id	sid	tid	token	lemma	pos
ejpam-2674	1	1	european	european	PROPN
ejpam-2674	1	2	journal	journal	PROPN
ejpam-2674	1	3	of	of	ADP
ejpam-2674	1	4	pure	pure	ADJ
ejpam-2674	1	5	and	and	CCONJ
ejpam-2674	1	6	applied	apply	VERB
ejpam-2674	1	7	mathematics	mathematic	NOUN
ejpam-2674	1	8	vol	vol	NOUN
ejpam-2674	1	9	.	.	PUNCT
ejpam-2674	2	1	11	11	NUM
ejpam-2674	2	2	,	,	PUNCT
ejpam-2674	2	3	no	no	INTJ
ejpam-2674	2	4	.	.	NOUN
ejpam-2674	2	5	2	2	NUM
ejpam-2674	2	6	,	,	PUNCT
ejpam-2674	2	7	2018	2018	NUM
ejpam-2674	2	8	,	,	PUNCT
ejpam-2674	2	9	505	505	NUM
ejpam-2674	2	10	-	-	SYM
ejpam-2674	2	11	516	516	NUM
ejpam-2674	2	12	issn	issn	PROPN
ejpam-2674	2	13	1307	1307	NUM
ejpam-2674	2	14	-	-	SYM
ejpam-2674	2	15	5543	5543	NUM
ejpam-2674	2	16	–	–	PUNCT
ejpam-2674	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2674	2	18	published	publish	VERB
ejpam-2674	2	19	by	by	ADP
ejpam-2674	2	20	new	new	PROPN
ejpam-2674	2	21	york	york	PROPN
ejpam-2674	2	22	business	business	PROPN
ejpam-2674	2	23	global	global	ADJ
ejpam-2674	2	24	near	near	ADP
ejpam-2674	2	25	ideals	ideal	NOUN
ejpam-2674	2	26	in	in	ADP
ejpam-2674	2	27	near	near	ADP
ejpam-2674	2	28	semigroups	semigroup	NOUN
ejpam-2674	2	29	nurettin	nurettin	PROPN
ejpam-2674	2	30	bağırmaz	bağırmaz	PROPN
ejpam-2674	2	31	mardin	mardin	PROPN
ejpam-2674	2	32	artuklu	artuklu	PROPN
ejpam-2674	2	33	university	university	PROPN
ejpam-2674	2	34	,	,	PUNCT
ejpam-2674	2	35	mardin	mardin	PROPN
ejpam-2674	2	36	,	,	PUNCT
ejpam-2674	2	37	turkey	turkey	NOUN
ejpam-2674	2	38	abstract	abstract	NOUN
ejpam-2674	2	39	.	.	PUNCT
ejpam-2674	3	1	in	in	ADP
ejpam-2674	3	2	this	this	DET
ejpam-2674	3	3	paper	paper	NOUN
ejpam-2674	3	4	,	,	PUNCT
ejpam-2674	3	5	we	we	PRON
ejpam-2674	3	6	introduced	introduce	VERB
ejpam-2674	3	7	the	the	DET
ejpam-2674	3	8	notion	notion	NOUN
ejpam-2674	3	9	of	of	ADP
ejpam-2674	3	10	near	near	ADJ
ejpam-2674	3	11	subsemigroups	subsemigroup	NOUN
ejpam-2674	3	12	,	,	PUNCT
ejpam-2674	3	13	near	near	ADP
ejpam-2674	3	14	ideals	ideal	NOUN
ejpam-2674	3	15	,	,	PUNCT
ejpam-2674	3	16	near	near	ADP
ejpam-2674	3	17	biideals	biideal	NOUN
ejpam-2674	3	18	and	and	CCONJ
ejpam-2674	3	19	homomorphisms	homomorphism	NOUN
ejpam-2674	3	20	of	of	ADP
ejpam-2674	3	21	near	near	ADJ
ejpam-2674	3	22	semigroups	semigroup	NOUN
ejpam-2674	3	23	on	on	ADP
ejpam-2674	3	24	near	near	ADJ
ejpam-2674	3	25	approximation	approximation	NOUN
ejpam-2674	3	26	spaces	space	NOUN
ejpam-2674	3	27	.	.	PUNCT
ejpam-2674	4	1	then	then	ADV
ejpam-2674	4	2	we	we	PRON
ejpam-2674	4	3	give	give	VERB
ejpam-2674	4	4	some	some	DET
ejpam-2674	4	5	properties	property	NOUN
ejpam-2674	4	6	of	of	ADP
ejpam-2674	4	7	these	these	DET
ejpam-2674	4	8	near	near	ADJ
ejpam-2674	4	9	structures	structure	NOUN
ejpam-2674	4	10	.	.	PUNCT
ejpam-2674	5	1	2010	2010	NUM
ejpam-2674	5	2	mathematics	mathematic	NOUN
ejpam-2674	5	3	subject	subject	NOUN
ejpam-2674	5	4	classifications	classification	NOUN
ejpam-2674	5	5	:	:	PUNCT
ejpam-2674	5	6	03e99	03e99	NUM
ejpam-2674	5	7	,	,	PUNCT
ejpam-2674	5	8	20m99	20m99	NUM
ejpam-2674	5	9	key	key	ADJ
ejpam-2674	5	10	words	word	NOUN
ejpam-2674	5	11	and	and	CCONJ
ejpam-2674	5	12	phrases	phrase	NOUN
ejpam-2674	5	13	:	:	PUNCT
ejpam-2674	5	14	near	near	ADP
ejpam-2674	5	15	set	set	NOUN
ejpam-2674	5	16	,	,	PUNCT
ejpam-2674	5	17	near	near	ADP
ejpam-2674	5	18	semigroup	semigroup	PROPN
ejpam-2674	5	19	,	,	PUNCT
ejpam-2674	5	20	near	near	ADP
ejpam-2674	5	21	ideal	ideal	ADJ
ejpam-2674	5	22	,	,	PUNCT
ejpam-2674	5	23	near	near	ADP
ejpam-2674	5	24	bi	bi	NOUN
ejpam-2674	5	25	-	-	NOUN
ejpam-2674	5	26	ideal	ideal	ADJ
ejpam-2674	5	27	,	,	PUNCT
ejpam-2674	5	28	homomorphism	homomorphism	PROPN
ejpam-2674	5	29	1	1	X
ejpam-2674	5	30	.	.	X
ejpam-2674	5	31	introduction	introduction	NOUN
ejpam-2674	5	32	rough	rough	ADJ
ejpam-2674	5	33	sets	set	NOUN
ejpam-2674	5	34	were	be	AUX
ejpam-2674	5	35	introduced	introduce	VERB
ejpam-2674	5	36	by	by	ADP
ejpam-2674	5	37	z.	z.	PROPN
ejpam-2674	5	38	pawlak	pawlak	PROPN
ejpam-2674	5	39	in	in	ADP
ejpam-2674	5	40	his	his	PRON
ejpam-2674	5	41	paper	paper	NOUN
ejpam-2674	6	1	[	[	X
ejpam-2674	6	2	16	16	NUM
ejpam-2674	6	3	]	]	PUNCT
ejpam-2674	6	4	.	.	PUNCT
ejpam-2674	7	1	algebraic	algebraic	ADJ
ejpam-2674	7	2	structures	structure	NOUN
ejpam-2674	7	3	of	of	ADP
ejpam-2674	7	4	rough	rough	ADJ
ejpam-2674	7	5	sets	set	NOUN
ejpam-2674	7	6	have	have	AUX
ejpam-2674	7	7	been	be	AUX
ejpam-2674	7	8	studied	study	VERB
ejpam-2674	7	9	by	by	ADP
ejpam-2674	7	10	many	many	ADJ
ejpam-2674	7	11	authors	author	NOUN
ejpam-2674	7	12	,	,	PUNCT
ejpam-2674	7	13	for	for	ADP
ejpam-2674	7	14	example	example	NOUN
ejpam-2674	7	15	,	,	PUNCT
ejpam-2674	7	16	bonikowaski	bonikowaski	PRON
ejpam-2674	8	1	[	[	X
ejpam-2674	8	2	4	4	NUM
ejpam-2674	8	3	]	]	PUNCT
ejpam-2674	8	4	,	,	PUNCT
ejpam-2674	8	5	iwinski	iwinski	VERB
ejpam-2674	9	1	[	[	X
ejpam-2674	9	2	8	8	NUM
ejpam-2674	9	3	]	]	PUNCT
ejpam-2674	9	4	,	,	PUNCT
ejpam-2674	9	5	and	and	CCONJ
ejpam-2674	9	6	pomykala	pomykala	VERB
ejpam-2674	9	7	and	and	CCONJ
ejpam-2674	9	8	pomykala	pomykala	NOUN
ejpam-2674	10	1	[	[	X
ejpam-2674	10	2	24	24	NUM
ejpam-2674	10	3	]	]	PUNCT
ejpam-2674	10	4	.	.	PUNCT
ejpam-2674	11	1	in	in	ADP
ejpam-2674	11	2	1994	1994	NUM
ejpam-2674	11	3	,	,	PUNCT
ejpam-2674	11	4	biswas	biswas	PROPN
ejpam-2674	11	5	and	and	CCONJ
ejpam-2674	11	6	nanda	nanda	ADV
ejpam-2674	11	7	[	[	X
ejpam-2674	11	8	3	3	X
ejpam-2674	11	9	]	]	PUNCT
ejpam-2674	11	10	introduced	introduce	VERB
ejpam-2674	11	11	the	the	DET
ejpam-2674	11	12	notion	notion	NOUN
ejpam-2674	11	13	of	of	ADP
ejpam-2674	11	14	rough	rough	ADJ
ejpam-2674	11	15	group	group	NOUN
ejpam-2674	11	16	and	and	CCONJ
ejpam-2674	11	17	rough	rough	ADJ
ejpam-2674	11	18	subgroups	subgroup	NOUN
ejpam-2674	11	19	that	that	SCONJ
ejpam-2674	11	20	their	their	PRON
ejpam-2674	11	21	notion	notion	NOUN
ejpam-2674	11	22	depends	depend	VERB
ejpam-2674	11	23	on	on	ADP
ejpam-2674	11	24	the	the	DET
ejpam-2674	11	25	upper	upper	ADJ
ejpam-2674	11	26	approximation	approximation	NOUN
ejpam-2674	11	27	and	and	CCONJ
ejpam-2674	11	28	does	do	AUX
ejpam-2674	11	29	not	not	PART
ejpam-2674	11	30	depend	depend	VERB
ejpam-2674	11	31	on	on	ADP
ejpam-2674	11	32	the	the	DET
ejpam-2674	11	33	lower	low	ADJ
ejpam-2674	11	34	approximation	approximation	NOUN
ejpam-2674	11	35	.	.	PUNCT
ejpam-2674	12	1	miao	miao	NOUN
ejpam-2674	12	2	et	et	PROPN
ejpam-2674	12	3	al	al	PROPN
ejpam-2674	12	4	.	.	PUNCT
ejpam-2674	13	1	[	[	X
ejpam-2674	13	2	14	14	NUM
ejpam-2674	13	3	]	]	PUNCT
ejpam-2674	13	4	improve	improve	VERB
ejpam-2674	13	5	definitions	definition	NOUN
ejpam-2674	13	6	of	of	ADP
ejpam-2674	13	7	rough	rough	ADJ
ejpam-2674	13	8	group	group	NOUN
ejpam-2674	13	9	and	and	CCONJ
ejpam-2674	13	10	rough	rough	ADJ
ejpam-2674	13	11	subgroup	subgroup	NOUN
ejpam-2674	13	12	,	,	PUNCT
ejpam-2674	13	13	and	and	CCONJ
ejpam-2674	13	14	prove	prove	VERB
ejpam-2674	13	15	their	their	PRON
ejpam-2674	13	16	new	new	ADJ
ejpam-2674	13	17	properties	property	NOUN
ejpam-2674	13	18	.	.	PUNCT
ejpam-2674	14	1	on	on	ADP
ejpam-2674	14	2	the	the	DET
ejpam-2674	14	3	other	other	ADJ
ejpam-2674	14	4	hand	hand	NOUN
ejpam-2674	14	5	,	,	PUNCT
ejpam-2674	14	6	kuroki	kuroki	PROPN
ejpam-2674	14	7	and	and	CCONJ
ejpam-2674	14	8	wang	wang	PROPN
ejpam-2674	15	1	[	[	X
ejpam-2674	15	2	11	11	NUM
ejpam-2674	15	3	]	]	PUNCT
ejpam-2674	15	4	presented	present	VERB
ejpam-2674	15	5	some	some	DET
ejpam-2674	15	6	properties	property	NOUN
ejpam-2674	15	7	of	of	ADP
ejpam-2674	15	8	the	the	DET
ejpam-2674	15	9	lower	low	ADJ
ejpam-2674	15	10	and	and	CCONJ
ejpam-2674	15	11	upper	upper	ADJ
ejpam-2674	15	12	approximations	approximation	NOUN
ejpam-2674	15	13	with	with	ADP
ejpam-2674	15	14	respect	respect	NOUN
ejpam-2674	15	15	to	to	ADP
ejpam-2674	15	16	the	the	DET
ejpam-2674	15	17	normal	normal	ADJ
ejpam-2674	15	18	subgroups	subgroup	NOUN
ejpam-2674	15	19	in	in	ADP
ejpam-2674	15	20	1996	1996	NUM
ejpam-2674	15	21	.	.	PUNCT
ejpam-2674	16	1	in	in	ADP
ejpam-2674	16	2	addition	addition	NOUN
ejpam-2674	16	3	,	,	PUNCT
ejpam-2674	16	4	some	some	DET
ejpam-2674	16	5	properties	property	NOUN
ejpam-2674	16	6	of	of	ADP
ejpam-2674	16	7	the	the	DET
ejpam-2674	16	8	lower	low	ADJ
ejpam-2674	16	9	and	and	CCONJ
ejpam-2674	16	10	the	the	DET
ejpam-2674	16	11	upper	upper	ADJ
ejpam-2674	16	12	approximations	approximation	NOUN
ejpam-2674	16	13	with	with	ADP
ejpam-2674	16	14	respect	respect	NOUN
ejpam-2674	16	15	to	to	ADP
ejpam-2674	16	16	the	the	DET
ejpam-2674	16	17	normal	normal	ADJ
ejpam-2674	16	18	subgroups	subgroup	NOUN
ejpam-2674	16	19	were	be	AUX
ejpam-2674	16	20	studied	study	VERB
ejpam-2674	16	21	in	in	ADP
ejpam-2674	16	22	[	[	X
ejpam-2674	16	23	5	5	NUM
ejpam-2674	16	24	,	,	PUNCT
ejpam-2674	16	25	13	13	NUM
ejpam-2674	16	26	,	,	PUNCT
ejpam-2674	16	27	26	26	NUM
ejpam-2674	16	28	–	–	PUNCT
ejpam-2674	16	29	28	28	NUM
ejpam-2674	16	30	]	]	PUNCT
ejpam-2674	16	31	.	.	PUNCT
ejpam-2674	17	1	also	also	ADV
ejpam-2674	17	2	,	,	PUNCT
ejpam-2674	17	3	kuroki	kuroki	X
ejpam-2674	17	4	[	[	X
ejpam-2674	17	5	12	12	NUM
ejpam-2674	17	6	]	]	PUNCT
ejpam-2674	17	7	,	,	PUNCT
ejpam-2674	17	8	introduced	introduce	VERB
ejpam-2674	17	9	the	the	DET
ejpam-2674	17	10	notion	notion	NOUN
ejpam-2674	17	11	of	of	ADP
ejpam-2674	17	12	a	a	DET
ejpam-2674	17	13	rough	rough	ADJ
ejpam-2674	17	14	ideal	ideal	NOUN
ejpam-2674	17	15	in	in	ADP
ejpam-2674	17	16	a	a	DET
ejpam-2674	17	17	semigroup	semigroup	NOUN
ejpam-2674	17	18	.	.	PUNCT
ejpam-2674	18	1	davvaz	davvaz	NOUN
ejpam-2674	19	1	[	[	X
ejpam-2674	19	2	6	6	NUM
ejpam-2674	19	3	]	]	PUNCT
ejpam-2674	19	4	,	,	PUNCT
ejpam-2674	19	5	introduced	introduce	VERB
ejpam-2674	19	6	the	the	DET
ejpam-2674	19	7	notion	notion	NOUN
ejpam-2674	19	8	of	of	ADP
ejpam-2674	19	9	rough	rough	ADJ
ejpam-2674	19	10	subring	subring	NOUN
ejpam-2674	19	11	with	with	ADP
ejpam-2674	19	12	respect	respect	NOUN
ejpam-2674	19	13	to	to	ADP
ejpam-2674	19	14	an	an	DET
ejpam-2674	19	15	ideal	ideal	NOUN
ejpam-2674	19	16	of	of	ADP
ejpam-2674	19	17	a	a	DET
ejpam-2674	19	18	ring	ring	NOUN
ejpam-2674	19	19	.	.	PUNCT
ejpam-2674	20	1	xiao	xiao	PROPN
ejpam-2674	20	2	and	and	CCONJ
ejpam-2674	20	3	zhang	zhang	PROPN
ejpam-2674	21	1	[	[	X
ejpam-2674	21	2	30	30	NUM
ejpam-2674	21	3	]	]	PUNCT
ejpam-2674	21	4	,	,	PUNCT
ejpam-2674	21	5	studied	study	VERB
ejpam-2674	21	6	the	the	DET
ejpam-2674	21	7	notions	notion	NOUN
ejpam-2674	21	8	of	of	ADP
ejpam-2674	21	9	rough	rough	ADJ
ejpam-2674	21	10	prime	prime	ADJ
ejpam-2674	21	11	ideals	ideal	NOUN
ejpam-2674	21	12	and	and	CCONJ
ejpam-2674	21	13	rough	rough	ADJ
ejpam-2674	21	14	fuzzy	fuzzy	ADJ
ejpam-2674	21	15	prime	prime	ADJ
ejpam-2674	21	16	ideals	ideal	NOUN
ejpam-2674	21	17	in	in	ADP
ejpam-2674	21	18	a	a	DET
ejpam-2674	21	19	semigroup	semigroup	NOUN
ejpam-2674	21	20	.	.	PUNCT
ejpam-2674	22	1	bağırmaz	bağırmaz	NOUN
ejpam-2674	22	2	and	and	CCONJ
ejpam-2674	22	3	özcan	özcan	PROPN
ejpam-2674	23	1	[	[	X
ejpam-2674	23	2	1	1	NUM
ejpam-2674	23	3	]	]	PUNCT
ejpam-2674	23	4	,	,	PUNCT
ejpam-2674	23	5	studied	study	VERB
ejpam-2674	23	6	the	the	DET
ejpam-2674	23	7	notion	notion	NOUN
ejpam-2674	23	8	of	of	ADP
ejpam-2674	23	9	rough	rough	ADJ
ejpam-2674	23	10	semigroup	semigroup	NOUN
ejpam-2674	23	11	on	on	ADP
ejpam-2674	23	12	approximation	approximation	NOUN
ejpam-2674	23	13	space	space	NOUN
ejpam-2674	23	14	.	.	PUNCT
ejpam-2674	24	1	moreover	moreover	ADV
ejpam-2674	24	2	,	,	PUNCT
ejpam-2674	24	3	bağırmaz	bağırmaz	NOUN
ejpam-2674	25	1	[	[	X
ejpam-2674	25	2	2	2	NUM
ejpam-2674	25	3	]	]	PUNCT
ejpam-2674	25	4	,	,	PUNCT
ejpam-2674	25	5	investigated	investigate	VERB
ejpam-2674	25	6	rough	rough	ADJ
ejpam-2674	25	7	prime	prime	ADJ
ejpam-2674	25	8	ideals	ideal	NOUN
ejpam-2674	25	9	on	on	ADP
ejpam-2674	25	10	approximation	approximation	NOUN
ejpam-2674	25	11	spaces	space	NOUN
ejpam-2674	25	12	.	.	PUNCT
ejpam-2674	26	1	near	near	ADP
ejpam-2674	26	2	sets	set	NOUN
ejpam-2674	26	3	were	be	AUX
ejpam-2674	26	4	introduced	introduce	VERB
ejpam-2674	26	5	by	by	ADP
ejpam-2674	26	6	peters	peters	PROPN
ejpam-2674	26	7	[	[	X
ejpam-2674	26	8	17	17	NUM
ejpam-2674	26	9	]	]	PUNCT
ejpam-2674	26	10	on	on	ADP
ejpam-2674	26	11	the	the	DET
ejpam-2674	26	12	basis	basis	NOUN
ejpam-2674	26	13	of	of	ADP
ejpam-2674	26	14	a	a	DET
ejpam-2674	26	15	generalization	generalization	NOUN
ejpam-2674	26	16	of	of	ADP
ejpam-2674	26	17	rough	rough	ADJ
ejpam-2674	26	18	set	set	NOUN
ejpam-2674	26	19	theory	theory	NOUN
ejpam-2674	26	20	.	.	PUNCT
ejpam-2674	27	1	the	the	DET
ejpam-2674	27	2	algebraic	algebraic	ADJ
ejpam-2674	27	3	properties	property	NOUN
ejpam-2674	27	4	of	of	ADP
ejpam-2674	27	5	near	near	ADJ
ejpam-2674	27	6	sets	set	NOUN
ejpam-2674	27	7	are	be	AUX
ejpam-2674	27	8	described	describe	VERB
ejpam-2674	27	9	in	in	ADP
ejpam-2674	27	10	[	[	X
ejpam-2674	27	11	19	19	NUM
ejpam-2674	27	12	]	]	PUNCT
ejpam-2674	27	13	.	.	PUNCT
ejpam-2674	28	1	recent	recent	ADJ
ejpam-2674	28	2	work	work	NOUN
ejpam-2674	28	3	has	have	AUX
ejpam-2674	28	4	considered	consider	VERB
ejpam-2674	28	5	near	near	ADP
ejpam-2674	28	6	groups	group	NOUN
ejpam-2674	28	7	[	[	X
ejpam-2674	28	8	9	9	NUM
ejpam-2674	28	9	]	]	PUNCT
ejpam-2674	28	10	and	and	CCONJ
ejpam-2674	28	11	near	near	ADP
ejpam-2674	28	12	semigroups	semigroup	NOUN
ejpam-2674	28	13	[	[	X
ejpam-2674	28	14	10	10	NUM
ejpam-2674	28	15	]	]	PUNCT
ejpam-2674	28	16	.	.	PUNCT
ejpam-2674	29	1	the	the	DET
ejpam-2674	29	2	fundamental	fundamental	ADJ
ejpam-2674	29	3	idea	idea	NOUN
ejpam-2674	29	4	of	of	ADP
ejpam-2674	29	5	near	near	ADP
ejpam-2674	29	6	set	set	ADJ
ejpam-2674	29	7	theory	theory	NOUN
ejpam-2674	29	8	is	be	AUX
ejpam-2674	29	9	object	object	NOUN
ejpam-2674	29	10	description	description	NOUN
ejpam-2674	29	11	and	and	CCONJ
ejpam-2674	29	12	classification	classification	NOUN
ejpam-2674	29	13	according	accord	VERB
ejpam-2674	29	14	to	to	ADP
ejpam-2674	29	15	perceptual	perceptual	ADJ
ejpam-2674	29	16	knowledge	knowledge	NOUN
ejpam-2674	29	17	.	.	PUNCT
ejpam-2674	30	1	it	it	PRON
ejpam-2674	30	2	is	be	AUX
ejpam-2674	30	3	supposed	suppose	VERB
ejpam-2674	30	4	that	that	SCONJ
ejpam-2674	30	5	perceptual	perceptual	ADJ
ejpam-2674	30	6	knowledge	knowledge	NOUN
ejpam-2674	30	7	about	about	ADP
ejpam-2674	30	8	objects	object	NOUN
ejpam-2674	30	9	is	be	AUX
ejpam-2674	30	10	always	always	ADV
ejpam-2674	30	11	given	give	VERB
ejpam-2674	30	12	with	with	ADP
ejpam-2674	30	13	respect	respect	NOUN
ejpam-2674	30	14	to	to	ADP
ejpam-2674	30	15	probe	probe	NOUN
ejpam-2674	30	16	functions	function	NOUN
ejpam-2674	30	17	,	,	PUNCT
ejpam-2674	30	18	i.e.	i.e.	X
ejpam-2674	30	19	,	,	PUNCT
ejpam-2674	30	20	real	real	ADV
ejpam-2674	30	21	-	-	PUNCT
ejpam-2674	30	22	valued	value	VERB
ejpam-2674	30	23	functions	function	NOUN
ejpam-2674	30	24	which	which	PRON
ejpam-2674	30	25	represent	represent	VERB
ejpam-2674	30	26	features	feature	NOUN
ejpam-2674	30	27	of	of	ADP
ejpam-2674	30	28	a	a	DET
ejpam-2674	30	29	physical	physical	ADJ
ejpam-2674	30	30	object	object	NOUN
ejpam-2674	30	31	[	[	X
ejpam-2674	30	32	7	7	NUM
ejpam-2674	30	33	,	,	PUNCT
ejpam-2674	30	34	15	15	NUM
ejpam-2674	30	35	,	,	PUNCT
ejpam-2674	30	36	20	20	NUM
ejpam-2674	30	37	–	–	PUNCT
ejpam-2674	30	38	23	23	NUM
ejpam-2674	30	39	,	,	PUNCT
ejpam-2674	30	40	25	25	NUM
ejpam-2674	30	41	,	,	PUNCT
ejpam-2674	30	42	29	29	NUM
ejpam-2674	30	43	]	]	PUNCT
ejpam-2674	30	44	.	.	PUNCT
ejpam-2674	31	1	email	email	NOUN
ejpam-2674	31	2	address	address	NOUN
ejpam-2674	31	3	:	:	PUNCT
ejpam-2674	31	4	nurettinbagirmaz@artuklu.edu.tr	nurettinbagirmaz@artuklu.edu.tr	PROPN
ejpam-2674	31	5	(	(	PUNCT
ejpam-2674	31	6	n.	n.	PROPN
ejpam-2674	31	7	bağırmaz	bağırmaz	NOUN
ejpam-2674	31	8	)	)	PUNCT
ejpam-2674	31	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2674	32	1	505	505	NUM
ejpam-2674	32	2	c	c	X
ejpam-2674	32	3	©	©	PROPN
ejpam-2674	32	4	2018	2018	NUM
ejpam-2674	32	5	ejpam	ejpam	VERB
ejpam-2674	32	6	all	all	DET
ejpam-2674	32	7	rights	right	NOUN
ejpam-2674	32	8	reserved	reserve	VERB
ejpam-2674	32	9	.	.	PUNCT
ejpam-2674	33	1	n.	n.	NOUN
ejpam-2674	33	2	bağırmaz	bağırmaz	PROPN
ejpam-2674	33	3	/	/	SYM
ejpam-2674	33	4	eur	eur	PROPN
ejpam-2674	33	5	.	.	PUNCT
ejpam-2674	34	1	j.	j.	PROPN
ejpam-2674	34	2	pure	pure	PROPN
ejpam-2674	34	3	appl	appl	PROPN
ejpam-2674	34	4	.	.	PROPN
ejpam-2674	34	5	math	math	PROPN
ejpam-2674	34	6	,	,	PUNCT
ejpam-2674	34	7	11	11	NUM
ejpam-2674	34	8	(	(	PUNCT
ejpam-2674	34	9	2	2	NUM
ejpam-2674	34	10	)	)	PUNCT
ejpam-2674	34	11	(	(	PUNCT
ejpam-2674	34	12	2018	2018	NUM
ejpam-2674	34	13	)	)	PUNCT
ejpam-2674	34	14	,	,	PUNCT
ejpam-2674	34	15	505	505	NUM
ejpam-2674	34	16	-	-	SYM
ejpam-2674	34	17	516	516	NUM
ejpam-2674	34	18	506	506	NUM
ejpam-2674	34	19	the	the	DET
ejpam-2674	34	20	main	main	ADJ
ejpam-2674	34	21	purpose	purpose	NOUN
ejpam-2674	34	22	of	of	ADP
ejpam-2674	34	23	this	this	DET
ejpam-2674	34	24	paper	paper	NOUN
ejpam-2674	34	25	is	be	AUX
ejpam-2674	34	26	to	to	PART
ejpam-2674	34	27	introduce	introduce	VERB
ejpam-2674	34	28	near	near	ADJ
ejpam-2674	34	29	ideals	ideal	NOUN
ejpam-2674	34	30	and	and	CCONJ
ejpam-2674	34	31	give	give	VERB
ejpam-2674	34	32	some	some	DET
ejpam-2674	34	33	properties	property	NOUN
ejpam-2674	34	34	of	of	ADP
ejpam-2674	34	35	such	such	ADJ
ejpam-2674	34	36	ideals	ideal	NOUN
ejpam-2674	34	37	on	on	ADP
ejpam-2674	34	38	nearness	nearness	NOUN
ejpam-2674	34	39	approximation	approximation	NOUN
ejpam-2674	34	40	spaces	space	NOUN
ejpam-2674	34	41	.	.	PUNCT
ejpam-2674	35	1	finally	finally	ADV
ejpam-2674	35	2	,	,	PUNCT
ejpam-2674	35	3	near	near	ADP
ejpam-2674	35	4	image	image	NOUN
ejpam-2674	35	5	and	and	CCONJ
ejpam-2674	35	6	near	near	ADJ
ejpam-2674	35	7	inverse	inverse	ADJ
ejpam-2674	35	8	image	image	NOUN
ejpam-2674	35	9	of	of	ADP
ejpam-2674	35	10	near	near	ADJ
ejpam-2674	35	11	ideal	ideal	NOUN
ejpam-2674	35	12	are	be	AUX
ejpam-2674	35	13	discussed	discuss	VERB
ejpam-2674	35	14	.	.	PUNCT
ejpam-2674	36	1	we	we	PRON
ejpam-2674	36	2	introduced	introduce	VERB
ejpam-2674	36	3	the	the	DET
ejpam-2674	36	4	notion	notion	NOUN
ejpam-2674	36	5	of	of	ADP
ejpam-2674	36	6	near	near	ADJ
ejpam-2674	36	7	ideal	ideal	NOUN
ejpam-2674	36	8	that	that	SCONJ
ejpam-2674	36	9	our	our	PRON
ejpam-2674	36	10	notion	notion	NOUN
ejpam-2674	36	11	depends	depend	VERB
ejpam-2674	36	12	on	on	ADP
ejpam-2674	36	13	the	the	DET
ejpam-2674	36	14	upper	upper	ADJ
ejpam-2674	36	15	approximation	approximation	NOUN
ejpam-2674	36	16	and	and	CCONJ
ejpam-2674	36	17	does	do	AUX
ejpam-2674	36	18	not	not	PART
ejpam-2674	36	19	depend	depend	VERB
ejpam-2674	36	20	on	on	ADP
ejpam-2674	36	21	the	the	DET
ejpam-2674	36	22	lower	low	ADJ
ejpam-2674	36	23	approximation	approximation	NOUN
ejpam-2674	36	24	.	.	PUNCT
ejpam-2674	37	1	so	so	ADV
ejpam-2674	37	2	,	,	PUNCT
ejpam-2674	37	3	our	our	PRON
ejpam-2674	37	4	definition	definition	NOUN
ejpam-2674	37	5	of	of	ADP
ejpam-2674	37	6	near	near	ADJ
ejpam-2674	37	7	ideal	ideal	NOUN
ejpam-2674	37	8	is	be	AUX
ejpam-2674	37	9	similar	similar	ADJ
ejpam-2674	37	10	to	to	ADP
ejpam-2674	37	11	the	the	DET
ejpam-2674	37	12	definition	definition	NOUN
ejpam-2674	37	13	of	of	ADP
ejpam-2674	37	14	rough	rough	ADJ
ejpam-2674	37	15	ideal	ideal	NOUN
ejpam-2674	38	1	[	[	X
ejpam-2674	38	2	1	1	NUM
ejpam-2674	38	3	]	]	PUNCT
ejpam-2674	38	4	.	.	PUNCT
ejpam-2674	39	1	2	2	X
ejpam-2674	39	2	.	.	X
ejpam-2674	39	3	preliminaries	preliminary	NOUN
ejpam-2674	39	4	in	in	ADP
ejpam-2674	39	5	this	this	DET
ejpam-2674	39	6	section	section	NOUN
ejpam-2674	39	7	,	,	PUNCT
ejpam-2674	39	8	we	we	PRON
ejpam-2674	39	9	will	will	AUX
ejpam-2674	39	10	give	give	VERB
ejpam-2674	39	11	some	some	DET
ejpam-2674	39	12	definitions	definition	NOUN
ejpam-2674	39	13	and	and	CCONJ
ejpam-2674	39	14	properties	property	NOUN
ejpam-2674	39	15	regarding	regard	VERB
ejpam-2674	39	16	near	near	ADJ
ejpam-2674	39	17	sets	set	NOUN
ejpam-2674	39	18	as	as	ADP
ejpam-2674	39	19	in	in	ADP
ejpam-2674	39	20	[	[	X
ejpam-2674	39	21	18	18	NUM
ejpam-2674	39	22	]	]	PUNCT
ejpam-2674	39	23	.	.	PUNCT
ejpam-2674	40	1	table	table	NOUN
ejpam-2674	40	2	1	1	NUM
ejpam-2674	40	3	:	:	PUNCT
ejpam-2674	40	4	description	description	NOUN
ejpam-2674	40	5	symbols	symbol	NOUN
ejpam-2674	40	6	symbol	symbol	NOUN
ejpam-2674	40	7	interpretation	interpretation	NOUN
ejpam-2674	40	8	r	r	NOUN
ejpam-2674	40	9	set	set	NOUN
ejpam-2674	40	10	of	of	ADP
ejpam-2674	40	11	real	real	ADJ
ejpam-2674	40	12	numbers	number	NOUN
ejpam-2674	40	13	,	,	PUNCT
ejpam-2674	40	14	o	o	PROPN
ejpam-2674	40	15	set	set	NOUN
ejpam-2674	40	16	of	of	ADP
ejpam-2674	40	17	perceptual	perceptual	ADJ
ejpam-2674	40	18	objects	object	NOUN
ejpam-2674	40	19	,	,	PUNCT
ejpam-2674	40	20	x	x	PUNCT
ejpam-2674	40	21	x	x	X
ejpam-2674	40	22	⊆	⊆	NUM
ejpam-2674	40	23	o	o	NOUN
ejpam-2674	40	24	,	,	PUNCT
ejpam-2674	40	25	set	set	VERB
ejpam-2674	40	26	of	of	ADP
ejpam-2674	40	27	sample	sample	NOUN
ejpam-2674	40	28	objects	object	NOUN
ejpam-2674	40	29	,	,	PUNCT
ejpam-2674	40	30	x	x	PUNCT
ejpam-2674	40	31	x	x	PUNCT
ejpam-2674	40	32	∈	∈	PROPN
ejpam-2674	40	33	o	o	NOUN
ejpam-2674	40	34	,	,	PUNCT
ejpam-2674	40	35	sample	sample	NOUN
ejpam-2674	40	36	objects	object	NOUN
ejpam-2674	40	37	,	,	PUNCT
ejpam-2674	40	38	f	f	PROPN
ejpam-2674	40	39	a	a	DET
ejpam-2674	40	40	set	set	NOUN
ejpam-2674	40	41	of	of	ADP
ejpam-2674	40	42	functions	function	NOUN
ejpam-2674	40	43	representing	represent	VERB
ejpam-2674	40	44	object	object	NOUN
ejpam-2674	40	45	features	feature	NOUN
ejpam-2674	40	46	,	,	PUNCT
ejpam-2674	40	47	b	b	PROPN
ejpam-2674	40	48	b	b	PROPN
ejpam-2674	40	49	⊆	⊆	NUM
ejpam-2674	40	50	f	f	PROPN
ejpam-2674	40	51	,	,	PUNCT
ejpam-2674	40	52	φ	φ	PROPN
ejpam-2674	40	53	φ	φ	PROPN
ejpam-2674	40	54	:	:	PUNCT
ejpam-2674	40	55	o	o	X
ejpam-2674	40	56	→	→	SYM
ejpam-2674	40	57	rl	rl	X
ejpam-2674	40	58	,	,	PUNCT
ejpam-2674	40	59	object	object	NOUN
ejpam-2674	40	60	description	description	NOUN
ejpam-2674	40	61	,	,	PUNCT
ejpam-2674	40	62	l	l	PROPN
ejpam-2674	40	63	l	l	NOUN
ejpam-2674	40	64	is	be	AUX
ejpam-2674	40	65	a	a	DET
ejpam-2674	40	66	description	description	NOUN
ejpam-2674	40	67	length	length	NOUN
ejpam-2674	40	68	,	,	PUNCT
ejpam-2674	41	1	i	i	PRON
ejpam-2674	41	2	i	i	VERB
ejpam-2674	41	3	≤	≤	ADV
ejpam-2674	42	1	l	l	NOUN
ejpam-2674	42	2	,	,	PUNCT
ejpam-2674	42	3	φ(x	φ(x	NOUN
ejpam-2674	42	4	)	)	PUNCT
ejpam-2674	42	5	φ(x	φ(x	NOUN
ejpam-2674	42	6	)	)	PUNCT
ejpam-2674	42	7	=	=	PUNCT
ejpam-2674	42	8	(	(	PUNCT
ejpam-2674	42	9	φ1(x	φ1(x	NOUN
ejpam-2674	42	10	)	)	PUNCT
ejpam-2674	42	11	,	,	PUNCT
ejpam-2674	42	12	φ2(x	φ2(x	NOUN
ejpam-2674	42	13	)	)	PUNCT
ejpam-2674	42	14	,	,	PUNCT
ejpam-2674	42	15	φ3(x	φ3(x	PROPN
ejpam-2674	42	16	)	)	PUNCT
ejpam-2674	42	17	,	,	PUNCT
ejpam-2674	42	18	...	...	PUNCT
ejpam-2674	42	19	,	,	PUNCT
ejpam-2674	42	20	φi(x	φi(x	NUM
ejpam-2674	42	21	)	)	PUNCT
ejpam-2674	42	22	,	,	PUNCT
ejpam-2674	42	23	...	...	PUNCT
ejpam-2674	42	24	,	,	PUNCT
ejpam-2674	42	25	φl(x	φl(x	PROPN
ejpam-2674	42	26	)	)	PUNCT
ejpam-2674	42	27	)	)	PUNCT
ejpam-2674	42	28	.	.	PUNCT
ejpam-2674	43	1	objects	object	NOUN
ejpam-2674	43	2	are	be	AUX
ejpam-2674	43	3	known	know	VERB
ejpam-2674	43	4	by	by	ADP
ejpam-2674	43	5	their	their	PRON
ejpam-2674	43	6	descriptions	description	NOUN
ejpam-2674	43	7	.	.	PUNCT
ejpam-2674	44	1	an	an	DET
ejpam-2674	44	2	object	object	NOUN
ejpam-2674	44	3	description	description	NOUN
ejpam-2674	44	4	is	be	AUX
ejpam-2674	44	5	defined	define	VERB
ejpam-2674	44	6	by	by	ADP
ejpam-2674	44	7	means	mean	NOUN
ejpam-2674	44	8	of	of	ADP
ejpam-2674	44	9	a	a	DET
ejpam-2674	44	10	tuple	tuple	NOUN
ejpam-2674	44	11	of	of	ADP
ejpam-2674	44	12	function	function	NOUN
ejpam-2674	44	13	values	value	NOUN
ejpam-2674	44	14	φ(x	φ(x	NOUN
ejpam-2674	44	15	)	)	PUNCT
ejpam-2674	44	16	associated	associate	VERB
ejpam-2674	44	17	with	with	ADP
ejpam-2674	44	18	an	an	DET
ejpam-2674	44	19	object	object	NOUN
ejpam-2674	44	20	x	x	SYM
ejpam-2674	44	21	∈	∈	NOUN
ejpam-2674	44	22	x.	x.	NOUN
ejpam-2674	45	1	the	the	DET
ejpam-2674	45	2	important	important	ADJ
ejpam-2674	45	3	thing	thing	NOUN
ejpam-2674	45	4	to	to	PART
ejpam-2674	45	5	notice	notice	VERB
ejpam-2674	45	6	is	be	AUX
ejpam-2674	45	7	the	the	DET
ejpam-2674	45	8	choice	choice	NOUN
ejpam-2674	45	9	of	of	ADP
ejpam-2674	45	10	functions	function	NOUN
ejpam-2674	45	11	φi	φi	ADP
ejpam-2674	45	12	∈	∈	PROPN
ejpam-2674	45	13	b	b	NUM
ejpam-2674	45	14	used	use	VERB
ejpam-2674	45	15	to	to	PART
ejpam-2674	45	16	describe	describe	VERB
ejpam-2674	45	17	an	an	DET
ejpam-2674	45	18	object	object	NOUN
ejpam-2674	45	19	of	of	ADP
ejpam-2674	45	20	interest	interest	NOUN
ejpam-2674	45	21	.	.	PUNCT
ejpam-2674	46	1	assume	assume	VERB
ejpam-2674	46	2	that	that	SCONJ
ejpam-2674	46	3	b	b	PROPN
ejpam-2674	46	4	⊆	⊆	NUM
ejpam-2674	46	5	f	f	X
ejpam-2674	46	6	(	(	PUNCT
ejpam-2674	46	7	see	see	VERB
ejpam-2674	46	8	table	table	NOUN
ejpam-2674	46	9	1	1	NUM
ejpam-2674	46	10	)	)	PUNCT
ejpam-2674	46	11	is	be	AUX
ejpam-2674	46	12	a	a	DET
ejpam-2674	46	13	given	give	VERB
ejpam-2674	46	14	set	set	NOUN
ejpam-2674	46	15	of	of	ADP
ejpam-2674	46	16	functions	function	NOUN
ejpam-2674	46	17	representing	represent	VERB
ejpam-2674	46	18	features	feature	NOUN
ejpam-2674	46	19	of	of	ADP
ejpam-2674	46	20	sample	sample	NOUN
ejpam-2674	46	21	objects	object	NOUN
ejpam-2674	46	22	x	x	SYM
ejpam-2674	46	23	⊆	⊆	NUM
ejpam-2674	46	24	o.	o.	NOUN
ejpam-2674	46	25	let	let	VERB
ejpam-2674	46	26	φi	φi	ADP
ejpam-2674	46	27	∈	∈	PROPN
ejpam-2674	46	28	b	b	PROPN
ejpam-2674	46	29	,	,	PUNCT
ejpam-2674	46	30	where	where	SCONJ
ejpam-2674	46	31	φi	φi	ADP
ejpam-2674	46	32	:	:	PUNCT
ejpam-2674	46	33	o	o	X
ejpam-2674	46	34	→	→	PUNCT
ejpam-2674	46	35	r.	r.	NOUN
ejpam-2674	46	36	in	in	ADP
ejpam-2674	46	37	combination	combination	NOUN
ejpam-2674	46	38	,	,	PUNCT
ejpam-2674	46	39	the	the	DET
ejpam-2674	46	40	functions	function	NOUN
ejpam-2674	46	41	representing	represent	VERB
ejpam-2674	46	42	object	object	NOUN
ejpam-2674	46	43	features	feature	NOUN
ejpam-2674	46	44	provide	provide	VERB
ejpam-2674	46	45	a	a	DET
ejpam-2674	46	46	basis	basis	NOUN
ejpam-2674	46	47	for	for	ADP
ejpam-2674	46	48	an	an	DET
ejpam-2674	46	49	object	object	NOUN
ejpam-2674	46	50	description	description	NOUN
ejpam-2674	46	51	φi	φi	ADP
ejpam-2674	46	52	:	:	PUNCT
ejpam-2674	46	53	o	o	X
ejpam-2674	46	54	→	→	PUNCT
ejpam-2674	46	55	rl	rl	X
ejpam-2674	46	56	,	,	PUNCT
ejpam-2674	46	57	a	a	DET
ejpam-2674	46	58	vector	vector	NOUN
ejpam-2674	46	59	containing	contain	VERB
ejpam-2674	46	60	measurements	measurement	NOUN
ejpam-2674	46	61	associated	associate	VERB
ejpam-2674	46	62	with	with	ADP
ejpam-2674	46	63	each	each	DET
ejpam-2674	46	64	functional	functional	ADJ
ejpam-2674	46	65	value	value	NOUN
ejpam-2674	46	66	φi	φi	ADP
ejpam-2674	46	67	(	(	PUNCT
ejpam-2674	46	68	x	x	X
ejpam-2674	46	69	)	)	PUNCT
ejpam-2674	46	70	,	,	PUNCT
ejpam-2674	46	71	where	where	SCONJ
ejpam-2674	46	72	the	the	DET
ejpam-2674	46	73	description	description	NOUN
ejpam-2674	46	74	length	length	X
ejpam-2674	46	75	|φ|	|φ|	PROPN
ejpam-2674	46	76	=	=	PUNCT
ejpam-2674	46	77	l.	l.	PROPN
ejpam-2674	46	78	object	object	PROPN
ejpam-2674	46	79	description	description	NOUN
ejpam-2674	46	80	:	:	PUNCT
ejpam-2674	46	81	φ(x	φ(x	VERB
ejpam-2674	46	82	)	)	PUNCT
ejpam-2674	46	83	=	=	PUNCT
ejpam-2674	46	84	(	(	PUNCT
ejpam-2674	46	85	φ1(x	φ1(x	NOUN
ejpam-2674	46	86	)	)	PUNCT
ejpam-2674	46	87	,	,	PUNCT
ejpam-2674	46	88	φ2(x	φ2(x	NOUN
ejpam-2674	46	89	)	)	PUNCT
ejpam-2674	46	90	,	,	PUNCT
ejpam-2674	46	91	φ3(x	φ3(x	PROPN
ejpam-2674	46	92	)	)	PUNCT
ejpam-2674	46	93	,	,	PUNCT
ejpam-2674	46	94	...	...	PUNCT
ejpam-2674	46	95	,	,	PUNCT
ejpam-2674	46	96	φi(x	φi(x	NUM
ejpam-2674	46	97	)	)	PUNCT
ejpam-2674	46	98	,	,	PUNCT
ejpam-2674	46	99	...	...	PUNCT
ejpam-2674	46	100	,	,	PUNCT
ejpam-2674	46	101	φl(x	φl(x	PROPN
ejpam-2674	46	102	)	)	PUNCT
ejpam-2674	46	103	)	)	PUNCT
ejpam-2674	46	104	.	.	PUNCT
ejpam-2674	47	1	the	the	DET
ejpam-2674	47	2	intuition	intuition	NOUN
ejpam-2674	47	3	underlying	underlie	VERB
ejpam-2674	47	4	a	a	DET
ejpam-2674	47	5	description	description	NOUN
ejpam-2674	47	6	φ(x	φ(x	NOUN
ejpam-2674	47	7	)	)	PUNCT
ejpam-2674	47	8	is	be	AUX
ejpam-2674	47	9	a	a	DET
ejpam-2674	47	10	recording	recording	NOUN
ejpam-2674	47	11	of	of	ADP
ejpam-2674	47	12	measurements	measurement	NOUN
ejpam-2674	47	13	from	from	ADP
ejpam-2674	47	14	sensors	sensor	NOUN
ejpam-2674	47	15	,	,	PUNCT
ejpam-2674	47	16	where	where	SCONJ
ejpam-2674	47	17	each	each	DET
ejpam-2674	47	18	sensor	sensor	NOUN
ejpam-2674	47	19	is	be	AUX
ejpam-2674	47	20	modelled	model	VERB
ejpam-2674	47	21	by	by	ADP
ejpam-2674	47	22	a	a	DET
ejpam-2674	47	23	function	function	NOUN
ejpam-2674	47	24	φi	φi	ADP
ejpam-2674	47	25	.	.	PUNCT
ejpam-2674	47	26	table	table	NOUN
ejpam-2674	47	27	2	2	NUM
ejpam-2674	47	28	:	:	PUNCT
ejpam-2674	47	29	nearness	nearness	NOUN
ejpam-2674	47	30	approximation	approximation	NOUN
ejpam-2674	47	31	space	space	NOUN
ejpam-2674	47	32	symbols	symbol	NOUN
ejpam-2674	47	33	n.	n.	PROPN
ejpam-2674	47	34	bağırmaz	bağırmaz	PROPN
ejpam-2674	47	35	/	/	SYM
ejpam-2674	47	36	eur	eur	PROPN
ejpam-2674	47	37	.	.	PUNCT
ejpam-2674	48	1	j.	j.	PROPN
ejpam-2674	48	2	pure	pure	PROPN
ejpam-2674	48	3	appl	appl	PROPN
ejpam-2674	48	4	.	.	PROPN
ejpam-2674	48	5	math	math	PROPN
ejpam-2674	48	6	,	,	PUNCT
ejpam-2674	48	7	11	11	NUM
ejpam-2674	48	8	(	(	PUNCT
ejpam-2674	48	9	2	2	NUM
ejpam-2674	48	10	)	)	PUNCT
ejpam-2674	48	11	(	(	PUNCT
ejpam-2674	48	12	2018	2018	NUM
ejpam-2674	48	13	)	)	PUNCT
ejpam-2674	48	14	,	,	PUNCT
ejpam-2674	48	15	505	505	NUM
ejpam-2674	48	16	-	-	SYM
ejpam-2674	48	17	516	516	NUM
ejpam-2674	48	18	507	507	NUM
ejpam-2674	48	19	symbol	symbol	NOUN
ejpam-2674	48	20	interpretation	interpretation	NOUN
ejpam-2674	48	21	b	b	PROPN
ejpam-2674	48	22	b	b	PROPN
ejpam-2674	48	23	⊆	⊆	NUM
ejpam-2674	48	24	f	f	PROPN
ejpam-2674	48	25	,	,	PUNCT
ejpam-2674	48	26	br	br	PROPN
ejpam-2674	48	27	r	r	NOUN
ejpam-2674	48	28	≤	≤	NOUN
ejpam-2674	48	29	|b|	|b|	VERB
ejpam-2674	48	30	probe	probe	NOUN
ejpam-2674	48	31	functions	function	NOUN
ejpam-2674	48	32	in	in	ADP
ejpam-2674	48	33	b	b	NUM
ejpam-2674	48	34	,	,	PUNCT
ejpam-2674	48	35	∼br	∼br	PROPN
ejpam-2674	48	36	indiscernibility	indiscernibility	NOUN
ejpam-2674	48	37	relation	relation	NOUN
ejpam-2674	48	38	defined	define	VERB
ejpam-2674	48	39	using	use	VERB
ejpam-2674	48	40	br	br	NOUN
ejpam-2674	48	41	,	,	PUNCT
ejpam-2674	48	42	[	[	X
ejpam-2674	48	43	x]br	x]br	X
ejpam-2674	49	1	[	[	X
ejpam-2674	49	2	x]br	x]br	SYM
ejpam-2674	49	3	=	=	SYM
ejpam-2674	49	4	{	{	PUNCT
ejpam-2674	49	5	x′	x′	PROPN
ejpam-2674	49	6	∈	∈	PROPN
ejpam-2674	49	7	o	o	NOUN
ejpam-2674	49	8	|	|	NOUN
ejpam-2674	49	9	x	x	SYM
ejpam-2674	49	10	∼br	∼br	NOUN
ejpam-2674	49	11	x	x	NOUN
ejpam-2674	49	12	′	′	NUM
ejpam-2674	49	13	}	}	PUNCT
ejpam-2674	49	14	,	,	PUNCT
ejpam-2674	49	15	equivalence	equivalence	NOUN
ejpam-2674	49	16	class	class	NOUN
ejpam-2674	49	17	,	,	PUNCT
ejpam-2674	49	18	o	o	NOUN
ejpam-2674	49	19	�	�	PROPN
ejpam-2674	49	20	∼br	∼br	PROPN
ejpam-2674	49	21	o	o	PROPN
ejpam-2674	49	22	�	�	PROPN
ejpam-2674	49	23	∼br=	∼br=	PROPN
ejpam-2674	49	24	{	{	PUNCT
ejpam-2674	50	1	[	[	X
ejpam-2674	50	2	x]br	x]br	X
ejpam-2674	50	3	|	|	ADV
ejpam-2674	50	4	x	x	ADP
ejpam-2674	50	5	′	′	NUM
ejpam-2674	51	1	∈	∈	NOUN
ejpam-2674	51	2	o	o	NOUN
ejpam-2674	51	3	}	}	PUNCT
ejpam-2674	51	4	,	,	PUNCT
ejpam-2674	51	5	quotient	quotient	NOUN
ejpam-2674	51	6	set	set	NOUN
ejpam-2674	51	7	,	,	PUNCT
ejpam-2674	51	8	ξo	ξo	PROPN
ejpam-2674	51	9	,	,	PUNCT
ejpam-2674	51	10	br	br	PROPN
ejpam-2674	51	11	partition	partition	PROPN
ejpam-2674	51	12	ξo	ξo	PROPN
ejpam-2674	51	13	,	,	PUNCT
ejpam-2674	51	14	br	br	NOUN
ejpam-2674	51	15	=	=	SYM
ejpam-2674	51	16	o	o	NOUN
ejpam-2674	51	17	�	�	PROPN
ejpam-2674	51	18	∼br	∼br	PROPN
ejpam-2674	51	19	,	,	PUNCT
ejpam-2674	51	20	r	r	NOUN
ejpam-2674	51	21	(	(	PUNCT
ejpam-2674	51	22	|b|	|b|	PROPN
ejpam-2674	51	23	r	r	NOUN
ejpam-2674	51	24	)	)	PUNCT
ejpam-2674	51	25	,	,	PUNCT
ejpam-2674	51	26	i.e.	i.e.	X
ejpam-2674	51	27	,	,	PUNCT
ejpam-2674	51	28	|b|	|b|	PROPN
ejpam-2674	51	29	functions	function	NOUN
ejpam-2674	51	30	φi	φi	ADP
ejpam-2674	51	31	∈	∈	PROPN
ejpam-2674	51	32	b	b	AUX
ejpam-2674	51	33	taken	take	VERB
ejpam-2674	51	34	r	r	NOUN
ejpam-2674	51	35	at	at	ADP
ejpam-2674	51	36	a	a	DET
ejpam-2674	51	37	time	time	NOUN
ejpam-2674	51	38	,	,	PUNCT
ejpam-2674	51	39	nr(b	nr(b	X
ejpam-2674	51	40	)	)	PUNCT
ejpam-2674	51	41	nr(b	nr(b	PUNCT
ejpam-2674	51	42	)	)	PUNCT
ejpam-2674	51	43	=	=	PRON
ejpam-2674	51	44	{	{	PUNCT
ejpam-2674	51	45	ξo	ξo	PROPN
ejpam-2674	51	46	,	,	PUNCT
ejpam-2674	51	47	br	br	PROPN
ejpam-2674	51	48	|br	|br	NUM
ejpam-2674	51	49	⊆	⊆	NUM
ejpam-2674	51	50	b	b	X
ejpam-2674	51	51	}	}	PUNCT
ejpam-2674	51	52	set	set	NOUN
ejpam-2674	51	53	of	of	ADP
ejpam-2674	51	54	partitions	partition	NOUN
ejpam-2674	51	55	,	,	PUNCT
ejpam-2674	51	56	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	51	57	nr(b)∗x	nr(b)∗x	ADV
ejpam-2674	51	58	=	=	SYM
ejpam-2674	51	59	∪	∪	X
ejpam-2674	51	60	x∈o	x∈o	NOUN
ejpam-2674	51	61	{	{	PUNCT
ejpam-2674	52	1	[	[	X
ejpam-2674	52	2	x]br	x]br	X
ejpam-2674	52	3	:	:	PUNCT
ejpam-2674	53	1	[	[	X
ejpam-2674	53	2	x]br	x]br	ADP
ejpam-2674	53	3	⊆	⊆	NUM
ejpam-2674	53	4	x	x	SYM
ejpam-2674	53	5	}	}	PUNCT
ejpam-2674	53	6	,	,	PUNCT
ejpam-2674	53	7	lower	low	ADJ
ejpam-2674	53	8	approximation	approximation	NOUN
ejpam-2674	53	9	,	,	PUNCT
ejpam-2674	53	10	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	53	11	nr(b)∗x	nr(b)∗x	ADV
ejpam-2674	53	12	=	=	SYM
ejpam-2674	53	13	∪	∪	X
ejpam-2674	53	14	x∈o	x∈o	NOUN
ejpam-2674	53	15	{	{	PUNCT
ejpam-2674	53	16	[	[	X
ejpam-2674	53	17	x]br	x]br	X
ejpam-2674	53	18	:	:	PUNCT
ejpam-2674	54	1	[	[	X
ejpam-2674	54	2	x]br	x]br	X
ejpam-2674	54	3	∩x	∩x	NOUN
ejpam-2674	54	4	6=	6=	ADP
ejpam-2674	54	5	∅	∅	NOUN
ejpam-2674	54	6	}	}	PUNCT
ejpam-2674	54	7	,	,	PUNCT
ejpam-2674	54	8	upper	upper	ADJ
ejpam-2674	54	9	approximation	approximation	NOUN
ejpam-2674	54	10	,	,	PUNCT
ejpam-2674	54	11	bndnr(b)(x	bndnr(b)(x	NOUN
ejpam-2674	54	12	)	)	PUNCT
ejpam-2674	54	13	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	54	14	�	�	NOUN
ejpam-2674	54	15	nr(b)∗x	nr(b)∗x	NOUN
ejpam-2674	54	16	=	=	SYM
ejpam-2674	54	17	{	{	PUNCT
ejpam-2674	54	18	x|x	x|x	PROPN
ejpam-2674	54	19	∈	∈	PROPN
ejpam-2674	54	20	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	54	21	and	and	CCONJ
ejpam-2674	54	22	x	x	PUNCT
ejpam-2674	54	23	/∈	/∈	PUNCT
ejpam-2674	54	24	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	54	25	.	.	PUNCT
ejpam-2674	55	1	a	a	DET
ejpam-2674	55	2	nearness	nearness	NOUN
ejpam-2674	55	3	approximation	approximation	NOUN
ejpam-2674	55	4	space	space	NOUN
ejpam-2674	55	5	(	(	PUNCT
ejpam-2674	55	6	nas	nas	PROPN
ejpam-2674	55	7	)	)	PUNCT
ejpam-2674	55	8	is	be	AUX
ejpam-2674	55	9	denoted	denote	VERB
ejpam-2674	55	10	by	by	ADP
ejpam-2674	55	11	nas	nas	PROPN
ejpam-2674	55	12	=	=	SYM
ejpam-2674	55	13	(	(	PUNCT
ejpam-2674	55	14	o	o	NOUN
ejpam-2674	55	15	,	,	PUNCT
ejpam-2674	55	16	f,∼br	f,∼br	NOUN
ejpam-2674	55	17	,	,	PUNCT
ejpam-2674	55	18	nr	nr	PROPN
ejpam-2674	55	19	,	,	PUNCT
ejpam-2674	55	20	vnr	vnr	PROPN
ejpam-2674	55	21	)	)	PUNCT
ejpam-2674	55	22	which	which	PRON
ejpam-2674	55	23	is	be	AUX
ejpam-2674	55	24	defined	define	VERB
ejpam-2674	55	25	with	with	ADP
ejpam-2674	55	26	a	a	DET
ejpam-2674	55	27	set	set	NOUN
ejpam-2674	55	28	of	of	ADP
ejpam-2674	55	29	perceived	perceive	VERB
ejpam-2674	55	30	objects	object	NOUN
ejpam-2674	55	31	o	o	NOUN
ejpam-2674	55	32	,	,	PUNCT
ejpam-2674	55	33	a	a	DET
ejpam-2674	55	34	set	set	NOUN
ejpam-2674	55	35	of	of	ADP
ejpam-2674	55	36	probe	probe	NOUN
ejpam-2674	55	37	functions	function	NOUN
ejpam-2674	56	1	f	f	X
ejpam-2674	56	2	representing	represent	VERB
ejpam-2674	56	3	object	object	NOUN
ejpam-2674	56	4	features	feature	NOUN
ejpam-2674	56	5	,	,	PUNCT
ejpam-2674	56	6	an	an	DET
ejpam-2674	56	7	indiscernibility	indiscernibility	NOUN
ejpam-2674	56	8	relation	relation	NOUN
ejpam-2674	56	9	∼br	∼br	PROPN
ejpam-2674	56	10	defined	define	VERB
ejpam-2674	56	11	relative	relative	ADJ
ejpam-2674	56	12	to	to	ADP
ejpam-2674	56	13	br	br	PROPN
ejpam-2674	56	14	⊆	⊆	NUM
ejpam-2674	56	15	b	b	PROPN
ejpam-2674	56	16	⊆	⊆	NUM
ejpam-2674	56	17	f	f	NOUN
ejpam-2674	56	18	,	,	PUNCT
ejpam-2674	56	19	a	a	DET
ejpam-2674	56	20	collection	collection	NOUN
ejpam-2674	56	21	of	of	ADP
ejpam-2674	56	22	partitions	partition	NOUN
ejpam-2674	56	23	(	(	PUNCT
ejpam-2674	56	24	families	family	NOUN
ejpam-2674	56	25	of	of	ADP
ejpam-2674	56	26	neighbourhoods	neighbourhood	NOUN
ejpam-2674	56	27	)	)	PUNCT
ejpam-2674	56	28	nr(b	nr(b	NUM
ejpam-2674	56	29	)	)	PUNCT
ejpam-2674	56	30	,	,	PUNCT
ejpam-2674	56	31	and	and	CCONJ
ejpam-2674	56	32	a	a	DET
ejpam-2674	56	33	neighbourhood	neighbourhood	NOUN
ejpam-2674	56	34	overlap	overlap	NOUN
ejpam-2674	56	35	function	function	NOUN
ejpam-2674	56	36	nr	nr	PROPN
ejpam-2674	56	37	.	.	PUNCT
ejpam-2674	57	1	the	the	DET
ejpam-2674	57	2	relation	relation	NOUN
ejpam-2674	57	3	∼br	∼br	PROPN
ejpam-2674	57	4	is	be	AUX
ejpam-2674	57	5	the	the	DET
ejpam-2674	57	6	usual	usual	ADJ
ejpam-2674	57	7	indiscernibility	indiscernibility	NOUN
ejpam-2674	57	8	relation	relation	NOUN
ejpam-2674	57	9	from	from	ADP
ejpam-2674	57	10	rough	rough	ADJ
ejpam-2674	57	11	set	set	NOUN
ejpam-2674	57	12	theory	theory	NOUN
ejpam-2674	57	13	restricted	restrict	VERB
ejpam-2674	57	14	to	to	ADP
ejpam-2674	57	15	a	a	DET
ejpam-2674	57	16	subset	subset	NOUN
ejpam-2674	57	17	br	br	PROPN
ejpam-2674	57	18	⊆	⊆	NUM
ejpam-2674	57	19	b.	b.	NOUN
ejpam-2674	57	20	the	the	DET
ejpam-2674	57	21	subscript	subscript	NOUN
ejpam-2674	57	22	r	r	NOUN
ejpam-2674	57	23	denotes	denote	VERB
ejpam-2674	57	24	the	the	DET
ejpam-2674	57	25	cardinality	cardinality	NOUN
ejpam-2674	57	26	of	of	ADP
ejpam-2674	57	27	the	the	DET
ejpam-2674	57	28	restricted	restrict	VERB
ejpam-2674	57	29	subset	subset	NOUN
ejpam-2674	57	30	br	br	PROPN
ejpam-2674	57	31	,	,	PUNCT
ejpam-2674	57	32	where	where	SCONJ
ejpam-2674	57	33	we	we	PRON
ejpam-2674	57	34	consider	consider	VERB
ejpam-2674	57	35	(	(	PUNCT
ejpam-2674	57	36	|b|	|b|	X
ejpam-2674	57	37	r	r	NOUN
ejpam-2674	57	38	)	)	PUNCT
ejpam-2674	57	39	,	,	PUNCT
ejpam-2674	57	40	i.e.	i.e.	X
ejpam-2674	57	41	,	,	PUNCT
ejpam-2674	57	42	|b|	|b|	PROPN
ejpam-2674	57	43	functions	function	VERB
ejpam-2674	57	44	i	i	PRON
ejpam-2674	57	45	∈	∈	PROPN
ejpam-2674	57	46	f	f	PROPN
ejpam-2674	57	47	taken	take	VERB
ejpam-2674	57	48	r	r	NOUN
ejpam-2674	57	49	at	at	ADP
ejpam-2674	57	50	a	a	DET
ejpam-2674	57	51	time	time	NOUN
ejpam-2674	57	52	to	to	PART
ejpam-2674	57	53	define	define	VERB
ejpam-2674	57	54	the	the	DET
ejpam-2674	57	55	relation	relation	NOUN
ejpam-2674	57	56	∼br	∼br	PROPN
ejpam-2674	57	57	.	.	PUNCT
ejpam-2674	58	1	this	this	DET
ejpam-2674	58	2	relation	relation	NOUN
ejpam-2674	58	3	defines	define	VERB
ejpam-2674	58	4	a	a	DET
ejpam-2674	58	5	partition	partition	NOUN
ejpam-2674	58	6	of	of	ADP
ejpam-2674	58	7	o	o	NOUN
ejpam-2674	58	8	into	into	ADP
ejpam-2674	58	9	non	non	ADJ
ejpam-2674	58	10	-	-	ADJ
ejpam-2674	58	11	empty	empty	ADJ
ejpam-2674	58	12	,	,	PUNCT
ejpam-2674	58	13	pairwise	pairwise	NOUN
ejpam-2674	58	14	disjoint	disjoint	NOUN
ejpam-2674	58	15	subsets	subset	NOUN
ejpam-2674	58	16	that	that	PRON
ejpam-2674	58	17	are	be	AUX
ejpam-2674	58	18	equivalence	equivalence	NOUN
ejpam-2674	58	19	classes	class	NOUN
ejpam-2674	58	20	denoted	denote	VERB
ejpam-2674	58	21	by	by	ADP
ejpam-2674	58	22	[	[	X
ejpam-2674	58	23	x]br	x]br	PROPN
ejpam-2674	58	24	,	,	PUNCT
ejpam-2674	58	25	where	where	SCONJ
ejpam-2674	59	1	[	[	X
ejpam-2674	59	2	x]br	x]br	X
ejpam-2674	59	3	=	=	SYM
ejpam-2674	59	4	{	{	PUNCT
ejpam-2674	59	5	x′	x′	PROPN
ejpam-2674	59	6	∈	∈	PROPN
ejpam-2674	59	7	o	o	NOUN
ejpam-2674	59	8	|	|	NOUN
ejpam-2674	59	9	x	x	SYM
ejpam-2674	59	10	∼br	∼br	NOUN
ejpam-2674	59	11	x	x	NOUN
ejpam-2674	59	12	′	′	NUM
ejpam-2674	59	13	}	}	PUNCT
ejpam-2674	59	14	.	.	PUNCT
ejpam-2674	60	1	these	these	DET
ejpam-2674	60	2	classes	class	NOUN
ejpam-2674	60	3	form	form	VERB
ejpam-2674	60	4	a	a	DET
ejpam-2674	60	5	new	new	ADJ
ejpam-2674	60	6	set	set	NOUN
ejpam-2674	60	7	called	call	VERB
ejpam-2674	60	8	the	the	DET
ejpam-2674	60	9	quotient	quotient	NOUN
ejpam-2674	60	10	seto	seto	NOUN
ejpam-2674	60	11	�	�	PROPN
ejpam-2674	60	12	∼br	∼br	PROPN
ejpam-2674	60	13	,	,	PUNCT
ejpam-2674	60	14	whereo	whereo	PROPN
ejpam-2674	60	15	�	�	PROPN
ejpam-2674	60	16	∼br=	∼br=	PROPN
ejpam-2674	60	17	{	{	PUNCT
ejpam-2674	61	1	[	[	X
ejpam-2674	61	2	x]br	x]br	X
ejpam-2674	61	3	|	|	ADV
ejpam-2674	61	4	x	x	ADP
ejpam-2674	61	5	′	′	NUM
ejpam-2674	62	1	∈	∈	NOUN
ejpam-2674	62	2	o	o	NOUN
ejpam-2674	62	3	}	}	PUNCT
ejpam-2674	62	4	.	.	PUNCT
ejpam-2674	63	1	in	in	ADP
ejpam-2674	63	2	effect	effect	NOUN
ejpam-2674	63	3	,	,	PUNCT
ejpam-2674	63	4	each	each	DET
ejpam-2674	63	5	choice	choice	NOUN
ejpam-2674	63	6	of	of	ADP
ejpam-2674	63	7	probe	probe	NOUN
ejpam-2674	63	8	functions	function	NOUN
ejpam-2674	63	9	br	br	PROPN
ejpam-2674	63	10	defines	define	VERB
ejpam-2674	63	11	a	a	DET
ejpam-2674	63	12	partition	partition	NOUN
ejpam-2674	63	13	ξo	ξo	ADP
ejpam-2674	63	14	,	,	PUNCT
ejpam-2674	63	15	br	br	VERB
ejpam-2674	63	16	on	on	ADP
ejpam-2674	63	17	a	a	DET
ejpam-2674	63	18	set	set	NOUN
ejpam-2674	63	19	of	of	ADP
ejpam-2674	63	20	objects	object	NOUN
ejpam-2674	63	21	o	o	NOUN
ejpam-2674	63	22	,	,	PUNCT
ejpam-2674	63	23	namely	namely	ADV
ejpam-2674	63	24	,	,	PUNCT
ejpam-2674	63	25	ξo	ξo	PROPN
ejpam-2674	63	26	,	,	PUNCT
ejpam-2674	63	27	br	br	NOUN
ejpam-2674	63	28	=	=	SYM
ejpam-2674	63	29	o	o	NOUN
ejpam-2674	63	30	�	�	PROPN
ejpam-2674	63	31	∼br	∼br	PROPN
ejpam-2674	63	32	.	.	PUNCT
ejpam-2674	64	1	every	every	DET
ejpam-2674	64	2	choice	choice	NOUN
ejpam-2674	64	3	of	of	ADP
ejpam-2674	64	4	the	the	DET
ejpam-2674	64	5	set	set	VERB
ejpam-2674	64	6	br	br	NOUN
ejpam-2674	64	7	leads	lead	VERB
ejpam-2674	64	8	to	to	ADP
ejpam-2674	64	9	a	a	DET
ejpam-2674	64	10	new	new	ADJ
ejpam-2674	64	11	partition	partition	NOUN
ejpam-2674	64	12	of	of	ADP
ejpam-2674	64	13	o.	o.	NOUN
ejpam-2674	64	14	let	let	VERB
ejpam-2674	64	15	f	f	PRON
ejpam-2674	64	16	denote	denote	VERB
ejpam-2674	64	17	a	a	DET
ejpam-2674	64	18	set	set	NOUN
ejpam-2674	64	19	of	of	ADP
ejpam-2674	64	20	features	feature	NOUN
ejpam-2674	64	21	for	for	ADP
ejpam-2674	64	22	objects	object	NOUN
ejpam-2674	64	23	in	in	ADP
ejpam-2674	64	24	a	a	DET
ejpam-2674	64	25	set	set	NOUN
ejpam-2674	64	26	x	x	NOUN
ejpam-2674	64	27	,	,	PUNCT
ejpam-2674	64	28	where	where	SCONJ
ejpam-2674	64	29	each	each	DET
ejpam-2674	64	30	φi	φi	ADP
ejpam-2674	64	31	∈	∈	PROPN
ejpam-2674	64	32	f	f	PROPN
ejpam-2674	64	33	that	that	PRON
ejpam-2674	64	34	maps	map	VERB
ejpam-2674	64	35	x	x	PUNCT
ejpam-2674	64	36	to	to	ADP
ejpam-2674	64	37	some	some	DET
ejpam-2674	64	38	value	value	NOUN
ejpam-2674	64	39	set	set	VERB
ejpam-2674	64	40	vφi	vφi	X
ejpam-2674	64	41	(	(	PUNCT
ejpam-2674	64	42	range	range	NOUN
ejpam-2674	64	43	of	of	ADP
ejpam-2674	64	44	φi	φi	NOUN
ejpam-2674	64	45	)	)	PUNCT
ejpam-2674	64	46	.	.	PUNCT
ejpam-2674	65	1	the	the	DET
ejpam-2674	65	2	value	value	NOUN
ejpam-2674	65	3	of	of	ADP
ejpam-2674	65	4	φi	φi	ADV
ejpam-2674	65	5	(	(	PUNCT
ejpam-2674	65	6	x	x	X
ejpam-2674	65	7	)	)	PUNCT
ejpam-2674	65	8	is	be	AUX
ejpam-2674	65	9	a	a	DET
ejpam-2674	65	10	measurement	measurement	NOUN
ejpam-2674	65	11	associated	associate	VERB
ejpam-2674	65	12	with	with	ADP
ejpam-2674	65	13	a	a	DET
ejpam-2674	65	14	feature	feature	NOUN
ejpam-2674	65	15	of	of	ADP
ejpam-2674	65	16	an	an	DET
ejpam-2674	65	17	object	object	NOUN
ejpam-2674	65	18	x	x	SYM
ejpam-2674	65	19	∈	∈	NOUN
ejpam-2674	65	20	x.	x.	NOUN
ejpam-2674	66	1	the	the	DET
ejpam-2674	66	2	overlap	overlap	NOUN
ejpam-2674	66	3	function	function	NOUN
ejpam-2674	66	4	vnr	vnr	NOUN
ejpam-2674	66	5	is	be	AUX
ejpam-2674	66	6	defined	define	VERB
ejpam-2674	66	7	by	by	ADP
ejpam-2674	66	8	vnr	vnr	NOUN
ejpam-2674	66	9	:	:	PUNCT
ejpam-2674	66	10	p	p	X
ejpam-2674	66	11	(	(	PUNCT
ejpam-2674	66	12	o)×p	o)×p	NOUN
ejpam-2674	66	13	(	(	PUNCT
ejpam-2674	66	14	o)→	o)→	NOUN
ejpam-2674	66	15	[	[	X
ejpam-2674	66	16	0	0	NUM
ejpam-2674	66	17	,	,	PUNCT
ejpam-2674	66	18	1],where	1],where	NUM
ejpam-2674	66	19	p	p	X
ejpam-2674	66	20	(	(	PUNCT
ejpam-2674	66	21	o	o	NOUN
ejpam-2674	66	22	)	)	PUNCT
ejpam-2674	66	23	is	be	AUX
ejpam-2674	66	24	the	the	DET
ejpam-2674	66	25	powerset	powerset	NOUN
ejpam-2674	66	26	of	of	ADP
ejpam-2674	66	27	o.	o.	NOUN
ejpam-2674	66	28	the	the	DET
ejpam-2674	66	29	overlap	overlap	NOUN
ejpam-2674	66	30	function	function	NOUN
ejpam-2674	66	31	vnr	vnr	PROPN
ejpam-2674	66	32	maps	map	VERB
ejpam-2674	66	33	a	a	DET
ejpam-2674	66	34	pair	pair	NOUN
ejpam-2674	66	35	of	of	ADP
ejpam-2674	66	36	sets	set	NOUN
ejpam-2674	66	37	to	to	ADP
ejpam-2674	66	38	a	a	DET
ejpam-2674	66	39	number	number	NOUN
ejpam-2674	66	40	in	in	ADP
ejpam-2674	66	41	[	[	X
ejpam-2674	66	42	0	0	NUM
ejpam-2674	66	43	,	,	PUNCT
ejpam-2674	66	44	1	1	NUM
ejpam-2674	66	45	]	]	PUNCT
ejpam-2674	66	46	representing	represent	VERB
ejpam-2674	66	47	the	the	DET
ejpam-2674	66	48	degree	degree	NOUN
ejpam-2674	66	49	of	of	ADP
ejpam-2674	66	50	overlap	overlap	NOUN
ejpam-2674	66	51	between	between	ADP
ejpam-2674	66	52	sets	set	NOUN
ejpam-2674	66	53	of	of	ADP
ejpam-2674	66	54	objects	object	NOUN
ejpam-2674	66	55	with	with	ADP
ejpam-2674	66	56	features	feature	NOUN
ejpam-2674	66	57	defined	define	VERB
ejpam-2674	66	58	by	by	ADP
ejpam-2674	66	59	probe	probe	NOUN
ejpam-2674	66	60	functions	function	NOUN
ejpam-2674	66	61	br	br	PROPN
ejpam-2674	66	62	⊆	⊆	NUM
ejpam-2674	66	63	b.	b.	NOUN
ejpam-2674	66	64	for	for	ADP
ejpam-2674	66	65	each	each	DET
ejpam-2674	66	66	subset	subset	NOUN
ejpam-2674	66	67	br	br	PROPN
ejpam-2674	66	68	⊆	⊆	NUM
ejpam-2674	66	69	b	b	PROPN
ejpam-2674	66	70	of	of	ADP
ejpam-2674	66	71	probe	probe	NOUN
ejpam-2674	66	72	functions	function	NOUN
ejpam-2674	66	73	,	,	PUNCT
ejpam-2674	66	74	define	define	VERB
ejpam-2674	66	75	the	the	DET
ejpam-2674	66	76	binary	binary	PROPN
ejpam-2674	66	77	relation	relation	PROPN
ejpam-2674	66	78	∼br=	∼br=	PROPN
ejpam-2674	66	79	{	{	PUNCT
ejpam-2674	66	80	(	(	PUNCT
ejpam-2674	66	81	x	x	X
ejpam-2674	66	82	,	,	PUNCT
ejpam-2674	66	83	x′	x′	PROPN
ejpam-2674	66	84	)	)	PUNCT
ejpam-2674	66	85	∈	∈	PROPN
ejpam-2674	67	1	o×o	o×o	X
ejpam-2674	67	2	:	:	PUNCT
ejpam-2674	67	3	∀φi	∀φi	PROPN
ejpam-2674	67	4	∈	∈	PROPN
ejpam-2674	67	5	br	br	PROPN
ejpam-2674	67	6	,	,	PUNCT
ejpam-2674	67	7	φi(x	φi(x	NUM
ejpam-2674	67	8	)	)	PUNCT
ejpam-2674	67	9	=	=	SYM
ejpam-2674	67	10	φi(x	φi(x	NUM
ejpam-2674	67	11	′	′	NOUN
ejpam-2674	67	12	)	)	PUNCT
ejpam-2674	67	13	}	}	PUNCT
ejpam-2674	67	14	.	.	PUNCT
ejpam-2674	68	1	since	since	SCONJ
ejpam-2674	68	2	each	each	DET
ejpam-2674	68	3	∼br	∼br	PROPN
ejpam-2674	68	4	is	be	AUX
ejpam-2674	68	5	,	,	PUNCT
ejpam-2674	68	6	in	in	ADP
ejpam-2674	68	7	fact	fact	NOUN
ejpam-2674	68	8	,	,	PUNCT
ejpam-2674	68	9	the	the	DET
ejpam-2674	68	10	usual	usual	ADJ
ejpam-2674	68	11	indiscernibility	indiscernibility	NOUN
ejpam-2674	68	12	relation	relation	NOUN
ejpam-2674	68	13	[	[	X
ejpam-2674	68	14	16	16	NUM
ejpam-2674	68	15	]	]	X
ejpam-2674	68	16	,	,	PUNCT
ejpam-2674	68	17	for	for	ADP
ejpam-2674	68	18	br	br	NOUN
ejpam-2674	68	19	⊆	⊆	NUM
ejpam-2674	68	20	b	b	NOUN
ejpam-2674	68	21	and	and	CCONJ
ejpam-2674	68	22	x	x	PUNCT
ejpam-2674	68	23	∈	∈	PROPN
ejpam-2674	69	1	o	o	NOUN
ejpam-2674	69	2	,	,	PUNCT
ejpam-2674	69	3	let	let	VERB
ejpam-2674	69	4	[	[	X
ejpam-2674	69	5	x]b	x]b	PROPN
ejpam-2674	69	6	denote	denote	VERB
ejpam-2674	69	7	the	the	DET
ejpam-2674	69	8	equivalence	equivalence	NOUN
ejpam-2674	69	9	class	class	NOUN
ejpam-2674	69	10	containing	contain	VERB
ejpam-2674	69	11	x	x	SYM
ejpam-2674	69	12	,	,	PUNCT
ejpam-2674	69	13	i.e.	i.e.	X
ejpam-2674	69	14	,	,	PUNCT
ejpam-2674	69	15	[	[	X
ejpam-2674	69	16	x]br	x]br	X
ejpam-2674	69	17	=	=	SYM
ejpam-2674	69	18	{	{	PUNCT
ejpam-2674	69	19	x′	x′	PROPN
ejpam-2674	69	20	∈	∈	PROPN
ejpam-2674	69	21	o|∀φ	o|∀φ	PROPN
ejpam-2674	69	22	∈	∈	PROPN
ejpam-2674	69	23	br	br	PROPN
ejpam-2674	69	24	,	,	PUNCT
ejpam-2674	69	25	φ(x	φ(x	PROPN
ejpam-2674	69	26	′	′	NUM
ejpam-2674	69	27	)	)	PUNCT
ejpam-2674	70	1	=	=	SYM
ejpam-2674	70	2	φ(x	φ(x	NOUN
ejpam-2674	70	3	)	)	PUNCT
ejpam-2674	70	4	}	}	PUNCT
ejpam-2674	70	5	.	.	PUNCT
ejpam-2674	71	1	if	if	SCONJ
ejpam-2674	71	2	(	(	PUNCT
ejpam-2674	71	3	x	x	X
ejpam-2674	71	4	,	,	PUNCT
ejpam-2674	71	5	x	x	NOUN
ejpam-2674	71	6	′	′	NUM
ejpam-2674	71	7	)	)	PUNCT
ejpam-2674	71	8	∈∼br	∈∼br	NOUN
ejpam-2674	71	9	(	(	PUNCT
ejpam-2674	71	10	also	also	ADV
ejpam-2674	71	11	written	write	VERB
ejpam-2674	71	12	x	x	PUNCT
ejpam-2674	71	13	∼br	∼br	NOUN
ejpam-2674	71	14	x	x	NOUN
ejpam-2674	71	15	′	′	NUM
ejpam-2674	71	16	)	)	PUNCT
ejpam-2674	71	17	,	,	PUNCT
ejpam-2674	71	18	then	then	ADV
ejpam-2674	71	19	x	x	PUNCT
ejpam-2674	71	20	and	and	CCONJ
ejpam-2674	71	21	x	x	AUX
ejpam-2674	71	22	′	′	NOUN
ejpam-2674	71	23	are	be	AUX
ejpam-2674	71	24	said	say	VERB
ejpam-2674	71	25	to	to	PART
ejpam-2674	71	26	be	be	AUX
ejpam-2674	71	27	b	b	NOUN
ejpam-2674	71	28	indiscernible	indiscernible	ADJ
ejpam-2674	71	29	with	with	ADP
ejpam-2674	71	30	respect	respect	NOUN
ejpam-2674	71	31	to	to	ADP
ejpam-2674	71	32	all	all	DET
ejpam-2674	71	33	feature	feature	NOUN
ejpam-2674	71	34	probe	probe	NOUN
ejpam-2674	71	35	functions	function	NOUN
ejpam-2674	71	36	in	in	ADP
ejpam-2674	71	37	br	br	PROPN
ejpam-2674	71	38	.	.	PUNCT
ejpam-2674	71	39	then	then	ADV
ejpam-2674	71	40	define	define	VERB
ejpam-2674	71	41	a	a	DET
ejpam-2674	71	42	collection	collection	NOUN
ejpam-2674	71	43	of	of	ADP
ejpam-2674	71	44	partitions	partition	NOUN
ejpam-2674	71	45	nr(b	nr(b	NOUN
ejpam-2674	71	46	)	)	PUNCT
ejpam-2674	71	47	(	(	PUNCT
ejpam-2674	71	48	families	family	NOUN
ejpam-2674	71	49	of	of	ADP
ejpam-2674	71	50	neighborhoods	neighborhood	NOUN
ejpam-2674	71	51	)	)	PUNCT
ejpam-2674	71	52	,	,	PUNCT
ejpam-2674	71	53	where	where	SCONJ
ejpam-2674	71	54	nr(b	nr(b	PUNCT
ejpam-2674	71	55	)	)	PUNCT
ejpam-2674	71	56	=	=	PRON
ejpam-2674	71	57	{	{	PUNCT
ejpam-2674	71	58	ξo	ξo	PROPN
ejpam-2674	71	59	,	,	PUNCT
ejpam-2674	71	60	br	br	PROPN
ejpam-2674	71	61	|br	|br	NUM
ejpam-2674	71	62	⊆	⊆	NUM
ejpam-2674	71	63	b	b	NOUN
ejpam-2674	71	64	}	}	PUNCT
ejpam-2674	71	65	.	.	PUNCT
ejpam-2674	72	1	families	family	NOUN
ejpam-2674	72	2	of	of	ADP
ejpam-2674	72	3	neighborhoods	neighborhood	NOUN
ejpam-2674	72	4	are	be	AUX
ejpam-2674	72	5	constructed	construct	VERB
ejpam-2674	72	6	for	for	ADP
ejpam-2674	72	7	each	each	DET
ejpam-2674	72	8	combination	combination	NOUN
ejpam-2674	72	9	of	of	ADP
ejpam-2674	72	10	probe	probe	NOUN
ejpam-2674	72	11	functions	function	NOUN
ejpam-2674	72	12	in	in	ADP
ejpam-2674	72	13	b	b	NOUN
ejpam-2674	72	14	using	use	VERB
ejpam-2674	72	15	(	(	PUNCT
ejpam-2674	72	16	|b|	|b|	X
ejpam-2674	72	17	r	r	NOUN
ejpam-2674	72	18	)	)	PUNCT
ejpam-2674	72	19	,	,	PUNCT
ejpam-2674	72	20	i.e.	i.e.	X
ejpam-2674	72	21	,	,	PUNCT
ejpam-2674	72	22	|b|	|b|	PROPN
ejpam-2674	72	23	probe	probe	NOUN
ejpam-2674	72	24	functions	function	NOUN
ejpam-2674	72	25	taken	take	VERB
ejpam-2674	72	26	r	r	NOUN
ejpam-2674	72	27	at	at	ADP
ejpam-2674	72	28	a	a	DET
ejpam-2674	72	29	time	time	NOUN
ejpam-2674	72	30	.	.	PUNCT
ejpam-2674	73	1	proposition	proposition	NOUN
ejpam-2674	73	2	1	1	NUM
ejpam-2674	73	3	.	.	PUNCT
ejpam-2674	74	1	[	[	X
ejpam-2674	74	2	10	10	NUM
ejpam-2674	74	3	]	]	X
ejpam-2674	74	4	let	let	AUX
ejpam-2674	74	5	(	(	PUNCT
ejpam-2674	74	6	o	o	NOUN
ejpam-2674	74	7	,	,	PUNCT
ejpam-2674	74	8	f,∼br	f,∼br	NOUN
ejpam-2674	74	9	,	,	PUNCT
ejpam-2674	74	10	nr	nr	PROPN
ejpam-2674	74	11	,	,	PUNCT
ejpam-2674	74	12	vnr	vnr	PROPN
ejpam-2674	74	13	)	)	PUNCT
ejpam-2674	74	14	be	be	AUX
ejpam-2674	74	15	a	a	DET
ejpam-2674	74	16	nearness	nearness	NOUN
ejpam-2674	74	17	approximation	approximation	NOUN
ejpam-2674	74	18	space	space	NOUN
ejpam-2674	74	19	and	and	CCONJ
ejpam-2674	74	20	x	x	NOUN
ejpam-2674	74	21	,	,	PUNCT
ejpam-2674	74	22	y	y	PROPN
ejpam-2674	74	23	⊆	⊆	NUM
ejpam-2674	75	1	o.	o.	NOUN
ejpam-2674	75	2	then	then	ADV
ejpam-2674	75	3	,	,	PUNCT
ejpam-2674	75	4	the	the	DET
ejpam-2674	75	5	approximations	approximation	NOUN
ejpam-2674	75	6	have	have	VERB
ejpam-2674	75	7	the	the	DET
ejpam-2674	75	8	following	follow	VERB
ejpam-2674	75	9	properties	property	NOUN
ejpam-2674	75	10	:	:	PUNCT
ejpam-2674	75	11	n.	n.	NOUN
ejpam-2674	75	12	bağırmaz	bağırmaz	PROPN
ejpam-2674	75	13	/	/	SYM
ejpam-2674	75	14	eur	eur	PROPN
ejpam-2674	75	15	.	.	PUNCT
ejpam-2674	76	1	j.	j.	PROPN
ejpam-2674	76	2	pure	pure	PROPN
ejpam-2674	76	3	appl	appl	PROPN
ejpam-2674	76	4	.	.	PROPN
ejpam-2674	76	5	math	math	PROPN
ejpam-2674	76	6	,	,	PUNCT
ejpam-2674	76	7	11	11	NUM
ejpam-2674	76	8	(	(	PUNCT
ejpam-2674	76	9	2	2	NUM
ejpam-2674	76	10	)	)	PUNCT
ejpam-2674	76	11	(	(	PUNCT
ejpam-2674	76	12	2018	2018	NUM
ejpam-2674	76	13	)	)	PUNCT
ejpam-2674	76	14	,	,	PUNCT
ejpam-2674	76	15	505	505	NUM
ejpam-2674	76	16	-	-	SYM
ejpam-2674	76	17	516	516	NUM
ejpam-2674	76	18	508	508	NUM
ejpam-2674	76	19	(	(	PUNCT
ejpam-2674	76	20	1	1	NUM
ejpam-2674	76	21	)	)	PUNCT
ejpam-2674	76	22	nr(b)∗x	nr(b)∗x	NOUN
ejpam-2674	76	23	⊆	⊆	NUM
ejpam-2674	76	24	x	x	SYM
ejpam-2674	76	25	⊆	⊆	NUM
ejpam-2674	76	26	nr(b)∗x	nr(b)∗x	NOUN
ejpam-2674	76	27	,	,	PUNCT
ejpam-2674	76	28	(	(	PUNCT
ejpam-2674	76	29	2	2	X
ejpam-2674	76	30	)	)	PUNCT
ejpam-2674	76	31	nr(b)∗	nr(b)∗	NOUN
ejpam-2674	76	32	(	(	PUNCT
ejpam-2674	76	33	x	x	SYM
ejpam-2674	76	34	∪	∪	PROPN
ejpam-2674	76	35	y	y	PROPN
ejpam-2674	76	36	)	)	PUNCT
ejpam-2674	77	1	=	=	SYM
ejpam-2674	77	2	nr(b)∗x	nr(b)∗x	NOUN
ejpam-2674	77	3	∪nr(b)∗y	∪nr(b)∗y	VERB
ejpam-2674	77	4	,	,	PUNCT
ejpam-2674	77	5	(	(	PUNCT
ejpam-2674	77	6	3	3	X
ejpam-2674	77	7	)	)	PUNCT
ejpam-2674	77	8	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	77	9	(	(	PUNCT
ejpam-2674	77	10	x	x	PROPN
ejpam-2674	77	11	∩	∩	ADJ
ejpam-2674	77	12	y	y	NOUN
ejpam-2674	77	13	)	)	PUNCT
ejpam-2674	77	14	=	=	SYM
ejpam-2674	77	15	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	77	16	∩nr(b)∗x	∩nr(b)∗x	NOUN
ejpam-2674	77	17	,	,	PUNCT
ejpam-2674	77	18	(	(	PUNCT
ejpam-2674	77	19	4	4	NUM
ejpam-2674	77	20	)	)	PUNCT
ejpam-2674	77	21	x	x	X
ejpam-2674	78	1	⊆	⊆	NUM
ejpam-2674	78	2	y	y	PROPN
ejpam-2674	78	3	implies	imply	VERB
ejpam-2674	78	4	nr(b)∗x	nr(b)∗x	PRON
ejpam-2674	78	5	⊆	⊆	NUM
ejpam-2674	78	6	nr(b)∗y	nr(b)∗y	NOUN
ejpam-2674	78	7	,	,	PUNCT
ejpam-2674	78	8	(	(	PUNCT
ejpam-2674	78	9	5	5	NUM
ejpam-2674	78	10	)	)	PUNCT
ejpam-2674	78	11	x	x	X
ejpam-2674	79	1	⊆	⊆	NUM
ejpam-2674	79	2	y	y	PROPN
ejpam-2674	79	3	implies	imply	VERB
ejpam-2674	79	4	nr(b)∗x	nr(b)∗x	PRON
ejpam-2674	79	5	⊆	⊆	NUM
ejpam-2674	79	6	nr(b)∗y	nr(b)∗y	NOUN
ejpam-2674	79	7	,	,	PUNCT
ejpam-2674	79	8	(	(	PUNCT
ejpam-2674	79	9	6	6	X
ejpam-2674	79	10	)	)	PUNCT
ejpam-2674	79	11	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	79	12	(	(	PUNCT
ejpam-2674	79	13	x	x	PROPN
ejpam-2674	79	14	∩	∩	ADJ
ejpam-2674	79	15	y	y	PROPN
ejpam-2674	79	16	)	)	PUNCT
ejpam-2674	79	17	⊆	⊆	NUM
ejpam-2674	79	18	nr(b)∗x	nr(b)∗x	NOUN
ejpam-2674	79	19	∩nr(b)∗y	∩nr(b)∗y	VERB
ejpam-2674	79	20	,	,	PUNCT
ejpam-2674	79	21	(	(	PUNCT
ejpam-2674	79	22	7	7	X
ejpam-2674	79	23	)	)	PUNCT
ejpam-2674	79	24	nr(b)∗	nr(b)∗	NOUN
ejpam-2674	79	25	(	(	PUNCT
ejpam-2674	79	26	x	x	AUX
ejpam-2674	79	27	∪	∪	PROPN
ejpam-2674	79	28	y	y	PROPN
ejpam-2674	79	29	)	)	PUNCT
ejpam-2674	79	30	⊇	⊇	PROPN
ejpam-2674	79	31	nr(b)∗x	nr(b)∗x	NOUN
ejpam-2674	79	32	∪nr(b)∗y	∪nr(b)∗y	VERB
ejpam-2674	79	33	.	.	PUNCT
ejpam-2674	80	1	a	a	DET
ejpam-2674	80	2	nonempty	nonempty	ADV
ejpam-2674	80	3	subset	subset	VERB
ejpam-2674	80	4	h	h	NOUN
ejpam-2674	80	5	of	of	ADP
ejpam-2674	80	6	a	a	DET
ejpam-2674	80	7	semigroup	semigroup	NOUN
ejpam-2674	80	8	s	s	NOUN
ejpam-2674	80	9	is	be	AUX
ejpam-2674	80	10	said	say	VERB
ejpam-2674	80	11	to	to	PART
ejpam-2674	80	12	be	be	AUX
ejpam-2674	80	13	a	a	DET
ejpam-2674	80	14	subsemigroup	subsemigroup	NOUN
ejpam-2674	80	15	of	of	ADP
ejpam-2674	80	16	s	s	SYM
ejpam-2674	80	17	,	,	PUNCT
ejpam-2674	80	18	if	if	SCONJ
ejpam-2674	80	19	ab	ab	PROPN
ejpam-2674	80	20	∈	∈	PROPN
ejpam-2674	80	21	h	h	NOUN
ejpam-2674	80	22	for	for	ADP
ejpam-2674	80	23	all	all	DET
ejpam-2674	80	24	a	a	PRON
ejpam-2674	80	25	,	,	PUNCT
ejpam-2674	80	26	b	b	PROPN
ejpam-2674	80	27	∈	∈	PROPN
ejpam-2674	80	28	t	t	NOUN
ejpam-2674	80	29	,	,	PUNCT
ejpam-2674	80	30	i.e.	i.e.	X
ejpam-2674	80	31	,	,	PUNCT
ejpam-2674	80	32	h2	h2	PROPN
ejpam-2674	80	33	⊆	⊆	NUM
ejpam-2674	80	34	h.	h.	NOUN
ejpam-2674	80	35	a	a	DET
ejpam-2674	80	36	nonempty	nonempty	NOUN
ejpam-2674	80	37	subset	subset	VERB
ejpam-2674	80	38	i	i	PRON
ejpam-2674	80	39	of	of	ADP
ejpam-2674	80	40	a	a	DET
ejpam-2674	80	41	semigroup	semigroup	NOUN
ejpam-2674	80	42	s	s	NOUN
ejpam-2674	80	43	is	be	AUX
ejpam-2674	80	44	said	say	VERB
ejpam-2674	80	45	to	to	PART
ejpam-2674	80	46	be	be	AUX
ejpam-2674	80	47	a	a	DET
ejpam-2674	80	48	left	left	ADJ
ejpam-2674	80	49	(	(	PUNCT
ejpam-2674	80	50	resp	resp	NOUN
ejpam-2674	80	51	.	.	PUNCT
ejpam-2674	81	1	right	right	ADJ
ejpam-2674	81	2	)	)	PUNCT
ejpam-2674	81	3	ideal	ideal	NOUN
ejpam-2674	81	4	of	of	ADP
ejpam-2674	81	5	s	s	PRON
ejpam-2674	81	6	if	if	SCONJ
ejpam-2674	81	7	si	si	PROPN
ejpam-2674	81	8	⊆	⊆	NUM
ejpam-2674	81	9	i	i	PROPN
ejpam-2674	81	10	(	(	PUNCT
ejpam-2674	81	11	resp	resp	PROPN
ejpam-2674	81	12	.	.	PUNCT
ejpam-2674	81	13	is	be	AUX
ejpam-2674	81	14	⊆	⊆	NUM
ejpam-2674	81	15	i	i	NOUN
ejpam-2674	81	16	)	)	PUNCT
ejpam-2674	81	17	.	.	PUNCT
ejpam-2674	82	1	a	a	DET
ejpam-2674	82	2	nonempty	nonempty	NOUN
ejpam-2674	82	3	subset	subset	VERB
ejpam-2674	82	4	i	i	PRON
ejpam-2674	82	5	of	of	ADP
ejpam-2674	82	6	s	s	PROPN
ejpam-2674	82	7	is	be	AUX
ejpam-2674	82	8	called	call	VERB
ejpam-2674	82	9	an	an	DET
ejpam-2674	82	10	ideal	ideal	NOUN
ejpam-2674	82	11	of	of	ADP
ejpam-2674	82	12	s	s	PRON
ejpam-2674	82	13	if	if	SCONJ
ejpam-2674	82	14	i	i	PRON
ejpam-2674	82	15	is	be	AUX
ejpam-2674	82	16	both	both	CCONJ
ejpam-2674	82	17	a	a	DET
ejpam-2674	82	18	left	left	NOUN
ejpam-2674	82	19	and	and	CCONJ
ejpam-2674	82	20	a	a	DET
ejpam-2674	82	21	right	right	ADJ
ejpam-2674	82	22	ideal	ideal	NOUN
ejpam-2674	82	23	of	of	ADP
ejpam-2674	82	24	s.	s.	PROPN
ejpam-2674	82	25	a	a	DET
ejpam-2674	82	26	subsemigroup	subsemigroup	PROPN
ejpam-2674	82	27	h	h	NOUN
ejpam-2674	82	28	of	of	ADP
ejpam-2674	82	29	s	s	PROPN
ejpam-2674	82	30	is	be	AUX
ejpam-2674	82	31	called	call	VERB
ejpam-2674	82	32	a	a	DET
ejpam-2674	82	33	bi	bi	NOUN
ejpam-2674	82	34	-	-	NOUN
ejpam-2674	82	35	ideal	ideal	NOUN
ejpam-2674	82	36	of	of	ADP
ejpam-2674	82	37	s	s	PRON
ejpam-2674	82	38	if	if	SCONJ
ejpam-2674	82	39	hsh	hsh	PROPN
ejpam-2674	82	40	⊆	⊆	NUM
ejpam-2674	82	41	h.	h.	NOUN
ejpam-2674	82	42	let	let	VERB
ejpam-2674	82	43	s	s	PRON
ejpam-2674	82	44	be	be	AUX
ejpam-2674	82	45	a	a	DET
ejpam-2674	82	46	semigroup	semigroup	NOUN
ejpam-2674	82	47	.	.	PUNCT
ejpam-2674	83	1	an	an	DET
ejpam-2674	83	2	element	element	NOUN
ejpam-2674	83	3	x	x	SYM
ejpam-2674	83	4	∈	∈	NOUN
ejpam-2674	83	5	s	s	NOUN
ejpam-2674	83	6	is	be	AUX
ejpam-2674	83	7	a	a	DET
ejpam-2674	83	8	left	left	ADJ
ejpam-2674	83	9	identity	identity	NOUN
ejpam-2674	83	10	of	of	ADP
ejpam-2674	83	11	s	s	NOUN
ejpam-2674	83	12	,	,	PUNCT
ejpam-2674	83	13	if	if	SCONJ
ejpam-2674	83	14	∀y	∀y	NUM
ejpam-2674	83	15	∈	∈	NOUN
ejpam-2674	83	16	s	s	VERB
ejpam-2674	83	17	:	:	PUNCT
ejpam-2674	83	18	xy	xy	PROPN
ejpam-2674	83	19	=	=	SYM
ejpam-2674	83	20	y	y	PROPN
ejpam-2674	83	21	.	.	PUNCT
ejpam-2674	84	1	similarly	similarly	ADV
ejpam-2674	84	2	,	,	PUNCT
ejpam-2674	84	3	x	x	X
ejpam-2674	84	4	is	be	AUX
ejpam-2674	84	5	a	a	DET
ejpam-2674	84	6	right	right	ADJ
ejpam-2674	84	7	identity	identity	NOUN
ejpam-2674	84	8	of	of	ADP
ejpam-2674	84	9	s	s	NOUN
ejpam-2674	84	10	,	,	PUNCT
ejpam-2674	84	11	if	if	SCONJ
ejpam-2674	84	12	∀y	∀y	NUM
ejpam-2674	84	13	∈	∈	NOUN
ejpam-2674	84	14	s	s	PART
ejpam-2674	84	15	:	:	PUNCT
ejpam-2674	84	16	yx	yx	PROPN
ejpam-2674	84	17	=	=	SYM
ejpam-2674	84	18	y	y	PROPN
ejpam-2674	84	19	.	.	PUNCT
ejpam-2674	85	1	if	if	SCONJ
ejpam-2674	85	2	x	x	PRON
ejpam-2674	85	3	is	be	AUX
ejpam-2674	85	4	both	both	CCONJ
ejpam-2674	85	5	a	a	DET
ejpam-2674	85	6	left	left	NOUN
ejpam-2674	85	7	and	and	CCONJ
ejpam-2674	85	8	a	a	DET
ejpam-2674	85	9	right	right	ADJ
ejpam-2674	85	10	identity	identity	NOUN
ejpam-2674	85	11	of	of	ADP
ejpam-2674	85	12	s	s	PROPN
ejpam-2674	85	13	,	,	PUNCT
ejpam-2674	85	14	then	then	ADV
ejpam-2674	85	15	x	x	PUNCT
ejpam-2674	85	16	is	be	AUX
ejpam-2674	85	17	called	call	VERB
ejpam-2674	85	18	an	an	DET
ejpam-2674	85	19	identity	identity	NOUN
ejpam-2674	85	20	of	of	ADP
ejpam-2674	85	21	s.	s.	PROPN
ejpam-2674	85	22	a	a	DET
ejpam-2674	85	23	semigroup	semigroup	PROPN
ejpam-2674	85	24	is	be	AUX
ejpam-2674	85	25	a	a	DET
ejpam-2674	85	26	monoid	monoid	NOUN
ejpam-2674	85	27	,	,	PUNCT
ejpam-2674	85	28	if	if	SCONJ
ejpam-2674	85	29	it	it	PRON
ejpam-2674	85	30	has	have	VERB
ejpam-2674	85	31	an	an	DET
ejpam-2674	85	32	identity	identity	NOUN
ejpam-2674	85	33	.	.	PUNCT
ejpam-2674	86	1	the	the	DET
ejpam-2674	86	2	identity	identity	NOUN
ejpam-2674	86	3	of	of	ADP
ejpam-2674	86	4	a	a	DET
ejpam-2674	86	5	monoid	monoid	NOUN
ejpam-2674	86	6	s	s	X
ejpam-2674	86	7	is	be	AUX
ejpam-2674	86	8	usually	usually	ADV
ejpam-2674	86	9	denoted	denote	VERB
ejpam-2674	86	10	by	by	ADP
ejpam-2674	86	11	1s	1	NOUN
ejpam-2674	86	12	,	,	PUNCT
ejpam-2674	86	13	or	or	CCONJ
ejpam-2674	86	14	just	just	ADV
ejpam-2674	86	15	by	by	ADP
ejpam-2674	86	16	1	1	NUM
ejpam-2674	86	17	,	,	PUNCT
ejpam-2674	86	18	for	for	ADP
ejpam-2674	86	19	short	short	ADJ
ejpam-2674	86	20	.	.	PUNCT
ejpam-2674	87	1	a	a	DET
ejpam-2674	87	2	monoid	monoid	NOUN
ejpam-2674	87	3	g	g	PROPN
ejpam-2674	87	4	is	be	AUX
ejpam-2674	87	5	a	a	DET
ejpam-2674	87	6	group	group	NOUN
ejpam-2674	87	7	,	,	PUNCT
ejpam-2674	87	8	if	if	SCONJ
ejpam-2674	87	9	every	every	DET
ejpam-2674	87	10	x	x	X
ejpam-2674	87	11	∈	∈	PROPN
ejpam-2674	87	12	g	g	PROPN
ejpam-2674	87	13	has	have	VERB
ejpam-2674	88	1	a	a	DET
ejpam-2674	88	2	(	(	PUNCT
ejpam-2674	88	3	group	group	NOUN
ejpam-2674	88	4	)	)	PUNCT
ejpam-2674	88	5	inverse	inverse	NOUN
ejpam-2674	88	6	x−1	x−1	PROPN
ejpam-2674	88	7	∈	∈	PROPN
ejpam-2674	88	8	g	g	NOUN
ejpam-2674	88	9	:	:	PUNCT
ejpam-2674	88	10	xx−1	xx−1	X
ejpam-2674	88	11	=	=	SYM
ejpam-2674	88	12	1	1	NUM
ejpam-2674	88	13	=	=	SYM
ejpam-2674	88	14	x−1x	x−1x	NOUN
ejpam-2674	88	15	3	3	NUM
ejpam-2674	88	16	.	.	PUNCT
ejpam-2674	89	1	near	near	ADP
ejpam-2674	89	2	ideals	ideal	NOUN
ejpam-2674	89	3	in	in	ADP
ejpam-2674	89	4	this	this	DET
ejpam-2674	89	5	section	section	NOUN
ejpam-2674	89	6	,	,	PUNCT
ejpam-2674	89	7	we	we	PRON
ejpam-2674	89	8	introduce	introduce	VERB
ejpam-2674	89	9	the	the	DET
ejpam-2674	89	10	notions	notion	NOUN
ejpam-2674	89	11	of	of	ADP
ejpam-2674	89	12	near	near	PROPN
ejpam-2674	89	13	subsemigroup	subsemigroup	NOUN
ejpam-2674	89	14	,	,	PUNCT
ejpam-2674	89	15	near	near	ADP
ejpam-2674	89	16	ideal	ideal	NOUN
ejpam-2674	89	17	and	and	CCONJ
ejpam-2674	89	18	near	near	ADP
ejpam-2674	89	19	bi	bi	NOUN
ejpam-2674	89	20	-	-	NOUN
ejpam-2674	89	21	ideal	ideal	NOUN
ejpam-2674	89	22	on	on	ADP
ejpam-2674	89	23	a	a	DET
ejpam-2674	89	24	near	near	ADJ
ejpam-2674	89	25	approximation	approximation	NOUN
ejpam-2674	89	26	space	space	NOUN
ejpam-2674	89	27	,	,	PUNCT
ejpam-2674	89	28	and	and	CCONJ
ejpam-2674	89	29	study	study	VERB
ejpam-2674	89	30	some	some	PRON
ejpam-2674	89	31	of	of	ADP
ejpam-2674	89	32	its	its	PRON
ejpam-2674	89	33	properties	property	NOUN
ejpam-2674	89	34	.	.	PUNCT
ejpam-2674	90	1	definition	definition	NOUN
ejpam-2674	90	2	1	1	NUM
ejpam-2674	90	3	.	.	PUNCT
ejpam-2674	91	1	[	[	X
ejpam-2674	91	2	10	10	NUM
ejpam-2674	91	3	]	]	X
ejpam-2674	91	4	let	let	AUX
ejpam-2674	91	5	(	(	PUNCT
ejpam-2674	91	6	o	o	NOUN
ejpam-2674	91	7	,	,	PUNCT
ejpam-2674	91	8	f,∼br	f,∼br	NOUN
ejpam-2674	91	9	,	,	PUNCT
ejpam-2674	91	10	nr	nr	PROPN
ejpam-2674	91	11	,	,	PUNCT
ejpam-2674	91	12	vnr	vnr	PROPN
ejpam-2674	91	13	)	)	PUNCT
ejpam-2674	91	14	be	be	AUX
ejpam-2674	91	15	a	a	DET
ejpam-2674	91	16	nearness	nearness	NOUN
ejpam-2674	91	17	approximation	approximation	NOUN
ejpam-2674	91	18	space	space	NOUN
ejpam-2674	91	19	and	and	CCONJ
ejpam-2674	91	20	let	let	VERB
ejpam-2674	91	21	(	(	PUNCT
ejpam-2674	91	22	·	·	PUNCT
ejpam-2674	91	23	)	)	PUNCT
ejpam-2674	91	24	be	be	AUX
ejpam-2674	91	25	a	a	DET
ejpam-2674	91	26	binary	binary	ADJ
ejpam-2674	91	27	operation	operation	NOUN
ejpam-2674	91	28	defined	define	VERB
ejpam-2674	91	29	on	on	ADP
ejpam-2674	91	30	o.	o.	PROPN
ejpam-2674	91	31	a	a	DET
ejpam-2674	91	32	subset	subset	NOUN
ejpam-2674	91	33	s	s	NOUN
ejpam-2674	91	34	of	of	ADP
ejpam-2674	91	35	the	the	DET
ejpam-2674	91	36	set	set	NOUN
ejpam-2674	91	37	of	of	ADP
ejpam-2674	91	38	perceptual	perceptual	ADJ
ejpam-2674	91	39	objects	object	NOUN
ejpam-2674	91	40	o	o	NOUN
ejpam-2674	91	41	is	be	AUX
ejpam-2674	91	42	called	call	VERB
ejpam-2674	91	43	a	a	DET
ejpam-2674	91	44	near	near	ADJ
ejpam-2674	91	45	semigroup	semigroup	NOUN
ejpam-2674	91	46	on	on	ADP
ejpam-2674	91	47	nearness	nearness	NOUN
ejpam-2674	91	48	approximation	approximation	NOUN
ejpam-2674	91	49	space	space	NOUN
ejpam-2674	91	50	,	,	PUNCT
ejpam-2674	91	51	provided	provide	VERB
ejpam-2674	91	52	the	the	DET
ejpam-2674	91	53	following	follow	VERB
ejpam-2674	91	54	properties	property	NOUN
ejpam-2674	91	55	are	be	AUX
ejpam-2674	91	56	satisfied	satisfied	ADJ
ejpam-2674	91	57	:	:	PUNCT
ejpam-2674	91	58	(	(	PUNCT
ejpam-2674	91	59	1	1	X
ejpam-2674	91	60	)	)	PUNCT
ejpam-2674	91	61	for	for	ADP
ejpam-2674	91	62	all	all	DET
ejpam-2674	91	63	x	x	NOUN
ejpam-2674	91	64	,	,	PUNCT
ejpam-2674	91	65	y	y	PROPN
ejpam-2674	91	66	∈	∈	PROPN
ejpam-2674	91	67	s	s	PROPN
ejpam-2674	91	68	,	,	PUNCT
ejpam-2674	91	69	x	x	PUNCT
ejpam-2674	91	70	·	·	PUNCT
ejpam-2674	91	71	y	y	PROPN
ejpam-2674	91	72	∈	∈	PROPN
ejpam-2674	91	73	nr(b)∗s	nr(b)∗s	PROPN
ejpam-2674	91	74	,	,	PUNCT
ejpam-2674	91	75	(	(	PUNCT
ejpam-2674	91	76	2	2	X
ejpam-2674	91	77	)	)	PUNCT
ejpam-2674	91	78	for	for	ADP
ejpam-2674	91	79	all	all	DET
ejpam-2674	91	80	x	x	NOUN
ejpam-2674	91	81	,	,	PUNCT
ejpam-2674	91	82	y	y	PROPN
ejpam-2674	91	83	,	,	PUNCT
ejpam-2674	91	84	z	z	PROPN
ejpam-2674	91	85	∈	∈	PROPN
ejpam-2674	91	86	s	s	PART
ejpam-2674	91	87	,	,	PUNCT
ejpam-2674	91	88	(	(	PUNCT
ejpam-2674	91	89	x	x	X
ejpam-2674	91	90	·	·	PUNCT
ejpam-2674	91	91	y	y	X
ejpam-2674	91	92	)	)	PUNCT
ejpam-2674	91	93	·	·	PUNCT
ejpam-2674	91	94	z	z	X
ejpam-2674	92	1	=	=	PUNCT
ejpam-2674	92	2	x	x	SYM
ejpam-2674	92	3	·	·	PUNCT
ejpam-2674	92	4	(	(	PUNCT
ejpam-2674	92	5	y	y	PROPN
ejpam-2674	92	6	·	·	PUNCT
ejpam-2674	92	7	z	z	X
ejpam-2674	92	8	)	)	PUNCT
ejpam-2674	92	9	property	property	NOUN
ejpam-2674	92	10	holds	hold	NOUN
ejpam-2674	92	11	in	in	ADP
ejpam-2674	92	12	nr(b)∗s	nr(b)∗s	NUM
ejpam-2674	92	13	.	.	PUNCT
ejpam-2674	93	1	let	let	AUX
ejpam-2674	93	2	(	(	PUNCT
ejpam-2674	93	3	o	o	NOUN
ejpam-2674	93	4	,	,	PUNCT
ejpam-2674	93	5	f,∼br	f,∼br	NOUN
ejpam-2674	93	6	,	,	PUNCT
ejpam-2674	93	7	nr	nr	PROPN
ejpam-2674	93	8	,	,	PUNCT
ejpam-2674	93	9	vnr	vnr	PROPN
ejpam-2674	93	10	)	)	PUNCT
ejpam-2674	93	11	be	be	AUX
ejpam-2674	93	12	a	a	DET
ejpam-2674	93	13	nearness	nearness	NOUN
ejpam-2674	93	14	approximation	approximation	NOUN
ejpam-2674	93	15	space	space	NOUN
ejpam-2674	93	16	and	and	CCONJ
ejpam-2674	93	17	(	(	PUNCT
ejpam-2674	93	18	·	·	PUNCT
ejpam-2674	93	19	)	)	PUNCT
ejpam-2674	93	20	be	be	AUX
ejpam-2674	93	21	a	a	DET
ejpam-2674	93	22	binary	binary	ADJ
ejpam-2674	93	23	operation	operation	NOUN
ejpam-2674	93	24	defined	define	VERB
ejpam-2674	93	25	on	on	ADP
ejpam-2674	93	26	o.	o.	NOUN
ejpam-2674	93	27	let	let	VERB
ejpam-2674	93	28	s	s	PRON
ejpam-2674	93	29	be	be	AUX
ejpam-2674	93	30	a	a	DET
ejpam-2674	93	31	near	near	ADJ
ejpam-2674	93	32	semigroup	semigroup	NOUN
ejpam-2674	93	33	.	.	PUNCT
ejpam-2674	94	1	there	there	PRON
ejpam-2674	94	2	is	be	VERB
ejpam-2674	94	3	only	only	ADV
ejpam-2674	94	4	one	one	NUM
ejpam-2674	94	5	an	an	DET
ejpam-2674	94	6	element	element	NOUN
ejpam-2674	94	7	x	x	SYM
ejpam-2674	94	8	∈	∈	NOUN
ejpam-2674	94	9	nr(b)∗s	nr(b)∗s	NOUN
ejpam-2674	94	10	is	be	AUX
ejpam-2674	94	11	a	a	DET
ejpam-2674	94	12	left	left	ADJ
ejpam-2674	94	13	identity	identity	NOUN
ejpam-2674	94	14	of	of	ADP
ejpam-2674	94	15	s	s	NOUN
ejpam-2674	94	16	,	,	PUNCT
ejpam-2674	94	17	if	if	SCONJ
ejpam-2674	94	18	∀y	∀y	NUM
ejpam-2674	94	19	∈	∈	NOUN
ejpam-2674	94	20	s	s	VERB
ejpam-2674	94	21	:	:	PUNCT
ejpam-2674	94	22	xy	xy	PROPN
ejpam-2674	94	23	=	=	SYM
ejpam-2674	94	24	y	y	PROPN
ejpam-2674	94	25	.	.	PUNCT
ejpam-2674	95	1	similarly	similarly	ADV
ejpam-2674	95	2	,	,	PUNCT
ejpam-2674	95	3	x	x	X
ejpam-2674	95	4	is	be	AUX
ejpam-2674	95	5	a	a	DET
ejpam-2674	95	6	right	right	ADJ
ejpam-2674	95	7	identity	identity	NOUN
ejpam-2674	95	8	of	of	ADP
ejpam-2674	95	9	s	s	NOUN
ejpam-2674	95	10	,	,	PUNCT
ejpam-2674	95	11	if	if	SCONJ
ejpam-2674	95	12	∀y	∀y	NUM
ejpam-2674	95	13	∈	∈	NOUN
ejpam-2674	95	14	s	s	PART
ejpam-2674	95	15	:	:	PUNCT
ejpam-2674	95	16	yx	yx	PROPN
ejpam-2674	95	17	=	=	SYM
ejpam-2674	95	18	y	y	PROPN
ejpam-2674	95	19	.	.	PUNCT
ejpam-2674	96	1	if	if	SCONJ
ejpam-2674	96	2	x	x	PRON
ejpam-2674	96	3	is	be	AUX
ejpam-2674	96	4	both	both	CCONJ
ejpam-2674	96	5	a	a	DET
ejpam-2674	96	6	left	left	NOUN
ejpam-2674	96	7	and	and	CCONJ
ejpam-2674	96	8	a	a	DET
ejpam-2674	96	9	right	right	ADJ
ejpam-2674	96	10	identity	identity	NOUN
ejpam-2674	96	11	of	of	ADP
ejpam-2674	96	12	s	s	PROPN
ejpam-2674	96	13	,	,	PUNCT
ejpam-2674	96	14	then	then	ADV
ejpam-2674	96	15	x	x	PUNCT
ejpam-2674	96	16	is	be	AUX
ejpam-2674	96	17	called	call	VERB
ejpam-2674	96	18	a	a	DET
ejpam-2674	96	19	near	near	ADJ
ejpam-2674	96	20	identity	identity	NOUN
ejpam-2674	96	21	of	of	ADP
ejpam-2674	96	22	s.	s.	PROPN
ejpam-2674	96	23	a	a	DET
ejpam-2674	96	24	near	near	ADJ
ejpam-2674	96	25	semigroup	semigroup	NOUN
ejpam-2674	96	26	is	be	AUX
ejpam-2674	96	27	a	a	DET
ejpam-2674	96	28	near	near	ADJ
ejpam-2674	96	29	monoid	monoid	NOUN
ejpam-2674	96	30	,	,	PUNCT
ejpam-2674	96	31	if	if	SCONJ
ejpam-2674	96	32	it	it	PRON
ejpam-2674	96	33	has	have	VERB
ejpam-2674	96	34	a	a	DET
ejpam-2674	96	35	near	near	ADJ
ejpam-2674	96	36	identity	identity	NOUN
ejpam-2674	96	37	.	.	PUNCT
ejpam-2674	97	1	n.	n.	NOUN
ejpam-2674	97	2	bağırmaz	bağırmaz	PROPN
ejpam-2674	97	3	/	/	SYM
ejpam-2674	97	4	eur	eur	PROPN
ejpam-2674	97	5	.	.	PUNCT
ejpam-2674	98	1	j.	j.	PROPN
ejpam-2674	98	2	pure	pure	PROPN
ejpam-2674	98	3	appl	appl	PROPN
ejpam-2674	98	4	.	.	PROPN
ejpam-2674	98	5	math	math	PROPN
ejpam-2674	98	6	,	,	PUNCT
ejpam-2674	98	7	11	11	NUM
ejpam-2674	98	8	(	(	PUNCT
ejpam-2674	98	9	2	2	NUM
ejpam-2674	98	10	)	)	PUNCT
ejpam-2674	98	11	(	(	PUNCT
ejpam-2674	98	12	2018	2018	NUM
ejpam-2674	98	13	)	)	PUNCT
ejpam-2674	98	14	,	,	PUNCT
ejpam-2674	98	15	505	505	NUM
ejpam-2674	98	16	-	-	SYM
ejpam-2674	98	17	516	516	NUM
ejpam-2674	98	18	509	509	NUM
ejpam-2674	98	19	lemma	lemma	PROPN
ejpam-2674	98	20	1	1	NUM
ejpam-2674	98	21	.	.	PUNCT
ejpam-2674	99	1	a	a	DET
ejpam-2674	99	2	near	near	ADJ
ejpam-2674	99	3	semigroup	semigroup	PROPN
ejpam-2674	99	4	s	s	PART
ejpam-2674	99	5	can	can	AUX
ejpam-2674	99	6	have	have	VERB
ejpam-2674	99	7	at	at	ADP
ejpam-2674	99	8	most	most	ADV
ejpam-2674	99	9	one	one	NUM
ejpam-2674	99	10	identity	identity	NOUN
ejpam-2674	99	11	.	.	PUNCT
ejpam-2674	100	1	in	in	ADP
ejpam-2674	100	2	fact	fact	NOUN
ejpam-2674	100	3	,	,	PUNCT
ejpam-2674	100	4	if	if	SCONJ
ejpam-2674	100	5	s	s	PROPN
ejpam-2674	100	6	has	have	VERB
ejpam-2674	100	7	a	a	DET
ejpam-2674	100	8	left	left	ADJ
ejpam-2674	100	9	identity	identity	NOUN
ejpam-2674	100	10	x	x	PUNCT
ejpam-2674	100	11	and	and	CCONJ
ejpam-2674	100	12	a	a	DET
ejpam-2674	100	13	right	right	ADJ
ejpam-2674	100	14	identity	identity	NOUN
ejpam-2674	100	15	y	y	NOUN
ejpam-2674	100	16	,	,	PUNCT
ejpam-2674	100	17	then	then	ADV
ejpam-2674	100	18	x	x	X
ejpam-2674	100	19	=	=	PUNCT
ejpam-2674	100	20	y.	y.	PROPN
ejpam-2674	100	21	in	in	ADP
ejpam-2674	100	22	particular	particular	ADJ
ejpam-2674	100	23	,	,	PUNCT
ejpam-2674	100	24	the	the	DET
ejpam-2674	100	25	identity	identity	NOUN
ejpam-2674	100	26	of	of	ADP
ejpam-2674	100	27	a	a	DET
ejpam-2674	100	28	near	near	ADJ
ejpam-2674	100	29	monoid	monoid	NOUN
ejpam-2674	100	30	is	be	AUX
ejpam-2674	100	31	unique	unique	ADJ
ejpam-2674	100	32	.	.	PUNCT
ejpam-2674	101	1	proof	proof	NOUN
ejpam-2674	101	2	.	.	PUNCT
ejpam-2674	102	1	by	by	ADP
ejpam-2674	102	2	the	the	DET
ejpam-2674	102	3	definitions	definition	NOUN
ejpam-2674	102	4	,	,	PUNCT
ejpam-2674	102	5	y	y	PROPN
ejpam-2674	102	6	=	=	PUNCT
ejpam-2674	102	7	xy	xy	PROPN
ejpam-2674	102	8	=	=	PUNCT
ejpam-2674	103	1	x.	x.	NOUN
ejpam-2674	103	2	the	the	DET
ejpam-2674	103	3	identity	identity	NOUN
ejpam-2674	103	4	of	of	ADP
ejpam-2674	103	5	a	a	DET
ejpam-2674	103	6	near	near	ADJ
ejpam-2674	103	7	monoid	monoid	PROPN
ejpam-2674	103	8	s	s	X
ejpam-2674	103	9	is	be	AUX
ejpam-2674	103	10	denoted	denote	VERB
ejpam-2674	103	11	by	by	ADP
ejpam-2674	103	12	e.	e.	PROPN
ejpam-2674	103	13	a	a	DET
ejpam-2674	103	14	near	near	PROPN
ejpam-2674	103	15	monoid	monoid	PROPN
ejpam-2674	103	16	g	g	PROPN
ejpam-2674	103	17	is	be	AUX
ejpam-2674	103	18	a	a	DET
ejpam-2674	103	19	near	near	ADJ
ejpam-2674	103	20	group	group	NOUN
ejpam-2674	103	21	,	,	PUNCT
ejpam-2674	103	22	if	if	SCONJ
ejpam-2674	103	23	every	every	DET
ejpam-2674	103	24	x	x	X
ejpam-2674	103	25	∈	∈	PROPN
ejpam-2674	103	26	g	g	NOUN
ejpam-2674	103	27	has	have	VERB
ejpam-2674	103	28	a	a	DET
ejpam-2674	103	29	inverse	inverse	NOUN
ejpam-2674	104	1	x−1	x−1	PROPN
ejpam-2674	104	2	∈	∈	PROPN
ejpam-2674	104	3	g	g	PROPN
ejpam-2674	104	4	:	:	PUNCT
ejpam-2674	104	5	x−1x	x−1x	X
ejpam-2674	104	6	=	=	SYM
ejpam-2674	104	7	e	e	X
ejpam-2674	104	8	=	=	SYM
ejpam-2674	104	9	x−1x	x−1x	PROPN
ejpam-2674	104	10	.	.	PUNCT
ejpam-2674	105	1	definition	definition	NOUN
ejpam-2674	105	2	2	2	NUM
ejpam-2674	105	3	.	.	PUNCT
ejpam-2674	106	1	let	let	AUX
ejpam-2674	106	2	(	(	PUNCT
ejpam-2674	106	3	o	o	NOUN
ejpam-2674	106	4	,	,	PUNCT
ejpam-2674	106	5	f,∼br	f,∼br	NOUN
ejpam-2674	106	6	,	,	PUNCT
ejpam-2674	106	7	nr	nr	PROPN
ejpam-2674	106	8	,	,	PUNCT
ejpam-2674	106	9	vnr	vnr	PROPN
ejpam-2674	106	10	)	)	PUNCT
ejpam-2674	106	11	be	be	AUX
ejpam-2674	106	12	a	a	DET
ejpam-2674	106	13	nearness	nearness	NOUN
ejpam-2674	106	14	approximation	approximation	NOUN
ejpam-2674	106	15	space	space	NOUN
ejpam-2674	106	16	and	and	CCONJ
ejpam-2674	106	17	(	(	PUNCT
ejpam-2674	106	18	·	·	PUNCT
ejpam-2674	106	19	)	)	PUNCT
ejpam-2674	106	20	be	be	AUX
ejpam-2674	106	21	a	a	DET
ejpam-2674	106	22	binary	binary	ADJ
ejpam-2674	106	23	operation	operation	NOUN
ejpam-2674	106	24	defined	define	VERB
ejpam-2674	106	25	on	on	ADP
ejpam-2674	106	26	o.	o.	NOUN
ejpam-2674	106	27	let	let	VERB
ejpam-2674	106	28	s	s	PRON
ejpam-2674	106	29	be	be	AUX
ejpam-2674	106	30	a	a	DET
ejpam-2674	106	31	near	near	ADJ
ejpam-2674	106	32	semigroup	semigroup	NOUN
ejpam-2674	106	33	and	and	CCONJ
ejpam-2674	106	34	h	h	NOUN
ejpam-2674	106	35	a	a	DET
ejpam-2674	106	36	nonempty	nonempty	NOUN
ejpam-2674	106	37	subset	subset	NOUN
ejpam-2674	106	38	of	of	ADP
ejpam-2674	106	39	s.	s.	PROPN
ejpam-2674	106	40	a	a	DET
ejpam-2674	106	41	nonempty	nonempty	ADV
ejpam-2674	106	42	subset	subset	VERB
ejpam-2674	106	43	h	h	NOUN
ejpam-2674	106	44	of	of	ADP
ejpam-2674	106	45	a	a	DET
ejpam-2674	106	46	near	near	ADJ
ejpam-2674	106	47	semigroup	semigroup	PROPN
ejpam-2674	106	48	s	s	PART
ejpam-2674	106	49	is	be	AUX
ejpam-2674	106	50	said	say	VERB
ejpam-2674	106	51	to	to	PART
ejpam-2674	106	52	be	be	AUX
ejpam-2674	106	53	a	a	DET
ejpam-2674	106	54	near	near	ADJ
ejpam-2674	106	55	subsemigroup	subsemigroup	NOUN
ejpam-2674	106	56	of	of	ADP
ejpam-2674	106	57	s	s	PROPN
ejpam-2674	106	58	,	,	PUNCT
ejpam-2674	106	59	if	if	SCONJ
ejpam-2674	106	60	ab	ab	PROPN
ejpam-2674	106	61	∈	∈	PROPN
ejpam-2674	106	62	nr(b)∗h	nr(b)∗h	NOUN
ejpam-2674	106	63	for	for	ADP
ejpam-2674	106	64	all	all	DET
ejpam-2674	106	65	a	a	DET
ejpam-2674	106	66	,	,	PUNCT
ejpam-2674	106	67	b	b	X
ejpam-2674	106	68	∈	∈	PROPN
ejpam-2674	106	69	h	h	NOUN
ejpam-2674	106	70	,	,	PUNCT
ejpam-2674	106	71	i.e.	i.e.	X
ejpam-2674	106	72	,	,	PUNCT
ejpam-2674	106	73	hh	hh	PROPN
ejpam-2674	106	74	⊆	⊆	NUM
ejpam-2674	106	75	nr(b)∗h	nr(b)∗h	NOUN
ejpam-2674	106	76	.	.	PUNCT
ejpam-2674	107	1	another	another	DET
ejpam-2674	107	2	difference	difference	NOUN
ejpam-2674	107	3	between	between	ADP
ejpam-2674	107	4	near	near	ADJ
ejpam-2674	107	5	semigroup	semigroup	PROPN
ejpam-2674	107	6	and	and	CCONJ
ejpam-2674	107	7	semigroup	semigroup	PROPN
ejpam-2674	107	8	is	be	AUX
ejpam-2674	107	9	the	the	DET
ejpam-2674	107	10	following	following	NOUN
ejpam-2674	107	11	:	:	PUNCT
ejpam-2674	107	12	proposition	proposition	NOUN
ejpam-2674	107	13	2	2	NUM
ejpam-2674	107	14	.	.	PUNCT
ejpam-2674	108	1	let	let	AUX
ejpam-2674	108	2	(	(	PUNCT
ejpam-2674	108	3	o	o	NOUN
ejpam-2674	108	4	,	,	PUNCT
ejpam-2674	108	5	f,∼br	f,∼br	NOUN
ejpam-2674	108	6	,	,	PUNCT
ejpam-2674	108	7	nr	nr	PROPN
ejpam-2674	108	8	,	,	PUNCT
ejpam-2674	108	9	vnr	vnr	PROPN
ejpam-2674	108	10	)	)	PUNCT
ejpam-2674	108	11	be	be	AUX
ejpam-2674	108	12	a	a	DET
ejpam-2674	108	13	nearness	nearness	NOUN
ejpam-2674	108	14	approximation	approximation	NOUN
ejpam-2674	108	15	space	space	NOUN
ejpam-2674	108	16	and	and	CCONJ
ejpam-2674	108	17	(	(	PUNCT
ejpam-2674	108	18	·	·	PUNCT
ejpam-2674	108	19	)	)	PUNCT
ejpam-2674	108	20	be	be	AUX
ejpam-2674	108	21	a	a	DET
ejpam-2674	108	22	binary	binary	ADJ
ejpam-2674	108	23	operation	operation	NOUN
ejpam-2674	108	24	defined	define	VERB
ejpam-2674	108	25	on	on	ADP
ejpam-2674	108	26	o.	o.	NOUN
ejpam-2674	108	27	let	let	VERB
ejpam-2674	108	28	h1	h1	VERB
ejpam-2674	108	29	and	and	CCONJ
ejpam-2674	108	30	h2	h2	NOUN
ejpam-2674	108	31	be	be	AUX
ejpam-2674	108	32	two	two	NUM
ejpam-2674	108	33	near	near	ADP
ejpam-2674	108	34	subsemigroups	subsemigroup	NOUN
ejpam-2674	108	35	of	of	ADP
ejpam-2674	108	36	the	the	DET
ejpam-2674	108	37	near	near	PROPN
ejpam-2674	108	38	semigroup	semigroup	PROPN
ejpam-2674	108	39	s.	s.	PROPN
ejpam-2674	108	40	a	a	DET
ejpam-2674	108	41	sufficient	sufficient	ADJ
ejpam-2674	108	42	condition	condition	NOUN
ejpam-2674	108	43	for	for	ADP
ejpam-2674	108	44	intersection	intersection	NOUN
ejpam-2674	108	45	of	of	ADP
ejpam-2674	108	46	two	two	NUM
ejpam-2674	108	47	near	near	ADP
ejpam-2674	108	48	subsemigroups	subsemigroup	NOUN
ejpam-2674	108	49	of	of	ADP
ejpam-2674	108	50	a	a	DET
ejpam-2674	108	51	near	near	ADJ
ejpam-2674	108	52	semigroup	semigroup	NOUN
ejpam-2674	108	53	to	to	PART
ejpam-2674	108	54	be	be	AUX
ejpam-2674	108	55	a	a	DET
ejpam-2674	108	56	near	near	ADJ
ejpam-2674	108	57	subsemigroup	subsemigroup	NOUN
ejpam-2674	108	58	is	be	AUX
ejpam-2674	108	59	nr(b)∗h1	nr(b)∗h1	ADJ
ejpam-2674	108	60	∩nr(b)∗h2	∩nr(b)∗h2	NOUN
ejpam-2674	108	61	=	=	X
ejpam-2674	108	62	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	108	63	(	(	PUNCT
ejpam-2674	108	64	h1	h1	PROPN
ejpam-2674	108	65	∩h2	∩h2	PROPN
ejpam-2674	108	66	)	)	PUNCT
ejpam-2674	108	67	.	.	PUNCT
ejpam-2674	109	1	proof	proof	NOUN
ejpam-2674	109	2	.	.	PUNCT
ejpam-2674	110	1	suppose	suppose	VERB
ejpam-2674	110	2	h1	h1	PROPN
ejpam-2674	110	3	and	and	CCONJ
ejpam-2674	110	4	h2	h2	NOUN
ejpam-2674	110	5	are	be	AUX
ejpam-2674	110	6	two	two	NUM
ejpam-2674	110	7	near	near	ADP
ejpam-2674	110	8	subsemigroups	subsemigroup	NOUN
ejpam-2674	110	9	of	of	ADP
ejpam-2674	110	10	s.	s.	PROPN
ejpam-2674	110	11	it	it	PRON
ejpam-2674	110	12	is	be	AUX
ejpam-2674	110	13	obvious	obvious	ADJ
ejpam-2674	110	14	that	that	SCONJ
ejpam-2674	110	15	h1	h1	PROPN
ejpam-2674	110	16	∩	∩	ADJ
ejpam-2674	110	17	h2	h2	PROPN
ejpam-2674	110	18	⊂	⊂	PROPN
ejpam-2674	110	19	s.	s.	PROPN
ejpam-2674	110	20	consider	consider	VERB
ejpam-2674	110	21	x	x	PRON
ejpam-2674	110	22	,	,	PUNCT
ejpam-2674	110	23	y	y	PROPN
ejpam-2674	110	24	∈	∈	PROPN
ejpam-2674	110	25	h1	h1	PROPN
ejpam-2674	110	26	∩	∩	ADJ
ejpam-2674	110	27	h2	h2	NOUN
ejpam-2674	110	28	.	.	PUNCT
ejpam-2674	111	1	because	because	SCONJ
ejpam-2674	111	2	h1	h1	PROPN
ejpam-2674	111	3	and	and	CCONJ
ejpam-2674	111	4	h2	h2	NOUN
ejpam-2674	111	5	are	be	AUX
ejpam-2674	111	6	near	near	ADP
ejpam-2674	111	7	subsemigroups	subsemigroup	NOUN
ejpam-2674	111	8	,	,	PUNCT
ejpam-2674	111	9	we	we	PRON
ejpam-2674	111	10	have	have	VERB
ejpam-2674	111	11	xy	xy	PROPN
ejpam-2674	111	12	∈	∈	PROPN
ejpam-2674	111	13	nr(b)∗h1	nr(b)∗h1	NOUN
ejpam-2674	111	14	,	,	PUNCT
ejpam-2674	111	15	xy	xy	PROPN
ejpam-2674	111	16	∈	∈	PROPN
ejpam-2674	111	17	nr(b)∗h2	nr(b)∗h2	PROPN
ejpam-2674	111	18	,	,	PUNCT
ejpam-2674	111	19	i.e.	i.e.	X
ejpam-2674	111	20	xy	xy	PROPN
ejpam-2674	111	21	∈	∈	PROPN
ejpam-2674	111	22	nr(b)∗h1	nr(b)∗h1	PROPN
ejpam-2674	111	23	∩	∩	ADJ
ejpam-2674	111	24	nr(b)∗h2	nr(b)∗h2	PROPN
ejpam-2674	111	25	.	.	PUNCT
ejpam-2674	112	1	assuming	assume	VERB
ejpam-2674	112	2	nr(b)∗h1	nr(b)∗h1	ADJ
ejpam-2674	112	3	∩	∩	ADJ
ejpam-2674	112	4	nr(b)∗h2	nr(b)∗h2	PROPN
ejpam-2674	112	5	=	=	SYM
ejpam-2674	112	6	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	112	7	(	(	PUNCT
ejpam-2674	112	8	h1	h1	PROPN
ejpam-2674	112	9	∩h2	∩h2	PROPN
ejpam-2674	112	10	)	)	PUNCT
ejpam-2674	112	11	,	,	PUNCT
ejpam-2674	112	12	we	we	PRON
ejpam-2674	112	13	have	have	VERB
ejpam-2674	112	14	xy	xy	PROPN
ejpam-2674	112	15	∈	∈	PROPN
ejpam-2674	112	16	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	112	17	(	(	PUNCT
ejpam-2674	112	18	h1	h1	PROPN
ejpam-2674	112	19	∩h2	∩h2	PROPN
ejpam-2674	112	20	)	)	PUNCT
ejpam-2674	112	21	.	.	PUNCT
ejpam-2674	113	1	thus	thus	ADV
ejpam-2674	113	2	h1	h1	VERB
ejpam-2674	113	3	∩h2	∩h2	PROPN
ejpam-2674	113	4	is	be	AUX
ejpam-2674	113	5	a	a	DET
ejpam-2674	113	6	near	near	ADJ
ejpam-2674	113	7	subsemigroup	subsemigroup	NOUN
ejpam-2674	113	8	of	of	ADP
ejpam-2674	113	9	s.	s.	PROPN
ejpam-2674	113	10	definition	definition	PROPN
ejpam-2674	113	11	3	3	X
ejpam-2674	113	12	.	.	PUNCT
ejpam-2674	114	1	let	let	AUX
ejpam-2674	114	2	(	(	PUNCT
ejpam-2674	114	3	o	o	NOUN
ejpam-2674	114	4	,	,	PUNCT
ejpam-2674	114	5	f,∼br	f,∼br	NOUN
ejpam-2674	114	6	,	,	PUNCT
ejpam-2674	114	7	nr	nr	PROPN
ejpam-2674	114	8	,	,	PUNCT
ejpam-2674	114	9	vnr	vnr	PROPN
ejpam-2674	114	10	)	)	PUNCT
ejpam-2674	114	11	be	be	AUX
ejpam-2674	114	12	a	a	DET
ejpam-2674	114	13	nearness	nearness	NOUN
ejpam-2674	114	14	approximation	approximation	NOUN
ejpam-2674	114	15	space	space	NOUN
ejpam-2674	114	16	and	and	CCONJ
ejpam-2674	114	17	(	(	PUNCT
ejpam-2674	114	18	·	·	PUNCT
ejpam-2674	114	19	)	)	PUNCT
ejpam-2674	114	20	be	be	AUX
ejpam-2674	114	21	a	a	DET
ejpam-2674	114	22	binary	binary	ADJ
ejpam-2674	114	23	operation	operation	NOUN
ejpam-2674	114	24	defined	define	VERB
ejpam-2674	114	25	on	on	ADP
ejpam-2674	114	26	o.	o.	PROPN
ejpam-2674	114	27	a	a	DET
ejpam-2674	114	28	nonempty	nonempty	NOUN
ejpam-2674	114	29	subset	subset	VERB
ejpam-2674	114	30	i	i	PRON
ejpam-2674	114	31	of	of	ADP
ejpam-2674	114	32	a	a	DET
ejpam-2674	114	33	near	near	ADJ
ejpam-2674	114	34	semigroup	semigroup	PROPN
ejpam-2674	114	35	s	s	PART
ejpam-2674	114	36	is	be	AUX
ejpam-2674	114	37	said	say	VERB
ejpam-2674	114	38	to	to	PART
ejpam-2674	114	39	be	be	AUX
ejpam-2674	114	40	a	a	DET
ejpam-2674	114	41	near	near	ADJ
ejpam-2674	114	42	left	left	ADJ
ejpam-2674	114	43	(	(	PUNCT
ejpam-2674	114	44	resp	resp	NOUN
ejpam-2674	114	45	.	.	PUNCT
ejpam-2674	115	1	right	right	ADJ
ejpam-2674	115	2	)	)	PUNCT
ejpam-2674	115	3	ideal	ideal	NOUN
ejpam-2674	115	4	of	of	ADP
ejpam-2674	115	5	s	s	PRON
ejpam-2674	115	6	if	if	SCONJ
ejpam-2674	115	7	si	si	PROPN
ejpam-2674	115	8	⊆	⊆	NUM
ejpam-2674	115	9	nr(b)∗i	nr(b)∗i	ADJ
ejpam-2674	115	10	(	(	PUNCT
ejpam-2674	115	11	resp	resp	NOUN
ejpam-2674	115	12	.	.	PUNCT
ejpam-2674	115	13	is	be	AUX
ejpam-2674	115	14	⊆	⊆	NUM
ejpam-2674	115	15	nr(b)∗i	nr(b)∗i	NOUN
ejpam-2674	115	16	)	)	PUNCT
ejpam-2674	115	17	.	.	PUNCT
ejpam-2674	116	1	a	a	DET
ejpam-2674	116	2	nonempty	nonempty	NOUN
ejpam-2674	116	3	subset	subset	VERB
ejpam-2674	116	4	i	i	PRON
ejpam-2674	116	5	of	of	ADP
ejpam-2674	116	6	s	s	PROPN
ejpam-2674	116	7	is	be	AUX
ejpam-2674	116	8	called	call	VERB
ejpam-2674	116	9	an	an	DET
ejpam-2674	116	10	near	near	ADJ
ejpam-2674	116	11	ideal	ideal	NOUN
ejpam-2674	116	12	of	of	ADP
ejpam-2674	116	13	s	s	PRON
ejpam-2674	116	14	if	if	SCONJ
ejpam-2674	116	15	i	i	PRON
ejpam-2674	116	16	is	be	AUX
ejpam-2674	116	17	both	both	CCONJ
ejpam-2674	116	18	a	a	DET
ejpam-2674	116	19	left	left	NOUN
ejpam-2674	116	20	and	and	CCONJ
ejpam-2674	116	21	a	a	DET
ejpam-2674	116	22	right	right	NOUN
ejpam-2674	116	23	near	near	ADP
ejpam-2674	116	24	ideal	ideal	NOUN
ejpam-2674	116	25	of	of	ADP
ejpam-2674	116	26	s.	s.	PROPN
ejpam-2674	116	27	proposition	proposition	PROPN
ejpam-2674	116	28	3	3	X
ejpam-2674	116	29	.	.	PUNCT
ejpam-2674	117	1	let	let	AUX
ejpam-2674	117	2	(	(	PUNCT
ejpam-2674	117	3	o	o	NOUN
ejpam-2674	117	4	,	,	PUNCT
ejpam-2674	117	5	f,∼br	f,∼br	NOUN
ejpam-2674	117	6	,	,	PUNCT
ejpam-2674	117	7	nr	nr	PROPN
ejpam-2674	117	8	,	,	PUNCT
ejpam-2674	117	9	vnr	vnr	PROPN
ejpam-2674	117	10	)	)	PUNCT
ejpam-2674	117	11	be	be	AUX
ejpam-2674	117	12	a	a	DET
ejpam-2674	117	13	nearness	nearness	NOUN
ejpam-2674	117	14	approximation	approximation	NOUN
ejpam-2674	117	15	space	space	NOUN
ejpam-2674	117	16	and	and	CCONJ
ejpam-2674	117	17	(	(	PUNCT
ejpam-2674	117	18	·	·	PUNCT
ejpam-2674	117	19	)	)	PUNCT
ejpam-2674	117	20	be	be	AUX
ejpam-2674	117	21	a	a	DET
ejpam-2674	117	22	binary	binary	ADJ
ejpam-2674	117	23	operation	operation	NOUN
ejpam-2674	117	24	defined	define	VERB
ejpam-2674	117	25	on	on	ADP
ejpam-2674	117	26	o	o	PROPN
ejpam-2674	117	27	and	and	CCONJ
ejpam-2674	117	28	s	s	PROPN
ejpam-2674	117	29	⊆	⊆	NUM
ejpam-2674	117	30	o.	o.	NOUN
ejpam-2674	117	31	then	then	ADV
ejpam-2674	117	32	(	(	PUNCT
ejpam-2674	117	33	1	1	X
ejpam-2674	117	34	)	)	PUNCT
ejpam-2674	117	35	if	if	SCONJ
ejpam-2674	117	36	h	h	NOUN
ejpam-2674	117	37	is	be	AUX
ejpam-2674	117	38	a	a	DET
ejpam-2674	117	39	subsemigroup	subsemigroup	NOUN
ejpam-2674	117	40	of	of	ADP
ejpam-2674	117	41	semigroup	semigroup	PROPN
ejpam-2674	117	42	s	s	PROPN
ejpam-2674	117	43	,	,	PUNCT
ejpam-2674	117	44	then	then	ADV
ejpam-2674	117	45	h	h	PROPN
ejpam-2674	117	46	is	be	AUX
ejpam-2674	117	47	a	a	DET
ejpam-2674	117	48	near	near	ADJ
ejpam-2674	117	49	subsemigroup	subsemigroup	NOUN
ejpam-2674	117	50	of	of	ADP
ejpam-2674	117	51	near	near	PROPN
ejpam-2674	117	52	semigroup	semigroup	PROPN
ejpam-2674	117	53	s.	s.	PROPN
ejpam-2674	117	54	(	(	PUNCT
ejpam-2674	117	55	2	2	X
ejpam-2674	117	56	)	)	PUNCT
ejpam-2674	117	57	if	if	SCONJ
ejpam-2674	117	58	i	i	PRON
ejpam-2674	117	59	is	be	AUX
ejpam-2674	117	60	a	a	DET
ejpam-2674	117	61	left	left	ADJ
ejpam-2674	117	62	(	(	PUNCT
ejpam-2674	117	63	right	right	ADJ
ejpam-2674	117	64	,	,	PUNCT
ejpam-2674	117	65	two	two	NUM
ejpam-2674	117	66	-	-	PUNCT
ejpam-2674	117	67	sided	sided	ADJ
ejpam-2674	117	68	)	)	PUNCT
ejpam-2674	117	69	ideal	ideal	NOUN
ejpam-2674	117	70	of	of	ADP
ejpam-2674	117	71	semigroup	semigroup	PROPN
ejpam-2674	117	72	s	s	PROPN
ejpam-2674	117	73	,	,	PUNCT
ejpam-2674	117	74	then	then	ADV
ejpam-2674	117	75	i	i	PRON
ejpam-2674	117	76	is	be	AUX
ejpam-2674	117	77	a	a	DET
ejpam-2674	117	78	near	near	ADJ
ejpam-2674	117	79	left	left	NOUN
ejpam-2674	117	80	(	(	PUNCT
ejpam-2674	117	81	right	right	ADJ
ejpam-2674	117	82	,	,	PUNCT
ejpam-2674	117	83	two	two	NUM
ejpam-2674	117	84	-	-	PUNCT
ejpam-2674	117	85	sided	sided	ADJ
ejpam-2674	117	86	)	)	PUNCT
ejpam-2674	117	87	ideal	ideal	NOUN
ejpam-2674	117	88	of	of	ADP
ejpam-2674	117	89	near	near	PROPN
ejpam-2674	117	90	semigroup	semigroup	PROPN
ejpam-2674	117	91	s.	s.	PROPN
ejpam-2674	117	92	proof	proof	PROPN
ejpam-2674	117	93	.	.	PUNCT
ejpam-2674	118	1	(	(	PUNCT
ejpam-2674	118	2	1	1	X
ejpam-2674	118	3	)	)	PUNCT
ejpam-2674	118	4	let	let	VERB
ejpam-2674	118	5	h	h	NOUN
ejpam-2674	118	6	be	be	AUX
ejpam-2674	118	7	a	a	DET
ejpam-2674	118	8	subsemigroup	subsemigroup	NOUN
ejpam-2674	118	9	of	of	ADP
ejpam-2674	118	10	semigroup	semigroup	PROPN
ejpam-2674	118	11	s	s	PROPN
ejpam-2674	118	12	,	,	PUNCT
ejpam-2674	118	13	that	that	ADV
ejpam-2674	118	14	is	is	ADV
ejpam-2674	118	15	,	,	PUNCT
ejpam-2674	118	16	hh	hh	PROPN
ejpam-2674	118	17	⊆	⊆	NUM
ejpam-2674	118	18	h.	h.	NOUN
ejpam-2674	118	19	by	by	ADP
ejpam-2674	118	20	proposition	proposition	NOUN
ejpam-2674	118	21	1	1	NUM
ejpam-2674	118	22	(	(	PUNCT
ejpam-2674	118	23	1	1	NUM
ejpam-2674	118	24	)	)	PUNCT
ejpam-2674	118	25	,	,	PUNCT
ejpam-2674	118	26	we	we	PRON
ejpam-2674	118	27	have	have	VERB
ejpam-2674	118	28	that	that	DET
ejpam-2674	118	29	h	h	NOUN
ejpam-2674	118	30	⊆	⊆	NUM
ejpam-2674	118	31	nr(b)∗h	nr(b)∗h	NOUN
ejpam-2674	118	32	.	.	PUNCT
ejpam-2674	119	1	thus	thus	ADV
ejpam-2674	119	2	hh	hh	VERB
ejpam-2674	119	3	⊆	⊆	NUM
ejpam-2674	119	4	nr(b)∗h	nr(b)∗h	NOUN
ejpam-2674	119	5	.	.	PUNCT
ejpam-2674	120	1	hence	hence	ADV
ejpam-2674	120	2	,	,	PUNCT
ejpam-2674	120	3	h	h	NOUN
ejpam-2674	120	4	is	be	AUX
ejpam-2674	120	5	a	a	DET
ejpam-2674	120	6	near	near	ADJ
ejpam-2674	120	7	subsemigroup	subsemigroup	NOUN
ejpam-2674	120	8	of	of	ADP
ejpam-2674	120	9	near	near	PROPN
ejpam-2674	120	10	semigroup	semigroup	PROPN
ejpam-2674	120	11	s.	s.	PROPN
ejpam-2674	120	12	(	(	PUNCT
ejpam-2674	120	13	2	2	X
ejpam-2674	120	14	)	)	PUNCT
ejpam-2674	120	15	let	let	VERB
ejpam-2674	120	16	i	i	PRON
ejpam-2674	120	17	be	be	AUX
ejpam-2674	120	18	a	a	DET
ejpam-2674	120	19	left	left	ADJ
ejpam-2674	120	20	ideal	ideal	NOUN
ejpam-2674	120	21	of	of	ADP
ejpam-2674	120	22	semigroup	semigroup	PROPN
ejpam-2674	120	23	s	s	PROPN
ejpam-2674	120	24	,	,	PUNCT
ejpam-2674	120	25	that	that	ADV
ejpam-2674	120	26	is	is	ADV
ejpam-2674	120	27	,	,	PUNCT
ejpam-2674	120	28	si	si	PROPN
ejpam-2674	120	29	⊆	⊆	NUM
ejpam-2674	120	30	i.	i.	NOUN
ejpam-2674	120	31	since	since	SCONJ
ejpam-2674	120	32	i	i	PRON
ejpam-2674	120	33	⊆	⊆	NUM
ejpam-2674	120	34	s	s	NOUN
ejpam-2674	120	35	,	,	PUNCT
ejpam-2674	120	36	by	by	ADP
ejpam-2674	120	37	proposition	proposition	NOUN
ejpam-2674	120	38	1	1	NUM
ejpam-2674	120	39	(	(	PUNCT
ejpam-2674	120	40	5	5	NUM
ejpam-2674	120	41	)	)	PUNCT
ejpam-2674	120	42	,	,	PUNCT
ejpam-2674	120	43	we	we	PRON
ejpam-2674	120	44	know	know	VERB
ejpam-2674	120	45	that	that	SCONJ
ejpam-2674	120	46	nr(b)∗i	nr(b)∗i	PROPN
ejpam-2674	120	47	⊆	⊆	NUM
ejpam-2674	120	48	nr(b)∗s	nr(b)∗s	NUM
ejpam-2674	120	49	.	.	PUNCT
ejpam-2674	121	1	then	then	ADV
ejpam-2674	121	2	,	,	PUNCT
ejpam-2674	121	3	by	by	ADP
ejpam-2674	121	4	proposition	proposition	NOUN
ejpam-2674	121	5	1.(1	1.(1	NUM
ejpam-2674	121	6	)	)	PUNCT
ejpam-2674	121	7	,	,	PUNCT
ejpam-2674	121	8	we	we	PRON
ejpam-2674	121	9	have	have	VERB
ejpam-2674	121	10	that	that	DET
ejpam-2674	121	11	n.	n.	PROPN
ejpam-2674	121	12	bağırmaz	bağırmaz	PROPN
ejpam-2674	121	13	/	/	SYM
ejpam-2674	121	14	eur	eur	PROPN
ejpam-2674	121	15	.	.	PUNCT
ejpam-2674	122	1	j.	j.	PROPN
ejpam-2674	122	2	pure	pure	PROPN
ejpam-2674	122	3	appl	appl	PROPN
ejpam-2674	122	4	.	.	PROPN
ejpam-2674	122	5	math	math	PROPN
ejpam-2674	122	6	,	,	PUNCT
ejpam-2674	122	7	11	11	NUM
ejpam-2674	122	8	(	(	PUNCT
ejpam-2674	122	9	2	2	NUM
ejpam-2674	122	10	)	)	PUNCT
ejpam-2674	122	11	(	(	PUNCT
ejpam-2674	122	12	2018	2018	NUM
ejpam-2674	122	13	)	)	PUNCT
ejpam-2674	122	14	,	,	PUNCT
ejpam-2674	122	15	505	505	NUM
ejpam-2674	122	16	-	-	SYM
ejpam-2674	122	17	516	516	NUM
ejpam-2674	122	18	510	510	NUM
ejpam-2674	122	19	i	i	PRON
ejpam-2674	122	20	⊆	⊆	NUM
ejpam-2674	122	21	nr(b)∗i	nr(b)∗i	NOUN
ejpam-2674	122	22	.	.	PUNCT
ejpam-2674	123	1	thus	thus	ADV
ejpam-2674	123	2	si	si	PROPN
ejpam-2674	123	3	⊆	⊆	NUM
ejpam-2674	123	4	i	i	PROPN
ejpam-2674	123	5	⊆	⊆	NUM
ejpam-2674	123	6	nr(b)∗i	nr(b)∗i	NOUN
ejpam-2674	123	7	.	.	PUNCT
ejpam-2674	124	1	this	this	PRON
ejpam-2674	124	2	means	mean	VERB
ejpam-2674	124	3	that	that	SCONJ
ejpam-2674	124	4	i	i	PRON
ejpam-2674	124	5	is	be	AUX
ejpam-2674	124	6	a	a	DET
ejpam-2674	124	7	near	near	ADJ
ejpam-2674	124	8	left	left	ADJ
ejpam-2674	124	9	ideal	ideal	NOUN
ejpam-2674	124	10	of	of	ADP
ejpam-2674	124	11	near	near	PROPN
ejpam-2674	124	12	semigroup	semigroup	PROPN
ejpam-2674	124	13	s.	s.	PROPN
ejpam-2674	124	14	also	also	ADV
ejpam-2674	124	15	,	,	PUNCT
ejpam-2674	124	16	we	we	PRON
ejpam-2674	124	17	can	can	AUX
ejpam-2674	124	18	easily	easily	ADV
ejpam-2674	124	19	show	show	VERB
ejpam-2674	124	20	that	that	SCONJ
ejpam-2674	124	21	i	i	PRON
ejpam-2674	124	22	is	be	AUX
ejpam-2674	124	23	a	a	DET
ejpam-2674	124	24	near	near	ADJ
ejpam-2674	124	25	right	right	ADJ
ejpam-2674	124	26	ideal	ideal	NOUN
ejpam-2674	124	27	of	of	ADP
ejpam-2674	124	28	near	near	PROPN
ejpam-2674	124	29	semigroup	semigroup	PROPN
ejpam-2674	124	30	s.	s.	PROPN
ejpam-2674	124	31	the	the	DET
ejpam-2674	124	32	other	other	ADJ
ejpam-2674	124	33	cases	case	NOUN
ejpam-2674	124	34	can	can	AUX
ejpam-2674	124	35	be	be	AUX
ejpam-2674	124	36	seen	see	VERB
ejpam-2674	124	37	in	in	ADP
ejpam-2674	124	38	a	a	DET
ejpam-2674	124	39	similar	similar	ADJ
ejpam-2674	124	40	way	way	NOUN
ejpam-2674	124	41	.	.	PUNCT
ejpam-2674	125	1	the	the	DET
ejpam-2674	125	2	following	follow	VERB
ejpam-2674	125	3	example	example	NOUN
ejpam-2674	125	4	shows	show	VERB
ejpam-2674	125	5	that	that	SCONJ
ejpam-2674	125	6	the	the	DET
ejpam-2674	125	7	converse	converse	NOUN
ejpam-2674	125	8	of	of	ADP
ejpam-2674	125	9	by	by	ADP
ejpam-2674	125	10	proposition	proposition	NOUN
ejpam-2674	125	11	3	3	NUM
ejpam-2674	125	12	is	be	AUX
ejpam-2674	125	13	not	not	PART
ejpam-2674	125	14	true	true	ADJ
ejpam-2674	125	15	.	.	PUNCT
ejpam-2674	126	1	example	example	NOUN
ejpam-2674	127	1	1	1	NUM
ejpam-2674	127	2	.	.	PUNCT
ejpam-2674	127	3	let	let	VERB
ejpam-2674	127	4	o	o	NOUN
ejpam-2674	127	5	=	=	PUNCT
ejpam-2674	127	6	{	{	PUNCT
ejpam-2674	127	7	1	1	NUM
ejpam-2674	127	8	,	,	PUNCT
ejpam-2674	127	9	2	2	NUM
ejpam-2674	127	10	,	,	PUNCT
ejpam-2674	127	11	3	3	NUM
ejpam-2674	127	12	,	,	PUNCT
ejpam-2674	127	13	4	4	NUM
ejpam-2674	127	14	,	,	PUNCT
ejpam-2674	127	15	5	5	NUM
ejpam-2674	127	16	}	}	PUNCT
ejpam-2674	127	17	be	be	AUX
ejpam-2674	127	18	a	a	DET
ejpam-2674	127	19	set	set	NOUN
ejpam-2674	127	20	of	of	ADP
ejpam-2674	127	21	perceptual	perceptual	ADJ
ejpam-2674	127	22	objects	object	NOUN
ejpam-2674	127	23	with	with	ADP
ejpam-2674	127	24	the	the	DET
ejpam-2674	127	25	following	follow	VERB
ejpam-2674	127	26	multiplication	multiplication	NOUN
ejpam-2674	127	27	table	table	NOUN
ejpam-2674	127	28	2	2	NUM
ejpam-2674	127	29	and	and	CCONJ
ejpam-2674	127	30	b	b	NOUN
ejpam-2674	127	31	=	=	SYM
ejpam-2674	127	32	{	{	PUNCT
ejpam-2674	127	33	φ1	φ1	PROPN
ejpam-2674	127	34	,	,	PUNCT
ejpam-2674	127	35	φ2	φ2	PROPN
ejpam-2674	127	36	,	,	PUNCT
ejpam-2674	127	37	φ3	φ3	NOUN
ejpam-2674	127	38	}	}	PUNCT
ejpam-2674	127	39	⊆	⊆	NUM
ejpam-2674	127	40	f	f	X
ejpam-2674	127	41	be	be	AUX
ejpam-2674	127	42	a	a	DET
ejpam-2674	127	43	set	set	NOUN
ejpam-2674	127	44	of	of	ADP
ejpam-2674	127	45	probe	probe	NOUN
ejpam-2674	127	46	functions	function	NOUN
ejpam-2674	127	47	with	with	ADP
ejpam-2674	127	48	the	the	DET
ejpam-2674	127	49	following	follow	VERB
ejpam-2674	127	50	multiplication	multiplication	NOUN
ejpam-2674	127	51	table	table	NOUN
ejpam-2674	127	52	3	3	NUM
ejpam-2674	127	53	,	,	PUNCT
ejpam-2674	127	54	respectively	respectively	ADV
ejpam-2674	127	55	.	.	PUNCT
ejpam-2674	127	56	·	·	PUNCT
ejpam-2674	128	1	a	a	DET
ejpam-2674	128	2	b	b	X
ejpam-2674	128	3	c	c	NOUN
ejpam-2674	128	4	d	d	X
ejpam-2674	128	5	e	e	X
ejpam-2674	128	6	f	f	PROPN
ejpam-2674	128	7	a	a	PRON
ejpam-2674	128	8	a	a	DET
ejpam-2674	128	9	a	a	DET
ejpam-2674	128	10	a	a	DET
ejpam-2674	128	11	b	b	PROPN
ejpam-2674	128	12	b	b	PROPN
ejpam-2674	128	13	a	a	DET
ejpam-2674	128	14	b	b	NOUN
ejpam-2674	128	15	a	a	DET
ejpam-2674	128	16	b	b	PROPN
ejpam-2674	128	17	b	b	PROPN
ejpam-2674	128	18	c	c	NOUN
ejpam-2674	129	1	d	d	NOUN
ejpam-2674	129	2	f	f	PROPN
ejpam-2674	129	3	c	c	NOUN
ejpam-2674	129	4	c	c	NOUN
ejpam-2674	129	5	c	c	NOUN
ejpam-2674	129	6	c	c	NOUN
ejpam-2674	129	7	e	e	PROPN
ejpam-2674	129	8	d	d	X
ejpam-2674	129	9	f	f	PROPN
ejpam-2674	129	10	d	d	PROPN
ejpam-2674	129	11	b	b	PROPN
ejpam-2674	129	12	a	a	DET
ejpam-2674	129	13	b	b	NOUN
ejpam-2674	129	14	d	d	X
ejpam-2674	129	15	f	f	PROPN
ejpam-2674	129	16	a	a	DET
ejpam-2674	129	17	e	e	NOUN
ejpam-2674	129	18	a	a	DET
ejpam-2674	129	19	b	b	NOUN
ejpam-2674	129	20	c	c	NOUN
ejpam-2674	129	21	d	d	PROPN
ejpam-2674	129	22	e	e	X
ejpam-2674	130	1	f	f	PROPN
ejpam-2674	130	2	f	f	PROPN
ejpam-2674	130	3	b	b	PROPN
ejpam-2674	130	4	f	f	PROPN
ejpam-2674	130	5	b	b	PROPN
ejpam-2674	131	1	f	f	PROPN
ejpam-2674	132	1	f	f	PROPN
ejpam-2674	133	1	a	a	DET
ejpam-2674	133	2	a	a	DET
ejpam-2674	133	3	b	b	NOUN
ejpam-2674	133	4	c	c	NOUN
ejpam-2674	133	5	d	d	X
ejpam-2674	133	6	e	e	PROPN
ejpam-2674	133	7	f	f	PROPN
ejpam-2674	133	8	φ1	φ1	PROPN
ejpam-2674	133	9	1	1	NUM
ejpam-2674	133	10	1	1	NUM
ejpam-2674	133	11	2	2	NUM
ejpam-2674	133	12	3	3	NUM
ejpam-2674	133	13	2	2	NUM
ejpam-2674	133	14	4	4	NUM
ejpam-2674	133	15	φ2	φ2	NOUN
ejpam-2674	133	16	1	1	NUM
ejpam-2674	133	17	2	2	NUM
ejpam-2674	133	18	2	2	NUM
ejpam-2674	133	19	3	3	NUM
ejpam-2674	133	20	4	4	NUM
ejpam-2674	133	21	4	4	NUM
ejpam-2674	133	22	φ3	φ3	NOUN
ejpam-2674	133	23	1	1	NUM
ejpam-2674	133	24	1	1	NUM
ejpam-2674	133	25	3	3	NUM
ejpam-2674	133	26	2	2	NUM
ejpam-2674	133	27	4	4	NUM
ejpam-2674	133	28	4	4	NUM
ejpam-2674	133	29	table	table	NOUN
ejpam-2674	133	30	2	2	NUM
ejpam-2674	133	31	.	.	PUNCT
ejpam-2674	133	32	table	table	NOUN
ejpam-2674	133	33	3	3	NUM
ejpam-2674	133	34	.	.	PUNCT
ejpam-2674	134	1	since	since	SCONJ
ejpam-2674	134	2	[	[	X
ejpam-2674	134	3	a]φ1	a]φ1	X
ejpam-2674	134	4	=	=	X
ejpam-2674	134	5	{	{	PUNCT
ejpam-2674	134	6	a	a	DET
ejpam-2674	134	7	,	,	PUNCT
ejpam-2674	134	8	b	b	NOUN
ejpam-2674	134	9	}	}	PUNCT
ejpam-2674	134	10	,	,	PUNCT
ejpam-2674	134	11	[	[	X
ejpam-2674	134	12	c]φ1	c]φ1	X
ejpam-2674	134	13	=	=	X
ejpam-2674	134	14	{	{	PUNCT
ejpam-2674	134	15	c	c	NOUN
ejpam-2674	134	16	,	,	PUNCT
ejpam-2674	134	17	e	e	NOUN
ejpam-2674	134	18	}	}	PUNCT
ejpam-2674	134	19	,	,	PUNCT
ejpam-2674	134	20	[	[	X
ejpam-2674	134	21	d]φ1	d]φ1	X
ejpam-2674	134	22	=	=	SYM
ejpam-2674	134	23	{	{	PUNCT
ejpam-2674	134	24	d	d	NOUN
ejpam-2674	134	25	}	}	PUNCT
ejpam-2674	134	26	,	,	PUNCT
ejpam-2674	134	27	[	[	X
ejpam-2674	134	28	f	f	X
ejpam-2674	134	29	]	]	X
ejpam-2674	134	30	φ1	φ1	NOUN
ejpam-2674	134	31	=	=	SYM
ejpam-2674	134	32	{	{	PUNCT
ejpam-2674	134	33	f	f	X
ejpam-2674	134	34	}	}	PUNCT
ejpam-2674	134	35	we	we	PRON
ejpam-2674	134	36	have	have	VERB
ejpam-2674	134	37	ξφ1	ξφ1	NOUN
ejpam-2674	134	38	=	=	PUNCT
ejpam-2674	134	39	{	{	PUNCT
ejpam-2674	134	40	[	[	X
ejpam-2674	134	41	a]φ1	a]φ1	X
ejpam-2674	134	42	,	,	PUNCT
ejpam-2674	134	43	[	[	X
ejpam-2674	134	44	c]φ1	c]φ1	X
ejpam-2674	134	45	,	,	PUNCT
ejpam-2674	134	46	[	[	X
ejpam-2674	134	47	d]φ1	d]φ1	X
ejpam-2674	134	48	,	,	PUNCT
ejpam-2674	134	49	[	[	X
ejpam-2674	134	50	f	f	X
ejpam-2674	134	51	]	]	X
ejpam-2674	134	52	φ1	φ1	PROPN
ejpam-2674	134	53	}	}	PUNCT
ejpam-2674	134	54	.	.	PUNCT
ejpam-2674	135	1	since	since	SCONJ
ejpam-2674	135	2	[	[	X
ejpam-2674	135	3	a]φ2	a]φ2	X
ejpam-2674	135	4	=	=	X
ejpam-2674	135	5	{	{	PUNCT
ejpam-2674	135	6	a	a	NOUN
ejpam-2674	135	7	}	}	PUNCT
ejpam-2674	135	8	,	,	PUNCT
ejpam-2674	135	9	[	[	X
ejpam-2674	135	10	b]φ2	b]φ2	NOUN
ejpam-2674	135	11	=	=	SYM
ejpam-2674	135	12	{	{	PUNCT
ejpam-2674	135	13	b	b	NOUN
ejpam-2674	135	14	,	,	PUNCT
ejpam-2674	135	15	c	c	NOUN
ejpam-2674	135	16	}	}	PUNCT
ejpam-2674	135	17	,	,	PUNCT
ejpam-2674	135	18	[	[	X
ejpam-2674	135	19	d]φ2	d]φ2	X
ejpam-2674	135	20	=	=	PUNCT
ejpam-2674	135	21	{	{	PUNCT
ejpam-2674	135	22	d	d	NOUN
ejpam-2674	135	23	}	}	PUNCT
ejpam-2674	135	24	,	,	PUNCT
ejpam-2674	135	25	[	[	X
ejpam-2674	135	26	e]φ2	e]φ2	X
ejpam-2674	135	27	=	=	SYM
ejpam-2674	135	28	{	{	PUNCT
ejpam-2674	135	29	e	e	NOUN
ejpam-2674	135	30	,	,	PUNCT
ejpam-2674	135	31	f	f	X
ejpam-2674	135	32	}	}	PUNCT
ejpam-2674	135	33	we	we	PRON
ejpam-2674	135	34	have	have	VERB
ejpam-2674	135	35	ξφ2	ξφ2	NOUN
ejpam-2674	135	36	=	=	SYM
ejpam-2674	135	37	{	{	PUNCT
ejpam-2674	136	1	[	[	X
ejpam-2674	136	2	a]φ2	a]φ2	NOUN
ejpam-2674	136	3	,	,	PUNCT
ejpam-2674	136	4	[	[	X
ejpam-2674	136	5	b]φ2	b]φ2	INTJ
ejpam-2674	136	6	,	,	PUNCT
ejpam-2674	136	7	[	[	X
ejpam-2674	136	8	d]φ2	d]φ2	X
ejpam-2674	136	9	,	,	PUNCT
ejpam-2674	136	10	[	[	X
ejpam-2674	136	11	e]φ2	e]φ2	X
ejpam-2674	136	12	}	}	PUNCT
ejpam-2674	136	13	.	.	PUNCT
ejpam-2674	137	1	since	since	SCONJ
ejpam-2674	137	2	[	[	X
ejpam-2674	137	3	a]φ3	a]φ3	X
ejpam-2674	137	4	=	=	X
ejpam-2674	137	5	{	{	PUNCT
ejpam-2674	137	6	a	a	DET
ejpam-2674	137	7	,	,	PUNCT
ejpam-2674	137	8	b	b	NOUN
ejpam-2674	137	9	}	}	PUNCT
ejpam-2674	137	10	,	,	PUNCT
ejpam-2674	137	11	[	[	X
ejpam-2674	137	12	c]φ3	c]φ3	NOUN
ejpam-2674	137	13	=	=	X
ejpam-2674	137	14	{	{	PUNCT
ejpam-2674	137	15	c	c	NOUN
ejpam-2674	137	16	}	}	PUNCT
ejpam-2674	137	17	,	,	PUNCT
ejpam-2674	137	18	[	[	X
ejpam-2674	137	19	d]φ3	d]φ3	X
ejpam-2674	137	20	=	=	SYM
ejpam-2674	137	21	{	{	PUNCT
ejpam-2674	137	22	d	d	NOUN
ejpam-2674	137	23	}	}	PUNCT
ejpam-2674	137	24	,	,	PUNCT
ejpam-2674	137	25	[	[	X
ejpam-2674	137	26	e]φ3	e]φ3	NOUN
ejpam-2674	137	27	=	=	SYM
ejpam-2674	137	28	{	{	PUNCT
ejpam-2674	137	29	e	e	NOUN
ejpam-2674	137	30	,	,	PUNCT
ejpam-2674	137	31	f	f	NOUN
ejpam-2674	137	32	}	}	PUNCT
ejpam-2674	137	33	.	.	PUNCT
ejpam-2674	138	1	we	we	PRON
ejpam-2674	138	2	have	have	VERB
ejpam-2674	138	3	ξφ3	ξφ3	NOUN
ejpam-2674	138	4	=	=	SYM
ejpam-2674	138	5	{	{	PUNCT
ejpam-2674	138	6	[	[	X
ejpam-2674	138	7	a]φ3	a]φ3	X
ejpam-2674	138	8	,	,	PUNCT
ejpam-2674	138	9	[	[	X
ejpam-2674	138	10	c]φ3	c]φ3	X
ejpam-2674	138	11	,	,	PUNCT
ejpam-2674	138	12	[	[	X
ejpam-2674	138	13	d]φ3	d]φ3	ADJ
ejpam-2674	138	14	,	,	PUNCT
ejpam-2674	138	15	[	[	X
ejpam-2674	138	16	e]φ3	e]φ3	ADV
ejpam-2674	138	17	}	}	PUNCT
ejpam-2674	138	18	.	.	PUNCT
ejpam-2674	139	1	therefore	therefore	ADV
ejpam-2674	139	2	,	,	PUNCT
ejpam-2674	139	3	for	for	ADP
ejpam-2674	139	4	r	r	NOUN
ejpam-2674	139	5	=	=	SYM
ejpam-2674	139	6	1	1	NUM
ejpam-2674	139	7	,	,	PUNCT
ejpam-2674	139	8	a	a	DET
ejpam-2674	139	9	set	set	VERB
ejpam-2674	139	10	partitions	partition	NOUN
ejpam-2674	139	11	of	of	ADP
ejpam-2674	139	12	o	o	PROPN
ejpam-2674	139	13	is	be	AUX
ejpam-2674	139	14	n1(b	n1(b	NOUN
ejpam-2674	139	15	)	)	PUNCT
ejpam-2674	139	16	=	=	SYM
ejpam-2674	139	17	{	{	PUNCT
ejpam-2674	139	18	ξφ1	ξφ1	PROPN
ejpam-2674	139	19	,	,	PUNCT
ejpam-2674	139	20	ξφ2	ξφ2	NOUN
ejpam-2674	139	21	,	,	PUNCT
ejpam-2674	139	22	ξφ3	ξφ3	PROPN
ejpam-2674	139	23	}	}	PUNCT
ejpam-2674	139	24	.	.	PUNCT
ejpam-2674	140	1	let	let	VERB
ejpam-2674	140	2	s	s	VERB
ejpam-2674	140	3	=	=	PUNCT
ejpam-2674	140	4	{	{	PUNCT
ejpam-2674	140	5	b	b	PROPN
ejpam-2674	140	6	,	,	PUNCT
ejpam-2674	140	7	c	c	X
ejpam-2674	140	8	,	,	PUNCT
ejpam-2674	140	9	d	d	X
ejpam-2674	140	10	}	}	PUNCT
ejpam-2674	140	11	be	be	AUX
ejpam-2674	140	12	a	a	DET
ejpam-2674	140	13	subset	subset	NOUN
ejpam-2674	140	14	of	of	ADP
ejpam-2674	140	15	perceptual	perceptual	ADJ
ejpam-2674	140	16	o	o	NOUN
ejpam-2674	140	17	as	as	ADP
ejpam-2674	140	18	in	in	ADP
ejpam-2674	140	19	table	table	NOUN
ejpam-2674	140	20	4	4	NUM
ejpam-2674	140	21	.	.	PUNCT
ejpam-2674	140	22	·	·	PUNCT
ejpam-2674	141	1	b	b	X
ejpam-2674	141	2	c	c	X
ejpam-2674	141	3	d	d	PROPN
ejpam-2674	141	4	b	b	PROPN
ejpam-2674	141	5	b	b	PROPN
ejpam-2674	141	6	b	b	PROPN
ejpam-2674	141	7	c	c	NOUN
ejpam-2674	141	8	c	c	NOUN
ejpam-2674	141	9	c	c	NOUN
ejpam-2674	141	10	c	c	NOUN
ejpam-2674	141	11	e	e	PROPN
ejpam-2674	141	12	d	d	X
ejpam-2674	141	13	a	a	DET
ejpam-2674	141	14	b	b	X
ejpam-2674	141	15	d	d	X
ejpam-2674	141	16	n.	n.	PROPN
ejpam-2674	141	17	bağırmaz	bağırmaz	PROPN
ejpam-2674	141	18	/	/	SYM
ejpam-2674	141	19	eur	eur	PROPN
ejpam-2674	141	20	.	.	PUNCT
ejpam-2674	142	1	j.	j.	PROPN
ejpam-2674	142	2	pure	pure	PROPN
ejpam-2674	142	3	appl	appl	PROPN
ejpam-2674	142	4	.	.	PROPN
ejpam-2674	142	5	math	math	PROPN
ejpam-2674	142	6	,	,	PUNCT
ejpam-2674	142	7	11	11	NUM
ejpam-2674	142	8	(	(	PUNCT
ejpam-2674	142	9	2	2	NUM
ejpam-2674	142	10	)	)	PUNCT
ejpam-2674	142	11	(	(	PUNCT
ejpam-2674	142	12	2018	2018	NUM
ejpam-2674	142	13	)	)	PUNCT
ejpam-2674	142	14	,	,	PUNCT
ejpam-2674	142	15	505	505	NUM
ejpam-2674	142	16	-	-	SYM
ejpam-2674	142	17	516	516	NUM
ejpam-2674	142	18	511	511	NUM
ejpam-2674	142	19	table	table	NOUN
ejpam-2674	142	20	4	4	NUM
ejpam-2674	142	21	.	.	PUNCT
ejpam-2674	143	1	then	then	ADV
ejpam-2674	143	2	,	,	PUNCT
ejpam-2674	143	3	we	we	PRON
ejpam-2674	143	4	have	have	VERB
ejpam-2674	143	5	that	that	DET
ejpam-2674	143	6	n1(b)∗s	n1(b)∗s	PROPN
ejpam-2674	143	7	=	=	SYM
ejpam-2674	143	8	∪	∪	ADP
ejpam-2674	143	9	x∈o	x∈o	NOUN
ejpam-2674	143	10	{	{	PUNCT
ejpam-2674	143	11	[	[	X
ejpam-2674	143	12	x]b1	x]b1	X
ejpam-2674	143	13	:	:	PUNCT
ejpam-2674	144	1	[	[	X
ejpam-2674	144	2	x]b1	x]b1	PUNCT
ejpam-2674	144	3	∩	∩	PROPN
ejpam-2674	144	4	s	s	PART
ejpam-2674	144	5	6=	6=	NUM
ejpam-2674	144	6	∅	∅	NOUN
ejpam-2674	144	7	}	}	PUNCT
ejpam-2674	144	8	=	=	SYM
ejpam-2674	144	9	{	{	PUNCT
ejpam-2674	144	10	a	a	DET
ejpam-2674	144	11	,	,	PUNCT
ejpam-2674	144	12	b	b	NOUN
ejpam-2674	144	13	}	}	PUNCT
ejpam-2674	144	14	∪	∪	X
ejpam-2674	144	15	{	{	PUNCT
ejpam-2674	144	16	c	c	NOUN
ejpam-2674	144	17	,	,	PUNCT
ejpam-2674	144	18	e	e	NOUN
ejpam-2674	144	19	}	}	PUNCT
ejpam-2674	144	20	∪	∪	ADJ
ejpam-2674	144	21	{	{	PUNCT
ejpam-2674	144	22	d	d	NOUN
ejpam-2674	144	23	}	}	PUNCT
ejpam-2674	144	24	∪	∪	ADJ
ejpam-2674	144	25	{	{	PUNCT
ejpam-2674	144	26	b	b	NOUN
ejpam-2674	144	27	,	,	PUNCT
ejpam-2674	144	28	c	c	NOUN
ejpam-2674	144	29	}	}	PUNCT
ejpam-2674	144	30	∪	∪	X
ejpam-2674	144	31	{	{	PUNCT
ejpam-2674	144	32	d	d	NOUN
ejpam-2674	144	33	}	}	PUNCT
ejpam-2674	144	34	∪	∪	ADJ
ejpam-2674	144	35	{	{	PUNCT
ejpam-2674	144	36	c	c	NOUN
ejpam-2674	144	37	}	}	PUNCT
ejpam-2674	144	38	=	=	SYM
ejpam-2674	144	39	{	{	PUNCT
ejpam-2674	144	40	a	a	PRON
ejpam-2674	144	41	,	,	PUNCT
ejpam-2674	144	42	b	b	NOUN
ejpam-2674	144	43	,	,	PUNCT
ejpam-2674	144	44	c	c	NOUN
ejpam-2674	144	45	,	,	PUNCT
ejpam-2674	144	46	d	d	NOUN
ejpam-2674	144	47	,	,	PUNCT
ejpam-2674	144	48	e	e	NOUN
ejpam-2674	144	49	}	}	PUNCT
ejpam-2674	144	50	.	.	PUNCT
ejpam-2674	145	1	from	from	ADP
ejpam-2674	145	2	definition	definition	NOUN
ejpam-2674	145	3	1	1	NUM
ejpam-2674	145	4	,	,	PUNCT
ejpam-2674	145	5	s	s	VERB
ejpam-2674	145	6	⊆	⊆	NUM
ejpam-2674	145	7	o	o	NOUN
ejpam-2674	145	8	is	be	AUX
ejpam-2674	145	9	a	a	DET
ejpam-2674	145	10	near	near	ADJ
ejpam-2674	145	11	semigroup	semigroup	NOUN
ejpam-2674	145	12	.	.	PUNCT
ejpam-2674	146	1	because	because	SCONJ
ejpam-2674	146	2	d	d	PROPN
ejpam-2674	146	3	·	·	PUNCT
ejpam-2674	146	4	b	b	X
ejpam-2674	146	5	=	=	PUNCT
ejpam-2674	146	6	a	a	PROPN
ejpam-2674	146	7	/∈	/∈	PUNCT
ejpam-2674	147	1	s	s	VERB
ejpam-2674	148	1	we	we	PRON
ejpam-2674	148	2	have	have	VERB
ejpam-2674	148	3	s	s	NOUN
ejpam-2674	148	4	is	be	AUX
ejpam-2674	148	5	not	not	PART
ejpam-2674	148	6	a	a	DET
ejpam-2674	148	7	semigroup	semigroup	NOUN
ejpam-2674	148	8	.	.	PUNCT
ejpam-2674	149	1	let	let	VERB
ejpam-2674	149	2	h	h	NOUN
ejpam-2674	149	3	=	=	PUNCT
ejpam-2674	149	4	{	{	PUNCT
ejpam-2674	149	5	b	b	PROPN
ejpam-2674	149	6	,	,	PUNCT
ejpam-2674	149	7	c	c	NOUN
ejpam-2674	149	8	}	}	PUNCT
ejpam-2674	149	9	,	,	PUNCT
ejpam-2674	149	10	then	then	ADV
ejpam-2674	149	11	n1(b)∗h	n1(b)∗h	PROPN
ejpam-2674	149	12	=	=	SYM
ejpam-2674	149	13	∪	∪	ADP
ejpam-2674	149	14	x∈o	x∈o	NOUN
ejpam-2674	149	15	{	{	PUNCT
ejpam-2674	149	16	[	[	X
ejpam-2674	149	17	x]b1	x]b1	X
ejpam-2674	149	18	:	:	PUNCT
ejpam-2674	150	1	[	[	X
ejpam-2674	150	2	x]b1	x]b1	X
ejpam-2674	150	3	∩h	∩h	PROPN
ejpam-2674	150	4	6=	6=	PUNCT
ejpam-2674	150	5	∅	∅	NOUN
ejpam-2674	150	6	}	}	PUNCT
ejpam-2674	150	7	=	=	SYM
ejpam-2674	150	8	{	{	PUNCT
ejpam-2674	150	9	a	a	PRON
ejpam-2674	150	10	,	,	PUNCT
ejpam-2674	150	11	b	b	NOUN
ejpam-2674	150	12	}	}	PUNCT
ejpam-2674	150	13	∪	∪	X
ejpam-2674	150	14	{	{	PUNCT
ejpam-2674	150	15	c	c	NOUN
ejpam-2674	150	16	,	,	PUNCT
ejpam-2674	150	17	e	e	NOUN
ejpam-2674	150	18	}	}	PUNCT
ejpam-2674	150	19	∪	∪	ADJ
ejpam-2674	150	20	{	{	PUNCT
ejpam-2674	150	21	a	a	DET
ejpam-2674	150	22	,	,	PUNCT
ejpam-2674	150	23	b	b	NOUN
ejpam-2674	150	24	,	,	PUNCT
ejpam-2674	150	25	c	c	NOUN
ejpam-2674	150	26	}	}	PUNCT
ejpam-2674	150	27	=	=	SYM
ejpam-2674	150	28	{	{	PUNCT
ejpam-2674	150	29	a	a	PRON
ejpam-2674	150	30	,	,	PUNCT
ejpam-2674	150	31	b	b	NOUN
ejpam-2674	150	32	,	,	PUNCT
ejpam-2674	150	33	c	c	NOUN
ejpam-2674	150	34	}	}	PUNCT
ejpam-2674	150	35	.	.	PUNCT
ejpam-2674	151	1	from	from	ADP
ejpam-2674	151	2	definition	definition	NOUN
ejpam-2674	151	3	2	2	NUM
ejpam-2674	151	4	,	,	PUNCT
ejpam-2674	151	5	h	h	NOUN
ejpam-2674	151	6	is	be	AUX
ejpam-2674	151	7	a	a	DET
ejpam-2674	151	8	near	near	ADJ
ejpam-2674	151	9	subsemigroup	subsemigroup	NOUN
ejpam-2674	151	10	of	of	ADP
ejpam-2674	151	11	near	near	PROPN
ejpam-2674	151	12	semigroup	semigroup	PROPN
ejpam-2674	151	13	s.	s.	PROPN
ejpam-2674	151	14	let	let	VERB
ejpam-2674	151	15	i	i	PRON
ejpam-2674	151	16	=	=	PUNCT
ejpam-2674	151	17	{	{	PUNCT
ejpam-2674	151	18	c	c	X
ejpam-2674	151	19	,	,	PUNCT
ejpam-2674	151	20	d	d	NOUN
ejpam-2674	151	21	}	}	PUNCT
ejpam-2674	151	22	,	,	PUNCT
ejpam-2674	151	23	then	then	ADV
ejpam-2674	151	24	n1(b)∗i	n1(b)∗i	ADV
ejpam-2674	151	25	=	=	SYM
ejpam-2674	151	26	∪	∪	ADP
ejpam-2674	151	27	x∈o	x∈o	NOUN
ejpam-2674	151	28	{	{	PUNCT
ejpam-2674	151	29	[	[	X
ejpam-2674	151	30	x]b1	x]b1	X
ejpam-2674	151	31	:	:	PUNCT
ejpam-2674	152	1	[	[	X
ejpam-2674	152	2	x]b1	x]b1	NOUN
ejpam-2674	152	3	∩	∩	X
ejpam-2674	152	4	i	i	ADP
ejpam-2674	152	5	6=	6=	NOUN
ejpam-2674	152	6	∅	∅	NOUN
ejpam-2674	152	7	}	}	PUNCT
ejpam-2674	152	8	=	=	SYM
ejpam-2674	152	9	{	{	PUNCT
ejpam-2674	152	10	c	c	NOUN
ejpam-2674	152	11	,	,	PUNCT
ejpam-2674	152	12	e	e	NOUN
ejpam-2674	152	13	}	}	PUNCT
ejpam-2674	152	14	∪	∪	ADJ
ejpam-2674	152	15	{	{	PUNCT
ejpam-2674	152	16	d	d	NOUN
ejpam-2674	152	17	}	}	PUNCT
ejpam-2674	152	18	∪	∪	ADJ
ejpam-2674	152	19	{	{	PUNCT
ejpam-2674	152	20	b	b	NOUN
ejpam-2674	152	21	,	,	PUNCT
ejpam-2674	152	22	c	c	NOUN
ejpam-2674	152	23	}	}	PUNCT
ejpam-2674	152	24	∪	∪	X
ejpam-2674	152	25	{	{	PUNCT
ejpam-2674	152	26	c	c	NOUN
ejpam-2674	152	27	}	}	PUNCT
ejpam-2674	152	28	=	=	SYM
ejpam-2674	152	29	{	{	PUNCT
ejpam-2674	152	30	b	b	PROPN
ejpam-2674	152	31	,	,	PUNCT
ejpam-2674	152	32	c	c	NOUN
ejpam-2674	152	33	,	,	PUNCT
ejpam-2674	152	34	d	d	NOUN
ejpam-2674	152	35	,	,	PUNCT
ejpam-2674	152	36	e	e	NOUN
ejpam-2674	152	37	}	}	PUNCT
ejpam-2674	152	38	.	.	PUNCT
ejpam-2674	153	1	from	from	ADP
ejpam-2674	153	2	definition	definition	NOUN
ejpam-2674	153	3	3	3	NUM
ejpam-2674	153	4	,	,	PUNCT
ejpam-2674	153	5	i	i	PRON
ejpam-2674	153	6	is	be	AUX
ejpam-2674	153	7	a	a	DET
ejpam-2674	153	8	near	near	ADJ
ejpam-2674	153	9	left	left	ADJ
ejpam-2674	153	10	ideal	ideal	NOUN
ejpam-2674	153	11	of	of	ADP
ejpam-2674	153	12	near	near	PROPN
ejpam-2674	153	13	semigroup	semigroup	PROPN
ejpam-2674	153	14	s.	s.	PROPN
ejpam-2674	154	1	the	the	DET
ejpam-2674	154	2	proposition	proposition	NOUN
ejpam-2674	154	3	3	3	NUM
ejpam-2674	154	4	shows	show	VERB
ejpam-2674	154	5	that	that	SCONJ
ejpam-2674	154	6	the	the	DET
ejpam-2674	154	7	notion	notion	NOUN
ejpam-2674	154	8	of	of	ADP
ejpam-2674	154	9	a	a	DET
ejpam-2674	154	10	near	near	ADJ
ejpam-2674	154	11	semigroup	semigroup	NOUN
ejpam-2674	154	12	(	(	PUNCT
ejpam-2674	154	13	left	leave	VERB
ejpam-2674	154	14	ideal	ideal	ADJ
ejpam-2674	154	15	,	,	PUNCT
ejpam-2674	154	16	right	right	ADJ
ejpam-2674	154	17	ideal	ideal	ADJ
ejpam-2674	154	18	,	,	PUNCT
ejpam-2674	154	19	two	two	NUM
ejpam-2674	154	20	-	-	PUNCT
ejpam-2674	154	21	sided	sided	ADJ
ejpam-2674	154	22	ideal	ideal	NOUN
ejpam-2674	154	23	)	)	PUNCT
ejpam-2674	154	24	is	be	AUX
ejpam-2674	154	25	an	an	DET
ejpam-2674	154	26	extended	extended	ADJ
ejpam-2674	154	27	notion	notion	NOUN
ejpam-2674	154	28	of	of	ADP
ejpam-2674	154	29	an	an	DET
ejpam-2674	154	30	ordinary	ordinary	ADJ
ejpam-2674	154	31	semigroup	semigroup	NOUN
ejpam-2674	154	32	(	(	PUNCT
ejpam-2674	154	33	left	leave	VERB
ejpam-2674	154	34	ideal	ideal	ADJ
ejpam-2674	154	35	,	,	PUNCT
ejpam-2674	154	36	right	right	ADJ
ejpam-2674	154	37	ideal	ideal	ADJ
ejpam-2674	154	38	,	,	PUNCT
ejpam-2674	154	39	two	two	NUM
ejpam-2674	154	40	-	-	PUNCT
ejpam-2674	154	41	sided	sided	ADJ
ejpam-2674	154	42	ideal	ideal	NOUN
ejpam-2674	154	43	)	)	PUNCT
ejpam-2674	154	44	.	.	PUNCT
ejpam-2674	155	1	another	another	DET
ejpam-2674	155	2	difference	difference	NOUN
ejpam-2674	155	3	between	between	ADP
ejpam-2674	155	4	near	near	ADP
ejpam-2674	155	5	left	left	ADJ
ejpam-2674	155	6	(	(	PUNCT
ejpam-2674	155	7	right	right	ADJ
ejpam-2674	155	8	,	,	PUNCT
ejpam-2674	155	9	two	two	NUM
ejpam-2674	155	10	-	-	PUNCT
ejpam-2674	155	11	sided	sided	ADJ
ejpam-2674	155	12	)	)	PUNCT
ejpam-2674	155	13	ideal	ideal	NOUN
ejpam-2674	155	14	and	and	CCONJ
ejpam-2674	155	15	left	leave	VERB
ejpam-2674	155	16	(	(	PUNCT
ejpam-2674	155	17	right	right	ADJ
ejpam-2674	155	18	,	,	PUNCT
ejpam-2674	155	19	two	two	NUM
ejpam-2674	155	20	-	-	PUNCT
ejpam-2674	155	21	sided	sided	ADJ
ejpam-2674	155	22	)	)	PUNCT
ejpam-2674	155	23	ideal	ideal	NOUN
ejpam-2674	155	24	is	be	AUX
ejpam-2674	155	25	the	the	DET
ejpam-2674	155	26	following	following	NOUN
ejpam-2674	155	27	:	:	PUNCT
ejpam-2674	155	28	proposition	proposition	NOUN
ejpam-2674	155	29	4	4	NUM
ejpam-2674	155	30	.	.	PUNCT
ejpam-2674	156	1	let	let	AUX
ejpam-2674	156	2	(	(	PUNCT
ejpam-2674	156	3	o	o	NOUN
ejpam-2674	156	4	,	,	PUNCT
ejpam-2674	156	5	f,∼br	f,∼br	NOUN
ejpam-2674	156	6	,	,	PUNCT
ejpam-2674	156	7	nr	nr	PROPN
ejpam-2674	156	8	,	,	PUNCT
ejpam-2674	156	9	vnr	vnr	PROPN
ejpam-2674	156	10	)	)	PUNCT
ejpam-2674	156	11	be	be	AUX
ejpam-2674	156	12	a	a	DET
ejpam-2674	156	13	nearness	nearness	NOUN
ejpam-2674	156	14	approximation	approximation	NOUN
ejpam-2674	156	15	space	space	NOUN
ejpam-2674	156	16	and	and	CCONJ
ejpam-2674	156	17	(	(	PUNCT
ejpam-2674	156	18	·	·	PUNCT
ejpam-2674	156	19	)	)	PUNCT
ejpam-2674	156	20	be	be	AUX
ejpam-2674	156	21	a	a	DET
ejpam-2674	156	22	binary	binary	ADJ
ejpam-2674	156	23	operation	operation	NOUN
ejpam-2674	156	24	defined	define	VERB
ejpam-2674	156	25	on	on	ADP
ejpam-2674	156	26	o.	o.	NOUN
ejpam-2674	156	27	let	let	VERB
ejpam-2674	156	28	i1	i1	PROPN
ejpam-2674	156	29	and	and	CCONJ
ejpam-2674	156	30	i2	i2	PROPN
ejpam-2674	156	31	be	be	VERB
ejpam-2674	156	32	two	two	NUM
ejpam-2674	156	33	left	left	ADJ
ejpam-2674	156	34	(	(	PUNCT
ejpam-2674	156	35	right	right	ADJ
ejpam-2674	156	36	,	,	PUNCT
ejpam-2674	156	37	two	two	NUM
ejpam-2674	156	38	-	-	PUNCT
ejpam-2674	156	39	sided	sided	ADJ
ejpam-2674	156	40	)	)	PUNCT
ejpam-2674	156	41	ideals	ideal	NOUN
ejpam-2674	156	42	of	of	ADP
ejpam-2674	156	43	the	the	DET
ejpam-2674	156	44	near	near	PROPN
ejpam-2674	156	45	semigroup	semigroup	PROPN
ejpam-2674	156	46	s.	s.	PROPN
ejpam-2674	156	47	a	a	DET
ejpam-2674	156	48	sufficient	sufficient	ADJ
ejpam-2674	156	49	condition	condition	NOUN
ejpam-2674	156	50	for	for	ADP
ejpam-2674	156	51	intersection	intersection	NOUN
ejpam-2674	156	52	of	of	ADP
ejpam-2674	156	53	two	two	NUM
ejpam-2674	156	54	left	left	ADJ
ejpam-2674	156	55	(	(	PUNCT
ejpam-2674	156	56	right	right	ADJ
ejpam-2674	156	57	,	,	PUNCT
ejpam-2674	156	58	two	two	NUM
ejpam-2674	156	59	-	-	PUNCT
ejpam-2674	156	60	sided	sided	ADJ
ejpam-2674	156	61	)	)	PUNCT
ejpam-2674	156	62	ideal	ideal	NOUN
ejpam-2674	156	63	of	of	ADP
ejpam-2674	156	64	a	a	DET
ejpam-2674	156	65	near	near	ADJ
ejpam-2674	156	66	semigroup	semigroup	NOUN
ejpam-2674	156	67	to	to	PART
ejpam-2674	156	68	be	be	AUX
ejpam-2674	156	69	a	a	DET
ejpam-2674	156	70	near	near	ADJ
ejpam-2674	156	71	left	left	NOUN
ejpam-2674	156	72	(	(	PUNCT
ejpam-2674	156	73	right	right	ADJ
ejpam-2674	156	74	,	,	PUNCT
ejpam-2674	156	75	two	two	NUM
ejpam-2674	156	76	-	-	PUNCT
ejpam-2674	156	77	sided	sided	ADJ
ejpam-2674	156	78	)	)	PUNCT
ejpam-2674	156	79	ideal	ideal	NOUN
ejpam-2674	156	80	is	be	AUX
ejpam-2674	156	81	nr(b)∗i1	nr(b)∗i1	ADJ
ejpam-2674	156	82	∩	∩	NOUN
ejpam-2674	156	83	nr(b)∗i2	nr(b)∗i2	NOUN
ejpam-2674	156	84	=	=	SYM
ejpam-2674	156	85	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	156	86	(	(	PUNCT
ejpam-2674	156	87	i1	i1	PROPN
ejpam-2674	156	88	∩	∩	PROPN
ejpam-2674	156	89	i2	i2	PROPN
ejpam-2674	156	90	)	)	PUNCT
ejpam-2674	156	91	.	.	PUNCT
ejpam-2674	157	1	proof	proof	NOUN
ejpam-2674	157	2	.	.	PUNCT
ejpam-2674	158	1	suppose	suppose	VERB
ejpam-2674	158	2	i1	i1	PROPN
ejpam-2674	158	3	and	and	CCONJ
ejpam-2674	158	4	i2	i2	PROPN
ejpam-2674	158	5	are	be	AUX
ejpam-2674	158	6	two	two	NUM
ejpam-2674	158	7	near	near	ADP
ejpam-2674	158	8	left	left	ADJ
ejpam-2674	158	9	ideals	ideal	NOUN
ejpam-2674	158	10	of	of	ADP
ejpam-2674	158	11	s.	s.	PROPN
ejpam-2674	158	12	it	it	PRON
ejpam-2674	158	13	is	be	AUX
ejpam-2674	158	14	obvious	obvious	ADJ
ejpam-2674	158	15	that	that	SCONJ
ejpam-2674	158	16	i1	i1	PROPN
ejpam-2674	158	17	∩	∩	PROPN
ejpam-2674	158	18	i2	i2	PROPN
ejpam-2674	158	19	⊂	⊂	PROPN
ejpam-2674	158	20	s.	s.	PROPN
ejpam-2674	158	21	consider	consider	VERB
ejpam-2674	158	22	x	x	X
ejpam-2674	158	23	∈	∈	PROPN
ejpam-2674	158	24	s	s	PART
ejpam-2674	158	25	and	and	CCONJ
ejpam-2674	158	26	y	y	PROPN
ejpam-2674	158	27	∈	∈	PROPN
ejpam-2674	158	28	i1	i1	PROPN
ejpam-2674	158	29	∩	∩	PROPN
ejpam-2674	158	30	i2	i2	PROPN
ejpam-2674	158	31	.	.	PUNCT
ejpam-2674	159	1	because	because	SCONJ
ejpam-2674	159	2	i1	i1	PROPN
ejpam-2674	159	3	and	and	CCONJ
ejpam-2674	159	4	i2	i2	PROPN
ejpam-2674	159	5	are	be	AUX
ejpam-2674	159	6	near	near	ADP
ejpam-2674	159	7	left	left	ADJ
ejpam-2674	159	8	ideals	ideal	NOUN
ejpam-2674	159	9	,	,	PUNCT
ejpam-2674	159	10	we	we	PRON
ejpam-2674	159	11	have	have	VERB
ejpam-2674	159	12	xy	xy	PROPN
ejpam-2674	159	13	∈	∈	PROPN
ejpam-2674	159	14	nr(b)∗i1	nr(b)∗i1	NOUN
ejpam-2674	159	15	,	,	PUNCT
ejpam-2674	159	16	xy	xy	PROPN
ejpam-2674	159	17	∈	∈	PROPN
ejpam-2674	159	18	nr(b)∗i2	nr(b)∗i2	NOUN
ejpam-2674	159	19	,	,	PUNCT
ejpam-2674	159	20	i.e.	i.e.	X
ejpam-2674	159	21	xy	xy	PROPN
ejpam-2674	159	22	∈	∈	PROPN
ejpam-2674	159	23	nr(b)∗i1	nr(b)∗i1	PROPN
ejpam-2674	159	24	∩	∩	PROPN
ejpam-2674	159	25	nr(b)∗i2	nr(b)∗i2	NOUN
ejpam-2674	159	26	.	.	PUNCT
ejpam-2674	160	1	assuming	assume	VERB
ejpam-2674	160	2	nr(b)∗i1	nr(b)∗i1	ADJ
ejpam-2674	160	3	∩	∩	NOUN
ejpam-2674	160	4	nr(b)∗i2	nr(b)∗i2	NOUN
ejpam-2674	160	5	=	=	SYM
ejpam-2674	160	6	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	160	7	(	(	PUNCT
ejpam-2674	160	8	i1	i1	PROPN
ejpam-2674	160	9	∩	∩	PROPN
ejpam-2674	160	10	i2	i2	PROPN
ejpam-2674	160	11	)	)	PUNCT
ejpam-2674	160	12	,	,	PUNCT
ejpam-2674	160	13	we	we	PRON
ejpam-2674	160	14	have	have	VERB
ejpam-2674	160	15	xy	xy	PROPN
ejpam-2674	160	16	∈	∈	PROPN
ejpam-2674	160	17	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	160	18	(	(	PUNCT
ejpam-2674	160	19	i1	i1	PROPN
ejpam-2674	160	20	∩	∩	PROPN
ejpam-2674	160	21	i2	i2	PROPN
ejpam-2674	160	22	)	)	PUNCT
ejpam-2674	160	23	.	.	PUNCT
ejpam-2674	161	1	thus	thus	ADV
ejpam-2674	161	2	i1	i1	PROPN
ejpam-2674	161	3	∩	∩	PROPN
ejpam-2674	161	4	i2	i2	PROPN
ejpam-2674	161	5	is	be	AUX
ejpam-2674	161	6	a	a	DET
ejpam-2674	161	7	near	near	ADJ
ejpam-2674	161	8	left	left	ADJ
ejpam-2674	161	9	ideal	ideal	NOUN
ejpam-2674	161	10	of	of	ADP
ejpam-2674	161	11	s.	s.	PROPN
ejpam-2674	161	12	the	the	DET
ejpam-2674	161	13	other	other	ADJ
ejpam-2674	161	14	cases	case	NOUN
ejpam-2674	161	15	can	can	AUX
ejpam-2674	161	16	be	be	AUX
ejpam-2674	161	17	seen	see	VERB
ejpam-2674	161	18	in	in	ADP
ejpam-2674	161	19	a	a	DET
ejpam-2674	161	20	similar	similar	ADJ
ejpam-2674	161	21	way	way	NOUN
ejpam-2674	161	22	.	.	PUNCT
ejpam-2674	162	1	n.	n.	NOUN
ejpam-2674	162	2	bağırmaz	bağırmaz	PROPN
ejpam-2674	162	3	/	/	SYM
ejpam-2674	162	4	eur	eur	PROPN
ejpam-2674	162	5	.	.	PUNCT
ejpam-2674	163	1	j.	j.	PROPN
ejpam-2674	163	2	pure	pure	PROPN
ejpam-2674	163	3	appl	appl	PROPN
ejpam-2674	163	4	.	.	PROPN
ejpam-2674	163	5	math	math	PROPN
ejpam-2674	163	6	,	,	PUNCT
ejpam-2674	163	7	11	11	NUM
ejpam-2674	163	8	(	(	PUNCT
ejpam-2674	163	9	2	2	NUM
ejpam-2674	163	10	)	)	PUNCT
ejpam-2674	163	11	(	(	PUNCT
ejpam-2674	163	12	2018	2018	NUM
ejpam-2674	163	13	)	)	PUNCT
ejpam-2674	163	14	,	,	PUNCT
ejpam-2674	163	15	505	505	NUM
ejpam-2674	163	16	-	-	SYM
ejpam-2674	163	17	516	516	NUM
ejpam-2674	163	18	512	512	NUM
ejpam-2674	163	19	definition	definition	NOUN
ejpam-2674	163	20	4	4	NUM
ejpam-2674	163	21	.	.	PUNCT
ejpam-2674	164	1	let	let	AUX
ejpam-2674	164	2	(	(	PUNCT
ejpam-2674	164	3	o	o	NOUN
ejpam-2674	164	4	,	,	PUNCT
ejpam-2674	164	5	f,∼br	f,∼br	NOUN
ejpam-2674	164	6	,	,	PUNCT
ejpam-2674	164	7	nr	nr	PROPN
ejpam-2674	164	8	,	,	PUNCT
ejpam-2674	164	9	vnr	vnr	PROPN
ejpam-2674	164	10	)	)	PUNCT
ejpam-2674	164	11	be	be	AUX
ejpam-2674	164	12	a	a	DET
ejpam-2674	164	13	nearness	nearness	NOUN
ejpam-2674	164	14	approximation	approximation	NOUN
ejpam-2674	164	15	space	space	NOUN
ejpam-2674	164	16	and	and	CCONJ
ejpam-2674	164	17	(	(	PUNCT
ejpam-2674	164	18	·	·	PUNCT
ejpam-2674	164	19	)	)	PUNCT
ejpam-2674	164	20	be	be	AUX
ejpam-2674	164	21	a	a	DET
ejpam-2674	164	22	binary	binary	ADJ
ejpam-2674	164	23	operation	operation	NOUN
ejpam-2674	164	24	defined	define	VERB
ejpam-2674	164	25	on	on	ADP
ejpam-2674	164	26	o.	o.	PROPN
ejpam-2674	164	27	a	a	PRON
ejpam-2674	165	1	near	near	ADJ
ejpam-2674	165	2	subsemigroup	subsemigroup	NOUN
ejpam-2674	166	1	i	i	PRON
ejpam-2674	166	2	of	of	ADP
ejpam-2674	166	3	near	near	PROPN
ejpam-2674	166	4	semigroup	semigroup	PROPN
ejpam-2674	166	5	s	s	PART
ejpam-2674	166	6	is	be	AUX
ejpam-2674	166	7	called	call	VERB
ejpam-2674	166	8	a	a	DET
ejpam-2674	166	9	near	near	ADJ
ejpam-2674	166	10	bi	bi	NOUN
ejpam-2674	166	11	-	-	NOUN
ejpam-2674	166	12	ideal	ideal	NOUN
ejpam-2674	166	13	of	of	ADP
ejpam-2674	166	14	s	s	PRON
ejpam-2674	166	15	if	if	SCONJ
ejpam-2674	166	16	isi	isi	PROPN
ejpam-2674	166	17	⊆	⊆	NUM
ejpam-2674	166	18	nr(b)∗i	nr(b)∗i	NOUN
ejpam-2674	166	19	.	.	PUNCT
ejpam-2674	167	1	proposition	proposition	NOUN
ejpam-2674	167	2	5	5	NUM
ejpam-2674	167	3	.	.	PUNCT
ejpam-2674	168	1	let	let	AUX
ejpam-2674	168	2	(	(	PUNCT
ejpam-2674	168	3	o	o	NOUN
ejpam-2674	168	4	,	,	PUNCT
ejpam-2674	168	5	f,∼br	f,∼br	NOUN
ejpam-2674	168	6	,	,	PUNCT
ejpam-2674	168	7	nr	nr	PROPN
ejpam-2674	168	8	,	,	PUNCT
ejpam-2674	168	9	vnr	vnr	PROPN
ejpam-2674	168	10	)	)	PUNCT
ejpam-2674	168	11	be	be	AUX
ejpam-2674	168	12	a	a	DET
ejpam-2674	168	13	nearness	nearness	NOUN
ejpam-2674	168	14	approximation	approximation	NOUN
ejpam-2674	168	15	space	space	NOUN
ejpam-2674	168	16	and	and	CCONJ
ejpam-2674	168	17	(	(	PUNCT
ejpam-2674	168	18	·	·	PUNCT
ejpam-2674	168	19	)	)	PUNCT
ejpam-2674	168	20	be	be	AUX
ejpam-2674	168	21	a	a	DET
ejpam-2674	168	22	binary	binary	ADJ
ejpam-2674	168	23	operation	operation	NOUN
ejpam-2674	168	24	defined	define	VERB
ejpam-2674	168	25	on	on	ADP
ejpam-2674	168	26	o.	o.	NOUN
ejpam-2674	168	27	let	let	VERB
ejpam-2674	168	28	s	s	PRON
ejpam-2674	168	29	⊆	⊆	NUM
ejpam-2674	168	30	o	o	NOUN
ejpam-2674	168	31	be	be	AUX
ejpam-2674	168	32	a	a	DET
ejpam-2674	168	33	semigroup	semigroup	NOUN
ejpam-2674	168	34	.	.	PUNCT
ejpam-2674	169	1	if	if	SCONJ
ejpam-2674	169	2	i	i	PRON
ejpam-2674	169	3	is	be	AUX
ejpam-2674	169	4	a	a	DET
ejpam-2674	169	5	biideal	biideal	NOUN
ejpam-2674	169	6	of	of	ADP
ejpam-2674	169	7	s	s	PROPN
ejpam-2674	169	8	,	,	PUNCT
ejpam-2674	169	9	then	then	ADV
ejpam-2674	169	10	i	i	PRON
ejpam-2674	169	11	is	be	AUX
ejpam-2674	169	12	a	a	DET
ejpam-2674	169	13	near	near	ADJ
ejpam-2674	169	14	biideal	biideal	NOUN
ejpam-2674	169	15	of	of	ADP
ejpam-2674	169	16	near	near	PROPN
ejpam-2674	169	17	semigroup	semigroup	PROPN
ejpam-2674	169	18	s.	s.	PROPN
ejpam-2674	169	19	proof	proof	PROPN
ejpam-2674	169	20	.	.	PUNCT
ejpam-2674	170	1	let	let	VERB
ejpam-2674	170	2	i	i	PRON
ejpam-2674	170	3	be	be	AUX
ejpam-2674	170	4	a	a	DET
ejpam-2674	170	5	bi	bi	NOUN
ejpam-2674	170	6	-	-	NOUN
ejpam-2674	170	7	ideal	ideal	NOUN
ejpam-2674	170	8	of	of	ADP
ejpam-2674	170	9	s	s	PROPN
ejpam-2674	170	10	,	,	PUNCT
ejpam-2674	170	11	i.e.	i.e.	X
ejpam-2674	170	12	,	,	PUNCT
ejpam-2674	170	13	isi	isi	PROPN
ejpam-2674	170	14	⊆	⊆	NUM
ejpam-2674	170	15	i.	i.	NOUN
ejpam-2674	170	16	since	since	SCONJ
ejpam-2674	170	17	i	i	PRON
ejpam-2674	170	18	⊆	⊆	NUM
ejpam-2674	170	19	s	s	NOUN
ejpam-2674	170	20	,	,	PUNCT
ejpam-2674	170	21	by	by	ADP
ejpam-2674	170	22	proposition	proposition	NOUN
ejpam-2674	170	23	1	1	NUM
ejpam-2674	170	24	(	(	PUNCT
ejpam-2674	170	25	5	5	NUM
ejpam-2674	170	26	)	)	PUNCT
ejpam-2674	170	27	,	,	PUNCT
ejpam-2674	170	28	we	we	PRON
ejpam-2674	170	29	know	know	VERB
ejpam-2674	170	30	that	that	SCONJ
ejpam-2674	170	31	nr(b)∗i	nr(b)∗i	PROPN
ejpam-2674	170	32	⊆	⊆	NUM
ejpam-2674	170	33	nr(b)∗s	nr(b)∗s	NUM
ejpam-2674	170	34	.	.	PUNCT
ejpam-2674	171	1	then	then	ADV
ejpam-2674	171	2	,	,	PUNCT
ejpam-2674	171	3	by	by	ADP
ejpam-2674	171	4	proposition	proposition	NOUN
ejpam-2674	171	5	1	1	NUM
ejpam-2674	171	6	(	(	PUNCT
ejpam-2674	171	7	1	1	NUM
ejpam-2674	171	8	)	)	PUNCT
ejpam-2674	171	9	,	,	PUNCT
ejpam-2674	171	10	we	we	PRON
ejpam-2674	171	11	have	have	VERB
ejpam-2674	171	12	that	that	SCONJ
ejpam-2674	171	13	i	i	PRON
ejpam-2674	171	14	⊆	⊆	NUM
ejpam-2674	171	15	nr(b)∗i	nr(b)∗i	NOUN
ejpam-2674	171	16	.	.	PUNCT
ejpam-2674	172	1	hence	hence	ADV
ejpam-2674	172	2	,	,	PUNCT
ejpam-2674	172	3	i	i	PRON
ejpam-2674	172	4	is	be	AUX
ejpam-2674	172	5	a	a	DET
ejpam-2674	172	6	near	near	ADJ
ejpam-2674	172	7	biideal	biideal	NOUN
ejpam-2674	172	8	of	of	ADP
ejpam-2674	172	9	near	near	PROPN
ejpam-2674	172	10	semigroup	semigroup	PROPN
ejpam-2674	172	11	s.	s.	PROPN
ejpam-2674	172	12	lemma	lemma	PROPN
ejpam-2674	173	1	2	2	X
ejpam-2674	173	2	.	.	PUNCT
ejpam-2674	174	1	let	let	AUX
ejpam-2674	174	2	(	(	PUNCT
ejpam-2674	174	3	o	o	NOUN
ejpam-2674	174	4	,	,	PUNCT
ejpam-2674	174	5	f,∼br	f,∼br	NOUN
ejpam-2674	174	6	,	,	PUNCT
ejpam-2674	174	7	nr	nr	PROPN
ejpam-2674	174	8	,	,	PUNCT
ejpam-2674	174	9	vnr	vnr	PROPN
ejpam-2674	174	10	)	)	PUNCT
ejpam-2674	174	11	be	be	AUX
ejpam-2674	174	12	a	a	DET
ejpam-2674	174	13	nearness	nearness	NOUN
ejpam-2674	174	14	approximation	approximation	NOUN
ejpam-2674	174	15	space	space	NOUN
ejpam-2674	174	16	and	and	CCONJ
ejpam-2674	174	17	(	(	PUNCT
ejpam-2674	174	18	·	·	PUNCT
ejpam-2674	174	19	)	)	PUNCT
ejpam-2674	174	20	be	be	AUX
ejpam-2674	174	21	a	a	DET
ejpam-2674	174	22	binary	binary	ADJ
ejpam-2674	174	23	operation	operation	NOUN
ejpam-2674	174	24	defined	define	VERB
ejpam-2674	174	25	on	on	ADP
ejpam-2674	174	26	o.	o.	INTJ
ejpam-2674	174	27	let	let	VERB
ejpam-2674	174	28	x	x	PUNCT
ejpam-2674	175	1	⊆	⊆	NUM
ejpam-2674	175	2	o.	o.	NOUN
ejpam-2674	175	3	then	then	ADV
ejpam-2674	175	4	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	175	5	(	(	PUNCT
ejpam-2674	175	6	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	175	7	)	)	PUNCT
ejpam-2674	176	1	=	=	SYM
ejpam-2674	177	1	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	177	2	(	(	PUNCT
ejpam-2674	177	3	x	x	NOUN
ejpam-2674	177	4	)	)	PUNCT
ejpam-2674	177	5	.	.	PUNCT
ejpam-2674	178	1	proof	proof	NOUN
ejpam-2674	178	2	.	.	PUNCT
ejpam-2674	179	1	since	since	SCONJ
ejpam-2674	179	2	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	179	3	(	(	PUNCT
ejpam-2674	179	4	x	x	NOUN
ejpam-2674	179	5	)	)	PUNCT
ejpam-2674	179	6	⊆	⊆	NUM
ejpam-2674	179	7	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	179	8	(	(	PUNCT
ejpam-2674	179	9	x	x	NOUN
ejpam-2674	179	10	)	)	PUNCT
ejpam-2674	179	11	,	,	PUNCT
ejpam-2674	179	12	then	then	ADV
ejpam-2674	179	13	,	,	PUNCT
ejpam-2674	179	14	by	by	ADP
ejpam-2674	179	15	proposition	proposition	NOUN
ejpam-2674	179	16	1	1	NUM
ejpam-2674	179	17	(	(	PUNCT
ejpam-2674	179	18	1	1	NUM
ejpam-2674	179	19	)	)	PUNCT
ejpam-2674	179	20	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	179	21	(	(	PUNCT
ejpam-2674	179	22	x	x	NOUN
ejpam-2674	179	23	)	)	PUNCT
ejpam-2674	179	24	⊆	⊆	NUM
ejpam-2674	179	25	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	179	26	(	(	PUNCT
ejpam-2674	179	27	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	179	28	)	)	PUNCT
ejpam-2674	179	29	.	.	PUNCT
ejpam-2674	180	1	conversely	conversely	ADV
ejpam-2674	180	2	,	,	PUNCT
ejpam-2674	180	3	let	let	VERB
ejpam-2674	180	4	[	[	X
ejpam-2674	180	5	x]br	x]br	ADP
ejpam-2674	180	6	∈	∈	PROPN
ejpam-2674	180	7	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	180	8	(	(	PUNCT
ejpam-2674	180	9	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	180	10	)	)	PUNCT
ejpam-2674	180	11	.	.	PUNCT
ejpam-2674	181	1	then	then	ADV
ejpam-2674	181	2	[	[	X
ejpam-2674	181	3	x]br	x]br	NUM
ejpam-2674	181	4	∩nr(b)∗x	∩nr(b)∗x	NOUN
ejpam-2674	181	5	6=	6=	ADP
ejpam-2674	181	6	∅.	∅.	VERB
ejpam-2674	181	7	thus	thus	ADV
ejpam-2674	181	8	[	[	X
ejpam-2674	181	9	x]br	x]br	PROPN
ejpam-2674	181	10	∈	∈	PROPN
ejpam-2674	181	11	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	181	12	.	.	PUNCT
ejpam-2674	182	1	hence	hence	ADV
ejpam-2674	182	2	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	182	3	(	(	PUNCT
ejpam-2674	182	4	nr(b)∗x	nr(b)∗x	PROPN
ejpam-2674	182	5	)	)	PUNCT
ejpam-2674	183	1	=	=	SYM
ejpam-2674	183	2	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	183	3	(	(	PUNCT
ejpam-2674	183	4	x	x	NOUN
ejpam-2674	183	5	)	)	PUNCT
ejpam-2674	183	6	.	.	PUNCT
ejpam-2674	184	1	proposition	proposition	NOUN
ejpam-2674	184	2	6	6	NUM
ejpam-2674	184	3	.	.	PUNCT
ejpam-2674	185	1	let	let	AUX
ejpam-2674	185	2	(	(	PUNCT
ejpam-2674	185	3	o	o	NOUN
ejpam-2674	185	4	,	,	PUNCT
ejpam-2674	185	5	f,∼br	f,∼br	NOUN
ejpam-2674	185	6	,	,	PUNCT
ejpam-2674	185	7	nr	nr	PROPN
ejpam-2674	185	8	,	,	PUNCT
ejpam-2674	185	9	vnr	vnr	PROPN
ejpam-2674	185	10	)	)	PUNCT
ejpam-2674	185	11	be	be	AUX
ejpam-2674	185	12	a	a	DET
ejpam-2674	185	13	nearness	nearness	NOUN
ejpam-2674	185	14	approximation	approximation	NOUN
ejpam-2674	185	15	space	space	NOUN
ejpam-2674	185	16	and	and	CCONJ
ejpam-2674	185	17	(	(	PUNCT
ejpam-2674	185	18	·	·	PUNCT
ejpam-2674	185	19	)	)	PUNCT
ejpam-2674	185	20	be	be	AUX
ejpam-2674	185	21	a	a	DET
ejpam-2674	185	22	binary	binary	ADJ
ejpam-2674	185	23	operation	operation	NOUN
ejpam-2674	185	24	defined	define	VERB
ejpam-2674	185	25	on	on	ADP
ejpam-2674	185	26	o	o	PROPN
ejpam-2674	185	27	and	and	CCONJ
ejpam-2674	185	28	s	s	PROPN
ejpam-2674	186	1	⊆	⊆	NUM
ejpam-2674	186	2	u	u	NOUN
ejpam-2674	186	3	be	be	VERB
ejpam-2674	186	4	a	a	DET
ejpam-2674	186	5	near	near	ADJ
ejpam-2674	186	6	semigroup	semigroup	NOUN
ejpam-2674	186	7	.	.	PUNCT
ejpam-2674	187	1	if	if	SCONJ
ejpam-2674	187	2	i	i	PRON
ejpam-2674	187	3	is	be	AUX
ejpam-2674	187	4	a	a	DET
ejpam-2674	187	5	near	near	ADJ
ejpam-2674	187	6	right	right	ADJ
ejpam-2674	187	7	ideal	ideal	NOUN
ejpam-2674	187	8	of	of	ADP
ejpam-2674	187	9	s	s	PRON
ejpam-2674	187	10	and	and	CCONJ
ejpam-2674	187	11	j	j	PROPN
ejpam-2674	187	12	is	be	AUX
ejpam-2674	187	13	a	a	DET
ejpam-2674	187	14	near	near	ADJ
ejpam-2674	187	15	left	left	ADJ
ejpam-2674	187	16	ideal	ideal	NOUN
ejpam-2674	187	17	of	of	ADP
ejpam-2674	187	18	s	s	PROPN
ejpam-2674	187	19	,	,	PUNCT
ejpam-2674	187	20	then	then	ADV
ejpam-2674	187	21	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	187	22	(	(	PUNCT
ejpam-2674	187	23	ij	ij	NOUN
ejpam-2674	187	24	)	)	PUNCT
ejpam-2674	187	25	⊆	⊆	NUM
ejpam-2674	187	26	nr(b)∗i	nr(b)∗i	ADJ
ejpam-2674	187	27	∩nr(b)∗j	∩nr(b)∗j	PROPN
ejpam-2674	187	28	.	.	PUNCT
ejpam-2674	188	1	proof	proof	NOUN
ejpam-2674	188	2	.	.	PUNCT
ejpam-2674	189	1	let	let	VERB
ejpam-2674	189	2	i	i	PRON
ejpam-2674	189	3	be	be	AUX
ejpam-2674	189	4	a	a	DET
ejpam-2674	189	5	near	near	ADJ
ejpam-2674	189	6	right	right	ADJ
ejpam-2674	189	7	ideal	ideal	NOUN
ejpam-2674	189	8	of	of	ADP
ejpam-2674	189	9	s	s	PRON
ejpam-2674	189	10	and	and	CCONJ
ejpam-2674	189	11	j	j	PROPN
ejpam-2674	189	12	be	be	AUX
ejpam-2674	189	13	a	a	DET
ejpam-2674	189	14	near	near	ADJ
ejpam-2674	189	15	left	left	ADJ
ejpam-2674	189	16	ideal	ideal	NOUN
ejpam-2674	189	17	of	of	ADP
ejpam-2674	189	18	s	s	PROPN
ejpam-2674	189	19	,	,	PUNCT
ejpam-2674	189	20	then	then	ADV
ejpam-2674	189	21	ij	ij	NOUN
ejpam-2674	189	22	⊆	⊆	NUM
ejpam-2674	189	23	is	be	AUX
ejpam-2674	189	24	⊆	⊆	NUM
ejpam-2674	189	25	nr(b)∗i	nr(b)∗i	ADJ
ejpam-2674	189	26	and	and	CCONJ
ejpam-2674	189	27	ij	ij	NOUN
ejpam-2674	189	28	⊆	⊆	NUM
ejpam-2674	189	29	sj	sj	ADP
ejpam-2674	189	30	⊆	⊆	NUM
ejpam-2674	189	31	nr(b)∗j	nr(b)∗j	NOUN
ejpam-2674	189	32	.	.	PUNCT
ejpam-2674	190	1	thus	thus	ADV
ejpam-2674	190	2	ij	ij	X
ejpam-2674	190	3	⊆	⊆	NUM
ejpam-2674	190	4	nr(b)∗i	nr(b)∗i	ADJ
ejpam-2674	190	5	∩nr(b)∗j	∩nr(b)∗j	PROPN
ejpam-2674	190	6	.	.	PUNCT
ejpam-2674	191	1	thus	thus	ADV
ejpam-2674	191	2	,	,	PUNCT
ejpam-2674	191	3	it	it	PRON
ejpam-2674	191	4	follows	follow	VERB
ejpam-2674	191	5	from	from	ADP
ejpam-2674	191	6	proposition	proposition	NOUN
ejpam-2674	191	7	1.(5	1.(5	NUM
ejpam-2674	191	8	)	)	PUNCT
ejpam-2674	191	9	and	and	CCONJ
ejpam-2674	191	10	(	(	PUNCT
ejpam-2674	191	11	6	6	NUM
ejpam-2674	191	12	)	)	PUNCT
ejpam-2674	192	1	that	that	PRON
ejpam-2674	192	2	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	192	3	(	(	PUNCT
ejpam-2674	192	4	ij	ij	NOUN
ejpam-2674	192	5	)	)	PUNCT
ejpam-2674	192	6	⊆	⊆	PROPN
ejpam-2674	192	7	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	192	8	(	(	PUNCT
ejpam-2674	192	9	nr(b)∗i	nr(b)∗i	PROPN
ejpam-2674	192	10	∩nr(b)∗j	∩nr(b)∗j	PROPN
ejpam-2674	192	11	)	)	PUNCT
ejpam-2674	192	12	⊆	⊆	NUM
ejpam-2674	192	13	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	192	14	(	(	PUNCT
ejpam-2674	192	15	nr(b)∗i	nr(b)∗i	ADJ
ejpam-2674	192	16	)	)	PUNCT
ejpam-2674	192	17	∩nr(b)∗	∩nr(b)∗	NOUN
ejpam-2674	192	18	(	(	PUNCT
ejpam-2674	192	19	nr(b)∗j	nr(b)∗j	NOUN
ejpam-2674	192	20	)	)	PUNCT
ejpam-2674	192	21	.	.	PUNCT
ejpam-2674	192	22	then	then	ADV
ejpam-2674	192	23	,	,	PUNCT
ejpam-2674	192	24	by	by	ADP
ejpam-2674	192	25	lemma	lemma	PROPN
ejpam-2674	192	26	2	2	NUM
ejpam-2674	192	27	,	,	PUNCT
ejpam-2674	192	28	we	we	PRON
ejpam-2674	192	29	have	have	VERB
ejpam-2674	192	30	that	that	PRON
ejpam-2674	192	31	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	192	32	(	(	PUNCT
ejpam-2674	192	33	nr(b)∗i	nr(b)∗i	ADJ
ejpam-2674	192	34	)	)	PUNCT
ejpam-2674	193	1	=	=	SYM
ejpam-2674	193	2	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	193	3	(	(	PUNCT
ejpam-2674	193	4	i	i	NOUN
ejpam-2674	193	5	)	)	PUNCT
ejpam-2674	193	6	and	and	CCONJ
ejpam-2674	193	7	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	193	8	(	(	PUNCT
ejpam-2674	193	9	nr(b)∗j	nr(b)∗j	NOUN
ejpam-2674	193	10	)	)	PUNCT
ejpam-2674	193	11	=	=	SYM
ejpam-2674	194	1	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	194	2	(	(	PUNCT
ejpam-2674	194	3	j	j	PROPN
ejpam-2674	194	4	)	)	PUNCT
ejpam-2674	194	5	.	.	PUNCT
ejpam-2674	195	1	hence	hence	ADV
ejpam-2674	195	2	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	195	3	(	(	PUNCT
ejpam-2674	195	4	ij	ij	NOUN
ejpam-2674	195	5	)	)	PUNCT
ejpam-2674	195	6	⊆	⊆	PROPN
ejpam-2674	195	7	nr(b)∗	nr(b)∗	PROPN
ejpam-2674	195	8	(	(	PUNCT
ejpam-2674	195	9	i	i	NOUN
ejpam-2674	195	10	)	)	PUNCT
ejpam-2674	195	11	∩nr(b)∗	∩nr(b)∗	PROPN
ejpam-2674	195	12	(	(	PUNCT
ejpam-2674	195	13	j	j	PROPN
ejpam-2674	195	14	)	)	PUNCT
ejpam-2674	195	15	.	.	PUNCT
ejpam-2674	196	1	4	4	X
ejpam-2674	196	2	.	.	X
ejpam-2674	196	3	homomorphisms	homomorphism	NOUN
ejpam-2674	196	4	of	of	ADP
ejpam-2674	196	5	near	near	ADJ
ejpam-2674	196	6	semigroups	semigroup	NOUN
ejpam-2674	196	7	let	let	VERB
ejpam-2674	196	8	(	(	PUNCT
ejpam-2674	196	9	o1	o1	NOUN
ejpam-2674	196	10	,	,	PUNCT
ejpam-2674	196	11	f1,∼br1	f1,∼br1	PROPN
ejpam-2674	196	12	,	,	PUNCT
ejpam-2674	196	13	nr1	nr1	PROPN
ejpam-2674	196	14	,	,	PUNCT
ejpam-2674	196	15	vnr1	vnr1	PROPN
ejpam-2674	196	16	)	)	PUNCT
ejpam-2674	196	17	,	,	PUNCT
ejpam-2674	196	18	(	(	PUNCT
ejpam-2674	196	19	o2	o2	PROPN
ejpam-2674	196	20	,	,	PUNCT
ejpam-2674	196	21	f2,∼br2	f2,∼br2	PROPN
ejpam-2674	196	22	,	,	PUNCT
ejpam-2674	196	23	nr2	nr2	PROPN
ejpam-2674	196	24	,	,	PUNCT
ejpam-2674	196	25	vnr2	vnr2	PROPN
ejpam-2674	196	26	)	)	PUNCT
ejpam-2674	196	27	be	be	AUX
ejpam-2674	196	28	two	two	NUM
ejpam-2674	196	29	nearness	nearness	NOUN
ejpam-2674	196	30	approximation	approximation	NOUN
ejpam-2674	196	31	spaces	space	NOUN
ejpam-2674	196	32	,	,	PUNCT
ejpam-2674	196	33	and	and	CCONJ
ejpam-2674	196	34	(	(	PUNCT
ejpam-2674	196	35	·	·	PUNCT
ejpam-2674	196	36	)	)	PUNCT
ejpam-2674	196	37	,	,	PUNCT
ejpam-2674	196	38	(	(	PUNCT
ejpam-2674	196	39	◦	◦	NOUN
ejpam-2674	196	40	)	)	PUNCT
ejpam-2674	196	41	be	be	AUX
ejpam-2674	196	42	binary	binary	ADJ
ejpam-2674	196	43	operations	operation	NOUN
ejpam-2674	196	44	over	over	ADP
ejpam-2674	196	45	universes	universe	NOUN
ejpam-2674	196	46	o1	o1	NOUN
ejpam-2674	196	47	and	and	CCONJ
ejpam-2674	196	48	o2	o2	PROPN
ejpam-2674	196	49	,	,	PUNCT
ejpam-2674	196	50	respectively	respectively	ADV
ejpam-2674	196	51	.	.	PUNCT
ejpam-2674	197	1	definition	definition	NOUN
ejpam-2674	197	2	5	5	NUM
ejpam-2674	197	3	.	.	PUNCT
ejpam-2674	198	1	let	let	VERB
ejpam-2674	198	2	s1	s1	PROPN
ejpam-2674	198	3	⊂	⊂	PROPN
ejpam-2674	198	4	o1	o1	PROPN
ejpam-2674	198	5	,	,	PUNCT
ejpam-2674	198	6	s2	s2	PROPN
ejpam-2674	198	7	⊂	⊂	PROPN
ejpam-2674	198	8	o2	o2	PROPN
ejpam-2674	198	9	be	be	AUX
ejpam-2674	198	10	near	near	ADP
ejpam-2674	198	11	semigroups	semigroup	NOUN
ejpam-2674	198	12	.	.	PUNCT
ejpam-2674	199	1	if	if	SCONJ
ejpam-2674	199	2	there	there	PRON
ejpam-2674	199	3	exists	exist	VERB
ejpam-2674	199	4	a	a	DET
ejpam-2674	199	5	surjection	surjection	NOUN
ejpam-2674	199	6	φ	φ	X
ejpam-2674	199	7	:	:	PUNCT
ejpam-2674	199	8	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	199	9	(	(	PUNCT
ejpam-2674	199	10	s1)→	s1)→	PROPN
ejpam-2674	199	11	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	199	12	(	(	PUNCT
ejpam-2674	199	13	s2	s2	PROPN
ejpam-2674	199	14	)	)	PUNCT
ejpam-2674	199	15	such	such	ADJ
ejpam-2674	199	16	that	that	SCONJ
ejpam-2674	199	17	φ(x	φ(x	PROPN
ejpam-2674	199	18	·	·	SYM
ejpam-2674	199	19	y	y	X
ejpam-2674	199	20	)	)	PUNCT
ejpam-2674	199	21	=	=	SYM
ejpam-2674	199	22	φ(x)	φ(x)	PROPN
ejpam-2674	199	23	◦	◦	NOUN
ejpam-2674	199	24	φ(y	φ(y	NOUN
ejpam-2674	199	25	)	)	PUNCT
ejpam-2674	199	26	for	for	ADP
ejpam-2674	199	27	all	all	DET
ejpam-2674	199	28	x	x	NOUN
ejpam-2674	199	29	,	,	PUNCT
ejpam-2674	199	30	y	y	PROPN
ejpam-2674	199	31	∈	∈	PROPN
ejpam-2674	199	32	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	199	33	(	(	PUNCT
ejpam-2674	199	34	s1	s1	PROPN
ejpam-2674	199	35	)	)	PUNCT
ejpam-2674	199	36	then	then	ADV
ejpam-2674	199	37	ϕ	ϕ	PROPN
ejpam-2674	199	38	is	be	AUX
ejpam-2674	199	39	called	call	VERB
ejpam-2674	199	40	a	a	PRON
ejpam-2674	199	41	near	near	ADJ
ejpam-2674	199	42	homomorphism	homomorphism	NOUN
ejpam-2674	199	43	and	and	CCONJ
ejpam-2674	199	44	s1	s1	NOUN
ejpam-2674	199	45	,	,	PUNCT
ejpam-2674	199	46	s2	s2	PROPN
ejpam-2674	199	47	are	be	AUX
ejpam-2674	199	48	called	call	VERB
ejpam-2674	199	49	near	near	ADP
ejpam-2674	199	50	homomorphic	homomorphic	ADJ
ejpam-2674	199	51	semigroups	semigroup	NOUN
ejpam-2674	199	52	.	.	PUNCT
ejpam-2674	200	1	proposition	proposition	NOUN
ejpam-2674	200	2	7	7	NUM
ejpam-2674	200	3	.	.	PUNCT
ejpam-2674	201	1	let	let	VERB
ejpam-2674	201	2	s1	s1	NOUN
ejpam-2674	201	3	and	and	CCONJ
ejpam-2674	201	4	s2	s2	NOUN
ejpam-2674	201	5	be	be	AUX
ejpam-2674	201	6	near	near	ADP
ejpam-2674	201	7	homomorphic	homomorphic	ADJ
ejpam-2674	201	8	semigroups	semigroup	NOUN
ejpam-2674	201	9	.	.	PUNCT
ejpam-2674	202	1	if	if	SCONJ
ejpam-2674	202	2	(	(	PUNCT
ejpam-2674	202	3	·	·	PUNCT
ejpam-2674	202	4	)	)	PUNCT
ejpam-2674	202	5	satisfies	satisfy	VERB
ejpam-2674	202	6	the	the	DET
ejpam-2674	202	7	commutative	commutative	ADJ
ejpam-2674	202	8	law	law	NOUN
ejpam-2674	202	9	,	,	PUNCT
ejpam-2674	202	10	then	then	ADV
ejpam-2674	202	11	(	(	PUNCT
ejpam-2674	202	12	◦	◦	NOUN
ejpam-2674	202	13	)	)	PUNCT
ejpam-2674	202	14	also	also	ADV
ejpam-2674	202	15	satisfies	satisfy	VERB
ejpam-2674	202	16	it	it	PRON
ejpam-2674	202	17	.	.	PUNCT
ejpam-2674	203	1	n.	n.	NOUN
ejpam-2674	203	2	bağırmaz	bağırmaz	PROPN
ejpam-2674	203	3	/	/	SYM
ejpam-2674	203	4	eur	eur	PROPN
ejpam-2674	203	5	.	.	PUNCT
ejpam-2674	204	1	j.	j.	PROPN
ejpam-2674	204	2	pure	pure	PROPN
ejpam-2674	204	3	appl	appl	PROPN
ejpam-2674	204	4	.	.	PROPN
ejpam-2674	204	5	math	math	PROPN
ejpam-2674	204	6	,	,	PUNCT
ejpam-2674	204	7	11	11	NUM
ejpam-2674	204	8	(	(	PUNCT
ejpam-2674	204	9	2	2	NUM
ejpam-2674	204	10	)	)	PUNCT
ejpam-2674	204	11	(	(	PUNCT
ejpam-2674	204	12	2018	2018	NUM
ejpam-2674	204	13	)	)	PUNCT
ejpam-2674	204	14	,	,	PUNCT
ejpam-2674	204	15	505	505	NUM
ejpam-2674	204	16	-	-	SYM
ejpam-2674	204	17	516	516	NUM
ejpam-2674	204	18	513	513	NUM
ejpam-2674	204	19	proof	proof	NOUN
ejpam-2674	204	20	.	.	PUNCT
ejpam-2674	205	1	consider	consider	VERB
ejpam-2674	205	2	s1	s1	NOUN
ejpam-2674	205	3	,	,	PUNCT
ejpam-2674	205	4	s2	s2	NOUN
ejpam-2674	205	5	,	,	PUNCT
ejpam-2674	205	6	and	and	CCONJ
ejpam-2674	205	7	φ	φ	NUM
ejpam-2674	205	8	such	such	ADJ
ejpam-2674	205	9	that	that	SCONJ
ejpam-2674	205	10	φ	φ	PROPN
ejpam-2674	205	11	(	(	PUNCT
ejpam-2674	205	12	x	x	PROPN
ejpam-2674	205	13	·	·	PUNCT
ejpam-2674	205	14	y	y	X
ejpam-2674	205	15	)	)	PUNCT
ejpam-2674	205	16	=	=	SYM
ejpam-2674	205	17	φ	φ	PROPN
ejpam-2674	205	18	(	(	PUNCT
ejpam-2674	205	19	x	x	NOUN
ejpam-2674	205	20	)	)	PUNCT
ejpam-2674	205	21	◦	◦	NOUN
ejpam-2674	205	22	φ(y	φ(y	NOUN
ejpam-2674	205	23	)	)	PUNCT
ejpam-2674	205	24	for	for	ADP
ejpam-2674	205	25	all	all	DET
ejpam-2674	205	26	x	x	NOUN
ejpam-2674	205	27	,	,	PUNCT
ejpam-2674	205	28	y	y	PROPN
ejpam-2674	205	29	∈	∈	PROPN
ejpam-2674	205	30	g1	g1	PROPN
ejpam-2674	205	31	.	.	PUNCT
ejpam-2674	206	1	for	for	ADP
ejpam-2674	206	2	every	every	DET
ejpam-2674	206	3	φ(x	φ(x	NOUN
ejpam-2674	206	4	)	)	PUNCT
ejpam-2674	206	5	,	,	PUNCT
ejpam-2674	206	6	φ(y	φ(y	NOUN
ejpam-2674	206	7	)	)	PUNCT
ejpam-2674	206	8	∈	∈	PROPN
ejpam-2674	206	9	s2	s2	PROPN
ejpam-2674	206	10	,	,	PUNCT
ejpam-2674	206	11	since	since	SCONJ
ejpam-2674	206	12	φ	φ	PROPN
ejpam-2674	206	13	is	be	AUX
ejpam-2674	206	14	surjection	surjection	NOUN
ejpam-2674	206	15	,	,	PUNCT
ejpam-2674	206	16	there	there	PRON
ejpam-2674	206	17	exist	exist	VERB
ejpam-2674	206	18	x	x	NOUN
ejpam-2674	206	19	,	,	PUNCT
ejpam-2674	206	20	y	y	PROPN
ejpam-2674	206	21	∈	∈	PROPN
ejpam-2674	206	22	s1	s1	NOUN
ejpam-2674	206	23	such	such	ADJ
ejpam-2674	206	24	that	that	SCONJ
ejpam-2674	206	25	x	x	PROPN
ejpam-2674	206	26	7→	7→	NUM
ejpam-2674	206	27	φ(x	φ(x	NOUN
ejpam-2674	206	28	)	)	PUNCT
ejpam-2674	206	29	,	,	PUNCT
ejpam-2674	206	30	y	y	PROPN
ejpam-2674	206	31	7→	7→	PROPN
ejpam-2674	206	32	φ(y	φ(y	NOUN
ejpam-2674	206	33	)	)	PUNCT
ejpam-2674	206	34	.	.	PUNCT
ejpam-2674	207	1	thus	thus	ADV
ejpam-2674	207	2	φ(x	φ(x	PROPN
ejpam-2674	207	3	·	·	PUNCT
ejpam-2674	207	4	y	y	X
ejpam-2674	207	5	)	)	PUNCT
ejpam-2674	207	6	=	=	SYM
ejpam-2674	207	7	φ(x	φ(x	NOUN
ejpam-2674	207	8	)	)	PUNCT
ejpam-2674	207	9	◦	◦	NOUN
ejpam-2674	207	10	φ(y	φ(y	NOUN
ejpam-2674	207	11	)	)	PUNCT
ejpam-2674	207	12	,	,	PUNCT
ejpam-2674	207	13	and	and	CCONJ
ejpam-2674	207	14	φ(y	φ(y	NOUN
ejpam-2674	207	15	·	·	PUNCT
ejpam-2674	207	16	x	x	X
ejpam-2674	207	17	)	)	PUNCT
ejpam-2674	207	18	=	=	SYM
ejpam-2674	207	19	φ(y	φ(y	NOUN
ejpam-2674	207	20	)	)	PUNCT
ejpam-2674	207	21	◦	◦	NOUN
ejpam-2674	207	22	φ(x	φ(x	NOUN
ejpam-2674	207	23	)	)	PUNCT
ejpam-2674	207	24	.	.	PUNCT
ejpam-2674	208	1	now	now	ADV
ejpam-2674	208	2	,	,	PUNCT
ejpam-2674	208	3	assuming	assume	VERB
ejpam-2674	208	4	x	x	X
ejpam-2674	208	5	·	·	PUNCT
ejpam-2674	208	6	y	y	X
ejpam-2674	208	7	=	=	SYM
ejpam-2674	208	8	y	y	PROPN
ejpam-2674	208	9	·	·	PUNCT
ejpam-2674	208	10	x	x	X
ejpam-2674	208	11	,	,	PUNCT
ejpam-2674	208	12	we	we	PRON
ejpam-2674	208	13	obtain	obtain	VERB
ejpam-2674	208	14	φ(x	φ(x	NOUN
ejpam-2674	208	15	)	)	PUNCT
ejpam-2674	208	16	◦	◦	NOUN
ejpam-2674	208	17	φ(y	φ(y	NOUN
ejpam-2674	208	18	)	)	PUNCT
ejpam-2674	208	19	=	=	SYM
ejpam-2674	208	20	φ(y	φ(y	NOUN
ejpam-2674	208	21	)	)	PUNCT
ejpam-2674	208	22	◦	◦	NOUN
ejpam-2674	208	23	φ(x	φ(x	NOUN
ejpam-2674	208	24	)	)	PUNCT
ejpam-2674	208	25	.	.	PUNCT
ejpam-2674	209	1	that	that	PRON
ejpam-2674	209	2	means	mean	VERB
ejpam-2674	209	3	that	that	SCONJ
ejpam-2674	209	4	(	(	PUNCT
ejpam-2674	209	5	◦	◦	NOUN
ejpam-2674	209	6	)	)	PUNCT
ejpam-2674	209	7	satisfies	satisfy	VERB
ejpam-2674	209	8	the	the	DET
ejpam-2674	209	9	commutative	commutative	ADJ
ejpam-2674	209	10	law	law	NOUN
ejpam-2674	209	11	.	.	PUNCT
ejpam-2674	210	1	proposition	proposition	NOUN
ejpam-2674	210	2	8	8	NUM
ejpam-2674	210	3	.	.	PUNCT
ejpam-2674	211	1	let	let	VERB
ejpam-2674	211	2	s1	s1	PROPN
ejpam-2674	211	3	⊂	⊂	PROPN
ejpam-2674	211	4	o1	o1	PROPN
ejpam-2674	211	5	,	,	PUNCT
ejpam-2674	211	6	s2	s2	PROPN
ejpam-2674	211	7	⊂	⊂	PROPN
ejpam-2674	211	8	o2	o2	PROPN
ejpam-2674	211	9	be	be	AUX
ejpam-2674	211	10	near	near	ADP
ejpam-2674	211	11	homomorphic	homomorphic	ADJ
ejpam-2674	211	12	semigroups	semigroup	NOUN
ejpam-2674	211	13	and	and	CCONJ
ejpam-2674	211	14	let	let	VERB
ejpam-2674	211	15	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	211	16	(	(	PUNCT
ejpam-2674	211	17	φ	φ	PROPN
ejpam-2674	211	18	(	(	PUNCT
ejpam-2674	211	19	s1	s1	NOUN
ejpam-2674	211	20	)	)	PUNCT
ejpam-2674	211	21	)	)	PUNCT
ejpam-2674	212	1	=	=	SYM
ejpam-2674	213	1	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	213	2	(	(	PUNCT
ejpam-2674	213	3	s2	s2	PROPN
ejpam-2674	213	4	)	)	PUNCT
ejpam-2674	213	5	.then	.then	X
ejpam-2674	214	1	φ	φ	PROPN
ejpam-2674	214	2	(	(	PUNCT
ejpam-2674	214	3	s1	s1	PROPN
ejpam-2674	214	4	)	)	PUNCT
ejpam-2674	214	5	is	be	AUX
ejpam-2674	214	6	a	a	DET
ejpam-2674	214	7	near	near	ADJ
ejpam-2674	214	8	semigroup	semigroup	NOUN
ejpam-2674	214	9	.	.	PUNCT
ejpam-2674	215	1	proof	proof	NOUN
ejpam-2674	215	2	.	.	PUNCT
ejpam-2674	216	1	(	(	PUNCT
ejpam-2674	216	2	1	1	X
ejpam-2674	216	3	)	)	PUNCT
ejpam-2674	216	4	∀x′	∀x′	NOUN
ejpam-2674	216	5	,	,	PUNCT
ejpam-2674	216	6	y′	y′	NOUN
ejpam-2674	216	7	∈	∈	PROPN
ejpam-2674	216	8	φ(s1	φ(s1	NOUN
ejpam-2674	216	9	)	)	PUNCT
ejpam-2674	216	10	,	,	PUNCT
ejpam-2674	216	11	consider	consider	VERB
ejpam-2674	216	12	x	x	PRON
ejpam-2674	216	13	,	,	PUNCT
ejpam-2674	216	14	y	y	PROPN
ejpam-2674	216	15	∈	∈	PROPN
ejpam-2674	216	16	s1	s1	NOUN
ejpam-2674	216	17	such	such	ADJ
ejpam-2674	216	18	that	that	SCONJ
ejpam-2674	216	19	x	x	PROPN
ejpam-2674	216	20	7→	7→	NUM
ejpam-2674	216	21	x′	x′	NUM
ejpam-2674	216	22	,	,	PUNCT
ejpam-2674	216	23	y	y	PROPN
ejpam-2674	216	24	7→	7→	PROPN
ejpam-2674	216	25	y′.	y′.	VERB
ejpam-2674	216	26	we	we	PRON
ejpam-2674	216	27	have	have	VERB
ejpam-2674	216	28	φ(x	φ(x	PROPN
ejpam-2674	216	29	·	·	SYM
ejpam-2674	216	30	y	y	PROPN
ejpam-2674	216	31	)	)	PUNCT
ejpam-2674	216	32	=	=	SYM
ejpam-2674	216	33	φ(x)	φ(x)	PROPN
ejpam-2674	216	34	◦	◦	NOUN
ejpam-2674	216	35	φ(y	φ(y	NOUN
ejpam-2674	216	36	)	)	PUNCT
ejpam-2674	216	37	∈	∈	PROPN
ejpam-2674	217	1	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	217	2	(	(	PUNCT
ejpam-2674	217	3	s2	s2	PROPN
ejpam-2674	217	4	)	)	PUNCT
ejpam-2674	217	5	=	=	SYM
ejpam-2674	218	1	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	218	2	(	(	PUNCT
ejpam-2674	218	3	φ	φ	PROPN
ejpam-2674	218	4	(	(	PUNCT
ejpam-2674	218	5	s1	s1	PROPN
ejpam-2674	218	6	)	)	PUNCT
ejpam-2674	218	7	)	)	PUNCT
ejpam-2674	218	8	,	,	PUNCT
ejpam-2674	218	9	that	that	PRON
ejpam-2674	218	10	is	be	AUX
ejpam-2674	218	11	x′	x′	PROPN
ejpam-2674	218	12	◦	◦	NOUN
ejpam-2674	218	13	y′	y′	NOUN
ejpam-2674	218	14	∈	∈	PROPN
ejpam-2674	219	1	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	219	2	(	(	PUNCT
ejpam-2674	219	3	φ	φ	PROPN
ejpam-2674	219	4	(	(	PUNCT
ejpam-2674	219	5	s1	s1	PROPN
ejpam-2674	219	6	)	)	PUNCT
ejpam-2674	219	7	)	)	PUNCT
ejpam-2674	219	8	.	.	PUNCT
ejpam-2674	220	1	(	(	PUNCT
ejpam-2674	220	2	2	2	X
ejpam-2674	220	3	)	)	PUNCT
ejpam-2674	220	4	s1	s1	NOUN
ejpam-2674	220	5	is	be	AUX
ejpam-2674	220	6	a	a	DET
ejpam-2674	220	7	near	near	ADJ
ejpam-2674	220	8	semigroup	semigroup	NOUN
ejpam-2674	220	9	,	,	PUNCT
ejpam-2674	220	10	so	so	ADV
ejpam-2674	220	11	∀x	∀x	NUM
ejpam-2674	220	12	,	,	PUNCT
ejpam-2674	220	13	y	y	PROPN
ejpam-2674	220	14	,	,	PUNCT
ejpam-2674	220	15	z	z	NOUN
ejpam-2674	220	16	∈	∈	PROPN
ejpam-2674	220	17	s1	s1	NOUN
ejpam-2674	220	18	,	,	PUNCT
ejpam-2674	220	19	x	x	X
ejpam-2674	220	20	·	·	PUNCT
ejpam-2674	220	21	(	(	PUNCT
ejpam-2674	220	22	y	y	PROPN
ejpam-2674	220	23	·	·	PUNCT
ejpam-2674	220	24	z	z	X
ejpam-2674	220	25	)	)	PUNCT
ejpam-2674	220	26	=	=	SYM
ejpam-2674	221	1	(	(	PUNCT
ejpam-2674	221	2	x	x	X
ejpam-2674	221	3	·	·	PUNCT
ejpam-2674	221	4	y	y	X
ejpam-2674	221	5	)	)	PUNCT
ejpam-2674	221	6	·	·	PUNCT
ejpam-2674	222	1	z.	z.	PROPN
ejpam-2674	222	2	hence	hence	ADV
ejpam-2674	222	3	,	,	PUNCT
ejpam-2674	222	4	φ(x	φ(x	PROPN
ejpam-2674	222	5	·	·	PUNCT
ejpam-2674	222	6	(	(	PUNCT
ejpam-2674	222	7	y	y	PROPN
ejpam-2674	222	8	·	·	PUNCT
ejpam-2674	222	9	z	z	NOUN
ejpam-2674	222	10	)	)	PUNCT
ejpam-2674	222	11	)	)	PUNCT
ejpam-2674	222	12	=	=	SYM
ejpam-2674	222	13	φ(x	φ(x	X
ejpam-2674	222	14	)	)	PUNCT
ejpam-2674	222	15	◦	◦	NOUN
ejpam-2674	222	16	φ(y	φ(y	PROPN
ejpam-2674	222	17	·	·	PUNCT
ejpam-2674	222	18	z	z	X
ejpam-2674	222	19	)	)	PUNCT
ejpam-2674	222	20	=	=	SYM
ejpam-2674	222	21	φ(x	φ(x	NOUN
ejpam-2674	222	22	)	)	PUNCT
ejpam-2674	222	23	◦	◦	NOUN
ejpam-2674	222	24	(	(	PUNCT
ejpam-2674	222	25	φ(y	φ(y	NOUN
ejpam-2674	222	26	)	)	PUNCT
ejpam-2674	222	27	◦	◦	NOUN
ejpam-2674	222	28	φ(z	φ(z	PROPN
ejpam-2674	222	29	)	)	PUNCT
ejpam-2674	222	30	)	)	PUNCT
ejpam-2674	222	31	φ((x	φ((x	PUNCT
ejpam-2674	222	32	·	·	PUNCT
ejpam-2674	222	33	y	y	X
ejpam-2674	222	34	)	)	PUNCT
ejpam-2674	222	35	·	·	PUNCT
ejpam-2674	223	1	z	z	X
ejpam-2674	223	2	)	)	PUNCT
ejpam-2674	223	3	=	=	SYM
ejpam-2674	223	4	φ(x	φ(x	PROPN
ejpam-2674	223	5	·	·	PUNCT
ejpam-2674	223	6	y	y	X
ejpam-2674	223	7	)	)	PUNCT
ejpam-2674	223	8	◦	◦	NOUN
ejpam-2674	223	9	φ(z	φ(z	PROPN
ejpam-2674	223	10	)	)	PUNCT
ejpam-2674	224	1	=	=	PUNCT
ejpam-2674	224	2	(	(	PUNCT
ejpam-2674	224	3	φ(x	φ(x	NOUN
ejpam-2674	224	4	)	)	PUNCT
ejpam-2674	224	5	◦	◦	NOUN
ejpam-2674	224	6	φ(y	φ(y	NOUN
ejpam-2674	224	7	)	)	PUNCT
ejpam-2674	224	8	)	)	PUNCT
ejpam-2674	225	1	◦	◦	NOUN
ejpam-2674	225	2	φ(z	φ(z	PROPN
ejpam-2674	225	3	)	)	PUNCT
ejpam-2674	225	4	,	,	PUNCT
ejpam-2674	225	5	i.e.	i.e.	X
ejpam-2674	225	6	,	,	PUNCT
ejpam-2674	225	7	(	(	PUNCT
ejpam-2674	225	8	φ(x	φ(x	NOUN
ejpam-2674	225	9	)	)	PUNCT
ejpam-2674	225	10	◦	◦	NOUN
ejpam-2674	225	11	φ(y	φ(y	NOUN
ejpam-2674	225	12	)	)	PUNCT
ejpam-2674	225	13	)	)	PUNCT
ejpam-2674	225	14	◦	◦	NOUN
ejpam-2674	225	15	φ(z	φ(z	PROPN
ejpam-2674	225	16	)	)	PUNCT
ejpam-2674	225	17	=	=	SYM
ejpam-2674	225	18	φ(x	φ(x	NOUN
ejpam-2674	225	19	)	)	PUNCT
ejpam-2674	225	20	◦	◦	NOUN
ejpam-2674	225	21	(	(	PUNCT
ejpam-2674	225	22	φ(y	φ(y	NOUN
ejpam-2674	225	23	)	)	PUNCT
ejpam-2674	225	24	◦	◦	NOUN
ejpam-2674	225	25	φ(z	φ(z	PROPN
ejpam-2674	225	26	)	)	PUNCT
ejpam-2674	225	27	)	)	PUNCT
ejpam-2674	225	28	.	.	PUNCT
ejpam-2674	226	1	consequently	consequently	ADV
ejpam-2674	226	2	,	,	PUNCT
ejpam-2674	226	3	we	we	PRON
ejpam-2674	226	4	can	can	AUX
ejpam-2674	226	5	conclude	conclude	VERB
ejpam-2674	226	6	that	that	SCONJ
ejpam-2674	226	7	φ	φ	PROPN
ejpam-2674	226	8	(	(	PUNCT
ejpam-2674	226	9	s1	s1	PROPN
ejpam-2674	226	10	)	)	PUNCT
ejpam-2674	226	11	is	be	AUX
ejpam-2674	226	12	a	a	DET
ejpam-2674	226	13	near	near	ADJ
ejpam-2674	226	14	semigroup	semigroup	NOUN
ejpam-2674	226	15	.	.	PUNCT
ejpam-2674	227	1	proposition	proposition	NOUN
ejpam-2674	227	2	9	9	NUM
ejpam-2674	227	3	.	.	PUNCT
ejpam-2674	228	1	let	let	VERB
ejpam-2674	228	2	s1	s1	PROPN
ejpam-2674	228	3	⊂	⊂	PROPN
ejpam-2674	228	4	o1	o1	PROPN
ejpam-2674	228	5	,	,	PUNCT
ejpam-2674	228	6	s2	s2	PROPN
ejpam-2674	228	7	⊂	⊂	PROPN
ejpam-2674	228	8	o2	o2	PROPN
ejpam-2674	228	9	be	be	AUX
ejpam-2674	228	10	near	near	ADP
ejpam-2674	228	11	homomorphic	homomorphic	ADJ
ejpam-2674	228	12	semigroups	semigroup	NOUN
ejpam-2674	228	13	and	and	CCONJ
ejpam-2674	228	14	let	let	VERB
ejpam-2674	228	15	h	h	NOUN
ejpam-2674	228	16	,	,	PUNCT
ejpam-2674	228	17	i	i	PRON
ejpam-2674	228	18	be	be	VERB
ejpam-2674	228	19	a	a	DET
ejpam-2674	228	20	near	near	ADJ
ejpam-2674	228	21	subsemigroup	subsemigroup	NOUN
ejpam-2674	228	22	and	and	CCONJ
ejpam-2674	228	23	a	a	DET
ejpam-2674	228	24	near	near	ADJ
ejpam-2674	228	25	left	left	NOUN
ejpam-2674	228	26	(	(	PUNCT
ejpam-2674	228	27	right	right	ADJ
ejpam-2674	228	28	,	,	PUNCT
ejpam-2674	228	29	two	two	NUM
ejpam-2674	228	30	-	-	PUNCT
ejpam-2674	228	31	sided	sided	ADJ
ejpam-2674	228	32	)	)	PUNCT
ejpam-2674	228	33	ideal	ideal	NOUN
ejpam-2674	228	34	of	of	ADP
ejpam-2674	228	35	s1	s1	NOUN
ejpam-2674	228	36	,	,	PUNCT
ejpam-2674	228	37	respectively	respectively	ADV
ejpam-2674	228	38	.	.	PUNCT
ejpam-2674	229	1	then	then	ADV
ejpam-2674	229	2	;	;	PUNCT
ejpam-2674	229	3	(	(	PUNCT
ejpam-2674	229	4	a	a	X
ejpam-2674	229	5	)	)	PUNCT
ejpam-2674	229	6	φ	φ	PROPN
ejpam-2674	229	7	(	(	PUNCT
ejpam-2674	229	8	h	h	NOUN
ejpam-2674	229	9	)	)	PUNCT
ejpam-2674	229	10	is	be	AUX
ejpam-2674	229	11	a	a	DET
ejpam-2674	229	12	near	near	ADJ
ejpam-2674	229	13	subsemigroup	subsemigroup	NOUN
ejpam-2674	229	14	of	of	ADP
ejpam-2674	229	15	s2	s2	PROPN
ejpam-2674	229	16	if	if	SCONJ
ejpam-2674	229	17	φ	φ	PROPN
ejpam-2674	229	18	(	(	PUNCT
ejpam-2674	229	19	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	229	20	(	(	PUNCT
ejpam-2674	229	21	h	h	NOUN
ejpam-2674	229	22	)	)	PUNCT
ejpam-2674	229	23	)	)	PUNCT
ejpam-2674	230	1	=	=	SYM
ejpam-2674	230	2	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	230	3	(	(	PUNCT
ejpam-2674	230	4	φ	φ	PROPN
ejpam-2674	230	5	(	(	PUNCT
ejpam-2674	230	6	h	h	NOUN
ejpam-2674	230	7	)	)	PUNCT
ejpam-2674	230	8	)	)	PUNCT
ejpam-2674	230	9	,	,	PUNCT
ejpam-2674	230	10	(	(	PUNCT
ejpam-2674	230	11	b	b	X
ejpam-2674	230	12	)	)	PUNCT
ejpam-2674	230	13	φ	φ	PROPN
ejpam-2674	230	14	(	(	PUNCT
ejpam-2674	230	15	i	i	NOUN
ejpam-2674	230	16	)	)	PUNCT
ejpam-2674	230	17	is	be	AUX
ejpam-2674	230	18	a	a	DET
ejpam-2674	230	19	near	near	ADJ
ejpam-2674	230	20	left	left	NOUN
ejpam-2674	230	21	(	(	PUNCT
ejpam-2674	230	22	right	right	ADJ
ejpam-2674	230	23	,	,	PUNCT
ejpam-2674	230	24	two	two	NUM
ejpam-2674	230	25	-	-	PUNCT
ejpam-2674	230	26	sided	sided	ADJ
ejpam-2674	230	27	)	)	PUNCT
ejpam-2674	230	28	ideal	ideal	NOUN
ejpam-2674	230	29	of	of	ADP
ejpam-2674	230	30	s2	s2	PROPN
ejpam-2674	230	31	if	if	SCONJ
ejpam-2674	230	32	φ	φ	PROPN
ejpam-2674	230	33	(	(	PUNCT
ejpam-2674	230	34	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	230	35	(	(	PUNCT
ejpam-2674	230	36	i	i	NOUN
ejpam-2674	230	37	)	)	PUNCT
ejpam-2674	230	38	)	)	PUNCT
ejpam-2674	231	1	=	=	SYM
ejpam-2674	231	2	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	231	3	(	(	PUNCT
ejpam-2674	231	4	φ	φ	PROPN
ejpam-2674	231	5	(	(	PUNCT
ejpam-2674	231	6	i	i	NOUN
ejpam-2674	231	7	)	)	PUNCT
ejpam-2674	231	8	)	)	PUNCT
ejpam-2674	231	9	.	.	PUNCT
ejpam-2674	232	1	proof	proof	NOUN
ejpam-2674	232	2	.	.	PUNCT
ejpam-2674	233	1	(	(	PUNCT
ejpam-2674	233	2	a	a	X
ejpam-2674	233	3	)	)	PUNCT
ejpam-2674	233	4	consider	consider	VERB
ejpam-2674	233	5	a	a	PRON
ejpam-2674	233	6	onto	onto	ADP
ejpam-2674	233	7	mapping	mapping	NOUN
ejpam-2674	233	8	φ	φ	NOUN
ejpam-2674	233	9	from	from	ADP
ejpam-2674	233	10	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	233	11	(	(	PUNCT
ejpam-2674	233	12	s1	s1	PROPN
ejpam-2674	233	13	)	)	PUNCT
ejpam-2674	233	14	to	to	ADP
ejpam-2674	233	15	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	233	16	(	(	PUNCT
ejpam-2674	233	17	s2	s2	PROPN
ejpam-2674	233	18	)	)	PUNCT
ejpam-2674	233	19	such	such	ADJ
ejpam-2674	233	20	that	that	SCONJ
ejpam-2674	233	21	∀x	∀x	NUM
ejpam-2674	233	22	,	,	PUNCT
ejpam-2674	233	23	y	y	PROPN
ejpam-2674	233	24	∈	∈	PROPN
ejpam-2674	233	25	nr1(b)∗s1	nr1(b)∗s1	PROPN
ejpam-2674	233	26	,	,	PUNCT
ejpam-2674	233	27	φ(x	φ(x	PROPN
ejpam-2674	233	28	·	·	PUNCT
ejpam-2674	233	29	y	y	X
ejpam-2674	233	30	)	)	PUNCT
ejpam-2674	233	31	=	=	SYM
ejpam-2674	233	32	φ(x	φ(x	NOUN
ejpam-2674	233	33	)	)	PUNCT
ejpam-2674	233	34	◦	◦	NOUN
ejpam-2674	233	35	φ(y	φ(y	NOUN
ejpam-2674	233	36	)	)	PUNCT
ejpam-2674	233	37	.	.	PUNCT
ejpam-2674	234	1	for	for	ADP
ejpam-2674	234	2	all	all	DET
ejpam-2674	234	3	φ(x	φ(x	NOUN
ejpam-2674	234	4	)	)	PUNCT
ejpam-2674	234	5	,	,	PUNCT
ejpam-2674	234	6	φ(y	φ(y	NOUN
ejpam-2674	234	7	)	)	PUNCT
ejpam-2674	234	8	∈	∈	PROPN
ejpam-2674	234	9	φ(h	φ(h	NOUN
ejpam-2674	234	10	)	)	PUNCT
ejpam-2674	234	11	,	,	PUNCT
ejpam-2674	234	12	by	by	ADP
ejpam-2674	234	13	the	the	DET
ejpam-2674	234	14	definition	definition	NOUN
ejpam-2674	234	15	of	of	ADP
ejpam-2674	234	16	φ	φ	PROPN
ejpam-2674	234	17	,	,	PUNCT
ejpam-2674	234	18	there	there	PRON
ejpam-2674	234	19	exists	exist	VERB
ejpam-2674	234	20	x	x	X
ejpam-2674	234	21	,	,	PUNCT
ejpam-2674	234	22	y	y	PROPN
ejpam-2674	234	23	∈	∈	PROPN
ejpam-2674	234	24	h	h	NOUN
ejpam-2674	234	25	such	such	ADJ
ejpam-2674	234	26	that	that	SCONJ
ejpam-2674	234	27	x	x	PROPN
ejpam-2674	234	28	7→	7→	NUM
ejpam-2674	234	29	φ(x	φ(x	NOUN
ejpam-2674	234	30	)	)	PUNCT
ejpam-2674	234	31	and	and	CCONJ
ejpam-2674	234	32	φ(x	φ(x	NOUN
ejpam-2674	234	33	)	)	PUNCT
ejpam-2674	234	34	◦	◦	NOUN
ejpam-2674	234	35	φ(y	φ(y	NOUN
ejpam-2674	234	36	)	)	PUNCT
ejpam-2674	234	37	=	=	SYM
ejpam-2674	234	38	φ(x	φ(x	PROPN
ejpam-2674	234	39	·	·	PUNCT
ejpam-2674	234	40	y	y	X
ejpam-2674	234	41	)	)	PUNCT
ejpam-2674	234	42	∈	∈	PROPN
ejpam-2674	234	43	φ(nr1(b)∗h	φ(nr1(b)∗h	NUM
ejpam-2674	234	44	)	)	PUNCT
ejpam-2674	234	45	.	.	PUNCT
ejpam-2674	235	1	since	since	SCONJ
ejpam-2674	235	2	φ	φ	PROPN
ejpam-2674	235	3	(	(	PUNCT
ejpam-2674	235	4	nr1(b)∗h	nr1(b)∗h	PROPN
ejpam-2674	235	5	)	)	PUNCT
ejpam-2674	235	6	=	=	SYM
ejpam-2674	235	7	nr2(b)∗φ	nr2(b)∗φ	PROPN
ejpam-2674	235	8	(	(	PUNCT
ejpam-2674	235	9	h	h	NOUN
ejpam-2674	235	10	)	)	PUNCT
ejpam-2674	235	11	,	,	PUNCT
ejpam-2674	235	12	we	we	PRON
ejpam-2674	235	13	have	have	VERB
ejpam-2674	235	14	φ(x	φ(x	NOUN
ejpam-2674	235	15	)	)	PUNCT
ejpam-2674	235	16	◦	◦	NOUN
ejpam-2674	235	17	φ(y	φ(y	NOUN
ejpam-2674	235	18	)	)	PUNCT
ejpam-2674	235	19	∈	∈	PROPN
ejpam-2674	235	20	nr2(b)∗φ	nr2(b)∗φ	ADP
ejpam-2674	235	21	(	(	PUNCT
ejpam-2674	235	22	h	h	NOUN
ejpam-2674	235	23	)	)	PUNCT
ejpam-2674	235	24	.	.	PUNCT
ejpam-2674	236	1	(	(	PUNCT
ejpam-2674	236	2	b	b	X
ejpam-2674	236	3	)	)	PUNCT
ejpam-2674	236	4	by	by	ADP
ejpam-2674	236	5	(	(	PUNCT
ejpam-2674	236	6	a	a	X
ejpam-2674	236	7	)	)	PUNCT
ejpam-2674	236	8	,	,	PUNCT
ejpam-2674	236	9	it	it	PRON
ejpam-2674	236	10	is	be	AUX
ejpam-2674	236	11	easy	easy	ADJ
ejpam-2674	236	12	to	to	PART
ejpam-2674	236	13	see	see	VERB
ejpam-2674	236	14	that	that	SCONJ
ejpam-2674	236	15	φ	φ	PROPN
ejpam-2674	236	16	(	(	PUNCT
ejpam-2674	236	17	i	i	NOUN
ejpam-2674	236	18	)	)	PUNCT
ejpam-2674	236	19	is	be	AUX
ejpam-2674	236	20	a	a	DET
ejpam-2674	236	21	near	near	ADJ
ejpam-2674	236	22	subsemigroup	subsemigroup	NOUN
ejpam-2674	236	23	of	of	ADP
ejpam-2674	236	24	s2	s2	PROPN
ejpam-2674	236	25	if	if	SCONJ
ejpam-2674	236	26	ϕ	ϕ	X
ejpam-2674	236	27	(	(	PUNCT
ejpam-2674	236	28	nr1(b)∗i	nr1(b)∗i	PROPN
ejpam-2674	236	29	)	)	PUNCT
ejpam-2674	237	1	=	=	SYM
ejpam-2674	237	2	nr2(b)∗φ	nr2(b)∗φ	X
ejpam-2674	237	3	(	(	PUNCT
ejpam-2674	237	4	i	i	NOUN
ejpam-2674	237	5	)	)	PUNCT
ejpam-2674	237	6	.	.	PUNCT
ejpam-2674	238	1	since	since	SCONJ
ejpam-2674	238	2	∀φ(x	∀φ(x	PROPN
ejpam-2674	238	3	)	)	PUNCT
ejpam-2674	238	4	∈	∈	PROPN
ejpam-2674	238	5	s2	s2	PROPN
ejpam-2674	238	6	,	,	PUNCT
ejpam-2674	238	7	φ(y	φ(y	NOUN
ejpam-2674	238	8	)	)	PUNCT
ejpam-2674	238	9	∈	∈	PROPN
ejpam-2674	238	10	φ(i	φ(i	PROPN
ejpam-2674	238	11	)	)	PUNCT
ejpam-2674	238	12	there	there	PRON
ejpam-2674	238	13	is	be	VERB
ejpam-2674	238	14	φ(x	φ(x	NOUN
ejpam-2674	238	15	)	)	PUNCT
ejpam-2674	238	16	◦	◦	NOUN
ejpam-2674	238	17	φ(y	φ(y	NOUN
ejpam-2674	238	18	)	)	PUNCT
ejpam-2674	239	1	=	=	SYM
ejpam-2674	239	2	φ(x	φ(x	PROPN
ejpam-2674	239	3	·	·	PUNCT
ejpam-2674	239	4	y	y	X
ejpam-2674	239	5	)	)	PUNCT
ejpam-2674	239	6	and	and	CCONJ
ejpam-2674	239	7	i	i	PRON
ejpam-2674	239	8	is	be	AUX
ejpam-2674	239	9	a	a	DET
ejpam-2674	239	10	near	near	ADJ
ejpam-2674	239	11	left	left	ADJ
ejpam-2674	239	12	ideal	ideal	NOUN
ejpam-2674	239	13	of	of	ADP
ejpam-2674	239	14	s1	s1	NOUN
ejpam-2674	239	15	,	,	PUNCT
ejpam-2674	239	16	we	we	PRON
ejpam-2674	239	17	have	have	VERB
ejpam-2674	239	18	x	x	X
ejpam-2674	239	19	·	·	PUNCT
ejpam-2674	239	20	y	y	PROPN
ejpam-2674	239	21	∈	∈	PROPN
ejpam-2674	239	22	nr1(b)∗i	nr1(b)∗i	PROPN
ejpam-2674	239	23	.	.	PUNCT
ejpam-2674	240	1	thus	thus	ADV
ejpam-2674	240	2	φ(x	φ(x	PROPN
ejpam-2674	240	3	·	·	PUNCT
ejpam-2674	240	4	y	y	X
ejpam-2674	240	5	)	)	PUNCT
ejpam-2674	240	6	∈	∈	PROPN
ejpam-2674	240	7	φ	φ	PROPN
ejpam-2674	240	8	(	(	PUNCT
ejpam-2674	240	9	nr1(b)∗i	nr1(b)∗i	PROPN
ejpam-2674	240	10	)	)	PUNCT
ejpam-2674	240	11	.	.	PUNCT
ejpam-2674	241	1	since	since	SCONJ
ejpam-2674	241	2	φ	φ	PROPN
ejpam-2674	241	3	(	(	PUNCT
ejpam-2674	241	4	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	241	5	(	(	PUNCT
ejpam-2674	241	6	i	i	NOUN
ejpam-2674	241	7	)	)	PUNCT
ejpam-2674	241	8	)	)	PUNCT
ejpam-2674	242	1	=	=	SYM
ejpam-2674	242	2	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	242	3	(	(	PUNCT
ejpam-2674	242	4	φ	φ	PROPN
ejpam-2674	242	5	(	(	PUNCT
ejpam-2674	242	6	i	i	NOUN
ejpam-2674	242	7	)	)	PUNCT
ejpam-2674	242	8	)	)	PUNCT
ejpam-2674	242	9	,	,	PUNCT
ejpam-2674	242	10	we	we	PRON
ejpam-2674	242	11	have	have	VERB
ejpam-2674	242	12	φ(x	φ(x	NOUN
ejpam-2674	242	13	)	)	PUNCT
ejpam-2674	242	14	◦	◦	NOUN
ejpam-2674	242	15	φ(y	φ(y	NOUN
ejpam-2674	242	16	)	)	PUNCT
ejpam-2674	242	17	∈	∈	PROPN
ejpam-2674	242	18	nr2(b)∗φ	nr2(b)∗φ	ADP
ejpam-2674	242	19	(	(	PUNCT
ejpam-2674	242	20	i	i	NOUN
ejpam-2674	242	21	)	)	PUNCT
ejpam-2674	242	22	.	.	PUNCT
ejpam-2674	243	1	hence	hence	ADV
ejpam-2674	243	2	ϕ	ϕ	X
ejpam-2674	243	3	(	(	PUNCT
ejpam-2674	243	4	i	i	NOUN
ejpam-2674	243	5	)	)	PUNCT
ejpam-2674	243	6	is	be	AUX
ejpam-2674	243	7	a	a	DET
ejpam-2674	243	8	rough	rough	ADJ
ejpam-2674	243	9	left	left	ADJ
ejpam-2674	243	10	ideal	ideal	NOUN
ejpam-2674	243	11	of	of	ADP
ejpam-2674	243	12	s2	s2	PROPN
ejpam-2674	243	13	.	.	PUNCT
ejpam-2674	244	1	similarly	similarly	ADV
ejpam-2674	244	2	,	,	PUNCT
ejpam-2674	244	3	we	we	PRON
ejpam-2674	244	4	can	can	AUX
ejpam-2674	244	5	prove	prove	VERB
ejpam-2674	244	6	the	the	DET
ejpam-2674	244	7	other	other	ADJ
ejpam-2674	244	8	statement	statement	NOUN
ejpam-2674	244	9	.	.	PUNCT
ejpam-2674	245	1	proposition	proposition	NOUN
ejpam-2674	245	2	10	10	NUM
ejpam-2674	245	3	.	.	PUNCT
ejpam-2674	246	1	let	let	VERB
ejpam-2674	246	2	s1	s1	PROPN
ejpam-2674	246	3	⊂	⊂	PROPN
ejpam-2674	246	4	o1	o1	PROPN
ejpam-2674	246	5	,	,	PUNCT
ejpam-2674	246	6	s2	s2	PROPN
ejpam-2674	246	7	⊂	⊂	PROPN
ejpam-2674	246	8	o2	o2	PROPN
ejpam-2674	246	9	be	be	AUX
ejpam-2674	246	10	near	near	ADP
ejpam-2674	246	11	homomorphic	homomorphic	ADJ
ejpam-2674	246	12	semigroups	semigroup	NOUN
ejpam-2674	246	13	and	and	CCONJ
ejpam-2674	246	14	let	let	VERB
ejpam-2674	246	15	i	i	PRON
ejpam-2674	246	16	be	be	AUX
ejpam-2674	246	17	a	a	DET
ejpam-2674	246	18	near	near	ADJ
ejpam-2674	246	19	bi	bi	NOUN
ejpam-2674	246	20	-	-	NOUN
ejpam-2674	246	21	ideal	ideal	NOUN
ejpam-2674	246	22	of	of	ADP
ejpam-2674	246	23	s1	s1	NOUN
ejpam-2674	246	24	.	.	PUNCT
ejpam-2674	247	1	then	then	ADV
ejpam-2674	247	2	,	,	PUNCT
ejpam-2674	247	3	φ	φ	PROPN
ejpam-2674	247	4	(	(	PUNCT
ejpam-2674	247	5	i	i	NOUN
ejpam-2674	247	6	)	)	PUNCT
ejpam-2674	247	7	is	be	AUX
ejpam-2674	247	8	a	a	DET
ejpam-2674	247	9	near	near	ADJ
ejpam-2674	247	10	bi	bi	NOUN
ejpam-2674	247	11	-	-	NOUN
ejpam-2674	247	12	ideal	ideal	NOUN
ejpam-2674	247	13	of	of	ADP
ejpam-2674	247	14	s2	s2	PROPN
ejpam-2674	247	15	if	if	SCONJ
ejpam-2674	247	16	φ	φ	PROPN
ejpam-2674	247	17	(	(	PUNCT
ejpam-2674	247	18	nr1(b)∗i	nr1(b)∗i	PROPN
ejpam-2674	247	19	)	)	PUNCT
ejpam-2674	248	1	=	=	SYM
ejpam-2674	248	2	nr2(b)∗φ	nr2(b)∗φ	X
ejpam-2674	248	3	(	(	PUNCT
ejpam-2674	248	4	i	i	NOUN
ejpam-2674	248	5	)	)	PUNCT
ejpam-2674	248	6	.	.	PUNCT
ejpam-2674	249	1	proof	proof	NOUN
ejpam-2674	249	2	.	.	PUNCT
ejpam-2674	250	1	by	by	ADP
ejpam-2674	250	2	proposition	proposition	NOUN
ejpam-2674	250	3	9	9	NUM
ejpam-2674	250	4	item	item	NOUN
ejpam-2674	250	5	(	(	PUNCT
ejpam-2674	250	6	a	a	NOUN
ejpam-2674	250	7	)	)	PUNCT
ejpam-2674	250	8	,	,	PUNCT
ejpam-2674	250	9	φ	φ	PROPN
ejpam-2674	250	10	(	(	PUNCT
ejpam-2674	250	11	i	i	NOUN
ejpam-2674	250	12	)	)	PUNCT
ejpam-2674	250	13	is	be	AUX
ejpam-2674	250	14	a	a	DET
ejpam-2674	250	15	near	near	ADJ
ejpam-2674	250	16	subsemigroup	subsemigroup	NOUN
ejpam-2674	250	17	of	of	ADP
ejpam-2674	250	18	s2	s2	PROPN
ejpam-2674	250	19	if	if	SCONJ
ejpam-2674	250	20	φ	φ	PROPN
ejpam-2674	250	21	(	(	PUNCT
ejpam-2674	250	22	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	250	23	(	(	PUNCT
ejpam-2674	250	24	i	i	NOUN
ejpam-2674	250	25	)	)	PUNCT
ejpam-2674	250	26	)	)	PUNCT
ejpam-2674	251	1	=	=	SYM
ejpam-2674	251	2	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	251	3	(	(	PUNCT
ejpam-2674	251	4	φ	φ	PROPN
ejpam-2674	251	5	(	(	PUNCT
ejpam-2674	251	6	i	i	NOUN
ejpam-2674	251	7	)	)	PUNCT
ejpam-2674	251	8	)	)	PUNCT
ejpam-2674	251	9	.	.	PUNCT
ejpam-2674	252	1	since	since	SCONJ
ejpam-2674	252	2	∀φ(x	∀φ(x	PROPN
ejpam-2674	252	3	)	)	PUNCT
ejpam-2674	252	4	∈	∈	PROPN
ejpam-2674	252	5	s2	s2	PROPN
ejpam-2674	252	6	,	,	PUNCT
ejpam-2674	252	7	φ(y	φ(y	NOUN
ejpam-2674	252	8	)	)	PUNCT
ejpam-2674	252	9	∈	∈	PROPN
ejpam-2674	252	10	φ(i	φ(i	PROPN
ejpam-2674	252	11	)	)	PUNCT
ejpam-2674	252	12	there	there	PRON
ejpam-2674	252	13	is	be	VERB
ejpam-2674	252	14	φ(y	φ(y	NOUN
ejpam-2674	252	15	)	)	PUNCT
ejpam-2674	252	16	◦	◦	NOUN
ejpam-2674	252	17	φ(x	φ(x	NOUN
ejpam-2674	252	18	)	)	PUNCT
ejpam-2674	252	19	◦	◦	NOUN
ejpam-2674	252	20	φ(y	φ(y	NOUN
ejpam-2674	252	21	)	)	PUNCT
ejpam-2674	253	1	=	=	SYM
ejpam-2674	253	2	φ(y	φ(y	NOUN
ejpam-2674	253	3	·	·	PUNCT
ejpam-2674	253	4	x	x	SYM
ejpam-2674	253	5	·	·	PUNCT
ejpam-2674	253	6	y	y	X
ejpam-2674	253	7	)	)	PUNCT
ejpam-2674	254	1	and	and	CCONJ
ejpam-2674	254	2	i	i	PRON
ejpam-2674	254	3	is	be	AUX
ejpam-2674	254	4	a	a	DET
ejpam-2674	254	5	near	near	ADJ
ejpam-2674	254	6	bi	bi	NOUN
ejpam-2674	254	7	-	-	NOUN
ejpam-2674	254	8	ideal	ideal	NOUN
ejpam-2674	254	9	of	of	ADP
ejpam-2674	254	10	s1	s1	NOUN
ejpam-2674	254	11	,	,	PUNCT
ejpam-2674	254	12	we	we	PRON
ejpam-2674	254	13	have	have	VERB
ejpam-2674	254	14	y	y	PROPN
ejpam-2674	254	15	·	·	PUNCT
ejpam-2674	254	16	x	x	X
ejpam-2674	254	17	·	·	PUNCT
ejpam-2674	254	18	y	y	SYM
ejpam-2674	254	19	∈	∈	PROPN
ejpam-2674	254	20	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	254	21	(	(	PUNCT
ejpam-2674	254	22	i	i	NOUN
ejpam-2674	254	23	)	)	PUNCT
ejpam-2674	254	24	.	.	PUNCT
ejpam-2674	255	1	thus	thus	ADV
ejpam-2674	255	2	φ(y	φ(y	ADJ
ejpam-2674	255	3	·	·	PUNCT
ejpam-2674	255	4	x	x	SYM
ejpam-2674	255	5	·	·	PUNCT
ejpam-2674	255	6	y	y	X
ejpam-2674	255	7	)	)	PUNCT
ejpam-2674	255	8	∈	∈	PROPN
ejpam-2674	255	9	φ	φ	PROPN
ejpam-2674	255	10	(	(	PUNCT
ejpam-2674	255	11	nr1(b)∗i	nr1(b)∗i	PROPN
ejpam-2674	255	12	)	)	PUNCT
ejpam-2674	255	13	.	.	PUNCT
ejpam-2674	256	1	since	since	SCONJ
ejpam-2674	256	2	φ	φ	PROPN
ejpam-2674	256	3	(	(	PUNCT
ejpam-2674	256	4	nr1(b)∗i	nr1(b)∗i	PROPN
ejpam-2674	256	5	)	)	PUNCT
ejpam-2674	256	6	=	=	SYM
ejpam-2674	256	7	nr2(b)∗φ	nr2(b)∗φ	X
ejpam-2674	256	8	(	(	PUNCT
ejpam-2674	256	9	i	i	NOUN
ejpam-2674	256	10	)	)	PUNCT
ejpam-2674	256	11	,	,	PUNCT
ejpam-2674	256	12	we	we	PRON
ejpam-2674	256	13	have	have	AUX
ejpam-2674	256	14	φ(y	φ(y	NOUN
ejpam-2674	256	15	)	)	PUNCT
ejpam-2674	256	16	◦	◦	NOUN
ejpam-2674	256	17	φ(x	φ(x	NOUN
ejpam-2674	256	18	)	)	PUNCT
ejpam-2674	256	19	◦	◦	NOUN
ejpam-2674	256	20	φ(y	φ(y	NOUN
ejpam-2674	256	21	)	)	PUNCT
ejpam-2674	256	22	∈	∈	PROPN
ejpam-2674	256	23	nr2(b)∗φ	nr2(b)∗φ	ADP
ejpam-2674	256	24	(	(	PUNCT
ejpam-2674	256	25	i	i	NOUN
ejpam-2674	256	26	)	)	PUNCT
ejpam-2674	256	27	.	.	PUNCT
ejpam-2674	257	1	hence	hence	ADV
ejpam-2674	257	2	φ	φ	PROPN
ejpam-2674	257	3	(	(	PUNCT
ejpam-2674	257	4	i	i	NOUN
ejpam-2674	257	5	)	)	PUNCT
ejpam-2674	257	6	is	be	AUX
ejpam-2674	257	7	a	a	DET
ejpam-2674	257	8	near	near	ADJ
ejpam-2674	257	9	bi	bi	NOUN
ejpam-2674	257	10	-	-	NOUN
ejpam-2674	257	11	ideal	ideal	NOUN
ejpam-2674	257	12	of	of	ADP
ejpam-2674	257	13	s2	s2	PROPN
ejpam-2674	257	14	.	.	PUNCT
ejpam-2674	258	1	proposition	proposition	NOUN
ejpam-2674	258	2	11	11	NUM
ejpam-2674	258	3	.	.	PUNCT
ejpam-2674	259	1	let	let	VERB
ejpam-2674	259	2	s1	s1	PROPN
ejpam-2674	259	3	⊂	⊂	PROPN
ejpam-2674	259	4	o1	o1	PROPN
ejpam-2674	259	5	,	,	PUNCT
ejpam-2674	259	6	s2	s2	PROPN
ejpam-2674	259	7	⊂	⊂	PROPN
ejpam-2674	259	8	o2	o2	PROPN
ejpam-2674	259	9	be	be	AUX
ejpam-2674	259	10	near	near	ADP
ejpam-2674	259	11	homomorphic	homomorphic	ADJ
ejpam-2674	259	12	semigroups	semigroup	NOUN
ejpam-2674	259	13	and	and	CCONJ
ejpam-2674	259	14	let	let	VERB
ejpam-2674	259	15	h2	h2	PROPN
ejpam-2674	259	16	,	,	PUNCT
ejpam-2674	259	17	i2	i2	PROPN
ejpam-2674	259	18	be	be	VERB
ejpam-2674	259	19	a	a	DET
ejpam-2674	259	20	near	near	ADJ
ejpam-2674	259	21	subsemigroup	subsemigroup	NOUN
ejpam-2674	259	22	and	and	CCONJ
ejpam-2674	259	23	a	a	DET
ejpam-2674	259	24	near	near	ADJ
ejpam-2674	259	25	left	left	NOUN
ejpam-2674	259	26	(	(	PUNCT
ejpam-2674	259	27	right	right	ADJ
ejpam-2674	259	28	,	,	PUNCT
ejpam-2674	259	29	two	two	NUM
ejpam-2674	259	30	-	-	PUNCT
ejpam-2674	259	31	sided	sided	ADJ
ejpam-2674	259	32	)	)	PUNCT
ejpam-2674	259	33	ideal	ideal	NOUN
ejpam-2674	259	34	of	of	ADP
ejpam-2674	259	35	s2	s2	PROPN
ejpam-2674	259	36	.	.	PUNCT
ejpam-2674	260	1	then	then	ADV
ejpam-2674	260	2	,	,	PUNCT
ejpam-2674	260	3	(	(	PUNCT
ejpam-2674	260	4	a	a	X
ejpam-2674	260	5	)	)	PUNCT
ejpam-2674	260	6	φ−1	φ−1	PROPN
ejpam-2674	260	7	(	(	PUNCT
ejpam-2674	260	8	h2	h2	NOUN
ejpam-2674	260	9	)	)	PUNCT
ejpam-2674	261	1	=	=	PRON
ejpam-2674	261	2	h1	h1	NOUN
ejpam-2674	261	3	is	be	AUX
ejpam-2674	261	4	a	a	DET
ejpam-2674	261	5	near	near	ADJ
ejpam-2674	261	6	subsemigroup	subsemigroup	NOUN
ejpam-2674	261	7	of	of	ADP
ejpam-2674	261	8	s1	s1	PROPN
ejpam-2674	261	9	if	if	SCONJ
ejpam-2674	261	10	φ	φ	PROPN
ejpam-2674	261	11	(	(	PUNCT
ejpam-2674	261	12	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	261	13	(	(	PUNCT
ejpam-2674	261	14	h1	h1	PROPN
ejpam-2674	261	15	)	)	PUNCT
ejpam-2674	261	16	)	)	PUNCT
ejpam-2674	262	1	=	=	SYM
ejpam-2674	263	1	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	263	2	(	(	PUNCT
ejpam-2674	263	3	φ	φ	PROPN
ejpam-2674	263	4	(	(	PUNCT
ejpam-2674	263	5	h1	h1	PROPN
ejpam-2674	263	6	)	)	PUNCT
ejpam-2674	263	7	)	)	PUNCT
ejpam-2674	263	8	,	,	PUNCT
ejpam-2674	263	9	references	reference	NOUN
ejpam-2674	263	10	514	514	NUM
ejpam-2674	263	11	(	(	PUNCT
ejpam-2674	263	12	b	b	NOUN
ejpam-2674	263	13	)	)	PUNCT
ejpam-2674	263	14	φ−1	φ−1	PROPN
ejpam-2674	263	15	(	(	PUNCT
ejpam-2674	263	16	i2	i2	PROPN
ejpam-2674	263	17	)	)	PUNCT
ejpam-2674	263	18	=	=	PROPN
ejpam-2674	263	19	i1	i1	PROPN
ejpam-2674	263	20	is	be	AUX
ejpam-2674	263	21	a	a	DET
ejpam-2674	263	22	near	near	ADJ
ejpam-2674	263	23	left	left	NOUN
ejpam-2674	263	24	(	(	PUNCT
ejpam-2674	263	25	right	right	ADJ
ejpam-2674	263	26	,	,	PUNCT
ejpam-2674	263	27	two	two	NUM
ejpam-2674	263	28	-	-	PUNCT
ejpam-2674	263	29	sided	sided	ADJ
ejpam-2674	263	30	)	)	PUNCT
ejpam-2674	263	31	ideal	ideal	NOUN
ejpam-2674	263	32	of	of	ADP
ejpam-2674	263	33	s1	s1	PROPN
ejpam-2674	263	34	if	if	SCONJ
ejpam-2674	263	35	φ	φ	PROPN
ejpam-2674	263	36	(	(	PUNCT
ejpam-2674	263	37	nr1(b)∗	nr1(b)∗	PROPN
ejpam-2674	263	38	(	(	PUNCT
ejpam-2674	263	39	i1	i1	PROPN
ejpam-2674	263	40	)	)	PUNCT
ejpam-2674	263	41	)	)	PUNCT
ejpam-2674	264	1	=	=	SYM
ejpam-2674	264	2	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	264	3	(	(	PUNCT
ejpam-2674	264	4	φ	φ	PROPN
ejpam-2674	264	5	(	(	PUNCT
ejpam-2674	264	6	i1	i1	PROPN
ejpam-2674	264	7	)	)	PUNCT
ejpam-2674	264	8	)	)	PUNCT
ejpam-2674	264	9	.	.	PUNCT
ejpam-2674	265	1	proof	proof	NOUN
ejpam-2674	265	2	.	.	PUNCT
ejpam-2674	266	1	(	(	PUNCT
ejpam-2674	266	2	a	a	X
ejpam-2674	266	3	)	)	PUNCT
ejpam-2674	266	4	since	since	SCONJ
ejpam-2674	266	5	φ−1	φ−1	PROPN
ejpam-2674	266	6	(	(	PUNCT
ejpam-2674	266	7	h2	h2	NOUN
ejpam-2674	266	8	)	)	PUNCT
ejpam-2674	267	1	=	=	SYM
ejpam-2674	267	2	h1	h1	PROPN
ejpam-2674	267	3	,	,	PUNCT
ejpam-2674	267	4	we	we	PRON
ejpam-2674	267	5	have	have	VERB
ejpam-2674	267	6	φ	φ	PROPN
ejpam-2674	267	7	(	(	PUNCT
ejpam-2674	267	8	h1	h1	PROPN
ejpam-2674	267	9	)	)	PUNCT
ejpam-2674	267	10	=	=	SYM
ejpam-2674	267	11	h2	h2	NOUN
ejpam-2674	267	12	,	,	PUNCT
ejpam-2674	267	13	and	and	CCONJ
ejpam-2674	267	14	so	so	ADV
ejpam-2674	267	15	nr2(b)∗h2	nr2(b)∗h2	NOUN
ejpam-2674	267	16	=	=	SYM
ejpam-2674	268	1	nr2(b)∗	nr2(b)∗	PROPN
ejpam-2674	268	2	(	(	PUNCT
ejpam-2674	268	3	φ	φ	PROPN
ejpam-2674	268	4	(	(	PUNCT
ejpam-2674	268	5	h1	h1	PROPN
ejpam-2674	268	6	)	)	PUNCT
ejpam-2674	268	7	)	)	PUNCT
ejpam-2674	269	1	=	=	SYM
ejpam-2674	269	2	φ	φ	PROPN
ejpam-2674	269	3	(	(	PUNCT
ejpam-2674	269	4	nr1(b)∗h1	nr1(b)∗h1	PROPN
ejpam-2674	269	5	)	)	PUNCT
ejpam-2674	269	6	.	.	PUNCT
ejpam-2674	270	1	∀x	∀x	X
ejpam-2674	270	2	,	,	PUNCT
ejpam-2674	270	3	y	y	PROPN
ejpam-2674	270	4	∈	∈	PROPN
ejpam-2674	270	5	h1	h1	PROPN
ejpam-2674	270	6	,	,	PUNCT
ejpam-2674	270	7	we	we	PRON
ejpam-2674	270	8	have	have	VERB
ejpam-2674	270	9	φ(x	φ(x	NOUN
ejpam-2674	270	10	)	)	PUNCT
ejpam-2674	270	11	,	,	PUNCT
ejpam-2674	270	12	φ(y	φ(y	NOUN
ejpam-2674	270	13	)	)	PUNCT
ejpam-2674	270	14	∈	∈	PROPN
ejpam-2674	270	15	h2	h2	NOUN
ejpam-2674	270	16	.	.	PUNCT
ejpam-2674	271	1	since	since	SCONJ
ejpam-2674	271	2	h2	h2	PROPN
ejpam-2674	271	3	is	be	AUX
ejpam-2674	271	4	a	a	DET
ejpam-2674	271	5	near	near	ADJ
ejpam-2674	271	6	subsemigroup	subsemigroup	NOUN
ejpam-2674	271	7	,	,	PUNCT
ejpam-2674	271	8	we	we	PRON
ejpam-2674	271	9	get	get	VERB
ejpam-2674	271	10	φ(x	φ(x	NOUN
ejpam-2674	271	11	)	)	PUNCT
ejpam-2674	271	12	◦	◦	NOUN
ejpam-2674	271	13	φ(y	φ(y	NOUN
ejpam-2674	271	14	)	)	PUNCT
ejpam-2674	271	15	∈	∈	PROPN
ejpam-2674	271	16	nr2(b)∗h2	nr2(b)∗h2	NOUN
ejpam-2674	271	17	.	.	PUNCT
ejpam-2674	272	1	thus	thus	ADV
ejpam-2674	272	2	φ(x	φ(x	PROPN
ejpam-2674	272	3	·	·	PUNCT
ejpam-2674	272	4	y	y	X
ejpam-2674	272	5	)	)	PUNCT
ejpam-2674	272	6	∈	∈	PROPN
ejpam-2674	272	7	φ	φ	PROPN
ejpam-2674	272	8	(	(	PUNCT
ejpam-2674	272	9	nr1(b)∗h1	nr1(b)∗h1	PROPN
ejpam-2674	272	10	)	)	PUNCT
ejpam-2674	272	11	.	.	PUNCT
ejpam-2674	273	1	thus	thus	ADV
ejpam-2674	273	2	x	x	X
ejpam-2674	273	3	·	·	PUNCT
ejpam-2674	273	4	y	y	PROPN
ejpam-2674	273	5	∈	∈	PROPN
ejpam-2674	273	6	nr1(b)∗h1	nr1(b)∗h1	VERB
ejpam-2674	273	7	.	.	PUNCT
ejpam-2674	274	1	(	(	PUNCT
ejpam-2674	274	2	b	b	X
ejpam-2674	274	3	)	)	PUNCT
ejpam-2674	274	4	by	by	ADP
ejpam-2674	274	5	(	(	PUNCT
ejpam-2674	274	6	a	a	X
ejpam-2674	274	7	)	)	PUNCT
ejpam-2674	274	8	,	,	PUNCT
ejpam-2674	274	9	it	it	PRON
ejpam-2674	274	10	is	be	AUX
ejpam-2674	274	11	easy	easy	ADJ
ejpam-2674	274	12	to	to	PART
ejpam-2674	274	13	see	see	VERB
ejpam-2674	274	14	that	that	SCONJ
ejpam-2674	275	1	ϕ−1	ϕ−1	PROPN
ejpam-2674	275	2	(	(	PUNCT
ejpam-2674	275	3	i2	i2	PROPN
ejpam-2674	275	4	)	)	PUNCT
ejpam-2674	275	5	=	=	PROPN
ejpam-2674	275	6	i1	i1	PROPN
ejpam-2674	275	7	is	be	AUX
ejpam-2674	275	8	a	a	DET
ejpam-2674	275	9	near	near	ADJ
ejpam-2674	275	10	subsemigroup	subsemigroup	NOUN
ejpam-2674	275	11	of	of	ADP
ejpam-2674	275	12	s1	s1	PROPN
ejpam-2674	275	13	if	if	SCONJ
ejpam-2674	275	14	φ	φ	PROPN
ejpam-2674	275	15	(	(	PUNCT
ejpam-2674	275	16	nr1(b)∗i1	nr1(b)∗i1	NOUN
ejpam-2674	275	17	)	)	PUNCT
ejpam-2674	275	18	=	=	SYM
ejpam-2674	276	1	nr2(b)∗φ	nr2(b)∗φ	PROPN
ejpam-2674	276	2	(	(	PUNCT
ejpam-2674	276	3	i1	i1	PROPN
ejpam-2674	276	4	)	)	PUNCT
ejpam-2674	276	5	.	.	PUNCT
ejpam-2674	277	1	since	since	SCONJ
ejpam-2674	277	2	φ−1	φ−1	PROPN
ejpam-2674	277	3	(	(	PUNCT
ejpam-2674	277	4	i2	i2	PROPN
ejpam-2674	277	5	)	)	PUNCT
ejpam-2674	277	6	=	=	SYM
ejpam-2674	277	7	i1	i1	PROPN
ejpam-2674	277	8	,	,	PUNCT
ejpam-2674	277	9	we	we	PRON
ejpam-2674	277	10	have	have	VERB
ejpam-2674	277	11	φ	φ	PROPN
ejpam-2674	277	12	(	(	PUNCT
ejpam-2674	277	13	i1	i1	PROPN
ejpam-2674	277	14	)	)	PUNCT
ejpam-2674	277	15	=	=	SYM
ejpam-2674	277	16	i2	i2	PROPN
ejpam-2674	277	17	,	,	PUNCT
ejpam-2674	277	18	and	and	CCONJ
ejpam-2674	277	19	so	so	ADV
ejpam-2674	277	20	nr2(b)∗i2	nr2(b)∗i2	NOUN
ejpam-2674	277	21	=	=	SYM
ejpam-2674	277	22	nr2(b)∗φ	nr2(b)∗φ	PROPN
ejpam-2674	277	23	(	(	PUNCT
ejpam-2674	277	24	i1	i1	PROPN
ejpam-2674	277	25	)	)	PUNCT
ejpam-2674	278	1	=	=	SYM
ejpam-2674	278	2	φ	φ	PROPN
ejpam-2674	278	3	(	(	PUNCT
ejpam-2674	278	4	nr1(b)∗i1	nr1(b)∗i1	NOUN
ejpam-2674	278	5	)	)	PUNCT
ejpam-2674	278	6	.	.	PUNCT
ejpam-2674	279	1	∀x	∀x	X
ejpam-2674	279	2	∈	∈	PROPN
ejpam-2674	279	3	s1	s1	NOUN
ejpam-2674	279	4	and	and	CCONJ
ejpam-2674	279	5	y	y	PROPN
ejpam-2674	279	6	∈	∈	PROPN
ejpam-2674	279	7	i1	i1	PROPN
ejpam-2674	279	8	,	,	PUNCT
ejpam-2674	279	9	we	we	PRON
ejpam-2674	279	10	have	have	VERB
ejpam-2674	279	11	φ(x	φ(x	NOUN
ejpam-2674	279	12	)	)	PUNCT
ejpam-2674	279	13	∈	∈	PROPN
ejpam-2674	279	14	φ	φ	PROPN
ejpam-2674	279	15	(	(	PUNCT
ejpam-2674	279	16	s1	s1	PROPN
ejpam-2674	279	17	)	)	PUNCT
ejpam-2674	279	18	and	and	CCONJ
ejpam-2674	279	19	φ(y	φ(y	ADJ
ejpam-2674	279	20	)	)	PUNCT
ejpam-2674	279	21	∈	∈	PROPN
ejpam-2674	279	22	i2	i2	PROPN
ejpam-2674	279	23	.	.	PUNCT
ejpam-2674	280	1	since	since	SCONJ
ejpam-2674	280	2	i2	i2	PROPN
ejpam-2674	280	3	is	be	AUX
ejpam-2674	280	4	a	a	DET
ejpam-2674	280	5	near	near	ADJ
ejpam-2674	280	6	left	left	ADJ
ejpam-2674	280	7	ideal	ideal	NOUN
ejpam-2674	280	8	of	of	ADP
ejpam-2674	280	9	s2	s2	PROPN
ejpam-2674	280	10	,	,	PUNCT
ejpam-2674	280	11	we	we	PRON
ejpam-2674	280	12	have	have	VERB
ejpam-2674	280	13	φ(x	φ(x	NOUN
ejpam-2674	280	14	)	)	PUNCT
ejpam-2674	280	15	◦	◦	NOUN
ejpam-2674	280	16	φ(y	φ(y	NOUN
ejpam-2674	280	17	)	)	PUNCT
ejpam-2674	280	18	∈	∈	PROPN
ejpam-2674	280	19	nr2(b)∗i2	nr2(b)∗i2	NOUN
ejpam-2674	280	20	.	.	PUNCT
ejpam-2674	281	1	thus	thus	ADV
ejpam-2674	281	2	φ(x	φ(x	PROPN
ejpam-2674	281	3	·	·	PUNCT
ejpam-2674	281	4	y	y	X
ejpam-2674	281	5	)	)	PUNCT
ejpam-2674	281	6	∈	∈	PROPN
ejpam-2674	281	7	φ	φ	PROPN
ejpam-2674	281	8	(	(	PUNCT
ejpam-2674	281	9	nr1(b)∗i1	nr1(b)∗i1	PROPN
ejpam-2674	281	10	)	)	PUNCT
ejpam-2674	281	11	.	.	PUNCT
ejpam-2674	282	1	thus	thus	ADV
ejpam-2674	282	2	x	x	X
ejpam-2674	282	3	·	·	PUNCT
ejpam-2674	282	4	y	y	PROPN
ejpam-2674	282	5	∈	∈	PROPN
ejpam-2674	282	6	nr1(b)∗i1	nr1(b)∗i1	PROPN
ejpam-2674	282	7	.	.	PUNCT
ejpam-2674	283	1	therefore	therefore	ADV
ejpam-2674	283	2	,	,	PUNCT
ejpam-2674	283	3	ϕ−1	ϕ−1	PROPN
ejpam-2674	283	4	(	(	PUNCT
ejpam-2674	283	5	i2	i2	PROPN
ejpam-2674	283	6	)	)	PUNCT
ejpam-2674	283	7	=	=	PROPN
ejpam-2674	283	8	i1	i1	PROPN
ejpam-2674	283	9	is	be	AUX
ejpam-2674	283	10	a	a	DET
ejpam-2674	283	11	near	near	ADJ
ejpam-2674	283	12	left	left	ADJ
ejpam-2674	283	13	ideal	ideal	NOUN
ejpam-2674	283	14	of	of	ADP
ejpam-2674	283	15	s1	s1	NOUN
ejpam-2674	283	16	.	.	PUNCT
ejpam-2674	284	1	similarly	similarly	ADV
ejpam-2674	284	2	,	,	PUNCT
ejpam-2674	284	3	we	we	PRON
ejpam-2674	284	4	can	can	AUX
ejpam-2674	284	5	prove	prove	VERB
ejpam-2674	284	6	the	the	DET
ejpam-2674	284	7	other	other	ADJ
ejpam-2674	284	8	statement	statement	NOUN
ejpam-2674	284	9	.	.	PUNCT
ejpam-2674	285	1	proposition	proposition	NOUN
ejpam-2674	285	2	12	12	NUM
ejpam-2674	285	3	.	.	PUNCT
ejpam-2674	286	1	let	let	VERB
ejpam-2674	286	2	s1	s1	PROPN
ejpam-2674	286	3	⊂	⊂	PROPN
ejpam-2674	286	4	o1	o1	PROPN
ejpam-2674	286	5	,	,	PUNCT
ejpam-2674	286	6	s2	s2	PROPN
ejpam-2674	286	7	⊂	⊂	PROPN
ejpam-2674	286	8	o2	o2	PROPN
ejpam-2674	286	9	be	be	AUX
ejpam-2674	286	10	near	near	ADP
ejpam-2674	286	11	homomorphic	homomorphic	ADJ
ejpam-2674	286	12	semigroups	semigroup	NOUN
ejpam-2674	286	13	and	and	CCONJ
ejpam-2674	286	14	let	let	VERB
ejpam-2674	286	15	i2	i2	PROPN
ejpam-2674	286	16	be	be	AUX
ejpam-2674	286	17	a	a	DET
ejpam-2674	286	18	near	near	ADJ
ejpam-2674	286	19	bi	bi	NOUN
ejpam-2674	286	20	-	-	NOUN
ejpam-2674	286	21	ideal	ideal	NOUN
ejpam-2674	286	22	of	of	ADP
ejpam-2674	286	23	s2	s2	PROPN
ejpam-2674	286	24	.	.	PUNCT
ejpam-2674	287	1	then	then	ADV
ejpam-2674	287	2	,	,	PUNCT
ejpam-2674	287	3	φ−1	φ−1	PROPN
ejpam-2674	287	4	(	(	PUNCT
ejpam-2674	287	5	i2	i2	PROPN
ejpam-2674	287	6	)	)	PUNCT
ejpam-2674	287	7	=	=	PROPN
ejpam-2674	287	8	i1	i1	PROPN
ejpam-2674	287	9	is	be	AUX
ejpam-2674	287	10	a	a	DET
ejpam-2674	287	11	near	near	ADJ
ejpam-2674	287	12	bi	bi	NOUN
ejpam-2674	287	13	-	-	NOUN
ejpam-2674	287	14	ideal	ideal	NOUN
ejpam-2674	287	15	of	of	ADP
ejpam-2674	287	16	s1	s1	PROPN
ejpam-2674	287	17	if	if	SCONJ
ejpam-2674	287	18	φ	φ	PROPN
ejpam-2674	287	19	(	(	PUNCT
ejpam-2674	287	20	nr1(b)∗i1	nr1(b)∗i1	NOUN
ejpam-2674	287	21	)	)	PUNCT
ejpam-2674	287	22	=	=	SYM
ejpam-2674	288	1	nr2(b)∗φ	nr2(b)∗φ	PROPN
ejpam-2674	288	2	(	(	PUNCT
ejpam-2674	288	3	i1	i1	PROPN
ejpam-2674	288	4	)	)	PUNCT
ejpam-2674	288	5	.	.	PUNCT
ejpam-2674	289	1	proof	proof	NOUN
ejpam-2674	289	2	.	.	PUNCT
ejpam-2674	290	1	by	by	ADP
ejpam-2674	290	2	proposition	proposition	NOUN
ejpam-2674	290	3	11	11	NUM
ejpam-2674	290	4	item	item	NOUN
ejpam-2674	290	5	(	(	PUNCT
ejpam-2674	290	6	a	a	NOUN
ejpam-2674	290	7	)	)	PUNCT
ejpam-2674	290	8	,	,	PUNCT
ejpam-2674	290	9	φ−1	φ−1	PROPN
ejpam-2674	290	10	(	(	PUNCT
ejpam-2674	290	11	i2	i2	PROPN
ejpam-2674	290	12	)	)	PUNCT
ejpam-2674	290	13	=	=	PROPN
ejpam-2674	290	14	i1	i1	PROPN
ejpam-2674	290	15	is	be	AUX
ejpam-2674	290	16	a	a	DET
ejpam-2674	290	17	near	near	ADJ
ejpam-2674	290	18	subsemigroup	subsemigroup	NOUN
ejpam-2674	290	19	of	of	ADP
ejpam-2674	290	20	s1	s1	PROPN
ejpam-2674	290	21	if	if	SCONJ
ejpam-2674	290	22	φ	φ	PROPN
ejpam-2674	290	23	(	(	PUNCT
ejpam-2674	290	24	nr1(b)∗i1	nr1(b)∗i1	NOUN
ejpam-2674	290	25	)	)	PUNCT
ejpam-2674	290	26	=	=	SYM
ejpam-2674	291	1	nr2(b)∗φ	nr2(b)∗φ	PROPN
ejpam-2674	291	2	(	(	PUNCT
ejpam-2674	291	3	i1	i1	PROPN
ejpam-2674	291	4	)	)	PUNCT
ejpam-2674	291	5	.	.	PUNCT
ejpam-2674	292	1	since	since	SCONJ
ejpam-2674	292	2	ϕ−1	ϕ−1	PROPN
ejpam-2674	292	3	(	(	PUNCT
ejpam-2674	292	4	i2	i2	PROPN
ejpam-2674	292	5	)	)	PUNCT
ejpam-2674	292	6	=	=	SYM
ejpam-2674	292	7	i1	i1	PROPN
ejpam-2674	292	8	,	,	PUNCT
ejpam-2674	292	9	we	we	PRON
ejpam-2674	292	10	have	have	VERB
ejpam-2674	292	11	ϕ	ϕ	NOUN
ejpam-2674	292	12	(	(	PUNCT
ejpam-2674	292	13	i1	i1	PROPN
ejpam-2674	292	14	)	)	PUNCT
ejpam-2674	292	15	=	=	SYM
ejpam-2674	292	16	i2	i2	PROPN
ejpam-2674	292	17	,	,	PUNCT
ejpam-2674	292	18	and	and	CCONJ
ejpam-2674	292	19	so	so	ADV
ejpam-2674	292	20	nr2(b)∗i2	nr2(b)∗i2	NOUN
ejpam-2674	292	21	=	=	SYM
ejpam-2674	292	22	nr2(b)∗φ	nr2(b)∗φ	PROPN
ejpam-2674	292	23	(	(	PUNCT
ejpam-2674	292	24	i1	i1	PROPN
ejpam-2674	292	25	)	)	PUNCT
ejpam-2674	293	1	=	=	SYM
ejpam-2674	293	2	φ	φ	PROPN
ejpam-2674	293	3	(	(	PUNCT
ejpam-2674	293	4	nr1(b)∗i1	nr1(b)∗i1	NOUN
ejpam-2674	293	5	)	)	PUNCT
ejpam-2674	293	6	.	.	PUNCT
ejpam-2674	294	1	∀x	∀x	X
ejpam-2674	294	2	∈	∈	PROPN
ejpam-2674	294	3	s1	s1	NOUN
ejpam-2674	294	4	and	and	CCONJ
ejpam-2674	294	5	y	y	PROPN
ejpam-2674	294	6	∈	∈	PROPN
ejpam-2674	294	7	i1	i1	PROPN
ejpam-2674	294	8	,	,	PUNCT
ejpam-2674	294	9	we	we	PRON
ejpam-2674	294	10	have	have	VERB
ejpam-2674	294	11	φ(x	φ(x	NOUN
ejpam-2674	294	12	)	)	PUNCT
ejpam-2674	294	13	∈	∈	PROPN
ejpam-2674	294	14	φ	φ	PROPN
ejpam-2674	294	15	(	(	PUNCT
ejpam-2674	294	16	s1	s1	PROPN
ejpam-2674	294	17	)	)	PUNCT
ejpam-2674	294	18	and	and	CCONJ
ejpam-2674	294	19	φ(y	φ(y	ADJ
ejpam-2674	294	20	)	)	PUNCT
ejpam-2674	294	21	∈	∈	PROPN
ejpam-2674	294	22	i2	i2	PROPN
ejpam-2674	294	23	.	.	PUNCT
ejpam-2674	295	1	since	since	SCONJ
ejpam-2674	295	2	i2	i2	PROPN
ejpam-2674	295	3	is	be	AUX
ejpam-2674	295	4	a	a	DET
ejpam-2674	295	5	near	near	ADJ
ejpam-2674	295	6	bi	bi	NOUN
ejpam-2674	295	7	-	-	NOUN
ejpam-2674	295	8	ideal	ideal	NOUN
ejpam-2674	295	9	of	of	ADP
ejpam-2674	295	10	s2	s2	PROPN
ejpam-2674	295	11	,	,	PUNCT
ejpam-2674	295	12	we	we	PRON
ejpam-2674	295	13	have	have	AUX
ejpam-2674	295	14	φ(y	φ(y	NOUN
ejpam-2674	295	15	)	)	PUNCT
ejpam-2674	295	16	◦	◦	NOUN
ejpam-2674	295	17	φ(x	φ(x	NOUN
ejpam-2674	295	18	)	)	PUNCT
ejpam-2674	295	19	◦	◦	NOUN
ejpam-2674	295	20	φ(y	φ(y	NOUN
ejpam-2674	295	21	)	)	PUNCT
ejpam-2674	295	22	∈	∈	PROPN
ejpam-2674	295	23	nr2(b)∗i2	nr2(b)∗i2	NOUN
ejpam-2674	295	24	.	.	PUNCT
ejpam-2674	296	1	thus	thus	ADV
ejpam-2674	296	2	φ(y	φ(y	NOUN
ejpam-2674	296	3	·	·	PUNCT
ejpam-2674	296	4	x	x	SYM
ejpam-2674	296	5	·	·	PUNCT
ejpam-2674	296	6	y	y	X
ejpam-2674	296	7	)	)	PUNCT
ejpam-2674	296	8	∈	∈	PROPN
ejpam-2674	296	9	φ	φ	PROPN
ejpam-2674	296	10	(	(	PUNCT
ejpam-2674	296	11	nr1(b)∗i1	nr1(b)∗i1	PROPN
ejpam-2674	296	12	)	)	PUNCT
ejpam-2674	296	13	.	.	PUNCT
ejpam-2674	297	1	thus	thus	ADV
ejpam-2674	297	2	y	y	PROPN
ejpam-2674	297	3	·	·	PUNCT
ejpam-2674	297	4	x	x	PUNCT
ejpam-2674	297	5	·	·	PUNCT
ejpam-2674	297	6	y	y	PROPN
ejpam-2674	297	7	∈	∈	PROPN
ejpam-2674	297	8	nr1(b)∗i1	nr1(b)∗i1	PROPN
ejpam-2674	297	9	.	.	PUNCT
ejpam-2674	298	1	therefore	therefore	ADV
ejpam-2674	298	2	,	,	PUNCT
ejpam-2674	298	3	φ−1	φ−1	PROPN
ejpam-2674	298	4	(	(	PUNCT
ejpam-2674	298	5	i2	i2	PROPN
ejpam-2674	298	6	)	)	PUNCT
ejpam-2674	298	7	=	=	PROPN
ejpam-2674	298	8	i1	i1	PROPN
ejpam-2674	298	9	is	be	AUX
ejpam-2674	298	10	a	a	DET
ejpam-2674	298	11	near	near	ADJ
ejpam-2674	298	12	bi	bi	NOUN
ejpam-2674	298	13	-	-	NOUN
ejpam-2674	298	14	ideal	ideal	NOUN
ejpam-2674	298	15	of	of	ADP
ejpam-2674	298	16	s1	s1	NOUN
ejpam-2674	298	17	.	.	PUNCT
ejpam-2674	299	1	references	reference	NOUN
ejpam-2674	299	2	[	[	X
ejpam-2674	299	3	1	1	NUM
ejpam-2674	299	4	]	]	X
ejpam-2674	299	5	n.	n.	NOUN
ejpam-2674	299	6	bağırmaz	bağırmaz	PROPN
ejpam-2674	299	7	and	and	CCONJ
ejpam-2674	299	8	a.	a.	PROPN
ejpam-2674	299	9	f.	f.	PROPN
ejpam-2674	299	10	özcan	özcan	PROPN
ejpam-2674	299	11	,	,	PUNCT
ejpam-2674	299	12	rough	rough	ADJ
ejpam-2674	299	13	semigroups	semigroup	NOUN
ejpam-2674	299	14	on	on	ADP
ejpam-2674	299	15	approximation	approximation	NOUN
ejpam-2674	299	16	spaces	space	NOUN
ejpam-2674	299	17	,	,	PUNCT
ejpam-2674	299	18	international	international	ADJ
ejpam-2674	299	19	journal	journal	NOUN
ejpam-2674	299	20	of	of	ADP
ejpam-2674	299	21	algebra	algebra	PROPN
ejpam-2674	299	22	,	,	PUNCT
ejpam-2674	299	23	vol	vol	NOUN
ejpam-2674	299	24	.	.	NOUN
ejpam-2674	299	25	9	9	NUM
ejpam-2674	299	26	,	,	PUNCT
ejpam-2674	299	27	no	no	INTJ
ejpam-2674	299	28	.	.	NOUN
ejpam-2674	299	29	7	7	NUM
ejpam-2674	299	30	,	,	PUNCT
ejpam-2674	299	31	339	339	NUM
ejpam-2674	299	32	-	-	SYM
ejpam-2674	299	33	350	350	NUM
ejpam-2674	299	34	,	,	PUNCT
ejpam-2674	299	35	2015	2015	NUM
ejpam-2674	299	36	.	.	PUNCT
ejpam-2674	300	1	[	[	X
ejpam-2674	300	2	2	2	NUM
ejpam-2674	300	3	]	]	X
ejpam-2674	300	4	n.	n.	NOUN
ejpam-2674	300	5	bağırmaz	bağırmaz	PROPN
ejpam-2674	300	6	,	,	PUNCT
ejpam-2674	300	7	rough	rough	ADJ
ejpam-2674	300	8	prime	prime	ADJ
ejpam-2674	300	9	ideals	ideal	NOUN
ejpam-2674	300	10	in	in	ADP
ejpam-2674	300	11	rough	rough	ADJ
ejpam-2674	300	12	semigroups	semigroup	NOUN
ejpam-2674	300	13	,	,	PUNCT
ejpam-2674	300	14	international	international	PROPN
ejpam-2674	300	15	mathematical	mathematical	ADJ
ejpam-2674	300	16	forum	forum	PROPN
ejpam-2674	300	17	,	,	PUNCT
ejpam-2674	300	18	vol	vol	NOUN
ejpam-2674	300	19	.	.	PROPN
ejpam-2674	300	20	11	11	NUM
ejpam-2674	300	21	,	,	PUNCT
ejpam-2674	300	22	no	no	INTJ
ejpam-2674	300	23	.	.	NOUN
ejpam-2674	300	24	8	8	NUM
ejpam-2674	300	25	,	,	PUNCT
ejpam-2674	300	26	369	369	NUM
ejpam-2674	300	27	377	377	NUM
ejpam-2674	300	28	,	,	PUNCT
ejpam-2674	300	29	2016	2016	NUM
ejpam-2674	300	30	.	.	PUNCT
ejpam-2674	301	1	[	[	X
ejpam-2674	301	2	3	3	X
ejpam-2674	301	3	]	]	X
ejpam-2674	301	4	r.	r.	PROPN
ejpam-2674	301	5	biswas	biswas	PROPN
ejpam-2674	301	6	and	and	CCONJ
ejpam-2674	301	7	s.	s.	PROPN
ejpam-2674	301	8	nanda	nanda	PROPN
ejpam-2674	301	9	,	,	PUNCT
ejpam-2674	301	10	rough	rough	ADJ
ejpam-2674	301	11	groups	group	NOUN
ejpam-2674	301	12	and	and	CCONJ
ejpam-2674	301	13	rough	rough	ADJ
ejpam-2674	301	14	subgroups	subgroup	NOUN
ejpam-2674	301	15	,	,	PUNCT
ejpam-2674	301	16	bull	bull	NOUN
ejpam-2674	301	17	.	.	PUNCT
ejpam-2674	302	1	polish	polish	PROPN
ejpam-2674	302	2	acad	acad	PROPN
ejpam-2674	302	3	.	.	PUNCT
ejpam-2674	303	1	sci	sci	PROPN
ejpam-2674	303	2	.	.	PROPN
ejpam-2674	303	3	math	math	PROPN
ejpam-2674	303	4	.	.	PUNCT
ejpam-2674	303	5	,	,	PUNCT
ejpam-2674	303	6	42	42	NUM
ejpam-2674	303	7	251–254	251–254	NUM
ejpam-2674	303	8	,	,	PUNCT
ejpam-2674	303	9	1994	1994	NUM
ejpam-2674	303	10	.	.	PUNCT
ejpam-2674	304	1	[	[	X
ejpam-2674	304	2	4	4	X
ejpam-2674	304	3	]	]	PUNCT
ejpam-2674	304	4	z.	z.	PROPN
ejpam-2674	304	5	bonikowaski	bonikowaski	PROPN
ejpam-2674	304	6	,	,	PUNCT
ejpam-2674	304	7	algebraic	algebraic	ADJ
ejpam-2674	304	8	structures	structure	NOUN
ejpam-2674	304	9	of	of	ADP
ejpam-2674	304	10	rough	rough	ADJ
ejpam-2674	304	11	sets	set	NOUN
ejpam-2674	304	12	,	,	PUNCT
ejpam-2674	304	13	in	in	ADP
ejpam-2674	304	14	:	:	PUNCT
ejpam-2674	304	15	w.p	w.p	PROPN
ejpam-2674	304	16	.	.	PROPN
ejpam-2674	304	17	ziarko	ziarko	PROPN
ejpam-2674	304	18	(	(	PUNCT
ejpam-2674	304	19	ed	ed	NOUN
ejpam-2674	304	20	.	.	PUNCT
ejpam-2674	304	21	)	)	PUNCT
ejpam-2674	304	22	,	,	PUNCT
ejpam-2674	304	23	rough	rough	ADJ
ejpam-2674	304	24	sets	set	NOUN
ejpam-2674	304	25	,	,	PUNCT
ejpam-2674	304	26	fuzzy	fuzzy	ADJ
ejpam-2674	304	27	sets	set	NOUN
ejpam-2674	304	28	and	and	CCONJ
ejpam-2674	304	29	knowledge	knowledge	NOUN
ejpam-2674	304	30	discovery	discovery	NOUN
ejpam-2674	304	31	,	,	PUNCT
ejpam-2674	304	32	springer	springer	NOUN
ejpam-2674	304	33	-	-	PUNCT
ejpam-2674	304	34	verlag	verlag	PROPN
ejpam-2674	304	35	,	,	PUNCT
ejpam-2674	304	36	berlin	berlin	PROPN
ejpam-2674	304	37	,	,	PUNCT
ejpam-2674	304	38	pp	pp	X
ejpam-2674	304	39	.	.	PUNCT
ejpam-2674	305	1	242–247	242–247	NUM
ejpam-2674	305	2	,	,	PUNCT
ejpam-2674	305	3	1995	1995	NUM
ejpam-2674	305	4	.	.	PUNCT
ejpam-2674	306	1	[	[	X
ejpam-2674	306	2	5	5	X
ejpam-2674	306	3	]	]	PUNCT
ejpam-2674	306	4	w.	w.	PROPN
ejpam-2674	306	5	cheng	cheng	PROPN
ejpam-2674	306	6	,	,	PUNCT
ejpam-2674	306	7	z.	z.	PROPN
ejpam-2674	306	8	mo	mo	PROPN
ejpam-2674	306	9	and	and	CCONJ
ejpam-2674	306	10	j.	j.	PROPN
ejpam-2674	306	11	wang	wang	PROPN
ejpam-2674	306	12	,	,	PUNCT
ejpam-2674	306	13	notes	note	VERB
ejpam-2674	306	14	on	on	ADP
ejpam-2674	306	15	“	"	PUNCT
ejpam-2674	306	16	the	the	DET
ejpam-2674	306	17	lower	low	ADJ
ejpam-2674	306	18	and	and	CCONJ
ejpam-2674	306	19	upper	upper	ADJ
ejpam-2674	306	20	approximations	approximation	NOUN
ejpam-2674	306	21	in	in	ADP
ejpam-2674	306	22	a	a	DET
ejpam-2674	306	23	fuzzy	fuzzy	ADJ
ejpam-2674	306	24	group	group	NOUN
ejpam-2674	306	25	”	"	PUNCT
ejpam-2674	306	26	and	and	CCONJ
ejpam-2674	306	27	“	"	PUNCT
ejpam-2674	306	28	rough	rough	ADJ
ejpam-2674	306	29	ideals	ideal	NOUN
ejpam-2674	306	30	in	in	ADP
ejpam-2674	306	31	semigroups	semigroup	NOUN
ejpam-2674	306	32	”	"	PUNCT
ejpam-2674	306	33	,	,	PUNCT
ejpam-2674	306	34	inform	inform	NOUN
ejpam-2674	306	35	.	.	PUNCT
ejpam-2674	307	1	sci	sci	PROPN
ejpam-2674	307	2	.	.	PROPN
ejpam-2674	307	3	,	,	PUNCT
ejpam-2674	307	4	177	177	NUM
ejpam-2674	307	5	5134	5134	NUM
ejpam-2674	307	6	-	-	SYM
ejpam-2674	307	7	5140	5140	NUM
ejpam-2674	307	8	,	,	PUNCT
ejpam-2674	307	9	2007	2007	NUM
ejpam-2674	307	10	.	.	PUNCT
ejpam-2674	308	1	[	[	X
ejpam-2674	308	2	6	6	NUM
ejpam-2674	308	3	]	]	PUNCT
ejpam-2674	308	4	b.	b.	PROPN
ejpam-2674	308	5	davvaz	davvaz	PROPN
ejpam-2674	308	6	,	,	PUNCT
ejpam-2674	308	7	roughness	roughness	NOUN
ejpam-2674	308	8	in	in	ADP
ejpam-2674	308	9	rings	ring	NOUN
ejpam-2674	308	10	,	,	PUNCT
ejpam-2674	308	11	inform	inform	NOUN
ejpam-2674	308	12	.	.	PUNCT
ejpam-2674	309	1	sci	sci	PROPN
ejpam-2674	309	2	.	.	PROPN
ejpam-2674	309	3	,	,	PUNCT
ejpam-2674	309	4	164	164	NUM
ejpam-2674	309	5	,	,	PUNCT
ejpam-2674	309	6	147–163	147–163	NUM
ejpam-2674	309	7	,	,	PUNCT
ejpam-2674	309	8	2004	2004	NUM
ejpam-2674	309	9	.	.	PUNCT
ejpam-2674	310	1	[	[	X
ejpam-2674	310	2	7	7	X
ejpam-2674	310	3	]	]	X
ejpam-2674	310	4	c.	c.	PROPN
ejpam-2674	310	5	henry	henry	PROPN
ejpam-2674	310	6	,	,	PUNCT
ejpam-2674	310	7	neighbourhoods	neighbourhood	NOUN
ejpam-2674	310	8	,	,	PUNCT
ejpam-2674	310	9	classes	class	NOUN
ejpam-2674	310	10	and	and	CCONJ
ejpam-2674	310	11	near	near	ADJ
ejpam-2674	310	12	sets	set	NOUN
ejpam-2674	310	13	,	,	PUNCT
ejpam-2674	310	14	applied	apply	VERB
ejpam-2674	310	15	mathematical	mathematical	ADJ
ejpam-2674	310	16	sciences	science	NOUN
ejpam-2674	310	17	,	,	PUNCT
ejpam-2674	310	18	vol	vol	NOUN
ejpam-2674	310	19	.	.	PROPN
ejpam-2674	310	20	5	5	NUM
ejpam-2674	310	21	,	,	PUNCT
ejpam-2674	310	22	no	no	INTJ
ejpam-2674	310	23	.	.	NOUN
ejpam-2674	310	24	35	35	NUM
ejpam-2674	310	25	,	,	PUNCT
ejpam-2674	310	26	1727	1727	NUM
ejpam-2674	310	27	1732	1732	NUM
ejpam-2674	310	28	,	,	PUNCT
ejpam-2674	310	29	2011	2011	NUM
ejpam-2674	310	30	.	.	PUNCT
ejpam-2674	311	1	[	[	X
ejpam-2674	311	2	8	8	X
ejpam-2674	311	3	]	]	PUNCT
ejpam-2674	311	4	t.	t.	NOUN
ejpam-2674	311	5	iwinski	iwinski	NOUN
ejpam-2674	311	6	,	,	PUNCT
ejpam-2674	311	7	algebraic	algebraic	ADJ
ejpam-2674	311	8	approach	approach	NOUN
ejpam-2674	311	9	to	to	ADP
ejpam-2674	311	10	rough	rough	ADJ
ejpam-2674	311	11	sets	set	NOUN
ejpam-2674	311	12	,	,	PUNCT
ejpam-2674	311	13	bull	bull	NOUN
ejpam-2674	311	14	.	.	PUNCT
ejpam-2674	312	1	polish	polish	PROPN
ejpam-2674	312	2	acad	acad	PROPN
ejpam-2674	312	3	.	.	PUNCT
ejpam-2674	313	1	sci	sci	PROPN
ejpam-2674	313	2	.	.	PROPN
ejpam-2674	313	3	math	math	PROPN
ejpam-2674	313	4	.	.	PUNCT
ejpam-2674	313	5	,	,	PUNCT
ejpam-2674	313	6	35	35	NUM
ejpam-2674	313	7	,	,	PUNCT
ejpam-2674	313	8	673–683	673–683	NUM
ejpam-2674	313	9	,	,	PUNCT
ejpam-2674	313	10	1987	1987	NUM
ejpam-2674	313	11	.	.	PUNCT
ejpam-2674	314	1	references	reference	NOUN
ejpam-2674	314	2	515	515	NUM
ejpam-2674	315	1	[	[	X
ejpam-2674	315	2	9	9	NUM
ejpam-2674	315	3	]	]	X
ejpam-2674	315	4	e.	e.	PROPN
ejpam-2674	315	5	i̇nan	i̇nan	PROPN
ejpam-2674	315	6	and	and	CCONJ
ejpam-2674	315	7	m.	m.	NOUN
ejpam-2674	315	8	öztürk	öztürk	PROPN
ejpam-2674	315	9	,	,	PUNCT
ejpam-2674	315	10	near	near	ADP
ejpam-2674	315	11	groups	group	NOUN
ejpam-2674	315	12	on	on	ADP
ejpam-2674	315	13	nearness	nearness	NOUN
ejpam-2674	315	14	approximation	approximation	NOUN
ejpam-2674	315	15	spaces	space	NOUN
ejpam-2674	315	16	,	,	PUNCT
ejpam-2674	315	17	hacettepe	hacettepe	ADJ
ejpam-2674	315	18	journal	journal	NOUN
ejpam-2674	315	19	of	of	ADP
ejpam-2674	315	20	mathematics	mathematic	NOUN
ejpam-2674	315	21	and	and	CCONJ
ejpam-2674	315	22	statistics	statistic	NOUN
ejpam-2674	315	23	,	,	PUNCT
ejpam-2674	315	24	4	4	NUM
ejpam-2674	315	25	,	,	PUNCT
ejpam-2674	315	26	545–558	545–558	NUM
ejpam-2674	315	27	,	,	PUNCT
ejpam-2674	315	28	2012	2012	NUM
ejpam-2674	315	29	.	.	PUNCT
ejpam-2674	316	1	[	[	X
ejpam-2674	316	2	10	10	NUM
ejpam-2674	316	3	]	]	X
ejpam-2674	316	4	e.	e.	PROPN
ejpam-2674	316	5	i̇nan	i̇nan	PROPN
ejpam-2674	316	6	and	and	CCONJ
ejpam-2674	316	7	m.	m.	NOUN
ejpam-2674	316	8	öztürk	öztürk	PROPN
ejpam-2674	316	9	,	,	PUNCT
ejpam-2674	316	10	near	near	ADP
ejpam-2674	316	11	semigroups	semigroup	NOUN
ejpam-2674	316	12	on	on	ADP
ejpam-2674	316	13	nearness	nearness	NOUN
ejpam-2674	316	14	approximation	approximation	NOUN
ejpam-2674	316	15	spaces	space	NOUN
ejpam-2674	316	16	,	,	PUNCT
ejpam-2674	316	17	annals	annal	NOUN
ejpam-2674	316	18	of	of	ADP
ejpam-2674	316	19	fuzzy	fuzzy	ADJ
ejpam-2674	316	20	mathematics	mathematic	NOUN
ejpam-2674	316	21	and	and	CCONJ
ejpam-2674	316	22	informatics	informatic	NOUN
ejpam-2674	316	23	,	,	PUNCT
ejpam-2674	316	24	2	2	NUM
ejpam-2674	316	25	,	,	PUNCT
ejpam-2674	316	26	279–281	279–281	NUM
ejpam-2674	316	27	,	,	PUNCT
ejpam-2674	316	28	2014	2014	NUM
ejpam-2674	316	29	.	.	PUNCT
ejpam-2674	317	1	[	[	X
ejpam-2674	317	2	11	11	NUM
ejpam-2674	317	3	]	]	X
ejpam-2674	317	4	n.	n.	NOUN
ejpam-2674	317	5	kuroki	kuroki	PROPN
ejpam-2674	317	6	and	and	CCONJ
ejpam-2674	317	7	p.	p.	PROPN
ejpam-2674	317	8	p.	p.	PROPN
ejpam-2674	317	9	wang	wang	PROPN
ejpam-2674	317	10	,	,	PUNCT
ejpam-2674	317	11	the	the	DET
ejpam-2674	317	12	lower	low	ADJ
ejpam-2674	317	13	and	and	CCONJ
ejpam-2674	317	14	upper	upper	ADJ
ejpam-2674	317	15	approximations	approximation	NOUN
ejpam-2674	317	16	in	in	ADP
ejpam-2674	317	17	a	a	DET
ejpam-2674	317	18	fuzzy	fuzzy	ADJ
ejpam-2674	317	19	group	group	NOUN
ejpam-2674	317	20	,	,	PUNCT
ejpam-2674	317	21	information	information	NOUN
ejpam-2674	317	22	sciences	science	NOUN
ejpam-2674	317	23	,	,	PUNCT
ejpam-2674	317	24	90	90	NUM
ejpam-2674	317	25	,	,	PUNCT
ejpam-2674	317	26	203–220	203–220	NUM
ejpam-2674	317	27	,	,	PUNCT
ejpam-2674	317	28	1996	1996	NUM
ejpam-2674	317	29	.	.	PUNCT
ejpam-2674	318	1	[	[	X
ejpam-2674	318	2	12	12	NUM
ejpam-2674	318	3	]	]	X
ejpam-2674	318	4	n.	n.	PROPN
ejpam-2674	318	5	kuroki	kuroki	PROPN
ejpam-2674	318	6	,	,	PUNCT
ejpam-2674	318	7	rough	rough	ADJ
ejpam-2674	318	8	ideals	ideal	NOUN
ejpam-2674	318	9	in	in	ADP
ejpam-2674	318	10	semigroups	semigroup	NOUN
ejpam-2674	318	11	,	,	PUNCT
ejpam-2674	318	12	information	information	NOUN
ejpam-2674	318	13	sciences	science	NOUN
ejpam-2674	318	14	,	,	PUNCT
ejpam-2674	318	15	100	100	NUM
ejpam-2674	318	16	,	,	PUNCT
ejpam-2674	318	17	139–163	139–163	NUM
ejpam-2674	318	18	,	,	PUNCT
ejpam-2674	318	19	1997	1997	NUM
ejpam-2674	318	20	.	.	PUNCT
ejpam-2674	319	1	[	[	X
ejpam-2674	319	2	13	13	NUM
ejpam-2674	319	3	]	]	X
ejpam-2674	319	4	f.	f.	PROPN
ejpam-2674	319	5	li	li	PROPN
ejpam-2674	319	6	and	and	CCONJ
ejpam-2674	319	7	z.	z.	PROPN
ejpam-2674	319	8	zang	zang	PROPN
ejpam-2674	319	9	,	,	PUNCT
ejpam-2674	319	10	the	the	DET
ejpam-2674	319	11	homomorphisms	homomorphism	NOUN
ejpam-2674	319	12	and	and	CCONJ
ejpam-2674	319	13	operations	operation	NOUN
ejpam-2674	319	14	of	of	ADP
ejpam-2674	319	15	rough	rough	ADJ
ejpam-2674	319	16	groups	group	NOUN
ejpam-2674	319	17	,	,	PUNCT
ejpam-2674	319	18	the	the	DET
ejpam-2674	319	19	scientific	scientific	ADJ
ejpam-2674	319	20	world	world	NOUN
ejpam-2674	319	21	journal	journal	NOUN
ejpam-2674	319	22	,	,	PUNCT
ejpam-2674	319	23	volume	volume	NOUN
ejpam-2674	319	24	2014	2014	NUM
ejpam-2674	319	25	,	,	PUNCT
ejpam-2674	319	26	article	article	NOUN
ejpam-2674	319	27	i	i	PROPN
ejpam-2674	319	28	d	d	PROPN
ejpam-2674	319	29	507972	507972	NUM
ejpam-2674	319	30	,	,	PUNCT
ejpam-2674	319	31	6	6	NUM
ejpam-2674	319	32	pages	page	NOUN
ejpam-2674	319	33	.	.	PUNCT
ejpam-2674	320	1	[	[	X
ejpam-2674	320	2	14	14	NUM
ejpam-2674	320	3	]	]	X
ejpam-2674	320	4	d.	d.	PROPN
ejpam-2674	320	5	miao	miao	PROPN
ejpam-2674	320	6	,	,	PUNCT
ejpam-2674	320	7	s.	s.	PROPN
ejpam-2674	320	8	han	han	PROPN
ejpam-2674	320	9	,	,	PUNCT
ejpam-2674	320	10	d.	d.	PROPN
ejpam-2674	320	11	li	li	PROPN
ejpam-2674	320	12	and	and	CCONJ
ejpam-2674	320	13	l.	l.	PROPN
ejpam-2674	320	14	sun	sun	PROPN
ejpam-2674	320	15	,	,	PUNCT
ejpam-2674	320	16	rough	rough	ADJ
ejpam-2674	320	17	group	group	NOUN
ejpam-2674	320	18	,	,	PUNCT
ejpam-2674	320	19	rough	rough	ADJ
ejpam-2674	320	20	subgroup	subgroup	NOUN
ejpam-2674	320	21	and	and	CCONJ
ejpam-2674	320	22	their	their	PRON
ejpam-2674	320	23	properties	property	NOUN
ejpam-2674	320	24	,	,	PUNCT
ejpam-2674	320	25	d.	d.	PROPN
ejpam-2674	320	26	ślkezak	ślkezak	PROPN
ejpam-2674	320	27	et	et	PROPN
ejpam-2674	320	28	al	al	PROPN
ejpam-2674	320	29	.	.	PROPN
ejpam-2674	320	30	(	(	PUNCT
ejpam-2674	320	31	eds	ed	NOUN
ejpam-2674	320	32	.	.	PUNCT
ejpam-2674	320	33	):	):	PUNCT
ejpam-2674	320	34	rsfdgrc	rsfdgrc	NOUN
ejpam-2674	320	35	2005	2005	NUM
ejpam-2674	320	36	,	,	PUNCT
ejpam-2674	320	37	lnai	lnai	ADJ
ejpam-2674	320	38	3641	3641	NUM
ejpam-2674	320	39	,	,	PUNCT
ejpam-2674	320	40	pp	pp	ADP
ejpam-2674	320	41	.	.	PUNCT
ejpam-2674	321	1	104–113	104–113	NUM
ejpam-2674	321	2	,	,	PUNCT
ejpam-2674	321	3	2005	2005	NUM
ejpam-2674	321	4	.	.	PUNCT
ejpam-2674	322	1	c	c	X
ejpam-2674	322	2	©	©	PROPN
ejpam-2674	322	3	springer	springer	NOUN
ejpam-2674	322	4	-	-	PUNCT
ejpam-2674	322	5	verlag	verlag	PROPN
ejpam-2674	322	6	berlin	berlin	PROPN
ejpam-2674	322	7	heidelberg	heidelberg	PROPN
ejpam-2674	322	8	,	,	PUNCT
ejpam-2674	322	9	2005	2005	NUM
ejpam-2674	322	10	.	.	PUNCT
ejpam-2674	323	1	[	[	X
ejpam-2674	323	2	15	15	NUM
ejpam-2674	323	3	]	]	X
ejpam-2674	323	4	a.	a.	NOUN
ejpam-2674	323	5	f.	f.	PROPN
ejpam-2674	323	6	özcan	özcan	PROPN
ejpam-2674	323	7	and	and	CCONJ
ejpam-2674	323	8	n.	n.	PROPN
ejpam-2674	323	9	bağırmaz	bağırmaz	PROPN
ejpam-2674	323	10	,	,	PUNCT
ejpam-2674	323	11	comparison	comparison	NOUN
ejpam-2674	323	12	of	of	ADP
ejpam-2674	323	13	near	near	ADJ
ejpam-2674	323	14	sets	set	NOUN
ejpam-2674	323	15	by	by	ADP
ejpam-2674	323	16	means	mean	NOUN
ejpam-2674	323	17	of	of	ADP
ejpam-2674	323	18	a	a	DET
ejpam-2674	323	19	chain	chain	NOUN
ejpam-2674	323	20	of	of	ADP
ejpam-2674	323	21	features	feature	NOUN
ejpam-2674	323	22	,	,	PUNCT
ejpam-2674	323	23	hacettepe	hacettepe	ADJ
ejpam-2674	323	24	journal	journal	NOUN
ejpam-2674	323	25	of	of	ADP
ejpam-2674	323	26	mathematics	mathematic	NOUN
ejpam-2674	323	27	and	and	CCONJ
ejpam-2674	323	28	statistics	statistic	NOUN
ejpam-2674	323	29	,	,	PUNCT
ejpam-2674	323	30	volume	volume	NOUN
ejpam-2674	323	31	45	45	NUM
ejpam-2674	323	32	(	(	PUNCT
ejpam-2674	323	33	1	1	NUM
ejpam-2674	323	34	)	)	PUNCT
ejpam-2674	323	35	,	,	PUNCT
ejpam-2674	323	36	69	69	NUM
ejpam-2674	323	37	–	–	SYM
ejpam-2674	323	38	76	76	NUM
ejpam-2674	323	39	,	,	PUNCT
ejpam-2674	323	40	2016	2016	NUM
ejpam-2674	323	41	.	.	PUNCT
ejpam-2674	324	1	[	[	X
ejpam-2674	324	2	16	16	NUM
ejpam-2674	324	3	]	]	PUNCT
ejpam-2674	324	4	z.	z.	PROPN
ejpam-2674	324	5	pawlak	pawlak	PROPN
ejpam-2674	324	6	,	,	PUNCT
ejpam-2674	324	7	rough	rough	ADJ
ejpam-2674	324	8	sets	set	NOUN
ejpam-2674	324	9	,	,	PUNCT
ejpam-2674	324	10	int	int	NOUN
ejpam-2674	324	11	.	.	PUNCT
ejpam-2674	325	1	j.	j.	PROPN
ejpam-2674	325	2	comput	comput	PROPN
ejpam-2674	325	3	.	.	PUNCT
ejpam-2674	326	1	inform	inform	NOUN
ejpam-2674	326	2	.	.	PUNCT
ejpam-2674	327	1	sci	sci	PROPN
ejpam-2674	327	2	.	.	PROPN
ejpam-2674	327	3	,	,	PUNCT
ejpam-2674	327	4	11	11	NUM
ejpam-2674	327	5	,	,	PUNCT
ejpam-2674	327	6	341–356	341–356	NUM
ejpam-2674	327	7	,	,	PUNCT
ejpam-2674	327	8	1982	1982	NUM
ejpam-2674	327	9	.	.	PUNCT
ejpam-2674	328	1	[	[	X
ejpam-2674	328	2	17	17	NUM
ejpam-2674	328	3	]	]	PUNCT
ejpam-2674	328	4	j.	j.	PROPN
ejpam-2674	328	5	f.	f.	PROPN
ejpam-2674	328	6	peters	peters	PROPN
ejpam-2674	328	7	,	,	PUNCT
ejpam-2674	328	8	near	near	ADP
ejpam-2674	328	9	sets	set	NOUN
ejpam-2674	328	10	,	,	PUNCT
ejpam-2674	328	11	general	general	ADJ
ejpam-2674	328	12	theory	theory	NOUN
ejpam-2674	328	13	about	about	ADP
ejpam-2674	328	14	nearness	nearness	NOUN
ejpam-2674	328	15	of	of	ADP
ejpam-2674	328	16	objects	object	NOUN
ejpam-2674	328	17	,	,	PUNCT
ejpam-2674	328	18	appl	appl	PROPN
ejpam-2674	328	19	.	.	PROPN
ejpam-2674	328	20	math	math	PROPN
ejpam-2674	328	21	.	.	PUNCT
ejpam-2674	329	1	sci	sci	PROPN
ejpam-2674	329	2	.	.	PROPN
ejpam-2674	329	3	,	,	PUNCT
ejpam-2674	329	4	1	1	NUM
ejpam-2674	329	5	(	(	PUNCT
ejpam-2674	329	6	53	53	NUM
ejpam-2674	329	7	)	)	PUNCT
ejpam-2674	329	8	,	,	PUNCT
ejpam-2674	329	9	2029–2609	2029–2609	NUM
ejpam-2674	329	10	,	,	PUNCT
ejpam-2674	329	11	2007	2007	NUM
ejpam-2674	329	12	.	.	PUNCT
ejpam-2674	330	1	[	[	X
ejpam-2674	330	2	18	18	NUM
ejpam-2674	330	3	]	]	PUNCT
ejpam-2674	330	4	j.	j.	PROPN
ejpam-2674	330	5	f.	f.	PROPN
ejpam-2674	330	6	peters	peters	PROPN
ejpam-2674	330	7	,	,	PUNCT
ejpam-2674	330	8	near	near	ADP
ejpam-2674	330	9	sets	set	NOUN
ejpam-2674	330	10	,	,	PUNCT
ejpam-2674	330	11	special	special	ADJ
ejpam-2674	330	12	theory	theory	NOUN
ejpam-2674	330	13	about	about	ADP
ejpam-2674	330	14	nearness	nearness	NOUN
ejpam-2674	330	15	of	of	ADP
ejpam-2674	330	16	objects	object	NOUN
ejpam-2674	330	17	,	,	PUNCT
ejpam-2674	330	18	fundam	fundam	ADJ
ejpam-2674	330	19	.	.	PUNCT
ejpam-2674	331	1	inform	inform	NOUN
ejpam-2674	331	2	.	.	PUNCT
ejpam-2674	331	3	,	,	PUNCT
ejpam-2674	331	4	75	75	NUM
ejpam-2674	331	5	(	(	PUNCT
ejpam-2674	331	6	1–4	1–4	NUM
ejpam-2674	331	7	)	)	PUNCT
ejpam-2674	331	8	,	,	PUNCT
ejpam-2674	331	9	407–433	407–433	NUM
ejpam-2674	331	10	,	,	PUNCT
ejpam-2674	331	11	2007	2007	NUM
ejpam-2674	331	12	.	.	PUNCT
ejpam-2674	332	1	[	[	X
ejpam-2674	332	2	19	19	NUM
ejpam-2674	332	3	]	]	PUNCT
ejpam-2674	332	4	j.	j.	PROPN
ejpam-2674	332	5	f.	f.	PROPN
ejpam-2674	332	6	peters	peters	PROPN
ejpam-2674	332	7	and	and	CCONJ
ejpam-2674	332	8	p.	p.	PROPN
ejpam-2674	332	9	wasilewsk	wasilewsk	PROPN
ejpam-2674	332	10	,	,	PUNCT
ejpam-2674	332	11	foundations	foundation	NOUN
ejpam-2674	332	12	of	of	ADP
ejpam-2674	332	13	near	near	ADJ
ejpam-2674	332	14	sets	set	NOUN
ejpam-2674	332	15	,	,	PUNCT
ejpam-2674	332	16	information	information	NOUN
ejpam-2674	332	17	sciences	science	NOUN
ejpam-2674	332	18	,	,	PUNCT
ejpam-2674	332	19	179	179	NUM
ejpam-2674	332	20	,	,	PUNCT
ejpam-2674	332	21	3091–3109	3091–3109	NUM
ejpam-2674	332	22	,	,	PUNCT
ejpam-2674	332	23	2009	2009	NUM
ejpam-2674	332	24	.	.	PUNCT
ejpam-2674	333	1	[	[	X
ejpam-2674	333	2	20	20	NUM
ejpam-2674	333	3	]	]	PUNCT
ejpam-2674	333	4	j.	j.	PROPN
ejpam-2674	333	5	f.	f.	PROPN
ejpam-2674	333	6	peters	peters	PROPN
ejpam-2674	333	7	,	,	PUNCT
ejpam-2674	333	8	classification	classification	NOUN
ejpam-2674	333	9	of	of	ADP
ejpam-2674	333	10	perceptual	perceptual	ADJ
ejpam-2674	333	11	objects	object	NOUN
ejpam-2674	333	12	by	by	ADP
ejpam-2674	333	13	means	mean	NOUN
ejpam-2674	333	14	of	of	ADP
ejpam-2674	333	15	features	feature	NOUN
ejpam-2674	333	16	,	,	PUNCT
ejpam-2674	333	17	int	int	NOUN
ejpam-2674	333	18	.	.	PUNCT
ejpam-2674	334	1	j.	j.	PROPN
ejpam-2674	334	2	info	info	PROPN
ejpam-2674	334	3	.	.	PUNCT
ejpam-2674	335	1	technol	technol	PROPN
ejpam-2674	335	2	.	.	PUNCT
ejpam-2674	335	3	intell	intell	PROPN
ejpam-2674	335	4	.	.	PUNCT
ejpam-2674	336	1	comput	comput	NOUN
ejpam-2674	336	2	.	.	PUNCT
ejpam-2674	337	1	3	3	NUM
ejpam-2674	337	2	(	(	PUNCT
ejpam-2674	337	3	2	2	NUM
ejpam-2674	337	4	)	)	PUNCT
ejpam-2674	337	5	,	,	PUNCT
ejpam-2674	337	6	1–35	1–35	NUM
ejpam-2674	337	7	,	,	PUNCT
ejpam-2674	337	8	2008	2008	NUM
ejpam-2674	337	9	.	.	PUNCT
ejpam-2674	338	1	[	[	X
ejpam-2674	338	2	21	21	NUM
ejpam-2674	338	3	]	]	X
ejpam-2674	338	4	j.	j.	PROPN
ejpam-2674	338	5	f.	f.	PROPN
ejpam-2674	338	6	peters	peters	PROPN
ejpam-2674	338	7	,	,	PUNCT
ejpam-2674	338	8	fuzzy	fuzzy	ADJ
ejpam-2674	338	9	sets	set	NOUN
ejpam-2674	338	10	,	,	PUNCT
ejpam-2674	338	11	near	near	ADP
ejpam-2674	338	12	sets	set	NOUN
ejpam-2674	338	13	,	,	PUNCT
ejpam-2674	338	14	and	and	CCONJ
ejpam-2674	338	15	rough	rough	ADJ
ejpam-2674	338	16	sets	set	NOUN
ejpam-2674	338	17	for	for	ADP
ejpam-2674	338	18	your	your	PRON
ejpam-2674	338	19	computational	computational	ADJ
ejpam-2674	338	20	intelligence	intelligence	NOUN
ejpam-2674	338	21	toolbox	toolbox	NOUN
ejpam-2674	338	22	,	,	PUNCT
ejpam-2674	338	23	foundations	foundation	NOUN
ejpam-2674	338	24	of	of	ADP
ejpam-2674	338	25	comput	comput	NOUN
ejpam-2674	338	26	.	.	PUNCT
ejpam-2674	339	1	intel	intel	PROPN
ejpam-2674	339	2	.	.	PUNCT
ejpam-2674	340	1	vol	vol	NOUN
ejpam-2674	340	2	.	.	PROPN
ejpam-2674	341	1	2	2	NUM
ejpam-2674	341	2	,	,	PUNCT
ejpam-2674	341	3	sci	sci	PROPN
ejpam-2674	341	4	202	202	NUM
ejpam-2674	341	5	,	,	PUNCT
ejpam-2674	341	6	pp	pp	ADJ
ejpam-2674	341	7	.	.	PUNCT
ejpam-2674	342	1	3	3	NUM
ejpam-2674	342	2	-	-	SYM
ejpam-2674	342	3	25	25	NUM
ejpam-2674	342	4	,	,	PUNCT
ejpam-2674	342	5	2009	2009	NUM
ejpam-2674	342	6	.	.	PUNCT
ejpam-2674	343	1	[	[	X
ejpam-2674	343	2	22	22	NUM
ejpam-2674	343	3	]	]	PUNCT
ejpam-2674	343	4	j.	j.	PROPN
ejpam-2674	343	5	f.	f.	PROPN
ejpam-2674	343	6	peters	peters	PROPN
ejpam-2674	343	7	and	and	CCONJ
ejpam-2674	343	8	r.	r.	PROPN
ejpam-2674	343	9	ramanna	ramanna	PROPN
ejpam-2674	343	10	,	,	PUNCT
ejpam-2674	343	11	feature	feature	NOUN
ejpam-2674	343	12	selection	selection	NOUN
ejpam-2674	343	13	:	:	PUNCT
ejpam-2674	343	14	a	a	DET
ejpam-2674	343	15	near	near	ADV
ejpam-2674	343	16	set	set	ADJ
ejpam-2674	343	17	approach	approach	NOUN
ejpam-2674	343	18	,	,	PUNCT
ejpam-2674	343	19	(	(	PUNCT
ejpam-2674	343	20	in	in	ADP
ejpam-2674	343	21	:	:	PUNCT
ejpam-2674	343	22	ecml	ecml	PROPN
ejpam-2674	343	23	&	&	CCONJ
ejpam-2674	343	24	pkdd	pkdd	PROPN
ejpam-2674	343	25	workshop	workshop	NOUN
ejpam-2674	343	26	on	on	ADP
ejpam-2674	343	27	mining	mining	NOUN
ejpam-2674	343	28	complex	complex	ADJ
ejpam-2674	343	29	data	datum	NOUN
ejpam-2674	343	30	,	,	PUNCT
ejpam-2674	343	31	warsaw	warsaw	PROPN
ejpam-2674	343	32	,	,	PUNCT
ejpam-2674	343	33	2007	2007	NUM
ejpam-2674	343	34	)	)	PUNCT
ejpam-2674	343	35	,	,	PUNCT
ejpam-2674	343	36	pp	pp	PROPN
ejpam-2674	343	37	.	.	PUNCT
ejpam-2674	343	38	1–12	1–12	NOUN
ejpam-2674	343	39	.	.	PUNCT
ejpam-2674	344	1	[	[	X
ejpam-2674	344	2	23	23	NUM
ejpam-2674	344	3	]	]	PUNCT
ejpam-2674	344	4	j.	j.	PROPN
ejpam-2674	344	5	f.	f.	PROPN
ejpam-2674	344	6	peters	peters	PROPN
ejpam-2674	344	7	and	and	CCONJ
ejpam-2674	344	8	s.	s.	PROPN
ejpam-2674	344	9	k.	k.	PROPN
ejpam-2674	344	10	pal	pal	PROPN
ejpam-2674	344	11	,	,	PUNCT
ejpam-2674	344	12	cantor	cantor	PROPN
ejpam-2674	344	13	,	,	PUNCT
ejpam-2674	344	14	fuzzy	fuzzy	ADJ
ejpam-2674	344	15	,	,	PUNCT
ejpam-2674	344	16	near	near	ADV
ejpam-2674	344	17	,	,	PUNCT
ejpam-2674	344	18	and	and	CCONJ
ejpam-2674	344	19	rough	rough	ADJ
ejpam-2674	344	20	sets	set	NOUN
ejpam-2674	344	21	in	in	ADP
ejpam-2674	344	22	image	image	NOUN
ejpam-2674	344	23	analysis	analysis	NOUN
ejpam-2674	344	24	,	,	PUNCT
ejpam-2674	344	25	(	(	PUNCT
ejpam-2674	344	26	in	in	ADP
ejpam-2674	344	27	:	:	PUNCT
ejpam-2674	344	28	pal	pal	NOUN
ejpam-2674	344	29	,	,	PUNCT
ejpam-2674	344	30	s.k	s.k	PROPN
ejpam-2674	344	31	.	.	PROPN
ejpam-2674	344	32	and	and	CCONJ
ejpam-2674	344	33	peters	peters	PROPN
ejpam-2674	344	34	,	,	PUNCT
ejpam-2674	344	35	j.	j.	PROPN
ejpam-2674	344	36	f.(eds	f.(eds	PROPN
ejpam-2674	344	37	.	.	PUNCT
ejpam-2674	344	38	)	)	PUNCT
ejpam-2674	345	1	rough	rough	ADJ
ejpam-2674	345	2	fuzzy	fuzzy	ADJ
ejpam-2674	345	3	image	image	NOUN
ejpam-2674	345	4	analysis	analysis	NOUN
ejpam-2674	345	5	:	:	PUNCT
ejpam-2674	345	6	foundations	foundation	NOUN
ejpam-2674	345	7	and	and	CCONJ
ejpam-2674	345	8	methodologies	methodology	NOUN
ejpam-2674	345	9	,	,	PUNCT
ejpam-2674	345	10	crc	crc	NOUN
ejpam-2674	345	11	pres	pres	PROPN
ejpam-2674	345	12	,	,	PUNCT
ejpam-2674	345	13	taylor	taylor	PROPN
ejpam-2674	345	14	and	and	CCONJ
ejpam-2674	345	15	francis	francis	PROPN
ejpam-2674	345	16	group	group	PROPN
ejpam-2674	345	17	,	,	PUNCT
ejpam-2674	345	18	boca	boca	PROPN
ejpam-2674	345	19	raton	raton	PROPN
ejpam-2674	345	20	,	,	PUNCT
ejpam-2674	345	21	u.s.a	u.s.a	PROPN
ejpam-2674	345	22	,	,	PUNCT
ejpam-2674	345	23	2010	2010	NUM
ejpam-2674	345	24	)	)	PUNCT
ejpam-2674	345	25	,	,	PUNCT
ejpam-2674	345	26	1.1	1.1	NUM
ejpam-2674	345	27	-	-	SYM
ejpam-2674	345	28	1.16	1.16	NUM
ejpam-2674	345	29	.	.	PUNCT
ejpam-2674	346	1	[	[	X
ejpam-2674	346	2	24	24	NUM
ejpam-2674	346	3	]	]	X
ejpam-2674	346	4	j.	j.	PROPN
ejpam-2674	346	5	pomykala	pomykala	PROPN
ejpam-2674	346	6	and	and	CCONJ
ejpam-2674	346	7	j.	j.	PROPN
ejpam-2674	346	8	a.	a.	NOUN
ejpam-2674	346	9	pomykala	pomykala	NOUN
ejpam-2674	346	10	,	,	PUNCT
ejpam-2674	346	11	the	the	DET
ejpam-2674	346	12	stone	stone	NOUN
ejpam-2674	346	13	algebra	algebra	NOUN
ejpam-2674	346	14	of	of	ADP
ejpam-2674	346	15	rough	rough	ADJ
ejpam-2674	346	16	sets	set	NOUN
ejpam-2674	346	17	,	,	PUNCT
ejpam-2674	346	18	bull	bull	NOUN
ejpam-2674	346	19	.	.	PUNCT
ejpam-2674	347	1	polish	polish	PROPN
ejpam-2674	347	2	acad	acad	PROPN
ejpam-2674	347	3	.	.	PUNCT
ejpam-2674	348	1	sci	sci	PROPN
ejpam-2674	348	2	.	.	PROPN
ejpam-2674	348	3	math	math	PROPN
ejpam-2674	348	4	.	.	PUNCT
ejpam-2674	348	5	,	,	PUNCT
ejpam-2674	348	6	36	36	NUM
ejpam-2674	348	7	,	,	PUNCT
ejpam-2674	348	8	495–508	495–508	NUM
ejpam-2674	348	9	,	,	PUNCT
ejpam-2674	348	10	1998	1998	NUM
ejpam-2674	348	11	.	.	PUNCT
ejpam-2674	349	1	references	reference	NOUN
ejpam-2674	349	2	516	516	NUM
ejpam-2674	349	3	[	[	X
ejpam-2674	349	4	25	25	NUM
ejpam-2674	349	5	]	]	PUNCT
ejpam-2674	349	6	h.	h.	PROPN
ejpam-2674	349	7	taşbozan	taşbozan	PROPN
ejpam-2674	349	8	,	,	PUNCT
ejpam-2674	349	9	i.	i.	PROPN
ejpam-2674	349	10	içen	içen	PROPN
ejpam-2674	349	11	,	,	PUNCT
ejpam-2674	349	12	n.	n.	PROPN
ejpam-2674	349	13	bağırmaz	bağırmaz	PROPN
ejpam-2674	349	14	and	and	CCONJ
ejpam-2674	349	15	a.	a.	PROPN
ejpam-2674	349	16	f.	f.	PROPN
ejpam-2674	349	17	özcan	özcan	PROPN
ejpam-2674	349	18	,	,	PUNCT
ejpam-2674	349	19	soft	soft	ADJ
ejpam-2674	349	20	sets	set	NOUN
ejpam-2674	349	21	and	and	CCONJ
ejpam-2674	349	22	soft	soft	ADJ
ejpam-2674	349	23	topology	topology	NOUN
ejpam-2674	349	24	on	on	ADP
ejpam-2674	349	25	nearness	nearness	NOUN
ejpam-2674	349	26	approximation	approximation	NOUN
ejpam-2674	349	27	spaces	space	NOUN
ejpam-2674	349	28	,	,	PUNCT
ejpam-2674	349	29	filomat	filomat	NOUN
ejpam-2674	349	30	,	,	PUNCT
ejpam-2674	349	31	31:13	31:13	NUM
ejpam-2674	349	32	,	,	PUNCT
ejpam-2674	349	33	4117–4125	4117–4125	NUM
ejpam-2674	349	34	,	,	PUNCT
ejpam-2674	349	35	2017	2017	NUM
ejpam-2674	349	36	.	.	PUNCT
ejpam-2674	350	1	[	[	X
ejpam-2674	350	2	26	26	NUM
ejpam-2674	350	3	]	]	X
ejpam-2674	350	4	c.	c.	PROPN
ejpam-2674	350	5	wang	wang	PROPN
ejpam-2674	350	6	,	,	PUNCT
ejpam-2674	350	7	d.	d.	PROPN
ejpam-2674	350	8	chen	chen	PROPN
ejpam-2674	350	9	and	and	CCONJ
ejpam-2674	350	10	q.	q.	PROPN
ejpam-2674	350	11	hu	hu	PROPN
ejpam-2674	350	12	,	,	PUNCT
ejpam-2674	350	13	on	on	ADP
ejpam-2674	350	14	rough	rough	ADJ
ejpam-2674	350	15	approximations	approximation	NOUN
ejpam-2674	350	16	of	of	ADP
ejpam-2674	350	17	groups	group	NOUN
ejpam-2674	350	18	,	,	PUNCT
ejpam-2674	350	19	int	int	NOUN
ejpam-2674	350	20	.	.	PUNCT
ejpam-2674	351	1	j.	j.	PROPN
ejpam-2674	351	2	mach	mach	PROPN
ejpam-2674	351	3	.	.	PUNCT
ejpam-2674	352	1	learn	learn	PROPN
ejpam-2674	352	2	.	.	PUNCT
ejpam-2674	352	3	&	&	CCONJ
ejpam-2674	352	4	cyber	cyber	PROPN
ejpam-2674	352	5	.	.	PUNCT
ejpam-2674	353	1	doi	doi	PROPN
ejpam-2674	353	2	10.1007	10.1007	NUM
ejpam-2674	353	3	/	/	SYM
ejpam-2674	353	4	s13042	s13042	PROPN
ejpam-2674	353	5	-	-	PUNCT
ejpam-2674	353	6	012	012	NUM
ejpam-2674	353	7	-	-	PUNCT
ejpam-2674	353	8	0108	0108	NUM
ejpam-2674	353	9	-	-	PUNCT
ejpam-2674	353	10	6	6	NUM
ejpam-2674	353	11	,	,	PUNCT
ejpam-2674	353	12	springer	springer	NOUN
ejpam-2674	353	13	-	-	PUNCT
ejpam-2674	353	14	verlag	verlag	PROPN
ejpam-2674	353	15	,	,	PUNCT
ejpam-2674	353	16	2012	2012	NUM
ejpam-2674	353	17	.	.	PUNCT
ejpam-2674	354	1	[	[	X
ejpam-2674	354	2	27	27	NUM
ejpam-2674	354	3	]	]	X
ejpam-2674	354	4	c.	c.	PROPN
ejpam-2674	354	5	z.	z.	PROPN
ejpam-2674	354	6	wang	wang	PROPN
ejpam-2674	354	7	and	and	CCONJ
ejpam-2674	354	8	d.g	d.g	PROPN
ejpam-2674	354	9	.	.	PROPN
ejpam-2674	354	10	chen	chen	PROPN
ejpam-2674	354	11	,	,	PUNCT
ejpam-2674	354	12	a	a	DET
ejpam-2674	354	13	short	short	ADJ
ejpam-2674	354	14	note	note	NOUN
ejpam-2674	354	15	on	on	ADP
ejpam-2674	354	16	some	some	DET
ejpam-2674	354	17	properties	property	NOUN
ejpam-2674	354	18	of	of	ADP
ejpam-2674	354	19	rough	rough	ADJ
ejpam-2674	354	20	groups	group	NOUN
ejpam-2674	354	21	,	,	PUNCT
ejpam-2674	354	22	comput	comput	NOUN
ejpam-2674	354	23	.	.	PUNCT
ejpam-2674	355	1	math	math	NOUN
ejpam-2674	355	2	.	.	PUNCT
ejpam-2674	356	1	appl	appl	PROPN
ejpam-2674	356	2	.	.	PROPN
ejpam-2674	356	3	,	,	PUNCT
ejpam-2674	356	4	59	59	NUM
ejpam-2674	356	5	,	,	PUNCT
ejpam-2674	356	6	431	431	NUM
ejpam-2674	356	7	-	-	SYM
ejpam-2674	356	8	436	436	NUM
ejpam-2674	356	9	,	,	PUNCT
ejpam-2674	356	10	2010	2010	NUM
ejpam-2674	356	11	.	.	PUNCT
ejpam-2674	357	1	[	[	X
ejpam-2674	357	2	28	28	NUM
ejpam-2674	357	3	]	]	PUNCT
ejpam-2674	357	4	z.	z.	PROPN
ejpam-2674	357	5	wang	wang	PROPN
ejpam-2674	357	6	and	and	CCONJ
ejpam-2674	357	7	l.	l.	PROPN
ejpam-2674	357	8	shu	shu	PROPN
ejpam-2674	357	9	,	,	PUNCT
ejpam-2674	357	10	the	the	DET
ejpam-2674	357	11	lower	low	ADJ
ejpam-2674	357	12	and	and	CCONJ
ejpam-2674	357	13	upper	upper	ADJ
ejpam-2674	357	14	approximations	approximation	NOUN
ejpam-2674	357	15	in	in	ADP
ejpam-2674	357	16	a	a	DET
ejpam-2674	357	17	group	group	NOUN
ejpam-2674	357	18	,	,	PUNCT
ejpam-2674	357	19	international	international	ADJ
ejpam-2674	357	20	journal	journal	NOUN
ejpam-2674	357	21	of	of	ADP
ejpam-2674	357	22	mathematical	mathematical	ADJ
ejpam-2674	357	23	and	and	CCONJ
ejpam-2674	357	24	computational	computational	ADJ
ejpam-2674	357	25	sciences	science	NOUN
ejpam-2674	357	26	,	,	PUNCT
ejpam-2674	357	27	6,158	6,158	NUM
ejpam-2674	357	28	-	-	SYM
ejpam-2674	357	29	162	162	NUM
ejpam-2674	357	30	,	,	PUNCT
ejpam-2674	357	31	2012	2012	NUM
ejpam-2674	357	32	.	.	PUNCT
ejpam-2674	358	1	[	[	X
ejpam-2674	358	2	29	29	NUM
ejpam-2674	358	3	]	]	X
ejpam-2674	358	4	w.	w.	PROPN
ejpam-2674	358	5	wolski	wolski	PROPN
ejpam-2674	358	6	,	,	PUNCT
ejpam-2674	358	7	perception	perception	NOUN
ejpam-2674	358	8	and	and	CCONJ
ejpam-2674	358	9	classification	classification	NOUN
ejpam-2674	358	10	.	.	PUNCT
ejpam-2674	359	1	a	a	DET
ejpam-2674	359	2	note	note	NOUN
ejpam-2674	359	3	on	on	ADP
ejpam-2674	359	4	near	near	ADJ
ejpam-2674	359	5	sets	set	NOUN
ejpam-2674	359	6	and	and	CCONJ
ejpam-2674	359	7	rough	rough	ADJ
ejpam-2674	359	8	sets	set	NOUN
ejpam-2674	359	9	,	,	PUNCT
ejpam-2674	359	10	foundamenta	foundamenta	ADJ
ejpam-2674	359	11	informaticae	informaticae	PROPN
ejpam-2674	359	12	,	,	PUNCT
ejpam-2674	359	13	101	101	NUM
ejpam-2674	359	14	,	,	PUNCT
ejpam-2674	359	15	143	143	NUM
ejpam-2674	359	16	-	-	SYM
ejpam-2674	359	17	155	155	NUM
ejpam-2674	359	18	,	,	PUNCT
ejpam-2674	359	19	2010	2010	NUM
ejpam-2674	359	20	.	.	PUNCT
ejpam-2674	360	1	[	[	X
ejpam-2674	360	2	30	30	NUM
ejpam-2674	360	3	]	]	X
ejpam-2674	360	4	q.	q.	PROPN
ejpam-2674	360	5	m.	m.	PROPN
ejpam-2674	360	6	xiao	xiao	PROPN
ejpam-2674	360	7	and	and	CCONJ
ejpam-2674	360	8	z.	z.	PROPN
ejpam-2674	360	9	l.	l.	PROPN
ejpam-2674	360	10	zhang	zhang	PROPN
ejpam-2674	360	11	,	,	PUNCT
ejpam-2674	360	12	rough	rough	ADJ
ejpam-2674	360	13	prime	prime	ADJ
ejpam-2674	360	14	ideals	ideal	NOUN
ejpam-2674	360	15	and	and	CCONJ
ejpam-2674	360	16	rough	rough	ADJ
ejpam-2674	360	17	fuzzy	fuzzy	ADJ
ejpam-2674	360	18	prime	prime	ADJ
ejpam-2674	360	19	ideals	ideal	NOUN
ejpam-2674	360	20	in	in	ADP
ejpam-2674	360	21	semigroups	semigroup	NOUN
ejpam-2674	360	22	,	,	PUNCT
ejpam-2674	360	23	information	information	NOUN
ejpam-2674	360	24	sciences	science	NOUN
ejpam-2674	360	25	,	,	PUNCT
ejpam-2674	360	26	176	176	NUM
ejpam-2674	360	27	,	,	PUNCT
ejpam-2674	360	28	725733	725733	NUM
ejpam-2674	360	29	,	,	PUNCT
ejpam-2674	360	30	2006	2006	NUM
ejpam-2674	360	31	.	.	PUNCT