id	sid	tid	token	lemma	pos
ejpam-6535	1	1	european	european	PROPN
ejpam-6535	1	2	journal	journal	PROPN
ejpam-6535	1	3	of	of	ADP
ejpam-6535	1	4	pure	pure	ADJ
ejpam-6535	1	5	and	and	CCONJ
ejpam-6535	1	6	applied	applied	ADJ
ejpam-6535	1	7	mathematics	mathematic	NOUN
ejpam-6535	1	8	2025	2025	NUM
ejpam-6535	1	9	,	,	PUNCT
ejpam-6535	1	10	vol	vol	NOUN
ejpam-6535	1	11	.	.	PROPN
ejpam-6535	1	12	18	18	NUM
ejpam-6535	1	13	,	,	PUNCT
ejpam-6535	1	14	issue	issue	NOUN
ejpam-6535	1	15	3	3	NUM
ejpam-6535	1	16	,	,	PUNCT
ejpam-6535	1	17	article	article	NOUN
ejpam-6535	1	18	number	number	NOUN
ejpam-6535	1	19	6535	6535	NUM
ejpam-6535	1	20	issn	issn	VERB
ejpam-6535	1	21	1307	1307	NUM
ejpam-6535	1	22	-	-	SYM
ejpam-6535	1	23	5543	5543	NUM
ejpam-6535	1	24	–	–	PUNCT
ejpam-6535	1	25	ejpam.com	ejpam.com	X
ejpam-6535	1	26	published	publish	VERB
ejpam-6535	1	27	by	by	ADP
ejpam-6535	1	28	new	new	PROPN
ejpam-6535	1	29	york	york	PROPN
ejpam-6535	1	30	business	business	PROPN
ejpam-6535	1	31	global	global	ADJ
ejpam-6535	1	32	on	on	ADP
ejpam-6535	1	33	some	some	DET
ejpam-6535	1	34	subcategories	subcategorie	NOUN
ejpam-6535	1	35	of	of	ADP
ejpam-6535	1	36	probabilistic	probabilistic	ADJ
ejpam-6535	1	37	convergence	convergence	NOUN
ejpam-6535	1	38	groups	group	NOUN
ejpam-6535	1	39	t.m.g	t.m.g	ADJ
ejpam-6535	1	40	.	.	PUNCT
ejpam-6535	1	41	ahsanullah1,∗	ahsanullah1,∗	PROPN
ejpam-6535	1	42	,	,	PUNCT
ejpam-6535	1	43	fawzi	fawzi	PROPN
ejpam-6535	1	44	al	al	PROPN
ejpam-6535	1	45	-	-	PUNCT
ejpam-6535	1	46	thukair	thukair	NOUN
ejpam-6535	1	47	1	1	NUM
ejpam-6535	1	48	department	department	NOUN
ejpam-6535	1	49	of	of	ADP
ejpam-6535	1	50	mathematics	mathematic	NOUN
ejpam-6535	1	51	,	,	PUNCT
ejpam-6535	1	52	college	college	NOUN
ejpam-6535	1	53	of	of	ADP
ejpam-6535	1	54	science	science	NOUN
ejpam-6535	1	55	,	,	PUNCT
ejpam-6535	1	56	king	king	NOUN
ejpam-6535	1	57	saud	saud	PROPN
ejpam-6535	1	58	university	university	PROPN
ejpam-6535	1	59	,	,	PUNCT
ejpam-6535	1	60	riyadh	riyadh	PROPN
ejpam-6535	1	61	,	,	PUNCT
ejpam-6535	1	62	saudi	saudi	PROPN
ejpam-6535	1	63	arabia	arabia	PROPN
ejpam-6535	1	64	dedicated	dedicate	VERB
ejpam-6535	1	65	to	to	PART
ejpam-6535	1	66	prof	prof	PROPN
ejpam-6535	1	67	.	.	PUNCT
ejpam-6535	2	1	dr	dr	PROPN
ejpam-6535	2	2	.	.	PROPN
ejpam-6535	2	3	abdul	abdul	PROPN
ejpam-6535	2	4	moyeen	moyeen	PROPN
ejpam-6535	2	5	khan	khan	PROPN
ejpam-6535	2	6	on	on	ADP
ejpam-6535	2	7	the	the	DET
ejpam-6535	2	8	occasion	occasion	NOUN
ejpam-6535	2	9	of	of	ADP
ejpam-6535	2	10	his	his	PRON
ejpam-6535	2	11	78th	78th	ADJ
ejpam-6535	2	12	birthday	birthday	NOUN
ejpam-6535	2	13	abstract	abstract	NOUN
ejpam-6535	2	14	.	.	PUNCT
ejpam-6535	3	1	in	in	ADP
ejpam-6535	3	2	this	this	DET
ejpam-6535	3	3	article	article	NOUN
ejpam-6535	3	4	,	,	PUNCT
ejpam-6535	3	5	we	we	PRON
ejpam-6535	3	6	focus	focus	VERB
ejpam-6535	3	7	on	on	ADP
ejpam-6535	3	8	discussing	discuss	VERB
ejpam-6535	3	9	some	some	DET
ejpam-6535	3	10	subcategories	subcategorie	NOUN
ejpam-6535	3	11	of	of	ADP
ejpam-6535	3	12	the	the	DET
ejpam-6535	3	13	category	category	NOUN
ejpam-6535	3	14	of	of	ADP
ejpam-6535	3	15	probabilistic	probabilistic	ADJ
ejpam-6535	3	16	convergence	convergence	NOUN
ejpam-6535	3	17	groups	group	NOUN
ejpam-6535	3	18	,	,	PUNCT
ejpam-6535	3	19	pconvgrp	pconvgrp	PROPN
ejpam-6535	3	20	.	.	PUNCT
ejpam-6535	4	1	in	in	ADP
ejpam-6535	4	2	so	so	ADV
ejpam-6535	4	3	doing	do	VERB
ejpam-6535	4	4	,	,	PUNCT
ejpam-6535	4	5	we	we	PRON
ejpam-6535	4	6	introduce	introduce	VERB
ejpam-6535	4	7	a	a	DET
ejpam-6535	4	8	category	category	NOUN
ejpam-6535	4	9	of	of	ADP
ejpam-6535	4	10	probabilistic	probabilistic	ADJ
ejpam-6535	4	11	neighborhood	neighborhood	NOUN
ejpam-6535	4	12	spaces	space	NOUN
ejpam-6535	4	13	,	,	PUNCT
ejpam-6535	4	14	pneigh	pneigh	NOUN
ejpam-6535	4	15	,	,	PUNCT
ejpam-6535	4	16	and	and	CCONJ
ejpam-6535	4	17	a	a	DET
ejpam-6535	4	18	category	category	NOUN
ejpam-6535	4	19	of	of	ADP
ejpam-6535	4	20	probabilistic	probabilistic	ADJ
ejpam-6535	4	21	topological	topological	ADJ
ejpam-6535	4	22	neighborhood	neighborhood	NOUN
ejpam-6535	4	23	spaces	space	NOUN
ejpam-6535	4	24	,	,	PUNCT
ejpam-6535	4	25	ptopneigh	ptopneigh	ADJ
ejpam-6535	4	26	.	.	PUNCT
ejpam-6535	5	1	we	we	PRON
ejpam-6535	5	2	identify	identify	VERB
ejpam-6535	5	3	probabilistic	probabilistic	ADJ
ejpam-6535	5	4	metric	metric	ADJ
ejpam-6535	5	5	spaces	space	NOUN
ejpam-6535	5	6	as	as	ADP
ejpam-6535	5	7	probabilistic	probabilistic	ADJ
ejpam-6535	5	8	neighborhood	neighborhood	NOUN
ejpam-6535	5	9	spaces	space	NOUN
ejpam-6535	5	10	.	.	PUNCT
ejpam-6535	6	1	introducing	introduce	VERB
ejpam-6535	6	2	a	a	DET
ejpam-6535	6	3	category	category	NOUN
ejpam-6535	6	4	of	of	ADP
ejpam-6535	6	5	probabilistic	probabilistic	ADJ
ejpam-6535	6	6	neighborhood	neighborhood	NOUN
ejpam-6535	6	7	groups	group	NOUN
ejpam-6535	6	8	,	,	PUNCT
ejpam-6535	6	9	pneighgrp	pneighgrp	NOUN
ejpam-6535	6	10	,	,	PUNCT
ejpam-6535	6	11	and	and	CCONJ
ejpam-6535	6	12	a	a	DET
ejpam-6535	6	13	category	category	NOUN
ejpam-6535	6	14	of	of	ADP
ejpam-6535	6	15	probabilistic	probabilistic	ADJ
ejpam-6535	6	16	topological	topological	ADJ
ejpam-6535	6	17	neighborhood	neighborhood	NOUN
ejpam-6535	6	18	groups	group	NOUN
ejpam-6535	6	19	,	,	PUNCT
ejpam-6535	6	20	ptopneighgrp	ptopneighgrp	NOUN
ejpam-6535	6	21	,	,	PUNCT
ejpam-6535	6	22	we	we	PRON
ejpam-6535	6	23	show	show	VERB
ejpam-6535	6	24	that	that	SCONJ
ejpam-6535	6	25	the	the	DET
ejpam-6535	6	26	category	category	NOUN
ejpam-6535	6	27	of	of	ADP
ejpam-6535	6	28	probabilistic	probabilistic	ADJ
ejpam-6535	6	29	neighborhood	neighborhood	NOUN
ejpam-6535	6	30	groups	group	NOUN
ejpam-6535	6	31	,	,	PUNCT
ejpam-6535	6	32	pneighgrp	pneighgrp	VERB
ejpam-6535	6	33	a	a	DET
ejpam-6535	6	34	topological	topological	ADJ
ejpam-6535	6	35	category	category	NOUN
ejpam-6535	6	36	,	,	PUNCT
ejpam-6535	6	37	and	and	CCONJ
ejpam-6535	6	38	the	the	DET
ejpam-6535	6	39	category	category	NOUN
ejpam-6535	6	40	of	of	ADP
ejpam-6535	6	41	probabilistic	probabilistic	ADJ
ejpam-6535	6	42	pretopological	pretopological	ADJ
ejpam-6535	6	43	groups	group	NOUN
ejpam-6535	6	44	,	,	PUNCT
ejpam-6535	6	45	ppretopgrp	ppretopgrp	NOUN
ejpam-6535	6	46	are	be	AUX
ejpam-6535	6	47	isomorphic	isomorphic	ADJ
ejpam-6535	6	48	,	,	PUNCT
ejpam-6535	6	49	and	and	CCONJ
ejpam-6535	6	50	find	find	VERB
ejpam-6535	6	51	a	a	DET
ejpam-6535	6	52	categorical	categorical	ADJ
ejpam-6535	6	53	relationship	relationship	NOUN
ejpam-6535	6	54	of	of	ADP
ejpam-6535	6	55	probabilistic	probabilistic	ADJ
ejpam-6535	6	56	neighborhood	neighborhood	NOUN
ejpam-6535	6	57	groups	group	NOUN
ejpam-6535	6	58	with	with	ADP
ejpam-6535	6	59	probabilistic	probabilistic	ADJ
ejpam-6535	6	60	convergence	convergence	NOUN
ejpam-6535	6	61	groups	group	NOUN
ejpam-6535	6	62	.	.	PUNCT
ejpam-6535	7	1	furthermore	furthermore	ADV
ejpam-6535	7	2	,	,	PUNCT
ejpam-6535	7	3	we	we	PRON
ejpam-6535	7	4	introduce	introduce	VERB
ejpam-6535	7	5	a	a	DET
ejpam-6535	7	6	category	category	NOUN
ejpam-6535	7	7	of	of	ADP
ejpam-6535	7	8	probabilistic	probabilistic	ADJ
ejpam-6535	7	9	pre	pre	ADJ
ejpam-6535	7	10	cauchy	cauchy	PROPN
ejpam-6535	7	11	groups	group	NOUN
ejpam-6535	7	12	,	,	PUNCT
ejpam-6535	7	13	pprechygrp	pprechygrp	NOUN
ejpam-6535	7	14	showing	show	VERB
ejpam-6535	7	15	that	that	SCONJ
ejpam-6535	7	16	the	the	DET
ejpam-6535	7	17	category	category	NOUN
ejpam-6535	7	18	of	of	ADP
ejpam-6535	7	19	probabilistic	probabilistic	ADJ
ejpam-6535	7	20	cauchy	cauchy	ADJ
ejpam-6535	7	21	groups	group	NOUN
ejpam-6535	7	22	,	,	PUNCT
ejpam-6535	7	23	pchygrp	pchygrp	VERB
ejpam-6535	7	24	a	a	DET
ejpam-6535	7	25	category	category	NOUN
ejpam-6535	7	26	introduced	introduce	VERB
ejpam-6535	7	27	earlier	early	ADV
ejpam-6535	7	28	,	,	PUNCT
ejpam-6535	7	29	is	be	AUX
ejpam-6535	7	30	a	a	DET
ejpam-6535	7	31	full	full	ADJ
ejpam-6535	7	32	subcategory	subcategory	NOUN
ejpam-6535	7	33	of	of	ADP
ejpam-6535	7	34	the	the	DET
ejpam-6535	7	35	category	category	NOUN
ejpam-6535	7	36	pprechygrp	pprechygrp	NOUN
ejpam-6535	7	37	.	.	PUNCT
ejpam-6535	8	1	in	in	ADP
ejpam-6535	8	2	this	this	DET
ejpam-6535	8	3	respect	respect	NOUN
ejpam-6535	8	4	,	,	PUNCT
ejpam-6535	8	5	we	we	PRON
ejpam-6535	8	6	prove	prove	VERB
ejpam-6535	8	7	that	that	SCONJ
ejpam-6535	8	8	in	in	ADP
ejpam-6535	8	9	presence	presence	NOUN
ejpam-6535	8	10	of	of	ADP
ejpam-6535	8	11	probabilistic	probabilistic	ADJ
ejpam-6535	8	12	convergence	convergence	NOUN
ejpam-6535	8	13	group	group	NOUN
ejpam-6535	8	14	,	,	PUNCT
ejpam-6535	8	15	the	the	DET
ejpam-6535	8	16	category	category	NOUN
ejpam-6535	8	17	of	of	ADP
ejpam-6535	8	18	probabilistic	probabilistic	ADJ
ejpam-6535	8	19	cauchy	cauchy	ADJ
ejpam-6535	8	20	groups	group	NOUN
ejpam-6535	8	21	,	,	PUNCT
ejpam-6535	8	22	pchygrp	pchygrp	NOUN
ejpam-6535	8	23	and	and	CCONJ
ejpam-6535	8	24	the	the	DET
ejpam-6535	8	25	category	category	NOUN
ejpam-6535	8	26	of	of	ADP
ejpam-6535	8	27	strongly	strongly	ADV
ejpam-6535	8	28	normal	normal	ADJ
ejpam-6535	8	29	probabilistic	probabilistic	ADJ
ejpam-6535	8	30	limit	limit	NOUN
ejpam-6535	8	31	groups	group	NOUN
ejpam-6535	8	32	,	,	PUNCT
ejpam-6535	8	33	snplimgrp	snplimgrp	NOUN
ejpam-6535	8	34	are	be	AUX
ejpam-6535	8	35	isomorphic	isomorphic	ADJ
ejpam-6535	8	36	.	.	PUNCT
ejpam-6535	9	1	moreover	moreover	ADV
ejpam-6535	9	2	,	,	PUNCT
ejpam-6535	9	3	following	follow	VERB
ejpam-6535	9	4	a	a	DET
ejpam-6535	9	5	notion	notion	NOUN
ejpam-6535	9	6	of	of	ADP
ejpam-6535	9	7	probabilistic	probabilistic	ADJ
ejpam-6535	9	8	normed	normed	PROPN
ejpam-6535	9	9	group	group	NOUN
ejpam-6535	9	10	a	a	DET
ejpam-6535	9	11	notion	notion	NOUN
ejpam-6535	9	12	studied	study	VERB
ejpam-6535	9	13	earlier	early	ADV
ejpam-6535	9	14	,	,	PUNCT
ejpam-6535	9	15	we	we	PRON
ejpam-6535	9	16	show	show	VERB
ejpam-6535	9	17	that	that	SCONJ
ejpam-6535	9	18	the	the	DET
ejpam-6535	9	19	category	category	NOUN
ejpam-6535	9	20	of	of	ADP
ejpam-6535	9	21	probabilistic	probabilistic	ADJ
ejpam-6535	9	22	normed	normed	ADJ
ejpam-6535	9	23	groups	group	NOUN
ejpam-6535	9	24	,	,	PUNCT
ejpam-6535	9	25	pnormedgrp	pnormedgrp	NOUN
ejpam-6535	9	26	is	be	AUX
ejpam-6535	9	27	isomorphic	isomorphic	ADJ
ejpam-6535	9	28	to	to	ADP
ejpam-6535	9	29	the	the	DET
ejpam-6535	9	30	well	well	ADV
ejpam-6535	9	31	-	-	PUNCT
ejpam-6535	9	32	known	know	VERB
ejpam-6535	9	33	category	category	NOUN
ejpam-6535	9	34	of	of	ADP
ejpam-6535	9	35	probabilistic	probabilistic	ADJ
ejpam-6535	9	36	metric	metric	ADJ
ejpam-6535	9	37	groups	group	NOUN
ejpam-6535	9	38	,	,	PUNCT
ejpam-6535	9	39	pmetgrp	pmetgrp	PROPN
ejpam-6535	9	40	;	;	PUNCT
ejpam-6535	9	41	finally	finally	ADV
ejpam-6535	9	42	,	,	PUNCT
ejpam-6535	9	43	we	we	PRON
ejpam-6535	9	44	present	present	VERB
ejpam-6535	9	45	probabilistic	probabilistic	ADJ
ejpam-6535	9	46	version	version	NOUN
ejpam-6535	9	47	of	of	ADP
ejpam-6535	9	48	so	so	ADV
ejpam-6535	9	49	-	-	PUNCT
ejpam-6535	9	50	called	call	VERB
ejpam-6535	9	51	invariance	invariance	NOUN
ejpam-6535	9	52	of	of	ADP
ejpam-6535	9	53	norm	norm	NOUN
ejpam-6535	9	54	theorem	theorem	VERB
ejpam-6535	9	55	.	.	PROPN
ejpam-6535	9	56	2020	2020	NUM
ejpam-6535	9	57	mathematics	mathematics	PROPN
ejpam-6535	9	58	subject	subject	NOUN
ejpam-6535	9	59	classifications	classification	NOUN
ejpam-6535	9	60	:	:	PUNCT
ejpam-6535	9	61	54a20	54a20	NUM
ejpam-6535	9	62	,	,	PUNCT
ejpam-6535	9	63	54e70	54e70	NUM
ejpam-6535	9	64	,	,	PUNCT
ejpam-6535	9	65	54h11	54h11	NUM
ejpam-6535	9	66	,	,	PUNCT
ejpam-6535	9	67	54b30	54b30	PRON
ejpam-6535	9	68	key	key	ADJ
ejpam-6535	9	69	words	word	NOUN
ejpam-6535	9	70	and	and	CCONJ
ejpam-6535	9	71	phrases	phrase	NOUN
ejpam-6535	9	72	:	:	PUNCT
ejpam-6535	9	73	probabilistic	probabilistic	ADJ
ejpam-6535	9	74	metric	metric	ADJ
ejpam-6535	9	75	space	space	NOUN
ejpam-6535	9	76	,	,	PUNCT
ejpam-6535	9	77	probabilistic	probabilistic	VERB
ejpam-6535	9	78	tardiff	tardiff	ADJ
ejpam-6535	9	79	neighborhood	neighborhood	NOUN
ejpam-6535	9	80	system	system	NOUN
ejpam-6535	9	81	,	,	PUNCT
ejpam-6535	9	82	probabilistic	probabilistic	ADJ
ejpam-6535	9	83	neighborhood	neighborhood	NOUN
ejpam-6535	9	84	space	space	NOUN
ejpam-6535	9	85	,	,	PUNCT
ejpam-6535	9	86	probabilistic	probabilistic	ADJ
ejpam-6535	9	87	convergence	convergence	NOUN
ejpam-6535	9	88	space	space	NOUN
ejpam-6535	9	89	,	,	PUNCT
ejpam-6535	9	90	probabilistic	probabilistic	ADJ
ejpam-6535	9	91	convergence	convergence	NOUN
ejpam-6535	9	92	groups	group	NOUN
ejpam-6535	9	93	,	,	PUNCT
ejpam-6535	9	94	probabilistic	probabilistic	ADJ
ejpam-6535	9	95	pre	pre	ADJ
ejpam-6535	9	96	-	-	ADJ
ejpam-6535	9	97	cauchy	cauchy	ADJ
ejpam-6535	9	98	space	space	NOUN
ejpam-6535	9	99	,	,	PUNCT
ejpam-6535	9	100	probabilistic	probabilistic	ADJ
ejpam-6535	9	101	neighborhood	neighborhood	NOUN
ejpam-6535	9	102	group	group	NOUN
ejpam-6535	9	103	,	,	PUNCT
ejpam-6535	9	104	probabilistic	probabilistic	ADJ
ejpam-6535	9	105	metric	metric	ADJ
ejpam-6535	9	106	group	group	NOUN
ejpam-6535	9	107	,	,	PUNCT
ejpam-6535	9	108	probabilistic	probabilistic	VERB
ejpam-6535	9	109	normed	normed	ADJ
ejpam-6535	9	110	group	group	NOUN
ejpam-6535	9	111	.	.	PUNCT
ejpam-6535	10	1	1	1	X
ejpam-6535	10	2	.	.	X
ejpam-6535	10	3	introduction	introduction	NOUN
ejpam-6535	10	4	since	since	SCONJ
ejpam-6535	10	5	the	the	DET
ejpam-6535	10	6	inception	inception	NOUN
ejpam-6535	10	7	of	of	ADP
ejpam-6535	10	8	the	the	DET
ejpam-6535	10	9	notion	notion	NOUN
ejpam-6535	10	10	of	of	ADP
ejpam-6535	10	11	menger	menger	PROPN
ejpam-6535	10	12	probabilistic	probabilistic	VERB
ejpam-6535	10	13	metric	metric	ADJ
ejpam-6535	10	14	spaces	space	NOUN
ejpam-6535	10	15	,	,	PUNCT
ejpam-6535	10	16	[	[	X
ejpam-6535	10	17	27	27	NUM
ejpam-6535	10	18	]	]	PUNCT
ejpam-6535	10	19	(	(	PUNCT
ejpam-6535	10	20	see	see	VERB
ejpam-6535	10	21	also	also	ADV
ejpam-6535	10	22	,	,	PUNCT
ejpam-6535	10	23	[	[	X
ejpam-6535	10	24	34	34	NUM
ejpam-6535	10	25	]	]	NUM
ejpam-6535	10	26	)	)	PUNCT
ejpam-6535	10	27	,	,	PUNCT
ejpam-6535	10	28	enormous	enormous	ADJ
ejpam-6535	10	29	quantity	quantity	NOUN
ejpam-6535	10	30	of	of	ADP
ejpam-6535	10	31	work	work	NOUN
ejpam-6535	10	32	surfaced	surface	VERB
ejpam-6535	10	33	over	over	ADP
ejpam-6535	10	34	the	the	DET
ejpam-6535	10	35	years	year	NOUN
ejpam-6535	10	36	in	in	ADP
ejpam-6535	10	37	a	a	DET
ejpam-6535	10	38	wide	wide	ADJ
ejpam-6535	10	39	variety	variety	NOUN
ejpam-6535	10	40	of	of	ADP
ejpam-6535	10	41	areas	area	NOUN
ejpam-6535	10	42	,	,	PUNCT
ejpam-6535	10	43	we	we	PRON
ejpam-6535	10	44	include	include	VERB
ejpam-6535	10	45	∗corresponding	∗corresponde	VERB
ejpam-6535	10	46	author	author	NOUN
ejpam-6535	10	47	.	.	PUNCT
ejpam-6535	11	1	doi	doi	NOUN
ejpam-6535	11	2	:	:	PUNCT
ejpam-6535	11	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6535	https://doi.org/10.29020/nybg.ejpam.v18i3.6535	PRON
ejpam-6535	11	4	email	email	NOUN
ejpam-6535	11	5	addresses	address	VERB
ejpam-6535	11	6	:	:	PUNCT
ejpam-6535	11	7	tmga1@ksu.edu.sa	tmga1@ksu.edu.sa	PROPN
ejpam-6535	11	8	(	(	PUNCT
ejpam-6535	11	9	t.m.g	t.m.g	X
ejpam-6535	11	10	.	.	PUNCT
ejpam-6535	12	1	ahsanullah	ahsanullah	NOUN
ejpam-6535	12	2	)	)	PUNCT
ejpam-6535	13	1	,	,	PUNCT
ejpam-6535	13	2	thukair@ksu.edu.sa	thukair@ksu.edu.sa	PROPN
ejpam-6535	13	3	(	(	PUNCT
ejpam-6535	13	4	fawzi	fawzi	PROPN
ejpam-6535	13	5	al	al	PROPN
ejpam-6535	13	6	-	-	PUNCT
ejpam-6535	13	7	thukair	thukair	NOUN
ejpam-6535	13	8	)	)	PUNCT
ejpam-6535	13	9	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6535	13	10	1	1	NUM
ejpam-6535	13	11	copyright	copyright	NOUN
ejpam-6535	13	12	:	:	PUNCT
ejpam-6535	13	13	©	©	PROPN
ejpam-6535	13	14	2025	2025	NUM
ejpam-6535	13	15	the	the	DET
ejpam-6535	13	16	author(s	author(s	NOUN
ejpam-6535	13	17	)	)	PUNCT
ejpam-6535	13	18	.	.	PUNCT
ejpam-6535	14	1	(	(	PUNCT
ejpam-6535	14	2	cc	cc	NOUN
ejpam-6535	14	3	by	by	ADP
ejpam-6535	14	4	-	-	PUNCT
ejpam-6535	14	5	nc	nc	PROPN
ejpam-6535	14	6	4.0	4.0	NUM
ejpam-6535	14	7	)	)	PUNCT
ejpam-6535	14	8	here	here	ADV
ejpam-6535	14	9	a	a	DET
ejpam-6535	14	10	tiny	tiny	ADJ
ejpam-6535	14	11	list	list	NOUN
ejpam-6535	14	12	for	for	ADP
ejpam-6535	14	13	the	the	DET
ejpam-6535	14	14	convenience	convenience	NOUN
ejpam-6535	14	15	of	of	ADP
ejpam-6535	14	16	the	the	DET
ejpam-6535	14	17	reader	reader	NOUN
ejpam-6535	14	18	,	,	PUNCT
ejpam-6535	14	19	[	[	X
ejpam-6535	14	20	3	3	NUM
ejpam-6535	14	21	,	,	PUNCT
ejpam-6535	14	22	5–8	5–8	NUM
ejpam-6535	14	23	,	,	PUNCT
ejpam-6535	14	24	14	14	NUM
ejpam-6535	14	25	,	,	PUNCT
ejpam-6535	14	26	18	18	NUM
ejpam-6535	14	27	,	,	PUNCT
ejpam-6535	14	28	22	22	NUM
ejpam-6535	14	29	,	,	PUNCT
ejpam-6535	14	30	23	23	NUM
ejpam-6535	14	31	,	,	PUNCT
ejpam-6535	14	32	29	29	NUM
ejpam-6535	14	33	,	,	PUNCT
ejpam-6535	14	34	31	31	NUM
ejpam-6535	14	35	,	,	PUNCT
ejpam-6535	14	36	33–39	33–39	NUM
ejpam-6535	14	37	]	]	PUNCT
ejpam-6535	14	38	.	.	PUNCT
ejpam-6535	15	1	following	follow	VERB
ejpam-6535	15	2	the	the	DET
ejpam-6535	15	3	category	category	NOUN
ejpam-6535	15	4	of	of	ADP
ejpam-6535	15	5	probabilistic	probabilistic	ADJ
ejpam-6535	15	6	convergence	convergence	NOUN
ejpam-6535	15	7	spaces	space	NOUN
ejpam-6535	15	8	,	,	PUNCT
ejpam-6535	15	9	pconv	pconv	ADJ
ejpam-6535	15	10	,	,	PUNCT
ejpam-6535	15	11	[	[	X
ejpam-6535	15	12	22	22	NUM
ejpam-6535	15	13	,	,	PUNCT
ejpam-6535	15	14	32	32	NUM
ejpam-6535	15	15	]	]	PUNCT
ejpam-6535	15	16	a	a	DET
ejpam-6535	15	17	supercategory	supercategory	NOUN
ejpam-6535	15	18	of	of	ADP
ejpam-6535	15	19	the	the	DET
ejpam-6535	15	20	category	category	NOUN
ejpam-6535	15	21	of	of	ADP
ejpam-6535	15	22	topological	topological	ADJ
ejpam-6535	15	23	spaces	space	NOUN
ejpam-6535	15	24	,	,	PUNCT
ejpam-6535	15	25	top(see	top(see	ADJ
ejpam-6535	15	26	also	also	ADV
ejpam-6535	15	27	,	,	PUNCT
ejpam-6535	15	28	[	[	X
ejpam-6535	15	29	30	30	NUM
ejpam-6535	15	30	]	]	NUM
ejpam-6535	15	31	)	)	PUNCT
ejpam-6535	15	32	,	,	PUNCT
ejpam-6535	15	33	in	in	ADP
ejpam-6535	15	34	[	[	X
ejpam-6535	15	35	3	3	X
ejpam-6535	15	36	]	]	PUNCT
ejpam-6535	15	37	the	the	DET
ejpam-6535	15	38	authors	author	NOUN
ejpam-6535	15	39	introduced	introduce	VERB
ejpam-6535	15	40	the	the	DET
ejpam-6535	15	41	concept	concept	NOUN
ejpam-6535	15	42	of	of	ADP
ejpam-6535	15	43	probabilistic	probabilistic	ADJ
ejpam-6535	15	44	convergence	convergence	NOUN
ejpam-6535	15	45	groups	group	NOUN
ejpam-6535	15	46	;	;	PUNCT
ejpam-6535	15	47	upon	upon	SCONJ
ejpam-6535	15	48	using	use	VERB
ejpam-6535	15	49	tardiff	tardiff	ADJ
ejpam-6535	15	50	neighborhood	neighborhood	NOUN
ejpam-6535	15	51	system	system	NOUN
ejpam-6535	15	52	as	as	SCONJ
ejpam-6535	15	53	introduced	introduce	VERB
ejpam-6535	15	54	in	in	ADP
ejpam-6535	15	55	[	[	X
ejpam-6535	15	56	38	38	NUM
ejpam-6535	15	57	]	]	PUNCT
ejpam-6535	15	58	,	,	PUNCT
ejpam-6535	15	59	they	they	PRON
ejpam-6535	15	60	showed	show	VERB
ejpam-6535	15	61	that	that	SCONJ
ejpam-6535	15	62	every	every	DET
ejpam-6535	15	63	probabilistic	probabilistic	ADJ
ejpam-6535	15	64	metric	metric	ADJ
ejpam-6535	15	65	group	group	NOUN
ejpam-6535	15	66	is	be	AUX
ejpam-6535	15	67	a	a	DET
ejpam-6535	15	68	probabilistic	probabilistic	ADJ
ejpam-6535	15	69	convergence	convergence	NOUN
ejpam-6535	15	70	group	group	NOUN
ejpam-6535	15	71	;	;	PUNCT
ejpam-6535	15	72	further	far	ADV
ejpam-6535	15	73	they	they	PRON
ejpam-6535	15	74	discussed	discuss	VERB
ejpam-6535	15	75	the	the	DET
ejpam-6535	15	76	unifmormizability	unifmormizability	NOUN
ejpam-6535	15	77	and	and	CCONJ
ejpam-6535	15	78	metrizability	metrizability	NOUN
ejpam-6535	15	79	of	of	ADP
ejpam-6535	15	80	probabilistic	probabilistic	ADJ
ejpam-6535	15	81	convergence	convergence	NOUN
ejpam-6535	15	82	groups	group	NOUN
ejpam-6535	15	83	.	.	PUNCT
ejpam-6535	16	1	it	it	PRON
ejpam-6535	16	2	goes	go	VERB
ejpam-6535	16	3	without	without	ADP
ejpam-6535	16	4	saying	say	VERB
ejpam-6535	16	5	that	that	SCONJ
ejpam-6535	16	6	the	the	DET
ejpam-6535	16	7	notion	notion	NOUN
ejpam-6535	16	8	of	of	ADP
ejpam-6535	16	9	probabilistic	probabilistic	ADJ
ejpam-6535	16	10	normed	norme	VERB
ejpam-6535	16	11	spaces	space	NOUN
ejpam-6535	16	12	play	play	VERB
ejpam-6535	16	13	a	a	DET
ejpam-6535	16	14	vital	vital	ADJ
ejpam-6535	16	15	role	role	NOUN
ejpam-6535	16	16	in	in	ADP
ejpam-6535	16	17	functional	functional	ADJ
ejpam-6535	16	18	analysis	analysis	NOUN
ejpam-6535	16	19	,	,	PUNCT
ejpam-6535	16	20	[	[	X
ejpam-6535	16	21	12	12	NUM
ejpam-6535	16	22	,	,	PUNCT
ejpam-6535	16	23	20	20	NUM
ejpam-6535	16	24	]	]	PUNCT
ejpam-6535	16	25	,	,	PUNCT
ejpam-6535	16	26	and	and	CCONJ
ejpam-6535	16	27	as	as	SCONJ
ejpam-6535	16	28	such	such	ADJ
ejpam-6535	16	29	,	,	PUNCT
ejpam-6535	16	30	quite	quite	DET
ejpam-6535	16	31	a	a	DET
ejpam-6535	16	32	good	good	ADJ
ejpam-6535	16	33	number	number	NOUN
ejpam-6535	16	34	of	of	ADP
ejpam-6535	16	35	papers	paper	NOUN
ejpam-6535	16	36	appeared	appear	VERB
ejpam-6535	16	37	in	in	ADP
ejpam-6535	16	38	recent	recent	ADJ
ejpam-6535	16	39	years	year	NOUN
ejpam-6535	16	40	,	,	PUNCT
ejpam-6535	16	41	see	see	VERB
ejpam-6535	16	42	f.i	f.i	PROPN
ejpam-6535	16	43	.	.	PROPN
ejpam-6535	16	44	,	,	PUNCT
ejpam-6535	17	1	[	[	X
ejpam-6535	17	2	29	29	NUM
ejpam-6535	17	3	,	,	PUNCT
ejpam-6535	17	4	31	31	NUM
ejpam-6535	17	5	]	]	PUNCT
ejpam-6535	17	6	where	where	SCONJ
ejpam-6535	17	7	the	the	DET
ejpam-6535	17	8	notion	notion	NOUN
ejpam-6535	17	9	of	of	ADP
ejpam-6535	17	10	probabilistic	probabilistic	ADJ
ejpam-6535	17	11	normed	normed	ADJ
ejpam-6535	17	12	groups	group	NOUN
ejpam-6535	17	13	and	and	CCONJ
ejpam-6535	17	14	their	their	PRON
ejpam-6535	17	15	non	non	ADJ
ejpam-6535	17	16	categorical	categorical	ADJ
ejpam-6535	17	17	aspects	aspect	NOUN
ejpam-6535	17	18	are	be	AUX
ejpam-6535	17	19	discussed	discuss	VERB
ejpam-6535	17	20	.	.	PUNCT
ejpam-6535	18	1	in	in	ADP
ejpam-6535	18	2	[	[	X
ejpam-6535	18	3	3	3	NUM
ejpam-6535	18	4	]	]	PUNCT
ejpam-6535	18	5	,	,	PUNCT
ejpam-6535	18	6	the	the	DET
ejpam-6535	18	7	authors	author	NOUN
ejpam-6535	18	8	of	of	ADP
ejpam-6535	18	9	this	this	DET
ejpam-6535	18	10	article	article	NOUN
ejpam-6535	18	11	also	also	ADV
ejpam-6535	18	12	introduced	introduce	VERB
ejpam-6535	18	13	the	the	DET
ejpam-6535	18	14	notion	notion	NOUN
ejpam-6535	18	15	of	of	ADP
ejpam-6535	18	16	norm	norm	NOUN
ejpam-6535	18	17	groups	group	NOUN
ejpam-6535	18	18	;	;	PUNCT
ejpam-6535	18	19	in	in	ADP
ejpam-6535	18	20	1963	1963	NUM
ejpam-6535	18	21	,	,	PUNCT
ejpam-6535	18	22	šerstnev	šerstnev	PROPN
ejpam-6535	18	23	,	,	PUNCT
ejpam-6535	18	24	[	[	X
ejpam-6535	18	25	35	35	NUM
ejpam-6535	18	26	]	]	PUNCT
ejpam-6535	18	27	studied	study	VERB
ejpam-6535	18	28	probabilistic	probabilistic	ADJ
ejpam-6535	18	29	norm	norm	NOUN
ejpam-6535	18	30	on	on	ADP
ejpam-6535	18	31	linear	linear	ADJ
ejpam-6535	18	32	spaces	space	NOUN
ejpam-6535	18	33	.	.	PUNCT
ejpam-6535	19	1	in	in	ADP
ejpam-6535	19	2	almost	almost	ADV
ejpam-6535	19	3	all	all	PRON
ejpam-6535	19	4	of	of	ADP
ejpam-6535	19	5	these	these	DET
ejpam-6535	19	6	work	work	NOUN
ejpam-6535	19	7	except	except	SCONJ
ejpam-6535	19	8	[	[	X
ejpam-6535	19	9	3	3	X
ejpam-6535	19	10	]	]	PUNCT
ejpam-6535	19	11	where	where	SCONJ
ejpam-6535	19	12	notion	notion	NOUN
ejpam-6535	19	13	of	of	ADP
ejpam-6535	19	14	tardiff	tardiff	ADJ
ejpam-6535	19	15	neighborhood	neighborhood	NOUN
ejpam-6535	19	16	system	system	NOUN
ejpam-6535	19	17	is	be	AUX
ejpam-6535	19	18	considered	consider	VERB
ejpam-6535	19	19	,	,	PUNCT
ejpam-6535	19	20	and	and	CCONJ
ejpam-6535	19	21	in	in	ADP
ejpam-6535	19	22	other	other	ADJ
ejpam-6535	19	23	cases	case	NOUN
ejpam-6535	19	24	,	,	PUNCT
ejpam-6535	19	25	the	the	DET
ejpam-6535	19	26	notion	notion	NOUN
ejpam-6535	19	27	of	of	ADP
ejpam-6535	19	28	so	so	ADV
ejpam-6535	19	29	-	-	PUNCT
ejpam-6535	19	30	called	call	VERB
ejpam-6535	19	31	strong	strong	ADJ
ejpam-6535	19	32	topology	topology	NOUN
ejpam-6535	19	33	,	,	PUNCT
ejpam-6535	19	34	[	[	X
ejpam-6535	19	35	34	34	NUM
ejpam-6535	19	36	]	]	PUNCT
ejpam-6535	19	37	are	be	AUX
ejpam-6535	19	38	used	use	VERB
ejpam-6535	19	39	.	.	PUNCT
ejpam-6535	20	1	our	our	PRON
ejpam-6535	20	2	motivations	motivation	NOUN
ejpam-6535	20	3	are	be	AUX
ejpam-6535	20	4	to	to	PART
ejpam-6535	20	5	introduce	introduce	VERB
ejpam-6535	20	6	a	a	DET
ejpam-6535	20	7	category	category	NOUN
ejpam-6535	20	8	of	of	ADP
ejpam-6535	20	9	probabilistic	probabilistic	ADJ
ejpam-6535	20	10	neighborhood	neighborhood	NOUN
ejpam-6535	20	11	groups	group	NOUN
ejpam-6535	20	12	a	a	DET
ejpam-6535	20	13	topological	topological	ADJ
ejpam-6535	20	14	category	category	NOUN
ejpam-6535	20	15	,	,	PUNCT
ejpam-6535	20	16	and	and	CCONJ
ejpam-6535	20	17	a	a	DET
ejpam-6535	20	18	subcategory	subcategory	ADJ
ejpam-6535	20	19	probabilistic	probabilistic	ADJ
ejpam-6535	20	20	topological	topological	ADJ
ejpam-6535	20	21	groups	group	NOUN
ejpam-6535	20	22	.	.	PUNCT
ejpam-6535	21	1	we	we	PRON
ejpam-6535	21	2	identify	identify	VERB
ejpam-6535	21	3	probabilistic	probabilistic	ADJ
ejpam-6535	21	4	neighborhood	neighborhood	NOUN
ejpam-6535	21	5	groups	group	NOUN
ejpam-6535	21	6	with	with	ADP
ejpam-6535	21	7	probabilistic	probabilistic	ADJ
ejpam-6535	21	8	metric	metric	ADJ
ejpam-6535	21	9	groups	group	NOUN
ejpam-6535	21	10	,	,	PUNCT
ejpam-6535	21	11	among	among	ADP
ejpam-6535	21	12	others	other	NOUN
ejpam-6535	21	13	fundamental	fundamental	ADJ
ejpam-6535	21	14	results	result	NOUN
ejpam-6535	21	15	,	,	PUNCT
ejpam-6535	21	16	show	show	VERB
ejpam-6535	21	17	that	that	SCONJ
ejpam-6535	21	18	the	the	DET
ejpam-6535	21	19	category	category	NOUN
ejpam-6535	21	20	of	of	ADP
ejpam-6535	21	21	probabilistic	probabilistic	ADJ
ejpam-6535	21	22	neighborhood	neighborhood	NOUN
ejpam-6535	21	23	groups	group	NOUN
ejpam-6535	21	24	is	be	AUX
ejpam-6535	21	25	isomorphic	isomorphic	ADJ
ejpam-6535	21	26	with	with	ADP
ejpam-6535	21	27	the	the	DET
ejpam-6535	21	28	category	category	NOUN
ejpam-6535	21	29	of	of	ADP
ejpam-6535	21	30	probabilistic	probabilistic	ADJ
ejpam-6535	21	31	pretopological	pretopological	ADJ
ejpam-6535	21	32	groups.this	groups.this	PRON
ejpam-6535	21	33	probabilistic	probabilistic	ADJ
ejpam-6535	21	34	metric	metric	ADJ
ejpam-6535	21	35	group	group	NOUN
ejpam-6535	21	36	gives	give	VERB
ejpam-6535	21	37	rise	rise	NOUN
ejpam-6535	21	38	to	to	ADP
ejpam-6535	21	39	a	a	DET
ejpam-6535	21	40	probabilistic	probabilistic	ADJ
ejpam-6535	21	41	convergence	convergence	NOUN
ejpam-6535	21	42	group	group	NOUN
ejpam-6535	21	43	,	,	PUNCT
ejpam-6535	21	44	[	[	X
ejpam-6535	21	45	3	3	NUM
ejpam-6535	21	46	]	]	PUNCT
ejpam-6535	21	47	.	.	PUNCT
ejpam-6535	22	1	a	a	DET
ejpam-6535	22	2	detail	detail	NOUN
ejpam-6535	22	3	study	study	NOUN
ejpam-6535	22	4	is	be	AUX
ejpam-6535	22	5	made	make	VERB
ejpam-6535	22	6	on	on	ADP
ejpam-6535	22	7	quantale	quantale	NOUN
ejpam-6535	22	8	-	-	PUNCT
ejpam-6535	22	9	valued	value	VERB
ejpam-6535	22	10	cauchy	cauchy	NOUN
ejpam-6535	22	11	tower	tower	NOUN
ejpam-6535	22	12	spaces	space	NOUN
ejpam-6535	22	13	and	and	CCONJ
ejpam-6535	22	14	quantale	quantale	NOUN
ejpam-6535	22	15	-	-	PUNCT
ejpam-6535	22	16	valued	value	VERB
ejpam-6535	22	17	convergence	convergence	NOUN
ejpam-6535	22	18	tower	tower	NOUN
ejpam-6535	22	19	in	in	ADP
ejpam-6535	22	20	[	[	X
ejpam-6535	22	21	23	23	NUM
ejpam-6535	22	22	]	]	PUNCT
ejpam-6535	22	23	presenting	present	VERB
ejpam-6535	22	24	their	their	PRON
ejpam-6535	22	25	various	various	ADJ
ejpam-6535	22	26	connection	connection	NOUN
ejpam-6535	22	27	with	with	ADP
ejpam-6535	22	28	quantale	quantale	NOUN
ejpam-6535	22	29	-	-	PUNCT
ejpam-6535	22	30	valued	value	VERB
ejpam-6535	22	31	metric	metric	ADJ
ejpam-6535	22	32	spaces	space	NOUN
ejpam-6535	22	33	;	;	PUNCT
ejpam-6535	22	34	moreover	moreover	ADV
ejpam-6535	22	35	,	,	PUNCT
ejpam-6535	22	36	in	in	ADP
ejpam-6535	22	37	[	[	X
ejpam-6535	22	38	23	23	NUM
ejpam-6535	22	39	]	]	PUNCT
ejpam-6535	22	40	a	a	DET
ejpam-6535	22	41	thorough	thorough	ADJ
ejpam-6535	22	42	investigation	investigation	NOUN
ejpam-6535	22	43	is	be	AUX
ejpam-6535	22	44	made	make	VERB
ejpam-6535	22	45	on	on	ADP
ejpam-6535	22	46	completeness	completeness	NOUN
ejpam-6535	22	47	of	of	ADP
ejpam-6535	22	48	quantale	quantale	NOUN
ejpam-6535	22	49	-	-	PUNCT
ejpam-6535	22	50	valued	value	VERB
ejpam-6535	22	51	cauchy	cauchy	NOUN
ejpam-6535	22	52	tower	tower	NOUN
ejpam-6535	22	53	spaces	space	NOUN
ejpam-6535	22	54	.	.	PUNCT
ejpam-6535	23	1	in	in	ADP
ejpam-6535	23	2	this	this	DET
ejpam-6535	23	3	article	article	NOUN
ejpam-6535	23	4	,	,	PUNCT
ejpam-6535	23	5	we	we	PRON
ejpam-6535	23	6	extract	extract	VERB
ejpam-6535	23	7	some	some	PRON
ejpam-6535	23	8	the	the	DET
ejpam-6535	23	9	results	result	NOUN
ejpam-6535	23	10	in	in	ADP
ejpam-6535	23	11	the	the	DET
ejpam-6535	23	12	light	light	NOUN
ejpam-6535	23	13	of	of	ADP
ejpam-6535	23	14	probabilistic	probabilistic	ADJ
ejpam-6535	23	15	cauchy	cauchy	ADJ
ejpam-6535	23	16	spaces	space	NOUN
ejpam-6535	23	17	,	,	PUNCT
ejpam-6535	23	18	and	and	CCONJ
ejpam-6535	23	19	more	more	ADV
ejpam-6535	23	20	importantly	importantly	ADV
ejpam-6535	23	21	,	,	PUNCT
ejpam-6535	23	22	we	we	PRON
ejpam-6535	23	23	discuss	discuss	VERB
ejpam-6535	23	24	the	the	DET
ejpam-6535	23	25	category	category	NOUN
ejpam-6535	23	26	of	of	ADP
ejpam-6535	23	27	probabilistic	probabilistic	ADJ
ejpam-6535	23	28	pre	pre	ADJ
ejpam-6535	23	29	-	-	ADJ
ejpam-6535	23	30	cauchy	cauchy	ADJ
ejpam-6535	23	31	spaces	space	NOUN
ejpam-6535	23	32	,	,	PUNCT
ejpam-6535	23	33	and	and	CCONJ
ejpam-6535	23	34	probabilistic	probabilistic	ADJ
ejpam-6535	23	35	pre	pre	ADJ
ejpam-6535	23	36	-	-	ADJ
ejpam-6535	23	37	cauchy	cauchy	ADJ
ejpam-6535	23	38	groups	group	NOUN
ejpam-6535	23	39	,	,	PUNCT
ejpam-6535	23	40	and	and	CCONJ
ejpam-6535	23	41	their	their	PRON
ejpam-6535	23	42	relationship	relationship	NOUN
ejpam-6535	23	43	with	with	ADP
ejpam-6535	23	44	probabilistic	probabilistic	ADJ
ejpam-6535	23	45	cauchy	cauchy	ADJ
ejpam-6535	23	46	groups	group	NOUN
ejpam-6535	23	47	.	.	PUNCT
ejpam-6535	24	1	following	follow	VERB
ejpam-6535	24	2	a	a	DET
ejpam-6535	24	3	notion	notion	NOUN
ejpam-6535	24	4	of	of	ADP
ejpam-6535	24	5	so	so	ADV
ejpam-6535	24	6	-	-	PUNCT
ejpam-6535	24	7	called	call	VERB
ejpam-6535	24	8	strong	strong	ADJ
ejpam-6535	24	9	normality	normality	NOUN
ejpam-6535	24	10	as	as	SCONJ
ejpam-6535	24	11	introduced	introduce	VERB
ejpam-6535	24	12	in	in	ADP
ejpam-6535	24	13	[	[	X
ejpam-6535	24	14	9	9	NUM
ejpam-6535	24	15	]	]	PUNCT
ejpam-6535	24	16	,	,	PUNCT
ejpam-6535	24	17	we	we	PRON
ejpam-6535	24	18	introduce	introduce	VERB
ejpam-6535	24	19	a	a	DET
ejpam-6535	24	20	notion	notion	NOUN
ejpam-6535	24	21	of	of	ADP
ejpam-6535	24	22	strongly	strongly	ADV
ejpam-6535	24	23	normal	normal	ADJ
ejpam-6535	24	24	probabilistic	probabilistic	ADJ
ejpam-6535	24	25	limit	limit	NOUN
ejpam-6535	24	26	group	group	NOUN
ejpam-6535	24	27	,	,	PUNCT
ejpam-6535	24	28	showing	show	VERB
ejpam-6535	24	29	that	that	SCONJ
ejpam-6535	24	30	the	the	DET
ejpam-6535	24	31	category	category	NOUN
ejpam-6535	24	32	of	of	ADP
ejpam-6535	24	33	probabilistic	probabilistic	ADJ
ejpam-6535	24	34	cauchy	cauchy	ADJ
ejpam-6535	24	35	groups	group	NOUN
ejpam-6535	24	36	is	be	AUX
ejpam-6535	24	37	isomorphic	isomorphic	ADJ
ejpam-6535	24	38	to	to	ADP
ejpam-6535	24	39	the	the	DET
ejpam-6535	24	40	category	category	NOUN
ejpam-6535	24	41	of	of	ADP
ejpam-6535	24	42	strongly	strongly	ADV
ejpam-6535	24	43	norm	norm	NOUN
ejpam-6535	24	44	limit	limit	NOUN
ejpam-6535	24	45	groups	group	NOUN
ejpam-6535	24	46	under	under	ADP
ejpam-6535	24	47	the	the	DET
ejpam-6535	24	48	largest	large	ADJ
ejpam-6535	24	49	triangle	triangle	NOUN
ejpam-6535	24	50	function	function	NOUN
ejpam-6535	24	51	τ	τ	PROPN
ejpam-6535	24	52	.	.	PUNCT
ejpam-6535	25	1	finally	finally	ADV
ejpam-6535	25	2	,	,	PUNCT
ejpam-6535	25	3	following	follow	VERB
ejpam-6535	25	4	the	the	DET
ejpam-6535	25	5	notion	notion	NOUN
ejpam-6535	25	6	of	of	ADP
ejpam-6535	25	7	probabilistic	probabilistic	ADJ
ejpam-6535	25	8	norm	norm	NOUN
ejpam-6535	25	9	group	group	NOUN
ejpam-6535	25	10	as	as	SCONJ
ejpam-6535	25	11	introduced	introduce	VERB
ejpam-6535	25	12	in	in	ADP
ejpam-6535	25	13	[	[	X
ejpam-6535	25	14	3	3	NUM
ejpam-6535	25	15	]	]	PUNCT
ejpam-6535	25	16	,	,	PUNCT
ejpam-6535	25	17	we	we	PRON
ejpam-6535	25	18	show	show	VERB
ejpam-6535	25	19	that	that	SCONJ
ejpam-6535	25	20	there	there	PRON
ejpam-6535	25	21	exists	exist	VERB
ejpam-6535	25	22	a	a	DET
ejpam-6535	25	23	one	one	NUM
ejpam-6535	25	24	-	-	PUNCT
ejpam-6535	25	25	to	to	ADP
ejpam-6535	25	26	-	-	PUNCT
ejpam-6535	25	27	one	one	NUM
ejpam-6535	25	28	correspondence	correspondence	NOUN
ejpam-6535	25	29	between	between	ADP
ejpam-6535	25	30	probabilistic	probabilistic	ADJ
ejpam-6535	25	31	metrics	metric	NOUN
ejpam-6535	25	32	on	on	ADP
ejpam-6535	25	33	groups	group	NOUN
ejpam-6535	25	34	and	and	CCONJ
ejpam-6535	25	35	probabilistic	probabilistic	ADJ
ejpam-6535	25	36	norm	norm	NOUN
ejpam-6535	25	37	-	-	PUNCT
ejpam-6535	25	38	groups	group	NOUN
ejpam-6535	25	39	leading	lead	VERB
ejpam-6535	25	40	to	to	ADP
ejpam-6535	25	41	the	the	DET
ejpam-6535	25	42	fact	fact	NOUN
ejpam-6535	25	43	that	that	SCONJ
ejpam-6535	25	44	the	the	DET
ejpam-6535	25	45	category	category	NOUN
ejpam-6535	25	46	of	of	ADP
ejpam-6535	25	47	probabilistic	probabilistic	ADJ
ejpam-6535	25	48	normed	normed	ADJ
ejpam-6535	25	49	groups	group	NOUN
ejpam-6535	25	50	is	be	AUX
ejpam-6535	25	51	isomorphic	isomorphic	ADJ
ejpam-6535	25	52	to	to	ADP
ejpam-6535	25	53	the	the	DET
ejpam-6535	25	54	category	category	NOUN
ejpam-6535	25	55	of	of	ADP
ejpam-6535	25	56	probabilistic	probabilistic	ADJ
ejpam-6535	25	57	metric	metric	ADJ
ejpam-6535	25	58	groups	group	NOUN
ejpam-6535	25	59	.	.	PUNCT
ejpam-6535	26	1	2	2	X
ejpam-6535	26	2	.	.	X
ejpam-6535	26	3	preliminaries	preliminary	NOUN
ejpam-6535	26	4	if	if	SCONJ
ejpam-6535	26	5	(	(	PUNCT
ejpam-6535	26	6	a,≤	a,≤	NOUN
ejpam-6535	26	7	)	)	PUNCT
ejpam-6535	26	8	is	be	AUX
ejpam-6535	26	9	an	an	DET
ejpam-6535	26	10	ordered	order	VERB
ejpam-6535	26	11	set	set	NOUN
ejpam-6535	26	12	,	,	PUNCT
ejpam-6535	26	13	we	we	PRON
ejpam-6535	26	14	denote	denote	VERB
ejpam-6535	26	15	by	by	ADP
ejpam-6535	26	16	∧	∧	PROPN
ejpam-6535	26	17	j∈j	j∈j	NOUN
ejpam-6535	26	18	αj	αj	ADP
ejpam-6535	26	19	the	the	DET
ejpam-6535	26	20	infimum	infimum	NOUN
ejpam-6535	26	21	,	,	PUNCT
ejpam-6535	26	22	while	while	SCONJ
ejpam-6535	26	23	∨	∨	PROPN
ejpam-6535	26	24	j∈j	j∈j	NOUN
ejpam-6535	26	25	αj	αj	PROPN
ejpam-6535	26	26	denotes	denote	VERB
ejpam-6535	26	27	the	the	DET
ejpam-6535	26	28	supremum	supremum	ADJ
ejpam-6535	26	29	,	,	PUNCT
ejpam-6535	26	30	if	if	SCONJ
ejpam-6535	26	31	they	they	PRON
ejpam-6535	26	32	exist	exist	VERB
ejpam-6535	26	33	,	,	PUNCT
ejpam-6535	26	34	of	of	ADP
ejpam-6535	26	35	the	the	DET
ejpam-6535	26	36	set	set	NOUN
ejpam-6535	26	37	{	{	PUNCT
ejpam-6535	26	38	αj	αj	NOUN
ejpam-6535	26	39	:	:	PUNCT
ejpam-6535	27	1	j	j	PROPN
ejpam-6535	27	2	∈	∈	PROPN
ejpam-6535	27	3	j	j	PROPN
ejpam-6535	27	4	}	}	PUNCT
ejpam-6535	27	5	⊆	⊆	NUM
ejpam-6535	27	6	a.	a.	NOUN
ejpam-6535	27	7	in	in	ADP
ejpam-6535	27	8	case	case	NOUN
ejpam-6535	27	9	of	of	ADP
ejpam-6535	27	10	a	a	DET
ejpam-6535	27	11	two	two	NUM
ejpam-6535	27	12	-	-	PUNCT
ejpam-6535	27	13	point	point	NOUN
ejpam-6535	27	14	set	set	NOUN
ejpam-6535	27	15	{	{	PUNCT
ejpam-6535	27	16	α	α	NOUN
ejpam-6535	27	17	,	,	PUNCT
ejpam-6535	27	18	β	β	X
ejpam-6535	27	19	}	}	PUNCT
ejpam-6535	27	20	we	we	PRON
ejpam-6535	27	21	write	write	VERB
ejpam-6535	27	22	α	α	PROPN
ejpam-6535	27	23	∧	∧	PROPN
ejpam-6535	27	24	β	β	X
ejpam-6535	27	25	and	and	CCONJ
ejpam-6535	27	26	α	α	PROPN
ejpam-6535	27	27	∨	∨	NUM
ejpam-6535	27	28	β	β	NOUN
ejpam-6535	27	29	,	,	PUNCT
ejpam-6535	27	30	respectively	respectively	ADV
ejpam-6535	27	31	.	.	PUNCT
ejpam-6535	28	1	a	a	DET
ejpam-6535	28	2	function	function	NOUN
ejpam-6535	28	3	φ	φ	NOUN
ejpam-6535	28	4	:	:	PUNCT
ejpam-6535	29	1	[	[	X
ejpam-6535	29	2	0,∞	0,∞	X
ejpam-6535	29	3	]	]	X
ejpam-6535	29	4	−→	−→	NOUN
ejpam-6535	29	5	[	[	X
ejpam-6535	29	6	0	0	NUM
ejpam-6535	29	7	,	,	PUNCT
ejpam-6535	29	8	1	1	NUM
ejpam-6535	29	9	]	]	PUNCT
ejpam-6535	29	10	,	,	PUNCT
ejpam-6535	29	11	which	which	PRON
ejpam-6535	29	12	is	be	AUX
ejpam-6535	29	13	non	non	ADJ
ejpam-6535	29	14	-	-	ADJ
ejpam-6535	29	15	decreasing	decrease	VERB
ejpam-6535	29	16	,	,	PUNCT
ejpam-6535	29	17	left	left	ADJ
ejpam-6535	29	18	-	-	PUNCT
ejpam-6535	29	19	continuous	continuous	ADJ
ejpam-6535	29	20	on	on	ADP
ejpam-6535	29	21	(	(	PUNCT
ejpam-6535	29	22	0,∞	0,∞	NOUN
ejpam-6535	29	23	)	)	PUNCT
ejpam-6535	29	24	and	and	CCONJ
ejpam-6535	29	25	satisfies	satisfy	VERB
ejpam-6535	29	26	φ(0	φ(0	ADJ
ejpam-6535	29	27	)	)	PUNCT
ejpam-6535	29	28	=	=	SYM
ejpam-6535	29	29	0	0	NUM
ejpam-6535	29	30	and	and	CCONJ
ejpam-6535	29	31	φ(∞	φ(∞	NOUN
ejpam-6535	29	32	)	)	PUNCT
ejpam-6535	29	33	=	=	SYM
ejpam-6535	29	34	1	1	NUM
ejpam-6535	29	35	,	,	PUNCT
ejpam-6535	29	36	is	be	AUX
ejpam-6535	29	37	called	call	VERB
ejpam-6535	29	38	a	a	DET
ejpam-6535	29	39	distance	distance	NOUN
ejpam-6535	29	40	distribution	distribution	NOUN
ejpam-6535	29	41	function	function	NOUN
ejpam-6535	29	42	[	[	X
ejpam-6535	29	43	34	34	NUM
ejpam-6535	29	44	]	]	PUNCT
ejpam-6535	29	45	.	.	PUNCT
ejpam-6535	30	1	the	the	DET
ejpam-6535	30	2	set	set	NOUN
ejpam-6535	30	3	of	of	ADP
ejpam-6535	30	4	all	all	DET
ejpam-6535	30	5	distance	distance	NOUN
ejpam-6535	30	6	distribution	distribution	NOUN
ejpam-6535	30	7	functions	function	NOUN
ejpam-6535	30	8	is	be	AUX
ejpam-6535	30	9	denoted	denote	VERB
ejpam-6535	30	10	by	by	ADP
ejpam-6535	30	11	∆+	∆+	NOUN
ejpam-6535	30	12	.	.	PUNCT
ejpam-6535	31	1	for	for	ADP
ejpam-6535	31	2	example	example	NOUN
ejpam-6535	31	3	,	,	PUNCT
ejpam-6535	31	4	for	for	SCONJ
ejpam-6535	31	5	each	each	DET
ejpam-6535	31	6	0	0	NUM
ejpam-6535	31	7	≤	≤	NOUN
ejpam-6535	31	8	a	a	DET
ejpam-6535	31	9	<	<	X
ejpam-6535	31	10	∞	∞	NUM
ejpam-6535	31	11	the	the	DET
ejpam-6535	31	12	functions	function	NOUN
ejpam-6535	31	13	ϵa(x	ϵa(x	PUNCT
ejpam-6535	31	14	)	)	PUNCT
ejpam-6535	31	15	=	=	PRON
ejpam-6535	31	16	{	{	PUNCT
ejpam-6535	31	17	0	0	NUM
ejpam-6535	31	18	if	if	SCONJ
ejpam-6535	31	19	0	0	NUM
ejpam-6535	31	20	≤	≤	NUM
ejpam-6535	31	21	x	x	SYM
ejpam-6535	31	22	≤	≤	NUM
ejpam-6535	31	23	a	a	DET
ejpam-6535	31	24	1	1	NUM
ejpam-6535	31	25	if	if	SCONJ
ejpam-6535	31	26	a	a	DET
ejpam-6535	31	27	<	<	X
ejpam-6535	31	28	x	x	SYM
ejpam-6535	31	29	≤	≤	NUM
ejpam-6535	31	30	∞	∞	NUM
ejpam-6535	31	31	and	and	CCONJ
ejpam-6535	31	32	ϵ∞(x	ϵ∞(x	NOUN
ejpam-6535	31	33	)	)	PUNCT
ejpam-6535	31	34	=	=	PRON
ejpam-6535	31	35	{	{	PUNCT
ejpam-6535	31	36	0	0	NUM
ejpam-6535	31	37	if	if	SCONJ
ejpam-6535	31	38	0	0	NUM
ejpam-6535	31	39	≤	≤	NUM
ejpam-6535	31	40	x	x	PUNCT
ejpam-6535	32	1	<	<	X
ejpam-6535	32	2	∞	∞	NUM
ejpam-6535	32	3	1	1	NUM
ejpam-6535	32	4	if	if	SCONJ
ejpam-6535	32	5	x	x	X
ejpam-6535	32	6	=	=	SYM
ejpam-6535	32	7	∞	∞	NUM
ejpam-6535	32	8	belong	belong	VERB
ejpam-6535	32	9	to	to	ADP
ejpam-6535	32	10	∆+	∆+	NOUN
ejpam-6535	32	11	.	.	PUNCT
ejpam-6535	33	1	it	it	PRON
ejpam-6535	33	2	is	be	AUX
ejpam-6535	33	3	well	well	ADV
ejpam-6535	33	4	-	-	PUNCT
ejpam-6535	33	5	known	know	VERB
ejpam-6535	33	6	that	that	SCONJ
ejpam-6535	33	7	(	(	PUNCT
ejpam-6535	33	8	∆+,≤	∆+,≤	NOUN
ejpam-6535	33	9	)	)	PUNCT
ejpam-6535	33	10	is	be	AUX
ejpam-6535	33	11	a	a	DET
ejpam-6535	33	12	complete	complete	ADJ
ejpam-6535	33	13	lattice	lattice	NOUN
ejpam-6535	33	14	with	with	ADP
ejpam-6535	33	15	minimal	minimal	ADJ
ejpam-6535	33	16	element	element	NOUN
ejpam-6535	33	17	ϵ∞	ϵ∞	PROPN
ejpam-6535	33	18	and	and	CCONJ
ejpam-6535	33	19	maximal	maximal	ADJ
ejpam-6535	33	20	element	element	NOUN
ejpam-6535	33	21	ϵ0	ϵ0	NOUN
ejpam-6535	33	22	.	.	PUNCT
ejpam-6535	34	1	thus	thus	ADV
ejpam-6535	34	2	for	for	ADP
ejpam-6535	34	3	any	any	DET
ejpam-6535	34	4	nonempty	nonempty	ADV
ejpam-6535	34	5	set	set	VERB
ejpam-6535	34	6	j	j	PROPN
ejpam-6535	34	7	and	and	CCONJ
ejpam-6535	34	8	any	any	DET
ejpam-6535	34	9	family	family	NOUN
ejpam-6535	34	10	(	(	PUNCT
ejpam-6535	34	11	φj)j∈j	φj)j∈j	NUM
ejpam-6535	34	12	of	of	ADP
ejpam-6535	34	13	distribution	distribution	NOUN
ejpam-6535	34	14	functions	function	NOUN
ejpam-6535	34	15	in	in	ADP
ejpam-6535	34	16	∆+	∆+	NOUN
ejpam-6535	34	17	,	,	PUNCT
ejpam-6535	34	18	the	the	DET
ejpam-6535	34	19	function	function	NOUN
ejpam-6535	34	20	φ	φ	X
ejpam-6535	34	21	=	=	SYM
ejpam-6535	34	22	∨	∨	PROPN
ejpam-6535	34	23	j∈j	j∈j	NOUN
ejpam-6535	34	24	φj	φj	PROPN
ejpam-6535	34	25	is	be	AUX
ejpam-6535	34	26	also	also	ADV
ejpam-6535	34	27	in	in	ADP
ejpam-6535	34	28	∆+	∆+	NOUN
ejpam-6535	34	29	.	.	PUNCT
ejpam-6535	35	1	the	the	DET
ejpam-6535	35	2	following	following	ADJ
ejpam-6535	35	3	result	result	NOUN
ejpam-6535	35	4	is	be	AUX
ejpam-6535	35	5	mentioned	mention	VERB
ejpam-6535	35	6	in	in	ADP
ejpam-6535	35	7	schweizer	schweizer	PROPN
ejpam-6535	35	8	and	and	CCONJ
ejpam-6535	35	9	sklar	sklar	ADJ
ejpam-6535	36	1	[	[	X
ejpam-6535	36	2	34	34	NUM
ejpam-6535	36	3	]	]	PUNCT
ejpam-6535	36	4	.	.	PUNCT
ejpam-6535	37	1	lemma	lemma	PROPN
ejpam-6535	37	2	1	1	NUM
ejpam-6535	37	3	.	.	PUNCT
ejpam-6535	38	1	(	(	PUNCT
ejpam-6535	38	2	i	i	NOUN
ejpam-6535	38	3	)	)	PUNCT
ejpam-6535	38	4	if	if	SCONJ
ejpam-6535	38	5	φ	φ	PROPN
ejpam-6535	38	6	,	,	PUNCT
ejpam-6535	38	7	ψ	ψ	X
ejpam-6535	38	8	∈	∈	PROPN
ejpam-6535	38	9	∆+	∆+	NOUN
ejpam-6535	38	10	,	,	PUNCT
ejpam-6535	38	11	then	then	ADV
ejpam-6535	38	12	also	also	ADV
ejpam-6535	38	13	φ	φ	PROPN
ejpam-6535	38	14	∧	∧	PROPN
ejpam-6535	38	15	ψ	ψ	ADP
ejpam-6535	38	16	∈	∈	PROPN
ejpam-6535	38	17	∆+	∆+	NOUN
ejpam-6535	38	18	.	.	PUNCT
ejpam-6535	39	1	(	(	PUNCT
ejpam-6535	39	2	ii	ii	NOUN
ejpam-6535	39	3	)	)	PUNCT
ejpam-6535	39	4	if	if	SCONJ
ejpam-6535	39	5	φj	φj	ADP
ejpam-6535	39	6	∈	∈	PROPN
ejpam-6535	39	7	∆+	∆+	NUM
ejpam-6535	39	8	for	for	ADP
ejpam-6535	39	9	all	all	DET
ejpam-6535	39	10	j	j	PROPN
ejpam-6535	39	11	∈	∈	PROPN
ejpam-6535	39	12	j	j	PROPN
ejpam-6535	39	13	,	,	PUNCT
ejpam-6535	39	14	then	then	ADV
ejpam-6535	39	15	also	also	ADV
ejpam-6535	39	16	∨	∨	NUM
ejpam-6535	39	17	j∈j	j∈j	PROPN
ejpam-6535	39	18	φj	φj	ADP
ejpam-6535	39	19	∈	∈	PROPN
ejpam-6535	39	20	∆+	∆+	NOUN
ejpam-6535	39	21	.	.	PUNCT
ejpam-6535	40	1	here	here	ADV
ejpam-6535	40	2	,	,	PUNCT
ejpam-6535	40	3	φ	φ	PROPN
ejpam-6535	40	4	∧	∧	PROPN
ejpam-6535	40	5	ψ	ψ	PROPN
ejpam-6535	40	6	denotes	denote	VERB
ejpam-6535	40	7	the	the	DET
ejpam-6535	40	8	point	point	ADV
ejpam-6535	40	9	-	-	PUNCT
ejpam-6535	40	10	wise	wise	ADJ
ejpam-6535	40	11	minimum	minimum	NOUN
ejpam-6535	40	12	of	of	ADP
ejpam-6535	40	13	φ	φ	PROPN
ejpam-6535	40	14	and	and	CCONJ
ejpam-6535	40	15	ψ	ψ	X
ejpam-6535	40	16	in	in	ADP
ejpam-6535	40	17	(	(	PUNCT
ejpam-6535	40	18	∆+,≤	∆+,≤	NOUN
ejpam-6535	40	19	)	)	PUNCT
ejpam-6535	40	20	and	and	CCONJ
ejpam-6535	40	21	∨	∨	NUM
ejpam-6535	40	22	j∈j	j∈j	PROPN
ejpam-6535	40	23	φj	φj	PROPN
ejpam-6535	40	24	denotes	denote	VERB
ejpam-6535	40	25	the	the	DET
ejpam-6535	40	26	pointwise	pointwise	PROPN
ejpam-6535	40	27	supremum	supremum	NOUN
ejpam-6535	40	28	of	of	ADP
ejpam-6535	40	29	the	the	DET
ejpam-6535	40	30	family	family	NOUN
ejpam-6535	40	31	{	{	PUNCT
ejpam-6535	40	32	φj	φj	X
ejpam-6535	40	33	:	:	PUNCT
ejpam-6535	40	34	j	j	PROPN
ejpam-6535	40	35	∈	∈	PROPN
ejpam-6535	40	36	j	j	PROPN
ejpam-6535	40	37	}	}	PUNCT
ejpam-6535	40	38	in	in	ADP
ejpam-6535	40	39	(	(	PUNCT
ejpam-6535	40	40	∆+,≤	∆+,≤	NOUN
ejpam-6535	40	41	)	)	PUNCT
ejpam-6535	40	42	.	.	PUNCT
ejpam-6535	41	1	on	on	ADP
ejpam-6535	41	2	the	the	DET
ejpam-6535	41	3	set	set	NOUN
ejpam-6535	41	4	∆+	∆+	AUX
ejpam-6535	41	5	we	we	PRON
ejpam-6535	41	6	consider	consider	VERB
ejpam-6535	41	7	the	the	DET
ejpam-6535	41	8	modified	modified	ADJ
ejpam-6535	41	9	lévy	lévy	X
ejpam-6535	41	10	metric	metric	NOUN
ejpam-6535	41	11	[	[	X
ejpam-6535	41	12	37	37	NUM
ejpam-6535	41	13	]	]	PUNCT
ejpam-6535	41	14	,	,	PUNCT
ejpam-6535	41	15	which	which	PRON
ejpam-6535	41	16	is	be	AUX
ejpam-6535	41	17	defined	define	VERB
ejpam-6535	41	18	below	below	ADP
ejpam-6535	41	19	for	for	ADP
ejpam-6535	41	20	the	the	DET
ejpam-6535	41	21	convenience	convenience	NOUN
ejpam-6535	41	22	of	of	ADP
ejpam-6535	41	23	the	the	DET
ejpam-6535	41	24	reader	reader	NOUN
ejpam-6535	41	25	.	.	PUNCT
ejpam-6535	42	1	let	let	VERB
ejpam-6535	42	2	φ	φ	NOUN
ejpam-6535	42	3	,	,	PUNCT
ejpam-6535	42	4	ψ	ψ	PROPN
ejpam-6535	42	5	∈	∈	PROPN
ejpam-6535	42	6	∆+	∆+	NUM
ejpam-6535	42	7	and	and	CCONJ
ejpam-6535	42	8	ϵ	ϵ	X
ejpam-6535	42	9	>	>	X
ejpam-6535	42	10	0	0	X
ejpam-6535	42	11	.	.	PUNCT
ejpam-6535	42	12	consider	consider	VERB
ejpam-6535	42	13	the	the	DET
ejpam-6535	42	14	following	follow	VERB
ejpam-6535	42	15	properties	property	NOUN
ejpam-6535	42	16	a	a	DET
ejpam-6535	42	17	(	(	PUNCT
ejpam-6535	42	18	φ	φ	PROPN
ejpam-6535	42	19	,	,	PUNCT
ejpam-6535	42	20	ψ	ψ	SYM
ejpam-6535	42	21	;	;	PUNCT
ejpam-6535	42	22	ϵ	ϵ	X
ejpam-6535	42	23	)	)	PUNCT
ejpam-6535	42	24	⇐	⇐	ADJ
ejpam-6535	42	25	⇒	⇒	NOUN
ejpam-6535	42	26	φ(x−	φ(x−	PROPN
ejpam-6535	42	27	ϵ)−	ϵ)−	PROPN
ejpam-6535	42	28	ϵ	ϵ	X
ejpam-6535	42	29	≤	≤	NUM
ejpam-6535	42	30	ψ(x	ψ(x	NOUN
ejpam-6535	42	31	)	)	PUNCT
ejpam-6535	42	32	,	,	PUNCT
ejpam-6535	43	1	if	if	SCONJ
ejpam-6535	43	2	x	x	PUNCT
ejpam-6535	43	3	∈	∈	PROPN
ejpam-6535	43	4	[	[	X
ejpam-6535	43	5	0	0	NUM
ejpam-6535	43	6	,	,	PUNCT
ejpam-6535	43	7	1ϵ	1ϵ	NUM
ejpam-6535	43	8	)	)	PUNCT
ejpam-6535	43	9	;	;	PUNCT
ejpam-6535	43	10	and	and	CCONJ
ejpam-6535	43	11	b	b	X
ejpam-6535	43	12	(	(	PUNCT
ejpam-6535	43	13	φ	φ	PROPN
ejpam-6535	43	14	,	,	PUNCT
ejpam-6535	43	15	ψ	ψ	SYM
ejpam-6535	43	16	;	;	PUNCT
ejpam-6535	43	17	ϵ	ϵ	X
ejpam-6535	43	18	)	)	PUNCT
ejpam-6535	43	19	⇐	⇐	ADJ
ejpam-6535	43	20	⇒	⇒	NOUN
ejpam-6535	43	21	φ(x+	φ(x+	PROPN
ejpam-6535	43	22	ϵ	ϵ	X
ejpam-6535	43	23	)	)	PUNCT
ejpam-6535	43	24	+	+	CCONJ
ejpam-6535	43	25	ϵ	ϵ	PRON
ejpam-6535	43	26	≥	≥	NOUN
ejpam-6535	43	27	ψ(x	ψ(x	NOUN
ejpam-6535	43	28	)	)	PUNCT
ejpam-6535	43	29	,	,	PUNCT
ejpam-6535	43	30	if	if	SCONJ
ejpam-6535	43	31	x	x	PUNCT
ejpam-6535	43	32	∈	∈	PROPN
ejpam-6535	44	1	[	[	X
ejpam-6535	44	2	0	0	NUM
ejpam-6535	44	3	,	,	PUNCT
ejpam-6535	44	4	1ϵ	1ϵ	NUM
ejpam-6535	44	5	)	)	PUNCT
ejpam-6535	44	6	.	.	PUNCT
ejpam-6535	45	1	then	then	ADV
ejpam-6535	45	2	the	the	DET
ejpam-6535	45	3	modified	modified	ADJ
ejpam-6535	45	4	lévy	lévy	X
ejpam-6535	45	5	metric	metric	ADJ
ejpam-6535	45	6	dl	dl	PROPN
ejpam-6535	45	7	on	on	ADP
ejpam-6535	45	8	∆+	∆+	NUM
ejpam-6535	45	9	×∆+	×∆+	NUM
ejpam-6535	45	10	is	be	AUX
ejpam-6535	45	11	given	give	VERB
ejpam-6535	45	12	by	by	ADP
ejpam-6535	45	13	dl	dl	PROPN
ejpam-6535	45	14	(	(	PUNCT
ejpam-6535	45	15	φ	φ	PROPN
ejpam-6535	45	16	,	,	PUNCT
ejpam-6535	45	17	ψ	ψ	NOUN
ejpam-6535	45	18	)	)	PUNCT
ejpam-6535	45	19	=	=	SYM
ejpam-6535	45	20	∧	∧	NOUN
ejpam-6535	45	21	{	{	PUNCT
ejpam-6535	45	22	ϵ	ϵ	X
ejpam-6535	45	23	>	>	X
ejpam-6535	45	24	0	0	NUM
ejpam-6535	45	25	:	:	PUNCT
ejpam-6535	45	26	a	a	PRON
ejpam-6535	45	27	(	(	PUNCT
ejpam-6535	45	28	φ	φ	PROPN
ejpam-6535	45	29	,	,	PUNCT
ejpam-6535	45	30	ψ	ψ	SYM
ejpam-6535	45	31	;	;	PUNCT
ejpam-6535	45	32	ϵ	ϵ	X
ejpam-6535	45	33	)	)	PUNCT
ejpam-6535	45	34	and	and	CCONJ
ejpam-6535	45	35	b	b	X
ejpam-6535	45	36	(	(	PUNCT
ejpam-6535	45	37	φ	φ	PROPN
ejpam-6535	45	38	,	,	PUNCT
ejpam-6535	45	39	ψ	ψ	SYM
ejpam-6535	45	40	;	;	PUNCT
ejpam-6535	45	41	ϵ	ϵ	X
ejpam-6535	45	42	)	)	PUNCT
ejpam-6535	45	43	hold	hold	NOUN
ejpam-6535	45	44	}	}	PUNCT
ejpam-6535	45	45	.	.	PUNCT
ejpam-6535	46	1	definition	definition	NOUN
ejpam-6535	46	2	1	1	NUM
ejpam-6535	46	3	.	.	PUNCT
ejpam-6535	47	1	a	a	DET
ejpam-6535	47	2	binary	binary	ADJ
ejpam-6535	47	3	operation	operation	NOUN
ejpam-6535	47	4	τ	τ	X
ejpam-6535	47	5	:	:	PUNCT
ejpam-6535	47	6	∆+×∆+	∆+×∆+	PROPN
ejpam-6535	47	7	−→	−→	NOUN
ejpam-6535	47	8	∆+	∆+	NOUN
ejpam-6535	47	9	,	,	PUNCT
ejpam-6535	47	10	which	which	PRON
ejpam-6535	47	11	is	be	AUX
ejpam-6535	47	12	commutative	commutative	ADJ
ejpam-6535	47	13	,	,	PUNCT
ejpam-6535	47	14	associative	associative	ADJ
ejpam-6535	47	15	,	,	PUNCT
ejpam-6535	47	16	non	non	ADJ
ejpam-6535	47	17	-	-	ADJ
ejpam-6535	47	18	decreasing	decrease	VERB
ejpam-6535	47	19	in	in	ADP
ejpam-6535	47	20	each	each	DET
ejpam-6535	47	21	place	place	NOUN
ejpam-6535	47	22	satisfying	satisfy	VERB
ejpam-6535	47	23	the	the	DET
ejpam-6535	47	24	boundary	boundary	ADJ
ejpam-6535	47	25	condition	condition	NOUN
ejpam-6535	47	26	τ(φ	τ(φ	ADV
ejpam-6535	47	27	,	,	PUNCT
ejpam-6535	47	28	ϵ0	ϵ0	NUM
ejpam-6535	47	29	)	)	PUNCT
ejpam-6535	47	30	=	=	PUNCT
ejpam-6535	47	31	φ	φ	PROPN
ejpam-6535	47	32	for	for	ADP
ejpam-6535	47	33	all	all	DET
ejpam-6535	47	34	φ	φ	PROPN
ejpam-6535	47	35	∈	∈	PROPN
ejpam-6535	47	36	∆+	∆+	NOUN
ejpam-6535	47	37	,	,	PUNCT
ejpam-6535	47	38	is	be	AUX
ejpam-6535	47	39	called	call	VERB
ejpam-6535	47	40	a	a	DET
ejpam-6535	47	41	triangle	triangle	NOUN
ejpam-6535	47	42	function	function	NOUN
ejpam-6535	47	43	[	[	X
ejpam-6535	47	44	34	34	NUM
ejpam-6535	47	45	]	]	PUNCT
ejpam-6535	47	46	.	.	PUNCT
ejpam-6535	48	1	the	the	DET
ejpam-6535	48	2	largest	large	ADJ
ejpam-6535	48	3	triangle	triangle	NOUN
ejpam-6535	48	4	function	function	NOUN
ejpam-6535	48	5	is	be	AUX
ejpam-6535	48	6	the	the	DET
ejpam-6535	48	7	point	point	ADV
ejpam-6535	48	8	-	-	PUNCT
ejpam-6535	48	9	wise	wise	ADJ
ejpam-6535	48	10	minimum	minimum	ADJ
ejpam-6535	48	11	µ(φ	µ(φ	NOUN
ejpam-6535	48	12	,	,	PUNCT
ejpam-6535	48	13	ψ	ψ	NOUN
ejpam-6535	48	14	)	)	PUNCT
ejpam-6535	48	15	=	=	SYM
ejpam-6535	49	1	φ	φ	NUM
ejpam-6535	49	2	∧	∧	PROPN
ejpam-6535	49	3	ψ	ψ	PROPN
ejpam-6535	49	4	.	.	PUNCT
ejpam-6535	50	1	it	it	PRON
ejpam-6535	50	2	is	be	AUX
ejpam-6535	50	3	easy	easy	ADJ
ejpam-6535	50	4	to	to	PART
ejpam-6535	50	5	prove	prove	VERB
ejpam-6535	50	6	that	that	SCONJ
ejpam-6535	50	7	a	a	DET
ejpam-6535	50	8	triangle	triangle	NOUN
ejpam-6535	50	9	function	function	NOUN
ejpam-6535	50	10	that	that	PRON
ejpam-6535	50	11	is	be	AUX
ejpam-6535	50	12	idempotent	idempotent	ADJ
ejpam-6535	50	13	,	,	PUNCT
ejpam-6535	50	14	i.e.	i.e.	X
ejpam-6535	50	15	,	,	PUNCT
ejpam-6535	50	16	for	for	ADP
ejpam-6535	50	17	which	which	PRON
ejpam-6535	50	18	τ(φ	τ(φ	ADP
ejpam-6535	50	19	,	,	PUNCT
ejpam-6535	50	20	φ	φ	NUM
ejpam-6535	50	21	)	)	PUNCT
ejpam-6535	50	22	=	=	SYM
ejpam-6535	50	23	φ	φ	PROPN
ejpam-6535	50	24	for	for	ADP
ejpam-6535	50	25	all	all	DET
ejpam-6535	50	26	φ	φ	PROPN
ejpam-6535	50	27	∈	∈	PROPN
ejpam-6535	50	28	∆+	∆+	NOUN
ejpam-6535	50	29	,	,	PUNCT
ejpam-6535	50	30	must	must	AUX
ejpam-6535	50	31	be	be	AUX
ejpam-6535	50	32	the	the	DET
ejpam-6535	50	33	largest	large	ADJ
ejpam-6535	50	34	triangle	triangle	NOUN
ejpam-6535	50	35	function	function	NOUN
ejpam-6535	50	36	.	.	PUNCT
ejpam-6535	51	1	for	for	ADP
ejpam-6535	51	2	a	a	DET
ejpam-6535	51	3	good	good	ADJ
ejpam-6535	51	4	survey	survey	NOUN
ejpam-6535	51	5	on	on	ADP
ejpam-6535	51	6	triangle	triangle	NOUN
ejpam-6535	51	7	functions	function	NOUN
ejpam-6535	51	8	,	,	PUNCT
ejpam-6535	51	9	see	see	VERB
ejpam-6535	51	10	e.g.	e.g.	ADV
ejpam-6535	51	11	[	[	X
ejpam-6535	51	12	33	33	NUM
ejpam-6535	51	13	]	]	PUNCT
ejpam-6535	51	14	.	.	PUNCT
ejpam-6535	52	1	a	a	DET
ejpam-6535	52	2	triangle	triangle	NOUN
ejpam-6535	52	3	function	function	NOUN
ejpam-6535	52	4	is	be	AUX
ejpam-6535	52	5	called	call	VERB
ejpam-6535	52	6	continuous	continuous	ADJ
ejpam-6535	52	7	[	[	X
ejpam-6535	52	8	34	34	NUM
ejpam-6535	52	9	,	,	PUNCT
ejpam-6535	52	10	38	38	NUM
ejpam-6535	52	11	]	]	PUNCT
ejpam-6535	52	12	if	if	SCONJ
ejpam-6535	52	13	it	it	PRON
ejpam-6535	52	14	is	be	AUX
ejpam-6535	52	15	a	a	DET
ejpam-6535	52	16	continuous	continuous	ADJ
ejpam-6535	52	17	function	function	NOUN
ejpam-6535	52	18	with	with	ADP
ejpam-6535	52	19	respect	respect	NOUN
ejpam-6535	52	20	to	to	ADP
ejpam-6535	52	21	the	the	DET
ejpam-6535	52	22	topology	topology	NOUN
ejpam-6535	52	23	and	and	CCONJ
ejpam-6535	52	24	product	product	NOUN
ejpam-6535	52	25	topology	topology	NOUN
ejpam-6535	52	26	induced	induce	VERB
ejpam-6535	52	27	by	by	ADP
ejpam-6535	52	28	the	the	DET
ejpam-6535	52	29	modified	modified	ADJ
ejpam-6535	52	30	lévy	lévy	X
ejpam-6535	52	31	metric	metric	ADJ
ejpam-6535	52	32	.	.	PUNCT
ejpam-6535	53	1	a	a	DET
ejpam-6535	53	2	triangle	triangle	NOUN
ejpam-6535	53	3	function	function	NOUN
ejpam-6535	53	4	is	be	AUX
ejpam-6535	53	5	called	call	VERB
ejpam-6535	53	6	sup	sup	NOUN
ejpam-6535	53	7	-	-	PUNCT
ejpam-6535	53	8	continuous	continuous	ADJ
ejpam-6535	53	9	[	[	X
ejpam-6535	53	10	34	34	NUM
ejpam-6535	53	11	,	,	PUNCT
ejpam-6535	53	12	38	38	NUM
ejpam-6535	53	13	]	]	PUNCT
ejpam-6535	53	14	if	if	SCONJ
ejpam-6535	53	15	τ	τ	PROPN
ejpam-6535	53	16	(	(	PUNCT
ejpam-6535	53	17	∨	∨	PROPN
ejpam-6535	53	18	j∈j	j∈j	NOUN
ejpam-6535	53	19	φj	φj	PROPN
ejpam-6535	53	20	,	,	PUNCT
ejpam-6535	53	21	ψ	ψ	X
ejpam-6535	53	22	)	)	PUNCT
ejpam-6535	53	23	=	=	SYM
ejpam-6535	53	24	∨	∨	NUM
ejpam-6535	53	25	j∈j	j∈j	NOUN
ejpam-6535	53	26	τ(φj	τ(φj	PROPN
ejpam-6535	53	27	,	,	PUNCT
ejpam-6535	53	28	ψ	ψ	X
ejpam-6535	53	29	)	)	PUNCT
ejpam-6535	53	30	for	for	ADP
ejpam-6535	53	31	all	all	DET
ejpam-6535	53	32	φj	φj	NOUN
ejpam-6535	53	33	,	,	PUNCT
ejpam-6535	53	34	ψ	ψ	X
ejpam-6535	53	35	∈	∈	PROPN
ejpam-6535	53	36	∆+	∆+	NUM
ejpam-6535	53	37	(	(	PUNCT
ejpam-6535	53	38	j	j	PROPN
ejpam-6535	53	39	∈	∈	PROPN
ejpam-6535	53	40	j	j	PROPN
ejpam-6535	53	41	)	)	PUNCT
ejpam-6535	53	42	.	.	PUNCT
ejpam-6535	54	1	for	for	ADP
ejpam-6535	54	2	further	further	ADJ
ejpam-6535	54	3	study	study	NOUN
ejpam-6535	54	4	on	on	ADP
ejpam-6535	54	5	sup	sup	NOUN
ejpam-6535	54	6	-	-	PUNCT
ejpam-6535	54	7	continuity	continuity	NOUN
ejpam-6535	54	8	and	and	CCONJ
ejpam-6535	54	9	its	its	PRON
ejpam-6535	54	10	relation	relation	NOUN
ejpam-6535	54	11	to	to	ADP
ejpam-6535	54	12	continuity	continuity	NOUN
ejpam-6535	54	13	,	,	PUNCT
ejpam-6535	54	14	we	we	PRON
ejpam-6535	54	15	refer	refer	VERB
ejpam-6535	54	16	to	to	ADP
ejpam-6535	54	17	[	[	X
ejpam-6535	54	18	34	34	NUM
ejpam-6535	54	19	]	]	PUNCT
ejpam-6535	54	20	.	.	PUNCT
ejpam-6535	55	1	for	for	ADP
ejpam-6535	55	2	a	a	DET
ejpam-6535	55	3	set	set	NOUN
ejpam-6535	55	4	s	s	PART
ejpam-6535	55	5	,	,	PUNCT
ejpam-6535	55	6	we	we	PRON
ejpam-6535	55	7	denote	denote	VERB
ejpam-6535	55	8	p	p	X
ejpam-6535	55	9	(	(	PUNCT
ejpam-6535	55	10	s	s	X
ejpam-6535	55	11	)	)	PUNCT
ejpam-6535	55	12	its	its	PRON
ejpam-6535	55	13	power	power	NOUN
ejpam-6535	55	14	set	set	NOUN
ejpam-6535	55	15	.	.	PUNCT
ejpam-6535	56	1	we	we	PRON
ejpam-6535	56	2	denote	denote	VERB
ejpam-6535	56	3	the	the	DET
ejpam-6535	56	4	set	set	NOUN
ejpam-6535	56	5	of	of	ADP
ejpam-6535	56	6	filters	filter	NOUN
ejpam-6535	56	7	on	on	ADP
ejpam-6535	56	8	the	the	DET
ejpam-6535	56	9	set	set	NOUN
ejpam-6535	56	10	s	s	X
ejpam-6535	56	11	by	by	ADP
ejpam-6535	56	12	f(s	f(	NOUN
ejpam-6535	56	13	)	)	PUNCT
ejpam-6535	56	14	.	.	PUNCT
ejpam-6535	57	1	we	we	PRON
ejpam-6535	57	2	order	order	VERB
ejpam-6535	57	3	this	this	DET
ejpam-6535	57	4	set	set	VERB
ejpam-6535	57	5	by	by	ADP
ejpam-6535	57	6	set	set	VERB
ejpam-6535	57	7	inclusion	inclusion	NOUN
ejpam-6535	57	8	and	and	CCONJ
ejpam-6535	57	9	we	we	PRON
ejpam-6535	57	10	denote	denote	VERB
ejpam-6535	57	11	for	for	ADP
ejpam-6535	57	12	p	p	PROPN
ejpam-6535	57	13	∈	∈	PROPN
ejpam-6535	57	14	s	s	VERB
ejpam-6535	57	15	the	the	DET
ejpam-6535	57	16	point	point	NOUN
ejpam-6535	57	17	filter	filter	NOUN
ejpam-6535	57	18	by	by	ADP
ejpam-6535	57	19	[	[	X
ejpam-6535	57	20	p	p	X
ejpam-6535	57	21	]	]	X
ejpam-6535	57	22	=	=	PUNCT
ejpam-6535	57	23	{	{	PUNCT
ejpam-6535	57	24	f	f	PROPN
ejpam-6535	57	25	⊆	⊆	NUM
ejpam-6535	57	26	s	s	VERB
ejpam-6535	57	27	:	:	PUNCT
ejpam-6535	57	28	p	p	X
ejpam-6535	57	29	∈	∈	PROPN
ejpam-6535	57	30	f	f	X
ejpam-6535	57	31	}	}	PUNCT
ejpam-6535	57	32	.	.	PUNCT
ejpam-6535	58	1	if	if	SCONJ
ejpam-6535	58	2	f	f	PROPN
ejpam-6535	58	3	∈	∈	PROPN
ejpam-6535	58	4	f(s	f(	VERB
ejpam-6535	58	5	)	)	PUNCT
ejpam-6535	58	6	and	and	CCONJ
ejpam-6535	58	7	g	g	PROPN
ejpam-6535	58	8	∈	∈	PROPN
ejpam-6535	58	9	f(t	f(t	PROPN
ejpam-6535	58	10	)	)	PUNCT
ejpam-6535	58	11	,	,	PUNCT
ejpam-6535	58	12	then	then	ADV
ejpam-6535	58	13	the	the	DET
ejpam-6535	58	14	filter	filter	NOUN
ejpam-6535	58	15	on	on	ADP
ejpam-6535	58	16	s	s	PRON
ejpam-6535	58	17	×	×	PROPN
ejpam-6535	58	18	t	t	NOUN
ejpam-6535	58	19	generated	generate	VERB
ejpam-6535	58	20	by	by	ADP
ejpam-6535	58	21	the	the	DET
ejpam-6535	58	22	sets	set	NOUN
ejpam-6535	58	23	of	of	ADP
ejpam-6535	58	24	the	the	DET
ejpam-6535	58	25	form	form	NOUN
ejpam-6535	58	26	{	{	PUNCT
ejpam-6535	58	27	f	f	NOUN
ejpam-6535	58	28	×	×	NOUN
ejpam-6535	58	29	g	g	PROPN
ejpam-6535	58	30	:	:	PUNCT
ejpam-6535	59	1	f	f	PROPN
ejpam-6535	59	2	∈	∈	PROPN
ejpam-6535	60	1	f	f	X
ejpam-6535	60	2	,	,	PUNCT
ejpam-6535	60	3	g	g	PROPN
ejpam-6535	60	4	∈	∈	PROPN
ejpam-6535	60	5	g	g	PROPN
ejpam-6535	60	6	}	}	PUNCT
ejpam-6535	60	7	is	be	AUX
ejpam-6535	60	8	denoted	denote	VERB
ejpam-6535	60	9	by	by	ADP
ejpam-6535	60	10	f	f	PROPN
ejpam-6535	60	11	×	×	PROPN
ejpam-6535	60	12	g.	g.	PROPN
ejpam-6535	60	13	if	if	SCONJ
ejpam-6535	60	14	(	(	PUNCT
ejpam-6535	60	15	s	s	X
ejpam-6535	60	16	,	,	PUNCT
ejpam-6535	60	17	·	·	PUNCT
ejpam-6535	60	18	)	)	PUNCT
ejpam-6535	60	19	is	be	AUX
ejpam-6535	60	20	a	a	DET
ejpam-6535	60	21	group	group	NOUN
ejpam-6535	60	22	and	and	CCONJ
ejpam-6535	60	23	f	f	NOUN
ejpam-6535	60	24	,	,	PUNCT
ejpam-6535	60	25	g	g	PROPN
ejpam-6535	60	26	∈	∈	PROPN
ejpam-6535	60	27	f(s	f(	NOUN
ejpam-6535	60	28	)	)	PUNCT
ejpam-6535	60	29	,	,	PUNCT
ejpam-6535	60	30	then	then	ADV
ejpam-6535	60	31	we	we	PRON
ejpam-6535	60	32	define	define	VERB
ejpam-6535	60	33	f	f	PROPN
ejpam-6535	60	34	⊙	⊙	PROPN
ejpam-6535	60	35	g	g	PROPN
ejpam-6535	60	36	as	as	ADP
ejpam-6535	60	37	a	a	DET
ejpam-6535	60	38	filter	filter	NOUN
ejpam-6535	60	39	generated	generate	VERB
ejpam-6535	60	40	by	by	ADP
ejpam-6535	60	41	the	the	DET
ejpam-6535	60	42	sets	set	NOUN
ejpam-6535	60	43	f	f	X
ejpam-6535	60	44	·	·	SYM
ejpam-6535	60	45	g	g	NOUN
ejpam-6535	60	46	=	=	SYM
ejpam-6535	60	47	{	{	PUNCT
ejpam-6535	60	48	pq	pq	INTJ
ejpam-6535	60	49	:	:	PUNCT
ejpam-6535	60	50	p	p	X
ejpam-6535	60	51	∈	∈	PROPN
ejpam-6535	60	52	f	f	X
ejpam-6535	60	53	,	,	PUNCT
ejpam-6535	60	54	q	q	PROPN
ejpam-6535	60	55	∈	∈	PROPN
ejpam-6535	60	56	g	g	NOUN
ejpam-6535	60	57	}	}	PUNCT
ejpam-6535	60	58	,	,	PUNCT
ejpam-6535	60	59	where	where	SCONJ
ejpam-6535	60	60	f	f	PROPN
ejpam-6535	60	61	∈	∈	PROPN
ejpam-6535	60	62	f	f	PROPN
ejpam-6535	60	63	and	and	CCONJ
ejpam-6535	60	64	g	g	PROPN
ejpam-6535	60	65	∈	∈	PROPN
ejpam-6535	60	66	g.	g.	NOUN
ejpam-6535	61	1	the	the	DET
ejpam-6535	61	2	filter	filter	NOUN
ejpam-6535	61	3	f−1	f−1	PROPN
ejpam-6535	61	4	is	be	AUX
ejpam-6535	61	5	generated	generate	VERB
ejpam-6535	61	6	by	by	ADP
ejpam-6535	61	7	the	the	DET
ejpam-6535	61	8	sets	set	NOUN
ejpam-6535	61	9	f−1	f−1	PROPN
ejpam-6535	61	10	=	=	SYM
ejpam-6535	61	11	{	{	PUNCT
ejpam-6535	61	12	p−1	p−1	NOUN
ejpam-6535	61	13	:	:	PUNCT
ejpam-6535	61	14	p	p	X
ejpam-6535	61	15	∈	∈	PROPN
ejpam-6535	61	16	f	f	X
ejpam-6535	61	17	}	}	PUNCT
ejpam-6535	61	18	for	for	ADP
ejpam-6535	61	19	f	f	PROPN
ejpam-6535	61	20	∈	∈	PROPN
ejpam-6535	61	21	f.	f.	PROPN
ejpam-6535	61	22	for	for	ADP
ejpam-6535	61	23	notions	notion	NOUN
ejpam-6535	61	24	of	of	ADP
ejpam-6535	61	25	category	category	NOUN
ejpam-6535	61	26	theory	theory	NOUN
ejpam-6535	61	27	we	we	PRON
ejpam-6535	61	28	refer	refer	VERB
ejpam-6535	61	29	to	to	ADP
ejpam-6535	61	30	adámek	adámek	PROPN
ejpam-6535	61	31	et	et	NOUN
ejpam-6535	61	32	.	.	PUNCT
ejpam-6535	62	1	al	al	PROPN
ejpam-6535	62	2	.	.	PUNCT
ejpam-6535	63	1	[	[	X
ejpam-6535	63	2	1	1	NUM
ejpam-6535	63	3	]	]	PUNCT
ejpam-6535	63	4	.	.	PUNCT
ejpam-6535	64	1	a	a	DET
ejpam-6535	64	2	construct	construct	NOUN
ejpam-6535	64	3	is	be	AUX
ejpam-6535	64	4	a	a	DET
ejpam-6535	64	5	category	category	NOUN
ejpam-6535	64	6	c	c	NOUN
ejpam-6535	64	7	whose	whose	DET
ejpam-6535	64	8	objects	object	NOUN
ejpam-6535	64	9	are	be	AUX
ejpam-6535	64	10	structured	structure	VERB
ejpam-6535	64	11	sets	set	NOUN
ejpam-6535	64	12	(	(	PUNCT
ejpam-6535	64	13	s	s	X
ejpam-6535	64	14	,	,	PUNCT
ejpam-6535	64	15	ξ	ξ	NOUN
ejpam-6535	64	16	)	)	PUNCT
ejpam-6535	64	17	and	and	CCONJ
ejpam-6535	64	18	morphisms	morphism	NOUN
ejpam-6535	64	19	are	be	AUX
ejpam-6535	64	20	suitable	suitable	ADJ
ejpam-6535	64	21	mappings	mapping	NOUN
ejpam-6535	64	22	between	between	ADP
ejpam-6535	64	23	the	the	DET
ejpam-6535	64	24	underlying	underlie	VERB
ejpam-6535	64	25	sets	set	NOUN
ejpam-6535	64	26	.	.	PUNCT
ejpam-6535	65	1	a	a	DET
ejpam-6535	65	2	construct	construct	NOUN
ejpam-6535	65	3	is	be	AUX
ejpam-6535	65	4	called	call	VERB
ejpam-6535	65	5	topological	topological	ADJ
ejpam-6535	65	6	if	if	SCONJ
ejpam-6535	65	7	it	it	PRON
ejpam-6535	65	8	allows	allow	VERB
ejpam-6535	65	9	initial	initial	ADJ
ejpam-6535	65	10	constructions	construction	NOUN
ejpam-6535	65	11	,	,	PUNCT
ejpam-6535	65	12	i.e.	i.e.	X
ejpam-6535	65	13	,	,	PUNCT
ejpam-6535	65	14	if	if	SCONJ
ejpam-6535	65	15	for	for	ADP
ejpam-6535	65	16	any	any	DET
ejpam-6535	65	17	source	source	NOUN
ejpam-6535	65	18	(	(	PUNCT
ejpam-6535	65	19	fj	fj	INTJ
ejpam-6535	65	20	:	:	PUNCT
ejpam-6535	65	21	s	s	AUX
ejpam-6535	65	22	−→	−→	NOUN
ejpam-6535	65	23	(	(	PUNCT
ejpam-6535	65	24	sj	sj	INTJ
ejpam-6535	65	25	,	,	PUNCT
ejpam-6535	65	26	ξj))j∈j	ξj))j∈j	PROPN
ejpam-6535	65	27	,	,	PUNCT
ejpam-6535	65	28	there	there	PRON
ejpam-6535	65	29	is	be	VERB
ejpam-6535	65	30	a	a	DET
ejpam-6535	65	31	unique	unique	ADJ
ejpam-6535	65	32	structure	structure	NOUN
ejpam-6535	65	33	ξ	ξ	X
ejpam-6535	65	34	on	on	ADP
ejpam-6535	65	35	s	s	PRON
ejpam-6535	65	36	such	such	ADJ
ejpam-6535	65	37	that	that	SCONJ
ejpam-6535	65	38	a	a	DET
ejpam-6535	65	39	mapping	mapping	NOUN
ejpam-6535	65	40	g	g	NOUN
ejpam-6535	65	41	:	:	PUNCT
ejpam-6535	65	42	(	(	PUNCT
ejpam-6535	65	43	t	t	PROPN
ejpam-6535	65	44	,	,	PUNCT
ejpam-6535	65	45	η	η	NOUN
ejpam-6535	65	46	)	)	PUNCT
ejpam-6535	65	47	−→	−→	NOUN
ejpam-6535	65	48	(	(	PUNCT
ejpam-6535	65	49	s	s	PROPN
ejpam-6535	65	50	,	,	PUNCT
ejpam-6535	65	51	ξ	ξ	X
ejpam-6535	65	52	)	)	PUNCT
ejpam-6535	65	53	is	be	AUX
ejpam-6535	65	54	a	a	DET
ejpam-6535	65	55	morphism	morphism	NOUN
ejpam-6535	65	56	if	if	SCONJ
ejpam-6535	65	57	and	and	CCONJ
ejpam-6535	65	58	only	only	ADV
ejpam-6535	65	59	if	if	SCONJ
ejpam-6535	65	60	for	for	ADP
ejpam-6535	65	61	each	each	DET
ejpam-6535	65	62	j	j	PROPN
ejpam-6535	65	63	∈	∈	PROPN
ejpam-6535	65	64	j	j	PROPN
ejpam-6535	65	65	the	the	DET
ejpam-6535	65	66	composition	composition	NOUN
ejpam-6535	65	67	fj	fj	INTJ
ejpam-6535	65	68	◦	◦	NOUN
ejpam-6535	65	69	g	g	NOUN
ejpam-6535	65	70	:	:	PUNCT
ejpam-6535	65	71	(	(	PUNCT
ejpam-6535	65	72	t	t	PROPN
ejpam-6535	65	73	,	,	PUNCT
ejpam-6535	65	74	η	η	NOUN
ejpam-6535	65	75	)	)	PUNCT
ejpam-6535	65	76	−→	−→	NOUN
ejpam-6535	65	77	(	(	PUNCT
ejpam-6535	65	78	sj	sj	INTJ
ejpam-6535	65	79	,	,	PUNCT
ejpam-6535	65	80	ξj	ξj	NOUN
ejpam-6535	65	81	)	)	PUNCT
ejpam-6535	65	82	is	be	AUX
ejpam-6535	65	83	a	a	DET
ejpam-6535	65	84	morphism	morphism	NOUN
ejpam-6535	65	85	,	,	PUNCT
ejpam-6535	65	86	where	where	SCONJ
ejpam-6535	65	87	(	(	PUNCT
ejpam-6535	65	88	t	t	PROPN
ejpam-6535	65	89	,	,	PUNCT
ejpam-6535	65	90	η	η	NOUN
ejpam-6535	65	91	)	)	PUNCT
ejpam-6535	65	92	is	be	AUX
ejpam-6535	65	93	a	a	DET
ejpam-6535	65	94	structured	structured	ADJ
ejpam-6535	65	95	set	set	NOUN
ejpam-6535	65	96	.	.	PUNCT
ejpam-6535	66	1	a	a	DET
ejpam-6535	66	2	topological	topological	ADJ
ejpam-6535	66	3	construct	construct	NOUN
ejpam-6535	66	4	is	be	AUX
ejpam-6535	66	5	called	call	VERB
ejpam-6535	66	6	cartesian	cartesian	ADJ
ejpam-6535	66	7	closed	close	VERB
ejpam-6535	66	8	if	if	SCONJ
ejpam-6535	66	9	for	for	ADP
ejpam-6535	66	10	each	each	DET
ejpam-6535	66	11	pair	pair	NOUN
ejpam-6535	66	12	of	of	ADP
ejpam-6535	66	13	objects	object	NOUN
ejpam-6535	66	14	(	(	PUNCT
ejpam-6535	66	15	s	s	X
ejpam-6535	66	16	,	,	PUNCT
ejpam-6535	66	17	ξ	ξ	NOUN
ejpam-6535	66	18	)	)	PUNCT
ejpam-6535	66	19	,	,	PUNCT
ejpam-6535	66	20	(	(	PUNCT
ejpam-6535	66	21	t	t	PROPN
ejpam-6535	66	22	,	,	PUNCT
ejpam-6535	66	23	η	η	PROPN
ejpam-6535	66	24	)	)	PUNCT
ejpam-6535	66	25	,	,	PUNCT
ejpam-6535	66	26	there	there	PRON
ejpam-6535	66	27	is	be	VERB
ejpam-6535	66	28	a	a	DET
ejpam-6535	66	29	structure	structure	NOUN
ejpam-6535	66	30	on	on	ADP
ejpam-6535	66	31	the	the	DET
ejpam-6535	66	32	set	set	NOUN
ejpam-6535	66	33	c(s	c(	NOUN
ejpam-6535	66	34	,	,	PUNCT
ejpam-6535	66	35	t	t	NOUN
ejpam-6535	66	36	)	)	PUNCT
ejpam-6535	66	37	of	of	ADP
ejpam-6535	66	38	morphisms	morphism	NOUN
ejpam-6535	66	39	from	from	ADP
ejpam-6535	66	40	s	s	PRON
ejpam-6535	66	41	to	to	ADP
ejpam-6535	66	42	t	t	NOUN
ejpam-6535	66	43	such	such	ADJ
ejpam-6535	66	44	that	that	DET
ejpam-6535	66	45	mapping	mapping	NOUN
ejpam-6535	66	46	ev	ev	X
ejpam-6535	66	47	:	:	PUNCT
ejpam-6535	66	48	c(s	c(s	NUM
ejpam-6535	66	49	,	,	PUNCT
ejpam-6535	66	50	t	t	NOUN
ejpam-6535	66	51	)	)	PUNCT
ejpam-6535	66	52	×	×	PROPN
ejpam-6535	66	53	s	s	PART
ejpam-6535	66	54	−→	−→	NOUN
ejpam-6535	66	55	t	t	NOUN
ejpam-6535	66	56	,	,	PUNCT
ejpam-6535	66	57	defined	define	VERB
ejpam-6535	66	58	for	for	ADP
ejpam-6535	66	59	any	any	DET
ejpam-6535	66	60	f	f	PROPN
ejpam-6535	66	61	∈	∈	PROPN
ejpam-6535	66	62	c(s	c(	NOUN
ejpam-6535	66	63	,	,	PUNCT
ejpam-6535	66	64	t	t	NOUN
ejpam-6535	66	65	)	)	PUNCT
ejpam-6535	66	66	and	and	CCONJ
ejpam-6535	66	67	s	s	PROPN
ejpam-6535	66	68	∈	∈	NOUN
ejpam-6535	66	69	s	s	X
ejpam-6535	66	70	by	by	ADP
ejpam-6535	66	71	ev(f	ev(f	NUM
ejpam-6535	66	72	,	,	PUNCT
ejpam-6535	66	73	s	s	AUX
ejpam-6535	66	74	)	)	PUNCT
ejpam-6535	66	75	=	=	PUNCT
ejpam-6535	66	76	f(s	f(	NOUN
ejpam-6535	66	77	)	)	PUNCT
ejpam-6535	66	78	(	(	PUNCT
ejpam-6535	66	79	called	call	VERB
ejpam-6535	66	80	an	an	DET
ejpam-6535	66	81	evaluation	evaluation	NOUN
ejpam-6535	66	82	mapping	mapping	NOUN
ejpam-6535	66	83	)	)	PUNCT
ejpam-6535	66	84	is	be	AUX
ejpam-6535	66	85	a	a	DET
ejpam-6535	66	86	morphism	morphism	NOUN
ejpam-6535	66	87	,	,	PUNCT
ejpam-6535	66	88	and	and	CCONJ
ejpam-6535	66	89	for	for	ADP
ejpam-6535	66	90	each	each	DET
ejpam-6535	66	91	object	object	NOUN
ejpam-6535	66	92	(	(	PUNCT
ejpam-6535	66	93	z	z	NOUN
ejpam-6535	66	94	,	,	PUNCT
ejpam-6535	66	95	ζ	ζ	NOUN
ejpam-6535	66	96	)	)	PUNCT
ejpam-6535	66	97	,	,	PUNCT
ejpam-6535	66	98	and	and	CCONJ
ejpam-6535	66	99	each	each	DET
ejpam-6535	66	100	morphism	morphism	NOUN
ejpam-6535	66	101	f	f	PROPN
ejpam-6535	66	102	:	:	PUNCT
ejpam-6535	66	103	s	s	AUX
ejpam-6535	66	104	×	×	NOUN
ejpam-6535	66	105	z	z	NOUN
ejpam-6535	66	106	−→	−→	NOUN
ejpam-6535	66	107	t	t	PROPN
ejpam-6535	66	108	the	the	DET
ejpam-6535	66	109	mapping	mapping	NOUN
ejpam-6535	66	110	f̂	f̂	NUM
ejpam-6535	66	111	:	:	PUNCT
ejpam-6535	66	112	z	z	NOUN
ejpam-6535	66	113	−→	−→	NOUN
ejpam-6535	66	114	c(s	c(	NOUN
ejpam-6535	66	115	,	,	PUNCT
ejpam-6535	66	116	t	t	NOUN
ejpam-6535	66	117	)	)	PUNCT
ejpam-6535	66	118	defined	define	VERB
ejpam-6535	66	119	by	by	ADP
ejpam-6535	66	120	f̂(z)(x	f̂(z)(x	PROPN
ejpam-6535	66	121	)	)	PUNCT
ejpam-6535	66	122	=	=	SYM
ejpam-6535	66	123	f(x	f(x	PROPN
ejpam-6535	66	124	,	,	PUNCT
ejpam-6535	66	125	z	z	NOUN
ejpam-6535	66	126	)	)	PUNCT
ejpam-6535	66	127	is	be	AUX
ejpam-6535	66	128	a	a	DET
ejpam-6535	66	129	morphism	morphism	NOUN
ejpam-6535	66	130	.	.	PUNCT
ejpam-6535	67	1	lemma	lemma	PROPN
ejpam-6535	67	2	2	2	NUM
ejpam-6535	67	3	.	.	PUNCT
ejpam-6535	68	1	[	[	X
ejpam-6535	68	2	2	2	X
ejpam-6535	68	3	]	]	PUNCT
ejpam-6535	68	4	let	let	VERB
ejpam-6535	68	5	s	s	PRON
ejpam-6535	68	6	and	and	CCONJ
ejpam-6535	68	7	t	t	PROPN
ejpam-6535	68	8	be	be	AUX
ejpam-6535	68	9	groups	group	NOUN
ejpam-6535	68	10	,	,	PUNCT
ejpam-6535	68	11	f	f	X
ejpam-6535	68	12	,	,	PUNCT
ejpam-6535	68	13	g	g	PROPN
ejpam-6535	68	14	,	,	PUNCT
ejpam-6535	68	15	h	h	NOUN
ejpam-6535	68	16	∈	∈	PROPN
ejpam-6535	68	17	f(s	f(	VERB
ejpam-6535	68	18	)	)	PUNCT
ejpam-6535	68	19	and	and	CCONJ
ejpam-6535	68	20	f	f	X
ejpam-6535	68	21	:	:	PUNCT
ejpam-6535	68	22	s	s	AUX
ejpam-6535	68	23	−→	−→	NOUN
ejpam-6535	68	24	t	t	PROPN
ejpam-6535	68	25	a	a	DET
ejpam-6535	68	26	group	group	NOUN
ejpam-6535	68	27	-	-	PUNCT
ejpam-6535	68	28	homomorphism	homomorphism	NOUN
ejpam-6535	68	29	,	,	PUNCT
ejpam-6535	68	30	then	then	ADV
ejpam-6535	68	31	we	we	PRON
ejpam-6535	68	32	have	have	AUX
ejpam-6535	68	33	(	(	PUNCT
ejpam-6535	68	34	a	a	PRON
ejpam-6535	68	35	)	)	PUNCT
ejpam-6535	68	36	f⊙	f⊙	NOUN
ejpam-6535	68	37	f−1	f−1	PROPN
ejpam-6535	68	38	≤	≤	NOUN
ejpam-6535	69	1	[	[	X
ejpam-6535	69	2	e	e	X
ejpam-6535	69	3	]	]	X
ejpam-6535	69	4	and	and	CCONJ
ejpam-6535	69	5	f−1	f−1	PROPN
ejpam-6535	69	6	⊙	⊙	NOUN
ejpam-6535	70	1	f	f	PROPN
ejpam-6535	70	2	≤	≤	PROPN
ejpam-6535	71	1	[	[	X
ejpam-6535	71	2	e	e	X
ejpam-6535	71	3	]	]	X
ejpam-6535	71	4	;	;	PUNCT
ejpam-6535	71	5	(	(	PUNCT
ejpam-6535	71	6	b	b	X
ejpam-6535	71	7	)	)	PUNCT
ejpam-6535	72	1	[	[	X
ejpam-6535	72	2	s]⊙	s]⊙	X
ejpam-6535	73	1	[	[	X
ejpam-6535	73	2	s]−1	s]−1	X
ejpam-6535	73	3	=	=	PUNCT
ejpam-6535	74	1	[	[	X
ejpam-6535	74	2	s]−1	s]−1	X
ejpam-6535	74	3	⊙	⊙	NOUN
ejpam-6535	75	1	[	[	X
ejpam-6535	75	2	s	s	X
ejpam-6535	75	3	]	]	X
ejpam-6535	75	4	=	=	PUNCT
ejpam-6535	76	1	[	[	X
ejpam-6535	76	2	e	e	X
ejpam-6535	76	3	]	]	X
ejpam-6535	76	4	;	;	PUNCT
ejpam-6535	76	5	(	(	PUNCT
ejpam-6535	76	6	c	c	X
ejpam-6535	76	7	)	)	PUNCT
ejpam-6535	77	1	[	[	X
ejpam-6535	77	2	s−1	s−1	X
ejpam-6535	77	3	]	]	X
ejpam-6535	77	4	=	=	PUNCT
ejpam-6535	78	1	[	[	X
ejpam-6535	78	2	s]−1	s]−1	X
ejpam-6535	78	3	;	;	PUNCT
ejpam-6535	78	4	(	(	PUNCT
ejpam-6535	78	5	d	d	X
ejpam-6535	78	6	)	)	PUNCT
ejpam-6535	79	1	[	[	X
ejpam-6535	79	2	s	s	X
ejpam-6535	79	3	·	·	PUNCT
ejpam-6535	79	4	t	t	X
ejpam-6535	79	5	]	]	X
ejpam-6535	79	6	=	=	PUNCT
ejpam-6535	80	1	[	[	X
ejpam-6535	80	2	s	s	X
ejpam-6535	80	3	]	]	X
ejpam-6535	80	4	·	·	PUNCT
ejpam-6535	81	1	[	[	X
ejpam-6535	81	2	t	t	X
ejpam-6535	81	3	]	]	X
ejpam-6535	81	4	;	;	PUNCT
ejpam-6535	81	5	(	(	PUNCT
ejpam-6535	81	6	e	e	X
ejpam-6535	81	7	)	)	PUNCT
ejpam-6535	81	8	(	(	PUNCT
ejpam-6535	81	9	f⊙g)⊙h	f⊙g)⊙h	NOUN
ejpam-6535	81	10	=	=	SYM
ejpam-6535	81	11	f⊙	f⊙	NOUN
ejpam-6535	81	12	(	(	PUNCT
ejpam-6535	81	13	g⊙h	g⊙h	ADJ
ejpam-6535	81	14	)	)	PUNCT
ejpam-6535	81	15	;	;	PUNCT
ejpam-6535	81	16	(	(	PUNCT
ejpam-6535	81	17	f	f	X
ejpam-6535	81	18	)	)	PUNCT
ejpam-6535	81	19	(	(	PUNCT
ejpam-6535	81	20	f−1)−1	f−1)−1	X
ejpam-6535	81	21	=	=	SYM
ejpam-6535	81	22	f	f	X
ejpam-6535	81	23	;	;	PUNCT
ejpam-6535	81	24	(	(	PUNCT
ejpam-6535	81	25	g	g	NOUN
ejpam-6535	81	26	)	)	PUNCT
ejpam-6535	81	27	(	(	PUNCT
ejpam-6535	81	28	f⊙g)−1	f⊙g)−1	NOUN
ejpam-6535	81	29	=	=	SYM
ejpam-6535	81	30	g−1	g−1	PROPN
ejpam-6535	81	31	⊙	⊙	PROPN
ejpam-6535	82	1	f−1	f−1	PROPN
ejpam-6535	82	2	;	;	PUNCT
ejpam-6535	82	3	(	(	PUNCT
ejpam-6535	82	4	h	h	NOUN
ejpam-6535	82	5	)	)	PUNCT
ejpam-6535	83	1	[	[	X
ejpam-6535	83	2	e]⊙	e]⊙	X
ejpam-6535	83	3	f	f	X
ejpam-6535	83	4	=	=	PUNCT
ejpam-6535	83	5	f⊙	f⊙	PROPN
ejpam-6535	83	6	[	[	X
ejpam-6535	83	7	e	e	X
ejpam-6535	83	8	]	]	X
ejpam-6535	83	9	=	=	SYM
ejpam-6535	83	10	f	f	X
ejpam-6535	83	11	;	;	PUNCT
ejpam-6535	83	12	(	(	PUNCT
ejpam-6535	83	13	i	i	NOUN
ejpam-6535	83	14	)	)	PUNCT
ejpam-6535	83	15	(	(	PUNCT
ejpam-6535	83	16	f	f	NOUN
ejpam-6535	83	17	∧g)−1	∧g)−1	NOUN
ejpam-6535	83	18	=	=	SYM
ejpam-6535	83	19	f−1	f−1	PROPN
ejpam-6535	83	20	∧g−1	∧g−1	NUM
ejpam-6535	83	21	;	;	PUNCT
ejpam-6535	83	22	(	(	PUNCT
ejpam-6535	83	23	j	j	NOUN
ejpam-6535	83	24	)	)	PUNCT
ejpam-6535	83	25	(	(	PUNCT
ejpam-6535	83	26	f	f	X
ejpam-6535	83	27	∧g)⊙h	∧g)⊙h	NUM
ejpam-6535	83	28	=	=	SYM
ejpam-6535	83	29	(	(	PUNCT
ejpam-6535	83	30	f⊙h	f⊙h	ADJ
ejpam-6535	83	31	)	)	PUNCT
ejpam-6535	83	32	∧	∧	NOUN
ejpam-6535	83	33	(	(	PUNCT
ejpam-6535	83	34	g⊙h	g⊙h	ADJ
ejpam-6535	83	35	)	)	PUNCT
ejpam-6535	83	36	;	;	PUNCT
ejpam-6535	83	37	(	(	PUNCT
ejpam-6535	83	38	k	k	NOUN
ejpam-6535	83	39	)	)	PUNCT
ejpam-6535	83	40	f(f⊙g	f(f⊙g	NUM
ejpam-6535	83	41	)	)	PUNCT
ejpam-6535	83	42	=	=	PRON
ejpam-6535	84	1	f(f)⊙	f(f)⊙	PROPN
ejpam-6535	84	2	f(g	f(g	PROPN
ejpam-6535	84	3	)	)	PUNCT
ejpam-6535	84	4	;	;	PUNCT
ejpam-6535	84	5	(	(	PUNCT
ejpam-6535	84	6	l	l	NOUN
ejpam-6535	84	7	)	)	PUNCT
ejpam-6535	84	8	f(f−1	f(f−1	PROPN
ejpam-6535	84	9	)	)	PUNCT
ejpam-6535	84	10	=	=	SYM
ejpam-6535	84	11	(	(	PUNCT
ejpam-6535	84	12	f(f))−1	f(f))−1	NOUN
ejpam-6535	84	13	.	.	PUNCT
ejpam-6535	85	1	3	3	X
ejpam-6535	85	2	.	.	X
ejpam-6535	85	3	probabilistic	probabilistic	ADJ
ejpam-6535	85	4	metric	metric	ADJ
ejpam-6535	85	5	spaces	space	NOUN
ejpam-6535	85	6	,	,	PUNCT
ejpam-6535	85	7	their	their	PRON
ejpam-6535	85	8	associated	associated	ADJ
ejpam-6535	85	9	tardiff	tardiff	NOUN
ejpam-6535	85	10	’s	’s	PART
ejpam-6535	85	11	neighborhood	neighborhood	NOUN
ejpam-6535	85	12	systems	system	NOUN
ejpam-6535	85	13	,	,	PUNCT
ejpam-6535	85	14	probabilistic	probabilistic	ADJ
ejpam-6535	85	15	closure	closure	NOUN
ejpam-6535	85	16	operator	operator	NOUN
ejpam-6535	85	17	and	and	CCONJ
ejpam-6535	85	18	probabilistic	probabilistic	ADJ
ejpam-6535	85	19	convergence	convergence	NOUN
ejpam-6535	85	20	structures	structure	NOUN
ejpam-6535	85	21	definition	definition	NOUN
ejpam-6535	85	22	2	2	NUM
ejpam-6535	85	23	.	.	PUNCT
ejpam-6535	86	1	[	[	X
ejpam-6535	86	2	34	34	NUM
ejpam-6535	86	3	]	]	X
ejpam-6535	86	4	a	a	DET
ejpam-6535	86	5	probabilistic	probabilistic	ADJ
ejpam-6535	86	6	metric	metric	ADJ
ejpam-6535	86	7	space	space	NOUN
ejpam-6535	86	8	under	under	ADP
ejpam-6535	86	9	a	a	DET
ejpam-6535	86	10	triangle	triangle	NOUN
ejpam-6535	86	11	function	function	NOUN
ejpam-6535	86	12	τ	τ	PROPN
ejpam-6535	86	13	is	be	AUX
ejpam-6535	86	14	a	a	DET
ejpam-6535	86	15	pair	pair	NOUN
ejpam-6535	86	16	(	(	PUNCT
ejpam-6535	86	17	s	s	X
ejpam-6535	86	18	,	,	PUNCT
ejpam-6535	86	19	f	f	PROPN
ejpam-6535	86	20	)	)	PUNCT
ejpam-6535	86	21	where	where	SCONJ
ejpam-6535	86	22	f	f	X
ejpam-6535	86	23	:	:	PUNCT
ejpam-6535	86	24	s	s	VERB
ejpam-6535	86	25	×	×	NOUN
ejpam-6535	86	26	s	s	PART
ejpam-6535	86	27	−→	−→	NOUN
ejpam-6535	86	28	∆+	∆+	NUM
ejpam-6535	86	29	such	such	ADJ
ejpam-6535	86	30	that	that	PRON
ejpam-6535	86	31	for	for	ADP
ejpam-6535	86	32	all	all	DET
ejpam-6535	86	33	p	p	NOUN
ejpam-6535	86	34	,	,	PUNCT
ejpam-6535	86	35	q	q	PROPN
ejpam-6535	86	36	∈	∈	PROPN
ejpam-6535	86	37	s	s	VERB
ejpam-6535	86	38	the	the	DET
ejpam-6535	86	39	following	follow	VERB
ejpam-6535	86	40	properties	property	NOUN
ejpam-6535	86	41	hold	hold	VERB
ejpam-6535	86	42	:	:	PUNCT
ejpam-6535	86	43	(	(	PUNCT
ejpam-6535	86	44	pm1	pm1	PROPN
ejpam-6535	86	45	)	)	PUNCT
ejpam-6535	86	46	f	f	PROPN
ejpam-6535	86	47	(	(	PUNCT
ejpam-6535	86	48	p	p	X
ejpam-6535	86	49	,	,	PUNCT
ejpam-6535	86	50	q	q	NOUN
ejpam-6535	86	51	)	)	PUNCT
ejpam-6535	86	52	=	=	SYM
ejpam-6535	87	1	ϵ0	ϵ0	NUM
ejpam-6535	87	2	⇐	⇐	ADJ
ejpam-6535	87	3	⇒	⇒	NOUN
ejpam-6535	87	4	p	p	X
ejpam-6535	87	5	=	=	ADJ
ejpam-6535	87	6	q	q	NOUN
ejpam-6535	87	7	;	;	PUNCT
ejpam-6535	87	8	(	(	PUNCT
ejpam-6535	87	9	pm2	pm2	NOUN
ejpam-6535	87	10	)	)	PUNCT
ejpam-6535	87	11	f	f	PROPN
ejpam-6535	87	12	(	(	PUNCT
ejpam-6535	87	13	p	p	X
ejpam-6535	87	14	,	,	PUNCT
ejpam-6535	87	15	q	q	NOUN
ejpam-6535	87	16	)	)	PUNCT
ejpam-6535	87	17	=	=	SYM
ejpam-6535	87	18	f	f	X
ejpam-6535	87	19	(	(	PUNCT
ejpam-6535	87	20	q	q	NOUN
ejpam-6535	87	21	,	,	PUNCT
ejpam-6535	87	22	p	p	NOUN
ejpam-6535	87	23	)	)	PUNCT
ejpam-6535	87	24	;	;	PUNCT
ejpam-6535	87	25	(	(	PUNCT
ejpam-6535	87	26	pm3	pm3	NOUN
ejpam-6535	87	27	)	)	PUNCT
ejpam-6535	87	28	τ(f	τ(f	NOUN
ejpam-6535	87	29	(	(	PUNCT
ejpam-6535	87	30	p	p	X
ejpam-6535	87	31	,	,	PUNCT
ejpam-6535	87	32	q	q	NOUN
ejpam-6535	87	33	)	)	PUNCT
ejpam-6535	87	34	,	,	PUNCT
ejpam-6535	87	35	f	f	PROPN
ejpam-6535	87	36	(	(	PUNCT
ejpam-6535	87	37	q	q	NOUN
ejpam-6535	87	38	,	,	PUNCT
ejpam-6535	87	39	r	r	NOUN
ejpam-6535	87	40	)	)	PUNCT
ejpam-6535	87	41	)	)	PUNCT
ejpam-6535	88	1	≤	≤	NUM
ejpam-6535	88	2	f	f	X
ejpam-6535	88	3	(	(	PUNCT
ejpam-6535	88	4	p	p	X
ejpam-6535	88	5	,	,	PUNCT
ejpam-6535	88	6	r	r	NOUN
ejpam-6535	88	7	)	)	PUNCT
ejpam-6535	88	8	.	.	PUNCT
ejpam-6535	89	1	we	we	PRON
ejpam-6535	89	2	use	use	VERB
ejpam-6535	89	3	the	the	DET
ejpam-6535	89	4	index	index	NOUN
ejpam-6535	89	5	notation	notation	NOUN
ejpam-6535	89	6	fp	fp	PROPN
ejpam-6535	89	7	,	,	PUNCT
ejpam-6535	89	8	q	q	PROPN
ejpam-6535	89	9	for	for	ADP
ejpam-6535	89	10	f	f	PROPN
ejpam-6535	89	11	(	(	PUNCT
ejpam-6535	89	12	p	p	X
ejpam-6535	89	13	,	,	PUNCT
ejpam-6535	89	14	q	q	NOUN
ejpam-6535	89	15	)	)	PUNCT
ejpam-6535	89	16	.	.	PUNCT
ejpam-6535	90	1	a	a	DET
ejpam-6535	90	2	mapping	mapping	NOUN
ejpam-6535	90	3	f	f	NOUN
ejpam-6535	90	4	:	:	PUNCT
ejpam-6535	90	5	(	(	PUNCT
ejpam-6535	90	6	s	s	X
ejpam-6535	90	7	,	,	PUNCT
ejpam-6535	90	8	f	f	NOUN
ejpam-6535	90	9	)	)	PUNCT
ejpam-6535	90	10	−→	−→	NOUN
ejpam-6535	90	11	(	(	PUNCT
ejpam-6535	90	12	s′	s′	PROPN
ejpam-6535	90	13	,	,	PUNCT
ejpam-6535	90	14	f	f	PROPN
ejpam-6535	90	15	′	′	NOUN
ejpam-6535	90	16	)	)	PUNCT
ejpam-6535	90	17	between	between	ADP
ejpam-6535	90	18	probabilistic	probabilistic	ADJ
ejpam-6535	90	19	metric	metric	ADJ
ejpam-6535	90	20	spaces	space	NOUN
ejpam-6535	90	21	is	be	AUX
ejpam-6535	90	22	called	call	VERB
ejpam-6535	90	23	non	non	ADJ
ejpam-6535	90	24	-	-	ADJ
ejpam-6535	90	25	expansive	expansive	ADJ
ejpam-6535	90	26	if	if	SCONJ
ejpam-6535	90	27	fp	fp	NOUN
ejpam-6535	90	28	,	,	PUNCT
ejpam-6535	90	29	q	q	PROPN
ejpam-6535	90	30	≤	≤	NUM
ejpam-6535	90	31	f	f	NOUN
ejpam-6535	90	32	′	′	NUM
ejpam-6535	90	33	f(p),f(q	f(p),f(q	NOUN
ejpam-6535	90	34	)	)	PUNCT
ejpam-6535	90	35	for	for	ADP
ejpam-6535	90	36	all	all	DET
ejpam-6535	90	37	p	p	NOUN
ejpam-6535	90	38	,	,	PUNCT
ejpam-6535	90	39	q	q	PROPN
ejpam-6535	90	40	∈	∈	PROPN
ejpam-6535	90	41	s.	s.	PROPN
ejpam-6535	90	42	the	the	DET
ejpam-6535	90	43	category	category	NOUN
ejpam-6535	90	44	of	of	ADP
ejpam-6535	90	45	all	all	DET
ejpam-6535	90	46	probabilistic	probabilistic	ADJ
ejpam-6535	90	47	metric	metric	ADJ
ejpam-6535	90	48	spaces	space	NOUN
ejpam-6535	90	49	and	and	CCONJ
ejpam-6535	90	50	non	non	ADJ
ejpam-6535	90	51	-	-	ADJ
ejpam-6535	90	52	expansive	expansive	ADJ
ejpam-6535	90	53	mappings	mapping	NOUN
ejpam-6535	90	54	is	be	AUX
ejpam-6535	90	55	denoted	denote	VERB
ejpam-6535	90	56	by	by	ADP
ejpam-6535	90	57	pmet	pmet	NOUN
ejpam-6535	90	58	.	.	PUNCT
ejpam-6535	91	1	we	we	PRON
ejpam-6535	91	2	recall	recall	VERB
ejpam-6535	91	3	tardiff	tardiff	PROPN
ejpam-6535	91	4	’s	’s	PART
ejpam-6535	91	5	neighborhood	neighborhood	NOUN
ejpam-6535	91	6	systems	system	NOUN
ejpam-6535	91	7	from	from	ADP
ejpam-6535	91	8	[	[	X
ejpam-6535	91	9	38	38	NUM
ejpam-6535	91	10	]	]	PUNCT
ejpam-6535	91	11	that	that	PRON
ejpam-6535	91	12	are	be	AUX
ejpam-6535	91	13	based	base	VERB
ejpam-6535	91	14	on	on	ADP
ejpam-6535	91	15	the	the	DET
ejpam-6535	91	16	so	so	ADV
ejpam-6535	91	17	-	-	PUNCT
ejpam-6535	91	18	called	call	VERB
ejpam-6535	91	19	profile	profile	NOUN
ejpam-6535	91	20	functions	function	NOUN
ejpam-6535	91	21	introduced	introduce	VERB
ejpam-6535	91	22	in	in	ADP
ejpam-6535	91	23	[	[	X
ejpam-6535	91	24	18	18	NUM
ejpam-6535	91	25	]	]	PUNCT
ejpam-6535	91	26	.	.	PUNCT
ejpam-6535	92	1	a	a	DET
ejpam-6535	92	2	profile	profile	NOUN
ejpam-6535	92	3	function	function	NOUN
ejpam-6535	92	4	is	be	AUX
ejpam-6535	92	5	in	in	ADP
ejpam-6535	92	6	fact	fact	NOUN
ejpam-6535	92	7	just	just	ADV
ejpam-6535	92	8	an	an	DET
ejpam-6535	92	9	element	element	NOUN
ejpam-6535	92	10	φ	φ	PROPN
ejpam-6535	92	11	∈	∈	PROPN
ejpam-6535	92	12	∆+	∆+	NOUN
ejpam-6535	92	13	,	,	PUNCT
ejpam-6535	92	14	where	where	SCONJ
ejpam-6535	92	15	φ(x	φ(x	NOUN
ejpam-6535	92	16	)	)	PUNCT
ejpam-6535	92	17	,	,	PUNCT
ejpam-6535	92	18	x	x	X
ejpam-6535	92	19	>	>	X
ejpam-6535	92	20	0	0	NUM
ejpam-6535	92	21	,	,	PUNCT
ejpam-6535	92	22	is	be	AUX
ejpam-6535	92	23	interpreted	interpret	VERB
ejpam-6535	92	24	as	as	ADP
ejpam-6535	92	25	the	the	DET
ejpam-6535	92	26	maximum	maximum	ADJ
ejpam-6535	92	27	probability	probability	NOUN
ejpam-6535	92	28	assigned	assign	VERB
ejpam-6535	92	29	to	to	ADP
ejpam-6535	92	30	the	the	DET
ejpam-6535	92	31	event	event	NOUN
ejpam-6535	92	32	that	that	SCONJ
ejpam-6535	92	33	the	the	DET
ejpam-6535	92	34	distance	distance	NOUN
ejpam-6535	92	35	between	between	ADP
ejpam-6535	92	36	p	p	PROPN
ejpam-6535	92	37	and	and	CCONJ
ejpam-6535	92	38	q	q	NOUN
ejpam-6535	92	39	is	be	AUX
ejpam-6535	92	40	less	less	ADJ
ejpam-6535	92	41	than	than	ADP
ejpam-6535	92	42	x.	x.	NOUN
ejpam-6535	92	43	given	give	VERB
ejpam-6535	92	44	a	a	DET
ejpam-6535	92	45	φ	φ	NUM
ejpam-6535	92	46	∈	∈	PROPN
ejpam-6535	92	47	∆+	∆+	NOUN
ejpam-6535	92	48	,	,	PUNCT
ejpam-6535	92	49	ϵ	ϵ	X
ejpam-6535	92	50	>	>	X
ejpam-6535	92	51	0	0	PUNCT
ejpam-6535	93	1	and	and	CCONJ
ejpam-6535	93	2	p	p	NOUN
ejpam-6535	93	3	∈	∈	PROPN
ejpam-6535	93	4	s	s	NOUN
ejpam-6535	93	5	,	,	PUNCT
ejpam-6535	93	6	the	the	DET
ejpam-6535	93	7	(	(	PUNCT
ejpam-6535	93	8	φ	φ	PROPN
ejpam-6535	93	9	,	,	PUNCT
ejpam-6535	93	10	ϵ)neighborhood	ϵ)neighborhood	NOUN
ejpam-6535	93	11	of	of	ADP
ejpam-6535	93	12	p	p	PROPN
ejpam-6535	93	13	is	be	AUX
ejpam-6535	93	14	defined	define	VERB
ejpam-6535	93	15	by	by	ADP
ejpam-6535	93	16	nφ,ϵ	nφ,ϵ	X
ejpam-6535	93	17	p	p	NOUN
ejpam-6535	93	18	=	=	X
ejpam-6535	93	19	{	{	PUNCT
ejpam-6535	93	20	q	q	PROPN
ejpam-6535	93	21	∈	∈	PROPN
ejpam-6535	93	22	s	s	PART
ejpam-6535	93	23	:	:	PUNCT
ejpam-6535	93	24	fp	fp	X
ejpam-6535	93	25	,	,	PUNCT
ejpam-6535	93	26	q(x+	q(x+	NOUN
ejpam-6535	93	27	ϵ	ϵ	NOUN
ejpam-6535	93	28	)	)	PUNCT
ejpam-6535	93	29	+	+	CCONJ
ejpam-6535	93	30	ϵ	ϵ	DET
ejpam-6535	93	31	≥	≥	NOUN
ejpam-6535	93	32	φ(x	φ(x	PROPN
ejpam-6535	93	33	)	)	PUNCT
ejpam-6535	93	34	,	,	PUNCT
ejpam-6535	93	35	∀x	∀x	VERB
ejpam-6535	93	36	∈	∈	PROPN
ejpam-6535	94	1	[	[	X
ejpam-6535	94	2	0	0	NUM
ejpam-6535	94	3	,	,	PUNCT
ejpam-6535	94	4	1	1	NUM
ejpam-6535	94	5	ϵ	ϵ	NOUN
ejpam-6535	94	6	)	)	PUNCT
ejpam-6535	94	7	}	}	PUNCT
ejpam-6535	94	8	.	.	PUNCT
ejpam-6535	95	1	the	the	DET
ejpam-6535	95	2	set	set	NOUN
ejpam-6535	95	3	{	{	PUNCT
ejpam-6535	95	4	nφ,ϵ	nφ,ϵ	NOUN
ejpam-6535	95	5	p	p	NOUN
ejpam-6535	95	6	:	:	PUNCT
ejpam-6535	95	7	ϵ	ϵ	X
ejpam-6535	95	8	>	>	X
ejpam-6535	95	9	0	0	NUM
ejpam-6535	95	10	}	}	PUNCT
ejpam-6535	95	11	is	be	AUX
ejpam-6535	95	12	a	a	DET
ejpam-6535	95	13	filter	filter	NOUN
ejpam-6535	95	14	basis	basis	NOUN
ejpam-6535	95	15	,	,	PUNCT
ejpam-6535	95	16	and	and	CCONJ
ejpam-6535	95	17	the	the	DET
ejpam-6535	95	18	filter	filter	NOUN
ejpam-6535	95	19	generated	generate	VERB
ejpam-6535	95	20	by	by	ADP
ejpam-6535	95	21	this	this	DET
ejpam-6535	95	22	basis	basis	NOUN
ejpam-6535	95	23	is	be	AUX
ejpam-6535	95	24	denoted	denote	VERB
ejpam-6535	95	25	by	by	ADP
ejpam-6535	95	26	nφ	nφ	PROPN
ejpam-6535	95	27	p	p	PROPN
ejpam-6535	95	28	.	.	PUNCT
ejpam-6535	96	1	note	note	VERB
ejpam-6535	96	2	that	that	SCONJ
ejpam-6535	96	3	nφ	nφ	PROPN
ejpam-6535	96	4	p	p	NOUN
ejpam-6535	96	5	satisfies	satisfie	NOUN
ejpam-6535	96	6	:	:	PUNCT
ejpam-6535	96	7	(	(	PUNCT
ejpam-6535	96	8	pmtn1	pmtn1	NOUN
ejpam-6535	96	9	)	)	PUNCT
ejpam-6535	96	10	nφ	nφ	ADP
ejpam-6535	96	11	p	p	PROPN
ejpam-6535	96	12	∈	∈	PROPN
ejpam-6535	96	13	f(s	f(	NOUN
ejpam-6535	96	14	)	)	PUNCT
ejpam-6535	96	15	;	;	PUNCT
ejpam-6535	96	16	(	(	PUNCT
ejpam-6535	96	17	pmtn2	pmtn2	PROPN
ejpam-6535	96	18	)	)	PUNCT
ejpam-6535	96	19	nφ	nφ	PROPN
ejpam-6535	96	20	p	p	NOUN
ejpam-6535	96	21	≤	≤	NOUN
ejpam-6535	97	1	[	[	X
ejpam-6535	97	2	p	p	X
ejpam-6535	97	3	]	]	X
ejpam-6535	97	4	;	;	PUNCT
ejpam-6535	97	5	(	(	PUNCT
ejpam-6535	97	6	pmtn3	pmtn3	NOUN
ejpam-6535	97	7	)	)	PUNCT
ejpam-6535	97	8	φ	φ	PROPN
ejpam-6535	97	9	≤	≤	NOUN
ejpam-6535	97	10	ψ	ψ	NOUN
ejpam-6535	97	11	implies	imply	VERB
ejpam-6535	97	12	nφ	nφ	PRON
ejpam-6535	97	13	p	p	NOUN
ejpam-6535	97	14	≤	≤	NUM
ejpam-6535	98	1	nψ	nψ	NOUN
ejpam-6535	99	1	p	p	NOUN
ejpam-6535	100	1	.	.	PUNCT
ejpam-6535	101	1	definition	definition	NOUN
ejpam-6535	101	2	3	3	NUM
ejpam-6535	101	3	.	.	PUNCT
ejpam-6535	102	1	[	[	X
ejpam-6535	102	2	22	22	NUM
ejpam-6535	102	3	]	]	PUNCT
ejpam-6535	102	4	let	let	VERB
ejpam-6535	102	5	s	s	PRON
ejpam-6535	102	6	be	be	AUX
ejpam-6535	102	7	a	a	DET
ejpam-6535	102	8	set	set	NOUN
ejpam-6535	102	9	.	.	PUNCT
ejpam-6535	103	1	a	a	DET
ejpam-6535	103	2	family	family	NOUN
ejpam-6535	103	3	of	of	ADP
ejpam-6535	103	4	mappings	mapping	NOUN
ejpam-6535	103	5	(	(	PUNCT
ejpam-6535	103	6	cφ	cφ	NOUN
ejpam-6535	103	7	:	:	PUNCT
ejpam-6535	103	8	f(s	f(	NOUN
ejpam-6535	103	9	)	)	PUNCT
ejpam-6535	103	10	−→	−→	NOUN
ejpam-6535	103	11	p	p	X
ejpam-6535	103	12	(	(	PUNCT
ejpam-6535	103	13	s))φ∈∆+	s))φ∈∆+	ADJ
ejpam-6535	103	14	which	which	PRON
ejpam-6535	103	15	satisfies	satisfy	VERB
ejpam-6535	103	16	the	the	DET
ejpam-6535	103	17	axioms	axiom	NOUN
ejpam-6535	103	18	(	(	PUNCT
ejpam-6535	103	19	pcs1	pcs1	NOUN
ejpam-6535	103	20	)	)	PUNCT
ejpam-6535	103	21	p	p	X
ejpam-6535	103	22	∈	∈	PROPN
ejpam-6535	103	23	cφ([p	cφ([p	PROPN
ejpam-6535	103	24	]	]	PUNCT
ejpam-6535	103	25	)	)	PUNCT
ejpam-6535	103	26	,	,	PUNCT
ejpam-6535	103	27	p	p	PROPN
ejpam-6535	103	28	∈	∈	PROPN
ejpam-6535	103	29	s	s	PART
ejpam-6535	103	30	,	,	PUNCT
ejpam-6535	103	31	φ	φ	PROPN
ejpam-6535	103	32	∈	∈	PROPN
ejpam-6535	103	33	∆+	∆+	NOUN
ejpam-6535	103	34	;	;	PUNCT
ejpam-6535	103	35	(	(	PUNCT
ejpam-6535	103	36	pcs2	pcs2	NOUN
ejpam-6535	103	37	)	)	PUNCT
ejpam-6535	103	38	if	if	SCONJ
ejpam-6535	103	39	f	f	PROPN
ejpam-6535	103	40	≤	≤	X
ejpam-6535	103	41	g	g	PROPN
ejpam-6535	103	42	,	,	PUNCT
ejpam-6535	103	43	then	then	ADV
ejpam-6535	103	44	cφ(f	cφ(f	PUNCT
ejpam-6535	103	45	)	)	PUNCT
ejpam-6535	103	46	⊆	⊆	NUM
ejpam-6535	103	47	cφ(g	cφ(g	NUM
ejpam-6535	103	48	)	)	PUNCT
ejpam-6535	103	49	,	,	PUNCT
ejpam-6535	103	50	∀f	∀f	PROPN
ejpam-6535	103	51	,	,	PUNCT
ejpam-6535	103	52	g	g	PROPN
ejpam-6535	103	53	∈	∈	PROPN
ejpam-6535	103	54	f(s	f(	VERB
ejpam-6535	103	55	)	)	PUNCT
ejpam-6535	103	56	and	and	CCONJ
ejpam-6535	103	57	∀φ	∀φ	NUM
ejpam-6535	103	58	∈	∈	PROPN
ejpam-6535	103	59	∆+	∆+	NOUN
ejpam-6535	103	60	;	;	PUNCT
ejpam-6535	103	61	(	(	PUNCT
ejpam-6535	103	62	pcs3	pcs3	NOUN
ejpam-6535	103	63	)	)	PUNCT
ejpam-6535	103	64	if	if	SCONJ
ejpam-6535	103	65	φ	φ	PROPN
ejpam-6535	103	66	≤	≤	X
ejpam-6535	103	67	ψ	ψ	NOUN
ejpam-6535	103	68	,	,	PUNCT
ejpam-6535	103	69	then	then	ADV
ejpam-6535	103	70	cψ(f	cψ(f	NOUN
ejpam-6535	103	71	)	)	PUNCT
ejpam-6535	103	72	⊆	⊆	NUM
ejpam-6535	103	73	cφ(f	cφ(f	NOUN
ejpam-6535	103	74	)	)	PUNCT
ejpam-6535	103	75	,	,	PUNCT
ejpam-6535	103	76	∀f	∀f	PROPN
ejpam-6535	103	77	,	,	PUNCT
ejpam-6535	103	78	g	g	PROPN
ejpam-6535	103	79	∈	∈	PROPN
ejpam-6535	103	80	f(s	f(	VERB
ejpam-6535	103	81	)	)	PUNCT
ejpam-6535	103	82	and	and	CCONJ
ejpam-6535	103	83	∀φ	∀φ	PROPN
ejpam-6535	103	84	,	,	PUNCT
ejpam-6535	103	85	ψ	ψ	X
ejpam-6535	103	86	∈	∈	PROPN
ejpam-6535	103	87	∆+	∆+	NUM
ejpam-6535	103	88	;	;	PUNCT
ejpam-6535	103	89	(	(	PUNCT
ejpam-6535	103	90	pcs4	pcs4	NOUN
ejpam-6535	103	91	)	)	PUNCT
ejpam-6535	103	92	p	p	PROPN
ejpam-6535	103	93	∈	∈	PROPN
ejpam-6535	103	94	cϵ∞(f	cϵ∞(f	NOUN
ejpam-6535	103	95	)	)	PUNCT
ejpam-6535	103	96	∀p	∀p	NOUN
ejpam-6535	103	97	∈	∈	PROPN
ejpam-6535	103	98	s	s	NOUN
ejpam-6535	103	99	,	,	PUNCT
ejpam-6535	103	100	f	f	PROPN
ejpam-6535	103	101	∈	∈	PROPN
ejpam-6535	103	102	f(s	f(	NOUN
ejpam-6535	103	103	)	)	PUNCT
ejpam-6535	103	104	,	,	PUNCT
ejpam-6535	103	105	is	be	AUX
ejpam-6535	103	106	called	call	VERB
ejpam-6535	103	107	a	a	DET
ejpam-6535	103	108	probabilistic	probabilistic	ADJ
ejpam-6535	103	109	convergence	convergence	NOUN
ejpam-6535	103	110	structure	structure	NOUN
ejpam-6535	103	111	on	on	ADP
ejpam-6535	103	112	s.	s.	PROPN
ejpam-6535	103	113	the	the	DET
ejpam-6535	103	114	pair	pair	NOUN
ejpam-6535	103	115	(	(	PUNCT
ejpam-6535	103	116	s	s	X
ejpam-6535	103	117	,	,	PUNCT
ejpam-6535	103	118	c	c	NOUN
ejpam-6535	103	119	=	=	SYM
ejpam-6535	103	120	(	(	PUNCT
ejpam-6535	103	121	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	103	122	)	)	PUNCT
ejpam-6535	103	123	is	be	AUX
ejpam-6535	103	124	called	call	VERB
ejpam-6535	103	125	a	a	DET
ejpam-6535	103	126	(	(	PUNCT
ejpam-6535	103	127	distance	distance	NOUN
ejpam-6535	103	128	distribution	distribution	NOUN
ejpam-6535	103	129	function	function	NOUN
ejpam-6535	103	130	indexed	index	VERB
ejpam-6535	103	131	)	)	PUNCT
ejpam-6535	103	132	probabilistic	probabilistic	ADJ
ejpam-6535	103	133	convergence	convergence	NOUN
ejpam-6535	103	134	space	space	NOUN
ejpam-6535	103	135	.	.	PUNCT
ejpam-6535	104	1	if	if	SCONJ
ejpam-6535	104	2	(	(	PUNCT
ejpam-6535	104	3	s	s	X
ejpam-6535	104	4	,	,	PUNCT
ejpam-6535	104	5	c	c	NOUN
ejpam-6535	104	6	)	)	PUNCT
ejpam-6535	104	7	satisfies	satisfie	NOUN
ejpam-6535	104	8	further	far	ADV
ejpam-6535	104	9	the	the	DET
ejpam-6535	104	10	axiom	axiom	NOUN
ejpam-6535	104	11	(	(	PUNCT
ejpam-6535	104	12	pcs5	pcs5	PROPN
ejpam-6535	104	13	)	)	PUNCT
ejpam-6535	104	14	cφ(f	cφ(f	NOUN
ejpam-6535	104	15	)	)	PUNCT
ejpam-6535	104	16	∩	∩	NOUN
ejpam-6535	104	17	cφ(g	cφ(g	NUM
ejpam-6535	104	18	)	)	PUNCT
ejpam-6535	104	19	⊆	⊆	NUM
ejpam-6535	104	20	cφ	cφ	NOUN
ejpam-6535	104	21	(	(	PUNCT
ejpam-6535	104	22	f	f	PROPN
ejpam-6535	104	23	∧g	∧g	PROPN
ejpam-6535	104	24	)	)	PUNCT
ejpam-6535	104	25	,	,	PUNCT
ejpam-6535	104	26	∀φ	∀φ	NUM
ejpam-6535	104	27	∈	∈	PROPN
ejpam-6535	104	28	∆+	∆+	NOUN
ejpam-6535	104	29	,	,	PUNCT
ejpam-6535	104	30	∀f	∀f	PROPN
ejpam-6535	104	31	,	,	PUNCT
ejpam-6535	104	32	g	g	PROPN
ejpam-6535	104	33	∈	∈	PROPN
ejpam-6535	104	34	f(s	f(	NOUN
ejpam-6535	104	35	)	)	PUNCT
ejpam-6535	104	36	,	,	PUNCT
ejpam-6535	104	37	then	then	ADV
ejpam-6535	104	38	we	we	PRON
ejpam-6535	104	39	speak	speak	VERB
ejpam-6535	104	40	of	of	ADP
ejpam-6535	104	41	a	a	DET
ejpam-6535	104	42	probabilistic	probabilistic	ADJ
ejpam-6535	104	43	limit	limit	NOUN
ejpam-6535	104	44	space	space	NOUN
ejpam-6535	104	45	.	.	PUNCT
ejpam-6535	105	1	the	the	DET
ejpam-6535	105	2	statement	statement	NOUN
ejpam-6535	105	3	:	:	PUNCT
ejpam-6535	105	4	p	p	X
ejpam-6535	105	5	∈	∈	PROPN
ejpam-6535	105	6	cφ(f	cφ(f	PUNCT
ejpam-6535	105	7	)	)	PUNCT
ejpam-6535	105	8	is	be	AUX
ejpam-6535	105	9	interpreted	interpret	VERB
ejpam-6535	105	10	in	in	ADP
ejpam-6535	105	11	[	[	X
ejpam-6535	105	12	22	22	NUM
ejpam-6535	105	13	]	]	PUNCT
ejpam-6535	105	14	as	as	ADP
ejpam-6535	105	15	,	,	PUNCT
ejpam-6535	105	16	the	the	DET
ejpam-6535	105	17	probability	probability	NOUN
ejpam-6535	105	18	that	that	SCONJ
ejpam-6535	105	19	the	the	DET
ejpam-6535	105	20	distance	distance	NOUN
ejpam-6535	105	21	between	between	ADP
ejpam-6535	105	22	p	p	PROPN
ejpam-6535	105	23	and	and	CCONJ
ejpam-6535	105	24	the	the	DET
ejpam-6535	105	25	limit	limit	NOUN
ejpam-6535	105	26	points	point	NOUN
ejpam-6535	105	27	of	of	ADP
ejpam-6535	105	28	f	f	PROPN
ejpam-6535	105	29	is	be	AUX
ejpam-6535	105	30	smaller	small	ADJ
ejpam-6535	105	31	than	than	SCONJ
ejpam-6535	105	32	x	x	PRON
ejpam-6535	105	33	is	be	AUX
ejpam-6535	105	34	at	at	ADP
ejpam-6535	105	35	least	least	ADJ
ejpam-6535	105	36	φ(x	φ(x	NOUN
ejpam-6535	105	37	)	)	PUNCT
ejpam-6535	105	38	.	.	PUNCT
ejpam-6535	106	1	a	a	DET
ejpam-6535	106	2	probabilistic	probabilistic	ADJ
ejpam-6535	106	3	convergence	convergence	NOUN
ejpam-6535	106	4	space	space	NOUN
ejpam-6535	106	5	(	(	PUNCT
ejpam-6535	106	6	s	s	X
ejpam-6535	106	7	,	,	PUNCT
ejpam-6535	106	8	c	c	NOUN
ejpam-6535	106	9	=	=	SYM
ejpam-6535	106	10	(	(	PUNCT
ejpam-6535	106	11	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	106	12	)	)	PUNCT
ejpam-6535	106	13	is	be	AUX
ejpam-6535	106	14	called	call	VERB
ejpam-6535	106	15	a	a	DET
ejpam-6535	106	16	probabilistic	probabilistic	ADJ
ejpam-6535	106	17	pretopological	pretopological	ADJ
ejpam-6535	106	18	space	space	NOUN
ejpam-6535	106	19	if	if	SCONJ
ejpam-6535	106	20	it	it	PRON
ejpam-6535	106	21	satisfies	satisfy	VERB
ejpam-6535	106	22	the	the	DET
ejpam-6535	106	23	axiom	axiom	NOUN
ejpam-6535	106	24	(	(	PUNCT
ejpam-6535	106	25	ppt	ppt	NOUN
ejpam-6535	106	26	):	):	PUNCT
ejpam-6535	106	27	for	for	ADP
ejpam-6535	106	28	all	all	PRON
ejpam-6535	106	29	p	p	NOUN
ejpam-6535	106	30	∈	∈	PROPN
ejpam-6535	106	31	s	s	NOUN
ejpam-6535	106	32	,	,	PUNCT
ejpam-6535	106	33	φ	φ	PROPN
ejpam-6535	106	34	∈	∈	PROPN
ejpam-6535	106	35	∆+	∆+	NOUN
ejpam-6535	106	36	and	and	CCONJ
ejpam-6535	106	37	f	f	PROPN
ejpam-6535	106	38	∈	∈	PROPN
ejpam-6535	106	39	f(s	f(	NOUN
ejpam-6535	106	40	)	)	PUNCT
ejpam-6535	106	41	,	,	PUNCT
ejpam-6535	106	42	we	we	PRON
ejpam-6535	106	43	have	have	VERB
ejpam-6535	106	44	p	p	NOUN
ejpam-6535	106	45	∈	∈	NOUN
ejpam-6535	106	46	cφ(f	cφ(f	PUNCT
ejpam-6535	106	47	)	)	PUNCT
ejpam-6535	106	48	if	if	SCONJ
ejpam-6535	107	1	and	and	CCONJ
ejpam-6535	107	2	only	only	ADV
ejpam-6535	107	3	if	if	SCONJ
ejpam-6535	107	4	f	f	PROPN
ejpam-6535	107	5	≥	≥	VERB
ejpam-6535	107	6	nφ	nφ	ADP
ejpam-6535	107	7	p	p	PROPN
ejpam-6535	107	8	whence	whence	PROPN
ejpam-6535	107	9	nφ	nφ	PROPN
ejpam-6535	107	10	p	p	PROPN
ejpam-6535	107	11	=	=	PROPN
ejpam-6535	107	12	∧	∧	PROPN
ejpam-6535	107	13	p∈cφ(f	p∈cφ(f	PROPN
ejpam-6535	107	14	)	)	PUNCT
ejpam-6535	107	15	f	f	PROPN
ejpam-6535	107	16	,	,	PUNCT
ejpam-6535	107	17	called	call	VERB
ejpam-6535	107	18	the	the	DET
ejpam-6535	107	19	φ	φ	ADJ
ejpam-6535	107	20	-	-	PUNCT
ejpam-6535	107	21	neighborhood	neighborhood	NOUN
ejpam-6535	107	22	filter	filter	NOUN
ejpam-6535	107	23	of	of	ADP
ejpam-6535	107	24	p.	p.	NOUN
ejpam-6535	107	25	it	it	PRON
ejpam-6535	107	26	is	be	AUX
ejpam-6535	107	27	pointed	point	VERB
ejpam-6535	107	28	out	out	ADP
ejpam-6535	107	29	in	in	ADP
ejpam-6535	107	30	[	[	X
ejpam-6535	107	31	22	22	NUM
ejpam-6535	107	32	]	]	PUNCT
ejpam-6535	107	33	that	that	SCONJ
ejpam-6535	107	34	the	the	DET
ejpam-6535	107	35	probabilistic	probabilistic	ADJ
ejpam-6535	107	36	convergence	convergence	NOUN
ejpam-6535	107	37	space	space	NOUN
ejpam-6535	107	38	(	(	PUNCT
ejpam-6535	107	39	s	s	X
ejpam-6535	107	40	,	,	PUNCT
ejpam-6535	107	41	cf	cf	NOUN
ejpam-6535	107	42	=	=	SYM
ejpam-6535	107	43	(	(	PUNCT
ejpam-6535	107	44	cfφ	cfφ	NOUN
ejpam-6535	107	45	)	)	PUNCT
ejpam-6535	107	46	φ∈∆+	φ∈∆+	PROPN
ejpam-6535	107	47	)	)	PUNCT
ejpam-6535	107	48	associated	associate	VERB
ejpam-6535	107	49	with	with	ADP
ejpam-6535	107	50	probabilistic	probabilistic	ADJ
ejpam-6535	107	51	metric	metric	ADJ
ejpam-6535	107	52	space	space	NOUN
ejpam-6535	107	53	(	(	PUNCT
ejpam-6535	107	54	s	s	PROPN
ejpam-6535	107	55	,	,	PUNCT
ejpam-6535	107	56	f	f	PROPN
ejpam-6535	107	57	)	)	PUNCT
ejpam-6535	107	58	,	,	PUNCT
ejpam-6535	107	59	is	be	AUX
ejpam-6535	107	60	a	a	DET
ejpam-6535	107	61	probabilistic	probabilistic	ADJ
ejpam-6535	107	62	pretopological	pretopological	ADJ
ejpam-6535	107	63	space	space	NOUN
ejpam-6535	107	64	.	.	PUNCT
ejpam-6535	108	1	a	a	DET
ejpam-6535	108	2	mapping	mapping	NOUN
ejpam-6535	108	3	f	f	NOUN
ejpam-6535	108	4	:	:	PUNCT
ejpam-6535	108	5	(	(	PUNCT
ejpam-6535	108	6	s	s	X
ejpam-6535	108	7	,	,	PUNCT
ejpam-6535	108	8	cs	cs	ADJ
ejpam-6535	108	9	)	)	PUNCT
ejpam-6535	108	10	−→	−→	NOUN
ejpam-6535	108	11	(	(	PUNCT
ejpam-6535	108	12	t	t	PROPN
ejpam-6535	108	13	,	,	PUNCT
ejpam-6535	108	14	ct	ct	PROPN
ejpam-6535	108	15	)	)	PUNCT
ejpam-6535	108	16	between	between	ADP
ejpam-6535	108	17	probabilistic	probabilistic	ADJ
ejpam-6535	108	18	convergence	convergence	NOUN
ejpam-6535	108	19	spaces	space	NOUN
ejpam-6535	108	20	(	(	PUNCT
ejpam-6535	108	21	resp	resp	NOUN
ejpam-6535	108	22	.	.	PUNCT
ejpam-6535	109	1	between	between	ADP
ejpam-6535	109	2	probabilistic	probabilistic	ADJ
ejpam-6535	109	3	pretopological	pretopological	ADJ
ejpam-6535	109	4	spaces	space	NOUN
ejpam-6535	109	5	)	)	PUNCT
ejpam-6535	109	6	is	be	AUX
ejpam-6535	109	7	called	call	VERB
ejpam-6535	109	8	continuous	continuous	ADJ
ejpam-6535	109	9	if	if	SCONJ
ejpam-6535	109	10	f(p	f(p	NOUN
ejpam-6535	109	11	)	)	PUNCT
ejpam-6535	109	12	∈	∈	PROPN
ejpam-6535	109	13	ctφ(f(f	ctφ(f(f	NOUN
ejpam-6535	109	14	)	)	PUNCT
ejpam-6535	109	15	)	)	PUNCT
ejpam-6535	110	1	whenever	whenever	SCONJ
ejpam-6535	110	2	p	p	PROPN
ejpam-6535	110	3	∈	∈	PROPN
ejpam-6535	110	4	csφ(f	csφ(f	PROPN
ejpam-6535	110	5	)	)	PUNCT
ejpam-6535	110	6	for	for	ADP
ejpam-6535	110	7	every	every	DET
ejpam-6535	110	8	p	p	PROPN
ejpam-6535	110	9	∈	∈	PROPN
ejpam-6535	110	10	s	s	NOUN
ejpam-6535	110	11	and	and	CCONJ
ejpam-6535	110	12	for	for	ADP
ejpam-6535	110	13	every	every	DET
ejpam-6535	110	14	f	f	PROPN
ejpam-6535	110	15	∈	∈	PROPN
ejpam-6535	110	16	f(s	f(	NOUN
ejpam-6535	110	17	)	)	PUNCT
ejpam-6535	110	18	,	,	PUNCT
ejpam-6535	110	19	and	and	CCONJ
ejpam-6535	110	20	φ	φ	NUM
ejpam-6535	110	21	∈	∈	PROPN
ejpam-6535	110	22	∆+	∆+	NOUN
ejpam-6535	110	23	;	;	PUNCT
ejpam-6535	110	24	for	for	ADP
ejpam-6535	110	25	convergence	convergence	NOUN
ejpam-6535	110	26	notations	notation	NOUN
ejpam-6535	110	27	,	,	PUNCT
ejpam-6535	110	28	we	we	PRON
ejpam-6535	110	29	will	will	AUX
ejpam-6535	110	30	suppress	suppress	VERB
ejpam-6535	110	31	s	s	PRON
ejpam-6535	110	32	and	and	CCONJ
ejpam-6535	110	33	t	t	PROPN
ejpam-6535	110	34	if	if	SCONJ
ejpam-6535	110	35	no	no	DET
ejpam-6535	110	36	confusion	confusion	NOUN
ejpam-6535	110	37	arises	arise	VERB
ejpam-6535	110	38	.	.	PUNCT
ejpam-6535	111	1	pconv	pconv	NOUN
ejpam-6535	111	2	denotes	denote	VERB
ejpam-6535	111	3	the	the	DET
ejpam-6535	111	4	category	category	NOUN
ejpam-6535	111	5	of	of	ADP
ejpam-6535	111	6	probabilistic	probabilistic	ADJ
ejpam-6535	111	7	convergence	convergence	NOUN
ejpam-6535	111	8	spaces	space	NOUN
ejpam-6535	111	9	as	as	ADP
ejpam-6535	111	10	objects	object	NOUN
ejpam-6535	111	11	and	and	CCONJ
ejpam-6535	111	12	continuous	continuous	ADJ
ejpam-6535	111	13	mappings	mapping	NOUN
ejpam-6535	111	14	as	as	ADP
ejpam-6535	111	15	morphisms	morphism	NOUN
ejpam-6535	111	16	while	while	SCONJ
ejpam-6535	111	17	ppretop	ppretop	ADJ
ejpam-6535	111	18	denotes	denote	VERB
ejpam-6535	111	19	the	the	DET
ejpam-6535	111	20	category	category	NOUN
ejpam-6535	111	21	of	of	ADP
ejpam-6535	111	22	probabilistic	probabilistic	ADJ
ejpam-6535	111	23	pretopological	pretopological	ADJ
ejpam-6535	111	24	spaces	space	NOUN
ejpam-6535	111	25	.	.	PUNCT
ejpam-6535	112	1	the	the	DET
ejpam-6535	112	2	dual	dual	ADJ
ejpam-6535	112	3	of	of	ADP
ejpam-6535	112	4	the	the	DET
ejpam-6535	112	5	following	follow	VERB
ejpam-6535	112	6	notion	notion	NOUN
ejpam-6535	112	7	called	call	VERB
ejpam-6535	112	8	φ	φ	NUM
ejpam-6535	112	9	-	-	ADJ
ejpam-6535	112	10	interior	interior	ADJ
ejpam-6535	112	11	operator	operator	NOUN
ejpam-6535	112	12	can	can	AUX
ejpam-6535	112	13	be	be	AUX
ejpam-6535	112	14	found	find	VERB
ejpam-6535	112	15	details	detail	NOUN
ejpam-6535	112	16	in	in	ADP
ejpam-6535	112	17	[	[	X
ejpam-6535	112	18	22	22	NUM
ejpam-6535	112	19	]	]	PUNCT
ejpam-6535	112	20	.	.	PUNCT
ejpam-6535	113	1	here	here	ADV
ejpam-6535	113	2	we	we	PRON
ejpam-6535	113	3	just	just	ADV
ejpam-6535	113	4	present	present	VERB
ejpam-6535	113	5	the	the	DET
ejpam-6535	113	6	notion	notion	NOUN
ejpam-6535	113	7	of	of	ADP
ejpam-6535	113	8	φ	φ	PROPN
ejpam-6535	113	9	-	-	PUNCT
ejpam-6535	113	10	closure	closure	NOUN
ejpam-6535	113	11	operator	operator	NOUN
ejpam-6535	113	12	for	for	ADP
ejpam-6535	113	13	a	a	DET
ejpam-6535	113	14	particular	particular	ADJ
ejpam-6535	113	15	result	result	NOUN
ejpam-6535	113	16	that	that	SCONJ
ejpam-6535	113	17	we	we	PRON
ejpam-6535	113	18	included	include	VERB
ejpam-6535	113	19	herein	herein	NOUN
ejpam-6535	113	20	this	this	DET
ejpam-6535	113	21	text	text	NOUN
ejpam-6535	113	22	without	without	ADP
ejpam-6535	113	23	further	further	ADJ
ejpam-6535	113	24	elaboration	elaboration	NOUN
ejpam-6535	113	25	.	.	PUNCT
ejpam-6535	114	1	we	we	PRON
ejpam-6535	114	2	intend	intend	VERB
ejpam-6535	114	3	to	to	PART
ejpam-6535	114	4	discuss	discuss	VERB
ejpam-6535	114	5	this	this	DET
ejpam-6535	114	6	issue	issue	NOUN
ejpam-6535	114	7	in	in	ADP
ejpam-6535	114	8	a	a	DET
ejpam-6535	114	9	future	future	ADJ
ejpam-6535	114	10	paper	paper	NOUN
ejpam-6535	114	11	in	in	ADP
ejpam-6535	114	12	conjunction	conjunction	NOUN
ejpam-6535	114	13	with	with	ADP
ejpam-6535	114	14	so	so	ADV
ejpam-6535	114	15	-	-	PUNCT
ejpam-6535	114	16	called	call	VERB
ejpam-6535	114	17	probabilistic	probabilistic	ADJ
ejpam-6535	114	18	approximation	approximation	NOUN
ejpam-6535	114	19	spaces	space	NOUN
ejpam-6535	114	20	.	.	PUNCT
ejpam-6535	115	1	definition	definition	NOUN
ejpam-6535	115	2	4	4	NUM
ejpam-6535	115	3	.	.	PUNCT
ejpam-6535	116	1	[	[	X
ejpam-6535	116	2	22	22	NUM
ejpam-6535	116	3	,	,	PUNCT
ejpam-6535	116	4	38	38	NUM
ejpam-6535	116	5	]	]	PUNCT
ejpam-6535	116	6	for	for	ADP
ejpam-6535	116	7	a	a	DET
ejpam-6535	116	8	φ	φ	PROPN
ejpam-6535	116	9	∈	∈	PROPN
ejpam-6535	116	10	∆+	∆+	NOUN
ejpam-6535	116	11	,	,	PUNCT
ejpam-6535	116	12	a	a	DET
ejpam-6535	116	13	φ	φ	VERB
ejpam-6535	116	14	-	-	PUNCT
ejpam-6535	116	15	closure	closure	NOUN
ejpam-6535	116	16	operator	operator	NOUN
ejpam-6535	116	17	on	on	ADP
ejpam-6535	116	18	a	a	DET
ejpam-6535	116	19	set	set	NOUN
ejpam-6535	116	20	s	s	NOUN
ejpam-6535	116	21	is	be	AUX
ejpam-6535	116	22	a	a	DET
ejpam-6535	116	23	mapping	mapping	NOUN
ejpam-6535	116	24	cφ	cφ	NOUN
ejpam-6535	116	25	:	:	PUNCT
ejpam-6535	116	26	p	p	X
ejpam-6535	116	27	(	(	PUNCT
ejpam-6535	116	28	s	s	NOUN
ejpam-6535	116	29	)	)	PUNCT
ejpam-6535	116	30	−→	−→	NOUN
ejpam-6535	116	31	p	p	X
ejpam-6535	116	32	(	(	PUNCT
ejpam-6535	116	33	s	s	NOUN
ejpam-6535	116	34	)	)	PUNCT
ejpam-6535	116	35	between	between	ADP
ejpam-6535	116	36	power	power	NOUN
ejpam-6535	116	37	set	set	NOUN
ejpam-6535	116	38	of	of	ADP
ejpam-6535	116	39	s	s	VERB
ejpam-6535	116	40	satisfying	satisfy	VERB
ejpam-6535	116	41	following	follow	VERB
ejpam-6535	116	42	conditions	condition	NOUN
ejpam-6535	116	43	:	:	PUNCT
ejpam-6535	116	44	(	(	PUNCT
ejpam-6535	116	45	c1	c1	NOUN
ejpam-6535	116	46	)	)	PUNCT
ejpam-6535	116	47	cφ(∅	cφ(∅	NOUN
ejpam-6535	116	48	)	)	PUNCT
ejpam-6535	117	1	=	=	NOUN
ejpam-6535	117	2	∅	∅	NOUN
ejpam-6535	117	3	for	for	ADP
ejpam-6535	117	4	all	all	DET
ejpam-6535	117	5	φ	φ	PROPN
ejpam-6535	117	6	∈	∈	PROPN
ejpam-6535	117	7	∆+	∆+	NOUN
ejpam-6535	117	8	;	;	PUNCT
ejpam-6535	117	9	(	(	PUNCT
ejpam-6535	117	10	c2	c2	PROPN
ejpam-6535	117	11	)	)	PUNCT
ejpam-6535	117	12	a	a	DET
ejpam-6535	117	13	⊆	⊆	NUM
ejpam-6535	117	14	cφ(a	cφ(a	NOUN
ejpam-6535	117	15	)	)	PUNCT
ejpam-6535	117	16	for	for	ADP
ejpam-6535	117	17	all	all	DET
ejpam-6535	117	18	a	a	DET
ejpam-6535	117	19	∈	∈	PROPN
ejpam-6535	117	20	p	p	X
ejpam-6535	117	21	(	(	PUNCT
ejpam-6535	117	22	s	s	NOUN
ejpam-6535	117	23	)	)	PUNCT
ejpam-6535	117	24	,	,	PUNCT
ejpam-6535	117	25	and	and	CCONJ
ejpam-6535	117	26	for	for	ADP
ejpam-6535	117	27	all	all	DET
ejpam-6535	117	28	φ	φ	PROPN
ejpam-6535	117	29	∈	∈	PROPN
ejpam-6535	117	30	∆+	∆+	NOUN
ejpam-6535	117	31	;	;	PUNCT
ejpam-6535	117	32	(	(	PUNCT
ejpam-6535	117	33	c3	c3	PROPN
ejpam-6535	117	34	)	)	PUNCT
ejpam-6535	117	35	a	a	DET
ejpam-6535	117	36	⊆	⊆	NUM
ejpam-6535	117	37	b	b	NOUN
ejpam-6535	117	38	implies	imply	VERB
ejpam-6535	117	39	cφ(a	cφ(a	NOUN
ejpam-6535	117	40	)	)	PUNCT
ejpam-6535	117	41	⊆	⊆	NUM
ejpam-6535	117	42	cφ(b	cφ(b	NUM
ejpam-6535	117	43	)	)	PUNCT
ejpam-6535	117	44	for	for	ADP
ejpam-6535	117	45	all	all	DET
ejpam-6535	117	46	a	a	DET
ejpam-6535	117	47	,	,	PUNCT
ejpam-6535	117	48	b	b	PROPN
ejpam-6535	117	49	∈	∈	PROPN
ejpam-6535	117	50	p	p	X
ejpam-6535	117	51	(	(	PUNCT
ejpam-6535	117	52	s	s	NOUN
ejpam-6535	117	53	)	)	PUNCT
ejpam-6535	117	54	and	and	CCONJ
ejpam-6535	117	55	for	for	ADP
ejpam-6535	117	56	all	all	DET
ejpam-6535	117	57	φ	φ	PROPN
ejpam-6535	117	58	∈	∈	PROPN
ejpam-6535	117	59	∆+	∆+	NOUN
ejpam-6535	117	60	;	;	PUNCT
ejpam-6535	117	61	(	(	PUNCT
ejpam-6535	117	62	c4	c4	NOUN
ejpam-6535	117	63	)	)	PUNCT
ejpam-6535	117	64	for	for	ADP
ejpam-6535	117	65	all	all	DET
ejpam-6535	117	66	φ	φ	NOUN
ejpam-6535	117	67	,	,	PUNCT
ejpam-6535	117	68	ψ	ψ	X
ejpam-6535	117	69	∈	∈	PROPN
ejpam-6535	117	70	∆+	∆+	NUM
ejpam-6535	117	71	with	with	ADP
ejpam-6535	117	72	φ	φ	PROPN
ejpam-6535	117	73	≤	≤	NOUN
ejpam-6535	117	74	ψ	ψ	PROPN
ejpam-6535	117	75	implies	implie	NOUN
ejpam-6535	117	76	cψ(a	cψ(a	NOUN
ejpam-6535	117	77	)	)	PUNCT
ejpam-6535	117	78	⊆	⊆	NUM
ejpam-6535	117	79	cφ(a	cφ(a	NOUN
ejpam-6535	117	80	)	)	PUNCT
ejpam-6535	117	81	for	for	ADP
ejpam-6535	117	82	all	all	DET
ejpam-6535	117	83	a	a	DET
ejpam-6535	117	84	∈	∈	PROPN
ejpam-6535	117	85	p	p	X
ejpam-6535	117	86	(	(	PUNCT
ejpam-6535	117	87	s	s	PROPN
ejpam-6535	117	88	)	)	PUNCT
ejpam-6535	117	89	;	;	PUNCT
ejpam-6535	117	90	then	then	ADV
ejpam-6535	117	91	the	the	DET
ejpam-6535	117	92	pair	pair	NOUN
ejpam-6535	117	93	(	(	PUNCT
ejpam-6535	117	94	s	s	X
ejpam-6535	117	95	,	,	PUNCT
ejpam-6535	117	96	(	(	PUNCT
ejpam-6535	117	97	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	117	98	)	)	PUNCT
ejpam-6535	117	99	is	be	AUX
ejpam-6535	117	100	called	call	VERB
ejpam-6535	117	101	a	a	DET
ejpam-6535	117	102	probabilistic	probabilistic	ADJ
ejpam-6535	117	103	closure	closure	NOUN
ejpam-6535	117	104	space	space	NOUN
ejpam-6535	117	105	.	.	PUNCT
ejpam-6535	118	1	it	it	PRON
ejpam-6535	118	2	is	be	AUX
ejpam-6535	118	3	called	call	VERB
ejpam-6535	118	4	probabilistic	probabilistic	ADJ
ejpam-6535	118	5	topological	topological	ADJ
ejpam-6535	118	6	space	space	NOUN
ejpam-6535	118	7	under	under	ADP
ejpam-6535	118	8	a	a	DET
ejpam-6535	118	9	triangle	triangle	NOUN
ejpam-6535	118	10	function	function	NOUN
ejpam-6535	118	11	τ	τ	X
ejpam-6535	118	12	if	if	SCONJ
ejpam-6535	118	13	it	it	PRON
ejpam-6535	118	14	further	far	ADV
ejpam-6535	118	15	satisfies	satisfie	NOUN
ejpam-6535	118	16	axiom	axiom	NOUN
ejpam-6535	118	17	(	(	PUNCT
ejpam-6535	118	18	c5	c5	PROPN
ejpam-6535	118	19	)	)	PUNCT
ejpam-6535	118	20	cφ	cφ	PROPN
ejpam-6535	118	21	(	(	PUNCT
ejpam-6535	118	22	cψ(a	cψ(a	NOUN
ejpam-6535	118	23	)	)	PUNCT
ejpam-6535	118	24	)	)	PUNCT
ejpam-6535	119	1	⊆	⊆	X
ejpam-6535	119	2	cτ(φ	cτ(φ	NUM
ejpam-6535	119	3	,	,	PUNCT
ejpam-6535	119	4	ψ	ψ	NOUN
ejpam-6535	119	5	)	)	PUNCT
ejpam-6535	119	6	for	for	ADP
ejpam-6535	119	7	all	all	DET
ejpam-6535	119	8	a	a	DET
ejpam-6535	119	9	̸=	̸=	PROPN
ejpam-6535	119	10	∅	∅	NOUN
ejpam-6535	119	11	and	and	CCONJ
ejpam-6535	119	12	for	for	ADP
ejpam-6535	119	13	all	all	PRON
ejpam-6535	119	14	(	(	PUNCT
ejpam-6535	119	15	φ	φ	PROPN
ejpam-6535	119	16	,	,	PUNCT
ejpam-6535	119	17	ψ	ψ	NOUN
ejpam-6535	119	18	)	)	PUNCT
ejpam-6535	119	19	∈	∈	PROPN
ejpam-6535	119	20	∆+	∆+	NUM
ejpam-6535	119	21	×∆+	×∆+	NUM
ejpam-6535	119	22	.	.	PUNCT
ejpam-6535	119	23	note	note	VERB
ejpam-6535	119	24	that	that	SCONJ
ejpam-6535	119	25	the	the	DET
ejpam-6535	119	26	axiom	axiom	NOUN
ejpam-6535	119	27	(	(	PUNCT
ejpam-6535	119	28	c3	c3	PROPN
ejpam-6535	119	29	)	)	PUNCT
ejpam-6535	119	30	is	be	AUX
ejpam-6535	119	31	equivalent	equivalent	ADJ
ejpam-6535	119	32	to	to	ADP
ejpam-6535	119	33	the	the	DET
ejpam-6535	119	34	axiom	axiom	NOUN
ejpam-6535	119	35	(	(	PUNCT
ejpam-6535	119	36	c3)′	c3)′	NOUN
ejpam-6535	119	37	:	:	PUNCT
ejpam-6535	119	38	cφ(a)∪cφ(b	cφ(a)∪cφ(b	PROPN
ejpam-6535	119	39	)	)	PUNCT
ejpam-6535	119	40	⊆	⊆	NUM
ejpam-6535	119	41	cφ(a∪b	cφ(a∪b	NOUN
ejpam-6535	119	42	)	)	PUNCT
ejpam-6535	119	43	.	.	PUNCT
ejpam-6535	120	1	if	if	SCONJ
ejpam-6535	120	2	(	(	PUNCT
ejpam-6535	120	3	s	s	X
ejpam-6535	120	4	,	,	PUNCT
ejpam-6535	120	5	c	c	NOUN
ejpam-6535	120	6	)	)	PUNCT
ejpam-6535	120	7	is	be	AUX
ejpam-6535	120	8	a	a	DET
ejpam-6535	120	9	probabilistic	probabilistic	ADJ
ejpam-6535	120	10	closure	closure	NOUN
ejpam-6535	120	11	space	space	NOUN
ejpam-6535	120	12	and	and	CCONJ
ejpam-6535	120	13	a	a	DET
ejpam-6535	120	14	⊆	⊆	NUM
ejpam-6535	120	15	s	s	NOUN
ejpam-6535	120	16	,	,	PUNCT
ejpam-6535	120	17	then	then	ADV
ejpam-6535	120	18	the	the	DET
ejpam-6535	120	19	set	set	NOUN
ejpam-6535	120	20	cφ(a	cφ(a	NOUN
ejpam-6535	120	21	)	)	PUNCT
ejpam-6535	120	22	is	be	AUX
ejpam-6535	120	23	called	call	VERB
ejpam-6535	120	24	the	the	DET
ejpam-6535	120	25	φ	φ	NOUN
ejpam-6535	120	26	-	-	NOUN
ejpam-6535	120	27	closure	closure	NOUN
ejpam-6535	120	28	of	of	ADP
ejpam-6535	120	29	a	a	DET
ejpam-6535	120	30	in	in	ADP
ejpam-6535	120	31	(	(	PUNCT
ejpam-6535	120	32	s	s	X
ejpam-6535	120	33	,	,	PUNCT
ejpam-6535	120	34	c	c	NOUN
ejpam-6535	120	35	)	)	PUNCT
ejpam-6535	120	36	.	.	PUNCT
ejpam-6535	121	1	remark	remark	PROPN
ejpam-6535	121	2	1	1	NUM
ejpam-6535	121	3	.	.	PUNCT
ejpam-6535	122	1	in	in	ADP
ejpam-6535	122	2	any	any	DET
ejpam-6535	122	3	probabilistic	probabilistic	ADJ
ejpam-6535	122	4	convergence	convergence	NOUN
ejpam-6535	122	5	space	space	NOUN
ejpam-6535	122	6	(	(	PUNCT
ejpam-6535	122	7	s	s	X
ejpam-6535	122	8	,	,	PUNCT
ejpam-6535	122	9	c	c	NOUN
ejpam-6535	122	10	=	=	SYM
ejpam-6535	122	11	(	(	PUNCT
ejpam-6535	122	12	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	122	13	)	)	PUNCT
ejpam-6535	122	14	,	,	PUNCT
ejpam-6535	122	15	one	one	PRON
ejpam-6535	122	16	can	can	AUX
ejpam-6535	122	17	define	define	VERB
ejpam-6535	122	18	φclosure	φclosure	NOUN
ejpam-6535	122	19	in	in	ADP
ejpam-6535	122	20	the	the	DET
ejpam-6535	122	21	following	following	ADJ
ejpam-6535	122	22	way	way	NOUN
ejpam-6535	122	23	:	:	PUNCT
ejpam-6535	122	24	cφ(a	cφ(a	X
ejpam-6535	122	25	)	)	PUNCT
ejpam-6535	123	1	=	=	PRON
ejpam-6535	123	2	{	{	PUNCT
ejpam-6535	123	3	p	p	X
ejpam-6535	123	4	∈	∈	PROPN
ejpam-6535	123	5	s	s	PART
ejpam-6535	123	6	:	:	PUNCT
ejpam-6535	123	7	∃	∃	PROPN
ejpam-6535	123	8	f	f	PROPN
ejpam-6535	123	9	∈	∈	PROPN
ejpam-6535	123	10	f(s	f(	NOUN
ejpam-6535	123	11	)	)	PUNCT
ejpam-6535	123	12	∋	∋	NOUN
ejpam-6535	124	1	p	p	PROPN
ejpam-6535	124	2	∈	∈	PROPN
ejpam-6535	124	3	cφ(f	cφ(f	PUNCT
ejpam-6535	124	4	)	)	PUNCT
ejpam-6535	124	5	⇒	⇒	VERB
ejpam-6535	124	6	a	a	DET
ejpam-6535	124	7	∈	∈	ADJ
ejpam-6535	124	8	f	f	X
ejpam-6535	124	9	}	}	PUNCT
ejpam-6535	124	10	,	,	PUNCT
ejpam-6535	124	11	for	for	ADP
ejpam-6535	124	12	any	any	DET
ejpam-6535	124	13	subset	subset	NOUN
ejpam-6535	124	14	a	a	DET
ejpam-6535	124	15	⊆	⊆	NUM
ejpam-6535	124	16	s.	s.	PROPN
ejpam-6535	124	17	remark	remark	NOUN
ejpam-6535	124	18	2	2	NUM
ejpam-6535	124	19	.	.	PUNCT
ejpam-6535	125	1	the	the	DET
ejpam-6535	125	2	category	category	NOUN
ejpam-6535	125	3	pconv	pconv	NOUN
ejpam-6535	125	4	is	be	AUX
ejpam-6535	125	5	a	a	DET
ejpam-6535	125	6	cartesian	cartesian	ADJ
ejpam-6535	125	7	closed	closed	ADJ
ejpam-6535	125	8	topological	topological	ADJ
ejpam-6535	125	9	category	category	NOUN
ejpam-6535	125	10	[	[	X
ejpam-6535	125	11	22	22	NUM
ejpam-6535	125	12	]	]	PUNCT
ejpam-6535	125	13	.	.	PUNCT
ejpam-6535	126	1	in	in	ADP
ejpam-6535	126	2	particular	particular	ADJ
ejpam-6535	126	3	,	,	PUNCT
ejpam-6535	126	4	the	the	DET
ejpam-6535	126	5	initial	initial	ADJ
ejpam-6535	126	6	probabilistic	probabilistic	ADJ
ejpam-6535	126	7	convergence	convergence	NOUN
ejpam-6535	126	8	structure	structure	NOUN
ejpam-6535	126	9	for	for	ADP
ejpam-6535	126	10	a	a	DET
ejpam-6535	126	11	given	give	VERB
ejpam-6535	126	12	source	source	NOUN
ejpam-6535	126	13	(	(	PUNCT
ejpam-6535	126	14	fi	fi	NOUN
ejpam-6535	126	15	:	:	PUNCT
ejpam-6535	126	16	s	s	AUX
ejpam-6535	126	17	−→	−→	ADJ
ejpam-6535	126	18	(	(	PUNCT
ejpam-6535	126	19	si	si	INTJ
ejpam-6535	126	20	,	,	PUNCT
ejpam-6535	126	21	(	(	PUNCT
ejpam-6535	126	22	c	c	VERB
ejpam-6535	126	23	i	i	PRON
ejpam-6535	126	24	φ)φ∈∆+	φ)φ∈∆+	NOUN
ejpam-6535	126	25	)	)	PUNCT
ejpam-6535	126	26	)	)	PUNCT
ejpam-6535	126	27	i∈j	i∈j	NOUN
ejpam-6535	126	28	is	be	AUX
ejpam-6535	126	29	given	give	VERB
ejpam-6535	126	30	by	by	ADP
ejpam-6535	126	31	p	p	NOUN
ejpam-6535	126	32	∈	∈	PROPN
ejpam-6535	126	33	cφ(f	cφ(f	NOUN
ejpam-6535	126	34	)	)	PUNCT
ejpam-6535	126	35	⇐	⇐	ADJ
ejpam-6535	126	36	⇒	⇒	NOUN
ejpam-6535	126	37	fi(p	fi(p	NOUN
ejpam-6535	126	38	)	)	PUNCT
ejpam-6535	126	39	∈	∈	PROPN
ejpam-6535	126	40	ciφ	ciφ	NOUN
ejpam-6535	126	41	(	(	PUNCT
ejpam-6535	126	42	fi(f	fi(f	NOUN
ejpam-6535	126	43	)	)	PUNCT
ejpam-6535	126	44	)	)	PUNCT
ejpam-6535	126	45	,	,	PUNCT
ejpam-6535	126	46	∀i	∀i	X
ejpam-6535	126	47	∈	∈	PROPN
ejpam-6535	126	48	j	j	NOUN
ejpam-6535	126	49	,	,	PUNCT
ejpam-6535	126	50	where	where	SCONJ
ejpam-6535	126	51	p	p	PROPN
ejpam-6535	126	52	∈	∈	PROPN
ejpam-6535	126	53	s	s	PROPN
ejpam-6535	126	54	,	,	PUNCT
ejpam-6535	126	55	f	f	PROPN
ejpam-6535	126	56	∈	∈	PROPN
ejpam-6535	126	57	f(s	f(	VERB
ejpam-6535	126	58	)	)	PUNCT
ejpam-6535	126	59	and	and	CCONJ
ejpam-6535	126	60	φ	φ	NUM
ejpam-6535	126	61	∈	∈	PROPN
ejpam-6535	126	62	∆+	∆+	NOUN
ejpam-6535	126	63	.	.	PUNCT
ejpam-6535	127	1	4	4	X
ejpam-6535	127	2	.	.	X
ejpam-6535	127	3	probabilistic	probabilistic	ADJ
ejpam-6535	127	4	neighborhood	neighborhood	NOUN
ejpam-6535	127	5	spaces	space	NOUN
ejpam-6535	127	6	and	and	CCONJ
ejpam-6535	127	7	probabilistic	probabilistic	ADJ
ejpam-6535	127	8	convergence	convergence	NOUN
ejpam-6535	127	9	spaces	space	NOUN
ejpam-6535	127	10	definition	definition	NOUN
ejpam-6535	127	11	5	5	NUM
ejpam-6535	127	12	.	.	PUNCT
ejpam-6535	128	1	a	a	DET
ejpam-6535	128	2	family	family	NOUN
ejpam-6535	128	3	of	of	ADP
ejpam-6535	128	4	filters	filter	NOUN
ejpam-6535	128	5	n	n	NOUN
ejpam-6535	128	6	=	=	SYM
ejpam-6535	128	7	(	(	PUNCT
ejpam-6535	128	8	nφ	nφ	PROPN
ejpam-6535	128	9	p	p	NOUN
ejpam-6535	128	10	)	)	PUNCT
ejpam-6535	128	11	(	(	PUNCT
ejpam-6535	128	12	p	p	X
ejpam-6535	128	13	,	,	PUNCT
ejpam-6535	128	14	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	128	15	,	,	PUNCT
ejpam-6535	128	16	where	where	SCONJ
ejpam-6535	128	17	for	for	ADP
ejpam-6535	128	18	each	each	DET
ejpam-6535	128	19	φ	φ	PROPN
ejpam-6535	128	20	∈	∈	PROPN
ejpam-6535	128	21	∆+	∆+	NOUN
ejpam-6535	128	22	,	,	PUNCT
ejpam-6535	128	23	nφ	nφ	NOUN
ejpam-6535	128	24	:	:	PUNCT
ejpam-6535	128	25	s	s	VERB
ejpam-6535	128	26	−→	−→	NOUN
ejpam-6535	128	27	p	p	X
ejpam-6535	128	28	(	(	PUNCT
ejpam-6535	128	29	p	p	X
ejpam-6535	128	30	(	(	PUNCT
ejpam-6535	128	31	s	s	NOUN
ejpam-6535	128	32	)	)	PUNCT
ejpam-6535	128	33	)	)	PUNCT
ejpam-6535	128	34	,	,	PUNCT
ejpam-6535	128	35	p	p	PROPN
ejpam-6535	128	36	7−→	7−→	PROPN
ejpam-6535	128	37	nφ	nφ	ADP
ejpam-6535	128	38	p	p	NOUN
ejpam-6535	128	39	is	be	AUX
ejpam-6535	128	40	said	say	VERB
ejpam-6535	128	41	to	to	PART
ejpam-6535	128	42	be	be	AUX
ejpam-6535	128	43	a	a	DET
ejpam-6535	128	44	probabilistic	probabilistic	ADJ
ejpam-6535	128	45	neighborhood	neighborhood	NOUN
ejpam-6535	128	46	system	system	NOUN
ejpam-6535	128	47	on	on	ADP
ejpam-6535	128	48	s	s	PRON
ejpam-6535	128	49	if	if	SCONJ
ejpam-6535	128	50	(	(	PUNCT
ejpam-6535	128	51	pns1	pns1	NOUN
ejpam-6535	128	52	)	)	PUNCT
ejpam-6535	128	53	∀	∀	PUNCT
ejpam-6535	129	1	p	p	NOUN
ejpam-6535	129	2	∈	∈	PROPN
ejpam-6535	129	3	s	s	NOUN
ejpam-6535	129	4	,	,	PUNCT
ejpam-6535	129	5	∀φ	∀φ	NOUN
ejpam-6535	129	6	∈	∈	PROPN
ejpam-6535	129	7	∆+	∆+	NOUN
ejpam-6535	129	8	,	,	PUNCT
ejpam-6535	129	9	nφ	nφ	ADP
ejpam-6535	129	10	p	p	NOUN
ejpam-6535	129	11	≤	≤	X
ejpam-6535	130	1	[	[	X
ejpam-6535	130	2	p	p	X
ejpam-6535	130	3	]	]	X
ejpam-6535	130	4	;	;	PUNCT
ejpam-6535	130	5	(	(	PUNCT
ejpam-6535	130	6	pns2	pns2	PROPN
ejpam-6535	130	7	)	)	PUNCT
ejpam-6535	130	8	∀	∀	PUNCT
ejpam-6535	130	9	φ	φ	X
ejpam-6535	130	10	,	,	PUNCT
ejpam-6535	130	11	ψ	ψ	X
ejpam-6535	130	12	∈	∈	PROPN
ejpam-6535	130	13	∆+	∆+	NUM
ejpam-6535	130	14	with	with	ADP
ejpam-6535	130	15	φ	φ	PROPN
ejpam-6535	130	16	≤	≤	NUM
ejpam-6535	130	17	ψ	ψ	NOUN
ejpam-6535	130	18	,	,	PUNCT
ejpam-6535	130	19	we	we	PRON
ejpam-6535	130	20	have	have	VERB
ejpam-6535	130	21	nφ	nφ	ADP
ejpam-6535	130	22	p	p	NOUN
ejpam-6535	130	23	≤	≤	NUM
ejpam-6535	131	1	nψ	nψ	NOUN
ejpam-6535	132	1	p	p	X
ejpam-6535	132	2	;	;	PUNCT
ejpam-6535	132	3	(	(	PUNCT
ejpam-6535	132	4	pns3	pns3	PROPN
ejpam-6535	132	5	)	)	PUNCT
ejpam-6535	132	6	nϵ∞	nϵ∞	PROPN
ejpam-6535	133	1	p	p	NOUN
ejpam-6535	133	2	=	=	X
ejpam-6535	134	1	[	[	X
ejpam-6535	134	2	s	s	X
ejpam-6535	134	3	]	]	X
ejpam-6535	134	4	,	,	PUNCT
ejpam-6535	134	5	∀p	∀p	X
ejpam-6535	134	6	∈	∈	PROPN
ejpam-6535	134	7	s.	s.	PROPN
ejpam-6535	134	8	then	then	ADV
ejpam-6535	134	9	the	the	DET
ejpam-6535	134	10	pair	pair	NOUN
ejpam-6535	134	11	(	(	PUNCT
ejpam-6535	134	12	s	s	NOUN
ejpam-6535	134	13	,	,	PUNCT
ejpam-6535	134	14	n	n	NOUN
ejpam-6535	134	15	=	=	SYM
ejpam-6535	134	16	(	(	PUNCT
ejpam-6535	134	17	nφ	nφ	PROPN
ejpam-6535	134	18	p	p	NOUN
ejpam-6535	134	19	)	)	PUNCT
ejpam-6535	134	20	(	(	PUNCT
ejpam-6535	134	21	p	p	X
ejpam-6535	134	22	,	,	PUNCT
ejpam-6535	134	23	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	134	24	)	)	PUNCT
ejpam-6535	134	25	is	be	AUX
ejpam-6535	134	26	called	call	VERB
ejpam-6535	134	27	a	a	DET
ejpam-6535	134	28	probabilistic	probabilistic	ADJ
ejpam-6535	134	29	neighborhood	neighborhood	NOUN
ejpam-6535	134	30	space	space	NOUN
ejpam-6535	134	31	.	.	PUNCT
ejpam-6535	135	1	we	we	PRON
ejpam-6535	135	2	call	call	VERB
ejpam-6535	135	3	nφ	nφ	INTJ
ejpam-6535	135	4	p	p	PRON
ejpam-6535	135	5	a	a	DET
ejpam-6535	135	6	φ	φ	NUM
ejpam-6535	135	7	-	-	PUNCT
ejpam-6535	135	8	neighborhood	neighborhood	NOUN
ejpam-6535	135	9	filter	filter	NOUN
ejpam-6535	135	10	in	in	ADP
ejpam-6535	135	11	p	p	NOUN
ejpam-6535	135	12	while	while	SCONJ
ejpam-6535	135	13	the	the	DET
ejpam-6535	135	14	elements	element	NOUN
ejpam-6535	135	15	of	of	ADP
ejpam-6535	135	16	nφ	nφ	NOUN
ejpam-6535	135	17	p	p	NOUN
ejpam-6535	135	18	are	be	AUX
ejpam-6535	135	19	called	call	VERB
ejpam-6535	135	20	a	a	DET
ejpam-6535	135	21	φneighborhood	φneighborhood	NOUN
ejpam-6535	135	22	of	of	ADP
ejpam-6535	135	23	p.	p.	NOUN
ejpam-6535	135	24	a	a	DET
ejpam-6535	135	25	mapping	mapping	NOUN
ejpam-6535	135	26	f	f	NOUN
ejpam-6535	135	27	:	:	PUNCT
ejpam-6535	135	28	(	(	PUNCT
ejpam-6535	135	29	s	s	X
ejpam-6535	135	30	,	,	PUNCT
ejpam-6535	135	31	n	n	CCONJ
ejpam-6535	135	32	)	)	PUNCT
ejpam-6535	135	33	−→	−→	NOUN
ejpam-6535	135	34	(	(	PUNCT
ejpam-6535	135	35	t	t	PROPN
ejpam-6535	135	36	,	,	PUNCT
ejpam-6535	135	37	m	m	PROPN
ejpam-6535	135	38	)	)	PUNCT
ejpam-6535	135	39	between	between	ADP
ejpam-6535	135	40	probabilistic	probabilistic	ADJ
ejpam-6535	135	41	neighborhood	neighborhood	NOUN
ejpam-6535	135	42	spaces	space	NOUN
ejpam-6535	135	43	(	(	PUNCT
ejpam-6535	135	44	s	s	NOUN
ejpam-6535	135	45	,	,	PUNCT
ejpam-6535	135	46	n	n	CCONJ
ejpam-6535	135	47	)	)	PUNCT
ejpam-6535	135	48	and	and	CCONJ
ejpam-6535	135	49	(	(	PUNCT
ejpam-6535	135	50	t	t	PROPN
ejpam-6535	135	51	,	,	PUNCT
ejpam-6535	135	52	m	m	PROPN
ejpam-6535	135	53	)	)	PUNCT
ejpam-6535	135	54	is	be	AUX
ejpam-6535	135	55	called	call	VERB
ejpam-6535	135	56	continuous	continuous	ADJ
ejpam-6535	135	57	if	if	SCONJ
ejpam-6535	135	58	mφ	mφ	PROPN
ejpam-6535	135	59	f(p	f(p	NOUN
ejpam-6535	135	60	)	)	PUNCT
ejpam-6535	136	1	≤	≤	NUM
ejpam-6535	136	2	f	f	X
ejpam-6535	136	3	(	(	PUNCT
ejpam-6535	136	4	nφ	nφ	PROPN
ejpam-6535	136	5	p	p	NOUN
ejpam-6535	136	6	)	)	PUNCT
ejpam-6535	136	7	.	.	PUNCT
ejpam-6535	137	1	the	the	DET
ejpam-6535	137	2	category	category	NOUN
ejpam-6535	137	3	of	of	ADP
ejpam-6535	137	4	probabilistic	probabilistic	ADJ
ejpam-6535	137	5	neighborhood	neighborhood	NOUN
ejpam-6535	137	6	spaces	space	NOUN
ejpam-6535	137	7	as	as	ADP
ejpam-6535	137	8	objects	object	NOUN
ejpam-6535	137	9	and	and	CCONJ
ejpam-6535	137	10	morphisms	morphism	NOUN
ejpam-6535	137	11	are	be	AUX
ejpam-6535	137	12	all	all	PRON
ejpam-6535	137	13	continuous	continuous	ADJ
ejpam-6535	137	14	mappings	mapping	NOUN
ejpam-6535	137	15	as	as	SCONJ
ejpam-6535	137	16	morphisms	morphism	NOUN
ejpam-6535	137	17	is	be	AUX
ejpam-6535	137	18	denoted	denote	VERB
ejpam-6535	137	19	by	by	ADP
ejpam-6535	137	20	pneigh	pneigh	NOUN
ejpam-6535	137	21	.	.	PUNCT
ejpam-6535	138	1	remark	remark	PROPN
ejpam-6535	138	2	3	3	NUM
ejpam-6535	138	3	.	.	PUNCT
ejpam-6535	139	1	a	a	DET
ejpam-6535	139	2	probabilistic	probabilistic	ADJ
ejpam-6535	139	3	neighborhood	neighborhood	NOUN
ejpam-6535	139	4	space	space	NOUN
ejpam-6535	139	5	(	(	PUNCT
ejpam-6535	139	6	s	s	X
ejpam-6535	139	7	,	,	PUNCT
ejpam-6535	139	8	n	n	NOUN
ejpam-6535	139	9	=	=	SYM
ejpam-6535	139	10	(	(	PUNCT
ejpam-6535	139	11	nφ	nφ	PROPN
ejpam-6535	139	12	p	p	NOUN
ejpam-6535	139	13	)	)	PUNCT
ejpam-6535	139	14	(	(	PUNCT
ejpam-6535	139	15	p	p	X
ejpam-6535	139	16	,	,	PUNCT
ejpam-6535	139	17	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	139	18	)	)	PUNCT
ejpam-6535	139	19	is	be	AUX
ejpam-6535	139	20	said	say	VERB
ejpam-6535	139	21	to	to	PART
ejpam-6535	139	22	be	be	AUX
ejpam-6535	139	23	a	a	DET
ejpam-6535	139	24	probabilistic	probabilistic	ADJ
ejpam-6535	139	25	topological	topological	ADJ
ejpam-6535	139	26	neighborhood	neighborhood	NOUN
ejpam-6535	139	27	space	space	NOUN
ejpam-6535	139	28	or	or	CCONJ
ejpam-6535	139	29	a	a	DET
ejpam-6535	139	30	probabilistic	probabilistic	ADJ
ejpam-6535	139	31	topological	topological	ADJ
ejpam-6535	139	32	space	space	NOUN
ejpam-6535	139	33	under	under	ADP
ejpam-6535	139	34	a	a	DET
ejpam-6535	139	35	continuous	continuous	ADJ
ejpam-6535	139	36	triangle	triangle	NOUN
ejpam-6535	139	37	function	function	NOUN
ejpam-6535	139	38	τ	τ	PROPN
ejpam-6535	139	39	if	if	SCONJ
ejpam-6535	139	40	(	(	PUNCT
ejpam-6535	139	41	plcc	plcc	NOUN
ejpam-6535	139	42	)	)	PUNCT
ejpam-6535	139	43	for	for	ADP
ejpam-6535	139	44	all	all	DET
ejpam-6535	139	45	∅	∅	NOUN
ejpam-6535	139	46	=	=	NOUN
ejpam-6535	139	47	̸m	̸m	NOUN
ejpam-6535	139	48	⊂	⊂	ADJ
ejpam-6535	139	49	∆+	∆+	NOUN
ejpam-6535	139	50	,	,	PUNCT
ejpam-6535	139	51	∨	∨	NUM
ejpam-6535	139	52	φ∈m	φ∈m	NUM
ejpam-6535	139	53	nφ	nφ	ADP
ejpam-6535	139	54	p	p	NOUN
ejpam-6535	139	55	=	=	PUNCT
ejpam-6535	139	56	n	n	PRON
ejpam-6535	139	57	∨	∨	NUM
ejpam-6535	139	58	m	m	PROPN
ejpam-6535	139	59	p	p	NOUN
ejpam-6535	139	60	;	;	PUNCT
ejpam-6535	139	61	(	(	PUNCT
ejpam-6535	139	62	τ	τ	X
ejpam-6535	139	63	-pk	-pk	ADJ
ejpam-6535	139	64	)	)	PUNCT
ejpam-6535	139	65	for	for	ADP
ejpam-6535	139	66	all	all	DET
ejpam-6535	139	67	p	p	NOUN
ejpam-6535	139	68	,	,	PUNCT
ejpam-6535	139	69	q	q	PROPN
ejpam-6535	139	70	∈	∈	PROPN
ejpam-6535	139	71	s	s	X
ejpam-6535	139	72	and	and	CCONJ
ejpam-6535	139	73	for	for	ADP
ejpam-6535	139	74	all	all	DET
ejpam-6535	139	75	φ	φ	NOUN
ejpam-6535	139	76	,	,	PUNCT
ejpam-6535	139	77	ψ	ψ	X
ejpam-6535	139	78	∈	∈	NOUN
ejpam-6535	139	79	∆+	∆+	NOUN
ejpam-6535	139	80	:	:	PUNCT
ejpam-6535	139	81	n	n	X
ejpam-6535	139	82	τ(φ	τ(φ	X
ejpam-6535	139	83	,	,	PUNCT
ejpam-6535	139	84	ψ	ψ	NOUN
ejpam-6535	139	85	)	)	PUNCT
ejpam-6535	139	86	p	p	NOUN
ejpam-6535	139	87	≤	≤	NUM
ejpam-6535	139	88	κ	κ	NOUN
ejpam-6535	139	89	(	(	PUNCT
ejpam-6535	139	90	nψ	nψ	INTJ
ejpam-6535	139	91	p	p	X
ejpam-6535	139	92	,	,	PUNCT
ejpam-6535	139	93	(	(	PUNCT
ejpam-6535	139	94	n	n	PROPN
ejpam-6535	139	95	φ	φ	NUM
ejpam-6535	139	96	q	q	PROPN
ejpam-6535	139	97	)	)	PUNCT
ejpam-6535	139	98	q∈s	q∈s	NOUN
ejpam-6535	139	99	)	)	PUNCT
ejpam-6535	139	100	.	.	PUNCT
ejpam-6535	140	1	the	the	DET
ejpam-6535	140	2	category	category	NOUN
ejpam-6535	140	3	of	of	ADP
ejpam-6535	140	4	probabilistic	probabilistic	ADJ
ejpam-6535	140	5	topological	topological	ADJ
ejpam-6535	140	6	neighborhood	neighborhood	NOUN
ejpam-6535	140	7	spaces	space	NOUN
ejpam-6535	140	8	under	under	ADP
ejpam-6535	140	9	continuous	continuous	ADJ
ejpam-6535	140	10	function	function	NOUN
ejpam-6535	140	11	τ	τ	PROPN
ejpam-6535	140	12	as	as	ADP
ejpam-6535	140	13	objects	object	NOUN
ejpam-6535	140	14	and	and	CCONJ
ejpam-6535	140	15	continuous	continuous	ADJ
ejpam-6535	140	16	mapping	mapping	NOUN
ejpam-6535	140	17	between	between	ADP
ejpam-6535	140	18	them	they	PRON
ejpam-6535	140	19	as	as	SCONJ
ejpam-6535	140	20	morphisms	morphism	NOUN
ejpam-6535	140	21	is	be	AUX
ejpam-6535	140	22	denoted	denote	VERB
ejpam-6535	140	23	by	by	ADP
ejpam-6535	140	24	ptopneigh	ptopneigh	ADJ
ejpam-6535	140	25	.	.	PUNCT
ejpam-6535	141	1	lemma	lemma	PROPN
ejpam-6535	141	2	3	3	X
ejpam-6535	141	3	.	.	PUNCT
ejpam-6535	142	1	let	let	AUX
ejpam-6535	142	2	(	(	PUNCT
ejpam-6535	142	3	s	s	X
ejpam-6535	142	4	,	,	PUNCT
ejpam-6535	142	5	n	n	NOUN
ejpam-6535	142	6	=	=	SYM
ejpam-6535	142	7	(	(	PUNCT
ejpam-6535	142	8	nφ	nφ	PROPN
ejpam-6535	142	9	p	p	NOUN
ejpam-6535	142	10	)	)	PUNCT
ejpam-6535	142	11	(	(	PUNCT
ejpam-6535	142	12	p	p	X
ejpam-6535	142	13	,	,	PUNCT
ejpam-6535	142	14	φ)∈s×∆	φ)∈s×∆	PROPN
ejpam-6535	142	15	)	)	PUNCT
ejpam-6535	142	16	be	be	AUX
ejpam-6535	142	17	a	a	DET
ejpam-6535	142	18	probabilistic	probabilistic	ADJ
ejpam-6535	142	19	neighborhood	neighborhood	NOUN
ejpam-6535	142	20	space	space	NOUN
ejpam-6535	142	21	.	.	PUNCT
ejpam-6535	143	1	define	define	VERB
ejpam-6535	143	2	a	a	DET
ejpam-6535	143	3	probabilistic	probabilistic	ADJ
ejpam-6535	143	4	convergence	convergence	NOUN
ejpam-6535	143	5	structure	structure	NOUN
ejpam-6535	143	6	cn	cn	NOUN
ejpam-6535	143	7	on	on	ADP
ejpam-6535	143	8	s	s	PRON
ejpam-6535	143	9	by	by	ADP
ejpam-6535	143	10	:	:	PUNCT
ejpam-6535	143	11	p	p	NOUN
ejpam-6535	143	12	∈	∈	PROPN
ejpam-6535	143	13	cnφ	cnφ	NOUN
ejpam-6535	143	14	(	(	PUNCT
ejpam-6535	143	15	f	f	X
ejpam-6535	143	16	)	)	PUNCT
ejpam-6535	143	17	⇐	⇐	ADJ
ejpam-6535	143	18	⇒	⇒	PROPN
ejpam-6535	143	19	f	f	PROPN
ejpam-6535	143	20	≥	≥	NOUN
ejpam-6535	143	21	nφ	nφ	ADP
ejpam-6535	143	22	p	p	PROPN
ejpam-6535	143	23	,	,	PUNCT
ejpam-6535	143	24	for	for	ADP
ejpam-6535	143	25	any	any	DET
ejpam-6535	143	26	f	f	PROPN
ejpam-6535	143	27	∈	∈	PROPN
ejpam-6535	143	28	f(s	f(	NOUN
ejpam-6535	143	29	)	)	PUNCT
ejpam-6535	143	30	,	,	PUNCT
ejpam-6535	143	31	and	and	CCONJ
ejpam-6535	143	32	φ	φ	NUM
ejpam-6535	143	33	∈	∈	PROPN
ejpam-6535	143	34	∆+	∆+	NOUN
ejpam-6535	143	35	.	.	PUNCT
ejpam-6535	144	1	then	then	ADV
ejpam-6535	144	2	(	(	PUNCT
ejpam-6535	144	3	s	s	X
ejpam-6535	144	4	,	,	PUNCT
ejpam-6535	144	5	cr	cr	NOUN
ejpam-6535	144	6	)	)	PUNCT
ejpam-6535	144	7	is	be	AUX
ejpam-6535	144	8	a	a	DET
ejpam-6535	144	9	probabilistic	probabilistic	ADJ
ejpam-6535	144	10	convergence	convergence	NOUN
ejpam-6535	144	11	space	space	NOUN
ejpam-6535	144	12	.	.	PUNCT
ejpam-6535	145	1	proof	proof	NOUN
ejpam-6535	145	2	.	.	PUNCT
ejpam-6535	146	1	(	(	PUNCT
ejpam-6535	146	2	pc1	pc1	PROPN
ejpam-6535	146	3	)	)	PUNCT
ejpam-6535	146	4	since	since	SCONJ
ejpam-6535	146	5	by	by	ADP
ejpam-6535	146	6	(	(	PUNCT
ejpam-6535	146	7	pns1	pns1	NOUN
ejpam-6535	146	8	)	)	PUNCT
ejpam-6535	146	9	,	,	PUNCT
ejpam-6535	146	10	for	for	ADP
ejpam-6535	146	11	any	any	DET
ejpam-6535	146	12	p	p	NOUN
ejpam-6535	146	13	∈	∈	PROPN
ejpam-6535	146	14	s	s	PART
ejpam-6535	146	15	and	and	CCONJ
ejpam-6535	146	16	φ	φ	PROPN
ejpam-6535	146	17	∈	∈	PROPN
ejpam-6535	146	18	∆+	∆+	NOUN
ejpam-6535	146	19	,	,	PUNCT
ejpam-6535	146	20	nφ	nφ	ADP
ejpam-6535	146	21	p	p	NOUN
ejpam-6535	146	22	≤	≤	X
ejpam-6535	147	1	[	[	X
ejpam-6535	147	2	p	p	X
ejpam-6535	147	3	]	]	X
ejpam-6535	147	4	,	,	PUNCT
ejpam-6535	147	5	immediately	immediately	ADV
ejpam-6535	147	6	,	,	PUNCT
ejpam-6535	147	7	we	we	PRON
ejpam-6535	147	8	get	get	VERB
ejpam-6535	147	9	p	p	NOUN
ejpam-6535	147	10	∈	∈	NOUN
ejpam-6535	147	11	cnφ	cnφ	NOUN
ejpam-6535	147	12	(	(	PUNCT
ejpam-6535	147	13	[	[	X
ejpam-6535	147	14	p	p	X
ejpam-6535	147	15	]	]	X
ejpam-6535	147	16	)	)	PUNCT
ejpam-6535	147	17	.	.	PUNCT
ejpam-6535	148	1	(	(	PUNCT
ejpam-6535	148	2	pc2	pc2	NOUN
ejpam-6535	148	3	)	)	PUNCT
ejpam-6535	148	4	let	let	VERB
ejpam-6535	148	5	f	f	X
ejpam-6535	148	6	,	,	PUNCT
ejpam-6535	148	7	g	g	PROPN
ejpam-6535	148	8	∈	∈	PROPN
ejpam-6535	148	9	f(s	f(	VERB
ejpam-6535	148	10	)	)	PUNCT
ejpam-6535	148	11	with	with	ADP
ejpam-6535	148	12	f	f	PROPN
ejpam-6535	148	13	≤	≤	PROPN
ejpam-6535	148	14	g	g	PROPN
ejpam-6535	148	15	,	,	PUNCT
ejpam-6535	148	16	and	and	CCONJ
ejpam-6535	148	17	p	p	NOUN
ejpam-6535	148	18	∈	∈	PROPN
ejpam-6535	148	19	cnφ	cnφ	NOUN
ejpam-6535	148	20	(	(	PUNCT
ejpam-6535	148	21	f	f	NOUN
ejpam-6535	148	22	)	)	PUNCT
ejpam-6535	148	23	.	.	PUNCT
ejpam-6535	149	1	then	then	ADV
ejpam-6535	149	2	f	f	PROPN
ejpam-6535	149	3	≥	≥	NOUN
ejpam-6535	149	4	nφ	nφ	ADP
ejpam-6535	149	5	p	p	PROPN
ejpam-6535	149	6	.	.	PUNCT
ejpam-6535	150	1	but	but	CCONJ
ejpam-6535	150	2	then	then	ADV
ejpam-6535	150	3	g	g	PROPN
ejpam-6535	150	4	≥	≥	PRON
ejpam-6535	150	5	nφ	nφ	ADP
ejpam-6535	150	6	p	p	NOUN
ejpam-6535	150	7	implying	imply	VERB
ejpam-6535	150	8	p	p	NOUN
ejpam-6535	150	9	∈	∈	PROPN
ejpam-6535	150	10	cnφ	cnφ	NOUN
ejpam-6535	150	11	(	(	PUNCT
ejpam-6535	150	12	g	g	NOUN
ejpam-6535	150	13	)	)	PUNCT
ejpam-6535	150	14	.	.	PUNCT
ejpam-6535	151	1	(	(	PUNCT
ejpam-6535	151	2	pc3	pc3	PROPN
ejpam-6535	151	3	)	)	PUNCT
ejpam-6535	151	4	let	let	VERB
ejpam-6535	151	5	φ	φ	NUM
ejpam-6535	151	6	,	,	PUNCT
ejpam-6535	151	7	ψ	ψ	X
ejpam-6535	151	8	∈	∈	PROPN
ejpam-6535	151	9	∆+	∆+	NUM
ejpam-6535	151	10	with	with	ADP
ejpam-6535	151	11	φ	φ	PROPN
ejpam-6535	151	12	≤	≤	NOUN
ejpam-6535	151	13	ψ	ψ	NOUN
ejpam-6535	151	14	and	and	CCONJ
ejpam-6535	151	15	let	let	VERB
ejpam-6535	151	16	f	f	PROPN
ejpam-6535	151	17	∈	∈	PROPN
ejpam-6535	151	18	f(s	f(	NOUN
ejpam-6535	151	19	)	)	PUNCT
ejpam-6535	151	20	.	.	PUNCT
ejpam-6535	152	1	if	if	SCONJ
ejpam-6535	152	2	p	p	PROPN
ejpam-6535	152	3	∈	∈	PROPN
ejpam-6535	152	4	cnψ	cnψ	NOUN
ejpam-6535	152	5	(	(	PUNCT
ejpam-6535	152	6	f	f	X
ejpam-6535	152	7	)	)	PUNCT
ejpam-6535	152	8	,	,	PUNCT
ejpam-6535	152	9	then	then	ADV
ejpam-6535	152	10	f	f	PROPN
ejpam-6535	152	11	≥	≥	X
ejpam-6535	152	12	nψ	nψ	INTJ
ejpam-6535	152	13	p	p	X
ejpam-6535	152	14	≥	≥	NOUN
ejpam-6535	152	15	nφ	nφ	ADP
ejpam-6535	152	16	p	p	NOUN
ejpam-6535	152	17	implying	imply	VERB
ejpam-6535	152	18	f	f	PROPN
ejpam-6535	152	19	≥	≥	NOUN
ejpam-6535	152	20	nφ	nφ	ADP
ejpam-6535	152	21	p	p	NOUN
ejpam-6535	152	22	which	which	PRON
ejpam-6535	152	23	yields	yield	VERB
ejpam-6535	152	24	that	that	SCONJ
ejpam-6535	152	25	p	p	PROPN
ejpam-6535	152	26	∈	∈	PROPN
ejpam-6535	152	27	cnφ	cnφ	NOUN
ejpam-6535	152	28	(	(	PUNCT
ejpam-6535	152	29	f	f	NOUN
ejpam-6535	152	30	)	)	PUNCT
ejpam-6535	152	31	.	.	PUNCT
ejpam-6535	153	1	finally	finally	ADV
ejpam-6535	153	2	,	,	PUNCT
ejpam-6535	153	3	to	to	PART
ejpam-6535	153	4	check	check	VERB
ejpam-6535	153	5	(	(	PUNCT
ejpam-6535	153	6	pc4	pc4	PROPN
ejpam-6535	153	7	)	)	PUNCT
ejpam-6535	153	8	,	,	PUNCT
ejpam-6535	153	9	let	let	VERB
ejpam-6535	153	10	f	f	PROPN
ejpam-6535	153	11	∈	∈	PROPN
ejpam-6535	153	12	f(s	f(	VERB
ejpam-6535	153	13	)	)	PUNCT
ejpam-6535	153	14	and	and	CCONJ
ejpam-6535	153	15	p	p	PROPN
ejpam-6535	153	16	∈	∈	PROPN
ejpam-6535	153	17	s.	s.	PROPN
ejpam-6535	154	1	then	then	ADV
ejpam-6535	154	2	nϵ∞	nϵ∞	PROPN
ejpam-6535	155	1	p	p	NOUN
ejpam-6535	156	1	=	=	PUNCT
ejpam-6535	157	1	[	[	X
ejpam-6535	157	2	{	{	PUNCT
ejpam-6535	157	3	s	s	NOUN
ejpam-6535	157	4	}	}	PUNCT
ejpam-6535	157	5	]	]	PUNCT
ejpam-6535	157	6	≤	≤	PROPN
ejpam-6535	157	7	f	f	X
ejpam-6535	157	8	,	,	PUNCT
ejpam-6535	157	9	i.e.	i.e.	X
ejpam-6535	157	10	,	,	PUNCT
ejpam-6535	157	11	nϵ∞	nϵ∞	PROPN
ejpam-6535	158	1	p	p	NOUN
ejpam-6535	158	2	≤	≤	PROPN
ejpam-6535	158	3	f	f	X
ejpam-6535	158	4	which	which	PRON
ejpam-6535	158	5	in	in	ADP
ejpam-6535	158	6	turn	turn	NOUN
ejpam-6535	158	7	yields	yield	NOUN
ejpam-6535	158	8	that	that	SCONJ
ejpam-6535	158	9	p	p	PROPN
ejpam-6535	158	10	∈	∈	PROPN
ejpam-6535	158	11	cnϵ∞(f	cnϵ∞(f	PROPN
ejpam-6535	158	12	)	)	PUNCT
ejpam-6535	158	13	.	.	PUNCT
ejpam-6535	159	1	remark	remark	PROPN
ejpam-6535	159	2	4	4	NUM
ejpam-6535	159	3	.	.	PUNCT
ejpam-6535	160	1	under	under	ADP
ejpam-6535	160	2	the	the	DET
ejpam-6535	160	3	definition	definition	NOUN
ejpam-6535	160	4	given	give	VERB
ejpam-6535	160	5	in	in	ADP
ejpam-6535	160	6	the	the	DET
ejpam-6535	160	7	preceding	precede	VERB
ejpam-6535	160	8	lemma	lemma	PROPN
ejpam-6535	160	9	3	3	NUM
ejpam-6535	160	10	,	,	PUNCT
ejpam-6535	160	11	essentially	essentially	ADV
ejpam-6535	160	12	,	,	PUNCT
ejpam-6535	160	13	this	this	DET
ejpam-6535	160	14	probabilistic	probabilistic	ADJ
ejpam-6535	160	15	convergence	convergence	NOUN
ejpam-6535	160	16	space	space	NOUN
ejpam-6535	160	17	is	be	AUX
ejpam-6535	160	18	a	a	DET
ejpam-6535	160	19	pretopological	pretopological	ADJ
ejpam-6535	160	20	space	space	NOUN
ejpam-6535	160	21	.	.	PUNCT
ejpam-6535	161	1	in	in	ADP
ejpam-6535	161	2	fact	fact	NOUN
ejpam-6535	161	3	,	,	PUNCT
ejpam-6535	161	4	in	in	ADP
ejpam-6535	161	5	view	view	NOUN
ejpam-6535	161	6	of	of	ADP
ejpam-6535	161	7	the	the	DET
ejpam-6535	161	8	lemma	lemma	PROPN
ejpam-6535	161	9	4.2	4.2	NUM
ejpam-6535	161	10	[	[	X
ejpam-6535	161	11	22	22	NUM
ejpam-6535	161	12	]	]	PUNCT
ejpam-6535	161	13	,	,	PUNCT
ejpam-6535	161	14	if	if	SCONJ
ejpam-6535	161	15	we	we	PRON
ejpam-6535	161	16	take	take	VERB
ejpam-6535	161	17	for	for	ADP
ejpam-6535	161	18	any	any	DET
ejpam-6535	161	19	φ	φ	PROPN
ejpam-6535	161	20	∈	∈	PROPN
ejpam-6535	161	21	∆+	∆+	NOUN
ejpam-6535	161	22	and	and	CCONJ
ejpam-6535	161	23	a	a	DET
ejpam-6535	161	24	family	family	NOUN
ejpam-6535	161	25	of	of	ADP
ejpam-6535	161	26	filters	filter	NOUN
ejpam-6535	161	27	(	(	PUNCT
ejpam-6535	161	28	fj)j∈j	fj)j∈j	NUM
ejpam-6535	161	29	,	,	PUNCT
ejpam-6535	161	30	p	p	PROPN
ejpam-6535	161	31	∈	∈	PROPN
ejpam-6535	161	32	⋂	⋂	PROPN
ejpam-6535	161	33	j∈j	j∈j	PROPN
ejpam-6535	161	34	cφ(fj	cφ(fj	PROPN
ejpam-6535	161	35	)	)	PUNCT
ejpam-6535	161	36	,	,	PUNCT
ejpam-6535	161	37	then	then	ADV
ejpam-6535	161	38	for	for	ADP
ejpam-6535	161	39	all	all	DET
ejpam-6535	161	40	j	j	PROPN
ejpam-6535	161	41	∈	∈	PROPN
ejpam-6535	161	42	j	j	PROPN
ejpam-6535	161	43	,	,	PUNCT
ejpam-6535	161	44	p	p	PROPN
ejpam-6535	161	45	∈	∈	PROPN
ejpam-6535	161	46	cφ(fj	cφ(fj	NOUN
ejpam-6535	161	47	)	)	PUNCT
ejpam-6535	161	48	which	which	PRON
ejpam-6535	161	49	is	be	AUX
ejpam-6535	161	50	equivalent	equivalent	ADJ
ejpam-6535	161	51	to	to	ADP
ejpam-6535	161	52	saying	say	VERB
ejpam-6535	161	53	fj	fj	PRON
ejpam-6535	161	54	≥	≥	NOUN
ejpam-6535	161	55	nφ	nφ	ADP
ejpam-6535	161	56	p	p	PROPN
ejpam-6535	161	57	,	,	PUNCT
ejpam-6535	161	58	this	this	PRON
ejpam-6535	161	59	is	be	AUX
ejpam-6535	161	60	true	true	ADJ
ejpam-6535	161	61	for	for	ADP
ejpam-6535	161	62	all	all	DET
ejpam-6535	161	63	j	j	PROPN
ejpam-6535	161	64	∈	∈	PROPN
ejpam-6535	161	65	j	j	PROPN
ejpam-6535	161	66	,	,	PUNCT
ejpam-6535	161	67	that	that	ADV
ejpam-6535	161	68	is	is	ADV
ejpam-6535	161	69	,	,	PUNCT
ejpam-6535	161	70	∧	∧	PROPN
ejpam-6535	161	71	j∈j	j∈j	NOUN
ejpam-6535	161	72	fj	fj	PROPN
ejpam-6535	161	73	≥	≥	NOUN
ejpam-6535	161	74	nφ	nφ	ADP
ejpam-6535	161	75	p	p	NOUN
ejpam-6535	161	76	which	which	PRON
ejpam-6535	161	77	is	be	AUX
ejpam-6535	161	78	again	again	ADV
ejpam-6535	161	79	equivalent	equivalent	ADJ
ejpam-6535	161	80	to	to	ADP
ejpam-6535	161	81	:	:	PUNCT
ejpam-6535	161	82	p	p	PROPN
ejpam-6535	161	83	∈	∈	PROPN
ejpam-6535	161	84	cφ	cφ	X
ejpam-6535	162	1	(	(	PUNCT
ejpam-6535	162	2	∧	∧	PROPN
ejpam-6535	162	3	j∈j	j∈j	PROPN
ejpam-6535	162	4	fj	fj	PROPN
ejpam-6535	162	5	)	)	PUNCT
ejpam-6535	162	6	)	)	PUNCT
ejpam-6535	162	7	.	.	PUNCT
ejpam-6535	163	1	hence⋂	hence⋂	X
ejpam-6535	163	2	j∈j	j∈j	PROPN
ejpam-6535	163	3	cφ(fj	cφ(fj	PROPN
ejpam-6535	163	4	)	)	PUNCT
ejpam-6535	164	1	⊆	⊆	NUM
ejpam-6535	164	2	cφ	cφ	NOUN
ejpam-6535	164	3	(	(	PUNCT
ejpam-6535	164	4	∧	∧	PROPN
ejpam-6535	164	5	j∈j	j∈j	PROPN
ejpam-6535	164	6	fj	fj	PROPN
ejpam-6535	164	7	)	)	PUNCT
ejpam-6535	164	8	)	)	PUNCT
ejpam-6535	164	9	which	which	PRON
ejpam-6535	164	10	is	be	AUX
ejpam-6535	164	11	precisely	precisely	ADV
ejpam-6535	164	12	the	the	DET
ejpam-6535	164	13	lemma	lemma	PROPN
ejpam-6535	164	14	4.2	4.2	NUM
ejpam-6535	165	1	[	[	X
ejpam-6535	165	2	22	22	NUM
ejpam-6535	165	3	]	]	PUNCT
ejpam-6535	165	4	.	.	PUNCT
ejpam-6535	166	1	lemma	lemma	PROPN
ejpam-6535	166	2	4	4	X
ejpam-6535	166	3	.	.	PUNCT
ejpam-6535	167	1	let	let	VERB
ejpam-6535	167	2	(	(	PUNCT
ejpam-6535	167	3	s	s	X
ejpam-6535	167	4	,	,	PUNCT
ejpam-6535	167	5	c	c	NOUN
ejpam-6535	167	6	=	=	SYM
ejpam-6535	167	7	(	(	PUNCT
ejpam-6535	167	8	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	167	9	)	)	PUNCT
ejpam-6535	167	10	be	be	AUX
ejpam-6535	167	11	a	a	DET
ejpam-6535	167	12	probabilistic	probabilistic	ADJ
ejpam-6535	167	13	pretopological	pretopological	ADJ
ejpam-6535	167	14	space	space	NOUN
ejpam-6535	167	15	.	.	PUNCT
ejpam-6535	168	1	then	then	ADV
ejpam-6535	168	2	(	(	PUNCT
ejpam-6535	168	3	s	s	PROPN
ejpam-6535	168	4	,	,	PUNCT
ejpam-6535	168	5	nc	nc	PROPN
ejpam-6535	168	6	,	,	PUNCT
ejpam-6535	168	7	φ	φ	PROPN
ejpam-6535	168	8	=	=	SYM
ejpam-6535	168	9	(	(	PUNCT
ejpam-6535	168	10	nc	nc	PROPN
ejpam-6535	168	11	,	,	PUNCT
ejpam-6535	168	12	φ	φ	PROPN
ejpam-6535	168	13	p	p	NOUN
ejpam-6535	168	14	)	)	PUNCT
ejpam-6535	168	15	(	(	PUNCT
ejpam-6535	168	16	p	p	X
ejpam-6535	168	17	,	,	PUNCT
ejpam-6535	168	18	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	168	19	)	)	PUNCT
ejpam-6535	168	20	is	be	AUX
ejpam-6535	168	21	a	a	DET
ejpam-6535	168	22	probabilistic	probabilistic	ADJ
ejpam-6535	168	23	neighborhood	neighborhood	NOUN
ejpam-6535	168	24	space	space	NOUN
ejpam-6535	168	25	.	.	PUNCT
ejpam-6535	169	1	proof	proof	NOUN
ejpam-6535	169	2	.	.	PUNCT
ejpam-6535	170	1	for	for	ADP
ejpam-6535	170	2	φ	φ	PROPN
ejpam-6535	170	3	∈	∈	PROPN
ejpam-6535	170	4	∆+	∆+	NOUN
ejpam-6535	170	5	and	and	CCONJ
ejpam-6535	170	6	p	p	PRON
ejpam-6535	170	7	∈	∈	PROPN
ejpam-6535	170	8	s	s	X
ejpam-6535	170	9	,	,	PUNCT
ejpam-6535	170	10	we	we	PRON
ejpam-6535	170	11	define	define	VERB
ejpam-6535	170	12	φ	φ	NUM
ejpam-6535	170	13	-	-	PUNCT
ejpam-6535	170	14	neighborhood	neighborhood	NOUN
ejpam-6535	170	15	filter	filter	NOUN
ejpam-6535	170	16	of	of	ADP
ejpam-6535	170	17	p	p	NOUN
ejpam-6535	170	18	bync	bync	NOUN
ejpam-6535	170	19	,	,	PUNCT
ejpam-6535	170	20	φ	φ	NOUN
ejpam-6535	170	21	p	p	NOUN
ejpam-6535	170	22	=	=	PUNCT
ejpam-6535	170	23	∧	∧	PROPN
ejpam-6535	170	24	p∈cφ(f	p∈cφ(f	PROPN
ejpam-6535	170	25	)	)	PUNCT
ejpam-6535	170	26	f.	f.	PROPN
ejpam-6535	171	1	then	then	ADV
ejpam-6535	171	2	the	the	DET
ejpam-6535	171	3	result	result	NOUN
ejpam-6535	171	4	follows	follow	VERB
ejpam-6535	171	5	from	from	ADP
ejpam-6535	171	6	the	the	DET
ejpam-6535	171	7	definition	definition	NOUN
ejpam-6535	171	8	.	.	PUNCT
ejpam-6535	172	1	lemma	lemma	PROPN
ejpam-6535	172	2	5	5	X
ejpam-6535	172	3	.	.	PUNCT
ejpam-6535	173	1	let	let	VERB
ejpam-6535	173	2	(	(	PUNCT
ejpam-6535	173	3	s	s	NOUN
ejpam-6535	173	4	,	,	PUNCT
ejpam-6535	173	5	n	n	CCONJ
ejpam-6535	173	6	)	)	PUNCT
ejpam-6535	173	7	and	and	CCONJ
ejpam-6535	173	8	(	(	PUNCT
ejpam-6535	173	9	t	t	PROPN
ejpam-6535	173	10	,	,	PUNCT
ejpam-6535	173	11	m	m	PRON
ejpam-6535	173	12	)	)	PUNCT
ejpam-6535	173	13	be	be	AUX
ejpam-6535	173	14	probabilistic	probabilistic	ADJ
ejpam-6535	173	15	neighborhood	neighborhood	NOUN
ejpam-6535	173	16	spaces	space	NOUN
ejpam-6535	173	17	and	and	CCONJ
ejpam-6535	173	18	f	f	X
ejpam-6535	173	19	:	:	PUNCT
ejpam-6535	173	20	s	s	AUX
ejpam-6535	173	21	−→	−→	NOUN
ejpam-6535	173	22	t	t	NOUN
ejpam-6535	173	23	be	be	AUX
ejpam-6535	173	24	a	a	DET
ejpam-6535	173	25	mapping	mapping	NOUN
ejpam-6535	173	26	.	.	PUNCT
ejpam-6535	174	1	then	then	ADV
ejpam-6535	174	2	the	the	DET
ejpam-6535	174	3	following	follow	VERB
ejpam-6535	174	4	are	be	AUX
ejpam-6535	174	5	equivalent	equivalent	ADJ
ejpam-6535	174	6	:	:	PUNCT
ejpam-6535	174	7	(	(	PUNCT
ejpam-6535	174	8	1	1	X
ejpam-6535	174	9	)	)	PUNCT
ejpam-6535	174	10	∀p	∀p	NOUN
ejpam-6535	174	11	∈	∈	PROPN
ejpam-6535	174	12	s	s	NOUN
ejpam-6535	174	13	,	,	PUNCT
ejpam-6535	174	14	∀φ	∀φ	NOUN
ejpam-6535	174	15	∈	∈	PROPN
ejpam-6535	174	16	∆+	∆+	NOUN
ejpam-6535	174	17	,	,	PUNCT
ejpam-6535	174	18	mφ	mφ	PRON
ejpam-6535	174	19	f(p	f(p	NOUN
ejpam-6535	174	20	)	)	PUNCT
ejpam-6535	175	1	≤	≤	NUM
ejpam-6535	175	2	f	f	X
ejpam-6535	175	3	(	(	PUNCT
ejpam-6535	175	4	nφ	nφ	PROPN
ejpam-6535	175	5	p	p	NOUN
ejpam-6535	175	6	)	)	PUNCT
ejpam-6535	175	7	;	;	PUNCT
ejpam-6535	175	8	(	(	PUNCT
ejpam-6535	175	9	2	2	X
ejpam-6535	175	10	)	)	PUNCT
ejpam-6535	175	11	∀p	∀p	NOUN
ejpam-6535	175	12	∈	∈	PROPN
ejpam-6535	175	13	s	s	NOUN
ejpam-6535	175	14	,	,	PUNCT
ejpam-6535	175	15	∀φ	∀φ	NOUN
ejpam-6535	175	16	∈	∈	PROPN
ejpam-6535	175	17	∆+	∆+	NOUN
ejpam-6535	175	18	,	,	PUNCT
ejpam-6535	175	19	∀u	∀u	NOUN
ejpam-6535	175	20	∈	∈	NOUN
ejpam-6535	175	21	mφ	mφ	ADP
ejpam-6535	175	22	f(p	f(p	NOUN
ejpam-6535	175	23	)	)	PUNCT
ejpam-6535	175	24	there	there	PRON
ejpam-6535	175	25	exists	exist	VERB
ejpam-6535	175	26	a	a	DET
ejpam-6535	175	27	v	v	NOUN
ejpam-6535	175	28	∈	∈	NOUN
ejpam-6535	175	29	nφ	nφ	ADP
ejpam-6535	175	30	p	p	NOUN
ejpam-6535	175	31	such	such	ADJ
ejpam-6535	175	32	that	that	SCONJ
ejpam-6535	175	33	f(v	f(v	PROPN
ejpam-6535	175	34	)	)	PUNCT
ejpam-6535	175	35	≤	≤	NUM
ejpam-6535	175	36	u	u	NOUN
ejpam-6535	175	37	;	;	PUNCT
ejpam-6535	175	38	(	(	PUNCT
ejpam-6535	175	39	3	3	X
ejpam-6535	175	40	)	)	PUNCT
ejpam-6535	175	41	∀p	∀p	NOUN
ejpam-6535	175	42	∈	∈	PROPN
ejpam-6535	175	43	s	s	NOUN
ejpam-6535	175	44	,	,	PUNCT
ejpam-6535	175	45	∀φ	∀φ	NOUN
ejpam-6535	175	46	∈	∈	PROPN
ejpam-6535	175	47	∆+	∆+	NOUN
ejpam-6535	175	48	,	,	PUNCT
ejpam-6535	175	49	∀f	∀f	PROPN
ejpam-6535	175	50	∈	∈	PROPN
ejpam-6535	175	51	f(s	f(	NOUN
ejpam-6535	175	52	)	)	PUNCT
ejpam-6535	175	53	,	,	PUNCT
ejpam-6535	175	54	p	p	PROPN
ejpam-6535	175	55	∈	∈	PROPN
ejpam-6535	175	56	cφ(f	cφ(f	PUNCT
ejpam-6535	175	57	)	)	PUNCT
ejpam-6535	175	58	implies	imply	VERB
ejpam-6535	175	59	f(p	f(p	NOUN
ejpam-6535	175	60	)	)	PUNCT
ejpam-6535	175	61	∈	∈	PROPN
ejpam-6535	175	62	cφ	cφ	X
ejpam-6535	175	63	(	(	PUNCT
ejpam-6535	175	64	f(f	f(f	PROPN
ejpam-6535	175	65	)	)	PUNCT
ejpam-6535	175	66	)	)	PUNCT
ejpam-6535	175	67	.	.	PUNCT
ejpam-6535	176	1	proof	proof	NOUN
ejpam-6535	176	2	.	.	PUNCT
ejpam-6535	177	1	(	(	PUNCT
ejpam-6535	177	2	1	1	X
ejpam-6535	177	3	)	)	PUNCT
ejpam-6535	177	4	⇐	⇐	ADJ
ejpam-6535	177	5	⇒	⇒	NOUN
ejpam-6535	177	6	(	(	PUNCT
ejpam-6535	177	7	2	2	X
ejpam-6535	177	8	)	)	PUNCT
ejpam-6535	177	9	follows	follow	VERB
ejpam-6535	177	10	from	from	ADP
ejpam-6535	177	11	the	the	DET
ejpam-6535	177	12	fact	fact	NOUN
ejpam-6535	177	13	that	that	SCONJ
ejpam-6535	177	14	f(v	f(v	NOUN
ejpam-6535	177	15	)	)	PUNCT
ejpam-6535	178	1	⊆	⊆	NUM
ejpam-6535	178	2	u	u	NOUN
ejpam-6535	178	3	⇐	⇐	ADJ
ejpam-6535	178	4	⇒	⇒	NOUN
ejpam-6535	178	5	v	v	ADP
ejpam-6535	178	6	⊆	⊆	NUM
ejpam-6535	178	7	f−1(u	f−1(u	NOUN
ejpam-6535	178	8	)	)	PUNCT
ejpam-6535	178	9	.	.	PUNCT
ejpam-6535	179	1	we	we	PRON
ejpam-6535	179	2	check	check	VERB
ejpam-6535	179	3	the	the	DET
ejpam-6535	179	4	equivalency	equivalency	NOUN
ejpam-6535	179	5	of	of	ADP
ejpam-6535	179	6	(	(	PUNCT
ejpam-6535	179	7	1	1	NUM
ejpam-6535	179	8	)	)	PUNCT
ejpam-6535	179	9	and	and	CCONJ
ejpam-6535	179	10	(	(	PUNCT
ejpam-6535	179	11	3	3	NUM
ejpam-6535	179	12	)	)	PUNCT
ejpam-6535	179	13	.	.	PUNCT
ejpam-6535	180	1	first	first	ADV
ejpam-6535	180	2	,	,	PUNCT
ejpam-6535	180	3	let	let	VERB
ejpam-6535	180	4	(	(	PUNCT
ejpam-6535	180	5	1	1	NUM
ejpam-6535	180	6	)	)	PUNCT
ejpam-6535	180	7	holds	hold	NOUN
ejpam-6535	180	8	,	,	PUNCT
ejpam-6535	180	9	and	and	CCONJ
ejpam-6535	180	10	let	let	VERB
ejpam-6535	180	11	p	p	X
ejpam-6535	180	12	∈	∈	PROPN
ejpam-6535	180	13	cφ(f	cφ(f	PUNCT
ejpam-6535	180	14	)	)	PUNCT
ejpam-6535	180	15	,	,	PUNCT
ejpam-6535	180	16	then	then	ADV
ejpam-6535	180	17	f	f	PROPN
ejpam-6535	180	18	≥	≥	NOUN
ejpam-6535	180	19	nφ	nφ	ADP
ejpam-6535	180	20	p	p	PROPN
ejpam-6535	180	21	.	.	PUNCT
ejpam-6535	181	1	but	but	CCONJ
ejpam-6535	181	2	then	then	ADV
ejpam-6535	181	3	f(f	f(f	PROPN
ejpam-6535	181	4	)	)	PUNCT
ejpam-6535	181	5	≥	≥	NOUN
ejpam-6535	182	1	f	f	PROPN
ejpam-6535	182	2	(	(	PUNCT
ejpam-6535	182	3	nφ	nφ	PROPN
ejpam-6535	182	4	p	p	NOUN
ejpam-6535	182	5	)	)	PUNCT
ejpam-6535	182	6	≥	≥	NOUN
ejpam-6535	182	7	mφ	mφ	ADP
ejpam-6535	182	8	f(p	f(p	NOUN
ejpam-6535	182	9	)	)	PUNCT
ejpam-6535	182	10	yields	yield	VERB
ejpam-6535	182	11	f(f	f(f	PROPN
ejpam-6535	182	12	)	)	PUNCT
ejpam-6535	182	13	≥	≥	NOUN
ejpam-6535	182	14	mφ	mφ	ADP
ejpam-6535	182	15	f(p	f(p	NOUN
ejpam-6535	182	16	)	)	PUNCT
ejpam-6535	182	17	which	which	PRON
ejpam-6535	182	18	is	be	AUX
ejpam-6535	182	19	equivalent	equivalent	ADJ
ejpam-6535	182	20	to	to	ADP
ejpam-6535	182	21	f(p	f(p	NOUN
ejpam-6535	182	22	)	)	PUNCT
ejpam-6535	183	1	∈	∈	PROPN
ejpam-6535	183	2	cφ	cφ	X
ejpam-6535	183	3	(	(	PUNCT
ejpam-6535	183	4	f(f	f(f	PROPN
ejpam-6535	183	5	)	)	PUNCT
ejpam-6535	183	6	)	)	PUNCT
ejpam-6535	183	7	.	.	PUNCT
ejpam-6535	184	1	next	next	ADV
ejpam-6535	184	2	,	,	PUNCT
ejpam-6535	184	3	assume	assume	VERB
ejpam-6535	184	4	(	(	PUNCT
ejpam-6535	184	5	3	3	NUM
ejpam-6535	184	6	)	)	PUNCT
ejpam-6535	184	7	holds	hold	VERB
ejpam-6535	184	8	.	.	PUNCT
ejpam-6535	185	1	then	then	ADV
ejpam-6535	185	2	f	f	PROPN
ejpam-6535	185	3	(	(	PUNCT
ejpam-6535	185	4	nφ	nφ	PROPN
ejpam-6535	185	5	p	p	NOUN
ejpam-6535	185	6	)	)	PUNCT
ejpam-6535	186	1	=	=	SYM
ejpam-6535	186	2	f	f	PROPN
ejpam-6535	186	3	(	(	PUNCT
ejpam-6535	186	4	∧	∧	PROPN
ejpam-6535	186	5	p∈cφ(f	p∈cφ(f	PROPN
ejpam-6535	186	6	)	)	PUNCT
ejpam-6535	186	7	f	f	NOUN
ejpam-6535	186	8	)	)	PUNCT
ejpam-6535	187	1	=	=	PUNCT
ejpam-6535	187	2	∧	∧	PROPN
ejpam-6535	187	3	p∈cφ(f	p∈cφ(f	PROPN
ejpam-6535	187	4	)	)	PUNCT
ejpam-6535	187	5	f(f	f(f	PROPN
ejpam-6535	187	6	)	)	PUNCT
ejpam-6535	187	7	≥∧	≥∧	NOUN
ejpam-6535	187	8	f(p)∈cφ(f(f	f(p)∈cφ(f(f	NOUN
ejpam-6535	187	9	)	)	PUNCT
ejpam-6535	187	10	)	)	PUNCT
ejpam-6535	188	1	f(f	f(f	PROPN
ejpam-6535	188	2	)	)	PUNCT
ejpam-6535	188	3	=	=	SYM
ejpam-6535	188	4	mφ	mφ	ADP
ejpam-6535	188	5	f(p	f(p	PROPN
ejpam-6535	188	6	)	)	PUNCT
ejpam-6535	188	7	.	.	PUNCT
ejpam-6535	189	1	lemma	lemma	PROPN
ejpam-6535	189	2	6	6	NUM
ejpam-6535	189	3	.	.	PUNCT
ejpam-6535	190	1	[	[	X
ejpam-6535	190	2	22	22	NUM
ejpam-6535	190	3	]	]	PUNCT
ejpam-6535	190	4	let	let	VERB
ejpam-6535	190	5	(	(	PUNCT
ejpam-6535	190	6	s	s	X
ejpam-6535	190	7	,	,	PUNCT
ejpam-6535	190	8	c	c	NOUN
ejpam-6535	190	9	)	)	PUNCT
ejpam-6535	190	10	and	and	CCONJ
ejpam-6535	190	11	(	(	PUNCT
ejpam-6535	190	12	t	t	PROPN
ejpam-6535	190	13	,	,	PUNCT
ejpam-6535	190	14	c′	c′	NOUN
ejpam-6535	190	15	)	)	PUNCT
ejpam-6535	190	16	be	be	AUX
ejpam-6535	190	17	probabilistic	probabilistic	ADJ
ejpam-6535	190	18	pretopological	pretopological	ADJ
ejpam-6535	190	19	spaces	space	NOUN
ejpam-6535	190	20	and	and	CCONJ
ejpam-6535	190	21	f	f	NOUN
ejpam-6535	190	22	:	:	PUNCT
ejpam-6535	190	23	s	s	AUX
ejpam-6535	190	24	−→	−→	NOUN
ejpam-6535	190	25	t	t	NOUN
ejpam-6535	190	26	be	be	AUX
ejpam-6535	190	27	a	a	DET
ejpam-6535	190	28	mapping	mapping	NOUN
ejpam-6535	190	29	.	.	PUNCT
ejpam-6535	191	1	then	then	ADV
ejpam-6535	191	2	f	f	PROPN
ejpam-6535	191	3	is	be	AUX
ejpam-6535	191	4	continuous	continuous	ADJ
ejpam-6535	191	5	if	if	SCONJ
ejpam-6535	191	6	and	and	CCONJ
ejpam-6535	191	7	only	only	ADV
ejpam-6535	191	8	if	if	SCONJ
ejpam-6535	191	9	for	for	ADP
ejpam-6535	191	10	all	all	PRON
ejpam-6535	191	11	p	p	NOUN
ejpam-6535	191	12	∈	∈	PROPN
ejpam-6535	191	13	s	s	NOUN
ejpam-6535	191	14	and	and	CCONJ
ejpam-6535	191	15	for	for	ADP
ejpam-6535	191	16	all	all	DET
ejpam-6535	191	17	φ	φ	PROPN
ejpam-6535	191	18	∈	∈	PROPN
ejpam-6535	191	19	∆+	∆+	NOUN
ejpam-6535	191	20	,	,	PUNCT
ejpam-6535	191	21	we	we	PRON
ejpam-6535	191	22	have	have	VERB
ejpam-6535	191	23	nc′,φ	nc′,φ	ADJ
ejpam-6535	191	24	f(p	f(p	NOUN
ejpam-6535	191	25	)	)	PUNCT
ejpam-6535	192	1	≤	≤	NUM
ejpam-6535	192	2	f	f	X
ejpam-6535	192	3	(	(	PUNCT
ejpam-6535	192	4	nc	nc	PROPN
ejpam-6535	192	5	,	,	PUNCT
ejpam-6535	192	6	φ	φ	PROPN
ejpam-6535	192	7	p	p	NOUN
ejpam-6535	192	8	)	)	PUNCT
ejpam-6535	192	9	.	.	PUNCT
ejpam-6535	193	1	lemma	lemma	PROPN
ejpam-6535	193	2	7	7	NUM
ejpam-6535	193	3	.	.	PUNCT
ejpam-6535	194	1	every	every	DET
ejpam-6535	194	2	probabilistic	probabilistic	ADJ
ejpam-6535	194	3	metric	metric	ADJ
ejpam-6535	194	4	space	space	NOUN
ejpam-6535	194	5	(	(	PUNCT
ejpam-6535	194	6	s	s	PROPN
ejpam-6535	194	7	,	,	PUNCT
ejpam-6535	194	8	f	f	PROPN
ejpam-6535	194	9	)	)	PUNCT
ejpam-6535	194	10	under	under	ADP
ejpam-6535	194	11	triangle	triangle	NOUN
ejpam-6535	194	12	function	function	NOUN
ejpam-6535	194	13	τ	τ	PROPN
ejpam-6535	194	14	gives	give	VERB
ejpam-6535	194	15	rise	rise	NOUN
ejpam-6535	194	16	to	to	ADP
ejpam-6535	194	17	a	a	DET
ejpam-6535	194	18	probabilistic	probabilistic	ADJ
ejpam-6535	194	19	neighborhood	neighborhood	NOUN
ejpam-6535	194	20	space	space	NOUN
ejpam-6535	194	21	(	(	PUNCT
ejpam-6535	194	22	s	s	X
ejpam-6535	194	23	,	,	PUNCT
ejpam-6535	194	24	(	(	PUNCT
ejpam-6535	194	25	fnφ	fnφ	NOUN
ejpam-6535	194	26	p	p	NOUN
ejpam-6535	194	27	)	)	PUNCT
ejpam-6535	194	28	(	(	PUNCT
ejpam-6535	194	29	p	p	X
ejpam-6535	194	30	,	,	PUNCT
ejpam-6535	194	31	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	194	32	)	)	PUNCT
ejpam-6535	194	33	.	.	PUNCT
ejpam-6535	195	1	proof	proof	NOUN
ejpam-6535	195	2	.	.	PUNCT
ejpam-6535	196	1	given	give	VERB
ejpam-6535	196	2	a	a	DET
ejpam-6535	196	3	φ	φ	NUM
ejpam-6535	196	4	∈	∈	PROPN
ejpam-6535	196	5	∆+	∆+	NOUN
ejpam-6535	196	6	,	,	PUNCT
ejpam-6535	196	7	ϵ	ϵ	X
ejpam-6535	196	8	>	>	X
ejpam-6535	196	9	0	0	PUNCT
ejpam-6535	196	10	and	and	CCONJ
ejpam-6535	196	11	p	p	NOUN
ejpam-6535	196	12	∈	∈	PROPN
ejpam-6535	196	13	s	s	NOUN
ejpam-6535	196	14	,	,	PUNCT
ejpam-6535	196	15	the	the	DET
ejpam-6535	196	16	(	(	PUNCT
ejpam-6535	196	17	φ	φ	PROPN
ejpam-6535	196	18	,	,	PUNCT
ejpam-6535	196	19	ϵ)-neighborhood	ϵ)-neighborhood	PUNCT
ejpam-6535	196	20	of	of	ADP
ejpam-6535	196	21	p	p	NOUN
ejpam-6535	196	22	defined	define	VERB
ejpam-6535	196	23	by	by	ADP
ejpam-6535	196	24	nφ,ϵ	nφ,ϵ	X
ejpam-6535	196	25	p	p	NOUN
ejpam-6535	196	26	=	=	X
ejpam-6535	196	27	{	{	PUNCT
ejpam-6535	196	28	q	q	PROPN
ejpam-6535	196	29	∈	∈	PROPN
ejpam-6535	196	30	s	s	PART
ejpam-6535	196	31	:	:	PUNCT
ejpam-6535	196	32	fp	fp	X
ejpam-6535	196	33	,	,	PUNCT
ejpam-6535	196	34	q(x+	q(x+	NOUN
ejpam-6535	196	35	ϵ	ϵ	NOUN
ejpam-6535	196	36	)	)	PUNCT
ejpam-6535	197	1	+	+	CCONJ
ejpam-6535	197	2	ϵ	ϵ	DET
ejpam-6535	197	3	≥	≥	NOUN
ejpam-6535	197	4	φ(x	φ(x	PROPN
ejpam-6535	197	5	)	)	PUNCT
ejpam-6535	197	6	,	,	PUNCT
ejpam-6535	197	7	∀x	∀x	VERB
ejpam-6535	197	8	∈	∈	PROPN
ejpam-6535	198	1	[	[	X
ejpam-6535	198	2	0	0	NUM
ejpam-6535	198	3	,	,	PUNCT
ejpam-6535	198	4	1ϵ	1ϵ	NUM
ejpam-6535	198	5	)	)	PUNCT
ejpam-6535	198	6	}	}	PUNCT
ejpam-6535	198	7	yields	yield	VERB
ejpam-6535	198	8	thatnφ	thatnφ	ADP
ejpam-6535	198	9	p	p	NOUN
ejpam-6535	199	1	=	=	PUNCT
ejpam-6535	200	1	[	[	X
ejpam-6535	200	2	{	{	PUNCT
ejpam-6535	200	3	nφ,ϵ	nφ,ϵ	NOUN
ejpam-6535	200	4	p	p	NOUN
ejpam-6535	200	5	:	:	PUNCT
ejpam-6535	200	6	ϵ	ϵ	X
ejpam-6535	200	7	>	>	X
ejpam-6535	200	8	0	0	NUM
ejpam-6535	200	9	}	}	PUNCT
ejpam-6535	200	10	]	]	PUNCT
ejpam-6535	200	11	the	the	DET
ejpam-6535	200	12	filter	filter	NOUN
ejpam-6535	200	13	satisfying	satisfy	VERB
ejpam-6535	200	14	all	all	DET
ejpam-6535	200	15	the	the	DET
ejpam-6535	200	16	conditions	condition	NOUN
ejpam-6535	200	17	(	(	PUNCT
ejpam-6535	200	18	pcs1)-(pcs3	pcs1)-(pcs3	NOUN
ejpam-6535	200	19	)	)	PUNCT
ejpam-6535	200	20	.	.	PUNCT
ejpam-6535	201	1	we	we	PRON
ejpam-6535	201	2	may	may	AUX
ejpam-6535	201	3	call	call	VERB
ejpam-6535	201	4	this	this	DET
ejpam-6535	201	5	probabilistic	probabilistic	ADJ
ejpam-6535	201	6	neighborhood	neighborhood	NOUN
ejpam-6535	201	7	space	space	NOUN
ejpam-6535	201	8	(	(	PUNCT
ejpam-6535	201	9	s	s	X
ejpam-6535	201	10	,	,	PUNCT
ejpam-6535	201	11	(	(	PUNCT
ejpam-6535	201	12	fnφ	fnφ	NOUN
ejpam-6535	201	13	p	p	NOUN
ejpam-6535	201	14	)	)	PUNCT
ejpam-6535	201	15	(	(	PUNCT
ejpam-6535	201	16	p	p	X
ejpam-6535	201	17	,	,	PUNCT
ejpam-6535	201	18	φ)∈s×∆	φ)∈s×∆	PROPN
ejpam-6535	201	19	)	)	PUNCT
ejpam-6535	201	20	a	a	DET
ejpam-6535	201	21	probabilistic	probabilistic	ADJ
ejpam-6535	201	22	metricgenerated	metricgenerate	VERB
ejpam-6535	201	23	probabilistic	probabilistic	ADJ
ejpam-6535	201	24	tardiff	tardiff	ADJ
ejpam-6535	201	25	-	-	PUNCT
ejpam-6535	201	26	neighborhood	neighborhood	NOUN
ejpam-6535	201	27	space	space	NOUN
ejpam-6535	201	28	.	.	PUNCT
ejpam-6535	202	1	hence	hence	ADV
ejpam-6535	202	2	in	in	ADP
ejpam-6535	202	3	view	view	NOUN
ejpam-6535	202	4	of	of	ADP
ejpam-6535	202	5	lemma	lemma	PROPN
ejpam-6535	202	6	6.4[22	6.4[22	PROPN
ejpam-6535	202	7	]	]	PUNCT
ejpam-6535	202	8	in	in	ADP
ejpam-6535	202	9	conjunction	conjunction	NOUN
ejpam-6535	202	10	with	with	ADP
ejpam-6535	202	11	preceding	precede	VERB
ejpam-6535	202	12	lemma	lemma	PROPN
ejpam-6535	202	13	4	4	NUM
ejpam-6535	202	14	,	,	PUNCT
ejpam-6535	202	15	and	and	CCONJ
ejpam-6535	202	16	denoting	denote	VERB
ejpam-6535	202	17	pmetneigh	pmetneigh	ADJ
ejpam-6535	202	18	the	the	DET
ejpam-6535	202	19	category	category	NOUN
ejpam-6535	202	20	having	having	AUX
ejpam-6535	202	21	probabilistic	probabilistic	ADJ
ejpam-6535	202	22	tardiff	tardiff	ADJ
ejpam-6535	202	23	-	-	PUNCT
ejpam-6535	202	24	neighborhood	neighborhood	NOUN
ejpam-6535	202	25	spaces	space	NOUN
ejpam-6535	202	26	as	as	ADP
ejpam-6535	202	27	objects	object	NOUN
ejpam-6535	202	28	and	and	CCONJ
ejpam-6535	202	29	morphisms	morphism	NOUN
ejpam-6535	202	30	as	as	SCONJ
ejpam-6535	202	31	described	describe	VERB
ejpam-6535	202	32	in	in	ADP
ejpam-6535	202	33	lemma	lemma	PROPN
ejpam-6535	202	34	6.4[22	6.4[22	PROPN
ejpam-6535	202	35	]	]	PUNCT
ejpam-6535	202	36	,	,	PUNCT
ejpam-6535	202	37	we	we	PRON
ejpam-6535	202	38	get	get	VERB
ejpam-6535	202	39	the	the	DET
ejpam-6535	202	40	following	follow	VERB
ejpam-6535	202	41	corollary	corollary	ADJ
ejpam-6535	202	42	1	1	NUM
ejpam-6535	202	43	.	.	PUNCT
ejpam-6535	203	1	b	b	X
ejpam-6535	203	2	:	:	PUNCT
ejpam-6535	203	3			PUNCT
ejpam-6535	203	4	pmetneigh	pmetneigh	ADJ
ejpam-6535	203	5	−→	−→	NOUN
ejpam-6535	203	6	pneigh	pneigh	NOUN
ejpam-6535	203	7	(	(	PUNCT
ejpam-6535	203	8	s	s	PROPN
ejpam-6535	203	9	,	,	PUNCT
ejpam-6535	203	10	nf	nf	ADJ
ejpam-6535	203	11	φ	φ	NOUN
ejpam-6535	203	12	)	)	PUNCT
ejpam-6535	203	13	7−→	7−→	PROPN
ejpam-6535	203	14	(	(	PUNCT
ejpam-6535	203	15	s	s	NOUN
ejpam-6535	203	16	,	,	PUNCT
ejpam-6535	203	17	n	n	CCONJ
ejpam-6535	203	18	)	)	PUNCT
ejpam-6535	203	19	f	f	PROPN
ejpam-6535	204	1	7−→	7−→	PROPN
ejpam-6535	204	2	f.	f.	NOUN
ejpam-6535	204	3	is	be	AUX
ejpam-6535	204	4	a	a	DET
ejpam-6535	204	5	functor	functor	PROPN
ejpam-6535	204	6	proposition	proposition	NOUN
ejpam-6535	204	7	1	1	NUM
ejpam-6535	204	8	.	.	X
ejpam-6535	205	1	pneigh	pneigh	NOUN
ejpam-6535	205	2	is	be	AUX
ejpam-6535	205	3	a	a	DET
ejpam-6535	205	4	topological	topological	ADJ
ejpam-6535	205	5	category	category	NOUN
ejpam-6535	205	6	.	.	PUNCT
ejpam-6535	206	1	proof	proof	NOUN
ejpam-6535	206	2	.	.	PUNCT
ejpam-6535	207	1	let	let	VERB
ejpam-6535	207	2	(	(	PUNCT
ejpam-6535	207	3	fj	fj	INTJ
ejpam-6535	207	4	:	:	PUNCT
ejpam-6535	207	5	s	s	X
ejpam-6535	207	6	−→	−→	NOUN
ejpam-6535	207	7	(	(	PUNCT
ejpam-6535	207	8	sj	sj	INTJ
ejpam-6535	207	9	,	,	PUNCT
ejpam-6535	207	10	n	n	PROPN
ejpam-6535	207	11	j	j	PROPN
ejpam-6535	207	12	,	,	PUNCT
ejpam-6535	207	13	φ	φ	PROPN
ejpam-6535	207	14	fj(p	fj(p	PROPN
ejpam-6535	207	15	)	)	PUNCT
ejpam-6535	207	16	)	)	PUNCT
ejpam-6535	207	17	)	)	PUNCT
ejpam-6535	208	1	j	j	PROPN
ejpam-6535	208	2	be	be	AUX
ejpam-6535	208	3	a	a	DET
ejpam-6535	208	4	source	source	NOUN
ejpam-6535	208	5	.	.	PUNCT
ejpam-6535	209	1	then	then	ADV
ejpam-6535	209	2	the	the	DET
ejpam-6535	209	3	initial	initial	ADJ
ejpam-6535	209	4	probabilistic	probabilistic	ADJ
ejpam-6535	209	5	neighborhood	neighborhood	NOUN
ejpam-6535	209	6	system	system	NOUN
ejpam-6535	209	7	on	on	ADP
ejpam-6535	209	8	s	s	PROPN
ejpam-6535	209	9	is	be	AUX
ejpam-6535	209	10	given	give	VERB
ejpam-6535	209	11	for	for	ADP
ejpam-6535	209	12	p	p	PROPN
ejpam-6535	209	13	∈	∈	PROPN
ejpam-6535	209	14	s	s	PART
ejpam-6535	209	15	and	and	CCONJ
ejpam-6535	209	16	φ	φ	PROPN
ejpam-6535	209	17	∈	∈	PROPN
ejpam-6535	209	18	∆+	∆+	NUM
ejpam-6535	209	19	by	by	ADP
ejpam-6535	209	20	nφ	nφ	PRON
ejpam-6535	209	21	p	p	PROPN
ejpam-6535	209	22	=	=	PROPN
ejpam-6535	209	23	∨	∨	NUM
ejpam-6535	209	24	j∈j	j∈j	NOUN
ejpam-6535	210	1	f	f	PROPN
ejpam-6535	210	2	−1	−1	PROPN
ejpam-6535	210	3	j	j	PROPN
ejpam-6535	210	4	(	(	PUNCT
ejpam-6535	210	5	nj	nj	PROPN
ejpam-6535	210	6	,	,	PUNCT
ejpam-6535	210	7	φ	φ	PROPN
ejpam-6535	210	8	fj(p	fj(p	PROPN
ejpam-6535	210	9	)	)	PUNCT
ejpam-6535	210	10	)	)	PUNCT
ejpam-6535	210	11	.	.	PUNCT
ejpam-6535	211	1	for	for	ADP
ejpam-6535	211	2	the	the	DET
ejpam-6535	211	3	remaining	remain	VERB
ejpam-6535	211	4	proof	proof	NOUN
ejpam-6535	211	5	see	see	VERB
ejpam-6535	211	6	f.i	f.i	PROPN
ejpam-6535	211	7	.	.	PUNCT
ejpam-6535	212	1	the	the	DET
ejpam-6535	212	2	proposition	proposition	NOUN
ejpam-6535	212	3	4.1	4.1	NUM
ejpam-6535	212	4	[	[	X
ejpam-6535	212	5	24	24	NUM
ejpam-6535	212	6	]	]	NUM
ejpam-6535	212	7	)	)	PUNCT
ejpam-6535	212	8	.	.	PUNCT
ejpam-6535	213	1	remark	remark	NOUN
ejpam-6535	213	2	5	5	NUM
ejpam-6535	213	3	.	.	PUNCT
ejpam-6535	214	1	if	if	SCONJ
ejpam-6535	214	2	(	(	PUNCT
ejpam-6535	214	3	s	s	X
ejpam-6535	214	4	,	,	PUNCT
ejpam-6535	214	5	n	n	CCONJ
ejpam-6535	214	6	)	)	PUNCT
ejpam-6535	214	7	is	be	AUX
ejpam-6535	214	8	a	a	DET
ejpam-6535	214	9	probabilistic	probabilistic	ADJ
ejpam-6535	214	10	neighborhood	neighborhood	NOUN
ejpam-6535	214	11	space	space	NOUN
ejpam-6535	214	12	and	and	CCONJ
ejpam-6535	214	13	a	a	DET
ejpam-6535	214	14	⊆	⊆	NUM
ejpam-6535	214	15	s	s	NOUN
ejpam-6535	214	16	,	,	PUNCT
ejpam-6535	214	17	then	then	ADV
ejpam-6535	214	18	the	the	DET
ejpam-6535	214	19	subspace	subspace	NOUN
ejpam-6535	214	20	(	(	PUNCT
ejpam-6535	214	21	a	a	DET
ejpam-6535	214	22	,	,	PUNCT
ejpam-6535	214	23	na	na	NOUN
ejpam-6535	214	24	)	)	PUNCT
ejpam-6535	214	25	,	,	PUNCT
ejpam-6535	214	26	the	the	DET
ejpam-6535	214	27	probabilistic	probabilistic	ADJ
ejpam-6535	214	28	neighborhood	neighborhood	NOUN
ejpam-6535	214	29	system	system	NOUN
ejpam-6535	214	30	on	on	ADP
ejpam-6535	214	31	a	a	PRON
ejpam-6535	214	32	is	be	AUX
ejpam-6535	214	33	given	give	VERB
ejpam-6535	214	34	for	for	ADP
ejpam-6535	214	35	any	any	DET
ejpam-6535	214	36	p	p	PROPN
ejpam-6535	214	37	∈	∈	PROPN
ejpam-6535	214	38	a	a	DET
ejpam-6535	214	39	by	by	ADP
ejpam-6535	214	40	anφ	anφ	NOUN
ejpam-6535	214	41	p	p	NOUN
ejpam-6535	214	42	=	=	PUNCT
ejpam-6535	214	43	{	{	PUNCT
ejpam-6535	214	44	a	a	DET
ejpam-6535	214	45	∩	∩	ADJ
ejpam-6535	214	46	v	v	NOUN
ejpam-6535	214	47	:	:	PUNCT
ejpam-6535	214	48	v	v	NUM
ejpam-6535	214	49	∈	∈	PROPN
ejpam-6535	214	50	nφ	nφ	ADP
ejpam-6535	214	51	p	p	NOUN
ejpam-6535	214	52	}	}	PUNCT
ejpam-6535	214	53	.	.	PUNCT
ejpam-6535	215	1	for	for	ADP
ejpam-6535	215	2	the	the	DET
ejpam-6535	215	3	product	product	NOUN
ejpam-6535	215	4	probabilistic	probabilistic	ADJ
ejpam-6535	215	5	neighborhood	neighborhood	NOUN
ejpam-6535	215	6	spaces	space	NOUN
ejpam-6535	215	7	,	,	PUNCT
ejpam-6535	215	8	we	we	PRON
ejpam-6535	215	9	just	just	ADV
ejpam-6535	215	10	consider	consider	VERB
ejpam-6535	215	11	fj	fj	NOUN
ejpam-6535	215	12	=	=	PUNCT
ejpam-6535	215	13	prj	prj	VERB
ejpam-6535	215	14	where	where	SCONJ
ejpam-6535	215	15	prj	prj	NOUN
ejpam-6535	215	16	:	:	PUNCT
ejpam-6535	216	1	∏	∏	NUM
ejpam-6535	216	2	i∈j	i∈j	NOUN
ejpam-6535	216	3	si	si	INTJ
ejpam-6535	216	4	−→	−→	NOUN
ejpam-6535	216	5	sj	sj	INTJ
ejpam-6535	216	6	are	be	AUX
ejpam-6535	216	7	the	the	DET
ejpam-6535	216	8	projections	projection	NOUN
ejpam-6535	216	9	.	.	PUNCT
ejpam-6535	217	1	in	in	ADP
ejpam-6535	217	2	fact	fact	NOUN
ejpam-6535	217	3	,	,	PUNCT
ejpam-6535	217	4	if	if	SCONJ
ejpam-6535	217	5	(	(	PUNCT
ejpam-6535	217	6	sj	sj	INTJ
ejpam-6535	217	7	,	,	PUNCT
ejpam-6535	217	8	nj	nj	PROPN
ejpam-6535	217	9	)	)	PUNCT
ejpam-6535	217	10	is	be	AUX
ejpam-6535	217	11	a	a	DET
ejpam-6535	217	12	family	family	NOUN
ejpam-6535	217	13	of	of	ADP
ejpam-6535	217	14	probabilistic	probabilistic	ADJ
ejpam-6535	217	15	neighborhood	neighborhood	NOUN
ejpam-6535	217	16	systems	system	NOUN
ejpam-6535	217	17	,	,	PUNCT
ejpam-6535	217	18	then	then	ADV
ejpam-6535	217	19	their	their	PRON
ejpam-6535	217	20	product	product	NOUN
ejpam-6535	217	21	structure	structure	NOUN
ejpam-6535	217	22	on	on	ADP
ejpam-6535	217	23	s	s	NOUN
ejpam-6535	217	24	=	=	SYM
ejpam-6535	217	25	∏	∏	PROPN
ejpam-6535	217	26	j∈j	j∈j	NOUN
ejpam-6535	217	27	sj	sj	NOUN
ejpam-6535	217	28	is	be	AUX
ejpam-6535	217	29	given	give	VERB
ejpam-6535	217	30	by	by	ADP
ejpam-6535	217	31	n	n	PROPN
ejpam-6535	217	32	=	=	PUNCT
ejpam-6535	217	33	∨	∨	NOUN
ejpam-6535	217	34	j∈j	j∈j	NOUN
ejpam-6535	217	35	pr	pr	PROPN
ejpam-6535	217	36	−1	−1	PROPN
ejpam-6535	217	37	j	j	PROPN
ejpam-6535	217	38	(	(	PUNCT
ejpam-6535	217	39	nj	nj	PROPN
ejpam-6535	217	40	,	,	PUNCT
ejpam-6535	217	41	φ	φ	PROPN
ejpam-6535	217	42	prj(p	prj(p	PROPN
ejpam-6535	217	43	)	)	PUNCT
ejpam-6535	217	44	)	)	PUNCT
ejpam-6535	217	45	,	,	PUNCT
ejpam-6535	217	46	for	for	ADP
ejpam-6535	217	47	p	p	PROPN
ejpam-6535	217	48	∈	∈	PROPN
ejpam-6535	217	49	s	s	PROPN
ejpam-6535	217	50	,	,	PUNCT
ejpam-6535	217	51	φ	φ	PROPN
ejpam-6535	217	52	∈	∈	PROPN
ejpam-6535	217	53	∆	∆	PROPN
ejpam-6535	217	54	,	,	PUNCT
ejpam-6535	217	55	where	where	SCONJ
ejpam-6535	217	56	prj	prj	NOUN
ejpam-6535	217	57	are	be	AUX
ejpam-6535	217	58	the	the	DET
ejpam-6535	217	59	projections	projection	NOUN
ejpam-6535	217	60	.	.	PUNCT
ejpam-6535	218	1	if	if	SCONJ
ejpam-6535	218	2	for	for	ADP
ejpam-6535	218	3	instance	instance	NOUN
ejpam-6535	218	4	j	j	PROPN
ejpam-6535	218	5	=	=	SYM
ejpam-6535	218	6	1	1	NUM
ejpam-6535	218	7	,	,	PUNCT
ejpam-6535	218	8	2	2	NUM
ejpam-6535	218	9	,	,	PUNCT
ejpam-6535	218	10	then	then	ADV
ejpam-6535	218	11	the	the	DET
ejpam-6535	218	12	product	product	NOUN
ejpam-6535	218	13	structure	structure	NOUN
ejpam-6535	218	14	(	(	PUNCT
ejpam-6535	218	15	n×m)(p	n×m)(p	PROPN
ejpam-6535	218	16	,	,	PUNCT
ejpam-6535	218	17	q	q	NOUN
ejpam-6535	218	18	)	)	PUNCT
ejpam-6535	218	19	on	on	ADP
ejpam-6535	218	20	s1	s1	PROPN
ejpam-6535	218	21	×	×	PROPN
ejpam-6535	218	22	s2	s2	NOUN
ejpam-6535	218	23	is	be	AUX
ejpam-6535	218	24	given	give	VERB
ejpam-6535	218	25	for	for	ADP
ejpam-6535	218	26	any	any	DET
ejpam-6535	218	27	(	(	PUNCT
ejpam-6535	218	28	p	p	X
ejpam-6535	218	29	,	,	PUNCT
ejpam-6535	218	30	q	q	NOUN
ejpam-6535	218	31	)	)	PUNCT
ejpam-6535	218	32	∈	∈	PROPN
ejpam-6535	218	33	s1	s1	NOUN
ejpam-6535	218	34	×	×	NOUN
ejpam-6535	218	35	s2	s2	NOUN
ejpam-6535	218	36	by	by	ADP
ejpam-6535	218	37	its	its	PRON
ejpam-6535	218	38	basis	basis	NOUN
ejpam-6535	218	39	b	b	NOUN
ejpam-6535	218	40	=	=	PUNCT
ejpam-6535	218	41	{	{	PUNCT
ejpam-6535	218	42	pr−1	pr−1	PROPN
ejpam-6535	218	43	1	1	NUM
ejpam-6535	218	44	(	(	PUNCT
ejpam-6535	218	45	u	u	NOUN
ejpam-6535	218	46	)	)	PUNCT
ejpam-6535	218	47	∩	∩	X
ejpam-6535	218	48	pr−1	pr−1	PROPN
ejpam-6535	218	49	2	2	NUM
ejpam-6535	218	50	(	(	PUNCT
ejpam-6535	218	51	v	v	NOUN
ejpam-6535	218	52	)	)	PUNCT
ejpam-6535	218	53	:	:	PUNCT
ejpam-6535	219	1	u	u	PROPN
ejpam-6535	219	2	∈	∈	PROPN
ejpam-6535	219	3	nφ	nφ	ADP
ejpam-6535	219	4	p	p	PROPN
ejpam-6535	219	5	,	,	PUNCT
ejpam-6535	219	6	v	v	NOUN
ejpam-6535	219	7	∈	∈	NOUN
ejpam-6535	219	8	mφ	mφ	ADP
ejpam-6535	219	9	q	q	NOUN
ejpam-6535	219	10	}	}	PUNCT
ejpam-6535	219	11	.	.	PUNCT
ejpam-6535	220	1	5	5	X
ejpam-6535	220	2	.	.	X
ejpam-6535	220	3	probabilistic	probabilistic	ADJ
ejpam-6535	220	4	neighborhood	neighborhood	NOUN
ejpam-6535	220	5	groups	group	NOUN
ejpam-6535	220	6	and	and	CCONJ
ejpam-6535	220	7	probabilistic	probabilistic	ADJ
ejpam-6535	220	8	convergence	convergence	NOUN
ejpam-6535	220	9	groups	group	NOUN
ejpam-6535	220	10	definition	definition	NOUN
ejpam-6535	220	11	6	6	NUM
ejpam-6535	220	12	.	.	PUNCT
ejpam-6535	221	1	let	let	VERB
ejpam-6535	221	2	(	(	PUNCT
ejpam-6535	221	3	s	s	X
ejpam-6535	221	4	,	,	PUNCT
ejpam-6535	221	5	·	·	PUNCT
ejpam-6535	221	6	)	)	PUNCT
ejpam-6535	221	7	be	be	AUX
ejpam-6535	221	8	a	a	DET
ejpam-6535	221	9	group	group	NOUN
ejpam-6535	221	10	,	,	PUNCT
ejpam-6535	221	11	and	and	CCONJ
ejpam-6535	221	12	(	(	PUNCT
ejpam-6535	221	13	s	s	X
ejpam-6535	221	14	,	,	PUNCT
ejpam-6535	221	15	n	n	CCONJ
ejpam-6535	221	16	)	)	PUNCT
ejpam-6535	221	17	a	a	DET
ejpam-6535	221	18	probabilistic	probabilistic	ADJ
ejpam-6535	221	19	neighborhood	neighborhood	NOUN
ejpam-6535	221	20	space	space	NOUN
ejpam-6535	221	21	.	.	PUNCT
ejpam-6535	222	1	then	then	ADV
ejpam-6535	222	2	the	the	DET
ejpam-6535	222	3	triple	triple	ADJ
ejpam-6535	222	4	(	(	PUNCT
ejpam-6535	222	5	s	s	NOUN
ejpam-6535	222	6	,	,	PUNCT
ejpam-6535	222	7	·	·	PUNCT
ejpam-6535	222	8	,	,	PUNCT
ejpam-6535	222	9	n	n	CCONJ
ejpam-6535	222	10	)	)	PUNCT
ejpam-6535	222	11	is	be	AUX
ejpam-6535	222	12	called	call	VERB
ejpam-6535	222	13	a	a	DET
ejpam-6535	222	14	probabilistic	probabilistic	ADJ
ejpam-6535	222	15	neighborhood	neighborhood	NOUN
ejpam-6535	222	16	group	group	NOUN
ejpam-6535	222	17	under	under	ADP
ejpam-6535	222	18	triangle	triangle	NOUN
ejpam-6535	222	19	function	function	NOUN
ejpam-6535	222	20	τ	τ	X
ejpam-6535	222	21	if	if	SCONJ
ejpam-6535	222	22	and	and	CCONJ
ejpam-6535	222	23	only	only	ADV
ejpam-6535	222	24	if	if	SCONJ
ejpam-6535	222	25	the	the	DET
ejpam-6535	222	26	following	follow	VERB
ejpam-6535	222	27	conditions	condition	NOUN
ejpam-6535	222	28	are	be	AUX
ejpam-6535	222	29	fulfilled	fulfil	VERB
ejpam-6535	222	30	:	:	PUNCT
ejpam-6535	222	31	(	(	PUNCT
ejpam-6535	222	32	pngm	pngm	ADJ
ejpam-6535	222	33	)	)	PUNCT
ejpam-6535	222	34	for	for	ADP
ejpam-6535	222	35	all	all	DET
ejpam-6535	222	36	p	p	NOUN
ejpam-6535	222	37	,	,	PUNCT
ejpam-6535	222	38	q	q	PROPN
ejpam-6535	222	39	∈	∈	PROPN
ejpam-6535	222	40	s	s	X
ejpam-6535	222	41	and	and	CCONJ
ejpam-6535	222	42	for	for	ADP
ejpam-6535	222	43	all	all	DET
ejpam-6535	222	44	φ	φ	NOUN
ejpam-6535	222	45	,	,	PUNCT
ejpam-6535	222	46	ψ	ψ	X
ejpam-6535	222	47	∈	∈	PROPN
ejpam-6535	222	48	∆	∆	X
ejpam-6535	222	49	,	,	PUNCT
ejpam-6535	222	50	n	n	CCONJ
ejpam-6535	222	51	τ(φ	τ(φ	X
ejpam-6535	222	52	,	,	PUNCT
ejpam-6535	222	53	ψ	ψ	NOUN
ejpam-6535	222	54	)	)	PUNCT
ejpam-6535	222	55	pq	pq	NOUN
ejpam-6535	222	56	≤	≤	NOUN
ejpam-6535	222	57	nφ	nφ	ADP
ejpam-6535	222	58	p	p	PROPN
ejpam-6535	222	59	⊙nψ	⊙nψ	NOUN
ejpam-6535	222	60	q	q	NOUN
ejpam-6535	222	61	;	;	PUNCT
ejpam-6535	222	62	(	(	PUNCT
ejpam-6535	222	63	pngi	pngi	NOUN
ejpam-6535	222	64	)	)	PUNCT
ejpam-6535	222	65	for	for	ADP
ejpam-6535	222	66	all	all	DET
ejpam-6535	222	67	p	p	NOUN
ejpam-6535	222	68	∈	∈	PROPN
ejpam-6535	222	69	s	s	NOUN
ejpam-6535	222	70	and	and	CCONJ
ejpam-6535	222	71	for	for	ADP
ejpam-6535	222	72	all	all	DET
ejpam-6535	222	73	∀φ	∀φ	NUM
ejpam-6535	222	74	∈	∈	PROPN
ejpam-6535	222	75	∆+	∆+	NOUN
ejpam-6535	222	76	,	,	PUNCT
ejpam-6535	222	77	nφ	nφ	PROPN
ejpam-6535	222	78	p−1	p−1	PROPN
ejpam-6535	222	79	≤	≤	NOUN
ejpam-6535	222	80	(	(	PUNCT
ejpam-6535	222	81	nφ	nφ	NOUN
ejpam-6535	222	82	p	p	NOUN
ejpam-6535	222	83	)	)	PUNCT
ejpam-6535	222	84	−1	−1	NOUN
ejpam-6535	222	85	.	.	PUNCT
ejpam-6535	223	1	lemma	lemma	PROPN
ejpam-6535	223	2	8	8	NUM
ejpam-6535	223	3	.	.	PUNCT
ejpam-6535	224	1	let	let	VERB
ejpam-6535	224	2	(	(	PUNCT
ejpam-6535	224	3	s	s	X
ejpam-6535	224	4	,	,	PUNCT
ejpam-6535	224	5	·	·	PUNCT
ejpam-6535	224	6	,	,	PUNCT
ejpam-6535	224	7	n	n	NOUN
ejpam-6535	224	8	=	=	SYM
ejpam-6535	224	9	(	(	PUNCT
ejpam-6535	224	10	nφ	nφ	PROPN
ejpam-6535	224	11	p	p	NOUN
ejpam-6535	224	12	)	)	PUNCT
ejpam-6535	224	13	(	(	PUNCT
ejpam-6535	224	14	p	p	X
ejpam-6535	224	15	,	,	PUNCT
ejpam-6535	224	16	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	224	17	)	)	PUNCT
ejpam-6535	224	18	be	be	AUX
ejpam-6535	224	19	a	a	DET
ejpam-6535	224	20	probabilistic	probabilistic	ADJ
ejpam-6535	224	21	neighborhood	neighborhood	NOUN
ejpam-6535	224	22	group	group	NOUN
ejpam-6535	224	23	.	.	PUNCT
ejpam-6535	225	1	then	then	ADV
ejpam-6535	225	2	the	the	DET
ejpam-6535	225	3	statement	statement	NOUN
ejpam-6535	225	4	(	(	PUNCT
ejpam-6535	225	5	pngm)′	pngm)′	PROPN
ejpam-6535	225	6	is	be	AUX
ejpam-6535	225	7	equivalent	equivalent	ADJ
ejpam-6535	225	8	to	to	ADP
ejpam-6535	225	9	the	the	DET
ejpam-6535	225	10	statements	statement	NOUN
ejpam-6535	225	11	(	(	PUNCT
ejpam-6535	225	12	pngm	pngm	ADJ
ejpam-6535	225	13	)	)	PUNCT
ejpam-6535	225	14	and	and	CCONJ
ejpam-6535	225	15	(	(	PUNCT
ejpam-6535	225	16	pngi	pngi	PROPN
ejpam-6535	225	17	)	)	PUNCT
ejpam-6535	225	18	as	as	SCONJ
ejpam-6535	225	19	given	give	VERB
ejpam-6535	225	20	below	below	ADV
ejpam-6535	225	21	:	:	PUNCT
ejpam-6535	225	22	(	(	PUNCT
ejpam-6535	225	23	pngm)′	pngm)′	VERB
ejpam-6535	225	24	for	for	ADP
ejpam-6535	225	25	all	all	DET
ejpam-6535	225	26	p	p	NOUN
ejpam-6535	225	27	,	,	PUNCT
ejpam-6535	225	28	q	q	PROPN
ejpam-6535	225	29	∈	∈	PROPN
ejpam-6535	225	30	s	s	X
ejpam-6535	225	31	and	and	CCONJ
ejpam-6535	225	32	for	for	ADP
ejpam-6535	225	33	all	all	DET
ejpam-6535	225	34	φ	φ	NOUN
ejpam-6535	225	35	,	,	PUNCT
ejpam-6535	225	36	ψ	ψ	X
ejpam-6535	225	37	∈	∈	PROPN
ejpam-6535	225	38	∆	∆	X
ejpam-6535	225	39	,	,	PUNCT
ejpam-6535	225	40	n	n	CCONJ
ejpam-6535	225	41	τ(φ	τ(φ	X
ejpam-6535	225	42	,	,	PUNCT
ejpam-6535	225	43	ψ	ψ	NOUN
ejpam-6535	225	44	)	)	PUNCT
ejpam-6535	225	45	p−1q	p−1q	NOUN
ejpam-6535	225	46	≤	≤	PROPN
ejpam-6535	225	47	(	(	PUNCT
ejpam-6535	225	48	nφ	nφ	NOUN
ejpam-6535	225	49	p	p	NOUN
ejpam-6535	225	50	)	)	PUNCT
ejpam-6535	225	51	−1	−1	NOUN
ejpam-6535	225	52	⊙nψ	⊙nψ	NOUN
ejpam-6535	225	53	q	q	NOUN
ejpam-6535	225	54	;	;	PUNCT
ejpam-6535	225	55	(	(	PUNCT
ejpam-6535	225	56	pngm	pngm	ADJ
ejpam-6535	225	57	)	)	PUNCT
ejpam-6535	225	58	for	for	ADP
ejpam-6535	225	59	all	all	DET
ejpam-6535	225	60	p	p	NOUN
ejpam-6535	225	61	,	,	PUNCT
ejpam-6535	225	62	q	q	PROPN
ejpam-6535	225	63	∈	∈	PROPN
ejpam-6535	225	64	s	s	X
ejpam-6535	225	65	and	and	CCONJ
ejpam-6535	225	66	for	for	ADP
ejpam-6535	225	67	all	all	DET
ejpam-6535	225	68	φ	φ	NOUN
ejpam-6535	225	69	,	,	PUNCT
ejpam-6535	225	70	ψ	ψ	X
ejpam-6535	225	71	∈	∈	PROPN
ejpam-6535	225	72	∆	∆	X
ejpam-6535	225	73	,	,	PUNCT
ejpam-6535	225	74	n	n	CCONJ
ejpam-6535	225	75	τ(φ	τ(φ	X
ejpam-6535	225	76	,	,	PUNCT
ejpam-6535	225	77	ψ	ψ	NOUN
ejpam-6535	225	78	)	)	PUNCT
ejpam-6535	225	79	pq	pq	NOUN
ejpam-6535	225	80	≤	≤	NOUN
ejpam-6535	225	81	nφ	nφ	ADP
ejpam-6535	225	82	p	p	PROPN
ejpam-6535	225	83	⊙nψ	⊙nψ	NOUN
ejpam-6535	225	84	q	q	NOUN
ejpam-6535	225	85	;	;	PUNCT
ejpam-6535	225	86	(	(	PUNCT
ejpam-6535	225	87	pngi	pngi	NOUN
ejpam-6535	225	88	)	)	PUNCT
ejpam-6535	225	89	for	for	ADP
ejpam-6535	225	90	all	all	DET
ejpam-6535	225	91	p	p	NOUN
ejpam-6535	225	92	∈	∈	PROPN
ejpam-6535	225	93	s	s	NOUN
ejpam-6535	225	94	and	and	CCONJ
ejpam-6535	225	95	for	for	ADP
ejpam-6535	225	96	all	all	DET
ejpam-6535	225	97	∀φ	∀φ	NUM
ejpam-6535	225	98	∈	∈	PROPN
ejpam-6535	225	99	∆+	∆+	NOUN
ejpam-6535	225	100	,	,	PUNCT
ejpam-6535	225	101	nφ	nφ	PROPN
ejpam-6535	225	102	p−1	p−1	PROPN
ejpam-6535	225	103	≤	≤	NOUN
ejpam-6535	225	104	(	(	PUNCT
ejpam-6535	225	105	nφ	nφ	NOUN
ejpam-6535	225	106	p	p	NOUN
ejpam-6535	225	107	)	)	PUNCT
ejpam-6535	225	108	−1	−1	NOUN
ejpam-6535	225	109	.	.	PUNCT
ejpam-6535	226	1	proof	proof	NOUN
ejpam-6535	226	2	.	.	PUNCT
ejpam-6535	227	1	(	(	PUNCT
ejpam-6535	227	2	pngm)′⇒	pngm)′⇒	PROPN
ejpam-6535	227	3	(	(	PUNCT
ejpam-6535	227	4	pngm)+(pngi	pngm)+(pngi	PROPN
ejpam-6535	227	5	):	):	PUNCT
ejpam-6535	227	6	first	first	ADV
ejpam-6535	227	7	,	,	PUNCT
ejpam-6535	227	8	we	we	PRON
ejpam-6535	227	9	prove	prove	VERB
ejpam-6535	227	10	(	(	PUNCT
ejpam-6535	227	11	pngi	pngi	PROPN
ejpam-6535	227	12	)	)	PUNCT
ejpam-6535	227	13	.	.	PUNCT
ejpam-6535	228	1	for	for	ADP
ejpam-6535	228	2	let	let	VERB
ejpam-6535	228	3	p	p	PROPN
ejpam-6535	228	4	∈	∈	PROPN
ejpam-6535	228	5	s	s	PART
ejpam-6535	228	6	and	and	CCONJ
ejpam-6535	228	7	φ	φ	PROPN
ejpam-6535	228	8	∈	∈	PROPN
ejpam-6535	228	9	∆+	∆+	NOUN
ejpam-6535	228	10	.	.	PUNCT
ejpam-6535	229	1	then	then	ADV
ejpam-6535	229	2	upon	upon	SCONJ
ejpam-6535	229	3	using	use	VERB
ejpam-6535	229	4	the	the	DET
ejpam-6535	229	5	boundary	boundary	ADJ
ejpam-6535	229	6	condition	condition	NOUN
ejpam-6535	229	7	τ(φ	τ(φ	ADV
ejpam-6535	229	8	,	,	PUNCT
ejpam-6535	229	9	ϵ0	ϵ0	NUM
ejpam-6535	229	10	)	)	PUNCT
ejpam-6535	229	11	=	=	SYM
ejpam-6535	230	1	φ	φ	NUM
ejpam-6535	230	2	,	,	PUNCT
ejpam-6535	230	3	we	we	PRON
ejpam-6535	230	4	havenφ	havenφ	VERB
ejpam-6535	230	5	p−1	p−1	PROPN
ejpam-6535	230	6	=	=	PROPN
ejpam-6535	230	7	n	n	X
ejpam-6535	230	8	τ(φ,ϵ0	τ(φ,ϵ0	ADJ
ejpam-6535	230	9	)	)	PUNCT
ejpam-6535	230	10	p−1e	p−1e	ADJ
ejpam-6535	230	11	≤	≤	NOUN
ejpam-6535	230	12	(	(	PUNCT
ejpam-6535	230	13	nφ	nφ	NOUN
ejpam-6535	230	14	p	p	NOUN
ejpam-6535	230	15	)	)	PUNCT
ejpam-6535	230	16	−1	−1	NOUN
ejpam-6535	230	17	⊙nϵ0	⊙nϵ0	PROPN
ejpam-6535	230	18	e	e	X
ejpam-6535	230	19	≤	≤	X
ejpam-6535	230	20	(	(	PUNCT
ejpam-6535	230	21	nφ	nφ	NOUN
ejpam-6535	230	22	p	p	NOUN
ejpam-6535	230	23	)	)	PUNCT
ejpam-6535	230	24	−1	−1	NOUN
ejpam-6535	230	25	⊙	⊙	NOUN
ejpam-6535	231	1	[	[	X
ejpam-6535	231	2	e	e	X
ejpam-6535	231	3	]	]	X
ejpam-6535	231	4	=	=	SYM
ejpam-6535	231	5	(	(	PUNCT
ejpam-6535	231	6	nφ	nφ	PROPN
ejpam-6535	231	7	p	p	NOUN
ejpam-6535	231	8	)	)	PUNCT
ejpam-6535	231	9	−1	−1	NOUN
ejpam-6535	231	10	,	,	PUNCT
ejpam-6535	231	11	i.e.	i.e.	X
ejpam-6535	231	12	,	,	PUNCT
ejpam-6535	231	13	nφ	nφ	PROPN
ejpam-6535	231	14	p−1	p−1	PROPN
ejpam-6535	231	15	≤	≤	NOUN
ejpam-6535	231	16	(	(	PUNCT
ejpam-6535	231	17	nφ	nφ	NOUN
ejpam-6535	231	18	p	p	NOUN
ejpam-6535	231	19	)	)	PUNCT
ejpam-6535	231	20	−1	−1	NOUN
ejpam-6535	231	21	.	.	PUNCT
ejpam-6535	232	1	next	next	ADJ
ejpam-6535	232	2	,	,	PUNCT
ejpam-6535	232	3	to	to	PART
ejpam-6535	232	4	prove	prove	VERB
ejpam-6535	232	5	(	(	PUNCT
ejpam-6535	232	6	pngm	pngm	ADJ
ejpam-6535	232	7	)	)	PUNCT
ejpam-6535	232	8	,	,	PUNCT
ejpam-6535	232	9	let	let	VERB
ejpam-6535	232	10	p	p	PRON
ejpam-6535	232	11	,	,	PUNCT
ejpam-6535	232	12	q	q	PROPN
ejpam-6535	232	13	∈	∈	PROPN
ejpam-6535	232	14	s	s	NOUN
ejpam-6535	232	15	and	and	CCONJ
ejpam-6535	232	16	φ	φ	NUM
ejpam-6535	232	17	,	,	PUNCT
ejpam-6535	232	18	ψ	ψ	X
ejpam-6535	232	19	∈	∈	PROPN
ejpam-6535	232	20	∆+	∆+	NOUN
ejpam-6535	232	21	.	.	PUNCT
ejpam-6535	233	1	then	then	ADV
ejpam-6535	233	2	using	use	VERB
ejpam-6535	233	3	(	(	PUNCT
ejpam-6535	233	4	pngi	pngi	PROPN
ejpam-6535	233	5	)	)	PUNCT
ejpam-6535	233	6	along	along	ADP
ejpam-6535	233	7	with	with	ADP
ejpam-6535	233	8	lemma	lemma	PROPN
ejpam-6535	233	9	2(f	2(f	NUM
ejpam-6535	233	10	)	)	PUNCT
ejpam-6535	233	11	and	and	CCONJ
ejpam-6535	233	12	the	the	DET
ejpam-6535	233	13	fact	fact	NOUN
ejpam-6535	233	14	that	that	SCONJ
ejpam-6535	233	15	pq	pq	INTJ
ejpam-6535	233	16	=	=	SYM
ejpam-6535	233	17	(	(	PUNCT
ejpam-6535	233	18	p−1)−1q	p−1)−1q	PROPN
ejpam-6535	233	19	,	,	PUNCT
ejpam-6535	233	20	we	we	PRON
ejpam-6535	233	21	have	have	AUX
ejpam-6535	233	22	from	from	ADP
ejpam-6535	233	23	the	the	DET
ejpam-6535	233	24	assumption	assumption	NOUN
ejpam-6535	233	25	thatn	thatn	ADV
ejpam-6535	233	26	τ(φ	τ(φ	NUM
ejpam-6535	233	27	,	,	PUNCT
ejpam-6535	233	28	ψ	ψ	NOUN
ejpam-6535	233	29	)	)	PUNCT
ejpam-6535	233	30	pq	pq	NOUN
ejpam-6535	233	31	=	=	SYM
ejpam-6535	233	32	n	n	CCONJ
ejpam-6535	233	33	τ(φ	τ(φ	X
ejpam-6535	233	34	,	,	PUNCT
ejpam-6535	233	35	ψ	ψ	NOUN
ejpam-6535	233	36	)	)	PUNCT
ejpam-6535	233	37	(	(	PUNCT
ejpam-6535	233	38	p−1)−1q	p−1)−1q	PROPN
ejpam-6535	233	39	≤	≤	PROPN
ejpam-6535	233	40	(	(	PUNCT
ejpam-6535	233	41	nφ	nφ	PROPN
ejpam-6535	233	42	p−1	p−1	PROPN
ejpam-6535	233	43	)	)	PUNCT
ejpam-6535	233	44	−1	−1	NOUN
ejpam-6535	233	45	⊙nψ	⊙nψ	NOUN
ejpam-6535	233	46	q	q	NOUN
ejpam-6535	234	1	=	=	PUNCT
ejpam-6535	234	2	nφ	nφ	PROPN
ejpam-6535	234	3	p	p	PROPN
ejpam-6535	234	4	⊙nψ	⊙nψ	PROPN
ejpam-6535	234	5	q	q	X
ejpam-6535	234	6	,	,	PUNCT
ejpam-6535	234	7	i.e.	i.e.	X
ejpam-6535	234	8	,	,	PUNCT
ejpam-6535	234	9	n	n	X
ejpam-6535	234	10	τ(φ	τ(φ	X
ejpam-6535	234	11	,	,	PUNCT
ejpam-6535	234	12	ψ	ψ	NOUN
ejpam-6535	234	13	)	)	PUNCT
ejpam-6535	234	14	pq	pq	NOUN
ejpam-6535	234	15	≤	≤	NOUN
ejpam-6535	234	16	nφ	nφ	ADP
ejpam-6535	234	17	p	p	PROPN
ejpam-6535	234	18	⊙nψ	⊙nψ	PROPN
ejpam-6535	234	19	q	q	X
ejpam-6535	234	20	.	.	PUNCT
ejpam-6535	235	1	conversely	conversely	ADV
ejpam-6535	235	2	,	,	PUNCT
ejpam-6535	235	3	we	we	PRON
ejpam-6535	235	4	prove	prove	VERB
ejpam-6535	235	5	(	(	PUNCT
ejpam-6535	235	6	pngm)+(pngi)⇒	pngm)+(pngi)⇒	ADV
ejpam-6535	235	7	(	(	PUNCT
ejpam-6535	235	8	pngm)′	pngm)′	NOUN
ejpam-6535	235	9	:	:	PUNCT
ejpam-6535	235	10	let	let	VERB
ejpam-6535	235	11	p	p	NOUN
ejpam-6535	235	12	,	,	PUNCT
ejpam-6535	235	13	q	q	PROPN
ejpam-6535	235	14	∈	∈	PROPN
ejpam-6535	235	15	s	s	NOUN
ejpam-6535	235	16	and	and	CCONJ
ejpam-6535	235	17	φ	φ	NUM
ejpam-6535	235	18	,	,	PUNCT
ejpam-6535	235	19	ψ	ψ	X
ejpam-6535	235	20	∈	∈	PROPN
ejpam-6535	235	21	∆+	∆+	NOUN
ejpam-6535	235	22	.	.	PUNCT
ejpam-6535	235	23	upon	upon	SCONJ
ejpam-6535	235	24	using	use	VERB
ejpam-6535	235	25	(	(	PUNCT
ejpam-6535	235	26	pngm	pngm	ADJ
ejpam-6535	235	27	)	)	PUNCT
ejpam-6535	235	28	and	and	CCONJ
ejpam-6535	235	29	then	then	ADV
ejpam-6535	235	30	using	use	VERB
ejpam-6535	235	31	(	(	PUNCT
ejpam-6535	235	32	pngi	pngi	PROPN
ejpam-6535	235	33	)	)	PUNCT
ejpam-6535	235	34	,	,	PUNCT
ejpam-6535	235	35	we	we	PRON
ejpam-6535	235	36	have	have	VERB
ejpam-6535	235	37	n	n	X
ejpam-6535	235	38	τ(φ	τ(φ	X
ejpam-6535	235	39	,	,	PUNCT
ejpam-6535	235	40	ψ	ψ	NOUN
ejpam-6535	235	41	)	)	PUNCT
ejpam-6535	235	42	p−1q	p−1q	NOUN
ejpam-6535	235	43	≤	≤	PROPN
ejpam-6535	235	44	nφ	nφ	ADP
ejpam-6535	235	45	p−1	p−1	PROPN
ejpam-6535	235	46	⊙	⊙	PROPN
ejpam-6535	236	1	nψ	nψ	PROPN
ejpam-6535	236	2	q	q	PROPN
ejpam-6535	236	3	≤	≤	X
ejpam-6535	236	4	(	(	PUNCT
ejpam-6535	236	5	nφ	nφ	NOUN
ejpam-6535	236	6	p	p	NOUN
ejpam-6535	236	7	)	)	PUNCT
ejpam-6535	237	1	−1	−1	NOUN
ejpam-6535	237	2	⊙	⊙	NOUN
ejpam-6535	238	1	nψ	nψ	PROPN
ejpam-6535	238	2	q	q	X
ejpam-6535	238	3	.	.	PUNCT
ejpam-6535	239	1	hence	hence	ADV
ejpam-6535	239	2	n	n	CCONJ
ejpam-6535	239	3	τ(φ	τ(φ	NUM
ejpam-6535	239	4	,	,	PUNCT
ejpam-6535	239	5	ψ	ψ	NOUN
ejpam-6535	239	6	)	)	PUNCT
ejpam-6535	239	7	p−1q	p−1q	NOUN
ejpam-6535	239	8	≤	≤	PROPN
ejpam-6535	239	9	(	(	PUNCT
ejpam-6535	239	10	nφ	nφ	NOUN
ejpam-6535	239	11	p	p	NOUN
ejpam-6535	239	12	)	)	PUNCT
ejpam-6535	239	13	−1	−1	NOUN
ejpam-6535	239	14	⊙nψ	⊙nψ	PROPN
ejpam-6535	240	1	q	q	NOUN
ejpam-6535	240	2	.	.	PUNCT
ejpam-6535	241	1	due	due	ADP
ejpam-6535	241	2	to	to	ADP
ejpam-6535	241	3	lemma	lemma	PROPN
ejpam-6535	241	4	6.5[3	6.5[3	NUM
ejpam-6535	241	5	]	]	PUNCT
ejpam-6535	241	6	and	and	CCONJ
ejpam-6535	241	7	lemma	lemma	PROPN
ejpam-6535	241	8	5	5	NUM
ejpam-6535	241	9	,	,	PUNCT
ejpam-6535	241	10	we	we	PRON
ejpam-6535	241	11	have	have	VERB
ejpam-6535	241	12	the	the	DET
ejpam-6535	241	13	following	follow	VERB
ejpam-6535	241	14	lemma	lemma	PROPN
ejpam-6535	241	15	9	9	NUM
ejpam-6535	241	16	.	.	PUNCT
ejpam-6535	242	1	if	if	SCONJ
ejpam-6535	242	2	(	(	PUNCT
ejpam-6535	242	3	s	s	X
ejpam-6535	242	4	,	,	PUNCT
ejpam-6535	242	5	·	·	PUNCT
ejpam-6535	242	6	,	,	PUNCT
ejpam-6535	242	7	nf	nf	X
ejpam-6535	242	8	φ	φ	PROPN
ejpam-6535	242	9	)	)	PUNCT
ejpam-6535	242	10	is	be	AUX
ejpam-6535	242	11	a	a	DET
ejpam-6535	242	12	probabilistic	probabilistic	ADJ
ejpam-6535	242	13	metric	metric	ADJ
ejpam-6535	242	14	topological	topological	ADJ
ejpam-6535	242	15	tardiff	tardiff	ADJ
ejpam-6535	242	16	-	-	PUNCT
ejpam-6535	242	17	neighborhood	neighborhood	NOUN
ejpam-6535	242	18	group	group	NOUN
ejpam-6535	242	19	under	under	ADP
ejpam-6535	242	20	continuous	continuous	ADJ
ejpam-6535	242	21	and	and	CCONJ
ejpam-6535	242	22	the	the	DET
ejpam-6535	242	23	largest	large	ADJ
ejpam-6535	242	24	triangle	triangle	NOUN
ejpam-6535	242	25	function	function	NOUN
ejpam-6535	242	26	τ	τ	PROPN
ejpam-6535	242	27	,	,	PUNCT
ejpam-6535	242	28	i.e.	i.e.	X
ejpam-6535	242	29	,	,	PUNCT
ejpam-6535	242	30	τ(φ	τ(φ	PROPN
ejpam-6535	242	31	,	,	PUNCT
ejpam-6535	242	32	φ	φ	NOUN
ejpam-6535	242	33	)	)	PUNCT
ejpam-6535	242	34	=	=	SYM
ejpam-6535	242	35	φ	φ	PROPN
ejpam-6535	242	36	,	,	PUNCT
ejpam-6535	242	37	then	then	ADV
ejpam-6535	242	38	it	it	PRON
ejpam-6535	242	39	is	be	AUX
ejpam-6535	242	40	a	a	DET
ejpam-6535	242	41	probabilistic	probabilistic	ADJ
ejpam-6535	242	42	topological	topological	ADJ
ejpam-6535	242	43	neighborhood	neighborhood	NOUN
ejpam-6535	242	44	group	group	NOUN
ejpam-6535	242	45	.	.	PUNCT
ejpam-6535	243	1	proof	proof	NOUN
ejpam-6535	243	2	.	.	PUNCT
ejpam-6535	244	1	we	we	PRON
ejpam-6535	244	2	only	only	ADV
ejpam-6535	244	3	need	need	AUX
ejpam-6535	244	4	check	check	VERB
ejpam-6535	244	5	the	the	DET
ejpam-6535	244	6	continuity	continuity	NOUN
ejpam-6535	244	7	of	of	ADP
ejpam-6535	244	8	the	the	DET
ejpam-6535	244	9	group	group	NOUN
ejpam-6535	244	10	operations	operation	NOUN
ejpam-6535	244	11	.	.	PUNCT
ejpam-6535	245	1	but	but	CCONJ
ejpam-6535	245	2	that	that	PRON
ejpam-6535	245	3	follows	follow	VERB
ejpam-6535	245	4	from	from	ADP
ejpam-6535	245	5	lemma	lemma	PROPN
ejpam-6535	245	6	6.5[3	6.5[3	NUM
ejpam-6535	245	7	]	]	X
ejpam-6535	245	8	in	in	ADP
ejpam-6535	245	9	conjunction	conjunction	NOUN
ejpam-6535	245	10	with	with	ADP
ejpam-6535	245	11	lemma	lemma	PROPN
ejpam-6535	245	12	8	8	NUM
ejpam-6535	245	13	,	,	PUNCT
ejpam-6535	245	14	i.e.	i.e.	X
ejpam-6535	245	15	,	,	PUNCT
ejpam-6535	245	16	for	for	ADP
ejpam-6535	245	17	any	any	DET
ejpam-6535	245	18	p	p	NOUN
ejpam-6535	245	19	,	,	PUNCT
ejpam-6535	245	20	q	q	PROPN
ejpam-6535	245	21	∈	∈	PROPN
ejpam-6535	245	22	s	s	X
ejpam-6535	245	23	and	and	CCONJ
ejpam-6535	245	24	ψ	ψ	NOUN
ejpam-6535	245	25	,	,	PUNCT
ejpam-6535	245	26	ψ	ψ	NOUN
ejpam-6535	245	27	∈	∈	PROPN
ejpam-6535	245	28	∆+	∆+	NUM
ejpam-6535	245	29	that	that	SCONJ
ejpam-6535	245	30	n	n	CCONJ
ejpam-6535	245	31	τ(φ	τ(φ	X
ejpam-6535	245	32	,	,	PUNCT
ejpam-6535	245	33	ψ	ψ	NOUN
ejpam-6535	245	34	)	)	PUNCT
ejpam-6535	245	35	p−1q	p−1q	NOUN
ejpam-6535	245	36	≤	≤	PROPN
ejpam-6535	245	37	(	(	PUNCT
ejpam-6535	245	38	nφ	nφ	NOUN
ejpam-6535	245	39	p	p	NOUN
ejpam-6535	245	40	)	)	PUNCT
ejpam-6535	245	41	−1	−1	NOUN
ejpam-6535	245	42	⊙nψ	⊙nψ	PROPN
ejpam-6535	246	1	q	q	X
ejpam-6535	246	2	.	.	PUNCT
ejpam-6535	247	1	lemma	lemma	PROPN
ejpam-6535	247	2	10	10	NUM
ejpam-6535	247	3	.	.	PUNCT
ejpam-6535	248	1	let	let	VERB
ejpam-6535	248	2	(	(	PUNCT
ejpam-6535	248	3	s	s	X
ejpam-6535	248	4	,	,	PUNCT
ejpam-6535	248	5	n	n	NOUN
ejpam-6535	248	6	=	=	SYM
ejpam-6535	248	7	(	(	PUNCT
ejpam-6535	248	8	nφ	nφ	PROPN
ejpam-6535	248	9	p	p	NOUN
ejpam-6535	248	10	)	)	PUNCT
ejpam-6535	248	11	(	(	PUNCT
ejpam-6535	248	12	p	p	X
ejpam-6535	248	13	,	,	PUNCT
ejpam-6535	248	14	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	248	15	)	)	PUNCT
ejpam-6535	248	16	be	be	AUX
ejpam-6535	248	17	a	a	DET
ejpam-6535	248	18	probabilistic	probabilistic	ADJ
ejpam-6535	248	19	neighborhood	neighborhood	NOUN
ejpam-6535	248	20	space	space	NOUN
ejpam-6535	248	21	.	.	PUNCT
ejpam-6535	249	1	if	if	SCONJ
ejpam-6535	249	2	τ(φ	τ(φ	PROPN
ejpam-6535	249	3	,	,	PUNCT
ejpam-6535	249	4	φ	φ	NUM
ejpam-6535	249	5	)	)	PUNCT
ejpam-6535	249	6	=	=	SYM
ejpam-6535	249	7	φ	φ	PROPN
ejpam-6535	249	8	for	for	ADP
ejpam-6535	249	9	all	all	DET
ejpam-6535	249	10	φ	φ	PROPN
ejpam-6535	249	11	∈	∈	PROPN
ejpam-6535	249	12	∆+	∆+	NOUN
ejpam-6535	249	13	.	.	PUNCT
ejpam-6535	250	1	then	then	ADV
ejpam-6535	250	2	(	(	PUNCT
ejpam-6535	250	3	s	s	X
ejpam-6535	250	4	,	,	PUNCT
ejpam-6535	250	5	·	·	PUNCT
ejpam-6535	250	6	,	,	PUNCT
ejpam-6535	250	7	n	n	CCONJ
ejpam-6535	250	8	)	)	PUNCT
ejpam-6535	250	9	is	be	AUX
ejpam-6535	250	10	a	a	DET
ejpam-6535	250	11	probabilistic	probabilistic	ADJ
ejpam-6535	250	12	neighborhood	neighborhood	NOUN
ejpam-6535	250	13	group	group	NOUN
ejpam-6535	250	14	under	under	ADP
ejpam-6535	250	15	a	a	DET
ejpam-6535	250	16	triangle	triangle	NOUN
ejpam-6535	250	17	function	function	NOUN
ejpam-6535	250	18	τ	τ	X
ejpam-6535	250	19	if	if	SCONJ
ejpam-6535	251	1	and	and	CCONJ
ejpam-6535	251	2	only	only	ADV
ejpam-6535	251	3	if	if	SCONJ
ejpam-6535	251	4	m	m	ADV
ejpam-6535	251	5	:	:	PUNCT
ejpam-6535	251	6	(	(	PUNCT
ejpam-6535	251	7	s	s	NUM
ejpam-6535	251	8	×	×	NOUN
ejpam-6535	251	9	s	s	NOUN
ejpam-6535	251	10	,	,	PUNCT
ejpam-6535	251	11	n×n	n×n	PROPN
ejpam-6535	251	12	)	)	PUNCT
ejpam-6535	251	13	−→	−→	NOUN
ejpam-6535	251	14	(	(	PUNCT
ejpam-6535	251	15	s	s	NOUN
ejpam-6535	251	16	,	,	PUNCT
ejpam-6535	251	17	n	n	CCONJ
ejpam-6535	251	18	)	)	PUNCT
ejpam-6535	251	19	,	,	PUNCT
ejpam-6535	251	20	(	(	PUNCT
ejpam-6535	251	21	p	p	X
ejpam-6535	251	22	,	,	PUNCT
ejpam-6535	251	23	q	q	NOUN
ejpam-6535	251	24	)	)	PUNCT
ejpam-6535	251	25	7−→	7−→	NOUN
ejpam-6535	251	26	pq	pq	NOUN
ejpam-6535	251	27	and	and	CCONJ
ejpam-6535	251	28	ȷ	ȷ	NOUN
ejpam-6535	251	29	:	:	PUNCT
ejpam-6535	251	30	(	(	PUNCT
ejpam-6535	251	31	s	s	X
ejpam-6535	251	32	,	,	PUNCT
ejpam-6535	251	33	n	n	CCONJ
ejpam-6535	251	34	)	)	PUNCT
ejpam-6535	251	35	−→	−→	NOUN
ejpam-6535	251	36	(	(	PUNCT
ejpam-6535	251	37	s	s	NOUN
ejpam-6535	251	38	,	,	PUNCT
ejpam-6535	251	39	n	n	CCONJ
ejpam-6535	251	40	)	)	PUNCT
ejpam-6535	251	41	,	,	PUNCT
ejpam-6535	251	42	p	p	PROPN
ejpam-6535	251	43	7−→	7−→	PROPN
ejpam-6535	251	44	p−1	p−1	PROPN
ejpam-6535	251	45	are	be	AUX
ejpam-6535	251	46	continuous	continuous	ADJ
ejpam-6535	251	47	.	.	PUNCT
ejpam-6535	252	1	proof	proof	NOUN
ejpam-6535	252	2	.	.	PUNCT
ejpam-6535	253	1	letw	letw	NOUN
ejpam-6535	253	2	τ(φ	τ(φ	PROPN
ejpam-6535	253	3	,	,	PUNCT
ejpam-6535	253	4	ψ	ψ	NOUN
ejpam-6535	253	5	)	)	PUNCT
ejpam-6535	253	6	pq	pq	NOUN
ejpam-6535	253	7	∈	∈	PROPN
ejpam-6535	253	8	n	n	CCONJ
ejpam-6535	253	9	τ(φ	τ(φ	X
ejpam-6535	253	10	,	,	PUNCT
ejpam-6535	253	11	ψ	ψ	NOUN
ejpam-6535	253	12	)	)	PUNCT
ejpam-6535	253	13	pq	pq	INTJ
ejpam-6535	253	14	.	.	PUNCT
ejpam-6535	254	1	sincem	sincem	PROPN
ejpam-6535	254	2	is	be	AUX
ejpam-6535	254	3	continuous	continuous	ADJ
ejpam-6535	254	4	,	,	PUNCT
ejpam-6535	254	5	we	we	PRON
ejpam-6535	254	6	choose	choose	VERB
ejpam-6535	254	7	uφp	uφp	NOUN
ejpam-6535	254	8	∈	∈	PROPN
ejpam-6535	254	9	nφ	nφ	ADP
ejpam-6535	254	10	p	p	PROPN
ejpam-6535	254	11	and	and	CCONJ
ejpam-6535	254	12	v	v	ADP
ejpam-6535	254	13	ψ	ψ	X
ejpam-6535	254	14	q	q	X
ejpam-6535	254	15	∈	∈	PROPN
ejpam-6535	255	1	nψ	nψ	NOUN
ejpam-6535	255	2	q	q	NOUN
ejpam-6535	255	3	such	such	ADJ
ejpam-6535	255	4	that	that	DET
ejpam-6535	255	5	uφp	uφp	NOUN
ejpam-6535	255	6	⊙v	⊙v	NOUN
ejpam-6535	255	7	ψ	ψ	NOUN
ejpam-6535	255	8	q	q	NOUN
ejpam-6535	255	9	⊆w	⊆w	NOUN
ejpam-6535	255	10	τ(φ	τ(φ	NUM
ejpam-6535	255	11	,	,	PUNCT
ejpam-6535	255	12	ψ	ψ	NOUN
ejpam-6535	255	13	)	)	PUNCT
ejpam-6535	255	14	pq	pq	INTJ
ejpam-6535	255	15	.	.	PUNCT
ejpam-6535	256	1	this	this	PRON
ejpam-6535	256	2	implies	imply	VERB
ejpam-6535	256	3	w	w	ADP
ejpam-6535	256	4	τ(φ	τ(φ	PROPN
ejpam-6535	256	5	,	,	PUNCT
ejpam-6535	256	6	ψ	ψ	X
ejpam-6535	256	7	pq	pq	NOUN
ejpam-6535	256	8	∈	∈	PROPN
ejpam-6535	256	9	n	n	CCONJ
ejpam-6535	256	10	τ(φ	τ(φ	X
ejpam-6535	256	11	,	,	PUNCT
ejpam-6535	256	12	ψ	ψ	NOUN
ejpam-6535	256	13	)	)	PUNCT
ejpam-6535	256	14	pq	pq	INTJ
ejpam-6535	256	15	.	.	PUNCT
ejpam-6535	257	1	hence	hence	ADV
ejpam-6535	257	2	n	n	CCONJ
ejpam-6535	257	3	τ(φ	τ(φ	NUM
ejpam-6535	257	4	,	,	PUNCT
ejpam-6535	257	5	ψ	ψ	NOUN
ejpam-6535	257	6	)	)	PUNCT
ejpam-6535	257	7	pq	pq	NOUN
ejpam-6535	257	8	≤	≤	NOUN
ejpam-6535	257	9	nφ	nφ	ADP
ejpam-6535	257	10	p	p	PROPN
ejpam-6535	257	11	⊙nψ	⊙nψ	PROPN
ejpam-6535	257	12	q	q	X
ejpam-6535	257	13	.	.	PUNCT
ejpam-6535	258	1	conversely	conversely	ADV
ejpam-6535	258	2	,	,	PUNCT
ejpam-6535	258	3	we	we	PRON
ejpam-6535	258	4	need	need	AUX
ejpam-6535	258	5	show	show	VERB
ejpam-6535	258	6	the	the	DET
ejpam-6535	258	7	mapping	mapping	NOUN
ejpam-6535	258	8	m	m	NOUN
ejpam-6535	258	9	is	be	AUX
ejpam-6535	258	10	continuous	continuous	ADJ
ejpam-6535	258	11	.	.	PUNCT
ejpam-6535	259	1	for	for	ADP
ejpam-6535	259	2	,	,	PUNCT
ejpam-6535	259	3	let	let	VERB
ejpam-6535	259	4	w	w	PROPN
ejpam-6535	259	5	∈	∈	PROPN
ejpam-6535	259	6	nφ	nφ	PROPN
ejpam-6535	259	7	pq	pq	PROPN
ejpam-6535	259	8	,	,	PUNCT
ejpam-6535	259	9	i.e.	i.e.	X
ejpam-6535	259	10	,	,	PUNCT
ejpam-6535	259	11	w	w	PROPN
ejpam-6535	259	12	∈	∈	PROPN
ejpam-6535	259	13	n	n	CCONJ
ejpam-6535	259	14	τ(φ	τ(φ	NUM
ejpam-6535	259	15	,	,	PUNCT
ejpam-6535	259	16	φ	φ	NOUN
ejpam-6535	259	17	)	)	PUNCT
ejpam-6535	259	18	pq	pq	PROPN
ejpam-6535	259	19	,	,	PUNCT
ejpam-6535	259	20	implying	imply	VERB
ejpam-6535	259	21	w	w	PRON
ejpam-6535	259	22	∈	∈	PROPN
ejpam-6535	259	23	nφ	nφ	ADP
ejpam-6535	259	24	p	p	PROPN
ejpam-6535	259	25	⊙	⊙	PROPN
ejpam-6535	260	1	nψ	nψ	INTJ
ejpam-6535	260	2	q	q	PROPN
ejpam-6535	261	1	=	=	VERB
ejpam-6535	261	2	m	m	PROPN
ejpam-6535	261	3	(	(	PUNCT
ejpam-6535	261	4	nφ	nφ	PROPN
ejpam-6535	261	5	p	p	PROPN
ejpam-6535	261	6	×nφ	×nφ	NOUN
ejpam-6535	261	7	q	q	PROPN
ejpam-6535	261	8	)	)	PUNCT
ejpam-6535	261	9	.	.	PUNCT
ejpam-6535	262	1	consequently	consequently	ADV
ejpam-6535	262	2	,	,	PUNCT
ejpam-6535	262	3	there	there	PRON
ejpam-6535	262	4	are	be	VERB
ejpam-6535	262	5	u	u	NOUN
ejpam-6535	262	6	∈	∈	PROPN
ejpam-6535	262	7	nφ	nφ	ADP
ejpam-6535	262	8	p	p	PROPN
ejpam-6535	262	9	and	and	CCONJ
ejpam-6535	262	10	v	v	ADP
ejpam-6535	262	11	∈	∈	PROPN
ejpam-6535	262	12	nφ	nφ	ADP
ejpam-6535	262	13	q	q	NOUN
ejpam-6535	262	14	such	such	ADJ
ejpam-6535	262	15	that	that	SCONJ
ejpam-6535	262	16	m(u	m(u	PROPN
ejpam-6535	262	17	×	×	NOUN
ejpam-6535	262	18	v	v	NOUN
ejpam-6535	262	19	)	)	PUNCT
ejpam-6535	262	20	⊆w	⊆w	NOUN
ejpam-6535	262	21	.	.	PUNCT
ejpam-6535	263	1	lemma	lemma	PROPN
ejpam-6535	263	2	11	11	NUM
ejpam-6535	263	3	.	.	PUNCT
ejpam-6535	264	1	let	let	VERB
ejpam-6535	264	2	(	(	PUNCT
ejpam-6535	264	3	s	s	X
ejpam-6535	264	4	,	,	PUNCT
ejpam-6535	264	5	·	·	PUNCT
ejpam-6535	264	6	,	,	PUNCT
ejpam-6535	264	7	n	n	CCONJ
ejpam-6535	264	8	)	)	PUNCT
ejpam-6535	264	9	be	be	AUX
ejpam-6535	264	10	a	a	DET
ejpam-6535	264	11	probabilistic	probabilistic	ADJ
ejpam-6535	264	12	neighborhood	neighborhood	NOUN
ejpam-6535	264	13	group	group	NOUN
ejpam-6535	264	14	and	and	CCONJ
ejpam-6535	264	15	x	x	SYM
ejpam-6535	264	16	∈	∈	PROPN
ejpam-6535	264	17	s.	s.	PROPN
ejpam-6535	264	18	then	then	ADV
ejpam-6535	264	19	(	(	PUNCT
ejpam-6535	264	20	1	1	X
ejpam-6535	264	21	)	)	PUNCT
ejpam-6535	264	22	the	the	DET
ejpam-6535	264	23	lx	lx	NOUN
ejpam-6535	264	24	:	:	PUNCT
ejpam-6535	264	25	s	s	AUX
ejpam-6535	264	26	−→	−→	NOUN
ejpam-6535	264	27	s	s	NOUN
ejpam-6535	264	28	,	,	PUNCT
ejpam-6535	264	29	z	z	PROPN
ejpam-6535	264	30	7−→	7−→	NOUN
ejpam-6535	264	31	zx	zx	NUM
ejpam-6535	264	32	the	the	DET
ejpam-6535	264	33	left	left	NOUN
ejpam-6535	264	34	and	and	CCONJ
ejpam-6535	264	35	rx	rx	VERB
ejpam-6535	264	36	:	:	PUNCT
ejpam-6535	264	37	s	s	VERB
ejpam-6535	264	38	−→	−→	NOUN
ejpam-6535	264	39	s	s	NOUN
ejpam-6535	264	40	,	,	PUNCT
ejpam-6535	264	41	z	z	PROPN
ejpam-6535	264	42	7−→	7−→	PROPN
ejpam-6535	264	43	xz	xz	NOUN
ejpam-6535	264	44	the	the	DET
ejpam-6535	264	45	right	right	ADJ
ejpam-6535	264	46	translations	translation	NOUN
ejpam-6535	264	47	,	,	PUNCT
ejpam-6535	264	48	and	and	CCONJ
ejpam-6535	265	1	the	the	DET
ejpam-6535	265	2	inversion	inversion	NOUN
ejpam-6535	265	3	mapping	mapping	NOUN
ejpam-6535	265	4	ȷ	ȷ	NOUN
ejpam-6535	265	5	:	:	PUNCT
ejpam-6535	265	6	s	s	AUX
ejpam-6535	265	7	−→	−→	NOUN
ejpam-6535	265	8	s	s	NOUN
ejpam-6535	265	9	,	,	PUNCT
ejpam-6535	265	10	z	z	NOUN
ejpam-6535	265	11	7−→	7−→	PROPN
ejpam-6535	265	12	z−1	z−1	PROPN
ejpam-6535	265	13	are	be	AUX
ejpam-6535	265	14	homeomorphisms	homeomorphism	NOUN
ejpam-6535	265	15	;	;	PUNCT
ejpam-6535	265	16	(	(	PUNCT
ejpam-6535	265	17	2	2	X
ejpam-6535	265	18	)	)	PUNCT
ejpam-6535	265	19	the	the	DET
ejpam-6535	265	20	inner	inner	ADJ
ejpam-6535	265	21	automorphism	automorphism	NOUN
ejpam-6535	265	22	operator	operator	NOUN
ejpam-6535	265	23	ix	ix	X
ejpam-6535	265	24	:	:	PUNCT
ejpam-6535	265	25	s	s	VERB
ejpam-6535	265	26	−→	−→	NOUN
ejpam-6535	265	27	s	s	NOUN
ejpam-6535	265	28	,	,	PUNCT
ejpam-6535	265	29	z	z	NOUN
ejpam-6535	265	30	7−→	7−→	NOUN
ejpam-6535	265	31	xzx−1	xzx−1	X
ejpam-6535	265	32	is	be	AUX
ejpam-6535	265	33	an	an	DET
ejpam-6535	265	34	isomorphism	isomorphism	NOUN
ejpam-6535	265	35	;	;	PUNCT
ejpam-6535	265	36	(	(	PUNCT
ejpam-6535	265	37	3	3	X
ejpam-6535	265	38	)	)	PUNCT
ejpam-6535	265	39	the	the	DET
ejpam-6535	265	40	mapping	mapping	NOUN
ejpam-6535	265	41	t(a	t(a	PROPN
ejpam-6535	265	42	,	,	PUNCT
ejpam-6535	265	43	b	b	NOUN
ejpam-6535	265	44	)	)	PUNCT
ejpam-6535	265	45	:	:	PUNCT
ejpam-6535	265	46	s	s	VERB
ejpam-6535	265	47	−→	−→	NOUN
ejpam-6535	265	48	s	s	NOUN
ejpam-6535	265	49	,	,	PUNCT
ejpam-6535	265	50	z	z	PROPN
ejpam-6535	265	51	7−→	7−→	PROPN
ejpam-6535	265	52	azb	azb	PROPN
ejpam-6535	265	53	is	be	AUX
ejpam-6535	265	54	a	a	DET
ejpam-6535	265	55	homeomorphism	homeomorphism	NOUN
ejpam-6535	265	56	;	;	PUNCT
ejpam-6535	265	57	(	(	PUNCT
ejpam-6535	265	58	4	4	X
ejpam-6535	265	59	)	)	PUNCT
ejpam-6535	266	1	n	n	NOUN
ejpam-6535	266	2	∈	∈	PROPN
ejpam-6535	266	3	nφ	nφ	ADP
ejpam-6535	266	4	e	e	X
ejpam-6535	266	5	⇐	⇐	PROPN
ejpam-6535	266	6	⇒	⇒	PROPN
ejpam-6535	266	7	n−1	n−1	PROPN
ejpam-6535	266	8	∈	∈	PROPN
ejpam-6535	266	9	nφ	nφ	PROPN
ejpam-6535	266	10	e	e	PROPN
ejpam-6535	266	11	,	,	PUNCT
ejpam-6535	266	12	or	or	CCONJ
ejpam-6535	266	13	alternatively	alternatively	ADV
ejpam-6535	266	14	,	,	PUNCT
ejpam-6535	266	15	(	(	PUNCT
ejpam-6535	266	16	nφ	nφ	PROPN
ejpam-6535	266	17	e	e	NOUN
ejpam-6535	266	18	)	)	PUNCT
ejpam-6535	266	19	−1	−1	NOUN
ejpam-6535	266	20	=	=	SYM
ejpam-6535	266	21	nφ	nφ	PROPN
ejpam-6535	266	22	e	e	PROPN
ejpam-6535	266	23	,	,	PUNCT
ejpam-6535	266	24	for	for	ADP
ejpam-6535	266	25	all	all	DET
ejpam-6535	266	26	φ	φ	PROPN
ejpam-6535	266	27	∈	∈	PROPN
ejpam-6535	266	28	∆+	∆+	NOUN
ejpam-6535	266	29	;	;	PUNCT
ejpam-6535	266	30	(	(	PUNCT
ejpam-6535	266	31	5	5	X
ejpam-6535	266	32	)	)	PUNCT
ejpam-6535	266	33	n	n	NOUN
ejpam-6535	266	34	∈	∈	NOUN
ejpam-6535	266	35	nφ	nφ	NOUN
ejpam-6535	266	36	x	x	SYM
ejpam-6535	266	37	⇐	⇐	ADJ
ejpam-6535	266	38	⇒	⇒	PROPN
ejpam-6535	266	39	x−1	x−1	PUNCT
ejpam-6535	267	1	⊙n	⊙n	PROPN
ejpam-6535	267	2	∈	∈	PROPN
ejpam-6535	267	3	nφ	nφ	ADP
ejpam-6535	267	4	e	e	X
ejpam-6535	267	5	⇐	⇐	PROPN
ejpam-6535	267	6	⇒	⇒	PROPN
ejpam-6535	267	7	n	n	X
ejpam-6535	267	8	⊙	⊙	NOUN
ejpam-6535	267	9	x−1	x−1	PROPN
ejpam-6535	268	1	∈	∈	PROPN
ejpam-6535	268	2	nφ	nφ	PROPN
ejpam-6535	268	3	e	e	PROPN
ejpam-6535	268	4	,	,	PUNCT
ejpam-6535	268	5	or	or	CCONJ
ejpam-6535	268	6	alternatively	alternatively	ADV
ejpam-6535	268	7	,	,	PUNCT
ejpam-6535	268	8	nφ	nφ	ADP
ejpam-6535	268	9	p	p	NOUN
ejpam-6535	269	1	=	=	PUNCT
ejpam-6535	269	2	[	[	X
ejpam-6535	269	3	p−1]⊙nφ	p−1]⊙nφ	X
ejpam-6535	269	4	e	e	NOUN
ejpam-6535	269	5	=	=	VERB
ejpam-6535	269	6	nφ	nφ	PROPN
ejpam-6535	269	7	e	e	PROPN
ejpam-6535	269	8	⊙	⊙	NOUN
ejpam-6535	270	1	[	[	X
ejpam-6535	270	2	p−1	p−1	PROPN
ejpam-6535	270	3	]	]	PUNCT
ejpam-6535	270	4	,	,	PUNCT
ejpam-6535	270	5	for	for	ADP
ejpam-6535	270	6	all	all	PRON
ejpam-6535	270	7	p	p	NOUN
ejpam-6535	270	8	∈	∈	PROPN
ejpam-6535	270	9	s	s	NOUN
ejpam-6535	270	10	and	and	CCONJ
ejpam-6535	270	11	for	for	ADP
ejpam-6535	270	12	all	all	DET
ejpam-6535	270	13	φ	φ	NOUN
ejpam-6535	270	14	∈	∈	PROPN
ejpam-6535	270	15	∆	∆	X
ejpam-6535	270	16	;	;	PUNCT
ejpam-6535	270	17	(	(	PUNCT
ejpam-6535	270	18	6	6	NUM
ejpam-6535	270	19	)	)	PUNCT
ejpam-6535	271	1	n	n	NOUN
ejpam-6535	271	2	∈	∈	PROPN
ejpam-6535	271	3	nφ	nφ	ADP
ejpam-6535	271	4	e	e	X
ejpam-6535	271	5	⇐	⇐	PROPN
ejpam-6535	271	6	⇒	⇒	PROPN
ejpam-6535	271	7	x⊙n	x⊙n	PROPN
ejpam-6535	271	8	∈	∈	PROPN
ejpam-6535	271	9	nφ	nφ	ADP
ejpam-6535	271	10	x	x	INTJ
ejpam-6535	271	11	⇐	⇐	ADJ
ejpam-6535	271	12	⇒	⇒	NOUN
ejpam-6535	271	13	n	n	X
ejpam-6535	271	14	⊙	⊙	X
ejpam-6535	271	15	x	x	PUNCT
ejpam-6535	271	16	∈	∈	PROPN
ejpam-6535	271	17	nφ	nφ	NOUN
ejpam-6535	271	18	x	x	X
ejpam-6535	271	19	,	,	PUNCT
ejpam-6535	271	20	or	or	CCONJ
ejpam-6535	271	21	alternatively	alternatively	ADV
ejpam-6535	271	22	,	,	PUNCT
ejpam-6535	271	23	nφ	nφ	PROPN
ejpam-6535	271	24	e	e	NOUN
ejpam-6535	271	25	=	=	PUNCT
ejpam-6535	272	1	[	[	X
ejpam-6535	272	2	p]⊙nφ	p]⊙nφ	X
ejpam-6535	272	3	p	p	X
ejpam-6535	272	4	=	=	PROPN
ejpam-6535	272	5	nφ	nφ	PROPN
ejpam-6535	272	6	p	p	NOUN
ejpam-6535	272	7	⊙	⊙	NOUN
ejpam-6535	273	1	[	[	X
ejpam-6535	273	2	p	p	X
ejpam-6535	273	3	]	]	X
ejpam-6535	273	4	,	,	PUNCT
ejpam-6535	273	5	for	for	ADP
ejpam-6535	273	6	all	all	PRON
ejpam-6535	273	7	p	p	NOUN
ejpam-6535	273	8	∈	∈	PROPN
ejpam-6535	273	9	s	s	NOUN
ejpam-6535	273	10	and	and	CCONJ
ejpam-6535	273	11	for	for	ADP
ejpam-6535	273	12	all	all	DET
ejpam-6535	273	13	φ	φ	NOUN
ejpam-6535	273	14	∈	∈	PROPN
ejpam-6535	273	15	∆.	∆.	ADJ
ejpam-6535	273	16	proof	proof	NOUN
ejpam-6535	273	17	.	.	PUNCT
ejpam-6535	273	18	follows	follow	VERB
ejpam-6535	273	19	almost	almost	ADV
ejpam-6535	273	20	similar	similar	ADJ
ejpam-6535	273	21	way	way	NOUN
ejpam-6535	273	22	as	as	ADP
ejpam-6535	273	23	in	in	ADP
ejpam-6535	273	24	classical	classical	ADJ
ejpam-6535	273	25	cases	case	NOUN
ejpam-6535	273	26	(	(	PUNCT
ejpam-6535	273	27	see	see	VERB
ejpam-6535	273	28	f.i	f.i	NOUN
ejpam-6535	273	29	.	.	PUNCT
ejpam-6535	274	1	[	[	X
ejpam-6535	274	2	13	13	NUM
ejpam-6535	274	3	,	,	PUNCT
ejpam-6535	274	4	15	15	NUM
ejpam-6535	274	5	]	]	NUM
ejpam-6535	274	6	)	)	PUNCT
ejpam-6535	274	7	.	.	PUNCT
ejpam-6535	275	1	definition	definition	NOUN
ejpam-6535	275	2	7	7	NUM
ejpam-6535	275	3	.	.	PUNCT
ejpam-6535	276	1	[	[	X
ejpam-6535	276	2	3	3	X
ejpam-6535	276	3	]	]	PUNCT
ejpam-6535	276	4	a	a	DET
ejpam-6535	276	5	triple	triple	ADJ
ejpam-6535	276	6	(	(	PUNCT
ejpam-6535	276	7	s	s	PROPN
ejpam-6535	276	8	,	,	PUNCT
ejpam-6535	276	9	·	·	PUNCT
ejpam-6535	276	10	,	,	PUNCT
ejpam-6535	276	11	c	c	X
ejpam-6535	276	12	=	=	SYM
ejpam-6535	276	13	(	(	PUNCT
ejpam-6535	276	14	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	276	15	)	)	PUNCT
ejpam-6535	276	16	is	be	AUX
ejpam-6535	276	17	called	call	VERB
ejpam-6535	276	18	a	a	DET
ejpam-6535	276	19	probabilistic	probabilistic	ADJ
ejpam-6535	276	20	convergence	convergence	NOUN
ejpam-6535	276	21	group	group	NOUN
ejpam-6535	276	22	under	under	ADP
ejpam-6535	276	23	the	the	DET
ejpam-6535	276	24	triangle	triangle	NOUN
ejpam-6535	276	25	function	function	NOUN
ejpam-6535	276	26	τ	τ	X
ejpam-6535	276	27	if	if	SCONJ
ejpam-6535	276	28	for	for	ADP
ejpam-6535	276	29	all	all	DET
ejpam-6535	276	30	φ	φ	NOUN
ejpam-6535	276	31	,	,	PUNCT
ejpam-6535	276	32	ψ	ψ	X
ejpam-6535	276	33	∈	∈	PROPN
ejpam-6535	276	34	∆+	∆+	NUM
ejpam-6535	276	35	and	and	CCONJ
ejpam-6535	276	36	for	for	ADP
ejpam-6535	276	37	all	all	DET
ejpam-6535	276	38	f	f	NOUN
ejpam-6535	276	39	,	,	PUNCT
ejpam-6535	276	40	g	g	PROPN
ejpam-6535	276	41	∈	∈	PROPN
ejpam-6535	276	42	f(s	f(	VERB
ejpam-6535	276	43	)	)	PUNCT
ejpam-6535	276	44	(	(	PUNCT
ejpam-6535	276	45	pcg1	pcg1	ADJ
ejpam-6535	276	46	)	)	PUNCT
ejpam-6535	276	47	(	(	PUNCT
ejpam-6535	276	48	s	s	X
ejpam-6535	276	49	,	,	PUNCT
ejpam-6535	276	50	·	·	PUNCT
ejpam-6535	276	51	)	)	PUNCT
ejpam-6535	276	52	is	be	AUX
ejpam-6535	276	53	a	a	DET
ejpam-6535	276	54	group	group	NOUN
ejpam-6535	276	55	;	;	PUNCT
ejpam-6535	276	56	(	(	PUNCT
ejpam-6535	276	57	pcg2	pcg2	NOUN
ejpam-6535	276	58	)	)	PUNCT
ejpam-6535	276	59	(	(	PUNCT
ejpam-6535	276	60	s	s	X
ejpam-6535	276	61	,	,	PUNCT
ejpam-6535	276	62	c	c	NOUN
ejpam-6535	276	63	)	)	PUNCT
ejpam-6535	276	64	is	be	AUX
ejpam-6535	276	65	a	a	DET
ejpam-6535	276	66	probabilistic	probabilistic	ADJ
ejpam-6535	276	67	convergence	convergence	NOUN
ejpam-6535	276	68	space	space	NOUN
ejpam-6535	276	69	;	;	PUNCT
ejpam-6535	276	70	(	(	PUNCT
ejpam-6535	276	71	pcgm	pcgm	NOUN
ejpam-6535	276	72	)	)	PUNCT
ejpam-6535	276	73	pq	pq	NOUN
ejpam-6535	276	74	∈	∈	PROPN
ejpam-6535	276	75	cτ(φ	cτ(φ	PRON
ejpam-6535	276	76	,	,	PUNCT
ejpam-6535	276	77	ψ)(f⊙g	ψ)(f⊙g	PROPN
ejpam-6535	276	78	)	)	PUNCT
ejpam-6535	276	79	whenever	whenever	SCONJ
ejpam-6535	276	80	p	p	PRON
ejpam-6535	276	81	∈	∈	PROPN
ejpam-6535	276	82	cφ(f	cφ(f	PUNCT
ejpam-6535	276	83	)	)	PUNCT
ejpam-6535	276	84	and	and	CCONJ
ejpam-6535	276	85	q	q	PROPN
ejpam-6535	276	86	∈	∈	PROPN
ejpam-6535	276	87	cψ(g	cψ(g	NOUN
ejpam-6535	276	88	)	)	PUNCT
ejpam-6535	276	89	;	;	PUNCT
ejpam-6535	276	90	(	(	PUNCT
ejpam-6535	276	91	pcgi	pcgi	NOUN
ejpam-6535	276	92	)	)	PUNCT
ejpam-6535	276	93	p−1	p−1	PROPN
ejpam-6535	276	94	∈	∈	PROPN
ejpam-6535	276	95	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	276	96	)	)	PUNCT
ejpam-6535	276	97	whenever	whenever	SCONJ
ejpam-6535	276	98	p	p	PRON
ejpam-6535	276	99	∈	∈	PROPN
ejpam-6535	276	100	cφ(f	cφ(f	PUNCT
ejpam-6535	276	101	)	)	PUNCT
ejpam-6535	276	102	.	.	PUNCT
ejpam-6535	277	1	furthermore	furthermore	ADV
ejpam-6535	277	2	,	,	PUNCT
ejpam-6535	277	3	if	if	SCONJ
ejpam-6535	277	4	we	we	PRON
ejpam-6535	277	5	consider	consider	VERB
ejpam-6535	277	6	in	in	ADP
ejpam-6535	277	7	(	(	PUNCT
ejpam-6535	277	8	pcg2	pcg2	NOUN
ejpam-6535	277	9	)	)	PUNCT
ejpam-6535	277	10	,	,	PUNCT
ejpam-6535	277	11	(	(	PUNCT
ejpam-6535	277	12	s	s	X
ejpam-6535	277	13	,	,	PUNCT
ejpam-6535	277	14	c	c	NOUN
ejpam-6535	277	15	)	)	PUNCT
ejpam-6535	277	16	a	a	DET
ejpam-6535	277	17	probabilistic	probabilistic	ADJ
ejpam-6535	277	18	limit	limit	NOUN
ejpam-6535	277	19	space	space	NOUN
ejpam-6535	277	20	,	,	PUNCT
ejpam-6535	277	21	then	then	ADV
ejpam-6535	277	22	the	the	DET
ejpam-6535	277	23	triple	triple	ADJ
ejpam-6535	277	24	(	(	PUNCT
ejpam-6535	277	25	s	s	PROPN
ejpam-6535	277	26	,	,	PUNCT
ejpam-6535	277	27	·	·	PUNCT
ejpam-6535	277	28	,	,	PUNCT
ejpam-6535	277	29	c	c	X
ejpam-6535	277	30	=	=	SYM
ejpam-6535	277	31	(	(	PUNCT
ejpam-6535	277	32	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	277	33	)	)	PUNCT
ejpam-6535	277	34	is	be	AUX
ejpam-6535	277	35	called	call	VERB
ejpam-6535	277	36	a	a	DET
ejpam-6535	277	37	probabilistic	probabilistic	ADJ
ejpam-6535	277	38	limit	limit	NOUN
ejpam-6535	277	39	group	group	NOUN
ejpam-6535	277	40	.	.	PUNCT
ejpam-6535	278	1	a	a	DET
ejpam-6535	278	2	probabilistic	probabilistic	ADJ
ejpam-6535	278	3	convergence	convergence	NOUN
ejpam-6535	278	4	group	group	NOUN
ejpam-6535	278	5	is	be	AUX
ejpam-6535	278	6	a	a	DET
ejpam-6535	278	7	probabilistic	probabilistic	ADJ
ejpam-6535	278	8	pretopological	pretopological	ADJ
ejpam-6535	278	9	group	group	NOUN
ejpam-6535	278	10	if	if	SCONJ
ejpam-6535	278	11	it	it	PRON
ejpam-6535	278	12	satisfies	satisfy	VERB
ejpam-6535	278	13	axiom	axiom	NOUN
ejpam-6535	278	14	(	(	PUNCT
ejpam-6535	278	15	plcc	plcc	NOUN
ejpam-6535	278	16	)	)	PUNCT
ejpam-6535	278	17	.	.	PUNCT
ejpam-6535	279	1	the	the	DET
ejpam-6535	279	2	category	category	NOUN
ejpam-6535	279	3	of	of	ADP
ejpam-6535	279	4	probabilistic	probabilistic	ADJ
ejpam-6535	279	5	convergence	convergence	NOUN
ejpam-6535	279	6	groups	group	NOUN
ejpam-6535	279	7	and	and	CCONJ
ejpam-6535	279	8	continuous	continuous	ADJ
ejpam-6535	279	9	group	group	NOUN
ejpam-6535	279	10	homomorphisms	homomorphism	NOUN
ejpam-6535	279	11	is	be	AUX
ejpam-6535	279	12	denoted	denote	VERB
ejpam-6535	279	13	by	by	ADP
ejpam-6535	279	14	pconvgrp	pconvgrp	NOUN
ejpam-6535	279	15	while	while	SCONJ
ejpam-6535	279	16	plimgrp	plimgrp	NOUN
ejpam-6535	279	17	denotes	denote	VERB
ejpam-6535	279	18	the	the	DET
ejpam-6535	279	19	category	category	NOUN
ejpam-6535	279	20	of	of	ADP
ejpam-6535	279	21	probabilistic	probabilistic	ADJ
ejpam-6535	279	22	limit	limit	NOUN
ejpam-6535	279	23	groups	group	NOUN
ejpam-6535	279	24	whence	whence	SCONJ
ejpam-6535	279	25	objects	object	NOUN
ejpam-6535	279	26	are	be	AUX
ejpam-6535	279	27	probabilistic	probabilistic	ADJ
ejpam-6535	279	28	limit	limit	NOUN
ejpam-6535	279	29	spaces	space	NOUN
ejpam-6535	279	30	and	and	CCONJ
ejpam-6535	279	31	morphisms	morphism	NOUN
ejpam-6535	279	32	are	be	AUX
ejpam-6535	279	33	continuous	continuous	ADJ
ejpam-6535	279	34	group	group	NOUN
ejpam-6535	279	35	homomorphisms	homomorphism	NOUN
ejpam-6535	279	36	.	.	PUNCT
ejpam-6535	280	1	we	we	PRON
ejpam-6535	280	2	denote	denote	VERB
ejpam-6535	280	3	by	by	ADP
ejpam-6535	280	4	ppretop	ppretop	NOUN
ejpam-6535	280	5	,	,	PUNCT
ejpam-6535	280	6	the	the	DET
ejpam-6535	280	7	category	category	NOUN
ejpam-6535	280	8	of	of	ADP
ejpam-6535	280	9	pretopological	pretopological	ADJ
ejpam-6535	280	10	groups	group	NOUN
ejpam-6535	280	11	.	.	PUNCT
ejpam-6535	281	1	lemma	lemma	PROPN
ejpam-6535	281	2	12	12	NUM
ejpam-6535	281	3	.	.	PUNCT
ejpam-6535	282	1	let	let	AUX
ejpam-6535	282	2	(	(	PUNCT
ejpam-6535	282	3	s	s	X
ejpam-6535	282	4	,	,	PUNCT
ejpam-6535	282	5	·	·	PUNCT
ejpam-6535	282	6	,	,	PUNCT
ejpam-6535	282	7	c	c	X
ejpam-6535	282	8	)	)	PUNCT
ejpam-6535	282	9	be	be	AUX
ejpam-6535	282	10	a	a	DET
ejpam-6535	282	11	probabilistic	probabilistic	ADJ
ejpam-6535	282	12	convergence	convergence	NOUN
ejpam-6535	282	13	group	group	NOUN
ejpam-6535	282	14	.	.	PUNCT
ejpam-6535	283	1	then	then	ADV
ejpam-6535	283	2	the	the	DET
ejpam-6535	283	3	statement	statement	NOUN
ejpam-6535	283	4	(	(	PUNCT
ejpam-6535	283	5	pcgm)′	pcgm)′	NOUN
ejpam-6535	283	6	is	be	AUX
ejpam-6535	283	7	equivalent	equivalent	ADJ
ejpam-6535	283	8	to	to	ADP
ejpam-6535	283	9	the	the	DET
ejpam-6535	283	10	statements	statement	NOUN
ejpam-6535	283	11	(	(	PUNCT
ejpam-6535	283	12	pcgm	pcgm	NOUN
ejpam-6535	283	13	)	)	PUNCT
ejpam-6535	283	14	and	and	CCONJ
ejpam-6535	283	15	(	(	PUNCT
ejpam-6535	283	16	pcgi	pcgi	PROPN
ejpam-6535	283	17	)	)	PUNCT
ejpam-6535	283	18	as	as	SCONJ
ejpam-6535	283	19	given	give	VERB
ejpam-6535	283	20	below	below	ADV
ejpam-6535	283	21	:	:	PUNCT
ejpam-6535	283	22	(	(	PUNCT
ejpam-6535	283	23	pcgm)′	pcgm)′	NOUN
ejpam-6535	283	24	if	if	SCONJ
ejpam-6535	283	25	for	for	ADP
ejpam-6535	283	26	all	all	DET
ejpam-6535	283	27	f	f	NOUN
ejpam-6535	283	28	,	,	PUNCT
ejpam-6535	283	29	g	g	PROPN
ejpam-6535	283	30	∈	∈	PROPN
ejpam-6535	283	31	f(s	f(	VERB
ejpam-6535	283	32	)	)	PUNCT
ejpam-6535	283	33	and	and	CCONJ
ejpam-6535	283	34	for	for	ADP
ejpam-6535	283	35	all	all	DET
ejpam-6535	283	36	φ	φ	NOUN
ejpam-6535	283	37	,	,	PUNCT
ejpam-6535	283	38	ψ	ψ	X
ejpam-6535	283	39	∈	∈	PROPN
ejpam-6535	283	40	∆+	∆+	NOUN
ejpam-6535	283	41	,	,	PUNCT
ejpam-6535	283	42	p	p	NOUN
ejpam-6535	283	43	∈	∈	PROPN
ejpam-6535	283	44	cφ(f	cφ(f	PUNCT
ejpam-6535	283	45	)	)	PUNCT
ejpam-6535	283	46	and	and	CCONJ
ejpam-6535	283	47	q	q	PROPN
ejpam-6535	283	48	∈	∈	PROPN
ejpam-6535	283	49	cψ(g	cψ(g	NOUN
ejpam-6535	283	50	)	)	PUNCT
ejpam-6535	283	51	,	,	PUNCT
ejpam-6535	283	52	then	then	ADV
ejpam-6535	283	53	p−1q	p−1q	PROPN
ejpam-6535	283	54	∈	∈	PROPN
ejpam-6535	283	55	cτ(φ	cτ(φ	NOUN
ejpam-6535	283	56	,	,	PUNCT
ejpam-6535	283	57	ψ	ψ	NOUN
ejpam-6535	283	58	)	)	PUNCT
ejpam-6535	283	59	(	(	PUNCT
ejpam-6535	283	60	f−1	f−1	PROPN
ejpam-6535	283	61	⊙g	⊙g	PROPN
ejpam-6535	283	62	)	)	PUNCT
ejpam-6535	283	63	.	.	PUNCT
ejpam-6535	284	1	(	(	PUNCT
ejpam-6535	284	2	pcgm	pcgm	NOUN
ejpam-6535	284	3	)	)	PUNCT
ejpam-6535	284	4	if	if	SCONJ
ejpam-6535	284	5	for	for	ADP
ejpam-6535	284	6	all	all	DET
ejpam-6535	284	7	f	f	NOUN
ejpam-6535	284	8	,	,	PUNCT
ejpam-6535	284	9	g	g	PROPN
ejpam-6535	284	10	∈	∈	PROPN
ejpam-6535	284	11	f(s	f(	VERB
ejpam-6535	284	12	)	)	PUNCT
ejpam-6535	284	13	and	and	CCONJ
ejpam-6535	284	14	for	for	ADP
ejpam-6535	284	15	all	all	DET
ejpam-6535	284	16	φ	φ	NOUN
ejpam-6535	284	17	,	,	PUNCT
ejpam-6535	284	18	ψ	ψ	X
ejpam-6535	284	19	∈	∈	PROPN
ejpam-6535	284	20	∆+	∆+	NOUN
ejpam-6535	284	21	,	,	PUNCT
ejpam-6535	284	22	p	p	NOUN
ejpam-6535	284	23	∈	∈	PROPN
ejpam-6535	284	24	cφ(f	cφ(f	PUNCT
ejpam-6535	284	25	)	)	PUNCT
ejpam-6535	284	26	and	and	CCONJ
ejpam-6535	284	27	q	q	PROPN
ejpam-6535	284	28	∈	∈	PROPN
ejpam-6535	284	29	cψ(g	cψ(g	NOUN
ejpam-6535	284	30	)	)	PUNCT
ejpam-6535	284	31	,	,	PUNCT
ejpam-6535	284	32	then	then	ADV
ejpam-6535	284	33	pq	pq	PROPN
ejpam-6535	284	34	∈	∈	PROPN
ejpam-6535	284	35	cτ(φ	cτ(φ	NOUN
ejpam-6535	284	36	,	,	PUNCT
ejpam-6535	284	37	ψ	ψ	NOUN
ejpam-6535	284	38	)	)	PUNCT
ejpam-6535	284	39	(	(	PUNCT
ejpam-6535	284	40	f⊙g	f⊙g	NOUN
ejpam-6535	284	41	)	)	PUNCT
ejpam-6535	284	42	;	;	PUNCT
ejpam-6535	284	43	(	(	PUNCT
ejpam-6535	284	44	pcgi	pcgi	NOUN
ejpam-6535	284	45	)	)	PUNCT
ejpam-6535	284	46	for	for	ADP
ejpam-6535	284	47	all	all	DET
ejpam-6535	284	48	f	f	PROPN
ejpam-6535	284	49	∈	∈	PROPN
ejpam-6535	284	50	f(s	f(	NOUN
ejpam-6535	284	51	)	)	PUNCT
ejpam-6535	284	52	and	and	CCONJ
ejpam-6535	284	53	for	for	ADP
ejpam-6535	284	54	all	all	DET
ejpam-6535	284	55	φ	φ	PROPN
ejpam-6535	284	56	∈	∈	PROPN
ejpam-6535	284	57	∆+	∆+	NOUN
ejpam-6535	284	58	,	,	PUNCT
ejpam-6535	284	59	p	p	NOUN
ejpam-6535	284	60	∈	∈	PROPN
ejpam-6535	284	61	cφ(f	cφ(f	NOUN
ejpam-6535	284	62	)	)	PUNCT
ejpam-6535	284	63	,	,	PUNCT
ejpam-6535	284	64	then	then	ADV
ejpam-6535	284	65	p−1	p−1	PROPN
ejpam-6535	284	66	∈	∈	PROPN
ejpam-6535	284	67	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	284	68	)	)	PUNCT
ejpam-6535	284	69	.	.	PUNCT
ejpam-6535	285	1	proof	proof	NOUN
ejpam-6535	285	2	.	.	PUNCT
ejpam-6535	286	1	assume	assume	VERB
ejpam-6535	286	2	(	(	PUNCT
ejpam-6535	286	3	pcgm)′	pcgm)′	NOUN
ejpam-6535	286	4	holds	hold	VERB
ejpam-6535	286	5	.	.	PUNCT
ejpam-6535	287	1	first	first	ADV
ejpam-6535	287	2	we	we	PRON
ejpam-6535	287	3	show	show	VERB
ejpam-6535	287	4	(	(	PUNCT
ejpam-6535	287	5	pcgi	pcgi	PROPN
ejpam-6535	287	6	):	):	PUNCT
ejpam-6535	287	7	let	let	VERB
ejpam-6535	287	8	f	f	PROPN
ejpam-6535	287	9	∈	∈	PROPN
ejpam-6535	287	10	f(s	f(	NOUN
ejpam-6535	287	11	)	)	PUNCT
ejpam-6535	287	12	,	,	PUNCT
ejpam-6535	287	13	φ	φ	PROPN
ejpam-6535	287	14	∈	∈	PROPN
ejpam-6535	287	15	∆+	∆+	NOUN
ejpam-6535	287	16	and	and	CCONJ
ejpam-6535	287	17	p	p	PRON
ejpam-6535	287	18	∈	∈	PROPN
ejpam-6535	287	19	cφ(f	cφ(f	PUNCT
ejpam-6535	287	20	)	)	PUNCT
ejpam-6535	287	21	.	.	PUNCT
ejpam-6535	288	1	then	then	ADV
ejpam-6535	288	2	by	by	ADP
ejpam-6535	288	3	(	(	PUNCT
ejpam-6535	288	4	pcmi	pcmi	NOUN
ejpam-6535	288	5	)	)	PUNCT
ejpam-6535	288	6	,	,	PUNCT
ejpam-6535	288	7	e	e	PROPN
ejpam-6535	288	8	∈	∈	PROPN
ejpam-6535	288	9	cϵ0([e	cϵ0([e	NOUN
ejpam-6535	288	10	]	]	PUNCT
ejpam-6535	288	11	)	)	PUNCT
ejpam-6535	288	12	and	and	CCONJ
ejpam-6535	288	13	hence	hence	ADV
ejpam-6535	288	14	by	by	ADP
ejpam-6535	288	15	(	(	PUNCT
ejpam-6535	288	16	pcgm)′	pcgm)′	PROPN
ejpam-6535	288	17	,	,	PUNCT
ejpam-6535	288	18	ep−1	ep−1	PROPN
ejpam-6535	288	19	∈	∈	PROPN
ejpam-6535	288	20	cτ(ϵ0,φ)([e]⊙f−1	cτ(ϵ0,φ)([e]⊙f−1	PROPN
ejpam-6535	288	21	)	)	PUNCT
ejpam-6535	288	22	which	which	PRON
ejpam-6535	288	23	implies	imply	VERB
ejpam-6535	288	24	p−1	p−1	PROPN
ejpam-6535	288	25	∈	∈	PROPN
ejpam-6535	288	26	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	288	27	)	)	PUNCT
ejpam-6535	288	28	since	since	SCONJ
ejpam-6535	288	29	τ(ϵ0	τ(ϵ0	ADV
ejpam-6535	288	30	,	,	PUNCT
ejpam-6535	288	31	φ	φ	NOUN
ejpam-6535	288	32	)	)	PUNCT
ejpam-6535	288	33	=	=	SYM
ejpam-6535	288	34	τ(φ	τ(φ	ADJ
ejpam-6535	288	35	,	,	PUNCT
ejpam-6535	288	36	ϵ0	ϵ0	NUM
ejpam-6535	288	37	)	)	PUNCT
ejpam-6535	288	38	=	=	SYM
ejpam-6535	289	1	φ	φ	PROPN
ejpam-6535	289	2	.	.	PUNCT
ejpam-6535	290	1	next	next	ADV
ejpam-6535	290	2	,	,	PUNCT
ejpam-6535	290	3	to	to	PART
ejpam-6535	290	4	show	show	VERB
ejpam-6535	290	5	(	(	PUNCT
ejpam-6535	290	6	pcgm	pcgm	PROPN
ejpam-6535	290	7	)	)	PUNCT
ejpam-6535	290	8	,	,	PUNCT
ejpam-6535	290	9	let	let	VERB
ejpam-6535	290	10	f	f	X
ejpam-6535	290	11	,	,	PUNCT
ejpam-6535	290	12	g	g	PROPN
ejpam-6535	290	13	∈	∈	PROPN
ejpam-6535	290	14	f(s	f(	VERB
ejpam-6535	290	15	)	)	PUNCT
ejpam-6535	290	16	and	and	CCONJ
ejpam-6535	290	17	φ	φ	NUM
ejpam-6535	290	18	,	,	PUNCT
ejpam-6535	290	19	ψ	ψ	X
ejpam-6535	290	20	∈	∈	PROPN
ejpam-6535	290	21	∆+	∆+	NOUN
ejpam-6535	290	22	.	.	PUNCT
ejpam-6535	291	1	furthermore	furthermore	ADV
ejpam-6535	291	2	,	,	PUNCT
ejpam-6535	291	3	assume	assume	VERB
ejpam-6535	291	4	p	p	X
ejpam-6535	291	5	∈	∈	PROPN
ejpam-6535	291	6	cφ(f	cφ(f	PUNCT
ejpam-6535	291	7	)	)	PUNCT
ejpam-6535	291	8	and	and	CCONJ
ejpam-6535	291	9	q	q	PROPN
ejpam-6535	291	10	∈	∈	PROPN
ejpam-6535	291	11	cψ(g	cψ(g	NOUN
ejpam-6535	291	12	)	)	PUNCT
ejpam-6535	291	13	.	.	PUNCT
ejpam-6535	292	1	since	since	SCONJ
ejpam-6535	292	2	p	p	PROPN
ejpam-6535	292	3	∈	∈	PROPN
ejpam-6535	292	4	cφ(f	cφ(f	PUNCT
ejpam-6535	292	5	)	)	PUNCT
ejpam-6535	292	6	and	and	CCONJ
ejpam-6535	292	7	,	,	PUNCT
ejpam-6535	292	8	by	by	ADP
ejpam-6535	292	9	(	(	PUNCT
ejpam-6535	292	10	pcgi	pcgi	PROPN
ejpam-6535	292	11	)	)	PUNCT
ejpam-6535	292	12	,	,	PUNCT
ejpam-6535	292	13	p−1	p−1	PROPN
ejpam-6535	292	14	∈	∈	PROPN
ejpam-6535	292	15	cψ(f−1	cψ(f−1	PROPN
ejpam-6535	292	16	)	)	PUNCT
ejpam-6535	292	17	,	,	PUNCT
ejpam-6535	292	18	these	these	PRON
ejpam-6535	292	19	together	together	ADV
ejpam-6535	292	20	in	in	ADP
ejpam-6535	292	21	conjunction	conjunction	NOUN
ejpam-6535	292	22	with	with	ADP
ejpam-6535	292	23	(	(	PUNCT
ejpam-6535	292	24	pcgm)′	pcgm)′	NOUN
ejpam-6535	292	25	imply	imply	VERB
ejpam-6535	292	26	that	that	PRON
ejpam-6535	292	27	(	(	PUNCT
ejpam-6535	292	28	p−1)−1q	p−1)−1q	PROPN
ejpam-6535	292	29	∈	∈	PROPN
ejpam-6535	292	30	cτ(φ	cτ(φ	NOUN
ejpam-6535	292	31	,	,	PUNCT
ejpam-6535	292	32	ψ	ψ	NOUN
ejpam-6535	292	33	)	)	PUNCT
ejpam-6535	292	34	(	(	PUNCT
ejpam-6535	292	35	(	(	PUNCT
ejpam-6535	292	36	f−1)−1	f−1)−1	NOUN
ejpam-6535	292	37	⊙g	⊙g	NOUN
ejpam-6535	292	38	)	)	PUNCT
ejpam-6535	292	39	meaning	mean	VERB
ejpam-6535	292	40	pq	pq	NOUN
ejpam-6535	293	1	=	=	SYM
ejpam-6535	293	2	(	(	PUNCT
ejpam-6535	293	3	p−1)−1q	p−1)−1q	PROPN
ejpam-6535	293	4	∈	∈	PROPN
ejpam-6535	293	5	cτ(φ	cτ(φ	NOUN
ejpam-6535	293	6	,	,	PUNCT
ejpam-6535	293	7	ψ	ψ	NOUN
ejpam-6535	293	8	)	)	PUNCT
ejpam-6535	293	9	(	(	PUNCT
ejpam-6535	293	10	f⊙g	f⊙g	NOUN
ejpam-6535	293	11	)	)	PUNCT
ejpam-6535	293	12	,	,	PUNCT
ejpam-6535	293	13	i.e.	i.e.	X
ejpam-6535	293	14	,	,	PUNCT
ejpam-6535	293	15	pq	pq	PROPN
ejpam-6535	293	16	∈	∈	PROPN
ejpam-6535	293	17	cτ(φ	cτ(φ	NOUN
ejpam-6535	293	18	,	,	PUNCT
ejpam-6535	293	19	ψ	ψ	NOUN
ejpam-6535	293	20	)	)	PUNCT
ejpam-6535	293	21	(	(	PUNCT
ejpam-6535	293	22	f⊙g	f⊙g	NOUN
ejpam-6535	293	23	)	)	PUNCT
ejpam-6535	293	24	.	.	PUNCT
ejpam-6535	294	1	now	now	ADV
ejpam-6535	294	2	assume	assume	VERB
ejpam-6535	294	3	that	that	SCONJ
ejpam-6535	294	4	the	the	DET
ejpam-6535	294	5	statements	statement	NOUN
ejpam-6535	294	6	(	(	PUNCT
ejpam-6535	294	7	pcgm	pcgm	NOUN
ejpam-6535	294	8	)	)	PUNCT
ejpam-6535	294	9	and	and	CCONJ
ejpam-6535	294	10	(	(	PUNCT
ejpam-6535	294	11	pcgi	pcgi	PROPN
ejpam-6535	294	12	)	)	PUNCT
ejpam-6535	294	13	hold	hold	VERB
ejpam-6535	294	14	;	;	PUNCT
ejpam-6535	294	15	we	we	PRON
ejpam-6535	294	16	verify	verify	VERB
ejpam-6535	294	17	(	(	PUNCT
ejpam-6535	294	18	pcgm)′.	pcgm)′.	NOUN
ejpam-6535	294	19	let	let	VERB
ejpam-6535	294	20	p	p	X
ejpam-6535	294	21	∈	∈	NOUN
ejpam-6535	294	22	cφ(f	cφ(f	PUNCT
ejpam-6535	294	23	)	)	PUNCT
ejpam-6535	294	24	and	and	CCONJ
ejpam-6535	294	25	q	q	PROPN
ejpam-6535	294	26	∈	∈	PROPN
ejpam-6535	294	27	cψ(g	cψ(g	NOUN
ejpam-6535	294	28	)	)	PUNCT
ejpam-6535	294	29	.	.	PUNCT
ejpam-6535	295	1	since	since	SCONJ
ejpam-6535	295	2	by	by	ADP
ejpam-6535	295	3	(	(	PUNCT
ejpam-6535	295	4	pcgi	pcgi	PROPN
ejpam-6535	295	5	)	)	PUNCT
ejpam-6535	295	6	,	,	PUNCT
ejpam-6535	295	7	p−1	p−1	PROPN
ejpam-6535	295	8	∈	∈	PROPN
ejpam-6535	295	9	cψ(f−1	cψ(f−1	PROPN
ejpam-6535	295	10	)	)	PUNCT
ejpam-6535	295	11	,	,	PUNCT
ejpam-6535	295	12	and	and	CCONJ
ejpam-6535	295	13	then	then	ADV
ejpam-6535	295	14	by	by	ADP
ejpam-6535	295	15	using	use	VERB
ejpam-6535	295	16	(	(	PUNCT
ejpam-6535	295	17	pcgm	pcgm	PROPN
ejpam-6535	295	18	)	)	PUNCT
ejpam-6535	295	19	,	,	PUNCT
ejpam-6535	295	20	we	we	PRON
ejpam-6535	295	21	get	get	VERB
ejpam-6535	295	22	p−1q	p−1q	PROPN
ejpam-6535	295	23	∈	∈	PROPN
ejpam-6535	295	24	cτ(φ	cτ(φ	NOUN
ejpam-6535	295	25	,	,	PUNCT
ejpam-6535	295	26	ψ	ψ	NOUN
ejpam-6535	295	27	)	)	PUNCT
ejpam-6535	295	28	(	(	PUNCT
ejpam-6535	295	29	f−1	f−1	PROPN
ejpam-6535	295	30	⊙g	⊙g	PROPN
ejpam-6535	295	31	)	)	PUNCT
ejpam-6535	295	32	which	which	PRON
ejpam-6535	295	33	is	be	AUX
ejpam-6535	295	34	precisely	precisely	ADV
ejpam-6535	295	35	statement	statement	NOUN
ejpam-6535	295	36	(	(	PUNCT
ejpam-6535	295	37	pcgm)′.	pcgm)′.	PROPN
ejpam-6535	295	38	lemma	lemma	PROPN
ejpam-6535	295	39	13	13	NUM
ejpam-6535	295	40	.	.	PUNCT
ejpam-6535	296	1	let	let	VERB
ejpam-6535	296	2	(	(	PUNCT
ejpam-6535	296	3	s	s	X
ejpam-6535	296	4	,	,	PUNCT
ejpam-6535	296	5	·	·	PUNCT
ejpam-6535	296	6	,	,	PUNCT
ejpam-6535	296	7	c	c	X
ejpam-6535	296	8	=	=	SYM
ejpam-6535	296	9	(	(	PUNCT
ejpam-6535	296	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	296	11	)	)	PUNCT
ejpam-6535	296	12	be	be	AUX
ejpam-6535	296	13	a	a	DET
ejpam-6535	296	14	probabilistic	probabilistic	ADJ
ejpam-6535	296	15	convergence	convergence	NOUN
ejpam-6535	296	16	group	group	NOUN
ejpam-6535	296	17	under	under	ADP
ejpam-6535	296	18	the	the	DET
ejpam-6535	296	19	largest	large	ADJ
ejpam-6535	296	20	triangle	triangle	NOUN
ejpam-6535	296	21	function	function	NOUN
ejpam-6535	296	22	τ	τ	PROPN
ejpam-6535	296	23	,	,	PUNCT
ejpam-6535	296	24	i.e.	i.e.	X
ejpam-6535	296	25	,	,	PUNCT
ejpam-6535	296	26	τ(φ	τ(φ	PROPN
ejpam-6535	296	27	,	,	PUNCT
ejpam-6535	296	28	φ	φ	NOUN
ejpam-6535	296	29	)	)	PUNCT
ejpam-6535	296	30	=	=	SYM
ejpam-6535	297	1	φ	φ	PROPN
ejpam-6535	297	2	.	.	PUNCT
ejpam-6535	298	1	then	then	ADV
ejpam-6535	298	2	for	for	ADP
ejpam-6535	298	3	all	all	PRON
ejpam-6535	298	4	p	p	NOUN
ejpam-6535	298	5	∈	∈	PROPN
ejpam-6535	298	6	s	s	NOUN
ejpam-6535	298	7	and	and	CCONJ
ejpam-6535	298	8	for	for	ADP
ejpam-6535	298	9	all	all	DET
ejpam-6535	298	10	φ	φ	PROPN
ejpam-6535	298	11	∈	∈	PROPN
ejpam-6535	298	12	∆+	∆+	NUM
ejpam-6535	298	13	the	the	DET
ejpam-6535	298	14	following	follow	VERB
ejpam-6535	298	15	holds	hold	VERB
ejpam-6535	298	16	:	:	PUNCT
ejpam-6535	298	17	(	(	PUNCT
ejpam-6535	298	18	a	a	X
ejpam-6535	298	19	)	)	PUNCT
ejpam-6535	298	20	p	p	NOUN
ejpam-6535	298	21	∈	∈	PROPN
ejpam-6535	298	22	cφ(f	cφ(f	NOUN
ejpam-6535	298	23	)	)	PUNCT
ejpam-6535	298	24	⇐	⇐	ADJ
ejpam-6535	298	25	⇒	⇒	NOUN
ejpam-6535	298	26	e	e	PROPN
ejpam-6535	298	27	∈	∈	PROPN
ejpam-6535	298	28	cφ([p	cφ([p	PROPN
ejpam-6535	298	29	−1]⊙f	−1]⊙f	PROPN
ejpam-6535	298	30	)	)	PUNCT
ejpam-6535	298	31	⇐	⇐	ADJ
ejpam-6535	298	32	⇒	⇒	NOUN
ejpam-6535	298	33	e	e	PROPN
ejpam-6535	298	34	∈	∈	PROPN
ejpam-6535	298	35	cφ	cφ	X
ejpam-6535	298	36	(	(	PUNCT
ejpam-6535	298	37	f⊙	f⊙	PROPN
ejpam-6535	298	38	[	[	X
ejpam-6535	298	39	p−1	p−1	X
ejpam-6535	298	40	]	]	PUNCT
ejpam-6535	298	41	)	)	PUNCT
ejpam-6535	298	42	,	,	PUNCT
ejpam-6535	298	43	∀f	∀f	PROPN
ejpam-6535	298	44	∈	∈	PROPN
ejpam-6535	298	45	f(s	f(	NOUN
ejpam-6535	298	46	)	)	PUNCT
ejpam-6535	298	47	(	(	PUNCT
ejpam-6535	298	48	homogeneity	homogeneity	NOUN
ejpam-6535	298	49	)	)	PUNCT
ejpam-6535	298	50	;	;	PUNCT
ejpam-6535	298	51	(	(	PUNCT
ejpam-6535	298	52	b	b	X
ejpam-6535	298	53	)	)	PUNCT
ejpam-6535	298	54	nc	nc	PROPN
ejpam-6535	298	55	,	,	PUNCT
ejpam-6535	298	56	φ	φ	NOUN
ejpam-6535	298	57	p	p	NOUN
ejpam-6535	299	1	=	=	X
ejpam-6535	300	1	[	[	X
ejpam-6535	300	2	p]⊙nc	p]⊙nc	PROPN
ejpam-6535	300	3	,	,	PUNCT
ejpam-6535	300	4	φ	φ	X
ejpam-6535	300	5	e	e	NOUN
ejpam-6535	300	6	=	=	SYM
ejpam-6535	300	7	nφ	nφ	PROPN
ejpam-6535	300	8	e	e	PROPN
ejpam-6535	300	9	⊙	⊙	NOUN
ejpam-6535	301	1	[	[	X
ejpam-6535	301	2	p	p	X
ejpam-6535	301	3	]	]	X
ejpam-6535	301	4	;	;	PUNCT
ejpam-6535	301	5	(	(	PUNCT
ejpam-6535	301	6	c	c	X
ejpam-6535	301	7	)	)	PUNCT
ejpam-6535	301	8	nc	nc	PROPN
ejpam-6535	301	9	,	,	PUNCT
ejpam-6535	301	10	φ	φ	NOUN
ejpam-6535	301	11	e	e	X
ejpam-6535	301	12	=	=	PUNCT
ejpam-6535	302	1	[	[	X
ejpam-6535	302	2	p−1]⊙nc	p−1]⊙nc	PRON
ejpam-6535	302	3	,	,	PUNCT
ejpam-6535	302	4	φ	φ	PROPN
ejpam-6535	302	5	p	p	X
ejpam-6535	302	6	=	=	PROPN
ejpam-6535	302	7	nc	nc	PROPN
ejpam-6535	302	8	,	,	PUNCT
ejpam-6535	302	9	φ	φ	PROPN
ejpam-6535	302	10	p	p	NOUN
ejpam-6535	302	11	⊙	⊙	PROPN
ejpam-6535	303	1	[	[	X
ejpam-6535	303	2	p−1	p−1	PROPN
ejpam-6535	303	3	]	]	X
ejpam-6535	303	4	;	;	PUNCT
ejpam-6535	303	5	(	(	PUNCT
ejpam-6535	303	6	d	d	X
ejpam-6535	303	7	)	)	PUNCT
ejpam-6535	303	8	(	(	PUNCT
ejpam-6535	303	9	nc	nc	PROPN
ejpam-6535	303	10	,	,	PUNCT
ejpam-6535	303	11	φ	φ	PROPN
ejpam-6535	303	12	p	p	NOUN
ejpam-6535	303	13	)	)	PUNCT
ejpam-6535	303	14	−1	−1	NOUN
ejpam-6535	303	15	=	=	PROPN
ejpam-6535	303	16	nc	nc	PROPN
ejpam-6535	303	17	,	,	PUNCT
ejpam-6535	303	18	φ	φ	PROPN
ejpam-6535	303	19	p−1	p−1	PROPN
ejpam-6535	303	20	proof	proof	NOUN
ejpam-6535	303	21	.	.	PUNCT
ejpam-6535	304	1	(	(	PUNCT
ejpam-6535	304	2	a	a	X
ejpam-6535	304	3	)	)	PUNCT
ejpam-6535	304	4	this	this	PRON
ejpam-6535	304	5	is	be	AUX
ejpam-6535	304	6	precisely	precisely	ADV
ejpam-6535	304	7	homogeneity	homogeneity	NOUN
ejpam-6535	304	8	of	of	ADP
ejpam-6535	304	9	probabilistic	probabilistic	ADJ
ejpam-6535	304	10	convergence	convergence	NOUN
ejpam-6535	304	11	group	group	NOUN
ejpam-6535	304	12	as	as	SCONJ
ejpam-6535	304	13	shown	show	VERB
ejpam-6535	304	14	in	in	ADP
ejpam-6535	304	15	lemma	lemma	PROPN
ejpam-6535	304	16	4.4[3	4.4[3	PROPN
ejpam-6535	304	17	]	]	PUNCT
ejpam-6535	304	18	.	.	PUNCT
ejpam-6535	305	1	(	(	PUNCT
ejpam-6535	305	2	b	b	X
ejpam-6535	305	3	)	)	PUNCT
ejpam-6535	305	4	we	we	PRON
ejpam-6535	305	5	show	show	VERB
ejpam-6535	305	6	here	here	ADV
ejpam-6535	305	7	the	the	DET
ejpam-6535	305	8	first	first	ADJ
ejpam-6535	305	9	part	part	NOUN
ejpam-6535	305	10	,	,	PUNCT
ejpam-6535	305	11	the	the	DET
ejpam-6535	305	12	other	other	ADJ
ejpam-6535	305	13	part	part	NOUN
ejpam-6535	305	14	follows	follow	VERB
ejpam-6535	305	15	similarly	similarly	ADV
ejpam-6535	305	16	.	.	PUNCT
ejpam-6535	306	1	for	for	ADP
ejpam-6535	306	2	this	this	PRON
ejpam-6535	306	3	,	,	PUNCT
ejpam-6535	306	4	we	we	PRON
ejpam-6535	306	5	have	have	VERB
ejpam-6535	306	6	[	[	X
ejpam-6535	306	7	p]⊙nc	p]⊙nc	PROPN
ejpam-6535	306	8	,	,	PUNCT
ejpam-6535	306	9	φ	φ	PROPN
ejpam-6535	306	10	e	e	PROPN
ejpam-6535	306	11	≥	≥	PROPN
ejpam-6535	306	12	nc	nc	PROPN
ejpam-6535	306	13	,	,	PUNCT
ejpam-6535	306	14	φ	φ	PROPN
ejpam-6535	306	15	p	p	PROPN
ejpam-6535	306	16	⊙nc	⊙nc	NOUN
ejpam-6535	306	17	,	,	PUNCT
ejpam-6535	306	18	φ	φ	PROPN
ejpam-6535	306	19	e	e	PROPN
ejpam-6535	306	20	≥	≥	PROPN
ejpam-6535	306	21	nc	nc	PROPN
ejpam-6535	306	22	,	,	PUNCT
ejpam-6535	306	23	τ(φ	τ(φ	PROPN
ejpam-6535	306	24	,	,	PUNCT
ejpam-6535	306	25	φ	φ	NOUN
ejpam-6535	306	26	)	)	PUNCT
ejpam-6535	306	27	pe	pe	PROPN
ejpam-6535	306	28	=	=	SYM
ejpam-6535	306	29	nc	nc	PROPN
ejpam-6535	306	30	,	,	PUNCT
ejpam-6535	306	31	φ	φ	PROPN
ejpam-6535	306	32	p	p	NOUN
ejpam-6535	306	33	.	.	PUNCT
ejpam-6535	307	1	on	on	ADP
ejpam-6535	307	2	the	the	DET
ejpam-6535	307	3	other	other	ADJ
ejpam-6535	307	4	hand	hand	NOUN
ejpam-6535	307	5	,	,	PUNCT
ejpam-6535	307	6	we	we	PRON
ejpam-6535	307	7	have	have	VERB
ejpam-6535	307	8	[	[	X
ejpam-6535	307	9	p]⊙nc	p]⊙nc	PROPN
ejpam-6535	307	10	,	,	PUNCT
ejpam-6535	307	11	φ	φ	X
ejpam-6535	307	12	e	e	X
ejpam-6535	308	1	=	=	PUNCT
ejpam-6535	309	1	[	[	X
ejpam-6535	309	2	p]⊙n	p]⊙n	NOUN
ejpam-6535	309	3	c	c	X
ejpam-6535	309	4	,	,	PUNCT
ejpam-6535	309	5	τ(φ	τ(φ	PROPN
ejpam-6535	309	6	,	,	PUNCT
ejpam-6535	309	7	φ	φ	NUM
ejpam-6535	309	8	)	)	PUNCT
ejpam-6535	309	9	p−1p	p−1p	NOUN
ejpam-6535	309	10	≤	≤	PUNCT
ejpam-6535	310	1	[	[	X
ejpam-6535	310	2	p]⊙	p]⊙	X
ejpam-6535	310	3	(	(	PUNCT
ejpam-6535	310	4	nc	nc	PROPN
ejpam-6535	310	5	,	,	PUNCT
ejpam-6535	310	6	φ	φ	PROPN
ejpam-6535	310	7	p−1	p−1	PROPN
ejpam-6535	310	8	⊙nc	⊙nc	NOUN
ejpam-6535	310	9	,	,	PUNCT
ejpam-6535	310	10	φ	φ	PROPN
ejpam-6535	310	11	p	p	NOUN
ejpam-6535	310	12	)	)	PUNCT
ejpam-6535	310	13	≤	≤	PUNCT
ejpam-6535	311	1	[	[	X
ejpam-6535	311	2	p]⊙	p]⊙	X
ejpam-6535	311	3	(	(	PUNCT
ejpam-6535	311	4	[	[	X
ejpam-6535	311	5	p−1]⊙nc	p−1]⊙nc	PRON
ejpam-6535	311	6	,	,	PUNCT
ejpam-6535	311	7	φ	φ	PROPN
ejpam-6535	311	8	p	p	NOUN
ejpam-6535	311	9	)	)	PUNCT
ejpam-6535	311	10	=	=	PUNCT
ejpam-6535	312	1	(	(	PUNCT
ejpam-6535	312	2	[	[	X
ejpam-6535	312	3	p]⊙	p]⊙	X
ejpam-6535	312	4	[	[	X
ejpam-6535	312	5	p−1	p−1	X
ejpam-6535	312	6	]	]	PUNCT
ejpam-6535	312	7	)	)	PUNCT
ejpam-6535	312	8	⊙nc	⊙nc	NOUN
ejpam-6535	312	9	,	,	PUNCT
ejpam-6535	312	10	φ	φ	NOUN
ejpam-6535	312	11	p	p	NOUN
ejpam-6535	312	12	=	=	X
ejpam-6535	313	1	[	[	X
ejpam-6535	313	2	e]⊙nc	e]⊙nc	PROPN
ejpam-6535	313	3	,	,	PUNCT
ejpam-6535	313	4	φ	φ	NOUN
ejpam-6535	313	5	p	p	X
ejpam-6535	313	6	=	=	PROPN
ejpam-6535	313	7	nc	nc	PROPN
ejpam-6535	313	8	,	,	PUNCT
ejpam-6535	313	9	φ	φ	PROPN
ejpam-6535	313	10	p	p	X
ejpam-6535	313	11	(	(	PUNCT
ejpam-6535	313	12	c	c	X
ejpam-6535	313	13	)	)	PUNCT
ejpam-6535	313	14	this	this	PRON
ejpam-6535	313	15	follows	follow	VERB
ejpam-6535	313	16	almost	almost	ADV
ejpam-6535	313	17	the	the	DET
ejpam-6535	313	18	same	same	ADJ
ejpam-6535	313	19	way	way	NOUN
ejpam-6535	313	20	as	as	ADP
ejpam-6535	313	21	in	in	ADP
ejpam-6535	313	22	(	(	PUNCT
ejpam-6535	313	23	b	b	NOUN
ejpam-6535	313	24	)	)	PUNCT
ejpam-6535	313	25	.	.	PUNCT
ejpam-6535	314	1	(	(	PUNCT
ejpam-6535	314	2	d	d	X
ejpam-6535	314	3	)	)	PUNCT
ejpam-6535	314	4	since	since	SCONJ
ejpam-6535	314	5	the	the	DET
ejpam-6535	314	6	inversion	inversion	NOUN
ejpam-6535	314	7	mapping	mapping	NOUN
ejpam-6535	314	8	ȷ	ȷ	NOUN
ejpam-6535	314	9	:	:	PUNCT
ejpam-6535	314	10	(	(	PUNCT
ejpam-6535	314	11	s	s	X
ejpam-6535	314	12	,	,	PUNCT
ejpam-6535	314	13	c	c	NOUN
ejpam-6535	314	14	)	)	PUNCT
ejpam-6535	314	15	−→	−→	NOUN
ejpam-6535	314	16	(	(	PUNCT
ejpam-6535	314	17	s	s	PROPN
ejpam-6535	314	18	,	,	PUNCT
ejpam-6535	314	19	c	c	NOUN
ejpam-6535	314	20	)	)	PUNCT
ejpam-6535	314	21	,	,	PUNCT
ejpam-6535	314	22	p	p	PROPN
ejpam-6535	314	23	7−→	7−→	PROPN
ejpam-6535	314	24	p−1	p−1	PROPN
ejpam-6535	314	25	is	be	AUX
ejpam-6535	314	26	a	a	DET
ejpam-6535	314	27	homeomorphism	homeomorphism	NOUN
ejpam-6535	314	28	,	,	PUNCT
ejpam-6535	314	29	one	one	PRON
ejpam-6535	314	30	can	can	AUX
ejpam-6535	314	31	easily	easily	ADV
ejpam-6535	314	32	obtain	obtain	VERB
ejpam-6535	314	33	the	the	DET
ejpam-6535	314	34	result	result	NOUN
ejpam-6535	314	35	in	in	ADP
ejpam-6535	314	36	this	this	DET
ejpam-6535	314	37	item	item	NOUN
ejpam-6535	314	38	.	.	PUNCT
ejpam-6535	315	1	lemma	lemma	PROPN
ejpam-6535	315	2	14	14	NUM
ejpam-6535	315	3	.	.	PUNCT
ejpam-6535	316	1	let	let	VERB
ejpam-6535	316	2	(	(	PUNCT
ejpam-6535	316	3	s	s	X
ejpam-6535	316	4	,	,	PUNCT
ejpam-6535	316	5	·	·	PUNCT
ejpam-6535	316	6	)	)	PUNCT
ejpam-6535	316	7	be	be	AUX
ejpam-6535	316	8	a	a	DET
ejpam-6535	316	9	group	group	NOUN
ejpam-6535	316	10	and	and	CCONJ
ejpam-6535	316	11	(	(	PUNCT
ejpam-6535	316	12	s	s	PROPN
ejpam-6535	316	13	,	,	PUNCT
ejpam-6535	316	14	n	n	NOUN
ejpam-6535	316	15	=	=	SYM
ejpam-6535	316	16	(	(	PUNCT
ejpam-6535	316	17	nφ	nφ	PROPN
ejpam-6535	316	18	p	p	NOUN
ejpam-6535	316	19	)	)	PUNCT
ejpam-6535	316	20	(	(	PUNCT
ejpam-6535	316	21	p	p	X
ejpam-6535	316	22	,	,	PUNCT
ejpam-6535	316	23	φ)∈s×∆+	φ)∈s×∆+	PROPN
ejpam-6535	316	24	)	)	PUNCT
ejpam-6535	316	25	be	be	AUX
ejpam-6535	316	26	a	a	DET
ejpam-6535	316	27	probabilistic	probabilistic	ADJ
ejpam-6535	316	28	neighborhood	neighborhood	NOUN
ejpam-6535	316	29	space	space	NOUN
ejpam-6535	316	30	and	and	CCONJ
ejpam-6535	316	31	let	let	VERB
ejpam-6535	316	32	τ	τ	PROPN
ejpam-6535	316	33	be	be	AUX
ejpam-6535	316	34	a	a	DET
ejpam-6535	316	35	triangle	triangle	NOUN
ejpam-6535	316	36	function	function	NOUN
ejpam-6535	316	37	.	.	PUNCT
ejpam-6535	317	1	define	define	VERB
ejpam-6535	317	2	p	p	PRON
ejpam-6535	317	3	∈	∈	PROPN
ejpam-6535	317	4	cφ(f	cφ(f	NOUN
ejpam-6535	317	5	)	)	PUNCT
ejpam-6535	317	6	⇐	⇐	ADJ
ejpam-6535	317	7	⇒	⇒	PROPN
ejpam-6535	317	8	f	f	PROPN
ejpam-6535	317	9	≥	≥	NOUN
ejpam-6535	317	10	nφ	nφ	ADP
ejpam-6535	317	11	p	p	PROPN
ejpam-6535	317	12	for	for	ADP
ejpam-6535	317	13	each	each	DET
ejpam-6535	317	14	f	f	PROPN
ejpam-6535	317	15	∈	∈	PROPN
ejpam-6535	317	16	f(s	f(	NOUN
ejpam-6535	317	17	)	)	PUNCT
ejpam-6535	317	18	,	,	PUNCT
ejpam-6535	317	19	where	where	SCONJ
ejpam-6535	317	20	nφ	nφ	ADP
ejpam-6535	317	21	p	p	NOUN
ejpam-6535	317	22	=	=	PROPN
ejpam-6535	317	23	∧	∧	PROPN
ejpam-6535	317	24	p∈cφ(f	p∈cφ(f	PROPN
ejpam-6535	317	25	)	)	PUNCT
ejpam-6535	317	26	f.	f.	PROPN
ejpam-6535	317	27	then	then	ADV
ejpam-6535	317	28	(	(	PUNCT
ejpam-6535	317	29	a	a	X
ejpam-6535	317	30	)	)	PUNCT
ejpam-6535	317	31	the	the	DET
ejpam-6535	317	32	mapping	mapping	NOUN
ejpam-6535	317	33	ȷ	ȷ	NOUN
ejpam-6535	317	34	:	:	PUNCT
ejpam-6535	317	35	(	(	PUNCT
ejpam-6535	317	36	s	s	X
ejpam-6535	317	37	,	,	PUNCT
ejpam-6535	317	38	n	n	CCONJ
ejpam-6535	317	39	)	)	PUNCT
ejpam-6535	317	40	−→	−→	NOUN
ejpam-6535	317	41	(	(	PUNCT
ejpam-6535	317	42	s	s	NOUN
ejpam-6535	317	43	,	,	PUNCT
ejpam-6535	317	44	n	n	CCONJ
ejpam-6535	317	45	)	)	PUNCT
ejpam-6535	317	46	is	be	AUX
ejpam-6535	317	47	continuous	continuous	ADJ
ejpam-6535	317	48	at	at	ADP
ejpam-6535	317	49	e	e	PROPN
ejpam-6535	317	50	∈	∈	NOUN
ejpam-6535	317	51	s	s	X
ejpam-6535	317	52	if	if	SCONJ
ejpam-6535	318	1	and	and	CCONJ
ejpam-6535	318	2	only	only	ADV
ejpam-6535	318	3	if	if	SCONJ
ejpam-6535	318	4	e	e	PROPN
ejpam-6535	318	5	∈	∈	PROPN
ejpam-6535	318	6	cφ(f	cφ(f	NOUN
ejpam-6535	318	7	)	)	PUNCT
ejpam-6535	318	8	⇒	⇒	NOUN
ejpam-6535	318	9	e	e	PROPN
ejpam-6535	318	10	∈	∈	PROPN
ejpam-6535	318	11	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	318	12	)	)	PUNCT
ejpam-6535	318	13	for	for	ADP
ejpam-6535	318	14	all	all	DET
ejpam-6535	318	15	f	f	PROPN
ejpam-6535	318	16	∈	∈	PROPN
ejpam-6535	318	17	f(s	f(	NOUN
ejpam-6535	318	18	)	)	PUNCT
ejpam-6535	318	19	and	and	CCONJ
ejpam-6535	318	20	for	for	ADP
ejpam-6535	318	21	all	all	DET
ejpam-6535	318	22	φ	φ	PROPN
ejpam-6535	318	23	∈	∈	PROPN
ejpam-6535	318	24	∆+	∆+	NOUN
ejpam-6535	318	25	.	.	PUNCT
ejpam-6535	319	1	(	(	PUNCT
ejpam-6535	319	2	b	b	X
ejpam-6535	319	3	)	)	PUNCT
ejpam-6535	319	4	the	the	DET
ejpam-6535	319	5	mapping	mapping	NOUN
ejpam-6535	319	6	m	m	VERB
ejpam-6535	319	7	:	:	PUNCT
ejpam-6535	319	8	(	(	PUNCT
ejpam-6535	319	9	s	s	NUM
ejpam-6535	319	10	×	×	NOUN
ejpam-6535	319	11	s	s	NOUN
ejpam-6535	319	12	,	,	PUNCT
ejpam-6535	319	13	n×n	n×n	PROPN
ejpam-6535	319	14	)	)	PUNCT
ejpam-6535	319	15	−→	−→	NOUN
ejpam-6535	319	16	(	(	PUNCT
ejpam-6535	319	17	s	s	NOUN
ejpam-6535	319	18	,	,	PUNCT
ejpam-6535	319	19	n	n	CCONJ
ejpam-6535	319	20	)	)	PUNCT
ejpam-6535	319	21	,	,	PUNCT
ejpam-6535	319	22	(	(	PUNCT
ejpam-6535	319	23	p	p	X
ejpam-6535	319	24	,	,	PUNCT
ejpam-6535	319	25	q	q	NOUN
ejpam-6535	319	26	)	)	PUNCT
ejpam-6535	319	27	7−→	7−→	NOUN
ejpam-6535	319	28	pq	pq	NOUN
ejpam-6535	319	29	is	be	AUX
ejpam-6535	319	30	continuous	continuous	ADJ
ejpam-6535	319	31	at	at	ADP
ejpam-6535	319	32	(	(	PUNCT
ejpam-6535	319	33	e	e	NOUN
ejpam-6535	319	34	,	,	PUNCT
ejpam-6535	319	35	e	e	NOUN
ejpam-6535	319	36	)	)	PUNCT
ejpam-6535	319	37	∈	∈	PROPN
ejpam-6535	319	38	s	s	PART
ejpam-6535	319	39	×	×	NOUN
ejpam-6535	319	40	s	s	X
ejpam-6535	319	41	if	if	SCONJ
ejpam-6535	320	1	and	and	CCONJ
ejpam-6535	320	2	only	only	ADV
ejpam-6535	320	3	if	if	SCONJ
ejpam-6535	320	4	e	e	PROPN
ejpam-6535	320	5	∈	∈	NOUN
ejpam-6535	320	6	cφ(f	cφ(f	NOUN
ejpam-6535	320	7	)	)	PUNCT
ejpam-6535	320	8	and	and	CCONJ
ejpam-6535	320	9	e	e	PROPN
ejpam-6535	320	10	∈	∈	PROPN
ejpam-6535	320	11	cψ(g	cψ(g	NOUN
ejpam-6535	320	12	)	)	PUNCT
ejpam-6535	320	13	⇒	⇒	NOUN
ejpam-6535	320	14	e	e	PROPN
ejpam-6535	320	15	∈	∈	PROPN
ejpam-6535	320	16	cτ(φ	cτ(φ	NOUN
ejpam-6535	320	17	,	,	PUNCT
ejpam-6535	320	18	ψ	ψ	NOUN
ejpam-6535	320	19	)	)	PUNCT
ejpam-6535	320	20	(	(	PUNCT
ejpam-6535	320	21	f⊙g	f⊙g	NOUN
ejpam-6535	320	22	)	)	PUNCT
ejpam-6535	320	23	,	,	PUNCT
ejpam-6535	320	24	for	for	ADP
ejpam-6535	320	25	all	all	DET
ejpam-6535	320	26	f	f	NOUN
ejpam-6535	320	27	,	,	PUNCT
ejpam-6535	320	28	g	g	PROPN
ejpam-6535	320	29	∈	∈	PROPN
ejpam-6535	320	30	f(s	f(	VERB
ejpam-6535	320	31	)	)	PUNCT
ejpam-6535	320	32	and	and	CCONJ
ejpam-6535	320	33	for	for	ADP
ejpam-6535	320	34	all	all	DET
ejpam-6535	320	35	φ	φ	NOUN
ejpam-6535	320	36	,	,	PUNCT
ejpam-6535	320	37	ψ	ψ	X
ejpam-6535	320	38	∈	∈	PROPN
ejpam-6535	320	39	∆+	∆+	NOUN
ejpam-6535	320	40	.	.	PUNCT
ejpam-6535	321	1	proof	proof	NOUN
ejpam-6535	321	2	.	.	PUNCT
ejpam-6535	322	1	(	(	PUNCT
ejpam-6535	322	2	a	a	X
ejpam-6535	322	3	)	)	PUNCT
ejpam-6535	322	4	note	note	NOUN
ejpam-6535	322	5	that	that	SCONJ
ejpam-6535	322	6	the	the	DET
ejpam-6535	322	7	inversion	inversion	NOUN
ejpam-6535	322	8	mapping	mapping	NOUN
ejpam-6535	322	9	ȷ	ȷ	NOUN
ejpam-6535	322	10	:	:	PUNCT
ejpam-6535	322	11	s	s	VERB
ejpam-6535	322	12	−→	−→	NOUN
ejpam-6535	322	13	s	s	NOUN
ejpam-6535	322	14	,	,	PUNCT
ejpam-6535	322	15	x	x	SYM
ejpam-6535	322	16	7−→	7−→	PROPN
ejpam-6535	322	17	x−1	x−1	PROPN
ejpam-6535	322	18	is	be	AUX
ejpam-6535	322	19	continuous	continuous	ADJ
ejpam-6535	322	20	e	e	NOUN
ejpam-6535	322	21	∈	∈	NOUN
ejpam-6535	322	22	s	s	X
ejpam-6535	322	23	if	if	SCONJ
ejpam-6535	323	1	and	and	CCONJ
ejpam-6535	323	2	only	only	ADV
ejpam-6535	323	3	if	if	SCONJ
ejpam-6535	323	4	nφ	nφ	PROPN
ejpam-6535	323	5	e−1	e−1	PROPN
ejpam-6535	323	6	≤	≤	NOUN
ejpam-6535	323	7	(	(	PUNCT
ejpam-6535	323	8	nφ	nφ	NOUN
ejpam-6535	323	9	e	e	NOUN
ejpam-6535	323	10	)	)	PUNCT
ejpam-6535	323	11	−1	−1	NOUN
ejpam-6535	323	12	.	.	PUNCT
ejpam-6535	324	1	now	now	ADV
ejpam-6535	324	2	for	for	ADP
ejpam-6535	324	3	any	any	DET
ejpam-6535	324	4	f	f	PROPN
ejpam-6535	324	5	∈	∈	PROPN
ejpam-6535	324	6	f(s	f(	NOUN
ejpam-6535	324	7	)	)	PUNCT
ejpam-6535	324	8	,	,	PUNCT
ejpam-6535	324	9	if	if	SCONJ
ejpam-6535	324	10	e	e	PROPN
ejpam-6535	324	11	∈	∈	PROPN
ejpam-6535	324	12	cφ(f	cφ(f	NOUN
ejpam-6535	324	13	)	)	PUNCT
ejpam-6535	324	14	,	,	PUNCT
ejpam-6535	324	15	then	then	ADV
ejpam-6535	324	16	f	f	PROPN
ejpam-6535	324	17	≥	≥	NOUN
ejpam-6535	324	18	nφ	nφ	PROPN
ejpam-6535	324	19	e	e	PROPN
ejpam-6535	324	20	.	.	PUNCT
ejpam-6535	325	1	so	so	ADV
ejpam-6535	325	2	,	,	PUNCT
ejpam-6535	325	3	f−1	f−1	PROPN
ejpam-6535	325	4	≥	≥	X
ejpam-6535	325	5	(	(	PUNCT
ejpam-6535	325	6	nφ	nφ	PROPN
ejpam-6535	325	7	e	e	PROPN
ejpam-6535	325	8	)	)	PUNCT
ejpam-6535	325	9	−1	−1	VERB
ejpam-6535	325	10	≥	≥	NOUN
ejpam-6535	325	11	nφ	nφ	ADP
ejpam-6535	325	12	e−1	e−1	PROPN
ejpam-6535	325	13	=	=	PUNCT
ejpam-6535	325	14	nφ	nφ	PROPN
ejpam-6535	325	15	e	e	NOUN
ejpam-6535	325	16	implying	imply	VERB
ejpam-6535	325	17	f−1	f−1	PROPN
ejpam-6535	325	18	≥	≥	NUM
ejpam-6535	325	19	nφ	nφ	ADP
ejpam-6535	325	20	e	e	NOUN
ejpam-6535	325	21	which	which	PRON
ejpam-6535	325	22	yields	yield	VERB
ejpam-6535	325	23	that	that	SCONJ
ejpam-6535	325	24	e	e	PROPN
ejpam-6535	325	25	∈	∈	PROPN
ejpam-6535	325	26	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	325	27	)	)	PUNCT
ejpam-6535	325	28	.	.	PUNCT
ejpam-6535	326	1	conversely	conversely	ADV
ejpam-6535	326	2	,	,	PUNCT
ejpam-6535	326	3	let	let	VERB
ejpam-6535	326	4	f	f	PROPN
ejpam-6535	326	5	∈	∈	PROPN
ejpam-6535	326	6	f(s	f(	VERB
ejpam-6535	326	7	)	)	PUNCT
ejpam-6535	326	8	and	and	CCONJ
ejpam-6535	326	9	φ	φ	NUM
ejpam-6535	326	10	∈	∈	PROPN
ejpam-6535	326	11	∆+	∆+	NOUN
ejpam-6535	326	12	.	.	PUNCT
ejpam-6535	327	1	then	then	ADV
ejpam-6535	327	2	nφ	nφ	PROPN
ejpam-6535	327	3	e−1	e−1	PROPN
ejpam-6535	327	4	=	=	SYM
ejpam-6535	327	5	∧	∧	PROPN
ejpam-6535	327	6	ȷ(e)∈cφ(f−1	ȷ(e)∈cφ(f−1	NOUN
ejpam-6535	327	7	)	)	PUNCT
ejpam-6535	327	8	f−1	f−1	PROPN
ejpam-6535	327	9	≤	≤	NOUN
ejpam-6535	327	10	∧	∧	PROPN
ejpam-6535	327	11	e∈cφ(f	e∈cφ(f	PROPN
ejpam-6535	327	12	)	)	PUNCT
ejpam-6535	327	13	f−1	f−1	PROPN
ejpam-6535	327	14	=	=	SYM
ejpam-6535	327	15	(	(	PUNCT
ejpam-6535	327	16	nφ	nφ	NOUN
ejpam-6535	327	17	e	e	NOUN
ejpam-6535	327	18	)	)	PUNCT
ejpam-6535	327	19	−1	−1	NOUN
ejpam-6535	327	20	.	.	PUNCT
ejpam-6535	328	1	this	this	PRON
ejpam-6535	328	2	implies	imply	VERB
ejpam-6535	328	3	nφ	nφ	ADP
ejpam-6535	328	4	e−1	e−1	PROPN
ejpam-6535	328	5	≤	≤	NOUN
ejpam-6535	328	6	(	(	PUNCT
ejpam-6535	328	7	nφ	nφ	NOUN
ejpam-6535	328	8	e	e	NOUN
ejpam-6535	328	9	)	)	PUNCT
ejpam-6535	328	10	−1	−1	NOUN
ejpam-6535	328	11	.	.	PUNCT
ejpam-6535	329	1	(	(	PUNCT
ejpam-6535	329	2	b	b	X
ejpam-6535	329	3	)	)	PUNCT
ejpam-6535	329	4	need	need	VERB
ejpam-6535	329	5	to	to	PART
ejpam-6535	329	6	show	show	VERB
ejpam-6535	329	7	that	that	SCONJ
ejpam-6535	329	8	for	for	ADP
ejpam-6535	329	9	a	a	DET
ejpam-6535	329	10	triangle	triangle	NOUN
ejpam-6535	329	11	function	function	NOUN
ejpam-6535	329	12	τ	τ	PROPN
ejpam-6535	329	13	,	,	PUNCT
ejpam-6535	329	14	n	n	CCONJ
ejpam-6535	329	15	τ(φ	τ(φ	NUM
ejpam-6535	329	16	,	,	PUNCT
ejpam-6535	329	17	ψ	ψ	NOUN
ejpam-6535	329	18	)	)	PUNCT
ejpam-6535	330	1	e	e	NOUN
ejpam-6535	330	2	≤	≤	NUM
ejpam-6535	330	3	nφ	nφ	ADP
ejpam-6535	330	4	e	e	NOUN
ejpam-6535	330	5	⊙nψ	⊙nψ	NOUN
ejpam-6535	330	6	e	e	NOUN
ejpam-6535	330	7	if	if	SCONJ
ejpam-6535	330	8	and	and	CCONJ
ejpam-6535	330	9	only	only	ADV
ejpam-6535	330	10	if	if	SCONJ
ejpam-6535	330	11	for	for	ADP
ejpam-6535	330	12	any	any	DET
ejpam-6535	330	13	f	f	NOUN
ejpam-6535	330	14	,	,	PUNCT
ejpam-6535	330	15	g	g	PROPN
ejpam-6535	330	16	∈	∈	PROPN
ejpam-6535	330	17	f(s	f(	VERB
ejpam-6535	330	18	)	)	PUNCT
ejpam-6535	330	19	and	and	CCONJ
ejpam-6535	330	20	for	for	ADP
ejpam-6535	330	21	all	all	DET
ejpam-6535	330	22	φ	φ	NOUN
ejpam-6535	330	23	,	,	PUNCT
ejpam-6535	330	24	ψ	ψ	X
ejpam-6535	330	25	∈	∈	NOUN
ejpam-6535	330	26	∆+	∆+	NOUN
ejpam-6535	330	27	,	,	PUNCT
ejpam-6535	330	28	e	e	X
ejpam-6535	330	29	∈	∈	PROPN
ejpam-6535	330	30	cφ(f	cφ(f	PUNCT
ejpam-6535	330	31	)	)	PUNCT
ejpam-6535	330	32	and	and	CCONJ
ejpam-6535	330	33	e	e	PROPN
ejpam-6535	330	34	∈	∈	PROPN
ejpam-6535	330	35	cψ(g	cψ(g	NOUN
ejpam-6535	330	36	)	)	PUNCT
ejpam-6535	330	37	imply	imply	VERB
ejpam-6535	330	38	e	e	PROPN
ejpam-6535	330	39	∈	∈	PROPN
ejpam-6535	330	40	cτ(φ	cτ(φ	NOUN
ejpam-6535	330	41	,	,	PUNCT
ejpam-6535	330	42	ψ	ψ	NOUN
ejpam-6535	330	43	)	)	PUNCT
ejpam-6535	330	44	(	(	PUNCT
ejpam-6535	330	45	f⊙g	f⊙g	NOUN
ejpam-6535	330	46	)	)	PUNCT
ejpam-6535	330	47	.	.	PUNCT
ejpam-6535	331	1	first	first	ADV
ejpam-6535	331	2	,	,	PUNCT
ejpam-6535	331	3	for	for	ADP
ejpam-6535	331	4	f	f	PROPN
ejpam-6535	331	5	,	,	PUNCT
ejpam-6535	331	6	g	g	PROPN
ejpam-6535	331	7	∈	∈	PROPN
ejpam-6535	331	8	f(s	f(	VERB
ejpam-6535	331	9	)	)	PUNCT
ejpam-6535	331	10	and	and	CCONJ
ejpam-6535	331	11	φ	φ	NUM
ejpam-6535	331	12	,	,	PUNCT
ejpam-6535	331	13	ψ	ψ	X
ejpam-6535	331	14	∈	∈	PROPN
ejpam-6535	331	15	∆+	∆+	NOUN
ejpam-6535	331	16	,	,	PUNCT
ejpam-6535	331	17	let	let	VERB
ejpam-6535	331	18	e	e	NOUN
ejpam-6535	331	19	∈	∈	PROPN
ejpam-6535	331	20	cφ(f	cφ(f	PUNCT
ejpam-6535	331	21	)	)	PUNCT
ejpam-6535	331	22	and	and	CCONJ
ejpam-6535	331	23	e	e	PROPN
ejpam-6535	331	24	∈	∈	PROPN
ejpam-6535	331	25	cψ(g	cψ(g	NOUN
ejpam-6535	331	26	)	)	PUNCT
ejpam-6535	331	27	.	.	PUNCT
ejpam-6535	332	1	consequently	consequently	ADV
ejpam-6535	332	2	,	,	PUNCT
ejpam-6535	332	3	we	we	PRON
ejpam-6535	332	4	have	have	VERB
ejpam-6535	332	5	f	f	PROPN
ejpam-6535	332	6	≥	≥	PROPN
ejpam-6535	332	7	nφ	nφ	PROPN
ejpam-6535	332	8	e	e	PROPN
ejpam-6535	332	9	and	and	CCONJ
ejpam-6535	332	10	g	g	PROPN
ejpam-6535	332	11	≥	≥	NOUN
ejpam-6535	332	12	nψ	nψ	PROPN
ejpam-6535	332	13	e	e	X
ejpam-6535	332	14	.	.	PUNCT
ejpam-6535	333	1	thus	thus	ADV
ejpam-6535	333	2	,	,	PUNCT
ejpam-6535	333	3	we	we	PRON
ejpam-6535	333	4	have	have	VERB
ejpam-6535	333	5	f⊙g	f⊙g	PROPN
ejpam-6535	333	6	≥	≥	PROPN
ejpam-6535	333	7	nφ	nφ	PROPN
ejpam-6535	333	8	e	e	PROPN
ejpam-6535	333	9	⊙nψ	⊙nψ	PROPN
ejpam-6535	333	10	e	e	X
ejpam-6535	333	11	.	.	PUNCT
ejpam-6535	334	1	due	due	ADP
ejpam-6535	334	2	to	to	ADP
ejpam-6535	334	3	the	the	DET
ejpam-6535	334	4	assumption	assumption	NOUN
ejpam-6535	334	5	,	,	PUNCT
ejpam-6535	334	6	we	we	PRON
ejpam-6535	334	7	obtain	obtain	VERB
ejpam-6535	334	8	:	:	PUNCT
ejpam-6535	334	9	f	f	PROPN
ejpam-6535	334	10	⊙	⊙	PROPN
ejpam-6535	334	11	g	g	PROPN
ejpam-6535	334	12	≥	≥	PROPN
ejpam-6535	334	13	n	n	CCONJ
ejpam-6535	334	14	τ(φ	τ(φ	X
ejpam-6535	334	15	,	,	PUNCT
ejpam-6535	334	16	ψ	ψ	NOUN
ejpam-6535	334	17	)	)	PUNCT
ejpam-6535	334	18	e	e	X
ejpam-6535	334	19	.	.	PUNCT
ejpam-6535	335	1	this	this	PRON
ejpam-6535	335	2	implies	imply	VERB
ejpam-6535	335	3	e	e	PROPN
ejpam-6535	335	4	∈	∈	PROPN
ejpam-6535	335	5	cτ(φ	cτ(φ	NOUN
ejpam-6535	335	6	,	,	PUNCT
ejpam-6535	335	7	ψ	ψ	NOUN
ejpam-6535	335	8	)	)	PUNCT
ejpam-6535	335	9	(	(	PUNCT
ejpam-6535	335	10	f⊙g	f⊙g	NOUN
ejpam-6535	335	11	)	)	PUNCT
ejpam-6535	335	12	,	,	PUNCT
ejpam-6535	335	13	given	give	VERB
ejpam-6535	335	14	the	the	DET
ejpam-6535	335	15	fact	fact	NOUN
ejpam-6535	335	16	that	that	SCONJ
ejpam-6535	335	17	f	f	PROPN
ejpam-6535	335	18	⊙	⊙	VERB
ejpam-6535	335	19	g	g	PROPN
ejpam-6535	335	20	∈	∈	PROPN
ejpam-6535	335	21	f(s	f(	NOUN
ejpam-6535	335	22	)	)	PUNCT
ejpam-6535	335	23	.	.	PUNCT
ejpam-6535	336	1	to	to	PART
ejpam-6535	336	2	prove	prove	VERB
ejpam-6535	336	3	the	the	DET
ejpam-6535	336	4	converse	converse	NOUN
ejpam-6535	336	5	part	part	NOUN
ejpam-6535	336	6	,	,	PUNCT
ejpam-6535	336	7	upon	upon	SCONJ
ejpam-6535	336	8	using	use	VERB
ejpam-6535	336	9	the	the	DET
ejpam-6535	336	10	assumption	assumption	NOUN
ejpam-6535	336	11	,	,	PUNCT
ejpam-6535	336	12	we	we	PRON
ejpam-6535	336	13	have	have	AUX
ejpam-6535	336	14	:	:	PUNCT
ejpam-6535	336	15	nφ	nφ	NOUN
ejpam-6535	336	16	e⊙nψ	e⊙nψ	NOUN
ejpam-6535	336	17	e	e	NOUN
ejpam-6535	336	18	=	=	NOUN
ejpam-6535	336	19	∧	∧	PROPN
ejpam-6535	336	20	e∈cφ(f	e∈cφ(f	PROPN
ejpam-6535	336	21	)	)	PUNCT
ejpam-6535	336	22	f⊙	f⊙	VERB
ejpam-6535	336	23	∧	∧	PROPN
ejpam-6535	336	24	e∈cψ(g	e∈cψ(g	PROPN
ejpam-6535	336	25	)	)	PUNCT
ejpam-6535	336	26	g	g	PROPN
ejpam-6535	336	27	=	=	PUNCT
ejpam-6535	336	28	∧	∧	PROPN
ejpam-6535	336	29	e∈cφ(f	e∈cφ(f	PROPN
ejpam-6535	336	30	)	)	PUNCT
ejpam-6535	336	31	∧	∧	PROPN
ejpam-6535	336	32	e∈cψ(g	e∈cψ(g	PROPN
ejpam-6535	336	33	)	)	PUNCT
ejpam-6535	336	34	f⊙g	f⊙g	NOUN
ejpam-6535	337	1	≥	≥	PROPN
ejpam-6535	337	2	∧	∧	PROPN
ejpam-6535	337	3	e∈cτ(φ	e∈cτ(φ	PROPN
ejpam-6535	337	4	,	,	PUNCT
ejpam-6535	337	5	ψ)(f⊙g	ψ)(f⊙g	PROPN
ejpam-6535	337	6	)	)	PUNCT
ejpam-6535	337	7	f⊙g	f⊙g	NOUN
ejpam-6535	338	1	=	=	SYM
ejpam-6535	338	2	∧	∧	PROPN
ejpam-6535	338	3	e∈cτ(φ	e∈cτ(φ	PROPN
ejpam-6535	338	4	,	,	PUNCT
ejpam-6535	338	5	ψ)(h	ψ)(h	NUM
ejpam-6535	338	6	)	)	PUNCT
ejpam-6535	338	7	h	h	NOUN
ejpam-6535	338	8	=	=	PUNCT
ejpam-6535	338	9	nτ(φ	nτ(φ	NUM
ejpam-6535	338	10	,	,	PUNCT
ejpam-6535	338	11	ψ	ψ	NOUN
ejpam-6535	338	12	)	)	PUNCT
ejpam-6535	338	13	e	e	NOUN
ejpam-6535	338	14	.	.	PUNCT
ejpam-6535	339	1	lemma	lemma	PROPN
ejpam-6535	339	2	15	15	NUM
ejpam-6535	339	3	.	.	PUNCT
ejpam-6535	340	1	let	let	VERB
ejpam-6535	340	2	(	(	PUNCT
ejpam-6535	340	3	s	s	X
ejpam-6535	340	4	,	,	PUNCT
ejpam-6535	340	5	c	c	AUX
ejpam-6535	340	6	)	)	PUNCT
ejpam-6535	340	7	be	be	AUX
ejpam-6535	340	8	a	a	DET
ejpam-6535	340	9	probabilistic	probabilistic	ADJ
ejpam-6535	340	10	convergence	convergence	NOUN
ejpam-6535	340	11	group	group	NOUN
ejpam-6535	340	12	under	under	ADP
ejpam-6535	340	13	a	a	DET
ejpam-6535	340	14	triangle	triangle	NOUN
ejpam-6535	340	15	function	function	NOUN
ejpam-6535	340	16	τ	τ	X
ejpam-6535	340	17	,	,	PUNCT
ejpam-6535	340	18	and	and	CCONJ
ejpam-6535	340	19	a	a	DET
ejpam-6535	340	20	∈	∈	PROPN
ejpam-6535	340	21	s.	s.	PROPN
ejpam-6535	340	22	then	then	ADV
ejpam-6535	340	23	the	the	DET
ejpam-6535	340	24	left	left	ADJ
ejpam-6535	340	25	translation	translation	NOUN
ejpam-6535	340	26	la	la	NOUN
ejpam-6535	340	27	:	:	PUNCT
ejpam-6535	340	28	(	(	PUNCT
ejpam-6535	340	29	s	s	X
ejpam-6535	340	30	,	,	PUNCT
ejpam-6535	340	31	c	c	NOUN
ejpam-6535	340	32	)	)	PUNCT
ejpam-6535	340	33	−→	−→	NOUN
ejpam-6535	340	34	(	(	PUNCT
ejpam-6535	340	35	s	s	PROPN
ejpam-6535	340	36	,	,	PUNCT
ejpam-6535	340	37	c	c	NOUN
ejpam-6535	340	38	)	)	PUNCT
ejpam-6535	340	39	,	,	PUNCT
ejpam-6535	340	40	p	p	PROPN
ejpam-6535	340	41	7−→	7−→	PROPN
ejpam-6535	340	42	ap	ap	PROPN
ejpam-6535	340	43	and	and	CCONJ
ejpam-6535	340	44	the	the	DET
ejpam-6535	340	45	right	right	ADJ
ejpam-6535	340	46	translation	translation	NOUN
ejpam-6535	340	47	ra	ra	PROPN
ejpam-6535	340	48	:	:	PUNCT
ejpam-6535	340	49	(	(	PUNCT
ejpam-6535	340	50	s	s	X
ejpam-6535	340	51	,	,	PUNCT
ejpam-6535	340	52	c	c	NOUN
ejpam-6535	340	53	)	)	PUNCT
ejpam-6535	340	54	−→	−→	NOUN
ejpam-6535	340	55	(	(	PUNCT
ejpam-6535	340	56	s	s	PROPN
ejpam-6535	340	57	,	,	PUNCT
ejpam-6535	340	58	c	c	NOUN
ejpam-6535	340	59	)	)	PUNCT
ejpam-6535	340	60	,	,	PUNCT
ejpam-6535	340	61	p	p	PROPN
ejpam-6535	340	62	7−→	7−→	PROPN
ejpam-6535	340	63	pa	pa	PROPN
ejpam-6535	340	64	,	,	PUNCT
ejpam-6535	340	65	the	the	DET
ejpam-6535	340	66	inversion	inversion	NOUN
ejpam-6535	340	67	ȷ	ȷ	NOUN
ejpam-6535	340	68	:	:	PUNCT
ejpam-6535	340	69	(	(	PUNCT
ejpam-6535	340	70	s	s	X
ejpam-6535	340	71	,	,	PUNCT
ejpam-6535	340	72	c	c	NOUN
ejpam-6535	340	73	)	)	PUNCT
ejpam-6535	340	74	−→	−→	NOUN
ejpam-6535	340	75	(	(	PUNCT
ejpam-6535	340	76	s	s	PROPN
ejpam-6535	340	77	,	,	PUNCT
ejpam-6535	340	78	c	c	NOUN
ejpam-6535	340	79	)	)	PUNCT
ejpam-6535	340	80	,	,	PUNCT
ejpam-6535	340	81	p	p	PROPN
ejpam-6535	340	82	7−→	7−→	PROPN
ejpam-6535	340	83	p−1	p−1	PROPN
ejpam-6535	340	84	are	be	AUX
ejpam-6535	340	85	homeomorphisms	homeomorphism	NOUN
ejpam-6535	340	86	;	;	PUNCT
ejpam-6535	340	87	and	and	CCONJ
ejpam-6535	340	88	the	the	DET
ejpam-6535	340	89	inner	inner	ADJ
ejpam-6535	340	90	automorphism	automorphism	NOUN
ejpam-6535	340	91	ia	ia	NOUN
ejpam-6535	340	92	:	:	PUNCT
ejpam-6535	340	93	(	(	PUNCT
ejpam-6535	340	94	s	s	X
ejpam-6535	340	95	,	,	PUNCT
ejpam-6535	340	96	c	c	NOUN
ejpam-6535	340	97	)	)	PUNCT
ejpam-6535	340	98	−→	−→	NOUN
ejpam-6535	340	99	(	(	PUNCT
ejpam-6535	340	100	s	s	PROPN
ejpam-6535	340	101	,	,	PUNCT
ejpam-6535	340	102	c	c	NOUN
ejpam-6535	340	103	)	)	PUNCT
ejpam-6535	340	104	,	,	PUNCT
ejpam-6535	340	105	p	p	PROPN
ejpam-6535	340	106	7−→	7−→	PROPN
ejpam-6535	340	107	apa−1	apa−1	PROPN
ejpam-6535	340	108	is	be	AUX
ejpam-6535	340	109	an	an	DET
ejpam-6535	340	110	isomorphism	isomorphism	NOUN
ejpam-6535	340	111	.	.	PUNCT
ejpam-6535	341	1	proof	proof	NOUN
ejpam-6535	341	2	.	.	PUNCT
ejpam-6535	342	1	let	let	VERB
ejpam-6535	342	2	a	a	DET
ejpam-6535	342	3	∈	∈	ADJ
ejpam-6535	342	4	s	s	NOUN
ejpam-6535	342	5	,	,	PUNCT
ejpam-6535	342	6	f	f	PROPN
ejpam-6535	342	7	∈	∈	PROPN
ejpam-6535	342	8	f(s	f(	VERB
ejpam-6535	342	9	)	)	PUNCT
ejpam-6535	342	10	and	and	CCONJ
ejpam-6535	342	11	φ	φ	NUM
ejpam-6535	342	12	∈	∈	PROPN
ejpam-6535	342	13	∆+	∆+	NOUN
ejpam-6535	342	14	.	.	PUNCT
ejpam-6535	343	1	since	since	SCONJ
ejpam-6535	343	2	,	,	PUNCT
ejpam-6535	343	3	in	in	ADP
ejpam-6535	343	4	particular	particular	ADJ
ejpam-6535	343	5	,	,	PUNCT
ejpam-6535	343	6	a	a	DET
ejpam-6535	343	7	∈	∈	PROPN
ejpam-6535	343	8	cϵ0([a	cϵ0([a	NOUN
ejpam-6535	343	9	]	]	PUNCT
ejpam-6535	343	10	)	)	PUNCT
ejpam-6535	343	11	by	by	ADP
ejpam-6535	343	12	(	(	PUNCT
ejpam-6535	343	13	pcs1	pcs1	NOUN
ejpam-6535	343	14	)	)	PUNCT
ejpam-6535	343	15	,	,	PUNCT
ejpam-6535	343	16	we	we	PRON
ejpam-6535	343	17	have	have	VERB
ejpam-6535	343	18	for	for	ADP
ejpam-6535	343	19	any	any	DET
ejpam-6535	343	20	p	p	NOUN
ejpam-6535	343	21	∈	∈	PROPN
ejpam-6535	343	22	cφ(f	cφ(f	NOUN
ejpam-6535	343	23	)	)	PUNCT
ejpam-6535	343	24	,	,	PUNCT
ejpam-6535	343	25	annd	annd	PROPN
ejpam-6535	343	26	(	(	PUNCT
ejpam-6535	343	27	pcgm	pcgm	PROPN
ejpam-6535	343	28	)	)	PUNCT
ejpam-6535	343	29	,	,	PUNCT
ejpam-6535	343	30	ap	ap	PROPN
ejpam-6535	343	31	∈	∈	PROPN
ejpam-6535	343	32	cτ(ϵ0,φ)([a	cτ(ϵ0,φ)([a	PROPN
ejpam-6535	343	33	]	]	X
ejpam-6535	343	34	⊙	⊙	PROPN
ejpam-6535	343	35	f	f	X
ejpam-6535	343	36	)	)	PUNCT
ejpam-6535	343	37	.	.	PUNCT
ejpam-6535	344	1	upon	upon	SCONJ
ejpam-6535	344	2	using	use	VERB
ejpam-6535	344	3	the	the	DET
ejpam-6535	344	4	commutativity	commutativity	NOUN
ejpam-6535	344	5	of	of	ADP
ejpam-6535	344	6	τ	τ	PROPN
ejpam-6535	344	7	and	and	CCONJ
ejpam-6535	344	8	the	the	DET
ejpam-6535	344	9	fact	fact	NOUN
ejpam-6535	344	10	that	that	SCONJ
ejpam-6535	344	11	τ(φ	τ(φ	ADV
ejpam-6535	344	12	,	,	PUNCT
ejpam-6535	344	13	ϵ0	ϵ0	NUM
ejpam-6535	344	14	)	)	PUNCT
ejpam-6535	344	15	=	=	SYM
ejpam-6535	344	16	φ	φ	PROPN
ejpam-6535	344	17	,	,	PUNCT
ejpam-6535	344	18	we	we	PRON
ejpam-6535	344	19	get	get	VERB
ejpam-6535	344	20	ap	ap	PROPN
ejpam-6535	344	21	∈	∈	PROPN
ejpam-6535	344	22	cφ([a	cφ([a	PROPN
ejpam-6535	344	23	]	]	PUNCT
ejpam-6535	344	24	⊙	⊙	PROPN
ejpam-6535	344	25	f	f	X
ejpam-6535	344	26	)	)	PUNCT
ejpam-6535	344	27	implying	imply	VERB
ejpam-6535	344	28	la(p	la(p	NOUN
ejpam-6535	344	29	)	)	PUNCT
ejpam-6535	344	30	∈	∈	PROPN
ejpam-6535	344	31	cφ	cφ	X
ejpam-6535	344	32	(	(	PUNCT
ejpam-6535	344	33	la(f	la(f	NOUN
ejpam-6535	344	34	)	)	PUNCT
ejpam-6535	344	35	)	)	PUNCT
ejpam-6535	344	36	;	;	PUNCT
ejpam-6535	344	37	this	this	PRON
ejpam-6535	344	38	means	mean	VERB
ejpam-6535	344	39	that	that	SCONJ
ejpam-6535	344	40	the	the	DET
ejpam-6535	344	41	left	left	ADJ
ejpam-6535	344	42	translation	translation	NOUN
ejpam-6535	344	43	is	be	AUX
ejpam-6535	344	44	continuous	continuous	ADJ
ejpam-6535	344	45	.	.	PUNCT
ejpam-6535	345	1	also	also	ADV
ejpam-6535	345	2	,	,	PUNCT
ejpam-6535	345	3	la−1	la−1	PROPN
ejpam-6535	345	4	is	be	AUX
ejpam-6535	345	5	continuous	continuous	ADJ
ejpam-6535	345	6	.	.	PUNCT
ejpam-6535	346	1	similarly	similarly	ADV
ejpam-6535	346	2	,	,	PUNCT
ejpam-6535	346	3	one	one	PRON
ejpam-6535	346	4	can	can	AUX
ejpam-6535	346	5	show	show	VERB
ejpam-6535	346	6	that	that	SCONJ
ejpam-6535	346	7	the	the	DET
ejpam-6535	346	8	right	right	ADJ
ejpam-6535	346	9	translation	translation	NOUN
ejpam-6535	346	10	ra	ra	PROPN
ejpam-6535	346	11	and	and	CCONJ
ejpam-6535	346	12	its	its	PRON
ejpam-6535	346	13	inverse	inverse	NOUN
ejpam-6535	346	14	ra−1	ra−1	NOUN
ejpam-6535	346	15	are	be	AUX
ejpam-6535	346	16	continuous	continuous	ADJ
ejpam-6535	346	17	.	.	PUNCT
ejpam-6535	347	1	note	note	VERB
ejpam-6535	347	2	that	that	SCONJ
ejpam-6535	347	3	ia	ia	PROPN
ejpam-6535	347	4	=	=	PUNCT
ejpam-6535	347	5	la	la	PROPN
ejpam-6535	347	6	◦	◦	NOUN
ejpam-6535	347	7	ra−1	ra−1	NOUN
ejpam-6535	347	8	,	,	PUNCT
ejpam-6535	347	9	so	so	ADV
ejpam-6535	347	10	their	their	PRON
ejpam-6535	347	11	composition	composition	NOUN
ejpam-6535	347	12	is	be	AUX
ejpam-6535	347	13	continuous	continuous	ADJ
ejpam-6535	347	14	.	.	PUNCT
ejpam-6535	348	1	we	we	PRON
ejpam-6535	348	2	leave	leave	VERB
ejpam-6535	348	3	the	the	DET
ejpam-6535	348	4	details	detail	NOUN
ejpam-6535	348	5	for	for	ADP
ejpam-6535	348	6	the	the	DET
ejpam-6535	348	7	interested	interested	ADJ
ejpam-6535	348	8	reader	reader	NOUN
ejpam-6535	348	9	.	.	PUNCT
ejpam-6535	349	1	in	in	ADP
ejpam-6535	349	2	view	view	NOUN
ejpam-6535	349	3	of	of	ADP
ejpam-6535	349	4	the	the	DET
ejpam-6535	349	5	lemma	lemma	PROPN
ejpam-6535	349	6	3	3	NUM
ejpam-6535	349	7	,	,	PUNCT
ejpam-6535	349	8	remark	remark	NOUN
ejpam-6535	349	9	5	5	NUM
ejpam-6535	349	10	,	,	PUNCT
ejpam-6535	349	11	and	and	CCONJ
ejpam-6535	349	12	lemma	lemma	PROPN
ejpam-6535	349	13	4	4	NUM
ejpam-6535	349	14	–	–	PUNCT
ejpam-6535	349	15	lemma	lemma	PROPN
ejpam-6535	349	16	6	6	NUM
ejpam-6535	349	17	,	,	PUNCT
ejpam-6535	349	18	we	we	PRON
ejpam-6535	349	19	arrive	arrive	VERB
ejpam-6535	349	20	at	at	ADP
ejpam-6535	349	21	the	the	DET
ejpam-6535	349	22	following	follow	VERB
ejpam-6535	349	23	theorem	theorem	NOUN
ejpam-6535	349	24	1	1	NUM
ejpam-6535	349	25	.	.	PUNCT
ejpam-6535	350	1	the	the	DET
ejpam-6535	350	2	category	category	NOUN
ejpam-6535	350	3	pneighgrp	pneighgrp	NOUN
ejpam-6535	350	4	is	be	AUX
ejpam-6535	350	5	isomorphic	isomorphic	ADJ
ejpam-6535	350	6	to	to	ADP
ejpam-6535	350	7	the	the	DET
ejpam-6535	350	8	category	category	NOUN
ejpam-6535	350	9	ppretopgrp	ppretopgrp	NOUN
ejpam-6535	350	10	.	.	PUNCT
ejpam-6535	351	1	proof	proof	NOUN
ejpam-6535	351	2	.	.	PUNCT
ejpam-6535	352	1	we	we	PRON
ejpam-6535	352	2	only	only	ADV
ejpam-6535	352	3	need	need	VERB
ejpam-6535	352	4	to	to	PART
ejpam-6535	352	5	check	check	VERB
ejpam-6535	352	6	(	(	PUNCT
ejpam-6535	352	7	pcgm	pcgm	PROPN
ejpam-6535	352	8	)	)	PUNCT
ejpam-6535	352	9	and	and	CCONJ
ejpam-6535	352	10	(	(	PUNCT
ejpam-6535	352	11	pcgi	pcgi	PROPN
ejpam-6535	352	12	)	)	PUNCT
ejpam-6535	352	13	.	.	PUNCT
ejpam-6535	353	1	recall	recall	VERB
ejpam-6535	353	2	that	that	PRON
ejpam-6535	353	3	for	for	ADP
ejpam-6535	353	4	any	any	DET
ejpam-6535	353	5	f	f	PROPN
ejpam-6535	353	6	∈	∈	PROPN
ejpam-6535	353	7	f(s	f(	NOUN
ejpam-6535	353	8	)	)	PUNCT
ejpam-6535	353	9	,	,	PUNCT
ejpam-6535	353	10	p	p	PROPN
ejpam-6535	353	11	∈	∈	PROPN
ejpam-6535	353	12	s	s	PART
ejpam-6535	353	13	and	and	CCONJ
ejpam-6535	353	14	φ	φ	PROPN
ejpam-6535	353	15	∈	∈	PROPN
ejpam-6535	353	16	∆+	∆+	NOUN
ejpam-6535	353	17	,	,	PUNCT
ejpam-6535	353	18	we	we	PRON
ejpam-6535	353	19	have	have	VERB
ejpam-6535	353	20	p	p	NOUN
ejpam-6535	353	21	∈	∈	PROPN
ejpam-6535	353	22	cφ(f	cφ(f	NOUN
ejpam-6535	353	23	)	)	PUNCT
ejpam-6535	353	24	⇐	⇐	ADJ
ejpam-6535	353	25	⇒	⇒	PROPN
ejpam-6535	353	26	f	f	PROPN
ejpam-6535	353	27	≥	≥	NOUN
ejpam-6535	353	28	nφ	nφ	ADP
ejpam-6535	353	29	p	p	PROPN
ejpam-6535	353	30	,	,	PUNCT
ejpam-6535	353	31	whence	whence	PROPN
ejpam-6535	353	32	nφ	nφ	PROPN
ejpam-6535	353	33	p	p	PROPN
ejpam-6535	353	34	=	=	PROPN
ejpam-6535	353	35	∧	∧	PROPN
ejpam-6535	353	36	p∈cφ(f	p∈cφ(f	PROPN
ejpam-6535	353	37	)	)	PUNCT
ejpam-6535	353	38	f.	f.	PROPN
ejpam-6535	353	39	now	now	ADV
ejpam-6535	353	40	first	first	ADV
ejpam-6535	353	41	,	,	PUNCT
ejpam-6535	353	42	assume	assume	VERB
ejpam-6535	353	43	n	n	X
ejpam-6535	353	44	τ(φ	τ(φ	X
ejpam-6535	353	45	,	,	PUNCT
ejpam-6535	353	46	ψ	ψ	NOUN
ejpam-6535	353	47	)	)	PUNCT
ejpam-6535	353	48	pq	pq	NOUN
ejpam-6535	353	49	≤	≤	NOUN
ejpam-6535	353	50	nφ	nφ	ADP
ejpam-6535	354	1	p	p	PROPN
ejpam-6535	354	2	⊙	⊙	PROPN
ejpam-6535	355	1	nψ	nψ	PROPN
ejpam-6535	355	2	q	q	PROPN
ejpam-6535	355	3	.	.	PUNCT
ejpam-6535	356	1	let	let	VERB
ejpam-6535	356	2	p	p	X
ejpam-6535	356	3	∈	∈	PROPN
ejpam-6535	356	4	cφ(f	cφ(f	PUNCT
ejpam-6535	356	5	)	)	PUNCT
ejpam-6535	356	6	and	and	CCONJ
ejpam-6535	356	7	q	q	PROPN
ejpam-6535	356	8	∈	∈	PROPN
ejpam-6535	356	9	cψ(g	cψ(g	NOUN
ejpam-6535	356	10	)	)	PUNCT
ejpam-6535	356	11	for	for	ADP
ejpam-6535	356	12	any	any	DET
ejpam-6535	356	13	f	f	NOUN
ejpam-6535	356	14	,	,	PUNCT
ejpam-6535	356	15	g	g	PROPN
ejpam-6535	356	16	∈	∈	PROPN
ejpam-6535	356	17	f(s	f(	NOUN
ejpam-6535	356	18	)	)	PUNCT
ejpam-6535	356	19	.	.	PUNCT
ejpam-6535	357	1	we	we	PRON
ejpam-6535	357	2	need	need	VERB
ejpam-6535	357	3	to	to	PART
ejpam-6535	357	4	show	show	VERB
ejpam-6535	357	5	that	that	SCONJ
ejpam-6535	357	6	pq	pq	PROPN
ejpam-6535	357	7	∈	∈	PROPN
ejpam-6535	357	8	cτ(φ	cτ(φ	NOUN
ejpam-6535	357	9	,	,	PUNCT
ejpam-6535	357	10	ψ	ψ	NOUN
ejpam-6535	357	11	)	)	PUNCT
ejpam-6535	357	12	(	(	PUNCT
ejpam-6535	357	13	f⊙g	f⊙g	NOUN
ejpam-6535	357	14	)	)	PUNCT
ejpam-6535	357	15	.	.	PUNCT
ejpam-6535	358	1	it	it	PRON
ejpam-6535	358	2	follows	follow	VERB
ejpam-6535	358	3	from	from	ADP
ejpam-6535	358	4	the	the	DET
ejpam-6535	358	5	assumption	assumption	NOUN
ejpam-6535	358	6	that	that	SCONJ
ejpam-6535	358	7	f	f	PROPN
ejpam-6535	358	8	≥	≥	VERB
ejpam-6535	358	9	nφ	nφ	ADP
ejpam-6535	358	10	p	p	PROPN
ejpam-6535	358	11	and	and	CCONJ
ejpam-6535	358	12	g	g	PROPN
ejpam-6535	358	13	≥	≥	PRON
ejpam-6535	358	14	nψ	nψ	PROPN
ejpam-6535	358	15	q	q	X
ejpam-6535	358	16	.	.	PUNCT
ejpam-6535	359	1	these	these	PRON
ejpam-6535	359	2	imply	imply	VERB
ejpam-6535	359	3	f	f	PROPN
ejpam-6535	359	4	⊙	⊙	PROPN
ejpam-6535	359	5	g	g	PROPN
ejpam-6535	359	6	≥	≥	PROPN
ejpam-6535	359	7	nφ	nφ	PROPN
ejpam-6535	359	8	p	p	PROPN
ejpam-6535	359	9	⊙	⊙	PROPN
ejpam-6535	360	1	nψ	nψ	PROPN
ejpam-6535	360	2	q	q	PROPN
ejpam-6535	360	3	≥	≥	NOUN
ejpam-6535	360	4	n	n	CCONJ
ejpam-6535	360	5	τ(φ	τ(φ	X
ejpam-6535	360	6	,	,	PUNCT
ejpam-6535	360	7	ψ	ψ	NOUN
ejpam-6535	360	8	)	)	PUNCT
ejpam-6535	360	9	pq	pq	NOUN
ejpam-6535	360	10	,	,	PUNCT
ejpam-6535	360	11	i.e.	i.e.	X
ejpam-6535	360	12	,	,	PUNCT
ejpam-6535	360	13	f	f	PROPN
ejpam-6535	360	14	⊙	⊙	PROPN
ejpam-6535	360	15	g	g	PROPN
ejpam-6535	360	16	≥	≥	PROPN
ejpam-6535	360	17	n	n	CCONJ
ejpam-6535	360	18	τ(φ	τ(φ	X
ejpam-6535	360	19	,	,	PUNCT
ejpam-6535	360	20	ψ	ψ	NOUN
ejpam-6535	360	21	)	)	PUNCT
ejpam-6535	360	22	pq	pq	NOUN
ejpam-6535	360	23	whence	whence	PROPN
ejpam-6535	360	24	f	f	PROPN
ejpam-6535	360	25	⊙	⊙	PROPN
ejpam-6535	360	26	g	g	PROPN
ejpam-6535	360	27	∈	∈	PROPN
ejpam-6535	360	28	f(s	f(	NOUN
ejpam-6535	360	29	)	)	PUNCT
ejpam-6535	360	30	,	,	PUNCT
ejpam-6535	360	31	and	and	CCONJ
ejpam-6535	360	32	hence	hence	ADV
ejpam-6535	360	33	pq	pq	NOUN
ejpam-6535	360	34	∈	∈	PROPN
ejpam-6535	360	35	cτ(φ	cτ(φ	NOUN
ejpam-6535	360	36	,	,	PUNCT
ejpam-6535	360	37	ψ	ψ	NOUN
ejpam-6535	360	38	)	)	PUNCT
ejpam-6535	360	39	(	(	PUNCT
ejpam-6535	360	40	f⊙g	f⊙g	NOUN
ejpam-6535	360	41	)	)	PUNCT
ejpam-6535	360	42	.	.	PUNCT
ejpam-6535	361	1	similarly	similarly	ADV
ejpam-6535	361	2	,	,	PUNCT
ejpam-6535	361	3	one	one	PRON
ejpam-6535	361	4	can	can	AUX
ejpam-6535	361	5	show	show	VERB
ejpam-6535	361	6	that	that	SCONJ
ejpam-6535	361	7	if	if	SCONJ
ejpam-6535	361	8	p	p	PROPN
ejpam-6535	361	9	∈	∈	PROPN
ejpam-6535	361	10	cφ(f	cφ(f	NOUN
ejpam-6535	361	11	)	)	PUNCT
ejpam-6535	361	12	,	,	PUNCT
ejpam-6535	361	13	then	then	ADV
ejpam-6535	361	14	p−1	p−1	PROPN
ejpam-6535	361	15	∈	∈	PROPN
ejpam-6535	361	16	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	361	17	)	)	PUNCT
ejpam-6535	361	18	.	.	PUNCT
ejpam-6535	362	1	for	for	ADP
ejpam-6535	362	2	the	the	DET
ejpam-6535	362	3	converse	converse	NOUN
ejpam-6535	362	4	part	part	NOUN
ejpam-6535	362	5	,	,	PUNCT
ejpam-6535	362	6	let	let	VERB
ejpam-6535	362	7	us	we	PRON
ejpam-6535	362	8	first	first	ADV
ejpam-6535	362	9	prove	prove	VERB
ejpam-6535	362	10	that	that	SCONJ
ejpam-6535	362	11	for	for	SCONJ
ejpam-6535	362	12	any	any	DET
ejpam-6535	362	13	(	(	PUNCT
ejpam-6535	362	14	s	s	PROPN
ejpam-6535	362	15	,	,	PUNCT
ejpam-6535	362	16	t	t	PROPN
ejpam-6535	362	17	)	)	PUNCT
ejpam-6535	362	18	∈	∈	PROPN
ejpam-6535	362	19	s	s	PART
ejpam-6535	362	20	×	×	NOUN
ejpam-6535	362	21	s	s	PROPN
ejpam-6535	362	22	,	,	PUNCT
ejpam-6535	362	23	φ	φ	X
ejpam-6535	362	24	,	,	PUNCT
ejpam-6535	362	25	ψ	ψ	PROPN
ejpam-6535	362	26	∈	∈	PROPN
ejpam-6535	362	27	∆+	∆+	NUM
ejpam-6535	362	28	and	and	CCONJ
ejpam-6535	362	29	f	f	X
ejpam-6535	362	30	,	,	PUNCT
ejpam-6535	362	31	g	g	PROPN
ejpam-6535	362	32	∈	∈	PROPN
ejpam-6535	362	33	f(s	f(	NOUN
ejpam-6535	362	34	)	)	PUNCT
ejpam-6535	362	35	,	,	PUNCT
ejpam-6535	362	36	nτ(φ	nτ(φ	NUM
ejpam-6535	362	37	,	,	PUNCT
ejpam-6535	362	38	ψ	ψ	NOUN
ejpam-6535	362	39	)	)	PUNCT
ejpam-6535	362	40	st	st	PROPN
ejpam-6535	362	41	≤	≤	PROPN
ejpam-6535	362	42	nφ	nφ	PROPN
ejpam-6535	362	43	s	s	PROPN
ejpam-6535	362	44	⊙	⊙	PROPN
ejpam-6535	362	45	nψ	nψ	PROPN
ejpam-6535	362	46	t	t	PROPN
ejpam-6535	362	47	.	.	PUNCT
ejpam-6535	363	1	this	this	PRON
ejpam-6535	363	2	follows	follow	VERB
ejpam-6535	363	3	from	from	ADP
ejpam-6535	363	4	the	the	DET
ejpam-6535	363	5	compositions	composition	NOUN
ejpam-6535	363	6	of	of	ADP
ejpam-6535	363	7	the	the	DET
ejpam-6535	363	8	continuities	continuity	NOUN
ejpam-6535	363	9	of	of	ADP
ejpam-6535	363	10	the	the	DET
ejpam-6535	363	11	mappings	mapping	NOUN
ejpam-6535	363	12	at	at	ADP
ejpam-6535	363	13	the	the	DET
ejpam-6535	363	14	identity	identity	NOUN
ejpam-6535	363	15	elements	element	NOUN
ejpam-6535	363	16	give	give	VERB
ejpam-6535	363	17	rise	rise	NOUN
ejpam-6535	363	18	to	to	ADP
ejpam-6535	363	19	the	the	DET
ejpam-6535	363	20	continuity	continuity	NOUN
ejpam-6535	363	21	of	of	ADP
ejpam-6535	363	22	h	h	NOUN
ejpam-6535	363	23	:	:	PUNCT
ejpam-6535	363	24	s	s	AUX
ejpam-6535	363	25	×	×	NOUN
ejpam-6535	363	26	s	s	PART
ejpam-6535	363	27	−→	−→	NOUN
ejpam-6535	363	28	s	s	NOUN
ejpam-6535	363	29	,	,	PUNCT
ejpam-6535	363	30	(	(	PUNCT
ejpam-6535	363	31	p	p	X
ejpam-6535	363	32	,	,	PUNCT
ejpam-6535	363	33	q	q	NOUN
ejpam-6535	363	34	)	)	PUNCT
ejpam-6535	363	35	7−→	7−→	NOUN
ejpam-6535	363	36	pq−1	pq−1	NOUN
ejpam-6535	363	37	at	at	ADP
ejpam-6535	363	38	any	any	DET
ejpam-6535	363	39	point	point	NOUN
ejpam-6535	363	40	(	(	PUNCT
ejpam-6535	363	41	s	s	PROPN
ejpam-6535	363	42	,	,	PUNCT
ejpam-6535	363	43	t	t	PROPN
ejpam-6535	363	44	)	)	PUNCT
ejpam-6535	363	45	in	in	ADP
ejpam-6535	363	46	the	the	DET
ejpam-6535	363	47	following	following	ADJ
ejpam-6535	363	48	way	way	NOUN
ejpam-6535	363	49	:	:	PUNCT
ejpam-6535	363	50	s	s	VERB
ejpam-6535	363	51	×	×	NOUN
ejpam-6535	363	52	s	s	X
ejpam-6535	363	53	ls−1×lt−1−→	ls−1×lt−1−→	NOUN
ejpam-6535	363	54	s	s	PART
ejpam-6535	363	55	×	×	NOUN
ejpam-6535	363	56	s	s	PART
ejpam-6535	363	57	m−→	m−→	NOUN
ejpam-6535	363	58	s	s	NOUN
ejpam-6535	363	59	it−→	it−→	NOUN
ejpam-6535	363	60	s	s	NOUN
ejpam-6535	363	61	lst−1−→	lst−1−→	NOUN
ejpam-6535	363	62	s	s	PROPN
ejpam-6535	363	63	,	,	PUNCT
ejpam-6535	363	64	(	(	PUNCT
ejpam-6535	363	65	s	s	X
ejpam-6535	363	66	,	,	PUNCT
ejpam-6535	363	67	t	t	PROPN
ejpam-6535	363	68	)	)	PUNCT
ejpam-6535	363	69	7−→	7−→	PROPN
ejpam-6535	363	70	(	(	PUNCT
ejpam-6535	363	71	e	e	NOUN
ejpam-6535	363	72	,	,	PUNCT
ejpam-6535	363	73	e	e	NOUN
ejpam-6535	363	74	)	)	PUNCT
ejpam-6535	363	75	7−→	7−→	NOUN
ejpam-6535	363	76	e	e	NOUN
ejpam-6535	363	77	7−→	7−→	NOUN
ejpam-6535	363	78	e	e	PROPN
ejpam-6535	363	79	7−→	7−→	PROPN
ejpam-6535	363	80	st−1	st−1	NOUN
ejpam-6535	363	81	.	.	PUNCT
ejpam-6535	364	1	the	the	DET
ejpam-6535	364	2	continuity	continuity	NOUN
ejpam-6535	364	3	at	at	ADP
ejpam-6535	364	4	any	any	DET
ejpam-6535	364	5	s	s	X
ejpam-6535	364	6	∈	∈	NOUN
ejpam-6535	364	7	s	s	NOUN
ejpam-6535	364	8	for	for	ADP
ejpam-6535	364	9	the	the	DET
ejpam-6535	364	10	mapping	mapping	NOUN
ejpam-6535	364	11	ȷ	ȷ	NOUN
ejpam-6535	364	12	:	:	PUNCT
ejpam-6535	364	13	s	s	AUX
ejpam-6535	364	14	−→	−→	NOUN
ejpam-6535	364	15	s	s	NOUN
ejpam-6535	364	16	,	,	PUNCT
ejpam-6535	364	17	s	s	VERB
ejpam-6535	364	18	7−→	7−→	NOUN
ejpam-6535	364	19	s−1	s−1	PROPN
ejpam-6535	364	20	follows	follow	VERB
ejpam-6535	364	21	directly	directly	ADV
ejpam-6535	364	22	from	from	ADP
ejpam-6535	364	23	the	the	DET
ejpam-6535	364	24	definition	definition	NOUN
ejpam-6535	364	25	.	.	PUNCT
ejpam-6535	365	1	lemma	lemma	PROPN
ejpam-6535	365	2	16	16	NUM
ejpam-6535	365	3	.	.	PUNCT
ejpam-6535	366	1	let	let	AUX
ejpam-6535	366	2	(	(	PUNCT
ejpam-6535	366	3	s	s	X
ejpam-6535	366	4	,	,	PUNCT
ejpam-6535	366	5	·	·	PUNCT
ejpam-6535	366	6	,	,	PUNCT
ejpam-6535	366	7	c	c	X
ejpam-6535	366	8	)	)	PUNCT
ejpam-6535	366	9	be	be	AUX
ejpam-6535	366	10	a	a	DET
ejpam-6535	366	11	probabilistic	probabilistic	ADJ
ejpam-6535	366	12	convergence	convergence	NOUN
ejpam-6535	366	13	group	group	NOUN
ejpam-6535	366	14	and	and	CCONJ
ejpam-6535	366	15	a	a	DET
ejpam-6535	366	16	⊆	⊆	NUM
ejpam-6535	366	17	s.	s.	PROPN
ejpam-6535	366	18	then	then	ADV
ejpam-6535	366	19	the	the	DET
ejpam-6535	366	20	following	follow	VERB
ejpam-6535	366	21	are	be	AUX
ejpam-6535	366	22	true	true	ADJ
ejpam-6535	366	23	:	:	PUNCT
ejpam-6535	366	24	(	(	PUNCT
ejpam-6535	366	25	a	a	X
ejpam-6535	366	26	)	)	PUNCT
ejpam-6535	366	27	if	if	SCONJ
ejpam-6535	366	28	a	a	PRON
ejpam-6535	366	29	is	be	AUX
ejpam-6535	366	30	a	a	DET
ejpam-6535	366	31	subgroup	subgroup	NOUN
ejpam-6535	366	32	of	of	ADP
ejpam-6535	366	33	s	s	PROPN
ejpam-6535	366	34	,	,	PUNCT
ejpam-6535	366	35	then	then	ADV
ejpam-6535	366	36	cφ(a	cφ(a	X
ejpam-6535	366	37	)	)	PUNCT
ejpam-6535	366	38	is	be	AUX
ejpam-6535	366	39	also	also	ADV
ejpam-6535	366	40	a	a	DET
ejpam-6535	366	41	subgroup	subgroup	NOUN
ejpam-6535	366	42	of	of	ADP
ejpam-6535	366	43	s	s	PROPN
ejpam-6535	366	44	;	;	PUNCT
ejpam-6535	366	45	(	(	PUNCT
ejpam-6535	366	46	b	b	X
ejpam-6535	366	47	)	)	PUNCT
ejpam-6535	366	48	if	if	SCONJ
ejpam-6535	366	49	n	n	PRON
ejpam-6535	366	50	is	be	AUX
ejpam-6535	366	51	a	a	DET
ejpam-6535	366	52	normal	normal	ADJ
ejpam-6535	366	53	subgroup	subgroup	NOUN
ejpam-6535	366	54	of	of	ADP
ejpam-6535	366	55	the	the	DET
ejpam-6535	366	56	subgroup	subgroup	NOUN
ejpam-6535	366	57	of	of	ADP
ejpam-6535	366	58	a	a	PRON
ejpam-6535	366	59	of	of	ADP
ejpam-6535	366	60	s	s	PROPN
ejpam-6535	366	61	,	,	PUNCT
ejpam-6535	366	62	then	then	ADV
ejpam-6535	366	63	cφ(n	cφ(n	NOUN
ejpam-6535	366	64	)	)	PUNCT
ejpam-6535	366	65	is	be	AUX
ejpam-6535	366	66	a	a	DET
ejpam-6535	366	67	normal	normal	ADJ
ejpam-6535	366	68	subgroup	subgroup	NOUN
ejpam-6535	366	69	of	of	ADP
ejpam-6535	366	70	the	the	DET
ejpam-6535	366	71	subgroup	subgroup	NOUN
ejpam-6535	366	72	cφ(a	cφ(a	NOUN
ejpam-6535	366	73	)	)	PUNCT
ejpam-6535	366	74	.	.	PUNCT
ejpam-6535	367	1	proof	proof	NOUN
ejpam-6535	367	2	.	.	PUNCT
ejpam-6535	368	1	(	(	PUNCT
ejpam-6535	368	2	a	a	X
ejpam-6535	368	3	)	)	PUNCT
ejpam-6535	368	4	if	if	SCONJ
ejpam-6535	368	5	p	p	X
ejpam-6535	368	6	,	,	PUNCT
ejpam-6535	368	7	q	q	PROPN
ejpam-6535	368	8	∈	∈	PROPN
ejpam-6535	368	9	a	a	PRON
ejpam-6535	368	10	,	,	PUNCT
ejpam-6535	368	11	then	then	ADV
ejpam-6535	368	12	p−1q	p−1q	PROPN
ejpam-6535	368	13	∈	∈	PROPN
ejpam-6535	368	14	a	a	DET
ejpam-6535	368	15	since	since	SCONJ
ejpam-6535	368	16	a	a	PRON
ejpam-6535	368	17	is	be	AUX
ejpam-6535	368	18	a	a	DET
ejpam-6535	368	19	subgroup	subgroup	NOUN
ejpam-6535	368	20	of	of	ADP
ejpam-6535	368	21	s.	s.	PROPN
ejpam-6535	368	22	let	let	VERB
ejpam-6535	368	23	p	p	PRON
ejpam-6535	368	24	,	,	PUNCT
ejpam-6535	368	25	q	q	NOUN
ejpam-6535	368	26	∈	∈	NOUN
ejpam-6535	368	27	cφ(a	cφ(a	NOUN
ejpam-6535	368	28	)	)	PUNCT
ejpam-6535	368	29	.	.	PUNCT
ejpam-6535	369	1	then	then	ADV
ejpam-6535	369	2	there	there	PRON
ejpam-6535	369	3	exists	exist	VERB
ejpam-6535	369	4	f	f	X
ejpam-6535	369	5	,	,	PUNCT
ejpam-6535	369	6	g	g	PROPN
ejpam-6535	369	7	∈	∈	PROPN
ejpam-6535	369	8	f(s	f(	VERB
ejpam-6535	369	9	)	)	PUNCT
ejpam-6535	369	10	such	such	ADJ
ejpam-6535	369	11	that	that	SCONJ
ejpam-6535	369	12	p	p	PROPN
ejpam-6535	369	13	∈	∈	PROPN
ejpam-6535	369	14	cφ(f	cφ(f	PUNCT
ejpam-6535	369	15	)	)	PUNCT
ejpam-6535	369	16	and	and	CCONJ
ejpam-6535	369	17	q	q	PROPN
ejpam-6535	369	18	∈	∈	PROPN
ejpam-6535	369	19	cψ(g	cψ(g	NOUN
ejpam-6535	369	20	)	)	PUNCT
ejpam-6535	369	21	implying	imply	VERB
ejpam-6535	369	22	a	a	DET
ejpam-6535	369	23	∈	∈	PROPN
ejpam-6535	369	24	f	f	NOUN
ejpam-6535	369	25	and	and	CCONJ
ejpam-6535	369	26	a	a	DET
ejpam-6535	369	27	∈	∈	PROPN
ejpam-6535	369	28	g.	g.	NOUN
ejpam-6535	369	29	by	by	ADP
ejpam-6535	369	30	(	(	PUNCT
ejpam-6535	369	31	pcgm)′	pcgm)′	PROPN
ejpam-6535	369	32	,	,	PUNCT
ejpam-6535	369	33	p−1q	p−1q	NOUN
ejpam-6535	369	34	∈	∈	PROPN
ejpam-6535	369	35	cτ(φ	cτ(φ	NOUN
ejpam-6535	369	36	,	,	PUNCT
ejpam-6535	369	37	ψ	ψ	NOUN
ejpam-6535	369	38	)	)	PUNCT
ejpam-6535	369	39	(	(	PUNCT
ejpam-6535	369	40	f−1	f−1	PROPN
ejpam-6535	369	41	⊙g	⊙g	PROPN
ejpam-6535	369	42	)	)	PUNCT
ejpam-6535	369	43	,	,	PUNCT
ejpam-6535	369	44	whence	whence	PROPN
ejpam-6535	369	45	a−1	a−1	PROPN
ejpam-6535	369	46	·	·	PUNCT
ejpam-6535	369	47	a	a	DET
ejpam-6535	369	48	∈	∈	PROPN
ejpam-6535	369	49	f−1	f−1	PROPN
ejpam-6535	369	50	⊙g	⊙g	NOUN
ejpam-6535	369	51	;	;	PUNCT
ejpam-6535	369	52	since	since	SCONJ
ejpam-6535	369	53	a	a	PRON
ejpam-6535	369	54	is	be	AUX
ejpam-6535	369	55	a	a	DET
ejpam-6535	369	56	subgroup	subgroup	NOUN
ejpam-6535	369	57	of	of	ADP
ejpam-6535	369	58	s	s	PRON
ejpam-6535	369	59	meaning	mean	VERB
ejpam-6535	369	60	a−1	a−1	PROPN
ejpam-6535	369	61	·	·	PUNCT
ejpam-6535	369	62	a	a	DET
ejpam-6535	369	63	⊆	⊆	NUM
ejpam-6535	369	64	a	a	NOUN
ejpam-6535	369	65	,	,	PUNCT
ejpam-6535	369	66	and	and	CCONJ
ejpam-6535	369	67	p−1q	p−1q	PROPN
ejpam-6535	369	68	∈	∈	PROPN
ejpam-6535	369	69	a	a	PRON
ejpam-6535	369	70	,	,	PUNCT
ejpam-6535	369	71	implying	imply	VERB
ejpam-6535	369	72	a	a	DET
ejpam-6535	369	73	∈	∈	PROPN
ejpam-6535	369	74	f−1⊙g	f−1⊙g	NOUN
ejpam-6535	369	75	.	.	PUNCT
ejpam-6535	370	1	thus	thus	ADV
ejpam-6535	370	2	,	,	PUNCT
ejpam-6535	370	3	we	we	PRON
ejpam-6535	370	4	have	have	VERB
ejpam-6535	370	5	we	we	PRON
ejpam-6535	370	6	obtained	obtain	VERB
ejpam-6535	370	7	a	a	DET
ejpam-6535	370	8	filter	filter	NOUN
ejpam-6535	370	9	f−1	f−1	PROPN
ejpam-6535	370	10	⊙g	⊙g	NOUN
ejpam-6535	370	11	∈	∈	PROPN
ejpam-6535	370	12	f(s	f(	NOUN
ejpam-6535	370	13	)	)	PUNCT
ejpam-6535	370	14	such	such	ADJ
ejpam-6535	370	15	that	that	DET
ejpam-6535	370	16	p−1q	p−1q	PROPN
ejpam-6535	370	17	∈	∈	PROPN
ejpam-6535	370	18	cτ(φ	cτ(φ	PRON
ejpam-6535	370	19	,	,	PUNCT
ejpam-6535	370	20	ψ)(f−1	ψ)(f−1	NOUN
ejpam-6535	370	21	⊙g	⊙g	NOUN
ejpam-6535	370	22	)	)	PUNCT
ejpam-6535	370	23	and	and	CCONJ
ejpam-6535	370	24	a	a	DET
ejpam-6535	370	25	∈	∈	PROPN
ejpam-6535	370	26	f−1	f−1	PROPN
ejpam-6535	370	27	⊙g	⊙g	NOUN
ejpam-6535	370	28	,	,	PUNCT
ejpam-6535	370	29	showing	show	VERB
ejpam-6535	370	30	that	that	SCONJ
ejpam-6535	370	31	p−1q	p−1q	PROPN
ejpam-6535	370	32	∈	∈	PROPN
ejpam-6535	370	33	cφ(a	cφ(a	NOUN
ejpam-6535	370	34	)	)	PUNCT
ejpam-6535	370	35	.	.	PUNCT
ejpam-6535	371	1	(	(	PUNCT
ejpam-6535	371	2	b	b	X
ejpam-6535	371	3	)	)	PUNCT
ejpam-6535	371	4	let	let	VERB
ejpam-6535	371	5	s	s	PRON
ejpam-6535	371	6	∈	∈	NOUN
ejpam-6535	371	7	cφ(a	cφ(a	NOUN
ejpam-6535	371	8	)	)	PUNCT
ejpam-6535	371	9	and	and	CCONJ
ejpam-6535	371	10	p	p	PROPN
ejpam-6535	371	11	∈	∈	PROPN
ejpam-6535	371	12	cψ(n	cψ(n	NOUN
ejpam-6535	371	13	)	)	PUNCT
ejpam-6535	371	14	,	,	PUNCT
ejpam-6535	371	15	we	we	PRON
ejpam-6535	371	16	show	show	VERB
ejpam-6535	371	17	that	that	SCONJ
ejpam-6535	371	18	sps−1	sps−1	PROPN
ejpam-6535	371	19	∈	∈	PROPN
ejpam-6535	371	20	cτ(φ	cτ(φ	PRON
ejpam-6535	371	21	,	,	PUNCT
ejpam-6535	371	22	φ)(n	φ)(n	NUM
ejpam-6535	371	23	)	)	PUNCT
ejpam-6535	371	24	.	.	PUNCT
ejpam-6535	372	1	then	then	ADV
ejpam-6535	372	2	there	there	PRON
ejpam-6535	372	3	are	be	VERB
ejpam-6535	372	4	filters	filter	NOUN
ejpam-6535	372	5	f	f	PROPN
ejpam-6535	372	6	and	and	CCONJ
ejpam-6535	372	7	g	g	PROPN
ejpam-6535	372	8	such	such	ADJ
ejpam-6535	372	9	that	that	DET
ejpam-6535	372	10	s	s	X
ejpam-6535	372	11	∈	∈	NOUN
ejpam-6535	372	12	cφ(f	cφ(f	PUNCT
ejpam-6535	372	13	)	)	PUNCT
ejpam-6535	372	14	and	and	CCONJ
ejpam-6535	372	15	p	p	PROPN
ejpam-6535	372	16	∈	∈	PROPN
ejpam-6535	372	17	cψ(g	cψ(g	NOUN
ejpam-6535	372	18	)	)	PUNCT
ejpam-6535	372	19	,	,	PUNCT
ejpam-6535	372	20	whence	whence	ADP
ejpam-6535	372	21	a	a	DET
ejpam-6535	372	22	∈	∈	PROPN
ejpam-6535	372	23	f	f	X
ejpam-6535	372	24	and	and	CCONJ
ejpam-6535	372	25	n	n	CCONJ
ejpam-6535	372	26	∈	∈	PROPN
ejpam-6535	372	27	g.	g.	NOUN
ejpam-6535	372	28	in	in	ADP
ejpam-6535	372	29	view	view	NOUN
ejpam-6535	372	30	of	of	ADP
ejpam-6535	372	31	the	the	DET
ejpam-6535	372	32	lemma	lemma	PROPN
ejpam-6535	372	33	15	15	NUM
ejpam-6535	372	34	,	,	PUNCT
ejpam-6535	372	35	it	it	PRON
ejpam-6535	372	36	follows	follow	VERB
ejpam-6535	372	37	from	from	ADP
ejpam-6535	372	38	the	the	DET
ejpam-6535	372	39	continuity	continuity	NOUN
ejpam-6535	372	40	of	of	ADP
ejpam-6535	372	41	the	the	DET
ejpam-6535	372	42	inner	inner	ADJ
ejpam-6535	372	43	automorphism	automorphism	NOUN
ejpam-6535	372	44	is(p	is(p	NOUN
ejpam-6535	372	45	)	)	PUNCT
ejpam-6535	372	46	=	=	PUNCT
ejpam-6535	373	1	sps−1	sps−1	PROPN
ejpam-6535	373	2	which	which	PRON
ejpam-6535	373	3	is	be	AUX
ejpam-6535	373	4	also	also	ADV
ejpam-6535	373	5	an	an	DET
ejpam-6535	373	6	isomorphism	isomorphism	NOUN
ejpam-6535	373	7	,	,	PUNCT
ejpam-6535	373	8	upon	upon	SCONJ
ejpam-6535	373	9	using	use	VERB
ejpam-6535	373	10	is(p	is(p	NOUN
ejpam-6535	373	11	)	)	PUNCT
ejpam-6535	373	12	=	=	SYM
ejpam-6535	374	1	sps−1	sps−1	PROPN
ejpam-6535	374	2	,	,	PUNCT
ejpam-6535	374	3	one	one	NUM
ejpam-6535	374	4	obtains	obtain	VERB
ejpam-6535	374	5	:	:	PUNCT
ejpam-6535	374	6	sps−1	sps−1	PROPN
ejpam-6535	374	7	∈	∈	PROPN
ejpam-6535	374	8	cτ(φ	cτ(φ	NOUN
ejpam-6535	374	9	,	,	PUNCT
ejpam-6535	374	10	ψ	ψ	NOUN
ejpam-6535	374	11	)	)	PUNCT
ejpam-6535	374	12	(	(	PUNCT
ejpam-6535	374	13	f⊙g⊙	f⊙g⊙	NOUN
ejpam-6535	374	14	f−1	f−1	PROPN
ejpam-6535	374	15	)	)	PUNCT
ejpam-6535	374	16	,	,	PUNCT
ejpam-6535	374	17	whence	whence	SCONJ
ejpam-6535	374	18	the	the	DET
ejpam-6535	374	19	filter	filter	NOUN
ejpam-6535	374	20	f⊙g⊙f−1	f⊙g⊙f−1	NOUN
ejpam-6535	374	21	is	be	AUX
ejpam-6535	374	22	generated	generate	VERB
ejpam-6535	374	23	by	by	ADP
ejpam-6535	374	24	the	the	DET
ejpam-6535	374	25	set	set	NOUN
ejpam-6535	374	26	{	{	PUNCT
ejpam-6535	374	27	f	f	PROPN
ejpam-6535	374	28	·	·	PROPN
ejpam-6535	374	29	m	m	PROPN
ejpam-6535	374	30	·	·	PUNCT
ejpam-6535	374	31	f−1	f−1	PROPN
ejpam-6535	374	32	:	:	PUNCT
ejpam-6535	374	33	f	f	PROPN
ejpam-6535	374	34	∈	∈	PROPN
ejpam-6535	375	1	f	f	X
ejpam-6535	375	2	,	,	PUNCT
ejpam-6535	375	3	m	m	VERB
ejpam-6535	375	4	∈	∈	NOUN
ejpam-6535	375	5	g	g	NOUN
ejpam-6535	375	6	}	}	PUNCT
ejpam-6535	375	7	,	,	PUNCT
ejpam-6535	375	8	where	where	SCONJ
ejpam-6535	375	9	f	f	PROPN
ejpam-6535	375	10	⊆	⊆	SYM
ejpam-6535	375	11	a	a	PRON
ejpam-6535	375	12	and	and	CCONJ
ejpam-6535	375	13	m	m	PROPN
ejpam-6535	375	14	⊆	⊆	NUM
ejpam-6535	375	15	n	n	NOUN
ejpam-6535	375	16	,	,	PUNCT
ejpam-6535	375	17	since	since	SCONJ
ejpam-6535	375	18	for	for	ADP
ejpam-6535	375	19	any	any	DET
ejpam-6535	375	20	a	a	DET
ejpam-6535	375	21	∈	∈	NOUN
ejpam-6535	375	22	f	f	NOUN
ejpam-6535	375	23	,	,	PUNCT
ejpam-6535	375	24	and	and	CCONJ
ejpam-6535	375	25	because	because	SCONJ
ejpam-6535	375	26	of	of	ADP
ejpam-6535	375	27	normality	normality	NOUN
ejpam-6535	375	28	of	of	ADP
ejpam-6535	375	29	n	n	PROPN
ejpam-6535	375	30	,	,	PUNCT
ejpam-6535	375	31	we	we	PRON
ejpam-6535	375	32	have	have	VERB
ejpam-6535	375	33	ana−1	ana−1	PROPN
ejpam-6535	375	34	=	=	SYM
ejpam-6535	375	35	n	n	PROPN
ejpam-6535	375	36	,	,	PUNCT
ejpam-6535	375	37	therefore	therefore	ADV
ejpam-6535	375	38	,	,	PUNCT
ejpam-6535	375	39	sps−1	sps−1	PROPN
ejpam-6535	375	40	∈	∈	PROPN
ejpam-6535	375	41	cτ(φ	cτ(φ	PRON
ejpam-6535	375	42	,	,	PUNCT
ejpam-6535	375	43	ψ)(n	ψ)(n	NUM
ejpam-6535	375	44	)	)	PUNCT
ejpam-6535	375	45	.	.	PUNCT
ejpam-6535	376	1	6	6	X
ejpam-6535	376	2	.	.	X
ejpam-6535	376	3	probabilistic	probabilistic	ADJ
ejpam-6535	376	4	cauchy	cauchy	NOUN
ejpam-6535	376	5	structures	structure	NOUN
ejpam-6535	376	6	and	and	CCONJ
ejpam-6535	376	7	their	their	PRON
ejpam-6535	376	8	relationships	relationship	NOUN
ejpam-6535	376	9	with	with	ADP
ejpam-6535	376	10	other	other	ADJ
ejpam-6535	376	11	probabilistic	probabilistic	ADJ
ejpam-6535	376	12	convergence	convergence	NOUN
ejpam-6535	376	13	structures	structure	NOUN
ejpam-6535	376	14	in	in	ADP
ejpam-6535	376	15	[	[	X
ejpam-6535	376	16	23	23	NUM
ejpam-6535	376	17	]	]	PUNCT
ejpam-6535	376	18	,	,	PUNCT
ejpam-6535	376	19	a	a	DET
ejpam-6535	376	20	general	general	ADJ
ejpam-6535	376	21	theory	theory	NOUN
ejpam-6535	376	22	of	of	ADP
ejpam-6535	376	23	quantale	quantale	NOUN
ejpam-6535	376	24	-	-	PUNCT
ejpam-6535	376	25	valued	value	VERB
ejpam-6535	376	26	cauchy	cauchy	NOUN
ejpam-6535	376	27	tower	tower	NOUN
ejpam-6535	376	28	spaces	space	NOUN
ejpam-6535	376	29	are	be	AUX
ejpam-6535	376	30	introduced	introduce	VERB
ejpam-6535	376	31	and	and	CCONJ
ejpam-6535	376	32	among	among	ADP
ejpam-6535	376	33	other	other	ADJ
ejpam-6535	376	34	interesting	interesting	ADJ
ejpam-6535	376	35	results	result	NOUN
ejpam-6535	376	36	,	,	PUNCT
ejpam-6535	376	37	they	they	PRON
ejpam-6535	376	38	proved	prove	VERB
ejpam-6535	376	39	that	that	SCONJ
ejpam-6535	376	40	the	the	DET
ejpam-6535	376	41	quantale	quantale	ADV
ejpam-6535	376	42	-	-	PUNCT
ejpam-6535	376	43	valued	value	VERB
ejpam-6535	376	44	tower	tower	NOUN
ejpam-6535	376	45	limit	limit	NOUN
ejpam-6535	376	46	space	space	NOUN
ejpam-6535	376	47	is	be	AUX
ejpam-6535	376	48	a	a	DET
ejpam-6535	376	49	quantale	quantale	NOUN
ejpam-6535	376	50	-	-	PUNCT
ejpam-6535	376	51	valued	value	VERB
ejpam-6535	376	52	cauchy	cauchy	PROPN
ejpam-6535	376	53	tower	tower	NOUN
ejpam-6535	376	54	space	space	NOUN
ejpam-6535	376	55	,	,	PUNCT
ejpam-6535	376	56	and	and	CCONJ
ejpam-6535	376	57	even	even	ADV
ejpam-6535	376	58	proved	prove	VERB
ejpam-6535	376	59	that	that	SCONJ
ejpam-6535	376	60	the	the	DET
ejpam-6535	376	61	category	category	NOUN
ejpam-6535	376	62	of	of	ADP
ejpam-6535	376	63	quantalevalued	quantalevalue	VERB
ejpam-6535	376	64	limit	limit	NOUN
ejpam-6535	376	65	tower	tower	NOUN
ejpam-6535	376	66	groups	group	NOUN
ejpam-6535	376	67	gives	give	VERB
ejpam-6535	376	68	rise	rise	NOUN
ejpam-6535	376	69	to	to	ADP
ejpam-6535	376	70	a	a	DET
ejpam-6535	376	71	quantale	quantale	NOUN
ejpam-6535	376	72	-	-	PUNCT
ejpam-6535	376	73	valued	value	VERB
ejpam-6535	376	74	cauchy	cauchy	NOUN
ejpam-6535	376	75	tower	tower	NOUN
ejpam-6535	376	76	groups	group	NOUN
ejpam-6535	376	77	;	;	PUNCT
ejpam-6535	376	78	furthermore	furthermore	ADV
ejpam-6535	376	79	,	,	PUNCT
ejpam-6535	376	80	cauchy	cauchy	PROPN
ejpam-6535	376	81	completeness	completeness	NOUN
ejpam-6535	376	82	are	be	AUX
ejpam-6535	376	83	also	also	ADV
ejpam-6535	376	84	considered	consider	VERB
ejpam-6535	376	85	there	there	ADV
ejpam-6535	376	86	in	in	ADP
ejpam-6535	376	87	a	a	DET
ejpam-6535	376	88	full	full	ADJ
ejpam-6535	376	89	length	length	NOUN
ejpam-6535	376	90	.	.	PUNCT
ejpam-6535	377	1	we	we	PRON
ejpam-6535	377	2	just	just	ADV
ejpam-6535	377	3	want	want	VERB
ejpam-6535	377	4	to	to	PART
ejpam-6535	377	5	take	take	VERB
ejpam-6535	377	6	a	a	DET
ejpam-6535	377	7	special	special	ADJ
ejpam-6535	377	8	case	case	NOUN
ejpam-6535	377	9	here	here	ADV
ejpam-6535	377	10	which	which	PRON
ejpam-6535	377	11	will	will	AUX
ejpam-6535	377	12	be	be	AUX
ejpam-6535	377	13	clear	clear	ADJ
ejpam-6535	377	14	from	from	ADP
ejpam-6535	377	15	the	the	DET
ejpam-6535	377	16	next	next	ADJ
ejpam-6535	377	17	section	section	NOUN
ejpam-6535	377	18	and	and	CCONJ
ejpam-6535	377	19	what	what	PRON
ejpam-6535	377	20	follows	follow	VERB
ejpam-6535	377	21	,	,	PUNCT
ejpam-6535	377	22	for	for	ADP
ejpam-6535	377	23	the	the	DET
ejpam-6535	377	24	details	detail	NOUN
ejpam-6535	377	25	we	we	PRON
ejpam-6535	377	26	refer	refer	VERB
ejpam-6535	377	27	to	to	ADP
ejpam-6535	377	28	[	[	X
ejpam-6535	377	29	23	23	NUM
ejpam-6535	377	30	]	]	PUNCT
ejpam-6535	377	31	.	.	PUNCT
ejpam-6535	378	1	furthermore	furthermore	ADV
ejpam-6535	378	2	,	,	PUNCT
ejpam-6535	378	3	we	we	PRON
ejpam-6535	378	4	note	note	VERB
ejpam-6535	378	5	here	here	ADV
ejpam-6535	378	6	that	that	SCONJ
ejpam-6535	378	7	in	in	ADP
ejpam-6535	378	8	[	[	X
ejpam-6535	378	9	10	10	NUM
ejpam-6535	378	10	]	]	PUNCT
ejpam-6535	378	11	,	,	PUNCT
ejpam-6535	378	12	it	it	PRON
ejpam-6535	378	13	is	be	AUX
ejpam-6535	378	14	showed	show	VERB
ejpam-6535	378	15	that	that	SCONJ
ejpam-6535	378	16	kt2convfco	kt2convfco	PROPN
ejpam-6535	378	17	,	,	PUNCT
ejpam-6535	378	18	the	the	DET
ejpam-6535	378	19	category	category	NOUN
ejpam-6535	378	20	of	of	ADP
ejpam-6535	378	21	kt2	kt2	PROPN
ejpam-6535	378	22	constant	constant	ADJ
ejpam-6535	378	23	convergence	convergence	NOUN
ejpam-6535	378	24	spaces	space	NOUN
ejpam-6535	378	25	and	and	CCONJ
ejpam-6535	378	26	continuous	continuous	ADJ
ejpam-6535	378	27	functions	function	NOUN
ejpam-6535	378	28	,	,	PUNCT
ejpam-6535	378	29	and	and	CCONJ
ejpam-6535	378	30	chy	chy	PROPN
ejpam-6535	378	31	,	,	PUNCT
ejpam-6535	378	32	the	the	DET
ejpam-6535	378	33	category	category	NOUN
ejpam-6535	378	34	of	of	ADP
ejpam-6535	378	35	cauchy	cauchy	PROPN
ejpam-6535	378	36	spaces	space	NOUN
ejpam-6535	378	37	and	and	CCONJ
ejpam-6535	378	38	cauchy	cauchy	PROPN
ejpam-6535	378	39	maps	map	NOUN
ejpam-6535	378	40	are	be	AUX
ejpam-6535	378	41	isomorphic	isomorphic	ADJ
ejpam-6535	378	42	.	.	PUNCT
ejpam-6535	379	1	also	also	ADV
ejpam-6535	379	2	,	,	PUNCT
ejpam-6535	379	3	it	it	PRON
ejpam-6535	379	4	is	be	AUX
ejpam-6535	379	5	proved	prove	VERB
ejpam-6535	379	6	there	there	ADV
ejpam-6535	379	7	that	that	SCONJ
ejpam-6535	379	8	convfco	convfco	NOUN
ejpam-6535	379	9	,	,	PUNCT
ejpam-6535	379	10	the	the	DET
ejpam-6535	379	11	category	category	NOUN
ejpam-6535	379	12	of	of	ADP
ejpam-6535	379	13	constant	constant	ADJ
ejpam-6535	379	14	convergence	convergence	NOUN
ejpam-6535	379	15	spaces	space	NOUN
ejpam-6535	379	16	and	and	CCONJ
ejpam-6535	379	17	continuous	continuous	ADJ
ejpam-6535	379	18	functions	function	NOUN
ejpam-6535	379	19	and	and	CCONJ
ejpam-6535	379	20	filprechy	filprechy	NOUN
ejpam-6535	379	21	,	,	PUNCT
ejpam-6535	379	22	the	the	DET
ejpam-6535	379	23	category	category	NOUN
ejpam-6535	379	24	of	of	ADP
ejpam-6535	379	25	filter	filter	NOUN
ejpam-6535	379	26	precauchy	precauchy	ADJ
ejpam-6535	379	27	spaces	space	NOUN
ejpam-6535	379	28	and	and	CCONJ
ejpam-6535	379	29	cauchy	cauchy	PROPN
ejpam-6535	379	30	maps	map	NOUN
ejpam-6535	379	31	are	be	AUX
ejpam-6535	379	32	isomorphic	isomorphic	ADJ
ejpam-6535	379	33	.	.	PUNCT
ejpam-6535	380	1	hence	hence	ADV
ejpam-6535	380	2	,	,	PUNCT
ejpam-6535	380	3	the	the	DET
ejpam-6535	380	4	category	category	NOUN
ejpam-6535	380	5	convfco	convfco	VERB
ejpam-6535	380	6	is	be	AUX
ejpam-6535	380	7	a	a	DET
ejpam-6535	380	8	link	link	NOUN
ejpam-6535	380	9	between	between	ADP
ejpam-6535	380	10	the	the	DET
ejpam-6535	380	11	categories	category	NOUN
ejpam-6535	380	12	filprechy	filprechy	ADJ
ejpam-6535	380	13	and	and	CCONJ
ejpam-6535	380	14	fcoconv	fcoconv	ADJ
ejpam-6535	380	15	.	.	PUNCT
ejpam-6535	381	1	interested	interested	ADJ
ejpam-6535	381	2	readers	reader	NOUN
ejpam-6535	381	3	are	be	AUX
ejpam-6535	381	4	referred	refer	VERB
ejpam-6535	381	5	to	to	ADP
ejpam-6535	381	6	[	[	X
ejpam-6535	381	7	10	10	NUM
ejpam-6535	381	8	]	]	PUNCT
ejpam-6535	381	9	for	for	ADP
ejpam-6535	381	10	a	a	DET
ejpam-6535	381	11	detail	detail	NOUN
ejpam-6535	381	12	study	study	NOUN
ejpam-6535	381	13	on	on	ADP
ejpam-6535	381	14	these	these	DET
ejpam-6535	381	15	categories	category	NOUN
ejpam-6535	381	16	and	and	CCONJ
ejpam-6535	381	17	their	their	PRON
ejpam-6535	381	18	terminologies	terminology	NOUN
ejpam-6535	381	19	.	.	PUNCT
ejpam-6535	382	1	one	one	NUM
ejpam-6535	382	2	can	can	AUX
ejpam-6535	382	3	also	also	ADV
ejpam-6535	382	4	look	look	VERB
ejpam-6535	382	5	into	into	ADP
ejpam-6535	382	6	the	the	DET
ejpam-6535	382	7	paper	paper	NOUN
ejpam-6535	382	8	[	[	X
ejpam-6535	382	9	11	11	NUM
ejpam-6535	382	10	]	]	PUNCT
ejpam-6535	382	11	to	to	PART
ejpam-6535	382	12	see	see	VERB
ejpam-6535	382	13	that	that	SCONJ
ejpam-6535	382	14	in	in	ADP
ejpam-6535	382	15	hausdorff	hausdorff	NOUN
ejpam-6535	382	16	objects	object	NOUN
ejpam-6535	382	17	,	,	PUNCT
ejpam-6535	382	18	it	it	PRON
ejpam-6535	382	19	is	be	AUX
ejpam-6535	382	20	proved	prove	VERB
ejpam-6535	382	21	that	that	SCONJ
ejpam-6535	382	22	culim	culim	PROPN
ejpam-6535	382	23	,	,	PUNCT
ejpam-6535	382	24	the	the	DET
ejpam-6535	382	25	category	category	NOUN
ejpam-6535	382	26	of	of	ADP
ejpam-6535	382	27	completely	completely	ADV
ejpam-6535	382	28	uniform	uniform	ADJ
ejpam-6535	382	29	limit	limit	NOUN
ejpam-6535	382	30	spaces	space	NOUN
ejpam-6535	382	31	and	and	CCONJ
ejpam-6535	382	32	uniformly	uniformly	ADV
ejpam-6535	382	33	continuous	continuous	ADJ
ejpam-6535	382	34	functions	function	NOUN
ejpam-6535	382	35	and	and	CCONJ
ejpam-6535	382	36	kt2lim	kt2lim	PROPN
ejpam-6535	382	37	,	,	PUNCT
ejpam-6535	382	38	the	the	DET
ejpam-6535	382	39	category	category	NOUN
ejpam-6535	382	40	of	of	ADP
ejpam-6535	382	41	limit	limit	NOUN
ejpam-6535	382	42	spaces	space	NOUN
ejpam-6535	382	43	and	and	CCONJ
ejpam-6535	382	44	continuous	continuous	ADJ
ejpam-6535	382	45	functions	function	NOUN
ejpam-6535	382	46	are	be	AUX
ejpam-6535	382	47	isomorphic	isomorphic	ADJ
ejpam-6535	382	48	;	;	PUNCT
ejpam-6535	382	49	and	and	CCONJ
ejpam-6535	382	50	deduce	deduce	VERB
ejpam-6535	382	51	that	that	SCONJ
ejpam-6535	382	52	every	every	DET
ejpam-6535	382	53	kt2	kt2	NOUN
ejpam-6535	382	54	limit	limit	NOUN
ejpam-6535	382	55	space	space	NOUN
ejpam-6535	382	56	induces	induce	VERB
ejpam-6535	382	57	the	the	DET
ejpam-6535	382	58	associated	associated	ADJ
ejpam-6535	382	59	complete	complete	ADJ
ejpam-6535	382	60	uniform	uniform	NOUN
ejpam-6535	382	61	limit	limit	NOUN
ejpam-6535	382	62	space	space	NOUN
ejpam-6535	382	63	.	.	PUNCT
ejpam-6535	383	1	definition	definition	NOUN
ejpam-6535	383	2	8	8	NUM
ejpam-6535	383	3	.	.	PUNCT
ejpam-6535	384	1	[	[	X
ejpam-6535	384	2	23	23	NUM
ejpam-6535	384	3	]	]	PUNCT
ejpam-6535	384	4	a	a	DET
ejpam-6535	384	5	probabilistic	probabilistic	ADJ
ejpam-6535	384	6	cauchy	cauchy	NOUN
ejpam-6535	384	7	space	space	NOUN
ejpam-6535	384	8	is	be	AUX
ejpam-6535	384	9	a	a	DET
ejpam-6535	384	10	pair	pair	NOUN
ejpam-6535	384	11	(	(	PUNCT
ejpam-6535	384	12	s	s	X
ejpam-6535	384	13	,	,	PUNCT
ejpam-6535	384	14	c	c	NOUN
ejpam-6535	384	15	=	=	SYM
ejpam-6535	384	16	(	(	PUNCT
ejpam-6535	384	17	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	384	18	)	)	PUNCT
ejpam-6535	384	19	,	,	PUNCT
ejpam-6535	384	20	where	where	SCONJ
ejpam-6535	384	21	cφ	cφ	ADV
ejpam-6535	384	22	⊆	⊆	NUM
ejpam-6535	384	23	f(s	f(	NOUN
ejpam-6535	384	24	)	)	PUNCT
ejpam-6535	384	25	is	be	AUX
ejpam-6535	384	26	called	call	VERB
ejpam-6535	384	27	the	the	DET
ejpam-6535	384	28	probabilistic	probabilistic	ADJ
ejpam-6535	384	29	cauchy	cauchy	NOUN
ejpam-6535	384	30	structure	structure	NOUN
ejpam-6535	384	31	on	on	ADP
ejpam-6535	384	32	s	s	PRON
ejpam-6535	384	33	under	under	ADP
ejpam-6535	384	34	a	a	DET
ejpam-6535	384	35	triangle	triangle	NOUN
ejpam-6535	384	36	function	function	NOUN
ejpam-6535	384	37	τ	τ	PROPN
ejpam-6535	384	38	if	if	SCONJ
ejpam-6535	384	39	the	the	DET
ejpam-6535	384	40	following	follow	VERB
ejpam-6535	384	41	conditions	condition	NOUN
ejpam-6535	384	42	are	be	AUX
ejpam-6535	384	43	satisfied	satisfied	ADJ
ejpam-6535	384	44	:	:	PUNCT
ejpam-6535	384	45	(	(	PUNCT
ejpam-6535	384	46	pchs1	pchs1	NOUN
ejpam-6535	384	47	)	)	PUNCT
ejpam-6535	385	1	[	[	X
ejpam-6535	385	2	p	p	X
ejpam-6535	385	3	]	]	X
ejpam-6535	385	4	∈	∈	PROPN
ejpam-6535	385	5	cφ	cφ	NOUN
ejpam-6535	385	6	,	,	PUNCT
ejpam-6535	385	7	∀p	∀p	PROPN
ejpam-6535	385	8	∈	∈	PROPN
ejpam-6535	385	9	s	s	NOUN
ejpam-6535	385	10	,	,	PUNCT
ejpam-6535	385	11	∀φ	∀φ	NOUN
ejpam-6535	385	12	∈	∈	PROPN
ejpam-6535	385	13	∆+	∆+	NOUN
ejpam-6535	385	14	;	;	PUNCT
ejpam-6535	385	15	(	(	PUNCT
ejpam-6535	385	16	pchs2	pchs2	NOUN
ejpam-6535	385	17	)	)	PUNCT
ejpam-6535	385	18	if	if	SCONJ
ejpam-6535	385	19	f	f	PROPN
ejpam-6535	385	20	∈	∈	PROPN
ejpam-6535	385	21	cφ	cφ	NOUN
ejpam-6535	385	22	and	and	CCONJ
ejpam-6535	385	23	f	f	PROPN
ejpam-6535	385	24	≤	≤	NOUN
ejpam-6535	385	25	g	g	PROPN
ejpam-6535	385	26	implies	imply	VERB
ejpam-6535	385	27	g	g	PROPN
ejpam-6535	385	28	∈	∈	PROPN
ejpam-6535	385	29	cφ	cφ	NOUN
ejpam-6535	385	30	;	;	PUNCT
ejpam-6535	385	31	(	(	PUNCT
ejpam-6535	385	32	pchs3	pchs3	X
ejpam-6535	385	33	)	)	PUNCT
ejpam-6535	385	34	∀φ	∀φ	NOUN
ejpam-6535	385	35	,	,	PUNCT
ejpam-6535	385	36	ψ	ψ	NOUN
ejpam-6535	385	37	∈	∈	PROPN
ejpam-6535	385	38	∆+	∆+	NUM
ejpam-6535	385	39	with	with	SCONJ
ejpam-6535	385	40	φ	φ	PROPN
ejpam-6535	385	41	≤	≤	NOUN
ejpam-6535	385	42	ψ	ψ	NOUN
ejpam-6535	385	43	implies	imply	VERB
ejpam-6535	385	44	cψ	cψ	PRON
ejpam-6535	385	45	≤	≤	NOUN
ejpam-6535	385	46	cφ	cφ	NOUN
ejpam-6535	385	47	;	;	PUNCT
ejpam-6535	385	48	(	(	PUNCT
ejpam-6535	385	49	pchs4	pchs4	X
ejpam-6535	385	50	)	)	PUNCT
ejpam-6535	385	51	cϵ∞	cϵ∞	PROPN
ejpam-6535	385	52	=	=	SYM
ejpam-6535	385	53	f(s	f(	NOUN
ejpam-6535	385	54	)	)	PUNCT
ejpam-6535	385	55	;	;	PUNCT
ejpam-6535	385	56	(	(	PUNCT
ejpam-6535	385	57	pchs5	pchs5	PROPN
ejpam-6535	385	58	)	)	PUNCT
ejpam-6535	385	59	if	if	SCONJ
ejpam-6535	385	60	f	f	PROPN
ejpam-6535	385	61	∈	∈	PROPN
ejpam-6535	385	62	cφ	cφ	NOUN
ejpam-6535	385	63	and	and	CCONJ
ejpam-6535	385	64	g	g	PROPN
ejpam-6535	385	65	∈	∈	PROPN
ejpam-6535	385	66	cψ	cψ	NOUN
ejpam-6535	385	67	for	for	ADP
ejpam-6535	385	68	φ	φ	NUM
ejpam-6535	385	69	,	,	PUNCT
ejpam-6535	385	70	ψ	ψ	X
ejpam-6535	385	71	∈	∈	PROPN
ejpam-6535	385	72	∆+	∆+	NUM
ejpam-6535	385	73	such	such	ADJ
ejpam-6535	385	74	that	that	DET
ejpam-6535	385	75	f∨g	f∨g	PROPN
ejpam-6535	385	76	exists	exist	VERB
ejpam-6535	385	77	implies	imply	VERB
ejpam-6535	385	78	that	that	SCONJ
ejpam-6535	385	79	f∧g	f∧g	PROPN
ejpam-6535	385	80	∈	∈	PROPN
ejpam-6535	385	81	cτ(φ	cτ(φ	NOUN
ejpam-6535	385	82	,	,	PUNCT
ejpam-6535	385	83	ψ	ψ	NOUN
ejpam-6535	385	84	)	)	PUNCT
ejpam-6535	385	85	.	.	PUNCT
ejpam-6535	386	1	a	a	DET
ejpam-6535	386	2	map	map	NOUN
ejpam-6535	386	3	f	f	X
ejpam-6535	386	4	:	:	PUNCT
ejpam-6535	386	5	(	(	PUNCT
ejpam-6535	386	6	s	s	X
ejpam-6535	386	7	,	,	PUNCT
ejpam-6535	386	8	c	c	NOUN
ejpam-6535	386	9	)	)	PUNCT
ejpam-6535	386	10	−→	−→	NOUN
ejpam-6535	386	11	(	(	PUNCT
ejpam-6535	386	12	s′	s′	X
ejpam-6535	386	13	,	,	PUNCT
ejpam-6535	386	14	c′	c′	NUM
ejpam-6535	386	15	)	)	PUNCT
ejpam-6535	386	16	between	between	ADP
ejpam-6535	386	17	probabilistic	probabilistic	ADJ
ejpam-6535	386	18	cauchy	cauchy	ADJ
ejpam-6535	386	19	spaces	space	NOUN
ejpam-6535	386	20	is	be	AUX
ejpam-6535	386	21	called	call	VERB
ejpam-6535	386	22	probabilistic	probabilistic	ADJ
ejpam-6535	386	23	cauchy	cauchy	NOUN
ejpam-6535	386	24	-	-	PUNCT
ejpam-6535	386	25	continuous	continuous	ADJ
ejpam-6535	386	26	if	if	SCONJ
ejpam-6535	386	27	∀φ	∀φ	NUM
ejpam-6535	386	28	∈	∈	PROPN
ejpam-6535	386	29	∆+	∆+	NOUN
ejpam-6535	386	30	,	,	PUNCT
ejpam-6535	386	31	∀f	∀f	PROPN
ejpam-6535	386	32	∈	∈	PROPN
ejpam-6535	386	33	f(s	f(	NOUN
ejpam-6535	386	34	)	)	PUNCT
ejpam-6535	386	35	,	,	PUNCT
ejpam-6535	386	36	f	f	PROPN
ejpam-6535	386	37	∈	∈	PROPN
ejpam-6535	386	38	cφ	cφ	PROPN
ejpam-6535	386	39	implies	imply	VERB
ejpam-6535	386	40	f(f	f(f	PROPN
ejpam-6535	386	41	)	)	PUNCT
ejpam-6535	386	42	∈	∈	PROPN
ejpam-6535	386	43	c′φ	c′φ	PROPN
ejpam-6535	386	44	.	.	PUNCT
ejpam-6535	387	1	the	the	DET
ejpam-6535	387	2	category	category	NOUN
ejpam-6535	387	3	of	of	ADP
ejpam-6535	387	4	probabilistic	probabilistic	ADJ
ejpam-6535	387	5	cauchy	cauchy	ADJ
ejpam-6535	387	6	spaces	space	NOUN
ejpam-6535	387	7	under	under	ADP
ejpam-6535	387	8	a	a	DET
ejpam-6535	387	9	triangle	triangle	NOUN
ejpam-6535	387	10	function	function	NOUN
ejpam-6535	387	11	τ	τ	PROPN
ejpam-6535	387	12	and	and	CCONJ
ejpam-6535	387	13	probabilistic	probabilistic	ADJ
ejpam-6535	387	14	cauchy	cauchy	NOUN
ejpam-6535	387	15	-	-	PUNCT
ejpam-6535	387	16	continuous	continuous	ADJ
ejpam-6535	387	17	mappings	mapping	NOUN
ejpam-6535	387	18	is	be	AUX
ejpam-6535	387	19	denoted	denote	VERB
ejpam-6535	387	20	by	by	ADP
ejpam-6535	387	21	pchy	pchy	NOUN
ejpam-6535	387	22	.	.	PUNCT
ejpam-6535	388	1	definition	definition	NOUN
ejpam-6535	388	2	9	9	NUM
ejpam-6535	388	3	.	.	PUNCT
ejpam-6535	389	1	[	[	X
ejpam-6535	389	2	23	23	NUM
ejpam-6535	389	3	]	]	PUNCT
ejpam-6535	389	4	a	a	DET
ejpam-6535	389	5	probabilistic	probabilistic	ADJ
ejpam-6535	389	6	cauchy	cauchy	NOUN
ejpam-6535	389	7	space	space	NOUN
ejpam-6535	389	8	under	under	ADP
ejpam-6535	389	9	t	t	NOUN
ejpam-6535	389	10	-	-	PUNCT
ejpam-6535	389	11	norm	norm	NOUN
ejpam-6535	389	12	∗	∗	NOUN
ejpam-6535	389	13	,	,	PUNCT
ejpam-6535	389	14	[	[	X
ejpam-6535	389	15	26	26	NUM
ejpam-6535	389	16	]	]	PUNCT
ejpam-6535	389	17	,	,	PUNCT
ejpam-6535	389	18	is	be	AUX
ejpam-6535	389	19	a	a	DET
ejpam-6535	389	20	pair	pair	NOUN
ejpam-6535	389	21	(	(	PUNCT
ejpam-6535	389	22	s	s	X
ejpam-6535	389	23	,	,	PUNCT
ejpam-6535	389	24	c	c	NOUN
ejpam-6535	389	25	=	=	SYM
ejpam-6535	389	26	(	(	PUNCT
ejpam-6535	389	27	cα)α∈[0,1	cα)α∈[0,1	NOUN
ejpam-6535	389	28	]	]	PUNCT
ejpam-6535	389	29	)	)	PUNCT
ejpam-6535	389	30	,	,	PUNCT
ejpam-6535	389	31	where	where	SCONJ
ejpam-6535	389	32	s	s	NOUN
ejpam-6535	389	33	is	be	AUX
ejpam-6535	389	34	a	a	DET
ejpam-6535	389	35	set	set	VERB
ejpam-6535	389	36	and	and	CCONJ
ejpam-6535	389	37	(	(	PUNCT
ejpam-6535	389	38	cα)α∈[0,1	cα)α∈[0,1	NOUN
ejpam-6535	389	39	]	]	PUNCT
ejpam-6535	389	40	is	be	AUX
ejpam-6535	389	41	a	a	DET
ejpam-6535	389	42	non	non	ADJ
ejpam-6535	389	43	-	-	ADJ
ejpam-6535	389	44	empty	empty	ADJ
ejpam-6535	389	45	family	family	NOUN
ejpam-6535	389	46	of	of	ADP
ejpam-6535	389	47	subsets	subset	NOUN
ejpam-6535	389	48	of	of	ADP
ejpam-6535	389	49	f(s	f(	NOUN
ejpam-6535	389	50	)	)	PUNCT
ejpam-6535	389	51	satisfying	satisfy	VERB
ejpam-6535	389	52	the	the	DET
ejpam-6535	389	53	following	following	NOUN
ejpam-6535	389	54	:	:	PUNCT
ejpam-6535	389	55	(	(	PUNCT
ejpam-6535	389	56	pch1	pch1	PROPN
ejpam-6535	389	57	)	)	PUNCT
ejpam-6535	390	1	[	[	X
ejpam-6535	390	2	p	p	X
ejpam-6535	390	3	]	]	X
ejpam-6535	390	4	∈	∈	NOUN
ejpam-6535	390	5	cα	cα	ADP
ejpam-6535	390	6	for	for	ADP
ejpam-6535	390	7	all	all	PRON
ejpam-6535	390	8	p	p	NOUN
ejpam-6535	390	9	∈	∈	PROPN
ejpam-6535	390	10	s	s	NOUN
ejpam-6535	390	11	and	and	CCONJ
ejpam-6535	390	12	α	α	NOUN
ejpam-6535	390	13	∈	∈	PROPN
ejpam-6535	391	1	[	[	X
ejpam-6535	391	2	0	0	NUM
ejpam-6535	391	3	,	,	PUNCT
ejpam-6535	391	4	1	1	NUM
ejpam-6535	391	5	]	]	PUNCT
ejpam-6535	391	6	;	;	PUNCT
ejpam-6535	391	7	(	(	PUNCT
ejpam-6535	391	8	pch2	pch2	PROPN
ejpam-6535	391	9	)	)	PUNCT
ejpam-6535	391	10	∀f	∀f	PROPN
ejpam-6535	391	11	,	,	PUNCT
ejpam-6535	391	12	g	g	PROPN
ejpam-6535	391	13	∈	∈	PROPN
ejpam-6535	391	14	f(s	f(	VERB
ejpam-6535	391	15	)	)	PUNCT
ejpam-6535	391	16	and	and	CCONJ
ejpam-6535	391	17	α	α	PRON
ejpam-6535	391	18	∈	∈	PROPN
ejpam-6535	392	1	[	[	X
ejpam-6535	392	2	0	0	NUM
ejpam-6535	392	3	,	,	PUNCT
ejpam-6535	392	4	1	1	NUM
ejpam-6535	392	5	]	]	PUNCT
ejpam-6535	392	6	with	with	ADP
ejpam-6535	392	7	f	f	PROPN
ejpam-6535	392	8	≤	≤	PROPN
ejpam-6535	392	9	g	g	PROPN
ejpam-6535	392	10	and	and	CCONJ
ejpam-6535	392	11	f	f	PROPN
ejpam-6535	392	12	∈	∈	PROPN
ejpam-6535	392	13	cα	cα	NOUN
ejpam-6535	392	14	implies	imply	VERB
ejpam-6535	392	15	g	g	PROPN
ejpam-6535	392	16	∈	∈	PROPN
ejpam-6535	392	17	cα	cα	ADP
ejpam-6535	392	18	;	;	PUNCT
ejpam-6535	392	19	(	(	PUNCT
ejpam-6535	392	20	pch3	pch3	PROPN
ejpam-6535	392	21	)	)	PUNCT
ejpam-6535	392	22	if	if	SCONJ
ejpam-6535	392	23	α	α	PRON
ejpam-6535	392	24	≤	≤	NOUN
ejpam-6535	392	25	β	β	X
ejpam-6535	392	26	,	,	PUNCT
ejpam-6535	392	27	then	then	ADV
ejpam-6535	392	28	cβ	cβ	PROPN
ejpam-6535	392	29	≤	≤	PROPN
ejpam-6535	392	30	cα	cα	ADP
ejpam-6535	392	31	;	;	PUNCT
ejpam-6535	392	32	(	(	PUNCT
ejpam-6535	392	33	pch4	pch4	PROPN
ejpam-6535	392	34	)	)	PUNCT
ejpam-6535	392	35	c0	c0	PROPN
ejpam-6535	392	36	=	=	PUNCT
ejpam-6535	392	37	f(s	f(	NOUN
ejpam-6535	392	38	)	)	PUNCT
ejpam-6535	392	39	;	;	PUNCT
ejpam-6535	392	40	(	(	PUNCT
ejpam-6535	392	41	pch5	pch5	PROPN
ejpam-6535	392	42	)	)	PUNCT
ejpam-6535	392	43	if	if	SCONJ
ejpam-6535	392	44	f	f	PROPN
ejpam-6535	392	45	∈	∈	PROPN
ejpam-6535	392	46	cα	cα	PROPN
ejpam-6535	392	47	,	,	PUNCT
ejpam-6535	392	48	g	g	PROPN
ejpam-6535	392	49	∈	∈	PROPN
ejpam-6535	392	50	cβ	cβ	NOUN
ejpam-6535	392	51	and	and	CCONJ
ejpam-6535	392	52	f	f	PROPN
ejpam-6535	392	53	∨g	∨g	PROPN
ejpam-6535	392	54	exists	exist	VERB
ejpam-6535	392	55	,	,	PUNCT
ejpam-6535	392	56	then	then	ADV
ejpam-6535	392	57	f	f	PROPN
ejpam-6535	392	58	∧g	∧g	PROPN
ejpam-6535	392	59	∈	∈	PROPN
ejpam-6535	392	60	cα∗β	cα∗β	PROPN
ejpam-6535	392	61	.	.	PUNCT
ejpam-6535	393	1	a	a	DET
ejpam-6535	393	2	map	map	NOUN
ejpam-6535	393	3	f	f	X
ejpam-6535	393	4	:	:	PUNCT
ejpam-6535	393	5	(	(	PUNCT
ejpam-6535	393	6	s	s	X
ejpam-6535	393	7	,	,	PUNCT
ejpam-6535	393	8	c	c	NOUN
ejpam-6535	393	9	)	)	PUNCT
ejpam-6535	393	10	−→	−→	NOUN
ejpam-6535	393	11	(	(	PUNCT
ejpam-6535	393	12	s′	s′	PROPN
ejpam-6535	393	13	,	,	PUNCT
ejpam-6535	393	14	c	c	NOUN
ejpam-6535	393	15	′	′	NOUN
ejpam-6535	393	16	)	)	PUNCT
ejpam-6535	393	17	between	between	ADP
ejpam-6535	393	18	probabilistic	probabilistic	ADJ
ejpam-6535	393	19	cauchy	cauchy	ADJ
ejpam-6535	393	20	spaces	space	NOUN
ejpam-6535	393	21	under	under	ADP
ejpam-6535	393	22	t	t	NOUN
ejpam-6535	393	23	-	-	PUNCT
ejpam-6535	393	24	norm	norm	NOUN
ejpam-6535	393	25	∗	∗	NOUN
ejpam-6535	393	26	is	be	AUX
ejpam-6535	393	27	called	call	VERB
ejpam-6535	393	28	cauchy	cauchy	NOUN
ejpam-6535	393	29	-	-	PUNCT
ejpam-6535	393	30	continuous	continuous	ADJ
ejpam-6535	393	31	if	if	SCONJ
ejpam-6535	394	1	and	and	CCONJ
ejpam-6535	394	2	only	only	ADV
ejpam-6535	394	3	if	if	SCONJ
ejpam-6535	394	4	for	for	ADP
ejpam-6535	394	5	all	all	DET
ejpam-6535	394	6	f	f	PROPN
ejpam-6535	394	7	∈	∈	PROPN
ejpam-6535	394	8	f(s	f(	NOUN
ejpam-6535	394	9	)	)	PUNCT
ejpam-6535	394	10	and	and	CCONJ
ejpam-6535	394	11	for	for	ADP
ejpam-6535	394	12	all	all	DET
ejpam-6535	394	13	α	α	PRON
ejpam-6535	394	14	∈	∈	PROPN
ejpam-6535	395	1	[	[	X
ejpam-6535	395	2	0	0	NUM
ejpam-6535	395	3	,	,	PUNCT
ejpam-6535	395	4	1	1	NUM
ejpam-6535	395	5	]	]	PUNCT
ejpam-6535	395	6	,	,	PUNCT
ejpam-6535	395	7	f	f	PROPN
ejpam-6535	395	8	∈	∈	PROPN
ejpam-6535	395	9	cα	cα	PROPN
ejpam-6535	395	10	implies	imply	VERB
ejpam-6535	395	11	f(f	f(f	PROPN
ejpam-6535	395	12	)	)	PUNCT
ejpam-6535	395	13	∈	∈	PROPN
ejpam-6535	395	14	c	c	NOUN
ejpam-6535	396	1	′	′	NUM
ejpam-6535	396	2	α	α	X
ejpam-6535	396	3	.	.	PUNCT
ejpam-6535	397	1	the	the	DET
ejpam-6535	397	2	category	category	NOUN
ejpam-6535	397	3	of	of	ADP
ejpam-6535	397	4	all	all	DET
ejpam-6535	397	5	probabilistic	probabilistic	ADJ
ejpam-6535	397	6	cauchy	cauchy	ADJ
ejpam-6535	397	7	spaces	space	NOUN
ejpam-6535	397	8	under	under	ADP
ejpam-6535	397	9	t	t	NOUN
ejpam-6535	397	10	-	-	PUNCT
ejpam-6535	397	11	norm	norm	NOUN
ejpam-6535	397	12	∗	∗	NOUN
ejpam-6535	397	13	and	and	CCONJ
ejpam-6535	397	14	cauchy	cauchy	NOUN
ejpam-6535	397	15	-	-	PUNCT
ejpam-6535	397	16	continuous	continuous	ADJ
ejpam-6535	397	17	mappings	mapping	NOUN
ejpam-6535	397	18	is	be	AUX
ejpam-6535	397	19	called	call	VERB
ejpam-6535	397	20	richarson	richarson	PROPN
ejpam-6535	397	21	-	-	PUNCT
ejpam-6535	397	22	kent	kent	PROPN
ejpam-6535	397	23	probabilistic	probabilistic	ADJ
ejpam-6535	397	24	convergence	convergence	NOUN
ejpam-6535	397	25	space	space	NOUN
ejpam-6535	397	26	and	and	CCONJ
ejpam-6535	397	27	denoted	denote	VERB
ejpam-6535	397	28	by	by	ADP
ejpam-6535	397	29	rkpchy	rkpchy	NOUN
ejpam-6535	397	30	.	.	PUNCT
ejpam-6535	398	1	example	example	NOUN
ejpam-6535	399	1	1	1	NUM
ejpam-6535	399	2	.	.	PUNCT
ejpam-6535	400	1	[	[	X
ejpam-6535	400	2	22	22	NUM
ejpam-6535	400	3	]	]	PUNCT
ejpam-6535	400	4	let	let	VERB
ejpam-6535	400	5	(	(	PUNCT
ejpam-6535	400	6	s	s	X
ejpam-6535	400	7	,	,	PUNCT
ejpam-6535	400	8	c	c	NOUN
ejpam-6535	400	9	=	=	SYM
ejpam-6535	400	10	(	(	PUNCT
ejpam-6535	400	11	cα)α∈[0,1	cα)α∈[0,1	NOUN
ejpam-6535	400	12	]	]	PUNCT
ejpam-6535	400	13	)	)	PUNCT
ejpam-6535	400	14	∈	∈	PROPN
ejpam-6535	400	15	|rk	|rk	NOUN
ejpam-6535	400	16	-	-	PUNCT
ejpam-6535	400	17	pchy|	pchy|	NOUN
ejpam-6535	400	18	.	.	PUNCT
ejpam-6535	401	1	for	for	ADP
ejpam-6535	401	2	φ	φ	PROPN
ejpam-6535	401	3	∈	∈	PROPN
ejpam-6535	401	4	∆+	∆+	AUX
ejpam-6535	401	5	we	we	PRON
ejpam-6535	401	6	denote	denote	VERB
ejpam-6535	401	7	φ(0	φ(0	PROPN
ejpam-6535	401	8	+	+	NOUN
ejpam-6535	401	9	)	)	PUNCT
ejpam-6535	401	10	=	=	SYM
ejpam-6535	402	1	limx→0	limx→0	ADV
ejpam-6535	402	2	+	+	ADJ
ejpam-6535	402	3	φ(x	φ(x	NOUN
ejpam-6535	402	4	)	)	PUNCT
ejpam-6535	402	5	the	the	DET
ejpam-6535	402	6	right	right	ADJ
ejpam-6535	402	7	-	-	PUNCT
ejpam-6535	402	8	hand	hand	NOUN
ejpam-6535	402	9	limit	limit	NOUN
ejpam-6535	402	10	of	of	ADP
ejpam-6535	402	11	φ	φ	PROPN
ejpam-6535	402	12	at	at	ADP
ejpam-6535	402	13	0	0	NUM
ejpam-6535	402	14	.	.	PUNCT
ejpam-6535	403	1	if	if	SCONJ
ejpam-6535	403	2	we	we	PRON
ejpam-6535	403	3	define	define	VERB
ejpam-6535	403	4	f	f	PROPN
ejpam-6535	403	5	∈	∈	PROPN
ejpam-6535	403	6	ccφ	ccφ	PROPN
ejpam-6535	403	7	iff	iff	PROPN
ejpam-6535	403	8	f	f	PROPN
ejpam-6535	403	9	∈	∈	PROPN
ejpam-6535	403	10	cφ(0	cφ(0	PROPN
ejpam-6535	403	11	+	+	PROPN
ejpam-6535	403	12	)	)	PUNCT
ejpam-6535	403	13	,	,	PUNCT
ejpam-6535	403	14	then	then	ADV
ejpam-6535	403	15	clearly	clearly	ADV
ejpam-6535	403	16	(	(	PUNCT
ejpam-6535	403	17	s	s	X
ejpam-6535	403	18	,	,	PUNCT
ejpam-6535	403	19	cc	cc	NOUN
ejpam-6535	403	20	)	)	PUNCT
ejpam-6535	403	21	∈	∈	PROPN
ejpam-6535	403	22	|pchy|	|pchy|	NUM
ejpam-6535	403	23	.	.	PUNCT
ejpam-6535	404	1	also	also	ADV
ejpam-6535	404	2	,	,	PUNCT
ejpam-6535	404	3	if	if	SCONJ
ejpam-6535	404	4	f	f	X
ejpam-6535	404	5	:	:	PUNCT
ejpam-6535	404	6	(	(	PUNCT
ejpam-6535	404	7	s	s	X
ejpam-6535	404	8	,	,	PUNCT
ejpam-6535	404	9	c	c	NOUN
ejpam-6535	404	10	=	=	SYM
ejpam-6535	404	11	(	(	PUNCT
ejpam-6535	404	12	cα)α∈[0,1	cα)α∈[0,1	NOUN
ejpam-6535	404	13	]	]	PUNCT
ejpam-6535	404	14	)	)	PUNCT
ejpam-6535	405	1	−→	−→	NOUN
ejpam-6535	405	2	(	(	PUNCT
ejpam-6535	405	3	s′	s′	PROPN
ejpam-6535	405	4	,	,	PUNCT
ejpam-6535	405	5	c	c	NOUN
ejpam-6535	405	6	′	′	NUM
ejpam-6535	406	1	=	=	SYM
ejpam-6535	406	2	(	(	PUNCT
ejpam-6535	406	3	cα)α∈[0,1	cα)α∈[0,1	NOUN
ejpam-6535	406	4	]	]	PUNCT
ejpam-6535	406	5	)	)	PUNCT
ejpam-6535	406	6	is	be	AUX
ejpam-6535	406	7	a	a	DET
ejpam-6535	406	8	continuous	continuous	ADJ
ejpam-6535	406	9	function	function	NOUN
ejpam-6535	406	10	,	,	PUNCT
ejpam-6535	406	11	then	then	ADV
ejpam-6535	406	12	f	f	X
ejpam-6535	406	13	:	:	PUNCT
ejpam-6535	406	14	(	(	PUNCT
ejpam-6535	406	15	s	s	X
ejpam-6535	406	16	,	,	PUNCT
ejpam-6535	406	17	ccφ	ccφ	NOUN
ejpam-6535	406	18	)	)	PUNCT
ejpam-6535	406	19	−→	−→	NOUN
ejpam-6535	406	20	(	(	PUNCT
ejpam-6535	406	21	s′	s′	PROPN
ejpam-6535	406	22	,	,	PUNCT
ejpam-6535	406	23	cc	cc	PROPN
ejpam-6535	406	24	′	′	NUM
ejpam-6535	406	25	φ	φ	PROPN
ejpam-6535	406	26	)	)	PUNCT
ejpam-6535	406	27	is	be	AUX
ejpam-6535	406	28	continuous	continuous	ADJ
ejpam-6535	406	29	.	.	PUNCT
ejpam-6535	407	1	thus	thus	ADV
ejpam-6535	407	2	we	we	PRON
ejpam-6535	407	3	obtain	obtain	VERB
ejpam-6535	407	4	an	an	DET
ejpam-6535	407	5	embedding	embed	VERB
ejpam-6535	407	6	functor	functor	PROPN
ejpam-6535	407	7	rk	rk	NOUN
ejpam-6535	407	8	-	-	PUNCT
ejpam-6535	407	9	pchy	pchy	ADJ
ejpam-6535	407	10	s−→	s−→	NOUN
ejpam-6535	407	11	pchy	pchy	ADJ
ejpam-6535	407	12	,	,	PUNCT
ejpam-6535	407	13	c	c	PROPN
ejpam-6535	407	14	7→	7→	NUM
ejpam-6535	407	15	cc	cc	NOUN
ejpam-6535	407	16	;	;	PUNCT
ejpam-6535	407	17	f	f	PROPN
ejpam-6535	407	18	7→	7→	NUM
ejpam-6535	407	19	f	f	NOUN
ejpam-6535	407	20	.	.	PUNCT
ejpam-6535	408	1	next	next	ADV
ejpam-6535	408	2	let	let	VERB
ejpam-6535	408	3	(	(	PUNCT
ejpam-6535	408	4	s	s	X
ejpam-6535	408	5	,	,	PUNCT
ejpam-6535	408	6	c	c	NOUN
ejpam-6535	408	7	=	=	SYM
ejpam-6535	408	8	(	(	PUNCT
ejpam-6535	408	9	cφ)φ∈∆+	cφ)φ∈∆+	ADJ
ejpam-6535	408	10	)	)	PUNCT
ejpam-6535	408	11	∈	∈	PROPN
ejpam-6535	408	12	|pchy|	|pchy|	NOUN
ejpam-6535	408	13	.	.	PUNCT
ejpam-6535	409	1	define	define	VERB
ejpam-6535	409	2	f	f	PROPN
ejpam-6535	409	3	∈	∈	PROPN
ejpam-6535	409	4	cc	cc	PROPN
ejpam-6535	409	5	α	α	PROPN
ejpam-6535	409	6	iff	iff	PROPN
ejpam-6535	409	7	∃φ	∃φ	PROPN
ejpam-6535	409	8	∈	∈	PROPN
ejpam-6535	409	9	∆+	∆+	NUM
ejpam-6535	409	10	such	such	ADJ
ejpam-6535	409	11	that	that	SCONJ
ejpam-6535	409	12	φ(0	φ(0	ADJ
ejpam-6535	409	13	+	+	NOUN
ejpam-6535	409	14	)	)	PUNCT
ejpam-6535	409	15	=	=	SYM
ejpam-6535	409	16	α	α	PROPN
ejpam-6535	409	17	and	and	CCONJ
ejpam-6535	409	18	f	f	PROPN
ejpam-6535	409	19	∈	∈	PROPN
ejpam-6535	410	1	cφ	cφ	NOUN
ejpam-6535	410	2	.	.	PUNCT
ejpam-6535	411	1	then	then	ADV
ejpam-6535	411	2	(	(	PUNCT
ejpam-6535	411	3	s	s	X
ejpam-6535	411	4	,	,	PUNCT
ejpam-6535	411	5	cc	cc	NOUN
ejpam-6535	411	6	α	α	NOUN
ejpam-6535	411	7	)	)	PUNCT
ejpam-6535	411	8	∈	∈	PROPN
ejpam-6535	411	9	|rk	|rk	NOUN
ejpam-6535	411	10	-	-	PUNCT
ejpam-6535	411	11	pchy|	pchy|	NOUN
ejpam-6535	411	12	.	.	PUNCT
ejpam-6535	412	1	also	also	ADV
ejpam-6535	412	2	,	,	PUNCT
ejpam-6535	412	3	if	if	SCONJ
ejpam-6535	412	4	f	f	X
ejpam-6535	412	5	:	:	PUNCT
ejpam-6535	412	6	(	(	PUNCT
ejpam-6535	412	7	s	s	X
ejpam-6535	412	8	,	,	PUNCT
ejpam-6535	412	9	c	c	NOUN
ejpam-6535	412	10	=	=	SYM
ejpam-6535	412	11	(	(	PUNCT
ejpam-6535	412	12	cφ)φ∈∆+	cφ)φ∈∆+	ADJ
ejpam-6535	412	13	)	)	PUNCT
ejpam-6535	412	14	−→	−→	NOUN
ejpam-6535	412	15	(	(	PUNCT
ejpam-6535	412	16	s′	s′	X
ejpam-6535	412	17	,	,	PUNCT
ejpam-6535	412	18	c′	c′	VERB
ejpam-6535	412	19	=	=	SYM
ejpam-6535	412	20	(	(	PUNCT
ejpam-6535	412	21	c′φ)φ∈∆+	c′φ)φ∈∆+	NOUN
ejpam-6535	412	22	)	)	PUNCT
ejpam-6535	412	23	is	be	AUX
ejpam-6535	412	24	a	a	DET
ejpam-6535	412	25	continuous	continuous	ADJ
ejpam-6535	412	26	function	function	NOUN
ejpam-6535	412	27	,	,	PUNCT
ejpam-6535	412	28	then	then	ADV
ejpam-6535	412	29	f	f	X
ejpam-6535	412	30	:	:	PUNCT
ejpam-6535	412	31	(	(	PUNCT
ejpam-6535	412	32	s	s	X
ejpam-6535	412	33	,	,	PUNCT
ejpam-6535	412	34	cc	cc	NOUN
ejpam-6535	412	35	α	α	NOUN
ejpam-6535	412	36	)	)	PUNCT
ejpam-6535	412	37	−→	−→	NOUN
ejpam-6535	412	38	(	(	PUNCT
ejpam-6535	412	39	s′	s′	PROPN
ejpam-6535	412	40	,	,	PUNCT
ejpam-6535	412	41	cc′	cc′	NOUN
ejpam-6535	412	42	α	α	NOUN
ejpam-6535	412	43	)	)	PUNCT
ejpam-6535	412	44	is	be	AUX
ejpam-6535	412	45	a	a	DET
ejpam-6535	412	46	continuous	continuous	ADJ
ejpam-6535	412	47	function	function	NOUN
ejpam-6535	412	48	.	.	PUNCT
ejpam-6535	413	1	thus	thus	ADV
ejpam-6535	413	2	,	,	PUNCT
ejpam-6535	413	3	one	one	PRON
ejpam-6535	413	4	obtains	obtain	VERB
ejpam-6535	413	5	the	the	DET
ejpam-6535	413	6	embedding	embed	VERB
ejpam-6535	413	7	functor	functor	PROPN
ejpam-6535	413	8	pchy	pchy	NOUN
ejpam-6535	413	9	t−→	t−→	NOUN
ejpam-6535	413	10	rk	rk	NOUN
ejpam-6535	413	11	-	-	PUNCT
ejpam-6535	413	12	pchy	pchy	ADJ
ejpam-6535	413	13	,	,	PUNCT
ejpam-6535	413	14	c	c	PROPN
ejpam-6535	413	15	7→	7→	NUM
ejpam-6535	413	16	c	c	NOUN
ejpam-6535	413	17	c	c	NOUN
ejpam-6535	413	18	;	;	PUNCT
ejpam-6535	413	19	f	f	PROPN
ejpam-6535	413	20	7→	7→	NUM
ejpam-6535	413	21	f	f	NOUN
ejpam-6535	413	22	.	.	PUNCT
ejpam-6535	414	1	as	as	ADP
ejpam-6535	414	2	t	t	PROPN
ejpam-6535	414	3	◦	◦	NOUN
ejpam-6535	414	4	s	s	PART
ejpam-6535	414	5	=	=	SYM
ejpam-6535	414	6	idrk	idrk	ADJ
ejpam-6535	414	7	-	-	PUNCT
ejpam-6535	414	8	pchy	pchy	NOUN
ejpam-6535	414	9	and	and	CCONJ
ejpam-6535	414	10	s	s	PROPN
ejpam-6535	414	11	◦	◦	NOUN
ejpam-6535	414	12	t	t	NOUN
ejpam-6535	414	13	≥	≥	NOUN
ejpam-6535	414	14	idpchy	idpchy	NOUN
ejpam-6535	414	15	,	,	PUNCT
ejpam-6535	414	16	we	we	PRON
ejpam-6535	414	17	have	have	VERB
ejpam-6535	414	18	that	that	SCONJ
ejpam-6535	414	19	the	the	DET
ejpam-6535	414	20	category	category	NOUN
ejpam-6535	414	21	rk	rk	NOUN
ejpam-6535	414	22	-	-	PUNCT
ejpam-6535	414	23	pchy	pchy	ADJ
ejpam-6535	414	24	is	be	AUX
ejpam-6535	414	25	a	a	DET
ejpam-6535	414	26	reflective	reflective	ADJ
ejpam-6535	414	27	subcategory	subcategory	NOUN
ejpam-6535	414	28	of	of	ADP
ejpam-6535	414	29	pchy	pchy	NOUN
ejpam-6535	414	30	.	.	PUNCT
ejpam-6535	415	1	proposition	proposition	NOUN
ejpam-6535	415	2	2	2	NUM
ejpam-6535	415	3	.	.	PUNCT
ejpam-6535	416	1	the	the	DET
ejpam-6535	416	2	category	category	NOUN
ejpam-6535	416	3	pchy	pchy	NOUN
ejpam-6535	416	4	is	be	AUX
ejpam-6535	416	5	a	a	DET
ejpam-6535	416	6	topological	topological	ADJ
ejpam-6535	416	7	category	category	NOUN
ejpam-6535	416	8	.	.	PUNCT
ejpam-6535	417	1	proof	proof	NOUN
ejpam-6535	417	2	.	.	PUNCT
ejpam-6535	418	1	this	this	PRON
ejpam-6535	418	2	follows	follow	VERB
ejpam-6535	418	3	from	from	ADP
ejpam-6535	418	4	the	the	DET
ejpam-6535	418	5	proposition	proposition	NOUN
ejpam-6535	418	6	3.2[23	3.2[23	PROPN
ejpam-6535	418	7	]	]	PUNCT
ejpam-6535	418	8	.	.	PUNCT
ejpam-6535	419	1	we	we	PRON
ejpam-6535	419	2	define	define	VERB
ejpam-6535	419	3	for	for	ADP
ejpam-6535	419	4	(	(	PUNCT
ejpam-6535	419	5	s	s	X
ejpam-6535	419	6	,	,	PUNCT
ejpam-6535	419	7	c	c	NOUN
ejpam-6535	419	8	=	=	SYM
ejpam-6535	419	9	(	(	PUNCT
ejpam-6535	419	10	cφ)φ∈∆+	cφ)φ∈∆+	ADJ
ejpam-6535	419	11	)	)	PUNCT
ejpam-6535	419	12	∈	∈	PROPN
ejpam-6535	419	13	|pchy|	|pchy|	NUM
ejpam-6535	419	14	,	,	PUNCT
ejpam-6535	419	15	the	the	DET
ejpam-6535	419	16	probabilistic	probabilistic	ADJ
ejpam-6535	419	17	convergence	convergence	NOUN
ejpam-6535	419	18	structure	structure	NOUN
ejpam-6535	419	19	cc	cc	NOUN
ejpam-6535	419	20	by	by	ADP
ejpam-6535	419	21	p	p	PROPN
ejpam-6535	419	22	∈	∈	PROPN
ejpam-6535	419	23	ccφ(f	ccφ(f	PROPN
ejpam-6535	419	24	)	)	PUNCT
ejpam-6535	419	25	⇐	⇐	ADJ
ejpam-6535	419	26	⇒	⇒	NOUN
ejpam-6535	420	1	f	f	PROPN
ejpam-6535	420	2	∧	∧	PROPN
ejpam-6535	421	1	[	[	X
ejpam-6535	421	2	p	p	X
ejpam-6535	421	3	]	]	X
ejpam-6535	421	4	∈	∈	PROPN
ejpam-6535	421	5	cφ	cφ	NOUN
ejpam-6535	421	6	,	,	PUNCT
ejpam-6535	421	7	∀φ	∀φ	PROPN
ejpam-6535	421	8	∈	∈	NOUN
ejpam-6535	421	9	∆+	∆+	NOUN
ejpam-6535	421	10	,	,	PUNCT
ejpam-6535	421	11	and	and	CCONJ
ejpam-6535	421	12	f	f	PROPN
ejpam-6535	421	13	∈	∈	PROPN
ejpam-6535	421	14	f(s	f(	NOUN
ejpam-6535	421	15	)	)	PUNCT
ejpam-6535	421	16	.	.	PUNCT
ejpam-6535	422	1	lemma	lemma	PROPN
ejpam-6535	422	2	17	17	NUM
ejpam-6535	422	3	.	.	PUNCT
ejpam-6535	423	1	let	let	VERB
ejpam-6535	423	2	(	(	PUNCT
ejpam-6535	423	3	s	s	X
ejpam-6535	423	4	,	,	PUNCT
ejpam-6535	423	5	c	c	NOUN
ejpam-6535	423	6	)	)	PUNCT
ejpam-6535	423	7	∈	∈	PROPN
ejpam-6535	423	8	|pchy|	|pchy|	VERB
ejpam-6535	423	9	under	under	ADP
ejpam-6535	423	10	the	the	DET
ejpam-6535	423	11	largest	large	ADJ
ejpam-6535	423	12	triangle	triangle	NOUN
ejpam-6535	423	13	function	function	NOUN
ejpam-6535	423	14	τ	τ	PROPN
ejpam-6535	423	15	.	.	PUNCT
ejpam-6535	424	1	then	then	ADV
ejpam-6535	424	2	(	(	PUNCT
ejpam-6535	424	3	s	s	X
ejpam-6535	424	4	,	,	PUNCT
ejpam-6535	424	5	cc	cc	NOUN
ejpam-6535	424	6	)	)	PUNCT
ejpam-6535	424	7	∈	∈	PROPN
ejpam-6535	424	8	|pconv|	|pconv|	ADV
ejpam-6535	424	9	and	and	CCONJ
ejpam-6535	424	10	satisfies	satisfy	VERB
ejpam-6535	424	11	the	the	DET
ejpam-6535	424	12	axiom	axiom	NOUN
ejpam-6535	424	13	(	(	PUNCT
ejpam-6535	424	14	pcs5	pcs5	PROPN
ejpam-6535	424	15	):	):	PUNCT
ejpam-6535	424	16	∀φ	∀φ	NUM
ejpam-6535	424	17	∈	∈	PROPN
ejpam-6535	424	18	∆+	∆+	NUM
ejpam-6535	424	19	and	and	CCONJ
ejpam-6535	424	20	∀	∀	NUM
ejpam-6535	424	21	f	f	X
ejpam-6535	424	22	,	,	PUNCT
ejpam-6535	424	23	g	g	PROPN
ejpam-6535	424	24	∈	∈	PROPN
ejpam-6535	424	25	f(s	f(	NOUN
ejpam-6535	424	26	)	)	PUNCT
ejpam-6535	424	27	,	,	PUNCT
ejpam-6535	424	28	ccφ(f	ccφ(f	PROPN
ejpam-6535	424	29	)	)	PUNCT
ejpam-6535	424	30	∩	∩	ADJ
ejpam-6535	424	31	ccφ(g	ccφ(g	NUM
ejpam-6535	424	32	)	)	PUNCT
ejpam-6535	424	33	≤	≤	NOUN
ejpam-6535	424	34	ccφ	ccφ	X
ejpam-6535	424	35	(	(	PUNCT
ejpam-6535	424	36	f	f	PROPN
ejpam-6535	424	37	∧g	∧g	PROPN
ejpam-6535	424	38	)	)	PUNCT
ejpam-6535	424	39	.	.	PUNCT
ejpam-6535	425	1	proof	proof	NOUN
ejpam-6535	425	2	.	.	PUNCT
ejpam-6535	426	1	(	(	PUNCT
ejpam-6535	426	2	pcs1	pcs1	NOUN
ejpam-6535	426	3	)	)	PUNCT
ejpam-6535	426	4	since	since	SCONJ
ejpam-6535	426	5	[	[	X
ejpam-6535	426	6	p	p	X
ejpam-6535	426	7	]	]	X
ejpam-6535	426	8	∈	∈	PROPN
ejpam-6535	426	9	cφ	cφ	NOUN
ejpam-6535	426	10	for	for	ADP
ejpam-6535	426	11	all	all	DET
ejpam-6535	426	12	φ	φ	PROPN
ejpam-6535	426	13	∈	∈	PROPN
ejpam-6535	426	14	∆+	∆+	NOUN
ejpam-6535	426	15	,	,	PUNCT
ejpam-6535	426	16	and	and	CCONJ
ejpam-6535	426	17	for	for	ADP
ejpam-6535	426	18	all	all	DET
ejpam-6535	426	19	p	p	NOUN
ejpam-6535	426	20	∈	∈	PROPN
ejpam-6535	426	21	s	s	VERB
ejpam-6535	426	22	we	we	PRON
ejpam-6535	426	23	have	have	VERB
ejpam-6535	426	24	[	[	X
ejpam-6535	426	25	p	p	X
ejpam-6535	426	26	]	]	X
ejpam-6535	426	27	=	=	PUNCT
ejpam-6535	427	1	[	[	X
ejpam-6535	427	2	p	p	X
ejpam-6535	427	3	]	]	X
ejpam-6535	427	4	∧	∧	PROPN
ejpam-6535	427	5	[	[	X
ejpam-6535	427	6	p	p	X
ejpam-6535	427	7	]	]	PUNCT
ejpam-6535	427	8	implies	imply	VERB
ejpam-6535	427	9	p	p	PROPN
ejpam-6535	427	10	∈	∈	PROPN
ejpam-6535	427	11	ccφ([p	ccφ([p	NOUN
ejpam-6535	427	12	]	]	PUNCT
ejpam-6535	427	13	)	)	PUNCT
ejpam-6535	427	14	.	.	PUNCT
ejpam-6535	428	1	(	(	PUNCT
ejpam-6535	428	2	pcs2	pcs2	NOUN
ejpam-6535	428	3	)	)	PUNCT
ejpam-6535	428	4	let	let	VERB
ejpam-6535	428	5	f	f	X
ejpam-6535	428	6	,	,	PUNCT
ejpam-6535	428	7	g	g	PROPN
ejpam-6535	428	8	∈	∈	PROPN
ejpam-6535	428	9	f(s	f(	VERB
ejpam-6535	428	10	)	)	PUNCT
ejpam-6535	428	11	with	with	ADP
ejpam-6535	428	12	f	f	PROPN
ejpam-6535	428	13	≤	≤	PROPN
ejpam-6535	428	14	g	g	PROPN
ejpam-6535	428	15	,	,	PUNCT
ejpam-6535	428	16	φ	φ	PROPN
ejpam-6535	428	17	∈	∈	PROPN
ejpam-6535	428	18	∆+	∆+	NOUN
ejpam-6535	428	19	,	,	PUNCT
ejpam-6535	428	20	and	and	CCONJ
ejpam-6535	428	21	p	p	PROPN
ejpam-6535	428	22	∈	∈	PROPN
ejpam-6535	428	23	ccφ(f	ccφ(f	PROPN
ejpam-6535	428	24	)	)	PUNCT
ejpam-6535	428	25	.	.	PUNCT
ejpam-6535	429	1	then	then	ADV
ejpam-6535	429	2	we	we	PRON
ejpam-6535	429	3	have	have	VERB
ejpam-6535	429	4	f	f	PROPN
ejpam-6535	429	5	∧	∧	PROPN
ejpam-6535	430	1	[	[	X
ejpam-6535	430	2	p	p	X
ejpam-6535	430	3	]	]	X
ejpam-6535	430	4	∈	∈	PROPN
ejpam-6535	430	5	cφ	cφ	NOUN
ejpam-6535	430	6	.	.	PUNCT
ejpam-6535	431	1	since	since	SCONJ
ejpam-6535	431	2	f	f	PROPN
ejpam-6535	431	3	∧	∧	PROPN
ejpam-6535	432	1	[	[	X
ejpam-6535	432	2	p	p	X
ejpam-6535	432	3	]	]	PUNCT
ejpam-6535	432	4	≤	≤	NUM
ejpam-6535	432	5	g	g	ADP
ejpam-6535	432	6	∧	∧	PROPN
ejpam-6535	433	1	[	[	X
ejpam-6535	433	2	p	p	X
ejpam-6535	433	3	]	]	X
ejpam-6535	433	4	,	,	PUNCT
ejpam-6535	433	5	we	we	PRON
ejpam-6535	433	6	have	have	VERB
ejpam-6535	433	7	g	g	PROPN
ejpam-6535	433	8	∧	∧	PROPN
ejpam-6535	434	1	[	[	X
ejpam-6535	434	2	p	p	X
ejpam-6535	434	3	]	]	X
ejpam-6535	434	4	∈	∈	PROPN
ejpam-6535	434	5	cφ	cφ	NOUN
ejpam-6535	434	6	by	by	ADP
ejpam-6535	434	7	(	(	PUNCT
ejpam-6535	434	8	pchs2	pchs2	NOUN
ejpam-6535	434	9	)	)	PUNCT
ejpam-6535	434	10	,	,	PUNCT
ejpam-6535	434	11	which	which	PRON
ejpam-6535	434	12	implies	imply	VERB
ejpam-6535	434	13	that	that	SCONJ
ejpam-6535	434	14	p	p	PROPN
ejpam-6535	434	15	∈	∈	PROPN
ejpam-6535	434	16	ccφ(g	ccφ(g	PROPN
ejpam-6535	434	17	)	)	PUNCT
ejpam-6535	434	18	.	.	PUNCT
ejpam-6535	435	1	(	(	PUNCT
ejpam-6535	435	2	pcs3	pcs3	NOUN
ejpam-6535	435	3	)	)	PUNCT
ejpam-6535	435	4	let	let	VERB
ejpam-6535	435	5	φ	φ	NUM
ejpam-6535	435	6	,	,	PUNCT
ejpam-6535	435	7	ψ	ψ	X
ejpam-6535	435	8	∈	∈	PROPN
ejpam-6535	435	9	∆+	∆+	NUM
ejpam-6535	435	10	with	with	ADP
ejpam-6535	435	11	φ	φ	PROPN
ejpam-6535	435	12	≤	≤	NOUN
ejpam-6535	435	13	ψ	ψ	X
ejpam-6535	435	14	and	and	CCONJ
ejpam-6535	435	15	f	f	PROPN
ejpam-6535	435	16	∈	∈	PROPN
ejpam-6535	435	17	f(s	f(	NOUN
ejpam-6535	435	18	)	)	PUNCT
ejpam-6535	435	19	.	.	PUNCT
ejpam-6535	436	1	if	if	SCONJ
ejpam-6535	436	2	p	p	PROPN
ejpam-6535	436	3	∈	∈	PROPN
ejpam-6535	436	4	ccψ(f	ccψ(f	PROPN
ejpam-6535	436	5	)	)	PUNCT
ejpam-6535	436	6	implies	imply	VERB
ejpam-6535	436	7	f	f	PROPN
ejpam-6535	436	8	∧	∧	PROPN
ejpam-6535	436	9	[	[	X
ejpam-6535	436	10	p	p	X
ejpam-6535	436	11	]	]	X
ejpam-6535	436	12	∈	∈	PROPN
ejpam-6535	436	13	cψ	cψ	NOUN
ejpam-6535	436	14	.	.	PUNCT
ejpam-6535	437	1	then	then	ADV
ejpam-6535	437	2	f	f	PROPN
ejpam-6535	437	3	∧	∧	PROPN
ejpam-6535	438	1	[	[	X
ejpam-6535	438	2	p	p	X
ejpam-6535	438	3	]	]	X
ejpam-6535	438	4	∈	∈	PROPN
ejpam-6535	438	5	cφ	cφ	NOUN
ejpam-6535	438	6	by	by	ADP
ejpam-6535	438	7	(	(	PUNCT
ejpam-6535	438	8	pchs3	pchs3	NOUN
ejpam-6535	438	9	)	)	PUNCT
ejpam-6535	438	10	,	,	PUNCT
ejpam-6535	438	11	implying	imply	VERB
ejpam-6535	438	12	p	p	NOUN
ejpam-6535	438	13	∈	∈	PROPN
ejpam-6535	438	14	ccφ(f	ccφ(f	PROPN
ejpam-6535	438	15	)	)	PUNCT
ejpam-6535	438	16	.	.	PUNCT
ejpam-6535	439	1	(	(	PUNCT
ejpam-6535	439	2	pcs4	pcs4	PROPN
ejpam-6535	439	3	)	)	PUNCT
ejpam-6535	439	4	obvious	obvious	ADJ
ejpam-6535	439	5	.	.	PUNCT
ejpam-6535	440	1	(	(	PUNCT
ejpam-6535	440	2	pcs5	pcs5	PROPN
ejpam-6535	440	3	)	)	PUNCT
ejpam-6535	440	4	let	let	VERB
ejpam-6535	440	5	φ	φ	PROPN
ejpam-6535	440	6	∈	∈	PROPN
ejpam-6535	440	7	∆+	∆+	PROPN
ejpam-6535	440	8	and	and	CCONJ
ejpam-6535	440	9	f	f	X
ejpam-6535	440	10	,	,	PUNCT
ejpam-6535	440	11	g	g	PROPN
ejpam-6535	440	12	∈	∈	PROPN
ejpam-6535	440	13	f(s	f(	NOUN
ejpam-6535	440	14	)	)	PUNCT
ejpam-6535	440	15	.	.	PUNCT
ejpam-6535	441	1	if	if	SCONJ
ejpam-6535	441	2	p	p	PROPN
ejpam-6535	441	3	∈	∈	PROPN
ejpam-6535	441	4	ccφ(f)∩ccφ(f	ccφ(f)∩ccφ(f	NOUN
ejpam-6535	441	5	)	)	PUNCT
ejpam-6535	441	6	,	,	PUNCT
ejpam-6535	441	7	then	then	ADV
ejpam-6535	441	8	f∧[p	f∧[p	X
ejpam-6535	441	9	]	]	X
ejpam-6535	441	10	∈	∈	PROPN
ejpam-6535	441	11	cφ	cφ	NOUN
ejpam-6535	441	12	and	and	CCONJ
ejpam-6535	441	13	g∧[p	g∧[p	PROPN
ejpam-6535	441	14	]	]	X
ejpam-6535	441	15	∈	∈	PROPN
ejpam-6535	441	16	cφ	cφ	NOUN
ejpam-6535	441	17	.	.	PUNCT
ejpam-6535	442	1	this	this	PRON
ejpam-6535	442	2	implies	imply	VERB
ejpam-6535	442	3	that	that	SCONJ
ejpam-6535	442	4	(	(	PUNCT
ejpam-6535	442	5	f	f	PROPN
ejpam-6535	442	6	∧g	∧g	PROPN
ejpam-6535	442	7	)	)	PUNCT
ejpam-6535	442	8	∧	∧	NOUN
ejpam-6535	442	9	[	[	X
ejpam-6535	442	10	p	p	X
ejpam-6535	442	11	]	]	X
ejpam-6535	442	12	∈	∈	PROPN
ejpam-6535	442	13	cφ	cφ	NOUN
ejpam-6535	442	14	by	by	ADP
ejpam-6535	442	15	(	(	PUNCT
ejpam-6535	442	16	pchs5	pchs5	PROPN
ejpam-6535	442	17	)	)	PUNCT
ejpam-6535	442	18	,	,	PUNCT
ejpam-6535	442	19	and	and	CCONJ
ejpam-6535	442	20	hence	hence	ADV
ejpam-6535	442	21	p	p	X
ejpam-6535	442	22	∈	∈	PROPN
ejpam-6535	442	23	ccφ	ccφ	NOUN
ejpam-6535	442	24	(	(	PUNCT
ejpam-6535	442	25	f	f	PROPN
ejpam-6535	442	26	∧g	∧g	PROPN
ejpam-6535	442	27	)	)	PUNCT
ejpam-6535	442	28	.	.	PUNCT
ejpam-6535	443	1	lemma	lemma	PROPN
ejpam-6535	443	2	18	18	NUM
ejpam-6535	443	3	.	.	PUNCT
ejpam-6535	444	1	let	let	VERB
ejpam-6535	444	2	(	(	PUNCT
ejpam-6535	444	3	s	s	X
ejpam-6535	444	4	,	,	PUNCT
ejpam-6535	444	5	c	c	NOUN
ejpam-6535	444	6	)	)	PUNCT
ejpam-6535	444	7	,	,	PUNCT
ejpam-6535	444	8	(	(	PUNCT
ejpam-6535	444	9	s	s	X
ejpam-6535	444	10	,	,	PUNCT
ejpam-6535	444	11	c′	c′	NUM
ejpam-6535	444	12	)	)	PUNCT
ejpam-6535	444	13	∈	∈	PROPN
ejpam-6535	444	14	|pchy|	|pchy|	NOUN
ejpam-6535	444	15	and	and	CCONJ
ejpam-6535	444	16	f	f	X
ejpam-6535	444	17	:	:	PUNCT
ejpam-6535	444	18	(	(	PUNCT
ejpam-6535	444	19	s	s	X
ejpam-6535	444	20	,	,	PUNCT
ejpam-6535	444	21	c	c	NOUN
ejpam-6535	444	22	)	)	PUNCT
ejpam-6535	444	23	−→	−→	NOUN
ejpam-6535	444	24	(	(	PUNCT
ejpam-6535	444	25	s′	s′	X
ejpam-6535	444	26	,	,	PUNCT
ejpam-6535	444	27	c′	c′	NUM
ejpam-6535	444	28	)	)	PUNCT
ejpam-6535	444	29	be	be	AUX
ejpam-6535	444	30	probabilistic	probabilistic	ADJ
ejpam-6535	444	31	cauchycontinuous	cauchycontinuous	ADJ
ejpam-6535	444	32	function	function	NOUN
ejpam-6535	444	33	.	.	PUNCT
ejpam-6535	445	1	then	then	ADV
ejpam-6535	445	2	f	f	X
ejpam-6535	445	3	:	:	PUNCT
ejpam-6535	445	4	(	(	PUNCT
ejpam-6535	445	5	s	s	X
ejpam-6535	445	6	,	,	PUNCT
ejpam-6535	445	7	cc	cc	NOUN
ejpam-6535	445	8	)	)	PUNCT
ejpam-6535	445	9	−→	−→	NOUN
ejpam-6535	445	10	(	(	PUNCT
ejpam-6535	445	11	s′	s′	PROPN
ejpam-6535	445	12	,	,	PUNCT
ejpam-6535	445	13	cc	cc	NOUN
ejpam-6535	445	14	′	′	NUM
ejpam-6535	445	15	)	)	PUNCT
ejpam-6535	445	16	is	be	AUX
ejpam-6535	445	17	continuous	continuous	ADJ
ejpam-6535	445	18	.	.	PUNCT
ejpam-6535	446	1	proof	proof	NOUN
ejpam-6535	446	2	.	.	PUNCT
ejpam-6535	447	1	let	let	VERB
ejpam-6535	447	2	p	p	PRON
ejpam-6535	447	3	∈	∈	PROPN
ejpam-6535	447	4	s	s	PART
ejpam-6535	447	5	,	,	PUNCT
ejpam-6535	447	6	φ	φ	PROPN
ejpam-6535	447	7	∈	∈	PROPN
ejpam-6535	447	8	∆+	∆+	NOUN
ejpam-6535	447	9	and	and	CCONJ
ejpam-6535	447	10	f	f	PROPN
ejpam-6535	447	11	∈	∈	PROPN
ejpam-6535	447	12	f(s	f(	NOUN
ejpam-6535	447	13	)	)	PUNCT
ejpam-6535	447	14	.	.	PUNCT
ejpam-6535	448	1	if	if	SCONJ
ejpam-6535	448	2	now	now	ADV
ejpam-6535	448	3	p	p	X
ejpam-6535	448	4	∈	∈	PROPN
ejpam-6535	448	5	ccφ(f	ccφ(f	PROPN
ejpam-6535	448	6	)	)	PUNCT
ejpam-6535	448	7	,	,	PUNCT
ejpam-6535	449	1	then	then	ADV
ejpam-6535	449	2	f	f	PROPN
ejpam-6535	449	3	∧	∧	PROPN
ejpam-6535	449	4	[	[	X
ejpam-6535	449	5	p	p	X
ejpam-6535	449	6	]	]	X
ejpam-6535	449	7	∈	∈	PROPN
ejpam-6535	449	8	cφ	cφ	NOUN
ejpam-6535	449	9	implying	imply	VERB
ejpam-6535	449	10	that	that	SCONJ
ejpam-6535	449	11	f	f	PROPN
ejpam-6535	449	12	(	(	PUNCT
ejpam-6535	449	13	f	f	X
ejpam-6535	449	14	∧	∧	PROPN
ejpam-6535	450	1	[	[	X
ejpam-6535	450	2	p	p	X
ejpam-6535	450	3	]	]	X
ejpam-6535	450	4	)	)	PUNCT
ejpam-6535	450	5	∈	∈	PROPN
ejpam-6535	450	6	c′φ	c′φ	PROPN
ejpam-6535	450	7	,	,	PUNCT
ejpam-6535	450	8	implying	imply	VERB
ejpam-6535	450	9	f(f	f(f	PROPN
ejpam-6535	450	10	)	)	PUNCT
ejpam-6535	450	11	∧	∧	PROPN
ejpam-6535	450	12	[	[	X
ejpam-6535	450	13	f(p	f(p	PROPN
ejpam-6535	450	14	)	)	PUNCT
ejpam-6535	450	15	]	]	PUNCT
ejpam-6535	451	1	∈	∈	PROPN
ejpam-6535	451	2	c′φ	c′φ	PROPN
ejpam-6535	451	3	.	.	PUNCT
ejpam-6535	452	1	hence	hence	ADV
ejpam-6535	452	2	f(p	f(p	NOUN
ejpam-6535	452	3	)	)	PUNCT
ejpam-6535	452	4	∈	∈	PROPN
ejpam-6535	452	5	cc	cc	NOUN
ejpam-6535	452	6	′	′	NUM
ejpam-6535	452	7	φ(f(f	φ(f(f	NOUN
ejpam-6535	452	8	)	)	PUNCT
ejpam-6535	452	9	)	)	PUNCT
ejpam-6535	452	10	.	.	PUNCT
ejpam-6535	453	1	then	then	ADV
ejpam-6535	453	2	lemma	lemma	PROPN
ejpam-6535	453	3	17	17	NUM
ejpam-6535	453	4	and	and	CCONJ
ejpam-6535	453	5	lemma	lemma	PROPN
ejpam-6535	453	6	18	18	NUM
ejpam-6535	453	7	yield	yield	NOUN
ejpam-6535	453	8	the	the	DET
ejpam-6535	453	9	following	follow	VERB
ejpam-6535	453	10	corollary	corollary	ADJ
ejpam-6535	453	11	2	2	NUM
ejpam-6535	453	12	.	.	PUNCT
ejpam-6535	453	13	f	f	NOUN
ejpam-6535	453	14	:	:	PUNCT
ejpam-6535	453	15			PUNCT
ejpam-6535	453	16	pchy	pchy	ADJ
ejpam-6535	453	17	−→	−→	ADJ
ejpam-6535	453	18	pconv	pconv	NOUN
ejpam-6535	453	19	(	(	PUNCT
ejpam-6535	453	20	x	x	NOUN
ejpam-6535	453	21	,	,	PUNCT
ejpam-6535	453	22	c	c	NOUN
ejpam-6535	453	23	)	)	PUNCT
ejpam-6535	453	24	7−→	7−→	NOUN
ejpam-6535	453	25	(	(	PUNCT
ejpam-6535	453	26	x	x	NOUN
ejpam-6535	453	27	,	,	PUNCT
ejpam-6535	453	28	cc	cc	NOUN
ejpam-6535	453	29	)	)	PUNCT
ejpam-6535	453	30	f	f	PROPN
ejpam-6535	454	1	7−→	7−→	PROPN
ejpam-6535	454	2	f	f	PROPN
ejpam-6535	454	3	,	,	PUNCT
ejpam-6535	454	4	is	be	AUX
ejpam-6535	454	5	a	a	DET
ejpam-6535	454	6	functor	functor	NOUN
ejpam-6535	454	7	.	.	PROPN
ejpam-6535	454	8	7	7	X
ejpam-6535	454	9	.	.	X
ejpam-6535	454	10	probabilistic	probabilistic	ADJ
ejpam-6535	454	11	pre	pre	ADJ
ejpam-6535	454	12	cauchy	cauchy	PROPN
ejpam-6535	454	13	groups	group	NOUN
ejpam-6535	454	14	and	and	CCONJ
ejpam-6535	454	15	their	their	PRON
ejpam-6535	454	16	relationship	relationship	NOUN
ejpam-6535	454	17	with	with	ADP
ejpam-6535	454	18	probabilistic	probabilistic	ADJ
ejpam-6535	454	19	cauchy	cauchy	ADJ
ejpam-6535	454	20	groups	group	NOUN
ejpam-6535	454	21	definition	definition	NOUN
ejpam-6535	454	22	10	10	NUM
ejpam-6535	454	23	.	.	PUNCT
ejpam-6535	455	1	let	let	VERB
ejpam-6535	455	2	(	(	PUNCT
ejpam-6535	455	3	s	s	X
ejpam-6535	455	4	,	,	PUNCT
ejpam-6535	455	5	·	·	PUNCT
ejpam-6535	455	6	)	)	PUNCT
ejpam-6535	455	7	be	be	AUX
ejpam-6535	455	8	a	a	DET
ejpam-6535	455	9	group	group	NOUN
ejpam-6535	455	10	.	.	PUNCT
ejpam-6535	456	1	a	a	DET
ejpam-6535	456	2	probabilistic	probabilistic	ADJ
ejpam-6535	456	3	pre	pre	ADJ
ejpam-6535	456	4	-	-	ADJ
ejpam-6535	456	5	cauchy	cauchy	ADJ
ejpam-6535	456	6	group	group	NOUN
ejpam-6535	456	7	is	be	AUX
ejpam-6535	456	8	a	a	DET
ejpam-6535	456	9	triple	triple	ADJ
ejpam-6535	456	10	(	(	PUNCT
ejpam-6535	456	11	s	s	PROPN
ejpam-6535	456	12	,	,	PUNCT
ejpam-6535	456	13	·	·	PUNCT
ejpam-6535	456	14	,	,	PUNCT
ejpam-6535	456	15	c	c	X
ejpam-6535	456	16	=	=	SYM
ejpam-6535	456	17	(	(	PUNCT
ejpam-6535	456	18	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	456	19	)	)	PUNCT
ejpam-6535	456	20	fulfilling	fulfil	VERB
ejpam-6535	456	21	the	the	DET
ejpam-6535	456	22	following	following	ADJ
ejpam-6535	456	23	conditions	condition	NOUN
ejpam-6535	456	24	:	:	PUNCT
ejpam-6535	456	25	(	(	PUNCT
ejpam-6535	456	26	pchs1	pchs1	NOUN
ejpam-6535	456	27	)	)	PUNCT
ejpam-6535	457	1	[	[	X
ejpam-6535	457	2	p	p	X
ejpam-6535	457	3	]	]	X
ejpam-6535	457	4	∈	∈	PROPN
ejpam-6535	457	5	cφ	cφ	NOUN
ejpam-6535	457	6	,	,	PUNCT
ejpam-6535	457	7	∀p	∀p	PROPN
ejpam-6535	457	8	∈	∈	PROPN
ejpam-6535	457	9	s	s	NOUN
ejpam-6535	457	10	,	,	PUNCT
ejpam-6535	457	11	∀φ	∀φ	NOUN
ejpam-6535	457	12	∈	∈	PROPN
ejpam-6535	457	13	∆+	∆+	NOUN
ejpam-6535	457	14	;	;	PUNCT
ejpam-6535	457	15	(	(	PUNCT
ejpam-6535	457	16	pchs2	pchs2	NOUN
ejpam-6535	457	17	)	)	PUNCT
ejpam-6535	457	18	if	if	SCONJ
ejpam-6535	457	19	f	f	PROPN
ejpam-6535	457	20	∈	∈	PROPN
ejpam-6535	457	21	cφ	cφ	NOUN
ejpam-6535	457	22	and	and	CCONJ
ejpam-6535	457	23	f	f	PROPN
ejpam-6535	457	24	≤	≤	NOUN
ejpam-6535	457	25	g	g	PROPN
ejpam-6535	457	26	⇒	⇒	NOUN
ejpam-6535	457	27	g	g	PROPN
ejpam-6535	457	28	∈	∈	PROPN
ejpam-6535	457	29	cφ	cφ	NOUN
ejpam-6535	457	30	;	;	PUNCT
ejpam-6535	457	31	(	(	PUNCT
ejpam-6535	457	32	pchs3	pchs3	X
ejpam-6535	457	33	)	)	PUNCT
ejpam-6535	457	34	∀φ	∀φ	NOUN
ejpam-6535	457	35	,	,	PUNCT
ejpam-6535	457	36	ψ	ψ	NOUN
ejpam-6535	457	37	∈	∈	PROPN
ejpam-6535	457	38	∆+	∆+	NUM
ejpam-6535	457	39	with	with	ADP
ejpam-6535	457	40	φ	φ	PROPN
ejpam-6535	457	41	≤	≤	NOUN
ejpam-6535	457	42	ψ	ψ	ADP
ejpam-6535	457	43	⇒	⇒	NOUN
ejpam-6535	457	44	cψ	cψ	PROPN
ejpam-6535	457	45	≤	≤	NOUN
ejpam-6535	457	46	cφ	cφ	NOUN
ejpam-6535	457	47	;	;	PUNCT
ejpam-6535	457	48	(	(	PUNCT
ejpam-6535	457	49	pchs4	pchs4	X
ejpam-6535	457	50	)	)	PUNCT
ejpam-6535	457	51	cϵ∞	cϵ∞	PROPN
ejpam-6535	457	52	=	=	SYM
ejpam-6535	457	53	f(s	f(	NOUN
ejpam-6535	457	54	)	)	PUNCT
ejpam-6535	457	55	;	;	PUNCT
ejpam-6535	457	56	(	(	PUNCT
ejpam-6535	457	57	pchgm)′	pchgm)′	NOUN
ejpam-6535	457	58	f	f	PROPN
ejpam-6535	457	59	∈	∈	PROPN
ejpam-6535	457	60	cφ	cφ	NOUN
ejpam-6535	457	61	and	and	CCONJ
ejpam-6535	457	62	g	g	PROPN
ejpam-6535	457	63	∈	∈	PROPN
ejpam-6535	457	64	cψ	cψ	NOUN
ejpam-6535	457	65	⇒	⇒	NOUN
ejpam-6535	457	66	f−1	f−1	PROPN
ejpam-6535	457	67	⊙g	⊙g	PROPN
ejpam-6535	457	68	∈	∈	PROPN
ejpam-6535	457	69	cτ(φ	cτ(φ	NOUN
ejpam-6535	457	70	,	,	PUNCT
ejpam-6535	457	71	ψ	ψ	NOUN
ejpam-6535	457	72	)	)	PUNCT
ejpam-6535	457	73	.	.	PUNCT
ejpam-6535	458	1	let	let	VERB
ejpam-6535	458	2	pprechygrp	pprechygrp	NOUN
ejpam-6535	458	3	denote	denote	VERB
ejpam-6535	458	4	the	the	DET
ejpam-6535	458	5	category	category	NOUN
ejpam-6535	458	6	consists	consist	VERB
ejpam-6535	458	7	of	of	ADP
ejpam-6535	458	8	all	all	DET
ejpam-6535	458	9	probabilistic	probabilistic	ADJ
ejpam-6535	458	10	pre	pre	ADJ
ejpam-6535	458	11	-	-	ADJ
ejpam-6535	458	12	cauchy	cauchy	ADJ
ejpam-6535	458	13	groups	group	NOUN
ejpam-6535	458	14	as	as	ADP
ejpam-6535	458	15	objects	object	NOUN
ejpam-6535	458	16	and	and	CCONJ
ejpam-6535	458	17	probabilistic	probabilistic	ADJ
ejpam-6535	458	18	cauchy	cauchy	NOUN
ejpam-6535	458	19	-	-	PUNCT
ejpam-6535	458	20	continuous	continuous	ADJ
ejpam-6535	458	21	group	group	NOUN
ejpam-6535	458	22	-	-	PUNCT
ejpam-6535	458	23	homomorphisms	homomorphism	NOUN
ejpam-6535	458	24	as	as	ADP
ejpam-6535	458	25	morphisms	morphism	NOUN
ejpam-6535	458	26	.	.	PUNCT
ejpam-6535	459	1	proposition	proposition	NOUN
ejpam-6535	459	2	3	3	X
ejpam-6535	459	3	.	.	PUNCT
ejpam-6535	460	1	let	let	VERB
ejpam-6535	460	2	(	(	PUNCT
ejpam-6535	460	3	s	s	X
ejpam-6535	460	4	,	,	PUNCT
ejpam-6535	460	5	·	·	PUNCT
ejpam-6535	460	6	,	,	PUNCT
ejpam-6535	460	7	c	c	X
ejpam-6535	460	8	=	=	SYM
ejpam-6535	460	9	(	(	PUNCT
ejpam-6535	460	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	460	11	)	)	PUNCT
ejpam-6535	460	12	∈	∈	PROPN
ejpam-6535	460	13	|pprechygrp|	|pprechygrp|	NUM
ejpam-6535	460	14	,	,	PUNCT
ejpam-6535	460	15	and	and	CCONJ
ejpam-6535	460	16	f	f	X
ejpam-6535	460	17	,	,	PUNCT
ejpam-6535	460	18	g	g	PROPN
ejpam-6535	460	19	∈	∈	PROPN
ejpam-6535	460	20	cφ	cφ	NOUN
ejpam-6535	460	21	,	,	PUNCT
ejpam-6535	460	22	and	and	CCONJ
ejpam-6535	460	23	φ	φ	NUM
ejpam-6535	460	24	∈	∈	PROPN
ejpam-6535	460	25	∆+	∆+	NOUN
ejpam-6535	460	26	.	.	PUNCT
ejpam-6535	461	1	if	if	SCONJ
ejpam-6535	461	2	τ	τ	PROPN
ejpam-6535	461	3	is	be	AUX
ejpam-6535	461	4	the	the	DET
ejpam-6535	461	5	largest	large	ADJ
ejpam-6535	461	6	triangle	triangle	NOUN
ejpam-6535	461	7	function	function	NOUN
ejpam-6535	461	8	,	,	PUNCT
ejpam-6535	461	9	i.e.	i.e.	X
ejpam-6535	461	10	,	,	PUNCT
ejpam-6535	461	11	τ(φ	τ(φ	PROPN
ejpam-6535	461	12	,	,	PUNCT
ejpam-6535	461	13	φ	φ	NOUN
ejpam-6535	461	14	)	)	PUNCT
ejpam-6535	461	15	=	=	SYM
ejpam-6535	461	16	φ	φ	PROPN
ejpam-6535	461	17	,	,	PUNCT
ejpam-6535	461	18	then	then	ADV
ejpam-6535	461	19	f	f	PROPN
ejpam-6535	461	20	∧	∧	PROPN
ejpam-6535	461	21	g	g	PROPN
ejpam-6535	461	22	∈	∈	PROPN
ejpam-6535	461	23	cφ	cφ	X
ejpam-6535	461	24	if	if	SCONJ
ejpam-6535	461	25	and	and	CCONJ
ejpam-6535	461	26	only	only	ADV
ejpam-6535	461	27	if	if	SCONJ
ejpam-6535	461	28	e	e	PROPN
ejpam-6535	461	29	∈	∈	PROPN
ejpam-6535	461	30	ccφ	ccφ	NOUN
ejpam-6535	461	31	(	(	PUNCT
ejpam-6535	461	32	f−1	f−1	PROPN
ejpam-6535	461	33	⊙g	⊙g	PROPN
ejpam-6535	461	34	)	)	PUNCT
ejpam-6535	461	35	.	.	PUNCT
ejpam-6535	462	1	proof	proof	NOUN
ejpam-6535	462	2	.	.	PUNCT
ejpam-6535	463	1	⇒	⇒	NOUN
ejpam-6535	463	2	:	:	PUNCT
ejpam-6535	463	3	let	let	VERB
ejpam-6535	463	4	f	f	X
ejpam-6535	463	5	,	,	PUNCT
ejpam-6535	463	6	g	g	PROPN
ejpam-6535	463	7	∈	∈	PROPN
ejpam-6535	463	8	cφ	cφ	NOUN
ejpam-6535	463	9	,	,	PUNCT
ejpam-6535	463	10	and	and	CCONJ
ejpam-6535	463	11	φ	φ	NUM
ejpam-6535	463	12	∈	∈	PROPN
ejpam-6535	463	13	∆+	∆+	NOUN
ejpam-6535	463	14	.	.	PUNCT
ejpam-6535	464	1	put	put	VERB
ejpam-6535	464	2	h	h	NOUN
ejpam-6535	465	1	=	=	SYM
ejpam-6535	465	2	f	f	PROPN
ejpam-6535	465	3	∧	∧	PROPN
ejpam-6535	465	4	g.	g.	PROPN
ejpam-6535	465	5	then	then	ADV
ejpam-6535	465	6	h−1	h−1	PROPN
ejpam-6535	465	7	≤	≤	X
ejpam-6535	465	8	f−1	f−1	PROPN
ejpam-6535	465	9	;	;	PUNCT
ejpam-6535	465	10	also	also	ADV
ejpam-6535	465	11	,	,	PUNCT
ejpam-6535	465	12	h	h	PROPN
ejpam-6535	465	13	≤	≤	NUM
ejpam-6535	465	14	g.	g.	PROPN
ejpam-6535	466	1	so	so	ADV
ejpam-6535	466	2	,	,	PUNCT
ejpam-6535	466	3	h−1	h−1	PROPN
ejpam-6535	466	4	⊙	⊙	PROPN
ejpam-6535	466	5	h	h	PROPN
ejpam-6535	467	1	≤	≤	PROPN
ejpam-6535	467	2	f−1	f−1	PROPN
ejpam-6535	467	3	⊙	⊙	VERB
ejpam-6535	467	4	g	g	PROPN
ejpam-6535	467	5	,	,	PUNCT
ejpam-6535	467	6	whence	whence	PROPN
ejpam-6535	467	7	f−1	f−1	PROPN
ejpam-6535	467	8	⊙	⊙	VERB
ejpam-6535	467	9	g	g	PROPN
ejpam-6535	467	10	∈	∈	PROPN
ejpam-6535	467	11	cφ	cφ	NOUN
ejpam-6535	467	12	.	.	PUNCT
ejpam-6535	468	1	by	by	ADP
ejpam-6535	468	2	lemma	lemma	PROPN
ejpam-6535	468	3	2(a	2(a	NUM
ejpam-6535	468	4	)	)	PUNCT
ejpam-6535	468	5	,	,	PUNCT
ejpam-6535	468	6	h−1	h−1	PROPN
ejpam-6535	468	7	⊙	⊙	PROPN
ejpam-6535	468	8	h	h	PROPN
ejpam-6535	469	1	≤	≤	X
ejpam-6535	470	1	[	[	X
ejpam-6535	470	2	e	e	X
ejpam-6535	470	3	]	]	X
ejpam-6535	470	4	and	and	CCONJ
ejpam-6535	470	5	so	so	ADV
ejpam-6535	470	6	,	,	PUNCT
ejpam-6535	470	7	h−1	h−1	PROPN
ejpam-6535	470	8	⊙	⊙	PROPN
ejpam-6535	470	9	h	h	PROPN
ejpam-6535	471	1	∧	∧	PROPN
ejpam-6535	472	1	[	[	X
ejpam-6535	472	2	e	e	X
ejpam-6535	472	3	]	]	X
ejpam-6535	472	4	∈	∈	PROPN
ejpam-6535	472	5	cφ	cφ	NOUN
ejpam-6535	472	6	which	which	PRON
ejpam-6535	472	7	yields	yield	VERB
ejpam-6535	472	8	that	that	SCONJ
ejpam-6535	472	9	e	e	PROPN
ejpam-6535	472	10	∈	∈	PROPN
ejpam-6535	472	11	ccφ	ccφ	NOUN
ejpam-6535	472	12	(	(	PUNCT
ejpam-6535	472	13	h−1	h−1	PROPN
ejpam-6535	472	14	⊙h	⊙h	NOUN
ejpam-6535	472	15	)	)	PUNCT
ejpam-6535	472	16	and	and	CCONJ
ejpam-6535	472	17	hence	hence	ADV
ejpam-6535	472	18	by	by	ADP
ejpam-6535	472	19	(	(	PUNCT
ejpam-6535	472	20	pcs2	pcs2	PROPN
ejpam-6535	472	21	)	)	PUNCT
ejpam-6535	472	22	,	,	PUNCT
ejpam-6535	472	23	e	e	PROPN
ejpam-6535	472	24	∈	∈	PROPN
ejpam-6535	472	25	ccφ	ccφ	NOUN
ejpam-6535	472	26	(	(	PUNCT
ejpam-6535	472	27	f−1	f−1	PROPN
ejpam-6535	472	28	⊙g	⊙g	PROPN
ejpam-6535	472	29	)	)	PUNCT
ejpam-6535	472	30	.	.	PUNCT
ejpam-6535	473	1	⇐	⇐	ADJ
ejpam-6535	473	2	:	:	PUNCT
ejpam-6535	473	3	if	if	SCONJ
ejpam-6535	473	4	e	e	PROPN
ejpam-6535	473	5	∈	∈	PROPN
ejpam-6535	473	6	ccφ	ccφ	NOUN
ejpam-6535	473	7	(	(	PUNCT
ejpam-6535	473	8	f−1	f−1	PROPN
ejpam-6535	473	9	⊙g	⊙g	PROPN
ejpam-6535	473	10	)	)	PUNCT
ejpam-6535	473	11	,	,	PUNCT
ejpam-6535	473	12	then	then	ADV
ejpam-6535	473	13	(	(	PUNCT
ejpam-6535	473	14	f−1	f−1	PROPN
ejpam-6535	473	15	⊙g	⊙g	ADJ
ejpam-6535	473	16	)	)	PUNCT
ejpam-6535	474	1	∧	∧	PROPN
ejpam-6535	474	2	[	[	X
ejpam-6535	474	3	e	e	X
ejpam-6535	474	4	]	]	X
ejpam-6535	474	5	∈	∈	PROPN
ejpam-6535	474	6	cφ	cφ	NOUN
ejpam-6535	474	7	.	.	PUNCT
ejpam-6535	475	1	since	since	SCONJ
ejpam-6535	475	2	f	f	PROPN
ejpam-6535	475	3	∈	∈	PROPN
ejpam-6535	475	4	cφ	cφ	NOUN
ejpam-6535	475	5	,	,	PUNCT
ejpam-6535	475	6	f⊙	f⊙	PROPN
ejpam-6535	475	7	(	(	PUNCT
ejpam-6535	475	8	(	(	PUNCT
ejpam-6535	475	9	f−1	f−1	PROPN
ejpam-6535	475	10	⊙g	⊙g	ADJ
ejpam-6535	475	11	)	)	PUNCT
ejpam-6535	476	1	∧	∧	PROPN
ejpam-6535	477	1	[	[	X
ejpam-6535	477	2	e	e	X
ejpam-6535	477	3	]	]	PUNCT
ejpam-6535	477	4	)	)	PUNCT
ejpam-6535	477	5	∈	∈	PROPN
ejpam-6535	477	6	cφ	cφ	NOUN
ejpam-6535	477	7	.	.	PUNCT
ejpam-6535	478	1	but	but	CCONJ
ejpam-6535	478	2	in	in	ADP
ejpam-6535	478	3	view	view	NOUN
ejpam-6535	478	4	of	of	ADP
ejpam-6535	478	5	lemma	lemma	PROPN
ejpam-6535	478	6	2	2	NUM
ejpam-6535	478	7	,	,	PUNCT
ejpam-6535	478	8	(	(	PUNCT
ejpam-6535	478	9	(	(	PUNCT
ejpam-6535	478	10	f⊙	f⊙	VERB
ejpam-6535	478	11	f−1)⊙g	f−1)⊙g	ADP
ejpam-6535	478	12	∧	∧	PROPN
ejpam-6535	478	13	[	[	X
ejpam-6535	478	14	e	e	NOUN
ejpam-6535	478	15	]	]	NOUN
ejpam-6535	478	16	)	)	PUNCT
ejpam-6535	478	17	)	)	PUNCT
ejpam-6535	479	1	=	=	PUNCT
ejpam-6535	479	2	(	(	PUNCT
ejpam-6535	479	3	(	(	PUNCT
ejpam-6535	479	4	f⊙	f⊙	VERB
ejpam-6535	479	5	f−1	f−1	PROPN
ejpam-6535	479	6	)	)	PUNCT
ejpam-6535	479	7	⊙g	⊙g	NOUN
ejpam-6535	479	8	)	)	PUNCT
ejpam-6535	479	9	∧(f⊙	∧(f⊙	ADP
ejpam-6535	479	10	[	[	X
ejpam-6535	479	11	e	e	X
ejpam-6535	479	12	]	]	X
ejpam-6535	479	13	)	)	PUNCT
ejpam-6535	479	14	≤	≤	NOUN
ejpam-6535	480	1	f∧g	f∧g	PROPN
ejpam-6535	480	2	.	.	PUNCT
ejpam-6535	481	1	thus	thus	ADV
ejpam-6535	481	2	we	we	PRON
ejpam-6535	481	3	have	have	VERB
ejpam-6535	481	4	f	f	PROPN
ejpam-6535	481	5	∧g	∧g	PROPN
ejpam-6535	481	6	∈	∈	PROPN
ejpam-6535	481	7	cφ	cφ	X
ejpam-6535	481	8	.	.	PUNCT
ejpam-6535	481	9	corollary	corollary	ADJ
ejpam-6535	481	10	3	3	NUM
ejpam-6535	481	11	.	.	PUNCT
ejpam-6535	482	1	if	if	SCONJ
ejpam-6535	482	2	(	(	PUNCT
ejpam-6535	482	3	x	x	X
ejpam-6535	482	4	,	,	PUNCT
ejpam-6535	482	5	·	·	PUNCT
ejpam-6535	482	6	,	,	PUNCT
ejpam-6535	482	7	c	c	X
ejpam-6535	482	8	=	=	SYM
ejpam-6535	482	9	(	(	PUNCT
ejpam-6535	482	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	482	11	)	)	PUNCT
ejpam-6535	482	12	is	be	AUX
ejpam-6535	482	13	a	a	DET
ejpam-6535	482	14	probabilistic	probabilistic	ADJ
ejpam-6535	482	15	pre	pre	ADJ
ejpam-6535	482	16	-	-	ADJ
ejpam-6535	482	17	cauchy	cauchy	ADJ
ejpam-6535	482	18	group	group	NOUN
ejpam-6535	482	19	under	under	ADP
ejpam-6535	482	20	a	a	DET
ejpam-6535	482	21	triangle	triangle	NOUN
ejpam-6535	482	22	function	function	NOUN
ejpam-6535	482	23	τ	τ	PROPN
ejpam-6535	482	24	,	,	PUNCT
ejpam-6535	482	25	then	then	ADV
ejpam-6535	482	26	it	it	PRON
ejpam-6535	482	27	is	be	AUX
ejpam-6535	482	28	probabilistic	probabilistic	ADJ
ejpam-6535	482	29	cauchy	cauchy	ADJ
ejpam-6535	482	30	space	space	NOUN
ejpam-6535	482	31	.	.	PUNCT
ejpam-6535	483	1	proof	proof	NOUN
ejpam-6535	483	2	.	.	PUNCT
ejpam-6535	484	1	we	we	PRON
ejpam-6535	484	2	only	only	ADV
ejpam-6535	484	3	need	need	VERB
ejpam-6535	484	4	to	to	PART
ejpam-6535	484	5	verify	verify	VERB
ejpam-6535	484	6	the	the	DET
ejpam-6535	484	7	axiom	axiom	NOUN
ejpam-6535	484	8	(	(	PUNCT
ejpam-6535	484	9	pchs5	pchs5	PROPN
ejpam-6535	484	10	)	)	PUNCT
ejpam-6535	484	11	.	.	PUNCT
ejpam-6535	485	1	for	for	ADP
ejpam-6535	485	2	,	,	PUNCT
ejpam-6535	485	3	let	let	VERB
ejpam-6535	485	4	φ	φ	PROPN
ejpam-6535	485	5	∈	∈	PROPN
ejpam-6535	485	6	∆+	∆+	PROPN
ejpam-6535	485	7	and	and	CCONJ
ejpam-6535	485	8	f	f	X
ejpam-6535	485	9	,	,	PUNCT
ejpam-6535	485	10	g	g	PROPN
ejpam-6535	485	11	∈	∈	PROPN
ejpam-6535	485	12	f(s	f(	NOUN
ejpam-6535	485	13	)	)	PUNCT
ejpam-6535	485	14	.	.	PUNCT
ejpam-6535	486	1	if	if	SCONJ
ejpam-6535	486	2	f	f	PROPN
ejpam-6535	486	3	∈	∈	PROPN
ejpam-6535	486	4	cφ	cφ	NOUN
ejpam-6535	486	5	,	,	PUNCT
ejpam-6535	486	6	and	and	CCONJ
ejpam-6535	486	7	g	g	PROPN
ejpam-6535	486	8	∈	∈	PROPN
ejpam-6535	486	9	cψ	cψ	PROPN
ejpam-6535	486	10	,	,	PUNCT
ejpam-6535	486	11	then	then	ADV
ejpam-6535	486	12	by	by	ADP
ejpam-6535	486	13	(	(	PUNCT
ejpam-6535	486	14	pchgm)′	pchgm)′	NOUN
ejpam-6535	486	15	,	,	PUNCT
ejpam-6535	486	16	f−1⊙g	f−1⊙g	PROPN
ejpam-6535	486	17	∈	∈	PROPN
ejpam-6535	486	18	cτ(φ	cτ(φ	NOUN
ejpam-6535	486	19	,	,	PUNCT
ejpam-6535	486	20	ψ	ψ	NOUN
ejpam-6535	486	21	)	)	PUNCT
ejpam-6535	486	22	,	,	PUNCT
ejpam-6535	486	23	since	since	SCONJ
ejpam-6535	486	24	f	f	PROPN
ejpam-6535	486	25	∈	∈	PROPN
ejpam-6535	486	26	cφ	cφ	NOUN
ejpam-6535	486	27	,	,	PUNCT
ejpam-6535	486	28	we	we	PRON
ejpam-6535	486	29	have	have	VERB
ejpam-6535	486	30	again	again	ADV
ejpam-6535	486	31	,	,	PUNCT
ejpam-6535	486	32	f⊙	f⊙	NOUN
ejpam-6535	486	33	(	(	PUNCT
ejpam-6535	486	34	f−1	f−1	PROPN
ejpam-6535	486	35	⊙g	⊙g	PROPN
ejpam-6535	486	36	)	)	PUNCT
ejpam-6535	486	37	∈	∈	PROPN
ejpam-6535	486	38	cτ(φ	cτ(φ	NOUN
ejpam-6535	486	39	,	,	PUNCT
ejpam-6535	486	40	ψ	ψ	NOUN
ejpam-6535	486	41	)	)	PUNCT
ejpam-6535	486	42	.	.	PUNCT
ejpam-6535	487	1	then	then	ADV
ejpam-6535	487	2	f⊙	f⊙	VERB
ejpam-6535	487	3	f−1	f−1	PROPN
ejpam-6535	487	4	⊙g	⊙g	ADJ
ejpam-6535	487	5	≤	≤	NUM
ejpam-6535	487	6	f	f	X
ejpam-6535	487	7	∧g	∧g	PROPN
ejpam-6535	487	8	with	with	ADP
ejpam-6535	487	9	[	[	X
ejpam-6535	487	10	e	e	X
ejpam-6535	487	11	]	]	X
ejpam-6535	487	12	≤	≤	ADJ
ejpam-6535	487	13	f	f	NOUN
ejpam-6535	487	14	,	,	PUNCT
ejpam-6535	487	15	whence	whence	PROPN
ejpam-6535	487	16	f	f	PROPN
ejpam-6535	487	17	∧g	∧g	PROPN
ejpam-6535	487	18	∈	∈	PROPN
ejpam-6535	487	19	cτ(φ	cτ(φ	X
ejpam-6535	487	20	,	,	PUNCT
ejpam-6535	487	21	ψ	ψ	NOUN
ejpam-6535	487	22	)	)	PUNCT
ejpam-6535	487	23	.	.	PUNCT
ejpam-6535	488	1	proposition	proposition	NOUN
ejpam-6535	488	2	4	4	NUM
ejpam-6535	488	3	.	.	X
ejpam-6535	489	1	pprechygrp	pprechygrp	PROPN
ejpam-6535	489	2	is	be	AUX
ejpam-6535	489	3	a	a	DET
ejpam-6535	489	4	topological	topological	ADJ
ejpam-6535	489	5	category	category	NOUN
ejpam-6535	489	6	with	with	ADP
ejpam-6535	489	7	respect	respect	NOUN
ejpam-6535	489	8	to	to	ADP
ejpam-6535	489	9	the	the	DET
ejpam-6535	489	10	forgetful	forgetful	ADJ
ejpam-6535	489	11	functor	functor	NOUN
ejpam-6535	489	12	.	.	PUNCT
ejpam-6535	490	1	proof	proof	NOUN
ejpam-6535	490	2	.	.	PUNCT
ejpam-6535	491	1	let	let	VERB
ejpam-6535	491	2	(	(	PUNCT
ejpam-6535	491	3	s	s	X
ejpam-6535	491	4	,	,	PUNCT
ejpam-6535	491	5	·	·	PUNCT
ejpam-6535	491	6	)	)	PUNCT
ejpam-6535	491	7	be	be	AUX
ejpam-6535	491	8	a	a	DET
ejpam-6535	491	9	group	group	NOUN
ejpam-6535	491	10	and	and	CCONJ
ejpam-6535	491	11	fj	fj	PROPN
ejpam-6535	491	12	:	:	PUNCT
ejpam-6535	491	13	s	s	AUX
ejpam-6535	491	14	−→	−→	NOUN
ejpam-6535	491	15	sj	sj	VERB
ejpam-6535	491	16	a	a	DET
ejpam-6535	491	17	group	group	NOUN
ejpam-6535	491	18	-	-	PUNCT
ejpam-6535	491	19	homomorphism	homomorphism	NOUN
ejpam-6535	491	20	,	,	PUNCT
ejpam-6535	491	21	and	and	CCONJ
ejpam-6535	491	22	(	(	PUNCT
ejpam-6535	491	23	sj	sj	INTJ
ejpam-6535	491	24	,	,	PUNCT
ejpam-6535	491	25	·	·	PUNCT
ejpam-6535	491	26	,	,	PUNCT
ejpam-6535	491	27	(	(	PUNCT
ejpam-6535	491	28	cjφ)φ∈∆+	cjφ)φ∈∆+	NOUN
ejpam-6535	491	29	)	)	PUNCT
ejpam-6535	491	30	be	be	AUX
ejpam-6535	491	31	a	a	DET
ejpam-6535	491	32	family	family	NOUN
ejpam-6535	491	33	of	of	ADP
ejpam-6535	491	34	probabilistic	probabilistic	ADJ
ejpam-6535	491	35	pre	pre	ADJ
ejpam-6535	491	36	-	-	ADJ
ejpam-6535	491	37	cauchy	cauchy	ADJ
ejpam-6535	491	38	spaces	space	NOUN
ejpam-6535	491	39	.	.	PUNCT
ejpam-6535	492	1	let	let	VERB
ejpam-6535	492	2	s	s	VERB
ejpam-6535	492	3	=	=	PUNCT
ejpam-6535	492	4	(	(	PUNCT
ejpam-6535	492	5	fj	fj	INTJ
ejpam-6535	492	6	:	:	PUNCT
ejpam-6535	492	7	s	s	X
ejpam-6535	492	8	−→	−→	NOUN
ejpam-6535	492	9	(	(	PUNCT
ejpam-6535	492	10	sj	sj	INTJ
ejpam-6535	492	11	,	,	PUNCT
ejpam-6535	492	12	·	·	PUNCT
ejpam-6535	492	13	,	,	PUNCT
ejpam-6535	492	14	cjφ	cjφ	PROPN
ejpam-6535	492	15	)	)	PUNCT
ejpam-6535	492	16	φ	φ	PROPN
ejpam-6535	492	17	)	)	PUNCT
ejpam-6535	492	18	j∈j	j∈j	NOUN
ejpam-6535	492	19	be	be	AUX
ejpam-6535	492	20	a	a	DET
ejpam-6535	492	21	source	source	NOUN
ejpam-6535	492	22	.	.	PUNCT
ejpam-6535	493	1	then	then	ADV
ejpam-6535	493	2	due	due	ADP
ejpam-6535	493	3	to	to	ADP
ejpam-6535	493	4	proposition	proposition	NOUN
ejpam-6535	493	5	2	2	NUM
ejpam-6535	493	6	,	,	PUNCT
ejpam-6535	493	7	for	for	ADP
ejpam-6535	493	8	any	any	DET
ejpam-6535	493	9	f	f	PROPN
ejpam-6535	493	10	∈	∈	PROPN
ejpam-6535	493	11	f(s	f(	NOUN
ejpam-6535	493	12	)	)	PUNCT
ejpam-6535	493	13	,	,	PUNCT
ejpam-6535	493	14	f	f	PROPN
ejpam-6535	493	15	∈	∈	PROPN
ejpam-6535	493	16	cφ	cφ	VERB
ejpam-6535	493	17	⇐	⇐	PROPN
ejpam-6535	493	18	⇒	⇒	PROPN
ejpam-6535	493	19	fj(f	fj(f	PUNCT
ejpam-6535	493	20	)	)	PUNCT
ejpam-6535	493	21	∈	∈	PROPN
ejpam-6535	493	22	cjφ	cjφ	NOUN
ejpam-6535	493	23	,	,	PUNCT
ejpam-6535	493	24	∀j	∀j	PROPN
ejpam-6535	493	25	∈	∈	PROPN
ejpam-6535	493	26	j	j	PROPN
ejpam-6535	493	27	,	,	PUNCT
ejpam-6535	493	28	∀φ	∀φ	PROPN
ejpam-6535	493	29	∈	∈	PROPN
ejpam-6535	493	30	∆+	∆+	NOUN
ejpam-6535	493	31	.	.	PUNCT
ejpam-6535	494	1	thus	thus	ADV
ejpam-6535	494	2	,	,	PUNCT
ejpam-6535	494	3	the	the	DET
ejpam-6535	494	4	source	source	NOUN
ejpam-6535	494	5	has	have	VERB
ejpam-6535	494	6	initial	initial	ADJ
ejpam-6535	494	7	lift	lift	NOUN
ejpam-6535	494	8	,	,	PUNCT
ejpam-6535	494	9	giving	give	VERB
ejpam-6535	494	10	that	that	SCONJ
ejpam-6535	494	11	(	(	PUNCT
ejpam-6535	494	12	s	s	X
ejpam-6535	494	13	,	,	PUNCT
ejpam-6535	494	14	·	·	PUNCT
ejpam-6535	494	15	,	,	PUNCT
ejpam-6535	494	16	c	c	X
ejpam-6535	494	17	)	)	PUNCT
ejpam-6535	494	18	is	be	AUX
ejpam-6535	494	19	a	a	DET
ejpam-6535	494	20	probabilistic	probabilistic	ADJ
ejpam-6535	494	21	precauchy	precauchy	ADJ
ejpam-6535	494	22	space	space	NOUN
ejpam-6535	494	23	.	.	PUNCT
ejpam-6535	495	1	we	we	PRON
ejpam-6535	495	2	only	only	ADV
ejpam-6535	495	3	prove	prove	VERB
ejpam-6535	495	4	the	the	DET
ejpam-6535	495	5	condition	condition	NOUN
ejpam-6535	495	6	(	(	PUNCT
ejpam-6535	495	7	pchgm)′.	pchgm)′.	NOUN
ejpam-6535	495	8	for	for	ADP
ejpam-6535	495	9	,	,	PUNCT
ejpam-6535	495	10	let	let	VERB
ejpam-6535	495	11	f	f	X
ejpam-6535	495	12	,	,	PUNCT
ejpam-6535	495	13	g	g	PROPN
ejpam-6535	495	14	∈	∈	PROPN
ejpam-6535	495	15	f(s	f(	NOUN
ejpam-6535	495	16	)	)	PUNCT
ejpam-6535	495	17	,	,	PUNCT
ejpam-6535	495	18	φ	φ	PROPN
ejpam-6535	495	19	,	,	PUNCT
ejpam-6535	495	20	ψ	ψ	X
ejpam-6535	495	21	∈	∈	PROPN
ejpam-6535	495	22	∆+	∆+	NOUN
ejpam-6535	495	23	,	,	PUNCT
ejpam-6535	495	24	f	f	PROPN
ejpam-6535	495	25	∈	∈	PROPN
ejpam-6535	495	26	cφ	cφ	NOUN
ejpam-6535	495	27	,	,	PUNCT
ejpam-6535	495	28	and	and	CCONJ
ejpam-6535	495	29	g	g	PROPN
ejpam-6535	495	30	∈	∈	PROPN
ejpam-6535	495	31	cψ	cψ	PROPN
ejpam-6535	495	32	.	.	PUNCT
ejpam-6535	496	1	since	since	SCONJ
ejpam-6535	496	2	for	for	ADP
ejpam-6535	496	3	each	each	DET
ejpam-6535	496	4	j	j	PROPN
ejpam-6535	496	5	∈	∈	PROPN
ejpam-6535	496	6	j	j	PROPN
ejpam-6535	496	7	,	,	PUNCT
ejpam-6535	496	8	fj(f	fj(f	PROPN
ejpam-6535	496	9	)	)	PUNCT
ejpam-6535	496	10	,	,	PUNCT
ejpam-6535	496	11	fj(g	fj(g	X
ejpam-6535	496	12	)	)	PUNCT
ejpam-6535	496	13	∈	∈	PROPN
ejpam-6535	496	14	f(sj	f(sj	PROPN
ejpam-6535	496	15	)	)	PUNCT
ejpam-6535	496	16	,	,	PUNCT
ejpam-6535	496	17	we	we	PRON
ejpam-6535	496	18	have	have	VERB
ejpam-6535	496	19	fj(f	fj(f	NOUN
ejpam-6535	496	20	)	)	PUNCT
ejpam-6535	496	21	∈	∈	PROPN
ejpam-6535	496	22	cjφ	cjφ	NOUN
ejpam-6535	496	23	and	and	CCONJ
ejpam-6535	496	24	fj(g	fj(g	X
ejpam-6535	496	25	)	)	PUNCT
ejpam-6535	496	26	∈	∈	PROPN
ejpam-6535	496	27	cjψ	cjψ	NOUN
ejpam-6535	496	28	implying	imply	VERB
ejpam-6535	496	29	that	that	SCONJ
ejpam-6535	496	30	(	(	PUNCT
ejpam-6535	496	31	fj(f))−1	fj(f))−1	X
ejpam-6535	496	32	⊙	⊙	NOUN
ejpam-6535	496	33	fj(g	fj(g	PUNCT
ejpam-6535	496	34	)	)	PUNCT
ejpam-6535	496	35	∈	∈	PROPN
ejpam-6535	496	36	cjτ(φ	cjτ(φ	PROPN
ejpam-6535	496	37	,	,	PUNCT
ejpam-6535	496	38	ψ	ψ	NOUN
ejpam-6535	496	39	)	)	PUNCT
ejpam-6535	496	40	.	.	PUNCT
ejpam-6535	497	1	now	now	ADV
ejpam-6535	497	2	using	use	VERB
ejpam-6535	497	3	lemma	lemma	PROPN
ejpam-6535	497	4	2(l	2(l	NUM
ejpam-6535	497	5	)	)	PUNCT
ejpam-6535	497	6	,	,	PUNCT
ejpam-6535	497	7	we	we	PRON
ejpam-6535	497	8	get	get	VERB
ejpam-6535	497	9	fj	fj	INTJ
ejpam-6535	497	10	(	(	PUNCT
ejpam-6535	497	11	f−1	f−1	PROPN
ejpam-6535	497	12	⊙g	⊙g	PROPN
ejpam-6535	497	13	)	)	PUNCT
ejpam-6535	498	1	=	=	SYM
ejpam-6535	498	2	(	(	PUNCT
ejpam-6535	498	3	fj(f))−1	fj(f))−1	X
ejpam-6535	498	4	⊙	⊙	NOUN
ejpam-6535	498	5	fj(g	fj(g	PUNCT
ejpam-6535	498	6	)	)	PUNCT
ejpam-6535	498	7	∈	∈	PROPN
ejpam-6535	498	8	cjτ(φ	cjτ(φ	PROPN
ejpam-6535	498	9	,	,	PUNCT
ejpam-6535	498	10	ψ	ψ	NOUN
ejpam-6535	498	11	)	)	PUNCT
ejpam-6535	498	12	,	,	PUNCT
ejpam-6535	498	13	yields	yield	VERB
ejpam-6535	498	14	that	that	PRON
ejpam-6535	498	15	f−1	f−1	PROPN
ejpam-6535	498	16	⊙	⊙	VERB
ejpam-6535	498	17	g	g	PROPN
ejpam-6535	498	18	∈	∈	PROPN
ejpam-6535	498	19	cτ(φ	cτ(φ	NOUN
ejpam-6535	498	20	,	,	PUNCT
ejpam-6535	498	21	ψ	ψ	NOUN
ejpam-6535	498	22	)	)	PUNCT
ejpam-6535	498	23	.	.	PUNCT
ejpam-6535	499	1	the	the	DET
ejpam-6535	499	2	missing	missing	ADJ
ejpam-6535	499	3	part	part	NOUN
ejpam-6535	499	4	follows	follow	VERB
ejpam-6535	499	5	by	by	ADP
ejpam-6535	499	6	using	use	VERB
ejpam-6535	499	7	definitions	definition	NOUN
ejpam-6535	499	8	.	.	PUNCT
ejpam-6535	500	1	definition	definition	NOUN
ejpam-6535	500	2	11	11	NUM
ejpam-6535	500	3	.	.	PUNCT
ejpam-6535	501	1	let	let	VERB
ejpam-6535	501	2	(	(	PUNCT
ejpam-6535	501	3	s	s	X
ejpam-6535	501	4	,	,	PUNCT
ejpam-6535	501	5	·	·	PUNCT
ejpam-6535	501	6	)	)	PUNCT
ejpam-6535	501	7	be	be	AUX
ejpam-6535	501	8	a	a	DET
ejpam-6535	501	9	group	group	NOUN
ejpam-6535	501	10	and	and	CCONJ
ejpam-6535	501	11	(	(	PUNCT
ejpam-6535	501	12	s	s	PROPN
ejpam-6535	501	13	,	,	PUNCT
ejpam-6535	501	14	c	c	NOUN
ejpam-6535	501	15	=	=	SYM
ejpam-6535	501	16	(	(	PUNCT
ejpam-6535	501	17	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	501	18	)	)	PUNCT
ejpam-6535	501	19	a	a	DET
ejpam-6535	501	20	probabilistic	probabilistic	ADJ
ejpam-6535	501	21	cauchy	cauchy	ADJ
ejpam-6535	501	22	space	space	NOUN
ejpam-6535	501	23	.	.	PUNCT
ejpam-6535	502	1	then	then	ADV
ejpam-6535	502	2	the	the	DET
ejpam-6535	502	3	triple	triple	ADJ
ejpam-6535	502	4	(	(	PUNCT
ejpam-6535	502	5	s	s	PROPN
ejpam-6535	502	6	,	,	PUNCT
ejpam-6535	502	7	·	·	PUNCT
ejpam-6535	502	8	,	,	PUNCT
ejpam-6535	502	9	c	c	X
ejpam-6535	502	10	=	=	SYM
ejpam-6535	502	11	(	(	PUNCT
ejpam-6535	502	12	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	502	13	)	)	PUNCT
ejpam-6535	502	14	is	be	AUX
ejpam-6535	502	15	called	call	VERB
ejpam-6535	502	16	a	a	DET
ejpam-6535	502	17	probabilistic	probabilistic	ADJ
ejpam-6535	502	18	cauchy	cauchy	NOUN
ejpam-6535	502	19	group	group	NOUN
ejpam-6535	502	20	under	under	ADP
ejpam-6535	502	21	a	a	DET
ejpam-6535	502	22	triangle	triangle	NOUN
ejpam-6535	502	23	function	function	NOUN
ejpam-6535	502	24	τ	τ	PROPN
ejpam-6535	502	25	if	if	SCONJ
ejpam-6535	502	26	the	the	DET
ejpam-6535	502	27	following	follow	VERB
ejpam-6535	502	28	assertions	assertion	NOUN
ejpam-6535	502	29	are	be	AUX
ejpam-6535	502	30	satisfied	satisfied	ADJ
ejpam-6535	502	31	:	:	PUNCT
ejpam-6535	502	32	(	(	PUNCT
ejpam-6535	502	33	pchgm	pchgm	NOUN
ejpam-6535	502	34	)	)	PUNCT
ejpam-6535	502	35	f	f	PROPN
ejpam-6535	502	36	∈	∈	PROPN
ejpam-6535	502	37	cφ	cφ	NOUN
ejpam-6535	502	38	and	and	CCONJ
ejpam-6535	502	39	g	g	PROPN
ejpam-6535	502	40	∈	∈	PROPN
ejpam-6535	502	41	cψ	cψ	PROPN
ejpam-6535	502	42	⇒	⇒	PROPN
ejpam-6535	502	43	f⊙g	f⊙g	PROPN
ejpam-6535	502	44	∈	∈	PROPN
ejpam-6535	502	45	cτ(φ	cτ(φ	X
ejpam-6535	502	46	,	,	PUNCT
ejpam-6535	502	47	ψ	ψ	NOUN
ejpam-6535	502	48	)	)	PUNCT
ejpam-6535	502	49	∀f	∀f	PROPN
ejpam-6535	502	50	,	,	PUNCT
ejpam-6535	502	51	g	g	PROPN
ejpam-6535	502	52	∈	∈	PROPN
ejpam-6535	502	53	f(s	f(	VERB
ejpam-6535	502	54	)	)	PUNCT
ejpam-6535	502	55	and	and	CCONJ
ejpam-6535	502	56	∀φ	∀φ	PROPN
ejpam-6535	502	57	,	,	PUNCT
ejpam-6535	502	58	ψ	ψ	X
ejpam-6535	502	59	∈	∈	NOUN
ejpam-6535	502	60	∆+	∆+	NOUN
ejpam-6535	502	61	;	;	PUNCT
ejpam-6535	502	62	(	(	PUNCT
ejpam-6535	502	63	pchgi	pchgi	ADJ
ejpam-6535	502	64	)	)	PUNCT
ejpam-6535	502	65	f	f	PROPN
ejpam-6535	502	66	∈	∈	PROPN
ejpam-6535	502	67	cφ	cφ	PART
ejpam-6535	502	68	⇒	⇒	PROPN
ejpam-6535	502	69	f−1	f−1	PROPN
ejpam-6535	502	70	∈	∈	PROPN
ejpam-6535	502	71	cφ	cφ	NOUN
ejpam-6535	502	72	,	,	PUNCT
ejpam-6535	502	73	∀f	∀f	PROPN
ejpam-6535	502	74	,	,	PUNCT
ejpam-6535	502	75	g	g	PROPN
ejpam-6535	502	76	∈	∈	PROPN
ejpam-6535	502	77	f(s	f(	VERB
ejpam-6535	502	78	)	)	PUNCT
ejpam-6535	502	79	and	and	CCONJ
ejpam-6535	502	80	∀φ	∀φ	PROPN
ejpam-6535	502	81	,	,	PUNCT
ejpam-6535	502	82	ψ	ψ	X
ejpam-6535	502	83	∈	∈	PROPN
ejpam-6535	502	84	∆+	∆+	NOUN
ejpam-6535	502	85	.	.	PUNCT
ejpam-6535	503	1	the	the	DET
ejpam-6535	503	2	category	category	NOUN
ejpam-6535	503	3	of	of	ADP
ejpam-6535	503	4	all	all	DET
ejpam-6535	503	5	probabilistic	probabilistic	ADJ
ejpam-6535	503	6	cauchy	cauchy	ADJ
ejpam-6535	503	7	groups	group	NOUN
ejpam-6535	503	8	and	and	CCONJ
ejpam-6535	503	9	probabilistic	probabilistic	ADJ
ejpam-6535	503	10	cauchy	cauchy	NOUN
ejpam-6535	503	11	-	-	PUNCT
ejpam-6535	503	12	continuous	continuous	ADJ
ejpam-6535	503	13	grouphomomorphisms	grouphomomorphism	NOUN
ejpam-6535	503	14	is	be	AUX
ejpam-6535	503	15	denoted	denote	VERB
ejpam-6535	503	16	by	by	ADP
ejpam-6535	503	17	pchygrp	pchygrp	NOUN
ejpam-6535	503	18	.	.	PUNCT
ejpam-6535	504	1	note	note	VERB
ejpam-6535	504	2	that	that	SCONJ
ejpam-6535	504	3	the	the	DET
ejpam-6535	504	4	category	category	NOUN
ejpam-6535	504	5	pchygrp	pchygrp	NOUN
ejpam-6535	504	6	is	be	AUX
ejpam-6535	504	7	a	a	DET
ejpam-6535	504	8	full	full	ADJ
ejpam-6535	504	9	subcategory	subcategory	NOUN
ejpam-6535	504	10	of	of	ADP
ejpam-6535	504	11	the	the	DET
ejpam-6535	504	12	category	category	NOUN
ejpam-6535	504	13	of	of	ADP
ejpam-6535	504	14	pprechygrp	pprechygrp	PROPN
ejpam-6535	504	15	.	.	PUNCT
ejpam-6535	505	1	lemma	lemma	PROPN
ejpam-6535	505	2	19	19	NUM
ejpam-6535	505	3	.	.	PUNCT
ejpam-6535	506	1	let	let	VERB
ejpam-6535	506	2	(	(	PUNCT
ejpam-6535	506	3	s	s	X
ejpam-6535	506	4	,	,	PUNCT
ejpam-6535	506	5	·	·	PUNCT
ejpam-6535	506	6	,	,	PUNCT
ejpam-6535	506	7	c	c	X
ejpam-6535	506	8	=	=	SYM
ejpam-6535	506	9	(	(	PUNCT
ejpam-6535	506	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	506	11	)	)	PUNCT
ejpam-6535	506	12	be	be	AUX
ejpam-6535	506	13	a	a	DET
ejpam-6535	506	14	probabilistic	probabilistic	ADJ
ejpam-6535	506	15	cauchy	cauchy	NOUN
ejpam-6535	506	16	group	group	NOUN
ejpam-6535	506	17	under	under	ADP
ejpam-6535	506	18	a	a	DET
ejpam-6535	506	19	triangle	triangle	NOUN
ejpam-6535	506	20	function	function	NOUN
ejpam-6535	506	21	τ	τ	PROPN
ejpam-6535	506	22	.	.	PUNCT
ejpam-6535	507	1	then	then	ADV
ejpam-6535	507	2	the	the	DET
ejpam-6535	507	3	condition	condition	NOUN
ejpam-6535	507	4	(	(	PUNCT
ejpam-6535	507	5	pchgm)′	pchgm)′	NOUN
ejpam-6535	507	6	is	be	AUX
ejpam-6535	507	7	equivalent	equivalent	ADJ
ejpam-6535	507	8	to	to	ADP
ejpam-6535	507	9	the	the	DET
ejpam-6535	507	10	conditions	condition	NOUN
ejpam-6535	507	11	(	(	PUNCT
ejpam-6535	507	12	pchgm	pchgm	NOUN
ejpam-6535	507	13	)	)	PUNCT
ejpam-6535	507	14	and	and	CCONJ
ejpam-6535	507	15	(	(	PUNCT
ejpam-6535	507	16	pchgi	pchgi	NOUN
ejpam-6535	507	17	)	)	PUNCT
ejpam-6535	507	18	as	as	SCONJ
ejpam-6535	507	19	shown	show	VERB
ejpam-6535	507	20	below	below	ADV
ejpam-6535	507	21	:	:	PUNCT
ejpam-6535	507	22	(	(	PUNCT
ejpam-6535	507	23	pchgm)′	pchgm)′	PROPN
ejpam-6535	507	24	∀f	∀f	PROPN
ejpam-6535	507	25	,	,	PUNCT
ejpam-6535	507	26	g	g	PROPN
ejpam-6535	507	27	∈	∈	PROPN
ejpam-6535	507	28	f(s	f(	NOUN
ejpam-6535	507	29	)	)	PUNCT
ejpam-6535	507	30	,	,	PUNCT
ejpam-6535	507	31	∀φ	∀φ	PROPN
ejpam-6535	507	32	,	,	PUNCT
ejpam-6535	507	33	ψ	ψ	NOUN
ejpam-6535	507	34	∈	∈	PROPN
ejpam-6535	507	35	∆+	∆+	NOUN
ejpam-6535	507	36	,	,	PUNCT
ejpam-6535	507	37	f	f	PROPN
ejpam-6535	507	38	∈	∈	PROPN
ejpam-6535	507	39	cφ	cφ	NOUN
ejpam-6535	507	40	,	,	PUNCT
ejpam-6535	507	41	g	g	PROPN
ejpam-6535	507	42	∈	∈	PROPN
ejpam-6535	507	43	cψ	cψ	NOUN
ejpam-6535	507	44	⇒	⇒	NOUN
ejpam-6535	507	45	f−1	f−1	PROPN
ejpam-6535	507	46	⊙g	⊙g	PROPN
ejpam-6535	507	47	∈	∈	PROPN
ejpam-6535	507	48	cτ(φ	cτ(φ	NOUN
ejpam-6535	507	49	,	,	PUNCT
ejpam-6535	507	50	ψ	ψ	NOUN
ejpam-6535	507	51	)	)	PUNCT
ejpam-6535	507	52	;	;	PUNCT
ejpam-6535	507	53	(	(	PUNCT
ejpam-6535	507	54	pchgm	pchgm	NOUN
ejpam-6535	507	55	)	)	PUNCT
ejpam-6535	507	56	∀f	∀f	PROPN
ejpam-6535	507	57	,	,	PUNCT
ejpam-6535	507	58	g	g	PROPN
ejpam-6535	507	59	∈	∈	PROPN
ejpam-6535	507	60	f(s	f(	NOUN
ejpam-6535	507	61	)	)	PUNCT
ejpam-6535	507	62	,	,	PUNCT
ejpam-6535	507	63	∀φ	∀φ	PROPN
ejpam-6535	507	64	,	,	PUNCT
ejpam-6535	507	65	ψ	ψ	NOUN
ejpam-6535	507	66	∈	∈	PROPN
ejpam-6535	507	67	∆+	∆+	NOUN
ejpam-6535	507	68	,	,	PUNCT
ejpam-6535	507	69	f	f	PROPN
ejpam-6535	507	70	∈	∈	PROPN
ejpam-6535	507	71	cφ	cφ	NOUN
ejpam-6535	507	72	,	,	PUNCT
ejpam-6535	507	73	g	g	PROPN
ejpam-6535	507	74	∈	∈	PROPN
ejpam-6535	507	75	cψ	cψ	PROPN
ejpam-6535	507	76	⇒	⇒	PROPN
ejpam-6535	507	77	f⊙g	f⊙g	PROPN
ejpam-6535	507	78	∈	∈	PROPN
ejpam-6535	507	79	cτ(φ	cτ(φ	X
ejpam-6535	507	80	,	,	PUNCT
ejpam-6535	507	81	ψ	ψ	NOUN
ejpam-6535	507	82	)	)	PUNCT
ejpam-6535	507	83	;	;	PUNCT
ejpam-6535	507	84	(	(	PUNCT
ejpam-6535	507	85	pchgi	pchgi	ADJ
ejpam-6535	507	86	)	)	PUNCT
ejpam-6535	507	87	∀f	∀f	PROPN
ejpam-6535	507	88	∈	∈	PROPN
ejpam-6535	507	89	f(s	f(	NOUN
ejpam-6535	507	90	)	)	PUNCT
ejpam-6535	507	91	,	,	PUNCT
ejpam-6535	507	92	∀φ	∀φ	X
ejpam-6535	507	93	∈	∈	PROPN
ejpam-6535	507	94	∆+	∆+	NOUN
ejpam-6535	507	95	,	,	PUNCT
ejpam-6535	507	96	f	f	PROPN
ejpam-6535	507	97	∈	∈	PROPN
ejpam-6535	507	98	cφ	cφ	PART
ejpam-6535	507	99	⇒	⇒	PROPN
ejpam-6535	507	100	f−1	f−1	PROPN
ejpam-6535	507	101	∈	∈	PROPN
ejpam-6535	507	102	cφ	cφ	NOUN
ejpam-6535	507	103	.	.	PUNCT
ejpam-6535	507	104	proof	proof	NOUN
ejpam-6535	507	105	.	.	PUNCT
ejpam-6535	508	1	(	(	PUNCT
ejpam-6535	508	2	pchgm)′⇒(pchgm)+(pchgi	pchgm)′⇒(pchgm)+(pchgi	PROPN
ejpam-6535	508	3	):	):	PUNCT
ejpam-6535	508	4	first	first	ADV
ejpam-6535	508	5	,	,	PUNCT
ejpam-6535	508	6	we	we	PRON
ejpam-6535	508	7	prove	prove	VERB
ejpam-6535	508	8	(	(	PUNCT
ejpam-6535	508	9	pchgi	pchgi	NOUN
ejpam-6535	508	10	)	)	PUNCT
ejpam-6535	508	11	.	.	PUNCT
ejpam-6535	509	1	let	let	VERB
ejpam-6535	509	2	f	f	PROPN
ejpam-6535	509	3	∈	∈	PROPN
ejpam-6535	509	4	f(s	f(	NOUN
ejpam-6535	509	5	)	)	PUNCT
ejpam-6535	509	6	,	,	PUNCT
ejpam-6535	509	7	φ	φ	PROPN
ejpam-6535	509	8	∈	∈	PROPN
ejpam-6535	509	9	∆+	∆+	NUM
ejpam-6535	509	10	and	and	CCONJ
ejpam-6535	509	11	f	f	PROPN
ejpam-6535	509	12	∈	∈	PROPN
ejpam-6535	509	13	cφ	cφ	NOUN
ejpam-6535	509	14	.	.	PUNCT
ejpam-6535	510	1	since	since	SCONJ
ejpam-6535	510	2	in	in	ADP
ejpam-6535	510	3	particular	particular	ADJ
ejpam-6535	510	4	,	,	PUNCT
ejpam-6535	510	5	[	[	X
ejpam-6535	510	6	e	e	X
ejpam-6535	510	7	]	]	X
ejpam-6535	510	8	∈	∈	PROPN
ejpam-6535	510	9	cϵ0	cϵ0	NOUN
ejpam-6535	510	10	,	,	PUNCT
ejpam-6535	510	11	we	we	PRON
ejpam-6535	510	12	get	get	VERB
ejpam-6535	510	13	by	by	ADP
ejpam-6535	510	14	assumption	assumption	NOUN
ejpam-6535	510	15	that	that	SCONJ
ejpam-6535	510	16	f−1	f−1	PROPN
ejpam-6535	510	17	=	=	SYM
ejpam-6535	510	18	f−1	f−1	PROPN
ejpam-6535	510	19	⊙	⊙	VERB
ejpam-6535	510	20	[	[	X
ejpam-6535	510	21	e	e	X
ejpam-6535	510	22	]	]	X
ejpam-6535	510	23	∈	∈	PROPN
ejpam-6535	510	24	cτ(φ,ϵ0	cτ(φ,ϵ0	PROPN
ejpam-6535	510	25	)	)	PUNCT
ejpam-6535	511	1	=	=	VERB
ejpam-6535	511	2	cφ	cφ	NOUN
ejpam-6535	511	3	because	because	SCONJ
ejpam-6535	511	4	of	of	ADP
ejpam-6535	511	5	the	the	DET
ejpam-6535	511	6	fact	fact	NOUN
ejpam-6535	511	7	that	that	SCONJ
ejpam-6535	511	8	τ(φ	τ(φ	ADV
ejpam-6535	511	9	,	,	PUNCT
ejpam-6535	511	10	ϵ0	ϵ0	NUM
ejpam-6535	511	11	)	)	PUNCT
ejpam-6535	511	12	=	=	SYM
ejpam-6535	512	1	φ	φ	PROPN
ejpam-6535	512	2	.	.	PUNCT
ejpam-6535	513	1	hence	hence	ADV
ejpam-6535	513	2	f−1	f−1	PROPN
ejpam-6535	513	3	∈	∈	PROPN
ejpam-6535	513	4	cφ	cφ	NOUN
ejpam-6535	513	5	.	.	PUNCT
ejpam-6535	514	1	to	to	PART
ejpam-6535	514	2	prove	prove	VERB
ejpam-6535	514	3	the	the	DET
ejpam-6535	514	4	other	other	ADJ
ejpam-6535	514	5	part	part	NOUN
ejpam-6535	514	6	,	,	PUNCT
ejpam-6535	514	7	let	let	VERB
ejpam-6535	514	8	f	f	X
ejpam-6535	514	9	,	,	PUNCT
ejpam-6535	514	10	g	g	PROPN
ejpam-6535	514	11	∈	∈	PROPN
ejpam-6535	514	12	f(s	f(	NOUN
ejpam-6535	514	13	)	)	PUNCT
ejpam-6535	514	14	,	,	PUNCT
ejpam-6535	514	15	and	and	CCONJ
ejpam-6535	514	16	φ	φ	NUM
ejpam-6535	514	17	,	,	PUNCT
ejpam-6535	514	18	ψ	ψ	X
ejpam-6535	514	19	∈	∈	PROPN
ejpam-6535	514	20	∆+	∆+	NOUN
ejpam-6535	514	21	.	.	PUNCT
ejpam-6535	515	1	if	if	SCONJ
ejpam-6535	515	2	now	now	ADV
ejpam-6535	515	3	f	f	PROPN
ejpam-6535	515	4	∈	∈	PROPN
ejpam-6535	515	5	cφ	cφ	NOUN
ejpam-6535	515	6	and	and	CCONJ
ejpam-6535	515	7	g	g	PROPN
ejpam-6535	515	8	∈	∈	PROPN
ejpam-6535	515	9	cψ	cψ	PROPN
ejpam-6535	515	10	,	,	PUNCT
ejpam-6535	515	11	then	then	ADV
ejpam-6535	515	12	by	by	ADP
ejpam-6535	515	13	using	use	VERB
ejpam-6535	515	14	(	(	PUNCT
ejpam-6535	515	15	pchgi	pchgi	ADJ
ejpam-6535	515	16	)	)	PUNCT
ejpam-6535	515	17	and	and	CCONJ
ejpam-6535	515	18	the	the	DET
ejpam-6535	515	19	assumption	assumption	NOUN
ejpam-6535	515	20	,	,	PUNCT
ejpam-6535	515	21	we	we	PRON
ejpam-6535	515	22	get	get	VERB
ejpam-6535	515	23	f⊙g	f⊙g	NOUN
ejpam-6535	516	1	=	=	SYM
ejpam-6535	516	2	(	(	PUNCT
ejpam-6535	516	3	f−1)−1	f−1)−1	NOUN
ejpam-6535	516	4	⊙g	⊙g	NOUN
ejpam-6535	516	5	∈	∈	PROPN
ejpam-6535	516	6	cτ(φ	cτ(φ	NOUN
ejpam-6535	516	7	,	,	PUNCT
ejpam-6535	516	8	ψ	ψ	NOUN
ejpam-6535	516	9	)	)	PUNCT
ejpam-6535	516	10	,	,	PUNCT
ejpam-6535	516	11	i.e.	i.e.	X
ejpam-6535	516	12	,	,	PUNCT
ejpam-6535	516	13	f⊙g	f⊙g	NOUN
ejpam-6535	516	14	∈	∈	PROPN
ejpam-6535	516	15	cτ(φ	cτ(φ	X
ejpam-6535	516	16	,	,	PUNCT
ejpam-6535	516	17	ψ	ψ	NOUN
ejpam-6535	516	18	)	)	PUNCT
ejpam-6535	516	19	.	.	PUNCT
ejpam-6535	517	1	conversely	conversely	ADV
ejpam-6535	517	2	,	,	PUNCT
ejpam-6535	517	3	we	we	PRON
ejpam-6535	517	4	prove	prove	VERB
ejpam-6535	517	5	(	(	PUNCT
ejpam-6535	517	6	pchgm)+(pchgi)⇒	pchgm)+(pchgi)⇒	NOUN
ejpam-6535	517	7	(	(	PUNCT
ejpam-6535	517	8	pchgm)′.	pchgm)′.	NOUN
ejpam-6535	517	9	if	if	SCONJ
ejpam-6535	517	10	f	f	PROPN
ejpam-6535	517	11	∈	∈	PROPN
ejpam-6535	517	12	cφ	cφ	NOUN
ejpam-6535	518	1	and	and	CCONJ
ejpam-6535	518	2	g	g	PROPN
ejpam-6535	518	3	∈	∈	PROPN
ejpam-6535	518	4	cψ	cψ	NOUN
ejpam-6535	518	5	,	,	PUNCT
ejpam-6535	518	6	then	then	ADV
ejpam-6535	518	7	because	because	SCONJ
ejpam-6535	518	8	of	of	ADP
ejpam-6535	518	9	(	(	PUNCT
ejpam-6535	518	10	pchgi	pchgi	PROPN
ejpam-6535	518	11	)	)	PUNCT
ejpam-6535	518	12	,	,	PUNCT
ejpam-6535	518	13	f−1	f−1	PROPN
ejpam-6535	518	14	∈	∈	PROPN
ejpam-6535	518	15	cφ	cφ	NOUN
ejpam-6535	518	16	and	and	CCONJ
ejpam-6535	518	17	hence	hence	ADV
ejpam-6535	518	18	by	by	ADP
ejpam-6535	518	19	using	use	VERB
ejpam-6535	518	20	(	(	PUNCT
ejpam-6535	518	21	pchgm	pchgm	NOUN
ejpam-6535	518	22	)	)	PUNCT
ejpam-6535	518	23	,	,	PUNCT
ejpam-6535	518	24	we	we	PRON
ejpam-6535	518	25	have	have	VERB
ejpam-6535	518	26	f−1	f−1	PROPN
ejpam-6535	518	27	⊙g	⊙g	NOUN
ejpam-6535	518	28	∈	∈	PROPN
ejpam-6535	518	29	cτ(φ	cτ(φ	NOUN
ejpam-6535	518	30	,	,	PUNCT
ejpam-6535	518	31	ψ	ψ	NOUN
ejpam-6535	518	32	)	)	PUNCT
ejpam-6535	518	33	.	.	PUNCT
ejpam-6535	519	1	proposition	proposition	NOUN
ejpam-6535	519	2	5	5	NUM
ejpam-6535	519	3	.	.	PUNCT
ejpam-6535	520	1	let	let	VERB
ejpam-6535	520	2	(	(	PUNCT
ejpam-6535	520	3	s	s	X
ejpam-6535	520	4	,	,	PUNCT
ejpam-6535	520	5	·	·	PUNCT
ejpam-6535	520	6	,	,	PUNCT
ejpam-6535	520	7	c	c	X
ejpam-6535	520	8	)	)	PUNCT
ejpam-6535	520	9	∈	∈	PROPN
ejpam-6535	520	10	|pchygrp|	|pchygrp|	PROPN
ejpam-6535	520	11	under	under	ADP
ejpam-6535	520	12	the	the	DET
ejpam-6535	520	13	a	a	DET
ejpam-6535	520	14	triangle	triangle	NOUN
ejpam-6535	520	15	function	function	NOUN
ejpam-6535	520	16	τ	τ	PROPN
ejpam-6535	520	17	.	.	PUNCT
ejpam-6535	521	1	then	then	ADV
ejpam-6535	521	2	(	(	PUNCT
ejpam-6535	521	3	s	s	X
ejpam-6535	521	4	,	,	PUNCT
ejpam-6535	521	5	·	·	PUNCT
ejpam-6535	521	6	,	,	PUNCT
ejpam-6535	521	7	cc	cc	NOUN
ejpam-6535	521	8	)	)	PUNCT
ejpam-6535	521	9	∈	∈	PROPN
ejpam-6535	521	10	|pconvgrp|	|pconvgrp|	NOUN
ejpam-6535	521	11	.	.	PUNCT
ejpam-6535	521	12	proof	proof	NOUN
ejpam-6535	521	13	.	.	PUNCT
ejpam-6535	522	1	let	let	VERB
ejpam-6535	522	2	(	(	PUNCT
ejpam-6535	522	3	s	s	X
ejpam-6535	522	4	,	,	PUNCT
ejpam-6535	522	5	·	·	PUNCT
ejpam-6535	522	6	,	,	PUNCT
ejpam-6535	522	7	c	c	X
ejpam-6535	522	8	=	=	SYM
ejpam-6535	522	9	(	(	PUNCT
ejpam-6535	522	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	522	11	)	)	PUNCT
ejpam-6535	522	12	be	be	AUX
ejpam-6535	522	13	a	a	DET
ejpam-6535	522	14	probabilistic	probabilistic	ADJ
ejpam-6535	522	15	cauchy	cauchy	NOUN
ejpam-6535	522	16	group	group	NOUN
ejpam-6535	522	17	.	.	PUNCT
ejpam-6535	523	1	define	define	VERB
ejpam-6535	523	2	p	p	PROPN
ejpam-6535	523	3	∈	∈	PROPN
ejpam-6535	523	4	ccφ(f	ccφ(f	PROPN
ejpam-6535	523	5	)	)	PUNCT
ejpam-6535	523	6	⇐	⇐	ADJ
ejpam-6535	523	7	⇒	⇒	NOUN
ejpam-6535	523	8	[	[	X
ejpam-6535	523	9	p	p	X
ejpam-6535	523	10	]	]	X
ejpam-6535	523	11	∧	∧	PROPN
ejpam-6535	523	12	f	f	PROPN
ejpam-6535	523	13	∈	∈	PROPN
ejpam-6535	523	14	cφ	cφ	NOUN
ejpam-6535	523	15	,	,	PUNCT
ejpam-6535	523	16	for	for	ADP
ejpam-6535	523	17	p	p	PROPN
ejpam-6535	523	18	∈	∈	PROPN
ejpam-6535	523	19	s	s	PROPN
ejpam-6535	523	20	,	,	PUNCT
ejpam-6535	523	21	φ	φ	PROPN
ejpam-6535	523	22	∈	∈	PROPN
ejpam-6535	523	23	∆+	∆+	NOUN
ejpam-6535	523	24	and	and	CCONJ
ejpam-6535	523	25	f	f	PROPN
ejpam-6535	523	26	∈	∈	PROPN
ejpam-6535	523	27	f(s	f(	NOUN
ejpam-6535	523	28	)	)	PUNCT
ejpam-6535	523	29	.	.	PUNCT
ejpam-6535	524	1	in	in	ADP
ejpam-6535	524	2	the	the	DET
ejpam-6535	524	3	light	light	NOUN
ejpam-6535	524	4	of	of	ADP
ejpam-6535	524	5	lemma	lemma	PROPN
ejpam-6535	524	6	17	17	NUM
ejpam-6535	524	7	,	,	PUNCT
ejpam-6535	524	8	we	we	PRON
ejpam-6535	524	9	only	only	ADV
ejpam-6535	524	10	need	need	VERB
ejpam-6535	524	11	to	to	PART
ejpam-6535	524	12	prove	prove	VERB
ejpam-6535	524	13	(	(	PUNCT
ejpam-6535	524	14	pchgm)′	pchgm)′	NOUN
ejpam-6535	524	15	:	:	PUNCT
ejpam-6535	524	16	let	let	VERB
ejpam-6535	524	17	p	p	NOUN
ejpam-6535	524	18	,	,	PUNCT
ejpam-6535	524	19	q	q	PROPN
ejpam-6535	524	20	∈	∈	PROPN
ejpam-6535	524	21	s	s	X
ejpam-6535	524	22	and	and	CCONJ
ejpam-6535	524	23	f	f	NOUN
ejpam-6535	524	24	,	,	PUNCT
ejpam-6535	524	25	g	g	PROPN
ejpam-6535	524	26	∈	∈	PROPN
ejpam-6535	524	27	f(s	f(	VERB
ejpam-6535	524	28	)	)	PUNCT
ejpam-6535	524	29	with	with	ADP
ejpam-6535	524	30	φ	φ	PROPN
ejpam-6535	524	31	,	,	PUNCT
ejpam-6535	524	32	ψ	ψ	X
ejpam-6535	524	33	∈	∈	PROPN
ejpam-6535	524	34	∆+	∆+	NOUN
ejpam-6535	524	35	.	.	PUNCT
ejpam-6535	525	1	if	if	SCONJ
ejpam-6535	525	2	p	p	PROPN
ejpam-6535	525	3	∈	∈	PROPN
ejpam-6535	525	4	ccφ(f	ccφ(f	PROPN
ejpam-6535	525	5	)	)	PUNCT
ejpam-6535	525	6	and	and	CCONJ
ejpam-6535	525	7	q	q	PROPN
ejpam-6535	525	8	∈	∈	PROPN
ejpam-6535	525	9	ccψ(g	ccψ(g	PROPN
ejpam-6535	525	10	)	)	PUNCT
ejpam-6535	525	11	,	,	PUNCT
ejpam-6535	525	12	then	then	ADV
ejpam-6535	525	13	[	[	X
ejpam-6535	525	14	p	p	X
ejpam-6535	525	15	]	]	X
ejpam-6535	525	16	∧	∧	PROPN
ejpam-6535	525	17	f	f	PROPN
ejpam-6535	525	18	∈	∈	PROPN
ejpam-6535	525	19	cφ	cφ	NOUN
ejpam-6535	526	1	and	and	CCONJ
ejpam-6535	526	2	[	[	X
ejpam-6535	526	3	q	q	X
ejpam-6535	526	4	]	]	X
ejpam-6535	526	5	∧	∧	NOUN
ejpam-6535	526	6	g	g	PROPN
ejpam-6535	526	7	∈	∈	PROPN
ejpam-6535	526	8	cψ	cψ	PROPN
ejpam-6535	526	9	,	,	PUNCT
ejpam-6535	526	10	whence	whence	NOUN
ejpam-6535	526	11	(	(	PUNCT
ejpam-6535	526	12	[	[	X
ejpam-6535	526	13	p	p	X
ejpam-6535	526	14	]	]	X
ejpam-6535	526	15	∧	∧	PROPN
ejpam-6535	526	16	f)−1	f)−1	NOUN
ejpam-6535	526	17	∈	∈	PROPN
ejpam-6535	526	18	cφ	cφ	NOUN
ejpam-6535	526	19	.	.	PUNCT
ejpam-6535	527	1	these	these	PRON
ejpam-6535	527	2	together	together	ADV
ejpam-6535	527	3	upon	upon	SCONJ
ejpam-6535	527	4	using	use	VERB
ejpam-6535	527	5	lemma	lemma	PROPN
ejpam-6535	527	6	2(i	2(i	NUM
ejpam-6535	527	7	)	)	PUNCT
ejpam-6535	527	8	imply	imply	VERB
ejpam-6535	527	9	that	that	SCONJ
ejpam-6535	527	10	(	(	PUNCT
ejpam-6535	527	11	[	[	X
ejpam-6535	527	12	p]−1	p]−1	X
ejpam-6535	527	13	∧	∧	PROPN
ejpam-6535	527	14	f−1	f−1	PROPN
ejpam-6535	527	15	)	)	PUNCT
ejpam-6535	527	16	⊙	⊙	NOUN
ejpam-6535	528	1	(	(	PUNCT
ejpam-6535	528	2	[	[	X
ejpam-6535	528	3	q	q	X
ejpam-6535	528	4	]	]	X
ejpam-6535	528	5	∧g	∧g	NUM
ejpam-6535	528	6	)	)	PUNCT
ejpam-6535	528	7	∈	∈	PROPN
ejpam-6535	528	8	cτ(φ	cτ(φ	NOUN
ejpam-6535	528	9	,	,	PUNCT
ejpam-6535	528	10	ψ	ψ	NOUN
ejpam-6535	528	11	)	)	PUNCT
ejpam-6535	528	12	.	.	PUNCT
ejpam-6535	529	1	again	again	ADV
ejpam-6535	529	2	using	use	VERB
ejpam-6535	529	3	lemma	lemma	PROPN
ejpam-6535	529	4	2(j	2(j	NUM
ejpam-6535	529	5	)	)	PUNCT
ejpam-6535	529	6	,	,	PUNCT
ejpam-6535	529	7	we	we	PRON
ejpam-6535	529	8	can	can	AUX
ejpam-6535	529	9	simplify	simplify	VERB
ejpam-6535	529	10	to	to	ADP
ejpam-6535	529	11	:	:	PUNCT
ejpam-6535	530	1	[	[	X
ejpam-6535	530	2	p−1q]∧	p−1q]∧	X
ejpam-6535	530	3	(	(	PUNCT
ejpam-6535	530	4	f−1	f−1	PROPN
ejpam-6535	530	5	⊙g	⊙g	PROPN
ejpam-6535	530	6	)	)	PUNCT
ejpam-6535	530	7	≥	≥	NOUN
ejpam-6535	530	8	(	(	PUNCT
ejpam-6535	530	9	[	[	X
ejpam-6535	530	10	p]−1	p]−1	X
ejpam-6535	530	11	∧	∧	PROPN
ejpam-6535	530	12	f−1	f−1	PROPN
ejpam-6535	530	13	)	)	PUNCT
ejpam-6535	530	14	⊙	⊙	NOUN
ejpam-6535	530	15	(	(	PUNCT
ejpam-6535	530	16	[	[	X
ejpam-6535	530	17	q	q	X
ejpam-6535	530	18	]	]	X
ejpam-6535	530	19	∧g	∧g	NUM
ejpam-6535	530	20	)	)	PUNCT
ejpam-6535	530	21	∈	∈	PROPN
ejpam-6535	530	22	cτ(φ	cτ(φ	NOUN
ejpam-6535	530	23	,	,	PUNCT
ejpam-6535	530	24	ψ	ψ	NOUN
ejpam-6535	530	25	)	)	PUNCT
ejpam-6535	530	26	.	.	PUNCT
ejpam-6535	531	1	hence	hence	ADV
ejpam-6535	531	2	we	we	PRON
ejpam-6535	531	3	obtain	obtain	VERB
ejpam-6535	531	4	p−1q	p−1q	PROPN
ejpam-6535	531	5	∈	∈	PROPN
ejpam-6535	531	6	ccτ(φ	ccτ(φ	PROPN
ejpam-6535	531	7	,	,	PUNCT
ejpam-6535	531	8	ψ	ψ	NOUN
ejpam-6535	531	9	)	)	PUNCT
ejpam-6535	531	10	(	(	PUNCT
ejpam-6535	531	11	f−1	f−1	PROPN
ejpam-6535	531	12	⊙g	⊙g	PROPN
ejpam-6535	531	13	)	)	PUNCT
ejpam-6535	531	14	,	,	PUNCT
ejpam-6535	531	15	which	which	PRON
ejpam-6535	531	16	in	in	ADP
ejpam-6535	531	17	the	the	DET
ejpam-6535	531	18	light	light	NOUN
ejpam-6535	531	19	of	of	ADP
ejpam-6535	531	20	lemma	lemma	PROPN
ejpam-6535	531	21	17	17	NUM
ejpam-6535	531	22	,	,	PUNCT
ejpam-6535	531	23	we	we	PRON
ejpam-6535	531	24	are	be	AUX
ejpam-6535	531	25	done	do	VERB
ejpam-6535	531	26	.	.	PUNCT
ejpam-6535	532	1	lemma	lemma	PROPN
ejpam-6535	532	2	20	20	NUM
ejpam-6535	532	3	.	.	PUNCT
ejpam-6535	533	1	let	let	VERB
ejpam-6535	533	2	(	(	PUNCT
ejpam-6535	533	3	s	s	X
ejpam-6535	533	4	,	,	PUNCT
ejpam-6535	533	5	·	·	PUNCT
ejpam-6535	533	6	,	,	PUNCT
ejpam-6535	533	7	c	c	X
ejpam-6535	533	8	=	=	SYM
ejpam-6535	533	9	(	(	PUNCT
ejpam-6535	533	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	533	11	)	)	PUNCT
ejpam-6535	533	12	∈	∈	PROPN
ejpam-6535	533	13	|plimgrp|	|plimgrp|	PROPN
ejpam-6535	533	14	.	.	PUNCT
ejpam-6535	534	1	then	then	ADV
ejpam-6535	534	2	(	(	PUNCT
ejpam-6535	534	3	s	s	X
ejpam-6535	534	4	,	,	PUNCT
ejpam-6535	534	5	·	·	PUNCT
ejpam-6535	534	6	,	,	PUNCT
ejpam-6535	534	7	cc	cc	NOUN
ejpam-6535	534	8	)	)	PUNCT
ejpam-6535	534	9	∈	∈	PROPN
ejpam-6535	534	10	|pchygrp|	|pchygrp|	NUM
ejpam-6535	534	11	⇐	⇐	ADJ
ejpam-6535	534	12	⇒	⇒	NOUN
ejpam-6535	534	13	(	(	PUNCT
ejpam-6535	534	14	♯	♯	PROPN
ejpam-6535	534	15	):	):	PUNCT
ejpam-6535	534	16	(	(	PUNCT
ejpam-6535	534	17	∀f	∀f	PROPN
ejpam-6535	534	18	,	,	PUNCT
ejpam-6535	534	19	g	g	PROPN
ejpam-6535	534	20	∈	∈	PROPN
ejpam-6535	534	21	f(s	f(	NOUN
ejpam-6535	534	22	)	)	PUNCT
ejpam-6535	534	23	,	,	PUNCT
ejpam-6535	534	24	φ	φ	PROPN
ejpam-6535	534	25	∈	∈	PROPN
ejpam-6535	534	26	∆+	∆+	NOUN
ejpam-6535	534	27	,	,	PUNCT
ejpam-6535	534	28	e	e	PROPN
ejpam-6535	534	29	∈	∈	PROPN
ejpam-6535	534	30	cφ	cφ	X
ejpam-6535	534	31	(	(	PUNCT
ejpam-6535	534	32	f−1	f−1	PROPN
ejpam-6535	534	33	⊙	⊙	PROPN
ejpam-6535	534	34	f	f	PROPN
ejpam-6535	534	35	)	)	PUNCT
ejpam-6535	534	36	,	,	PUNCT
ejpam-6535	534	37	e	e	PROPN
ejpam-6535	534	38	∈	∈	PROPN
ejpam-6535	534	39	cφ	cφ	X
ejpam-6535	534	40	(	(	PUNCT
ejpam-6535	534	41	f⊙	f⊙	VERB
ejpam-6535	534	42	f−1	f−1	PROPN
ejpam-6535	534	43	)	)	PUNCT
ejpam-6535	534	44	,	,	PUNCT
ejpam-6535	534	45	and	and	CCONJ
ejpam-6535	534	46	e	e	PROPN
ejpam-6535	534	47	∈	∈	PROPN
ejpam-6535	534	48	cφ(g	cφ(g	NOUN
ejpam-6535	534	49	)	)	PUNCT
ejpam-6535	534	50	)	)	PUNCT
ejpam-6535	535	1	=	=	SYM
ejpam-6535	535	2	⇒	⇒	NOUN
ejpam-6535	535	3	e	e	X
ejpam-6535	535	4	∈	∈	PROPN
ejpam-6535	535	5	cφ	cφ	NOUN
ejpam-6535	535	6	(	(	PUNCT
ejpam-6535	535	7	f⊙g⊙	f⊙g⊙	NOUN
ejpam-6535	535	8	f−1	f−1	PROPN
ejpam-6535	535	9	)	)	PUNCT
ejpam-6535	535	10	.	.	PUNCT
ejpam-6535	536	1	proof	proof	NOUN
ejpam-6535	536	2	.	.	PUNCT
ejpam-6535	537	1	define	define	VERB
ejpam-6535	537	2	f	f	PROPN
ejpam-6535	537	3	∈	∈	PROPN
ejpam-6535	537	4	cφ	cφ	VERB
ejpam-6535	537	5	⇐	⇐	ADJ
ejpam-6535	537	6	⇒	⇒	PROPN
ejpam-6535	537	7	e	e	PROPN
ejpam-6535	537	8	∈	∈	PROPN
ejpam-6535	537	9	ccφ	ccφ	NOUN
ejpam-6535	537	10	(	(	PUNCT
ejpam-6535	537	11	f−1	f−1	PROPN
ejpam-6535	537	12	⊙	⊙	NOUN
ejpam-6535	537	13	f	f	PROPN
ejpam-6535	537	14	)	)	PUNCT
ejpam-6535	537	15	and	and	CCONJ
ejpam-6535	537	16	e	e	X
ejpam-6535	537	17	∈	∈	PROPN
ejpam-6535	537	18	ccφ	ccφ	NOUN
ejpam-6535	537	19	(	(	PUNCT
ejpam-6535	537	20	f⊙	f⊙	VERB
ejpam-6535	537	21	f−1	f−1	PROPN
ejpam-6535	537	22	)	)	PUNCT
ejpam-6535	537	23	,	,	PUNCT
ejpam-6535	537	24	∀f	∀f	PROPN
ejpam-6535	537	25	∈	∈	PROPN
ejpam-6535	537	26	f(s	f(	NOUN
ejpam-6535	537	27	)	)	PUNCT
ejpam-6535	537	28	,	,	PUNCT
ejpam-6535	537	29	∀φ	∀φ	X
ejpam-6535	537	30	∈	∈	PROPN
ejpam-6535	537	31	∆+	∆+	NOUN
ejpam-6535	537	32	.	.	PUNCT
ejpam-6535	538	1	(	(	PUNCT
ejpam-6535	538	2	pchs1	pchs1	NOUN
ejpam-6535	538	3	)	)	PUNCT
ejpam-6535	538	4	since	since	SCONJ
ejpam-6535	538	5	in	in	ADP
ejpam-6535	538	6	particular	particular	ADJ
ejpam-6535	538	7	,	,	PUNCT
ejpam-6535	538	8	e	e	PROPN
ejpam-6535	538	9	∈	∈	PROPN
ejpam-6535	538	10	ccφ	ccφ	NOUN
ejpam-6535	538	11	(	(	PUNCT
ejpam-6535	538	12	[	[	X
ejpam-6535	538	13	p]−1	p]−1	X
ejpam-6535	538	14	⊙	⊙	NOUN
ejpam-6535	539	1	[	[	X
ejpam-6535	539	2	p	p	X
ejpam-6535	539	3	]	]	PUNCT
ejpam-6535	539	4	)	)	PUNCT
ejpam-6535	539	5	,	,	PUNCT
ejpam-6535	539	6	we	we	PRON
ejpam-6535	539	7	have	have	VERB
ejpam-6535	539	8	p	p	PROPN
ejpam-6535	539	9	∈	∈	PROPN
ejpam-6535	539	10	ccφ([p	ccφ([p	NOUN
ejpam-6535	539	11	]	]	PUNCT
ejpam-6535	539	12	)	)	PUNCT
ejpam-6535	539	13	and	and	CCONJ
ejpam-6535	539	14	hence	hence	ADV
ejpam-6535	539	15	[	[	X
ejpam-6535	539	16	p	p	X
ejpam-6535	539	17	]	]	X
ejpam-6535	539	18	∈	∈	PROPN
ejpam-6535	539	19	cφ	cφ	NOUN
ejpam-6535	539	20	.	.	PUNCT
ejpam-6535	540	1	(	(	PUNCT
ejpam-6535	540	2	pchs2	pchs2	NOUN
ejpam-6535	540	3	)	)	PUNCT
ejpam-6535	540	4	let	let	VERB
ejpam-6535	540	5	f	f	PROPN
ejpam-6535	540	6	∈	∈	PROPN
ejpam-6535	540	7	cφ	cφ	X
ejpam-6535	540	8	with	with	ADP
ejpam-6535	540	9	f	f	PROPN
ejpam-6535	540	10	≤	≤	PROPN
ejpam-6535	540	11	g.	g.	PROPN
ejpam-6535	540	12	then	then	ADV
ejpam-6535	540	13	e	e	PROPN
ejpam-6535	540	14	∈	∈	PROPN
ejpam-6535	540	15	ccφ	ccφ	NOUN
ejpam-6535	540	16	(	(	PUNCT
ejpam-6535	540	17	f−1	f−1	PROPN
ejpam-6535	540	18	⊙	⊙	NOUN
ejpam-6535	540	19	f	f	PROPN
ejpam-6535	540	20	)	)	PUNCT
ejpam-6535	540	21	.	.	PUNCT
ejpam-6535	541	1	because	because	SCONJ
ejpam-6535	541	2	of	of	ADP
ejpam-6535	541	3	f−1⊙f	f−1⊙f	PROPN
ejpam-6535	541	4	≤	≤	PROPN
ejpam-6535	541	5	g−1⊙g	g−1⊙g	NOUN
ejpam-6535	541	6	,	,	PUNCT
ejpam-6535	541	7	by	by	ADP
ejpam-6535	541	8	using	use	VERB
ejpam-6535	541	9	(	(	PUNCT
ejpam-6535	541	10	pcs2	pcs2	PROPN
ejpam-6535	541	11	)	)	PUNCT
ejpam-6535	541	12	,	,	PUNCT
ejpam-6535	541	13	e	e	PROPN
ejpam-6535	541	14	∈	∈	PROPN
ejpam-6535	541	15	ccφ	ccφ	NOUN
ejpam-6535	541	16	(	(	PUNCT
ejpam-6535	541	17	g−1	g−1	PROPN
ejpam-6535	541	18	⊙g	⊙g	PROPN
ejpam-6535	541	19	)	)	PUNCT
ejpam-6535	541	20	.	.	PUNCT
ejpam-6535	542	1	hence	hence	ADV
ejpam-6535	542	2	g	g	PROPN
ejpam-6535	542	3	∈	∈	PROPN
ejpam-6535	542	4	cφ	cφ	NOUN
ejpam-6535	542	5	.	.	PUNCT
ejpam-6535	542	6	(	(	PUNCT
ejpam-6535	542	7	pchs3	pchs3	X
ejpam-6535	542	8	)	)	PUNCT
ejpam-6535	542	9	let	let	VERB
ejpam-6535	542	10	φ	φ	NUM
ejpam-6535	542	11	,	,	PUNCT
ejpam-6535	542	12	ψ	ψ	X
ejpam-6535	542	13	∈	∈	PROPN
ejpam-6535	542	14	∆+	∆+	NUM
ejpam-6535	542	15	with	with	ADP
ejpam-6535	542	16	φ	φ	PROPN
ejpam-6535	542	17	≤	≤	NUM
ejpam-6535	542	18	ψ	ψ	NOUN
ejpam-6535	542	19	.	.	PUNCT
ejpam-6535	543	1	if	if	SCONJ
ejpam-6535	543	2	f	f	PROPN
ejpam-6535	543	3	∈	∈	PROPN
ejpam-6535	543	4	cψ	cψ	PROPN
ejpam-6535	543	5	,	,	PUNCT
ejpam-6535	543	6	then	then	ADV
ejpam-6535	543	7	e	e	PROPN
ejpam-6535	543	8	∈	∈	PROPN
ejpam-6535	543	9	ccψ	ccψ	VERB
ejpam-6535	543	10	(	(	PUNCT
ejpam-6535	543	11	f−1	f−1	PROPN
ejpam-6535	543	12	⊙	⊙	NOUN
ejpam-6535	543	13	f	f	PROPN
ejpam-6535	543	14	)	)	PUNCT
ejpam-6535	543	15	.	.	PUNCT
ejpam-6535	544	1	by	by	ADP
ejpam-6535	544	2	(	(	PUNCT
ejpam-6535	544	3	pcs3	pcs3	PROPN
ejpam-6535	544	4	)	)	PUNCT
ejpam-6535	544	5	,	,	PUNCT
ejpam-6535	544	6	e	e	PROPN
ejpam-6535	544	7	∈	∈	PROPN
ejpam-6535	544	8	ccφ	ccφ	NOUN
ejpam-6535	544	9	(	(	PUNCT
ejpam-6535	544	10	f−1	f−1	PROPN
ejpam-6535	544	11	⊙	⊙	PROPN
ejpam-6535	544	12	f	f	PROPN
ejpam-6535	544	13	)	)	PUNCT
ejpam-6535	544	14	implies	imply	VERB
ejpam-6535	544	15	that	that	SCONJ
ejpam-6535	544	16	f	f	PROPN
ejpam-6535	544	17	∈	∈	PROPN
ejpam-6535	544	18	cφ	cφ	X
ejpam-6535	544	19	.	.	PUNCT
ejpam-6535	544	20	(	(	PUNCT
ejpam-6535	544	21	pchs4	pchs4	NOUN
ejpam-6535	544	22	)	)	PUNCT
ejpam-6535	544	23	is	be	AUX
ejpam-6535	544	24	obviously	obviously	ADV
ejpam-6535	544	25	true	true	ADJ
ejpam-6535	544	26	.	.	PUNCT
ejpam-6535	545	1	(	(	PUNCT
ejpam-6535	545	2	pchs5	pchs5	PROPN
ejpam-6535	545	3	)	)	PUNCT
ejpam-6535	545	4	let	let	VERB
ejpam-6535	545	5	f	f	PROPN
ejpam-6535	545	6	∈	∈	PROPN
ejpam-6535	545	7	cφ	cφ	NOUN
ejpam-6535	545	8	,	,	PUNCT
ejpam-6535	545	9	then	then	ADV
ejpam-6535	545	10	f−1	f−1	PROPN
ejpam-6535	545	11	∈	∈	PROPN
ejpam-6535	545	12	cφ	cφ	NOUN
ejpam-6535	545	13	.	.	PUNCT
ejpam-6535	545	14	consider	consider	VERB
ejpam-6535	545	15	f	f	NOUN
ejpam-6535	545	16	,	,	PUNCT
ejpam-6535	545	17	g	g	PROPN
ejpam-6535	545	18	∈	∈	PROPN
ejpam-6535	545	19	cφ	cφ	NOUN
ejpam-6535	545	20	.	.	PUNCT
ejpam-6535	546	1	then	then	ADV
ejpam-6535	546	2	by	by	ADP
ejpam-6535	546	3	lemma	lemma	PROPN
ejpam-6535	546	4	2(g	2(g	NUM
ejpam-6535	546	5	)	)	PUNCT
ejpam-6535	546	6	,	,	PUNCT
ejpam-6535	546	7	(	(	PUNCT
ejpam-6535	546	8	f⊙g)⊙	f⊙g)⊙	PROPN
ejpam-6535	546	9	(	(	PUNCT
ejpam-6535	546	10	f⊙g)−1	f⊙g)−1	NOUN
ejpam-6535	546	11	=	=	SYM
ejpam-6535	546	12	f⊙g⊙g−1⊙f−1	f⊙g⊙g−1⊙f−1	PROPN
ejpam-6535	546	13	.	.	PUNCT
ejpam-6535	547	1	but	but	CCONJ
ejpam-6535	547	2	e	e	PROPN
ejpam-6535	547	3	∈	∈	PROPN
ejpam-6535	547	4	cφ(g⊙g−1	cφ(g⊙g−1	PROPN
ejpam-6535	547	5	)	)	PUNCT
ejpam-6535	547	6	sinceg	sinceg	PROPN
ejpam-6535	547	7	∈	∈	PROPN
ejpam-6535	547	8	cφ	cφ	X
ejpam-6535	547	9	and	and	CCONJ
ejpam-6535	547	10	e	e	PROPN
ejpam-6535	547	11	∈	∈	PROPN
ejpam-6535	547	12	cφ	cφ	NOUN
ejpam-6535	547	13	(	(	PUNCT
ejpam-6535	547	14	f⊙g⊙g−1⊙	f⊙g⊙g−1⊙	PROPN
ejpam-6535	547	15	f−1	f−1	PROPN
ejpam-6535	547	16	)	)	PUNCT
ejpam-6535	547	17	.	.	PUNCT
ejpam-6535	548	1	similarly	similarly	ADV
ejpam-6535	548	2	,	,	PUNCT
ejpam-6535	548	3	one	one	NOUN
ejpam-6535	548	4	obtains	obtain	VERB
ejpam-6535	548	5	e	e	NOUN
ejpam-6535	548	6	∈	∈	PROPN
ejpam-6535	548	7	cφ	cφ	X
ejpam-6535	548	8	(	(	PUNCT
ejpam-6535	548	9	(	(	PUNCT
ejpam-6535	548	10	f⊙g)−1⊙	f⊙g)−1⊙	X
ejpam-6535	548	11	(	(	PUNCT
ejpam-6535	548	12	f⊙g	f⊙g	NOUN
ejpam-6535	548	13	)	)	PUNCT
ejpam-6535	548	14	)	)	PUNCT
ejpam-6535	548	15	.	.	PUNCT
ejpam-6535	549	1	hence	hence	ADV
ejpam-6535	549	2	f⊙g	f⊙g	PROPN
ejpam-6535	549	3	∈	∈	PROPN
ejpam-6535	549	4	cφ	cφ	NOUN
ejpam-6535	549	5	.	.	PUNCT
ejpam-6535	550	1	conversely	conversely	ADV
ejpam-6535	550	2	,	,	PUNCT
ejpam-6535	550	3	assume	assume	VERB
ejpam-6535	550	4	that	that	SCONJ
ejpam-6535	550	5	∀f	∀f	PRON
ejpam-6535	550	6	,	,	PUNCT
ejpam-6535	550	7	g	g	PROPN
ejpam-6535	550	8	∈	∈	PROPN
ejpam-6535	550	9	f(s	f(	NOUN
ejpam-6535	550	10	)	)	PUNCT
ejpam-6535	550	11	,	,	PUNCT
ejpam-6535	550	12	e	e	PROPN
ejpam-6535	550	13	∈	∈	PROPN
ejpam-6535	550	14	cφ	cφ	X
ejpam-6535	551	1	(	(	PUNCT
ejpam-6535	551	2	f−1	f−1	PROPN
ejpam-6535	551	3	⊙	⊙	PROPN
ejpam-6535	551	4	f	f	PROPN
ejpam-6535	551	5	)	)	PUNCT
ejpam-6535	551	6	,	,	PUNCT
ejpam-6535	551	7	e	e	PROPN
ejpam-6535	551	8	∈	∈	PROPN
ejpam-6535	551	9	cφ	cφ	X
ejpam-6535	551	10	(	(	PUNCT
ejpam-6535	551	11	f⊙	f⊙	VERB
ejpam-6535	551	12	f−1	f−1	PROPN
ejpam-6535	551	13	)	)	PUNCT
ejpam-6535	551	14	)	)	PUNCT
ejpam-6535	551	15	,	,	PUNCT
ejpam-6535	551	16	and	and	CCONJ
ejpam-6535	551	17	e	e	PROPN
ejpam-6535	551	18	∈	∈	PROPN
ejpam-6535	551	19	cφ(g	cφ(g	NUM
ejpam-6535	551	20	)	)	PUNCT
ejpam-6535	551	21	.	.	PUNCT
ejpam-6535	552	1	by	by	ADP
ejpam-6535	552	2	definition	definition	NOUN
ejpam-6535	552	3	f	f	X
ejpam-6535	552	4	,	,	PUNCT
ejpam-6535	552	5	g	g	PROPN
ejpam-6535	552	6	∈	∈	PROPN
ejpam-6535	552	7	cφ	cφ	NOUN
ejpam-6535	552	8	,	,	PUNCT
ejpam-6535	552	9	so	so	ADV
ejpam-6535	552	10	f⊙g	f⊙g	PROPN
ejpam-6535	552	11	∈	∈	PROPN
ejpam-6535	552	12	cφ	cφ	NOUN
ejpam-6535	552	13	.	.	PUNCT
ejpam-6535	553	1	but	but	CCONJ
ejpam-6535	553	2	this	this	PRON
ejpam-6535	553	3	implies	imply	VERB
ejpam-6535	553	4	that	that	SCONJ
ejpam-6535	553	5	e	e	PROPN
ejpam-6535	553	6	∈	∈	PROPN
ejpam-6535	553	7	cφ	cφ	X
ejpam-6535	553	8	(	(	PUNCT
ejpam-6535	553	9	(	(	PUNCT
ejpam-6535	553	10	f⊙g)⊙	f⊙g)⊙	PROPN
ejpam-6535	553	11	(	(	PUNCT
ejpam-6535	553	12	f⊙g)−1	f⊙g)−1	NOUN
ejpam-6535	553	13	)	)	PUNCT
ejpam-6535	553	14	.	.	PUNCT
ejpam-6535	554	1	if	if	SCONJ
ejpam-6535	554	2	we	we	PRON
ejpam-6535	554	3	assume	assume	VERB
ejpam-6535	554	4	[	[	X
ejpam-6535	554	5	e	e	X
ejpam-6535	554	6	]	]	X
ejpam-6535	554	7	≤	≤	ADJ
ejpam-6535	554	8	g	g	NOUN
ejpam-6535	554	9	,	,	PUNCT
ejpam-6535	554	10	then	then	ADV
ejpam-6535	554	11	by	by	ADP
ejpam-6535	554	12	using	use	VERB
ejpam-6535	554	13	lemma	lemma	PROPN
ejpam-6535	554	14	2	2	NUM
ejpam-6535	554	15	,	,	PUNCT
ejpam-6535	554	16	we	we	PRON
ejpam-6535	554	17	obtain	obtain	VERB
ejpam-6535	554	18	f⊙g⊙g−1	f⊙g⊙g−1	NOUN
ejpam-6535	554	19	⊙f−1	⊙f−1	NOUN
ejpam-6535	554	20	≤	≤	NUM
ejpam-6535	554	21	f⊙g⊙f−1	f⊙g⊙f−1	NOUN
ejpam-6535	554	22	and	and	CCONJ
ejpam-6535	554	23	hence	hence	ADV
ejpam-6535	554	24	e	e	PROPN
ejpam-6535	554	25	∈	∈	PROPN
ejpam-6535	554	26	cφ	cφ	NOUN
ejpam-6535	554	27	(	(	PUNCT
ejpam-6535	554	28	f⊙g⊙	f⊙g⊙	NOUN
ejpam-6535	554	29	f−1	f−1	PROPN
ejpam-6535	554	30	)	)	PUNCT
ejpam-6535	554	31	.	.	PUNCT
ejpam-6535	555	1	lemma	lemma	PROPN
ejpam-6535	555	2	21	21	NUM
ejpam-6535	555	3	.	.	PUNCT
ejpam-6535	556	1	let	let	VERB
ejpam-6535	556	2	(	(	PUNCT
ejpam-6535	556	3	s	s	X
ejpam-6535	556	4	,	,	PUNCT
ejpam-6535	556	5	·	·	PUNCT
ejpam-6535	556	6	,	,	PUNCT
ejpam-6535	556	7	c	c	NOUN
ejpam-6535	556	8	)	)	PUNCT
ejpam-6535	556	9	,	,	PUNCT
ejpam-6535	556	10	(	(	PUNCT
ejpam-6535	556	11	s′	s′	X
ejpam-6535	556	12	,	,	PUNCT
ejpam-6535	556	13	·	·	PUNCT
ejpam-6535	556	14	,	,	PUNCT
ejpam-6535	556	15	c′	c′	NUM
ejpam-6535	556	16	)	)	PUNCT
ejpam-6535	556	17	∈	∈	PROPN
ejpam-6535	556	18	|plimgrp|	|plimgrp|	NUM
ejpam-6535	556	19	under	under	ADP
ejpam-6535	556	20	the	the	DET
ejpam-6535	556	21	largest	large	ADJ
ejpam-6535	556	22	triangle	triangle	NOUN
ejpam-6535	556	23	function	function	NOUN
ejpam-6535	556	24	τ	τ	PROPN
ejpam-6535	556	25	,	,	PUNCT
ejpam-6535	556	26	and	and	CCONJ
ejpam-6535	556	27	satisfies	satisfie	NOUN
ejpam-6535	556	28	(	(	PUNCT
ejpam-6535	556	29	♯	♯	PROPN
ejpam-6535	556	30	)	)	PUNCT
ejpam-6535	556	31	.	.	PUNCT
ejpam-6535	557	1	if	if	SCONJ
ejpam-6535	557	2	f	f	PROPN
ejpam-6535	557	3	:	:	PUNCT
ejpam-6535	557	4	s	s	AUX
ejpam-6535	557	5	−→	−→	NOUN
ejpam-6535	557	6	s′	s′	ADJ
ejpam-6535	557	7	a	a	DET
ejpam-6535	557	8	group	group	NOUN
ejpam-6535	557	9	homomorphism	homomorphism	NOUN
ejpam-6535	557	10	,	,	PUNCT
ejpam-6535	557	11	then	then	ADV
ejpam-6535	557	12	the	the	DET
ejpam-6535	557	13	following	follow	VERB
ejpam-6535	557	14	assertions	assertion	NOUN
ejpam-6535	557	15	are	be	AUX
ejpam-6535	557	16	equivalent	equivalent	ADJ
ejpam-6535	557	17	.	.	PUNCT
ejpam-6535	558	1	(	(	PUNCT
ejpam-6535	558	2	i	i	NOUN
ejpam-6535	558	3	)	)	PUNCT
ejpam-6535	558	4	f	f	NOUN
ejpam-6535	558	5	:	:	PUNCT
ejpam-6535	558	6	(	(	PUNCT
ejpam-6535	558	7	s	s	X
ejpam-6535	558	8	,	,	PUNCT
ejpam-6535	558	9	c	c	NOUN
ejpam-6535	558	10	)	)	PUNCT
ejpam-6535	558	11	−→	−→	NOUN
ejpam-6535	558	12	(	(	PUNCT
ejpam-6535	558	13	s′	s′	X
ejpam-6535	558	14	,	,	PUNCT
ejpam-6535	558	15	c′	c′	NUM
ejpam-6535	558	16	)	)	PUNCT
ejpam-6535	558	17	is	be	AUX
ejpam-6535	558	18	continuous	continuous	ADJ
ejpam-6535	558	19	;	;	PUNCT
ejpam-6535	558	20	(	(	PUNCT
ejpam-6535	558	21	ii	ii	NOUN
ejpam-6535	558	22	)	)	PUNCT
ejpam-6535	558	23	f	f	NOUN
ejpam-6535	558	24	:	:	PUNCT
ejpam-6535	558	25	(	(	PUNCT
ejpam-6535	558	26	s	s	X
ejpam-6535	558	27	,	,	PUNCT
ejpam-6535	558	28	cc	cc	NOUN
ejpam-6535	558	29	)	)	PUNCT
ejpam-6535	558	30	−→	−→	NOUN
ejpam-6535	558	31	(	(	PUNCT
ejpam-6535	558	32	s′	s′	PROPN
ejpam-6535	558	33	,	,	PUNCT
ejpam-6535	558	34	cc	cc	NOUN
ejpam-6535	558	35	′	′	NUM
ejpam-6535	558	36	)	)	PUNCT
ejpam-6535	558	37	is	be	AUX
ejpam-6535	558	38	cauchy	cauchy	NOUN
ejpam-6535	558	39	-	-	PUNCT
ejpam-6535	558	40	continuous	continuous	ADJ
ejpam-6535	558	41	.	.	PUNCT
ejpam-6535	559	1	proof	proof	NOUN
ejpam-6535	559	2	.	.	PUNCT
ejpam-6535	560	1	assume	assume	VERB
ejpam-6535	560	2	(	(	PUNCT
ejpam-6535	560	3	i	i	NOUN
ejpam-6535	560	4	)	)	PUNCT
ejpam-6535	560	5	holds	hold	VERB
ejpam-6535	560	6	.	.	PUNCT
ejpam-6535	561	1	let	let	VERB
ejpam-6535	561	2	f	f	PROPN
ejpam-6535	561	3	∈	∈	PROPN
ejpam-6535	561	4	ccφ	ccφ	PROPN
ejpam-6535	561	5	.	.	PUNCT
ejpam-6535	562	1	then	then	ADV
ejpam-6535	562	2	e	e	PROPN
ejpam-6535	562	3	∈	∈	PROPN
ejpam-6535	562	4	cφ	cφ	X
ejpam-6535	563	1	(	(	PUNCT
ejpam-6535	563	2	f−1	f−1	PROPN
ejpam-6535	563	3	⊙	⊙	PROPN
ejpam-6535	563	4	f	f	PROPN
ejpam-6535	563	5	)	)	PUNCT
ejpam-6535	563	6	implies	imply	VERB
ejpam-6535	563	7	that	that	SCONJ
ejpam-6535	563	8	e′	e′	PUNCT
ejpam-6535	563	9	=	=	SYM
ejpam-6535	563	10	f(e	f(e	PROPN
ejpam-6535	563	11	)	)	PUNCT
ejpam-6535	563	12	∈	∈	PROPN
ejpam-6535	563	13	cφ	cφ	NOUN
ejpam-6535	564	1	(	(	PUNCT
ejpam-6535	564	2	f(f)−1	f(f)−1	PROPN
ejpam-6535	564	3	⊙	⊙	PROPN
ejpam-6535	564	4	f(f	f(f	PROPN
ejpam-6535	564	5	)	)	PUNCT
ejpam-6535	564	6	)	)	PUNCT
ejpam-6535	565	1	by	by	ADP
ejpam-6535	565	2	lemma	lemma	PROPN
ejpam-6535	565	3	2(k),(l	2(k),(l	PROPN
ejpam-6535	565	4	)	)	PUNCT
ejpam-6535	565	5	.	.	PUNCT
ejpam-6535	566	1	similarly	similarly	ADV
ejpam-6535	566	2	,	,	PUNCT
ejpam-6535	566	3	e′	e′	PROPN
ejpam-6535	566	4	∈	∈	PROPN
ejpam-6535	566	5	cφ	cφ	X
ejpam-6535	566	6	(	(	PUNCT
ejpam-6535	566	7	f(f)⊙	f(f)⊙	PROPN
ejpam-6535	566	8	f(f)−1	f(f)−1	PROPN
ejpam-6535	566	9	)	)	PUNCT
ejpam-6535	566	10	.	.	PUNCT
ejpam-6535	567	1	hence	hence	ADV
ejpam-6535	567	2	f(f	f(f	PROPN
ejpam-6535	567	3	)	)	PUNCT
ejpam-6535	567	4	∈	∈	PROPN
ejpam-6535	567	5	ccφ	ccφ	NOUN
ejpam-6535	567	6	.	.	PUNCT
ejpam-6535	568	1	conversely	conversely	ADV
ejpam-6535	568	2	,	,	PUNCT
ejpam-6535	568	3	assume	assume	VERB
ejpam-6535	568	4	(	(	PUNCT
ejpam-6535	568	5	ii	ii	NOUN
ejpam-6535	568	6	)	)	PUNCT
ejpam-6535	568	7	holds	hold	VERB
ejpam-6535	568	8	.	.	PUNCT
ejpam-6535	569	1	then	then	ADV
ejpam-6535	569	2	for	for	ADP
ejpam-6535	569	3	any	any	DET
ejpam-6535	569	4	p	p	NOUN
ejpam-6535	569	5	∈	∈	PROPN
ejpam-6535	569	6	s	s	NOUN
ejpam-6535	569	7	,	,	PUNCT
ejpam-6535	569	8	φ	φ	PROPN
ejpam-6535	569	9	∈	∈	PROPN
ejpam-6535	569	10	∆+	∆+	NOUN
ejpam-6535	569	11	and	and	CCONJ
ejpam-6535	569	12	f	f	PROPN
ejpam-6535	569	13	∈	∈	PROPN
ejpam-6535	569	14	f(s	f(	NOUN
ejpam-6535	569	15	)	)	PUNCT
ejpam-6535	569	16	,	,	PUNCT
ejpam-6535	569	17	if	if	SCONJ
ejpam-6535	569	18	p	p	PROPN
ejpam-6535	569	19	∈	∈	PROPN
ejpam-6535	569	20	cφ(f	cφ(f	NOUN
ejpam-6535	569	21	)	)	PUNCT
ejpam-6535	569	22	,	,	PUNCT
ejpam-6535	569	23	then	then	ADV
ejpam-6535	569	24	because	because	SCONJ
ejpam-6535	569	25	of	of	ADP
ejpam-6535	569	26	p−1	p−1	PROPN
ejpam-6535	569	27	∈	∈	PROPN
ejpam-6535	569	28	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	569	29	)	)	PUNCT
ejpam-6535	569	30	,	,	PUNCT
ejpam-6535	569	31	e	e	X
ejpam-6535	569	32	=	=	PUNCT
ejpam-6535	569	33	p−1p	p−1p	PROPN
ejpam-6535	569	34	∈	∈	PROPN
ejpam-6535	569	35	cτ(φ	cτ(φ	NOUN
ejpam-6535	569	36	,	,	PUNCT
ejpam-6535	569	37	φ)(f−1	φ)(f−1	PUNCT
ejpam-6535	569	38	⊙	⊙	X
ejpam-6535	569	39	f	f	X
ejpam-6535	569	40	)	)	PUNCT
ejpam-6535	570	1	=	=	PRON
ejpam-6535	570	2	cφ	cφ	NOUN
ejpam-6535	571	1	(	(	PUNCT
ejpam-6535	571	2	f−1	f−1	PROPN
ejpam-6535	571	3	⊙	⊙	PROPN
ejpam-6535	571	4	f	f	PROPN
ejpam-6535	571	5	)	)	PUNCT
ejpam-6535	571	6	implies	imply	VERB
ejpam-6535	571	7	that	that	SCONJ
ejpam-6535	571	8	f	f	PROPN
ejpam-6535	571	9	∈	∈	PROPN
ejpam-6535	571	10	cφ	cφ	NOUN
ejpam-6535	571	11	.	.	PUNCT
ejpam-6535	572	1	then	then	ADV
ejpam-6535	572	2	f	f	PROPN
ejpam-6535	572	3	(	(	PUNCT
ejpam-6535	572	4	f	f	X
ejpam-6535	572	5	)	)	PUNCT
ejpam-6535	572	6	∈	∈	PROPN
ejpam-6535	572	7	c′φ	c′φ	PROPN
ejpam-6535	572	8	.	.	PUNCT
ejpam-6535	573	1	by	by	ADP
ejpam-6535	573	2	(	(	PUNCT
ejpam-6535	573	3	pchs5	pchs5	PROPN
ejpam-6535	573	4	)	)	PUNCT
ejpam-6535	573	5	,	,	PUNCT
ejpam-6535	573	6	we	we	PRON
ejpam-6535	573	7	have	have	VERB
ejpam-6535	573	8	(	(	PUNCT
ejpam-6535	573	9	f(f	f(f	PROPN
ejpam-6535	573	10	)	)	PUNCT
ejpam-6535	573	11	∧	∧	PROPN
ejpam-6535	573	12	[	[	X
ejpam-6535	573	13	f(p	f(p	PROPN
ejpam-6535	573	14	)	)	PUNCT
ejpam-6535	573	15	]	]	PUNCT
ejpam-6535	573	16	)	)	PUNCT
ejpam-6535	574	1	∈	∈	PROPN
ejpam-6535	574	2	c′φ	c′φ	PROPN
ejpam-6535	574	3	.	.	PUNCT
ejpam-6535	575	1	this	this	DET
ejpam-6535	575	2	yields	yield	NOUN
ejpam-6535	575	3	that	that	PRON
ejpam-6535	575	4	e′	e′	PROPN
ejpam-6535	575	5	∈	∈	PROPN
ejpam-6535	575	6	cφ	cφ	X
ejpam-6535	575	7	(	(	PUNCT
ejpam-6535	575	8	(	(	PUNCT
ejpam-6535	575	9	f(f	f(f	PROPN
ejpam-6535	575	10	)	)	PUNCT
ejpam-6535	575	11	∧	∧	PROPN
ejpam-6535	576	1	[	[	X
ejpam-6535	576	2	f(p)])−1	f(p)])−1	NOUN
ejpam-6535	576	3	⊙	⊙	NOUN
ejpam-6535	576	4	(	(	PUNCT
ejpam-6535	576	5	f(f	f(f	PROPN
ejpam-6535	576	6	)	)	PUNCT
ejpam-6535	576	7	∧	∧	PROPN
ejpam-6535	576	8	[	[	X
ejpam-6535	576	9	f(p	f(p	PROPN
ejpam-6535	576	10	)	)	PUNCT
ejpam-6535	576	11	]	]	PUNCT
ejpam-6535	576	12	)	)	PUNCT
ejpam-6535	576	13	)	)	PUNCT
ejpam-6535	576	14	.	.	PUNCT
ejpam-6535	577	1	but	but	CCONJ
ejpam-6535	577	2	it	it	PRON
ejpam-6535	577	3	follows	follow	VERB
ejpam-6535	577	4	immediately	immediately	ADV
ejpam-6535	577	5	that	that	SCONJ
ejpam-6535	577	6	(	(	PUNCT
ejpam-6535	577	7	(	(	PUNCT
ejpam-6535	577	8	f(f	f(f	PROPN
ejpam-6535	577	9	)	)	PUNCT
ejpam-6535	577	10	∧	∧	PROPN
ejpam-6535	578	1	[	[	X
ejpam-6535	578	2	f(p)])−1	f(p)])−1	NOUN
ejpam-6535	578	3	⊙	⊙	NOUN
ejpam-6535	578	4	(	(	PUNCT
ejpam-6535	578	5	f(f	f(f	PROPN
ejpam-6535	578	6	)	)	PUNCT
ejpam-6535	578	7	∧	∧	PROPN
ejpam-6535	578	8	[	[	X
ejpam-6535	578	9	f(p	f(p	PROPN
ejpam-6535	578	10	)	)	PUNCT
ejpam-6535	578	11	]	]	PUNCT
ejpam-6535	578	12	)	)	PUNCT
ejpam-6535	578	13	)	)	PUNCT
ejpam-6535	579	1	≤	≤	NOUN
ejpam-6535	579	2	(	(	PUNCT
ejpam-6535	579	3	[	[	X
ejpam-6535	579	4	f(p)]−1	f(p)]−1	X
ejpam-6535	579	5	⊙	⊙	X
ejpam-6535	579	6	f(f	f(f	PROPN
ejpam-6535	579	7	)	)	PUNCT
ejpam-6535	579	8	)	)	PUNCT
ejpam-6535	579	9	which	which	PRON
ejpam-6535	579	10	implies	imply	VERB
ejpam-6535	579	11	that	that	SCONJ
ejpam-6535	579	12	e′	e′	PROPN
ejpam-6535	579	13	∈	∈	PROPN
ejpam-6535	579	14	cφ	cφ	X
ejpam-6535	579	15	(	(	PUNCT
ejpam-6535	579	16	[	[	X
ejpam-6535	579	17	f(p)]−1	f(p)]−1	X
ejpam-6535	579	18	⊙	⊙	X
ejpam-6535	579	19	f(f	f(f	PROPN
ejpam-6535	579	20	)	)	PUNCT
ejpam-6535	579	21	)	)	PUNCT
ejpam-6535	579	22	.	.	PUNCT
ejpam-6535	580	1	hence	hence	ADV
ejpam-6535	580	2	because	because	SCONJ
ejpam-6535	580	3	of	of	ADP
ejpam-6535	580	4	homogeneity	homogeneity	NOUN
ejpam-6535	580	5	,	,	PUNCT
ejpam-6535	580	6	by	by	ADP
ejpam-6535	580	7	lemma	lemma	PROPN
ejpam-6535	580	8	13(a	13(a	NUM
ejpam-6535	580	9	)	)	PUNCT
ejpam-6535	580	10	,	,	PUNCT
ejpam-6535	580	11	we	we	PRON
ejpam-6535	580	12	get	get	VERB
ejpam-6535	580	13	f(p	f(p	NOUN
ejpam-6535	580	14	)	)	PUNCT
ejpam-6535	580	15	∈	∈	PROPN
ejpam-6535	580	16	c′φ(f(f	c′φ(f(f	PROPN
ejpam-6535	580	17	)	)	PUNCT
ejpam-6535	580	18	)	)	PUNCT
ejpam-6535	580	19	.	.	PUNCT
ejpam-6535	581	1	thus	thus	ADV
ejpam-6535	581	2	we	we	PRON
ejpam-6535	581	3	get	get	VERB
ejpam-6535	581	4	the	the	DET
ejpam-6535	581	5	following	follow	VERB
ejpam-6535	581	6	corollary	corollary	ADJ
ejpam-6535	581	7	4	4	NUM
ejpam-6535	581	8	.	.	PUNCT
ejpam-6535	582	1	g	g	NOUN
ejpam-6535	582	2	:	:	PUNCT
ejpam-6535	582	3			PUNCT
ejpam-6535	582	4	snplimgrp	snplimgrp	NOUN
ejpam-6535	582	5	−→	−→	ADJ
ejpam-6535	582	6	pchygrp	pchygrp	NOUN
ejpam-6535	582	7	(	(	PUNCT
ejpam-6535	582	8	s	s	X
ejpam-6535	582	9	,	,	PUNCT
ejpam-6535	582	10	c	c	NOUN
ejpam-6535	582	11	)	)	PUNCT
ejpam-6535	582	12	7−→	7−→	NOUN
ejpam-6535	582	13	(	(	PUNCT
ejpam-6535	582	14	s′	s′	PROPN
ejpam-6535	582	15	,	,	PUNCT
ejpam-6535	582	16	cc	cc	NOUN
ejpam-6535	582	17	)	)	PUNCT
ejpam-6535	582	18	f	f	PROPN
ejpam-6535	583	1	7−→	7−→	PROPN
ejpam-6535	583	2	f	f	PROPN
ejpam-6535	583	3	,	,	PUNCT
ejpam-6535	583	4	is	be	AUX
ejpam-6535	583	5	a	a	DET
ejpam-6535	583	6	functor	functor	NOUN
ejpam-6535	583	7	,	,	PUNCT
ejpam-6535	583	8	where	where	SCONJ
ejpam-6535	583	9	snplimgrp	snplimgrp	NOUN
ejpam-6535	583	10	denotes	denote	VERB
ejpam-6535	583	11	the	the	DET
ejpam-6535	583	12	category	category	NOUN
ejpam-6535	583	13	of	of	ADP
ejpam-6535	583	14	all	all	DET
ejpam-6535	583	15	objects	object	NOUN
ejpam-6535	583	16	(	(	PUNCT
ejpam-6535	583	17	strongly	strongly	ADV
ejpam-6535	583	18	normal	normal	ADJ
ejpam-6535	583	19	probabilistic	probabilistic	ADJ
ejpam-6535	583	20	limit	limit	NOUN
ejpam-6535	583	21	groups	group	NOUN
ejpam-6535	583	22	under	under	ADP
ejpam-6535	583	23	the	the	DET
ejpam-6535	583	24	largest	large	ADJ
ejpam-6535	583	25	triangle	triangle	NOUN
ejpam-6535	583	26	function	function	NOUN
ejpam-6535	583	27	τ	τ	NOUN
ejpam-6535	583	28	)	)	PUNCT
ejpam-6535	583	29	satisfying	satisfy	VERB
ejpam-6535	583	30	condition	condition	NOUN
ejpam-6535	583	31	(	(	PUNCT
ejpam-6535	583	32	♯	♯	PROPN
ejpam-6535	583	33	)	)	PUNCT
ejpam-6535	583	34	and	and	CCONJ
ejpam-6535	583	35	morphisms	morphism	VERB
ejpam-6535	583	36	as	as	ADP
ejpam-6535	583	37	continuous	continuous	ADJ
ejpam-6535	583	38	mappings	mapping	NOUN
ejpam-6535	583	39	between	between	ADP
ejpam-6535	583	40	them	they	PRON
ejpam-6535	583	41	.	.	PUNCT
ejpam-6535	584	1	remark	remark	VERB
ejpam-6535	584	2	6	6	NUM
ejpam-6535	584	3	.	.	PUNCT
ejpam-6535	585	1	this	this	DET
ejpam-6535	585	2	notion	notion	NOUN
ejpam-6535	585	3	of	of	ADP
ejpam-6535	585	4	strongly	strongly	ADV
ejpam-6535	585	5	normal	normal	ADJ
ejpam-6535	585	6	originally	originally	ADV
ejpam-6535	585	7	introduced	introduce	VERB
ejpam-6535	585	8	by	by	ADP
ejpam-6535	585	9	r.	r.	PROPN
ejpam-6535	585	10	n.	n.	PROPN
ejpam-6535	585	11	ball	ball	PROPN
ejpam-6535	585	12	[	[	X
ejpam-6535	585	13	9	9	NUM
ejpam-6535	585	14	]	]	PUNCT
ejpam-6535	585	15	in	in	ADP
ejpam-6535	585	16	relation	relation	NOUN
ejpam-6535	585	17	to	to	ADP
ejpam-6535	585	18	his	his	PRON
ejpam-6535	585	19	notion	notion	NOUN
ejpam-6535	585	20	of	of	ADP
ejpam-6535	585	21	convergence	convergence	NOUN
ejpam-6535	585	22	structures	structure	NOUN
ejpam-6535	585	23	and	and	CCONJ
ejpam-6535	585	24	cauchy	cauchy	NOUN
ejpam-6535	585	25	structures	structure	NOUN
ejpam-6535	585	26	for	for	ADP
ejpam-6535	585	27	lattice	lattice	ADJ
ejpam-6535	585	28	order	order	NOUN
ejpam-6535	585	29	groups	group	NOUN
ejpam-6535	585	30	or	or	CCONJ
ejpam-6535	585	31	so	so	ADV
ejpam-6535	585	32	-	-	PUNCT
ejpam-6535	585	33	called	call	VERB
ejpam-6535	585	34	l	l	NOUN
ejpam-6535	585	35	-	-	NOUN
ejpam-6535	585	36	groups	group	NOUN
ejpam-6535	585	37	;	;	PUNCT
ejpam-6535	585	38	some	some	DET
ejpam-6535	585	39	other	other	ADJ
ejpam-6535	585	40	authors	author	NOUN
ejpam-6535	585	41	also	also	ADV
ejpam-6535	585	42	used	use	VERB
ejpam-6535	585	43	this	this	DET
ejpam-6535	585	44	idea	idea	NOUN
ejpam-6535	585	45	towards	towards	ADP
ejpam-6535	585	46	the	the	DET
ejpam-6535	585	47	construction	construction	NOUN
ejpam-6535	585	48	of	of	ADP
ejpam-6535	585	49	cauchy	cauchy	PROPN
ejpam-6535	585	50	completion	completion	NOUN
ejpam-6535	585	51	,	,	PUNCT
ejpam-6535	585	52	cf	cf	NOUN
ejpam-6535	585	53	.	.	PUNCT
ejpam-6535	586	1	[	[	X
ejpam-6535	586	2	17	17	NUM
ejpam-6535	586	3	]	]	PUNCT
ejpam-6535	586	4	(	(	PUNCT
ejpam-6535	586	5	see	see	VERB
ejpam-6535	586	6	also	also	ADV
ejpam-6535	586	7	,	,	PUNCT
ejpam-6535	586	8	[	[	X
ejpam-6535	586	9	23	23	NUM
ejpam-6535	586	10	]	]	PUNCT
ejpam-6535	586	11	)	)	PUNCT
ejpam-6535	586	12	.	.	PUNCT
ejpam-6535	587	1	proposition	proposition	NOUN
ejpam-6535	587	2	6	6	NUM
ejpam-6535	587	3	.	.	PUNCT
ejpam-6535	588	1	(	(	PUNCT
ejpam-6535	588	2	i	i	NOUN
ejpam-6535	588	3	)	)	PUNCT
ejpam-6535	588	4	let	let	VERB
ejpam-6535	588	5	(	(	PUNCT
ejpam-6535	588	6	s	s	X
ejpam-6535	588	7	,	,	PUNCT
ejpam-6535	588	8	·	·	PUNCT
ejpam-6535	588	9	,	,	PUNCT
ejpam-6535	588	10	c	c	X
ejpam-6535	588	11	=	=	SYM
ejpam-6535	588	12	(	(	PUNCT
ejpam-6535	588	13	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	588	14	)	)	PUNCT
ejpam-6535	588	15	be	be	AUX
ejpam-6535	588	16	a	a	DET
ejpam-6535	588	17	probabilistic	probabilistic	ADJ
ejpam-6535	588	18	pre	pre	ADJ
ejpam-6535	588	19	-	-	ADJ
ejpam-6535	588	20	cauchy	cauchy	ADJ
ejpam-6535	588	21	group	group	NOUN
ejpam-6535	588	22	,	,	PUNCT
ejpam-6535	588	23	then	then	ADV
ejpam-6535	588	24	(	(	PUNCT
ejpam-6535	588	25	s	s	PROPN
ejpam-6535	588	26	,	,	PUNCT
ejpam-6535	588	27	·	·	PUNCT
ejpam-6535	588	28	,	,	PUNCT
ejpam-6535	588	29	ccφ	ccφ	X
ejpam-6535	588	30	)	)	PUNCT
ejpam-6535	588	31	is	be	AUX
ejpam-6535	588	32	a	a	DET
ejpam-6535	588	33	probabilistic	probabilistic	ADJ
ejpam-6535	588	34	limit	limit	NOUN
ejpam-6535	588	35	group	group	NOUN
ejpam-6535	588	36	.	.	PUNCT
ejpam-6535	589	1	(	(	PUNCT
ejpam-6535	589	2	ii	ii	NOUN
ejpam-6535	589	3	)	)	PUNCT
ejpam-6535	589	4	if	if	SCONJ
ejpam-6535	589	5	(	(	PUNCT
ejpam-6535	589	6	s	s	X
ejpam-6535	589	7	,	,	PUNCT
ejpam-6535	589	8	·	·	PUNCT
ejpam-6535	589	9	,	,	PUNCT
ejpam-6535	589	10	c	c	X
ejpam-6535	589	11	)	)	PUNCT
ejpam-6535	589	12	is	be	AUX
ejpam-6535	589	13	a	a	DET
ejpam-6535	589	14	probabilistic	probabilistic	ADJ
ejpam-6535	589	15	limit	limit	NOUN
ejpam-6535	589	16	group	group	NOUN
ejpam-6535	589	17	,	,	PUNCT
ejpam-6535	589	18	then	then	ADV
ejpam-6535	589	19	(	(	PUNCT
ejpam-6535	589	20	s	s	X
ejpam-6535	589	21	,	,	PUNCT
ejpam-6535	589	22	cc	cc	NOUN
ejpam-6535	589	23	)	)	PUNCT
ejpam-6535	589	24	is	be	AUX
ejpam-6535	589	25	a	a	DET
ejpam-6535	589	26	probabilistic	probabilistic	ADJ
ejpam-6535	589	27	pre	pre	ADJ
ejpam-6535	589	28	-	-	ADJ
ejpam-6535	589	29	cauchy	cauchy	ADJ
ejpam-6535	589	30	group	group	NOUN
ejpam-6535	589	31	if	if	SCONJ
ejpam-6535	589	32	and	and	CCONJ
ejpam-6535	589	33	only	only	ADV
ejpam-6535	589	34	if	if	SCONJ
ejpam-6535	589	35	(	(	PUNCT
ejpam-6535	589	36	s	s	X
ejpam-6535	589	37	,	,	PUNCT
ejpam-6535	589	38	·	·	PUNCT
ejpam-6535	589	39	,	,	PUNCT
ejpam-6535	589	40	c	c	X
ejpam-6535	589	41	)	)	PUNCT
ejpam-6535	589	42	is	be	AUX
ejpam-6535	589	43	probabilistic	probabilistic	ADJ
ejpam-6535	589	44	limit	limit	NOUN
ejpam-6535	589	45	group	group	NOUN
ejpam-6535	589	46	satisfying	satisfy	VERB
ejpam-6535	589	47	♯.	♯.	PROPN
ejpam-6535	589	48	(	(	PUNCT
ejpam-6535	589	49	iii	iii	NOUN
ejpam-6535	589	50	)	)	PUNCT
ejpam-6535	589	51	if	if	SCONJ
ejpam-6535	589	52	(	(	PUNCT
ejpam-6535	589	53	s	s	X
ejpam-6535	589	54	,	,	PUNCT
ejpam-6535	589	55	·	·	PUNCT
ejpam-6535	589	56	,	,	PUNCT
ejpam-6535	589	57	c	c	X
ejpam-6535	589	58	)	)	PUNCT
ejpam-6535	589	59	is	be	AUX
ejpam-6535	589	60	a	a	DET
ejpam-6535	589	61	probabilistic	probabilistic	ADJ
ejpam-6535	589	62	limit	limit	NOUN
ejpam-6535	589	63	group	group	NOUN
ejpam-6535	589	64	and	and	CCONJ
ejpam-6535	589	65	(	(	PUNCT
ejpam-6535	589	66	s	s	PROPN
ejpam-6535	589	67	,	,	PUNCT
ejpam-6535	589	68	·	·	PUNCT
ejpam-6535	589	69	,	,	PUNCT
ejpam-6535	589	70	cc	cc	NOUN
ejpam-6535	589	71	)	)	PUNCT
ejpam-6535	589	72	a	a	DET
ejpam-6535	589	73	probabilistic	probabilistic	ADJ
ejpam-6535	589	74	pre	pre	ADJ
ejpam-6535	589	75	-	-	ADJ
ejpam-6535	589	76	cauchy	cauchy	ADJ
ejpam-6535	589	77	group	group	NOUN
ejpam-6535	589	78	,	,	PUNCT
ejpam-6535	589	79	then	then	ADV
ejpam-6535	589	80	(	(	PUNCT
ejpam-6535	589	81	s	s	X
ejpam-6535	589	82	,	,	PUNCT
ejpam-6535	589	83	·	·	PUNCT
ejpam-6535	589	84	,	,	PUNCT
ejpam-6535	589	85	c	c	X
ejpam-6535	589	86	=	=	SYM
ejpam-6535	589	87	(	(	PUNCT
ejpam-6535	589	88	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	589	89	)	)	PUNCT
ejpam-6535	589	90	is	be	AUX
ejpam-6535	589	91	a	a	DET
ejpam-6535	589	92	probabilistic	probabilistic	ADJ
ejpam-6535	589	93	cauchy	cauchy	NOUN
ejpam-6535	589	94	group	group	NOUN
ejpam-6535	589	95	.	.	PUNCT
ejpam-6535	590	1	proof	proof	NOUN
ejpam-6535	590	2	.	.	PUNCT
ejpam-6535	591	1	we	we	PRON
ejpam-6535	591	2	only	only	ADV
ejpam-6535	591	3	prove	prove	VERB
ejpam-6535	591	4	item(i	item(i	PROPN
ejpam-6535	591	5	)	)	PUNCT
ejpam-6535	591	6	.	.	PUNCT
ejpam-6535	592	1	(	(	PUNCT
ejpam-6535	592	2	i	i	NOUN
ejpam-6535	592	3	)	)	PUNCT
ejpam-6535	592	4	let	let	VERB
ejpam-6535	592	5	p	p	PROPN
ejpam-6535	592	6	∈	∈	PROPN
ejpam-6535	592	7	ccφ(f	ccφ(f	PROPN
ejpam-6535	592	8	)	)	PUNCT
ejpam-6535	592	9	and	and	CCONJ
ejpam-6535	592	10	q	q	PROPN
ejpam-6535	592	11	∈	∈	PROPN
ejpam-6535	592	12	ccψ(g	ccψ(g	PROPN
ejpam-6535	592	13	)	)	PUNCT
ejpam-6535	592	14	.	.	PUNCT
ejpam-6535	593	1	then	then	ADV
ejpam-6535	593	2	as	as	SCONJ
ejpam-6535	593	3	[	[	X
ejpam-6535	593	4	p	p	X
ejpam-6535	593	5	]	]	X
ejpam-6535	593	6	∧	∧	PROPN
ejpam-6535	593	7	f	f	PROPN
ejpam-6535	593	8	∈	∈	PROPN
ejpam-6535	593	9	cφ	cφ	AUX
ejpam-6535	593	10	implying	imply	VERB
ejpam-6535	593	11	(	(	PUNCT
ejpam-6535	593	12	[	[	X
ejpam-6535	593	13	p	p	X
ejpam-6535	593	14	]	]	X
ejpam-6535	593	15	∧	∧	PROPN
ejpam-6535	593	16	f)−1	f)−1	NOUN
ejpam-6535	593	17	∈	∈	PROPN
ejpam-6535	593	18	cφ	cφ	X
ejpam-6535	593	19	which	which	PRON
ejpam-6535	593	20	in	in	ADP
ejpam-6535	593	21	turn	turn	NOUN
ejpam-6535	593	22	upon	upon	SCONJ
ejpam-6535	593	23	using	use	VERB
ejpam-6535	593	24	lemma	lemma	PROPN
ejpam-6535	593	25	2(g	2(g	NUM
ejpam-6535	593	26	)	)	PUNCT
ejpam-6535	593	27	implies	imply	VERB
ejpam-6535	593	28	that	that	SCONJ
ejpam-6535	593	29	f−1	f−1	PROPN
ejpam-6535	593	30	∧	∧	NOUN
ejpam-6535	594	1	[	[	X
ejpam-6535	594	2	p]−1	p]−1	X
ejpam-6535	594	3	∈	∈	NOUN
ejpam-6535	594	4	cφ	cφ	NOUN
ejpam-6535	594	5	and	and	CCONJ
ejpam-6535	594	6	g	g	PROPN
ejpam-6535	594	7	∧	∧	PROPN
ejpam-6535	595	1	[	[	X
ejpam-6535	595	2	q	q	X
ejpam-6535	595	3	]	]	X
ejpam-6535	595	4	∈	∈	PROPN
ejpam-6535	595	5	cψ	cψ	NOUN
ejpam-6535	595	6	.	.	PUNCT
ejpam-6535	596	1	these	these	PRON
ejpam-6535	596	2	together	together	ADV
ejpam-6535	596	3	imply	imply	VERB
ejpam-6535	596	4	that	that	DET
ejpam-6535	596	5	p−1q	p−1q	PROPN
ejpam-6535	596	6	∈	∈	PROPN
ejpam-6535	596	7	ccτ(φ	ccτ(φ	PROPN
ejpam-6535	596	8	,	,	PUNCT
ejpam-6535	596	9	ψ)(f	ψ)(f	X
ejpam-6535	596	10	−1	−1	NOUN
ejpam-6535	596	11	⊙	⊙	NOUN
ejpam-6535	596	12	g	g	NOUN
ejpam-6535	596	13	)	)	PUNCT
ejpam-6535	596	14	.	.	PUNCT
ejpam-6535	597	1	in	in	ADP
ejpam-6535	597	2	fact	fact	NOUN
ejpam-6535	597	3	,	,	PUNCT
ejpam-6535	597	4	(	(	PUNCT
ejpam-6535	597	5	f−1	f−1	PROPN
ejpam-6535	597	6	∧	∧	PROPN
ejpam-6535	597	7	[	[	X
ejpam-6535	597	8	p]−1	p]−1	X
ejpam-6535	597	9	)	)	PUNCT
ejpam-6535	597	10	⊙	⊙	NOUN
ejpam-6535	597	11	(	(	PUNCT
ejpam-6535	597	12	g	g	PROPN
ejpam-6535	597	13	∧	∧	PROPN
ejpam-6535	597	14	[	[	X
ejpam-6535	597	15	q	q	X
ejpam-6535	597	16	]	]	X
ejpam-6535	597	17	)	)	PUNCT
ejpam-6535	597	18	∈	∈	PROPN
ejpam-6535	597	19	cτ(φ	cτ(φ	NOUN
ejpam-6535	597	20	,	,	PUNCT
ejpam-6535	597	21	ψ	ψ	NOUN
ejpam-6535	597	22	)	)	PUNCT
ejpam-6535	597	23	,	,	PUNCT
ejpam-6535	597	24	and	and	CCONJ
ejpam-6535	597	25	upon	upon	SCONJ
ejpam-6535	597	26	using	use	VERB
ejpam-6535	597	27	lemma	lemma	PROPN
ejpam-6535	597	28	2(j	2(j	NUM
ejpam-6535	597	29	)	)	PUNCT
ejpam-6535	597	30	twice	twice	ADV
ejpam-6535	597	31	,	,	PUNCT
ejpam-6535	597	32	one	one	PRON
ejpam-6535	597	33	obtains	obtain	VERB
ejpam-6535	597	34	:	:	PUNCT
ejpam-6535	597	35	(	(	PUNCT
ejpam-6535	597	36	f−1	f−1	PROPN
ejpam-6535	597	37	∧	∧	PROPN
ejpam-6535	597	38	[	[	X
ejpam-6535	597	39	p]−1	p]−1	X
ejpam-6535	597	40	)	)	PUNCT
ejpam-6535	597	41	⊙	⊙	NOUN
ejpam-6535	597	42	(	(	PUNCT
ejpam-6535	597	43	g	g	PROPN
ejpam-6535	597	44	∧	∧	PROPN
ejpam-6535	598	1	[	[	X
ejpam-6535	598	2	q	q	X
ejpam-6535	598	3	]	]	X
ejpam-6535	598	4	)	)	PUNCT
ejpam-6535	598	5	≤	≤	NOUN
ejpam-6535	598	6	(	(	PUNCT
ejpam-6535	598	7	f−1	f−1	PROPN
ejpam-6535	598	8	⊙g	⊙g	ADJ
ejpam-6535	598	9	)	)	PUNCT
ejpam-6535	598	10	∧	∧	NOUN
ejpam-6535	598	11	(	(	PUNCT
ejpam-6535	598	12	[	[	X
ejpam-6535	598	13	p]−1	p]−1	X
ejpam-6535	598	14	⊙	⊙	NOUN
ejpam-6535	599	1	[	[	X
ejpam-6535	599	2	q	q	X
ejpam-6535	599	3	]	]	X
ejpam-6535	599	4	)	)	PUNCT
ejpam-6535	599	5	=	=	SYM
ejpam-6535	599	6	(	(	PUNCT
ejpam-6535	599	7	f−1	f−1	PROPN
ejpam-6535	599	8	⊙g	⊙g	ADJ
ejpam-6535	599	9	)	)	PUNCT
ejpam-6535	600	1	∧	∧	NOUN
ejpam-6535	600	2	(	(	PUNCT
ejpam-6535	600	3	[	[	X
ejpam-6535	600	4	p−1q	p−1q	X
ejpam-6535	600	5	]	]	X
ejpam-6535	600	6	)	)	PUNCT
ejpam-6535	600	7	,	,	PUNCT
ejpam-6535	600	8	whence	whence	X
ejpam-6535	600	9	(	(	PUNCT
ejpam-6535	600	10	f−1	f−1	PROPN
ejpam-6535	600	11	⊙g	⊙g	ADJ
ejpam-6535	600	12	)	)	PUNCT
ejpam-6535	601	1	∧	∧	PROPN
ejpam-6535	601	2	[	[	X
ejpam-6535	601	3	p−1q	p−1q	X
ejpam-6535	601	4	]	]	X
ejpam-6535	601	5	∈	∈	PROPN
ejpam-6535	601	6	cτ(φ	cτ(φ	X
ejpam-6535	601	7	,	,	PUNCT
ejpam-6535	601	8	ψ	ψ	NOUN
ejpam-6535	601	9	)	)	PUNCT
ejpam-6535	601	10	showing	show	VERB
ejpam-6535	601	11	that	that	DET
ejpam-6535	601	12	p−1q	p−1q	PROPN
ejpam-6535	601	13	∈	∈	PROPN
ejpam-6535	601	14	ccτ(φ	ccτ(φ	PROPN
ejpam-6535	601	15	,	,	PUNCT
ejpam-6535	601	16	ψ)(f	ψ)(f	X
ejpam-6535	601	17	−1	−1	NOUN
ejpam-6535	601	18	⊙g	⊙g	NOUN
ejpam-6535	601	19	)	)	PUNCT
ejpam-6535	601	20	.	.	PUNCT
ejpam-6535	602	1	theorem	theorem	NOUN
ejpam-6535	602	2	2	2	NUM
ejpam-6535	602	3	.	.	PUNCT
ejpam-6535	603	1	if	if	SCONJ
ejpam-6535	603	2	(	(	PUNCT
ejpam-6535	603	3	s	s	X
ejpam-6535	603	4	,	,	PUNCT
ejpam-6535	603	5	·	·	PUNCT
ejpam-6535	603	6	,	,	PUNCT
ejpam-6535	603	7	c	c	X
ejpam-6535	603	8	=	=	SYM
ejpam-6535	603	9	(	(	PUNCT
ejpam-6535	603	10	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	603	11	)	)	PUNCT
ejpam-6535	603	12	∈	∈	PROPN
ejpam-6535	603	13	|pchygrp|	|pchygrp|	PROPN
ejpam-6535	603	14	,	,	PUNCT
ejpam-6535	603	15	then	then	ADV
ejpam-6535	603	16	(	(	PUNCT
ejpam-6535	603	17	s	s	X
ejpam-6535	603	18	,	,	PUNCT
ejpam-6535	603	19	cc	cc	NOUN
ejpam-6535	603	20	)	)	PUNCT
ejpam-6535	603	21	∈	∈	PROPN
ejpam-6535	603	22	|snplimgrp|	|snplimgrp|	NUM
ejpam-6535	603	23	.	.	PUNCT
ejpam-6535	604	1	conversely	conversely	ADV
ejpam-6535	604	2	,	,	PUNCT
ejpam-6535	604	3	if	if	SCONJ
ejpam-6535	604	4	(	(	PUNCT
ejpam-6535	604	5	s	s	X
ejpam-6535	604	6	,	,	PUNCT
ejpam-6535	604	7	c	c	NOUN
ejpam-6535	604	8	)	)	PUNCT
ejpam-6535	604	9	∈	∈	PROPN
ejpam-6535	604	10	|snplimgrp|	|snplimgrp|	NUM
ejpam-6535	604	11	,	,	PUNCT
ejpam-6535	604	12	then	then	ADV
ejpam-6535	604	13	(	(	PUNCT
ejpam-6535	604	14	s	s	X
ejpam-6535	604	15	,	,	PUNCT
ejpam-6535	604	16	cc	cc	NOUN
ejpam-6535	604	17	)	)	PUNCT
ejpam-6535	604	18	∈	∈	PROPN
ejpam-6535	604	19	|pchygrp|	|pchygrp|	PROPN
ejpam-6535	604	20	.	.	PUNCT
ejpam-6535	605	1	furthermore	furthermore	ADV
ejpam-6535	605	2	,	,	PUNCT
ejpam-6535	605	3	there	there	PRON
ejpam-6535	605	4	are	be	VERB
ejpam-6535	605	5	functors	functor	NOUN
ejpam-6535	605	6	pchygrp	pchygrp	NOUN
ejpam-6535	605	7	snplimgrp	snplimgrp	NOUN
ejpam-6535	605	8	f	f	PROPN
ejpam-6535	605	9	g	g	PROPN
ejpam-6535	605	10	such	such	ADJ
ejpam-6535	605	11	that	that	SCONJ
ejpam-6535	605	12	fg	fg	PROPN
ejpam-6535	605	13	=	=	PUNCT
ejpam-6535	605	14	idpchygrp	idpchygrp	PROPN
ejpam-6535	605	15	and	and	CCONJ
ejpam-6535	605	16	st	st	PROPN
ejpam-6535	605	17	=	=	PROPN
ejpam-6535	605	18	idsnplimgrp	idsnplimgrp	PROPN
ejpam-6535	605	19	.	.	PUNCT
ejpam-6535	606	1	that	that	PRON
ejpam-6535	606	2	is	is	ADV
ejpam-6535	606	3	,	,	PUNCT
ejpam-6535	606	4	the	the	DET
ejpam-6535	606	5	categories	category	NOUN
ejpam-6535	606	6	pchygrp	pchygrp	VERB
ejpam-6535	606	7	and	and	CCONJ
ejpam-6535	606	8	snplimgrp	snplimgrp	NOUN
ejpam-6535	606	9	are	be	AUX
ejpam-6535	606	10	isomorphic	isomorphic	ADJ
ejpam-6535	606	11	under	under	ADP
ejpam-6535	606	12	the	the	DET
ejpam-6535	606	13	largest	large	ADJ
ejpam-6535	606	14	triangle	triangle	NOUN
ejpam-6535	606	15	function	function	NOUN
ejpam-6535	606	16	τ	τ	PROPN
ejpam-6535	606	17	,	,	PUNCT
ejpam-6535	606	18	i.e.	i.e.	X
ejpam-6535	606	19	,	,	PUNCT
ejpam-6535	606	20	τ(φ	τ(φ	PROPN
ejpam-6535	606	21	,	,	PUNCT
ejpam-6535	606	22	φ	φ	NOUN
ejpam-6535	606	23	)	)	PUNCT
ejpam-6535	606	24	=	=	SYM
ejpam-6535	606	25	φ	φ	PROPN
ejpam-6535	606	26	.	.	PUNCT
ejpam-6535	607	1	proof	proof	NOUN
ejpam-6535	607	2	.	.	PUNCT
ejpam-6535	608	1	observe	observe	VERB
ejpam-6535	608	2	that	that	SCONJ
ejpam-6535	608	3	pchygrp	pchygrp	NOUN
ejpam-6535	608	4	f−→	f−→	NOUN
ejpam-6535	608	5	snlimgrp	snlimgrp	NOUN
ejpam-6535	608	6	g−→	g−→	NOUN
ejpam-6535	608	7	pchygrp	pchygrp	NOUN
ejpam-6535	608	8	:	:	PUNCT
ejpam-6535	608	9	(	(	PUNCT
ejpam-6535	608	10	s	s	X
ejpam-6535	608	11	,	,	PUNCT
ejpam-6535	608	12	c	c	NOUN
ejpam-6535	608	13	)	)	PUNCT
ejpam-6535	608	14	7−→	7−→	NOUN
ejpam-6535	608	15	(	(	PUNCT
ejpam-6535	608	16	s	s	X
ejpam-6535	608	17	,	,	PUNCT
ejpam-6535	608	18	cc	cc	NOUN
ejpam-6535	608	19	)	)	PUNCT
ejpam-6535	608	20	7−→	7−→	PROPN
ejpam-6535	608	21	(	(	PUNCT
ejpam-6535	608	22	s	s	PROPN
ejpam-6535	608	23	,	,	PUNCT
ejpam-6535	608	24	c	c	NOUN
ejpam-6535	608	25	)	)	PUNCT
ejpam-6535	608	26	;	;	PUNCT
ejpam-6535	608	27	then	then	ADV
ejpam-6535	608	28	one	one	PRON
ejpam-6535	608	29	can	can	AUX
ejpam-6535	608	30	check	check	VERB
ejpam-6535	608	31	that	that	DET
ejpam-6535	608	32	g	g	PROPN
ejpam-6535	608	33	◦	◦	NOUN
ejpam-6535	608	34	f	f	X
ejpam-6535	608	35	=	=	SYM
ejpam-6535	608	36	idpchygrp	idpchygrp	PROPN
ejpam-6535	608	37	,	,	PUNCT
ejpam-6535	608	38	i.e.	i.e.	X
ejpam-6535	608	39	,	,	PUNCT
ejpam-6535	608	40	c	c	PROPN
ejpam-6535	608	41	cc	cc	PROPN
ejpam-6535	608	42	=	=	PROPN
ejpam-6535	608	43	c.	c.	PROPN
ejpam-6535	608	44	in	in	ADP
ejpam-6535	608	45	fact	fact	NOUN
ejpam-6535	608	46	,	,	PUNCT
ejpam-6535	608	47	for	for	ADP
ejpam-6535	608	48	any	any	DET
ejpam-6535	608	49	f	f	PROPN
ejpam-6535	608	50	∈	∈	PROPN
ejpam-6535	608	51	f(s	f(	NOUN
ejpam-6535	608	52	)	)	PUNCT
ejpam-6535	608	53	and	and	CCONJ
ejpam-6535	608	54	φ	φ	NUM
ejpam-6535	608	55	∈	∈	PROPN
ejpam-6535	608	56	∆+	∆+	NOUN
ejpam-6535	608	57	,	,	PUNCT
ejpam-6535	608	58	f	f	PROPN
ejpam-6535	608	59	∈	∈	PROPN
ejpam-6535	608	60	cc	cc	PROPN
ejpam-6535	608	61	c	c	PROPN
ejpam-6535	608	62	φ	φ	X
ejpam-6535	608	63	⇐	⇐	PROPN
ejpam-6535	608	64	⇒	⇒	PROPN
ejpam-6535	608	65	e	e	PROPN
ejpam-6535	608	66	∈	∈	PROPN
ejpam-6535	608	67	ccφ(f−1	ccφ(f−1	NOUN
ejpam-6535	608	68	⊙	⊙	NOUN
ejpam-6535	608	69	f	f	X
ejpam-6535	608	70	)	)	PUNCT
ejpam-6535	608	71	⇐	⇐	ADJ
ejpam-6535	608	72	⇒	⇒	PROPN
ejpam-6535	608	73	f	f	PROPN
ejpam-6535	608	74	∈	∈	PROPN
ejpam-6535	608	75	cφ	cφ	NOUN
ejpam-6535	608	76	;	;	PUNCT
ejpam-6535	608	77	so	so	SCONJ
ejpam-6535	608	78	cc	cc	ADP
ejpam-6535	608	79	c	c	PROPN
ejpam-6535	608	80	=	=	PROPN
ejpam-6535	608	81	c.	c.	PROPN
ejpam-6535	608	82	on	on	ADP
ejpam-6535	608	83	the	the	DET
ejpam-6535	608	84	other	other	ADJ
ejpam-6535	608	85	hand	hand	NOUN
ejpam-6535	608	86	,	,	PUNCT
ejpam-6535	608	87	snlimgrp	snlimgrp	NOUN
ejpam-6535	608	88	g−→	g−→	NOUN
ejpam-6535	608	89	pchygrp	pchygrp	NOUN
ejpam-6535	608	90	f−→	f−→	NOUN
ejpam-6535	608	91	snlimgrp	snlimgrp	NOUN
ejpam-6535	608	92	:	:	PUNCT
ejpam-6535	608	93	(	(	PUNCT
ejpam-6535	608	94	s	s	X
ejpam-6535	608	95	,	,	PUNCT
ejpam-6535	608	96	c	c	NOUN
ejpam-6535	608	97	)	)	PUNCT
ejpam-6535	608	98	7−→	7−→	NOUN
ejpam-6535	608	99	(	(	PUNCT
ejpam-6535	608	100	s	s	X
ejpam-6535	608	101	,	,	PUNCT
ejpam-6535	608	102	cc	cc	NOUN
ejpam-6535	608	103	)	)	PUNCT
ejpam-6535	608	104	7−→	7−→	PROPN
ejpam-6535	608	105	(	(	PUNCT
ejpam-6535	608	106	s	s	PROPN
ejpam-6535	608	107	,	,	PUNCT
ejpam-6535	608	108	c	c	NOUN
ejpam-6535	608	109	)	)	PUNCT
ejpam-6535	608	110	,	,	PUNCT
ejpam-6535	608	111	which	which	PRON
ejpam-6535	608	112	yields	yield	VERB
ejpam-6535	608	113	that	that	SCONJ
ejpam-6535	608	114	f	f	PROPN
ejpam-6535	608	115	◦	◦	NOUN
ejpam-6535	608	116	g	g	NOUN
ejpam-6535	608	117	=	=	SYM
ejpam-6535	608	118	idsnplimgrp	idsnplimgrp	NOUN
ejpam-6535	608	119	,	,	PUNCT
ejpam-6535	608	120	i.e.	i.e.	X
ejpam-6535	608	121	,	,	PUNCT
ejpam-6535	608	122	c	c	PROPN
ejpam-6535	608	123	cc	cc	PROPN
ejpam-6535	608	124	=	=	PROPN
ejpam-6535	608	125	c.	c.	PROPN
ejpam-6535	608	126	in	in	ADP
ejpam-6535	608	127	fact	fact	NOUN
ejpam-6535	608	128	,	,	PUNCT
ejpam-6535	608	129	for	for	ADP
ejpam-6535	608	130	any	any	DET
ejpam-6535	608	131	p	p	NOUN
ejpam-6535	608	132	∈	∈	PROPN
ejpam-6535	608	133	s	s	PROPN
ejpam-6535	608	134	,	,	PUNCT
ejpam-6535	608	135	f	f	PROPN
ejpam-6535	608	136	∈	∈	PROPN
ejpam-6535	608	137	f(s	f(	VERB
ejpam-6535	608	138	)	)	PUNCT
ejpam-6535	608	139	and	and	CCONJ
ejpam-6535	608	140	φ	φ	NUM
ejpam-6535	608	141	∈	∈	PROPN
ejpam-6535	608	142	∆+	∆+	NOUN
ejpam-6535	608	143	,	,	PUNCT
ejpam-6535	608	144	let	let	VERB
ejpam-6535	608	145	p	p	PRON
ejpam-6535	608	146	∈	∈	PROPN
ejpam-6535	608	147	cc	cc	ADP
ejpam-6535	608	148	c	c	PROPN
ejpam-6535	608	149	φ	φ	PROPN
ejpam-6535	608	150	(	(	PUNCT
ejpam-6535	608	151	f	f	PROPN
ejpam-6535	608	152	)	)	PUNCT
ejpam-6535	608	153	.	.	PUNCT
ejpam-6535	609	1	then	then	ADV
ejpam-6535	609	2	f	f	PROPN
ejpam-6535	609	3	∧	∧	PROPN
ejpam-6535	610	1	[	[	X
ejpam-6535	610	2	p	p	X
ejpam-6535	610	3	]	]	X
ejpam-6535	610	4	∈	∈	PROPN
ejpam-6535	610	5	ccφ	ccφ	NOUN
ejpam-6535	610	6	and	and	CCONJ
ejpam-6535	610	7	so	so	ADV
ejpam-6535	610	8	e	e	PROPN
ejpam-6535	610	9	∈	∈	PROPN
ejpam-6535	610	10	cφ	cφ	X
ejpam-6535	611	1	(	(	PUNCT
ejpam-6535	611	2	(	(	PUNCT
ejpam-6535	611	3	f	f	X
ejpam-6535	611	4	∧	∧	PROPN
ejpam-6535	611	5	[	[	X
ejpam-6535	611	6	p])−1	p])−1	X
ejpam-6535	611	7	∧	∧	NOUN
ejpam-6535	611	8	⊙(f	⊙(f	X
ejpam-6535	612	1	∧	∧	PROPN
ejpam-6535	613	1	[	[	X
ejpam-6535	613	2	p	p	X
ejpam-6535	613	3	]	]	X
ejpam-6535	613	4	)	)	PUNCT
ejpam-6535	613	5	)	)	PUNCT
ejpam-6535	613	6	.	.	PUNCT
ejpam-6535	614	1	upon	upon	SCONJ
ejpam-6535	614	2	using	use	VERB
ejpam-6535	614	3	lemma	lemma	PROPN
ejpam-6535	614	4	2	2	NUM
ejpam-6535	614	5	,	,	PUNCT
ejpam-6535	614	6	then	then	ADV
ejpam-6535	614	7	one	one	NUM
ejpam-6535	614	8	obtains	obtain	VERB
ejpam-6535	614	9	:	:	PUNCT
ejpam-6535	614	10	(	(	PUNCT
ejpam-6535	614	11	f−1	f−1	PROPN
ejpam-6535	614	12	∧	∧	PROPN
ejpam-6535	615	1	[	[	X
ejpam-6535	615	2	p−1	p−1	X
ejpam-6535	615	3	]	]	PUNCT
ejpam-6535	615	4	)	)	PUNCT
ejpam-6535	615	5	⊙	⊙	NOUN
ejpam-6535	615	6	(	(	PUNCT
ejpam-6535	615	7	f	f	PROPN
ejpam-6535	615	8	∧	∧	PROPN
ejpam-6535	616	1	[	[	X
ejpam-6535	616	2	p	p	X
ejpam-6535	616	3	]	]	X
ejpam-6535	616	4	)	)	PUNCT
ejpam-6535	616	5	≤	≤	NOUN
ejpam-6535	617	1	[	[	X
ejpam-6535	617	2	p−1	p−1	X
ejpam-6535	617	3	]	]	X
ejpam-6535	617	4	∧	∧	PROPN
ejpam-6535	617	5	f.	f.	PROPN
ejpam-6535	617	6	by	by	ADP
ejpam-6535	617	7	(	(	PUNCT
ejpam-6535	617	8	pcs2	pcs2	PROPN
ejpam-6535	617	9	)	)	PUNCT
ejpam-6535	617	10	and	and	CCONJ
ejpam-6535	617	11	,	,	PUNCT
ejpam-6535	617	12	then	then	ADV
ejpam-6535	617	13	by	by	ADP
ejpam-6535	617	14	homogeneity	homogeneity	NOUN
ejpam-6535	617	15	,	,	PUNCT
ejpam-6535	617	16	one	one	PRON
ejpam-6535	617	17	gets	get	VERB
ejpam-6535	617	18	p	p	NOUN
ejpam-6535	617	19	∈	∈	NOUN
ejpam-6535	617	20	cφ(f	cφ(f	PUNCT
ejpam-6535	617	21	)	)	PUNCT
ejpam-6535	617	22	.	.	PUNCT
ejpam-6535	618	1	conversely	conversely	ADV
ejpam-6535	618	2	,	,	PUNCT
ejpam-6535	618	3	let	let	VERB
ejpam-6535	618	4	p	p	X
ejpam-6535	618	5	∈	∈	NOUN
ejpam-6535	618	6	cφ(f	cφ(f	PUNCT
ejpam-6535	618	7	)	)	PUNCT
ejpam-6535	618	8	,	,	PUNCT
ejpam-6535	618	9	then	then	ADV
ejpam-6535	618	10	e	e	PROPN
ejpam-6535	618	11	∈	∈	PROPN
ejpam-6535	618	12	cφ	cφ	X
ejpam-6535	618	13	(	(	PUNCT
ejpam-6535	618	14	[	[	X
ejpam-6535	618	15	p]−1	p]−1	X
ejpam-6535	618	16	⊙	⊙	NOUN
ejpam-6535	618	17	f	f	PROPN
ejpam-6535	618	18	)	)	PUNCT
ejpam-6535	618	19	and	and	CCONJ
ejpam-6535	618	20	as	as	ADP
ejpam-6535	618	21	because	because	SCONJ
ejpam-6535	618	22	of	of	ADP
ejpam-6535	618	23	p−1	p−1	PROPN
ejpam-6535	618	24	∈	∈	PROPN
ejpam-6535	618	25	cφ(f−1	cφ(f−1	PROPN
ejpam-6535	618	26	)	)	PUNCT
ejpam-6535	618	27	,	,	PUNCT
ejpam-6535	618	28	we	we	PRON
ejpam-6535	618	29	have	have	VERB
ejpam-6535	618	30	e	e	NOUN
ejpam-6535	618	31	=	=	NOUN
ejpam-6535	618	32	p−1p	p−1p	PUNCT
ejpam-6535	618	33	∈	∈	NOUN
ejpam-6535	618	34	cφ	cφ	X
ejpam-6535	619	1	(	(	PUNCT
ejpam-6535	619	2	f−1	f−1	PROPN
ejpam-6535	619	3	⊙	⊙	PROPN
ejpam-6535	619	4	f	f	PROPN
ejpam-6535	619	5	)	)	PUNCT
ejpam-6535	619	6	,	,	PUNCT
ejpam-6535	619	7	taking	take	VERB
ejpam-6535	619	8	into	into	ADP
ejpam-6535	619	9	account	account	NOUN
ejpam-6535	619	10	that	that	SCONJ
ejpam-6535	619	11	τ(φ	τ(φ	PROPN
ejpam-6535	619	12	,	,	PUNCT
ejpam-6535	619	13	φ	φ	NUM
ejpam-6535	619	14	)	)	PUNCT
ejpam-6535	619	15	=	=	SYM
ejpam-6535	619	16	φ	φ	PROPN
ejpam-6535	619	17	,	,	PUNCT
ejpam-6535	619	18	i.e.	i.e.	X
ejpam-6535	619	19	,	,	PUNCT
ejpam-6535	619	20	because	because	SCONJ
ejpam-6535	619	21	of	of	ADP
ejpam-6535	619	22	our	our	PRON
ejpam-6535	619	23	assumption	assumption	NOUN
ejpam-6535	619	24	of	of	ADP
ejpam-6535	619	25	the	the	DET
ejpam-6535	619	26	largest	large	ADJ
ejpam-6535	619	27	triangle	triangle	NOUN
ejpam-6535	619	28	function	function	NOUN
ejpam-6535	619	29	τ	τ	PROPN
ejpam-6535	619	30	.	.	PUNCT
ejpam-6535	620	1	now	now	ADV
ejpam-6535	620	2	since	since	SCONJ
ejpam-6535	620	3	we	we	PRON
ejpam-6535	620	4	have	have	AUX
ejpam-6535	620	5	by	by	ADP
ejpam-6535	620	6	lemma	lemma	PROPN
ejpam-6535	620	7	2	2	NUM
ejpam-6535	620	8	,	,	PUNCT
ejpam-6535	620	9	(	(	PUNCT
ejpam-6535	620	10	f	f	PROPN
ejpam-6535	620	11	∧	∧	PROPN
ejpam-6535	621	1	[	[	X
ejpam-6535	621	2	p])−1⊙	p])−1⊙	NOUN
ejpam-6535	621	3	(	(	PUNCT
ejpam-6535	621	4	f	f	X
ejpam-6535	621	5	∧	∧	PROPN
ejpam-6535	622	1	[	[	X
ejpam-6535	622	2	p	p	X
ejpam-6535	622	3	]	]	X
ejpam-6535	622	4	)	)	PUNCT
ejpam-6535	622	5	=	=	SYM
ejpam-6535	623	1	(	(	PUNCT
ejpam-6535	623	2	f−1⊙f)∧	f−1⊙f)∧	NOUN
ejpam-6535	623	3	(	(	PUNCT
ejpam-6535	623	4	f⊙	f⊙	VERB
ejpam-6535	623	5	[	[	X
ejpam-6535	623	6	p])∧	p])∧	NOUN
ejpam-6535	623	7	(	(	PUNCT
ejpam-6535	623	8	[	[	X
ejpam-6535	623	9	p]−1⊙f)∧	p]−1⊙f)∧	X
ejpam-6535	623	10	[	[	X
ejpam-6535	623	11	e	e	X
ejpam-6535	623	12	]	]	X
ejpam-6535	623	13	we	we	PRON
ejpam-6535	623	14	get	get	VERB
ejpam-6535	623	15	e	e	PROPN
ejpam-6535	623	16	∈	∈	PROPN
ejpam-6535	623	17	cφ	cφ	X
ejpam-6535	624	1	(	(	PUNCT
ejpam-6535	624	2	(	(	PUNCT
ejpam-6535	624	3	f	f	X
ejpam-6535	624	4	∧	∧	PROPN
ejpam-6535	625	1	[	[	X
ejpam-6535	625	2	p])−1	p])−1	X
ejpam-6535	625	3	⊙	⊙	PROPN
ejpam-6535	625	4	(	(	PUNCT
ejpam-6535	625	5	f	f	PROPN
ejpam-6535	625	6	∧	∧	PROPN
ejpam-6535	626	1	[	[	X
ejpam-6535	626	2	p	p	X
ejpam-6535	626	3	]	]	X
ejpam-6535	626	4	)	)	PUNCT
ejpam-6535	626	5	)	)	PUNCT
ejpam-6535	627	1	which	which	PRON
ejpam-6535	627	2	implies	imply	VERB
ejpam-6535	627	3	that	that	SCONJ
ejpam-6535	627	4	f∧	f∧	PROPN
ejpam-6535	628	1	[	[	X
ejpam-6535	628	2	p	p	X
ejpam-6535	628	3	]	]	X
ejpam-6535	628	4	∈	∈	PROPN
ejpam-6535	628	5	cφ	cφ	NOUN
ejpam-6535	629	1	and	and	CCONJ
ejpam-6535	629	2	hence	hence	ADV
ejpam-6535	629	3	p	p	X
ejpam-6535	629	4	∈	∈	PROPN
ejpam-6535	629	5	cc	cc	ADP
ejpam-6535	629	6	c	c	PROPN
ejpam-6535	629	7	φ	φ	PROPN
ejpam-6535	629	8	(	(	PUNCT
ejpam-6535	629	9	f	f	PROPN
ejpam-6535	629	10	)	)	PUNCT
ejpam-6535	629	11	.	.	PUNCT
ejpam-6535	630	1	this	this	PRON
ejpam-6535	630	2	end	end	VERB
ejpam-6535	630	3	the	the	DET
ejpam-6535	630	4	proof	proof	NOUN
ejpam-6535	630	5	.	.	PUNCT
ejpam-6535	631	1	corollary	corollary	ADJ
ejpam-6535	631	2	5	5	NUM
ejpam-6535	631	3	.	.	PUNCT
ejpam-6535	632	1	if	if	SCONJ
ejpam-6535	632	2	the	the	DET
ejpam-6535	632	3	group	group	NOUN
ejpam-6535	632	4	under	under	AUX
ejpam-6535	632	5	consider	consider	VERB
ejpam-6535	632	6	is	be	AUX
ejpam-6535	632	7	abelian	abelian	ADJ
ejpam-6535	632	8	,	,	PUNCT
ejpam-6535	632	9	then	then	ADV
ejpam-6535	632	10	pchygrp	pchygrp	NOUN
ejpam-6535	632	11	is	be	AUX
ejpam-6535	632	12	isomorphic	isomorphic	ADJ
ejpam-6535	632	13	to	to	ADP
ejpam-6535	632	14	plimgrp	plimgrp	NOUN
ejpam-6535	632	15	.	.	PUNCT
ejpam-6535	633	1	proposition	proposition	NOUN
ejpam-6535	633	2	7	7	NUM
ejpam-6535	633	3	.	.	PUNCT
ejpam-6535	634	1	(	(	PUNCT
ejpam-6535	634	2	a	a	X
ejpam-6535	634	3	)	)	PUNCT
ejpam-6535	634	4	if	if	SCONJ
ejpam-6535	634	5	for	for	ADP
ejpam-6535	634	6	each	each	DET
ejpam-6535	634	7	φ	φ	PROPN
ejpam-6535	634	8	∈	∈	PROPN
ejpam-6535	634	9	∆+	∆+	NOUN
ejpam-6535	634	10	,	,	PUNCT
ejpam-6535	634	11	f	f	X
ejpam-6535	634	12	:	:	PUNCT
ejpam-6535	634	13	(	(	PUNCT
ejpam-6535	634	14	s	s	X
ejpam-6535	634	15	,	,	PUNCT
ejpam-6535	634	16	·	·	PUNCT
ejpam-6535	634	17	,	,	PUNCT
ejpam-6535	634	18	cφ	cφ	NOUN
ejpam-6535	634	19	)	)	PUNCT
ejpam-6535	634	20	−→	−→	NOUN
ejpam-6535	634	21	(	(	PUNCT
ejpam-6535	634	22	s′	s′	PROPN
ejpam-6535	634	23	,	,	PUNCT
ejpam-6535	634	24	·	·	PUNCT
ejpam-6535	634	25	,	,	PUNCT
ejpam-6535	634	26	c′φ	c′φ	PROPN
ejpam-6535	634	27	)	)	PUNCT
ejpam-6535	634	28	is	be	AUX
ejpam-6535	634	29	a	a	DET
ejpam-6535	634	30	cauchy	cauchy	NOUN
ejpam-6535	634	31	-	-	PUNCT
ejpam-6535	634	32	continuous	continuous	ADJ
ejpam-6535	634	33	mapping	mapping	NOUN
ejpam-6535	634	34	between	between	ADP
ejpam-6535	634	35	probabilistic	probabilistic	ADJ
ejpam-6535	634	36	pre	pre	ADJ
ejpam-6535	634	37	-	-	ADJ
ejpam-6535	634	38	cauchy	cauchy	ADJ
ejpam-6535	634	39	groups	group	NOUN
ejpam-6535	634	40	,	,	PUNCT
ejpam-6535	634	41	then	then	ADV
ejpam-6535	634	42	f	f	X
ejpam-6535	634	43	:	:	PUNCT
ejpam-6535	634	44	(	(	PUNCT
ejpam-6535	634	45	s	s	X
ejpam-6535	634	46	,	,	PUNCT
ejpam-6535	634	47	·	·	PUNCT
ejpam-6535	634	48	,	,	PUNCT
ejpam-6535	634	49	ccφ	ccφ	X
ejpam-6535	634	50	)	)	PUNCT
ejpam-6535	634	51	−→	−→	NOUN
ejpam-6535	634	52	(	(	PUNCT
ejpam-6535	634	53	s′	s′	PROPN
ejpam-6535	634	54	,	,	PUNCT
ejpam-6535	634	55	·	·	PUNCT
ejpam-6535	634	56	,	,	PUNCT
ejpam-6535	634	57	cc′φ	cc′φ	PROPN
ejpam-6535	634	58	)	)	PUNCT
ejpam-6535	634	59	is	be	AUX
ejpam-6535	634	60	a	a	DET
ejpam-6535	634	61	continuous	continuous	ADJ
ejpam-6535	634	62	mapping	mapping	NOUN
ejpam-6535	634	63	between	between	ADP
ejpam-6535	634	64	associated	associated	ADJ
ejpam-6535	634	65	probabilistic	probabilistic	ADJ
ejpam-6535	634	66	convergence	convergence	NOUN
ejpam-6535	634	67	spaces	space	NOUN
ejpam-6535	634	68	;	;	PUNCT
ejpam-6535	634	69	(	(	PUNCT
ejpam-6535	634	70	b	b	X
ejpam-6535	634	71	)	)	PUNCT
ejpam-6535	634	72	let	let	VERB
ejpam-6535	634	73	(	(	PUNCT
ejpam-6535	634	74	s	s	X
ejpam-6535	634	75	,	,	PUNCT
ejpam-6535	634	76	·	·	PUNCT
ejpam-6535	634	77	,	,	PUNCT
ejpam-6535	634	78	c	c	X
ejpam-6535	634	79	=	=	SYM
ejpam-6535	634	80	(	(	PUNCT
ejpam-6535	634	81	cφ)φ∈∆+	cφ)φ∈∆+	NOUN
ejpam-6535	634	82	)	)	PUNCT
ejpam-6535	634	83	,	,	PUNCT
ejpam-6535	634	84	(	(	PUNCT
ejpam-6535	634	85	s′	s′	X
ejpam-6535	634	86	,	,	PUNCT
ejpam-6535	634	87	·	·	PUNCT
ejpam-6535	634	88	,	,	PUNCT
ejpam-6535	634	89	c′	c′	NOUN
ejpam-6535	634	90	=	=	SYM
ejpam-6535	634	91	(	(	PUNCT
ejpam-6535	634	92	c′φ)φ∈∆+	c′φ)φ∈∆+	INTJ
ejpam-6535	634	93	)	)	PUNCT
ejpam-6535	634	94	∈	∈	PROPN
ejpam-6535	634	95	|snplimgrp|	|snplimgrp|	NUM
ejpam-6535	634	96	.	.	PUNCT
ejpam-6535	635	1	if	if	SCONJ
ejpam-6535	635	2	for	for	ADP
ejpam-6535	635	3	each	each	DET
ejpam-6535	635	4	φ	φ	PROPN
ejpam-6535	635	5	∈	∈	PROPN
ejpam-6535	635	6	∆+	∆+	NOUN
ejpam-6535	635	7	,	,	PUNCT
ejpam-6535	635	8	f	f	X
ejpam-6535	635	9	:	:	PUNCT
ejpam-6535	635	10	(	(	PUNCT
ejpam-6535	635	11	s	s	X
ejpam-6535	635	12	,	,	PUNCT
ejpam-6535	635	13	·	·	PUNCT
ejpam-6535	635	14	,	,	PUNCT
ejpam-6535	635	15	cφ	cφ	NOUN
ejpam-6535	635	16	)	)	PUNCT
ejpam-6535	635	17	−→	−→	NOUN
ejpam-6535	635	18	(	(	PUNCT
ejpam-6535	635	19	s′	s′	PROPN
ejpam-6535	635	20	,	,	PUNCT
ejpam-6535	635	21	·	·	PUNCT
ejpam-6535	635	22	,	,	PUNCT
ejpam-6535	635	23	c′φ	c′φ	PROPN
ejpam-6535	635	24	)	)	PUNCT
ejpam-6535	635	25	is	be	AUX
ejpam-6535	635	26	a	a	DET
ejpam-6535	635	27	continuous	continuous	ADJ
ejpam-6535	635	28	group	group	NOUN
ejpam-6535	635	29	-	-	PUNCT
ejpam-6535	635	30	homomorphism	homomorphism	NOUN
ejpam-6535	635	31	,	,	PUNCT
ejpam-6535	635	32	then	then	ADV
ejpam-6535	635	33	f	f	X
ejpam-6535	635	34	:	:	PUNCT
ejpam-6535	635	35	(	(	PUNCT
ejpam-6535	635	36	ccφ	ccφ	NOUN
ejpam-6535	635	37	)	)	PUNCT
ejpam-6535	635	38	−→	−→	NOUN
ejpam-6535	635	39	(	(	PUNCT
ejpam-6535	635	40	s′	s′	PROPN
ejpam-6535	635	41	,	,	PUNCT
ejpam-6535	635	42	·	·	PUNCT
ejpam-6535	635	43	,	,	PUNCT
ejpam-6535	635	44	cc′φ	cc′φ	PROPN
ejpam-6535	635	45	)	)	PUNCT
ejpam-6535	635	46	is	be	AUX
ejpam-6535	635	47	cauchy	cauchy	NOUN
ejpam-6535	635	48	-	-	PUNCT
ejpam-6535	635	49	continuous	continuous	ADJ
ejpam-6535	635	50	between	between	ADP
ejpam-6535	635	51	probabilistic	probabilistic	ADJ
ejpam-6535	635	52	pre	pre	ADJ
ejpam-6535	635	53	-	-	ADJ
ejpam-6535	635	54	cauchy	cauchy	ADJ
ejpam-6535	635	55	groups	group	NOUN
ejpam-6535	635	56	.	.	PUNCT
ejpam-6535	636	1	proof	proof	NOUN
ejpam-6535	636	2	.	.	PUNCT
ejpam-6535	637	1	(	(	PUNCT
ejpam-6535	637	2	a	a	X
ejpam-6535	637	3	)	)	PUNCT
ejpam-6535	637	4	let	let	VERB
ejpam-6535	637	5	p	p	PROPN
ejpam-6535	637	6	∈	∈	PROPN
ejpam-6535	637	7	s	s	PROPN
ejpam-6535	637	8	,	,	PUNCT
ejpam-6535	637	9	f	f	PROPN
ejpam-6535	637	10	∈	∈	PROPN
ejpam-6535	637	11	f(s	f(	NOUN
ejpam-6535	637	12	)	)	PUNCT
ejpam-6535	637	13	,	,	PUNCT
ejpam-6535	637	14	and	and	CCONJ
ejpam-6535	637	15	φ	φ	NUM
ejpam-6535	637	16	∈	∈	PROPN
ejpam-6535	637	17	∆+	∆+	NOUN
ejpam-6535	637	18	.	.	PUNCT
ejpam-6535	638	1	now	now	ADV
ejpam-6535	638	2	if	if	SCONJ
ejpam-6535	638	3	p	p	PROPN
ejpam-6535	638	4	∈	∈	PROPN
ejpam-6535	638	5	ccφ(f	ccφ(f	PROPN
ejpam-6535	638	6	)	)	PUNCT
ejpam-6535	638	7	,	,	PUNCT
ejpam-6535	638	8	then	then	ADV
ejpam-6535	638	9	we	we	PRON
ejpam-6535	638	10	have	have	VERB
ejpam-6535	638	11	[	[	X
ejpam-6535	638	12	p]∧f	p]∧f	NUM
ejpam-6535	638	13	∈	∈	PROPN
ejpam-6535	638	14	c	c	NOUN
ejpam-6535	638	15	and	and	CCONJ
ejpam-6535	638	16	then	then	ADV
ejpam-6535	638	17	by	by	ADP
ejpam-6535	638	18	cauchy	cauchy	NOUN
ejpam-6535	638	19	-	-	PUNCT
ejpam-6535	638	20	continuity	continuity	NOUN
ejpam-6535	638	21	,	,	PUNCT
ejpam-6535	638	22	f	f	X
ejpam-6535	639	1	(	(	PUNCT
ejpam-6535	639	2	[	[	X
ejpam-6535	639	3	p	p	X
ejpam-6535	639	4	]	]	X
ejpam-6535	639	5	∧	∧	PROPN
ejpam-6535	639	6	f	f	X
ejpam-6535	639	7	)	)	PUNCT
ejpam-6535	639	8	∈	∈	PROPN
ejpam-6535	639	9	c′φ	c′φ	PROPN
ejpam-6535	639	10	,	,	PUNCT
ejpam-6535	639	11	and	and	CCONJ
ejpam-6535	639	12	upon	upon	SCONJ
ejpam-6535	639	13	using	use	VERB
ejpam-6535	639	14	lemma	lemma	PROPN
ejpam-6535	639	15	2	2	PROPN
ejpam-6535	639	16	and	and	CCONJ
ejpam-6535	639	17	(	(	PUNCT
ejpam-6535	639	18	pchs2	pchs2	NOUN
ejpam-6535	639	19	)	)	PUNCT
ejpam-6535	639	20	,	,	PUNCT
ejpam-6535	639	21	we	we	PRON
ejpam-6535	639	22	have	have	VERB
ejpam-6535	639	23	f	f	X
ejpam-6535	639	24	(	(	PUNCT
ejpam-6535	639	25	[	[	X
ejpam-6535	639	26	p	p	X
ejpam-6535	639	27	]	]	X
ejpam-6535	639	28	∧	∧	PROPN
ejpam-6535	639	29	f	f	PROPN
ejpam-6535	639	30	)	)	PUNCT
ejpam-6535	639	31	≤	≤	NOUN
ejpam-6535	640	1	f([p	f([p	PROPN
ejpam-6535	640	2	]	]	X
ejpam-6535	640	3	)	)	PUNCT
ejpam-6535	640	4	∧	∧	PROPN
ejpam-6535	640	5	f(f	f(f	PROPN
ejpam-6535	640	6	)	)	PUNCT
ejpam-6535	640	7	=	=	PUNCT
ejpam-6535	641	1	[	[	X
ejpam-6535	641	2	f(p	f(p	PROPN
ejpam-6535	641	3	)	)	PUNCT
ejpam-6535	641	4	]	]	PUNCT
ejpam-6535	642	1	∧	∧	PROPN
ejpam-6535	642	2	f(f	f(f	PROPN
ejpam-6535	642	3	)	)	PUNCT
ejpam-6535	642	4	∈	∈	PROPN
ejpam-6535	642	5	c′φ	c′φ	PROPN
ejpam-6535	642	6	,	,	PUNCT
ejpam-6535	642	7	i.e.	i.e.	X
ejpam-6535	642	8	,	,	PUNCT
ejpam-6535	642	9	[	[	X
ejpam-6535	642	10	f(p	f(p	NOUN
ejpam-6535	642	11	)	)	PUNCT
ejpam-6535	642	12	]	]	PUNCT
ejpam-6535	643	1	∧	∧	PROPN
ejpam-6535	643	2	f(f	f(f	PROPN
ejpam-6535	643	3	)	)	PUNCT
ejpam-6535	643	4	∈	∈	PROPN
ejpam-6535	643	5	c′φ	c′φ	PROPN
ejpam-6535	643	6	which	which	PRON
ejpam-6535	643	7	in	in	ADP
ejpam-6535	643	8	turn	turn	NOUN
ejpam-6535	643	9	yields	yield	NOUN
ejpam-6535	643	10	that	that	SCONJ
ejpam-6535	643	11	f(p	f(p	NOUN
ejpam-6535	643	12	)	)	PUNCT
ejpam-6535	643	13	∈	∈	PROPN
ejpam-6535	643	14	cc	cc	NOUN
ejpam-6535	643	15	′	′	NUM
ejpam-6535	643	16	φ(f(f	φ(f(f	NOUN
ejpam-6535	643	17	)	)	PUNCT
ejpam-6535	643	18	.	.	PUNCT
ejpam-6535	644	1	(	(	PUNCT
ejpam-6535	644	2	b	b	X
ejpam-6535	644	3	)	)	PUNCT
ejpam-6535	644	4	let	let	VERB
ejpam-6535	644	5	f	f	PROPN
ejpam-6535	644	6	∈	∈	PROPN
ejpam-6535	644	7	cc	cc	PROPN
ejpam-6535	644	8	.	.	PUNCT
ejpam-6535	644	9	then	then	ADV
ejpam-6535	644	10	e	e	PROPN
ejpam-6535	644	11	∈	∈	PROPN
ejpam-6535	644	12	cφ	cφ	X
ejpam-6535	645	1	(	(	PUNCT
ejpam-6535	645	2	f−1	f−1	PROPN
ejpam-6535	645	3	⊙	⊙	PROPN
ejpam-6535	645	4	f	f	PROPN
ejpam-6535	645	5	)	)	PUNCT
ejpam-6535	645	6	implies	imply	VERB
ejpam-6535	645	7	e	e	NOUN
ejpam-6535	645	8	=	=	SYM
ejpam-6535	645	9	f(e	f(e	NOUN
ejpam-6535	645	10	)	)	PUNCT
ejpam-6535	645	11	∈	∈	PROPN
ejpam-6535	645	12	c′φ	c′φ	PROPN
ejpam-6535	645	13	(	(	PUNCT
ejpam-6535	645	14	f(f−1	f(f−1	PROPN
ejpam-6535	645	15	⊙	⊙	PROPN
ejpam-6535	645	16	f	f	NOUN
ejpam-6535	645	17	)	)	PUNCT
ejpam-6535	645	18	)	)	PUNCT
ejpam-6535	646	1	=	=	SYM
ejpam-6535	646	2	c′φ	c′φ	PROPN
ejpam-6535	646	3	(	(	PUNCT
ejpam-6535	646	4	f(f)−1	f(f)−1	PROPN
ejpam-6535	646	5	⊙	⊙	PROPN
ejpam-6535	646	6	f(f	f(f	PROPN
ejpam-6535	646	7	)	)	PUNCT
ejpam-6535	646	8	)	)	PUNCT
ejpam-6535	646	9	by	by	ADP
ejpam-6535	646	10	using	use	VERB
ejpam-6535	646	11	lemma	lemma	PROPN
ejpam-6535	646	12	2(k),(l	2(k),(l	X
ejpam-6535	646	13	)	)	PUNCT
ejpam-6535	646	14	.	.	PUNCT
ejpam-6535	647	1	hence	hence	ADV
ejpam-6535	647	2	e	e	PROPN
ejpam-6535	647	3	∈	∈	PROPN
ejpam-6535	647	4	c′φ	c′φ	PROPN
ejpam-6535	647	5	(	(	PUNCT
ejpam-6535	647	6	f(f)−1	f(f)−1	PROPN
ejpam-6535	647	7	⊙	⊙	PROPN
ejpam-6535	647	8	f(f	f(f	PROPN
ejpam-6535	647	9	)	)	PUNCT
ejpam-6535	647	10	)	)	PUNCT
ejpam-6535	647	11	proving	prove	VERB
ejpam-6535	647	12	that	that	SCONJ
ejpam-6535	647	13	f(f	f(f	PROPN
ejpam-6535	647	14	)	)	PUNCT
ejpam-6535	647	15	∈	∈	PROPN
ejpam-6535	647	16	cc	cc	NOUN
ejpam-6535	647	17	′	′	NUM
ejpam-6535	647	18	.	.	PUNCT
ejpam-6535	648	1	8	8	X
ejpam-6535	648	2	.	.	X
ejpam-6535	648	3	category	category	NOUN
ejpam-6535	648	4	of	of	ADP
ejpam-6535	648	5	probabilistic	probabilistic	ADJ
ejpam-6535	648	6	normed	normed	ADJ
ejpam-6535	648	7	groups	group	NOUN
ejpam-6535	648	8	definition	definition	NOUN
ejpam-6535	648	9	12	12	NUM
ejpam-6535	648	10	.	.	PUNCT
ejpam-6535	649	1	[	[	X
ejpam-6535	649	2	3	3	NUM
ejpam-6535	649	3	,	,	PUNCT
ejpam-6535	649	4	25	25	NUM
ejpam-6535	649	5	]	]	PUNCT
ejpam-6535	649	6	let	let	VERB
ejpam-6535	649	7	(	(	PUNCT
ejpam-6535	649	8	s	s	X
ejpam-6535	649	9	,	,	PUNCT
ejpam-6535	649	10	·	·	PUNCT
ejpam-6535	649	11	)	)	PUNCT
ejpam-6535	649	12	be	be	AUX
ejpam-6535	649	13	a	a	DET
ejpam-6535	649	14	group	group	NOUN
ejpam-6535	649	15	.	.	PUNCT
ejpam-6535	650	1	a	a	DET
ejpam-6535	650	2	probabilistic	probabilistic	ADJ
ejpam-6535	650	3	metric	metric	ADJ
ejpam-6535	650	4	f	f	NOUN
ejpam-6535	650	5	:	:	PUNCT
ejpam-6535	650	6	s	s	VERB
ejpam-6535	650	7	×	×	NOUN
ejpam-6535	650	8	s	s	PART
ejpam-6535	650	9	−→	−→	NOUN
ejpam-6535	650	10	∆+	∆+	NUM
ejpam-6535	650	11	under	under	ADP
ejpam-6535	650	12	a	a	DET
ejpam-6535	650	13	triangle	triangle	NOUN
ejpam-6535	650	14	function	function	NOUN
ejpam-6535	650	15	τ	τ	PROPN
ejpam-6535	650	16	is	be	AUX
ejpam-6535	650	17	called	call	VERB
ejpam-6535	650	18	left	left	ADJ
ejpam-6535	650	19	-	-	PUNCT
ejpam-6535	650	20	invariant	invariant	ADJ
ejpam-6535	651	1	if	if	SCONJ
ejpam-6535	651	2	f	f	PROPN
ejpam-6535	651	3	(	(	PUNCT
ejpam-6535	651	4	zx	zx	PROPN
ejpam-6535	651	5	,	,	PUNCT
ejpam-6535	651	6	zy	zy	NOUN
ejpam-6535	651	7	)	)	PUNCT
ejpam-6535	651	8	=	=	SYM
ejpam-6535	651	9	f	f	X
ejpam-6535	651	10	(	(	PUNCT
ejpam-6535	651	11	x	x	PROPN
ejpam-6535	651	12	,	,	PUNCT
ejpam-6535	651	13	y	y	PROPN
ejpam-6535	651	14	)	)	PUNCT
ejpam-6535	651	15	,	,	PUNCT
ejpam-6535	651	16	right	right	ADJ
ejpam-6535	651	17	-	-	PUNCT
ejpam-6535	651	18	invariant	invariant	ADJ
ejpam-6535	651	19	if	if	SCONJ
ejpam-6535	651	20	f	f	PROPN
ejpam-6535	651	21	(	(	PUNCT
ejpam-6535	651	22	xz	xz	PROPN
ejpam-6535	651	23	,	,	PUNCT
ejpam-6535	651	24	yz	yz	PROPN
ejpam-6535	651	25	)	)	PUNCT
ejpam-6535	652	1	=	=	SYM
ejpam-6535	652	2	f	f	PROPN
ejpam-6535	652	3	(	(	PUNCT
ejpam-6535	652	4	x	x	PROPN
ejpam-6535	652	5	,	,	PUNCT
ejpam-6535	652	6	y	y	PROPN
ejpam-6535	652	7	)	)	PUNCT
ejpam-6535	652	8	,	,	PUNCT
ejpam-6535	652	9	and	and	CCONJ
ejpam-6535	652	10	invariant	invariant	ADJ
ejpam-6535	652	11	if	if	SCONJ
ejpam-6535	652	12	f	f	PROPN
ejpam-6535	652	13	(	(	PUNCT
ejpam-6535	652	14	zx	zx	PROPN
ejpam-6535	652	15	,	,	PUNCT
ejpam-6535	652	16	zy	zy	NOUN
ejpam-6535	652	17	)	)	PUNCT
ejpam-6535	652	18	=	=	SYM
ejpam-6535	653	1	f	f	PROPN
ejpam-6535	653	2	(	(	PUNCT
ejpam-6535	653	3	xz	xz	PROPN
ejpam-6535	653	4	,	,	PUNCT
ejpam-6535	653	5	yz	yz	PROPN
ejpam-6535	653	6	)	)	PUNCT
ejpam-6535	653	7	=	=	SYM
ejpam-6535	654	1	f	f	PROPN
ejpam-6535	654	2	(	(	PUNCT
ejpam-6535	654	3	x	x	PROPN
ejpam-6535	654	4	,	,	PUNCT
ejpam-6535	654	5	y	y	PROPN
ejpam-6535	654	6	)	)	PUNCT
ejpam-6535	654	7	,	,	PUNCT
ejpam-6535	654	8	for	for	ADP
ejpam-6535	654	9	all	all	DET
ejpam-6535	654	10	x	x	NOUN
ejpam-6535	654	11	,	,	PUNCT
ejpam-6535	654	12	y	y	PROPN
ejpam-6535	654	13	,	,	PUNCT
ejpam-6535	654	14	z	z	PROPN
ejpam-6535	654	15	∈	∈	PROPN
ejpam-6535	654	16	s.	s.	PROPN
ejpam-6535	654	17	definition	definition	NOUN
ejpam-6535	654	18	13	13	NUM
ejpam-6535	654	19	.	.	PUNCT
ejpam-6535	655	1	[	[	X
ejpam-6535	655	2	3	3	X
ejpam-6535	655	3	]	]	PUNCT
ejpam-6535	655	4	a	a	DET
ejpam-6535	655	5	triple	triple	ADJ
ejpam-6535	655	6	(	(	PUNCT
ejpam-6535	655	7	s	s	NOUN
ejpam-6535	655	8	,	,	PUNCT
ejpam-6535	655	9	·	·	PUNCT
ejpam-6535	655	10	,	,	PUNCT
ejpam-6535	655	11	f	f	PROPN
ejpam-6535	655	12	)	)	PUNCT
ejpam-6535	655	13	is	be	AUX
ejpam-6535	655	14	called	call	VERB
ejpam-6535	655	15	a	a	DET
ejpam-6535	655	16	probabilistic	probabilistic	ADJ
ejpam-6535	655	17	metric	metric	ADJ
ejpam-6535	655	18	group	group	NOUN
ejpam-6535	655	19	if	if	SCONJ
ejpam-6535	655	20	(	(	PUNCT
ejpam-6535	655	21	s	s	X
ejpam-6535	655	22	,	,	PUNCT
ejpam-6535	655	23	·	·	PUNCT
ejpam-6535	655	24	)	)	PUNCT
ejpam-6535	655	25	is	be	AUX
ejpam-6535	655	26	a	a	DET
ejpam-6535	655	27	group	group	NOUN
ejpam-6535	655	28	and	and	CCONJ
ejpam-6535	655	29	(	(	PUNCT
ejpam-6535	655	30	s	s	PROPN
ejpam-6535	655	31	,	,	PUNCT
ejpam-6535	655	32	f	f	PROPN
ejpam-6535	655	33	)	)	PUNCT
ejpam-6535	655	34	is	be	AUX
ejpam-6535	655	35	a	a	DET
ejpam-6535	655	36	probabilistic	probabilistic	ADJ
ejpam-6535	655	37	metric	metric	ADJ
ejpam-6535	655	38	space	space	NOUN
ejpam-6535	655	39	under	under	ADP
ejpam-6535	655	40	the	the	DET
ejpam-6535	655	41	triangle	triangle	NOUN
ejpam-6535	655	42	function	function	NOUN
ejpam-6535	655	43	τ	τ	PRON
ejpam-6535	655	44	such	such	DET
ejpam-6535	655	45	the	the	DET
ejpam-6535	655	46	mappings	mapping	NOUN
ejpam-6535	655	47	m	m	VERB
ejpam-6535	655	48	:	:	PUNCT
ejpam-6535	655	49	(	(	PUNCT
ejpam-6535	655	50	s	s	AUX
ejpam-6535	655	51	×	×	NOUN
ejpam-6535	655	52	s	s	PROPN
ejpam-6535	655	53	,	,	PUNCT
ejpam-6535	655	54	f	f	PROPN
ejpam-6535	655	55	⊗	⊗	PROPN
ejpam-6535	655	56	f	f	PROPN
ejpam-6535	655	57	)	)	PUNCT
ejpam-6535	655	58	−→	−→	NOUN
ejpam-6535	655	59	(	(	PUNCT
ejpam-6535	655	60	s	s	PROPN
ejpam-6535	655	61	,	,	PUNCT
ejpam-6535	655	62	f	f	PROPN
ejpam-6535	655	63	)	)	PUNCT
ejpam-6535	655	64	,	,	PUNCT
ejpam-6535	655	65	(	(	PUNCT
ejpam-6535	655	66	p	p	X
ejpam-6535	655	67	,	,	PUNCT
ejpam-6535	655	68	q	q	NOUN
ejpam-6535	655	69	)	)	PUNCT
ejpam-6535	655	70	7→	7→	NUM
ejpam-6535	655	71	pq	pq	NOUN
ejpam-6535	655	72	and	and	CCONJ
ejpam-6535	655	73	ȷ	ȷ	NOUN
ejpam-6535	655	74	:	:	PUNCT
ejpam-6535	655	75	(	(	PUNCT
ejpam-6535	655	76	s	s	X
ejpam-6535	655	77	,	,	PUNCT
ejpam-6535	655	78	f	f	NOUN
ejpam-6535	655	79	)	)	PUNCT
ejpam-6535	655	80	−→	−→	NOUN
ejpam-6535	655	81	(	(	PUNCT
ejpam-6535	655	82	s	s	PROPN
ejpam-6535	655	83	,	,	PUNCT
ejpam-6535	655	84	f	f	PROPN
ejpam-6535	655	85	)	)	PUNCT
ejpam-6535	655	86	,	,	PUNCT
ejpam-6535	655	87	p	p	PROPN
ejpam-6535	655	88	7→	7→	NUM
ejpam-6535	655	89	p−1	p−1	PROPN
ejpam-6535	655	90	are	be	AUX
ejpam-6535	655	91	non	non	ADJ
ejpam-6535	655	92	-	-	ADJ
ejpam-6535	655	93	expansive	expansive	ADJ
ejpam-6535	655	94	,	,	PUNCT
ejpam-6535	655	95	where	where	SCONJ
ejpam-6535	655	96	the	the	DET
ejpam-6535	655	97	product	product	NOUN
ejpam-6535	655	98	probabilistic	probabilistic	VERB
ejpam-6535	655	99	metric	metric	ADJ
ejpam-6535	655	100	f	f	PROPN
ejpam-6535	655	101	⊗	⊗	PROPN
ejpam-6535	655	102	f	f	PROPN
ejpam-6535	655	103	on	on	ADP
ejpam-6535	655	104	s	s	PRON
ejpam-6535	655	105	×	×	NOUN
ejpam-6535	655	106	s	s	VERB
ejpam-6535	655	107	is	be	AUX
ejpam-6535	655	108	defined	define	VERB
ejpam-6535	655	109	by	by	ADP
ejpam-6535	655	110	[	[	X
ejpam-6535	655	111	38	38	NUM
ejpam-6535	655	112	]	]	PUNCT
ejpam-6535	655	113	f	f	PROPN
ejpam-6535	656	1	⊗	⊗	PROPN
ejpam-6535	656	2	f	f	PROPN
ejpam-6535	656	3	(	(	PUNCT
ejpam-6535	656	4	(	(	PUNCT
ejpam-6535	656	5	p1	p1	NOUN
ejpam-6535	656	6	,	,	PUNCT
ejpam-6535	656	7	p2	p2	PROPN
ejpam-6535	656	8	)	)	PUNCT
ejpam-6535	656	9	,	,	PUNCT
ejpam-6535	656	10	(	(	PUNCT
ejpam-6535	656	11	q1	q1	PROPN
ejpam-6535	656	12	,	,	PUNCT
ejpam-6535	656	13	q2	q2	NOUN
ejpam-6535	656	14	)	)	PUNCT
ejpam-6535	656	15	)	)	PUNCT
ejpam-6535	657	1	=	=	PUNCT
ejpam-6535	657	2	τ	τ	PROPN
ejpam-6535	657	3	(	(	PUNCT
ejpam-6535	657	4	fp1,q1	fp1,q1	NOUN
ejpam-6535	657	5	,	,	PUNCT
ejpam-6535	657	6	fp2,q2	fp2,q2	PROPN
ejpam-6535	657	7	)	)	PUNCT
ejpam-6535	657	8	,	,	PUNCT
ejpam-6535	657	9	∀(p1	∀(p1	PROPN
ejpam-6535	657	10	,	,	PUNCT
ejpam-6535	657	11	p2	p2	PROPN
ejpam-6535	657	12	)	)	PUNCT
ejpam-6535	657	13	,	,	PUNCT
ejpam-6535	657	14	(	(	PUNCT
ejpam-6535	657	15	q1	q1	PROPN
ejpam-6535	657	16	,	,	PUNCT
ejpam-6535	657	17	q2	q2	NOUN
ejpam-6535	657	18	)	)	PUNCT
ejpam-6535	657	19	∈	∈	PROPN
ejpam-6535	657	20	s	s	PART
ejpam-6535	657	21	×	×	NOUN
ejpam-6535	657	22	s.	s.	PROPN
ejpam-6535	657	23	it	it	PRON
ejpam-6535	657	24	is	be	AUX
ejpam-6535	657	25	pointed	point	VERB
ejpam-6535	657	26	out	out	ADP
ejpam-6535	657	27	in	in	ADP
ejpam-6535	657	28	[	[	X
ejpam-6535	657	29	3	3	X
ejpam-6535	657	30	]	]	PUNCT
ejpam-6535	657	31	that	that	SCONJ
ejpam-6535	657	32	a	a	DET
ejpam-6535	657	33	probabilistic	probabilistic	ADJ
ejpam-6535	657	34	metric	metric	ADJ
ejpam-6535	657	35	groups	group	NOUN
ejpam-6535	657	36	are	be	AUX
ejpam-6535	657	37	precisely	precisely	ADV
ejpam-6535	657	38	groups	group	NOUN
ejpam-6535	657	39	equipped	equip	VERB
ejpam-6535	657	40	with	with	ADP
ejpam-6535	657	41	invariant	invariant	ADJ
ejpam-6535	657	42	probabilistic	probabilistic	ADJ
ejpam-6535	657	43	metric	metric	NOUN
ejpam-6535	657	44	.	.	PUNCT
ejpam-6535	658	1	the	the	DET
ejpam-6535	658	2	category	category	NOUN
ejpam-6535	658	3	of	of	ADP
ejpam-6535	658	4	probabilistic	probabilistic	ADJ
ejpam-6535	658	5	metric	metric	ADJ
ejpam-6535	658	6	groups	group	NOUN
ejpam-6535	658	7	and	and	CCONJ
ejpam-6535	658	8	nonexpansive	nonexpansive	PROPN
ejpam-6535	658	9	group	group	NOUN
ejpam-6535	658	10	-	-	PUNCT
ejpam-6535	658	11	homomorphisms	homomorphisms	PROPN
ejpam-6535	658	12	is	be	AUX
ejpam-6535	658	13	denoted	denote	VERB
ejpam-6535	658	14	by	by	ADP
ejpam-6535	658	15	pmetgrp	pmetgrp	PROPN
ejpam-6535	658	16	.	.	PUNCT
ejpam-6535	659	1	definition	definition	NOUN
ejpam-6535	659	2	14	14	NUM
ejpam-6535	659	3	.	.	PUNCT
ejpam-6535	660	1	[	[	X
ejpam-6535	660	2	3	3	X
ejpam-6535	660	3	]	]	PUNCT
ejpam-6535	660	4	a	a	DET
ejpam-6535	660	5	mapping	mapping	NOUN
ejpam-6535	660	6	ν	ν	NOUN
ejpam-6535	660	7	:	:	PUNCT
ejpam-6535	660	8	s	s	AUX
ejpam-6535	660	9	−→	−→	ADJ
ejpam-6535	660	10	∆+	∆+	NUM
ejpam-6535	660	11	is	be	AUX
ejpam-6535	660	12	called	call	VERB
ejpam-6535	660	13	probabilistic	probabilistic	ADJ
ejpam-6535	660	14	norm	norm	NOUN
ejpam-6535	660	15	group	group	NOUN
ejpam-6535	660	16	on	on	ADP
ejpam-6535	660	17	s	s	PRON
ejpam-6535	660	18	under	under	ADP
ejpam-6535	660	19	a	a	DET
ejpam-6535	660	20	triangle	triangle	NOUN
ejpam-6535	660	21	function	function	NOUN
ejpam-6535	660	22	τ	τ	X
ejpam-6535	660	23	if	if	SCONJ
ejpam-6535	660	24	for	for	ADP
ejpam-6535	660	25	all	all	DET
ejpam-6535	660	26	p	p	NOUN
ejpam-6535	660	27	,	,	PUNCT
ejpam-6535	660	28	q	q	ADJ
ejpam-6535	660	29	,	,	PUNCT
ejpam-6535	660	30	r	r	NOUN
ejpam-6535	660	31	∈	∈	PROPN
ejpam-6535	660	32	s	s	PART
ejpam-6535	660	33	:	:	PUNCT
ejpam-6535	660	34	(	(	PUNCT
ejpam-6535	660	35	pgn1	pgn1	NOUN
ejpam-6535	660	36	)	)	PUNCT
ejpam-6535	660	37	ν(p	ν(p	PROPN
ejpam-6535	660	38	)	)	PUNCT
ejpam-6535	660	39	=	=	VERB
ejpam-6535	660	40	ϵ0	ϵ0	VERB
ejpam-6535	661	1	if	if	SCONJ
ejpam-6535	661	2	and	and	CCONJ
ejpam-6535	661	3	only	only	ADV
ejpam-6535	661	4	if	if	SCONJ
ejpam-6535	661	5	p	p	X
ejpam-6535	661	6	=	=	SYM
ejpam-6535	661	7	e	e	NOUN
ejpam-6535	661	8	;	;	PUNCT
ejpam-6535	661	9	(	(	PUNCT
ejpam-6535	661	10	png2	png2	NOUN
ejpam-6535	661	11	)	)	PUNCT
ejpam-6535	661	12	ν(p−1	ν(p−1	PROPN
ejpam-6535	661	13	)	)	PUNCT
ejpam-6535	661	14	=	=	SYM
ejpam-6535	661	15	ν(p	ν(p	PROPN
ejpam-6535	661	16	)	)	PUNCT
ejpam-6535	661	17	;	;	PUNCT
ejpam-6535	661	18	(	(	PUNCT
ejpam-6535	661	19	png3	png3	PROPN
ejpam-6535	661	20	)	)	PUNCT
ejpam-6535	661	21	τ	τ	PROPN
ejpam-6535	661	22	(	(	PUNCT
ejpam-6535	661	23	ν(p	ν(p	PROPN
ejpam-6535	661	24	)	)	PUNCT
ejpam-6535	661	25	,	,	PUNCT
ejpam-6535	661	26	ν(q	ν(q	NOUN
ejpam-6535	661	27	)	)	PUNCT
ejpam-6535	661	28	)	)	PUNCT
ejpam-6535	661	29	≤	≤	NOUN
ejpam-6535	661	30	ν(pq	ν(pq	PROPN
ejpam-6535	661	31	)	)	PUNCT
ejpam-6535	661	32	.	.	PUNCT
ejpam-6535	662	1	we	we	PRON
ejpam-6535	662	2	call	call	VERB
ejpam-6535	662	3	the	the	DET
ejpam-6535	662	4	quadruple	quadruple	NOUN
ejpam-6535	662	5	(	(	PUNCT
ejpam-6535	662	6	s	s	X
ejpam-6535	662	7	,	,	PUNCT
ejpam-6535	662	8	·	·	PUNCT
ejpam-6535	662	9	,	,	PUNCT
ejpam-6535	662	10	ν	ν	PROPN
ejpam-6535	662	11	,	,	PUNCT
ejpam-6535	662	12	τ	τ	X
ejpam-6535	662	13	)	)	PUNCT
ejpam-6535	662	14	of	of	ADP
ejpam-6535	662	15	a	a	DET
ejpam-6535	662	16	group	group	NOUN
ejpam-6535	662	17	(	(	PUNCT
ejpam-6535	662	18	s	s	PROPN
ejpam-6535	662	19	,	,	PUNCT
ejpam-6535	662	20	·	·	PUNCT
ejpam-6535	662	21	)	)	PUNCT
ejpam-6535	662	22	and	and	CCONJ
ejpam-6535	662	23	a	a	DET
ejpam-6535	662	24	probabilistic	probabilistic	ADJ
ejpam-6535	662	25	group	group	NOUN
ejpam-6535	662	26	norm	norm	NOUN
ejpam-6535	662	27	ν	ν	NOUN
ejpam-6535	662	28	on	on	ADP
ejpam-6535	662	29	s	s	PRON
ejpam-6535	662	30	a	a	DET
ejpam-6535	662	31	probabilistic	probabilistic	ADJ
ejpam-6535	662	32	normed	normed	ADJ
ejpam-6535	662	33	group	group	NOUN
ejpam-6535	662	34	.	.	PUNCT
ejpam-6535	663	1	let	let	VERB
ejpam-6535	663	2	the	the	DET
ejpam-6535	663	3	category	category	NOUN
ejpam-6535	663	4	of	of	ADP
ejpam-6535	663	5	probabilistic	probabilistic	ADJ
ejpam-6535	663	6	normed	normed	ADJ
ejpam-6535	663	7	groups	group	NOUN
ejpam-6535	663	8	with	with	ADP
ejpam-6535	663	9	abelian	abelian	PROPN
ejpam-6535	663	10	group	group	NOUN
ejpam-6535	663	11	norms	norm	VERB
ejpam-6535	663	12	as	as	ADP
ejpam-6535	663	13	objects	object	NOUN
ejpam-6535	663	14	and	and	CCONJ
ejpam-6535	663	15	norm	norm	NOUN
ejpam-6535	663	16	-	-	PUNCT
ejpam-6535	663	17	preserving	preserve	VERB
ejpam-6535	663	18	mappings	mapping	NOUN
ejpam-6535	663	19	as	as	SCONJ
ejpam-6535	663	20	morphisms	morphism	NOUN
ejpam-6535	663	21	be	be	AUX
ejpam-6535	663	22	denoted	denote	VERB
ejpam-6535	663	23	by	by	ADP
ejpam-6535	663	24	pnormedgrp	pnormedgrp	NOUN
ejpam-6535	663	25	.	.	PUNCT
ejpam-6535	664	1	theorem	theorem	NOUN
ejpam-6535	664	2	3	3	NUM
ejpam-6535	664	3	.	.	PUNCT
ejpam-6535	665	1	[	[	X
ejpam-6535	665	2	3	3	NUM
ejpam-6535	665	3	,	,	PUNCT
ejpam-6535	665	4	12	12	NUM
ejpam-6535	665	5	,	,	PUNCT
ejpam-6535	665	6	29	29	NUM
ejpam-6535	665	7	]	]	PUNCT
ejpam-6535	665	8	let	let	VERB
ejpam-6535	665	9	(	(	PUNCT
ejpam-6535	665	10	s	s	X
ejpam-6535	665	11	,	,	PUNCT
ejpam-6535	665	12	·	·	PUNCT
ejpam-6535	665	13	,	,	PUNCT
ejpam-6535	665	14	ν	ν	PROPN
ejpam-6535	665	15	,	,	PUNCT
ejpam-6535	665	16	τ	τ	X
ejpam-6535	665	17	)	)	PUNCT
ejpam-6535	665	18	be	be	VERB
ejpam-6535	665	19	a	a	DET
ejpam-6535	665	20	probabilistic	probabilistic	ADJ
ejpam-6535	665	21	normed	normed	ADJ
ejpam-6535	665	22	group	group	NOUN
ejpam-6535	665	23	.	.	PUNCT
ejpam-6535	666	1	then	then	ADV
ejpam-6535	666	2	fp	fp	X
ejpam-6535	666	3	,	,	PUNCT
ejpam-6535	666	4	q	q	NOUN
ejpam-6535	666	5	=	=	NOUN
ejpam-6535	666	6	ν(pq−1	ν(pq−1	X
ejpam-6535	666	7	)	)	PUNCT
ejpam-6535	666	8	is	be	AUX
ejpam-6535	666	9	a	a	DET
ejpam-6535	666	10	right	right	ADJ
ejpam-6535	666	11	-	-	PUNCT
ejpam-6535	666	12	invariant	invariant	ADJ
ejpam-6535	666	13	probabilistic	probabilistic	ADJ
ejpam-6535	666	14	metric	metric	NOUN
ejpam-6535	666	15	on	on	ADP
ejpam-6535	666	16	s.	s.	PROPN
ejpam-6535	666	17	also	also	ADV
ejpam-6535	666	18	,	,	PUNCT
ejpam-6535	666	19	f̃p	f̃p	NOUN
ejpam-6535	666	20	,	,	PUNCT
ejpam-6535	666	21	q	q	NOUN
ejpam-6535	666	22	=	=	PUNCT
ejpam-6535	666	23	fp−1,q−1	fp−1,q−1	NOUN
ejpam-6535	666	24	=	=	SYM
ejpam-6535	666	25	ν(p−1q	ν(p−1q	NOUN
ejpam-6535	666	26	)	)	PUNCT
ejpam-6535	666	27	is	be	AUX
ejpam-6535	666	28	a	a	DET
ejpam-6535	666	29	left	left	ADJ
ejpam-6535	666	30	-	-	PUNCT
ejpam-6535	666	31	invariant	invariant	ADJ
ejpam-6535	666	32	probabilistic	probabilistic	ADJ
ejpam-6535	666	33	metric	metric	NOUN
ejpam-6535	666	34	on	on	ADP
ejpam-6535	666	35	s.	s.	PROPN
ejpam-6535	666	36	conversely	conversely	ADV
ejpam-6535	666	37	,	,	PUNCT
ejpam-6535	666	38	if	if	SCONJ
ejpam-6535	666	39	f	f	PROPN
ejpam-6535	666	40	is	be	AUX
ejpam-6535	666	41	a	a	DET
ejpam-6535	666	42	right	right	ADJ
ejpam-6535	666	43	invariant	invariant	ADJ
ejpam-6535	666	44	probabilistic	probabilistic	ADJ
ejpam-6535	666	45	metric	metric	NOUN
ejpam-6535	666	46	on	on	ADP
ejpam-6535	666	47	a	a	DET
ejpam-6535	666	48	group	group	NOUN
ejpam-6535	666	49	s	s	PART
ejpam-6535	666	50	and	and	CCONJ
ejpam-6535	666	51	τ	τ	PROPN
ejpam-6535	666	52	is	be	AUX
ejpam-6535	666	53	a	a	DET
ejpam-6535	666	54	continuous	continuous	ADJ
ejpam-6535	666	55	triangle	triangle	NOUN
ejpam-6535	666	56	function	function	NOUN
ejpam-6535	666	57	,	,	PUNCT
ejpam-6535	666	58	then	then	ADV
ejpam-6535	666	59	for	for	ADP
ejpam-6535	666	60	ν(x	ν(x	PROPN
ejpam-6535	666	61	)	)	PUNCT
ejpam-6535	666	62	=	=	SYM
ejpam-6535	666	63	fe	fe	X
ejpam-6535	666	64	,	,	PUNCT
ejpam-6535	666	65	p	p	NOUN
ejpam-6535	666	66	=	=	NOUN
ejpam-6535	666	67	f̃e	f̃e	NOUN
ejpam-6535	666	68	,	,	PUNCT
ejpam-6535	666	69	p	p	X
ejpam-6535	666	70	,	,	PUNCT
ejpam-6535	666	71	the	the	DET
ejpam-6535	666	72	quadruple	quadruple	NOUN
ejpam-6535	666	73	(	(	PUNCT
ejpam-6535	666	74	s	s	X
ejpam-6535	666	75	,	,	PUNCT
ejpam-6535	666	76	·	·	PUNCT
ejpam-6535	666	77	,	,	PUNCT
ejpam-6535	666	78	ν	ν	PROPN
ejpam-6535	666	79	,	,	PUNCT
ejpam-6535	666	80	τ	τ	X
ejpam-6535	666	81	)	)	PUNCT
ejpam-6535	666	82	is	be	AUX
ejpam-6535	666	83	a	a	DET
ejpam-6535	666	84	probabilistic	probabilistic	ADJ
ejpam-6535	666	85	normed	normed	ADJ
ejpam-6535	666	86	group	group	NOUN
ejpam-6535	666	87	.	.	PUNCT
ejpam-6535	667	1	consequently	consequently	ADV
ejpam-6535	667	2	,	,	PUNCT
ejpam-6535	667	3	probabilistic	probabilistic	ADJ
ejpam-6535	667	4	metric	metric	ADJ
ejpam-6535	667	5	f	f	PROPN
ejpam-6535	667	6	is	be	AUX
ejpam-6535	667	7	invariant	invariant	ADJ
ejpam-6535	667	8	of	of	ADP
ejpam-6535	667	9	and	and	CCONJ
ejpam-6535	667	10	only	only	ADV
ejpam-6535	667	11	if	if	SCONJ
ejpam-6535	667	12	ν(pq−1	ν(pq−1	NOUN
ejpam-6535	667	13	)	)	PUNCT
ejpam-6535	668	1	=	=	SYM
ejpam-6535	668	2	ν(p−1q	ν(p−1q	NOUN
ejpam-6535	668	3	)	)	PUNCT
ejpam-6535	668	4	=	=	SYM
ejpam-6535	669	1	ν(q−1p	ν(q−1p	NOUN
ejpam-6535	669	2	)	)	PUNCT
ejpam-6535	669	3	,	,	PUNCT
ejpam-6535	669	4	it	it	PRON
ejpam-6535	669	5	means	mean	VERB
ejpam-6535	669	6	that	that	SCONJ
ejpam-6535	669	7	the	the	DET
ejpam-6535	669	8	probabilistic	probabilistic	ADJ
ejpam-6535	669	9	group	group	NOUN
ejpam-6535	669	10	norm	norm	NOUN
ejpam-6535	669	11	ν	ν	NOUN
ejpam-6535	669	12	is	be	AUX
ejpam-6535	669	13	abelian	abelian	ADJ
ejpam-6535	669	14	.	.	PUNCT
ejpam-6535	670	1	furthermore	furthermore	ADV
ejpam-6535	670	2	,	,	PUNCT
ejpam-6535	670	3	for	for	ADP
ejpam-6535	670	4	a	a	DET
ejpam-6535	670	5	probabilistic	probabilistic	ADJ
ejpam-6535	670	6	norm	norm	NOUN
ejpam-6535	670	7	group	group	NOUN
ejpam-6535	670	8	(	(	PUNCT
ejpam-6535	670	9	s	s	PROPN
ejpam-6535	670	10	,	,	PUNCT
ejpam-6535	670	11	·	·	PUNCT
ejpam-6535	670	12	,	,	PUNCT
ejpam-6535	670	13	ν	ν	NOUN
ejpam-6535	670	14	)	)	PUNCT
ejpam-6535	670	15	,	,	PUNCT
ejpam-6535	670	16	the	the	DET
ejpam-6535	670	17	inversion	inversion	NOUN
ejpam-6535	670	18	ȷ	ȷ	NOUN
ejpam-6535	670	19	:	:	PUNCT
ejpam-6535	670	20	(	(	PUNCT
ejpam-6535	670	21	s	s	X
ejpam-6535	670	22	,	,	PUNCT
ejpam-6535	670	23	·	·	PUNCT
ejpam-6535	670	24	,	,	PUNCT
ejpam-6535	670	25	ν	ν	NOUN
ejpam-6535	670	26	)	)	PUNCT
ejpam-6535	670	27	−→	−→	NOUN
ejpam-6535	670	28	(	(	PUNCT
ejpam-6535	670	29	s	s	PROPN
ejpam-6535	670	30	,	,	PUNCT
ejpam-6535	670	31	·	·	PUNCT
ejpam-6535	670	32	,	,	PUNCT
ejpam-6535	670	33	f̃	f̃	PROPN
ejpam-6535	670	34	)	)	PUNCT
ejpam-6535	670	35	is	be	AUX
ejpam-6535	670	36	an	an	DET
ejpam-6535	670	37	isometry	isometry	NOUN
ejpam-6535	670	38	and	and	CCONJ
ejpam-6535	670	39	hence	hence	ADV
ejpam-6535	670	40	a	a	DET
ejpam-6535	670	41	homeomorphism	homeomorphism	NOUN
ejpam-6535	670	42	.	.	PUNCT
ejpam-6535	671	1	let	let	VERB
ejpam-6535	671	2	us	we	PRON
ejpam-6535	671	3	denote	denote	VERB
ejpam-6535	671	4	the	the	DET
ejpam-6535	671	5	class	class	NOUN
ejpam-6535	671	6	of	of	ADP
ejpam-6535	671	7	all	all	DET
ejpam-6535	671	8	left	left	ADJ
ejpam-6535	671	9	-	-	PUNCT
ejpam-6535	671	10	invariant	invariant	ADJ
ejpam-6535	671	11	(	(	PUNCT
ejpam-6535	671	12	resp	resp	NOUN
ejpam-6535	671	13	.	.	PUNCT
ejpam-6535	672	1	right	right	ADJ
ejpam-6535	672	2	-	-	PUNCT
ejpam-6535	672	3	invariant	invariant	ADJ
ejpam-6535	672	4	,	,	PUNCT
ejpam-6535	672	5	invariant	invariant	ADJ
ejpam-6535	672	6	)	)	PUNCT
ejpam-6535	672	7	probabilistic	probabilistic	ADJ
ejpam-6535	672	8	metrics	metric	NOUN
ejpam-6535	672	9	by	by	ADP
ejpam-6535	672	10	ltinvpmet	ltinvpmet	NOUN
ejpam-6535	672	11	(	(	PUNCT
ejpam-6535	672	12	resp	resp	NOUN
ejpam-6535	672	13	.	.	PUNCT
ejpam-6535	673	1	rtinvpmet	rtinvpmet	PROPN
ejpam-6535	673	2	,	,	PUNCT
ejpam-6535	673	3	invpmet	invpmet	ADJ
ejpam-6535	673	4	)	)	PUNCT
ejpam-6535	673	5	and	and	CCONJ
ejpam-6535	673	6	class	class	NOUN
ejpam-6535	673	7	of	of	ADP
ejpam-6535	673	8	all	all	DET
ejpam-6535	673	9	probabilistic	probabilistic	ADJ
ejpam-6535	673	10	group	group	NOUN
ejpam-6535	673	11	norms	norm	NOUN
ejpam-6535	673	12	by	by	ADP
ejpam-6535	673	13	pgrpn	pgrpn	NOUN
ejpam-6535	673	14	.	.	PUNCT
ejpam-6535	674	1	then	then	ADV
ejpam-6535	674	2	in	in	ADP
ejpam-6535	674	3	view	view	NOUN
ejpam-6535	674	4	of	of	ADP
ejpam-6535	674	5	the	the	DET
ejpam-6535	674	6	content	content	NOUN
ejpam-6535	674	7	of	of	ADP
ejpam-6535	674	8	the	the	DET
ejpam-6535	674	9	theorem	theorem	NOUN
ejpam-6535	674	10	5.3[6	5.3[6	NUM
ejpam-6535	674	11	]	]	PUNCT
ejpam-6535	674	12	and	and	CCONJ
ejpam-6535	674	13	the	the	DET
ejpam-6535	674	14	theorem	theorem	NOUN
ejpam-6535	674	15	7	7	NUM
ejpam-6535	674	16	,	,	PUNCT
ejpam-6535	674	17	we	we	PRON
ejpam-6535	674	18	have	have	VERB
ejpam-6535	674	19	the	the	DET
ejpam-6535	674	20	following	follow	VERB
ejpam-6535	674	21	theorem	theorem	VERB
ejpam-6535	674	22	.	.	PUNCT
ejpam-6535	674	23	theorem	theorem	NOUN
ejpam-6535	674	24	4	4	NUM
ejpam-6535	674	25	.	.	PUNCT
ejpam-6535	675	1	let	let	VERB
ejpam-6535	675	2	(	(	PUNCT
ejpam-6535	675	3	s	s	X
ejpam-6535	675	4	,	,	PUNCT
ejpam-6535	675	5	·	·	PUNCT
ejpam-6535	675	6	)	)	PUNCT
ejpam-6535	675	7	be	be	AUX
ejpam-6535	675	8	a	a	DET
ejpam-6535	675	9	group	group	NOUN
ejpam-6535	675	10	.	.	PUNCT
ejpam-6535	676	1	then	then	ADV
ejpam-6535	676	2	the	the	DET
ejpam-6535	676	3	following	follow	VERB
ejpam-6535	676	4	are	be	AUX
ejpam-6535	676	5	true	true	ADJ
ejpam-6535	676	6	:	:	PUNCT
ejpam-6535	676	7	(	(	PUNCT
ejpam-6535	676	8	a	a	X
ejpam-6535	676	9	)	)	PUNCT
ejpam-6535	676	10	there	there	PRON
ejpam-6535	676	11	is	be	VERB
ejpam-6535	676	12	a	a	DET
ejpam-6535	676	13	1−	1−	NUM
ejpam-6535	676	14	1	1	NUM
ejpam-6535	676	15	correspondence	correspondence	NOUN
ejpam-6535	676	16	t	t	NOUN
ejpam-6535	676	17	:	:	PUNCT
ejpam-6535	676	18	ltinvpmet	ltinvpmet	VERB
ejpam-6535	676	19	−→	−→	NOUN
ejpam-6535	676	20	pgrpn	pgrpn	NOUN
ejpam-6535	676	21	,	,	PUNCT
ejpam-6535	676	22	f	f	PROPN
ejpam-6535	676	23	7→	7→	NUM
ejpam-6535	676	24	t(f	t(f	NOUN
ejpam-6535	676	25	)	)	PUNCT
ejpam-6535	676	26	defined	define	VERB
ejpam-6535	676	27	by	by	ADP
ejpam-6535	676	28	t(f	t(f	NOUN
ejpam-6535	676	29	)	)	PUNCT
ejpam-6535	676	30	(	(	PUNCT
ejpam-6535	676	31	p	p	X
ejpam-6535	676	32	)	)	PUNCT
ejpam-6535	677	1	=	=	SYM
ejpam-6535	677	2	f	f	X
ejpam-6535	677	3	(	(	PUNCT
ejpam-6535	677	4	p	p	X
ejpam-6535	677	5	,	,	PUNCT
ejpam-6535	677	6	e	e	NOUN
ejpam-6535	677	7	)	)	PUNCT
ejpam-6535	677	8	,	,	PUNCT
ejpam-6535	677	9	x	x	PROPN
ejpam-6535	677	10	∈	∈	PROPN
ejpam-6535	677	11	s.	s.	PROPN
ejpam-6535	677	12	the	the	DET
ejpam-6535	677	13	inverse	inverse	NOUN
ejpam-6535	677	14	transformation	transformation	NOUN
ejpam-6535	677	15	t−1	t−1	PROPN
ejpam-6535	677	16	:	:	PUNCT
ejpam-6535	677	17	pgrpn	pgrpn	VERB
ejpam-6535	677	18	−→	−→	ADJ
ejpam-6535	677	19	ltinvpmet	ltinvpmet	NOUN
ejpam-6535	677	20	,	,	PUNCT
ejpam-6535	677	21	ν	ν	PROPN
ejpam-6535	677	22	7→	7→	PROPN
ejpam-6535	677	23	t−1(ν	t−1(ν	PROPN
ejpam-6535	677	24	)	)	PUNCT
ejpam-6535	677	25	is	be	AUX
ejpam-6535	677	26	defined	define	VERB
ejpam-6535	677	27	by	by	ADP
ejpam-6535	677	28	t−1(ν)(p	t−1(ν)(p	PROPN
ejpam-6535	677	29	,	,	PUNCT
ejpam-6535	677	30	q	q	ADJ
ejpam-6535	677	31	)	)	PUNCT
ejpam-6535	677	32	=	=	SYM
ejpam-6535	677	33	ν(q−1p	ν(q−1p	PROPN
ejpam-6535	677	34	)	)	PUNCT
ejpam-6535	677	35	,	,	PUNCT
ejpam-6535	677	36	p	p	X
ejpam-6535	677	37	,	,	PUNCT
ejpam-6535	677	38	q	q	PROPN
ejpam-6535	677	39	∈	∈	PROPN
ejpam-6535	677	40	s.	s.	PROPN
ejpam-6535	677	41	(	(	PUNCT
ejpam-6535	677	42	b	b	X
ejpam-6535	677	43	)	)	PUNCT
ejpam-6535	677	44	there	there	PRON
ejpam-6535	677	45	is	be	VERB
ejpam-6535	677	46	a	a	DET
ejpam-6535	677	47	1−	1−	NUM
ejpam-6535	677	48	1	1	NUM
ejpam-6535	677	49	correspondence	correspondence	NOUN
ejpam-6535	677	50	s	s	PART
ejpam-6535	677	51	:	:	PUNCT
ejpam-6535	677	52	rtinvpmet	rtinvpmet	PROPN
ejpam-6535	677	53	−→	−→	NOUN
ejpam-6535	677	54	pgrpn	pgrpn	NOUN
ejpam-6535	677	55	,	,	PUNCT
ejpam-6535	677	56	f̃	f̃	PROPN
ejpam-6535	677	57	7→	7→	NUM
ejpam-6535	677	58	s(f̃	s(f̃	NOUN
ejpam-6535	677	59	)	)	PUNCT
ejpam-6535	677	60	defined	define	VERB
ejpam-6535	677	61	by	by	ADP
ejpam-6535	677	62	s(f̃	s(f̃	PROPN
ejpam-6535	677	63	)	)	PUNCT
ejpam-6535	677	64	(	(	PUNCT
ejpam-6535	677	65	p	p	X
ejpam-6535	677	66	)	)	PUNCT
ejpam-6535	677	67	=	=	SYM
ejpam-6535	677	68	f̃	f̃	PROPN
ejpam-6535	677	69	(	(	PUNCT
ejpam-6535	677	70	p	p	X
ejpam-6535	677	71	,	,	PUNCT
ejpam-6535	677	72	e	e	NOUN
ejpam-6535	677	73	)	)	PUNCT
ejpam-6535	677	74	,	,	PUNCT
ejpam-6535	677	75	p	p	PROPN
ejpam-6535	677	76	∈	∈	PROPN
ejpam-6535	677	77	s.	s.	PROPN
ejpam-6535	677	78	the	the	DET
ejpam-6535	677	79	inverse	inverse	NOUN
ejpam-6535	677	80	transformation	transformation	NOUN
ejpam-6535	677	81	s−1	s−1	PROPN
ejpam-6535	677	82	:	:	PUNCT
ejpam-6535	677	83	s(f̃	s(f̃	PROPN
ejpam-6535	677	84	)	)	PUNCT
ejpam-6535	677	85	−→	−→	NOUN
ejpam-6535	677	86	rtinvpmet	rtinvpmet	NOUN
ejpam-6535	677	87	,	,	PUNCT
ejpam-6535	677	88	ν	ν	PROPN
ejpam-6535	677	89	7→	7→	PROPN
ejpam-6535	677	90	s−1(ν	s−1(ν	PROPN
ejpam-6535	677	91	)	)	PUNCT
ejpam-6535	677	92	defined	define	VERB
ejpam-6535	677	93	by	by	ADP
ejpam-6535	677	94	s−1(ν)(p	s−1(ν)(p	PROPN
ejpam-6535	677	95	,	,	PUNCT
ejpam-6535	677	96	q	q	NOUN
ejpam-6535	677	97	)	)	PUNCT
ejpam-6535	677	98	=	=	SYM
ejpam-6535	677	99	ν(pq−1	ν(pq−1	NOUN
ejpam-6535	677	100	)	)	PUNCT
ejpam-6535	677	101	,	,	PUNCT
ejpam-6535	677	102	p	p	X
ejpam-6535	677	103	,	,	PUNCT
ejpam-6535	677	104	q	q	PROPN
ejpam-6535	677	105	∈	∈	PROPN
ejpam-6535	677	106	s.	s.	PROPN
ejpam-6535	677	107	(	(	PUNCT
ejpam-6535	677	108	c	c	X
ejpam-6535	677	109	)	)	PUNCT
ejpam-6535	677	110	the	the	DET
ejpam-6535	677	111	canonical	canonical	ADJ
ejpam-6535	677	112	1−	1−	NUM
ejpam-6535	677	113	1	1	NUM
ejpam-6535	677	114	correspondence	correspondence	NOUN
ejpam-6535	677	115	s−1	s−1	PROPN
ejpam-6535	677	116	◦	◦	NOUN
ejpam-6535	677	117	t	t	NOUN
ejpam-6535	677	118	:	:	PUNCT
ejpam-6535	677	119	invpmet	invpmet	ADV
ejpam-6535	677	120	−→	−→	NOUN
ejpam-6535	677	121	rtinvpmet	rtinvpmet	NOUN
ejpam-6535	677	122	,	,	PUNCT
ejpam-6535	677	123	f	f	PROPN
ejpam-6535	677	124	7→	7→	NUM
ejpam-6535	677	125	s−1	s−1	PROPN
ejpam-6535	677	126	◦	◦	NOUN
ejpam-6535	677	127	t(f	t(f	NOUN
ejpam-6535	677	128	)	)	PUNCT
ejpam-6535	677	129	given	give	VERB
ejpam-6535	677	130	by	by	ADP
ejpam-6535	677	131	s−1	s−1	PROPN
ejpam-6535	677	132	◦	◦	NOUN
ejpam-6535	677	133	t(f	t(f	NOUN
ejpam-6535	677	134	)	)	PUNCT
ejpam-6535	677	135	(	(	PUNCT
ejpam-6535	677	136	p	p	X
ejpam-6535	677	137	,	,	PUNCT
ejpam-6535	677	138	q	q	NOUN
ejpam-6535	677	139	)	)	PUNCT
ejpam-6535	677	140	=	=	SYM
ejpam-6535	677	141	f	f	PROPN
ejpam-6535	677	142	(	(	PUNCT
ejpam-6535	677	143	p−1	p−1	PROPN
ejpam-6535	677	144	,	,	PUNCT
ejpam-6535	677	145	q−1	q−1	PROPN
ejpam-6535	677	146	)	)	PUNCT
ejpam-6535	677	147	,	,	PUNCT
ejpam-6535	677	148	p	p	X
ejpam-6535	677	149	,	,	PUNCT
ejpam-6535	677	150	q	q	PROPN
ejpam-6535	677	151	∈	∈	PROPN
ejpam-6535	677	152	s.	s.	PROPN
ejpam-6535	677	153	the	the	DET
ejpam-6535	677	154	inverse	inverse	ADJ
ejpam-6535	677	155	transformation	transformation	NOUN
ejpam-6535	677	156	t−1	t−1	PROPN
ejpam-6535	677	157	◦	◦	NOUN
ejpam-6535	677	158	s	s	PART
ejpam-6535	677	159	:	:	PUNCT
ejpam-6535	677	160	rtinvpmet	rtinvpmet	PROPN
ejpam-6535	677	161	−→	−→	NOUN
ejpam-6535	677	162	ltinvpmet	ltinvpmet	NOUN
ejpam-6535	677	163	,	,	PUNCT
ejpam-6535	677	164	f̃	f̃	PROPN
ejpam-6535	677	165	7→	7→	PROPN
ejpam-6535	677	166	t−1	t−1	NOUN
ejpam-6535	677	167	◦	◦	NOUN
ejpam-6535	677	168	s(f̃	s(f̃	NOUN
ejpam-6535	677	169	)	)	PUNCT
ejpam-6535	677	170	given	give	VERB
ejpam-6535	677	171	by	by	ADP
ejpam-6535	677	172	t−1	t−1	PROPN
ejpam-6535	677	173	◦	◦	NOUN
ejpam-6535	677	174	s(f̃	s(f̃	NOUN
ejpam-6535	677	175	)	)	PUNCT
ejpam-6535	677	176	(	(	PUNCT
ejpam-6535	677	177	p	p	X
ejpam-6535	677	178	,	,	PUNCT
ejpam-6535	677	179	q	q	NOUN
ejpam-6535	677	180	)	)	PUNCT
ejpam-6535	677	181	=	=	SYM
ejpam-6535	677	182	f̃	f̃	PROPN
ejpam-6535	677	183	(	(	PUNCT
ejpam-6535	677	184	p−1	p−1	PROPN
ejpam-6535	677	185	,	,	PUNCT
ejpam-6535	677	186	q−1	q−1	PROPN
ejpam-6535	677	187	)	)	PUNCT
ejpam-6535	677	188	,	,	PUNCT
ejpam-6535	677	189	p	p	X
ejpam-6535	677	190	,	,	PUNCT
ejpam-6535	677	191	q	q	PROPN
ejpam-6535	677	192	∈	∈	PROPN
ejpam-6535	677	193	s.	s.	PROPN
ejpam-6535	677	194	proof	proof	PROPN
ejpam-6535	677	195	.	.	PUNCT
ejpam-6535	678	1	this	this	PRON
ejpam-6535	678	2	follows	follow	VERB
ejpam-6535	678	3	from	from	ADP
ejpam-6535	678	4	the	the	DET
ejpam-6535	678	5	lemmas	lemmas	ADJ
ejpam-6535	678	6	6.2	6.2	NUM
ejpam-6535	678	7	,	,	PUNCT
ejpam-6535	678	8	6.3	6.3	NUM
ejpam-6535	678	9	and	and	CCONJ
ejpam-6535	678	10	6.4	6.4	NUM
ejpam-6535	678	11	in	in	ADP
ejpam-6535	678	12	[	[	X
ejpam-6535	678	13	3	3	NUM
ejpam-6535	678	14	]	]	PUNCT
ejpam-6535	678	15	.	.	PUNCT
ejpam-6535	679	1	see	see	VERB
ejpam-6535	679	2	also	also	ADV
ejpam-6535	679	3	[	[	X
ejpam-6535	679	4	6	6	NUM
ejpam-6535	679	5	]	]	PUNCT
ejpam-6535	679	6	.	.	PUNCT
ejpam-6535	680	1	theorem	theorem	NOUN
ejpam-6535	680	2	5	5	NUM
ejpam-6535	680	3	.	.	PUNCT
ejpam-6535	681	1	let	let	VERB
ejpam-6535	681	2	f	f	PRON
ejpam-6535	681	3	be	be	AUX
ejpam-6535	681	4	a	a	DET
ejpam-6535	681	5	left	left	ADJ
ejpam-6535	681	6	-	-	PUNCT
ejpam-6535	681	7	invariant	invariant	ADJ
ejpam-6535	681	8	,	,	PUNCT
ejpam-6535	681	9	or	or	CCONJ
ejpam-6535	681	10	right	right	ADV
ejpam-6535	681	11	-	-	PUNCT
ejpam-6535	681	12	invariant	invariant	ADJ
ejpam-6535	681	13	probabilistic	probabilistic	ADJ
ejpam-6535	681	14	metric	metric	NOUN
ejpam-6535	681	15	on	on	ADP
ejpam-6535	681	16	a	a	DET
ejpam-6535	681	17	group	group	NOUN
ejpam-6535	681	18	(	(	PUNCT
ejpam-6535	681	19	s	s	PROPN
ejpam-6535	681	20	,	,	PUNCT
ejpam-6535	681	21	·	·	PUNCT
ejpam-6535	681	22	)	)	PUNCT
ejpam-6535	681	23	,	,	PUNCT
ejpam-6535	681	24	and	and	CCONJ
ejpam-6535	681	25	let	let	VERB
ejpam-6535	681	26	νf	νf	NOUN
ejpam-6535	681	27	be	be	AUX
ejpam-6535	681	28	its	its	PRON
ejpam-6535	681	29	probabilistic	probabilistic	ADJ
ejpam-6535	681	30	group	group	NOUN
ejpam-6535	681	31	norm	norm	NOUN
ejpam-6535	681	32	.	.	PUNCT
ejpam-6535	682	1	then	then	ADV
ejpam-6535	682	2	the	the	DET
ejpam-6535	682	3	following	follow	VERB
ejpam-6535	682	4	statements	statement	NOUN
ejpam-6535	682	5	are	be	AUX
ejpam-6535	682	6	equivalent	equivalent	ADJ
ejpam-6535	682	7	:	:	PUNCT
ejpam-6535	682	8	(	(	PUNCT
ejpam-6535	682	9	i	i	NOUN
ejpam-6535	682	10	)	)	PUNCT
ejpam-6535	682	11	f	f	PROPN
ejpam-6535	682	12	is	be	AUX
ejpam-6535	682	13	invariant	invariant	ADJ
ejpam-6535	682	14	,	,	PUNCT
ejpam-6535	682	15	that	that	PRON
ejpam-6535	682	16	is	be	AUX
ejpam-6535	682	17	both	both	PRON
ejpam-6535	682	18	left	left	ADJ
ejpam-6535	682	19	and	and	CCONJ
ejpam-6535	682	20	right	right	ADJ
ejpam-6535	682	21	invariant	invariant	ADJ
ejpam-6535	682	22	.	.	PUNCT
ejpam-6535	683	1	(	(	PUNCT
ejpam-6535	683	2	ii	ii	PROPN
ejpam-6535	683	3	)	)	PUNCT
ejpam-6535	683	4	f	f	PROPN
ejpam-6535	683	5	(	(	PUNCT
ejpam-6535	683	6	p	p	X
ejpam-6535	683	7	,	,	PUNCT
ejpam-6535	683	8	q	q	NOUN
ejpam-6535	683	9	)	)	PUNCT
ejpam-6535	684	1	=	=	SYM
ejpam-6535	684	2	f	f	PROPN
ejpam-6535	684	3	(	(	PUNCT
ejpam-6535	684	4	p−1	p−1	PROPN
ejpam-6535	684	5	,	,	PUNCT
ejpam-6535	684	6	q−1	q−1	PROPN
ejpam-6535	684	7	)	)	PUNCT
ejpam-6535	684	8	,	,	PUNCT
ejpam-6535	684	9	p	p	X
ejpam-6535	684	10	,	,	PUNCT
ejpam-6535	684	11	q	q	PROPN
ejpam-6535	684	12	∈	∈	PROPN
ejpam-6535	684	13	s.	s.	PROPN
ejpam-6535	684	14	(	(	PUNCT
ejpam-6535	684	15	iii	iii	NOUN
ejpam-6535	684	16	)	)	PUNCT
ejpam-6535	684	17	νf	νf	NOUN
ejpam-6535	684	18	(	(	PUNCT
ejpam-6535	684	19	pq	pq	NOUN
ejpam-6535	684	20	)	)	PUNCT
ejpam-6535	684	21	=	=	SYM
ejpam-6535	685	1	νf	νf	NOUN
ejpam-6535	685	2	(	(	PUNCT
ejpam-6535	685	3	qp	qp	NOUN
ejpam-6535	685	4	)	)	PUNCT
ejpam-6535	685	5	,	,	PUNCT
ejpam-6535	685	6	p	p	X
ejpam-6535	685	7	,	,	PUNCT
ejpam-6535	685	8	q	q	PROPN
ejpam-6535	685	9	∈	∈	PROPN
ejpam-6535	685	10	s.	s.	PROPN
ejpam-6535	685	11	conversely	conversely	ADV
ejpam-6535	685	12	,	,	PUNCT
ejpam-6535	685	13	a	a	DET
ejpam-6535	685	14	probabilistic	probabilistic	ADJ
ejpam-6535	685	15	metric	metric	NOUN
ejpam-6535	685	16	on	on	ADP
ejpam-6535	685	17	an	an	DET
ejpam-6535	685	18	abelian	abelian	ADJ
ejpam-6535	685	19	group	group	NOUN
ejpam-6535	685	20	is	be	AUX
ejpam-6535	685	21	left	leave	VERB
ejpam-6535	685	22	-	-	PUNCT
ejpam-6535	685	23	invariant	invariant	ADJ
ejpam-6535	685	24	if	if	SCONJ
ejpam-6535	685	25	and	and	CCONJ
ejpam-6535	685	26	only	only	ADV
ejpam-6535	685	27	if	if	SCONJ
ejpam-6535	685	28	it	it	PRON
ejpam-6535	685	29	is	be	AUX
ejpam-6535	685	30	right	right	ADJ
ejpam-6535	685	31	-	-	PUNCT
ejpam-6535	685	32	invariant	invariant	ADJ
ejpam-6535	685	33	if	if	SCONJ
ejpam-6535	685	34	and	and	CCONJ
ejpam-6535	685	35	only	only	ADV
ejpam-6535	685	36	if	if	SCONJ
ejpam-6535	685	37	it	it	PRON
ejpam-6535	685	38	is	be	AUX
ejpam-6535	685	39	invariant	invariant	ADJ
ejpam-6535	685	40	.	.	PUNCT
ejpam-6535	686	1	proof	proof	NOUN
ejpam-6535	686	2	.	.	PUNCT
ejpam-6535	687	1	applying	apply	VERB
ejpam-6535	687	2	the	the	DET
ejpam-6535	687	3	above	above	ADJ
ejpam-6535	687	4	theorem	theorem	ADJ
ejpam-6535	687	5	3	3	NUM
ejpam-6535	687	6	,	,	PUNCT
ejpam-6535	687	7	one	one	PRON
ejpam-6535	687	8	reach	reach	VERB
ejpam-6535	687	9	the	the	DET
ejpam-6535	687	10	conclusion	conclusion	NOUN
ejpam-6535	687	11	.	.	PUNCT
ejpam-6535	688	1	lemma	lemma	PROPN
ejpam-6535	688	2	22	22	NUM
ejpam-6535	688	3	.	.	PUNCT
ejpam-6535	689	1	let	let	VERB
ejpam-6535	689	2	(	(	PUNCT
ejpam-6535	689	3	s	s	X
ejpam-6535	689	4	,	,	PUNCT
ejpam-6535	689	5	·	·	PUNCT
ejpam-6535	689	6	,	,	PUNCT
ejpam-6535	689	7	ν	ν	NOUN
ejpam-6535	689	8	)	)	PUNCT
ejpam-6535	689	9	,	,	PUNCT
ejpam-6535	689	10	(	(	PUNCT
ejpam-6535	689	11	s′	s′	X
ejpam-6535	689	12	,	,	PUNCT
ejpam-6535	689	13	·	·	PUNCT
ejpam-6535	689	14	,	,	PUNCT
ejpam-6535	689	15	ν	ν	NOUN
ejpam-6535	689	16	′	′	NOUN
ejpam-6535	689	17	)	)	PUNCT
ejpam-6535	689	18	∈	∈	PROPN
ejpam-6535	689	19	|pnormedgrp|	|pnormedgrp|	NOUN
ejpam-6535	689	20	.	.	PUNCT
ejpam-6535	690	1	if	if	SCONJ
ejpam-6535	690	2	f	f	PROPN
ejpam-6535	690	3	:	:	PUNCT
ejpam-6535	690	4	(	(	PUNCT
ejpam-6535	690	5	s	s	X
ejpam-6535	690	6	,	,	PUNCT
ejpam-6535	690	7	ν	ν	NOUN
ejpam-6535	690	8	)	)	PUNCT
ejpam-6535	690	9	−→	−→	NOUN
ejpam-6535	690	10	(	(	PUNCT
ejpam-6535	690	11	s′	s′	PROPN
ejpam-6535	690	12	,	,	PUNCT
ejpam-6535	690	13	ν	ν	NOUN
ejpam-6535	690	14	′	′	NOUN
ejpam-6535	690	15	)	)	PUNCT
ejpam-6535	690	16	is	be	AUX
ejpam-6535	690	17	a	a	DET
ejpam-6535	690	18	normed	norme	VERB
ejpam-6535	690	19	-	-	PUNCT
ejpam-6535	690	20	preserving	preserve	VERB
ejpam-6535	690	21	group	group	NOUN
ejpam-6535	690	22	-	-	PUNCT
ejpam-6535	690	23	homomorphism	homomorphism	NOUN
ejpam-6535	690	24	,	,	PUNCT
ejpam-6535	690	25	then	then	ADV
ejpam-6535	690	26	f	f	X
ejpam-6535	690	27	:	:	PUNCT
ejpam-6535	690	28	(	(	PUNCT
ejpam-6535	690	29	s	s	X
ejpam-6535	690	30	,	,	PUNCT
ejpam-6535	690	31	f	f	PROPN
ejpam-6535	690	32	ν	ν	NOUN
ejpam-6535	690	33	)	)	PUNCT
ejpam-6535	690	34	−→	−→	NOUN
ejpam-6535	690	35	(	(	PUNCT
ejpam-6535	690	36	s′	s′	PROPN
ejpam-6535	690	37	,	,	PUNCT
ejpam-6535	690	38	f	f	PROPN
ejpam-6535	690	39	′ν′	′ν′	PROPN
ejpam-6535	690	40	)	)	PUNCT
ejpam-6535	690	41	is	be	AUX
ejpam-6535	690	42	non	non	ADJ
ejpam-6535	690	43	-	-	ADJ
ejpam-6535	690	44	expansive	expansive	ADJ
ejpam-6535	690	45	.	.	PUNCT
ejpam-6535	691	1	conversely	conversely	ADV
ejpam-6535	691	2	,	,	PUNCT
ejpam-6535	691	3	if	if	SCONJ
ejpam-6535	691	4	(	(	PUNCT
ejpam-6535	691	5	s	s	X
ejpam-6535	691	6	,	,	PUNCT
ejpam-6535	691	7	·	·	PUNCT
ejpam-6535	691	8	,	,	PUNCT
ejpam-6535	691	9	f	f	PROPN
ejpam-6535	691	10	)	)	PUNCT
ejpam-6535	691	11	,	,	PUNCT
ejpam-6535	691	12	(	(	PUNCT
ejpam-6535	691	13	s′	s′	X
ejpam-6535	691	14	,	,	PUNCT
ejpam-6535	691	15	·	·	PUNCT
ejpam-6535	691	16	,	,	PUNCT
ejpam-6535	691	17	f	f	PROPN
ejpam-6535	691	18	′	′	NOUN
ejpam-6535	691	19	)	)	PUNCT
ejpam-6535	691	20	∈	∈	PROPN
ejpam-6535	691	21	|pmetgrp|	|pmetgrp|	NOUN
ejpam-6535	691	22	and	and	CCONJ
ejpam-6535	691	23	f	f	X
ejpam-6535	691	24	:	:	PUNCT
ejpam-6535	691	25	(	(	PUNCT
ejpam-6535	691	26	s	s	X
ejpam-6535	691	27	,	,	PUNCT
ejpam-6535	691	28	f	f	NOUN
ejpam-6535	691	29	)	)	PUNCT
ejpam-6535	691	30	−→	−→	NOUN
ejpam-6535	691	31	(	(	PUNCT
ejpam-6535	691	32	s′	s′	PROPN
ejpam-6535	691	33	,	,	PUNCT
ejpam-6535	691	34	f	f	PROPN
ejpam-6535	691	35	′	′	NOUN
ejpam-6535	691	36	)	)	PUNCT
ejpam-6535	691	37	is	be	AUX
ejpam-6535	691	38	non	non	ADJ
ejpam-6535	691	39	-	-	ADJ
ejpam-6535	691	40	expansive	expansive	ADJ
ejpam-6535	691	41	,	,	PUNCT
ejpam-6535	691	42	then	then	ADV
ejpam-6535	691	43	f	f	X
ejpam-6535	691	44	:	:	PUNCT
ejpam-6535	691	45	(	(	PUNCT
ejpam-6535	691	46	s	s	X
ejpam-6535	691	47	,	,	PUNCT
ejpam-6535	691	48	ν	ν	NOUN
ejpam-6535	691	49	′f	′f	NOUN
ejpam-6535	691	50	)	)	PUNCT
ejpam-6535	691	51	−→	−→	NOUN
ejpam-6535	691	52	(	(	PUNCT
ejpam-6535	691	53	s′	s′	X
ejpam-6535	691	54	,	,	PUNCT
ejpam-6535	691	55	νf	νf	NOUN
ejpam-6535	691	56	′	′	NOUN
ejpam-6535	691	57	)	)	PUNCT
ejpam-6535	691	58	is	be	AUX
ejpam-6535	691	59	normed	normed	ADJ
ejpam-6535	691	60	-	-	PUNCT
ejpam-6535	691	61	preserving	preserve	VERB
ejpam-6535	691	62	group	group	NOUN
ejpam-6535	691	63	homomorphism	homomorphism	NOUN
ejpam-6535	691	64	.	.	PUNCT
ejpam-6535	692	1	proof	proof	NOUN
ejpam-6535	692	2	.	.	PUNCT
ejpam-6535	693	1	this	this	PRON
ejpam-6535	693	2	is	be	AUX
ejpam-6535	693	3	immediate	immediate	ADJ
ejpam-6535	693	4	from	from	ADP
ejpam-6535	693	5	the	the	DET
ejpam-6535	693	6	observation	observation	NOUN
ejpam-6535	693	7	that	that	SCONJ
ejpam-6535	693	8	for	for	ADP
ejpam-6535	693	9	any	any	DET
ejpam-6535	693	10	p	p	NOUN
ejpam-6535	693	11	,	,	PUNCT
ejpam-6535	693	12	q	q	PROPN
ejpam-6535	693	13	∈	∈	PROPN
ejpam-6535	693	14	s	s	PROPN
ejpam-6535	693	15	,	,	PUNCT
ejpam-6535	693	16	f	f	PROPN
ejpam-6535	693	17	ν(p	ν(p	PROPN
ejpam-6535	693	18	,	,	PUNCT
ejpam-6535	693	19	q	q	NOUN
ejpam-6535	693	20	)	)	PUNCT
ejpam-6535	693	21	=	=	SYM
ejpam-6535	693	22	ν(p−1q	ν(p−1q	NOUN
ejpam-6535	693	23	)	)	PUNCT
ejpam-6535	693	24	≤	≤	NUM
ejpam-6535	693	25	ν	ν	ADP
ejpam-6535	693	26	′(f(p−1q	′(f(p−1q	PROPN
ejpam-6535	693	27	)	)	PUNCT
ejpam-6535	693	28	)	)	PUNCT
ejpam-6535	694	1	=	=	PUNCT
ejpam-6535	694	2	ν	ν	X
ejpam-6535	694	3	′((f(p))−1f(q	′((f(p))−1f(q	ADJ
ejpam-6535	694	4	)	)	PUNCT
ejpam-6535	694	5	)	)	PUNCT
ejpam-6535	695	1	=	=	SYM
ejpam-6535	695	2	f	f	PROPN
ejpam-6535	695	3	′ν′(f(p	′ν′(f(p	PROPN
ejpam-6535	695	4	)	)	PUNCT
ejpam-6535	695	5	,	,	PUNCT
ejpam-6535	695	6	f(q	f(q	PROPN
ejpam-6535	695	7	)	)	PUNCT
ejpam-6535	695	8	)	)	PUNCT
ejpam-6535	695	9	.	.	PUNCT
ejpam-6535	696	1	for	for	ADP
ejpam-6535	696	2	the	the	DET
ejpam-6535	696	3	converse	converse	NOUN
ejpam-6535	696	4	part	part	NOUN
ejpam-6535	696	5	,	,	PUNCT
ejpam-6535	696	6	we	we	PRON
ejpam-6535	696	7	only	only	ADV
ejpam-6535	696	8	need	need	VERB
ejpam-6535	696	9	to	to	PART
ejpam-6535	696	10	see	see	VERB
ejpam-6535	696	11	the	the	DET
ejpam-6535	696	12	following	following	NOUN
ejpam-6535	696	13	.	.	PUNCT
ejpam-6535	697	1	for	for	ADP
ejpam-6535	697	2	any	any	DET
ejpam-6535	697	3	p	p	NOUN
ejpam-6535	697	4	,	,	PUNCT
ejpam-6535	697	5	q	q	PROPN
ejpam-6535	697	6	∈	∈	PROPN
ejpam-6535	697	7	s	s	X
ejpam-6535	697	8	,	,	PUNCT
ejpam-6535	697	9	we	we	PRON
ejpam-6535	697	10	have	have	VERB
ejpam-6535	697	11	νf	νf	NOUN
ejpam-6535	697	12	(	(	PUNCT
ejpam-6535	697	13	p	p	NOUN
ejpam-6535	697	14	)	)	PUNCT
ejpam-6535	697	15	≤	≤	NUM
ejpam-6535	697	16	νf	νf	NOUN
ejpam-6535	697	17	′	′	NOUN
ejpam-6535	697	18	(	(	PUNCT
ejpam-6535	697	19	f(p	f(p	PROPN
ejpam-6535	697	20	)	)	PUNCT
ejpam-6535	697	21	)	)	PUNCT
ejpam-6535	697	22	.	.	PUNCT
ejpam-6535	698	1	so	so	ADV
ejpam-6535	698	2	,	,	PUNCT
ejpam-6535	698	3	we	we	PRON
ejpam-6535	698	4	have	have	VERB
ejpam-6535	698	5	,	,	PUNCT
ejpam-6535	698	6	νf	νf	X
ejpam-6535	698	7	(	(	PUNCT
ejpam-6535	698	8	p	p	NOUN
ejpam-6535	698	9	)	)	PUNCT
ejpam-6535	699	1	=	=	SYM
ejpam-6535	699	2	f	f	X
ejpam-6535	699	3	(	(	PUNCT
ejpam-6535	699	4	p	p	X
ejpam-6535	699	5	,	,	PUNCT
ejpam-6535	699	6	e	e	NOUN
ejpam-6535	699	7	)	)	PUNCT
ejpam-6535	699	8	≤	≤	NUM
ejpam-6535	699	9	f	f	PROPN
ejpam-6535	699	10	′(f(p	′(f(p	PROPN
ejpam-6535	699	11	)	)	PUNCT
ejpam-6535	699	12	,	,	PUNCT
ejpam-6535	699	13	f(e	f(e	NOUN
ejpam-6535	699	14	)	)	PUNCT
ejpam-6535	699	15	)	)	PUNCT
ejpam-6535	700	1	=	=	PUNCT
ejpam-6535	700	2	f	f	X
ejpam-6535	700	3	′(f(p	′(f(p	X
ejpam-6535	700	4	)	)	PUNCT
ejpam-6535	700	5	,	,	PUNCT
ejpam-6535	700	6	e	e	X
ejpam-6535	700	7	)	)	PUNCT
ejpam-6535	700	8	=	=	NOUN
ejpam-6535	700	9	ν	ν	PART
ejpam-6535	700	10	′f	′f	NOUN
ejpam-6535	700	11	′	′	NUM
ejpam-6535	700	12	(	(	PUNCT
ejpam-6535	700	13	f(p	f(p	PROPN
ejpam-6535	700	14	)	)	PUNCT
ejpam-6535	700	15	)	)	PUNCT
ejpam-6535	700	16	.	.	PUNCT
ejpam-6535	701	1	theorem	theorem	VERB
ejpam-6535	701	2	6	6	NUM
ejpam-6535	701	3	.	.	PUNCT
ejpam-6535	702	1	if	if	SCONJ
ejpam-6535	702	2	(	(	PUNCT
ejpam-6535	702	3	s	s	X
ejpam-6535	702	4	,	,	PUNCT
ejpam-6535	702	5	·	·	PUNCT
ejpam-6535	702	6	,	,	PUNCT
ejpam-6535	702	7	f	f	PROPN
ejpam-6535	702	8	)	)	PUNCT
ejpam-6535	702	9	∈	∈	PROPN
ejpam-6535	702	10	|pmetgrp|	|pmetgrp|	NOUN
ejpam-6535	702	11	,	,	PUNCT
ejpam-6535	702	12	then	then	ADV
ejpam-6535	702	13	(	(	PUNCT
ejpam-6535	702	14	s	s	X
ejpam-6535	702	15	,	,	PUNCT
ejpam-6535	702	16	·	·	PUNCT
ejpam-6535	702	17	,	,	PUNCT
ejpam-6535	702	18	νf	νf	NOUN
ejpam-6535	702	19	)	)	PUNCT
ejpam-6535	702	20	∈	∈	PROPN
ejpam-6535	702	21	|pnormedgrp|	|pnormedgrp|	NOUN
ejpam-6535	702	22	.	.	PUNCT
ejpam-6535	703	1	conversely	conversely	ADV
ejpam-6535	703	2	,	,	PUNCT
ejpam-6535	703	3	if	if	SCONJ
ejpam-6535	703	4	(	(	PUNCT
ejpam-6535	703	5	s	s	X
ejpam-6535	703	6	,	,	PUNCT
ejpam-6535	703	7	·	·	PUNCT
ejpam-6535	703	8	,	,	PUNCT
ejpam-6535	703	9	ν	ν	NOUN
ejpam-6535	703	10	)	)	PUNCT
ejpam-6535	703	11	∈	∈	PROPN
ejpam-6535	703	12	|pnormedgrp|	|pnormedgrp|	NOUN
ejpam-6535	703	13	,	,	PUNCT
ejpam-6535	703	14	then	then	ADV
ejpam-6535	703	15	(	(	PUNCT
ejpam-6535	703	16	s	s	X
ejpam-6535	703	17	,	,	PUNCT
ejpam-6535	703	18	·	·	PUNCT
ejpam-6535	703	19	,	,	PUNCT
ejpam-6535	703	20	f	f	PROPN
ejpam-6535	703	21	ν	ν	PROPN
ejpam-6535	703	22	)	)	PUNCT
ejpam-6535	703	23	∈	∈	NOUN
ejpam-6535	703	24	|pmetgrp|	|pmetgrp|	NOUN
ejpam-6535	703	25	.	.	PUNCT
ejpam-6535	704	1	furthermore	furthermore	ADV
ejpam-6535	704	2	,	,	PUNCT
ejpam-6535	704	3	there	there	PRON
ejpam-6535	704	4	are	be	VERB
ejpam-6535	704	5	functors	functor	NOUN
ejpam-6535	704	6	pmetgrp	pmetgrp	PROPN
ejpam-6535	704	7	pnormedgrp	pnormedgrp	PROPN
ejpam-6535	704	8	t	t	PROPN
ejpam-6535	704	9	s	s	PRON
ejpam-6535	704	10	such	such	ADJ
ejpam-6535	704	11	that	that	PRON
ejpam-6535	704	12	ts	ts	X
ejpam-6535	704	13	=	=	SYM
ejpam-6535	704	14	idpnormedgrp	idpnormedgrp	PROPN
ejpam-6535	704	15	and	and	CCONJ
ejpam-6535	704	16	st	st	NOUN
ejpam-6535	704	17	=	=	NOUN
ejpam-6535	704	18	idpmetgrp	idpmetgrp	PROPN
ejpam-6535	704	19	.	.	PUNCT
ejpam-6535	705	1	that	that	PRON
ejpam-6535	705	2	is	is	ADV
ejpam-6535	705	3	,	,	PUNCT
ejpam-6535	705	4	the	the	DET
ejpam-6535	705	5	categories	category	NOUN
ejpam-6535	705	6	pmetgrp	pmetgrp	VERB
ejpam-6535	705	7	and	and	CCONJ
ejpam-6535	705	8	pnormedgrp	pnormedgrp	NOUN
ejpam-6535	705	9	.	.	PUNCT
ejpam-6535	706	1	proof	proof	NOUN
ejpam-6535	706	2	.	.	PUNCT
ejpam-6535	707	1	in	in	ADP
ejpam-6535	707	2	view	view	NOUN
ejpam-6535	707	3	of	of	ADP
ejpam-6535	707	4	the	the	DET
ejpam-6535	707	5	lemmas	lemmas	ADJ
ejpam-6535	707	6	6.2	6.2	NUM
ejpam-6535	707	7	,	,	PUNCT
ejpam-6535	707	8	6.3	6.3	NUM
ejpam-6535	707	9	and	and	CCONJ
ejpam-6535	707	10	6.4[3	6.4[3	NUM
ejpam-6535	707	11	]	]	PUNCT
ejpam-6535	707	12	,	,	PUNCT
ejpam-6535	707	13	we	we	PRON
ejpam-6535	707	14	have	have	VERB
ejpam-6535	707	15	the	the	DET
ejpam-6535	707	16	following	follow	VERB
ejpam-6535	707	17	functors	functor	NOUN
ejpam-6535	707	18	:	:	PUNCT
ejpam-6535	707	19	t	t	NOUN
ejpam-6535	707	20	:	:	PUNCT
ejpam-6535	707	21			PUNCT
ejpam-6535	708	1	pmetgrp	pmetgrp	NOUN
ejpam-6535	708	2	−→	−→	NOUN
ejpam-6535	708	3	pnormedgrp	pnormedgrp	NOUN
ejpam-6535	708	4	(	(	PUNCT
ejpam-6535	708	5	s	s	NOUN
ejpam-6535	708	6	,	,	PUNCT
ejpam-6535	708	7	·	·	PUNCT
ejpam-6535	708	8	,	,	PUNCT
ejpam-6535	708	9	f	f	PROPN
ejpam-6535	708	10	)	)	PUNCT
ejpam-6535	708	11	7−→	7−→	PROPN
ejpam-6535	708	12	(	(	PUNCT
ejpam-6535	708	13	s	s	PROPN
ejpam-6535	708	14	,	,	PUNCT
ejpam-6535	708	15	·	·	PUNCT
ejpam-6535	708	16	,	,	PUNCT
ejpam-6535	708	17	νf	νf	NOUN
ejpam-6535	708	18	)	)	PUNCT
ejpam-6535	708	19	f	f	PROPN
ejpam-6535	709	1	7−→	7−→	NOUN
ejpam-6535	709	2	f	f	NOUN
ejpam-6535	709	3	,	,	PUNCT
ejpam-6535	709	4	and	and	CCONJ
ejpam-6535	709	5	s	s	VERB
ejpam-6535	709	6	:	:	PUNCT
ejpam-6535	709	7			PUNCT
ejpam-6535	709	8	pnormedgrp	pnormedgrp	VERB
ejpam-6535	709	9	−→	−→	ADJ
ejpam-6535	709	10	pmetgrp	pmetgrp	PROPN
ejpam-6535	709	11	(	(	PUNCT
ejpam-6535	709	12	s	s	X
ejpam-6535	709	13	,	,	PUNCT
ejpam-6535	709	14	·	·	PUNCT
ejpam-6535	709	15	,	,	PUNCT
ejpam-6535	709	16	ν	ν	NOUN
ejpam-6535	709	17	)	)	PUNCT
ejpam-6535	709	18	7−→	7−→	PROPN
ejpam-6535	709	19	(	(	PUNCT
ejpam-6535	709	20	s	s	PROPN
ejpam-6535	709	21	,	,	PUNCT
ejpam-6535	709	22	·	·	PUNCT
ejpam-6535	709	23	,	,	PUNCT
ejpam-6535	709	24	f	f	PROPN
ejpam-6535	709	25	ν	ν	PROPN
ejpam-6535	709	26	)	)	PUNCT
ejpam-6535	710	1	f	f	PROPN
ejpam-6535	710	2	7−→	7−→	NUM
ejpam-6535	710	3	f	f	NOUN
ejpam-6535	710	4	.	.	PUNCT
ejpam-6535	711	1	then	then	ADV
ejpam-6535	711	2	we	we	PRON
ejpam-6535	711	3	have	have	VERB
ejpam-6535	711	4	for	for	ADP
ejpam-6535	711	5	any	any	DET
ejpam-6535	711	6	(	(	PUNCT
ejpam-6535	711	7	s	s	NOUN
ejpam-6535	711	8	,	,	PUNCT
ejpam-6535	711	9	·	·	PUNCT
ejpam-6535	711	10	,	,	PUNCT
ejpam-6535	711	11	ν	ν	NOUN
ejpam-6535	711	12	)	)	PUNCT
ejpam-6535	711	13	∈	∈	PROPN
ejpam-6535	711	14	|pnormedgrp|	|pnormedgrp|	NUM
ejpam-6535	711	15	,	,	PUNCT
ejpam-6535	711	16	t	t	PROPN
ejpam-6535	711	17	◦	◦	NOUN
ejpam-6535	711	18	s	s	X
ejpam-6535	711	19	(	(	PUNCT
ejpam-6535	711	20	s	s	PROPN
ejpam-6535	711	21	,	,	PUNCT
ejpam-6535	711	22	·	·	PUNCT
ejpam-6535	711	23	,	,	PUNCT
ejpam-6535	711	24	ν	ν	NOUN
ejpam-6535	711	25	)	)	PUNCT
ejpam-6535	711	26	=	=	SYM
ejpam-6535	711	27	t	t	PROPN
ejpam-6535	711	28	(	(	PUNCT
ejpam-6535	711	29	s	s	X
ejpam-6535	711	30	,	,	PUNCT
ejpam-6535	711	31	·	·	PUNCT
ejpam-6535	711	32	,	,	PUNCT
ejpam-6535	711	33	f	f	PROPN
ejpam-6535	711	34	ν	ν	PROPN
ejpam-6535	711	35	)	)	PUNCT
ejpam-6535	711	36	=	=	SYM
ejpam-6535	711	37	(	(	PUNCT
ejpam-6535	711	38	s	s	PROPN
ejpam-6535	711	39	,	,	PUNCT
ejpam-6535	711	40	·	·	PUNCT
ejpam-6535	711	41	,	,	PUNCT
ejpam-6535	711	42	νf	νf	NOUN
ejpam-6535	711	43	ν	ν	NOUN
ejpam-6535	711	44	=	=	SYM
ejpam-6535	711	45	ν	ν	NOUN
ejpam-6535	711	46	)	)	PUNCT
ejpam-6535	712	1	=	=	PRON
ejpam-6535	712	2	idpnormedgrp	idpnormedgrp	VERB
ejpam-6535	712	3	(	(	PUNCT
ejpam-6535	712	4	s	s	X
ejpam-6535	712	5	,	,	PUNCT
ejpam-6535	712	6	·	·	PUNCT
ejpam-6535	712	7	,	,	PUNCT
ejpam-6535	712	8	ν	ν	NOUN
ejpam-6535	712	9	)	)	PUNCT
ejpam-6535	712	10	.	.	PUNCT
ejpam-6535	713	1	in	in	ADP
ejpam-6535	713	2	fact	fact	NOUN
ejpam-6535	713	3	,	,	PUNCT
ejpam-6535	713	4	for	for	ADP
ejpam-6535	713	5	any	any	DET
ejpam-6535	713	6	p	p	NOUN
ejpam-6535	713	7	∈	∈	PROPN
ejpam-6535	713	8	s	s	NOUN
ejpam-6535	713	9	,	,	PUNCT
ejpam-6535	713	10	one	one	PRON
ejpam-6535	713	11	obtains	obtain	VERB
ejpam-6535	713	12	:	:	PUNCT
ejpam-6535	713	13	νf	νf	NOUN
ejpam-6535	713	14	ν	ν	X
ejpam-6535	713	15	(	(	PUNCT
ejpam-6535	713	16	p	p	NOUN
ejpam-6535	713	17	)	)	PUNCT
ejpam-6535	713	18	=	=	SYM
ejpam-6535	713	19	f	f	PROPN
ejpam-6535	713	20	ν(p	ν(p	PROPN
ejpam-6535	713	21	,	,	PUNCT
ejpam-6535	713	22	e	e	NOUN
ejpam-6535	713	23	)	)	PUNCT
ejpam-6535	713	24	=	=	SYM
ejpam-6535	713	25	ν(p−1e	ν(p−1e	NOUN
ejpam-6535	713	26	)	)	PUNCT
ejpam-6535	713	27	=	=	SYM
ejpam-6535	713	28	ν(p	ν(p	PROPN
ejpam-6535	713	29	)	)	PUNCT
ejpam-6535	713	30	.	.	PUNCT
ejpam-6535	714	1	next	next	ADV
ejpam-6535	714	2	,	,	PUNCT
ejpam-6535	714	3	for	for	ADP
ejpam-6535	714	4	any	any	DET
ejpam-6535	714	5	(	(	PUNCT
ejpam-6535	714	6	s	s	NOUN
ejpam-6535	714	7	,	,	PUNCT
ejpam-6535	714	8	·	·	PUNCT
ejpam-6535	714	9	,	,	PUNCT
ejpam-6535	714	10	f	f	PROPN
ejpam-6535	714	11	)	)	PUNCT
ejpam-6535	714	12	∈	∈	PROPN
ejpam-6535	714	13	|pmetgrp|	|pmetgrp|	NOUN
ejpam-6535	714	14	,	,	PUNCT
ejpam-6535	714	15	we	we	PRON
ejpam-6535	714	16	have	have	VERB
ejpam-6535	714	17	:	:	PUNCT
ejpam-6535	714	18	s	s	VERB
ejpam-6535	714	19	◦	◦	NOUN
ejpam-6535	714	20	t	t	PROPN
ejpam-6535	714	21	(	(	PUNCT
ejpam-6535	714	22	(	(	PUNCT
ejpam-6535	714	23	s	s	X
ejpam-6535	714	24	,	,	PUNCT
ejpam-6535	714	25	·	·	PUNCT
ejpam-6535	714	26	,	,	PUNCT
ejpam-6535	714	27	f	f	PROPN
ejpam-6535	714	28	)	)	PUNCT
ejpam-6535	714	29	)	)	PUNCT
ejpam-6535	715	1	=	=	SYM
ejpam-6535	715	2	s	s	X
ejpam-6535	715	3	(	(	PUNCT
ejpam-6535	715	4	(	(	PUNCT
ejpam-6535	715	5	s	s	X
ejpam-6535	715	6	,	,	PUNCT
ejpam-6535	715	7	·	·	PUNCT
ejpam-6535	715	8	,	,	PUNCT
ejpam-6535	715	9	νf	νf	NOUN
ejpam-6535	715	10	)	)	PUNCT
ejpam-6535	715	11	)	)	PUNCT
ejpam-6535	715	12	=	=	PRON
ejpam-6535	715	13	(	(	PUNCT
ejpam-6535	715	14	s	s	PROPN
ejpam-6535	715	15	,	,	PUNCT
ejpam-6535	715	16	·	·	PUNCT
ejpam-6535	715	17	,	,	PUNCT
ejpam-6535	715	18	f	f	PROPN
ejpam-6535	715	19	νf	νf	NOUN
ejpam-6535	715	20	=	=	PUNCT
ejpam-6535	715	21	f	f	PROPN
ejpam-6535	715	22	)	)	PUNCT
ejpam-6535	715	23	=	=	PUNCT
ejpam-6535	715	24	(	(	PUNCT
ejpam-6535	715	25	s	s	X
ejpam-6535	715	26	,	,	PUNCT
ejpam-6535	715	27	·	·	PUNCT
ejpam-6535	715	28	,	,	PUNCT
ejpam-6535	715	29	f	f	PROPN
ejpam-6535	715	30	)	)	PUNCT
ejpam-6535	715	31	=	=	SYM
ejpam-6535	715	32	idpmetgrp	idpmetgrp	NOUN
ejpam-6535	715	33	(	(	PUNCT
ejpam-6535	715	34	s	s	NOUN
ejpam-6535	715	35	,	,	PUNCT
ejpam-6535	715	36	·	·	PUNCT
ejpam-6535	715	37	,	,	PUNCT
ejpam-6535	715	38	f	f	PROPN
ejpam-6535	715	39	)	)	PUNCT
ejpam-6535	715	40	.	.	PUNCT
ejpam-6535	716	1	in	in	ADP
ejpam-6535	716	2	fact	fact	NOUN
ejpam-6535	716	3	,	,	PUNCT
ejpam-6535	716	4	for	for	ADP
ejpam-6535	716	5	any	any	DET
ejpam-6535	716	6	p	p	NOUN
ejpam-6535	716	7	,	,	PUNCT
ejpam-6535	716	8	q	q	PUNCT
ejpam-6535	716	9	∈	∈	PROPN
ejpam-6535	716	10	r	r	NOUN
ejpam-6535	716	11	,	,	PUNCT
ejpam-6535	716	12	one	one	NUM
ejpam-6535	716	13	obtains	obtain	VERB
ejpam-6535	716	14	:	:	PUNCT
ejpam-6535	716	15	f	f	PROPN
ejpam-6535	716	16	ν	ν	X
ejpam-6535	716	17	f	f	X
ejpam-6535	716	18	(	(	PUNCT
ejpam-6535	716	19	p	p	X
ejpam-6535	716	20	,	,	PUNCT
ejpam-6535	716	21	q	q	NOUN
ejpam-6535	716	22	)	)	PUNCT
ejpam-6535	716	23	=	=	SYM
ejpam-6535	716	24	νf	νf	NOUN
ejpam-6535	716	25	(	(	PUNCT
ejpam-6535	716	26	p−1q	p−1q	NOUN
ejpam-6535	716	27	)	)	PUNCT
ejpam-6535	716	28	=	=	SYM
ejpam-6535	717	1	f	f	PROPN
ejpam-6535	717	2	(	(	PUNCT
ejpam-6535	717	3	p−1q	p−1q	PROPN
ejpam-6535	717	4	,	,	PUNCT
ejpam-6535	717	5	e	e	NOUN
ejpam-6535	717	6	)	)	PUNCT
ejpam-6535	717	7	=	=	SYM
ejpam-6535	718	1	f	f	X
ejpam-6535	718	2	(	(	PUNCT
ejpam-6535	718	3	p	p	X
ejpam-6535	718	4	,	,	PUNCT
ejpam-6535	718	5	q	q	NOUN
ejpam-6535	718	6	)	)	PUNCT
ejpam-6535	718	7	.	.	PUNCT
ejpam-6535	719	1	thus	thus	ADV
ejpam-6535	719	2	,	,	PUNCT
ejpam-6535	719	3	we	we	PRON
ejpam-6535	719	4	arrive	arrive	VERB
ejpam-6535	719	5	at	at	ADP
ejpam-6535	719	6	:	:	PUNCT
ejpam-6535	719	7	t	t	PROPN
ejpam-6535	719	8	◦	◦	NOUN
ejpam-6535	719	9	s	s	PART
ejpam-6535	719	10	=	=	NOUN
ejpam-6535	719	11	idpmetgrp	idpmetgrp	NOUN
ejpam-6535	719	12	and	and	CCONJ
ejpam-6535	719	13	s	s	VERB
ejpam-6535	719	14	◦	◦	NOUN
ejpam-6535	719	15	t	t	NOUN
ejpam-6535	719	16	=	=	PUNCT
ejpam-6535	719	17	idpmetgrp	idpmetgrp	NOUN
ejpam-6535	719	18	.	.	PUNCT
ejpam-6535	720	1	this	this	PRON
ejpam-6535	720	2	ends	end	VERB
ejpam-6535	720	3	the	the	DET
ejpam-6535	720	4	proof	proof	NOUN
ejpam-6535	720	5	.	.	PUNCT
ejpam-6535	721	1	theorem	theorem	ADJ
ejpam-6535	721	2	7	7	NUM
ejpam-6535	721	3	.	.	PUNCT
ejpam-6535	722	1	(	(	PUNCT
ejpam-6535	722	2	invariance	invariance	NOUN
ejpam-6535	722	3	of	of	ADP
ejpam-6535	722	4	probabilistic	probabilistic	ADJ
ejpam-6535	722	5	norm	norm	NOUN
ejpam-6535	722	6	theorem	theorem	VERB
ejpam-6535	722	7	)	)	PUNCT
ejpam-6535	722	8	(	(	PUNCT
ejpam-6535	722	9	a	a	X
ejpam-6535	722	10	)	)	PUNCT
ejpam-6535	722	11	the	the	DET
ejpam-6535	722	12	group	group	NOUN
ejpam-6535	722	13	norm	norm	NOUN
ejpam-6535	722	14	ν	ν	PROPN
ejpam-6535	722	15	is	be	AUX
ejpam-6535	722	16	abelian	abelian	ADJ
ejpam-6535	722	17	(	(	PUNCT
ejpam-6535	722	18	and	and	CCONJ
ejpam-6535	722	19	probabilistic	probabilistic	ADJ
ejpam-6535	722	20	metric	metric	NOUN
ejpam-6535	722	21	is	be	AUX
ejpam-6535	722	22	invariant	invariant	ADJ
ejpam-6535	722	23	)	)	PUNCT
ejpam-6535	723	1	if	if	SCONJ
ejpam-6535	723	2	and	and	CCONJ
ejpam-6535	723	3	only	only	ADV
ejpam-6535	723	4	if	if	SCONJ
ejpam-6535	723	5	τ(ν(xa−1	τ(ν(xa−1	NOUN
ejpam-6535	723	6	)	)	PUNCT
ejpam-6535	723	7	,	,	PUNCT
ejpam-6535	723	8	ν(yb−1	ν(yb−1	NOUN
ejpam-6535	723	9	)	)	PUNCT
ejpam-6535	723	10	≤	≤	NUM
ejpam-6535	723	11	ν(xy(ab)−1	ν(xy(ab)−1	NOUN
ejpam-6535	723	12	)	)	PUNCT
ejpam-6535	723	13	,	,	PUNCT
ejpam-6535	723	14	for	for	ADP
ejpam-6535	723	15	all	all	DET
ejpam-6535	723	16	x	x	NOUN
ejpam-6535	723	17	,	,	PUNCT
ejpam-6535	723	18	y	y	PROPN
ejpam-6535	723	19	,	,	PUNCT
ejpam-6535	723	20	a	a	PRON
ejpam-6535	723	21	,	,	PUNCT
ejpam-6535	723	22	b	b	NOUN
ejpam-6535	723	23	;	;	PUNCT
ejpam-6535	723	24	(	(	PUNCT
ejpam-6535	723	25	b	b	X
ejpam-6535	723	26	)	)	PUNCT
ejpam-6535	723	27	a	a	DET
ejpam-6535	723	28	probabilistic	probabilistic	ADJ
ejpam-6535	723	29	metric	metric	ADJ
ejpam-6535	723	30	f	f	NOUN
ejpam-6535	723	31	on	on	ADP
ejpam-6535	723	32	a	a	DET
ejpam-6535	723	33	group	group	NOUN
ejpam-6535	723	34	(	(	PUNCT
ejpam-6535	723	35	s	s	PROPN
ejpam-6535	723	36	,	,	PUNCT
ejpam-6535	723	37	·	·	PUNCT
ejpam-6535	723	38	)	)	PUNCT
ejpam-6535	723	39	is	be	AUX
ejpam-6535	723	40	invariant	invariant	ADJ
ejpam-6535	723	41	if	if	SCONJ
ejpam-6535	723	42	and	and	CCONJ
ejpam-6535	723	43	only	only	ADV
ejpam-6535	723	44	if	if	SCONJ
ejpam-6535	723	45	τ	τ	PROPN
ejpam-6535	723	46	(	(	PUNCT
ejpam-6535	723	47	f	f	PROPN
ejpam-6535	723	48	(	(	PUNCT
ejpam-6535	723	49	a	a	PRON
ejpam-6535	723	50	,	,	PUNCT
ejpam-6535	723	51	x	x	NOUN
ejpam-6535	723	52	)	)	PUNCT
ejpam-6535	723	53	,	,	PUNCT
ejpam-6535	723	54	f	f	PROPN
ejpam-6535	723	55	(	(	PUNCT
ejpam-6535	723	56	b	b	PROPN
ejpam-6535	723	57	,	,	PUNCT
ejpam-6535	723	58	y	y	NOUN
ejpam-6535	723	59	)	)	PUNCT
ejpam-6535	723	60	)	)	PUNCT
ejpam-6535	724	1	≤	≤	NUM
ejpam-6535	724	2	f	f	X
ejpam-6535	724	3	(	(	PUNCT
ejpam-6535	724	4	ab	ab	PROPN
ejpam-6535	724	5	,	,	PUNCT
ejpam-6535	724	6	xy	xy	PROPN
ejpam-6535	724	7	)	)	PUNCT
ejpam-6535	724	8	;	;	PUNCT
ejpam-6535	724	9	in	in	ADP
ejpam-6535	724	10	particular	particular	ADJ
ejpam-6535	724	11	,	,	PUNCT
ejpam-6535	724	12	this	this	PRON
ejpam-6535	724	13	holds	hold	VERB
ejpam-6535	724	14	if	if	SCONJ
ejpam-6535	724	15	s	s	NOUN
ejpam-6535	724	16	is	be	AUX
ejpam-6535	724	17	abelian	abelian	ADJ
ejpam-6535	724	18	.	.	PUNCT
ejpam-6535	725	1	(	(	PUNCT
ejpam-6535	725	2	c	c	X
ejpam-6535	725	3	)	)	PUNCT
ejpam-6535	725	4	the	the	DET
ejpam-6535	725	5	group	group	NOUN
ejpam-6535	725	6	norm	norm	NOUN
ejpam-6535	725	7	is	be	AUX
ejpam-6535	725	8	abelian	abelian	ADJ
ejpam-6535	725	9	if	if	SCONJ
ejpam-6535	725	10	and	and	CCONJ
ejpam-6535	725	11	only	only	ADV
ejpam-6535	725	12	if	if	SCONJ
ejpam-6535	725	13	the	the	DET
ejpam-6535	725	14	probabilistic	probabilistic	ADJ
ejpam-6535	725	15	norm	norm	NOUN
ejpam-6535	725	16	is	be	AUX
ejpam-6535	725	17	preserved	preserve	VERB
ejpam-6535	725	18	under	under	ADP
ejpam-6535	725	19	conjugacy	conjugacy	PROPN
ejpam-6535	725	20	(	(	PUNCT
ejpam-6535	725	21	under	under	ADP
ejpam-6535	725	22	automorphism	automorphism	NOUN
ejpam-6535	725	23	)	)	PUNCT
ejpam-6535	725	24	.	.	PUNCT
ejpam-6535	726	1	proof	proof	NOUN
ejpam-6535	726	2	.	.	PUNCT
ejpam-6535	727	1	(	(	PUNCT
ejpam-6535	727	2	a	a	X
ejpam-6535	727	3	)	)	PUNCT
ejpam-6535	727	4	let	let	VERB
ejpam-6535	727	5	us	we	PRON
ejpam-6535	727	6	assume	assume	VERB
ejpam-6535	727	7	that	that	SCONJ
ejpam-6535	727	8	the	the	DET
ejpam-6535	727	9	group	group	NOUN
ejpam-6535	727	10	norm	norm	NOUN
ejpam-6535	727	11	is	be	AUX
ejpam-6535	727	12	abelian	abelian	ADJ
ejpam-6535	727	13	.	.	PUNCT
ejpam-6535	728	1	then	then	ADV
ejpam-6535	728	2	we	we	PRON
ejpam-6535	728	3	have	have	AUX
ejpam-6535	728	4	ν(xy(ab)−1	ν(xy(ab)−1	NOUN
ejpam-6535	728	5	)	)	PUNCT
ejpam-6535	728	6	=	=	SYM
ejpam-6535	728	7	ν(xyb−1.a−1	ν(xyb−1.a−1	NOUN
ejpam-6535	728	8	)	)	PUNCT
ejpam-6535	728	9	=	=	SYM
ejpam-6535	728	10	ν(a−1xyb−1	ν(a−1xyb−1	NOUN
ejpam-6535	728	11	)	)	PUNCT
ejpam-6535	728	12	≥	≥	NOUN
ejpam-6535	728	13	τ	τ	PROPN
ejpam-6535	728	14	(	(	PUNCT
ejpam-6535	728	15	ν(a−1x	ν(a−1x	PROPN
ejpam-6535	728	16	)	)	PUNCT
ejpam-6535	728	17	,	,	PUNCT
ejpam-6535	728	18	ν(yb−1	ν(yb−1	NOUN
ejpam-6535	728	19	)	)	PUNCT
ejpam-6535	728	20	)	)	PUNCT
ejpam-6535	729	1	=	=	SYM
ejpam-6535	729	2	τ	τ	PROPN
ejpam-6535	729	3	(	(	PUNCT
ejpam-6535	729	4	ν(xa−1	ν(xa−1	PROPN
ejpam-6535	729	5	)	)	PUNCT
ejpam-6535	729	6	,	,	PUNCT
ejpam-6535	729	7	ν(b−1y	ν(b−1y	PROPN
ejpam-6535	729	8	)	)	PUNCT
ejpam-6535	729	9	)	)	PUNCT
ejpam-6535	729	10	.	.	PUNCT
ejpam-6535	730	1	for	for	ADP
ejpam-6535	730	2	the	the	DET
ejpam-6535	730	3	converse	converse	NOUN
ejpam-6535	730	4	part	part	NOUN
ejpam-6535	730	5	,	,	PUNCT
ejpam-6535	730	6	we	we	PRON
ejpam-6535	730	7	show	show	VERB
ejpam-6535	730	8	the	the	DET
ejpam-6535	730	9	invariance	invariance	NOUN
ejpam-6535	730	10	by	by	ADP
ejpam-6535	730	11	using	use	VERB
ejpam-6535	730	12	ν(ba−1	ν(ba−1	NOUN
ejpam-6535	730	13	)	)	PUNCT
ejpam-6535	730	14	=	=	SYM
ejpam-6535	730	15	ν(a−1b	ν(a−1b	PROPN
ejpam-6535	730	16	)	)	PUNCT
ejpam-6535	730	17	.	.	PUNCT
ejpam-6535	731	1	in	in	ADP
ejpam-6535	731	2	fact	fact	NOUN
ejpam-6535	731	3	,	,	PUNCT
ejpam-6535	731	4	it	it	PRON
ejpam-6535	731	5	suffices	suffice	VERB
ejpam-6535	731	6	to	to	PART
ejpam-6535	731	7	show	show	VERB
ejpam-6535	731	8	that	that	PRON
ejpam-6535	731	9	ν(yx−1	ν(yx−1	NOUN
ejpam-6535	731	10	)	)	PUNCT
ejpam-6535	731	11	≥	≥	NOUN
ejpam-6535	731	12	ν(x−1y	ν(x−1y	PROPN
ejpam-6535	731	13	)	)	PUNCT
ejpam-6535	731	14	.	.	PUNCT
ejpam-6535	732	1	take	take	VERB
ejpam-6535	732	2	x	x	PUNCT
ejpam-6535	732	3	=	=	PUNCT
ejpam-6535	732	4	a	a	PROPN
ejpam-6535	732	5	and	and	CCONJ
ejpam-6535	732	6	y	y	PROPN
ejpam-6535	732	7	=	=	SYM
ejpam-6535	732	8	b	b	PROPN
ejpam-6535	732	9	,	,	PUNCT
ejpam-6535	732	10	then	then	ADV
ejpam-6535	732	11	ν(ba−1	ν(ba−1	PROPN
ejpam-6535	732	12	)	)	PUNCT
ejpam-6535	732	13	≥	≥	NOUN
ejpam-6535	732	14	ν(a−1b	ν(a−1b	PROPN
ejpam-6535	732	15	)	)	PUNCT
ejpam-6535	732	16	,	,	PUNCT
ejpam-6535	732	17	and	and	CCONJ
ejpam-6535	732	18	taking	take	VERB
ejpam-6535	732	19	x	x	X
ejpam-6535	732	20	=	=	SYM
ejpam-6535	732	21	b−1	b−1	NOUN
ejpam-6535	732	22	,	,	PUNCT
ejpam-6535	732	23	and	and	CCONJ
ejpam-6535	732	24	y	y	PROPN
ejpam-6535	732	25	=	=	SYM
ejpam-6535	732	26	a−1	a−1	PROPN
ejpam-6535	732	27	,	,	PUNCT
ejpam-6535	732	28	we	we	PRON
ejpam-6535	732	29	get	get	VERB
ejpam-6535	732	30	ν(a−1b	ν(a−1b	X
ejpam-6535	732	31	)	)	PUNCT
ejpam-6535	732	32	≥	≥	NOUN
ejpam-6535	732	33	ν(ba−1	ν(ba−1	NOUN
ejpam-6535	732	34	)	)	PUNCT
ejpam-6535	732	35	.	.	PUNCT
ejpam-6535	733	1	observe	observe	VERB
ejpam-6535	733	2	upon	upon	SCONJ
ejpam-6535	733	3	using	use	VERB
ejpam-6535	733	4	the	the	DET
ejpam-6535	733	5	property	property	NOUN
ejpam-6535	733	6	of	of	ADP
ejpam-6535	733	7	norm	norm	NOUN
ejpam-6535	733	8	group	group	NOUN
ejpam-6535	733	9	that	that	PRON
ejpam-6535	733	10	ν(yx−1	ν(yx−1	VERB
ejpam-6535	733	11	)	)	PUNCT
ejpam-6535	733	12	=	=	SYM
ejpam-6535	733	13	ν(yy−1xy−1	ν(yy−1xy−1	PROPN
ejpam-6535	733	14	)	)	PUNCT
ejpam-6535	733	15	≥	≥	PROPN
ejpam-6535	733	16	τ	τ	PROPN
ejpam-6535	733	17	(	(	PUNCT
ejpam-6535	733	18	ν(yy−1	ν(yy−1	PROPN
ejpam-6535	733	19	)	)	PUNCT
ejpam-6535	733	20	,	,	PUNCT
ejpam-6535	733	21	ν(x−1y	ν(x−1y	ADJ
ejpam-6535	733	22	)	)	PUNCT
ejpam-6535	733	23	)	)	PUNCT
ejpam-6535	734	1	=	=	SYM
ejpam-6535	734	2	τ	τ	PROPN
ejpam-6535	734	3	(	(	PUNCT
ejpam-6535	734	4	ν(e	ν(e	PROPN
ejpam-6535	734	5	)	)	PUNCT
ejpam-6535	734	6	,	,	PUNCT
ejpam-6535	734	7	ν(x−1y	ν(x−1y	ADJ
ejpam-6535	734	8	)	)	PUNCT
ejpam-6535	734	9	)	)	PUNCT
ejpam-6535	735	1	=	=	SYM
ejpam-6535	735	2	τ	τ	PROPN
ejpam-6535	735	3	(	(	PUNCT
ejpam-6535	735	4	ϵ0	ϵ0	PROPN
ejpam-6535	735	5	,	,	PUNCT
ejpam-6535	735	6	ν(x	ν(x	PROPN
ejpam-6535	735	7	−1y	−1y	NOUN
ejpam-6535	735	8	)	)	PUNCT
ejpam-6535	735	9	)	)	PUNCT
ejpam-6535	736	1	=	=	SYM
ejpam-6535	736	2	ν(x−1y	ν(x−1y	ADJ
ejpam-6535	736	3	)	)	PUNCT
ejpam-6535	736	4	.	.	PUNCT
ejpam-6535	737	1	(	(	PUNCT
ejpam-6535	737	2	b	b	X
ejpam-6535	737	3	)	)	PUNCT
ejpam-6535	737	4	if	if	SCONJ
ejpam-6535	737	5	f	f	PROPN
ejpam-6535	737	6	is	be	AUX
ejpam-6535	737	7	invariant	invariant	ADJ
ejpam-6535	737	8	,	,	PUNCT
ejpam-6535	737	9	then	then	ADV
ejpam-6535	737	10	ν	ν	NOUN
ejpam-6535	737	11	is	be	AUX
ejpam-6535	737	12	abelian	abelian	ADJ
ejpam-6535	737	13	.	.	PUNCT
ejpam-6535	738	1	conversely	conversely	ADV
ejpam-6535	738	2	,	,	PUNCT
ejpam-6535	738	3	for	for	ADP
ejpam-6535	738	4	a	a	DET
ejpam-6535	738	5	probabilistic	probabilistic	ADJ
ejpam-6535	738	6	metric	metric	ADJ
ejpam-6535	738	7	f	f	NOUN
ejpam-6535	738	8	,	,	PUNCT
ejpam-6535	738	9	let	let	VERB
ejpam-6535	738	10	ν(x	ν(x	NOUN
ejpam-6535	738	11	)	)	PUNCT
ejpam-6535	739	1	=	=	SYM
ejpam-6535	739	2	f	f	X
ejpam-6535	739	3	(	(	PUNCT
ejpam-6535	739	4	e	e	NOUN
ejpam-6535	739	5	,	,	PUNCT
ejpam-6535	739	6	x	x	NOUN
ejpam-6535	739	7	)	)	PUNCT
ejpam-6535	739	8	.	.	PUNCT
ejpam-6535	740	1	then	then	ADV
ejpam-6535	740	2	ν	ν	PROPN
ejpam-6535	740	3	is	be	AUX
ejpam-6535	740	4	a	a	DET
ejpam-6535	740	5	group	group	NOUN
ejpam-6535	740	6	norm	norm	NOUN
ejpam-6535	740	7	since	since	SCONJ
ejpam-6535	740	8	τ	τ	PROPN
ejpam-6535	740	9	(	(	PUNCT
ejpam-6535	740	10	f	f	X
ejpam-6535	740	11	(	(	PUNCT
ejpam-6535	740	12	e	e	NOUN
ejpam-6535	740	13	,	,	PUNCT
ejpam-6535	740	14	x	x	NOUN
ejpam-6535	740	15	)	)	PUNCT
ejpam-6535	740	16	,	,	PUNCT
ejpam-6535	740	17	f	f	PROPN
ejpam-6535	740	18	(	(	PUNCT
ejpam-6535	740	19	e	e	NOUN
ejpam-6535	740	20	,	,	PUNCT
ejpam-6535	740	21	y	y	NOUN
ejpam-6535	740	22	)	)	PUNCT
ejpam-6535	740	23	)	)	PUNCT
ejpam-6535	740	24	≤	≤	NUM
ejpam-6535	741	1	f	f	X
ejpam-6535	741	2	(	(	PUNCT
ejpam-6535	741	3	ee	ee	PROPN
ejpam-6535	741	4	,	,	PUNCT
ejpam-6535	741	5	xy	xy	PROPN
ejpam-6535	741	6	)	)	PUNCT
ejpam-6535	742	1	=	=	SYM
ejpam-6535	742	2	f	f	X
ejpam-6535	742	3	(	(	PUNCT
ejpam-6535	742	4	e	e	NOUN
ejpam-6535	742	5	,	,	PUNCT
ejpam-6535	742	6	xy	xy	PROPN
ejpam-6535	742	7	)	)	PUNCT
ejpam-6535	742	8	.	.	PUNCT
ejpam-6535	743	1	hence	hence	ADV
ejpam-6535	743	2	f	f	PROPN
ejpam-6535	743	3	is	be	AUX
ejpam-6535	743	4	right	right	ADV
ejpam-6535	743	5	-	-	PUNCT
ejpam-6535	743	6	invariant	invariant	ADJ
ejpam-6535	743	7	,	,	PUNCT
ejpam-6535	743	8	and	and	CCONJ
ejpam-6535	743	9	f	f	PROPN
ejpam-6535	743	10	(	(	PUNCT
ejpam-6535	743	11	p	p	X
ejpam-6535	743	12	,	,	PUNCT
ejpam-6535	743	13	q	q	NOUN
ejpam-6535	743	14	)	)	PUNCT
ejpam-6535	743	15	=	=	NOUN
ejpam-6535	743	16	ν(pq−1	ν(pq−1	NOUN
ejpam-6535	743	17	)	)	PUNCT
ejpam-6535	743	18	.	.	PUNCT
ejpam-6535	744	1	now	now	ADV
ejpam-6535	744	2	we	we	PRON
ejpam-6535	744	3	show	show	VERB
ejpam-6535	744	4	that	that	SCONJ
ejpam-6535	744	5	the	the	DET
ejpam-6535	744	6	group	group	NOUN
ejpam-6535	744	7	norm	norm	NOUN
ejpam-6535	744	8	is	be	AUX
ejpam-6535	744	9	abelian	abelian	ADJ
ejpam-6535	744	10	since	since	SCONJ
ejpam-6535	744	11	ν(xy(ab)−1	ν(xy(ab)−1	NOUN
ejpam-6535	744	12	)	)	PUNCT
ejpam-6535	745	1	=	=	SYM
ejpam-6535	745	2	f	f	PROPN
ejpam-6535	745	3	(	(	PUNCT
ejpam-6535	745	4	xy	xy	PROPN
ejpam-6535	745	5	,	,	PUNCT
ejpam-6535	745	6	ab	ab	PROPN
ejpam-6535	745	7	)	)	PUNCT
ejpam-6535	745	8	≥	≥	PROPN
ejpam-6535	745	9	τ	τ	PROPN
ejpam-6535	745	10	(	(	PUNCT
ejpam-6535	745	11	f	f	X
ejpam-6535	745	12	(	(	PUNCT
ejpam-6535	745	13	x	x	PROPN
ejpam-6535	745	14	,	,	PUNCT
ejpam-6535	745	15	a	a	NOUN
ejpam-6535	745	16	)	)	PUNCT
ejpam-6535	745	17	,	,	PUNCT
ejpam-6535	745	18	f	f	PROPN
ejpam-6535	745	19	(	(	PUNCT
ejpam-6535	745	20	y	y	PROPN
ejpam-6535	745	21	,	,	PUNCT
ejpam-6535	745	22	b	b	NOUN
ejpam-6535	745	23	)	)	PUNCT
ejpam-6535	745	24	)	)	PUNCT
ejpam-6535	746	1	=	=	SYM
ejpam-6535	746	2	τ	τ	PROPN
ejpam-6535	746	3	(	(	PUNCT
ejpam-6535	746	4	ν(xa−1	ν(xa−1	PROPN
ejpam-6535	746	5	)	)	PUNCT
ejpam-6535	746	6	,	,	PUNCT
ejpam-6535	746	7	ν(yb−1	ν(yb−1	NOUN
ejpam-6535	746	8	)	)	PUNCT
ejpam-6535	746	9	)	)	PUNCT
ejpam-6535	746	10	hence	hence	ADV
ejpam-6535	746	11	f	f	PROPN
ejpam-6535	746	12	is	be	AUX
ejpam-6535	746	13	also	also	ADV
ejpam-6535	746	14	left	leave	VERB
ejpam-6535	746	15	-	-	PUNCT
ejpam-6535	746	16	invariant	invariant	ADJ
ejpam-6535	746	17	.	.	PUNCT
ejpam-6535	747	1	(	(	PUNCT
ejpam-6535	747	2	c	c	X
ejpam-6535	747	3	)	)	PUNCT
ejpam-6535	747	4	suppose	suppose	VERB
ejpam-6535	747	5	the	the	DET
ejpam-6535	747	6	probabilistic	probabilistic	ADJ
ejpam-6535	747	7	norm	norm	NOUN
ejpam-6535	747	8	is	be	AUX
ejpam-6535	747	9	abelian	abelian	ADJ
ejpam-6535	747	10	..	..	PUNCT
ejpam-6535	747	11	then	then	ADV
ejpam-6535	747	12	for	for	ADP
ejpam-6535	747	13	any	any	DET
ejpam-6535	747	14	g	g	NOUN
ejpam-6535	747	15	,	,	PUNCT
ejpam-6535	747	16	by	by	ADP
ejpam-6535	747	17	the	the	DET
ejpam-6535	747	18	cyclic	cyclic	ADJ
ejpam-6535	747	19	property	property	NOUN
ejpam-6535	747	20	ν(g−1bg	ν(g−1bg	NOUN
ejpam-6535	747	21	)	)	PUNCT
ejpam-6535	747	22	=	=	SYM
ejpam-6535	747	23	ν(gg−1b	ν(gg−1b	NOUN
ejpam-6535	747	24	)	)	PUNCT
ejpam-6535	747	25	=	=	SYM
ejpam-6535	748	1	ν(b	ν(b	PROPN
ejpam-6535	748	2	)	)	PUNCT
ejpam-6535	748	3	.	.	PUNCT
ejpam-6535	749	1	conversely	conversely	ADV
ejpam-6535	749	2	,	,	PUNCT
ejpam-6535	749	3	if	if	SCONJ
ejpam-6535	749	4	the	the	DET
ejpam-6535	749	5	probabilistic	probabilistic	ADJ
ejpam-6535	749	6	norm	norm	NOUN
ejpam-6535	749	7	is	be	AUX
ejpam-6535	749	8	preserved	preserve	VERB
ejpam-6535	749	9	under	under	ADP
ejpam-6535	749	10	automorphism	automorphism	NOUN
ejpam-6535	749	11	,	,	PUNCT
ejpam-6535	749	12	then	then	ADV
ejpam-6535	749	13	we	we	PRON
ejpam-6535	749	14	have	have	VERB
ejpam-6535	749	15	invariance	invariance	NOUN
ejpam-6535	749	16	,	,	PUNCT
ejpam-6535	749	17	since	since	SCONJ
ejpam-6535	749	18	ν(ba−1	ν(ba−1	NOUN
ejpam-6535	749	19	)	)	PUNCT
ejpam-6535	749	20	=	=	PUNCT
ejpam-6535	749	21	ν(a−1(ba−1a	ν(a−1(ba−1a	PROPN
ejpam-6535	749	22	)	)	PUNCT
ejpam-6535	749	23	)	)	PUNCT
ejpam-6535	750	1	=	=	PUNCT
ejpam-6535	750	2	ν(a−1b	ν(a−1b	PROPN
ejpam-6535	750	3	)	)	PUNCT
ejpam-6535	750	4	.	.	PUNCT
ejpam-6535	751	1	9	9	X
ejpam-6535	751	2	.	.	X
ejpam-6535	751	3	conclusion	conclusion	NOUN
ejpam-6535	751	4	in	in	ADP
ejpam-6535	751	5	this	this	DET
ejpam-6535	751	6	article	article	NOUN
ejpam-6535	751	7	,	,	PUNCT
ejpam-6535	751	8	we	we	PRON
ejpam-6535	751	9	studied	study	VERB
ejpam-6535	751	10	various	various	ADJ
ejpam-6535	751	11	subcategories	subcategorie	NOUN
ejpam-6535	751	12	of	of	ADP
ejpam-6535	751	13	the	the	DET
ejpam-6535	751	14	category	category	NOUN
ejpam-6535	751	15	of	of	ADP
ejpam-6535	751	16	probabilistic	probabilistic	ADJ
ejpam-6535	751	17	convergence	convergence	NOUN
ejpam-6535	751	18	groups	group	NOUN
ejpam-6535	751	19	in	in	ADP
ejpam-6535	751	20	a	a	DET
ejpam-6535	751	21	continuation	continuation	NOUN
ejpam-6535	751	22	of	of	ADP
ejpam-6535	751	23	the	the	DET
ejpam-6535	751	24	previous	previous	ADJ
ejpam-6535	751	25	works	work	NOUN
ejpam-6535	751	26	undertaken	undertake	VERB
ejpam-6535	751	27	in	in	ADP
ejpam-6535	751	28	these	these	DET
ejpam-6535	751	29	areas	area	NOUN
ejpam-6535	751	30	,	,	PUNCT
ejpam-6535	751	31	cf	cf	INTJ
ejpam-6535	751	32	.	.	PUNCT
ejpam-6535	752	1	[	[	X
ejpam-6535	752	2	3	3	NUM
ejpam-6535	752	3	,	,	PUNCT
ejpam-6535	752	4	5	5	NUM
ejpam-6535	752	5	]	]	PUNCT
ejpam-6535	752	6	.	.	PUNCT
ejpam-6535	753	1	in	in	ADP
ejpam-6535	753	2	doing	do	VERB
ejpam-6535	753	3	so	so	ADV
ejpam-6535	753	4	,	,	PUNCT
ejpam-6535	753	5	we	we	PRON
ejpam-6535	753	6	introduced	introduce	VERB
ejpam-6535	753	7	a	a	DET
ejpam-6535	753	8	category	category	NOUN
ejpam-6535	753	9	of	of	ADP
ejpam-6535	753	10	probabilistic	probabilistic	ADJ
ejpam-6535	753	11	neighborhood	neighborhood	NOUN
ejpam-6535	753	12	spaces	space	NOUN
ejpam-6535	753	13	,	,	PUNCT
ejpam-6535	753	14	pneigh	pneigh	NOUN
ejpam-6535	753	15	,	,	PUNCT
ejpam-6535	753	16	and	and	CCONJ
ejpam-6535	753	17	probabilistic	probabilistic	ADJ
ejpam-6535	753	18	neighborhood	neighborhood	NOUN
ejpam-6535	753	19	groups	group	NOUN
ejpam-6535	753	20	,	,	PUNCT
ejpam-6535	753	21	pneighgrp	pneighgrp	NOUN
ejpam-6535	753	22	,	,	PUNCT
ejpam-6535	753	23	showing	show	VERB
ejpam-6535	753	24	that	that	SCONJ
ejpam-6535	753	25	every	every	DET
ejpam-6535	753	26	probabilistic	probabilistic	ADJ
ejpam-6535	753	27	metric	metric	ADJ
ejpam-6535	753	28	group	group	NOUN
ejpam-6535	753	29	is	be	AUX
ejpam-6535	753	30	a	a	DET
ejpam-6535	753	31	probabilistic	probabilistic	ADJ
ejpam-6535	753	32	neighborhood	neighborhood	NOUN
ejpam-6535	753	33	group	group	NOUN
ejpam-6535	753	34	.	.	PUNCT
ejpam-6535	754	1	moreover	moreover	ADV
ejpam-6535	754	2	,	,	PUNCT
ejpam-6535	754	3	we	we	PRON
ejpam-6535	754	4	talked	talk	VERB
ejpam-6535	754	5	about	about	ADP
ejpam-6535	754	6	the	the	DET
ejpam-6535	754	7	category	category	NOUN
ejpam-6535	754	8	of	of	ADP
ejpam-6535	754	9	probabilistic	probabilistic	ADJ
ejpam-6535	754	10	pre	pre	ADJ
ejpam-6535	754	11	-	-	ADJ
ejpam-6535	754	12	cauchy	cauchy	ADJ
ejpam-6535	754	13	groups	group	NOUN
ejpam-6535	754	14	,	,	PUNCT
ejpam-6535	754	15	pprechygrp	pprechygrp	NOUN
ejpam-6535	754	16	,	,	PUNCT
ejpam-6535	754	17	and	and	CCONJ
ejpam-6535	754	18	its	its	PRON
ejpam-6535	754	19	relation	relation	NOUN
ejpam-6535	754	20	with	with	ADP
ejpam-6535	754	21	an	an	DET
ejpam-6535	754	22	already	already	ADV
ejpam-6535	754	23	known	know	VERB
ejpam-6535	754	24	category	category	NOUN
ejpam-6535	754	25	of	of	ADP
ejpam-6535	754	26	probabilistic	probabilistic	ADJ
ejpam-6535	754	27	cauchy	cauchy	ADJ
ejpam-6535	754	28	groups	group	NOUN
ejpam-6535	754	29	,	,	PUNCT
ejpam-6535	754	30	pchygrp	pchygrp	NOUN
ejpam-6535	754	31	,	,	PUNCT
ejpam-6535	754	32	where	where	SCONJ
ejpam-6535	754	33	it	it	PRON
ejpam-6535	754	34	is	be	AUX
ejpam-6535	754	35	observed	observe	VERB
ejpam-6535	754	36	that	that	SCONJ
ejpam-6535	754	37	pchygrp	pchygrp	NOUN
ejpam-6535	754	38	is	be	AUX
ejpam-6535	754	39	a	a	DET
ejpam-6535	754	40	full	full	ADJ
ejpam-6535	754	41	subcategory	subcategory	NOUN
ejpam-6535	754	42	of	of	ADP
ejpam-6535	754	43	pprechygrp	pprechygrp	PROPN
ejpam-6535	754	44	.	.	PUNCT
ejpam-6535	755	1	moreover	moreover	ADV
ejpam-6535	755	2	,	,	PUNCT
ejpam-6535	755	3	we	we	PRON
ejpam-6535	755	4	discussed	discuss	VERB
ejpam-6535	755	5	the	the	DET
ejpam-6535	755	6	fact	fact	NOUN
ejpam-6535	755	7	that	that	SCONJ
ejpam-6535	755	8	there	there	PRON
ejpam-6535	755	9	exists	exist	VERB
ejpam-6535	755	10	a	a	DET
ejpam-6535	755	11	one	one	NUM
ejpam-6535	755	12	-	-	PUNCT
ejpam-6535	755	13	to	to	ADP
ejpam-6535	755	14	-	-	PUNCT
ejpam-6535	755	15	one	one	NUM
ejpam-6535	755	16	correspondence	correspondence	NOUN
ejpam-6535	755	17	between	between	ADP
ejpam-6535	755	18	probabilistic	probabilistic	ADJ
ejpam-6535	755	19	metrics	metric	NOUN
ejpam-6535	755	20	on	on	ADP
ejpam-6535	755	21	groups	group	NOUN
ejpam-6535	755	22	and	and	CCONJ
ejpam-6535	755	23	probabilistic	probabilistic	ADJ
ejpam-6535	755	24	group	group	NOUN
ejpam-6535	755	25	norms	norm	NOUN
ejpam-6535	755	26	,	,	PUNCT
ejpam-6535	755	27	here	here	ADV
ejpam-6535	755	28	we	we	PRON
ejpam-6535	755	29	showed	show	VERB
ejpam-6535	755	30	that	that	SCONJ
ejpam-6535	755	31	the	the	DET
ejpam-6535	755	32	category	category	NOUN
ejpam-6535	755	33	of	of	ADP
ejpam-6535	755	34	probabilistic	probabilistic	ADJ
ejpam-6535	755	35	normed	normed	ADJ
ejpam-6535	755	36	groups	group	NOUN
ejpam-6535	755	37	,	,	PUNCT
ejpam-6535	755	38	normedgrp	normedgrp	VERB
ejpam-6535	755	39	is	be	AUX
ejpam-6535	755	40	isomorphic	isomorphic	ADJ
ejpam-6535	755	41	to	to	ADP
ejpam-6535	755	42	the	the	DET
ejpam-6535	755	43	category	category	NOUN
ejpam-6535	755	44	of	of	ADP
ejpam-6535	755	45	probabilistic	probabilistic	ADJ
ejpam-6535	755	46	metric	metric	ADJ
ejpam-6535	755	47	groups	group	NOUN
ejpam-6535	755	48	,	,	PUNCT
ejpam-6535	755	49	pmetgrp	pmetgrp	PROPN
ejpam-6535	755	50	.	.	PUNCT
ejpam-6535	756	1	on	on	ADP
ejpam-6535	756	2	the	the	DET
ejpam-6535	756	3	other	other	ADJ
ejpam-6535	756	4	hand	hand	NOUN
ejpam-6535	756	5	,	,	PUNCT
ejpam-6535	756	6	it	it	PRON
ejpam-6535	756	7	is	be	AUX
ejpam-6535	756	8	proved	prove	VERB
ejpam-6535	756	9	in	in	ADP
ejpam-6535	756	10	[	[	X
ejpam-6535	756	11	4	4	X
ejpam-6535	756	12	]	]	PUNCT
ejpam-6535	756	13	that	that	SCONJ
ejpam-6535	756	14	the	the	DET
ejpam-6535	756	15	category	category	NOUN
ejpam-6535	756	16	pmetgrp	pmetgrp	VERB
ejpam-6535	756	17	is	be	AUX
ejpam-6535	756	18	isomorphic	isomorphic	ADJ
ejpam-6535	756	19	to	to	ADP
ejpam-6535	756	20	the	the	DET
ejpam-6535	756	21	category	category	NOUN
ejpam-6535	756	22	pmetconvgrp	pmetconvgrp	NOUN
ejpam-6535	756	23	under	under	ADP
ejpam-6535	756	24	sup	sup	ADJ
ejpam-6535	756	25	-	-	PUNCT
ejpam-6535	756	26	continuous	continuous	ADJ
ejpam-6535	756	27	triangle	triangle	NOUN
ejpam-6535	756	28	function	function	NOUN
ejpam-6535	756	29	τ	τ	PROPN
ejpam-6535	756	30	,	,	PUNCT
ejpam-6535	756	31	i.e.	i.e.	X
ejpam-6535	756	32	,	,	PUNCT
ejpam-6535	756	33	pmetgrp∼=pmetconvgrp	pmetgrp∼=pmetconvgrp	NOUN
ejpam-6535	756	34	under	under	ADP
ejpam-6535	756	35	sup	sup	ADJ
ejpam-6535	756	36	-	-	PUNCT
ejpam-6535	756	37	continuous	continuous	ADJ
ejpam-6535	756	38	triangle	triangle	NOUN
ejpam-6535	756	39	function	function	NOUN
ejpam-6535	756	40	τ	τ	X
ejpam-6535	756	41	.	.	PUNCT
ejpam-6535	757	1	question	question	NOUN
ejpam-6535	757	2	remains	remain	VERB
ejpam-6535	757	3	how	how	SCONJ
ejpam-6535	757	4	to	to	PART
ejpam-6535	757	5	give	give	VERB
ejpam-6535	757	6	a	a	DET
ejpam-6535	757	7	direct	direct	ADJ
ejpam-6535	757	8	proof	proof	NOUN
ejpam-6535	757	9	that	that	SCONJ
ejpam-6535	757	10	the	the	DET
ejpam-6535	757	11	category	category	NOUN
ejpam-6535	757	12	normedgrp	normedgrp	VERB
ejpam-6535	757	13	is	be	AUX
ejpam-6535	757	14	isomorphic	isomorphic	ADJ
ejpam-6535	757	15	to	to	ADP
ejpam-6535	757	16	pmetconvgrp	pmetconvgrp	VERB
ejpam-6535	757	17	,	,	PUNCT
ejpam-6535	757	18	i.e.	i.e.	X
ejpam-6535	757	19	,	,	PUNCT
ejpam-6535	757	20	normedgrp∼=	normedgrp∼=	PROPN
ejpam-6535	757	21	pmetconvgrp	pmetconvgrp	NOUN
ejpam-6535	757	22	?	?	PUNCT
ejpam-6535	758	1	while	while	SCONJ
ejpam-6535	758	2	completing	complete	VERB
ejpam-6535	758	3	this	this	DET
ejpam-6535	758	4	paper	paper	NOUN
ejpam-6535	758	5	,	,	PUNCT
ejpam-6535	758	6	we	we	PRON
ejpam-6535	758	7	further	far	ADV
ejpam-6535	758	8	observe	observe	VERB
ejpam-6535	758	9	some	some	DET
ejpam-6535	758	10	open	open	ADJ
ejpam-6535	758	11	problems	problem	NOUN
ejpam-6535	758	12	relating	relate	VERB
ejpam-6535	758	13	to	to	ADP
ejpam-6535	758	14	this	this	DET
ejpam-6535	758	15	work	work	NOUN
ejpam-6535	758	16	,	,	PUNCT
ejpam-6535	758	17	such	such	ADJ
ejpam-6535	758	18	as	as	ADP
ejpam-6535	758	19	,	,	PUNCT
ejpam-6535	758	20	(	(	PUNCT
ejpam-6535	758	21	a	a	X
ejpam-6535	758	22	)	)	PUNCT
ejpam-6535	758	23	probabilistic	probabilistic	ADJ
ejpam-6535	758	24	norms	norm	NOUN
ejpam-6535	758	25	on	on	ADP
ejpam-6535	758	26	the	the	DET
ejpam-6535	758	27	class	class	NOUN
ejpam-6535	758	28	of	of	ADP
ejpam-6535	758	29	homeomorphisms	homeomorphism	NOUN
ejpam-6535	758	30	of	of	ADP
ejpam-6535	758	31	groups	group	NOUN
ejpam-6535	758	32	in	in	ADP
ejpam-6535	758	33	relation	relation	NOUN
ejpam-6535	758	34	to	to	ADP
ejpam-6535	758	35	tardiff	tardiff	NOUN
ejpam-6535	758	36	neighborhood	neighborhood	NOUN
ejpam-6535	758	37	system	system	NOUN
ejpam-6535	758	38	of	of	ADP
ejpam-6535	758	39	probabilistic	probabilistic	ADJ
ejpam-6535	758	40	metrics	metric	NOUN
ejpam-6535	758	41	,	,	PUNCT
ejpam-6535	758	42	and	and	CCONJ
ejpam-6535	758	43	their	their	PRON
ejpam-6535	758	44	relationship	relationship	NOUN
ejpam-6535	758	45	with	with	ADP
ejpam-6535	758	46	the	the	DET
ejpam-6535	758	47	work	work	NOUN
ejpam-6535	758	48	undertaken	undertake	VERB
ejpam-6535	758	49	in	in	ADP
ejpam-6535	758	50	[	[	X
ejpam-6535	758	51	31	31	NUM
ejpam-6535	758	52	]	]	PUNCT
ejpam-6535	758	53	;	;	PUNCT
ejpam-6535	758	54	(	(	PUNCT
ejpam-6535	758	55	b	b	X
ejpam-6535	758	56	)	)	PUNCT
ejpam-6535	758	57	probabilistic	probabilistic	ADJ
ejpam-6535	758	58	neighborhood	neighborhood	NOUN
ejpam-6535	758	59	topological	topological	ADJ
ejpam-6535	758	60	groups	group	NOUN
ejpam-6535	758	61	in	in	ADP
ejpam-6535	758	62	relation	relation	NOUN
ejpam-6535	758	63	to	to	PART
ejpam-6535	758	64	probabilistic	probabilistic	VERB
ejpam-6535	758	65	normed	normed	ADJ
ejpam-6535	758	66	groups	group	NOUN
ejpam-6535	758	67	;	;	PUNCT
ejpam-6535	758	68	(	(	PUNCT
ejpam-6535	758	69	c	c	X
ejpam-6535	758	70	)	)	PUNCT
ejpam-6535	758	71	although	although	SCONJ
ejpam-6535	758	72	for	for	ADP
ejpam-6535	758	73	a	a	DET
ejpam-6535	758	74	specific	specific	ADJ
ejpam-6535	758	75	purpose	purpose	NOUN
ejpam-6535	758	76	,	,	PUNCT
ejpam-6535	758	77	we	we	PRON
ejpam-6535	758	78	brought	bring	VERB
ejpam-6535	758	79	into	into	ADP
ejpam-6535	758	80	light	light	NOUN
ejpam-6535	758	81	the	the	DET
ejpam-6535	758	82	notion	notion	NOUN
ejpam-6535	758	83	of	of	ADP
ejpam-6535	758	84	probabilistic	probabilistic	ADJ
ejpam-6535	758	85	closure	closure	NOUN
ejpam-6535	758	86	operator	operator	NOUN
ejpam-6535	758	87	a	a	DET
ejpam-6535	758	88	dual	dual	ADJ
ejpam-6535	758	89	to	to	PART
ejpam-6535	758	90	probabilistic	probabilistic	VERB
ejpam-6535	758	91	interior	interior	ADJ
ejpam-6535	758	92	operator	operator	NOUN
ejpam-6535	758	93	that	that	PRON
ejpam-6535	758	94	studied	study	VERB
ejpam-6535	758	95	in	in	ADP
ejpam-6535	758	96	[	[	X
ejpam-6535	758	97	22	22	NUM
ejpam-6535	758	98	]	]	PUNCT
ejpam-6535	758	99	,	,	PUNCT
ejpam-6535	758	100	we	we	PRON
ejpam-6535	758	101	intend	intend	VERB
ejpam-6535	758	102	to	to	PART
ejpam-6535	758	103	discuss	discuss	VERB
ejpam-6535	758	104	this	this	DET
ejpam-6535	758	105	probabilistic	probabilistic	ADJ
ejpam-6535	758	106	closure	closure	NOUN
ejpam-6535	758	107	operator	operator	NOUN
ejpam-6535	758	108	in	in	ADP
ejpam-6535	758	109	relation	relation	NOUN
ejpam-6535	758	110	to	to	PART
ejpam-6535	758	111	probabilistic	probabilistic	ADJ
ejpam-6535	758	112	approximation	approximation	NOUN
ejpam-6535	758	113	spaces	space	NOUN
ejpam-6535	758	114	.	.	PUNCT
ejpam-6535	759	1	all	all	PRON
ejpam-6535	759	2	of	of	ADP
ejpam-6535	759	3	these	these	DET
ejpam-6535	759	4	open	open	ADJ
ejpam-6535	759	5	problems	problem	NOUN
ejpam-6535	759	6	could	could	AUX
ejpam-6535	759	7	t.m.g	t.m.g	VERB
ejpam-6535	759	8	.	.	PUNCT
ejpam-6535	760	1	ahsanullah	ahsanullah	VERB
ejpam-6535	760	2	,	,	PUNCT
ejpam-6535	760	3	fawzi	fawzi	PROPN
ejpam-6535	760	4	al	al	PROPN
ejpam-6535	760	5	-	-	PUNCT
ejpam-6535	760	6	thukair	thukair	NOUN
ejpam-6535	760	7	/	/	SYM
ejpam-6535	760	8	eur	eur	NOUN
ejpam-6535	760	9	.	.	PUNCT
ejpam-6535	761	1	j.	j.	PROPN
ejpam-6535	761	2	pure	pure	PROPN
ejpam-6535	761	3	appl	appl	PROPN
ejpam-6535	761	4	.	.	PROPN
ejpam-6535	761	5	math	math	PROPN
ejpam-6535	761	6	,	,	PUNCT
ejpam-6535	761	7	18	18	NUM
ejpam-6535	761	8	(	(	PUNCT
ejpam-6535	761	9	3	3	NUM
ejpam-6535	761	10	)	)	PUNCT
ejpam-6535	761	11	(	(	PUNCT
ejpam-6535	761	12	2025	2025	NUM
ejpam-6535	761	13	)	)	PUNCT
ejpam-6535	761	14	,	,	PUNCT
ejpam-6535	761	15	6535	6535	NUM
ejpam-6535	761	16	26	26	NUM
ejpam-6535	761	17	of	of	ADP
ejpam-6535	761	18	28	28	NUM
ejpam-6535	761	19	be	be	AUX
ejpam-6535	761	20	discussed	discuss	VERB
ejpam-6535	761	21	in	in	ADP
ejpam-6535	761	22	separate	separate	ADJ
ejpam-6535	761	23	papers	paper	NOUN
ejpam-6535	761	24	in	in	ADP
ejpam-6535	761	25	near	near	ADJ
ejpam-6535	761	26	future	future	NOUN
ejpam-6535	761	27	.	.	PUNCT
ejpam-6535	762	1	finally	finally	ADV
ejpam-6535	762	2	,	,	PUNCT
ejpam-6535	762	3	we	we	PRON
ejpam-6535	762	4	would	would	AUX
ejpam-6535	762	5	like	like	VERB
ejpam-6535	762	6	to	to	PART
ejpam-6535	762	7	add	add	VERB
ejpam-6535	762	8	here	here	ADV
ejpam-6535	762	9	as	as	SCONJ
ejpam-6535	762	10	already	already	ADV
ejpam-6535	762	11	mentioned	mention	VERB
ejpam-6535	762	12	in	in	ADP
ejpam-6535	762	13	section	section	NOUN
ejpam-6535	762	14	6	6	NUM
ejpam-6535	762	15	that	that	SCONJ
ejpam-6535	762	16	in	in	ADP
ejpam-6535	762	17	[	[	X
ejpam-6535	762	18	10	10	NUM
ejpam-6535	762	19	]	]	PUNCT
ejpam-6535	762	20	,	,	PUNCT
ejpam-6535	762	21	it	it	PRON
ejpam-6535	762	22	is	be	AUX
ejpam-6535	762	23	shown	show	VERB
ejpam-6535	762	24	that	that	SCONJ
ejpam-6535	762	25	kt2convfco	kt2convfco	PROPN
ejpam-6535	762	26	,	,	PUNCT
ejpam-6535	762	27	the	the	DET
ejpam-6535	762	28	category	category	NOUN
ejpam-6535	762	29	of	of	ADP
ejpam-6535	762	30	kt2	kt2	PROPN
ejpam-6535	762	31	constant	constant	ADJ
ejpam-6535	762	32	convergence	convergence	NOUN
ejpam-6535	762	33	spaces	space	NOUN
ejpam-6535	762	34	and	and	CCONJ
ejpam-6535	762	35	continuous	continuous	ADJ
ejpam-6535	762	36	functions	function	NOUN
ejpam-6535	762	37	,	,	PUNCT
ejpam-6535	762	38	and	and	CCONJ
ejpam-6535	762	39	chy	chy	PROPN
ejpam-6535	762	40	,	,	PUNCT
ejpam-6535	762	41	the	the	DET
ejpam-6535	762	42	category	category	NOUN
ejpam-6535	762	43	of	of	ADP
ejpam-6535	762	44	cauchy	cauchy	PROPN
ejpam-6535	762	45	spaces	space	NOUN
ejpam-6535	762	46	and	and	CCONJ
ejpam-6535	762	47	cauchy	cauchy	PROPN
ejpam-6535	762	48	maps	map	NOUN
ejpam-6535	762	49	are	be	AUX
ejpam-6535	762	50	isomorphic	isomorphic	ADJ
ejpam-6535	762	51	.	.	PUNCT
ejpam-6535	763	1	also	also	ADV
ejpam-6535	763	2	,	,	PUNCT
ejpam-6535	763	3	it	it	PRON
ejpam-6535	763	4	is	be	AUX
ejpam-6535	763	5	proved	prove	VERB
ejpam-6535	763	6	there	there	ADV
ejpam-6535	763	7	that	that	SCONJ
ejpam-6535	763	8	convfco	convfco	NOUN
ejpam-6535	763	9	,	,	PUNCT
ejpam-6535	763	10	the	the	DET
ejpam-6535	763	11	category	category	NOUN
ejpam-6535	763	12	of	of	ADP
ejpam-6535	763	13	constant	constant	ADJ
ejpam-6535	763	14	convergence	convergence	NOUN
ejpam-6535	763	15	spaces	space	NOUN
ejpam-6535	763	16	and	and	CCONJ
ejpam-6535	763	17	continuous	continuous	ADJ
ejpam-6535	763	18	functions	function	NOUN
ejpam-6535	763	19	and	and	CCONJ
ejpam-6535	763	20	filprechy	filprechy	NOUN
ejpam-6535	763	21	,	,	PUNCT
ejpam-6535	763	22	the	the	DET
ejpam-6535	763	23	category	category	NOUN
ejpam-6535	763	24	of	of	ADP
ejpam-6535	763	25	filter	filter	NOUN
ejpam-6535	763	26	precauchy	precauchy	ADJ
ejpam-6535	763	27	spaces	space	NOUN
ejpam-6535	763	28	and	and	CCONJ
ejpam-6535	763	29	cauchy	cauchy	PROPN
ejpam-6535	763	30	maps	map	NOUN
ejpam-6535	763	31	are	be	AUX
ejpam-6535	763	32	isomorphic	isomorphic	ADJ
ejpam-6535	763	33	.	.	PUNCT
ejpam-6535	764	1	it	it	PRON
ejpam-6535	764	2	would	would	AUX
ejpam-6535	764	3	be	be	AUX
ejpam-6535	764	4	interesting	interesting	ADJ
ejpam-6535	764	5	to	to	PART
ejpam-6535	764	6	see	see	VERB
ejpam-6535	764	7	if	if	SCONJ
ejpam-6535	764	8	one	one	PRON
ejpam-6535	764	9	can	can	AUX
ejpam-6535	764	10	study	study	VERB
ejpam-6535	764	11	these	these	DET
ejpam-6535	764	12	new	new	ADJ
ejpam-6535	764	13	categories	category	NOUN
ejpam-6535	764	14	from	from	ADP
ejpam-6535	764	15	the	the	DET
ejpam-6535	764	16	perspective	perspective	NOUN
ejpam-6535	764	17	of	of	ADP
ejpam-6535	764	18	algebraic	algebraic	ADJ
ejpam-6535	764	19	structures	structure	NOUN
ejpam-6535	764	20	;	;	PUNCT
ejpam-6535	764	21	for	for	ADP
ejpam-6535	764	22	instance	instance	NOUN
ejpam-6535	764	23	,	,	PUNCT
ejpam-6535	764	24	search	search	NOUN
ejpam-6535	764	25	for	for	ADP
ejpam-6535	764	26	group	group	NOUN
ejpam-6535	764	27	objects	object	NOUN
ejpam-6535	764	28	in	in	ADP
ejpam-6535	764	29	these	these	DET
ejpam-6535	764	30	categories	category	NOUN
ejpam-6535	764	31	and	and	CCONJ
ejpam-6535	764	32	their	their	PRON
ejpam-6535	764	33	relationship	relationship	NOUN
ejpam-6535	764	34	.	.	PUNCT
ejpam-6535	765	1	acknowledgements	acknowledgement	NOUN
ejpam-6535	765	2	we	we	PRON
ejpam-6535	765	3	sincerely	sincerely	ADV
ejpam-6535	765	4	express	express	VERB
ejpam-6535	765	5	our	our	PRON
ejpam-6535	765	6	cordial	cordial	ADJ
ejpam-6535	765	7	thanks	thank	NOUN
ejpam-6535	765	8	to	to	ADP
ejpam-6535	765	9	the	the	DET
ejpam-6535	765	10	anonymous	anonymous	ADJ
ejpam-6535	765	11	referees	referee	NOUN
ejpam-6535	765	12	for	for	ADP
ejpam-6535	765	13	carefully	carefully	ADV
ejpam-6535	765	14	reading	read	VERB
ejpam-6535	765	15	the	the	DET
ejpam-6535	765	16	manuscript	manuscript	NOUN
ejpam-6535	765	17	and	and	CCONJ
ejpam-6535	765	18	offering	offer	VERB
ejpam-6535	765	19	various	various	ADJ
ejpam-6535	765	20	suggestions	suggestion	NOUN
ejpam-6535	765	21	.	.	PUNCT
ejpam-6535	766	1	references	reference	NOUN
ejpam-6535	766	2	[	[	X
ejpam-6535	766	3	1	1	X
ejpam-6535	766	4	]	]	PUNCT
ejpam-6535	766	5	j.	j.	PROPN
ejpam-6535	766	6	adámek	adámek	PROPN
ejpam-6535	766	7	,	,	PUNCT
ejpam-6535	766	8	h.	h.	PROPN
ejpam-6535	766	9	herrlich	herrlich	PROPN
ejpam-6535	766	10	and	and	CCONJ
ejpam-6535	766	11	g.	g.	PROPN
ejpam-6535	766	12	e.	e.	PROPN
ejpam-6535	766	13	strecker	strecker	PROPN
ejpam-6535	766	14	.	.	PUNCT
ejpam-6535	767	1	abstract	abstract	ADJ
ejpam-6535	767	2	and	and	CCONJ
ejpam-6535	767	3	concrete	concrete	ADJ
ejpam-6535	767	4	categories	category	NOUN
ejpam-6535	767	5	.	.	PUNCT
ejpam-6535	768	1	j.	j.	PROPN
ejpam-6535	768	2	wiley	wiley	PROPN
ejpam-6535	768	3	&	&	CCONJ
ejpam-6535	768	4	sons	son	NOUN
ejpam-6535	768	5	,	,	PUNCT
ejpam-6535	768	6	new	new	PROPN
ejpam-6535	768	7	york	york	PROPN
ejpam-6535	768	8	,	,	PUNCT
ejpam-6535	768	9	1990	1990	NUM
ejpam-6535	768	10	.	.	PUNCT
ejpam-6535	769	1	[	[	X
ejpam-6535	769	2	2	2	X
ejpam-6535	769	3	]	]	PUNCT
ejpam-6535	769	4	t.	t.	NOUN
ejpam-6535	769	5	m.	m.	NOUN
ejpam-6535	769	6	g.	g.	PROPN
ejpam-6535	769	7	ahsanullah	ahsanullah	PROPN
ejpam-6535	769	8	and	and	CCONJ
ejpam-6535	769	9	g.	g.	PROPN
ejpam-6535	769	10	jäger.on	jäger.on	ADJ
ejpam-6535	769	11	approach	approach	NOUN
ejpam-6535	769	12	limit	limit	NOUN
ejpam-6535	769	13	groups	group	NOUN
ejpam-6535	769	14	and	and	CCONJ
ejpam-6535	769	15	their	their	PRON
ejpam-6535	769	16	uniformization	uniformization	NOUN
ejpam-6535	769	17	,	,	PUNCT
ejpam-6535	769	18	int	int	NOUN
ejpam-6535	769	19	.	.	PUNCT
ejpam-6535	770	1	j.	j.	PROPN
ejpam-6535	770	2	contemp	contemp	PROPN
ejpam-6535	770	3	.	.	PUNCT
ejpam-6535	771	1	math	math	NOUN
ejpam-6535	771	2	.	.	PUNCT
ejpam-6535	772	1	sci	sci	PROPN
ejpam-6535	772	2	.	.	PROPN
ejpam-6535	772	3	9(5)(2014	9(5)(2014	NUM
ejpam-6535	772	4	)	)	PUNCT
ejpam-6535	772	5	,	,	PUNCT
ejpam-6535	772	6	195–213	195–213	NUM
ejpam-6535	772	7	.	.	PUNCT
ejpam-6535	773	1	[	[	X
ejpam-6535	773	2	3	3	X
ejpam-6535	773	3	]	]	PUNCT
ejpam-6535	773	4	t.	t.	PROPN
ejpam-6535	773	5	m.	m.	NOUN
ejpam-6535	773	6	g.	g.	PROPN
ejpam-6535	773	7	ahsanullah	ahsanullah	PROPN
ejpam-6535	773	8	and	and	CCONJ
ejpam-6535	773	9	g.	g.	PROPN
ejpam-6535	773	10	jäger	jäger	PROPN
ejpam-6535	773	11	.	.	PUNCT
ejpam-6535	774	1	probabilistic	probabilistic	ADJ
ejpam-6535	774	2	uniformization	uniformization	NOUN
ejpam-6535	774	3	and	and	CCONJ
ejpam-6535	774	4	probabilistic	probabilistic	ADJ
ejpam-6535	774	5	metrization	metrization	NOUN
ejpam-6535	774	6	of	of	ADP
ejpam-6535	774	7	probabilistic	probabilistic	ADJ
ejpam-6535	774	8	convergence	convergence	NOUN
ejpam-6535	774	9	groups	group	NOUN
ejpam-6535	774	10	,	,	PUNCT
ejpam-6535	774	11	math	math	NOUN
ejpam-6535	774	12	.	.	PUNCT
ejpam-6535	775	1	slovaca	slovaca	PROPN
ejpam-6535	775	2	67(4)(2017	67(4)(2017	NUM
ejpam-6535	775	3	)	)	PUNCT
ejpam-6535	775	4	,	,	PUNCT
ejpam-6535	775	5	985–1000	985–1000	NUM
ejpam-6535	775	6	.	.	PUNCT
ejpam-6535	776	1	[	[	X
ejpam-6535	776	2	4	4	X
ejpam-6535	776	3	]	]	PUNCT
ejpam-6535	776	4	t.	t.	NOUN
ejpam-6535	776	5	m.	m.	NOUN
ejpam-6535	776	6	g.	g.	PROPN
ejpam-6535	776	7	ahsanullah	ahsanullah	PROPN
ejpam-6535	776	8	,	,	PUNCT
ejpam-6535	776	9	tesnim	tesnim	ADJ
ejpam-6535	776	10	meryem	meryem	NOUN
ejpam-6535	776	11	baran	baran	NOUN
ejpam-6535	776	12	and	and	CCONJ
ejpam-6535	776	13	fawzi	fawzi	VERB
ejpam-6535	776	14	al	al	PROPN
ejpam-6535	776	15	-	-	PUNCT
ejpam-6535	776	16	thukair	thukair	NOUN
ejpam-6535	776	17	.	.	PUNCT
ejpam-6535	777	1	on	on	ADP
ejpam-6535	777	2	the	the	DET
ejpam-6535	777	3	probabilistic	probabilistic	ADJ
ejpam-6535	777	4	convergence	convergence	NOUN
ejpam-6535	777	5	spaces	space	VERB
ejpam-6535	777	6	:	:	PUNCT
ejpam-6535	777	7	monad	monad	PROPN
ejpam-6535	777	8	and	and	CCONJ
ejpam-6535	777	9	its	its	PRON
ejpam-6535	777	10	eilenberg	eilenberg	NOUN
ejpam-6535	777	11	-	-	PUNCT
ejpam-6535	777	12	moore	moore	PROPN
ejpam-6535	777	13	category	category	NOUN
ejpam-6535	777	14	,	,	PUNCT
ejpam-6535	777	15	new	new	ADJ
ejpam-6535	777	16	math	math	NOUN
ejpam-6535	777	17	.	.	PUNCT
ejpam-6535	778	1	&	&	CCONJ
ejpam-6535	778	2	nat	nat	PROPN
ejpam-6535	778	3	.	.	PUNCT
ejpam-6535	779	1	comput	comput	NOUN
ejpam-6535	779	2	.	.	PUNCT
ejpam-6535	780	1	18(2022	18(2022	NUM
ejpam-6535	780	2	)	)	PUNCT
ejpam-6535	780	3	,	,	PUNCT
ejpam-6535	781	1	1–21	1–21	PROPN
ejpam-6535	781	2	.	.	PUNCT
ejpam-6535	782	1	[	[	X
ejpam-6535	782	2	5	5	X
ejpam-6535	782	3	]	]	PUNCT
ejpam-6535	782	4	t.	t.	NOUN
ejpam-6535	782	5	m.	m.	NOUN
ejpam-6535	782	6	g.	g.	PROPN
ejpam-6535	782	7	ahsanullah	ahsanullah	PROPN
ejpam-6535	782	8	,	,	PUNCT
ejpam-6535	782	9	fawzi	fawzi	PROPN
ejpam-6535	782	10	al	al	PROPN
ejpam-6535	782	11	-	-	PUNCT
ejpam-6535	782	12	thukair	thukair	PROPN
ejpam-6535	782	13	and	and	CCONJ
ejpam-6535	782	14	bhamini	bhamini	PROPN
ejpam-6535	782	15	nayar	nayar	PROPN
ejpam-6535	782	16	.	.	PUNCT
ejpam-6535	783	1	on	on	ADP
ejpam-6535	783	2	the	the	DET
ejpam-6535	783	3	categories	category	NOUN
ejpam-6535	783	4	of	of	ADP
ejpam-6535	783	5	probabilistic	probabilistic	ADJ
ejpam-6535	783	6	approach	approach	NOUN
ejpam-6535	783	7	groups	group	NOUN
ejpam-6535	783	8	:	:	PUNCT
ejpam-6535	783	9	actions	action	NOUN
ejpam-6535	783	10	,	,	PUNCT
ejpam-6535	783	11	filomat	filomat	PROPN
ejpam-6535	783	12	37(16)(2023	37(16)(2023	NUM
ejpam-6535	783	13	)	)	PUNCT
ejpam-6535	783	14	,	,	PUNCT
ejpam-6535	783	15	5413–5426	5413–5426	NUM
ejpam-6535	783	16	.	.	PUNCT
ejpam-6535	784	1	[	[	X
ejpam-6535	784	2	6	6	NUM
ejpam-6535	784	3	]	]	PUNCT
ejpam-6535	784	4	t.	t.	PROPN
ejpam-6535	784	5	m.	m.	NOUN
ejpam-6535	784	6	g.	g.	PROPN
ejpam-6535	784	7	ahsanullah	ahsanullah	PROPN
ejpam-6535	784	8	and	and	CCONJ
ejpam-6535	784	9	n.	n.	PROPN
ejpam-6535	784	10	n.	n.	PROPN
ejpam-6535	784	11	morsi	morsi	PROPN
ejpam-6535	784	12	.	.	PUNCT
ejpam-6535	785	1	invariant	invariant	PROPN
ejpam-6535	785	2	probabilistic	probabilistic	ADJ
ejpam-6535	785	3	metrizability	metrizability	NOUN
ejpam-6535	785	4	of	of	ADP
ejpam-6535	785	5	fuzzy	fuzzy	ADJ
ejpam-6535	785	6	neighborhood	neighborhood	NOUN
ejpam-6535	785	7	groups	group	NOUN
ejpam-6535	785	8	,	,	PUNCT
ejpam-6535	785	9	fuzzy	fuzzy	ADJ
ejpam-6535	785	10	sets	set	NOUN
ejpam-6535	785	11	syst	syst	NOUN
ejpam-6535	785	12	.	.	PUNCT
ejpam-6535	786	1	47(1992	47(1992	NUM
ejpam-6535	786	2	)	)	PUNCT
ejpam-6535	786	3	,	,	PUNCT
ejpam-6535	787	1	233–245	233–245	NUM
ejpam-6535	787	2	.	.	PUNCT
ejpam-6535	788	1	[	[	X
ejpam-6535	788	2	7	7	X
ejpam-6535	788	3	]	]	X
ejpam-6535	788	4	c.	c.	PROPN
ejpam-6535	788	5	alsina	alsina	PROPN
ejpam-6535	788	6	,	,	PUNCT
ejpam-6535	788	7	b.	b.	PROPN
ejpam-6535	788	8	schweizer	schweizer	PROPN
ejpam-6535	788	9	and	and	CCONJ
ejpam-6535	788	10	a.	a.	NOUN
ejpam-6535	788	11	sklar	sklar	PROPN
ejpam-6535	788	12	.	.	PUNCT
ejpam-6535	789	1	on	on	ADP
ejpam-6535	789	2	the	the	DET
ejpam-6535	789	3	definition	definition	NOUN
ejpam-6535	789	4	of	of	ADP
ejpam-6535	789	5	a	a	DET
ejpam-6535	789	6	probabilistic	probabilistic	ADJ
ejpam-6535	789	7	normed	normed	ADJ
ejpam-6535	789	8	space	space	NOUN
ejpam-6535	789	9	,	,	PUNCT
ejpam-6535	789	10	aequat	aequat	PROPN
ejpam-6535	789	11	.	.	PUNCT
ejpam-6535	789	12	math	math	NOUN
ejpam-6535	789	13	.	.	PUNCT
ejpam-6535	790	1	46(1993	46(1993	NUM
ejpam-6535	790	2	)	)	PUNCT
ejpam-6535	790	3	,	,	PUNCT
ejpam-6535	790	4	91–98	91–98	NUM
ejpam-6535	790	5	.	.	PUNCT
ejpam-6535	791	1	[	[	X
ejpam-6535	791	2	8	8	NUM
ejpam-6535	791	3	]	]	PUNCT
ejpam-6535	791	4	m.	m.	NOUN
ejpam-6535	791	5	bachir	bachir	NOUN
ejpam-6535	791	6	.	.	PUNCT
ejpam-6535	792	1	the	the	DET
ejpam-6535	792	2	space	space	NOUN
ejpam-6535	792	3	of	of	ADP
ejpam-6535	792	4	probabilistic	probabilistic	ADJ
ejpam-6535	792	5	1	1	NUM
ejpam-6535	792	6	-	-	PUNCT
ejpam-6535	792	7	lipschitz	lipschitz	NOUN
ejpam-6535	792	8	maps	map	NOUN
ejpam-6535	792	9	,	,	PUNCT
ejpam-6535	792	10	aequat	aequat	PROPN
ejpam-6535	792	11	.	.	PUNCT
ejpam-6535	792	12	math	math	NOUN
ejpam-6535	792	13	.	.	PUNCT
ejpam-6535	793	1	93(2019	93(2019	NUM
ejpam-6535	793	2	)	)	PUNCT
ejpam-6535	793	3	,	,	PUNCT
ejpam-6535	793	4	955	955	NUM
ejpam-6535	793	5	–	–	PUNCT
ejpam-6535	793	6	983	983	NUM
ejpam-6535	793	7	.	.	PUNCT
ejpam-6535	794	1	[	[	X
ejpam-6535	794	2	9	9	NUM
ejpam-6535	794	3	]	]	SYM
ejpam-6535	794	4	r.	r.	PROPN
ejpam-6535	794	5	n.	n.	PROPN
ejpam-6535	794	6	ball	ball	PROPN
ejpam-6535	794	7	.	.	PUNCT
ejpam-6535	795	1	convergence	convergence	NOUN
ejpam-6535	795	2	and	and	CCONJ
ejpam-6535	795	3	cauchy	cauchy	NOUN
ejpam-6535	795	4	structures	structure	NOUN
ejpam-6535	795	5	on	on	ADP
ejpam-6535	795	6	lattice	lattice	NOUN
ejpam-6535	795	7	ordered	order	VERB
ejpam-6535	795	8	groups	group	NOUN
ejpam-6535	795	9	,	,	PUNCT
ejpam-6535	795	10	trans	trans	PROPN
ejpam-6535	795	11	.	.	PROPN
ejpam-6535	796	1	amer	amer	PROPN
ejpam-6535	796	2	.	.	PUNCT
ejpam-6535	796	3	math	math	PROPN
ejpam-6535	796	4	.	.	PUNCT
ejpam-6535	797	1	soc	soc	PROPN
ejpam-6535	797	2	.	.	PUNCT
ejpam-6535	798	1	259(2)(1980	259(2)(1980	X
ejpam-6535	798	2	)	)	PUNCT
ejpam-6535	798	3	,	,	PUNCT
ejpam-6535	798	4	357–392	357–392	NUM
ejpam-6535	798	5	.	.	PUNCT
ejpam-6535	799	1	[	[	X
ejpam-6535	799	2	10	10	NUM
ejpam-6535	799	3	]	]	PUNCT
ejpam-6535	799	4	m.	m.	NOUN
ejpam-6535	799	5	baran	baran	NOUN
ejpam-6535	799	6	.	.	PUNCT
ejpam-6535	800	1	separation	separation	NOUN
ejpam-6535	800	2	and	and	CCONJ
ejpam-6535	800	3	compactness	compactness	NOUN
ejpam-6535	800	4	in	in	ADP
ejpam-6535	800	5	topological	topological	ADJ
ejpam-6535	800	6	categories	category	NOUN
ejpam-6535	800	7	,	,	PUNCT
ejpam-6535	800	8	filomat	filomat	NOUN
ejpam-6535	800	9	93(3)(2025	93(3)(2025	NUM
ejpam-6535	800	10	)	)	PUNCT
ejpam-6535	800	11	,	,	PUNCT
ejpam-6535	800	12	871–881	871–881	NUM
ejpam-6535	800	13	.	.	PUNCT
ejpam-6535	801	1	[	[	X
ejpam-6535	801	2	11	11	NUM
ejpam-6535	801	3	]	]	PUNCT
ejpam-6535	801	4	m.	m.	NOUN
ejpam-6535	801	5	baran	baran	NOUN
ejpam-6535	801	6	.	.	PUNCT
ejpam-6535	802	1	hausdorff	hausdorff	NOUN
ejpam-6535	802	2	objects	object	NOUN
ejpam-6535	802	3	,	,	PUNCT
ejpam-6535	802	4	hacet	hacet	PROPN
ejpam-6535	802	5	.	.	PUNCT
ejpam-6535	803	1	j.	j.	PROPN
ejpam-6535	803	2	math	math	PROPN
ejpam-6535	803	3	.	.	PUNCT
ejpam-6535	804	1	stat	stat	PROPN
ejpam-6535	804	2	.	.	PUNCT
ejpam-6535	805	1	54(3)(2025	54(3)(2025	NUM
ejpam-6535	805	2	)	)	PUNCT
ejpam-6535	805	3	,	,	PUNCT
ejpam-6535	806	1	928–938	928–938	NUM
ejpam-6535	806	2	.	.	PUNCT
ejpam-6535	807	1	[	[	X
ejpam-6535	807	2	12	12	NUM
ejpam-6535	807	3	]	]	X
ejpam-6535	807	4	n.	n.	PROPN
ejpam-6535	807	5	h.	h.	PROPN
ejpam-6535	807	6	bingham	bingham	PROPN
ejpam-6535	807	7	and	and	CCONJ
ejpam-6535	807	8	a.	a.	PROPN
ejpam-6535	807	9	j.	j.	PROPN
ejpam-6535	807	10	ostaszewski	ostaszewski	PROPN
ejpam-6535	807	11	.	.	PUNCT
ejpam-6535	808	1	normed	normed	PROPN
ejpam-6535	808	2	versus	versus	ADP
ejpam-6535	808	3	topological	topological	ADJ
ejpam-6535	808	4	groups	group	NOUN
ejpam-6535	808	5	:	:	PUNCT
ejpam-6535	808	6	dichotomy	dichotomy	NOUN
ejpam-6535	808	7	and	and	CCONJ
ejpam-6535	808	8	duality	duality	NOUN
ejpam-6535	808	9	,	,	PUNCT
ejpam-6535	808	10	dissertations	dissertation	NOUN
ejpam-6535	808	11	math	math	NOUN
ejpam-6535	808	12	.	.	PUNCT
ejpam-6535	809	1	472(2010	472(2010	NUM
ejpam-6535	809	2	)	)	PUNCT
ejpam-6535	809	3	,	,	PUNCT
ejpam-6535	809	4	138p	138p	NOUN
ejpam-6535	809	5	.	.	PUNCT
ejpam-6535	810	1	[	[	X
ejpam-6535	810	2	13	13	NUM
ejpam-6535	810	3	]	]	X
ejpam-6535	810	4	n.	n.	NOUN
ejpam-6535	810	5	bourbaki	bourbaki	PROPN
ejpam-6535	810	6	.	.	PUNCT
ejpam-6535	811	1	elements	element	NOUN
ejpam-6535	811	2	of	of	ADP
ejpam-6535	811	3	mathematics	mathematic	NOUN
ejpam-6535	811	4	,	,	PUNCT
ejpam-6535	811	5	part	part	NOUN
ejpam-6535	811	6	1	1	NUM
ejpam-6535	811	7	,	,	PUNCT
ejpam-6535	811	8	2	2	NUM
ejpam-6535	811	9	,	,	PUNCT
ejpam-6535	811	10	adison	adison	PROPN
ejpam-6535	811	11	-	-	PUNCT
ejpam-6535	811	12	wesley	wesley	PROPN
ejpam-6535	811	13	,	,	PUNCT
ejpam-6535	811	14	publishing	publish	VERB
ejpam-6535	811	15	company	company	NOUN
ejpam-6535	811	16	,	,	PUNCT
ejpam-6535	811	17	reading	reading	NOUN
ejpam-6535	811	18	,	,	PUNCT
ejpam-6535	811	19	massachusetts	massachusetts	PROPN
ejpam-6535	811	20	,	,	PUNCT
ejpam-6535	811	21	1996	1996	NUM
ejpam-6535	811	22	.	.	PUNCT
ejpam-6535	812	1	t.m.g	t.m.g	ADJ
ejpam-6535	812	2	.	.	PUNCT
ejpam-6535	813	1	ahsanullah	ahsanullah	PROPN
ejpam-6535	813	2	,	,	PUNCT
ejpam-6535	813	3	fawzi	fawzi	PROPN
ejpam-6535	813	4	al	al	PROPN
ejpam-6535	813	5	-	-	PUNCT
ejpam-6535	813	6	thukair	thukair	NOUN
ejpam-6535	813	7	/	/	SYM
ejpam-6535	813	8	eur	eur	NOUN
ejpam-6535	813	9	.	.	PUNCT
ejpam-6535	814	1	j.	j.	PROPN
ejpam-6535	814	2	pure	pure	PROPN
ejpam-6535	814	3	appl	appl	PROPN
ejpam-6535	814	4	.	.	PROPN
ejpam-6535	814	5	math	math	PROPN
ejpam-6535	814	6	,	,	PUNCT
ejpam-6535	814	7	18	18	NUM
ejpam-6535	814	8	(	(	PUNCT
ejpam-6535	814	9	3	3	NUM
ejpam-6535	814	10	)	)	PUNCT
ejpam-6535	814	11	(	(	PUNCT
ejpam-6535	814	12	2025	2025	NUM
ejpam-6535	814	13	)	)	PUNCT
ejpam-6535	814	14	,	,	PUNCT
ejpam-6535	814	15	6535	6535	NUM
ejpam-6535	814	16	27	27	NUM
ejpam-6535	814	17	of	of	ADP
ejpam-6535	814	18	28	28	NUM
ejpam-6535	815	1	[	[	X
ejpam-6535	815	2	14	14	NUM
ejpam-6535	815	3	]	]	PUNCT
ejpam-6535	815	4	p.	p.	NOUN
ejpam-6535	815	5	brock	brock	PROPN
ejpam-6535	815	6	.	.	PUNCT
ejpam-6535	816	1	probabilistic	probabilistic	ADJ
ejpam-6535	816	2	convergence	convergence	NOUN
ejpam-6535	816	3	spaces	space	NOUN
ejpam-6535	816	4	and	and	CCONJ
ejpam-6535	816	5	generalized	generalize	VERB
ejpam-6535	816	6	metric	metric	ADJ
ejpam-6535	816	7	spaces	space	NOUN
ejpam-6535	816	8	,	,	PUNCT
ejpam-6535	816	9	int	int	NOUN
ejpam-6535	816	10	.	.	PUNCT
ejpam-6535	817	1	j.	j.	PROPN
ejpam-6535	817	2	math	math	PROPN
ejpam-6535	817	3	.	.	PUNCT
ejpam-6535	817	4	&	&	CCONJ
ejpam-6535	817	5	math	math	PROPN
ejpam-6535	817	6	.	.	PUNCT
ejpam-6535	818	1	sci	sci	PROPN
ejpam-6535	818	2	.	.	PUNCT
ejpam-6535	819	1	21(1998	21(1998	NUM
ejpam-6535	819	2	)	)	PUNCT
ejpam-6535	819	3	,	,	PUNCT
ejpam-6535	820	1	439–452	439–452	NUM
ejpam-6535	820	2	.	.	PUNCT
ejpam-6535	821	1	[	[	X
ejpam-6535	821	2	15	15	NUM
ejpam-6535	821	3	]	]	X
ejpam-6535	821	4	e.	e.	PROPN
ejpam-6535	821	5	ćech	ćech	PROPN
ejpam-6535	821	6	.	.	PUNCT
ejpam-6535	822	1	topological	topological	ADJ
ejpam-6535	822	2	spaces	space	NOUN
ejpam-6535	822	3	,	,	PUNCT
ejpam-6535	822	4	interscience	interscience	NOUN
ejpam-6535	822	5	publishers	publisher	NOUN
ejpam-6535	822	6	(	(	PUNCT
ejpam-6535	822	7	john	john	PROPN
ejpam-6535	822	8	wiley	wiley	PROPN
ejpam-6535	822	9	&	&	CCONJ
ejpam-6535	822	10	sons	sons	PROPN
ejpam-6535	822	11	,	,	PUNCT
ejpam-6535	822	12	london	london	PROPN
ejpam-6535	822	13	)	)	PUNCT
ejpam-6535	822	14	,	,	PUNCT
ejpam-6535	822	15	1966	1966	NUM
ejpam-6535	822	16	.	.	PUNCT
ejpam-6535	823	1	[	[	X
ejpam-6535	823	2	16	16	NUM
ejpam-6535	823	3	]	]	PUNCT
ejpam-6535	823	4	m.	m.	NOUN
ejpam-6535	823	5	j.	j.	PROPN
ejpam-6535	823	6	frank	frank	PROPN
ejpam-6535	823	7	.	.	PUNCT
ejpam-6535	824	1	probabilistic	probabilistic	ADJ
ejpam-6535	824	2	topological	topological	ADJ
ejpam-6535	824	3	spaces	space	NOUN
ejpam-6535	824	4	,	,	PUNCT
ejpam-6535	824	5	j.	j.	PROPN
ejpam-6535	824	6	math	math	PROPN
ejpam-6535	824	7	.	.	PUNCT
ejpam-6535	825	1	anal	anal	PROPN
ejpam-6535	825	2	.	.	PUNCT
ejpam-6535	825	3	appl	appl	PROPN
ejpam-6535	825	4	.	.	PUNCT
ejpam-6535	826	1	34(1971	34(1971	NUM
ejpam-6535	826	2	)	)	PUNCT
ejpam-6535	826	3	,	,	PUNCT
ejpam-6535	827	1	67–81	67–81	NUM
ejpam-6535	827	2	.	.	PUNCT
ejpam-6535	828	1	[	[	X
ejpam-6535	828	2	17	17	NUM
ejpam-6535	828	3	]	]	X
ejpam-6535	828	4	r.	r.	PROPN
ejpam-6535	828	5	fric	fric	PROPN
ejpam-6535	828	6	and	and	CCONJ
ejpam-6535	828	7	d.	d.	PROPN
ejpam-6535	828	8	c.	c.	PROPN
ejpam-6535	828	9	kent	kent	PROPN
ejpam-6535	828	10	.	.	PUNCT
ejpam-6535	829	1	a	a	DET
ejpam-6535	829	2	completion	completion	NOUN
ejpam-6535	829	3	functor	functor	NOUN
ejpam-6535	829	4	for	for	ADP
ejpam-6535	829	5	cauchy	cauchy	NOUN
ejpam-6535	829	6	groups	group	NOUN
ejpam-6535	829	7	,	,	PUNCT
ejpam-6535	829	8	internat	internat	PROPN
ejpam-6535	829	9	.	.	PUNCT
ejpam-6535	830	1	j.	j.	PROPN
ejpam-6535	830	2	math	math	PROPN
ejpam-6535	830	3	.	.	PUNCT
ejpam-6535	830	4	&	&	CCONJ
ejpam-6535	830	5	math	math	PROPN
ejpam-6535	830	6	.	.	PUNCT
ejpam-6535	831	1	sci	sci	PROPN
ejpam-6535	831	2	.	.	PROPN
ejpam-6535	831	3	4(1)(1981	4(1)(1981	NUM
ejpam-6535	831	4	)	)	PUNCT
ejpam-6535	831	5	,	,	PUNCT
ejpam-6535	831	6	55–65	55–65	NUM
ejpam-6535	831	7	.	.	PUNCT
ejpam-6535	832	1	[	[	X
ejpam-6535	832	2	18	18	NUM
ejpam-6535	832	3	]	]	X
ejpam-6535	832	4	r.	r.	PROPN
ejpam-6535	832	5	fritsche	fritsche	PROPN
ejpam-6535	832	6	.	.	PUNCT
ejpam-6535	833	1	topologies	topology	NOUN
ejpam-6535	833	2	for	for	ADP
ejpam-6535	833	3	probabilistic	probabilistic	ADJ
ejpam-6535	833	4	metric	metric	ADJ
ejpam-6535	833	5	spaces	space	NOUN
ejpam-6535	833	6	,	,	PUNCT
ejpam-6535	833	7	fund	fund	PROPN
ejpam-6535	833	8	.	.	PUNCT
ejpam-6535	833	9	math	math	NOUN
ejpam-6535	833	10	.	.	PUNCT
ejpam-6535	834	1	72(1971	72(1971	NUM
ejpam-6535	834	2	)	)	PUNCT
ejpam-6535	834	3	,	,	PUNCT
ejpam-6535	834	4	7–16	7–16	PROPN
ejpam-6535	834	5	.	.	PUNCT
ejpam-6535	835	1	[	[	X
ejpam-6535	835	2	19	19	NUM
ejpam-6535	835	3	]	]	PUNCT
ejpam-6535	835	4	w.	w.	NOUN
ejpam-6535	835	5	gähler	gähler	NOUN
ejpam-6535	835	6	.	.	PUNCT
ejpam-6535	836	1	a	a	DET
ejpam-6535	836	2	topological	topological	ADJ
ejpam-6535	836	3	approach	approach	NOUN
ejpam-6535	836	4	to	to	ADP
ejpam-6535	836	5	structure	structure	NOUN
ejpam-6535	836	6	theory	theory	NOUN
ejpam-6535	836	7	,	,	PUNCT
ejpam-6535	836	8	math	math	NOUN
ejpam-6535	836	9	.	.	PUNCT
ejpam-6535	837	1	nachr	nachr	PROPN
ejpam-6535	837	2	.	.	PUNCT
ejpam-6535	838	1	100(1981	100(1981	NUM
ejpam-6535	838	2	)	)	PUNCT
ejpam-6535	838	3	,	,	PUNCT
ejpam-6535	838	4	93	93	NUM
ejpam-6535	838	5	–	–	PUNCT
ejpam-6535	838	6	144	144	NUM
ejpam-6535	838	7	.	.	PUNCT
ejpam-6535	839	1	[	[	X
ejpam-6535	839	2	20	20	NUM
ejpam-6535	839	3	]	]	PUNCT
ejpam-6535	839	4	b.	b.	PROPN
ejpam-6535	839	5	l.	l.	PROPN
ejpam-6535	839	6	guillen	guillen	PROPN
ejpam-6535	839	7	and	and	CCONJ
ejpam-6535	839	8	p.	p.	PROPN
ejpam-6535	839	9	hariceishnan	hariceishnan	PROPN
ejpam-6535	839	10	.	.	PUNCT
ejpam-6535	840	1	probabilistic	probabilistic	VERB
ejpam-6535	840	2	normed	normed	ADJ
ejpam-6535	840	3	spaces	space	NOUN
ejpam-6535	840	4	,	,	PUNCT
ejpam-6535	840	5	world	world	NOUN
ejpam-6535	840	6	scientific	scientific	NOUN
ejpam-6535	840	7	,	,	PUNCT
ejpam-6535	840	8	singapore,2024	singapore,2024	NOUN
ejpam-6535	840	9	[	[	X
ejpam-6535	840	10	21	21	NUM
ejpam-6535	840	11	]	]	X
ejpam-6535	840	12	p.	p.	PROPN
ejpam-6535	840	13	eklund	eklund	PROPN
ejpam-6535	840	14	and	and	CCONJ
ejpam-6535	840	15	w.	w.	PROPN
ejpam-6535	840	16	gähler	gähler	NOUN
ejpam-6535	840	17	.	.	PUNCT
ejpam-6535	841	1	generalized	generalize	VERB
ejpam-6535	841	2	cauchy	cauchy	ADJ
ejpam-6535	841	3	spaces	space	NOUN
ejpam-6535	841	4	,	,	PUNCT
ejpam-6535	841	5	math	math	NOUN
ejpam-6535	841	6	.	.	PUNCT
ejpam-6535	842	1	nachr	nachr	PROPN
ejpam-6535	842	2	.	.	PUNCT
ejpam-6535	843	1	147(1990	147(1990	NUM
ejpam-6535	843	2	)	)	PUNCT
ejpam-6535	843	3	,	,	PUNCT
ejpam-6535	843	4	219	219	NUM
ejpam-6535	843	5	–	–	SYM
ejpam-6535	843	6	233	233	NUM
ejpam-6535	843	7	.	.	PUNCT
ejpam-6535	844	1	[	[	X
ejpam-6535	844	2	22	22	NUM
ejpam-6535	844	3	]	]	X
ejpam-6535	844	4	g.	g.	PROPN
ejpam-6535	844	5	jäger	jäger	PROPN
ejpam-6535	844	6	.	.	PUNCT
ejpam-6535	845	1	a	a	DET
ejpam-6535	845	2	convergence	convergence	NOUN
ejpam-6535	845	3	theory	theory	NOUN
ejpam-6535	845	4	for	for	ADP
ejpam-6535	845	5	probabilistic	probabilistic	ADJ
ejpam-6535	845	6	metric	metric	ADJ
ejpam-6535	845	7	spaces	space	NOUN
ejpam-6535	845	8	,	,	PUNCT
ejpam-6535	845	9	quaest	quaest	NOUN
ejpam-6535	845	10	.	.	PUNCT
ejpam-6535	846	1	math	math	NOUN
ejpam-6535	846	2	.	.	PUNCT
ejpam-6535	847	1	38(2015	38(2015	NUM
ejpam-6535	847	2	)	)	PUNCT
ejpam-6535	847	3	,	,	PUNCT
ejpam-6535	848	1	587–599	587–599	NUM
ejpam-6535	848	2	.	.	PUNCT
ejpam-6535	849	1	[	[	X
ejpam-6535	849	2	23	23	NUM
ejpam-6535	849	3	]	]	PUNCT
ejpam-6535	849	4	g.	g.	PROPN
ejpam-6535	849	5	jäger	jäger	PROPN
ejpam-6535	849	6	and	and	CCONJ
ejpam-6535	849	7	t.	t.	PROPN
ejpam-6535	849	8	m.	m.	NOUN
ejpam-6535	849	9	g.	g.	PROPN
ejpam-6535	849	10	ahsanullah	ahsanullah	PROPN
ejpam-6535	849	11	.	.	PUNCT
ejpam-6535	850	1	quantale	quantale	NOUN
ejpam-6535	850	2	-	-	PUNCT
ejpam-6535	850	3	valued	value	VERB
ejpam-6535	850	4	cauchy	cauchy	NOUN
ejpam-6535	850	5	tower	tower	NOUN
ejpam-6535	850	6	spaces	space	NOUN
ejpam-6535	850	7	and	and	CCONJ
ejpam-6535	850	8	completeness	completeness	NOUN
ejpam-6535	850	9	,	,	PUNCT
ejpam-6535	850	10	appl	appl	PROPN
ejpam-6535	850	11	.	.	PUNCT
ejpam-6535	851	1	gen	gen	PROPN
ejpam-6535	851	2	.	.	PROPN
ejpam-6535	851	3	topol	topol	PROPN
ejpam-6535	851	4	.	.	PUNCT
ejpam-6535	852	1	22(2)(2021	22(2)(2021	NUM
ejpam-6535	852	2	)	)	PUNCT
ejpam-6535	852	3	,	,	PUNCT
ejpam-6535	853	1	461–481	461–481	NUM
ejpam-6535	853	2	.	.	PUNCT
ejpam-6535	854	1	[	[	X
ejpam-6535	854	2	24	24	NUM
ejpam-6535	854	3	]	]	X
ejpam-6535	854	4	d.	d.	PROPN
ejpam-6535	854	5	c.	c.	PROPN
ejpam-6535	854	6	kent	kent	PROPN
ejpam-6535	854	7	and	and	CCONJ
ejpam-6535	854	8	w.	w.	PROPN
ejpam-6535	854	9	keun	keun	PROPN
ejpam-6535	854	10	min	min	PROPN
ejpam-6535	854	11	.	.	PROPN
ejpam-6535	854	12	neighborhood	neighborhood	NOUN
ejpam-6535	854	13	spaces	space	NOUN
ejpam-6535	854	14	,	,	PUNCT
ejpam-6535	854	15	internat	internat	PROPN
ejpam-6535	854	16	.	.	PUNCT
ejpam-6535	855	1	j.	j.	PROPN
ejpam-6535	855	2	math	math	PROPN
ejpam-6535	855	3	&	&	CCONJ
ejpam-6535	855	4	math	math	PROPN
ejpam-6535	855	5	.	.	PUNCT
ejpam-6535	856	1	sci	sci	PROPN
ejpam-6535	856	2	.	.	PROPN
ejpam-6535	856	3	32(7)(2002	32(7)(2002	NUM
ejpam-6535	856	4	)	)	PUNCT
ejpam-6535	856	5	,	,	PUNCT
ejpam-6535	856	6	387–399	387–399	NUM
ejpam-6535	856	7	.	.	PUNCT
ejpam-6535	857	1	[	[	X
ejpam-6535	857	2	25	25	NUM
ejpam-6535	857	3	]	]	X
ejpam-6535	857	4	v.	v.	PROPN
ejpam-6535	857	5	l.	l.	PROPN
ejpam-6535	857	6	klee	klee	PROPN
ejpam-6535	857	7	.	.	PUNCT
ejpam-6535	858	1	invariant	invariant	ADJ
ejpam-6535	858	2	metrices	metrice	NOUN
ejpam-6535	858	3	in	in	ADP
ejpam-6535	858	4	groups	group	NOUN
ejpam-6535	858	5	(	(	PUNCT
ejpam-6535	858	6	solution	solution	NOUN
ejpam-6535	858	7	of	of	ADP
ejpam-6535	858	8	a	a	DET
ejpam-6535	858	9	problem	problem	NOUN
ejpam-6535	858	10	of	of	ADP
ejpam-6535	858	11	banach	banach	NOUN
ejpam-6535	858	12	)	)	PUNCT
ejpam-6535	858	13	,	,	PUNCT
ejpam-6535	858	14	procd	procd	PROPN
ejpam-6535	858	15	.	.	PUNCT
ejpam-6535	859	1	amer	amer	PROPN
ejpam-6535	859	2	.	.	PUNCT
ejpam-6535	859	3	math	math	PROPN
ejpam-6535	859	4	.	.	PUNCT
ejpam-6535	860	1	soc	soc	PROPN
ejpam-6535	860	2	.	.	PUNCT
ejpam-6535	861	1	3(1952	3(1952	NUM
ejpam-6535	861	2	)	)	PUNCT
ejpam-6535	861	3	,	,	PUNCT
ejpam-6535	862	1	484–487	484–487	NUM
ejpam-6535	862	2	.	.	PUNCT
ejpam-6535	863	1	[	[	X
ejpam-6535	863	2	26	26	NUM
ejpam-6535	863	3	]	]	PUNCT
ejpam-6535	863	4	p.	p.	NOUN
ejpam-6535	863	5	klement	klement	PROPN
ejpam-6535	863	6	,	,	PUNCT
ejpam-6535	863	7	r.	r.	PROPN
ejpam-6535	863	8	mesiar	mesiar	PROPN
ejpam-6535	863	9	and	and	CCONJ
ejpam-6535	863	10	e.	e.	PROPN
ejpam-6535	863	11	pap	pap	PROPN
ejpam-6535	863	12	.	.	PUNCT
ejpam-6535	864	1	triangular	triangular	NOUN
ejpam-6535	864	2	norms	norm	NOUN
ejpam-6535	864	3	,	,	PUNCT
ejpam-6535	864	4	kluwer	kluwer	NOUN
ejpam-6535	864	5	academic	academic	ADJ
ejpam-6535	864	6	publishers	publisher	NOUN
ejpam-6535	864	7	,	,	PUNCT
ejpam-6535	864	8	dordrecht	dordrecht	PROPN
ejpam-6535	864	9	,	,	PUNCT
ejpam-6535	864	10	2000	2000	NUM
ejpam-6535	864	11	.	.	PUNCT
ejpam-6535	865	1	[	[	X
ejpam-6535	865	2	27	27	NUM
ejpam-6535	865	3	]	]	PUNCT
ejpam-6535	865	4	k.	k.	PROPN
ejpam-6535	865	5	menger	menger	PROPN
ejpam-6535	865	6	.	.	PUNCT
ejpam-6535	866	1	statistical	statistical	ADJ
ejpam-6535	866	2	metrics	metric	NOUN
ejpam-6535	866	3	,	,	PUNCT
ejpam-6535	866	4	proc	proc	NOUN
ejpam-6535	866	5	.	.	PUNCT
ejpam-6535	867	1	nat	nat	PROPN
ejpam-6535	867	2	.	.	PUNCT
ejpam-6535	868	1	acad	acad	PROPN
ejpam-6535	868	2	.	.	PUNCT
ejpam-6535	869	1	sci	sci	PROPN
ejpam-6535	869	2	.	.	PUNCT
ejpam-6535	869	3	u.	u.	PROPN
ejpam-6535	869	4	s.	s.	PROPN
ejpam-6535	869	5	a.	a.	PROPN
ejpam-6535	869	6	28(1942	28(1942	NUM
ejpam-6535	869	7	)	)	PUNCT
ejpam-6535	869	8	,	,	PUNCT
ejpam-6535	869	9	535–537	535–537	NUM
ejpam-6535	869	10	.	.	PUNCT
ejpam-6535	870	1	[	[	X
ejpam-6535	870	2	28	28	NUM
ejpam-6535	870	3	]	]	X
ejpam-6535	870	4	j.	j.	PROPN
ejpam-6535	870	5	novác	novác	PROPN
ejpam-6535	870	6	.	.	PUNCT
ejpam-6535	871	1	on	on	ADP
ejpam-6535	871	2	convergence	convergence	NOUN
ejpam-6535	871	3	groups	group	NOUN
ejpam-6535	871	4	,	,	PUNCT
ejpam-6535	871	5	czech	czech	PROPN
ejpam-6535	871	6	.	.	PUNCT
ejpam-6535	871	7	math	math	PROPN
ejpam-6535	871	8	.	.	PUNCT
ejpam-6535	872	1	j.	j.	PROPN
ejpam-6535	872	2	20(1970	20(1970	PROPN
ejpam-6535	872	3	)	)	PUNCT
ejpam-6535	872	4	,	,	PUNCT
ejpam-6535	872	5	357–374	357–374	NUM
ejpam-6535	872	6	.	.	PUNCT
ejpam-6535	873	1	[	[	X
ejpam-6535	873	2	29	29	NUM
ejpam-6535	873	3	]	]	PUNCT
ejpam-6535	873	4	k.	k.	PROPN
ejpam-6535	873	5	nourouzi	nourouzi	PROPN
ejpam-6535	873	6	and	and	CCONJ
ejpam-6535	873	7	a.	a.	PROPN
ejpam-6535	873	8	r.	r.	PROPN
ejpam-6535	873	9	pourmoslemi	pourmoslemi	PROPN
ejpam-6535	873	10	.	.	PUNCT
ejpam-6535	874	1	probabilistic	probabilistic	VERB
ejpam-6535	874	2	normed	normed	ADJ
ejpam-6535	874	3	groups	group	NOUN
ejpam-6535	874	4	,	,	PUNCT
ejpam-6535	874	5	iranian	iranian	ADJ
ejpam-6535	874	6	j.	j.	PROPN
ejpam-6535	874	7	fuzzy	fuzzy	PROPN
ejpam-6535	874	8	systs	syst	NOUN
ejpam-6535	874	9	.	.	PUNCT
ejpam-6535	875	1	14(1)(2017	14(1)(2017	NUM
ejpam-6535	875	2	)	)	PUNCT
ejpam-6535	875	3	,	,	PUNCT
ejpam-6535	875	4	99–113	99–113	PROPN
ejpam-6535	875	5	.	.	PUNCT
ejpam-6535	876	1	[	[	X
ejpam-6535	876	2	30	30	NUM
ejpam-6535	876	3	]	]	X
ejpam-6535	876	4	g.	g.	PROPN
ejpam-6535	876	5	preuss	preuss	PROPN
ejpam-6535	876	6	.	.	PUNCT
ejpam-6535	877	1	foundations	foundation	NOUN
ejpam-6535	877	2	of	of	ADP
ejpam-6535	877	3	topology	topology	NOUN
ejpam-6535	877	4	:	:	PUNCT
ejpam-6535	877	5	an	an	DET
ejpam-6535	877	6	approach	approach	NOUN
ejpam-6535	877	7	to	to	ADP
ejpam-6535	877	8	convenient	convenient	ADJ
ejpam-6535	877	9	topology	topology	NOUN
ejpam-6535	877	10	,	,	PUNCT
ejpam-6535	877	11	kluwer	kluwer	NOUN
ejpam-6535	877	12	academic	academic	ADJ
ejpam-6535	877	13	publishers	publisher	NOUN
ejpam-6535	877	14	,	,	PUNCT
ejpam-6535	877	15	dordrecht	dordrecht	PROPN
ejpam-6535	877	16	,	,	PUNCT
ejpam-6535	877	17	2002	2002	NUM
ejpam-6535	877	18	.	.	PUNCT
ejpam-6535	878	1	[	[	X
ejpam-6535	878	2	31	31	NUM
ejpam-6535	878	3	]	]	PUNCT
ejpam-6535	878	4	p.	p.	PROPN
ejpam-6535	878	5	pourmoslemi	pourmoslemi	PROPN
ejpam-6535	878	6	,	,	PUNCT
ejpam-6535	878	7	m.	m.	NOUN
ejpam-6535	878	8	ferrara	ferrara	PROPN
ejpam-6535	878	9	,	,	PUNCT
ejpam-6535	878	10	b.	b.	PROPN
ejpam-6535	878	11	a.	a.	PROPN
ejpam-6535	878	12	pansra	pansra	PROPN
ejpam-6535	878	13	and	and	CCONJ
ejpam-6535	878	14	m.	m.	PROPN
ejpam-6535	878	15	salimi	salimi	PROPN
ejpam-6535	878	16	.	.	PUNCT
ejpam-6535	879	1	probabilistic	probabilistic	ADJ
ejpam-6535	879	2	norms	norm	NOUN
ejpam-6535	879	3	on	on	ADP
ejpam-6535	879	4	the	the	DET
ejpam-6535	879	5	homeomorphisms	homeomorphism	NOUN
ejpam-6535	879	6	of	of	ADP
ejpam-6535	879	7	a	a	DET
ejpam-6535	879	8	group	group	NOUN
ejpam-6535	879	9	,	,	PUNCT
ejpam-6535	879	10	soft	soft	ADJ
ejpam-6535	879	11	computing	computing	NOUN
ejpam-6535	879	12	.	.	PUNCT
ejpam-6535	880	1	24(2020	24(2020	NOUN
ejpam-6535	880	2	)	)	PUNCT
ejpam-6535	880	3	,	,	PUNCT
ejpam-6535	881	1	7021–7028	7021–7028	NUM
ejpam-6535	881	2	.	.	PUNCT
ejpam-6535	882	1	[	[	X
ejpam-6535	882	2	32	32	NUM
ejpam-6535	882	3	]	]	PUNCT
ejpam-6535	882	4	g.	g.	PROPN
ejpam-6535	882	5	d.	d.	PROPN
ejpam-6535	882	6	richardson	richardson	PROPN
ejpam-6535	882	7	and	and	CCONJ
ejpam-6535	882	8	d.	d.	PROPN
ejpam-6535	882	9	c.	c.	PROPN
ejpam-6535	882	10	kent	kent	PROPN
ejpam-6535	882	11	.	.	PUNCT
ejpam-6535	883	1	probabilistic	probabilistic	ADJ
ejpam-6535	883	2	convergence	convergence	NOUN
ejpam-6535	883	3	spaces	space	NOUN
ejpam-6535	883	4	,	,	PUNCT
ejpam-6535	883	5	j.	j.	PROPN
ejpam-6535	883	6	austral	austral	PROPN
ejpam-6535	883	7	.	.	PUNCT
ejpam-6535	884	1	math	math	NOUN
ejpam-6535	884	2	.	.	PUNCT
ejpam-6535	885	1	soc	soc	PROPN
ejpam-6535	885	2	.	.	PUNCT
ejpam-6535	886	1	61(1996	61(1996	X
ejpam-6535	886	2	)	)	PUNCT
ejpam-6535	886	3	,	,	PUNCT
ejpam-6535	887	1	400–42	400–42	NUM
ejpam-6535	887	2	.	.	PUNCT
ejpam-6535	888	1	[	[	X
ejpam-6535	888	2	33	33	NUM
ejpam-6535	888	3	]	]	PUNCT
ejpam-6535	888	4	s.	s.	PROPN
ejpam-6535	888	5	saminger	saminger	PROPN
ejpam-6535	888	6	and	and	CCONJ
ejpam-6535	888	7	c.	c.	PROPN
ejpam-6535	888	8	sempi	sempi	PROPN
ejpam-6535	888	9	.	.	PUNCT
ejpam-6535	889	1	a	a	DET
ejpam-6535	889	2	primer	primer	NOUN
ejpam-6535	889	3	on	on	ADP
ejpam-6535	889	4	triangle	triangle	NOUN
ejpam-6535	889	5	functions	function	NOUN
ejpam-6535	889	6	i	i	PRON
ejpam-6535	889	7	,	,	PUNCT
ejpam-6535	889	8	aequat	aequat	PROPN
ejpam-6535	889	9	.	.	PUNCT
ejpam-6535	889	10	math	math	NOUN
ejpam-6535	889	11	.	.	PUNCT
ejpam-6535	890	1	76(2008	76(2008	X
ejpam-6535	890	2	)	)	PUNCT
ejpam-6535	890	3	,	,	PUNCT
ejpam-6535	891	1	201–240	201–240	NUM
ejpam-6535	891	2	.	.	PUNCT
ejpam-6535	892	1	[	[	X
ejpam-6535	892	2	34	34	NUM
ejpam-6535	892	3	]	]	X
ejpam-6535	892	4	b.	b.	PROPN
ejpam-6535	892	5	schweizer	schweizer	PROPN
ejpam-6535	892	6	and	and	CCONJ
ejpam-6535	892	7	a.	a.	NOUN
ejpam-6535	892	8	sklar	sklar	PROPN
ejpam-6535	892	9	.	.	PUNCT
ejpam-6535	893	1	probabilistic	probabilistic	ADJ
ejpam-6535	893	2	metric	metric	ADJ
ejpam-6535	893	3	spaces	space	NOUN
ejpam-6535	893	4	,	,	PUNCT
ejpam-6535	893	5	north	north	NOUN
ejpam-6535	893	6	-	-	PUNCT
ejpam-6535	893	7	holland	holland	PROPN
ejpam-6535	893	8	,	,	PUNCT
ejpam-6535	893	9	new	new	PROPN
ejpam-6535	893	10	york	york	PROPN
ejpam-6535	893	11	,	,	PUNCT
ejpam-6535	893	12	1983	1983	NUM
ejpam-6535	893	13	.	.	PUNCT
ejpam-6535	894	1	[	[	X
ejpam-6535	894	2	35	35	NUM
ejpam-6535	894	3	]	]	PUNCT
ejpam-6535	894	4	a.	a.	NOUN
ejpam-6535	894	5	n.	n.	PROPN
ejpam-6535	894	6	šerstnev	šerstnev	PROPN
ejpam-6535	894	7	.	.	PROPN
ejpam-6535	895	1	on	on	ADP
ejpam-6535	895	2	the	the	DET
ejpam-6535	895	3	notion	notion	NOUN
ejpam-6535	895	4	of	of	ADP
ejpam-6535	895	5	a	a	DET
ejpam-6535	895	6	random	random	ADJ
ejpam-6535	895	7	normed	normed	ADJ
ejpam-6535	895	8	space	space	NOUN
ejpam-6535	895	9	,	,	PUNCT
ejpam-6535	895	10	dokl	dokl	NOUN
ejpam-6535	895	11	.	.	PUNCT
ejpam-6535	895	12	akad	akad	PROPN
ejpam-6535	895	13	.	.	PUNCT
ejpam-6535	896	1	nauk	nauk	PROPN
ejpam-6535	896	2	sssr	sssr	NOUN
ejpam-6535	896	3	149	149	NUM
ejpam-6535	896	4	(	(	PUNCT
ejpam-6535	896	5	1963	1963	NUM
ejpam-6535	896	6	)	)	PUNCT
ejpam-6535	896	7	,	,	PUNCT
ejpam-6535	896	8	280–283	280–283	NUM
ejpam-6535	896	9	.	.	PUNCT
ejpam-6535	897	1	[	[	X
ejpam-6535	897	2	36	36	NUM
ejpam-6535	897	3	]	]	X
ejpam-6535	897	4	h.	h.	PROPN
ejpam-6535	897	5	sherwood	sherwood	PROPN
ejpam-6535	897	6	.	.	PUNCT
ejpam-6535	898	1	on	on	ADP
ejpam-6535	898	2	e	e	NOUN
ejpam-6535	898	3	-	-	NOUN
ejpam-6535	898	4	spaces	space	NOUN
ejpam-6535	898	5	and	and	CCONJ
ejpam-6535	898	6	their	their	PRON
ejpam-6535	898	7	relation	relation	NOUN
ejpam-6535	898	8	to	to	ADP
ejpam-6535	898	9	other	other	ADJ
ejpam-6535	898	10	classes	class	NOUN
ejpam-6535	898	11	of	of	ADP
ejpam-6535	898	12	probabilistic	probabilistic	ADJ
ejpam-6535	898	13	metric	metric	ADJ
ejpam-6535	898	14	spaces	space	NOUN
ejpam-6535	898	15	,	,	PUNCT
ejpam-6535	898	16	j.	j.	PROPN
ejpam-6535	898	17	london	london	PROPN
ejpam-6535	898	18	math	math	PROPN
ejpam-6535	898	19	.	.	PUNCT
ejpam-6535	899	1	soc	soc	PROPN
ejpam-6535	899	2	.	.	PUNCT
ejpam-6535	900	1	44	44	NUM
ejpam-6535	900	2	(	(	PUNCT
ejpam-6535	900	3	1969	1969	NUM
ejpam-6535	900	4	)	)	PUNCT
ejpam-6535	900	5	,	,	PUNCT
ejpam-6535	900	6	441	441	NUM
ejpam-6535	900	7	–	–	PUNCT
ejpam-6535	900	8	448	448	NUM
ejpam-6535	900	9	.	.	PUNCT
ejpam-6535	901	1	[	[	X
ejpam-6535	901	2	37	37	NUM
ejpam-6535	901	3	]	]	X
ejpam-6535	901	4	d.	d.	PROPN
ejpam-6535	901	5	a.	a.	PROPN
ejpam-6535	901	6	sibley	sibley	PROPN
ejpam-6535	901	7	.	.	PUNCT
ejpam-6535	902	1	a	a	DET
ejpam-6535	902	2	metric	metric	NOUN
ejpam-6535	902	3	for	for	ADP
ejpam-6535	902	4	weak	weak	ADJ
ejpam-6535	902	5	convergence	convergence	NOUN
ejpam-6535	902	6	of	of	ADP
ejpam-6535	902	7	distribution	distribution	NOUN
ejpam-6535	902	8	functions	function	NOUN
ejpam-6535	902	9	,	,	PUNCT
ejpam-6535	902	10	rocky	rocky	ADJ
ejpam-6535	902	11	mountain	mountain	NOUN
ejpam-6535	902	12	j.	j.	PROPN
ejpam-6535	902	13	math	math	PROPN
ejpam-6535	902	14	.	.	PUNCT
ejpam-6535	903	1	1	1	NUM
ejpam-6535	903	2	(	(	PUNCT
ejpam-6535	903	3	1971	1971	NUM
ejpam-6535	903	4	)	)	PUNCT
ejpam-6535	903	5	,	,	PUNCT
ejpam-6535	903	6	427	427	NUM
ejpam-6535	903	7	–	–	SYM
ejpam-6535	903	8	430	430	NUM
ejpam-6535	903	9	.	.	PUNCT
ejpam-6535	904	1	[	[	X
ejpam-6535	904	2	38	38	NUM
ejpam-6535	904	3	]	]	PUNCT
ejpam-6535	904	4	r.	r.	PROPN
ejpam-6535	904	5	m.	m.	PROPN
ejpam-6535	904	6	tardiff	tardiff	PROPN
ejpam-6535	904	7	.	.	PUNCT
ejpam-6535	905	1	topologies	topology	NOUN
ejpam-6535	905	2	for	for	ADP
ejpam-6535	905	3	probabilistic	probabilistic	ADJ
ejpam-6535	905	4	metric	metric	ADJ
ejpam-6535	905	5	spaces	space	NOUN
ejpam-6535	905	6	,	,	PUNCT
ejpam-6535	905	7	pacific	pacific	PROPN
ejpam-6535	905	8	j.	j.	PROPN
ejpam-6535	905	9	math	math	PROPN
ejpam-6535	905	10	.	.	PUNCT
ejpam-6535	906	1	65(1976	65(1976	X
ejpam-6535	906	2	)	)	PUNCT
ejpam-6535	906	3	,	,	PUNCT
ejpam-6535	907	1	233–251	233–251	NUM
ejpam-6535	907	2	.	.	PUNCT
ejpam-6535	908	1	[	[	X
ejpam-6535	908	2	39	39	NUM
ejpam-6535	908	3	]	]	PUNCT
ejpam-6535	908	4	e.	e.	PROPN
ejpam-6535	908	5	thorp	thorp	PROPN
ejpam-6535	908	6	.	.	PUNCT
ejpam-6535	909	1	generalized	generalize	VERB
ejpam-6535	909	2	topologies	topology	NOUN
ejpam-6535	909	3	for	for	ADP
ejpam-6535	909	4	statistical	statistical	ADJ
ejpam-6535	909	5	metric	metric	ADJ
ejpam-6535	909	6	spaces	space	NOUN
ejpam-6535	909	7	,	,	PUNCT
ejpam-6535	909	8	fund	fund	PROPN
ejpam-6535	909	9	.	.	PUNCT
ejpam-6535	910	1	math	math	NOUN
ejpam-6535	910	2	.	.	PUNCT
ejpam-6535	911	1	51(1962	51(1962	NUM
ejpam-6535	911	2	)	)	PUNCT
ejpam-6535	911	3	,	,	PUNCT
ejpam-6535	911	4	9–12	9–12	PROPN
ejpam-6535	911	5	.	.	PUNCT