id	sid	tid	token	lemma	pos
ejpam-5051	1	1	european	european	PROPN
ejpam-5051	1	2	journal	journal	PROPN
ejpam-5051	1	3	of	of	ADP
ejpam-5051	1	4	pure	pure	ADJ
ejpam-5051	1	5	and	and	CCONJ
ejpam-5051	1	6	applied	apply	VERB
ejpam-5051	1	7	mathematics	mathematic	NOUN
ejpam-5051	1	8	vol	vol	NOUN
ejpam-5051	1	9	.	.	PROPN
ejpam-5051	2	1	17	17	NUM
ejpam-5051	2	2	,	,	PUNCT
ejpam-5051	2	3	no	no	INTJ
ejpam-5051	2	4	.	.	NOUN
ejpam-5051	2	5	1	1	NUM
ejpam-5051	2	6	,	,	PUNCT
ejpam-5051	2	7	2024	2024	NUM
ejpam-5051	2	8	,	,	PUNCT
ejpam-5051	2	9	519	519	NUM
ejpam-5051	2	10	-	-	SYM
ejpam-5051	2	11	545	545	NUM
ejpam-5051	2	12	issn	issn	PROPN
ejpam-5051	2	13	1307	1307	NUM
ejpam-5051	2	14	-	-	SYM
ejpam-5051	2	15	5543	5543	NUM
ejpam-5051	2	16	–	–	PUNCT
ejpam-5051	3	1	ejpam.com	ejpam.com	X
ejpam-5051	3	2	published	publish	VERB
ejpam-5051	3	3	by	by	ADP
ejpam-5051	3	4	new	new	PROPN
ejpam-5051	3	5	york	york	PROPN
ejpam-5051	3	6	business	business	PROPN
ejpam-5051	3	7	global	global	PROPN
ejpam-5051	3	8	on	on	ADP
ejpam-5051	3	9	the	the	DET
ejpam-5051	3	10	construction	construction	NOUN
ejpam-5051	3	11	of	of	ADP
ejpam-5051	3	12	a	a	DET
ejpam-5051	3	13	groupoid	groupoid	NOUN
ejpam-5051	3	14	from	from	ADP
ejpam-5051	3	15	an	an	DET
ejpam-5051	3	16	ample	ample	ADJ
ejpam-5051	3	17	hausdorff	hausdorff	NOUN
ejpam-5051	3	18	groupoid	groupoid	NOUN
ejpam-5051	3	19	with	with	ADP
ejpam-5051	3	20	twisted	twisted	ADJ
ejpam-5051	3	21	steinberg	steinberg	PROPN
ejpam-5051	3	22	algebra	algebra	NOUN
ejpam-5051	3	23	not	not	PART
ejpam-5051	3	24	isomorphic	isomorphic	ADJ
ejpam-5051	3	25	to	to	ADP
ejpam-5051	3	26	its	its	PRON
ejpam-5051	3	27	non	non	ADJ
ejpam-5051	3	28	-	-	ADJ
ejpam-5051	3	29	twisted	twisted	ADJ
ejpam-5051	3	30	steinberg	steinberg	PROPN
ejpam-5051	3	31	algebra	algebra	PROPN
ejpam-5051	3	32	rizalyn	rizalyn	PROPN
ejpam-5051	3	33	s.	s.	PROPN
ejpam-5051	3	34	bongcawel	bongcawel	PROPN
ejpam-5051	3	35	1,∗	1,∗	PROPN
ejpam-5051	3	36	,	,	PUNCT
ejpam-5051	3	37	lyster	lyster	PROPN
ejpam-5051	3	38	rey	rey	PROPN
ejpam-5051	3	39	b.	b.	PROPN
ejpam-5051	3	40	cabardo1	cabardo1	PROPN
ejpam-5051	3	41	,	,	PUNCT
ejpam-5051	3	42	gaudencio	gaudencio	PROPN
ejpam-5051	3	43	c.	c.	PROPN
ejpam-5051	3	44	petalcorin	petalcorin	PROPN
ejpam-5051	3	45	jr.1	jr.1	PROPN
ejpam-5051	3	46	,	,	PUNCT
ejpam-5051	3	47	jocelyn	jocelyn	PROPN
ejpam-5051	3	48	p.	p.	PROPN
ejpam-5051	3	49	vilela1	vilela1	NOUN
ejpam-5051	4	1	1	1	NUM
ejpam-5051	4	2	department	department	NOUN
ejpam-5051	4	3	of	of	ADP
ejpam-5051	4	4	mathematics	mathematic	NOUN
ejpam-5051	4	5	and	and	CCONJ
ejpam-5051	4	6	statistics	statistic	NOUN
ejpam-5051	4	7	,	,	PUNCT
ejpam-5051	4	8	college	college	NOUN
ejpam-5051	4	9	of	of	ADP
ejpam-5051	4	10	science	science	NOUN
ejpam-5051	4	11	and	and	CCONJ
ejpam-5051	4	12	mathematics	mathematic	NOUN
ejpam-5051	4	13	,	,	PUNCT
ejpam-5051	4	14	center	center	NOUN
ejpam-5051	4	15	of	of	ADP
ejpam-5051	4	16	mathematical	mathematical	ADJ
ejpam-5051	4	17	and	and	CCONJ
ejpam-5051	4	18	theoretical	theoretical	ADJ
ejpam-5051	4	19	physical	physical	ADJ
ejpam-5051	4	20	sciences	science	NOUN
ejpam-5051	4	21	-	-	PUNCT
ejpam-5051	4	22	prism	prism	NOUN
ejpam-5051	4	23	,	,	PUNCT
ejpam-5051	4	24	msu	msu	PROPN
ejpam-5051	4	25	-	-	PUNCT
ejpam-5051	4	26	iligan	iligan	PROPN
ejpam-5051	4	27	institute	institute	PROPN
ejpam-5051	4	28	of	of	ADP
ejpam-5051	4	29	technology	technology	PROPN
ejpam-5051	4	30	,	,	PUNCT
ejpam-5051	4	31	9200	9200	NUM
ejpam-5051	4	32	iligan	iligan	ADJ
ejpam-5051	4	33	city	city	NOUN
ejpam-5051	4	34	,	,	PUNCT
ejpam-5051	4	35	philippines	philippine	NOUN
ejpam-5051	4	36	abstract	abstract	ADJ
ejpam-5051	4	37	.	.	PUNCT
ejpam-5051	5	1	this	this	DET
ejpam-5051	5	2	study	study	NOUN
ejpam-5051	5	3	introduces	introduce	VERB
ejpam-5051	5	4	an	an	DET
ejpam-5051	5	5	ample	ample	ADJ
ejpam-5051	5	6	hausdorff	hausdorff	NOUN
ejpam-5051	5	7	groupoid	groupoid	PROPN
ejpam-5051	5	8	â	â	PUNCT
ejpam-5051	6	1	⋊r	⋊r	PROPN
ejpam-5051	6	2	extracted	extract	VERB
ejpam-5051	6	3	from	from	ADP
ejpam-5051	6	4	an	an	DET
ejpam-5051	6	5	ample	ample	ADJ
ejpam-5051	6	6	hausdorff	hausdorff	NOUN
ejpam-5051	6	7	groupoid	groupoid	PROPN
ejpam-5051	6	8	g	g	PROPN
ejpam-5051	6	9	and	and	CCONJ
ejpam-5051	6	10	a	a	DET
ejpam-5051	6	11	unital	unital	ADJ
ejpam-5051	6	12	commutative	commutative	ADJ
ejpam-5051	6	13	ring	ring	NOUN
ejpam-5051	6	14	r	r	NOUN
ejpam-5051	6	15	;	;	PUNCT
ejpam-5051	6	16	a	a	DET
ejpam-5051	6	17	hausdorff	hausdorff	NOUN
ejpam-5051	6	18	groupoid	groupoid	PROPN
ejpam-5051	6	19	d	d	X
ejpam-5051	6	20	which	which	PRON
ejpam-5051	6	21	is	be	AUX
ejpam-5051	6	22	the	the	DET
ejpam-5051	6	23	discrete	discrete	ADJ
ejpam-5051	6	24	twist	twist	NOUN
ejpam-5051	6	25	over	over	ADP
ejpam-5051	6	26	â	â	DET
ejpam-5051	6	27	⋊	⋊	PROPN
ejpam-5051	6	28	r.	r.	X
ejpam-5051	6	29	in	in	ADP
ejpam-5051	6	30	the	the	DET
ejpam-5051	6	31	groupoid	groupoid	PROPN
ejpam-5051	6	32	c*-algebra	c*-algebra	PROPN
ejpam-5051	6	33	perspective	perspective	NOUN
ejpam-5051	6	34	,	,	PUNCT
ejpam-5051	6	35	when	when	SCONJ
ejpam-5051	6	36	r	r	NOUN
ejpam-5051	6	37	=	=	PUNCT
ejpam-5051	6	38	c	c	NOUN
ejpam-5051	6	39	there	there	PRON
ejpam-5051	6	40	is	be	VERB
ejpam-5051	6	41	an	an	DET
ejpam-5051	6	42	isomorphism	isomorphism	NOUN
ejpam-5051	6	43	between	between	ADP
ejpam-5051	6	44	the	the	DET
ejpam-5051	6	45	non	non	ADJ
ejpam-5051	6	46	-	-	ADJ
ejpam-5051	6	47	twisted	twisted	ADJ
ejpam-5051	6	48	groupoid	groupoid	NOUN
ejpam-5051	6	49	c*-algebra	c*-algebra	PROPN
ejpam-5051	6	50	(	(	PUNCT
ejpam-5051	6	51	c∗(g	c∗(g	PROPN
ejpam-5051	6	52	)	)	PUNCT
ejpam-5051	6	53	)	)	PUNCT
ejpam-5051	6	54	and	and	CCONJ
ejpam-5051	6	55	the	the	DET
ejpam-5051	6	56	twisted	twisted	ADJ
ejpam-5051	6	57	groupoid	groupoid	NOUN
ejpam-5051	6	58	c*algebra	c*algebra	PROPN
ejpam-5051	6	59	(	(	PUNCT
ejpam-5051	6	60	c∗(â	c∗(â	NOUN
ejpam-5051	6	61	⋊	⋊	NOUN
ejpam-5051	6	62	r;d	r;d	NUM
ejpam-5051	6	63	)	)	PUNCT
ejpam-5051	6	64	)	)	PUNCT
ejpam-5051	6	65	.	.	PUNCT
ejpam-5051	7	1	however	however	ADV
ejpam-5051	7	2	,	,	PUNCT
ejpam-5051	7	3	in	in	ADP
ejpam-5051	7	4	this	this	DET
ejpam-5051	7	5	paper	paper	NOUN
ejpam-5051	7	6	,	,	PUNCT
ejpam-5051	7	7	in	in	ADP
ejpam-5051	7	8	a	a	DET
ejpam-5051	7	9	purely	purely	ADV
ejpam-5051	7	10	algebraic	algebraic	ADJ
ejpam-5051	7	11	setting	setting	NOUN
ejpam-5051	7	12	,	,	PUNCT
ejpam-5051	7	13	the	the	DET
ejpam-5051	7	14	non	non	ADJ
ejpam-5051	7	15	-	-	ADJ
ejpam-5051	7	16	twisted	twisted	ADJ
ejpam-5051	7	17	steinberg	steinberg	PROPN
ejpam-5051	7	18	algebra	algebra	PROPN
ejpam-5051	7	19	(	(	PUNCT
ejpam-5051	7	20	ar(g	ar(g	ADJ
ejpam-5051	7	21	)	)	PUNCT
ejpam-5051	7	22	)	)	PUNCT
ejpam-5051	7	23	and	and	CCONJ
ejpam-5051	7	24	the	the	DET
ejpam-5051	7	25	twisted	twisted	ADJ
ejpam-5051	7	26	steinberg	steinberg	PROPN
ejpam-5051	7	27	algebra	algebra	PROPN
ejpam-5051	7	28	(	(	PUNCT
ejpam-5051	7	29	ar(d	ar(d	ADV
ejpam-5051	7	30	;	;	PUNCT
ejpam-5051	7	31	â⋊r	â⋊r	NOUN
ejpam-5051	7	32	)	)	PUNCT
ejpam-5051	7	33	)	)	PUNCT
ejpam-5051	7	34	are	be	AUX
ejpam-5051	7	35	non	non	ADJ
ejpam-5051	7	36	-	-	ADJ
ejpam-5051	7	37	isomorphic	isomorphic	ADJ
ejpam-5051	7	38	.	.	PUNCT
ejpam-5051	8	1	2020	2020	NUM
ejpam-5051	8	2	mathematics	mathematic	NOUN
ejpam-5051	8	3	subject	subject	NOUN
ejpam-5051	8	4	classifications	classification	NOUN
ejpam-5051	8	5	:	:	PUNCT
ejpam-5051	8	6	20l05	20l05	NUM
ejpam-5051	8	7	,	,	PUNCT
ejpam-5051	8	8	22a22	22a22	NUM
ejpam-5051	8	9	key	key	ADJ
ejpam-5051	8	10	words	word	NOUN
ejpam-5051	8	11	and	and	CCONJ
ejpam-5051	8	12	phrases	phrase	NOUN
ejpam-5051	8	13	:	:	PUNCT
ejpam-5051	8	14	groupoids	groupoid	NOUN
ejpam-5051	8	15	,	,	PUNCT
ejpam-5051	8	16	steinberg	steinberg	PROPN
ejpam-5051	8	17	algebra	algebra	PROPN
ejpam-5051	8	18	,	,	PUNCT
ejpam-5051	8	19	twisted	twisted	ADJ
ejpam-5051	8	20	steinberg	steinberg	PROPN
ejpam-5051	8	21	algebra	algebra	PROPN
ejpam-5051	8	22	,	,	PUNCT
ejpam-5051	8	23	nontwisted	nontwiste	VERB
ejpam-5051	8	24	steinberg	steinberg	PROPN
ejpam-5051	8	25	algebra	algebra	PROPN
ejpam-5051	8	26	1	1	NUM
ejpam-5051	8	27	.	.	PUNCT
ejpam-5051	8	28	introduction	introduction	NOUN
ejpam-5051	8	29	the	the	DET
ejpam-5051	8	30	study	study	NOUN
ejpam-5051	8	31	of	of	ADP
ejpam-5051	8	32	groupoids	groupoid	NOUN
ejpam-5051	8	33	was	be	AUX
ejpam-5051	8	34	initiated	initiate	VERB
ejpam-5051	8	35	by	by	ADP
ejpam-5051	8	36	brandt	brandt	PROPN
ejpam-5051	8	37	in	in	ADP
ejpam-5051	8	38	1926	1926	NUM
ejpam-5051	8	39	in	in	ADP
ejpam-5051	8	40	[	[	X
ejpam-5051	8	41	2	2	NUM
ejpam-5051	8	42	]	]	PUNCT
ejpam-5051	8	43	.	.	PUNCT
ejpam-5051	9	1	brandt	brandt	PROPN
ejpam-5051	9	2	utilizes	utilize	VERB
ejpam-5051	9	3	the	the	DET
ejpam-5051	9	4	notion	notion	NOUN
ejpam-5051	9	5	of	of	ADP
ejpam-5051	9	6	groupoid	groupoid	PROPN
ejpam-5051	9	7	in	in	ADP
ejpam-5051	9	8	[	[	X
ejpam-5051	9	9	4	4	NUM
ejpam-5051	9	10	]	]	PUNCT
ejpam-5051	9	11	and	and	CCONJ
ejpam-5051	9	12	other	other	ADJ
ejpam-5051	9	13	researchers	researcher	NOUN
ejpam-5051	9	14	produced	produce	VERB
ejpam-5051	9	15	more	more	ADJ
ejpam-5051	9	16	studies	study	NOUN
ejpam-5051	9	17	related	relate	VERB
ejpam-5051	9	18	to	to	ADP
ejpam-5051	9	19	groupoids	groupoid	NOUN
ejpam-5051	9	20	.	.	PUNCT
ejpam-5051	10	1	in	in	ADP
ejpam-5051	10	2	[	[	X
ejpam-5051	10	3	12	12	NUM
ejpam-5051	10	4	]	]	PUNCT
ejpam-5051	10	5	,	,	PUNCT
ejpam-5051	10	6	groupoid	groupoid	PROPN
ejpam-5051	10	7	is	be	AUX
ejpam-5051	10	8	defined	define	VERB
ejpam-5051	10	9	as	as	ADP
ejpam-5051	10	10	a	a	DET
ejpam-5051	10	11	small	small	ADJ
ejpam-5051	10	12	category	category	NOUN
ejpam-5051	10	13	in	in	ADP
ejpam-5051	10	14	which	which	PRON
ejpam-5051	10	15	every	every	DET
ejpam-5051	10	16	morphism	morphism	NOUN
ejpam-5051	10	17	is	be	AUX
ejpam-5051	10	18	invertible	invertible	ADJ
ejpam-5051	10	19	.	.	PUNCT
ejpam-5051	11	1	groupoid	groupoid	PROPN
ejpam-5051	11	2	was	be	AUX
ejpam-5051	11	3	used	use	VERB
ejpam-5051	11	4	in	in	ADP
ejpam-5051	11	5	various	various	ADJ
ejpam-5051	11	6	areas	area	NOUN
ejpam-5051	11	7	like	like	ADP
ejpam-5051	11	8	the	the	DET
ejpam-5051	11	9	fibre	fibre	NOUN
ejpam-5051	11	10	bundle	bundle	NOUN
ejpam-5051	11	11	theory	theory	NOUN
ejpam-5051	11	12	,	,	PUNCT
ejpam-5051	11	13	in	in	ADP
ejpam-5051	11	14	differential	differential	ADJ
ejpam-5051	11	15	theory	theory	NOUN
ejpam-5051	11	16	,	,	PUNCT
ejpam-5051	11	17	in	in	ADP
ejpam-5051	11	18	foliation	foliation	NOUN
ejpam-5051	11	19	theory	theory	NOUN
ejpam-5051	11	20	and	and	CCONJ
ejpam-5051	11	21	in	in	ADP
ejpam-5051	11	22	differential	differential	ADJ
ejpam-5051	11	23	topology	topology	NOUN
ejpam-5051	11	24	.	.	PUNCT
ejpam-5051	12	1	in	in	ADP
ejpam-5051	12	2	1980s	1980s	NUM
ejpam-5051	12	3	,	,	PUNCT
ejpam-5051	12	4	renault	renault	PROPN
ejpam-5051	12	5	was	be	AUX
ejpam-5051	12	6	motivated	motivate	VERB
ejpam-5051	12	7	by	by	ADP
ejpam-5051	12	8	the	the	DET
ejpam-5051	12	9	works	work	NOUN
ejpam-5051	12	10	of	of	ADP
ejpam-5051	12	11	feldman	feldman	PROPN
ejpam-5051	12	12	and	and	CCONJ
ejpam-5051	12	13	moore	moore	PROPN
ejpam-5051	13	1	[	[	X
ejpam-5051	13	2	5	5	NUM
ejpam-5051	13	3	,	,	PUNCT
ejpam-5051	13	4	6	6	NUM
ejpam-5051	13	5	]	]	PUNCT
ejpam-5051	13	6	for	for	ADP
ejpam-5051	13	7	von	von	PROPN
ejpam-5051	13	8	neumann	neumann	PROPN
ejpam-5051	13	9	algebras	algebras	PROPN
ejpam-5051	13	10	and	and	CCONJ
ejpam-5051	13	11	initiated	initiate	VERB
ejpam-5051	13	12	the	the	DET
ejpam-5051	13	13	study	study	NOUN
ejpam-5051	13	14	of	of	ADP
ejpam-5051	13	15	c*-algebras	c*-algebra	NOUN
ejpam-5051	13	16	associated	associate	VERB
ejpam-5051	13	17	to	to	ADP
ejpam-5051	13	18	groupoids	groupoid	NOUN
ejpam-5051	13	19	in	in	ADP
ejpam-5051	13	20	his	his	PRON
ejpam-5051	13	21	phd	phd	NOUN
ejpam-5051	13	22	thesis	thesis	NOUN
ejpam-5051	14	1	[	[	X
ejpam-5051	14	2	10	10	NUM
ejpam-5051	14	3	]	]	PUNCT
ejpam-5051	14	4	.	.	PUNCT
ejpam-5051	15	1	this	this	DET
ejpam-5051	15	2	study	study	NOUN
ejpam-5051	15	3	proved	prove	VERB
ejpam-5051	15	4	itself	itself	PRON
ejpam-5051	15	5	useful	useful	ADJ
ejpam-5051	15	6	as	as	SCONJ
ejpam-5051	15	7	it	it	PRON
ejpam-5051	15	8	caters	cater	VERB
ejpam-5051	15	9	many	many	ADJ
ejpam-5051	15	10	problem	problem	NOUN
ejpam-5051	15	11	in	in	ADP
ejpam-5051	15	12	c*-algebras	c*-algebras	ADJ
ejpam-5051	15	13	.	.	PUNCT
ejpam-5051	16	1	∗corresponding	∗corresponde	VERB
ejpam-5051	16	2	author	author	NOUN
ejpam-5051	16	3	.	.	PUNCT
ejpam-5051	17	1	doi	doi	NOUN
ejpam-5051	17	2	:	:	PUNCT
ejpam-5051	17	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5051	https://doi.org/10.29020/nybg.ejpam.v17i1.5051	PROPN
ejpam-5051	17	4	email	email	NOUN
ejpam-5051	17	5	addresses	address	NOUN
ejpam-5051	17	6	:	:	PUNCT
ejpam-5051	17	7	rizalyn.bongcawel@g.msuiit.edu.ph	rizalyn.bongcawel@g.msuiit.edu.ph	PROPN
ejpam-5051	17	8	(	(	PUNCT
ejpam-5051	17	9	r.	r.	PROPN
ejpam-5051	17	10	s.	s.	PROPN
ejpam-5051	17	11	bongcawel	bongcawel	PROPN
ejpam-5051	17	12	)	)	PUNCT
ejpam-5051	17	13	,	,	PUNCT
ejpam-5051	17	14	lysterrey.cabardo@g.msuiit.edu.ph	lysterrey.cabardo@g.msuiit.edu.ph	PROPN
ejpam-5051	17	15	(	(	PUNCT
ejpam-5051	17	16	l.	l.	PROPN
ejpam-5051	17	17	b.	b.	PROPN
ejpam-5051	17	18	cabardo	cabardo	PROPN
ejpam-5051	17	19	)	)	PUNCT
ejpam-5051	17	20	,	,	PUNCT
ejpam-5051	17	21	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-5051	17	22	(	(	PUNCT
ejpam-5051	17	23	g.	g.	PROPN
ejpam-5051	17	24	c.	c.	PROPN
ejpam-5051	17	25	petalcorin	petalcorin	PROPN
ejpam-5051	17	26	)	)	PUNCT
ejpam-5051	17	27	,	,	PUNCT
ejpam-5051	17	28	jocelyn.vilela@g.msuiit.edu.ph	jocelyn.vilela@g.msuiit.edu.ph	PROPN
ejpam-5051	17	29	(	(	PUNCT
ejpam-5051	17	30	j.	j.	PROPN
ejpam-5051	17	31	p.	p.	PROPN
ejpam-5051	17	32	vilela	vilela	PROPN
ejpam-5051	17	33	)	)	PUNCT
ejpam-5051	17	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5051	18	1	519	519	NUM
ejpam-5051	18	2	©	©	PROPN
ejpam-5051	18	3	2024	2024	NUM
ejpam-5051	18	4	ejpam	ejpam	NOUN
ejpam-5051	18	5	all	all	DET
ejpam-5051	18	6	rights	right	NOUN
ejpam-5051	18	7	reserved	reserve	VERB
ejpam-5051	18	8	.	.	PUNCT
ejpam-5051	19	1	r.	r.	PROPN
ejpam-5051	19	2	s.	s.	PROPN
ejpam-5051	19	3	bongcawel	bongcawel	PROPN
ejpam-5051	20	1	et	et	PROPN
ejpam-5051	20	2	al	al	PROPN
ejpam-5051	20	3	.	.	PUNCT
ejpam-5051	20	4	/	/	SYM
ejpam-5051	20	5	eur	eur	PROPN
ejpam-5051	20	6	.	.	PUNCT
ejpam-5051	21	1	j.	j.	PROPN
ejpam-5051	21	2	pure	pure	PROPN
ejpam-5051	21	3	appl	appl	PROPN
ejpam-5051	21	4	.	.	PROPN
ejpam-5051	21	5	math	math	PROPN
ejpam-5051	21	6	,	,	PUNCT
ejpam-5051	21	7	17	17	NUM
ejpam-5051	21	8	(	(	PUNCT
ejpam-5051	21	9	1	1	NUM
ejpam-5051	21	10	)	)	PUNCT
ejpam-5051	21	11	(	(	PUNCT
ejpam-5051	21	12	2024	2024	NUM
ejpam-5051	21	13	)	)	PUNCT
ejpam-5051	21	14	,	,	PUNCT
ejpam-5051	21	15	519	519	NUM
ejpam-5051	21	16	-	-	SYM
ejpam-5051	21	17	545	545	NUM
ejpam-5051	21	18	520	520	NUM
ejpam-5051	21	19	significant	significant	ADJ
ejpam-5051	21	20	works	work	NOUN
ejpam-5051	21	21	on	on	ADP
ejpam-5051	21	22	characterization	characterization	NOUN
ejpam-5051	21	23	of	of	ADP
ejpam-5051	21	24	lei	lei	ADJ
ejpam-5051	21	25	-	-	PUNCT
ejpam-5051	21	26	type	type	NOUN
ejpam-5051	21	27	maps	map	NOUN
ejpam-5051	21	28	with	with	ADP
ejpam-5051	21	29	c*-algebra	c*-algebra	PROPN
ejpam-5051	21	30	are	be	AUX
ejpam-5051	21	31	in	in	ADP
ejpam-5051	21	32	[	[	X
ejpam-5051	21	33	13	13	NUM
ejpam-5051	21	34	]	]	PUNCT
ejpam-5051	21	35	and	and	CCONJ
ejpam-5051	22	1	[	[	X
ejpam-5051	22	2	8	8	NUM
ejpam-5051	22	3	]	]	PUNCT
ejpam-5051	22	4	.	.	PUNCT
ejpam-5051	23	1	renault	renault	PROPN
ejpam-5051	23	2	then	then	ADV
ejpam-5051	23	3	introduced	introduce	VERB
ejpam-5051	23	4	the	the	DET
ejpam-5051	23	5	twisted	twisted	ADJ
ejpam-5051	23	6	groupoid	groupoid	NOUN
ejpam-5051	23	7	c*-algebras	c*-algebra	NOUN
ejpam-5051	23	8	where	where	SCONJ
ejpam-5051	23	9	the	the	DET
ejpam-5051	23	10	twist	twist	NOUN
ejpam-5051	23	11	is	be	AUX
ejpam-5051	23	12	done	do	VERB
ejpam-5051	23	13	by	by	ADP
ejpam-5051	23	14	incorporating	incorporate	VERB
ejpam-5051	23	15	a	a	DET
ejpam-5051	23	16	t	t	NOUN
ejpam-5051	23	17	-	-	PUNCT
ejpam-5051	23	18	valued	value	VERB
ejpam-5051	23	19	2	2	NUM
ejpam-5051	23	20	-	-	PUNCT
ejpam-5051	23	21	cocycle	cocycle	NOUN
ejpam-5051	23	22	to	to	ADP
ejpam-5051	23	23	its	its	PRON
ejpam-5051	23	24	multiplication	multiplication	NOUN
ejpam-5051	23	25	and	and	CCONJ
ejpam-5051	23	26	involution	involution	NOUN
ejpam-5051	23	27	.	.	PUNCT
ejpam-5051	24	1	this	this	DET
ejpam-5051	24	2	study	study	NOUN
ejpam-5051	24	3	yields	yield	VERB
ejpam-5051	24	4	extreme	extreme	ADJ
ejpam-5051	24	5	importance	importance	NOUN
ejpam-5051	24	6	in	in	ADP
ejpam-5051	24	7	the	the	DET
ejpam-5051	24	8	structures	structure	NOUN
ejpam-5051	24	9	of	of	ADP
ejpam-5051	24	10	large	large	ADJ
ejpam-5051	24	11	classes	class	NOUN
ejpam-5051	24	12	of	of	ADP
ejpam-5051	24	13	c*-algebras	c*-algebra	NOUN
ejpam-5051	24	14	as	as	SCONJ
ejpam-5051	24	15	seen	see	VERB
ejpam-5051	24	16	in	in	ADP
ejpam-5051	24	17	the	the	DET
ejpam-5051	24	18	works	work	NOUN
ejpam-5051	24	19	of	of	ADP
ejpam-5051	24	20	renault[11	renault[11	NOUN
ejpam-5051	24	21	]	]	X
ejpam-5051	24	22	,	,	PUNCT
ejpam-5051	24	23	tu[14	tu[14	PROPN
ejpam-5051	24	24	]	]	PUNCT
ejpam-5051	24	25	and	and	CCONJ
ejpam-5051	24	26	barlak	barlak	NOUN
ejpam-5051	24	27	and	and	CCONJ
ejpam-5051	24	28	li[4	li[4	PROPN
ejpam-5051	24	29	]	]	PUNCT
ejpam-5051	24	30	.	.	PUNCT
ejpam-5051	25	1	in	in	ADP
ejpam-5051	25	2	[	[	X
ejpam-5051	25	3	15	15	NUM
ejpam-5051	25	4	]	]	PUNCT
ejpam-5051	25	5	,	,	PUNCT
ejpam-5051	25	6	williams	williams	PROPN
ejpam-5051	25	7	,	,	PUNCT
ejpam-5051	25	8	renault	renault	PROPN
ejpam-5051	25	9	and	and	CCONJ
ejpam-5051	25	10	muhly	muhly	ADV
ejpam-5051	25	11	proved	prove	VERB
ejpam-5051	25	12	that	that	SCONJ
ejpam-5051	25	13	the	the	DET
ejpam-5051	25	14	groupoid	groupoid	PROPN
ejpam-5051	25	15	c*-algebra	c*-algebra	PROPN
ejpam-5051	25	16	(	(	PUNCT
ejpam-5051	25	17	c∗(g	c∗(g	PROPN
ejpam-5051	25	18	)	)	PUNCT
ejpam-5051	25	19	)	)	PUNCT
ejpam-5051	25	20	and	and	CCONJ
ejpam-5051	25	21	the	the	DET
ejpam-5051	25	22	twisted	twisted	ADJ
ejpam-5051	25	23	groupoid	groupoid	NOUN
ejpam-5051	25	24	c*-algebra	c*-algebra	PROPN
ejpam-5051	25	25	(	(	PUNCT
ejpam-5051	25	26	c∗(â⋊r;d	c∗(â⋊r;d	NUM
ejpam-5051	25	27	)	)	PUNCT
ejpam-5051	25	28	)	)	PUNCT
ejpam-5051	25	29	are	be	AUX
ejpam-5051	25	30	isomorphic	isomorphic	ADJ
ejpam-5051	25	31	when	when	SCONJ
ejpam-5051	25	32	r	r	NOUN
ejpam-5051	25	33	=	=	SYM
ejpam-5051	25	34	c	c	NOUN
ejpam-5051	25	35	with	with	ADP
ejpam-5051	25	36	the	the	DET
ejpam-5051	25	37	additional	additional	ADJ
ejpam-5051	25	38	conditions	condition	NOUN
ejpam-5051	25	39	for	for	SCONJ
ejpam-5051	25	40	g	g	NOUN
ejpam-5051	25	41	to	to	PART
ejpam-5051	25	42	be	be	AUX
ejpam-5051	25	43	second	second	ADV
ejpam-5051	25	44	countable	countable	ADJ
ejpam-5051	25	45	locally	locally	ADV
ejpam-5051	25	46	compact	compact	ADJ
ejpam-5051	25	47	groupoid	groupoid	NOUN
ejpam-5051	25	48	with	with	ADP
ejpam-5051	25	49	a	a	DET
ejpam-5051	25	50	haar	haar	NOUN
ejpam-5051	25	51	system	system	NOUN
ejpam-5051	25	52	and	and	CCONJ
ejpam-5051	25	53	abelian	abelian	NOUN
ejpam-5051	25	54	isotropy	isotropy	PROPN
ejpam-5051	25	55	.	.	PUNCT
ejpam-5051	26	1	last	last	ADJ
ejpam-5051	26	2	2010	2010	NUM
ejpam-5051	26	3	,	,	PUNCT
ejpam-5051	26	4	thirty	thirty	NUM
ejpam-5051	26	5	years	year	NOUN
ejpam-5051	26	6	after	after	ADP
ejpam-5051	26	7	the	the	DET
ejpam-5051	26	8	introduction	introduction	NOUN
ejpam-5051	26	9	of	of	ADP
ejpam-5051	26	10	twisted	twisted	ADJ
ejpam-5051	26	11	groupoid	groupoid	PROPN
ejpam-5051	26	12	c*-algebras	c*-algebras	PROPN
ejpam-5051	26	13	,	,	PUNCT
ejpam-5051	26	14	steinberg	steinberg	PROPN
ejpam-5051	26	15	algebra	algebra	PROPN
ejpam-5051	26	16	was	be	AUX
ejpam-5051	26	17	introduced	introduce	VERB
ejpam-5051	26	18	independently	independently	ADV
ejpam-5051	26	19	in	in	ADP
ejpam-5051	26	20	[	[	X
ejpam-5051	26	21	3	3	NUM
ejpam-5051	26	22	,	,	PUNCT
ejpam-5051	26	23	9	9	NUM
ejpam-5051	26	24	]	]	PUNCT
ejpam-5051	26	25	.	.	PUNCT
ejpam-5051	27	1	it	it	PRON
ejpam-5051	27	2	is	be	AUX
ejpam-5051	27	3	an	an	DET
ejpam-5051	27	4	algebraic	algebraic	ADJ
ejpam-5051	27	5	analogue	analogue	NOUN
ejpam-5051	27	6	of	of	ADP
ejpam-5051	27	7	groupoid	groupoid	PROPN
ejpam-5051	27	8	c*-algebra	c*-algebra	PROPN
ejpam-5051	27	9	.	.	PUNCT
ejpam-5051	28	1	in	in	ADP
ejpam-5051	28	2	2021	2021	NUM
ejpam-5051	28	3	,	,	PUNCT
ejpam-5051	28	4	becky	becky	PROPN
ejpam-5051	28	5	armstrong	armstrong	PROPN
ejpam-5051	28	6	,	,	PUNCT
ejpam-5051	28	7	lisa	lisa	PROPN
ejpam-5051	28	8	clark	clark	PROPN
ejpam-5051	28	9	,	,	PUNCT
ejpam-5051	28	10	et	et	PROPN
ejpam-5051	28	11	al	al	PROPN
ejpam-5051	28	12	.	.	PROPN
ejpam-5051	28	13	introduced	introduce	VERB
ejpam-5051	28	14	the	the	DET
ejpam-5051	28	15	twisted	twisted	ADJ
ejpam-5051	28	16	steinberg	steinberg	PROPN
ejpam-5051	28	17	algebra	algebra	PROPN
ejpam-5051	28	18	in	in	ADP
ejpam-5051	28	19	[	[	X
ejpam-5051	28	20	1	1	NUM
ejpam-5051	28	21	]	]	PUNCT
ejpam-5051	28	22	.	.	PUNCT
ejpam-5051	29	1	it	it	PRON
ejpam-5051	29	2	is	be	AUX
ejpam-5051	29	3	a	a	DET
ejpam-5051	29	4	purely	purely	ADV
ejpam-5051	29	5	algebraic	algebraic	ADJ
ejpam-5051	29	6	analogue	analogue	NOUN
ejpam-5051	29	7	of	of	ADP
ejpam-5051	29	8	renault	renault	PROPN
ejpam-5051	29	9	’s	’s	PART
ejpam-5051	29	10	twisted	twisted	ADJ
ejpam-5051	29	11	groupoid	groupoid	PROPN
ejpam-5051	29	12	c*-algebra	c*-algebra	PROPN
ejpam-5051	29	13	.	.	PUNCT
ejpam-5051	30	1	this	this	DET
ejpam-5051	30	2	study	study	NOUN
ejpam-5051	30	3	is	be	AUX
ejpam-5051	30	4	a	a	DET
ejpam-5051	30	5	generalisation	generalisation	NOUN
ejpam-5051	30	6	of	of	ADP
ejpam-5051	30	7	steinberg	steinberg	PROPN
ejpam-5051	30	8	algebra	algebra	PROPN
ejpam-5051	30	9	by	by	ADP
ejpam-5051	30	10	twisting	twist	VERB
ejpam-5051	30	11	the	the	DET
ejpam-5051	30	12	convolution	convolution	NOUN
ejpam-5051	30	13	and	and	CCONJ
ejpam-5051	30	14	involution	involution	NOUN
ejpam-5051	30	15	in	in	ADP
ejpam-5051	30	16	two	two	NUM
ejpam-5051	30	17	ways	way	NOUN
ejpam-5051	30	18	:	:	PUNCT
ejpam-5051	30	19	a	a	DET
ejpam-5051	30	20	locally	locally	ADV
ejpam-5051	30	21	constant	constant	ADJ
ejpam-5051	30	22	2	2	NUM
ejpam-5051	30	23	-	-	PUNCT
ejpam-5051	30	24	cocyle	cocyle	NOUN
ejpam-5051	30	25	σ	σ	NOUN
ejpam-5051	30	26	and	and	CCONJ
ejpam-5051	30	27	a	a	DET
ejpam-5051	30	28	discrete	discrete	ADJ
ejpam-5051	30	29	twist	twist	NOUN
ejpam-5051	30	30	σ	σ	NOUN
ejpam-5051	30	31	over	over	ADP
ejpam-5051	30	32	a	a	DET
ejpam-5051	30	33	hausdorff	hausdorff	NOUN
ejpam-5051	30	34	étale	étale	PROPN
ejpam-5051	30	35	groupoid	groupoid	PROPN
ejpam-5051	30	36	g.	g.	NOUN
ejpam-5051	30	37	in	in	ADP
ejpam-5051	30	38	this	this	DET
ejpam-5051	30	39	paper	paper	NOUN
ejpam-5051	30	40	,	,	PUNCT
ejpam-5051	30	41	we	we	PRON
ejpam-5051	30	42	consider	consider	VERB
ejpam-5051	30	43	a	a	DET
ejpam-5051	30	44	purely	purely	ADV
ejpam-5051	30	45	algebraic	algebraic	ADJ
ejpam-5051	30	46	perspective	perspective	NOUN
ejpam-5051	30	47	,	,	PUNCT
ejpam-5051	30	48	that	that	ADV
ejpam-5051	30	49	is	is	ADV
ejpam-5051	30	50	,	,	PUNCT
ejpam-5051	30	51	in	in	ADP
ejpam-5051	30	52	the	the	DET
ejpam-5051	30	53	notion	notion	NOUN
ejpam-5051	30	54	of	of	ADP
ejpam-5051	30	55	steinberg	steinberg	PROPN
ejpam-5051	30	56	algebra	algebra	PROPN
ejpam-5051	30	57	.	.	PUNCT
ejpam-5051	31	1	without	without	ADP
ejpam-5051	31	2	the	the	DET
ejpam-5051	31	3	analysis	analysis	NOUN
ejpam-5051	31	4	requirements	requirement	NOUN
ejpam-5051	31	5	for	for	ADP
ejpam-5051	31	6	our	our	PRON
ejpam-5051	31	7	groupoid	groupoid	NOUN
ejpam-5051	31	8	,	,	PUNCT
ejpam-5051	31	9	our	our	PRON
ejpam-5051	31	10	goal	goal	NOUN
ejpam-5051	31	11	is	be	AUX
ejpam-5051	31	12	to	to	PART
ejpam-5051	31	13	show	show	VERB
ejpam-5051	31	14	that	that	SCONJ
ejpam-5051	31	15	the	the	DET
ejpam-5051	31	16	non	non	ADJ
ejpam-5051	31	17	-	-	ADJ
ejpam-5051	31	18	twisted	twisted	ADJ
ejpam-5051	31	19	steinberg	steinberg	PROPN
ejpam-5051	31	20	algebra	algebra	PROPN
ejpam-5051	31	21	and	and	CCONJ
ejpam-5051	31	22	the	the	DET
ejpam-5051	31	23	twisted	twisted	ADJ
ejpam-5051	31	24	steinberg	steinberg	PROPN
ejpam-5051	31	25	algebra	algebra	PROPN
ejpam-5051	31	26	are	be	AUX
ejpam-5051	31	27	nonisomorphic	nonisomorphic	ADJ
ejpam-5051	31	28	.	.	PUNCT
ejpam-5051	32	1	our	our	PRON
ejpam-5051	32	2	first	first	ADJ
ejpam-5051	32	3	task	task	NOUN
ejpam-5051	32	4	is	be	AUX
ejpam-5051	32	5	to	to	PART
ejpam-5051	32	6	construct	construct	VERB
ejpam-5051	32	7	an	an	DET
ejpam-5051	32	8	ample	ample	ADJ
ejpam-5051	32	9	hausdorff	hausdorff	NOUN
ejpam-5051	32	10	groupoid	groupoid	PROPN
ejpam-5051	32	11	â	â	ADP
ejpam-5051	32	12	⋊	⋊	SYM
ejpam-5051	32	13	r	r	NOUN
ejpam-5051	32	14	from	from	ADP
ejpam-5051	32	15	an	an	DET
ejpam-5051	32	16	ample	ample	ADJ
ejpam-5051	32	17	hausdorff	hausdorff	NOUN
ejpam-5051	32	18	groupoid	groupoid	PROPN
ejpam-5051	32	19	g	g	PROPN
ejpam-5051	32	20	and	and	CCONJ
ejpam-5051	32	21	a	a	DET
ejpam-5051	32	22	unital	unital	ADJ
ejpam-5051	32	23	commutative	commutative	ADJ
ejpam-5051	32	24	ring	ring	NOUN
ejpam-5051	32	25	r	r	NOUN
ejpam-5051	32	26	with	with	ADP
ejpam-5051	32	27	r×	r×	NOUN
ejpam-5051	32	28	as	as	ADP
ejpam-5051	32	29	the	the	DET
ejpam-5051	32	30	set	set	NOUN
ejpam-5051	32	31	of	of	ADP
ejpam-5051	32	32	units	unit	NOUN
ejpam-5051	32	33	of	of	ADP
ejpam-5051	32	34	r.	r.	PROPN
ejpam-5051	32	35	from	from	ADP
ejpam-5051	32	36	the	the	DET
ejpam-5051	32	37	unit	unit	NOUN
ejpam-5051	32	38	space	space	NOUN
ejpam-5051	32	39	of	of	ADP
ejpam-5051	32	40	â⋊r	â⋊r	PROPN
ejpam-5051	32	41	,	,	PUNCT
ejpam-5051	32	42	we	we	PRON
ejpam-5051	32	43	then	then	ADV
ejpam-5051	32	44	construct	construct	VERB
ejpam-5051	32	45	a	a	DET
ejpam-5051	32	46	sequence	sequence	NOUN
ejpam-5051	32	47	â×	â×	NOUN
ejpam-5051	32	48	t	t	PROPN
ejpam-5051	32	49	i	i	NOUN
ejpam-5051	32	50	↪	↪	PROPN
ejpam-5051	32	51	→	→	SYM
ejpam-5051	32	52	d	d	X
ejpam-5051	32	53	q	q	X
ejpam-5051	32	54	↪	↪	PROPN
ejpam-5051	32	55	→	→	SYM
ejpam-5051	32	56	â⋊r	â⋊r	NOUN
ejpam-5051	32	57	where	where	SCONJ
ejpam-5051	32	58	d	d	NOUN
ejpam-5051	32	59	is	be	AUX
ejpam-5051	32	60	a	a	DET
ejpam-5051	32	61	hausdorff	hausdorff	NOUN
ejpam-5051	32	62	groupoid	groupoid	NOUN
ejpam-5051	32	63	,	,	PUNCT
ejpam-5051	32	64	t	t	NOUN
ejpam-5051	32	65	≤	≤	NUM
ejpam-5051	32	66	r×	r×	PROPN
ejpam-5051	33	1	and	and	CCONJ
ejpam-5051	33	2	(	(	PUNCT
ejpam-5051	33	3	d	d	X
ejpam-5051	33	4	,	,	PUNCT
ejpam-5051	33	5	i	i	PRON
ejpam-5051	33	6	,	,	PUNCT
ejpam-5051	33	7	q	q	X
ejpam-5051	33	8	)	)	PUNCT
ejpam-5051	33	9	is	be	AUX
ejpam-5051	33	10	our	our	PRON
ejpam-5051	33	11	desired	desire	VERB
ejpam-5051	33	12	twist	twist	NOUN
ejpam-5051	33	13	over	over	ADP
ejpam-5051	33	14	â	â	PROPN
ejpam-5051	33	15	⋊r	⋊r	PROPN
ejpam-5051	33	16	.	.	PUNCT
ejpam-5051	34	1	we	we	PRON
ejpam-5051	34	2	then	then	ADV
ejpam-5051	34	3	investigate	investigate	VERB
ejpam-5051	34	4	properties	property	NOUN
ejpam-5051	34	5	of	of	ADP
ejpam-5051	34	6	the	the	DET
ejpam-5051	34	7	steinberg	steinberg	PROPN
ejpam-5051	34	8	algebra	algebra	PROPN
ejpam-5051	34	9	of	of	ADP
ejpam-5051	34	10	g	g	NOUN
ejpam-5051	34	11	over	over	ADP
ejpam-5051	34	12	r	r	NOUN
ejpam-5051	34	13	or	or	CCONJ
ejpam-5051	34	14	ar(g	ar(g	ADP
ejpam-5051	34	15	)	)	PUNCT
ejpam-5051	34	16	and	and	CCONJ
ejpam-5051	34	17	the	the	DET
ejpam-5051	34	18	twisted	twisted	ADJ
ejpam-5051	34	19	steinberg	steinberg	PROPN
ejpam-5051	34	20	algebra	algebra	PROPN
ejpam-5051	34	21	associated	associate	VERB
ejpam-5051	34	22	to	to	ADP
ejpam-5051	34	23	the	the	DET
ejpam-5051	34	24	pair	pair	NOUN
ejpam-5051	34	25	(	(	PUNCT
ejpam-5051	34	26	â⋊r	â⋊r	PROPN
ejpam-5051	34	27	,	,	PUNCT
ejpam-5051	34	28	d	d	NOUN
ejpam-5051	34	29	)	)	PUNCT
ejpam-5051	34	30	or	or	CCONJ
ejpam-5051	34	31	ar(d	ar(d	NUM
ejpam-5051	34	32	;	;	PUNCT
ejpam-5051	34	33	â⋊r	â⋊r	NOUN
ejpam-5051	34	34	)	)	PUNCT
ejpam-5051	34	35	and	and	CCONJ
ejpam-5051	34	36	look	look	VERB
ejpam-5051	34	37	at	at	ADP
ejpam-5051	34	38	when	when	SCONJ
ejpam-5051	34	39	isomorphism	isomorphism	NOUN
ejpam-5051	34	40	between	between	ADP
ejpam-5051	34	41	the	the	DET
ejpam-5051	34	42	two	two	NUM
ejpam-5051	34	43	fails	fail	VERB
ejpam-5051	34	44	to	to	PART
ejpam-5051	34	45	hold	hold	VERB
ejpam-5051	34	46	.	.	PUNCT
ejpam-5051	35	1	2	2	X
ejpam-5051	35	2	.	.	NUM
ejpam-5051	35	3	preliminaries	preliminary	NOUN
ejpam-5051	35	4	in	in	ADP
ejpam-5051	35	5	this	this	DET
ejpam-5051	35	6	section	section	NOUN
ejpam-5051	35	7	,	,	PUNCT
ejpam-5051	35	8	important	important	ADJ
ejpam-5051	35	9	concepts	concept	NOUN
ejpam-5051	35	10	and	and	CCONJ
ejpam-5051	35	11	notations	notation	NOUN
ejpam-5051	35	12	on	on	ADP
ejpam-5051	35	13	topological	topological	ADJ
ejpam-5051	35	14	groupoids	groupoid	NOUN
ejpam-5051	35	15	,	,	PUNCT
ejpam-5051	35	16	steinberg	steinberg	PROPN
ejpam-5051	35	17	algebra	algebra	PROPN
ejpam-5051	35	18	and	and	CCONJ
ejpam-5051	35	19	twisted	twisted	ADJ
ejpam-5051	35	20	steinberg	steinberg	PROPN
ejpam-5051	35	21	algebra	algebra	PROPN
ejpam-5051	35	22	arising	arise	VERB
ejpam-5051	35	23	from	from	ADP
ejpam-5051	35	24	a	a	DET
ejpam-5051	35	25	discrete	discrete	ADJ
ejpam-5051	35	26	twist	twist	NOUN
ejpam-5051	35	27	are	be	AUX
ejpam-5051	35	28	presented	present	VERB
ejpam-5051	35	29	.	.	PUNCT
ejpam-5051	36	1	definition	definition	NOUN
ejpam-5051	36	2	1	1	NUM
ejpam-5051	36	3	.	.	PUNCT
ejpam-5051	37	1	[	[	X
ejpam-5051	37	2	7	7	X
ejpam-5051	37	3	]	]	PUNCT
ejpam-5051	37	4	let	let	VERB
ejpam-5051	37	5	g	g	PRON
ejpam-5051	37	6	be	be	AUX
ejpam-5051	37	7	a	a	DET
ejpam-5051	37	8	set	set	NOUN
ejpam-5051	37	9	and	and	CCONJ
ejpam-5051	37	10	g(2	g(2	PROPN
ejpam-5051	37	11	)	)	PUNCT
ejpam-5051	37	12	be	be	VERB
ejpam-5051	37	13	a	a	DET
ejpam-5051	37	14	subset	subset	NOUN
ejpam-5051	37	15	of	of	ADP
ejpam-5051	37	16	g	g	PROPN
ejpam-5051	37	17	×	×	NOUN
ejpam-5051	37	18	g	g	NOUN
ejpam-5051	37	19	such	such	ADJ
ejpam-5051	37	20	that	that	SCONJ
ejpam-5051	37	21	there	there	PRON
ejpam-5051	37	22	is	be	VERB
ejpam-5051	37	23	a	a	DET
ejpam-5051	37	24	(	(	PUNCT
ejpam-5051	37	25	composition	composition	NOUN
ejpam-5051	37	26	)	)	PUNCT
ejpam-5051	37	27	map	map	NOUN
ejpam-5051	37	28	(	(	PUNCT
ejpam-5051	37	29	γ	γ	X
ejpam-5051	37	30	,	,	PUNCT
ejpam-5051	37	31	α	α	NOUN
ejpam-5051	37	32	)	)	PUNCT
ejpam-5051	37	33	7→	7→	NOUN
ejpam-5051	37	34	γα	γα	ADP
ejpam-5051	37	35	from	from	ADP
ejpam-5051	37	36	g(2	g(2	PROPN
ejpam-5051	37	37	)	)	PUNCT
ejpam-5051	37	38	to	to	ADP
ejpam-5051	37	39	g.	g.	PROPN
ejpam-5051	37	40	suppose	suppose	VERB
ejpam-5051	37	41	that	that	SCONJ
ejpam-5051	37	42	there	there	PRON
ejpam-5051	37	43	is	be	VERB
ejpam-5051	37	44	an	an	DET
ejpam-5051	37	45	inverse	inverse	NOUN
ejpam-5051	37	46	map	map	NOUN
ejpam-5051	37	47	γ	γ	PROPN
ejpam-5051	37	48	7→	7→	PROPN
ejpam-5051	37	49	γ−1	γ−1	PROPN
ejpam-5051	37	50	on	on	ADP
ejpam-5051	37	51	g	g	PROPN
ejpam-5051	37	52	such	such	ADJ
ejpam-5051	37	53	that	that	PRON
ejpam-5051	37	54	(	(	PUNCT
ejpam-5051	37	55	γ−1)−1	γ−1)−1	NOUN
ejpam-5051	37	56	=	=	SYM
ejpam-5051	37	57	γ	γ	X
ejpam-5051	37	58	.	.	PUNCT
ejpam-5051	38	1	then	then	ADV
ejpam-5051	38	2	we	we	PRON
ejpam-5051	38	3	say	say	VERB
ejpam-5051	38	4	that	that	SCONJ
ejpam-5051	38	5	g	g	PROPN
ejpam-5051	38	6	is	be	AUX
ejpam-5051	38	7	a	a	DET
ejpam-5051	38	8	groupoid	groupoid	NOUN
ejpam-5051	38	9	if	if	SCONJ
ejpam-5051	38	10	the	the	DET
ejpam-5051	38	11	following	following	NOUN
ejpam-5051	38	12	are	be	AUX
ejpam-5051	38	13	satisfied	satisfied	ADJ
ejpam-5051	38	14	:	:	PUNCT
ejpam-5051	38	15	(	(	PUNCT
ejpam-5051	38	16	g1	g1	PROPN
ejpam-5051	38	17	)	)	PUNCT
ejpam-5051	38	18	if	if	SCONJ
ejpam-5051	38	19	(	(	PUNCT
ejpam-5051	38	20	γ	γ	X
ejpam-5051	38	21	,	,	PUNCT
ejpam-5051	38	22	α	α	NOUN
ejpam-5051	38	23	)	)	PUNCT
ejpam-5051	38	24	,	,	PUNCT
ejpam-5051	38	25	(	(	PUNCT
ejpam-5051	38	26	α	α	X
ejpam-5051	38	27	,	,	PUNCT
ejpam-5051	38	28	β	β	NOUN
ejpam-5051	38	29	)	)	PUNCT
ejpam-5051	38	30	∈	∈	PROPN
ejpam-5051	38	31	g(2	g(2	PROPN
ejpam-5051	38	32	)	)	PUNCT
ejpam-5051	38	33	,	,	PUNCT
ejpam-5051	38	34	then	then	ADV
ejpam-5051	38	35	(	(	PUNCT
ejpam-5051	38	36	γα	γα	INTJ
ejpam-5051	38	37	,	,	PUNCT
ejpam-5051	38	38	β	β	NOUN
ejpam-5051	38	39	)	)	PUNCT
ejpam-5051	38	40	,	,	PUNCT
ejpam-5051	38	41	(	(	PUNCT
ejpam-5051	38	42	γ	γ	X
ejpam-5051	38	43	,	,	PUNCT
ejpam-5051	38	44	αβ	αβ	INTJ
ejpam-5051	38	45	)	)	PUNCT
ejpam-5051	38	46	∈	∈	PROPN
ejpam-5051	38	47	g(2	g(2	PROPN
ejpam-5051	38	48	)	)	PUNCT
ejpam-5051	38	49	and	and	CCONJ
ejpam-5051	38	50	the	the	DET
ejpam-5051	38	51	following	follow	VERB
ejpam-5051	38	52	equation	equation	NOUN
ejpam-5051	38	53	is	be	AUX
ejpam-5051	38	54	satisfied	satisfied	ADJ
ejpam-5051	38	55	:	:	PUNCT
ejpam-5051	38	56	(	(	PUNCT
ejpam-5051	38	57	γα)β	γα)β	PROPN
ejpam-5051	38	58	=	=	PUNCT
ejpam-5051	38	59	γ(αβ	γ(αβ	NUM
ejpam-5051	38	60	)	)	PUNCT
ejpam-5051	38	61	;	;	PUNCT
ejpam-5051	38	62	(	(	PUNCT
ejpam-5051	38	63	g2	g2	PROPN
ejpam-5051	38	64	)	)	PUNCT
ejpam-5051	38	65	for	for	ADP
ejpam-5051	38	66	all	all	DET
ejpam-5051	38	67	γ	γ	PROPN
ejpam-5051	38	68	∈	∈	PROPN
ejpam-5051	38	69	g	g	NOUN
ejpam-5051	38	70	,	,	PUNCT
ejpam-5051	38	71	(	(	PUNCT
ejpam-5051	38	72	γ−1	γ−1	ADJ
ejpam-5051	38	73	,	,	PUNCT
ejpam-5051	38	74	γ	γ	NOUN
ejpam-5051	38	75	)	)	PUNCT
ejpam-5051	38	76	∈	∈	PROPN
ejpam-5051	38	77	g(2	g(2	PROPN
ejpam-5051	38	78	)	)	PUNCT
ejpam-5051	38	79	;	;	PUNCT
ejpam-5051	38	80	(	(	PUNCT
ejpam-5051	38	81	g3	g3	NOUN
ejpam-5051	38	82	)	)	PUNCT
ejpam-5051	38	83	if	if	SCONJ
ejpam-5051	38	84	(	(	PUNCT
ejpam-5051	38	85	γ	γ	X
ejpam-5051	38	86	,	,	PUNCT
ejpam-5051	38	87	α	α	NOUN
ejpam-5051	38	88	)	)	PUNCT
ejpam-5051	38	89	∈	∈	PROPN
ejpam-5051	38	90	g(2	g(2	PROPN
ejpam-5051	38	91	)	)	PUNCT
ejpam-5051	38	92	,	,	PUNCT
ejpam-5051	38	93	then	then	ADV
ejpam-5051	38	94	(	(	PUNCT
ejpam-5051	38	95	γ−1γ)α	γ−1γ)α	NOUN
ejpam-5051	38	96	=	=	SYM
ejpam-5051	38	97	α	α	NOUN
ejpam-5051	38	98	and	and	CCONJ
ejpam-5051	38	99	γ(αα−1	γ(αα−1	NOUN
ejpam-5051	38	100	)	)	PUNCT
ejpam-5051	38	101	=	=	SYM
ejpam-5051	39	1	γ	γ	X
ejpam-5051	39	2	.	.	PUNCT
ejpam-5051	40	1	we	we	PRON
ejpam-5051	40	2	call	call	VERB
ejpam-5051	40	3	g(2	g(2	NOUN
ejpam-5051	40	4	)	)	PUNCT
ejpam-5051	40	5	as	as	ADP
ejpam-5051	40	6	the	the	DET
ejpam-5051	40	7	set	set	NOUN
ejpam-5051	40	8	of	of	ADP
ejpam-5051	40	9	all	all	DET
ejpam-5051	40	10	composable	composable	ADJ
ejpam-5051	40	11	pairs	pair	NOUN
ejpam-5051	40	12	.	.	PUNCT
ejpam-5051	41	1	we	we	PRON
ejpam-5051	41	2	write	write	VERB
ejpam-5051	41	3	g(3	g(3	PROPN
ejpam-5051	41	4	)	)	PUNCT
ejpam-5051	41	5	for	for	ADP
ejpam-5051	41	6	the	the	DET
ejpam-5051	41	7	set	set	NOUN
ejpam-5051	41	8	of	of	ADP
ejpam-5051	41	9	composable	composable	ADJ
ejpam-5051	41	10	triples	triple	NOUN
ejpam-5051	41	11	in	in	ADP
ejpam-5051	41	12	g	g	PROPN
ejpam-5051	41	13	,	,	PUNCT
ejpam-5051	41	14	that	that	ADV
ejpam-5051	41	15	is	is	ADV
ejpam-5051	41	16	,	,	PUNCT
ejpam-5051	41	17	g(3	g(3	PROPN
ejpam-5051	41	18	)	)	PUNCT
ejpam-5051	41	19	=	=	PRON
ejpam-5051	41	20	{	{	PUNCT
ejpam-5051	41	21	(	(	PUNCT
ejpam-5051	41	22	α	α	NOUN
ejpam-5051	41	23	,	,	PUNCT
ejpam-5051	41	24	β	β	X
ejpam-5051	41	25	,	,	PUNCT
ejpam-5051	41	26	γ	γ	NOUN
ejpam-5051	41	27	)	)	PUNCT
ejpam-5051	41	28	:	:	PUNCT
ejpam-5051	41	29	(	(	PUNCT
ejpam-5051	41	30	α	α	X
ejpam-5051	41	31	,	,	PUNCT
ejpam-5051	41	32	β	β	NOUN
ejpam-5051	41	33	)	)	PUNCT
ejpam-5051	41	34	,	,	PUNCT
ejpam-5051	41	35	(	(	PUNCT
ejpam-5051	41	36	β	β	X
ejpam-5051	41	37	,	,	PUNCT
ejpam-5051	41	38	γ	γ	NOUN
ejpam-5051	41	39	)	)	PUNCT
ejpam-5051	41	40	∈	∈	PROPN
ejpam-5051	41	41	g(2	g(2	PROPN
ejpam-5051	41	42	)	)	PUNCT
ejpam-5051	41	43	}	}	PUNCT
ejpam-5051	41	44	.	.	PUNCT
ejpam-5051	42	1	r.	r.	PROPN
ejpam-5051	42	2	s.	s.	PROPN
ejpam-5051	42	3	bongcawel	bongcawel	PROPN
ejpam-5051	43	1	et	et	PROPN
ejpam-5051	43	2	al	al	PROPN
ejpam-5051	43	3	.	.	PUNCT
ejpam-5051	43	4	/	/	SYM
ejpam-5051	43	5	eur	eur	PROPN
ejpam-5051	43	6	.	.	PUNCT
ejpam-5051	44	1	j.	j.	PROPN
ejpam-5051	44	2	pure	pure	PROPN
ejpam-5051	44	3	appl	appl	PROPN
ejpam-5051	44	4	.	.	PROPN
ejpam-5051	44	5	math	math	PROPN
ejpam-5051	44	6	,	,	PUNCT
ejpam-5051	44	7	17	17	NUM
ejpam-5051	44	8	(	(	PUNCT
ejpam-5051	44	9	1	1	NUM
ejpam-5051	44	10	)	)	PUNCT
ejpam-5051	44	11	(	(	PUNCT
ejpam-5051	44	12	2024	2024	NUM
ejpam-5051	44	13	)	)	PUNCT
ejpam-5051	44	14	,	,	PUNCT
ejpam-5051	44	15	519	519	NUM
ejpam-5051	44	16	-	-	SYM
ejpam-5051	44	17	545	545	NUM
ejpam-5051	44	18	521	521	NUM
ejpam-5051	44	19	lemma	lemma	PROPN
ejpam-5051	44	20	1	1	NUM
ejpam-5051	44	21	.	.	PUNCT
ejpam-5051	45	1	[	[	X
ejpam-5051	45	2	12	12	NUM
ejpam-5051	45	3	]	]	PUNCT
ejpam-5051	45	4	let	let	VERB
ejpam-5051	45	5	g	g	PRON
ejpam-5051	45	6	be	be	AUX
ejpam-5051	45	7	a	a	DET
ejpam-5051	45	8	groupoid	groupoid	NOUN
ejpam-5051	45	9	and	and	CCONJ
ejpam-5051	45	10	γ	γ	PROPN
ejpam-5051	45	11	,	,	PUNCT
ejpam-5051	45	12	β	β	X
ejpam-5051	45	13	∈	∈	PROPN
ejpam-5051	45	14	g.	g.	NOUN
ejpam-5051	46	1	we	we	PRON
ejpam-5051	46	2	say	say	VERB
ejpam-5051	46	3	that	that	SCONJ
ejpam-5051	46	4	(	(	PUNCT
ejpam-5051	46	5	γ	γ	X
ejpam-5051	46	6	,	,	PUNCT
ejpam-5051	46	7	β	β	NOUN
ejpam-5051	46	8	)	)	PUNCT
ejpam-5051	46	9	∈	∈	PROPN
ejpam-5051	46	10	g(2	g(2	PROPN
ejpam-5051	46	11	)	)	PUNCT
ejpam-5051	46	12	if	if	SCONJ
ejpam-5051	47	1	and	and	CCONJ
ejpam-5051	47	2	only	only	ADV
ejpam-5051	47	3	if	if	SCONJ
ejpam-5051	47	4	s(γ	s(γ	PROPN
ejpam-5051	47	5	)	)	PUNCT
ejpam-5051	47	6	=	=	SYM
ejpam-5051	47	7	r(β	r(β	PROPN
ejpam-5051	47	8	)	)	PUNCT
ejpam-5051	47	9	.	.	PUNCT
ejpam-5051	48	1	definition	definition	NOUN
ejpam-5051	48	2	2	2	NUM
ejpam-5051	48	3	.	.	PUNCT
ejpam-5051	49	1	[	[	X
ejpam-5051	49	2	12	12	NUM
ejpam-5051	49	3	]	]	PUNCT
ejpam-5051	49	4	define	define	VERB
ejpam-5051	49	5	the	the	DET
ejpam-5051	49	6	functions	function	NOUN
ejpam-5051	49	7	s	s	PART
ejpam-5051	49	8	and	and	CCONJ
ejpam-5051	49	9	r	r	NOUN
ejpam-5051	49	10	from	from	ADP
ejpam-5051	49	11	g	g	NOUN
ejpam-5051	49	12	to	to	ADP
ejpam-5051	49	13	itself	itself	PRON
ejpam-5051	49	14	by	by	ADP
ejpam-5051	49	15	s(α	s(α	NOUN
ejpam-5051	49	16	)	)	PUNCT
ejpam-5051	50	1	=	=	NOUN
ejpam-5051	50	2	α−1α	α−1α	NOUN
ejpam-5051	50	3	called	call	VERB
ejpam-5051	50	4	the	the	DET
ejpam-5051	50	5	source	source	NOUN
ejpam-5051	50	6	of	of	ADP
ejpam-5051	50	7	α	α	PROPN
ejpam-5051	50	8	∈	∈	PROPN
ejpam-5051	50	9	g	g	PROPN
ejpam-5051	50	10	and	and	CCONJ
ejpam-5051	50	11	r(α	r(α	PROPN
ejpam-5051	50	12	)	)	PUNCT
ejpam-5051	50	13	=	=	SYM
ejpam-5051	51	1	αα−1	αα−1	NOUN
ejpam-5051	51	2	called	call	VERB
ejpam-5051	51	3	the	the	DET
ejpam-5051	51	4	range	range	NOUN
ejpam-5051	51	5	of	of	ADP
ejpam-5051	51	6	α	α	PROPN
ejpam-5051	51	7	∈	∈	PROPN
ejpam-5051	51	8	g	g	NOUN
ejpam-5051	51	9	,	,	PUNCT
ejpam-5051	51	10	respectively	respectively	ADV
ejpam-5051	51	11	.	.	PUNCT
ejpam-5051	52	1	the	the	DET
ejpam-5051	52	2	common	common	ADJ
ejpam-5051	52	3	image	image	NOUN
ejpam-5051	52	4	of	of	ADP
ejpam-5051	52	5	r	r	NOUN
ejpam-5051	52	6	and	and	CCONJ
ejpam-5051	52	7	s	s	NOUN
ejpam-5051	52	8	is	be	AUX
ejpam-5051	52	9	the	the	DET
ejpam-5051	52	10	unit	unit	NOUN
ejpam-5051	52	11	space	space	NOUN
ejpam-5051	52	12	of	of	ADP
ejpam-5051	52	13	g	g	NOUN
ejpam-5051	52	14	and	and	CCONJ
ejpam-5051	52	15	is	be	AUX
ejpam-5051	52	16	denoted	denote	VERB
ejpam-5051	52	17	by	by	ADP
ejpam-5051	52	18	g(0	g(0	NOUN
ejpam-5051	52	19	)	)	PUNCT
ejpam-5051	52	20	,	,	PUNCT
ejpam-5051	52	21	that	that	ADV
ejpam-5051	52	22	is	is	ADV
ejpam-5051	52	23	,	,	PUNCT
ejpam-5051	52	24	g(0	g(0	PROPN
ejpam-5051	52	25	)	)	PUNCT
ejpam-5051	52	26	:	:	PUNCT
ejpam-5051	52	27	=	=	SYM
ejpam-5051	52	28	s(g	s(g	PROPN
ejpam-5051	52	29	)	)	PUNCT
ejpam-5051	52	30	=	=	PUNCT
ejpam-5051	52	31	r(g	r(g	NUM
ejpam-5051	52	32	)	)	PUNCT
ejpam-5051	52	33	.	.	PUNCT
ejpam-5051	53	1	example	example	NOUN
ejpam-5051	54	1	1	1	NUM
ejpam-5051	54	2	.	.	PUNCT
ejpam-5051	55	1	[	[	X
ejpam-5051	55	2	12	12	NUM
ejpam-5051	55	3	]	]	PUNCT
ejpam-5051	55	4	(	(	PUNCT
ejpam-5051	55	5	i	i	NOUN
ejpam-5051	55	6	)	)	PUNCT
ejpam-5051	55	7	let	let	VERB
ejpam-5051	55	8	g	g	NOUN
ejpam-5051	55	9	be	be	AUX
ejpam-5051	55	10	a	a	DET
ejpam-5051	55	11	group	group	NOUN
ejpam-5051	55	12	with	with	ADP
ejpam-5051	55	13	identity	identity	NOUN
ejpam-5051	55	14	e.	e.	PROPN
ejpam-5051	55	15	then	then	ADV
ejpam-5051	55	16	g	g	PROPN
ejpam-5051	55	17	is	be	AUX
ejpam-5051	55	18	a	a	DET
ejpam-5051	55	19	groupoid	groupoid	NOUN
ejpam-5051	55	20	with	with	ADP
ejpam-5051	55	21	g(2	g(2	PROPN
ejpam-5051	55	22	)	)	PUNCT
ejpam-5051	55	23	=	=	SYM
ejpam-5051	55	24	g×g	g×g	PROPN
ejpam-5051	55	25	;	;	PUNCT
ejpam-5051	55	26	s(γ	s(γ	PROPN
ejpam-5051	55	27	)	)	PUNCT
ejpam-5051	56	1	=	=	PUNCT
ejpam-5051	57	1	γ−1γ	γ−1γ	NOUN
ejpam-5051	57	2	=	=	SYM
ejpam-5051	57	3	e	e	NOUN
ejpam-5051	57	4	;	;	PUNCT
ejpam-5051	57	5	r(γ	r(γ	VERB
ejpam-5051	57	6	)	)	PUNCT
ejpam-5051	57	7	=	=	PUNCT
ejpam-5051	57	8	γγ−1	γγ−1	NOUN
ejpam-5051	57	9	=	=	PUNCT
ejpam-5051	57	10	e	e	NOUN
ejpam-5051	57	11	;	;	PUNCT
ejpam-5051	57	12	and	and	CCONJ
ejpam-5051	57	13	g(0	g(0	NOUN
ejpam-5051	57	14	)	)	PUNCT
ejpam-5051	57	15	=	=	PRON
ejpam-5051	57	16	{	{	PUNCT
ejpam-5051	57	17	e	e	NOUN
ejpam-5051	57	18	}	}	PUNCT
ejpam-5051	57	19	.	.	PUNCT
ejpam-5051	58	1	(	(	PUNCT
ejpam-5051	58	2	ii	ii	NOUN
ejpam-5051	58	3	)	)	PUNCT
ejpam-5051	58	4	if	if	SCONJ
ejpam-5051	58	5	{	{	PUNCT
ejpam-5051	58	6	gi|i	gi|i	NOUN
ejpam-5051	58	7	∈	∈	PROPN
ejpam-5051	58	8	i	i	PRON
ejpam-5051	58	9	}	}	PUNCT
ejpam-5051	58	10	is	be	AUX
ejpam-5051	58	11	a	a	DET
ejpam-5051	58	12	family	family	NOUN
ejpam-5051	58	13	of	of	ADP
ejpam-5051	58	14	groups	group	NOUN
ejpam-5051	58	15	with	with	ADP
ejpam-5051	58	16	identities	identity	NOUN
ejpam-5051	58	17	{	{	PUNCT
ejpam-5051	58	18	ϵ1|i	ϵ1|i	PROPN
ejpam-5051	58	19	∈	∈	PROPN
ejpam-5051	59	1	i	i	X
ejpam-5051	59	2	}	}	PUNCT
ejpam-5051	59	3	,	,	PUNCT
ejpam-5051	59	4	then	then	ADV
ejpam-5051	59	5	the	the	DET
ejpam-5051	59	6	disjoint	disjoint	NOUN
ejpam-5051	59	7	union⋃	union⋃	NOUN
ejpam-5051	59	8	i∈i	i∈i	ADJ
ejpam-5051	59	9	gi	gi	INTJ
ejpam-5051	59	10	has	have	VERB
ejpam-5051	59	11	a	a	DET
ejpam-5051	59	12	groupoid	groupoid	NOUN
ejpam-5051	59	13	structure	structure	NOUN
ejpam-5051	59	14	with	with	ADP
ejpam-5051	59	15	d(g	d(g	PROPN
ejpam-5051	59	16	)	)	PUNCT
ejpam-5051	59	17	=	=	SYM
ejpam-5051	59	18	c(g	c(g	PROPN
ejpam-5051	59	19	)	)	PUNCT
ejpam-5051	60	1	=	=	SYM
ejpam-5051	60	2	ϵi	ϵi	NOUN
ejpam-5051	60	3	for	for	ADP
ejpam-5051	60	4	every	every	DET
ejpam-5051	60	5	g	g	PROPN
ejpam-5051	60	6	∈	∈	PROPN
ejpam-5051	60	7	gi	gi	NOUN
ejpam-5051	60	8	.	.	PUNCT
ejpam-5051	61	1	the	the	DET
ejpam-5051	61	2	composition	composition	NOUN
ejpam-5051	61	3	,	,	PUNCT
ejpam-5051	61	4	defined	define	VERB
ejpam-5051	61	5	only	only	ADV
ejpam-5051	61	6	for	for	ADP
ejpam-5051	61	7	pairs	pair	NOUN
ejpam-5051	61	8	(	(	PUNCT
ejpam-5051	61	9	g	g	NOUN
ejpam-5051	61	10	,	,	PUNCT
ejpam-5051	61	11	h	h	NOUN
ejpam-5051	61	12	)	)	PUNCT
ejpam-5051	61	13	∈	∈	PROPN
ejpam-5051	61	14	⋃	⋃	NOUN
ejpam-5051	61	15	i∈i	i∈i	ADJ
ejpam-5051	61	16	gi	gi	NOUN
ejpam-5051	61	17	×gi	×gi	PROPN
ejpam-5051	61	18	,	,	PUNCT
ejpam-5051	61	19	is	be	AUX
ejpam-5051	61	20	just	just	ADV
ejpam-5051	61	21	the	the	DET
ejpam-5051	61	22	relevant	relevant	ADJ
ejpam-5051	61	23	group	group	NOUN
ejpam-5051	61	24	law	law	NOUN
ejpam-5051	61	25	.	.	PUNCT
ejpam-5051	62	1	this	this	PRON
ejpam-5051	62	2	is	be	AUX
ejpam-5051	62	3	known	know	VERB
ejpam-5051	62	4	as	as	ADP
ejpam-5051	62	5	a	a	DET
ejpam-5051	62	6	group	group	NOUN
ejpam-5051	62	7	bundle	bundle	NOUN
ejpam-5051	62	8	.	.	PUNCT
ejpam-5051	63	1	lemma	lemma	PROPN
ejpam-5051	63	2	2	2	NUM
ejpam-5051	63	3	.	.	PUNCT
ejpam-5051	64	1	[	[	X
ejpam-5051	64	2	7	7	X
ejpam-5051	64	3	]	]	PUNCT
ejpam-5051	64	4	let	let	VERB
ejpam-5051	64	5	g	g	PRON
ejpam-5051	64	6	be	be	AUX
ejpam-5051	64	7	a	a	DET
ejpam-5051	64	8	groupoid	groupoid	NOUN
ejpam-5051	64	9	.	.	PUNCT
ejpam-5051	65	1	we	we	PRON
ejpam-5051	65	2	have	have	VERB
ejpam-5051	65	3	(	(	PUNCT
ejpam-5051	65	4	i	i	NOUN
ejpam-5051	65	5	)	)	PUNCT
ejpam-5051	65	6	(	(	PUNCT
ejpam-5051	65	7	α	α	X
ejpam-5051	65	8	,	,	PUNCT
ejpam-5051	65	9	γ	γ	NOUN
ejpam-5051	65	10	)	)	PUNCT
ejpam-5051	65	11	,	,	PUNCT
ejpam-5051	65	12	(	(	PUNCT
ejpam-5051	65	13	γ	γ	X
ejpam-5051	65	14	,	,	PUNCT
ejpam-5051	65	15	β	β	NOUN
ejpam-5051	65	16	)	)	PUNCT
ejpam-5051	65	17	∈	∈	PROPN
ejpam-5051	65	18	g(2	g(2	PROPN
ejpam-5051	65	19	)	)	PUNCT
ejpam-5051	65	20	and	and	CCONJ
ejpam-5051	65	21	αγ	αγ	X
ejpam-5051	66	1	=	=	NOUN
ejpam-5051	66	2	βγ	βγ	PRON
ejpam-5051	66	3	imply	imply	VERB
ejpam-5051	66	4	α	α	X
ejpam-5051	66	5	=	=	PUNCT
ejpam-5051	66	6	β	β	X
ejpam-5051	66	7	.	.	PUNCT
ejpam-5051	67	1	similarly	similarly	ADV
ejpam-5051	67	2	,	,	PUNCT
ejpam-5051	67	3	if	if	SCONJ
ejpam-5051	67	4	(	(	PUNCT
ejpam-5051	67	5	γ	γ	X
ejpam-5051	67	6	,	,	PUNCT
ejpam-5051	67	7	α	α	NOUN
ejpam-5051	67	8	)	)	PUNCT
ejpam-5051	67	9	,	,	PUNCT
ejpam-5051	67	10	(	(	PUNCT
ejpam-5051	67	11	γ	γ	X
ejpam-5051	67	12	,	,	PUNCT
ejpam-5051	67	13	β	β	NOUN
ejpam-5051	67	14	)	)	PUNCT
ejpam-5051	67	15	∈	∈	PROPN
ejpam-5051	67	16	g(2	g(2	PROPN
ejpam-5051	67	17	)	)	PUNCT
ejpam-5051	67	18	and	and	CCONJ
ejpam-5051	67	19	γα	γα	ADP
ejpam-5051	67	20	=	=	NOUN
ejpam-5051	67	21	γβ	γβ	PROPN
ejpam-5051	67	22	,	,	PUNCT
ejpam-5051	67	23	then	then	ADV
ejpam-5051	67	24	α	α	PROPN
ejpam-5051	67	25	=	=	SYM
ejpam-5051	67	26	β	β	X
ejpam-5051	67	27	.	.	PUNCT
ejpam-5051	67	28	(	(	PUNCT
ejpam-5051	67	29	ii	ii	NOUN
ejpam-5051	67	30	)	)	PUNCT
ejpam-5051	67	31	r(αβ	r(αβ	NOUN
ejpam-5051	67	32	)	)	PUNCT
ejpam-5051	67	33	=	=	SYM
ejpam-5051	67	34	r(β	r(β	PROPN
ejpam-5051	67	35	)	)	PUNCT
ejpam-5051	67	36	and	and	CCONJ
ejpam-5051	67	37	s(αβ	s(αβ	NOUN
ejpam-5051	67	38	)	)	PUNCT
ejpam-5051	67	39	=	=	SYM
ejpam-5051	67	40	s(β	s(β	PROPN
ejpam-5051	67	41	)	)	PUNCT
ejpam-5051	67	42	for	for	ADP
ejpam-5051	67	43	all	all	DET
ejpam-5051	67	44	α	α	NOUN
ejpam-5051	67	45	,	,	PUNCT
ejpam-5051	67	46	β	β	PROPN
ejpam-5051	67	47	∈	∈	PROPN
ejpam-5051	67	48	g(2	g(2	PROPN
ejpam-5051	67	49	)	)	PUNCT
ejpam-5051	67	50	.	.	PUNCT
ejpam-5051	68	1	(	(	PUNCT
ejpam-5051	68	2	iii	iii	X
ejpam-5051	68	3	)	)	PUNCT
ejpam-5051	68	4	(	(	PUNCT
ejpam-5051	68	5	αβ)−1	αβ)−1	X
ejpam-5051	68	6	=	=	SYM
ejpam-5051	68	7	β−1α−1	β−1α−1	PROPN
ejpam-5051	68	8	for	for	ADP
ejpam-5051	68	9	all	all	DET
ejpam-5051	68	10	α	α	NOUN
ejpam-5051	68	11	,	,	PUNCT
ejpam-5051	68	12	β	β	PROPN
ejpam-5051	68	13	∈	∈	PROPN
ejpam-5051	68	14	g(2	g(2	PROPN
ejpam-5051	68	15	)	)	PUNCT
ejpam-5051	68	16	.	.	PUNCT
ejpam-5051	69	1	(	(	PUNCT
ejpam-5051	69	2	iv	iv	X
ejpam-5051	69	3	)	)	PUNCT
ejpam-5051	69	4	r(x	r(x	PROPN
ejpam-5051	69	5	)	)	PUNCT
ejpam-5051	70	1	=	=	SYM
ejpam-5051	70	2	x	x	SYM
ejpam-5051	70	3	=	=	SYM
ejpam-5051	70	4	s(x	s(x	PROPN
ejpam-5051	70	5	)	)	PUNCT
ejpam-5051	70	6	for	for	ADP
ejpam-5051	70	7	all	all	DET
ejpam-5051	70	8	x	x	SYM
ejpam-5051	70	9	∈	∈	PROPN
ejpam-5051	70	10	g(0	g(0	PROPN
ejpam-5051	70	11	)	)	PUNCT
ejpam-5051	70	12	.	.	PUNCT
ejpam-5051	71	1	if	if	SCONJ
ejpam-5051	71	2	γ	γ	X
ejpam-5051	71	3	∈	∈	PROPN
ejpam-5051	71	4	g	g	NOUN
ejpam-5051	71	5	,	,	PUNCT
ejpam-5051	71	6	then	then	ADV
ejpam-5051	71	7	(	(	PUNCT
ejpam-5051	71	8	r(γ	r(γ	NOUN
ejpam-5051	71	9	)	)	PUNCT
ejpam-5051	71	10	,	,	PUNCT
ejpam-5051	71	11	γ	γ	X
ejpam-5051	71	12	)	)	PUNCT
ejpam-5051	71	13	and	and	CCONJ
ejpam-5051	71	14	(	(	PUNCT
ejpam-5051	71	15	γ	γ	X
ejpam-5051	71	16	,	,	PUNCT
ejpam-5051	71	17	s(γ	s(γ	PROPN
ejpam-5051	71	18	)	)	PUNCT
ejpam-5051	71	19	)	)	PUNCT
ejpam-5051	71	20	belong	belong	VERB
ejpam-5051	71	21	to	to	ADP
ejpam-5051	71	22	g(2	g(2	PROPN
ejpam-5051	71	23	)	)	PUNCT
ejpam-5051	71	24	,	,	PUNCT
ejpam-5051	71	25	and	and	CCONJ
ejpam-5051	71	26	r(γ)γ	r(γ)γ	VERB
ejpam-5051	71	27	=	=	PUNCT
ejpam-5051	71	28	γ	γ	X
ejpam-5051	71	29	=	=	PUNCT
ejpam-5051	71	30	γs(γ	γs(γ	NUM
ejpam-5051	71	31	)	)	PUNCT
ejpam-5051	71	32	.	.	PUNCT
ejpam-5051	72	1	definition	definition	NOUN
ejpam-5051	72	2	3	3	NUM
ejpam-5051	72	3	.	.	PUNCT
ejpam-5051	73	1	[	[	X
ejpam-5051	73	2	12	12	NUM
ejpam-5051	73	3	]	]	PUNCT
ejpam-5051	73	4	let	let	VERB
ejpam-5051	73	5	xg	xg	PROPN
ejpam-5051	73	6	=	=	PROPN
ejpam-5051	73	7	r−1(x	r−1(x	PROPN
ejpam-5051	73	8	)	)	PUNCT
ejpam-5051	73	9	,	,	PUNCT
ejpam-5051	73	10	gx	gx	PROPN
ejpam-5051	73	11	=	=	PROPN
ejpam-5051	73	12	s−1(x	s−1(x	PROPN
ejpam-5051	73	13	)	)	PUNCT
ejpam-5051	73	14	,	,	PUNCT
ejpam-5051	73	15	and	and	CCONJ
ejpam-5051	73	16	xgy	xgy	PROPN
ejpam-5051	73	17	=	=	PROPN
ejpam-5051	73	18	xg	xg	PROPN
ejpam-5051	73	19	∩gy	∩gy	PROPN
ejpam-5051	73	20	.	.	PUNCT
ejpam-5051	74	1	the	the	DET
ejpam-5051	74	2	isotropy	isotropy	NOUN
ejpam-5051	74	3	of	of	ADP
ejpam-5051	74	4	a	a	DET
ejpam-5051	74	5	groupoid	groupoid	PROPN
ejpam-5051	74	6	g	g	PROPN
ejpam-5051	74	7	is	be	AUX
ejpam-5051	74	8	the	the	DET
ejpam-5051	74	9	set	set	NOUN
ejpam-5051	74	10	iso(g	iso(g	NOUN
ejpam-5051	74	11	)	)	PUNCT
ejpam-5051	74	12	:	:	PUNCT
ejpam-5051	74	13	=	=	SYM
ejpam-5051	74	14	{	{	PUNCT
ejpam-5051	74	15	γ	γ	X
ejpam-5051	74	16	∈	∈	PROPN
ejpam-5051	74	17	g	g	NOUN
ejpam-5051	74	18	:	:	PUNCT
ejpam-5051	74	19	r(γ	r(γ	NOUN
ejpam-5051	74	20	)	)	PUNCT
ejpam-5051	74	21	=	=	SYM
ejpam-5051	74	22	s(γ	s(γ	PROPN
ejpam-5051	74	23	)	)	PUNCT
ejpam-5051	74	24	}	}	PUNCT
ejpam-5051	75	1	=	=	SYM
ejpam-5051	75	2	⋃	⋃	NOUN
ejpam-5051	75	3	x∈g(0	x∈g(0	NOUN
ejpam-5051	75	4	)	)	PUNCT
ejpam-5051	75	5	xgx	xgx	PROPN
ejpam-5051	75	6	.	.	PUNCT
ejpam-5051	76	1	we	we	PRON
ejpam-5051	76	2	say	say	VERB
ejpam-5051	76	3	that	that	SCONJ
ejpam-5051	76	4	g	g	PROPN
ejpam-5051	76	5	is	be	AUX
ejpam-5051	76	6	principal	principal	ADJ
ejpam-5051	76	7	if	if	SCONJ
ejpam-5051	76	8	iso(g	iso(g	VERB
ejpam-5051	76	9	)	)	PUNCT
ejpam-5051	76	10	=	=	SYM
ejpam-5051	76	11	g(0	g(0	PROPN
ejpam-5051	76	12	)	)	PUNCT
ejpam-5051	76	13	.	.	PUNCT
ejpam-5051	77	1	remark	remark	PROPN
ejpam-5051	77	2	1	1	NUM
ejpam-5051	77	3	.	.	PUNCT
ejpam-5051	78	1	[	[	X
ejpam-5051	78	2	12	12	NUM
ejpam-5051	78	3	]	]	PUNCT
ejpam-5051	78	4	the	the	DET
ejpam-5051	78	5	isotropy	isotropy	NOUN
ejpam-5051	78	6	of	of	ADP
ejpam-5051	78	7	any	any	DET
ejpam-5051	78	8	groupoid	groupoid	NOUN
ejpam-5051	78	9	is	be	AUX
ejpam-5051	78	10	a	a	DET
ejpam-5051	78	11	group	group	NOUN
ejpam-5051	78	12	bundle	bundle	NOUN
ejpam-5051	78	13	.	.	PUNCT
ejpam-5051	79	1	lemma	lemma	PROPN
ejpam-5051	79	2	3	3	X
ejpam-5051	79	3	.	.	PUNCT
ejpam-5051	80	1	[	[	X
ejpam-5051	80	2	7	7	X
ejpam-5051	80	3	]	]	X
ejpam-5051	80	4	a	a	DET
ejpam-5051	80	5	groupoid	groupoid	PROPN
ejpam-5051	80	6	g	g	PROPN
ejpam-5051	80	7	is	be	AUX
ejpam-5051	80	8	principal	principal	ADJ
ejpam-5051	80	9	if	if	SCONJ
ejpam-5051	80	10	γ	γ	X
ejpam-5051	80	11	7→	7→	PROPN
ejpam-5051	80	12	(	(	PUNCT
ejpam-5051	80	13	r(γ	r(γ	NOUN
ejpam-5051	80	14	)	)	PUNCT
ejpam-5051	80	15	,	,	PUNCT
ejpam-5051	80	16	s(γ	s(γ	PROPN
ejpam-5051	80	17	)	)	PUNCT
ejpam-5051	80	18	)	)	PUNCT
ejpam-5051	80	19	is	be	AUX
ejpam-5051	80	20	injective	injective	ADJ
ejpam-5051	80	21	.	.	PUNCT
ejpam-5051	81	1	definition	definition	NOUN
ejpam-5051	81	2	4	4	NUM
ejpam-5051	81	3	.	.	PUNCT
ejpam-5051	82	1	[	[	X
ejpam-5051	82	2	12	12	NUM
ejpam-5051	82	3	]	]	PUNCT
ejpam-5051	82	4	a	a	DET
ejpam-5051	82	5	groupoid	groupoid	PROPN
ejpam-5051	82	6	g	g	PROPN
ejpam-5051	82	7	is	be	AUX
ejpam-5051	82	8	effective	effective	ADJ
ejpam-5051	82	9	if	if	SCONJ
ejpam-5051	82	10	the	the	DET
ejpam-5051	82	11	interior	interior	NOUN
ejpam-5051	82	12	of	of	ADP
ejpam-5051	82	13	the	the	DET
ejpam-5051	82	14	isotropy	isotropy	ADJ
ejpam-5051	82	15	group	group	NOUN
ejpam-5051	82	16	of	of	ADP
ejpam-5051	82	17	g	g	PROPN
ejpam-5051	82	18	is	be	AUX
ejpam-5051	82	19	equal	equal	ADJ
ejpam-5051	82	20	to	to	ADP
ejpam-5051	82	21	its	its	PRON
ejpam-5051	82	22	unit	unit	NOUN
ejpam-5051	82	23	space	space	NOUN
ejpam-5051	82	24	.	.	PUNCT
ejpam-5051	83	1	definition	definition	NOUN
ejpam-5051	83	2	5	5	NUM
ejpam-5051	83	3	.	.	PUNCT
ejpam-5051	84	1	[	[	X
ejpam-5051	84	2	12	12	NUM
ejpam-5051	84	3	]	]	PUNCT
ejpam-5051	84	4	given	give	VERB
ejpam-5051	84	5	groupoid	groupoid	PROPN
ejpam-5051	84	6	g	g	PROPN
ejpam-5051	84	7	and	and	CCONJ
ejpam-5051	84	8	h	h	NOUN
ejpam-5051	84	9	,	,	PUNCT
ejpam-5051	84	10	we	we	PRON
ejpam-5051	84	11	call	call	VERB
ejpam-5051	84	12	a	a	DET
ejpam-5051	84	13	map	map	NOUN
ejpam-5051	84	14	ϕ	ϕ	NOUN
ejpam-5051	84	15	:	:	PUNCT
ejpam-5051	84	16	g	g	PROPN
ejpam-5051	84	17	→	→	SYM
ejpam-5051	84	18	h	h	NOUN
ejpam-5051	84	19	a	a	DET
ejpam-5051	84	20	groupoid	groupoid	PROPN
ejpam-5051	84	21	homomorphism	homomorphism	PROPN
ejpam-5051	84	22	if	if	SCONJ
ejpam-5051	84	23	(	(	PUNCT
ejpam-5051	84	24	ϕ×	ϕ×	PROPN
ejpam-5051	84	25	ϕ)(g(2	ϕ)(g(2	NOUN
ejpam-5051	84	26	)	)	PUNCT
ejpam-5051	84	27	)	)	PUNCT
ejpam-5051	85	1	⊆	⊆	NUM
ejpam-5051	85	2	h(2	h(2	NOUN
ejpam-5051	85	3	)	)	PUNCT
ejpam-5051	85	4	and	and	CCONJ
ejpam-5051	85	5	ϕ(α)ϕ(β	ϕ(α)ϕ(β	NOUN
ejpam-5051	85	6	)	)	PUNCT
ejpam-5051	85	7	=	=	SYM
ejpam-5051	85	8	ϕ(αβ	ϕ(αβ	PROPN
ejpam-5051	85	9	)	)	PUNCT
ejpam-5051	85	10	for	for	ADP
ejpam-5051	85	11	all	all	PRON
ejpam-5051	85	12	(	(	PUNCT
ejpam-5051	85	13	α	α	NOUN
ejpam-5051	85	14	,	,	PUNCT
ejpam-5051	85	15	β	β	NOUN
ejpam-5051	85	16	)	)	PUNCT
ejpam-5051	85	17	∈	∈	PROPN
ejpam-5051	85	18	g(2	g(2	PROPN
ejpam-5051	85	19	)	)	PUNCT
ejpam-5051	85	20	.	.	PUNCT
ejpam-5051	86	1	the	the	DET
ejpam-5051	86	2	following	follow	VERB
ejpam-5051	86	3	concepts	concept	NOUN
ejpam-5051	86	4	is	be	AUX
ejpam-5051	86	5	taken	take	VERB
ejpam-5051	86	6	from	from	ADP
ejpam-5051	86	7	[	[	X
ejpam-5051	86	8	12	12	NUM
ejpam-5051	86	9	]	]	PUNCT
ejpam-5051	86	10	.	.	PUNCT
ejpam-5051	87	1	a	a	DET
ejpam-5051	87	2	topological	topological	ADJ
ejpam-5051	87	3	groupoid	groupoid	NOUN
ejpam-5051	87	4	consists	consist	VERB
ejpam-5051	87	5	of	of	ADP
ejpam-5051	87	6	a	a	DET
ejpam-5051	87	7	groupoid	groupoid	PROPN
ejpam-5051	87	8	g	g	PROPN
ejpam-5051	87	9	and	and	CCONJ
ejpam-5051	87	10	a	a	DET
ejpam-5051	87	11	topology	topology	NOUN
ejpam-5051	87	12	compatible	compatible	ADJ
ejpam-5051	87	13	with	with	ADP
ejpam-5051	87	14	the	the	DET
ejpam-5051	87	15	groupoid	groupoid	PROPN
ejpam-5051	87	16	structure	structure	NOUN
ejpam-5051	87	17	such	such	ADJ
ejpam-5051	87	18	that	that	SCONJ
ejpam-5051	87	19	the	the	DET
ejpam-5051	87	20	composition	composition	NOUN
ejpam-5051	87	21	and	and	CCONJ
ejpam-5051	87	22	involution	involution	NOUN
ejpam-5051	87	23	are	be	AUX
ejpam-5051	87	24	continuous	continuous	ADJ
ejpam-5051	87	25	and	and	CCONJ
ejpam-5051	87	26	g(2	g(2	PROPN
ejpam-5051	87	27	)	)	PUNCT
ejpam-5051	87	28	has	have	VERB
ejpam-5051	87	29	the	the	DET
ejpam-5051	87	30	induced	induced	ADJ
ejpam-5051	87	31	topology	topology	NOUN
ejpam-5051	87	32	from	from	ADP
ejpam-5051	87	33	the	the	DET
ejpam-5051	87	34	product	product	NOUN
ejpam-5051	87	35	topology	topology	NOUN
ejpam-5051	87	36	.	.	PUNCT
ejpam-5051	88	1	every	every	DET
ejpam-5051	88	2	groupoid	groupoid	PROPN
ejpam-5051	88	3	is	be	AUX
ejpam-5051	88	4	a	a	DET
ejpam-5051	88	5	topological	topological	ADJ
ejpam-5051	88	6	groupoid	groupoid	PROPN
ejpam-5051	88	7	r.	r.	PROPN
ejpam-5051	88	8	s.	s.	PROPN
ejpam-5051	88	9	bongcawel	bongcawel	PROPN
ejpam-5051	88	10	et	et	PROPN
ejpam-5051	88	11	al	al	PROPN
ejpam-5051	88	12	.	.	PUNCT
ejpam-5051	88	13	/	/	SYM
ejpam-5051	88	14	eur	eur	PROPN
ejpam-5051	88	15	.	.	PUNCT
ejpam-5051	89	1	j.	j.	PROPN
ejpam-5051	89	2	pure	pure	PROPN
ejpam-5051	89	3	appl	appl	PROPN
ejpam-5051	89	4	.	.	PROPN
ejpam-5051	89	5	math	math	PROPN
ejpam-5051	89	6	,	,	PUNCT
ejpam-5051	89	7	17	17	NUM
ejpam-5051	89	8	(	(	PUNCT
ejpam-5051	89	9	1	1	NUM
ejpam-5051	89	10	)	)	PUNCT
ejpam-5051	89	11	(	(	PUNCT
ejpam-5051	89	12	2024	2024	NUM
ejpam-5051	89	13	)	)	PUNCT
ejpam-5051	89	14	,	,	PUNCT
ejpam-5051	89	15	519	519	NUM
ejpam-5051	89	16	-	-	SYM
ejpam-5051	89	17	545	545	NUM
ejpam-5051	89	18	522	522	NUM
ejpam-5051	89	19	with	with	ADP
ejpam-5051	89	20	the	the	DET
ejpam-5051	89	21	discrete	discrete	ADJ
ejpam-5051	89	22	topology	topology	NOUN
ejpam-5051	89	23	.	.	PUNCT
ejpam-5051	90	1	an	an	DET
ejpam-5051	90	2	open	open	ADJ
ejpam-5051	90	3	set	set	NOUN
ejpam-5051	90	4	b	b	NOUN
ejpam-5051	90	5	⊆	⊆	NUM
ejpam-5051	90	6	g	g	NOUN
ejpam-5051	90	7	is	be	AUX
ejpam-5051	90	8	an	an	DET
ejpam-5051	90	9	open	open	ADJ
ejpam-5051	90	10	bisection	bisection	NOUN
ejpam-5051	90	11	if	if	SCONJ
ejpam-5051	90	12	r|b	r|b	PROPN
ejpam-5051	90	13	and	and	CCONJ
ejpam-5051	90	14	s|b	s|b	PRON
ejpam-5051	90	15	are	be	AUX
ejpam-5051	90	16	homeomorphisms	homeomorphism	NOUN
ejpam-5051	90	17	onto	onto	ADP
ejpam-5051	90	18	an	an	DET
ejpam-5051	90	19	open	open	ADJ
ejpam-5051	90	20	subset	subset	NOUN
ejpam-5051	90	21	of	of	ADP
ejpam-5051	90	22	g.	g.	PROPN
ejpam-5051	90	23	a	a	DET
ejpam-5051	90	24	topological	topological	ADJ
ejpam-5051	90	25	groupoid	groupoid	NOUN
ejpam-5051	90	26	is	be	AUX
ejpam-5051	90	27	étale	étale	ADJ
ejpam-5051	90	28	if	if	SCONJ
ejpam-5051	90	29	r	r	NOUN
ejpam-5051	90	30	(	(	PUNCT
ejpam-5051	90	31	or	or	CCONJ
ejpam-5051	90	32	equivalently	equivalently	ADV
ejpam-5051	90	33	s	s	PART
ejpam-5051	90	34	)	)	PUNCT
ejpam-5051	90	35	is	be	AUX
ejpam-5051	90	36	a	a	DET
ejpam-5051	90	37	local	local	ADJ
ejpam-5051	90	38	homeomorphism	homeomorphism	NOUN
ejpam-5051	90	39	.	.	PUNCT
ejpam-5051	91	1	an	an	DET
ejpam-5051	91	2	étale	étale	ADJ
ejpam-5051	91	3	groupoid	groupoid	NOUN
ejpam-5051	91	4	is	be	AUX
ejpam-5051	91	5	ample	ample	ADJ
ejpam-5051	91	6	if	if	SCONJ
ejpam-5051	91	7	the	the	DET
ejpam-5051	91	8	topology	topology	NOUN
ejpam-5051	91	9	of	of	ADP
ejpam-5051	91	10	g	g	PROPN
ejpam-5051	91	11	has	have	VERB
ejpam-5051	91	12	a	a	DET
ejpam-5051	91	13	basis	basis	NOUN
ejpam-5051	91	14	of	of	ADP
ejpam-5051	91	15	compact	compact	ADJ
ejpam-5051	91	16	open	open	ADJ
ejpam-5051	91	17	bisections	bisection	NOUN
ejpam-5051	91	18	.	.	PUNCT
ejpam-5051	92	1	discrete	discrete	ADJ
ejpam-5051	92	2	group	group	NOUN
ejpam-5051	92	3	,	,	PUNCT
ejpam-5051	92	4	discrete	discrete	ADJ
ejpam-5051	92	5	groupoids	groupoid	NOUN
ejpam-5051	92	6	,	,	PUNCT
ejpam-5051	92	7	and	and	CCONJ
ejpam-5051	92	8	discrete	discrete	ADJ
ejpam-5051	92	9	space	space	NOUN
ejpam-5051	92	10	are	be	AUX
ejpam-5051	92	11	some	some	DET
ejpam-5051	92	12	examples	example	NOUN
ejpam-5051	92	13	of	of	ADP
ejpam-5051	92	14	an	an	DET
ejpam-5051	92	15	ample	ample	ADJ
ejpam-5051	92	16	groupoid	groupoid	NOUN
ejpam-5051	92	17	with	with	ADP
ejpam-5051	92	18	the	the	DET
ejpam-5051	92	19	discrete	discrete	ADJ
ejpam-5051	92	20	topology	topology	NOUN
ejpam-5051	92	21	.	.	PUNCT
ejpam-5051	93	1	definition	definition	NOUN
ejpam-5051	93	2	6	6	NUM
ejpam-5051	93	3	.	.	PUNCT
ejpam-5051	94	1	[	[	X
ejpam-5051	94	2	12	12	NUM
ejpam-5051	94	3	]	]	PUNCT
ejpam-5051	94	4	given	give	VERB
ejpam-5051	94	5	a	a	DET
ejpam-5051	94	6	topological	topological	ADJ
ejpam-5051	94	7	space	space	NOUN
ejpam-5051	94	8	x	x	PUNCT
ejpam-5051	94	9	and	and	CCONJ
ejpam-5051	94	10	a	a	DET
ejpam-5051	94	11	topological	topological	ADJ
ejpam-5051	94	12	ring	ring	NOUN
ejpam-5051	94	13	r	r	NOUN
ejpam-5051	94	14	,	,	PUNCT
ejpam-5051	94	15	the	the	DET
ejpam-5051	94	16	open	open	ADJ
ejpam-5051	94	17	support	support	NOUN
ejpam-5051	94	18	of	of	ADP
ejpam-5051	94	19	a	a	DET
ejpam-5051	94	20	function	function	NOUN
ejpam-5051	94	21	f	f	NOUN
ejpam-5051	94	22	:	:	PUNCT
ejpam-5051	94	23	x	x	X
ejpam-5051	94	24	→	→	PUNCT
ejpam-5051	94	25	r	r	NOUN
ejpam-5051	94	26	is	be	AUX
ejpam-5051	94	27	the	the	DET
ejpam-5051	94	28	set	set	VERB
ejpam-5051	94	29	supp(f	supp(f	PROPN
ejpam-5051	94	30	)	)	PUNCT
ejpam-5051	94	31	:	:	PUNCT
ejpam-5051	94	32	=	=	SYM
ejpam-5051	94	33	{	{	PUNCT
ejpam-5051	94	34	x	x	PUNCT
ejpam-5051	94	35	∈	∈	PROPN
ejpam-5051	94	36	x	x	X
ejpam-5051	94	37	:	:	PUNCT
ejpam-5051	94	38	f(x	f(x	PROPN
ejpam-5051	94	39	)	)	PUNCT
ejpam-5051	94	40	̸=	̸=	PROPN
ejpam-5051	94	41	0	0	NUM
ejpam-5051	94	42	}	}	PUNCT
ejpam-5051	94	43	=	=	SYM
ejpam-5051	94	44	f−1(r\{0	f−1(r\{0	ADJ
ejpam-5051	94	45	}	}	PUNCT
ejpam-5051	94	46	)	)	PUNCT
ejpam-5051	94	47	.	.	PUNCT
ejpam-5051	95	1	we	we	PRON
ejpam-5051	95	2	say	say	VERB
ejpam-5051	95	3	that	that	SCONJ
ejpam-5051	95	4	f	f	PROPN
ejpam-5051	95	5	is	be	AUX
ejpam-5051	95	6	compactly	compactly	ADV
ejpam-5051	95	7	supported	support	VERB
ejpam-5051	95	8	if	if	SCONJ
ejpam-5051	95	9	supp(f	supp(f	PROPN
ejpam-5051	95	10	)	)	PUNCT
ejpam-5051	95	11	is	be	AUX
ejpam-5051	95	12	contained	contain	VERB
ejpam-5051	95	13	in	in	ADP
ejpam-5051	95	14	a	a	DET
ejpam-5051	95	15	compact	compact	ADJ
ejpam-5051	95	16	set	set	NOUN
ejpam-5051	95	17	.	.	PUNCT
ejpam-5051	96	1	we	we	PRON
ejpam-5051	96	2	use	use	VERB
ejpam-5051	96	3	the	the	DET
ejpam-5051	96	4	following	follow	VERB
ejpam-5051	96	5	notion	notion	NOUN
ejpam-5051	96	6	for	for	ADP
ejpam-5051	96	7	the	the	DET
ejpam-5051	96	8	characteristic	characteristic	ADJ
ejpam-5051	96	9	function	function	NOUN
ejpam-5051	96	10	of	of	ADP
ejpam-5051	96	11	a	a	DET
ejpam-5051	96	12	subset	subset	ADJ
ejpam-5051	96	13	u	u	NOUN
ejpam-5051	96	14	of	of	ADP
ejpam-5051	96	15	g	g	NOUN
ejpam-5051	96	16	:	:	PUNCT
ejpam-5051	96	17	1u	1u	NUM
ejpam-5051	96	18	:	:	PUNCT
ejpam-5051	96	19	g	g	NOUN
ejpam-5051	96	20	→	→	SYM
ejpam-5051	96	21	r	r	NOUN
ejpam-5051	96	22	defined	define	VERB
ejpam-5051	96	23	by	by	ADP
ejpam-5051	96	24	1u	1u	NUM
ejpam-5051	96	25	(	(	PUNCT
ejpam-5051	96	26	g	g	NOUN
ejpam-5051	96	27	)	)	PUNCT
ejpam-5051	96	28	=	=	PRON
ejpam-5051	96	29	{	{	PUNCT
ejpam-5051	96	30	1	1	NUM
ejpam-5051	96	31	if	if	SCONJ
ejpam-5051	96	32	g	g	PROPN
ejpam-5051	96	33	∈	∈	PROPN
ejpam-5051	96	34	u	u	NOUN
ejpam-5051	96	35	0	0	PUNCT
ejpam-5051	96	36	if	if	SCONJ
ejpam-5051	96	37	g	g	PROPN
ejpam-5051	96	38	/∈	/∈	PUNCT
ejpam-5051	96	39	u	u	NOUN
ejpam-5051	96	40	let	let	VERB
ejpam-5051	96	41	rg	rg	PRON
ejpam-5051	96	42	be	be	AUX
ejpam-5051	96	43	the	the	DET
ejpam-5051	96	44	set	set	NOUN
ejpam-5051	96	45	of	of	ADP
ejpam-5051	96	46	all	all	DET
ejpam-5051	96	47	functions	function	NOUN
ejpam-5051	97	1	f	f	NOUN
ejpam-5051	97	2	:	:	PUNCT
ejpam-5051	97	3	g	g	PROPN
ejpam-5051	97	4	→	→	SYM
ejpam-5051	97	5	r.	r.	PROPN
ejpam-5051	97	6	canonically	canonically	ADV
ejpam-5051	97	7	rg	rg	PROPN
ejpam-5051	97	8	has	have	VERB
ejpam-5051	97	9	the	the	DET
ejpam-5051	97	10	structure	structure	NOUN
ejpam-5051	97	11	of	of	ADP
ejpam-5051	97	12	an	an	DET
ejpam-5051	97	13	r	r	NOUN
ejpam-5051	97	14	-	-	PUNCT
ejpam-5051	97	15	module	module	NOUN
ejpam-5051	97	16	with	with	ADP
ejpam-5051	97	17	operations	operation	NOUN
ejpam-5051	97	18	defined	define	VERB
ejpam-5051	97	19	pointwise	pointwise	NOUN
ejpam-5051	97	20	.	.	PUNCT
ejpam-5051	98	1	definition	definition	NOUN
ejpam-5051	98	2	7	7	NUM
ejpam-5051	98	3	.	.	PUNCT
ejpam-5051	99	1	[	[	X
ejpam-5051	99	2	12	12	NUM
ejpam-5051	99	3	]	]	PUNCT
ejpam-5051	99	4	let	let	VERB
ejpam-5051	99	5	ar(g	ar(g	PUNCT
ejpam-5051	99	6	)	)	PUNCT
ejpam-5051	99	7	be	be	AUX
ejpam-5051	99	8	the	the	DET
ejpam-5051	99	9	r	r	NOUN
ejpam-5051	99	10	-	-	PUNCT
ejpam-5051	99	11	submodule	submodule	NOUN
ejpam-5051	99	12	of	of	ADP
ejpam-5051	99	13	rg	rg	PROPN
ejpam-5051	99	14	generated	generate	VERB
ejpam-5051	99	15	by	by	ADP
ejpam-5051	99	16	the	the	DET
ejpam-5051	99	17	set	set	NOUN
ejpam-5051	99	18	{	{	PUNCT
ejpam-5051	99	19	1u	1u	NUM
ejpam-5051	99	20	|u	|u	ADJ
ejpam-5051	99	21	is	be	AUX
ejpam-5051	99	22	a	a	DET
ejpam-5051	99	23	hausdorff	hausdorff	NOUN
ejpam-5051	99	24	compact	compact	ADJ
ejpam-5051	99	25	open	open	ADJ
ejpam-5051	99	26	subset	subset	NOUN
ejpam-5051	99	27	of	of	ADP
ejpam-5051	99	28	g	g	NOUN
ejpam-5051	99	29	}	}	PUNCT
ejpam-5051	99	30	,	,	PUNCT
ejpam-5051	99	31	that	that	ADV
ejpam-5051	99	32	is	is	ADV
ejpam-5051	99	33	,	,	PUNCT
ejpam-5051	99	34	ar(g	ar(g	ADJ
ejpam-5051	99	35	)	)	PUNCT
ejpam-5051	99	36	=	=	SYM
ejpam-5051	100	1	{	{	PUNCT
ejpam-5051	100	2	f	f	X
ejpam-5051	100	3	:	:	PUNCT
ejpam-5051	100	4	g	g	NOUN
ejpam-5051	100	5	→	→	SYM
ejpam-5051	100	6	r|f	r|f	NOUN
ejpam-5051	100	7	is	be	AUX
ejpam-5051	100	8	continuous	continuous	ADJ
ejpam-5051	100	9	and	and	CCONJ
ejpam-5051	100	10	supp(f	supp(f	NUM
ejpam-5051	100	11	)	)	PUNCT
ejpam-5051	100	12	is	be	AUX
ejpam-5051	100	13	compact	compact	ADJ
ejpam-5051	100	14	}	}	PUNCT
ejpam-5051	100	15	.	.	PUNCT
ejpam-5051	101	1	the	the	DET
ejpam-5051	101	2	convolution	convolution	NOUN
ejpam-5051	101	3	of	of	ADP
ejpam-5051	101	4	f	f	PROPN
ejpam-5051	101	5	,	,	PUNCT
ejpam-5051	101	6	g	g	PROPN
ejpam-5051	101	7	∈	∈	PROPN
ejpam-5051	101	8	ar(g	ar(g	PUNCT
ejpam-5051	101	9	)	)	PUNCT
ejpam-5051	101	10	is	be	AUX
ejpam-5051	101	11	defined	define	VERB
ejpam-5051	101	12	as	as	ADP
ejpam-5051	101	13	(	(	PUNCT
ejpam-5051	101	14	f	f	PROPN
ejpam-5051	101	15	∗	∗	PROPN
ejpam-5051	101	16	g)(x	g)(x	PROPN
ejpam-5051	101	17	)	)	PUNCT
ejpam-5051	101	18	:	:	PUNCT
ejpam-5051	102	1	=	=	PUNCT
ejpam-5051	102	2	∑	∑	PUNCT
ejpam-5051	102	3	y∈g	y∈g	NOUN
ejpam-5051	102	4	,	,	PUNCT
ejpam-5051	102	5	s(y)=s(x	s(y)=s(x	NOUN
ejpam-5051	102	6	)	)	PUNCT
ejpam-5051	102	7	f(xy−1)g(y	f(xy−1)g(y	PROPN
ejpam-5051	102	8	)	)	PUNCT
ejpam-5051	102	9	=	=	PUNCT
ejpam-5051	102	10	∑	∑	PUNCT
ejpam-5051	102	11	(	(	PUNCT
ejpam-5051	102	12	z	z	NOUN
ejpam-5051	102	13	,	,	PUNCT
ejpam-5051	102	14	y)∈g(2	y)∈g(2	NOUN
ejpam-5051	102	15	)	)	PUNCT
ejpam-5051	102	16	,	,	PUNCT
ejpam-5051	102	17	zy	zy	NOUN
ejpam-5051	102	18	=	=	NOUN
ejpam-5051	102	19	x	x	NOUN
ejpam-5051	102	20	f(z)g(y	f(z)g(y	NOUN
ejpam-5051	102	21	)	)	PUNCT
ejpam-5051	102	22	for	for	ADP
ejpam-5051	102	23	all	all	PRON
ejpam-5051	102	24	x	x	SYM
ejpam-5051	102	25	∈	∈	PROPN
ejpam-5051	102	26	g.	g.	NOUN
ejpam-5051	102	27	the	the	DET
ejpam-5051	102	28	r	r	NOUN
ejpam-5051	102	29	-	-	PUNCT
ejpam-5051	102	30	module	module	NOUN
ejpam-5051	102	31	ar(g	ar(g	NOUN
ejpam-5051	102	32	)	)	PUNCT
ejpam-5051	102	33	with	with	ADP
ejpam-5051	102	34	the	the	DET
ejpam-5051	102	35	convolution	convolution	NOUN
ejpam-5051	102	36	,	,	PUNCT
ejpam-5051	102	37	is	be	AUX
ejpam-5051	102	38	called	call	VERB
ejpam-5051	102	39	the	the	DET
ejpam-5051	102	40	steinberg	steinberg	PROPN
ejpam-5051	102	41	algebra	algebra	PROPN
ejpam-5051	102	42	of	of	ADP
ejpam-5051	102	43	g	g	PROPN
ejpam-5051	102	44	over	over	ADP
ejpam-5051	102	45	r.	r.	PROPN
ejpam-5051	102	46	the	the	DET
ejpam-5051	102	47	following	follow	VERB
ejpam-5051	102	48	example	example	NOUN
ejpam-5051	102	49	is	be	AUX
ejpam-5051	102	50	a	a	DET
ejpam-5051	102	51	steinberg	steinberg	PROPN
ejpam-5051	102	52	algebra	algebra	NOUN
ejpam-5051	102	53	of	of	ADP
ejpam-5051	102	54	r	r	NOUN
ejpam-5051	102	55	over	over	ADP
ejpam-5051	102	56	z.	z.	PROPN
ejpam-5051	102	57	example	example	NOUN
ejpam-5051	103	1	2	2	NUM
ejpam-5051	103	2	.	.	PUNCT
ejpam-5051	104	1	[	[	X
ejpam-5051	104	2	12	12	NUM
ejpam-5051	104	3	]	]	PUNCT
ejpam-5051	104	4	consider	consider	VERB
ejpam-5051	104	5	the	the	DET
ejpam-5051	104	6	set	set	NOUN
ejpam-5051	104	7	of	of	ADP
ejpam-5051	104	8	g	g	PROPN
ejpam-5051	104	9	=	=	SYM
ejpam-5051	104	10	r\{0	r\{0	PROPN
ejpam-5051	104	11	}	}	PUNCT
ejpam-5051	104	12	which	which	PRON
ejpam-5051	104	13	is	be	AUX
ejpam-5051	104	14	a	a	DET
ejpam-5051	104	15	group	group	NOUN
ejpam-5051	104	16	under	under	ADP
ejpam-5051	104	17	multiplication	multiplication	NOUN
ejpam-5051	104	18	.	.	PUNCT
ejpam-5051	105	1	by	by	ADP
ejpam-5051	105	2	example	example	NOUN
ejpam-5051	105	3	1	1	NUM
ejpam-5051	105	4	,	,	PUNCT
ejpam-5051	105	5	g	g	PROPN
ejpam-5051	105	6	is	be	AUX
ejpam-5051	105	7	a	a	DET
ejpam-5051	105	8	groupoid	groupoid	NOUN
ejpam-5051	105	9	with	with	ADP
ejpam-5051	105	10	the	the	DET
ejpam-5051	105	11	following	follow	VERB
ejpam-5051	105	12	structures	structure	NOUN
ejpam-5051	105	13	:	:	PUNCT
ejpam-5051	105	14	g(2	g(2	ADJ
ejpam-5051	105	15	)	)	PUNCT
ejpam-5051	105	16	=	=	SYM
ejpam-5051	105	17	g×g	g×g	PROPN
ejpam-5051	105	18	,	,	PUNCT
ejpam-5051	105	19	s(γ	s(γ	PROPN
ejpam-5051	105	20	)	)	PUNCT
ejpam-5051	105	21	=	=	PUNCT
ejpam-5051	106	1	γ−1γ	γ−1γ	NOUN
ejpam-5051	106	2	=	=	SYM
ejpam-5051	106	3	1	1	NUM
ejpam-5051	106	4	,	,	PUNCT
ejpam-5051	106	5	r(γ	r(γ	NOUN
ejpam-5051	106	6	)	)	PUNCT
ejpam-5051	107	1	=	=	VERB
ejpam-5051	107	2	γγ−1	γγ−1	NOUN
ejpam-5051	107	3	=	=	SYM
ejpam-5051	107	4	1	1	NUM
ejpam-5051	107	5	and	and	CCONJ
ejpam-5051	107	6	g(0	g(0	PROPN
ejpam-5051	107	7	)	)	PUNCT
ejpam-5051	107	8	=	=	PUNCT
ejpam-5051	107	9	{	{	PUNCT
ejpam-5051	107	10	1	1	NUM
ejpam-5051	107	11	}	}	PUNCT
ejpam-5051	107	12	.	.	PUNCT
ejpam-5051	108	1	we	we	PRON
ejpam-5051	108	2	note	note	VERB
ejpam-5051	108	3	that	that	SCONJ
ejpam-5051	108	4	g	g	PROPN
ejpam-5051	108	5	is	be	AUX
ejpam-5051	108	6	an	an	DET
ejpam-5051	108	7	ample	ample	ADJ
ejpam-5051	108	8	hausdorff	hausdorff	NOUN
ejpam-5051	108	9	groupoid	groupoid	NOUN
ejpam-5051	108	10	with	with	ADP
ejpam-5051	108	11	respect	respect	NOUN
ejpam-5051	108	12	to	to	ADP
ejpam-5051	108	13	the	the	DET
ejpam-5051	108	14	discrete	discrete	ADJ
ejpam-5051	108	15	topology	topology	NOUN
ejpam-5051	108	16	.	.	PUNCT
ejpam-5051	109	1	its	its	PRON
ejpam-5051	109	2	base	base	NOUN
ejpam-5051	109	3	is	be	AUX
ejpam-5051	109	4	composed	compose	VERB
ejpam-5051	109	5	of	of	ADP
ejpam-5051	109	6	singletons	singleton	NOUN
ejpam-5051	109	7	{	{	PUNCT
ejpam-5051	109	8	r	r	NOUN
ejpam-5051	109	9	}	}	PUNCT
ejpam-5051	109	10	where	where	SCONJ
ejpam-5051	109	11	r	r	NOUN
ejpam-5051	109	12	∈	∈	PROPN
ejpam-5051	109	13	g.	g.	NOUN
ejpam-5051	109	14	we	we	PRON
ejpam-5051	109	15	let	let	VERB
ejpam-5051	109	16	g	g	NOUN
ejpam-5051	109	17	as	as	ADP
ejpam-5051	109	18	our	our	PRON
ejpam-5051	109	19	unital	unital	ADJ
ejpam-5051	109	20	commutative	commutative	ADJ
ejpam-5051	109	21	ring	ring	NOUN
ejpam-5051	109	22	and	and	CCONJ
ejpam-5051	109	23	1{r	1{r	NUM
ejpam-5051	109	24	}	}	PUNCT
ejpam-5051	109	25	:	:	PUNCT
ejpam-5051	109	26	g	g	X
ejpam-5051	109	27	→	→	SYM
ejpam-5051	109	28	z	z	NOUN
ejpam-5051	109	29	is	be	AUX
ejpam-5051	109	30	the	the	DET
ejpam-5051	109	31	characteristic	characteristic	ADJ
ejpam-5051	109	32	function	function	NOUN
ejpam-5051	109	33	of	of	ADP
ejpam-5051	109	34	a	a	DET
ejpam-5051	109	35	subset	subset	NOUN
ejpam-5051	109	36	{	{	PUNCT
ejpam-5051	109	37	r	r	NOUN
ejpam-5051	109	38	}	}	PUNCT
ejpam-5051	109	39	of	of	ADP
ejpam-5051	109	40	g.	g.	PROPN
ejpam-5051	109	41	then	then	ADV
ejpam-5051	109	42	az(g	az(g	NUM
ejpam-5051	109	43	)	)	PUNCT
ejpam-5051	109	44	:	:	PUNCT
ejpam-5051	109	45	=	=	SYM
ejpam-5051	109	46	spanz{1{r	spanz{1{r	PROPN
ejpam-5051	109	47	}	}	PUNCT
ejpam-5051	109	48	:	:	PUNCT
ejpam-5051	109	49	{	{	PUNCT
ejpam-5051	109	50	r}is	r}is	PROPN
ejpam-5051	109	51	a	a	DET
ejpam-5051	109	52	compact	compact	ADJ
ejpam-5051	109	53	open	open	ADJ
ejpam-5051	109	54	bisection	bisection	NOUN
ejpam-5051	109	55	}	}	PUNCT
ejpam-5051	109	56	:	:	PUNCT
ejpam-5051	109	57	=	=	SYM
ejpam-5051	109	58	{	{	PUNCT
ejpam-5051	109	59	f	f	X
ejpam-5051	109	60	:	:	PUNCT
ejpam-5051	109	61	g	g	PROPN
ejpam-5051	109	62	→	→	SYM
ejpam-5051	109	63	z	z	NOUN
ejpam-5051	109	64	}	}	PUNCT
ejpam-5051	109	65	.	.	PUNCT
ejpam-5051	110	1	(	(	PUNCT
ejpam-5051	110	2	1	1	X
ejpam-5051	110	3	)	)	PUNCT
ejpam-5051	110	4	hence	hence	ADV
ejpam-5051	110	5	,	,	PUNCT
ejpam-5051	110	6	az(g	az(g	NUM
ejpam-5051	110	7	)	)	PUNCT
ejpam-5051	110	8	together	together	ADV
ejpam-5051	110	9	with	with	ADP
ejpam-5051	110	10	the	the	DET
ejpam-5051	110	11	convolution	convolution	NOUN
ejpam-5051	110	12	(	(	PUNCT
ejpam-5051	110	13	f	f	PROPN
ejpam-5051	110	14	∗	∗	PROPN
ejpam-5051	110	15	g)(x	g)(x	PROPN
ejpam-5051	110	16	)	)	PUNCT
ejpam-5051	110	17	:	:	PUNCT
ejpam-5051	110	18	=	=	PUNCT
ejpam-5051	110	19	∑	∑	PUNCT
ejpam-5051	110	20	y∈g	y∈g	NOUN
ejpam-5051	110	21	,	,	PUNCT
ejpam-5051	110	22	s(y)=s(x	s(y)=s(x	NOUN
ejpam-5051	110	23	)	)	PUNCT
ejpam-5051	110	24	f(xy−1)g(y	f(xy−1)g(y	PROPN
ejpam-5051	110	25	)	)	PUNCT
ejpam-5051	110	26	=	=	PUNCT
ejpam-5051	110	27	∑	∑	PUNCT
ejpam-5051	110	28	(	(	PUNCT
ejpam-5051	110	29	z	z	NOUN
ejpam-5051	110	30	,	,	PUNCT
ejpam-5051	110	31	y)∈g(2	y)∈g(2	NOUN
ejpam-5051	110	32	)	)	PUNCT
ejpam-5051	110	33	,	,	PUNCT
ejpam-5051	110	34	zy	zy	NOUN
ejpam-5051	110	35	=	=	NOUN
ejpam-5051	110	36	x	x	SYM
ejpam-5051	110	37	f(z)g(y	f(z)g(y	NOUN
ejpam-5051	110	38	)	)	PUNCT
ejpam-5051	110	39	is	be	AUX
ejpam-5051	110	40	a	a	DET
ejpam-5051	110	41	steinberg	steinberg	PROPN
ejpam-5051	110	42	algebra	algebra	NOUN
ejpam-5051	110	43	of	of	ADP
ejpam-5051	110	44	z	z	PROPN
ejpam-5051	110	45	over	over	ADP
ejpam-5051	110	46	g.	g.	PROPN
ejpam-5051	110	47	r.	r.	PROPN
ejpam-5051	110	48	s.	s.	PROPN
ejpam-5051	110	49	bongcawel	bongcawel	PROPN
ejpam-5051	110	50	et	et	PROPN
ejpam-5051	110	51	al	al	PROPN
ejpam-5051	110	52	.	.	PUNCT
ejpam-5051	110	53	/	/	SYM
ejpam-5051	110	54	eur	eur	PROPN
ejpam-5051	110	55	.	.	PUNCT
ejpam-5051	111	1	j.	j.	PROPN
ejpam-5051	111	2	pure	pure	PROPN
ejpam-5051	111	3	appl	appl	PROPN
ejpam-5051	111	4	.	.	PROPN
ejpam-5051	111	5	math	math	PROPN
ejpam-5051	111	6	,	,	PUNCT
ejpam-5051	111	7	17	17	NUM
ejpam-5051	111	8	(	(	PUNCT
ejpam-5051	111	9	1	1	NUM
ejpam-5051	111	10	)	)	PUNCT
ejpam-5051	111	11	(	(	PUNCT
ejpam-5051	111	12	2024	2024	NUM
ejpam-5051	111	13	)	)	PUNCT
ejpam-5051	111	14	,	,	PUNCT
ejpam-5051	111	15	519	519	NUM
ejpam-5051	111	16	-	-	SYM
ejpam-5051	111	17	545	545	NUM
ejpam-5051	111	18	523	523	NUM
ejpam-5051	111	19	the	the	DET
ejpam-5051	111	20	following	follow	VERB
ejpam-5051	111	21	discussions	discussion	NOUN
ejpam-5051	111	22	is	be	AUX
ejpam-5051	111	23	taken	take	VERB
ejpam-5051	111	24	from	from	ADP
ejpam-5051	111	25	[	[	X
ejpam-5051	111	26	1	1	X
ejpam-5051	111	27	]	]	PUNCT
ejpam-5051	111	28	where	where	SCONJ
ejpam-5051	111	29	the	the	DET
ejpam-5051	111	30	steinberg	steinberg	PROPN
ejpam-5051	111	31	algebra	algebra	PROPN
ejpam-5051	111	32	is	be	AUX
ejpam-5051	111	33	twisted	twist	VERB
ejpam-5051	111	34	via	via	ADP
ejpam-5051	111	35	the	the	DET
ejpam-5051	111	36	discrete	discrete	ADJ
ejpam-5051	111	37	twist	twist	NOUN
ejpam-5051	111	38	.	.	PUNCT
ejpam-5051	112	1	definition	definition	NOUN
ejpam-5051	112	2	8	8	NUM
ejpam-5051	112	3	.	.	PUNCT
ejpam-5051	113	1	let	let	VERB
ejpam-5051	113	2	g	g	PRON
ejpam-5051	113	3	be	be	AUX
ejpam-5051	113	4	a	a	DET
ejpam-5051	113	5	hausdorff	hausdorff	NOUN
ejpam-5051	113	6	étale	étale	NOUN
ejpam-5051	113	7	groupoid	groupoid	NOUN
ejpam-5051	113	8	,	,	PUNCT
ejpam-5051	113	9	and	and	CCONJ
ejpam-5051	113	10	r	r	NOUN
ejpam-5051	113	11	be	be	VERB
ejpam-5051	113	12	a	a	DET
ejpam-5051	113	13	commutative	commutative	ADJ
ejpam-5051	113	14	unital	unital	ADJ
ejpam-5051	113	15	ring	ring	NOUN
ejpam-5051	113	16	,	,	PUNCT
ejpam-5051	113	17	and	and	CCONJ
ejpam-5051	113	18	let	let	VERB
ejpam-5051	113	19	t	t	PROPN
ejpam-5051	113	20	<	<	X
ejpam-5051	113	21	r×.	r×.	ADP
ejpam-5051	113	22	a	a	DET
ejpam-5051	113	23	discrete	discrete	ADJ
ejpam-5051	113	24	twist	twist	NOUN
ejpam-5051	113	25	by	by	ADP
ejpam-5051	113	26	t	t	PROPN
ejpam-5051	113	27	over	over	ADP
ejpam-5051	113	28	g	g	PROPN
ejpam-5051	113	29	is	be	AUX
ejpam-5051	113	30	a	a	DET
ejpam-5051	113	31	sequence	sequence	NOUN
ejpam-5051	113	32	g(0)×t	g(0)×t	X
ejpam-5051	113	33	i	i	NOUN
ejpam-5051	113	34	↪	↪	PROPN
ejpam-5051	113	35	→	→	SYM
ejpam-5051	113	36	σ	σ	X
ejpam-5051	113	37	q	q	ADJ
ejpam-5051	113	38	↪	↪	PROPN
ejpam-5051	113	39	→	→	SYM
ejpam-5051	113	40	g	g	PROPN
ejpam-5051	113	41	,	,	PUNCT
ejpam-5051	113	42	where	where	SCONJ
ejpam-5051	113	43	the	the	DET
ejpam-5051	113	44	groupoid	groupoid	PROPN
ejpam-5051	113	45	g(0)×t	g(0)×t	PROPN
ejpam-5051	113	46	is	be	AUX
ejpam-5051	113	47	regarded	regard	VERB
ejpam-5051	113	48	as	as	ADP
ejpam-5051	113	49	trivial	trivial	ADJ
ejpam-5051	113	50	group	group	NOUN
ejpam-5051	113	51	bundle	bundle	NOUN
ejpam-5051	113	52	with	with	ADP
ejpam-5051	113	53	fibres	fibre	NOUN
ejpam-5051	113	54	t	t	PROPN
ejpam-5051	113	55	,	,	PUNCT
ejpam-5051	113	56	σ	σ	PROPN
ejpam-5051	113	57	is	be	AUX
ejpam-5051	113	58	a	a	DET
ejpam-5051	113	59	hausdorff	hausdorff	NOUN
ejpam-5051	113	60	étale	étale	NOUN
ejpam-5051	113	61	groupoid	groupoid	NOUN
ejpam-5051	113	62	with	with	ADP
ejpam-5051	113	63	σ(0	σ(0	PROPN
ejpam-5051	113	64	)	)	PUNCT
ejpam-5051	113	65	=	=	SYM
ejpam-5051	113	66	i(g(0	i(g(0	PROPN
ejpam-5051	113	67	)	)	PUNCT
ejpam-5051	113	68	×{1	×{1	NOUN
ejpam-5051	113	69	}	}	PUNCT
ejpam-5051	113	70	)	)	PUNCT
ejpam-5051	113	71	,	,	PUNCT
ejpam-5051	113	72	and	and	CCONJ
ejpam-5051	113	73	i	i	PRON
ejpam-5051	113	74	and	and	CCONJ
ejpam-5051	113	75	q	q	PROPN
ejpam-5051	113	76	are	be	AUX
ejpam-5051	113	77	continuous	continuous	ADJ
ejpam-5051	113	78	groupoid	groupoid	PROPN
ejpam-5051	113	79	homomorphisms	homomorphism	NOUN
ejpam-5051	113	80	that	that	PRON
ejpam-5051	113	81	restricts	restrict	VERB
ejpam-5051	113	82	to	to	ADP
ejpam-5051	113	83	homeomorphism	homeomorphism	PROPN
ejpam-5051	113	84	of	of	ADP
ejpam-5051	113	85	unit	unit	NOUN
ejpam-5051	113	86	spaces	space	NOUN
ejpam-5051	113	87	,	,	PUNCT
ejpam-5051	113	88	such	such	ADJ
ejpam-5051	113	89	that	that	SCONJ
ejpam-5051	113	90	the	the	DET
ejpam-5051	113	91	following	follow	VERB
ejpam-5051	113	92	condition	condition	NOUN
ejpam-5051	113	93	holds	hold	VERB
ejpam-5051	113	94	:	:	PUNCT
ejpam-5051	113	95	(	(	PUNCT
ejpam-5051	113	96	1	1	X
ejpam-5051	113	97	)	)	PUNCT
ejpam-5051	113	98	the	the	DET
ejpam-5051	113	99	sequence	sequence	NOUN
ejpam-5051	113	100	is	be	AUX
ejpam-5051	113	101	exact	exact	ADJ
ejpam-5051	113	102	,	,	PUNCT
ejpam-5051	113	103	in	in	ADP
ejpam-5051	113	104	the	the	DET
ejpam-5051	113	105	sense	sense	NOUN
ejpam-5051	113	106	that	that	SCONJ
ejpam-5051	113	107	i({x	i({x	PROPN
ejpam-5051	113	108	}	}	PUNCT
ejpam-5051	113	109	×	×	PROPN
ejpam-5051	113	110	t	t	NOUN
ejpam-5051	113	111	)	)	PUNCT
ejpam-5051	113	112	=	=	SYM
ejpam-5051	113	113	q−1(x	q−1(x	NOUN
ejpam-5051	113	114	)	)	PUNCT
ejpam-5051	113	115	for	for	ADP
ejpam-5051	113	116	every	every	DET
ejpam-5051	113	117	x	x	PROPN
ejpam-5051	113	118	∈	∈	PROPN
ejpam-5051	113	119	g(0	g(0	PROPN
ejpam-5051	113	120	)	)	PUNCT
ejpam-5051	113	121	,	,	PUNCT
ejpam-5051	113	122	i	i	PRON
ejpam-5051	113	123	is	be	AUX
ejpam-5051	113	124	injective	injective	ADJ
ejpam-5051	113	125	,	,	PUNCT
ejpam-5051	113	126	and	and	CCONJ
ejpam-5051	113	127	q	q	NOUN
ejpam-5051	113	128	is	be	AUX
ejpam-5051	113	129	a	a	DET
ejpam-5051	113	130	quotient	quotient	NOUN
ejpam-5051	113	131	map	map	NOUN
ejpam-5051	113	132	(	(	PUNCT
ejpam-5051	113	133	2	2	NUM
ejpam-5051	113	134	)	)	PUNCT
ejpam-5051	113	135	the	the	DET
ejpam-5051	113	136	groupoid	groupoid	PROPN
ejpam-5051	113	137	σ	σ	PROPN
ejpam-5051	113	138	is	be	AUX
ejpam-5051	113	139	a	a	DET
ejpam-5051	113	140	locally	locally	ADV
ejpam-5051	113	141	trivial	trivial	ADJ
ejpam-5051	113	142	g	g	NOUN
ejpam-5051	113	143	-	-	PUNCT
ejpam-5051	113	144	bundle	bundle	NOUN
ejpam-5051	113	145	,	,	PUNCT
ejpam-5051	114	1	in	in	ADP
ejpam-5051	114	2	the	the	DET
ejpam-5051	114	3	sense	sense	NOUN
ejpam-5051	114	4	that	that	SCONJ
ejpam-5051	114	5	for	for	ADP
ejpam-5051	114	6	each	each	DET
ejpam-5051	114	7	α	α	NOUN
ejpam-5051	114	8	∈	∈	PROPN
ejpam-5051	114	9	g	g	NOUN
ejpam-5051	114	10	,	,	PUNCT
ejpam-5051	114	11	there	there	PRON
ejpam-5051	114	12	is	be	VERB
ejpam-5051	114	13	an	an	DET
ejpam-5051	114	14	open	open	ADJ
ejpam-5051	114	15	bisection	bisection	NOUN
ejpam-5051	114	16	bα	bα	NOUN
ejpam-5051	114	17	of	of	ADP
ejpam-5051	114	18	g	g	NOUN
ejpam-5051	114	19	containing	contain	VERB
ejpam-5051	114	20	α	α	NOUN
ejpam-5051	114	21	,	,	PUNCT
ejpam-5051	114	22	and	and	CCONJ
ejpam-5051	114	23	a	a	DET
ejpam-5051	114	24	continuous	continuous	ADJ
ejpam-5051	114	25	map	map	NOUN
ejpam-5051	114	26	pα	pα	INTJ
ejpam-5051	114	27	:	:	PUNCT
ejpam-5051	114	28	bα	bα	PROPN
ejpam-5051	114	29	→	→	PUNCT
ejpam-5051	114	30	σ	σ	NOUN
ejpam-5051	114	31	such	such	ADJ
ejpam-5051	114	32	that	that	SCONJ
ejpam-5051	114	33	(	(	PUNCT
ejpam-5051	114	34	i	i	NOUN
ejpam-5051	114	35	)	)	PUNCT
ejpam-5051	114	36	q	q	PROPN
ejpam-5051	115	1	◦	◦	NOUN
ejpam-5051	115	2	pα	pα	NOUN
ejpam-5051	115	3	=	=	NOUN
ejpam-5051	115	4	idbα	idbα	NOUN
ejpam-5051	115	5	(	(	PUNCT
ejpam-5051	115	6	ii	ii	NOUN
ejpam-5051	115	7	)	)	PUNCT
ejpam-5051	115	8	the	the	DET
ejpam-5051	115	9	map	map	NOUN
ejpam-5051	115	10	(	(	PUNCT
ejpam-5051	115	11	β	β	X
ejpam-5051	115	12	,	,	PUNCT
ejpam-5051	115	13	z	z	NOUN
ejpam-5051	115	14	)	)	PUNCT
ejpam-5051	115	15	→	→	SYM
ejpam-5051	115	16	i(r(β	i(r(β	NOUN
ejpam-5051	115	17	)	)	PUNCT
ejpam-5051	115	18	,	,	PUNCT
ejpam-5051	115	19	z)pα(β	z)pα(β	NUM
ejpam-5051	115	20	)	)	PUNCT
ejpam-5051	115	21	is	be	AUX
ejpam-5051	115	22	a	a	DET
ejpam-5051	115	23	homeomorphism	homeomorphism	NOUN
ejpam-5051	115	24	from	from	ADP
ejpam-5051	115	25	bα×t	bα×t	NOUN
ejpam-5051	115	26	to	to	ADP
ejpam-5051	115	27	q−1(bα	q−1(bα	NOUN
ejpam-5051	115	28	)	)	PUNCT
ejpam-5051	115	29	.	.	PUNCT
ejpam-5051	116	1	(	(	PUNCT
ejpam-5051	116	2	3	3	X
ejpam-5051	116	3	)	)	PUNCT
ejpam-5051	116	4	the	the	DET
ejpam-5051	116	5	image	image	NOUN
ejpam-5051	116	6	of	of	ADP
ejpam-5051	116	7	i	i	PRON
ejpam-5051	116	8	is	be	AUX
ejpam-5051	116	9	central	central	ADJ
ejpam-5051	116	10	in	in	ADP
ejpam-5051	116	11	σ	σ	PROPN
ejpam-5051	116	12	,	,	PUNCT
ejpam-5051	116	13	in	in	ADP
ejpam-5051	116	14	the	the	DET
ejpam-5051	116	15	sense	sense	NOUN
ejpam-5051	116	16	that	that	SCONJ
ejpam-5051	116	17	i(r(ϵ	i(r(ϵ	PROPN
ejpam-5051	116	18	)	)	PUNCT
ejpam-5051	116	19	,	,	PUNCT
ejpam-5051	116	20	z)ϵ	z)ϵ	PUNCT
ejpam-5051	117	1	=	=	SYM
ejpam-5051	117	2	ϵi(s(ϵ	ϵi(s(ϵ	X
ejpam-5051	117	3	)	)	PUNCT
ejpam-5051	117	4	,	,	PUNCT
ejpam-5051	117	5	z	z	NOUN
ejpam-5051	117	6	)	)	PUNCT
ejpam-5051	117	7	for	for	ADP
ejpam-5051	117	8	all	all	PRON
ejpam-5051	117	9	ϵ	ϵ	PROPN
ejpam-5051	117	10	∈	∈	PROPN
ejpam-5051	117	11	σ	σ	NOUN
ejpam-5051	117	12	and	and	CCONJ
ejpam-5051	117	13	z	z	PROPN
ejpam-5051	117	14	∈	∈	PROPN
ejpam-5051	117	15	t	t	NOUN
ejpam-5051	117	16	.	.	PUNCT
ejpam-5051	118	1	we	we	PRON
ejpam-5051	118	2	will	will	AUX
ejpam-5051	118	3	denote	denote	VERB
ejpam-5051	118	4	a	a	DET
ejpam-5051	118	5	discrete	discrete	ADJ
ejpam-5051	118	6	twist	twist	NOUN
ejpam-5051	118	7	over	over	ADP
ejpam-5051	118	8	g	g	NOUN
ejpam-5051	118	9	by	by	ADP
ejpam-5051	118	10	(	(	PUNCT
ejpam-5051	118	11	σ	σ	PROPN
ejpam-5051	118	12	,	,	PUNCT
ejpam-5051	118	13	i	i	PRON
ejpam-5051	118	14	,	,	PUNCT
ejpam-5051	118	15	q	q	NOUN
ejpam-5051	118	16	)	)	PUNCT
ejpam-5051	118	17	.	.	PUNCT
ejpam-5051	119	1	the	the	DET
ejpam-5051	119	2	following	follow	VERB
ejpam-5051	119	3	is	be	AUX
ejpam-5051	119	4	an	an	DET
ejpam-5051	119	5	example	example	NOUN
ejpam-5051	119	6	of	of	ADP
ejpam-5051	119	7	a	a	DET
ejpam-5051	119	8	discrete	discrete	ADJ
ejpam-5051	119	9	twist	twist	NOUN
ejpam-5051	119	10	.	.	PUNCT
ejpam-5051	120	1	example	example	NOUN
ejpam-5051	121	1	3	3	X
ejpam-5051	121	2	.	.	X
ejpam-5051	121	3	consider	consider	VERB
ejpam-5051	121	4	the	the	DET
ejpam-5051	121	5	the	the	DET
ejpam-5051	121	6	set	set	NOUN
ejpam-5051	121	7	of	of	ADP
ejpam-5051	121	8	integers	integer	NOUN
ejpam-5051	121	9	z	z	PROPN
ejpam-5051	121	10	as	as	ADP
ejpam-5051	121	11	our	our	PRON
ejpam-5051	121	12	groupoid	groupoid	NOUN
ejpam-5051	121	13	and	and	CCONJ
ejpam-5051	121	14	unital	unital	ADJ
ejpam-5051	121	15	commutative	commutative	ADJ
ejpam-5051	121	16	ring	ring	NOUN
ejpam-5051	121	17	.	.	PUNCT
ejpam-5051	122	1	then	then	ADV
ejpam-5051	122	2	our	our	PRON
ejpam-5051	122	3	groupoid	groupoid	PROPN
ejpam-5051	122	4	z	z	PROPN
ejpam-5051	122	5	will	will	AUX
ejpam-5051	122	6	have	have	VERB
ejpam-5051	122	7	the	the	DET
ejpam-5051	122	8	following	follow	VERB
ejpam-5051	122	9	structures	structure	NOUN
ejpam-5051	122	10	:	:	PUNCT
ejpam-5051	122	11	z×	z×	NUM
ejpam-5051	122	12	=	=	SYM
ejpam-5051	122	13	{	{	PUNCT
ejpam-5051	122	14	−1	−1	NOUN
ejpam-5051	122	15	,	,	PUNCT
ejpam-5051	122	16	1	1	NUM
ejpam-5051	122	17	}	}	PUNCT
ejpam-5051	122	18	,	,	PUNCT
ejpam-5051	122	19	s(x	s(x	PROPN
ejpam-5051	122	20	)	)	PUNCT
ejpam-5051	122	21	=	=	PUNCT
ejpam-5051	123	1	x−1	x−1	PROPN
ejpam-5051	124	1	+	+	NUM
ejpam-5051	124	2	x	x	X
ejpam-5051	124	3	=	=	X
ejpam-5051	124	4	{	{	PUNCT
ejpam-5051	124	5	0	0	NUM
ejpam-5051	124	6	}	}	PUNCT
ejpam-5051	124	7	,	,	PUNCT
ejpam-5051	124	8	r(x	r(x	PROPN
ejpam-5051	124	9	)	)	PUNCT
ejpam-5051	124	10	=	=	PUNCT
ejpam-5051	125	1	x+	x+	PUNCT
ejpam-5051	125	2	x−1	x−1	PUNCT
ejpam-5051	125	3	=	=	PUNCT
ejpam-5051	125	4	{	{	PUNCT
ejpam-5051	125	5	0	0	NUM
ejpam-5051	125	6	}	}	PUNCT
ejpam-5051	125	7	,	,	PUNCT
ejpam-5051	125	8	z(0	z(0	PROPN
ejpam-5051	125	9	)	)	PUNCT
ejpam-5051	125	10	=	=	PUNCT
ejpam-5051	125	11	{	{	PUNCT
ejpam-5051	125	12	0	0	NUM
ejpam-5051	125	13	}	}	PUNCT
ejpam-5051	125	14	and	and	CCONJ
ejpam-5051	125	15	z(2	z(2	NUM
ejpam-5051	125	16	)	)	PUNCT
ejpam-5051	125	17	=	=	PRON
ejpam-5051	125	18	{	{	PUNCT
ejpam-5051	125	19	(	(	PUNCT
ejpam-5051	125	20	x	x	NOUN
ejpam-5051	125	21	,	,	PUNCT
ejpam-5051	125	22	y	y	NOUN
ejpam-5051	125	23	)	)	PUNCT
ejpam-5051	125	24	∈	∈	PROPN
ejpam-5051	125	25	z×z|s(x	z×z|s(x	NOUN
ejpam-5051	125	26	)	)	PUNCT
ejpam-5051	125	27	=	=	SYM
ejpam-5051	125	28	r(y	r(y	VERB
ejpam-5051	125	29	)	)	PUNCT
ejpam-5051	125	30	}	}	PUNCT
ejpam-5051	125	31	.	.	PUNCT
ejpam-5051	126	1	note	note	VERB
ejpam-5051	126	2	that	that	SCONJ
ejpam-5051	126	3	z	z	NOUN
ejpam-5051	126	4	is	be	AUX
ejpam-5051	126	5	a	a	DET
ejpam-5051	126	6	hausdorff	hausdorff	NOUN
ejpam-5051	126	7	étale	étale	NOUN
ejpam-5051	126	8	groupoid	groupoid	NOUN
ejpam-5051	126	9	having	have	VERB
ejpam-5051	126	10	the	the	DET
ejpam-5051	126	11	discrete	discrete	ADJ
ejpam-5051	126	12	topology	topology	NOUN
ejpam-5051	126	13	.	.	PUNCT
ejpam-5051	127	1	let	let	VERB
ejpam-5051	127	2	the	the	DET
ejpam-5051	127	3	function	function	NOUN
ejpam-5051	127	4	σ	σ	NOUN
ejpam-5051	127	5	:	:	PUNCT
ejpam-5051	127	6	z(2	z(2	NUM
ejpam-5051	127	7	)	)	PUNCT
ejpam-5051	127	8	→	→	SYM
ejpam-5051	127	9	t	t	NOUN
ejpam-5051	127	10	≤	≤	NUM
ejpam-5051	128	1	r×	r×	NOUN
ejpam-5051	128	2	be	be	AUX
ejpam-5051	128	3	a	a	DET
ejpam-5051	128	4	continuous	continuous	ADJ
ejpam-5051	128	5	2	2	NUM
ejpam-5051	128	6	-	-	PUNCT
ejpam-5051	128	7	cocycle	cocycle	NOUN
ejpam-5051	128	8	.	.	PUNCT
ejpam-5051	129	1	choose	choose	VERB
ejpam-5051	129	2	t	t	PROPN
ejpam-5051	129	3	≤	≤	PROPN
ejpam-5051	129	4	z×	z×	PUNCT
ejpam-5051	129	5	=	=	PUNCT
ejpam-5051	129	6	{	{	PUNCT
ejpam-5051	129	7	1	1	NUM
ejpam-5051	129	8	}	}	PUNCT
ejpam-5051	129	9	.	.	PUNCT
ejpam-5051	130	1	then	then	ADV
ejpam-5051	130	2	z	z	PROPN
ejpam-5051	130	3	×	×	PROPN
ejpam-5051	130	4	t	t	PROPN
ejpam-5051	130	5	is	be	AUX
ejpam-5051	130	6	a	a	DET
ejpam-5051	130	7	hausdorff	hausdorff	NOUN
ejpam-5051	130	8	groupoid	groupoid	NOUN
ejpam-5051	130	9	with	with	ADP
ejpam-5051	130	10	respect	respect	NOUN
ejpam-5051	130	11	to	to	ADP
ejpam-5051	130	12	the	the	DET
ejpam-5051	130	13	product	product	NOUN
ejpam-5051	130	14	topology	topology	NOUN
ejpam-5051	130	15	with	with	ADP
ejpam-5051	130	16	multiplication	multiplication	NOUN
ejpam-5051	130	17	given	give	VERB
ejpam-5051	130	18	by	by	ADP
ejpam-5051	130	19	(	(	PUNCT
ejpam-5051	130	20	α	α	X
ejpam-5051	130	21	,	,	PUNCT
ejpam-5051	130	22	z)(β	z)(β	NOUN
ejpam-5051	130	23	,	,	PUNCT
ejpam-5051	130	24	w	w	NOUN
ejpam-5051	130	25	)	)	PUNCT
ejpam-5051	130	26	:	:	PUNCT
ejpam-5051	131	1	=	=	SYM
ejpam-5051	131	2	(	(	PUNCT
ejpam-5051	131	3	αβ	αβ	INTJ
ejpam-5051	131	4	,	,	PUNCT
ejpam-5051	131	5	σ(α	σ(α	PROPN
ejpam-5051	131	6	,	,	PUNCT
ejpam-5051	131	7	β)zw	β)zw	PROPN
ejpam-5051	131	8	)	)	PUNCT
ejpam-5051	131	9	,	,	PUNCT
ejpam-5051	131	10	and	and	CCONJ
ejpam-5051	131	11	inversion	inversion	NOUN
ejpam-5051	131	12	given	give	VERB
ejpam-5051	131	13	by	by	ADP
ejpam-5051	131	14	(	(	PUNCT
ejpam-5051	131	15	α	α	X
ejpam-5051	131	16	,	,	PUNCT
ejpam-5051	131	17	z)−1	z)−1	NUM
ejpam-5051	131	18	:	:	PUNCT
ejpam-5051	131	19	=	=	SYM
ejpam-5051	131	20	(	(	PUNCT
ejpam-5051	131	21	α−1	α−1	PROPN
ejpam-5051	131	22	,	,	PUNCT
ejpam-5051	131	23	σ(α	σ(α	PROPN
ejpam-5051	131	24	,	,	PUNCT
ejpam-5051	131	25	α−1)−1z−1	α−1)−1z−1	ADJ
ejpam-5051	131	26	)	)	PUNCT
ejpam-5051	131	27	=	=	SYM
ejpam-5051	131	28	(	(	PUNCT
ejpam-5051	131	29	α−1	α−1	PROPN
ejpam-5051	131	30	,	,	PUNCT
ejpam-5051	131	31	σ(α−1	σ(α−1	NOUN
ejpam-5051	131	32	,	,	PUNCT
ejpam-5051	131	33	α)−1z−1	α)−1z−1	NOUN
ejpam-5051	131	34	)	)	PUNCT
ejpam-5051	131	35	,	,	PUNCT
ejpam-5051	131	36	for	for	ADP
ejpam-5051	131	37	all	all	DET
ejpam-5051	131	38	(	(	PUNCT
ejpam-5051	131	39	α	α	NOUN
ejpam-5051	131	40	,	,	PUNCT
ejpam-5051	131	41	β	β	NOUN
ejpam-5051	131	42	)	)	PUNCT
ejpam-5051	131	43	∈	∈	PROPN
ejpam-5051	131	44	z(2	z(2	PROPN
ejpam-5051	131	45	)	)	PUNCT
ejpam-5051	131	46	and	and	CCONJ
ejpam-5051	131	47	z	z	NOUN
ejpam-5051	131	48	,	,	PUNCT
ejpam-5051	131	49	w	w	PROPN
ejpam-5051	131	50	∈	∈	PROPN
ejpam-5051	131	51	t	t	NOUN
ejpam-5051	131	52	.	.	PUNCT
ejpam-5051	132	1	then	then	ADV
ejpam-5051	132	2	,	,	PUNCT
ejpam-5051	132	3	(	(	PUNCT
ejpam-5051	132	4	z×	z×	NUM
ejpam-5051	132	5	t	t	PROPN
ejpam-5051	132	6	,	,	PUNCT
ejpam-5051	132	7	i	i	PRON
ejpam-5051	132	8	,	,	PUNCT
ejpam-5051	132	9	q	q	X
ejpam-5051	132	10	)	)	PUNCT
ejpam-5051	132	11	is	be	AUX
ejpam-5051	132	12	a	a	DET
ejpam-5051	132	13	discrete	discrete	ADJ
ejpam-5051	132	14	twist	twist	NOUN
ejpam-5051	132	15	by	by	ADP
ejpam-5051	132	16	t	t	PROPN
ejpam-5051	132	17	over	over	ADP
ejpam-5051	132	18	z	z	PROPN
ejpam-5051	132	19	with	with	ADP
ejpam-5051	132	20	the	the	DET
ejpam-5051	132	21	sequence	sequence	NOUN
ejpam-5051	132	22	z(0	z(0	NOUN
ejpam-5051	132	23	)	)	PUNCT
ejpam-5051	132	24	×	×	NOUN
ejpam-5051	132	25	t	t	NOUN
ejpam-5051	133	1	i	i	NOUN
ejpam-5051	133	2	↪	↪	PROPN
ejpam-5051	133	3	→	→	SYM
ejpam-5051	133	4	z×	z×	NUM
ejpam-5051	133	5	t	t	PROPN
ejpam-5051	133	6	q	q	X
ejpam-5051	133	7	↪	↪	PROPN
ejpam-5051	133	8	→	→	SYM
ejpam-5051	133	9	z	z	NOUN
ejpam-5051	133	10	where	where	SCONJ
ejpam-5051	133	11	i(x	i(x	PROPN
ejpam-5051	133	12	,	,	PUNCT
ejpam-5051	133	13	z	z	NOUN
ejpam-5051	133	14	)	)	PUNCT
ejpam-5051	133	15	=	=	SYM
ejpam-5051	133	16	(	(	PUNCT
ejpam-5051	133	17	x	x	X
ejpam-5051	133	18	,	,	PUNCT
ejpam-5051	133	19	z	z	NOUN
ejpam-5051	133	20	)	)	PUNCT
ejpam-5051	133	21	and	and	CCONJ
ejpam-5051	133	22	q(γ	q(γ	PROPN
ejpam-5051	133	23	,	,	PUNCT
ejpam-5051	133	24	z	z	NOUN
ejpam-5051	133	25	)	)	PUNCT
ejpam-5051	133	26	=	=	SYM
ejpam-5051	133	27	γ	γ	NOUN
ejpam-5051	133	28	for	for	ADP
ejpam-5051	133	29	all	all	DET
ejpam-5051	133	30	x	x	NOUN
ejpam-5051	133	31	,	,	PUNCT
ejpam-5051	133	32	γ	γ	PROPN
ejpam-5051	133	33	∈	∈	PROPN
ejpam-5051	133	34	z	z	PROPN
ejpam-5051	133	35	and	and	CCONJ
ejpam-5051	133	36	z	z	PROPN
ejpam-5051	133	37	∈	∈	PROPN
ejpam-5051	133	38	t	t	PROPN
ejpam-5051	133	39	.	.	PUNCT
ejpam-5051	134	1	definition	definition	NOUN
ejpam-5051	134	2	9	9	NUM
ejpam-5051	134	3	.	.	PUNCT
ejpam-5051	135	1	a	a	DET
ejpam-5051	135	2	continuous	continuous	ADJ
ejpam-5051	135	3	map	map	NOUN
ejpam-5051	135	4	pα	pα	INTJ
ejpam-5051	135	5	:	:	PUNCT
ejpam-5051	135	6	bα	bα	PROPN
ejpam-5051	135	7	→	→	PUNCT
ejpam-5051	135	8	σ	σ	PROPN
ejpam-5051	135	9	is	be	AUX
ejpam-5051	135	10	called	call	VERB
ejpam-5051	135	11	a	a	DET
ejpam-5051	135	12	continuous	continuous	ADJ
ejpam-5051	135	13	local	local	ADJ
ejpam-5051	135	14	section	section	NOUN
ejpam-5051	135	15	if	if	SCONJ
ejpam-5051	135	16	it	it	PRON
ejpam-5051	135	17	satisfies	satisfy	VERB
ejpam-5051	135	18	definition	definition	NOUN
ejpam-5051	135	19	8(2i	8(2i	NUM
ejpam-5051	135	20	)	)	PUNCT
ejpam-5051	135	21	.	.	PUNCT
ejpam-5051	136	1	if	if	SCONJ
ejpam-5051	136	2	p	p	PROPN
ejpam-5051	136	3	(	(	PUNCT
ejpam-5051	136	4	g(0	g(0	NOUN
ejpam-5051	136	5	)	)	PUNCT
ejpam-5051	136	6	)	)	PUNCT
ejpam-5051	137	1	=	=	SYM
ejpam-5051	137	2	σ(0	σ(0	PROPN
ejpam-5051	137	3	)	)	PUNCT
ejpam-5051	137	4	=	=	SYM
ejpam-5051	137	5	i(g(0	i(g(0	PROPN
ejpam-5051	137	6	)	)	PUNCT
ejpam-5051	137	7	×	×	NOUN
ejpam-5051	137	8	1	1	NUM
ejpam-5051	137	9	)	)	PUNCT
ejpam-5051	137	10	,	,	PUNCT
ejpam-5051	137	11	then	then	ADV
ejpam-5051	137	12	pα	pα	INTJ
ejpam-5051	137	13	is	be	AUX
ejpam-5051	137	14	a	a	DET
ejpam-5051	137	15	continuous	continuous	ADJ
ejpam-5051	137	16	global	global	ADJ
ejpam-5051	137	17	section	section	NOUN
ejpam-5051	137	18	.	.	PUNCT
ejpam-5051	138	1	r.	r.	PROPN
ejpam-5051	138	2	s.	s.	PROPN
ejpam-5051	138	3	bongcawel	bongcawel	PROPN
ejpam-5051	139	1	et	et	PROPN
ejpam-5051	139	2	al	al	PROPN
ejpam-5051	139	3	.	.	PUNCT
ejpam-5051	139	4	/	/	SYM
ejpam-5051	139	5	eur	eur	PROPN
ejpam-5051	139	6	.	.	PUNCT
ejpam-5051	140	1	j.	j.	PROPN
ejpam-5051	140	2	pure	pure	PROPN
ejpam-5051	140	3	appl	appl	PROPN
ejpam-5051	140	4	.	.	PROPN
ejpam-5051	140	5	math	math	PROPN
ejpam-5051	140	6	,	,	PUNCT
ejpam-5051	140	7	17	17	NUM
ejpam-5051	140	8	(	(	PUNCT
ejpam-5051	140	9	1	1	NUM
ejpam-5051	140	10	)	)	PUNCT
ejpam-5051	140	11	(	(	PUNCT
ejpam-5051	140	12	2024	2024	NUM
ejpam-5051	140	13	)	)	PUNCT
ejpam-5051	140	14	,	,	PUNCT
ejpam-5051	140	15	519	519	NUM
ejpam-5051	140	16	-	-	SYM
ejpam-5051	140	17	545	545	NUM
ejpam-5051	140	18	524	524	NUM
ejpam-5051	140	19	definition	definition	NOUN
ejpam-5051	140	20	10	10	NUM
ejpam-5051	140	21	.	.	PUNCT
ejpam-5051	141	1	let	let	VERB
ejpam-5051	141	2	g	g	PRON
ejpam-5051	141	3	be	be	AUX
ejpam-5051	141	4	an	an	DET
ejpam-5051	141	5	ample	ample	ADJ
ejpam-5051	141	6	hausdorff	hausdorff	NOUN
ejpam-5051	141	7	groupoid	groupoid	NOUN
ejpam-5051	141	8	and	and	CCONJ
ejpam-5051	141	9	let	let	VERB
ejpam-5051	141	10	(	(	PUNCT
ejpam-5051	141	11	σ	σ	NOUN
ejpam-5051	141	12	,	,	PUNCT
ejpam-5051	141	13	i	i	PRON
ejpam-5051	141	14	,	,	PUNCT
ejpam-5051	141	15	q	q	X
ejpam-5051	141	16	)	)	PUNCT
ejpam-5051	141	17	be	be	AUX
ejpam-5051	141	18	a	a	DET
ejpam-5051	141	19	discrete	discrete	ADJ
ejpam-5051	141	20	twist	twist	NOUN
ejpam-5051	141	21	by	by	ADP
ejpam-5051	141	22	t	t	NOUN
ejpam-5051	141	23	≤	≤	NUM
ejpam-5051	141	24	r×	r×	NOUN
ejpam-5051	141	25	over	over	ADP
ejpam-5051	141	26	g.	g.	PROPN
ejpam-5051	141	27	denote	denote	PROPN
ejpam-5051	141	28	c(σ	c(σ	PROPN
ejpam-5051	141	29	,	,	PUNCT
ejpam-5051	141	30	r	r	NOUN
ejpam-5051	141	31	)	)	PUNCT
ejpam-5051	141	32	as	as	ADP
ejpam-5051	141	33	the	the	DET
ejpam-5051	141	34	collection	collection	NOUN
ejpam-5051	141	35	of	of	ADP
ejpam-5051	141	36	continuous	continuous	ADJ
ejpam-5051	141	37	functions	function	NOUN
ejpam-5051	141	38	from	from	ADP
ejpam-5051	141	39	σ	σ	PROPN
ejpam-5051	141	40	to	to	ADP
ejpam-5051	141	41	r.	r.	PROPN
ejpam-5051	141	42	we	we	PRON
ejpam-5051	141	43	say	say	VERB
ejpam-5051	141	44	that	that	SCONJ
ejpam-5051	141	45	f	f	PROPN
ejpam-5051	141	46	∈	∈	PROPN
ejpam-5051	141	47	c(σ	c(σ	PROPN
ejpam-5051	141	48	,	,	PUNCT
ejpam-5051	141	49	r	r	NOUN
ejpam-5051	141	50	)	)	PUNCT
ejpam-5051	141	51	is	be	AUX
ejpam-5051	141	52	t	t	NOUN
ejpam-5051	141	53	-equivariant	-equivariant	ADJ
ejpam-5051	141	54	if	if	SCONJ
ejpam-5051	141	55	f(z	f(z	NOUN
ejpam-5051	141	56	·	·	PUNCT
ejpam-5051	142	1	ϵ	ϵ	X
ejpam-5051	142	2	)	)	PUNCT
ejpam-5051	142	3	=	=	PUNCT
ejpam-5051	142	4	zf(ϵ	zf(ϵ	NOUN
ejpam-5051	142	5	)	)	PUNCT
ejpam-5051	142	6	for	for	ADP
ejpam-5051	142	7	all	all	DET
ejpam-5051	142	8	z	z	NOUN
ejpam-5051	142	9	∈	∈	PROPN
ejpam-5051	142	10	t	t	NOUN
ejpam-5051	142	11	and	and	CCONJ
ejpam-5051	142	12	ϵ	ϵ	PROPN
ejpam-5051	142	13	∈	∈	PROPN
ejpam-5051	142	14	σ	σ	PROPN
ejpam-5051	142	15	,	,	PUNCT
ejpam-5051	142	16	and	and	CCONJ
ejpam-5051	142	17	we	we	PRON
ejpam-5051	142	18	define	define	VERB
ejpam-5051	142	19	ar(g	ar(g	ADP
ejpam-5051	142	20	;	;	PUNCT
ejpam-5051	142	21	σ	σ	X
ejpam-5051	142	22	)	)	PUNCT
ejpam-5051	142	23	:	:	PUNCT
ejpam-5051	143	1	=	=	SYM
ejpam-5051	143	2	{	{	PUNCT
ejpam-5051	143	3	f	f	PROPN
ejpam-5051	143	4	∈	∈	PROPN
ejpam-5051	143	5	c(σ	c(σ	PROPN
ejpam-5051	143	6	,	,	PUNCT
ejpam-5051	143	7	r	r	NOUN
ejpam-5051	143	8	)	)	PUNCT
ejpam-5051	143	9	:	:	PUNCT
ejpam-5051	143	10	f	f	PROPN
ejpam-5051	143	11	is	be	AUX
ejpam-5051	143	12	t	t	X
ejpam-5051	143	13	-equivariant	-equivariant	ADJ
ejpam-5051	143	14	and	and	CCONJ
ejpam-5051	143	15	q(supp(f	q(supp(f	NOUN
ejpam-5051	143	16	)	)	PUNCT
ejpam-5051	143	17	)	)	PUNCT
ejpam-5051	143	18	is	be	AUX
ejpam-5051	143	19	compact	compact	ADJ
ejpam-5051	143	20	}	}	PUNCT
ejpam-5051	143	21	.	.	PUNCT
ejpam-5051	144	1	lemma	lemma	PROPN
ejpam-5051	144	2	4	4	X
ejpam-5051	144	3	.	.	PUNCT
ejpam-5051	145	1	let	let	VERB
ejpam-5051	145	2	g	g	PRON
ejpam-5051	145	3	be	be	AUX
ejpam-5051	145	4	an	an	DET
ejpam-5051	145	5	ample	ample	ADJ
ejpam-5051	145	6	hausdorff	hausdorff	NOUN
ejpam-5051	145	7	groupoid	groupoid	NOUN
ejpam-5051	145	8	,	,	PUNCT
ejpam-5051	145	9	and	and	CCONJ
ejpam-5051	145	10	let	let	AUX
ejpam-5051	145	11	(	(	PUNCT
ejpam-5051	145	12	σ	σ	NOUN
ejpam-5051	145	13	,	,	PUNCT
ejpam-5051	145	14	i	i	PRON
ejpam-5051	145	15	,	,	PUNCT
ejpam-5051	145	16	q	q	X
ejpam-5051	145	17	)	)	PUNCT
ejpam-5051	145	18	be	be	AUX
ejpam-5051	145	19	a	a	DET
ejpam-5051	145	20	discrete	discrete	ADJ
ejpam-5051	145	21	twist	twist	NOUN
ejpam-5051	145	22	by	by	ADP
ejpam-5051	145	23	t	t	NOUN
ejpam-5051	145	24	≤	≤	NUM
ejpam-5051	145	25	r×	r×	NOUN
ejpam-5051	145	26	over	over	ADP
ejpam-5051	145	27	g.	g.	PROPN
ejpam-5051	145	28	then	then	ADV
ejpam-5051	145	29	ar(g	ar(g	PROPN
ejpam-5051	145	30	;	;	PUNCT
ejpam-5051	145	31	σ	σ	X
ejpam-5051	145	32	)	)	PUNCT
ejpam-5051	145	33	is	be	AUX
ejpam-5051	145	34	an	an	DET
ejpam-5051	145	35	r	r	NOUN
ejpam-5051	145	36	-	-	PUNCT
ejpam-5051	145	37	submodule	submodule	NOUN
ejpam-5051	145	38	of	of	ADP
ejpam-5051	145	39	c(σ	c(σ	PROPN
ejpam-5051	145	40	,	,	PUNCT
ejpam-5051	145	41	r	r	NOUN
ejpam-5051	145	42	)	)	PUNCT
ejpam-5051	145	43	.	.	PUNCT
ejpam-5051	146	1	definition	definition	NOUN
ejpam-5051	146	2	11	11	NUM
ejpam-5051	146	3	.	.	PUNCT
ejpam-5051	147	1	let	let	VERB
ejpam-5051	147	2	g	g	PRON
ejpam-5051	147	3	be	be	AUX
ejpam-5051	147	4	an	an	DET
ejpam-5051	147	5	ample	ample	ADJ
ejpam-5051	147	6	hausdorff	hausdorff	NOUN
ejpam-5051	147	7	groupoid	groupoid	NOUN
ejpam-5051	147	8	,	,	PUNCT
ejpam-5051	147	9	and	and	CCONJ
ejpam-5051	147	10	let	let	AUX
ejpam-5051	147	11	(	(	PUNCT
ejpam-5051	147	12	σ	σ	NOUN
ejpam-5051	147	13	,	,	PUNCT
ejpam-5051	147	14	i	i	PRON
ejpam-5051	147	15	,	,	PUNCT
ejpam-5051	147	16	q	q	X
ejpam-5051	147	17	)	)	PUNCT
ejpam-5051	147	18	be	be	AUX
ejpam-5051	147	19	a	a	DET
ejpam-5051	147	20	discrete	discrete	ADJ
ejpam-5051	147	21	twist	twist	NOUN
ejpam-5051	147	22	by	by	ADP
ejpam-5051	147	23	t	t	NOUN
ejpam-5051	147	24	≤	≤	NUM
ejpam-5051	147	25	r×	r×	NOUN
ejpam-5051	147	26	over	over	ADP
ejpam-5051	147	27	g.	g.	PROPN
ejpam-5051	147	28	let	let	VERB
ejpam-5051	147	29	p	p	NOUN
ejpam-5051	147	30	:	:	PUNCT
ejpam-5051	147	31	g	g	PROPN
ejpam-5051	147	32	→	→	SYM
ejpam-5051	147	33	σ	σ	X
ejpam-5051	147	34	be	be	AUX
ejpam-5051	147	35	any	any	DET
ejpam-5051	147	36	continuous	continuous	ADJ
ejpam-5051	147	37	global	global	ADJ
ejpam-5051	147	38	section	section	NOUN
ejpam-5051	147	39	.	.	PUNCT
ejpam-5051	148	1	there	there	PRON
ejpam-5051	148	2	is	be	VERB
ejpam-5051	148	3	a	a	DET
ejpam-5051	148	4	multiplication	multiplication	NOUN
ejpam-5051	148	5	called	call	VERB
ejpam-5051	148	6	convolution	convolution	NOUN
ejpam-5051	148	7	on	on	ADP
ejpam-5051	148	8	the	the	DET
ejpam-5051	148	9	r	r	NOUN
ejpam-5051	148	10	-	-	PUNCT
ejpam-5051	148	11	module	module	NOUN
ejpam-5051	148	12	ar(g	ar(g	NOUN
ejpam-5051	148	13	;	;	PUNCT
ejpam-5051	148	14	σ	σ	PROPN
ejpam-5051	148	15	)	)	PUNCT
ejpam-5051	148	16	,	,	PUNCT
ejpam-5051	148	17	given	give	VERB
ejpam-5051	148	18	by	by	ADP
ejpam-5051	148	19	(	(	PUNCT
ejpam-5051	148	20	f	f	PROPN
ejpam-5051	148	21	∗σ	∗σ	PROPN
ejpam-5051	148	22	g)(ϵ	g)(ϵ	NOUN
ejpam-5051	148	23	)	)	PUNCT
ejpam-5051	148	24	:	:	PUNCT
ejpam-5051	149	1	=	=	PUNCT
ejpam-5051	149	2	∑	∑	PUNCT
ejpam-5051	149	3	γ∈gs(q(ϵ	γ∈gs(q(ϵ	PROPN
ejpam-5051	149	4	)	)	PUNCT
ejpam-5051	149	5	)	)	PUNCT
ejpam-5051	150	1	f(ϵp	f(ϵp	PROPN
ejpam-5051	150	2	(	(	PUNCT
ejpam-5051	150	3	γ))g(p	γ))g(p	PROPN
ejpam-5051	150	4	(	(	PUNCT
ejpam-5051	150	5	γ)−1	γ)−1	NOUN
ejpam-5051	150	6	)	)	PUNCT
ejpam-5051	150	7	,	,	PUNCT
ejpam-5051	150	8	under	under	ADP
ejpam-5051	150	9	which	which	PRON
ejpam-5051	150	10	ar(g	ar(g	NOUN
ejpam-5051	150	11	;	;	PUNCT
ejpam-5051	150	12	σ	σ	X
ejpam-5051	150	13	)	)	PUNCT
ejpam-5051	150	14	is	be	AUX
ejpam-5051	150	15	an	an	DET
ejpam-5051	150	16	r	r	NOUN
ejpam-5051	150	17	-	-	PUNCT
ejpam-5051	150	18	algebra	algebra	NOUN
ejpam-5051	150	19	.	.	PUNCT
ejpam-5051	151	1	we	we	PRON
ejpam-5051	151	2	call	call	VERB
ejpam-5051	151	3	ar(g	ar(g	ADP
ejpam-5051	151	4	;	;	PUNCT
ejpam-5051	151	5	σ	σ	X
ejpam-5051	151	6	)	)	PUNCT
ejpam-5051	151	7	the	the	DET
ejpam-5051	151	8	twisted	twisted	ADJ
ejpam-5051	151	9	steinberg	steinberg	PROPN
ejpam-5051	151	10	algebra	algebra	PROPN
ejpam-5051	151	11	of	of	ADP
ejpam-5051	151	12	g	g	PROPN
ejpam-5051	151	13	associated	associate	VERB
ejpam-5051	151	14	to	to	ADP
ejpam-5051	151	15	the	the	DET
ejpam-5051	151	16	pair	pair	NOUN
ejpam-5051	151	17	(	(	PUNCT
ejpam-5051	151	18	g	g	PROPN
ejpam-5051	151	19	,	,	PUNCT
ejpam-5051	151	20	σ	σ	PROPN
ejpam-5051	151	21	)	)	PUNCT
ejpam-5051	151	22	.	.	PUNCT
ejpam-5051	152	1	the	the	DET
ejpam-5051	152	2	following	follow	VERB
ejpam-5051	152	3	is	be	AUX
ejpam-5051	152	4	an	an	DET
ejpam-5051	152	5	example	example	NOUN
ejpam-5051	152	6	of	of	ADP
ejpam-5051	152	7	a	a	DET
ejpam-5051	152	8	twisted	twisted	ADJ
ejpam-5051	152	9	steinberg	steinberg	PROPN
ejpam-5051	152	10	algebra	algebra	NOUN
ejpam-5051	152	11	of	of	ADP
ejpam-5051	152	12	a	a	DET
ejpam-5051	152	13	discrete	discrete	ADJ
ejpam-5051	152	14	group	group	NOUN
ejpam-5051	152	15	z	z	PROPN
ejpam-5051	152	16	over	over	ADP
ejpam-5051	152	17	a	a	DET
ejpam-5051	152	18	commutative	commutative	ADJ
ejpam-5051	152	19	ring	ring	NOUN
ejpam-5051	152	20	r	r	NOUN
ejpam-5051	152	21	called	call	VERB
ejpam-5051	152	22	the	the	DET
ejpam-5051	152	23	twisted	twisted	ADJ
ejpam-5051	152	24	discrete	discrete	ADJ
ejpam-5051	152	25	group	group	NOUN
ejpam-5051	152	26	algebra	algebra	NOUN
ejpam-5051	152	27	.	.	PUNCT
ejpam-5051	152	28	example	example	NOUN
ejpam-5051	153	1	4	4	NUM
ejpam-5051	153	2	.	.	PUNCT
ejpam-5051	154	1	let	let	VERB
ejpam-5051	154	2	r	r	PRON
ejpam-5051	154	3	be	be	AUX
ejpam-5051	154	4	a	a	DET
ejpam-5051	154	5	discrete	discrete	ADJ
ejpam-5051	154	6	commutative	commutative	ADJ
ejpam-5051	154	7	unital	unital	ADJ
ejpam-5051	154	8	ring	ring	NOUN
ejpam-5051	154	9	and	and	CCONJ
ejpam-5051	154	10	consider	consider	VERB
ejpam-5051	154	11	an	an	DET
ejpam-5051	154	12	ample	ample	ADJ
ejpam-5051	154	13	hausdorff	hausdorff	NOUN
ejpam-5051	154	14	groupoid	groupoid	PROPN
ejpam-5051	154	15	z	z	PROPN
ejpam-5051	154	16	with	with	ADP
ejpam-5051	154	17	the	the	DET
ejpam-5051	154	18	discrete	discrete	ADJ
ejpam-5051	154	19	topology	topology	NOUN
ejpam-5051	154	20	.	.	PUNCT
ejpam-5051	155	1	let	let	VERB
ejpam-5051	155	2	σ	σ	NOUN
ejpam-5051	155	3	:	:	PUNCT
ejpam-5051	155	4	z	z	NOUN
ejpam-5051	155	5	7→	7→	NUM
ejpam-5051	155	6	r×	r×	NOUN
ejpam-5051	155	7	be	be	AUX
ejpam-5051	155	8	a	a	DET
ejpam-5051	155	9	continuous	continuous	ADJ
ejpam-5051	155	10	2	2	NUM
ejpam-5051	155	11	-	-	PUNCT
ejpam-5051	155	12	cocycle	cocycle	NOUN
ejpam-5051	155	13	which	which	PRON
ejpam-5051	155	14	is	be	AUX
ejpam-5051	155	15	locally	locally	ADV
ejpam-5051	155	16	constant	constant	ADJ
ejpam-5051	155	17	.	.	PUNCT
ejpam-5051	156	1	then	then	ADV
ejpam-5051	156	2	the	the	DET
ejpam-5051	156	3	set	set	PROPN
ejpam-5051	156	4	ar(z	ar(z	PROPN
ejpam-5051	156	5	,	,	PUNCT
ejpam-5051	156	6	σ	σ	PROPN
ejpam-5051	156	7	)	)	PUNCT
ejpam-5051	156	8	=	=	PRON
ejpam-5051	156	9	span	span	NOUN
ejpam-5051	156	10	{	{	PUNCT
ejpam-5051	156	11	1{z	1{z	NUM
ejpam-5051	156	12	}	}	PUNCT
ejpam-5051	156	13	:	:	PUNCT
ejpam-5051	156	14	z	z	X
ejpam-5051	156	15	7→	7→	NUM
ejpam-5051	156	16	r	r	NOUN
ejpam-5051	156	17	|{z	|{z	NOUN
ejpam-5051	156	18	}	}	PUNCT
ejpam-5051	156	19	is	be	AUX
ejpam-5051	156	20	compact	compact	ADJ
ejpam-5051	156	21	open	open	ADJ
ejpam-5051	156	22	bisection	bisection	NOUN
ejpam-5051	156	23	of	of	ADP
ejpam-5051	156	24	z	z	NOUN
ejpam-5051	156	25	}	}	PUNCT
ejpam-5051	156	26	with	with	ADP
ejpam-5051	156	27	the	the	DET
ejpam-5051	156	28	twisted	twisted	ADJ
ejpam-5051	156	29	convolution	convolution	NOUN
ejpam-5051	156	30	(	(	PUNCT
ejpam-5051	156	31	f	f	PROPN
ejpam-5051	156	32	∗σ	∗σ	PROPN
ejpam-5051	156	33	g)(z	g)(z	PUNCT
ejpam-5051	156	34	)	)	PUNCT
ejpam-5051	156	35	:	:	PUNCT
ejpam-5051	157	1	=	=	PUNCT
ejpam-5051	157	2	∑	∑	PUNCT
ejpam-5051	157	3	(	(	PUNCT
ejpam-5051	157	4	x	x	NOUN
ejpam-5051	157	5	,	,	PUNCT
ejpam-5051	157	6	y)∈z(2	y)∈z(2	NOUN
ejpam-5051	157	7	)	)	PUNCT
ejpam-5051	157	8	xy	xy	PROPN
ejpam-5051	158	1	=	=	PROPN
ejpam-5051	158	2	z	z	PROPN
ejpam-5051	158	3	σ(x	σ(x	PROPN
ejpam-5051	158	4	,	,	PUNCT
ejpam-5051	158	5	y)f(x)g(y	y)f(x)g(y	NUM
ejpam-5051	158	6	)	)	PUNCT
ejpam-5051	158	7	is	be	AUX
ejpam-5051	158	8	the	the	DET
ejpam-5051	158	9	twisted	twisted	ADJ
ejpam-5051	158	10	steinberg	steinberg	PROPN
ejpam-5051	158	11	algebra	algebra	PROPN
ejpam-5051	158	12	of	of	ADP
ejpam-5051	158	13	z	z	NOUN
ejpam-5051	158	14	over	over	ADP
ejpam-5051	158	15	r	r	NOUN
ejpam-5051	158	16	associated	associate	VERB
ejpam-5051	158	17	to	to	ADP
ejpam-5051	158	18	the	the	DET
ejpam-5051	158	19	pair	pair	NOUN
ejpam-5051	158	20	(	(	PUNCT
ejpam-5051	158	21	z	z	NOUN
ejpam-5051	158	22	,	,	PUNCT
ejpam-5051	158	23	σ	σ	PROPN
ejpam-5051	158	24	)	)	PUNCT
ejpam-5051	158	25	denoted	denote	VERB
ejpam-5051	158	26	as	as	ADP
ejpam-5051	158	27	ar(z	ar(z	PROPN
ejpam-5051	158	28	,	,	PUNCT
ejpam-5051	158	29	σ	σ	PROPN
ejpam-5051	158	30	)	)	PUNCT
ejpam-5051	158	31	.	.	PUNCT
ejpam-5051	159	1	3	3	X
ejpam-5051	159	2	.	.	X
ejpam-5051	159	3	the	the	DET
ejpam-5051	159	4	groupoid	groupoid	PROPN
ejpam-5051	159	5	â⋊r	â⋊r	PROPN
ejpam-5051	159	6	and	and	CCONJ
ejpam-5051	159	7	discrete	discrete	ADJ
ejpam-5051	159	8	twist	twist	NOUN
ejpam-5051	159	9	(	(	PUNCT
ejpam-5051	159	10	d	d	NOUN
ejpam-5051	159	11	,	,	PUNCT
ejpam-5051	159	12	i	i	PRON
ejpam-5051	159	13	,	,	PUNCT
ejpam-5051	159	14	q	q	NOUN
ejpam-5051	159	15	)	)	PUNCT
ejpam-5051	159	16	in	in	ADP
ejpam-5051	159	17	this	this	DET
ejpam-5051	159	18	section	section	NOUN
ejpam-5051	159	19	,	,	PUNCT
ejpam-5051	159	20	we	we	PRON
ejpam-5051	159	21	will	will	AUX
ejpam-5051	159	22	define	define	VERB
ejpam-5051	159	23	what	what	PRON
ejpam-5051	159	24	is	be	AUX
ejpam-5051	159	25	â⋊r	â⋊r	NOUN
ejpam-5051	159	26	from	from	ADP
ejpam-5051	159	27	a	a	DET
ejpam-5051	159	28	groupoid	groupoid	PROPN
ejpam-5051	159	29	g	g	PROPN
ejpam-5051	159	30	and	and	CCONJ
ejpam-5051	159	31	a	a	DET
ejpam-5051	159	32	commutative	commutative	ADJ
ejpam-5051	159	33	unital	unital	ADJ
ejpam-5051	159	34	ring	ring	NOUN
ejpam-5051	159	35	r	r	NOUN
ejpam-5051	159	36	,	,	PUNCT
ejpam-5051	159	37	investigate	investigate	VERB
ejpam-5051	159	38	its	its	PRON
ejpam-5051	159	39	properties	property	NOUN
ejpam-5051	159	40	and	and	CCONJ
ejpam-5051	159	41	construct	construct	VERB
ejpam-5051	159	42	the	the	DET
ejpam-5051	159	43	discrete	discrete	ADJ
ejpam-5051	159	44	twist	twist	NOUN
ejpam-5051	159	45	(	(	PUNCT
ejpam-5051	159	46	d	d	NOUN
ejpam-5051	159	47	,	,	PUNCT
ejpam-5051	159	48	i	i	PRON
ejpam-5051	159	49	,	,	PUNCT
ejpam-5051	159	50	q	q	NOUN
ejpam-5051	159	51	)	)	PUNCT
ejpam-5051	159	52	.	.	PUNCT
ejpam-5051	160	1	throughout	throughout	ADP
ejpam-5051	160	2	,	,	PUNCT
ejpam-5051	160	3	g	g	PROPN
ejpam-5051	160	4	is	be	AUX
ejpam-5051	160	5	an	an	DET
ejpam-5051	160	6	ample	ample	ADJ
ejpam-5051	160	7	hausdorff	hausdorff	NOUN
ejpam-5051	160	8	groupoid	groupoid	PROPN
ejpam-5051	160	9	.	.	PUNCT
ejpam-5051	161	1	let	let	VERB
ejpam-5051	161	2	a	a	DET
ejpam-5051	161	3	=	=	PUNCT
ejpam-5051	161	4	iso(g	iso(g	VERB
ejpam-5051	161	5	)	)	PUNCT
ejpam-5051	161	6	=	=	SYM
ejpam-5051	161	7	{	{	PUNCT
ejpam-5051	161	8	γ	γ	X
ejpam-5051	161	9	∈	∈	PROPN
ejpam-5051	161	10	g	g	NOUN
ejpam-5051	161	11	:	:	PUNCT
ejpam-5051	161	12	s(γ	s(γ	PROPN
ejpam-5051	161	13	)	)	PUNCT
ejpam-5051	161	14	=	=	PUNCT
ejpam-5051	162	1	r(γ	r(γ	NOUN
ejpam-5051	162	2	)	)	PUNCT
ejpam-5051	162	3	}	}	PUNCT
ejpam-5051	162	4	be	be	AUX
ejpam-5051	162	5	the	the	DET
ejpam-5051	162	6	isotropy	isotropy	NOUN
ejpam-5051	162	7	of	of	ADP
ejpam-5051	162	8	g.	g.	PROPN
ejpam-5051	162	9	for	for	ADP
ejpam-5051	162	10	u	u	PROPN
ejpam-5051	162	11	∈	∈	PROPN
ejpam-5051	162	12	g(0	g(0	PROPN
ejpam-5051	162	13	)	)	PUNCT
ejpam-5051	162	14	,	,	PUNCT
ejpam-5051	162	15	we	we	PRON
ejpam-5051	162	16	let	let	VERB
ejpam-5051	162	17	au	au	ADV
ejpam-5051	162	18	=	=	VERB
ejpam-5051	162	19	{	{	PUNCT
ejpam-5051	162	20	γ	γ	X
ejpam-5051	162	21	∈	∈	PROPN
ejpam-5051	162	22	a	a	DET
ejpam-5051	162	23	:	:	PUNCT
ejpam-5051	162	24	s(γ	s(γ	PROPN
ejpam-5051	162	25	)	)	PUNCT
ejpam-5051	163	1	=	=	SYM
ejpam-5051	163	2	u	u	NOUN
ejpam-5051	163	3	}	}	PUNCT
ejpam-5051	163	4	.	.	PUNCT
ejpam-5051	164	1	we	we	PRON
ejpam-5051	164	2	define	define	VERB
ejpam-5051	164	3	âu	âu	PUNCT
ejpam-5051	164	4	=	=	PUNCT
ejpam-5051	164	5	{	{	PUNCT
ejpam-5051	164	6	χ	χ	NOUN
ejpam-5051	164	7	:	:	PUNCT
ejpam-5051	164	8	au	au	X
ejpam-5051	164	9	→	→	X
ejpam-5051	164	10	r×|χ	r×|χ	NUM
ejpam-5051	164	11	is	be	AUX
ejpam-5051	164	12	a	a	DET
ejpam-5051	164	13	continuous	continuous	ADJ
ejpam-5051	164	14	group	group	NOUN
ejpam-5051	164	15	homomorphism	homomorphism	NOUN
ejpam-5051	164	16	}	}	PUNCT
ejpam-5051	164	17	with	with	ADP
ejpam-5051	164	18	au	au	ADV
ejpam-5051	164	19	and	and	CCONJ
ejpam-5051	164	20	r×	r×	NOUN
ejpam-5051	164	21	having	have	VERB
ejpam-5051	164	22	the	the	DET
ejpam-5051	164	23	subspace	subspace	NOUN
ejpam-5051	164	24	and	and	CCONJ
ejpam-5051	164	25	discrete	discrete	ADJ
ejpam-5051	164	26	topology	topology	NOUN
ejpam-5051	164	27	,	,	PUNCT
ejpam-5051	164	28	respectively	respectively	ADV
ejpam-5051	164	29	.	.	PUNCT
ejpam-5051	165	1	define	define	VERB
ejpam-5051	165	2	r	r	NOUN
ejpam-5051	165	3	=	=	SYM
ejpam-5051	165	4	g	g	NOUN
ejpam-5051	165	5	/	/	SYM
ejpam-5051	165	6	a	a	NOUN
ejpam-5051	165	7	=	=	X
ejpam-5051	165	8	{	{	PUNCT
ejpam-5051	165	9	γa	γa	NOUN
ejpam-5051	165	10	:	:	PUNCT
ejpam-5051	165	11	γ	γ	X
ejpam-5051	165	12	∈	∈	PROPN
ejpam-5051	165	13	g	g	NOUN
ejpam-5051	165	14	}	}	PUNCT
ejpam-5051	165	15	.	.	PUNCT
ejpam-5051	166	1	let	let	VERB
ejpam-5051	166	2	γ̇	γ̇	NOUN
ejpam-5051	166	3	=	=	PRON
ejpam-5051	166	4	γa	γa	NOUN
ejpam-5051	166	5	∈	∈	PROPN
ejpam-5051	166	6	r	r	PROPN
ejpam-5051	166	7	,	,	PUNCT
ejpam-5051	166	8	â	â	X
ejpam-5051	166	9	=	=	X
ejpam-5051	166	10	{	{	PUNCT
ejpam-5051	166	11	(	(	PUNCT
ejpam-5051	166	12	χ	χ	NOUN
ejpam-5051	166	13	,	,	PUNCT
ejpam-5051	166	14	u	u	NOUN
ejpam-5051	166	15	)	)	PUNCT
ejpam-5051	166	16	:	:	PUNCT
ejpam-5051	166	17	u	u	PROPN
ejpam-5051	166	18	∈	∈	PROPN
ejpam-5051	166	19	g(0	g(0	PROPN
ejpam-5051	166	20	)	)	PUNCT
ejpam-5051	166	21	,	,	PUNCT
ejpam-5051	166	22	χ	χ	PROPN
ejpam-5051	166	23	∈	∈	PROPN
ejpam-5051	166	24	âu	âu	PROPN
ejpam-5051	166	25	}	}	PUNCT
ejpam-5051	166	26	and	and	CCONJ
ejpam-5051	166	27	â⋊r	â⋊r	PROPN
ejpam-5051	166	28	=	=	SYM
ejpam-5051	166	29	{	{	PUNCT
ejpam-5051	166	30	(	(	PUNCT
ejpam-5051	166	31	χ	χ	NOUN
ejpam-5051	166	32	,	,	PUNCT
ejpam-5051	166	33	u	u	NOUN
ejpam-5051	166	34	,	,	PUNCT
ejpam-5051	166	35	γ̇	γ̇	PROPN
ejpam-5051	166	36	)	)	PUNCT
ejpam-5051	166	37	:	:	PUNCT
ejpam-5051	166	38	(	(	PUNCT
ejpam-5051	166	39	χ	χ	X
ejpam-5051	166	40	,	,	PUNCT
ejpam-5051	166	41	u	u	NOUN
ejpam-5051	166	42	)	)	PUNCT
ejpam-5051	166	43	∈	∈	PROPN
ejpam-5051	166	44	â	â	PROPN
ejpam-5051	166	45	,	,	PUNCT
ejpam-5051	166	46	r(γ	r(γ	NOUN
ejpam-5051	166	47	)	)	PUNCT
ejpam-5051	166	48	=	=	SYM
ejpam-5051	166	49	u	u	NOUN
ejpam-5051	166	50	}	}	PUNCT
ejpam-5051	166	51	.	.	PUNCT
ejpam-5051	167	1	theorem	theorem	NOUN
ejpam-5051	167	2	1	1	NUM
ejpam-5051	167	3	.	.	PUNCT
ejpam-5051	168	1	let	let	VERB
ejpam-5051	168	2	g	g	PRON
ejpam-5051	168	3	be	be	AUX
ejpam-5051	168	4	an	an	DET
ejpam-5051	168	5	ample	ample	ADJ
ejpam-5051	168	6	hausdorff	hausdorff	NOUN
ejpam-5051	168	7	groupoid	groupoid	PROPN
ejpam-5051	168	8	and	and	CCONJ
ejpam-5051	168	9	r	r	NOUN
ejpam-5051	168	10	be	be	VERB
ejpam-5051	168	11	a	a	DET
ejpam-5051	168	12	commutative	commutative	ADJ
ejpam-5051	168	13	unital	unital	ADJ
ejpam-5051	168	14	ring	ring	NOUN
ejpam-5051	168	15	.	.	PUNCT
ejpam-5051	169	1	then	then	ADV
ejpam-5051	169	2	r	r	NOUN
ejpam-5051	169	3	is	be	AUX
ejpam-5051	169	4	an	an	DET
ejpam-5051	169	5	ample	ample	ADJ
ejpam-5051	169	6	hausdorff	hausdorff	NOUN
ejpam-5051	169	7	groupoid	groupoid	PROPN
ejpam-5051	169	8	.	.	PUNCT
ejpam-5051	170	1	proof	proof	NOUN
ejpam-5051	170	2	.	.	PUNCT
ejpam-5051	171	1	let	let	VERB
ejpam-5051	171	2	m	m	PRON
ejpam-5051	171	3	:	:	PUNCT
ejpam-5051	171	4	r(2	r(2	NOUN
ejpam-5051	171	5	)	)	PUNCT
ejpam-5051	171	6	→	→	PUNCT
ejpam-5051	171	7	r	r	NOUN
ejpam-5051	171	8	be	be	VERB
ejpam-5051	171	9	the	the	DET
ejpam-5051	171	10	composition	composition	NOUN
ejpam-5051	171	11	map	map	NOUN
ejpam-5051	171	12	defined	define	VERB
ejpam-5051	171	13	by	by	ADP
ejpam-5051	171	14	m((α̇	m((α̇	NOUN
ejpam-5051	171	15	,	,	PUNCT
ejpam-5051	171	16	β̇	β̇	NOUN
ejpam-5051	171	17	)	)	PUNCT
ejpam-5051	171	18	)	)	PUNCT
ejpam-5051	172	1	=	=	SYM
ejpam-5051	172	2	α̇β	α̇β	PROPN
ejpam-5051	172	3	=	=	PUNCT
ejpam-5051	172	4	αβa	αβa	PROPN
ejpam-5051	172	5	where	where	SCONJ
ejpam-5051	172	6	αβ	αβ	DET
ejpam-5051	172	7	∈	∈	PROPN
ejpam-5051	172	8	g	g	PROPN
ejpam-5051	172	9	and	and	CCONJ
ejpam-5051	172	10	(	(	PUNCT
ejpam-5051	172	11	α	α	NOUN
ejpam-5051	172	12	,	,	PUNCT
ejpam-5051	172	13	β	β	NOUN
ejpam-5051	172	14	)	)	PUNCT
ejpam-5051	172	15	∈	∈	PROPN
ejpam-5051	172	16	g(2	g(2	PROPN
ejpam-5051	172	17	)	)	PUNCT
ejpam-5051	172	18	and	and	CCONJ
ejpam-5051	172	19	i	i	PRON
ejpam-5051	172	20	:	:	PUNCT
ejpam-5051	172	21	r	r	NOUN
ejpam-5051	172	22	→	→	SYM
ejpam-5051	172	23	r	r	NOUN
ejpam-5051	172	24	be	be	AUX
ejpam-5051	172	25	defined	define	VERB
ejpam-5051	172	26	by	by	ADP
ejpam-5051	172	27	i(γ̇	i(γ̇	PROPN
ejpam-5051	172	28	)	)	PUNCT
ejpam-5051	172	29	=	=	SYM
ejpam-5051	172	30	γ̇−1	γ̇−1	NOUN
ejpam-5051	172	31	=	=	SYM
ejpam-5051	172	32	γ−1a	γ−1a	PROPN
ejpam-5051	172	33	.	.	PUNCT
ejpam-5051	173	1	r.	r.	PROPN
ejpam-5051	173	2	s.	s.	PROPN
ejpam-5051	173	3	bongcawel	bongcawel	PROPN
ejpam-5051	174	1	et	et	PROPN
ejpam-5051	174	2	al	al	PROPN
ejpam-5051	174	3	.	.	PUNCT
ejpam-5051	174	4	/	/	SYM
ejpam-5051	174	5	eur	eur	PROPN
ejpam-5051	174	6	.	.	PUNCT
ejpam-5051	175	1	j.	j.	PROPN
ejpam-5051	175	2	pure	pure	PROPN
ejpam-5051	175	3	appl	appl	PROPN
ejpam-5051	175	4	.	.	PROPN
ejpam-5051	175	5	math	math	PROPN
ejpam-5051	175	6	,	,	PUNCT
ejpam-5051	175	7	17	17	NUM
ejpam-5051	175	8	(	(	PUNCT
ejpam-5051	175	9	1	1	NUM
ejpam-5051	175	10	)	)	PUNCT
ejpam-5051	175	11	(	(	PUNCT
ejpam-5051	175	12	2024	2024	NUM
ejpam-5051	175	13	)	)	PUNCT
ejpam-5051	175	14	,	,	PUNCT
ejpam-5051	175	15	519	519	NUM
ejpam-5051	175	16	-	-	SYM
ejpam-5051	175	17	545	545	NUM
ejpam-5051	175	18	525	525	NUM
ejpam-5051	175	19	let	let	VERB
ejpam-5051	175	20	(	(	PUNCT
ejpam-5051	175	21	α̇	α̇	NOUN
ejpam-5051	175	22	,	,	PUNCT
ejpam-5051	175	23	β̇	β̇	PROPN
ejpam-5051	175	24	)	)	PUNCT
ejpam-5051	175	25	,	,	PUNCT
ejpam-5051	175	26	(	(	PUNCT
ejpam-5051	175	27	γ̇	γ̇	ADV
ejpam-5051	175	28	,	,	PUNCT
ejpam-5051	175	29	µ̇	µ̇	INTJ
ejpam-5051	175	30	)	)	PUNCT
ejpam-5051	175	31	∈	∈	PROPN
ejpam-5051	175	32	r(2	r(2	PROPN
ejpam-5051	175	33	)	)	PUNCT
ejpam-5051	175	34	such	such	ADJ
ejpam-5051	175	35	that	that	SCONJ
ejpam-5051	175	36	(	(	PUNCT
ejpam-5051	175	37	α̇	α̇	NOUN
ejpam-5051	175	38	,	,	PUNCT
ejpam-5051	175	39	β̇	β̇	PROPN
ejpam-5051	175	40	)	)	PUNCT
ejpam-5051	175	41	=	=	SYM
ejpam-5051	176	1	(	(	PUNCT
ejpam-5051	176	2	γ̇	γ̇	PROPN
ejpam-5051	176	3	,	,	PUNCT
ejpam-5051	176	4	µ̇	µ̇	PROPN
ejpam-5051	176	5	)	)	PUNCT
ejpam-5051	176	6	.	.	PUNCT
ejpam-5051	177	1	then	then	ADV
ejpam-5051	177	2	αa	αa	ADV
ejpam-5051	177	3	=	=	VERB
ejpam-5051	177	4	γa	γa	PROPN
ejpam-5051	177	5	and	and	CCONJ
ejpam-5051	177	6	βa	βa	INTJ
ejpam-5051	178	1	=	=	SYM
ejpam-5051	178	2	µa	µa	PROPN
ejpam-5051	178	3	.	.	PUNCT
ejpam-5051	179	1	so	so	SCONJ
ejpam-5051	179	2	that	that	SCONJ
ejpam-5051	179	3	m((α̇	m((α̇	NOUN
ejpam-5051	179	4	,	,	PUNCT
ejpam-5051	179	5	β̇	β̇	NOUN
ejpam-5051	179	6	)	)	PUNCT
ejpam-5051	179	7	)	)	PUNCT
ejpam-5051	180	1	=	=	SYM
ejpam-5051	180	2	αβa	αβa	NOUN
ejpam-5051	180	3	=	=	SYM
ejpam-5051	180	4	αaβa	αaβa	NOUN
ejpam-5051	180	5	=	=	NOUN
ejpam-5051	180	6	γaµa	γaµa	NOUN
ejpam-5051	180	7	=	=	SYM
ejpam-5051	180	8	γµa	γµa	NOUN
ejpam-5051	180	9	=	=	SYM
ejpam-5051	180	10	m((γ̇	m((γ̇	PROPN
ejpam-5051	180	11	,	,	PUNCT
ejpam-5051	180	12	µ̇	µ̇	PROPN
ejpam-5051	180	13	)	)	PUNCT
ejpam-5051	180	14	)	)	PUNCT
ejpam-5051	180	15	.	.	PUNCT
ejpam-5051	181	1	thus	thus	ADV
ejpam-5051	181	2	,	,	PUNCT
ejpam-5051	181	3	m	m	VERB
ejpam-5051	181	4	is	be	AUX
ejpam-5051	181	5	well	well	ADV
ejpam-5051	181	6	-	-	PUNCT
ejpam-5051	181	7	defined	define	VERB
ejpam-5051	181	8	.	.	PUNCT
ejpam-5051	182	1	for	for	ADP
ejpam-5051	182	2	α̇	α̇	PROPN
ejpam-5051	182	3	,	,	PUNCT
ejpam-5051	182	4	γ̇	γ̇	PROPN
ejpam-5051	182	5	∈	∈	NOUN
ejpam-5051	182	6	r	r	NOUN
ejpam-5051	182	7	with	with	ADP
ejpam-5051	182	8	α̇	α̇	NOUN
ejpam-5051	182	9	=	=	SYM
ejpam-5051	182	10	γ̇	γ̇	PROPN
ejpam-5051	182	11	,	,	PUNCT
ejpam-5051	182	12	i(γ̇	i(γ̇	PROPN
ejpam-5051	182	13	)	)	PUNCT
ejpam-5051	182	14	=	=	VERB
ejpam-5051	183	1	γ−1a	γ−1a	PUNCT
ejpam-5051	183	2	=	=	PUNCT
ejpam-5051	183	3	α−1a	α−1a	PROPN
ejpam-5051	183	4	=	=	PUNCT
ejpam-5051	183	5	i(α̇	i(α̇	X
ejpam-5051	183	6	)	)	PUNCT
ejpam-5051	183	7	.	.	PUNCT
ejpam-5051	184	1	also	also	ADV
ejpam-5051	184	2	,	,	PUNCT
ejpam-5051	184	3	for	for	ADP
ejpam-5051	184	4	γ̇	γ̇	NOUN
ejpam-5051	184	5	,	,	PUNCT
ejpam-5051	184	6	β̇	β̇	PROPN
ejpam-5051	184	7	∈	∈	PROPN
ejpam-5051	184	8	r	r	NOUN
ejpam-5051	184	9	with	with	ADP
ejpam-5051	184	10	γ̇	γ̇	NOUN
ejpam-5051	184	11	=	=	SYM
ejpam-5051	184	12	β̇	β̇	PROPN
ejpam-5051	184	13	,	,	PUNCT
ejpam-5051	184	14	s(γ̇	s(γ̇	PROPN
ejpam-5051	184	15	)	)	PUNCT
ejpam-5051	184	16	=	=	SYM
ejpam-5051	184	17	γ̇−1γ̇	γ̇−1γ̇	NOUN
ejpam-5051	184	18	=	=	SYM
ejpam-5051	184	19	(	(	PUNCT
ejpam-5051	184	20	γa)−1γa	γa)−1γa	NOUN
ejpam-5051	184	21	=	=	SYM
ejpam-5051	184	22	γ−1aγa	γ−1aγa	NOUN
ejpam-5051	184	23	=	=	PUNCT
ejpam-5051	184	24	β−1aβa	β−1aβa	PROPN
ejpam-5051	184	25	=	=	SYM
ejpam-5051	184	26	β̇−1β̇	β̇−1β̇	NOUN
ejpam-5051	184	27	=	=	SYM
ejpam-5051	184	28	s(β̇	s(β̇	NOUN
ejpam-5051	184	29	)	)	PUNCT
ejpam-5051	184	30	;	;	PUNCT
ejpam-5051	184	31	r(γ̇	r(γ̇	X
ejpam-5051	184	32	)	)	PUNCT
ejpam-5051	184	33	=	=	SYM
ejpam-5051	185	1	γ̇γ̇−1	γ̇γ̇−1	NOUN
ejpam-5051	185	2	=	=	SYM
ejpam-5051	185	3	γaγ−1a	γaγ−1a	PROPN
ejpam-5051	185	4	=	=	PUNCT
ejpam-5051	186	1	βaβ−1a	βaβ−1a	PROPN
ejpam-5051	186	2	=	=	PUNCT
ejpam-5051	187	1	β̇β̇−1	β̇β̇−1	PUNCT
ejpam-5051	187	2	=	=	PUNCT
ejpam-5051	188	1	r(β̇	r(β̇	NOUN
ejpam-5051	188	2	)	)	PUNCT
ejpam-5051	188	3	.	.	PUNCT
ejpam-5051	189	1	thus	thus	ADV
ejpam-5051	189	2	,	,	PUNCT
ejpam-5051	189	3	the	the	DET
ejpam-5051	189	4	inverse	inverse	NOUN
ejpam-5051	189	5	,	,	PUNCT
ejpam-5051	189	6	source	source	NOUN
ejpam-5051	189	7	and	and	CCONJ
ejpam-5051	189	8	range	range	NOUN
ejpam-5051	189	9	maps	map	NOUN
ejpam-5051	189	10	are	be	AUX
ejpam-5051	189	11	also	also	ADV
ejpam-5051	189	12	well	well	ADV
ejpam-5051	189	13	-	-	PUNCT
ejpam-5051	189	14	defined	define	VERB
ejpam-5051	189	15	.	.	PUNCT
ejpam-5051	190	1	let	let	VERB
ejpam-5051	190	2	(	(	PUNCT
ejpam-5051	190	3	α̇	α̇	NOUN
ejpam-5051	190	4	,	,	PUNCT
ejpam-5051	190	5	β̇	β̇	PROPN
ejpam-5051	190	6	)	)	PUNCT
ejpam-5051	190	7	,	,	PUNCT
ejpam-5051	190	8	(	(	PUNCT
ejpam-5051	190	9	β̇	β̇	NOUN
ejpam-5051	190	10	,	,	PUNCT
ejpam-5051	190	11	γ̇	γ̇	ADJ
ejpam-5051	190	12	)	)	PUNCT
ejpam-5051	190	13	∈	∈	PROPN
ejpam-5051	190	14	r(2	r(2	PROPN
ejpam-5051	190	15	)	)	PUNCT
ejpam-5051	190	16	.	.	PUNCT
ejpam-5051	191	1	then	then	ADV
ejpam-5051	191	2	s(α̇	s(α̇	X
ejpam-5051	191	3	)	)	PUNCT
ejpam-5051	191	4	=	=	SYM
ejpam-5051	192	1	β̇β̇−1	β̇β̇−1	NOUN
ejpam-5051	192	2	and	and	CCONJ
ejpam-5051	192	3	s(β̇	s(β̇	ADJ
ejpam-5051	192	4	)	)	PUNCT
ejpam-5051	193	1	=	=	NOUN
ejpam-5051	193	2	γ̇γ̇−1	γ̇γ̇−1	NOUN
ejpam-5051	193	3	since	since	SCONJ
ejpam-5051	193	4	α	α	PROPN
ejpam-5051	193	5	and	and	CCONJ
ejpam-5051	193	6	β	β	X
ejpam-5051	193	7	are	be	AUX
ejpam-5051	193	8	composable	composable	ADJ
ejpam-5051	193	9	.	.	PUNCT
ejpam-5051	194	1	hence	hence	ADV
ejpam-5051	194	2	,	,	PUNCT
ejpam-5051	194	3	s(α̇β	s(α̇β	PROPN
ejpam-5051	194	4	)	)	PUNCT
ejpam-5051	194	5	=	=	SYM
ejpam-5051	194	6	(	(	PUNCT
ejpam-5051	194	7	α̇β)−1(α̇β	α̇β)−1(α̇β	NOUN
ejpam-5051	194	8	)	)	PUNCT
ejpam-5051	194	9	=	=	SYM
ejpam-5051	194	10	(	(	PUNCT
ejpam-5051	194	11	αβa)−1(αβa	αβa)−1(αβa	PROPN
ejpam-5051	194	12	)	)	PUNCT
ejpam-5051	194	13	=	=	SYM
ejpam-5051	195	1	β−1α−1aαβa	β−1α−1aαβa	PUNCT
ejpam-5051	196	1	=	=	PUNCT
ejpam-5051	196	2	α−1αβ−1βa	α−1αβ−1βa	NOUN
ejpam-5051	196	3	=	=	SYM
ejpam-5051	196	4	s(αβ)a	s(αβ)a	PROPN
ejpam-5051	196	5	=	=	PUNCT
ejpam-5051	196	6	s(β)a	s(β)a	PROPN
ejpam-5051	196	7	,	,	PUNCT
ejpam-5051	196	8	=	=	SYM
ejpam-5051	196	9	β−1βa	β−1βa	NOUN
ejpam-5051	196	10	.	.	PUNCT
ejpam-5051	197	1	also	also	ADV
ejpam-5051	197	2	,	,	PUNCT
ejpam-5051	197	3	r(γ̇	r(γ̇	PROPN
ejpam-5051	197	4	)	)	PUNCT
ejpam-5051	197	5	=	=	SYM
ejpam-5051	198	1	γ̇γ̇−1	γ̇γ̇−1	NOUN
ejpam-5051	198	2	=	=	SYM
ejpam-5051	198	3	β̇−1β̇	β̇−1β̇	NOUN
ejpam-5051	198	4	=	=	X
ejpam-5051	198	5	β−1β	β−1β	PUNCT
ejpam-5051	198	6	a.	a.	NOUN
ejpam-5051	198	7	hence	hence	ADV
ejpam-5051	198	8	,	,	PUNCT
ejpam-5051	198	9	s(α̇β	s(α̇β	PROPN
ejpam-5051	198	10	)	)	PUNCT
ejpam-5051	198	11	=	=	SYM
ejpam-5051	198	12	r(γ̇	r(γ̇	PROPN
ejpam-5051	198	13	)	)	PUNCT
ejpam-5051	198	14	.	.	PUNCT
ejpam-5051	199	1	thus	thus	ADV
ejpam-5051	199	2	,	,	PUNCT
ejpam-5051	199	3	(	(	PUNCT
ejpam-5051	199	4	α̇β̇	α̇β̇	NOUN
ejpam-5051	199	5	,	,	PUNCT
ejpam-5051	199	6	γ̇	γ̇	NOUN
ejpam-5051	199	7	)	)	PUNCT
ejpam-5051	199	8	∈	∈	PROPN
ejpam-5051	199	9	r(2	r(2	PROPN
ejpam-5051	199	10	)	)	PUNCT
ejpam-5051	199	11	.	.	PUNCT
ejpam-5051	200	1	we	we	PRON
ejpam-5051	200	2	also	also	ADV
ejpam-5051	200	3	have	have	VERB
ejpam-5051	200	4	β̇γ̇	β̇γ̇	NOUN
ejpam-5051	200	5	=	=	PUNCT
ejpam-5051	200	6	β̇γ	β̇γ	PROPN
ejpam-5051	200	7	.	.	PROPN
ejpam-5051	201	1	hence	hence	ADV
ejpam-5051	201	2	,	,	PUNCT
ejpam-5051	201	3	r(β̇γ	r(β̇γ	PROPN
ejpam-5051	201	4	)	)	PUNCT
ejpam-5051	201	5	=	=	PRON
ejpam-5051	202	1	(	(	PUNCT
ejpam-5051	202	2	β̇γ)(β̇γ)−1	β̇γ)(β̇γ)−1	SYM
ejpam-5051	202	3	=	=	SYM
ejpam-5051	202	4	(	(	PUNCT
ejpam-5051	202	5	βγa)(βγa	βγa)(βγa	ADV
ejpam-5051	202	6	=	=	SYM
ejpam-5051	202	7	βγaγ−1β−1a	βγaγ−1β−1a	PROPN
ejpam-5051	202	8	=	=	PUNCT
ejpam-5051	202	9	ββ−1γγ−1a	ββ−1γγ−1a	PUNCT
ejpam-5051	203	1	=	=	PUNCT
ejpam-5051	203	2	r(βγ)a	r(βγ)a	NOUN
ejpam-5051	203	3	=	=	PUNCT
ejpam-5051	203	4	r(β)a	r(β)a	PROPN
ejpam-5051	203	5	=	=	PUNCT
ejpam-5051	204	1	ββ−1a	ββ−1a	PROPN
ejpam-5051	204	2	.	.	PUNCT
ejpam-5051	205	1	since	since	SCONJ
ejpam-5051	205	2	s(α̇	s(α̇	X
ejpam-5051	205	3	)	)	PUNCT
ejpam-5051	205	4	=	=	SYM
ejpam-5051	205	5	α̇−1α̇	α̇−1α̇	NOUN
ejpam-5051	205	6	=	=	PUNCT
ejpam-5051	205	7	β̇β̇−1	β̇β̇−1	NOUN
ejpam-5051	206	1	=	=	PUNCT
ejpam-5051	207	1	βaβ−1a	βaβ−1a	PUNCT
ejpam-5051	207	2	=	=	PUNCT
ejpam-5051	208	1	ββ−1a	ββ−1a	PROPN
ejpam-5051	208	2	,	,	PUNCT
ejpam-5051	208	3	then	then	ADV
ejpam-5051	208	4	r(β̇γ̇	r(β̇γ̇	X
ejpam-5051	208	5	)	)	PUNCT
ejpam-5051	208	6	=	=	SYM
ejpam-5051	208	7	s(α̇	s(α̇	X
ejpam-5051	208	8	)	)	PUNCT
ejpam-5051	208	9	and	and	CCONJ
ejpam-5051	208	10	(	(	PUNCT
ejpam-5051	208	11	α̇	α̇	NOUN
ejpam-5051	208	12	,	,	PUNCT
ejpam-5051	208	13	β̇γ̇	β̇γ̇	NOUN
ejpam-5051	208	14	)	)	PUNCT
ejpam-5051	208	15	∈	∈	PROPN
ejpam-5051	208	16	r(2	r(2	PROPN
ejpam-5051	208	17	)	)	PUNCT
ejpam-5051	208	18	.	.	PUNCT
ejpam-5051	209	1	now	now	ADV
ejpam-5051	209	2	,	,	PUNCT
ejpam-5051	209	3	(	(	PUNCT
ejpam-5051	209	4	α̇β̇)γ̇	α̇β̇)γ̇	NOUN
ejpam-5051	209	5	=	=	SYM
ejpam-5051	209	6	(	(	PUNCT
ejpam-5051	209	7	αβa)γa	αβa)γa	NOUN
ejpam-5051	209	8	=	=	SYM
ejpam-5051	209	9	(	(	PUNCT
ejpam-5051	209	10	αa(βγa	αa(βγa	ADJ
ejpam-5051	209	11	)	)	PUNCT
ejpam-5051	209	12	)	)	PUNCT
ejpam-5051	209	13	=	=	SYM
ejpam-5051	209	14	α̇(β̇γ	α̇(β̇γ	NOUN
ejpam-5051	209	15	)	)	PUNCT
ejpam-5051	209	16	=	=	SYM
ejpam-5051	209	17	α̇(β̇γ̇	α̇(β̇γ̇	NOUN
ejpam-5051	209	18	)	)	PUNCT
ejpam-5051	209	19	.	.	PUNCT
ejpam-5051	210	1	let	let	VERB
ejpam-5051	210	2	γ̇	γ̇	PROPN
ejpam-5051	210	3	∈	∈	PROPN
ejpam-5051	210	4	r.	r.	PROPN
ejpam-5051	210	5	now	now	ADV
ejpam-5051	210	6	,	,	PUNCT
ejpam-5051	210	7	(	(	PUNCT
ejpam-5051	210	8	γ̇−1)−1	γ̇−1)−1	X
ejpam-5051	210	9	=	=	SYM
ejpam-5051	210	10	(	(	PUNCT
ejpam-5051	210	11	γ−1a)−1	γ−1a)−1	NOUN
ejpam-5051	210	12	=	=	SYM
ejpam-5051	210	13	(	(	PUNCT
ejpam-5051	210	14	γ1)−1a	γ1)−1a	NOUN
ejpam-5051	210	15	=	=	X
ejpam-5051	210	16	γa	γa	PROPN
ejpam-5051	210	17	=	=	PUNCT
ejpam-5051	210	18	γ̇.	γ̇.	NUM
ejpam-5051	210	19	for	for	ADP
ejpam-5051	210	20	γ̇	γ̇	PROPN
ejpam-5051	210	21	∈	∈	PROPN
ejpam-5051	210	22	r	r	NOUN
ejpam-5051	210	23	,	,	PUNCT
ejpam-5051	210	24	r(γ̇−1	r(γ̇−1	NOUN
ejpam-5051	210	25	)	)	PUNCT
ejpam-5051	210	26	=	=	SYM
ejpam-5051	210	27	γ̇−1(γ̇−1)−1	γ̇−1(γ̇−1)−1	NUM
ejpam-5051	210	28	=	=	SYM
ejpam-5051	210	29	γ̇−1γ̇.	γ̇−1γ̇.	PUNCT
ejpam-5051	210	30	hence	hence	ADV
ejpam-5051	210	31	,	,	PUNCT
ejpam-5051	210	32	(	(	PUNCT
ejpam-5051	210	33	γ̇	γ̇	NOUN
ejpam-5051	210	34	,	,	PUNCT
ejpam-5051	210	35	γ̇−1	γ̇−1	PROPN
ejpam-5051	210	36	)	)	PUNCT
ejpam-5051	210	37	∈	∈	PROPN
ejpam-5051	210	38	r(2	r(2	PROPN
ejpam-5051	210	39	)	)	PUNCT
ejpam-5051	210	40	.	.	PUNCT
ejpam-5051	211	1	let	let	VERB
ejpam-5051	211	2	(	(	PUNCT
ejpam-5051	211	3	β̇	β̇	NOUN
ejpam-5051	211	4	,	,	PUNCT
ejpam-5051	211	5	γ̇	γ̇	ADJ
ejpam-5051	211	6	)	)	PUNCT
ejpam-5051	211	7	∈	∈	PROPN
ejpam-5051	211	8	r(2	r(2	PROPN
ejpam-5051	211	9	)	)	PUNCT
ejpam-5051	211	10	.	.	PUNCT
ejpam-5051	212	1	then	then	ADV
ejpam-5051	212	2	,	,	PUNCT
ejpam-5051	212	3	(	(	PUNCT
ejpam-5051	212	4	β̇γ̇)γ̇−1	β̇γ̇)γ̇−1	NOUN
ejpam-5051	212	5	=	=	SYM
ejpam-5051	212	6	β̇(γ̇γ̇−1	β̇(γ̇γ̇−1	PROPN
ejpam-5051	212	7	)	)	PUNCT
ejpam-5051	212	8	=	=	SYM
ejpam-5051	212	9	β̇r(γ̇	β̇r(γ̇	X
ejpam-5051	212	10	)	)	PUNCT
ejpam-5051	212	11	=	=	SYM
ejpam-5051	212	12	β̇s(β̇	β̇s(β̇	X
ejpam-5051	212	13	)	)	PUNCT
ejpam-5051	212	14	=	=	SYM
ejpam-5051	212	15	β̇	β̇	PROPN
ejpam-5051	212	16	and	and	CCONJ
ejpam-5051	212	17	γ̇−1(γ̇β̇	γ̇−1(γ̇β̇	NOUN
ejpam-5051	212	18	)	)	PUNCT
ejpam-5051	212	19	=	=	PUNCT
ejpam-5051	212	20	(	(	PUNCT
ejpam-5051	212	21	γ̇−1γ̇)β̇	γ̇−1γ̇)β̇	NOUN
ejpam-5051	212	22	=	=	SYM
ejpam-5051	212	23	s(γ̇)β̇	s(γ̇)β̇	NOUN
ejpam-5051	212	24	=	=	SYM
ejpam-5051	212	25	r(β̇)β̇	r(β̇)β̇	NOUN
ejpam-5051	212	26	=	=	PUNCT
ejpam-5051	212	27	β̇.	β̇.	NUM
ejpam-5051	212	28	thus	thus	ADV
ejpam-5051	212	29	,	,	PUNCT
ejpam-5051	212	30	r	r	NOUN
ejpam-5051	212	31	is	be	AUX
ejpam-5051	212	32	a	a	DET
ejpam-5051	212	33	groupoid	groupoid	NOUN
ejpam-5051	212	34	.	.	PUNCT
ejpam-5051	213	1	let	let	VERB
ejpam-5051	213	2	r	r	PRON
ejpam-5051	213	3	be	be	AUX
ejpam-5051	213	4	a	a	DET
ejpam-5051	213	5	topological	topological	ADJ
ejpam-5051	213	6	space	space	NOUN
ejpam-5051	213	7	with	with	ADP
ejpam-5051	213	8	the	the	DET
ejpam-5051	213	9	quotient	quotient	NOUN
ejpam-5051	213	10	topology	topology	NOUN
ejpam-5051	213	11	τr	τr	AUX
ejpam-5051	213	12	.	.	PUNCT
ejpam-5051	213	13	define	define	VERB
ejpam-5051	213	14	the	the	DET
ejpam-5051	213	15	quotient	quotient	NOUN
ejpam-5051	213	16	map	map	NOUN
ejpam-5051	214	1	πr	πr	SCONJ
ejpam-5051	214	2	:	:	PUNCT
ejpam-5051	214	3	g	g	NOUN
ejpam-5051	214	4	→	→	SYM
ejpam-5051	214	5	r	r	NOUN
ejpam-5051	214	6	by	by	ADP
ejpam-5051	214	7	πr(α	πr(α	NOUN
ejpam-5051	214	8	)	)	PUNCT
ejpam-5051	214	9	=	=	SYM
ejpam-5051	214	10	αa	αa	NOUN
ejpam-5051	214	11	=	=	PUNCT
ejpam-5051	214	12	α̇.	α̇.	PUNCT
ejpam-5051	214	13	define	define	VERB
ejpam-5051	214	14	the	the	DET
ejpam-5051	214	15	topology	topology	NOUN
ejpam-5051	214	16	for	for	ADP
ejpam-5051	214	17	r	r	NOUN
ejpam-5051	214	18	×	×	PROPN
ejpam-5051	214	19	r	r	NOUN
ejpam-5051	214	20	and	and	CCONJ
ejpam-5051	214	21	r(2	r(2	PROPN
ejpam-5051	214	22	)	)	PUNCT
ejpam-5051	214	23	as	as	SCONJ
ejpam-5051	214	24	follow	follow	VERB
ejpam-5051	214	25	:	:	PUNCT
ejpam-5051	214	26	τr×r	τr×r	PROPN
ejpam-5051	214	27	=	=	SYM
ejpam-5051	214	28	{	{	PUNCT
ejpam-5051	214	29	u	u	NOUN
ejpam-5051	214	30	×	×	PROPN
ejpam-5051	214	31	v	v	NOUN
ejpam-5051	214	32	:	:	PUNCT
ejpam-5051	214	33	u	u	NOUN
ejpam-5051	214	34	,	,	PUNCT
ejpam-5051	214	35	v	v	NOUN
ejpam-5051	214	36	∈	∈	PROPN
ejpam-5051	214	37	τr	τr	PUNCT
ejpam-5051	214	38	}	}	PUNCT
ejpam-5051	214	39	and	and	CCONJ
ejpam-5051	214	40	τr(2	τr(2	NOUN
ejpam-5051	214	41	)	)	PUNCT
ejpam-5051	214	42	=	=	PRON
ejpam-5051	214	43	{	{	PUNCT
ejpam-5051	214	44	(	(	PUNCT
ejpam-5051	214	45	u	u	NOUN
ejpam-5051	214	46	×	×	PROPN
ejpam-5051	214	47	v	v	NOUN
ejpam-5051	214	48	)	)	PUNCT
ejpam-5051	214	49	∩	∩	NOUN
ejpam-5051	214	50	r(2	r(2	NOUN
ejpam-5051	214	51	)	)	PUNCT
ejpam-5051	214	52	:	:	PUNCT
ejpam-5051	215	1	u	u	NOUN
ejpam-5051	215	2	×	×	NOUN
ejpam-5051	215	3	v	v	ADP
ejpam-5051	215	4	∈	∈	PROPN
ejpam-5051	215	5	τr×r	τr×r	NOUN
ejpam-5051	215	6	}	}	PUNCT
ejpam-5051	215	7	.	.	PUNCT
ejpam-5051	216	1	let	let	VERB
ejpam-5051	216	2	u	u	PRON
ejpam-5051	216	3	r.	r.	PROPN
ejpam-5051	216	4	s.	s.	PROPN
ejpam-5051	216	5	bongcawel	bongcawel	PROPN
ejpam-5051	216	6	et	et	PROPN
ejpam-5051	216	7	al	al	PROPN
ejpam-5051	216	8	.	.	PUNCT
ejpam-5051	216	9	/	/	SYM
ejpam-5051	216	10	eur	eur	PROPN
ejpam-5051	216	11	.	.	PUNCT
ejpam-5051	217	1	j.	j.	PROPN
ejpam-5051	217	2	pure	pure	PROPN
ejpam-5051	217	3	appl	appl	PROPN
ejpam-5051	217	4	.	.	PROPN
ejpam-5051	217	5	math	math	PROPN
ejpam-5051	217	6	,	,	PUNCT
ejpam-5051	217	7	17	17	NUM
ejpam-5051	217	8	(	(	PUNCT
ejpam-5051	217	9	1	1	NUM
ejpam-5051	217	10	)	)	PUNCT
ejpam-5051	217	11	(	(	PUNCT
ejpam-5051	217	12	2024	2024	NUM
ejpam-5051	217	13	)	)	PUNCT
ejpam-5051	217	14	,	,	PUNCT
ejpam-5051	217	15	519	519	NUM
ejpam-5051	217	16	-	-	SYM
ejpam-5051	217	17	545	545	NUM
ejpam-5051	217	18	526	526	NUM
ejpam-5051	217	19	be	be	AUX
ejpam-5051	217	20	an	an	DET
ejpam-5051	217	21	open	open	ADJ
ejpam-5051	217	22	set	set	NOUN
ejpam-5051	217	23	in	in	ADP
ejpam-5051	217	24	r.	r.	PROPN
ejpam-5051	217	25	then	then	ADV
ejpam-5051	217	26	v	v	ADP
ejpam-5051	217	27	=	=	SYM
ejpam-5051	218	1	π−1	π−1	PROPN
ejpam-5051	218	2	r	r	NOUN
ejpam-5051	218	3	(	(	PUNCT
ejpam-5051	218	4	u	u	NOUN
ejpam-5051	218	5	)	)	PUNCT
ejpam-5051	218	6	is	be	AUX
ejpam-5051	218	7	open	open	ADJ
ejpam-5051	218	8	in	in	ADP
ejpam-5051	218	9	g.	g.	PROPN
ejpam-5051	218	10	let	let	VERB
ejpam-5051	218	11	(	(	PUNCT
ejpam-5051	218	12	γ̇	γ̇	ADV
ejpam-5051	218	13	,	,	PUNCT
ejpam-5051	218	14	β̇	β̇	PROPN
ejpam-5051	218	15	)	)	PUNCT
ejpam-5051	218	16	∈	∈	PROPN
ejpam-5051	218	17	m−1(u	m−1(u	PROPN
ejpam-5051	218	18	)	)	PUNCT
ejpam-5051	219	1	⊆	⊆	NUM
ejpam-5051	219	2	r(2	r(2	NOUN
ejpam-5051	219	3	)	)	PUNCT
ejpam-5051	219	4	.	.	PUNCT
ejpam-5051	220	1	then	then	ADV
ejpam-5051	220	2	π(γ)π(β	π(γ)π(β	NOUN
ejpam-5051	220	3	)	)	PUNCT
ejpam-5051	220	4	∈	∈	PROPN
ejpam-5051	220	5	u	u	NOUN
ejpam-5051	220	6	,	,	PUNCT
ejpam-5051	220	7	i.e.	i.e.	X
ejpam-5051	220	8	,	,	PUNCT
ejpam-5051	220	9	(	(	PUNCT
ejpam-5051	220	10	γ̇	γ̇	ADV
ejpam-5051	220	11	,	,	PUNCT
ejpam-5051	220	12	β̇	β̇	PROPN
ejpam-5051	220	13	)	)	PUNCT
ejpam-5051	220	14	∈	∈	NOUN
ejpam-5051	220	15	u	u	NOUN
ejpam-5051	220	16	×	×	PROPN
ejpam-5051	220	17	u	u	NOUN
ejpam-5051	220	18	and	and	CCONJ
ejpam-5051	220	19	(	(	PUNCT
ejpam-5051	220	20	γ̇	γ̇	PROPN
ejpam-5051	220	21	,	,	PUNCT
ejpam-5051	220	22	β̇	β̇	NOUN
ejpam-5051	220	23	)	)	PUNCT
ejpam-5051	220	24	∈	∈	PROPN
ejpam-5051	220	25	(	(	PUNCT
ejpam-5051	220	26	u	u	NOUN
ejpam-5051	220	27	×	×	PROPN
ejpam-5051	220	28	u	u	NOUN
ejpam-5051	220	29	)	)	PUNCT
ejpam-5051	220	30	∩	∩	ADJ
ejpam-5051	220	31	r(2	r(2	PROPN
ejpam-5051	220	32	)	)	PUNCT
ejpam-5051	220	33	∈	∈	PROPN
ejpam-5051	220	34	τr(2	τr(2	NOUN
ejpam-5051	220	35	)	)	PUNCT
ejpam-5051	220	36	since	since	SCONJ
ejpam-5051	220	37	u	u	PRON
ejpam-5051	220	38	×	×	PROPN
ejpam-5051	220	39	u	u	X
ejpam-5051	220	40	∈	∈	PROPN
ejpam-5051	220	41	τr×r	τr×r	NOUN
ejpam-5051	220	42	.	.	PUNCT
ejpam-5051	221	1	since	since	SCONJ
ejpam-5051	221	2	(	(	PUNCT
ejpam-5051	221	3	α̇	α̇	NOUN
ejpam-5051	221	4	,	,	PUNCT
ejpam-5051	221	5	β̇	β̇	PROPN
ejpam-5051	221	6	)	)	PUNCT
ejpam-5051	221	7	is	be	AUX
ejpam-5051	221	8	chosen	choose	VERB
ejpam-5051	221	9	arbitrarily	arbitrarily	ADV
ejpam-5051	221	10	,	,	PUNCT
ejpam-5051	221	11	every	every	DET
ejpam-5051	221	12	element	element	NOUN
ejpam-5051	221	13	in	in	ADP
ejpam-5051	221	14	m−1(u	m−1(u	PROPN
ejpam-5051	221	15	)	)	PUNCT
ejpam-5051	221	16	is	be	AUX
ejpam-5051	221	17	contained	contain	VERB
ejpam-5051	221	18	in	in	ADP
ejpam-5051	221	19	some	some	DET
ejpam-5051	221	20	open	open	ADJ
ejpam-5051	221	21	set	set	NOUN
ejpam-5051	221	22	in	in	ADP
ejpam-5051	221	23	τr(2	τr(2	NOUN
ejpam-5051	221	24	)	)	PUNCT
ejpam-5051	221	25	and	and	CCONJ
ejpam-5051	221	26	m	m	PROPN
ejpam-5051	221	27	is	be	AUX
ejpam-5051	221	28	continuous	continuous	ADJ
ejpam-5051	221	29	.	.	PUNCT
ejpam-5051	222	1	also	also	ADV
ejpam-5051	222	2	,	,	PUNCT
ejpam-5051	222	3	let	let	VERB
ejpam-5051	222	4	m	m	PRON
ejpam-5051	222	5	be	be	AUX
ejpam-5051	222	6	an	an	DET
ejpam-5051	222	7	open	open	ADJ
ejpam-5051	222	8	set	set	NOUN
ejpam-5051	222	9	in	in	ADP
ejpam-5051	222	10	r.	r.	PROPN
ejpam-5051	222	11	then	then	ADV
ejpam-5051	222	12	there	there	PRON
ejpam-5051	222	13	exists	exist	VERB
ejpam-5051	222	14	v	v	ADP
ejpam-5051	222	15	=	=	SYM
ejpam-5051	222	16	π−1	π−1	PROPN
ejpam-5051	222	17	r	r	NOUN
ejpam-5051	222	18	(	(	PUNCT
ejpam-5051	222	19	m	m	NOUN
ejpam-5051	222	20	)	)	PUNCT
ejpam-5051	222	21	=	=	SYM
ejpam-5051	222	22	{	{	PUNCT
ejpam-5051	222	23	γ	γ	X
ejpam-5051	222	24	∈	∈	PROPN
ejpam-5051	222	25	g	g	NOUN
ejpam-5051	222	26	:	:	PUNCT
ejpam-5051	222	27	πr(γ	πr(γ	PUNCT
ejpam-5051	222	28	)	)	PUNCT
ejpam-5051	222	29	∈	∈	PROPN
ejpam-5051	222	30	m	m	NOUN
ejpam-5051	222	31	}	}	PUNCT
ejpam-5051	222	32	⊂	⊂	PROPN
ejpam-5051	222	33	g.	g.	PROPN
ejpam-5051	222	34	note	note	VERB
ejpam-5051	222	35	that	that	SCONJ
ejpam-5051	222	36	i−1(m	i−1(m	PROPN
ejpam-5051	222	37	)	)	PUNCT
ejpam-5051	222	38	=	=	SYM
ejpam-5051	222	39	πr(v	πr(v	PRON
ejpam-5051	222	40	)	)	PUNCT
ejpam-5051	223	1	=	=	SYM
ejpam-5051	223	2	{	{	PUNCT
ejpam-5051	223	3	γ	γ	X
ejpam-5051	223	4	∈	∈	PROPN
ejpam-5051	223	5	g	g	NOUN
ejpam-5051	223	6	:	:	PUNCT
ejpam-5051	223	7	πr(γ	πr(γ	PUNCT
ejpam-5051	223	8	−1	−1	NOUN
ejpam-5051	223	9	)	)	PUNCT
ejpam-5051	223	10	∈	∈	PROPN
ejpam-5051	223	11	m	m	NOUN
ejpam-5051	223	12	}	}	PUNCT
ejpam-5051	223	13	=	=	SYM
ejpam-5051	223	14	{	{	PUNCT
ejpam-5051	223	15	γ	γ	X
ejpam-5051	223	16	∈	∈	PROPN
ejpam-5051	223	17	g	g	NOUN
ejpam-5051	223	18	:	:	PUNCT
ejpam-5051	223	19	γ−1	γ−1	PROPN
ejpam-5051	223	20	∈	∈	PROPN
ejpam-5051	223	21	m	m	PRON
ejpam-5051	223	22	}	}	PUNCT
ejpam-5051	223	23	.	.	PUNCT
ejpam-5051	224	1	for	for	ADP
ejpam-5051	224	2	any	any	DET
ejpam-5051	224	3	open	open	ADJ
ejpam-5051	224	4	set	set	NOUN
ejpam-5051	224	5	u	u	NOUN
ejpam-5051	224	6	′	′	NOUN
ejpam-5051	224	7	∈	∈	PROPN
ejpam-5051	224	8	r	r	NOUN
ejpam-5051	224	9	,	,	PUNCT
ejpam-5051	224	10	π−1	π−1	PROPN
ejpam-5051	224	11	r	r	NOUN
ejpam-5051	224	12	(	(	PUNCT
ejpam-5051	224	13	u	u	NOUN
ejpam-5051	224	14	′	′	NOUN
ejpam-5051	224	15	)	)	PUNCT
ejpam-5051	224	16	is	be	AUX
ejpam-5051	224	17	open	open	ADJ
ejpam-5051	224	18	in	in	ADP
ejpam-5051	224	19	g.	g.	PROPN
ejpam-5051	224	20	in	in	ADP
ejpam-5051	224	21	particular	particular	ADJ
ejpam-5051	224	22	,	,	PUNCT
ejpam-5051	224	23	v	v	NOUN
ejpam-5051	224	24	=	=	SYM
ejpam-5051	224	25	π−1	π−1	PROPN
ejpam-5051	224	26	r	r	NOUN
ejpam-5051	224	27	(	(	PUNCT
ejpam-5051	224	28	m	m	NOUN
ejpam-5051	224	29	)	)	PUNCT
ejpam-5051	224	30	is	be	AUX
ejpam-5051	224	31	open	open	ADJ
ejpam-5051	224	32	in	in	ADP
ejpam-5051	224	33	g.	g.	PROPN
ejpam-5051	225	1	it	it	PRON
ejpam-5051	225	2	follows	follow	VERB
ejpam-5051	225	3	that	that	SCONJ
ejpam-5051	225	4	πr(v	πr(v	PUNCT
ejpam-5051	225	5	)	)	PUNCT
ejpam-5051	225	6	is	be	AUX
ejpam-5051	225	7	open	open	ADJ
ejpam-5051	225	8	in	in	ADP
ejpam-5051	225	9	r.	r.	PROPN
ejpam-5051	225	10	hence	hence	ADV
ejpam-5051	225	11	,	,	PUNCT
ejpam-5051	225	12	i−1(m	i−1(m	PROPN
ejpam-5051	225	13	)	)	PUNCT
ejpam-5051	225	14	is	be	AUX
ejpam-5051	225	15	open	open	ADJ
ejpam-5051	225	16	in	in	ADP
ejpam-5051	225	17	r	r	NOUN
ejpam-5051	225	18	and	and	CCONJ
ejpam-5051	225	19	i	i	PRON
ejpam-5051	225	20	is	be	AUX
ejpam-5051	225	21	continuous	continuous	ADJ
ejpam-5051	225	22	.	.	PUNCT
ejpam-5051	226	1	thus	thus	ADV
ejpam-5051	226	2	,	,	PUNCT
ejpam-5051	226	3	r	r	NOUN
ejpam-5051	226	4	is	be	AUX
ejpam-5051	226	5	a	a	DET
ejpam-5051	226	6	topological	topological	ADJ
ejpam-5051	226	7	groupoid	groupoid	NOUN
ejpam-5051	226	8	.	.	PUNCT
ejpam-5051	227	1	suppose	suppose	VERB
ejpam-5051	227	2	that	that	SCONJ
ejpam-5051	227	3	γ̇	γ̇	PROPN
ejpam-5051	227	4	and	and	CCONJ
ejpam-5051	227	5	β̇	β̇	PROPN
ejpam-5051	227	6	are	be	AUX
ejpam-5051	227	7	distinct	distinct	ADJ
ejpam-5051	227	8	points	point	NOUN
ejpam-5051	227	9	in	in	ADP
ejpam-5051	227	10	r.	r.	PROPN
ejpam-5051	227	11	then	then	ADV
ejpam-5051	227	12	for	for	ADP
ejpam-5051	227	13	γ	γ	PROPN
ejpam-5051	227	14	,	,	PUNCT
ejpam-5051	227	15	β	β	X
ejpam-5051	227	16	∈	∈	NOUN
ejpam-5051	227	17	g	g	PROPN
ejpam-5051	227	18	,	,	PUNCT
ejpam-5051	227	19	πr(γ	πr(γ	PUNCT
ejpam-5051	227	20	)	)	PUNCT
ejpam-5051	227	21	=	=	SYM
ejpam-5051	227	22	γa	γa	NOUN
ejpam-5051	227	23	and	and	CCONJ
ejpam-5051	227	24	πr(β	πr(β	PUNCT
ejpam-5051	227	25	)	)	PUNCT
ejpam-5051	228	1	=	=	SYM
ejpam-5051	228	2	βa	βa	INTJ
ejpam-5051	228	3	where	where	SCONJ
ejpam-5051	228	4	γa	γa	PROPN
ejpam-5051	228	5	̸=	̸=	PROPN
ejpam-5051	228	6	βa	βa	NUM
ejpam-5051	228	7	.	.	PUNCT
ejpam-5051	228	8	let	let	VERB
ejpam-5051	228	9	u̇	u̇	PRON
ejpam-5051	228	10	be	be	AUX
ejpam-5051	228	11	an	an	DET
ejpam-5051	228	12	open	open	ADJ
ejpam-5051	228	13	set	set	NOUN
ejpam-5051	228	14	in	in	ADP
ejpam-5051	228	15	g	g	PROPN
ejpam-5051	228	16	defined	define	VERB
ejpam-5051	228	17	as	as	ADP
ejpam-5051	228	18	u̇	u̇	NOUN
ejpam-5051	228	19	=	=	NOUN
ejpam-5051	228	20	{	{	PUNCT
ejpam-5051	228	21	α	α	NOUN
ejpam-5051	228	22	∈	∈	PROPN
ejpam-5051	228	23	g	g	NOUN
ejpam-5051	228	24	:	:	PUNCT
ejpam-5051	228	25	πr(α	πr(α	NOUN
ejpam-5051	228	26	)	)	PUNCT
ejpam-5051	228	27	̸=	̸=	PROPN
ejpam-5051	228	28	βa	βa	NUM
ejpam-5051	228	29	}	}	PUNCT
ejpam-5051	228	30	.	.	PUNCT
ejpam-5051	229	1	since	since	SCONJ
ejpam-5051	229	2	γa	γa	PROPN
ejpam-5051	229	3	̸=	̸=	PROPN
ejpam-5051	229	4	βa	βa	NUM
ejpam-5051	229	5	,	,	PUNCT
ejpam-5051	229	6	then	then	ADV
ejpam-5051	229	7	γ	γ	PROPN
ejpam-5051	229	8	∈	∈	PROPN
ejpam-5051	229	9	u̇	u̇	PROPN
ejpam-5051	229	10	.	.	PUNCT
ejpam-5051	230	1	hence	hence	ADV
ejpam-5051	230	2	,	,	PUNCT
ejpam-5051	230	3	u̇	u̇	PROPN
ejpam-5051	230	4	is	be	AUX
ejpam-5051	230	5	an	an	DET
ejpam-5051	230	6	open	open	ADJ
ejpam-5051	230	7	neighborhood	neighborhood	NOUN
ejpam-5051	230	8	in	in	ADP
ejpam-5051	230	9	g	g	NOUN
ejpam-5051	230	10	containing	contain	VERB
ejpam-5051	230	11	γ	γ	PROPN
ejpam-5051	230	12	.	.	PUNCT
ejpam-5051	231	1	now	now	ADV
ejpam-5051	231	2	,	,	PUNCT
ejpam-5051	231	3	let	let	VERB
ejpam-5051	231	4	v̇	v̇	PRON
ejpam-5051	231	5	be	be	AUX
ejpam-5051	231	6	an	an	DET
ejpam-5051	231	7	open	open	ADJ
ejpam-5051	231	8	set	set	NOUN
ejpam-5051	231	9	in	in	ADP
ejpam-5051	231	10	g	g	PROPN
ejpam-5051	231	11	defined	define	VERB
ejpam-5051	231	12	as	as	ADP
ejpam-5051	231	13	v̇	v̇	NOUN
ejpam-5051	231	14	=	=	PUNCT
ejpam-5051	231	15	{	{	PUNCT
ejpam-5051	231	16	α	α	NOUN
ejpam-5051	231	17	∈	∈	PROPN
ejpam-5051	231	18	g	g	NOUN
ejpam-5051	231	19	:	:	PUNCT
ejpam-5051	231	20	πr(α	πr(α	NOUN
ejpam-5051	231	21	)	)	PUNCT
ejpam-5051	231	22	̸=	̸=	PROPN
ejpam-5051	231	23	γa	γa	NOUN
ejpam-5051	231	24	}	}	PUNCT
ejpam-5051	231	25	.	.	PUNCT
ejpam-5051	232	1	since	since	SCONJ
ejpam-5051	232	2	βa	βa	INTJ
ejpam-5051	232	3	̸=	̸=	PROPN
ejpam-5051	232	4	γa	γa	NOUN
ejpam-5051	232	5	,	,	PUNCT
ejpam-5051	232	6	then	then	ADV
ejpam-5051	232	7	β	β	PROPN
ejpam-5051	232	8	∈	∈	PROPN
ejpam-5051	232	9	v̇	v̇	NOUN
ejpam-5051	232	10	.	.	PUNCT
ejpam-5051	233	1	hence	hence	ADV
ejpam-5051	233	2	,	,	PUNCT
ejpam-5051	233	3	v̇	v̇	NOUN
ejpam-5051	233	4	is	be	AUX
ejpam-5051	233	5	an	an	DET
ejpam-5051	233	6	open	open	ADJ
ejpam-5051	233	7	neighborhood	neighborhood	NOUN
ejpam-5051	233	8	containing	contain	VERB
ejpam-5051	233	9	β	β	X
ejpam-5051	233	10	.	.	PUNCT
ejpam-5051	234	1	let	let	VERB
ejpam-5051	234	2	α	α	PRON
ejpam-5051	234	3	∈	∈	PROPN
ejpam-5051	234	4	u̇	u̇	PROPN
ejpam-5051	234	5	∩	∩	PROPN
ejpam-5051	234	6	v̇	v̇	VERB
ejpam-5051	234	7	.	.	PUNCT
ejpam-5051	235	1	then	then	ADV
ejpam-5051	235	2	,	,	PUNCT
ejpam-5051	235	3	πr(α	πr(α	X
ejpam-5051	235	4	)	)	PUNCT
ejpam-5051	235	5	̸=	̸=	PROPN
ejpam-5051	235	6	γa	γa	PROPN
ejpam-5051	235	7	and	and	CCONJ
ejpam-5051	235	8	πr(α	πr(α	PUNCT
ejpam-5051	235	9	)	)	PUNCT
ejpam-5051	235	10	̸=	̸=	PROPN
ejpam-5051	235	11	βa	βa	NUM
ejpam-5051	235	12	which	which	PRON
ejpam-5051	235	13	is	be	AUX
ejpam-5051	235	14	a	a	DET
ejpam-5051	235	15	contradiction	contradiction	NOUN
ejpam-5051	235	16	since	since	SCONJ
ejpam-5051	235	17	γa	γa	PRON
ejpam-5051	235	18	and	and	CCONJ
ejpam-5051	235	19	βa	βa	NUM
ejpam-5051	235	20	are	be	AUX
ejpam-5051	235	21	distinct	distinct	ADJ
ejpam-5051	235	22	.	.	PUNCT
ejpam-5051	236	1	thus	thus	ADV
ejpam-5051	236	2	,	,	PUNCT
ejpam-5051	236	3	we	we	PRON
ejpam-5051	236	4	have	have	AUX
ejpam-5051	236	5	found	find	VERB
ejpam-5051	236	6	open	open	ADJ
ejpam-5051	236	7	sets	set	NOUN
ejpam-5051	236	8	u̇	u̇	PROPN
ejpam-5051	236	9	and	and	CCONJ
ejpam-5051	236	10	v̇	v̇	VERB
ejpam-5051	236	11	in	in	ADP
ejpam-5051	236	12	g	g	PROPN
ejpam-5051	236	13	such	such	ADJ
ejpam-5051	236	14	that	that	PRON
ejpam-5051	236	15	u̇	u̇	PROPN
ejpam-5051	236	16	∩	∩	NOUN
ejpam-5051	236	17	v̇	v̇	NOUN
ejpam-5051	236	18	is	be	AUX
ejpam-5051	236	19	empty	empty	ADJ
ejpam-5051	236	20	.	.	PUNCT
ejpam-5051	237	1	it	it	PRON
ejpam-5051	237	2	follows	follow	VERB
ejpam-5051	237	3	that	that	PRON
ejpam-5051	237	4	π(v̇	π(v̇	X
ejpam-5051	237	5	)	)	PUNCT
ejpam-5051	237	6	and	and	CCONJ
ejpam-5051	237	7	π(v̇	π(v̇	NUM
ejpam-5051	237	8	)	)	PUNCT
ejpam-5051	237	9	are	be	AUX
ejpam-5051	237	10	open	open	ADJ
ejpam-5051	237	11	in	in	ADP
ejpam-5051	237	12	r	r	NOUN
ejpam-5051	237	13	with	with	ADP
ejpam-5051	237	14	π(v̇	π(v̇	NUM
ejpam-5051	237	15	)	)	PUNCT
ejpam-5051	238	1	∩π(v̇	∩π(v̇	NOUN
ejpam-5051	238	2	)	)	PUNCT
ejpam-5051	239	1	=	=	NOUN
ejpam-5051	239	2	∅	∅	NOUN
ejpam-5051	239	3	and	and	CCONJ
ejpam-5051	239	4	each	each	PRON
ejpam-5051	239	5	contains	contain	VERB
ejpam-5051	239	6	distinct	distinct	ADJ
ejpam-5051	239	7	equivalence	equivalence	NOUN
ejpam-5051	239	8	classes	class	NOUN
ejpam-5051	239	9	.	.	PUNCT
ejpam-5051	240	1	thus	thus	ADV
ejpam-5051	240	2	,	,	PUNCT
ejpam-5051	240	3	r	r	NOUN
ejpam-5051	240	4	is	be	AUX
ejpam-5051	240	5	hausdorff	hausdorff	NOUN
ejpam-5051	240	6	.	.	PUNCT
ejpam-5051	241	1	since	since	SCONJ
ejpam-5051	241	2	r	r	NOUN
ejpam-5051	241	3	is	be	AUX
ejpam-5051	241	4	hausdorff	hausdorff	NOUN
ejpam-5051	241	5	then	then	ADV
ejpam-5051	241	6	r(0	r(0	PROPN
ejpam-5051	241	7	)	)	PUNCT
ejpam-5051	241	8	is	be	AUX
ejpam-5051	241	9	hausdorff	hausdorff	NOUN
ejpam-5051	241	10	.	.	PUNCT
ejpam-5051	242	1	let	let	VERB
ejpam-5051	242	2	b	b	X
ejpam-5051	242	3	be	be	AUX
ejpam-5051	242	4	a	a	DET
ejpam-5051	242	5	basis	basis	NOUN
ejpam-5051	242	6	for	for	ADP
ejpam-5051	242	7	a	a	DET
ejpam-5051	242	8	topology	topology	NOUN
ejpam-5051	242	9	in	in	ADP
ejpam-5051	242	10	g.	g.	PROPN
ejpam-5051	242	11	then	then	ADV
ejpam-5051	242	12	πr(b	πr(b	PUNCT
ejpam-5051	242	13	)	)	PUNCT
ejpam-5051	243	1	=	=	PRON
ejpam-5051	243	2	{	{	PUNCT
ejpam-5051	243	3	πr(b	πr(b	NUM
ejpam-5051	243	4	)	)	PUNCT
ejpam-5051	243	5	:	:	PUNCT
ejpam-5051	244	1	b	b	X
ejpam-5051	244	2	∈	∈	PROPN
ejpam-5051	244	3	b	b	AUX
ejpam-5051	244	4	}	}	PUNCT
ejpam-5051	244	5	is	be	AUX
ejpam-5051	244	6	a	a	DET
ejpam-5051	244	7	basis	basis	NOUN
ejpam-5051	244	8	for	for	ADP
ejpam-5051	244	9	the	the	DET
ejpam-5051	244	10	quotient	quotient	NOUN
ejpam-5051	244	11	topology	topology	NOUN
ejpam-5051	244	12	in	in	ADP
ejpam-5051	244	13	r.	r.	PROPN
ejpam-5051	244	14	let	let	VERB
ejpam-5051	244	15	v	v	PART
ejpam-5051	244	16	be	be	AUX
ejpam-5051	244	17	an	an	DET
ejpam-5051	244	18	open	open	ADJ
ejpam-5051	244	19	subset	subset	NOUN
ejpam-5051	244	20	of	of	ADP
ejpam-5051	244	21	r	r	NOUN
ejpam-5051	244	22	and	and	CCONJ
ejpam-5051	244	23	consider	consider	VERB
ejpam-5051	244	24	s|πr(b	s|πr(b	NOUN
ejpam-5051	244	25	)	)	PUNCT
ejpam-5051	244	26	:	:	PUNCT
ejpam-5051	244	27	πr(b	πr(b	X
ejpam-5051	244	28	)	)	PUNCT
ejpam-5051	244	29	→	→	SYM
ejpam-5051	244	30	v	v	NOUN
ejpam-5051	244	31	.	.	PUNCT
ejpam-5051	245	1	we	we	PRON
ejpam-5051	245	2	denote	denote	VERB
ejpam-5051	245	3	s1	s1	PROPN
ejpam-5051	245	4	=	=	SYM
ejpam-5051	245	5	s|πr(b	s|πr(b	NOUN
ejpam-5051	245	6	)	)	PUNCT
ejpam-5051	245	7	.	.	PUNCT
ejpam-5051	246	1	let	let	VERB
ejpam-5051	246	2	u	u	PRON
ejpam-5051	246	3	be	be	AUX
ejpam-5051	246	4	an	an	DET
ejpam-5051	246	5	open	open	ADJ
ejpam-5051	246	6	subset	subset	NOUN
ejpam-5051	246	7	of	of	ADP
ejpam-5051	246	8	v	v	NOUN
ejpam-5051	246	9	.	.	PUNCT
ejpam-5051	247	1	then	then	ADV
ejpam-5051	247	2	π−1	π−1	PROPN
ejpam-5051	247	3	r	r	NOUN
ejpam-5051	247	4	(	(	PUNCT
ejpam-5051	247	5	u	u	NOUN
ejpam-5051	247	6	)	)	PUNCT
ejpam-5051	247	7	is	be	AUX
ejpam-5051	247	8	open	open	ADJ
ejpam-5051	247	9	in	in	ADP
ejpam-5051	247	10	g.	g.	PROPN
ejpam-5051	247	11	since	since	SCONJ
ejpam-5051	247	12	πr(b	πr(b	NUM
ejpam-5051	247	13	)	)	PUNCT
ejpam-5051	247	14	is	be	AUX
ejpam-5051	247	15	a	a	DET
ejpam-5051	247	16	basis	basis	NOUN
ejpam-5051	247	17	for	for	ADP
ejpam-5051	247	18	the	the	DET
ejpam-5051	247	19	topology	topology	NOUN
ejpam-5051	247	20	on	on	ADP
ejpam-5051	247	21	r	r	NOUN
ejpam-5051	247	22	,	,	PUNCT
ejpam-5051	247	23	then	then	ADV
ejpam-5051	247	24	there	there	PRON
ejpam-5051	247	25	exists	exist	VERB
ejpam-5051	247	26	basic	basic	ADJ
ejpam-5051	247	27	element	element	NOUN
ejpam-5051	247	28	πr(b	πr(b	NUM
ejpam-5051	247	29	)	)	PUNCT
ejpam-5051	247	30	in	in	ADP
ejpam-5051	247	31	πr(b	πr(b	NUM
ejpam-5051	247	32	)	)	PUNCT
ejpam-5051	247	33	containing	contain	VERB
ejpam-5051	247	34	s−1	s−1	PROPN
ejpam-5051	247	35	1	1	NUM
ejpam-5051	247	36	(	(	PUNCT
ejpam-5051	247	37	u	u	NOUN
ejpam-5051	247	38	)	)	PUNCT
ejpam-5051	247	39	.	.	PUNCT
ejpam-5051	248	1	now	now	ADV
ejpam-5051	248	2	,	,	PUNCT
ejpam-5051	248	3	let	let	VERB
ejpam-5051	248	4	s−1	s−1	PROPN
ejpam-5051	248	5	1	1	NUM
ejpam-5051	248	6	=	=	SYM
ejpam-5051	248	7	(	(	PUNCT
ejpam-5051	248	8	s|πr(b	s|πr(b	NOUN
ejpam-5051	248	9	)	)	PUNCT
ejpam-5051	248	10	)	)	PUNCT
ejpam-5051	249	1	−1	−1	NOUN
ejpam-5051	249	2	:	:	PUNCT
ejpam-5051	249	3	v	v	NOUN
ejpam-5051	249	4	→	→	SYM
ejpam-5051	249	5	πr(b	πr(b	NUM
ejpam-5051	249	6	)	)	PUNCT
ejpam-5051	249	7	.	.	PUNCT
ejpam-5051	250	1	let	let	VERB
ejpam-5051	250	2	b	b	NOUN
ejpam-5051	250	3	⊆	⊆	NUM
ejpam-5051	250	4	πr(b	πr(b	NUM
ejpam-5051	250	5	)	)	PUNCT
ejpam-5051	250	6	which	which	PRON
ejpam-5051	250	7	is	be	AUX
ejpam-5051	250	8	open	open	ADJ
ejpam-5051	250	9	in	in	ADP
ejpam-5051	250	10	r.	r.	PROPN
ejpam-5051	250	11	then	then	ADV
ejpam-5051	250	12	there	there	PRON
ejpam-5051	250	13	exists	exist	VERB
ejpam-5051	250	14	w	w	ADP
ejpam-5051	250	15	⊆	⊆	NUM
ejpam-5051	250	16	g	g	ADP
ejpam-5051	250	17	such	such	ADJ
ejpam-5051	250	18	that	that	PRON
ejpam-5051	250	19	w	w	NOUN
ejpam-5051	250	20	is	be	AUX
ejpam-5051	250	21	the	the	DET
ejpam-5051	250	22	inverse	inverse	ADJ
ejpam-5051	250	23	image	image	NOUN
ejpam-5051	250	24	of	of	ADP
ejpam-5051	250	25	of	of	ADP
ejpam-5051	250	26	b	b	PROPN
ejpam-5051	250	27	under	under	ADP
ejpam-5051	250	28	πr	πr	PROPN
ejpam-5051	250	29	.	.	PUNCT
ejpam-5051	251	1	then	then	ADV
ejpam-5051	251	2	w	w	PROPN
ejpam-5051	251	3	=	=	SYM
ejpam-5051	251	4	π−1	π−1	PROPN
ejpam-5051	251	5	r	r	NOUN
ejpam-5051	251	6	(	(	PUNCT
ejpam-5051	251	7	b	b	NOUN
ejpam-5051	251	8	)	)	PUNCT
ejpam-5051	251	9	=	=	SYM
ejpam-5051	251	10	{	{	PUNCT
ejpam-5051	251	11	γ	γ	X
ejpam-5051	251	12	∈	∈	PROPN
ejpam-5051	251	13	g	g	NOUN
ejpam-5051	251	14	:	:	PUNCT
ejpam-5051	251	15	πr(γ	πr(γ	PUNCT
ejpam-5051	251	16	)	)	PUNCT
ejpam-5051	251	17	∈	∈	PROPN
ejpam-5051	252	1	b	b	X
ejpam-5051	252	2	}	}	PUNCT
ejpam-5051	252	3	.	.	PUNCT
ejpam-5051	253	1	since	since	SCONJ
ejpam-5051	253	2	πr	πr	PROPN
ejpam-5051	253	3	is	be	AUX
ejpam-5051	253	4	surjective	surjective	ADJ
ejpam-5051	253	5	,	,	PUNCT
ejpam-5051	253	6	s−1	s−1	PROPN
ejpam-5051	253	7	1	1	NUM
ejpam-5051	253	8	(	(	PUNCT
ejpam-5051	253	9	b	b	NOUN
ejpam-5051	253	10	)	)	PUNCT
ejpam-5051	253	11	=	=	NOUN
ejpam-5051	253	12	πr(w	πr(w	X
ejpam-5051	253	13	)	)	PUNCT
ejpam-5051	253	14	.	.	PUNCT
ejpam-5051	254	1	since	since	SCONJ
ejpam-5051	254	2	πr	πr	PROPN
ejpam-5051	254	3	is	be	AUX
ejpam-5051	254	4	a	a	DET
ejpam-5051	254	5	quotient	quotient	NOUN
ejpam-5051	254	6	map	map	NOUN
ejpam-5051	254	7	then	then	ADV
ejpam-5051	254	8	it	it	PRON
ejpam-5051	254	9	is	be	AUX
ejpam-5051	254	10	an	an	DET
ejpam-5051	254	11	open	open	ADJ
ejpam-5051	254	12	map	map	NOUN
ejpam-5051	254	13	.	.	PUNCT
ejpam-5051	255	1	thus	thus	ADV
ejpam-5051	255	2	,	,	PUNCT
ejpam-5051	255	3	for	for	ADP
ejpam-5051	255	4	any	any	DET
ejpam-5051	255	5	open	open	ADJ
ejpam-5051	255	6	set	set	NOUN
ejpam-5051	255	7	u	u	NOUN
ejpam-5051	255	8	′	′	NOUN
ejpam-5051	255	9	in	in	ADP
ejpam-5051	255	10	r	r	NOUN
ejpam-5051	255	11	,	,	PUNCT
ejpam-5051	255	12	πr(u	πr(u	NOUN
ejpam-5051	255	13	)	)	PUNCT
ejpam-5051	255	14	is	be	AUX
ejpam-5051	255	15	open	open	ADJ
ejpam-5051	255	16	in	in	ADP
ejpam-5051	255	17	g.	g.	PROPN
ejpam-5051	255	18	in	in	ADP
ejpam-5051	255	19	particular	particular	ADJ
ejpam-5051	255	20	,	,	PUNCT
ejpam-5051	255	21	w	w	PROPN
ejpam-5051	255	22	=	=	SYM
ejpam-5051	255	23	π−1	π−1	PROPN
ejpam-5051	255	24	r	r	NOUN
ejpam-5051	255	25	(	(	PUNCT
ejpam-5051	255	26	b	b	NOUN
ejpam-5051	255	27	)	)	PUNCT
ejpam-5051	255	28	is	be	AUX
ejpam-5051	255	29	open	open	ADJ
ejpam-5051	255	30	in	in	ADP
ejpam-5051	255	31	g.	g.	PROPN
ejpam-5051	255	32	it	it	PRON
ejpam-5051	255	33	follows	follow	VERB
ejpam-5051	255	34	that	that	PRON
ejpam-5051	255	35	πr(w	πr(w	PUNCT
ejpam-5051	255	36	)	)	PUNCT
ejpam-5051	255	37	is	be	AUX
ejpam-5051	255	38	open	open	ADJ
ejpam-5051	255	39	in	in	ADP
ejpam-5051	255	40	r.	r.	PROPN
ejpam-5051	255	41	hence	hence	ADV
ejpam-5051	255	42	,	,	PUNCT
ejpam-5051	255	43	s−1	s−1	PROPN
ejpam-5051	255	44	1	1	NUM
ejpam-5051	255	45	(	(	PUNCT
ejpam-5051	255	46	w	w	NOUN
ejpam-5051	255	47	)	)	PUNCT
ejpam-5051	255	48	is	be	AUX
ejpam-5051	255	49	open	open	ADJ
ejpam-5051	255	50	and	and	CCONJ
ejpam-5051	255	51	the	the	DET
ejpam-5051	255	52	source	source	NOUN
ejpam-5051	255	53	map	map	NOUN
ejpam-5051	255	54	is	be	AUX
ejpam-5051	255	55	a	a	DET
ejpam-5051	255	56	homeomorphism	homeomorphism	NOUN
ejpam-5051	255	57	onto	onto	ADP
ejpam-5051	255	58	an	an	DET
ejpam-5051	255	59	open	open	ADJ
ejpam-5051	255	60	subset	subset	NOUN
ejpam-5051	255	61	of	of	ADP
ejpam-5051	255	62	r.	r.	PROPN
ejpam-5051	255	63	similarly	similarly	ADV
ejpam-5051	255	64	,	,	PUNCT
ejpam-5051	255	65	the	the	DET
ejpam-5051	255	66	range	range	NOUN
ejpam-5051	255	67	map	map	NOUN
ejpam-5051	255	68	is	be	AUX
ejpam-5051	255	69	also	also	ADV
ejpam-5051	255	70	homeomorphic	homeomorphic	ADJ
ejpam-5051	255	71	onto	onto	ADP
ejpam-5051	255	72	an	an	DET
ejpam-5051	255	73	open	open	ADJ
ejpam-5051	255	74	subset	subset	NOUN
ejpam-5051	255	75	of	of	ADP
ejpam-5051	255	76	r.	r.	PROPN
ejpam-5051	255	77	therefore	therefore	ADV
ejpam-5051	255	78	,	,	PUNCT
ejpam-5051	255	79	r	r	NOUN
ejpam-5051	255	80	is	be	AUX
ejpam-5051	255	81	an	an	DET
ejpam-5051	255	82	ample	ample	ADJ
ejpam-5051	255	83	hausdorff	hausdorff	NOUN
ejpam-5051	255	84	groupoid	groupoid	NOUN
ejpam-5051	255	85	with	with	ADP
ejpam-5051	255	86	respect	respect	NOUN
ejpam-5051	255	87	to	to	ADP
ejpam-5051	255	88	the	the	DET
ejpam-5051	255	89	quotient	quotient	NOUN
ejpam-5051	255	90	topology	topology	NOUN
ejpam-5051	255	91	.	.	PUNCT
ejpam-5051	256	1	from	from	ADP
ejpam-5051	256	2	now	now	ADV
ejpam-5051	256	3	on	on	ADV
ejpam-5051	256	4	,	,	PUNCT
ejpam-5051	256	5	we	we	PRON
ejpam-5051	256	6	denote	denote	VERB
ejpam-5051	256	7	the	the	DET
ejpam-5051	256	8	elements	element	NOUN
ejpam-5051	256	9	of	of	ADP
ejpam-5051	256	10	â	â	PRON
ejpam-5051	256	11	⋊	⋊	SYM
ejpam-5051	256	12	r	r	NOUN
ejpam-5051	256	13	by	by	ADP
ejpam-5051	256	14	(	(	PUNCT
ejpam-5051	256	15	χ	χ	ADJ
ejpam-5051	256	16	,	,	PUNCT
ejpam-5051	256	17	γ̇	γ̇	NOUN
ejpam-5051	256	18	)	)	PUNCT
ejpam-5051	256	19	with	with	ADP
ejpam-5051	256	20	χ	χ	PROPN
ejpam-5051	256	21	∈	∈	PROPN
ejpam-5051	256	22	âr(γ	âr(γ	PROPN
ejpam-5051	256	23	)	)	PUNCT
ejpam-5051	256	24	.	.	PUNCT
ejpam-5051	257	1	a	a	DET
ejpam-5051	257	2	subset	subset	NOUN
ejpam-5051	257	3	c	c	NOUN
ejpam-5051	257	4	of	of	ADP
ejpam-5051	257	5	â	â	PROPN
ejpam-5051	257	6	is	be	AUX
ejpam-5051	257	7	closed	close	VERB
ejpam-5051	257	8	if	if	SCONJ
ejpam-5051	257	9	and	and	CCONJ
ejpam-5051	257	10	only	only	ADV
ejpam-5051	257	11	if	if	SCONJ
ejpam-5051	257	12	for	for	ADP
ejpam-5051	257	13	all	all	DET
ejpam-5051	257	14	sequences	sequence	NOUN
ejpam-5051	257	15	where	where	SCONJ
ejpam-5051	257	16	xn	xn	PROPN
ejpam-5051	257	17	converges	converge	VERB
ejpam-5051	257	18	to	to	ADP
ejpam-5051	257	19	x	x	SYM
ejpam-5051	257	20	such	such	ADJ
ejpam-5051	257	21	that	that	SCONJ
ejpam-5051	257	22	xn	xn	PROPN
ejpam-5051	257	23	∈	∈	PROPN
ejpam-5051	257	24	c	c	NOUN
ejpam-5051	257	25	,	,	PUNCT
ejpam-5051	257	26	then	then	ADV
ejpam-5051	257	27	x	x	PART
ejpam-5051	257	28	∈	∈	PROPN
ejpam-5051	257	29	c.	c.	NOUN
ejpam-5051	257	30	we	we	PRON
ejpam-5051	257	31	will	will	AUX
ejpam-5051	257	32	denote	denote	VERB
ejpam-5051	257	33	our	our	PRON
ejpam-5051	257	34	topology	topology	NOUN
ejpam-5051	257	35	for	for	ADP
ejpam-5051	257	36	â	â	PROPN
ejpam-5051	257	37	as	as	ADP
ejpam-5051	257	38	τâ	τâ	NUM
ejpam-5051	257	39	=	=	SYM
ejpam-5051	257	40	{	{	PUNCT
ejpam-5051	257	41	d	d	NOUN
ejpam-5051	257	42	:	:	PUNCT
ejpam-5051	257	43	d	d	X
ejpam-5051	257	44	=	=	SYM
ejpam-5051	257	45	cc	cc	PROPN
ejpam-5051	257	46	,	,	PUNCT
ejpam-5051	257	47	c	c	PROPN
ejpam-5051	257	48	is	be	AUX
ejpam-5051	257	49	closed	close	VERB
ejpam-5051	257	50	in	in	ADP
ejpam-5051	257	51	â	â	ADJ
ejpam-5051	257	52	}	}	PUNCT
ejpam-5051	257	53	and	and	CCONJ
ejpam-5051	257	54	cc	cc	PROPN
ejpam-5051	257	55	stands	stand	VERB
ejpam-5051	257	56	for	for	ADP
ejpam-5051	257	57	the	the	DET
ejpam-5051	257	58	compliment	compliment	NOUN
ejpam-5051	257	59	of	of	ADP
ejpam-5051	257	60	c.	c.	PROPN
ejpam-5051	257	61	also	also	ADV
ejpam-5051	257	62	,	,	PUNCT
ejpam-5051	257	63	τâ×r	τâ×r	PROPN
ejpam-5051	257	64	=	=	PUNCT
ejpam-5051	257	65	{	{	PUNCT
ejpam-5051	257	66	u	u	NOUN
ejpam-5051	257	67	×	×	NOUN
ejpam-5051	257	68	v	v	NOUN
ejpam-5051	257	69	:	:	PUNCT
ejpam-5051	257	70	u	u	NOUN
ejpam-5051	257	71	∈	∈	PROPN
ejpam-5051	257	72	τâ	τâ	NOUN
ejpam-5051	257	73	and	and	CCONJ
ejpam-5051	257	74	v	v	ADP
ejpam-5051	257	75	∈	∈	PROPN
ejpam-5051	257	76	τr	τr	ADP
ejpam-5051	257	77	}	}	PUNCT
ejpam-5051	257	78	,	,	PUNCT
ejpam-5051	257	79	and	and	CCONJ
ejpam-5051	257	80	τ(â⋊r)×(â⋊r	τ(â⋊r)×(â⋊r	PROPN
ejpam-5051	257	81	)	)	PUNCT
ejpam-5051	257	82	=	=	PRON
ejpam-5051	257	83	{	{	PUNCT
ejpam-5051	257	84	a	a	DET
ejpam-5051	257	85	×	×	PROPN
ejpam-5051	257	86	b	b	NOUN
ejpam-5051	257	87	:	:	PUNCT
ejpam-5051	257	88	a	a	DET
ejpam-5051	257	89	,	,	PUNCT
ejpam-5051	257	90	b	b	X
ejpam-5051	257	91	∈	∈	PROPN
ejpam-5051	257	92	τâ⋊r	τâ⋊r	PROPN
ejpam-5051	257	93	}	}	PUNCT
ejpam-5051	257	94	which	which	PRON
ejpam-5051	257	95	gives	give	VERB
ejpam-5051	257	96	us	we	PRON
ejpam-5051	257	97	the	the	DET
ejpam-5051	257	98	relative	relative	ADJ
ejpam-5051	257	99	topology	topology	NOUN
ejpam-5051	257	100	for	for	ADP
ejpam-5051	257	101	(	(	PUNCT
ejpam-5051	257	102	â	â	X
ejpam-5051	257	103	⋊r)(2	⋊r)(2	NOUN
ejpam-5051	257	104	)	)	PUNCT
ejpam-5051	257	105	as	as	ADP
ejpam-5051	257	106	τ(â⋊r)(2	τ(â⋊r)(2	NOUN
ejpam-5051	257	107	)	)	PUNCT
ejpam-5051	258	1	=	=	PRON
ejpam-5051	258	2	{	{	PUNCT
ejpam-5051	258	3	(	(	PUNCT
ejpam-5051	258	4	a	a	DET
ejpam-5051	258	5	×	×	PROPN
ejpam-5051	258	6	b	b	NOUN
ejpam-5051	258	7	)	)	PUNCT
ejpam-5051	258	8	∩	∩	NOUN
ejpam-5051	258	9	(	(	PUNCT
ejpam-5051	258	10	â	â	X
ejpam-5051	258	11	⋊r)(2	⋊r)(2	NOUN
ejpam-5051	258	12	)	)	PUNCT
ejpam-5051	258	13	:	:	PUNCT
ejpam-5051	258	14	a	a	DET
ejpam-5051	258	15	×	×	PROPN
ejpam-5051	258	16	b	b	X
ejpam-5051	258	17	∈	∈	PROPN
ejpam-5051	258	18	τ(â⋊r)×(â⋊r	τ(â⋊r)×(â⋊r	PROPN
ejpam-5051	258	19	)	)	PUNCT
ejpam-5051	258	20	}	}	PUNCT
ejpam-5051	258	21	.	.	PUNCT
ejpam-5051	259	1	let	let	VERB
ejpam-5051	259	2	r((χ	r((χ	NOUN
ejpam-5051	259	3	,	,	PUNCT
ejpam-5051	259	4	γ̇	γ̇	NOUN
ejpam-5051	259	5	)	)	PUNCT
ejpam-5051	259	6	)	)	PUNCT
ejpam-5051	260	1	=	=	PUNCT
ejpam-5051	260	2	(	(	PUNCT
ejpam-5051	260	3	χ	χ	NOUN
ejpam-5051	260	4	,	,	PUNCT
ejpam-5051	260	5	r(γ	r(γ	NOUN
ejpam-5051	260	6	)	)	PUNCT
ejpam-5051	260	7	)	)	PUNCT
ejpam-5051	260	8	and	and	CCONJ
ejpam-5051	260	9	s((χ	s((χ	NOUN
ejpam-5051	260	10	,	,	PUNCT
ejpam-5051	260	11	γ̇	γ̇	NOUN
ejpam-5051	260	12	)	)	PUNCT
ejpam-5051	260	13	)	)	PUNCT
ejpam-5051	261	1	=	=	PUNCT
ejpam-5051	261	2	(	(	PUNCT
ejpam-5051	261	3	χ	χ	X
ejpam-5051	261	4	·	·	PUNCT
ejpam-5051	261	5	γ	γ	X
ejpam-5051	261	6	,	,	PUNCT
ejpam-5051	261	7	s(γ	s(γ	PROPN
ejpam-5051	261	8	)	)	PUNCT
ejpam-5051	261	9	)	)	PUNCT
ejpam-5051	261	10	,	,	PUNCT
ejpam-5051	261	11	respectively	respectively	ADV
ejpam-5051	261	12	.	.	PUNCT
ejpam-5051	262	1	the	the	DET
ejpam-5051	262	2	set	set	NOUN
ejpam-5051	262	3	of	of	ADP
ejpam-5051	262	4	composable	composable	ADJ
ejpam-5051	262	5	pairs	pair	NOUN
ejpam-5051	262	6	is	be	AUX
ejpam-5051	262	7	(	(	PUNCT
ejpam-5051	262	8	â	â	X
ejpam-5051	262	9	⋊r)(2	⋊r)(2	X
ejpam-5051	262	10	)	)	PUNCT
ejpam-5051	262	11	=	=	PRON
ejpam-5051	262	12	{	{	PUNCT
ejpam-5051	262	13	(	(	PUNCT
ejpam-5051	262	14	(	(	PUNCT
ejpam-5051	262	15	χ	χ	X
ejpam-5051	262	16	,	,	PUNCT
ejpam-5051	262	17	γ̇	γ̇	NOUN
ejpam-5051	262	18	)	)	PUNCT
ejpam-5051	262	19	,	,	PUNCT
ejpam-5051	262	20	(	(	PUNCT
ejpam-5051	262	21	χ′	χ′	PROPN
ejpam-5051	262	22	,	,	PUNCT
ejpam-5051	262	23	γ̇′))|χ′	γ̇′))|χ′	ADJ
ejpam-5051	262	24	=	=	SYM
ejpam-5051	262	25	χ	χ	X
ejpam-5051	262	26	·	·	PUNCT
ejpam-5051	262	27	γ	γ	X
ejpam-5051	262	28	}	}	PUNCT
ejpam-5051	262	29	.	.	PUNCT
ejpam-5051	263	1	note	note	VERB
ejpam-5051	263	2	that	that	SCONJ
ejpam-5051	263	3	χ	χ	X
ejpam-5051	263	4	·	·	PUNCT
ejpam-5051	263	5	γ(a	γ(a	NUM
ejpam-5051	263	6	)	)	PUNCT
ejpam-5051	263	7	=	=	SYM
ejpam-5051	264	1	χ(γaγ−1	χ(γaγ−1	NUM
ejpam-5051	264	2	)	)	PUNCT
ejpam-5051	264	3	.	.	PUNCT
ejpam-5051	265	1	also	also	ADV
ejpam-5051	265	2	,	,	PUNCT
ejpam-5051	265	3	r.	r.	PROPN
ejpam-5051	265	4	s.	s.	PROPN
ejpam-5051	265	5	bongcawel	bongcawel	PROPN
ejpam-5051	265	6	et	et	PROPN
ejpam-5051	265	7	al	al	PROPN
ejpam-5051	265	8	.	.	PUNCT
ejpam-5051	265	9	/	/	SYM
ejpam-5051	265	10	eur	eur	PROPN
ejpam-5051	265	11	.	.	PUNCT
ejpam-5051	266	1	j.	j.	PROPN
ejpam-5051	266	2	pure	pure	PROPN
ejpam-5051	266	3	appl	appl	PROPN
ejpam-5051	266	4	.	.	PROPN
ejpam-5051	266	5	math	math	PROPN
ejpam-5051	266	6	,	,	PUNCT
ejpam-5051	266	7	17	17	NUM
ejpam-5051	266	8	(	(	PUNCT
ejpam-5051	266	9	1	1	NUM
ejpam-5051	266	10	)	)	PUNCT
ejpam-5051	266	11	(	(	PUNCT
ejpam-5051	266	12	2024	2024	NUM
ejpam-5051	266	13	)	)	PUNCT
ejpam-5051	266	14	,	,	PUNCT
ejpam-5051	266	15	519	519	NUM
ejpam-5051	266	16	-	-	SYM
ejpam-5051	266	17	545	545	NUM
ejpam-5051	266	18	527	527	NUM
ejpam-5051	266	19	for	for	ADP
ejpam-5051	266	20	every	every	DET
ejpam-5051	266	21	u	u	PROPN
ejpam-5051	266	22	∈	∈	PROPN
ejpam-5051	266	23	g	g	PROPN
ejpam-5051	266	24	,	,	PUNCT
ejpam-5051	266	25	χ	χ	X
ejpam-5051	266	26	·	·	PUNCT
ejpam-5051	266	27	u	u	NOUN
ejpam-5051	266	28	=	=	PUNCT
ejpam-5051	266	29	χ	χ	NOUN
ejpam-5051	266	30	since	since	SCONJ
ejpam-5051	266	31	χ	χ	PROPN
ejpam-5051	266	32	·	·	PUNCT
ejpam-5051	266	33	u(a	u(a	PROPN
ejpam-5051	266	34	)	)	PUNCT
ejpam-5051	266	35	=	=	SYM
ejpam-5051	266	36	χ(uau−1	χ(uau−1	PROPN
ejpam-5051	266	37	)	)	PUNCT
ejpam-5051	266	38	=	=	SYM
ejpam-5051	266	39	χ(auu−1	χ(auu−1	PROPN
ejpam-5051	266	40	)	)	PUNCT
ejpam-5051	266	41	=	=	SYM
ejpam-5051	266	42	χ(ar(u	χ(ar(u	PROPN
ejpam-5051	266	43	)	)	PUNCT
ejpam-5051	266	44	)	)	PUNCT
ejpam-5051	266	45	=	=	SYM
ejpam-5051	266	46	χ(au	χ(au	PROPN
ejpam-5051	266	47	)	)	PUNCT
ejpam-5051	267	1	=	=	PUNCT
ejpam-5051	267	2	χ(as(a	χ(as(a	NOUN
ejpam-5051	267	3	)	)	PUNCT
ejpam-5051	267	4	)	)	PUNCT
ejpam-5051	268	1	=	=	SYM
ejpam-5051	268	2	χ(a	χ(a	NOUN
ejpam-5051	268	3	)	)	PUNCT
ejpam-5051	268	4	.	.	PUNCT
ejpam-5051	269	1	also	also	ADV
ejpam-5051	269	2	,	,	PUNCT
ejpam-5051	269	3	i((χ	i((χ	NOUN
ejpam-5051	269	4	,	,	PUNCT
ejpam-5051	269	5	γ̇	γ̇	NOUN
ejpam-5051	269	6	)	)	PUNCT
ejpam-5051	269	7	)	)	PUNCT
ejpam-5051	270	1	=	=	PUNCT
ejpam-5051	270	2	(	(	PUNCT
ejpam-5051	270	3	χ	χ	X
ejpam-5051	270	4	·	·	PUNCT
ejpam-5051	270	5	γ	γ	X
ejpam-5051	270	6	,	,	PUNCT
ejpam-5051	270	7	γ̇−1	γ̇−1	PROPN
ejpam-5051	270	8	)	)	PUNCT
ejpam-5051	270	9	and	and	CCONJ
ejpam-5051	270	10	m((χ	m((χ	NOUN
ejpam-5051	270	11	,	,	PUNCT
ejpam-5051	270	12	γ̇	γ̇	PROPN
ejpam-5051	270	13	)	)	PUNCT
ejpam-5051	270	14	,	,	PUNCT
ejpam-5051	270	15	(	(	PUNCT
ejpam-5051	270	16	χ′	χ′	PROPN
ejpam-5051	270	17	,	,	PUNCT
ejpam-5051	270	18	γ̇′	γ̇′	NOUN
ejpam-5051	270	19	)	)	PUNCT
ejpam-5051	270	20	)	)	PUNCT
ejpam-5051	271	1	=	=	PUNCT
ejpam-5051	271	2	(	(	PUNCT
ejpam-5051	271	3	χ	χ	X
ejpam-5051	271	4	,	,	PUNCT
ejpam-5051	271	5	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	271	6	)	)	PUNCT
ejpam-5051	271	7	are	be	AUX
ejpam-5051	271	8	the	the	DET
ejpam-5051	271	9	inversion	inversion	NOUN
ejpam-5051	271	10	and	and	CCONJ
ejpam-5051	271	11	composition	composition	NOUN
ejpam-5051	271	12	maps	map	NOUN
ejpam-5051	271	13	,	,	PUNCT
ejpam-5051	271	14	respectively	respectively	ADV
ejpam-5051	271	15	.	.	PUNCT
ejpam-5051	272	1	theorem	theorem	NOUN
ejpam-5051	272	2	2	2	NUM
ejpam-5051	272	3	.	.	PUNCT
ejpam-5051	273	1	let	let	VERB
ejpam-5051	273	2	g	g	PRON
ejpam-5051	273	3	be	be	AUX
ejpam-5051	273	4	an	an	DET
ejpam-5051	273	5	ample	ample	ADJ
ejpam-5051	273	6	hausdorff	hausdorff	NOUN
ejpam-5051	273	7	groupoid	groupoid	PROPN
ejpam-5051	273	8	and	and	CCONJ
ejpam-5051	273	9	r	r	NOUN
ejpam-5051	273	10	be	be	VERB
ejpam-5051	273	11	a	a	DET
ejpam-5051	273	12	commutative	commutative	ADJ
ejpam-5051	273	13	unital	unital	ADJ
ejpam-5051	273	14	ring	ring	NOUN
ejpam-5051	273	15	.	.	PUNCT
ejpam-5051	274	1	then	then	ADV
ejpam-5051	274	2	â⋊r	â⋊r	PROPN
ejpam-5051	274	3	=	=	SYM
ejpam-5051	274	4	{	{	PUNCT
ejpam-5051	274	5	(	(	PUNCT
ejpam-5051	274	6	χ	χ	NOUN
ejpam-5051	274	7	,	,	PUNCT
ejpam-5051	274	8	u	u	NOUN
ejpam-5051	274	9	,	,	PUNCT
ejpam-5051	274	10	γ̇	γ̇	PROPN
ejpam-5051	274	11	)	)	PUNCT
ejpam-5051	274	12	:	:	PUNCT
ejpam-5051	274	13	(	(	PUNCT
ejpam-5051	274	14	χ	χ	X
ejpam-5051	274	15	,	,	PUNCT
ejpam-5051	274	16	u	u	NOUN
ejpam-5051	274	17	)	)	PUNCT
ejpam-5051	274	18	∈	∈	PROPN
ejpam-5051	274	19	â	â	PROPN
ejpam-5051	274	20	,	,	PUNCT
ejpam-5051	274	21	r(γ	r(γ	NOUN
ejpam-5051	274	22	)	)	PUNCT
ejpam-5051	274	23	=	=	SYM
ejpam-5051	274	24	u	u	NOUN
ejpam-5051	274	25	}	}	PUNCT
ejpam-5051	274	26	is	be	AUX
ejpam-5051	274	27	a	a	DET
ejpam-5051	274	28	groupoid	groupoid	NOUN
ejpam-5051	274	29	.	.	PUNCT
ejpam-5051	275	1	proof	proof	NOUN
ejpam-5051	275	2	.	.	PUNCT
ejpam-5051	276	1	suppose	suppose	VERB
ejpam-5051	276	2	that	that	SCONJ
ejpam-5051	276	3	(	(	PUNCT
ejpam-5051	276	4	(	(	PUNCT
ejpam-5051	276	5	χ1	χ1	NOUN
ejpam-5051	276	6	,	,	PUNCT
ejpam-5051	276	7	γ̇1	γ̇1	PROPN
ejpam-5051	276	8	)	)	PUNCT
ejpam-5051	276	9	,	,	PUNCT
ejpam-5051	276	10	(	(	PUNCT
ejpam-5051	276	11	χ	χ	X
ejpam-5051	276	12	′	′	NUM
ejpam-5051	276	13	1	1	NUM
ejpam-5051	276	14	,	,	PUNCT
ejpam-5051	276	15	γ̇	γ̇	PROPN
ejpam-5051	276	16	′	′	NOUN
ejpam-5051	276	17	1	1	NUM
ejpam-5051	276	18	)	)	PUNCT
ejpam-5051	276	19	)	)	PUNCT
ejpam-5051	276	20	,	,	PUNCT
ejpam-5051	276	21	(	(	PUNCT
ejpam-5051	276	22	(	(	PUNCT
ejpam-5051	276	23	χ2	χ2	PROPN
ejpam-5051	276	24	,	,	PUNCT
ejpam-5051	276	25	γ̇2	γ̇2	PROPN
ejpam-5051	276	26	)	)	PUNCT
ejpam-5051	276	27	,	,	PUNCT
ejpam-5051	276	28	(	(	PUNCT
ejpam-5051	276	29	χ	χ	X
ejpam-5051	276	30	′	′	NUM
ejpam-5051	276	31	2	2	NUM
ejpam-5051	276	32	,	,	PUNCT
ejpam-5051	276	33	γ̇	γ̇	PROPN
ejpam-5051	276	34	′	′	NOUN
ejpam-5051	276	35	2	2	NUM
ejpam-5051	276	36	)	)	PUNCT
ejpam-5051	276	37	)	)	PUNCT
ejpam-5051	276	38	∈	∈	PROPN
ejpam-5051	276	39	(	(	PUNCT
ejpam-5051	276	40	â⋊r)(2	â⋊r)(2	ADV
ejpam-5051	276	41	)	)	PUNCT
ejpam-5051	276	42	with	with	ADP
ejpam-5051	276	43	(	(	PUNCT
ejpam-5051	276	44	(	(	PUNCT
ejpam-5051	276	45	χ1	χ1	NOUN
ejpam-5051	276	46	,	,	PUNCT
ejpam-5051	276	47	γ̇1	γ̇1	PROPN
ejpam-5051	276	48	)	)	PUNCT
ejpam-5051	276	49	,	,	PUNCT
ejpam-5051	276	50	(	(	PUNCT
ejpam-5051	276	51	χ	χ	X
ejpam-5051	276	52	′	′	NUM
ejpam-5051	276	53	1	1	NUM
ejpam-5051	276	54	,	,	PUNCT
ejpam-5051	276	55	γ̇	γ̇	PROPN
ejpam-5051	276	56	′	′	NOUN
ejpam-5051	276	57	1	1	NUM
ejpam-5051	276	58	)	)	PUNCT
ejpam-5051	276	59	)	)	PUNCT
ejpam-5051	277	1	=	=	SYM
ejpam-5051	277	2	(	(	PUNCT
ejpam-5051	277	3	(	(	PUNCT
ejpam-5051	277	4	χ2	χ2	PROPN
ejpam-5051	277	5	,	,	PUNCT
ejpam-5051	277	6	γ̇2	γ̇2	PROPN
ejpam-5051	277	7	)	)	PUNCT
ejpam-5051	277	8	,	,	PUNCT
ejpam-5051	277	9	(	(	PUNCT
ejpam-5051	277	10	χ	χ	X
ejpam-5051	277	11	′	′	NUM
ejpam-5051	277	12	2	2	NUM
ejpam-5051	277	13	,	,	PUNCT
ejpam-5051	277	14	γ̇	γ̇	PROPN
ejpam-5051	277	15	′	′	NOUN
ejpam-5051	277	16	2	2	NUM
ejpam-5051	277	17	)	)	PUNCT
ejpam-5051	277	18	)	)	PUNCT
ejpam-5051	277	19	.	.	PUNCT
ejpam-5051	278	1	then	then	ADV
ejpam-5051	278	2	,	,	PUNCT
ejpam-5051	278	3	(	(	PUNCT
ejpam-5051	278	4	χ1	χ1	NOUN
ejpam-5051	278	5	,	,	PUNCT
ejpam-5051	278	6	γ̇1	γ̇1	PROPN
ejpam-5051	278	7	)	)	PUNCT
ejpam-5051	278	8	=	=	SYM
ejpam-5051	278	9	(	(	PUNCT
ejpam-5051	278	10	χ2	χ2	PROPN
ejpam-5051	278	11	,	,	PUNCT
ejpam-5051	278	12	γ̇2	γ̇2	PROPN
ejpam-5051	278	13	)	)	PUNCT
ejpam-5051	278	14	and	and	CCONJ
ejpam-5051	278	15	(	(	PUNCT
ejpam-5051	278	16	χ′	χ′	PROPN
ejpam-5051	278	17	1	1	NUM
ejpam-5051	278	18	,	,	PUNCT
ejpam-5051	278	19	γ̇	γ̇	PROPN
ejpam-5051	278	20	′	′	NUM
ejpam-5051	278	21	1	1	NUM
ejpam-5051	278	22	)	)	PUNCT
ejpam-5051	278	23	=	=	SYM
ejpam-5051	278	24	(	(	PUNCT
ejpam-5051	278	25	χ′	χ′	PROPN
ejpam-5051	278	26	2	2	NUM
ejpam-5051	278	27	,	,	PUNCT
ejpam-5051	278	28	γ̇	γ̇	PROPN
ejpam-5051	278	29	′	′	NOUN
ejpam-5051	278	30	2	2	NUM
ejpam-5051	278	31	)	)	PUNCT
ejpam-5051	278	32	.	.	PUNCT
ejpam-5051	279	1	now	now	ADV
ejpam-5051	279	2	,	,	PUNCT
ejpam-5051	279	3	m(((χ1	m(((χ1	ADJ
ejpam-5051	279	4	,	,	PUNCT
ejpam-5051	279	5	γ̇1	γ̇1	NOUN
ejpam-5051	279	6	)	)	PUNCT
ejpam-5051	279	7	,	,	PUNCT
ejpam-5051	279	8	(	(	PUNCT
ejpam-5051	279	9	χ	χ	X
ejpam-5051	279	10	′	′	NUM
ejpam-5051	279	11	1	1	NUM
ejpam-5051	279	12	,	,	PUNCT
ejpam-5051	279	13	γ̇	γ̇	PROPN
ejpam-5051	279	14	′	′	NOUN
ejpam-5051	279	15	1	1	NUM
ejpam-5051	279	16	)	)	PUNCT
ejpam-5051	279	17	)	)	PUNCT
ejpam-5051	279	18	)	)	PUNCT
ejpam-5051	280	1	=	=	SYM
ejpam-5051	280	2	(	(	PUNCT
ejpam-5051	280	3	χ1	χ1	NOUN
ejpam-5051	280	4	,	,	PUNCT
ejpam-5051	280	5	γ̇1γ̇	γ̇1γ̇	NOUN
ejpam-5051	280	6	′	′	NUM
ejpam-5051	281	1	1	1	NUM
ejpam-5051	281	2	)	)	PUNCT
ejpam-5051	281	3	=	=	SYM
ejpam-5051	281	4	(	(	PUNCT
ejpam-5051	281	5	χ2	χ2	PROPN
ejpam-5051	281	6	,	,	PUNCT
ejpam-5051	281	7	γ̇2γ̇	γ̇2γ̇	ADJ
ejpam-5051	281	8	′	′	NUM
ejpam-5051	281	9	2	2	NUM
ejpam-5051	281	10	)	)	PUNCT
ejpam-5051	281	11	=	=	PUNCT
ejpam-5051	282	1	m(((χ2	m(((χ2	NOUN
ejpam-5051	282	2	,	,	PUNCT
ejpam-5051	282	3	γ̇2	γ̇2	PROPN
ejpam-5051	282	4	)	)	PUNCT
ejpam-5051	282	5	,	,	PUNCT
ejpam-5051	282	6	(	(	PUNCT
ejpam-5051	282	7	χ	χ	X
ejpam-5051	282	8	′	′	NUM
ejpam-5051	282	9	2	2	NUM
ejpam-5051	282	10	,	,	PUNCT
ejpam-5051	282	11	γ̇	γ̇	PROPN
ejpam-5051	282	12	′	′	NOUN
ejpam-5051	282	13	2	2	NUM
ejpam-5051	282	14	)	)	PUNCT
ejpam-5051	282	15	)	)	PUNCT
ejpam-5051	282	16	)	)	PUNCT
ejpam-5051	282	17	.	.	PUNCT
ejpam-5051	283	1	let	let	VERB
ejpam-5051	283	2	(	(	PUNCT
ejpam-5051	283	3	χ	χ	X
ejpam-5051	283	4	,	,	PUNCT
ejpam-5051	283	5	γ̇	γ̇	NOUN
ejpam-5051	283	6	)	)	PUNCT
ejpam-5051	283	7	,	,	PUNCT
ejpam-5051	283	8	(	(	PUNCT
ejpam-5051	283	9	χ′	χ′	PROPN
ejpam-5051	283	10	,	,	PUNCT
ejpam-5051	283	11	γ̇′	γ̇′	NOUN
ejpam-5051	283	12	)	)	PUNCT
ejpam-5051	283	13	∈	∈	PROPN
ejpam-5051	283	14	â⋊r	â⋊r	NOUN
ejpam-5051	283	15	such	such	ADJ
ejpam-5051	283	16	that	that	SCONJ
ejpam-5051	283	17	(	(	PUNCT
ejpam-5051	283	18	χ	χ	X
ejpam-5051	283	19	,	,	PUNCT
ejpam-5051	283	20	γ̇	γ̇	NOUN
ejpam-5051	283	21	)	)	PUNCT
ejpam-5051	283	22	=	=	SYM
ejpam-5051	283	23	(	(	PUNCT
ejpam-5051	283	24	χ′	χ′	PROPN
ejpam-5051	283	25	,	,	PUNCT
ejpam-5051	283	26	γ̇′	γ̇′	NOUN
ejpam-5051	283	27	)	)	PUNCT
ejpam-5051	283	28	.	.	PUNCT
ejpam-5051	284	1	then	then	ADV
ejpam-5051	284	2	i((χ	i((χ	NOUN
ejpam-5051	284	3	,	,	PUNCT
ejpam-5051	284	4	γ̇	γ̇	NOUN
ejpam-5051	284	5	)	)	PUNCT
ejpam-5051	284	6	)	)	PUNCT
ejpam-5051	285	1	=	=	PUNCT
ejpam-5051	285	2	(	(	PUNCT
ejpam-5051	285	3	χ	χ	X
ejpam-5051	285	4	·	·	PUNCT
ejpam-5051	285	5	γ̇	γ̇	ADJ
ejpam-5051	285	6	,	,	PUNCT
ejpam-5051	285	7	γ̇−1	γ̇−1	PROPN
ejpam-5051	285	8	)	)	PUNCT
ejpam-5051	285	9	=	=	SYM
ejpam-5051	286	1	i((χ′	i((χ′	NOUN
ejpam-5051	286	2	,	,	PUNCT
ejpam-5051	286	3	γ̇′	γ̇′	NOUN
ejpam-5051	286	4	)	)	PUNCT
ejpam-5051	286	5	)	)	PUNCT
ejpam-5051	286	6	;	;	PUNCT
ejpam-5051	286	7	r((χ	r((χ	X
ejpam-5051	286	8	,	,	PUNCT
ejpam-5051	286	9	γ̇	γ̇	NOUN
ejpam-5051	286	10	)	)	PUNCT
ejpam-5051	286	11	)	)	PUNCT
ejpam-5051	287	1	=	=	PUNCT
ejpam-5051	287	2	(	(	PUNCT
ejpam-5051	287	3	χ	χ	NOUN
ejpam-5051	287	4	,	,	PUNCT
ejpam-5051	287	5	r(γ	r(γ	NOUN
ejpam-5051	287	6	)	)	PUNCT
ejpam-5051	287	7	)	)	PUNCT
ejpam-5051	288	1	=	=	SYM
ejpam-5051	288	2	(	(	PUNCT
ejpam-5051	288	3	χ′	χ′	PROPN
ejpam-5051	288	4	,	,	PUNCT
ejpam-5051	288	5	r(γ′	r(γ′	NOUN
ejpam-5051	288	6	)	)	PUNCT
ejpam-5051	288	7	)	)	PUNCT
ejpam-5051	289	1	=	=	PUNCT
ejpam-5051	289	2	r((χ′	r((χ′	NOUN
ejpam-5051	289	3	,	,	PUNCT
ejpam-5051	289	4	γ̇′	γ̇′	NOUN
ejpam-5051	289	5	)	)	PUNCT
ejpam-5051	289	6	)	)	PUNCT
ejpam-5051	289	7	;	;	PUNCT
ejpam-5051	289	8	s((χ	s((χ	NOUN
ejpam-5051	289	9	,	,	PUNCT
ejpam-5051	289	10	γ̇	γ̇	NOUN
ejpam-5051	289	11	)	)	PUNCT
ejpam-5051	289	12	)	)	PUNCT
ejpam-5051	290	1	=	=	PUNCT
ejpam-5051	290	2	(	(	PUNCT
ejpam-5051	290	3	χ	χ	X
ejpam-5051	290	4	·	·	PUNCT
ejpam-5051	290	5	γ	γ	X
ejpam-5051	290	6	,	,	PUNCT
ejpam-5051	290	7	s(γ	s(γ	PROPN
ejpam-5051	290	8	)	)	PUNCT
ejpam-5051	290	9	)	)	PUNCT
ejpam-5051	290	10	=	=	SYM
ejpam-5051	290	11	(	(	PUNCT
ejpam-5051	290	12	χ′	χ′	PROPN
ejpam-5051	290	13	·	·	PUNCT
ejpam-5051	290	14	γ′	γ′	PROPN
ejpam-5051	290	15	,	,	PUNCT
ejpam-5051	290	16	s(γ′	s(γ′	NOUN
ejpam-5051	290	17	)	)	PUNCT
ejpam-5051	290	18	)	)	PUNCT
ejpam-5051	290	19	=	=	SYM
ejpam-5051	291	1	s((χ′	s((χ′	NOUN
ejpam-5051	291	2	,	,	PUNCT
ejpam-5051	291	3	γ̇′	γ̇′	NOUN
ejpam-5051	291	4	)	)	PUNCT
ejpam-5051	291	5	)	)	PUNCT
ejpam-5051	291	6	.	.	PUNCT
ejpam-5051	292	1	thus	thus	ADV
ejpam-5051	292	2	,	,	PUNCT
ejpam-5051	292	3	the	the	DET
ejpam-5051	292	4	composition	composition	NOUN
ejpam-5051	292	5	,	,	PUNCT
ejpam-5051	292	6	inverse	inverse	NOUN
ejpam-5051	292	7	,	,	PUNCT
ejpam-5051	292	8	range	range	NOUN
ejpam-5051	292	9	and	and	CCONJ
ejpam-5051	292	10	source	source	NOUN
ejpam-5051	292	11	maps	map	NOUN
ejpam-5051	292	12	are	be	AUX
ejpam-5051	292	13	well	well	ADV
ejpam-5051	292	14	-	-	PUNCT
ejpam-5051	292	15	defined	define	VERB
ejpam-5051	292	16	.	.	PUNCT
ejpam-5051	293	1	let	let	VERB
ejpam-5051	293	2	(	(	PUNCT
ejpam-5051	293	3	(	(	PUNCT
ejpam-5051	293	4	χ	χ	X
ejpam-5051	293	5	,	,	PUNCT
ejpam-5051	293	6	γ̇	γ̇	NOUN
ejpam-5051	293	7	)	)	PUNCT
ejpam-5051	293	8	,	,	PUNCT
ejpam-5051	293	9	(	(	PUNCT
ejpam-5051	293	10	χ′	χ′	PROPN
ejpam-5051	293	11	,	,	PUNCT
ejpam-5051	293	12	γ̇′	γ̇′	NOUN
ejpam-5051	293	13	)	)	PUNCT
ejpam-5051	293	14	)	)	PUNCT
ejpam-5051	293	15	,	,	PUNCT
ejpam-5051	293	16	(	(	PUNCT
ejpam-5051	293	17	(	(	PUNCT
ejpam-5051	293	18	χ′	χ′	PROPN
ejpam-5051	293	19	,	,	PUNCT
ejpam-5051	293	20	γ̇′	γ̇′	NOUN
ejpam-5051	293	21	)	)	PUNCT
ejpam-5051	293	22	,	,	PUNCT
ejpam-5051	293	23	(	(	PUNCT
ejpam-5051	293	24	χ′′	χ′′	PROPN
ejpam-5051	293	25	,	,	PUNCT
ejpam-5051	293	26	γ̇′′	γ̇′′	NOUN
ejpam-5051	293	27	)	)	PUNCT
ejpam-5051	293	28	)	)	PUNCT
ejpam-5051	294	1	∈	∈	PROPN
ejpam-5051	294	2	(	(	PUNCT
ejpam-5051	294	3	â⋊r)(2	â⋊r)(2	ADJ
ejpam-5051	294	4	)	)	PUNCT
ejpam-5051	294	5	.	.	PUNCT
ejpam-5051	295	1	then	then	ADV
ejpam-5051	295	2	s((χ	s((χ	NOUN
ejpam-5051	295	3	,	,	PUNCT
ejpam-5051	295	4	γ̇	γ̇	NOUN
ejpam-5051	295	5	)	)	PUNCT
ejpam-5051	295	6	)	)	PUNCT
ejpam-5051	296	1	=	=	PUNCT
ejpam-5051	296	2	(	(	PUNCT
ejpam-5051	296	3	χ	χ	X
ejpam-5051	296	4	·	·	PUNCT
ejpam-5051	296	5	γ	γ	X
ejpam-5051	296	6	,	,	PUNCT
ejpam-5051	296	7	s(γ	s(γ	PROPN
ejpam-5051	296	8	)	)	PUNCT
ejpam-5051	296	9	)	)	PUNCT
ejpam-5051	296	10	=	=	PUNCT
ejpam-5051	297	1	r((χ′	r((χ′	NOUN
ejpam-5051	297	2	,	,	PUNCT
ejpam-5051	297	3	γ̇′	γ̇′	NOUN
ejpam-5051	297	4	)	)	PUNCT
ejpam-5051	297	5	)	)	PUNCT
ejpam-5051	298	1	=	=	SYM
ejpam-5051	298	2	(	(	PUNCT
ejpam-5051	298	3	χ′	χ′	PROPN
ejpam-5051	298	4	,	,	PUNCT
ejpam-5051	298	5	r(γ′	r(γ′	NOUN
ejpam-5051	298	6	)	)	PUNCT
ejpam-5051	298	7	)	)	PUNCT
ejpam-5051	298	8	;	;	PUNCT
ejpam-5051	298	9	s((χ′	s((χ′	NOUN
ejpam-5051	298	10	,	,	PUNCT
ejpam-5051	298	11	γ̇′	γ̇′	NOUN
ejpam-5051	298	12	)	)	PUNCT
ejpam-5051	298	13	)	)	PUNCT
ejpam-5051	298	14	=	=	SYM
ejpam-5051	298	15	(	(	PUNCT
ejpam-5051	298	16	χ′	χ′	PROPN
ejpam-5051	298	17	·	·	PUNCT
ejpam-5051	298	18	γ′	γ′	PROPN
ejpam-5051	298	19	,	,	PUNCT
ejpam-5051	298	20	s(γ′	s(γ′	NOUN
ejpam-5051	298	21	)	)	PUNCT
ejpam-5051	298	22	)	)	PUNCT
ejpam-5051	299	1	=	=	PRON
ejpam-5051	299	2	r((χ′′	r((χ′′	ADJ
ejpam-5051	299	3	,	,	PUNCT
ejpam-5051	299	4	γ̇′′	γ̇′′	NOUN
ejpam-5051	299	5	)	)	PUNCT
ejpam-5051	299	6	)	)	PUNCT
ejpam-5051	300	1	=	=	PRON
ejpam-5051	300	2	(	(	PUNCT
ejpam-5051	300	3	χ′′	χ′′	PROPN
ejpam-5051	300	4	,	,	PUNCT
ejpam-5051	300	5	r(γ′′	r(γ′′	PROPN
ejpam-5051	300	6	)	)	PUNCT
ejpam-5051	300	7	)	)	PUNCT
ejpam-5051	300	8	.	.	PUNCT
ejpam-5051	301	1	now	now	ADV
ejpam-5051	301	2	,	,	PUNCT
ejpam-5051	301	3	s((χ	s((χ	NOUN
ejpam-5051	301	4	,	,	PUNCT
ejpam-5051	301	5	γ̇	γ̇	NOUN
ejpam-5051	301	6	)	)	PUNCT
ejpam-5051	301	7	,	,	PUNCT
ejpam-5051	301	8	(	(	PUNCT
ejpam-5051	301	9	χ′	χ′	PROPN
ejpam-5051	301	10	,	,	PUNCT
ejpam-5051	301	11	γ̇′	γ̇′	NOUN
ejpam-5051	301	12	)	)	PUNCT
ejpam-5051	301	13	)	)	PUNCT
ejpam-5051	302	1	=	=	SYM
ejpam-5051	302	2	s((χ	s((χ	NOUN
ejpam-5051	302	3	,	,	PUNCT
ejpam-5051	302	4	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	302	5	)	)	PUNCT
ejpam-5051	302	6	)	)	PUNCT
ejpam-5051	303	1	=	=	PUNCT
ejpam-5051	303	2	(	(	PUNCT
ejpam-5051	303	3	χ	χ	X
ejpam-5051	303	4	·	·	SYM
ejpam-5051	303	5	γγ′	γγ′	PROPN
ejpam-5051	303	6	,	,	PUNCT
ejpam-5051	303	7	s(γγ′	s(γγ′	PROPN
ejpam-5051	303	8	)	)	PUNCT
ejpam-5051	303	9	)	)	PUNCT
ejpam-5051	304	1	=	=	PUNCT
ejpam-5051	304	2	(	(	PUNCT
ejpam-5051	304	3	χ	χ	X
ejpam-5051	304	4	·	·	SYM
ejpam-5051	304	5	γγ′	γγ′	NOUN
ejpam-5051	304	6	,	,	PUNCT
ejpam-5051	304	7	s(γ′	s(γ′	NOUN
ejpam-5051	304	8	)	)	PUNCT
ejpam-5051	304	9	)	)	PUNCT
ejpam-5051	305	1	=	=	PUNCT
ejpam-5051	305	2	(	(	PUNCT
ejpam-5051	305	3	χ	χ	X
ejpam-5051	305	4	·	·	SYM
ejpam-5051	305	5	γγ′	γγ′	NOUN
ejpam-5051	305	6	,	,	PUNCT
ejpam-5051	305	7	r(γ′′	r(γ′′	NOUN
ejpam-5051	305	8	)	)	PUNCT
ejpam-5051	305	9	)	)	PUNCT
ejpam-5051	306	1	=	=	SYM
ejpam-5051	306	2	(	(	PUNCT
ejpam-5051	306	3	χ′	χ′	PROPN
ejpam-5051	306	4	·	·	PUNCT
ejpam-5051	306	5	γ′	γ′	PROPN
ejpam-5051	306	6	,	,	PUNCT
ejpam-5051	306	7	r(γ′′	r(γ′′	PROPN
ejpam-5051	306	8	)	)	PUNCT
ejpam-5051	306	9	)	)	PUNCT
ejpam-5051	307	1	=	=	PRON
ejpam-5051	307	2	(	(	PUNCT
ejpam-5051	307	3	χ′′	χ′′	PROPN
ejpam-5051	307	4	,	,	PUNCT
ejpam-5051	307	5	r(γ′′	r(γ′′	PROPN
ejpam-5051	307	6	)	)	PUNCT
ejpam-5051	307	7	)	)	PUNCT
ejpam-5051	307	8	=	=	PUNCT
ejpam-5051	308	1	r(χ′′	r(χ′′	VERB
ejpam-5051	308	2	,	,	PUNCT
ejpam-5051	308	3	γ̇′′	γ̇′′	NOUN
ejpam-5051	308	4	)	)	PUNCT
ejpam-5051	308	5	;	;	PUNCT
ejpam-5051	308	6	r[(χ′	r[(χ′	NOUN
ejpam-5051	308	7	,	,	PUNCT
ejpam-5051	308	8	γ̇′)(χ′′	γ̇′)(χ′′	PROPN
ejpam-5051	308	9	,	,	PUNCT
ejpam-5051	308	10	γ̇′′	γ̇′′	NOUN
ejpam-5051	308	11	)	)	PUNCT
ejpam-5051	308	12	]	]	PUNCT
ejpam-5051	308	13	=	=	PUNCT
ejpam-5051	308	14	r((χ′	r((χ′	NOUN
ejpam-5051	308	15	,	,	PUNCT
ejpam-5051	308	16	γ̇′γ̇′′	γ̇′γ̇′′	NOUN
ejpam-5051	308	17	)	)	PUNCT
ejpam-5051	308	18	)	)	PUNCT
ejpam-5051	309	1	=	=	PRON
ejpam-5051	309	2	(	(	PUNCT
ejpam-5051	309	3	χ′	χ′	PROPN
ejpam-5051	309	4	,	,	PUNCT
ejpam-5051	309	5	r(γ′γ′′	r(γ′γ′′	NUM
ejpam-5051	309	6	)	)	PUNCT
ejpam-5051	309	7	)	)	PUNCT
ejpam-5051	310	1	=	=	SYM
ejpam-5051	310	2	(	(	PUNCT
ejpam-5051	310	3	χ′	χ′	PROPN
ejpam-5051	310	4	,	,	PUNCT
ejpam-5051	310	5	r(γ′	r(γ′	NOUN
ejpam-5051	310	6	)	)	PUNCT
ejpam-5051	310	7	)	)	PUNCT
ejpam-5051	311	1	=	=	PUNCT
ejpam-5051	311	2	(	(	PUNCT
ejpam-5051	311	3	χ	χ	X
ejpam-5051	311	4	·	·	PUNCT
ejpam-5051	311	5	γ	γ	X
ejpam-5051	311	6	,	,	PUNCT
ejpam-5051	311	7	s(γ	s(γ	PROPN
ejpam-5051	311	8	)	)	PUNCT
ejpam-5051	311	9	)	)	PUNCT
ejpam-5051	311	10	=	=	SYM
ejpam-5051	312	1	s((χ	s((χ	NOUN
ejpam-5051	312	2	,	,	PUNCT
ejpam-5051	312	3	γ̇	γ̇	NOUN
ejpam-5051	312	4	)	)	PUNCT
ejpam-5051	312	5	)	)	PUNCT
ejpam-5051	312	6	.	.	PUNCT
ejpam-5051	313	1	hence	hence	ADV
ejpam-5051	313	2	,	,	PUNCT
ejpam-5051	313	3	(	(	PUNCT
ejpam-5051	313	4	(	(	PUNCT
ejpam-5051	313	5	χ	χ	X
ejpam-5051	313	6	,	,	PUNCT
ejpam-5051	313	7	γ̇)(χ′	γ̇)(χ′	NOUN
ejpam-5051	313	8	,	,	PUNCT
ejpam-5051	313	9	γ̇′	γ̇′	NOUN
ejpam-5051	313	10	)	)	PUNCT
ejpam-5051	313	11	,	,	PUNCT
ejpam-5051	313	12	(	(	PUNCT
ejpam-5051	313	13	χ′′	χ′′	PROPN
ejpam-5051	313	14	,	,	PUNCT
ejpam-5051	313	15	γ̇′′	γ̇′′	NOUN
ejpam-5051	313	16	)	)	PUNCT
ejpam-5051	313	17	)	)	PUNCT
ejpam-5051	313	18	∈	∈	PROPN
ejpam-5051	313	19	(	(	PUNCT
ejpam-5051	313	20	â⋊r)(2	â⋊r)(2	ADV
ejpam-5051	313	21	)	)	PUNCT
ejpam-5051	313	22	and	and	CCONJ
ejpam-5051	313	23	(	(	PUNCT
ejpam-5051	313	24	(	(	PUNCT
ejpam-5051	313	25	χ	χ	X
ejpam-5051	313	26	,	,	PUNCT
ejpam-5051	313	27	γ̇	γ̇	NOUN
ejpam-5051	313	28	)	)	PUNCT
ejpam-5051	313	29	,	,	PUNCT
ejpam-5051	313	30	(	(	PUNCT
ejpam-5051	313	31	χ′	χ′	PROPN
ejpam-5051	313	32	,	,	PUNCT
ejpam-5051	313	33	γ̇′)(χ′′	γ̇′)(χ′′	PROPN
ejpam-5051	313	34	,	,	PUNCT
ejpam-5051	313	35	γ̇′′	γ̇′′	NOUN
ejpam-5051	313	36	)	)	PUNCT
ejpam-5051	313	37	)	)	PUNCT
ejpam-5051	313	38	∈	∈	PROPN
ejpam-5051	313	39	(	(	PUNCT
ejpam-5051	313	40	â⋊r)(2	â⋊r)(2	ADJ
ejpam-5051	313	41	)	)	PUNCT
ejpam-5051	313	42	.	.	PUNCT
ejpam-5051	314	1	now	now	ADV
ejpam-5051	314	2	,	,	PUNCT
ejpam-5051	314	3	[	[	X
ejpam-5051	314	4	(	(	PUNCT
ejpam-5051	314	5	χ	χ	NOUN
ejpam-5051	314	6	,	,	PUNCT
ejpam-5051	314	7	γ̇)(χ′	γ̇)(χ′	PROPN
ejpam-5051	314	8	,	,	PUNCT
ejpam-5051	314	9	γ̇′)](χ′′	γ̇′)](χ′′	NOUN
ejpam-5051	314	10	,	,	PUNCT
ejpam-5051	314	11	γ̇′′	γ̇′′	NOUN
ejpam-5051	314	12	)	)	PUNCT
ejpam-5051	314	13	=	=	SYM
ejpam-5051	314	14	(	(	PUNCT
ejpam-5051	314	15	χ	χ	X
ejpam-5051	314	16	,	,	PUNCT
ejpam-5051	314	17	γ̇γ̇′)(χ′′	γ̇γ̇′)(χ′′	PROPN
ejpam-5051	314	18	,	,	PUNCT
ejpam-5051	314	19	γ̇′′	γ̇′′	NOUN
ejpam-5051	314	20	)	)	PUNCT
ejpam-5051	314	21	=	=	SYM
ejpam-5051	314	22	(	(	PUNCT
ejpam-5051	314	23	χ	χ	X
ejpam-5051	314	24	,	,	PUNCT
ejpam-5051	314	25	γ̇γ̇′γ̇′′	γ̇γ̇′γ̇′′	PROPN
ejpam-5051	314	26	)	)	PUNCT
ejpam-5051	314	27	=	=	PUNCT
ejpam-5051	314	28	(	(	PUNCT
ejpam-5051	314	29	χ	χ	NOUN
ejpam-5051	314	30	,	,	PUNCT
ejpam-5051	314	31	γ̇)(χ′	γ̇)(χ′	NOUN
ejpam-5051	314	32	,	,	PUNCT
ejpam-5051	314	33	γ̇′γ̇′′	γ̇′γ̇′′	NOUN
ejpam-5051	314	34	)	)	PUNCT
ejpam-5051	314	35	=	=	PUNCT
ejpam-5051	314	36	(	(	PUNCT
ejpam-5051	314	37	χ	χ	NOUN
ejpam-5051	314	38	,	,	PUNCT
ejpam-5051	314	39	γ̇)[(χ′	γ̇)[(χ′	NOUN
ejpam-5051	314	40	,	,	PUNCT
ejpam-5051	314	41	γ̇′)(χ′′	γ̇′)(χ′′	NOUN
ejpam-5051	314	42	,	,	PUNCT
ejpam-5051	314	43	γ̇′′	γ̇′′	NOUN
ejpam-5051	314	44	)	)	PUNCT
ejpam-5051	314	45	]	]	PUNCT
ejpam-5051	314	46	.	.	PUNCT
ejpam-5051	314	47	r.	r.	PROPN
ejpam-5051	314	48	s.	s.	PROPN
ejpam-5051	314	49	bongcawel	bongcawel	PROPN
ejpam-5051	314	50	et	et	PROPN
ejpam-5051	314	51	al	al	PROPN
ejpam-5051	314	52	.	.	PUNCT
ejpam-5051	314	53	/	/	SYM
ejpam-5051	314	54	eur	eur	PROPN
ejpam-5051	314	55	.	.	PUNCT
ejpam-5051	315	1	j.	j.	PROPN
ejpam-5051	315	2	pure	pure	PROPN
ejpam-5051	315	3	appl	appl	PROPN
ejpam-5051	315	4	.	.	PROPN
ejpam-5051	315	5	math	math	PROPN
ejpam-5051	315	6	,	,	PUNCT
ejpam-5051	315	7	17	17	NUM
ejpam-5051	315	8	(	(	PUNCT
ejpam-5051	315	9	1	1	NUM
ejpam-5051	315	10	)	)	PUNCT
ejpam-5051	315	11	(	(	PUNCT
ejpam-5051	315	12	2024	2024	NUM
ejpam-5051	315	13	)	)	PUNCT
ejpam-5051	315	14	,	,	PUNCT
ejpam-5051	315	15	519	519	NUM
ejpam-5051	315	16	-	-	SYM
ejpam-5051	315	17	545	545	NUM
ejpam-5051	315	18	528	528	NUM
ejpam-5051	315	19	let	let	VERB
ejpam-5051	315	20	(	(	PUNCT
ejpam-5051	315	21	χ	χ	X
ejpam-5051	315	22	,	,	PUNCT
ejpam-5051	315	23	γ̇	γ̇	NOUN
ejpam-5051	315	24	)	)	PUNCT
ejpam-5051	315	25	∈	∈	PROPN
ejpam-5051	315	26	â⋊r	â⋊r	NOUN
ejpam-5051	315	27	.	.	PUNCT
ejpam-5051	316	1	then	then	ADV
ejpam-5051	316	2	(	(	PUNCT
ejpam-5051	316	3	(	(	PUNCT
ejpam-5051	316	4	χ	χ	X
ejpam-5051	316	5	,	,	PUNCT
ejpam-5051	316	6	γ̇)−1)−1	γ̇)−1)−1	PROPN
ejpam-5051	316	7	=	=	SYM
ejpam-5051	316	8	(	(	PUNCT
ejpam-5051	316	9	χ	χ	X
ejpam-5051	316	10	·	·	PUNCT
ejpam-5051	316	11	γ	γ	X
ejpam-5051	316	12	,	,	PUNCT
ejpam-5051	316	13	γ̇−1	γ̇−1	PROPN
ejpam-5051	316	14	)	)	PUNCT
ejpam-5051	316	15	=	=	PUNCT
ejpam-5051	316	16	(	(	PUNCT
ejpam-5051	316	17	χ	χ	X
ejpam-5051	316	18	·	·	PUNCT
ejpam-5051	316	19	γγ−1	γγ−1	PROPN
ejpam-5051	316	20	,	,	PUNCT
ejpam-5051	316	21	(	(	PUNCT
ejpam-5051	316	22	γ̇−1)−1	γ̇−1)−1	NUM
ejpam-5051	316	23	)	)	PUNCT
ejpam-5051	316	24	=	=	PUNCT
ejpam-5051	316	25	(	(	PUNCT
ejpam-5051	316	26	χ	χ	X
ejpam-5051	316	27	·	·	PUNCT
ejpam-5051	316	28	r(γ	r(γ	NOUN
ejpam-5051	316	29	)	)	PUNCT
ejpam-5051	316	30	,	,	PUNCT
ejpam-5051	316	31	γ̇	γ̇	NOUN
ejpam-5051	316	32	)	)	PUNCT
ejpam-5051	316	33	=	=	PUNCT
ejpam-5051	316	34	(	(	PUNCT
ejpam-5051	316	35	χ	χ	X
ejpam-5051	316	36	·	·	PUNCT
ejpam-5051	316	37	u	u	NOUN
ejpam-5051	316	38	,	,	PUNCT
ejpam-5051	316	39	γ̇	γ̇	NOUN
ejpam-5051	316	40	)	)	PUNCT
ejpam-5051	316	41	=	=	PUNCT
ejpam-5051	316	42	(	(	PUNCT
ejpam-5051	316	43	χ	χ	NOUN
ejpam-5051	316	44	,	,	PUNCT
ejpam-5051	316	45	γ̇	γ̇	NOUN
ejpam-5051	316	46	)	)	PUNCT
ejpam-5051	316	47	;	;	PUNCT
ejpam-5051	317	1	r((χ	r((χ	ADJ
ejpam-5051	317	2	,	,	PUNCT
ejpam-5051	317	3	γ̇)−1	γ̇)−1	NOUN
ejpam-5051	317	4	)	)	PUNCT
ejpam-5051	317	5	=	=	SYM
ejpam-5051	317	6	r((χ	r((χ	X
ejpam-5051	317	7	·	·	PUNCT
ejpam-5051	318	1	γ	γ	X
ejpam-5051	318	2	,	,	PUNCT
ejpam-5051	318	3	γ̇−1	γ̇−1	PROPN
ejpam-5051	318	4	)	)	PUNCT
ejpam-5051	318	5	)	)	PUNCT
ejpam-5051	319	1	=	=	PUNCT
ejpam-5051	319	2	(	(	PUNCT
ejpam-5051	319	3	χ	χ	X
ejpam-5051	319	4	·	·	PUNCT
ejpam-5051	319	5	γ	γ	X
ejpam-5051	319	6	,	,	PUNCT
ejpam-5051	319	7	r(γ−1	r(γ−1	ADJ
ejpam-5051	319	8	)	)	PUNCT
ejpam-5051	319	9	=	=	SYM
ejpam-5051	319	10	(	(	PUNCT
ejpam-5051	319	11	χ	χ	X
ejpam-5051	319	12	·	·	PUNCT
ejpam-5051	319	13	γ	γ	X
ejpam-5051	319	14	,	,	PUNCT
ejpam-5051	319	15	s(γ	s(γ	PROPN
ejpam-5051	319	16	)	)	PUNCT
ejpam-5051	319	17	)	)	PUNCT
ejpam-5051	319	18	=	=	SYM
ejpam-5051	320	1	s((χ	s((χ	NOUN
ejpam-5051	320	2	,	,	PUNCT
ejpam-5051	320	3	γ̇	γ̇	NOUN
ejpam-5051	320	4	)	)	PUNCT
ejpam-5051	320	5	)	)	PUNCT
ejpam-5051	320	6	.	.	PUNCT
ejpam-5051	321	1	hence	hence	ADV
ejpam-5051	321	2	,	,	PUNCT
ejpam-5051	321	3	(	(	PUNCT
ejpam-5051	321	4	(	(	PUNCT
ejpam-5051	321	5	χ	χ	X
ejpam-5051	321	6	,	,	PUNCT
ejpam-5051	321	7	γ̇	γ̇	NOUN
ejpam-5051	321	8	)	)	PUNCT
ejpam-5051	321	9	,	,	PUNCT
ejpam-5051	321	10	(	(	PUNCT
ejpam-5051	321	11	χ	χ	ADJ
ejpam-5051	321	12	,	,	PUNCT
ejpam-5051	321	13	γ̇)−1	γ̇)−1	NOUN
ejpam-5051	321	14	)	)	PUNCT
ejpam-5051	321	15	∈	∈	PROPN
ejpam-5051	321	16	(	(	PUNCT
ejpam-5051	321	17	â⋊r)(2	â⋊r)(2	ADV
ejpam-5051	321	18	)	)	PUNCT
ejpam-5051	321	19	.	.	PUNCT
ejpam-5051	321	20	suppose	suppose	VERB
ejpam-5051	321	21	that	that	SCONJ
ejpam-5051	321	22	(	(	PUNCT
ejpam-5051	321	23	(	(	PUNCT
ejpam-5051	321	24	χ′	χ′	PROPN
ejpam-5051	321	25	,	,	PUNCT
ejpam-5051	321	26	γ̇′	γ̇′	NOUN
ejpam-5051	321	27	)	)	PUNCT
ejpam-5051	321	28	,	,	PUNCT
ejpam-5051	321	29	(	(	PUNCT
ejpam-5051	321	30	χ	χ	X
ejpam-5051	321	31	,	,	PUNCT
ejpam-5051	321	32	γ̇	γ̇	NOUN
ejpam-5051	321	33	)	)	PUNCT
ejpam-5051	321	34	)	)	PUNCT
ejpam-5051	321	35	∈	∈	PROPN
ejpam-5051	321	36	(	(	PUNCT
ejpam-5051	321	37	â⋊r)(2	â⋊r)(2	ADJ
ejpam-5051	321	38	)	)	PUNCT
ejpam-5051	321	39	.	.	PUNCT
ejpam-5051	322	1	then	then	ADV
ejpam-5051	322	2	,	,	PUNCT
ejpam-5051	322	3	[	[	X
ejpam-5051	322	4	(	(	PUNCT
ejpam-5051	322	5	χ′	χ′	PROPN
ejpam-5051	322	6	,	,	PUNCT
ejpam-5051	322	7	γ̇′)(χ	γ̇′)(χ	NOUN
ejpam-5051	322	8	,	,	PUNCT
ejpam-5051	322	9	γ̇)](χ	γ̇)](χ	NOUN
ejpam-5051	322	10	,	,	PUNCT
ejpam-5051	322	11	γ̇)−1	γ̇)−1	NOUN
ejpam-5051	322	12	=	=	SYM
ejpam-5051	322	13	(	(	PUNCT
ejpam-5051	322	14	χ	χ	NOUN
ejpam-5051	322	15	,	,	PUNCT
ejpam-5051	322	16	γ̇γ̇′)(χ′	γ̇γ̇′)(χ′	PROPN
ejpam-5051	322	17	,	,	PUNCT
ejpam-5051	322	18	γ̇′)−1	γ̇′)−1	PROPN
ejpam-5051	322	19	=	=	SYM
ejpam-5051	322	20	(	(	PUNCT
ejpam-5051	322	21	χ	χ	NOUN
ejpam-5051	322	22	,	,	PUNCT
ejpam-5051	322	23	γ̇γ̇′)(χ′	γ̇γ̇′)(χ′	NOUN
ejpam-5051	322	24	·	·	PUNCT
ejpam-5051	322	25	γ′	γ′	PROPN
ejpam-5051	322	26	,	,	PUNCT
ejpam-5051	322	27	(	(	PUNCT
ejpam-5051	322	28	γ̇′)−1	γ̇′)−1	PROPN
ejpam-5051	322	29	)	)	PUNCT
ejpam-5051	322	30	=	=	PUNCT
ejpam-5051	323	1	(	(	PUNCT
ejpam-5051	323	2	χ	χ	NOUN
ejpam-5051	323	3	,	,	PUNCT
ejpam-5051	323	4	γ̇γ̇′(γ̇′)−1	γ̇γ̇′(γ̇′)−1	NOUN
ejpam-5051	323	5	)	)	PUNCT
ejpam-5051	324	1	=	=	PUNCT
ejpam-5051	324	2	(	(	PUNCT
ejpam-5051	324	3	χ	χ	NOUN
ejpam-5051	324	4	,	,	PUNCT
ejpam-5051	324	5	γ̇r((γ̇′	γ̇r((γ̇′	NOUN
ejpam-5051	324	6	)	)	PUNCT
ejpam-5051	324	7	)	)	PUNCT
ejpam-5051	325	1	=	=	PUNCT
ejpam-5051	325	2	(	(	PUNCT
ejpam-5051	325	3	χ	χ	NOUN
ejpam-5051	325	4	,	,	PUNCT
ejpam-5051	325	5	γ̇s(γ̇	γ̇s(γ̇	NOUN
ejpam-5051	325	6	)	)	PUNCT
ejpam-5051	325	7	)	)	PUNCT
ejpam-5051	326	1	=	=	PUNCT
ejpam-5051	326	2	(	(	PUNCT
ejpam-5051	326	3	χ	χ	X
ejpam-5051	326	4	,	,	PUNCT
ejpam-5051	326	5	γ̇	γ̇	NOUN
ejpam-5051	326	6	)	)	PUNCT
ejpam-5051	326	7	also	also	ADV
ejpam-5051	326	8	,	,	PUNCT
ejpam-5051	326	9	(	(	PUNCT
ejpam-5051	326	10	χ	χ	X
ejpam-5051	326	11	,	,	PUNCT
ejpam-5051	326	12	γ̇)−1[(χ	γ̇)−1[(χ	NOUN
ejpam-5051	326	13	,	,	PUNCT
ejpam-5051	326	14	γ̇)(χ′	γ̇)(χ′	NOUN
ejpam-5051	326	15	,	,	PUNCT
ejpam-5051	326	16	γ̇′	γ̇′	NOUN
ejpam-5051	326	17	)	)	PUNCT
ejpam-5051	326	18	]	]	PUNCT
ejpam-5051	327	1	=	=	PUNCT
ejpam-5051	327	2	(	(	PUNCT
ejpam-5051	327	3	χ	χ	NOUN
ejpam-5051	327	4	,	,	PUNCT
ejpam-5051	327	5	γ̇)−1(χ	γ̇)−1(χ	NOUN
ejpam-5051	327	6	,	,	PUNCT
ejpam-5051	327	7	γ̇γ̇′	γ̇γ̇′	NUM
ejpam-5051	327	8	)	)	PUNCT
ejpam-5051	327	9	=	=	PUNCT
ejpam-5051	327	10	(	(	PUNCT
ejpam-5051	327	11	χ	χ	X
ejpam-5051	327	12	·	·	PUNCT
ejpam-5051	327	13	γ	γ	X
ejpam-5051	327	14	,	,	PUNCT
ejpam-5051	327	15	γ̇−1)(χ	γ̇−1)(χ	PROPN
ejpam-5051	327	16	,	,	PUNCT
ejpam-5051	327	17	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	327	18	)	)	PUNCT
ejpam-5051	327	19	=	=	PUNCT
ejpam-5051	327	20	(	(	PUNCT
ejpam-5051	327	21	χ	χ	X
ejpam-5051	327	22	·	·	PUNCT
ejpam-5051	327	23	γ	γ	NOUN
ejpam-5051	327	24	,	,	PUNCT
ejpam-5051	327	25	γ̇−1γ̇γ̇′	γ̇−1γ̇γ̇′	NOUN
ejpam-5051	327	26	)	)	PUNCT
ejpam-5051	327	27	=	=	PUNCT
ejpam-5051	328	1	(	(	PUNCT
ejpam-5051	328	2	χ	χ	X
ejpam-5051	328	3	·	·	PUNCT
ejpam-5051	328	4	γ	γ	X
ejpam-5051	328	5	,	,	PUNCT
ejpam-5051	328	6	s(γ̇)γ̇′	s(γ̇)γ̇′	NOUN
ejpam-5051	328	7	)	)	PUNCT
ejpam-5051	328	8	=	=	PUNCT
ejpam-5051	328	9	(	(	PUNCT
ejpam-5051	328	10	χ	χ	X
ejpam-5051	328	11	·	·	PUNCT
ejpam-5051	328	12	γ	γ	NOUN
ejpam-5051	328	13	,	,	PUNCT
ejpam-5051	328	14	r(γ̇′)γ̇′	r(γ̇′)γ̇′	NOUN
ejpam-5051	328	15	)	)	PUNCT
ejpam-5051	329	1	=	=	SYM
ejpam-5051	329	2	(	(	PUNCT
ejpam-5051	329	3	χ′	χ′	PROPN
ejpam-5051	329	4	,	,	PUNCT
ejpam-5051	329	5	γ̇′	γ̇′	NOUN
ejpam-5051	329	6	)	)	PUNCT
ejpam-5051	329	7	therefore	therefore	ADV
ejpam-5051	329	8	,	,	PUNCT
ejpam-5051	329	9	â⋊r	â⋊r	PROPN
ejpam-5051	329	10	is	be	AUX
ejpam-5051	329	11	a	a	DET
ejpam-5051	329	12	groupoid	groupoid	PROPN
ejpam-5051	329	13	.	.	PUNCT
ejpam-5051	330	1	lemma	lemma	PROPN
ejpam-5051	330	2	5	5	NUM
ejpam-5051	330	3	.	.	PUNCT
ejpam-5051	331	1	â⋊r	â⋊r	PROPN
ejpam-5051	331	2	is	be	AUX
ejpam-5051	331	3	an	an	DET
ejpam-5051	331	4	ample	ample	ADJ
ejpam-5051	331	5	hausdorff	hausdorff	NOUN
ejpam-5051	331	6	groupoid	groupoid	PROPN
ejpam-5051	331	7	.	.	PUNCT
ejpam-5051	332	1	proof	proof	NOUN
ejpam-5051	332	2	.	.	PUNCT
ejpam-5051	333	1	let	let	VERB
ejpam-5051	333	2	u	u	PRON
ejpam-5051	333	3	be	be	AUX
ejpam-5051	333	4	open	open	ADJ
ejpam-5051	333	5	in	in	ADP
ejpam-5051	333	6	â	â	PRON
ejpam-5051	333	7	⋊	⋊	PROPN
ejpam-5051	333	8	r.	r.	NOUN
ejpam-5051	333	9	then	then	ADV
ejpam-5051	333	10	u	u	X
ejpam-5051	333	11	=	=	PUNCT
ejpam-5051	333	12	(	(	PUNCT
ejpam-5051	333	13	a	a	DET
ejpam-5051	333	14	×	×	PROPN
ejpam-5051	333	15	b	b	NOUN
ejpam-5051	333	16	)	)	PUNCT
ejpam-5051	333	17	∩	∩	NOUN
ejpam-5051	333	18	(	(	PUNCT
ejpam-5051	333	19	â	â	X
ejpam-5051	333	20	⋊	⋊	X
ejpam-5051	333	21	r	r	NOUN
ejpam-5051	333	22	)	)	PUNCT
ejpam-5051	333	23	where	where	SCONJ
ejpam-5051	333	24	a	a	DET
ejpam-5051	333	25	×	×	PROPN
ejpam-5051	333	26	b	b	NOUN
ejpam-5051	333	27	is	be	AUX
ejpam-5051	333	28	open	open	ADJ
ejpam-5051	333	29	in	in	ADP
ejpam-5051	333	30	â	â	PROPN
ejpam-5051	333	31	×	×	PROPN
ejpam-5051	333	32	r.	r.	PROPN
ejpam-5051	333	33	let	let	VERB
ejpam-5051	333	34	(	(	PUNCT
ejpam-5051	333	35	(	(	PUNCT
ejpam-5051	333	36	χ	χ	X
ejpam-5051	333	37	,	,	PUNCT
ejpam-5051	333	38	γ̇	γ̇	NOUN
ejpam-5051	333	39	)	)	PUNCT
ejpam-5051	333	40	,	,	PUNCT
ejpam-5051	333	41	(	(	PUNCT
ejpam-5051	333	42	χ′	χ′	PROPN
ejpam-5051	333	43	,	,	PUNCT
ejpam-5051	333	44	γ̇′	γ̇′	NOUN
ejpam-5051	333	45	)	)	PUNCT
ejpam-5051	333	46	)	)	PUNCT
ejpam-5051	334	1	∈	∈	PROPN
ejpam-5051	334	2	m−1(u	m−1(u	PROPN
ejpam-5051	334	3	)	)	PUNCT
ejpam-5051	334	4	.	.	PUNCT
ejpam-5051	335	1	then	then	ADV
ejpam-5051	335	2	(	(	PUNCT
ejpam-5051	335	3	χ	χ	X
ejpam-5051	335	4	,	,	PUNCT
ejpam-5051	335	5	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	335	6	)	)	PUNCT
ejpam-5051	335	7	∈	∈	PROPN
ejpam-5051	335	8	(	(	PUNCT
ejpam-5051	335	9	a	a	DET
ejpam-5051	335	10	×	×	PROPN
ejpam-5051	335	11	b	b	NOUN
ejpam-5051	335	12	)	)	PUNCT
ejpam-5051	335	13	and	and	CCONJ
ejpam-5051	335	14	(	(	PUNCT
ejpam-5051	335	15	χ	χ	X
ejpam-5051	335	16	,	,	PUNCT
ejpam-5051	335	17	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	335	18	)	)	PUNCT
ejpam-5051	335	19	∈	∈	PROPN
ejpam-5051	335	20	â	â	X
ejpam-5051	335	21	⋊	⋊	PROPN
ejpam-5051	335	22	r.	r.	NOUN
ejpam-5051	335	23	since	since	SCONJ
ejpam-5051	335	24	a	a	DET
ejpam-5051	335	25	×	×	PROPN
ejpam-5051	335	26	b	b	NOUN
ejpam-5051	335	27	is	be	AUX
ejpam-5051	335	28	open	open	ADJ
ejpam-5051	335	29	in	in	ADP
ejpam-5051	335	30	â	â	X
ejpam-5051	335	31	×	×	PROPN
ejpam-5051	335	32	r	r	NOUN
ejpam-5051	335	33	,	,	PUNCT
ejpam-5051	335	34	then	then	ADV
ejpam-5051	335	35	there	there	PRON
ejpam-5051	335	36	exists	exist	VERB
ejpam-5051	335	37	open	open	ADJ
ejpam-5051	335	38	set	set	NOUN
ejpam-5051	335	39	(	(	PUNCT
ejpam-5051	335	40	a	a	DET
ejpam-5051	335	41	×	×	NOUN
ejpam-5051	336	1	b)′	b)′	NOUN
ejpam-5051	336	2	containing	contain	VERB
ejpam-5051	336	3	(	(	PUNCT
ejpam-5051	336	4	χ	χ	ADJ
ejpam-5051	336	5	,	,	PUNCT
ejpam-5051	336	6	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	336	7	)	)	PUNCT
ejpam-5051	336	8	such	such	ADJ
ejpam-5051	336	9	that	that	SCONJ
ejpam-5051	336	10	(	(	PUNCT
ejpam-5051	336	11	a	a	DET
ejpam-5051	336	12	×	×	NOUN
ejpam-5051	336	13	b)′	b)′	PROPN
ejpam-5051	336	14	⊆	⊆	NUM
ejpam-5051	336	15	a	a	DET
ejpam-5051	336	16	×	×	PROPN
ejpam-5051	336	17	b.	b.	NOUN
ejpam-5051	336	18	also	also	ADV
ejpam-5051	336	19	there	there	PRON
ejpam-5051	336	20	exists	exist	VERB
ejpam-5051	336	21	open	open	ADJ
ejpam-5051	336	22	set	set	VERB
ejpam-5051	336	23	w	w	NOUN
ejpam-5051	336	24	in	in	ADP
ejpam-5051	336	25	â	â	PROPN
ejpam-5051	336	26	⋊r	⋊r	PROPN
ejpam-5051	336	27	containing	contain	VERB
ejpam-5051	336	28	(	(	PUNCT
ejpam-5051	336	29	χ	χ	NOUN
ejpam-5051	336	30	,	,	PUNCT
ejpam-5051	336	31	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	336	32	)	)	PUNCT
ejpam-5051	336	33	.	.	PUNCT
ejpam-5051	337	1	since	since	SCONJ
ejpam-5051	337	2	â	â	PRON
ejpam-5051	337	3	⋊	⋊	NUM
ejpam-5051	337	4	r	r	NOUN
ejpam-5051	337	5	⊆	⊆	NUM
ejpam-5051	337	6	â	â	X
ejpam-5051	337	7	×	×	PROPN
ejpam-5051	337	8	r	r	NOUN
ejpam-5051	337	9	,	,	PUNCT
ejpam-5051	337	10	then	then	ADV
ejpam-5051	337	11	there	there	PRON
ejpam-5051	337	12	exists	exist	VERB
ejpam-5051	337	13	open	open	ADJ
ejpam-5051	337	14	set	set	VERB
ejpam-5051	337	15	w	w	ADP
ejpam-5051	337	16	′	′	NUM
ejpam-5051	337	17	in	in	ADP
ejpam-5051	337	18	â	â	X
ejpam-5051	337	19	×	×	NOUN
ejpam-5051	337	20	r	r	NOUN
ejpam-5051	337	21	containing	contain	VERB
ejpam-5051	337	22	(	(	PUNCT
ejpam-5051	337	23	χ	χ	NOUN
ejpam-5051	337	24	,	,	PUNCT
ejpam-5051	337	25	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	337	26	)	)	PUNCT
ejpam-5051	337	27	where	where	SCONJ
ejpam-5051	337	28	w	w	ADP
ejpam-5051	337	29	′	′	NOUN
ejpam-5051	337	30	=	=	PUNCT
ejpam-5051	337	31	w	w	PROPN
ejpam-5051	337	32	∩	∩	X
ejpam-5051	337	33	â	â	PRON
ejpam-5051	337	34	⋊r	⋊r	PROPN
ejpam-5051	337	35	.	.	PUNCT
ejpam-5051	338	1	consider	consider	VERB
ejpam-5051	338	2	the	the	DET
ejpam-5051	338	3	set	set	NOUN
ejpam-5051	338	4	(	(	PUNCT
ejpam-5051	338	5	a	a	DET
ejpam-5051	338	6	×	×	NOUN
ejpam-5051	338	7	b)′	b)′	NOUN
ejpam-5051	338	8	×w	×w	NOUN
ejpam-5051	338	9	′	′	NUM
ejpam-5051	338	10	⊆	⊆	NUM
ejpam-5051	338	11	(	(	PUNCT
ejpam-5051	338	12	â	â	X
ejpam-5051	338	13	×r	×r	NUM
ejpam-5051	338	14	)	)	PUNCT
ejpam-5051	338	15	×	×	NOUN
ejpam-5051	338	16	(	(	PUNCT
ejpam-5051	338	17	â	â	X
ejpam-5051	338	18	×r	×r	NOUN
ejpam-5051	338	19	)	)	PUNCT
ejpam-5051	338	20	where	where	SCONJ
ejpam-5051	338	21	(	(	PUNCT
ejpam-5051	338	22	a	a	DET
ejpam-5051	338	23	×	×	NOUN
ejpam-5051	338	24	b)′	b)′	PROPN
ejpam-5051	338	25	∈	∈	PROPN
ejpam-5051	338	26	τâ×r	τâ×r	PROPN
ejpam-5051	338	27	and	and	CCONJ
ejpam-5051	338	28	w	w	NOUN
ejpam-5051	338	29	′	′	NUM
ejpam-5051	338	30	∈	∈	PROPN
ejpam-5051	338	31	τâ×r	τâ×r	NOUN
ejpam-5051	338	32	.	.	PUNCT
ejpam-5051	339	1	it	it	PRON
ejpam-5051	339	2	follows	follow	VERB
ejpam-5051	339	3	that	that	SCONJ
ejpam-5051	339	4	(	(	PUNCT
ejpam-5051	339	5	a	a	DET
ejpam-5051	339	6	×	×	NOUN
ejpam-5051	339	7	b)′	b)′	NOUN
ejpam-5051	339	8	×	×	NOUN
ejpam-5051	339	9	w	w	NOUN
ejpam-5051	339	10	′	′	NUM
ejpam-5051	339	11	is	be	AUX
ejpam-5051	339	12	open	open	ADJ
ejpam-5051	339	13	in	in	ADP
ejpam-5051	339	14	(	(	PUNCT
ejpam-5051	339	15	â	â	X
ejpam-5051	339	16	×	×	PROPN
ejpam-5051	339	17	r	r	NOUN
ejpam-5051	339	18	)	)	PUNCT
ejpam-5051	339	19	×	×	NOUN
ejpam-5051	339	20	(	(	PUNCT
ejpam-5051	339	21	â	â	X
ejpam-5051	339	22	×	×	PROPN
ejpam-5051	339	23	r	r	NOUN
ejpam-5051	339	24	)	)	PUNCT
ejpam-5051	339	25	.	.	PUNCT
ejpam-5051	340	1	define	define	VERB
ejpam-5051	340	2	m	m	NOUN
ejpam-5051	340	3	=	=	SYM
ejpam-5051	340	4	(	(	PUNCT
ejpam-5051	340	5	(	(	PUNCT
ejpam-5051	340	6	a	a	DET
ejpam-5051	340	7	×	×	NOUN
ejpam-5051	340	8	b)′	b)′	X
ejpam-5051	340	9	×	×	PROPN
ejpam-5051	340	10	w	w	PROPN
ejpam-5051	340	11	′	′	NOUN
ejpam-5051	340	12	)	)	PUNCT
ejpam-5051	340	13	∩	∩	NOUN
ejpam-5051	340	14	(	(	PUNCT
ejpam-5051	340	15	â	â	X
ejpam-5051	340	16	⋊	⋊	X
ejpam-5051	340	17	r)(2	r)(2	X
ejpam-5051	340	18	)	)	PUNCT
ejpam-5051	340	19	=	=	PRON
ejpam-5051	340	20	{	{	PUNCT
ejpam-5051	340	21	(	(	PUNCT
ejpam-5051	340	22	(	(	PUNCT
ejpam-5051	340	23	χ	χ	X
ejpam-5051	340	24	,	,	PUNCT
ejpam-5051	340	25	γ̇	γ̇	NOUN
ejpam-5051	340	26	)	)	PUNCT
ejpam-5051	340	27	,	,	PUNCT
ejpam-5051	340	28	(	(	PUNCT
ejpam-5051	340	29	χ′	χ′	PROPN
ejpam-5051	340	30	,	,	PUNCT
ejpam-5051	340	31	γ̇′	γ̇′	NOUN
ejpam-5051	340	32	)	)	PUNCT
ejpam-5051	340	33	)	)	PUNCT
ejpam-5051	341	1	∈	∈	PROPN
ejpam-5051	341	2	r.	r.	PROPN
ejpam-5051	341	3	s.	s.	PROPN
ejpam-5051	341	4	bongcawel	bongcawel	PROPN
ejpam-5051	341	5	et	et	PROPN
ejpam-5051	341	6	al	al	PROPN
ejpam-5051	341	7	.	.	PUNCT
ejpam-5051	341	8	/	/	SYM
ejpam-5051	341	9	eur	eur	PROPN
ejpam-5051	341	10	.	.	PUNCT
ejpam-5051	342	1	j.	j.	PROPN
ejpam-5051	342	2	pure	pure	PROPN
ejpam-5051	342	3	appl	appl	PROPN
ejpam-5051	342	4	.	.	PROPN
ejpam-5051	342	5	math	math	PROPN
ejpam-5051	342	6	,	,	PUNCT
ejpam-5051	342	7	17	17	NUM
ejpam-5051	342	8	(	(	PUNCT
ejpam-5051	342	9	1	1	NUM
ejpam-5051	342	10	)	)	PUNCT
ejpam-5051	342	11	(	(	PUNCT
ejpam-5051	342	12	2024	2024	NUM
ejpam-5051	342	13	)	)	PUNCT
ejpam-5051	342	14	,	,	PUNCT
ejpam-5051	342	15	519	519	NUM
ejpam-5051	342	16	-	-	SYM
ejpam-5051	342	17	545	545	NUM
ejpam-5051	342	18	529	529	NUM
ejpam-5051	342	19	(	(	PUNCT
ejpam-5051	342	20	â	â	X
ejpam-5051	342	21	⋊	⋊	X
ejpam-5051	342	22	r)(2	r)(2	X
ejpam-5051	342	23	)	)	PUNCT
ejpam-5051	342	24	:	:	PUNCT
ejpam-5051	343	1	m(((χ	m(((χ	PROPN
ejpam-5051	343	2	,	,	PUNCT
ejpam-5051	343	3	γ̇	γ̇	PROPN
ejpam-5051	343	4	)	)	PUNCT
ejpam-5051	343	5	,	,	PUNCT
ejpam-5051	343	6	(	(	PUNCT
ejpam-5051	343	7	χ′	χ′	PROPN
ejpam-5051	343	8	,	,	PUNCT
ejpam-5051	343	9	γ̇′	γ̇′	NOUN
ejpam-5051	343	10	)	)	PUNCT
ejpam-5051	343	11	)	)	PUNCT
ejpam-5051	343	12	)	)	PUNCT
ejpam-5051	344	1	∈	∈	PROPN
ejpam-5051	344	2	(	(	PUNCT
ejpam-5051	344	3	a	a	DET
ejpam-5051	344	4	×	×	NOUN
ejpam-5051	344	5	b)′	b)′	PROPN
ejpam-5051	344	6	∩	∩	NOUN
ejpam-5051	344	7	w	w	PROPN
ejpam-5051	344	8	′	′	NOUN
ejpam-5051	344	9	}	}	PUNCT
ejpam-5051	344	10	.	.	PUNCT
ejpam-5051	345	1	we	we	PRON
ejpam-5051	345	2	claim	claim	VERB
ejpam-5051	345	3	that	that	SCONJ
ejpam-5051	345	4	m	m	PROPN
ejpam-5051	345	5	⊂	⊂	PROPN
ejpam-5051	345	6	m−1(u	m−1(u	PROPN
ejpam-5051	345	7	)	)	PUNCT
ejpam-5051	345	8	.	.	PUNCT
ejpam-5051	346	1	let	let	VERB
ejpam-5051	346	2	(	(	PUNCT
ejpam-5051	346	3	(	(	PUNCT
ejpam-5051	346	4	χ	χ	X
ejpam-5051	346	5	,	,	PUNCT
ejpam-5051	346	6	γ̇	γ̇	NOUN
ejpam-5051	346	7	)	)	PUNCT
ejpam-5051	346	8	,	,	PUNCT
ejpam-5051	346	9	(	(	PUNCT
ejpam-5051	346	10	χ′	χ′	PROPN
ejpam-5051	346	11	,	,	PUNCT
ejpam-5051	346	12	γ̇′	γ̇′	NOUN
ejpam-5051	346	13	)	)	PUNCT
ejpam-5051	346	14	)	)	PUNCT
ejpam-5051	347	1	∈	∈	PROPN
ejpam-5051	347	2	m	m	VERB
ejpam-5051	347	3	.	.	PUNCT
ejpam-5051	348	1	then	then	ADV
ejpam-5051	348	2	m(((χ	m(((χ	PROPN
ejpam-5051	348	3	,	,	PUNCT
ejpam-5051	348	4	γ̇	γ̇	PROPN
ejpam-5051	348	5	)	)	PUNCT
ejpam-5051	348	6	,	,	PUNCT
ejpam-5051	348	7	(	(	PUNCT
ejpam-5051	348	8	χ′	χ′	PROPN
ejpam-5051	348	9	,	,	PUNCT
ejpam-5051	348	10	γ̇′	γ̇′	NOUN
ejpam-5051	348	11	)	)	PUNCT
ejpam-5051	348	12	)	)	PUNCT
ejpam-5051	348	13	)	)	PUNCT
ejpam-5051	348	14	∈	∈	PROPN
ejpam-5051	348	15	(	(	PUNCT
ejpam-5051	348	16	a×	a×	NOUN
ejpam-5051	348	17	b)′	b)′	NOUN
ejpam-5051	349	1	∩w	∩w	NOUN
ejpam-5051	350	1	′	′	NUM
ejpam-5051	351	1	⊆	⊆	NUM
ejpam-5051	351	2	(	(	PUNCT
ejpam-5051	351	3	a×	a×	NOUN
ejpam-5051	351	4	b	b	NOUN
ejpam-5051	351	5	)	)	PUNCT
ejpam-5051	351	6	∩	∩	ADJ
ejpam-5051	351	7	â⋊r	â⋊r	NOUN
ejpam-5051	351	8	and	and	CCONJ
ejpam-5051	351	9	m(((χ	m(((χ	PROPN
ejpam-5051	351	10	,	,	PUNCT
ejpam-5051	351	11	γ̇	γ̇	PROPN
ejpam-5051	351	12	)	)	PUNCT
ejpam-5051	351	13	,	,	PUNCT
ejpam-5051	351	14	(	(	PUNCT
ejpam-5051	351	15	χ′	χ′	PROPN
ejpam-5051	351	16	,	,	PUNCT
ejpam-5051	351	17	γ̇′	γ̇′	NOUN
ejpam-5051	351	18	)	)	PUNCT
ejpam-5051	351	19	)	)	PUNCT
ejpam-5051	351	20	)	)	PUNCT
ejpam-5051	352	1	∈	∈	PROPN
ejpam-5051	352	2	(	(	PUNCT
ejpam-5051	352	3	a×b)∩	a×b)∩	NOUN
ejpam-5051	352	4	â⋊r	â⋊r	NOUN
ejpam-5051	352	5	,	,	PUNCT
ejpam-5051	352	6	i.e.	i.e.	X
ejpam-5051	352	7	,	,	PUNCT
ejpam-5051	352	8	(	(	PUNCT
ejpam-5051	352	9	(	(	PUNCT
ejpam-5051	352	10	χ	χ	X
ejpam-5051	352	11	,	,	PUNCT
ejpam-5051	352	12	γ̇	γ̇	NOUN
ejpam-5051	352	13	)	)	PUNCT
ejpam-5051	352	14	,	,	PUNCT
ejpam-5051	352	15	(	(	PUNCT
ejpam-5051	352	16	χ′	χ′	PROPN
ejpam-5051	352	17	,	,	PUNCT
ejpam-5051	352	18	γ̇′	γ̇′	NOUN
ejpam-5051	352	19	)	)	PUNCT
ejpam-5051	352	20	)	)	PUNCT
ejpam-5051	353	1	∈	∈	PROPN
ejpam-5051	353	2	m−1(u	m−1(u	PROPN
ejpam-5051	353	3	)	)	PUNCT
ejpam-5051	353	4	and	and	CCONJ
ejpam-5051	353	5	m	m	PROPN
ejpam-5051	353	6	⊂	⊂	PROPN
ejpam-5051	353	7	m−1(u	m−1(u	PROPN
ejpam-5051	353	8	)	)	PUNCT
ejpam-5051	353	9	.	.	PUNCT
ejpam-5051	354	1	since	since	SCONJ
ejpam-5051	354	2	(	(	PUNCT
ejpam-5051	354	3	a×b)′×w	a×b)′×w	ADP
ejpam-5051	354	4	′	′	NOUN
ejpam-5051	354	5	is	be	AUX
ejpam-5051	354	6	open	open	ADJ
ejpam-5051	354	7	in	in	ADP
ejpam-5051	354	8	(	(	PUNCT
ejpam-5051	354	9	â×r)×	â×r)×	PROPN
ejpam-5051	354	10	(	(	PUNCT
ejpam-5051	354	11	â×r	â×r	ADJ
ejpam-5051	354	12	)	)	PUNCT
ejpam-5051	354	13	,	,	PUNCT
ejpam-5051	354	14	then	then	ADV
ejpam-5051	354	15	m	m	VERB
ejpam-5051	354	16	is	be	AUX
ejpam-5051	354	17	open	open	ADJ
ejpam-5051	354	18	in	in	ADP
ejpam-5051	354	19	(	(	PUNCT
ejpam-5051	354	20	â⋊r)(2	â⋊r)(2	ADV
ejpam-5051	354	21	)	)	PUNCT
ejpam-5051	354	22	.	.	PUNCT
ejpam-5051	355	1	it	it	PRON
ejpam-5051	355	2	follows	follow	VERB
ejpam-5051	355	3	that	that	SCONJ
ejpam-5051	355	4	m−1(u	m−1(u	PROPN
ejpam-5051	355	5	)	)	PUNCT
ejpam-5051	355	6	is	be	AUX
ejpam-5051	355	7	open	open	ADJ
ejpam-5051	355	8	and	and	CCONJ
ejpam-5051	355	9	m	m	VERB
ejpam-5051	355	10	is	be	AUX
ejpam-5051	355	11	continuous	continuous	ADJ
ejpam-5051	355	12	.	.	PUNCT
ejpam-5051	356	1	let	let	VERB
ejpam-5051	356	2	u	u	PRON
ejpam-5051	356	3	be	be	AUX
ejpam-5051	356	4	an	an	DET
ejpam-5051	356	5	open	open	ADJ
ejpam-5051	356	6	set	set	NOUN
ejpam-5051	356	7	in	in	ADP
ejpam-5051	356	8	â⋊r	â⋊r	NOUN
ejpam-5051	356	9	.	.	PUNCT
ejpam-5051	357	1	then	then	ADV
ejpam-5051	357	2	u	u	X
ejpam-5051	357	3	=	=	SYM
ejpam-5051	357	4	v	v	NOUN
ejpam-5051	357	5	∩	∩	NOUN
ejpam-5051	357	6	â⋊r	â⋊r	NOUN
ejpam-5051	357	7	where	where	SCONJ
ejpam-5051	357	8	v	v	NOUN
ejpam-5051	357	9	is	be	AUX
ejpam-5051	357	10	open	open	ADJ
ejpam-5051	357	11	in	in	ADP
ejpam-5051	357	12	â×r	â×r	PROPN
ejpam-5051	357	13	.	.	PUNCT
ejpam-5051	358	1	let	let	VERB
ejpam-5051	358	2	(	(	PUNCT
ejpam-5051	358	3	χ	χ	X
ejpam-5051	358	4	,	,	PUNCT
ejpam-5051	358	5	γ̇	γ̇	NOUN
ejpam-5051	358	6	)	)	PUNCT
ejpam-5051	358	7	∈	∈	PROPN
ejpam-5051	358	8	i−1(u	i−1(u	PROPN
ejpam-5051	358	9	)	)	PUNCT
ejpam-5051	358	10	.	.	PUNCT
ejpam-5051	359	1	then	then	ADV
ejpam-5051	359	2	,	,	PUNCT
ejpam-5051	359	3	i((χ	i((χ	NOUN
ejpam-5051	359	4	,	,	PUNCT
ejpam-5051	359	5	γ̇	γ̇	PROPN
ejpam-5051	359	6	)	)	PUNCT
ejpam-5051	359	7	)	)	PUNCT
ejpam-5051	359	8	∈	∈	PROPN
ejpam-5051	359	9	v	v	ADP
ejpam-5051	359	10	∩	∩	ADJ
ejpam-5051	359	11	â⋊r	â⋊r	NOUN
ejpam-5051	359	12	.	.	PUNCT
ejpam-5051	360	1	since	since	SCONJ
ejpam-5051	360	2	v	v	NOUN
ejpam-5051	360	3	is	be	AUX
ejpam-5051	360	4	open	open	ADJ
ejpam-5051	360	5	in	in	ADP
ejpam-5051	360	6	â×r	â×r	PROPN
ejpam-5051	360	7	,	,	PUNCT
ejpam-5051	360	8	then	then	ADV
ejpam-5051	360	9	there	there	PRON
ejpam-5051	360	10	exists	exist	VERB
ejpam-5051	360	11	open	open	ADJ
ejpam-5051	360	12	set	set	VERB
ejpam-5051	360	13	uv	uv	NOUN
ejpam-5051	360	14	containing	contain	VERB
ejpam-5051	360	15	(	(	PUNCT
ejpam-5051	360	16	χ	χ	ADJ
ejpam-5051	360	17	,	,	PUNCT
ejpam-5051	360	18	γ̇	γ̇	NOUN
ejpam-5051	360	19	)	)	PUNCT
ejpam-5051	360	20	where	where	SCONJ
ejpam-5051	360	21	uv	uv	NOUN
ejpam-5051	360	22	⊆	⊆	NUM
ejpam-5051	360	23	v	v	NOUN
ejpam-5051	360	24	.	.	PUNCT
ejpam-5051	361	1	also	also	ADV
ejpam-5051	361	2	,	,	PUNCT
ejpam-5051	361	3	there	there	PRON
ejpam-5051	361	4	exists	exist	VERB
ejpam-5051	361	5	open	open	ADJ
ejpam-5051	361	6	set	set	VERB
ejpam-5051	361	7	w	w	NOUN
ejpam-5051	361	8	containing	contain	VERB
ejpam-5051	361	9	(	(	PUNCT
ejpam-5051	361	10	χ	χ	ADJ
ejpam-5051	361	11	,	,	PUNCT
ejpam-5051	361	12	γ̇)−1	γ̇)−1	ADJ
ejpam-5051	361	13	where	where	SCONJ
ejpam-5051	361	14	w	w	PROPN
ejpam-5051	361	15	⊆	⊆	NUM
ejpam-5051	361	16	â	â	PRON
ejpam-5051	361	17	⋊	⋊	PROPN
ejpam-5051	361	18	r.	r.	AUX
ejpam-5051	361	19	define	define	VERB
ejpam-5051	361	20	u	u	NOUN
ejpam-5051	361	21	′	′	NOUN
ejpam-5051	361	22	v	v	NOUN
ejpam-5051	361	23	=	=	SYM
ejpam-5051	361	24	{	{	PUNCT
ejpam-5051	361	25	(	(	PUNCT
ejpam-5051	361	26	χ′	χ′	PROPN
ejpam-5051	361	27	,	,	PUNCT
ejpam-5051	361	28	γ̇′	γ̇′	PROPN
ejpam-5051	361	29	)	)	PUNCT
ejpam-5051	361	30	∈	∈	PROPN
ejpam-5051	361	31	â	â	ADP
ejpam-5051	361	32	⋊	⋊	NUM
ejpam-5051	361	33	r	r	NOUN
ejpam-5051	361	34	:	:	PUNCT
ejpam-5051	361	35	i((χ′	i((χ′	NOUN
ejpam-5051	361	36	,	,	PUNCT
ejpam-5051	361	37	γ̇′	γ̇′	NOUN
ejpam-5051	361	38	)	)	PUNCT
ejpam-5051	361	39	)	)	PUNCT
ejpam-5051	362	1	∈	∈	PROPN
ejpam-5051	362	2	uv	uv	NOUN
ejpam-5051	362	3	∩	∩	NOUN
ejpam-5051	362	4	w	w	NOUN
ejpam-5051	362	5	}	}	PUNCT
ejpam-5051	362	6	.	.	PUNCT
ejpam-5051	363	1	let	let	VERB
ejpam-5051	363	2	(	(	PUNCT
ejpam-5051	363	3	χ′	χ′	PROPN
ejpam-5051	363	4	,	,	PUNCT
ejpam-5051	363	5	γ̇′	γ̇′	NOUN
ejpam-5051	363	6	,	,	PUNCT
ejpam-5051	363	7	)	)	PUNCT
ejpam-5051	364	1	∈	∈	PROPN
ejpam-5051	364	2	u	u	NOUN
ejpam-5051	364	3	′	′	NOUN
ejpam-5051	365	1	v.	v.	ADP
ejpam-5051	365	2	by	by	ADP
ejpam-5051	365	3	definition	definition	NOUN
ejpam-5051	365	4	,	,	PUNCT
ejpam-5051	365	5	i((χ′	i((χ′	NOUN
ejpam-5051	365	6	,	,	PUNCT
ejpam-5051	365	7	γ̇′	γ̇′	NOUN
ejpam-5051	365	8	)	)	PUNCT
ejpam-5051	365	9	)	)	PUNCT
ejpam-5051	366	1	∈	∈	PROPN
ejpam-5051	366	2	uv	uv	NOUN
ejpam-5051	366	3	∩	∩	PROPN
ejpam-5051	366	4	w	w	PROPN
ejpam-5051	366	5	⊂	⊂	PROPN
ejpam-5051	366	6	v	v	ADP
ejpam-5051	366	7	∩	∩	NOUN
ejpam-5051	366	8	â	â	ADP
ejpam-5051	366	9	⋊	⋊	SYM
ejpam-5051	366	10	r	r	NOUN
ejpam-5051	366	11	which	which	PRON
ejpam-5051	366	12	means	mean	VERB
ejpam-5051	366	13	that	that	SCONJ
ejpam-5051	366	14	(	(	PUNCT
ejpam-5051	366	15	χ′	χ′	PROPN
ejpam-5051	366	16	,	,	PUNCT
ejpam-5051	366	17	γ̇′	γ̇′	PROPN
ejpam-5051	366	18	)	)	PUNCT
ejpam-5051	366	19	∈	∈	PROPN
ejpam-5051	366	20	i−1(u	i−1(u	PROPN
ejpam-5051	366	21	)	)	PUNCT
ejpam-5051	366	22	.	.	PUNCT
ejpam-5051	367	1	hence	hence	ADV
ejpam-5051	367	2	,	,	PUNCT
ejpam-5051	367	3	u	u	NOUN
ejpam-5051	367	4	′	′	NOUN
ejpam-5051	367	5	v	v	NUM
ejpam-5051	367	6	⊆	⊆	NUM
ejpam-5051	367	7	i−1(u	i−1(u	NOUN
ejpam-5051	367	8	)	)	PUNCT
ejpam-5051	367	9	.	.	PUNCT
ejpam-5051	368	1	since	since	SCONJ
ejpam-5051	368	2	uv	uv	NOUN
ejpam-5051	368	3	⊆	⊆	NUM
ejpam-5051	368	4	v	v	NOUN
ejpam-5051	368	5	,	,	PUNCT
ejpam-5051	368	6	then	then	ADV
ejpam-5051	368	7	u	u	NOUN
ejpam-5051	368	8	′	′	NOUN
ejpam-5051	368	9	v	v	NUM
ejpam-5051	368	10	⊆	⊆	NUM
ejpam-5051	368	11	v	v	NOUN
ejpam-5051	368	12	∩	∩	PROPN
ejpam-5051	368	13	w	w	PROPN
ejpam-5051	368	14	.	.	PUNCT
ejpam-5051	369	1	notice	notice	VERB
ejpam-5051	369	2	that	that	SCONJ
ejpam-5051	369	3	v	v	ADP
ejpam-5051	369	4	∩	∩	NOUN
ejpam-5051	369	5	w	w	NOUN
ejpam-5051	369	6	is	be	AUX
ejpam-5051	369	7	open	open	ADJ
ejpam-5051	369	8	in	in	ADP
ejpam-5051	369	9	â	â	PRON
ejpam-5051	369	10	⋊	⋊	PROPN
ejpam-5051	369	11	r.	r.	NOUN
ejpam-5051	369	12	hence	hence	ADV
ejpam-5051	369	13	,	,	PUNCT
ejpam-5051	369	14	u	u	NOUN
ejpam-5051	369	15	′	′	NOUN
ejpam-5051	369	16	v	v	NOUN
ejpam-5051	369	17	is	be	AUX
ejpam-5051	369	18	open	open	ADJ
ejpam-5051	369	19	in	in	ADP
ejpam-5051	369	20	â	â	PRON
ejpam-5051	369	21	⋊	⋊	PROPN
ejpam-5051	369	22	r.	r.	PROPN
ejpam-5051	369	23	thus	thus	ADV
ejpam-5051	369	24	,	,	PUNCT
ejpam-5051	369	25	i−1(u	i−1(u	PROPN
ejpam-5051	369	26	)	)	PUNCT
ejpam-5051	369	27	is	be	AUX
ejpam-5051	369	28	open	open	ADJ
ejpam-5051	369	29	and	and	CCONJ
ejpam-5051	369	30	our	our	PRON
ejpam-5051	369	31	inverse	inverse	NOUN
ejpam-5051	369	32	map	map	NOUN
ejpam-5051	369	33	is	be	AUX
ejpam-5051	369	34	continuous	continuous	ADJ
ejpam-5051	369	35	.	.	PUNCT
ejpam-5051	370	1	let	let	AUX
ejpam-5051	370	2	(	(	PUNCT
ejpam-5051	370	3	χ	χ	X
ejpam-5051	370	4	,	,	PUNCT
ejpam-5051	370	5	γ̇	γ̇	NOUN
ejpam-5051	370	6	)	)	PUNCT
ejpam-5051	370	7	and	and	CCONJ
ejpam-5051	370	8	(	(	PUNCT
ejpam-5051	370	9	χ′	χ′	PROPN
ejpam-5051	370	10	,	,	PUNCT
ejpam-5051	370	11	γ̇′	γ̇′	NOUN
ejpam-5051	370	12	)	)	PUNCT
ejpam-5051	370	13	be	be	AUX
ejpam-5051	370	14	distinct	distinct	ADJ
ejpam-5051	370	15	points	point	NOUN
ejpam-5051	370	16	in	in	ADP
ejpam-5051	370	17	â⋊r	â⋊r	NOUN
ejpam-5051	370	18	.	.	PUNCT
ejpam-5051	371	1	we	we	PRON
ejpam-5051	371	2	can	can	AUX
ejpam-5051	371	3	choose	choose	VERB
ejpam-5051	371	4	open	open	ADJ
ejpam-5051	371	5	sets	set	NOUN
ejpam-5051	371	6	u	u	NOUN
ejpam-5051	371	7	and	and	CCONJ
ejpam-5051	371	8	v	v	NOUN
ejpam-5051	371	9	in	in	ADP
ejpam-5051	371	10	â	â	X
ejpam-5051	371	11	×	×	NOUN
ejpam-5051	371	12	r	r	NOUN
ejpam-5051	371	13	such	such	ADJ
ejpam-5051	371	14	that	that	SCONJ
ejpam-5051	371	15	u	u	PROPN
ejpam-5051	371	16	∩	∩	NOUN
ejpam-5051	371	17	v	v	NOUN
ejpam-5051	371	18	=	=	NOUN
ejpam-5051	371	19	∅	∅	NOUN
ejpam-5051	371	20	with	with	ADP
ejpam-5051	371	21	(	(	PUNCT
ejpam-5051	371	22	χ	χ	X
ejpam-5051	371	23	,	,	PUNCT
ejpam-5051	371	24	γ̇	γ̇	NOUN
ejpam-5051	371	25	)	)	PUNCT
ejpam-5051	371	26	∈	∈	PROPN
ejpam-5051	371	27	u	u	NOUN
ejpam-5051	371	28	and	and	CCONJ
ejpam-5051	371	29	(	(	PUNCT
ejpam-5051	371	30	χ′	χ′	PROPN
ejpam-5051	371	31	,	,	PUNCT
ejpam-5051	371	32	γ̇′	γ̇′	NOUN
ejpam-5051	371	33	)	)	PUNCT
ejpam-5051	371	34	∈	∈	PROPN
ejpam-5051	371	35	v	v	NOUN
ejpam-5051	371	36	.	.	PUNCT
ejpam-5051	372	1	let	let	VERB
ejpam-5051	372	2	u	u	PRON
ejpam-5051	372	3	′	′	NOUN
ejpam-5051	372	4	=	=	SYM
ejpam-5051	372	5	u	u	NOUN
ejpam-5051	372	6	∩	∩	NOUN
ejpam-5051	372	7	â	â	ADP
ejpam-5051	372	8	⋊	⋊	SYM
ejpam-5051	372	9	r	r	NOUN
ejpam-5051	372	10	and	and	CCONJ
ejpam-5051	372	11	v	v	NOUN
ejpam-5051	372	12	′	′	NUM
ejpam-5051	372	13	=	=	SYM
ejpam-5051	372	14	v	v	NOUN
ejpam-5051	372	15	∩	∩	ADJ
ejpam-5051	372	16	â⋊r	â⋊r	NOUN
ejpam-5051	372	17	.	.	PUNCT
ejpam-5051	373	1	since	since	SCONJ
ejpam-5051	373	2	u	u	PROPN
ejpam-5051	373	3	and	and	CCONJ
ejpam-5051	373	4	v	v	NOUN
ejpam-5051	373	5	are	be	AUX
ejpam-5051	373	6	in	in	ADP
ejpam-5051	373	7	τâ⋊r	τâ⋊r	ADV
ejpam-5051	373	8	,	,	PUNCT
ejpam-5051	373	9	then	then	ADV
ejpam-5051	373	10	u	u	NOUN
ejpam-5051	373	11	′	′	NOUN
ejpam-5051	373	12	and	and	CCONJ
ejpam-5051	373	13	v	v	NOUN
ejpam-5051	373	14	′	′	NOUN
ejpam-5051	373	15	are	be	AUX
ejpam-5051	373	16	open	open	ADJ
ejpam-5051	373	17	sets	set	NOUN
ejpam-5051	373	18	in	in	ADP
ejpam-5051	373	19	â⋊r	â⋊r	NOUN
ejpam-5051	373	20	containing	contain	VERB
ejpam-5051	373	21	(	(	PUNCT
ejpam-5051	373	22	χ	χ	ADJ
ejpam-5051	373	23	,	,	PUNCT
ejpam-5051	373	24	γ̇	γ̇	NOUN
ejpam-5051	373	25	)	)	PUNCT
ejpam-5051	373	26	and	and	CCONJ
ejpam-5051	373	27	(	(	PUNCT
ejpam-5051	373	28	χ′	χ′	PROPN
ejpam-5051	373	29	,	,	PUNCT
ejpam-5051	373	30	γ̇′	γ̇′	NOUN
ejpam-5051	373	31	)	)	PUNCT
ejpam-5051	373	32	,	,	PUNCT
ejpam-5051	373	33	respectively	respectively	ADV
ejpam-5051	373	34	.	.	PUNCT
ejpam-5051	374	1	note	note	VERB
ejpam-5051	374	2	that	that	SCONJ
ejpam-5051	374	3	u	u	PROPN
ejpam-5051	374	4	and	and	CCONJ
ejpam-5051	374	5	v	v	NOUN
ejpam-5051	374	6	are	be	AUX
ejpam-5051	374	7	disjoint	disjoint	ADJ
ejpam-5051	374	8	,	,	PUNCT
ejpam-5051	374	9	hence	hence	ADV
ejpam-5051	374	10	u	u	NOUN
ejpam-5051	374	11	′	′	NOUN
ejpam-5051	374	12	and	and	CCONJ
ejpam-5051	374	13	v	v	NOUN
ejpam-5051	374	14	′	′	NOUN
ejpam-5051	374	15	are	be	AUX
ejpam-5051	374	16	also	also	ADV
ejpam-5051	374	17	disjoint	disjoint	ADJ
ejpam-5051	375	1	and	and	CCONJ
ejpam-5051	375	2	we	we	PRON
ejpam-5051	375	3	have	have	AUX
ejpam-5051	375	4	proved	prove	VERB
ejpam-5051	375	5	that	that	SCONJ
ejpam-5051	375	6	â⋊r	â⋊r	NOUN
ejpam-5051	375	7	is	be	AUX
ejpam-5051	375	8	a	a	DET
ejpam-5051	375	9	hausdorff	hausdorff	NOUN
ejpam-5051	375	10	groupoid	groupoid	NOUN
ejpam-5051	375	11	.	.	PUNCT
ejpam-5051	376	1	since	since	SCONJ
ejpam-5051	376	2	â	â	PROPN
ejpam-5051	376	3	⋊r	⋊r	PROPN
ejpam-5051	376	4	is	be	AUX
ejpam-5051	376	5	hausdorff	hausdorff	NOUN
ejpam-5051	376	6	,	,	PUNCT
ejpam-5051	376	7	(	(	PUNCT
ejpam-5051	376	8	â	â	X
ejpam-5051	376	9	⋊r)(0	⋊r)(0	PROPN
ejpam-5051	376	10	)	)	PUNCT
ejpam-5051	376	11	is	be	AUX
ejpam-5051	376	12	hausdorff	hausdorff	NOUN
ejpam-5051	376	13	.	.	PUNCT
ejpam-5051	377	1	let	let	VERB
ejpam-5051	377	2	b	b	X
ejpam-5051	377	3	be	be	AUX
ejpam-5051	377	4	a	a	DET
ejpam-5051	377	5	basis	basis	NOUN
ejpam-5051	377	6	for	for	ADP
ejpam-5051	377	7	the	the	DET
ejpam-5051	377	8	product	product	NOUN
ejpam-5051	377	9	topology	topology	NOUN
ejpam-5051	377	10	on	on	ADP
ejpam-5051	377	11	â×r	â×r	PROPN
ejpam-5051	377	12	.	.	PUNCT
ejpam-5051	378	1	then	then	ADV
ejpam-5051	378	2	,	,	PUNCT
ejpam-5051	378	3	b′	b′	NUM
ejpam-5051	378	4	=	=	PUNCT
ejpam-5051	378	5	{	{	PUNCT
ejpam-5051	378	6	b∩	b∩	NOUN
ejpam-5051	378	7	â⋊r	â⋊r	NOUN
ejpam-5051	378	8	:	:	PUNCT
ejpam-5051	378	9	b	b	X
ejpam-5051	378	10	∈	∈	ADP
ejpam-5051	378	11	b	b	AUX
ejpam-5051	378	12	}	}	PUNCT
ejpam-5051	378	13	is	be	AUX
ejpam-5051	378	14	a	a	DET
ejpam-5051	378	15	basis	basis	NOUN
ejpam-5051	378	16	for	for	ADP
ejpam-5051	378	17	the	the	DET
ejpam-5051	378	18	relative	relative	ADJ
ejpam-5051	378	19	topology	topology	NOUN
ejpam-5051	378	20	on	on	ADP
ejpam-5051	378	21	â⋊r	â⋊r	PROPN
ejpam-5051	378	22	.	.	PUNCT
ejpam-5051	379	1	now	now	ADV
ejpam-5051	379	2	,	,	PUNCT
ejpam-5051	379	3	let	let	VERB
ejpam-5051	379	4	r1	r1	PROPN
ejpam-5051	379	5	=	=	SYM
ejpam-5051	379	6	r|b′	r|b′	PROPN
ejpam-5051	379	7	:	:	PUNCT
ejpam-5051	379	8	b′	b′	NUM
ejpam-5051	379	9	→	→	SYM
ejpam-5051	379	10	u	u	NOUN
ejpam-5051	379	11	where	where	SCONJ
ejpam-5051	379	12	u	u	NOUN
ejpam-5051	379	13	is	be	AUX
ejpam-5051	379	14	an	an	DET
ejpam-5051	379	15	open	open	ADJ
ejpam-5051	379	16	subset	subset	NOUN
ejpam-5051	379	17	of	of	ADP
ejpam-5051	379	18	â⋊r	â⋊r	NOUN
ejpam-5051	379	19	and	and	CCONJ
ejpam-5051	379	20	let	let	VERB
ejpam-5051	379	21	v	v	PART
ejpam-5051	379	22	be	be	AUX
ejpam-5051	379	23	an	an	DET
ejpam-5051	379	24	open	open	ADJ
ejpam-5051	379	25	subset	subset	NOUN
ejpam-5051	379	26	of	of	ADP
ejpam-5051	379	27	u	u	PROPN
ejpam-5051	379	28	.	.	PUNCT
ejpam-5051	380	1	then	then	ADV
ejpam-5051	380	2	v	v	X
ejpam-5051	380	3	=	=	SYM
ejpam-5051	380	4	(	(	PUNCT
ejpam-5051	380	5	a×b)∩	a×b)∩	NOUN
ejpam-5051	380	6	â⋊r	â⋊r	NOUN
ejpam-5051	380	7	where	where	SCONJ
ejpam-5051	380	8	a×b	a×b	PROPN
ejpam-5051	380	9	is	be	AUX
ejpam-5051	380	10	open	open	ADJ
ejpam-5051	380	11	in	in	ADP
ejpam-5051	380	12	â×r	â×r	PROPN
ejpam-5051	380	13	.	.	PUNCT
ejpam-5051	381	1	since	since	SCONJ
ejpam-5051	381	2	b′	b′	NOUN
ejpam-5051	381	3	is	be	AUX
ejpam-5051	381	4	a	a	DET
ejpam-5051	381	5	base	base	NOUN
ejpam-5051	381	6	for	for	ADP
ejpam-5051	381	7	the	the	DET
ejpam-5051	381	8	topology	topology	NOUN
ejpam-5051	381	9	on	on	ADP
ejpam-5051	381	10	â⋊r	â⋊r	NOUN
ejpam-5051	381	11	,	,	PUNCT
ejpam-5051	381	12	then	then	ADV
ejpam-5051	381	13	there	there	PRON
ejpam-5051	381	14	exists	exist	VERB
ejpam-5051	381	15	a	a	DET
ejpam-5051	381	16	basic	basic	ADJ
ejpam-5051	381	17	element	element	NOUN
ejpam-5051	381	18	b	b	NOUN
ejpam-5051	381	19	containing	contain	VERB
ejpam-5051	381	20	(	(	PUNCT
ejpam-5051	381	21	χ	χ	ADJ
ejpam-5051	381	22	,	,	PUNCT
ejpam-5051	381	23	γ̇	γ̇	NOUN
ejpam-5051	381	24	)	)	PUNCT
ejpam-5051	381	25	such	such	ADJ
ejpam-5051	381	26	that	that	SCONJ
ejpam-5051	381	27	r1(χ	r1(χ	PROPN
ejpam-5051	381	28	,	,	PUNCT
ejpam-5051	381	29	γ̇	γ̇	NOUN
ejpam-5051	381	30	)	)	PUNCT
ejpam-5051	381	31	∈	∈	PROPN
ejpam-5051	381	32	v	v	NOUN
ejpam-5051	381	33	.	.	PUNCT
ejpam-5051	382	1	then	then	ADV
ejpam-5051	382	2	r−1	r−1	PROPN
ejpam-5051	382	3	1	1	NUM
ejpam-5051	382	4	(	(	PUNCT
ejpam-5051	382	5	u	u	NOUN
ejpam-5051	382	6	)	)	PUNCT
ejpam-5051	382	7	is	be	AUX
ejpam-5051	382	8	open	open	ADJ
ejpam-5051	382	9	in	in	ADP
ejpam-5051	382	10	â⋊r	â⋊r	NOUN
ejpam-5051	382	11	.	.	PUNCT
ejpam-5051	383	1	now	now	ADV
ejpam-5051	383	2	,	,	PUNCT
ejpam-5051	383	3	denote	denote	VERB
ejpam-5051	383	4	r−1	r−1	PROPN
ejpam-5051	383	5	1	1	NUM
ejpam-5051	383	6	=	=	SYM
ejpam-5051	383	7	(	(	PUNCT
ejpam-5051	383	8	r|b′)−1	r|b′)−1	NOUN
ejpam-5051	383	9	:	:	PUNCT
ejpam-5051	383	10	u	u	X
ejpam-5051	383	11	→	→	SYM
ejpam-5051	383	12	b′.	b′.	PROPN
ejpam-5051	383	13	let	let	VERB
ejpam-5051	383	14	b	b	X
ejpam-5051	383	15	be	be	AUX
ejpam-5051	383	16	open	open	ADJ
ejpam-5051	383	17	subset	subset	NOUN
ejpam-5051	383	18	of	of	ADP
ejpam-5051	383	19	b′.	b′.	PROPN
ejpam-5051	383	20	then	then	ADV
ejpam-5051	383	21	b	b	X
ejpam-5051	383	22	=	=	PUNCT
ejpam-5051	383	23	a	a	DET
ejpam-5051	383	24	∩	∩	NOUN
ejpam-5051	383	25	(	(	PUNCT
ejpam-5051	383	26	â	â	X
ejpam-5051	383	27	⋊	⋊	X
ejpam-5051	383	28	r	r	NOUN
ejpam-5051	383	29	)	)	PUNCT
ejpam-5051	383	30	where	where	SCONJ
ejpam-5051	383	31	a	a	DET
ejpam-5051	383	32	∈	∈	PROPN
ejpam-5051	383	33	b.	b.	NOUN
ejpam-5051	383	34	let	let	VERB
ejpam-5051	383	35	(	(	PUNCT
ejpam-5051	383	36	χ	χ	X
ejpam-5051	383	37	,	,	PUNCT
ejpam-5051	383	38	γ̇	γ̇	NOUN
ejpam-5051	383	39	)	)	PUNCT
ejpam-5051	383	40	∈	∈	PROPN
ejpam-5051	383	41	r1(b	r1(b	PROPN
ejpam-5051	383	42	)	)	PUNCT
ejpam-5051	383	43	.	.	PUNCT
ejpam-5051	384	1	then	then	ADV
ejpam-5051	384	2	r−1	r−1	PROPN
ejpam-5051	384	3	1	1	NUM
ejpam-5051	384	4	(	(	PUNCT
ejpam-5051	384	5	χ	χ	NOUN
ejpam-5051	384	6	,	,	PUNCT
ejpam-5051	384	7	γ̇	γ̇	NOUN
ejpam-5051	384	8	)	)	PUNCT
ejpam-5051	384	9	∈	∈	PROPN
ejpam-5051	384	10	a	a	DET
ejpam-5051	384	11	∩	∩	NOUN
ejpam-5051	384	12	(	(	PUNCT
ejpam-5051	384	13	â	â	X
ejpam-5051	384	14	⋊	⋊	X
ejpam-5051	384	15	r	r	NOUN
ejpam-5051	384	16	)	)	PUNCT
ejpam-5051	384	17	.	.	PUNCT
ejpam-5051	385	1	since	since	SCONJ
ejpam-5051	385	2	a	a	PRON
ejpam-5051	385	3	is	be	AUX
ejpam-5051	385	4	open	open	ADJ
ejpam-5051	385	5	in	in	ADP
ejpam-5051	385	6	â	â	X
ejpam-5051	385	7	×	×	PROPN
ejpam-5051	385	8	r	r	NOUN
ejpam-5051	385	9	,	,	PUNCT
ejpam-5051	385	10	then	then	ADV
ejpam-5051	385	11	there	there	PRON
ejpam-5051	385	12	exists	exist	VERB
ejpam-5051	385	13	open	open	ADJ
ejpam-5051	385	14	set	set	VERB
ejpam-5051	385	15	a′	a′	NOUN
ejpam-5051	385	16	containing	contain	VERB
ejpam-5051	385	17	(	(	PUNCT
ejpam-5051	385	18	χ	χ	ADJ
ejpam-5051	385	19	,	,	PUNCT
ejpam-5051	385	20	γ̇	γ̇	NOUN
ejpam-5051	385	21	)	)	PUNCT
ejpam-5051	385	22	where	where	SCONJ
ejpam-5051	385	23	a′	a′	PROPN
ejpam-5051	385	24	⊆	⊆	NUM
ejpam-5051	385	25	a.	a.	NOUN
ejpam-5051	385	26	also	also	ADV
ejpam-5051	385	27	,	,	PUNCT
ejpam-5051	385	28	there	there	PRON
ejpam-5051	385	29	exists	exist	VERB
ejpam-5051	385	30	open	open	ADJ
ejpam-5051	385	31	set	set	VERB
ejpam-5051	385	32	w	w	ADP
ejpam-5051	385	33	⊆	⊆	NUM
ejpam-5051	385	34	â	â	PRON
ejpam-5051	385	35	⋊	⋊	NUM
ejpam-5051	385	36	r	r	NOUN
ejpam-5051	385	37	containing	contain	VERB
ejpam-5051	385	38	(	(	PUNCT
ejpam-5051	385	39	χ	χ	NOUN
ejpam-5051	385	40	,	,	PUNCT
ejpam-5051	385	41	γ̇	γ̇	NOUN
ejpam-5051	385	42	)	)	PUNCT
ejpam-5051	385	43	.	.	PUNCT
ejpam-5051	386	1	define	define	VERB
ejpam-5051	386	2	a′′	a′′	PROPN
ejpam-5051	386	3	=	=	SYM
ejpam-5051	386	4	{	{	PUNCT
ejpam-5051	386	5	(	(	PUNCT
ejpam-5051	386	6	χ′	χ′	PROPN
ejpam-5051	386	7	,	,	PUNCT
ejpam-5051	386	8	γ̇′	γ̇′	NOUN
ejpam-5051	386	9	)	)	PUNCT
ejpam-5051	387	1	∈	∈	PROPN
ejpam-5051	387	2	u	u	NOUN
ejpam-5051	387	3	:	:	PUNCT
ejpam-5051	387	4	r−1	r−1	PROPN
ejpam-5051	387	5	1	1	NUM
ejpam-5051	387	6	(	(	PUNCT
ejpam-5051	387	7	χ′	χ′	PROPN
ejpam-5051	387	8	,	,	PUNCT
ejpam-5051	387	9	γ̇′	γ̇′	PROPN
ejpam-5051	387	10	)	)	PUNCT
ejpam-5051	387	11	∈	∈	PROPN
ejpam-5051	387	12	a′	a′	NOUN
ejpam-5051	387	13	∩w	∩w	NOUN
ejpam-5051	387	14	}	}	PUNCT
ejpam-5051	387	15	.	.	PUNCT
ejpam-5051	388	1	let	let	VERB
ejpam-5051	388	2	(	(	PUNCT
ejpam-5051	388	3	χ′	χ′	PROPN
ejpam-5051	388	4	,	,	PUNCT
ejpam-5051	388	5	γ̇′	γ̇′	PROPN
ejpam-5051	388	6	)	)	PUNCT
ejpam-5051	388	7	∈	∈	PROPN
ejpam-5051	388	8	a′′.	a′′.	PROPN
ejpam-5051	388	9	by	by	ADP
ejpam-5051	388	10	definition	definition	NOUN
ejpam-5051	388	11	,	,	PUNCT
ejpam-5051	389	1	r−1	r−1	PROPN
ejpam-5051	389	2	1	1	NUM
ejpam-5051	389	3	(	(	PUNCT
ejpam-5051	389	4	χ′	χ′	PROPN
ejpam-5051	389	5	,	,	PUNCT
ejpam-5051	389	6	γ̇′	γ̇′	NOUN
ejpam-5051	389	7	)	)	PUNCT
ejpam-5051	389	8	∈	∈	PROPN
ejpam-5051	389	9	a′′	a′′	NOUN
ejpam-5051	389	10	∩w	∩w	PROPN
ejpam-5051	389	11	⊂	⊂	PROPN
ejpam-5051	390	1	a	a	DET
ejpam-5051	390	2	∩	∩	NOUN
ejpam-5051	390	3	(	(	PUNCT
ejpam-5051	390	4	â⋊r	â⋊r	NOUN
ejpam-5051	390	5	)	)	PUNCT
ejpam-5051	390	6	.	.	PUNCT
ejpam-5051	391	1	hence	hence	ADV
ejpam-5051	391	2	,	,	PUNCT
ejpam-5051	391	3	r−1	r−1	PROPN
ejpam-5051	391	4	1	1	NUM
ejpam-5051	391	5	(	(	PUNCT
ejpam-5051	391	6	χ′	χ′	PROPN
ejpam-5051	391	7	,	,	PUNCT
ejpam-5051	391	8	γ̇′	γ̇′	NOUN
ejpam-5051	391	9	)	)	PUNCT
ejpam-5051	391	10	∈	∈	PROPN
ejpam-5051	391	11	a	a	DET
ejpam-5051	391	12	∩	∩	NOUN
ejpam-5051	391	13	(	(	PUNCT
ejpam-5051	391	14	â⋊r	â⋊r	PROPN
ejpam-5051	391	15	)	)	PUNCT
ejpam-5051	391	16	which	which	PRON
ejpam-5051	391	17	means	mean	VERB
ejpam-5051	391	18	that	that	SCONJ
ejpam-5051	391	19	(	(	PUNCT
ejpam-5051	391	20	χ′	χ′	PROPN
ejpam-5051	391	21	,	,	PUNCT
ejpam-5051	391	22	γ̇′	γ̇′	NOUN
ejpam-5051	391	23	)	)	PUNCT
ejpam-5051	391	24	∈	∈	PROPN
ejpam-5051	391	25	r1(b	r1(b	PROPN
ejpam-5051	391	26	)	)	PUNCT
ejpam-5051	391	27	.	.	PUNCT
ejpam-5051	392	1	hence	hence	ADV
ejpam-5051	392	2	,	,	PUNCT
ejpam-5051	392	3	a′′	a′′	PROPN
ejpam-5051	392	4	⊂	⊂	X
ejpam-5051	392	5	r1(b	r1(b	PROPN
ejpam-5051	392	6	)	)	PUNCT
ejpam-5051	392	7	.	.	PUNCT
ejpam-5051	393	1	since	since	SCONJ
ejpam-5051	393	2	a′′	a′′	PROPN
ejpam-5051	393	3	⊆	⊆	NUM
ejpam-5051	393	4	a′∪w	a′∪w	NOUN
ejpam-5051	393	5	and	and	CCONJ
ejpam-5051	393	6	a′	a′	PROPN
ejpam-5051	393	7	⊂	⊂	PROPN
ejpam-5051	393	8	a	a	X
ejpam-5051	393	9	,	,	PUNCT
ejpam-5051	393	10	a′′	a′′	PROPN
ejpam-5051	393	11	⊆	⊆	NUM
ejpam-5051	393	12	a∩w	a∩w	PROPN
ejpam-5051	393	13	.	.	PUNCT
ejpam-5051	394	1	notice	notice	VERB
ejpam-5051	394	2	that	that	SCONJ
ejpam-5051	394	3	a	a	DET
ejpam-5051	394	4	∩w	∩w	NOUN
ejpam-5051	394	5	is	be	AUX
ejpam-5051	394	6	open	open	ADJ
ejpam-5051	394	7	in	in	ADP
ejpam-5051	394	8	â⋊r	â⋊r	NOUN
ejpam-5051	394	9	.	.	PUNCT
ejpam-5051	395	1	hence	hence	ADV
ejpam-5051	395	2	,	,	PUNCT
ejpam-5051	395	3	a′′	a′′	NOUN
ejpam-5051	395	4	is	be	AUX
ejpam-5051	395	5	open	open	ADJ
ejpam-5051	395	6	in	in	ADP
ejpam-5051	395	7	â⋊r	â⋊r	NOUN
ejpam-5051	395	8	.	.	PUNCT
ejpam-5051	396	1	thus	thus	ADV
ejpam-5051	396	2	,	,	PUNCT
ejpam-5051	396	3	r1(b	r1(b	PROPN
ejpam-5051	396	4	)	)	PUNCT
ejpam-5051	396	5	is	be	AUX
ejpam-5051	396	6	open	open	ADJ
ejpam-5051	396	7	and	and	CCONJ
ejpam-5051	396	8	r	r	NOUN
ejpam-5051	396	9	is	be	AUX
ejpam-5051	396	10	a	a	DET
ejpam-5051	396	11	homeomorphism	homeomorphism	NOUN
ejpam-5051	396	12	onto	onto	ADP
ejpam-5051	396	13	an	an	DET
ejpam-5051	396	14	open	open	ADJ
ejpam-5051	396	15	subset	subset	NOUN
ejpam-5051	396	16	of	of	ADP
ejpam-5051	396	17	â	â	PROPN
ejpam-5051	396	18	⋊r	⋊r	PROPN
ejpam-5051	396	19	.	.	PUNCT
ejpam-5051	397	1	similarly	similarly	ADV
ejpam-5051	397	2	,	,	PUNCT
ejpam-5051	397	3	s	s	VERB
ejpam-5051	397	4	is	be	AUX
ejpam-5051	397	5	homeomorphic	homeomorphic	ADJ
ejpam-5051	397	6	onto	onto	ADP
ejpam-5051	397	7	an	an	DET
ejpam-5051	397	8	open	open	ADJ
ejpam-5051	397	9	subset	subset	NOUN
ejpam-5051	397	10	of	of	ADP
ejpam-5051	397	11	â⋊r	â⋊r	PROPN
ejpam-5051	397	12	.	.	PUNCT
ejpam-5051	398	1	proposition	proposition	NOUN
ejpam-5051	398	2	1	1	NUM
ejpam-5051	398	3	.	.	PUNCT
ejpam-5051	399	1	â⋊r	â⋊r	NOUN
ejpam-5051	399	2	is	be	AUX
ejpam-5051	399	3	a	a	DET
ejpam-5051	399	4	principal	principal	ADJ
ejpam-5051	399	5	groupoid	groupoid	NOUN
ejpam-5051	399	6	with	with	ADP
ejpam-5051	399	7	unit	unit	NOUN
ejpam-5051	399	8	space	space	NOUN
ejpam-5051	399	9	â.	â.	ADJ
ejpam-5051	399	10	proof	proof	NOUN
ejpam-5051	399	11	.	.	PUNCT
ejpam-5051	400	1	let	let	VERB
ejpam-5051	400	2	(	(	PUNCT
ejpam-5051	400	3	χ	χ	X
ejpam-5051	400	4	,	,	PUNCT
ejpam-5051	400	5	u	u	NOUN
ejpam-5051	400	6	)	)	PUNCT
ejpam-5051	400	7	∈	∈	PROPN
ejpam-5051	400	8	â	â	X
ejpam-5051	400	9	where	where	SCONJ
ejpam-5051	400	10	u	u	PROPN
ejpam-5051	400	11	∈	∈	PROPN
ejpam-5051	400	12	g(0	g(0	PROPN
ejpam-5051	400	13	)	)	PUNCT
ejpam-5051	400	14	.	.	PUNCT
ejpam-5051	401	1	then	then	ADV
ejpam-5051	401	2	,	,	PUNCT
ejpam-5051	401	3	s(γ	s(γ	PROPN
ejpam-5051	401	4	)	)	PUNCT
ejpam-5051	402	1	=	=	SYM
ejpam-5051	402	2	u	u	NOUN
ejpam-5051	402	3	for	for	ADP
ejpam-5051	402	4	γ	γ	X
ejpam-5051	402	5	∈	∈	PROPN
ejpam-5051	402	6	au	au	X
ejpam-5051	402	7	and	and	CCONJ
ejpam-5051	402	8	s(γ	s(γ	PROPN
ejpam-5051	402	9	)	)	PUNCT
ejpam-5051	402	10	=	=	PUNCT
ejpam-5051	402	11	r(γ	r(γ	NOUN
ejpam-5051	402	12	)	)	PUNCT
ejpam-5051	402	13	for	for	ADP
ejpam-5051	402	14	γ	γ	PROPN
ejpam-5051	402	15	∈	∈	PROPN
ejpam-5051	402	16	a.	a.	NOUN
ejpam-5051	402	17	hence	hence	ADV
ejpam-5051	402	18	,	,	PUNCT
ejpam-5051	402	19	(	(	PUNCT
ejpam-5051	402	20	χ	χ	X
ejpam-5051	402	21	,	,	PUNCT
ejpam-5051	402	22	u	u	NOUN
ejpam-5051	402	23	)	)	PUNCT
ejpam-5051	402	24	=	=	SYM
ejpam-5051	402	25	(	(	PUNCT
ejpam-5051	402	26	χ	χ	NOUN
ejpam-5051	402	27	,	,	PUNCT
ejpam-5051	402	28	s(γ	s(γ	PROPN
ejpam-5051	402	29	)	)	PUNCT
ejpam-5051	402	30	)	)	PUNCT
ejpam-5051	403	1	=	=	PUNCT
ejpam-5051	403	2	(	(	PUNCT
ejpam-5051	403	3	χ	χ	NOUN
ejpam-5051	403	4	,	,	PUNCT
ejpam-5051	403	5	r(γ	r(γ	NOUN
ejpam-5051	403	6	)	)	PUNCT
ejpam-5051	403	7	)	)	PUNCT
ejpam-5051	404	1	=	=	PUNCT
ejpam-5051	404	2	(	(	PUNCT
ejpam-5051	404	3	χ	χ	X
ejpam-5051	404	4	·	·	PUNCT
ejpam-5051	404	5	γ	γ	X
ejpam-5051	404	6	,	,	PUNCT
ejpam-5051	404	7	s(γ	s(γ	PROPN
ejpam-5051	404	8	)	)	PUNCT
ejpam-5051	404	9	)	)	PUNCT
ejpam-5051	404	10	.	.	PUNCT
ejpam-5051	405	1	thus	thus	ADV
ejpam-5051	405	2	,	,	PUNCT
ejpam-5051	405	3	(	(	PUNCT
ejpam-5051	405	4	χ	χ	X
ejpam-5051	405	5	,	,	PUNCT
ejpam-5051	405	6	u	u	NOUN
ejpam-5051	405	7	)	)	PUNCT
ejpam-5051	405	8	∈	∈	PROPN
ejpam-5051	405	9	(	(	PUNCT
ejpam-5051	405	10	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	405	11	)	)	PUNCT
ejpam-5051	405	12	and	and	CCONJ
ejpam-5051	405	13	â	â	X
ejpam-5051	405	14	⊆	⊆	NUM
ejpam-5051	405	15	(	(	PUNCT
ejpam-5051	405	16	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	405	17	)	)	PUNCT
ejpam-5051	405	18	.	.	PUNCT
ejpam-5051	406	1	let	let	VERB
ejpam-5051	406	2	(	(	PUNCT
ejpam-5051	406	3	χ	χ	X
ejpam-5051	406	4	·	·	PUNCT
ejpam-5051	406	5	γ	γ	X
ejpam-5051	406	6	,	,	PUNCT
ejpam-5051	406	7	s(γ	s(γ	PROPN
ejpam-5051	406	8	)	)	PUNCT
ejpam-5051	406	9	)	)	PUNCT
ejpam-5051	407	1	∈	∈	PROPN
ejpam-5051	407	2	(	(	PUNCT
ejpam-5051	407	3	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	407	4	)	)	PUNCT
ejpam-5051	407	5	where	where	SCONJ
ejpam-5051	407	6	(	(	PUNCT
ejpam-5051	407	7	χ	χ	X
ejpam-5051	407	8	,	,	PUNCT
ejpam-5051	407	9	γ̇	γ̇	NOUN
ejpam-5051	407	10	)	)	PUNCT
ejpam-5051	407	11	∈	∈	PROPN
ejpam-5051	407	12	â⋊r	â⋊r	NOUN
ejpam-5051	407	13	.	.	PUNCT
ejpam-5051	408	1	then	then	ADV
ejpam-5051	408	2	(	(	PUNCT
ejpam-5051	408	3	χ	χ	X
ejpam-5051	408	4	·	·	PUNCT
ejpam-5051	408	5	γ	γ	X
ejpam-5051	408	6	,	,	PUNCT
ejpam-5051	408	7	s(γ	s(γ	PROPN
ejpam-5051	408	8	)	)	PUNCT
ejpam-5051	408	9	)	)	PUNCT
ejpam-5051	409	1	=	=	PUNCT
ejpam-5051	409	2	(	(	PUNCT
ejpam-5051	409	3	χ	χ	NOUN
ejpam-5051	409	4	,	,	PUNCT
ejpam-5051	409	5	r(γ	r(γ	NOUN
ejpam-5051	409	6	)	)	PUNCT
ejpam-5051	409	7	)	)	PUNCT
ejpam-5051	410	1	=	=	PUNCT
ejpam-5051	410	2	(	(	PUNCT
ejpam-5051	410	3	χ	χ	X
ejpam-5051	410	4	·	·	PUNCT
ejpam-5051	410	5	γ	γ	X
ejpam-5051	410	6	,	,	PUNCT
ejpam-5051	410	7	u	u	NOUN
ejpam-5051	410	8	)	)	PUNCT
ejpam-5051	410	9	since	since	SCONJ
ejpam-5051	410	10	r(γ	r(γ	VERB
ejpam-5051	410	11	)	)	PUNCT
ejpam-5051	410	12	=	=	VERB
ejpam-5051	411	1	u.	u.	PROPN
ejpam-5051	411	2	thus	thus	ADV
ejpam-5051	411	3	,	,	PUNCT
ejpam-5051	411	4	(	(	PUNCT
ejpam-5051	411	5	â	â	X
ejpam-5051	411	6	⋊	⋊	NUM
ejpam-5051	411	7	r)(0	r)(0	NUM
ejpam-5051	411	8	)	)	PUNCT
ejpam-5051	411	9	⊆	⊆	NUM
ejpam-5051	411	10	â	â	X
ejpam-5051	411	11	and	and	CCONJ
ejpam-5051	411	12	â	â	X
ejpam-5051	411	13	is	be	AUX
ejpam-5051	411	14	the	the	DET
ejpam-5051	411	15	unit	unit	NOUN
ejpam-5051	411	16	space	space	NOUN
ejpam-5051	411	17	of	of	ADP
ejpam-5051	411	18	â⋊r	â⋊r	PROPN
ejpam-5051	411	19	.	.	PUNCT
ejpam-5051	412	1	let	let	VERB
ejpam-5051	412	2	θ	θ	NOUN
ejpam-5051	412	3	:	:	PUNCT
ejpam-5051	412	4	â	â	X
ejpam-5051	412	5	⋊	⋊	PUNCT
ejpam-5051	412	6	r	r	NOUN
ejpam-5051	412	7	→	→	SYM
ejpam-5051	412	8	â	â	X
ejpam-5051	412	9	×	×	NOUN
ejpam-5051	412	10	â	â	AUX
ejpam-5051	412	11	be	be	AUX
ejpam-5051	412	12	defined	define	VERB
ejpam-5051	412	13	by	by	ADP
ejpam-5051	412	14	θ((χ	θ((χ	PROPN
ejpam-5051	412	15	,	,	PUNCT
ejpam-5051	412	16	γ̇	γ̇	NOUN
ejpam-5051	412	17	)	)	PUNCT
ejpam-5051	412	18	)	)	PUNCT
ejpam-5051	413	1	=	=	PRON
ejpam-5051	413	2	(	(	PUNCT
ejpam-5051	413	3	r((χ	r((χ	ADJ
ejpam-5051	413	4	,	,	PUNCT
ejpam-5051	413	5	γ̇	γ̇	NOUN
ejpam-5051	413	6	)	)	PUNCT
ejpam-5051	413	7	)	)	PUNCT
ejpam-5051	413	8	,	,	PUNCT
ejpam-5051	413	9	s((χ	s((χ	NOUN
ejpam-5051	413	10	,	,	PUNCT
ejpam-5051	413	11	γ̇	γ̇	NOUN
ejpam-5051	413	12	)	)	PUNCT
ejpam-5051	413	13	)	)	PUNCT
ejpam-5051	413	14	)	)	PUNCT
ejpam-5051	414	1	and	and	CCONJ
ejpam-5051	414	2	let	let	VERB
ejpam-5051	414	3	r.	r.	PROPN
ejpam-5051	414	4	s.	s.	PROPN
ejpam-5051	414	5	bongcawel	bongcawel	PROPN
ejpam-5051	414	6	et	et	PROPN
ejpam-5051	414	7	al	al	PROPN
ejpam-5051	414	8	.	.	PUNCT
ejpam-5051	414	9	/	/	SYM
ejpam-5051	414	10	eur	eur	PROPN
ejpam-5051	414	11	.	.	PUNCT
ejpam-5051	415	1	j.	j.	PROPN
ejpam-5051	415	2	pure	pure	PROPN
ejpam-5051	415	3	appl	appl	PROPN
ejpam-5051	415	4	.	.	PROPN
ejpam-5051	415	5	math	math	PROPN
ejpam-5051	415	6	,	,	PUNCT
ejpam-5051	415	7	17	17	NUM
ejpam-5051	415	8	(	(	PUNCT
ejpam-5051	415	9	1	1	NUM
ejpam-5051	415	10	)	)	PUNCT
ejpam-5051	415	11	(	(	PUNCT
ejpam-5051	415	12	2024	2024	NUM
ejpam-5051	415	13	)	)	PUNCT
ejpam-5051	415	14	,	,	PUNCT
ejpam-5051	415	15	519	519	NUM
ejpam-5051	415	16	-	-	SYM
ejpam-5051	415	17	545	545	NUM
ejpam-5051	415	18	530	530	NUM
ejpam-5051	415	19	(	(	PUNCT
ejpam-5051	415	20	χ1	χ1	NOUN
ejpam-5051	415	21	,	,	PUNCT
ejpam-5051	415	22	γ̇1	γ̇1	PROPN
ejpam-5051	415	23	)	)	PUNCT
ejpam-5051	415	24	,	,	PUNCT
ejpam-5051	415	25	(	(	PUNCT
ejpam-5051	415	26	χ2	χ2	PROPN
ejpam-5051	415	27	,	,	PUNCT
ejpam-5051	415	28	γ̇2	γ̇2	PROPN
ejpam-5051	415	29	)	)	PUNCT
ejpam-5051	415	30	∈	∈	PROPN
ejpam-5051	415	31	â⋊r	â⋊r	NOUN
ejpam-5051	415	32	such	such	ADJ
ejpam-5051	415	33	that	that	DET
ejpam-5051	415	34	θ((χ1	θ((χ1	NOUN
ejpam-5051	415	35	,	,	PUNCT
ejpam-5051	415	36	γ̇1	γ̇1	NOUN
ejpam-5051	415	37	)	)	PUNCT
ejpam-5051	415	38	)	)	PUNCT
ejpam-5051	415	39	=	=	SYM
ejpam-5051	416	1	θ((χ2	θ((χ2	NOUN
ejpam-5051	416	2	,	,	PUNCT
ejpam-5051	416	3	γ̇2	γ̇2	PROPN
ejpam-5051	416	4	)	)	PUNCT
ejpam-5051	416	5	)	)	PUNCT
ejpam-5051	416	6	.	.	PUNCT
ejpam-5051	417	1	then	then	ADV
ejpam-5051	417	2	(	(	PUNCT
ejpam-5051	417	3	r((χ1	r((χ1	X
ejpam-5051	417	4	,	,	PUNCT
ejpam-5051	417	5	γ̇1	γ̇1	PROPN
ejpam-5051	417	6	)	)	PUNCT
ejpam-5051	417	7	)	)	PUNCT
ejpam-5051	417	8	,	,	PUNCT
ejpam-5051	417	9	s((χ1	s((χ1	NOUN
ejpam-5051	417	10	,	,	PUNCT
ejpam-5051	417	11	γ̇1	γ̇1	PROPN
ejpam-5051	417	12	)	)	PUNCT
ejpam-5051	417	13	)	)	PUNCT
ejpam-5051	417	14	)	)	PUNCT
ejpam-5051	418	1	=	=	PUNCT
ejpam-5051	418	2	(	(	PUNCT
ejpam-5051	418	3	r((χ2	r((χ2	PROPN
ejpam-5051	418	4	,	,	PUNCT
ejpam-5051	418	5	γ̇2	γ̇2	PROPN
ejpam-5051	418	6	)	)	PUNCT
ejpam-5051	418	7	)	)	PUNCT
ejpam-5051	418	8	,	,	PUNCT
ejpam-5051	418	9	s((χ2	s((χ2	NOUN
ejpam-5051	418	10	,	,	PUNCT
ejpam-5051	418	11	γ̇2	γ̇2	PROPN
ejpam-5051	418	12	)	)	PUNCT
ejpam-5051	418	13	)	)	PUNCT
ejpam-5051	418	14	)	)	PUNCT
ejpam-5051	418	15	.	.	PUNCT
ejpam-5051	419	1	also	also	ADV
ejpam-5051	419	2	,	,	PUNCT
ejpam-5051	419	3	r((χ1	r((χ1	X
ejpam-5051	419	4	,	,	PUNCT
ejpam-5051	419	5	γ̇1	γ̇1	NOUN
ejpam-5051	419	6	)	)	PUNCT
ejpam-5051	419	7	)	)	PUNCT
ejpam-5051	420	1	=	=	SYM
ejpam-5051	420	2	(	(	PUNCT
ejpam-5051	420	3	χ1	χ1	NOUN
ejpam-5051	420	4	,	,	PUNCT
ejpam-5051	420	5	r(γ1	r(γ1	NOUN
ejpam-5051	420	6	)	)	PUNCT
ejpam-5051	420	7	)	)	PUNCT
ejpam-5051	420	8	=	=	PUNCT
ejpam-5051	421	1	r((χ2	r((χ2	NOUN
ejpam-5051	421	2	,	,	PUNCT
ejpam-5051	421	3	γ̇2	γ̇2	PROPN
ejpam-5051	421	4	)	)	PUNCT
ejpam-5051	421	5	)	)	PUNCT
ejpam-5051	422	1	=	=	SYM
ejpam-5051	422	2	(	(	PUNCT
ejpam-5051	422	3	χ2	χ2	PROPN
ejpam-5051	422	4	,	,	PUNCT
ejpam-5051	422	5	r(γ2	r(γ2	NOUN
ejpam-5051	422	6	)	)	PUNCT
ejpam-5051	422	7	)	)	PUNCT
ejpam-5051	422	8	and	and	CCONJ
ejpam-5051	422	9	s((χ1	s((χ1	NOUN
ejpam-5051	422	10	,	,	PUNCT
ejpam-5051	422	11	γ̇1	γ̇1	PROPN
ejpam-5051	422	12	)	)	PUNCT
ejpam-5051	422	13	)	)	PUNCT
ejpam-5051	423	1	=	=	SYM
ejpam-5051	423	2	(	(	PUNCT
ejpam-5051	423	3	χ1·γ1	χ1·γ1	PROPN
ejpam-5051	423	4	,	,	PUNCT
ejpam-5051	423	5	s(γ1	s(γ1	NOUN
ejpam-5051	423	6	)	)	PUNCT
ejpam-5051	423	7	)	)	PUNCT
ejpam-5051	424	1	=	=	SYM
ejpam-5051	424	2	s((χ2	s((χ2	NOUN
ejpam-5051	424	3	,	,	PUNCT
ejpam-5051	424	4	γ̇2	γ̇2	NOUN
ejpam-5051	424	5	)	)	PUNCT
ejpam-5051	424	6	)	)	PUNCT
ejpam-5051	424	7	=	=	SYM
ejpam-5051	424	8	(	(	PUNCT
ejpam-5051	424	9	χ2	χ2	PROPN
ejpam-5051	424	10	·	·	PUNCT
ejpam-5051	424	11	γ2	γ2	PROPN
ejpam-5051	424	12	,	,	PUNCT
ejpam-5051	424	13	s(γ2	s(γ2	NOUN
ejpam-5051	424	14	)	)	PUNCT
ejpam-5051	424	15	)	)	PUNCT
ejpam-5051	424	16	.	.	PUNCT
ejpam-5051	425	1	hence	hence	ADV
ejpam-5051	425	2	,	,	PUNCT
ejpam-5051	425	3	χ1	χ1	NOUN
ejpam-5051	425	4	=	=	SYM
ejpam-5051	425	5	χ2	χ2	PROPN
ejpam-5051	425	6	and	and	CCONJ
ejpam-5051	425	7	γ1	γ1	PROPN
ejpam-5051	425	8	=	=	SYM
ejpam-5051	425	9	γ2	γ2	PROPN
ejpam-5051	425	10	.	.	PUNCT
ejpam-5051	426	1	thus	thus	ADV
ejpam-5051	426	2	,	,	PUNCT
ejpam-5051	426	3	(	(	PUNCT
ejpam-5051	426	4	χ1	χ1	NOUN
ejpam-5051	426	5	,	,	PUNCT
ejpam-5051	426	6	γ̇1	γ̇1	PROPN
ejpam-5051	426	7	)	)	PUNCT
ejpam-5051	426	8	=	=	SYM
ejpam-5051	426	9	(	(	PUNCT
ejpam-5051	426	10	χ2	χ2	PROPN
ejpam-5051	426	11	,	,	PUNCT
ejpam-5051	426	12	γ̇2	γ̇2	PROPN
ejpam-5051	426	13	)	)	PUNCT
ejpam-5051	426	14	and	and	CCONJ
ejpam-5051	426	15	θ	θ	PROPN
ejpam-5051	426	16	is	be	AUX
ejpam-5051	426	17	injective	injective	ADJ
ejpam-5051	426	18	.	.	PUNCT
ejpam-5051	427	1	therefore	therefore	ADV
ejpam-5051	427	2	,	,	PUNCT
ejpam-5051	427	3	â⋊r	â⋊r	PROPN
ejpam-5051	427	4	is	be	AUX
ejpam-5051	427	5	a	a	DET
ejpam-5051	427	6	principal	principal	ADJ
ejpam-5051	427	7	groupoid	groupoid	NOUN
ejpam-5051	427	8	.	.	PUNCT
ejpam-5051	428	1	we	we	PRON
ejpam-5051	428	2	now	now	ADV
ejpam-5051	428	3	introduce	introduce	VERB
ejpam-5051	428	4	a	a	DET
ejpam-5051	428	5	sequence	sequence	NOUN
ejpam-5051	428	6	of	of	ADP
ejpam-5051	428	7	groupoids	groupoid	NOUN
ejpam-5051	428	8	and	and	CCONJ
ejpam-5051	428	9	investigate	investigate	VERB
ejpam-5051	428	10	whether	whether	SCONJ
ejpam-5051	428	11	it	it	PRON
ejpam-5051	428	12	is	be	AUX
ejpam-5051	428	13	our	our	PRON
ejpam-5051	428	14	desired	desire	VERB
ejpam-5051	428	15	discrete	discrete	ADJ
ejpam-5051	428	16	twist	twist	NOUN
ejpam-5051	428	17	over	over	ADP
ejpam-5051	428	18	â	â	PROPN
ejpam-5051	428	19	⋊r	⋊r	PROPN
ejpam-5051	428	20	.	.	PUNCT
ejpam-5051	428	21	define	define	VERB
ejpam-5051	428	22	â	â	ADP
ejpam-5051	428	23	∗	∗	NOUN
ejpam-5051	428	24	g	g	PROPN
ejpam-5051	428	25	×	×	PROPN
ejpam-5051	428	26	t	t	NOUN
ejpam-5051	428	27	=	=	SYM
ejpam-5051	428	28	{	{	PUNCT
ejpam-5051	428	29	(	(	PUNCT
ejpam-5051	428	30	χ	χ	NOUN
ejpam-5051	428	31	,	,	PUNCT
ejpam-5051	428	32	z	z	PROPN
ejpam-5051	428	33	,	,	PUNCT
ejpam-5051	428	34	γ	γ	NOUN
ejpam-5051	428	35	)	)	PUNCT
ejpam-5051	428	36	:	:	PUNCT
ejpam-5051	428	37	χ	χ	X
ejpam-5051	428	38	∈	∈	PROPN
ejpam-5051	428	39	âr(γ	âr(γ	PROPN
ejpam-5051	428	40	)	)	PUNCT
ejpam-5051	428	41	,	,	PUNCT
ejpam-5051	428	42	z	z	PROPN
ejpam-5051	428	43	∈	∈	PROPN
ejpam-5051	428	44	t	t	PROPN
ejpam-5051	428	45	,	,	PUNCT
ejpam-5051	428	46	and	and	CCONJ
ejpam-5051	428	47	γ	γ	PROPN
ejpam-5051	428	48	∈	∈	PROPN
ejpam-5051	428	49	g	g	NOUN
ejpam-5051	428	50	}	}	PUNCT
ejpam-5051	428	51	.	.	PUNCT
ejpam-5051	429	1	let	let	VERB
ejpam-5051	429	2	r((χ	r((χ	PROPN
ejpam-5051	429	3	,	,	PUNCT
ejpam-5051	429	4	z	z	PROPN
ejpam-5051	429	5	,	,	PUNCT
ejpam-5051	429	6	γ	γ	NOUN
ejpam-5051	429	7	)	)	PUNCT
ejpam-5051	429	8	)	)	PUNCT
ejpam-5051	430	1	=	=	PUNCT
ejpam-5051	430	2	(	(	PUNCT
ejpam-5051	430	3	χ	χ	NOUN
ejpam-5051	430	4	,	,	PUNCT
ejpam-5051	430	5	r(γ	r(γ	NOUN
ejpam-5051	430	6	)	)	PUNCT
ejpam-5051	430	7	)	)	PUNCT
ejpam-5051	430	8	and	and	CCONJ
ejpam-5051	430	9	s((χ	s((χ	NOUN
ejpam-5051	430	10	,	,	PUNCT
ejpam-5051	430	11	z	z	PROPN
ejpam-5051	430	12	,	,	PUNCT
ejpam-5051	430	13	γ	γ	NOUN
ejpam-5051	430	14	)	)	PUNCT
ejpam-5051	430	15	)	)	PUNCT
ejpam-5051	431	1	=	=	PUNCT
ejpam-5051	431	2	(	(	PUNCT
ejpam-5051	431	3	χ	χ	X
ejpam-5051	431	4	·	·	PUNCT
ejpam-5051	431	5	γ	γ	X
ejpam-5051	431	6	,	,	PUNCT
ejpam-5051	431	7	s(γ	s(γ	PROPN
ejpam-5051	431	8	)	)	PUNCT
ejpam-5051	431	9	)	)	PUNCT
ejpam-5051	431	10	be	be	AUX
ejpam-5051	431	11	the	the	DET
ejpam-5051	431	12	range	range	NOUN
ejpam-5051	431	13	and	and	CCONJ
ejpam-5051	431	14	source	source	NOUN
ejpam-5051	431	15	maps	map	NOUN
ejpam-5051	431	16	,	,	PUNCT
ejpam-5051	431	17	respectively	respectively	ADV
ejpam-5051	431	18	.	.	PUNCT
ejpam-5051	432	1	the	the	DET
ejpam-5051	432	2	composition	composition	NOUN
ejpam-5051	432	3	map	map	NOUN
ejpam-5051	432	4	and	and	CCONJ
ejpam-5051	432	5	inverse	inverse	NOUN
ejpam-5051	432	6	map	map	NOUN
ejpam-5051	432	7	is	be	AUX
ejpam-5051	432	8	(	(	PUNCT
ejpam-5051	432	9	χ	χ	X
ejpam-5051	432	10	,	,	PUNCT
ejpam-5051	432	11	z	z	NOUN
ejpam-5051	432	12	,	,	PUNCT
ejpam-5051	432	13	γ)(χ′	γ)(χ′	NUM
ejpam-5051	432	14	,	,	PUNCT
ejpam-5051	432	15	z′	z′	NOUN
ejpam-5051	432	16	,	,	PUNCT
ejpam-5051	432	17	γ′	γ′	NUM
ejpam-5051	432	18	)	)	PUNCT
ejpam-5051	432	19	=	=	PUNCT
ejpam-5051	432	20	(	(	PUNCT
ejpam-5051	432	21	χ	χ	NOUN
ejpam-5051	432	22	,	,	PUNCT
ejpam-5051	432	23	zz′	zz′	NUM
ejpam-5051	432	24	,	,	PUNCT
ejpam-5051	432	25	γγ′	γγ′	NOUN
ejpam-5051	432	26	)	)	PUNCT
ejpam-5051	432	27	and	and	CCONJ
ejpam-5051	432	28	(	(	PUNCT
ejpam-5051	432	29	χ	χ	X
ejpam-5051	432	30	,	,	PUNCT
ejpam-5051	432	31	z	z	NOUN
ejpam-5051	432	32	,	,	PUNCT
ejpam-5051	432	33	γ)−1	γ)−1	NOUN
ejpam-5051	432	34	=	=	PRON
ejpam-5051	432	35	(	(	PUNCT
ejpam-5051	432	36	χ	χ	X
ejpam-5051	432	37	·	·	PUNCT
ejpam-5051	432	38	γ	γ	X
ejpam-5051	432	39	,	,	PUNCT
ejpam-5051	432	40	z−1	z−1	PROPN
ejpam-5051	432	41	,	,	PUNCT
ejpam-5051	432	42	γ−1	γ−1	PROPN
ejpam-5051	432	43	)	)	PUNCT
ejpam-5051	432	44	,	,	PUNCT
ejpam-5051	432	45	respectively	respectively	ADV
ejpam-5051	432	46	.	.	PUNCT
ejpam-5051	433	1	we	we	PRON
ejpam-5051	433	2	note	note	VERB
ejpam-5051	433	3	that	that	SCONJ
ejpam-5051	433	4	(	(	PUNCT
ejpam-5051	433	5	χ	χ	X
ejpam-5051	433	6	,	,	PUNCT
ejpam-5051	433	7	z	z	PROPN
ejpam-5051	433	8	,	,	PUNCT
ejpam-5051	433	9	γ	γ	NOUN
ejpam-5051	433	10	)	)	PUNCT
ejpam-5051	433	11	and	and	CCONJ
ejpam-5051	433	12	(	(	PUNCT
ejpam-5051	433	13	χ′	χ′	PROPN
ejpam-5051	433	14	,	,	PUNCT
ejpam-5051	433	15	z′	z′	PROPN
ejpam-5051	433	16	,	,	PUNCT
ejpam-5051	433	17	γ′	γ′	NUM
ejpam-5051	433	18	)	)	PUNCT
ejpam-5051	433	19	are	be	AUX
ejpam-5051	433	20	composable	composable	ADJ
ejpam-5051	433	21	pairs	pair	NOUN
ejpam-5051	433	22	if	if	SCONJ
ejpam-5051	433	23	we	we	PRON
ejpam-5051	433	24	have	have	VERB
ejpam-5051	433	25	χ′	χ′	PROPN
ejpam-5051	433	26	=	=	SYM
ejpam-5051	434	1	χ	χ	ADJ
ejpam-5051	434	2	·	·	PUNCT
ejpam-5051	434	3	γ	γ	X
ejpam-5051	434	4	and	and	CCONJ
ejpam-5051	434	5	χ	χ	PROPN
ejpam-5051	434	6	·	·	PUNCT
ejpam-5051	434	7	γ	γ	X
ejpam-5051	434	8	is	be	AUX
ejpam-5051	434	9	defined	define	VERB
ejpam-5051	434	10	by	by	ADP
ejpam-5051	434	11	χ	χ	PROPN
ejpam-5051	434	12	·	·	PUNCT
ejpam-5051	434	13	γ(a	γ(a	NUM
ejpam-5051	434	14	)	)	PUNCT
ejpam-5051	434	15	=	=	SYM
ejpam-5051	435	1	χ(γaγ−1	χ(γaγ−1	NOUN
ejpam-5051	435	2	)	)	PUNCT
ejpam-5051	436	1	where	where	SCONJ
ejpam-5051	436	2	χ	χ	X
ejpam-5051	436	3	·	·	PUNCT
ejpam-5051	436	4	u	u	NOUN
ejpam-5051	436	5	=	=	SYM
ejpam-5051	436	6	χ	χ	X
ejpam-5051	436	7	.	.	PUNCT
ejpam-5051	436	8	lemma	lemma	PROPN
ejpam-5051	436	9	6	6	NUM
ejpam-5051	436	10	.	.	PUNCT
ejpam-5051	437	1	â	â	ADP
ejpam-5051	437	2	∗	∗	NOUN
ejpam-5051	437	3	g	g	PROPN
ejpam-5051	437	4	×	×	PROPN
ejpam-5051	437	5	t	t	PROPN
ejpam-5051	437	6	is	be	AUX
ejpam-5051	437	7	a	a	DET
ejpam-5051	437	8	hausdorff	hausdorff	NOUN
ejpam-5051	437	9	groupoid	groupoid	NOUN
ejpam-5051	437	10	.	.	PUNCT
ejpam-5051	438	1	proof	proof	NOUN
ejpam-5051	438	2	.	.	PUNCT
ejpam-5051	439	1	let	let	VERB
ejpam-5051	439	2	(	(	PUNCT
ejpam-5051	439	3	χ	χ	X
ejpam-5051	439	4	,	,	PUNCT
ejpam-5051	439	5	z	z	PROPN
ejpam-5051	439	6	,	,	PUNCT
ejpam-5051	439	7	γ	γ	NOUN
ejpam-5051	439	8	)	)	PUNCT
ejpam-5051	439	9	,	,	PUNCT
ejpam-5051	439	10	(	(	PUNCT
ejpam-5051	439	11	χ′	χ′	PROPN
ejpam-5051	439	12	,	,	PUNCT
ejpam-5051	439	13	z′	z′	PROPN
ejpam-5051	439	14	,	,	PUNCT
ejpam-5051	439	15	γ′	γ′	NOUN
ejpam-5051	439	16	)	)	PUNCT
ejpam-5051	439	17	∈	∈	PROPN
ejpam-5051	439	18	â	â	ADP
ejpam-5051	439	19	∗	∗	NOUN
ejpam-5051	439	20	g	g	PROPN
ejpam-5051	439	21	×	×	PROPN
ejpam-5051	439	22	t	t	PROPN
ejpam-5051	439	23	with	with	ADP
ejpam-5051	439	24	(	(	PUNCT
ejpam-5051	439	25	χ	χ	X
ejpam-5051	439	26	,	,	PUNCT
ejpam-5051	439	27	z	z	PROPN
ejpam-5051	439	28	,	,	PUNCT
ejpam-5051	439	29	γ	γ	NOUN
ejpam-5051	439	30	)	)	PUNCT
ejpam-5051	439	31	=	=	SYM
ejpam-5051	439	32	(	(	PUNCT
ejpam-5051	439	33	χ′	χ′	PROPN
ejpam-5051	439	34	,	,	PUNCT
ejpam-5051	439	35	z′	z′	PROPN
ejpam-5051	439	36	,	,	PUNCT
ejpam-5051	439	37	γ′	γ′	PROPN
ejpam-5051	439	38	)	)	PUNCT
ejpam-5051	439	39	.	.	PUNCT
ejpam-5051	440	1	now	now	ADV
ejpam-5051	440	2	,	,	PUNCT
ejpam-5051	440	3	(	(	PUNCT
ejpam-5051	440	4	χ	χ	X
ejpam-5051	440	5	,	,	PUNCT
ejpam-5051	440	6	z	z	NOUN
ejpam-5051	440	7	,	,	PUNCT
ejpam-5051	440	8	γ)−1	γ)−1	NOUN
ejpam-5051	440	9	=	=	PRON
ejpam-5051	440	10	(	(	PUNCT
ejpam-5051	440	11	χ	χ	X
ejpam-5051	440	12	·	·	PUNCT
ejpam-5051	440	13	γ	γ	X
ejpam-5051	440	14	,	,	PUNCT
ejpam-5051	440	15	z−1	z−1	PROPN
ejpam-5051	440	16	,	,	PUNCT
ejpam-5051	440	17	γ−1	γ−1	PROPN
ejpam-5051	440	18	)	)	PUNCT
ejpam-5051	440	19	=	=	SYM
ejpam-5051	440	20	(	(	PUNCT
ejpam-5051	440	21	χ′	χ′	PROPN
ejpam-5051	440	22	·	·	PUNCT
ejpam-5051	441	1	γ′	γ′	PROPN
ejpam-5051	441	2	,	,	PUNCT
ejpam-5051	441	3	(	(	PUNCT
ejpam-5051	441	4	z−1)′	z−1)′	NOUN
ejpam-5051	441	5	,	,	PUNCT
ejpam-5051	441	6	γ′−1	γ′−1	NUM
ejpam-5051	441	7	)	)	PUNCT
ejpam-5051	441	8	=	=	PRON
ejpam-5051	441	9	(	(	PUNCT
ejpam-5051	441	10	χ′	χ′	PROPN
ejpam-5051	441	11	,	,	PUNCT
ejpam-5051	441	12	z′	z′	NUM
ejpam-5051	441	13	,	,	PUNCT
ejpam-5051	441	14	γ′)−1	γ′)−1	NOUN
ejpam-5051	441	15	.	.	PUNCT
ejpam-5051	442	1	also	also	ADV
ejpam-5051	442	2	,	,	PUNCT
ejpam-5051	442	3	r((χ	r((χ	ADJ
ejpam-5051	442	4	,	,	PUNCT
ejpam-5051	442	5	z	z	PROPN
ejpam-5051	442	6	,	,	PUNCT
ejpam-5051	442	7	γ	γ	NOUN
ejpam-5051	442	8	)	)	PUNCT
ejpam-5051	442	9	)	)	PUNCT
ejpam-5051	443	1	=	=	PUNCT
ejpam-5051	443	2	(	(	PUNCT
ejpam-5051	443	3	χ	χ	NOUN
ejpam-5051	443	4	,	,	PUNCT
ejpam-5051	443	5	r(γ	r(γ	NOUN
ejpam-5051	443	6	)	)	PUNCT
ejpam-5051	443	7	)	)	PUNCT
ejpam-5051	444	1	=	=	PUNCT
ejpam-5051	444	2	(	(	PUNCT
ejpam-5051	444	3	χ	χ	NOUN
ejpam-5051	444	4	,	,	PUNCT
ejpam-5051	444	5	s(γ′	s(γ′	NOUN
ejpam-5051	444	6	)	)	PUNCT
ejpam-5051	444	7	)	)	PUNCT
ejpam-5051	445	1	=	=	PUNCT
ejpam-5051	445	2	r((χ′	r((χ′	NOUN
ejpam-5051	445	3	,	,	PUNCT
ejpam-5051	445	4	z′	z′	PROPN
ejpam-5051	445	5	,	,	PUNCT
ejpam-5051	445	6	γ′	γ′	NOUN
ejpam-5051	445	7	)	)	PUNCT
ejpam-5051	445	8	)	)	PUNCT
ejpam-5051	445	9	;	;	PUNCT
ejpam-5051	445	10	s((χ	s((χ	NOUN
ejpam-5051	445	11	,	,	PUNCT
ejpam-5051	445	12	z	z	PROPN
ejpam-5051	445	13	,	,	PUNCT
ejpam-5051	445	14	γ	γ	NOUN
ejpam-5051	445	15	)	)	PUNCT
ejpam-5051	445	16	)	)	PUNCT
ejpam-5051	445	17	=	=	PUNCT
ejpam-5051	445	18	(	(	PUNCT
ejpam-5051	445	19	χ	χ	X
ejpam-5051	445	20	·	·	PUNCT
ejpam-5051	445	21	γ	γ	X
ejpam-5051	445	22	,	,	PUNCT
ejpam-5051	445	23	s(γ	s(γ	PROPN
ejpam-5051	445	24	)	)	PUNCT
ejpam-5051	445	25	)	)	PUNCT
ejpam-5051	445	26	=	=	SYM
ejpam-5051	445	27	(	(	PUNCT
ejpam-5051	445	28	χ′	χ′	PROPN
ejpam-5051	445	29	·	·	PUNCT
ejpam-5051	445	30	γ′	γ′	PROPN
ejpam-5051	445	31	,	,	PUNCT
ejpam-5051	445	32	s(γ′	s(γ′	NOUN
ejpam-5051	445	33	)	)	PUNCT
ejpam-5051	445	34	)	)	PUNCT
ejpam-5051	446	1	=	=	SYM
ejpam-5051	446	2	s((χ′	s((χ′	PROPN
ejpam-5051	446	3	,	,	PUNCT
ejpam-5051	446	4	z′	z′	PROPN
ejpam-5051	446	5	,	,	PUNCT
ejpam-5051	446	6	γ′	γ′	NOUN
ejpam-5051	446	7	)	)	PUNCT
ejpam-5051	446	8	)	)	PUNCT
ejpam-5051	446	9	.	.	PUNCT
ejpam-5051	447	1	hence	hence	ADV
ejpam-5051	447	2	,	,	PUNCT
ejpam-5051	447	3	the	the	DET
ejpam-5051	447	4	inverse	inverse	ADJ
ejpam-5051	447	5	range	range	NOUN
ejpam-5051	447	6	and	and	CCONJ
ejpam-5051	447	7	source	source	NOUN
ejpam-5051	447	8	maps	map	NOUN
ejpam-5051	447	9	are	be	AUX
ejpam-5051	447	10	well	well	ADV
ejpam-5051	447	11	-	-	PUNCT
ejpam-5051	447	12	defined	define	VERB
ejpam-5051	447	13	.	.	PUNCT
ejpam-5051	448	1	composition	composition	NOUN
ejpam-5051	448	2	is	be	AUX
ejpam-5051	448	3	well	well	ADV
ejpam-5051	448	4	-	-	PUNCT
ejpam-5051	448	5	defined	define	VERB
ejpam-5051	448	6	since	since	SCONJ
ejpam-5051	448	7	for	for	ADP
ejpam-5051	448	8	(	(	PUNCT
ejpam-5051	448	9	(	(	PUNCT
ejpam-5051	448	10	χ1	χ1	NOUN
ejpam-5051	448	11	,	,	PUNCT
ejpam-5051	448	12	z1	z1	NOUN
ejpam-5051	448	13	,	,	PUNCT
ejpam-5051	448	14	γ1	γ1	PROPN
ejpam-5051	448	15	)	)	PUNCT
ejpam-5051	448	16	,	,	PUNCT
ejpam-5051	448	17	(	(	PUNCT
ejpam-5051	448	18	χ	χ	X
ejpam-5051	448	19	′	′	NUM
ejpam-5051	448	20	1	1	NUM
ejpam-5051	448	21	,	,	PUNCT
ejpam-5051	448	22	z	z	NOUN
ejpam-5051	448	23	′	′	NUM
ejpam-5051	448	24	1	1	NUM
ejpam-5051	448	25	,	,	PUNCT
ejpam-5051	448	26	γ	γ	NOUN
ejpam-5051	448	27	′	′	NOUN
ejpam-5051	448	28	1	1	NUM
ejpam-5051	448	29	)	)	PUNCT
ejpam-5051	448	30	)	)	PUNCT
ejpam-5051	448	31	,	,	PUNCT
ejpam-5051	448	32	(	(	PUNCT
ejpam-5051	448	33	(	(	PUNCT
ejpam-5051	448	34	χ2	χ2	PROPN
ejpam-5051	448	35	,	,	PUNCT
ejpam-5051	448	36	z2	z2	PROPN
ejpam-5051	448	37	,	,	PUNCT
ejpam-5051	448	38	γ2	γ2	PROPN
ejpam-5051	448	39	)	)	PUNCT
ejpam-5051	448	40	,	,	PUNCT
ejpam-5051	448	41	(	(	PUNCT
ejpam-5051	448	42	χ	χ	X
ejpam-5051	448	43	′	′	NUM
ejpam-5051	448	44	2	2	NUM
ejpam-5051	448	45	,	,	PUNCT
ejpam-5051	448	46	z	z	NOUN
ejpam-5051	448	47	′	′	NUM
ejpam-5051	448	48	2	2	NUM
ejpam-5051	448	49	,	,	PUNCT
ejpam-5051	448	50	γ	γ	NOUN
ejpam-5051	448	51	′	′	NOUN
ejpam-5051	448	52	2	2	NUM
ejpam-5051	448	53	)	)	PUNCT
ejpam-5051	448	54	)	)	PUNCT
ejpam-5051	449	1	∈	∈	PROPN
ejpam-5051	449	2	â∗g×t	â∗g×t	ADV
ejpam-5051	449	3	(	(	PUNCT
ejpam-5051	449	4	2	2	NUM
ejpam-5051	449	5	)	)	PUNCT
ejpam-5051	449	6	with	with	ADP
ejpam-5051	449	7	(	(	PUNCT
ejpam-5051	449	8	(	(	PUNCT
ejpam-5051	449	9	χ1	χ1	NOUN
ejpam-5051	449	10	,	,	PUNCT
ejpam-5051	449	11	z1	z1	NOUN
ejpam-5051	449	12	,	,	PUNCT
ejpam-5051	449	13	γ1	γ1	PROPN
ejpam-5051	449	14	)	)	PUNCT
ejpam-5051	449	15	,	,	PUNCT
ejpam-5051	449	16	(	(	PUNCT
ejpam-5051	449	17	χ	χ	X
ejpam-5051	449	18	′	′	NUM
ejpam-5051	449	19	1	1	NUM
ejpam-5051	449	20	,	,	PUNCT
ejpam-5051	449	21	z	z	NOUN
ejpam-5051	449	22	′	′	NUM
ejpam-5051	449	23	1	1	NUM
ejpam-5051	449	24	,	,	PUNCT
ejpam-5051	449	25	γ	γ	NOUN
ejpam-5051	449	26	′	′	NOUN
ejpam-5051	449	27	1	1	NUM
ejpam-5051	449	28	)	)	PUNCT
ejpam-5051	449	29	)	)	PUNCT
ejpam-5051	450	1	=	=	SYM
ejpam-5051	450	2	(	(	PUNCT
ejpam-5051	450	3	(	(	PUNCT
ejpam-5051	450	4	χ2	χ2	PROPN
ejpam-5051	450	5	,	,	PUNCT
ejpam-5051	450	6	z2	z2	PROPN
ejpam-5051	450	7	,	,	PUNCT
ejpam-5051	450	8	γ2	γ2	PROPN
ejpam-5051	450	9	)	)	PUNCT
ejpam-5051	450	10	,	,	PUNCT
ejpam-5051	450	11	(	(	PUNCT
ejpam-5051	450	12	χ	χ	X
ejpam-5051	450	13	′	′	NUM
ejpam-5051	450	14	2	2	NUM
ejpam-5051	450	15	,	,	PUNCT
ejpam-5051	450	16	z	z	NOUN
ejpam-5051	450	17	′	′	NUM
ejpam-5051	450	18	2	2	NUM
ejpam-5051	450	19	,	,	PUNCT
ejpam-5051	450	20	γ	γ	X
ejpam-5051	450	21	′	′	NOUN
ejpam-5051	450	22	2)),m(((χ1	2)),m(((χ1	NUM
ejpam-5051	450	23	,	,	PUNCT
ejpam-5051	450	24	z1	z1	NOUN
ejpam-5051	450	25	,	,	PUNCT
ejpam-5051	450	26	γ1)(χ	γ1)(χ	ADV
ejpam-5051	450	27	′	′	NUM
ejpam-5051	450	28	1	1	NUM
ejpam-5051	450	29	,	,	PUNCT
ejpam-5051	450	30	z	z	NOUN
ejpam-5051	450	31	′	′	NUM
ejpam-5051	450	32	1	1	NUM
ejpam-5051	450	33	,	,	PUNCT
ejpam-5051	450	34	γ	γ	NOUN
ejpam-5051	450	35	′	′	NOUN
ejpam-5051	450	36	1	1	NUM
ejpam-5051	450	37	)	)	PUNCT
ejpam-5051	450	38	)	)	PUNCT
ejpam-5051	450	39	)	)	PUNCT
ejpam-5051	451	1	=	=	SYM
ejpam-5051	451	2	(	(	PUNCT
ejpam-5051	451	3	χ1	χ1	NOUN
ejpam-5051	451	4	,	,	PUNCT
ejpam-5051	451	5	z1z	z1z	PROPN
ejpam-5051	451	6	′	′	NUM
ejpam-5051	451	7	1	1	NUM
ejpam-5051	451	8	,	,	PUNCT
ejpam-5051	451	9	γ1γ	γ1γ	NOUN
ejpam-5051	451	10	′	′	NUM
ejpam-5051	451	11	1	1	NUM
ejpam-5051	451	12	)	)	PUNCT
ejpam-5051	451	13	=	=	SYM
ejpam-5051	451	14	(	(	PUNCT
ejpam-5051	451	15	χ2	χ2	PROPN
ejpam-5051	451	16	,	,	PUNCT
ejpam-5051	451	17	z2z	z2z	PROPN
ejpam-5051	451	18	′	′	NUM
ejpam-5051	451	19	2	2	NUM
ejpam-5051	451	20	,	,	PUNCT
ejpam-5051	451	21	γ2γ	γ2γ	ADV
ejpam-5051	451	22	′	′	NOUN
ejpam-5051	451	23	2	2	X
ejpam-5051	451	24	)	)	PUNCT
ejpam-5051	451	25	=	=	SYM
ejpam-5051	452	1	m(((χ2	m(((χ2	NOUN
ejpam-5051	452	2	,	,	PUNCT
ejpam-5051	452	3	z2	z2	NOUN
ejpam-5051	452	4	,	,	PUNCT
ejpam-5051	452	5	γ2	γ2	PROPN
ejpam-5051	452	6	)	)	PUNCT
ejpam-5051	452	7	,	,	PUNCT
ejpam-5051	452	8	(	(	PUNCT
ejpam-5051	452	9	χ	χ	X
ejpam-5051	452	10	′	′	NUM
ejpam-5051	452	11	2	2	NUM
ejpam-5051	452	12	,	,	PUNCT
ejpam-5051	452	13	z	z	NOUN
ejpam-5051	452	14	′	′	NUM
ejpam-5051	452	15	2	2	NUM
ejpam-5051	452	16	,	,	PUNCT
ejpam-5051	452	17	γ	γ	NOUN
ejpam-5051	452	18	′	′	NOUN
ejpam-5051	452	19	2	2	NUM
ejpam-5051	452	20	)	)	PUNCT
ejpam-5051	452	21	)	)	PUNCT
ejpam-5051	452	22	)	)	PUNCT
ejpam-5051	452	23	.	.	PUNCT
ejpam-5051	453	1	now	now	ADV
ejpam-5051	453	2	,	,	PUNCT
ejpam-5051	453	3	let	let	VERB
ejpam-5051	453	4	(	(	PUNCT
ejpam-5051	453	5	(	(	PUNCT
ejpam-5051	453	6	χ1	χ1	NOUN
ejpam-5051	453	7	,	,	PUNCT
ejpam-5051	453	8	z1	z1	NOUN
ejpam-5051	453	9	,	,	PUNCT
ejpam-5051	453	10	γ1	γ1	PROPN
ejpam-5051	453	11	)	)	PUNCT
ejpam-5051	453	12	,	,	PUNCT
ejpam-5051	453	13	(	(	PUNCT
ejpam-5051	453	14	χ2	χ2	PROPN
ejpam-5051	453	15	,	,	PUNCT
ejpam-5051	453	16	z2	z2	PROPN
ejpam-5051	453	17	,	,	PUNCT
ejpam-5051	453	18	γ2	γ2	NOUN
ejpam-5051	453	19	)	)	PUNCT
ejpam-5051	453	20	)	)	PUNCT
ejpam-5051	453	21	,	,	PUNCT
ejpam-5051	453	22	(	(	PUNCT
ejpam-5051	453	23	(	(	PUNCT
ejpam-5051	453	24	χ2	χ2	PROPN
ejpam-5051	453	25	,	,	PUNCT
ejpam-5051	453	26	z2	z2	PROPN
ejpam-5051	453	27	,	,	PUNCT
ejpam-5051	453	28	γ2	γ2	PROPN
ejpam-5051	453	29	)	)	PUNCT
ejpam-5051	453	30	,	,	PUNCT
ejpam-5051	453	31	(	(	PUNCT
ejpam-5051	453	32	χ3	χ3	NOUN
ejpam-5051	453	33	,	,	PUNCT
ejpam-5051	453	34	z3	z3	PROPN
ejpam-5051	453	35	,	,	PUNCT
ejpam-5051	453	36	γ3	γ3	NOUN
ejpam-5051	453	37	)	)	PUNCT
ejpam-5051	453	38	)	)	PUNCT
ejpam-5051	454	1	∈	∈	PROPN
ejpam-5051	454	2	â	â	ADP
ejpam-5051	454	3	∗	∗	NOUN
ejpam-5051	454	4	g	g	PROPN
ejpam-5051	454	5	×	×	PROPN
ejpam-5051	454	6	t	t	PROPN
ejpam-5051	454	7	(	(	PUNCT
ejpam-5051	454	8	2	2	NUM
ejpam-5051	454	9	)	)	PUNCT
ejpam-5051	454	10	.	.	PUNCT
ejpam-5051	455	1	then	then	ADV
ejpam-5051	455	2	s((χ1	s((χ1	NOUN
ejpam-5051	455	3	,	,	PUNCT
ejpam-5051	455	4	z1	z1	PROPN
ejpam-5051	455	5	,	,	PUNCT
ejpam-5051	455	6	γ1)(χ2	γ1)(χ2	PROPN
ejpam-5051	455	7	,	,	PUNCT
ejpam-5051	455	8	z2	z2	PROPN
ejpam-5051	455	9	,	,	PUNCT
ejpam-5051	455	10	γ2	γ2	NOUN
ejpam-5051	455	11	)	)	PUNCT
ejpam-5051	455	12	)	)	PUNCT
ejpam-5051	456	1	=	=	SYM
ejpam-5051	456	2	s((χ1	s((χ1	PROPN
ejpam-5051	456	3	,	,	PUNCT
ejpam-5051	456	4	z1z2	z1z2	PROPN
ejpam-5051	456	5	,	,	PUNCT
ejpam-5051	456	6	γ1γ2	γ1γ2	NOUN
ejpam-5051	456	7	)	)	PUNCT
ejpam-5051	456	8	)	)	PUNCT
ejpam-5051	457	1	=	=	SYM
ejpam-5051	457	2	(	(	PUNCT
ejpam-5051	457	3	χ1	χ1	NOUN
ejpam-5051	457	4	·	·	PUNCT
ejpam-5051	457	5	γ1γ2	γ1γ2	ADJ
ejpam-5051	457	6	,	,	PUNCT
ejpam-5051	457	7	s(γ1γ2	s(γ1γ2	NOUN
ejpam-5051	457	8	)	)	PUNCT
ejpam-5051	457	9	)	)	PUNCT
ejpam-5051	457	10	=	=	SYM
ejpam-5051	458	1	(	(	PUNCT
ejpam-5051	458	2	χ2	χ2	PROPN
ejpam-5051	458	3	·	·	PUNCT
ejpam-5051	458	4	γ2	γ2	PROPN
ejpam-5051	458	5	,	,	PUNCT
ejpam-5051	458	6	s(γ2	s(γ2	NOUN
ejpam-5051	458	7	)	)	PUNCT
ejpam-5051	458	8	)	)	PUNCT
ejpam-5051	459	1	=	=	PRON
ejpam-5051	459	2	(	(	PUNCT
ejpam-5051	459	3	χ3	χ3	PROPN
ejpam-5051	459	4	,	,	PUNCT
ejpam-5051	459	5	r(γ3	r(γ3	NOUN
ejpam-5051	459	6	)	)	PUNCT
ejpam-5051	459	7	)	)	PUNCT
ejpam-5051	460	1	=	=	SYM
ejpam-5051	460	2	(	(	PUNCT
ejpam-5051	460	3	(	(	PUNCT
ejpam-5051	460	4	χ3	χ3	NOUN
ejpam-5051	460	5	,	,	PUNCT
ejpam-5051	460	6	z3	z3	PROPN
ejpam-5051	460	7	,	,	PUNCT
ejpam-5051	460	8	γ3	γ3	NOUN
ejpam-5051	460	9	)	)	PUNCT
ejpam-5051	460	10	)	)	PUNCT
ejpam-5051	460	11	.	.	PUNCT
ejpam-5051	461	1	also	also	ADV
ejpam-5051	461	2	,	,	PUNCT
ejpam-5051	461	3	r((χ2	r((χ2	PROPN
ejpam-5051	461	4	,	,	PUNCT
ejpam-5051	461	5	z2	z2	PROPN
ejpam-5051	461	6	,	,	PUNCT
ejpam-5051	461	7	γ2)(χ3	γ2)(χ3	ADJ
ejpam-5051	461	8	,	,	PUNCT
ejpam-5051	461	9	z3	z3	PROPN
ejpam-5051	461	10	,	,	PUNCT
ejpam-5051	461	11	γ3	γ3	NOUN
ejpam-5051	461	12	)	)	PUNCT
ejpam-5051	461	13	)	)	PUNCT
ejpam-5051	462	1	=	=	PUNCT
ejpam-5051	462	2	r((χ2	r((χ2	NOUN
ejpam-5051	462	3	,	,	PUNCT
ejpam-5051	462	4	z2z3	z2z3	X
ejpam-5051	462	5	,	,	PUNCT
ejpam-5051	462	6	γ2γ3	γ2γ3	NOUN
ejpam-5051	462	7	)	)	PUNCT
ejpam-5051	462	8	)	)	PUNCT
ejpam-5051	463	1	=	=	SYM
ejpam-5051	463	2	(	(	PUNCT
ejpam-5051	463	3	χ2	χ2	PROPN
ejpam-5051	463	4	,	,	PUNCT
ejpam-5051	463	5	r(γ2γ3	r(γ2γ3	NOUN
ejpam-5051	463	6	)	)	PUNCT
ejpam-5051	463	7	)	)	PUNCT
ejpam-5051	464	1	=	=	PRON
ejpam-5051	464	2	(	(	PUNCT
ejpam-5051	464	3	χ2	χ2	PROPN
ejpam-5051	464	4	,	,	PUNCT
ejpam-5051	464	5	r(γ2	r(γ2	NOUN
ejpam-5051	464	6	)	)	PUNCT
ejpam-5051	464	7	)	)	PUNCT
ejpam-5051	464	8	=	=	SYM
ejpam-5051	465	1	(	(	PUNCT
ejpam-5051	465	2	χ1	χ1	NOUN
ejpam-5051	465	3	·	·	PUNCT
ejpam-5051	465	4	γ1	γ1	NOUN
ejpam-5051	465	5	,	,	PUNCT
ejpam-5051	465	6	s(γ1	s(γ1	NOUN
ejpam-5051	465	7	)	)	PUNCT
ejpam-5051	465	8	)	)	PUNCT
ejpam-5051	466	1	r.	r.	PROPN
ejpam-5051	466	2	s.	s.	PROPN
ejpam-5051	466	3	bongcawel	bongcawel	PROPN
ejpam-5051	466	4	et	et	PROPN
ejpam-5051	466	5	al	al	PROPN
ejpam-5051	466	6	.	.	PUNCT
ejpam-5051	466	7	/	/	SYM
ejpam-5051	466	8	eur	eur	PROPN
ejpam-5051	466	9	.	.	PUNCT
ejpam-5051	467	1	j.	j.	PROPN
ejpam-5051	467	2	pure	pure	PROPN
ejpam-5051	467	3	appl	appl	PROPN
ejpam-5051	467	4	.	.	PROPN
ejpam-5051	467	5	math	math	PROPN
ejpam-5051	467	6	,	,	PUNCT
ejpam-5051	467	7	17	17	NUM
ejpam-5051	467	8	(	(	PUNCT
ejpam-5051	467	9	1	1	NUM
ejpam-5051	467	10	)	)	PUNCT
ejpam-5051	467	11	(	(	PUNCT
ejpam-5051	467	12	2024	2024	NUM
ejpam-5051	467	13	)	)	PUNCT
ejpam-5051	467	14	,	,	PUNCT
ejpam-5051	467	15	519	519	NUM
ejpam-5051	467	16	-	-	SYM
ejpam-5051	467	17	545	545	NUM
ejpam-5051	467	18	531	531	NUM
ejpam-5051	467	19	=	=	NOUN
ejpam-5051	467	20	s((χ1	s((χ1	NOUN
ejpam-5051	467	21	,	,	PUNCT
ejpam-5051	467	22	z1	z1	NOUN
ejpam-5051	467	23	,	,	PUNCT
ejpam-5051	467	24	γ1	γ1	NOUN
ejpam-5051	467	25	)	)	PUNCT
ejpam-5051	467	26	)	)	PUNCT
ejpam-5051	467	27	.	.	PUNCT
ejpam-5051	468	1	thus	thus	ADV
ejpam-5051	468	2	,	,	PUNCT
ejpam-5051	468	3	(	(	PUNCT
ejpam-5051	468	4	(	(	PUNCT
ejpam-5051	468	5	χ1	χ1	NOUN
ejpam-5051	468	6	,	,	PUNCT
ejpam-5051	468	7	z1	z1	NOUN
ejpam-5051	468	8	,	,	PUNCT
ejpam-5051	468	9	γ1)(χ2	γ1)(χ2	PROPN
ejpam-5051	468	10	,	,	PUNCT
ejpam-5051	468	11	z2	z2	PROPN
ejpam-5051	468	12	,	,	PUNCT
ejpam-5051	468	13	γ2	γ2	PROPN
ejpam-5051	468	14	)	)	PUNCT
ejpam-5051	468	15	,	,	PUNCT
ejpam-5051	468	16	(	(	PUNCT
ejpam-5051	468	17	χ3	χ3	NOUN
ejpam-5051	468	18	,	,	PUNCT
ejpam-5051	468	19	z3	z3	PROPN
ejpam-5051	468	20	,	,	PUNCT
ejpam-5051	468	21	γ3)),((χ1	γ3)),((χ1	PROPN
ejpam-5051	468	22	,	,	PUNCT
ejpam-5051	468	23	z1	z1	NOUN
ejpam-5051	468	24	,	,	PUNCT
ejpam-5051	468	25	γ1	γ1	PROPN
ejpam-5051	468	26	)	)	PUNCT
ejpam-5051	468	27	,	,	PUNCT
ejpam-5051	468	28	(	(	PUNCT
ejpam-5051	468	29	χ2	χ2	PROPN
ejpam-5051	468	30	,	,	PUNCT
ejpam-5051	468	31	z2	z2	PROPN
ejpam-5051	468	32	,	,	PUNCT
ejpam-5051	468	33	γ2)(χ3	γ2)(χ3	ADJ
ejpam-5051	468	34	,	,	PUNCT
ejpam-5051	468	35	z3	z3	PROPN
ejpam-5051	468	36	,	,	PUNCT
ejpam-5051	468	37	γ3	γ3	NOUN
ejpam-5051	468	38	)	)	PUNCT
ejpam-5051	468	39	)	)	PUNCT
ejpam-5051	468	40	∈	∈	PROPN
ejpam-5051	468	41	(	(	PUNCT
ejpam-5051	468	42	â	â	X
ejpam-5051	468	43	∗	∗	NOUN
ejpam-5051	468	44	g	g	PROPN
ejpam-5051	468	45	×	×	PROPN
ejpam-5051	468	46	t	t	NOUN
ejpam-5051	468	47	)	)	PUNCT
ejpam-5051	468	48	(	(	PUNCT
ejpam-5051	468	49	2	2	NUM
ejpam-5051	468	50	)	)	PUNCT
ejpam-5051	468	51	.	.	PUNCT
ejpam-5051	469	1	composition	composition	NOUN
ejpam-5051	469	2	in	in	ADP
ejpam-5051	469	3	â	â	PROPN
ejpam-5051	469	4	∗	∗	NOUN
ejpam-5051	469	5	g	g	PROPN
ejpam-5051	469	6	×	×	PROPN
ejpam-5051	469	7	t	t	PROPN
ejpam-5051	469	8	is	be	AUX
ejpam-5051	469	9	associative	associative	ADJ
ejpam-5051	469	10	since	since	SCONJ
ejpam-5051	469	11	(	(	PUNCT
ejpam-5051	469	12	(	(	PUNCT
ejpam-5051	469	13	χ1	χ1	NOUN
ejpam-5051	469	14	,	,	PUNCT
ejpam-5051	469	15	z1	z1	NOUN
ejpam-5051	469	16	,	,	PUNCT
ejpam-5051	469	17	γ1)(χ2	γ1)(χ2	PROPN
ejpam-5051	469	18	,	,	PUNCT
ejpam-5051	469	19	z2	z2	PROPN
ejpam-5051	469	20	,	,	PUNCT
ejpam-5051	469	21	γ2))(χ3	γ2))(χ3	NOUN
ejpam-5051	469	22	,	,	PUNCT
ejpam-5051	469	23	z3	z3	PROPN
ejpam-5051	469	24	,	,	PUNCT
ejpam-5051	469	25	γ3	γ3	NOUN
ejpam-5051	469	26	)	)	PUNCT
ejpam-5051	469	27	=	=	PUNCT
ejpam-5051	470	1	(	(	PUNCT
ejpam-5051	470	2	χ1	χ1	NOUN
ejpam-5051	470	3	,	,	PUNCT
ejpam-5051	470	4	z1z2	z1z2	PROPN
ejpam-5051	470	5	,	,	PUNCT
ejpam-5051	470	6	γ1γ2)(χ3	γ1γ2)(χ3	NOUN
ejpam-5051	470	7	,	,	PUNCT
ejpam-5051	470	8	z3	z3	PROPN
ejpam-5051	470	9	,	,	PUNCT
ejpam-5051	470	10	γ3	γ3	NOUN
ejpam-5051	470	11	)	)	PUNCT
ejpam-5051	470	12	=	=	PUNCT
ejpam-5051	470	13	(	(	PUNCT
ejpam-5051	470	14	χ1	χ1	PROPN
ejpam-5051	470	15	,	,	PUNCT
ejpam-5051	470	16	z1z2z3	z1z2z3	PROPN
ejpam-5051	470	17	,	,	PUNCT
ejpam-5051	470	18	γ1γ2γ3	γ1γ2γ3	NOUN
ejpam-5051	470	19	)	)	PUNCT
ejpam-5051	470	20	=	=	PUNCT
ejpam-5051	470	21	(	(	PUNCT
ejpam-5051	470	22	χ1	χ1	NOUN
ejpam-5051	470	23	,	,	PUNCT
ejpam-5051	470	24	z1	z1	PROPN
ejpam-5051	470	25	,	,	PUNCT
ejpam-5051	470	26	γ1)(χ2	γ1)(χ2	PROPN
ejpam-5051	470	27	,	,	PUNCT
ejpam-5051	470	28	z2z3	z2z3	X
ejpam-5051	470	29	,	,	PUNCT
ejpam-5051	470	30	γ2γ3	γ2γ3	NOUN
ejpam-5051	470	31	)	)	PUNCT
ejpam-5051	470	32	=	=	SYM
ejpam-5051	470	33	(	(	PUNCT
ejpam-5051	470	34	χ1	χ1	NOUN
ejpam-5051	470	35	,	,	PUNCT
ejpam-5051	470	36	z1	z1	NOUN
ejpam-5051	470	37	,	,	PUNCT
ejpam-5051	470	38	γ1)((χ2	γ1)((χ2	NUM
ejpam-5051	470	39	,	,	PUNCT
ejpam-5051	470	40	z2	z2	NOUN
ejpam-5051	470	41	,	,	PUNCT
ejpam-5051	470	42	γ2)(χ3	γ2)(χ3	ADJ
ejpam-5051	470	43	,	,	PUNCT
ejpam-5051	470	44	z3	z3	NOUN
ejpam-5051	470	45	,	,	PUNCT
ejpam-5051	470	46	γ3	γ3	NOUN
ejpam-5051	470	47	)	)	PUNCT
ejpam-5051	470	48	)	)	PUNCT
ejpam-5051	470	49	.	.	PUNCT
ejpam-5051	471	1	for	for	ADP
ejpam-5051	471	2	(	(	PUNCT
ejpam-5051	471	3	χ	χ	X
ejpam-5051	471	4	,	,	PUNCT
ejpam-5051	471	5	z	z	PROPN
ejpam-5051	471	6	,	,	PUNCT
ejpam-5051	471	7	γ	γ	PROPN
ejpam-5051	471	8	)	)	PUNCT
ejpam-5051	471	9	∈	∈	PROPN
ejpam-5051	471	10	â	â	ADP
ejpam-5051	471	11	∗	∗	NOUN
ejpam-5051	471	12	g	g	PROPN
ejpam-5051	471	13	×	×	PROPN
ejpam-5051	471	14	t	t	NOUN
ejpam-5051	471	15	,	,	PUNCT
ejpam-5051	471	16	(	(	PUNCT
ejpam-5051	471	17	(	(	PUNCT
ejpam-5051	471	18	χ	χ	X
ejpam-5051	471	19	,	,	PUNCT
ejpam-5051	471	20	z	z	PROPN
ejpam-5051	471	21	,	,	PUNCT
ejpam-5051	471	22	γ)−1)−1	γ)−1)−1	PROPN
ejpam-5051	471	23	=	=	PUNCT
ejpam-5051	471	24	(	(	PUNCT
ejpam-5051	471	25	χ	χ	X
ejpam-5051	471	26	·	·	PUNCT
ejpam-5051	471	27	γ	γ	X
ejpam-5051	471	28	,	,	PUNCT
ejpam-5051	471	29	z−1	z−1	PROPN
ejpam-5051	471	30	,	,	PUNCT
ejpam-5051	471	31	γ−1)−1	γ−1)−1	NOUN
ejpam-5051	471	32	=	=	SYM
ejpam-5051	471	33	(	(	PUNCT
ejpam-5051	471	34	χ	χ	X
ejpam-5051	471	35	·	·	PUNCT
ejpam-5051	471	36	γ	γ	X
ejpam-5051	471	37	·	·	PUNCT
ejpam-5051	471	38	γ−1	γ−1	ADJ
ejpam-5051	471	39	,	,	PUNCT
ejpam-5051	471	40	(	(	PUNCT
ejpam-5051	471	41	z−1)−1	z−1)−1	NOUN
ejpam-5051	471	42	,	,	PUNCT
ejpam-5051	471	43	(	(	PUNCT
ejpam-5051	471	44	γ−1)−1	γ−1)−1	NOUN
ejpam-5051	471	45	)	)	PUNCT
ejpam-5051	471	46	=	=	PUNCT
ejpam-5051	471	47	(	(	PUNCT
ejpam-5051	471	48	χ	χ	X
ejpam-5051	471	49	·	·	PUNCT
ejpam-5051	471	50	r(γ	r(γ	NOUN
ejpam-5051	471	51	)	)	PUNCT
ejpam-5051	471	52	,	,	PUNCT
ejpam-5051	471	53	z	z	PROPN
ejpam-5051	471	54	,	,	PUNCT
ejpam-5051	471	55	γ	γ	NOUN
ejpam-5051	471	56	)	)	PUNCT
ejpam-5051	471	57	=	=	PUNCT
ejpam-5051	471	58	(	(	PUNCT
ejpam-5051	471	59	χ	χ	X
ejpam-5051	471	60	·	·	PUNCT
ejpam-5051	471	61	u	u	NOUN
ejpam-5051	471	62	,	,	PUNCT
ejpam-5051	471	63	z	z	PROPN
ejpam-5051	471	64	,	,	PUNCT
ejpam-5051	471	65	γ	γ	NOUN
ejpam-5051	471	66	)	)	PUNCT
ejpam-5051	471	67	=	=	PUNCT
ejpam-5051	471	68	(	(	PUNCT
ejpam-5051	471	69	χ	χ	X
ejpam-5051	471	70	,	,	PUNCT
ejpam-5051	471	71	z	z	PROPN
ejpam-5051	471	72	,	,	PUNCT
ejpam-5051	471	73	γ	γ	NOUN
ejpam-5051	471	74	)	)	PUNCT
ejpam-5051	471	75	.	.	PUNCT
ejpam-5051	472	1	also	also	ADV
ejpam-5051	472	2	,	,	PUNCT
ejpam-5051	472	3	r((χ	r((χ	ADJ
ejpam-5051	472	4	,	,	PUNCT
ejpam-5051	472	5	z	z	NOUN
ejpam-5051	472	6	,	,	PUNCT
ejpam-5051	472	7	γ)−1	γ)−1	NOUN
ejpam-5051	472	8	)	)	PUNCT
ejpam-5051	472	9	=	=	SYM
ejpam-5051	472	10	r((χ	r((χ	X
ejpam-5051	472	11	·	·	PUNCT
ejpam-5051	473	1	γ	γ	X
ejpam-5051	473	2	,	,	PUNCT
ejpam-5051	473	3	z−1	z−1	PROPN
ejpam-5051	473	4	,	,	PUNCT
ejpam-5051	473	5	γ−1	γ−1	PROPN
ejpam-5051	473	6	)	)	PUNCT
ejpam-5051	473	7	)	)	PUNCT
ejpam-5051	474	1	=	=	PUNCT
ejpam-5051	474	2	(	(	PUNCT
ejpam-5051	474	3	χ	χ	X
ejpam-5051	474	4	·	·	PUNCT
ejpam-5051	474	5	γ	γ	X
ejpam-5051	474	6	,	,	PUNCT
ejpam-5051	474	7	r(γ−1	r(γ−1	ADJ
ejpam-5051	474	8	)	)	PUNCT
ejpam-5051	474	9	)	)	PUNCT
ejpam-5051	475	1	=	=	PUNCT
ejpam-5051	475	2	(	(	PUNCT
ejpam-5051	475	3	χ	χ	X
ejpam-5051	475	4	·	·	PUNCT
ejpam-5051	475	5	γ	γ	X
ejpam-5051	475	6	,	,	PUNCT
ejpam-5051	475	7	s(γ	s(γ	PROPN
ejpam-5051	475	8	)	)	PUNCT
ejpam-5051	475	9	)	)	PUNCT
ejpam-5051	475	10	=	=	SYM
ejpam-5051	476	1	s((χ	s((χ	NOUN
ejpam-5051	476	2	,	,	PUNCT
ejpam-5051	476	3	z	z	PROPN
ejpam-5051	476	4	,	,	PUNCT
ejpam-5051	476	5	γ	γ	NOUN
ejpam-5051	476	6	)	)	PUNCT
ejpam-5051	476	7	)	)	PUNCT
ejpam-5051	476	8	.	.	PUNCT
ejpam-5051	477	1	hence	hence	ADV
ejpam-5051	477	2	,	,	PUNCT
ejpam-5051	477	3	(	(	PUNCT
ejpam-5051	477	4	(	(	PUNCT
ejpam-5051	477	5	χ	χ	X
ejpam-5051	477	6	,	,	PUNCT
ejpam-5051	477	7	z	z	PROPN
ejpam-5051	477	8	,	,	PUNCT
ejpam-5051	477	9	γ	γ	NOUN
ejpam-5051	477	10	)	)	PUNCT
ejpam-5051	477	11	,	,	PUNCT
ejpam-5051	477	12	(	(	PUNCT
ejpam-5051	477	13	χ	χ	X
ejpam-5051	477	14	,	,	PUNCT
ejpam-5051	477	15	z	z	NOUN
ejpam-5051	477	16	,	,	PUNCT
ejpam-5051	477	17	γ)−1	γ)−1	NOUN
ejpam-5051	477	18	)	)	PUNCT
ejpam-5051	477	19	∈	∈	PROPN
ejpam-5051	477	20	â	â	ADP
ejpam-5051	477	21	∗	∗	NOUN
ejpam-5051	477	22	g	g	PROPN
ejpam-5051	477	23	×	×	PROPN
ejpam-5051	477	24	t	t	PROPN
ejpam-5051	477	25	(	(	PUNCT
ejpam-5051	477	26	2	2	NUM
ejpam-5051	477	27	)	)	PUNCT
ejpam-5051	477	28	.	.	PUNCT
ejpam-5051	477	29	notice	notice	VERB
ejpam-5051	477	30	that	that	SCONJ
ejpam-5051	477	31	(	(	PUNCT
ejpam-5051	477	32	(	(	PUNCT
ejpam-5051	477	33	χ1	χ1	NOUN
ejpam-5051	477	34	,	,	PUNCT
ejpam-5051	477	35	z1	z1	NOUN
ejpam-5051	477	36	,	,	PUNCT
ejpam-5051	477	37	γ1)(χ2	γ1)(χ2	NOUN
ejpam-5051	477	38	,	,	PUNCT
ejpam-5051	477	39	z2	z2	PROPN
ejpam-5051	477	40	,	,	PUNCT
ejpam-5051	477	41	γ2))(χ2	γ2))(χ2	NUM
ejpam-5051	477	42	,	,	PUNCT
ejpam-5051	477	43	z2	z2	NOUN
ejpam-5051	477	44	,	,	PUNCT
ejpam-5051	477	45	γ2	γ2	ADJ
ejpam-5051	477	46	)	)	PUNCT
ejpam-5051	477	47	−1	−1	NOUN
ejpam-5051	478	1	=	=	SYM
ejpam-5051	479	1	(	(	PUNCT
ejpam-5051	480	1	χ1	χ1	NOUN
ejpam-5051	480	2	,	,	PUNCT
ejpam-5051	480	3	z1z2	z1z2	PROPN
ejpam-5051	480	4	,	,	PUNCT
ejpam-5051	480	5	γ1γ2)(χ2	γ1γ2)(χ2	NUM
ejpam-5051	480	6	,	,	PUNCT
ejpam-5051	480	7	z2	z2	NOUN
ejpam-5051	480	8	,	,	PUNCT
ejpam-5051	480	9	γ2	γ2	ADJ
ejpam-5051	480	10	)	)	PUNCT
ejpam-5051	480	11	−1	−1	NOUN
ejpam-5051	480	12	=	=	SYM
ejpam-5051	480	13	(	(	PUNCT
ejpam-5051	480	14	χ1	χ1	NOUN
ejpam-5051	480	15	,	,	PUNCT
ejpam-5051	480	16	z1z2	z1z2	PROPN
ejpam-5051	480	17	,	,	PUNCT
ejpam-5051	480	18	γ1γ2)(χ2	γ1γ2)(χ2	VERB
ejpam-5051	480	19	·	·	PUNCT
ejpam-5051	480	20	γ2	γ2	ADJ
ejpam-5051	480	21	,	,	PUNCT
ejpam-5051	480	22	z−1	z−1	PROPN
ejpam-5051	480	23	2	2	NUM
ejpam-5051	480	24	,	,	PUNCT
ejpam-5051	480	25	γ−1	γ−1	PROPN
ejpam-5051	480	26	2	2	NUM
ejpam-5051	480	27	)	)	PUNCT
ejpam-5051	480	28	=	=	SYM
ejpam-5051	480	29	(	(	PUNCT
ejpam-5051	480	30	χ1	χ1	PROPN
ejpam-5051	480	31	,	,	PUNCT
ejpam-5051	480	32	z1z2z3	z1z2z3	PROPN
ejpam-5051	480	33	,	,	PUNCT
ejpam-5051	480	34	γ1γ2γ	γ1γ2γ	NUM
ejpam-5051	480	35	−1	−1	NOUN
ejpam-5051	480	36	3	3	X
ejpam-5051	480	37	)	)	PUNCT
ejpam-5051	480	38	=	=	SYM
ejpam-5051	480	39	(	(	PUNCT
ejpam-5051	480	40	χ1	χ1	NOUN
ejpam-5051	480	41	,	,	PUNCT
ejpam-5051	480	42	z1	z1	NOUN
ejpam-5051	480	43	,	,	PUNCT
ejpam-5051	480	44	γ1r(γ2	γ1r(γ2	NOUN
ejpam-5051	480	45	)	)	PUNCT
ejpam-5051	480	46	)	)	PUNCT
ejpam-5051	481	1	=	=	SYM
ejpam-5051	481	2	(	(	PUNCT
ejpam-5051	481	3	χ1	χ1	NOUN
ejpam-5051	481	4	,	,	PUNCT
ejpam-5051	481	5	z1	z1	PROPN
ejpam-5051	481	6	,	,	PUNCT
ejpam-5051	481	7	γ1s(γ1	γ1s(γ1	NOUN
ejpam-5051	481	8	)	)	PUNCT
ejpam-5051	481	9	)	)	PUNCT
ejpam-5051	481	10	=	=	SYM
ejpam-5051	481	11	(	(	PUNCT
ejpam-5051	481	12	χ1	χ1	NOUN
ejpam-5051	481	13	,	,	PUNCT
ejpam-5051	481	14	z1	z1	NOUN
ejpam-5051	481	15	,	,	PUNCT
ejpam-5051	481	16	γ1	γ1	PROPN
ejpam-5051	481	17	)	)	PUNCT
ejpam-5051	481	18	.	.	PUNCT
ejpam-5051	482	1	also	also	ADV
ejpam-5051	482	2	,	,	PUNCT
ejpam-5051	482	3	(	(	PUNCT
ejpam-5051	482	4	χ1	χ1	NOUN
ejpam-5051	482	5	,	,	PUNCT
ejpam-5051	482	6	z1	z1	NOUN
ejpam-5051	482	7	,	,	PUNCT
ejpam-5051	482	8	γ1	γ1	PROPN
ejpam-5051	482	9	)	)	PUNCT
ejpam-5051	482	10	−1((χ1	−1((χ1	X
ejpam-5051	482	11	,	,	PUNCT
ejpam-5051	482	12	z1	z1	NOUN
ejpam-5051	482	13	,	,	PUNCT
ejpam-5051	482	14	γ1)(χ2	γ1)(χ2	PROPN
ejpam-5051	482	15	,	,	PUNCT
ejpam-5051	482	16	z2	z2	PROPN
ejpam-5051	482	17	,	,	PUNCT
ejpam-5051	482	18	γ2	γ2	NOUN
ejpam-5051	482	19	)	)	PUNCT
ejpam-5051	482	20	)	)	PUNCT
ejpam-5051	483	1	=	=	SYM
ejpam-5051	483	2	(	(	PUNCT
ejpam-5051	483	3	χ1	χ1	NOUN
ejpam-5051	483	4	,	,	PUNCT
ejpam-5051	483	5	z1	z1	NOUN
ejpam-5051	483	6	,	,	PUNCT
ejpam-5051	483	7	γ1	γ1	PROPN
ejpam-5051	483	8	)	)	PUNCT
ejpam-5051	483	9	−1(χ1	−1(χ1	X
ejpam-5051	483	10	,	,	PUNCT
ejpam-5051	483	11	z1z2	z1z2	PROPN
ejpam-5051	483	12	,	,	PUNCT
ejpam-5051	483	13	γ1γ2	γ1γ2	NOUN
ejpam-5051	483	14	)	)	PUNCT
ejpam-5051	483	15	=	=	SYM
ejpam-5051	483	16	(	(	PUNCT
ejpam-5051	483	17	χ1	χ1	NOUN
ejpam-5051	483	18	·	·	PUNCT
ejpam-5051	483	19	γ1	γ1	NOUN
ejpam-5051	483	20	,	,	PUNCT
ejpam-5051	483	21	z−1	z−1	PROPN
ejpam-5051	483	22	1	1	NUM
ejpam-5051	483	23	,	,	PUNCT
ejpam-5051	483	24	γ−1	γ−1	PROPN
ejpam-5051	483	25	1	1	NUM
ejpam-5051	483	26	)	)	PUNCT
ejpam-5051	483	27	(	(	PUNCT
ejpam-5051	483	28	χ1	χ1	NOUN
ejpam-5051	483	29	,	,	PUNCT
ejpam-5051	483	30	z1z2	z1z2	PROPN
ejpam-5051	483	31	,	,	PUNCT
ejpam-5051	483	32	γ1γ2	γ1γ2	NOUN
ejpam-5051	483	33	)	)	PUNCT
ejpam-5051	483	34	=	=	SYM
ejpam-5051	483	35	(	(	PUNCT
ejpam-5051	483	36	χ1	χ1	NOUN
ejpam-5051	483	37	·	·	PUNCT
ejpam-5051	483	38	γ1	γ1	NOUN
ejpam-5051	483	39	,	,	PUNCT
ejpam-5051	483	40	z−1	z−1	PROPN
ejpam-5051	483	41	1	1	NUM
ejpam-5051	483	42	z1z2	z1z2	NOUN
ejpam-5051	483	43	,	,	PUNCT
ejpam-5051	483	44	γ	γ	X
ejpam-5051	483	45	−1	−1	NOUN
ejpam-5051	483	46	1	1	NUM
ejpam-5051	483	47	γ1γ2	γ1γ2	NOUN
ejpam-5051	483	48	)	)	PUNCT
ejpam-5051	483	49	=	=	SYM
ejpam-5051	483	50	(	(	PUNCT
ejpam-5051	483	51	χ2	χ2	PROPN
ejpam-5051	483	52	,	,	PUNCT
ejpam-5051	483	53	z2	z2	NOUN
ejpam-5051	483	54	,	,	PUNCT
ejpam-5051	483	55	s(γ1)γ2	s(γ1)γ2	NOUN
ejpam-5051	483	56	)	)	PUNCT
ejpam-5051	483	57	=	=	SYM
ejpam-5051	483	58	(	(	PUNCT
ejpam-5051	483	59	χ2	χ2	PROPN
ejpam-5051	483	60	,	,	PUNCT
ejpam-5051	483	61	z2	z2	NOUN
ejpam-5051	483	62	,	,	PUNCT
ejpam-5051	483	63	r(γ2)γ2	r(γ2)γ2	NOUN
ejpam-5051	483	64	)	)	PUNCT
ejpam-5051	483	65	=	=	SYM
ejpam-5051	483	66	(	(	PUNCT
ejpam-5051	483	67	χ2	χ2	PROPN
ejpam-5051	483	68	,	,	PUNCT
ejpam-5051	483	69	z2	z2	PROPN
ejpam-5051	483	70	,	,	PUNCT
ejpam-5051	483	71	γ2	γ2	NOUN
ejpam-5051	483	72	)	)	PUNCT
ejpam-5051	483	73	.	.	PUNCT
ejpam-5051	484	1	hence	hence	ADV
ejpam-5051	484	2	,	,	PUNCT
ejpam-5051	484	3	â	â	X
ejpam-5051	484	4	∗	∗	NOUN
ejpam-5051	484	5	g	g	PROPN
ejpam-5051	484	6	×	×	PROPN
ejpam-5051	484	7	t	t	PROPN
ejpam-5051	484	8	is	be	AUX
ejpam-5051	484	9	a	a	DET
ejpam-5051	484	10	groupoid	groupoid	PROPN
ejpam-5051	484	11	.	.	PUNCT
ejpam-5051	485	1	endowed	endow	VERB
ejpam-5051	485	2	â	â	ADP
ejpam-5051	485	3	∗	∗	NOUN
ejpam-5051	485	4	g	g	PROPN
ejpam-5051	485	5	×	×	PROPN
ejpam-5051	485	6	t	t	NOUN
ejpam-5051	485	7	with	with	ADP
ejpam-5051	485	8	the	the	DET
ejpam-5051	485	9	product	product	NOUN
ejpam-5051	485	10	topology	topology	NOUN
ejpam-5051	485	11	define	define	VERB
ejpam-5051	485	12	as	as	ADP
ejpam-5051	485	13	τâ∗×g	τâ∗×g	PUNCT
ejpam-5051	485	14	=	=	SYM
ejpam-5051	485	15	{	{	PUNCT
ejpam-5051	485	16	(	(	PUNCT
ejpam-5051	485	17	a	a	DET
ejpam-5051	485	18	∗	∗	NOUN
ejpam-5051	485	19	b	b	NOUN
ejpam-5051	485	20	×	×	PROPN
ejpam-5051	485	21	c	c	NOUN
ejpam-5051	485	22	)	)	PUNCT
ejpam-5051	485	23	∈	∈	PROPN
ejpam-5051	485	24	â	â	ADP
ejpam-5051	485	25	∗	∗	NOUN
ejpam-5051	485	26	g	g	PROPN
ejpam-5051	485	27	×	×	PROPN
ejpam-5051	485	28	t	t	NOUN
ejpam-5051	485	29	:	:	PUNCT
ejpam-5051	485	30	a	a	DET
ejpam-5051	485	31	∈	∈	PROPN
ejpam-5051	485	32	τâ	τâ	PROPN
ejpam-5051	485	33	,	,	PUNCT
ejpam-5051	485	34	b	b	PROPN
ejpam-5051	485	35	∈	∈	PROPN
ejpam-5051	485	36	τg	τg	NUM
ejpam-5051	485	37	,	,	PUNCT
ejpam-5051	485	38	c	c	PROPN
ejpam-5051	485	39	∈	∈	PROPN
ejpam-5051	485	40	τt	τt	ADP
ejpam-5051	485	41	}	}	PUNCT
ejpam-5051	485	42	.	.	PUNCT
ejpam-5051	486	1	since	since	SCONJ
ejpam-5051	486	2	g	g	PROPN
ejpam-5051	486	3	,	,	PUNCT
ejpam-5051	486	4	t	t	PROPN
ejpam-5051	486	5	and	and	CCONJ
ejpam-5051	486	6	â	â	PRON
ejpam-5051	486	7	⋊	⋊	SYM
ejpam-5051	486	8	r	r	NOUN
ejpam-5051	486	9	are	be	AUX
ejpam-5051	486	10	hausdorff	hausdorff	NOUN
ejpam-5051	486	11	,	,	PUNCT
ejpam-5051	486	12	â	â	X
ejpam-5051	486	13	is	be	AUX
ejpam-5051	487	1	r.	r.	PROPN
ejpam-5051	487	2	s.	s.	PROPN
ejpam-5051	487	3	bongcawel	bongcawel	PROPN
ejpam-5051	487	4	et	et	PROPN
ejpam-5051	487	5	al	al	PROPN
ejpam-5051	487	6	.	.	PUNCT
ejpam-5051	487	7	/	/	SYM
ejpam-5051	487	8	eur	eur	PROPN
ejpam-5051	487	9	.	.	PUNCT
ejpam-5051	488	1	j.	j.	PROPN
ejpam-5051	488	2	pure	pure	PROPN
ejpam-5051	488	3	appl	appl	PROPN
ejpam-5051	488	4	.	.	PROPN
ejpam-5051	488	5	math	math	PROPN
ejpam-5051	488	6	,	,	PUNCT
ejpam-5051	488	7	17	17	NUM
ejpam-5051	488	8	(	(	PUNCT
ejpam-5051	488	9	1	1	NUM
ejpam-5051	488	10	)	)	PUNCT
ejpam-5051	488	11	(	(	PUNCT
ejpam-5051	488	12	2024	2024	NUM
ejpam-5051	488	13	)	)	PUNCT
ejpam-5051	488	14	,	,	PUNCT
ejpam-5051	488	15	519	519	NUM
ejpam-5051	488	16	-	-	SYM
ejpam-5051	488	17	545	545	NUM
ejpam-5051	488	18	532	532	NUM
ejpam-5051	488	19	also	also	ADV
ejpam-5051	488	20	hausdorff	hausdorff	NOUN
ejpam-5051	488	21	.	.	PUNCT
ejpam-5051	489	1	let	let	VERB
ejpam-5051	489	2	(	(	PUNCT
ejpam-5051	489	3	χ	χ	X
ejpam-5051	489	4	,	,	PUNCT
ejpam-5051	489	5	z	z	PROPN
ejpam-5051	489	6	,	,	PUNCT
ejpam-5051	489	7	γ	γ	NOUN
ejpam-5051	489	8	)	)	PUNCT
ejpam-5051	489	9	and	and	CCONJ
ejpam-5051	489	10	(	(	PUNCT
ejpam-5051	489	11	χ′	χ′	PROPN
ejpam-5051	489	12	,	,	PUNCT
ejpam-5051	489	13	z′	z′	PROPN
ejpam-5051	489	14	,	,	PUNCT
ejpam-5051	489	15	γ′	γ′	PROPN
ejpam-5051	489	16	)	)	PUNCT
ejpam-5051	489	17	be	be	VERB
ejpam-5051	489	18	distinct	distinct	ADJ
ejpam-5051	489	19	points	point	NOUN
ejpam-5051	489	20	in	in	ADP
ejpam-5051	489	21	â	â	ADP
ejpam-5051	489	22	∗	∗	NOUN
ejpam-5051	489	23	g	g	PROPN
ejpam-5051	489	24	×	×	PROPN
ejpam-5051	489	25	t	t	PROPN
ejpam-5051	489	26	.	.	PUNCT
ejpam-5051	490	1	since	since	SCONJ
ejpam-5051	490	2	â	â	PROPN
ejpam-5051	490	3	is	be	AUX
ejpam-5051	490	4	hausdorff	hausdorff	NOUN
ejpam-5051	490	5	,	,	PUNCT
ejpam-5051	490	6	then	then	ADV
ejpam-5051	490	7	there	there	PRON
ejpam-5051	490	8	exists	exist	VERB
ejpam-5051	490	9	open	open	ADJ
ejpam-5051	490	10	neighborhoods	neighborhood	NOUN
ejpam-5051	490	11	a1	a1	NOUN
ejpam-5051	490	12	and	and	CCONJ
ejpam-5051	490	13	a2	a2	PROPN
ejpam-5051	490	14	in	in	ADP
ejpam-5051	490	15	â	â	X
ejpam-5051	490	16	containing	contain	VERB
ejpam-5051	490	17	χ	χ	X
ejpam-5051	490	18	and	and	CCONJ
ejpam-5051	490	19	χ′	χ′	PROPN
ejpam-5051	490	20	,	,	PUNCT
ejpam-5051	490	21	respectively	respectively	ADV
ejpam-5051	490	22	such	such	ADJ
ejpam-5051	490	23	that	that	DET
ejpam-5051	490	24	a1	a1	NOUN
ejpam-5051	490	25	∩a2	∩a2	PUNCT
ejpam-5051	491	1	=	=	PRON
ejpam-5051	491	2	∅.	∅.	PRON
ejpam-5051	491	3	also	also	ADV
ejpam-5051	491	4	,	,	PUNCT
ejpam-5051	491	5	there	there	PRON
ejpam-5051	491	6	exists	exist	VERB
ejpam-5051	491	7	open	open	ADJ
ejpam-5051	491	8	neighborhoods	neighborhood	NOUN
ejpam-5051	491	9	g1	g1	NOUN
ejpam-5051	491	10	and	and	CCONJ
ejpam-5051	491	11	g2	g2	PROPN
ejpam-5051	491	12	in	in	ADP
ejpam-5051	491	13	g	g	NOUN
ejpam-5051	491	14	containing	contain	VERB
ejpam-5051	491	15	γ	γ	NOUN
ejpam-5051	491	16	and	and	CCONJ
ejpam-5051	491	17	γ′	γ′	PROPN
ejpam-5051	491	18	,	,	PUNCT
ejpam-5051	491	19	respectively	respectively	ADV
ejpam-5051	491	20	such	such	ADJ
ejpam-5051	491	21	that	that	SCONJ
ejpam-5051	491	22	g1	g1	NOUN
ejpam-5051	491	23	∩	∩	ADJ
ejpam-5051	491	24	g2	g2	PROPN
ejpam-5051	491	25	=	=	PUNCT
ejpam-5051	491	26	∅.	∅.	NOUN
ejpam-5051	491	27	for	for	ADP
ejpam-5051	491	28	the	the	DET
ejpam-5051	491	29	hausdorff	hausdorff	PROPN
ejpam-5051	491	30	space	space	PROPN
ejpam-5051	491	31	t	t	PROPN
ejpam-5051	491	32	,	,	PUNCT
ejpam-5051	491	33	there	there	PRON
ejpam-5051	491	34	exists	exist	VERB
ejpam-5051	491	35	open	open	ADJ
ejpam-5051	491	36	neighborhoods	neighborhood	NOUN
ejpam-5051	491	37	t1	t1	VERB
ejpam-5051	491	38	and	and	CCONJ
ejpam-5051	491	39	t2	t2	PROPN
ejpam-5051	491	40	in	in	ADP
ejpam-5051	491	41	t	t	NOUN
ejpam-5051	491	42	containing	contain	VERB
ejpam-5051	491	43	z	z	PROPN
ejpam-5051	491	44	and	and	CCONJ
ejpam-5051	491	45	z′	z′	PROPN
ejpam-5051	491	46	,	,	PUNCT
ejpam-5051	491	47	respectively	respectively	ADV
ejpam-5051	491	48	wherein	wherein	ADJ
ejpam-5051	491	49	t1	t1	NOUN
ejpam-5051	491	50	∩	∩	ADJ
ejpam-5051	491	51	t2	t2	NOUN
ejpam-5051	491	52	=	=	PUNCT
ejpam-5051	491	53	∅.	∅.	NOUN
ejpam-5051	491	54	then	then	ADV
ejpam-5051	491	55	by	by	ADP
ejpam-5051	491	56	definition	definition	NOUN
ejpam-5051	491	57	of	of	ADP
ejpam-5051	491	58	τâ∗g×t	τâ∗g×t	PUNCT
ejpam-5051	491	59	,	,	PUNCT
ejpam-5051	491	60	u	u	NOUN
ejpam-5051	491	61	=	=	NOUN
ejpam-5051	491	62	a1	a1	NOUN
ejpam-5051	491	63	∗g1	∗g1	NOUN
ejpam-5051	491	64	×	×	NOUN
ejpam-5051	491	65	t1	t1	NOUN
ejpam-5051	491	66	and	and	CCONJ
ejpam-5051	491	67	v	v	NOUN
ejpam-5051	491	68	=	=	SYM
ejpam-5051	491	69	a2	a2	PROPN
ejpam-5051	492	1	∗g2	∗g2	SCONJ
ejpam-5051	492	2	×	×	NOUN
ejpam-5051	492	3	t2	t2	NOUN
ejpam-5051	492	4	are	be	AUX
ejpam-5051	492	5	open	open	ADJ
ejpam-5051	492	6	neighboorhoods	neighboorhood	NOUN
ejpam-5051	492	7	in	in	ADP
ejpam-5051	492	8	â	â	PROPN
ejpam-5051	492	9	∗	∗	NOUN
ejpam-5051	492	10	g	g	PROPN
ejpam-5051	492	11	×	×	PROPN
ejpam-5051	492	12	t	t	NOUN
ejpam-5051	492	13	containing	contain	VERB
ejpam-5051	492	14	(	(	PUNCT
ejpam-5051	492	15	χ	χ	X
ejpam-5051	492	16	,	,	PUNCT
ejpam-5051	492	17	z	z	PROPN
ejpam-5051	492	18	,	,	PUNCT
ejpam-5051	492	19	γ	γ	NOUN
ejpam-5051	492	20	)	)	PUNCT
ejpam-5051	492	21	and	and	CCONJ
ejpam-5051	492	22	(	(	PUNCT
ejpam-5051	492	23	χ′	χ′	PROPN
ejpam-5051	492	24	,	,	PUNCT
ejpam-5051	492	25	z′	z′	PROPN
ejpam-5051	492	26	,	,	PUNCT
ejpam-5051	492	27	γ′	γ′	PROPN
ejpam-5051	492	28	)	)	PUNCT
ejpam-5051	492	29	,	,	PUNCT
ejpam-5051	492	30	respectively	respectively	ADV
ejpam-5051	492	31	such	such	ADJ
ejpam-5051	492	32	that	that	SCONJ
ejpam-5051	492	33	u	u	PROPN
ejpam-5051	492	34	∩	∩	NOUN
ejpam-5051	492	35	v	v	NOUN
ejpam-5051	492	36	=	=	PUNCT
ejpam-5051	492	37	∅.	∅.	VERB
ejpam-5051	492	38	therefore	therefore	ADV
ejpam-5051	492	39	,	,	PUNCT
ejpam-5051	492	40	â	â	X
ejpam-5051	492	41	∗	∗	NOUN
ejpam-5051	492	42	g	g	PROPN
ejpam-5051	492	43	×	×	PROPN
ejpam-5051	492	44	t	t	PROPN
ejpam-5051	492	45	is	be	AUX
ejpam-5051	492	46	hausdorff	hausdorff	NOUN
ejpam-5051	492	47	.	.	PUNCT
ejpam-5051	493	1	lemma	lemma	PROPN
ejpam-5051	493	2	7	7	X
ejpam-5051	493	3	.	.	PUNCT
ejpam-5051	494	1	let	let	VERB
ejpam-5051	494	2	â	â	X
ejpam-5051	494	3	×	×	PROPN
ejpam-5051	494	4	t	t	PROPN
ejpam-5051	494	5	=	=	SYM
ejpam-5051	494	6	{	{	PUNCT
ejpam-5051	494	7	(	(	PUNCT
ejpam-5051	494	8	χ	χ	NOUN
ejpam-5051	494	9	,	,	PUNCT
ejpam-5051	494	10	z	z	NOUN
ejpam-5051	494	11	,	,	PUNCT
ejpam-5051	494	12	u	u	NOUN
ejpam-5051	494	13	)	)	PUNCT
ejpam-5051	494	14	:	:	PUNCT
ejpam-5051	494	15	(	(	PUNCT
ejpam-5051	494	16	χ	χ	X
ejpam-5051	494	17	,	,	PUNCT
ejpam-5051	494	18	u	u	NOUN
ejpam-5051	494	19	)	)	PUNCT
ejpam-5051	494	20	∈	∈	PROPN
ejpam-5051	494	21	â	â	X
ejpam-5051	494	22	and	and	CCONJ
ejpam-5051	494	23	z	z	PROPN
ejpam-5051	494	24	∈	∈	PROPN
ejpam-5051	494	25	t	t	PROPN
ejpam-5051	494	26	}	}	PUNCT
ejpam-5051	494	27	.	.	PUNCT
ejpam-5051	495	1	then	then	ADV
ejpam-5051	495	2	â	â	X
ejpam-5051	495	3	×	×	PROPN
ejpam-5051	495	4	t	t	PROPN
ejpam-5051	495	5	is	be	AUX
ejpam-5051	495	6	the	the	DET
ejpam-5051	495	7	isotropy	isotropy	ADJ
ejpam-5051	495	8	group	group	NOUN
ejpam-5051	495	9	of	of	ADP
ejpam-5051	495	10	â	â	PROPN
ejpam-5051	495	11	∗	∗	NOUN
ejpam-5051	495	12	g	g	PROPN
ejpam-5051	495	13	×	×	PROPN
ejpam-5051	495	14	t	t	NOUN
ejpam-5051	495	15	.	.	PUNCT
ejpam-5051	496	1	proof	proof	NOUN
ejpam-5051	496	2	.	.	PUNCT
ejpam-5051	497	1	note	note	VERB
ejpam-5051	497	2	that	that	SCONJ
ejpam-5051	497	3	iso(â	iso(â	VERB
ejpam-5051	497	4	∗	∗	NOUN
ejpam-5051	497	5	g	g	PROPN
ejpam-5051	497	6	×	×	PROPN
ejpam-5051	497	7	t	t	NOUN
ejpam-5051	497	8	)	)	PUNCT
ejpam-5051	497	9	=	=	PUNCT
ejpam-5051	498	1	{	{	PUNCT
ejpam-5051	498	2	(	(	PUNCT
ejpam-5051	498	3	χ	χ	NOUN
ejpam-5051	498	4	,	,	PUNCT
ejpam-5051	498	5	z	z	PROPN
ejpam-5051	498	6	,	,	PUNCT
ejpam-5051	498	7	γ	γ	PROPN
ejpam-5051	498	8	)	)	PUNCT
ejpam-5051	498	9	∈	∈	PROPN
ejpam-5051	498	10	â	â	ADP
ejpam-5051	498	11	∗	∗	NOUN
ejpam-5051	498	12	g	g	PROPN
ejpam-5051	498	13	×	×	PROPN
ejpam-5051	498	14	t	t	NOUN
ejpam-5051	498	15	:	:	PUNCT
ejpam-5051	498	16	s(χ	s(χ	PROPN
ejpam-5051	498	17	,	,	PUNCT
ejpam-5051	498	18	z	z	NOUN
ejpam-5051	498	19	,	,	PUNCT
ejpam-5051	498	20	γ	γ	NOUN
ejpam-5051	498	21	)	)	PUNCT
ejpam-5051	498	22	=	=	SYM
ejpam-5051	498	23	r(χ	r(χ	PROPN
ejpam-5051	498	24	,	,	PUNCT
ejpam-5051	498	25	z	z	PROPN
ejpam-5051	498	26	,	,	PUNCT
ejpam-5051	498	27	γ	γ	NOUN
ejpam-5051	498	28	)	)	PUNCT
ejpam-5051	498	29	}	}	PUNCT
ejpam-5051	498	30	.	.	PUNCT
ejpam-5051	499	1	let	let	VERB
ejpam-5051	499	2	(	(	PUNCT
ejpam-5051	499	3	χ	χ	X
ejpam-5051	499	4	,	,	PUNCT
ejpam-5051	499	5	z	z	PROPN
ejpam-5051	499	6	,	,	PUNCT
ejpam-5051	499	7	γ	γ	NOUN
ejpam-5051	499	8	)	)	PUNCT
ejpam-5051	499	9	∈	∈	NOUN
ejpam-5051	499	10	iso(â∗g×t	iso(â∗g×t	NOUN
ejpam-5051	499	11	)	)	PUNCT
ejpam-5051	499	12	.	.	PUNCT
ejpam-5051	500	1	then	then	ADV
ejpam-5051	500	2	s(χ	s(χ	PROPN
ejpam-5051	500	3	,	,	PUNCT
ejpam-5051	500	4	z	z	PROPN
ejpam-5051	500	5	,	,	PUNCT
ejpam-5051	500	6	γ	γ	NOUN
ejpam-5051	500	7	)	)	PUNCT
ejpam-5051	500	8	=	=	SYM
ejpam-5051	500	9	r(χ	r(χ	PROPN
ejpam-5051	500	10	,	,	PUNCT
ejpam-5051	500	11	z	z	PROPN
ejpam-5051	500	12	,	,	PUNCT
ejpam-5051	500	13	γ	γ	PROPN
ejpam-5051	500	14	)	)	PUNCT
ejpam-5051	500	15	,	,	PUNCT
ejpam-5051	500	16	that	that	ADV
ejpam-5051	500	17	is	is	ADV
ejpam-5051	500	18	,	,	PUNCT
ejpam-5051	500	19	(	(	PUNCT
ejpam-5051	500	20	χ·γ	χ·γ	NOUN
ejpam-5051	500	21	,	,	PUNCT
ejpam-5051	500	22	s(γ	s(γ	PROPN
ejpam-5051	500	23	)	)	PUNCT
ejpam-5051	500	24	)	)	PUNCT
ejpam-5051	501	1	=	=	PUNCT
ejpam-5051	501	2	(	(	PUNCT
ejpam-5051	501	3	χ	χ	NOUN
ejpam-5051	501	4	,	,	PUNCT
ejpam-5051	501	5	r(γ	r(γ	NOUN
ejpam-5051	501	6	)	)	PUNCT
ejpam-5051	501	7	)	)	PUNCT
ejpam-5051	501	8	.	.	PUNCT
ejpam-5051	502	1	note	note	VERB
ejpam-5051	502	2	that	that	SCONJ
ejpam-5051	502	3	χ	χ	X
ejpam-5051	502	4	·	·	PUNCT
ejpam-5051	502	5	γ	γ	X
ejpam-5051	502	6	=	=	SYM
ejpam-5051	502	7	χ	χ	NOUN
ejpam-5051	502	8	if	if	SCONJ
ejpam-5051	503	1	and	and	CCONJ
ejpam-5051	503	2	only	only	ADV
ejpam-5051	503	3	if	if	SCONJ
ejpam-5051	503	4	γ	γ	X
ejpam-5051	503	5	=	=	SYM
ejpam-5051	503	6	u	u	PROPN
ejpam-5051	503	7	where	where	SCONJ
ejpam-5051	503	8	u	u	PROPN
ejpam-5051	503	9	∈	∈	PROPN
ejpam-5051	503	10	g(0	g(0	PROPN
ejpam-5051	503	11	)	)	PUNCT
ejpam-5051	503	12	.	.	PUNCT
ejpam-5051	504	1	also	also	ADV
ejpam-5051	504	2	,	,	PUNCT
ejpam-5051	504	3	s(γ	s(γ	PROPN
ejpam-5051	504	4	)	)	PUNCT
ejpam-5051	505	1	=	=	PUNCT
ejpam-5051	505	2	r(γ	r(γ	NOUN
ejpam-5051	505	3	)	)	PUNCT
ejpam-5051	505	4	means	mean	VERB
ejpam-5051	505	5	γ	γ	X
ejpam-5051	505	6	=	=	SYM
ejpam-5051	505	7	u	u	PROPN
ejpam-5051	505	8	∈	∈	PROPN
ejpam-5051	505	9	g(0	g(0	PROPN
ejpam-5051	505	10	)	)	PUNCT
ejpam-5051	505	11	.	.	PUNCT
ejpam-5051	506	1	thus	thus	ADV
ejpam-5051	506	2	,	,	PUNCT
ejpam-5051	506	3	(	(	PUNCT
ejpam-5051	506	4	χ	χ	X
ejpam-5051	506	5	,	,	PUNCT
ejpam-5051	506	6	z	z	PROPN
ejpam-5051	506	7	,	,	PUNCT
ejpam-5051	506	8	γ	γ	NOUN
ejpam-5051	506	9	)	)	PUNCT
ejpam-5051	506	10	=	=	PUNCT
ejpam-5051	506	11	(	(	PUNCT
ejpam-5051	506	12	χ	χ	X
ejpam-5051	506	13	,	,	PUNCT
ejpam-5051	506	14	z	z	NOUN
ejpam-5051	506	15	,	,	PUNCT
ejpam-5051	506	16	u	u	NOUN
ejpam-5051	506	17	)	)	PUNCT
ejpam-5051	506	18	and	and	CCONJ
ejpam-5051	506	19	iso(â	iso(â	NOUN
ejpam-5051	506	20	∗	∗	NOUN
ejpam-5051	506	21	g	g	PROPN
ejpam-5051	506	22	×	×	PROPN
ejpam-5051	506	23	t	t	NOUN
ejpam-5051	506	24	)	)	PUNCT
ejpam-5051	506	25	=	=	PUNCT
ejpam-5051	506	26	{	{	PUNCT
ejpam-5051	506	27	(	(	PUNCT
ejpam-5051	506	28	χ	χ	NOUN
ejpam-5051	506	29	,	,	PUNCT
ejpam-5051	506	30	z	z	NOUN
ejpam-5051	506	31	,	,	PUNCT
ejpam-5051	506	32	u	u	NOUN
ejpam-5051	506	33	)	)	PUNCT
ejpam-5051	506	34	∈	∈	PROPN
ejpam-5051	506	35	â	â	ADP
ejpam-5051	506	36	∗	∗	NOUN
ejpam-5051	506	37	g	g	PROPN
ejpam-5051	506	38	×	×	PROPN
ejpam-5051	506	39	t	t	NOUN
ejpam-5051	506	40	:	:	PUNCT
ejpam-5051	506	41	(	(	PUNCT
ejpam-5051	506	42	χ	χ	X
ejpam-5051	506	43	,	,	PUNCT
ejpam-5051	506	44	u	u	NOUN
ejpam-5051	506	45	)	)	PUNCT
ejpam-5051	506	46	∈	∈	PROPN
ejpam-5051	506	47	â	â	PROPN
ejpam-5051	506	48	,	,	PUNCT
ejpam-5051	506	49	z	z	PROPN
ejpam-5051	506	50	∈	∈	PROPN
ejpam-5051	506	51	t	t	PROPN
ejpam-5051	506	52	}	}	PUNCT
ejpam-5051	506	53	=	=	SYM
ejpam-5051	506	54	â×	â×	PROPN
ejpam-5051	506	55	t.	t.	NOUN
ejpam-5051	506	56	therefore	therefore	ADV
ejpam-5051	506	57	,	,	PUNCT
ejpam-5051	506	58	â×	â×	PROPN
ejpam-5051	506	59	t	t	PROPN
ejpam-5051	506	60	is	be	AUX
ejpam-5051	506	61	the	the	DET
ejpam-5051	506	62	isotropy	isotropy	ADJ
ejpam-5051	506	63	group	group	NOUN
ejpam-5051	506	64	for	for	ADP
ejpam-5051	506	65	â	â	PROPN
ejpam-5051	506	66	∗	∗	NOUN
ejpam-5051	506	67	g	g	PROPN
ejpam-5051	506	68	×	×	PROPN
ejpam-5051	506	69	t	t	PROPN
ejpam-5051	506	70	.	.	PUNCT
ejpam-5051	507	1	lemma	lemma	PROPN
ejpam-5051	507	2	8	8	NUM
ejpam-5051	507	3	.	.	PUNCT
ejpam-5051	507	4	define	define	VERB
ejpam-5051	507	5	∼	∼	NOUN
ejpam-5051	507	6	on	on	ADP
ejpam-5051	507	7	â	â	X
ejpam-5051	507	8	∗g	∗g	NOUN
ejpam-5051	507	9	×t	×t	NOUN
ejpam-5051	507	10	by	by	ADP
ejpam-5051	507	11	(	(	PUNCT
ejpam-5051	507	12	χ	χ	X
ejpam-5051	507	13	,	,	PUNCT
ejpam-5051	507	14	z	z	PROPN
ejpam-5051	507	15	,	,	PUNCT
ejpam-5051	507	16	γ	γ	NOUN
ejpam-5051	507	17	)	)	PUNCT
ejpam-5051	507	18	∼	∼	NOUN
ejpam-5051	507	19	(	(	PUNCT
ejpam-5051	507	20	χ′	χ′	PROPN
ejpam-5051	507	21	,	,	PUNCT
ejpam-5051	507	22	z′	z′	PROPN
ejpam-5051	507	23	,	,	PUNCT
ejpam-5051	507	24	γ′	γ′	NUM
ejpam-5051	507	25	)	)	PUNCT
ejpam-5051	507	26	if	if	SCONJ
ejpam-5051	508	1	and	and	CCONJ
ejpam-5051	508	2	only	only	ADV
ejpam-5051	508	3	if	if	SCONJ
ejpam-5051	508	4	χ	χ	ADJ
ejpam-5051	508	5	=	=	SYM
ejpam-5051	508	6	χ′	χ′	PROPN
ejpam-5051	508	7	and	and	CCONJ
ejpam-5051	508	8	there	there	PRON
ejpam-5051	508	9	exists	exist	VERB
ejpam-5051	508	10	a	a	DET
ejpam-5051	508	11	∈	∈	NOUN
ejpam-5051	508	12	au	au	ADP
ejpam-5051	508	13	such	such	ADJ
ejpam-5051	508	14	that	that	PRON
ejpam-5051	508	15	χ(a)z	χ(a)z	PROPN
ejpam-5051	508	16	=	=	SYM
ejpam-5051	508	17	z′	z′	NUM
ejpam-5051	508	18	and	and	CCONJ
ejpam-5051	508	19	γ	γ	X
ejpam-5051	508	20	=	=	VERB
ejpam-5051	508	21	a	a	PRON
ejpam-5051	508	22	·	·	PUNCT
ejpam-5051	508	23	γ′.	γ′.	VERB
ejpam-5051	508	24	then	then	ADV
ejpam-5051	508	25	∼	∼	NOUN
ejpam-5051	508	26	is	be	AUX
ejpam-5051	508	27	an	an	DET
ejpam-5051	508	28	equivalence	equivalence	NOUN
ejpam-5051	508	29	relation	relation	NOUN
ejpam-5051	508	30	on	on	ADP
ejpam-5051	508	31	â	â	X
ejpam-5051	508	32	∗	∗	NOUN
ejpam-5051	508	33	g	g	PROPN
ejpam-5051	508	34	×	×	PROPN
ejpam-5051	508	35	t	t	NOUN
ejpam-5051	508	36	.	.	PUNCT
ejpam-5051	509	1	proof	proof	NOUN
ejpam-5051	509	2	.	.	PUNCT
ejpam-5051	510	1	let	let	VERB
ejpam-5051	510	2	(	(	PUNCT
ejpam-5051	510	3	χ	χ	X
ejpam-5051	510	4	,	,	PUNCT
ejpam-5051	510	5	z	z	PROPN
ejpam-5051	510	6	,	,	PUNCT
ejpam-5051	510	7	γ	γ	PROPN
ejpam-5051	510	8	)	)	PUNCT
ejpam-5051	510	9	∈	∈	PROPN
ejpam-5051	510	10	â	â	ADP
ejpam-5051	510	11	∗	∗	VERB
ejpam-5051	510	12	g	g	PROPN
ejpam-5051	510	13	×	×	PROPN
ejpam-5051	510	14	t	t	PROPN
ejpam-5051	510	15	.	.	PUNCT
ejpam-5051	511	1	choose	choose	VERB
ejpam-5051	511	2	a	a	DET
ejpam-5051	511	3	∈	∈	NOUN
ejpam-5051	511	4	au	au	ADP
ejpam-5051	511	5	such	such	ADJ
ejpam-5051	511	6	that	that	SCONJ
ejpam-5051	511	7	χ(a	χ(a	NOUN
ejpam-5051	511	8	)	)	PUNCT
ejpam-5051	511	9	=	=	SYM
ejpam-5051	511	10	1	1	NUM
ejpam-5051	511	11	∈	∈	NOUN
ejpam-5051	511	12	r×.	r×.	ADP
ejpam-5051	511	13	then	then	ADV
ejpam-5051	511	14	χ(a)z	χ(a)z	PROPN
ejpam-5051	511	15	=	=	SYM
ejpam-5051	511	16	1(z	1(z	X
ejpam-5051	511	17	)	)	PUNCT
ejpam-5051	511	18	=	=	SYM
ejpam-5051	511	19	z	z	NOUN
ejpam-5051	511	20	and	and	CCONJ
ejpam-5051	511	21	s(a	s(a	PROPN
ejpam-5051	511	22	)	)	PUNCT
ejpam-5051	511	23	=	=	PUNCT
ejpam-5051	512	1	u.	u.	VERB
ejpam-5051	512	2	since	since	SCONJ
ejpam-5051	512	3	γ	γ	PROPN
ejpam-5051	512	4	∈	∈	PROPN
ejpam-5051	512	5	au	au	PROPN
ejpam-5051	512	6	,	,	PUNCT
ejpam-5051	512	7	s(γ	s(γ	PROPN
ejpam-5051	512	8	)	)	PUNCT
ejpam-5051	512	9	=	=	SYM
ejpam-5051	512	10	u	u	PROPN
ejpam-5051	512	11	,	,	PUNCT
ejpam-5051	512	12	s(γ	s(γ	PROPN
ejpam-5051	512	13	)	)	PUNCT
ejpam-5051	513	1	=	=	SYM
ejpam-5051	513	2	u	u	NOUN
ejpam-5051	513	3	=	=	NOUN
ejpam-5051	513	4	s(a	s(a	PROPN
ejpam-5051	513	5	)	)	PUNCT
ejpam-5051	513	6	=	=	SYM
ejpam-5051	513	7	r(a	r(a	VERB
ejpam-5051	513	8	)	)	PUNCT
ejpam-5051	513	9	and	and	CCONJ
ejpam-5051	513	10	a	a	PRON
ejpam-5051	513	11	and	and	CCONJ
ejpam-5051	513	12	γ	γ	NOUN
ejpam-5051	513	13	are	be	AUX
ejpam-5051	513	14	composable	composable	ADJ
ejpam-5051	513	15	pairs	pair	NOUN
ejpam-5051	513	16	in	in	ADP
ejpam-5051	513	17	g.	g.	PROPN
ejpam-5051	513	18	then	then	ADV
ejpam-5051	513	19	,	,	PUNCT
ejpam-5051	513	20	(	(	PUNCT
ejpam-5051	513	21	aa−1)γ	aa−1)γ	X
ejpam-5051	513	22	=	=	PUNCT
ejpam-5051	513	23	γ	γ	X
ejpam-5051	513	24	where	where	SCONJ
ejpam-5051	513	25	aa−1	aa−1	PROPN
ejpam-5051	513	26	∈	∈	PROPN
ejpam-5051	513	27	au	au	PROPN
ejpam-5051	513	28	.	.	PROPN
ejpam-5051	514	1	hence	hence	ADV
ejpam-5051	514	2	(	(	PUNCT
ejpam-5051	514	3	χ	χ	X
ejpam-5051	514	4	,	,	PUNCT
ejpam-5051	514	5	z	z	PROPN
ejpam-5051	514	6	,	,	PUNCT
ejpam-5051	514	7	γ	γ	NOUN
ejpam-5051	514	8	)	)	PUNCT
ejpam-5051	514	9	∼	∼	NOUN
ejpam-5051	514	10	(	(	PUNCT
ejpam-5051	514	11	χ	χ	NOUN
ejpam-5051	514	12	,	,	PUNCT
ejpam-5051	514	13	z	z	PROPN
ejpam-5051	514	14	,	,	PUNCT
ejpam-5051	514	15	γ	γ	NOUN
ejpam-5051	514	16	)	)	PUNCT
ejpam-5051	514	17	.	.	PUNCT
ejpam-5051	515	1	let	let	VERB
ejpam-5051	515	2	(	(	PUNCT
ejpam-5051	515	3	χ	χ	X
ejpam-5051	515	4	,	,	PUNCT
ejpam-5051	515	5	z	z	PROPN
ejpam-5051	515	6	,	,	PUNCT
ejpam-5051	515	7	γ	γ	NOUN
ejpam-5051	515	8	)	)	PUNCT
ejpam-5051	515	9	,	,	PUNCT
ejpam-5051	515	10	(	(	PUNCT
ejpam-5051	515	11	χ′	χ′	PROPN
ejpam-5051	515	12	,	,	PUNCT
ejpam-5051	515	13	z′	z′	PROPN
ejpam-5051	515	14	,	,	PUNCT
ejpam-5051	515	15	γ′	γ′	NOUN
ejpam-5051	515	16	)	)	PUNCT
ejpam-5051	515	17	∈	∈	PROPN
ejpam-5051	515	18	â∗g×t	â∗g×t	ADJ
ejpam-5051	515	19	such	such	ADJ
ejpam-5051	515	20	that	that	SCONJ
ejpam-5051	515	21	(	(	PUNCT
ejpam-5051	515	22	χ	χ	X
ejpam-5051	515	23	,	,	PUNCT
ejpam-5051	515	24	z	z	PROPN
ejpam-5051	515	25	,	,	PUNCT
ejpam-5051	515	26	γ	γ	NOUN
ejpam-5051	515	27	)	)	PUNCT
ejpam-5051	515	28	∼	∼	NOUN
ejpam-5051	515	29	(	(	PUNCT
ejpam-5051	515	30	χ′	χ′	PROPN
ejpam-5051	515	31	,	,	PUNCT
ejpam-5051	515	32	z′	z′	PROPN
ejpam-5051	515	33	,	,	PUNCT
ejpam-5051	515	34	γ′	γ′	PROPN
ejpam-5051	515	35	)	)	PUNCT
ejpam-5051	515	36	.	.	PUNCT
ejpam-5051	516	1	then	then	ADV
ejpam-5051	516	2	χ(a)χ(a)−1z	χ(a)χ(a)−1z	PROPN
ejpam-5051	516	3	=	=	SYM
ejpam-5051	516	4	χ(a)−1z′	χ(a)−1z′	PROPN
ejpam-5051	516	5	and	and	CCONJ
ejpam-5051	516	6	we	we	PRON
ejpam-5051	516	7	have	have	VERB
ejpam-5051	516	8	z	z	NOUN
ejpam-5051	516	9	=	=	SYM
ejpam-5051	516	10	χ(a)−1z′.	χ(a)−1z′.	PROPN
ejpam-5051	516	11	also	also	ADV
ejpam-5051	516	12	since	since	SCONJ
ejpam-5051	516	13	γ′	γ′	PROPN
ejpam-5051	516	14	∈	∈	PROPN
ejpam-5051	516	15	au	au	VERB
ejpam-5051	516	16	then	then	ADV
ejpam-5051	516	17	s(γ′	s(γ′	NOUN
ejpam-5051	516	18	)	)	PUNCT
ejpam-5051	516	19	=	=	SYM
ejpam-5051	516	20	u	u	NOUN
ejpam-5051	516	21	=	=	SYM
ejpam-5051	516	22	r(a	r(a	PROPN
ejpam-5051	516	23	)	)	PUNCT
ejpam-5051	516	24	,	,	PUNCT
ejpam-5051	516	25	that	that	ADV
ejpam-5051	516	26	is	is	ADV
ejpam-5051	516	27	,	,	PUNCT
ejpam-5051	516	28	(	(	PUNCT
ejpam-5051	516	29	γ′	γ′	PROPN
ejpam-5051	516	30	,	,	PUNCT
ejpam-5051	516	31	a	a	PRON
ejpam-5051	516	32	)	)	PUNCT
ejpam-5051	516	33	∈	∈	PROPN
ejpam-5051	516	34	g(2	g(2	PROPN
ejpam-5051	516	35	)	)	PUNCT
ejpam-5051	516	36	and	and	CCONJ
ejpam-5051	516	37	aa−1γ′	aa−1γ′	PUNCT
ejpam-5051	516	38	=	=	PUNCT
ejpam-5051	516	39	a−1γ	a−1γ	X
ejpam-5051	516	40	which	which	PRON
ejpam-5051	516	41	is	be	AUX
ejpam-5051	516	42	γ′	γ′	NOUN
ejpam-5051	516	43	=	=	SYM
ejpam-5051	516	44	a−1γ	a−1γ	NOUN
ejpam-5051	516	45	,	,	PUNCT
ejpam-5051	516	46	a−1	a−1	PROPN
ejpam-5051	516	47	∈	∈	PROPN
ejpam-5051	516	48	au	au	PROPN
ejpam-5051	516	49	.	.	PUNCT
ejpam-5051	516	50	thus	thus	ADV
ejpam-5051	516	51	,	,	PUNCT
ejpam-5051	516	52	(	(	PUNCT
ejpam-5051	516	53	χ′	χ′	PROPN
ejpam-5051	516	54	,	,	PUNCT
ejpam-5051	516	55	z′	z′	PROPN
ejpam-5051	516	56	,	,	PUNCT
ejpam-5051	516	57	γ′	γ′	NOUN
ejpam-5051	516	58	)	)	PUNCT
ejpam-5051	516	59	∼	∼	NOUN
ejpam-5051	516	60	(	(	PUNCT
ejpam-5051	516	61	χ	χ	NOUN
ejpam-5051	516	62	,	,	PUNCT
ejpam-5051	516	63	z	z	PROPN
ejpam-5051	516	64	,	,	PUNCT
ejpam-5051	516	65	γ	γ	NOUN
ejpam-5051	516	66	)	)	PUNCT
ejpam-5051	516	67	.	.	PUNCT
ejpam-5051	517	1	let	let	VERB
ejpam-5051	517	2	(	(	PUNCT
ejpam-5051	517	3	χ1	χ1	NOUN
ejpam-5051	517	4	,	,	PUNCT
ejpam-5051	517	5	z1	z1	NOUN
ejpam-5051	517	6	,	,	PUNCT
ejpam-5051	517	7	γ1	γ1	NOUN
ejpam-5051	517	8	)	)	PUNCT
ejpam-5051	517	9	∼	∼	NOUN
ejpam-5051	517	10	(	(	PUNCT
ejpam-5051	517	11	χ2	χ2	PROPN
ejpam-5051	517	12	,	,	PUNCT
ejpam-5051	517	13	z2	z2	PROPN
ejpam-5051	517	14	,	,	PUNCT
ejpam-5051	517	15	γ2	γ2	NOUN
ejpam-5051	517	16	)	)	PUNCT
ejpam-5051	517	17	and	and	CCONJ
ejpam-5051	517	18	(	(	PUNCT
ejpam-5051	517	19	χ2	χ2	PROPN
ejpam-5051	517	20	,	,	PUNCT
ejpam-5051	517	21	z2	z2	PROPN
ejpam-5051	517	22	,	,	PUNCT
ejpam-5051	517	23	γ2	γ2	ADJ
ejpam-5051	517	24	)	)	PUNCT
ejpam-5051	517	25	∼	∼	NOUN
ejpam-5051	517	26	(	(	PUNCT
ejpam-5051	517	27	χ3	χ3	NOUN
ejpam-5051	517	28	,	,	PUNCT
ejpam-5051	517	29	z3	z3	PROPN
ejpam-5051	517	30	,	,	PUNCT
ejpam-5051	517	31	γ3	γ3	NOUN
ejpam-5051	517	32	)	)	PUNCT
ejpam-5051	517	33	.	.	PUNCT
ejpam-5051	518	1	then	then	ADV
ejpam-5051	518	2	χ1	χ1	NOUN
ejpam-5051	518	3	=	=	PUNCT
ejpam-5051	518	4	χ3	χ3	PROPN
ejpam-5051	518	5	and	and	CCONJ
ejpam-5051	518	6	z3	z3	PROPN
ejpam-5051	518	7	=	=	SYM
ejpam-5051	518	8	χ2(a)χ1(a)z1	χ2(a)χ1(a)z1	NOUN
ejpam-5051	518	9	=	=	PUNCT
ejpam-5051	518	10	χ1(a)χ1(a)z1	χ1(a)χ1(a)z1	NOUN
ejpam-5051	518	11	=	=	SYM
ejpam-5051	518	12	χ1(a)z1	χ1(a)z1	NOUN
ejpam-5051	518	13	.	.	PUNCT
ejpam-5051	519	1	also	also	ADV
ejpam-5051	519	2	,	,	PUNCT
ejpam-5051	519	3	γ1	γ1	PROPN
ejpam-5051	519	4	=	=	PUNCT
ejpam-5051	519	5	a	a	DET
ejpam-5051	519	6	·	·	PUNCT
ejpam-5051	519	7	γ2	γ2	NOUN
ejpam-5051	519	8	=	=	PUNCT
ejpam-5051	519	9	a	a	X
ejpam-5051	519	10	·	·	PUNCT
ejpam-5051	519	11	a	a	DET
ejpam-5051	519	12	·	·	PUNCT
ejpam-5051	519	13	γ3	γ3	NOUN
ejpam-5051	519	14	=	=	PUNCT
ejpam-5051	519	15	a	a	DET
ejpam-5051	519	16	·	·	PUNCT
ejpam-5051	519	17	γ3	γ3	NOUN
ejpam-5051	519	18	.	.	PUNCT
ejpam-5051	520	1	thus	thus	ADV
ejpam-5051	520	2	(	(	PUNCT
ejpam-5051	520	3	χ1	χ1	NOUN
ejpam-5051	520	4	,	,	PUNCT
ejpam-5051	520	5	z2	z2	PROPN
ejpam-5051	520	6	,	,	PUNCT
ejpam-5051	520	7	γ1	γ1	NOUN
ejpam-5051	520	8	)	)	PUNCT
ejpam-5051	520	9	∼	∼	NOUN
ejpam-5051	520	10	(	(	PUNCT
ejpam-5051	520	11	χ3	χ3	NOUN
ejpam-5051	520	12	,	,	PUNCT
ejpam-5051	520	13	z3	z3	PROPN
ejpam-5051	520	14	,	,	PUNCT
ejpam-5051	520	15	γ3	γ3	NOUN
ejpam-5051	520	16	)	)	PUNCT
ejpam-5051	520	17	.	.	PUNCT
ejpam-5051	521	1	therefore	therefore	ADV
ejpam-5051	521	2	,	,	PUNCT
ejpam-5051	521	3	∼	∼	NOUN
ejpam-5051	521	4	is	be	AUX
ejpam-5051	521	5	an	an	DET
ejpam-5051	521	6	equivalence	equivalence	NOUN
ejpam-5051	521	7	relation	relation	NOUN
ejpam-5051	521	8	on	on	ADP
ejpam-5051	521	9	â	â	X
ejpam-5051	521	10	∗	∗	NOUN
ejpam-5051	521	11	g	g	PROPN
ejpam-5051	521	12	×	×	PROPN
ejpam-5051	521	13	t	t	PROPN
ejpam-5051	521	14	.	.	PUNCT
ejpam-5051	522	1	denote	denote	VERB
ejpam-5051	522	2	the	the	DET
ejpam-5051	522	3	set	set	NOUN
ejpam-5051	522	4	of	of	ADP
ejpam-5051	522	5	equivalence	equivalence	NOUN
ejpam-5051	522	6	classes	class	NOUN
ejpam-5051	522	7	of	of	ADP
ejpam-5051	522	8	â	â	PROPN
ejpam-5051	522	9	∗	∗	NOUN
ejpam-5051	522	10	g	g	PROPN
ejpam-5051	522	11	×	×	PROPN
ejpam-5051	522	12	t	t	NOUN
ejpam-5051	522	13	with	with	ADP
ejpam-5051	522	14	respect	respect	NOUN
ejpam-5051	522	15	to	to	ADP
ejpam-5051	522	16	the	the	DET
ejpam-5051	522	17	equivalence	equivalence	NOUN
ejpam-5051	522	18	relation	relation	NOUN
ejpam-5051	522	19	∼	∼	NOUN
ejpam-5051	522	20	on	on	ADP
ejpam-5051	522	21	lemma	lemma	PROPN
ejpam-5051	522	22	8	8	NUM
ejpam-5051	522	23	by	by	ADP
ejpam-5051	522	24	d	d	PROPN
ejpam-5051	522	25	=	=	SYM
ejpam-5051	522	26	â	â	PROPN
ejpam-5051	522	27	∗	∗	NOUN
ejpam-5051	522	28	g	g	PROPN
ejpam-5051	522	29	×	×	PROPN
ejpam-5051	522	30	t/	t/	ADV
ejpam-5051	522	31	∼=	∼=	PROPN
ejpam-5051	522	32	{	{	PUNCT
ejpam-5051	522	33	[	[	X
ejpam-5051	522	34	χ	χ	X
ejpam-5051	522	35	,	,	PUNCT
ejpam-5051	522	36	z	z	PROPN
ejpam-5051	522	37	,	,	PUNCT
ejpam-5051	522	38	γ	γ	X
ejpam-5051	522	39	]	]	X
ejpam-5051	522	40	:	:	PUNCT
ejpam-5051	522	41	(	(	PUNCT
ejpam-5051	522	42	χ	χ	X
ejpam-5051	522	43	,	,	PUNCT
ejpam-5051	522	44	z	z	PROPN
ejpam-5051	522	45	,	,	PUNCT
ejpam-5051	522	46	γ	γ	PROPN
ejpam-5051	522	47	)	)	PUNCT
ejpam-5051	522	48	∈	∈	PROPN
ejpam-5051	522	49	â	â	ADP
ejpam-5051	522	50	∗	∗	NOUN
ejpam-5051	522	51	g	g	PROPN
ejpam-5051	522	52	×	×	PROPN
ejpam-5051	522	53	t	t	PROPN
ejpam-5051	522	54	}	}	PUNCT
ejpam-5051	522	55	.	.	PUNCT
ejpam-5051	523	1	define	define	VERB
ejpam-5051	523	2	the	the	DET
ejpam-5051	523	3	following	follow	VERB
ejpam-5051	523	4	structure	structure	NOUN
ejpam-5051	523	5	for	for	ADP
ejpam-5051	523	6	d	d	NOUN
ejpam-5051	523	7	and	and	CCONJ
ejpam-5051	523	8	verify	verify	VERB
ejpam-5051	523	9	whether	whether	SCONJ
ejpam-5051	523	10	it	it	PRON
ejpam-5051	523	11	is	be	AUX
ejpam-5051	523	12	a	a	DET
ejpam-5051	523	13	groupoid	groupoid	NOUN
ejpam-5051	523	14	.	.	PUNCT
ejpam-5051	524	1	the	the	DET
ejpam-5051	524	2	range	range	NOUN
ejpam-5051	524	3	and	and	CCONJ
ejpam-5051	524	4	source	source	NOUN
ejpam-5051	524	5	maps	map	NOUN
ejpam-5051	524	6	will	will	AUX
ejpam-5051	524	7	be	be	AUX
ejpam-5051	524	8	r([χ	r([χ	NOUN
ejpam-5051	524	9	,	,	PUNCT
ejpam-5051	524	10	z	z	PROPN
ejpam-5051	524	11	,	,	PUNCT
ejpam-5051	524	12	γ	γ	X
ejpam-5051	524	13	]	]	X
ejpam-5051	524	14	)	)	PUNCT
ejpam-5051	524	15	=	=	PUNCT
ejpam-5051	525	1	[	[	X
ejpam-5051	525	2	χ	χ	X
ejpam-5051	525	3	,	,	PUNCT
ejpam-5051	525	4	r(γ	r(γ	NOUN
ejpam-5051	525	5	)	)	PUNCT
ejpam-5051	525	6	]	]	PUNCT
ejpam-5051	525	7	and	and	CCONJ
ejpam-5051	525	8	s([χ	s([χ	ADP
ejpam-5051	525	9	,	,	PUNCT
ejpam-5051	525	10	z	z	PROPN
ejpam-5051	525	11	,	,	PUNCT
ejpam-5051	525	12	γ	γ	X
ejpam-5051	525	13	]	]	X
ejpam-5051	525	14	)	)	PUNCT
ejpam-5051	525	15	=	=	PUNCT
ejpam-5051	526	1	[	[	X
ejpam-5051	526	2	χ	χ	X
ejpam-5051	526	3	·	·	PUNCT
ejpam-5051	526	4	γ	γ	X
ejpam-5051	526	5	,	,	PUNCT
ejpam-5051	526	6	s(γ	s(γ	PROPN
ejpam-5051	526	7	)	)	PUNCT
ejpam-5051	526	8	]	]	X
ejpam-5051	526	9	,	,	PUNCT
ejpam-5051	526	10	respectively	respectively	ADV
ejpam-5051	526	11	.	.	PUNCT
ejpam-5051	527	1	the	the	DET
ejpam-5051	527	2	composition	composition	NOUN
ejpam-5051	527	3	and	and	CCONJ
ejpam-5051	527	4	inverse	inverse	NOUN
ejpam-5051	527	5	map	map	NOUN
ejpam-5051	527	6	is	be	AUX
ejpam-5051	527	7	[	[	X
ejpam-5051	527	8	χ	χ	ADP
ejpam-5051	527	9	,	,	PUNCT
ejpam-5051	527	10	z	z	PROPN
ejpam-5051	527	11	,	,	PUNCT
ejpam-5051	527	12	γ][χ′	γ][χ′	PROPN
ejpam-5051	527	13	,	,	PUNCT
ejpam-5051	527	14	z′	z′	PROPN
ejpam-5051	527	15	,	,	PUNCT
ejpam-5051	527	16	γ′	γ′	PROPN
ejpam-5051	527	17	]	]	X
ejpam-5051	528	1	=	=	PUNCT
ejpam-5051	529	1	[	[	X
ejpam-5051	529	2	χ	χ	X
ejpam-5051	529	3	,	,	PUNCT
ejpam-5051	529	4	zz′	zz′	NUM
ejpam-5051	529	5	,	,	PUNCT
ejpam-5051	529	6	γγ′	γγ′	NOUN
ejpam-5051	529	7	]	]	PUNCT
ejpam-5051	529	8	and	and	CCONJ
ejpam-5051	529	9	[	[	X
ejpam-5051	529	10	χ	χ	X
ejpam-5051	529	11	,	,	PUNCT
ejpam-5051	529	12	z	z	NOUN
ejpam-5051	529	13	,	,	PUNCT
ejpam-5051	529	14	γ]−1	γ]−1	X
ejpam-5051	529	15	=	=	PUNCT
ejpam-5051	530	1	[	[	X
ejpam-5051	530	2	χ	χ	X
ejpam-5051	530	3	·	·	PUNCT
ejpam-5051	530	4	γ	γ	X
ejpam-5051	530	5	,	,	PUNCT
ejpam-5051	530	6	z−1	z−1	PROPN
ejpam-5051	530	7	,	,	PUNCT
ejpam-5051	530	8	γ−1	γ−1	PROPN
ejpam-5051	530	9	]	]	PUNCT
ejpam-5051	530	10	,	,	PUNCT
ejpam-5051	530	11	respectively	respectively	ADV
ejpam-5051	530	12	.	.	PUNCT
ejpam-5051	531	1	we	we	PRON
ejpam-5051	531	2	note	note	VERB
ejpam-5051	531	3	that	that	SCONJ
ejpam-5051	531	4	[	[	X
ejpam-5051	531	5	χ	χ	X
ejpam-5051	531	6	,	,	PUNCT
ejpam-5051	531	7	z	z	PROPN
ejpam-5051	531	8	,	,	PUNCT
ejpam-5051	531	9	γ	γ	X
ejpam-5051	531	10	]	]	X
ejpam-5051	531	11	and	and	CCONJ
ejpam-5051	531	12	[	[	X
ejpam-5051	531	13	χ′	χ′	PROPN
ejpam-5051	531	14	,	,	PUNCT
ejpam-5051	531	15	z′	z′	PROPN
ejpam-5051	531	16	,	,	PUNCT
ejpam-5051	531	17	γ′	γ′	PROPN
ejpam-5051	531	18	]	]	PUNCT
ejpam-5051	531	19	are	be	AUX
ejpam-5051	531	20	composable	composable	ADJ
ejpam-5051	531	21	pairs	pair	NOUN
ejpam-5051	531	22	if	if	SCONJ
ejpam-5051	531	23	χ′	χ′	PROPN
ejpam-5051	531	24	=	=	SYM
ejpam-5051	531	25	χ	χ	X
ejpam-5051	531	26	·	·	PUNCT
ejpam-5051	531	27	γ	γ	X
ejpam-5051	531	28	where	where	SCONJ
ejpam-5051	531	29	χ	χ	X
ejpam-5051	531	30	·	·	PUNCT
ejpam-5051	531	31	γ	γ	X
ejpam-5051	531	32	is	be	AUX
ejpam-5051	531	33	defined	define	VERB
ejpam-5051	531	34	by	by	ADP
ejpam-5051	531	35	χ	χ	PROPN
ejpam-5051	531	36	·	·	PUNCT
ejpam-5051	531	37	γ(a	γ(a	NUM
ejpam-5051	531	38	)	)	PUNCT
ejpam-5051	531	39	=	=	SYM
ejpam-5051	532	1	χ(γaγ−1	χ(γaγ−1	PUNCT
ejpam-5051	532	2	)	)	PUNCT
ejpam-5051	532	3	and	and	CCONJ
ejpam-5051	532	4	χ	χ	X
ejpam-5051	532	5	·	·	PUNCT
ejpam-5051	532	6	u	u	NOUN
ejpam-5051	532	7	=	=	SYM
ejpam-5051	532	8	χ	χ	X
ejpam-5051	532	9	.	.	PUNCT
ejpam-5051	532	10	theorem	theorem	NOUN
ejpam-5051	532	11	3	3	NUM
ejpam-5051	532	12	.	.	X
ejpam-5051	533	1	d	d	NOUN
ejpam-5051	533	2	is	be	AUX
ejpam-5051	533	3	a	a	DET
ejpam-5051	533	4	hausdorff	hausdorff	NOUN
ejpam-5051	533	5	étale	étale	NOUN
ejpam-5051	533	6	groupoid	groupoid	NOUN
ejpam-5051	533	7	with	with	ADP
ejpam-5051	533	8	respect	respect	NOUN
ejpam-5051	533	9	to	to	ADP
ejpam-5051	533	10	the	the	DET
ejpam-5051	533	11	quotient	quotient	NOUN
ejpam-5051	533	12	topology	topology	NOUN
ejpam-5051	533	13	with	with	ADP
ejpam-5051	533	14	d(0	d(0	NOUN
ejpam-5051	533	15	)	)	PUNCT
ejpam-5051	533	16	=	=	PUNCT
ejpam-5051	534	1	i(â×	i(â×	NOUN
ejpam-5051	534	2	{	{	PUNCT
ejpam-5051	534	3	1	1	NUM
ejpam-5051	534	4	}	}	PUNCT
ejpam-5051	534	5	)	)	PUNCT
ejpam-5051	534	6	.	.	PUNCT
ejpam-5051	535	1	r.	r.	PROPN
ejpam-5051	535	2	s.	s.	PROPN
ejpam-5051	535	3	bongcawel	bongcawel	PROPN
ejpam-5051	536	1	et	et	PROPN
ejpam-5051	536	2	al	al	PROPN
ejpam-5051	536	3	.	.	PUNCT
ejpam-5051	536	4	/	/	SYM
ejpam-5051	536	5	eur	eur	PROPN
ejpam-5051	536	6	.	.	PUNCT
ejpam-5051	537	1	j.	j.	PROPN
ejpam-5051	537	2	pure	pure	PROPN
ejpam-5051	537	3	appl	appl	PROPN
ejpam-5051	537	4	.	.	PROPN
ejpam-5051	537	5	math	math	PROPN
ejpam-5051	537	6	,	,	PUNCT
ejpam-5051	537	7	17	17	NUM
ejpam-5051	537	8	(	(	PUNCT
ejpam-5051	537	9	1	1	NUM
ejpam-5051	537	10	)	)	PUNCT
ejpam-5051	537	11	(	(	PUNCT
ejpam-5051	537	12	2024	2024	NUM
ejpam-5051	537	13	)	)	PUNCT
ejpam-5051	537	14	,	,	PUNCT
ejpam-5051	537	15	519	519	NUM
ejpam-5051	537	16	-	-	SYM
ejpam-5051	537	17	545	545	NUM
ejpam-5051	537	18	533	533	NUM
ejpam-5051	537	19	proof	proof	NOUN
ejpam-5051	537	20	.	.	PUNCT
ejpam-5051	538	1	let	let	VERB
ejpam-5051	538	2	[	[	X
ejpam-5051	538	3	χ	χ	X
ejpam-5051	538	4	,	,	PUNCT
ejpam-5051	538	5	z	z	PROPN
ejpam-5051	538	6	,	,	PUNCT
ejpam-5051	538	7	γ	γ	X
ejpam-5051	538	8	]	]	X
ejpam-5051	538	9	,	,	PUNCT
ejpam-5051	538	10	[	[	X
ejpam-5051	538	11	χ′	χ′	PROPN
ejpam-5051	538	12	,	,	PUNCT
ejpam-5051	538	13	z′	z′	PROPN
ejpam-5051	538	14	,	,	PUNCT
ejpam-5051	538	15	γ′	γ′	PROPN
ejpam-5051	538	16	]	]	X
ejpam-5051	538	17	∈	∈	PROPN
ejpam-5051	539	1	d	d	X
ejpam-5051	539	2	with	with	ADP
ejpam-5051	539	3	[	[	X
ejpam-5051	539	4	χ	χ	X
ejpam-5051	539	5	,	,	PUNCT
ejpam-5051	539	6	z	z	PROPN
ejpam-5051	539	7	,	,	PUNCT
ejpam-5051	539	8	γ	γ	X
ejpam-5051	539	9	]	]	X
ejpam-5051	539	10	=	=	SYM
ejpam-5051	540	1	[	[	X
ejpam-5051	540	2	χ′	χ′	PROPN
ejpam-5051	540	3	,	,	PUNCT
ejpam-5051	540	4	z′	z′	PROPN
ejpam-5051	540	5	,	,	PUNCT
ejpam-5051	540	6	γ′	γ′	PROPN
ejpam-5051	540	7	]	]	PUNCT
ejpam-5051	540	8	.	.	PUNCT
ejpam-5051	541	1	now	now	ADV
ejpam-5051	541	2	,	,	PUNCT
ejpam-5051	541	3	[	[	X
ejpam-5051	541	4	χ	χ	X
ejpam-5051	541	5	,	,	PUNCT
ejpam-5051	541	6	z	z	NOUN
ejpam-5051	541	7	,	,	PUNCT
ejpam-5051	541	8	γ]−1	γ]−1	X
ejpam-5051	541	9	=	=	PUNCT
ejpam-5051	542	1	[	[	X
ejpam-5051	542	2	χ	χ	X
ejpam-5051	542	3	·	·	PUNCT
ejpam-5051	542	4	γ	γ	X
ejpam-5051	542	5	,	,	PUNCT
ejpam-5051	542	6	z−1	z−1	PROPN
ejpam-5051	542	7	,	,	PUNCT
ejpam-5051	542	8	γ−1	γ−1	PROPN
ejpam-5051	542	9	]	]	X
ejpam-5051	542	10	=	=	SYM
ejpam-5051	543	1	[	[	X
ejpam-5051	543	2	χ′	χ′	PROPN
ejpam-5051	543	3	·	·	PUNCT
ejpam-5051	544	1	γ′	γ′	PROPN
ejpam-5051	544	2	,	,	PUNCT
ejpam-5051	544	3	(	(	PUNCT
ejpam-5051	544	4	z−1)′	z−1)′	NOUN
ejpam-5051	544	5	,	,	PUNCT
ejpam-5051	544	6	γ′−1	γ′−1	PROPN
ejpam-5051	544	7	]	]	PUNCT
ejpam-5051	544	8	=	=	X
ejpam-5051	545	1	[	[	X
ejpam-5051	545	2	χ′	χ′	PROPN
ejpam-5051	545	3	,	,	PUNCT
ejpam-5051	545	4	z′	z′	NUM
ejpam-5051	545	5	,	,	PUNCT
ejpam-5051	545	6	γ′]−1	γ′]−1	PROPN
ejpam-5051	545	7	.	.	PUNCT
ejpam-5051	546	1	also	also	ADV
ejpam-5051	546	2	,	,	PUNCT
ejpam-5051	546	3	r([χ	r([χ	NOUN
ejpam-5051	546	4	,	,	PUNCT
ejpam-5051	546	5	z	z	PROPN
ejpam-5051	546	6	,	,	PUNCT
ejpam-5051	546	7	γ	γ	X
ejpam-5051	546	8	]	]	X
ejpam-5051	546	9	)	)	PUNCT
ejpam-5051	546	10	=	=	PUNCT
ejpam-5051	547	1	[	[	X
ejpam-5051	547	2	χ	χ	X
ejpam-5051	547	3	,	,	PUNCT
ejpam-5051	547	4	r(γ	r(γ	NOUN
ejpam-5051	547	5	)	)	PUNCT
ejpam-5051	547	6	]	]	PUNCT
ejpam-5051	548	1	=	=	PUNCT
ejpam-5051	549	1	[	[	X
ejpam-5051	549	2	χ	χ	X
ejpam-5051	549	3	,	,	PUNCT
ejpam-5051	549	4	s(γ′	s(γ′	NOUN
ejpam-5051	549	5	)	)	PUNCT
ejpam-5051	549	6	]	]	PUNCT
ejpam-5051	550	1	=	=	PUNCT
ejpam-5051	550	2	r([χ′	r([χ′	NOUN
ejpam-5051	550	3	,	,	PUNCT
ejpam-5051	550	4	z′	z′	PROPN
ejpam-5051	550	5	,	,	PUNCT
ejpam-5051	550	6	γ′	γ′	PROPN
ejpam-5051	550	7	]	]	X
ejpam-5051	550	8	)	)	PUNCT
ejpam-5051	550	9	;	;	PUNCT
ejpam-5051	550	10	s([χ	s([χ	NOUN
ejpam-5051	550	11	,	,	PUNCT
ejpam-5051	550	12	z	z	PROPN
ejpam-5051	550	13	,	,	PUNCT
ejpam-5051	550	14	γ	γ	X
ejpam-5051	550	15	]	]	X
ejpam-5051	550	16	)	)	PUNCT
ejpam-5051	550	17	=	=	PUNCT
ejpam-5051	551	1	[	[	X
ejpam-5051	551	2	χ	χ	X
ejpam-5051	551	3	·	·	PUNCT
ejpam-5051	551	4	γ	γ	X
ejpam-5051	551	5	,	,	PUNCT
ejpam-5051	551	6	s(γ	s(γ	PROPN
ejpam-5051	551	7	)	)	PUNCT
ejpam-5051	551	8	]	]	PUNCT
ejpam-5051	552	1	=	=	PUNCT
ejpam-5051	553	1	[	[	X
ejpam-5051	553	2	χ′	χ′	PROPN
ejpam-5051	553	3	·	·	PUNCT
ejpam-5051	553	4	γ′	γ′	NOUN
ejpam-5051	553	5	,	,	PUNCT
ejpam-5051	553	6	s(γ′	s(γ′	NOUN
ejpam-5051	553	7	)	)	PUNCT
ejpam-5051	553	8	]	]	PUNCT
ejpam-5051	553	9	=	=	SYM
ejpam-5051	553	10	s([χ′	s([χ′	NOUN
ejpam-5051	553	11	,	,	PUNCT
ejpam-5051	553	12	z′	z′	PROPN
ejpam-5051	553	13	,	,	PUNCT
ejpam-5051	553	14	γ′	γ′	PROPN
ejpam-5051	553	15	]	]	PUNCT
ejpam-5051	553	16	)	)	PUNCT
ejpam-5051	553	17	.	.	PUNCT
ejpam-5051	554	1	hence	hence	ADV
ejpam-5051	554	2	,	,	PUNCT
ejpam-5051	554	3	the	the	DET
ejpam-5051	554	4	inverse	inverse	NOUN
ejpam-5051	554	5	,	,	PUNCT
ejpam-5051	554	6	range	range	NOUN
ejpam-5051	554	7	and	and	CCONJ
ejpam-5051	554	8	source	source	NOUN
ejpam-5051	554	9	maps	map	NOUN
ejpam-5051	554	10	are	be	AUX
ejpam-5051	554	11	well	well	ADV
ejpam-5051	554	12	-	-	PUNCT
ejpam-5051	554	13	defined	define	VERB
ejpam-5051	554	14	.	.	PUNCT
ejpam-5051	555	1	let	let	VERB
ejpam-5051	555	2	(	(	PUNCT
ejpam-5051	555	3	[	[	X
ejpam-5051	555	4	χ1	χ1	NOUN
ejpam-5051	555	5	,	,	PUNCT
ejpam-5051	555	6	z1	z1	NOUN
ejpam-5051	555	7	,	,	PUNCT
ejpam-5051	555	8	γ1	γ1	NOUN
ejpam-5051	555	9	]	]	PUNCT
ejpam-5051	555	10	,	,	PUNCT
ejpam-5051	556	1	[	[	X
ejpam-5051	556	2	χ	χ	X
ejpam-5051	556	3	′	′	NUM
ejpam-5051	556	4	1	1	NUM
ejpam-5051	556	5	,	,	PUNCT
ejpam-5051	556	6	z	z	NOUN
ejpam-5051	556	7	′	′	NUM
ejpam-5051	556	8	1	1	NUM
ejpam-5051	556	9	,	,	PUNCT
ejpam-5051	556	10	γ	γ	NOUN
ejpam-5051	556	11	′	′	NOUN
ejpam-5051	556	12	1	1	NUM
ejpam-5051	556	13	]	]	PUNCT
ejpam-5051	556	14	)	)	PUNCT
ejpam-5051	556	15	,	,	PUNCT
ejpam-5051	556	16	(	(	PUNCT
ejpam-5051	556	17	[	[	X
ejpam-5051	556	18	χ2	χ2	PROPN
ejpam-5051	556	19	,	,	PUNCT
ejpam-5051	556	20	z2	z2	PROPN
ejpam-5051	556	21	,	,	PUNCT
ejpam-5051	556	22	γ2	γ2	PROPN
ejpam-5051	556	23	]	]	PUNCT
ejpam-5051	556	24	,	,	PUNCT
ejpam-5051	556	25	[	[	X
ejpam-5051	556	26	χ	χ	X
ejpam-5051	556	27	′	′	NUM
ejpam-5051	556	28	2	2	NUM
ejpam-5051	556	29	,	,	PUNCT
ejpam-5051	556	30	z	z	NOUN
ejpam-5051	556	31	′	′	NUM
ejpam-5051	556	32	2	2	NUM
ejpam-5051	556	33	,	,	PUNCT
ejpam-5051	556	34	γ	γ	NOUN
ejpam-5051	556	35	′	′	NOUN
ejpam-5051	556	36	2	2	NUM
ejpam-5051	556	37	]	]	PUNCT
ejpam-5051	556	38	)	)	PUNCT
ejpam-5051	556	39	∈	∈	PROPN
ejpam-5051	556	40	d(2	d(2	PROPN
ejpam-5051	556	41	)	)	PUNCT
ejpam-5051	556	42	with	with	ADP
ejpam-5051	556	43	(	(	PUNCT
ejpam-5051	556	44	[	[	X
ejpam-5051	556	45	χ1	χ1	NOUN
ejpam-5051	556	46	,	,	PUNCT
ejpam-5051	556	47	z1	z1	NOUN
ejpam-5051	556	48	,	,	PUNCT
ejpam-5051	556	49	γ1	γ1	NOUN
ejpam-5051	556	50	]	]	PUNCT
ejpam-5051	556	51	,	,	PUNCT
ejpam-5051	556	52	[	[	X
ejpam-5051	556	53	χ	χ	X
ejpam-5051	556	54	′	′	NUM
ejpam-5051	556	55	1	1	NUM
ejpam-5051	556	56	,	,	PUNCT
ejpam-5051	556	57	z	z	NOUN
ejpam-5051	556	58	′	′	NUM
ejpam-5051	556	59	1	1	NUM
ejpam-5051	556	60	,	,	PUNCT
ejpam-5051	556	61	γ	γ	NOUN
ejpam-5051	556	62	′	′	NOUN
ejpam-5051	556	63	1	1	NUM
ejpam-5051	556	64	]	]	PUNCT
ejpam-5051	556	65	)	)	PUNCT
ejpam-5051	556	66	=	=	SYM
ejpam-5051	557	1	(	(	PUNCT
ejpam-5051	557	2	[	[	X
ejpam-5051	557	3	χ2	χ2	PROPN
ejpam-5051	557	4	,	,	PUNCT
ejpam-5051	557	5	z2	z2	PROPN
ejpam-5051	557	6	,	,	PUNCT
ejpam-5051	557	7	γ2	γ2	PROPN
ejpam-5051	557	8	]	]	PUNCT
ejpam-5051	557	9	,	,	PUNCT
ejpam-5051	558	1	[	[	X
ejpam-5051	558	2	χ	χ	X
ejpam-5051	558	3	′	′	NUM
ejpam-5051	558	4	2	2	NUM
ejpam-5051	558	5	,	,	PUNCT
ejpam-5051	558	6	z	z	NOUN
ejpam-5051	558	7	′	′	NUM
ejpam-5051	558	8	2	2	NUM
ejpam-5051	558	9	,	,	PUNCT
ejpam-5051	558	10	γ	γ	NOUN
ejpam-5051	558	11	′	′	NOUN
ejpam-5051	558	12	2	2	NUM
ejpam-5051	558	13	]	]	PUNCT
ejpam-5051	558	14	)	)	PUNCT
ejpam-5051	558	15	.	.	PUNCT
ejpam-5051	559	1	composition	composition	NOUN
ejpam-5051	559	2	is	be	AUX
ejpam-5051	559	3	well	well	ADV
ejpam-5051	559	4	-	-	PUNCT
ejpam-5051	559	5	defined	define	VERB
ejpam-5051	559	6	since	since	SCONJ
ejpam-5051	559	7	m(([χ1	m(([χ1	NOUN
ejpam-5051	559	8	,	,	PUNCT
ejpam-5051	559	9	z1	z1	NOUN
ejpam-5051	559	10	,	,	PUNCT
ejpam-5051	559	11	γ1	γ1	NOUN
ejpam-5051	559	12	]	]	PUNCT
ejpam-5051	559	13	,	,	PUNCT
ejpam-5051	560	1	[	[	X
ejpam-5051	560	2	χ	χ	X
ejpam-5051	560	3	′	′	NUM
ejpam-5051	560	4	1	1	NUM
ejpam-5051	560	5	,	,	PUNCT
ejpam-5051	560	6	z	z	NOUN
ejpam-5051	560	7	′	′	NUM
ejpam-5051	560	8	1	1	NUM
ejpam-5051	560	9	,	,	PUNCT
ejpam-5051	560	10	γ	γ	NOUN
ejpam-5051	560	11	′	′	NOUN
ejpam-5051	560	12	1	1	NUM
ejpam-5051	560	13	]	]	PUNCT
ejpam-5051	560	14	)	)	PUNCT
ejpam-5051	560	15	)	)	PUNCT
ejpam-5051	561	1	=	=	PUNCT
ejpam-5051	562	1	[	[	X
ejpam-5051	562	2	χ1	χ1	NOUN
ejpam-5051	562	3	,	,	PUNCT
ejpam-5051	562	4	z1z	z1z	PROPN
ejpam-5051	562	5	′	′	NUM
ejpam-5051	562	6	1	1	NUM
ejpam-5051	562	7	,	,	PUNCT
ejpam-5051	562	8	γ1γ	γ1γ	NOUN
ejpam-5051	562	9	′	′	NUM
ejpam-5051	562	10	1	1	NUM
ejpam-5051	562	11	]	]	PUNCT
ejpam-5051	562	12	=	=	PUNCT
ejpam-5051	563	1	[	[	X
ejpam-5051	563	2	χ2	χ2	PROPN
ejpam-5051	563	3	,	,	PUNCT
ejpam-5051	563	4	z2z	z2z	PROPN
ejpam-5051	563	5	′	′	NUM
ejpam-5051	563	6	2	2	NUM
ejpam-5051	563	7	,	,	PUNCT
ejpam-5051	563	8	γ2γ	γ2γ	ADV
ejpam-5051	563	9	′	′	NOUN
ejpam-5051	563	10	2	2	NUM
ejpam-5051	563	11	]	]	PUNCT
ejpam-5051	563	12	=	=	SYM
ejpam-5051	563	13	m(([χ2	m(([χ2	NOUN
ejpam-5051	563	14	,	,	PUNCT
ejpam-5051	563	15	z2	z2	PROPN
ejpam-5051	563	16	,	,	PUNCT
ejpam-5051	563	17	γ2	γ2	PROPN
ejpam-5051	563	18	]	]	PUNCT
ejpam-5051	563	19	,	,	PUNCT
ejpam-5051	564	1	[	[	X
ejpam-5051	564	2	χ	χ	X
ejpam-5051	564	3	′	′	NUM
ejpam-5051	564	4	2	2	NUM
ejpam-5051	564	5	,	,	PUNCT
ejpam-5051	564	6	z	z	NOUN
ejpam-5051	564	7	′	′	NUM
ejpam-5051	564	8	2	2	NUM
ejpam-5051	564	9	,	,	PUNCT
ejpam-5051	564	10	γ	γ	NOUN
ejpam-5051	564	11	′	′	NOUN
ejpam-5051	564	12	2	2	NUM
ejpam-5051	564	13	]	]	PUNCT
ejpam-5051	564	14	)	)	PUNCT
ejpam-5051	564	15	)	)	PUNCT
ejpam-5051	564	16	.	.	PUNCT
ejpam-5051	565	1	now	now	ADV
ejpam-5051	565	2	,	,	PUNCT
ejpam-5051	565	3	let	let	VERB
ejpam-5051	565	4	(	(	PUNCT
ejpam-5051	565	5	[	[	X
ejpam-5051	565	6	χ1	χ1	NOUN
ejpam-5051	565	7	,	,	PUNCT
ejpam-5051	565	8	z1	z1	NOUN
ejpam-5051	565	9	,	,	PUNCT
ejpam-5051	565	10	γ1	γ1	NOUN
ejpam-5051	565	11	]	]	PUNCT
ejpam-5051	565	12	,	,	PUNCT
ejpam-5051	565	13	[	[	X
ejpam-5051	565	14	χ2	χ2	PROPN
ejpam-5051	565	15	,	,	PUNCT
ejpam-5051	565	16	z2	z2	PROPN
ejpam-5051	565	17	,	,	PUNCT
ejpam-5051	565	18	γ2	γ2	PROPN
ejpam-5051	565	19	]	]	PUNCT
ejpam-5051	565	20	)	)	PUNCT
ejpam-5051	565	21	,	,	PUNCT
ejpam-5051	565	22	(	(	PUNCT
ejpam-5051	565	23	[	[	X
ejpam-5051	565	24	χ2	χ2	PROPN
ejpam-5051	565	25	,	,	PUNCT
ejpam-5051	565	26	z2	z2	PROPN
ejpam-5051	565	27	,	,	PUNCT
ejpam-5051	565	28	γ2	γ2	PROPN
ejpam-5051	565	29	]	]	PUNCT
ejpam-5051	565	30	,	,	PUNCT
ejpam-5051	566	1	[	[	X
ejpam-5051	566	2	χ3	χ3	NOUN
ejpam-5051	566	3	,	,	PUNCT
ejpam-5051	566	4	z3	z3	PROPN
ejpam-5051	566	5	,	,	PUNCT
ejpam-5051	566	6	γ3	γ3	NOUN
ejpam-5051	566	7	]	]	PUNCT
ejpam-5051	566	8	)	)	PUNCT
ejpam-5051	566	9	∈	∈	PROPN
ejpam-5051	566	10	d(2	d(2	PROPN
ejpam-5051	566	11	)	)	PUNCT
ejpam-5051	566	12	.	.	PUNCT
ejpam-5051	567	1	then	then	ADV
ejpam-5051	567	2	s([χ1	s([χ1	PROPN
ejpam-5051	567	3	,	,	PUNCT
ejpam-5051	567	4	z1	z1	PROPN
ejpam-5051	567	5	,	,	PUNCT
ejpam-5051	567	6	γ1][χ2	γ1][χ2	NOUN
ejpam-5051	567	7	,	,	PUNCT
ejpam-5051	567	8	z2	z2	PROPN
ejpam-5051	567	9	,	,	PUNCT
ejpam-5051	567	10	γ2	γ2	PROPN
ejpam-5051	567	11	]	]	X
ejpam-5051	567	12	)	)	PUNCT
ejpam-5051	567	13	=	=	SYM
ejpam-5051	567	14	s([χ1	s([χ1	PROPN
ejpam-5051	567	15	,	,	PUNCT
ejpam-5051	567	16	z1z2	z1z2	PROPN
ejpam-5051	567	17	,	,	PUNCT
ejpam-5051	567	18	γ1γ2	γ1γ2	NOUN
ejpam-5051	567	19	]	]	X
ejpam-5051	567	20	)	)	PUNCT
ejpam-5051	567	21	=	=	PUNCT
ejpam-5051	568	1	[	[	X
ejpam-5051	568	2	χ1	χ1	NOUN
ejpam-5051	568	3	·	·	PUNCT
ejpam-5051	568	4	γ1γ2	γ1γ2	ADJ
ejpam-5051	568	5	,	,	PUNCT
ejpam-5051	568	6	s(γ1γ2	s(γ1γ2	NOUN
ejpam-5051	568	7	)	)	PUNCT
ejpam-5051	568	8	]	]	PUNCT
ejpam-5051	569	1	=	=	PUNCT
ejpam-5051	570	1	[	[	X
ejpam-5051	570	2	χ2	χ2	PROPN
ejpam-5051	570	3	·	·	PUNCT
ejpam-5051	570	4	γ2	γ2	ADJ
ejpam-5051	570	5	,	,	PUNCT
ejpam-5051	570	6	s(γ2	s(γ2	NOUN
ejpam-5051	570	7	)	)	PUNCT
ejpam-5051	570	8	]	]	PUNCT
ejpam-5051	571	1	=	=	PUNCT
ejpam-5051	572	1	[	[	X
ejpam-5051	572	2	χ3	χ3	NOUN
ejpam-5051	572	3	,	,	PUNCT
ejpam-5051	572	4	r(γ3	r(γ3	NOUN
ejpam-5051	572	5	)	)	PUNCT
ejpam-5051	572	6	]	]	PUNCT
ejpam-5051	573	1	=	=	PUNCT
ejpam-5051	573	2	r([χ3	r([χ3	NOUN
ejpam-5051	573	3	,	,	PUNCT
ejpam-5051	573	4	z3	z3	NOUN
ejpam-5051	573	5	,	,	PUNCT
ejpam-5051	573	6	γ3	γ3	NOUN
ejpam-5051	573	7	]	]	PUNCT
ejpam-5051	573	8	)	)	PUNCT
ejpam-5051	573	9	.	.	PUNCT
ejpam-5051	574	1	also	also	ADV
ejpam-5051	574	2	,	,	PUNCT
ejpam-5051	574	3	r([χ2	r([χ2	NOUN
ejpam-5051	574	4	,	,	PUNCT
ejpam-5051	574	5	z2	z2	PROPN
ejpam-5051	574	6	,	,	PUNCT
ejpam-5051	574	7	γ2][χ3	γ2][χ3	PROPN
ejpam-5051	574	8	,	,	PUNCT
ejpam-5051	574	9	z3	z3	PROPN
ejpam-5051	574	10	,	,	PUNCT
ejpam-5051	574	11	γ3	γ3	NOUN
ejpam-5051	574	12	]	]	PUNCT
ejpam-5051	574	13	)	)	PUNCT
ejpam-5051	574	14	=	=	SYM
ejpam-5051	574	15	r([χ2	r([χ2	NOUN
ejpam-5051	574	16	,	,	PUNCT
ejpam-5051	574	17	z2z3	z2z3	X
ejpam-5051	574	18	,	,	PUNCT
ejpam-5051	574	19	γ2γ3	γ2γ3	NOUN
ejpam-5051	574	20	]	]	X
ejpam-5051	574	21	)	)	PUNCT
ejpam-5051	575	1	=	=	PUNCT
ejpam-5051	576	1	[	[	X
ejpam-5051	576	2	χ2	χ2	PROPN
ejpam-5051	576	3	,	,	PUNCT
ejpam-5051	576	4	r(γ2γ3	r(γ2γ3	NOUN
ejpam-5051	576	5	)	)	PUNCT
ejpam-5051	576	6	]	]	PUNCT
ejpam-5051	577	1	=	=	PUNCT
ejpam-5051	577	2	[	[	X
ejpam-5051	577	3	χ2	χ2	PROPN
ejpam-5051	577	4	,	,	PUNCT
ejpam-5051	577	5	r(γ2	r(γ2	NOUN
ejpam-5051	577	6	)	)	PUNCT
ejpam-5051	577	7	]	]	PUNCT
ejpam-5051	577	8	=	=	PUNCT
ejpam-5051	578	1	[	[	X
ejpam-5051	578	2	χ1	χ1	NOUN
ejpam-5051	578	3	·	·	PUNCT
ejpam-5051	578	4	γ1	γ1	NOUN
ejpam-5051	578	5	,	,	PUNCT
ejpam-5051	578	6	s(γ1	s(γ1	NOUN
ejpam-5051	578	7	)	)	PUNCT
ejpam-5051	578	8	]	]	PUNCT
ejpam-5051	579	1	=	=	SYM
ejpam-5051	579	2	s([χ1	s([χ1	PROPN
ejpam-5051	579	3	,	,	PUNCT
ejpam-5051	579	4	z1	z1	NOUN
ejpam-5051	579	5	,	,	PUNCT
ejpam-5051	579	6	γ1	γ1	NOUN
ejpam-5051	579	7	]	]	PUNCT
ejpam-5051	579	8	)	)	PUNCT
ejpam-5051	579	9	.	.	PUNCT
ejpam-5051	580	1	thus	thus	ADV
ejpam-5051	580	2	,	,	PUNCT
ejpam-5051	580	3	(	(	PUNCT
ejpam-5051	580	4	[	[	X
ejpam-5051	580	5	χ1	χ1	NOUN
ejpam-5051	580	6	,	,	PUNCT
ejpam-5051	580	7	z1	z1	NOUN
ejpam-5051	580	8	,	,	PUNCT
ejpam-5051	580	9	γ1][χ2	γ1][χ2	NOUN
ejpam-5051	580	10	,	,	PUNCT
ejpam-5051	580	11	z2	z2	PROPN
ejpam-5051	580	12	,	,	PUNCT
ejpam-5051	580	13	γ2	γ2	PROPN
ejpam-5051	580	14	]	]	PUNCT
ejpam-5051	580	15	,	,	PUNCT
ejpam-5051	580	16	[	[	X
ejpam-5051	580	17	χ3	χ3	NOUN
ejpam-5051	580	18	,	,	PUNCT
ejpam-5051	580	19	z3	z3	PROPN
ejpam-5051	580	20	,	,	PUNCT
ejpam-5051	580	21	γ3	γ3	NOUN
ejpam-5051	580	22	]	]	PUNCT
ejpam-5051	580	23	)	)	PUNCT
ejpam-5051	580	24	and	and	CCONJ
ejpam-5051	580	25	(	(	PUNCT
ejpam-5051	580	26	[	[	X
ejpam-5051	580	27	χ1	χ1	NOUN
ejpam-5051	580	28	,	,	PUNCT
ejpam-5051	580	29	z1	z1	NOUN
ejpam-5051	580	30	,	,	PUNCT
ejpam-5051	580	31	γ1	γ1	NOUN
ejpam-5051	580	32	]	]	PUNCT
ejpam-5051	580	33	,	,	PUNCT
ejpam-5051	580	34	[	[	X
ejpam-5051	580	35	χ2	χ2	PROPN
ejpam-5051	580	36	,	,	PUNCT
ejpam-5051	580	37	z2	z2	PROPN
ejpam-5051	580	38	,	,	PUNCT
ejpam-5051	580	39	γ2][χ3	γ2][χ3	PROPN
ejpam-5051	580	40	,	,	PUNCT
ejpam-5051	580	41	z3	z3	PROPN
ejpam-5051	580	42	,	,	PUNCT
ejpam-5051	580	43	γ3	γ3	NOUN
ejpam-5051	580	44	]	]	PUNCT
ejpam-5051	580	45	)	)	PUNCT
ejpam-5051	580	46	are	be	AUX
ejpam-5051	580	47	composable	composable	ADJ
ejpam-5051	580	48	pairs	pair	NOUN
ejpam-5051	580	49	.	.	PUNCT
ejpam-5051	581	1	to	to	PART
ejpam-5051	581	2	show	show	VERB
ejpam-5051	581	3	that	that	SCONJ
ejpam-5051	581	4	composition	composition	NOUN
ejpam-5051	581	5	in	in	ADP
ejpam-5051	581	6	d	d	PROPN
ejpam-5051	581	7	is	be	AUX
ejpam-5051	581	8	associative	associative	ADJ
ejpam-5051	581	9	,	,	PUNCT
ejpam-5051	581	10	(	(	PUNCT
ejpam-5051	581	11	[	[	X
ejpam-5051	581	12	χ1	χ1	NOUN
ejpam-5051	581	13	,	,	PUNCT
ejpam-5051	581	14	z1	z1	NOUN
ejpam-5051	581	15	,	,	PUNCT
ejpam-5051	581	16	γ1][χ2	γ1][χ2	NOUN
ejpam-5051	581	17	,	,	PUNCT
ejpam-5051	581	18	z2	z2	PROPN
ejpam-5051	581	19	,	,	PUNCT
ejpam-5051	581	20	γ2])[χ3	γ2])[χ3	NOUN
ejpam-5051	581	21	,	,	PUNCT
ejpam-5051	581	22	z3	z3	NOUN
ejpam-5051	581	23	,	,	PUNCT
ejpam-5051	581	24	γ3	γ3	NOUN
ejpam-5051	581	25	]	]	PUNCT
ejpam-5051	582	1	=	=	PUNCT
ejpam-5051	583	1	[	[	X
ejpam-5051	583	2	χ1	χ1	NOUN
ejpam-5051	583	3	,	,	PUNCT
ejpam-5051	583	4	z1z2	z1z2	PROPN
ejpam-5051	583	5	,	,	PUNCT
ejpam-5051	583	6	γ1γ2][χ3	γ1γ2][χ3	NOUN
ejpam-5051	583	7	,	,	PUNCT
ejpam-5051	583	8	z3	z3	PROPN
ejpam-5051	583	9	,	,	PUNCT
ejpam-5051	583	10	γ3	γ3	NOUN
ejpam-5051	583	11	]	]	PUNCT
ejpam-5051	583	12	=	=	PUNCT
ejpam-5051	584	1	[	[	X
ejpam-5051	584	2	χ1	χ1	NOUN
ejpam-5051	584	3	,	,	PUNCT
ejpam-5051	584	4	z1z2z3	z1z2z3	PROPN
ejpam-5051	584	5	,	,	PUNCT
ejpam-5051	584	6	γ1γ2γ3	γ1γ2γ3	NOUN
ejpam-5051	584	7	]	]	X
ejpam-5051	584	8	=	=	PUNCT
ejpam-5051	585	1	[	[	X
ejpam-5051	585	2	χ1	χ1	NOUN
ejpam-5051	585	3	,	,	PUNCT
ejpam-5051	585	4	z1	z1	PROPN
ejpam-5051	585	5	,	,	PUNCT
ejpam-5051	585	6	γ1][χ2	γ1][χ2	PROPN
ejpam-5051	585	7	,	,	PUNCT
ejpam-5051	585	8	z2z3	z2z3	NOUN
ejpam-5051	585	9	,	,	PUNCT
ejpam-5051	585	10	γ2γ3	γ2γ3	NOUN
ejpam-5051	585	11	]	]	X
ejpam-5051	585	12	=	=	PUNCT
ejpam-5051	586	1	[	[	X
ejpam-5051	586	2	χ1	χ1	NOUN
ejpam-5051	586	3	,	,	PUNCT
ejpam-5051	586	4	z1	z1	NOUN
ejpam-5051	586	5	,	,	PUNCT
ejpam-5051	586	6	γ1]([χ2	γ1]([χ2	NOUN
ejpam-5051	586	7	,	,	PUNCT
ejpam-5051	586	8	z2	z2	PROPN
ejpam-5051	586	9	,	,	PUNCT
ejpam-5051	586	10	γ2][χ3	γ2][χ3	PROPN
ejpam-5051	586	11	,	,	PUNCT
ejpam-5051	586	12	z3	z3	PROPN
ejpam-5051	586	13	,	,	PUNCT
ejpam-5051	586	14	γ3	γ3	NOUN
ejpam-5051	586	15	]	]	PUNCT
ejpam-5051	586	16	)	)	PUNCT
ejpam-5051	586	17	.	.	PUNCT
ejpam-5051	587	1	r.	r.	PROPN
ejpam-5051	587	2	s.	s.	PROPN
ejpam-5051	587	3	bongcawel	bongcawel	PROPN
ejpam-5051	588	1	et	et	PROPN
ejpam-5051	588	2	al	al	PROPN
ejpam-5051	588	3	.	.	PUNCT
ejpam-5051	588	4	/	/	SYM
ejpam-5051	588	5	eur	eur	PROPN
ejpam-5051	588	6	.	.	PUNCT
ejpam-5051	589	1	j.	j.	PROPN
ejpam-5051	589	2	pure	pure	PROPN
ejpam-5051	589	3	appl	appl	PROPN
ejpam-5051	589	4	.	.	PROPN
ejpam-5051	589	5	math	math	PROPN
ejpam-5051	589	6	,	,	PUNCT
ejpam-5051	589	7	17	17	NUM
ejpam-5051	589	8	(	(	PUNCT
ejpam-5051	589	9	1	1	NUM
ejpam-5051	589	10	)	)	PUNCT
ejpam-5051	589	11	(	(	PUNCT
ejpam-5051	589	12	2024	2024	NUM
ejpam-5051	589	13	)	)	PUNCT
ejpam-5051	589	14	,	,	PUNCT
ejpam-5051	589	15	519	519	NUM
ejpam-5051	589	16	-	-	SYM
ejpam-5051	589	17	545	545	NUM
ejpam-5051	589	18	534	534	NUM
ejpam-5051	589	19	for	for	ADP
ejpam-5051	589	20	[	[	NOUN
ejpam-5051	589	21	χ	χ	X
ejpam-5051	589	22	,	,	PUNCT
ejpam-5051	589	23	z	z	PROPN
ejpam-5051	589	24	,	,	PUNCT
ejpam-5051	589	25	γ	γ	X
ejpam-5051	589	26	]	]	X
ejpam-5051	589	27	∈	∈	PROPN
ejpam-5051	589	28	d	d	X
ejpam-5051	589	29	we	we	PRON
ejpam-5051	589	30	have	have	VERB
ejpam-5051	589	31	,	,	PUNCT
ejpam-5051	589	32	(	(	PUNCT
ejpam-5051	590	1	[	[	X
ejpam-5051	590	2	χ	χ	X
ejpam-5051	590	3	,	,	PUNCT
ejpam-5051	590	4	z	z	NOUN
ejpam-5051	590	5	,	,	PUNCT
ejpam-5051	590	6	γ]−1)−1	γ]−1)−1	PUNCT
ejpam-5051	590	7	=	=	PUNCT
ejpam-5051	591	1	[	[	X
ejpam-5051	591	2	χ	χ	X
ejpam-5051	591	3	·	·	PUNCT
ejpam-5051	591	4	γ	γ	X
ejpam-5051	591	5	,	,	PUNCT
ejpam-5051	591	6	z−1	z−1	PROPN
ejpam-5051	591	7	,	,	PUNCT
ejpam-5051	591	8	γ−1]−1	γ−1]−1	NOUN
ejpam-5051	591	9	=	=	PUNCT
ejpam-5051	592	1	[	[	X
ejpam-5051	592	2	χ	χ	X
ejpam-5051	592	3	·	·	PUNCT
ejpam-5051	592	4	γ	γ	X
ejpam-5051	592	5	·	·	PUNCT
ejpam-5051	592	6	γ−1	γ−1	ADJ
ejpam-5051	592	7	,	,	PUNCT
ejpam-5051	592	8	(	(	PUNCT
ejpam-5051	592	9	z−1)−1	z−1)−1	NOUN
ejpam-5051	592	10	,	,	PUNCT
ejpam-5051	592	11	(	(	PUNCT
ejpam-5051	592	12	γ−1)−1	γ−1)−1	NOUN
ejpam-5051	592	13	]	]	PUNCT
ejpam-5051	592	14	=	=	PUNCT
ejpam-5051	593	1	[	[	X
ejpam-5051	593	2	χ	χ	X
ejpam-5051	593	3	·	·	PUNCT
ejpam-5051	593	4	r(γ	r(γ	NUM
ejpam-5051	593	5	)	)	PUNCT
ejpam-5051	593	6	,	,	PUNCT
ejpam-5051	594	1	z	z	PROPN
ejpam-5051	594	2	,	,	PUNCT
ejpam-5051	594	3	γ	γ	X
ejpam-5051	594	4	]	]	X
ejpam-5051	594	5	=	=	PUNCT
ejpam-5051	595	1	[	[	X
ejpam-5051	595	2	χ	χ	X
ejpam-5051	595	3	·	·	PUNCT
ejpam-5051	595	4	u	u	NOUN
ejpam-5051	595	5	,	,	PUNCT
ejpam-5051	595	6	z	z	PROPN
ejpam-5051	595	7	,	,	PUNCT
ejpam-5051	595	8	γ	γ	X
ejpam-5051	595	9	]	]	X
ejpam-5051	595	10	=	=	PUNCT
ejpam-5051	596	1	[	[	X
ejpam-5051	596	2	χ	χ	X
ejpam-5051	596	3	,	,	PUNCT
ejpam-5051	596	4	z	z	PROPN
ejpam-5051	596	5	,	,	PUNCT
ejpam-5051	596	6	γ	γ	X
ejpam-5051	596	7	]	]	X
ejpam-5051	596	8	.	.	PUNCT
ejpam-5051	597	1	also	also	ADV
ejpam-5051	597	2	,	,	PUNCT
ejpam-5051	597	3	r([χ	r([χ	NOUN
ejpam-5051	597	4	,	,	PUNCT
ejpam-5051	597	5	z	z	NOUN
ejpam-5051	597	6	,	,	PUNCT
ejpam-5051	597	7	γ]−1	γ]−1	NOUN
ejpam-5051	597	8	)	)	PUNCT
ejpam-5051	597	9	=	=	SYM
ejpam-5051	597	10	r([χ	r([χ	NOUN
ejpam-5051	597	11	·	·	SYM
ejpam-5051	597	12	γ	γ	X
ejpam-5051	597	13	,	,	PUNCT
ejpam-5051	597	14	z−1	z−1	PROPN
ejpam-5051	597	15	,	,	PUNCT
ejpam-5051	597	16	γ−1	γ−1	PROPN
ejpam-5051	597	17	]	]	X
ejpam-5051	597	18	)	)	PUNCT
ejpam-5051	597	19	=	=	PUNCT
ejpam-5051	598	1	[	[	X
ejpam-5051	598	2	χ	χ	X
ejpam-5051	598	3	·	·	SYM
ejpam-5051	598	4	γ	γ	X
ejpam-5051	598	5	,	,	PUNCT
ejpam-5051	598	6	r(γ−1	r(γ−1	ADJ
ejpam-5051	598	7	)	)	PUNCT
ejpam-5051	598	8	]	]	PUNCT
ejpam-5051	599	1	=	=	PUNCT
ejpam-5051	600	1	[	[	X
ejpam-5051	600	2	χ	χ	X
ejpam-5051	600	3	·	·	SYM
ejpam-5051	600	4	γ	γ	X
ejpam-5051	600	5	,	,	PUNCT
ejpam-5051	600	6	s(γ	s(γ	PROPN
ejpam-5051	600	7	)	)	PUNCT
ejpam-5051	600	8	]	]	PUNCT
ejpam-5051	601	1	=	=	PUNCT
ejpam-5051	601	2	s([χ	s([χ	NOUN
ejpam-5051	601	3	,	,	PUNCT
ejpam-5051	601	4	z	z	PROPN
ejpam-5051	601	5	,	,	PUNCT
ejpam-5051	601	6	γ	γ	NOUN
ejpam-5051	601	7	]	]	X
ejpam-5051	601	8	)	)	PUNCT
ejpam-5051	601	9	.	.	PUNCT
ejpam-5051	602	1	hence	hence	ADV
ejpam-5051	602	2	,	,	PUNCT
ejpam-5051	602	3	(	(	PUNCT
ejpam-5051	602	4	[	[	X
ejpam-5051	602	5	χ	χ	X
ejpam-5051	602	6	,	,	PUNCT
ejpam-5051	602	7	z	z	PROPN
ejpam-5051	602	8	,	,	PUNCT
ejpam-5051	602	9	γ	γ	X
ejpam-5051	602	10	]	]	X
ejpam-5051	602	11	,	,	PUNCT
ejpam-5051	602	12	[	[	X
ejpam-5051	602	13	χ	χ	X
ejpam-5051	602	14	,	,	PUNCT
ejpam-5051	602	15	z	z	NOUN
ejpam-5051	602	16	,	,	PUNCT
ejpam-5051	602	17	γ]−1	γ]−1	NOUN
ejpam-5051	602	18	)	)	PUNCT
ejpam-5051	602	19	∈	∈	PROPN
ejpam-5051	602	20	d(2	d(2	PROPN
ejpam-5051	602	21	)	)	PUNCT
ejpam-5051	602	22	.	.	PUNCT
ejpam-5051	603	1	notice	notice	VERB
ejpam-5051	603	2	that	that	SCONJ
ejpam-5051	603	3	(	(	PUNCT
ejpam-5051	603	4	[	[	X
ejpam-5051	603	5	χ1	χ1	NOUN
ejpam-5051	603	6	,	,	PUNCT
ejpam-5051	603	7	z1	z1	NOUN
ejpam-5051	603	8	,	,	PUNCT
ejpam-5051	603	9	γ1][χ2	γ1][χ2	NOUN
ejpam-5051	603	10	,	,	PUNCT
ejpam-5051	603	11	z2	z2	PROPN
ejpam-5051	603	12	,	,	PUNCT
ejpam-5051	603	13	γ2])[χ2	γ2])[χ2	ADJ
ejpam-5051	603	14	,	,	PUNCT
ejpam-5051	603	15	z2	z2	PROPN
ejpam-5051	603	16	,	,	PUNCT
ejpam-5051	603	17	γ2	γ2	NOUN
ejpam-5051	603	18	]	]	PUNCT
ejpam-5051	603	19	−1	−1	NOUN
ejpam-5051	604	1	=	=	SYM
ejpam-5051	605	1	[	[	X
ejpam-5051	605	2	χ1	χ1	NOUN
ejpam-5051	605	3	,	,	PUNCT
ejpam-5051	605	4	z1z2	z1z2	PROPN
ejpam-5051	605	5	,	,	PUNCT
ejpam-5051	605	6	γ1γ2][χ2	γ1γ2][χ2	NOUN
ejpam-5051	605	7	,	,	PUNCT
ejpam-5051	605	8	z2	z2	NOUN
ejpam-5051	605	9	,	,	PUNCT
ejpam-5051	605	10	γ2	γ2	NOUN
ejpam-5051	605	11	]	]	PUNCT
ejpam-5051	605	12	−1	−1	NOUN
ejpam-5051	605	13	=	=	SYM
ejpam-5051	606	1	[	[	X
ejpam-5051	606	2	χ1	χ1	NOUN
ejpam-5051	606	3	,	,	PUNCT
ejpam-5051	606	4	z1z2	z1z2	PROPN
ejpam-5051	606	5	,	,	PUNCT
ejpam-5051	606	6	γ1γ2][χ2	γ1γ2][χ2	NOUN
ejpam-5051	606	7	·	·	PUNCT
ejpam-5051	606	8	γ2	γ2	ADJ
ejpam-5051	606	9	,	,	PUNCT
ejpam-5051	606	10	z−1	z−1	PROPN
ejpam-5051	606	11	2	2	NUM
ejpam-5051	606	12	,	,	PUNCT
ejpam-5051	606	13	γ−1	γ−1	PROPN
ejpam-5051	606	14	2	2	NUM
ejpam-5051	606	15	]	]	PUNCT
ejpam-5051	606	16	=	=	PUNCT
ejpam-5051	607	1	[	[	X
ejpam-5051	607	2	χ1	χ1	NOUN
ejpam-5051	607	3	,	,	PUNCT
ejpam-5051	607	4	z1z2z3	z1z2z3	PROPN
ejpam-5051	607	5	,	,	PUNCT
ejpam-5051	607	6	γ1γ2γ	γ1γ2γ	NUM
ejpam-5051	607	7	−1	−1	NOUN
ejpam-5051	607	8	3	3	NUM
ejpam-5051	607	9	]	]	PUNCT
ejpam-5051	607	10	=	=	PUNCT
ejpam-5051	608	1	[	[	X
ejpam-5051	608	2	χ1	χ1	NOUN
ejpam-5051	608	3	,	,	PUNCT
ejpam-5051	608	4	z1	z1	NOUN
ejpam-5051	608	5	,	,	PUNCT
ejpam-5051	608	6	γ1r(γ2	γ1r(γ2	NOUN
ejpam-5051	608	7	)	)	PUNCT
ejpam-5051	608	8	]	]	PUNCT
ejpam-5051	609	1	=	=	PUNCT
ejpam-5051	610	1	[	[	X
ejpam-5051	610	2	χ1	χ1	NOUN
ejpam-5051	610	3	,	,	PUNCT
ejpam-5051	610	4	z1	z1	PROPN
ejpam-5051	610	5	,	,	PUNCT
ejpam-5051	610	6	γ1s(γ1	γ1s(γ1	NOUN
ejpam-5051	610	7	)	)	PUNCT
ejpam-5051	610	8	]	]	PUNCT
ejpam-5051	611	1	=	=	PUNCT
ejpam-5051	612	1	[	[	X
ejpam-5051	612	2	χ1	χ1	NOUN
ejpam-5051	612	3	,	,	PUNCT
ejpam-5051	612	4	z1	z1	NOUN
ejpam-5051	612	5	,	,	PUNCT
ejpam-5051	612	6	γ1	γ1	NOUN
ejpam-5051	612	7	]	]	PUNCT
ejpam-5051	612	8	.	.	PUNCT
ejpam-5051	613	1	also	also	ADV
ejpam-5051	613	2	,	,	PUNCT
ejpam-5051	613	3	[	[	X
ejpam-5051	613	4	χ1	χ1	NOUN
ejpam-5051	613	5	,	,	PUNCT
ejpam-5051	613	6	z1	z1	NOUN
ejpam-5051	613	7	,	,	PUNCT
ejpam-5051	613	8	γ1	γ1	PROPN
ejpam-5051	613	9	]	]	PUNCT
ejpam-5051	613	10	−1([χ1	−1([χ1	PROPN
ejpam-5051	613	11	,	,	PUNCT
ejpam-5051	613	12	z1	z1	NOUN
ejpam-5051	613	13	,	,	PUNCT
ejpam-5051	613	14	γ1][χ2	γ1][χ2	NOUN
ejpam-5051	613	15	,	,	PUNCT
ejpam-5051	613	16	z2	z2	PROPN
ejpam-5051	613	17	,	,	PUNCT
ejpam-5051	613	18	γ2	γ2	PROPN
ejpam-5051	613	19	]	]	PUNCT
ejpam-5051	613	20	)	)	PUNCT
ejpam-5051	614	1	=	=	PUNCT
ejpam-5051	615	1	[	[	X
ejpam-5051	615	2	χ1	χ1	NOUN
ejpam-5051	615	3	,	,	PUNCT
ejpam-5051	615	4	z1	z1	NOUN
ejpam-5051	615	5	,	,	PUNCT
ejpam-5051	615	6	γ1	γ1	PROPN
ejpam-5051	615	7	]	]	PUNCT
ejpam-5051	615	8	−1[χ1	−1[χ1	PROPN
ejpam-5051	615	9	,	,	PUNCT
ejpam-5051	615	10	z1z2	z1z2	PROPN
ejpam-5051	615	11	,	,	PUNCT
ejpam-5051	615	12	γ1γ2	γ1γ2	X
ejpam-5051	615	13	]	]	PUNCT
ejpam-5051	615	14	=	=	PUNCT
ejpam-5051	616	1	[	[	X
ejpam-5051	616	2	χ1	χ1	NOUN
ejpam-5051	616	3	·	·	PUNCT
ejpam-5051	616	4	γ1	γ1	NOUN
ejpam-5051	616	5	,	,	PUNCT
ejpam-5051	616	6	z−1	z−1	PROPN
ejpam-5051	616	7	1	1	NUM
ejpam-5051	616	8	,	,	PUNCT
ejpam-5051	616	9	γ−1	γ−1	PROPN
ejpam-5051	616	10	1	1	NUM
ejpam-5051	616	11	]	]	PUNCT
ejpam-5051	616	12	[	[	X
ejpam-5051	616	13	χ1	χ1	NOUN
ejpam-5051	616	14	,	,	PUNCT
ejpam-5051	616	15	z1z2	z1z2	PROPN
ejpam-5051	616	16	,	,	PUNCT
ejpam-5051	616	17	γ1γ2	γ1γ2	X
ejpam-5051	616	18	]	]	PUNCT
ejpam-5051	616	19	=	=	PUNCT
ejpam-5051	617	1	[	[	X
ejpam-5051	617	2	χ1	χ1	NOUN
ejpam-5051	617	3	·	·	PUNCT
ejpam-5051	617	4	γ1	γ1	NOUN
ejpam-5051	617	5	,	,	PUNCT
ejpam-5051	617	6	z−1	z−1	PROPN
ejpam-5051	617	7	1	1	NUM
ejpam-5051	617	8	z1z2	z1z2	NOUN
ejpam-5051	617	9	,	,	PUNCT
ejpam-5051	617	10	γ	γ	X
ejpam-5051	617	11	−1	−1	NOUN
ejpam-5051	617	12	1	1	NUM
ejpam-5051	617	13	γ1γ2	γ1γ2	NOUN
ejpam-5051	617	14	]	]	X
ejpam-5051	617	15	=	=	PUNCT
ejpam-5051	618	1	[	[	X
ejpam-5051	618	2	χ2	χ2	PROPN
ejpam-5051	618	3	,	,	PUNCT
ejpam-5051	618	4	z2	z2	NOUN
ejpam-5051	618	5	,	,	PUNCT
ejpam-5051	618	6	s(γ1)γ2	s(γ1)γ2	NOUN
ejpam-5051	618	7	]	]	X
ejpam-5051	618	8	=	=	PUNCT
ejpam-5051	619	1	[	[	X
ejpam-5051	619	2	χ2	χ2	PROPN
ejpam-5051	619	3	,	,	PUNCT
ejpam-5051	619	4	z2	z2	NOUN
ejpam-5051	619	5	,	,	PUNCT
ejpam-5051	619	6	r(γ2)γ2	r(γ2)γ2	NOUN
ejpam-5051	619	7	]	]	PUNCT
ejpam-5051	619	8	=	=	PUNCT
ejpam-5051	620	1	[	[	X
ejpam-5051	620	2	χ2	χ2	PROPN
ejpam-5051	620	3	,	,	PUNCT
ejpam-5051	620	4	z2	z2	PROPN
ejpam-5051	620	5	,	,	PUNCT
ejpam-5051	620	6	γ2	γ2	PROPN
ejpam-5051	620	7	]	]	PUNCT
ejpam-5051	620	8	.	.	PUNCT
ejpam-5051	621	1	hence	hence	ADV
ejpam-5051	621	2	,	,	PUNCT
ejpam-5051	621	3	d	d	PROPN
ejpam-5051	621	4	is	be	AUX
ejpam-5051	621	5	a	a	DET
ejpam-5051	621	6	groupoid	groupoid	NOUN
ejpam-5051	621	7	.	.	PUNCT
ejpam-5051	622	1	let	let	VERB
ejpam-5051	622	2	d	d	PRON
ejpam-5051	622	3	be	be	AUX
ejpam-5051	622	4	a	a	DET
ejpam-5051	622	5	topological	topological	ADJ
ejpam-5051	622	6	space	space	NOUN
ejpam-5051	622	7	with	with	ADP
ejpam-5051	622	8	the	the	DET
ejpam-5051	622	9	quotient	quotient	NOUN
ejpam-5051	622	10	topology	topology	NOUN
ejpam-5051	622	11	τd	τd	NOUN
ejpam-5051	622	12	.	.	PUNCT
ejpam-5051	623	1	we	we	PRON
ejpam-5051	623	2	define	define	VERB
ejpam-5051	623	3	the	the	DET
ejpam-5051	623	4	quotient	quotient	NOUN
ejpam-5051	623	5	map	map	NOUN
ejpam-5051	623	6	πd	πd	ADP
ejpam-5051	623	7	:	:	PUNCT
ejpam-5051	623	8	â∗g×t	â∗g×t	ADV
ejpam-5051	623	9	→	→	SYM
ejpam-5051	623	10	d	d	X
ejpam-5051	623	11	by	by	ADP
ejpam-5051	623	12	πd((χ	πd((χ	PRON
ejpam-5051	623	13	,	,	PUNCT
ejpam-5051	623	14	z	z	PROPN
ejpam-5051	623	15	,	,	PUNCT
ejpam-5051	623	16	γ	γ	NOUN
ejpam-5051	623	17	)	)	PUNCT
ejpam-5051	623	18	)	)	PUNCT
ejpam-5051	624	1	=	=	PUNCT
ejpam-5051	625	1	[	[	X
ejpam-5051	625	2	χ	χ	X
ejpam-5051	625	3	,	,	PUNCT
ejpam-5051	625	4	z	z	PROPN
ejpam-5051	625	5	,	,	PUNCT
ejpam-5051	625	6	γ	γ	X
ejpam-5051	625	7	]	]	X
ejpam-5051	625	8	for	for	ADP
ejpam-5051	625	9	(	(	PUNCT
ejpam-5051	625	10	χ	χ	X
ejpam-5051	625	11	,	,	PUNCT
ejpam-5051	625	12	z	z	PROPN
ejpam-5051	625	13	,	,	PUNCT
ejpam-5051	625	14	γ	γ	NOUN
ejpam-5051	625	15	)	)	PUNCT
ejpam-5051	625	16	∈	∈	PROPN
ejpam-5051	625	17	â∗g×t	â∗g×t	ADV
ejpam-5051	625	18	and	and	CCONJ
ejpam-5051	625	19	[	[	X
ejpam-5051	625	20	χ	χ	X
ejpam-5051	625	21	,	,	PUNCT
ejpam-5051	625	22	z	z	PROPN
ejpam-5051	625	23	,	,	PUNCT
ejpam-5051	625	24	γ	γ	X
ejpam-5051	625	25	]	]	X
ejpam-5051	625	26	∈	∈	PROPN
ejpam-5051	625	27	d	d	NOUN
ejpam-5051	625	28	and	and	CCONJ
ejpam-5051	625	29	τâ∗g×t	τâ∗g×t	PUNCT
ejpam-5051	625	30	=	=	SYM
ejpam-5051	625	31	{	{	PUNCT
ejpam-5051	625	32	u	u	NOUN
ejpam-5051	625	33	×	×	NOUN
ejpam-5051	625	34	v	v	NOUN
ejpam-5051	625	35	:	:	PUNCT
ejpam-5051	625	36	u	u	PROPN
ejpam-5051	625	37	∈	∈	PROPN
ejpam-5051	625	38	τâ	τâ	PROPN
ejpam-5051	625	39	,	,	PUNCT
ejpam-5051	625	40	v	v	ADP
ejpam-5051	625	41	∈	∈	NOUN
ejpam-5051	625	42	τg×t	τg×t	NOUN
ejpam-5051	625	43	}	}	PUNCT
ejpam-5051	625	44	where	where	SCONJ
ejpam-5051	625	45	τg×t	τg×t	NOUN
ejpam-5051	625	46	is	be	AUX
ejpam-5051	625	47	the	the	DET
ejpam-5051	625	48	product	product	NOUN
ejpam-5051	625	49	topology	topology	NOUN
ejpam-5051	625	50	with	with	ADP
ejpam-5051	625	51	the	the	DET
ejpam-5051	625	52	topology	topology	NOUN
ejpam-5051	625	53	in	in	ADP
ejpam-5051	625	54	g	g	PROPN
ejpam-5051	625	55	and	and	CCONJ
ejpam-5051	625	56	t	t	NOUN
ejpam-5051	625	57	having	have	VERB
ejpam-5051	625	58	the	the	DET
ejpam-5051	625	59	discrete	discrete	ADJ
ejpam-5051	625	60	topology	topology	NOUN
ejpam-5051	625	61	.	.	PUNCT
ejpam-5051	626	1	let	let	VERB
ejpam-5051	627	1	[	[	X
ejpam-5051	627	2	χ	χ	X
ejpam-5051	627	3	,	,	PUNCT
ejpam-5051	627	4	z	z	PROPN
ejpam-5051	627	5	,	,	PUNCT
ejpam-5051	627	6	γ	γ	X
ejpam-5051	627	7	]	]	X
ejpam-5051	627	8	and	and	CCONJ
ejpam-5051	627	9	[	[	X
ejpam-5051	627	10	χ′	χ′	PROPN
ejpam-5051	627	11	,	,	PUNCT
ejpam-5051	627	12	z′	z′	PROPN
ejpam-5051	627	13	,	,	PUNCT
ejpam-5051	627	14	γ′	γ′	PROPN
ejpam-5051	627	15	]	]	PUNCT
ejpam-5051	627	16	be	be	AUX
ejpam-5051	627	17	distinct	distinct	ADJ
ejpam-5051	627	18	elements	element	NOUN
ejpam-5051	627	19	of	of	ADP
ejpam-5051	627	20	d.	d.	PROPN
ejpam-5051	627	21	then	then	ADV
ejpam-5051	627	22	there	there	PRON
ejpam-5051	627	23	exists	exist	VERB
ejpam-5051	627	24	(	(	PUNCT
ejpam-5051	627	25	χ	χ	X
ejpam-5051	627	26	,	,	PUNCT
ejpam-5051	627	27	z	z	PROPN
ejpam-5051	627	28	,	,	PUNCT
ejpam-5051	627	29	γ	γ	NOUN
ejpam-5051	627	30	)	)	PUNCT
ejpam-5051	627	31	≁	≁	PROPN
ejpam-5051	627	32	(	(	PUNCT
ejpam-5051	627	33	χ′	χ′	PROPN
ejpam-5051	627	34	,	,	PUNCT
ejpam-5051	627	35	z′	z′	PROPN
ejpam-5051	627	36	,	,	PUNCT
ejpam-5051	627	37	γ′	γ′	NUM
ejpam-5051	627	38	)	)	PUNCT
ejpam-5051	627	39	in	in	ADP
ejpam-5051	627	40	â	â	PROPN
ejpam-5051	627	41	∗g	∗g	NOUN
ejpam-5051	627	42	×t	×t	NOUN
ejpam-5051	627	43	,	,	PUNCT
ejpam-5051	627	44	that	that	ADV
ejpam-5051	627	45	is	is	ADV
ejpam-5051	627	46	,	,	PUNCT
ejpam-5051	627	47	(	(	PUNCT
ejpam-5051	627	48	χ	χ	X
ejpam-5051	627	49	,	,	PUNCT
ejpam-5051	627	50	z	z	PROPN
ejpam-5051	627	51	,	,	PUNCT
ejpam-5051	627	52	γ	γ	NOUN
ejpam-5051	627	53	)	)	PUNCT
ejpam-5051	627	54	̸=	̸=	PROPN
ejpam-5051	627	55	(	(	PUNCT
ejpam-5051	627	56	χ′	χ′	PROPN
ejpam-5051	627	57	,	,	PUNCT
ejpam-5051	627	58	z′	z′	PROPN
ejpam-5051	627	59	,	,	PUNCT
ejpam-5051	627	60	γ′	γ′	PROPN
ejpam-5051	627	61	)	)	PUNCT
ejpam-5051	627	62	such	such	ADJ
ejpam-5051	627	63	that	that	SCONJ
ejpam-5051	627	64	πd((χ	πd((χ	ADJ
ejpam-5051	627	65	,	,	PUNCT
ejpam-5051	627	66	z	z	PROPN
ejpam-5051	627	67	,	,	PUNCT
ejpam-5051	627	68	γ	γ	NOUN
ejpam-5051	627	69	)	)	PUNCT
ejpam-5051	627	70	)	)	PUNCT
ejpam-5051	628	1	=	=	PUNCT
ejpam-5051	629	1	[	[	X
ejpam-5051	629	2	χ	χ	X
ejpam-5051	629	3	,	,	PUNCT
ejpam-5051	629	4	z	z	PROPN
ejpam-5051	629	5	,	,	PUNCT
ejpam-5051	629	6	γ	γ	X
ejpam-5051	629	7	]	]	X
ejpam-5051	629	8	and	and	CCONJ
ejpam-5051	629	9	πd((χ	πd((χ	ADP
ejpam-5051	629	10	′	′	PROPN
ejpam-5051	629	11	,	,	PUNCT
ejpam-5051	629	12	z′	z′	PROPN
ejpam-5051	629	13	,	,	PUNCT
ejpam-5051	629	14	γ′	γ′	NOUN
ejpam-5051	629	15	)	)	PUNCT
ejpam-5051	629	16	)	)	PUNCT
ejpam-5051	630	1	=	=	PUNCT
ejpam-5051	631	1	[	[	X
ejpam-5051	631	2	χ′	χ′	PROPN
ejpam-5051	631	3	,	,	PUNCT
ejpam-5051	631	4	z′	z′	PROPN
ejpam-5051	631	5	,	,	PUNCT
ejpam-5051	631	6	γ′	γ′	PROPN
ejpam-5051	631	7	]	]	PUNCT
ejpam-5051	631	8	.	.	PUNCT
ejpam-5051	632	1	since	since	SCONJ
ejpam-5051	632	2	â	â	ADP
ejpam-5051	632	3	∗	∗	NOUN
ejpam-5051	632	4	g	g	NOUN
ejpam-5051	632	5	×t	×t	NOUN
ejpam-5051	632	6	is	be	AUX
ejpam-5051	632	7	hausdorff	hausdorff	NOUN
ejpam-5051	632	8	,	,	PUNCT
ejpam-5051	632	9	there	there	PRON
ejpam-5051	632	10	exists	exist	VERB
ejpam-5051	632	11	open	open	ADJ
ejpam-5051	632	12	neighborhoods	neighborhood	NOUN
ejpam-5051	632	13	u	u	NOUN
ejpam-5051	632	14	and	and	CCONJ
ejpam-5051	632	15	v	v	NOUN
ejpam-5051	632	16	in	in	ADP
ejpam-5051	632	17	â∗g×t	â∗g×t	ADJ
ejpam-5051	632	18	containing	contain	VERB
ejpam-5051	632	19	(	(	PUNCT
ejpam-5051	632	20	χ	χ	NOUN
ejpam-5051	632	21	,	,	PUNCT
ejpam-5051	632	22	z	z	PROPN
ejpam-5051	632	23	,	,	PUNCT
ejpam-5051	632	24	γ	γ	NOUN
ejpam-5051	632	25	)	)	PUNCT
ejpam-5051	632	26	and	and	CCONJ
ejpam-5051	632	27	(	(	PUNCT
ejpam-5051	632	28	χ′	χ′	PROPN
ejpam-5051	632	29	,	,	PUNCT
ejpam-5051	632	30	z′	z′	PROPN
ejpam-5051	632	31	,	,	PUNCT
ejpam-5051	632	32	γ′	γ′	PROPN
ejpam-5051	632	33	)	)	PUNCT
ejpam-5051	632	34	,	,	PUNCT
ejpam-5051	632	35	respectively	respectively	ADV
ejpam-5051	632	36	such	such	ADJ
ejpam-5051	632	37	that	that	SCONJ
ejpam-5051	632	38	u	u	NOUN
ejpam-5051	632	39	∩v	∩v	NOUN
ejpam-5051	632	40	=	=	PUNCT
ejpam-5051	632	41	∅.	∅.	NOUN
ejpam-5051	632	42	then	then	ADV
ejpam-5051	632	43	,	,	PUNCT
ejpam-5051	632	44	πd(u	πd(u	X
ejpam-5051	632	45	)	)	PUNCT
ejpam-5051	632	46	and	and	CCONJ
ejpam-5051	632	47	πd(v	πd(v	PUNCT
ejpam-5051	632	48	)	)	PUNCT
ejpam-5051	632	49	are	be	AUX
ejpam-5051	632	50	open	open	ADJ
ejpam-5051	632	51	neighborhoods	neighborhood	NOUN
ejpam-5051	632	52	in	in	ADP
ejpam-5051	632	53	d	d	NOUN
ejpam-5051	632	54	containing	contain	VERB
ejpam-5051	632	55	[	[	X
ejpam-5051	632	56	χ	χ	X
ejpam-5051	632	57	,	,	PUNCT
ejpam-5051	632	58	z	z	PROPN
ejpam-5051	632	59	,	,	PUNCT
ejpam-5051	632	60	γ	γ	X
ejpam-5051	632	61	]	]	X
ejpam-5051	632	62	and	and	CCONJ
ejpam-5051	632	63	[	[	X
ejpam-5051	632	64	χ′	χ′	PROPN
ejpam-5051	632	65	,	,	PUNCT
ejpam-5051	632	66	z′	z′	PROPN
ejpam-5051	632	67	,	,	PUNCT
ejpam-5051	632	68	γ′	γ′	PROPN
ejpam-5051	632	69	]	]	X
ejpam-5051	632	70	,	,	PUNCT
ejpam-5051	632	71	respectively	respectively	ADV
ejpam-5051	632	72	such	such	ADJ
ejpam-5051	632	73	that	that	SCONJ
ejpam-5051	632	74	πd(u	πd(u	PRON
ejpam-5051	632	75	)	)	PUNCT
ejpam-5051	632	76	∩	∩	NOUN
ejpam-5051	632	77	πd(v	πd(v	PUNCT
ejpam-5051	632	78	)	)	PUNCT
ejpam-5051	632	79	=	=	VERB
ejpam-5051	632	80	∅.	∅.	AUX
ejpam-5051	632	81	let	let	VERB
ejpam-5051	632	82	[	[	X
ejpam-5051	632	83	χ	χ	X
ejpam-5051	632	84	,	,	PUNCT
ejpam-5051	632	85	z	z	PROPN
ejpam-5051	632	86	,	,	PUNCT
ejpam-5051	632	87	γ	γ	X
ejpam-5051	632	88	]	]	X
ejpam-5051	632	89	∈	∈	PROPN
ejpam-5051	632	90	d	d	NOUN
ejpam-5051	632	91	and	and	CCONJ
ejpam-5051	632	92	u	u	PROPN
ejpam-5051	632	93	and	and	CCONJ
ejpam-5051	632	94	v	v	NOUN
ejpam-5051	632	95	be	be	AUX
ejpam-5051	632	96	open	open	ADJ
ejpam-5051	632	97	subsets	subset	NOUN
ejpam-5051	632	98	of	of	ADP
ejpam-5051	632	99	d	d	PROPN
ejpam-5051	632	100	where	where	SCONJ
ejpam-5051	632	101	[	[	X
ejpam-5051	632	102	χ	χ	X
ejpam-5051	632	103	,	,	PUNCT
ejpam-5051	632	104	z	z	PROPN
ejpam-5051	632	105	,	,	PUNCT
ejpam-5051	632	106	γ	γ	X
ejpam-5051	632	107	]	]	X
ejpam-5051	632	108	∈	∈	PROPN
ejpam-5051	632	109	u	u	NOUN
ejpam-5051	632	110	.	.	PUNCT
ejpam-5051	633	1	we	we	PRON
ejpam-5051	633	2	need	need	VERB
ejpam-5051	633	3	to	to	PART
ejpam-5051	633	4	show	show	VERB
ejpam-5051	633	5	that	that	SCONJ
ejpam-5051	633	6	r	r	NOUN
ejpam-5051	633	7	:	:	PUNCT
ejpam-5051	633	8	u	u	NOUN
ejpam-5051	633	9	→	→	SYM
ejpam-5051	633	10	v	v	PROPN
ejpam-5051	633	11	is	be	AUX
ejpam-5051	633	12	a	a	DET
ejpam-5051	633	13	homeomorphism	homeomorphism	NOUN
ejpam-5051	633	14	.	.	PUNCT
ejpam-5051	634	1	let	let	VERB
ejpam-5051	634	2	v1	v1	NOUN
ejpam-5051	634	3	be	be	AUX
ejpam-5051	634	4	an	an	DET
ejpam-5051	634	5	open	open	ADJ
ejpam-5051	634	6	subset	subset	NOUN
ejpam-5051	634	7	of	of	ADP
ejpam-5051	634	8	v	v	NOUN
ejpam-5051	634	9	such	such	ADJ
ejpam-5051	634	10	that	that	DET
ejpam-5051	634	11	r−1(v1	r−1(v1	NOUN
ejpam-5051	634	12	)	)	PUNCT
ejpam-5051	634	13	⊆	⊆	NUM
ejpam-5051	634	14	u	u	NOUN
ejpam-5051	634	15	.	.	PUNCT
ejpam-5051	635	1	then	then	ADV
ejpam-5051	635	2	,	,	PUNCT
ejpam-5051	635	3	m	m	VERB
ejpam-5051	635	4	=	=	SYM
ejpam-5051	635	5	π−1	π−1	ADJ
ejpam-5051	635	6	d	d	PROPN
ejpam-5051	635	7	(	(	PUNCT
ejpam-5051	635	8	v1	v1	NOUN
ejpam-5051	635	9	)	)	PUNCT
ejpam-5051	635	10	is	be	AUX
ejpam-5051	635	11	open	open	ADJ
ejpam-5051	635	12	in	in	ADP
ejpam-5051	635	13	â∗g×t	â∗g×t	NOUN
ejpam-5051	635	14	so	so	SCONJ
ejpam-5051	635	15	that	that	SCONJ
ejpam-5051	635	16	r−1(v1	r−1(v1	NOUN
ejpam-5051	635	17	)	)	PUNCT
ejpam-5051	635	18	=	=	SYM
ejpam-5051	635	19	πd(m	πd(m	NUM
ejpam-5051	635	20	)	)	PUNCT
ejpam-5051	635	21	is	be	AUX
ejpam-5051	636	1	open	open	ADJ
ejpam-5051	636	2	d.	d.	PROPN
ejpam-5051	636	3	r.	r.	PROPN
ejpam-5051	636	4	s.	s.	PROPN
ejpam-5051	636	5	bongcawel	bongcawel	PROPN
ejpam-5051	636	6	et	et	PROPN
ejpam-5051	636	7	al	al	PROPN
ejpam-5051	636	8	.	.	PUNCT
ejpam-5051	636	9	/	/	SYM
ejpam-5051	636	10	eur	eur	PROPN
ejpam-5051	636	11	.	.	PUNCT
ejpam-5051	637	1	j.	j.	PROPN
ejpam-5051	637	2	pure	pure	PROPN
ejpam-5051	637	3	appl	appl	PROPN
ejpam-5051	637	4	.	.	PROPN
ejpam-5051	637	5	math	math	PROPN
ejpam-5051	637	6	,	,	PUNCT
ejpam-5051	637	7	17	17	NUM
ejpam-5051	637	8	(	(	PUNCT
ejpam-5051	637	9	1	1	NUM
ejpam-5051	637	10	)	)	PUNCT
ejpam-5051	637	11	(	(	PUNCT
ejpam-5051	637	12	2024	2024	NUM
ejpam-5051	637	13	)	)	PUNCT
ejpam-5051	637	14	,	,	PUNCT
ejpam-5051	637	15	519	519	NUM
ejpam-5051	637	16	-	-	SYM
ejpam-5051	637	17	545	545	NUM
ejpam-5051	637	18	535	535	NUM
ejpam-5051	637	19	hence	hence	ADV
ejpam-5051	637	20	,	,	PUNCT
ejpam-5051	637	21	r	r	NOUN
ejpam-5051	637	22	is	be	AUX
ejpam-5051	637	23	continuous	continuous	ADJ
ejpam-5051	637	24	.	.	PUNCT
ejpam-5051	638	1	similarly	similarly	ADV
ejpam-5051	638	2	,	,	PUNCT
ejpam-5051	638	3	r−1	r−1	PROPN
ejpam-5051	638	4	is	be	AUX
ejpam-5051	638	5	continuous	continuous	ADJ
ejpam-5051	638	6	.	.	PUNCT
ejpam-5051	639	1	thus	thus	ADV
ejpam-5051	639	2	,	,	PUNCT
ejpam-5051	639	3	r	r	NOUN
ejpam-5051	639	4	is	be	AUX
ejpam-5051	639	5	a	a	DET
ejpam-5051	639	6	local	local	ADJ
ejpam-5051	639	7	homeomorphism	homeomorphism	NOUN
ejpam-5051	639	8	.	.	PUNCT
ejpam-5051	640	1	therefore	therefore	ADV
ejpam-5051	640	2	,	,	PUNCT
ejpam-5051	640	3	d	d	X
ejpam-5051	640	4	is	be	AUX
ejpam-5051	640	5	a	a	DET
ejpam-5051	640	6	hausdorff	hausdorff	NOUN
ejpam-5051	640	7	étale	étale	NOUN
ejpam-5051	640	8	groupoid	groupoid	NOUN
ejpam-5051	640	9	.	.	PUNCT
ejpam-5051	641	1	let	let	VERB
ejpam-5051	641	2	[	[	X
ejpam-5051	641	3	χ	χ	ADP
ejpam-5051	641	4	,	,	PUNCT
ejpam-5051	641	5	z	z	PROPN
ejpam-5051	641	6	,	,	PUNCT
ejpam-5051	641	7	γ	γ	X
ejpam-5051	641	8	]	]	X
ejpam-5051	641	9	∈	∈	PROPN
ejpam-5051	642	1	d	d	X
ejpam-5051	642	2	such	such	ADJ
ejpam-5051	642	3	that	that	DET
ejpam-5051	642	4	s([χ	s([χ	NOUN
ejpam-5051	642	5	,	,	PUNCT
ejpam-5051	642	6	z	z	PROPN
ejpam-5051	642	7	,	,	PUNCT
ejpam-5051	642	8	γ	γ	X
ejpam-5051	642	9	]	]	X
ejpam-5051	642	10	)	)	PUNCT
ejpam-5051	642	11	=	=	SYM
ejpam-5051	642	12	r([χ	r([χ	NOUN
ejpam-5051	642	13	,	,	PUNCT
ejpam-5051	642	14	z	z	PROPN
ejpam-5051	642	15	,	,	PUNCT
ejpam-5051	642	16	γ	γ	NOUN
ejpam-5051	642	17	]	]	X
ejpam-5051	642	18	)	)	PUNCT
ejpam-5051	642	19	.	.	PUNCT
ejpam-5051	643	1	note	note	VERB
ejpam-5051	643	2	that	that	DET
ejpam-5051	643	3	s([χ	s([χ	NOUN
ejpam-5051	643	4	,	,	PUNCT
ejpam-5051	643	5	z	z	PROPN
ejpam-5051	643	6	,	,	PUNCT
ejpam-5051	643	7	γ	γ	X
ejpam-5051	643	8	]	]	X
ejpam-5051	643	9	)	)	PUNCT
ejpam-5051	643	10	=	=	PUNCT
ejpam-5051	644	1	[	[	X
ejpam-5051	644	2	χ	χ	X
ejpam-5051	644	3	,	,	PUNCT
ejpam-5051	644	4	z	z	NOUN
ejpam-5051	644	5	,	,	PUNCT
ejpam-5051	644	6	γ]−1[χ	γ]−1[χ	PROPN
ejpam-5051	644	7	,	,	PUNCT
ejpam-5051	644	8	z	z	PROPN
ejpam-5051	644	9	,	,	PUNCT
ejpam-5051	644	10	γ	γ	X
ejpam-5051	644	11	]	]	X
ejpam-5051	644	12	=	=	PUNCT
ejpam-5051	645	1	[	[	X
ejpam-5051	645	2	χ	χ	X
ejpam-5051	645	3	·	·	PUNCT
ejpam-5051	645	4	γ	γ	X
ejpam-5051	645	5	,	,	PUNCT
ejpam-5051	645	6	z−1	z−1	ADJ
ejpam-5051	645	7	,	,	PUNCT
ejpam-5051	645	8	γ−1][χ	γ−1][χ	ADJ
ejpam-5051	645	9	,	,	PUNCT
ejpam-5051	645	10	z	z	PROPN
ejpam-5051	645	11	,	,	PUNCT
ejpam-5051	645	12	γ	γ	X
ejpam-5051	645	13	]	]	X
ejpam-5051	645	14	=	=	PUNCT
ejpam-5051	646	1	[	[	X
ejpam-5051	646	2	χ	χ	X
ejpam-5051	646	3	·	·	PUNCT
ejpam-5051	646	4	γ	γ	X
ejpam-5051	646	5	,	,	PUNCT
ejpam-5051	646	6	z−1z	z−1z	NOUN
ejpam-5051	646	7	,	,	PUNCT
ejpam-5051	646	8	γ−1γ	γ−1γ	NOUN
ejpam-5051	646	9	]	]	X
ejpam-5051	646	10	=	=	PUNCT
ejpam-5051	647	1	[	[	X
ejpam-5051	647	2	χ	χ	X
ejpam-5051	647	3	·	·	PUNCT
ejpam-5051	647	4	γ	γ	X
ejpam-5051	647	5	,	,	PUNCT
ejpam-5051	647	6	1	1	NUM
ejpam-5051	647	7	,	,	PUNCT
ejpam-5051	647	8	s(γ	s(γ	PROPN
ejpam-5051	647	9	)	)	PUNCT
ejpam-5051	647	10	]	]	PUNCT
ejpam-5051	648	1	r([χ	r([χ	NOUN
ejpam-5051	648	2	,	,	PUNCT
ejpam-5051	648	3	z	z	PROPN
ejpam-5051	648	4	,	,	PUNCT
ejpam-5051	648	5	γ	γ	X
ejpam-5051	648	6	]	]	X
ejpam-5051	648	7	)	)	PUNCT
ejpam-5051	648	8	=	=	PUNCT
ejpam-5051	649	1	[	[	X
ejpam-5051	649	2	χ	χ	X
ejpam-5051	649	3	,	,	PUNCT
ejpam-5051	649	4	z	z	NOUN
ejpam-5051	649	5	,	,	PUNCT
ejpam-5051	649	6	γ][χ	γ][χ	PROPN
ejpam-5051	649	7	,	,	PUNCT
ejpam-5051	649	8	z	z	NOUN
ejpam-5051	649	9	,	,	PUNCT
ejpam-5051	649	10	γ]−1	γ]−1	X
ejpam-5051	649	11	=	=	PUNCT
ejpam-5051	650	1	[	[	X
ejpam-5051	650	2	χ	χ	X
ejpam-5051	650	3	,	,	PUNCT
ejpam-5051	650	4	z	z	NOUN
ejpam-5051	650	5	,	,	PUNCT
ejpam-5051	650	6	γ][χ	γ][χ	NOUN
ejpam-5051	650	7	·	·	PUNCT
ejpam-5051	650	8	γ	γ	X
ejpam-5051	650	9	,	,	PUNCT
ejpam-5051	650	10	z−1	z−1	PROPN
ejpam-5051	650	11	,	,	PUNCT
ejpam-5051	650	12	γ−1	γ−1	PROPN
ejpam-5051	650	13	]	]	X
ejpam-5051	650	14	=	=	PUNCT
ejpam-5051	651	1	[	[	X
ejpam-5051	651	2	χ	χ	X
ejpam-5051	651	3	,	,	PUNCT
ejpam-5051	651	4	zz−1	zz−1	PROPN
ejpam-5051	651	5	,	,	PUNCT
ejpam-5051	651	6	γγ−1	γγ−1	PROPN
ejpam-5051	651	7	]	]	X
ejpam-5051	651	8	=	=	PUNCT
ejpam-5051	652	1	[	[	X
ejpam-5051	652	2	χ	χ	X
ejpam-5051	652	3	,	,	PUNCT
ejpam-5051	652	4	1	1	NUM
ejpam-5051	652	5	,	,	PUNCT
ejpam-5051	652	6	r(γ	r(γ	NOUN
ejpam-5051	652	7	)	)	PUNCT
ejpam-5051	652	8	]	]	PUNCT
ejpam-5051	652	9	.	.	PUNCT
ejpam-5051	653	1	hence	hence	ADV
ejpam-5051	653	2	,	,	PUNCT
ejpam-5051	653	3	[	[	X
ejpam-5051	653	4	χ	χ	X
ejpam-5051	653	5	·	·	PUNCT
ejpam-5051	653	6	γ	γ	X
ejpam-5051	653	7	,	,	PUNCT
ejpam-5051	653	8	1	1	NUM
ejpam-5051	653	9	,	,	PUNCT
ejpam-5051	653	10	s(γ	s(γ	PROPN
ejpam-5051	653	11	)	)	PUNCT
ejpam-5051	653	12	]	]	PUNCT
ejpam-5051	654	1	=	=	PUNCT
ejpam-5051	655	1	[	[	X
ejpam-5051	655	2	χ	χ	X
ejpam-5051	655	3	,	,	PUNCT
ejpam-5051	655	4	1	1	NUM
ejpam-5051	655	5	,	,	PUNCT
ejpam-5051	655	6	r(γ	r(γ	NOUN
ejpam-5051	655	7	)	)	PUNCT
ejpam-5051	655	8	]	]	PUNCT
ejpam-5051	655	9	,	,	PUNCT
ejpam-5051	655	10	that	that	ADV
ejpam-5051	655	11	is	is	ADV
ejpam-5051	655	12	,	,	PUNCT
ejpam-5051	655	13	χ	χ	X
ejpam-5051	655	14	·	·	PUNCT
ejpam-5051	655	15	γ	γ	X
ejpam-5051	655	16	=	=	SYM
ejpam-5051	655	17	χ	χ	NOUN
ejpam-5051	655	18	and	and	CCONJ
ejpam-5051	655	19	r(γ	r(γ	NOUN
ejpam-5051	655	20	)	)	PUNCT
ejpam-5051	656	1	=	=	SYM
ejpam-5051	656	2	s(γ	s(γ	PROPN
ejpam-5051	656	3	)	)	PUNCT
ejpam-5051	656	4	.	.	PUNCT
ejpam-5051	657	1	then	then	ADV
ejpam-5051	657	2	γ	γ	PROPN
ejpam-5051	657	3	=	=	SYM
ejpam-5051	657	4	u	u	PROPN
ejpam-5051	657	5	∈	∈	PROPN
ejpam-5051	657	6	g(0	g(0	PROPN
ejpam-5051	657	7	)	)	PUNCT
ejpam-5051	657	8	.	.	PUNCT
ejpam-5051	658	1	hence	hence	ADV
ejpam-5051	658	2	,	,	PUNCT
ejpam-5051	658	3	the	the	DET
ejpam-5051	658	4	elements	element	NOUN
ejpam-5051	658	5	in	in	ADP
ejpam-5051	658	6	d(0	d(0	NOUN
ejpam-5051	658	7	)	)	PUNCT
ejpam-5051	658	8	will	will	AUX
ejpam-5051	658	9	look	look	VERB
ejpam-5051	658	10	like	like	ADP
ejpam-5051	658	11	[	[	X
ejpam-5051	658	12	χ	χ	X
ejpam-5051	658	13	,	,	PUNCT
ejpam-5051	658	14	1	1	NUM
ejpam-5051	658	15	,	,	PUNCT
ejpam-5051	658	16	u	u	NOUN
ejpam-5051	658	17	]	]	X
ejpam-5051	658	18	.	.	PUNCT
ejpam-5051	659	1	now	now	ADV
ejpam-5051	659	2	,	,	PUNCT
ejpam-5051	659	3	i(â×	i(â×	X
ejpam-5051	659	4	{	{	PUNCT
ejpam-5051	659	5	1	1	NUM
ejpam-5051	659	6	}	}	PUNCT
ejpam-5051	659	7	)	)	PUNCT
ejpam-5051	659	8	=	=	SYM
ejpam-5051	659	9	i(χ	i(χ	PROPN
ejpam-5051	659	10	,	,	PUNCT
ejpam-5051	659	11	1	1	NUM
ejpam-5051	659	12	,	,	PUNCT
ejpam-5051	659	13	u	u	NOUN
ejpam-5051	659	14	)	)	PUNCT
ejpam-5051	659	15	=	=	PUNCT
ejpam-5051	660	1	[	[	X
ejpam-5051	660	2	χ	χ	X
ejpam-5051	660	3	,	,	PUNCT
ejpam-5051	660	4	1	1	NUM
ejpam-5051	660	5	,	,	PUNCT
ejpam-5051	660	6	u	u	NOUN
ejpam-5051	660	7	]	]	X
ejpam-5051	660	8	.	.	PUNCT
ejpam-5051	661	1	therefore	therefore	ADV
ejpam-5051	661	2	,	,	PUNCT
ejpam-5051	661	3	d(0	d(0	NOUN
ejpam-5051	661	4	)	)	PUNCT
ejpam-5051	661	5	=	=	PUNCT
ejpam-5051	662	1	i(â×	i(â×	NOUN
ejpam-5051	662	2	{	{	PUNCT
ejpam-5051	662	3	1	1	NUM
ejpam-5051	662	4	}	}	PUNCT
ejpam-5051	662	5	)	)	PUNCT
ejpam-5051	662	6	.	.	PUNCT
ejpam-5051	663	1	note	note	VERB
ejpam-5051	663	2	that	that	SCONJ
ejpam-5051	663	3	â	â	PROPN
ejpam-5051	663	4	×	×	PROPN
ejpam-5051	663	5	t	t	PROPN
ejpam-5051	663	6	is	be	AUX
ejpam-5051	663	7	the	the	DET
ejpam-5051	663	8	isotropy	isotropy	ADJ
ejpam-5051	663	9	group	group	NOUN
ejpam-5051	663	10	of	of	ADP
ejpam-5051	663	11	â	â	PROPN
ejpam-5051	663	12	∗	∗	NOUN
ejpam-5051	663	13	g	g	PROPN
ejpam-5051	663	14	×	×	PROPN
ejpam-5051	663	15	t	t	NOUN
ejpam-5051	663	16	by	by	ADP
ejpam-5051	663	17	lemma	lemma	PROPN
ejpam-5051	663	18	7	7	NUM
ejpam-5051	663	19	.	.	PUNCT
ejpam-5051	664	1	hence	hence	ADV
ejpam-5051	664	2	,	,	PUNCT
ejpam-5051	664	3	â	â	X
ejpam-5051	664	4	×	×	PROPN
ejpam-5051	664	5	t	t	PROPN
ejpam-5051	664	6	is	be	AUX
ejpam-5051	664	7	a	a	DET
ejpam-5051	664	8	group	group	NOUN
ejpam-5051	664	9	bundle	bundle	NOUN
ejpam-5051	664	10	by	by	ADP
ejpam-5051	664	11	remark	remark	NOUN
ejpam-5051	664	12	1	1	NUM
ejpam-5051	664	13	.	.	PUNCT
ejpam-5051	665	1	then	then	ADV
ejpam-5051	665	2	,	,	PUNCT
ejpam-5051	665	3	define	define	VERB
ejpam-5051	665	4	the	the	DET
ejpam-5051	665	5	sequence	sequence	NOUN
ejpam-5051	665	6	â	â	X
ejpam-5051	665	7	×	×	PROPN
ejpam-5051	665	8	t	t	X
ejpam-5051	666	1	i	i	NOUN
ejpam-5051	666	2	↪	↪	PROPN
ejpam-5051	666	3	→	→	SYM
ejpam-5051	666	4	d	d	X
ejpam-5051	666	5	q	q	X
ejpam-5051	666	6	↪	↪	PROPN
ejpam-5051	666	7	→	→	SYM
ejpam-5051	666	8	â	â	X
ejpam-5051	666	9	⋊	⋊	SYM
ejpam-5051	666	10	r	r	NOUN
ejpam-5051	666	11	where	where	SCONJ
ejpam-5051	666	12	d	d	NOUN
ejpam-5051	666	13	is	be	AUX
ejpam-5051	666	14	a	a	DET
ejpam-5051	666	15	hausdorff	hausdorff	NOUN
ejpam-5051	666	16	étale	étale	NOUN
ejpam-5051	666	17	groupoid	groupoid	NOUN
ejpam-5051	666	18	by	by	ADP
ejpam-5051	666	19	proposition	proposition	NOUN
ejpam-5051	666	20	3	3	NUM
ejpam-5051	666	21	,	,	PUNCT
ejpam-5051	666	22	and	and	CCONJ
ejpam-5051	666	23	the	the	DET
ejpam-5051	666	24	maps	map	NOUN
ejpam-5051	666	25	i	i	PRON
ejpam-5051	666	26	and	and	CCONJ
ejpam-5051	666	27	q	q	NOUN
ejpam-5051	666	28	are	be	AUX
ejpam-5051	666	29	defined	define	VERB
ejpam-5051	666	30	by	by	ADP
ejpam-5051	666	31	i((χ	i((χ	NOUN
ejpam-5051	666	32	,	,	PUNCT
ejpam-5051	666	33	z	z	PROPN
ejpam-5051	666	34	,	,	PUNCT
ejpam-5051	666	35	u	u	NOUN
ejpam-5051	666	36	)	)	PUNCT
ejpam-5051	666	37	)	)	PUNCT
ejpam-5051	667	1	=	=	PUNCT
ejpam-5051	668	1	[	[	X
ejpam-5051	668	2	χ	χ	X
ejpam-5051	668	3	,	,	PUNCT
ejpam-5051	668	4	z	z	NOUN
ejpam-5051	668	5	,	,	PUNCT
ejpam-5051	668	6	u	u	NOUN
ejpam-5051	668	7	]	]	X
ejpam-5051	668	8	and	and	CCONJ
ejpam-5051	668	9	q([χ	q([χ	NOUN
ejpam-5051	668	10	,	,	PUNCT
ejpam-5051	668	11	z	z	PROPN
ejpam-5051	668	12	,	,	PUNCT
ejpam-5051	668	13	γ	γ	X
ejpam-5051	668	14	]	]	X
ejpam-5051	668	15	)	)	PUNCT
ejpam-5051	668	16	=	=	SYM
ejpam-5051	668	17	(	(	PUNCT
ejpam-5051	668	18	χ	χ	NOUN
ejpam-5051	668	19	,	,	PUNCT
ejpam-5051	668	20	γ̇	γ̇	NOUN
ejpam-5051	668	21	)	)	PUNCT
ejpam-5051	668	22	,	,	PUNCT
ejpam-5051	668	23	respectively	respectively	ADV
ejpam-5051	668	24	.	.	PUNCT
ejpam-5051	669	1	lemma	lemma	PROPN
ejpam-5051	669	2	9	9	NUM
ejpam-5051	669	3	.	.	PUNCT
ejpam-5051	670	1	the	the	DET
ejpam-5051	670	2	maps	map	NOUN
ejpam-5051	670	3	i	i	PRON
ejpam-5051	670	4	and	and	CCONJ
ejpam-5051	670	5	q	q	NOUN
ejpam-5051	670	6	are	be	AUX
ejpam-5051	670	7	continuous	continuous	ADJ
ejpam-5051	670	8	groupoid	groupoid	PROPN
ejpam-5051	670	9	homomorphism	homomorphism	NOUN
ejpam-5051	670	10	that	that	PRON
ejpam-5051	670	11	restricts	restrict	VERB
ejpam-5051	670	12	to	to	ADP
ejpam-5051	670	13	homeomorphism	homeomorphism	PROPN
ejpam-5051	670	14	of	of	ADP
ejpam-5051	670	15	unit	unit	NOUN
ejpam-5051	670	16	spaces	space	VERB
ejpam-5051	670	17	.	.	PUNCT
ejpam-5051	671	1	proof	proof	NOUN
ejpam-5051	671	2	.	.	PUNCT
ejpam-5051	672	1	let	let	VERB
ejpam-5051	672	2	(	(	PUNCT
ejpam-5051	672	3	χ	χ	X
ejpam-5051	672	4	,	,	PUNCT
ejpam-5051	672	5	z	z	PROPN
ejpam-5051	672	6	,	,	PUNCT
ejpam-5051	672	7	u	u	NOUN
ejpam-5051	672	8	)	)	PUNCT
ejpam-5051	672	9	,	,	PUNCT
ejpam-5051	672	10	(	(	PUNCT
ejpam-5051	672	11	χ′	χ′	PROPN
ejpam-5051	672	12	,	,	PUNCT
ejpam-5051	672	13	z′	z′	PROPN
ejpam-5051	672	14	,	,	PUNCT
ejpam-5051	672	15	u′	u′	SYM
ejpam-5051	672	16	)	)	PUNCT
ejpam-5051	672	17	∈	∈	PROPN
ejpam-5051	672	18	â×t	â×t	ADP
ejpam-5051	672	19	such	such	ADJ
ejpam-5051	672	20	that	that	SCONJ
ejpam-5051	672	21	(	(	PUNCT
ejpam-5051	672	22	χ	χ	X
ejpam-5051	672	23	,	,	PUNCT
ejpam-5051	672	24	z	z	NOUN
ejpam-5051	672	25	,	,	PUNCT
ejpam-5051	672	26	u	u	NOUN
ejpam-5051	672	27	)	)	PUNCT
ejpam-5051	672	28	=	=	SYM
ejpam-5051	672	29	(	(	PUNCT
ejpam-5051	672	30	χ′	χ′	PROPN
ejpam-5051	672	31	,	,	PUNCT
ejpam-5051	672	32	z′	z′	PROPN
ejpam-5051	672	33	,	,	PUNCT
ejpam-5051	672	34	u′	u′	PROPN
ejpam-5051	672	35	)	)	PUNCT
ejpam-5051	672	36	.	.	PUNCT
ejpam-5051	673	1	then	then	ADV
ejpam-5051	673	2	[	[	X
ejpam-5051	673	3	χ	χ	X
ejpam-5051	673	4	,	,	PUNCT
ejpam-5051	673	5	z	z	NOUN
ejpam-5051	673	6	,	,	PUNCT
ejpam-5051	673	7	u	u	NOUN
ejpam-5051	673	8	]	]	X
ejpam-5051	673	9	=	=	PUNCT
ejpam-5051	674	1	[	[	X
ejpam-5051	674	2	χ′	χ′	PROPN
ejpam-5051	674	3	,	,	PUNCT
ejpam-5051	674	4	z′	z′	PROPN
ejpam-5051	674	5	,	,	PUNCT
ejpam-5051	674	6	u′	u′	PROPN
ejpam-5051	674	7	]	]	PUNCT
ejpam-5051	674	8	.	.	PUNCT
ejpam-5051	675	1	thus	thus	ADV
ejpam-5051	675	2	,	,	PUNCT
ejpam-5051	675	3	i((χ	i((χ	NOUN
ejpam-5051	675	4	,	,	PUNCT
ejpam-5051	675	5	z	z	PROPN
ejpam-5051	675	6	,	,	PUNCT
ejpam-5051	675	7	u	u	NOUN
ejpam-5051	675	8	)	)	PUNCT
ejpam-5051	675	9	)	)	PUNCT
ejpam-5051	676	1	=	=	SYM
ejpam-5051	676	2	i((χ′	i((χ′	PROPN
ejpam-5051	676	3	,	,	PUNCT
ejpam-5051	676	4	z′	z′	PROPN
ejpam-5051	676	5	,	,	PUNCT
ejpam-5051	676	6	u′	u′	PROPN
ejpam-5051	676	7	)	)	PUNCT
ejpam-5051	676	8	)	)	PUNCT
ejpam-5051	677	1	and	and	CCONJ
ejpam-5051	677	2	i	i	PRON
ejpam-5051	677	3	is	be	AUX
ejpam-5051	677	4	well	well	ADV
ejpam-5051	677	5	-	-	PUNCT
ejpam-5051	677	6	defined	define	VERB
ejpam-5051	677	7	.	.	PUNCT
ejpam-5051	678	1	let	let	VERB
ejpam-5051	678	2	[	[	X
ejpam-5051	678	3	χ1	χ1	NOUN
ejpam-5051	678	4	,	,	PUNCT
ejpam-5051	678	5	z1	z1	NOUN
ejpam-5051	678	6	,	,	PUNCT
ejpam-5051	678	7	γ1	γ1	NOUN
ejpam-5051	678	8	]	]	PUNCT
ejpam-5051	678	9	and	and	CCONJ
ejpam-5051	678	10	[	[	X
ejpam-5051	678	11	χ2	χ2	PROPN
ejpam-5051	678	12	,	,	PUNCT
ejpam-5051	678	13	z2	z2	PROPN
ejpam-5051	678	14	,	,	PUNCT
ejpam-5051	678	15	γ2	γ2	PROPN
ejpam-5051	678	16	]	]	PUNCT
ejpam-5051	678	17	be	be	VERB
ejpam-5051	678	18	elements	element	NOUN
ejpam-5051	678	19	in	in	ADP
ejpam-5051	678	20	d	d	PROPN
ejpam-5051	678	21	such	such	ADJ
ejpam-5051	678	22	that	that	DET
ejpam-5051	678	23	q[χ1	q[χ1	NOUN
ejpam-5051	678	24	,	,	PUNCT
ejpam-5051	678	25	z1	z1	PROPN
ejpam-5051	678	26	,	,	PUNCT
ejpam-5051	678	27	γ1	γ1	PROPN
ejpam-5051	678	28	]	]	PUNCT
ejpam-5051	678	29	̸=	̸=	PROPN
ejpam-5051	678	30	q[χ2	q[χ2	NOUN
ejpam-5051	678	31	,	,	PUNCT
ejpam-5051	678	32	z2	z2	PROPN
ejpam-5051	678	33	,	,	PUNCT
ejpam-5051	678	34	γ2	γ2	PROPN
ejpam-5051	678	35	]	]	PUNCT
ejpam-5051	678	36	.	.	PUNCT
ejpam-5051	679	1	then	then	ADV
ejpam-5051	679	2	(	(	PUNCT
ejpam-5051	679	3	χ1	χ1	NOUN
ejpam-5051	679	4	,	,	PUNCT
ejpam-5051	679	5	γ̇1	γ̇1	PROPN
ejpam-5051	679	6	)	)	PUNCT
ejpam-5051	679	7	̸=	̸=	PROPN
ejpam-5051	679	8	(	(	PUNCT
ejpam-5051	679	9	χ2	χ2	PROPN
ejpam-5051	679	10	,	,	PUNCT
ejpam-5051	679	11	γ̇2	γ̇2	PROPN
ejpam-5051	679	12	)	)	PUNCT
ejpam-5051	679	13	.	.	PUNCT
ejpam-5051	680	1	if	if	SCONJ
ejpam-5051	680	2	χ1	χ1	PROPN
ejpam-5051	680	3	̸=	̸=	PROPN
ejpam-5051	680	4	χ2	χ2	PROPN
ejpam-5051	680	5	,	,	PUNCT
ejpam-5051	680	6	then	then	ADV
ejpam-5051	680	7	(	(	PUNCT
ejpam-5051	680	8	χ1	χ1	NOUN
ejpam-5051	680	9	,	,	PUNCT
ejpam-5051	680	10	z1	z1	NOUN
ejpam-5051	680	11	,	,	PUNCT
ejpam-5051	680	12	γ1	γ1	PROPN
ejpam-5051	680	13	)	)	PUNCT
ejpam-5051	680	14	≁	≁	PROPN
ejpam-5051	680	15	(	(	PUNCT
ejpam-5051	680	16	χ2	χ2	PROPN
ejpam-5051	680	17	,	,	PUNCT
ejpam-5051	680	18	z2	z2	PROPN
ejpam-5051	680	19	,	,	PUNCT
ejpam-5051	680	20	γ	γ	X
ejpam-5051	680	21	,	,	PUNCT
ejpam-5051	680	22	)	)	PUNCT
ejpam-5051	680	23	.	.	PUNCT
ejpam-5051	681	1	if	if	SCONJ
ejpam-5051	681	2	γ̇1	γ̇1	PROPN
ejpam-5051	681	3	̸=	̸=	PROPN
ejpam-5051	681	4	γ̇2	γ̇2	PROPN
ejpam-5051	681	5	,	,	PUNCT
ejpam-5051	681	6	then	then	ADV
ejpam-5051	681	7	γ1a	γ1a	PROPN
ejpam-5051	681	8	̸=	̸=	PROPN
ejpam-5051	681	9	γ2a	γ2a	NOUN
ejpam-5051	681	10	.	.	PUNCT
ejpam-5051	682	1	since	since	SCONJ
ejpam-5051	682	2	au	au	PROPN
ejpam-5051	682	3	⊂	⊂	PROPN
ejpam-5051	682	4	a	a	X
ejpam-5051	682	5	,	,	PUNCT
ejpam-5051	682	6	then	then	ADV
ejpam-5051	682	7	we	we	PRON
ejpam-5051	682	8	can	can	AUX
ejpam-5051	682	9	not	not	PART
ejpam-5051	682	10	find	find	VERB
ejpam-5051	682	11	a	a	DET
ejpam-5051	682	12	∈	∈	NOUN
ejpam-5051	682	13	au	au	ADP
ejpam-5051	682	14	such	such	ADJ
ejpam-5051	682	15	that	that	DET
ejpam-5051	682	16	γ1	γ1	NOUN
ejpam-5051	682	17	=	=	PUNCT
ejpam-5051	682	18	a	a	DET
ejpam-5051	682	19	·	·	PUNCT
ejpam-5051	682	20	γ2	γ2	NOUN
ejpam-5051	682	21	.	.	PUNCT
ejpam-5051	683	1	hence	hence	ADV
ejpam-5051	683	2	,	,	PUNCT
ejpam-5051	683	3	(	(	PUNCT
ejpam-5051	683	4	χ1	χ1	NOUN
ejpam-5051	683	5	,	,	PUNCT
ejpam-5051	683	6	z1	z1	NOUN
ejpam-5051	683	7	,	,	PUNCT
ejpam-5051	683	8	γ1	γ1	PROPN
ejpam-5051	683	9	)	)	PUNCT
ejpam-5051	683	10	≁	≁	PROPN
ejpam-5051	683	11	(	(	PUNCT
ejpam-5051	683	12	χ2	χ2	PROPN
ejpam-5051	683	13	,	,	PUNCT
ejpam-5051	683	14	z2	z2	PROPN
ejpam-5051	683	15	,	,	PUNCT
ejpam-5051	683	16	γ2	γ2	NOUN
ejpam-5051	683	17	)	)	PUNCT
ejpam-5051	683	18	.	.	PUNCT
ejpam-5051	684	1	in	in	ADP
ejpam-5051	684	2	both	both	DET
ejpam-5051	684	3	cases	case	NOUN
ejpam-5051	684	4	(	(	PUNCT
ejpam-5051	684	5	χ1	χ1	NOUN
ejpam-5051	684	6	,	,	PUNCT
ejpam-5051	684	7	z1	z1	NOUN
ejpam-5051	684	8	,	,	PUNCT
ejpam-5051	684	9	γ1	γ1	PROPN
ejpam-5051	684	10	)	)	PUNCT
ejpam-5051	684	11	≁	≁	PROPN
ejpam-5051	684	12	(	(	PUNCT
ejpam-5051	684	13	χ2	χ2	PROPN
ejpam-5051	684	14	,	,	PUNCT
ejpam-5051	684	15	z2	z2	PROPN
ejpam-5051	684	16	,	,	PUNCT
ejpam-5051	684	17	γ2	γ2	PROPN
ejpam-5051	684	18	)	)	PUNCT
ejpam-5051	684	19	which	which	PRON
ejpam-5051	684	20	means	mean	VERB
ejpam-5051	684	21	that	that	SCONJ
ejpam-5051	685	1	[	[	X
ejpam-5051	685	2	χ1	χ1	NOUN
ejpam-5051	685	3	,	,	PUNCT
ejpam-5051	685	4	z1	z1	NOUN
ejpam-5051	685	5	,	,	PUNCT
ejpam-5051	685	6	γ1	γ1	NOUN
ejpam-5051	685	7	]	]	PUNCT
ejpam-5051	685	8	̸=	̸=	PROPN
ejpam-5051	685	9	[	[	X
ejpam-5051	685	10	χ2	χ2	PROPN
ejpam-5051	685	11	,	,	PUNCT
ejpam-5051	685	12	z2	z2	PROPN
ejpam-5051	685	13	,	,	PUNCT
ejpam-5051	685	14	γ2	γ2	PROPN
ejpam-5051	685	15	]	]	PUNCT
ejpam-5051	685	16	.	.	PUNCT
ejpam-5051	686	1	thus	thus	ADV
ejpam-5051	686	2	,	,	PUNCT
ejpam-5051	686	3	q	q	PROPN
ejpam-5051	686	4	is	be	AUX
ejpam-5051	686	5	well	well	ADV
ejpam-5051	686	6	-	-	PUNCT
ejpam-5051	686	7	defined	define	VERB
ejpam-5051	686	8	.	.	PUNCT
ejpam-5051	687	1	we	we	PRON
ejpam-5051	687	2	need	need	VERB
ejpam-5051	687	3	â	â	PROPN
ejpam-5051	687	4	×	×	PROPN
ejpam-5051	687	5	t	t	PROPN
ejpam-5051	687	6	⊂	⊂	PROPN
ejpam-5051	687	7	â	â	ADP
ejpam-5051	687	8	∗	∗	VERB
ejpam-5051	687	9	g	g	PROPN
ejpam-5051	687	10	×	×	PROPN
ejpam-5051	687	11	t	t	PROPN
ejpam-5051	687	12	to	to	PART
ejpam-5051	687	13	show	show	VERB
ejpam-5051	687	14	that	that	SCONJ
ejpam-5051	687	15	i	i	PRON
ejpam-5051	687	16	is	be	AUX
ejpam-5051	687	17	continuous	continuous	ADJ
ejpam-5051	687	18	.	.	PUNCT
ejpam-5051	688	1	let	let	VERB
ejpam-5051	688	2	(	(	PUNCT
ejpam-5051	688	3	χ	χ	X
ejpam-5051	688	4	,	,	PUNCT
ejpam-5051	688	5	z	z	NOUN
ejpam-5051	688	6	,	,	PUNCT
ejpam-5051	688	7	u	u	NOUN
ejpam-5051	688	8	)	)	PUNCT
ejpam-5051	688	9	∈	∈	PROPN
ejpam-5051	688	10	â	â	X
ejpam-5051	688	11	×	×	PROPN
ejpam-5051	688	12	t	t	NOUN
ejpam-5051	688	13	where	where	SCONJ
ejpam-5051	688	14	(	(	PUNCT
ejpam-5051	688	15	χ	χ	X
ejpam-5051	688	16	,	,	PUNCT
ejpam-5051	688	17	u	u	NOUN
ejpam-5051	688	18	)	)	PUNCT
ejpam-5051	688	19	∈	∈	PROPN
ejpam-5051	688	20	â	â	ADJ
ejpam-5051	688	21	,	,	PUNCT
ejpam-5051	688	22	and	and	CCONJ
ejpam-5051	688	23	u	u	PROPN
ejpam-5051	688	24	∈	∈	PROPN
ejpam-5051	688	25	g(0	g(0	PROPN
ejpam-5051	688	26	)	)	PUNCT
ejpam-5051	688	27	.	.	PUNCT
ejpam-5051	689	1	since	since	SCONJ
ejpam-5051	689	2	g(0	g(0	PROPN
ejpam-5051	689	3	)	)	PUNCT
ejpam-5051	689	4	⊂	⊂	PROPN
ejpam-5051	689	5	g	g	PROPN
ejpam-5051	689	6	,	,	PUNCT
ejpam-5051	689	7	then	then	ADV
ejpam-5051	689	8	(	(	PUNCT
ejpam-5051	689	9	χ	χ	X
ejpam-5051	689	10	,	,	PUNCT
ejpam-5051	689	11	z	z	NOUN
ejpam-5051	689	12	,	,	PUNCT
ejpam-5051	689	13	u	u	NOUN
ejpam-5051	689	14	)	)	PUNCT
ejpam-5051	689	15	∈	∈	PROPN
ejpam-5051	689	16	â	â	ADP
ejpam-5051	689	17	∗	∗	VERB
ejpam-5051	689	18	g	g	PROPN
ejpam-5051	689	19	×	×	PROPN
ejpam-5051	689	20	t	t	PROPN
ejpam-5051	689	21	.	.	PUNCT
ejpam-5051	690	1	since	since	SCONJ
ejpam-5051	690	2	πd	πd	PRON
ejpam-5051	690	3	:	:	PUNCT
ejpam-5051	690	4	â	â	X
ejpam-5051	690	5	∗	∗	NOUN
ejpam-5051	690	6	g	g	PROPN
ejpam-5051	690	7	×	×	PROPN
ejpam-5051	690	8	t	t	PROPN
ejpam-5051	690	9	→	→	PUNCT
ejpam-5051	690	10	d	d	NOUN
ejpam-5051	690	11	is	be	AUX
ejpam-5051	690	12	continuous	continuous	ADJ
ejpam-5051	690	13	,	,	PUNCT
ejpam-5051	690	14	i	i	PRON
ejpam-5051	690	15	=	=	PUNCT
ejpam-5051	690	16	πd|â×t	πd|â×t	ADV
ejpam-5051	690	17	:	:	PUNCT
ejpam-5051	690	18	â×	â×	PROPN
ejpam-5051	690	19	t	t	PROPN
ejpam-5051	690	20	→	→	PUNCT
ejpam-5051	690	21	d	d	X
ejpam-5051	690	22	is	be	AUX
ejpam-5051	690	23	also	also	ADV
ejpam-5051	690	24	continuous	continuous	ADJ
ejpam-5051	690	25	.	.	PUNCT
ejpam-5051	691	1	let	let	VERB
ejpam-5051	691	2	q	q	PRON
ejpam-5051	691	3	◦	◦	VERB
ejpam-5051	691	4	πd	πd	ADP
ejpam-5051	691	5	:	:	PUNCT
ejpam-5051	691	6	â	â	X
ejpam-5051	691	7	∗	∗	NOUN
ejpam-5051	691	8	g	g	PROPN
ejpam-5051	691	9	×	×	PROPN
ejpam-5051	691	10	t	t	PROPN
ejpam-5051	691	11	→	→	PUNCT
ejpam-5051	691	12	â	â	X
ejpam-5051	691	13	⋊	⋊	SYM
ejpam-5051	691	14	r	r	NOUN
ejpam-5051	691	15	be	be	AUX
ejpam-5051	691	16	defined	define	VERB
ejpam-5051	691	17	by	by	ADP
ejpam-5051	691	18	(	(	PUNCT
ejpam-5051	691	19	q	q	PART
ejpam-5051	691	20	◦	◦	NOUN
ejpam-5051	691	21	πd)(χ	πd)(χ	PROPN
ejpam-5051	691	22	,	,	PUNCT
ejpam-5051	691	23	z	z	PROPN
ejpam-5051	691	24	,	,	PUNCT
ejpam-5051	691	25	γ	γ	NOUN
ejpam-5051	691	26	)	)	PUNCT
ejpam-5051	691	27	=	=	SYM
ejpam-5051	692	1	q(πd(χ	q(πd(χ	PROPN
ejpam-5051	692	2	,	,	PUNCT
ejpam-5051	692	3	z	z	PROPN
ejpam-5051	692	4	,	,	PUNCT
ejpam-5051	692	5	γ	γ	NOUN
ejpam-5051	692	6	)	)	PUNCT
ejpam-5051	692	7	)	)	PUNCT
ejpam-5051	693	1	and	and	CCONJ
ejpam-5051	693	2	let	let	VERB
ejpam-5051	693	3	u	u	PRON
ejpam-5051	693	4	be	be	AUX
ejpam-5051	693	5	an	an	DET
ejpam-5051	693	6	open	open	ADJ
ejpam-5051	693	7	subset	subset	NOUN
ejpam-5051	693	8	of	of	ADP
ejpam-5051	693	9	â	â	DET
ejpam-5051	693	10	⋊	⋊	PROPN
ejpam-5051	693	11	r.	r.	NOUN
ejpam-5051	693	12	then	then	ADV
ejpam-5051	693	13	u	u	X
ejpam-5051	693	14	=	=	PUNCT
ejpam-5051	693	15	(	(	PUNCT
ejpam-5051	693	16	a	a	DET
ejpam-5051	693	17	×	×	PROPN
ejpam-5051	693	18	b	b	NOUN
ejpam-5051	693	19	)	)	PUNCT
ejpam-5051	693	20	∩	∩	NOUN
ejpam-5051	693	21	â	â	ADP
ejpam-5051	693	22	⋊	⋊	SYM
ejpam-5051	693	23	r	r	NOUN
ejpam-5051	693	24	where	where	SCONJ
ejpam-5051	693	25	a	a	DET
ejpam-5051	693	26	×	×	PROPN
ejpam-5051	693	27	b	b	NOUN
ejpam-5051	693	28	is	be	AUX
ejpam-5051	693	29	open	open	ADJ
ejpam-5051	693	30	in	in	ADP
ejpam-5051	693	31	â	â	PROPN
ejpam-5051	693	32	×	×	PROPN
ejpam-5051	693	33	r.	r.	PROPN
ejpam-5051	693	34	let	let	VERB
ejpam-5051	693	35	(	(	PUNCT
ejpam-5051	693	36	χ	χ	X
ejpam-5051	693	37	,	,	PUNCT
ejpam-5051	693	38	z	z	PROPN
ejpam-5051	693	39	,	,	PUNCT
ejpam-5051	693	40	γ	γ	NOUN
ejpam-5051	693	41	)	)	PUNCT
ejpam-5051	693	42	∈	∈	PROPN
ejpam-5051	693	43	(	(	PUNCT
ejpam-5051	693	44	q	q	NOUN
ejpam-5051	693	45	◦	◦	NOUN
ejpam-5051	693	46	πd	πd	NOUN
ejpam-5051	693	47	)	)	PUNCT
ejpam-5051	693	48	−1(u	−1(u	NOUN
ejpam-5051	693	49	)	)	PUNCT
ejpam-5051	693	50	.	.	PUNCT
ejpam-5051	694	1	then	then	ADV
ejpam-5051	694	2	q	q	X
ejpam-5051	694	3	◦	◦	NOUN
ejpam-5051	694	4	πd(χ	πd(χ	PUNCT
ejpam-5051	694	5	,	,	PUNCT
ejpam-5051	694	6	z	z	NOUN
ejpam-5051	694	7	,	,	PUNCT
ejpam-5051	694	8	γ	γ	NOUN
ejpam-5051	694	9	)	)	PUNCT
ejpam-5051	694	10	∈	∈	PROPN
ejpam-5051	694	11	u	u	NOUN
ejpam-5051	694	12	,	,	PUNCT
ejpam-5051	694	13	that	that	ADV
ejpam-5051	694	14	is	is	ADV
ejpam-5051	694	15	,	,	PUNCT
ejpam-5051	694	16	q(πd(χ	q(πd(χ	PROPN
ejpam-5051	694	17	,	,	PUNCT
ejpam-5051	694	18	z	z	PROPN
ejpam-5051	694	19	,	,	PUNCT
ejpam-5051	694	20	γ	γ	NOUN
ejpam-5051	694	21	)	)	PUNCT
ejpam-5051	694	22	)	)	PUNCT
ejpam-5051	695	1	=	=	PUNCT
ejpam-5051	695	2	q([χ	q([χ	NOUN
ejpam-5051	695	3	,	,	PUNCT
ejpam-5051	695	4	z	z	PROPN
ejpam-5051	695	5	,	,	PUNCT
ejpam-5051	695	6	γ	γ	X
ejpam-5051	695	7	]	]	X
ejpam-5051	695	8	)	)	PUNCT
ejpam-5051	695	9	=	=	SYM
ejpam-5051	695	10	(	(	PUNCT
ejpam-5051	695	11	χ	χ	X
ejpam-5051	695	12	,	,	PUNCT
ejpam-5051	695	13	γ̇	γ̇	NOUN
ejpam-5051	695	14	)	)	PUNCT
ejpam-5051	695	15	∈	∈	NOUN
ejpam-5051	695	16	a×b∩	a×b∩	NOUN
ejpam-5051	695	17	â⋊r	â⋊r	NOUN
ejpam-5051	695	18	.	.	PUNCT
ejpam-5051	696	1	then	then	ADV
ejpam-5051	696	2	(	(	PUNCT
ejpam-5051	696	3	χ	χ	X
ejpam-5051	696	4	,	,	PUNCT
ejpam-5051	696	5	γ̇	γ̇	NOUN
ejpam-5051	696	6	)	)	PUNCT
ejpam-5051	696	7	∈	∈	PROPN
ejpam-5051	696	8	a×b	a×b	PROPN
ejpam-5051	696	9	,	,	PUNCT
ejpam-5051	696	10	that	that	ADV
ejpam-5051	696	11	is	is	ADV
ejpam-5051	696	12	,	,	PUNCT
ejpam-5051	696	13	χ	χ	PROPN
ejpam-5051	696	14	∈	∈	PROPN
ejpam-5051	696	15	a	a	PRON
ejpam-5051	696	16	and	and	CCONJ
ejpam-5051	696	17	γ̇	γ̇	PROPN
ejpam-5051	696	18	∈	∈	PROPN
ejpam-5051	696	19	b.	b.	PROPN
ejpam-5051	696	20	since	since	SCONJ
ejpam-5051	696	21	πr	πr	PRON
ejpam-5051	696	22	is	be	AUX
ejpam-5051	696	23	continuous	continuous	ADJ
ejpam-5051	696	24	,	,	PUNCT
ejpam-5051	696	25	π−1	π−1	PROPN
ejpam-5051	696	26	r	r	NOUN
ejpam-5051	696	27	(	(	PUNCT
ejpam-5051	696	28	b	b	NOUN
ejpam-5051	696	29	)	)	PUNCT
ejpam-5051	696	30	is	be	AUX
ejpam-5051	696	31	open	open	ADJ
ejpam-5051	696	32	in	in	ADP
ejpam-5051	696	33	g	g	NOUN
ejpam-5051	696	34	containing	contain	VERB
ejpam-5051	696	35	γ	γ	X
ejpam-5051	696	36	.	.	PUNCT
ejpam-5051	697	1	let	let	VERB
ejpam-5051	697	2	m	m	VERB
ejpam-5051	697	3	=	=	VERB
ejpam-5051	697	4	a	a	DET
ejpam-5051	697	5	∗b2	∗b2	PROPN
ejpam-5051	697	6	×	×	NOUN
ejpam-5051	697	7	{	{	PUNCT
ejpam-5051	697	8	z	z	NOUN
ejpam-5051	697	9	}	}	PUNCT
ejpam-5051	697	10	=	=	SYM
ejpam-5051	697	11	{	{	PUNCT
ejpam-5051	697	12	(	(	PUNCT
ejpam-5051	697	13	χ	χ	NOUN
ejpam-5051	697	14	,	,	PUNCT
ejpam-5051	697	15	z	z	PROPN
ejpam-5051	697	16	,	,	PUNCT
ejpam-5051	697	17	γ	γ	PROPN
ejpam-5051	697	18	)	)	PUNCT
ejpam-5051	697	19	∈	∈	PROPN
ejpam-5051	697	20	â	â	ADP
ejpam-5051	697	21	∗	∗	NOUN
ejpam-5051	697	22	g	g	PROPN
ejpam-5051	697	23	×	×	PROPN
ejpam-5051	697	24	t	t	PROPN
ejpam-5051	697	25	:	:	PUNCT
ejpam-5051	697	26	πd(χ	πd(χ	NUM
ejpam-5051	697	27	,	,	PUNCT
ejpam-5051	697	28	z	z	NOUN
ejpam-5051	697	29	,	,	PUNCT
ejpam-5051	697	30	γ	γ	NOUN
ejpam-5051	697	31	)	)	PUNCT
ejpam-5051	697	32	∈	∈	PROPN
ejpam-5051	697	33	(	(	PUNCT
ejpam-5051	697	34	q	q	NOUN
ejpam-5051	697	35	◦	◦	NOUN
ejpam-5051	697	36	πd)−1(u	πd)−1(u	PROPN
ejpam-5051	697	37	)	)	PUNCT
ejpam-5051	697	38	}	}	PUNCT
ejpam-5051	697	39	.	.	PUNCT
ejpam-5051	698	1	r.	r.	PROPN
ejpam-5051	698	2	s.	s.	PROPN
ejpam-5051	698	3	bongcawel	bongcawel	PROPN
ejpam-5051	699	1	et	et	PROPN
ejpam-5051	699	2	al	al	PROPN
ejpam-5051	699	3	.	.	PUNCT
ejpam-5051	699	4	/	/	SYM
ejpam-5051	699	5	eur	eur	PROPN
ejpam-5051	699	6	.	.	PUNCT
ejpam-5051	700	1	j.	j.	PROPN
ejpam-5051	700	2	pure	pure	PROPN
ejpam-5051	700	3	appl	appl	PROPN
ejpam-5051	700	4	.	.	PROPN
ejpam-5051	700	5	math	math	PROPN
ejpam-5051	700	6	,	,	PUNCT
ejpam-5051	700	7	17	17	NUM
ejpam-5051	700	8	(	(	PUNCT
ejpam-5051	700	9	1	1	NUM
ejpam-5051	700	10	)	)	PUNCT
ejpam-5051	700	11	(	(	PUNCT
ejpam-5051	700	12	2024	2024	NUM
ejpam-5051	700	13	)	)	PUNCT
ejpam-5051	700	14	,	,	PUNCT
ejpam-5051	700	15	519	519	NUM
ejpam-5051	700	16	-	-	SYM
ejpam-5051	700	17	545	545	NUM
ejpam-5051	700	18	536	536	NUM
ejpam-5051	700	19	then	then	ADV
ejpam-5051	700	20	m	m	VERB
ejpam-5051	700	21	⊆	⊆	NUM
ejpam-5051	700	22	(	(	PUNCT
ejpam-5051	700	23	q	q	NOUN
ejpam-5051	700	24	◦	◦	NOUN
ejpam-5051	700	25	πd)−1(u	πd)−1(u	PROPN
ejpam-5051	700	26	)	)	PUNCT
ejpam-5051	700	27	and	and	CCONJ
ejpam-5051	700	28	m	m	PROPN
ejpam-5051	700	29	is	be	AUX
ejpam-5051	700	30	open	open	ADJ
ejpam-5051	700	31	in	in	ADP
ejpam-5051	700	32	â	â	PROPN
ejpam-5051	700	33	∗	∗	NOUN
ejpam-5051	700	34	g	g	PROPN
ejpam-5051	700	35	×	×	PROPN
ejpam-5051	700	36	t	t	PROPN
ejpam-5051	700	37	.	.	PUNCT
ejpam-5051	701	1	thus	thus	ADV
ejpam-5051	701	2	,	,	PUNCT
ejpam-5051	701	3	(	(	PUNCT
ejpam-5051	701	4	q	q	PUNCT
ejpam-5051	701	5	◦	◦	NOUN
ejpam-5051	701	6	πd)−1(u	πd)−1(u	PROPN
ejpam-5051	701	7	)	)	PUNCT
ejpam-5051	701	8	is	be	AUX
ejpam-5051	701	9	open	open	ADJ
ejpam-5051	701	10	and	and	CCONJ
ejpam-5051	701	11	q	q	ADJ
ejpam-5051	701	12	◦	◦	NOUN
ejpam-5051	701	13	πd	πd	SCONJ
ejpam-5051	701	14	is	be	AUX
ejpam-5051	701	15	continuous	continuous	ADJ
ejpam-5051	701	16	.	.	PUNCT
ejpam-5051	702	1	since	since	SCONJ
ejpam-5051	702	2	πd	πd	ADV
ejpam-5051	702	3	is	be	AUX
ejpam-5051	702	4	continuous	continuous	ADJ
ejpam-5051	702	5	,	,	PUNCT
ejpam-5051	702	6	q	q	X
ejpam-5051	702	7	is	be	AUX
ejpam-5051	702	8	continuous	continuous	ADJ
ejpam-5051	702	9	.	.	PUNCT
ejpam-5051	703	1	consider	consider	VERB
ejpam-5051	703	2	i×	i×	PROPN
ejpam-5051	704	1	i	i	PRON
ejpam-5051	704	2	:	:	PUNCT
ejpam-5051	704	3	(	(	PUNCT
ejpam-5051	704	4	â×	â×	PROPN
ejpam-5051	704	5	t	t	PROPN
ejpam-5051	704	6	)	)	PUNCT
ejpam-5051	704	7	(	(	PUNCT
ejpam-5051	704	8	2	2	NUM
ejpam-5051	704	9	)	)	PUNCT
ejpam-5051	704	10	→	→	SYM
ejpam-5051	704	11	d(2	d(2	PROPN
ejpam-5051	704	12	)	)	PUNCT
ejpam-5051	704	13	defined	define	VERB
ejpam-5051	704	14	by	by	ADP
ejpam-5051	704	15	(	(	PUNCT
ejpam-5051	704	16	i×	i×	PROPN
ejpam-5051	704	17	i)(((χ	i)(((χ	PROPN
ejpam-5051	704	18	,	,	PUNCT
ejpam-5051	704	19	z	z	PROPN
ejpam-5051	704	20	,	,	PUNCT
ejpam-5051	704	21	u	u	NOUN
ejpam-5051	704	22	)	)	PUNCT
ejpam-5051	704	23	,	,	PUNCT
ejpam-5051	704	24	(	(	PUNCT
ejpam-5051	704	25	χ′	χ′	PROPN
ejpam-5051	704	26	,	,	PUNCT
ejpam-5051	704	27	z′	z′	PROPN
ejpam-5051	704	28	,	,	PUNCT
ejpam-5051	704	29	u′	u′	PROPN
ejpam-5051	704	30	)	)	PUNCT
ejpam-5051	704	31	)	)	PUNCT
ejpam-5051	704	32	)	)	PUNCT
ejpam-5051	705	1	=	=	PUNCT
ejpam-5051	705	2	(	(	PUNCT
ejpam-5051	705	3	(	(	PUNCT
ejpam-5051	705	4	[	[	X
ejpam-5051	705	5	χ	χ	X
ejpam-5051	705	6	,	,	PUNCT
ejpam-5051	705	7	z	z	PROPN
ejpam-5051	705	8	,	,	PUNCT
ejpam-5051	705	9	u	u	NOUN
ejpam-5051	705	10	]	]	X
ejpam-5051	705	11	,	,	PUNCT
ejpam-5051	705	12	[	[	X
ejpam-5051	705	13	χ′	χ′	PROPN
ejpam-5051	705	14	,	,	PUNCT
ejpam-5051	705	15	z′	z′	PROPN
ejpam-5051	705	16	,	,	PUNCT
ejpam-5051	705	17	u′	u′	PROPN
ejpam-5051	705	18	]	]	PUNCT
ejpam-5051	705	19	)	)	PUNCT
ejpam-5051	705	20	)	)	PUNCT
ejpam-5051	706	1	∈	∈	PROPN
ejpam-5051	706	2	d(2	d(2	PROPN
ejpam-5051	706	3	)	)	PUNCT
ejpam-5051	706	4	.	.	PUNCT
ejpam-5051	707	1	also	also	ADV
ejpam-5051	707	2	,	,	PUNCT
ejpam-5051	707	3	q	q	PUNCT
ejpam-5051	707	4	×	×	NOUN
ejpam-5051	707	5	q	q	NOUN
ejpam-5051	707	6	:	:	PUNCT
ejpam-5051	707	7	d(2	d(2	PROPN
ejpam-5051	707	8	)	)	PUNCT
ejpam-5051	707	9	→	→	SYM
ejpam-5051	707	10	(	(	PUNCT
ejpam-5051	707	11	â×r)(2	â×r)(2	NOUN
ejpam-5051	707	12	)	)	PUNCT
ejpam-5051	707	13	defined	define	VERB
ejpam-5051	707	14	by	by	ADP
ejpam-5051	707	15	(	(	PUNCT
ejpam-5051	707	16	q	q	PROPN
ejpam-5051	707	17	×	×	PROPN
ejpam-5051	707	18	q)(([χ	q)(([χ	NOUN
ejpam-5051	707	19	,	,	PUNCT
ejpam-5051	707	20	z	z	PROPN
ejpam-5051	707	21	,	,	PUNCT
ejpam-5051	707	22	γ	γ	X
ejpam-5051	707	23	]	]	X
ejpam-5051	707	24	,	,	PUNCT
ejpam-5051	707	25	[	[	X
ejpam-5051	707	26	χ′	χ′	PROPN
ejpam-5051	707	27	,	,	PUNCT
ejpam-5051	707	28	z′	z′	PROPN
ejpam-5051	707	29	,	,	PUNCT
ejpam-5051	707	30	γ′	γ′	PROPN
ejpam-5051	707	31	]	]	X
ejpam-5051	707	32	)	)	PUNCT
ejpam-5051	707	33	)	)	PUNCT
ejpam-5051	708	1	=	=	SYM
ejpam-5051	708	2	(	(	PUNCT
ejpam-5051	708	3	(	(	PUNCT
ejpam-5051	708	4	χ	χ	X
ejpam-5051	708	5	,	,	PUNCT
ejpam-5051	708	6	γ̇	γ̇	NOUN
ejpam-5051	708	7	)	)	PUNCT
ejpam-5051	708	8	,	,	PUNCT
ejpam-5051	708	9	(	(	PUNCT
ejpam-5051	708	10	χ′	χ′	PROPN
ejpam-5051	708	11	,	,	PUNCT
ejpam-5051	708	12	γ̇′	γ̇′	NOUN
ejpam-5051	708	13	)	)	PUNCT
ejpam-5051	708	14	)	)	PUNCT
ejpam-5051	709	1	∈	∈	PROPN
ejpam-5051	709	2	(	(	PUNCT
ejpam-5051	709	3	â⋊r)(2	â⋊r)(2	ADJ
ejpam-5051	709	4	)	)	PUNCT
ejpam-5051	709	5	.	.	PUNCT
ejpam-5051	710	1	now	now	ADV
ejpam-5051	710	2	,	,	PUNCT
ejpam-5051	710	3	i((χ	i((χ	NOUN
ejpam-5051	710	4	,	,	PUNCT
ejpam-5051	710	5	z	z	PROPN
ejpam-5051	710	6	,	,	PUNCT
ejpam-5051	710	7	u)(χ′	u)(χ′	PROPN
ejpam-5051	710	8	,	,	PUNCT
ejpam-5051	710	9	z′	z′	PROPN
ejpam-5051	710	10	,	,	PUNCT
ejpam-5051	710	11	u′	u′	PROPN
ejpam-5051	710	12	)	)	PUNCT
ejpam-5051	710	13	)	)	PUNCT
ejpam-5051	711	1	=	=	SYM
ejpam-5051	711	2	i((χ	i((χ	NOUN
ejpam-5051	711	3	,	,	PUNCT
ejpam-5051	711	4	zz′	zz′	NUM
ejpam-5051	711	5	,	,	PUNCT
ejpam-5051	711	6	uu′	uu′	PROPN
ejpam-5051	711	7	)	)	PUNCT
ejpam-5051	711	8	)	)	PUNCT
ejpam-5051	712	1	=	=	PUNCT
ejpam-5051	713	1	[	[	X
ejpam-5051	713	2	χ	χ	X
ejpam-5051	713	3	,	,	PUNCT
ejpam-5051	713	4	zz′	zz′	NUM
ejpam-5051	713	5	,	,	PUNCT
ejpam-5051	713	6	uu′	uu′	PROPN
ejpam-5051	713	7	]	]	X
ejpam-5051	713	8	;	;	PUNCT
ejpam-5051	713	9	i((χ	i((χ	NOUN
ejpam-5051	713	10	,	,	PUNCT
ejpam-5051	713	11	z	z	PROPN
ejpam-5051	713	12	,	,	PUNCT
ejpam-5051	713	13	u))i((χ′	u))i((χ′	PROPN
ejpam-5051	713	14	,	,	PUNCT
ejpam-5051	713	15	z′	z′	PROPN
ejpam-5051	713	16	,	,	PUNCT
ejpam-5051	713	17	u′	u′	PROPN
ejpam-5051	713	18	)	)	PUNCT
ejpam-5051	713	19	)	)	PUNCT
ejpam-5051	714	1	=	=	PUNCT
ejpam-5051	715	1	[	[	X
ejpam-5051	715	2	χ	χ	X
ejpam-5051	715	3	,	,	PUNCT
ejpam-5051	715	4	z	z	NOUN
ejpam-5051	715	5	,	,	PUNCT
ejpam-5051	715	6	u][χ′	u][χ′	PROPN
ejpam-5051	715	7	,	,	PUNCT
ejpam-5051	715	8	z′	z′	NUM
ejpam-5051	715	9	,	,	PUNCT
ejpam-5051	715	10	u′	u′	X
ejpam-5051	715	11	]	]	PUNCT
ejpam-5051	716	1	=	=	PUNCT
ejpam-5051	717	1	[	[	X
ejpam-5051	717	2	χ	χ	X
ejpam-5051	717	3	,	,	PUNCT
ejpam-5051	717	4	zz′	zz′	NUM
ejpam-5051	717	5	,	,	PUNCT
ejpam-5051	717	6	uu′	uu′	PROPN
ejpam-5051	717	7	]	]	PUNCT
ejpam-5051	717	8	.	.	PUNCT
ejpam-5051	718	1	also	also	ADV
ejpam-5051	718	2	,	,	PUNCT
ejpam-5051	718	3	q([χ	q([χ	NOUN
ejpam-5051	718	4	,	,	PUNCT
ejpam-5051	718	5	z	z	PROPN
ejpam-5051	718	6	,	,	PUNCT
ejpam-5051	718	7	γ][χ′	γ][χ′	PROPN
ejpam-5051	718	8	,	,	PUNCT
ejpam-5051	718	9	z′	z′	PROPN
ejpam-5051	718	10	,	,	PUNCT
ejpam-5051	718	11	γ′	γ′	PROPN
ejpam-5051	718	12	]	]	X
ejpam-5051	718	13	)	)	PUNCT
ejpam-5051	718	14	=	=	SYM
ejpam-5051	718	15	q([χ	q([χ	NOUN
ejpam-5051	718	16	,	,	PUNCT
ejpam-5051	718	17	zz′	zz′	NUM
ejpam-5051	718	18	,	,	PUNCT
ejpam-5051	718	19	γγ′	γγ′	NOUN
ejpam-5051	718	20	]	]	PUNCT
ejpam-5051	718	21	)	)	PUNCT
ejpam-5051	718	22	=	=	SYM
ejpam-5051	718	23	(	(	PUNCT
ejpam-5051	718	24	χ	χ	NOUN
ejpam-5051	718	25	,	,	PUNCT
ejpam-5051	718	26	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	718	27	)	)	PUNCT
ejpam-5051	718	28	;	;	PUNCT
ejpam-5051	718	29	q([χ	q([χ	NOUN
ejpam-5051	718	30	,	,	PUNCT
ejpam-5051	718	31	z	z	NOUN
ejpam-5051	718	32	,	,	PUNCT
ejpam-5051	718	33	γ])q([χ′	γ])q([χ′	VERB
ejpam-5051	718	34	,	,	PUNCT
ejpam-5051	718	35	z′	z′	PROPN
ejpam-5051	718	36	,	,	PUNCT
ejpam-5051	718	37	γ′	γ′	PROPN
ejpam-5051	718	38	]	]	X
ejpam-5051	718	39	)	)	PUNCT
ejpam-5051	718	40	=	=	SYM
ejpam-5051	718	41	(	(	PUNCT
ejpam-5051	718	42	χ	χ	NOUN
ejpam-5051	718	43	,	,	PUNCT
ejpam-5051	718	44	γ̇)(χ′	γ̇)(χ′	NOUN
ejpam-5051	718	45	,	,	PUNCT
ejpam-5051	718	46	γ̇′	γ̇′	NOUN
ejpam-5051	718	47	)	)	PUNCT
ejpam-5051	718	48	=	=	PUNCT
ejpam-5051	718	49	(	(	PUNCT
ejpam-5051	718	50	χ	χ	NOUN
ejpam-5051	718	51	,	,	PUNCT
ejpam-5051	718	52	γ̇γ̇′	γ̇γ̇′	PROPN
ejpam-5051	718	53	)	)	PUNCT
ejpam-5051	718	54	.	.	PUNCT
ejpam-5051	719	1	thus	thus	ADV
ejpam-5051	719	2	,	,	PUNCT
ejpam-5051	719	3	i	i	PRON
ejpam-5051	719	4	and	and	CCONJ
ejpam-5051	719	5	q	q	PROPN
ejpam-5051	719	6	are	be	AUX
ejpam-5051	719	7	continuous	continuous	ADJ
ejpam-5051	719	8	groupoid	groupoid	PROPN
ejpam-5051	719	9	homomorphism	homomorphism	PROPN
ejpam-5051	719	10	.	.	PUNCT
ejpam-5051	720	1	let	let	VERB
ejpam-5051	720	2	i|(â×t	i|(â×t	ADV
ejpam-5051	720	3	)	)	PUNCT
ejpam-5051	720	4	(	(	PUNCT
ejpam-5051	720	5	0	0	NUM
ejpam-5051	720	6	)	)	PUNCT
ejpam-5051	720	7	:	:	PUNCT
ejpam-5051	721	1	(	(	PUNCT
ejpam-5051	721	2	â	â	X
ejpam-5051	721	3	×	×	PROPN
ejpam-5051	721	4	t	t	PROPN
ejpam-5051	721	5	)	)	PUNCT
ejpam-5051	721	6	(	(	PUNCT
ejpam-5051	721	7	0	0	NUM
ejpam-5051	721	8	)	)	PUNCT
ejpam-5051	721	9	→	→	SYM
ejpam-5051	721	10	d(0	d(0	NOUN
ejpam-5051	721	11	)	)	PUNCT
ejpam-5051	721	12	.	.	PUNCT
ejpam-5051	722	1	since	since	SCONJ
ejpam-5051	722	2	i	i	PRON
ejpam-5051	722	3	is	be	AUX
ejpam-5051	722	4	continuous	continuous	ADJ
ejpam-5051	722	5	by	by	ADP
ejpam-5051	722	6	lemma	lemma	PROPN
ejpam-5051	722	7	9	9	NUM
ejpam-5051	722	8	,	,	PUNCT
ejpam-5051	722	9	then	then	ADV
ejpam-5051	722	10	i|(â×t	i|(â×t	ADJ
ejpam-5051	722	11	)	)	PUNCT
ejpam-5051	722	12	(	(	PUNCT
ejpam-5051	722	13	0	0	NUM
ejpam-5051	722	14	)	)	PUNCT
ejpam-5051	722	15	is	be	AUX
ejpam-5051	722	16	continuous	continuous	ADJ
ejpam-5051	722	17	.	.	PUNCT
ejpam-5051	723	1	let	let	VERB
ejpam-5051	723	2	v	v	PART
ejpam-5051	723	3	be	be	AUX
ejpam-5051	723	4	open	open	ADJ
ejpam-5051	723	5	in	in	ADP
ejpam-5051	723	6	(	(	PUNCT
ejpam-5051	723	7	â×	â×	NOUN
ejpam-5051	723	8	t	t	PROPN
ejpam-5051	723	9	)	)	PUNCT
ejpam-5051	723	10	(	(	PUNCT
ejpam-5051	723	11	0	0	NUM
ejpam-5051	723	12	)	)	PUNCT
ejpam-5051	723	13	.	.	PUNCT
ejpam-5051	724	1	then	then	ADV
ejpam-5051	724	2	v	v	X
ejpam-5051	724	3	=	=	SYM
ejpam-5051	724	4	a×	a×	PROPN
ejpam-5051	724	5	b	b	NOUN
ejpam-5051	724	6	where	where	SCONJ
ejpam-5051	724	7	a	a	PRON
ejpam-5051	724	8	is	be	AUX
ejpam-5051	724	9	open	open	ADJ
ejpam-5051	724	10	in	in	ADP
ejpam-5051	724	11	â	â	PROPN
ejpam-5051	724	12	and	and	CCONJ
ejpam-5051	724	13	b	b	NOUN
ejpam-5051	724	14	is	be	AUX
ejpam-5051	724	15	open	open	ADJ
ejpam-5051	724	16	in	in	ADP
ejpam-5051	724	17	t	t	PROPN
ejpam-5051	724	18	.	.	PUNCT
ejpam-5051	725	1	let	let	VERB
ejpam-5051	725	2	m	m	VERB
ejpam-5051	725	3	=	=	VERB
ejpam-5051	725	4	a	a	DET
ejpam-5051	725	5	∗	∗	NOUN
ejpam-5051	725	6	g(0	g(0	NOUN
ejpam-5051	725	7	)	)	PUNCT
ejpam-5051	725	8	×	×	PROPN
ejpam-5051	725	9	b	b	NOUN
ejpam-5051	725	10	=	=	PRON
ejpam-5051	725	11	{	{	PUNCT
ejpam-5051	725	12	(	(	PUNCT
ejpam-5051	725	13	χ	χ	NOUN
ejpam-5051	725	14	,	,	PUNCT
ejpam-5051	725	15	z	z	NOUN
ejpam-5051	725	16	,	,	PUNCT
ejpam-5051	725	17	u	u	NOUN
ejpam-5051	725	18	)	)	PUNCT
ejpam-5051	725	19	∈	∈	PROPN
ejpam-5051	725	20	â	â	ADP
ejpam-5051	725	21	∗	∗	NOUN
ejpam-5051	725	22	g	g	PROPN
ejpam-5051	725	23	×	×	PROPN
ejpam-5051	725	24	t	t	PROPN
ejpam-5051	725	25	:	:	PUNCT
ejpam-5051	725	26	πd(χ	πd(χ	NUM
ejpam-5051	725	27	,	,	PUNCT
ejpam-5051	725	28	z	z	NOUN
ejpam-5051	725	29	,	,	PUNCT
ejpam-5051	725	30	u	u	NOUN
ejpam-5051	725	31	)	)	PUNCT
ejpam-5051	725	32	∈	∈	PROPN
ejpam-5051	725	33	i(v	i(v	NOUN
ejpam-5051	725	34	)	)	PUNCT
ejpam-5051	725	35	}	}	PUNCT
ejpam-5051	725	36	.	.	PUNCT
ejpam-5051	726	1	then	then	ADV
ejpam-5051	726	2	m	m	VERB
ejpam-5051	726	3	=	=	SYM
ejpam-5051	726	4	π−1	π−1	ADJ
ejpam-5051	726	5	d	d	NOUN
ejpam-5051	726	6	(	(	PUNCT
ejpam-5051	726	7	i(v	i(v	NOUN
ejpam-5051	726	8	)	)	PUNCT
ejpam-5051	726	9	)	)	PUNCT
ejpam-5051	726	10	and	and	CCONJ
ejpam-5051	726	11	m	m	PROPN
ejpam-5051	726	12	is	be	AUX
ejpam-5051	726	13	open	open	ADJ
ejpam-5051	726	14	in	in	ADP
ejpam-5051	726	15	â	â	PROPN
ejpam-5051	726	16	∗	∗	NOUN
ejpam-5051	726	17	g	g	PROPN
ejpam-5051	726	18	×	×	PROPN
ejpam-5051	726	19	t	t	PROPN
ejpam-5051	726	20	since	since	SCONJ
ejpam-5051	726	21	a	a	PRON
ejpam-5051	726	22	is	be	AUX
ejpam-5051	726	23	open	open	ADJ
ejpam-5051	726	24	in	in	ADP
ejpam-5051	726	25	â	â	PROPN
ejpam-5051	726	26	,	,	PUNCT
ejpam-5051	726	27	g(0	g(0	PROPN
ejpam-5051	726	28	)	)	PUNCT
ejpam-5051	726	29	is	be	AUX
ejpam-5051	726	30	open	open	ADJ
ejpam-5051	726	31	in	in	ADP
ejpam-5051	726	32	g	g	PROPN
ejpam-5051	726	33	and	and	CCONJ
ejpam-5051	726	34	b	b	NOUN
ejpam-5051	726	35	is	be	AUX
ejpam-5051	726	36	open	open	ADJ
ejpam-5051	726	37	in	in	ADP
ejpam-5051	726	38	t	t	PROPN
ejpam-5051	726	39	.	.	PUNCT
ejpam-5051	727	1	hence	hence	ADV
ejpam-5051	727	2	,	,	PUNCT
ejpam-5051	727	3	i(v	i(v	PROPN
ejpam-5051	727	4	)	)	PUNCT
ejpam-5051	727	5	is	be	AUX
ejpam-5051	727	6	open	open	ADJ
ejpam-5051	727	7	in	in	ADP
ejpam-5051	727	8	d(0	d(0	NOUN
ejpam-5051	727	9	)	)	PUNCT
ejpam-5051	727	10	and	and	CCONJ
ejpam-5051	727	11	i−1	i−1	PROPN
ejpam-5051	727	12	is	be	AUX
ejpam-5051	727	13	continuous	continuous	ADJ
ejpam-5051	727	14	.	.	PUNCT
ejpam-5051	728	1	thus	thus	ADV
ejpam-5051	728	2	,	,	PUNCT
ejpam-5051	728	3	i|â×t	i|â×t	PRON
ejpam-5051	728	4	is	be	AUX
ejpam-5051	728	5	a	a	DET
ejpam-5051	728	6	homeomorphism	homeomorphism	NOUN
ejpam-5051	728	7	of	of	ADP
ejpam-5051	728	8	unit	unit	NOUN
ejpam-5051	728	9	spaces	space	VERB
ejpam-5051	728	10	.	.	PUNCT
ejpam-5051	729	1	now	now	ADV
ejpam-5051	729	2	,	,	PUNCT
ejpam-5051	729	3	let	let	VERB
ejpam-5051	729	4	q|d(0	q|d(0	PROPN
ejpam-5051	729	5	)	)	PUNCT
ejpam-5051	729	6	:	:	PUNCT
ejpam-5051	730	1	d(0	d(0	NOUN
ejpam-5051	730	2	)	)	PUNCT
ejpam-5051	730	3	→	→	SYM
ejpam-5051	730	4	(	(	PUNCT
ejpam-5051	730	5	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	730	6	)	)	PUNCT
ejpam-5051	730	7	.	.	PUNCT
ejpam-5051	731	1	since	since	SCONJ
ejpam-5051	731	2	q	q	PROPN
ejpam-5051	731	3	is	be	AUX
ejpam-5051	731	4	continuous	continuous	ADJ
ejpam-5051	731	5	by	by	ADP
ejpam-5051	731	6	lemma	lemma	PROPN
ejpam-5051	731	7	9	9	NUM
ejpam-5051	731	8	,	,	PUNCT
ejpam-5051	731	9	then	then	ADV
ejpam-5051	731	10	q|d(0	q|d(0	PROPN
ejpam-5051	731	11	)	)	PUNCT
ejpam-5051	731	12	is	be	AUX
ejpam-5051	731	13	continuous	continuous	ADJ
ejpam-5051	731	14	.	.	PUNCT
ejpam-5051	732	1	let	let	VERB
ejpam-5051	732	2	y	y	PRON
ejpam-5051	732	3	be	be	AUX
ejpam-5051	732	4	an	an	DET
ejpam-5051	732	5	open	open	ADJ
ejpam-5051	732	6	subset	subset	NOUN
ejpam-5051	732	7	of	of	ADP
ejpam-5051	732	8	d(0	d(0	NOUN
ejpam-5051	732	9	)	)	PUNCT
ejpam-5051	732	10	.	.	PUNCT
ejpam-5051	733	1	then	then	ADV
ejpam-5051	733	2	π−1	π−1	PROPN
ejpam-5051	733	3	d	d	X
ejpam-5051	733	4	(	(	PUNCT
ejpam-5051	733	5	y	y	PROPN
ejpam-5051	733	6	)	)	PUNCT
ejpam-5051	733	7	is	be	AUX
ejpam-5051	733	8	open	open	ADJ
ejpam-5051	733	9	in	in	ADP
ejpam-5051	733	10	â	â	PROPN
ejpam-5051	733	11	∗	∗	NOUN
ejpam-5051	733	12	g	g	PROPN
ejpam-5051	733	13	×	×	PROPN
ejpam-5051	733	14	t	t	NOUN
ejpam-5051	733	15	,	,	PUNCT
ejpam-5051	733	16	that	that	ADV
ejpam-5051	733	17	is	is	ADV
ejpam-5051	733	18	,	,	PUNCT
ejpam-5051	733	19	π−1	π−1	PROPN
ejpam-5051	733	20	d	d	X
ejpam-5051	733	21	(	(	PUNCT
ejpam-5051	733	22	y	y	PROPN
ejpam-5051	733	23	)	)	PUNCT
ejpam-5051	733	24	=	=	PUNCT
ejpam-5051	733	25	a	a	DET
ejpam-5051	733	26	∗	∗	NOUN
ejpam-5051	733	27	b	b	SYM
ejpam-5051	733	28	×	×	NOUN
ejpam-5051	733	29	c	c	NOUN
ejpam-5051	733	30	where	where	SCONJ
ejpam-5051	733	31	a	a	PRON
ejpam-5051	733	32	is	be	AUX
ejpam-5051	733	33	open	open	ADJ
ejpam-5051	733	34	in	in	ADP
ejpam-5051	733	35	â	â	PROPN
ejpam-5051	733	36	,	,	PUNCT
ejpam-5051	733	37	b	b	PROPN
ejpam-5051	733	38	is	be	AUX
ejpam-5051	733	39	open	open	ADJ
ejpam-5051	733	40	in	in	ADP
ejpam-5051	733	41	g	g	PROPN
ejpam-5051	733	42	and	and	CCONJ
ejpam-5051	733	43	c	c	PROPN
ejpam-5051	733	44	is	be	AUX
ejpam-5051	733	45	open	open	ADJ
ejpam-5051	733	46	in	in	ADP
ejpam-5051	733	47	t	t	PROPN
ejpam-5051	733	48	.	.	PUNCT
ejpam-5051	734	1	let	let	VERB
ejpam-5051	734	2	m	m	VERB
ejpam-5051	734	3	=	=	PUNCT
ejpam-5051	734	4	a	a	DET
ejpam-5051	734	5	×	×	NOUN
ejpam-5051	734	6	πr(b	πr(b	NUM
ejpam-5051	734	7	)	)	PUNCT
ejpam-5051	734	8	∩	∩	NOUN
ejpam-5051	734	9	(	(	PUNCT
ejpam-5051	734	10	â	â	X
ejpam-5051	734	11	⋊r)(0	⋊r)(0	PROPN
ejpam-5051	734	12	)	)	PUNCT
ejpam-5051	734	13	=	=	SYM
ejpam-5051	734	14	{	{	PUNCT
ejpam-5051	734	15	(	(	PUNCT
ejpam-5051	734	16	χ	χ	NOUN
ejpam-5051	734	17	,	,	PUNCT
ejpam-5051	734	18	γ̇	γ̇	NOUN
ejpam-5051	734	19	)	)	PUNCT
ejpam-5051	734	20	∈	∈	PROPN
ejpam-5051	734	21	(	(	PUNCT
ejpam-5051	734	22	â	â	X
ejpam-5051	734	23	⋊r)(0	⋊r)(0	PROPN
ejpam-5051	734	24	)	)	PUNCT
ejpam-5051	734	25	:	:	PUNCT
ejpam-5051	735	1	q−1(χ	q−1(χ	PROPN
ejpam-5051	735	2	,	,	PUNCT
ejpam-5051	735	3	γ̇	γ̇	NOUN
ejpam-5051	735	4	)	)	PUNCT
ejpam-5051	735	5	∈	∈	PROPN
ejpam-5051	735	6	y	y	PROPN
ejpam-5051	735	7	}	}	PUNCT
ejpam-5051	735	8	.	.	PUNCT
ejpam-5051	736	1	then	then	ADV
ejpam-5051	736	2	m	m	VERB
ejpam-5051	736	3	=	=	ADJ
ejpam-5051	736	4	q(y	q(y	PROPN
ejpam-5051	736	5	)	)	PUNCT
ejpam-5051	736	6	and	and	CCONJ
ejpam-5051	736	7	m	m	PROPN
ejpam-5051	736	8	is	be	AUX
ejpam-5051	736	9	open	open	ADJ
ejpam-5051	736	10	in	in	ADP
ejpam-5051	736	11	(	(	PUNCT
ejpam-5051	736	12	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	736	13	)	)	PUNCT
ejpam-5051	736	14	since	since	SCONJ
ejpam-5051	736	15	a	a	PRON
ejpam-5051	736	16	is	be	AUX
ejpam-5051	736	17	open	open	ADJ
ejpam-5051	736	18	in	in	ADP
ejpam-5051	736	19	â	â	PROPN
ejpam-5051	736	20	and	and	CCONJ
ejpam-5051	736	21	πr(b	πr(b	NUM
ejpam-5051	736	22	)	)	PUNCT
ejpam-5051	736	23	is	be	AUX
ejpam-5051	736	24	open	open	ADJ
ejpam-5051	736	25	in	in	ADP
ejpam-5051	736	26	r.	r.	PROPN
ejpam-5051	736	27	then	then	ADV
ejpam-5051	736	28	q(y	q(y	PROPN
ejpam-5051	736	29	)	)	PUNCT
ejpam-5051	736	30	is	be	AUX
ejpam-5051	736	31	open	open	ADJ
ejpam-5051	736	32	in	in	ADP
ejpam-5051	736	33	(	(	PUNCT
ejpam-5051	736	34	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	736	35	)	)	PUNCT
ejpam-5051	736	36	and	and	CCONJ
ejpam-5051	736	37	q−1	q−1	PROPN
ejpam-5051	736	38	is	be	AUX
ejpam-5051	736	39	continuous	continuous	ADJ
ejpam-5051	736	40	.	.	PUNCT
ejpam-5051	737	1	therefore	therefore	ADV
ejpam-5051	737	2	,	,	PUNCT
ejpam-5051	737	3	q|d(0	q|d(0	PROPN
ejpam-5051	737	4	)	)	PUNCT
ejpam-5051	737	5	is	be	AUX
ejpam-5051	737	6	a	a	DET
ejpam-5051	737	7	homeomorphism	homeomorphism	NOUN
ejpam-5051	737	8	.	.	PUNCT
ejpam-5051	738	1	in	in	ADP
ejpam-5051	738	2	order	order	NOUN
ejpam-5051	738	3	to	to	PART
ejpam-5051	738	4	show	show	VERB
ejpam-5051	738	5	that	that	SCONJ
ejpam-5051	738	6	(	(	PUNCT
ejpam-5051	738	7	d	d	X
ejpam-5051	738	8	,	,	PUNCT
ejpam-5051	738	9	i	i	PRON
ejpam-5051	738	10	,	,	PUNCT
ejpam-5051	738	11	q	q	X
ejpam-5051	738	12	)	)	PUNCT
ejpam-5051	738	13	is	be	AUX
ejpam-5051	738	14	a	a	DET
ejpam-5051	738	15	discrete	discrete	ADJ
ejpam-5051	738	16	twist	twist	NOUN
ejpam-5051	738	17	over	over	ADP
ejpam-5051	738	18	â	â	PRON
ejpam-5051	738	19	⋊	⋊	PROPN
ejpam-5051	738	20	r.	r.	NOUN
ejpam-5051	738	21	we	we	PRON
ejpam-5051	738	22	prove	prove	VERB
ejpam-5051	738	23	first	first	ADV
ejpam-5051	738	24	the	the	DET
ejpam-5051	738	25	following	following	ADJ
ejpam-5051	738	26	results	result	NOUN
ejpam-5051	738	27	.	.	PUNCT
ejpam-5051	739	1	theorem	theorem	ADJ
ejpam-5051	739	2	4	4	NUM
ejpam-5051	739	3	.	.	PUNCT
ejpam-5051	740	1	the	the	DET
ejpam-5051	740	2	sequence	sequence	NOUN
ejpam-5051	740	3	â×	â×	PROPN
ejpam-5051	740	4	t	t	PROPN
ejpam-5051	740	5	i	i	NOUN
ejpam-5051	740	6	↪	↪	PROPN
ejpam-5051	740	7	→	→	SYM
ejpam-5051	740	8	d	d	X
ejpam-5051	740	9	q	q	ADJ
ejpam-5051	740	10	↪	↪	PROPN
ejpam-5051	740	11	→	→	SYM
ejpam-5051	740	12	â⋊r	â⋊r	NOUN
ejpam-5051	740	13	is	be	AUX
ejpam-5051	740	14	exact	exact	ADJ
ejpam-5051	740	15	,	,	PUNCT
ejpam-5051	740	16	that	that	ADV
ejpam-5051	740	17	is	is	ADV
ejpam-5051	740	18	,	,	PUNCT
ejpam-5051	740	19	(	(	PUNCT
ejpam-5051	740	20	i	i	NOUN
ejpam-5051	740	21	)	)	PUNCT
ejpam-5051	740	22	i({(χ	i({(χ	PROPN
ejpam-5051	740	23	,	,	PUNCT
ejpam-5051	740	24	u)×	u)×	PROPN
ejpam-5051	740	25	t	t	NOUN
ejpam-5051	740	26	}	}	PUNCT
ejpam-5051	740	27	)	)	PUNCT
ejpam-5051	741	1	=	=	PUNCT
ejpam-5051	741	2	q−1((χ	q−1((χ	PROPN
ejpam-5051	741	3	,	,	PUNCT
ejpam-5051	741	4	u	u	NOUN
ejpam-5051	741	5	)	)	PUNCT
ejpam-5051	741	6	)	)	PUNCT
ejpam-5051	741	7	for	for	ADP
ejpam-5051	741	8	(	(	PUNCT
ejpam-5051	741	9	χ	χ	X
ejpam-5051	741	10	,	,	PUNCT
ejpam-5051	741	11	u	u	NOUN
ejpam-5051	741	12	)	)	PUNCT
ejpam-5051	741	13	∈	∈	PROPN
ejpam-5051	741	14	(	(	PUNCT
ejpam-5051	741	15	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	741	16	)	)	PUNCT
ejpam-5051	741	17	,	,	PUNCT
ejpam-5051	741	18	(	(	PUNCT
ejpam-5051	741	19	ii	ii	X
ejpam-5051	741	20	)	)	PUNCT
ejpam-5051	742	1	i	i	PRON
ejpam-5051	742	2	is	be	AUX
ejpam-5051	742	3	injective	injective	ADJ
ejpam-5051	742	4	,	,	PUNCT
ejpam-5051	742	5	and	and	CCONJ
ejpam-5051	742	6	(	(	PUNCT
ejpam-5051	742	7	iii	iii	X
ejpam-5051	742	8	)	)	PUNCT
ejpam-5051	742	9	q	q	PUNCT
ejpam-5051	742	10	is	be	AUX
ejpam-5051	742	11	a	a	DET
ejpam-5051	742	12	quotient	quotient	NOUN
ejpam-5051	742	13	map	map	NOUN
ejpam-5051	742	14	.	.	PUNCT
ejpam-5051	743	1	proof	proof	NOUN
ejpam-5051	743	2	.	.	PUNCT
ejpam-5051	744	1	(	(	PUNCT
ejpam-5051	744	2	i	i	NOUN
ejpam-5051	744	3	)	)	PUNCT
ejpam-5051	744	4	let	let	VERB
ejpam-5051	744	5	(	(	PUNCT
ejpam-5051	744	6	χ	χ	X
ejpam-5051	744	7	,	,	PUNCT
ejpam-5051	744	8	u	u	NOUN
ejpam-5051	744	9	)	)	PUNCT
ejpam-5051	744	10	∈	∈	PROPN
ejpam-5051	744	11	â.	â.	NOUN
ejpam-5051	744	12	then	then	ADV
ejpam-5051	744	13	i({(χ	i({(χ	PROPN
ejpam-5051	744	14	,	,	PUNCT
ejpam-5051	744	15	u	u	NOUN
ejpam-5051	744	16	)	)	PUNCT
ejpam-5051	744	17	}	}	PUNCT
ejpam-5051	744	18	×	×	PROPN
ejpam-5051	744	19	t	t	PROPN
ejpam-5051	744	20	}	}	PUNCT
ejpam-5051	744	21	)	)	PUNCT
ejpam-5051	745	1	=	=	PUNCT
ejpam-5051	746	1	[	[	X
ejpam-5051	746	2	χ	χ	X
ejpam-5051	746	3	,	,	PUNCT
ejpam-5051	746	4	z	z	PROPN
ejpam-5051	746	5	,	,	PUNCT
ejpam-5051	746	6	u	u	X
ejpam-5051	746	7	]	]	X
ejpam-5051	746	8	for	for	ADP
ejpam-5051	746	9	some	some	DET
ejpam-5051	746	10	z	z	PROPN
ejpam-5051	746	11	∈	∈	PROPN
ejpam-5051	746	12	t	t	PROPN
ejpam-5051	746	13	and	and	CCONJ
ejpam-5051	746	14	q−1((χ	q−1((χ	PROPN
ejpam-5051	746	15	,	,	PUNCT
ejpam-5051	746	16	u	u	NOUN
ejpam-5051	746	17	)	)	PUNCT
ejpam-5051	746	18	)	)	PUNCT
ejpam-5051	747	1	=	=	PUNCT
ejpam-5051	748	1	[	[	X
ejpam-5051	748	2	χ	χ	X
ejpam-5051	748	3	,	,	PUNCT
ejpam-5051	748	4	z	z	PROPN
ejpam-5051	748	5	,	,	PUNCT
ejpam-5051	748	6	u	u	X
ejpam-5051	748	7	]	]	X
ejpam-5051	748	8	for	for	ADP
ejpam-5051	748	9	some	some	DET
ejpam-5051	748	10	z	z	PROPN
ejpam-5051	748	11	∈	∈	PROPN
ejpam-5051	748	12	t	t	NOUN
ejpam-5051	748	13	.	.	PUNCT
ejpam-5051	749	1	hence	hence	ADV
ejpam-5051	749	2	,	,	PUNCT
ejpam-5051	749	3	i({(χ	i({(χ	PROPN
ejpam-5051	749	4	,	,	PUNCT
ejpam-5051	749	5	u)×t	u)×t	NOUN
ejpam-5051	749	6	}	}	PUNCT
ejpam-5051	749	7	)	)	PUNCT
ejpam-5051	750	1	=	=	PUNCT
ejpam-5051	750	2	q−1((χ	q−1((χ	PROPN
ejpam-5051	750	3	,	,	PUNCT
ejpam-5051	750	4	u	u	NOUN
ejpam-5051	750	5	)	)	PUNCT
ejpam-5051	750	6	)	)	PUNCT
ejpam-5051	750	7	for	for	ADP
ejpam-5051	750	8	(	(	PUNCT
ejpam-5051	750	9	χ	χ	X
ejpam-5051	750	10	,	,	PUNCT
ejpam-5051	750	11	u	u	NOUN
ejpam-5051	750	12	)	)	PUNCT
ejpam-5051	750	13	∈	∈	PROPN
ejpam-5051	750	14	(	(	PUNCT
ejpam-5051	750	15	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	750	16	)	)	PUNCT
ejpam-5051	750	17	.	.	PUNCT
ejpam-5051	751	1	r.	r.	PROPN
ejpam-5051	751	2	s.	s.	PROPN
ejpam-5051	751	3	bongcawel	bongcawel	PROPN
ejpam-5051	752	1	et	et	PROPN
ejpam-5051	752	2	al	al	PROPN
ejpam-5051	752	3	.	.	PUNCT
ejpam-5051	752	4	/	/	SYM
ejpam-5051	752	5	eur	eur	PROPN
ejpam-5051	752	6	.	.	PUNCT
ejpam-5051	753	1	j.	j.	PROPN
ejpam-5051	753	2	pure	pure	PROPN
ejpam-5051	753	3	appl	appl	PROPN
ejpam-5051	753	4	.	.	PROPN
ejpam-5051	753	5	math	math	PROPN
ejpam-5051	753	6	,	,	PUNCT
ejpam-5051	753	7	17	17	NUM
ejpam-5051	753	8	(	(	PUNCT
ejpam-5051	753	9	1	1	NUM
ejpam-5051	753	10	)	)	PUNCT
ejpam-5051	753	11	(	(	PUNCT
ejpam-5051	753	12	2024	2024	NUM
ejpam-5051	753	13	)	)	PUNCT
ejpam-5051	753	14	,	,	PUNCT
ejpam-5051	753	15	519	519	NUM
ejpam-5051	753	16	-	-	SYM
ejpam-5051	753	17	545	545	NUM
ejpam-5051	753	18	537	537	NUM
ejpam-5051	753	19	(	(	PUNCT
ejpam-5051	753	20	ii	ii	NOUN
ejpam-5051	753	21	)	)	PUNCT
ejpam-5051	753	22	let	let	VERB
ejpam-5051	753	23	(	(	PUNCT
ejpam-5051	753	24	χ1	χ1	NOUN
ejpam-5051	753	25	,	,	PUNCT
ejpam-5051	753	26	z1	z1	NOUN
ejpam-5051	753	27	,	,	PUNCT
ejpam-5051	753	28	u1	u1	NOUN
ejpam-5051	753	29	)	)	PUNCT
ejpam-5051	753	30	,	,	PUNCT
ejpam-5051	753	31	(	(	PUNCT
ejpam-5051	753	32	χ2	χ2	PROPN
ejpam-5051	753	33	,	,	PUNCT
ejpam-5051	753	34	z2	z2	PROPN
ejpam-5051	753	35	,	,	PUNCT
ejpam-5051	753	36	u2	u2	PROPN
ejpam-5051	753	37	)	)	PUNCT
ejpam-5051	753	38	∈	∈	PROPN
ejpam-5051	753	39	â	â	ADP
ejpam-5051	753	40	⋊	⋊	PROPN
ejpam-5051	753	41	t	t	NOUN
ejpam-5051	753	42	with	with	ADP
ejpam-5051	753	43	q((χ1	q((χ1	PROPN
ejpam-5051	753	44	,	,	PUNCT
ejpam-5051	753	45	z1	z1	NOUN
ejpam-5051	753	46	,	,	PUNCT
ejpam-5051	753	47	u1	u1	NOUN
ejpam-5051	753	48	)	)	PUNCT
ejpam-5051	753	49	)	)	PUNCT
ejpam-5051	754	1	=	=	SYM
ejpam-5051	754	2	q((χ2	q((χ2	NOUN
ejpam-5051	754	3	,	,	PUNCT
ejpam-5051	754	4	z2	z2	PROPN
ejpam-5051	754	5	,	,	PUNCT
ejpam-5051	754	6	u2	u2	NOUN
ejpam-5051	754	7	)	)	PUNCT
ejpam-5051	754	8	)	)	PUNCT
ejpam-5051	754	9	.	.	PUNCT
ejpam-5051	755	1	then	then	ADV
ejpam-5051	755	2	,	,	PUNCT
ejpam-5051	755	3	[	[	X
ejpam-5051	755	4	χ1	χ1	NOUN
ejpam-5051	755	5	,	,	PUNCT
ejpam-5051	755	6	z1	z1	NOUN
ejpam-5051	755	7	,	,	PUNCT
ejpam-5051	755	8	γ1	γ1	NOUN
ejpam-5051	755	9	]	]	PUNCT
ejpam-5051	755	10	=	=	PUNCT
ejpam-5051	756	1	[	[	X
ejpam-5051	756	2	χ2	χ2	PROPN
ejpam-5051	756	3	,	,	PUNCT
ejpam-5051	756	4	z2	z2	PROPN
ejpam-5051	756	5	,	,	PUNCT
ejpam-5051	756	6	γ2	γ2	PROPN
ejpam-5051	756	7	]	]	PUNCT
ejpam-5051	756	8	,	,	PUNCT
ejpam-5051	756	9	that	that	ADV
ejpam-5051	756	10	is	is	ADV
ejpam-5051	756	11	,	,	PUNCT
ejpam-5051	756	12	(	(	PUNCT
ejpam-5051	756	13	χ1	χ1	NOUN
ejpam-5051	756	14	,	,	PUNCT
ejpam-5051	756	15	z1	z1	NOUN
ejpam-5051	756	16	,	,	PUNCT
ejpam-5051	756	17	γ1	γ1	NOUN
ejpam-5051	756	18	)	)	PUNCT
ejpam-5051	756	19	∼	∼	NOUN
ejpam-5051	756	20	(	(	PUNCT
ejpam-5051	756	21	χ2	χ2	PROPN
ejpam-5051	756	22	,	,	PUNCT
ejpam-5051	756	23	z2	z2	PROPN
ejpam-5051	756	24	,	,	PUNCT
ejpam-5051	756	25	γ2	γ2	NOUN
ejpam-5051	756	26	)	)	PUNCT
ejpam-5051	756	27	.	.	PUNCT
ejpam-5051	757	1	then	then	ADV
ejpam-5051	757	2	χ1	χ1	NOUN
ejpam-5051	757	3	=	=	SYM
ejpam-5051	757	4	χ2	χ2	PROPN
ejpam-5051	757	5	and	and	CCONJ
ejpam-5051	757	6	we	we	PRON
ejpam-5051	757	7	can	can	AUX
ejpam-5051	757	8	choose	choose	VERB
ejpam-5051	757	9	a	a	DET
ejpam-5051	757	10	∈	∈	NOUN
ejpam-5051	757	11	au	au	ADP
ejpam-5051	757	12	such	such	ADJ
ejpam-5051	757	13	that	that	SCONJ
ejpam-5051	757	14	χ(a	χ(a	NOUN
ejpam-5051	757	15	)	)	PUNCT
ejpam-5051	757	16	=	=	SYM
ejpam-5051	757	17	1	1	NUM
ejpam-5051	757	18	∈	∈	NOUN
ejpam-5051	757	19	r×	r×	NOUN
ejpam-5051	757	20	such	such	ADJ
ejpam-5051	757	21	that	that	DET
ejpam-5051	757	22	z1	z1	ADJ
ejpam-5051	757	23	=	=	SYM
ejpam-5051	757	24	χ(a)z2	χ(a)z2	NOUN
ejpam-5051	757	25	=	=	SYM
ejpam-5051	757	26	(	(	PUNCT
ejpam-5051	757	27	1)z2	1)z2	NOUN
ejpam-5051	757	28	=	=	SYM
ejpam-5051	757	29	z2	z2	PROPN
ejpam-5051	757	30	.	.	PUNCT
ejpam-5051	758	1	also	also	ADV
ejpam-5051	758	2	,	,	PUNCT
ejpam-5051	758	3	choose	choose	VERB
ejpam-5051	758	4	a′	a′	PROPN
ejpam-5051	758	5	∈	∈	PROPN
ejpam-5051	758	6	au	au	ADP
ejpam-5051	758	7	such	such	ADJ
ejpam-5051	758	8	that	that	SCONJ
ejpam-5051	758	9	a;∈	a;∈	PROPN
ejpam-5051	758	10	g(0	g(0	PROPN
ejpam-5051	758	11	)	)	PUNCT
ejpam-5051	758	12	.	.	PUNCT
ejpam-5051	759	1	then	then	ADV
ejpam-5051	759	2	γ1	γ1	PROPN
ejpam-5051	759	3	=	=	PUNCT
ejpam-5051	759	4	a	a	DET
ejpam-5051	759	5	·	·	PUNCT
ejpam-5051	759	6	γ2	γ2	NOUN
ejpam-5051	759	7	=	=	SYM
ejpam-5051	759	8	γ2	γ2	NOUN
ejpam-5051	759	9	.	.	PUNCT
ejpam-5051	760	1	thus	thus	ADV
ejpam-5051	760	2	,	,	PUNCT
ejpam-5051	760	3	(	(	PUNCT
ejpam-5051	760	4	χ1	χ1	NOUN
ejpam-5051	760	5	,	,	PUNCT
ejpam-5051	760	6	z1	z1	NOUN
ejpam-5051	760	7	,	,	PUNCT
ejpam-5051	760	8	γ1	γ1	NOUN
ejpam-5051	760	9	)	)	PUNCT
ejpam-5051	760	10	=	=	SYM
ejpam-5051	760	11	(	(	PUNCT
ejpam-5051	760	12	χ2	χ2	PROPN
ejpam-5051	760	13	,	,	PUNCT
ejpam-5051	760	14	z2	z2	PROPN
ejpam-5051	760	15	,	,	PUNCT
ejpam-5051	760	16	γ2	γ2	NOUN
ejpam-5051	760	17	)	)	PUNCT
ejpam-5051	760	18	and	and	CCONJ
ejpam-5051	760	19	i	i	PRON
ejpam-5051	760	20	is	be	AUX
ejpam-5051	760	21	injective	injective	ADJ
ejpam-5051	760	22	.	.	PUNCT
ejpam-5051	761	1	(	(	PUNCT
ejpam-5051	761	2	iii	iii	X
ejpam-5051	761	3	)	)	PUNCT
ejpam-5051	761	4	by	by	ADP
ejpam-5051	761	5	lemma	lemma	PROPN
ejpam-5051	761	6	9	9	NUM
ejpam-5051	761	7	,	,	PUNCT
ejpam-5051	761	8	q	q	PRON
ejpam-5051	761	9	is	be	AUX
ejpam-5051	761	10	continuous	continuous	ADJ
ejpam-5051	761	11	.	.	PUNCT
ejpam-5051	762	1	let	let	VERB
ejpam-5051	762	2	(	(	PUNCT
ejpam-5051	762	3	χ	χ	X
ejpam-5051	762	4	,	,	PUNCT
ejpam-5051	762	5	γ̇	γ̇	NOUN
ejpam-5051	762	6	)	)	PUNCT
ejpam-5051	762	7	∈	∈	PROPN
ejpam-5051	762	8	â⋊r	â⋊r	NOUN
ejpam-5051	762	9	.	.	PUNCT
ejpam-5051	763	1	then	then	ADV
ejpam-5051	763	2	[	[	X
ejpam-5051	763	3	χ	χ	X
ejpam-5051	763	4	,	,	PUNCT
ejpam-5051	763	5	z	z	PROPN
ejpam-5051	763	6	,	,	PUNCT
ejpam-5051	763	7	γ	γ	X
ejpam-5051	763	8	]	]	X
ejpam-5051	763	9	where	where	SCONJ
ejpam-5051	763	10	r(γ	r(γ	NOUN
ejpam-5051	763	11	)	)	PUNCT
ejpam-5051	763	12	=	=	SYM
ejpam-5051	763	13	u	u	NOUN
ejpam-5051	763	14	is	be	AUX
ejpam-5051	763	15	the	the	DET
ejpam-5051	763	16	pre	pre	NOUN
ejpam-5051	763	17	-	-	NOUN
ejpam-5051	763	18	image	image	NOUN
ejpam-5051	763	19	of	of	ADP
ejpam-5051	763	20	(	(	PUNCT
ejpam-5051	763	21	χ	χ	ADJ
ejpam-5051	763	22	,	,	PUNCT
ejpam-5051	763	23	γ̇	γ̇	NOUN
ejpam-5051	763	24	)	)	PUNCT
ejpam-5051	763	25	in	in	ADP
ejpam-5051	763	26	d.	d.	PROPN
ejpam-5051	763	27	thus	thus	ADV
ejpam-5051	763	28	,	,	PUNCT
ejpam-5051	763	29	q	q	PROPN
ejpam-5051	763	30	is	be	AUX
ejpam-5051	763	31	surjective	surjective	ADJ
ejpam-5051	763	32	and	and	CCONJ
ejpam-5051	763	33	a	a	DET
ejpam-5051	763	34	quotient	quotient	NOUN
ejpam-5051	763	35	map	map	NOUN
ejpam-5051	763	36	.	.	PUNCT
ejpam-5051	764	1	theorem	theorem	VERB
ejpam-5051	764	2	5	5	NUM
ejpam-5051	764	3	.	.	PUNCT
ejpam-5051	765	1	d	d	NOUN
ejpam-5051	765	2	is	be	AUX
ejpam-5051	765	3	a	a	DET
ejpam-5051	765	4	locally	locally	ADV
ejpam-5051	765	5	trivial	trivial	ADJ
ejpam-5051	765	6	g	g	NOUN
ejpam-5051	765	7	-	-	PUNCT
ejpam-5051	765	8	bundle	bundle	NOUN
ejpam-5051	765	9	in	in	ADP
ejpam-5051	765	10	the	the	DET
ejpam-5051	765	11	sense	sense	NOUN
ejpam-5051	765	12	that	that	SCONJ
ejpam-5051	765	13	for	for	ADP
ejpam-5051	765	14	each	each	DET
ejpam-5051	765	15	(	(	PUNCT
ejpam-5051	765	16	χ	χ	NOUN
ejpam-5051	765	17	,	,	PUNCT
ejpam-5051	765	18	γ̇	γ̇	NOUN
ejpam-5051	765	19	)	)	PUNCT
ejpam-5051	765	20	∈	∈	PROPN
ejpam-5051	765	21	â⋊r	â⋊r	NOUN
ejpam-5051	765	22	,	,	PUNCT
ejpam-5051	765	23	there	there	PRON
ejpam-5051	765	24	is	be	VERB
ejpam-5051	765	25	an	an	DET
ejpam-5051	765	26	open	open	ADJ
ejpam-5051	765	27	bisection	bisection	NOUN
ejpam-5051	765	28	bα	bα	NOUN
ejpam-5051	765	29	of	of	ADP
ejpam-5051	765	30	â⋊r	â⋊r	NOUN
ejpam-5051	765	31	containing	contain	VERB
ejpam-5051	765	32	(	(	PUNCT
ejpam-5051	765	33	χ	χ	ADJ
ejpam-5051	765	34	,	,	PUNCT
ejpam-5051	765	35	γ̇	γ̇	NOUN
ejpam-5051	765	36	)	)	PUNCT
ejpam-5051	765	37	,	,	PUNCT
ejpam-5051	765	38	and	and	CCONJ
ejpam-5051	765	39	a	a	DET
ejpam-5051	765	40	continuous	continuous	ADJ
ejpam-5051	765	41	map	map	NOUN
ejpam-5051	765	42	pα	pα	INTJ
ejpam-5051	765	43	:	:	PUNCT
ejpam-5051	765	44	bα	bα	PROPN
ejpam-5051	765	45	→	→	PUNCT
ejpam-5051	765	46	d	d	X
ejpam-5051	765	47	such	such	ADJ
ejpam-5051	765	48	that	that	SCONJ
ejpam-5051	765	49	(	(	PUNCT
ejpam-5051	765	50	i	i	NOUN
ejpam-5051	765	51	)	)	PUNCT
ejpam-5051	765	52	q	q	PROPN
ejpam-5051	765	53	◦	◦	NOUN
ejpam-5051	765	54	pα	pα	NOUN
ejpam-5051	765	55	=	=	NOUN
ejpam-5051	765	56	idbα	idbα	NOUN
ejpam-5051	765	57	(	(	PUNCT
ejpam-5051	765	58	ii	ii	NOUN
ejpam-5051	765	59	)	)	PUNCT
ejpam-5051	765	60	the	the	DET
ejpam-5051	765	61	map	map	NOUN
ejpam-5051	765	62	(	(	PUNCT
ejpam-5051	765	63	β	β	X
ejpam-5051	765	64	,	,	PUNCT
ejpam-5051	765	65	z	z	NOUN
ejpam-5051	765	66	)	)	PUNCT
ejpam-5051	765	67	→	→	SYM
ejpam-5051	765	68	i(r(β	i(r(β	NOUN
ejpam-5051	765	69	)	)	PUNCT
ejpam-5051	765	70	,	,	PUNCT
ejpam-5051	765	71	z)pα(β	z)pα(β	NUM
ejpam-5051	765	72	)	)	PUNCT
ejpam-5051	765	73	is	be	AUX
ejpam-5051	765	74	a	a	DET
ejpam-5051	765	75	homeomorphism	homeomorphism	NOUN
ejpam-5051	765	76	from	from	ADP
ejpam-5051	765	77	bα	bα	PROPN
ejpam-5051	765	78	×	×	PROPN
ejpam-5051	765	79	t	t	NOUN
ejpam-5051	765	80	to	to	ADP
ejpam-5051	765	81	q−1(bα	q−1(bα	NOUN
ejpam-5051	765	82	)	)	PUNCT
ejpam-5051	765	83	.	.	PUNCT
ejpam-5051	766	1	proof	proof	NOUN
ejpam-5051	766	2	.	.	PUNCT
ejpam-5051	767	1	(	(	PUNCT
ejpam-5051	767	2	i	i	NOUN
ejpam-5051	767	3	)	)	PUNCT
ejpam-5051	767	4	let	let	VERB
ejpam-5051	767	5	(	(	PUNCT
ejpam-5051	767	6	χ	χ	X
ejpam-5051	767	7	,	,	PUNCT
ejpam-5051	767	8	γ̇	γ̇	NOUN
ejpam-5051	767	9	)	)	PUNCT
ejpam-5051	767	10	∈	∈	PROPN
ejpam-5051	767	11	â⋊r	â⋊r	NOUN
ejpam-5051	767	12	and	and	CCONJ
ejpam-5051	767	13	bα	bα	PROPN
ejpam-5051	767	14	be	be	AUX
ejpam-5051	767	15	an	an	DET
ejpam-5051	767	16	open	open	ADJ
ejpam-5051	767	17	bisection	bisection	NOUN
ejpam-5051	767	18	of	of	ADP
ejpam-5051	767	19	â⋊r	â⋊r	NOUN
ejpam-5051	767	20	containing	contain	VERB
ejpam-5051	767	21	(	(	PUNCT
ejpam-5051	767	22	χ	χ	ADJ
ejpam-5051	767	23	,	,	PUNCT
ejpam-5051	767	24	γ̇	γ̇	NOUN
ejpam-5051	767	25	)	)	PUNCT
ejpam-5051	767	26	and	and	CCONJ
ejpam-5051	767	27	let	let	VERB
ejpam-5051	767	28	pα	pα	VERB
ejpam-5051	767	29	:	:	PUNCT
ejpam-5051	767	30	bα	bα	PROPN
ejpam-5051	767	31	→	→	SYM
ejpam-5051	767	32	d	d	NOUN
ejpam-5051	767	33	defined	define	VERB
ejpam-5051	767	34	by	by	ADP
ejpam-5051	767	35	pα((χ	pα((χ	NOUN
ejpam-5051	767	36	,	,	PUNCT
ejpam-5051	767	37	γ̇	γ̇	NOUN
ejpam-5051	767	38	)	)	PUNCT
ejpam-5051	767	39	)	)	PUNCT
ejpam-5051	768	1	=	=	PUNCT
ejpam-5051	769	1	[	[	X
ejpam-5051	769	2	χ	χ	X
ejpam-5051	769	3	,	,	PUNCT
ejpam-5051	769	4	z	z	PROPN
ejpam-5051	769	5	,	,	PUNCT
ejpam-5051	769	6	γ	γ	X
ejpam-5051	769	7	]	]	X
ejpam-5051	769	8	.	.	PUNCT
ejpam-5051	770	1	let	let	VERB
ejpam-5051	770	2	u	u	PRON
ejpam-5051	770	3	be	be	AUX
ejpam-5051	770	4	an	an	DET
ejpam-5051	770	5	open	open	ADJ
ejpam-5051	770	6	subset	subset	NOUN
ejpam-5051	770	7	of	of	ADP
ejpam-5051	770	8	d.	d.	PROPN
ejpam-5051	770	9	then	then	ADV
ejpam-5051	770	10	π−1	π−1	PROPN
ejpam-5051	770	11	d	d	X
ejpam-5051	770	12	(	(	PUNCT
ejpam-5051	770	13	u	u	NOUN
ejpam-5051	770	14	)	)	PUNCT
ejpam-5051	770	15	is	be	AUX
ejpam-5051	770	16	open	open	ADJ
ejpam-5051	770	17	in	in	ADP
ejpam-5051	770	18	â	â	PROPN
ejpam-5051	770	19	∗	∗	NOUN
ejpam-5051	770	20	g	g	PROPN
ejpam-5051	770	21	×	×	PROPN
ejpam-5051	770	22	t	t	NOUN
ejpam-5051	770	23	,	,	PUNCT
ejpam-5051	770	24	that	that	ADV
ejpam-5051	770	25	is	is	ADV
ejpam-5051	770	26	,	,	PUNCT
ejpam-5051	771	1	π−1	π−1	PROPN
ejpam-5051	771	2	d	d	X
ejpam-5051	771	3	(	(	PUNCT
ejpam-5051	771	4	u	u	NOUN
ejpam-5051	771	5	)	)	PUNCT
ejpam-5051	771	6	=	=	PUNCT
ejpam-5051	771	7	a	a	DET
ejpam-5051	771	8	∗b	∗b	NOUN
ejpam-5051	771	9	×c	×c	PRON
ejpam-5051	771	10	where	where	SCONJ
ejpam-5051	771	11	a	a	PRON
ejpam-5051	771	12	is	be	AUX
ejpam-5051	771	13	open	open	ADJ
ejpam-5051	771	14	in	in	ADP
ejpam-5051	771	15	â	â	PROPN
ejpam-5051	771	16	,	,	PUNCT
ejpam-5051	771	17	b	b	PROPN
ejpam-5051	771	18	is	be	AUX
ejpam-5051	771	19	open	open	ADJ
ejpam-5051	771	20	in	in	ADP
ejpam-5051	771	21	g	g	PROPN
ejpam-5051	771	22	and	and	CCONJ
ejpam-5051	771	23	c	c	PROPN
ejpam-5051	771	24	is	be	AUX
ejpam-5051	771	25	open	open	ADJ
ejpam-5051	771	26	in	in	ADP
ejpam-5051	771	27	t	t	PROPN
ejpam-5051	771	28	.	.	PUNCT
ejpam-5051	772	1	let	let	VERB
ejpam-5051	772	2	(	(	PUNCT
ejpam-5051	772	3	χ	χ	X
ejpam-5051	772	4	,	,	PUNCT
ejpam-5051	772	5	z	z	PROPN
ejpam-5051	772	6	,	,	PUNCT
ejpam-5051	772	7	γ	γ	NOUN
ejpam-5051	772	8	)	)	PUNCT
ejpam-5051	772	9	∈	∈	NOUN
ejpam-5051	772	10	π−1	π−1	PROPN
ejpam-5051	772	11	d	d	X
ejpam-5051	772	12	(	(	PUNCT
ejpam-5051	772	13	u	u	NOUN
ejpam-5051	772	14	)	)	PUNCT
ejpam-5051	772	15	.	.	PUNCT
ejpam-5051	773	1	then	then	ADV
ejpam-5051	773	2	(	(	PUNCT
ejpam-5051	773	3	χ	χ	X
ejpam-5051	773	4	,	,	PUNCT
ejpam-5051	773	5	z	z	PROPN
ejpam-5051	773	6	,	,	PUNCT
ejpam-5051	773	7	γ	γ	NOUN
ejpam-5051	773	8	)	)	PUNCT
ejpam-5051	773	9	∈	∈	PROPN
ejpam-5051	773	10	a	a	DET
ejpam-5051	773	11	∗b×c	∗b×c	NOUN
ejpam-5051	773	12	,	,	PUNCT
ejpam-5051	773	13	that	that	ADV
ejpam-5051	773	14	is	is	ADV
ejpam-5051	773	15	,	,	PUNCT
ejpam-5051	773	16	χ	χ	PROPN
ejpam-5051	773	17	∈	∈	PROPN
ejpam-5051	773	18	a	a	PRON
ejpam-5051	773	19	and	and	CCONJ
ejpam-5051	773	20	γ	γ	PROPN
ejpam-5051	773	21	∈	∈	PROPN
ejpam-5051	773	22	b.	b.	PROPN
ejpam-5051	773	23	since	since	SCONJ
ejpam-5051	773	24	b	b	PROPN
ejpam-5051	773	25	is	be	AUX
ejpam-5051	773	26	open	open	ADJ
ejpam-5051	773	27	in	in	ADP
ejpam-5051	773	28	g	g	PROPN
ejpam-5051	773	29	,	,	PUNCT
ejpam-5051	773	30	then	then	ADV
ejpam-5051	773	31	πr(b	πr(b	PUNCT
ejpam-5051	773	32	)	)	PUNCT
ejpam-5051	773	33	is	be	AUX
ejpam-5051	773	34	open	open	ADJ
ejpam-5051	773	35	in	in	ADP
ejpam-5051	773	36	d	d	NOUN
ejpam-5051	773	37	containing	contain	VERB
ejpam-5051	773	38	γ̇.	γ̇.	NOUN
ejpam-5051	773	39	let	let	VERB
ejpam-5051	773	40	m	m	VERB
ejpam-5051	773	41	=	=	VERB
ejpam-5051	773	42	a	a	DET
ejpam-5051	773	43	×	×	NOUN
ejpam-5051	773	44	πr(b	πr(b	NUM
ejpam-5051	773	45	)	)	PUNCT
ejpam-5051	773	46	∩	∩	NOUN
ejpam-5051	773	47	â	â	ADP
ejpam-5051	773	48	⋊	⋊	SYM
ejpam-5051	773	49	r.	r.	NOUN
ejpam-5051	773	50	then	then	ADV
ejpam-5051	773	51	(	(	PUNCT
ejpam-5051	773	52	χ	χ	X
ejpam-5051	773	53	,	,	PUNCT
ejpam-5051	773	54	γ̇	γ̇	NOUN
ejpam-5051	773	55	)	)	PUNCT
ejpam-5051	773	56	∈	∈	PROPN
ejpam-5051	773	57	m	m	NOUN
ejpam-5051	773	58	and	and	CCONJ
ejpam-5051	773	59	m	m	VERB
ejpam-5051	773	60	is	be	AUX
ejpam-5051	773	61	open	open	ADJ
ejpam-5051	773	62	in	in	ADP
ejpam-5051	773	63	â	â	DET
ejpam-5051	773	64	⋊	⋊	PROPN
ejpam-5051	773	65	r.	r.	NOUN
ejpam-5051	773	66	since	since	SCONJ
ejpam-5051	773	67	(	(	PUNCT
ejpam-5051	773	68	χ	χ	X
ejpam-5051	773	69	,	,	PUNCT
ejpam-5051	773	70	γ̇	γ̇	NOUN
ejpam-5051	773	71	)	)	PUNCT
ejpam-5051	773	72	is	be	AUX
ejpam-5051	773	73	chosen	choose	VERB
ejpam-5051	773	74	arbitrarily	arbitrarily	ADV
ejpam-5051	773	75	,	,	PUNCT
ejpam-5051	773	76	then	then	ADV
ejpam-5051	773	77	for	for	ADP
ejpam-5051	773	78	every	every	DET
ejpam-5051	773	79	element	element	NOUN
ejpam-5051	773	80	in	in	ADP
ejpam-5051	773	81	p−1	p−1	PROPN
ejpam-5051	773	82	α	α	PROPN
ejpam-5051	773	83	(	(	PUNCT
ejpam-5051	773	84	u	u	NOUN
ejpam-5051	773	85	)	)	PUNCT
ejpam-5051	773	86	there	there	PRON
ejpam-5051	773	87	exists	exist	VERB
ejpam-5051	773	88	an	an	DET
ejpam-5051	773	89	open	open	ADJ
ejpam-5051	773	90	neighborhoodm	neighborhoodm	NOUN
ejpam-5051	773	91	containing	contain	VERB
ejpam-5051	773	92	(	(	PUNCT
ejpam-5051	773	93	χ	χ	NOUN
ejpam-5051	773	94	,	,	PUNCT
ejpam-5051	773	95	γ̇	γ̇	NOUN
ejpam-5051	773	96	)	)	PUNCT
ejpam-5051	773	97	.	.	PUNCT
ejpam-5051	774	1	thus	thus	ADV
ejpam-5051	774	2	,	,	PUNCT
ejpam-5051	774	3	p−1	p−1	PROPN
ejpam-5051	774	4	α	α	PROPN
ejpam-5051	774	5	(	(	PUNCT
ejpam-5051	774	6	u	u	NOUN
ejpam-5051	774	7	)	)	PUNCT
ejpam-5051	774	8	is	be	AUX
ejpam-5051	774	9	open	open	ADJ
ejpam-5051	774	10	and	and	CCONJ
ejpam-5051	774	11	pα	pα	INTJ
ejpam-5051	774	12	is	be	AUX
ejpam-5051	774	13	continuous	continuous	ADJ
ejpam-5051	774	14	.	.	PUNCT
ejpam-5051	775	1	now	now	ADV
ejpam-5051	775	2	,	,	PUNCT
ejpam-5051	775	3	q	q	NOUN
ejpam-5051	775	4	◦	◦	NOUN
ejpam-5051	775	5	pα	pα	VERB
ejpam-5051	775	6	:	:	PUNCT
ejpam-5051	775	7	bα	bα	PROPN
ejpam-5051	775	8	→	→	SYM
ejpam-5051	775	9	â⋊r	â⋊r	PROPN
ejpam-5051	775	10	.	.	PUNCT
ejpam-5051	776	1	then	then	ADV
ejpam-5051	776	2	,	,	PUNCT
ejpam-5051	776	3	q	q	NOUN
ejpam-5051	776	4	◦	◦	NOUN
ejpam-5051	776	5	pα((χ	pα((χ	NOUN
ejpam-5051	776	6	,	,	PUNCT
ejpam-5051	776	7	γ̇	γ̇	NOUN
ejpam-5051	776	8	)	)	PUNCT
ejpam-5051	776	9	)	)	PUNCT
ejpam-5051	777	1	=	=	SYM
ejpam-5051	777	2	q(pα((χ	q(pα((χ	ADJ
ejpam-5051	777	3	,	,	PUNCT
ejpam-5051	777	4	γ̇	γ̇	NOUN
ejpam-5051	777	5	)	)	PUNCT
ejpam-5051	777	6	)	)	PUNCT
ejpam-5051	777	7	)	)	PUNCT
ejpam-5051	778	1	=	=	PUNCT
ejpam-5051	778	2	q([χ	q([χ	NOUN
ejpam-5051	778	3	,	,	PUNCT
ejpam-5051	778	4	z	z	PROPN
ejpam-5051	778	5	,	,	PUNCT
ejpam-5051	778	6	γ	γ	X
ejpam-5051	778	7	]	]	X
ejpam-5051	778	8	)	)	PUNCT
ejpam-5051	778	9	=	=	SYM
ejpam-5051	778	10	(	(	PUNCT
ejpam-5051	778	11	χ	χ	NOUN
ejpam-5051	778	12	,	,	PUNCT
ejpam-5051	778	13	γ̇	γ̇	NOUN
ejpam-5051	778	14	)	)	PUNCT
ejpam-5051	778	15	.	.	PUNCT
ejpam-5051	779	1	hence	hence	ADV
ejpam-5051	779	2	,	,	PUNCT
ejpam-5051	779	3	the	the	DET
ejpam-5051	779	4	image	image	NOUN
ejpam-5051	779	5	of	of	ADP
ejpam-5051	779	6	bα	bα	NOUN
ejpam-5051	779	7	in	in	ADP
ejpam-5051	779	8	pα	pα	NOUN
ejpam-5051	779	9	is	be	AUX
ejpam-5051	779	10	just	just	ADV
ejpam-5051	779	11	itself	itself	PRON
ejpam-5051	779	12	and	and	CCONJ
ejpam-5051	779	13	we	we	PRON
ejpam-5051	779	14	have	have	VERB
ejpam-5051	779	15	q	q	NOUN
ejpam-5051	779	16	◦	◦	NOUN
ejpam-5051	779	17	pα	pα	NOUN
ejpam-5051	779	18	=	=	NOUN
ejpam-5051	779	19	idbα	idbα	NOUN
ejpam-5051	779	20	.	.	PUNCT
ejpam-5051	780	1	(	(	PUNCT
ejpam-5051	780	2	ii	ii	NOUN
ejpam-5051	780	3	)	)	PUNCT
ejpam-5051	780	4	let	let	VERB
ejpam-5051	780	5	θ	θ	NOUN
ejpam-5051	780	6	:	:	PUNCT
ejpam-5051	780	7	βα	βα	VERB
ejpam-5051	780	8	×	×	PROPN
ejpam-5051	780	9	t	t	PROPN
ejpam-5051	780	10	→	→	SYM
ejpam-5051	780	11	q−1(βα	q−1(βα	NOUN
ejpam-5051	780	12	)	)	PUNCT
ejpam-5051	781	1	where	where	SCONJ
ejpam-5051	781	2	βα	βα	AUX
ejpam-5051	781	3	×	×	PROPN
ejpam-5051	781	4	t	t	PROPN
ejpam-5051	781	5	⊆	⊆	NUM
ejpam-5051	781	6	â	â	X
ejpam-5051	781	7	⋊	⋊	NUM
ejpam-5051	781	8	r	r	NOUN
ejpam-5051	781	9	×	×	NOUN
ejpam-5051	781	10	t	t	NOUN
ejpam-5051	781	11	and	and	CCONJ
ejpam-5051	781	12	q−1(βα	q−1(βα	NOUN
ejpam-5051	781	13	)	)	PUNCT
ejpam-5051	781	14	⊆	⊆	NUM
ejpam-5051	781	15	d.	d.	NOUN
ejpam-5051	781	16	let	let	VERB
ejpam-5051	781	17	u	u	PRON
ejpam-5051	781	18	be	be	AUX
ejpam-5051	781	19	an	an	DET
ejpam-5051	781	20	open	open	ADJ
ejpam-5051	781	21	subset	subset	NOUN
ejpam-5051	781	22	of	of	ADP
ejpam-5051	781	23	q−1(βα	q−1(βα	NOUN
ejpam-5051	781	24	)	)	PUNCT
ejpam-5051	781	25	.	.	PUNCT
ejpam-5051	782	1	then	then	ADV
ejpam-5051	782	2	there	there	PRON
ejpam-5051	782	3	exists	exist	VERB
ejpam-5051	782	4	u	u	NOUN
ejpam-5051	782	5	′	′	NOUN
ejpam-5051	782	6	∈	∈	PROPN
ejpam-5051	782	7	â	â	ADP
ejpam-5051	782	8	∗	∗	NOUN
ejpam-5051	782	9	g	g	PROPN
ejpam-5051	782	10	×	×	PROPN
ejpam-5051	782	11	t	t	NOUN
ejpam-5051	782	12	such	such	ADJ
ejpam-5051	782	13	that	that	PRON
ejpam-5051	782	14	u	u	NOUN
ejpam-5051	782	15	=	=	PUNCT
ejpam-5051	782	16	u	u	NOUN
ejpam-5051	782	17	′/	′/	NUM
ejpam-5051	782	18	∼	∼	NOUN
ejpam-5051	782	19	∈	∈	PROPN
ejpam-5051	782	20	d	d	X
ejpam-5051	782	21	where	where	SCONJ
ejpam-5051	782	22	u	u	NOUN
ejpam-5051	782	23	′	′	VERB
ejpam-5051	782	24	is	be	AUX
ejpam-5051	782	25	open	open	ADJ
ejpam-5051	782	26	in	in	ADP
ejpam-5051	782	27	â	â	PROPN
ejpam-5051	782	28	∗	∗	NOUN
ejpam-5051	782	29	g	g	PROPN
ejpam-5051	782	30	×	×	PROPN
ejpam-5051	782	31	t	t	PROPN
ejpam-5051	782	32	.	.	PUNCT
ejpam-5051	783	1	here	here	ADV
ejpam-5051	783	2	,	,	PUNCT
ejpam-5051	783	3	u	u	NOUN
ejpam-5051	783	4	′	′	NOUN
ejpam-5051	783	5	is	be	AUX
ejpam-5051	783	6	the	the	DET
ejpam-5051	783	7	pre	pre	NOUN
ejpam-5051	783	8	-	-	NOUN
ejpam-5051	783	9	image	image	NOUN
ejpam-5051	783	10	of	of	ADP
ejpam-5051	783	11	u	u	NOUN
ejpam-5051	783	12	under	under	ADP
ejpam-5051	783	13	πd	πd	PROPN
ejpam-5051	783	14	.	.	PUNCT
ejpam-5051	784	1	since	since	SCONJ
ejpam-5051	784	2	u	u	NOUN
ejpam-5051	784	3	′	′	NOUN
ejpam-5051	784	4	is	be	AUX
ejpam-5051	784	5	open	open	ADJ
ejpam-5051	784	6	in	in	ADP
ejpam-5051	784	7	â	â	PROPN
ejpam-5051	784	8	∗	∗	NOUN
ejpam-5051	784	9	g	g	PROPN
ejpam-5051	784	10	×	×	PROPN
ejpam-5051	784	11	t	t	NOUN
ejpam-5051	784	12	,	,	PUNCT
ejpam-5051	784	13	then	then	ADV
ejpam-5051	784	14	u	u	NOUN
ejpam-5051	784	15	′	′	NOUN
ejpam-5051	784	16	=	=	PUNCT
ejpam-5051	784	17	(	(	PUNCT
ejpam-5051	784	18	a	a	DET
ejpam-5051	784	19	×	×	PROPN
ejpam-5051	784	20	b	b	NOUN
ejpam-5051	784	21	)	)	PUNCT
ejpam-5051	784	22	×	×	NOUN
ejpam-5051	784	23	c	c	NOUN
ejpam-5051	784	24	where	where	SCONJ
ejpam-5051	784	25	a	a	PRON
ejpam-5051	784	26	is	be	AUX
ejpam-5051	784	27	open	open	ADJ
ejpam-5051	784	28	in	in	ADP
ejpam-5051	784	29	â	â	PROPN
ejpam-5051	784	30	,	,	PUNCT
ejpam-5051	784	31	b	b	PROPN
ejpam-5051	784	32	is	be	AUX
ejpam-5051	784	33	open	open	ADJ
ejpam-5051	784	34	in	in	ADP
ejpam-5051	784	35	g	g	PROPN
ejpam-5051	784	36	and	and	CCONJ
ejpam-5051	784	37	c	c	PROPN
ejpam-5051	784	38	is	be	AUX
ejpam-5051	784	39	open	open	ADJ
ejpam-5051	784	40	in	in	ADP
ejpam-5051	784	41	the	the	DET
ejpam-5051	784	42	discrete	discrete	ADJ
ejpam-5051	784	43	topology	topology	NOUN
ejpam-5051	784	44	for	for	ADP
ejpam-5051	784	45	t	t	PROPN
ejpam-5051	784	46	.	.	PUNCT
ejpam-5051	785	1	note	note	VERB
ejpam-5051	785	2	that	that	SCONJ
ejpam-5051	785	3	θ−1(u	θ−1(u	PROPN
ejpam-5051	785	4	)	)	PUNCT
ejpam-5051	786	1	=	=	PRON
ejpam-5051	786	2	{	{	PUNCT
ejpam-5051	786	3	(	(	PUNCT
ejpam-5051	786	4	χ	χ	NOUN
ejpam-5051	786	5	,	,	PUNCT
ejpam-5051	786	6	z	z	NOUN
ejpam-5051	786	7	,	,	PUNCT
ejpam-5051	786	8	γ̇	γ̇	NOUN
ejpam-5051	786	9	)	)	PUNCT
ejpam-5051	786	10	∈	∈	PROPN
ejpam-5051	786	11	â	â	ADP
ejpam-5051	786	12	⋊	⋊	SYM
ejpam-5051	786	13	r	r	NOUN
ejpam-5051	786	14	×	×	NOUN
ejpam-5051	786	15	t	t	NOUN
ejpam-5051	786	16	:	:	PUNCT
ejpam-5051	786	17	θ(χ	θ(χ	PROPN
ejpam-5051	786	18	,	,	PUNCT
ejpam-5051	786	19	z	z	NOUN
ejpam-5051	786	20	,	,	PUNCT
ejpam-5051	786	21	γ̇	γ̇	NOUN
ejpam-5051	786	22	)	)	PUNCT
ejpam-5051	786	23	∈	∈	PROPN
ejpam-5051	786	24	u	u	NOUN
ejpam-5051	786	25	)	)	PUNCT
ejpam-5051	786	26	}	}	PUNCT
ejpam-5051	786	27	.	.	PUNCT
ejpam-5051	787	1	since	since	SCONJ
ejpam-5051	787	2	u	u	NOUN
ejpam-5051	787	3	=	=	PROPN
ejpam-5051	787	4	u	u	NOUN
ejpam-5051	787	5	′/	′/	NUM
ejpam-5051	787	6	∼	∼	NOUN
ejpam-5051	787	7	,	,	PUNCT
ejpam-5051	787	8	then	then	ADV
ejpam-5051	787	9	there	there	PRON
ejpam-5051	787	10	exists	exist	VERB
ejpam-5051	787	11	an	an	DET
ejpam-5051	787	12	element	element	NOUN
ejpam-5051	787	13	(	(	PUNCT
ejpam-5051	787	14	χ	χ	NOUN
ejpam-5051	787	15	,	,	PUNCT
ejpam-5051	787	16	z	z	PROPN
ejpam-5051	787	17	,	,	PUNCT
ejpam-5051	787	18	γ	γ	NOUN
ejpam-5051	787	19	)	)	PUNCT
ejpam-5051	787	20	in	in	ADP
ejpam-5051	787	21	u	u	NOUN
ejpam-5051	787	22	′	′	ADP
ejpam-5051	787	23	whose	whose	DET
ejpam-5051	787	24	equivalence	equivalence	NOUN
ejpam-5051	787	25	class	class	NOUN
ejpam-5051	787	26	in	in	ADP
ejpam-5051	787	27	d	d	PROPN
ejpam-5051	787	28	is	be	AUX
ejpam-5051	787	29	in	in	ADP
ejpam-5051	787	30	u	u	PROPN
ejpam-5051	787	31	.	.	PUNCT
ejpam-5051	788	1	since	since	SCONJ
ejpam-5051	788	2	(	(	PUNCT
ejpam-5051	788	3	χ	χ	X
ejpam-5051	788	4	,	,	PUNCT
ejpam-5051	788	5	z	z	PROPN
ejpam-5051	788	6	,	,	PUNCT
ejpam-5051	788	7	γ	γ	NOUN
ejpam-5051	788	8	)	)	PUNCT
ejpam-5051	788	9	∈	∈	PROPN
ejpam-5051	788	10	u	u	NOUN
ejpam-5051	788	11	′	′	NOUN
ejpam-5051	788	12	,	,	PUNCT
ejpam-5051	788	13	then	then	ADV
ejpam-5051	788	14	χ	χ	PROPN
ejpam-5051	788	15	∈	∈	PROPN
ejpam-5051	788	16	â	â	PROPN
ejpam-5051	788	17	,	,	PUNCT
ejpam-5051	788	18	z	z	PROPN
ejpam-5051	788	19	∈	∈	PROPN
ejpam-5051	788	20	c	c	NOUN
ejpam-5051	788	21	which	which	PRON
ejpam-5051	788	22	is	be	AUX
ejpam-5051	788	23	open	open	ADJ
ejpam-5051	788	24	in	in	ADP
ejpam-5051	788	25	t	t	PROPN
ejpam-5051	788	26	,	,	PUNCT
ejpam-5051	788	27	and	and	CCONJ
ejpam-5051	788	28	γ	γ	PROPN
ejpam-5051	788	29	∈	∈	PROPN
ejpam-5051	788	30	b	b	PROPN
ejpam-5051	788	31	which	which	PRON
ejpam-5051	788	32	is	be	AUX
ejpam-5051	788	33	open	open	ADJ
ejpam-5051	788	34	in	in	ADP
ejpam-5051	788	35	g.	g.	PROPN
ejpam-5051	788	36	since	since	SCONJ
ejpam-5051	788	37	we	we	PRON
ejpam-5051	788	38	have	have	VERB
ejpam-5051	788	39	b	b	NOUN
ejpam-5051	788	40	to	to	PART
ejpam-5051	788	41	be	be	AUX
ejpam-5051	788	42	an	an	DET
ejpam-5051	788	43	open	open	ADJ
ejpam-5051	788	44	set	set	NOUN
ejpam-5051	788	45	in	in	ADP
ejpam-5051	788	46	g	g	NOUN
ejpam-5051	788	47	containing	contain	VERB
ejpam-5051	788	48	γ	γ	NOUN
ejpam-5051	788	49	,	,	PUNCT
ejpam-5051	788	50	then	then	ADV
ejpam-5051	788	51	there	there	PRON
ejpam-5051	788	52	exists	exist	VERB
ejpam-5051	788	53	open	open	ADJ
ejpam-5051	788	54	set	set	VERB
ejpam-5051	788	55	m	m	NOUN
ejpam-5051	788	56	in	in	ADP
ejpam-5051	788	57	r	r	NOUN
ejpam-5051	788	58	containing	contain	VERB
ejpam-5051	788	59	γ̇.	γ̇.	NOUN
ejpam-5051	788	60	hence	hence	ADV
ejpam-5051	788	61	,	,	PUNCT
ejpam-5051	788	62	(	(	PUNCT
ejpam-5051	788	63	a×m)×c	a×m)×c	PROPN
ejpam-5051	788	64	is	be	AUX
ejpam-5051	788	65	an	an	DET
ejpam-5051	788	66	open	open	ADJ
ejpam-5051	788	67	set	set	NOUN
ejpam-5051	788	68	in	in	ADP
ejpam-5051	788	69	â⋊r×	â⋊r×	PROPN
ejpam-5051	788	70	t	t	NOUN
ejpam-5051	788	71	.	.	PUNCT
ejpam-5051	789	1	since	since	SCONJ
ejpam-5051	789	2	(	(	PUNCT
ejpam-5051	789	3	χ	χ	X
ejpam-5051	789	4	,	,	PUNCT
ejpam-5051	789	5	z	z	NOUN
ejpam-5051	789	6	,	,	PUNCT
ejpam-5051	789	7	γ̇	γ̇	NOUN
ejpam-5051	789	8	)	)	PUNCT
ejpam-5051	789	9	is	be	AUX
ejpam-5051	789	10	arbitrary	arbitrary	ADJ
ejpam-5051	789	11	,	,	PUNCT
ejpam-5051	789	12	we	we	PRON
ejpam-5051	789	13	have	have	AUX
ejpam-5051	789	14	shown	show	VERB
ejpam-5051	789	15	that	that	SCONJ
ejpam-5051	789	16	every	every	DET
ejpam-5051	789	17	element	element	NOUN
ejpam-5051	789	18	in	in	ADP
ejpam-5051	789	19	θ−1(u	θ−1(u	PROPN
ejpam-5051	789	20	)	)	PUNCT
ejpam-5051	789	21	is	be	AUX
ejpam-5051	789	22	contained	contain	VERB
ejpam-5051	789	23	in	in	ADP
ejpam-5051	789	24	some	some	DET
ejpam-5051	789	25	open	open	ADJ
ejpam-5051	789	26	set	set	NOUN
ejpam-5051	789	27	in	in	ADP
ejpam-5051	789	28	â⋊r×	â⋊r×	PROPN
ejpam-5051	789	29	t	t	NOUN
ejpam-5051	789	30	.	.	PUNCT
ejpam-5051	790	1	thus	thus	ADV
ejpam-5051	790	2	,	,	PUNCT
ejpam-5051	790	3	θ	θ	PROPN
ejpam-5051	790	4	is	be	AUX
ejpam-5051	790	5	continuous	continuous	ADJ
ejpam-5051	790	6	.	.	PUNCT
ejpam-5051	791	1	note	note	VERB
ejpam-5051	791	2	that	that	SCONJ
ejpam-5051	791	3	θ−1	θ−1	PROPN
ejpam-5051	791	4	:	:	PUNCT
ejpam-5051	791	5	q−1(βα	q−1(βα	NOUN
ejpam-5051	791	6	)	)	PUNCT
ejpam-5051	791	7	→	→	SYM
ejpam-5051	791	8	βα	βα	VERB
ejpam-5051	791	9	×	×	PROPN
ejpam-5051	791	10	t	t	PROPN
ejpam-5051	791	11	.	.	PUNCT
ejpam-5051	792	1	let	let	VERB
ejpam-5051	792	2	u	u	PRON
ejpam-5051	792	3	be	be	AUX
ejpam-5051	792	4	an	an	DET
ejpam-5051	792	5	open	open	ADJ
ejpam-5051	792	6	subset	subset	NOUN
ejpam-5051	792	7	of	of	ADP
ejpam-5051	792	8	βα	βα	PROPN
ejpam-5051	792	9	×	×	PROPN
ejpam-5051	792	10	t	t	PROPN
ejpam-5051	792	11	.	.	PUNCT
ejpam-5051	793	1	then	then	ADV
ejpam-5051	793	2	,	,	PUNCT
ejpam-5051	793	3	u	u	NOUN
ejpam-5051	793	4	=	=	X
ejpam-5051	793	5	v	v	NUM
ejpam-5051	793	6	×t	×t	NOUN
ejpam-5051	793	7	′	′	VERB
ejpam-5051	793	8	where	where	SCONJ
ejpam-5051	793	9	v	v	NOUN
ejpam-5051	793	10	is	be	AUX
ejpam-5051	793	11	open	open	ADJ
ejpam-5051	793	12	in	in	ADP
ejpam-5051	793	13	â⋊r	â⋊r	PROPN
ejpam-5051	793	14	and	and	CCONJ
ejpam-5051	793	15	t	t	NOUN
ejpam-5051	793	16	′	′	NUM
ejpam-5051	793	17	is	be	AUX
ejpam-5051	793	18	open	open	ADJ
ejpam-5051	793	19	in	in	ADP
ejpam-5051	793	20	t	t	PROPN
ejpam-5051	793	21	.	.	PUNCT
ejpam-5051	794	1	let	let	VERB
ejpam-5051	794	2	[	[	X
ejpam-5051	794	3	χ	χ	X
ejpam-5051	794	4	,	,	PUNCT
ejpam-5051	794	5	z	z	PROPN
ejpam-5051	794	6	,	,	PUNCT
ejpam-5051	794	7	γ	γ	X
ejpam-5051	794	8	]	]	X
ejpam-5051	794	9	∈	∈	PROPN
ejpam-5051	794	10	θ(u	θ(u	PROPN
ejpam-5051	794	11	)	)	PUNCT
ejpam-5051	794	12	.	.	PUNCT
ejpam-5051	795	1	then	then	ADV
ejpam-5051	795	2	r.	r.	PROPN
ejpam-5051	795	3	s.	s.	PROPN
ejpam-5051	795	4	bongcawel	bongcawel	PROPN
ejpam-5051	795	5	et	et	PROPN
ejpam-5051	795	6	al	al	PROPN
ejpam-5051	795	7	.	.	PUNCT
ejpam-5051	795	8	/	/	SYM
ejpam-5051	795	9	eur	eur	PROPN
ejpam-5051	795	10	.	.	PUNCT
ejpam-5051	796	1	j.	j.	PROPN
ejpam-5051	796	2	pure	pure	PROPN
ejpam-5051	796	3	appl	appl	PROPN
ejpam-5051	796	4	.	.	PROPN
ejpam-5051	796	5	math	math	PROPN
ejpam-5051	796	6	,	,	PUNCT
ejpam-5051	796	7	17	17	NUM
ejpam-5051	796	8	(	(	PUNCT
ejpam-5051	796	9	1	1	NUM
ejpam-5051	796	10	)	)	PUNCT
ejpam-5051	796	11	(	(	PUNCT
ejpam-5051	796	12	2024	2024	NUM
ejpam-5051	796	13	)	)	PUNCT
ejpam-5051	796	14	,	,	PUNCT
ejpam-5051	796	15	519	519	NUM
ejpam-5051	796	16	-	-	SYM
ejpam-5051	796	17	545	545	NUM
ejpam-5051	796	18	538	538	NUM
ejpam-5051	796	19	θ−1([χ	θ−1([χ	NOUN
ejpam-5051	796	20	,	,	PUNCT
ejpam-5051	796	21	z	z	PROPN
ejpam-5051	796	22	,	,	PUNCT
ejpam-5051	796	23	γ	γ	NOUN
ejpam-5051	796	24	]	]	X
ejpam-5051	796	25	)	)	PUNCT
ejpam-5051	796	26	∈	∈	NOUN
ejpam-5051	796	27	v	v	NOUN
ejpam-5051	796	28	×t	×t	NOUN
ejpam-5051	796	29	′	′	NOUN
ejpam-5051	796	30	,	,	PUNCT
ejpam-5051	796	31	that	that	ADV
ejpam-5051	796	32	is	is	ADV
ejpam-5051	796	33	,	,	PUNCT
ejpam-5051	796	34	(	(	PUNCT
ejpam-5051	796	35	χ	χ	X
ejpam-5051	796	36	,	,	PUNCT
ejpam-5051	796	37	z	z	PROPN
ejpam-5051	796	38	,	,	PUNCT
ejpam-5051	796	39	γ	γ	NOUN
ejpam-5051	796	40	)	)	PUNCT
ejpam-5051	796	41	∈	∈	PROPN
ejpam-5051	796	42	v	v	NOUN
ejpam-5051	796	43	×t	×t	NOUN
ejpam-5051	796	44	′.	′.	NOUN
ejpam-5051	796	45	hence	hence	ADV
ejpam-5051	796	46	,	,	PUNCT
ejpam-5051	796	47	z	z	PROPN
ejpam-5051	796	48	∈	∈	PROPN
ejpam-5051	796	49	t	t	NOUN
ejpam-5051	796	50	′	′	NOUN
ejpam-5051	797	1	and	and	CCONJ
ejpam-5051	797	2	(	(	PUNCT
ejpam-5051	797	3	χ	χ	X
ejpam-5051	797	4	,	,	PUNCT
ejpam-5051	797	5	γ̇	γ̇	NOUN
ejpam-5051	797	6	)	)	PUNCT
ejpam-5051	797	7	∈	∈	PROPN
ejpam-5051	797	8	v	v	NOUN
ejpam-5051	797	9	.	.	PUNCT
ejpam-5051	798	1	since	since	SCONJ
ejpam-5051	798	2	v	v	NOUN
ejpam-5051	798	3	is	be	AUX
ejpam-5051	798	4	open	open	ADJ
ejpam-5051	798	5	in	in	ADP
ejpam-5051	798	6	â⋊r	â⋊r	NOUN
ejpam-5051	798	7	,	,	PUNCT
ejpam-5051	798	8	then	then	ADV
ejpam-5051	798	9	v	v	NOUN
ejpam-5051	798	10	=	=	SYM
ejpam-5051	798	11	a×b	a×b	PROPN
ejpam-5051	798	12	∩	∩	ADJ
ejpam-5051	798	13	â⋊r	â⋊r	NOUN
ejpam-5051	798	14	where	where	SCONJ
ejpam-5051	798	15	χ	χ	PROPN
ejpam-5051	798	16	∈	∈	PROPN
ejpam-5051	798	17	a	a	X
ejpam-5051	798	18	,	,	PUNCT
ejpam-5051	798	19	a	a	DET
ejpam-5051	798	20	open	open	NOUN
ejpam-5051	798	21	in	in	ADP
ejpam-5051	798	22	â	â	PROPN
ejpam-5051	798	23	and	and	CCONJ
ejpam-5051	798	24	γ̇	γ̇	PROPN
ejpam-5051	798	25	∈	∈	PROPN
ejpam-5051	798	26	b	b	PROPN
ejpam-5051	798	27	,	,	PUNCT
ejpam-5051	798	28	b	b	X
ejpam-5051	798	29	open	open	ADJ
ejpam-5051	798	30	in	in	ADP
ejpam-5051	798	31	r.	r.	PROPN
ejpam-5051	798	32	thus	thus	ADV
ejpam-5051	798	33	,	,	PUNCT
ejpam-5051	798	34	π−1	π−1	PROPN
ejpam-5051	798	35	r	r	NOUN
ejpam-5051	798	36	(	(	PUNCT
ejpam-5051	798	37	b	b	NOUN
ejpam-5051	798	38	)	)	PUNCT
ejpam-5051	798	39	is	be	AUX
ejpam-5051	798	40	open	open	ADJ
ejpam-5051	798	41	in	in	ADP
ejpam-5051	798	42	g.	g.	PROPN
ejpam-5051	798	43	let	let	VERB
ejpam-5051	798	44	π−1	π−1	PROPN
ejpam-5051	798	45	d	d	X
ejpam-5051	798	46	(	(	PUNCT
ejpam-5051	798	47	θ(u	θ(u	NUM
ejpam-5051	798	48	)	)	PUNCT
ejpam-5051	798	49	)	)	PUNCT
ejpam-5051	799	1	=	=	PUNCT
ejpam-5051	799	2	m	m	X
ejpam-5051	799	3	=	=	PUNCT
ejpam-5051	799	4	a	a	DET
ejpam-5051	799	5	∗	∗	NOUN
ejpam-5051	799	6	π−1	π−1	PROPN
ejpam-5051	799	7	r	r	NOUN
ejpam-5051	799	8	(	(	PUNCT
ejpam-5051	799	9	b	b	NOUN
ejpam-5051	799	10	)	)	PUNCT
ejpam-5051	799	11	×	×	NOUN
ejpam-5051	799	12	t	t	NOUN
ejpam-5051	799	13	′	′	NUM
ejpam-5051	799	14	which	which	PRON
ejpam-5051	799	15	is	be	AUX
ejpam-5051	799	16	open	open	ADJ
ejpam-5051	799	17	in	in	ADP
ejpam-5051	799	18	â	â	PROPN
ejpam-5051	799	19	∗	∗	NOUN
ejpam-5051	799	20	g	g	PROPN
ejpam-5051	799	21	×	×	PROPN
ejpam-5051	799	22	t	t	PROPN
ejpam-5051	799	23	.	.	PUNCT
ejpam-5051	800	1	hence	hence	ADV
ejpam-5051	800	2	,	,	PUNCT
ejpam-5051	800	3	θ(u	θ(u	PROPN
ejpam-5051	800	4	)	)	PUNCT
ejpam-5051	800	5	is	be	AUX
ejpam-5051	800	6	open	open	ADJ
ejpam-5051	800	7	q−1(bα	q−1(bα	NOUN
ejpam-5051	800	8	)	)	PUNCT
ejpam-5051	800	9	and	and	CCONJ
ejpam-5051	800	10	θ−1	θ−1	PROPN
ejpam-5051	800	11	is	be	AUX
ejpam-5051	800	12	continuous	continuous	ADJ
ejpam-5051	800	13	.	.	PUNCT
ejpam-5051	801	1	therefore	therefore	ADV
ejpam-5051	801	2	,	,	PUNCT
ejpam-5051	801	3	θ	θ	PROPN
ejpam-5051	801	4	is	be	AUX
ejpam-5051	801	5	a	a	DET
ejpam-5051	801	6	homeomorphism	homeomorphism	NOUN
ejpam-5051	801	7	.	.	PUNCT
ejpam-5051	802	1	theorem	theorem	NOUN
ejpam-5051	802	2	6	6	NUM
ejpam-5051	802	3	.	.	PUNCT
ejpam-5051	803	1	the	the	DET
ejpam-5051	803	2	image	image	NOUN
ejpam-5051	803	3	i(â×t	i(â×t	VERB
ejpam-5051	803	4	)	)	PUNCT
ejpam-5051	803	5	is	be	AUX
ejpam-5051	803	6	central	central	ADJ
ejpam-5051	803	7	in	in	ADP
ejpam-5051	803	8	d	d	PROPN
ejpam-5051	803	9	in	in	ADP
ejpam-5051	803	10	the	the	DET
ejpam-5051	803	11	sense	sense	NOUN
ejpam-5051	803	12	that	that	SCONJ
ejpam-5051	803	13	i(r([χ	i(r([χ	NOUN
ejpam-5051	803	14	,	,	PUNCT
ejpam-5051	803	15	z	z	PROPN
ejpam-5051	803	16	,	,	PUNCT
ejpam-5051	803	17	γ	γ	NOUN
ejpam-5051	803	18	]	]	X
ejpam-5051	803	19	)	)	PUNCT
ejpam-5051	803	20	,	,	PUNCT
ejpam-5051	803	21	z)[χ	z)[χ	PROPN
ejpam-5051	803	22	,	,	PUNCT
ejpam-5051	803	23	z	z	PROPN
ejpam-5051	803	24	,	,	PUNCT
ejpam-5051	803	25	γ	γ	X
ejpam-5051	803	26	]	]	X
ejpam-5051	803	27	=	=	PUNCT
ejpam-5051	804	1	[	[	X
ejpam-5051	804	2	χ	χ	X
ejpam-5051	804	3	,	,	PUNCT
ejpam-5051	804	4	z	z	PROPN
ejpam-5051	804	5	,	,	PUNCT
ejpam-5051	804	6	γ]i(s([χ	γ]i(s([χ	PROPN
ejpam-5051	804	7	,	,	PUNCT
ejpam-5051	804	8	z	z	PROPN
ejpam-5051	804	9	,	,	PUNCT
ejpam-5051	804	10	γ	γ	NOUN
ejpam-5051	804	11	]	]	X
ejpam-5051	804	12	)	)	PUNCT
ejpam-5051	804	13	,	,	PUNCT
ejpam-5051	804	14	z	z	NOUN
ejpam-5051	804	15	)	)	PUNCT
ejpam-5051	804	16	for	for	ADP
ejpam-5051	804	17	all	all	PRON
ejpam-5051	804	18	[	[	X
ejpam-5051	804	19	χ	χ	X
ejpam-5051	804	20	,	,	PUNCT
ejpam-5051	804	21	z	z	PROPN
ejpam-5051	804	22	,	,	PUNCT
ejpam-5051	804	23	γ	γ	X
ejpam-5051	804	24	]	]	X
ejpam-5051	804	25	∈	∈	PROPN
ejpam-5051	804	26	d	d	NOUN
ejpam-5051	804	27	and	and	CCONJ
ejpam-5051	804	28	z	z	PROPN
ejpam-5051	804	29	∈	∈	PROPN
ejpam-5051	804	30	t	t	NOUN
ejpam-5051	804	31	.	.	PUNCT
ejpam-5051	805	1	proof	proof	NOUN
ejpam-5051	805	2	.	.	PUNCT
ejpam-5051	806	1	let	let	VERB
ejpam-5051	806	2	[	[	X
ejpam-5051	806	3	χ	χ	X
ejpam-5051	806	4	,	,	PUNCT
ejpam-5051	806	5	z	z	PROPN
ejpam-5051	806	6	,	,	PUNCT
ejpam-5051	806	7	γ	γ	X
ejpam-5051	806	8	]	]	X
ejpam-5051	806	9	∈	∈	PROPN
ejpam-5051	806	10	d	d	NOUN
ejpam-5051	806	11	and	and	CCONJ
ejpam-5051	806	12	z′	z′	NUM
ejpam-5051	806	13	∈	∈	PROPN
ejpam-5051	806	14	t	t	NOUN
ejpam-5051	806	15	.	.	PUNCT
ejpam-5051	807	1	now	now	ADV
ejpam-5051	807	2	,	,	PUNCT
ejpam-5051	807	3	i(r([χ	i(r([χ	NOUN
ejpam-5051	807	4	,	,	PUNCT
ejpam-5051	807	5	z	z	PROPN
ejpam-5051	807	6	,	,	PUNCT
ejpam-5051	807	7	γ	γ	NOUN
ejpam-5051	807	8	]	]	X
ejpam-5051	807	9	)	)	PUNCT
ejpam-5051	807	10	,	,	PUNCT
ejpam-5051	807	11	z′)[χ	z′)[χ	PROPN
ejpam-5051	807	12	,	,	PUNCT
ejpam-5051	807	13	z	z	PROPN
ejpam-5051	807	14	,	,	PUNCT
ejpam-5051	807	15	γ	γ	X
ejpam-5051	807	16	]	]	X
ejpam-5051	807	17	=	=	SYM
ejpam-5051	807	18	i((χ	i((χ	NOUN
ejpam-5051	807	19	,	,	PUNCT
ejpam-5051	807	20	r(γ	r(γ	NOUN
ejpam-5051	807	21	)	)	PUNCT
ejpam-5051	807	22	)	)	PUNCT
ejpam-5051	807	23	,	,	PUNCT
ejpam-5051	807	24	z′)[χ	z′)[χ	PROPN
ejpam-5051	807	25	,	,	PUNCT
ejpam-5051	807	26	z	z	PROPN
ejpam-5051	807	27	,	,	PUNCT
ejpam-5051	807	28	γ	γ	X
ejpam-5051	807	29	]	]	X
ejpam-5051	807	30	=	=	PUNCT
ejpam-5051	808	1	[	[	X
ejpam-5051	808	2	χ	χ	X
ejpam-5051	808	3	,	,	PUNCT
ejpam-5051	808	4	z′	z′	PROPN
ejpam-5051	808	5	,	,	PUNCT
ejpam-5051	808	6	r(γ)][χ	r(γ)][χ	NOUN
ejpam-5051	808	7	,	,	PUNCT
ejpam-5051	808	8	z	z	PROPN
ejpam-5051	808	9	,	,	PUNCT
ejpam-5051	808	10	γ	γ	X
ejpam-5051	808	11	]	]	X
ejpam-5051	808	12	=	=	PUNCT
ejpam-5051	809	1	[	[	X
ejpam-5051	809	2	χ	χ	X
ejpam-5051	809	3	,	,	PUNCT
ejpam-5051	809	4	z′z	z′z	NOUN
ejpam-5051	809	5	,	,	PUNCT
ejpam-5051	809	6	r(γ)γ	r(γ)γ	VERB
ejpam-5051	809	7	]	]	PUNCT
ejpam-5051	809	8	=	=	PUNCT
ejpam-5051	810	1	[	[	X
ejpam-5051	810	2	χ	χ	X
ejpam-5051	810	3	,	,	PUNCT
ejpam-5051	810	4	z′z	z′z	NOUN
ejpam-5051	810	5	,	,	PUNCT
ejpam-5051	810	6	γ	γ	X
ejpam-5051	810	7	]	]	X
ejpam-5051	810	8	.	.	PUNCT
ejpam-5051	811	1	also	also	ADV
ejpam-5051	811	2	,	,	PUNCT
ejpam-5051	811	3	[	[	X
ejpam-5051	811	4	χ	χ	X
ejpam-5051	811	5	,	,	PUNCT
ejpam-5051	811	6	z	z	PROPN
ejpam-5051	811	7	,	,	PUNCT
ejpam-5051	811	8	γ]i(s([χ	γ]i(s([χ	PROPN
ejpam-5051	811	9	,	,	PUNCT
ejpam-5051	811	10	z	z	PROPN
ejpam-5051	811	11	,	,	PUNCT
ejpam-5051	811	12	γ	γ	NOUN
ejpam-5051	811	13	]	]	X
ejpam-5051	811	14	)	)	PUNCT
ejpam-5051	811	15	,	,	PUNCT
ejpam-5051	811	16	z′	z′	NUM
ejpam-5051	811	17	)	)	PUNCT
ejpam-5051	812	1	=	=	PUNCT
ejpam-5051	813	1	[	[	X
ejpam-5051	813	2	χ	χ	X
ejpam-5051	813	3	,	,	PUNCT
ejpam-5051	813	4	z	z	NOUN
ejpam-5051	813	5	,	,	PUNCT
ejpam-5051	813	6	γ]i((χ	γ]i((χ	PROPN
ejpam-5051	813	7	·	·	PUNCT
ejpam-5051	813	8	γ	γ	X
ejpam-5051	813	9	,	,	PUNCT
ejpam-5051	813	10	s(γ	s(γ	PROPN
ejpam-5051	813	11	)	)	PUNCT
ejpam-5051	813	12	,	,	PUNCT
ejpam-5051	813	13	z′	z′	NUM
ejpam-5051	813	14	)	)	PUNCT
ejpam-5051	813	15	)	)	PUNCT
ejpam-5051	813	16	=	=	PUNCT
ejpam-5051	814	1	[	[	X
ejpam-5051	814	2	χ	χ	X
ejpam-5051	814	3	,	,	PUNCT
ejpam-5051	814	4	z	z	NOUN
ejpam-5051	814	5	,	,	PUNCT
ejpam-5051	814	6	γ][χ	γ][χ	NOUN
ejpam-5051	814	7	·	·	PUNCT
ejpam-5051	814	8	γ	γ	X
ejpam-5051	814	9	,	,	PUNCT
ejpam-5051	814	10	z′	z′	PROPN
ejpam-5051	814	11	,	,	PUNCT
ejpam-5051	814	12	s(γ	s(γ	PROPN
ejpam-5051	814	13	)	)	PUNCT
ejpam-5051	814	14	)	)	PUNCT
ejpam-5051	814	15	]	]	PUNCT
ejpam-5051	815	1	=	=	PUNCT
ejpam-5051	816	1	[	[	X
ejpam-5051	816	2	χ	χ	X
ejpam-5051	816	3	,	,	PUNCT
ejpam-5051	816	4	zz′	zz′	NUM
ejpam-5051	816	5	,	,	PUNCT
ejpam-5051	816	6	γs(γ	γs(γ	NUM
ejpam-5051	816	7	)	)	PUNCT
ejpam-5051	816	8	]	]	PUNCT
ejpam-5051	817	1	=	=	PUNCT
ejpam-5051	818	1	[	[	X
ejpam-5051	818	2	χ	χ	X
ejpam-5051	818	3	,	,	PUNCT
ejpam-5051	818	4	zz′	zz′	NUM
ejpam-5051	818	5	,	,	PUNCT
ejpam-5051	818	6	γ	γ	NOUN
ejpam-5051	818	7	]	]	X
ejpam-5051	818	8	.	.	PUNCT
ejpam-5051	819	1	hence	hence	ADV
ejpam-5051	819	2	,	,	PUNCT
ejpam-5051	819	3	i(r([χ	i(r([χ	NOUN
ejpam-5051	819	4	,	,	PUNCT
ejpam-5051	819	5	z	z	PROPN
ejpam-5051	819	6	,	,	PUNCT
ejpam-5051	819	7	γ	γ	NOUN
ejpam-5051	819	8	]	]	X
ejpam-5051	819	9	)	)	PUNCT
ejpam-5051	819	10	,	,	PUNCT
ejpam-5051	819	11	z′)[χ	z′)[χ	PROPN
ejpam-5051	819	12	,	,	PUNCT
ejpam-5051	819	13	z	z	PROPN
ejpam-5051	819	14	,	,	PUNCT
ejpam-5051	819	15	γ	γ	X
ejpam-5051	819	16	]	]	X
ejpam-5051	819	17	=	=	PUNCT
ejpam-5051	820	1	[	[	X
ejpam-5051	820	2	χ	χ	X
ejpam-5051	820	3	,	,	PUNCT
ejpam-5051	820	4	z	z	PROPN
ejpam-5051	820	5	,	,	PUNCT
ejpam-5051	820	6	γ]i(s([χ	γ]i(s([χ	PROPN
ejpam-5051	820	7	,	,	PUNCT
ejpam-5051	820	8	z	z	PROPN
ejpam-5051	820	9	,	,	PUNCT
ejpam-5051	820	10	γ	γ	NOUN
ejpam-5051	820	11	]	]	X
ejpam-5051	820	12	)	)	PUNCT
ejpam-5051	820	13	,	,	PUNCT
ejpam-5051	820	14	z′	z′	NUM
ejpam-5051	820	15	)	)	PUNCT
ejpam-5051	820	16	and	and	CCONJ
ejpam-5051	820	17	so	so	ADV
ejpam-5051	820	18	the	the	DET
ejpam-5051	820	19	image	image	NOUN
ejpam-5051	820	20	of	of	ADP
ejpam-5051	820	21	i	i	PRON
ejpam-5051	820	22	is	be	AUX
ejpam-5051	820	23	central	central	ADJ
ejpam-5051	820	24	in	in	ADP
ejpam-5051	820	25	d.	d.	PROPN
ejpam-5051	820	26	the	the	DET
ejpam-5051	820	27	following	follow	VERB
ejpam-5051	820	28	corollary	corollary	NOUN
ejpam-5051	820	29	follows	follow	VERB
ejpam-5051	820	30	from	from	ADP
ejpam-5051	820	31	theorems	theorem	NOUN
ejpam-5051	820	32	4	4	NUM
ejpam-5051	820	33	,	,	PUNCT
ejpam-5051	820	34	5	5	NUM
ejpam-5051	820	35	and	and	CCONJ
ejpam-5051	820	36	lemma	lemma	PROPN
ejpam-5051	820	37	6	6	NUM
ejpam-5051	820	38	.	.	PUNCT
ejpam-5051	820	39	corollary	corollary	ADJ
ejpam-5051	820	40	1	1	NUM
ejpam-5051	820	41	.	.	PUNCT
ejpam-5051	821	1	(	(	PUNCT
ejpam-5051	821	2	d	d	X
ejpam-5051	821	3	,	,	PUNCT
ejpam-5051	821	4	i	i	PRON
ejpam-5051	821	5	,	,	PUNCT
ejpam-5051	821	6	q	q	X
ejpam-5051	821	7	)	)	PUNCT
ejpam-5051	821	8	is	be	AUX
ejpam-5051	821	9	a	a	DET
ejpam-5051	821	10	discrete	discrete	ADJ
ejpam-5051	821	11	twist	twist	NOUN
ejpam-5051	821	12	over	over	ADP
ejpam-5051	821	13	â⋊r	â⋊r	NOUN
ejpam-5051	821	14	.	.	PUNCT
ejpam-5051	822	1	4	4	X
ejpam-5051	822	2	.	.	X
ejpam-5051	822	3	non	non	ADJ
ejpam-5051	822	4	-	-	ADJ
ejpam-5051	822	5	isomorphic	isomorphic	ADJ
ejpam-5051	822	6	property	property	NOUN
ejpam-5051	822	7	of	of	ADP
ejpam-5051	822	8	az(z	az(z	NOUN
ejpam-5051	822	9	)	)	PUNCT
ejpam-5051	822	10	and	and	CCONJ
ejpam-5051	822	11	az(d	az(d	NUM
ejpam-5051	822	12	;	;	PUNCT
ejpam-5051	822	13	â⋊r	â⋊r	NOUN
ejpam-5051	822	14	)	)	PUNCT
ejpam-5051	822	15	in	in	ADP
ejpam-5051	822	16	this	this	DET
ejpam-5051	822	17	section	section	NOUN
ejpam-5051	822	18	we	we	PRON
ejpam-5051	822	19	present	present	VERB
ejpam-5051	822	20	a	a	DET
ejpam-5051	822	21	case	case	NOUN
ejpam-5051	822	22	in	in	ADP
ejpam-5051	822	23	which	which	PRON
ejpam-5051	822	24	the	the	DET
ejpam-5051	822	25	non	non	ADJ
ejpam-5051	822	26	-	-	ADJ
ejpam-5051	822	27	twisted	twisted	ADJ
ejpam-5051	822	28	steinberg	steinberg	PROPN
ejpam-5051	822	29	algebra	algebra	PROPN
ejpam-5051	822	30	(	(	PUNCT
ejpam-5051	822	31	ar(g	ar(g	ADJ
ejpam-5051	822	32	)	)	PUNCT
ejpam-5051	822	33	)	)	PUNCT
ejpam-5051	822	34	and	and	CCONJ
ejpam-5051	822	35	twisted	twist	VERB
ejpam-5051	822	36	steinberg	steinberg	PROPN
ejpam-5051	822	37	algebra	algebra	PROPN
ejpam-5051	822	38	(	(	PUNCT
ejpam-5051	822	39	ar(d	ar(d	ADV
ejpam-5051	822	40	;	;	PUNCT
ejpam-5051	822	41	â⋊r	â⋊r	NOUN
ejpam-5051	822	42	)	)	PUNCT
ejpam-5051	822	43	)	)	PUNCT
ejpam-5051	822	44	is	be	AUX
ejpam-5051	822	45	not	not	PART
ejpam-5051	822	46	isomorphic	isomorphic	ADJ
ejpam-5051	822	47	when	when	SCONJ
ejpam-5051	822	48	g	g	PROPN
ejpam-5051	822	49	=	=	PROPN
ejpam-5051	822	50	z	z	PROPN
ejpam-5051	822	51	and	and	CCONJ
ejpam-5051	822	52	r	r	PROPN
ejpam-5051	822	53	=	=	PUNCT
ejpam-5051	822	54	z.	z.	PROPN
ejpam-5051	822	55	let	let	VERB
ejpam-5051	823	1	g	g	PROPN
ejpam-5051	823	2	=	=	PROPN
ejpam-5051	823	3	z	z	PROPN
ejpam-5051	823	4	and	and	CCONJ
ejpam-5051	823	5	r	r	NOUN
ejpam-5051	823	6	=	=	PUNCT
ejpam-5051	823	7	z.	z.	X
ejpam-5051	823	8	the	the	DET
ejpam-5051	823	9	set	set	NOUN
ejpam-5051	823	10	of	of	ADP
ejpam-5051	823	11	multiplicative	multiplicative	ADJ
ejpam-5051	823	12	units	unit	NOUN
ejpam-5051	823	13	of	of	ADP
ejpam-5051	823	14	z	z	PROPN
ejpam-5051	823	15	is	be	AUX
ejpam-5051	823	16	z×	z×	NOUN
ejpam-5051	823	17	=	=	PUNCT
ejpam-5051	823	18	{	{	PUNCT
ejpam-5051	823	19	−1	−1	NOUN
ejpam-5051	823	20	,	,	PUNCT
ejpam-5051	823	21	1	1	NUM
ejpam-5051	823	22	}	}	PUNCT
ejpam-5051	823	23	=	=	SYM
ejpam-5051	823	24	t	t	NOUN
ejpam-5051	823	25	and	and	CCONJ
ejpam-5051	823	26	the	the	DET
ejpam-5051	823	27	unit	unit	NOUN
ejpam-5051	823	28	space	space	NOUN
ejpam-5051	823	29	of	of	ADP
ejpam-5051	823	30	z	z	PROPN
ejpam-5051	823	31	is	be	AUX
ejpam-5051	823	32	z(0	z(0	ADV
ejpam-5051	823	33	)	)	PUNCT
ejpam-5051	823	34	=	=	PRON
ejpam-5051	824	1	{	{	PUNCT
ejpam-5051	824	2	x	x	PUNCT
ejpam-5051	824	3	∈	∈	PROPN
ejpam-5051	824	4	z	z	NOUN
ejpam-5051	824	5	:	:	PUNCT
ejpam-5051	824	6	x	x	X
ejpam-5051	824	7	=	=	SYM
ejpam-5051	824	8	s(y	s(y	NOUN
ejpam-5051	824	9	)	)	PUNCT
ejpam-5051	824	10	=	=	PUNCT
ejpam-5051	825	1	r(y	r(y	VERB
ejpam-5051	825	2	)	)	PUNCT
ejpam-5051	825	3	,	,	PUNCT
ejpam-5051	825	4	y	y	PROPN
ejpam-5051	825	5	∈	∈	PROPN
ejpam-5051	826	1	z	z	X
ejpam-5051	826	2	}	}	PUNCT
ejpam-5051	826	3	=	=	PUNCT
ejpam-5051	826	4	{	{	PUNCT
ejpam-5051	826	5	0	0	NUM
ejpam-5051	826	6	}	}	PUNCT
ejpam-5051	826	7	.	.	PUNCT
ejpam-5051	827	1	the	the	DET
ejpam-5051	827	2	source	source	NOUN
ejpam-5051	827	3	and	and	CCONJ
ejpam-5051	827	4	range	range	NOUN
ejpam-5051	827	5	maps	map	NOUN
ejpam-5051	827	6	are	be	AUX
ejpam-5051	827	7	s(x	s(x	NOUN
ejpam-5051	827	8	)	)	PUNCT
ejpam-5051	828	1	=	=	SYM
ejpam-5051	828	2	(	(	PUNCT
ejpam-5051	828	3	−x	−x	NOUN
ejpam-5051	828	4	)	)	PUNCT
ejpam-5051	829	1	+	+	NOUN
ejpam-5051	829	2	x	x	X
ejpam-5051	829	3	=	=	SYM
ejpam-5051	829	4	{	{	PUNCT
ejpam-5051	829	5	0	0	NUM
ejpam-5051	829	6	}	}	PUNCT
ejpam-5051	829	7	and	and	CCONJ
ejpam-5051	829	8	r(x	r(x	NOUN
ejpam-5051	829	9	)	)	PUNCT
ejpam-5051	829	10	=	=	PUNCT
ejpam-5051	830	1	x	x	PUNCT
ejpam-5051	830	2	+	+	CCONJ
ejpam-5051	830	3	(	(	PUNCT
ejpam-5051	830	4	−x	−x	NOUN
ejpam-5051	830	5	)	)	PUNCT
ejpam-5051	830	6	=	=	PUNCT
ejpam-5051	830	7	{	{	PUNCT
ejpam-5051	830	8	0	0	NUM
ejpam-5051	830	9	}	}	PUNCT
ejpam-5051	830	10	,	,	PUNCT
ejpam-5051	830	11	respectively	respectively	ADV
ejpam-5051	830	12	.	.	PUNCT
ejpam-5051	831	1	the	the	DET
ejpam-5051	831	2	isotropy	isotropy	ADJ
ejpam-5051	831	3	group	group	NOUN
ejpam-5051	831	4	for	for	ADP
ejpam-5051	831	5	z	z	PROPN
ejpam-5051	831	6	is	be	AUX
ejpam-5051	831	7	a	a	DET
ejpam-5051	831	8	=	=	PUNCT
ejpam-5051	831	9	z.	z.	PROPN
ejpam-5051	831	10	also	also	ADV
ejpam-5051	831	11	,	,	PUNCT
ejpam-5051	831	12	r	r	NOUN
ejpam-5051	831	13	=	=	PUNCT
ejpam-5051	831	14	zz	zz	PROPN
ejpam-5051	831	15	=	=	SYM
ejpam-5051	831	16	{	{	PUNCT
ejpam-5051	831	17	x	x	X
ejpam-5051	832	1	+	+	NUM
ejpam-5051	832	2	z	z	NOUN
ejpam-5051	832	3	:	:	PUNCT
ejpam-5051	832	4	x	x	SYM
ejpam-5051	832	5	∈	∈	PROPN
ejpam-5051	832	6	z	z	X
ejpam-5051	832	7	}	}	PUNCT
ejpam-5051	832	8	=	=	SYM
ejpam-5051	832	9	{	{	PUNCT
ejpam-5051	832	10	0̇	0̇	NOUN
ejpam-5051	832	11	}	}	PUNCT
ejpam-5051	832	12	where	where	SCONJ
ejpam-5051	832	13	{	{	PUNCT
ejpam-5051	832	14	0̇	0̇	NOUN
ejpam-5051	832	15	}	}	PUNCT
ejpam-5051	832	16	=	=	SYM
ejpam-5051	832	17	0	0	PUNCT
ejpam-5051	833	1	+	+	CCONJ
ejpam-5051	833	2	z.	z.	PROPN
ejpam-5051	833	3	for	for	ADP
ejpam-5051	833	4	u	u	PROPN
ejpam-5051	833	5	∈	∈	PROPN
ejpam-5051	833	6	z(0	z(0	AUX
ejpam-5051	833	7	)	)	PUNCT
ejpam-5051	833	8	,	,	PUNCT
ejpam-5051	833	9	we	we	PRON
ejpam-5051	833	10	have	have	VERB
ejpam-5051	833	11	a0	a0	NOUN
ejpam-5051	833	12	=	=	SYM
ejpam-5051	833	13	z.	z.	PROPN
ejpam-5051	833	14	also	also	ADV
ejpam-5051	833	15	,	,	PUNCT
ejpam-5051	833	16	â0	â0	NOUN
ejpam-5051	833	17	=	=	PUNCT
ejpam-5051	833	18	{	{	PUNCT
ejpam-5051	833	19	χ1	χ1	NOUN
ejpam-5051	833	20	,	,	PUNCT
ejpam-5051	833	21	χ2|χi	χ2|χi	PROPN
ejpam-5051	833	22	:	:	PUNCT
ejpam-5051	833	23	z	z	X
ejpam-5051	833	24	→	→	PUNCT
ejpam-5051	833	25	{	{	PUNCT
ejpam-5051	833	26	1,−1	1,−1	NUM
ejpam-5051	833	27	}	}	PUNCT
ejpam-5051	833	28	is	be	AUX
ejpam-5051	833	29	a	a	DET
ejpam-5051	833	30	continuous	continuous	ADJ
ejpam-5051	833	31	group	group	NOUN
ejpam-5051	833	32	homomorphism	homomorphism	NOUN
ejpam-5051	833	33	}	}	PUNCT
ejpam-5051	833	34	,	,	PUNCT
ejpam-5051	833	35	i	i	PRON
ejpam-5051	833	36	=	=	NOUN
ejpam-5051	833	37	1	1	NUM
ejpam-5051	833	38	,	,	PUNCT
ejpam-5051	833	39	2	2	NUM
ejpam-5051	833	40	where	where	SCONJ
ejpam-5051	833	41	χ1	χ1	NOUN
ejpam-5051	833	42	:	:	PUNCT
ejpam-5051	833	43	z	z	X
ejpam-5051	833	44	→	→	SYM
ejpam-5051	833	45	z×	z×	NOUN
ejpam-5051	833	46	defined	define	VERB
ejpam-5051	833	47	by	by	ADP
ejpam-5051	833	48	χ1(a	χ1(a	PROPN
ejpam-5051	833	49	)	)	PUNCT
ejpam-5051	833	50	=	=	SYM
ejpam-5051	833	51	1	1	NUM
ejpam-5051	833	52	and	and	CCONJ
ejpam-5051	833	53	χ2	χ2	PROPN
ejpam-5051	833	54	:	:	PUNCT
ejpam-5051	833	55	z	z	X
ejpam-5051	833	56	→	→	SYM
ejpam-5051	833	57	z×	z×	NOUN
ejpam-5051	833	58	defined	define	VERB
ejpam-5051	833	59	by	by	ADP
ejpam-5051	833	60	χ2(a	χ2(a	NOUN
ejpam-5051	833	61	)	)	PUNCT
ejpam-5051	833	62	=	=	PRON
ejpam-5051	833	63	{	{	PUNCT
ejpam-5051	833	64	1	1	NUM
ejpam-5051	833	65	if	if	SCONJ
ejpam-5051	833	66	a	a	DET
ejpam-5051	833	67	∈	∈	PROPN
ejpam-5051	833	68	2z	2z	NUM
ejpam-5051	833	69	−1	−1	NOUN
ejpam-5051	833	70	if	if	SCONJ
ejpam-5051	833	71	a	a	DET
ejpam-5051	833	72	∈	∈	PROPN
ejpam-5051	833	73	2z+	2z+	NUM
ejpam-5051	833	74	1	1	NUM
ejpam-5051	833	75	.	.	PUNCT
ejpam-5051	833	76	r.	r.	PROPN
ejpam-5051	833	77	s.	s.	PROPN
ejpam-5051	833	78	bongcawel	bongcawel	PROPN
ejpam-5051	834	1	et	et	PROPN
ejpam-5051	834	2	al	al	PROPN
ejpam-5051	834	3	.	.	PUNCT
ejpam-5051	834	4	/	/	SYM
ejpam-5051	834	5	eur	eur	PROPN
ejpam-5051	834	6	.	.	PUNCT
ejpam-5051	835	1	j.	j.	PROPN
ejpam-5051	835	2	pure	pure	PROPN
ejpam-5051	835	3	appl	appl	PROPN
ejpam-5051	835	4	.	.	PROPN
ejpam-5051	835	5	math	math	PROPN
ejpam-5051	835	6	,	,	PUNCT
ejpam-5051	835	7	17	17	NUM
ejpam-5051	835	8	(	(	PUNCT
ejpam-5051	835	9	1	1	NUM
ejpam-5051	835	10	)	)	PUNCT
ejpam-5051	835	11	(	(	PUNCT
ejpam-5051	835	12	2024	2024	NUM
ejpam-5051	835	13	)	)	PUNCT
ejpam-5051	835	14	,	,	PUNCT
ejpam-5051	835	15	519	519	NUM
ejpam-5051	835	16	-	-	SYM
ejpam-5051	835	17	545	545	NUM
ejpam-5051	835	18	539	539	NUM
ejpam-5051	835	19	note	note	VERB
ejpam-5051	835	20	that	that	SCONJ
ejpam-5051	835	21	â	â	ADP
ejpam-5051	835	22	∗	∗	NOUN
ejpam-5051	835	23	z×	z×	PROPN
ejpam-5051	835	24	t	t	PROPN
ejpam-5051	835	25	=	=	SYM
ejpam-5051	835	26	{	{	PUNCT
ejpam-5051	835	27	(	(	PUNCT
ejpam-5051	835	28	χ	χ	NOUN
ejpam-5051	835	29	,	,	PUNCT
ejpam-5051	835	30	z	z	NOUN
ejpam-5051	835	31	,	,	PUNCT
ejpam-5051	835	32	x	x	NOUN
ejpam-5051	835	33	)	)	PUNCT
ejpam-5051	835	34	:	:	PUNCT
ejpam-5051	836	1	χ	χ	X
ejpam-5051	836	2	∈	∈	NOUN
ejpam-5051	836	3	â0	â0	NOUN
ejpam-5051	836	4	,	,	PUNCT
ejpam-5051	836	5	z	z	PROPN
ejpam-5051	836	6	∈	∈	PROPN
ejpam-5051	836	7	t	t	PROPN
ejpam-5051	836	8	,	,	PUNCT
ejpam-5051	836	9	x	x	X
ejpam-5051	836	10	∈	∈	PROPN
ejpam-5051	836	11	z	z	X
ejpam-5051	836	12	}	}	PUNCT
ejpam-5051	836	13	=	=	SYM
ejpam-5051	836	14	{	{	PUNCT
ejpam-5051	836	15	(	(	PUNCT
ejpam-5051	836	16	χ1	χ1	NOUN
ejpam-5051	836	17	,	,	PUNCT
ejpam-5051	836	18	1	1	NUM
ejpam-5051	836	19	,	,	PUNCT
ejpam-5051	836	20	x	x	NOUN
ejpam-5051	836	21	)	)	PUNCT
ejpam-5051	836	22	,	,	PUNCT
ejpam-5051	836	23	(	(	PUNCT
ejpam-5051	836	24	χ1,−1	χ1,−1	PROPN
ejpam-5051	836	25	,	,	PUNCT
ejpam-5051	836	26	x	x	NOUN
ejpam-5051	836	27	)	)	PUNCT
ejpam-5051	836	28	,	,	PUNCT
ejpam-5051	836	29	(	(	PUNCT
ejpam-5051	836	30	χ2	χ2	PROPN
ejpam-5051	836	31	,	,	PUNCT
ejpam-5051	836	32	1	1	NUM
ejpam-5051	836	33	,	,	PUNCT
ejpam-5051	836	34	x	x	NOUN
ejpam-5051	836	35	)	)	PUNCT
ejpam-5051	836	36	,	,	PUNCT
ejpam-5051	836	37	(	(	PUNCT
ejpam-5051	836	38	χ2,−1	χ2,−1	INTJ
ejpam-5051	836	39	,	,	PUNCT
ejpam-5051	836	40	x	x	NOUN
ejpam-5051	836	41	)	)	PUNCT
ejpam-5051	836	42	}	}	PUNCT
ejpam-5051	836	43	.	.	PUNCT
ejpam-5051	837	1	so	so	ADV
ejpam-5051	837	2	,	,	PUNCT
ejpam-5051	837	3	d	d	PROPN
ejpam-5051	837	4	=	=	SYM
ejpam-5051	837	5	(	(	PUNCT
ejpam-5051	837	6	â	â	X
ejpam-5051	837	7	∗	∗	PROPN
ejpam-5051	837	8	z×	z×	NUM
ejpam-5051	837	9	t/	t/	ADJ
ejpam-5051	837	10	∼	∼	NOUN
ejpam-5051	837	11	)	)	PUNCT
ejpam-5051	837	12	=	=	PRON
ejpam-5051	837	13	{	{	PUNCT
ejpam-5051	838	1	[	[	X
ejpam-5051	838	2	χ1	χ1	NOUN
ejpam-5051	838	3	,	,	PUNCT
ejpam-5051	838	4	1	1	NUM
ejpam-5051	838	5	,	,	PUNCT
ejpam-5051	838	6	x	x	NOUN
ejpam-5051	838	7	]	]	X
ejpam-5051	838	8	,	,	PUNCT
ejpam-5051	838	9	[	[	X
ejpam-5051	838	10	χ1,−1	χ1,−1	NOUN
ejpam-5051	838	11	,	,	PUNCT
ejpam-5051	838	12	x	x	X
ejpam-5051	838	13	]	]	X
ejpam-5051	838	14	,	,	PUNCT
ejpam-5051	838	15	[	[	X
ejpam-5051	838	16	χ2	χ2	PROPN
ejpam-5051	838	17	,	,	PUNCT
ejpam-5051	838	18	1	1	NUM
ejpam-5051	838	19	,	,	PUNCT
ejpam-5051	838	20	x	x	NOUN
ejpam-5051	838	21	]	]	X
ejpam-5051	838	22	,	,	PUNCT
ejpam-5051	838	23	[	[	X
ejpam-5051	838	24	χ2,−1	χ2,−1	X
ejpam-5051	838	25	,	,	PUNCT
ejpam-5051	838	26	x]|x	x]|x	PROPN
ejpam-5051	838	27	∈	∈	PROPN
ejpam-5051	839	1	z	z	X
ejpam-5051	839	2	}	}	PUNCT
ejpam-5051	839	3	.	.	PUNCT
ejpam-5051	840	1	claim	claim	NOUN
ejpam-5051	840	2	1	1	NUM
ejpam-5051	840	3	:	:	PUNCT
ejpam-5051	841	1	d	d	NOUN
ejpam-5051	841	2	=	=	SYM
ejpam-5051	841	3	{	{	PUNCT
ejpam-5051	841	4	[	[	X
ejpam-5051	841	5	χ1	χ1	NOUN
ejpam-5051	841	6	,	,	PUNCT
ejpam-5051	841	7	1	1	NUM
ejpam-5051	841	8	,	,	PUNCT
ejpam-5051	841	9	0	0	NUM
ejpam-5051	841	10	]	]	PUNCT
ejpam-5051	841	11	,	,	PUNCT
ejpam-5051	842	1	[	[	X
ejpam-5051	842	2	χ1,−1	χ1,−1	X
ejpam-5051	842	3	,	,	PUNCT
ejpam-5051	842	4	0	0	NUM
ejpam-5051	842	5	]	]	PUNCT
ejpam-5051	842	6	,	,	PUNCT
ejpam-5051	842	7	[	[	X
ejpam-5051	842	8	χ2	χ2	PROPN
ejpam-5051	842	9	,	,	PUNCT
ejpam-5051	842	10	1	1	NUM
ejpam-5051	842	11	,	,	PUNCT
ejpam-5051	842	12	0	0	NUM
ejpam-5051	842	13	]	]	PUNCT
ejpam-5051	842	14	,	,	PUNCT
ejpam-5051	843	1	[	[	X
ejpam-5051	843	2	χ2,−1	χ2,−1	X
ejpam-5051	843	3	,	,	PUNCT
ejpam-5051	843	4	0	0	NUM
ejpam-5051	843	5	]	]	PUNCT
ejpam-5051	843	6	}	}	PUNCT
ejpam-5051	843	7	.	.	PUNCT
ejpam-5051	844	1	for	for	ADP
ejpam-5051	844	2	i	i	PRON
ejpam-5051	844	3	=	=	NOUN
ejpam-5051	844	4	1	1	NUM
ejpam-5051	844	5	,	,	PUNCT
ejpam-5051	844	6	2	2	NUM
ejpam-5051	844	7	,	,	PUNCT
ejpam-5051	844	8	[	[	X
ejpam-5051	844	9	χi	χi	NOUN
ejpam-5051	844	10	,	,	PUNCT
ejpam-5051	844	11	1	1	NUM
ejpam-5051	844	12	,	,	PUNCT
ejpam-5051	844	13	x	x	X
ejpam-5051	844	14	]	]	X
ejpam-5051	844	15	=	=	SYM
ejpam-5051	844	16	{	{	PUNCT
ejpam-5051	844	17	(	(	PUNCT
ejpam-5051	844	18	χ′	χ′	PROPN
ejpam-5051	844	19	,	,	PUNCT
ejpam-5051	844	20	z′	z′	PROPN
ejpam-5051	844	21	,	,	PUNCT
ejpam-5051	844	22	x′)|χi	x′)|χi	PUNCT
ejpam-5051	845	1	=	=	PROPN
ejpam-5051	845	2	χ′,∃	χ′,∃	PROPN
ejpam-5051	845	3	a	a	DET
ejpam-5051	845	4	∈	∈	PROPN
ejpam-5051	845	5	zwhereχi(a)(1	zwhereχi(a)(1	NOUN
ejpam-5051	845	6	)	)	PUNCT
ejpam-5051	846	1	=	=	SYM
ejpam-5051	847	1	z′	z′	NUM
ejpam-5051	847	2	andx	andx	NOUN
ejpam-5051	847	3	=	=	SYM
ejpam-5051	847	4	a	a	PRON
ejpam-5051	847	5	·	·	PUNCT
ejpam-5051	847	6	x′	x′	NUM
ejpam-5051	847	7	}	}	PUNCT
ejpam-5051	847	8	=	=	SYM
ejpam-5051	847	9	{	{	PUNCT
ejpam-5051	847	10	(	(	PUNCT
ejpam-5051	847	11	χi	χi	NOUN
ejpam-5051	847	12	,	,	PUNCT
ejpam-5051	847	13	z	z	NOUN
ejpam-5051	847	14	′	′	NOUN
ejpam-5051	847	15	,	,	PUNCT
ejpam-5051	847	16	x′)|∃	x′)|∃	PROPN
ejpam-5051	848	1	a	a	DET
ejpam-5051	848	2	∈	∈	PROPN
ejpam-5051	848	3	zwhere	zwhere	ADP
ejpam-5051	848	4	1	1	NUM
ejpam-5051	848	5	=	=	SYM
ejpam-5051	848	6	χi(a)(1	χi(a)(1	PROPN
ejpam-5051	848	7	)	)	PUNCT
ejpam-5051	848	8	=	=	PUNCT
ejpam-5051	849	1	z′	z′	NUM
ejpam-5051	849	2	andx	andx	NOUN
ejpam-5051	849	3	=	=	SYM
ejpam-5051	849	4	a	a	PRON
ejpam-5051	849	5	·	·	PUNCT
ejpam-5051	849	6	x′	x′	NUM
ejpam-5051	849	7	}	}	PUNCT
ejpam-5051	849	8	=	=	SYM
ejpam-5051	849	9	{	{	PUNCT
ejpam-5051	849	10	(	(	PUNCT
ejpam-5051	849	11	χi	χi	NOUN
ejpam-5051	849	12	,	,	PUNCT
ejpam-5051	849	13	1	1	NUM
ejpam-5051	849	14	,	,	PUNCT
ejpam-5051	849	15	x	x	PROPN
ejpam-5051	849	16	′)|∃	′)|∃	PROPN
ejpam-5051	849	17	a	a	DET
ejpam-5051	849	18	∈	∈	PROPN
ejpam-5051	849	19	z	z	PROPN
ejpam-5051	849	20	,	,	PUNCT
ejpam-5051	849	21	x	x	PUNCT
ejpam-5051	849	22	=	=	PUNCT
ejpam-5051	849	23	a	a	PRON
ejpam-5051	849	24	·	·	PUNCT
ejpam-5051	849	25	x′	x′	NUM
ejpam-5051	849	26	}	}	PUNCT
ejpam-5051	849	27	=	=	SYM
ejpam-5051	849	28	{	{	PUNCT
ejpam-5051	849	29	(	(	PUNCT
ejpam-5051	849	30	χi	χi	NOUN
ejpam-5051	849	31	,	,	PUNCT
ejpam-5051	849	32	1	1	NUM
ejpam-5051	849	33	,	,	PUNCT
ejpam-5051	849	34	x	x	X
ejpam-5051	849	35	/	/	SYM
ejpam-5051	849	36	a)|a	a)|a	VERB
ejpam-5051	849	37	∈	∈	PROPN
ejpam-5051	849	38	z	z	PROPN
ejpam-5051	849	39	,	,	PUNCT
ejpam-5051	849	40	x	x	SYM
ejpam-5051	849	41	∈	∈	PROPN
ejpam-5051	849	42	z	z	X
ejpam-5051	849	43	}	}	PUNCT
ejpam-5051	849	44	=	=	SYM
ejpam-5051	849	45	{	{	PUNCT
ejpam-5051	849	46	(	(	PUNCT
ejpam-5051	849	47	χi	χi	NOUN
ejpam-5051	849	48	,	,	PUNCT
ejpam-5051	849	49	1	1	NUM
ejpam-5051	849	50	,	,	PUNCT
ejpam-5051	849	51	x)|a	x)|a	NOUN
ejpam-5051	849	52	=	=	SYM
ejpam-5051	849	53	1	1	NUM
ejpam-5051	849	54	,	,	PUNCT
ejpam-5051	849	55	x	x	SYM
ejpam-5051	849	56	∈	∈	PROPN
ejpam-5051	849	57	z	z	NOUN
ejpam-5051	849	58	}	}	PUNCT
ejpam-5051	849	59	=	=	SYM
ejpam-5051	849	60	{	{	PUNCT
ejpam-5051	849	61	·	·	PUNCT
ejpam-5051	849	62	·	·	PUNCT
ejpam-5051	849	63	·	·	PUNCT
ejpam-5051	849	64	(	(	PUNCT
ejpam-5051	849	65	χi	χi	X
ejpam-5051	849	66	,	,	PUNCT
ejpam-5051	849	67	1,−1	1,−1	NUM
ejpam-5051	849	68	)	)	PUNCT
ejpam-5051	849	69	,	,	PUNCT
ejpam-5051	849	70	(	(	PUNCT
ejpam-5051	849	71	χi	χi	NOUN
ejpam-5051	849	72	,	,	PUNCT
ejpam-5051	849	73	1	1	NUM
ejpam-5051	849	74	,	,	PUNCT
ejpam-5051	849	75	0	0	NUM
ejpam-5051	849	76	)	)	PUNCT
ejpam-5051	849	77	,	,	PUNCT
ejpam-5051	849	78	(	(	PUNCT
ejpam-5051	849	79	χi	χi	NOUN
ejpam-5051	849	80	,	,	PUNCT
ejpam-5051	849	81	1	1	NUM
ejpam-5051	849	82	,	,	PUNCT
ejpam-5051	849	83	1	1	NUM
ejpam-5051	849	84	)	)	PUNCT
ejpam-5051	849	85	·	·	PUNCT
ejpam-5051	849	86	·	·	PUNCT
ejpam-5051	849	87	·	·	PUNCT
ejpam-5051	849	88	}	}	PUNCT
ejpam-5051	850	1	[	[	X
ejpam-5051	850	2	χi,−1	χi,−1	INTJ
ejpam-5051	850	3	,	,	PUNCT
ejpam-5051	850	4	x	x	X
ejpam-5051	850	5	]	]	X
ejpam-5051	850	6	=	=	SYM
ejpam-5051	850	7	{	{	PUNCT
ejpam-5051	850	8	(	(	PUNCT
ejpam-5051	850	9	χ′	χ′	PROPN
ejpam-5051	850	10	,	,	PUNCT
ejpam-5051	850	11	z′	z′	PROPN
ejpam-5051	850	12	,	,	PUNCT
ejpam-5051	850	13	x′)|χi	x′)|χi	PUNCT
ejpam-5051	850	14	=	=	PROPN
ejpam-5051	850	15	χ′,∃	χ′,∃	PROPN
ejpam-5051	850	16	a	a	DET
ejpam-5051	850	17	∈	∈	PROPN
ejpam-5051	850	18	zwhereχi(a)(−1	zwhereχi(a)(−1	X
ejpam-5051	850	19	)	)	PUNCT
ejpam-5051	851	1	=	=	SYM
ejpam-5051	852	1	z′	z′	NUM
ejpam-5051	852	2	andx	andx	NOUN
ejpam-5051	852	3	=	=	SYM
ejpam-5051	852	4	a	a	PRON
ejpam-5051	852	5	·	·	PUNCT
ejpam-5051	852	6	x′	x′	NUM
ejpam-5051	852	7	}	}	PUNCT
ejpam-5051	852	8	=	=	SYM
ejpam-5051	852	9	{	{	PUNCT
ejpam-5051	852	10	(	(	PUNCT
ejpam-5051	852	11	χi	χi	NOUN
ejpam-5051	852	12	,	,	PUNCT
ejpam-5051	852	13	z	z	NOUN
ejpam-5051	852	14	′	′	NOUN
ejpam-5051	852	15	,	,	PUNCT
ejpam-5051	852	16	x′)|∃	x′)|∃	PROPN
ejpam-5051	852	17	a	a	DET
ejpam-5051	852	18	∈	∈	PROPN
ejpam-5051	852	19	zwhere	zwhere	PUNCT
ejpam-5051	853	1	−	−	NOUN
ejpam-5051	853	2	1	1	NUM
ejpam-5051	853	3	=	=	SYM
ejpam-5051	853	4	χi(a)(−1	χi(a)(−1	NOUN
ejpam-5051	853	5	)	)	PUNCT
ejpam-5051	854	1	=	=	SYM
ejpam-5051	854	2	z′	z′	NUM
ejpam-5051	854	3	andx	andx	NOUN
ejpam-5051	854	4	=	=	SYM
ejpam-5051	854	5	a	a	PRON
ejpam-5051	854	6	·	·	PUNCT
ejpam-5051	854	7	x′	x′	NUM
ejpam-5051	854	8	}	}	PUNCT
ejpam-5051	854	9	=	=	SYM
ejpam-5051	854	10	{	{	PUNCT
ejpam-5051	854	11	(	(	PUNCT
ejpam-5051	854	12	χi,−1	χi,−1	PROPN
ejpam-5051	854	13	,	,	PUNCT
ejpam-5051	854	14	x′)|∃	x′)|∃	PROPN
ejpam-5051	854	15	a	a	DET
ejpam-5051	854	16	∈	∈	PROPN
ejpam-5051	854	17	z	z	PROPN
ejpam-5051	854	18	,	,	PUNCT
ejpam-5051	854	19	x	x	PUNCT
ejpam-5051	854	20	=	=	PUNCT
ejpam-5051	854	21	a	a	PRON
ejpam-5051	854	22	·	·	PUNCT
ejpam-5051	854	23	x′	x′	NUM
ejpam-5051	854	24	}	}	PUNCT
ejpam-5051	854	25	=	=	SYM
ejpam-5051	854	26	{	{	PUNCT
ejpam-5051	854	27	(	(	PUNCT
ejpam-5051	854	28	χi,−1	χi,−1	INTJ
ejpam-5051	854	29	,	,	PUNCT
ejpam-5051	854	30	x	x	X
ejpam-5051	854	31	/	/	SYM
ejpam-5051	854	32	a)|a	a)|a	VERB
ejpam-5051	854	33	∈	∈	PROPN
ejpam-5051	854	34	z	z	PROPN
ejpam-5051	854	35	,	,	PUNCT
ejpam-5051	854	36	x	x	SYM
ejpam-5051	854	37	∈	∈	PROPN
ejpam-5051	854	38	z	z	X
ejpam-5051	854	39	}	}	PUNCT
ejpam-5051	854	40	=	=	SYM
ejpam-5051	854	41	{	{	PUNCT
ejpam-5051	854	42	(	(	PUNCT
ejpam-5051	854	43	χi,−1	χi,−1	PROPN
ejpam-5051	854	44	,	,	PUNCT
ejpam-5051	854	45	x)|a	x)|a	NOUN
ejpam-5051	854	46	=	=	SYM
ejpam-5051	854	47	1	1	NUM
ejpam-5051	854	48	,	,	PUNCT
ejpam-5051	854	49	x	x	SYM
ejpam-5051	854	50	∈	∈	PROPN
ejpam-5051	854	51	z	z	NOUN
ejpam-5051	854	52	}	}	PUNCT
ejpam-5051	854	53	=	=	SYM
ejpam-5051	854	54	{	{	PUNCT
ejpam-5051	854	55	·	·	PUNCT
ejpam-5051	854	56	·	·	PUNCT
ejpam-5051	854	57	·	·	PUNCT
ejpam-5051	854	58	(	(	PUNCT
ejpam-5051	854	59	χi,−1,−1	χi,−1,−1	PROPN
ejpam-5051	854	60	)	)	PUNCT
ejpam-5051	854	61	,	,	PUNCT
ejpam-5051	854	62	(	(	PUNCT
ejpam-5051	854	63	χi,−1	χi,−1	ADV
ejpam-5051	854	64	,	,	PUNCT
ejpam-5051	854	65	0	0	NUM
ejpam-5051	854	66	)	)	PUNCT
ejpam-5051	854	67	,	,	PUNCT
ejpam-5051	854	68	(	(	PUNCT
ejpam-5051	854	69	χi,−1	χi,−1	ADV
ejpam-5051	854	70	,	,	PUNCT
ejpam-5051	854	71	1	1	NUM
ejpam-5051	854	72	)	)	PUNCT
ejpam-5051	854	73	·	·	PUNCT
ejpam-5051	854	74	·	·	PUNCT
ejpam-5051	854	75	·	·	PUNCT
ejpam-5051	854	76	}	}	PUNCT
ejpam-5051	854	77	hence	hence	ADV
ejpam-5051	854	78	,	,	PUNCT
ejpam-5051	854	79	(	(	PUNCT
ejpam-5051	854	80	χi	χi	NOUN
ejpam-5051	854	81	,	,	PUNCT
ejpam-5051	854	82	1	1	NUM
ejpam-5051	854	83	,	,	PUNCT
ejpam-5051	854	84	0	0	NUM
ejpam-5051	854	85	)	)	PUNCT
ejpam-5051	854	86	∈	∈	PROPN
ejpam-5051	855	1	[	[	X
ejpam-5051	855	2	χi	χi	NOUN
ejpam-5051	855	3	,	,	PUNCT
ejpam-5051	855	4	1	1	NUM
ejpam-5051	855	5	,	,	PUNCT
ejpam-5051	855	6	x	x	X
ejpam-5051	855	7	]	]	PUNCT
ejpam-5051	855	8	and	and	CCONJ
ejpam-5051	855	9	(	(	PUNCT
ejpam-5051	855	10	χi,−1	χi,−1	ADJ
ejpam-5051	855	11	,	,	PUNCT
ejpam-5051	855	12	0	0	X
ejpam-5051	855	13	)	)	PUNCT
ejpam-5051	855	14	∈	∈	NOUN
ejpam-5051	856	1	[	[	X
ejpam-5051	856	2	χi,−1	χi,−1	NOUN
ejpam-5051	856	3	,	,	PUNCT
ejpam-5051	856	4	x	x	X
ejpam-5051	856	5	]	]	X
ejpam-5051	856	6	imply	imply	VERB
ejpam-5051	856	7	that	that	SCONJ
ejpam-5051	856	8	[	[	X
ejpam-5051	856	9	χi	χi	NOUN
ejpam-5051	856	10	,	,	PUNCT
ejpam-5051	856	11	1	1	NUM
ejpam-5051	856	12	,	,	PUNCT
ejpam-5051	856	13	x	x	X
ejpam-5051	856	14	]	]	X
ejpam-5051	856	15	=	=	PUNCT
ejpam-5051	857	1	[	[	X
ejpam-5051	857	2	χi	χi	X
ejpam-5051	857	3	,	,	PUNCT
ejpam-5051	857	4	1	1	NUM
ejpam-5051	857	5	,	,	PUNCT
ejpam-5051	857	6	0	0	NUM
ejpam-5051	857	7	]	]	PUNCT
ejpam-5051	857	8	and	and	CCONJ
ejpam-5051	857	9	[	[	X
ejpam-5051	857	10	χi,−1	χi,−1	INTJ
ejpam-5051	857	11	,	,	PUNCT
ejpam-5051	857	12	x	x	X
ejpam-5051	857	13	]	]	X
ejpam-5051	857	14	=	=	PUNCT
ejpam-5051	858	1	[	[	X
ejpam-5051	858	2	χi,−1	χi,−1	NOUN
ejpam-5051	858	3	,	,	PUNCT
ejpam-5051	858	4	0	0	NUM
ejpam-5051	858	5	]	]	PUNCT
ejpam-5051	858	6	.	.	PUNCT
ejpam-5051	859	1	therefore	therefore	ADV
ejpam-5051	859	2	,	,	PUNCT
ejpam-5051	859	3	d	d	PROPN
ejpam-5051	859	4	=	=	PRON
ejpam-5051	859	5	{	{	PUNCT
ejpam-5051	859	6	[	[	X
ejpam-5051	859	7	χ1	χ1	NOUN
ejpam-5051	859	8	,	,	PUNCT
ejpam-5051	859	9	1	1	NUM
ejpam-5051	859	10	,	,	PUNCT
ejpam-5051	859	11	0	0	NUM
ejpam-5051	859	12	]	]	PUNCT
ejpam-5051	859	13	,	,	PUNCT
ejpam-5051	860	1	[	[	X
ejpam-5051	860	2	χ1,−1	χ1,−1	X
ejpam-5051	860	3	,	,	PUNCT
ejpam-5051	860	4	0	0	NUM
ejpam-5051	860	5	]	]	PUNCT
ejpam-5051	860	6	,	,	PUNCT
ejpam-5051	860	7	[	[	X
ejpam-5051	860	8	χ2	χ2	PROPN
ejpam-5051	860	9	,	,	PUNCT
ejpam-5051	860	10	1	1	NUM
ejpam-5051	860	11	,	,	PUNCT
ejpam-5051	860	12	0	0	NUM
ejpam-5051	860	13	]	]	PUNCT
ejpam-5051	860	14	,	,	PUNCT
ejpam-5051	860	15	[	[	X
ejpam-5051	860	16	χ2,−1	χ2,−1	X
ejpam-5051	860	17	,	,	PUNCT
ejpam-5051	860	18	0	0	NUM
ejpam-5051	860	19	]	]	PUNCT
ejpam-5051	860	20	}	}	PUNCT
ejpam-5051	860	21	.	.	PUNCT
ejpam-5051	861	1	and	and	CCONJ
ejpam-5051	861	2	claim	claim	NOUN
ejpam-5051	861	3	1	1	NUM
ejpam-5051	861	4	is	be	AUX
ejpam-5051	861	5	proved	prove	VERB
ejpam-5051	861	6	.	.	PUNCT
ejpam-5051	862	1	now	now	ADV
ejpam-5051	862	2	,	,	PUNCT
ejpam-5051	862	3	the	the	DET
ejpam-5051	862	4	source	source	NOUN
ejpam-5051	862	5	of	of	ADP
ejpam-5051	862	6	[	[	X
ejpam-5051	862	7	χ1,−1	χ1,−1	PROPN
ejpam-5051	862	8	,	,	PUNCT
ejpam-5051	862	9	0	0	NUM
ejpam-5051	862	10	]	]	PUNCT
ejpam-5051	862	11	in	in	ADP
ejpam-5051	862	12	d	d	PROPN
ejpam-5051	862	13	is	be	AUX
ejpam-5051	862	14	,	,	PUNCT
ejpam-5051	862	15	s([χ1,−1	s([χ1,−1	NOUN
ejpam-5051	862	16	,	,	PUNCT
ejpam-5051	862	17	0	0	NUM
ejpam-5051	862	18	]	]	PUNCT
ejpam-5051	862	19	)	)	PUNCT
ejpam-5051	863	1	=	=	PUNCT
ejpam-5051	864	1	[	[	X
ejpam-5051	864	2	χ1,−1	χ1,−1	NOUN
ejpam-5051	864	3	,	,	PUNCT
ejpam-5051	864	4	0]−1[χ1,−1	0]−1[χ1,−1	NUM
ejpam-5051	864	5	,	,	PUNCT
ejpam-5051	864	6	0	0	NUM
ejpam-5051	864	7	]	]	PUNCT
ejpam-5051	864	8	=	=	PUNCT
ejpam-5051	865	1	[	[	X
ejpam-5051	865	2	χ1	χ1	PROPN
ejpam-5051	865	3	·	·	PUNCT
ejpam-5051	865	4	0	0	NUM
ejpam-5051	865	5	,	,	PUNCT
ejpam-5051	865	6	(	(	PUNCT
ejpam-5051	865	7	−1)−1	−1)−1	NOUN
ejpam-5051	865	8	,	,	PUNCT
ejpam-5051	865	9	0][χ1,−1	0][χ1,−1	PROPN
ejpam-5051	865	10	,	,	PUNCT
ejpam-5051	865	11	0	0	NUM
ejpam-5051	865	12	]	]	PUNCT
ejpam-5051	865	13	=	=	PUNCT
ejpam-5051	866	1	[	[	X
ejpam-5051	866	2	χ1	χ1	NOUN
ejpam-5051	866	3	,	,	PUNCT
ejpam-5051	866	4	(	(	PUNCT
ejpam-5051	866	5	−1)−1(−1	−1)−1(−1	PROPN
ejpam-5051	866	6	)	)	PUNCT
ejpam-5051	866	7	,	,	PUNCT
ejpam-5051	866	8	0(0	0(0	NUM
ejpam-5051	866	9	)	)	PUNCT
ejpam-5051	866	10	]	]	PUNCT
ejpam-5051	867	1	=	=	PUNCT
ejpam-5051	868	1	[	[	X
ejpam-5051	868	2	χ1	χ1	NOUN
ejpam-5051	868	3	,	,	PUNCT
ejpam-5051	868	4	1	1	NUM
ejpam-5051	868	5	,	,	PUNCT
ejpam-5051	868	6	0	0	NUM
ejpam-5051	868	7	]	]	PUNCT
ejpam-5051	868	8	.	.	PUNCT
ejpam-5051	869	1	also	also	ADV
ejpam-5051	869	2	,	,	PUNCT
ejpam-5051	869	3	the	the	DET
ejpam-5051	869	4	range	range	NOUN
ejpam-5051	869	5	of	of	ADP
ejpam-5051	869	6	[	[	X
ejpam-5051	869	7	χ1,−1	χ1,−1	PROPN
ejpam-5051	869	8	,	,	PUNCT
ejpam-5051	869	9	0	0	NUM
ejpam-5051	869	10	]	]	PUNCT
ejpam-5051	869	11	in	in	ADP
ejpam-5051	869	12	d	d	PROPN
ejpam-5051	869	13	is	be	AUX
ejpam-5051	869	14	,	,	PUNCT
ejpam-5051	869	15	r([χ1,−1	r([χ1,−1	ADJ
ejpam-5051	869	16	,	,	PUNCT
ejpam-5051	869	17	0	0	NUM
ejpam-5051	869	18	]	]	PUNCT
ejpam-5051	869	19	)	)	PUNCT
ejpam-5051	870	1	=	=	PUNCT
ejpam-5051	871	1	[	[	X
ejpam-5051	871	2	χ1,−1	χ1,−1	PROPN
ejpam-5051	871	3	,	,	PUNCT
ejpam-5051	871	4	0][χ1,−1	0][χ1,−1	PROPN
ejpam-5051	871	5	,	,	PUNCT
ejpam-5051	871	6	0]−1	0]−1	NOUN
ejpam-5051	871	7	=	=	PUNCT
ejpam-5051	872	1	[	[	X
ejpam-5051	872	2	χ1,−1	χ1,−1	NOUN
ejpam-5051	872	3	,	,	PUNCT
ejpam-5051	872	4	0][χ1	0][χ1	X
ejpam-5051	872	5	·	·	PUNCT
ejpam-5051	872	6	0	0	NUM
ejpam-5051	872	7	,	,	PUNCT
ejpam-5051	872	8	(	(	PUNCT
ejpam-5051	872	9	−1)−1	−1)−1	NOUN
ejpam-5051	872	10	,	,	PUNCT
ejpam-5051	872	11	0	0	NUM
ejpam-5051	872	12	]	]	PUNCT
ejpam-5051	872	13	r.	r.	PROPN
ejpam-5051	872	14	s.	s.	PROPN
ejpam-5051	872	15	bongcawel	bongcawel	PROPN
ejpam-5051	872	16	et	et	PROPN
ejpam-5051	872	17	al	al	PROPN
ejpam-5051	872	18	.	.	PUNCT
ejpam-5051	872	19	/	/	SYM
ejpam-5051	872	20	eur	eur	PROPN
ejpam-5051	872	21	.	.	PUNCT
ejpam-5051	873	1	j.	j.	PROPN
ejpam-5051	873	2	pure	pure	PROPN
ejpam-5051	873	3	appl	appl	PROPN
ejpam-5051	873	4	.	.	PROPN
ejpam-5051	873	5	math	math	PROPN
ejpam-5051	873	6	,	,	PUNCT
ejpam-5051	873	7	17	17	NUM
ejpam-5051	873	8	(	(	PUNCT
ejpam-5051	873	9	1	1	NUM
ejpam-5051	873	10	)	)	PUNCT
ejpam-5051	873	11	(	(	PUNCT
ejpam-5051	873	12	2024	2024	NUM
ejpam-5051	873	13	)	)	PUNCT
ejpam-5051	873	14	,	,	PUNCT
ejpam-5051	873	15	519	519	NUM
ejpam-5051	873	16	-	-	SYM
ejpam-5051	873	17	545	545	NUM
ejpam-5051	873	18	540	540	NUM
ejpam-5051	873	19	=	=	PUNCT
ejpam-5051	874	1	[	[	X
ejpam-5051	874	2	χ1	χ1	NOUN
ejpam-5051	874	3	,	,	PUNCT
ejpam-5051	874	4	(	(	PUNCT
ejpam-5051	874	5	−1)(−1)−1	−1)(−1)−1	NOUN
ejpam-5051	874	6	,	,	PUNCT
ejpam-5051	874	7	(	(	PUNCT
ejpam-5051	874	8	0)0	0)0	NOUN
ejpam-5051	874	9	]	]	X
ejpam-5051	874	10	=	=	PUNCT
ejpam-5051	875	1	[	[	X
ejpam-5051	875	2	χ1	χ1	NOUN
ejpam-5051	875	3	,	,	PUNCT
ejpam-5051	875	4	1	1	NUM
ejpam-5051	875	5	,	,	PUNCT
ejpam-5051	875	6	0	0	NUM
ejpam-5051	875	7	]	]	PUNCT
ejpam-5051	875	8	for	for	ADP
ejpam-5051	875	9	[	[	X
ejpam-5051	875	10	χ2,−1	χ2,−1	ADJ
ejpam-5051	875	11	,	,	PUNCT
ejpam-5051	875	12	0	0	NUM
ejpam-5051	875	13	]	]	PUNCT
ejpam-5051	875	14	in	in	ADP
ejpam-5051	875	15	d	d	PROPN
ejpam-5051	875	16	,	,	PUNCT
ejpam-5051	875	17	s([χ2,−1	s([χ2,−1	ADV
ejpam-5051	875	18	,	,	PUNCT
ejpam-5051	875	19	0	0	NUM
ejpam-5051	875	20	]	]	PUNCT
ejpam-5051	875	21	)	)	PUNCT
ejpam-5051	876	1	=	=	PUNCT
ejpam-5051	877	1	[	[	X
ejpam-5051	877	2	χ2,−1	χ2,−1	X
ejpam-5051	877	3	,	,	PUNCT
ejpam-5051	877	4	0]−1[χ2,−1	0]−1[χ2,−1	PRON
ejpam-5051	877	5	,	,	PUNCT
ejpam-5051	877	6	0	0	NUM
ejpam-5051	877	7	]	]	PUNCT
ejpam-5051	877	8	=	=	PUNCT
ejpam-5051	878	1	[	[	X
ejpam-5051	878	2	χ2	χ2	PROPN
ejpam-5051	878	3	·	·	PUNCT
ejpam-5051	878	4	0	0	NUM
ejpam-5051	878	5	,	,	PUNCT
ejpam-5051	878	6	(	(	PUNCT
ejpam-5051	878	7	−1)−1	−1)−1	NOUN
ejpam-5051	878	8	,	,	PUNCT
ejpam-5051	878	9	0][χ2,−1	0][χ2,−1	NOUN
ejpam-5051	878	10	,	,	PUNCT
ejpam-5051	878	11	0	0	NUM
ejpam-5051	878	12	]	]	PUNCT
ejpam-5051	878	13	=	=	PUNCT
ejpam-5051	879	1	[	[	X
ejpam-5051	879	2	χ2	χ2	PROPN
ejpam-5051	879	3	,	,	PUNCT
ejpam-5051	879	4	(	(	PUNCT
ejpam-5051	879	5	−1)−1(−1	−1)−1(−1	PROPN
ejpam-5051	879	6	)	)	PUNCT
ejpam-5051	879	7	,	,	PUNCT
ejpam-5051	879	8	0(0	0(0	NUM
ejpam-5051	879	9	)	)	PUNCT
ejpam-5051	879	10	]	]	PUNCT
ejpam-5051	880	1	=	=	PUNCT
ejpam-5051	881	1	[	[	X
ejpam-5051	881	2	χ2	χ2	PROPN
ejpam-5051	881	3	,	,	PUNCT
ejpam-5051	881	4	1	1	NUM
ejpam-5051	881	5	,	,	PUNCT
ejpam-5051	881	6	0	0	NUM
ejpam-5051	881	7	]	]	PUNCT
ejpam-5051	881	8	.	.	PUNCT
ejpam-5051	882	1	and	and	CCONJ
ejpam-5051	882	2	r([χ2,−1	r([χ2,−1	ADJ
ejpam-5051	882	3	,	,	PUNCT
ejpam-5051	882	4	0	0	NUM
ejpam-5051	882	5	]	]	PUNCT
ejpam-5051	882	6	)	)	PUNCT
ejpam-5051	883	1	=	=	PUNCT
ejpam-5051	884	1	[	[	X
ejpam-5051	884	2	χ2,−1	χ2,−1	X
ejpam-5051	884	3	,	,	PUNCT
ejpam-5051	884	4	0][χ2,−1	0][χ2,−1	NOUN
ejpam-5051	884	5	,	,	PUNCT
ejpam-5051	884	6	0]−1	0]−1	NOUN
ejpam-5051	884	7	=	=	PUNCT
ejpam-5051	885	1	[	[	X
ejpam-5051	885	2	χ2,−1	χ2,−1	X
ejpam-5051	885	3	,	,	PUNCT
ejpam-5051	885	4	0][χ2	0][χ2	X
ejpam-5051	885	5	·	·	PUNCT
ejpam-5051	885	6	0	0	NUM
ejpam-5051	885	7	,	,	PUNCT
ejpam-5051	885	8	(	(	PUNCT
ejpam-5051	885	9	−1)−1	−1)−1	NOUN
ejpam-5051	885	10	,	,	PUNCT
ejpam-5051	885	11	0	0	NUM
ejpam-5051	885	12	]	]	PUNCT
ejpam-5051	885	13	=	=	PUNCT
ejpam-5051	886	1	[	[	X
ejpam-5051	886	2	χ2	χ2	PROPN
ejpam-5051	886	3	,	,	PUNCT
ejpam-5051	886	4	(	(	PUNCT
ejpam-5051	886	5	−1)(−1)−1	−1)(−1)−1	NOUN
ejpam-5051	886	6	,	,	PUNCT
ejpam-5051	886	7	(	(	PUNCT
ejpam-5051	886	8	0)0	0)0	NOUN
ejpam-5051	886	9	]	]	X
ejpam-5051	886	10	=	=	PUNCT
ejpam-5051	887	1	[	[	X
ejpam-5051	887	2	χ2	χ2	PROPN
ejpam-5051	887	3	,	,	PUNCT
ejpam-5051	887	4	1	1	NUM
ejpam-5051	887	5	,	,	PUNCT
ejpam-5051	887	6	0	0	NUM
ejpam-5051	887	7	]	]	PUNCT
ejpam-5051	887	8	our	our	PRON
ejpam-5051	887	9	groupoid	groupoid	PROPN
ejpam-5051	887	10	d	d	PROPN
ejpam-5051	887	11	is	be	AUX
ejpam-5051	887	12	best	well	ADV
ejpam-5051	887	13	understood	understand	VERB
ejpam-5051	887	14	with	with	ADP
ejpam-5051	887	15	this	this	DET
ejpam-5051	887	16	illustration	illustration	NOUN
ejpam-5051	887	17	:	:	PUNCT
ejpam-5051	888	1	[	[	X
ejpam-5051	888	2	x1	x1	X
ejpam-5051	888	3	,	,	PUNCT
ejpam-5051	888	4	1	1	NUM
ejpam-5051	888	5	,	,	PUNCT
ejpam-5051	888	6	0	0	NUM
ejpam-5051	888	7	]	]	PUNCT
ejpam-5051	889	1	[	[	X
ejpam-5051	889	2	x1,−1	x1,−1	X
ejpam-5051	889	3	,	,	PUNCT
ejpam-5051	889	4	0	0	NUM
ejpam-5051	889	5	]	]	PUNCT
ejpam-5051	890	1	[	[	X
ejpam-5051	890	2	x2,−1	x2,−1	NOUN
ejpam-5051	890	3	,	,	PUNCT
ejpam-5051	890	4	0	0	NUM
ejpam-5051	890	5	]	]	PUNCT
ejpam-5051	891	1	[	[	X
ejpam-5051	891	2	x2	x2	X
ejpam-5051	891	3	,	,	PUNCT
ejpam-5051	891	4	1	1	NUM
ejpam-5051	891	5	,	,	PUNCT
ejpam-5051	891	6	0	0	NUM
ejpam-5051	891	7	]	]	PUNCT
ejpam-5051	891	8	figure	figure	NOUN
ejpam-5051	891	9	1	1	NUM
ejpam-5051	891	10	:	:	PUNCT
ejpam-5051	891	11	morphisms	morphism	VERB
ejpam-5051	891	12	in	in	ADP
ejpam-5051	891	13	d	d	PROPN
ejpam-5051	891	14	hence	hence	ADV
ejpam-5051	891	15	,	,	PUNCT
ejpam-5051	891	16	the	the	DET
ejpam-5051	891	17	unit	unit	NOUN
ejpam-5051	891	18	space	space	NOUN
ejpam-5051	891	19	for	for	ADP
ejpam-5051	891	20	d	d	PROPN
ejpam-5051	891	21	is	be	AUX
ejpam-5051	891	22	d(0	d(0	NOUN
ejpam-5051	891	23	)	)	PUNCT
ejpam-5051	892	1	=	=	PRON
ejpam-5051	893	1	{	{	PUNCT
ejpam-5051	894	1	[	[	X
ejpam-5051	894	2	χ1	χ1	NOUN
ejpam-5051	894	3	,	,	PUNCT
ejpam-5051	894	4	1	1	NUM
ejpam-5051	894	5	,	,	PUNCT
ejpam-5051	894	6	0	0	NUM
ejpam-5051	894	7	]	]	PUNCT
ejpam-5051	894	8	,	,	PUNCT
ejpam-5051	894	9	[	[	X
ejpam-5051	894	10	χ2	χ2	PROPN
ejpam-5051	894	11	,	,	PUNCT
ejpam-5051	894	12	1	1	NUM
ejpam-5051	894	13	,	,	PUNCT
ejpam-5051	894	14	0	0	NUM
ejpam-5051	894	15	]	]	PUNCT
ejpam-5051	894	16	}	}	PUNCT
ejpam-5051	894	17	.	.	PUNCT
ejpam-5051	895	1	when	when	SCONJ
ejpam-5051	895	2	z	z	NOUN
ejpam-5051	895	3	is	be	AUX
ejpam-5051	895	4	endowed	endow	VERB
ejpam-5051	895	5	with	with	ADP
ejpam-5051	895	6	the	the	DET
ejpam-5051	895	7	discrete	discrete	ADJ
ejpam-5051	895	8	topology	topology	NOUN
ejpam-5051	895	9	,	,	PUNCT
ejpam-5051	895	10	its	its	PRON
ejpam-5051	895	11	base	base	NOUN
ejpam-5051	895	12	will	will	AUX
ejpam-5051	895	13	be	be	AUX
ejpam-5051	895	14	composed	compose	VERB
ejpam-5051	895	15	of	of	ADP
ejpam-5051	895	16	singletons	singleton	NOUN
ejpam-5051	895	17	{	{	PUNCT
ejpam-5051	895	18	z	z	NOUN
ejpam-5051	895	19	}	}	PUNCT
ejpam-5051	895	20	,	,	PUNCT
ejpam-5051	895	21	for	for	ADP
ejpam-5051	895	22	all	all	DET
ejpam-5051	895	23	z	z	NOUN
ejpam-5051	895	24	∈	∈	PROPN
ejpam-5051	895	25	z.	z.	PROPN
ejpam-5051	895	26	let	let	VERB
ejpam-5051	895	27	1{z	1{z	NUM
ejpam-5051	895	28	}	}	PUNCT
ejpam-5051	895	29	denotes	denote	VERB
ejpam-5051	895	30	the	the	DET
ejpam-5051	895	31	characteristic	characteristic	ADJ
ejpam-5051	895	32	function	function	NOUN
ejpam-5051	895	33	of	of	ADP
ejpam-5051	895	34	{	{	PUNCT
ejpam-5051	895	35	z	z	NOUN
ejpam-5051	895	36	}	}	PUNCT
ejpam-5051	895	37	from	from	ADP
ejpam-5051	895	38	z	z	PROPN
ejpam-5051	895	39	to	to	ADP
ejpam-5051	895	40	z.	z.	PROPN
ejpam-5051	895	41	the	the	DET
ejpam-5051	895	42	steinberg	steinberg	PROPN
ejpam-5051	895	43	algebra	algebra	PROPN
ejpam-5051	895	44	associated	associate	VERB
ejpam-5051	895	45	to	to	ADP
ejpam-5051	895	46	z	z	PROPN
ejpam-5051	895	47	is	be	AUX
ejpam-5051	895	48	az(z	az(z	NOUN
ejpam-5051	895	49	)	)	PUNCT
ejpam-5051	896	1	:	:	PUNCT
ejpam-5051	896	2	=	=	SYM
ejpam-5051	896	3	span{1{z	span{1{z	PROPN
ejpam-5051	896	4	}	}	PUNCT
ejpam-5051	896	5	:	:	PUNCT
ejpam-5051	896	6	z	z	X
ejpam-5051	896	7	→	→	SYM
ejpam-5051	896	8	z|{z	z|{z	PROPN
ejpam-5051	896	9	}	}	PUNCT
ejpam-5051	896	10	is	be	AUX
ejpam-5051	896	11	a	a	DET
ejpam-5051	896	12	compact	compact	ADJ
ejpam-5051	896	13	open	open	ADJ
ejpam-5051	896	14	bisection	bisection	NOUN
ejpam-5051	896	15	of	of	ADP
ejpam-5051	896	16	z	z	NOUN
ejpam-5051	896	17	}	}	PUNCT
ejpam-5051	896	18	equipped	equip	VERB
ejpam-5051	896	19	with	with	ADP
ejpam-5051	896	20	pointwise	pointwise	ADJ
ejpam-5051	896	21	addition	addition	NOUN
ejpam-5051	896	22	,	,	PUNCT
ejpam-5051	896	23	a11{z1	a11{z1	NOUN
ejpam-5051	896	24	}	}	PUNCT
ejpam-5051	896	25	+	+	CCONJ
ejpam-5051	896	26	a21{z2	a21{z2	NOUN
ejpam-5051	896	27	}	}	PUNCT
ejpam-5051	896	28	=	=	SYM
ejpam-5051	896	29	(	(	PUNCT
ejpam-5051	896	30	a1	a1	NOUN
ejpam-5051	896	31	+	+	CCONJ
ejpam-5051	896	32	a2)1{z1+z2	a2)1{z1+z2	NOUN
ejpam-5051	896	33	}	}	PUNCT
ejpam-5051	896	34	and	and	CCONJ
ejpam-5051	896	35	multiplication	multiplication	NOUN
ejpam-5051	896	36	as	as	SCONJ
ejpam-5051	896	37	follows	follow	VERB
ejpam-5051	896	38	;	;	PUNCT
ejpam-5051	896	39	a11{z1	a11{z1	NOUN
ejpam-5051	896	40	}	}	PUNCT
ejpam-5051	896	41	·	·	PUNCT
ejpam-5051	896	42	a21{z2	a21{z2	NOUN
ejpam-5051	896	43	}	}	PUNCT
ejpam-5051	896	44	=	=	PUNCT
ejpam-5051	896	45	a1a21{z1+z2	a1a21{z1+z2	X
ejpam-5051	896	46	}	}	PUNCT
ejpam-5051	896	47	.	.	PUNCT
ejpam-5051	897	1	claim	claim	NOUN
ejpam-5051	897	2	2	2	NUM
ejpam-5051	897	3	:	:	PUNCT
ejpam-5051	897	4	â⋊r	â⋊r	PROPN
ejpam-5051	897	5	=	=	SYM
ejpam-5051	897	6	(	(	PUNCT
ejpam-5051	897	7	â⋊r)(0	â⋊r)(0	PROPN
ejpam-5051	897	8	)	)	PUNCT
ejpam-5051	897	9	the	the	DET
ejpam-5051	897	10	source	source	NOUN
ejpam-5051	897	11	and	and	CCONJ
ejpam-5051	897	12	range	range	NOUN
ejpam-5051	897	13	of	of	ADP
ejpam-5051	897	14	(	(	PUNCT
ejpam-5051	897	15	χ1	χ1	NOUN
ejpam-5051	897	16	,	,	PUNCT
ejpam-5051	897	17	0	0	NUM
ejpam-5051	897	18	,	,	PUNCT
ejpam-5051	897	19	0̇	0̇	NUM
ejpam-5051	897	20	)	)	PUNCT
ejpam-5051	897	21	∈	∈	PROPN
ejpam-5051	897	22	â⋊r	â⋊r	NOUN
ejpam-5051	897	23	are	be	AUX
ejpam-5051	897	24	:	:	PUNCT
ejpam-5051	897	25	s((χ1	s((χ1	NOUN
ejpam-5051	897	26	,	,	PUNCT
ejpam-5051	897	27	0	0	NUM
ejpam-5051	897	28	,	,	PUNCT
ejpam-5051	897	29	0̇	0̇	NUM
ejpam-5051	897	30	)	)	PUNCT
ejpam-5051	897	31	)	)	PUNCT
ejpam-5051	898	1	=	=	SYM
ejpam-5051	898	2	(	(	PUNCT
ejpam-5051	898	3	χ1	χ1	NOUN
ejpam-5051	898	4	,	,	PUNCT
ejpam-5051	898	5	0	0	NUM
ejpam-5051	898	6	,	,	PUNCT
ejpam-5051	898	7	0̇	0̇	NUM
ejpam-5051	898	8	)	)	PUNCT
ejpam-5051	898	9	−1(χ1	−1(χ1	X
ejpam-5051	898	10	,	,	PUNCT
ejpam-5051	898	11	0	0	NUM
ejpam-5051	898	12	,	,	PUNCT
ejpam-5051	898	13	0̇	0̇	NUM
ejpam-5051	898	14	)	)	PUNCT
ejpam-5051	898	15	=	=	SYM
ejpam-5051	898	16	(	(	PUNCT
ejpam-5051	898	17	χ1	χ1	NOUN
ejpam-5051	898	18	·	·	PUNCT
ejpam-5051	898	19	0	0	NUM
ejpam-5051	898	20	,	,	PUNCT
ejpam-5051	898	21	0	0	NUM
ejpam-5051	898	22	,	,	PUNCT
ejpam-5051	898	23	0̇)(χ1	0̇)(χ1	NUM
ejpam-5051	898	24	,	,	PUNCT
ejpam-5051	898	25	0	0	NUM
ejpam-5051	898	26	,	,	PUNCT
ejpam-5051	898	27	0̇	0̇	NUM
ejpam-5051	898	28	)	)	PUNCT
ejpam-5051	898	29	=	=	SYM
ejpam-5051	898	30	(	(	PUNCT
ejpam-5051	898	31	χ1	χ1	NOUN
ejpam-5051	898	32	,	,	PUNCT
ejpam-5051	898	33	0	0	NUM
ejpam-5051	898	34	,	,	PUNCT
ejpam-5051	898	35	0̇	0̇	NUM
ejpam-5051	898	36	)	)	PUNCT
ejpam-5051	898	37	r.	r.	PROPN
ejpam-5051	898	38	s.	s.	PROPN
ejpam-5051	898	39	bongcawel	bongcawel	PROPN
ejpam-5051	898	40	et	et	PROPN
ejpam-5051	898	41	al	al	PROPN
ejpam-5051	898	42	.	.	PUNCT
ejpam-5051	898	43	/	/	SYM
ejpam-5051	898	44	eur	eur	PROPN
ejpam-5051	898	45	.	.	PUNCT
ejpam-5051	899	1	j.	j.	PROPN
ejpam-5051	899	2	pure	pure	PROPN
ejpam-5051	899	3	appl	appl	PROPN
ejpam-5051	899	4	.	.	PROPN
ejpam-5051	899	5	math	math	PROPN
ejpam-5051	899	6	,	,	PUNCT
ejpam-5051	899	7	17	17	NUM
ejpam-5051	899	8	(	(	PUNCT
ejpam-5051	899	9	1	1	NUM
ejpam-5051	899	10	)	)	PUNCT
ejpam-5051	899	11	(	(	PUNCT
ejpam-5051	899	12	2024	2024	NUM
ejpam-5051	899	13	)	)	PUNCT
ejpam-5051	899	14	,	,	PUNCT
ejpam-5051	899	15	519	519	NUM
ejpam-5051	899	16	-	-	SYM
ejpam-5051	899	17	545	545	NUM
ejpam-5051	899	18	541	541	NUM
ejpam-5051	899	19	r((χ1	r((χ1	PROPN
ejpam-5051	899	20	,	,	PUNCT
ejpam-5051	899	21	0	0	NUM
ejpam-5051	899	22	,	,	PUNCT
ejpam-5051	899	23	0̇	0̇	NUM
ejpam-5051	899	24	)	)	PUNCT
ejpam-5051	899	25	)	)	PUNCT
ejpam-5051	900	1	=	=	SYM
ejpam-5051	900	2	(	(	PUNCT
ejpam-5051	900	3	χ1	χ1	NOUN
ejpam-5051	900	4	,	,	PUNCT
ejpam-5051	900	5	0	0	NUM
ejpam-5051	900	6	,	,	PUNCT
ejpam-5051	900	7	0̇)(χ1	0̇)(χ1	NUM
ejpam-5051	900	8	,	,	PUNCT
ejpam-5051	900	9	0	0	NUM
ejpam-5051	900	10	,	,	PUNCT
ejpam-5051	900	11	0̇	0̇	NUM
ejpam-5051	900	12	)	)	PUNCT
ejpam-5051	900	13	−1	−1	NOUN
ejpam-5051	900	14	=	=	SYM
ejpam-5051	900	15	(	(	PUNCT
ejpam-5051	900	16	χ1	χ1	NOUN
ejpam-5051	900	17	,	,	PUNCT
ejpam-5051	900	18	0	0	NUM
ejpam-5051	900	19	,	,	PUNCT
ejpam-5051	900	20	0̇)(χ1	0̇)(χ1	X
ejpam-5051	900	21	·	·	PUNCT
ejpam-5051	900	22	0	0	NUM
ejpam-5051	900	23	,	,	PUNCT
ejpam-5051	900	24	0	0	NUM
ejpam-5051	900	25	,	,	PUNCT
ejpam-5051	900	26	0̇	0̇	NUM
ejpam-5051	900	27	)	)	PUNCT
ejpam-5051	900	28	=	=	SYM
ejpam-5051	900	29	(	(	PUNCT
ejpam-5051	900	30	χ1	χ1	NOUN
ejpam-5051	900	31	,	,	PUNCT
ejpam-5051	900	32	0	0	NUM
ejpam-5051	900	33	,	,	PUNCT
ejpam-5051	900	34	0̇	0̇	NUM
ejpam-5051	900	35	)	)	PUNCT
ejpam-5051	900	36	.	.	PUNCT
ejpam-5051	901	1	also	also	ADV
ejpam-5051	901	2	,	,	PUNCT
ejpam-5051	901	3	the	the	DET
ejpam-5051	901	4	source	source	NOUN
ejpam-5051	901	5	and	and	CCONJ
ejpam-5051	901	6	range	range	VERB
ejpam-5051	901	7	for	for	ADP
ejpam-5051	901	8	(	(	PUNCT
ejpam-5051	901	9	χ2	χ2	PROPN
ejpam-5051	901	10	,	,	PUNCT
ejpam-5051	901	11	0	0	NUM
ejpam-5051	901	12	,	,	PUNCT
ejpam-5051	901	13	0̇	0̇	NUM
ejpam-5051	901	14	)	)	PUNCT
ejpam-5051	901	15	∈	∈	PROPN
ejpam-5051	901	16	â⋊r	â⋊r	NOUN
ejpam-5051	901	17	are	be	AUX
ejpam-5051	901	18	:	:	PUNCT
ejpam-5051	901	19	s((χ2	s((χ2	NOUN
ejpam-5051	901	20	,	,	PUNCT
ejpam-5051	901	21	0	0	NUM
ejpam-5051	901	22	,	,	PUNCT
ejpam-5051	901	23	0̇	0̇	NUM
ejpam-5051	901	24	)	)	PUNCT
ejpam-5051	901	25	)	)	PUNCT
ejpam-5051	902	1	=	=	PRON
ejpam-5051	902	2	(	(	PUNCT
ejpam-5051	902	3	χ2	χ2	PROPN
ejpam-5051	902	4	,	,	PUNCT
ejpam-5051	902	5	0	0	NUM
ejpam-5051	902	6	,	,	PUNCT
ejpam-5051	902	7	0̇	0̇	NUM
ejpam-5051	902	8	)	)	PUNCT
ejpam-5051	902	9	−1(χ2	−1(χ2	X
ejpam-5051	902	10	,	,	PUNCT
ejpam-5051	902	11	0	0	NUM
ejpam-5051	902	12	,	,	PUNCT
ejpam-5051	902	13	0̇	0̇	NUM
ejpam-5051	902	14	)	)	PUNCT
ejpam-5051	902	15	=	=	SYM
ejpam-5051	903	1	(	(	PUNCT
ejpam-5051	903	2	χ2	χ2	PROPN
ejpam-5051	903	3	·	·	PUNCT
ejpam-5051	903	4	0	0	NUM
ejpam-5051	903	5	,	,	PUNCT
ejpam-5051	903	6	0	0	NUM
ejpam-5051	903	7	,	,	PUNCT
ejpam-5051	903	8	0̇)(χ2	0̇)(χ2	NOUN
ejpam-5051	903	9	,	,	PUNCT
ejpam-5051	903	10	0	0	NUM
ejpam-5051	903	11	,	,	PUNCT
ejpam-5051	903	12	0̇	0̇	NUM
ejpam-5051	903	13	)	)	PUNCT
ejpam-5051	903	14	=	=	SYM
ejpam-5051	903	15	(	(	PUNCT
ejpam-5051	903	16	χ2	χ2	PROPN
ejpam-5051	903	17	,	,	PUNCT
ejpam-5051	903	18	0	0	NUM
ejpam-5051	903	19	,	,	PUNCT
ejpam-5051	903	20	0̇	0̇	NUM
ejpam-5051	903	21	)	)	PUNCT
ejpam-5051	903	22	r((χ2	r((χ2	NOUN
ejpam-5051	903	23	,	,	PUNCT
ejpam-5051	903	24	0	0	NUM
ejpam-5051	903	25	,	,	PUNCT
ejpam-5051	903	26	0̇	0̇	NUM
ejpam-5051	903	27	)	)	PUNCT
ejpam-5051	903	28	)	)	PUNCT
ejpam-5051	904	1	=	=	PRON
ejpam-5051	904	2	(	(	PUNCT
ejpam-5051	904	3	χ2	χ2	PROPN
ejpam-5051	904	4	,	,	PUNCT
ejpam-5051	904	5	0	0	NUM
ejpam-5051	904	6	,	,	PUNCT
ejpam-5051	904	7	0̇)(χ2	0̇)(χ2	NOUN
ejpam-5051	904	8	,	,	PUNCT
ejpam-5051	904	9	0	0	NUM
ejpam-5051	904	10	,	,	PUNCT
ejpam-5051	904	11	0̇	0̇	NUM
ejpam-5051	904	12	)	)	PUNCT
ejpam-5051	904	13	−1	−1	NOUN
ejpam-5051	904	14	=	=	SYM
ejpam-5051	904	15	(	(	PUNCT
ejpam-5051	904	16	χ2	χ2	PROPN
ejpam-5051	904	17	,	,	PUNCT
ejpam-5051	904	18	0	0	NUM
ejpam-5051	904	19	,	,	PUNCT
ejpam-5051	904	20	0̇)(χ2	0̇)(χ2	X
ejpam-5051	904	21	·	·	PUNCT
ejpam-5051	904	22	0	0	NUM
ejpam-5051	904	23	,	,	PUNCT
ejpam-5051	904	24	0	0	NUM
ejpam-5051	904	25	,	,	PUNCT
ejpam-5051	904	26	0̇	0̇	NUM
ejpam-5051	904	27	)	)	PUNCT
ejpam-5051	904	28	=	=	SYM
ejpam-5051	904	29	(	(	PUNCT
ejpam-5051	904	30	χ2	χ2	PROPN
ejpam-5051	904	31	,	,	PUNCT
ejpam-5051	904	32	0	0	NUM
ejpam-5051	904	33	,	,	PUNCT
ejpam-5051	904	34	0̇	0̇	NUM
ejpam-5051	904	35	)	)	PUNCT
ejpam-5051	904	36	.	.	PUNCT
ejpam-5051	905	1	hence	hence	ADV
ejpam-5051	905	2	,	,	PUNCT
ejpam-5051	905	3	(	(	PUNCT
ejpam-5051	905	4	â⋊r)(0	â⋊r)(0	ADV
ejpam-5051	905	5	)	)	PUNCT
ejpam-5051	905	6	=	=	PRON
ejpam-5051	905	7	{	{	PUNCT
ejpam-5051	905	8	(	(	PUNCT
ejpam-5051	905	9	χ1	χ1	NOUN
ejpam-5051	905	10	,	,	PUNCT
ejpam-5051	905	11	0	0	NUM
ejpam-5051	905	12	,	,	PUNCT
ejpam-5051	905	13	0̇	0̇	NUM
ejpam-5051	905	14	)	)	PUNCT
ejpam-5051	905	15	,	,	PUNCT
ejpam-5051	905	16	(	(	PUNCT
ejpam-5051	905	17	χ2	χ2	PROPN
ejpam-5051	905	18	,	,	PUNCT
ejpam-5051	905	19	0	0	NUM
ejpam-5051	905	20	,	,	PUNCT
ejpam-5051	905	21	0̇	0̇	NUM
ejpam-5051	905	22	)	)	PUNCT
ejpam-5051	905	23	}	}	PUNCT
ejpam-5051	905	24	=	=	SYM
ejpam-5051	905	25	â⋊r	â⋊r	NOUN
ejpam-5051	905	26	.	.	PUNCT
ejpam-5051	906	1	theorem	theorem	NOUN
ejpam-5051	906	2	7	7	NUM
ejpam-5051	906	3	.	.	PUNCT
ejpam-5051	907	1	if	if	SCONJ
ejpam-5051	907	2	â⋊r	â⋊r	PROPN
ejpam-5051	907	3	=	=	SYM
ejpam-5051	907	4	(	(	PUNCT
ejpam-5051	907	5	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	907	6	)	)	PUNCT
ejpam-5051	907	7	,	,	PUNCT
ejpam-5051	907	8	then	then	ADV
ejpam-5051	907	9	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	907	10	)	)	PUNCT
ejpam-5051	907	11	∼=	∼=	PROPN
ejpam-5051	907	12	az(d	az(d	NUM
ejpam-5051	907	13	;	;	PUNCT
ejpam-5051	907	14	â⋊r	â⋊r	NOUN
ejpam-5051	907	15	)	)	PUNCT
ejpam-5051	907	16	.	.	PUNCT
ejpam-5051	908	1	proof	proof	NOUN
ejpam-5051	908	2	.	.	PUNCT
ejpam-5051	909	1	let	let	VERB
ejpam-5051	909	2	f	f	PROPN
ejpam-5051	909	3	:	:	PUNCT
ejpam-5051	909	4	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	909	5	)	)	PUNCT
ejpam-5051	909	6	→	→	SYM
ejpam-5051	909	7	az(d	az(d	NUM
ejpam-5051	909	8	;	;	PUNCT
ejpam-5051	909	9	â⋊r	â⋊r	NOUN
ejpam-5051	909	10	)	)	PUNCT
ejpam-5051	909	11	be	be	AUX
ejpam-5051	909	12	defined	define	VERB
ejpam-5051	909	13	by	by	ADP
ejpam-5051	909	14	f	f	PROPN
ejpam-5051	909	15	(	(	PUNCT
ejpam-5051	909	16	f)([χi	f)([χi	PROPN
ejpam-5051	909	17	,	,	PUNCT
ejpam-5051	909	18	z	z	PROPN
ejpam-5051	909	19	,	,	PUNCT
ejpam-5051	909	20	γ	γ	NOUN
ejpam-5051	909	21	]	]	X
ejpam-5051	909	22	)	)	PUNCT
ejpam-5051	910	1	=	=	SYM
ejpam-5051	910	2	z	z	X
ejpam-5051	910	3	·	·	PUNCT
ejpam-5051	910	4	f(r((χi	f(r((χi	NUM
ejpam-5051	910	5	,	,	PUNCT
ejpam-5051	910	6	γ̇	γ̇	NOUN
ejpam-5051	910	7	)	)	PUNCT
ejpam-5051	910	8	)	)	PUNCT
ejpam-5051	910	9	)	)	PUNCT
ejpam-5051	911	1	where	where	SCONJ
ejpam-5051	911	2	z	z	PROPN
ejpam-5051	911	3	∈	∈	PROPN
ejpam-5051	911	4	t	t	PROPN
ejpam-5051	911	5	,	,	PUNCT
ejpam-5051	911	6	(	(	PUNCT
ejpam-5051	911	7	χi	χi	NOUN
ejpam-5051	911	8	,	,	PUNCT
ejpam-5051	911	9	γ̇	γ̇	NOUN
ejpam-5051	911	10	)	)	PUNCT
ejpam-5051	911	11	∈	∈	PROPN
ejpam-5051	911	12	â⋊r	â⋊r	NOUN
ejpam-5051	911	13	.	.	PUNCT
ejpam-5051	912	1	linearity	linearity	NOUN
ejpam-5051	912	2	holds	hold	VERB
ejpam-5051	912	3	since	since	SCONJ
ejpam-5051	912	4	for	for	ADP
ejpam-5051	912	5	all	all	DET
ejpam-5051	912	6	f	f	NOUN
ejpam-5051	912	7	,	,	PUNCT
ejpam-5051	912	8	g	g	PROPN
ejpam-5051	912	9	∈	∈	PROPN
ejpam-5051	912	10	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	912	11	)	)	PUNCT
ejpam-5051	912	12	and	and	CCONJ
ejpam-5051	912	13	n	n	PRON
ejpam-5051	912	14	∈	∈	PROPN
ejpam-5051	912	15	z	z	PROPN
ejpam-5051	912	16	,	,	PUNCT
ejpam-5051	912	17	f	f	PROPN
ejpam-5051	912	18	(	(	PUNCT
ejpam-5051	912	19	f	f	PROPN
ejpam-5051	913	1	+	+	CCONJ
ejpam-5051	913	2	g)([χi	g)([χi	NOUN
ejpam-5051	913	3	,	,	PUNCT
ejpam-5051	913	4	z	z	PROPN
ejpam-5051	913	5	,	,	PUNCT
ejpam-5051	913	6	γ	γ	NOUN
ejpam-5051	913	7	]	]	X
ejpam-5051	913	8	)	)	PUNCT
ejpam-5051	913	9	=	=	SYM
ejpam-5051	914	1	z(f	z(f	NOUN
ejpam-5051	914	2	+	+	CCONJ
ejpam-5051	914	3	g)(r((χi	g)(r((χi	VERB
ejpam-5051	914	4	,	,	PUNCT
ejpam-5051	914	5	γ̇	γ̇	NOUN
ejpam-5051	914	6	)	)	PUNCT
ejpam-5051	914	7	)	)	PUNCT
ejpam-5051	914	8	)	)	PUNCT
ejpam-5051	915	1	=	=	SYM
ejpam-5051	915	2	zf(r((χi	zf(r((χi	X
ejpam-5051	915	3	,	,	PUNCT
ejpam-5051	915	4	γ̇	γ̇	NOUN
ejpam-5051	915	5	)	)	PUNCT
ejpam-5051	915	6	)	)	PUNCT
ejpam-5051	915	7	)	)	PUNCT
ejpam-5051	916	1	+	+	CCONJ
ejpam-5051	916	2	zg(r((χi	zg(r((χi	NUM
ejpam-5051	916	3	,	,	PUNCT
ejpam-5051	916	4	γ̇	γ̇	NOUN
ejpam-5051	916	5	)	)	PUNCT
ejpam-5051	916	6	)	)	PUNCT
ejpam-5051	916	7	)	)	PUNCT
ejpam-5051	917	1	=	=	PUNCT
ejpam-5051	917	2	(	(	PUNCT
ejpam-5051	917	3	f	f	X
ejpam-5051	917	4	(	(	PUNCT
ejpam-5051	917	5	f	f	X
ejpam-5051	917	6	)	)	PUNCT
ejpam-5051	918	1	+	+	NUM
ejpam-5051	918	2	f	f	X
ejpam-5051	918	3	(	(	PUNCT
ejpam-5051	918	4	g))([χi	g))([χi	NOUN
ejpam-5051	918	5	,	,	PUNCT
ejpam-5051	918	6	z	z	PROPN
ejpam-5051	918	7	,	,	PUNCT
ejpam-5051	918	8	γ	γ	X
ejpam-5051	918	9	]	]	X
ejpam-5051	918	10	)	)	PUNCT
ejpam-5051	918	11	and	and	CCONJ
ejpam-5051	918	12	f	f	PROPN
ejpam-5051	918	13	(	(	PUNCT
ejpam-5051	918	14	nf	nf	INTJ
ejpam-5051	918	15	)	)	PUNCT
ejpam-5051	918	16	=	=	SYM
ejpam-5051	918	17	znf(r((χi	znf(r((χi	VERB
ejpam-5051	918	18	,	,	PUNCT
ejpam-5051	918	19	γ̇	γ̇	NOUN
ejpam-5051	918	20	)	)	PUNCT
ejpam-5051	918	21	)	)	PUNCT
ejpam-5051	918	22	)	)	PUNCT
ejpam-5051	919	1	=	=	PRON
ejpam-5051	919	2	nzf(r(χi	nzf(r(χi	VERB
ejpam-5051	919	3	,	,	PUNCT
ejpam-5051	919	4	γ̇	γ̇	NOUN
ejpam-5051	919	5	)	)	PUNCT
ejpam-5051	919	6	)	)	PUNCT
ejpam-5051	919	7	)	)	PUNCT
ejpam-5051	920	1	=	=	PUNCT
ejpam-5051	920	2	nf	nf	INTJ
ejpam-5051	920	3	(	(	PUNCT
ejpam-5051	920	4	f	f	NOUN
ejpam-5051	920	5	)	)	PUNCT
ejpam-5051	920	6	.	.	PUNCT
ejpam-5051	921	1	now	now	ADV
ejpam-5051	921	2	,	,	PUNCT
ejpam-5051	921	3	observe	observe	VERB
ejpam-5051	921	4	that	that	SCONJ
ejpam-5051	921	5	f	f	PROPN
ejpam-5051	921	6	(	(	PUNCT
ejpam-5051	921	7	fg)([χi	fg)([χi	PROPN
ejpam-5051	921	8	,	,	PUNCT
ejpam-5051	921	9	z	z	PROPN
ejpam-5051	921	10	,	,	PUNCT
ejpam-5051	921	11	γ	γ	NOUN
ejpam-5051	921	12	]	]	X
ejpam-5051	921	13	)	)	PUNCT
ejpam-5051	921	14	=	=	SYM
ejpam-5051	921	15	z(fg)(r((χi	z(fg)(r((χi	VERB
ejpam-5051	921	16	,	,	PUNCT
ejpam-5051	921	17	γ̇	γ̇	PROPN
ejpam-5051	921	18	)	)	PUNCT
ejpam-5051	921	19	)	)	PUNCT
ejpam-5051	921	20	)	)	PUNCT
ejpam-5051	922	1	=	=	SYM
ejpam-5051	922	2	zf(r((χi	zf(r((χi	X
ejpam-5051	922	3	,	,	PUNCT
ejpam-5051	922	4	γ̇)))g(r((χi	γ̇)))g(r((χi	VERB
ejpam-5051	922	5	,	,	PUNCT
ejpam-5051	922	6	γ̇	γ̇	NOUN
ejpam-5051	922	7	)	)	PUNCT
ejpam-5051	922	8	)	)	PUNCT
ejpam-5051	922	9	)	)	PUNCT
ejpam-5051	922	10	.	.	PUNCT
ejpam-5051	923	1	also	also	ADV
ejpam-5051	923	2	,	,	PUNCT
ejpam-5051	923	3	(	(	PUNCT
ejpam-5051	923	4	f	f	X
ejpam-5051	923	5	(	(	PUNCT
ejpam-5051	923	6	f)f	f)f	X
ejpam-5051	923	7	(	(	PUNCT
ejpam-5051	923	8	g))([χi	g))([χi	NOUN
ejpam-5051	923	9	,	,	PUNCT
ejpam-5051	923	10	z	z	NOUN
ejpam-5051	923	11	,	,	PUNCT
ejpam-5051	923	12	γ])(χi	γ])(χi	ADJ
ejpam-5051	923	13	,	,	PUNCT
ejpam-5051	923	14	γ̇	γ̇	NOUN
ejpam-5051	923	15	)	)	PUNCT
ejpam-5051	923	16	=	=	SYM
ejpam-5051	923	17	∑	∑	PUNCT
ejpam-5051	923	18	(	(	PUNCT
ejpam-5051	923	19	(	(	PUNCT
ejpam-5051	923	20	χ′	χ′	PROPN
ejpam-5051	923	21	i	i	PRON
ejpam-5051	923	22	,	,	PUNCT
ejpam-5051	923	23	γ̇	γ̇	PROPN
ejpam-5051	923	24	′),(χ′′	′),(χ′′	PROPN
ejpam-5051	923	25	i	i	PRON
ejpam-5051	923	26	,	,	PUNCT
ejpam-5051	923	27	γ̇	γ̇	PROPN
ejpam-5051	923	28	′′)∈(â⋊r)(2	′′)∈(â⋊r)(2	NOUN
ejpam-5051	923	29	)	)	PUNCT
ejpam-5051	923	30	,	,	PUNCT
ejpam-5051	923	31	(	(	PUNCT
ejpam-5051	923	32	χ′	χ′	PROPN
ejpam-5051	923	33	i	i	PRON
ejpam-5051	923	34	,	,	PUNCT
ejpam-5051	923	35	γ̇	γ̇	PROPN
ejpam-5051	923	36	′))(χ′′	′))(χ′′	PROPN
ejpam-5051	923	37	i	i	PRON
ejpam-5051	923	38	,	,	PUNCT
ejpam-5051	923	39	γ̇	γ̇	PROPN
ejpam-5051	923	40	′′)=(χi	′′)=(χi	PROPN
ejpam-5051	923	41	,	,	PUNCT
ejpam-5051	923	42	γ̇	γ̇	PROPN
ejpam-5051	923	43	)	)	PUNCT
ejpam-5051	923	44	f	f	NOUN
ejpam-5051	924	1	(	(	PUNCT
ejpam-5051	924	2	f)(χ′	f)(χ′	NOUN
ejpam-5051	924	3	i	i	PRON
ejpam-5051	924	4	,	,	PUNCT
ejpam-5051	924	5	γ̇	γ̇	PROPN
ejpam-5051	924	6	′)f	′)f	PROPN
ejpam-5051	924	7	(	(	PUNCT
ejpam-5051	924	8	g)(χ′′	g)(χ′′	INTJ
ejpam-5051	924	9	i	i	PRON
ejpam-5051	924	10	,	,	PUNCT
ejpam-5051	924	11	γ̇	γ̇	PROPN
ejpam-5051	924	12	′′)−1	′′)−1	NOUN
ejpam-5051	924	13	since	since	SCONJ
ejpam-5051	924	14	â⋊r	â⋊r	PROPN
ejpam-5051	924	15	=	=	SYM
ejpam-5051	924	16	(	(	PUNCT
ejpam-5051	924	17	â⋊r)(0	â⋊r)(0	NOUN
ejpam-5051	924	18	)	)	PUNCT
ejpam-5051	924	19	,	,	PUNCT
ejpam-5051	924	20	then	then	ADV
ejpam-5051	924	21	for	for	ADP
ejpam-5051	924	22	all	all	DET
ejpam-5051	924	23	(	(	PUNCT
ejpam-5051	924	24	χi	χi	NOUN
ejpam-5051	924	25	,	,	PUNCT
ejpam-5051	924	26	γ̇	γ̇	NOUN
ejpam-5051	924	27	)	)	PUNCT
ejpam-5051	924	28	∈	∈	PROPN
ejpam-5051	924	29	â⋊r	â⋊r	NOUN
ejpam-5051	924	30	the	the	DET
ejpam-5051	924	31	only	only	ADJ
ejpam-5051	924	32	composable	composable	ADJ
ejpam-5051	924	33	pairs	pair	NOUN
ejpam-5051	924	34	in	in	ADP
ejpam-5051	924	35	â⋊r	â⋊r	NOUN
ejpam-5051	924	36	is	be	AUX
ejpam-5051	924	37	of	of	ADP
ejpam-5051	924	38	the	the	DET
ejpam-5051	924	39	form	form	NOUN
ejpam-5051	924	40	(	(	PUNCT
ejpam-5051	924	41	(	(	PUNCT
ejpam-5051	924	42	χi	χi	NOUN
ejpam-5051	924	43	,	,	PUNCT
ejpam-5051	924	44	γ̇	γ̇	NOUN
ejpam-5051	924	45	)	)	PUNCT
ejpam-5051	924	46	,	,	PUNCT
ejpam-5051	924	47	(	(	PUNCT
ejpam-5051	924	48	χi	χi	NOUN
ejpam-5051	924	49	,	,	PUNCT
ejpam-5051	924	50	γ̇	γ̇	NOUN
ejpam-5051	924	51	)	)	PUNCT
ejpam-5051	924	52	)	)	PUNCT
ejpam-5051	924	53	where	where	SCONJ
ejpam-5051	924	54	s(χi	s(χi	VERB
ejpam-5051	924	55	,	,	PUNCT
ejpam-5051	924	56	γ̇	γ̇	NOUN
ejpam-5051	924	57	)	)	PUNCT
ejpam-5051	924	58	=	=	SYM
ejpam-5051	924	59	(	(	PUNCT
ejpam-5051	924	60	χi	χi	NOUN
ejpam-5051	924	61	,	,	PUNCT
ejpam-5051	924	62	γ̇	γ̇	NOUN
ejpam-5051	924	63	)	)	PUNCT
ejpam-5051	924	64	=	=	PRON
ejpam-5051	924	65	r(χi	r(χi	VERB
ejpam-5051	924	66	,	,	PUNCT
ejpam-5051	924	67	γ̇	γ̇	NOUN
ejpam-5051	924	68	)	)	PUNCT
ejpam-5051	924	69	.	.	PUNCT
ejpam-5051	925	1	but	but	CCONJ
ejpam-5051	925	2	(	(	PUNCT
ejpam-5051	925	3	χ1	χ1	NOUN
ejpam-5051	925	4	,	,	PUNCT
ejpam-5051	925	5	0̇)(χ2	0̇)(χ2	INTJ
ejpam-5051	925	6	,	,	PUNCT
ejpam-5051	925	7	0̇	0̇	NUM
ejpam-5051	925	8	)	)	PUNCT
ejpam-5051	925	9	̸=	̸=	PROPN
ejpam-5051	925	10	(	(	PUNCT
ejpam-5051	925	11	χ1	χ1	NOUN
ejpam-5051	925	12	,	,	PUNCT
ejpam-5051	925	13	0̇	0̇	NUM
ejpam-5051	925	14	)	)	PUNCT
ejpam-5051	925	15	.	.	PUNCT
ejpam-5051	926	1	hence	hence	ADV
ejpam-5051	926	2	,	,	PUNCT
ejpam-5051	926	3	(	(	PUNCT
ejpam-5051	926	4	f	f	X
ejpam-5051	926	5	(	(	PUNCT
ejpam-5051	926	6	f)f	f)f	X
ejpam-5051	926	7	(	(	PUNCT
ejpam-5051	926	8	g))([χi	g))([χi	NOUN
ejpam-5051	926	9	,	,	PUNCT
ejpam-5051	926	10	z	z	NOUN
ejpam-5051	926	11	,	,	PUNCT
ejpam-5051	926	12	γ])(χ1	γ])(χ1	PROPN
ejpam-5051	926	13	,	,	PUNCT
ejpam-5051	926	14	0̇	0̇	NUM
ejpam-5051	926	15	)	)	PUNCT
ejpam-5051	926	16	=	=	PUNCT
ejpam-5051	926	17	∑	∑	PUNCT
ejpam-5051	926	18	(	(	PUNCT
ejpam-5051	926	19	(	(	PUNCT
ejpam-5051	926	20	χ1,0̇),(χ1,0̇)∈(â⋊r)(2	χ1,0̇),(χ1,0̇)∈(â⋊r)(2	NOUN
ejpam-5051	926	21	)	)	PUNCT
ejpam-5051	926	22	,	,	PUNCT
ejpam-5051	926	23	(	(	PUNCT
ejpam-5051	926	24	χ1,0̇))(χ1,0̇)=(χ1,0̇	χ1,0̇))(χ1,0̇)=(χ1,0̇	NOUN
ejpam-5051	926	25	)	)	PUNCT
ejpam-5051	926	26	f	f	PROPN
ejpam-5051	926	27	(	(	PUNCT
ejpam-5051	926	28	f)(χ1	f)(χ1	PROPN
ejpam-5051	926	29	,	,	PUNCT
ejpam-5051	926	30	0̇)f	0̇)f	X
ejpam-5051	926	31	(	(	PUNCT
ejpam-5051	926	32	g)(χ1	g)(χ1	ADJ
ejpam-5051	926	33	,	,	PUNCT
ejpam-5051	926	34	0̇	0̇	NUM
ejpam-5051	926	35	)	)	PUNCT
ejpam-5051	926	36	−1	−1	NOUN
ejpam-5051	927	1	=	=	SYM
ejpam-5051	927	2	f	f	PROPN
ejpam-5051	927	3	(	(	PUNCT
ejpam-5051	927	4	f)(χ1	f)(χ1	PROPN
ejpam-5051	927	5	,	,	PUNCT
ejpam-5051	927	6	0̇)f	0̇)f	X
ejpam-5051	927	7	(	(	PUNCT
ejpam-5051	927	8	g)(χ1	g)(χ1	ADJ
ejpam-5051	927	9	,	,	PUNCT
ejpam-5051	927	10	0̇	0̇	NUM
ejpam-5051	927	11	)	)	PUNCT
ejpam-5051	927	12	−1	−1	NOUN
ejpam-5051	928	1	=	=	SYM
ejpam-5051	928	2	f	f	PROPN
ejpam-5051	928	3	(	(	PUNCT
ejpam-5051	928	4	f)(χ1	f)(χ1	PROPN
ejpam-5051	928	5	,	,	PUNCT
ejpam-5051	928	6	0̇)f	0̇)f	X
ejpam-5051	928	7	(	(	PUNCT
ejpam-5051	928	8	g)(χ1	g)(χ1	ADJ
ejpam-5051	928	9	,	,	PUNCT
ejpam-5051	928	10	0̇	0̇	NUM
ejpam-5051	928	11	)	)	PUNCT
ejpam-5051	928	12	=	=	SYM
ejpam-5051	928	13	zf(r((χ1	zf(r((χ1	PROPN
ejpam-5051	928	14	,	,	PUNCT
ejpam-5051	928	15	0̇)))g(r((χ1	0̇)))g(r((χ1	NUM
ejpam-5051	928	16	,	,	PUNCT
ejpam-5051	928	17	0̇	0̇	NUM
ejpam-5051	928	18	)	)	PUNCT
ejpam-5051	928	19	)	)	PUNCT
ejpam-5051	928	20	)	)	PUNCT
ejpam-5051	928	21	.	.	PUNCT
ejpam-5051	929	1	r.	r.	PROPN
ejpam-5051	929	2	s.	s.	PROPN
ejpam-5051	929	3	bongcawel	bongcawel	PROPN
ejpam-5051	930	1	et	et	PROPN
ejpam-5051	930	2	al	al	PROPN
ejpam-5051	930	3	.	.	PUNCT
ejpam-5051	930	4	/	/	SYM
ejpam-5051	930	5	eur	eur	PROPN
ejpam-5051	930	6	.	.	PUNCT
ejpam-5051	931	1	j.	j.	PROPN
ejpam-5051	931	2	pure	pure	PROPN
ejpam-5051	931	3	appl	appl	PROPN
ejpam-5051	931	4	.	.	PROPN
ejpam-5051	931	5	math	math	PROPN
ejpam-5051	931	6	,	,	PUNCT
ejpam-5051	931	7	17	17	NUM
ejpam-5051	931	8	(	(	PUNCT
ejpam-5051	931	9	1	1	NUM
ejpam-5051	931	10	)	)	PUNCT
ejpam-5051	931	11	(	(	PUNCT
ejpam-5051	931	12	2024	2024	NUM
ejpam-5051	931	13	)	)	PUNCT
ejpam-5051	931	14	,	,	PUNCT
ejpam-5051	931	15	519	519	NUM
ejpam-5051	931	16	-	-	SYM
ejpam-5051	931	17	545	545	NUM
ejpam-5051	931	18	542	542	NUM
ejpam-5051	931	19	also	also	ADV
ejpam-5051	931	20	,	,	PUNCT
ejpam-5051	931	21	since	since	SCONJ
ejpam-5051	931	22	(	(	PUNCT
ejpam-5051	931	23	χ2	χ2	PROPN
ejpam-5051	931	24	,	,	PUNCT
ejpam-5051	931	25	0̇)(χ1	0̇)(χ1	ADJ
ejpam-5051	931	26	,	,	PUNCT
ejpam-5051	931	27	0̇	0̇	NUM
ejpam-5051	931	28	)	)	PUNCT
ejpam-5051	931	29	̸=	̸=	PROPN
ejpam-5051	931	30	(	(	PUNCT
ejpam-5051	931	31	χ2	χ2	PROPN
ejpam-5051	931	32	,	,	PUNCT
ejpam-5051	931	33	0̇	0̇	NUM
ejpam-5051	931	34	)	)	PUNCT
ejpam-5051	931	35	,	,	PUNCT
ejpam-5051	931	36	we	we	PRON
ejpam-5051	931	37	get	get	VERB
ejpam-5051	931	38	(	(	PUNCT
ejpam-5051	931	39	f	f	X
ejpam-5051	931	40	(	(	PUNCT
ejpam-5051	931	41	f)f	f)f	X
ejpam-5051	931	42	(	(	PUNCT
ejpam-5051	931	43	g))([χi	g))([χi	NOUN
ejpam-5051	931	44	,	,	PUNCT
ejpam-5051	931	45	z	z	NOUN
ejpam-5051	931	46	,	,	PUNCT
ejpam-5051	931	47	γ])(χ2	γ])(χ2	NOUN
ejpam-5051	931	48	,	,	PUNCT
ejpam-5051	931	49	0̇	0̇	NUM
ejpam-5051	931	50	)	)	PUNCT
ejpam-5051	931	51	=	=	PUNCT
ejpam-5051	932	1	∑	∑	PUNCT
ejpam-5051	932	2	(	(	PUNCT
ejpam-5051	932	3	(	(	PUNCT
ejpam-5051	932	4	χ2,0̇),(χ2,0̇)∈(â⋊r)(2	χ2,0̇),(χ2,0̇)∈(â⋊r)(2	NOUN
ejpam-5051	932	5	)	)	PUNCT
ejpam-5051	932	6	,	,	PUNCT
ejpam-5051	932	7	(	(	PUNCT
ejpam-5051	932	8	χ2,0̇))(χ2,0̇)=(χ2,0̇	χ2,0̇))(χ2,0̇)=(χ2,0̇	X
ejpam-5051	932	9	)	)	PUNCT
ejpam-5051	932	10	f	f	PROPN
ejpam-5051	932	11	(	(	PUNCT
ejpam-5051	932	12	f)(χ2	f)(χ2	PROPN
ejpam-5051	932	13	,	,	PUNCT
ejpam-5051	932	14	0̇)f	0̇)f	X
ejpam-5051	932	15	(	(	PUNCT
ejpam-5051	932	16	g)(χ2	g)(χ2	X
ejpam-5051	932	17	,	,	PUNCT
ejpam-5051	932	18	0̇	0̇	NUM
ejpam-5051	932	19	)	)	PUNCT
ejpam-5051	932	20	−1	−1	NOUN
ejpam-5051	933	1	=	=	SYM
ejpam-5051	933	2	f	f	PROPN
ejpam-5051	933	3	(	(	PUNCT
ejpam-5051	933	4	f)(χ2	f)(χ2	PROPN
ejpam-5051	933	5	,	,	PUNCT
ejpam-5051	933	6	0̇)f	0̇)f	X
ejpam-5051	933	7	(	(	PUNCT
ejpam-5051	933	8	g)(χ2	g)(χ2	X
ejpam-5051	933	9	,	,	PUNCT
ejpam-5051	933	10	0̇	0̇	NUM
ejpam-5051	933	11	)	)	PUNCT
ejpam-5051	933	12	−1	−1	NOUN
ejpam-5051	934	1	=	=	SYM
ejpam-5051	934	2	f	f	PROPN
ejpam-5051	934	3	(	(	PUNCT
ejpam-5051	934	4	f)(χ2	f)(χ2	PROPN
ejpam-5051	934	5	,	,	PUNCT
ejpam-5051	934	6	0̇)f	0̇)f	X
ejpam-5051	934	7	(	(	PUNCT
ejpam-5051	934	8	g)(χ2	g)(χ2	X
ejpam-5051	934	9	,	,	PUNCT
ejpam-5051	934	10	0̇	0̇	NUM
ejpam-5051	934	11	)	)	PUNCT
ejpam-5051	934	12	=	=	SYM
ejpam-5051	934	13	zf(r((χ2	zf(r((χ2	PROPN
ejpam-5051	934	14	,	,	PUNCT
ejpam-5051	934	15	0̇)))g(r((χ2	0̇)))g(r((χ2	NUM
ejpam-5051	934	16	,	,	PUNCT
ejpam-5051	934	17	0̇	0̇	NUM
ejpam-5051	934	18	)	)	PUNCT
ejpam-5051	934	19	)	)	PUNCT
ejpam-5051	934	20	)	)	PUNCT
ejpam-5051	934	21	.	.	PUNCT
ejpam-5051	935	1	thus	thus	ADV
ejpam-5051	935	2	,	,	PUNCT
ejpam-5051	935	3	for	for	ADP
ejpam-5051	935	4	all	all	DET
ejpam-5051	935	5	(	(	PUNCT
ejpam-5051	935	6	χi	χi	NOUN
ejpam-5051	935	7	,	,	PUNCT
ejpam-5051	935	8	γ̇	γ̇	NOUN
ejpam-5051	935	9	)	)	PUNCT
ejpam-5051	935	10	∈	∈	PROPN
ejpam-5051	935	11	â⋊r	â⋊r	NOUN
ejpam-5051	935	12	,	,	PUNCT
ejpam-5051	935	13	f	f	X
ejpam-5051	935	14	(	(	PUNCT
ejpam-5051	935	15	f)f	f)f	X
ejpam-5051	935	16	(	(	PUNCT
ejpam-5051	935	17	g)([χi	g)([χi	NOUN
ejpam-5051	935	18	,	,	PUNCT
ejpam-5051	935	19	z	z	PROPN
ejpam-5051	935	20	,	,	PUNCT
ejpam-5051	935	21	γ])(χi	γ])(χi	ADJ
ejpam-5051	935	22	,	,	PUNCT
ejpam-5051	935	23	γ̇	γ̇	NOUN
ejpam-5051	935	24	)	)	PUNCT
ejpam-5051	935	25	=	=	SYM
ejpam-5051	935	26	zf(r((χi	zf(r((χi	X
ejpam-5051	935	27	,	,	PUNCT
ejpam-5051	935	28	γ̇)))zg(r((χi	γ̇)))zg(r((χi	ADJ
ejpam-5051	935	29	,	,	PUNCT
ejpam-5051	935	30	γ̇	γ̇	NOUN
ejpam-5051	935	31	)	)	PUNCT
ejpam-5051	935	32	)	)	PUNCT
ejpam-5051	935	33	)	)	PUNCT
ejpam-5051	936	1	=	=	SYM
ejpam-5051	936	2	f	f	PROPN
ejpam-5051	936	3	(	(	PUNCT
ejpam-5051	936	4	fg)([χi	fg)([χi	PROPN
ejpam-5051	936	5	,	,	PUNCT
ejpam-5051	936	6	z	z	PROPN
ejpam-5051	936	7	,	,	PUNCT
ejpam-5051	936	8	γ	γ	X
ejpam-5051	936	9	]	]	X
ejpam-5051	936	10	)	)	PUNCT
ejpam-5051	936	11	and	and	CCONJ
ejpam-5051	936	12	f	f	PROPN
ejpam-5051	936	13	is	be	AUX
ejpam-5051	936	14	a	a	DET
ejpam-5051	936	15	z	z	NOUN
ejpam-5051	936	16	-	-	PUNCT
ejpam-5051	936	17	module	module	NOUN
ejpam-5051	936	18	homomorphism	homomorphism	NOUN
ejpam-5051	936	19	.	.	PUNCT
ejpam-5051	937	1	suppose	suppose	VERB
ejpam-5051	938	1	that	that	SCONJ
ejpam-5051	938	2	f	f	PROPN
ejpam-5051	938	3	(	(	PUNCT
ejpam-5051	938	4	f)([χi	f)([χi	PROPN
ejpam-5051	938	5	,	,	PUNCT
ejpam-5051	938	6	z	z	PROPN
ejpam-5051	938	7	,	,	PUNCT
ejpam-5051	938	8	γ	γ	X
ejpam-5051	938	9	]	]	X
ejpam-5051	938	10	)	)	PUNCT
ejpam-5051	938	11	=	=	SYM
ejpam-5051	938	12	0	0	NUM
ejpam-5051	938	13	for	for	ADP
ejpam-5051	938	14	[	[	X
ejpam-5051	938	15	χi	χi	NOUN
ejpam-5051	938	16	,	,	PUNCT
ejpam-5051	938	17	z	z	PROPN
ejpam-5051	938	18	,	,	PUNCT
ejpam-5051	938	19	γ	γ	X
ejpam-5051	938	20	]	]	X
ejpam-5051	938	21	∈	∈	PROPN
ejpam-5051	938	22	d.	d.	NOUN
ejpam-5051	938	23	then	then	ADV
ejpam-5051	938	24	,	,	PUNCT
ejpam-5051	938	25	zf(r((χi	zf(r((χi	X
ejpam-5051	938	26	,	,	PUNCT
ejpam-5051	938	27	γ̇	γ̇	NOUN
ejpam-5051	938	28	)	)	PUNCT
ejpam-5051	938	29	)	)	PUNCT
ejpam-5051	938	30	)	)	PUNCT
ejpam-5051	939	1	=	=	SYM
ejpam-5051	939	2	0	0	NUM
ejpam-5051	939	3	for	for	ADP
ejpam-5051	939	4	all	all	DET
ejpam-5051	939	5	z	z	NOUN
ejpam-5051	939	6	∈	∈	PROPN
ejpam-5051	939	7	t	t	NOUN
ejpam-5051	939	8	and	and	CCONJ
ejpam-5051	939	9	γ	γ	X
ejpam-5051	939	10	∈	∈	PROPN
ejpam-5051	939	11	z	z	NOUN
ejpam-5051	939	12	which	which	PRON
ejpam-5051	939	13	means	mean	VERB
ejpam-5051	939	14	that	that	SCONJ
ejpam-5051	939	15	f(r((χi	f(r((χi	NUM
ejpam-5051	939	16	,	,	PUNCT
ejpam-5051	939	17	γ̇	γ̇	NOUN
ejpam-5051	939	18	)	)	PUNCT
ejpam-5051	939	19	)	)	PUNCT
ejpam-5051	939	20	)	)	PUNCT
ejpam-5051	940	1	=	=	PUNCT
ejpam-5051	940	2	0	0	X
ejpam-5051	940	3	.	.	PUNCT
ejpam-5051	940	4	since	since	SCONJ
ejpam-5051	940	5	â	â	PRON
ejpam-5051	940	6	⋊	⋊	NUM
ejpam-5051	940	7	r	r	NOUN
ejpam-5051	940	8	=	=	PUNCT
ejpam-5051	940	9	(	(	PUNCT
ejpam-5051	940	10	â	â	X
ejpam-5051	940	11	⋊	⋊	X
ejpam-5051	940	12	r)(0	r)(0	NUM
ejpam-5051	940	13	)	)	PUNCT
ejpam-5051	940	14	,	,	PUNCT
ejpam-5051	940	15	then	then	ADV
ejpam-5051	940	16	for	for	ADP
ejpam-5051	940	17	all	all	DET
ejpam-5051	940	18	(	(	PUNCT
ejpam-5051	940	19	χi	χi	NOUN
ejpam-5051	940	20	,	,	PUNCT
ejpam-5051	940	21	γ̇	γ̇	NOUN
ejpam-5051	940	22	)	)	PUNCT
ejpam-5051	940	23	∈	∈	PROPN
ejpam-5051	940	24	â	â	ADP
ejpam-5051	940	25	⋊	⋊	SYM
ejpam-5051	940	26	r	r	NOUN
ejpam-5051	940	27	,	,	PUNCT
ejpam-5051	940	28	r((χi	r((χi	VERB
ejpam-5051	940	29	,	,	PUNCT
ejpam-5051	940	30	γ̇	γ̇	NOUN
ejpam-5051	940	31	)	)	PUNCT
ejpam-5051	940	32	)	)	PUNCT
ejpam-5051	941	1	=	=	SYM
ejpam-5051	941	2	(	(	PUNCT
ejpam-5051	941	3	χi	χi	NOUN
ejpam-5051	941	4	,	,	PUNCT
ejpam-5051	941	5	γ̇	γ̇	NOUN
ejpam-5051	941	6	)	)	PUNCT
ejpam-5051	941	7	.	.	PUNCT
ejpam-5051	942	1	hence	hence	ADV
ejpam-5051	942	2	for	for	ADP
ejpam-5051	942	3	all	all	DET
ejpam-5051	942	4	(	(	PUNCT
ejpam-5051	942	5	χi	χi	NOUN
ejpam-5051	942	6	,	,	PUNCT
ejpam-5051	942	7	γ̇	γ̇	NOUN
ejpam-5051	942	8	)	)	PUNCT
ejpam-5051	942	9	∈	∈	PROPN
ejpam-5051	942	10	â	â	ADP
ejpam-5051	942	11	⋊	⋊	PUNCT
ejpam-5051	942	12	r	r	NOUN
ejpam-5051	942	13	,	,	PUNCT
ejpam-5051	942	14	f((χi	f((χi	PROPN
ejpam-5051	942	15	,	,	PUNCT
ejpam-5051	942	16	γ̇	γ̇	NOUN
ejpam-5051	942	17	)	)	PUNCT
ejpam-5051	942	18	)	)	PUNCT
ejpam-5051	942	19	=	=	SYM
ejpam-5051	942	20	f(r((χi	f(r((χi	PROPN
ejpam-5051	942	21	,	,	PUNCT
ejpam-5051	942	22	γ̇	γ̇	NOUN
ejpam-5051	942	23	)	)	PUNCT
ejpam-5051	942	24	)	)	PUNCT
ejpam-5051	942	25	)	)	PUNCT
ejpam-5051	943	1	=	=	SYM
ejpam-5051	943	2	0	0	NUM
ejpam-5051	943	3	which	which	PRON
ejpam-5051	943	4	implies	imply	VERB
ejpam-5051	943	5	that	that	SCONJ
ejpam-5051	943	6	f	f	PROPN
ejpam-5051	943	7	=	=	SYM
ejpam-5051	943	8	0	0	PROPN
ejpam-5051	943	9	.	.	PUNCT
ejpam-5051	944	1	thus	thus	ADV
ejpam-5051	944	2	,	,	PUNCT
ejpam-5051	944	3	f	f	PROPN
ejpam-5051	944	4	is	be	AUX
ejpam-5051	944	5	injective	injective	ADJ
ejpam-5051	944	6	.	.	PUNCT
ejpam-5051	945	1	now	now	ADV
ejpam-5051	945	2	let	let	VERB
ejpam-5051	945	3	h	h	PROPN
ejpam-5051	945	4	∈	∈	PROPN
ejpam-5051	945	5	az(d	az(d	NUM
ejpam-5051	945	6	;	;	PUNCT
ejpam-5051	945	7	â⋊r	â⋊r	NOUN
ejpam-5051	945	8	)	)	PUNCT
ejpam-5051	945	9	and	and	CCONJ
ejpam-5051	945	10	define	define	VERB
ejpam-5051	945	11	fh	fh	PROPN
ejpam-5051	945	12	:	:	PUNCT
ejpam-5051	945	13	â	â	X
ejpam-5051	945	14	⋊	⋊	SYM
ejpam-5051	945	15	r	r	NOUN
ejpam-5051	945	16	→	→	SYM
ejpam-5051	945	17	z	z	NOUN
ejpam-5051	945	18	by	by	ADP
ejpam-5051	945	19	fh((χi	fh((χi	NOUN
ejpam-5051	945	20	,	,	PUNCT
ejpam-5051	945	21	0̇	0̇	NUM
ejpam-5051	945	22	)	)	PUNCT
ejpam-5051	945	23	)	)	PUNCT
ejpam-5051	946	1	=	=	PUNCT
ejpam-5051	946	2	h([χi	h([χi	PROPN
ejpam-5051	946	3	,	,	PUNCT
ejpam-5051	946	4	1	1	NUM
ejpam-5051	946	5	,	,	PUNCT
ejpam-5051	946	6	0	0	NUM
ejpam-5051	946	7	]	]	PUNCT
ejpam-5051	946	8	)	)	PUNCT
ejpam-5051	946	9	.	.	PUNCT
ejpam-5051	947	1	notice	notice	VERB
ejpam-5051	947	2	that	that	SCONJ
ejpam-5051	947	3	every	every	DET
ejpam-5051	947	4	element	element	NOUN
ejpam-5051	947	5	in	in	ADP
ejpam-5051	947	6	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	947	7	)	)	PUNCT
ejpam-5051	947	8	is	be	AUX
ejpam-5051	947	9	a	a	DET
ejpam-5051	947	10	mapping	mapping	NOUN
ejpam-5051	947	11	from	from	ADP
ejpam-5051	947	12	â⋊r	â⋊r	PROPN
ejpam-5051	947	13	to	to	ADP
ejpam-5051	947	14	z.	z.	PROPN
ejpam-5051	947	15	we	we	PRON
ejpam-5051	947	16	are	be	AUX
ejpam-5051	947	17	left	leave	VERB
ejpam-5051	947	18	to	to	PART
ejpam-5051	947	19	show	show	VERB
ejpam-5051	947	20	that	that	SCONJ
ejpam-5051	947	21	fh	fh	PROPN
ejpam-5051	947	22	is	be	AUX
ejpam-5051	947	23	continuous	continuous	ADJ
ejpam-5051	947	24	and	and	CCONJ
ejpam-5051	947	25	supp(fh	supp(fh	NOUN
ejpam-5051	947	26	)	)	PUNCT
ejpam-5051	947	27	is	be	AUX
ejpam-5051	947	28	compact	compact	ADJ
ejpam-5051	947	29	.	.	PUNCT
ejpam-5051	948	1	since	since	SCONJ
ejpam-5051	948	2	â	â	PRON
ejpam-5051	948	3	⋊r	⋊r	PROPN
ejpam-5051	948	4	and	and	CCONJ
ejpam-5051	948	5	z	z	PROPN
ejpam-5051	948	6	are	be	AUX
ejpam-5051	948	7	both	both	ADV
ejpam-5051	948	8	discrete	discrete	ADJ
ejpam-5051	948	9	,	,	PUNCT
ejpam-5051	948	10	then	then	ADV
ejpam-5051	948	11	fh	fh	PROPN
ejpam-5051	948	12	is	be	AUX
ejpam-5051	948	13	continuous	continuous	ADJ
ejpam-5051	948	14	.	.	PUNCT
ejpam-5051	949	1	since	since	SCONJ
ejpam-5051	949	2	h	h	PROPN
ejpam-5051	949	3	∈	∈	PROPN
ejpam-5051	949	4	az(d	az(d	NUM
ejpam-5051	949	5	;	;	PUNCT
ejpam-5051	949	6	â⋊r	â⋊r	NOUN
ejpam-5051	949	7	)	)	PUNCT
ejpam-5051	949	8	,	,	PUNCT
ejpam-5051	949	9	h	h	NOUN
ejpam-5051	949	10	=	=	SYM
ejpam-5051	949	11	a11{[χ1,1,0	a11{[χ1,1,0	PROPN
ejpam-5051	949	12	]	]	PUNCT
ejpam-5051	949	13	}	}	PUNCT
ejpam-5051	949	14	+	+	CCONJ
ejpam-5051	949	15	a21{[χ1,−1,0	a21{[χ1,−1,0	NOUN
ejpam-5051	949	16	]	]	X
ejpam-5051	949	17	}	}	PUNCT
ejpam-5051	950	1	+	+	CCONJ
ejpam-5051	950	2	a31{[χ2,1,0	a31{[χ2,1,0	NOUN
ejpam-5051	950	3	]	]	X
ejpam-5051	950	4	}	}	PUNCT
ejpam-5051	950	5	+	+	CCONJ
ejpam-5051	950	6	a41{[χ2,−1,0	a41{[χ2,−1,0	NOUN
ejpam-5051	950	7	]	]	NUM
ejpam-5051	950	8	}	}	PUNCT
ejpam-5051	950	9	.	.	PUNCT
ejpam-5051	951	1	thus	thus	ADV
ejpam-5051	951	2	,	,	PUNCT
ejpam-5051	951	3	fh(χi	fh(χi	NOUN
ejpam-5051	951	4	,	,	PUNCT
ejpam-5051	951	5	γ̇	γ̇	NOUN
ejpam-5051	951	6	)	)	PUNCT
ejpam-5051	951	7	=	=	SYM
ejpam-5051	951	8	h([χi	h([χi	PROPN
ejpam-5051	951	9	,	,	PUNCT
ejpam-5051	951	10	z	z	PROPN
ejpam-5051	951	11	,	,	PUNCT
ejpam-5051	951	12	γ	γ	X
ejpam-5051	951	13	]	]	X
ejpam-5051	951	14	)	)	PUNCT
ejpam-5051	951	15	=	=	SYM
ejpam-5051	951	16	(	(	PUNCT
ejpam-5051	951	17	a11{[χ1,1,0	a11{[χ1,1,0	X
ejpam-5051	951	18	]	]	PUNCT
ejpam-5051	951	19	}	}	PUNCT
ejpam-5051	951	20	+	+	CCONJ
ejpam-5051	951	21	a21{[χ1,−1,0	a21{[χ1,−1,0	NOUN
ejpam-5051	951	22	]	]	X
ejpam-5051	951	23	}	}	PUNCT
ejpam-5051	952	1	+	+	CCONJ
ejpam-5051	952	2	a31{[χ2,1,0	a31{[χ2,1,0	NOUN
ejpam-5051	952	3	]	]	X
ejpam-5051	952	4	}	}	PUNCT
ejpam-5051	952	5	+	+	CCONJ
ejpam-5051	952	6	a41{[χ2,−1,0]})([χi	a41{[χ2,−1,0]})([χi	PROPN
ejpam-5051	952	7	,	,	PUNCT
ejpam-5051	952	8	z	z	PROPN
ejpam-5051	952	9	,	,	PUNCT
ejpam-5051	952	10	γ	γ	X
ejpam-5051	952	11	]	]	X
ejpam-5051	952	12	)	)	PUNCT
ejpam-5051	952	13	hence	hence	ADV
ejpam-5051	952	14	,	,	PUNCT
ejpam-5051	952	15	fh(χ1	fh(χ1	NOUN
ejpam-5051	952	16	,	,	PUNCT
ejpam-5051	952	17	0̇	0̇	NUM
ejpam-5051	952	18	)	)	PUNCT
ejpam-5051	952	19	=	=	PUNCT
ejpam-5051	952	20	h([χ1	h([χ1	NOUN
ejpam-5051	952	21	,	,	PUNCT
ejpam-5051	952	22	1	1	NUM
ejpam-5051	952	23	,	,	PUNCT
ejpam-5051	952	24	0	0	NUM
ejpam-5051	952	25	]	]	PUNCT
ejpam-5051	952	26	)	)	PUNCT
ejpam-5051	952	27	=	=	SYM
ejpam-5051	952	28	(	(	PUNCT
ejpam-5051	952	29	a11{[χ1,1,0	a11{[χ1,1,0	X
ejpam-5051	952	30	]	]	PUNCT
ejpam-5051	952	31	}	}	PUNCT
ejpam-5051	952	32	+	+	CCONJ
ejpam-5051	952	33	a21{[χ1,−1,0	a21{[χ1,−1,0	NOUN
ejpam-5051	952	34	]	]	X
ejpam-5051	952	35	}	}	PUNCT
ejpam-5051	952	36	+	+	CCONJ
ejpam-5051	952	37	a31{[χ2,1,0	a31{[χ2,1,0	NOUN
ejpam-5051	952	38	]	]	X
ejpam-5051	952	39	}	}	PUNCT
ejpam-5051	952	40	+	+	CCONJ
ejpam-5051	952	41	a41{[χ2,−1,0]})([χ1	a41{[χ2,−1,0]})([χ1	PROPN
ejpam-5051	952	42	,	,	PUNCT
ejpam-5051	952	43	1	1	NUM
ejpam-5051	952	44	,	,	PUNCT
ejpam-5051	952	45	0	0	NUM
ejpam-5051	952	46	]	]	PUNCT
ejpam-5051	952	47	)	)	PUNCT
ejpam-5051	952	48	=	=	SYM
ejpam-5051	952	49	a1	a1	NOUN
ejpam-5051	952	50	fh(χ2	fh(χ2	NOUN
ejpam-5051	952	51	,	,	PUNCT
ejpam-5051	952	52	0̇	0̇	NUM
ejpam-5051	952	53	)	)	PUNCT
ejpam-5051	952	54	=	=	PUNCT
ejpam-5051	952	55	h([χ2	h([χ2	NOUN
ejpam-5051	952	56	,	,	PUNCT
ejpam-5051	952	57	1	1	NUM
ejpam-5051	952	58	,	,	PUNCT
ejpam-5051	952	59	0	0	NUM
ejpam-5051	952	60	]	]	PUNCT
ejpam-5051	952	61	)	)	PUNCT
ejpam-5051	952	62	=	=	SYM
ejpam-5051	952	63	(	(	PUNCT
ejpam-5051	952	64	a11{[χ1,1,0	a11{[χ1,1,0	X
ejpam-5051	952	65	]	]	PUNCT
ejpam-5051	952	66	}	}	PUNCT
ejpam-5051	952	67	+	+	CCONJ
ejpam-5051	952	68	a21{[χ1,−1,0	a21{[χ1,−1,0	NOUN
ejpam-5051	952	69	]	]	X
ejpam-5051	952	70	}	}	PUNCT
ejpam-5051	952	71	+	+	CCONJ
ejpam-5051	952	72	a31{[χ2,1,0	a31{[χ2,1,0	NOUN
ejpam-5051	952	73	]	]	X
ejpam-5051	952	74	}	}	PUNCT
ejpam-5051	952	75	+	+	CCONJ
ejpam-5051	952	76	a41{[χ2,−1,0]})([χ2	a41{[χ2,−1,0]})([χ2	PROPN
ejpam-5051	952	77	,	,	PUNCT
ejpam-5051	952	78	1	1	NUM
ejpam-5051	952	79	,	,	PUNCT
ejpam-5051	952	80	0	0	NUM
ejpam-5051	952	81	]	]	PUNCT
ejpam-5051	952	82	)	)	PUNCT
ejpam-5051	952	83	=	=	NOUN
ejpam-5051	952	84	a3	a3	NOUN
ejpam-5051	952	85	if	if	SCONJ
ejpam-5051	952	86	a1	a1	NOUN
ejpam-5051	952	87	=	=	NOUN
ejpam-5051	952	88	a3	a3	NOUN
ejpam-5051	952	89	=	=	SYM
ejpam-5051	952	90	0	0	NUM
ejpam-5051	952	91	,	,	PUNCT
ejpam-5051	952	92	then	then	ADV
ejpam-5051	952	93	supp(fh	supp(fh	ADJ
ejpam-5051	952	94	)	)	PUNCT
ejpam-5051	952	95	=	=	NOUN
ejpam-5051	952	96	∅	∅	NOUN
ejpam-5051	952	97	which	which	PRON
ejpam-5051	952	98	is	be	AUX
ejpam-5051	952	99	closed	close	VERB
ejpam-5051	952	100	and	and	CCONJ
ejpam-5051	952	101	bounded	bound	VERB
ejpam-5051	952	102	,	,	PUNCT
ejpam-5051	952	103	that	that	ADV
ejpam-5051	952	104	is	be	AUX
ejpam-5051	952	105	,	,	PUNCT
ejpam-5051	952	106	compact	compact	ADJ
ejpam-5051	952	107	.	.	PUNCT
ejpam-5051	953	1	if	if	SCONJ
ejpam-5051	953	2	a1	a1	PROPN
ejpam-5051	953	3	,	,	PUNCT
ejpam-5051	953	4	a2	a2	PROPN
ejpam-5051	953	5	∈	∈	PROPN
ejpam-5051	953	6	z	z	NOUN
ejpam-5051	953	7	\	\	PUNCT
ejpam-5051	953	8	{	{	PUNCT
ejpam-5051	953	9	0	0	NUM
ejpam-5051	953	10	}	}	PUNCT
ejpam-5051	953	11	,	,	PUNCT
ejpam-5051	953	12	then	then	ADV
ejpam-5051	953	13	supp(fh	supp(fh	ADJ
ejpam-5051	953	14	)	)	PUNCT
ejpam-5051	953	15	=	=	SYM
ejpam-5051	953	16	{	{	PUNCT
ejpam-5051	953	17	(	(	PUNCT
ejpam-5051	953	18	χi	χi	NOUN
ejpam-5051	953	19	,	,	PUNCT
ejpam-5051	953	20	γ̇	γ̇	NOUN
ejpam-5051	953	21	)	)	PUNCT
ejpam-5051	953	22	∈	∈	PROPN
ejpam-5051	953	23	â	â	PUNCT
ejpam-5051	954	1	⋊r	⋊r	X
ejpam-5051	954	2	:	:	PUNCT
ejpam-5051	954	3	fh((χi	fh((χi	ADJ
ejpam-5051	954	4	,	,	PUNCT
ejpam-5051	954	5	γ̇	γ̇	NOUN
ejpam-5051	954	6	)	)	PUNCT
ejpam-5051	954	7	)	)	PUNCT
ejpam-5051	955	1	̸=	̸=	PROPN
ejpam-5051	955	2	0	0	NUM
ejpam-5051	955	3	)	)	PUNCT
ejpam-5051	955	4	)	)	PUNCT
ejpam-5051	955	5	}	}	PUNCT
ejpam-5051	955	6	=	=	SYM
ejpam-5051	955	7	â	â	X
ejpam-5051	955	8	⋊r	⋊r	X
ejpam-5051	955	9	which	which	PRON
ejpam-5051	955	10	is	be	AUX
ejpam-5051	955	11	compact	compact	ADJ
ejpam-5051	955	12	.	.	PUNCT
ejpam-5051	956	1	thus	thus	ADV
ejpam-5051	956	2	,	,	PUNCT
ejpam-5051	956	3	fh	fh	PROPN
ejpam-5051	956	4	∈	∈	PROPN
ejpam-5051	956	5	az(â	az(â	PROPN
ejpam-5051	956	6	⋊r	⋊r	PROPN
ejpam-5051	956	7	)	)	PUNCT
ejpam-5051	956	8	.	.	PUNCT
ejpam-5051	957	1	now	now	ADV
ejpam-5051	957	2	for	for	ADP
ejpam-5051	957	3	[	[	X
ejpam-5051	957	4	χi	χi	X
ejpam-5051	957	5	,	,	PUNCT
ejpam-5051	957	6	z	z	PROPN
ejpam-5051	957	7	,	,	PUNCT
ejpam-5051	957	8	γ	γ	X
ejpam-5051	957	9	]	]	X
ejpam-5051	957	10	∈	∈	PROPN
ejpam-5051	957	11	d	d	NOUN
ejpam-5051	957	12	and	and	CCONJ
ejpam-5051	957	13	since	since	SCONJ
ejpam-5051	957	14	[	[	X
ejpam-5051	957	15	χi	χi	NOUN
ejpam-5051	957	16	,	,	PUNCT
ejpam-5051	957	17	z	z	PROPN
ejpam-5051	957	18	,	,	PUNCT
ejpam-5051	957	19	0	0	NUM
ejpam-5051	957	20	]	]	PUNCT
ejpam-5051	957	21	and	and	CCONJ
ejpam-5051	957	22	[	[	X
ejpam-5051	957	23	χi	χi	X
ejpam-5051	957	24	,	,	PUNCT
ejpam-5051	957	25	z	z	PROPN
ejpam-5051	957	26	,	,	PUNCT
ejpam-5051	957	27	γ	γ	X
ejpam-5051	957	28	]	]	X
ejpam-5051	957	29	are	be	AUX
ejpam-5051	957	30	the	the	DET
ejpam-5051	957	31	same	same	ADJ
ejpam-5051	957	32	equivalence	equivalence	NOUN
ejpam-5051	957	33	classes	class	NOUN
ejpam-5051	957	34	in	in	ADP
ejpam-5051	957	35	d	d	PROPN
ejpam-5051	957	36	,	,	PUNCT
ejpam-5051	957	37	f	f	PROPN
ejpam-5051	957	38	(	(	PUNCT
ejpam-5051	957	39	fh)([χi	fh)([χi	PROPN
ejpam-5051	957	40	,	,	PUNCT
ejpam-5051	957	41	z	z	PROPN
ejpam-5051	957	42	,	,	PUNCT
ejpam-5051	957	43	γ	γ	NOUN
ejpam-5051	957	44	]	]	X
ejpam-5051	957	45	)	)	PUNCT
ejpam-5051	957	46	=	=	SYM
ejpam-5051	957	47	zfh(r((χi	zfh(r((χi	VERB
ejpam-5051	957	48	,	,	PUNCT
ejpam-5051	957	49	γ̇	γ̇	NOUN
ejpam-5051	957	50	)	)	PUNCT
ejpam-5051	957	51	)	)	PUNCT
ejpam-5051	957	52	)	)	PUNCT
ejpam-5051	958	1	r.	r.	PROPN
ejpam-5051	958	2	s.	s.	PROPN
ejpam-5051	958	3	bongcawel	bongcawel	PROPN
ejpam-5051	958	4	et	et	PROPN
ejpam-5051	958	5	al	al	PROPN
ejpam-5051	958	6	.	.	PUNCT
ejpam-5051	958	7	/	/	SYM
ejpam-5051	958	8	eur	eur	PROPN
ejpam-5051	958	9	.	.	PUNCT
ejpam-5051	959	1	j.	j.	PROPN
ejpam-5051	959	2	pure	pure	PROPN
ejpam-5051	959	3	appl	appl	PROPN
ejpam-5051	959	4	.	.	PROPN
ejpam-5051	959	5	math	math	PROPN
ejpam-5051	959	6	,	,	PUNCT
ejpam-5051	959	7	17	17	NUM
ejpam-5051	959	8	(	(	PUNCT
ejpam-5051	959	9	1	1	NUM
ejpam-5051	959	10	)	)	PUNCT
ejpam-5051	959	11	(	(	PUNCT
ejpam-5051	959	12	2024	2024	NUM
ejpam-5051	959	13	)	)	PUNCT
ejpam-5051	959	14	,	,	PUNCT
ejpam-5051	959	15	519	519	NUM
ejpam-5051	959	16	-	-	SYM
ejpam-5051	959	17	545	545	NUM
ejpam-5051	959	18	543	543	NUM
ejpam-5051	959	19	=	=	NOUN
ejpam-5051	959	20	zfh(χi	zfh(χi	NOUN
ejpam-5051	959	21	,	,	PUNCT
ejpam-5051	959	22	r(γ	r(γ	NOUN
ejpam-5051	959	23	)	)	PUNCT
ejpam-5051	959	24	)	)	PUNCT
ejpam-5051	960	1	=	=	SYM
ejpam-5051	960	2	zfh(χi	zfh(χi	X
ejpam-5051	960	3	,	,	PUNCT
ejpam-5051	960	4	γ	γ	NOUN
ejpam-5051	960	5	)	)	PUNCT
ejpam-5051	960	6	=	=	SYM
ejpam-5051	960	7	zh([χ,1	zh([χ,1	PROPN
ejpam-5051	960	8	,	,	PUNCT
ejpam-5051	960	9	0	0	NUM
ejpam-5051	960	10	]	]	PUNCT
ejpam-5051	960	11	)	)	PUNCT
ejpam-5051	960	12	=	=	SYM
ejpam-5051	960	13	h([χi	h([χi	PROPN
ejpam-5051	960	14	,	,	PUNCT
ejpam-5051	960	15	z	z	PROPN
ejpam-5051	960	16	,	,	PUNCT
ejpam-5051	960	17	0	0	NUM
ejpam-5051	960	18	]	]	PUNCT
ejpam-5051	960	19	)	)	PUNCT
ejpam-5051	961	1	=	=	SYM
ejpam-5051	961	2	h([χi	h([χi	PROPN
ejpam-5051	961	3	,	,	PUNCT
ejpam-5051	961	4	z	z	PROPN
ejpam-5051	961	5	,	,	PUNCT
ejpam-5051	961	6	γ	γ	X
ejpam-5051	961	7	]	]	X
ejpam-5051	961	8	)	)	PUNCT
ejpam-5051	962	1	=	=	SYM
ejpam-5051	963	1	h.	h.	PROPN
ejpam-5051	963	2	then	then	ADV
ejpam-5051	963	3	f	f	PROPN
ejpam-5051	963	4	is	be	AUX
ejpam-5051	963	5	surjective	surjective	ADJ
ejpam-5051	963	6	.	.	PUNCT
ejpam-5051	964	1	therefore	therefore	ADV
ejpam-5051	964	2	,	,	PUNCT
ejpam-5051	964	3	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	964	4	)	)	PUNCT
ejpam-5051	964	5	∼=	∼=	PROPN
ejpam-5051	964	6	az(d	az(d	PUNCT
ejpam-5051	964	7	;	;	PUNCT
ejpam-5051	964	8	â⋊r	â⋊r	NOUN
ejpam-5051	964	9	)	)	PUNCT
ejpam-5051	964	10	.	.	PUNCT
ejpam-5051	965	1	since	since	SCONJ
ejpam-5051	965	2	â	â	DET
ejpam-5051	965	3	⋊	⋊	NUM
ejpam-5051	965	4	r	r	NOUN
ejpam-5051	965	5	=	=	SYM
ejpam-5051	965	6	{	{	PUNCT
ejpam-5051	965	7	(	(	PUNCT
ejpam-5051	965	8	χ1	χ1	NOUN
ejpam-5051	965	9	,	,	PUNCT
ejpam-5051	965	10	0̇	0̇	NUM
ejpam-5051	965	11	)	)	PUNCT
ejpam-5051	965	12	,	,	PUNCT
ejpam-5051	965	13	(	(	PUNCT
ejpam-5051	965	14	χ2	χ2	PROPN
ejpam-5051	965	15	,	,	PUNCT
ejpam-5051	965	16	0̇	0̇	NUM
ejpam-5051	965	17	)	)	PUNCT
ejpam-5051	965	18	}	}	PUNCT
ejpam-5051	965	19	is	be	AUX
ejpam-5051	965	20	a	a	DET
ejpam-5051	965	21	topological	topological	ADJ
ejpam-5051	965	22	space	space	NOUN
ejpam-5051	965	23	with	with	ADP
ejpam-5051	965	24	the	the	DET
ejpam-5051	965	25	discrete	discrete	ADJ
ejpam-5051	965	26	topology	topology	NOUN
ejpam-5051	965	27	,	,	PUNCT
ejpam-5051	965	28	{	{	PUNCT
ejpam-5051	965	29	(	(	PUNCT
ejpam-5051	965	30	χ1	χ1	NOUN
ejpam-5051	965	31	,	,	PUNCT
ejpam-5051	965	32	0̇	0̇	NUM
ejpam-5051	965	33	)	)	PUNCT
ejpam-5051	965	34	}	}	PUNCT
ejpam-5051	965	35	and	and	CCONJ
ejpam-5051	965	36	{	{	PUNCT
ejpam-5051	965	37	(	(	PUNCT
ejpam-5051	965	38	χ2	χ2	PROPN
ejpam-5051	965	39	,	,	PUNCT
ejpam-5051	965	40	0̇	0̇	NUM
ejpam-5051	965	41	)	)	PUNCT
ejpam-5051	965	42	}	}	PUNCT
ejpam-5051	965	43	are	be	AUX
ejpam-5051	965	44	the	the	DET
ejpam-5051	965	45	basic	basic	ADJ
ejpam-5051	965	46	elements	element	NOUN
ejpam-5051	965	47	of	of	ADP
ejpam-5051	965	48	its	its	PRON
ejpam-5051	965	49	base	base	NOUN
ejpam-5051	965	50	which	which	PRON
ejpam-5051	965	51	are	be	AUX
ejpam-5051	965	52	compact	compact	ADJ
ejpam-5051	965	53	and	and	CCONJ
ejpam-5051	965	54	an	an	DET
ejpam-5051	965	55	open	open	ADJ
ejpam-5051	965	56	bisection	bisection	NOUN
ejpam-5051	965	57	since	since	SCONJ
ejpam-5051	965	58	they	they	PRON
ejpam-5051	965	59	are	be	AUX
ejpam-5051	965	60	singletons	singleton	NOUN
ejpam-5051	965	61	.	.	PUNCT
ejpam-5051	966	1	hence	hence	ADV
ejpam-5051	966	2	,	,	PUNCT
ejpam-5051	966	3	we	we	PRON
ejpam-5051	966	4	introduce	introduce	VERB
ejpam-5051	966	5	our	our	PRON
ejpam-5051	966	6	characterictic	characterictic	ADJ
ejpam-5051	966	7	functions	function	NOUN
ejpam-5051	966	8	that	that	PRON
ejpam-5051	966	9	spans	span	VERB
ejpam-5051	966	10	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	966	11	)	)	PUNCT
ejpam-5051	966	12	as	as	ADP
ejpam-5051	966	13	1{(χ	1{(χ	NUM
ejpam-5051	966	14	,	,	PUNCT
ejpam-5051	966	15	γ̇	γ̇	NOUN
ejpam-5051	966	16	)	)	PUNCT
ejpam-5051	966	17	}	}	PUNCT
ejpam-5051	966	18	:	:	PUNCT
ejpam-5051	966	19	â⋊r	â⋊r	PROPN
ejpam-5051	966	20	→	→	SYM
ejpam-5051	966	21	z	z	NOUN
ejpam-5051	966	22	defined	define	VERB
ejpam-5051	966	23	by	by	ADP
ejpam-5051	966	24	1{(χ	1{(χ	NUM
ejpam-5051	966	25	,	,	PUNCT
ejpam-5051	966	26	γ̇)}(g	γ̇)}(g	NOUN
ejpam-5051	966	27	)	)	PUNCT
ejpam-5051	966	28	=	=	PRON
ejpam-5051	966	29	{	{	PUNCT
ejpam-5051	966	30	1	1	NUM
ejpam-5051	966	31	if	if	SCONJ
ejpam-5051	966	32	g	g	PROPN
ejpam-5051	966	33	∈	∈	PROPN
ejpam-5051	966	34	{	{	PUNCT
ejpam-5051	966	35	(	(	PUNCT
ejpam-5051	966	36	χ	χ	NOUN
ejpam-5051	966	37	,	,	PUNCT
ejpam-5051	966	38	γ̇	γ̇	NOUN
ejpam-5051	966	39	)	)	PUNCT
ejpam-5051	966	40	}	}	PUNCT
ejpam-5051	966	41	0	0	PUNCT
ejpam-5051	967	1	if	if	SCONJ
ejpam-5051	967	2	g	g	PROPN
ejpam-5051	967	3	/∈	/∈	PUNCT
ejpam-5051	967	4	{	{	PUNCT
ejpam-5051	967	5	(	(	PUNCT
ejpam-5051	967	6	χ	χ	NOUN
ejpam-5051	967	7	,	,	PUNCT
ejpam-5051	967	8	γ̇	γ̇	NOUN
ejpam-5051	967	9	)	)	PUNCT
ejpam-5051	967	10	}	}	PUNCT
ejpam-5051	967	11	.	.	PUNCT
ejpam-5051	968	1	define	define	VERB
ejpam-5051	968	2	the	the	DET
ejpam-5051	968	3	steinberg	steinberg	PROPN
ejpam-5051	968	4	algbera	algbera	PROPN
ejpam-5051	968	5	of	of	ADP
ejpam-5051	968	6	â	â	PRON
ejpam-5051	968	7	⋊	⋊	SYM
ejpam-5051	968	8	r	r	NOUN
ejpam-5051	968	9	over	over	ADP
ejpam-5051	968	10	z	z	NOUN
ejpam-5051	968	11	as	as	ADP
ejpam-5051	968	12	az(â	az(â	NOUN
ejpam-5051	968	13	⋊	⋊	NUM
ejpam-5051	968	14	r	r	NOUN
ejpam-5051	968	15	)	)	PUNCT
ejpam-5051	968	16	=	=	PRON
ejpam-5051	968	17	span	span	NOUN
ejpam-5051	968	18	{	{	PUNCT
ejpam-5051	968	19	1{(χ1,0̇	1{(χ1,0̇	NUM
ejpam-5051	968	20	)	)	PUNCT
ejpam-5051	968	21	}	}	PUNCT
ejpam-5051	968	22	,	,	PUNCT
ejpam-5051	968	23	1{(χ2,0̇	1{(χ2,0̇	NUM
ejpam-5051	968	24	)	)	PUNCT
ejpam-5051	968	25	}	}	PUNCT
ejpam-5051	968	26	}	}	PUNCT
ejpam-5051	968	27	equipped	equip	VERB
ejpam-5051	968	28	with	with	ADP
ejpam-5051	968	29	the	the	DET
ejpam-5051	968	30	pointwise	pointwise	NOUN
ejpam-5051	968	31	addition	addition	NOUN
ejpam-5051	968	32	and	and	CCONJ
ejpam-5051	968	33	multiplication	multiplication	NOUN
ejpam-5051	968	34	as	as	SCONJ
ejpam-5051	968	35	follows	follow	VERB
ejpam-5051	968	36	:	:	PUNCT
ejpam-5051	968	37	a11{(χ1,0̇	a11{(χ1,0̇	NOUN
ejpam-5051	968	38	)	)	PUNCT
ejpam-5051	968	39	}	}	PUNCT
ejpam-5051	968	40	+	+	CCONJ
ejpam-5051	968	41	a21{(χ1,0̇	a21{(χ1,0̇	NOUN
ejpam-5051	968	42	)	)	PUNCT
ejpam-5051	968	43	}	}	PUNCT
ejpam-5051	969	1	=	=	SYM
ejpam-5051	969	2	(	(	PUNCT
ejpam-5051	969	3	a1	a1	NOUN
ejpam-5051	969	4	+	+	CCONJ
ejpam-5051	969	5	a2)1{(χ1,0̇)}+{(χ2,0̇	a2)1{(χ1,0̇)}+{(χ2,0̇	NOUN
ejpam-5051	969	6	)	)	PUNCT
ejpam-5051	969	7	}	}	PUNCT
ejpam-5051	969	8	a11{(χ1,0̇	a11{(χ1,0̇	NOUN
ejpam-5051	969	9	)	)	PUNCT
ejpam-5051	969	10	}	}	PUNCT
ejpam-5051	969	11	·	·	PUNCT
ejpam-5051	969	12	a21{(χ2,0̇	a21{(χ2,0̇	NOUN
ejpam-5051	969	13	)	)	PUNCT
ejpam-5051	969	14	}	}	PUNCT
ejpam-5051	969	15	=	=	SYM
ejpam-5051	969	16	(	(	PUNCT
ejpam-5051	969	17	a1	a1	NOUN
ejpam-5051	969	18	·	·	PUNCT
ejpam-5051	969	19	a2)1{(χ1,0̇)}{(χ2,0̇	a2)1{(χ1,0̇)}{(χ2,0̇	NOUN
ejpam-5051	969	20	)	)	PUNCT
ejpam-5051	969	21	}	}	PUNCT
ejpam-5051	969	22	.	.	PUNCT
ejpam-5051	970	1	by	by	ADP
ejpam-5051	970	2	theorem	theorem	NOUN
ejpam-5051	970	3	7	7	NUM
ejpam-5051	970	4	,	,	PUNCT
ejpam-5051	970	5	az(â⋊r	az(â⋊r	PROPN
ejpam-5051	970	6	)	)	PUNCT
ejpam-5051	970	7	∼=	∼=	PROPN
ejpam-5051	970	8	az(d	az(d	PUNCT
ejpam-5051	970	9	;	;	PUNCT
ejpam-5051	970	10	â⋊r	â⋊r	NOUN
ejpam-5051	970	11	)	)	PUNCT
ejpam-5051	970	12	.	.	PUNCT
ejpam-5051	971	1	then	then	ADV
ejpam-5051	971	2	the	the	DET
ejpam-5051	971	3	twisted	twisted	ADJ
ejpam-5051	971	4	steinberg	steinberg	PROPN
ejpam-5051	971	5	algebra	algebra	PROPN
ejpam-5051	971	6	of	of	ADP
ejpam-5051	971	7	â⋊r	â⋊r	PROPN
ejpam-5051	971	8	over	over	ADP
ejpam-5051	971	9	the	the	DET
ejpam-5051	971	10	pair	pair	NOUN
ejpam-5051	971	11	(	(	PUNCT
ejpam-5051	971	12	d	d	NOUN
ejpam-5051	971	13	,	,	PUNCT
ejpam-5051	971	14	z	z	NOUN
ejpam-5051	971	15	)	)	PUNCT
ejpam-5051	971	16	is	be	AUX
ejpam-5051	971	17	defined	define	VERB
ejpam-5051	971	18	as	as	ADP
ejpam-5051	971	19	az(d	az(d	NUM
ejpam-5051	971	20	;	;	PUNCT
ejpam-5051	971	21	â⋊r	â⋊r	NOUN
ejpam-5051	971	22	)	)	PUNCT
ejpam-5051	971	23	∼=	∼=	PROPN
ejpam-5051	971	24	span	span	NOUN
ejpam-5051	971	25	{	{	PUNCT
ejpam-5051	971	26	1{(χ1,0̇	1{(χ1,0̇	NUM
ejpam-5051	971	27	)	)	PUNCT
ejpam-5051	971	28	}	}	PUNCT
ejpam-5051	971	29	,	,	PUNCT
ejpam-5051	971	30	1{(χ2,0̇	1{(χ2,0̇	NUM
ejpam-5051	971	31	)	)	PUNCT
ejpam-5051	971	32	}	}	PUNCT
ejpam-5051	971	33	}	}	PUNCT
ejpam-5051	971	34	.	.	PUNCT
ejpam-5051	972	1	thus	thus	ADV
ejpam-5051	972	2	,	,	PUNCT
ejpam-5051	972	3	dimension	dimension	NOUN
ejpam-5051	972	4	of	of	ADP
ejpam-5051	972	5	az(d	az(d	NUM
ejpam-5051	972	6	;	;	PUNCT
ejpam-5051	972	7	â	â	X
ejpam-5051	972	8	⋊	⋊	X
ejpam-5051	972	9	r	r	X
ejpam-5051	972	10	)	)	PUNCT
ejpam-5051	972	11	is	be	AUX
ejpam-5051	972	12	less	less	ADJ
ejpam-5051	972	13	than	than	ADP
ejpam-5051	972	14	or	or	CCONJ
ejpam-5051	972	15	equal	equal	ADJ
ejpam-5051	972	16	to	to	ADP
ejpam-5051	972	17	2	2	NUM
ejpam-5051	972	18	.	.	PUNCT
ejpam-5051	972	19	note	note	VERB
ejpam-5051	972	20	that	that	PRON
ejpam-5051	972	21	az(z	az(z	VERB
ejpam-5051	972	22	)	)	PUNCT
ejpam-5051	972	23	is	be	AUX
ejpam-5051	972	24	a	a	DET
ejpam-5051	972	25	z	z	NOUN
ejpam-5051	972	26	-	-	PUNCT
ejpam-5051	972	27	module	module	NOUN
ejpam-5051	972	28	.	.	PUNCT
ejpam-5051	973	1	since	since	SCONJ
ejpam-5051	973	2	az(z	az(z	NUM
ejpam-5051	973	3	)	)	PUNCT
ejpam-5051	973	4	is	be	AUX
ejpam-5051	973	5	generated	generate	VERB
ejpam-5051	973	6	by	by	ADP
ejpam-5051	973	7	the	the	DET
ejpam-5051	973	8	characteristic	characteristic	ADJ
ejpam-5051	973	9	functions	function	NOUN
ejpam-5051	973	10	of	of	ADP
ejpam-5051	973	11	the	the	DET
ejpam-5051	973	12	form	form	NOUN
ejpam-5051	973	13	1{z	1{z	NUM
ejpam-5051	973	14	}	}	PUNCT
ejpam-5051	973	15	where	where	SCONJ
ejpam-5051	973	16	z	z	PROPN
ejpam-5051	973	17	∈	∈	PROPN
ejpam-5051	973	18	z	z	NOUN
ejpam-5051	973	19	which	which	PRON
ejpam-5051	973	20	is	be	AUX
ejpam-5051	973	21	infinite	infinite	ADJ
ejpam-5051	973	22	,	,	PUNCT
ejpam-5051	973	23	then	then	ADV
ejpam-5051	973	24	az(z	az(z	NUM
ejpam-5051	973	25	)	)	PUNCT
ejpam-5051	973	26	is	be	AUX
ejpam-5051	973	27	infinite	infinite	ADJ
ejpam-5051	973	28	dimensional	dimensional	ADJ
ejpam-5051	973	29	.	.	PUNCT
ejpam-5051	974	1	hence	hence	ADV
ejpam-5051	974	2	,	,	PUNCT
ejpam-5051	974	3	if	if	SCONJ
ejpam-5051	974	4	we	we	PRON
ejpam-5051	974	5	map	map	VERB
ejpam-5051	974	6	az(z	az(z	NOUN
ejpam-5051	974	7	)	)	PUNCT
ejpam-5051	974	8	to	to	PART
ejpam-5051	974	9	az(d	az(d	NUM
ejpam-5051	974	10	;	;	PUNCT
ejpam-5051	974	11	â⋊r	â⋊r	NOUN
ejpam-5051	974	12	)	)	PUNCT
ejpam-5051	974	13	it	it	PRON
ejpam-5051	974	14	will	will	AUX
ejpam-5051	974	15	never	never	ADV
ejpam-5051	974	16	be	be	AUX
ejpam-5051	974	17	injective	injective	ADJ
ejpam-5051	974	18	.	.	PUNCT
ejpam-5051	975	1	thus	thus	ADV
ejpam-5051	975	2	,	,	PUNCT
ejpam-5051	975	3	isomorphism	isomorphism	NOUN
ejpam-5051	975	4	fails	fail	VERB
ejpam-5051	975	5	to	to	PART
ejpam-5051	975	6	hold	hold	VERB
ejpam-5051	975	7	.	.	PUNCT
ejpam-5051	976	1	note	note	VERB
ejpam-5051	976	2	that	that	SCONJ
ejpam-5051	976	3	from	from	ADP
ejpam-5051	976	4	section	section	NOUN
ejpam-5051	976	5	3	3	NUM
ejpam-5051	976	6	,	,	PUNCT
ejpam-5051	976	7	the	the	DET
ejpam-5051	976	8	isotropy	isotropy	ADJ
ejpam-5051	976	9	group	group	NOUN
ejpam-5051	976	10	of	of	ADP
ejpam-5051	976	11	z	z	PROPN
ejpam-5051	976	12	is	be	AUX
ejpam-5051	976	13	itself	itself	PRON
ejpam-5051	976	14	,	,	PUNCT
ejpam-5051	976	15	that	that	ADV
ejpam-5051	976	16	is	is	ADV
ejpam-5051	976	17	,	,	PUNCT
ejpam-5051	976	18	iso(z	iso(z	X
ejpam-5051	976	19	)	)	PUNCT
ejpam-5051	976	20	=	=	SYM
ejpam-5051	976	21	z	z	NOUN
ejpam-5051	976	22	and	and	CCONJ
ejpam-5051	976	23	the	the	DET
ejpam-5051	976	24	unit	unit	NOUN
ejpam-5051	976	25	space	space	NOUN
ejpam-5051	976	26	of	of	ADP
ejpam-5051	976	27	z	z	PROPN
ejpam-5051	976	28	is	be	AUX
ejpam-5051	976	29	z(0	z(0	ADV
ejpam-5051	976	30	)	)	PUNCT
ejpam-5051	976	31	=	=	PUNCT
ejpam-5051	976	32	{	{	PUNCT
ejpam-5051	976	33	0	0	NUM
ejpam-5051	976	34	}	}	PUNCT
ejpam-5051	976	35	.	.	PUNCT
ejpam-5051	977	1	now	now	ADV
ejpam-5051	977	2	,	,	PUNCT
ejpam-5051	977	3	the	the	DET
ejpam-5051	977	4	interior	interior	NOUN
ejpam-5051	977	5	of	of	ADP
ejpam-5051	977	6	iso(z	iso(z	NOUN
ejpam-5051	977	7	)	)	PUNCT
ejpam-5051	977	8	=	=	PUNCT
ejpam-5051	978	1	z	z	X
ejpam-5051	978	2	̸=	̸=	PROPN
ejpam-5051	978	3	z(0	z(0	NOUN
ejpam-5051	978	4	)	)	PUNCT
ejpam-5051	978	5	.	.	PUNCT
ejpam-5051	979	1	by	by	ADP
ejpam-5051	979	2	definition	definition	NOUN
ejpam-5051	979	3	4	4	NUM
ejpam-5051	979	4	,	,	PUNCT
ejpam-5051	979	5	z	z	NOUN
ejpam-5051	979	6	is	be	AUX
ejpam-5051	979	7	not	not	PART
ejpam-5051	979	8	an	an	DET
ejpam-5051	979	9	effective	effective	ADJ
ejpam-5051	979	10	groupoid	groupoid	NOUN
ejpam-5051	979	11	.	.	PUNCT
ejpam-5051	980	1	conjecture	conjecture	NOUN
ejpam-5051	980	2	:	:	PUNCT
ejpam-5051	980	3	let	let	VERB
ejpam-5051	980	4	g	g	PRON
ejpam-5051	980	5	be	be	AUX
ejpam-5051	980	6	an	an	DET
ejpam-5051	980	7	effective	effective	ADJ
ejpam-5051	980	8	ample	ample	ADJ
ejpam-5051	980	9	hausdorff	hausdorff	NOUN
ejpam-5051	980	10	groupoid	groupoid	PROPN
ejpam-5051	980	11	and	and	CCONJ
ejpam-5051	980	12	r	r	NOUN
ejpam-5051	980	13	be	be	VERB
ejpam-5051	980	14	a	a	DET
ejpam-5051	980	15	unital	unital	ADJ
ejpam-5051	980	16	commutative	commutative	ADJ
ejpam-5051	980	17	ring	ring	NOUN
ejpam-5051	980	18	.	.	PUNCT
ejpam-5051	981	1	then	then	ADV
ejpam-5051	981	2	ar(g	ar(g	ADV
ejpam-5051	981	3	)	)	PUNCT
ejpam-5051	981	4	∼=	∼=	NOUN
ejpam-5051	981	5	ar(d	ar(d	NUM
ejpam-5051	981	6	;	;	PUNCT
ejpam-5051	981	7	â⋊r	â⋊r	NOUN
ejpam-5051	981	8	)	)	PUNCT
ejpam-5051	981	9	.	.	PUNCT
ejpam-5051	982	1	conclusion	conclusion	NOUN
ejpam-5051	982	2	:	:	PUNCT
ejpam-5051	982	3	we	we	PRON
ejpam-5051	982	4	have	have	AUX
ejpam-5051	982	5	defined	define	VERB
ejpam-5051	982	6	a	a	DET
ejpam-5051	982	7	groupoid	groupoid	NOUN
ejpam-5051	982	8	â	â	ADP
ejpam-5051	982	9	⋊	⋊	SYM
ejpam-5051	982	10	r	r	NOUN
ejpam-5051	982	11	coming	come	VERB
ejpam-5051	982	12	from	from	ADP
ejpam-5051	982	13	the	the	DET
ejpam-5051	982	14	isotropy	isotropy	NOUN
ejpam-5051	982	15	of	of	ADP
ejpam-5051	982	16	an	an	DET
ejpam-5051	982	17	ample	ample	ADJ
ejpam-5051	982	18	hausdorff	hausdorff	NOUN
ejpam-5051	982	19	groupoid	groupoid	PROPN
ejpam-5051	982	20	g.	g.	PROPN
ejpam-5051	983	1	we	we	PRON
ejpam-5051	983	2	have	have	AUX
ejpam-5051	983	3	examined	examine	VERB
ejpam-5051	983	4	the	the	DET
ejpam-5051	983	5	properties	property	NOUN
ejpam-5051	983	6	of	of	ADP
ejpam-5051	983	7	the	the	DET
ejpam-5051	983	8	groupoid	groupoid	NOUN
ejpam-5051	983	9	â	â	PRON
ejpam-5051	983	10	⋊	⋊	PROPN
ejpam-5051	983	11	r.	r.	NOUN
ejpam-5051	983	12	we	we	PRON
ejpam-5051	983	13	have	have	AUX
ejpam-5051	983	14	successfully	successfully	ADV
ejpam-5051	983	15	constructed	construct	VERB
ejpam-5051	983	16	a	a	DET
ejpam-5051	983	17	discrete	discrete	ADJ
ejpam-5051	983	18	twist	twist	NOUN
ejpam-5051	983	19	on	on	ADP
ejpam-5051	983	20	â	â	DET
ejpam-5051	983	21	⋊	⋊	NUM
ejpam-5051	983	22	r	r	NOUN
ejpam-5051	983	23	thereby	thereby	ADV
ejpam-5051	983	24	the	the	DET
ejpam-5051	983	25	presence	presence	NOUN
ejpam-5051	983	26	of	of	ADP
ejpam-5051	983	27	a	a	DET
ejpam-5051	983	28	twisted	twisted	ADJ
ejpam-5051	983	29	steinberg	steinberg	PROPN
ejpam-5051	983	30	algebra	algebra	PROPN
ejpam-5051	983	31	over	over	ADP
ejpam-5051	983	32	â	â	PRON
ejpam-5051	983	33	⋊	⋊	NUM
ejpam-5051	983	34	r	r	NOUN
ejpam-5051	983	35	via	via	ADP
ejpam-5051	983	36	the	the	DET
ejpam-5051	983	37	discrete	discrete	ADJ
ejpam-5051	983	38	twist	twist	NOUN
ejpam-5051	983	39	(	(	PUNCT
ejpam-5051	983	40	d	d	NOUN
ejpam-5051	983	41	,	,	PUNCT
ejpam-5051	983	42	i	i	PRON
ejpam-5051	983	43	,	,	PUNCT
ejpam-5051	983	44	q	q	NOUN
ejpam-5051	983	45	)	)	PUNCT
ejpam-5051	983	46	.	.	PUNCT
ejpam-5051	984	1	finally	finally	ADV
ejpam-5051	984	2	,	,	PUNCT
ejpam-5051	984	3	we	we	PRON
ejpam-5051	984	4	have	have	AUX
ejpam-5051	984	5	shown	show	VERB
ejpam-5051	984	6	that	that	SCONJ
ejpam-5051	984	7	for	for	ADP
ejpam-5051	984	8	g	g	PROPN
ejpam-5051	984	9	=	=	SYM
ejpam-5051	984	10	z	z	PROPN
ejpam-5051	984	11	and	and	CCONJ
ejpam-5051	984	12	r	r	NOUN
ejpam-5051	984	13	=	=	SYM
ejpam-5051	984	14	z	z	NOUN
ejpam-5051	984	15	isomorphism	isomorphism	NOUN
ejpam-5051	984	16	between	between	ADP
ejpam-5051	984	17	ar(g	ar(g	NOUN
ejpam-5051	984	18	)	)	PUNCT
ejpam-5051	984	19	and	and	CCONJ
ejpam-5051	984	20	ar(d	ar(d	NUM
ejpam-5051	984	21	;	;	PUNCT
ejpam-5051	984	22	â⋊r	â⋊r	NOUN
ejpam-5051	984	23	)	)	PUNCT
ejpam-5051	984	24	fails	fail	VERB
ejpam-5051	984	25	to	to	PART
ejpam-5051	984	26	hold	hold	VERB
ejpam-5051	984	27	.	.	PUNCT
ejpam-5051	985	1	references	reference	NOUN
ejpam-5051	985	2	544	544	NUM
ejpam-5051	985	3	acknowledgements	acknowledgement	NOUN
ejpam-5051	985	4	the	the	DET
ejpam-5051	985	5	authors	author	NOUN
ejpam-5051	985	6	would	would	AUX
ejpam-5051	985	7	like	like	VERB
ejpam-5051	985	8	to	to	PART
ejpam-5051	985	9	thank	thank	VERB
ejpam-5051	985	10	the	the	DET
ejpam-5051	985	11	department	department	NOUN
ejpam-5051	985	12	of	of	ADP
ejpam-5051	985	13	science	science	NOUN
ejpam-5051	985	14	and	and	CCONJ
ejpam-5051	985	15	technology	technology	NOUN
ejpam-5051	985	16	accelerated	accelerate	VERB
ejpam-5051	985	17	science	science	NOUN
ejpam-5051	985	18	and	and	CCONJ
ejpam-5051	985	19	technology	technology	NOUN
ejpam-5051	985	20	human	human	ADJ
ejpam-5051	985	21	resource	resource	NOUN
ejpam-5051	985	22	development	development	NOUN
ejpam-5051	985	23	program	program	NOUN
ejpam-5051	985	24	(	(	PUNCT
ejpam-5051	985	25	dost	dost	NOUN
ejpam-5051	985	26	-	-	PUNCT
ejpam-5051	985	27	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-5051	985	28	,	,	PUNCT
ejpam-5051	985	29	and	and	CCONJ
ejpam-5051	985	30	msu	msu	PROPN
ejpam-5051	985	31	-	-	PUNCT
ejpam-5051	985	32	iligan	iligan	PROPN
ejpam-5051	985	33	institute	institute	PROPN
ejpam-5051	985	34	of	of	ADP
ejpam-5051	985	35	technology	technology	NOUN
ejpam-5051	985	36	for	for	ADP
ejpam-5051	985	37	funding	fund	VERB
ejpam-5051	985	38	this	this	DET
ejpam-5051	985	39	research	research	NOUN
ejpam-5051	985	40	.	.	PUNCT
ejpam-5051	986	1	references	reference	NOUN
ejpam-5051	986	2	[	[	X
ejpam-5051	986	3	1	1	NUM
ejpam-5051	986	4	]	]	X
ejpam-5051	986	5	b.	b.	PROPN
ejpam-5051	986	6	armstrong	armstrong	PROPN
ejpam-5051	986	7	,	,	PUNCT
ejpam-5051	986	8	l.	l.	PROPN
ejpam-5051	986	9	orloff	orloff	PROPN
ejpam-5051	986	10	clark	clark	PROPN
ejpam-5051	986	11	,	,	PUNCT
ejpam-5051	986	12	k.	k.	PROPN
ejpam-5051	986	13	courtney	courtney	PROPN
ejpam-5051	986	14	,	,	PUNCT
ejpam-5051	986	15	y.	y.	PROPN
ejpam-5051	986	16	lin	lin	PROPN
ejpam-5051	986	17	,	,	PUNCT
ejpam-5051	986	18	k.	k.	PROPN
ejpam-5051	986	19	mccormick	mccormick	PROPN
ejpam-5051	986	20	,	,	PUNCT
ejpam-5051	986	21	and	and	CCONJ
ejpam-5051	986	22	j.	j.	PROPN
ejpam-5051	986	23	ramagge	ramagge	PROPN
ejpam-5051	986	24	.	.	PUNCT
ejpam-5051	987	1	twisted	twisted	PROPN
ejpam-5051	987	2	steinberg	steinberg	PROPN
ejpam-5051	987	3	algebras	algebras	PROPN
ejpam-5051	987	4	.	.	PROPN
ejpam-5051	987	5	journal	journal	PROPN
ejpam-5051	987	6	of	of	ADP
ejpam-5051	987	7	pure	pure	ADJ
ejpam-5051	987	8	and	and	CCONJ
ejpam-5051	987	9	applied	applied	ADJ
ejpam-5051	987	10	algebra	algebra	NOUN
ejpam-5051	987	11	,	,	PUNCT
ejpam-5051	987	12	226:6–28	226:6–28	NUM
ejpam-5051	987	13	,	,	PUNCT
ejpam-5051	987	14	2022	2022	NUM
ejpam-5051	987	15	.	.	PUNCT
ejpam-5051	988	1	[	[	X
ejpam-5051	988	2	2	2	X
ejpam-5051	988	3	]	]	PUNCT
ejpam-5051	988	4	h.	h.	PROPN
ejpam-5051	988	5	brandt	brandt	PROPN
ejpam-5051	988	6	.	.	PUNCT
ejpam-5051	989	1	idealtheorie	idealtheorie	PROPN
ejpam-5051	989	2	in	in	ADP
ejpam-5051	989	3	quatemionenalgebren	quatemionenalgebren	PROPN
ejpam-5051	989	4	.	.	PUNCT
ejpam-5051	990	1	mathematische	mathematische	PROPN
ejpam-5051	990	2	annalen	annalen	PROPN
ejpam-5051	990	3	,	,	PUNCT
ejpam-5051	990	4	99:1–29	99:1–29	NUM
ejpam-5051	990	5	,	,	PUNCT
ejpam-5051	990	6	1928	1928	NUM
ejpam-5051	990	7	.	.	PUNCT
ejpam-5051	991	1	[	[	X
ejpam-5051	991	2	3	3	X
ejpam-5051	991	3	]	]	X
ejpam-5051	991	4	l.g	l.g	PROPN
ejpam-5051	991	5	.	.	PROPN
ejpam-5051	991	6	brown	brown	PROPN
ejpam-5051	991	7	,	,	PUNCT
ejpam-5051	991	8	p.	p.	NOUN
ejpam-5051	991	9	green	green	NOUN
ejpam-5051	991	10	,	,	PUNCT
ejpam-5051	991	11	and	and	CCONJ
ejpam-5051	991	12	m.a	m.a	PROPN
ejpam-5051	991	13	rieffel	rieffel	NOUN
ejpam-5051	991	14	.	.	PUNCT
ejpam-5051	992	1	stable	stable	ADJ
ejpam-5051	992	2	isomorphism	isomorphism	NOUN
ejpam-5051	992	3	and	and	CCONJ
ejpam-5051	992	4	strong	strong	ADJ
ejpam-5051	992	5	morita	morita	NOUN
ejpam-5051	992	6	equivalence	equivalence	NOUN
ejpam-5051	992	7	of	of	ADP
ejpam-5051	992	8	c*-algebras	c*-algebras	PROPN
ejpam-5051	992	9	.	.	PUNCT
ejpam-5051	993	1	pacific	pacific	PROPN
ejpam-5051	993	2	j.	j.	PROPN
ejpam-5051	993	3	math	math	PROPN
ejpam-5051	993	4	,	,	PUNCT
ejpam-5051	993	5	71:394–407	71:394–407	PROPN
ejpam-5051	993	6	,	,	PUNCT
ejpam-5051	993	7	1977	1977	NUM
ejpam-5051	993	8	.	.	PUNCT
ejpam-5051	994	1	[	[	X
ejpam-5051	994	2	4	4	X
ejpam-5051	994	3	]	]	PUNCT
ejpam-5051	994	4	s.	s.	PROPN
ejpam-5051	994	5	eilenberg	eilenberg	PROPN
ejpam-5051	994	6	and	and	CCONJ
ejpam-5051	994	7	s.	s.	PROPN
ejpam-5051	994	8	maclane	maclane	PROPN
ejpam-5051	994	9	.	.	PUNCT
ejpam-5051	995	1	the	the	DET
ejpam-5051	995	2	general	general	ADJ
ejpam-5051	995	3	theory	theory	NOUN
ejpam-5051	995	4	of	of	ADP
ejpam-5051	995	5	natural	natural	ADJ
ejpam-5051	995	6	equivalence	equivalence	NOUN
ejpam-5051	995	7	.	.	PUNCT
ejpam-5051	996	1	american	american	PROPN
ejpam-5051	996	2	mathematical	mathematical	PROPN
ejpam-5051	996	3	society	society	NOUN
ejpam-5051	996	4	,	,	PUNCT
ejpam-5051	996	5	58:231–294	58:231–294	NUM
ejpam-5051	996	6	,	,	PUNCT
ejpam-5051	996	7	1945	1945	NUM
ejpam-5051	996	8	.	.	PUNCT
ejpam-5051	997	1	[	[	X
ejpam-5051	997	2	5	5	X
ejpam-5051	997	3	]	]	PUNCT
ejpam-5051	997	4	j.	j.	PROPN
ejpam-5051	997	5	feldman	feldman	PROPN
ejpam-5051	997	6	and	and	CCONJ
ejpam-5051	997	7	c.c	c.c	PROPN
ejpam-5051	997	8	.	.	PROPN
ejpam-5051	997	9	moore	moore	PROPN
ejpam-5051	997	10	.	.	PUNCT
ejpam-5051	998	1	ergodic	ergodic	ADJ
ejpam-5051	998	2	equivalence	equivalence	NOUN
ejpam-5051	998	3	relations	relation	NOUN
ejpam-5051	998	4	,	,	PUNCT
ejpam-5051	998	5	cohomology	cohomology	NOUN
ejpam-5051	998	6	,	,	PUNCT
ejpam-5051	998	7	and	and	CCONJ
ejpam-5051	998	8	von	von	PROPN
ejpam-5051	998	9	neumann	neumann	PROPN
ejpam-5051	998	10	algebras	algebras	PROPN
ejpam-5051	998	11	.	.	PUNCT
ejpam-5051	998	12	i.	i.	PROPN
ejpam-5051	998	13	american	american	PROPN
ejpam-5051	998	14	mathematical	mathematical	PROPN
ejpam-5051	998	15	society	society	NOUN
ejpam-5051	998	16	,	,	PUNCT
ejpam-5051	998	17	234:289–324	234:289–324	NUM
ejpam-5051	998	18	,	,	PUNCT
ejpam-5051	998	19	1977	1977	NUM
ejpam-5051	998	20	.	.	PUNCT
ejpam-5051	999	1	[	[	X
ejpam-5051	999	2	6	6	NUM
ejpam-5051	999	3	]	]	PUNCT
ejpam-5051	999	4	j.	j.	PROPN
ejpam-5051	999	5	feldman	feldman	PROPN
ejpam-5051	999	6	and	and	CCONJ
ejpam-5051	999	7	c.c	c.c	PROPN
ejpam-5051	999	8	.	.	PROPN
ejpam-5051	999	9	moore	moore	PROPN
ejpam-5051	999	10	.	.	PUNCT
ejpam-5051	1000	1	ergodic	ergodic	ADJ
ejpam-5051	1000	2	equivalence	equivalence	NOUN
ejpam-5051	1000	3	relations	relation	NOUN
ejpam-5051	1000	4	,	,	PUNCT
ejpam-5051	1000	5	cohomology	cohomology	NOUN
ejpam-5051	1000	6	,	,	PUNCT
ejpam-5051	1000	7	and	and	CCONJ
ejpam-5051	1000	8	von	von	PROPN
ejpam-5051	1000	9	neumann	neumann	PROPN
ejpam-5051	1000	10	algebras	algebras	PROPN
ejpam-5051	1000	11	.	.	PUNCT
ejpam-5051	1001	1	ii	ii	PROPN
ejpam-5051	1001	2	.	.	PUNCT
ejpam-5051	1002	1	american	american	PROPN
ejpam-5051	1002	2	mathematical	mathematical	PROPN
ejpam-5051	1002	3	society	society	NOUN
ejpam-5051	1002	4	,	,	PUNCT
ejpam-5051	1002	5	234:325–359	234:325–359	NUM
ejpam-5051	1002	6	,	,	PUNCT
ejpam-5051	1002	7	1977	1977	NUM
ejpam-5051	1002	8	.	.	PUNCT
ejpam-5051	1003	1	[	[	X
ejpam-5051	1003	2	7	7	X
ejpam-5051	1003	3	]	]	X
ejpam-5051	1003	4	p.	p.	PROPN
ejpam-5051	1003	5	hahn	hahn	PROPN
ejpam-5051	1003	6	.	.	PUNCT
ejpam-5051	1004	1	haar	haar	PROPN
ejpam-5051	1004	2	measure	measure	NOUN
ejpam-5051	1004	3	for	for	ADP
ejpam-5051	1004	4	measure	measure	NOUN
ejpam-5051	1004	5	groupoids	groupoid	NOUN
ejpam-5051	1004	6	.	.	PUNCT
ejpam-5051	1005	1	american	american	PROPN
ejpam-5051	1005	2	mathematical	mathematical	PROPN
ejpam-5051	1005	3	society	society	NOUN
ejpam-5051	1005	4	,	,	PUNCT
ejpam-5051	1005	5	242:1–33	242:1–33	NUM
ejpam-5051	1005	6	,	,	PUNCT
ejpam-5051	1005	7	1978	1978	NUM
ejpam-5051	1005	8	.	.	PUNCT
ejpam-5051	1006	1	[	[	X
ejpam-5051	1006	2	8	8	NUM
ejpam-5051	1006	3	]	]	X
ejpam-5051	1006	4	f.	f.	PROPN
ejpam-5051	1006	5	bruno	bruno	PROPN
ejpam-5051	1006	6	leonardo	leonardo	PROPN
ejpam-5051	1006	7	macedo	macedo	PROPN
ejpam-5051	1006	8	and	and	CCONJ
ejpam-5051	1006	9	c.	c.	PROPN
ejpam-5051	1006	10	bruno	bruno	PROPN
ejpam-5051	1006	11	tadeu	tadeu	PROPN
ejpam-5051	1006	12	.	.	PUNCT
ejpam-5051	1007	1	*	*	PUNCT
ejpam-5051	1007	2	lie	lie	NOUN
ejpam-5051	1007	3	-	-	PUNCT
ejpam-5051	1007	4	jordan	jordan	NOUN
ejpam-5051	1007	5	-	-	PUNCT
ejpam-5051	1007	6	type	type	NOUN
ejpam-5051	1007	7	maps	map	NOUN
ejpam-5051	1007	8	on	on	ADP
ejpam-5051	1007	9	c*algebras	c*algebra	NOUN
ejpam-5051	1007	10	.	.	NOUN
ejpam-5051	1007	11	bulletin	bulletin	NOUN
ejpam-5051	1007	12	of	of	ADP
ejpam-5051	1007	13	the	the	DET
ejpam-5051	1007	14	iranian	iranian	PROPN
ejpam-5051	1007	15	mathematical	mathematical	ADJ
ejpam-5051	1007	16	society	society	NOUN
ejpam-5051	1007	17	,	,	PUNCT
ejpam-5051	1007	18	48:1679–1690	48:1679–1690	NOUN
ejpam-5051	1007	19	,	,	PUNCT
ejpam-5051	1007	20	2022	2022	NUM
ejpam-5051	1007	21	.	.	PUNCT
ejpam-5051	1008	1	[	[	X
ejpam-5051	1008	2	9	9	NUM
ejpam-5051	1008	3	]	]	PUNCT
ejpam-5051	1008	4	i.	i.	NOUN
ejpam-5051	1008	5	raebum	raebum	NOUN
ejpam-5051	1008	6	and	and	CCONJ
ejpam-5051	1008	7	j.l	j.l	PROPN
ejpam-5051	1008	8	.	.	PROPN
ejpam-5051	1008	9	taylor	taylor	PROPN
ejpam-5051	1008	10	.	.	PUNCT
ejpam-5051	1009	1	continuous	continuous	ADJ
ejpam-5051	1009	2	trace	trace	NOUN
ejpam-5051	1009	3	c*-algebras	c*-algebra	NOUN
ejpam-5051	1009	4	with	with	ADP
ejpam-5051	1009	5	given	give	VERB
ejpam-5051	1009	6	dixmier	dixmier	NOUN
ejpam-5051	1009	7	-	-	PUNCT
ejpam-5051	1009	8	douady	douady	PROPN
ejpam-5051	1009	9	class	class	NOUN
ejpam-5051	1009	10	.	.	PUNCT
ejpam-5051	1010	1	australian	australian	ADJ
ejpam-5051	1010	2	mathematical	mathematical	ADJ
ejpam-5051	1010	3	society	society	NOUN
ejpam-5051	1010	4	,	,	PUNCT
ejpam-5051	1010	5	38:394–407	38:394–407	PROPN
ejpam-5051	1010	6	,	,	PUNCT
ejpam-5051	1010	7	1985	1985	NUM
ejpam-5051	1010	8	.	.	PUNCT
ejpam-5051	1011	1	[	[	X
ejpam-5051	1011	2	10	10	NUM
ejpam-5051	1011	3	]	]	X
ejpam-5051	1011	4	j.	j.	PROPN
ejpam-5051	1011	5	renault	renault	PROPN
ejpam-5051	1011	6	.	.	PUNCT
ejpam-5051	1012	1	a	a	DET
ejpam-5051	1012	2	groupoid	groupoid	PROPN
ejpam-5051	1012	3	approach	approach	NOUN
ejpam-5051	1012	4	to	to	ADP
ejpam-5051	1012	5	c*-algebras	c*-algebras	PROPN
ejpam-5051	1012	6	.	.	PUNCT
ejpam-5051	1012	7	springer	springer	NOUN
ejpam-5051	1012	8	,	,	PUNCT
ejpam-5051	1012	9	berlin	berlin	PROPN
ejpam-5051	1012	10	,	,	PUNCT
ejpam-5051	1012	11	germany	germany	PROPN
ejpam-5051	1012	12	,	,	PUNCT
ejpam-5051	1012	13	1980	1980	NUM
ejpam-5051	1012	14	.	.	PUNCT
ejpam-5051	1013	1	[	[	X
ejpam-5051	1013	2	11	11	NUM
ejpam-5051	1013	3	]	]	PUNCT
ejpam-5051	1013	4	j.	j.	PROPN
ejpam-5051	1013	5	renault	renault	PROPN
ejpam-5051	1013	6	.	.	PUNCT
ejpam-5051	1014	1	cartan	cartan	PROPN
ejpam-5051	1014	2	subalgebras	subalgebras	PROPN
ejpam-5051	1014	3	in	in	ADP
ejpam-5051	1014	4	c*-algebras	c*-algebras	PROPN
ejpam-5051	1014	5	.	.	PUNCT
ejpam-5051	1015	1	ireland	ireland	PROPN
ejpam-5051	1015	2	mathematical	mathematical	PROPN
ejpam-5051	1015	3	society	society	NOUN
ejpam-5051	1015	4	,	,	PUNCT
ejpam-5051	1015	5	61:29	61:29	NUM
ejpam-5051	1015	6	–	–	PUNCT
ejpam-5051	1015	7	63	63	NUM
ejpam-5051	1015	8	,	,	PUNCT
ejpam-5051	1015	9	2008	2008	NUM
ejpam-5051	1015	10	.	.	PUNCT
ejpam-5051	1016	1	[	[	X
ejpam-5051	1016	2	12	12	NUM
ejpam-5051	1016	3	]	]	PUNCT
ejpam-5051	1016	4	s.	s.	PROPN
ejpam-5051	1016	5	rigby	rigby	PROPN
ejpam-5051	1016	6	.	.	PUNCT
ejpam-5051	1017	1	steinberg	steinberg	PROPN
ejpam-5051	1017	2	algebras	algebras	PROPN
ejpam-5051	1017	3	and	and	CCONJ
ejpam-5051	1017	4	leavitt	leavitt	PROPN
ejpam-5051	1017	5	path	path	PROPN
ejpam-5051	1017	6	algebras	algebras	PROPN
ejpam-5051	1017	7	.	.	PUNCT
ejpam-5051	1018	1	masteral	masteral	ADJ
ejpam-5051	1018	2	thesis	thesis	NOUN
ejpam-5051	1018	3	,	,	PUNCT
ejpam-5051	1018	4	university	university	NOUN
ejpam-5051	1018	5	of	of	ADP
ejpam-5051	1018	6	cape	cape	NOUN
ejpam-5051	1018	7	town	town	NOUN
ejpam-5051	1018	8	,	,	PUNCT
ejpam-5051	1018	9	2018	2018	NUM
ejpam-5051	1018	10	.	.	PUNCT
ejpam-5051	1019	1	[	[	X
ejpam-5051	1019	2	13	13	NUM
ejpam-5051	1019	3	]	]	X
ejpam-5051	1019	4	n.	n.	PROPN
ejpam-5051	1019	5	ruth	ruth	PROPN
ejpam-5051	1019	6	,	,	PUNCT
ejpam-5051	1019	7	m.	m.	PROPN
ejpam-5051	1019	8	ferreira	ferreira	PROPN
ejpam-5051	1019	9	,	,	PUNCT
ejpam-5051	1019	10	b.	b.	PROPN
ejpam-5051	1019	11	leonardo	leonardo	PROPN
ejpam-5051	1019	12	,	,	PUNCT
ejpam-5051	1019	13	g.	g.	PROPN
ejpam-5051	1019	14	henrique	henrique	PROPN
ejpam-5051	1019	15	,	,	PUNCT
ejpam-5051	1019	16	and	and	CCONJ
ejpam-5051	1019	17	c.	c.	PROPN
ejpam-5051	1019	18	bruno	bruno	PROPN
ejpam-5051	1019	19	tadeu	tadeu	PROPN
ejpam-5051	1019	20	.	.	PUNCT
ejpam-5051	1020	1	*	*	PUNCT
ejpam-5051	1020	2	lie	lie	NOUN
ejpam-5051	1020	3	-	-	PUNCT
ejpam-5051	1020	4	type	type	NOUN
ejpam-5051	1020	5	maps	map	NOUN
ejpam-5051	1020	6	on	on	ADP
ejpam-5051	1020	7	c*-algebras	c*-algebra	NOUN
ejpam-5051	1020	8	.	.	PUNCT
ejpam-5051	1021	1	communications	communication	NOUN
ejpam-5051	1021	2	in	in	ADP
ejpam-5051	1021	3	algebra	algebra	NOUN
ejpam-5051	1021	4	(	(	PUNCT
ejpam-5051	1021	5	online	online	ADJ
ejpam-5051	1021	6	)	)	PUNCT
ejpam-5051	1021	7	,	,	PUNCT
ejpam-5051	1021	8	50:5145–5154	50:5145–5154	NUM
ejpam-5051	1021	9	,	,	PUNCT
ejpam-5051	1021	10	2022	2022	NUM
ejpam-5051	1021	11	.	.	PUNCT
ejpam-5051	1022	1	[	[	X
ejpam-5051	1022	2	14	14	NUM
ejpam-5051	1022	3	]	]	X
ejpam-5051	1022	4	j.l	j.l	PROPN
ejpam-5051	1022	5	.	.	PROPN
ejpam-5051	1022	6	tu	tu	PROPN
ejpam-5051	1022	7	.	.	PUNCT
ejpam-5051	1023	1	la	la	PROPN
ejpam-5051	1023	2	conjecture	conjecture	NOUN
ejpam-5051	1023	3	de	de	SCONJ
ejpam-5051	1023	4	baum	baum	PROPN
ejpam-5051	1023	5	-	-	PUNCT
ejpam-5051	1023	6	connes	conne	NOUN
ejpam-5051	1023	7	pour	pour	VERB
ejpam-5051	1023	8	les	le	NOUN
ejpam-5051	1023	9	feuilletages	feuilletage	NOUN
ejpam-5051	1023	10	moyennables	moyennable	NOUN
ejpam-5051	1023	11	.	.	PUNCT
ejpam-5051	1024	1	k	k	X
ejpam-5051	1024	2	-	-	NOUN
ejpam-5051	1024	3	theory	theory	NOUN
ejpam-5051	1024	4	,	,	PUNCT
ejpam-5051	1024	5	17:215–264	17:215–264	PROPN
ejpam-5051	1024	6	,	,	PUNCT
ejpam-5051	1024	7	1999	1999	NUM
ejpam-5051	1024	8	.	.	PUNCT
ejpam-5051	1025	1	references	reference	NOUN
ejpam-5051	1025	2	545	545	NUM
ejpam-5051	1025	3	[	[	X
ejpam-5051	1025	4	15	15	NUM
ejpam-5051	1025	5	]	]	X
ejpam-5051	1025	6	d.	d.	PROPN
ejpam-5051	1025	7	williams	williams	PROPN
ejpam-5051	1025	8	,	,	PUNCT
ejpam-5051	1025	9	j.	j.	PROPN
ejpam-5051	1025	10	renault	renault	PROPN
ejpam-5051	1025	11	,	,	PUNCT
ejpam-5051	1025	12	and	and	CCONJ
ejpam-5051	1025	13	p.	p.	NOUN
ejpam-5051	1025	14	muhly	muhly	ADV
ejpam-5051	1025	15	.	.	PUNCT
ejpam-5051	1026	1	continuous	continuous	ADJ
ejpam-5051	1026	2	-	-	PUNCT
ejpam-5051	1026	3	trace	trace	NOUN
ejpam-5051	1026	4	groupoid	groupoid	PROPN
ejpam-5051	1026	5	c*-algebras	c*-algebras	AUX
ejpam-5051	1026	6	.	.	PUNCT
ejpam-5051	1027	1	iii	iii	X
ejpam-5051	1027	2	.	.	PUNCT
ejpam-5051	1028	1	american	american	PROPN
ejpam-5051	1028	2	mathematical	mathematical	PROPN
ejpam-5051	1028	3	society	society	NOUN
ejpam-5051	1028	4	,	,	PUNCT
ejpam-5051	1028	5	348:3621–3641	348:3621–3641	NUM
ejpam-5051	1028	6	,	,	PUNCT
ejpam-5051	1028	7	1996	1996	NUM
ejpam-5051	1028	8	.	.	PUNCT