id	sid	tid	token	lemma	pos
ejpam-2753	1	1	european	european	PROPN
ejpam-2753	1	2	journal	journal	PROPN
ejpam-2753	1	3	of	of	ADP
ejpam-2753	1	4	pure	pure	ADJ
ejpam-2753	1	5	and	and	CCONJ
ejpam-2753	1	6	applied	apply	VERB
ejpam-2753	1	7	mathematics	mathematic	NOUN
ejpam-2753	1	8	vol	vol	NOUN
ejpam-2753	1	9	.	.	PROPN
ejpam-2753	2	1	10	10	NUM
ejpam-2753	2	2	,	,	PUNCT
ejpam-2753	2	3	no	no	INTJ
ejpam-2753	2	4	.	.	NOUN
ejpam-2753	2	5	4	4	NUM
ejpam-2753	2	6	,	,	PUNCT
ejpam-2753	2	7	2017	2017	NUM
ejpam-2753	2	8	,	,	PUNCT
ejpam-2753	2	9	702	702	NUM
ejpam-2753	2	10	-	-	SYM
ejpam-2753	2	11	716	716	NUM
ejpam-2753	2	12	issn	issn	PROPN
ejpam-2753	2	13	1307	1307	NUM
ejpam-2753	2	14	-	-	SYM
ejpam-2753	2	15	5543	5543	NUM
ejpam-2753	2	16	–	–	PUNCT
ejpam-2753	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2753	2	18	published	publish	VERB
ejpam-2753	2	19	by	by	ADP
ejpam-2753	2	20	new	new	PROPN
ejpam-2753	2	21	york	york	PROPN
ejpam-2753	2	22	business	business	PROPN
ejpam-2753	2	23	global	global	ADJ
ejpam-2753	2	24	tensor	tensor	NOUN
ejpam-2753	2	25	product	product	NOUN
ejpam-2753	2	26	of	of	ADP
ejpam-2753	2	27	hypervector	hypervector	NOUN
ejpam-2753	2	28	spaces	space	NOUN
ejpam-2753	2	29	r.	r.	PROPN
ejpam-2753	2	30	ameri1,∗	ameri1,∗	PROPN
ejpam-2753	2	31	,	,	PUNCT
ejpam-2753	2	32	k.	k.	PROPN
ejpam-2753	2	33	ghadimi2	ghadimi2	PROPN
ejpam-2753	2	34	,	,	PUNCT
ejpam-2753	2	35	r.	r.	PROPN
ejpam-2753	2	36	a.	a.	PROPN
ejpam-2753	2	37	borzooei3	borzooei3	PROPN
ejpam-2753	3	1	1	1	NUM
ejpam-2753	3	2	school	school	NOUN
ejpam-2753	3	3	of	of	ADP
ejpam-2753	3	4	mathematics	mathematic	NOUN
ejpam-2753	3	5	,	,	PUNCT
ejpam-2753	3	6	statistic	statistic	NOUN
ejpam-2753	3	7	and	and	CCONJ
ejpam-2753	3	8	computer	computer	NOUN
ejpam-2753	3	9	sciences	science	NOUN
ejpam-2753	3	10	,	,	PUNCT
ejpam-2753	3	11	university	university	NOUN
ejpam-2753	3	12	of	of	ADP
ejpam-2753	3	13	tehran	tehran	PROPN
ejpam-2753	3	14	,	,	PUNCT
ejpam-2753	3	15	iran	iran	PROPN
ejpam-2753	3	16	2	2	NUM
ejpam-2753	3	17	department	department	NOUN
ejpam-2753	3	18	of	of	ADP
ejpam-2753	3	19	mathematics	mathematic	NOUN
ejpam-2753	3	20	,	,	PUNCT
ejpam-2753	3	21	payame	payame	NOUN
ejpam-2753	3	22	noor	noor	PROPN
ejpam-2753	3	23	university	university	PROPN
ejpam-2753	3	24	,	,	PUNCT
ejpam-2753	3	25	iran	iran	PROPN
ejpam-2753	3	26	3	3	NUM
ejpam-2753	3	27	department	department	NOUN
ejpam-2753	3	28	of	of	ADP
ejpam-2753	3	29	mathematics	mathematic	NOUN
ejpam-2753	3	30	,	,	PUNCT
ejpam-2753	3	31	shahid	shahid	PROPN
ejpam-2753	3	32	beheshti	beheshti	PROPN
ejpam-2753	3	33	university	university	NOUN
ejpam-2753	3	34	,	,	PUNCT
ejpam-2753	3	35	iran	iran	PROPN
ejpam-2753	3	36	abstract	abstract	ADJ
ejpam-2753	3	37	.	.	PUNCT
ejpam-2753	4	1	we	we	PRON
ejpam-2753	4	2	introduce	introduce	VERB
ejpam-2753	4	3	and	and	CCONJ
ejpam-2753	4	4	study	study	VERB
ejpam-2753	4	5	tensor	tensor	NOUN
ejpam-2753	4	6	product	product	NOUN
ejpam-2753	4	7	of	of	ADP
ejpam-2753	4	8	hypervector	hypervector	NOUN
ejpam-2753	4	9	spaces	space	NOUN
ejpam-2753	4	10	(	(	PUNCT
ejpam-2753	4	11	or	or	CCONJ
ejpam-2753	4	12	hyperspaces	hyperspace	NOUN
ejpam-2753	4	13	)	)	PUNCT
ejpam-2753	4	14	based	base	VERB
ejpam-2753	4	15	on	on	ADP
ejpam-2753	4	16	tallini	tallini	ADJ
ejpam-2753	4	17	hypervector	hypervector	NOUN
ejpam-2753	4	18	spaces	space	NOUN
ejpam-2753	4	19	.	.	PUNCT
ejpam-2753	5	1	here	here	ADV
ejpam-2753	5	2	we	we	PRON
ejpam-2753	5	3	introduce	introduce	VERB
ejpam-2753	5	4	the	the	DET
ejpam-2753	5	5	(	(	PUNCT
ejpam-2753	5	6	resp	resp	NOUN
ejpam-2753	5	7	.	.	PUNCT
ejpam-2753	5	8	multivalued	multivalue	VERB
ejpam-2753	5	9	)	)	PUNCT
ejpam-2753	5	10	middle	middle	ADJ
ejpam-2753	5	11	linear	linear	NOUN
ejpam-2753	5	12	maps	map	NOUN
ejpam-2753	5	13	of	of	ADP
ejpam-2753	5	14	hyperspaces	hyperspace	NOUN
ejpam-2753	5	15	and	and	CCONJ
ejpam-2753	5	16	construct	construct	VERB
ejpam-2753	5	17	the	the	DET
ejpam-2753	5	18	categories	category	NOUN
ejpam-2753	5	19	of	of	ADP
ejpam-2753	5	20	linear	linear	PROPN
ejpam-2753	5	21	maps	map	NOUN
ejpam-2753	5	22	and	and	CCONJ
ejpam-2753	5	23	multivalued	multivalue	VERB
ejpam-2753	5	24	linear	linear	ADJ
ejpam-2753	5	25	maps	map	NOUN
ejpam-2753	5	26	of	of	ADP
ejpam-2753	5	27	hyperspaces	hyperspace	NOUN
ejpam-2753	5	28	.	.	PUNCT
ejpam-2753	6	1	it	it	PRON
ejpam-2753	6	2	is	be	AUX
ejpam-2753	6	3	shown	show	VERB
ejpam-2753	6	4	the	the	DET
ejpam-2753	6	5	tensor	tensor	NOUN
ejpam-2753	6	6	product	product	NOUN
ejpam-2753	6	7	of	of	ADP
ejpam-2753	6	8	two	two	NUM
ejpam-2753	6	9	hypespaces	hypespace	NOUN
ejpam-2753	6	10	,	,	PUNCT
ejpam-2753	6	11	as	as	ADP
ejpam-2753	6	12	an	an	DET
ejpam-2753	6	13	initial	initial	ADJ
ejpam-2753	6	14	object	object	NOUN
ejpam-2753	6	15	in	in	ADP
ejpam-2753	6	16	this	this	DET
ejpam-2753	6	17	category	category	NOUN
ejpam-2753	6	18	,	,	PUNCT
ejpam-2753	6	19	exists	exist	VERB
ejpam-2753	6	20	.	.	PUNCT
ejpam-2753	7	1	also	also	ADV
ejpam-2753	7	2	,	,	PUNCT
ejpam-2753	7	3	notion	notion	NOUN
ejpam-2753	7	4	of	of	ADP
ejpam-2753	7	5	a	a	DET
ejpam-2753	7	6	quasi	quasi	ADJ
ejpam-2753	7	7	-	-	ADJ
ejpam-2753	7	8	free	free	ADJ
ejpam-2753	7	9	object	object	NOUN
ejpam-2753	7	10	in	in	ADP
ejpam-2753	7	11	category	category	NOUN
ejpam-2753	7	12	of	of	ADP
ejpam-2753	7	13	hyperspaces	hyperspace	NOUN
ejpam-2753	7	14	is	be	AUX
ejpam-2753	7	15	introduced	introduce	VERB
ejpam-2753	7	16	and	and	CCONJ
ejpam-2753	7	17	it	it	PRON
ejpam-2753	7	18	is	be	AUX
ejpam-2753	7	19	proved	prove	VERB
ejpam-2753	7	20	that	that	SCONJ
ejpam-2753	7	21	in	in	ADP
ejpam-2753	7	22	this	this	DET
ejpam-2753	7	23	category	category	NOUN
ejpam-2753	7	24	a	a	DET
ejpam-2753	7	25	quasi	quasi	ADJ
ejpam-2753	7	26	-	-	ADJ
ejpam-2753	7	27	free	free	ADJ
ejpam-2753	7	28	object	object	NOUN
ejpam-2753	7	29	up	up	ADP
ejpam-2753	7	30	to	to	ADP
ejpam-2753	7	31	maximum	maximum	NOUN
ejpam-2753	7	32	is	be	AUX
ejpam-2753	7	33	unique	unique	ADJ
ejpam-2753	7	34	.	.	PUNCT
ejpam-2753	8	1	2010	2010	NUM
ejpam-2753	8	2	mathematics	mathematic	NOUN
ejpam-2753	8	3	subject	subject	NOUN
ejpam-2753	8	4	classifications	classification	NOUN
ejpam-2753	8	5	:	:	PUNCT
ejpam-2753	8	6	20n20	20n20	NUM
ejpam-2753	8	7	key	key	ADJ
ejpam-2753	8	8	words	word	NOUN
ejpam-2753	8	9	and	and	CCONJ
ejpam-2753	8	10	phrases	phrase	NOUN
ejpam-2753	8	11	:	:	PUNCT
ejpam-2753	8	12	hypervector	hypervector	NOUN
ejpam-2753	8	13	space	space	NOUN
ejpam-2753	8	14	,	,	PUNCT
ejpam-2753	8	15	multivalued	multivalue	VERB
ejpam-2753	8	16	middle	middle	ADJ
ejpam-2753	8	17	linear	linear	PROPN
ejpam-2753	8	18	map	map	NOUN
ejpam-2753	8	19	,	,	PUNCT
ejpam-2753	8	20	quasi	quasi	ADJ
ejpam-2753	8	21	-	-	ADJ
ejpam-2753	8	22	free	free	ADJ
ejpam-2753	8	23	,	,	PUNCT
ejpam-2753	8	24	tensor	tensor	NOUN
ejpam-2753	8	25	product	product	NOUN
ejpam-2753	8	26	1	1	NUM
ejpam-2753	8	27	.	.	PUNCT
ejpam-2753	8	28	introduction	introduction	NOUN
ejpam-2753	8	29	the	the	DET
ejpam-2753	8	30	theory	theory	NOUN
ejpam-2753	8	31	of	of	ADP
ejpam-2753	8	32	algebraic	algebraic	PROPN
ejpam-2753	8	33	hyperstructures	hyperstructure	NOUN
ejpam-2753	8	34	is	be	AUX
ejpam-2753	8	35	a	a	DET
ejpam-2753	8	36	well	well	ADV
ejpam-2753	8	37	-	-	PUNCT
ejpam-2753	8	38	established	establish	VERB
ejpam-2753	8	39	branch	branch	NOUN
ejpam-2753	8	40	of	of	ADP
ejpam-2753	8	41	classical	classical	ADJ
ejpam-2753	8	42	algebraic	algebraic	ADJ
ejpam-2753	8	43	theory	theory	NOUN
ejpam-2753	8	44	.	.	PUNCT
ejpam-2753	9	1	hyperstructure	hyperstructure	PROPN
ejpam-2753	9	2	theory	theory	NOUN
ejpam-2753	9	3	was	be	AUX
ejpam-2753	9	4	first	first	ADV
ejpam-2753	9	5	proposed	propose	VERB
ejpam-2753	9	6	in	in	ADP
ejpam-2753	9	7	1934	1934	NUM
ejpam-2753	9	8	by	by	ADP
ejpam-2753	9	9	marty	marty	PROPN
ejpam-2753	9	10	,	,	PUNCT
ejpam-2753	9	11	who	who	PRON
ejpam-2753	9	12	defined	define	VERB
ejpam-2753	9	13	hypergroups	hypergroup	NOUN
ejpam-2753	9	14	and	and	CCONJ
ejpam-2753	9	15	began	begin	VERB
ejpam-2753	9	16	to	to	PART
ejpam-2753	9	17	investigate	investigate	VERB
ejpam-2753	9	18	their	their	PRON
ejpam-2753	9	19	properties	property	NOUN
ejpam-2753	9	20	with	with	ADP
ejpam-2753	9	21	applications	application	NOUN
ejpam-2753	9	22	to	to	ADP
ejpam-2753	9	23	groups	group	NOUN
ejpam-2753	9	24	,	,	PUNCT
ejpam-2753	9	25	rational	rational	ADJ
ejpam-2753	9	26	fractions	fraction	NOUN
ejpam-2753	9	27	and	and	CCONJ
ejpam-2753	9	28	algebraic	algebraic	ADJ
ejpam-2753	9	29	functions	function	NOUN
ejpam-2753	9	30	[	[	X
ejpam-2753	9	31	19	19	NUM
ejpam-2753	9	32	]	]	PUNCT
ejpam-2753	9	33	.	.	PUNCT
ejpam-2753	10	1	it	it	PRON
ejpam-2753	10	2	was	be	AUX
ejpam-2753	10	3	later	later	ADV
ejpam-2753	10	4	observed	observe	VERB
ejpam-2753	10	5	that	that	SCONJ
ejpam-2753	10	6	the	the	DET
ejpam-2753	10	7	theory	theory	NOUN
ejpam-2753	10	8	of	of	ADP
ejpam-2753	10	9	hyperstructures	hyperstructure	NOUN
ejpam-2753	10	10	has	have	VERB
ejpam-2753	10	11	many	many	ADJ
ejpam-2753	10	12	applications	application	NOUN
ejpam-2753	10	13	in	in	ADP
ejpam-2753	10	14	both	both	CCONJ
ejpam-2753	10	15	pure	pure	ADJ
ejpam-2753	10	16	and	and	CCONJ
ejpam-2753	10	17	applied	applied	ADJ
ejpam-2753	10	18	sciences	science	NOUN
ejpam-2753	10	19	;	;	PUNCT
ejpam-2753	10	20	for	for	ADP
ejpam-2753	10	21	example	example	NOUN
ejpam-2753	10	22	,	,	PUNCT
ejpam-2753	10	23	semihypergroups	semihypergroup	NOUN
ejpam-2753	10	24	are	be	AUX
ejpam-2753	10	25	the	the	DET
ejpam-2753	10	26	simplest	simple	ADJ
ejpam-2753	10	27	algebraic	algebraic	ADJ
ejpam-2753	10	28	hyperstructures	hyperstructure	VERB
ejpam-2753	10	29	that	that	PRON
ejpam-2753	10	30	possess	possess	VERB
ejpam-2753	10	31	the	the	DET
ejpam-2753	10	32	properties	property	NOUN
ejpam-2753	10	33	of	of	ADP
ejpam-2753	10	34	closure	closure	NOUN
ejpam-2753	10	35	and	and	CCONJ
ejpam-2753	10	36	associativity	associativity	NOUN
ejpam-2753	10	37	.	.	PUNCT
ejpam-2753	11	1	the	the	DET
ejpam-2753	11	2	theory	theory	NOUN
ejpam-2753	11	3	of	of	ADP
ejpam-2753	11	4	hyperstructures	hyperstructure	NOUN
ejpam-2753	11	5	has	have	AUX
ejpam-2753	11	6	been	be	AUX
ejpam-2753	11	7	widely	widely	ADV
ejpam-2753	11	8	reviewed	review	VERB
ejpam-2753	11	9	(	(	PUNCT
ejpam-2753	11	10	[	[	X
ejpam-2753	11	11	14	14	NUM
ejpam-2753	11	12	]	]	PUNCT
ejpam-2753	11	13	,	,	PUNCT
ejpam-2753	11	14	[	[	X
ejpam-2753	11	15	15	15	NUM
ejpam-2753	11	16	]	]	PUNCT
ejpam-2753	11	17	,	,	PUNCT
ejpam-2753	12	1	[	[	X
ejpam-2753	12	2	16],[17	16],[17	NUM
ejpam-2753	12	3	]	]	PUNCT
ejpam-2753	12	4	and	and	CCONJ
ejpam-2753	12	5	[	[	X
ejpam-2753	12	6	23	23	NUM
ejpam-2753	12	7	]	]	PUNCT
ejpam-2753	12	8	)	)	PUNCT
ejpam-2753	12	9	(	(	PUNCT
ejpam-2753	12	10	for	for	ADP
ejpam-2753	12	11	more	more	ADJ
ejpam-2753	12	12	see	see	NOUN
ejpam-2753	12	13	[	[	X
ejpam-2753	12	14	1	1	NUM
ejpam-2753	12	15	,	,	PUNCT
ejpam-2753	12	16	2	2	NUM
ejpam-2753	12	17	,	,	PUNCT
ejpam-2753	12	18	3	3	NUM
ejpam-2753	12	19	,	,	PUNCT
ejpam-2753	12	20	6	6	NUM
ejpam-2753	12	21	,	,	PUNCT
ejpam-2753	12	22	5	5	NUM
ejpam-2753	12	23	,	,	PUNCT
ejpam-2753	12	24	4	4	NUM
ejpam-2753	12	25	,	,	PUNCT
ejpam-2753	12	26	7	7	NUM
ejpam-2753	12	27	,	,	PUNCT
ejpam-2753	12	28	8	8	NUM
ejpam-2753	12	29	,	,	PUNCT
ejpam-2753	12	30	9	9	NUM
ejpam-2753	12	31	]	]	NUM
ejpam-2753	12	32	)	)	PUNCT
ejpam-2753	12	33	.	.	PUNCT
ejpam-2753	13	1	m.s	m.s	PROPN
ejpam-2753	13	2	.	.	PROPN
ejpam-2753	13	3	tallini	tallini	PROPN
ejpam-2753	13	4	introduced	introduce	VERB
ejpam-2753	13	5	the	the	DET
ejpam-2753	13	6	notion	notion	NOUN
ejpam-2753	13	7	of	of	ADP
ejpam-2753	13	8	hyperspaces	hyperspace	NOUN
ejpam-2753	13	9	(	(	PUNCT
ejpam-2753	13	10	or	or	CCONJ
ejpam-2753	13	11	hypervector	hypervector	NOUN
ejpam-2753	13	12	spaces	space	NOUN
ejpam-2753	13	13	)	)	PUNCT
ejpam-2753	13	14	(	(	PUNCT
ejpam-2753	14	1	[	[	X
ejpam-2753	14	2	20	20	NUM
ejpam-2753	14	3	]	]	PUNCT
ejpam-2753	14	4	,	,	PUNCT
ejpam-2753	15	1	[	[	X
ejpam-2753	15	2	21	21	NUM
ejpam-2753	15	3	]	]	PUNCT
ejpam-2753	15	4	and	and	CCONJ
ejpam-2753	15	5	[	[	X
ejpam-2753	15	6	22	22	NUM
ejpam-2753	15	7	]	]	PUNCT
ejpam-2753	15	8	)	)	PUNCT
ejpam-2753	15	9	and	and	CCONJ
ejpam-2753	15	10	studied	study	VERB
ejpam-2753	15	11	basic	basic	ADJ
ejpam-2753	15	12	properties	property	NOUN
ejpam-2753	15	13	of	of	ADP
ejpam-2753	15	14	them	they	PRON
ejpam-2753	15	15	.	.	PUNCT
ejpam-2753	16	1	r.	r.	PROPN
ejpam-2753	16	2	ameri	ameri	PROPN
ejpam-2753	16	3	and	and	CCONJ
ejpam-2753	16	4	o.	o.	PROPN
ejpam-2753	16	5	r.	r.	PROPN
ejpam-2753	16	6	dehghan	dehghan	PROPN
ejpam-2753	16	7	introduced	introduce	VERB
ejpam-2753	16	8	and	and	CCONJ
ejpam-2753	16	9	studied	study	VERB
ejpam-2753	16	10	dimension	dimension	NOUN
ejpam-2753	16	11	of	of	ADP
ejpam-2753	16	12	hyperspaces	hyperspace	NOUN
ejpam-2753	16	13	[	[	X
ejpam-2753	16	14	2	2	NUM
ejpam-2753	16	15	]	]	PUNCT
ejpam-2753	16	16	.	.	PUNCT
ejpam-2753	17	1	r.	r.	PROPN
ejpam-2753	17	2	ameri	ameri	PROPN
ejpam-2753	17	3	in	in	ADP
ejpam-2753	17	4	[	[	X
ejpam-2753	17	5	1	1	NUM
ejpam-2753	17	6	]	]	PUNCT
ejpam-2753	17	7	introduced	introduce	VERB
ejpam-2753	17	8	and	and	CCONJ
ejpam-2753	17	9	studied	study	VERB
ejpam-2753	17	10	categories	category	NOUN
ejpam-2753	17	11	of	of	ADP
ejpam-2753	17	12	hypermodules	hypermodule	NOUN
ejpam-2753	17	13	.	.	PUNCT
ejpam-2753	18	1	let	let	VERB
ejpam-2753	18	2	v	v	NOUN
ejpam-2753	18	3	and	and	CCONJ
ejpam-2753	18	4	w	w	NOUN
ejpam-2753	18	5	be	be	AUX
ejpam-2753	18	6	two	two	NUM
ejpam-2753	18	7	hyperspaces	hyperspace	NOUN
ejpam-2753	18	8	over	over	ADP
ejpam-2753	18	9	the	the	DET
ejpam-2753	18	10	fixed	fix	VERB
ejpam-2753	18	11	filed	file	VERB
ejpam-2753	18	12	k	k	PROPN
ejpam-2753	18	13	(	(	PUNCT
ejpam-2753	18	14	of	of	ADP
ejpam-2753	18	15	real	real	ADJ
ejpam-2753	18	16	or	or	CCONJ
ejpam-2753	18	17	complex	complex	ADJ
ejpam-2753	18	18	numbers	number	NOUN
ejpam-2753	18	19	)	)	PUNCT
ejpam-2753	18	20	.	.	PUNCT
ejpam-2753	19	1	the	the	DET
ejpam-2753	19	2	purpose	purpose	NOUN
ejpam-2753	19	3	of	of	ADP
ejpam-2753	19	4	this	this	DET
ejpam-2753	19	5	paper	paper	NOUN
ejpam-2753	19	6	is	be	AUX
ejpam-2753	19	7	the	the	DET
ejpam-2753	19	8	study	study	NOUN
ejpam-2753	19	9	of	of	ADP
ejpam-2753	19	10	tensor	tensor	NOUN
ejpam-2753	19	11	product	product	NOUN
ejpam-2753	19	12	of	of	ADP
ejpam-2753	19	13	hypervector	hypervector	NOUN
ejpam-2753	19	14	spaces	space	NOUN
ejpam-2753	19	15	on	on	ADP
ejpam-2753	19	16	the	the	DET
ejpam-2753	19	17	sense	sense	NOUN
ejpam-2753	19	18	of	of	ADP
ejpam-2753	19	19	tallini	tallini	NOUN
ejpam-2753	19	20	.	.	PUNCT
ejpam-2753	20	1	we	we	PRON
ejpam-2753	20	2	introduce	introduce	VERB
ejpam-2753	20	3	the	the	DET
ejpam-2753	20	4	category	category	NOUN
ejpam-2753	20	5	of	of	ADP
ejpam-2753	20	6	multivalued	multivalue	VERB
ejpam-2753	20	7	linear	linear	ADJ
ejpam-2753	20	8	maps	map	NOUN
ejpam-2753	20	9	of	of	ADP
ejpam-2753	20	10	hyperspaces	hyperspace	NOUN
ejpam-2753	20	11	and	and	CCONJ
ejpam-2753	20	12	then	then	ADV
ejpam-2753	20	13	construct	construct	VERB
ejpam-2753	20	14	the	the	DET
ejpam-2753	20	15	tensor	tensor	NOUN
ejpam-2753	20	16	product	product	NOUN
ejpam-2753	20	17	of	of	ADP
ejpam-2753	20	18	v	v	NOUN
ejpam-2753	20	19	and	and	CCONJ
ejpam-2753	20	20	w	w	NOUN
ejpam-2753	20	21	as	as	ADP
ejpam-2753	20	22	initial	initial	ADJ
ejpam-2753	20	23	object	object	NOUN
ejpam-2753	20	24	in	in	ADP
ejpam-2753	20	25	this	this	DET
ejpam-2753	20	26	category	category	NOUN
ejpam-2753	20	27	.	.	PUNCT
ejpam-2753	21	1	∗corresponding	∗corresponde	VERB
ejpam-2753	21	2	author	author	NOUN
ejpam-2753	21	3	.	.	PUNCT
ejpam-2753	22	1	email	email	NOUN
ejpam-2753	22	2	addresses	address	NOUN
ejpam-2753	22	3	:	:	PUNCT
ejpam-2753	22	4	rameri@ut.ac.ir	rameri@ut.ac.ir	PROPN
ejpam-2753	22	5	(	(	PUNCT
ejpam-2753	22	6	r.	r.	PROPN
ejpam-2753	22	7	ameri	ameri	PROPN
ejpam-2753	22	8	)	)	PUNCT
ejpam-2753	22	9	,	,	PUNCT
ejpam-2753	22	10	ghadimi@phd.pnu.ac.ir	ghadimi@phd.pnu.ac.ir	NOUN
ejpam-2753	22	11	(	(	PUNCT
ejpam-2753	22	12	k.	k.	PROPN
ejpam-2753	22	13	ghadimi	ghadimi	PROPN
ejpam-2753	22	14	)	)	PUNCT
ejpam-2753	22	15	,	,	PUNCT
ejpam-2753	22	16	borzooei@sbu.ac.ir	borzooei@sbu.ac.ir	NOUN
ejpam-2753	22	17	(	(	PUNCT
ejpam-2753	22	18	r.	r.	PROPN
ejpam-2753	22	19	a.	a.	PROPN
ejpam-2753	22	20	borzooei	borzooei	PROPN
ejpam-2753	22	21	)	)	PUNCT
ejpam-2753	22	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2753	23	1	702	702	NUM
ejpam-2753	23	2	c	c	NOUN
ejpam-2753	23	3	©	©	PROPN
ejpam-2753	23	4	2017	2017	NUM
ejpam-2753	23	5	ejpam	ejpam	NOUN
ejpam-2753	23	6	all	all	DET
ejpam-2753	23	7	rights	right	NOUN
ejpam-2753	23	8	reserved	reserve	VERB
ejpam-2753	23	9	.	.	PUNCT
ejpam-2753	24	1	r.	r.	PROPN
ejpam-2753	24	2	ameri	ameri	PROPN
ejpam-2753	24	3	,	,	PUNCT
ejpam-2753	24	4	k.	k.	PROPN
ejpam-2753	24	5	ghadimi	ghadimi	PROPN
ejpam-2753	24	6	,	,	PUNCT
ejpam-2753	24	7	r.	r.	PROPN
ejpam-2753	24	8	a.	a.	PROPN
ejpam-2753	24	9	borzooei	borzooei	PROPN
ejpam-2753	24	10	/	/	SYM
ejpam-2753	24	11	eur	eur	PROPN
ejpam-2753	24	12	.	.	PUNCT
ejpam-2753	25	1	j.	j.	PROPN
ejpam-2753	25	2	pure	pure	PROPN
ejpam-2753	25	3	appl	appl	PROPN
ejpam-2753	25	4	.	.	PROPN
ejpam-2753	25	5	math	math	PROPN
ejpam-2753	25	6	,	,	PUNCT
ejpam-2753	25	7	10	10	NUM
ejpam-2753	25	8	(	(	PUNCT
ejpam-2753	25	9	4	4	NUM
ejpam-2753	25	10	)	)	PUNCT
ejpam-2753	25	11	(	(	PUNCT
ejpam-2753	25	12	2017	2017	NUM
ejpam-2753	25	13	)	)	PUNCT
ejpam-2753	25	14	,	,	PUNCT
ejpam-2753	25	15	702	702	NUM
ejpam-2753	25	16	-	-	SYM
ejpam-2753	25	17	716	716	NUM
ejpam-2753	25	18	703	703	NUM
ejpam-2753	25	19	2	2	NUM
ejpam-2753	25	20	.	.	PUNCT
ejpam-2753	25	21	preliminaries	preliminary	NOUN
ejpam-2753	25	22	which	which	PRON
ejpam-2753	25	23	we	we	PRON
ejpam-2753	25	24	need	need	VERB
ejpam-2753	25	25	to	to	PART
ejpam-2753	25	26	develop	develop	VERB
ejpam-2753	25	27	our	our	PRON
ejpam-2753	25	28	paper	paper	NOUN
ejpam-2753	25	29	.	.	PUNCT
ejpam-2753	26	1	definition	definition	NOUN
ejpam-2753	26	2	1	1	NUM
ejpam-2753	26	3	.	.	PUNCT
ejpam-2753	27	1	let	let	VERB
ejpam-2753	27	2	h	h	PRON
ejpam-2753	27	3	be	be	AUX
ejpam-2753	27	4	a	a	DET
ejpam-2753	27	5	nonempty	nonempty	ADV
ejpam-2753	27	6	set	set	VERB
ejpam-2753	27	7	.	.	PUNCT
ejpam-2753	28	1	a	a	DET
ejpam-2753	28	2	map	map	NOUN
ejpam-2753	28	3	·	·	PUNCT
ejpam-2753	28	4	:	:	PUNCT
ejpam-2753	28	5	h	h	NOUN
ejpam-2753	28	6	×h	×h	VERB
ejpam-2753	28	7	−→	−→	ADJ
ejpam-2753	28	8	p	p	PROPN
ejpam-2753	28	9	∗(h	∗(h	PROPN
ejpam-2753	28	10	)	)	PUNCT
ejpam-2753	28	11	is	be	AUX
ejpam-2753	28	12	called	call	VERB
ejpam-2753	28	13	hyperoperation	hyperoperation	NOUN
ejpam-2753	28	14	or	or	CCONJ
ejpam-2753	28	15	join	join	VERB
ejpam-2753	28	16	operation	operation	NOUN
ejpam-2753	28	17	,	,	PUNCT
ejpam-2753	28	18	where	where	SCONJ
ejpam-2753	28	19	p	p	PROPN
ejpam-2753	28	20	∗(h	∗(h	PROPN
ejpam-2753	28	21	)	)	PUNCT
ejpam-2753	28	22	is	be	AUX
ejpam-2753	28	23	the	the	DET
ejpam-2753	28	24	set	set	NOUN
ejpam-2753	28	25	of	of	ADP
ejpam-2753	28	26	all	all	DET
ejpam-2753	28	27	nonempty	nonempty	ADJ
ejpam-2753	28	28	subsets	subset	NOUN
ejpam-2753	28	29	of	of	ADP
ejpam-2753	28	30	h.	h.	PROPN
ejpam-2753	28	31	the	the	DET
ejpam-2753	28	32	join	join	NOUN
ejpam-2753	28	33	operation	operation	NOUN
ejpam-2753	28	34	is	be	AUX
ejpam-2753	28	35	extended	extend	VERB
ejpam-2753	28	36	to	to	ADP
ejpam-2753	28	37	nonempty	nonempty	VERB
ejpam-2753	28	38	subsets	subset	NOUN
ejpam-2753	28	39	of	of	ADP
ejpam-2753	28	40	h	h	NOUN
ejpam-2753	28	41	in	in	ADP
ejpam-2753	28	42	natural	natural	ADJ
ejpam-2753	28	43	way	way	NOUN
ejpam-2753	28	44	,	,	PUNCT
ejpam-2753	28	45	so	so	SCONJ
ejpam-2753	28	46	that	that	SCONJ
ejpam-2753	28	47	a	a	DET
ejpam-2753	28	48	·	·	SYM
ejpam-2753	28	49	b	b	NOUN
ejpam-2753	28	50	is	be	AUX
ejpam-2753	28	51	given	give	VERB
ejpam-2753	28	52	by	by	ADP
ejpam-2753	28	53	a	a	DET
ejpam-2753	28	54	·	·	SYM
ejpam-2753	28	55	b	b	NOUN
ejpam-2753	28	56	=	=	PUNCT
ejpam-2753	28	57	⋃	⋃	NOUN
ejpam-2753	28	58	{	{	PUNCT
ejpam-2753	28	59	a	a	DET
ejpam-2753	28	60	·	·	PUNCT
ejpam-2753	28	61	b	b	NOUN
ejpam-2753	28	62	|	|	ADV
ejpam-2753	28	63	a	a	DET
ejpam-2753	28	64	∈	∈	PROPN
ejpam-2753	28	65	a	a	PRON
ejpam-2753	28	66	and	and	CCONJ
ejpam-2753	28	67	b	b	NOUN
ejpam-2753	28	68	∈	∈	PROPN
ejpam-2753	28	69	b	b	NOUN
ejpam-2753	28	70	}	}	PUNCT
ejpam-2753	28	71	.	.	PUNCT
ejpam-2753	29	1	the	the	DET
ejpam-2753	29	2	notations	notation	NOUN
ejpam-2753	29	3	a	a	DET
ejpam-2753	29	4	·	·	PUNCT
ejpam-2753	29	5	a	a	PRON
ejpam-2753	29	6	and	and	CCONJ
ejpam-2753	29	7	a	a	PRON
ejpam-2753	29	8	·	·	PUNCT
ejpam-2753	29	9	a	a	PRON
ejpam-2753	29	10	are	be	AUX
ejpam-2753	29	11	used	use	VERB
ejpam-2753	29	12	for	for	ADP
ejpam-2753	29	13	{	{	PUNCT
ejpam-2753	29	14	a	a	PRON
ejpam-2753	29	15	}	}	PUNCT
ejpam-2753	29	16	·	·	PUNCT
ejpam-2753	29	17	a	a	PRON
ejpam-2753	29	18	and	and	CCONJ
ejpam-2753	29	19	a	a	PRON
ejpam-2753	29	20	·	·	PUNCT
ejpam-2753	29	21	{	{	PUNCT
ejpam-2753	29	22	a	a	NOUN
ejpam-2753	29	23	}	}	PUNCT
ejpam-2753	29	24	respectively	respectively	ADV
ejpam-2753	29	25	.	.	PUNCT
ejpam-2753	30	1	generally	generally	ADV
ejpam-2753	30	2	,	,	PUNCT
ejpam-2753	30	3	the	the	DET
ejpam-2753	30	4	singleton	singleton	NOUN
ejpam-2753	30	5	{	{	PUNCT
ejpam-2753	30	6	a	a	PRON
ejpam-2753	30	7	}	}	PUNCT
ejpam-2753	30	8	is	be	AUX
ejpam-2753	30	9	identified	identify	VERB
ejpam-2753	30	10	by	by	ADP
ejpam-2753	30	11	its	its	PRON
ejpam-2753	30	12	element	element	NOUN
ejpam-2753	30	13	a.	a.	NOUN
ejpam-2753	30	14	definition	definition	NOUN
ejpam-2753	30	15	2	2	NUM
ejpam-2753	30	16	.	.	PUNCT
ejpam-2753	31	1	[	[	X
ejpam-2753	31	2	14	14	NUM
ejpam-2753	31	3	]	]	PUNCT
ejpam-2753	31	4	a	a	DET
ejpam-2753	31	5	hypergroup	hypergroup	NOUN
ejpam-2753	31	6	is	be	AUX
ejpam-2753	31	7	a	a	DET
ejpam-2753	31	8	nonempty	nonempty	ADV
ejpam-2753	31	9	set	set	VERB
ejpam-2753	31	10	h	h	NOUN
ejpam-2753	31	11	equipped	equip	VERB
ejpam-2753	31	12	with	with	ADP
ejpam-2753	31	13	an	an	DET
ejpam-2753	31	14	associative	associative	ADJ
ejpam-2753	31	15	hyperoperation	hyperoperation	NOUN
ejpam-2753	31	16	·	·	PUNCT
ejpam-2753	31	17	:	:	PUNCT
ejpam-2753	32	1	h	h	NOUN
ejpam-2753	32	2	×h	×h	VERB
ejpam-2753	33	1	−→	−→	ADJ
ejpam-2753	33	2	p	p	PROPN
ejpam-2753	33	3	∗(h	∗(h	PROPN
ejpam-2753	33	4	)	)	PUNCT
ejpam-2753	33	5	which	which	PRON
ejpam-2753	33	6	satisfies	satisfy	VERB
ejpam-2753	33	7	the	the	DET
ejpam-2753	33	8	property	property	NOUN
ejpam-2753	33	9	x	x	PUNCT
ejpam-2753	33	10	·	·	PUNCT
ejpam-2753	33	11	h	h	NOUN
ejpam-2753	33	12	=	=	NOUN
ejpam-2753	33	13	h	h	NOUN
ejpam-2753	33	14	·	·	PUNCT
ejpam-2753	33	15	x	x	PUNCT
ejpam-2753	34	1	=	=	SYM
ejpam-2753	34	2	h	h	NOUN
ejpam-2753	34	3	,	,	PUNCT
ejpam-2753	34	4	for	for	ADP
ejpam-2753	34	5	all	all	DET
ejpam-2753	34	6	x	x	SYM
ejpam-2753	34	7	∈	∈	PROPN
ejpam-2753	34	8	h.	h.	NOUN
ejpam-2753	34	9	if	if	SCONJ
ejpam-2753	34	10	the	the	DET
ejpam-2753	34	11	hyperoperation	hyperoperation	NOUN
ejpam-2753	34	12	·	·	PUNCT
ejpam-2753	34	13	is	be	AUX
ejpam-2753	34	14	associative	associative	ADJ
ejpam-2753	34	15	then	then	ADV
ejpam-2753	34	16	h	h	NOUN
ejpam-2753	34	17	is	be	AUX
ejpam-2753	34	18	called	call	VERB
ejpam-2753	34	19	a	a	DET
ejpam-2753	34	20	semihypergroup	semihypergroup	NOUN
ejpam-2753	34	21	.	.	PUNCT
ejpam-2753	35	1	a	a	DET
ejpam-2753	35	2	quasicanonical	quasicanonical	ADJ
ejpam-2753	35	3	hypergroup	hypergroup	NOUN
ejpam-2753	35	4	is	be	AUX
ejpam-2753	35	5	a	a	DET
ejpam-2753	35	6	special	special	ADJ
ejpam-2753	35	7	kind	kind	NOUN
ejpam-2753	35	8	of	of	ADP
ejpam-2753	35	9	a	a	DET
ejpam-2753	35	10	hypergroup	hypergroup	NOUN
ejpam-2753	35	11	,	,	PUNCT
ejpam-2753	35	12	that	that	SCONJ
ejpam-2753	35	13	first	first	ADJ
ejpam-2753	35	14	time	time	NOUN
ejpam-2753	35	15	introduced	introduce	VERB
ejpam-2753	35	16	and	and	CCONJ
ejpam-2753	35	17	studied	study	VERB
ejpam-2753	35	18	by	by	ADP
ejpam-2753	35	19	bonansinga	bonansinga	NOUN
ejpam-2753	35	20	and	and	CCONJ
ejpam-2753	35	21	corsini	corsini	ADJ
ejpam-2753	35	22	in	in	ADP
ejpam-2753	35	23	[	[	X
ejpam-2753	35	24	10	10	NUM
ejpam-2753	35	25	,	,	PUNCT
ejpam-2753	35	26	11	11	NUM
ejpam-2753	35	27	]	]	PUNCT
ejpam-2753	35	28	.	.	PUNCT
ejpam-2753	36	1	after	after	ADP
ejpam-2753	36	2	that	that	PRON
ejpam-2753	36	3	this	this	DET
ejpam-2753	36	4	kind	kind	NOUN
ejpam-2753	36	5	of	of	ADP
ejpam-2753	36	6	hypergroups	hypergroup	NOUN
ejpam-2753	36	7	studied	study	VERB
ejpam-2753	36	8	by	by	ADP
ejpam-2753	36	9	comer	comer	NOUN
ejpam-2753	36	10	[	[	X
ejpam-2753	36	11	13	13	NUM
ejpam-2753	36	12	,	,	PUNCT
ejpam-2753	36	13	12	12	NUM
ejpam-2753	36	14	]	]	PUNCT
ejpam-2753	36	15	as	as	ADP
ejpam-2753	36	16	the	the	DET
ejpam-2753	36	17	name	name	NOUN
ejpam-2753	36	18	of	of	ADP
ejpam-2753	36	19	polygroups	polygroup	NOUN
ejpam-2753	36	20	.	.	PUNCT
ejpam-2753	37	1	definition	definition	NOUN
ejpam-2753	37	2	3	3	NUM
ejpam-2753	37	3	.	.	PUNCT
ejpam-2753	38	1	[	[	X
ejpam-2753	38	2	14	14	NUM
ejpam-2753	38	3	,	,	PUNCT
ejpam-2753	38	4	16	16	NUM
ejpam-2753	38	5	]	]	PUNCT
ejpam-2753	38	6	a	a	DET
ejpam-2753	38	7	polygroup	polygroup	NOUN
ejpam-2753	38	8	is	be	AUX
ejpam-2753	38	9	a	a	DET
ejpam-2753	38	10	system	system	NOUN
ejpam-2753	38	11	p	p	NOUN
ejpam-2753	38	12	=	=	PUNCT
ejpam-2753	38	13	〈	〈	PROPN
ejpam-2753	38	14	p	p	NOUN
ejpam-2753	38	15	,	,	PUNCT
ejpam-2753	38	16	·	·	PUNCT
ejpam-2753	38	17	,	,	PUNCT
ejpam-2753	38	18	e,−1	e,−1	PROPN
ejpam-2753	38	19	〉	〉	PROPN
ejpam-2753	38	20	,	,	PUNCT
ejpam-2753	38	21	where	where	SCONJ
ejpam-2753	38	22	e	e	PROPN
ejpam-2753	38	23	∈	∈	PROPN
ejpam-2753	38	24	p	p	PROPN
ejpam-2753	38	25	,	,	PUNCT
ejpam-2753	38	26	−1	−1	NOUN
ejpam-2753	38	27	is	be	AUX
ejpam-2753	38	28	a	a	DET
ejpam-2753	38	29	unary	unary	ADJ
ejpam-2753	38	30	operation	operation	NOUN
ejpam-2753	38	31	on	on	ADP
ejpam-2753	38	32	p	p	PROPN
ejpam-2753	38	33	,	,	PUNCT
ejpam-2753	38	34	·	·	PUNCT
ejpam-2753	38	35	maps	map	VERB
ejpam-2753	38	36	p	p	NOUN
ejpam-2753	38	37	×p	×p	NOUN
ejpam-2753	38	38	into	into	ADP
ejpam-2753	38	39	nonempty	nonempty	ADJ
ejpam-2753	38	40	subsets	subset	NOUN
ejpam-2753	38	41	of	of	ADP
ejpam-2753	38	42	p	p	NOUN
ejpam-2753	38	43	,	,	PUNCT
ejpam-2753	38	44	and	and	CCONJ
ejpam-2753	38	45	the	the	DET
ejpam-2753	38	46	following	following	ADJ
ejpam-2753	38	47	axioms	axiom	NOUN
ejpam-2753	38	48	hold	hold	VERB
ejpam-2753	38	49	for	for	ADP
ejpam-2753	38	50	all	all	DET
ejpam-2753	38	51	x	x	NOUN
ejpam-2753	38	52	,	,	PUNCT
ejpam-2753	38	53	y	y	PROPN
ejpam-2753	38	54	,	,	PUNCT
ejpam-2753	38	55	z	z	PROPN
ejpam-2753	38	56	∈	∈	PROPN
ejpam-2753	38	57	p	p	X
ejpam-2753	38	58	:	:	PUNCT
ejpam-2753	38	59	(	(	PUNCT
ejpam-2753	38	60	p1	p1	NOUN
ejpam-2753	38	61	)	)	PUNCT
ejpam-2753	38	62	(	(	PUNCT
ejpam-2753	38	63	x	x	X
ejpam-2753	38	64	·	·	PUNCT
ejpam-2753	38	65	y	y	X
ejpam-2753	38	66	)	)	PUNCT
ejpam-2753	38	67	·	·	PUNCT
ejpam-2753	39	1	z	z	X
ejpam-2753	39	2	=	=	PUNCT
ejpam-2753	39	3	x	x	SYM
ejpam-2753	39	4	·	·	PUNCT
ejpam-2753	39	5	(	(	PUNCT
ejpam-2753	39	6	y	y	PROPN
ejpam-2753	39	7	·	·	PUNCT
ejpam-2753	39	8	z	z	X
ejpam-2753	39	9	)	)	PUNCT
ejpam-2753	39	10	;	;	PUNCT
ejpam-2753	39	11	(	(	PUNCT
ejpam-2753	39	12	p2	p2	X
ejpam-2753	39	13	)	)	PUNCT
ejpam-2753	39	14	x	x	X
ejpam-2753	39	15	·	·	PUNCT
ejpam-2753	39	16	e	e	X
ejpam-2753	39	17	=	=	SYM
ejpam-2753	39	18	e	e	X
ejpam-2753	39	19	·	·	PUNCT
ejpam-2753	39	20	x	x	SYM
ejpam-2753	39	21	=	=	SYM
ejpam-2753	39	22	x	x	X
ejpam-2753	39	23	;	;	PUNCT
ejpam-2753	39	24	(	(	PUNCT
ejpam-2753	39	25	p3	p3	NOUN
ejpam-2753	39	26	)	)	PUNCT
ejpam-2753	39	27	x	x	PUNCT
ejpam-2753	39	28	∈	∈	PROPN
ejpam-2753	39	29	y	y	PROPN
ejpam-2753	39	30	·	·	PUNCT
ejpam-2753	39	31	z	z	PROPN
ejpam-2753	39	32	implies	imply	VERB
ejpam-2753	39	33	y	y	PROPN
ejpam-2753	39	34	∈	∈	PROPN
ejpam-2753	39	35	x	x	PUNCT
ejpam-2753	39	36	·	·	PUNCT
ejpam-2753	39	37	z−1	z−1	ADJ
ejpam-2753	39	38	and	and	CCONJ
ejpam-2753	39	39	z	z	NOUN
ejpam-2753	39	40	∈	∈	PROPN
ejpam-2753	39	41	y−1	y−1	PROPN
ejpam-2753	39	42	·	·	PUNCT
ejpam-2753	39	43	x.	x.	NOUN
ejpam-2753	40	1	the	the	DET
ejpam-2753	40	2	following	follow	VERB
ejpam-2753	40	3	elementary	elementary	ADJ
ejpam-2753	40	4	facts	fact	NOUN
ejpam-2753	40	5	about	about	ADP
ejpam-2753	40	6	polygroups	polygroup	NOUN
ejpam-2753	40	7	follow	follow	VERB
ejpam-2753	40	8	easily	easily	ADV
ejpam-2753	40	9	from	from	ADP
ejpam-2753	40	10	the	the	DET
ejpam-2753	40	11	axioms	axiom	NOUN
ejpam-2753	40	12	:	:	PUNCT
ejpam-2753	40	13	e	e	X
ejpam-2753	40	14	∈	∈	PROPN
ejpam-2753	40	15	x·x−1∩x−1·x	x·x−1∩x−1·x	PROPN
ejpam-2753	40	16	,	,	PUNCT
ejpam-2753	40	17	e−1	e−1	PROPN
ejpam-2753	40	18	=	=	SYM
ejpam-2753	40	19	e	e	PROPN
ejpam-2753	40	20	,	,	PUNCT
ejpam-2753	40	21	(	(	PUNCT
ejpam-2753	40	22	x−1)−1	x−1)−1	X
ejpam-2753	40	23	=	=	SYM
ejpam-2753	40	24	x	x	NOUN
ejpam-2753	40	25	,	,	PUNCT
ejpam-2753	40	26	and	and	CCONJ
ejpam-2753	40	27	(	(	PUNCT
ejpam-2753	40	28	x·y)−1	x·y)−1	X
ejpam-2753	40	29	=	=	SYM
ejpam-2753	40	30	y−1·x−1	y−1·x−1	PROPN
ejpam-2753	40	31	,	,	PUNCT
ejpam-2753	40	32	where	where	SCONJ
ejpam-2753	40	33	a−1	a−1	PROPN
ejpam-2753	40	34	=	=	PRON
ejpam-2753	40	35	{	{	PUNCT
ejpam-2753	40	36	a−1	a−1	PROPN
ejpam-2753	40	37	|	|	ADV
ejpam-2753	40	38	a	a	DET
ejpam-2753	40	39	∈	∈	PROPN
ejpam-2753	40	40	a	a	PRON
ejpam-2753	40	41	}	}	PUNCT
ejpam-2753	40	42	.	.	PUNCT
ejpam-2753	41	1	a	a	DET
ejpam-2753	41	2	polygroup	polygroup	NOUN
ejpam-2753	41	3	in	in	ADP
ejpam-2753	41	4	which	which	PRON
ejpam-2753	41	5	every	every	DET
ejpam-2753	41	6	element	element	NOUN
ejpam-2753	41	7	has	have	VERB
ejpam-2753	41	8	order	order	NOUN
ejpam-2753	41	9	2	2	NUM
ejpam-2753	41	10	(	(	PUNCT
ejpam-2753	41	11	i.e.	i.e.	X
ejpam-2753	41	12	,	,	PUNCT
ejpam-2753	41	13	x−1	x−1	PUNCT
ejpam-2753	41	14	=	=	PUNCT
ejpam-2753	41	15	x	x	PROPN
ejpam-2753	41	16	for	for	ADP
ejpam-2753	41	17	all	all	DET
ejpam-2753	41	18	x	x	NOUN
ejpam-2753	41	19	)	)	PUNCT
ejpam-2753	41	20	is	be	AUX
ejpam-2753	41	21	called	call	VERB
ejpam-2753	41	22	symmetric	symmetric	ADJ
ejpam-2753	41	23	.	.	PUNCT
ejpam-2753	42	1	as	as	ADP
ejpam-2753	42	2	in	in	ADP
ejpam-2753	42	3	group	group	NOUN
ejpam-2753	42	4	theory	theory	NOUN
ejpam-2753	42	5	it	it	PRON
ejpam-2753	42	6	can	can	AUX
ejpam-2753	42	7	be	be	AUX
ejpam-2753	42	8	shown	show	VERB
ejpam-2753	42	9	that	that	SCONJ
ejpam-2753	42	10	a	a	DET
ejpam-2753	42	11	symmetric	symmetric	ADJ
ejpam-2753	42	12	polygroup	polygroup	NOUN
ejpam-2753	42	13	is	be	AUX
ejpam-2753	42	14	commutative	commutative	ADJ
ejpam-2753	42	15	.	.	PUNCT
ejpam-2753	43	1	definition	definition	NOUN
ejpam-2753	43	2	4	4	NUM
ejpam-2753	43	3	.	.	PUNCT
ejpam-2753	44	1	[	[	X
ejpam-2753	44	2	15	15	NUM
ejpam-2753	44	3	]	]	X
ejpam-2753	44	4	a	a	DET
ejpam-2753	44	5	semihypergroup	semihypergroup	NOUN
ejpam-2753	44	6	(	(	PUNCT
ejpam-2753	44	7	h,+	h,+	PROPN
ejpam-2753	44	8	)	)	PUNCT
ejpam-2753	44	9	is	be	AUX
ejpam-2753	44	10	called	call	VERB
ejpam-2753	44	11	a	a	DET
ejpam-2753	44	12	canonical	canonical	ADJ
ejpam-2753	44	13	hypergroup	hypergroup	NOUN
ejpam-2753	44	14	if	if	SCONJ
ejpam-2753	44	15	the	the	DET
ejpam-2753	44	16	following	follow	VERB
ejpam-2753	44	17	conditions	condition	NOUN
ejpam-2753	44	18	are	be	AUX
ejpam-2753	44	19	satisfied	satisfied	ADJ
ejpam-2753	44	20	:	:	PUNCT
ejpam-2753	44	21	(	(	PUNCT
ejpam-2753	44	22	i	i	NOUN
ejpam-2753	44	23	)	)	PUNCT
ejpam-2753	44	24	x+	x+	PUNCT
ejpam-2753	45	1	y	y	NOUN
ejpam-2753	45	2	=	=	SYM
ejpam-2753	45	3	y	y	PROPN
ejpam-2753	46	1	+	+	CCONJ
ejpam-2753	46	2	x	x	X
ejpam-2753	46	3	for	for	ADP
ejpam-2753	46	4	all	all	DET
ejpam-2753	46	5	x	x	NOUN
ejpam-2753	46	6	,	,	PUNCT
ejpam-2753	46	7	y	y	PROPN
ejpam-2753	46	8	∈	∈	PROPN
ejpam-2753	46	9	r	r	NOUN
ejpam-2753	46	10	;	;	PUNCT
ejpam-2753	46	11	(	(	PUNCT
ejpam-2753	46	12	ii	ii	NOUN
ejpam-2753	46	13	)	)	PUNCT
ejpam-2753	46	14	there	there	PRON
ejpam-2753	46	15	exists	exist	VERB
ejpam-2753	46	16	0	0	NUM
ejpam-2753	46	17	∈	∈	PROPN
ejpam-2753	46	18	r	r	NOUN
ejpam-2753	46	19	(	(	PUNCT
ejpam-2753	46	20	unique	unique	ADJ
ejpam-2753	46	21	)	)	PUNCT
ejpam-2753	46	22	such	such	ADJ
ejpam-2753	46	23	that	that	PRON
ejpam-2753	46	24	for	for	ADP
ejpam-2753	46	25	every	every	DET
ejpam-2753	46	26	x	x	SYM
ejpam-2753	46	27	∈	∈	PROPN
ejpam-2753	46	28	r	r	NOUN
ejpam-2753	46	29	,	,	PUNCT
ejpam-2753	46	30	x	x	SYM
ejpam-2753	46	31	∈	∈	NOUN
ejpam-2753	46	32	0	0	PUNCT
ejpam-2753	47	1	+	+	CCONJ
ejpam-2753	47	2	x	x	SYM
ejpam-2753	47	3	=	=	SYM
ejpam-2753	47	4	x	x	X
ejpam-2753	47	5	;	;	PUNCT
ejpam-2753	47	6	(	(	PUNCT
ejpam-2753	47	7	iii	iii	NOUN
ejpam-2753	47	8	)	)	PUNCT
ejpam-2753	47	9	for	for	ADP
ejpam-2753	47	10	every	every	DET
ejpam-2753	47	11	x	x	SYM
ejpam-2753	47	12	∈	∈	PROPN
ejpam-2753	47	13	r	r	NOUN
ejpam-2753	47	14	,	,	PUNCT
ejpam-2753	47	15	there	there	PRON
ejpam-2753	47	16	exists	exist	VERB
ejpam-2753	47	17	a	a	DET
ejpam-2753	47	18	unique	unique	ADJ
ejpam-2753	47	19	element	element	NOUN
ejpam-2753	47	20	,	,	PUNCT
ejpam-2753	47	21	say	say	VERB
ejpam-2753	47	22	x′	x′	PROPN
ejpam-2753	48	1	such	such	ADJ
ejpam-2753	48	2	that	that	DET
ejpam-2753	48	3	0	0	NUM
ejpam-2753	48	4	∈	∈	NOUN
ejpam-2753	48	5	x	x	X
ejpam-2753	49	1	+	+	NUM
ejpam-2753	49	2	x′	x′	PROPN
ejpam-2753	49	3	(	(	PUNCT
ejpam-2753	49	4	we	we	PRON
ejpam-2753	49	5	denote	denote	VERB
ejpam-2753	49	6	x′	x′	PROPN
ejpam-2753	49	7	=	=	PUNCT
ejpam-2753	49	8	−x	−x	NOUN
ejpam-2753	49	9	)	)	PUNCT
ejpam-2753	49	10	;	;	PUNCT
ejpam-2753	49	11	(	(	PUNCT
ejpam-2753	49	12	iv	iv	X
ejpam-2753	49	13	)	)	PUNCT
ejpam-2753	49	14	for	for	ADP
ejpam-2753	49	15	every	every	DET
ejpam-2753	49	16	x	x	PROPN
ejpam-2753	49	17	,	,	PUNCT
ejpam-2753	49	18	y	y	PROPN
ejpam-2753	49	19	,	,	PUNCT
ejpam-2753	49	20	z	z	NOUN
ejpam-2753	49	21	∈	∈	PROPN
ejpam-2753	49	22	r	r	NOUN
ejpam-2753	49	23	,	,	PUNCT
ejpam-2753	49	24	z	z	NOUN
ejpam-2753	49	25	∈	∈	PROPN
ejpam-2753	49	26	x+	x+	NUM
ejpam-2753	49	27	y	y	PROPN
ejpam-2753	49	28	⇐	⇐	PROPN
ejpam-2753	49	29	⇒	⇒	PROPN
ejpam-2753	49	30	x	x	SYM
ejpam-2753	50	1	∈	∈	PROPN
ejpam-2753	50	2	z	z	NOUN
ejpam-2753	50	3	−	−	PROPN
ejpam-2753	50	4	y	y	PROPN
ejpam-2753	50	5	⇐	⇐	PROPN
ejpam-2753	50	6	⇒	⇒	PROPN
ejpam-2753	50	7	y	y	PROPN
ejpam-2753	50	8	∈	∈	PROPN
ejpam-2753	50	9	z	z	NOUN
ejpam-2753	51	1	−	−	PROPN
ejpam-2753	51	2	x	x	SYM
ejpam-2753	51	3	;	;	PUNCT
ejpam-2753	51	4	from	from	ADP
ejpam-2753	51	5	the	the	DET
ejpam-2753	51	6	definition	definition	NOUN
ejpam-2753	51	7	it	it	PRON
ejpam-2753	51	8	can	can	AUX
ejpam-2753	51	9	be	be	AUX
ejpam-2753	51	10	easily	easily	ADV
ejpam-2753	51	11	verified	verify	VERB
ejpam-2753	51	12	that	that	SCONJ
ejpam-2753	51	13	−(−x	−(−x	NOUN
ejpam-2753	51	14	)	)	PUNCT
ejpam-2753	52	1	=	=	PUNCT
ejpam-2753	53	1	x	x	PUNCT
ejpam-2753	53	2	and	and	CCONJ
ejpam-2753	53	3	−(x+	−(x+	ADP
ejpam-2753	53	4	y	y	NOUN
ejpam-2753	53	5	)	)	PUNCT
ejpam-2753	53	6	=	=	VERB
ejpam-2753	53	7	−x−	−x−	NOUN
ejpam-2753	53	8	y.	y.	NOUN
ejpam-2753	53	9	the	the	DET
ejpam-2753	53	10	concept	concept	NOUN
ejpam-2753	53	11	of	of	ADP
ejpam-2753	53	12	hyperspace	hyperspace	NOUN
ejpam-2753	53	13	,	,	PUNCT
ejpam-2753	53	14	which	which	PRON
ejpam-2753	53	15	is	be	AUX
ejpam-2753	53	16	a	a	DET
ejpam-2753	53	17	generalization	generalization	NOUN
ejpam-2753	53	18	of	of	ADP
ejpam-2753	53	19	the	the	DET
ejpam-2753	53	20	concept	concept	NOUN
ejpam-2753	53	21	of	of	ADP
ejpam-2753	53	22	ordinary	ordinary	ADJ
ejpam-2753	53	23	vector	vector	NOUN
ejpam-2753	53	24	space	space	NOUN
ejpam-2753	53	25	.	.	PUNCT
ejpam-2753	54	1	r.	r.	PROPN
ejpam-2753	54	2	ameri	ameri	PROPN
ejpam-2753	54	3	,	,	PUNCT
ejpam-2753	54	4	k.	k.	PROPN
ejpam-2753	54	5	ghadimi	ghadimi	PROPN
ejpam-2753	54	6	,	,	PUNCT
ejpam-2753	54	7	r.	r.	PROPN
ejpam-2753	54	8	a.	a.	PROPN
ejpam-2753	54	9	borzooei	borzooei	PROPN
ejpam-2753	54	10	/	/	SYM
ejpam-2753	54	11	eur	eur	PROPN
ejpam-2753	54	12	.	.	PUNCT
ejpam-2753	55	1	j.	j.	PROPN
ejpam-2753	55	2	pure	pure	PROPN
ejpam-2753	55	3	appl	appl	PROPN
ejpam-2753	55	4	.	.	PROPN
ejpam-2753	55	5	math	math	PROPN
ejpam-2753	55	6	,	,	PUNCT
ejpam-2753	55	7	10	10	NUM
ejpam-2753	55	8	(	(	PUNCT
ejpam-2753	55	9	4	4	NUM
ejpam-2753	55	10	)	)	PUNCT
ejpam-2753	55	11	(	(	PUNCT
ejpam-2753	55	12	2017	2017	NUM
ejpam-2753	55	13	)	)	PUNCT
ejpam-2753	55	14	,	,	PUNCT
ejpam-2753	55	15	702	702	NUM
ejpam-2753	55	16	-	-	SYM
ejpam-2753	55	17	716	716	NUM
ejpam-2753	55	18	704	704	NUM
ejpam-2753	55	19	definition	definition	NOUN
ejpam-2753	55	20	5	5	NUM
ejpam-2753	55	21	.	.	PUNCT
ejpam-2753	56	1	[	[	X
ejpam-2753	56	2	20	20	NUM
ejpam-2753	56	3	]	]	PUNCT
ejpam-2753	56	4	let	let	VERB
ejpam-2753	56	5	k	k	PRON
ejpam-2753	56	6	be	be	AUX
ejpam-2753	56	7	a	a	DET
ejpam-2753	56	8	field	field	NOUN
ejpam-2753	56	9	and	and	CCONJ
ejpam-2753	56	10	(	(	PUNCT
ejpam-2753	56	11	v,+	v,+	NUM
ejpam-2753	56	12	)	)	PUNCT
ejpam-2753	56	13	be	be	AUX
ejpam-2753	56	14	an	an	DET
ejpam-2753	56	15	abelian	abelian	ADJ
ejpam-2753	56	16	group	group	NOUN
ejpam-2753	56	17	.	.	PUNCT
ejpam-2753	57	1	we	we	PRON
ejpam-2753	57	2	define	define	VERB
ejpam-2753	57	3	a	a	DET
ejpam-2753	57	4	hyperspace	hyperspace	NOUN
ejpam-2753	57	5	over	over	ADP
ejpam-2753	57	6	k	k	PROPN
ejpam-2753	57	7	(	(	PUNCT
ejpam-2753	57	8	k	k	NOUN
ejpam-2753	57	9	-	-	NOUN
ejpam-2753	57	10	hyperspace	hyperspace	NOUN
ejpam-2753	57	11	)	)	PUNCT
ejpam-2753	57	12	to	to	PART
ejpam-2753	57	13	be	be	AUX
ejpam-2753	57	14	the	the	DET
ejpam-2753	57	15	quadruplet	quadruplet	NOUN
ejpam-2753	57	16	(	(	PUNCT
ejpam-2753	57	17	v,+	v,+	NUM
ejpam-2753	57	18	,	,	PUNCT
ejpam-2753	57	19	◦	◦	NOUN
ejpam-2753	57	20	,	,	PUNCT
ejpam-2753	57	21	k	k	NOUN
ejpam-2753	57	22	)	)	PUNCT
ejpam-2753	57	23	,	,	PUNCT
ejpam-2753	57	24	where	where	SCONJ
ejpam-2753	57	25	◦	◦	NOUN
ejpam-2753	57	26	is	be	AUX
ejpam-2753	57	27	a	a	DET
ejpam-2753	57	28	mapping	mapping	NOUN
ejpam-2753	57	29	◦	◦	NOUN
ejpam-2753	57	30	:	:	PUNCT
ejpam-2753	58	1	k	k	X
ejpam-2753	58	2	×	×	NOUN
ejpam-2753	58	3	v	v	INTJ
ejpam-2753	58	4	−→	−→	NOUN
ejpam-2753	58	5	p	p	X
ejpam-2753	58	6	∗(v	∗(v	PROPN
ejpam-2753	58	7	)	)	PUNCT
ejpam-2753	58	8	,	,	PUNCT
ejpam-2753	58	9	such	such	ADJ
ejpam-2753	58	10	that	that	SCONJ
ejpam-2753	58	11	the	the	DET
ejpam-2753	58	12	following	follow	VERB
ejpam-2753	58	13	conditions	condition	NOUN
ejpam-2753	58	14	hold	hold	VERB
ejpam-2753	58	15	(	(	PUNCT
ejpam-2753	58	16	for	for	ADP
ejpam-2753	58	17	all	all	DET
ejpam-2753	58	18	x	x	NOUN
ejpam-2753	58	19	,	,	PUNCT
ejpam-2753	58	20	y	y	PROPN
ejpam-2753	58	21	∈	∈	PROPN
ejpam-2753	58	22	v	v	NOUN
ejpam-2753	58	23	,	,	PUNCT
ejpam-2753	58	24	and	and	CCONJ
ejpam-2753	58	25	a	a	DET
ejpam-2753	58	26	,	,	PUNCT
ejpam-2753	58	27	b	b	PROPN
ejpam-2753	58	28	∈	∈	PROPN
ejpam-2753	58	29	k	k	NOUN
ejpam-2753	58	30	):	):	PUNCT
ejpam-2753	58	31	(	(	PUNCT
ejpam-2753	58	32	h1	h1	PROPN
ejpam-2753	58	33	)	)	PUNCT
ejpam-2753	58	34	a	a	DET
ejpam-2753	58	35	◦	◦	NOUN
ejpam-2753	58	36	(	(	PUNCT
ejpam-2753	58	37	x+	x+	ADJ
ejpam-2753	58	38	y	y	NOUN
ejpam-2753	58	39	)	)	PUNCT
ejpam-2753	58	40	⊆	⊆	PROPN
ejpam-2753	58	41	a	a	DET
ejpam-2753	58	42	◦	◦	NOUN
ejpam-2753	58	43	x+	x+	PUNCT
ejpam-2753	58	44	a	a	DET
ejpam-2753	58	45	◦	◦	NOUN
ejpam-2753	58	46	y	y	NOUN
ejpam-2753	58	47	,	,	PUNCT
ejpam-2753	58	48	right	right	ADJ
ejpam-2753	58	49	distributive	distributive	ADJ
ejpam-2753	58	50	law	law	NOUN
ejpam-2753	58	51	;	;	PUNCT
ejpam-2753	58	52	(	(	PUNCT
ejpam-2753	58	53	h2	h2	NOUN
ejpam-2753	58	54	)	)	PUNCT
ejpam-2753	58	55	(	(	PUNCT
ejpam-2753	58	56	a+	a+	PUNCT
ejpam-2753	58	57	b	b	X
ejpam-2753	58	58	)	)	PUNCT
ejpam-2753	58	59	◦	◦	NOUN
ejpam-2753	58	60	x	x	SYM
ejpam-2753	58	61	⊆	⊆	NUM
ejpam-2753	58	62	a	a	DET
ejpam-2753	58	63	◦	◦	NOUN
ejpam-2753	58	64	x+	x+	X
ejpam-2753	58	65	b	b	NOUN
ejpam-2753	58	66	◦	◦	NOUN
ejpam-2753	58	67	x	x	NOUN
ejpam-2753	58	68	,	,	PUNCT
ejpam-2753	58	69	left	leave	VERB
ejpam-2753	58	70	distributive	distributive	ADJ
ejpam-2753	58	71	law	law	NOUN
ejpam-2753	58	72	;	;	PUNCT
ejpam-2753	58	73	(	(	PUNCT
ejpam-2753	58	74	h3	h3	NOUN
ejpam-2753	58	75	)	)	PUNCT
ejpam-2753	58	76	a	a	DET
ejpam-2753	58	77	◦	◦	NOUN
ejpam-2753	58	78	(	(	PUNCT
ejpam-2753	58	79	b	b	X
ejpam-2753	58	80	◦	◦	NOUN
ejpam-2753	58	81	x	x	NOUN
ejpam-2753	58	82	)	)	PUNCT
ejpam-2753	58	83	=	=	SYM
ejpam-2753	58	84	(	(	PUNCT
ejpam-2753	58	85	ab	ab	NOUN
ejpam-2753	58	86	)	)	PUNCT
ejpam-2753	58	87	◦	◦	NOUN
ejpam-2753	58	88	x	x	SYM
ejpam-2753	58	89	,	,	PUNCT
ejpam-2753	58	90	associative	associative	ADJ
ejpam-2753	58	91	law	law	NOUN
ejpam-2753	58	92	;	;	PUNCT
ejpam-2753	58	93	(	(	PUNCT
ejpam-2753	58	94	h4	h4	PROPN
ejpam-2753	58	95	)	)	PUNCT
ejpam-2753	58	96	a	a	DET
ejpam-2753	58	97	◦	◦	NOUN
ejpam-2753	58	98	(	(	PUNCT
ejpam-2753	58	99	−x	−x	NOUN
ejpam-2753	58	100	)	)	PUNCT
ejpam-2753	58	101	=	=	PUNCT
ejpam-2753	58	102	(	(	PUNCT
ejpam-2753	58	103	−a	−a	ADJ
ejpam-2753	58	104	)	)	PUNCT
ejpam-2753	58	105	◦	◦	NOUN
ejpam-2753	58	106	x	x	X
ejpam-2753	58	107	=	=	SYM
ejpam-2753	58	108	−(a	−(a	ADJ
ejpam-2753	58	109	◦	◦	NOUN
ejpam-2753	58	110	x	x	X
ejpam-2753	58	111	)	)	PUNCT
ejpam-2753	58	112	;	;	PUNCT
ejpam-2753	58	113	(	(	PUNCT
ejpam-2753	58	114	h5	h5	PROPN
ejpam-2753	58	115	)	)	PUNCT
ejpam-2753	58	116	x	x	SYM
ejpam-2753	58	117	∈	∈	PROPN
ejpam-2753	58	118	1	1	NUM
ejpam-2753	58	119	◦	◦	NOUN
ejpam-2753	58	120	x.	x.	NOUN
ejpam-2753	58	121	remark	remark	NOUN
ejpam-2753	58	122	1	1	NUM
ejpam-2753	58	123	.	.	PUNCT
ejpam-2753	59	1	(	(	PUNCT
ejpam-2753	59	2	i	i	NOUN
ejpam-2753	59	3	)	)	PUNCT
ejpam-2753	59	4	in	in	ADP
ejpam-2753	59	5	the	the	DET
ejpam-2753	59	6	right	right	ADJ
ejpam-2753	59	7	hand	hand	NOUN
ejpam-2753	59	8	side	side	NOUN
ejpam-2753	59	9	of	of	ADP
ejpam-2753	59	10	(	(	PUNCT
ejpam-2753	59	11	h1	h1	PROPN
ejpam-2753	59	12	)	)	PUNCT
ejpam-2753	59	13	the	the	DET
ejpam-2753	59	14	sum	sum	NOUN
ejpam-2753	59	15	is	be	AUX
ejpam-2753	59	16	meant	mean	VERB
ejpam-2753	59	17	in	in	ADP
ejpam-2753	59	18	the	the	DET
ejpam-2753	59	19	sense	sense	NOUN
ejpam-2753	59	20	of	of	ADP
ejpam-2753	59	21	frobenius	frobenius	NOUN
ejpam-2753	59	22	,	,	PUNCT
ejpam-2753	59	23	that	that	PRON
ejpam-2753	59	24	is	is	ADV
ejpam-2753	59	25	we	we	PRON
ejpam-2753	59	26	consider	consider	VERB
ejpam-2753	59	27	the	the	DET
ejpam-2753	59	28	set	set	NOUN
ejpam-2753	59	29	of	of	ADP
ejpam-2753	59	30	all	all	DET
ejpam-2753	59	31	sums	sum	NOUN
ejpam-2753	59	32	of	of	ADP
ejpam-2753	59	33	an	an	DET
ejpam-2753	59	34	element	element	NOUN
ejpam-2753	59	35	of	of	ADP
ejpam-2753	59	36	a	a	DET
ejpam-2753	59	37	◦	◦	NOUN
ejpam-2753	59	38	x	x	PUNCT
ejpam-2753	59	39	with	with	ADP
ejpam-2753	59	40	an	an	DET
ejpam-2753	59	41	element	element	NOUN
ejpam-2753	59	42	of	of	ADP
ejpam-2753	59	43	a	a	DET
ejpam-2753	59	44	◦	◦	NOUN
ejpam-2753	60	1	y.	y.	NOUN
ejpam-2753	61	1	similarly	similarly	ADV
ejpam-2753	61	2	we	we	PRON
ejpam-2753	61	3	have	have	VERB
ejpam-2753	61	4	in	in	ADP
ejpam-2753	61	5	(	(	PUNCT
ejpam-2753	61	6	h2	h2	NOUN
ejpam-2753	61	7	)	)	PUNCT
ejpam-2753	61	8	.	.	PUNCT
ejpam-2753	62	1	(	(	PUNCT
ejpam-2753	62	2	ii	ii	X
ejpam-2753	62	3	)	)	PUNCT
ejpam-2753	62	4	we	we	PRON
ejpam-2753	62	5	say	say	VERB
ejpam-2753	62	6	that	that	SCONJ
ejpam-2753	62	7	(	(	PUNCT
ejpam-2753	62	8	v,+	v,+	NUM
ejpam-2753	62	9	,	,	PUNCT
ejpam-2753	62	10	◦	◦	NOUN
ejpam-2753	62	11	,	,	PUNCT
ejpam-2753	62	12	k	k	NOUN
ejpam-2753	62	13	)	)	PUNCT
ejpam-2753	62	14	is	be	AUX
ejpam-2753	62	15	anti	anti	ADJ
ejpam-2753	62	16	-	-	ADJ
ejpam-2753	62	17	left	left	ADJ
ejpam-2753	62	18	distributive	distributive	ADJ
ejpam-2753	62	19	,	,	PUNCT
ejpam-2753	62	20	if	if	SCONJ
ejpam-2753	62	21	(	(	PUNCT
ejpam-2753	62	22	a+	a+	NOUN
ejpam-2753	62	23	b	b	X
ejpam-2753	62	24	)	)	PUNCT
ejpam-2753	62	25	◦	◦	NOUN
ejpam-2753	62	26	x	x	SYM
ejpam-2753	62	27	⊇	⊇	NOUN
ejpam-2753	62	28	a	a	DET
ejpam-2753	62	29	◦	◦	NOUN
ejpam-2753	62	30	x+	x+	X
ejpam-2753	62	31	b	b	NOUN
ejpam-2753	63	1	◦	◦	NOUN
ejpam-2753	63	2	x	x	SYM
ejpam-2753	63	3	for	for	ADP
ejpam-2753	63	4	all	all	DET
ejpam-2753	63	5	a	a	PRON
ejpam-2753	63	6	,	,	PUNCT
ejpam-2753	63	7	b	b	X
ejpam-2753	63	8	∈	∈	PROPN
ejpam-2753	63	9	k	k	NOUN
ejpam-2753	63	10	,	,	PUNCT
ejpam-2753	63	11	x	x	PROPN
ejpam-2753	63	12	∈	∈	PROPN
ejpam-2753	63	13	v	v	NOUN
ejpam-2753	63	14	,	,	PUNCT
ejpam-2753	63	15	and	and	CCONJ
ejpam-2753	63	16	strongly	strongly	ADV
ejpam-2753	63	17	left	leave	VERB
ejpam-2753	63	18	distributive	distributive	ADJ
ejpam-2753	63	19	,	,	PUNCT
ejpam-2753	63	20	if	if	SCONJ
ejpam-2753	63	21	(	(	PUNCT
ejpam-2753	63	22	a+	a+	NOUN
ejpam-2753	63	23	b	b	X
ejpam-2753	63	24	)	)	PUNCT
ejpam-2753	63	25	◦	◦	NOUN
ejpam-2753	63	26	x	x	X
ejpam-2753	63	27	=	=	PUNCT
ejpam-2753	63	28	a	a	DET
ejpam-2753	63	29	◦	◦	NOUN
ejpam-2753	63	30	x+	x+	X
ejpam-2753	63	31	b	b	NOUN
ejpam-2753	63	32	◦	◦	NOUN
ejpam-2753	63	33	x	x	SYM
ejpam-2753	63	34	for	for	ADP
ejpam-2753	63	35	all	all	DET
ejpam-2753	63	36	a	a	PRON
ejpam-2753	63	37	,	,	PUNCT
ejpam-2753	63	38	b	b	X
ejpam-2753	63	39	∈	∈	PROPN
ejpam-2753	63	40	k	k	NOUN
ejpam-2753	63	41	,	,	PUNCT
ejpam-2753	63	42	x	x	PROPN
ejpam-2753	63	43	∈	∈	PROPN
ejpam-2753	63	44	v	v	NOUN
ejpam-2753	63	45	,	,	PUNCT
ejpam-2753	63	46	in	in	ADP
ejpam-2753	63	47	a	a	DET
ejpam-2753	63	48	similar	similar	ADJ
ejpam-2753	63	49	way	way	NOUN
ejpam-2753	63	50	we	we	PRON
ejpam-2753	63	51	define	define	VERB
ejpam-2753	63	52	the	the	DET
ejpam-2753	63	53	anti	anti	ADJ
ejpam-2753	63	54	-	-	ADJ
ejpam-2753	63	55	right	right	ADJ
ejpam-2753	63	56	distributive	distributive	ADJ
ejpam-2753	63	57	and	and	CCONJ
ejpam-2753	63	58	strongly	strongly	ADV
ejpam-2753	63	59	right	right	ADJ
ejpam-2753	63	60	distributive	distributive	ADJ
ejpam-2753	63	61	hyperspaces	hyperspace	NOUN
ejpam-2753	63	62	,	,	PUNCT
ejpam-2753	63	63	respectvely	respectvely	ADV
ejpam-2753	63	64	.	.	PUNCT
ejpam-2753	64	1	v	v	NOUN
ejpam-2753	64	2	is	be	AUX
ejpam-2753	64	3	called	call	VERB
ejpam-2753	64	4	strongly	strongly	ADV
ejpam-2753	64	5	distributive	distributive	ADJ
ejpam-2753	64	6	if	if	SCONJ
ejpam-2753	64	7	it	it	PRON
ejpam-2753	64	8	is	be	AUX
ejpam-2753	64	9	both	both	PRON
ejpam-2753	64	10	strongly	strongly	ADV
ejpam-2753	64	11	left	left	ADJ
ejpam-2753	64	12	and	and	CCONJ
ejpam-2753	64	13	strongly	strongly	ADV
ejpam-2753	64	14	right	right	ADV
ejpam-2753	64	15	distributive	distributive	ADJ
ejpam-2753	64	16	.	.	PUNCT
ejpam-2753	65	1	(	(	PUNCT
ejpam-2753	65	2	iii	iii	X
ejpam-2753	65	3	)	)	PUNCT
ejpam-2753	65	4	the	the	DET
ejpam-2753	65	5	left	left	ADJ
ejpam-2753	65	6	hand	hand	NOUN
ejpam-2753	65	7	side	side	NOUN
ejpam-2753	65	8	of	of	ADP
ejpam-2753	65	9	(	(	PUNCT
ejpam-2753	65	10	h3	h3	NOUN
ejpam-2753	65	11	)	)	PUNCT
ejpam-2753	65	12	means	mean	VERB
ejpam-2753	65	13	the	the	DET
ejpam-2753	65	14	set	set	VERB
ejpam-2753	65	15	-	-	PUNCT
ejpam-2753	65	16	theoretical	theoretical	ADJ
ejpam-2753	65	17	union	union	NOUN
ejpam-2753	65	18	of	of	ADP
ejpam-2753	65	19	all	all	DET
ejpam-2753	65	20	the	the	DET
ejpam-2753	65	21	sets	set	NOUN
ejpam-2753	65	22	a	a	DET
ejpam-2753	65	23	◦	◦	NOUN
ejpam-2753	65	24	y	y	PROPN
ejpam-2753	65	25	,	,	PUNCT
ejpam-2753	65	26	where	where	SCONJ
ejpam-2753	65	27	y	y	PROPN
ejpam-2753	65	28	runs	run	VERB
ejpam-2753	65	29	over	over	ADP
ejpam-2753	65	30	the	the	DET
ejpam-2753	65	31	set	set	NOUN
ejpam-2753	65	32	b	b	PROPN
ejpam-2753	65	33	◦	◦	NOUN
ejpam-2753	65	34	x	x	SYM
ejpam-2753	65	35	,	,	PUNCT
ejpam-2753	65	36	i.e.	i.e.	X
ejpam-2753	65	37	for	for	ADP
ejpam-2753	65	38	all	all	DET
ejpam-2753	65	39	a	a	PRON
ejpam-2753	65	40	,	,	PUNCT
ejpam-2753	65	41	b	b	PROPN
ejpam-2753	65	42	∈	∈	PROPN
ejpam-2753	65	43	k	k	NOUN
ejpam-2753	65	44	,	,	PUNCT
ejpam-2753	65	45	and	and	CCONJ
ejpam-2753	65	46	x	x	X
ejpam-2753	65	47	∈	∈	NOUN
ejpam-2753	65	48	v	v	X
ejpam-2753	65	49	:	:	PUNCT
ejpam-2753	65	50	a	a	DET
ejpam-2753	65	51	◦	◦	NOUN
ejpam-2753	65	52	(	(	PUNCT
ejpam-2753	65	53	b	b	X
ejpam-2753	65	54	◦	◦	NOUN
ejpam-2753	65	55	x	x	NOUN
ejpam-2753	65	56	)	)	PUNCT
ejpam-2753	65	57	=	=	PUNCT
ejpam-2753	66	1	⋃	⋃	NOUN
ejpam-2753	66	2	y∈b	y∈b	NOUN
ejpam-2753	66	3	◦	◦	NOUN
ejpam-2753	66	4	x	x	SYM
ejpam-2753	66	5	a	a	DET
ejpam-2753	66	6	◦	◦	NOUN
ejpam-2753	66	7	y.	y.	NOUN
ejpam-2753	66	8	(	(	PUNCT
ejpam-2753	66	9	iv	iv	X
ejpam-2753	66	10	)	)	PUNCT
ejpam-2753	66	11	let	let	VERB
ejpam-2753	66	12	ωv	ωv	ADV
ejpam-2753	66	13	=	=	SYM
ejpam-2753	66	14	0	0	NUM
ejpam-2753	66	15	◦	◦	NOUN
ejpam-2753	66	16	0v	0v	NOUN
ejpam-2753	66	17	,	,	PUNCT
ejpam-2753	66	18	where	where	SCONJ
ejpam-2753	66	19	0v	0v	PROPN
ejpam-2753	66	20	is	be	AUX
ejpam-2753	66	21	the	the	DET
ejpam-2753	66	22	zero	zero	NUM
ejpam-2753	66	23	of	of	ADP
ejpam-2753	66	24	(	(	PUNCT
ejpam-2753	66	25	v,+	v,+	NUM
ejpam-2753	66	26	)	)	PUNCT
ejpam-2753	66	27	,	,	PUNCT
ejpam-2753	66	28	in	in	ADP
ejpam-2753	66	29	[	[	X
ejpam-2753	66	30	20	20	NUM
ejpam-2753	66	31	]	]	X
ejpam-2753	66	32	it	it	PRON
ejpam-2753	66	33	is	be	AUX
ejpam-2753	66	34	shown	show	VERB
ejpam-2753	66	35	if	if	SCONJ
ejpam-2753	66	36	v	v	NOUN
ejpam-2753	66	37	is	be	AUX
ejpam-2753	66	38	either	either	CCONJ
ejpam-2753	66	39	strongly	strongly	ADV
ejpam-2753	66	40	right	right	ADJ
ejpam-2753	66	41	or	or	CCONJ
ejpam-2753	66	42	left	leave	VERB
ejpam-2753	66	43	distributive	distributive	ADJ
ejpam-2753	66	44	,	,	PUNCT
ejpam-2753	66	45	then	then	ADV
ejpam-2753	66	46	ωv	ωv	PROPN
ejpam-2753	66	47	is	be	AUX
ejpam-2753	66	48	a	a	DET
ejpam-2753	66	49	subgroup	subgroup	NOUN
ejpam-2753	66	50	of	of	ADP
ejpam-2753	66	51	(	(	PUNCT
ejpam-2753	66	52	v,+	v,+	NUM
ejpam-2753	66	53	)	)	PUNCT
ejpam-2753	66	54	.	.	PUNCT
ejpam-2753	67	1	definition	definition	NOUN
ejpam-2753	67	2	6	6	NUM
ejpam-2753	67	3	.	.	PUNCT
ejpam-2753	68	1	[	[	X
ejpam-2753	68	2	2	2	X
ejpam-2753	68	3	]	]	PUNCT
ejpam-2753	68	4	let	let	VERB
ejpam-2753	68	5	v	v	PART
ejpam-2753	68	6	be	be	AUX
ejpam-2753	68	7	a	a	DET
ejpam-2753	68	8	hyperspace	hyperspace	NOUN
ejpam-2753	68	9	over	over	ADP
ejpam-2753	68	10	a	a	DET
ejpam-2753	68	11	field	field	NOUN
ejpam-2753	68	12	k.	k.	INTJ
ejpam-2753	69	1	a	a	DET
ejpam-2753	69	2	nonempty	nonempty	NOUN
ejpam-2753	69	3	subset	subset	VERB
ejpam-2753	69	4	w	w	NOUN
ejpam-2753	69	5	of	of	ADP
ejpam-2753	69	6	v	v	NOUN
ejpam-2753	69	7	is	be	AUX
ejpam-2753	69	8	called	call	VERB
ejpam-2753	69	9	a	a	DET
ejpam-2753	69	10	subhyperspace	subhyperspace	NOUN
ejpam-2753	69	11	if	if	SCONJ
ejpam-2753	69	12	w	w	NOUN
ejpam-2753	69	13	is	be	AUX
ejpam-2753	69	14	itself	itself	PRON
ejpam-2753	69	15	a	a	DET
ejpam-2753	69	16	hyperspace	hyperspace	NOUN
ejpam-2753	69	17	with	with	ADP
ejpam-2753	69	18	the	the	DET
ejpam-2753	69	19	hyperoperation	hyperoperation	NOUN
ejpam-2753	69	20	on	on	ADP
ejpam-2753	69	21	v	v	NUM
ejpam-2753	69	22	,	,	PUNCT
ejpam-2753	69	23	i.e.	i.e.	X
ejpam-2753	69	24	w	w	NOUN
ejpam-2753	69	25	6=	6=	ADP
ejpam-2753	69	26	∅	∅	NOUN
ejpam-2753	69	27	,	,	PUNCT
ejpam-2753	69	28	w	w	PROPN
ejpam-2753	69	29	−w	−w	ADV
ejpam-2753	69	30	⊆w	⊆w	PROPN
ejpam-2753	69	31	,	,	PUNCT
ejpam-2753	69	32	a	a	DET
ejpam-2753	69	33	◦	◦	NOUN
ejpam-2753	69	34	w	w	NOUN
ejpam-2753	69	35	⊆w	⊆w	NOUN
ejpam-2753	69	36	for	for	ADP
ejpam-2753	69	37	all	all	DET
ejpam-2753	69	38	a	a	DET
ejpam-2753	69	39	∈	∈	PROPN
ejpam-2753	69	40	k.	k.	NOUN
ejpam-2753	69	41	in	in	ADP
ejpam-2753	69	42	this	this	DET
ejpam-2753	69	43	case	case	NOUN
ejpam-2753	69	44	we	we	PRON
ejpam-2753	69	45	write	write	VERB
ejpam-2753	69	46	w	w	PROPN
ejpam-2753	69	47	≤	≤	NUM
ejpam-2753	69	48	v	v	NOUN
ejpam-2753	69	49	.	.	PUNCT
ejpam-2753	70	1	definition	definition	NOUN
ejpam-2753	70	2	7	7	NUM
ejpam-2753	70	3	.	.	PUNCT
ejpam-2753	71	1	[	[	X
ejpam-2753	71	2	2	2	X
ejpam-2753	71	3	]	]	PUNCT
ejpam-2753	71	4	let	let	VERB
ejpam-2753	71	5	v	v	PART
ejpam-2753	71	6	be	be	AUX
ejpam-2753	71	7	a	a	DET
ejpam-2753	71	8	hyperspace	hyperspace	NOUN
ejpam-2753	71	9	over	over	ADP
ejpam-2753	71	10	a	a	DET
ejpam-2753	71	11	field	field	NOUN
ejpam-2753	71	12	k.	k.	NOUN
ejpam-2753	72	1	if	if	SCONJ
ejpam-2753	72	2	w	w	PROPN
ejpam-2753	72	3	is	be	AUX
ejpam-2753	72	4	a	a	DET
ejpam-2753	72	5	nonempty	nonempty	ADJ
ejpam-2753	72	6	subset	subset	NOUN
ejpam-2753	72	7	of	of	ADP
ejpam-2753	72	8	v	v	NOUN
ejpam-2753	72	9	,	,	PUNCT
ejpam-2753	72	10	then	then	ADV
ejpam-2753	72	11	the	the	DET
ejpam-2753	72	12	linear	linear	ADJ
ejpam-2753	72	13	span	span	NOUN
ejpam-2753	72	14	of	of	ADP
ejpam-2753	72	15	w	w	PROPN
ejpam-2753	72	16	is	be	AUX
ejpam-2753	72	17	defined	define	VERB
ejpam-2753	72	18	by	by	ADP
ejpam-2753	72	19	l(w	l(w	PROPN
ejpam-2753	72	20	)	)	PUNCT
ejpam-2753	72	21	=	=	PRON
ejpam-2753	73	1	{	{	PUNCT
ejpam-2753	73	2	t	t	NOUN
ejpam-2753	73	3	∈	∈	PROPN
ejpam-2753	73	4	v	v	ADP
ejpam-2753	73	5	|	|	ADV
ejpam-2753	73	6	t	t	PROPN
ejpam-2753	73	7	∈	∈	PROPN
ejpam-2753	74	1	n∑	n∑	INTJ
ejpam-2753	74	2	i=1	i=1	PROPN
ejpam-2753	74	3	ai	ai	VERB
ejpam-2753	74	4	◦	◦	PROPN
ejpam-2753	74	5	wi	wi	PROPN
ejpam-2753	74	6	,	,	PUNCT
ejpam-2753	74	7	ai	ai	VERB
ejpam-2753	74	8	∈	∈	PROPN
ejpam-2753	74	9	k	k	PROPN
ejpam-2753	74	10	,	,	PUNCT
ejpam-2753	74	11	wi	wi	PROPN
ejpam-2753	74	12	∈w	∈w	PROPN
ejpam-2753	74	13	,	,	PUNCT
ejpam-2753	74	14	n	n	PRON
ejpam-2753	74	15	∈	∈	PROPN
ejpam-2753	74	16	n	n	CCONJ
ejpam-2753	74	17	}	}	PUNCT
ejpam-2753	74	18	=	=	SYM
ejpam-2753	74	19	{	{	PUNCT
ejpam-2753	74	20	t1	t1	NOUN
ejpam-2753	74	21	+	+	CCONJ
ejpam-2753	74	22	t2	t2	PROPN
ejpam-2753	74	23	+	+	CCONJ
ejpam-2753	74	24	...	...	PUNCT
ejpam-2753	74	25	+	+	X
ejpam-2753	74	26	tn	tn	NOUN
ejpam-2753	74	27	|	|	ADV
ejpam-2753	74	28	ti	ti	PROPN
ejpam-2753	74	29	∈	∈	PROPN
ejpam-2753	74	30	ai	ai	VERB
ejpam-2753	74	31	◦	◦	PROPN
ejpam-2753	74	32	wi	wi	PROPN
ejpam-2753	74	33	,	,	PUNCT
ejpam-2753	74	34	ai	ai	VERB
ejpam-2753	74	35	∈	∈	PROPN
ejpam-2753	74	36	k	k	PROPN
ejpam-2753	74	37	,	,	PUNCT
ejpam-2753	74	38	wi	wi	PROPN
ejpam-2753	74	39	∈w	∈w	PROPN
ejpam-2753	74	40	,	,	PUNCT
ejpam-2753	74	41	n	n	PRON
ejpam-2753	74	42	∈	∈	PROPN
ejpam-2753	74	43	n	n	CCONJ
ejpam-2753	74	44	}	}	PUNCT
ejpam-2753	74	45	.	.	PUNCT
ejpam-2753	75	1	r.	r.	PROPN
ejpam-2753	75	2	ameri	ameri	PROPN
ejpam-2753	75	3	,	,	PUNCT
ejpam-2753	75	4	k.	k.	PROPN
ejpam-2753	75	5	ghadimi	ghadimi	PROPN
ejpam-2753	75	6	,	,	PUNCT
ejpam-2753	75	7	r.	r.	PROPN
ejpam-2753	75	8	a.	a.	PROPN
ejpam-2753	75	9	borzooei	borzooei	PROPN
ejpam-2753	75	10	/	/	SYM
ejpam-2753	75	11	eur	eur	PROPN
ejpam-2753	75	12	.	.	PUNCT
ejpam-2753	76	1	j.	j.	PROPN
ejpam-2753	76	2	pure	pure	PROPN
ejpam-2753	76	3	appl	appl	PROPN
ejpam-2753	76	4	.	.	PROPN
ejpam-2753	76	5	math	math	PROPN
ejpam-2753	76	6	,	,	PUNCT
ejpam-2753	76	7	10	10	NUM
ejpam-2753	76	8	(	(	PUNCT
ejpam-2753	76	9	4	4	NUM
ejpam-2753	76	10	)	)	PUNCT
ejpam-2753	76	11	(	(	PUNCT
ejpam-2753	76	12	2017	2017	NUM
ejpam-2753	76	13	)	)	PUNCT
ejpam-2753	76	14	,	,	PUNCT
ejpam-2753	76	15	702	702	NUM
ejpam-2753	76	16	-	-	SYM
ejpam-2753	76	17	716	716	NUM
ejpam-2753	76	18	705	705	NUM
ejpam-2753	76	19	lemma	lemma	PROPN
ejpam-2753	76	20	1	1	NUM
ejpam-2753	76	21	.	.	PUNCT
ejpam-2753	77	1	[	[	X
ejpam-2753	77	2	2	2	NUM
ejpam-2753	77	3	]	]	X
ejpam-2753	77	4	l(w	l(w	PROPN
ejpam-2753	77	5	)	)	PUNCT
ejpam-2753	77	6	is	be	AUX
ejpam-2753	77	7	the	the	DET
ejpam-2753	77	8	smallest	small	ADJ
ejpam-2753	77	9	subhyperspace	subhyperspace	NOUN
ejpam-2753	77	10	of	of	ADP
ejpam-2753	77	11	v	v	NOUN
ejpam-2753	77	12	containing	contain	VERB
ejpam-2753	77	13	w	w	PROPN
ejpam-2753	77	14	.	.	PUNCT
ejpam-2753	78	1	definition	definition	NOUN
ejpam-2753	78	2	8	8	NUM
ejpam-2753	78	3	.	.	PUNCT
ejpam-2753	79	1	[	[	X
ejpam-2753	79	2	2	2	X
ejpam-2753	79	3	]	]	PUNCT
ejpam-2753	79	4	let	let	VERB
ejpam-2753	79	5	v	v	PART
ejpam-2753	79	6	be	be	AUX
ejpam-2753	79	7	a	a	DET
ejpam-2753	79	8	hyperspace	hyperspace	NOUN
ejpam-2753	79	9	over	over	ADP
ejpam-2753	79	10	a	a	DET
ejpam-2753	79	11	field	field	NOUN
ejpam-2753	79	12	k.	k.	PROPN
ejpam-2753	80	1	a	a	DET
ejpam-2753	80	2	subset	subset	PROPN
ejpam-2753	80	3	w	w	NOUN
ejpam-2753	80	4	of	of	ADP
ejpam-2753	80	5	v	v	NOUN
ejpam-2753	80	6	is	be	AUX
ejpam-2753	80	7	called	call	VERB
ejpam-2753	80	8	linearly	linearly	ADV
ejpam-2753	80	9	independent	independent	ADJ
ejpam-2753	80	10	if	if	SCONJ
ejpam-2753	80	11	for	for	ADP
ejpam-2753	80	12	every	every	DET
ejpam-2753	80	13	vectors	vector	NOUN
ejpam-2753	80	14	v1	v1	NOUN
ejpam-2753	80	15	,	,	PUNCT
ejpam-2753	80	16	v2	v2	PROPN
ejpam-2753	80	17	,	,	PUNCT
ejpam-2753	80	18	...	...	PUNCT
ejpam-2753	80	19	,	,	PUNCT
ejpam-2753	80	20	vn	vn	X
ejpam-2753	80	21	in	in	ADP
ejpam-2753	80	22	w	w	PROPN
ejpam-2753	80	23	,	,	PUNCT
ejpam-2753	80	24	c1	c1	PROPN
ejpam-2753	80	25	,	,	PUNCT
ejpam-2753	80	26	c2	c2	PROPN
ejpam-2753	80	27	,	,	PUNCT
ejpam-2753	80	28	...	...	PUNCT
ejpam-2753	80	29	,	,	PUNCT
ejpam-2753	80	30	cn	cn	PROPN
ejpam-2753	80	31	∈	∈	PROPN
ejpam-2753	80	32	k	k	PROPN
ejpam-2753	80	33	,	,	PUNCT
ejpam-2753	80	34	and	and	CCONJ
ejpam-2753	80	35	0v	0v	PROPN
ejpam-2753	80	36	∈	∈	PROPN
ejpam-2753	80	37	c1	c1	PROPN
ejpam-2753	80	38	◦	◦	NOUN
ejpam-2753	80	39	v1	v1	PROPN
ejpam-2753	80	40	+	+	X
ejpam-2753	80	41	...	...	PUNCT
ejpam-2753	81	1	+	+	CCONJ
ejpam-2753	81	2	cn	cn	PROPN
ejpam-2753	81	3	◦	◦	PROPN
ejpam-2753	81	4	vn	vn	PROPN
ejpam-2753	81	5	,	,	PUNCT
ejpam-2753	81	6	implies	imply	VERB
ejpam-2753	81	7	that	that	DET
ejpam-2753	81	8	c1	c1	PROPN
ejpam-2753	81	9	=	=	PROPN
ejpam-2753	81	10	c2	c2	PROPN
ejpam-2753	81	11	=	=	PUNCT
ejpam-2753	81	12	...	...	PUNCT
ejpam-2753	82	1	=	=	PUNCT
ejpam-2753	82	2	cn	cn	PROPN
ejpam-2753	82	3	=	=	NOUN
ejpam-2753	82	4	0	0	PROPN
ejpam-2753	82	5	.	.	PUNCT
ejpam-2753	83	1	a	a	DET
ejpam-2753	83	2	subset	subset	NOUN
ejpam-2753	83	3	w	w	NOUN
ejpam-2753	83	4	of	of	ADP
ejpam-2753	83	5	v	v	NOUN
ejpam-2753	83	6	is	be	AUX
ejpam-2753	83	7	called	call	VERB
ejpam-2753	83	8	linearly	linearly	ADV
ejpam-2753	83	9	dependent	dependent	ADJ
ejpam-2753	83	10	if	if	SCONJ
ejpam-2753	83	11	it	it	PRON
ejpam-2753	83	12	is	be	AUX
ejpam-2753	83	13	not	not	PART
ejpam-2753	83	14	linearly	linearly	ADV
ejpam-2753	83	15	independent	independent	ADJ
ejpam-2753	83	16	.	.	PUNCT
ejpam-2753	84	1	definition	definition	NOUN
ejpam-2753	84	2	9	9	NUM
ejpam-2753	84	3	.	.	PUNCT
ejpam-2753	85	1	[	[	X
ejpam-2753	85	2	2	2	X
ejpam-2753	85	3	]	]	PUNCT
ejpam-2753	85	4	let	let	VERB
ejpam-2753	85	5	v	v	PART
ejpam-2753	85	6	be	be	AUX
ejpam-2753	85	7	a	a	DET
ejpam-2753	85	8	hyperspace	hyperspace	NOUN
ejpam-2753	85	9	over	over	ADP
ejpam-2753	85	10	a	a	DET
ejpam-2753	85	11	field	field	NOUN
ejpam-2753	85	12	k.	k.	NOUN
ejpam-2753	86	1	a	a	DET
ejpam-2753	86	2	basis	basis	NOUN
ejpam-2753	86	3	for	for	ADP
ejpam-2753	86	4	v	v	NOUN
ejpam-2753	86	5	is	be	AUX
ejpam-2753	86	6	a	a	DET
ejpam-2753	86	7	linearly	linearly	ADV
ejpam-2753	86	8	independent	independent	ADJ
ejpam-2753	86	9	subset	subset	NOUN
ejpam-2753	86	10	of	of	ADP
ejpam-2753	86	11	v	v	NOUN
ejpam-2753	86	12	such	such	ADJ
ejpam-2753	86	13	that	that	DET
ejpam-2753	86	14	span	span	NOUN
ejpam-2753	86	15	v	v	NOUN
ejpam-2753	86	16	.	.	PUNCT
ejpam-2753	87	1	we	we	PRON
ejpam-2753	87	2	say	say	VERB
ejpam-2753	87	3	that	that	SCONJ
ejpam-2753	87	4	v	v	NOUN
ejpam-2753	87	5	has	have	AUX
ejpam-2753	87	6	finite	finite	VERB
ejpam-2753	87	7	dimensional	dimensional	ADJ
ejpam-2753	87	8	if	if	SCONJ
ejpam-2753	87	9	it	it	PRON
ejpam-2753	87	10	has	have	VERB
ejpam-2753	87	11	a	a	DET
ejpam-2753	87	12	finite	finite	ADJ
ejpam-2753	87	13	basis	basis	NOUN
ejpam-2753	87	14	.	.	PUNCT
ejpam-2753	88	1	example	example	NOUN
ejpam-2753	89	1	1	1	NUM
ejpam-2753	89	2	.	.	PUNCT
ejpam-2753	90	1	[	[	X
ejpam-2753	90	2	2	2	NUM
ejpam-2753	90	3	]	]	PUNCT
ejpam-2753	90	4	consider	consider	VERB
ejpam-2753	90	5	abelian	abelian	ADJ
ejpam-2753	90	6	group	group	NOUN
ejpam-2753	90	7	(	(	PUNCT
ejpam-2753	90	8	r2,+	r2,+	NOUN
ejpam-2753	90	9	)	)	PUNCT
ejpam-2753	90	10	.	.	PUNCT
ejpam-2753	91	1	define	define	VERB
ejpam-2753	91	2	hyper	hyper	NOUN
ejpam-2753	91	3	-	-	NOUN
ejpam-2753	91	4	compositions	composition	NOUN
ejpam-2753	91	5	{	{	PUNCT
ejpam-2753	91	6	◦	◦	NOUN
ejpam-2753	91	7	:	:	PUNCT
ejpam-2753	91	8	r×	r×	NOUN
ejpam-2753	91	9	r2	r2	NOUN
ejpam-2753	91	10	−→	−→	NOUN
ejpam-2753	91	11	p	p	PROPN
ejpam-2753	91	12	∗(r2	∗(r2	NOUN
ejpam-2753	91	13	)	)	PUNCT
ejpam-2753	91	14	a	a	DET
ejpam-2753	91	15	◦	◦	NOUN
ejpam-2753	91	16	(	(	PUNCT
ejpam-2753	91	17	x	x	NOUN
ejpam-2753	91	18	,	,	PUNCT
ejpam-2753	91	19	y	y	PROPN
ejpam-2753	91	20	)	)	PUNCT
ejpam-2753	91	21	=	=	NOUN
ejpam-2753	92	1	ax×	ax×	NOUN
ejpam-2753	92	2	r	r	NOUN
ejpam-2753	92	3	and	and	CCONJ
ejpam-2753	92	4	{	{	PUNCT
ejpam-2753	92	5	�	�	PROPN
ejpam-2753	92	6	:	:	PUNCT
ejpam-2753	92	7	r×	r×	NOUN
ejpam-2753	92	8	r2	r2	NOUN
ejpam-2753	92	9	−→	−→	NOUN
ejpam-2753	92	10	p	p	PROPN
ejpam-2753	92	11	∗(r2	∗(r2	NOUN
ejpam-2753	92	12	)	)	PUNCT
ejpam-2753	92	13	a	a	DET
ejpam-2753	92	14	�	�	PROPN
ejpam-2753	92	15	(	(	PUNCT
ejpam-2753	92	16	x	x	NOUN
ejpam-2753	92	17	,	,	PUNCT
ejpam-2753	92	18	y	y	NOUN
ejpam-2753	92	19	)	)	PUNCT
ejpam-2753	92	20	=	=	PUNCT
ejpam-2753	92	21	r×	r×	NOUN
ejpam-2753	92	22	ay	ay	NOUN
ejpam-2753	92	23	.	.	PUNCT
ejpam-2753	93	1	then	then	ADV
ejpam-2753	93	2	(	(	PUNCT
ejpam-2753	93	3	r2,+	r2,+	NOUN
ejpam-2753	93	4	,	,	PUNCT
ejpam-2753	93	5	◦	◦	NOUN
ejpam-2753	93	6	,	,	PUNCT
ejpam-2753	93	7	r	r	NOUN
ejpam-2753	93	8	)	)	PUNCT
ejpam-2753	93	9	and	and	CCONJ
ejpam-2753	93	10	(	(	PUNCT
ejpam-2753	93	11	r2,+	r2,+	NOUN
ejpam-2753	93	12	,	,	PUNCT
ejpam-2753	93	13	�	�	PROPN
ejpam-2753	93	14	,	,	PUNCT
ejpam-2753	93	15	r	r	NOUN
ejpam-2753	93	16	)	)	PUNCT
ejpam-2753	93	17	are	be	AUX
ejpam-2753	93	18	a	a	DET
ejpam-2753	93	19	strongly	strongly	ADV
ejpam-2753	93	20	distributive	distributive	ADJ
ejpam-2753	93	21	hyperspaces	hyperspace	NOUN
ejpam-2753	93	22	.	.	PUNCT
ejpam-2753	93	23	example	example	NOUN
ejpam-2753	94	1	2	2	NUM
ejpam-2753	94	2	.	.	PUNCT
ejpam-2753	95	1	[	[	X
ejpam-2753	95	2	20	20	NUM
ejpam-2753	95	3	]	]	PUNCT
ejpam-2753	95	4	in	in	ADP
ejpam-2753	95	5	(	(	PUNCT
ejpam-2753	95	6	r2,+	r2,+	NOUN
ejpam-2753	95	7	)	)	PUNCT
ejpam-2753	95	8	define	define	VERB
ejpam-2753	95	9	the	the	DET
ejpam-2753	95	10	hyper	hyper	NOUN
ejpam-2753	95	11	-	-	NOUN
ejpam-2753	95	12	composition	composition	NOUN
ejpam-2753	95	13	◦	◦	NOUN
ejpam-2753	95	14	as	as	SCONJ
ejpam-2753	95	15	follows	follow	VERB
ejpam-2753	95	16	(	(	PUNCT
ejpam-2753	95	17	for	for	ADP
ejpam-2753	95	18	all	all	DET
ejpam-2753	95	19	a	a	DET
ejpam-2753	95	20	∈	∈	NOUN
ejpam-2753	95	21	r	r	NOUN
ejpam-2753	95	22	,	,	PUNCT
ejpam-2753	95	23	and	and	CCONJ
ejpam-2753	95	24	x	x	PUNCT
ejpam-2753	95	25	∈	∈	NOUN
ejpam-2753	95	26	r2	r2	NOUN
ejpam-2753	95	27	):	):	PUNCT
ejpam-2753	95	28	a	a	DET
ejpam-2753	95	29	◦	◦	NOUN
ejpam-2753	95	30	x	x	SYM
ejpam-2753	95	31	=	=	NOUN
ejpam-2753	95	32	{	{	PUNCT
ejpam-2753	95	33	line	line	NOUN
ejpam-2753	95	34	ox	ox	NOUN
ejpam-2753	95	35	if	if	SCONJ
ejpam-2753	95	36	x	x	PROPN
ejpam-2753	95	37	6=	6=	ADP
ejpam-2753	95	38	0v	0v	NOUN
ejpam-2753	95	39	{	{	PUNCT
ejpam-2753	95	40	0v	0v	NOUN
ejpam-2753	95	41	}	}	PUNCT
ejpam-2753	95	42	if	if	SCONJ
ejpam-2753	95	43	x	x	X
ejpam-2753	95	44	=	=	SYM
ejpam-2753	95	45	0v	0v	NOUN
ejpam-2753	95	46	,	,	PUNCT
ejpam-2753	95	47	where	where	SCONJ
ejpam-2753	95	48	0v	0v	X
ejpam-2753	95	49	=	=	SYM
ejpam-2753	95	50	(	(	PUNCT
ejpam-2753	95	51	0	0	NUM
ejpam-2753	95	52	,	,	PUNCT
ejpam-2753	95	53	0	0	NUM
ejpam-2753	95	54	)	)	PUNCT
ejpam-2753	95	55	.	.	PUNCT
ejpam-2753	96	1	then	then	ADV
ejpam-2753	96	2	(	(	PUNCT
ejpam-2753	96	3	r2,+	r2,+	NOUN
ejpam-2753	96	4	,	,	PUNCT
ejpam-2753	96	5	◦	◦	NOUN
ejpam-2753	96	6	,	,	PUNCT
ejpam-2753	96	7	r	r	NOUN
ejpam-2753	96	8	)	)	PUNCT
ejpam-2753	96	9	is	be	AUX
ejpam-2753	96	10	a	a	DET
ejpam-2753	96	11	strongly	strongly	ADV
ejpam-2753	96	12	left	leave	VERB
ejpam-2753	96	13	,	,	PUNCT
ejpam-2753	96	14	but	but	CCONJ
ejpam-2753	96	15	not	not	PART
ejpam-2753	96	16	right	right	ADJ
ejpam-2753	96	17	distributive	distributive	ADJ
ejpam-2753	96	18	hyperspace	hyperspace	NOUN
ejpam-2753	96	19	.	.	PUNCT
ejpam-2753	97	1	proposition	proposition	NOUN
ejpam-2753	97	2	1	1	NUM
ejpam-2753	97	3	.	.	PUNCT
ejpam-2753	98	1	[	[	X
ejpam-2753	98	2	20	20	NUM
ejpam-2753	98	3	]	]	PUNCT
ejpam-2753	98	4	every	every	DET
ejpam-2753	98	5	strongly	strongly	ADV
ejpam-2753	98	6	right	right	ADJ
ejpam-2753	98	7	distributive	distributive	ADJ
ejpam-2753	98	8	hyperspace	hyperspace	NOUN
ejpam-2753	98	9	is	be	AUX
ejpam-2753	98	10	strongly	strongly	ADV
ejpam-2753	98	11	left	leave	VERB
ejpam-2753	98	12	distributive	distributive	ADJ
ejpam-2753	98	13	hyperspace	hyperspace	NOUN
ejpam-2753	98	14	.	.	PUNCT
ejpam-2753	99	1	let	let	AUX
ejpam-2753	99	2	(	(	PUNCT
ejpam-2753	99	3	v,+	v,+	NUM
ejpam-2753	99	4	)	)	PUNCT
ejpam-2753	99	5	be	be	AUX
ejpam-2753	99	6	an	an	DET
ejpam-2753	99	7	abelian	abelian	ADJ
ejpam-2753	99	8	group	group	NOUN
ejpam-2753	99	9	,	,	PUNCT
ejpam-2753	99	10	ω	ω	PROPN
ejpam-2753	99	11	a	a	DET
ejpam-2753	99	12	subgroup	subgroup	NOUN
ejpam-2753	99	13	of	of	ADP
ejpam-2753	99	14	v	v	NOUN
ejpam-2753	99	15	and	and	CCONJ
ejpam-2753	99	16	k	k	NOUN
ejpam-2753	99	17	a	a	DET
ejpam-2753	99	18	field	field	NOUN
ejpam-2753	99	19	such	such	ADJ
ejpam-2753	99	20	that	that	PRON
ejpam-2753	99	21	w	w	PROPN
ejpam-2753	99	22	=	=	SYM
ejpam-2753	99	23	v	v	NOUN
ejpam-2753	99	24	/	/	SYM
ejpam-2753	99	25	ω	ω	PROPN
ejpam-2753	99	26	is	be	AUX
ejpam-2753	99	27	a	a	DET
ejpam-2753	99	28	classical	classical	ADJ
ejpam-2753	99	29	vector	vector	NOUN
ejpam-2753	99	30	space	space	NOUN
ejpam-2753	99	31	over	over	ADP
ejpam-2753	99	32	a	a	DET
ejpam-2753	99	33	field	field	NOUN
ejpam-2753	99	34	k.	k.	NOUN
ejpam-2753	100	1	if	if	SCONJ
ejpam-2753	100	2	p	p	X
ejpam-2753	100	3	:	:	PUNCT
ejpam-2753	100	4	v	v	ADP
ejpam-2753	100	5	−→	−→	NOUN
ejpam-2753	100	6	w	w	NOUN
ejpam-2753	100	7	is	be	AUX
ejpam-2753	100	8	the	the	DET
ejpam-2753	100	9	canonical	canonical	ADJ
ejpam-2753	100	10	projection	projection	NOUN
ejpam-2753	100	11	of	of	ADP
ejpam-2753	100	12	(	(	PUNCT
ejpam-2753	100	13	v,+	v,+	NUM
ejpam-2753	100	14	)	)	PUNCT
ejpam-2753	100	15	onto	onto	ADP
ejpam-2753	100	16	(	(	PUNCT
ejpam-2753	100	17	w,+	w,+	NOUN
ejpam-2753	100	18	)	)	PUNCT
ejpam-2753	100	19	and	and	CCONJ
ejpam-2753	100	20	set	set	VERB
ejpam-2753	100	21	:	:	PUNCT
ejpam-2753	100	22	{	{	PUNCT
ejpam-2753	100	23	◦	◦	NOUN
ejpam-2753	100	24	:	:	PUNCT
ejpam-2753	100	25	k	k	X
ejpam-2753	100	26	×	×	NOUN
ejpam-2753	100	27	v	v	INTJ
ejpam-2753	100	28	−→	−→	NOUN
ejpam-2753	100	29	p	p	X
ejpam-2753	100	30	∗(v	∗(v	PROPN
ejpam-2753	100	31	)	)	PUNCT
ejpam-2753	100	32	a	a	DET
ejpam-2753	100	33	◦	◦	NOUN
ejpam-2753	100	34	x	x	X
ejpam-2753	100	35	=	=	VERB
ejpam-2753	100	36	p−1(a	p−1(a	NOUN
ejpam-2753	100	37	·	·	PUNCT
ejpam-2753	100	38	p(x	p(x	PROPN
ejpam-2753	100	39	)	)	PUNCT
ejpam-2753	100	40	)	)	PUNCT
ejpam-2753	100	41	.	.	PUNCT
ejpam-2753	101	1	then	then	ADV
ejpam-2753	101	2	(	(	PUNCT
ejpam-2753	101	3	v,+	v,+	NUM
ejpam-2753	101	4	,	,	PUNCT
ejpam-2753	101	5	◦	◦	NOUN
ejpam-2753	101	6	,	,	PUNCT
ejpam-2753	101	7	k	k	NOUN
ejpam-2753	101	8	)	)	PUNCT
ejpam-2753	101	9	is	be	AUX
ejpam-2753	101	10	a	a	DET
ejpam-2753	101	11	strongly	strongly	ADV
ejpam-2753	101	12	distributive	distributive	ADJ
ejpam-2753	101	13	hyperspace	hyperspace	NOUN
ejpam-2753	101	14	over	over	ADP
ejpam-2753	101	15	a	a	DET
ejpam-2753	101	16	field	field	NOUN
ejpam-2753	101	17	k.	k.	NOUN
ejpam-2753	102	1	moreover	moreover	ADV
ejpam-2753	102	2	every	every	DET
ejpam-2753	102	3	strongly	strongly	ADV
ejpam-2753	102	4	distributive	distributive	ADJ
ejpam-2753	102	5	hyperspace	hyperspace	NOUN
ejpam-2753	102	6	can	can	AUX
ejpam-2753	102	7	be	be	AUX
ejpam-2753	102	8	obtained	obtain	VERB
ejpam-2753	102	9	in	in	ADP
ejpam-2753	102	10	such	such	DET
ejpam-2753	102	11	a	a	DET
ejpam-2753	102	12	way	way	NOUN
ejpam-2753	102	13	.	.	PUNCT
ejpam-2753	103	1	proposition	proposition	NOUN
ejpam-2753	103	2	2	2	NUM
ejpam-2753	103	3	.	.	PUNCT
ejpam-2753	104	1	[	[	X
ejpam-2753	104	2	20	20	NUM
ejpam-2753	104	3	]	]	X
ejpam-2753	104	4	if	if	SCONJ
ejpam-2753	104	5	(	(	PUNCT
ejpam-2753	104	6	v,+	v,+	NUM
ejpam-2753	104	7	,	,	PUNCT
ejpam-2753	104	8	◦	◦	NOUN
ejpam-2753	104	9	,	,	PUNCT
ejpam-2753	104	10	k	k	NOUN
ejpam-2753	104	11	)	)	PUNCT
ejpam-2753	104	12	is	be	AUX
ejpam-2753	104	13	a	a	DET
ejpam-2753	104	14	left	left	ADJ
ejpam-2753	104	15	distributive	distributive	ADJ
ejpam-2753	104	16	hyperspace	hyperspace	NOUN
ejpam-2753	104	17	,	,	PUNCT
ejpam-2753	104	18	then	then	ADV
ejpam-2753	104	19	for	for	ADP
ejpam-2753	104	20	all	all	DET
ejpam-2753	104	21	a	a	DET
ejpam-2753	104	22	∈	∈	NOUN
ejpam-2753	104	23	k	k	NOUN
ejpam-2753	104	24	and	and	CCONJ
ejpam-2753	104	25	x	x	PROPN
ejpam-2753	104	26	∈	∈	PROPN
ejpam-2753	104	27	v	v	X
ejpam-2753	104	28	:	:	PUNCT
ejpam-2753	104	29	(	(	PUNCT
ejpam-2753	104	30	i	i	NOUN
ejpam-2753	104	31	)	)	PUNCT
ejpam-2753	104	32	0	0	PUNCT
ejpam-2753	105	1	◦	◦	NOUN
ejpam-2753	105	2	x	x	PUNCT
ejpam-2753	105	3	is	be	AUX
ejpam-2753	105	4	a	a	DET
ejpam-2753	105	5	subgroup	subgroup	NOUN
ejpam-2753	105	6	of	of	ADP
ejpam-2753	105	7	(	(	PUNCT
ejpam-2753	105	8	v,+	v,+	NUM
ejpam-2753	105	9	)	)	PUNCT
ejpam-2753	105	10	;	;	PUNCT
ejpam-2753	105	11	(	(	PUNCT
ejpam-2753	105	12	ii	ii	NOUN
ejpam-2753	105	13	)	)	PUNCT
ejpam-2753	105	14	ωv	ωv	ADP
ejpam-2753	105	15	is	be	AUX
ejpam-2753	105	16	a	a	DET
ejpam-2753	105	17	subgroup	subgroup	NOUN
ejpam-2753	105	18	of	of	ADP
ejpam-2753	105	19	(	(	PUNCT
ejpam-2753	105	20	v,+	v,+	NUM
ejpam-2753	105	21	)	)	PUNCT
ejpam-2753	105	22	;	;	PUNCT
ejpam-2753	106	1	r.	r.	PROPN
ejpam-2753	106	2	ameri	ameri	PROPN
ejpam-2753	106	3	,	,	PUNCT
ejpam-2753	106	4	k.	k.	PROPN
ejpam-2753	106	5	ghadimi	ghadimi	PROPN
ejpam-2753	106	6	,	,	PUNCT
ejpam-2753	106	7	r.	r.	PROPN
ejpam-2753	106	8	a.	a.	PROPN
ejpam-2753	106	9	borzooei	borzooei	PROPN
ejpam-2753	106	10	/	/	SYM
ejpam-2753	106	11	eur	eur	PROPN
ejpam-2753	106	12	.	.	PUNCT
ejpam-2753	107	1	j.	j.	PROPN
ejpam-2753	107	2	pure	pure	PROPN
ejpam-2753	107	3	appl	appl	PROPN
ejpam-2753	107	4	.	.	PROPN
ejpam-2753	107	5	math	math	PROPN
ejpam-2753	107	6	,	,	PUNCT
ejpam-2753	107	7	10	10	NUM
ejpam-2753	107	8	(	(	PUNCT
ejpam-2753	107	9	4	4	NUM
ejpam-2753	107	10	)	)	PUNCT
ejpam-2753	107	11	(	(	PUNCT
ejpam-2753	107	12	2017	2017	NUM
ejpam-2753	107	13	)	)	PUNCT
ejpam-2753	107	14	,	,	PUNCT
ejpam-2753	107	15	702	702	NUM
ejpam-2753	107	16	-	-	SYM
ejpam-2753	107	17	716	716	NUM
ejpam-2753	107	18	706	706	NUM
ejpam-2753	107	19	(	(	PUNCT
ejpam-2753	107	20	iii	iii	NOUN
ejpam-2753	107	21	)	)	PUNCT
ejpam-2753	107	22	a	a	DET
ejpam-2753	107	23	◦	◦	NOUN
ejpam-2753	107	24	0v	0v	NOUN
ejpam-2753	107	25	=	=	PUNCT
ejpam-2753	107	26	ωv	ωv	PUNCT
ejpam-2753	107	27	=	=	PUNCT
ejpam-2753	107	28	a	a	DET
ejpam-2753	107	29	◦	◦	NOUN
ejpam-2753	107	30	ωv	ωv	ADP
ejpam-2753	107	31	;	;	PUNCT
ejpam-2753	107	32	(	(	PUNCT
ejpam-2753	107	33	iv	iv	X
ejpam-2753	107	34	)	)	PUNCT
ejpam-2753	107	35	ωv	ωv	ADP
ejpam-2753	107	36	⊆	⊆	NUM
ejpam-2753	107	37	0	0	NUM
ejpam-2753	107	38	◦	◦	NOUN
ejpam-2753	107	39	x	x	SYM
ejpam-2753	107	40	;	;	PUNCT
ejpam-2753	107	41	(	(	PUNCT
ejpam-2753	107	42	v	v	NOUN
ejpam-2753	107	43	)	)	PUNCT
ejpam-2753	107	44	x	x	SYM
ejpam-2753	107	45	∈	∈	NOUN
ejpam-2753	107	46	0	0	NUM
ejpam-2753	108	1	◦	◦	NOUN
ejpam-2753	108	2	x	x	SYM
ejpam-2753	108	3	⇐	⇐	ADJ
ejpam-2753	108	4	⇒	⇒	NOUN
ejpam-2753	108	5	1	1	NUM
ejpam-2753	108	6	◦	◦	NOUN
ejpam-2753	108	7	x	x	SYM
ejpam-2753	108	8	=	=	SYM
ejpam-2753	108	9	0	0	NUM
ejpam-2753	108	10	◦	◦	NOUN
ejpam-2753	108	11	x	x	SYM
ejpam-2753	108	12	⇐	⇐	ADJ
ejpam-2753	108	13	⇒	⇒	NOUN
ejpam-2753	108	14	a	a	DET
ejpam-2753	108	15	◦	◦	NOUN
ejpam-2753	108	16	x	x	PUNCT
ejpam-2753	108	17	=	=	SYM
ejpam-2753	108	18	0	0	NUM
ejpam-2753	108	19	◦	◦	NOUN
ejpam-2753	108	20	x.	x.	NOUN
ejpam-2753	108	21	remark	remark	NOUN
ejpam-2753	108	22	2	2	NUM
ejpam-2753	108	23	.	.	PUNCT
ejpam-2753	109	1	let	let	AUX
ejpam-2753	109	2	(	(	PUNCT
ejpam-2753	109	3	v,+	v,+	NUM
ejpam-2753	109	4	,	,	PUNCT
ejpam-2753	109	5	◦	◦	NOUN
ejpam-2753	109	6	,	,	PUNCT
ejpam-2753	109	7	k	k	NOUN
ejpam-2753	109	8	)	)	PUNCT
ejpam-2753	109	9	be	be	AUX
ejpam-2753	109	10	a	a	DET
ejpam-2753	109	11	hyperspace	hyperspace	NOUN
ejpam-2753	109	12	and	and	CCONJ
ejpam-2753	109	13	w	w	AUX
ejpam-2753	109	14	be	be	AUX
ejpam-2753	109	15	a	a	DET
ejpam-2753	109	16	subhyperspace	subhyperspace	NOUN
ejpam-2753	109	17	of	of	ADP
ejpam-2753	109	18	v	v	NOUN
ejpam-2753	109	19	.	.	PUNCT
ejpam-2753	110	1	consider	consider	VERB
ejpam-2753	110	2	the	the	DET
ejpam-2753	110	3	quotient	quotient	NOUN
ejpam-2753	110	4	abelian	abelian	PROPN
ejpam-2753	110	5	group	group	PROPN
ejpam-2753	110	6	(	(	PUNCT
ejpam-2753	110	7	v	v	NOUN
ejpam-2753	110	8	/	/	SYM
ejpam-2753	110	9	w,+	w,+	NOUN
ejpam-2753	110	10	)	)	PUNCT
ejpam-2753	110	11	.	.	PUNCT
ejpam-2753	111	1	define	define	VERB
ejpam-2753	111	2	the	the	DET
ejpam-2753	111	3	rule	rule	NOUN
ejpam-2753	111	4	{	{	PUNCT
ejpam-2753	111	5	∗	∗	NOUN
ejpam-2753	111	6	:	:	PUNCT
ejpam-2753	112	1	k	k	PROPN
ejpam-2753	112	2	×	×	PROPN
ejpam-2753	112	3	v	v	NOUN
ejpam-2753	112	4	/	/	SYM
ejpam-2753	112	5	w	w	NOUN
ejpam-2753	112	6	−→	−→	NOUN
ejpam-2753	112	7	p	p	PROPN
ejpam-2753	112	8	∗(v	∗(v	PROPN
ejpam-2753	112	9	/	/	SYM
ejpam-2753	112	10	w	w	PROPN
ejpam-2753	112	11	)	)	PUNCT
ejpam-2753	112	12	(	(	PUNCT
ejpam-2753	112	13	a	a	PRON
ejpam-2753	112	14	,	,	PUNCT
ejpam-2753	112	15	x+w	x+w	NUM
ejpam-2753	112	16	)	)	PUNCT
ejpam-2753	112	17	7−→	7−→	NOUN
ejpam-2753	112	18	a	a	DET
ejpam-2753	112	19	◦	◦	NOUN
ejpam-2753	112	20	x+w	x+w	NUM
ejpam-2753	112	21	.	.	PUNCT
ejpam-2753	113	1	then	then	ADV
ejpam-2753	113	2	it	it	PRON
ejpam-2753	113	3	is	be	AUX
ejpam-2753	113	4	easy	easy	ADJ
ejpam-2753	113	5	to	to	PART
ejpam-2753	113	6	verify	verify	VERB
ejpam-2753	113	7	that	that	SCONJ
ejpam-2753	113	8	(	(	PUNCT
ejpam-2753	113	9	v	v	NOUN
ejpam-2753	113	10	/	/	SYM
ejpam-2753	113	11	w,+	w,+	NOUN
ejpam-2753	113	12	,	,	PUNCT
ejpam-2753	113	13	∗,k	∗,k	NOUN
ejpam-2753	113	14	)	)	PUNCT
ejpam-2753	113	15	is	be	AUX
ejpam-2753	113	16	a	a	DET
ejpam-2753	113	17	hyperspace	hyperspace	NOUN
ejpam-2753	113	18	over	over	ADP
ejpam-2753	113	19	k	k	PROPN
ejpam-2753	113	20	and	and	CCONJ
ejpam-2753	113	21	it	it	PRON
ejpam-2753	113	22	is	be	AUX
ejpam-2753	113	23	called	call	VERB
ejpam-2753	113	24	the	the	DET
ejpam-2753	113	25	quotient	quotient	NOUN
ejpam-2753	113	26	hyperspace	hyperspace	NOUN
ejpam-2753	113	27	of	of	ADP
ejpam-2753	113	28	v	v	NOUN
ejpam-2753	113	29	over	over	ADP
ejpam-2753	113	30	w	w	PROPN
ejpam-2753	113	31	.	.	PUNCT
ejpam-2753	114	1	definition	definition	NOUN
ejpam-2753	114	2	10	10	NUM
ejpam-2753	114	3	.	.	PUNCT
ejpam-2753	115	1	[	[	X
ejpam-2753	115	2	2	2	X
ejpam-2753	115	3	]	]	PUNCT
ejpam-2753	115	4	let	let	VERB
ejpam-2753	115	5	v	v	NOUN
ejpam-2753	115	6	and	and	CCONJ
ejpam-2753	115	7	w	w	NOUN
ejpam-2753	115	8	be	be	AUX
ejpam-2753	115	9	two	two	NUM
ejpam-2753	115	10	hyperspaces	hyperspace	NOUN
ejpam-2753	115	11	over	over	ADP
ejpam-2753	115	12	a	a	DET
ejpam-2753	115	13	field	field	NOUN
ejpam-2753	115	14	k.	k.	PROPN
ejpam-2753	116	1	a	a	DET
ejpam-2753	116	2	mapping	mapping	NOUN
ejpam-2753	116	3	t	t	NOUN
ejpam-2753	116	4	:	:	PUNCT
ejpam-2753	116	5	v	v	SCONJ
ejpam-2753	116	6	−→	−→	NOUN
ejpam-2753	116	7	w	w	NOUN
ejpam-2753	116	8	is	be	AUX
ejpam-2753	116	9	called	call	VERB
ejpam-2753	116	10	(	(	PUNCT
ejpam-2753	116	11	for	for	ADP
ejpam-2753	116	12	all	all	DET
ejpam-2753	116	13	x	x	NOUN
ejpam-2753	116	14	,	,	PUNCT
ejpam-2753	116	15	y	y	PROPN
ejpam-2753	116	16	∈	∈	PROPN
ejpam-2753	116	17	v	v	NOUN
ejpam-2753	116	18	,	,	PUNCT
ejpam-2753	116	19	and	and	CCONJ
ejpam-2753	116	20	a	a	DET
ejpam-2753	116	21	∈	∈	PROPN
ejpam-2753	116	22	k	k	NOUN
ejpam-2753	116	23	):	):	PUNCT
ejpam-2753	116	24	(	(	PUNCT
ejpam-2753	116	25	i	i	NOUN
ejpam-2753	116	26	)	)	PUNCT
ejpam-2753	116	27	weak	weak	ADJ
ejpam-2753	116	28	linear	linear	ADJ
ejpam-2753	116	29	transformation	transformation	NOUN
ejpam-2753	116	30	(	(	PUNCT
ejpam-2753	116	31	wlt	wlt	PROPN
ejpam-2753	116	32	)	)	PUNCT
ejpam-2753	117	1	iff	iff	PROPN
ejpam-2753	117	2	t	t	PROPN
ejpam-2753	117	3	(	(	PUNCT
ejpam-2753	117	4	x+	x+	PROPN
ejpam-2753	117	5	y	y	NOUN
ejpam-2753	117	6	)	)	PUNCT
ejpam-2753	118	1	=	=	SYM
ejpam-2753	118	2	t	t	PROPN
ejpam-2753	118	3	(	(	PUNCT
ejpam-2753	118	4	x	x	X
ejpam-2753	118	5	)	)	PUNCT
ejpam-2753	119	1	+	+	NUM
ejpam-2753	119	2	t	t	PROPN
ejpam-2753	119	3	(	(	PUNCT
ejpam-2753	119	4	y	y	NOUN
ejpam-2753	119	5	)	)	PUNCT
ejpam-2753	119	6	and	and	CCONJ
ejpam-2753	119	7	t	t	PROPN
ejpam-2753	119	8	(	(	PUNCT
ejpam-2753	119	9	a	a	DET
ejpam-2753	119	10	◦	◦	NOUN
ejpam-2753	119	11	x	x	SYM
ejpam-2753	119	12	)	)	PUNCT
ejpam-2753	119	13	∩	∩	NOUN
ejpam-2753	119	14	a	a	DET
ejpam-2753	119	15	◦	◦	NOUN
ejpam-2753	119	16	t	t	X
ejpam-2753	119	17	(	(	PUNCT
ejpam-2753	119	18	x	x	X
ejpam-2753	119	19	)	)	PUNCT
ejpam-2753	119	20	6=	6=	NUM
ejpam-2753	119	21	∅	∅	NOUN
ejpam-2753	119	22	;	;	PUNCT
ejpam-2753	119	23	(	(	PUNCT
ejpam-2753	119	24	ii	ii	NOUN
ejpam-2753	119	25	)	)	PUNCT
ejpam-2753	119	26	linear	linear	PROPN
ejpam-2753	119	27	transformation	transformation	NOUN
ejpam-2753	119	28	(	(	PUNCT
ejpam-2753	119	29	lt	lt	NOUN
ejpam-2753	119	30	)	)	PUNCT
ejpam-2753	119	31	iff	iff	PROPN
ejpam-2753	119	32	t	t	PROPN
ejpam-2753	119	33	(	(	PUNCT
ejpam-2753	119	34	x+	x+	PROPN
ejpam-2753	119	35	y	y	NOUN
ejpam-2753	119	36	)	)	PUNCT
ejpam-2753	119	37	=	=	SYM
ejpam-2753	119	38	t	t	PROPN
ejpam-2753	119	39	(	(	PUNCT
ejpam-2753	119	40	x	x	X
ejpam-2753	119	41	)	)	PUNCT
ejpam-2753	120	1	+	+	NUM
ejpam-2753	120	2	t	t	PROPN
ejpam-2753	120	3	(	(	PUNCT
ejpam-2753	120	4	y	y	NOUN
ejpam-2753	120	5	)	)	PUNCT
ejpam-2753	120	6	and	and	CCONJ
ejpam-2753	120	7	t	t	PROPN
ejpam-2753	120	8	(	(	PUNCT
ejpam-2753	120	9	a	a	DET
ejpam-2753	120	10	◦	◦	NOUN
ejpam-2753	120	11	x	x	SYM
ejpam-2753	120	12	)	)	PUNCT
ejpam-2753	120	13	⊆	⊆	NUM
ejpam-2753	120	14	a	a	DET
ejpam-2753	120	15	◦	◦	NOUN
ejpam-2753	120	16	t	t	X
ejpam-2753	120	17	(	(	PUNCT
ejpam-2753	120	18	x	x	NOUN
ejpam-2753	120	19	)	)	PUNCT
ejpam-2753	120	20	;	;	PUNCT
ejpam-2753	120	21	(	(	PUNCT
ejpam-2753	120	22	iii	iii	X
ejpam-2753	120	23	)	)	PUNCT
ejpam-2753	120	24	strong	strong	ADJ
ejpam-2753	120	25	linear	linear	ADJ
ejpam-2753	120	26	transformation	transformation	NOUN
ejpam-2753	120	27	(	(	PUNCT
ejpam-2753	120	28	slt	slt	PROPN
ejpam-2753	120	29	)	)	PUNCT
ejpam-2753	120	30	iff	iff	PROPN
ejpam-2753	120	31	t	t	PROPN
ejpam-2753	120	32	(	(	PUNCT
ejpam-2753	120	33	x+	x+	PROPN
ejpam-2753	120	34	y	y	NOUN
ejpam-2753	120	35	)	)	PUNCT
ejpam-2753	121	1	=	=	SYM
ejpam-2753	121	2	t	t	PROPN
ejpam-2753	121	3	(	(	PUNCT
ejpam-2753	121	4	x	x	X
ejpam-2753	121	5	)	)	PUNCT
ejpam-2753	122	1	+	+	NUM
ejpam-2753	122	2	t	t	PROPN
ejpam-2753	122	3	(	(	PUNCT
ejpam-2753	122	4	y	y	NOUN
ejpam-2753	122	5	)	)	PUNCT
ejpam-2753	122	6	and	and	CCONJ
ejpam-2753	122	7	t	t	PROPN
ejpam-2753	122	8	(	(	PUNCT
ejpam-2753	122	9	a	a	DET
ejpam-2753	122	10	◦	◦	NOUN
ejpam-2753	122	11	x	x	X
ejpam-2753	122	12	)	)	PUNCT
ejpam-2753	122	13	=	=	SYM
ejpam-2753	122	14	a	a	DET
ejpam-2753	122	15	◦	◦	NOUN
ejpam-2753	122	16	t	t	X
ejpam-2753	122	17	(	(	PUNCT
ejpam-2753	122	18	x	x	NOUN
ejpam-2753	122	19	)	)	PUNCT
ejpam-2753	122	20	.	.	PUNCT
ejpam-2753	123	1	a	a	DET
ejpam-2753	123	2	(	(	PUNCT
ejpam-2753	123	3	resp	resp	NOUN
ejpam-2753	123	4	.	.	PUNCT
ejpam-2753	124	1	weak	weak	ADJ
ejpam-2753	124	2	,	,	PUNCT
ejpam-2753	124	3	strong	strong	ADJ
ejpam-2753	124	4	)	)	PUNCT
ejpam-2753	124	5	linear	linear	PROPN
ejpam-2753	124	6	isomorphism	isomorphism	NOUN
ejpam-2753	124	7	is	be	AUX
ejpam-2753	124	8	defined	define	VERB
ejpam-2753	124	9	as	as	ADP
ejpam-2753	124	10	usual	usual	ADJ
ejpam-2753	124	11	.	.	PUNCT
ejpam-2753	125	1	if	if	SCONJ
ejpam-2753	125	2	t	t	PROPN
ejpam-2753	125	3	:	:	PUNCT
ejpam-2753	125	4	v	v	ADP
ejpam-2753	125	5	−→	−→	NOUN
ejpam-2753	125	6	w	w	NOUN
ejpam-2753	125	7	is	be	AUX
ejpam-2753	125	8	a	a	DET
ejpam-2753	125	9	(	(	PUNCT
ejpam-2753	125	10	resp	resp	NOUN
ejpam-2753	125	11	.	.	PUNCT
ejpam-2753	126	1	weak	weak	ADJ
ejpam-2753	126	2	,	,	PUNCT
ejpam-2753	126	3	strong	strong	ADJ
ejpam-2753	126	4	)	)	PUNCT
ejpam-2753	126	5	linear	linear	PROPN
ejpam-2753	126	6	isomorphism	isomorphism	NOUN
ejpam-2753	126	7	,	,	PUNCT
ejpam-2753	126	8	then	then	ADV
ejpam-2753	126	9	it	it	PRON
ejpam-2753	126	10	is	be	AUX
ejpam-2753	126	11	denoted	denote	VERB
ejpam-2753	126	12	by	by	ADP
ejpam-2753	126	13	(	(	PUNCT
ejpam-2753	126	14	resp	resp	NOUN
ejpam-2753	126	15	.	.	PUNCT
ejpam-2753	127	1	v	v	NUM
ejpam-2753	127	2	∼=w	∼=w	NOUN
ejpam-2753	127	3	w	w	PROPN
ejpam-2753	127	4	,	,	PUNCT
ejpam-2753	127	5	v	v	PRON
ejpam-2753	127	6	∼=s	∼=s	PROPN
ejpam-2753	127	7	w	w	PROPN
ejpam-2753	127	8	)	)	PUNCT
ejpam-2753	127	9	v	v	ADP
ejpam-2753	127	10	∼=	∼=	PROPN
ejpam-2753	127	11	w	w	NOUN
ejpam-2753	127	12	.	.	PUNCT
ejpam-2753	128	1	definition	definition	NOUN
ejpam-2753	128	2	11	11	NUM
ejpam-2753	128	3	.	.	PUNCT
ejpam-2753	129	1	[	[	X
ejpam-2753	129	2	2	2	X
ejpam-2753	129	3	]	]	PUNCT
ejpam-2753	129	4	let	let	VERB
ejpam-2753	129	5	v	v	NOUN
ejpam-2753	129	6	and	and	CCONJ
ejpam-2753	129	7	w	w	NOUN
ejpam-2753	129	8	be	be	AUX
ejpam-2753	129	9	two	two	NUM
ejpam-2753	129	10	hyperspaces	hyperspace	NOUN
ejpam-2753	129	11	over	over	ADP
ejpam-2753	129	12	a	a	DET
ejpam-2753	129	13	field	field	NOUN
ejpam-2753	130	1	k	k	PROPN
ejpam-2753	130	2	and	and	CCONJ
ejpam-2753	130	3	t	t	PROPN
ejpam-2753	130	4	:	:	PUNCT
ejpam-2753	130	5	v	v	AUX
ejpam-2753	130	6	−→	−→	NOUN
ejpam-2753	130	7	w	w	NOUN
ejpam-2753	130	8	be	be	AUX
ejpam-2753	130	9	a	a	DET
ejpam-2753	130	10	linear	linear	ADJ
ejpam-2753	130	11	transformation	transformation	NOUN
ejpam-2753	130	12	.	.	PUNCT
ejpam-2753	131	1	the	the	DET
ejpam-2753	131	2	kernel	kernel	NOUN
ejpam-2753	131	3	and	and	CCONJ
ejpam-2753	131	4	image	image	NOUN
ejpam-2753	131	5	of	of	ADP
ejpam-2753	131	6	t	t	PROPN
ejpam-2753	131	7	are	be	AUX
ejpam-2753	131	8	denoted	denote	VERB
ejpam-2753	131	9	by	by	ADP
ejpam-2753	131	10	kert	kert	PROPN
ejpam-2753	131	11	and	and	CCONJ
ejpam-2753	131	12	imt	imt	PROPN
ejpam-2753	131	13	,	,	PUNCT
ejpam-2753	131	14	respectively	respectively	ADV
ejpam-2753	131	15	,	,	PUNCT
ejpam-2753	131	16	are	be	AUX
ejpam-2753	131	17	defined	define	VERB
ejpam-2753	131	18	by	by	ADP
ejpam-2753	131	19	kert	kert	PROPN
ejpam-2753	131	20	=	=	PUNCT
ejpam-2753	131	21	{	{	PUNCT
ejpam-2753	131	22	x	x	SYM
ejpam-2753	131	23	∈	∈	PROPN
ejpam-2753	131	24	v	v	ADP
ejpam-2753	131	25	|	|	ADV
ejpam-2753	131	26	t	t	PROPN
ejpam-2753	131	27	(	(	PUNCT
ejpam-2753	131	28	x	x	X
ejpam-2753	131	29	)	)	PUNCT
ejpam-2753	131	30	∈	∈	PROPN
ejpam-2753	131	31	ωw	ωw	X
ejpam-2753	131	32	}	}	PUNCT
ejpam-2753	131	33	.	.	PUNCT
ejpam-2753	132	1	and	and	CCONJ
ejpam-2753	132	2	imt	imt	PROPN
ejpam-2753	132	3	=	=	SYM
ejpam-2753	132	4	{	{	PUNCT
ejpam-2753	132	5	y	y	PROPN
ejpam-2753	132	6	∈w	∈w	VERB
ejpam-2753	132	7	|	|	ADV
ejpam-2753	132	8	y	y	PROPN
ejpam-2753	132	9	=	=	SYM
ejpam-2753	132	10	t	t	PROPN
ejpam-2753	132	11	(	(	PUNCT
ejpam-2753	132	12	x	x	NOUN
ejpam-2753	132	13	)	)	PUNCT
ejpam-2753	132	14	for	for	ADP
ejpam-2753	132	15	some	some	DET
ejpam-2753	132	16	x	x	SYM
ejpam-2753	132	17	∈	∈	PROPN
ejpam-2753	132	18	v	v	NOUN
ejpam-2753	132	19	}	}	PUNCT
ejpam-2753	132	20	.	.	PUNCT
ejpam-2753	133	1	proposition	proposition	NOUN
ejpam-2753	133	2	3	3	NUM
ejpam-2753	133	3	.	.	PUNCT
ejpam-2753	134	1	[	[	X
ejpam-2753	134	2	2	2	X
ejpam-2753	134	3	]	]	PUNCT
ejpam-2753	134	4	let	let	VERB
ejpam-2753	134	5	t	t	NOUN
ejpam-2753	134	6	:	:	PUNCT
ejpam-2753	134	7	v	v	AUX
ejpam-2753	134	8	−→w	−→w	NOUN
ejpam-2753	134	9	be	be	AUX
ejpam-2753	134	10	a	a	DET
ejpam-2753	134	11	strong	strong	ADJ
ejpam-2753	134	12	linear	linear	ADJ
ejpam-2753	134	13	transformation	transformation	NOUN
ejpam-2753	134	14	.	.	PUNCT
ejpam-2753	135	1	(	(	PUNCT
ejpam-2753	135	2	i	i	NOUN
ejpam-2753	135	3	)	)	PUNCT
ejpam-2753	135	4	if	if	SCONJ
ejpam-2753	135	5	z	z	NOUN
ejpam-2753	135	6	is	be	AUX
ejpam-2753	135	7	a	a	DET
ejpam-2753	135	8	subhyperspace	subhyperspace	NOUN
ejpam-2753	135	9	of	of	ADP
ejpam-2753	135	10	v	v	NOUN
ejpam-2753	135	11	,	,	PUNCT
ejpam-2753	135	12	then	then	ADV
ejpam-2753	135	13	the	the	DET
ejpam-2753	135	14	image	image	NOUN
ejpam-2753	135	15	of	of	ADP
ejpam-2753	135	16	z	z	PROPN
ejpam-2753	135	17	,	,	PUNCT
ejpam-2753	135	18	t	t	PROPN
ejpam-2753	135	19	(	(	PUNCT
ejpam-2753	135	20	z	z	NOUN
ejpam-2753	135	21	)	)	PUNCT
ejpam-2753	135	22	is	be	AUX
ejpam-2753	135	23	a	a	DET
ejpam-2753	135	24	subhyperspace	subhyperspace	NOUN
ejpam-2753	135	25	of	of	ADP
ejpam-2753	135	26	w	w	PROPN
ejpam-2753	135	27	.	.	PUNCT
ejpam-2753	136	1	in	in	ADP
ejpam-2753	136	2	particular	particular	ADJ
ejpam-2753	136	3	imt	imt	PROPN
ejpam-2753	136	4	is	be	AUX
ejpam-2753	136	5	a	a	DET
ejpam-2753	136	6	subhyperspace	subhyperspace	NOUN
ejpam-2753	136	7	of	of	ADP
ejpam-2753	136	8	w	w	PROPN
ejpam-2753	136	9	.	.	PUNCT
ejpam-2753	137	1	r.	r.	PROPN
ejpam-2753	137	2	ameri	ameri	PROPN
ejpam-2753	137	3	,	,	PUNCT
ejpam-2753	137	4	k.	k.	PROPN
ejpam-2753	137	5	ghadimi	ghadimi	PROPN
ejpam-2753	137	6	,	,	PUNCT
ejpam-2753	137	7	r.	r.	PROPN
ejpam-2753	137	8	a.	a.	PROPN
ejpam-2753	137	9	borzooei	borzooei	PROPN
ejpam-2753	137	10	/	/	SYM
ejpam-2753	137	11	eur	eur	PROPN
ejpam-2753	137	12	.	.	PUNCT
ejpam-2753	138	1	j.	j.	PROPN
ejpam-2753	138	2	pure	pure	PROPN
ejpam-2753	138	3	appl	appl	PROPN
ejpam-2753	138	4	.	.	PROPN
ejpam-2753	138	5	math	math	PROPN
ejpam-2753	138	6	,	,	PUNCT
ejpam-2753	138	7	10	10	NUM
ejpam-2753	138	8	(	(	PUNCT
ejpam-2753	138	9	4	4	NUM
ejpam-2753	138	10	)	)	PUNCT
ejpam-2753	138	11	(	(	PUNCT
ejpam-2753	138	12	2017	2017	NUM
ejpam-2753	138	13	)	)	PUNCT
ejpam-2753	138	14	,	,	PUNCT
ejpam-2753	138	15	702	702	NUM
ejpam-2753	138	16	-	-	SYM
ejpam-2753	138	17	716	716	NUM
ejpam-2753	138	18	707	707	NUM
ejpam-2753	138	19	(	(	PUNCT
ejpam-2753	138	20	ii	ii	NOUN
ejpam-2753	138	21	)	)	PUNCT
ejpam-2753	138	22	if	if	SCONJ
ejpam-2753	138	23	l	l	NOUN
ejpam-2753	138	24	is	be	AUX
ejpam-2753	138	25	a	a	DET
ejpam-2753	138	26	subhyperspace	subhyperspace	NOUN
ejpam-2753	138	27	of	of	ADP
ejpam-2753	138	28	w	w	NOUN
ejpam-2753	138	29	,	,	PUNCT
ejpam-2753	138	30	then	then	ADV
ejpam-2753	138	31	the	the	DET
ejpam-2753	138	32	preimage	preimage	NOUN
ejpam-2753	138	33	of	of	ADP
ejpam-2753	138	34	l	l	PROPN
ejpam-2753	138	35	,	,	PUNCT
ejpam-2753	138	36	t−1(l	t−1(l	PROPN
ejpam-2753	138	37	)	)	PUNCT
ejpam-2753	138	38	is	be	AUX
ejpam-2753	138	39	a	a	DET
ejpam-2753	138	40	subhyperspace	subhyperspace	NOUN
ejpam-2753	138	41	of	of	ADP
ejpam-2753	138	42	v	v	NOUN
ejpam-2753	138	43	containing	contain	VERB
ejpam-2753	138	44	kert	kert	PROPN
ejpam-2753	138	45	.	.	PUNCT
ejpam-2753	139	1	definition	definition	NOUN
ejpam-2753	139	2	12	12	NUM
ejpam-2753	139	3	.	.	PUNCT
ejpam-2753	140	1	let	let	VERB
ejpam-2753	140	2	v	v	NOUN
ejpam-2753	140	3	and	and	CCONJ
ejpam-2753	140	4	w	w	NOUN
ejpam-2753	140	5	be	be	AUX
ejpam-2753	140	6	two	two	NUM
ejpam-2753	140	7	hyperspaces	hyperspace	NOUN
ejpam-2753	140	8	over	over	ADP
ejpam-2753	140	9	a	a	DET
ejpam-2753	140	10	field	field	NOUN
ejpam-2753	140	11	k.	k.	NOUN
ejpam-2753	141	1	a	a	DET
ejpam-2753	141	2	multivalued	multivalue	VERB
ejpam-2753	141	3	linear	linear	ADJ
ejpam-2753	141	4	transformation	transformation	NOUN
ejpam-2753	141	5	(	(	PUNCT
ejpam-2753	141	6	mlt	mlt	PROPN
ejpam-2753	141	7	)	)	PUNCT
ejpam-2753	141	8	,	,	PUNCT
ejpam-2753	141	9	t	t	PROPN
ejpam-2753	141	10	:	:	PUNCT
ejpam-2753	141	11	v	v	ADP
ejpam-2753	141	12	−→	−→	NOUN
ejpam-2753	141	13	p	p	X
ejpam-2753	141	14	∗(w	∗(w	NOUN
ejpam-2753	141	15	)	)	PUNCT
ejpam-2753	141	16	is	be	AUX
ejpam-2753	141	17	a	a	DET
ejpam-2753	141	18	mapping	mapping	NOUN
ejpam-2753	141	19	such	such	ADJ
ejpam-2753	141	20	that	that	PRON
ejpam-2753	141	21	for	for	ADP
ejpam-2753	141	22	all	all	DET
ejpam-2753	141	23	x	x	NOUN
ejpam-2753	141	24	,	,	PUNCT
ejpam-2753	141	25	y	y	PROPN
ejpam-2753	141	26	∈	∈	PROPN
ejpam-2753	141	27	v	v	NOUN
ejpam-2753	141	28	,	,	PUNCT
ejpam-2753	141	29	and	and	CCONJ
ejpam-2753	141	30	a	a	DET
ejpam-2753	141	31	∈	∈	ADJ
ejpam-2753	141	32	k	k	NOUN
ejpam-2753	141	33	:	:	PUNCT
ejpam-2753	141	34	(	(	PUNCT
ejpam-2753	141	35	i	i	NOUN
ejpam-2753	141	36	)	)	PUNCT
ejpam-2753	141	37	t	t	PROPN
ejpam-2753	141	38	(	(	PUNCT
ejpam-2753	141	39	x+	x+	PROPN
ejpam-2753	141	40	y	y	PROPN
ejpam-2753	141	41	)	)	PUNCT
ejpam-2753	141	42	⊆	⊆	NUM
ejpam-2753	141	43	t	t	NOUN
ejpam-2753	141	44	(	(	PUNCT
ejpam-2753	141	45	x	x	X
ejpam-2753	141	46	)	)	PUNCT
ejpam-2753	142	1	+	+	NUM
ejpam-2753	142	2	t	t	PROPN
ejpam-2753	142	3	(	(	PUNCT
ejpam-2753	142	4	y	y	PROPN
ejpam-2753	142	5	)	)	PUNCT
ejpam-2753	142	6	;	;	PUNCT
ejpam-2753	142	7	(	(	PUNCT
ejpam-2753	142	8	ii	ii	NOUN
ejpam-2753	142	9	)	)	PUNCT
ejpam-2753	142	10	t	t	PROPN
ejpam-2753	142	11	(	(	PUNCT
ejpam-2753	142	12	a	a	DET
ejpam-2753	142	13	◦	◦	NOUN
ejpam-2753	142	14	x	x	SYM
ejpam-2753	142	15	)	)	PUNCT
ejpam-2753	142	16	⊆	⊆	NUM
ejpam-2753	142	17	a	a	DET
ejpam-2753	142	18	◦	◦	NOUN
ejpam-2753	142	19	t	t	X
ejpam-2753	142	20	(	(	PUNCT
ejpam-2753	142	21	x	x	NOUN
ejpam-2753	142	22	)	)	PUNCT
ejpam-2753	142	23	;	;	PUNCT
ejpam-2753	142	24	(	(	PUNCT
ejpam-2753	142	25	iii	iii	X
ejpam-2753	142	26	)	)	PUNCT
ejpam-2753	142	27	t	t	NOUN
ejpam-2753	142	28	(	(	PUNCT
ejpam-2753	142	29	−x	−x	NOUN
ejpam-2753	142	30	)	)	PUNCT
ejpam-2753	142	31	=	=	SYM
ejpam-2753	142	32	−t	−t	NOUN
ejpam-2753	142	33	(	(	PUNCT
ejpam-2753	142	34	x	x	NOUN
ejpam-2753	142	35	)	)	PUNCT
ejpam-2753	142	36	;	;	PUNCT
ejpam-2753	142	37	(	(	PUNCT
ejpam-2753	142	38	iv	iv	X
ejpam-2753	142	39	)	)	PUNCT
ejpam-2753	142	40	t	t	NOUN
ejpam-2753	142	41	(	(	PUNCT
ejpam-2753	142	42	0	0	NUM
ejpam-2753	142	43	)	)	PUNCT
ejpam-2753	142	44	=	=	PRON
ejpam-2753	142	45	{	{	PUNCT
ejpam-2753	142	46	0	0	NUM
ejpam-2753	142	47	}	}	PUNCT
ejpam-2753	142	48	.	.	PUNCT
ejpam-2753	143	1	remark	remark	NOUN
ejpam-2753	143	2	3	3	NUM
ejpam-2753	143	3	.	.	PUNCT
ejpam-2753	144	1	(	(	PUNCT
ejpam-2753	144	2	i	i	NOUN
ejpam-2753	144	3	)	)	PUNCT
ejpam-2753	144	4	in	in	ADP
ejpam-2753	144	5	definition	definition	NOUN
ejpam-2753	144	6	12(i	12(i	NUM
ejpam-2753	144	7	)	)	PUNCT
ejpam-2753	144	8	and	and	CCONJ
ejpam-2753	144	9	(	(	PUNCT
ejpam-2753	144	10	ii	ii	NOUN
ejpam-2753	144	11	)	)	PUNCT
ejpam-2753	144	12	,	,	PUNCT
ejpam-2753	144	13	if	if	SCONJ
ejpam-2753	144	14	the	the	DET
ejpam-2753	144	15	equality	equality	NOUN
ejpam-2753	144	16	holds	hold	VERB
ejpam-2753	144	17	,	,	PUNCT
ejpam-2753	144	18	then	then	ADV
ejpam-2753	144	19	t	t	PROPN
ejpam-2753	144	20	is	be	AUX
ejpam-2753	144	21	called	call	VERB
ejpam-2753	144	22	a	a	DET
ejpam-2753	144	23	strong	strong	ADJ
ejpam-2753	144	24	multivalued	multivalued	ADJ
ejpam-2753	144	25	linear	linear	ADJ
ejpam-2753	144	26	transformation	transformation	NOUN
ejpam-2753	144	27	(	(	PUNCT
ejpam-2753	144	28	smlt	smlt	NOUN
ejpam-2753	144	29	)	)	PUNCT
ejpam-2753	144	30	.	.	PUNCT
ejpam-2753	145	1	(	(	PUNCT
ejpam-2753	145	2	ii	ii	NOUN
ejpam-2753	145	3	)	)	PUNCT
ejpam-2753	145	4	in	in	ADP
ejpam-2753	145	5	definition	definition	NOUN
ejpam-2753	145	6	12	12	NUM
ejpam-2753	145	7	,	,	PUNCT
ejpam-2753	145	8	if	if	SCONJ
ejpam-2753	145	9	we	we	PRON
ejpam-2753	145	10	consider	consider	VERB
ejpam-2753	145	11	t	t	NOUN
ejpam-2753	145	12	as	as	ADP
ejpam-2753	145	13	a	a	DET
ejpam-2753	145	14	mapping	mapping	NOUN
ejpam-2753	145	15	t	t	NOUN
ejpam-2753	145	16	:	:	PUNCT
ejpam-2753	145	17	v	v	ADP
ejpam-2753	145	18	−→w	−→w	NOUN
ejpam-2753	145	19	,	,	PUNCT
ejpam-2753	145	20	then	then	ADV
ejpam-2753	145	21	it	it	PRON
ejpam-2753	145	22	is	be	AUX
ejpam-2753	145	23	called	call	VERB
ejpam-2753	145	24	a	a	DET
ejpam-2753	145	25	linear	linear	ADJ
ejpam-2753	145	26	transformation	transformation	NOUN
ejpam-2753	145	27	.	.	PUNCT
ejpam-2753	146	1	here	here	ADV
ejpam-2753	146	2	we	we	PRON
ejpam-2753	146	3	consider	consider	VERB
ejpam-2753	146	4	only	only	ADV
ejpam-2753	146	5	inclusion	inclusion	NOUN
ejpam-2753	146	6	and	and	CCONJ
ejpam-2753	146	7	equality	equality	NOUN
ejpam-2753	146	8	cases	case	NOUN
ejpam-2753	146	9	.	.	PUNCT
ejpam-2753	147	1	definition	definition	NOUN
ejpam-2753	147	2	13	13	NUM
ejpam-2753	147	3	.	.	PUNCT
ejpam-2753	148	1	the	the	DET
ejpam-2753	148	2	category	category	NOUN
ejpam-2753	148	3	of	of	ADP
ejpam-2753	148	4	hyperspaces	hyperspace	NOUN
ejpam-2753	148	5	over	over	ADP
ejpam-2753	148	6	a	a	DET
ejpam-2753	148	7	field	field	NOUN
ejpam-2753	148	8	k	k	NOUN
ejpam-2753	148	9	denoted	denote	VERB
ejpam-2753	148	10	by	by	ADP
ejpam-2753	148	11	hvk	hvk	PROPN
ejpam-2753	148	12	is	be	AUX
ejpam-2753	148	13	defined	define	VERB
ejpam-2753	148	14	as	as	SCONJ
ejpam-2753	148	15	follows	follow	VERB
ejpam-2753	148	16	:	:	PUNCT
ejpam-2753	148	17	(	(	PUNCT
ejpam-2753	148	18	i	i	NOUN
ejpam-2753	148	19	)	)	PUNCT
ejpam-2753	148	20	the	the	DET
ejpam-2753	148	21	objects	object	NOUN
ejpam-2753	148	22	of	of	ADP
ejpam-2753	148	23	hvk	hvk	PROPN
ejpam-2753	148	24	are	be	AUX
ejpam-2753	148	25	all	all	PRON
ejpam-2753	148	26	hyperspaces	hyperspace	NOUN
ejpam-2753	148	27	over	over	ADP
ejpam-2753	148	28	k	k	NOUN
ejpam-2753	148	29	;	;	PUNCT
ejpam-2753	148	30	(	(	PUNCT
ejpam-2753	148	31	ii	ii	NOUN
ejpam-2753	148	32	)	)	PUNCT
ejpam-2753	148	33	for	for	ADP
ejpam-2753	148	34	the	the	DET
ejpam-2753	148	35	objects	object	NOUN
ejpam-2753	148	36	v	v	ADP
ejpam-2753	148	37	and	and	CCONJ
ejpam-2753	148	38	w	w	PROPN
ejpam-2753	148	39	of	of	ADP
ejpam-2753	148	40	hvk	hvk	PROPN
ejpam-2753	148	41	,	,	PUNCT
ejpam-2753	148	42	the	the	DET
ejpam-2753	148	43	set	set	NOUN
ejpam-2753	148	44	of	of	ADP
ejpam-2753	148	45	all	all	DET
ejpam-2753	148	46	morphisms	morphism	NOUN
ejpam-2753	148	47	from	from	ADP
ejpam-2753	148	48	v	v	NUM
ejpam-2753	148	49	to	to	ADP
ejpam-2753	148	50	w	w	NOUN
ejpam-2753	148	51	denoted	denote	VERB
ejpam-2753	148	52	by	by	ADP
ejpam-2753	148	53	homk(v	homk(v	PROPN
ejpam-2753	148	54	,	,	PUNCT
ejpam-2753	148	55	w	w	NOUN
ejpam-2753	148	56	)	)	PUNCT
ejpam-2753	148	57	,	,	PUNCT
ejpam-2753	148	58	is	be	AUX
ejpam-2753	148	59	the	the	DET
ejpam-2753	148	60	set	set	NOUN
ejpam-2753	148	61	of	of	ADP
ejpam-2753	148	62	all	all	DET
ejpam-2753	148	63	mlt	mlt	NOUN
ejpam-2753	148	64	from	from	ADP
ejpam-2753	148	65	v	v	NUM
ejpam-2753	148	66	to	to	ADP
ejpam-2753	148	67	w	w	PROPN
ejpam-2753	148	68	.	.	PUNCT
ejpam-2753	149	1	(	(	PUNCT
ejpam-2753	149	2	iii	iii	X
ejpam-2753	149	3	)	)	PUNCT
ejpam-2753	149	4	the	the	DET
ejpam-2753	149	5	composition	composition	NOUN
ejpam-2753	149	6	st	st	NOUN
ejpam-2753	149	7	:	:	PUNCT
ejpam-2753	149	8	v	v	ADP
ejpam-2753	149	9	−→	−→	NOUN
ejpam-2753	149	10	p	p	X
ejpam-2753	149	11	∗(w	∗(w	NOUN
ejpam-2753	149	12	)	)	PUNCT
ejpam-2753	149	13	of	of	ADP
ejpam-2753	149	14	morphisms	morphism	NOUN
ejpam-2753	149	15	t	t	NOUN
ejpam-2753	149	16	:	:	PUNCT
ejpam-2753	149	17	v	v	ADP
ejpam-2753	149	18	−→	−→	NOUN
ejpam-2753	149	19	p	p	X
ejpam-2753	149	20	∗(l	∗(l	PROPN
ejpam-2753	149	21	)	)	PUNCT
ejpam-2753	149	22	and	and	CCONJ
ejpam-2753	149	23	s	s	VERB
ejpam-2753	149	24	:	:	PUNCT
ejpam-2753	149	25	l	l	NOUN
ejpam-2753	149	26	−→	−→	NOUN
ejpam-2753	149	27	p	p	X
ejpam-2753	149	28	∗(w	∗(w	NOUN
ejpam-2753	149	29	)	)	PUNCT
ejpam-2753	149	30	is	be	AUX
ejpam-2753	149	31	defined	define	VERB
ejpam-2753	149	32	as	as	SCONJ
ejpam-2753	149	33	follows	follow	VERB
ejpam-2753	149	34	:	:	PUNCT
ejpam-2753	149	35	st	st	PROPN
ejpam-2753	149	36	(	(	PUNCT
ejpam-2753	149	37	x	x	NOUN
ejpam-2753	149	38	)	)	PUNCT
ejpam-2753	149	39	=	=	PUNCT
ejpam-2753	150	1	⋃	⋃	NOUN
ejpam-2753	150	2	t∈t	t∈t	NOUN
ejpam-2753	150	3	(	(	PUNCT
ejpam-2753	150	4	x	x	NOUN
ejpam-2753	150	5	)	)	PUNCT
ejpam-2753	150	6	s(t	s(t	PROPN
ejpam-2753	150	7	)	)	PUNCT
ejpam-2753	150	8	.	.	PUNCT
ejpam-2753	151	1	(	(	PUNCT
ejpam-2753	151	2	iv	iv	X
ejpam-2753	151	3	)	)	PUNCT
ejpam-2753	151	4	for	for	ADP
ejpam-2753	151	5	any	any	DET
ejpam-2753	151	6	object	object	NOUN
ejpam-2753	151	7	v	v	NOUN
ejpam-2753	151	8	,	,	PUNCT
ejpam-2753	151	9	the	the	DET
ejpam-2753	151	10	morphism	morphism	NOUN
ejpam-2753	151	11	1v	1v	NUM
ejpam-2753	151	12	:	:	PUNCT
ejpam-2753	151	13	v	v	X
ejpam-2753	151	14	−→	−→	NOUN
ejpam-2753	151	15	p	p	X
ejpam-2753	151	16	∗(v	∗(v	PROPN
ejpam-2753	151	17	)	)	PUNCT
ejpam-2753	151	18	,	,	PUNCT
ejpam-2753	151	19	x	x	PUNCT
ejpam-2753	151	20	−→	−→	ADJ
ejpam-2753	151	21	{	{	PUNCT
ejpam-2753	151	22	x	x	NOUN
ejpam-2753	151	23	}	}	PUNCT
ejpam-2753	151	24	is	be	AUX
ejpam-2753	151	25	the	the	DET
ejpam-2753	151	26	identity	identity	NOUN
ejpam-2753	151	27	.	.	PUNCT
ejpam-2753	152	1	(	(	PUNCT
ejpam-2753	152	2	v	v	NOUN
ejpam-2753	152	3	)	)	PUNCT
ejpam-2753	152	4	the	the	DET
ejpam-2753	152	5	category	category	NOUN
ejpam-2753	152	6	of	of	ADP
ejpam-2753	152	7	hyperspaces	hyperspace	NOUN
ejpam-2753	152	8	over	over	ADP
ejpam-2753	152	9	a	a	DET
ejpam-2753	152	10	field	field	NOUN
ejpam-2753	152	11	k	k	NOUN
ejpam-2753	152	12	with	with	ADP
ejpam-2753	152	13	(	(	PUNCT
ejpam-2753	152	14	resp	resp	NOUN
ejpam-2753	152	15	.	.	PUNCT
ejpam-2753	153	1	slt	slt	X
ejpam-2753	153	2	)	)	PUNCT
ejpam-2753	153	3	lt	lt	NOUN
ejpam-2753	153	4	is	be	AUX
ejpam-2753	153	5	denoted	denote	VERB
ejpam-2753	153	6	by	by	ADP
ejpam-2753	153	7	(	(	PUNCT
ejpam-2753	153	8	resp	resp	PROPN
ejpam-2753	153	9	.	.	PUNCT
ejpam-2753	154	1	hs	hs	PROPN
ejpam-2753	154	2	k	k	PROPN
ejpam-2753	154	3	)	)	PUNCT
ejpam-2753	155	1	hk	hk	PROPN
ejpam-2753	155	2	.	.	PUNCT
ejpam-2753	156	1	remark	remark	PROPN
ejpam-2753	156	2	4	4	NUM
ejpam-2753	156	3	.	.	PUNCT
ejpam-2753	157	1	if	if	SCONJ
ejpam-2753	157	2	in	in	ADP
ejpam-2753	157	3	definition	definition	NOUN
ejpam-2753	157	4	13	13	NUM
ejpam-2753	157	5	part	part	NOUN
ejpam-2753	157	6	(	(	PUNCT
ejpam-2753	157	7	ii	ii	NOUN
ejpam-2753	157	8	)	)	PUNCT
ejpam-2753	157	9	we	we	PRON
ejpam-2753	157	10	replace	replace	VERB
ejpam-2753	157	11	homk(v	homk(v	PROPN
ejpam-2753	157	12	,	,	PUNCT
ejpam-2753	157	13	w	w	NOUN
ejpam-2753	157	14	)	)	PUNCT
ejpam-2753	157	15	by	by	ADP
ejpam-2753	157	16	homs	hom	NOUN
ejpam-2753	157	17	k(v	k(v	PROPN
ejpam-2753	157	18	,	,	PUNCT
ejpam-2753	157	19	w	w	PROPN
ejpam-2753	157	20	)	)	PUNCT
ejpam-2753	157	21	,	,	PUNCT
ejpam-2753	157	22	the	the	DET
ejpam-2753	157	23	set	set	NOUN
ejpam-2753	157	24	of	of	ADP
ejpam-2753	157	25	all	all	DET
ejpam-2753	157	26	smlt	smlt	NOUN
ejpam-2753	157	27	,	,	PUNCT
ejpam-2753	157	28	then	then	ADV
ejpam-2753	157	29	we	we	PRON
ejpam-2753	157	30	will	will	AUX
ejpam-2753	157	31	obtain	obtain	VERB
ejpam-2753	157	32	a	a	DET
ejpam-2753	157	33	new	new	ADJ
ejpam-2753	157	34	category	category	NOUN
ejpam-2753	157	35	,	,	PUNCT
ejpam-2753	157	36	which	which	PRON
ejpam-2753	157	37	it	it	PRON
ejpam-2753	157	38	denotes	denote	VERB
ejpam-2753	157	39	by	by	ADP
ejpam-2753	157	40	hvsk	hvsk	NOUN
ejpam-2753	157	41	.	.	PUNCT
ejpam-2753	158	1	in	in	ADP
ejpam-2753	158	2	fact	fact	NOUN
ejpam-2753	158	3	,	,	PUNCT
ejpam-2753	158	4	hvsk	hvsk	VERB
ejpam-2753	158	5	�	�	PROPN
ejpam-2753	158	6	hvk	hvk	PROPN
ejpam-2753	158	7	(	(	PUNCT
ejpam-2753	158	8	by	by	ADP
ejpam-2753	158	9	a	a	DET
ejpam-2753	158	10	�	�	PROPN
ejpam-2753	158	11	b	b	NOUN
ejpam-2753	158	12	we	we	PRON
ejpam-2753	158	13	mean	mean	VERB
ejpam-2753	158	14	a	a	PRON
ejpam-2753	158	15	is	be	AUX
ejpam-2753	158	16	a	a	DET
ejpam-2753	158	17	subcategory	subcategory	NOUN
ejpam-2753	158	18	of	of	ADP
ejpam-2753	158	19	b	b	PROPN
ejpam-2753	158	20	)	)	PUNCT
ejpam-2753	158	21	.	.	PUNCT
ejpam-2753	159	1	also	also	ADV
ejpam-2753	159	2	,	,	PUNCT
ejpam-2753	159	3	denote	denote	VERB
ejpam-2753	159	4	the	the	DET
ejpam-2753	159	5	category	category	NOUN
ejpam-2753	159	6	of	of	ADP
ejpam-2753	159	7	all	all	DET
ejpam-2753	159	8	vector	vector	NOUN
ejpam-2753	159	9	spaces	space	NOUN
ejpam-2753	159	10	over	over	ADP
ejpam-2753	159	11	a	a	DET
ejpam-2753	159	12	field	field	NOUN
ejpam-2753	159	13	k	k	NOUN
ejpam-2753	159	14	(	(	PUNCT
ejpam-2753	159	15	k	k	ADJ
ejpam-2753	159	16	-	-	ADJ
ejpam-2753	159	17	vector	vector	NOUN
ejpam-2753	159	18	spaces	space	NOUN
ejpam-2753	159	19	)	)	PUNCT
ejpam-2753	159	20	by	by	ADP
ejpam-2753	159	21	vk	vk	NOUN
ejpam-2753	159	22	.	.	PUNCT
ejpam-2753	160	1	clearly	clearly	ADV
ejpam-2753	160	2	,	,	PUNCT
ejpam-2753	160	3	vk	vk	AUX
ejpam-2753	160	4	�	�	PROPN
ejpam-2753	160	5	hk	hk	PROPN
ejpam-2753	160	6	�	�	PROPN
ejpam-2753	160	7	hs	hs	PROPN
ejpam-2753	160	8	k	k	PROPN
ejpam-2753	160	9	�	�	PROPN
ejpam-2753	160	10	hvsk	hvsk	VERB
ejpam-2753	160	11	�	�	PROPN
ejpam-2753	160	12	hvk	hvk	PROPN
ejpam-2753	160	13	(	(	PUNCT
ejpam-2753	160	14	for	for	ADP
ejpam-2753	160	15	more	more	ADJ
ejpam-2753	160	16	details	detail	NOUN
ejpam-2753	160	17	see	see	VERB
ejpam-2753	160	18	[	[	X
ejpam-2753	160	19	1	1	NUM
ejpam-2753	160	20	]	]	NUM
ejpam-2753	160	21	)	)	PUNCT
ejpam-2753	160	22	.	.	PUNCT
ejpam-2753	161	1	r.	r.	PROPN
ejpam-2753	161	2	ameri	ameri	PROPN
ejpam-2753	161	3	,	,	PUNCT
ejpam-2753	161	4	k.	k.	PROPN
ejpam-2753	161	5	ghadimi	ghadimi	PROPN
ejpam-2753	161	6	,	,	PUNCT
ejpam-2753	161	7	r.	r.	PROPN
ejpam-2753	161	8	a.	a.	PROPN
ejpam-2753	161	9	borzooei	borzooei	PROPN
ejpam-2753	161	10	/	/	SYM
ejpam-2753	161	11	eur	eur	PROPN
ejpam-2753	161	12	.	.	PUNCT
ejpam-2753	162	1	j.	j.	PROPN
ejpam-2753	162	2	pure	pure	PROPN
ejpam-2753	162	3	appl	appl	PROPN
ejpam-2753	162	4	.	.	PROPN
ejpam-2753	162	5	math	math	PROPN
ejpam-2753	162	6	,	,	PUNCT
ejpam-2753	162	7	10	10	NUM
ejpam-2753	162	8	(	(	PUNCT
ejpam-2753	162	9	4	4	NUM
ejpam-2753	162	10	)	)	PUNCT
ejpam-2753	162	11	(	(	PUNCT
ejpam-2753	162	12	2017	2017	NUM
ejpam-2753	162	13	)	)	PUNCT
ejpam-2753	162	14	,	,	PUNCT
ejpam-2753	162	15	702	702	NUM
ejpam-2753	162	16	-	-	SYM
ejpam-2753	162	17	716	716	NUM
ejpam-2753	162	18	708	708	NUM
ejpam-2753	162	19	definition	definition	NOUN
ejpam-2753	162	20	14	14	NUM
ejpam-2753	162	21	.	.	PUNCT
ejpam-2753	163	1	[	[	X
ejpam-2753	163	2	1	1	X
ejpam-2753	163	3	]	]	PUNCT
ejpam-2753	163	4	let	let	VERB
ejpam-2753	163	5	v	v	NOUN
ejpam-2753	163	6	and	and	CCONJ
ejpam-2753	163	7	w	w	NOUN
ejpam-2753	163	8	be	be	AUX
ejpam-2753	163	9	two	two	NUM
ejpam-2753	163	10	hyperspaces	hyperspace	NOUN
ejpam-2753	163	11	over	over	ADP
ejpam-2753	163	12	a	a	DET
ejpam-2753	163	13	field	field	NOUN
ejpam-2753	164	1	k	k	PROPN
ejpam-2753	164	2	and	and	CCONJ
ejpam-2753	164	3	t	t	PROPN
ejpam-2753	164	4	:	:	PUNCT
ejpam-2753	164	5	v	v	ADP
ejpam-2753	164	6	−→	−→	NOUN
ejpam-2753	164	7	p	p	X
ejpam-2753	164	8	∗(w	∗(w	PROPN
ejpam-2753	164	9	)	)	PUNCT
ejpam-2753	164	10	be	be	AUX
ejpam-2753	164	11	a	a	DET
ejpam-2753	164	12	smlt	smlt	NOUN
ejpam-2753	164	13	.	.	PUNCT
ejpam-2753	165	1	then	then	ADV
ejpam-2753	165	2	multivalued	multivalued	ADJ
ejpam-2753	165	3	kernel	kernel	NOUN
ejpam-2753	165	4	and	and	CCONJ
ejpam-2753	165	5	multivalued	multivalued	ADJ
ejpam-2753	165	6	image	image	NOUN
ejpam-2753	165	7	of	of	ADP
ejpam-2753	165	8	t	t	PROPN
ejpam-2753	165	9	,	,	PUNCT
ejpam-2753	165	10	denoted	denote	VERB
ejpam-2753	165	11	by	by	ADP
ejpam-2753	165	12	kert	kert	PROPN
ejpam-2753	165	13	and	and	CCONJ
ejpam-2753	165	14	imt	imt	PROPN
ejpam-2753	165	15	,	,	PUNCT
ejpam-2753	165	16	respectively	respectively	ADV
ejpam-2753	165	17	,	,	PUNCT
ejpam-2753	165	18	are	be	AUX
ejpam-2753	165	19	defined	define	VERB
ejpam-2753	165	20	as	as	SCONJ
ejpam-2753	165	21	follows	follow	VERB
ejpam-2753	165	22	:	:	PUNCT
ejpam-2753	165	23	kert	kert	PROPN
ejpam-2753	165	24	=	=	PUNCT
ejpam-2753	165	25	{	{	PUNCT
ejpam-2753	165	26	x	x	SYM
ejpam-2753	165	27	∈	∈	PROPN
ejpam-2753	165	28	v	v	ADP
ejpam-2753	165	29	|	|	ADV
ejpam-2753	165	30	0w	0w	NOUN
ejpam-2753	165	31	∈	∈	PROPN
ejpam-2753	165	32	t	t	PROPN
ejpam-2753	165	33	(	(	PUNCT
ejpam-2753	165	34	x	x	NOUN
ejpam-2753	165	35	)	)	PUNCT
ejpam-2753	165	36	}	}	PUNCT
ejpam-2753	165	37	;	;	PUNCT
ejpam-2753	165	38	and	and	CCONJ
ejpam-2753	165	39	imt	imt	PROPN
ejpam-2753	165	40	=	=	SYM
ejpam-2753	165	41	{	{	PUNCT
ejpam-2753	165	42	y	y	PROPN
ejpam-2753	165	43	∈w	∈w	VERB
ejpam-2753	165	44	|	|	ADV
ejpam-2753	165	45	y	y	PROPN
ejpam-2753	165	46	∈	∈	PROPN
ejpam-2753	165	47	t	t	PROPN
ejpam-2753	165	48	(	(	PUNCT
ejpam-2753	165	49	x	x	X
ejpam-2753	165	50	)	)	PUNCT
ejpam-2753	165	51	for	for	ADP
ejpam-2753	165	52	some	some	DET
ejpam-2753	165	53	x	x	SYM
ejpam-2753	165	54	∈	∈	PROPN
ejpam-2753	165	55	v	v	NOUN
ejpam-2753	165	56	}	}	PUNCT
ejpam-2753	165	57	.	.	PUNCT
ejpam-2753	166	1	remark	remark	NOUN
ejpam-2753	166	2	5	5	NUM
ejpam-2753	166	3	.	.	PUNCT
ejpam-2753	167	1	(	(	PUNCT
ejpam-2753	167	2	i	i	NOUN
ejpam-2753	167	3	)	)	PUNCT
ejpam-2753	167	4	note	note	VERB
ejpam-2753	167	5	that	that	SCONJ
ejpam-2753	167	6	kert	kert	PROPN
ejpam-2753	167	7	6=	6=	PROPN
ejpam-2753	167	8	∅	∅	NOUN
ejpam-2753	167	9	,	,	PUNCT
ejpam-2753	167	10	by	by	ADP
ejpam-2753	167	11	definition	definition	NOUN
ejpam-2753	167	12	12(iv	12(iv	NUM
ejpam-2753	167	13	)	)	PUNCT
ejpam-2753	167	14	.	.	PUNCT
ejpam-2753	168	1	(	(	PUNCT
ejpam-2753	168	2	ii	ii	NOUN
ejpam-2753	168	3	)	)	PUNCT
ejpam-2753	168	4	for	for	ADP
ejpam-2753	168	5	hyperspaces	hyperspace	NOUN
ejpam-2753	168	6	v	v	ADP
ejpam-2753	168	7	and	and	CCONJ
ejpam-2753	168	8	w	w	NOUN
ejpam-2753	168	9	over	over	ADP
ejpam-2753	168	10	a	a	DET
ejpam-2753	168	11	field	field	NOUN
ejpam-2753	168	12	k	k	NOUN
ejpam-2753	168	13	,	,	PUNCT
ejpam-2753	168	14	by	by	ADP
ejpam-2753	168	15	homk(v	homk(v	PROPN
ejpam-2753	168	16	,	,	PUNCT
ejpam-2753	168	17	w	w	NOUN
ejpam-2753	168	18	)	)	PUNCT
ejpam-2753	168	19	and	and	CCONJ
ejpam-2753	168	20	homs	hom	NOUN
ejpam-2753	168	21	k(v	k(v	PROPN
ejpam-2753	168	22	,	,	PUNCT
ejpam-2753	168	23	w	w	PROPN
ejpam-2753	168	24	)	)	PUNCT
ejpam-2753	168	25	,	,	PUNCT
ejpam-2753	168	26	we	we	PRON
ejpam-2753	168	27	mean	mean	VERB
ejpam-2753	168	28	the	the	DET
ejpam-2753	168	29	set	set	NOUN
ejpam-2753	168	30	of	of	ADP
ejpam-2753	168	31	all	all	DET
ejpam-2753	168	32	mlt	mlt	NOUN
ejpam-2753	168	33	and	and	CCONJ
ejpam-2753	168	34	smlt	smlt	NOUN
ejpam-2753	168	35	,	,	PUNCT
ejpam-2753	168	36	respectively	respectively	ADV
ejpam-2753	168	37	and	and	CCONJ
ejpam-2753	168	38	sometimes	sometimes	ADV
ejpam-2753	168	39	we	we	PRON
ejpam-2753	168	40	use	use	VERB
ejpam-2753	168	41	morphism	morphism	NOUN
ejpam-2753	168	42	instead	instead	ADV
ejpam-2753	168	43	multivalued	multivalue	VERB
ejpam-2753	168	44	linear	linear	ADJ
ejpam-2753	168	45	transformation	transformation	NOUN
ejpam-2753	168	46	,	,	PUNCT
ejpam-2753	168	47	respectively	respectively	ADV
ejpam-2753	168	48	.	.	PUNCT
ejpam-2753	169	1	definition	definition	NOUN
ejpam-2753	169	2	15	15	NUM
ejpam-2753	169	3	.	.	PUNCT
ejpam-2753	170	1	let	let	VERB
ejpam-2753	170	2	t	t	NOUN
ejpam-2753	170	3	:	:	PUNCT
ejpam-2753	170	4	v	v	ADP
ejpam-2753	170	5	−→	−→	NOUN
ejpam-2753	170	6	p	p	X
ejpam-2753	170	7	∗(w	∗(w	PROPN
ejpam-2753	170	8	)	)	PUNCT
ejpam-2753	170	9	be	be	AUX
ejpam-2753	170	10	a	a	DET
ejpam-2753	170	11	smlt	smlt	NOUN
ejpam-2753	170	12	of	of	ADP
ejpam-2753	170	13	hyperspaces	hyperspace	NOUN
ejpam-2753	170	14	.	.	PUNCT
ejpam-2753	171	1	we	we	PRON
ejpam-2753	171	2	say	say	VERB
ejpam-2753	171	3	that	that	SCONJ
ejpam-2753	171	4	t	t	PROPN
ejpam-2753	171	5	is	be	AUX
ejpam-2753	171	6	weakly	weakly	ADV
ejpam-2753	171	7	injective	injective	ADJ
ejpam-2753	171	8	if	if	SCONJ
ejpam-2753	171	9	for	for	ADP
ejpam-2753	171	10	all	all	DET
ejpam-2753	171	11	x	x	NOUN
ejpam-2753	171	12	,	,	PUNCT
ejpam-2753	171	13	y	y	PROPN
ejpam-2753	171	14	∈	∈	PROPN
ejpam-2753	171	15	v	v	ADP
ejpam-2753	171	16	:	:	PUNCT
ejpam-2753	171	17	t	t	PROPN
ejpam-2753	171	18	(	(	PUNCT
ejpam-2753	171	19	x	x	NOUN
ejpam-2753	171	20	)	)	PUNCT
ejpam-2753	171	21	∩	∩	ADJ
ejpam-2753	171	22	t	t	PROPN
ejpam-2753	171	23	(	(	PUNCT
ejpam-2753	171	24	y	y	PROPN
ejpam-2753	171	25	)	)	PUNCT
ejpam-2753	171	26	6=	6=	ADP
ejpam-2753	171	27	∅	∅	NOUN
ejpam-2753	172	1	=	=	NOUN
ejpam-2753	172	2	⇒	⇒	NOUN
ejpam-2753	172	3	x	x	PUNCT
ejpam-2753	173	1	=	=	PUNCT
ejpam-2753	173	2	y.	y.	NOUN
ejpam-2753	173	3	we	we	PRON
ejpam-2753	173	4	say	say	VERB
ejpam-2753	173	5	that	that	SCONJ
ejpam-2753	173	6	t	t	PROPN
ejpam-2753	173	7	is	be	AUX
ejpam-2753	173	8	strongly	strongly	ADV
ejpam-2753	173	9	injective	injective	ADJ
ejpam-2753	173	10	if	if	SCONJ
ejpam-2753	173	11	for	for	ADP
ejpam-2753	173	12	all	all	DET
ejpam-2753	173	13	x	x	NOUN
ejpam-2753	173	14	,	,	PUNCT
ejpam-2753	173	15	y	y	PROPN
ejpam-2753	173	16	∈	∈	PROPN
ejpam-2753	173	17	v	v	ADP
ejpam-2753	173	18	:	:	PUNCT
ejpam-2753	173	19	t	t	PROPN
ejpam-2753	173	20	(	(	PUNCT
ejpam-2753	173	21	x	x	X
ejpam-2753	173	22	)	)	PUNCT
ejpam-2753	173	23	=	=	SYM
ejpam-2753	173	24	t	t	PROPN
ejpam-2753	173	25	(	(	PUNCT
ejpam-2753	173	26	y	y	NOUN
ejpam-2753	173	27	)	)	PUNCT
ejpam-2753	174	1	=	=	NOUN
ejpam-2753	174	2	⇒	⇒	NOUN
ejpam-2753	174	3	x	x	PUNCT
ejpam-2753	175	1	=	=	PUNCT
ejpam-2753	175	2	y.	y.	NOUN
ejpam-2753	175	3	remark	remark	VERB
ejpam-2753	175	4	6	6	NUM
ejpam-2753	175	5	.	.	PUNCT
ejpam-2753	176	1	clearly	clearly	ADV
ejpam-2753	176	2	,	,	PUNCT
ejpam-2753	176	3	every	every	DET
ejpam-2753	176	4	weakly	weakly	ADJ
ejpam-2753	176	5	injective	injective	ADJ
ejpam-2753	176	6	morphism	morphism	NOUN
ejpam-2753	176	7	is	be	AUX
ejpam-2753	176	8	also	also	ADV
ejpam-2753	176	9	strongly	strongly	ADV
ejpam-2753	176	10	injective	injective	ADJ
ejpam-2753	176	11	.	.	PUNCT
ejpam-2753	177	1	note	note	VERB
ejpam-2753	177	2	that	that	SCONJ
ejpam-2753	177	3	t	t	PROPN
ejpam-2753	177	4	is	be	AUX
ejpam-2753	177	5	strongly	strongly	ADV
ejpam-2753	177	6	injective	injective	ADJ
ejpam-2753	177	7	,	,	PUNCT
ejpam-2753	177	8	means	mean	VERB
ejpam-2753	177	9	that	that	SCONJ
ejpam-2753	177	10	t	t	PROPN
ejpam-2753	177	11	is	be	AUX
ejpam-2753	177	12	injective	injective	ADJ
ejpam-2753	177	13	as	as	ADP
ejpam-2753	177	14	a	a	DET
ejpam-2753	177	15	function	function	NOUN
ejpam-2753	177	16	with	with	ADP
ejpam-2753	177	17	values	value	NOUN
ejpam-2753	177	18	in	in	ADP
ejpam-2753	177	19	p	p	NOUN
ejpam-2753	177	20	∗(w	∗(w	NOUN
ejpam-2753	177	21	)	)	PUNCT
ejpam-2753	177	22	.	.	PUNCT
ejpam-2753	178	1	in	in	ADP
ejpam-2753	178	2	the	the	DET
ejpam-2753	178	3	following	following	ADJ
ejpam-2753	178	4	example	example	NOUN
ejpam-2753	178	5	we	we	PRON
ejpam-2753	178	6	show	show	VERB
ejpam-2753	178	7	that	that	SCONJ
ejpam-2753	178	8	a	a	DET
ejpam-2753	178	9	strongly	strongly	ADV
ejpam-2753	178	10	injective	injective	ADJ
ejpam-2753	178	11	morphism	morphism	NOUN
ejpam-2753	178	12	need	need	VERB
ejpam-2753	178	13	not	not	PART
ejpam-2753	178	14	to	to	PART
ejpam-2753	178	15	be	be	AUX
ejpam-2753	178	16	weakly	weakly	ADV
ejpam-2753	178	17	injective	injective	ADJ
ejpam-2753	178	18	.	.	PUNCT
ejpam-2753	179	1	similarly	similarly	ADV
ejpam-2753	179	2	,	,	PUNCT
ejpam-2753	179	3	we	we	PRON
ejpam-2753	179	4	introduce	introduce	VERB
ejpam-2753	179	5	the	the	DET
ejpam-2753	179	6	notions	notion	NOUN
ejpam-2753	179	7	of	of	ADP
ejpam-2753	179	8	weakly	weakly	ADJ
ejpam-2753	179	9	and	and	CCONJ
ejpam-2753	179	10	strongly	strongly	ADV
ejpam-2753	179	11	surjective	surjective	ADJ
ejpam-2753	179	12	.	.	PUNCT
ejpam-2753	180	1	a	a	DET
ejpam-2753	180	2	morphism	morphism	NOUN
ejpam-2753	180	3	t	t	PROPN
ejpam-2753	180	4	:	:	PUNCT
ejpam-2753	180	5	v	v	ADP
ejpam-2753	180	6	−→	−→	NOUN
ejpam-2753	180	7	p	p	X
ejpam-2753	180	8	∗(w	∗(w	NOUN
ejpam-2753	180	9	)	)	PUNCT
ejpam-2753	180	10	of	of	ADP
ejpam-2753	180	11	hyperspaces	hyperspace	NOUN
ejpam-2753	180	12	is	be	AUX
ejpam-2753	180	13	said	say	VERB
ejpam-2753	180	14	to	to	PART
ejpam-2753	180	15	be	be	AUX
ejpam-2753	180	16	weakly	weakly	ADV
ejpam-2753	180	17	surjective	surjective	ADJ
ejpam-2753	180	18	if	if	SCONJ
ejpam-2753	180	19	for	for	ADP
ejpam-2753	180	20	every	every	DET
ejpam-2753	180	21	y	y	PROPN
ejpam-2753	180	22	∈	∈	PROPN
ejpam-2753	180	23	w	w	NOUN
ejpam-2753	180	24	there	there	PRON
ejpam-2753	180	25	exists	exist	VERB
ejpam-2753	180	26	x	x	X
ejpam-2753	180	27	∈	∈	NOUN
ejpam-2753	180	28	v	v	ADP
ejpam-2753	180	29	such	such	ADJ
ejpam-2753	180	30	that	that	SCONJ
ejpam-2753	180	31	y	y	PROPN
ejpam-2753	180	32	∈	∈	PROPN
ejpam-2753	180	33	t	t	PROPN
ejpam-2753	180	34	(	(	PUNCT
ejpam-2753	180	35	x	x	NOUN
ejpam-2753	180	36	)	)	PUNCT
ejpam-2753	180	37	and	and	CCONJ
ejpam-2753	180	38	is	be	AUX
ejpam-2753	180	39	strongly	strongly	ADV
ejpam-2753	180	40	surjective	surjective	ADJ
ejpam-2753	180	41	,	,	PUNCT
ejpam-2753	180	42	if	if	SCONJ
ejpam-2753	180	43	for	for	ADP
ejpam-2753	180	44	every	every	DET
ejpam-2753	180	45	nonempty	nonempty	NOUN
ejpam-2753	180	46	subset	subset	VERB
ejpam-2753	180	47	z	z	NOUN
ejpam-2753	180	48	of	of	ADP
ejpam-2753	180	49	w	w	PROPN
ejpam-2753	180	50	,	,	PUNCT
ejpam-2753	180	51	there	there	PRON
ejpam-2753	180	52	exists	exist	VERB
ejpam-2753	180	53	x	x	X
ejpam-2753	180	54	∈	∈	NOUN
ejpam-2753	180	55	v	v	ADP
ejpam-2753	180	56	such	such	ADJ
ejpam-2753	180	57	that	that	DET
ejpam-2753	180	58	z	z	NOUN
ejpam-2753	180	59	=	=	SYM
ejpam-2753	180	60	t	t	PROPN
ejpam-2753	180	61	(	(	PUNCT
ejpam-2753	180	62	x	x	NOUN
ejpam-2753	180	63	)	)	PUNCT
ejpam-2753	180	64	.	.	PUNCT
ejpam-2753	181	1	remark	remark	PROPN
ejpam-2753	181	2	7	7	NUM
ejpam-2753	181	3	.	.	PUNCT
ejpam-2753	182	1	clearly	clearly	ADV
ejpam-2753	182	2	,	,	PUNCT
ejpam-2753	182	3	every	every	DET
ejpam-2753	182	4	strongly	strongly	ADV
ejpam-2753	182	5	surjective	surjective	ADJ
ejpam-2753	182	6	morphism	morphism	NOUN
ejpam-2753	182	7	is	be	AUX
ejpam-2753	182	8	weakly	weakly	ADV
ejpam-2753	182	9	surjective	surjective	ADJ
ejpam-2753	182	10	.	.	PUNCT
ejpam-2753	183	1	but	but	CCONJ
ejpam-2753	183	2	the	the	DET
ejpam-2753	183	3	converse	converse	NOUN
ejpam-2753	183	4	is	be	AUX
ejpam-2753	183	5	not	not	PART
ejpam-2753	183	6	true	true	ADJ
ejpam-2753	183	7	.	.	PUNCT
ejpam-2753	184	1	for	for	ADP
ejpam-2753	184	2	example	example	NOUN
ejpam-2753	184	3	the	the	DET
ejpam-2753	184	4	identity	identity	NOUN
ejpam-2753	184	5	function	function	NOUN
ejpam-2753	184	6	on	on	ADP
ejpam-2753	184	7	every	every	DET
ejpam-2753	184	8	hyperspace	hyperspace	NOUN
ejpam-2753	184	9	is	be	AUX
ejpam-2753	184	10	weakly	weakly	ADV
ejpam-2753	184	11	surjective	surjective	ADJ
ejpam-2753	184	12	,	,	PUNCT
ejpam-2753	184	13	but	but	CCONJ
ejpam-2753	184	14	is	be	AUX
ejpam-2753	184	15	not	not	PART
ejpam-2753	184	16	strongly	strongly	ADV
ejpam-2753	184	17	surjective	surjective	ADJ
ejpam-2753	184	18	.	.	PUNCT
ejpam-2753	185	1	theorem	theorem	NOUN
ejpam-2753	185	2	2	2	NUM
ejpam-2753	185	3	.	.	PUNCT
ejpam-2753	186	1	[	[	X
ejpam-2753	186	2	18	18	NUM
ejpam-2753	186	3	]	]	PUNCT
ejpam-2753	186	4	let	let	VERB
ejpam-2753	186	5	k	k	PRON
ejpam-2753	186	6	be	be	AUX
ejpam-2753	186	7	a	a	DET
ejpam-2753	186	8	field	field	NOUN
ejpam-2753	186	9	.	.	PUNCT
ejpam-2753	187	1	the	the	DET
ejpam-2753	187	2	following	follow	VERB
ejpam-2753	187	3	conditions	condition	NOUN
ejpam-2753	187	4	on	on	ADP
ejpam-2753	187	5	a	a	DET
ejpam-2753	187	6	k	k	ADJ
ejpam-2753	187	7	-	-	ADJ
ejpam-2753	187	8	vector	vector	NOUN
ejpam-2753	187	9	space	space	NOUN
ejpam-2753	187	10	f	f	PROPN
ejpam-2753	187	11	are	be	AUX
ejpam-2753	187	12	equivalent	equivalent	ADJ
ejpam-2753	187	13	:	:	PUNCT
ejpam-2753	187	14	(	(	PUNCT
ejpam-2753	187	15	i	i	NOUN
ejpam-2753	187	16	)	)	PUNCT
ejpam-2753	187	17	f	f	PROPN
ejpam-2753	187	18	has	have	VERB
ejpam-2753	187	19	a	a	DET
ejpam-2753	187	20	nonempty	nonempty	ADJ
ejpam-2753	187	21	basis	basis	NOUN
ejpam-2753	187	22	;	;	PUNCT
ejpam-2753	187	23	(	(	PUNCT
ejpam-2753	187	24	ii	ii	NOUN
ejpam-2753	187	25	)	)	PUNCT
ejpam-2753	187	26	f	f	PROPN
ejpam-2753	187	27	is	be	AUX
ejpam-2753	187	28	the	the	DET
ejpam-2753	187	29	internal	internal	ADJ
ejpam-2753	187	30	direct	direct	ADJ
ejpam-2753	187	31	sum	sum	NOUN
ejpam-2753	187	32	of	of	ADP
ejpam-2753	187	33	a	a	DET
ejpam-2753	187	34	family	family	NOUN
ejpam-2753	187	35	of	of	ADP
ejpam-2753	187	36	cyclic	cyclic	ADJ
ejpam-2753	187	37	k	k	ADJ
ejpam-2753	187	38	-	-	ADJ
ejpam-2753	187	39	vector	vector	NOUN
ejpam-2753	187	40	spaces	space	NOUN
ejpam-2753	187	41	,	,	PUNCT
ejpam-2753	187	42	each	each	PRON
ejpam-2753	187	43	of	of	ADP
ejpam-2753	187	44	which	which	PRON
ejpam-2753	187	45	is	be	AUX
ejpam-2753	187	46	isomorphic	isomorphic	ADJ
ejpam-2753	187	47	as	as	ADP
ejpam-2753	187	48	a	a	DET
ejpam-2753	187	49	k	k	ADJ
ejpam-2753	187	50	-	-	ADJ
ejpam-2753	187	51	vector	vector	NOUN
ejpam-2753	187	52	space	space	NOUN
ejpam-2753	187	53	to	to	ADP
ejpam-2753	187	54	k	k	NOUN
ejpam-2753	187	55	;	;	PUNCT
ejpam-2753	187	56	(	(	PUNCT
ejpam-2753	187	57	iii	iii	X
ejpam-2753	187	58	)	)	PUNCT
ejpam-2753	187	59	f	f	PROPN
ejpam-2753	187	60	is	be	AUX
ejpam-2753	187	61	k	k	ADJ
ejpam-2753	187	62	-	-	ADJ
ejpam-2753	187	63	vector	vector	NOUN
ejpam-2753	187	64	space	space	NOUN
ejpam-2753	187	65	isomorphic	isomorphic	ADJ
ejpam-2753	187	66	to	to	ADP
ejpam-2753	187	67	a	a	DET
ejpam-2753	187	68	direct	direct	ADJ
ejpam-2753	187	69	sum	sum	NOUN
ejpam-2753	187	70	of	of	ADP
ejpam-2753	187	71	copies	copy	NOUN
ejpam-2753	187	72	of	of	ADP
ejpam-2753	187	73	the	the	DET
ejpam-2753	187	74	k	k	ADJ
ejpam-2753	187	75	-	-	ADJ
ejpam-2753	187	76	vector	vector	NOUN
ejpam-2753	187	77	space	space	NOUN
ejpam-2753	187	78	k	k	PROPN
ejpam-2753	187	79	;	;	PUNCT
ejpam-2753	187	80	r.	r.	PROPN
ejpam-2753	187	81	ameri	ameri	PROPN
ejpam-2753	187	82	,	,	PUNCT
ejpam-2753	187	83	k.	k.	PROPN
ejpam-2753	187	84	ghadimi	ghadimi	PROPN
ejpam-2753	187	85	,	,	PUNCT
ejpam-2753	187	86	r.	r.	PROPN
ejpam-2753	187	87	a.	a.	PROPN
ejpam-2753	187	88	borzooei	borzooei	PROPN
ejpam-2753	187	89	/	/	SYM
ejpam-2753	187	90	eur	eur	PROPN
ejpam-2753	187	91	.	.	PUNCT
ejpam-2753	188	1	j.	j.	PROPN
ejpam-2753	188	2	pure	pure	PROPN
ejpam-2753	188	3	appl	appl	PROPN
ejpam-2753	188	4	.	.	PROPN
ejpam-2753	188	5	math	math	PROPN
ejpam-2753	188	6	,	,	PUNCT
ejpam-2753	188	7	10	10	NUM
ejpam-2753	188	8	(	(	PUNCT
ejpam-2753	188	9	4	4	NUM
ejpam-2753	188	10	)	)	PUNCT
ejpam-2753	188	11	(	(	PUNCT
ejpam-2753	188	12	2017	2017	NUM
ejpam-2753	188	13	)	)	PUNCT
ejpam-2753	188	14	,	,	PUNCT
ejpam-2753	188	15	702	702	NUM
ejpam-2753	188	16	-	-	SYM
ejpam-2753	188	17	716	716	NUM
ejpam-2753	188	18	709	709	NUM
ejpam-2753	188	19	(	(	PUNCT
ejpam-2753	188	20	iv	iv	X
ejpam-2753	188	21	)	)	PUNCT
ejpam-2753	188	22	there	there	PRON
ejpam-2753	188	23	exists	exist	VERB
ejpam-2753	188	24	a	a	DET
ejpam-2753	188	25	nonempty	nonempty	ADV
ejpam-2753	188	26	set	set	VERB
ejpam-2753	188	27	x	x	PUNCT
ejpam-2753	188	28	and	and	CCONJ
ejpam-2753	188	29	a	a	DET
ejpam-2753	188	30	function	function	NOUN
ejpam-2753	188	31	ι	ι	X
ejpam-2753	188	32	:	:	PUNCT
ejpam-2753	188	33	x	x	PUNCT
ejpam-2753	188	34	−→	−→	NOUN
ejpam-2753	188	35	f	f	X
ejpam-2753	188	36	with	with	ADP
ejpam-2753	188	37	the	the	DET
ejpam-2753	188	38	following	follow	VERB
ejpam-2753	188	39	property	property	NOUN
ejpam-2753	188	40	:	:	PUNCT
ejpam-2753	188	41	given	give	VERB
ejpam-2753	188	42	any	any	DET
ejpam-2753	188	43	k	k	ADJ
ejpam-2753	188	44	-	-	ADJ
ejpam-2753	188	45	vector	vector	NOUN
ejpam-2753	188	46	space	space	NOUN
ejpam-2753	188	47	v	v	NOUN
ejpam-2753	188	48	and	and	CCONJ
ejpam-2753	188	49	function	function	VERB
ejpam-2753	188	50	f	f	NOUN
ejpam-2753	188	51	:	:	PUNCT
ejpam-2753	188	52	x	x	PUNCT
ejpam-2753	188	53	−→	−→	NOUN
ejpam-2753	188	54	v	v	X
ejpam-2753	188	55	,	,	PUNCT
ejpam-2753	188	56	there	there	PRON
ejpam-2753	188	57	exists	exist	VERB
ejpam-2753	188	58	a	a	DET
ejpam-2753	188	59	unique	unique	ADJ
ejpam-2753	188	60	k	k	ADJ
ejpam-2753	188	61	-	-	ADJ
ejpam-2753	188	62	vector	vector	NOUN
ejpam-2753	188	63	space	space	NOUN
ejpam-2753	188	64	homomorphism	homomorphism	PROPN
ejpam-2753	188	65	f	f	X
ejpam-2753	188	66	:	:	PUNCT
ejpam-2753	188	67	f	f	X
ejpam-2753	189	1	−→	−→	NOUN
ejpam-2753	189	2	v	v	ADP
ejpam-2753	189	3	such	such	ADJ
ejpam-2753	189	4	that	that	PRON
ejpam-2753	189	5	fι	fι	VERB
ejpam-2753	189	6	=	=	SYM
ejpam-2753	189	7	f	f	PROPN
ejpam-2753	189	8	.	.	PUNCT
ejpam-2753	190	1	in	in	ADP
ejpam-2753	190	2	other	other	ADJ
ejpam-2753	190	3	words	word	NOUN
ejpam-2753	190	4	,	,	PUNCT
ejpam-2753	190	5	f	f	PROPN
ejpam-2753	190	6	is	be	AUX
ejpam-2753	190	7	a	a	DET
ejpam-2753	190	8	free	free	ADJ
ejpam-2753	190	9	object	object	NOUN
ejpam-2753	190	10	in	in	ADP
ejpam-2753	190	11	the	the	DET
ejpam-2753	190	12	category	category	NOUN
ejpam-2753	190	13	of	of	ADP
ejpam-2753	190	14	k	k	ADJ
ejpam-2753	190	15	-	-	ADJ
ejpam-2753	190	16	vector	vector	NOUN
ejpam-2753	190	17	spaces	space	NOUN
ejpam-2753	190	18	.	.	PUNCT
ejpam-2753	191	1	remark	remark	PROPN
ejpam-2753	191	2	8	8	NUM
ejpam-2753	191	3	.	.	PUNCT
ejpam-2753	192	1	a	a	DET
ejpam-2753	192	2	vector	vector	NOUN
ejpam-2753	192	3	space	space	NOUN
ejpam-2753	192	4	f	f	PROPN
ejpam-2753	192	5	over	over	ADP
ejpam-2753	192	6	a	a	DET
ejpam-2753	192	7	field	field	NOUN
ejpam-2753	192	8	k	k	NOUN
ejpam-2753	192	9	,	,	PUNCT
ejpam-2753	192	10	which	which	PRON
ejpam-2753	192	11	satisfies	satisfy	VERB
ejpam-2753	192	12	the	the	DET
ejpam-2753	192	13	equivalent	equivalent	ADJ
ejpam-2753	192	14	conditions	condition	NOUN
ejpam-2753	192	15	of	of	ADP
ejpam-2753	192	16	theorem	theorem	NOUN
ejpam-2753	192	17	2	2	NUM
ejpam-2753	192	18	,	,	PUNCT
ejpam-2753	192	19	is	be	AUX
ejpam-2753	192	20	called	call	VERB
ejpam-2753	192	21	a	a	DET
ejpam-2753	192	22	free	free	ADJ
ejpam-2753	192	23	k	k	ADJ
ejpam-2753	192	24	-	-	ADJ
ejpam-2753	192	25	vector	vector	NOUN
ejpam-2753	192	26	space	space	NOUN
ejpam-2753	192	27	on	on	ADP
ejpam-2753	192	28	the	the	DET
ejpam-2753	192	29	set	set	NOUN
ejpam-2753	192	30	x.	x.	NOUN
ejpam-2753	192	31	by	by	ADP
ejpam-2753	192	32	theorem	theorem	NOUN
ejpam-2753	192	33	2	2	NUM
ejpam-2753	192	34	(	(	PUNCT
ejpam-2753	192	35	iv	iv	NUM
ejpam-2753	192	36	)	)	PUNCT
ejpam-2753	192	37	,	,	PUNCT
ejpam-2753	192	38	f	f	PROPN
ejpam-2753	192	39	is	be	AUX
ejpam-2753	192	40	a	a	DET
ejpam-2753	192	41	free	free	ADJ
ejpam-2753	192	42	object	object	NOUN
ejpam-2753	192	43	in	in	ADP
ejpam-2753	192	44	the	the	DET
ejpam-2753	192	45	category	category	NOUN
ejpam-2753	192	46	of	of	ADP
ejpam-2753	192	47	all	all	DET
ejpam-2753	192	48	k	k	ADJ
ejpam-2753	192	49	-	-	ADJ
ejpam-2753	192	50	vector	vector	NOUN
ejpam-2753	192	51	spaces	space	NOUN
ejpam-2753	192	52	.	.	PUNCT
ejpam-2753	193	1	definition	definition	NOUN
ejpam-2753	193	2	16	16	NUM
ejpam-2753	193	3	.	.	PUNCT
ejpam-2753	194	1	[	[	X
ejpam-2753	194	2	18	18	NUM
ejpam-2753	194	3	]	]	PUNCT
ejpam-2753	194	4	let	let	VERB
ejpam-2753	194	5	v	v	NOUN
ejpam-2753	194	6	and	and	CCONJ
ejpam-2753	194	7	w	w	NOUN
ejpam-2753	194	8	be	be	AUX
ejpam-2753	194	9	two	two	NUM
ejpam-2753	194	10	vector	vector	NOUN
ejpam-2753	194	11	space	space	NOUN
ejpam-2753	194	12	over	over	ADP
ejpam-2753	194	13	a	a	DET
ejpam-2753	194	14	field	field	NOUN
ejpam-2753	194	15	k	k	NOUN
ejpam-2753	194	16	,	,	PUNCT
ejpam-2753	194	17	and	and	CCONJ
ejpam-2753	194	18	z	z	NOUN
ejpam-2753	194	19	is	be	AUX
ejpam-2753	194	20	an	an	DET
ejpam-2753	194	21	(	(	PUNCT
ejpam-2753	194	22	additive	additive	NOUN
ejpam-2753	194	23	)	)	PUNCT
ejpam-2753	194	24	abelian	abelian	PROPN
ejpam-2753	194	25	group	group	NOUN
ejpam-2753	194	26	.	.	PUNCT
ejpam-2753	195	1	then	then	ADV
ejpam-2753	195	2	a	a	DET
ejpam-2753	195	3	middle	middle	ADJ
ejpam-2753	195	4	linear	linear	NOUN
ejpam-2753	195	5	map	map	NOUN
ejpam-2753	195	6	from	from	ADP
ejpam-2753	195	7	v	v	NOUN
ejpam-2753	195	8	×w	×w	NOUN
ejpam-2753	195	9	to	to	ADP
ejpam-2753	195	10	z	z	PROPN
ejpam-2753	195	11	is	be	AUX
ejpam-2753	195	12	a	a	DET
ejpam-2753	195	13	function	function	NOUN
ejpam-2753	195	14	f	f	NOUN
ejpam-2753	195	15	:	:	PUNCT
ejpam-2753	195	16	v	v	NUM
ejpam-2753	195	17	×w	×w	NOUN
ejpam-2753	195	18	−→	−→	NOUN
ejpam-2753	195	19	z	z	NOUN
ejpam-2753	195	20	such	such	ADJ
ejpam-2753	195	21	that	that	PRON
ejpam-2753	195	22	(	(	PUNCT
ejpam-2753	195	23	for	for	ADP
ejpam-2753	195	24	all	all	DET
ejpam-2753	195	25	v	v	NOUN
ejpam-2753	195	26	,	,	PUNCT
ejpam-2753	195	27	vi	vi	PROPN
ejpam-2753	195	28	∈	∈	PROPN
ejpam-2753	195	29	v	v	NOUN
ejpam-2753	195	30	,	,	PUNCT
ejpam-2753	195	31	w	w	PROPN
ejpam-2753	195	32	,	,	PUNCT
ejpam-2753	195	33	wi	wi	PROPN
ejpam-2753	195	34	∈w	∈w	PROPN
ejpam-2753	195	35	,	,	PUNCT
ejpam-2753	195	36	a	a	DET
ejpam-2753	195	37	∈	∈	PROPN
ejpam-2753	195	38	k	k	NOUN
ejpam-2753	195	39	,	,	PUNCT
ejpam-2753	195	40	and	and	CCONJ
ejpam-2753	195	41	i	i	NOUN
ejpam-2753	195	42	=	=	NOUN
ejpam-2753	195	43	1	1	NUM
ejpam-2753	195	44	,	,	PUNCT
ejpam-2753	195	45	2	2	NUM
ejpam-2753	195	46	):	):	PUNCT
ejpam-2753	195	47	(	(	PUNCT
ejpam-2753	195	48	i	i	NOUN
ejpam-2753	195	49	)	)	PUNCT
ejpam-2753	195	50	f(v1	f(v1	VERB
ejpam-2753	195	51	+	+	X
ejpam-2753	195	52	v2	v2	NOUN
ejpam-2753	195	53	,	,	PUNCT
ejpam-2753	195	54	w	w	NOUN
ejpam-2753	195	55	)	)	PUNCT
ejpam-2753	195	56	=	=	SYM
ejpam-2753	195	57	f(v1	f(v1	NOUN
ejpam-2753	195	58	,	,	PUNCT
ejpam-2753	195	59	w	w	NOUN
ejpam-2753	195	60	)	)	PUNCT
ejpam-2753	195	61	+	+	NOUN
ejpam-2753	195	62	f(v2	f(v2	NOUN
ejpam-2753	195	63	,	,	PUNCT
ejpam-2753	195	64	w	w	NOUN
ejpam-2753	195	65	)	)	PUNCT
ejpam-2753	195	66	;	;	PUNCT
ejpam-2753	195	67	(	(	PUNCT
ejpam-2753	195	68	ii	ii	NOUN
ejpam-2753	195	69	)	)	PUNCT
ejpam-2753	195	70	f(v	f(v	PROPN
ejpam-2753	195	71	,	,	PUNCT
ejpam-2753	195	72	w1	w1	NOUN
ejpam-2753	195	73	+	+	NOUN
ejpam-2753	195	74	w2	w2	NOUN
ejpam-2753	195	75	)	)	PUNCT
ejpam-2753	195	76	=	=	SYM
ejpam-2753	195	77	f(v	f(v	NOUN
ejpam-2753	195	78	,	,	PUNCT
ejpam-2753	195	79	w1	w1	NOUN
ejpam-2753	195	80	)	)	PUNCT
ejpam-2753	196	1	+	+	NUM
ejpam-2753	196	2	f(v	f(v	NOUN
ejpam-2753	196	3	,	,	PUNCT
ejpam-2753	196	4	w2	w2	NOUN
ejpam-2753	196	5	)	)	PUNCT
ejpam-2753	196	6	;	;	PUNCT
ejpam-2753	196	7	(	(	PUNCT
ejpam-2753	196	8	iii	iii	X
ejpam-2753	196	9	)	)	PUNCT
ejpam-2753	196	10	f(av	f(av	PROPN
ejpam-2753	196	11	,	,	PUNCT
ejpam-2753	196	12	w	w	NOUN
ejpam-2753	196	13	)	)	PUNCT
ejpam-2753	196	14	=	=	PUNCT
ejpam-2753	196	15	f(v	f(v	NOUN
ejpam-2753	196	16	,	,	PUNCT
ejpam-2753	196	17	aw	aw	INTJ
ejpam-2753	196	18	)	)	PUNCT
ejpam-2753	196	19	.	.	PUNCT
ejpam-2753	197	1	for	for	ADP
ejpam-2753	197	2	fixed	fix	VERB
ejpam-2753	197	3	v	v	NOUN
ejpam-2753	197	4	and	and	CCONJ
ejpam-2753	197	5	w	w	NOUN
ejpam-2753	197	6	consider	consider	VERB
ejpam-2753	197	7	the	the	DET
ejpam-2753	197	8	categoryml(v	categoryml(v	NOUN
ejpam-2753	197	9	,	,	PUNCT
ejpam-2753	197	10	w	w	NOUN
ejpam-2753	197	11	)	)	PUNCT
ejpam-2753	197	12	whose	whose	DET
ejpam-2753	197	13	objects	object	NOUN
ejpam-2753	197	14	are	be	AUX
ejpam-2753	197	15	all	all	PRON
ejpam-2753	197	16	middle	middle	ADJ
ejpam-2753	197	17	linear	linear	ADJ
ejpam-2753	197	18	maps	map	NOUN
ejpam-2753	197	19	on	on	ADP
ejpam-2753	197	20	v	v	NOUN
ejpam-2753	197	21	×w	×w	NOUN
ejpam-2753	197	22	.	.	PUNCT
ejpam-2753	198	1	by	by	ADP
ejpam-2753	198	2	definition	definition	NOUN
ejpam-2753	198	3	a	a	DET
ejpam-2753	198	4	morphism	morphism	NOUN
ejpam-2753	198	5	in	in	ADP
ejpam-2753	198	6	ml(v	ml(v	NOUN
ejpam-2753	198	7	,	,	PUNCT
ejpam-2753	198	8	w	w	NOUN
ejpam-2753	198	9	)	)	PUNCT
ejpam-2753	198	10	from	from	ADP
ejpam-2753	198	11	the	the	DET
ejpam-2753	198	12	middle	middle	ADJ
ejpam-2753	198	13	linear	linear	PROPN
ejpam-2753	198	14	map	map	NOUN
ejpam-2753	199	1	f	f	X
ejpam-2753	199	2	:	:	PUNCT
ejpam-2753	199	3	v	v	NUM
ejpam-2753	199	4	×w	×w	NOUN
ejpam-2753	199	5	−→	−→	NOUN
ejpam-2753	199	6	z	z	NOUN
ejpam-2753	199	7	to	to	ADP
ejpam-2753	199	8	the	the	DET
ejpam-2753	199	9	middle	middle	ADJ
ejpam-2753	199	10	linear	linear	PROPN
ejpam-2753	199	11	map	map	NOUN
ejpam-2753	199	12	g	g	NOUN
ejpam-2753	199	13	:	:	PUNCT
ejpam-2753	199	14	v	v	NOUN
ejpam-2753	199	15	×w	×w	NOUN
ejpam-2753	199	16	−→	−→	NOUN
ejpam-2753	199	17	z	z	NOUN
ejpam-2753	199	18	′	′	NOUN
ejpam-2753	200	1	is	be	AUX
ejpam-2753	200	2	a	a	DET
ejpam-2753	200	3	group	group	NOUN
ejpam-2753	200	4	homomorphism	homomorphism	NOUN
ejpam-2753	200	5	h	h	NOUN
ejpam-2753	200	6	:	:	PUNCT
ejpam-2753	200	7	z	z	VERB
ejpam-2753	201	1	−→	−→	NOUN
ejpam-2753	201	2	z	z	NOUN
ejpam-2753	201	3	′	′	NUM
ejpam-2753	202	1	such	such	ADJ
ejpam-2753	202	2	that	that	SCONJ
ejpam-2753	202	3	the	the	DET
ejpam-2753	202	4	diagram	diagram	NOUN
ejpam-2753	202	5	z	z	NOUN
ejpam-2753	202	6	′	′	NUM
ejpam-2753	202	7	z	z	NOUN
ejpam-2753	202	8	v	v	NOUN
ejpam-2753	202	9	×w	×w	NOUN
ejpam-2753	202	10	f	f	PROPN
ejpam-2753	202	11	g	g	PROPN
ejpam-2753	202	12	h	h	NOUN
ejpam-2753	202	13	is	be	AUX
ejpam-2753	202	14	commutative	commutative	ADJ
ejpam-2753	202	15	.	.	PUNCT
ejpam-2753	203	1	verify	verify	VERB
ejpam-2753	203	2	thatml(v	thatml(v	PROPN
ejpam-2753	203	3	,	,	PUNCT
ejpam-2753	203	4	w	w	PROPN
ejpam-2753	203	5	)	)	PUNCT
ejpam-2753	203	6	is	be	AUX
ejpam-2753	203	7	a	a	DET
ejpam-2753	203	8	category	category	NOUN
ejpam-2753	203	9	,	,	PUNCT
ejpam-2753	203	10	that	that	SCONJ
ejpam-2753	203	11	1h	1h	NUM
ejpam-2753	203	12	is	be	AUX
ejpam-2753	203	13	the	the	DET
ejpam-2753	203	14	identity	identity	NOUN
ejpam-2753	203	15	morphism	morphism	NOUN
ejpam-2753	203	16	from	from	ADP
ejpam-2753	203	17	f	f	PROPN
ejpam-2753	203	18	to	to	ADP
ejpam-2753	203	19	f	f	PROPN
ejpam-2753	203	20	,	,	PUNCT
ejpam-2753	203	21	and	and	CCONJ
ejpam-2753	203	22	that	that	SCONJ
ejpam-2753	203	23	h	h	NOUN
ejpam-2753	203	24	is	be	AUX
ejpam-2753	203	25	an	an	DET
ejpam-2753	203	26	equivalence	equivalence	NOUN
ejpam-2753	203	27	inml(v	inml(v	NOUN
ejpam-2753	203	28	,	,	PUNCT
ejpam-2753	203	29	w	w	NOUN
ejpam-2753	203	30	)	)	PUNCT
ejpam-2753	204	1	if	if	SCONJ
ejpam-2753	204	2	and	and	CCONJ
ejpam-2753	204	3	only	only	ADV
ejpam-2753	204	4	if	if	SCONJ
ejpam-2753	204	5	h	h	NOUN
ejpam-2753	204	6	is	be	AUX
ejpam-2753	204	7	an	an	DET
ejpam-2753	204	8	isomorphism	isomorphism	NOUN
ejpam-2753	204	9	of	of	ADP
ejpam-2753	204	10	groups	group	NOUN
ejpam-2753	204	11	.	.	PUNCT
ejpam-2753	205	1	3	3	X
ejpam-2753	205	2	.	.	X
ejpam-2753	205	3	quasi	quasi	ADJ
ejpam-2753	205	4	-	-	ADJ
ejpam-2753	205	5	free	free	ADJ
ejpam-2753	205	6	object	object	NOUN
ejpam-2753	205	7	definition	definition	NOUN
ejpam-2753	205	8	17	17	NUM
ejpam-2753	205	9	.	.	PUNCT
ejpam-2753	206	1	let	let	VERB
ejpam-2753	206	2	(	(	PUNCT
ejpam-2753	206	3	f	f	X
ejpam-2753	206	4	,	,	PUNCT
ejpam-2753	206	5	·	·	PUNCT
ejpam-2753	206	6	)	)	PUNCT
ejpam-2753	206	7	is	be	AUX
ejpam-2753	206	8	an	an	DET
ejpam-2753	206	9	object	object	NOUN
ejpam-2753	206	10	in	in	ADP
ejpam-2753	206	11	the	the	DET
ejpam-2753	206	12	category	category	NOUN
ejpam-2753	206	13	hvsk	hvsk	VERB
ejpam-2753	207	1	and	and	CCONJ
ejpam-2753	207	2	i	i	PRON
ejpam-2753	207	3	:	:	PUNCT
ejpam-2753	207	4	x	x	X
ejpam-2753	207	5	↪	↪	PROPN
ejpam-2753	207	6	→	→	SYM
ejpam-2753	207	7	f	f	PROPN
ejpam-2753	207	8	is	be	AUX
ejpam-2753	207	9	an	an	DET
ejpam-2753	207	10	inclusion	inclusion	NOUN
ejpam-2753	207	11	map	map	NOUN
ejpam-2753	207	12	of	of	ADP
ejpam-2753	207	13	sets	set	NOUN
ejpam-2753	207	14	.	.	PUNCT
ejpam-2753	208	1	we	we	PRON
ejpam-2753	208	2	say	say	VERB
ejpam-2753	208	3	that	that	SCONJ
ejpam-2753	208	4	f	f	PROPN
ejpam-2753	208	5	is	be	AUX
ejpam-2753	208	6	quasi	quasi	ADJ
ejpam-2753	208	7	-	-	ADJ
ejpam-2753	208	8	free	free	ADJ
ejpam-2753	208	9	on	on	ADP
ejpam-2753	208	10	the	the	DET
ejpam-2753	208	11	subset	subset	NOUN
ejpam-2753	208	12	x	x	PUNCT
ejpam-2753	208	13	provided	provide	VERB
ejpam-2753	208	14	that	that	SCONJ
ejpam-2753	208	15	:	:	PUNCT
ejpam-2753	208	16	(	(	PUNCT
ejpam-2753	208	17	i	i	NOUN
ejpam-2753	208	18	)	)	PUNCT
ejpam-2753	208	19	f	f	PROPN
ejpam-2753	209	1	=	=	SYM
ejpam-2753	209	2	〈	〈	PROPN
ejpam-2753	209	3	x	x	SYM
ejpam-2753	209	4	〉	〉	PROPN
ejpam-2753	209	5	;	;	PUNCT
ejpam-2753	209	6	(	(	PUNCT
ejpam-2753	209	7	ii	ii	NOUN
ejpam-2753	209	8	)	)	PUNCT
ejpam-2753	209	9	for	for	ADP
ejpam-2753	209	10	any	any	DET
ejpam-2753	209	11	object	object	NOUN
ejpam-2753	209	12	v	v	NOUN
ejpam-2753	209	13	in	in	ADP
ejpam-2753	209	14	hvsk	hvsk	NOUN
ejpam-2753	209	15	and	and	CCONJ
ejpam-2753	209	16	any	any	DET
ejpam-2753	209	17	multivalued	multivalue	VERB
ejpam-2753	209	18	map	map	NOUN
ejpam-2753	209	19	λ	λ	NOUN
ejpam-2753	209	20	:	:	PUNCT
ejpam-2753	209	21	x	x	PUNCT
ejpam-2753	209	22	−→	−→	NOUN
ejpam-2753	209	23	p	p	PROPN
ejpam-2753	209	24	∗(v	∗(v	PROPN
ejpam-2753	209	25	)	)	PUNCT
ejpam-2753	209	26	,	,	PUNCT
ejpam-2753	209	27	there	there	PRON
ejpam-2753	209	28	is	be	VERB
ejpam-2753	209	29	a	a	DET
ejpam-2753	209	30	maximum	maximum	ADJ
ejpam-2753	209	31	smlt	smlt	NOUN
ejpam-2753	209	32	,	,	PUNCT
ejpam-2753	209	33	λ	λ	X
ejpam-2753	209	34	:	:	PUNCT
ejpam-2753	209	35	f	f	X
ejpam-2753	210	1	−→	−→	NOUN
ejpam-2753	210	2	p	p	PROPN
ejpam-2753	210	3	∗(v	∗(v	PROPN
ejpam-2753	210	4	)	)	PUNCT
ejpam-2753	210	5	such	such	ADJ
ejpam-2753	210	6	that	that	PRON
ejpam-2753	210	7	for	for	ADP
ejpam-2753	210	8	all	all	DET
ejpam-2753	210	9	x	x	SYM
ejpam-2753	210	10	∈	∈	NOUN
ejpam-2753	210	11	x	x	NOUN
ejpam-2753	210	12	,	,	PUNCT
ejpam-2753	210	13	we	we	PRON
ejpam-2753	210	14	have	have	VERB
ejpam-2753	210	15	λi(x	λi(x	NUM
ejpam-2753	210	16	)	)	PUNCT
ejpam-2753	210	17	=	=	SYM
ejpam-2753	211	1	λ(x	λ(x	X
ejpam-2753	211	2	)	)	PUNCT
ejpam-2753	211	3	.	.	PUNCT
ejpam-2753	212	1	r.	r.	PROPN
ejpam-2753	212	2	ameri	ameri	PROPN
ejpam-2753	212	3	,	,	PUNCT
ejpam-2753	212	4	k.	k.	PROPN
ejpam-2753	212	5	ghadimi	ghadimi	PROPN
ejpam-2753	212	6	,	,	PUNCT
ejpam-2753	212	7	r.	r.	PROPN
ejpam-2753	212	8	a.	a.	PROPN
ejpam-2753	212	9	borzooei	borzooei	PROPN
ejpam-2753	212	10	/	/	SYM
ejpam-2753	212	11	eur	eur	PROPN
ejpam-2753	212	12	.	.	PUNCT
ejpam-2753	213	1	j.	j.	PROPN
ejpam-2753	213	2	pure	pure	PROPN
ejpam-2753	213	3	appl	appl	PROPN
ejpam-2753	213	4	.	.	PROPN
ejpam-2753	213	5	math	math	PROPN
ejpam-2753	213	6	,	,	PUNCT
ejpam-2753	213	7	10	10	NUM
ejpam-2753	213	8	(	(	PUNCT
ejpam-2753	213	9	4	4	NUM
ejpam-2753	213	10	)	)	PUNCT
ejpam-2753	213	11	(	(	PUNCT
ejpam-2753	213	12	2017	2017	NUM
ejpam-2753	213	13	)	)	PUNCT
ejpam-2753	213	14	,	,	PUNCT
ejpam-2753	213	15	702	702	NUM
ejpam-2753	213	16	-	-	SYM
ejpam-2753	213	17	716	716	NUM
ejpam-2753	213	18	710	710	NUM
ejpam-2753	213	19	theorem	theorem	NOUN
ejpam-2753	213	20	3	3	X
ejpam-2753	213	21	.	.	PUNCT
ejpam-2753	214	1	let	let	VERB
ejpam-2753	214	2	f	f	PRON
ejpam-2753	214	3	be	be	AUX
ejpam-2753	214	4	a	a	DET
ejpam-2753	214	5	strongly	strongly	ADV
ejpam-2753	214	6	distributive	distributive	ADJ
ejpam-2753	214	7	hyperspace	hyperspace	NOUN
ejpam-2753	214	8	over	over	ADP
ejpam-2753	214	9	a	a	DET
ejpam-2753	214	10	field	field	NOUN
ejpam-2753	215	1	k	k	PROPN
ejpam-2753	216	1	and	and	CCONJ
ejpam-2753	216	2	x	x	AUX
ejpam-2753	216	3	be	be	AUX
ejpam-2753	216	4	a	a	DET
ejpam-2753	216	5	basis	basis	NOUN
ejpam-2753	216	6	for	for	ADP
ejpam-2753	216	7	f	f	PROPN
ejpam-2753	216	8	.	.	PUNCT
ejpam-2753	217	1	then	then	ADV
ejpam-2753	217	2	(	(	PUNCT
ejpam-2753	217	3	i	i	NOUN
ejpam-2753	217	4	)	)	PUNCT
ejpam-2753	217	5	if	if	SCONJ
ejpam-2753	217	6	j	j	PROPN
ejpam-2753	217	7	:	:	PUNCT
ejpam-2753	217	8	x	x	SYM
ejpam-2753	217	9	↪	↪	PROPN
ejpam-2753	217	10	→	→	SYM
ejpam-2753	217	11	f	f	PROPN
ejpam-2753	217	12	is	be	AUX
ejpam-2753	217	13	a	a	DET
ejpam-2753	217	14	inclusion	inclusion	NOUN
ejpam-2753	217	15	map	map	NOUN
ejpam-2753	217	16	,	,	PUNCT
ejpam-2753	217	17	then	then	ADV
ejpam-2753	217	18	for	for	ADP
ejpam-2753	217	19	all	all	DET
ejpam-2753	217	20	k	k	NOUN
ejpam-2753	217	21	-	-	NOUN
ejpam-2753	217	22	hyperspace	hyperspace	NOUN
ejpam-2753	217	23	v	v	NOUN
ejpam-2753	217	24	and	and	CCONJ
ejpam-2753	217	25	map	map	VERB
ejpam-2753	217	26	f	f	X
ejpam-2753	217	27	:	:	PUNCT
ejpam-2753	217	28	x	x	PUNCT
ejpam-2753	217	29	−→	−→	NOUN
ejpam-2753	217	30	p	p	PROPN
ejpam-2753	217	31	∗(v	∗(v	PROPN
ejpam-2753	217	32	)	)	PUNCT
ejpam-2753	217	33	,	,	PUNCT
ejpam-2753	217	34	there	there	PRON
ejpam-2753	217	35	is	be	VERB
ejpam-2753	217	36	a	a	DET
ejpam-2753	217	37	maximum	maximum	ADJ
ejpam-2753	217	38	smlt	smlt	NOUN
ejpam-2753	217	39	,	,	PUNCT
ejpam-2753	217	40	ϕ	ϕ	NOUN
ejpam-2753	217	41	:	:	PUNCT
ejpam-2753	217	42	f	f	PROPN
ejpam-2753	217	43	−→	−→	NOUN
ejpam-2753	217	44	p	p	PROPN
ejpam-2753	217	45	∗(v	∗(v	PROPN
ejpam-2753	217	46	)	)	PUNCT
ejpam-2753	217	47	such	such	ADJ
ejpam-2753	217	48	that	that	SCONJ
ejpam-2753	217	49	the	the	DET
ejpam-2753	217	50	diagram	diagram	NOUN
ejpam-2753	217	51	x	x	X
ejpam-2753	217	52	f	f	PROPN
ejpam-2753	217	53	p	p	PROPN
ejpam-2753	217	54	∗(v	∗(v	PROPN
ejpam-2753	217	55	)	)	PUNCT
ejpam-2753	218	1	j	j	PROPN
ejpam-2753	219	1	ϕf	ϕf	PROPN
ejpam-2753	219	2	is	be	AUX
ejpam-2753	219	3	commutative	commutative	ADJ
ejpam-2753	219	4	.	.	PUNCT
ejpam-2753	220	1	(	(	PUNCT
ejpam-2753	220	2	ii	ii	NOUN
ejpam-2753	220	3	)	)	PUNCT
ejpam-2753	220	4	for	for	ADP
ejpam-2753	220	5	all	all	DET
ejpam-2753	220	6	k	k	PROPN
ejpam-2753	220	7	-	-	NOUN
ejpam-2753	220	8	hyperspace	hyperspace	NOUN
ejpam-2753	220	9	v	v	NOUN
ejpam-2753	220	10	and	and	CCONJ
ejpam-2753	220	11	f	f	NOUN
ejpam-2753	220	12	:	:	PUNCT
ejpam-2753	220	13	x	x	PUNCT
ejpam-2753	220	14	−→	−→	NOUN
ejpam-2753	220	15	p	p	X
ejpam-2753	220	16	∗(v	∗(v	PROPN
ejpam-2753	220	17	)	)	PUNCT
ejpam-2753	220	18	induced	induce	VERB
ejpam-2753	220	19	maximum	maximum	ADJ
ejpam-2753	220	20	smlt	smlt	NOUN
ejpam-2753	220	21	,	,	PUNCT
ejpam-2753	220	22	ϕ	ϕ	NOUN
ejpam-2753	220	23	:	:	PUNCT
ejpam-2753	220	24	f	f	PROPN
ejpam-2753	220	25	−→	−→	NOUN
ejpam-2753	220	26	p	p	PROPN
ejpam-2753	220	27	∗(v	∗(v	PROPN
ejpam-2753	220	28	)	)	PUNCT
ejpam-2753	220	29	,	,	PUNCT
ejpam-2753	220	30	means	mean	VERB
ejpam-2753	220	31	there	there	PRON
ejpam-2753	220	32	is	be	VERB
ejpam-2753	220	33	a	a	DET
ejpam-2753	220	34	maximum	maximum	ADJ
ejpam-2753	220	35	smlt	smlt	NOUN
ejpam-2753	220	36	,	,	PUNCT
ejpam-2753	220	37	ϕ	ϕ	NOUN
ejpam-2753	220	38	:	:	PUNCT
ejpam-2753	220	39	f	f	PROPN
ejpam-2753	220	40	−→	−→	NOUN
ejpam-2753	220	41	p	p	PROPN
ejpam-2753	220	42	∗(v	∗(v	PROPN
ejpam-2753	220	43	)	)	PUNCT
ejpam-2753	220	44	such	such	ADJ
ejpam-2753	220	45	that	that	SCONJ
ejpam-2753	220	46	ϕ|x	ϕ|x	PUNCT
ejpam-2753	221	1	=	=	PUNCT
ejpam-2753	221	2	f	f	PROPN
ejpam-2753	221	3	.	.	PUNCT
ejpam-2753	222	1	proof	proof	NOUN
ejpam-2753	222	2	.	.	PUNCT
ejpam-2753	223	1	(	(	PUNCT
ejpam-2753	223	2	i	i	NOUN
ejpam-2753	223	3	)	)	PUNCT
ejpam-2753	223	4	since	since	SCONJ
ejpam-2753	223	5	for	for	ADP
ejpam-2753	223	6	every	every	DET
ejpam-2753	223	7	u	u	PROPN
ejpam-2753	223	8	∈	∈	PROPN
ejpam-2753	223	9	f	f	NOUN
ejpam-2753	223	10	,	,	PUNCT
ejpam-2753	223	11	there	there	PRON
ejpam-2753	223	12	exists	exist	VERB
ejpam-2753	223	13	scalars	scalars	PROPN
ejpam-2753	223	14	c1	c1	PROPN
ejpam-2753	223	15	,	,	PUNCT
ejpam-2753	223	16	...	...	PUNCT
ejpam-2753	223	17	,	,	PUNCT
ejpam-2753	223	18	cn	cn	PROPN
ejpam-2753	223	19	∈	∈	PROPN
ejpam-2753	224	1	k	k	PROPN
ejpam-2753	224	2	such	such	ADJ
ejpam-2753	224	3	that	that	DET
ejpam-2753	224	4	(	(	PUNCT
ejpam-2753	224	5	∗	∗	NOUN
ejpam-2753	224	6	)	)	PUNCT
ejpam-2753	224	7	u	u	NOUN
ejpam-2753	224	8	∈	∈	PROPN
ejpam-2753	224	9	n∑	n∑	PROPN
ejpam-2753	225	1	i=1	i=1	PROPN
ejpam-2753	225	2	ci	ci	PROPN
ejpam-2753	225	3	◦	◦	NOUN
ejpam-2753	225	4	xi	xi	PROPN
ejpam-2753	225	5	,	,	PUNCT
ejpam-2753	225	6	then	then	ADV
ejpam-2753	225	7	we	we	PRON
ejpam-2753	225	8	define	define	VERB
ejpam-2753	225	9	a	a	DET
ejpam-2753	225	10	map	map	NOUN
ejpam-2753	225	11	ϕ	ϕ	NOUN
ejpam-2753	225	12	:	:	PUNCT
ejpam-2753	225	13	f	f	PROPN
ejpam-2753	225	14	−→	−→	NOUN
ejpam-2753	225	15	p	p	PROPN
ejpam-2753	225	16	∗(v	∗(v	PROPN
ejpam-2753	225	17	)	)	PUNCT
ejpam-2753	225	18	as	as	SCONJ
ejpam-2753	225	19	follows	follow	VERB
ejpam-2753	225	20	:	:	PUNCT
ejpam-2753	225	21	ϕ(u	ϕ(u	X
ejpam-2753	225	22	)	)	PUNCT
ejpam-2753	226	1	=	=	SYM
ejpam-2753	226	2	ϕ	ϕ	PROPN
ejpam-2753	226	3	(	(	PUNCT
ejpam-2753	226	4	n∑	n∑	NOUN
ejpam-2753	226	5	i=1	i=1	PROPN
ejpam-2753	226	6	ci	ci	PROPN
ejpam-2753	227	1	◦	◦	NOUN
ejpam-2753	227	2	xi	xi	NUM
ejpam-2753	227	3	)	)	PUNCT
ejpam-2753	228	1	=	=	SYM
ejpam-2753	229	1	n∑	n∑	PROPN
ejpam-2753	229	2	i=1	i=1	PROPN
ejpam-2753	229	3	ci	ci	PROPN
ejpam-2753	229	4	◦	◦	NOUN
ejpam-2753	229	5	f(xi	f(xi	NUM
ejpam-2753	229	6	)	)	PUNCT
ejpam-2753	229	7	.	.	PUNCT
ejpam-2753	230	1	since	since	SCONJ
ejpam-2753	230	2	(	(	PUNCT
ejpam-2753	230	3	∗	∗	NOUN
ejpam-2753	230	4	)	)	PUNCT
ejpam-2753	230	5	is	be	AUX
ejpam-2753	230	6	unique	unique	ADJ
ejpam-2753	230	7	,	,	PUNCT
ejpam-2753	230	8	then	then	ADV
ejpam-2753	230	9	ϕ	ϕ	PROPN
ejpam-2753	230	10	is	be	AUX
ejpam-2753	230	11	well	well	ADV
ejpam-2753	230	12	-	-	PUNCT
ejpam-2753	230	13	defined	define	VERB
ejpam-2753	230	14	.	.	PUNCT
ejpam-2753	231	1	now	now	ADV
ejpam-2753	231	2	,	,	PUNCT
ejpam-2753	231	3	we	we	PRON
ejpam-2753	231	4	check	check	VERB
ejpam-2753	231	5	that	that	SCONJ
ejpam-2753	231	6	ϕ	ϕ	NOUN
ejpam-2753	231	7	is	be	AUX
ejpam-2753	231	8	a	a	DET
ejpam-2753	231	9	smlt	smlt	NOUN
ejpam-2753	231	10	.	.	PUNCT
ejpam-2753	232	1	let	let	VERB
ejpam-2753	232	2	u	u	NOUN
ejpam-2753	232	3	,	,	PUNCT
ejpam-2753	232	4	v	v	PROPN
ejpam-2753	232	5	∈	∈	ADJ
ejpam-2753	232	6	f	f	NOUN
ejpam-2753	232	7	and	and	CCONJ
ejpam-2753	232	8	scalars	scalar	VERB
ejpam-2753	232	9	d1	d1	PROPN
ejpam-2753	232	10	,	,	PUNCT
ejpam-2753	232	11	...	...	PUNCT
ejpam-2753	232	12	,	,	PUNCT
ejpam-2753	232	13	dn	dn	PROPN
ejpam-2753	232	14	∈	∈	PROPN
ejpam-2753	233	1	k.	k.	PROPN
ejpam-2753	234	1	then	then	ADV
ejpam-2753	234	2	u	u	PROPN
ejpam-2753	234	3	∈	∈	PROPN
ejpam-2753	234	4	∑n	∑n	PROPN
ejpam-2753	234	5	i=1	i=1	PROPN
ejpam-2753	234	6	ci	ci	PROPN
ejpam-2753	234	7	◦	◦	NOUN
ejpam-2753	234	8	xi	xi	X
ejpam-2753	234	9	and	and	CCONJ
ejpam-2753	234	10	v	v	NOUN
ejpam-2753	234	11	∈	∈	NOUN
ejpam-2753	234	12	∑n	∑n	PROPN
ejpam-2753	234	13	i=1	i=1	PROPN
ejpam-2753	234	14	di	di	NOUN
ejpam-2753	234	15	◦	◦	NOUN
ejpam-2753	234	16	xi	xi	PROPN
ejpam-2753	234	17	,	,	PUNCT
ejpam-2753	234	18	thus	thus	ADV
ejpam-2753	234	19	we	we	PRON
ejpam-2753	234	20	have	have	VERB
ejpam-2753	234	21	ϕ(u	ϕ(u	X
ejpam-2753	234	22	)	)	PUNCT
ejpam-2753	235	1	=	=	PUNCT
ejpam-2753	236	1	∑n	∑n	PROPN
ejpam-2753	236	2	i=1	i=1	PROPN
ejpam-2753	236	3	ci	ci	PROPN
ejpam-2753	236	4	◦	◦	NOUN
ejpam-2753	236	5	f(xi	f(xi	PROPN
ejpam-2753	236	6	)	)	PUNCT
ejpam-2753	236	7	and	and	CCONJ
ejpam-2753	236	8	ϕ(v	ϕ(v	PROPN
ejpam-2753	236	9	)	)	PUNCT
ejpam-2753	237	1	=	=	SYM
ejpam-2753	237	2	∑n	∑n	PROPN
ejpam-2753	237	3	i=1	i=1	PROPN
ejpam-2753	237	4	di	di	NOUN
ejpam-2753	237	5	◦	◦	NOUN
ejpam-2753	237	6	f(xi	f(xi	NUM
ejpam-2753	237	7	)	)	PUNCT
ejpam-2753	237	8	.	.	PUNCT
ejpam-2753	238	1	now	now	ADV
ejpam-2753	238	2	since	since	SCONJ
ejpam-2753	238	3	u+	u+	NUM
ejpam-2753	238	4	v	v	PRON
ejpam-2753	238	5	∈∑n	∈∑n	PROPN
ejpam-2753	238	6	i=1(ci	i=1(ci	PROPN
ejpam-2753	238	7	+	+	CCONJ
ejpam-2753	238	8	di	di	NOUN
ejpam-2753	238	9	)	)	PUNCT
ejpam-2753	238	10	◦	◦	NOUN
ejpam-2753	238	11	xi	xi	ADP
ejpam-2753	238	12	,	,	PUNCT
ejpam-2753	238	13	then	then	ADV
ejpam-2753	238	14	we	we	PRON
ejpam-2753	238	15	obtain	obtain	VERB
ejpam-2753	238	16	:	:	PUNCT
ejpam-2753	238	17	ϕ(u+	ϕ(u+	NUM
ejpam-2753	238	18	v	v	NOUN
ejpam-2753	238	19	)	)	PUNCT
ejpam-2753	238	20	=	=	SYM
ejpam-2753	239	1	ϕ	ϕ	PROPN
ejpam-2753	239	2	(	(	PUNCT
ejpam-2753	239	3	n∑	n∑	NOUN
ejpam-2753	239	4	i=1	i=1	PROPN
ejpam-2753	239	5	(	(	PUNCT
ejpam-2753	239	6	ci	ci	NOUN
ejpam-2753	239	7	+	+	CCONJ
ejpam-2753	239	8	di	di	NOUN
ejpam-2753	239	9	)	)	PUNCT
ejpam-2753	239	10	◦	◦	NOUN
ejpam-2753	239	11	xi	xi	NUM
ejpam-2753	239	12	)	)	PUNCT
ejpam-2753	239	13	=	=	SYM
ejpam-2753	240	1	n∑	n∑	NOUN
ejpam-2753	240	2	i=1	i=1	PROPN
ejpam-2753	241	1	(	(	PUNCT
ejpam-2753	241	2	ci	ci	NOUN
ejpam-2753	241	3	+	+	CCONJ
ejpam-2753	241	4	di	di	NOUN
ejpam-2753	241	5	)	)	PUNCT
ejpam-2753	241	6	◦	◦	NOUN
ejpam-2753	241	7	f(xi	f(xi	NUM
ejpam-2753	241	8	)	)	PUNCT
ejpam-2753	241	9	=	=	SYM
ejpam-2753	241	10	n∑	n∑	PROPN
ejpam-2753	241	11	i=1	i=1	PROPN
ejpam-2753	241	12	ci	ci	PROPN
ejpam-2753	241	13	◦	◦	NOUN
ejpam-2753	241	14	f(xi	f(xi	PROPN
ejpam-2753	241	15	)	)	PUNCT
ejpam-2753	242	1	+	+	NUM
ejpam-2753	242	2	n∑	n∑	PROPN
ejpam-2753	242	3	i=1	i=1	PROPN
ejpam-2753	242	4	di	di	PROPN
ejpam-2753	242	5	◦	◦	PROPN
ejpam-2753	242	6	f(xi	f(xi	PROPN
ejpam-2753	242	7	)	)	PUNCT
ejpam-2753	242	8	r.	r.	PROPN
ejpam-2753	242	9	ameri	ameri	PROPN
ejpam-2753	242	10	,	,	PUNCT
ejpam-2753	242	11	k.	k.	PROPN
ejpam-2753	242	12	ghadimi	ghadimi	PROPN
ejpam-2753	242	13	,	,	PUNCT
ejpam-2753	242	14	r.	r.	PROPN
ejpam-2753	242	15	a.	a.	PROPN
ejpam-2753	242	16	borzooei	borzooei	PROPN
ejpam-2753	242	17	/	/	SYM
ejpam-2753	242	18	eur	eur	PROPN
ejpam-2753	242	19	.	.	PUNCT
ejpam-2753	243	1	j.	j.	PROPN
ejpam-2753	243	2	pure	pure	PROPN
ejpam-2753	243	3	appl	appl	PROPN
ejpam-2753	243	4	.	.	PROPN
ejpam-2753	243	5	math	math	PROPN
ejpam-2753	243	6	,	,	PUNCT
ejpam-2753	243	7	10	10	NUM
ejpam-2753	243	8	(	(	PUNCT
ejpam-2753	243	9	4	4	NUM
ejpam-2753	243	10	)	)	PUNCT
ejpam-2753	243	11	(	(	PUNCT
ejpam-2753	243	12	2017	2017	NUM
ejpam-2753	243	13	)	)	PUNCT
ejpam-2753	243	14	,	,	PUNCT
ejpam-2753	243	15	702	702	NUM
ejpam-2753	243	16	-	-	SYM
ejpam-2753	243	17	716	716	NUM
ejpam-2753	243	18	711	711	NUM
ejpam-2753	243	19	=	=	SYM
ejpam-2753	243	20	ϕ(u	ϕ(u	NOUN
ejpam-2753	243	21	)	)	PUNCT
ejpam-2753	243	22	+	+	CCONJ
ejpam-2753	243	23	ϕ(v	ϕ(v	NOUN
ejpam-2753	243	24	)	)	PUNCT
ejpam-2753	243	25	.	.	PUNCT
ejpam-2753	244	1	also	also	ADV
ejpam-2753	244	2	,	,	PUNCT
ejpam-2753	244	3	it	it	PRON
ejpam-2753	244	4	is	be	AUX
ejpam-2753	244	5	clear	clear	ADJ
ejpam-2753	244	6	that	that	SCONJ
ejpam-2753	244	7	(	(	PUNCT
ejpam-2753	244	8	c	c	NOUN
ejpam-2753	244	9	◦	◦	NOUN
ejpam-2753	244	10	ϕ)(xi	ϕ)(xi	NUM
ejpam-2753	244	11	)	)	PUNCT
ejpam-2753	245	1	=	=	PUNCT
ejpam-2753	246	1	c	c	X
ejpam-2753	246	2	◦	◦	NOUN
ejpam-2753	246	3	ϕ(xi	ϕ(xi	PROPN
ejpam-2753	246	4	)	)	PUNCT
ejpam-2753	246	5	.	.	PUNCT
ejpam-2753	247	1	hence	hence	ADV
ejpam-2753	247	2	,	,	PUNCT
ejpam-2753	247	3	ϕ	ϕ	PROPN
ejpam-2753	247	4	is	be	AUX
ejpam-2753	247	5	a	a	DET
ejpam-2753	247	6	multivalued	multivalue	VERB
ejpam-2753	247	7	linear	linear	ADJ
ejpam-2753	247	8	transformation	transformation	NOUN
ejpam-2753	247	9	.	.	PUNCT
ejpam-2753	248	1	also	also	ADV
ejpam-2753	248	2	,	,	PUNCT
ejpam-2753	248	3	for	for	ADP
ejpam-2753	248	4	all	all	DET
ejpam-2753	248	5	x	x	SYM
ejpam-2753	248	6	∈	∈	PROPN
ejpam-2753	248	7	x	x	X
ejpam-2753	248	8	,	,	PUNCT
ejpam-2753	248	9	ϕj(x	ϕj(x	PUNCT
ejpam-2753	248	10	)	)	PUNCT
ejpam-2753	248	11	=	=	SYM
ejpam-2753	248	12	ϕ(x	ϕ(x	X
ejpam-2753	248	13	)	)	PUNCT
ejpam-2753	248	14	=	=	SYM
ejpam-2753	248	15	f(x	f(x	PROPN
ejpam-2753	248	16	)	)	PUNCT
ejpam-2753	248	17	,	,	PUNCT
ejpam-2753	248	18	thus	thus	ADV
ejpam-2753	248	19	ϕj	ϕj	ADP
ejpam-2753	248	20	=	=	SYM
ejpam-2753	248	21	f	f	PROPN
ejpam-2753	248	22	,	,	PUNCT
ejpam-2753	248	23	means	mean	VERB
ejpam-2753	248	24	that	that	SCONJ
ejpam-2753	248	25	ϕ	ϕ	NOUN
ejpam-2753	248	26	is	be	AUX
ejpam-2753	248	27	a	a	DET
ejpam-2753	248	28	smlt	smlt	NOUN
ejpam-2753	248	29	,	,	PUNCT
ejpam-2753	248	30	where	where	SCONJ
ejpam-2753	248	31	the	the	DET
ejpam-2753	248	32	diagram	diagram	NOUN
ejpam-2753	248	33	is	be	AUX
ejpam-2753	248	34	commutative	commutative	ADJ
ejpam-2753	248	35	.	.	PUNCT
ejpam-2753	249	1	now	now	ADV
ejpam-2753	249	2	,	,	PUNCT
ejpam-2753	249	3	if	if	SCONJ
ejpam-2753	249	4	there	there	PRON
ejpam-2753	249	5	is	be	VERB
ejpam-2753	249	6	a	a	DET
ejpam-2753	249	7	smlt	smlt	NOUN
ejpam-2753	249	8	,	,	PUNCT
ejpam-2753	249	9	ψ	ψ	X
ejpam-2753	249	10	:	:	PUNCT
ejpam-2753	249	11	f	f	X
ejpam-2753	249	12	−→	−→	NOUN
ejpam-2753	249	13	p	p	PROPN
ejpam-2753	249	14	∗(v	∗(v	PROPN
ejpam-2753	249	15	)	)	PUNCT
ejpam-2753	249	16	such	such	ADJ
ejpam-2753	249	17	that	that	SCONJ
ejpam-2753	249	18	the	the	DET
ejpam-2753	249	19	diagram	diagram	NOUN
ejpam-2753	249	20	is	be	AUX
ejpam-2753	249	21	commutative	commutative	ADJ
ejpam-2753	249	22	,	,	PUNCT
ejpam-2753	249	23	then	then	ADV
ejpam-2753	249	24	for	for	ADP
ejpam-2753	249	25	all	all	PRON
ejpam-2753	249	26	u	u	NOUN
ejpam-2753	249	27	∈	∈	PROPN
ejpam-2753	249	28	f	f	X
ejpam-2753	249	29	:	:	PUNCT
ejpam-2753	249	30	ϕ(u	ϕ(u	X
ejpam-2753	249	31	)	)	PUNCT
ejpam-2753	250	1	=	=	SYM
ejpam-2753	250	2	ϕ	ϕ	PROPN
ejpam-2753	250	3	(	(	PUNCT
ejpam-2753	250	4	n∑	n∑	NOUN
ejpam-2753	250	5	i=1	i=1	PROPN
ejpam-2753	250	6	ci	ci	PROPN
ejpam-2753	251	1	◦	◦	NOUN
ejpam-2753	251	2	xi	xi	NUM
ejpam-2753	251	3	)	)	PUNCT
ejpam-2753	252	1	=	=	SYM
ejpam-2753	253	1	n∑	n∑	PROPN
ejpam-2753	253	2	i=1	i=1	PROPN
ejpam-2753	253	3	ci	ci	PROPN
ejpam-2753	253	4	◦	◦	NOUN
ejpam-2753	253	5	f(xi	f(xi	PROPN
ejpam-2753	253	6	)	)	PUNCT
ejpam-2753	254	1	=	=	SYM
ejpam-2753	255	1	n∑	n∑	PROPN
ejpam-2753	255	2	i=1	i=1	PROPN
ejpam-2753	255	3	ci	ci	PROPN
ejpam-2753	255	4	◦	◦	PROPN
ejpam-2753	255	5	ψj(xi	ψj(xi	PROPN
ejpam-2753	255	6	)	)	PUNCT
ejpam-2753	256	1	=	=	PUNCT
ejpam-2753	257	1	n∑	n∑	PROPN
ejpam-2753	257	2	i=1	i=1	PROPN
ejpam-2753	258	1	ci	ci	PROPN
ejpam-2753	258	2	◦	◦	NOUN
ejpam-2753	258	3	ψ(xi	ψ(xi	PROPN
ejpam-2753	258	4	)	)	PUNCT
ejpam-2753	259	1	=	=	SYM
ejpam-2753	260	1	ψ	ψ	X
ejpam-2753	260	2	(	(	PUNCT
ejpam-2753	260	3	n∑	n∑	NOUN
ejpam-2753	260	4	i=1	i=1	PROPN
ejpam-2753	260	5	ci	ci	PROPN
ejpam-2753	260	6	◦	◦	NOUN
ejpam-2753	260	7	xi	xi	NOUN
ejpam-2753	260	8	)	)	PUNCT
ejpam-2753	260	9	⊇	⊇	PROPN
ejpam-2753	260	10	ψ(u	ψ(u	PROPN
ejpam-2753	260	11	)	)	PUNCT
ejpam-2753	260	12	,	,	PUNCT
ejpam-2753	260	13	therfore	therfore	ADP
ejpam-2753	260	14	ϕ	ϕ	PROPN
ejpam-2753	260	15	⊇	⊇	PROPN
ejpam-2753	260	16	ψ	ψ	PROPN
ejpam-2753	260	17	.	.	PUNCT
ejpam-2753	260	18	(	(	PUNCT
ejpam-2753	260	19	ii	ii	NOUN
ejpam-2753	260	20	)	)	PUNCT
ejpam-2753	260	21	let	let	VERB
ejpam-2753	260	22	v	v	PART
ejpam-2753	260	23	be	be	AUX
ejpam-2753	260	24	a	a	DET
ejpam-2753	260	25	k	k	NOUN
ejpam-2753	260	26	-	-	NOUN
ejpam-2753	260	27	hyperspace	hyperspace	NOUN
ejpam-2753	260	28	and	and	CCONJ
ejpam-2753	260	29	f	f	NOUN
ejpam-2753	260	30	:	:	PUNCT
ejpam-2753	260	31	x	x	PUNCT
ejpam-2753	260	32	−→	−→	NOUN
ejpam-2753	260	33	p	p	X
ejpam-2753	260	34	∗(v	∗(v	PROPN
ejpam-2753	260	35	)	)	PUNCT
ejpam-2753	260	36	be	be	AUX
ejpam-2753	260	37	a	a	DET
ejpam-2753	260	38	map	map	NOUN
ejpam-2753	260	39	.	.	PUNCT
ejpam-2753	261	1	by	by	ADP
ejpam-2753	261	2	part	part	NOUN
ejpam-2753	261	3	(	(	PUNCT
ejpam-2753	261	4	i	i	NOUN
ejpam-2753	261	5	)	)	PUNCT
ejpam-2753	261	6	,	,	PUNCT
ejpam-2753	261	7	there	there	PRON
ejpam-2753	261	8	exists	exist	VERB
ejpam-2753	261	9	maximum	maximum	ADJ
ejpam-2753	261	10	smlt	smlt	NOUN
ejpam-2753	261	11	,	,	PUNCT
ejpam-2753	261	12	ϕ	ϕ	NOUN
ejpam-2753	261	13	:	:	PUNCT
ejpam-2753	261	14	f	f	PROPN
ejpam-2753	261	15	−→	−→	NOUN
ejpam-2753	261	16	p	p	PROPN
ejpam-2753	261	17	∗(v	∗(v	PROPN
ejpam-2753	261	18	)	)	PUNCT
ejpam-2753	261	19	such	such	ADJ
ejpam-2753	261	20	that	that	SCONJ
ejpam-2753	261	21	the	the	DET
ejpam-2753	261	22	diagram	diagram	NOUN
ejpam-2753	261	23	x	x	X
ejpam-2753	261	24	f	f	PROPN
ejpam-2753	261	25	p	p	PROPN
ejpam-2753	261	26	∗(v	∗(v	PROPN
ejpam-2753	261	27	)	)	PUNCT
ejpam-2753	262	1	j	j	PROPN
ejpam-2753	263	1	ϕf	ϕf	PROPN
ejpam-2753	263	2	is	be	AUX
ejpam-2753	263	3	commutative	commutative	ADJ
ejpam-2753	263	4	,	,	PUNCT
ejpam-2753	263	5	means	mean	VERB
ejpam-2753	263	6	that	that	SCONJ
ejpam-2753	264	1	ϕj	ϕj	ADP
ejpam-2753	264	2	=	=	SYM
ejpam-2753	264	3	f	f	PROPN
ejpam-2753	264	4	.	.	PUNCT
ejpam-2753	265	1	therefore	therefore	ADV
ejpam-2753	265	2	for	for	ADP
ejpam-2753	265	3	all	all	DET
ejpam-2753	265	4	x	x	SYM
ejpam-2753	265	5	∈	∈	PROPN
ejpam-2753	265	6	x	x	NOUN
ejpam-2753	265	7	,	,	PUNCT
ejpam-2753	265	8	ϕ(x	ϕ(x	X
ejpam-2753	265	9	)	)	PUNCT
ejpam-2753	265	10	=	=	SYM
ejpam-2753	265	11	ϕj(x	ϕj(x	X
ejpam-2753	265	12	)	)	PUNCT
ejpam-2753	265	13	=	=	SYM
ejpam-2753	265	14	f(x	f(x	PROPN
ejpam-2753	265	15	)	)	PUNCT
ejpam-2753	265	16	.	.	PUNCT
ejpam-2753	266	1	so	so	ADV
ejpam-2753	266	2	ϕ|x	ϕ|x	PUNCT
ejpam-2753	267	1	=	=	PUNCT
ejpam-2753	267	2	f	f	X
ejpam-2753	267	3	.	.	PUNCT
ejpam-2753	268	1	remark	remark	PROPN
ejpam-2753	268	2	9	9	NUM
ejpam-2753	268	3	.	.	PUNCT
ejpam-2753	269	1	by	by	ADP
ejpam-2753	269	2	theorem	theorem	NOUN
ejpam-2753	269	3	3	3	NUM
ejpam-2753	269	4	every	every	DET
ejpam-2753	269	5	strongly	strongly	ADV
ejpam-2753	269	6	distributive	distributive	ADJ
ejpam-2753	269	7	hyperspace	hyperspace	NOUN
ejpam-2753	269	8	is	be	AUX
ejpam-2753	269	9	a	a	DET
ejpam-2753	269	10	quasi	quasi	NOUN
ejpam-2753	269	11	-	-	ADJ
ejpam-2753	269	12	free	free	ADJ
ejpam-2753	269	13	on	on	ADP
ejpam-2753	269	14	every	every	PRON
ejpam-2753	269	15	of	of	ADP
ejpam-2753	269	16	its	its	PRON
ejpam-2753	269	17	basis	basis	NOUN
ejpam-2753	269	18	.	.	PUNCT
ejpam-2753	270	1	r.	r.	PROPN
ejpam-2753	270	2	ameri	ameri	PROPN
ejpam-2753	270	3	,	,	PUNCT
ejpam-2753	270	4	k.	k.	PROPN
ejpam-2753	270	5	ghadimi	ghadimi	PROPN
ejpam-2753	270	6	,	,	PUNCT
ejpam-2753	270	7	r.	r.	PROPN
ejpam-2753	270	8	a.	a.	PROPN
ejpam-2753	270	9	borzooei	borzooei	PROPN
ejpam-2753	270	10	/	/	SYM
ejpam-2753	270	11	eur	eur	PROPN
ejpam-2753	270	12	.	.	PUNCT
ejpam-2753	271	1	j.	j.	PROPN
ejpam-2753	271	2	pure	pure	PROPN
ejpam-2753	271	3	appl	appl	PROPN
ejpam-2753	271	4	.	.	PROPN
ejpam-2753	271	5	math	math	PROPN
ejpam-2753	271	6	,	,	PUNCT
ejpam-2753	271	7	10	10	NUM
ejpam-2753	271	8	(	(	PUNCT
ejpam-2753	271	9	4	4	NUM
ejpam-2753	271	10	)	)	PUNCT
ejpam-2753	271	11	(	(	PUNCT
ejpam-2753	271	12	2017	2017	NUM
ejpam-2753	271	13	)	)	PUNCT
ejpam-2753	271	14	,	,	PUNCT
ejpam-2753	271	15	702	702	NUM
ejpam-2753	271	16	-	-	SYM
ejpam-2753	271	17	716	716	NUM
ejpam-2753	271	18	712	712	NUM
ejpam-2753	271	19	4	4	NUM
ejpam-2753	271	20	.	.	PUNCT
ejpam-2753	271	21	tensor	tensor	NOUN
ejpam-2753	271	22	product	product	NOUN
ejpam-2753	271	23	definition	definition	NOUN
ejpam-2753	271	24	18	18	NUM
ejpam-2753	271	25	.	.	PUNCT
ejpam-2753	272	1	let	let	VERB
ejpam-2753	272	2	v	v	X
ejpam-2753	272	3	,	,	PUNCT
ejpam-2753	272	4	w	w	PROPN
ejpam-2753	272	5	be	be	AUX
ejpam-2753	272	6	two	two	NUM
ejpam-2753	272	7	hyperspaces	hyperspace	NOUN
ejpam-2753	272	8	over	over	ADP
ejpam-2753	272	9	a	a	DET
ejpam-2753	272	10	field	field	NOUN
ejpam-2753	272	11	k	k	NOUN
ejpam-2753	272	12	,	,	PUNCT
ejpam-2753	272	13	and	and	CCONJ
ejpam-2753	272	14	z	z	NOUN
ejpam-2753	272	15	be	be	AUX
ejpam-2753	272	16	an	an	DET
ejpam-2753	272	17	(	(	PUNCT
ejpam-2753	272	18	additive	additive	NOUN
ejpam-2753	272	19	)	)	PUNCT
ejpam-2753	272	20	abelian	abelian	PROPN
ejpam-2753	272	21	group	group	NOUN
ejpam-2753	272	22	.	.	PUNCT
ejpam-2753	273	1	then	then	ADV
ejpam-2753	273	2	a	a	DET
ejpam-2753	273	3	multivalued	multivalue	VERB
ejpam-2753	273	4	middle	middle	ADJ
ejpam-2753	273	5	linear	linear	PROPN
ejpam-2753	273	6	map	map	NOUN
ejpam-2753	273	7	from	from	ADP
ejpam-2753	273	8	v	v	NUM
ejpam-2753	273	9	×	×	NOUN
ejpam-2753	273	10	w	w	NOUN
ejpam-2753	273	11	to	to	ADP
ejpam-2753	273	12	p	p	PROPN
ejpam-2753	273	13	∗(z	∗(z	PROPN
ejpam-2753	273	14	)	)	PUNCT
ejpam-2753	273	15	is	be	AUX
ejpam-2753	273	16	a	a	DET
ejpam-2753	273	17	multivalued	multivalue	VERB
ejpam-2753	273	18	function	function	NOUN
ejpam-2753	273	19	f	f	NOUN
ejpam-2753	273	20	:	:	PUNCT
ejpam-2753	273	21	v	v	NUM
ejpam-2753	273	22	×	×	NOUN
ejpam-2753	273	23	w	w	NOUN
ejpam-2753	273	24	−→	−→	NOUN
ejpam-2753	273	25	p	p	PROPN
ejpam-2753	273	26	∗(z	∗(z	NOUN
ejpam-2753	273	27	)	)	PUNCT
ejpam-2753	273	28	such	such	ADJ
ejpam-2753	273	29	that	that	SCONJ
ejpam-2753	273	30	(	(	PUNCT
ejpam-2753	273	31	for	for	ADP
ejpam-2753	273	32	all	all	DET
ejpam-2753	273	33	v	v	NOUN
ejpam-2753	273	34	,	,	PUNCT
ejpam-2753	273	35	vi	vi	PROPN
ejpam-2753	273	36	∈	∈	PROPN
ejpam-2753	273	37	v	v	NOUN
ejpam-2753	273	38	,	,	PUNCT
ejpam-2753	273	39	w	w	PROPN
ejpam-2753	273	40	,	,	PUNCT
ejpam-2753	273	41	wi	wi	PROPN
ejpam-2753	273	42	∈	∈	PROPN
ejpam-2753	273	43	w	w	PROPN
ejpam-2753	273	44	,	,	PUNCT
ejpam-2753	273	45	a	a	DET
ejpam-2753	273	46	∈	∈	PROPN
ejpam-2753	273	47	k	k	NOUN
ejpam-2753	273	48	,	,	PUNCT
ejpam-2753	273	49	and	and	CCONJ
ejpam-2753	273	50	i	i	NOUN
ejpam-2753	273	51	=	=	NOUN
ejpam-2753	273	52	1	1	NUM
ejpam-2753	273	53	,	,	PUNCT
ejpam-2753	273	54	2	2	NUM
ejpam-2753	273	55	):	):	PUNCT
ejpam-2753	273	56	(	(	PUNCT
ejpam-2753	273	57	i	i	NOUN
ejpam-2753	273	58	)	)	PUNCT
ejpam-2753	273	59	f(v1	f(v1	VERB
ejpam-2753	273	60	+	+	X
ejpam-2753	273	61	v2	v2	NOUN
ejpam-2753	273	62	,	,	PUNCT
ejpam-2753	273	63	w	w	NOUN
ejpam-2753	273	64	)	)	PUNCT
ejpam-2753	273	65	=	=	SYM
ejpam-2753	273	66	f(v1	f(v1	NOUN
ejpam-2753	273	67	,	,	PUNCT
ejpam-2753	273	68	w	w	NOUN
ejpam-2753	273	69	)	)	PUNCT
ejpam-2753	273	70	+	+	NOUN
ejpam-2753	273	71	f(v2	f(v2	NOUN
ejpam-2753	273	72	,	,	PUNCT
ejpam-2753	273	73	w	w	NOUN
ejpam-2753	273	74	)	)	PUNCT
ejpam-2753	273	75	;	;	PUNCT
ejpam-2753	273	76	(	(	PUNCT
ejpam-2753	273	77	ii	ii	NOUN
ejpam-2753	273	78	)	)	PUNCT
ejpam-2753	273	79	f(v	f(v	PROPN
ejpam-2753	273	80	,	,	PUNCT
ejpam-2753	273	81	w1	w1	NOUN
ejpam-2753	273	82	+	+	NOUN
ejpam-2753	273	83	w2	w2	NOUN
ejpam-2753	273	84	)	)	PUNCT
ejpam-2753	273	85	=	=	SYM
ejpam-2753	273	86	f(v	f(v	NOUN
ejpam-2753	273	87	,	,	PUNCT
ejpam-2753	273	88	w1	w1	NOUN
ejpam-2753	273	89	)	)	PUNCT
ejpam-2753	274	1	+	+	NUM
ejpam-2753	274	2	f(v	f(v	NOUN
ejpam-2753	274	3	,	,	PUNCT
ejpam-2753	274	4	w2	w2	NOUN
ejpam-2753	274	5	)	)	PUNCT
ejpam-2753	274	6	;	;	PUNCT
ejpam-2753	274	7	(	(	PUNCT
ejpam-2753	274	8	iii	iii	X
ejpam-2753	274	9	)	)	PUNCT
ejpam-2753	274	10	f(a	f(a	NOUN
ejpam-2753	274	11	◦	◦	NOUN
ejpam-2753	274	12	v	v	ADP
ejpam-2753	274	13	,	,	PUNCT
ejpam-2753	274	14	w	w	NOUN
ejpam-2753	274	15	)	)	PUNCT
ejpam-2753	274	16	=	=	PUNCT
ejpam-2753	274	17	f(v	f(v	NOUN
ejpam-2753	274	18	,	,	PUNCT
ejpam-2753	274	19	a	a	DET
ejpam-2753	274	20	◦	◦	NOUN
ejpam-2753	274	21	w	w	PROPN
ejpam-2753	274	22	)	)	PUNCT
ejpam-2753	274	23	,	,	PUNCT
ejpam-2753	274	24	where	where	SCONJ
ejpam-2753	274	25	f(a	f(a	NOUN
ejpam-2753	274	26	◦	◦	NOUN
ejpam-2753	274	27	v	v	ADP
ejpam-2753	274	28	,	,	PUNCT
ejpam-2753	274	29	w	w	NOUN
ejpam-2753	274	30	)	)	PUNCT
ejpam-2753	274	31	=	=	SYM
ejpam-2753	274	32	⋃	⋃	NOUN
ejpam-2753	274	33	t∈a	t∈a	NOUN
ejpam-2753	274	34	◦	◦	NOUN
ejpam-2753	274	35	v	v	NOUN
ejpam-2753	274	36	f(t	f(t	NOUN
ejpam-2753	274	37	,	,	PUNCT
ejpam-2753	274	38	w	w	NOUN
ejpam-2753	274	39	)	)	PUNCT
ejpam-2753	274	40	.	.	PUNCT
ejpam-2753	275	1	for	for	ADP
ejpam-2753	275	2	fixed	fix	VERB
ejpam-2753	275	3	v	v	NOUN
ejpam-2753	275	4	and	and	CCONJ
ejpam-2753	275	5	w	w	NOUN
ejpam-2753	275	6	consider	consider	VERB
ejpam-2753	275	7	the	the	DET
ejpam-2753	275	8	category	category	NOUN
ejpam-2753	275	9	mml(v	mml(v	PROPN
ejpam-2753	275	10	,	,	PUNCT
ejpam-2753	275	11	w	w	NOUN
ejpam-2753	275	12	)	)	PUNCT
ejpam-2753	275	13	whose	whose	DET
ejpam-2753	275	14	objects	object	NOUN
ejpam-2753	275	15	are	be	AUX
ejpam-2753	275	16	all	all	PRON
ejpam-2753	275	17	multivalued	multivalued	ADJ
ejpam-2753	275	18	middle	middle	ADJ
ejpam-2753	275	19	linear	linear	PROPN
ejpam-2753	275	20	maps	map	NOUN
ejpam-2753	275	21	on	on	ADP
ejpam-2753	275	22	v	v	NOUN
ejpam-2753	275	23	×w	×w	NOUN
ejpam-2753	275	24	.	.	PUNCT
ejpam-2753	276	1	by	by	ADP
ejpam-2753	276	2	definition	definition	NOUN
ejpam-2753	276	3	a	a	DET
ejpam-2753	276	4	morphism	morphism	NOUN
ejpam-2753	276	5	in	in	ADP
ejpam-2753	276	6	mml(v	mml(v	PROPN
ejpam-2753	276	7	,	,	PUNCT
ejpam-2753	276	8	w	w	NOUN
ejpam-2753	276	9	)	)	PUNCT
ejpam-2753	276	10	from	from	ADP
ejpam-2753	276	11	the	the	DET
ejpam-2753	276	12	multivalued	multivalue	VERB
ejpam-2753	276	13	middle	middle	ADJ
ejpam-2753	276	14	linear	linear	PROPN
ejpam-2753	276	15	map	map	NOUN
ejpam-2753	277	1	f	f	X
ejpam-2753	277	2	:	:	PUNCT
ejpam-2753	277	3	v	v	NUM
ejpam-2753	277	4	×w	×w	NOUN
ejpam-2753	277	5	−→	−→	ADJ
ejpam-2753	277	6	p	p	PROPN
ejpam-2753	277	7	∗(z	∗(z	PROPN
ejpam-2753	277	8	)	)	PUNCT
ejpam-2753	277	9	to	to	ADP
ejpam-2753	277	10	the	the	DET
ejpam-2753	277	11	multivalued	multivalue	VERB
ejpam-2753	277	12	middle	middle	ADJ
ejpam-2753	277	13	linear	linear	PROPN
ejpam-2753	277	14	map	map	NOUN
ejpam-2753	277	15	g	g	NOUN
ejpam-2753	277	16	:	:	PUNCT
ejpam-2753	277	17	v	v	NOUN
ejpam-2753	277	18	×w	×w	NOUN
ejpam-2753	277	19	−→	−→	NOUN
ejpam-2753	277	20	p	p	X
ejpam-2753	277	21	∗(z	∗(z	PROPN
ejpam-2753	277	22	′	′	NOUN
ejpam-2753	277	23	)	)	PUNCT
ejpam-2753	277	24	is	be	AUX
ejpam-2753	277	25	a	a	DET
ejpam-2753	277	26	map	map	NOUN
ejpam-2753	277	27	h	h	NOUN
ejpam-2753	277	28	:	:	PUNCT
ejpam-2753	277	29	p	p	PROPN
ejpam-2753	277	30	∗(z	∗(z	PROPN
ejpam-2753	277	31	)	)	PUNCT
ejpam-2753	277	32	−→	−→	NOUN
ejpam-2753	277	33	p	p	PROPN
ejpam-2753	277	34	∗(z	∗(z	PROPN
ejpam-2753	277	35	′	′	NOUN
ejpam-2753	277	36	)	)	PUNCT
ejpam-2753	277	37	such	such	ADJ
ejpam-2753	277	38	that	that	SCONJ
ejpam-2753	277	39	the	the	DET
ejpam-2753	277	40	diagram	diagram	NOUN
ejpam-2753	277	41	p	p	PROPN
ejpam-2753	277	42	∗(z	∗(z	PROPN
ejpam-2753	277	43	′	′	NOUN
ejpam-2753	277	44	)	)	PUNCT
ejpam-2753	277	45	p	p	PROPN
ejpam-2753	277	46	∗(z	∗(z	PROPN
ejpam-2753	277	47	)	)	PUNCT
ejpam-2753	277	48	v	v	NOUN
ejpam-2753	277	49	×w	×w	NOUN
ejpam-2753	277	50	f	f	PROPN
ejpam-2753	277	51	g	g	PROPN
ejpam-2753	277	52	h	h	NOUN
ejpam-2753	277	53	is	be	AUX
ejpam-2753	277	54	commutative	commutative	ADJ
ejpam-2753	277	55	.	.	PUNCT
ejpam-2753	278	1	verify	verify	VERB
ejpam-2753	278	2	that	that	SCONJ
ejpam-2753	278	3	mml(v	mml(v	PROPN
ejpam-2753	278	4	,	,	PUNCT
ejpam-2753	278	5	w	w	NOUN
ejpam-2753	278	6	)	)	PUNCT
ejpam-2753	278	7	is	be	AUX
ejpam-2753	278	8	a	a	DET
ejpam-2753	278	9	category	category	NOUN
ejpam-2753	278	10	,	,	PUNCT
ejpam-2753	278	11	that	that	SCONJ
ejpam-2753	278	12	1h	1h	NUM
ejpam-2753	278	13	is	be	AUX
ejpam-2753	278	14	the	the	DET
ejpam-2753	278	15	identity	identity	NOUN
ejpam-2753	278	16	morphism	morphism	NOUN
ejpam-2753	278	17	from	from	ADP
ejpam-2753	278	18	f	f	PROPN
ejpam-2753	278	19	to	to	ADP
ejpam-2753	278	20	f	f	PROPN
ejpam-2753	278	21	.	.	PUNCT
ejpam-2753	279	1	in	in	ADP
ejpam-2753	279	2	theorem	theorem	NOUN
ejpam-2753	279	3	4	4	NUM
ejpam-2753	279	4	we	we	PRON
ejpam-2753	279	5	shall	shall	AUX
ejpam-2753	279	6	construct	construct	VERB
ejpam-2753	279	7	a	a	DET
ejpam-2753	279	8	universal	universal	ADJ
ejpam-2753	279	9	object	object	NOUN
ejpam-2753	279	10	in	in	ADP
ejpam-2753	279	11	the	the	DET
ejpam-2753	279	12	category	category	NOUN
ejpam-2753	279	13	mml(v	mml(v	PROPN
ejpam-2753	279	14	,	,	PUNCT
ejpam-2753	279	15	w	w	NOUN
ejpam-2753	279	16	)	)	PUNCT
ejpam-2753	279	17	.	.	PUNCT
ejpam-2753	280	1	first	first	ADV
ejpam-2753	280	2	,	,	PUNCT
ejpam-2753	280	3	however	however	ADV
ejpam-2753	280	4	,	,	PUNCT
ejpam-2753	280	5	we	we	PRON
ejpam-2753	280	6	need	need	VERB
ejpam-2753	280	7	definition	definition	NOUN
ejpam-2753	280	8	19	19	NUM
ejpam-2753	280	9	.	.	PUNCT
ejpam-2753	281	1	let	let	VERB
ejpam-2753	281	2	v	v	NOUN
ejpam-2753	281	3	and	and	CCONJ
ejpam-2753	281	4	w	w	NOUN
ejpam-2753	281	5	be	be	AUX
ejpam-2753	281	6	two	two	NUM
ejpam-2753	281	7	hyperspaces	hyperspace	NOUN
ejpam-2753	281	8	over	over	ADP
ejpam-2753	281	9	a	a	DET
ejpam-2753	281	10	field	field	NOUN
ejpam-2753	282	1	k.	k.	NOUN
ejpam-2753	282	2	let	let	VERB
ejpam-2753	282	3	f	f	PRON
ejpam-2753	282	4	be	be	AUX
ejpam-2753	282	5	the	the	DET
ejpam-2753	282	6	free	free	ADJ
ejpam-2753	282	7	abelian	abelian	ADJ
ejpam-2753	282	8	group	group	NOUN
ejpam-2753	282	9	on	on	ADP
ejpam-2753	282	10	the	the	DET
ejpam-2753	282	11	set	set	NOUN
ejpam-2753	282	12	v	v	NOUN
ejpam-2753	282	13	×w	×w	NOUN
ejpam-2753	282	14	.	.	PUNCT
ejpam-2753	283	1	let	let	VERB
ejpam-2753	283	2	h	h	PRON
ejpam-2753	283	3	be	be	AUX
ejpam-2753	283	4	the	the	DET
ejpam-2753	283	5	subgroup	subgroup	NOUN
ejpam-2753	283	6	of	of	ADP
ejpam-2753	283	7	f	f	PROPN
ejpam-2753	283	8	generated	generate	VERB
ejpam-2753	283	9	by	by	ADP
ejpam-2753	283	10	all	all	DET
ejpam-2753	283	11	elements	element	NOUN
ejpam-2753	283	12	of	of	ADP
ejpam-2753	283	13	the	the	DET
ejpam-2753	283	14	following	follow	VERB
ejpam-2753	283	15	forms	form	NOUN
ejpam-2753	283	16	(	(	PUNCT
ejpam-2753	283	17	for	for	ADP
ejpam-2753	283	18	all	all	DET
ejpam-2753	283	19	v	v	NOUN
ejpam-2753	283	20	,	,	PUNCT
ejpam-2753	283	21	v′	v′	NOUN
ejpam-2753	283	22	∈	∈	PROPN
ejpam-2753	283	23	v	v	PROPN
ejpam-2753	283	24	,	,	PUNCT
ejpam-2753	283	25	w	w	PROPN
ejpam-2753	283	26	,	,	PUNCT
ejpam-2753	283	27	w′	w′	NOUN
ejpam-2753	283	28	∈w	∈w	NOUN
ejpam-2753	283	29	,	,	PUNCT
ejpam-2753	283	30	and	and	CCONJ
ejpam-2753	283	31	a	a	DET
ejpam-2753	283	32	∈	∈	PROPN
ejpam-2753	283	33	k	k	NOUN
ejpam-2753	283	34	):	):	PUNCT
ejpam-2753	283	35	(	(	PUNCT
ejpam-2753	283	36	i	i	NOUN
ejpam-2753	283	37	)	)	PUNCT
ejpam-2753	283	38	(	(	PUNCT
ejpam-2753	283	39	v	v	X
ejpam-2753	283	40	+	+	NUM
ejpam-2753	283	41	v′	v′	NOUN
ejpam-2753	283	42	,	,	PUNCT
ejpam-2753	283	43	w)−	w)−	PROPN
ejpam-2753	283	44	(	(	PUNCT
ejpam-2753	283	45	v	v	NOUN
ejpam-2753	283	46	,	,	PUNCT
ejpam-2753	283	47	w)−	w)−	PROPN
ejpam-2753	283	48	(	(	PUNCT
ejpam-2753	283	49	v′	v′	PROPN
ejpam-2753	283	50	,	,	PUNCT
ejpam-2753	283	51	w	w	NOUN
ejpam-2753	283	52	)	)	PUNCT
ejpam-2753	283	53	;	;	PUNCT
ejpam-2753	283	54	(	(	PUNCT
ejpam-2753	283	55	ii	ii	NOUN
ejpam-2753	283	56	)	)	PUNCT
ejpam-2753	283	57	(	(	PUNCT
ejpam-2753	283	58	v	v	NOUN
ejpam-2753	283	59	,	,	PUNCT
ejpam-2753	283	60	w	w	PROPN
ejpam-2753	284	1	+	+	PUNCT
ejpam-2753	284	2	w′)−	w′)−	PROPN
ejpam-2753	284	3	(	(	PUNCT
ejpam-2753	284	4	v	v	NOUN
ejpam-2753	284	5	,	,	PUNCT
ejpam-2753	284	6	w)−	w)−	PROPN
ejpam-2753	284	7	(	(	PUNCT
ejpam-2753	284	8	v	v	NOUN
ejpam-2753	284	9	,	,	PUNCT
ejpam-2753	284	10	w′	w′	PROPN
ejpam-2753	284	11	)	)	PUNCT
ejpam-2753	284	12	;	;	PUNCT
ejpam-2753	284	13	(	(	PUNCT
ejpam-2753	284	14	iii	iii	X
ejpam-2753	284	15	)	)	PUNCT
ejpam-2753	284	16	(	(	PUNCT
ejpam-2753	284	17	a	a	DET
ejpam-2753	284	18	◦	◦	NOUN
ejpam-2753	284	19	v	v	NOUN
ejpam-2753	284	20	,	,	PUNCT
ejpam-2753	284	21	w)−	w)−	PROPN
ejpam-2753	284	22	(	(	PUNCT
ejpam-2753	284	23	v	v	NOUN
ejpam-2753	284	24	,	,	PUNCT
ejpam-2753	284	25	a	a	DET
ejpam-2753	284	26	◦	◦	NOUN
ejpam-2753	284	27	w	w	PROPN
ejpam-2753	284	28	)	)	PUNCT
ejpam-2753	284	29	,	,	PUNCT
ejpam-2753	284	30	where	where	SCONJ
ejpam-2753	284	31	(	(	PUNCT
ejpam-2753	284	32	a	a	DET
ejpam-2753	284	33	◦	◦	NOUN
ejpam-2753	284	34	v	v	ADP
ejpam-2753	284	35	,	,	PUNCT
ejpam-2753	284	36	w	w	NOUN
ejpam-2753	284	37	)	)	PUNCT
ejpam-2753	284	38	=	=	SYM
ejpam-2753	284	39	⋃	⋃	NOUN
ejpam-2753	284	40	t∈a	t∈a	NOUN
ejpam-2753	284	41	◦	◦	NOUN
ejpam-2753	284	42	v(t	v(t	NOUN
ejpam-2753	284	43	,	,	PUNCT
ejpam-2753	284	44	w	w	NOUN
ejpam-2753	284	45	)	)	PUNCT
ejpam-2753	284	46	.	.	PUNCT
ejpam-2753	285	1	the	the	DET
ejpam-2753	285	2	quotient	quotient	NOUN
ejpam-2753	285	3	group	group	NOUN
ejpam-2753	285	4	f	f	PROPN
ejpam-2753	285	5	/	/	SYM
ejpam-2753	285	6	h	h	PROPN
ejpam-2753	285	7	is	be	AUX
ejpam-2753	285	8	called	call	VERB
ejpam-2753	285	9	the	the	DET
ejpam-2753	285	10	tensor	tensor	NOUN
ejpam-2753	285	11	product	product	NOUN
ejpam-2753	285	12	of	of	ADP
ejpam-2753	285	13	v	v	NOUN
ejpam-2753	285	14	and	and	CCONJ
ejpam-2753	285	15	w	w	NOUN
ejpam-2753	285	16	;	;	PUNCT
ejpam-2753	285	17	it	it	PRON
ejpam-2753	285	18	is	be	AUX
ejpam-2753	285	19	denoted	denote	VERB
ejpam-2753	285	20	v	v	ADP
ejpam-2753	285	21	⊗k	⊗k	ADJ
ejpam-2753	285	22	w	w	NOUN
ejpam-2753	285	23	.	.	PUNCT
ejpam-2753	286	1	the	the	DET
ejpam-2753	286	2	coset	coset	NOUN
ejpam-2753	286	3	(	(	PUNCT
ejpam-2753	286	4	v	v	NOUN
ejpam-2753	286	5	,	,	PUNCT
ejpam-2753	286	6	w	w	NOUN
ejpam-2753	286	7	)	)	PUNCT
ejpam-2753	286	8	+	+	CCONJ
ejpam-2753	286	9	k	k	X
ejpam-2753	286	10	of	of	ADP
ejpam-2753	286	11	the	the	DET
ejpam-2753	286	12	element	element	NOUN
ejpam-2753	286	13	(	(	PUNCT
ejpam-2753	286	14	v	v	NOUN
ejpam-2753	286	15	,	,	PUNCT
ejpam-2753	286	16	w	w	NOUN
ejpam-2753	286	17	)	)	PUNCT
ejpam-2753	286	18	in	in	ADP
ejpam-2753	286	19	f	f	PROPN
ejpam-2753	286	20	is	be	AUX
ejpam-2753	286	21	denoted	denote	VERB
ejpam-2753	286	22	v	v	ADP
ejpam-2753	286	23	⊗	⊗	PROPN
ejpam-2753	286	24	w	w	PROPN
ejpam-2753	286	25	;	;	PUNCT
ejpam-2753	286	26	the	the	DET
ejpam-2753	286	27	coset	coset	NOUN
ejpam-2753	286	28	of	of	ADP
ejpam-2753	286	29	(	(	PUNCT
ejpam-2753	286	30	0	0	NUM
ejpam-2753	286	31	,	,	PUNCT
ejpam-2753	286	32	0	0	NUM
ejpam-2753	286	33	)	)	PUNCT
ejpam-2753	286	34	is	be	AUX
ejpam-2753	286	35	denoted	denote	VERB
ejpam-2753	286	36	0	0	NUM
ejpam-2753	286	37	.	.	PUNCT
ejpam-2753	286	38	r.	r.	PROPN
ejpam-2753	286	39	ameri	ameri	PROPN
ejpam-2753	286	40	,	,	PUNCT
ejpam-2753	286	41	k.	k.	PROPN
ejpam-2753	286	42	ghadimi	ghadimi	PROPN
ejpam-2753	286	43	,	,	PUNCT
ejpam-2753	286	44	r.	r.	PROPN
ejpam-2753	286	45	a.	a.	PROPN
ejpam-2753	286	46	borzooei	borzooei	PROPN
ejpam-2753	286	47	/	/	SYM
ejpam-2753	286	48	eur	eur	PROPN
ejpam-2753	286	49	.	.	PUNCT
ejpam-2753	287	1	j.	j.	PROPN
ejpam-2753	287	2	pure	pure	PROPN
ejpam-2753	287	3	appl	appl	PROPN
ejpam-2753	287	4	.	.	PROPN
ejpam-2753	287	5	math	math	PROPN
ejpam-2753	287	6	,	,	PUNCT
ejpam-2753	287	7	10	10	NUM
ejpam-2753	287	8	(	(	PUNCT
ejpam-2753	287	9	4	4	NUM
ejpam-2753	287	10	)	)	PUNCT
ejpam-2753	287	11	(	(	PUNCT
ejpam-2753	287	12	2017	2017	NUM
ejpam-2753	287	13	)	)	PUNCT
ejpam-2753	287	14	,	,	PUNCT
ejpam-2753	287	15	702	702	NUM
ejpam-2753	287	16	-	-	SYM
ejpam-2753	287	17	716	716	NUM
ejpam-2753	287	18	713	713	NUM
ejpam-2753	287	19	since	since	SCONJ
ejpam-2753	287	20	f	f	PROPN
ejpam-2753	287	21	is	be	AUX
ejpam-2753	287	22	generated	generate	VERB
ejpam-2753	287	23	by	by	ADP
ejpam-2753	287	24	the	the	DET
ejpam-2753	287	25	set	set	NOUN
ejpam-2753	287	26	v	v	NOUN
ejpam-2753	287	27	×w	×w	NOUN
ejpam-2753	287	28	,	,	PUNCT
ejpam-2753	287	29	the	the	DET
ejpam-2753	287	30	quotient	quotient	NOUN
ejpam-2753	287	31	group	group	NOUN
ejpam-2753	287	32	f	f	PROPN
ejpam-2753	287	33	/	/	SYM
ejpam-2753	287	34	h	h	NOUN
ejpam-2753	287	35	=	=	NOUN
ejpam-2753	287	36	v	v	NOUN
ejpam-2753	287	37	⊗kw	⊗kw	ADJ
ejpam-2753	287	38	is	be	AUX
ejpam-2753	287	39	generated	generate	VERB
ejpam-2753	287	40	by	by	ADP
ejpam-2753	287	41	all	all	DET
ejpam-2753	287	42	elements	element	NOUN
ejpam-2753	287	43	(	(	PUNCT
ejpam-2753	287	44	cosets	coset	NOUN
ejpam-2753	287	45	)	)	PUNCT
ejpam-2753	287	46	of	of	ADP
ejpam-2753	287	47	the	the	DET
ejpam-2753	287	48	form	form	NOUN
ejpam-2753	287	49	v	v	ADP
ejpam-2753	287	50	⊗	⊗	PROPN
ejpam-2753	287	51	w	w	PROPN
ejpam-2753	287	52	(	(	PUNCT
ejpam-2753	287	53	v	v	NOUN
ejpam-2753	287	54	∈	∈	PROPN
ejpam-2753	287	55	v	v	NOUN
ejpam-2753	287	56	,	,	PUNCT
ejpam-2753	287	57	w	w	PROPN
ejpam-2753	287	58	∈	∈	PROPN
ejpam-2753	287	59	w	w	PROPN
ejpam-2753	287	60	)	)	PUNCT
ejpam-2753	287	61	.	.	PUNCT
ejpam-2753	288	1	but	but	CCONJ
ejpam-2753	288	2	it	it	PRON
ejpam-2753	288	3	is	be	AUX
ejpam-2753	288	4	not	not	PART
ejpam-2753	288	5	true	true	ADJ
ejpam-2753	288	6	that	that	SCONJ
ejpam-2753	288	7	every	every	DET
ejpam-2753	288	8	element	element	NOUN
ejpam-2753	288	9	of	of	ADP
ejpam-2753	288	10	v⊗kw	v⊗kw	PROPN
ejpam-2753	288	11	is	be	AUX
ejpam-2753	288	12	of	of	ADP
ejpam-2753	288	13	the	the	DET
ejpam-2753	288	14	form	form	NOUN
ejpam-2753	288	15	v×w	v×w	PROPN
ejpam-2753	288	16	.	.	PUNCT
ejpam-2753	289	1	for	for	ADP
ejpam-2753	289	2	the	the	DET
ejpam-2753	289	3	typical	typical	ADJ
ejpam-2753	289	4	element	element	NOUN
ejpam-2753	289	5	of	of	ADP
ejpam-2753	289	6	f	f	PROPN
ejpam-2753	289	7	is	be	AUX
ejpam-2753	289	8	a	a	DET
ejpam-2753	289	9	sum	sum	NOUN
ejpam-2753	289	10	∑r	∑r	PROPN
ejpam-2753	289	11	i=1	i=1	PROPN
ejpam-2753	289	12	ni(vi	ni(vi	PROPN
ejpam-2753	289	13	,	,	PUNCT
ejpam-2753	289	14	wi	wi	PROPN
ejpam-2753	289	15	)	)	PUNCT
ejpam-2753	289	16	(	(	PUNCT
ejpam-2753	289	17	ni	ni	PROPN
ejpam-2753	289	18	∈	∈	PROPN
ejpam-2753	289	19	z	z	PROPN
ejpam-2753	289	20	,	,	PUNCT
ejpam-2753	289	21	vi	vi	PROPN
ejpam-2753	289	22	∈	∈	PROPN
ejpam-2753	289	23	v	v	NOUN
ejpam-2753	289	24	,	,	PUNCT
ejpam-2753	289	25	and	and	CCONJ
ejpam-2753	289	26	wi	wi	PROPN
ejpam-2753	289	27	∈	∈	PROPN
ejpam-2753	289	28	w	w	PROPN
ejpam-2753	289	29	)	)	PUNCT
ejpam-2753	289	30	and	and	CCONJ
ejpam-2753	289	31	hence	hence	ADV
ejpam-2753	289	32	its	its	PRON
ejpam-2753	289	33	coset	coset	NOUN
ejpam-2753	289	34	in	in	ADP
ejpam-2753	289	35	v	v	NUM
ejpam-2753	289	36	⊗k	⊗k	NOUN
ejpam-2753	289	37	w	w	NOUN
ejpam-2753	289	38	=	=	SYM
ejpam-2753	289	39	f	f	X
ejpam-2753	289	40	/	/	SYM
ejpam-2753	289	41	h	h	PROPN
ejpam-2753	289	42	is	be	AUX
ejpam-2753	289	43	of	of	ADP
ejpam-2753	289	44	the	the	DET
ejpam-2753	289	45	form∑r	form∑r	ADJ
ejpam-2753	289	46	i=1	i=1	PROPN
ejpam-2753	290	1	ni(vi	ni(vi	ADP
ejpam-2753	290	2	⊗	⊗	PROPN
ejpam-2753	290	3	wi	wi	PROPN
ejpam-2753	290	4	)	)	PUNCT
ejpam-2753	290	5	.	.	PUNCT
ejpam-2753	291	1	furthermore	furthermore	ADV
ejpam-2753	291	2	,	,	PUNCT
ejpam-2753	291	3	since	since	SCONJ
ejpam-2753	291	4	it	it	PRON
ejpam-2753	291	5	is	be	AUX
ejpam-2753	291	6	possible	possible	ADJ
ejpam-2753	291	7	to	to	PART
ejpam-2753	291	8	choose	choose	VERB
ejpam-2753	291	9	different	different	ADJ
ejpam-2753	291	10	representatives	representative	NOUN
ejpam-2753	291	11	for	for	ADP
ejpam-2753	291	12	a	a	DET
ejpam-2753	291	13	coset	coset	NOUN
ejpam-2753	291	14	,	,	PUNCT
ejpam-2753	291	15	one	one	PRON
ejpam-2753	291	16	may	may	AUX
ejpam-2753	291	17	have	have	VERB
ejpam-2753	291	18	v	v	ADP
ejpam-2753	291	19	⊗	⊗	PROPN
ejpam-2753	291	20	w	w	PROPN
ejpam-2753	291	21	=	=	SYM
ejpam-2753	291	22	v′	v′	PROPN
ejpam-2753	291	23	⊗	⊗	NUM
ejpam-2753	291	24	w′	w′	NOUN
ejpam-2753	291	25	in	in	ADP
ejpam-2753	291	26	v	v	NUM
ejpam-2753	291	27	⊗k	⊗k	ADJ
ejpam-2753	291	28	w	w	NOUN
ejpam-2753	291	29	,	,	PUNCT
ejpam-2753	291	30	but	but	CCONJ
ejpam-2753	291	31	v	v	X
ejpam-2753	291	32	6=	6=	NUM
ejpam-2753	291	33	v′	v′	NOUN
ejpam-2753	291	34	and	and	CCONJ
ejpam-2753	291	35	w	w	PROPN
ejpam-2753	291	36	6=	6=	PROPN
ejpam-2753	291	37	w′.	w′.	X
ejpam-2753	292	1	it	it	PRON
ejpam-2753	292	2	is	be	AUX
ejpam-2753	292	3	also	also	ADV
ejpam-2753	292	4	possible	possible	ADJ
ejpam-2753	292	5	to	to	PART
ejpam-2753	292	6	have	have	VERB
ejpam-2753	292	7	v	v	NUM
ejpam-2753	292	8	⊗k	⊗k	ADJ
ejpam-2753	292	9	w	w	NOUN
ejpam-2753	292	10	=	=	NOUN
ejpam-2753	292	11	0	0	PUNCT
ejpam-2753	292	12	even	even	ADV
ejpam-2753	292	13	though	though	SCONJ
ejpam-2753	292	14	v	v	NUM
ejpam-2753	292	15	6=	6=	NUM
ejpam-2753	292	16	0	0	NUM
ejpam-2753	292	17	and	and	CCONJ
ejpam-2753	292	18	w	w	ADP
ejpam-2753	292	19	6=	6=	PROPN
ejpam-2753	292	20	0	0	NUM
ejpam-2753	292	21	.	.	PUNCT
ejpam-2753	293	1	definition	definition	NOUN
ejpam-2753	293	2	19	19	NUM
ejpam-2753	293	3	implies	imply	VERB
ejpam-2753	293	4	that	that	SCONJ
ejpam-2753	293	5	the	the	DET
ejpam-2753	293	6	generators	generator	NOUN
ejpam-2753	293	7	v⊗w	v⊗w	X
ejpam-2753	293	8	of	of	ADP
ejpam-2753	293	9	v	v	NOUN
ejpam-2753	293	10	⊗kw	⊗kw	NOUN
ejpam-2753	293	11	satisfy	satisfy	VERB
ejpam-2753	293	12	the	the	DET
ejpam-2753	293	13	following	follow	VERB
ejpam-2753	293	14	relations	relation	NOUN
ejpam-2753	293	15	(	(	PUNCT
ejpam-2753	293	16	for	for	ADP
ejpam-2753	293	17	all	all	DET
ejpam-2753	293	18	v	v	NOUN
ejpam-2753	293	19	,	,	PUNCT
ejpam-2753	293	20	vi	vi	PROPN
ejpam-2753	293	21	∈	∈	PROPN
ejpam-2753	293	22	v	v	NOUN
ejpam-2753	293	23	,	,	PUNCT
ejpam-2753	293	24	w	w	PROPN
ejpam-2753	293	25	,	,	PUNCT
ejpam-2753	293	26	wi	wi	PROPN
ejpam-2753	293	27	∈w	∈w	PROPN
ejpam-2753	293	28	,	,	PUNCT
ejpam-2753	293	29	a	a	DET
ejpam-2753	293	30	∈	∈	PROPN
ejpam-2753	293	31	k	k	NOUN
ejpam-2753	293	32	,	,	PUNCT
ejpam-2753	293	33	and	and	CCONJ
ejpam-2753	293	34	i	i	NOUN
ejpam-2753	293	35	=	=	NOUN
ejpam-2753	293	36	1	1	NUM
ejpam-2753	293	37	,	,	PUNCT
ejpam-2753	293	38	2	2	NUM
ejpam-2753	293	39	):	):	PUNCT
ejpam-2753	293	40	(	(	PUNCT
ejpam-2753	293	41	v1	v1	NOUN
ejpam-2753	293	42	+	+	CCONJ
ejpam-2753	293	43	v2)⊗	v2)⊗	PROPN
ejpam-2753	293	44	w	w	NOUN
ejpam-2753	293	45	=	=	SYM
ejpam-2753	293	46	v1	v1	PROPN
ejpam-2753	294	1	⊗	⊗	PROPN
ejpam-2753	294	2	w	w	PROPN
ejpam-2753	294	3	+	+	NUM
ejpam-2753	294	4	v2	v2	PROPN
ejpam-2753	294	5	⊗	⊗	PROPN
ejpam-2753	294	6	w	w	NOUN
ejpam-2753	294	7	;	;	PUNCT
ejpam-2753	294	8	(	(	PUNCT
ejpam-2753	294	9	1	1	X
ejpam-2753	294	10	)	)	PUNCT
ejpam-2753	294	11	v	v	NOUN
ejpam-2753	294	12	⊗	⊗	PROPN
ejpam-2753	294	13	(	(	PUNCT
ejpam-2753	294	14	w1	w1	NOUN
ejpam-2753	294	15	+	+	SYM
ejpam-2753	294	16	w2	w2	NOUN
ejpam-2753	294	17	)	)	PUNCT
ejpam-2753	294	18	=	=	PROPN
ejpam-2753	295	1	v	v	ADP
ejpam-2753	295	2	⊗	⊗	PROPN
ejpam-2753	295	3	w1	w1	NOUN
ejpam-2753	295	4	+	+	CCONJ
ejpam-2753	295	5	v	v	PROPN
ejpam-2753	295	6	⊗	⊗	PROPN
ejpam-2753	295	7	w2	w2	NOUN
ejpam-2753	295	8	;	;	PUNCT
ejpam-2753	295	9	(	(	PUNCT
ejpam-2753	295	10	2	2	X
ejpam-2753	295	11	)	)	PUNCT
ejpam-2753	295	12	(	(	PUNCT
ejpam-2753	295	13	a	a	DET
ejpam-2753	295	14	◦	◦	NOUN
ejpam-2753	295	15	v)⊗	v)⊗	NOUN
ejpam-2753	295	16	w	w	PROPN
ejpam-2753	295	17	=	=	SYM
ejpam-2753	295	18	v	v	ADP
ejpam-2753	295	19	⊗	⊗	PROPN
ejpam-2753	295	20	(	(	PUNCT
ejpam-2753	295	21	a	a	DET
ejpam-2753	295	22	◦	◦	NOUN
ejpam-2753	295	23	w	w	NOUN
ejpam-2753	295	24	)	)	PUNCT
ejpam-2753	295	25	.	.	PUNCT
ejpam-2753	296	1	(	(	PUNCT
ejpam-2753	296	2	3	3	X
ejpam-2753	296	3	)	)	PUNCT
ejpam-2753	296	4	the	the	DET
ejpam-2753	296	5	proof	proof	NOUN
ejpam-2753	296	6	of	of	ADP
ejpam-2753	296	7	these	these	DET
ejpam-2753	296	8	facts	fact	NOUN
ejpam-2753	296	9	is	be	AUX
ejpam-2753	296	10	straightforward	straightforward	ADJ
ejpam-2753	296	11	;	;	PUNCT
ejpam-2753	296	12	for	for	ADP
ejpam-2753	296	13	example	example	NOUN
ejpam-2753	296	14	,	,	PUNCT
ejpam-2753	296	15	since	since	SCONJ
ejpam-2753	296	16	(	(	PUNCT
ejpam-2753	296	17	v1	v1	VERB
ejpam-2753	296	18	+	+	CCONJ
ejpam-2753	296	19	v2	v2	PROPN
ejpam-2753	296	20	,	,	PUNCT
ejpam-2753	296	21	w	w	NOUN
ejpam-2753	296	22	)	)	PUNCT
ejpam-2753	296	23	−	−	PROPN
ejpam-2753	296	24	(	(	PUNCT
ejpam-2753	296	25	v1	v1	NOUN
ejpam-2753	296	26	,	,	PUNCT
ejpam-2753	296	27	w	w	NOUN
ejpam-2753	296	28	)	)	PUNCT
ejpam-2753	296	29	−	−	PROPN
ejpam-2753	296	30	(	(	PUNCT
ejpam-2753	296	31	v2	v2	PROPN
ejpam-2753	296	32	,	,	PUNCT
ejpam-2753	296	33	w	w	NOUN
ejpam-2753	296	34	)	)	PUNCT
ejpam-2753	296	35	∈	∈	PROPN
ejpam-2753	296	36	h	h	NOUN
ejpam-2753	296	37	,	,	PUNCT
ejpam-2753	296	38	the	the	DET
ejpam-2753	296	39	zero	zero	NUM
ejpam-2753	296	40	coset	coset	NOUN
ejpam-2753	296	41	,	,	PUNCT
ejpam-2753	296	42	we	we	PRON
ejpam-2753	296	43	have	have	VERB
ejpam-2753	296	44	[	[	X
ejpam-2753	296	45	(	(	PUNCT
ejpam-2753	296	46	v1	v1	NOUN
ejpam-2753	296	47	+	+	CCONJ
ejpam-2753	296	48	v2	v2	PROPN
ejpam-2753	296	49	,	,	PUNCT
ejpam-2753	296	50	w	w	NOUN
ejpam-2753	296	51	)	)	PUNCT
ejpam-2753	297	1	+	+	NOUN
ejpam-2753	297	2	h]−	h]−	X
ejpam-2753	297	3	[	[	X
ejpam-2753	297	4	(	(	PUNCT
ejpam-2753	297	5	v1	v1	NOUN
ejpam-2753	297	6	,	,	PUNCT
ejpam-2753	297	7	w	w	NOUN
ejpam-2753	297	8	)	)	PUNCT
ejpam-2753	298	1	+	+	NOUN
ejpam-2753	298	2	h]−	h]−	X
ejpam-2753	299	1	[	[	X
ejpam-2753	299	2	(	(	PUNCT
ejpam-2753	299	3	v2	v2	PROPN
ejpam-2753	299	4	,	,	PUNCT
ejpam-2753	299	5	w	w	NOUN
ejpam-2753	299	6	)	)	PUNCT
ejpam-2753	299	7	+	+	NOUN
ejpam-2753	299	8	h	h	NOUN
ejpam-2753	299	9	]	]	X
ejpam-2753	299	10	=	=	SYM
ejpam-2753	299	11	h	h	NOUN
ejpam-2753	299	12	;	;	PUNCT
ejpam-2753	299	13	or	or	CCONJ
ejpam-2753	299	14	in	in	ADP
ejpam-2753	299	15	the	the	DET
ejpam-2753	299	16	notation	notation	NOUN
ejpam-2753	299	17	(	(	PUNCT
ejpam-2753	299	18	v	v	NOUN
ejpam-2753	299	19	,	,	PUNCT
ejpam-2753	299	20	w	w	NOUN
ejpam-2753	299	21	)	)	PUNCT
ejpam-2753	300	1	+	+	NOUN
ejpam-2753	300	2	h	h	NOUN
ejpam-2753	300	3	=	=	X
ejpam-2753	300	4	v	v	ADP
ejpam-2753	300	5	⊗	⊗	PROPN
ejpam-2753	300	6	w	w	PROPN
ejpam-2753	300	7	,	,	PUNCT
ejpam-2753	300	8	(	(	PUNCT
ejpam-2753	300	9	v1	v1	NOUN
ejpam-2753	300	10	+	+	CCONJ
ejpam-2753	300	11	v2)⊗	v2)⊗	PROPN
ejpam-2753	300	12	w	w	PROPN
ejpam-2753	300	13	−	−	PROPN
ejpam-2753	300	14	v1	v1	PROPN
ejpam-2753	300	15	⊗	⊗	PROPN
ejpam-2753	300	16	w	w	PROPN
ejpam-2753	300	17	−	−	PROPN
ejpam-2753	300	18	v2	v2	PROPN
ejpam-2753	300	19	⊗	⊗	PROPN
ejpam-2753	300	20	w	w	PROPN
ejpam-2753	301	1	=	=	NOUN
ejpam-2753	301	2	0	0	NUM
ejpam-2753	301	3	.	.	PUNCT
ejpam-2753	302	1	also	also	ADV
ejpam-2753	302	2	,	,	PUNCT
ejpam-2753	302	3	since	since	SCONJ
ejpam-2753	302	4	(	(	PUNCT
ejpam-2753	302	5	a	a	DET
ejpam-2753	302	6	◦	◦	NOUN
ejpam-2753	302	7	v	v	NOUN
ejpam-2753	302	8	,	,	PUNCT
ejpam-2753	302	9	w)−	w)−	PROPN
ejpam-2753	302	10	(	(	PUNCT
ejpam-2753	302	11	v	v	NOUN
ejpam-2753	302	12	,	,	PUNCT
ejpam-2753	302	13	a	a	DET
ejpam-2753	302	14	◦	◦	NOUN
ejpam-2753	302	15	w	w	NOUN
ejpam-2753	302	16	)	)	PUNCT
ejpam-2753	302	17	=	=	SYM
ejpam-2753	302	18	⋃	⋃	NOUN
ejpam-2753	302	19	t∈a	t∈a	NOUN
ejpam-2753	302	20	◦	◦	NOUN
ejpam-2753	302	21	v(t	v(t	NOUN
ejpam-2753	302	22	,	,	PUNCT
ejpam-2753	302	23	w)−	w)−	PROPN
ejpam-2753	302	24	⋃	⋃	PROPN
ejpam-2753	302	25	s∈a	s∈a	ADJ
ejpam-2753	302	26	◦	◦	NOUN
ejpam-2753	302	27	w(v	w(v	PROPN
ejpam-2753	302	28	,	,	PUNCT
ejpam-2753	302	29	s	s	X
ejpam-2753	302	30	)	)	PUNCT
ejpam-2753	302	31	∈	∈	PROPN
ejpam-2753	302	32	h	h	NOUN
ejpam-2753	302	33	,	,	PUNCT
ejpam-2753	302	34	the	the	DET
ejpam-2753	302	35	zero	zero	NUM
ejpam-2753	302	36	coset	coset	NOUN
ejpam-2753	302	37	,	,	PUNCT
ejpam-2753	302	38	we	we	PRON
ejpam-2753	302	39	have	have	VERB
ejpam-2753	302	40	[	[	X
ejpam-2753	302	41	(	(	PUNCT
ejpam-2753	302	42	a	a	DET
ejpam-2753	302	43	◦	◦	NOUN
ejpam-2753	302	44	v	v	ADP
ejpam-2753	302	45	,	,	PUNCT
ejpam-2753	302	46	w	w	NOUN
ejpam-2753	302	47	)	)	PUNCT
ejpam-2753	303	1	+	+	NOUN
ejpam-2753	303	2	h]−	h]−	X
ejpam-2753	303	3	[	[	X
ejpam-2753	303	4	(	(	PUNCT
ejpam-2753	303	5	v	v	NOUN
ejpam-2753	303	6	,	,	PUNCT
ejpam-2753	303	7	a	a	DET
ejpam-2753	303	8	◦	◦	NOUN
ejpam-2753	303	9	w	w	NOUN
ejpam-2753	303	10	)	)	PUNCT
ejpam-2753	304	1	+	+	NOUN
ejpam-2753	304	2	h	h	NOUN
ejpam-2753	304	3	]	]	X
ejpam-2753	304	4	=	=	X
ejpam-2753	304	5	[	[	PUNCT
ejpam-2753	304	6	⋃	⋃	NOUN
ejpam-2753	304	7	t∈a	t∈a	NOUN
ejpam-2753	304	8	◦	◦	NOUN
ejpam-2753	304	9	v	v	NOUN
ejpam-2753	304	10	(	(	PUNCT
ejpam-2753	304	11	t	t	PROPN
ejpam-2753	304	12	,	,	PUNCT
ejpam-2753	304	13	w	w	NOUN
ejpam-2753	304	14	)	)	PUNCT
ejpam-2753	305	1	+	+	NOUN
ejpam-2753	305	2	h]−	h]−	X
ejpam-2753	305	3	[	[	PUNCT
ejpam-2753	305	4	⋃	⋃	NOUN
ejpam-2753	305	5	s∈a	s∈a	PROPN
ejpam-2753	305	6	◦	◦	PROPN
ejpam-2753	305	7	w	w	PROPN
ejpam-2753	305	8	(	(	PUNCT
ejpam-2753	305	9	v	v	NOUN
ejpam-2753	305	10	,	,	PUNCT
ejpam-2753	305	11	s	s	PART
ejpam-2753	305	12	)	)	PUNCT
ejpam-2753	306	1	+	+	NOUN
ejpam-2753	306	2	h	h	NOUN
ejpam-2753	306	3	]	]	X
ejpam-2753	306	4	=	=	SYM
ejpam-2753	306	5	h	h	NOUN
ejpam-2753	306	6	;	;	PUNCT
ejpam-2753	306	7	or	or	CCONJ
ejpam-2753	306	8	in	in	ADP
ejpam-2753	306	9	the	the	DET
ejpam-2753	306	10	notation	notation	NOUN
ejpam-2753	306	11	⋃	⋃	PUNCT
ejpam-2753	306	12	t∈a	t∈a	NOUN
ejpam-2753	306	13	◦	◦	NOUN
ejpam-2753	306	14	v(t	v(t	NOUN
ejpam-2753	306	15	,	,	PUNCT
ejpam-2753	306	16	w	w	NOUN
ejpam-2753	306	17	)	)	PUNCT
ejpam-2753	307	1	+	+	NOUN
ejpam-2753	307	2	h	h	NOUN
ejpam-2753	308	1	=	=	SYM
ejpam-2753	308	2	(	(	PUNCT
ejpam-2753	308	3	a	a	DET
ejpam-2753	308	4	◦	◦	NOUN
ejpam-2753	308	5	v)⊗	v)⊗	NOUN
ejpam-2753	308	6	w	w	ADP
ejpam-2753	308	7	,	,	PUNCT
ejpam-2753	308	8	(	(	PUNCT
ejpam-2753	308	9	a	a	DET
ejpam-2753	308	10	◦	◦	NOUN
ejpam-2753	308	11	v)⊗	v)⊗	NOUN
ejpam-2753	308	12	w	w	ADP
ejpam-2753	308	13	−	−	PROPN
ejpam-2753	308	14	v	v	ADP
ejpam-2753	308	15	⊗	⊗	PROPN
ejpam-2753	308	16	(	(	PUNCT
ejpam-2753	308	17	a	a	DET
ejpam-2753	308	18	◦	◦	NOUN
ejpam-2753	308	19	w	w	NOUN
ejpam-2753	308	20	)	)	PUNCT
ejpam-2753	308	21	=	=	SYM
ejpam-2753	308	22	0	0	X
ejpam-2753	308	23	.	.	PUNCT
ejpam-2753	309	1	indeed	indeed	ADV
ejpam-2753	309	2	an	an	DET
ejpam-2753	309	3	alternate	alternate	ADJ
ejpam-2753	309	4	definition	definition	NOUN
ejpam-2753	309	5	of	of	ADP
ejpam-2753	309	6	v	v	NUM
ejpam-2753	309	7	⊗k	⊗k	ADJ
ejpam-2753	309	8	w	w	NOUN
ejpam-2753	309	9	is	be	AUX
ejpam-2753	309	10	that	that	SCONJ
ejpam-2753	309	11	it	it	PRON
ejpam-2753	309	12	is	be	AUX
ejpam-2753	309	13	the	the	DET
ejpam-2753	309	14	abelian	abelian	ADJ
ejpam-2753	309	15	group	group	NOUN
ejpam-2753	309	16	with	with	ADP
ejpam-2753	309	17	generators	generator	NOUN
ejpam-2753	309	18	all	all	DET
ejpam-2753	309	19	symbols	symbol	NOUN
ejpam-2753	309	20	v	v	PROPN
ejpam-2753	309	21	⊗w	⊗w	NOUN
ejpam-2753	309	22	(	(	PUNCT
ejpam-2753	309	23	v	v	NOUN
ejpam-2753	309	24	∈	∈	PROPN
ejpam-2753	309	25	v	v	NOUN
ejpam-2753	309	26	,	,	PUNCT
ejpam-2753	309	27	w	w	NOUN
ejpam-2753	309	28	∈w	∈w	NOUN
ejpam-2753	309	29	)	)	PUNCT
ejpam-2753	309	30	,	,	PUNCT
ejpam-2753	309	31	subject	subject	ADJ
ejpam-2753	309	32	to	to	ADP
ejpam-2753	309	33	the	the	DET
ejpam-2753	309	34	relations	relation	NOUN
ejpam-2753	309	35	(	(	PUNCT
ejpam-2753	309	36	1)−	1)−	PROPN
ejpam-2753	309	37	(	(	PUNCT
ejpam-2753	309	38	3	3	NUM
ejpam-2753	309	39	)	)	PUNCT
ejpam-2753	309	40	above	above	ADV
ejpam-2753	309	41	.	.	PUNCT
ejpam-2753	310	1	furthermore	furthermore	ADV
ejpam-2753	310	2	,	,	PUNCT
ejpam-2753	310	3	since	since	SCONJ
ejpam-2753	310	4	0	0	NUM
ejpam-2753	310	5	is	be	AUX
ejpam-2753	310	6	the	the	DET
ejpam-2753	310	7	only	only	ADJ
ejpam-2753	310	8	element	element	NOUN
ejpam-2753	310	9	of	of	ADP
ejpam-2753	310	10	a	a	DET
ejpam-2753	310	11	group	group	NOUN
ejpam-2753	310	12	satisfying	satisfy	VERB
ejpam-2753	310	13	x	x	PUNCT
ejpam-2753	311	1	+	+	NUM
ejpam-2753	311	2	x	x	SYM
ejpam-2753	311	3	=	=	SYM
ejpam-2753	311	4	x	x	NOUN
ejpam-2753	311	5	,	,	PUNCT
ejpam-2753	311	6	it	it	PRON
ejpam-2753	311	7	is	be	AUX
ejpam-2753	311	8	easy	easy	ADJ
ejpam-2753	311	9	to	to	PART
ejpam-2753	311	10	see	see	VERB
ejpam-2753	311	11	that	that	PRON
ejpam-2753	311	12	for	for	ADP
ejpam-2753	311	13	all	all	DET
ejpam-2753	311	14	v	v	ADP
ejpam-2753	311	15	∈	∈	PROPN
ejpam-2753	311	16	v	v	NOUN
ejpam-2753	311	17	,	,	PUNCT
ejpam-2753	311	18	w	w	NOUN
ejpam-2753	311	19	∈w	∈w	NOUN
ejpam-2753	311	20	:	:	PUNCT
ejpam-2753	311	21	v	v	X
ejpam-2753	311	22	⊗	⊗	NOUN
ejpam-2753	311	23	0	0	NUM
ejpam-2753	312	1	=	=	SYM
ejpam-2753	312	2	0⊗	0⊗	NUM
ejpam-2753	313	1	w	w	NOUN
ejpam-2753	313	2	=	=	NOUN
ejpam-2753	313	3	0⊗	0⊗	NOUN
ejpam-2753	313	4	0	0	NUM
ejpam-2753	313	5	=	=	SYM
ejpam-2753	313	6	0	0	X
ejpam-2753	313	7	.	.	PUNCT
ejpam-2753	313	8	given	give	VERB
ejpam-2753	313	9	hyperspaces	hyperspace	NOUN
ejpam-2753	313	10	v	v	ADP
ejpam-2753	313	11	and	and	CCONJ
ejpam-2753	313	12	w	w	NOUN
ejpam-2753	313	13	over	over	ADP
ejpam-2753	313	14	a	a	DET
ejpam-2753	313	15	field	field	NOUN
ejpam-2753	313	16	k	k	NOUN
ejpam-2753	313	17	,	,	PUNCT
ejpam-2753	313	18	it	it	PRON
ejpam-2753	313	19	is	be	AUX
ejpam-2753	313	20	easy	easy	ADJ
ejpam-2753	313	21	to	to	PART
ejpam-2753	313	22	verify	verify	VERB
ejpam-2753	313	23	that	that	SCONJ
ejpam-2753	313	24	the	the	DET
ejpam-2753	313	25	map	map	NOUN
ejpam-2753	313	26	i	i	PRON
ejpam-2753	313	27	:	:	PUNCT
ejpam-2753	313	28	v	v	X
ejpam-2753	313	29	×w	×w	NOUN
ejpam-2753	313	30	−→	−→	NOUN
ejpam-2753	313	31	v	v	NOUN
ejpam-2753	313	32	⊗kw	⊗kw	NUM
ejpam-2753	313	33	given	give	VERB
ejpam-2753	313	34	by	by	ADP
ejpam-2753	313	35	(	(	PUNCT
ejpam-2753	313	36	v	v	NOUN
ejpam-2753	313	37	,	,	PUNCT
ejpam-2753	313	38	w	w	NOUN
ejpam-2753	313	39	)	)	PUNCT
ejpam-2753	313	40	7−→	7−→	NOUN
ejpam-2753	313	41	v⊗w	v⊗w	NOUN
ejpam-2753	313	42	is	be	AUX
ejpam-2753	313	43	a	a	DET
ejpam-2753	313	44	middle	middle	ADJ
ejpam-2753	313	45	linear	linear	PROPN
ejpam-2753	313	46	map	map	NOUN
ejpam-2753	313	47	.	.	PUNCT
ejpam-2753	314	1	the	the	DET
ejpam-2753	314	2	map	map	NOUN
ejpam-2753	314	3	i	i	PRON
ejpam-2753	314	4	is	be	AUX
ejpam-2753	314	5	called	call	VERB
ejpam-2753	314	6	canonical	canonical	ADJ
ejpam-2753	314	7	middle	middle	ADJ
ejpam-2753	314	8	linear	linear	PROPN
ejpam-2753	314	9	map	map	NOUN
ejpam-2753	314	10	.	.	PUNCT
ejpam-2753	315	1	its	its	PRON
ejpam-2753	315	2	importance	importance	NOUN
ejpam-2753	315	3	is	be	AUX
ejpam-2753	315	4	seen	see	VERB
ejpam-2753	315	5	in	in	ADP
ejpam-2753	315	6	theorem	theorem	NOUN
ejpam-2753	315	7	4	4	NUM
ejpam-2753	315	8	.	.	PUNCT
ejpam-2753	316	1	let	let	VERB
ejpam-2753	316	2	v	v	NOUN
ejpam-2753	316	3	,	,	PUNCT
ejpam-2753	316	4	w	w	PROPN
ejpam-2753	316	5	be	be	AUX
ejpam-2753	316	6	two	two	NUM
ejpam-2753	316	7	hyperspaces	hyperspace	NOUN
ejpam-2753	316	8	over	over	ADP
ejpam-2753	316	9	a	a	DET
ejpam-2753	316	10	field	field	NOUN
ejpam-2753	316	11	k	k	NOUN
ejpam-2753	316	12	,	,	PUNCT
ejpam-2753	316	13	and	and	CCONJ
ejpam-2753	316	14	z	z	NOUN
ejpam-2753	316	15	be	be	AUX
ejpam-2753	316	16	an	an	DET
ejpam-2753	316	17	abelian	abelian	ADJ
ejpam-2753	316	18	group	group	NOUN
ejpam-2753	316	19	.	.	PUNCT
ejpam-2753	317	1	if	if	SCONJ
ejpam-2753	317	2	g	g	NOUN
ejpam-2753	317	3	:	:	PUNCT
ejpam-2753	317	4	v	v	NOUN
ejpam-2753	317	5	×w	×w	NOUN
ejpam-2753	317	6	−→	−→	NOUN
ejpam-2753	317	7	z	z	NOUN
ejpam-2753	317	8	is	be	AUX
ejpam-2753	317	9	a	a	DET
ejpam-2753	317	10	middle	middle	ADJ
ejpam-2753	317	11	linear	linear	PROPN
ejpam-2753	317	12	map	map	NOUN
ejpam-2753	317	13	,	,	PUNCT
ejpam-2753	317	14	then	then	ADV
ejpam-2753	317	15	there	there	PRON
ejpam-2753	317	16	exists	exist	VERB
ejpam-2753	317	17	a	a	DET
ejpam-2753	317	18	unique	unique	ADJ
ejpam-2753	317	19	group	group	NOUN
ejpam-2753	317	20	homomorphism	homomorphism	NOUN
ejpam-2753	317	21	g	g	NOUN
ejpam-2753	317	22	:	:	PUNCT
ejpam-2753	317	23	v	v	NOUN
ejpam-2753	317	24	⊗kw	⊗kw	NOUN
ejpam-2753	317	25	−→	−→	NOUN
ejpam-2753	317	26	z	z	NOUN
ejpam-2753	317	27	such	such	ADJ
ejpam-2753	317	28	that	that	DET
ejpam-2753	317	29	gi	gi	NOUN
ejpam-2753	317	30	=	=	SYM
ejpam-2753	317	31	g	g	NOUN
ejpam-2753	317	32	,	,	PUNCT
ejpam-2753	317	33	where	where	SCONJ
ejpam-2753	317	34	i	i	PRON
ejpam-2753	317	35	:	:	PUNCT
ejpam-2753	317	36	v	v	X
ejpam-2753	317	37	×w	×w	NOUN
ejpam-2753	317	38	−→	−→	NOUN
ejpam-2753	317	39	v	v	NOUN
ejpam-2753	317	40	⊗kw	⊗kw	NUM
ejpam-2753	317	41	is	be	AUX
ejpam-2753	317	42	the	the	DET
ejpam-2753	317	43	canonical	canonical	ADJ
ejpam-2753	317	44	middle	middle	ADJ
ejpam-2753	317	45	linear	linear	PROPN
ejpam-2753	317	46	map	map	NOUN
ejpam-2753	317	47	.	.	PUNCT
ejpam-2753	318	1	v	v	X
ejpam-2753	318	2	⊗k	⊗k	ADJ
ejpam-2753	318	3	w	w	NOUN
ejpam-2753	318	4	is	be	AUX
ejpam-2753	318	5	uniquely	uniquely	ADV
ejpam-2753	318	6	determined	determine	VERB
ejpam-2753	318	7	up	up	ADP
ejpam-2753	318	8	to	to	ADP
ejpam-2753	318	9	isomorphism	isomorphism	NOUN
ejpam-2753	318	10	by	by	ADP
ejpam-2753	318	11	this	this	DET
ejpam-2753	318	12	property	property	NOUN
ejpam-2753	318	13	.	.	PUNCT
ejpam-2753	319	1	in	in	ADP
ejpam-2753	319	2	other	other	ADJ
ejpam-2753	319	3	words	word	NOUN
ejpam-2753	319	4	i	i	PRON
ejpam-2753	319	5	:	:	PUNCT
ejpam-2753	319	6	v	v	X
ejpam-2753	319	7	×w	×w	NOUN
ejpam-2753	319	8	−→	−→	NOUN
ejpam-2753	319	9	v	v	ADP
ejpam-2753	319	10	⊗k	⊗k	ADJ
ejpam-2753	319	11	w	w	NOUN
ejpam-2753	319	12	is	be	AUX
ejpam-2753	319	13	universal	universal	ADJ
ejpam-2753	319	14	in	in	ADP
ejpam-2753	319	15	the	the	DET
ejpam-2753	319	16	category	category	NOUN
ejpam-2753	319	17	ml(v	ml(v	NOUN
ejpam-2753	319	18	,	,	PUNCT
ejpam-2753	319	19	w	w	NOUN
ejpam-2753	319	20	)	)	PUNCT
ejpam-2753	319	21	of	of	ADP
ejpam-2753	319	22	all	all	DET
ejpam-2753	319	23	middle	middle	ADJ
ejpam-2753	319	24	linear	linear	PROPN
ejpam-2753	319	25	maps	map	NOUN
ejpam-2753	319	26	on	on	ADP
ejpam-2753	319	27	v	v	NOUN
ejpam-2753	319	28	×w	×w	NOUN
ejpam-2753	319	29	.	.	PUNCT
ejpam-2753	320	1	references	reference	NOUN
ejpam-2753	320	2	714	714	NUM
ejpam-2753	320	3	proof	proof	NOUN
ejpam-2753	320	4	.	.	PUNCT
ejpam-2753	321	1	let	let	VERB
ejpam-2753	321	2	f	f	PRON
ejpam-2753	321	3	be	be	AUX
ejpam-2753	321	4	the	the	DET
ejpam-2753	321	5	free	free	ADJ
ejpam-2753	321	6	abelian	abelian	ADJ
ejpam-2753	321	7	group	group	NOUN
ejpam-2753	321	8	on	on	ADP
ejpam-2753	321	9	the	the	DET
ejpam-2753	321	10	set	set	NOUN
ejpam-2753	321	11	v	v	NOUN
ejpam-2753	321	12	×w	×w	NOUN
ejpam-2753	321	13	,	,	PUNCT
ejpam-2753	321	14	and	and	CCONJ
ejpam-2753	321	15	let	let	VERB
ejpam-2753	321	16	h	h	NOUN
ejpam-2753	321	17	be	be	AUX
ejpam-2753	321	18	the	the	DET
ejpam-2753	321	19	subgroup	subgroup	NOUN
ejpam-2753	321	20	described	describe	VERB
ejpam-2753	321	21	in	in	ADP
ejpam-2753	321	22	definition	definition	NOUN
ejpam-2753	321	23	19	19	NUM
ejpam-2753	321	24	.	.	PUNCT
ejpam-2753	322	1	since	since	SCONJ
ejpam-2753	322	2	f	f	PROPN
ejpam-2753	322	3	is	be	AUX
ejpam-2753	322	4	free	free	ADJ
ejpam-2753	322	5	,	,	PUNCT
ejpam-2753	322	6	the	the	DET
ejpam-2753	322	7	assignment	assignment	NOUN
ejpam-2753	322	8	(	(	PUNCT
ejpam-2753	322	9	v	v	NOUN
ejpam-2753	322	10	,	,	PUNCT
ejpam-2753	322	11	w	w	NOUN
ejpam-2753	322	12	)	)	PUNCT
ejpam-2753	322	13	7→	7→	NUM
ejpam-2753	322	14	g(v	g(v	PROPN
ejpam-2753	322	15	,	,	PUNCT
ejpam-2753	322	16	w	w	NOUN
ejpam-2753	322	17	)	)	PUNCT
ejpam-2753	322	18	∈	∈	PROPN
ejpam-2753	322	19	z	z	NOUN
ejpam-2753	322	20	determines	determine	VERB
ejpam-2753	322	21	a	a	DET
ejpam-2753	322	22	unique	unique	ADJ
ejpam-2753	322	23	group	group	NOUN
ejpam-2753	322	24	homomorphism	homomorphism	NOUN
ejpam-2753	322	25	g1	g1	PROPN
ejpam-2753	322	26	:	:	PUNCT
ejpam-2753	322	27	f	f	PROPN
ejpam-2753	322	28	−→	−→	NOUN
ejpam-2753	322	29	z	z	PROPN
ejpam-2753	322	30	by	by	ADP
ejpam-2753	322	31	theorem	theorem	NOUN
ejpam-2753	322	32	2	2	NUM
ejpam-2753	322	33	.	.	X
ejpam-2753	322	34	use	use	VERB
ejpam-2753	322	35	the	the	DET
ejpam-2753	322	36	fact	fact	NOUN
ejpam-2753	322	37	that	that	SCONJ
ejpam-2753	322	38	g	g	PROPN
ejpam-2753	322	39	is	be	AUX
ejpam-2753	322	40	middle	middle	ADJ
ejpam-2753	322	41	linear	linear	ADJ
ejpam-2753	322	42	to	to	PART
ejpam-2753	322	43	show	show	VERB
ejpam-2753	322	44	that	that	SCONJ
ejpam-2753	322	45	g1	g1	PROPN
ejpam-2753	322	46	maps	map	VERB
ejpam-2753	322	47	every	every	DET
ejpam-2753	322	48	generator	generator	NOUN
ejpam-2753	322	49	of	of	ADP
ejpam-2753	322	50	h	h	NOUN
ejpam-2753	322	51	to	to	ADP
ejpam-2753	322	52	0	0	NUM
ejpam-2753	322	53	.	.	PUNCT
ejpam-2753	323	1	hence	hence	ADV
ejpam-2753	323	2	h	h	PROPN
ejpam-2753	324	1	⊂	⊂	PROPN
ejpam-2753	324	2	kerg1	kerg1	PROPN
ejpam-2753	324	3	.	.	PUNCT
ejpam-2753	325	1	g1	g1	PROPN
ejpam-2753	325	2	induces	induce	VERB
ejpam-2753	325	3	a	a	DET
ejpam-2753	325	4	homomorphism	homomorphism	NOUN
ejpam-2753	325	5	g	g	NOUN
ejpam-2753	325	6	:	:	PUNCT
ejpam-2753	325	7	f	f	X
ejpam-2753	325	8	/	/	SYM
ejpam-2753	325	9	h	h	NOUN
ejpam-2753	325	10	−→	−→	ADJ
ejpam-2753	325	11	z	z	NOUN
ejpam-2753	325	12	such	such	ADJ
ejpam-2753	325	13	that	that	DET
ejpam-2753	325	14	g[(v	g[(v	NOUN
ejpam-2753	325	15	,	,	PUNCT
ejpam-2753	325	16	w	w	NOUN
ejpam-2753	325	17	)	)	PUNCT
ejpam-2753	326	1	+	+	CCONJ
ejpam-2753	326	2	h	h	X
ejpam-2753	326	3	]	]	X
ejpam-2753	326	4	=	=	PUNCT
ejpam-2753	326	5	g1(v	g1(v	PROPN
ejpam-2753	326	6	,	,	PUNCT
ejpam-2753	326	7	w	w	PROPN
ejpam-2753	326	8	)	)	PUNCT
ejpam-2753	326	9	=	=	SYM
ejpam-2753	326	10	g(v	g(v	X
ejpam-2753	326	11	,	,	PUNCT
ejpam-2753	326	12	w	w	NOUN
ejpam-2753	326	13	)	)	PUNCT
ejpam-2753	326	14	.	.	PUNCT
ejpam-2753	327	1	but	but	CCONJ
ejpam-2753	327	2	f	f	X
ejpam-2753	327	3	/	/	SYM
ejpam-2753	327	4	h	h	NOUN
ejpam-2753	327	5	=	=	NOUN
ejpam-2753	328	1	v	v	NUM
ejpam-2753	328	2	⊗k	⊗k	ADJ
ejpam-2753	328	3	w	w	PROPN
ejpam-2753	328	4	and	and	CCONJ
ejpam-2753	328	5	(	(	PUNCT
ejpam-2753	328	6	v	v	NOUN
ejpam-2753	328	7	,	,	PUNCT
ejpam-2753	328	8	w	w	NOUN
ejpam-2753	328	9	)	)	PUNCT
ejpam-2753	328	10	+	+	NUM
ejpam-2753	329	1	h	h	NOUN
ejpam-2753	329	2	=	=	SYM
ejpam-2753	329	3	v	v	PROPN
ejpam-2753	329	4	⊗	⊗	PROPN
ejpam-2753	329	5	w.	w.	PROPN
ejpam-2753	329	6	therefore	therefore	ADV
ejpam-2753	329	7	,	,	PUNCT
ejpam-2753	329	8	g	g	NOUN
ejpam-2753	329	9	:	:	PUNCT
ejpam-2753	329	10	v	v	NOUN
ejpam-2753	329	11	⊗k	⊗k	NOUN
ejpam-2753	329	12	w	w	ADP
ejpam-2753	329	13	−→	−→	NOUN
ejpam-2753	329	14	z	z	NOUN
ejpam-2753	329	15	is	be	AUX
ejpam-2753	329	16	a	a	DET
ejpam-2753	329	17	homomorphism	homomorphism	NOUN
ejpam-2753	329	18	such	such	ADJ
ejpam-2753	329	19	that	that	DET
ejpam-2753	329	20	gi(v	gi(v	NOUN
ejpam-2753	329	21	,	,	PUNCT
ejpam-2753	329	22	w	w	NOUN
ejpam-2753	329	23	)	)	PUNCT
ejpam-2753	330	1	=	=	SYM
ejpam-2753	331	1	g(v	g(v	PROPN
ejpam-2753	331	2	⊗	⊗	PROPN
ejpam-2753	331	3	w	w	PROPN
ejpam-2753	331	4	)	)	PUNCT
ejpam-2753	331	5	=	=	SYM
ejpam-2753	331	6	g(v	g(v	X
ejpam-2753	331	7	,	,	PUNCT
ejpam-2753	331	8	w	w	NOUN
ejpam-2753	331	9	)	)	PUNCT
ejpam-2753	331	10	for	for	ADP
ejpam-2753	331	11	all	all	DET
ejpam-2753	331	12	(	(	PUNCT
ejpam-2753	331	13	v	v	NOUN
ejpam-2753	331	14	,	,	PUNCT
ejpam-2753	331	15	w	w	NOUN
ejpam-2753	331	16	)	)	PUNCT
ejpam-2753	331	17	∈	∈	NOUN
ejpam-2753	331	18	v	v	NOUN
ejpam-2753	331	19	×w	×w	NOUN
ejpam-2753	331	20	;	;	PUNCT
ejpam-2753	331	21	that	that	PRON
ejpam-2753	331	22	is	be	AUX
ejpam-2753	331	23	,	,	PUNCT
ejpam-2753	331	24	gi	gi	X
ejpam-2753	331	25	=	=	PUNCT
ejpam-2753	331	26	g.	g.	NOUN
ejpam-2753	331	27	if	if	SCONJ
ejpam-2753	331	28	h	h	NOUN
ejpam-2753	331	29	:	:	PUNCT
ejpam-2753	331	30	v	v	X
ejpam-2753	331	31	⊗k	⊗k	NOUN
ejpam-2753	331	32	w	w	ADP
ejpam-2753	331	33	−→	−→	NOUN
ejpam-2753	331	34	z	z	NOUN
ejpam-2753	331	35	is	be	AUX
ejpam-2753	331	36	any	any	DET
ejpam-2753	331	37	homomorphism	homomorphism	NOUN
ejpam-2753	331	38	with	with	ADP
ejpam-2753	331	39	hi	hi	NOUN
ejpam-2753	331	40	=	=	SYM
ejpam-2753	331	41	g	g	NOUN
ejpam-2753	331	42	,	,	PUNCT
ejpam-2753	331	43	then	then	ADV
ejpam-2753	331	44	for	for	ADP
ejpam-2753	331	45	any	any	DET
ejpam-2753	331	46	generator	generator	NOUN
ejpam-2753	331	47	v	v	ADP
ejpam-2753	331	48	⊗	⊗	PROPN
ejpam-2753	331	49	w	w	PROPN
ejpam-2753	331	50	of	of	ADP
ejpam-2753	331	51	v	v	NUM
ejpam-2753	331	52	⊗k	⊗k	ADJ
ejpam-2753	331	53	w	w	NOUN
ejpam-2753	331	54	,	,	PUNCT
ejpam-2753	331	55	h(v	h(v	PROPN
ejpam-2753	331	56	⊗	⊗	PROPN
ejpam-2753	331	57	w	w	PROPN
ejpam-2753	331	58	)	)	PUNCT
ejpam-2753	331	59	=	=	SYM
ejpam-2753	331	60	hi(v	hi(v	X
ejpam-2753	331	61	,	,	PUNCT
ejpam-2753	331	62	w	w	NOUN
ejpam-2753	331	63	)	)	PUNCT
ejpam-2753	331	64	=	=	SYM
ejpam-2753	331	65	g(v	g(v	X
ejpam-2753	331	66	,	,	PUNCT
ejpam-2753	331	67	w	w	NOUN
ejpam-2753	331	68	)	)	PUNCT
ejpam-2753	331	69	=	=	SYM
ejpam-2753	331	70	gi(v	gi(v	PROPN
ejpam-2753	331	71	,	,	PUNCT
ejpam-2753	331	72	w	w	NOUN
ejpam-2753	331	73	)	)	PUNCT
ejpam-2753	331	74	=	=	SYM
ejpam-2753	332	1	g(v	g(v	PROPN
ejpam-2753	332	2	⊗	⊗	PROPN
ejpam-2753	332	3	w	w	PROPN
ejpam-2753	332	4	)	)	PUNCT
ejpam-2753	332	5	.	.	PUNCT
ejpam-2753	333	1	since	since	SCONJ
ejpam-2753	333	2	h	h	PROPN
ejpam-2753	333	3	and	and	CCONJ
ejpam-2753	333	4	g	g	PROPN
ejpam-2753	333	5	are	be	AUX
ejpam-2753	333	6	homomorphisms	homomorphism	NOUN
ejpam-2753	333	7	that	that	PRON
ejpam-2753	333	8	agree	agree	VERB
ejpam-2753	333	9	on	on	ADP
ejpam-2753	333	10	the	the	DET
ejpam-2753	333	11	generators	generator	NOUN
ejpam-2753	333	12	of	of	ADP
ejpam-2753	333	13	v	v	NOUN
ejpam-2753	333	14	⊗kw	⊗kw	NUM
ejpam-2753	333	15	,	,	PUNCT
ejpam-2753	333	16	we	we	PRON
ejpam-2753	333	17	must	must	AUX
ejpam-2753	333	18	have	have	VERB
ejpam-2753	333	19	h	h	NOUN
ejpam-2753	333	20	=	=	SYM
ejpam-2753	333	21	g	g	NOUN
ejpam-2753	333	22	,	,	PUNCT
ejpam-2753	333	23	whence	whence	ADP
ejpam-2753	333	24	g	g	PROPN
ejpam-2753	333	25	is	be	AUX
ejpam-2753	333	26	unique	unique	ADJ
ejpam-2753	333	27	.	.	PUNCT
ejpam-2753	334	1	this	this	PRON
ejpam-2753	334	2	proves	prove	VERB
ejpam-2753	334	3	that	that	SCONJ
ejpam-2753	334	4	i	i	PRON
ejpam-2753	334	5	:	:	PUNCT
ejpam-2753	334	6	v	v	X
ejpam-2753	334	7	×w	×w	NOUN
ejpam-2753	334	8	−→	−→	NOUN
ejpam-2753	334	9	v	v	NOUN
ejpam-2753	334	10	⊗kw	⊗kw	NUM
ejpam-2753	334	11	is	be	AUX
ejpam-2753	334	12	a	a	DET
ejpam-2753	334	13	universal	universal	ADJ
ejpam-2753	334	14	object	object	NOUN
ejpam-2753	334	15	in	in	ADP
ejpam-2753	334	16	the	the	DET
ejpam-2753	334	17	category	category	NOUN
ejpam-2753	334	18	of	of	ADP
ejpam-2753	334	19	all	all	DET
ejpam-2753	334	20	middle	middle	ADJ
ejpam-2753	334	21	linear	linear	PROPN
ejpam-2753	334	22	maps	map	NOUN
ejpam-2753	334	23	on	on	ADP
ejpam-2753	334	24	v	v	NOUN
ejpam-2753	334	25	×w	×w	NOUN
ejpam-2753	334	26	,	,	PUNCT
ejpam-2753	334	27	whence	whence	ADP
ejpam-2753	334	28	v	v	NOUN
ejpam-2753	334	29	⊗kw	⊗kw	NUM
ejpam-2753	334	30	is	be	AUX
ejpam-2753	334	31	uniquely	uniquely	ADV
ejpam-2753	334	32	determined	determine	VERB
ejpam-2753	334	33	up	up	ADP
ejpam-2753	334	34	to	to	ADP
ejpam-2753	334	35	isomorphism	isomorphism	NOUN
ejpam-2753	334	36	(	(	PUNCT
ejpam-2753	334	37	equivalence	equivalence	NOUN
ejpam-2753	334	38	)	)	PUNCT
ejpam-2753	334	39	.	.	PUNCT
ejpam-2753	335	1	corollary	corollary	ADJ
ejpam-2753	335	2	1	1	NUM
ejpam-2753	335	3	.	.	PUNCT
ejpam-2753	336	1	if	if	SCONJ
ejpam-2753	336	2	v	v	NUM
ejpam-2753	336	3	,	,	PUNCT
ejpam-2753	336	4	v	v	NOUN
ejpam-2753	336	5	′	′	NUM
ejpam-2753	336	6	,	,	PUNCT
ejpam-2753	336	7	w	w	NOUN
ejpam-2753	336	8	,	,	PUNCT
ejpam-2753	336	9	and	and	CCONJ
ejpam-2753	336	10	w	w	PROPN
ejpam-2753	336	11	′	′	NOUN
ejpam-2753	336	12	are	be	AUX
ejpam-2753	336	13	hyperspaces	hyperspace	NOUN
ejpam-2753	336	14	over	over	ADP
ejpam-2753	336	15	a	a	DET
ejpam-2753	336	16	field	field	NOUN
ejpam-2753	337	1	k	k	PROPN
ejpam-2753	337	2	and	and	CCONJ
ejpam-2753	337	3	f	f	PROPN
ejpam-2753	337	4	:	:	PUNCT
ejpam-2753	337	5	v	v	AUX
ejpam-2753	337	6	−→	−→	NOUN
ejpam-2753	337	7	v	v	ADP
ejpam-2753	337	8	′	′	NUM
ejpam-2753	337	9	,	,	PUNCT
ejpam-2753	337	10	g	g	NOUN
ejpam-2753	337	11	:	:	PUNCT
ejpam-2753	337	12	w	w	X
ejpam-2753	337	13	−→w	−→w	NOUN
ejpam-2753	337	14	′	′	NOUN
ejpam-2753	337	15	are	be	AUX
ejpam-2753	337	16	k	k	ADJ
ejpam-2753	337	17	-	-	PUNCT
ejpam-2753	337	18	hyperspace	hyperspace	NOUN
ejpam-2753	337	19	homomorphisms	homomorphism	NOUN
ejpam-2753	337	20	,	,	PUNCT
ejpam-2753	337	21	then	then	ADV
ejpam-2753	337	22	there	there	PRON
ejpam-2753	337	23	is	be	VERB
ejpam-2753	337	24	a	a	DET
ejpam-2753	337	25	unique	unique	ADJ
ejpam-2753	337	26	group	group	NOUN
ejpam-2753	337	27	homomorphism	homomorphism	NOUN
ejpam-2753	337	28	v	v	ADP
ejpam-2753	337	29	⊗k	⊗k	ADJ
ejpam-2753	337	30	w	w	ADP
ejpam-2753	337	31	−→	−→	NOUN
ejpam-2753	337	32	v	v	NOUN
ejpam-2753	337	33	′	′	NOUN
ejpam-2753	337	34	⊗k	⊗k	ADJ
ejpam-2753	338	1	w	w	NOUN
ejpam-2753	339	1	′	′	NUM
ejpam-2753	339	2	such	such	ADJ
ejpam-2753	339	3	that	that	DET
ejpam-2753	339	4	(	(	PUNCT
ejpam-2753	339	5	v	v	NOUN
ejpam-2753	339	6	,	,	PUNCT
ejpam-2753	339	7	w	w	NOUN
ejpam-2753	339	8	)	)	PUNCT
ejpam-2753	339	9	7−→	7−→	NOUN
ejpam-2753	339	10	f(v)⊗	f(v)⊗	NOUN
ejpam-2753	339	11	g(w	g(w	PROPN
ejpam-2753	339	12	)	)	PUNCT
ejpam-2753	339	13	for	for	ADP
ejpam-2753	339	14	all	all	DET
ejpam-2753	339	15	v	v	ADP
ejpam-2753	339	16	∈	∈	PROPN
ejpam-2753	339	17	v	v	NOUN
ejpam-2753	339	18	,	,	PUNCT
ejpam-2753	339	19	w	w	NOUN
ejpam-2753	339	20	∈w	∈w	NOUN
ejpam-2753	339	21	.	.	PUNCT
ejpam-2753	340	1	proof	proof	NOUN
ejpam-2753	340	2	.	.	PUNCT
ejpam-2753	341	1	verify	verify	VERB
ejpam-2753	341	2	that	that	SCONJ
ejpam-2753	341	3	the	the	DET
ejpam-2753	341	4	assignment	assignment	NOUN
ejpam-2753	341	5	(	(	PUNCT
ejpam-2753	341	6	v	v	NOUN
ejpam-2753	341	7	,	,	PUNCT
ejpam-2753	341	8	w	w	NOUN
ejpam-2753	341	9	)	)	PUNCT
ejpam-2753	341	10	7−→	7−→	NOUN
ejpam-2753	341	11	f(v	f(v	NOUN
ejpam-2753	341	12	)	)	PUNCT
ejpam-2753	341	13	⊗	⊗	PROPN
ejpam-2753	341	14	g(w	g(w	PROPN
ejpam-2753	341	15	)	)	PUNCT
ejpam-2753	341	16	defines	define	VERB
ejpam-2753	341	17	a	a	DET
ejpam-2753	341	18	middle	middle	ADJ
ejpam-2753	341	19	linear	linear	NOUN
ejpam-2753	341	20	map	map	NOUN
ejpam-2753	341	21	h	h	NOUN
ejpam-2753	341	22	:	:	PUNCT
ejpam-2753	342	1	v	v	NUM
ejpam-2753	342	2	×w	×w	NOUN
ejpam-2753	342	3	−→	−→	NOUN
ejpam-2753	342	4	c	c	NOUN
ejpam-2753	342	5	=	=	SYM
ejpam-2753	342	6	v	v	NOUN
ejpam-2753	342	7	′	′	NUM
ejpam-2753	342	8	⊗k	⊗k	ADJ
ejpam-2753	342	9	w	w	NOUN
ejpam-2753	342	10	′.	′.	NOUN
ejpam-2753	342	11	by	by	ADP
ejpam-2753	342	12	theorem	theorem	NOUN
ejpam-2753	342	13	4	4	NUM
ejpam-2753	342	14	there	there	PRON
ejpam-2753	342	15	is	be	VERB
ejpam-2753	342	16	a	a	DET
ejpam-2753	342	17	unique	unique	ADJ
ejpam-2753	342	18	homomorphism	homomorphism	NOUN
ejpam-2753	342	19	h	h	NOUN
ejpam-2753	342	20	:	:	PUNCT
ejpam-2753	343	1	v	v	X
ejpam-2753	343	2	⊗k	⊗k	NOUN
ejpam-2753	343	3	w	w	ADP
ejpam-2753	343	4	−→	−→	NOUN
ejpam-2753	343	5	v	v	NOUN
ejpam-2753	343	6	′	′	NUM
ejpam-2753	343	7	⊗w	⊗w	NOUN
ejpam-2753	343	8	′	′	NUM
ejpam-2753	343	9	such	such	ADJ
ejpam-2753	343	10	that	that	SCONJ
ejpam-2753	343	11	h(v	h(v	PROPN
ejpam-2753	343	12	⊗	⊗	PROPN
ejpam-2753	343	13	w	w	PROPN
ejpam-2753	343	14	)	)	PUNCT
ejpam-2753	343	15	=	=	SYM
ejpam-2753	343	16	hi(v	hi(v	X
ejpam-2753	343	17	,	,	PUNCT
ejpam-2753	343	18	w	w	NOUN
ejpam-2753	343	19	)	)	PUNCT
ejpam-2753	343	20	=	=	SYM
ejpam-2753	344	1	h(v	h(v	PROPN
ejpam-2753	344	2	,	,	PUNCT
ejpam-2753	344	3	w	w	NOUN
ejpam-2753	344	4	)	)	PUNCT
ejpam-2753	344	5	=	=	PUNCT
ejpam-2753	344	6	f(v	f(v	NOUN
ejpam-2753	344	7	)	)	PUNCT
ejpam-2753	344	8	⊗	⊗	PROPN
ejpam-2753	344	9	g(w	g(w	PROPN
ejpam-2753	344	10	)	)	PUNCT
ejpam-2753	344	11	for	for	ADP
ejpam-2753	344	12	all	all	DET
ejpam-2753	344	13	v	v	ADP
ejpam-2753	344	14	∈	∈	PROPN
ejpam-2753	344	15	v	v	NOUN
ejpam-2753	344	16	,	,	PUNCT
ejpam-2753	344	17	w	w	PROPN
ejpam-2753	344	18	∈w	∈w	NOUN
ejpam-2753	344	19	.	.	PUNCT
ejpam-2753	345	1	the	the	DET
ejpam-2753	345	2	unique	unique	ADJ
ejpam-2753	345	3	homomorphism	homomorphism	NOUN
ejpam-2753	345	4	of	of	ADP
ejpam-2753	345	5	corollary	corollary	ADJ
ejpam-2753	345	6	1	1	NUM
ejpam-2753	345	7	is	be	AUX
ejpam-2753	345	8	denoted	denote	VERB
ejpam-2753	345	9	f	f	PROPN
ejpam-2753	345	10	⊗	⊗	PROPN
ejpam-2753	345	11	g	g	PROPN
ejpam-2753	345	12	:	:	PUNCT
ejpam-2753	345	13	v	v	NOUN
ejpam-2753	345	14	⊗k	⊗k	NOUN
ejpam-2753	345	15	w	w	ADP
ejpam-2753	345	16	−→	−→	NOUN
ejpam-2753	345	17	v	v	NOUN
ejpam-2753	345	18	′	′	NUM
ejpam-2753	345	19	⊗k	⊗k	ADJ
ejpam-2753	345	20	w	w	PROPN
ejpam-2753	345	21	′.	′.	NOUN
ejpam-2753	345	22	if	if	SCONJ
ejpam-2753	345	23	f	f	PROPN
ejpam-2753	346	1	′	′	NUM
ejpam-2753	346	2	:	:	PUNCT
ejpam-2753	347	1	v	v	X
ejpam-2753	347	2	′	′	NUM
ejpam-2753	348	1	−→	−→	NOUN
ejpam-2753	348	2	v	v	ADP
ejpam-2753	348	3	′′	′′	PROPN
ejpam-2753	348	4	and	and	CCONJ
ejpam-2753	348	5	g′	g′	NOUN
ejpam-2753	348	6	:	:	PUNCT
ejpam-2753	349	1	w	w	X
ejpam-2753	349	2	′	′	NUM
ejpam-2753	349	3	−→	−→	NOUN
ejpam-2753	349	4	w	w	PROPN
ejpam-2753	349	5	′′	′′	PROPN
ejpam-2753	349	6	are	be	AUX
ejpam-2753	349	7	also	also	ADV
ejpam-2753	349	8	k	k	ADJ
ejpam-2753	349	9	-	-	PUNCT
ejpam-2753	349	10	hyperspace	hyperspace	NOUN
ejpam-2753	349	11	homomorphisms	homomorphism	NOUN
ejpam-2753	349	12	,	,	PUNCT
ejpam-2753	349	13	then	then	ADV
ejpam-2753	349	14	it	it	PRON
ejpam-2753	349	15	is	be	AUX
ejpam-2753	349	16	easy	easy	ADJ
ejpam-2753	349	17	to	to	PART
ejpam-2753	349	18	verify	verify	VERB
ejpam-2753	349	19	that	that	SCONJ
ejpam-2753	349	20	(	(	PUNCT
ejpam-2753	349	21	f	f	X
ejpam-2753	349	22	′	′	PROPN
ejpam-2753	349	23	⊗	⊗	PROPN
ejpam-2753	349	24	g′)(f	g′)(f	VERB
ejpam-2753	349	25	⊗	⊗	PROPN
ejpam-2753	349	26	g	g	NOUN
ejpam-2753	349	27	)	)	PUNCT
ejpam-2753	349	28	=	=	PUNCT
ejpam-2753	350	1	(	(	PUNCT
ejpam-2753	350	2	f	f	PROPN
ejpam-2753	350	3	′f	′f	PROPN
ejpam-2753	350	4	⊗	⊗	PROPN
ejpam-2753	350	5	g′g	g′g	NOUN
ejpam-2753	350	6	)	)	PUNCT
ejpam-2753	350	7	:	:	PUNCT
ejpam-2753	351	1	v	v	X
ejpam-2753	351	2	⊗k	⊗k	ADJ
ejpam-2753	351	3	w	w	ADP
ejpam-2753	351	4	−→	−→	NOUN
ejpam-2753	351	5	v	v	ADP
ejpam-2753	351	6	′′	′′	PROPN
ejpam-2753	351	7	⊗k	⊗k	ADJ
ejpam-2753	351	8	w	w	PRON
ejpam-2753	351	9	′′.	′′.	NOUN
ejpam-2753	351	10	it	it	PRON
ejpam-2753	351	11	follows	follow	VERB
ejpam-2753	351	12	readily	readily	ADV
ejpam-2753	351	13	that	that	SCONJ
ejpam-2753	351	14	if	if	SCONJ
ejpam-2753	351	15	f	f	PROPN
ejpam-2753	351	16	and	and	CCONJ
ejpam-2753	351	17	g	g	PROPN
ejpam-2753	351	18	are	be	AUX
ejpam-2753	351	19	k	k	ADJ
ejpam-2753	351	20	-	-	PUNCT
ejpam-2753	351	21	hyperspace	hyperspace	PROPN
ejpam-2753	351	22	isomorphisms	isomorphism	NOUN
ejpam-2753	351	23	,	,	PUNCT
ejpam-2753	351	24	then	then	ADV
ejpam-2753	351	25	f	f	PROPN
ejpam-2753	351	26	⊗	⊗	PROPN
ejpam-2753	351	27	g	g	PROPN
ejpam-2753	351	28	is	be	AUX
ejpam-2753	351	29	a	a	DET
ejpam-2753	351	30	group	group	NOUN
ejpam-2753	351	31	isomorphism	isomorphism	NOUN
ejpam-2753	351	32	with	with	ADP
ejpam-2753	351	33	inverse	inverse	NOUN
ejpam-2753	351	34	f−1	f−1	PROPN
ejpam-2753	351	35	⊗	⊗	PROPN
ejpam-2753	351	36	g−1	g−1	PROPN
ejpam-2753	351	37	.	.	PUNCT
ejpam-2753	352	1	references	reference	NOUN
ejpam-2753	352	2	[	[	X
ejpam-2753	352	3	1	1	NUM
ejpam-2753	352	4	]	]	X
ejpam-2753	352	5	r	r	NOUN
ejpam-2753	352	6	ameri	ameri	PROPN
ejpam-2753	352	7	.	.	PUNCT
ejpam-2753	353	1	on	on	ADP
ejpam-2753	353	2	categories	category	NOUN
ejpam-2753	353	3	of	of	ADP
ejpam-2753	353	4	hypergroups	hypergroup	NOUN
ejpam-2753	353	5	and	and	CCONJ
ejpam-2753	353	6	hypermodules	hypermodule	NOUN
ejpam-2753	353	7	.	.	PUNCT
ejpam-2753	354	1	journal	journal	PROPN
ejpam-2753	354	2	of	of	ADP
ejpam-2753	354	3	discrete	discrete	ADJ
ejpam-2753	354	4	mathematical	mathematical	ADJ
ejpam-2753	354	5	sciences	science	NOUN
ejpam-2753	354	6	and	and	CCONJ
ejpam-2753	354	7	cryptography	cryptography	NOUN
ejpam-2753	354	8	,	,	PUNCT
ejpam-2753	354	9	6(2	6(2	NUM
ejpam-2753	354	10	-	-	PUNCT
ejpam-2753	354	11	3):121	3):121	NUM
ejpam-2753	354	12	-	-	PUNCT
ejpam-2753	354	13	132	132	NUM
ejpam-2753	354	14	,	,	PUNCT
ejpam-2753	354	15	2003	2003	NUM
ejpam-2753	354	16	.	.	PUNCT
ejpam-2753	355	1	[	[	X
ejpam-2753	355	2	2	2	NUM
ejpam-2753	355	3	]	]	X
ejpam-2753	355	4	r	r	NOUN
ejpam-2753	355	5	ameri	ameri	NOUN
ejpam-2753	355	6	and	and	CCONJ
ejpam-2753	355	7	o	o	NOUN
ejpam-2753	355	8	r	r	NOUN
ejpam-2753	355	9	dehghan	dehghan	NOUN
ejpam-2753	355	10	.	.	PUNCT
ejpam-2753	356	1	on	on	ADP
ejpam-2753	356	2	dimension	dimension	NOUN
ejpam-2753	356	3	of	of	ADP
ejpam-2753	356	4	hypervector	hypervector	NOUN
ejpam-2753	356	5	spaces	space	NOUN
ejpam-2753	356	6	.	.	PUNCT
ejpam-2753	357	1	european	european	ADJ
ejpam-2753	357	2	journal	journal	PROPN
ejpam-2753	357	3	of	of	ADP
ejpam-2753	357	4	pure	pure	ADJ
ejpam-2753	357	5	and	and	CCONJ
ejpam-2753	357	6	applied	applied	ADJ
ejpam-2753	357	7	mathematics	mathematic	NOUN
ejpam-2753	357	8	,	,	PUNCT
ejpam-2753	357	9	1(2):32	1(2):32	NOUN
ejpam-2753	357	10	-	-	PUNCT
ejpam-2753	357	11	50	50	NUM
ejpam-2753	357	12	,	,	PUNCT
ejpam-2753	357	13	2008	2008	NUM
ejpam-2753	357	14	.	.	PUNCT
ejpam-2753	358	1	[	[	X
ejpam-2753	358	2	3	3	NUM
ejpam-2753	358	3	]	]	X
ejpam-2753	358	4	r	r	NOUN
ejpam-2753	358	5	ameri	ameri	PROPN
ejpam-2753	358	6	,	,	PUNCT
ejpam-2753	358	7	k	k	PROPN
ejpam-2753	358	8	ghadimi	ghadimi	PROPN
ejpam-2753	358	9	and	and	CCONJ
ejpam-2753	358	10	r	r	NOUN
ejpam-2753	358	11	a	a	DET
ejpam-2753	358	12	borzooei	borzooei	NOUN
ejpam-2753	358	13	.	.	PUNCT
ejpam-2753	359	1	categories	category	NOUN
ejpam-2753	359	2	of	of	ADP
ejpam-2753	359	3	hypervector	hypervector	NOUN
ejpam-2753	359	4	spaces	space	NOUN
ejpam-2753	359	5	,	,	PUNCT
ejpam-2753	359	6	submitted	submit	VERB
ejpam-2753	359	7	.	.	PUNCT
ejpam-2753	360	1	[	[	X
ejpam-2753	360	2	4	4	NUM
ejpam-2753	360	3	]	]	X
ejpam-2753	360	4	r	r	NOUN
ejpam-2753	360	5	ameri	ameri	PROPN
ejpam-2753	360	6	and	and	CCONJ
ejpam-2753	360	7	m	m	PROPN
ejpam-2753	360	8	norouzi	norouzi	PROPN
ejpam-2753	360	9	.	.	PUNCT
ejpam-2753	361	1	prime	prime	ADJ
ejpam-2753	361	2	and	and	CCONJ
ejpam-2753	361	3	primary	primary	ADJ
ejpam-2753	361	4	hyperideals	hyperideal	NOUN
ejpam-2753	361	5	in	in	ADP
ejpam-2753	361	6	krasner	krasner	NOUN
ejpam-2753	361	7	.	.	PUNCT
ejpam-2753	362	1	european	european	PROPN
ejpam-2753	362	2	journal	journal	PROPN
ejpam-2753	362	3	of	of	ADP
ejpam-2753	362	4	combinatorics	combinatoric	NOUN
ejpam-2753	362	5	,	,	PUNCT
ejpam-2753	362	6	34:379	34:379	NUM
ejpam-2753	362	7	-	-	SYM
ejpam-2753	362	8	390	390	NUM
ejpam-2753	362	9	,	,	PUNCT
ejpam-2753	362	10	2013	2013	NUM
ejpam-2753	362	11	.	.	PUNCT
ejpam-2753	363	1	references	reference	NOUN
ejpam-2753	363	2	715	715	NUM
ejpam-2753	364	1	[	[	X
ejpam-2753	364	2	5	5	NUM
ejpam-2753	364	3	]	]	SYM
ejpam-2753	364	4	r	r	NOUN
ejpam-2753	364	5	ameri	ameri	PROPN
ejpam-2753	364	6	and	and	CCONJ
ejpam-2753	364	7	m	m	AUX
ejpam-2753	364	8	norouzi	norouzi	ADJ
ejpam-2753	364	9	.	.	PUNCT
ejpam-2753	365	1	new	new	ADJ
ejpam-2753	365	2	fundamental	fundamental	ADJ
ejpam-2753	365	3	relation	relation	NOUN
ejpam-2753	365	4	of	of	ADP
ejpam-2753	365	5	hyperrings	hyperring	NOUN
ejpam-2753	365	6	.	.	PUNCT
ejpam-2753	366	1	european	european	PROPN
ejpam-2753	366	2	journal	journal	PROPN
ejpam-2753	366	3	of	of	ADP
ejpam-2753	366	4	combinatorics	combinatorics	PROPN
ejpam-2753	366	5	,	,	PUNCT
ejpam-2753	366	6	34:884	34:884	NUM
ejpam-2753	366	7	-	-	PUNCT
ejpam-2753	366	8	891	891	NUM
ejpam-2753	366	9	,	,	PUNCT
ejpam-2753	366	10	2013	2013	NUM
ejpam-2753	366	11	.	.	PUNCT
ejpam-2753	367	1	[	[	X
ejpam-2753	367	2	6	6	NUM
ejpam-2753	367	3	]	]	SYM
ejpam-2753	367	4	r	r	NOUN
ejpam-2753	367	5	ameri	ameri	PROPN
ejpam-2753	367	6	and	and	CCONJ
ejpam-2753	367	7	m	m	AUX
ejpam-2753	367	8	norouzi	norouzi	ADJ
ejpam-2753	367	9	.	.	PUNCT
ejpam-2753	368	1	on	on	ADP
ejpam-2753	368	2	multiplication	multiplication	NOUN
ejpam-2753	368	3	(	(	PUNCT
ejpam-2753	368	4	m	m	PROPN
ejpam-2753	368	5	,	,	PUNCT
ejpam-2753	368	6	n)-hypermodules	n)-hypermodule	NOUN
ejpam-2753	368	7	.	.	PUNCT
ejpam-2753	368	8	european	european	PROPN
ejpam-2753	368	9	journal	journal	PROPN
ejpam-2753	368	10	of	of	ADP
ejpam-2753	368	11	combinatorics	combinatoric	NOUN
ejpam-2753	368	12	,	,	PUNCT
ejpam-2753	368	13	44:153	44:153	NUM
ejpam-2753	368	14	-	-	SYM
ejpam-2753	368	15	171	171	NUM
ejpam-2753	368	16	,	,	PUNCT
ejpam-2753	368	17	2015	2015	NUM
ejpam-2753	368	18	.	.	PUNCT
ejpam-2753	369	1	[	[	X
ejpam-2753	369	2	7	7	NUM
ejpam-2753	369	3	]	]	X
ejpam-2753	369	4	r	r	NOUN
ejpam-2753	369	5	ameri	ameri	PROPN
ejpam-2753	369	6	,	,	PUNCT
ejpam-2753	369	7	m	m	VERB
ejpam-2753	369	8	norouzi	norouzi	VERB
ejpam-2753	369	9	and	and	CCONJ
ejpam-2753	369	10	v	v	ADP
ejpam-2753	369	11	leoreanu	leoreanu	NOUN
ejpam-2753	369	12	-	-	PUNCT
ejpam-2753	369	13	fotea	fotea	NOUN
ejpam-2753	369	14	.	.	PUNCT
ejpam-2753	370	1	on	on	ADP
ejpam-2753	370	2	prime	prime	ADJ
ejpam-2753	370	3	and	and	CCONJ
ejpam-2753	370	4	primary	primary	ADJ
ejpam-2753	370	5	subhypermodules	subhypermodule	NOUN
ejpam-2753	370	6	of	of	ADP
ejpam-2753	370	7	(	(	PUNCT
ejpam-2753	370	8	m	m	PROPN
ejpam-2753	370	9	,	,	PUNCT
ejpam-2753	370	10	n)-hypermodules	n)-hypermodule	NOUN
ejpam-2753	370	11	.	.	PUNCT
ejpam-2753	371	1	european	european	PROPN
ejpam-2753	371	2	journal	journal	PROPN
ejpam-2753	371	3	of	of	ADP
ejpam-2753	371	4	combinatorics	combinatorics	PROPN
ejpam-2753	371	5	,	,	PUNCT
ejpam-2753	371	6	44:175	44:175	NUM
ejpam-2753	371	7	-	-	SYM
ejpam-2753	371	8	190	190	NUM
ejpam-2753	371	9	,	,	PUNCT
ejpam-2753	371	10	2015	2015	NUM
ejpam-2753	371	11	.	.	PUNCT
ejpam-2753	372	1	[	[	X
ejpam-2753	372	2	8	8	NUM
ejpam-2753	372	3	]	]	X
ejpam-2753	372	4	r	r	NOUN
ejpam-2753	372	5	ameri	ameri	PROPN
ejpam-2753	372	6	and	and	CCONJ
ejpam-2753	372	7	i	i	PRON
ejpam-2753	372	8	g	g	PROPN
ejpam-2753	372	9	rosenberg	rosenberg	PROPN
ejpam-2753	372	10	.	.	PUNCT
ejpam-2753	373	1	congruences	congruence	NOUN
ejpam-2753	373	2	of	of	ADP
ejpam-2753	373	3	multialgebras	multialgebra	NOUN
ejpam-2753	373	4	.	.	PUNCT
ejpam-2753	374	1	multivalued	multivalue	VERB
ejpam-2753	374	2	logic	logic	NOUN
ejpam-2753	374	3	and	and	CCONJ
ejpam-2753	374	4	soft	soft	ADJ
ejpam-2753	374	5	computing	computing	NOUN
ejpam-2753	374	6	,	,	PUNCT
ejpam-2753	374	7	15(5	15(5	NUM
ejpam-2753	374	8	-	-	PUNCT
ejpam-2753	374	9	6):525	6):525	NOUN
ejpam-2753	374	10	-	-	PUNCT
ejpam-2753	374	11	536	536	NUM
ejpam-2753	374	12	,	,	PUNCT
ejpam-2753	374	13	2009	2009	NUM
ejpam-2753	374	14	.	.	PUNCT
ejpam-2753	375	1	[	[	X
ejpam-2753	375	2	9	9	NUM
ejpam-2753	375	3	]	]	SYM
ejpam-2753	375	4	r	r	NOUN
ejpam-2753	375	5	ameri	ameri	PROPN
ejpam-2753	375	6	and	and	CCONJ
ejpam-2753	375	7	m	m	PROPN
ejpam-2753	375	8	m	m	PROPN
ejpam-2753	375	9	zahedi	zahedi	PROPN
ejpam-2753	375	10	.	.	PUNCT
ejpam-2753	376	1	hyperalgebraic	hyperalgebraic	PROPN
ejpam-2753	376	2	systems	systems	PROPN
ejpam-2753	376	3	.	.	PUNCT
ejpam-2753	377	1	italian	italian	ADJ
ejpam-2753	377	2	journal	journal	NOUN
ejpam-2753	377	3	of	of	ADP
ejpam-2753	377	4	pure	pure	ADJ
ejpam-2753	377	5	and	and	CCONJ
ejpam-2753	377	6	applied	applied	ADJ
ejpam-2753	377	7	mathematics	mathematic	NOUN
ejpam-2753	377	8	,	,	PUNCT
ejpam-2753	377	9	6:21	6:21	NUM
ejpam-2753	377	10	-	-	SYM
ejpam-2753	377	11	32	32	NUM
ejpam-2753	377	12	,	,	PUNCT
ejpam-2753	377	13	1999	1999	NUM
ejpam-2753	377	14	.	.	PUNCT
ejpam-2753	378	1	[	[	X
ejpam-2753	378	2	10	10	NUM
ejpam-2753	378	3	]	]	X
ejpam-2753	378	4	p	p	NOUN
ejpam-2753	378	5	bonansinga	bonansinga	NOUN
ejpam-2753	378	6	.	.	PUNCT
ejpam-2753	379	1	sugli	sugli	PROPN
ejpam-2753	379	2	ipergruppi	ipergruppi	PROPN
ejpam-2753	379	3	quasicanonici	quasicanonici	PROPN
ejpam-2753	379	4	.	.	PUNCT
ejpam-2753	380	1	atti	atti	PROPN
ejpam-2753	380	2	soc	soc	PROPN
ejpam-2753	380	3	.	.	PUNCT
ejpam-2753	381	1	peloritana	peloritana	PROPN
ejpam-2753	381	2	sci	sci	PROPN
ejpam-2753	381	3	.	.	PROPN
ejpam-2753	381	4	fis	fis	PROPN
ejpam-2753	381	5	.	.	PUNCT
ejpam-2753	382	1	mat	mat	PROPN
ejpam-2753	382	2	.	.	PUNCT
ejpam-2753	382	3	natur	natur	PROPN
ejpam-2753	382	4	.	.	PROPN
ejpam-2753	382	5	,	,	PUNCT
ejpam-2753	382	6	27:9	27:9	NUM
ejpam-2753	382	7	-	-	SYM
ejpam-2753	382	8	17	17	NUM
ejpam-2753	382	9	,	,	PUNCT
ejpam-2753	382	10	1981	1981	NUM
ejpam-2753	382	11	.	.	PUNCT
ejpam-2753	383	1	[	[	X
ejpam-2753	383	2	11	11	NUM
ejpam-2753	383	3	]	]	X
ejpam-2753	383	4	p	p	X
ejpam-2753	383	5	bonansinga	bonansinga	NOUN
ejpam-2753	383	6	and	and	CCONJ
ejpam-2753	383	7	p	p	NOUN
ejpam-2753	383	8	corsini	corsini	PROPN
ejpam-2753	383	9	.	.	PUNCT
ejpam-2753	384	1	sugli	sugli	PROPN
ejpam-2753	384	2	omomorfismi	omomorfismi	NOUN
ejpam-2753	384	3	di	di	X
ejpam-2753	384	4	semi	semi	ADJ
ejpam-2753	384	5	-	-	ADJ
ejpam-2753	384	6	ipergruppi	ipergruppi	ADJ
ejpam-2753	384	7	e	e	PROPN
ejpam-2753	384	8	di	di	X
ejpam-2753	384	9	ipergruppi	ipergruppi	PROPN
ejpam-2753	384	10	.	.	PROPN
ejpam-2753	384	11	boll	boll	PROPN
ejpam-2753	384	12	.	.	PUNCT
ejpam-2753	385	1	un	un	PROPN
ejpam-2753	385	2	.	.	PROPN
ejpam-2753	385	3	mat	mat	PROPN
ejpam-2753	385	4	.	.	PROPN
ejpam-2753	385	5	italy	italy	PROPN
ejpam-2753	385	6	,	,	PUNCT
ejpam-2753	385	7	1	1	NUM
ejpam-2753	385	8	-	-	PUNCT
ejpam-2753	385	9	b:717	b:717	NOUN
ejpam-2753	385	10	-	-	PUNCT
ejpam-2753	385	11	727	727	NUM
ejpam-2753	385	12	,	,	PUNCT
ejpam-2753	385	13	1982	1982	NUM
ejpam-2753	385	14	.	.	PUNCT
ejpam-2753	386	1	[	[	X
ejpam-2753	386	2	12	12	NUM
ejpam-2753	386	3	]	]	X
ejpam-2753	386	4	s	s	PART
ejpam-2753	386	5	comer	comer	NOUN
ejpam-2753	386	6	.	.	PUNCT
ejpam-2753	387	1	extension	extension	NOUN
ejpam-2753	387	2	of	of	ADP
ejpam-2753	387	3	polygroups	polygroup	NOUN
ejpam-2753	387	4	by	by	ADP
ejpam-2753	387	5	polygroups	polygroup	NOUN
ejpam-2753	387	6	and	and	CCONJ
ejpam-2753	387	7	their	their	PRON
ejpam-2753	387	8	representations	representation	NOUN
ejpam-2753	387	9	using	use	VERB
ejpam-2753	387	10	color	color	NOUN
ejpam-2753	387	11	schemes	scheme	NOUN
ejpam-2753	387	12	.	.	PUNCT
ejpam-2753	388	1	lecture	lecture	NOUN
ejpam-2753	388	2	notes	note	NOUN
ejpam-2753	388	3	in	in	ADP
ejpam-2753	388	4	mathematics	mathematic	NOUN
ejpam-2753	388	5	,	,	PUNCT
ejpam-2753	388	6	no	no	INTJ
ejpam-2753	388	7	.	.	NOUN
ejpam-2753	388	8	1004	1004	NUM
ejpam-2753	388	9	,	,	PUNCT
ejpam-2753	388	10	universal	universal	ADJ
ejpam-2753	388	11	algebra	algebra	NOUN
ejpam-2753	388	12	and	and	CCONJ
ejpam-2753	388	13	lattice	lattice	PROPN
ejpam-2753	388	14	theory	theory	NOUN
ejpam-2753	388	15	,	,	PUNCT
ejpam-2753	388	16	91	91	NUM
ejpam-2753	388	17	-	-	SYM
ejpam-2753	388	18	103	103	NUM
ejpam-2753	388	19	,	,	PUNCT
ejpam-2753	388	20	1982	1982	NUM
ejpam-2753	388	21	.	.	PUNCT
ejpam-2753	389	1	[	[	X
ejpam-2753	389	2	13	13	NUM
ejpam-2753	389	3	]	]	SYM
ejpam-2753	389	4	s	s	PART
ejpam-2753	389	5	comer	comer	NOUN
ejpam-2753	389	6	.	.	PUNCT
ejpam-2753	390	1	polygroups	polygroup	NOUN
ejpam-2753	390	2	derived	derive	VERB
ejpam-2753	390	3	from	from	ADP
ejpam-2753	390	4	cogroups	cogroup	NOUN
ejpam-2753	390	5	.	.	PUNCT
ejpam-2753	391	1	j.	j.	PROPN
ejpam-2753	391	2	algebra	algebra	PROPN
ejpam-2753	391	3	,	,	PUNCT
ejpam-2753	391	4	89(2):397	89(2):397	PROPN
ejpam-2753	391	5	-	-	SYM
ejpam-2753	391	6	405	405	NUM
ejpam-2753	391	7	,	,	PUNCT
ejpam-2753	391	8	1984	1984	NUM
ejpam-2753	391	9	.	.	PUNCT
ejpam-2753	392	1	[	[	X
ejpam-2753	392	2	14	14	NUM
ejpam-2753	392	3	]	]	X
ejpam-2753	392	4	p	p	X
ejpam-2753	392	5	corsini	corsini	PROPN
ejpam-2753	392	6	.	.	PUNCT
ejpam-2753	393	1	prolegomena	prolegomenon	NOUN
ejpam-2753	393	2	of	of	ADP
ejpam-2753	393	3	hypergroup	hypergroup	PROPN
ejpam-2753	393	4	theory	theory	NOUN
ejpam-2753	393	5	.	.	PUNCT
ejpam-2753	394	1	second	second	ADJ
ejpam-2753	394	2	edition	edition	PROPN
ejpam-2753	394	3	,	,	PUNCT
ejpam-2753	394	4	aviani	aviani	PROPN
ejpam-2753	394	5	editor	editor	NOUN
ejpam-2753	394	6	,	,	PUNCT
ejpam-2753	394	7	1993	1993	NUM
ejpam-2753	394	8	.	.	PUNCT
ejpam-2753	395	1	[	[	X
ejpam-2753	395	2	15	15	NUM
ejpam-2753	395	3	]	]	X
ejpam-2753	395	4	p	p	X
ejpam-2753	395	5	corsini	corsini	NOUN
ejpam-2753	395	6	and	and	CCONJ
ejpam-2753	395	7	v	v	ADP
ejpam-2753	395	8	leoreanu	leoreanu	NOUN
ejpam-2753	395	9	-	-	PUNCT
ejpam-2753	395	10	fotea	fotea	NOUN
ejpam-2753	395	11	.	.	PUNCT
ejpam-2753	396	1	applications	application	NOUN
ejpam-2753	396	2	of	of	ADP
ejpam-2753	396	3	hyperstructure	hyperstructure	NOUN
ejpam-2753	396	4	theory	theory	PROPN
ejpam-2753	396	5	.	.	PUNCT
ejpam-2753	397	1	kluwer	kluwer	NOUN
ejpam-2753	397	2	academic	academic	ADJ
ejpam-2753	397	3	publishers	publisher	NOUN
ejpam-2753	397	4	,	,	PUNCT
ejpam-2753	397	5	dordrecht	dordrecht	NOUN
ejpam-2753	397	6	,	,	PUNCT
ejpam-2753	397	7	hardbound	hardbound	NOUN
ejpam-2753	397	8	,	,	PUNCT
ejpam-2753	397	9	2003	2003	NUM
ejpam-2753	397	10	.	.	PUNCT
ejpam-2753	398	1	[	[	X
ejpam-2753	398	2	16	16	NUM
ejpam-2753	398	3	]	]	SYM
ejpam-2753	398	4	b	b	X
ejpam-2753	398	5	davvaz	davvaz	NOUN
ejpam-2753	398	6	.	.	PUNCT
ejpam-2753	399	1	polygroup	polygroup	PROPN
ejpam-2753	399	2	theory	theory	NOUN
ejpam-2753	399	3	and	and	CCONJ
ejpam-2753	399	4	related	related	ADJ
ejpam-2753	399	5	systems	system	NOUN
ejpam-2753	399	6	.	.	PUNCT
ejpam-2753	400	1	world	world	NOUN
ejpam-2753	400	2	scientific	scientific	PROPN
ejpam-2753	400	3	,	,	PUNCT
ejpam-2753	400	4	2013	2013	NUM
ejpam-2753	400	5	.	.	PUNCT
ejpam-2753	401	1	[	[	X
ejpam-2753	401	2	17	17	NUM
ejpam-2753	401	3	]	]	SYM
ejpam-2753	401	4	b	b	NOUN
ejpam-2753	401	5	davvaz	davvaz	NOUN
ejpam-2753	401	6	and	and	CCONJ
ejpam-2753	401	7	v	v	ADP
ejpam-2753	401	8	leoreanu	leoreanu	NOUN
ejpam-2753	401	9	-	-	PUNCT
ejpam-2753	401	10	fotea	fotea	NOUN
ejpam-2753	401	11	.	.	PUNCT
ejpam-2753	402	1	hyperring	hyperre	VERB
ejpam-2753	402	2	theory	theory	NOUN
ejpam-2753	402	3	and	and	CCONJ
ejpam-2753	402	4	applications	application	NOUN
ejpam-2753	402	5	.	.	PUNCT
ejpam-2753	403	1	international	international	ADJ
ejpam-2753	403	2	academic	academic	ADJ
ejpam-2753	403	3	press	press	NOUN
ejpam-2753	403	4	,	,	PUNCT
ejpam-2753	403	5	usa	usa	PROPN
ejpam-2753	403	6	,	,	PUNCT
ejpam-2753	403	7	2007	2007	NUM
ejpam-2753	403	8	.	.	PUNCT
ejpam-2753	404	1	[	[	X
ejpam-2753	404	2	18	18	NUM
ejpam-2753	404	3	]	]	X
ejpam-2753	404	4	t	t	PROPN
ejpam-2753	404	5	w	w	PROPN
ejpam-2753	404	6	hungerford	hungerford	PROPN
ejpam-2753	404	7	.	.	PUNCT
ejpam-2753	405	1	algebra	algebra	PROPN
ejpam-2753	405	2	,	,	PUNCT
ejpam-2753	405	3	graduate	graduate	NOUN
ejpam-2753	405	4	texts	text	NOUN
ejpam-2753	405	5	in	in	ADP
ejpam-2753	405	6	mathematics	mathematic	NOUN
ejpam-2753	405	7	.	.	PUNCT
ejpam-2753	406	1	73	73	NUM
ejpam-2753	406	2	.	.	PUNCT
ejpam-2753	406	3	springer	springer	NOUN
ejpam-2753	406	4	-	-	PUNCT
ejpam-2753	406	5	verlag	verlag	PROPN
ejpam-2753	406	6	,	,	PUNCT
ejpam-2753	406	7	new	new	PROPN
ejpam-2753	406	8	york	york	PROPN
ejpam-2753	406	9	-	-	PUNCT
ejpam-2753	406	10	berlin	berlin	PROPN
ejpam-2753	406	11	,	,	PUNCT
ejpam-2753	406	12	1980	1980	NUM
ejpam-2753	406	13	.	.	PUNCT
ejpam-2753	407	1	[	[	X
ejpam-2753	407	2	19	19	NUM
ejpam-2753	407	3	]	]	X
ejpam-2753	407	4	f	f	PROPN
ejpam-2753	407	5	marty	marty	PROPN
ejpam-2753	407	6	.	.	PUNCT
ejpam-2753	408	1	sur	sur	PROPN
ejpam-2753	408	2	une	une	PROPN
ejpam-2753	408	3	gnralisation	gnralisation	PROPN
ejpam-2753	408	4	de	de	X
ejpam-2753	408	5	la	la	X
ejpam-2753	408	6	notion	notion	NOUN
ejpam-2753	408	7	de	de	X
ejpam-2753	408	8	groupe	groupe	PROPN
ejpam-2753	408	9	.	.	PUNCT
ejpam-2753	409	1	8th	8th	ADJ
ejpam-2753	409	2	congrs	congrs	PROPN
ejpam-2753	410	1	des	des	PROPN
ejpam-2753	410	2	mathmaticiens	mathmaticien	NOUN
ejpam-2753	410	3	scandinaves	scandinave	NOUN
ejpam-2753	410	4	,	,	PUNCT
ejpam-2753	410	5	pages	page	NOUN
ejpam-2753	410	6	45	45	NUM
ejpam-2753	410	7	-	-	SYM
ejpam-2753	410	8	49	49	NUM
ejpam-2753	410	9	,	,	PUNCT
ejpam-2753	410	10	stockholm	stockholm	PROPN
ejpam-2753	410	11	,	,	PUNCT
ejpam-2753	410	12	1934	1934	NUM
ejpam-2753	410	13	.	.	PUNCT
ejpam-2753	411	1	[	[	X
ejpam-2753	411	2	20	20	NUM
ejpam-2753	411	3	]	]	X
ejpam-2753	411	4	m	m	NOUN
ejpam-2753	411	5	s	s	NOUN
ejpam-2753	411	6	tallini	tallini	ADJ
ejpam-2753	411	7	.	.	PUNCT
ejpam-2753	412	1	hypervector	hypervector	NOUN
ejpam-2753	412	2	spaces	space	NOUN
ejpam-2753	412	3	.	.	PUNCT
ejpam-2753	413	1	4th	4th	ADJ
ejpam-2753	413	2	aha	aha	INTJ
ejpam-2753	413	3	,	,	PUNCT
ejpam-2753	413	4	world	world	NOUN
ejpam-2753	413	5	scientific	scientific	ADJ
ejpam-2753	413	6	,	,	PUNCT
ejpam-2753	413	7	pages	page	NOUN
ejpam-2753	413	8	167	167	NUM
ejpam-2753	413	9	-	-	SYM
ejpam-2753	413	10	174	174	NUM
ejpam-2753	413	11	,	,	PUNCT
ejpam-2753	413	12	xanthi	xanthi	PROPN
ejpam-2753	413	13	,	,	PUNCT
ejpam-2753	413	14	1990	1990	NUM
ejpam-2753	413	15	.	.	PUNCT
ejpam-2753	414	1	greece	greece	PROPN
ejpam-2753	414	2	.	.	PUNCT
ejpam-2753	415	1	[	[	X
ejpam-2753	415	2	21	21	NUM
ejpam-2753	415	3	]	]	X
ejpam-2753	415	4	m	m	PROPN
ejpam-2753	415	5	s	s	NOUN
ejpam-2753	415	6	tallini	tallini	ADJ
ejpam-2753	415	7	.	.	PUNCT
ejpam-2753	416	1	weak	weak	ADJ
ejpam-2753	416	2	hypervector	hypervector	NOUN
ejpam-2753	416	3	spaces	space	NOUN
ejpam-2753	416	4	and	and	CCONJ
ejpam-2753	416	5	norms	norm	NOUN
ejpam-2753	416	6	in	in	ADP
ejpam-2753	416	7	such	such	ADJ
ejpam-2753	416	8	spaces	space	NOUN
ejpam-2753	416	9	.	.	PUNCT
ejpam-2753	417	1	proceedings	proceeding	NOUN
ejpam-2753	417	2	of	of	ADP
ejpam-2753	417	3	the	the	DET
ejpam-2753	417	4	fifth	fifth	ADJ
ejpam-2753	417	5	international	international	ADJ
ejpam-2753	417	6	congress	congress	PROPN
ejpam-2753	417	7	on	on	ADP
ejpam-2753	417	8	algebraic	algebraic	PROPN
ejpam-2753	417	9	hyperstructures	hyperstructure	NOUN
ejpam-2753	417	10	and	and	CCONJ
ejpam-2753	417	11	applications	application	NOUN
ejpam-2753	417	12	,	,	PUNCT
ejpam-2753	417	13	hadronic	hadronic	ADJ
ejpam-2753	417	14	press	press	NOUN
ejpam-2753	417	15	,	,	PUNCT
ejpam-2753	417	16	pages	page	NOUN
ejpam-2753	417	17	199	199	NUM
ejpam-2753	417	18	-	-	SYM
ejpam-2753	417	19	206	206	NUM
ejpam-2753	417	20	,	,	PUNCT
ejpam-2753	417	21	jasi	jasi	PROPN
ejpam-2753	417	22	,	,	PUNCT
ejpam-2753	417	23	1994	1994	NUM
ejpam-2753	417	24	.	.	PUNCT
ejpam-2753	418	1	rumania	rumania	PROPN
ejpam-2753	418	2	.	.	PUNCT
ejpam-2753	419	1	references	reference	NOUN
ejpam-2753	419	2	716	716	NUM
ejpam-2753	420	1	[	[	X
ejpam-2753	420	2	22	22	NUM
ejpam-2753	420	3	]	]	PUNCT
ejpam-2753	420	4	m	m	PROPN
ejpam-2753	420	5	s	s	NOUN
ejpam-2753	420	6	tallini	tallini	NOUN
ejpam-2753	420	7	.	.	PUNCT
ejpam-2753	421	1	dimensions	dimension	NOUN
ejpam-2753	421	2	in	in	ADP
ejpam-2753	421	3	multivalued	multivalued	ADJ
ejpam-2753	421	4	algebraic	algebraic	ADJ
ejpam-2753	421	5	structures	structure	NOUN
ejpam-2753	421	6	.	.	PUNCT
ejpam-2753	422	1	italian	italian	ADJ
ejpam-2753	422	2	journal	journal	NOUN
ejpam-2753	422	3	of	of	ADP
ejpam-2753	422	4	pure	pure	ADJ
ejpam-2753	422	5	and	and	CCONJ
ejpam-2753	422	6	applied	applied	ADJ
ejpam-2753	422	7	mathematics	mathematic	NOUN
ejpam-2753	422	8	,	,	PUNCT
ejpam-2753	422	9	1:51	1:51	NUM
ejpam-2753	422	10	-	-	SYM
ejpam-2753	422	11	64	64	NUM
ejpam-2753	422	12	,	,	PUNCT
ejpam-2753	422	13	1997	1997	NUM
ejpam-2753	422	14	.	.	PUNCT
ejpam-2753	423	1	[	[	X
ejpam-2753	423	2	23	23	NUM
ejpam-2753	423	3	]	]	X
ejpam-2753	423	4	t	t	PROPN
ejpam-2753	423	5	vougiouklis	vougioukli	VERB
ejpam-2753	423	6	.	.	PUNCT
ejpam-2753	424	1	hyperstructures	hyperstructure	NOUN
ejpam-2753	424	2	and	and	CCONJ
ejpam-2753	424	3	their	their	PRON
ejpam-2753	424	4	representations	representation	NOUN
ejpam-2753	424	5	.	.	PUNCT
ejpam-2753	425	1	hadronic	hadronic	ADJ
ejpam-2753	425	2	press	press	PROPN
ejpam-2753	425	3	,	,	PUNCT
ejpam-2753	425	4	inc	inc	PROPN
ejpam-2753	425	5	.	.	PROPN
ejpam-2753	425	6	,	,	PUNCT
ejpam-2753	425	7	115	115	NUM
ejpam-2753	425	8	,	,	PUNCT
ejpam-2753	425	9	palm	palm	NOUN
ejpam-2753	425	10	harber	harber	PROPN
ejpam-2753	425	11	,	,	PUNCT
ejpam-2753	425	12	usa	usa	PROPN
ejpam-2753	425	13	,	,	PUNCT
ejpam-2753	425	14	1994	1994	NUM
ejpam-2753	425	15	.	.	PUNCT