id	sid	tid	token	lemma	pos
ejpam-4624	1	1	european	european	PROPN
ejpam-4624	1	2	journal	journal	PROPN
ejpam-4624	1	3	of	of	ADP
ejpam-4624	1	4	pure	pure	ADJ
ejpam-4624	1	5	and	and	CCONJ
ejpam-4624	1	6	applied	applied	ADJ
ejpam-4624	1	7	mathematics	mathematic	NOUN
ejpam-4624	1	8	2025	2025	NUM
ejpam-4624	1	9	,	,	PUNCT
ejpam-4624	1	10	vol	vol	NOUN
ejpam-4624	1	11	.	.	PROPN
ejpam-4624	1	12	18	18	NUM
ejpam-4624	1	13	,	,	PUNCT
ejpam-4624	1	14	issue	issue	NOUN
ejpam-4624	1	15	2	2	NUM
ejpam-4624	1	16	,	,	PUNCT
ejpam-4624	1	17	article	article	NOUN
ejpam-4624	1	18	number	number	NOUN
ejpam-4624	1	19	4624	4624	NUM
ejpam-4624	1	20	issn	issn	VERB
ejpam-4624	1	21	1307	1307	NUM
ejpam-4624	1	22	-	-	SYM
ejpam-4624	1	23	5543	5543	NUM
ejpam-4624	1	24	–	–	PUNCT
ejpam-4624	1	25	ejpam.com	ejpam.com	X
ejpam-4624	1	26	published	publish	VERB
ejpam-4624	1	27	by	by	ADP
ejpam-4624	1	28	new	new	PROPN
ejpam-4624	1	29	york	york	PROPN
ejpam-4624	1	30	business	business	PROPN
ejpam-4624	1	31	global	global	PROPN
ejpam-4624	1	32	double	double	ADJ
ejpam-4624	1	33	fuzzy	fuzzy	ADJ
ejpam-4624	1	34	δ	δ	NOUN
ejpam-4624	1	35	-	-	ADJ
ejpam-4624	1	36	continuous	continuous	ADJ
ejpam-4624	1	37	functions	function	NOUN
ejpam-4624	1	38	in	in	ADP
ejpam-4624	1	39	double	double	ADJ
ejpam-4624	1	40	fuzzy	fuzzy	ADJ
ejpam-4624	1	41	topological	topological	ADJ
ejpam-4624	1	42	spaces	space	NOUN
ejpam-4624	1	43	wadei	wadei	VERB
ejpam-4624	1	44	al	al	PROPN
ejpam-4624	1	45	-	-	PUNCT
ejpam-4624	1	46	omeri	omeri	PROPN
ejpam-4624	1	47	department	department	NOUN
ejpam-4624	1	48	of	of	ADP
ejpam-4624	1	49	mathematics	mathematic	NOUN
ejpam-4624	1	50	,	,	PUNCT
ejpam-4624	1	51	faculty	faculty	NOUN
ejpam-4624	1	52	of	of	ADP
ejpam-4624	1	53	science	science	NOUN
ejpam-4624	1	54	,	,	PUNCT
ejpam-4624	1	55	jadara	jadara	PROPN
ejpam-4624	1	56	university	university	PROPN
ejpam-4624	1	57	,	,	PUNCT
ejpam-4624	1	58	irbid	irbid	PROPN
ejpam-4624	1	59	,	,	PUNCT
ejpam-4624	1	60	jordan	jordan	PROPN
ejpam-4624	1	61	abstract	abstract	PROPN
ejpam-4624	1	62	.	.	PUNCT
ejpam-4624	2	1	in	in	ADP
ejpam-4624	2	2	this	this	DET
ejpam-4624	2	3	paper	paper	NOUN
ejpam-4624	2	4	,	,	PUNCT
ejpam-4624	2	5	we	we	PRON
ejpam-4624	2	6	introduce	introduce	VERB
ejpam-4624	2	7	(	(	PUNCT
ejpam-4624	2	8	r	r	NOUN
ejpam-4624	2	9	,	,	PUNCT
ejpam-4624	2	10	s)-δ	s)-δ	NOUN
ejpam-4624	2	11	-	-	PUNCT
ejpam-4624	2	12	fuzzy	fuzzy	ADJ
ejpam-4624	2	13	closed	close	VERB
ejpam-4624	2	14	sets	set	NOUN
ejpam-4624	2	15	in	in	ADP
ejpam-4624	2	16	double	double	ADJ
ejpam-4624	2	17	fuzzy	fuzzy	ADJ
ejpam-4624	2	18	topological	topological	ADJ
ejpam-4624	2	19	spaces	space	NOUN
ejpam-4624	2	20	and	and	CCONJ
ejpam-4624	2	21	investigate	investigate	VERB
ejpam-4624	2	22	some	some	PRON
ejpam-4624	2	23	of	of	ADP
ejpam-4624	2	24	their	their	PRON
ejpam-4624	2	25	properties	property	NOUN
ejpam-4624	2	26	.	.	PUNCT
ejpam-4624	3	1	moreover	moreover	ADV
ejpam-4624	3	2	,	,	PUNCT
ejpam-4624	3	3	we	we	PRON
ejpam-4624	3	4	introduce	introduce	VERB
ejpam-4624	3	5	the	the	DET
ejpam-4624	3	6	concept	concept	NOUN
ejpam-4624	3	7	of	of	ADP
ejpam-4624	3	8	double	double	ADJ
ejpam-4624	3	9	fuzzy	fuzzy	ADJ
ejpam-4624	3	10	δ	δ	NOUN
ejpam-4624	3	11	-	-	ADJ
ejpam-4624	3	12	continuous	continuous	ADJ
ejpam-4624	3	13	functions	function	NOUN
ejpam-4624	3	14	.	.	PUNCT
ejpam-4624	4	1	several	several	ADJ
ejpam-4624	4	2	interesting	interesting	ADJ
ejpam-4624	4	3	properties	property	NOUN
ejpam-4624	4	4	and	and	CCONJ
ejpam-4624	4	5	characterizations	characterization	NOUN
ejpam-4624	4	6	are	be	AUX
ejpam-4624	4	7	introduced	introduce	VERB
ejpam-4624	4	8	and	and	CCONJ
ejpam-4624	4	9	discussed	discuss	VERB
ejpam-4624	4	10	.	.	PUNCT
ejpam-4624	5	1	furthermore	furthermore	ADV
ejpam-4624	5	2	,	,	PUNCT
ejpam-4624	5	3	the	the	DET
ejpam-4624	5	4	relationships	relationship	NOUN
ejpam-4624	5	5	among	among	ADP
ejpam-4624	5	6	the	the	DET
ejpam-4624	5	7	new	new	ADJ
ejpam-4624	5	8	concepts	concept	NOUN
ejpam-4624	5	9	are	be	AUX
ejpam-4624	5	10	introduced	introduce	VERB
ejpam-4624	5	11	and	and	CCONJ
ejpam-4624	5	12	established	establish	VERB
ejpam-4624	5	13	with	with	ADP
ejpam-4624	5	14	some	some	DET
ejpam-4624	5	15	interesting	interesting	ADJ
ejpam-4624	5	16	counterexamples	counterexample	NOUN
ejpam-4624	5	17	.	.	PUNCT
ejpam-4624	6	1	2020	2020	NUM
ejpam-4624	6	2	mathematics	mathematic	NOUN
ejpam-4624	6	3	subject	subject	NOUN
ejpam-4624	6	4	classifications	classification	NOUN
ejpam-4624	6	5	:	:	PUNCT
ejpam-4624	6	6	54a40	54a40	NUM
ejpam-4624	6	7	,	,	PUNCT
ejpam-4624	6	8	45d05	45d05	NUM
ejpam-4624	6	9	,	,	PUNCT
ejpam-4624	6	10	03e72	03e72	X
ejpam-4624	6	11	key	key	ADJ
ejpam-4624	6	12	words	word	NOUN
ejpam-4624	6	13	and	and	CCONJ
ejpam-4624	6	14	phrases	phrase	NOUN
ejpam-4624	6	15	:	:	PUNCT
ejpam-4624	6	16	fuzzy	fuzzy	ADJ
ejpam-4624	6	17	sets	set	NOUN
ejpam-4624	6	18	,	,	PUNCT
ejpam-4624	6	19	double	double	ADJ
ejpam-4624	6	20	fuzzy	fuzzy	ADJ
ejpam-4624	6	21	topological	topological	ADJ
ejpam-4624	6	22	spaces	space	NOUN
ejpam-4624	6	23	,	,	PUNCT
ejpam-4624	6	24	(	(	PUNCT
ejpam-4624	6	25	r	r	NOUN
ejpam-4624	6	26	,	,	PUNCT
ejpam-4624	6	27	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	6	28	δ	δ	PROPN
ejpam-4624	6	29	-	-	PUNCT
ejpam-4624	6	30	closed	close	VERB
ejpam-4624	6	31	sets	set	NOUN
ejpam-4624	6	32	,	,	PUNCT
ejpam-4624	6	33	(	(	PUNCT
ejpam-4624	6	34	r	r	NOUN
ejpam-4624	6	35	,	,	PUNCT
ejpam-4624	6	36	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	6	37	δ	δ	ADJ
ejpam-4624	6	38	-	-	PUNCT
ejpam-4624	6	39	continuous	continuous	ADJ
ejpam-4624	6	40	functions	function	NOUN
ejpam-4624	6	41	1	1	NUM
ejpam-4624	6	42	.	.	PUNCT
ejpam-4624	6	43	preliminaries	preliminary	NOUN
ejpam-4624	6	44	the	the	DET
ejpam-4624	6	45	concept	concept	NOUN
ejpam-4624	6	46	of	of	ADP
ejpam-4624	6	47	fuzzy	fuzzy	ADJ
ejpam-4624	6	48	sets	set	NOUN
ejpam-4624	6	49	was	be	AUX
ejpam-4624	6	50	introduced	introduce	VERB
ejpam-4624	6	51	by	by	ADP
ejpam-4624	6	52	zadeh	zadeh	PROPN
ejpam-4624	6	53	in	in	ADP
ejpam-4624	6	54	his	his	PRON
ejpam-4624	6	55	classical	classical	ADJ
ejpam-4624	6	56	paper	paper	NOUN
ejpam-4624	7	1	[	[	X
ejpam-4624	7	2	1	1	NUM
ejpam-4624	7	3	]	]	PUNCT
ejpam-4624	7	4	.	.	PUNCT
ejpam-4624	8	1	in	in	ADP
ejpam-4624	8	2	1968	1968	NUM
ejpam-4624	8	3	,	,	PUNCT
ejpam-4624	8	4	chang	chang	PROPN
ejpam-4624	8	5	[	[	X
ejpam-4624	8	6	2	2	NUM
ejpam-4624	8	7	]	]	PUNCT
ejpam-4624	8	8	used	use	VERB
ejpam-4624	8	9	fuzzy	fuzzy	ADJ
ejpam-4624	8	10	sets	set	NOUN
ejpam-4624	8	11	to	to	PART
ejpam-4624	8	12	introduce	introduce	VERB
ejpam-4624	8	13	the	the	DET
ejpam-4624	8	14	notion	notion	NOUN
ejpam-4624	8	15	of	of	ADP
ejpam-4624	8	16	fuzzy	fuzzy	ADJ
ejpam-4624	8	17	topological	topological	ADJ
ejpam-4624	8	18	spaces	space	NOUN
ejpam-4624	8	19	.	.	PUNCT
ejpam-4624	9	1	çoker	çoker	NOUN
ejpam-4624	10	1	[	[	X
ejpam-4624	10	2	3	3	NUM
ejpam-4624	10	3	,	,	PUNCT
ejpam-4624	10	4	4	4	NUM
ejpam-4624	10	5	]	]	PUNCT
ejpam-4624	10	6	defined	define	VERB
ejpam-4624	10	7	the	the	DET
ejpam-4624	10	8	intuitionistic	intuitionistic	ADJ
ejpam-4624	10	9	fuzzy	fuzzy	ADJ
ejpam-4624	10	10	topological	topological	ADJ
ejpam-4624	10	11	spaces	space	NOUN
ejpam-4624	10	12	using	use	VERB
ejpam-4624	10	13	intuitionistic	intuitionistic	ADJ
ejpam-4624	10	14	fuzzy	fuzzy	ADJ
ejpam-4624	10	15	sets	set	NOUN
ejpam-4624	10	16	.	.	PUNCT
ejpam-4624	11	1	later	later	ADV
ejpam-4624	11	2	on	on	ADV
ejpam-4624	11	3	,	,	PUNCT
ejpam-4624	11	4	demirci	demirci	NOUN
ejpam-4624	11	5	and	and	CCONJ
ejpam-4624	11	6	çoker	çoker	NOUN
ejpam-4624	12	1	[	[	X
ejpam-4624	12	2	5	5	NUM
ejpam-4624	12	3	]	]	PUNCT
ejpam-4624	12	4	defined	define	VERB
ejpam-4624	12	5	intuitionistic	intuitionistic	ADJ
ejpam-4624	12	6	fuzzy	fuzzy	ADJ
ejpam-4624	12	7	topological	topological	ADJ
ejpam-4624	12	8	spaces	space	NOUN
ejpam-4624	12	9	which	which	PRON
ejpam-4624	12	10	is	be	AUX
ejpam-4624	12	11	a	a	DET
ejpam-4624	12	12	generalization	generalization	NOUN
ejpam-4624	12	13	of	of	ADP
ejpam-4624	12	14	fuzzy	fuzzy	ADJ
ejpam-4624	12	15	topological	topological	ADJ
ejpam-4624	12	16	spaces	space	NOUN
ejpam-4624	12	17	and	and	CCONJ
ejpam-4624	12	18	intuitionistic	intuitionistic	ADJ
ejpam-4624	12	19	fuzzy	fuzzy	ADJ
ejpam-4624	12	20	topological	topological	ADJ
ejpam-4624	12	21	spaces	space	NOUN
ejpam-4624	12	22	.	.	PUNCT
ejpam-4624	13	1	mondal	mondal	PROPN
ejpam-4624	13	2	and	and	CCONJ
ejpam-4624	13	3	samanta	samanta	PROPN
ejpam-4624	13	4	[	[	X
ejpam-4624	13	5	6	6	NUM
ejpam-4624	13	6	]	]	PUNCT
ejpam-4624	13	7	succeeded	succeed	VERB
ejpam-4624	13	8	to	to	PART
ejpam-4624	13	9	make	make	VERB
ejpam-4624	13	10	the	the	DET
ejpam-4624	13	11	topology	topology	NOUN
ejpam-4624	13	12	itself	itself	PRON
ejpam-4624	13	13	intuitionistic	intuitionistic	ADJ
ejpam-4624	13	14	.	.	PUNCT
ejpam-4624	14	1	the	the	DET
ejpam-4624	14	2	resulting	result	VERB
ejpam-4624	14	3	structure	structure	NOUN
ejpam-4624	14	4	is	be	AUX
ejpam-4624	14	5	given	give	VERB
ejpam-4624	14	6	the	the	DET
ejpam-4624	14	7	new	new	ADJ
ejpam-4624	14	8	name	name	NOUN
ejpam-4624	14	9	”	"	PUNCT
ejpam-4624	14	10	intuitionistic	intuitionistic	ADJ
ejpam-4624	14	11	gradation	gradation	NOUN
ejpam-4624	14	12	of	of	ADP
ejpam-4624	14	13	openness	openness	NOUN
ejpam-4624	14	14	”	"	PUNCT
ejpam-4624	14	15	.	.	PUNCT
ejpam-4624	15	1	the	the	DET
ejpam-4624	15	2	name	name	NOUN
ejpam-4624	15	3	”	"	PUNCT
ejpam-4624	15	4	intuitionistic	intuitionistic	ADJ
ejpam-4624	15	5	”	"	PUNCT
ejpam-4624	15	6	did	do	AUX
ejpam-4624	15	7	not	not	PART
ejpam-4624	15	8	continue	continue	VERB
ejpam-4624	15	9	due	due	ADP
ejpam-4624	15	10	to	to	ADP
ejpam-4624	15	11	some	some	DET
ejpam-4624	15	12	doubts	doubt	NOUN
ejpam-4624	15	13	that	that	PRON
ejpam-4624	15	14	were	be	AUX
ejpam-4624	15	15	thrown	throw	VERB
ejpam-4624	15	16	about	about	ADP
ejpam-4624	15	17	the	the	DET
ejpam-4624	15	18	suitability	suitability	NOUN
ejpam-4624	15	19	of	of	ADP
ejpam-4624	15	20	this	this	DET
ejpam-4624	15	21	term	term	NOUN
ejpam-4624	15	22	.	.	PUNCT
ejpam-4624	16	1	these	these	DET
ejpam-4624	16	2	doubts	doubt	NOUN
ejpam-4624	16	3	were	be	AUX
ejpam-4624	16	4	quickly	quickly	ADV
ejpam-4624	16	5	ended	end	VERB
ejpam-4624	16	6	in	in	ADP
ejpam-4624	16	7	2005	2005	NUM
ejpam-4624	16	8	by	by	ADP
ejpam-4624	16	9	gutiérrez	gutiérrez	NOUN
ejpam-4624	16	10	garcía	garcía	ADJ
ejpam-4624	16	11	and	and	CCONJ
ejpam-4624	16	12	rodabaugh	rodabaugh	ADJ
ejpam-4624	16	13	[	[	X
ejpam-4624	16	14	7	7	NUM
ejpam-4624	16	15	]	]	PUNCT
ejpam-4624	16	16	.	.	PUNCT
ejpam-4624	17	1	they	they	PRON
ejpam-4624	17	2	proved	prove	VERB
ejpam-4624	17	3	that	that	SCONJ
ejpam-4624	17	4	this	this	DET
ejpam-4624	17	5	term	term	NOUN
ejpam-4624	17	6	is	be	AUX
ejpam-4624	17	7	unsuitable	unsuitable	ADJ
ejpam-4624	17	8	in	in	ADP
ejpam-4624	17	9	mathematics	mathematic	NOUN
ejpam-4624	17	10	and	and	CCONJ
ejpam-4624	17	11	applications	application	NOUN
ejpam-4624	17	12	.	.	PUNCT
ejpam-4624	18	1	therefore	therefore	ADV
ejpam-4624	18	2	,	,	PUNCT
ejpam-4624	18	3	they	they	PRON
ejpam-4624	18	4	replaced	replace	VERB
ejpam-4624	18	5	the	the	DET
ejpam-4624	18	6	word	word	NOUN
ejpam-4624	18	7	”	"	PUNCT
ejpam-4624	18	8	intuitionistic	intuitionistic	ADJ
ejpam-4624	18	9	”	"	PUNCT
ejpam-4624	18	10	by	by	ADP
ejpam-4624	18	11	”	"	PUNCT
ejpam-4624	18	12	double	double	ADJ
ejpam-4624	18	13	”	"	PUNCT
ejpam-4624	18	14	and	and	CCONJ
ejpam-4624	18	15	renamed	rename	VERB
ejpam-4624	18	16	its	its	PRON
ejpam-4624	18	17	related	related	ADJ
ejpam-4624	18	18	topologies	topology	NOUN
ejpam-4624	18	19	.	.	PUNCT
ejpam-4624	19	1	the	the	DET
ejpam-4624	19	2	notion	notion	NOUN
ejpam-4624	19	3	of	of	ADP
ejpam-4624	19	4	intuitionistic	intuitionistic	ADJ
ejpam-4624	19	5	gradation	gradation	NOUN
ejpam-4624	19	6	of	of	ADP
ejpam-4624	19	7	openness	openness	NOUN
ejpam-4624	19	8	is	be	AUX
ejpam-4624	19	9	given	give	VERB
ejpam-4624	19	10	the	the	DET
ejpam-4624	19	11	new	new	ADJ
ejpam-4624	19	12	name	name	NOUN
ejpam-4624	19	13	”	"	PUNCT
ejpam-4624	19	14	double	double	ADJ
ejpam-4624	19	15	fuzzy	fuzzy	ADJ
ejpam-4624	19	16	topological	topological	ADJ
ejpam-4624	19	17	spaces	space	NOUN
ejpam-4624	19	18	”	"	PUNCT
ejpam-4624	19	19	see	see	VERB
ejpam-4624	19	20	[	[	X
ejpam-4624	19	21	8–10	8–10	NOUN
ejpam-4624	19	22	]	]	PUNCT
ejpam-4624	19	23	.	.	PUNCT
ejpam-4624	20	1	the	the	DET
ejpam-4624	20	2	fuzzy	fuzzy	ADJ
ejpam-4624	20	3	type	type	NOUN
ejpam-4624	20	4	of	of	ADP
ejpam-4624	20	5	the	the	DET
ejpam-4624	20	6	notion	notion	NOUN
ejpam-4624	20	7	of	of	ADP
ejpam-4624	20	8	topology	topology	NOUN
ejpam-4624	20	9	can	can	AUX
ejpam-4624	20	10	be	be	AUX
ejpam-4624	20	11	studied	study	VERB
ejpam-4624	20	12	in	in	ADP
ejpam-4624	20	13	the	the	DET
ejpam-4624	20	14	fuzzy	fuzzy	ADJ
ejpam-4624	20	15	mathematics	mathematic	NOUN
ejpam-4624	20	16	see	see	VERB
ejpam-4624	20	17	[	[	X
ejpam-4624	20	18	11–13	11–13	NUM
ejpam-4624	20	19	]	]	X
ejpam-4624	20	20	,	,	PUNCT
ejpam-4624	20	21	which	which	PRON
ejpam-4624	20	22	has	have	VERB
ejpam-4624	20	23	many	many	ADJ
ejpam-4624	20	24	applications	application	NOUN
ejpam-4624	20	25	in	in	ADP
ejpam-4624	20	26	different	different	ADJ
ejpam-4624	20	27	branches	branch	NOUN
ejpam-4624	20	28	of	of	ADP
ejpam-4624	20	29	mathematics	mathematic	NOUN
ejpam-4624	20	30	and	and	CCONJ
ejpam-4624	20	31	physics	physics	NOUN
ejpam-4624	20	32	theory	theory	NOUN
ejpam-4624	20	33	.	.	PUNCT
ejpam-4624	21	1	for	for	ADP
ejpam-4624	21	2	example	example	NOUN
ejpam-4624	21	3	,	,	PUNCT
ejpam-4624	21	4	fuzzy	fuzzy	ADJ
ejpam-4624	21	5	topological	topological	ADJ
ejpam-4624	21	6	spaces	space	NOUN
ejpam-4624	21	7	can	can	AUX
ejpam-4624	21	8	be	be	AUX
ejpam-4624	21	9	applied	apply	VERB
ejpam-4624	21	10	in	in	ADP
ejpam-4624	21	11	the	the	DET
ejpam-4624	21	12	modeling	modeling	NOUN
ejpam-4624	21	13	of	of	ADP
ejpam-4624	21	14	spatial	spatial	ADJ
ejpam-4624	21	15	objects	object	NOUN
ejpam-4624	21	16	such	such	ADJ
ejpam-4624	21	17	as	as	ADP
ejpam-4624	21	18	rivers	river	NOUN
ejpam-4624	21	19	,	,	PUNCT
ejpam-4624	21	20	roads	road	NOUN
ejpam-4624	21	21	,	,	PUNCT
ejpam-4624	21	22	trees	tree	NOUN
ejpam-4624	21	23	,	,	PUNCT
ejpam-4624	21	24	and	and	CCONJ
ejpam-4624	21	25	buildings	building	NOUN
ejpam-4624	21	26	.	.	PUNCT
ejpam-4624	22	1	since	since	SCONJ
ejpam-4624	22	2	double	double	ADJ
ejpam-4624	22	3	fuzzy	fuzzy	ADJ
ejpam-4624	22	4	topology	topology	NOUN
ejpam-4624	22	5	forms	form	VERB
ejpam-4624	22	6	an	an	DET
ejpam-4624	22	7	doi	doi	NOUN
ejpam-4624	22	8	:	:	PUNCT
ejpam-4624	22	9	https://doi.org/10.29020/nybg.ejpam.v18i2.4624	https://doi.org/10.29020/nybg.ejpam.v18i2.4624	DET
ejpam-4624	22	10	email	email	NOUN
ejpam-4624	22	11	addresses	address	NOUN
ejpam-4624	22	12	:	:	PUNCT
ejpam-4624	22	13	wadeimoon1@hotmail.com	wadeimoon1@hotmail.com	X
ejpam-4624	22	14	(	(	PUNCT
ejpam-4624	22	15	w.	w.	PROPN
ejpam-4624	22	16	f.	f.	PROPN
ejpam-4624	22	17	al	al	PROPN
ejpam-4624	22	18	-	-	PUNCT
ejpam-4624	22	19	omeri	omeri	ADJ
ejpam-4624	22	20	)	)	PUNCT
ejpam-4624	22	21	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4624	22	22	1	1	NUM
ejpam-4624	22	23	copyright	copyright	NOUN
ejpam-4624	22	24	:	:	PUNCT
ejpam-4624	22	25	©	©	PROPN
ejpam-4624	22	26	2025	2025	NUM
ejpam-4624	22	27	the	the	DET
ejpam-4624	22	28	author(s	author(s	NOUN
ejpam-4624	22	29	)	)	PUNCT
ejpam-4624	22	30	.	.	PUNCT
ejpam-4624	23	1	(	(	PUNCT
ejpam-4624	23	2	cc	cc	NOUN
ejpam-4624	23	3	by	by	ADP
ejpam-4624	23	4	-	-	PUNCT
ejpam-4624	23	5	nc	nc	PROPN
ejpam-4624	23	6	4.0	4.0	NUM
ejpam-4624	23	7	)	)	PUNCT
ejpam-4624	23	8	w.	w.	PROPN
ejpam-4624	23	9	f.	f.	PROPN
ejpam-4624	23	10	al	al	PROPN
ejpam-4624	23	11	-	-	PUNCT
ejpam-4624	23	12	omeri	omeri	ADJ
ejpam-4624	23	13	/	/	SYM
ejpam-4624	23	14	eur	eur	PROPN
ejpam-4624	23	15	.	.	PUNCT
ejpam-4624	24	1	j.	j.	PROPN
ejpam-4624	24	2	pure	pure	PROPN
ejpam-4624	24	3	appl	appl	PROPN
ejpam-4624	24	4	.	.	PROPN
ejpam-4624	24	5	math	math	PROPN
ejpam-4624	24	6	,	,	PUNCT
ejpam-4624	24	7	18	18	NUM
ejpam-4624	24	8	(	(	PUNCT
ejpam-4624	24	9	2	2	NUM
ejpam-4624	24	10	)	)	PUNCT
ejpam-4624	24	11	(	(	PUNCT
ejpam-4624	24	12	2025	2025	NUM
ejpam-4624	24	13	)	)	PUNCT
ejpam-4624	24	14	,	,	PUNCT
ejpam-4624	24	15	4624	4624	NUM
ejpam-4624	24	16	2	2	NUM
ejpam-4624	24	17	of	of	ADP
ejpam-4624	24	18	15	15	NUM
ejpam-4624	24	19	extension	extension	NOUN
ejpam-4624	24	20	of	of	ADP
ejpam-4624	24	21	fuzzy	fuzzy	ADJ
ejpam-4624	24	22	topology	topology	NOUN
ejpam-4624	24	23	and	and	CCONJ
ejpam-4624	24	24	general	general	ADJ
ejpam-4624	24	25	topology	topology	NOUN
ejpam-4624	25	1	,	,	PUNCT
ejpam-4624	25	2	we	we	PRON
ejpam-4624	25	3	think	think	VERB
ejpam-4624	25	4	that	that	SCONJ
ejpam-4624	25	5	our	our	PRON
ejpam-4624	25	6	results	result	NOUN
ejpam-4624	25	7	can	can	AUX
ejpam-4624	25	8	be	be	AUX
ejpam-4624	25	9	applied	apply	VERB
ejpam-4624	25	10	in	in	ADP
ejpam-4624	25	11	modern	modern	ADJ
ejpam-4624	25	12	physics	physics	NOUN
ejpam-4624	25	13	and	and	CCONJ
ejpam-4624	25	14	gis	gis	NOUN
ejpam-4624	25	15	problems	problem	NOUN
ejpam-4624	25	16	.	.	PUNCT
ejpam-4624	26	1	in	in	ADP
ejpam-4624	26	2	this	this	DET
ejpam-4624	26	3	paper	paper	NOUN
ejpam-4624	26	4	,	,	PUNCT
ejpam-4624	26	5	we	we	PRON
ejpam-4624	26	6	define	define	VERB
ejpam-4624	26	7	and	and	CCONJ
ejpam-4624	26	8	study	study	NOUN
ejpam-4624	26	9	(	(	PUNCT
ejpam-4624	26	10	r	r	NOUN
ejpam-4624	26	11	,	,	PUNCT
ejpam-4624	26	12	s)-δ	s)-δ	NOUN
ejpam-4624	26	13	-	-	PUNCT
ejpam-4624	26	14	fuzzy	fuzzy	ADJ
ejpam-4624	26	15	closed	close	VERB
ejpam-4624	26	16	sets	set	NOUN
ejpam-4624	26	17	in	in	ADP
ejpam-4624	26	18	double	double	ADJ
ejpam-4624	26	19	fuzzy	fuzzy	ADJ
ejpam-4624	26	20	topological	topological	ADJ
ejpam-4624	26	21	spaces	space	NOUN
ejpam-4624	26	22	and	and	CCONJ
ejpam-4624	26	23	investigate	investigate	VERB
ejpam-4624	26	24	some	some	PRON
ejpam-4624	26	25	of	of	ADP
ejpam-4624	26	26	their	their	PRON
ejpam-4624	26	27	properties	property	NOUN
ejpam-4624	26	28	.	.	PUNCT
ejpam-4624	27	1	moreover	moreover	ADV
ejpam-4624	27	2	,	,	PUNCT
ejpam-4624	27	3	we	we	PRON
ejpam-4624	27	4	introduce	introduce	VERB
ejpam-4624	27	5	the	the	DET
ejpam-4624	27	6	concepts	concept	NOUN
ejpam-4624	27	7	of	of	ADP
ejpam-4624	27	8	double	double	ADJ
ejpam-4624	27	9	fuzzy	fuzzy	ADJ
ejpam-4624	27	10	δ	δ	NOUN
ejpam-4624	27	11	-	-	ADJ
ejpam-4624	27	12	continuous	continuous	ADJ
ejpam-4624	27	13	functions	function	NOUN
ejpam-4624	27	14	.	.	PUNCT
ejpam-4624	28	1	several	several	ADJ
ejpam-4624	28	2	interesting	interesting	ADJ
ejpam-4624	28	3	properties	property	NOUN
ejpam-4624	28	4	and	and	CCONJ
ejpam-4624	28	5	characterizations	characterization	NOUN
ejpam-4624	28	6	are	be	AUX
ejpam-4624	28	7	introduced	introduce	VERB
ejpam-4624	28	8	and	and	CCONJ
ejpam-4624	28	9	discussed	discuss	VERB
ejpam-4624	28	10	.	.	PUNCT
ejpam-4624	29	1	throughout	throughout	ADP
ejpam-4624	29	2	this	this	DET
ejpam-4624	29	3	paper	paper	NOUN
ejpam-4624	29	4	,	,	PUNCT
ejpam-4624	29	5	let	let	VERB
ejpam-4624	29	6	x	x	PRON
ejpam-4624	29	7	be	be	AUX
ejpam-4624	29	8	a	a	DET
ejpam-4624	29	9	nonempty	nonempty	ADV
ejpam-4624	29	10	set	set	VERB
ejpam-4624	30	1	and	and	CCONJ
ejpam-4624	30	2	i	i	PRON
ejpam-4624	30	3	be	be	VERB
ejpam-4624	30	4	the	the	DET
ejpam-4624	30	5	closed	closed	ADJ
ejpam-4624	30	6	unit	unit	NOUN
ejpam-4624	30	7	interval	interval	NOUN
ejpam-4624	30	8	[	[	X
ejpam-4624	30	9	0	0	NUM
ejpam-4624	30	10	,	,	PUNCT
ejpam-4624	30	11	1	1	NUM
ejpam-4624	30	12	]	]	PUNCT
ejpam-4624	30	13	,	,	PUNCT
ejpam-4624	30	14	i0	i0	PROPN
ejpam-4624	30	15	=	=	PUNCT
ejpam-4624	30	16	(	(	PUNCT
ejpam-4624	30	17	0	0	NUM
ejpam-4624	30	18	,	,	PUNCT
ejpam-4624	30	19	1	1	NUM
ejpam-4624	30	20	]	]	PUNCT
ejpam-4624	30	21	and	and	CCONJ
ejpam-4624	30	22	i1	i1	PROPN
ejpam-4624	30	23	=	=	PUNCT
ejpam-4624	31	1	[	[	X
ejpam-4624	31	2	0	0	NUM
ejpam-4624	31	3	,	,	PUNCT
ejpam-4624	31	4	1	1	NUM
ejpam-4624	31	5	)	)	PUNCT
ejpam-4624	31	6	.	.	PUNCT
ejpam-4624	32	1	the	the	DET
ejpam-4624	32	2	family	family	NOUN
ejpam-4624	32	3	of	of	ADP
ejpam-4624	32	4	all	all	DET
ejpam-4624	32	5	fuzzy	fuzzy	ADJ
ejpam-4624	32	6	subsets	subset	NOUN
ejpam-4624	32	7	on	on	ADP
ejpam-4624	32	8	x	x	PUNCT
ejpam-4624	32	9	is	be	AUX
ejpam-4624	32	10	denoted	denote	VERB
ejpam-4624	32	11	by	by	ADP
ejpam-4624	32	12	ix	ix	PRON
ejpam-4624	32	13	.	.	PUNCT
ejpam-4624	33	1	by	by	ADP
ejpam-4624	33	2	0	0	NUM
ejpam-4624	33	3	and	and	CCONJ
ejpam-4624	33	4	1	1	NUM
ejpam-4624	33	5	,	,	PUNCT
ejpam-4624	33	6	we	we	PRON
ejpam-4624	33	7	denote	denote	VERB
ejpam-4624	33	8	the	the	DET
ejpam-4624	33	9	smallest	small	ADJ
ejpam-4624	33	10	and	and	CCONJ
ejpam-4624	33	11	the	the	DET
ejpam-4624	33	12	greatest	great	ADJ
ejpam-4624	33	13	fuzzy	fuzzy	ADJ
ejpam-4624	33	14	subsets	subset	NOUN
ejpam-4624	33	15	on	on	ADP
ejpam-4624	33	16	x.	x.	NOUN
ejpam-4624	33	17	for	for	ADP
ejpam-4624	33	18	a	a	DET
ejpam-4624	33	19	fuzzy	fuzzy	ADJ
ejpam-4624	33	20	subset	subset	NOUN
ejpam-4624	33	21	ρ	ρ	PROPN
ejpam-4624	33	22	∈	∈	PROPN
ejpam-4624	33	23	ix	ix	X
ejpam-4624	33	24	,	,	PUNCT
ejpam-4624	33	25	1	1	NUM
ejpam-4624	33	26	−	−	PROPN
ejpam-4624	33	27	ρ	ρ	PROPN
ejpam-4624	33	28	denotes	denote	VERB
ejpam-4624	33	29	it	it	PRON
ejpam-4624	33	30	’s	’	VERB
ejpam-4624	33	31	complement	complement	NOUN
ejpam-4624	33	32	.	.	PUNCT
ejpam-4624	34	1	given	give	VERB
ejpam-4624	34	2	a	a	DET
ejpam-4624	34	3	function	function	NOUN
ejpam-4624	34	4	f	f	NOUN
ejpam-4624	34	5	:	:	PUNCT
ejpam-4624	34	6	x	x	X
ejpam-4624	34	7	→	→	SYM
ejpam-4624	34	8	y	y	PROPN
ejpam-4624	34	9	,	,	PUNCT
ejpam-4624	34	10	f(ρ	f(ρ	NOUN
ejpam-4624	34	11	)	)	PUNCT
ejpam-4624	34	12	and	and	CCONJ
ejpam-4624	34	13	f−1(ρ	f−1(ρ	NOUN
ejpam-4624	34	14	)	)	PUNCT
ejpam-4624	34	15	define	define	VERB
ejpam-4624	34	16	the	the	DET
ejpam-4624	34	17	direct	direct	ADJ
ejpam-4624	34	18	image	image	NOUN
ejpam-4624	34	19	and	and	CCONJ
ejpam-4624	34	20	the	the	DET
ejpam-4624	34	21	inverse	inverse	ADJ
ejpam-4624	34	22	image	image	NOUN
ejpam-4624	34	23	of	of	ADP
ejpam-4624	34	24	f	f	PROPN
ejpam-4624	34	25	,	,	PUNCT
ejpam-4624	34	26	by	by	ADP
ejpam-4624	34	27	f(ρ)(y	f(ρ)(y	NOUN
ejpam-4624	34	28	)	)	PUNCT
ejpam-4624	34	29	=	=	PUNCT
ejpam-4624	34	30	∨	∨	NUM
ejpam-4624	34	31	f(x)=y	f(x)=y	NOUN
ejpam-4624	34	32	ρ(x	ρ(x	NOUN
ejpam-4624	34	33	)	)	PUNCT
ejpam-4624	34	34	and	and	CCONJ
ejpam-4624	34	35	f−1(ν)(x	f−1(ν)(x	PROPN
ejpam-4624	34	36	)	)	PUNCT
ejpam-4624	34	37	=	=	SYM
ejpam-4624	34	38	ν(f(x	ν(f(x	PROPN
ejpam-4624	34	39	)	)	PUNCT
ejpam-4624	34	40	)	)	PUNCT
ejpam-4624	34	41	,	,	PUNCT
ejpam-4624	34	42	for	for	ADP
ejpam-4624	34	43	each	each	DET
ejpam-4624	34	44	ρ	ρ	PROPN
ejpam-4624	34	45	∈	∈	PROPN
ejpam-4624	34	46	ix	ix	ADV
ejpam-4624	34	47	,	,	PUNCT
ejpam-4624	34	48	ν	ν	PROPN
ejpam-4624	34	49	∈	∈	PROPN
ejpam-4624	34	50	iy	iy	PROPN
ejpam-4624	34	51	and	and	CCONJ
ejpam-4624	34	52	x	x	PUNCT
ejpam-4624	34	53	∈	∈	PROPN
ejpam-4624	34	54	x	x	NOUN
ejpam-4624	34	55	,	,	PUNCT
ejpam-4624	34	56	respectively	respectively	ADV
ejpam-4624	34	57	.	.	PUNCT
ejpam-4624	35	1	for	for	ADP
ejpam-4624	35	2	fuzzy	fuzzy	ADJ
ejpam-4624	35	3	subsets	subset	NOUN
ejpam-4624	35	4	ρ	ρ	PROPN
ejpam-4624	35	5	and	and	CCONJ
ejpam-4624	35	6	ϕ	ϕ	NOUN
ejpam-4624	35	7	in	in	ADP
ejpam-4624	35	8	x	x	SYM
ejpam-4624	35	9	,	,	PUNCT
ejpam-4624	35	10	we	we	PRON
ejpam-4624	35	11	write	write	VERB
ejpam-4624	35	12	ρqϕ	ρqϕ	NOUN
ejpam-4624	35	13	to	to	PART
ejpam-4624	35	14	mean	mean	VERB
ejpam-4624	35	15	that	that	SCONJ
ejpam-4624	35	16	ρ	ρ	PROPN
ejpam-4624	35	17	is	be	AUX
ejpam-4624	35	18	quasi	quasi	ADJ
ejpam-4624	35	19	coincident	coincident	NOUN
ejpam-4624	35	20	(	(	PUNCT
ejpam-4624	35	21	q	q	NOUN
ejpam-4624	35	22	-	-	NOUN
ejpam-4624	35	23	coincident	coincident	NOUN
ejpam-4624	35	24	)	)	PUNCT
ejpam-4624	35	25	with	with	ADP
ejpam-4624	35	26	ϕ	ϕ	PRON
ejpam-4624	35	27	that	that	PRON
ejpam-4624	35	28	is	be	AUX
ejpam-4624	35	29	,	,	PUNCT
ejpam-4624	35	30	there	there	PRON
ejpam-4624	35	31	exists	exist	VERB
ejpam-4624	35	32	at	at	ADV
ejpam-4624	35	33	least	least	ADV
ejpam-4624	35	34	one	one	NUM
ejpam-4624	35	35	point	point	NOUN
ejpam-4624	35	36	x	x	X
ejpam-4624	35	37	∈	∈	NOUN
ejpam-4624	35	38	x	x	PUNCT
ejpam-4624	35	39	such	such	ADJ
ejpam-4624	35	40	that	that	DET
ejpam-4624	35	41	ρ(x	ρ(x	NOUN
ejpam-4624	35	42	)	)	PUNCT
ejpam-4624	35	43	+	+	CCONJ
ejpam-4624	35	44	ϕ(x	ϕ(x	NOUN
ejpam-4624	35	45	)	)	PUNCT
ejpam-4624	35	46	>	>	X
ejpam-4624	36	1	1	1	NUM
ejpam-4624	36	2	.	.	PUNCT
ejpam-4624	36	3	negation	negation	NOUN
ejpam-4624	36	4	of	of	ADP
ejpam-4624	36	5	such	such	DET
ejpam-4624	36	6	a	a	DET
ejpam-4624	36	7	statement	statement	NOUN
ejpam-4624	36	8	is	be	AUX
ejpam-4624	36	9	denoted	denote	VERB
ejpam-4624	36	10	as	as	ADP
ejpam-4624	36	11	ρqϕ.	ρqϕ.	X
ejpam-4624	36	12	notions	notion	NOUN
ejpam-4624	36	13	and	and	CCONJ
ejpam-4624	36	14	notations	notation	NOUN
ejpam-4624	36	15	not	not	PART
ejpam-4624	36	16	described	describe	VERB
ejpam-4624	36	17	in	in	ADP
ejpam-4624	36	18	this	this	DET
ejpam-4624	36	19	paper	paper	NOUN
ejpam-4624	36	20	are	be	AUX
ejpam-4624	36	21	standard	standard	ADJ
ejpam-4624	36	22	and	and	CCONJ
ejpam-4624	36	23	usual	usual	ADJ
ejpam-4624	36	24	.	.	PUNCT
ejpam-4624	37	1	definition	definition	NOUN
ejpam-4624	37	2	1.1	1.1	NUM
ejpam-4624	37	3	.	.	PUNCT
ejpam-4624	38	1	[	[	X
ejpam-4624	38	2	8	8	NUM
ejpam-4624	38	3	,	,	PUNCT
ejpam-4624	38	4	14	14	NUM
ejpam-4624	38	5	,	,	PUNCT
ejpam-4624	38	6	15	15	NUM
ejpam-4624	38	7	]	]	PUNCT
ejpam-4624	38	8	the	the	DET
ejpam-4624	38	9	pair	pair	NOUN
ejpam-4624	38	10	of	of	ADP
ejpam-4624	38	11	functions	function	NOUN
ejpam-4624	38	12	t	t	PROPN
ejpam-4624	38	13	,	,	PUNCT
ejpam-4624	38	14	t	t	PROPN
ejpam-4624	38	15	∗	∗	NOUN
ejpam-4624	38	16	:	:	PUNCT
ejpam-4624	38	17	ix	ix	PROPN
ejpam-4624	38	18	→	→	PUNCT
ejpam-4624	38	19	i	i	PRON
ejpam-4624	38	20	is	be	AUX
ejpam-4624	38	21	called	call	VERB
ejpam-4624	38	22	a	a	DET
ejpam-4624	38	23	double	double	ADJ
ejpam-4624	38	24	fuzzy	fuzzy	ADJ
ejpam-4624	38	25	topology	topology	NOUN
ejpam-4624	38	26	on	on	ADP
ejpam-4624	38	27	x	x	SYM
ejpam-4624	38	28	if	if	SCONJ
ejpam-4624	38	29	it	it	PRON
ejpam-4624	38	30	satisfies	satisfy	VERB
ejpam-4624	38	31	the	the	DET
ejpam-4624	38	32	following	follow	VERB
ejpam-4624	38	33	conditions	condition	NOUN
ejpam-4624	38	34	:	:	PUNCT
ejpam-4624	38	35	(	(	PUNCT
ejpam-4624	38	36	i	i	NOUN
ejpam-4624	38	37	)	)	PUNCT
ejpam-4624	38	38	t	t	PROPN
ejpam-4624	38	39	(	(	PUNCT
ejpam-4624	38	40	ρ	ρ	PROPN
ejpam-4624	38	41	)	)	PUNCT
ejpam-4624	38	42	+	+	NUM
ejpam-4624	38	43	t	t	NOUN
ejpam-4624	38	44	∗(ρ	∗(ρ	NOUN
ejpam-4624	38	45	)	)	PUNCT
ejpam-4624	38	46	≤	≤	NUM
ejpam-4624	38	47	1	1	NUM
ejpam-4624	38	48	,	,	PUNCT
ejpam-4624	38	49	(	(	PUNCT
ejpam-4624	38	50	ii	ii	NOUN
ejpam-4624	38	51	)	)	PUNCT
ejpam-4624	38	52	t	t	NOUN
ejpam-4624	38	53	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	38	54	∧	∧	PROPN
ejpam-4624	38	55	ρ2	ρ2	PROPN
ejpam-4624	38	56	)	)	PUNCT
ejpam-4624	38	57	≥	≥	NOUN
ejpam-4624	38	58	t	t	PROPN
ejpam-4624	38	59	∗(ρ1	∗(ρ1	NOUN
ejpam-4624	38	60	)	)	PUNCT
ejpam-4624	38	61	∧	∧	PROPN
ejpam-4624	38	62	t	t	PROPN
ejpam-4624	38	63	∗(ρ2	∗(ρ2	PROPN
ejpam-4624	38	64	)	)	PUNCT
ejpam-4624	38	65	and	and	CCONJ
ejpam-4624	38	66	t	t	PROPN
ejpam-4624	38	67	(	(	PUNCT
ejpam-4624	38	68	ρ1	ρ1	NOUN
ejpam-4624	38	69	∧	∧	PROPN
ejpam-4624	38	70	ρ2	ρ2	PROPN
ejpam-4624	38	71	)	)	PUNCT
ejpam-4624	38	72	≤	≤	NOUN
ejpam-4624	38	73	t	t	PROPN
ejpam-4624	38	74	(	(	PUNCT
ejpam-4624	38	75	ρ1	ρ1	PROPN
ejpam-4624	38	76	)	)	PUNCT
ejpam-4624	38	77	∨	∨	PROPN
ejpam-4624	38	78	t	t	PROPN
ejpam-4624	38	79	(	(	PUNCT
ejpam-4624	38	80	ρ2	ρ2	PROPN
ejpam-4624	38	81	)	)	PUNCT
ejpam-4624	38	82	,	,	PUNCT
ejpam-4624	38	83	(	(	PUNCT
ejpam-4624	38	84	iii	iii	X
ejpam-4624	38	85	)	)	PUNCT
ejpam-4624	38	86	t	t	PROPN
ejpam-4624	38	87	(	(	PUNCT
ejpam-4624	38	88	∨	∨	PROPN
ejpam-4624	38	89	i∈i	i∈i	PROPN
ejpam-4624	38	90	ρi	ρi	PROPN
ejpam-4624	38	91	)	)	PUNCT
ejpam-4624	38	92	≥	≥	NOUN
ejpam-4624	38	93	∧	∧	PROPN
ejpam-4624	38	94	i∈i	i∈i	ADJ
ejpam-4624	38	95	t	t	PROPN
ejpam-4624	38	96	(	(	PUNCT
ejpam-4624	38	97	ρi	ρi	NOUN
ejpam-4624	38	98	)	)	PUNCT
ejpam-4624	38	99	and	and	CCONJ
ejpam-4624	38	100	t	t	PROPN
ejpam-4624	38	101	∗	∗	NOUN
ejpam-4624	38	102	(	(	PUNCT
ejpam-4624	38	103	∨	∨	NUM
ejpam-4624	38	104	i∈i	i∈i	ADJ
ejpam-4624	38	105	ρi	ρi	PROPN
ejpam-4624	38	106	)	)	PUNCT
ejpam-4624	38	107	≤	≤	NOUN
ejpam-4624	38	108	∨	∨	NUM
ejpam-4624	38	109	i∈i	i∈i	ADJ
ejpam-4624	38	110	t	t	PROPN
ejpam-4624	38	111	∗(ρi	∗(ρi	ADJ
ejpam-4624	38	112	)	)	PUNCT
ejpam-4624	38	113	for	for	ADP
ejpam-4624	38	114	each	each	DET
ejpam-4624	38	115	ρi	ρi	PROPN
ejpam-4624	38	116	∈	∈	PROPN
ejpam-4624	38	117	ix	ix	ADV
ejpam-4624	38	118	,	,	PUNCT
ejpam-4624	38	119	i	i	PRON
ejpam-4624	38	120	∈	∈	PROPN
ejpam-4624	38	121	i.	i.	NOUN
ejpam-4624	38	122	the	the	DET
ejpam-4624	38	123	triplet	triplet	NOUN
ejpam-4624	38	124	(	(	PUNCT
ejpam-4624	38	125	x	x	NOUN
ejpam-4624	38	126	,	,	PUNCT
ejpam-4624	38	127	t	t	PROPN
ejpam-4624	38	128	,	,	PUNCT
ejpam-4624	38	129	t	t	PROPN
ejpam-4624	38	130	∗	∗	NOUN
ejpam-4624	38	131	)	)	PUNCT
ejpam-4624	38	132	is	be	AUX
ejpam-4624	38	133	called	call	VERB
ejpam-4624	38	134	a	a	DET
ejpam-4624	38	135	double	double	ADJ
ejpam-4624	38	136	fuzzy	fuzzy	ADJ
ejpam-4624	38	137	topological	topological	ADJ
ejpam-4624	38	138	space	space	NOUN
ejpam-4624	38	139	(	(	PUNCT
ejpam-4624	38	140	dfts	dft	NOUN
ejpam-4624	38	141	,	,	PUNCT
ejpam-4624	38	142	for	for	ADP
ejpam-4624	38	143	short	short	ADJ
ejpam-4624	38	144	)	)	PUNCT
ejpam-4624	38	145	.	.	PUNCT
ejpam-4624	39	1	t	t	PROPN
ejpam-4624	39	2	(	(	PUNCT
ejpam-4624	39	3	ρ	ρ	PROPN
ejpam-4624	39	4	)	)	PUNCT
ejpam-4624	39	5	and	and	CCONJ
ejpam-4624	39	6	t	t	PROPN
ejpam-4624	39	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	39	8	)	)	PUNCT
ejpam-4624	39	9	may	may	AUX
ejpam-4624	39	10	be	be	AUX
ejpam-4624	39	11	interpreted	interpret	VERB
ejpam-4624	39	12	as	as	ADP
ejpam-4624	39	13	a	a	DET
ejpam-4624	39	14	gradation	gradation	NOUN
ejpam-4624	39	15	of	of	ADP
ejpam-4624	39	16	openness	openness	NOUN
ejpam-4624	39	17	and	and	CCONJ
ejpam-4624	39	18	gradation	gradation	NOUN
ejpam-4624	39	19	of	of	ADP
ejpam-4624	39	20	non	non	ADJ
ejpam-4624	39	21	-	-	NOUN
ejpam-4624	39	22	openness	openness	NOUN
ejpam-4624	39	23	for	for	ADP
ejpam-4624	39	24	ρ	ρ	PROPN
ejpam-4624	39	25	.	.	PUNCT
ejpam-4624	40	1	a	a	DET
ejpam-4624	40	2	function	function	NOUN
ejpam-4624	40	3	f	f	NOUN
ejpam-4624	40	4	:	:	PUNCT
ejpam-4624	40	5	(	(	PUNCT
ejpam-4624	40	6	x	x	X
ejpam-4624	40	7	,	,	PUNCT
ejpam-4624	40	8	t1	t1	PROPN
ejpam-4624	40	9	,	,	PUNCT
ejpam-4624	40	10	t	t	PROPN
ejpam-4624	40	11	∗	∗	X
ejpam-4624	40	12	1	1	NUM
ejpam-4624	40	13	)	)	PUNCT
ejpam-4624	40	14	→	→	SYM
ejpam-4624	40	15	(	(	PUNCT
ejpam-4624	40	16	y	y	PROPN
ejpam-4624	40	17	,	,	PUNCT
ejpam-4624	40	18	t2	t2	PROPN
ejpam-4624	40	19	,	,	PUNCT
ejpam-4624	40	20	t	t	PROPN
ejpam-4624	40	21	∗	∗	X
ejpam-4624	40	22	2	2	NUM
ejpam-4624	40	23	)	)	PUNCT
ejpam-4624	40	24	is	be	AUX
ejpam-4624	40	25	said	say	VERB
ejpam-4624	40	26	to	to	PART
ejpam-4624	40	27	be	be	AUX
ejpam-4624	40	28	double	double	ADV
ejpam-4624	40	29	fuzzy	fuzzy	ADJ
ejpam-4624	40	30	continuous	continuous	ADJ
ejpam-4624	40	31	if	if	SCONJ
ejpam-4624	40	32	t1(f−1(ν	t1(f−1(ν	PROPN
ejpam-4624	40	33	)	)	PUNCT
ejpam-4624	40	34	)	)	PUNCT
ejpam-4624	40	35	≥	≥	NOUN
ejpam-4624	40	36	t2(ν	t2(ν	VERB
ejpam-4624	40	37	)	)	PUNCT
ejpam-4624	40	38	and	and	CCONJ
ejpam-4624	40	39	t	t	PROPN
ejpam-4624	40	40	∗	∗	NOUN
ejpam-4624	40	41	1	1	NUM
ejpam-4624	40	42	(	(	PUNCT
ejpam-4624	40	43	f	f	PROPN
ejpam-4624	40	44	−1(ν	−1(ν	NUM
ejpam-4624	40	45	)	)	PUNCT
ejpam-4624	40	46	)	)	PUNCT
ejpam-4624	40	47	≤	≤	PROPN
ejpam-4624	41	1	t	t	PROPN
ejpam-4624	41	2	∗	∗	X
ejpam-4624	41	3	2	2	NUM
ejpam-4624	41	4	(	(	PUNCT
ejpam-4624	41	5	ν	ν	NOUN
ejpam-4624	41	6	)	)	PUNCT
ejpam-4624	41	7	for	for	ADP
ejpam-4624	41	8	each	each	DET
ejpam-4624	41	9	ν	ν	NOUN
ejpam-4624	41	10	∈	∈	PROPN
ejpam-4624	41	11	iy	iy	PROPN
ejpam-4624	41	12	.	.	PUNCT
ejpam-4624	42	1	theorem	theorem	VERB
ejpam-4624	42	2	1.2	1.2	NUM
ejpam-4624	42	3	.	.	PUNCT
ejpam-4624	43	1	[	[	X
ejpam-4624	43	2	8	8	NUM
ejpam-4624	43	3	,	,	PUNCT
ejpam-4624	43	4	14	14	NUM
ejpam-4624	43	5	]	]	PUNCT
ejpam-4624	43	6	let	let	VERB
ejpam-4624	43	7	(	(	PUNCT
ejpam-4624	43	8	x	x	X
ejpam-4624	43	9	,	,	PUNCT
ejpam-4624	43	10	t	t	PROPN
ejpam-4624	43	11	,	,	PUNCT
ejpam-4624	43	12	t	t	PROPN
ejpam-4624	43	13	∗	∗	NOUN
ejpam-4624	43	14	)	)	PUNCT
ejpam-4624	43	15	be	be	AUX
ejpam-4624	43	16	an	an	DET
ejpam-4624	43	17	dfts	dft	NOUN
ejpam-4624	43	18	.	.	PUNCT
ejpam-4624	44	1	then	then	ADV
ejpam-4624	44	2	,	,	PUNCT
ejpam-4624	44	3	for	for	ADP
ejpam-4624	44	4	each	each	DET
ejpam-4624	44	5	r	r	NOUN
ejpam-4624	44	6	∈	∈	PROPN
ejpam-4624	44	7	i0	i0	PROPN
ejpam-4624	44	8	,	,	PUNCT
ejpam-4624	44	9	s	s	PROPN
ejpam-4624	44	10	∈	∈	PROPN
ejpam-4624	44	11	i1	i1	NOUN
ejpam-4624	44	12	,	,	PUNCT
ejpam-4624	44	13	and	and	CCONJ
ejpam-4624	44	14	ρ	ρ	PROPN
ejpam-4624	44	15	∈	∈	PROPN
ejpam-4624	44	16	ix	ix	ADV
ejpam-4624	44	17	,	,	PUNCT
ejpam-4624	44	18	we	we	PRON
ejpam-4624	44	19	define	define	VERB
ejpam-4624	44	20	an	an	DET
ejpam-4624	44	21	operator	operator	NOUN
ejpam-4624	44	22	ct	ct	NOUN
ejpam-4624	44	23	,	,	PUNCT
ejpam-4624	44	24	t	t	PROPN
ejpam-4624	44	25	∗	∗	NOUN
ejpam-4624	44	26	:	:	PUNCT
ejpam-4624	44	27	ix	ix	PROPN
ejpam-4624	44	28	×	×	PROPN
ejpam-4624	44	29	i1	i1	PROPN
ejpam-4624	44	30	×	×	PROPN
ejpam-4624	44	31	i0	i0	PROPN
ejpam-4624	44	32	−→	−→	NOUN
ejpam-4624	44	33	ix	ix	ADV
ejpam-4624	44	34	as	as	SCONJ
ejpam-4624	44	35	follows	follow	VERB
ejpam-4624	44	36	:	:	PUNCT
ejpam-4624	44	37	ct	ct	NUM
ejpam-4624	44	38	,	,	PUNCT
ejpam-4624	44	39	t	t	NOUN
ejpam-4624	44	40	∗(ρ	∗(ρ	NOUN
ejpam-4624	44	41	,	,	PUNCT
ejpam-4624	44	42	r	r	NOUN
ejpam-4624	44	43	,	,	PUNCT
ejpam-4624	44	44	s	s	NOUN
ejpam-4624	44	45	)	)	PUNCT
ejpam-4624	45	1	=	=	SYM
ejpam-4624	45	2	∧	∧	PROPN
ejpam-4624	45	3	{	{	PUNCT
ejpam-4624	45	4	ϕ	ϕ	NOUN
ejpam-4624	45	5	∈	∈	PROPN
ejpam-4624	45	6	ix	ix	ADP
ejpam-4624	45	7	|ρ	|ρ	ADJ
ejpam-4624	45	8	≤	≤	NUM
ejpam-4624	45	9	ϕ	ϕ	PROPN
ejpam-4624	45	10	,	,	PUNCT
ejpam-4624	45	11	t	t	PROPN
ejpam-4624	45	12	(	(	PUNCT
ejpam-4624	45	13	1−	1−	NUM
ejpam-4624	45	14	ϕ	ϕ	NOUN
ejpam-4624	45	15	)	)	PUNCT
ejpam-4624	45	16	≥	≥	NOUN
ejpam-4624	45	17	r	r	NOUN
ejpam-4624	45	18	,	,	PUNCT
ejpam-4624	45	19	t	t	NOUN
ejpam-4624	45	20	∗(1−	∗(1−	PROPN
ejpam-4624	45	21	ϕ	ϕ	X
ejpam-4624	45	22	)	)	PUNCT
ejpam-4624	45	23	≤	≤	NOUN
ejpam-4624	45	24	s	s	PART
ejpam-4624	45	25	}	}	PUNCT
ejpam-4624	45	26	.	.	PUNCT
ejpam-4624	46	1	for	for	ADP
ejpam-4624	46	2	each	each	DET
ejpam-4624	46	3	ρ	ρ	NOUN
ejpam-4624	46	4	,	,	PUNCT
ejpam-4624	46	5	ϕ	ϕ	PROPN
ejpam-4624	46	6	∈	∈	PROPN
ejpam-4624	46	7	ix	ix	X
ejpam-4624	46	8	,	,	PUNCT
ejpam-4624	46	9	r	r	NOUN
ejpam-4624	46	10	,	,	PUNCT
ejpam-4624	46	11	r1	r1	PROPN
ejpam-4624	46	12	∈	∈	PROPN
ejpam-4624	46	13	i0	i0	PROPN
ejpam-4624	46	14	and	and	CCONJ
ejpam-4624	46	15	s	s	PROPN
ejpam-4624	46	16	,	,	PUNCT
ejpam-4624	46	17	s1	s1	PROPN
ejpam-4624	46	18	∈	∈	PROPN
ejpam-4624	46	19	i1	i1	PROPN
ejpam-4624	46	20	,	,	PUNCT
ejpam-4624	46	21	the	the	DET
ejpam-4624	46	22	operator	operator	NOUN
ejpam-4624	46	23	ct	ct	PRON
ejpam-4624	46	24	,	,	PUNCT
ejpam-4624	46	25	t	t	PROPN
ejpam-4624	46	26	∗	∗	NOUN
ejpam-4624	46	27	satisfies	satisfy	VERB
ejpam-4624	46	28	the	the	DET
ejpam-4624	46	29	following	following	ADJ
ejpam-4624	46	30	statements	statement	NOUN
ejpam-4624	46	31	:	:	PUNCT
ejpam-4624	46	32	(	(	PUNCT
ejpam-4624	46	33	i	i	NOUN
ejpam-4624	46	34	)	)	PUNCT
ejpam-4624	46	35	ct	ct	PROPN
ejpam-4624	46	36	,	,	PUNCT
ejpam-4624	46	37	t	t	PROPN
ejpam-4624	46	38	∗(0	∗(0	PROPN
ejpam-4624	46	39	,	,	PUNCT
ejpam-4624	46	40	r	r	NOUN
ejpam-4624	46	41	,	,	PUNCT
ejpam-4624	46	42	s	s	PART
ejpam-4624	46	43	)	)	PUNCT
ejpam-4624	46	44	=	=	SYM
ejpam-4624	47	1	0	0	X
ejpam-4624	47	2	.	.	PUNCT
ejpam-4624	47	3	(	(	PUNCT
ejpam-4624	47	4	ii	ii	NOUN
ejpam-4624	47	5	)	)	PUNCT
ejpam-4624	47	6	ρ	ρ	PROPN
ejpam-4624	47	7	≤	≤	PROPN
ejpam-4624	47	8	ct	ct	NUM
ejpam-4624	47	9	,	,	PUNCT
ejpam-4624	47	10	t	t	NOUN
ejpam-4624	47	11	∗(ρ	∗(ρ	NOUN
ejpam-4624	47	12	,	,	PUNCT
ejpam-4624	47	13	r	r	NOUN
ejpam-4624	47	14	,	,	PUNCT
ejpam-4624	47	15	s	s	NOUN
ejpam-4624	47	16	)	)	PUNCT
ejpam-4624	47	17	.	.	PUNCT
ejpam-4624	48	1	(	(	PUNCT
ejpam-4624	48	2	iii	iii	X
ejpam-4624	48	3	)	)	PUNCT
ejpam-4624	48	4	ct	ct	NOUN
ejpam-4624	48	5	,	,	PUNCT
ejpam-4624	48	6	t	t	NOUN
ejpam-4624	48	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	48	8	,	,	PUNCT
ejpam-4624	48	9	r	r	NOUN
ejpam-4624	48	10	,	,	PUNCT
ejpam-4624	48	11	s	s	NOUN
ejpam-4624	48	12	)	)	PUNCT
ejpam-4624	48	13	∧	∧	PROPN
ejpam-4624	48	14	ct	ct	PROPN
ejpam-4624	48	15	,	,	PUNCT
ejpam-4624	48	16	t	t	PROPN
ejpam-4624	48	17	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	48	18	,	,	PUNCT
ejpam-4624	48	19	r	r	NOUN
ejpam-4624	48	20	,	,	PUNCT
ejpam-4624	48	21	s	s	PART
ejpam-4624	48	22	)	)	PUNCT
ejpam-4624	48	23	=	=	SYM
ejpam-4624	48	24	ct	ct	PROPN
ejpam-4624	48	25	,	,	PUNCT
ejpam-4624	48	26	t	t	PROPN
ejpam-4624	48	27	∗(ρ	∗(ρ	PROPN
ejpam-4624	48	28	∧	∧	PROPN
ejpam-4624	48	29	ϕ	ϕ	PROPN
ejpam-4624	48	30	,	,	PUNCT
ejpam-4624	48	31	r	r	NOUN
ejpam-4624	48	32	,	,	PUNCT
ejpam-4624	48	33	s	s	NOUN
ejpam-4624	48	34	)	)	PUNCT
ejpam-4624	48	35	.	.	PUNCT
ejpam-4624	49	1	(	(	PUNCT
ejpam-4624	49	2	iv	iv	X
ejpam-4624	49	3	)	)	PUNCT
ejpam-4624	49	4	ct	ct	PROPN
ejpam-4624	49	5	,	,	PUNCT
ejpam-4624	49	6	t	t	NOUN
ejpam-4624	49	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	49	8	,	,	PUNCT
ejpam-4624	49	9	r	r	NOUN
ejpam-4624	49	10	,	,	PUNCT
ejpam-4624	49	11	s	s	NOUN
ejpam-4624	49	12	)	)	PUNCT
ejpam-4624	49	13	≤	≤	NOUN
ejpam-4624	49	14	ct	ct	NUM
ejpam-4624	49	15	,	,	PUNCT
ejpam-4624	49	16	t	t	NOUN
ejpam-4624	49	17	∗(ρ	∗(ρ	NOUN
ejpam-4624	49	18	,	,	PUNCT
ejpam-4624	49	19	r1	r1	NOUN
ejpam-4624	49	20	,	,	PUNCT
ejpam-4624	49	21	s1	s1	NOUN
ejpam-4624	49	22	)	)	PUNCT
ejpam-4624	49	23	,	,	PUNCT
ejpam-4624	49	24	if	if	SCONJ
ejpam-4624	49	25	r	r	NOUN
ejpam-4624	49	26	≤	≤	PUNCT
ejpam-4624	49	27	r1	r1	NOUN
ejpam-4624	49	28	and	and	CCONJ
ejpam-4624	49	29	s	s	NOUN
ejpam-4624	49	30	≥	≥	NOUN
ejpam-4624	49	31	s1	s1	NOUN
ejpam-4624	49	32	.	.	PUNCT
ejpam-4624	50	1	w.	w.	PROPN
ejpam-4624	50	2	f.	f.	PROPN
ejpam-4624	50	3	al	al	PROPN
ejpam-4624	50	4	-	-	PUNCT
ejpam-4624	50	5	omeri	omeri	ADJ
ejpam-4624	50	6	/	/	SYM
ejpam-4624	50	7	eur	eur	PROPN
ejpam-4624	50	8	.	.	PUNCT
ejpam-4624	51	1	j.	j.	PROPN
ejpam-4624	51	2	pure	pure	PROPN
ejpam-4624	51	3	appl	appl	PROPN
ejpam-4624	51	4	.	.	PROPN
ejpam-4624	51	5	math	math	PROPN
ejpam-4624	51	6	,	,	PUNCT
ejpam-4624	51	7	18	18	NUM
ejpam-4624	51	8	(	(	PUNCT
ejpam-4624	51	9	2	2	NUM
ejpam-4624	51	10	)	)	PUNCT
ejpam-4624	51	11	(	(	PUNCT
ejpam-4624	51	12	2025	2025	NUM
ejpam-4624	51	13	)	)	PUNCT
ejpam-4624	51	14	,	,	PUNCT
ejpam-4624	51	15	4624	4624	NUM
ejpam-4624	51	16	3	3	NUM
ejpam-4624	51	17	of	of	ADP
ejpam-4624	51	18	15	15	NUM
ejpam-4624	51	19	(	(	PUNCT
ejpam-4624	51	20	v	v	NOUN
ejpam-4624	51	21	)	)	PUNCT
ejpam-4624	51	22	ct	ct	PROPN
ejpam-4624	51	23	,	,	PUNCT
ejpam-4624	51	24	t	t	PROPN
ejpam-4624	51	25	∗(ct	∗(ct	PROPN
ejpam-4624	51	26	,	,	PUNCT
ejpam-4624	51	27	t	t	NOUN
ejpam-4624	51	28	∗(ρ	∗(ρ	NOUN
ejpam-4624	51	29	,	,	PUNCT
ejpam-4624	51	30	r	r	NOUN
ejpam-4624	51	31	,	,	PUNCT
ejpam-4624	51	32	s	s	PART
ejpam-4624	51	33	)	)	PUNCT
ejpam-4624	51	34	,	,	PUNCT
ejpam-4624	51	35	r	r	NOUN
ejpam-4624	51	36	,	,	PUNCT
ejpam-4624	51	37	s	s	PART
ejpam-4624	51	38	)	)	PUNCT
ejpam-4624	51	39	=	=	SYM
ejpam-4624	51	40	ct	ct	PROPN
ejpam-4624	51	41	,	,	PUNCT
ejpam-4624	51	42	t	t	NOUN
ejpam-4624	51	43	∗(ρ	∗(ρ	NOUN
ejpam-4624	51	44	,	,	PUNCT
ejpam-4624	51	45	r	r	NOUN
ejpam-4624	51	46	,	,	PUNCT
ejpam-4624	51	47	s	s	PART
ejpam-4624	51	48	)	)	PUNCT
ejpam-4624	51	49	.	.	PUNCT
ejpam-4624	52	1	theorem	theorem	VERB
ejpam-4624	52	2	1.3	1.3	NUM
ejpam-4624	52	3	.	.	PUNCT
ejpam-4624	53	1	(	(	PUNCT
ejpam-4624	53	2	see	see	VERB
ejpam-4624	53	3	[	[	X
ejpam-4624	53	4	12	12	NUM
ejpam-4624	53	5	-	-	SYM
ejpam-4624	53	6	14	14	NUM
ejpam-4624	53	7	]	]	PUNCT
ejpam-4624	53	8	)	)	PUNCT
ejpam-4624	53	9	let	let	VERB
ejpam-4624	53	10	(	(	PUNCT
ejpam-4624	53	11	x	x	X
ejpam-4624	53	12	,	,	PUNCT
ejpam-4624	53	13	t	t	PROPN
ejpam-4624	53	14	,	,	PUNCT
ejpam-4624	53	15	t	t	PROPN
ejpam-4624	53	16	∗	∗	NOUN
ejpam-4624	53	17	)	)	PUNCT
ejpam-4624	53	18	be	be	AUX
ejpam-4624	53	19	an	an	DET
ejpam-4624	53	20	dfts	dft	NOUN
ejpam-4624	53	21	.	.	PUNCT
ejpam-4624	54	1	then	then	ADV
ejpam-4624	54	2	for	for	ADP
ejpam-4624	54	3	each	each	DET
ejpam-4624	54	4	r	r	NOUN
ejpam-4624	54	5	∈	∈	PROPN
ejpam-4624	54	6	i0	i0	PROPN
ejpam-4624	54	7	,	,	PUNCT
ejpam-4624	54	8	s	s	PROPN
ejpam-4624	54	9	∈	∈	PROPN
ejpam-4624	54	10	i1	i1	NOUN
ejpam-4624	54	11	,	,	PUNCT
ejpam-4624	54	12	and	and	CCONJ
ejpam-4624	54	13	ρ	ρ	PROPN
ejpam-4624	54	14	∈	∈	PROPN
ejpam-4624	54	15	ix	ix	ADV
ejpam-4624	54	16	,	,	PUNCT
ejpam-4624	54	17	we	we	PRON
ejpam-4624	54	18	define	define	VERB
ejpam-4624	54	19	an	an	DET
ejpam-4624	54	20	operator	operator	NOUN
ejpam-4624	54	21	it	it	PRON
ejpam-4624	54	22	,	,	PUNCT
ejpam-4624	54	23	t	t	PROPN
ejpam-4624	54	24	∗	∗	NOUN
ejpam-4624	54	25	:	:	PUNCT
ejpam-4624	54	26	ix	ix	PROPN
ejpam-4624	54	27	×	×	PROPN
ejpam-4624	54	28	i1	i1	PROPN
ejpam-4624	54	29	×	×	PROPN
ejpam-4624	54	30	i0	i0	PROPN
ejpam-4624	54	31	−→	−→	NOUN
ejpam-4624	54	32	ix	ix	ADV
ejpam-4624	54	33	as	as	SCONJ
ejpam-4624	54	34	follows	follow	VERB
ejpam-4624	54	35	:	:	PUNCT
ejpam-4624	54	36	it	it	PRON
ejpam-4624	54	37	,	,	PUNCT
ejpam-4624	54	38	t	t	NOUN
ejpam-4624	54	39	∗(ρ	∗(ρ	NOUN
ejpam-4624	54	40	,	,	PUNCT
ejpam-4624	54	41	r	r	NOUN
ejpam-4624	54	42	,	,	PUNCT
ejpam-4624	54	43	s	s	PART
ejpam-4624	54	44	)	)	PUNCT
ejpam-4624	54	45	=	=	SYM
ejpam-4624	54	46	∨	∨	X
ejpam-4624	54	47	{	{	PUNCT
ejpam-4624	54	48	ϕ	ϕ	NOUN
ejpam-4624	54	49	∈	∈	PROPN
ejpam-4624	54	50	ix	ix	X
ejpam-4624	54	51	:	:	PUNCT
ejpam-4624	54	52	ϕ	ϕ	PROPN
ejpam-4624	54	53	≤	≤	PROPN
ejpam-4624	54	54	ρ	ρ	PROPN
ejpam-4624	54	55	,	,	PUNCT
ejpam-4624	54	56	t	t	PROPN
ejpam-4624	54	57	(	(	PUNCT
ejpam-4624	54	58	ϕ	ϕ	NOUN
ejpam-4624	54	59	)	)	PUNCT
ejpam-4624	54	60	≥	≥	NOUN
ejpam-4624	54	61	r	r	NOUN
ejpam-4624	54	62	,	,	PUNCT
ejpam-4624	54	63	t	t	NOUN
ejpam-4624	54	64	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	54	65	)	)	PUNCT
ejpam-4624	54	66	≤	≤	PROPN
ejpam-4624	54	67	s	s	PART
ejpam-4624	54	68	}	}	PUNCT
ejpam-4624	54	69	.	.	PUNCT
ejpam-4624	55	1	for	for	ADP
ejpam-4624	55	2	each	each	DET
ejpam-4624	55	3	ρ	ρ	NOUN
ejpam-4624	55	4	,	,	PUNCT
ejpam-4624	55	5	ϕ	ϕ	PROPN
ejpam-4624	55	6	∈	∈	PROPN
ejpam-4624	55	7	ix	ix	X
ejpam-4624	55	8	,	,	PUNCT
ejpam-4624	55	9	r	r	NOUN
ejpam-4624	55	10	,	,	PUNCT
ejpam-4624	55	11	r1	r1	PROPN
ejpam-4624	55	12	∈	∈	PROPN
ejpam-4624	55	13	i0	i0	PROPN
ejpam-4624	55	14	and	and	CCONJ
ejpam-4624	55	15	s	s	PROPN
ejpam-4624	55	16	,	,	PUNCT
ejpam-4624	55	17	s1	s1	PROPN
ejpam-4624	55	18	∈	∈	PROPN
ejpam-4624	55	19	i1	i1	PROPN
ejpam-4624	55	20	,	,	PUNCT
ejpam-4624	55	21	the	the	DET
ejpam-4624	55	22	operator	operator	NOUN
ejpam-4624	55	23	it	it	PRON
ejpam-4624	55	24	,	,	PUNCT
ejpam-4624	55	25	t	t	PROPN
ejpam-4624	55	26	∗	∗	NOUN
ejpam-4624	55	27	satisfies	satisfy	VERB
ejpam-4624	55	28	the	the	DET
ejpam-4624	55	29	following	following	ADJ
ejpam-4624	55	30	statements	statement	NOUN
ejpam-4624	55	31	:	:	PUNCT
ejpam-4624	55	32	(	(	PUNCT
ejpam-4624	55	33	i	i	NOUN
ejpam-4624	55	34	)	)	PUNCT
ejpam-4624	55	35	it	it	PRON
ejpam-4624	55	36	,	,	PUNCT
ejpam-4624	55	37	t	t	PROPN
ejpam-4624	55	38	∗(1−	∗(1−	PROPN
ejpam-4624	55	39	ρ	ρ	PROPN
ejpam-4624	55	40	,	,	PUNCT
ejpam-4624	55	41	r	r	NOUN
ejpam-4624	55	42	,	,	PUNCT
ejpam-4624	55	43	s	s	NOUN
ejpam-4624	55	44	)	)	PUNCT
ejpam-4624	55	45	=	=	SYM
ejpam-4624	56	1	1−	1−	NUM
ejpam-4624	56	2	ct	ct	NUM
ejpam-4624	56	3	,	,	PUNCT
ejpam-4624	56	4	t	t	NOUN
ejpam-4624	56	5	∗(ρ	∗(ρ	NOUN
ejpam-4624	56	6	,	,	PUNCT
ejpam-4624	56	7	r	r	NOUN
ejpam-4624	56	8	,	,	PUNCT
ejpam-4624	56	9	s	s	NOUN
ejpam-4624	56	10	)	)	PUNCT
ejpam-4624	56	11	.	.	PUNCT
ejpam-4624	57	1	(	(	PUNCT
ejpam-4624	57	2	ii	ii	X
ejpam-4624	57	3	)	)	PUNCT
ejpam-4624	57	4	it	it	PRON
ejpam-4624	57	5	,	,	PUNCT
ejpam-4624	57	6	t	t	PROPN
ejpam-4624	57	7	∗(1	∗(1	PROPN
ejpam-4624	57	8	,	,	PUNCT
ejpam-4624	57	9	r	r	NOUN
ejpam-4624	57	10	,	,	PUNCT
ejpam-4624	57	11	s	s	PART
ejpam-4624	57	12	)	)	PUNCT
ejpam-4624	57	13	=	=	SYM
ejpam-4624	57	14	1	1	X
ejpam-4624	57	15	.	.	PUNCT
ejpam-4624	57	16	(	(	PUNCT
ejpam-4624	57	17	iii	iii	X
ejpam-4624	57	18	)	)	PUNCT
ejpam-4624	57	19	it	it	PRON
ejpam-4624	57	20	,	,	PUNCT
ejpam-4624	57	21	t	t	NOUN
ejpam-4624	57	22	∗(ρ	∗(ρ	NOUN
ejpam-4624	57	23	,	,	PUNCT
ejpam-4624	57	24	r	r	NOUN
ejpam-4624	57	25	,	,	PUNCT
ejpam-4624	57	26	s	s	NOUN
ejpam-4624	57	27	)	)	PUNCT
ejpam-4624	57	28	≤	≤	NUM
ejpam-4624	57	29	ρ	ρ	NOUN
ejpam-4624	57	30	.	.	PUNCT
ejpam-4624	58	1	(	(	PUNCT
ejpam-4624	58	2	iv	iv	X
ejpam-4624	58	3	)	)	PUNCT
ejpam-4624	58	4	it	it	PRON
ejpam-4624	58	5	,	,	PUNCT
ejpam-4624	58	6	t	t	NOUN
ejpam-4624	58	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	58	8	,	,	PUNCT
ejpam-4624	58	9	r	r	NOUN
ejpam-4624	58	10	,	,	PUNCT
ejpam-4624	58	11	s	s	PART
ejpam-4624	58	12	)	)	PUNCT
ejpam-4624	58	13	∨	∨	NUM
ejpam-4624	58	14	it	it	PRON
ejpam-4624	58	15	,	,	PUNCT
ejpam-4624	58	16	t	t	PROPN
ejpam-4624	58	17	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	58	18	,	,	PUNCT
ejpam-4624	58	19	r	r	NOUN
ejpam-4624	58	20	,	,	PUNCT
ejpam-4624	58	21	s	s	PART
ejpam-4624	58	22	)	)	PUNCT
ejpam-4624	58	23	=	=	VERB
ejpam-4624	58	24	it	it	PRON
ejpam-4624	58	25	,	,	PUNCT
ejpam-4624	58	26	t	t	PROPN
ejpam-4624	58	27	∗(ρ	∗(ρ	PROPN
ejpam-4624	58	28	∨	∨	NUM
ejpam-4624	58	29	ϕ	ϕ	PROPN
ejpam-4624	58	30	,	,	PUNCT
ejpam-4624	58	31	r	r	NOUN
ejpam-4624	58	32	,	,	PUNCT
ejpam-4624	58	33	s	s	NOUN
ejpam-4624	58	34	)	)	PUNCT
ejpam-4624	58	35	.	.	PUNCT
ejpam-4624	59	1	(	(	PUNCT
ejpam-4624	59	2	v	v	X
ejpam-4624	59	3	)	)	PUNCT
ejpam-4624	59	4	it	it	PRON
ejpam-4624	59	5	,	,	PUNCT
ejpam-4624	59	6	t	t	PROPN
ejpam-4624	59	7	∗(ρ	∗(ρ	PROPN
ejpam-4624	59	8	∨	∨	NUM
ejpam-4624	59	9	ϕ	ϕ	PROPN
ejpam-4624	59	10	,	,	PUNCT
ejpam-4624	59	11	r	r	NOUN
ejpam-4624	59	12	,	,	PUNCT
ejpam-4624	59	13	s	s	PART
ejpam-4624	59	14	)	)	PUNCT
ejpam-4624	59	15	≥	≥	NOUN
ejpam-4624	59	16	it	it	PRON
ejpam-4624	59	17	,	,	PUNCT
ejpam-4624	59	18	t	t	PROPN
ejpam-4624	59	19	∗(ρ	∗(ρ	PROPN
ejpam-4624	59	20	∨	∨	NUM
ejpam-4624	59	21	ϕ	ϕ	PROPN
ejpam-4624	59	22	,	,	PUNCT
ejpam-4624	59	23	r1	r1	NOUN
ejpam-4624	59	24	,	,	PUNCT
ejpam-4624	59	25	s1	s1	NOUN
ejpam-4624	59	26	)	)	PUNCT
ejpam-4624	59	27	if	if	SCONJ
ejpam-4624	59	28	r	r	NOUN
ejpam-4624	59	29	≤	≤	PUNCT
ejpam-4624	59	30	r1	r1	NOUN
ejpam-4624	59	31	and	and	CCONJ
ejpam-4624	59	32	s	s	NOUN
ejpam-4624	59	33	≥	≥	NOUN
ejpam-4624	59	34	s1	s1	NOUN
ejpam-4624	59	35	.	.	PUNCT
ejpam-4624	60	1	(	(	PUNCT
ejpam-4624	60	2	vi	vi	X
ejpam-4624	60	3	)	)	PUNCT
ejpam-4624	60	4	it	it	PRON
ejpam-4624	60	5	,	,	PUNCT
ejpam-4624	60	6	t	t	PROPN
ejpam-4624	60	7	∗(it	∗(it	VERB
ejpam-4624	60	8	,	,	PUNCT
ejpam-4624	60	9	t	t	NOUN
ejpam-4624	60	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	60	11	,	,	PUNCT
ejpam-4624	60	12	r	r	NOUN
ejpam-4624	60	13	,	,	PUNCT
ejpam-4624	60	14	s	s	PART
ejpam-4624	60	15	)	)	PUNCT
ejpam-4624	60	16	,	,	PUNCT
ejpam-4624	60	17	r	r	NOUN
ejpam-4624	60	18	,	,	PUNCT
ejpam-4624	60	19	s	s	PART
ejpam-4624	60	20	)	)	PUNCT
ejpam-4624	61	1	=	=	VERB
ejpam-4624	61	2	it	it	PRON
ejpam-4624	61	3	,	,	PUNCT
ejpam-4624	61	4	t	t	NOUN
ejpam-4624	61	5	∗(ρ	∗(ρ	NOUN
ejpam-4624	61	6	,	,	PUNCT
ejpam-4624	61	7	r	r	NOUN
ejpam-4624	61	8	,	,	PUNCT
ejpam-4624	61	9	s	s	NOUN
ejpam-4624	61	10	)	)	PUNCT
ejpam-4624	61	11	.	.	PUNCT
ejpam-4624	62	1	(	(	PUNCT
ejpam-4624	62	2	vii	vii	PROPN
ejpam-4624	62	3	)	)	PUNCT
ejpam-4624	62	4	it	it	PRON
ejpam-4624	62	5	,	,	PUNCT
ejpam-4624	62	6	t	t	PROPN
ejpam-4624	62	7	∗(ct	∗(ct	NOUN
ejpam-4624	62	8	,	,	PUNCT
ejpam-4624	62	9	t	t	NOUN
ejpam-4624	62	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	62	11	,	,	PUNCT
ejpam-4624	62	12	r	r	NOUN
ejpam-4624	62	13	,	,	PUNCT
ejpam-4624	62	14	s	s	PART
ejpam-4624	62	15	)	)	PUNCT
ejpam-4624	62	16	,	,	PUNCT
ejpam-4624	62	17	r	r	NOUN
ejpam-4624	62	18	,	,	PUNCT
ejpam-4624	62	19	s	s	NOUN
ejpam-4624	62	20	)	)	PUNCT
ejpam-4624	62	21	=	=	SYM
ejpam-4624	62	22	ρ	ρ	PROPN
ejpam-4624	62	23	,	,	PUNCT
ejpam-4624	62	24	then	then	ADV
ejpam-4624	62	25	ct	ct	PROPN
ejpam-4624	62	26	,	,	PUNCT
ejpam-4624	62	27	t	t	PROPN
ejpam-4624	62	28	∗(it	∗(it	NUM
ejpam-4624	62	29	,	,	PUNCT
ejpam-4624	62	30	t	t	PROPN
ejpam-4624	62	31	∗(1−	∗(1−	PROPN
ejpam-4624	62	32	ρ	ρ	PROPN
ejpam-4624	62	33	,	,	PUNCT
ejpam-4624	62	34	r	r	NOUN
ejpam-4624	62	35	,	,	PUNCT
ejpam-4624	62	36	s	s	PART
ejpam-4624	62	37	)	)	PUNCT
ejpam-4624	62	38	,	,	PUNCT
ejpam-4624	62	39	r	r	NOUN
ejpam-4624	62	40	,	,	PUNCT
ejpam-4624	62	41	s	s	NOUN
ejpam-4624	62	42	)	)	PUNCT
ejpam-4624	62	43	=	=	SYM
ejpam-4624	62	44	1−	1−	NUM
ejpam-4624	62	45	ρ	ρ	NOUN
ejpam-4624	62	46	.	.	PUNCT
ejpam-4624	63	1	definition	definition	NOUN
ejpam-4624	63	2	1.4	1.4	NUM
ejpam-4624	63	3	.	.	PUNCT
ejpam-4624	64	1	[	[	X
ejpam-4624	64	2	16	16	NUM
ejpam-4624	64	3	]	]	X
ejpam-4624	64	4	let	let	VERB
ejpam-4624	64	5	(	(	PUNCT
ejpam-4624	64	6	x	x	X
ejpam-4624	64	7	,	,	PUNCT
ejpam-4624	64	8	t	t	PROPN
ejpam-4624	64	9	,	,	PUNCT
ejpam-4624	64	10	t	t	PROPN
ejpam-4624	64	11	∗	∗	NOUN
ejpam-4624	64	12	)	)	PUNCT
ejpam-4624	64	13	be	be	VERB
ejpam-4624	64	14	an	an	DET
ejpam-4624	64	15	dfts	dft	NOUN
ejpam-4624	64	16	.	.	PUNCT
ejpam-4624	65	1	ρ	ρ	PROPN
ejpam-4624	65	2	∈	∈	PROPN
ejpam-4624	65	3	ix	ix	ADV
ejpam-4624	65	4	,	,	PUNCT
ejpam-4624	65	5	xi	xi	PROPN
ejpam-4624	65	6	∈	∈	PROPN
ejpam-4624	65	7	fp	fp	PROPN
ejpam-4624	65	8	(	(	PUNCT
ejpam-4624	65	9	x	x	X
ejpam-4624	65	10	)	)	PUNCT
ejpam-4624	65	11	,	,	PUNCT
ejpam-4624	65	12	r	r	PROPN
ejpam-4624	65	13	∈	∈	PROPN
ejpam-4624	65	14	i0	i0	PROPN
ejpam-4624	65	15	,	,	PUNCT
ejpam-4624	65	16	s	s	PROPN
ejpam-4624	65	17	∈	∈	PROPN
ejpam-4624	65	18	i1	i1	PROPN
ejpam-4624	65	19	,	,	PUNCT
ejpam-4624	65	20	a	a	DET
ejpam-4624	65	21	fuzzy	fuzzy	ADJ
ejpam-4624	65	22	set	set	VERB
ejpam-4624	65	23	ρ	ρ	PROPN
ejpam-4624	65	24	is	be	AUX
ejpam-4624	65	25	called	call	VERB
ejpam-4624	65	26	(	(	PUNCT
ejpam-4624	65	27	r	r	NOUN
ejpam-4624	65	28	,	,	PUNCT
ejpam-4624	65	29	s)-q	s)-q	NOUN
ejpam-4624	65	30	-	-	PUNCT
ejpam-4624	65	31	neighborhood	neighborhood	NOUN
ejpam-4624	65	32	of	of	ADP
ejpam-4624	65	33	xi	xi	PROPN
ejpam-4624	65	34	,	,	PUNCT
ejpam-4624	65	35	if	if	SCONJ
ejpam-4624	65	36	t	t	PROPN
ejpam-4624	65	37	(	(	PUNCT
ejpam-4624	65	38	ρ	ρ	PROPN
ejpam-4624	65	39	)	)	PUNCT
ejpam-4624	65	40	≥	≥	NOUN
ejpam-4624	65	41	r	r	NOUN
ejpam-4624	65	42	,	,	PUNCT
ejpam-4624	65	43	t	t	NOUN
ejpam-4624	65	44	∗(ρ	∗(ρ	NOUN
ejpam-4624	65	45	)	)	PUNCT
ejpam-4624	65	46	≤	≤	NOUN
ejpam-4624	65	47	s	s	PROPN
ejpam-4624	65	48	,	,	PUNCT
ejpam-4624	65	49	and	and	CCONJ
ejpam-4624	65	50	xiqρ	xiqρ	PROPN
ejpam-4624	65	51	.	.	PUNCT
ejpam-4624	66	1	definition	definition	NOUN
ejpam-4624	66	2	1.5	1.5	NUM
ejpam-4624	66	3	.	.	PUNCT
ejpam-4624	67	1	[	[	X
ejpam-4624	67	2	17	17	NUM
ejpam-4624	67	3	]	]	X
ejpam-4624	67	4	let	let	VERB
ejpam-4624	67	5	(	(	PUNCT
ejpam-4624	67	6	x	x	X
ejpam-4624	67	7	,	,	PUNCT
ejpam-4624	67	8	t	t	PROPN
ejpam-4624	67	9	,	,	PUNCT
ejpam-4624	67	10	t	t	PROPN
ejpam-4624	67	11	∗	∗	NOUN
ejpam-4624	67	12	)	)	PUNCT
ejpam-4624	67	13	be	be	AUX
ejpam-4624	67	14	an	an	DET
ejpam-4624	67	15	dfts	dft	NOUN
ejpam-4624	67	16	.	.	PUNCT
ejpam-4624	68	1	then	then	ADV
ejpam-4624	68	2	,	,	PUNCT
ejpam-4624	68	3	for	for	ADP
ejpam-4624	68	4	each	each	DET
ejpam-4624	68	5	r	r	NOUN
ejpam-4624	68	6	∈	∈	PROPN
ejpam-4624	68	7	i0	i0	PROPN
ejpam-4624	68	8	,	,	PUNCT
ejpam-4624	68	9	s	s	PROPN
ejpam-4624	68	10	∈	∈	PROPN
ejpam-4624	68	11	i1	i1	PROPN
ejpam-4624	68	12	and	and	CCONJ
ejpam-4624	68	13	ρ	ρ	PROPN
ejpam-4624	68	14	∈	∈	PROPN
ejpam-4624	68	15	ix	ix	ADV
ejpam-4624	68	16	is	be	AUX
ejpam-4624	68	17	called	call	VERB
ejpam-4624	68	18	(	(	PUNCT
ejpam-4624	68	19	r	r	NOUN
ejpam-4624	68	20	,	,	PUNCT
ejpam-4624	68	21	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	68	22	regular	regular	ADJ
ejpam-4624	68	23	open	open	ADJ
ejpam-4624	68	24	(	(	PUNCT
ejpam-4624	68	25	(	(	PUNCT
ejpam-4624	68	26	r	r	NOUN
ejpam-4624	68	27	,	,	PUNCT
ejpam-4624	68	28	s)-fro	s)-fro	NOUN
ejpam-4624	68	29	,	,	PUNCT
ejpam-4624	68	30	for	for	ADP
ejpam-4624	68	31	short	short	ADJ
ejpam-4624	68	32	)	)	PUNCT
ejpam-4624	68	33	if	if	SCONJ
ejpam-4624	68	34	ρ	ρ	PROPN
ejpam-4624	68	35	=	=	PUNCT
ejpam-4624	68	36	it	it	PRON
ejpam-4624	68	37	,	,	PUNCT
ejpam-4624	68	38	t	t	PROPN
ejpam-4624	68	39	∗(ct	∗(ct	NOUN
ejpam-4624	68	40	,	,	PUNCT
ejpam-4624	68	41	t	t	NOUN
ejpam-4624	68	42	∗(ρ	∗(ρ	NOUN
ejpam-4624	68	43	,	,	PUNCT
ejpam-4624	68	44	r	r	NOUN
ejpam-4624	68	45	,	,	PUNCT
ejpam-4624	68	46	s	s	PART
ejpam-4624	68	47	)	)	PUNCT
ejpam-4624	68	48	,	,	PUNCT
ejpam-4624	68	49	r	r	NOUN
ejpam-4624	68	50	,	,	PUNCT
ejpam-4624	68	51	s	s	NOUN
ejpam-4624	68	52	)	)	PUNCT
ejpam-4624	68	53	.	.	PUNCT
ejpam-4624	69	1	a	a	DET
ejpam-4624	69	2	fuzzy	fuzzy	ADJ
ejpam-4624	69	3	set	set	VERB
ejpam-4624	69	4	ρ	ρ	PROPN
ejpam-4624	69	5	is	be	AUX
ejpam-4624	69	6	called	call	VERB
ejpam-4624	69	7	a	a	DET
ejpam-4624	69	8	(	(	PUNCT
ejpam-4624	69	9	r	r	NOUN
ejpam-4624	69	10	,	,	PUNCT
ejpam-4624	69	11	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	69	12	regular	regular	ADJ
ejpam-4624	69	13	closed	closed	ADJ
ejpam-4624	69	14	(	(	PUNCT
ejpam-4624	69	15	(	(	PUNCT
ejpam-4624	69	16	r	r	NOUN
ejpam-4624	69	17	,	,	PUNCT
ejpam-4624	69	18	s)-frc	s)-frc	NOUN
ejpam-4624	69	19	,	,	PUNCT
ejpam-4624	69	20	for	for	ADP
ejpam-4624	69	21	short	short	ADJ
ejpam-4624	69	22	)	)	PUNCT
ejpam-4624	69	23	iff	iff	VERB
ejpam-4624	69	24	1	1	NUM
ejpam-4624	69	25	−	−	PROPN
ejpam-4624	70	1	ρ	ρ	NOUN
ejpam-4624	71	1	is	be	AUX
ejpam-4624	71	2	a	a	DET
ejpam-4624	71	3	(	(	PUNCT
ejpam-4624	71	4	r	r	NOUN
ejpam-4624	71	5	,	,	PUNCT
ejpam-4624	71	6	s)-fro	s)-fro	NOUN
ejpam-4624	71	7	set	set	NOUN
ejpam-4624	71	8	.	.	PUNCT
ejpam-4624	72	1	2	2	X
ejpam-4624	72	2	.	.	X
ejpam-4624	72	3	(	(	PUNCT
ejpam-4624	72	4	r	r	NOUN
ejpam-4624	72	5	,	,	PUNCT
ejpam-4624	72	6	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	72	7	δ	δ	PROPN
ejpam-4624	72	8	-	-	PUNCT
ejpam-4624	72	9	closed	close	VERB
ejpam-4624	72	10	sets	set	NOUN
ejpam-4624	72	11	definition	definition	NOUN
ejpam-4624	72	12	2.1	2.1	NUM
ejpam-4624	72	13	.	.	PUNCT
ejpam-4624	73	1	let	let	AUX
ejpam-4624	73	2	(	(	PUNCT
ejpam-4624	73	3	x	x	X
ejpam-4624	73	4	,	,	PUNCT
ejpam-4624	73	5	t	t	PROPN
ejpam-4624	73	6	,	,	PUNCT
ejpam-4624	73	7	t	t	PROPN
ejpam-4624	73	8	∗	∗	NOUN
ejpam-4624	73	9	)	)	PUNCT
ejpam-4624	73	10	be	be	VERB
ejpam-4624	73	11	a	a	DET
ejpam-4624	73	12	double	double	ADJ
ejpam-4624	73	13	fuzzy	fuzzy	ADJ
ejpam-4624	73	14	topological	topological	ADJ
ejpam-4624	73	15	spaces	space	NOUN
ejpam-4624	73	16	.	.	PUNCT
ejpam-4624	74	1	then	then	ADV
ejpam-4624	74	2	for	for	ADP
ejpam-4624	74	3	each	each	DET
ejpam-4624	74	4	r	r	NOUN
ejpam-4624	74	5	∈	∈	PROPN
ejpam-4624	74	6	i0	i0	PROPN
ejpam-4624	74	7	,	,	PUNCT
ejpam-4624	74	8	s	s	PROPN
ejpam-4624	74	9	∈	∈	PROPN
ejpam-4624	74	10	i1	i1	NOUN
ejpam-4624	74	11	,	,	PUNCT
ejpam-4624	74	12	and	and	CCONJ
ejpam-4624	74	13	ρ	ρ	PROPN
ejpam-4624	74	14	∈	∈	PROPN
ejpam-4624	74	15	ix	ix	X
ejpam-4624	74	16	,	,	PUNCT
ejpam-4624	74	17	x(α	x(α	PROPN
ejpam-4624	74	18	,	,	PUNCT
ejpam-4624	74	19	β	β	X
ejpam-4624	74	20	)	)	PUNCT
ejpam-4624	74	21	∈	∈	PROPN
ejpam-4624	74	22	fp	fp	X
ejpam-4624	74	23	(	(	PUNCT
ejpam-4624	74	24	x	x	X
ejpam-4624	74	25	)	)	PUNCT
ejpam-4624	74	26	,	,	PUNCT
ejpam-4624	74	27	where	where	SCONJ
ejpam-4624	74	28	fp	fp	X
ejpam-4624	74	29	(	(	PUNCT
ejpam-4624	74	30	x	x	X
ejpam-4624	74	31	)	)	PUNCT
ejpam-4624	74	32	is	be	AUX
ejpam-4624	74	33	the	the	DET
ejpam-4624	74	34	family	family	NOUN
ejpam-4624	74	35	of	of	ADP
ejpam-4624	74	36	all	all	DET
ejpam-4624	74	37	fuzzy	fuzzy	ADJ
ejpam-4624	74	38	points	point	NOUN
ejpam-4624	74	39	in	in	ADP
ejpam-4624	74	40	x.	x.	NOUN
ejpam-4624	74	41	a	a	DET
ejpam-4624	74	42	double	double	ADJ
ejpam-4624	74	43	fuzzy	fuzzy	ADJ
ejpam-4624	74	44	point	point	NOUN
ejpam-4624	74	45	x(α	x(α	PROPN
ejpam-4624	74	46	,	,	PUNCT
ejpam-4624	74	47	β	β	X
ejpam-4624	74	48	)	)	PUNCT
ejpam-4624	74	49	is	be	AUX
ejpam-4624	74	50	said	say	VERB
ejpam-4624	74	51	to	to	PART
ejpam-4624	74	52	be	be	AUX
ejpam-4624	74	53	a	a	DET
ejpam-4624	74	54	double	double	ADJ
ejpam-4624	74	55	fuzzy	fuzzy	ADJ
ejpam-4624	74	56	δ	δ	NOUN
ejpam-4624	74	57	-	-	PUNCT
ejpam-4624	74	58	cluster	cluster	NOUN
ejpam-4624	74	59	point	point	NOUN
ejpam-4624	74	60	of	of	ADP
ejpam-4624	74	61	a	a	DET
ejpam-4624	74	62	fuzzy	fuzzy	ADJ
ejpam-4624	74	63	set	set	VERB
ejpam-4624	74	64	ρ	ρ	NOUN
ejpam-4624	74	65	in	in	ADP
ejpam-4624	74	66	an	an	DET
ejpam-4624	74	67	dfts	dft	NOUN
ejpam-4624	74	68	x	x	SYM
ejpam-4624	74	69	iff	iff	NOUN
ejpam-4624	74	70	every	every	DET
ejpam-4624	74	71	(	(	PUNCT
ejpam-4624	74	72	r	r	NOUN
ejpam-4624	74	73	,	,	PUNCT
ejpam-4624	74	74	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	74	75	regular	regular	ADJ
ejpam-4624	74	76	open	open	ADJ
ejpam-4624	74	77	set	set	NOUN
ejpam-4624	74	78	containing	contain	VERB
ejpam-4624	74	79	a	a	DET
ejpam-4624	74	80	double	double	ADJ
ejpam-4624	74	81	fuzzy	fuzzy	ADJ
ejpam-4624	74	82	point	point	NOUN
ejpam-4624	74	83	x(α	x(α	PROPN
ejpam-4624	74	84	,	,	PUNCT
ejpam-4624	74	85	β	β	X
ejpam-4624	74	86	)	)	PUNCT
ejpam-4624	74	87	(	(	PUNCT
ejpam-4624	74	88	having	have	VERB
ejpam-4624	74	89	same	same	ADJ
ejpam-4624	74	90	support	support	NOUN
ejpam-4624	74	91	as	as	ADP
ejpam-4624	74	92	x(α	x(α	PROPN
ejpam-4624	74	93	,	,	PUNCT
ejpam-4624	74	94	β	β	NOUN
ejpam-4624	74	95	)	)	PUNCT
ejpam-4624	74	96	)	)	PUNCT
ejpam-4624	74	97	has	have	VERB
ejpam-4624	74	98	non	non	ADJ
ejpam-4624	74	99	-	-	ADJ
ejpam-4624	74	100	null	null	ADJ
ejpam-4624	74	101	intersection	intersection	NOUN
ejpam-4624	74	102	with	with	ADP
ejpam-4624	74	103	ρ	ρ	PROPN
ejpam-4624	74	104	,	,	PUNCT
ejpam-4624	74	105	or	or	CCONJ
ejpam-4624	74	106	if	if	SCONJ
ejpam-4624	74	107	for	for	ADP
ejpam-4624	74	108	every	every	DET
ejpam-4624	74	109	(	(	PUNCT
ejpam-4624	74	110	r	r	NOUN
ejpam-4624	74	111	,	,	PUNCT
ejpam-4624	74	112	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	74	113	regular	regular	ADJ
ejpam-4624	74	114	open	open	ADJ
ejpam-4624	74	115	q	q	ADJ
ejpam-4624	74	116	-	-	PUNCT
ejpam-4624	74	117	neighborhood	neighborhood	NOUN
ejpam-4624	74	118	ϕ	ϕ	NOUN
ejpam-4624	74	119	of	of	ADP
ejpam-4624	74	120	x(α	x(α	PROPN
ejpam-4624	74	121	,	,	PUNCT
ejpam-4624	74	122	β	β	X
ejpam-4624	74	123	)	)	PUNCT
ejpam-4624	74	124	is	be	AUX
ejpam-4624	74	125	q	q	ADJ
ejpam-4624	74	126	-	-	NOUN
ejpam-4624	74	127	coincident	coincident	ADJ
ejpam-4624	74	128	with	with	ADP
ejpam-4624	74	129	ρ	ρ	PROPN
ejpam-4624	74	130	,	,	PUNCT
ejpam-4624	74	131	by	by	ADP
ejpam-4624	74	132	other	other	ADJ
ejpam-4624	74	133	words	word	NOUN
ejpam-4624	74	134	it	it	PRON
ejpam-4624	74	135	,	,	PUNCT
ejpam-4624	74	136	t	t	PROPN
ejpam-4624	74	137	∗(ct	∗(ct	PROPN
ejpam-4624	74	138	,	,	PUNCT
ejpam-4624	74	139	t	t	PROPN
ejpam-4624	74	140	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	74	141	,	,	PUNCT
ejpam-4624	74	142	r	r	NOUN
ejpam-4624	74	143	,	,	PUNCT
ejpam-4624	74	144	s	s	PART
ejpam-4624	74	145	)	)	PUNCT
ejpam-4624	74	146	,	,	PUNCT
ejpam-4624	74	147	r	r	NOUN
ejpam-4624	74	148	,	,	PUNCT
ejpam-4624	74	149	s)qρ	s)qρ	PROPN
ejpam-4624	74	150	.	.	PROPN
ejpam-4624	74	151	definition	definition	NOUN
ejpam-4624	74	152	2.2	2.2	NUM
ejpam-4624	74	153	.	.	PUNCT
ejpam-4624	75	1	let	let	VERB
ejpam-4624	75	2	(	(	PUNCT
ejpam-4624	75	3	x	x	X
ejpam-4624	75	4	,	,	PUNCT
ejpam-4624	75	5	t	t	PROPN
ejpam-4624	75	6	,	,	PUNCT
ejpam-4624	75	7	t	t	PROPN
ejpam-4624	75	8	∗	∗	NOUN
ejpam-4624	75	9	)	)	PUNCT
ejpam-4624	75	10	be	be	AUX
ejpam-4624	75	11	an	an	DET
ejpam-4624	75	12	dfts	dft	NOUN
ejpam-4624	75	13	.	.	PUNCT
ejpam-4624	76	1	then	then	ADV
ejpam-4624	76	2	,	,	PUNCT
ejpam-4624	76	3	for	for	SCONJ
ejpam-4624	76	4	each	each	DET
ejpam-4624	76	5	r	r	NOUN
ejpam-4624	76	6	∈	∈	PROPN
ejpam-4624	76	7	i0	i0	PROPN
ejpam-4624	76	8	,	,	PUNCT
ejpam-4624	76	9	s	s	PROPN
ejpam-4624	76	10	∈	∈	PROPN
ejpam-4624	76	11	i1	i1	NOUN
ejpam-4624	76	12	,	,	PUNCT
ejpam-4624	76	13	and	and	CCONJ
ejpam-4624	76	14	ρ	ρ	PROPN
ejpam-4624	76	15	∈	∈	PROPN
ejpam-4624	76	16	ix	ix	X
ejpam-4624	76	17	,	,	PUNCT
ejpam-4624	76	18	where	where	SCONJ
ejpam-4624	76	19	ρ	ρ	PROPN
ejpam-4624	76	20	be	be	VERB
ejpam-4624	76	21	a	a	DET
ejpam-4624	76	22	fuzzy	fuzzy	ADJ
ejpam-4624	76	23	subset	subset	NOUN
ejpam-4624	76	24	of	of	ADP
ejpam-4624	76	25	an	an	DET
ejpam-4624	76	26	dfts	dft	NOUN
ejpam-4624	76	27	x.	x.	NOUN
ejpam-4624	76	28	let	let	VERB
ejpam-4624	76	29	ϕ	ϕ	NOUN
ejpam-4624	76	30	be	be	AUX
ejpam-4624	76	31	a	a	DET
ejpam-4624	76	32	fuzzy	fuzzy	ADJ
ejpam-4624	76	33	subset	subset	NOUN
ejpam-4624	76	34	of	of	ADP
ejpam-4624	76	35	x	x	PUNCT
ejpam-4624	76	36	satisfying	satisfy	VERB
ejpam-4624	76	37	the	the	DET
ejpam-4624	76	38	following	follow	VERB
ejpam-4624	76	39	conditions	condition	NOUN
ejpam-4624	76	40	:	:	PUNCT
ejpam-4624	76	41	(	(	PUNCT
ejpam-4624	76	42	a	a	X
ejpam-4624	76	43	)	)	PUNCT
ejpam-4624	76	44	every	every	DET
ejpam-4624	76	45	double	double	ADJ
ejpam-4624	76	46	fuzzy	fuzzy	ADJ
ejpam-4624	76	47	point	point	NOUN
ejpam-4624	76	48	x(α	x(α	PROPN
ejpam-4624	76	49	,	,	PUNCT
ejpam-4624	76	50	β	β	NOUN
ejpam-4624	76	51	)	)	PUNCT
ejpam-4624	76	52	in	in	ADP
ejpam-4624	76	53	ϕ	ϕ	PROPN
ejpam-4624	76	54	is	be	AUX
ejpam-4624	76	55	a	a	DET
ejpam-4624	76	56	double	double	ADJ
ejpam-4624	76	57	fuzzy	fuzzy	ADJ
ejpam-4624	76	58	δ	δ	NOUN
ejpam-4624	76	59	-	-	PUNCT
ejpam-4624	76	60	cluster	cluster	NOUN
ejpam-4624	76	61	point	point	NOUN
ejpam-4624	76	62	of	of	ADP
ejpam-4624	76	63	ρ	ρ	PROPN
ejpam-4624	76	64	,	,	PUNCT
ejpam-4624	76	65	(	(	PUNCT
ejpam-4624	76	66	b	b	X
ejpam-4624	76	67	)	)	PUNCT
ejpam-4624	76	68	if	if	SCONJ
ejpam-4624	76	69	ν	ν	PROPN
ejpam-4624	76	70	is	be	AUX
ejpam-4624	76	71	a	a	DET
ejpam-4624	76	72	double	double	ADJ
ejpam-4624	76	73	fuzzy	fuzzy	ADJ
ejpam-4624	76	74	set	set	NOUN
ejpam-4624	76	75	,	,	PUNCT
ejpam-4624	76	76	such	such	ADJ
ejpam-4624	76	77	that	that	SCONJ
ejpam-4624	76	78	ϕ	ϕ	PROPN
ejpam-4624	76	79	≤	≤	NUM
ejpam-4624	76	80	ν	ν	NOUN
ejpam-4624	76	81	,	,	PUNCT
ejpam-4624	76	82	then	then	ADV
ejpam-4624	76	83	there	there	PRON
ejpam-4624	76	84	is	be	VERB
ejpam-4624	76	85	a	a	DET
ejpam-4624	76	86	double	double	ADJ
ejpam-4624	76	87	fuzzy	fuzzy	ADJ
ejpam-4624	76	88	point	point	NOUN
ejpam-4624	76	89	.	.	PUNCT
ejpam-4624	77	1	x(α	x(α	PROPN
ejpam-4624	77	2	,	,	PUNCT
ejpam-4624	77	3	β	β	NOUN
ejpam-4624	77	4	)	)	PUNCT
ejpam-4624	77	5	in	in	ADP
ejpam-4624	77	6	ν	ν	NOUN
ejpam-4624	77	7	which	which	PRON
ejpam-4624	77	8	is	be	AUX
ejpam-4624	77	9	not	not	PART
ejpam-4624	77	10	a	a	DET
ejpam-4624	77	11	double	double	ADJ
ejpam-4624	77	12	fuzzy	fuzzy	ADJ
ejpam-4624	77	13	δ	δ	NOUN
ejpam-4624	77	14	-	-	PUNCT
ejpam-4624	77	15	cluster	cluster	NOUN
ejpam-4624	77	16	point	point	NOUN
ejpam-4624	77	17	of	of	ADP
ejpam-4624	77	18	ρ	ρ	PROPN
ejpam-4624	77	19	.	.	PUNCT
ejpam-4624	78	1	w.	w.	PROPN
ejpam-4624	78	2	f.	f.	PROPN
ejpam-4624	78	3	al	al	PROPN
ejpam-4624	78	4	-	-	PUNCT
ejpam-4624	78	5	omeri	omeri	ADJ
ejpam-4624	78	6	/	/	SYM
ejpam-4624	78	7	eur	eur	PROPN
ejpam-4624	78	8	.	.	PUNCT
ejpam-4624	79	1	j.	j.	PROPN
ejpam-4624	79	2	pure	pure	PROPN
ejpam-4624	79	3	appl	appl	PROPN
ejpam-4624	79	4	.	.	PROPN
ejpam-4624	79	5	math	math	PROPN
ejpam-4624	79	6	,	,	PUNCT
ejpam-4624	79	7	18	18	NUM
ejpam-4624	79	8	(	(	PUNCT
ejpam-4624	79	9	2	2	NUM
ejpam-4624	79	10	)	)	PUNCT
ejpam-4624	79	11	(	(	PUNCT
ejpam-4624	79	12	2025	2025	NUM
ejpam-4624	79	13	)	)	PUNCT
ejpam-4624	79	14	,	,	PUNCT
ejpam-4624	79	15	4624	4624	NUM
ejpam-4624	79	16	4	4	NUM
ejpam-4624	79	17	of	of	ADP
ejpam-4624	79	18	15	15	NUM
ejpam-4624	79	19	any	any	DET
ejpam-4624	79	20	double	double	ADJ
ejpam-4624	79	21	fuzzy	fuzzy	ADJ
ejpam-4624	79	22	subset	subset	NOUN
ejpam-4624	79	23	of	of	ADP
ejpam-4624	79	24	x	x	PUNCT
ejpam-4624	79	25	having	have	VERB
ejpam-4624	79	26	same	same	ADJ
ejpam-4624	79	27	support	support	NOUN
ejpam-4624	79	28	as	as	SCONJ
ejpam-4624	79	29	ϕ	ϕ	NOUN
ejpam-4624	79	30	is	be	AUX
ejpam-4624	79	31	defined	define	VERB
ejpam-4624	79	32	to	to	PART
ejpam-4624	79	33	be	be	AUX
ejpam-4624	79	34	(	(	PUNCT
ejpam-4624	79	35	r	r	NOUN
ejpam-4624	79	36	,	,	PUNCT
ejpam-4624	79	37	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	79	38	δ	δ	PROPN
ejpam-4624	79	39	-	-	PUNCT
ejpam-4624	79	40	closure	closure	NOUN
ejpam-4624	79	41	of	of	ADP
ejpam-4624	79	42	ρ	ρ	PROPN
ejpam-4624	79	43	.	.	PUNCT
ejpam-4624	80	1	definition	definition	NOUN
ejpam-4624	80	2	2.3	2.3	NUM
ejpam-4624	80	3	.	.	PUNCT
ejpam-4624	81	1	the	the	DET
ejpam-4624	81	2	set	set	NOUN
ejpam-4624	81	3	of	of	ADP
ejpam-4624	81	4	all	all	DET
ejpam-4624	81	5	double	double	ADJ
ejpam-4624	81	6	fuzzy	fuzzy	ADJ
ejpam-4624	81	7	δ	δ	NOUN
ejpam-4624	81	8	-	-	PUNCT
ejpam-4624	81	9	cluster	cluster	NOUN
ejpam-4624	81	10	points	point	NOUN
ejpam-4624	81	11	of	of	ADP
ejpam-4624	81	12	ρ	ρ	PROPN
ejpam-4624	81	13	is	be	AUX
ejpam-4624	81	14	called	call	VERB
ejpam-4624	81	15	the	the	DET
ejpam-4624	81	16	(	(	PUNCT
ejpam-4624	81	17	r	r	NOUN
ejpam-4624	81	18	,	,	PUNCT
ejpam-4624	81	19	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	81	20	δ	δ	PROPN
ejpam-4624	81	21	-	-	PUNCT
ejpam-4624	81	22	closure	closure	NOUN
ejpam-4624	81	23	of	of	ADP
ejpam-4624	81	24	ρ	ρ	NOUN
ejpam-4624	81	25	and	and	CCONJ
ejpam-4624	81	26	denoted	denote	VERB
ejpam-4624	81	27	by	by	ADP
ejpam-4624	81	28	δct	δct	NOUN
ejpam-4624	81	29	,	,	PUNCT
ejpam-4624	81	30	t	t	NOUN
ejpam-4624	81	31	∗	∗	NOUN
ejpam-4624	81	32	.	.	PUNCT
ejpam-4624	82	1	thus	thus	ADV
ejpam-4624	82	2	a	a	DET
ejpam-4624	82	3	property	property	NOUN
ejpam-4624	82	4	related	relate	VERB
ejpam-4624	82	5	with	with	ADP
ejpam-4624	82	6	the	the	DET
ejpam-4624	82	7	notation	notation	NOUN
ejpam-4624	82	8	δct	δct	NOUN
ejpam-4624	82	9	,	,	PUNCT
ejpam-4624	82	10	t	t	NOUN
ejpam-4624	82	11	∗	∗	NOUN
ejpam-4624	82	12	,	,	PUNCT
ejpam-4624	82	13	will	will	AUX
ejpam-4624	82	14	always	always	ADV
ejpam-4624	82	15	imply	imply	VERB
ejpam-4624	82	16	that	that	SCONJ
ejpam-4624	82	17	the	the	DET
ejpam-4624	82	18	property	property	NOUN
ejpam-4624	82	19	holds	hold	VERB
ejpam-4624	82	20	for	for	ADP
ejpam-4624	82	21	all	all	DET
ejpam-4624	82	22	(	(	PUNCT
ejpam-4624	82	23	r	r	NOUN
ejpam-4624	82	24	,	,	PUNCT
ejpam-4624	82	25	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	82	26	δ	δ	PROPN
ejpam-4624	82	27	-	-	PUNCT
ejpam-4624	82	28	closure	closure	NOUN
ejpam-4624	82	29	of	of	ADP
ejpam-4624	82	30	ρ	ρ	PROPN
ejpam-4624	82	31	.	.	PUNCT
ejpam-4624	83	1	a	a	DET
ejpam-4624	83	2	double	double	ADJ
ejpam-4624	83	3	fuzzy	fuzzy	ADJ
ejpam-4624	83	4	set	set	VERB
ejpam-4624	83	5	ρ	ρ	PROPN
ejpam-4624	83	6	is	be	AUX
ejpam-4624	83	7	said	say	VERB
ejpam-4624	83	8	to	to	PART
ejpam-4624	83	9	be	be	AUX
ejpam-4624	83	10	a	a	DET
ejpam-4624	83	11	(	(	PUNCT
ejpam-4624	83	12	r	r	NOUN
ejpam-4624	83	13	,	,	PUNCT
ejpam-4624	83	14	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	83	15	δ	δ	PROPN
ejpam-4624	83	16	-	-	PUNCT
ejpam-4624	83	17	closed	close	VERB
ejpam-4624	83	18	set	set	NOUN
ejpam-4624	83	19	if	if	SCONJ
ejpam-4624	83	20	ρ	ρ	NOUN
ejpam-4624	83	21	=	=	NOUN
ejpam-4624	83	22	δct	δct	NOUN
ejpam-4624	83	23	,	,	PUNCT
ejpam-4624	83	24	t	t	NOUN
ejpam-4624	83	25	∗(ρ	∗(ρ	NOUN
ejpam-4624	83	26	,	,	PUNCT
ejpam-4624	83	27	r	r	NOUN
ejpam-4624	83	28	,	,	PUNCT
ejpam-4624	83	29	s	s	NOUN
ejpam-4624	83	30	)	)	PUNCT
ejpam-4624	83	31	.	.	PUNCT
ejpam-4624	84	1	the	the	DET
ejpam-4624	84	2	complement	complement	NOUN
ejpam-4624	84	3	of	of	ADP
ejpam-4624	84	4	a	a	PRON
ejpam-4624	84	5	(	(	PUNCT
ejpam-4624	84	6	r	r	NOUN
ejpam-4624	84	7	,	,	PUNCT
ejpam-4624	84	8	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	84	9	δ	δ	PROPN
ejpam-4624	84	10	-	-	PUNCT
ejpam-4624	84	11	closed	close	VERB
ejpam-4624	84	12	set	set	NOUN
ejpam-4624	84	13	is	be	AUX
ejpam-4624	84	14	said	say	VERB
ejpam-4624	84	15	to	to	PART
ejpam-4624	84	16	be	be	AUX
ejpam-4624	84	17	a	a	DET
ejpam-4624	84	18	(	(	PUNCT
ejpam-4624	84	19	r	r	NOUN
ejpam-4624	84	20	,	,	PUNCT
ejpam-4624	84	21	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	84	22	δ	δ	PROPN
ejpam-4624	84	23	-	-	PUNCT
ejpam-4624	84	24	open	open	ADJ
ejpam-4624	84	25	set	set	NOUN
ejpam-4624	84	26	.	.	PUNCT
ejpam-4624	85	1	definition	definition	NOUN
ejpam-4624	85	2	2.4	2.4	NUM
ejpam-4624	85	3	.	.	PUNCT
ejpam-4624	86	1	let	let	AUX
ejpam-4624	86	2	(	(	PUNCT
ejpam-4624	86	3	x	x	X
ejpam-4624	86	4	,	,	PUNCT
ejpam-4624	86	5	t	t	PROPN
ejpam-4624	86	6	,	,	PUNCT
ejpam-4624	86	7	t	t	PROPN
ejpam-4624	86	8	∗	∗	NOUN
ejpam-4624	86	9	)	)	PUNCT
ejpam-4624	86	10	be	be	AUX
ejpam-4624	86	11	an	an	DET
ejpam-4624	86	12	dfts	dft	NOUN
ejpam-4624	86	13	.	.	PUNCT
ejpam-4624	87	1	then	then	ADV
ejpam-4624	87	2	,	,	PUNCT
ejpam-4624	87	3	for	for	SCONJ
ejpam-4624	87	4	each	each	DET
ejpam-4624	87	5	r	r	NOUN
ejpam-4624	87	6	∈	∈	PROPN
ejpam-4624	87	7	i0	i0	PROPN
ejpam-4624	87	8	,	,	PUNCT
ejpam-4624	87	9	s	s	PROPN
ejpam-4624	87	10	∈	∈	PROPN
ejpam-4624	87	11	i1	i1	NOUN
ejpam-4624	87	12	,	,	PUNCT
ejpam-4624	87	13	and	and	CCONJ
ejpam-4624	87	14	ρ	ρ	PROPN
ejpam-4624	87	15	∈	∈	PROPN
ejpam-4624	87	16	ix	ix	X
ejpam-4624	87	17	,	,	PUNCT
ejpam-4624	87	18	the	the	DET
ejpam-4624	87	19	δct	δct	NOUN
ejpam-4624	87	20	,	,	PUNCT
ejpam-4624	87	21	t	t	NOUN
ejpam-4624	87	22	∗	∗	NOUN
ejpam-4624	87	23	and	and	CCONJ
ejpam-4624	87	24	it	it	PRON
ejpam-4624	87	25	,	,	PUNCT
ejpam-4624	87	26	t	t	PROPN
ejpam-4624	87	27	∗	∗	NOUN
ejpam-4624	87	28	operators	operator	NOUN
ejpam-4624	87	29	are	be	AUX
ejpam-4624	87	30	define	define	ADJ
ejpam-4624	87	31	as	as	SCONJ
ejpam-4624	87	32	follows	follow	VERB
ejpam-4624	87	33	:	:	PUNCT
ejpam-4624	87	34	(	(	PUNCT
ejpam-4624	87	35	i	i	NOUN
ejpam-4624	87	36	)	)	PUNCT
ejpam-4624	87	37	δct	δct	NOUN
ejpam-4624	87	38	,	,	PUNCT
ejpam-4624	87	39	t	t	NOUN
ejpam-4624	87	40	∗(ρ	∗(ρ	NOUN
ejpam-4624	87	41	,	,	PUNCT
ejpam-4624	87	42	r	r	NOUN
ejpam-4624	87	43	,	,	PUNCT
ejpam-4624	87	44	s	s	NOUN
ejpam-4624	87	45	)	)	PUNCT
ejpam-4624	87	46	=	=	SYM
ejpam-4624	87	47	∧	∧	PROPN
ejpam-4624	87	48	{	{	PUNCT
ejpam-4624	87	49	ϕ	ϕ	NOUN
ejpam-4624	87	50	∈	∈	PROPN
ejpam-4624	87	51	ix	ix	ADP
ejpam-4624	87	52	|ρ	|ρ	ADJ
ejpam-4624	87	53	≤	≤	NUM
ejpam-4624	87	54	ϕ	ϕ	PROPN
ejpam-4624	87	55	,	,	PUNCT
ejpam-4624	87	56	ϕ	ϕ	NOUN
ejpam-4624	87	57	is	be	AUX
ejpam-4624	87	58	(	(	PUNCT
ejpam-4624	87	59	r	r	NOUN
ejpam-4624	87	60	,	,	PUNCT
ejpam-4624	87	61	s)−	s)−	PROPN
ejpam-4624	87	62	frc	frc	NOUN
ejpam-4624	87	63	}	}	PUNCT
ejpam-4624	87	64	.	.	PUNCT
ejpam-4624	88	1	(	(	PUNCT
ejpam-4624	88	2	ii	ii	NOUN
ejpam-4624	88	3	)	)	PUNCT
ejpam-4624	88	4	δit	δit	NOUN
ejpam-4624	88	5	,	,	PUNCT
ejpam-4624	88	6	t	t	NOUN
ejpam-4624	88	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	88	8	,	,	PUNCT
ejpam-4624	88	9	r	r	NOUN
ejpam-4624	88	10	,	,	PUNCT
ejpam-4624	88	11	s	s	PART
ejpam-4624	88	12	)	)	PUNCT
ejpam-4624	88	13	=	=	SYM
ejpam-4624	88	14	∨	∨	X
ejpam-4624	88	15	{	{	PUNCT
ejpam-4624	88	16	ϕ	ϕ	NOUN
ejpam-4624	88	17	∈	∈	PROPN
ejpam-4624	88	18	ix	ix	ADP
ejpam-4624	88	19	|ρ	|ρ	ADJ
ejpam-4624	88	20	≥	≥	PROPN
ejpam-4624	88	21	ϕ	ϕ	NOUN
ejpam-4624	88	22	,	,	PUNCT
ejpam-4624	88	23	ϕ	ϕ	NOUN
ejpam-4624	88	24	is	be	AUX
ejpam-4624	88	25	(	(	PUNCT
ejpam-4624	88	26	r	r	NOUN
ejpam-4624	88	27	,	,	PUNCT
ejpam-4624	88	28	s)−	s)−	PROPN
ejpam-4624	88	29	fro	fro	NOUN
ejpam-4624	88	30	}	}	PUNCT
ejpam-4624	88	31	.	.	PUNCT
ejpam-4624	89	1	from	from	ADP
ejpam-4624	89	2	the	the	DET
ejpam-4624	89	3	above	above	ADJ
ejpam-4624	89	4	definition	definition	NOUN
ejpam-4624	89	5	,	,	PUNCT
ejpam-4624	89	6	we	we	PRON
ejpam-4624	89	7	have	have	VERB
ejpam-4624	89	8	the	the	DET
ejpam-4624	89	9	following	follow	VERB
ejpam-4624	89	10	relations	relation	NOUN
ejpam-4624	89	11	:	:	PUNCT
ejpam-4624	89	12	(	(	PUNCT
ejpam-4624	89	13	i	i	NOUN
ejpam-4624	89	14	)	)	PUNCT
ejpam-4624	89	15	δct	δct	NOUN
ejpam-4624	89	16	,	,	PUNCT
ejpam-4624	89	17	t	t	PROPN
ejpam-4624	89	18	∗(1−	∗(1−	PROPN
ejpam-4624	89	19	ρ	ρ	PROPN
ejpam-4624	89	20	,	,	PUNCT
ejpam-4624	89	21	r	r	NOUN
ejpam-4624	89	22	,	,	PUNCT
ejpam-4624	89	23	s	s	NOUN
ejpam-4624	89	24	)	)	PUNCT
ejpam-4624	89	25	=	=	SYM
ejpam-4624	89	26	1−	1−	NUM
ejpam-4624	89	27	δit	δit	NOUN
ejpam-4624	89	28	,	,	PUNCT
ejpam-4624	89	29	t	t	NOUN
ejpam-4624	89	30	∗(ρ	∗(ρ	NOUN
ejpam-4624	89	31	,	,	PUNCT
ejpam-4624	89	32	r	r	NOUN
ejpam-4624	89	33	,	,	PUNCT
ejpam-4624	89	34	s	s	PART
ejpam-4624	89	35	)	)	PUNCT
ejpam-4624	89	36	,	,	PUNCT
ejpam-4624	89	37	(	(	PUNCT
ejpam-4624	89	38	ii	ii	NOUN
ejpam-4624	89	39	)	)	PUNCT
ejpam-4624	89	40	1−	1−	NUM
ejpam-4624	89	41	δct	δct	NOUN
ejpam-4624	89	42	,	,	PUNCT
ejpam-4624	89	43	t	t	NOUN
ejpam-4624	89	44	∗(ρ	∗(ρ	NOUN
ejpam-4624	89	45	,	,	PUNCT
ejpam-4624	89	46	r	r	NOUN
ejpam-4624	89	47	,	,	PUNCT
ejpam-4624	89	48	s	s	NOUN
ejpam-4624	89	49	)	)	PUNCT
ejpam-4624	89	50	)	)	PUNCT
ejpam-4624	90	1	=	=	NOUN
ejpam-4624	90	2	δit	δit	NOUN
ejpam-4624	90	3	,	,	PUNCT
ejpam-4624	90	4	t	t	PROPN
ejpam-4624	90	5	∗(1−	∗(1−	PROPN
ejpam-4624	90	6	ρ	ρ	PROPN
ejpam-4624	90	7	,	,	PUNCT
ejpam-4624	90	8	r	r	NOUN
ejpam-4624	90	9	,	,	PUNCT
ejpam-4624	90	10	s	s	PART
ejpam-4624	90	11	)	)	PUNCT
ejpam-4624	90	12	.	.	PUNCT
ejpam-4624	91	1	note	note	VERB
ejpam-4624	91	2	:	:	PUNCT
ejpam-4624	91	3	(	(	PUNCT
ejpam-4624	91	4	r	r	NOUN
ejpam-4624	91	5	,	,	PUNCT
ejpam-4624	91	6	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	91	7	δ	δ	PROPN
ejpam-4624	91	8	-	-	PUNCT
ejpam-4624	91	9	closure	closure	NOUN
ejpam-4624	91	10	of	of	ADP
ejpam-4624	91	11	a	a	DET
ejpam-4624	91	12	fuzzy	fuzzy	ADJ
ejpam-4624	91	13	set	set	NOUN
ejpam-4624	91	14	in	in	ADP
ejpam-4624	91	15	an	an	DET
ejpam-4624	91	16	dfts	dft	NOUN
ejpam-4624	91	17	is	be	AUX
ejpam-4624	91	18	not	not	PART
ejpam-4624	91	19	unique	unique	ADJ
ejpam-4624	91	20	.	.	PUNCT
ejpam-4624	92	1	however	however	ADV
ejpam-4624	92	2	,	,	PUNCT
ejpam-4624	92	3	it	it	PRON
ejpam-4624	92	4	is	be	AUX
ejpam-4624	92	5	unique	unique	ADJ
ejpam-4624	92	6	up	up	ADP
ejpam-4624	92	7	to	to	ADP
ejpam-4624	92	8	it	it	PRON
ejpam-4624	92	9	’s	’	VERB
ejpam-4624	92	10	support	support	NOUN
ejpam-4624	92	11	,	,	PUNCT
ejpam-4624	92	12	and	and	CCONJ
ejpam-4624	92	13	any	any	DET
ejpam-4624	92	14	(	(	PUNCT
ejpam-4624	92	15	r	r	NOUN
ejpam-4624	92	16	,	,	PUNCT
ejpam-4624	92	17	s)-fro	s)-fro	NOUN
ejpam-4624	92	18	set	set	NOUN
ejpam-4624	92	19	of	of	ADP
ejpam-4624	92	20	an	an	DET
ejpam-4624	92	21	dfts	dft	NOUN
ejpam-4624	92	22	x	x	PUNCT
ejpam-4624	92	23	is	be	AUX
ejpam-4624	92	24	a	a	DET
ejpam-4624	92	25	(	(	PUNCT
ejpam-4624	92	26	r	r	NOUN
ejpam-4624	92	27	,	,	PUNCT
ejpam-4624	92	28	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	92	29	open	open	ADJ
ejpam-4624	92	30	set	set	NOUN
ejpam-4624	92	31	of	of	ADP
ejpam-4624	92	32	x.	x.	NOUN
ejpam-4624	92	33	therefore	therefore	ADV
ejpam-4624	92	34	,	,	PUNCT
ejpam-4624	92	35	the	the	DET
ejpam-4624	92	36	set	set	NOUN
ejpam-4624	92	37	of	of	ADP
ejpam-4624	92	38	all	all	DET
ejpam-4624	92	39	(	(	PUNCT
ejpam-4624	92	40	r	r	NOUN
ejpam-4624	92	41	,	,	PUNCT
ejpam-4624	92	42	s)-fro	s)-fro	NOUN
ejpam-4624	92	43	sets	set	NOUN
ejpam-4624	92	44	is	be	AUX
ejpam-4624	92	45	subset	subset	VERB
ejpam-4624	92	46	of	of	ADP
ejpam-4624	92	47	the	the	DET
ejpam-4624	92	48	set	set	NOUN
ejpam-4624	92	49	of	of	ADP
ejpam-4624	92	50	all	all	DET
ejpam-4624	92	51	(	(	PUNCT
ejpam-4624	92	52	r	r	NOUN
ejpam-4624	92	53	,	,	PUNCT
ejpam-4624	92	54	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	92	55	open	open	ADJ
ejpam-4624	92	56	sets	set	NOUN
ejpam-4624	92	57	of	of	ADP
ejpam-4624	92	58	an	an	DET
ejpam-4624	92	59	dfts	dft	NOUN
ejpam-4624	92	60	.	.	PUNCT
ejpam-4624	93	1	so	so	ADV
ejpam-4624	93	2	,	,	PUNCT
ejpam-4624	93	3	if	if	SCONJ
ejpam-4624	93	4	a	a	DET
ejpam-4624	93	5	double	double	ADJ
ejpam-4624	93	6	fuzzy	fuzzy	ADJ
ejpam-4624	93	7	point	point	NOUN
ejpam-4624	93	8	x(α	x(α	PROPN
ejpam-4624	93	9	,	,	PUNCT
ejpam-4624	93	10	β	β	NOUN
ejpam-4624	93	11	)	)	PUNCT
ejpam-4624	93	12	of	of	ADP
ejpam-4624	93	13	a	a	DET
ejpam-4624	93	14	double	double	ADJ
ejpam-4624	93	15	fuzzy	fuzzy	ADJ
ejpam-4624	93	16	set	set	VERB
ejpam-4624	93	17	ρ	ρ	NOUN
ejpam-4624	93	18	in	in	ADP
ejpam-4624	93	19	an	an	DET
ejpam-4624	93	20	dfts	dft	NOUN
ejpam-4624	93	21	x	x	PUNCT
ejpam-4624	93	22	is	be	AUX
ejpam-4624	93	23	a	a	DET
ejpam-4624	93	24	double	double	ADJ
ejpam-4624	93	25	fuzzy	fuzzy	ADJ
ejpam-4624	93	26	δ	δ	NOUN
ejpam-4624	93	27	-	-	PUNCT
ejpam-4624	93	28	cluster	cluster	NOUN
ejpam-4624	93	29	point	point	NOUN
ejpam-4624	93	30	of	of	ADP
ejpam-4624	93	31	ρ	ρ	PROPN
ejpam-4624	93	32	,	,	PUNCT
ejpam-4624	93	33	then	then	ADV
ejpam-4624	93	34	x(α	x(α	PROPN
ejpam-4624	93	35	,	,	PUNCT
ejpam-4624	93	36	β	β	X
ejpam-4624	93	37	)	)	PUNCT
ejpam-4624	93	38	is	be	AUX
ejpam-4624	93	39	also	also	ADV
ejpam-4624	93	40	a	a	DET
ejpam-4624	93	41	double	double	ADJ
ejpam-4624	93	42	fuzzy	fuzzy	ADJ
ejpam-4624	93	43	cluster	cluster	NOUN
ejpam-4624	93	44	point	point	NOUN
ejpam-4624	93	45	of	of	ADP
ejpam-4624	93	46	ρ	ρ	PROPN
ejpam-4624	93	47	.	.	PUNCT
ejpam-4624	94	1	proposition	proposition	NOUN
ejpam-4624	94	2	2.5	2.5	NUM
ejpam-4624	94	3	.	.	PUNCT
ejpam-4624	95	1	let	let	VERB
ejpam-4624	95	2	(	(	PUNCT
ejpam-4624	95	3	x	x	X
ejpam-4624	95	4	,	,	PUNCT
ejpam-4624	95	5	t	t	PROPN
ejpam-4624	95	6	,	,	PUNCT
ejpam-4624	95	7	t	t	PROPN
ejpam-4624	95	8	∗	∗	NOUN
ejpam-4624	95	9	)	)	PUNCT
ejpam-4624	95	10	be	be	AUX
ejpam-4624	95	11	an	an	DET
ejpam-4624	95	12	dfts	dft	NOUN
ejpam-4624	95	13	.	.	PUNCT
ejpam-4624	96	1	then	then	ADV
ejpam-4624	96	2	,	,	PUNCT
ejpam-4624	96	3	for	for	SCONJ
ejpam-4624	96	4	each	each	DET
ejpam-4624	96	5	r	r	NOUN
ejpam-4624	96	6	,	,	PUNCT
ejpam-4624	96	7	r1	r1	PROPN
ejpam-4624	96	8	∈	∈	PROPN
ejpam-4624	96	9	i0	i0	PROPN
ejpam-4624	96	10	,	,	PUNCT
ejpam-4624	96	11	s	s	PROPN
ejpam-4624	96	12	,	,	PUNCT
ejpam-4624	96	13	s1	s1	PROPN
ejpam-4624	96	14	∈	∈	PROPN
ejpam-4624	96	15	i1	i1	PROPN
ejpam-4624	96	16	,	,	PUNCT
ejpam-4624	96	17	and	and	CCONJ
ejpam-4624	96	18	ρ	ρ	PROPN
ejpam-4624	96	19	∈	∈	PROPN
ejpam-4624	96	20	ix	ix	ADV
ejpam-4624	96	21	,	,	PUNCT
ejpam-4624	96	22	the	the	DET
ejpam-4624	96	23	operator	operator	NOUN
ejpam-4624	96	24	δit	δit	VERB
ejpam-4624	96	25	,	,	PUNCT
ejpam-4624	96	26	t	t	PROPN
ejpam-4624	96	27	∗	∗	NOUN
ejpam-4624	96	28	satisfies	satisfy	VERB
ejpam-4624	96	29	the	the	DET
ejpam-4624	96	30	following	following	ADJ
ejpam-4624	96	31	statements	statement	NOUN
ejpam-4624	96	32	:	:	PUNCT
ejpam-4624	96	33	(	(	PUNCT
ejpam-4624	96	34	i	i	NOUN
ejpam-4624	96	35	)	)	PUNCT
ejpam-4624	96	36	δit	δit	NOUN
ejpam-4624	96	37	,	,	PUNCT
ejpam-4624	96	38	t	t	PROPN
ejpam-4624	96	39	∗(0	∗(0	PROPN
ejpam-4624	96	40	,	,	PUNCT
ejpam-4624	96	41	r	r	NOUN
ejpam-4624	96	42	,	,	PUNCT
ejpam-4624	96	43	s	s	PART
ejpam-4624	96	44	)	)	PUNCT
ejpam-4624	96	45	=	=	SYM
ejpam-4624	96	46	0	0	NUM
ejpam-4624	96	47	,	,	PUNCT
ejpam-4624	96	48	δit	δit	NOUN
ejpam-4624	96	49	,	,	PUNCT
ejpam-4624	96	50	t	t	PROPN
ejpam-4624	96	51	∗(1	∗(1	PROPN
ejpam-4624	96	52	,	,	PUNCT
ejpam-4624	96	53	r	r	NOUN
ejpam-4624	96	54	,	,	PUNCT
ejpam-4624	96	55	s	s	PART
ejpam-4624	96	56	)	)	PUNCT
ejpam-4624	96	57	=	=	SYM
ejpam-4624	96	58	1	1	X
ejpam-4624	96	59	.	.	PUNCT
ejpam-4624	96	60	(	(	PUNCT
ejpam-4624	96	61	ii	ii	NOUN
ejpam-4624	96	62	)	)	PUNCT
ejpam-4624	96	63	δit	δit	NOUN
ejpam-4624	96	64	,	,	PUNCT
ejpam-4624	96	65	t	t	NOUN
ejpam-4624	96	66	∗(ρ	∗(ρ	NOUN
ejpam-4624	96	67	,	,	PUNCT
ejpam-4624	96	68	r	r	NOUN
ejpam-4624	96	69	,	,	PUNCT
ejpam-4624	96	70	s	s	NOUN
ejpam-4624	96	71	)	)	PUNCT
ejpam-4624	96	72	≤	≤	NUM
ejpam-4624	96	73	ρ	ρ	NOUN
ejpam-4624	96	74	.	.	PUNCT
ejpam-4624	97	1	(	(	PUNCT
ejpam-4624	97	2	iii	iii	NOUN
ejpam-4624	97	3	)	)	PUNCT
ejpam-4624	97	4	δit	δit	NOUN
ejpam-4624	97	5	,	,	PUNCT
ejpam-4624	97	6	t	t	NOUN
ejpam-4624	97	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	97	8	,	,	PUNCT
ejpam-4624	97	9	r	r	NOUN
ejpam-4624	97	10	,	,	PUNCT
ejpam-4624	97	11	s	s	NOUN
ejpam-4624	97	12	)	)	PUNCT
ejpam-4624	97	13	≤	≤	NUM
ejpam-4624	97	14	δit	δit	NOUN
ejpam-4624	97	15	,	,	PUNCT
ejpam-4624	97	16	t	t	NOUN
ejpam-4624	97	17	∗(ρ	∗(ρ	NOUN
ejpam-4624	97	18	,	,	PUNCT
ejpam-4624	97	19	r1	r1	NOUN
ejpam-4624	97	20	,	,	PUNCT
ejpam-4624	97	21	s1	s1	NOUN
ejpam-4624	97	22	)	)	PUNCT
ejpam-4624	97	23	,	,	PUNCT
ejpam-4624	97	24	if	if	SCONJ
ejpam-4624	97	25	r	r	NOUN
ejpam-4624	97	26	≥	≥	NOUN
ejpam-4624	97	27	r1	r1	NOUN
ejpam-4624	97	28	and	and	CCONJ
ejpam-4624	97	29	s	s	NOUN
ejpam-4624	97	30	≤	≤	NUM
ejpam-4624	97	31	s1	s1	NOUN
ejpam-4624	97	32	.	.	PUNCT
ejpam-4624	98	1	(	(	PUNCT
ejpam-4624	98	2	iv	iv	X
ejpam-4624	98	3	)	)	PUNCT
ejpam-4624	98	4	δit	δit	NOUN
ejpam-4624	98	5	,	,	PUNCT
ejpam-4624	98	6	t	t	PROPN
ejpam-4624	98	7	∗(ρ	∗(ρ	PROPN
ejpam-4624	98	8	∧	∧	PROPN
ejpam-4624	98	9	ϕ	ϕ	PROPN
ejpam-4624	98	10	,	,	PUNCT
ejpam-4624	98	11	r	r	NOUN
ejpam-4624	98	12	,	,	PUNCT
ejpam-4624	98	13	s	s	PART
ejpam-4624	98	14	)	)	PUNCT
ejpam-4624	99	1	=	=	NOUN
ejpam-4624	99	2	δit	δit	NOUN
ejpam-4624	99	3	,	,	PUNCT
ejpam-4624	99	4	t	t	NOUN
ejpam-4624	99	5	∗(ρ	∗(ρ	NOUN
ejpam-4624	99	6	,	,	PUNCT
ejpam-4624	99	7	r	r	NOUN
ejpam-4624	99	8	,	,	PUNCT
ejpam-4624	99	9	s	s	NOUN
ejpam-4624	99	10	)	)	PUNCT
ejpam-4624	99	11	∧	∧	NOUN
ejpam-4624	99	12	δit	δit	NOUN
ejpam-4624	99	13	,	,	PUNCT
ejpam-4624	99	14	t	t	PROPN
ejpam-4624	99	15	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	99	16	,	,	PUNCT
ejpam-4624	99	17	r	r	NOUN
ejpam-4624	99	18	,	,	PUNCT
ejpam-4624	99	19	s	s	NOUN
ejpam-4624	99	20	)	)	PUNCT
ejpam-4624	99	21	.	.	PUNCT
ejpam-4624	100	1	(	(	PUNCT
ejpam-4624	100	2	v	v	NOUN
ejpam-4624	100	3	)	)	PUNCT
ejpam-4624	100	4	δit	δit	NOUN
ejpam-4624	100	5	,	,	PUNCT
ejpam-4624	100	6	t	t	PROPN
ejpam-4624	100	7	∗(δit	∗(δit	NOUN
ejpam-4624	100	8	,	,	PUNCT
ejpam-4624	100	9	t	t	PROPN
ejpam-4624	100	10	∗((ρ	∗((ρ	PROPN
ejpam-4624	100	11	,	,	PUNCT
ejpam-4624	100	12	r	r	NOUN
ejpam-4624	100	13	,	,	PUNCT
ejpam-4624	100	14	s	s	PART
ejpam-4624	100	15	)	)	PUNCT
ejpam-4624	100	16	,	,	PUNCT
ejpam-4624	100	17	r	r	NOUN
ejpam-4624	100	18	,	,	PUNCT
ejpam-4624	100	19	s	s	NOUN
ejpam-4624	100	20	)	)	PUNCT
ejpam-4624	100	21	)	)	PUNCT
ejpam-4624	101	1	=	=	NOUN
ejpam-4624	101	2	δit	δit	NOUN
ejpam-4624	101	3	,	,	PUNCT
ejpam-4624	101	4	t	t	NOUN
ejpam-4624	101	5	∗(ρ	∗(ρ	NOUN
ejpam-4624	101	6	,	,	PUNCT
ejpam-4624	101	7	r	r	NOUN
ejpam-4624	101	8	,	,	PUNCT
ejpam-4624	101	9	s	s	NOUN
ejpam-4624	101	10	)	)	PUNCT
ejpam-4624	101	11	.	.	PUNCT
ejpam-4624	102	1	proof	proof	NOUN
ejpam-4624	102	2	.	.	PUNCT
ejpam-4624	103	1	(	(	PUNCT
ejpam-4624	103	2	i	i	NOUN
ejpam-4624	103	3	)	)	PUNCT
ejpam-4624	103	4	,	,	PUNCT
ejpam-4624	103	5	(	(	PUNCT
ejpam-4624	103	6	ii	ii	NOUN
ejpam-4624	103	7	)	)	PUNCT
ejpam-4624	103	8	,	,	PUNCT
ejpam-4624	103	9	(	(	PUNCT
ejpam-4624	103	10	v	v	NOUN
ejpam-4624	103	11	)	)	PUNCT
ejpam-4624	103	12	are	be	AUX
ejpam-4624	103	13	obvious	obvious	ADJ
ejpam-4624	103	14	by	by	ADP
ejpam-4624	103	15	using	use	VERB
ejpam-4624	103	16	the	the	DET
ejpam-4624	103	17	definition	definition	NOUN
ejpam-4624	103	18	2.4	2.4	NUM
ejpam-4624	103	19	.	.	PUNCT
ejpam-4624	104	1	(	(	PUNCT
ejpam-4624	104	2	iii	iii	X
ejpam-4624	104	3	)	)	PUNCT
ejpam-4624	104	4	let	let	VERB
ejpam-4624	104	5	r	r	NOUN
ejpam-4624	104	6	≥	≥	NOUN
ejpam-4624	104	7	r1	r1	NOUN
ejpam-4624	104	8	and	and	CCONJ
ejpam-4624	104	9	s	s	NOUN
ejpam-4624	104	10	≤	≤	NUM
ejpam-4624	104	11	s1	s1	NOUN
ejpam-4624	104	12	.	.	PUNCT
ejpam-4624	105	1	then	then	ADV
ejpam-4624	105	2	for	for	ADP
ejpam-4624	105	3	each	each	DET
ejpam-4624	105	4	(	(	PUNCT
ejpam-4624	105	5	r	r	NOUN
ejpam-4624	105	6	,	,	PUNCT
ejpam-4624	105	7	s)-fro	s)-fro	NOUN
ejpam-4624	105	8	and	and	CCONJ
ejpam-4624	105	9	(	(	PUNCT
ejpam-4624	105	10	r1	r1	PROPN
ejpam-4624	105	11	,	,	PUNCT
ejpam-4624	105	12	s1)-fro	s1)-fro	PROPN
ejpam-4624	105	13	sets	set	VERB
ejpam-4624	105	14	,	,	PUNCT
ejpam-4624	105	15	we	we	PRON
ejpam-4624	105	16	have	have	VERB
ejpam-4624	105	17	:	:	PUNCT
ejpam-4624	105	18	δi(ρ	δi(ρ	NOUN
ejpam-4624	105	19	,	,	PUNCT
ejpam-4624	105	20	r	r	NOUN
ejpam-4624	105	21	,	,	PUNCT
ejpam-4624	105	22	s	s	PART
ejpam-4624	105	23	)	)	PUNCT
ejpam-4624	105	24	=	=	SYM
ejpam-4624	105	25	∨	∨	X
ejpam-4624	105	26	{	{	PUNCT
ejpam-4624	105	27	ϕ	ϕ	NOUN
ejpam-4624	105	28	∈	∈	PROPN
ejpam-4624	105	29	ix	ix	ADP
ejpam-4624	105	30	|ρ	|ρ	ADJ
ejpam-4624	105	31	≥	≥	PROPN
ejpam-4624	105	32	ϕ	ϕ	NOUN
ejpam-4624	105	33	,	,	PUNCT
ejpam-4624	105	34	ϕ	ϕ	NOUN
ejpam-4624	105	35	is	be	AUX
ejpam-4624	105	36	(	(	PUNCT
ejpam-4624	105	37	r	r	NOUN
ejpam-4624	105	38	,	,	PUNCT
ejpam-4624	105	39	s)−	s)−	PROPN
ejpam-4624	105	40	fro	fro	NOUN
ejpam-4624	105	41	}	}	PUNCT
ejpam-4624	105	42	=	=	SYM
ejpam-4624	105	43	∨	∨	X
ejpam-4624	105	44	{	{	PUNCT
ejpam-4624	105	45	ϕ	ϕ	NOUN
ejpam-4624	105	46	∈	∈	PROPN
ejpam-4624	105	47	ix	ix	ADP
ejpam-4624	105	48	|ρ	|ρ	ADJ
ejpam-4624	105	49	≥	≥	PROPN
ejpam-4624	105	50	ϕ	ϕ	NOUN
ejpam-4624	105	51	,	,	PUNCT
ejpam-4624	105	52	ϕ	ϕ	NOUN
ejpam-4624	105	53	is	be	AUX
ejpam-4624	105	54	(	(	PUNCT
ejpam-4624	105	55	r1	r1	NOUN
ejpam-4624	105	56	,	,	PUNCT
ejpam-4624	105	57	s1)−	s1)−	NOUN
ejpam-4624	105	58	fro	fro	NOUN
ejpam-4624	105	59	}	}	PUNCT
ejpam-4624	105	60	w.	w.	PROPN
ejpam-4624	105	61	f.	f.	PROPN
ejpam-4624	105	62	al	al	PROPN
ejpam-4624	105	63	-	-	PUNCT
ejpam-4624	105	64	omeri	omeri	ADJ
ejpam-4624	105	65	/	/	SYM
ejpam-4624	105	66	eur	eur	PROPN
ejpam-4624	105	67	.	.	PUNCT
ejpam-4624	106	1	j.	j.	PROPN
ejpam-4624	106	2	pure	pure	PROPN
ejpam-4624	106	3	appl	appl	PROPN
ejpam-4624	106	4	.	.	PROPN
ejpam-4624	106	5	math	math	PROPN
ejpam-4624	106	6	,	,	PUNCT
ejpam-4624	106	7	18	18	NUM
ejpam-4624	106	8	(	(	PUNCT
ejpam-4624	106	9	2	2	NUM
ejpam-4624	106	10	)	)	PUNCT
ejpam-4624	106	11	(	(	PUNCT
ejpam-4624	106	12	2025	2025	NUM
ejpam-4624	106	13	)	)	PUNCT
ejpam-4624	106	14	,	,	PUNCT
ejpam-4624	106	15	4624	4624	NUM
ejpam-4624	106	16	5	5	NUM
ejpam-4624	106	17	of	of	ADP
ejpam-4624	106	18	15	15	NUM
ejpam-4624	106	19	=	=	SYM
ejpam-4624	106	20	δi(ρ	δi(ρ	NOUN
ejpam-4624	106	21	,	,	PUNCT
ejpam-4624	106	22	r1	r1	NOUN
ejpam-4624	106	23	,	,	PUNCT
ejpam-4624	106	24	s1	s1	PROPN
ejpam-4624	106	25	)	)	PUNCT
ejpam-4624	106	26	.	.	PUNCT
ejpam-4624	107	1	(	(	PUNCT
ejpam-4624	107	2	iv	iv	X
ejpam-4624	107	3	)	)	PUNCT
ejpam-4624	107	4	since	since	SCONJ
ejpam-4624	107	5	ρ	ρ	PROPN
ejpam-4624	107	6	∧	∧	PROPN
ejpam-4624	107	7	ϕ	ϕ	PROPN
ejpam-4624	107	8	≤	≤	PROPN
ejpam-4624	107	9	ρ	ρ	PROPN
ejpam-4624	107	10	and	and	CCONJ
ejpam-4624	107	11	ρ	ρ	NUM
ejpam-4624	107	12	∧	∧	PROPN
ejpam-4624	107	13	ϕ	ϕ	PROPN
ejpam-4624	107	14	≤	≤	PROPN
ejpam-4624	107	15	ϕ	ϕ	NOUN
ejpam-4624	107	16	,	,	PUNCT
ejpam-4624	107	17	then	then	ADV
ejpam-4624	107	18	we	we	PRON
ejpam-4624	107	19	have	have	VERB
ejpam-4624	107	20	δi(ρ	δi(ρ	VERB
ejpam-4624	107	21	∧	∧	PROPN
ejpam-4624	107	22	ϕ	ϕ	PROPN
ejpam-4624	107	23	,	,	PUNCT
ejpam-4624	107	24	r	r	NOUN
ejpam-4624	107	25	,	,	PUNCT
ejpam-4624	107	26	s	s	PART
ejpam-4624	107	27	)	)	PUNCT
ejpam-4624	107	28	≤	≤	X
ejpam-4624	107	29	δi(ρ	δi(ρ	VERB
ejpam-4624	107	30	,	,	PUNCT
ejpam-4624	107	31	r	r	NOUN
ejpam-4624	107	32	,	,	PUNCT
ejpam-4624	107	33	s	s	NOUN
ejpam-4624	107	34	)	)	PUNCT
ejpam-4624	107	35	,	,	PUNCT
ejpam-4624	107	36	and	and	CCONJ
ejpam-4624	107	37	δi(ρ	δi(ρ	VERB
ejpam-4624	107	38	∧	∧	PROPN
ejpam-4624	107	39	ϕ	ϕ	PROPN
ejpam-4624	107	40	,	,	PUNCT
ejpam-4624	107	41	r	r	NOUN
ejpam-4624	107	42	,	,	PUNCT
ejpam-4624	107	43	s	s	NOUN
ejpam-4624	107	44	)	)	PUNCT
ejpam-4624	107	45	≤	≤	NOUN
ejpam-4624	107	46	δi(ϕ	δi(ϕ	PUNCT
ejpam-4624	107	47	,	,	PUNCT
ejpam-4624	107	48	r	r	NOUN
ejpam-4624	107	49	,	,	PUNCT
ejpam-4624	107	50	s	s	NOUN
ejpam-4624	107	51	)	)	PUNCT
ejpam-4624	107	52	.	.	PUNCT
ejpam-4624	108	1	thus	thus	ADV
ejpam-4624	108	2	,	,	PUNCT
ejpam-4624	108	3	δi(ρ	δi(ρ	VERB
ejpam-4624	108	4	∧	∧	PROPN
ejpam-4624	108	5	ϕ	ϕ	PROPN
ejpam-4624	108	6	,	,	PUNCT
ejpam-4624	108	7	r	r	NOUN
ejpam-4624	108	8	,	,	PUNCT
ejpam-4624	108	9	s	s	NOUN
ejpam-4624	108	10	)	)	PUNCT
ejpam-4624	108	11	≤	≤	NUM
ejpam-4624	108	12	δit	δit	NOUN
ejpam-4624	108	13	,	,	PUNCT
ejpam-4624	108	14	t	t	NOUN
ejpam-4624	108	15	∗(ρ	∗(ρ	NOUN
ejpam-4624	108	16	,	,	PUNCT
ejpam-4624	108	17	r	r	NOUN
ejpam-4624	108	18	,	,	PUNCT
ejpam-4624	108	19	s	s	NOUN
ejpam-4624	108	20	)	)	PUNCT
ejpam-4624	108	21	∧	∧	NOUN
ejpam-4624	108	22	δit	δit	NOUN
ejpam-4624	108	23	,	,	PUNCT
ejpam-4624	108	24	t	t	PROPN
ejpam-4624	108	25	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	108	26	,	,	PUNCT
ejpam-4624	108	27	r	r	NOUN
ejpam-4624	108	28	,	,	PUNCT
ejpam-4624	108	29	s	s	NOUN
ejpam-4624	108	30	)	)	PUNCT
ejpam-4624	108	31	.	.	PUNCT
ejpam-4624	109	1	conversely	conversely	ADV
ejpam-4624	109	2	,	,	PUNCT
ejpam-4624	109	3	it	it	PRON
ejpam-4624	109	4	is	be	AUX
ejpam-4624	109	5	clear	clear	ADJ
ejpam-4624	109	6	that	that	SCONJ
ejpam-4624	109	7	δit	δit	NOUN
ejpam-4624	109	8	,	,	PUNCT
ejpam-4624	109	9	t	t	NOUN
ejpam-4624	109	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	109	11	,	,	PUNCT
ejpam-4624	109	12	r	r	NOUN
ejpam-4624	109	13	,	,	PUNCT
ejpam-4624	109	14	s	s	NOUN
ejpam-4624	109	15	)	)	PUNCT
ejpam-4624	109	16	∧	∧	NOUN
ejpam-4624	109	17	δit	δit	NOUN
ejpam-4624	109	18	,	,	PUNCT
ejpam-4624	109	19	t	t	PROPN
ejpam-4624	109	20	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	109	21	,	,	PUNCT
ejpam-4624	109	22	r	r	NOUN
ejpam-4624	109	23	,	,	PUNCT
ejpam-4624	109	24	s	s	NOUN
ejpam-4624	109	25	)	)	PUNCT
ejpam-4624	109	26	≤	≤	NUM
ejpam-4624	109	27	ρ	ρ	NUM
ejpam-4624	109	28	∧	∧	PROPN
ejpam-4624	109	29	ϕ.	ϕ.	PROPN
ejpam-4624	109	30	also	also	ADV
ejpam-4624	109	31	,	,	PUNCT
ejpam-4624	109	32	t	t	PROPN
ejpam-4624	109	33	(	(	PUNCT
ejpam-4624	109	34	δit	δit	NOUN
ejpam-4624	109	35	,	,	PUNCT
ejpam-4624	109	36	t	t	NOUN
ejpam-4624	109	37	∗(ρ	∗(ρ	NOUN
ejpam-4624	109	38	,	,	PUNCT
ejpam-4624	109	39	r	r	NOUN
ejpam-4624	109	40	,	,	PUNCT
ejpam-4624	109	41	s	s	NOUN
ejpam-4624	109	42	)	)	PUNCT
ejpam-4624	109	43	∧	∧	NOUN
ejpam-4624	109	44	δit	δit	NOUN
ejpam-4624	109	45	,	,	PUNCT
ejpam-4624	109	46	t	t	PROPN
ejpam-4624	109	47	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	109	48	,	,	PUNCT
ejpam-4624	109	49	r	r	NOUN
ejpam-4624	109	50	,	,	PUNCT
ejpam-4624	109	51	s	s	NOUN
ejpam-4624	109	52	)	)	PUNCT
ejpam-4624	109	53	)	)	PUNCT
ejpam-4624	109	54	≥	≥	PROPN
ejpam-4624	109	55	t	t	NOUN
ejpam-4624	109	56	(	(	PUNCT
ejpam-4624	109	57	δit	δit	NOUN
ejpam-4624	109	58	,	,	PUNCT
ejpam-4624	109	59	t	t	NOUN
ejpam-4624	109	60	∗(ρ	∗(ρ	NOUN
ejpam-4624	109	61	,	,	PUNCT
ejpam-4624	109	62	r	r	NOUN
ejpam-4624	109	63	,	,	PUNCT
ejpam-4624	109	64	s	s	NOUN
ejpam-4624	109	65	)	)	PUNCT
ejpam-4624	109	66	)	)	PUNCT
ejpam-4624	110	1	∧	∧	PROPN
ejpam-4624	110	2	t	t	PROPN
ejpam-4624	110	3	(	(	PUNCT
ejpam-4624	110	4	δit	δit	NOUN
ejpam-4624	110	5	,	,	PUNCT
ejpam-4624	110	6	t	t	PROPN
ejpam-4624	110	7	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	110	8	,	,	PUNCT
ejpam-4624	110	9	r	r	NOUN
ejpam-4624	110	10	,	,	PUNCT
ejpam-4624	110	11	s	s	NOUN
ejpam-4624	110	12	)	)	PUNCT
ejpam-4624	110	13	)	)	PUNCT
ejpam-4624	110	14	≥	≥	NOUN
ejpam-4624	110	15	r	r	NOUN
ejpam-4624	110	16	∧	∧	PROPN
ejpam-4624	110	17	r	r	NOUN
ejpam-4624	110	18	=	=	SYM
ejpam-4624	110	19	r	r	NOUN
ejpam-4624	110	20	,	,	PUNCT
ejpam-4624	110	21	and	and	CCONJ
ejpam-4624	110	22	t	t	PROPN
ejpam-4624	110	23	∗(δit	∗(δit	NOUN
ejpam-4624	110	24	,	,	PUNCT
ejpam-4624	110	25	t	t	NOUN
ejpam-4624	110	26	∗(ρ	∗(ρ	NOUN
ejpam-4624	110	27	,	,	PUNCT
ejpam-4624	110	28	r	r	NOUN
ejpam-4624	110	29	,	,	PUNCT
ejpam-4624	110	30	s	s	NOUN
ejpam-4624	110	31	)	)	PUNCT
ejpam-4624	110	32	∧	∧	NOUN
ejpam-4624	110	33	δit	δit	NOUN
ejpam-4624	110	34	,	,	PUNCT
ejpam-4624	110	35	t	t	PROPN
ejpam-4624	110	36	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	110	37	,	,	PUNCT
ejpam-4624	110	38	r	r	NOUN
ejpam-4624	110	39	,	,	PUNCT
ejpam-4624	110	40	s	s	NOUN
ejpam-4624	110	41	)	)	PUNCT
ejpam-4624	110	42	)	)	PUNCT
ejpam-4624	110	43	≤	≤	NOUN
ejpam-4624	110	44	t	t	NOUN
ejpam-4624	110	45	∗(δit	∗(δit	NOUN
ejpam-4624	110	46	,	,	PUNCT
ejpam-4624	110	47	t	t	NOUN
ejpam-4624	110	48	∗(ρ	∗(ρ	NOUN
ejpam-4624	110	49	,	,	PUNCT
ejpam-4624	110	50	r	r	NOUN
ejpam-4624	110	51	,	,	PUNCT
ejpam-4624	110	52	s	s	NOUN
ejpam-4624	110	53	)	)	PUNCT
ejpam-4624	110	54	)	)	PUNCT
ejpam-4624	111	1	∧	∧	PROPN
ejpam-4624	111	2	t	t	PROPN
ejpam-4624	111	3	∗(δit	∗(δit	NOUN
ejpam-4624	111	4	,	,	PUNCT
ejpam-4624	111	5	t	t	PROPN
ejpam-4624	111	6	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	111	7	,	,	PUNCT
ejpam-4624	111	8	r	r	NOUN
ejpam-4624	111	9	,	,	PUNCT
ejpam-4624	111	10	s	s	NOUN
ejpam-4624	111	11	)	)	PUNCT
ejpam-4624	111	12	)	)	PUNCT
ejpam-4624	111	13	≤	≤	NUM
ejpam-4624	111	14	s	s	PART
ejpam-4624	111	15	∧	∧	PROPN
ejpam-4624	111	16	s	s	PART
ejpam-4624	111	17	=	=	PUNCT
ejpam-4624	111	18	s.	s.	PROPN
ejpam-4624	111	19	by	by	ADP
ejpam-4624	111	20	the	the	DET
ejpam-4624	111	21	definition	definition	NOUN
ejpam-4624	111	22	of	of	ADP
ejpam-4624	111	23	δit	δit	NOUN
ejpam-4624	111	24	,	,	PUNCT
ejpam-4624	111	25	t	t	NOUN
ejpam-4624	111	26	∗	∗	NOUN
ejpam-4624	111	27	,	,	PUNCT
ejpam-4624	111	28	we	we	PRON
ejpam-4624	111	29	get	get	VERB
ejpam-4624	111	30	δit	δit	NOUN
ejpam-4624	111	31	,	,	PUNCT
ejpam-4624	111	32	t	t	NOUN
ejpam-4624	111	33	∗(ρ	∗(ρ	NOUN
ejpam-4624	111	34	,	,	PUNCT
ejpam-4624	111	35	r	r	NOUN
ejpam-4624	111	36	,	,	PUNCT
ejpam-4624	111	37	s	s	NOUN
ejpam-4624	111	38	)	)	PUNCT
ejpam-4624	111	39	∧	∧	NOUN
ejpam-4624	111	40	δit	δit	NOUN
ejpam-4624	111	41	,	,	PUNCT
ejpam-4624	111	42	t	t	PROPN
ejpam-4624	111	43	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	111	44	,	,	PUNCT
ejpam-4624	111	45	r	r	NOUN
ejpam-4624	111	46	,	,	PUNCT
ejpam-4624	111	47	s	s	NOUN
ejpam-4624	111	48	)	)	PUNCT
ejpam-4624	111	49	≤	≤	NOUN
ejpam-4624	111	50	δi(ρ	δi(ρ	VERB
ejpam-4624	111	51	∧	∧	PROPN
ejpam-4624	111	52	ϕ	ϕ	PROPN
ejpam-4624	111	53	,	,	PUNCT
ejpam-4624	111	54	r	r	NOUN
ejpam-4624	111	55	,	,	PUNCT
ejpam-4624	111	56	s	s	NOUN
ejpam-4624	111	57	)	)	PUNCT
ejpam-4624	111	58	.	.	PUNCT
ejpam-4624	112	1	hence	hence	ADV
ejpam-4624	112	2	,	,	PUNCT
ejpam-4624	112	3	δit	δit	NOUN
ejpam-4624	112	4	,	,	PUNCT
ejpam-4624	112	5	t	t	PROPN
ejpam-4624	112	6	∗(ρ	∗(ρ	PROPN
ejpam-4624	112	7	∧	∧	PROPN
ejpam-4624	112	8	ϕ	ϕ	PROPN
ejpam-4624	112	9	,	,	PUNCT
ejpam-4624	112	10	r	r	NOUN
ejpam-4624	112	11	,	,	PUNCT
ejpam-4624	112	12	s	s	PART
ejpam-4624	112	13	)	)	PUNCT
ejpam-4624	112	14	=	=	NOUN
ejpam-4624	112	15	δit	δit	NOUN
ejpam-4624	112	16	,	,	PUNCT
ejpam-4624	112	17	t	t	NOUN
ejpam-4624	112	18	∗(ρ	∗(ρ	NOUN
ejpam-4624	112	19	,	,	PUNCT
ejpam-4624	112	20	r	r	NOUN
ejpam-4624	112	21	,	,	PUNCT
ejpam-4624	112	22	s	s	NOUN
ejpam-4624	112	23	)	)	PUNCT
ejpam-4624	112	24	∧	∧	NOUN
ejpam-4624	112	25	δit	δit	NOUN
ejpam-4624	112	26	,	,	PUNCT
ejpam-4624	112	27	t	t	PROPN
ejpam-4624	112	28	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	112	29	,	,	PUNCT
ejpam-4624	112	30	r	r	NOUN
ejpam-4624	112	31	,	,	PUNCT
ejpam-4624	112	32	s	s	PART
ejpam-4624	112	33	)	)	PUNCT
ejpam-4624	112	34	.	.	PUNCT
ejpam-4624	113	1	proposition	proposition	NOUN
ejpam-4624	113	2	2.6	2.6	NUM
ejpam-4624	113	3	.	.	PUNCT
ejpam-4624	114	1	let	let	AUX
ejpam-4624	114	2	(	(	PUNCT
ejpam-4624	114	3	x	x	X
ejpam-4624	114	4	,	,	PUNCT
ejpam-4624	114	5	t	t	PROPN
ejpam-4624	114	6	,	,	PUNCT
ejpam-4624	114	7	t	t	PROPN
ejpam-4624	114	8	∗	∗	NOUN
ejpam-4624	114	9	)	)	PUNCT
ejpam-4624	114	10	be	be	AUX
ejpam-4624	114	11	an	an	DET
ejpam-4624	114	12	dfts	dft	NOUN
ejpam-4624	114	13	.	.	PUNCT
ejpam-4624	115	1	then	then	ADV
ejpam-4624	115	2	,	,	PUNCT
ejpam-4624	115	3	for	for	SCONJ
ejpam-4624	115	4	each	each	DET
ejpam-4624	115	5	r	r	NOUN
ejpam-4624	115	6	,	,	PUNCT
ejpam-4624	115	7	r1	r1	PROPN
ejpam-4624	115	8	∈	∈	PROPN
ejpam-4624	115	9	i0	i0	PROPN
ejpam-4624	115	10	,	,	PUNCT
ejpam-4624	115	11	s	s	PROPN
ejpam-4624	115	12	,	,	PUNCT
ejpam-4624	115	13	s1	s1	PROPN
ejpam-4624	115	14	∈	∈	PROPN
ejpam-4624	115	15	i1	i1	PROPN
ejpam-4624	115	16	,	,	PUNCT
ejpam-4624	115	17	and	and	CCONJ
ejpam-4624	115	18	ρ	ρ	PROPN
ejpam-4624	115	19	∈	∈	PROPN
ejpam-4624	115	20	ix	ix	ADV
ejpam-4624	115	21	,	,	PUNCT
ejpam-4624	115	22	the	the	DET
ejpam-4624	115	23	operator	operator	NOUN
ejpam-4624	115	24	δct	δct	NOUN
ejpam-4624	115	25	,	,	PUNCT
ejpam-4624	115	26	t	t	PROPN
ejpam-4624	115	27	∗	∗	NOUN
ejpam-4624	115	28	satisfies	satisfy	VERB
ejpam-4624	115	29	the	the	DET
ejpam-4624	115	30	following	following	ADJ
ejpam-4624	115	31	statements	statement	NOUN
ejpam-4624	115	32	:	:	PUNCT
ejpam-4624	115	33	(	(	PUNCT
ejpam-4624	115	34	i	i	NOUN
ejpam-4624	115	35	)	)	PUNCT
ejpam-4624	115	36	δct	δct	NOUN
ejpam-4624	115	37	,	,	PUNCT
ejpam-4624	115	38	t	t	PROPN
ejpam-4624	115	39	∗(0	∗(0	PROPN
ejpam-4624	115	40	,	,	PUNCT
ejpam-4624	115	41	r	r	NOUN
ejpam-4624	115	42	,	,	PUNCT
ejpam-4624	115	43	s	s	PART
ejpam-4624	115	44	)	)	PUNCT
ejpam-4624	115	45	=	=	SYM
ejpam-4624	115	46	0	0	NUM
ejpam-4624	115	47	,	,	PUNCT
ejpam-4624	115	48	δct	δct	NOUN
ejpam-4624	115	49	,	,	PUNCT
ejpam-4624	115	50	t	t	NOUN
ejpam-4624	115	51	∗(1	∗(1	PROPN
ejpam-4624	115	52	,	,	PUNCT
ejpam-4624	115	53	r	r	NOUN
ejpam-4624	115	54	,	,	PUNCT
ejpam-4624	115	55	s	s	PART
ejpam-4624	115	56	)	)	PUNCT
ejpam-4624	115	57	=	=	SYM
ejpam-4624	115	58	1	1	X
ejpam-4624	115	59	.	.	PUNCT
ejpam-4624	115	60	(	(	PUNCT
ejpam-4624	115	61	ii	ii	NOUN
ejpam-4624	115	62	)	)	PUNCT
ejpam-4624	115	63	δct	δct	NOUN
ejpam-4624	115	64	,	,	PUNCT
ejpam-4624	115	65	t	t	NOUN
ejpam-4624	115	66	∗(ρ	∗(ρ	NOUN
ejpam-4624	115	67	,	,	PUNCT
ejpam-4624	115	68	r	r	NOUN
ejpam-4624	115	69	,	,	PUNCT
ejpam-4624	115	70	s	s	PART
ejpam-4624	115	71	)	)	PUNCT
ejpam-4624	115	72	≥	≥	NOUN
ejpam-4624	115	73	ρ	ρ	PROPN
ejpam-4624	115	74	.	.	PUNCT
ejpam-4624	116	1	(	(	PUNCT
ejpam-4624	116	2	iii	iii	NOUN
ejpam-4624	116	3	)	)	PUNCT
ejpam-4624	116	4	δct	δct	NOUN
ejpam-4624	116	5	,	,	PUNCT
ejpam-4624	116	6	t	t	NOUN
ejpam-4624	116	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	116	8	,	,	PUNCT
ejpam-4624	116	9	r	r	NOUN
ejpam-4624	116	10	,	,	PUNCT
ejpam-4624	116	11	s	s	NOUN
ejpam-4624	116	12	)	)	PUNCT
ejpam-4624	116	13	≤	≤	NOUN
ejpam-4624	116	14	δct	δct	NOUN
ejpam-4624	116	15	,	,	PUNCT
ejpam-4624	116	16	t	t	NOUN
ejpam-4624	116	17	∗(ρ	∗(ρ	NOUN
ejpam-4624	116	18	,	,	PUNCT
ejpam-4624	116	19	r1	r1	NOUN
ejpam-4624	116	20	,	,	PUNCT
ejpam-4624	116	21	s1	s1	NOUN
ejpam-4624	116	22	)	)	PUNCT
ejpam-4624	116	23	,	,	PUNCT
ejpam-4624	116	24	if	if	SCONJ
ejpam-4624	116	25	r	r	NOUN
ejpam-4624	116	26	≤	≤	PUNCT
ejpam-4624	116	27	r1	r1	NOUN
ejpam-4624	116	28	and	and	CCONJ
ejpam-4624	116	29	s	s	NOUN
ejpam-4624	116	30	≥	≥	NOUN
ejpam-4624	116	31	s1	s1	NOUN
ejpam-4624	116	32	.	.	PUNCT
ejpam-4624	117	1	(	(	PUNCT
ejpam-4624	117	2	iv	iv	X
ejpam-4624	117	3	)	)	PUNCT
ejpam-4624	117	4	δct	δct	NOUN
ejpam-4624	117	5	,	,	PUNCT
ejpam-4624	117	6	t	t	PROPN
ejpam-4624	117	7	∗(ρ	∗(ρ	PROPN
ejpam-4624	117	8	∨	∨	NUM
ejpam-4624	117	9	ϕ	ϕ	PROPN
ejpam-4624	117	10	,	,	PUNCT
ejpam-4624	117	11	r	r	NOUN
ejpam-4624	117	12	,	,	PUNCT
ejpam-4624	117	13	s	s	NOUN
ejpam-4624	117	14	)	)	PUNCT
ejpam-4624	117	15	=	=	NOUN
ejpam-4624	117	16	δct	δct	NOUN
ejpam-4624	117	17	,	,	PUNCT
ejpam-4624	117	18	t	t	NOUN
ejpam-4624	117	19	∗(ρ	∗(ρ	NOUN
ejpam-4624	117	20	,	,	PUNCT
ejpam-4624	117	21	r	r	NOUN
ejpam-4624	117	22	,	,	PUNCT
ejpam-4624	117	23	s	s	PART
ejpam-4624	117	24	)	)	PUNCT
ejpam-4624	117	25	∨	∨	NUM
ejpam-4624	117	26	δct	δct	NOUN
ejpam-4624	117	27	,	,	PUNCT
ejpam-4624	117	28	t	t	PROPN
ejpam-4624	117	29	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	117	30	,	,	PUNCT
ejpam-4624	117	31	r	r	NOUN
ejpam-4624	117	32	,	,	PUNCT
ejpam-4624	117	33	s	s	NOUN
ejpam-4624	117	34	)	)	PUNCT
ejpam-4624	117	35	.	.	PUNCT
ejpam-4624	118	1	(	(	PUNCT
ejpam-4624	118	2	v	v	NOUN
ejpam-4624	118	3	)	)	PUNCT
ejpam-4624	118	4	δct	δct	NOUN
ejpam-4624	118	5	,	,	PUNCT
ejpam-4624	118	6	t	t	PROPN
ejpam-4624	118	7	∗(δct	∗(δct	NOUN
ejpam-4624	118	8	,	,	PUNCT
ejpam-4624	118	9	t	t	PROPN
ejpam-4624	118	10	∗((ρ	∗((ρ	PROPN
ejpam-4624	118	11	,	,	PUNCT
ejpam-4624	118	12	r	r	NOUN
ejpam-4624	118	13	,	,	PUNCT
ejpam-4624	118	14	s	s	PART
ejpam-4624	118	15	)	)	PUNCT
ejpam-4624	118	16	,	,	PUNCT
ejpam-4624	118	17	r	r	NOUN
ejpam-4624	118	18	,	,	PUNCT
ejpam-4624	118	19	s	s	NOUN
ejpam-4624	118	20	)	)	PUNCT
ejpam-4624	118	21	)	)	PUNCT
ejpam-4624	119	1	=	=	NOUN
ejpam-4624	119	2	δct	δct	NOUN
ejpam-4624	119	3	,	,	PUNCT
ejpam-4624	119	4	t	t	NOUN
ejpam-4624	119	5	∗(ρ	∗(ρ	NOUN
ejpam-4624	119	6	,	,	PUNCT
ejpam-4624	119	7	r	r	NOUN
ejpam-4624	119	8	,	,	PUNCT
ejpam-4624	119	9	s	s	NOUN
ejpam-4624	119	10	)	)	PUNCT
ejpam-4624	119	11	.	.	PUNCT
ejpam-4624	120	1	proof	proof	NOUN
ejpam-4624	120	2	.	.	PUNCT
ejpam-4624	121	1	similar	similar	ADJ
ejpam-4624	121	2	to	to	PART
ejpam-4624	121	3	proposition	proposition	VERB
ejpam-4624	121	4	2.5	2.5	NUM
ejpam-4624	121	5	.	.	PUNCT
ejpam-4624	122	1	w.	w.	PROPN
ejpam-4624	122	2	f.	f.	PROPN
ejpam-4624	122	3	al	al	PROPN
ejpam-4624	122	4	-	-	PUNCT
ejpam-4624	122	5	omeri	omeri	ADJ
ejpam-4624	122	6	/	/	SYM
ejpam-4624	122	7	eur	eur	PROPN
ejpam-4624	122	8	.	.	PUNCT
ejpam-4624	123	1	j.	j.	PROPN
ejpam-4624	123	2	pure	pure	PROPN
ejpam-4624	123	3	appl	appl	PROPN
ejpam-4624	123	4	.	.	PROPN
ejpam-4624	123	5	math	math	PROPN
ejpam-4624	123	6	,	,	PUNCT
ejpam-4624	123	7	18	18	NUM
ejpam-4624	123	8	(	(	PUNCT
ejpam-4624	123	9	2	2	NUM
ejpam-4624	123	10	)	)	PUNCT
ejpam-4624	123	11	(	(	PUNCT
ejpam-4624	123	12	2025	2025	NUM
ejpam-4624	123	13	)	)	PUNCT
ejpam-4624	123	14	,	,	PUNCT
ejpam-4624	123	15	4624	4624	NUM
ejpam-4624	123	16	6	6	NUM
ejpam-4624	123	17	of	of	ADP
ejpam-4624	123	18	15	15	NUM
ejpam-4624	123	19	lemma	lemma	PROPN
ejpam-4624	123	20	2.7	2.7	NUM
ejpam-4624	123	21	.	.	PUNCT
ejpam-4624	124	1	(	(	PUNCT
ejpam-4624	124	2	i	i	NOUN
ejpam-4624	124	3	)	)	PUNCT
ejpam-4624	124	4	for	for	ADP
ejpam-4624	124	5	any	any	DET
ejpam-4624	124	6	double	double	ADJ
ejpam-4624	124	7	fuzzy	fuzzy	NOUN
ejpam-4624	124	8	set	set	VERB
ejpam-4624	124	9	ρ	ρ	NOUN
ejpam-4624	124	10	in	in	ADP
ejpam-4624	124	11	an	an	DET
ejpam-4624	124	12	double	double	ADJ
ejpam-4624	124	13	fuzzy	fuzzy	ADJ
ejpam-4624	124	14	topology	topology	NOUN
ejpam-4624	124	15	(	(	PUNCT
ejpam-4624	124	16	t	t	PROPN
ejpam-4624	124	17	,	,	PUNCT
ejpam-4624	124	18	t	t	PROPN
ejpam-4624	124	19	∗	∗	NOUN
ejpam-4624	124	20	)	)	PUNCT
ejpam-4624	124	21	on	on	ADP
ejpam-4624	124	22	x	x	SYM
ejpam-4624	124	23	,	,	PUNCT
ejpam-4624	124	24	it	it	PRON
ejpam-4624	124	25	,	,	PUNCT
ejpam-4624	124	26	t	t	PROPN
ejpam-4624	124	27	∗(ct	∗(ct	NOUN
ejpam-4624	124	28	,	,	PUNCT
ejpam-4624	124	29	t	t	NOUN
ejpam-4624	124	30	∗(ρ	∗(ρ	NOUN
ejpam-4624	124	31	,	,	PUNCT
ejpam-4624	124	32	r	r	NOUN
ejpam-4624	124	33	,	,	PUNCT
ejpam-4624	124	34	s	s	NOUN
ejpam-4624	124	35	)	)	PUNCT
ejpam-4624	124	36	)	)	PUNCT
ejpam-4624	124	37	is	be	AUX
ejpam-4624	124	38	a	a	DET
ejpam-4624	124	39	(	(	PUNCT
ejpam-4624	124	40	r	r	NOUN
ejpam-4624	124	41	,	,	PUNCT
ejpam-4624	124	42	s)-fro	s)-fro	NOUN
ejpam-4624	124	43	set	set	NOUN
ejpam-4624	124	44	.	.	PUNCT
ejpam-4624	125	1	(	(	PUNCT
ejpam-4624	125	2	ii	ii	NOUN
ejpam-4624	125	3	)	)	PUNCT
ejpam-4624	125	4	double	double	ADJ
ejpam-4624	125	5	fuzzy	fuzzy	ADJ
ejpam-4624	125	6	set	set	VERB
ejpam-4624	125	7	ρ	ρ	NOUN
ejpam-4624	125	8	in	in	ADP
ejpam-4624	125	9	an	an	DET
ejpam-4624	125	10	double	double	ADJ
ejpam-4624	125	11	fuzzy	fuzzy	ADJ
ejpam-4624	125	12	topology	topology	NOUN
ejpam-4624	125	13	(	(	PUNCT
ejpam-4624	125	14	t	t	PROPN
ejpam-4624	125	15	,	,	PUNCT
ejpam-4624	125	16	t	t	PROPN
ejpam-4624	125	17	∗	∗	NOUN
ejpam-4624	125	18	)	)	PUNCT
ejpam-4624	125	19	on	on	ADP
ejpam-4624	125	20	x	x	PRON
ejpam-4624	125	21	,	,	PUNCT
ejpam-4624	125	22	such	such	ADJ
ejpam-4624	125	23	that	that	SCONJ
ejpam-4624	125	24	xiqρ	xiqρ	PROPN
ejpam-4624	125	25	,	,	PUNCT
ejpam-4624	125	26	it	it	PRON
ejpam-4624	125	27	,	,	PUNCT
ejpam-4624	125	28	t	t	PROPN
ejpam-4624	125	29	∗(ct	∗(ct	NOUN
ejpam-4624	125	30	,	,	PUNCT
ejpam-4624	125	31	t	t	NOUN
ejpam-4624	125	32	∗(ρ	∗(ρ	NOUN
ejpam-4624	125	33	,	,	PUNCT
ejpam-4624	125	34	r	r	NOUN
ejpam-4624	125	35	,	,	PUNCT
ejpam-4624	125	36	s	s	NOUN
ejpam-4624	125	37	)	)	PUNCT
ejpam-4624	125	38	)	)	PUNCT
ejpam-4624	125	39	is	be	AUX
ejpam-4624	125	40	a	a	DET
ejpam-4624	125	41	(	(	PUNCT
ejpam-4624	125	42	r	r	NOUN
ejpam-4624	125	43	,	,	PUNCT
ejpam-4624	125	44	s)-fro	s)-fro	ADJ
ejpam-4624	125	45	q	q	NOUN
ejpam-4624	125	46	-	-	PUNCT
ejpam-4624	125	47	neighborhood	neighborhood	NOUN
ejpam-4624	125	48	of	of	ADP
ejpam-4624	125	49	xi	xi	PROPN
ejpam-4624	125	50	.	.	PUNCT
ejpam-4624	126	1	proof	proof	NOUN
ejpam-4624	126	2	.	.	PUNCT
ejpam-4624	127	1	(	(	PUNCT
ejpam-4624	127	2	i	i	NOUN
ejpam-4624	127	3	)	)	PUNCT
ejpam-4624	127	4	it	it	PRON
ejpam-4624	127	5	’s	’	VERB
ejpam-4624	127	6	enough	enough	ADV
ejpam-4624	127	7	to	to	PART
ejpam-4624	127	8	show	show	VERB
ejpam-4624	127	9	that	that	SCONJ
ejpam-4624	127	10	it	it	PRON
ejpam-4624	127	11	,	,	PUNCT
ejpam-4624	127	12	t	t	PROPN
ejpam-4624	127	13	∗(ct	∗(ct	NOUN
ejpam-4624	127	14	,	,	PUNCT
ejpam-4624	127	15	t	t	NOUN
ejpam-4624	127	16	∗(ρ	∗(ρ	NOUN
ejpam-4624	127	17	,	,	PUNCT
ejpam-4624	127	18	r	r	NOUN
ejpam-4624	127	19	,	,	PUNCT
ejpam-4624	127	20	s	s	NOUN
ejpam-4624	127	21	)	)	PUNCT
ejpam-4624	127	22	)	)	PUNCT
ejpam-4624	128	1	=	=	SYM
ejpam-4624	128	2	it	it	PRON
ejpam-4624	128	3	,	,	PUNCT
ejpam-4624	128	4	t	t	PROPN
ejpam-4624	128	5	∗(ct	∗(ct	PROPN
ejpam-4624	128	6	,	,	PUNCT
ejpam-4624	128	7	t	t	PROPN
ejpam-4624	128	8	∗(it	∗(it	NUM
ejpam-4624	128	9	,	,	PUNCT
ejpam-4624	128	10	t	t	PROPN
ejpam-4624	128	11	∗(ct	∗(ct	NOUN
ejpam-4624	128	12	,	,	PUNCT
ejpam-4624	128	13	t	t	NOUN
ejpam-4624	128	14	∗(ρ	∗(ρ	NOUN
ejpam-4624	128	15	,	,	PUNCT
ejpam-4624	128	16	r	r	NOUN
ejpam-4624	128	17	,	,	PUNCT
ejpam-4624	128	18	s	s	NOUN
ejpam-4624	128	19	)	)	PUNCT
ejpam-4624	128	20	)	)	PUNCT
ejpam-4624	128	21	)	)	PUNCT
ejpam-4624	128	22	.	.	PUNCT
ejpam-4624	129	1	since	since	SCONJ
ejpam-4624	129	2	it	it	PRON
ejpam-4624	129	3	,	,	PUNCT
ejpam-4624	129	4	t	t	PROPN
ejpam-4624	129	5	∗(ct	∗(ct	NOUN
ejpam-4624	129	6	,	,	PUNCT
ejpam-4624	129	7	t	t	NOUN
ejpam-4624	129	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	129	9	,	,	PUNCT
ejpam-4624	129	10	r	r	NOUN
ejpam-4624	129	11	,	,	PUNCT
ejpam-4624	129	12	s	s	NOUN
ejpam-4624	129	13	)	)	PUNCT
ejpam-4624	129	14	)	)	PUNCT
ejpam-4624	129	15	≤	≤	NUM
ejpam-4624	130	1	ct	ct	NUM
ejpam-4624	130	2	,	,	PUNCT
ejpam-4624	130	3	t	t	PROPN
ejpam-4624	130	4	∗(it	∗(it	NUM
ejpam-4624	130	5	,	,	PUNCT
ejpam-4624	130	6	t	t	PROPN
ejpam-4624	130	7	∗(ct	∗(ct	NOUN
ejpam-4624	130	8	,	,	PUNCT
ejpam-4624	130	9	t	t	NOUN
ejpam-4624	130	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	130	11	,	,	PUNCT
ejpam-4624	130	12	r	r	NOUN
ejpam-4624	130	13	,	,	PUNCT
ejpam-4624	130	14	s	s	NOUN
ejpam-4624	130	15	)	)	PUNCT
ejpam-4624	130	16	)	)	PUNCT
ejpam-4624	130	17	)	)	PUNCT
ejpam-4624	130	18	,	,	PUNCT
ejpam-4624	130	19	and	and	CCONJ
ejpam-4624	130	20	we	we	PRON
ejpam-4624	130	21	have	have	VERB
ejpam-4624	130	22	it	it	PRON
ejpam-4624	130	23	,	,	PUNCT
ejpam-4624	130	24	t	t	PROPN
ejpam-4624	130	25	∗(it	∗(it	VERB
ejpam-4624	130	26	,	,	PUNCT
ejpam-4624	130	27	t	t	PROPN
ejpam-4624	130	28	∗(ct	∗(ct	NOUN
ejpam-4624	130	29	,	,	PUNCT
ejpam-4624	130	30	t	t	NOUN
ejpam-4624	130	31	∗(ρ	∗(ρ	NOUN
ejpam-4624	130	32	,	,	PUNCT
ejpam-4624	130	33	r	r	NOUN
ejpam-4624	130	34	,	,	PUNCT
ejpam-4624	130	35	s	s	NOUN
ejpam-4624	130	36	)	)	PUNCT
ejpam-4624	130	37	)	)	PUNCT
ejpam-4624	131	1	≤	≤	ADV
ejpam-4624	131	2	it	it	PRON
ejpam-4624	131	3	,	,	PUNCT
ejpam-4624	131	4	t	t	PROPN
ejpam-4624	131	5	∗(ct	∗(ct	PROPN
ejpam-4624	131	6	,	,	PUNCT
ejpam-4624	131	7	t	t	PROPN
ejpam-4624	131	8	∗(it	∗(it	NUM
ejpam-4624	131	9	,	,	PUNCT
ejpam-4624	131	10	t	t	PROPN
ejpam-4624	131	11	∗(ct	∗(ct	NOUN
ejpam-4624	131	12	,	,	PUNCT
ejpam-4624	131	13	t	t	NOUN
ejpam-4624	131	14	∗(ρ	∗(ρ	NOUN
ejpam-4624	131	15	,	,	PUNCT
ejpam-4624	131	16	r	r	NOUN
ejpam-4624	131	17	,	,	PUNCT
ejpam-4624	131	18	s	s	NOUN
ejpam-4624	131	19	)	)	PUNCT
ejpam-4624	131	20	)	)	PUNCT
ejpam-4624	131	21	)	)	PUNCT
ejpam-4624	131	22	.	.	PUNCT
ejpam-4624	132	1	thus	thus	ADV
ejpam-4624	132	2	it	it	PRON
ejpam-4624	132	3	,	,	PUNCT
ejpam-4624	132	4	t	t	PROPN
ejpam-4624	132	5	∗(ct	∗(ct	NOUN
ejpam-4624	132	6	,	,	PUNCT
ejpam-4624	132	7	t	t	NOUN
ejpam-4624	132	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	132	9	,	,	PUNCT
ejpam-4624	132	10	r	r	NOUN
ejpam-4624	132	11	,	,	PUNCT
ejpam-4624	132	12	s	s	NOUN
ejpam-4624	132	13	)	)	PUNCT
ejpam-4624	132	14	)	)	PUNCT
ejpam-4624	132	15	≤	≤	ADV
ejpam-4624	132	16	it	it	PRON
ejpam-4624	132	17	,	,	PUNCT
ejpam-4624	132	18	t	t	PROPN
ejpam-4624	132	19	∗(ct	∗(ct	PROPN
ejpam-4624	132	20	,	,	PUNCT
ejpam-4624	132	21	t	t	PROPN
ejpam-4624	132	22	∗(it	∗(it	NUM
ejpam-4624	132	23	,	,	PUNCT
ejpam-4624	132	24	t	t	PROPN
ejpam-4624	132	25	∗(ct	∗(ct	NOUN
ejpam-4624	132	26	,	,	PUNCT
ejpam-4624	132	27	t	t	NOUN
ejpam-4624	132	28	∗(ρ	∗(ρ	NOUN
ejpam-4624	132	29	,	,	PUNCT
ejpam-4624	132	30	r	r	NOUN
ejpam-4624	132	31	,	,	PUNCT
ejpam-4624	132	32	s	s	NOUN
ejpam-4624	132	33	)	)	PUNCT
ejpam-4624	132	34	)	)	PUNCT
ejpam-4624	132	35	)	)	PUNCT
ejpam-4624	132	36	.	.	PUNCT
ejpam-4624	133	1	conversely	conversely	ADV
ejpam-4624	133	2	,	,	PUNCT
ejpam-4624	133	3	since	since	SCONJ
ejpam-4624	133	4	it	it	PRON
ejpam-4624	133	5	,	,	PUNCT
ejpam-4624	133	6	t	t	PROPN
ejpam-4624	133	7	∗(ct	∗(ct	NOUN
ejpam-4624	133	8	,	,	PUNCT
ejpam-4624	133	9	t	t	NOUN
ejpam-4624	133	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	133	11	,	,	PUNCT
ejpam-4624	133	12	r	r	NOUN
ejpam-4624	133	13	,	,	PUNCT
ejpam-4624	133	14	s	s	NOUN
ejpam-4624	133	15	)	)	PUNCT
ejpam-4624	133	16	)	)	PUNCT
ejpam-4624	133	17	≤	≤	NUM
ejpam-4624	133	18	ct	ct	NUM
ejpam-4624	133	19	,	,	PUNCT
ejpam-4624	133	20	t	t	NOUN
ejpam-4624	133	21	∗(ρ	∗(ρ	NOUN
ejpam-4624	133	22	,	,	PUNCT
ejpam-4624	133	23	r	r	NOUN
ejpam-4624	133	24	,	,	PUNCT
ejpam-4624	133	25	s	s	NOUN
ejpam-4624	133	26	)	)	PUNCT
ejpam-4624	133	27	,	,	PUNCT
ejpam-4624	133	28	and	and	CCONJ
ejpam-4624	133	29	we	we	PRON
ejpam-4624	133	30	have	have	VERB
ejpam-4624	133	31	ct	ct	NUM
ejpam-4624	133	32	,	,	PUNCT
ejpam-4624	133	33	t	t	PROPN
ejpam-4624	133	34	∗(it	∗(it	NUM
ejpam-4624	133	35	,	,	PUNCT
ejpam-4624	133	36	t	t	PROPN
ejpam-4624	133	37	∗(ct	∗(ct	NOUN
ejpam-4624	133	38	,	,	PUNCT
ejpam-4624	133	39	t	t	NOUN
ejpam-4624	133	40	∗(ρ	∗(ρ	NOUN
ejpam-4624	133	41	,	,	PUNCT
ejpam-4624	133	42	r	r	NOUN
ejpam-4624	133	43	,	,	PUNCT
ejpam-4624	133	44	s	s	NOUN
ejpam-4624	133	45	)	)	PUNCT
ejpam-4624	133	46	)	)	PUNCT
ejpam-4624	134	1	≤	≤	NUM
ejpam-4624	134	2	ct	ct	NUM
ejpam-4624	134	3	,	,	PUNCT
ejpam-4624	134	4	t	t	PROPN
ejpam-4624	134	5	∗(ct	∗(ct	PROPN
ejpam-4624	134	6	,	,	PUNCT
ejpam-4624	134	7	t	t	NOUN
ejpam-4624	134	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	134	9	,	,	PUNCT
ejpam-4624	134	10	r	r	NOUN
ejpam-4624	134	11	,	,	PUNCT
ejpam-4624	134	12	s	s	NOUN
ejpam-4624	134	13	)	)	PUNCT
ejpam-4624	134	14	)	)	PUNCT
ejpam-4624	135	1	=	=	SYM
ejpam-4624	135	2	ct	ct	PROPN
ejpam-4624	135	3	,	,	PUNCT
ejpam-4624	135	4	t	t	PROPN
ejpam-4624	135	5	∗((ρ	∗((ρ	PROPN
ejpam-4624	135	6	,	,	PUNCT
ejpam-4624	135	7	r	r	NOUN
ejpam-4624	135	8	,	,	PUNCT
ejpam-4624	135	9	s	s	PART
ejpam-4624	135	10	)	)	PUNCT
ejpam-4624	135	11	,	,	PUNCT
ejpam-4624	135	12	r	r	NOUN
ejpam-4624	135	13	,	,	PUNCT
ejpam-4624	135	14	s	s	NOUN
ejpam-4624	135	15	)	)	PUNCT
ejpam-4624	135	16	.	.	PUNCT
ejpam-4624	136	1	thus	thus	ADV
ejpam-4624	136	2	it	it	PRON
ejpam-4624	136	3	,	,	PUNCT
ejpam-4624	136	4	t	t	PROPN
ejpam-4624	136	5	∗(ct	∗(ct	PROPN
ejpam-4624	136	6	,	,	PUNCT
ejpam-4624	136	7	t	t	PROPN
ejpam-4624	136	8	∗(it	∗(it	NUM
ejpam-4624	136	9	,	,	PUNCT
ejpam-4624	136	10	t	t	PROPN
ejpam-4624	136	11	∗(ct	∗(ct	NOUN
ejpam-4624	136	12	,	,	PUNCT
ejpam-4624	136	13	t	t	NOUN
ejpam-4624	136	14	∗(ρ	∗(ρ	NOUN
ejpam-4624	136	15	,	,	PUNCT
ejpam-4624	136	16	r	r	NOUN
ejpam-4624	136	17	,	,	PUNCT
ejpam-4624	136	18	s	s	NOUN
ejpam-4624	136	19	)	)	PUNCT
ejpam-4624	136	20	)	)	PUNCT
ejpam-4624	136	21	)	)	PUNCT
ejpam-4624	137	1	≤	≤	ADV
ejpam-4624	137	2	it	it	PRON
ejpam-4624	137	3	,	,	PUNCT
ejpam-4624	137	4	t	t	PROPN
ejpam-4624	137	5	∗(ct	∗(ct	NOUN
ejpam-4624	137	6	,	,	PUNCT
ejpam-4624	137	7	t	t	NOUN
ejpam-4624	137	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	137	9	,	,	PUNCT
ejpam-4624	137	10	r	r	NOUN
ejpam-4624	137	11	,	,	PUNCT
ejpam-4624	137	12	s	s	NOUN
ejpam-4624	137	13	)	)	PUNCT
ejpam-4624	137	14	)	)	PUNCT
ejpam-4624	137	15	.	.	PUNCT
ejpam-4624	138	1	hence	hence	ADV
ejpam-4624	138	2	it	it	PRON
ejpam-4624	138	3	,	,	PUNCT
ejpam-4624	138	4	t	t	PROPN
ejpam-4624	138	5	∗(ct	∗(ct	PROPN
ejpam-4624	138	6	,	,	PUNCT
ejpam-4624	138	7	t	t	NOUN
ejpam-4624	138	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	138	9	,	,	PUNCT
ejpam-4624	138	10	r	r	NOUN
ejpam-4624	138	11	,	,	PUNCT
ejpam-4624	138	12	s	s	NOUN
ejpam-4624	138	13	)	)	PUNCT
ejpam-4624	138	14	)	)	PUNCT
ejpam-4624	138	15	is	be	AUX
ejpam-4624	138	16	a	a	DET
ejpam-4624	138	17	(	(	PUNCT
ejpam-4624	138	18	r	r	NOUN
ejpam-4624	138	19	,	,	PUNCT
ejpam-4624	138	20	s)-fro	s)-fro	NOUN
ejpam-4624	138	21	set	set	NOUN
ejpam-4624	138	22	.	.	PUNCT
ejpam-4624	139	1	(	(	PUNCT
ejpam-4624	139	2	ii	ii	NOUN
ejpam-4624	139	3	)	)	PUNCT
ejpam-4624	139	4	clearly	clearly	ADV
ejpam-4624	139	5	,	,	PUNCT
ejpam-4624	139	6	it	it	PRON
ejpam-4624	139	7	,	,	PUNCT
ejpam-4624	139	8	t	t	NOUN
ejpam-4624	139	9	∗(ρ	∗(ρ	NOUN
ejpam-4624	139	10	,	,	PUNCT
ejpam-4624	139	11	r	r	NOUN
ejpam-4624	139	12	,	,	PUNCT
ejpam-4624	139	13	s	s	NOUN
ejpam-4624	139	14	)	)	PUNCT
ejpam-4624	139	15	≤	≤	NOUN
ejpam-4624	139	16	it	it	PRON
ejpam-4624	139	17	,	,	PUNCT
ejpam-4624	139	18	t	t	PROPN
ejpam-4624	139	19	∗(ct	∗(ct	NOUN
ejpam-4624	139	20	,	,	PUNCT
ejpam-4624	139	21	t	t	NOUN
ejpam-4624	139	22	∗(ρ	∗(ρ	NOUN
ejpam-4624	139	23	,	,	PUNCT
ejpam-4624	139	24	r	r	NOUN
ejpam-4624	139	25	,	,	PUNCT
ejpam-4624	139	26	s	s	NOUN
ejpam-4624	139	27	)	)	PUNCT
ejpam-4624	139	28	)	)	PUNCT
ejpam-4624	139	29	.	.	PUNCT
ejpam-4624	140	1	since	since	SCONJ
ejpam-4624	140	2	ρ	ρ	PROPN
ejpam-4624	140	3	is	be	AUX
ejpam-4624	140	4	a	a	DET
ejpam-4624	140	5	(	(	PUNCT
ejpam-4624	140	6	r	r	NOUN
ejpam-4624	140	7	,	,	PUNCT
ejpam-4624	140	8	s)-fro	s)-fro	NOUN
ejpam-4624	140	9	set	set	NOUN
ejpam-4624	140	10	,	,	PUNCT
ejpam-4624	140	11	we	we	PRON
ejpam-4624	140	12	have	have	VERB
ejpam-4624	140	13	ρ	ρ	NOUN
ejpam-4624	140	14	=	=	PUNCT
ejpam-4624	140	15	it	it	PRON
ejpam-4624	140	16	,	,	PUNCT
ejpam-4624	140	17	t	t	NOUN
ejpam-4624	140	18	∗(ρ	∗(ρ	NOUN
ejpam-4624	140	19	,	,	PUNCT
ejpam-4624	140	20	r	r	NOUN
ejpam-4624	140	21	,	,	PUNCT
ejpam-4624	140	22	s	s	NOUN
ejpam-4624	140	23	)	)	PUNCT
ejpam-4624	140	24	≤	≤	NOUN
ejpam-4624	140	25	it	it	PRON
ejpam-4624	140	26	,	,	PUNCT
ejpam-4624	140	27	t	t	PROPN
ejpam-4624	140	28	∗(ct	∗(ct	NOUN
ejpam-4624	140	29	,	,	PUNCT
ejpam-4624	140	30	t	t	NOUN
ejpam-4624	140	31	∗(ρ	∗(ρ	NOUN
ejpam-4624	140	32	,	,	PUNCT
ejpam-4624	140	33	r	r	NOUN
ejpam-4624	140	34	,	,	PUNCT
ejpam-4624	140	35	s	s	NOUN
ejpam-4624	140	36	)	)	PUNCT
ejpam-4624	140	37	)	)	PUNCT
ejpam-4624	140	38	.	.	PUNCT
ejpam-4624	141	1	by	by	ADP
ejpam-4624	141	2	(	(	PUNCT
ejpam-4624	141	3	1	1	NUM
ejpam-4624	141	4	)	)	PUNCT
ejpam-4624	141	5	,	,	PUNCT
ejpam-4624	141	6	it	it	PRON
ejpam-4624	141	7	,	,	PUNCT
ejpam-4624	141	8	t	t	PROPN
ejpam-4624	141	9	∗(ct	∗(ct	NOUN
ejpam-4624	141	10	,	,	PUNCT
ejpam-4624	141	11	t	t	NOUN
ejpam-4624	141	12	∗(ρ	∗(ρ	NOUN
ejpam-4624	141	13	,	,	PUNCT
ejpam-4624	141	14	r	r	NOUN
ejpam-4624	141	15	,	,	PUNCT
ejpam-4624	141	16	s	s	NOUN
ejpam-4624	141	17	)	)	PUNCT
ejpam-4624	141	18	)	)	PUNCT
ejpam-4624	141	19	is	be	AUX
ejpam-4624	141	20	a	a	DET
ejpam-4624	141	21	(	(	PUNCT
ejpam-4624	141	22	r	r	NOUN
ejpam-4624	141	23	,	,	PUNCT
ejpam-4624	141	24	s)-fro	s)-fro	NOUN
ejpam-4624	141	25	set	set	NOUN
ejpam-4624	141	26	.	.	PUNCT
ejpam-4624	142	1	therefore	therefore	ADV
ejpam-4624	142	2	it	it	PRON
ejpam-4624	142	3	,	,	PUNCT
ejpam-4624	142	4	t	t	PROPN
ejpam-4624	142	5	∗(ct	∗(ct	PROPN
ejpam-4624	142	6	,	,	PUNCT
ejpam-4624	142	7	t	t	NOUN
ejpam-4624	142	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	142	9	,	,	PUNCT
ejpam-4624	142	10	r	r	NOUN
ejpam-4624	142	11	,	,	PUNCT
ejpam-4624	142	12	s	s	PART
ejpam-4624	142	13	)	)	PUNCT
ejpam-4624	142	14	is	be	AUX
ejpam-4624	142	15	a	a	DET
ejpam-4624	142	16	(	(	PUNCT
ejpam-4624	142	17	r	r	NOUN
ejpam-4624	142	18	,	,	PUNCT
ejpam-4624	142	19	s)-fro	s)-fro	ADJ
ejpam-4624	142	20	q	q	NOUN
ejpam-4624	142	21	-	-	PUNCT
ejpam-4624	142	22	neighborhood	neighborhood	NOUN
ejpam-4624	142	23	of	of	ADP
ejpam-4624	142	24	xi	xi	PROPN
ejpam-4624	142	25	.	.	PUNCT
ejpam-4624	143	1	a	a	PRON
ejpam-4624	143	2	(	(	PUNCT
ejpam-4624	143	3	r	r	NOUN
ejpam-4624	143	4	,	,	PUNCT
ejpam-4624	143	5	s)-frc	s)-frc	NOUN
ejpam-4624	143	6	set	set	NOUN
ejpam-4624	143	7	is	be	AUX
ejpam-4624	143	8	not	not	PART
ejpam-4624	143	9	always	always	ADV
ejpam-4624	143	10	(	(	PUNCT
ejpam-4624	143	11	r	r	NOUN
ejpam-4624	143	12	,	,	PUNCT
ejpam-4624	143	13	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	143	14	δ	δ	PROPN
ejpam-4624	143	15	-	-	PUNCT
ejpam-4624	143	16	closed	closed	ADJ
ejpam-4624	143	17	set	set	NOUN
ejpam-4624	143	18	.	.	PUNCT
ejpam-4624	144	1	for	for	ADP
ejpam-4624	144	2	example	example	NOUN
ejpam-4624	144	3	,	,	PUNCT
ejpam-4624	144	4	example	example	NOUN
ejpam-4624	144	5	2.8	2.8	NUM
ejpam-4624	144	6	.	.	PUNCT
ejpam-4624	145	1	let	let	VERB
ejpam-4624	145	2	x	x	PUNCT
ejpam-4624	145	3	=	=	PRON
ejpam-4624	145	4	{	{	PUNCT
ejpam-4624	145	5	a	a	DET
ejpam-4624	145	6	,	,	PUNCT
ejpam-4624	145	7	b	b	NOUN
ejpam-4624	145	8	}	}	PUNCT
ejpam-4624	145	9	and	and	CCONJ
ejpam-4624	145	10	the	the	DET
ejpam-4624	145	11	fuzzy	fuzzy	ADJ
ejpam-4624	145	12	set	set	VERB
ejpam-4624	145	13	µ1	µ1	NOUN
ejpam-4624	145	14	define	define	NOUN
ejpam-4624	145	15	as	as	SCONJ
ejpam-4624	145	16	follows	follow	VERB
ejpam-4624	145	17	:	:	PUNCT
ejpam-4624	145	18	µ1(a	µ1(a	ADP
ejpam-4624	145	19	)	)	PUNCT
ejpam-4624	145	20	=	=	SYM
ejpam-4624	145	21	0.5	0.5	NUM
ejpam-4624	145	22	,	,	PUNCT
ejpam-4624	145	23	µ1(b	µ1(b	NOUN
ejpam-4624	145	24	)	)	PUNCT
ejpam-4624	145	25	=	=	SYM
ejpam-4624	145	26	0.6	0.6	NUM
ejpam-4624	145	27	,	,	PUNCT
ejpam-4624	145	28	w.	w.	PROPN
ejpam-4624	145	29	f.	f.	PROPN
ejpam-4624	145	30	al	al	PROPN
ejpam-4624	145	31	-	-	PUNCT
ejpam-4624	145	32	omeri	omeri	ADJ
ejpam-4624	145	33	/	/	SYM
ejpam-4624	145	34	eur	eur	PROPN
ejpam-4624	145	35	.	.	PUNCT
ejpam-4624	146	1	j.	j.	PROPN
ejpam-4624	146	2	pure	pure	PROPN
ejpam-4624	146	3	appl	appl	PROPN
ejpam-4624	146	4	.	.	PROPN
ejpam-4624	146	5	math	math	PROPN
ejpam-4624	146	6	,	,	PUNCT
ejpam-4624	146	7	18	18	NUM
ejpam-4624	146	8	(	(	PUNCT
ejpam-4624	146	9	2	2	NUM
ejpam-4624	146	10	)	)	PUNCT
ejpam-4624	146	11	(	(	PUNCT
ejpam-4624	146	12	2025	2025	NUM
ejpam-4624	146	13	)	)	PUNCT
ejpam-4624	146	14	,	,	PUNCT
ejpam-4624	146	15	4624	4624	NUM
ejpam-4624	146	16	7	7	NUM
ejpam-4624	146	17	of	of	ADP
ejpam-4624	146	18	15	15	NUM
ejpam-4624	146	19	the	the	DET
ejpam-4624	146	20	double	double	ADJ
ejpam-4624	146	21	fuzzy	fuzzy	ADJ
ejpam-4624	146	22	space	space	NOUN
ejpam-4624	146	23	(	(	PUNCT
ejpam-4624	146	24	t	t	PROPN
ejpam-4624	146	25	,	,	PUNCT
ejpam-4624	146	26	t	t	PROPN
ejpam-4624	146	27	∗	∗	NOUN
ejpam-4624	146	28	)	)	PUNCT
ejpam-4624	146	29	is	be	AUX
ejpam-4624	146	30	define	define	VERB
ejpam-4624	146	31	on	on	ADP
ejpam-4624	146	32	x	x	PUNCT
ejpam-4624	146	33	as	as	SCONJ
ejpam-4624	146	34	follows	follow	VERB
ejpam-4624	146	35	:	:	PUNCT
ejpam-4624	146	36	:	:	PUNCT
ejpam-4624	146	37	t	t	X
ejpam-4624	146	38	(	(	PUNCT
ejpam-4624	146	39	ρ	ρ	NOUN
ejpam-4624	146	40	)	)	PUNCT
ejpam-4624	146	41	=	=	PUNCT
ejpam-4624	146	42			PROPN
ejpam-4624	146	43	1	1	NUM
ejpam-4624	146	44	,	,	PUNCT
ejpam-4624	146	45	if	if	SCONJ
ejpam-4624	146	46	ρ	ρ	PROPN
ejpam-4624	146	47	∈	∈	PROPN
ejpam-4624	146	48	{	{	PUNCT
ejpam-4624	146	49	0	0	NUM
ejpam-4624	146	50	,	,	PUNCT
ejpam-4624	146	51	1	1	NUM
ejpam-4624	146	52	}	}	PUNCT
ejpam-4624	146	53	,	,	PUNCT
ejpam-4624	146	54	1	1	NUM
ejpam-4624	146	55	2	2	NUM
ejpam-4624	146	56	,	,	PUNCT
ejpam-4624	146	57	if	if	SCONJ
ejpam-4624	146	58	ρ	ρ	PROPN
ejpam-4624	146	59	=	=	SYM
ejpam-4624	146	60	µ1	µ1	PROPN
ejpam-4624	146	61	,	,	PUNCT
ejpam-4624	146	62	0	0	NUM
ejpam-4624	146	63	,	,	PUNCT
ejpam-4624	146	64	otherwise	otherwise	ADV
ejpam-4624	146	65	.	.	PUNCT
ejpam-4624	147	1	t	t	NOUN
ejpam-4624	147	2	∗(ρ	∗(ρ	NOUN
ejpam-4624	147	3	)	)	PUNCT
ejpam-4624	147	4	=	=	PUNCT
ejpam-4624	148	1			PROPN
ejpam-4624	148	2	0	0	NUM
ejpam-4624	148	3	,	,	PUNCT
ejpam-4624	148	4	if	if	SCONJ
ejpam-4624	148	5	ρ	ρ	PROPN
ejpam-4624	148	6	∈	∈	PROPN
ejpam-4624	148	7	{	{	PUNCT
ejpam-4624	148	8	0	0	NUM
ejpam-4624	148	9	,	,	PUNCT
ejpam-4624	148	10	1	1	NUM
ejpam-4624	148	11	}	}	PUNCT
ejpam-4624	148	12	,	,	PUNCT
ejpam-4624	148	13	1	1	NUM
ejpam-4624	148	14	2	2	NUM
ejpam-4624	148	15	,	,	PUNCT
ejpam-4624	148	16	if	if	SCONJ
ejpam-4624	148	17	ρ	ρ	PROPN
ejpam-4624	148	18	=	=	SYM
ejpam-4624	148	19	µ1	µ1	PROPN
ejpam-4624	148	20	,	,	PUNCT
ejpam-4624	148	21	1	1	NUM
ejpam-4624	148	22	,	,	PUNCT
ejpam-4624	148	23	otherwise	otherwise	ADV
ejpam-4624	148	24	.	.	PUNCT
ejpam-4624	149	1	since	since	SCONJ
ejpam-4624	149	2	µ1	µ1	PROPN
ejpam-4624	149	3	=	=	SYM
ejpam-4624	149	4	ct	ct	PROPN
ejpam-4624	149	5	,	,	PUNCT
ejpam-4624	149	6	t	t	PROPN
ejpam-4624	149	7	∗(it	∗(it	NUM
ejpam-4624	149	8	,	,	PUNCT
ejpam-4624	149	9	t	t	NOUN
ejpam-4624	149	10	∗(µ1	∗(µ1	NOUN
ejpam-4624	149	11	,	,	PUNCT
ejpam-4624	149	12	r	r	NOUN
ejpam-4624	149	13	,	,	PUNCT
ejpam-4624	149	14	s	s	PART
ejpam-4624	149	15	)	)	PUNCT
ejpam-4624	149	16	,	,	PUNCT
ejpam-4624	149	17	r	r	NOUN
ejpam-4624	149	18	,	,	PUNCT
ejpam-4624	149	19	s	s	NOUN
ejpam-4624	149	20	)	)	PUNCT
ejpam-4624	149	21	.	.	PUNCT
ejpam-4624	150	1	then	then	ADV
ejpam-4624	150	2	,	,	PUNCT
ejpam-4624	150	3	µ1	µ1	PROPN
ejpam-4624	150	4	is	be	AUX
ejpam-4624	150	5	(	(	PUNCT
ejpam-4624	150	6	12	12	NUM
ejpam-4624	150	7	,	,	PUNCT
ejpam-4624	150	8	1	1	NUM
ejpam-4624	150	9	2)-frc	2)-frc	NUM
ejpam-4624	150	10	set	set	NOUN
ejpam-4624	150	11	,	,	PUNCT
ejpam-4624	150	12	but	but	CCONJ
ejpam-4624	150	13	is	be	AUX
ejpam-4624	150	14	not	not	PART
ejpam-4624	150	15	(	(	PUNCT
ejpam-4624	150	16	12	12	NUM
ejpam-4624	150	17	)	)	PUNCT
ejpam-4624	150	18	,	,	PUNCT
ejpam-4624	150	19	1	1	NUM
ejpam-4624	150	20	2)-fuzzy	2)-fuzzy	NUM
ejpam-4624	150	21	δ	δ	NOUN
ejpam-4624	150	22	-	-	PUNCT
ejpam-4624	150	23	closed	close	VERB
ejpam-4624	150	24	set	set	NOUN
ejpam-4624	150	25	.	.	PUNCT
ejpam-4624	151	1	theorem	theorem	VERB
ejpam-4624	151	2	2.9	2.9	NUM
ejpam-4624	151	3	.	.	PUNCT
ejpam-4624	152	1	for	for	ADP
ejpam-4624	152	2	any	any	DET
ejpam-4624	152	3	dfs	dfs	PROPN
ejpam-4624	152	4	ρ	ρ	NOUN
ejpam-4624	152	5	in	in	ADP
ejpam-4624	152	6	an	an	DET
ejpam-4624	152	7	dfts	dft	NOUN
ejpam-4624	152	8	(	(	PUNCT
ejpam-4624	152	9	x	x	X
ejpam-4624	152	10	,	,	PUNCT
ejpam-4624	152	11	t	t	PROPN
ejpam-4624	152	12	,	,	PUNCT
ejpam-4624	152	13	t	t	PROPN
ejpam-4624	152	14	∗	∗	NOUN
ejpam-4624	152	15	)	)	PUNCT
ejpam-4624	152	16	,	,	PUNCT
ejpam-4624	152	17	we	we	PRON
ejpam-4624	152	18	have	have	VERB
ejpam-4624	152	19	:	:	PUNCT
ejpam-4624	152	20	(	(	PUNCT
ejpam-4624	152	21	i	i	NOUN
ejpam-4624	152	22	)	)	PUNCT
ejpam-4624	152	23	ct	ct	PROPN
ejpam-4624	152	24	,	,	PUNCT
ejpam-4624	152	25	t	t	NOUN
ejpam-4624	152	26	∗(ρ	∗(ρ	NOUN
ejpam-4624	152	27	,	,	PUNCT
ejpam-4624	152	28	r	r	NOUN
ejpam-4624	152	29	,	,	PUNCT
ejpam-4624	152	30	s	s	NOUN
ejpam-4624	152	31	)	)	PUNCT
ejpam-4624	152	32	≤	≤	NOUN
ejpam-4624	152	33	δct	δct	NOUN
ejpam-4624	152	34	,	,	PUNCT
ejpam-4624	152	35	t	t	NOUN
ejpam-4624	152	36	∗(ρ	∗(ρ	NOUN
ejpam-4624	152	37	,	,	PUNCT
ejpam-4624	152	38	r	r	NOUN
ejpam-4624	152	39	,	,	PUNCT
ejpam-4624	152	40	s	s	NOUN
ejpam-4624	152	41	)	)	PUNCT
ejpam-4624	152	42	.	.	PUNCT
ejpam-4624	153	1	(	(	PUNCT
ejpam-4624	153	2	ii	ii	NOUN
ejpam-4624	153	3	)	)	PUNCT
ejpam-4624	153	4	δit	δit	NOUN
ejpam-4624	153	5	,	,	PUNCT
ejpam-4624	153	6	t	t	NOUN
ejpam-4624	153	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	153	8	,	,	PUNCT
ejpam-4624	153	9	r	r	NOUN
ejpam-4624	153	10	,	,	PUNCT
ejpam-4624	153	11	s	s	NOUN
ejpam-4624	153	12	)	)	PUNCT
ejpam-4624	153	13	≤	≤	NOUN
ejpam-4624	153	14	it	it	PRON
ejpam-4624	153	15	,	,	PUNCT
ejpam-4624	153	16	t	t	NOUN
ejpam-4624	153	17	∗(ρ	∗(ρ	NOUN
ejpam-4624	153	18	,	,	PUNCT
ejpam-4624	153	19	r	r	NOUN
ejpam-4624	153	20	,	,	PUNCT
ejpam-4624	153	21	s	s	NOUN
ejpam-4624	153	22	)	)	PUNCT
ejpam-4624	153	23	.	.	PUNCT
ejpam-4624	154	1	proof	proof	NOUN
ejpam-4624	154	2	.	.	PUNCT
ejpam-4624	155	1	it	it	PRON
ejpam-4624	155	2	is	be	AUX
ejpam-4624	155	3	obvious	obvious	ADJ
ejpam-4624	155	4	.	.	PUNCT
ejpam-4624	156	1	theorem	theorem	VERB
ejpam-4624	156	2	2.10	2.10	NUM
ejpam-4624	156	3	.	.	PUNCT
ejpam-4624	157	1	let	let	VERB
ejpam-4624	157	2	ρ	ρ	NOUN
ejpam-4624	157	3	,	,	PUNCT
ejpam-4624	157	4	ϕ	ϕ	PROPN
ejpam-4624	157	5	∈	∈	PROPN
ejpam-4624	157	6	ix	ix	ADV
ejpam-4624	157	7	.	.	PUNCT
ejpam-4624	158	1	the	the	DET
ejpam-4624	158	2	finite	finite	PROPN
ejpam-4624	158	3	union	union	PROPN
ejpam-4624	158	4	of	of	ADP
ejpam-4624	158	5	(	(	PUNCT
ejpam-4624	158	6	r	r	NOUN
ejpam-4624	158	7	,	,	PUNCT
ejpam-4624	158	8	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	158	9	δ	δ	PROPN
ejpam-4624	158	10	-	-	PUNCT
ejpam-4624	158	11	closed	closed	ADJ
ejpam-4624	158	12	sets	set	NOUN
ejpam-4624	158	13	is	be	AUX
ejpam-4624	158	14	also	also	ADV
ejpam-4624	158	15	(	(	PUNCT
ejpam-4624	158	16	r	r	NOUN
ejpam-4624	158	17	,	,	PUNCT
ejpam-4624	158	18	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	158	19	δ	δ	PROPN
ejpam-4624	158	20	-	-	PUNCT
ejpam-4624	158	21	closed	closed	ADJ
ejpam-4624	158	22	,	,	PUNCT
ejpam-4624	158	23	where	where	SCONJ
ejpam-4624	158	24	r	r	NOUN
ejpam-4624	158	25	∈	∈	PROPN
ejpam-4624	158	26	i0	i0	PROPN
ejpam-4624	158	27	and	and	CCONJ
ejpam-4624	158	28	s	s	PROPN
ejpam-4624	158	29	∈	∈	PROPN
ejpam-4624	158	30	i1	i1	PROPN
ejpam-4624	158	31	.	.	PUNCT
ejpam-4624	159	1	that	that	PRON
ejpam-4624	159	2	is	be	AUX
ejpam-4624	159	3	,	,	PUNCT
ejpam-4624	159	4	if	if	SCONJ
ejpam-4624	159	5	ρ	ρ	PROPN
ejpam-4624	159	6	=	=	NOUN
ejpam-4624	159	7	δct	δct	NOUN
ejpam-4624	159	8	,	,	PUNCT
ejpam-4624	159	9	t	t	NOUN
ejpam-4624	159	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	159	11	,	,	PUNCT
ejpam-4624	159	12	r	r	NOUN
ejpam-4624	159	13	,	,	PUNCT
ejpam-4624	159	14	s	s	PART
ejpam-4624	159	15	)	)	PUNCT
ejpam-4624	159	16	and	and	CCONJ
ejpam-4624	159	17	ϕ	ϕ	X
ejpam-4624	159	18	=	=	NOUN
ejpam-4624	159	19	δct	δct	NOUN
ejpam-4624	159	20	,	,	PUNCT
ejpam-4624	159	21	t	t	PROPN
ejpam-4624	159	22	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	159	23	,	,	PUNCT
ejpam-4624	159	24	r	r	NOUN
ejpam-4624	159	25	,	,	PUNCT
ejpam-4624	159	26	s	s	PART
ejpam-4624	159	27	)	)	PUNCT
ejpam-4624	159	28	,	,	PUNCT
ejpam-4624	159	29	then	then	ADV
ejpam-4624	159	30	ρ	ρ	PROPN
ejpam-4624	159	31	∨	∨	PROPN
ejpam-4624	159	32	ϕ	ϕ	X
ejpam-4624	159	33	=	=	NOUN
ejpam-4624	159	34	δct	δct	NOUN
ejpam-4624	159	35	,	,	PUNCT
ejpam-4624	159	36	t	t	PROPN
ejpam-4624	159	37	∗(ρ	∗(ρ	PROPN
ejpam-4624	159	38	∨	∨	NUM
ejpam-4624	159	39	ϕ	ϕ	PROPN
ejpam-4624	159	40	,	,	PUNCT
ejpam-4624	159	41	r	r	NOUN
ejpam-4624	159	42	,	,	PUNCT
ejpam-4624	159	43	s	s	NOUN
ejpam-4624	159	44	)	)	PUNCT
ejpam-4624	159	45	.	.	PUNCT
ejpam-4624	160	1	proof	proof	NOUN
ejpam-4624	160	2	.	.	PUNCT
ejpam-4624	161	1	clearly	clearly	ADV
ejpam-4624	161	2	(	(	PUNCT
ejpam-4624	161	3	ρ	ρ	PROPN
ejpam-4624	161	4	∨	∨	PROPN
ejpam-4624	161	5	ϕ	ϕ	NOUN
ejpam-4624	161	6	)	)	PUNCT
ejpam-4624	161	7	≤	≤	NOUN
ejpam-4624	161	8	δct	δct	NOUN
ejpam-4624	161	9	,	,	PUNCT
ejpam-4624	161	10	t	t	PROPN
ejpam-4624	161	11	∗(ρ	∗(ρ	PROPN
ejpam-4624	161	12	∨	∨	NUM
ejpam-4624	161	13	ϕ	ϕ	PROPN
ejpam-4624	161	14	,	,	PUNCT
ejpam-4624	161	15	r	r	NOUN
ejpam-4624	161	16	,	,	PUNCT
ejpam-4624	161	17	s	s	NOUN
ejpam-4624	161	18	)	)	PUNCT
ejpam-4624	161	19	.	.	PUNCT
ejpam-4624	162	1	we	we	PRON
ejpam-4624	162	2	will	will	AUX
ejpam-4624	162	3	show	show	VERB
ejpam-4624	162	4	that	that	SCONJ
ejpam-4624	162	5	δct	δct	NOUN
ejpam-4624	162	6	,	,	PUNCT
ejpam-4624	162	7	t	t	PROPN
ejpam-4624	162	8	∗((ρ	∗((ρ	NOUN
ejpam-4624	162	9	∨	∨	NUM
ejpam-4624	162	10	ϕ	ϕ	NOUN
ejpam-4624	162	11	)	)	PUNCT
ejpam-4624	162	12	,	,	PUNCT
ejpam-4624	162	13	r	r	NOUN
ejpam-4624	162	14	,	,	PUNCT
ejpam-4624	162	15	s	s	NOUN
ejpam-4624	162	16	)	)	PUNCT
ejpam-4624	162	17	≤	≤	NUM
ejpam-4624	162	18	ρ	ρ	PROPN
ejpam-4624	162	19	∨	∨	PROPN
ejpam-4624	162	20	ϕ.	ϕ.	PROPN
ejpam-4624	162	21	let	let	VERB
ejpam-4624	162	22	xi	xi	PROPN
ejpam-4624	162	23	for	for	ADP
ejpam-4624	162	24	each	each	DET
ejpam-4624	162	25	i	i	PRON
ejpam-4624	162	26	∈	∈	PROPN
ejpam-4624	162	27	i	i	PRON
ejpam-4624	162	28	be	be	VERB
ejpam-4624	162	29	a	a	DET
ejpam-4624	162	30	double	double	ADJ
ejpam-4624	162	31	fuzzy	fuzzy	ADJ
ejpam-4624	162	32	point	point	NOUN
ejpam-4624	162	33	.	.	PUNCT
ejpam-4624	162	34	suppose	suppose	VERB
ejpam-4624	162	35	that	that	SCONJ
ejpam-4624	162	36	xi	xi	PROPN
ejpam-4624	162	37	∈	∈	PROPN
ejpam-4624	162	38	δct	δct	NOUN
ejpam-4624	162	39	,	,	PUNCT
ejpam-4624	162	40	t	t	PROPN
ejpam-4624	162	41	∗((ρ∨ϕ	∗((ρ∨ϕ	NOUN
ejpam-4624	162	42	)	)	PUNCT
ejpam-4624	162	43	,	,	PUNCT
ejpam-4624	162	44	r	r	NOUN
ejpam-4624	162	45	,	,	PUNCT
ejpam-4624	162	46	s	s	NOUN
ejpam-4624	162	47	)	)	PUNCT
ejpam-4624	162	48	.	.	PUNCT
ejpam-4624	163	1	then	then	ADV
ejpam-4624	163	2	for	for	ADP
ejpam-4624	163	3	any	any	DET
ejpam-4624	163	4	(	(	PUNCT
ejpam-4624	163	5	r	r	NOUN
ejpam-4624	163	6	,	,	PUNCT
ejpam-4624	163	7	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	163	8	regular	regular	ADJ
ejpam-4624	163	9	q	q	ADJ
ejpam-4624	163	10	-	-	PUNCT
ejpam-4624	163	11	neighborhood	neighborhood	NOUN
ejpam-4624	163	12	γ	γ	NOUN
ejpam-4624	163	13	of	of	ADP
ejpam-4624	163	14	xα	xα	PROPN
ejpam-4624	163	15	∈	∈	PROPN
ejpam-4624	163	16	γq(ρ	γq(ρ	PUNCT
ejpam-4624	163	17	∨	∨	NUM
ejpam-4624	163	18	ϕ	ϕ	NOUN
ejpam-4624	163	19	)	)	PUNCT
ejpam-4624	163	20	.	.	PUNCT
ejpam-4624	164	1	thus	thus	ADV
ejpam-4624	164	2	γqρ	γqρ	PROPN
ejpam-4624	164	3	or	or	CCONJ
ejpam-4624	164	4	γqϕ.	γqϕ.	VERB
ejpam-4624	164	5	hence	hence	ADV
ejpam-4624	164	6	xα	xα	PUNCT
ejpam-4624	164	7	∈	∈	PROPN
ejpam-4624	164	8	δct	δct	NOUN
ejpam-4624	164	9	,	,	PUNCT
ejpam-4624	164	10	t	t	NOUN
ejpam-4624	164	11	∗(ρ	∗(ρ	NOUN
ejpam-4624	164	12	,	,	PUNCT
ejpam-4624	164	13	r	r	NOUN
ejpam-4624	164	14	,	,	PUNCT
ejpam-4624	164	15	s	s	PART
ejpam-4624	164	16	)	)	PUNCT
ejpam-4624	164	17	∨	∨	NUM
ejpam-4624	164	18	δct	δct	NOUN
ejpam-4624	164	19	,	,	PUNCT
ejpam-4624	164	20	t	t	PROPN
ejpam-4624	164	21	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	164	22	,	,	PUNCT
ejpam-4624	164	23	r	r	NOUN
ejpam-4624	164	24	,	,	PUNCT
ejpam-4624	164	25	s	s	NOUN
ejpam-4624	164	26	)	)	PUNCT
ejpam-4624	164	27	.	.	PUNCT
ejpam-4624	165	1	that	that	PRON
ejpam-4624	165	2	is	be	AUX
ejpam-4624	165	3	,	,	PUNCT
ejpam-4624	165	4	xα	xα	ADP
ejpam-4624	165	5	∈	∈	PROPN
ejpam-4624	165	6	(	(	PUNCT
ejpam-4624	165	7	ρ	ρ	PROPN
ejpam-4624	165	8	∨	∨	PROPN
ejpam-4624	165	9	ϕ	ϕ	NOUN
ejpam-4624	165	10	)	)	PUNCT
ejpam-4624	165	11	.	.	PUNCT
ejpam-4624	166	1	corollary	corollary	ADJ
ejpam-4624	166	2	2.11	2.11	NUM
ejpam-4624	166	3	.	.	PUNCT
ejpam-4624	167	1	if	if	SCONJ
ejpam-4624	167	2	ρ	ρ	PROPN
ejpam-4624	167	3	is	be	AUX
ejpam-4624	167	4	a	a	DET
ejpam-4624	167	5	(	(	PUNCT
ejpam-4624	167	6	r	r	NOUN
ejpam-4624	167	7	,	,	PUNCT
ejpam-4624	167	8	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	167	9	δ	δ	PROPN
ejpam-4624	167	10	-	-	PUNCT
ejpam-4624	167	11	closed	close	VERB
ejpam-4624	167	12	set	set	NOUN
ejpam-4624	167	13	in	in	ADP
ejpam-4624	167	14	an	an	DET
ejpam-4624	167	15	dfts	dft	NOUN
ejpam-4624	167	16	(	(	PUNCT
ejpam-4624	167	17	x	x	X
ejpam-4624	167	18	,	,	PUNCT
ejpam-4624	167	19	t	t	PROPN
ejpam-4624	167	20	,	,	PUNCT
ejpam-4624	167	21	t	t	PROPN
ejpam-4624	167	22	∗	∗	NOUN
ejpam-4624	167	23	)	)	PUNCT
ejpam-4624	167	24	,	,	PUNCT
ejpam-4624	167	25	then	then	ADV
ejpam-4624	167	26	ρ	ρ	PROPN
ejpam-4624	167	27	is	be	AUX
ejpam-4624	167	28	double	double	ADJ
ejpam-4624	167	29	fuzzy	fuzzy	ADJ
ejpam-4624	167	30	closed	closed	ADJ
ejpam-4624	167	31	.	.	PUNCT
ejpam-4624	168	1	the	the	DET
ejpam-4624	168	2	converse	converse	NOUN
ejpam-4624	168	3	do	do	AUX
ejpam-4624	168	4	n’t	not	PART
ejpam-4624	168	5	holds	hold	VERB
ejpam-4624	168	6	,	,	PUNCT
ejpam-4624	168	7	the	the	DET
ejpam-4624	168	8	following	follow	VERB
ejpam-4624	168	9	example	example	NOUN
ejpam-4624	168	10	shows	show	VERB
ejpam-4624	168	11	it	it	PRON
ejpam-4624	168	12	.	.	PUNCT
ejpam-4624	169	1	example	example	NOUN
ejpam-4624	170	1	2.12	2.12	NUM
ejpam-4624	170	2	.	.	PUNCT
ejpam-4624	171	1	let	let	VERB
ejpam-4624	171	2	x	x	PUNCT
ejpam-4624	171	3	=	=	PRON
ejpam-4624	171	4	{	{	PUNCT
ejpam-4624	171	5	a	a	DET
ejpam-4624	171	6	,	,	PUNCT
ejpam-4624	171	7	b	b	NOUN
ejpam-4624	171	8	}	}	PUNCT
ejpam-4624	171	9	and	and	CCONJ
ejpam-4624	171	10	the	the	DET
ejpam-4624	171	11	fuzzy	fuzzy	ADJ
ejpam-4624	171	12	set	set	VERB
ejpam-4624	171	13	µ1	µ1	PROPN
ejpam-4624	171	14	is	be	AUX
ejpam-4624	171	15	fuzzy	fuzzy	ADJ
ejpam-4624	171	16	set	set	VERB
ejpam-4624	171	17	define	define	NOUN
ejpam-4624	171	18	by	by	ADP
ejpam-4624	171	19	µ1(a	µ1(a	NOUN
ejpam-4624	171	20	)	)	PUNCT
ejpam-4624	171	21	=	=	SYM
ejpam-4624	171	22	0.5	0.5	NUM
ejpam-4624	171	23	and	and	CCONJ
ejpam-4624	171	24	µ1(b	µ1(b	NUM
ejpam-4624	171	25	)	)	PUNCT
ejpam-4624	171	26	=	=	SYM
ejpam-4624	171	27	0.3	0.3	NUM
ejpam-4624	171	28	,	,	PUNCT
ejpam-4624	171	29	take	take	VERB
ejpam-4624	171	30	the	the	DET
ejpam-4624	171	31	(	(	PUNCT
ejpam-4624	171	32	t	t	PROPN
ejpam-4624	171	33	,	,	PUNCT
ejpam-4624	171	34	t	t	PROPN
ejpam-4624	171	35	∗	∗	NOUN
ejpam-4624	171	36	)	)	PUNCT
ejpam-4624	171	37	on	on	ADP
ejpam-4624	171	38	x	x	PUNCT
ejpam-4624	171	39	as	as	ADP
ejpam-4624	171	40	in	in	ADP
ejpam-4624	171	41	example	example	NOUN
ejpam-4624	171	42	2.8	2.8	NUM
ejpam-4624	171	43	.	.	PUNCT
ejpam-4624	172	1	since	since	SCONJ
ejpam-4624	172	2	µ1	µ1	NOUN
ejpam-4624	172	3	=	=	NOUN
ejpam-4624	172	4	δct	δct	NOUN
ejpam-4624	172	5	,	,	PUNCT
ejpam-4624	172	6	t	t	NOUN
ejpam-4624	172	7	∗(µ1	∗(µ1	NOUN
ejpam-4624	172	8	,	,	PUNCT
ejpam-4624	172	9	r	r	NOUN
ejpam-4624	172	10	,	,	PUNCT
ejpam-4624	172	11	s	s	NOUN
ejpam-4624	172	12	)	)	PUNCT
ejpam-4624	172	13	.	.	PUNCT
ejpam-4624	173	1	then	then	ADV
ejpam-4624	173	2	,	,	PUNCT
ejpam-4624	173	3	µ1	µ1	PROPN
ejpam-4624	173	4	is	be	AUX
ejpam-4624	173	5	(	(	PUNCT
ejpam-4624	173	6	12	12	NUM
ejpam-4624	173	7	)	)	PUNCT
ejpam-4624	173	8	,	,	PUNCT
ejpam-4624	173	9	1	1	NUM
ejpam-4624	173	10	2)-fuzzy	2)-fuzzy	NUM
ejpam-4624	173	11	δ	δ	NOUN
ejpam-4624	173	12	-	-	PUNCT
ejpam-4624	173	13	closed	close	VERB
ejpam-4624	173	14	set	set	NOUN
ejpam-4624	173	15	,	,	PUNCT
ejpam-4624	173	16	but	but	CCONJ
ejpam-4624	173	17	is	be	AUX
ejpam-4624	173	18	not	not	PART
ejpam-4624	173	19	(	(	PUNCT
ejpam-4624	173	20	12	12	NUM
ejpam-4624	173	21	,	,	PUNCT
ejpam-4624	173	22	1	1	NUM
ejpam-4624	173	23	2)-frc	2)-frc	NUM
ejpam-4624	173	24	set	set	NOUN
ejpam-4624	173	25	.	.	PUNCT
ejpam-4624	174	1	theorem	theorem	VERB
ejpam-4624	174	2	2.13	2.13	NUM
ejpam-4624	174	3	.	.	PUNCT
ejpam-4624	175	1	if	if	SCONJ
ejpam-4624	175	2	ρ	ρ	PROPN
ejpam-4624	175	3	is	be	AUX
ejpam-4624	175	4	a	a	DET
ejpam-4624	175	5	(	(	PUNCT
ejpam-4624	175	6	r	r	NOUN
ejpam-4624	175	7	,	,	PUNCT
ejpam-4624	175	8	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	175	9	δ	δ	PROPN
ejpam-4624	175	10	-	-	PUNCT
ejpam-4624	175	11	open	open	ADJ
ejpam-4624	175	12	set	set	NOUN
ejpam-4624	175	13	in	in	ADP
ejpam-4624	175	14	an	an	DET
ejpam-4624	175	15	dfts	dft	NOUN
ejpam-4624	175	16	(	(	PUNCT
ejpam-4624	175	17	x	x	X
ejpam-4624	175	18	,	,	PUNCT
ejpam-4624	175	19	t	t	PROPN
ejpam-4624	175	20	,	,	PUNCT
ejpam-4624	175	21	t	t	PROPN
ejpam-4624	175	22	∗	∗	NOUN
ejpam-4624	175	23	)	)	PUNCT
ejpam-4624	175	24	,	,	PUNCT
ejpam-4624	175	25	then	then	ADV
ejpam-4624	175	26	the	the	DET
ejpam-4624	175	27	double	double	ADJ
ejpam-4624	175	28	fuzzy	fuzzy	ADJ
ejpam-4624	175	29	closure	closure	NOUN
ejpam-4624	175	30	and	and	CCONJ
ejpam-4624	175	31	(	(	PUNCT
ejpam-4624	175	32	r	r	NOUN
ejpam-4624	175	33	,	,	PUNCT
ejpam-4624	175	34	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	175	35	δ	δ	PROPN
ejpam-4624	175	36	-	-	PUNCT
ejpam-4624	175	37	closure	closure	NOUN
ejpam-4624	175	38	are	be	AUX
ejpam-4624	175	39	the	the	DET
ejpam-4624	175	40	same	same	ADJ
ejpam-4624	175	41	,	,	PUNCT
ejpam-4624	175	42	i.e.	i.e.	X
ejpam-4624	175	43	ct	ct	NUM
ejpam-4624	175	44	,	,	PUNCT
ejpam-4624	175	45	t	t	NOUN
ejpam-4624	175	46	∗(ρ	∗(ρ	NOUN
ejpam-4624	175	47	,	,	PUNCT
ejpam-4624	175	48	r	r	NOUN
ejpam-4624	175	49	,	,	PUNCT
ejpam-4624	175	50	s	s	NOUN
ejpam-4624	175	51	)	)	PUNCT
ejpam-4624	175	52	=	=	NOUN
ejpam-4624	175	53	δct	δct	NOUN
ejpam-4624	175	54	,	,	PUNCT
ejpam-4624	175	55	t	t	NOUN
ejpam-4624	175	56	∗(ρ	∗(ρ	NOUN
ejpam-4624	175	57	,	,	PUNCT
ejpam-4624	175	58	r	r	NOUN
ejpam-4624	175	59	,	,	PUNCT
ejpam-4624	175	60	s	s	NOUN
ejpam-4624	175	61	)	)	PUNCT
ejpam-4624	175	62	.	.	PUNCT
ejpam-4624	176	1	proof	proof	NOUN
ejpam-4624	176	2	.	.	PUNCT
ejpam-4624	177	1	by	by	ADP
ejpam-4624	177	2	theorem	theorem	NOUN
ejpam-4624	177	3	2.9	2.9	NUM
ejpam-4624	177	4	,	,	PUNCT
ejpam-4624	177	5	it	it	PRON
ejpam-4624	177	6	is	be	AUX
ejpam-4624	177	7	sufficient	sufficient	ADJ
ejpam-4624	177	8	to	to	PART
ejpam-4624	177	9	show	show	VERB
ejpam-4624	177	10	that	that	SCONJ
ejpam-4624	177	11	δct	δct	NOUN
ejpam-4624	177	12	,	,	PUNCT
ejpam-4624	177	13	t	t	NOUN
ejpam-4624	177	14	∗(ρ	∗(ρ	NOUN
ejpam-4624	177	15	,	,	PUNCT
ejpam-4624	177	16	r	r	NOUN
ejpam-4624	177	17	,	,	PUNCT
ejpam-4624	177	18	s	s	NOUN
ejpam-4624	177	19	)	)	PUNCT
ejpam-4624	177	20	≤	≤	NOUN
ejpam-4624	177	21	ct	ct	NUM
ejpam-4624	177	22	,	,	PUNCT
ejpam-4624	177	23	t	t	NOUN
ejpam-4624	177	24	∗(ρ	∗(ρ	NOUN
ejpam-4624	177	25	,	,	PUNCT
ejpam-4624	177	26	r	r	NOUN
ejpam-4624	177	27	,	,	PUNCT
ejpam-4624	177	28	s	s	PART
ejpam-4624	177	29	)	)	PUNCT
ejpam-4624	177	30	.	.	PUNCT
ejpam-4624	178	1	take	take	VERB
ejpam-4624	178	2	any	any	DET
ejpam-4624	178	3	xi	xi	ADP
ejpam-4624	178	4	∈	∈	PROPN
ejpam-4624	178	5	δct	δct	NOUN
ejpam-4624	178	6	,	,	PUNCT
ejpam-4624	178	7	t	t	NOUN
ejpam-4624	178	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	178	9	,	,	PUNCT
ejpam-4624	178	10	r	r	NOUN
ejpam-4624	178	11	,	,	PUNCT
ejpam-4624	178	12	s	s	PART
ejpam-4624	178	13	)	)	PUNCT
ejpam-4624	178	14	.	.	PUNCT
ejpam-4624	179	1	suppose	suppose	VERB
ejpam-4624	179	2	that	that	SCONJ
ejpam-4624	179	3	xi	xi	PROPN
ejpam-4624	179	4	/∈	/∈	PUNCT
ejpam-4624	180	1	ct	ct	INTJ
ejpam-4624	180	2	,	,	PUNCT
ejpam-4624	180	3	t	t	NOUN
ejpam-4624	180	4	∗(ρ	∗(ρ	NOUN
ejpam-4624	180	5	,	,	PUNCT
ejpam-4624	180	6	r	r	NOUN
ejpam-4624	180	7	,	,	PUNCT
ejpam-4624	180	8	s	s	NOUN
ejpam-4624	180	9	)	)	PUNCT
ejpam-4624	180	10	.	.	PUNCT
ejpam-4624	181	1	then	then	ADV
ejpam-4624	181	2	there	there	PRON
ejpam-4624	181	3	exists	exist	VERB
ejpam-4624	181	4	a	a	DET
ejpam-4624	181	5	(	(	PUNCT
ejpam-4624	181	6	r	r	NOUN
ejpam-4624	181	7	,	,	PUNCT
ejpam-4624	181	8	s)fuzzy	s)fuzzy	X
ejpam-4624	181	9	open	open	VERB
ejpam-4624	181	10	q	q	ADJ
ejpam-4624	181	11	-	-	PUNCT
ejpam-4624	181	12	neighborhood	neighborhood	NOUN
ejpam-4624	181	13	ϕ	ϕ	NOUN
ejpam-4624	181	14	of	of	ADP
ejpam-4624	181	15	xi	xi	INTJ
ejpam-4624	181	16	such	such	ADJ
ejpam-4624	181	17	that	that	SCONJ
ejpam-4624	181	18	ϕq̃ρ	ϕq̃ρ	PROPN
ejpam-4624	181	19	.	.	PUNCT
ejpam-4624	182	1	since	since	SCONJ
ejpam-4624	182	2	ϕq̃ρ	ϕq̃ρ	PROPN
ejpam-4624	182	3	,	,	PUNCT
ejpam-4624	182	4	we	we	PRON
ejpam-4624	182	5	have	have	VERB
ejpam-4624	182	6	ϕ	ϕ	NOUN
ejpam-4624	182	7	≤	≤	PROPN
ejpam-4624	182	8	1−	1−	NUM
ejpam-4624	182	9	ρ	ρ	NOUN
ejpam-4624	182	10	.	.	PUNCT
ejpam-4624	183	1	since	since	SCONJ
ejpam-4624	183	2	(	(	PUNCT
ejpam-4624	183	3	1−	1−	NUM
ejpam-4624	183	4	ρ	ρ	NOUN
ejpam-4624	183	5	)	)	PUNCT
ejpam-4624	183	6	is	be	AUX
ejpam-4624	183	7	a	a	DET
ejpam-4624	183	8	(	(	PUNCT
ejpam-4624	183	9	r	r	NOUN
ejpam-4624	183	10	,	,	PUNCT
ejpam-4624	183	11	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	183	12	δ	δ	PROPN
ejpam-4624	183	13	-	-	PUNCT
ejpam-4624	183	14	closed	close	VERB
ejpam-4624	183	15	set	set	NOUN
ejpam-4624	183	16	,	,	PUNCT
ejpam-4624	183	17	ct	ct	PRON
ejpam-4624	183	18	,	,	PUNCT
ejpam-4624	183	19	t	t	PROPN
ejpam-4624	183	20	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	183	21	,	,	PUNCT
ejpam-4624	183	22	r	r	NOUN
ejpam-4624	183	23	,	,	PUNCT
ejpam-4624	183	24	s	s	NOUN
ejpam-4624	183	25	)	)	PUNCT
ejpam-4624	183	26	≤	≤	NOUN
ejpam-4624	183	27	ct	ct	NUM
ejpam-4624	183	28	,	,	PUNCT
ejpam-4624	183	29	t	t	PROPN
ejpam-4624	183	30	∗(1−	∗(1−	PROPN
ejpam-4624	183	31	ρ	ρ	PROPN
ejpam-4624	183	32	,	,	PUNCT
ejpam-4624	183	33	r	r	NOUN
ejpam-4624	183	34	,	,	PUNCT
ejpam-4624	183	35	s	s	NOUN
ejpam-4624	183	36	)	)	PUNCT
ejpam-4624	183	37	=	=	SYM
ejpam-4624	183	38	1−	1−	NUM
ejpam-4624	183	39	ρ	ρ	NOUN
ejpam-4624	183	40	.	.	PUNCT
ejpam-4624	184	1	therefore	therefore	ADV
ejpam-4624	184	2	,	,	PUNCT
ejpam-4624	184	3	it	it	PRON
ejpam-4624	184	4	,	,	PUNCT
ejpam-4624	184	5	t	t	PROPN
ejpam-4624	184	6	∗(ct	∗(ct	PROPN
ejpam-4624	184	7	,	,	PUNCT
ejpam-4624	184	8	t	t	PROPN
ejpam-4624	184	9	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	184	10	,	,	PUNCT
ejpam-4624	184	11	r	r	NOUN
ejpam-4624	184	12	,	,	PUNCT
ejpam-4624	184	13	s	s	NOUN
ejpam-4624	184	14	)	)	PUNCT
ejpam-4624	184	15	)	)	PUNCT
ejpam-4624	184	16	≤	≤	ADV
ejpam-4624	184	17	it	it	PRON
ejpam-4624	184	18	,	,	PUNCT
ejpam-4624	184	19	t	t	PROPN
ejpam-4624	184	20	∗(1−	∗(1−	PROPN
ejpam-4624	184	21	ρ	ρ	PROPN
ejpam-4624	184	22	,	,	PUNCT
ejpam-4624	184	23	r	r	NOUN
ejpam-4624	184	24	,	,	PUNCT
ejpam-4624	184	25	s	s	NOUN
ejpam-4624	184	26	)	)	PUNCT
ejpam-4624	184	27	≤	≤	NOUN
ejpam-4624	184	28	1−	1−	NUM
ejpam-4624	184	29	ρ	ρ	NOUN
ejpam-4624	184	30	,	,	PUNCT
ejpam-4624	184	31	i.e.	i.e.	X
ejpam-4624	184	32	it	it	PRON
ejpam-4624	184	33	,	,	PUNCT
ejpam-4624	184	34	t	t	PROPN
ejpam-4624	184	35	∗(ct	∗(ct	PROPN
ejpam-4624	184	36	,	,	PUNCT
ejpam-4624	184	37	t	t	PROPN
ejpam-4624	184	38	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	184	39	,	,	PUNCT
ejpam-4624	184	40	r	r	NOUN
ejpam-4624	184	41	,	,	PUNCT
ejpam-4624	184	42	s))q̃ρ	s))q̃ρ	NOUN
ejpam-4624	184	43	.	.	PUNCT
ejpam-4624	185	1	by	by	ADP
ejpam-4624	185	2	lemma	lemma	PROPN
ejpam-4624	185	3	2.7	2.7	NUM
ejpam-4624	185	4	,	,	PUNCT
ejpam-4624	185	5	it	it	PRON
ejpam-4624	185	6	,	,	PUNCT
ejpam-4624	185	7	t	t	PROPN
ejpam-4624	185	8	∗(ct	∗(ct	NOUN
ejpam-4624	185	9	,	,	PUNCT
ejpam-4624	185	10	t	t	NOUN
ejpam-4624	185	11	∗(ρ	∗(ρ	NOUN
ejpam-4624	185	12	,	,	PUNCT
ejpam-4624	185	13	r	r	NOUN
ejpam-4624	185	14	,	,	PUNCT
ejpam-4624	185	15	s	s	NOUN
ejpam-4624	185	16	)	)	PUNCT
ejpam-4624	185	17	)	)	PUNCT
ejpam-4624	185	18	is	be	AUX
ejpam-4624	185	19	a	a	DET
ejpam-4624	185	20	(	(	PUNCT
ejpam-4624	185	21	r	r	NOUN
ejpam-4624	185	22	,	,	PUNCT
ejpam-4624	185	23	s)-fro	s)-fro	NOUN
ejpam-4624	185	24	set	set	VERB
ejpam-4624	185	25	q	q	NOUN
ejpam-4624	185	26	-	-	PUNCT
ejpam-4624	185	27	neighborhood	neighborhood	NOUN
ejpam-4624	185	28	of	of	ADP
ejpam-4624	185	29	xi	xi	INTJ
ejpam-4624	185	30	such	such	ADJ
ejpam-4624	185	31	that	that	SCONJ
ejpam-4624	185	32	it	it	PRON
ejpam-4624	185	33	,	,	PUNCT
ejpam-4624	185	34	t	t	PROPN
ejpam-4624	185	35	∗(ct	∗(ct	PROPN
ejpam-4624	185	36	,	,	PUNCT
ejpam-4624	185	37	t	t	PROPN
ejpam-4624	185	38	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	185	39	,	,	PUNCT
ejpam-4624	185	40	r	r	NOUN
ejpam-4624	185	41	,	,	PUNCT
ejpam-4624	185	42	s))q̃ρ	s))q̃ρ	NOUN
ejpam-4624	185	43	.	.	PUNCT
ejpam-4624	186	1	hence	hence	ADV
ejpam-4624	186	2	xi	xi	PROPN
ejpam-4624	186	3	/∈	/∈	PUNCT
ejpam-4624	187	1	δct	δct	NOUN
ejpam-4624	187	2	,	,	PUNCT
ejpam-4624	187	3	t	t	NOUN
ejpam-4624	187	4	∗(ρ	∗(ρ	NOUN
ejpam-4624	187	5	,	,	PUNCT
ejpam-4624	187	6	r	r	NOUN
ejpam-4624	187	7	,	,	PUNCT
ejpam-4624	187	8	s	s	NOUN
ejpam-4624	187	9	)	)	PUNCT
ejpam-4624	187	10	.	.	PUNCT
ejpam-4624	188	1	w.	w.	PROPN
ejpam-4624	188	2	f.	f.	PROPN
ejpam-4624	188	3	al	al	PROPN
ejpam-4624	188	4	-	-	PUNCT
ejpam-4624	188	5	omeri	omeri	ADJ
ejpam-4624	188	6	/	/	SYM
ejpam-4624	188	7	eur	eur	PROPN
ejpam-4624	188	8	.	.	PUNCT
ejpam-4624	189	1	j.	j.	PROPN
ejpam-4624	189	2	pure	pure	PROPN
ejpam-4624	189	3	appl	appl	PROPN
ejpam-4624	189	4	.	.	PROPN
ejpam-4624	189	5	math	math	PROPN
ejpam-4624	189	6	,	,	PUNCT
ejpam-4624	189	7	18	18	NUM
ejpam-4624	189	8	(	(	PUNCT
ejpam-4624	189	9	2	2	NUM
ejpam-4624	189	10	)	)	PUNCT
ejpam-4624	189	11	(	(	PUNCT
ejpam-4624	189	12	2025	2025	NUM
ejpam-4624	189	13	)	)	PUNCT
ejpam-4624	189	14	,	,	PUNCT
ejpam-4624	189	15	4624	4624	NUM
ejpam-4624	189	16	8	8	NUM
ejpam-4624	189	17	of	of	ADP
ejpam-4624	189	18	15	15	NUM
ejpam-4624	189	19	theorem	theorem	VERB
ejpam-4624	189	20	2.14	2.14	NUM
ejpam-4624	189	21	.	.	PUNCT
ejpam-4624	190	1	for	for	ADP
ejpam-4624	190	2	any	any	DET
ejpam-4624	190	3	(	(	PUNCT
ejpam-4624	190	4	r	r	NOUN
ejpam-4624	190	5	,	,	PUNCT
ejpam-4624	190	6	s)-fso	s)-fso	VERB
ejpam-4624	190	7	set	set	VERB
ejpam-4624	190	8	ρ	ρ	PROPN
ejpam-4624	190	9	,	,	PUNCT
ejpam-4624	190	10	ct	ct	PRON
ejpam-4624	190	11	,	,	PUNCT
ejpam-4624	190	12	t	t	NOUN
ejpam-4624	190	13	∗(ρ	∗(ρ	NOUN
ejpam-4624	190	14	,	,	PUNCT
ejpam-4624	190	15	r	r	NOUN
ejpam-4624	190	16	,	,	PUNCT
ejpam-4624	190	17	s	s	NOUN
ejpam-4624	190	18	)	)	PUNCT
ejpam-4624	190	19	=	=	NOUN
ejpam-4624	190	20	δct	δct	NOUN
ejpam-4624	190	21	,	,	PUNCT
ejpam-4624	190	22	t	t	NOUN
ejpam-4624	190	23	∗(ρ	∗(ρ	NOUN
ejpam-4624	190	24	,	,	PUNCT
ejpam-4624	190	25	r	r	NOUN
ejpam-4624	190	26	,	,	PUNCT
ejpam-4624	190	27	s	s	NOUN
ejpam-4624	190	28	)	)	PUNCT
ejpam-4624	190	29	.	.	PUNCT
ejpam-4624	191	1	proof	proof	NOUN
ejpam-4624	191	2	.	.	PUNCT
ejpam-4624	192	1	it	it	PRON
ejpam-4624	192	2	’s	’	VERB
ejpam-4624	192	3	enough	enough	ADV
ejpam-4624	192	4	to	to	PART
ejpam-4624	192	5	show	show	VERB
ejpam-4624	192	6	that	that	SCONJ
ejpam-4624	192	7	δct	δct	NOUN
ejpam-4624	192	8	,	,	PUNCT
ejpam-4624	192	9	t	t	NOUN
ejpam-4624	192	10	∗(ρ	∗(ρ	NOUN
ejpam-4624	192	11	,	,	PUNCT
ejpam-4624	192	12	r	r	NOUN
ejpam-4624	192	13	,	,	PUNCT
ejpam-4624	192	14	s	s	NOUN
ejpam-4624	192	15	)	)	PUNCT
ejpam-4624	192	16	≤	≤	NOUN
ejpam-4624	192	17	ct	ct	NUM
ejpam-4624	192	18	,	,	PUNCT
ejpam-4624	192	19	t	t	NOUN
ejpam-4624	192	20	∗(ρ	∗(ρ	NOUN
ejpam-4624	192	21	,	,	PUNCT
ejpam-4624	192	22	r	r	NOUN
ejpam-4624	192	23	,	,	PUNCT
ejpam-4624	192	24	s	s	PART
ejpam-4624	192	25	)	)	PUNCT
ejpam-4624	192	26	.	.	PUNCT
ejpam-4624	193	1	take	take	VERB
ejpam-4624	193	2	any	any	DET
ejpam-4624	193	3	xi	xi	ADP
ejpam-4624	193	4	∈	∈	PROPN
ejpam-4624	193	5	δct	δct	NOUN
ejpam-4624	193	6	,	,	PUNCT
ejpam-4624	193	7	t	t	NOUN
ejpam-4624	193	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	193	9	,	,	PUNCT
ejpam-4624	193	10	r	r	NOUN
ejpam-4624	193	11	,	,	PUNCT
ejpam-4624	193	12	s	s	PART
ejpam-4624	193	13	)	)	PUNCT
ejpam-4624	193	14	and	and	CCONJ
ejpam-4624	193	15	suppose	suppose	VERB
ejpam-4624	193	16	that	that	SCONJ
ejpam-4624	193	17	xi	xi	PROPN
ejpam-4624	193	18	/∈	/∈	PUNCT
ejpam-4624	194	1	ct	ct	INTJ
ejpam-4624	194	2	,	,	PUNCT
ejpam-4624	194	3	t	t	NOUN
ejpam-4624	194	4	∗(ρ	∗(ρ	NOUN
ejpam-4624	194	5	,	,	PUNCT
ejpam-4624	194	6	r	r	NOUN
ejpam-4624	194	7	,	,	PUNCT
ejpam-4624	194	8	s	s	NOUN
ejpam-4624	194	9	)	)	PUNCT
ejpam-4624	194	10	.	.	PUNCT
ejpam-4624	195	1	now	now	ADV
ejpam-4624	195	2	,	,	PUNCT
ejpam-4624	195	3	xi	xi	PROPN
ejpam-4624	195	4	/∈	/∈	PUNCT
ejpam-4624	196	1	ct	ct	INTJ
ejpam-4624	196	2	,	,	PUNCT
ejpam-4624	196	3	t	t	NOUN
ejpam-4624	196	4	∗(ρ	∗(ρ	NOUN
ejpam-4624	196	5	,	,	PUNCT
ejpam-4624	196	6	r	r	NOUN
ejpam-4624	196	7	,	,	PUNCT
ejpam-4624	196	8	s	s	PART
ejpam-4624	196	9	)	)	PUNCT
ejpam-4624	196	10	,	,	PUNCT
ejpam-4624	196	11	then	then	ADV
ejpam-4624	196	12	there	there	PRON
ejpam-4624	196	13	exists	exist	VERB
ejpam-4624	196	14	a	a	DET
ejpam-4624	196	15	(	(	PUNCT
ejpam-4624	196	16	r	r	NOUN
ejpam-4624	196	17	,	,	PUNCT
ejpam-4624	196	18	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	196	19	open	open	ADJ
ejpam-4624	196	20	q	q	ADJ
ejpam-4624	196	21	-	-	PUNCT
ejpam-4624	196	22	neighborhood	neighborhood	NOUN
ejpam-4624	196	23	ν	ν	NOUN
ejpam-4624	196	24	of	of	ADP
ejpam-4624	196	25	xi	xi	INTJ
ejpam-4624	196	26	such	such	ADJ
ejpam-4624	196	27	that	that	SCONJ
ejpam-4624	196	28	ϕq̃ρ	ϕq̃ρ	PROPN
ejpam-4624	196	29	.	.	PUNCT
ejpam-4624	197	1	by	by	ADP
ejpam-4624	197	2	definition	definition	NOUN
ejpam-4624	197	3	of	of	ADP
ejpam-4624	197	4	(	(	PUNCT
ejpam-4624	197	5	r	r	NOUN
ejpam-4624	197	6	,	,	PUNCT
ejpam-4624	197	7	s)-fso	s)-fso	NOUN
ejpam-4624	197	8	set	set	NOUN
ejpam-4624	197	9	,	,	PUNCT
ejpam-4624	197	10	there	there	PRON
ejpam-4624	197	11	exists	exist	VERB
ejpam-4624	197	12	a	a	DET
ejpam-4624	197	13	t	t	NOUN
ejpam-4624	197	14	(	(	PUNCT
ejpam-4624	197	15	ϕ	ϕ	NOUN
ejpam-4624	197	16	)	)	PUNCT
ejpam-4624	197	17	≥	≥	NOUN
ejpam-4624	197	18	r	r	NOUN
ejpam-4624	197	19	and	and	CCONJ
ejpam-4624	197	20	t	t	NOUN
ejpam-4624	197	21	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	197	22	)	)	PUNCT
ejpam-4624	198	1	≤	≤	PROPN
ejpam-4624	199	1	s	s	VERB
ejpam-4624	199	2	such	such	ADJ
ejpam-4624	199	3	that	that	SCONJ
ejpam-4624	199	4	ϕ	ϕ	PROPN
ejpam-4624	199	5	≤	≤	PROPN
ejpam-4624	199	6	ρ	ρ	PROPN
ejpam-4624	199	7	≤	≤	NUM
ejpam-4624	199	8	ct	ct	NUM
ejpam-4624	199	9	,	,	PUNCT
ejpam-4624	199	10	t	t	PROPN
ejpam-4624	199	11	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	199	12	,	,	PUNCT
ejpam-4624	199	13	r	r	NOUN
ejpam-4624	199	14	,	,	PUNCT
ejpam-4624	199	15	s	s	PART
ejpam-4624	199	16	)	)	PUNCT
ejpam-4624	199	17	whenever	whenever	SCONJ
ejpam-4624	199	18	,	,	PUNCT
ejpam-4624	199	19	r	r	PROPN
ejpam-4624	199	20	∈	∈	PROPN
ejpam-4624	199	21	i0	i0	PROPN
ejpam-4624	199	22	,	,	PUNCT
ejpam-4624	199	23	s	s	PROPN
ejpam-4624	199	24	∈	∈	PROPN
ejpam-4624	199	25	i1	i1	PROPN
ejpam-4624	199	26	.	.	PUNCT
ejpam-4624	200	1	thus	thus	ADV
ejpam-4624	200	2	ν	ν	X
ejpam-4624	200	3	≤	≤	NOUN
ejpam-4624	200	4	1−	1−	NUM
ejpam-4624	200	5	ρ	ρ	PROPN
ejpam-4624	200	6	≤	≤	PROPN
ejpam-4624	200	7	1−	1−	NUM
ejpam-4624	200	8	ϕ.	ϕ.	NOUN
ejpam-4624	200	9	hence	hence	ADV
ejpam-4624	200	10	,	,	PUNCT
ejpam-4624	200	11	ct	ct	INTJ
ejpam-4624	200	12	,	,	PUNCT
ejpam-4624	200	13	t	t	PROPN
ejpam-4624	200	14	∗(ν	∗(ν	PROPN
ejpam-4624	200	15	,	,	PUNCT
ejpam-4624	200	16	r	r	NOUN
ejpam-4624	200	17	,	,	PUNCT
ejpam-4624	200	18	s	s	NOUN
ejpam-4624	200	19	)	)	PUNCT
ejpam-4624	200	20	≤	≤	NOUN
ejpam-4624	200	21	ct	ct	NUM
ejpam-4624	200	22	,	,	PUNCT
ejpam-4624	200	23	t	t	PROPN
ejpam-4624	200	24	∗(1−	∗(1−	PROPN
ejpam-4624	200	25	ρ	ρ	PROPN
ejpam-4624	200	26	,	,	PUNCT
ejpam-4624	200	27	r	r	NOUN
ejpam-4624	200	28	,	,	PUNCT
ejpam-4624	200	29	s	s	NOUN
ejpam-4624	200	30	)	)	PUNCT
ejpam-4624	200	31	≤	≤	NOUN
ejpam-4624	200	32	ct	ct	NUM
ejpam-4624	200	33	,	,	PUNCT
ejpam-4624	200	34	t	t	PROPN
ejpam-4624	201	1	∗(1−	∗(1−	PROPN
ejpam-4624	201	2	ϕ	ϕ	PROPN
ejpam-4624	201	3	,	,	PUNCT
ejpam-4624	201	4	r	r	NOUN
ejpam-4624	201	5	,	,	PUNCT
ejpam-4624	201	6	s	s	NOUN
ejpam-4624	201	7	)	)	PUNCT
ejpam-4624	201	8	=	=	SYM
ejpam-4624	202	1	1−	1−	NUM
ejpam-4624	202	2	ϕ.	ϕ.	NOUN
ejpam-4624	202	3	also	also	ADV
ejpam-4624	202	4	,	,	PUNCT
ejpam-4624	202	5	it	it	PRON
ejpam-4624	202	6	,	,	PUNCT
ejpam-4624	202	7	t	t	PROPN
ejpam-4624	202	8	∗(ct	∗(ct	PROPN
ejpam-4624	202	9	,	,	PUNCT
ejpam-4624	202	10	t	t	PROPN
ejpam-4624	202	11	∗(ν	∗(ν	PROPN
ejpam-4624	202	12	,	,	PUNCT
ejpam-4624	202	13	r	r	NOUN
ejpam-4624	202	14	,	,	PUNCT
ejpam-4624	202	15	s	s	NOUN
ejpam-4624	202	16	)	)	PUNCT
ejpam-4624	202	17	)	)	PUNCT
ejpam-4624	202	18	≤	≤	ADV
ejpam-4624	202	19	it	it	PRON
ejpam-4624	202	20	,	,	PUNCT
ejpam-4624	202	21	t	t	PROPN
ejpam-4624	202	22	∗(ct	∗(ct	NOUN
ejpam-4624	202	23	,	,	PUNCT
ejpam-4624	202	24	t	t	PROPN
ejpam-4624	202	25	∗(1−	∗(1−	PROPN
ejpam-4624	202	26	ρ	ρ	PROPN
ejpam-4624	202	27	,	,	PUNCT
ejpam-4624	202	28	r	r	NOUN
ejpam-4624	202	29	,	,	PUNCT
ejpam-4624	202	30	s	s	NOUN
ejpam-4624	202	31	)	)	PUNCT
ejpam-4624	202	32	)	)	PUNCT
ejpam-4624	202	33	≤	≤	ADV
ejpam-4624	203	1	it	it	PRON
ejpam-4624	203	2	,	,	PUNCT
ejpam-4624	203	3	t	t	PROPN
ejpam-4624	203	4	∗(ct	∗(ct	NOUN
ejpam-4624	203	5	,	,	PUNCT
ejpam-4624	203	6	t	t	PROPN
ejpam-4624	203	7	∗(1−	∗(1−	PROPN
ejpam-4624	203	8	ϕ	ϕ	PROPN
ejpam-4624	203	9	,	,	PUNCT
ejpam-4624	203	10	r	r	NOUN
ejpam-4624	203	11	,	,	PUNCT
ejpam-4624	203	12	s	s	NOUN
ejpam-4624	203	13	)	)	PUNCT
ejpam-4624	203	14	)	)	PUNCT
ejpam-4624	204	1	=	=	SYM
ejpam-4624	204	2	it	it	PRON
ejpam-4624	204	3	,	,	PUNCT
ejpam-4624	204	4	t	t	PROPN
ejpam-4624	204	5	∗(1−	∗(1−	PROPN
ejpam-4624	205	1	ϕ	ϕ	PROPN
ejpam-4624	205	2	,	,	PUNCT
ejpam-4624	205	3	r	r	NOUN
ejpam-4624	205	4	,	,	PUNCT
ejpam-4624	205	5	s	s	NOUN
ejpam-4624	205	6	)	)	PUNCT
ejpam-4624	205	7	≤	≤	NOUN
ejpam-4624	205	8	1−	1−	NUM
ejpam-4624	205	9	ϕ	ϕ	NOUN
ejpam-4624	205	10	,	,	PUNCT
ejpam-4624	205	11	i.e.	i.e.	X
ejpam-4624	205	12	it	it	PRON
ejpam-4624	205	13	,	,	PUNCT
ejpam-4624	205	14	t	t	PROPN
ejpam-4624	205	15	∗(ct	∗(ct	PROPN
ejpam-4624	205	16	,	,	PUNCT
ejpam-4624	205	17	t	t	PROPN
ejpam-4624	205	18	∗(ν	∗(ν	PROPN
ejpam-4624	205	19	,	,	PUNCT
ejpam-4624	205	20	r	r	NOUN
ejpam-4624	205	21	,	,	PUNCT
ejpam-4624	205	22	s	s	NOUN
ejpam-4624	205	23	)	)	PUNCT
ejpam-4624	205	24	)	)	PUNCT
ejpam-4624	205	25	≤	≤	NOUN
ejpam-4624	206	1	1−	1−	NUM
ejpam-4624	206	2	ϕ.	ϕ.	NOUN
ejpam-4624	206	3	therefore	therefore	ADV
ejpam-4624	206	4	,	,	PUNCT
ejpam-4624	206	5	ϕ	ϕ	PROPN
ejpam-4624	206	6	≤	≤	NUM
ejpam-4624	206	7	(	(	PUNCT
ejpam-4624	206	8	1−	1−	NUM
ejpam-4624	206	9	it	it	PRON
ejpam-4624	206	10	,	,	PUNCT
ejpam-4624	206	11	t	t	PROPN
ejpam-4624	206	12	∗(ct	∗(ct	PROPN
ejpam-4624	206	13	,	,	PUNCT
ejpam-4624	206	14	t	t	PROPN
ejpam-4624	206	15	∗(ν	∗(ν	PROPN
ejpam-4624	206	16	,	,	PUNCT
ejpam-4624	206	17	r	r	NOUN
ejpam-4624	206	18	,	,	PUNCT
ejpam-4624	206	19	s	s	NOUN
ejpam-4624	206	20	)	)	PUNCT
ejpam-4624	206	21	)	)	PUNCT
ejpam-4624	206	22	)	)	PUNCT
ejpam-4624	206	23	.	.	PUNCT
ejpam-4624	207	1	hence	hence	ADV
ejpam-4624	207	2	,	,	PUNCT
ejpam-4624	207	3	ρ	ρ	PROPN
ejpam-4624	207	4	≤	≤	PROPN
ejpam-4624	207	5	ct	ct	NUM
ejpam-4624	207	6	,	,	PUNCT
ejpam-4624	207	7	t	t	PROPN
ejpam-4624	207	8	∗(ϕ	∗(ϕ	NOUN
ejpam-4624	207	9	,	,	PUNCT
ejpam-4624	207	10	r	r	NOUN
ejpam-4624	207	11	,	,	PUNCT
ejpam-4624	207	12	s	s	NOUN
ejpam-4624	207	13	)	)	PUNCT
ejpam-4624	207	14	≤	≤	NOUN
ejpam-4624	207	15	ct	ct	NUM
ejpam-4624	207	16	,	,	PUNCT
ejpam-4624	207	17	t	t	PROPN
ejpam-4624	207	18	∗(1−	∗(1−	PROPN
ejpam-4624	208	1	it	it	PRON
ejpam-4624	208	2	,	,	PUNCT
ejpam-4624	208	3	t	t	PROPN
ejpam-4624	208	4	∗(ct	∗(ct	PROPN
ejpam-4624	208	5	,	,	PUNCT
ejpam-4624	208	6	t	t	PROPN
ejpam-4624	208	7	∗(ν	∗(ν	PROPN
ejpam-4624	208	8	,	,	PUNCT
ejpam-4624	208	9	r	r	NOUN
ejpam-4624	208	10	,	,	PUNCT
ejpam-4624	208	11	s	s	NOUN
ejpam-4624	208	12	)	)	PUNCT
ejpam-4624	208	13	)	)	PUNCT
ejpam-4624	208	14	)	)	PUNCT
ejpam-4624	209	1	=	=	PUNCT
ejpam-4624	209	2	(	(	PUNCT
ejpam-4624	209	3	1−	1−	NUM
ejpam-4624	209	4	it	it	PRON
ejpam-4624	209	5	,	,	PUNCT
ejpam-4624	209	6	t	t	PROPN
ejpam-4624	209	7	∗(ct	∗(ct	PROPN
ejpam-4624	209	8	,	,	PUNCT
ejpam-4624	209	9	t	t	PROPN
ejpam-4624	209	10	∗(ν	∗(ν	PROPN
ejpam-4624	209	11	,	,	PUNCT
ejpam-4624	209	12	r	r	NOUN
ejpam-4624	209	13	,	,	PUNCT
ejpam-4624	209	14	s	s	NOUN
ejpam-4624	209	15	)	)	PUNCT
ejpam-4624	209	16	)	)	PUNCT
ejpam-4624	209	17	.	.	PUNCT
ejpam-4624	210	1	because	because	SCONJ
ejpam-4624	210	2	of	of	ADP
ejpam-4624	210	3	(	(	PUNCT
ejpam-4624	210	4	1	1	NUM
ejpam-4624	210	5	−	−	NOUN
ejpam-4624	210	6	(	(	PUNCT
ejpam-4624	210	7	1	1	NUM
ejpam-4624	210	8	−	−	NOUN
ejpam-4624	210	9	it	it	PRON
ejpam-4624	210	10	,	,	PUNCT
ejpam-4624	210	11	t	t	PROPN
ejpam-4624	210	12	∗(ct	∗(ct	PROPN
ejpam-4624	210	13	,	,	PUNCT
ejpam-4624	210	14	t	t	PROPN
ejpam-4624	210	15	∗(ν	∗(ν	PROPN
ejpam-4624	210	16	,	,	PUNCT
ejpam-4624	210	17	r	r	NOUN
ejpam-4624	210	18	,	,	PUNCT
ejpam-4624	210	19	s	s	NOUN
ejpam-4624	210	20	)	)	PUNCT
ejpam-4624	210	21	)	)	PUNCT
ejpam-4624	210	22	)	)	PUNCT
ejpam-4624	210	23	)	)	PUNCT
ejpam-4624	211	1	≥	≥	NOUN
ejpam-4624	211	2	r	r	NOUN
ejpam-4624	211	3	and	and	CCONJ
ejpam-4624	211	4	(	(	PUNCT
ejpam-4624	211	5	1	1	NUM
ejpam-4624	211	6	−	−	PROPN
ejpam-4624	211	7	(	(	PUNCT
ejpam-4624	211	8	1	1	NUM
ejpam-4624	211	9	−	−	NOUN
ejpam-4624	211	10	it	it	PRON
ejpam-4624	211	11	,	,	PUNCT
ejpam-4624	211	12	t	t	PROPN
ejpam-4624	211	13	∗(ct	∗(ct	PROPN
ejpam-4624	211	14	,	,	PUNCT
ejpam-4624	211	15	t	t	PROPN
ejpam-4624	211	16	∗(ν	∗(ν	PROPN
ejpam-4624	211	17	,	,	PUNCT
ejpam-4624	211	18	r	r	NOUN
ejpam-4624	211	19	,	,	PUNCT
ejpam-4624	211	20	s	s	NOUN
ejpam-4624	211	21	)	)	PUNCT
ejpam-4624	211	22	)	)	PUNCT
ejpam-4624	211	23	)	)	PUNCT
ejpam-4624	212	1	≤	≤	PROPN
ejpam-4624	212	2	s.	s.	PROPN
ejpam-4624	212	3	thus	thus	ADV
ejpam-4624	212	4	it	it	PRON
ejpam-4624	212	5	,	,	PUNCT
ejpam-4624	212	6	t	t	PROPN
ejpam-4624	212	7	∗(ct	∗(ct	PROPN
ejpam-4624	212	8	,	,	PUNCT
ejpam-4624	212	9	t	t	PROPN
ejpam-4624	212	10	∗(ν	∗(ν	PROPN
ejpam-4624	212	11	,	,	PUNCT
ejpam-4624	212	12	r	r	NOUN
ejpam-4624	212	13	,	,	PUNCT
ejpam-4624	212	14	s))q̃ρ	s))q̃ρ	NOUN
ejpam-4624	212	15	.	.	PUNCT
ejpam-4624	213	1	by	by	ADP
ejpam-4624	213	2	lemma	lemma	PROPN
ejpam-4624	213	3	2.7	2.7	NUM
ejpam-4624	213	4	,	,	PUNCT
ejpam-4624	213	5	it	it	PRON
ejpam-4624	213	6	,	,	PUNCT
ejpam-4624	213	7	t	t	PROPN
ejpam-4624	213	8	∗(ct	∗(ct	PROPN
ejpam-4624	213	9	,	,	PUNCT
ejpam-4624	213	10	t	t	PROPN
ejpam-4624	213	11	∗(ν	∗(ν	PROPN
ejpam-4624	213	12	,	,	PUNCT
ejpam-4624	213	13	r	r	NOUN
ejpam-4624	213	14	,	,	PUNCT
ejpam-4624	213	15	s	s	NOUN
ejpam-4624	213	16	)	)	PUNCT
ejpam-4624	213	17	)	)	PUNCT
ejpam-4624	213	18	is	be	AUX
ejpam-4624	213	19	a	a	DET
ejpam-4624	213	20	(	(	PUNCT
ejpam-4624	213	21	r	r	NOUN
ejpam-4624	213	22	,	,	PUNCT
ejpam-4624	213	23	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-4624	213	24	regular	regular	ADJ
ejpam-4624	213	25	open	open	ADJ
ejpam-4624	213	26	q	q	ADJ
ejpam-4624	213	27	-	-	PUNCT
ejpam-4624	213	28	neighborhood	neighborhood	NOUN
ejpam-4624	213	29	ν	ν	NOUN
ejpam-4624	213	30	of	of	ADP
ejpam-4624	213	31	xi	xi	INTJ
ejpam-4624	213	32	such	such	ADJ
ejpam-4624	213	33	that	that	SCONJ
ejpam-4624	213	34	it	it	PRON
ejpam-4624	213	35	,	,	PUNCT
ejpam-4624	213	36	t	t	PROPN
ejpam-4624	213	37	∗(ct	∗(ct	PROPN
ejpam-4624	213	38	,	,	PUNCT
ejpam-4624	213	39	t	t	PROPN
ejpam-4624	213	40	∗(ν	∗(ν	PROPN
ejpam-4624	213	41	,	,	PUNCT
ejpam-4624	213	42	r	r	NOUN
ejpam-4624	213	43	,	,	PUNCT
ejpam-4624	213	44	s))q̃ρ	s))q̃ρ	NOUN
ejpam-4624	213	45	.	.	PUNCT
ejpam-4624	214	1	hence	hence	ADV
ejpam-4624	214	2	,	,	PUNCT
ejpam-4624	214	3	xi	xi	PROPN
ejpam-4624	214	4	/∈	/∈	PUNCT
ejpam-4624	214	5	δct	δct	NOUN
ejpam-4624	214	6	,	,	PUNCT
ejpam-4624	214	7	t	t	NOUN
ejpam-4624	214	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	214	9	,	,	PUNCT
ejpam-4624	214	10	r	r	NOUN
ejpam-4624	214	11	,	,	PUNCT
ejpam-4624	214	12	s	s	PART
ejpam-4624	214	13	)	)	PUNCT
ejpam-4624	214	14	.	.	PUNCT
ejpam-4624	215	1	proposition	proposition	NOUN
ejpam-4624	215	2	2.15	2.15	NUM
ejpam-4624	215	3	.	.	PUNCT
ejpam-4624	216	1	let	let	VERB
ejpam-4624	216	2	(	(	PUNCT
ejpam-4624	216	3	x	x	X
ejpam-4624	216	4	,	,	PUNCT
ejpam-4624	216	5	t	t	PROPN
ejpam-4624	216	6	,	,	PUNCT
ejpam-4624	216	7	t	t	PROPN
ejpam-4624	216	8	∗	∗	NOUN
ejpam-4624	216	9	)	)	PUNCT
ejpam-4624	216	10	be	be	AUX
ejpam-4624	216	11	an	an	DET
ejpam-4624	216	12	dfts	dft	NOUN
ejpam-4624	216	13	.	.	PUNCT
ejpam-4624	217	1	then	then	ADV
ejpam-4624	217	2	,	,	PUNCT
ejpam-4624	217	3	for	for	ADP
ejpam-4624	217	4	each	each	DET
ejpam-4624	217	5	r	r	NOUN
ejpam-4624	217	6	∈	∈	PROPN
ejpam-4624	217	7	i0	i0	PROPN
ejpam-4624	217	8	,	,	PUNCT
ejpam-4624	217	9	s	s	PROPN
ejpam-4624	217	10	∈	∈	PROPN
ejpam-4624	217	11	i1	i1	NOUN
ejpam-4624	217	12	,	,	PUNCT
ejpam-4624	217	13	and	and	CCONJ
ejpam-4624	217	14	ρ	ρ	PROPN
ejpam-4624	217	15	∈	∈	PROPN
ejpam-4624	217	16	ix	ix	ADV
ejpam-4624	217	17	.	.	PUNCT
ejpam-4624	218	1	let	let	VERB
ejpam-4624	218	2	δit	δit	NOUN
ejpam-4624	218	3	,	,	PUNCT
ejpam-4624	218	4	t	t	PROPN
ejpam-4624	218	5	∗	∗	NOUN
ejpam-4624	218	6	:	:	PUNCT
ejpam-4624	219	1	ix	ix	PROPN
ejpam-4624	219	2	×	×	PROPN
ejpam-4624	219	3	i0	i0	PROPN
ejpam-4624	219	4	×	×	PROPN
ejpam-4624	219	5	i1	i1	PROPN
ejpam-4624	219	6	−→	−→	NOUN
ejpam-4624	219	7	ix	ix	PROPN
ejpam-4624	219	8	be	be	AUX
ejpam-4624	219	9	a	a	DET
ejpam-4624	219	10	function	function	NOUN
ejpam-4624	219	11	satisfy	satisfy	VERB
ejpam-4624	219	12	the	the	DET
ejpam-4624	219	13	conditions	condition	NOUN
ejpam-4624	219	14	(	(	PUNCT
ejpam-4624	219	15	1	1	NUM
ejpam-4624	219	16	-	-	SYM
ejpam-4624	219	17	5	5	NUM
ejpam-4624	219	18	)	)	PUNCT
ejpam-4624	219	19	in	in	ADP
ejpam-4624	219	20	proposition	proposition	NOUN
ejpam-4624	219	21	2.5	2.5	NUM
ejpam-4624	219	22	such	such	ADJ
ejpam-4624	219	23	that	that	DET
ejpam-4624	219	24	t	t	PROPN
ejpam-4624	219	25	,	,	PUNCT
ejpam-4624	219	26	t	t	PROPN
ejpam-4624	219	27	∗	∗	NOUN
ejpam-4624	219	28	:	:	PUNCT
ejpam-4624	219	29	ix	ix	PROPN
ejpam-4624	219	30	→	→	PUNCT
ejpam-4624	219	31	i	i	PRON
ejpam-4624	219	32	be	be	VERB
ejpam-4624	219	33	functions	function	NOUN
ejpam-4624	219	34	defined	define	VERB
ejpam-4624	219	35	by	by	ADP
ejpam-4624	219	36	t	t	PROPN
ejpam-4624	219	37	(	(	PUNCT
ejpam-4624	219	38	ρ	ρ	NOUN
ejpam-4624	219	39	)	)	PUNCT
ejpam-4624	219	40	=	=	SYM
ejpam-4624	219	41	∨	∨	X
ejpam-4624	219	42	{	{	PUNCT
ejpam-4624	219	43	r	r	NOUN
ejpam-4624	219	44	∈	∈	PROPN
ejpam-4624	219	45	i|δit	i|δit	NOUN
ejpam-4624	219	46	,	,	PUNCT
ejpam-4624	219	47	t	t	NOUN
ejpam-4624	219	48	∗(ρ	∗(ρ	NOUN
ejpam-4624	219	49	,	,	PUNCT
ejpam-4624	219	50	r	r	NOUN
ejpam-4624	219	51	,	,	PUNCT
ejpam-4624	219	52	s	s	NOUN
ejpam-4624	219	53	)	)	PUNCT
ejpam-4624	219	54	=	=	SYM
ejpam-4624	219	55	ρ	ρ	PROPN
ejpam-4624	219	56	}	}	PUNCT
ejpam-4624	219	57	and	and	CCONJ
ejpam-4624	219	58	t	t	NOUN
ejpam-4624	219	59	∗(ρ	∗(ρ	NOUN
ejpam-4624	219	60	)	)	PUNCT
ejpam-4624	219	61	=	=	SYM
ejpam-4624	220	1	∧	∧	NOUN
ejpam-4624	220	2	{	{	PUNCT
ejpam-4624	220	3	s	s	NOUN
ejpam-4624	220	4	∈	∈	PROPN
ejpam-4624	220	5	i|δit	i|δit	NOUN
ejpam-4624	220	6	,	,	PUNCT
ejpam-4624	220	7	t	t	NOUN
ejpam-4624	220	8	∗(ρ	∗(ρ	NOUN
ejpam-4624	220	9	,	,	PUNCT
ejpam-4624	220	10	r	r	NOUN
ejpam-4624	220	11	,	,	PUNCT
ejpam-4624	220	12	s	s	PART
ejpam-4624	220	13	)	)	PUNCT
ejpam-4624	220	14	=	=	SYM
ejpam-4624	220	15	ρ	ρ	PROPN
ejpam-4624	220	16	}	}	PUNCT
ejpam-4624	220	17	.	.	PUNCT
ejpam-4624	221	1	then	then	ADV
ejpam-4624	221	2	ζ	ζ	X
ejpam-4624	221	3	=	=	SYM
ejpam-4624	221	4	(	(	PUNCT
ejpam-4624	221	5	t	t	PROPN
ejpam-4624	221	6	,	,	PUNCT
ejpam-4624	221	7	t	t	PROPN
ejpam-4624	221	8	∗	∗	NOUN
ejpam-4624	221	9	)	)	PUNCT
ejpam-4624	221	10	is	be	AUX
ejpam-4624	221	11	double	double	ADJ
ejpam-4624	221	12	fuzzy	fuzzy	ADJ
ejpam-4624	221	13	topology	topology	NOUN
ejpam-4624	221	14	in	in	ADP
ejpam-4624	221	15	x.	x.	NOUN
ejpam-4624	221	16	proof	proof	NOUN
ejpam-4624	221	17	.	.	PUNCT
ejpam-4624	222	1	(	(	PUNCT
ejpam-4624	222	2	a	a	X
ejpam-4624	222	3	)	)	PUNCT
ejpam-4624	222	4	since	since	SCONJ
ejpam-4624	222	5	(	(	PUNCT
ejpam-4624	222	6	r	r	NOUN
ejpam-4624	222	7	,	,	PUNCT
ejpam-4624	222	8	s	s	PART
ejpam-4624	222	9	)	)	PUNCT
ejpam-4624	222	10	∈	∈	PROPN
ejpam-4624	222	11	i0	i0	PROPN
ejpam-4624	222	12	×	×	PROPN
ejpam-4624	222	13	i1	i1	PROPN
ejpam-4624	223	1	and	and	CCONJ
ejpam-4624	223	2	we	we	PRON
ejpam-4624	223	3	have	have	AUX
ejpam-4624	223	4	r+	r+	X
ejpam-4624	223	5	s	s	VERB
ejpam-4624	223	6	≤	≤	NOUN
ejpam-4624	223	7	1	1	NUM
ejpam-4624	223	8	.	.	PUNCT
ejpam-4624	224	1	hence	hence	ADV
ejpam-4624	224	2	s	s	VERB
ejpam-4624	224	3	≤	≤	NUM
ejpam-4624	224	4	1−	1−	NUM
ejpam-4624	224	5	r	r	NOUN
ejpam-4624	224	6	,	,	PUNCT
ejpam-4624	224	7	thus	thus	ADV
ejpam-4624	224	8	,	,	PUNCT
ejpam-4624	224	9	1−	1−	NUM
ejpam-4624	224	10	t	t	PROPN
ejpam-4624	224	11	(	(	PUNCT
ejpam-4624	224	12	ρ	ρ	NOUN
ejpam-4624	224	13	)	)	PUNCT
ejpam-4624	224	14	=	=	SYM
ejpam-4624	224	15	1−	1−	NUM
ejpam-4624	224	16	∨	∨	NUM
ejpam-4624	224	17	{	{	PUNCT
ejpam-4624	224	18	r	r	NOUN
ejpam-4624	224	19	∈	∈	PROPN
ejpam-4624	224	20	i|δit	i|δit	NOUN
ejpam-4624	224	21	,	,	PUNCT
ejpam-4624	224	22	t	t	NOUN
ejpam-4624	224	23	∗(ρ	∗(ρ	NOUN
ejpam-4624	224	24	,	,	PUNCT
ejpam-4624	224	25	r	r	NOUN
ejpam-4624	224	26	,	,	PUNCT
ejpam-4624	224	27	s	s	NOUN
ejpam-4624	224	28	)	)	PUNCT
ejpam-4624	224	29	=	=	SYM
ejpam-4624	224	30	ρ	ρ	PROPN
ejpam-4624	224	31	}	}	PUNCT
ejpam-4624	224	32	=	=	SYM
ejpam-4624	224	33	∧	∧	NOUN
ejpam-4624	224	34	{	{	PUNCT
ejpam-4624	224	35	1−	1−	NUM
ejpam-4624	224	36	r	r	NOUN
ejpam-4624	224	37	∈	∈	PROPN
ejpam-4624	224	38	i|δit	i|δit	NOUN
ejpam-4624	224	39	,	,	PUNCT
ejpam-4624	224	40	t	t	NOUN
ejpam-4624	224	41	∗(ρ	∗(ρ	NOUN
ejpam-4624	224	42	,	,	PUNCT
ejpam-4624	224	43	r	r	NOUN
ejpam-4624	224	44	,	,	PUNCT
ejpam-4624	224	45	s	s	NOUN
ejpam-4624	224	46	)	)	PUNCT
ejpam-4624	224	47	=	=	SYM
ejpam-4624	224	48	ρ	ρ	PROPN
ejpam-4624	224	49	}	}	PUNCT
ejpam-4624	224	50	≥	≥	NOUN
ejpam-4624	224	51	∧	∧	NOUN
ejpam-4624	224	52	{	{	PUNCT
ejpam-4624	224	53	s	s	NOUN
ejpam-4624	224	54	∈	∈	PROPN
ejpam-4624	224	55	i|δit	i|δit	NOUN
ejpam-4624	224	56	,	,	PUNCT
ejpam-4624	224	57	t	t	NOUN
ejpam-4624	224	58	∗(ρ	∗(ρ	NOUN
ejpam-4624	224	59	,	,	PUNCT
ejpam-4624	224	60	r	r	NOUN
ejpam-4624	224	61	,	,	PUNCT
ejpam-4624	224	62	s	s	NOUN
ejpam-4624	224	63	)	)	PUNCT
ejpam-4624	224	64	=	=	SYM
ejpam-4624	224	65	ρ	ρ	PROPN
ejpam-4624	224	66	}	}	PUNCT
ejpam-4624	224	67	=	=	SYM
ejpam-4624	224	68	t	t	NOUN
ejpam-4624	224	69	∗	∗	NOUN
ejpam-4624	224	70	.	.	PUNCT
ejpam-4624	225	1	(	(	PUNCT
ejpam-4624	225	2	b	b	X
ejpam-4624	225	3	)	)	PUNCT
ejpam-4624	225	4	suppose	suppose	VERB
ejpam-4624	225	5	that	that	SCONJ
ejpam-4624	225	6	t	t	PROPN
ejpam-4624	225	7	(	(	PUNCT
ejpam-4624	225	8	ρ1	ρ1	NOUN
ejpam-4624	225	9	∧	∧	PROPN
ejpam-4624	225	10	ρ2	ρ2	PROPN
ejpam-4624	225	11	)	)	PUNCT
ejpam-4624	225	12	≤	≤	NOUN
ejpam-4624	225	13	t	t	PROPN
ejpam-4624	225	14	(	(	PUNCT
ejpam-4624	225	15	ρ1	ρ1	NOUN
ejpam-4624	225	16	)	)	PUNCT
ejpam-4624	225	17	∧	∧	PROPN
ejpam-4624	225	18	t	t	PROPN
ejpam-4624	225	19	(	(	PUNCT
ejpam-4624	225	20	ρ2	ρ2	PROPN
ejpam-4624	225	21	)	)	PUNCT
ejpam-4624	225	22	.	.	PUNCT
ejpam-4624	226	1	then	then	ADV
ejpam-4624	226	2	there	there	PRON
ejpam-4624	226	3	is	be	VERB
ejpam-4624	226	4	a	a	DET
ejpam-4624	226	5	ξ	ξ	PROPN
ejpam-4624	226	6	∈	∈	NOUN
ejpam-4624	226	7	i	i	PRON
ejpam-4624	226	8	such	such	ADJ
ejpam-4624	226	9	that	that	SCONJ
ejpam-4624	226	10	t	t	PROPN
ejpam-4624	226	11	(	(	PUNCT
ejpam-4624	226	12	ρ1	ρ1	NOUN
ejpam-4624	226	13	∧	∧	PROPN
ejpam-4624	226	14	ρ2	ρ2	NOUN
ejpam-4624	226	15	)	)	PUNCT
ejpam-4624	226	16	≤	≤	NUM
ejpam-4624	226	17	ξ	ξ	X
ejpam-4624	226	18	≤	≤	PROPN
ejpam-4624	226	19	t	t	PROPN
ejpam-4624	226	20	(	(	PUNCT
ejpam-4624	226	21	ρ1	ρ1	NOUN
ejpam-4624	226	22	)	)	PUNCT
ejpam-4624	226	23	∧	∧	PROPN
ejpam-4624	226	24	t	t	PROPN
ejpam-4624	226	25	(	(	PUNCT
ejpam-4624	226	26	ρ2	ρ2	PROPN
ejpam-4624	226	27	)	)	PUNCT
ejpam-4624	226	28	.	.	PUNCT
ejpam-4624	227	1	w.	w.	PROPN
ejpam-4624	227	2	f.	f.	PROPN
ejpam-4624	227	3	al	al	PROPN
ejpam-4624	227	4	-	-	PUNCT
ejpam-4624	227	5	omeri	omeri	ADJ
ejpam-4624	227	6	/	/	SYM
ejpam-4624	227	7	eur	eur	PROPN
ejpam-4624	227	8	.	.	PUNCT
ejpam-4624	228	1	j.	j.	PROPN
ejpam-4624	228	2	pure	pure	PROPN
ejpam-4624	228	3	appl	appl	PROPN
ejpam-4624	228	4	.	.	PROPN
ejpam-4624	228	5	math	math	PROPN
ejpam-4624	228	6	,	,	PUNCT
ejpam-4624	228	7	18	18	NUM
ejpam-4624	228	8	(	(	PUNCT
ejpam-4624	228	9	2	2	NUM
ejpam-4624	228	10	)	)	PUNCT
ejpam-4624	228	11	(	(	PUNCT
ejpam-4624	228	12	2025	2025	NUM
ejpam-4624	228	13	)	)	PUNCT
ejpam-4624	228	14	,	,	PUNCT
ejpam-4624	228	15	4624	4624	NUM
ejpam-4624	228	16	9	9	NUM
ejpam-4624	228	17	of	of	ADP
ejpam-4624	228	18	15	15	NUM
ejpam-4624	228	19	since	since	ADV
ejpam-4624	228	20	,	,	PUNCT
ejpam-4624	228	21	ξ	ξ	PROPN
ejpam-4624	228	22	≤	≤	PROPN
ejpam-4624	228	23	t	t	PROPN
ejpam-4624	228	24	(	(	PUNCT
ejpam-4624	228	25	ρi	ρi	NOUN
ejpam-4624	228	26	)	)	PUNCT
ejpam-4624	228	27	=	=	PUNCT
ejpam-4624	229	1	∨	∨	X
ejpam-4624	229	2	{	{	PUNCT
ejpam-4624	229	3	r	r	NOUN
ejpam-4624	229	4	∈	∈	PROPN
ejpam-4624	229	5	i|δit	i|δit	NOUN
ejpam-4624	229	6	,	,	PUNCT
ejpam-4624	229	7	t	t	PROPN
ejpam-4624	229	8	∗(ρξ	∗(ρξ	NOUN
ejpam-4624	229	9	,	,	PUNCT
ejpam-4624	229	10	r	r	NOUN
ejpam-4624	229	11	,	,	PUNCT
ejpam-4624	229	12	s	s	NOUN
ejpam-4624	229	13	)	)	PUNCT
ejpam-4624	229	14	=	=	SYM
ejpam-4624	229	15	ρi	ρi	PROPN
ejpam-4624	229	16	}	}	PUNCT
ejpam-4624	229	17	,	,	PUNCT
ejpam-4624	229	18	for	for	ADP
ejpam-4624	229	19	each	each	DET
ejpam-4624	229	20	i	i	NOUN
ejpam-4624	229	21	=	=	NOUN
ejpam-4624	229	22	1	1	NUM
ejpam-4624	229	23	,	,	PUNCT
ejpam-4624	229	24	2	2	NUM
ejpam-4624	229	25	there	there	PRON
ejpam-4624	229	26	exist	exist	VERB
ejpam-4624	229	27	(	(	PUNCT
ejpam-4624	229	28	r1	r1	PROPN
ejpam-4624	229	29	,	,	PUNCT
ejpam-4624	229	30	s1	s1	NOUN
ejpam-4624	229	31	)	)	PUNCT
ejpam-4624	229	32	,	,	PUNCT
ejpam-4624	229	33	(	(	PUNCT
ejpam-4624	229	34	r2	r2	PROPN
ejpam-4624	229	35	,	,	PUNCT
ejpam-4624	229	36	s2	s2	PROPN
ejpam-4624	229	37	)	)	PUNCT
ejpam-4624	229	38	∈	∈	PROPN
ejpam-4624	229	39	i0	i0	PROPN
ejpam-4624	229	40	×	×	PROPN
ejpam-4624	229	41	i1	i1	PROPN
ejpam-4624	230	1	such	such	ADJ
ejpam-4624	230	2	that	that	SCONJ
ejpam-4624	230	3	ξ	ξ	PROPN
ejpam-4624	230	4	≤	≤	NUM
ejpam-4624	230	5	ri	ri	X
ejpam-4624	230	6	≤	≤	PROPN
ejpam-4624	230	7	t	t	PROPN
ejpam-4624	230	8	(	(	PUNCT
ejpam-4624	230	9	ρi	ρi	NOUN
ejpam-4624	230	10	)	)	PUNCT
ejpam-4624	230	11	and	and	CCONJ
ejpam-4624	230	12	δit	δit	NOUN
ejpam-4624	230	13	,	,	PUNCT
ejpam-4624	230	14	t	t	PROPN
ejpam-4624	230	15	∗(ρi	∗(ρi	ADJ
ejpam-4624	230	16	,	,	PUNCT
ejpam-4624	230	17	ri	ri	PROPN
ejpam-4624	230	18	,	,	PUNCT
ejpam-4624	230	19	si	si	NOUN
ejpam-4624	230	20	)	)	PUNCT
ejpam-4624	230	21	=	=	SYM
ejpam-4624	230	22	ρi	ρi	NOUN
ejpam-4624	230	23	.	.	PUNCT
ejpam-4624	231	1	now	now	ADV
ejpam-4624	231	2	,	,	PUNCT
ejpam-4624	231	3	for	for	ADP
ejpam-4624	231	4	each	each	DET
ejpam-4624	231	5	i	i	NOUN
ejpam-4624	231	6	=	=	NOUN
ejpam-4624	231	7	1	1	NUM
ejpam-4624	231	8	,	,	PUNCT
ejpam-4624	231	9	2	2	NUM
ejpam-4624	231	10	,	,	PUNCT
ejpam-4624	231	11	let	let	VERB
ejpam-4624	231	12	r	r	NOUN
ejpam-4624	231	13	=	=	SYM
ejpam-4624	231	14	r1	r1	NOUN
ejpam-4624	231	15	∧	∧	PROPN
ejpam-4624	231	16	r2	r2	PROPN
ejpam-4624	231	17	and	and	CCONJ
ejpam-4624	231	18	s	s	NOUN
ejpam-4624	231	19	=	=	PROPN
ejpam-4624	231	20	s1	s1	PROPN
ejpam-4624	231	21	∨	∨	NUM
ejpam-4624	231	22	s2	s2	PROPN
ejpam-4624	231	23	.	.	PUNCT
ejpam-4624	232	1	since	since	SCONJ
ejpam-4624	232	2	(	(	PUNCT
ejpam-4624	232	3	r1	r1	PROPN
ejpam-4624	232	4	,	,	PUNCT
ejpam-4624	232	5	s1	s1	NOUN
ejpam-4624	232	6	)	)	PUNCT
ejpam-4624	232	7	,	,	PUNCT
ejpam-4624	232	8	(	(	PUNCT
ejpam-4624	232	9	r2	r2	PROPN
ejpam-4624	232	10	,	,	PUNCT
ejpam-4624	232	11	s2	s2	PROPN
ejpam-4624	232	12	)	)	PUNCT
ejpam-4624	232	13	∈	∈	PROPN
ejpam-4624	232	14	i0	i0	PROPN
ejpam-4624	232	15	×	×	PROPN
ejpam-4624	232	16	i1	i1	PROPN
ejpam-4624	232	17	,	,	PUNCT
ejpam-4624	232	18	we	we	PRON
ejpam-4624	232	19	have	have	VERB
ejpam-4624	232	20	:	:	PUNCT
ejpam-4624	232	21	1−	1−	NUM
ejpam-4624	232	22	r	r	NOUN
ejpam-4624	232	23	=	=	SYM
ejpam-4624	232	24	1−	1−	NUM
ejpam-4624	232	25	(	(	PUNCT
ejpam-4624	232	26	r1	r1	NOUN
ejpam-4624	232	27	∧	∧	PROPN
ejpam-4624	232	28	r2	r2	PROPN
ejpam-4624	232	29	)	)	PUNCT
ejpam-4624	232	30	=	=	PUNCT
ejpam-4624	232	31	(	(	PUNCT
ejpam-4624	232	32	1−	1−	NUM
ejpam-4624	232	33	r1	r1	PROPN
ejpam-4624	232	34	)	)	PUNCT
ejpam-4624	232	35	∨	∨	NUM
ejpam-4624	232	36	(	(	PUNCT
ejpam-4624	232	37	1−	1−	NUM
ejpam-4624	232	38	r2	r2	PROPN
ejpam-4624	232	39	)	)	PUNCT
ejpam-4624	232	40	≥	≥	NOUN
ejpam-4624	232	41	s1	s1	PROPN
ejpam-4624	232	42	∨	∨	NUM
ejpam-4624	232	43	s2	s2	PROPN
ejpam-4624	232	44	=	=	SYM
ejpam-4624	232	45	s	s	PART
ejpam-4624	232	46	hence	hence	ADV
ejpam-4624	232	47	,	,	PUNCT
ejpam-4624	232	48	(	(	PUNCT
ejpam-4624	232	49	r	r	NOUN
ejpam-4624	232	50	,	,	PUNCT
ejpam-4624	232	51	s	s	PART
ejpam-4624	232	52	)	)	PUNCT
ejpam-4624	232	53	∈	∈	PROPN
ejpam-4624	232	54	i0	i0	PROPN
ejpam-4624	232	55	×	×	PROPN
ejpam-4624	232	56	i1	i1	PROPN
ejpam-4624	232	57	.	.	PUNCT
ejpam-4624	233	1	since	since	SCONJ
ejpam-4624	233	2	r	r	NOUN
ejpam-4624	233	3	≤	≤	NUM
ejpam-4624	233	4	ri	ri	NOUN
ejpam-4624	233	5	and	and	CCONJ
ejpam-4624	233	6	s	s	X
ejpam-4624	233	7	≥	≥	NOUN
ejpam-4624	233	8	si	si	X
ejpam-4624	233	9	for	for	ADP
ejpam-4624	233	10	each	each	DET
ejpam-4624	233	11	i	i	NOUN
ejpam-4624	233	12	=	=	NOUN
ejpam-4624	233	13	1	1	NUM
ejpam-4624	233	14	,	,	PUNCT
ejpam-4624	233	15	2	2	NUM
ejpam-4624	233	16	we	we	PRON
ejpam-4624	233	17	have	have	VERB
ejpam-4624	233	18	,	,	PUNCT
ejpam-4624	233	19	δit	δit	NOUN
ejpam-4624	233	20	,	,	PUNCT
ejpam-4624	233	21	t	t	PROPN
ejpam-4624	233	22	∗(ρξ	∗(ρξ	NOUN
ejpam-4624	233	23	,	,	PUNCT
ejpam-4624	233	24	r	r	NOUN
ejpam-4624	233	25	,	,	PUNCT
ejpam-4624	233	26	s	s	PART
ejpam-4624	233	27	)	)	PUNCT
ejpam-4624	233	28	≥	≥	NOUN
ejpam-4624	233	29	δit	δit	NOUN
ejpam-4624	233	30	,	,	PUNCT
ejpam-4624	234	1	t	t	PROPN
ejpam-4624	234	2	∗(ρi	∗(ρi	ADJ
ejpam-4624	234	3	,	,	PUNCT
ejpam-4624	234	4	ri	ri	PROPN
ejpam-4624	234	5	,	,	PUNCT
ejpam-4624	234	6	si	si	NOUN
ejpam-4624	234	7	)	)	PUNCT
ejpam-4624	234	8	=	=	SYM
ejpam-4624	234	9	ρξ	ρξ	X
ejpam-4624	234	10	.	.	PUNCT
ejpam-4624	235	1	hence	hence	ADV
ejpam-4624	235	2	,	,	PUNCT
ejpam-4624	235	3	δit	δit	NOUN
ejpam-4624	235	4	,	,	PUNCT
ejpam-4624	235	5	t	t	PROPN
ejpam-4624	235	6	∗(ρi	∗(ρi	ADJ
ejpam-4624	235	7	,	,	PUNCT
ejpam-4624	235	8	r	r	NOUN
ejpam-4624	235	9	,	,	PUNCT
ejpam-4624	235	10	s	s	NOUN
ejpam-4624	235	11	)	)	PUNCT
ejpam-4624	235	12	=	=	SYM
ejpam-4624	235	13	ρi	ρi	NOUN
ejpam-4624	235	14	for	for	ADP
ejpam-4624	235	15	each	each	DET
ejpam-4624	235	16	i	i	NOUN
ejpam-4624	235	17	=	=	NOUN
ejpam-4624	235	18	1	1	NUM
ejpam-4624	235	19	,	,	PUNCT
ejpam-4624	235	20	2	2	NUM
ejpam-4624	235	21	,	,	PUNCT
ejpam-4624	235	22	we	we	PRON
ejpam-4624	235	23	get	get	VERB
ejpam-4624	235	24	δit	δit	NOUN
ejpam-4624	235	25	,	,	PUNCT
ejpam-4624	235	26	t	t	PROPN
ejpam-4624	235	27	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	235	28	∧	∧	PROPN
ejpam-4624	235	29	ρ2	ρ2	PROPN
ejpam-4624	235	30	,	,	PUNCT
ejpam-4624	235	31	r	r	NOUN
ejpam-4624	235	32	,	,	PUNCT
ejpam-4624	235	33	s	s	PART
ejpam-4624	235	34	)	)	PUNCT
ejpam-4624	235	35	=	=	NOUN
ejpam-4624	235	36	δit	δit	NOUN
ejpam-4624	235	37	,	,	PUNCT
ejpam-4624	235	38	t	t	NOUN
ejpam-4624	235	39	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	235	40	,	,	PUNCT
ejpam-4624	235	41	r	r	NOUN
ejpam-4624	235	42	,	,	PUNCT
ejpam-4624	235	43	s	s	NOUN
ejpam-4624	235	44	)	)	PUNCT
ejpam-4624	235	45	∧	∧	NOUN
ejpam-4624	235	46	δit	δit	NOUN
ejpam-4624	235	47	,	,	PUNCT
ejpam-4624	235	48	t	t	PROPN
ejpam-4624	235	49	∗(ρ2	∗(ρ2	NOUN
ejpam-4624	235	50	,	,	PUNCT
ejpam-4624	235	51	r	r	NOUN
ejpam-4624	235	52	,	,	PUNCT
ejpam-4624	235	53	s	s	NOUN
ejpam-4624	235	54	)	)	PUNCT
ejpam-4624	235	55	=	=	SYM
ejpam-4624	235	56	ρ1	ρ1	NOUN
ejpam-4624	235	57	∧	∧	PROPN
ejpam-4624	235	58	ρ2	ρ2	NOUN
ejpam-4624	235	59	.	.	PUNCT
ejpam-4624	236	1	thus	thus	ADV
ejpam-4624	236	2	,	,	PUNCT
ejpam-4624	236	3	ξ	ξ	PROPN
ejpam-4624	236	4	≥	≥	NOUN
ejpam-4624	236	5	t	t	PROPN
ejpam-4624	236	6	(	(	PUNCT
ejpam-4624	236	7	ρ1	ρ1	NOUN
ejpam-4624	236	8	∧	∧	PROPN
ejpam-4624	236	9	ρ2	ρ2	NOUN
ejpam-4624	236	10	)	)	PUNCT
ejpam-4624	236	11	=	=	SYM
ejpam-4624	236	12	∨	∨	X
ejpam-4624	236	13	{	{	PUNCT
ejpam-4624	236	14	r∗	r∗	PROPN
ejpam-4624	236	15	∈	∈	PROPN
ejpam-4624	236	16	i|δit	i|δit	NOUN
ejpam-4624	236	17	,	,	PUNCT
ejpam-4624	236	18	t	t	PROPN
ejpam-4624	236	19	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	236	20	∧	∧	PROPN
ejpam-4624	236	21	ρ2	ρ2	PROPN
ejpam-4624	236	22	,	,	PUNCT
ejpam-4624	236	23	r	r	NOUN
ejpam-4624	236	24	,	,	PUNCT
ejpam-4624	236	25	s	s	NOUN
ejpam-4624	236	26	)	)	PUNCT
ejpam-4624	236	27	=	=	SYM
ejpam-4624	236	28	ρ1	ρ1	NOUN
ejpam-4624	236	29	∧	∧	PROPN
ejpam-4624	236	30	ρ2	ρ2	PROPN
ejpam-4624	236	31	}	}	PUNCT
ejpam-4624	236	32	≥	≥	NOUN
ejpam-4624	236	33	r	r	NOUN
ejpam-4624	236	34	=	=	SYM
ejpam-4624	236	35	r1	r1	NOUN
ejpam-4624	236	36	∧	∧	PROPN
ejpam-4624	236	37	r2	r2	PROPN
ejpam-4624	236	38	≥	≥	NUM
ejpam-4624	236	39	ξ	ξ	X
ejpam-4624	236	40	.	.	PUNCT
ejpam-4624	236	41	which	which	PRON
ejpam-4624	236	42	is	be	AUX
ejpam-4624	236	43	a	a	DET
ejpam-4624	236	44	contradiction	contradiction	NOUN
ejpam-4624	236	45	.	.	PUNCT
ejpam-4624	237	1	hence	hence	ADV
ejpam-4624	237	2	,	,	PUNCT
ejpam-4624	237	3	t	t	PROPN
ejpam-4624	237	4	(	(	PUNCT
ejpam-4624	237	5	ρ1	ρ1	NOUN
ejpam-4624	237	6	∧	∧	PROPN
ejpam-4624	237	7	ρ2	ρ2	PROPN
ejpam-4624	237	8	)	)	PUNCT
ejpam-4624	237	9	≥	≥	PROPN
ejpam-4624	237	10	t	t	PROPN
ejpam-4624	237	11	(	(	PUNCT
ejpam-4624	237	12	ρ1	ρ1	NOUN
ejpam-4624	237	13	)	)	PUNCT
ejpam-4624	237	14	∧	∧	PROPN
ejpam-4624	237	15	t	t	PROPN
ejpam-4624	237	16	(	(	PUNCT
ejpam-4624	237	17	ρ2	ρ2	PROPN
ejpam-4624	237	18	)	)	PUNCT
ejpam-4624	237	19	.	.	PUNCT
ejpam-4624	238	1	next	next	ADV
ejpam-4624	238	2	,	,	PUNCT
ejpam-4624	238	3	suppose	suppose	VERB
ejpam-4624	238	4	that	that	SCONJ
ejpam-4624	238	5	t	t	PROPN
ejpam-4624	238	6	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	238	7	∧	∧	PROPN
ejpam-4624	238	8	ρ2	ρ2	PROPN
ejpam-4624	238	9	)	)	PUNCT
ejpam-4624	238	10	≥	≥	NOUN
ejpam-4624	238	11	t	t	NOUN
ejpam-4624	238	12	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	238	13	)	)	PUNCT
ejpam-4624	238	14	∨	∨	PROPN
ejpam-4624	238	15	t	t	PROPN
ejpam-4624	238	16	∗(ρ2	∗(ρ2	PROPN
ejpam-4624	238	17	)	)	PUNCT
ejpam-4624	238	18	.	.	PUNCT
ejpam-4624	239	1	then	then	ADV
ejpam-4624	239	2	,	,	PUNCT
ejpam-4624	239	3	there	there	PRON
ejpam-4624	239	4	is	be	VERB
ejpam-4624	239	5	a	a	DET
ejpam-4624	239	6	ξ	ξ	PROPN
ejpam-4624	239	7	∈	∈	NOUN
ejpam-4624	239	8	i	i	PRON
ejpam-4624	239	9	such	such	ADJ
ejpam-4624	239	10	that	that	SCONJ
ejpam-4624	239	11	t	t	NOUN
ejpam-4624	239	12	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	239	13	∧	∧	PROPN
ejpam-4624	239	14	ρ2	ρ2	PROPN
ejpam-4624	239	15	)	)	PUNCT
ejpam-4624	239	16	≥	≥	NOUN
ejpam-4624	239	17	ξ	ξ	PROPN
ejpam-4624	239	18	≥	≥	NOUN
ejpam-4624	239	19	t	t	NOUN
ejpam-4624	239	20	∗(ρ1	∗(ρ1	NOUN
ejpam-4624	239	21	)	)	PUNCT
ejpam-4624	239	22	∨	∨	PROPN
ejpam-4624	239	23	t	t	PROPN
ejpam-4624	239	24	∗(ρ2	∗(ρ2	PROPN
ejpam-4624	239	25	)	)	PUNCT
ejpam-4624	239	26	.	.	PUNCT
ejpam-4624	240	1	since	since	SCONJ
ejpam-4624	240	2	ξ	ξ	PROPN
ejpam-4624	240	3	≥	≥	PROPN
ejpam-4624	240	4	t	t	X
ejpam-4624	240	5	∗(ρi	∗(ρi	ADJ
ejpam-4624	240	6	)	)	PUNCT
ejpam-4624	240	7	=	=	SYM
ejpam-4624	240	8	∧	∧	NOUN
ejpam-4624	240	9	{	{	PUNCT
ejpam-4624	240	10	s	s	NOUN
ejpam-4624	240	11	∈	∈	PROPN
ejpam-4624	240	12	i|δit	i|δit	NOUN
ejpam-4624	240	13	,	,	PUNCT
ejpam-4624	240	14	t	t	PROPN
ejpam-4624	240	15	∗(ρi	∗(ρi	ADJ
ejpam-4624	240	16	,	,	PUNCT
ejpam-4624	240	17	r	r	NOUN
ejpam-4624	240	18	,	,	PUNCT
ejpam-4624	240	19	s	s	PART
ejpam-4624	240	20	)	)	PUNCT
ejpam-4624	240	21	=	=	SYM
ejpam-4624	240	22	ρξ	ρξ	VERB
ejpam-4624	240	23	}	}	PUNCT
ejpam-4624	240	24	for	for	ADP
ejpam-4624	240	25	each	each	DET
ejpam-4624	240	26	i	i	NOUN
ejpam-4624	240	27	=	=	NOUN
ejpam-4624	240	28	1	1	NUM
ejpam-4624	240	29	,	,	PUNCT
ejpam-4624	240	30	2	2	NUM
ejpam-4624	240	31	there	there	PRON
ejpam-4624	240	32	are	be	VERB
ejpam-4624	240	33	(	(	PUNCT
ejpam-4624	240	34	r1	r1	PROPN
ejpam-4624	240	35	,	,	PUNCT
ejpam-4624	240	36	s1	s1	NOUN
ejpam-4624	240	37	)	)	PUNCT
ejpam-4624	240	38	,	,	PUNCT
ejpam-4624	240	39	(	(	PUNCT
ejpam-4624	240	40	r2	r2	PROPN
ejpam-4624	240	41	,	,	PUNCT
ejpam-4624	240	42	s2	s2	PROPN
ejpam-4624	240	43	)	)	PUNCT
ejpam-4624	240	44	∈	∈	PROPN
ejpam-4624	240	45	i0	i0	PROPN
ejpam-4624	240	46	×	×	PROPN
ejpam-4624	240	47	i1	i1	PROPN
ejpam-4624	240	48	such	such	ADJ
ejpam-4624	240	49	that	that	SCONJ
ejpam-4624	240	50	ξ	ξ	PROPN
ejpam-4624	240	51	≥	≥	NOUN
ejpam-4624	240	52	sξ	sξ	ADP
ejpam-4624	240	53	≥	≥	PROPN
ejpam-4624	240	54	t	t	PROPN
ejpam-4624	240	55	(	(	PUNCT
ejpam-4624	240	56	ρi	ρi	NOUN
ejpam-4624	240	57	)	)	PUNCT
ejpam-4624	240	58	and	and	CCONJ
ejpam-4624	240	59	δit	δit	NOUN
ejpam-4624	240	60	,	,	PUNCT
ejpam-4624	240	61	t	t	PROPN
ejpam-4624	240	62	∗(ρi	∗(ρi	ADJ
ejpam-4624	240	63	,	,	PUNCT
ejpam-4624	240	64	ri	ri	PROPN
ejpam-4624	240	65	,	,	PUNCT
ejpam-4624	240	66	si	si	NOUN
ejpam-4624	240	67	)	)	PUNCT
ejpam-4624	240	68	=	=	SYM
ejpam-4624	240	69	ρi	ρi	NOUN
ejpam-4624	240	70	.	.	PUNCT
ejpam-4624	241	1	now	now	ADV
ejpam-4624	241	2	,	,	PUNCT
ejpam-4624	241	3	let	let	VERB
ejpam-4624	241	4	r	r	NOUN
ejpam-4624	241	5	=	=	SYM
ejpam-4624	241	6	r1	r1	NOUN
ejpam-4624	241	7	∧	∧	PROPN
ejpam-4624	241	8	r2	r2	PROPN
ejpam-4624	241	9	and	and	CCONJ
ejpam-4624	241	10	s	s	NOUN
ejpam-4624	241	11	=	=	PROPN
ejpam-4624	241	12	s1	s1	PROPN
ejpam-4624	241	13	∨	∨	NUM
ejpam-4624	241	14	s2	s2	PROPN
ejpam-4624	241	15	.	.	PUNCT
ejpam-4624	242	1	then	then	ADV
ejpam-4624	242	2	(	(	PUNCT
ejpam-4624	242	3	r	r	NOUN
ejpam-4624	242	4	,	,	PUNCT
ejpam-4624	242	5	s	s	PART
ejpam-4624	242	6	)	)	PUNCT
ejpam-4624	242	7	∈	∈	PROPN
ejpam-4624	242	8	i0	i0	PROPN
ejpam-4624	242	9	×	×	PROPN
ejpam-4624	242	10	i1	i1	PROPN
ejpam-4624	242	11	and	and	CCONJ
ejpam-4624	242	12	δit	δit	NOUN
ejpam-4624	242	13	,	,	PUNCT
ejpam-4624	242	14	t	t	PROPN
ejpam-4624	242	15	∗(ρi	∗(ρi	ADJ
ejpam-4624	242	16	,	,	PUNCT
ejpam-4624	242	17	r	r	NOUN
ejpam-4624	242	18	,	,	PUNCT
ejpam-4624	242	19	si	si	NOUN
ejpam-4624	242	20	)	)	PUNCT
ejpam-4624	242	21	=	=	SYM
ejpam-4624	243	1	ρi	ρi	NOUN
ejpam-4624	243	2	for	for	ADP
ejpam-4624	243	3	each	each	DET
ejpam-4624	243	4	i	i	NOUN
ejpam-4624	243	5	=	=	NOUN
ejpam-4624	243	6	1	1	NUM
ejpam-4624	243	7	,	,	PUNCT
ejpam-4624	243	8	2	2	NUM
ejpam-4624	243	9	.	.	X
ejpam-4624	243	10	δit	δit	NOUN
ejpam-4624	243	11	,	,	PUNCT
ejpam-4624	243	12	t	t	PROPN
ejpam-4624	243	13	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	243	14	∧	∧	PROPN
ejpam-4624	243	15	ρ2	ρ2	PROPN
ejpam-4624	243	16	,	,	PUNCT
ejpam-4624	243	17	r	r	NOUN
ejpam-4624	243	18	,	,	PUNCT
ejpam-4624	243	19	s	s	PART
ejpam-4624	243	20	)	)	PUNCT
ejpam-4624	243	21	=	=	NOUN
ejpam-4624	243	22	δit	δit	NOUN
ejpam-4624	243	23	,	,	PUNCT
ejpam-4624	243	24	t	t	NOUN
ejpam-4624	243	25	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	243	26	,	,	PUNCT
ejpam-4624	243	27	r	r	NOUN
ejpam-4624	243	28	,	,	PUNCT
ejpam-4624	243	29	s	s	NOUN
ejpam-4624	243	30	)	)	PUNCT
ejpam-4624	243	31	∧	∧	NOUN
ejpam-4624	243	32	δit	δit	NOUN
ejpam-4624	243	33	,	,	PUNCT
ejpam-4624	243	34	t	t	PROPN
ejpam-4624	243	35	∗(ρ2	∗(ρ2	NOUN
ejpam-4624	243	36	,	,	PUNCT
ejpam-4624	243	37	r	r	NOUN
ejpam-4624	243	38	,	,	PUNCT
ejpam-4624	243	39	s	s	NOUN
ejpam-4624	243	40	)	)	PUNCT
ejpam-4624	243	41	=	=	SYM
ejpam-4624	243	42	ρ1	ρ1	NOUN
ejpam-4624	243	43	∧	∧	PROPN
ejpam-4624	243	44	ρ2	ρ2	NOUN
ejpam-4624	243	45	.	.	PUNCT
ejpam-4624	244	1	thus	thus	ADV
ejpam-4624	244	2	,	,	PUNCT
ejpam-4624	244	3	ξ	ξ	PROPN
ejpam-4624	244	4	≥	≥	NOUN
ejpam-4624	244	5	t	t	NOUN
ejpam-4624	244	6	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	244	7	∧	∧	PROPN
ejpam-4624	244	8	ρ2	ρ2	NOUN
ejpam-4624	244	9	)	)	PUNCT
ejpam-4624	244	10	=	=	SYM
ejpam-4624	245	1	∧	∧	NOUN
ejpam-4624	245	2	{	{	PUNCT
ejpam-4624	245	3	r∗	r∗	PROPN
ejpam-4624	245	4	∈	∈	PROPN
ejpam-4624	245	5	i|δit	i|δit	NOUN
ejpam-4624	245	6	,	,	PUNCT
ejpam-4624	245	7	t	t	PROPN
ejpam-4624	245	8	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	245	9	∧	∧	PROPN
ejpam-4624	245	10	ρ2	ρ2	PROPN
ejpam-4624	245	11	,	,	PUNCT
ejpam-4624	245	12	r	r	NOUN
ejpam-4624	245	13	,	,	PUNCT
ejpam-4624	245	14	s	s	NOUN
ejpam-4624	245	15	)	)	PUNCT
ejpam-4624	245	16	=	=	SYM
ejpam-4624	245	17	ρ1	ρ1	NOUN
ejpam-4624	245	18	∧	∧	PROPN
ejpam-4624	245	19	ρ2	ρ2	PROPN
ejpam-4624	245	20	}	}	PUNCT
ejpam-4624	245	21	≤	≤	PROPN
ejpam-4624	245	22	s	s	PART
ejpam-4624	245	23	=	=	SYM
ejpam-4624	245	24	s1	s1	PROPN
ejpam-4624	245	25	∧	∧	PROPN
ejpam-4624	245	26	s2	s2	NOUN
ejpam-4624	245	27	≤	≤	NUM
ejpam-4624	245	28	ξ	ξ	NOUN
ejpam-4624	245	29	.	.	PUNCT
ejpam-4624	245	30	which	which	PRON
ejpam-4624	245	31	is	be	AUX
ejpam-4624	245	32	a	a	DET
ejpam-4624	245	33	contradiction	contradiction	NOUN
ejpam-4624	245	34	.	.	PUNCT
ejpam-4624	246	1	hence	hence	ADV
ejpam-4624	246	2	,	,	PUNCT
ejpam-4624	246	3	t	t	PROPN
ejpam-4624	246	4	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	246	5	∧	∧	PROPN
ejpam-4624	246	6	ρ2	ρ2	PROPN
ejpam-4624	246	7	)	)	PUNCT
ejpam-4624	246	8	≤	≤	NOUN
ejpam-4624	246	9	t	t	PROPN
ejpam-4624	246	10	∗(ρ1	∗(ρ1	PROPN
ejpam-4624	246	11	)	)	PUNCT
ejpam-4624	246	12	∨	∨	PROPN
ejpam-4624	246	13	t	t	PROPN
ejpam-4624	246	14	∗(ρ2	∗(ρ2	PROPN
ejpam-4624	246	15	)	)	PUNCT
ejpam-4624	246	16	.	.	PUNCT
ejpam-4624	247	1	(	(	PUNCT
ejpam-4624	247	2	c	c	X
ejpam-4624	247	3	)	)	PUNCT
ejpam-4624	247	4	first	first	ADV
ejpam-4624	247	5	suppose	suppose	VERB
ejpam-4624	247	6	that	that	SCONJ
ejpam-4624	247	7	,	,	PUNCT
ejpam-4624	247	8	t	t	PROPN
ejpam-4624	247	9	(	(	PUNCT
ejpam-4624	247	10	∨	∨	NUM
ejpam-4624	247	11	ρi	ρi	NOUN
ejpam-4624	247	12	)	)	PUNCT
ejpam-4624	247	13	≤	≤	NUM
ejpam-4624	247	14	∧	∧	PROPN
ejpam-4624	247	15	t	t	PROPN
ejpam-4624	247	16	(	(	PUNCT
ejpam-4624	247	17	ρi	ρi	NOUN
ejpam-4624	247	18	)	)	PUNCT
ejpam-4624	247	19	.	.	PUNCT
ejpam-4624	248	1	then	then	ADV
ejpam-4624	248	2	,	,	PUNCT
ejpam-4624	248	3	there	there	PRON
ejpam-4624	248	4	exist	exist	VERB
ejpam-4624	248	5	ξ	ξ	PRON
ejpam-4624	248	6	such	such	ADJ
ejpam-4624	248	7	that	that	DET
ejpam-4624	248	8	t	t	PROPN
ejpam-4624	248	9	(	(	PUNCT
ejpam-4624	248	10	∨	∨	NUM
ejpam-4624	248	11	ρi	ρi	NOUN
ejpam-4624	248	12	)	)	PUNCT
ejpam-4624	248	13	≤	≤	NUM
ejpam-4624	248	14	ξ	ξ	PRON
ejpam-4624	248	15	≤	≤	NOUN
ejpam-4624	248	16	∧	∧	PROPN
ejpam-4624	248	17	t	t	PROPN
ejpam-4624	248	18	(	(	PUNCT
ejpam-4624	248	19	ρi	ρi	NOUN
ejpam-4624	248	20	)	)	PUNCT
ejpam-4624	248	21	.	.	PUNCT
ejpam-4624	249	1	since	since	SCONJ
ejpam-4624	249	2	ξ	ξ	X
ejpam-4624	249	3	≤	≤	NUM
ejpam-4624	249	4	∨	∨	NUM
ejpam-4624	249	5	{	{	PUNCT
ejpam-4624	249	6	r	r	NOUN
ejpam-4624	249	7	∈	∈	PROPN
ejpam-4624	249	8	i|δit	i|δit	NOUN
ejpam-4624	249	9	,	,	PUNCT
ejpam-4624	249	10	t	t	PROPN
ejpam-4624	249	11	∗(ρi	∗(ρi	ADJ
ejpam-4624	249	12	,	,	PUNCT
ejpam-4624	249	13	r	r	NOUN
ejpam-4624	249	14	,	,	PUNCT
ejpam-4624	249	15	s	s	NOUN
ejpam-4624	249	16	)	)	PUNCT
ejpam-4624	249	17	=	=	SYM
ejpam-4624	249	18	ρi	ρi	NOUN
ejpam-4624	249	19	}	}	PUNCT
ejpam-4624	249	20	for	for	ADP
ejpam-4624	249	21	each	each	PRON
ejpam-4624	249	22	i	i	PRON
ejpam-4624	249	23	there	there	ADV
ejpam-4624	249	24	exist	exist	VERB
ejpam-4624	249	25	(	(	PUNCT
ejpam-4624	249	26	ri	ri	NOUN
ejpam-4624	249	27	,	,	PUNCT
ejpam-4624	249	28	si	si	NOUN
ejpam-4624	249	29	)	)	PUNCT
ejpam-4624	249	30	∈	∈	PROPN
ejpam-4624	249	31	i0×i1	i0×i1	PROPN
ejpam-4624	249	32	w.	w.	PROPN
ejpam-4624	249	33	f.	f.	PROPN
ejpam-4624	249	34	al	al	PROPN
ejpam-4624	249	35	-	-	PUNCT
ejpam-4624	249	36	omeri	omeri	ADJ
ejpam-4624	249	37	/	/	SYM
ejpam-4624	249	38	eur	eur	PROPN
ejpam-4624	249	39	.	.	PUNCT
ejpam-4624	250	1	j.	j.	PROPN
ejpam-4624	250	2	pure	pure	PROPN
ejpam-4624	250	3	appl	appl	PROPN
ejpam-4624	250	4	.	.	PROPN
ejpam-4624	250	5	math	math	PROPN
ejpam-4624	250	6	,	,	PUNCT
ejpam-4624	250	7	18	18	NUM
ejpam-4624	250	8	(	(	PUNCT
ejpam-4624	250	9	2	2	NUM
ejpam-4624	250	10	)	)	PUNCT
ejpam-4624	250	11	(	(	PUNCT
ejpam-4624	250	12	2025	2025	NUM
ejpam-4624	250	13	)	)	PUNCT
ejpam-4624	250	14	,	,	PUNCT
ejpam-4624	250	15	4624	4624	NUM
ejpam-4624	250	16	10	10	NUM
ejpam-4624	250	17	of	of	ADP
ejpam-4624	250	18	15	15	NUM
ejpam-4624	251	1	such	such	ADJ
ejpam-4624	251	2	that	that	SCONJ
ejpam-4624	251	3	ξ	ξ	PROPN
ejpam-4624	251	4	≤	≤	NUM
ejpam-4624	251	5	ri	ri	X
ejpam-4624	251	6	≤	≤	PROPN
ejpam-4624	251	7	t	t	PROPN
ejpam-4624	251	8	(	(	PUNCT
ejpam-4624	251	9	ρi	ρi	NOUN
ejpam-4624	251	10	)	)	PUNCT
ejpam-4624	251	11	and	and	CCONJ
ejpam-4624	251	12	δit	δit	NOUN
ejpam-4624	251	13	,	,	PUNCT
ejpam-4624	251	14	t	t	PROPN
ejpam-4624	251	15	∗(ρi	∗(ρi	ADJ
ejpam-4624	251	16	,	,	PUNCT
ejpam-4624	251	17	ri	ri	PROPN
ejpam-4624	251	18	,	,	PUNCT
ejpam-4624	251	19	si	si	NOUN
ejpam-4624	251	20	)	)	PUNCT
ejpam-4624	251	21	=	=	SYM
ejpam-4624	251	22	ρi	ρi	NOUN
ejpam-4624	251	23	.	.	PUNCT
ejpam-4624	252	1	now	now	ADV
ejpam-4624	252	2	,	,	PUNCT
ejpam-4624	252	3	let	let	VERB
ejpam-4624	252	4	r	r	NOUN
ejpam-4624	252	5	=	=	SYM
ejpam-4624	252	6	∧	∧	PROPN
ejpam-4624	252	7	ri	ri	NOUN
ejpam-4624	252	8	and	and	CCONJ
ejpam-4624	252	9	s	s	NOUN
ejpam-4624	252	10	=	=	X
ejpam-4624	252	11	∨	∨	PROPN
ejpam-4624	252	12	si	si	X
ejpam-4624	252	13	.	.	PUNCT
ejpam-4624	253	1	since	since	SCONJ
ejpam-4624	253	2	(	(	PUNCT
ejpam-4624	253	3	ri	ri	PROPN
ejpam-4624	253	4	,	,	PUNCT
ejpam-4624	253	5	si	si	NOUN
ejpam-4624	253	6	)	)	PUNCT
ejpam-4624	253	7	∈	∈	PROPN
ejpam-4624	253	8	i0	i0	PROPN
ejpam-4624	253	9	×	×	PROPN
ejpam-4624	253	10	i1	i1	PROPN
ejpam-4624	253	11	for	for	ADP
ejpam-4624	253	12	each	each	PRON
ejpam-4624	253	13	i	i	PRON
ejpam-4624	253	14	we	we	PRON
ejpam-4624	253	15	have	have	VERB
ejpam-4624	253	16	,	,	PUNCT
ejpam-4624	253	17	1−	1−	NUM
ejpam-4624	253	18	r	r	NOUN
ejpam-4624	253	19	=	=	SYM
ejpam-4624	253	20	1−	1−	NUM
ejpam-4624	253	21	∧	∧	PROPN
ejpam-4624	253	22	(	(	PUNCT
ejpam-4624	253	23	ri	ri	NOUN
ejpam-4624	253	24	)	)	PUNCT
ejpam-4624	253	25	=	=	SYM
ejpam-4624	253	26	∨	∨	X
ejpam-4624	253	27	(	(	PUNCT
ejpam-4624	253	28	1−	1−	NUM
ejpam-4624	253	29	ri	ri	PROPN
ejpam-4624	253	30	)	)	PUNCT
ejpam-4624	253	31	≥	≥	NOUN
ejpam-4624	253	32	∨	∨	NUM
ejpam-4624	253	33	si	si	X
ejpam-4624	253	34	=	=	PROPN
ejpam-4624	253	35	s.	s.	PROPN
ejpam-4624	253	36	hence	hence	ADV
ejpam-4624	253	37	,	,	PUNCT
ejpam-4624	253	38	(	(	PUNCT
ejpam-4624	253	39	r	r	NOUN
ejpam-4624	253	40	,	,	PUNCT
ejpam-4624	253	41	s	s	PART
ejpam-4624	253	42	)	)	PUNCT
ejpam-4624	253	43	∈	∈	PROPN
ejpam-4624	253	44	i0	i0	PROPN
ejpam-4624	253	45	×	×	PROPN
ejpam-4624	253	46	i1	i1	PROPN
ejpam-4624	253	47	.	.	PUNCT
ejpam-4624	254	1	and	and	CCONJ
ejpam-4624	254	2	since	since	SCONJ
ejpam-4624	254	3	r	r	NOUN
ejpam-4624	254	4	≤	≤	NUM
ejpam-4624	254	5	∧	∧	PROPN
ejpam-4624	254	6	ri	ri	NOUN
ejpam-4624	254	7	and	and	CCONJ
ejpam-4624	254	8	s	s	PROPN
ejpam-4624	254	9	≥	≥	NOUN
ejpam-4624	254	10	∨	∨	NUM
ejpam-4624	254	11	si	si	X
ejpam-4624	254	12	for	for	ADP
ejpam-4624	254	13	each	each	DET
ejpam-4624	254	14	i	i	PROPN
ejpam-4624	254	15	,	,	PUNCT
ejpam-4624	254	16	δit	δit	NOUN
ejpam-4624	254	17	,	,	PUNCT
ejpam-4624	254	18	t	t	PROPN
ejpam-4624	254	19	∗(ρi	∗(ρi	ADJ
ejpam-4624	254	20	,	,	PUNCT
ejpam-4624	254	21	r	r	NOUN
ejpam-4624	254	22	,	,	PUNCT
ejpam-4624	254	23	s	s	PART
ejpam-4624	254	24	)	)	PUNCT
ejpam-4624	254	25	≥	≥	NOUN
ejpam-4624	254	26	δit	δit	NOUN
ejpam-4624	254	27	,	,	PUNCT
ejpam-4624	255	1	t	t	PROPN
ejpam-4624	255	2	∗(ρi	∗(ρi	ADJ
ejpam-4624	255	3	,	,	PUNCT
ejpam-4624	255	4	ri	ri	PROPN
ejpam-4624	255	5	,	,	PUNCT
ejpam-4624	255	6	si	si	NOUN
ejpam-4624	255	7	)	)	PUNCT
ejpam-4624	255	8	=	=	SYM
ejpam-4624	255	9	ρi	ρi	NOUN
ejpam-4624	255	10	.	.	PUNCT
ejpam-4624	256	1	hence	hence	ADV
ejpam-4624	256	2	,	,	PUNCT
ejpam-4624	256	3	δit	δit	NOUN
ejpam-4624	256	4	,	,	PUNCT
ejpam-4624	256	5	t	t	PROPN
ejpam-4624	256	6	∗	∗	NOUN
ejpam-4624	256	7	(	(	PUNCT
ejpam-4624	256	8	∨	∨	NUM
ejpam-4624	256	9	ρi	ρi	PROPN
ejpam-4624	256	10	,	,	PUNCT
ejpam-4624	256	11	r	r	NOUN
ejpam-4624	256	12	,	,	PUNCT
ejpam-4624	256	13	s	s	PART
ejpam-4624	256	14	)	)	PUNCT
ejpam-4624	256	15	≥	≥	NOUN
ejpam-4624	256	16	δit	δit	NOUN
ejpam-4624	256	17	,	,	PUNCT
ejpam-4624	256	18	t	t	PROPN
ejpam-4624	256	19	∗(ρi	∗(ρi	ADJ
ejpam-4624	256	20	,	,	PUNCT
ejpam-4624	256	21	r	r	NOUN
ejpam-4624	256	22	,	,	PUNCT
ejpam-4624	256	23	s	s	PART
ejpam-4624	256	24	)	)	PUNCT
ejpam-4624	256	25	≥	≥	NOUN
ejpam-4624	256	26	ρi	ρi	NOUN
ejpam-4624	256	27	for	for	ADP
ejpam-4624	256	28	each	each	DET
ejpam-4624	256	29	i.	i.	NOUN
ejpam-4624	256	30	so	so	ADV
ejpam-4624	256	31	,	,	PUNCT
ejpam-4624	256	32	δit	δit	NOUN
ejpam-4624	256	33	,	,	PUNCT
ejpam-4624	256	34	t	t	PROPN
ejpam-4624	256	35	∗	∗	NOUN
ejpam-4624	256	36	(	(	PUNCT
ejpam-4624	256	37	∨	∨	NUM
ejpam-4624	256	38	ρi	ρi	PROPN
ejpam-4624	256	39	,	,	PUNCT
ejpam-4624	256	40	r	r	NOUN
ejpam-4624	256	41	,	,	PUNCT
ejpam-4624	256	42	s	s	PART
ejpam-4624	256	43	)	)	PUNCT
ejpam-4624	256	44	≥	≥	NOUN
ejpam-4624	256	45	∨	∨	NUM
ejpam-4624	256	46	ρi	ρi	NOUN
ejpam-4624	256	47	,	,	PUNCT
ejpam-4624	256	48	and	and	CCONJ
ejpam-4624	256	49	hence	hence	ADV
ejpam-4624	256	50	,	,	PUNCT
ejpam-4624	256	51	δit	δit	NOUN
ejpam-4624	256	52	,	,	PUNCT
ejpam-4624	256	53	t	t	PROPN
ejpam-4624	256	54	∗	∗	NOUN
ejpam-4624	256	55	(	(	PUNCT
ejpam-4624	256	56	∨	∨	NUM
ejpam-4624	256	57	ρi	ρi	PROPN
ejpam-4624	256	58	,	,	PUNCT
ejpam-4624	256	59	r	r	NOUN
ejpam-4624	256	60	,	,	PUNCT
ejpam-4624	256	61	s	s	PART
ejpam-4624	256	62	)	)	PUNCT
ejpam-4624	256	63	=	=	SYM
ejpam-4624	257	1	∨	∨	NUM
ejpam-4624	257	2	ρi	ρi	NOUN
ejpam-4624	257	3	.	.	PUNCT
ejpam-4624	258	1	thus	thus	ADV
ejpam-4624	258	2	,	,	PUNCT
ejpam-4624	258	3	ξ	ξ	PROPN
ejpam-4624	258	4	≥	≥	NOUN
ejpam-4624	258	5	t	t	PROPN
ejpam-4624	258	6	(	(	PUNCT
ejpam-4624	258	7	∨	∨	NUM
ejpam-4624	258	8	ρi	ρi	NOUN
ejpam-4624	258	9	)	)	PUNCT
ejpam-4624	258	10	=	=	SYM
ejpam-4624	258	11	∨	∨	X
ejpam-4624	258	12	{	{	PUNCT
ejpam-4624	258	13	r∗	r∗	PROPN
ejpam-4624	258	14	∈	∈	PROPN
ejpam-4624	258	15	i|δit	i|δit	NOUN
ejpam-4624	258	16	,	,	PUNCT
ejpam-4624	258	17	t	t	PROPN
ejpam-4624	258	18	∗	∗	NOUN
ejpam-4624	258	19	(	(	PUNCT
ejpam-4624	258	20	∨	∨	NUM
ejpam-4624	258	21	ρi	ρi	NOUN
ejpam-4624	258	22	,	,	PUNCT
ejpam-4624	258	23	r	r	NOUN
ejpam-4624	258	24	∗	∗	NOUN
ejpam-4624	258	25	,	,	PUNCT
ejpam-4624	258	26	s∗	s∗	PROPN
ejpam-4624	258	27	)	)	PUNCT
ejpam-4624	258	28	=	=	PUNCT
ejpam-4624	259	1	∨	∨	NUM
ejpam-4624	259	2	ρi	ρi	PROPN
ejpam-4624	259	3	}	}	PUNCT
ejpam-4624	259	4	≥	≥	NOUN
ejpam-4624	259	5	r	r	NOUN
ejpam-4624	259	6	=	=	SYM
ejpam-4624	259	7	∧	∧	PROPN
ejpam-4624	259	8	ri	ri	PROPN
ejpam-4624	259	9	≥	≥	X
ejpam-4624	259	10	ξ	ξ	X
ejpam-4624	259	11	.	.	PUNCT
ejpam-4624	259	12	which	which	PRON
ejpam-4624	259	13	is	be	AUX
ejpam-4624	259	14	a	a	DET
ejpam-4624	259	15	contradiction	contradiction	NOUN
ejpam-4624	259	16	.	.	PUNCT
ejpam-4624	260	1	hence	hence	ADV
ejpam-4624	260	2	,	,	PUNCT
ejpam-4624	260	3	t	t	PROPN
ejpam-4624	260	4	(	(	PUNCT
ejpam-4624	260	5	∨	∨	PROPN
ejpam-4624	260	6	ρi	ρi	PROPN
ejpam-4624	260	7	)	)	PUNCT
ejpam-4624	260	8	≥	≥	NOUN
ejpam-4624	260	9	∧	∧	PROPN
ejpam-4624	260	10	t	t	PROPN
ejpam-4624	260	11	(	(	PUNCT
ejpam-4624	260	12	ρi	ρi	PROPN
ejpam-4624	260	13	)	)	PUNCT
ejpam-4624	260	14	.	.	PUNCT
ejpam-4624	261	1	similar	similar	ADJ
ejpam-4624	261	2	for	for	ADP
ejpam-4624	261	3	s.	s.	PROPN
ejpam-4624	261	4	therefor	therefor	PROPN
ejpam-4624	261	5	,	,	PUNCT
ejpam-4624	261	6	ζ	ζ	NOUN
ejpam-4624	261	7	=	=	SYM
ejpam-4624	261	8	(	(	PUNCT
ejpam-4624	261	9	t	t	PROPN
ejpam-4624	261	10	,	,	PUNCT
ejpam-4624	261	11	t	t	PROPN
ejpam-4624	261	12	∗	∗	NOUN
ejpam-4624	261	13	)	)	PUNCT
ejpam-4624	261	14	is	be	AUX
ejpam-4624	261	15	double	double	ADJ
ejpam-4624	261	16	fuzzy	fuzzy	ADJ
ejpam-4624	261	17	topology	topology	NOUN
ejpam-4624	261	18	in	in	ADP
ejpam-4624	261	19	x.	x.	PROPN
ejpam-4624	261	20	proposition	proposition	PROPN
ejpam-4624	261	21	2.16	2.16	NUM
ejpam-4624	261	22	.	.	PUNCT
ejpam-4624	262	1	let	let	VERB
ejpam-4624	262	2	(	(	PUNCT
ejpam-4624	262	3	x	x	X
ejpam-4624	262	4	,	,	PUNCT
ejpam-4624	262	5	t	t	PROPN
ejpam-4624	262	6	,	,	PUNCT
ejpam-4624	262	7	t	t	PROPN
ejpam-4624	262	8	∗	∗	NOUN
ejpam-4624	262	9	)	)	PUNCT
ejpam-4624	262	10	be	be	AUX
ejpam-4624	262	11	an	an	DET
ejpam-4624	262	12	dfts	dft	NOUN
ejpam-4624	262	13	.	.	PUNCT
ejpam-4624	263	1	then	then	ADV
ejpam-4624	263	2	,	,	PUNCT
ejpam-4624	263	3	for	for	ADP
ejpam-4624	263	4	each	each	DET
ejpam-4624	263	5	r	r	NOUN
ejpam-4624	263	6	∈	∈	PROPN
ejpam-4624	263	7	i0	i0	PROPN
ejpam-4624	263	8	,	,	PUNCT
ejpam-4624	263	9	s	s	PROPN
ejpam-4624	263	10	∈	∈	PROPN
ejpam-4624	263	11	i1	i1	NOUN
ejpam-4624	263	12	,	,	PUNCT
ejpam-4624	263	13	and	and	CCONJ
ejpam-4624	263	14	ρ	ρ	PROPN
ejpam-4624	263	15	∈	∈	PROPN
ejpam-4624	263	16	ix	ix	ADV
ejpam-4624	263	17	.	.	PUNCT
ejpam-4624	264	1	let	let	VERB
ejpam-4624	264	2	δct	δct	NOUN
ejpam-4624	264	3	,	,	PUNCT
ejpam-4624	264	4	t	t	PROPN
ejpam-4624	264	5	∗	∗	NOUN
ejpam-4624	264	6	:	:	PUNCT
ejpam-4624	265	1	ix	ix	PROPN
ejpam-4624	265	2	×	×	PROPN
ejpam-4624	265	3	i0	i0	PROPN
ejpam-4624	265	4	×	×	PROPN
ejpam-4624	265	5	i1	i1	PROPN
ejpam-4624	265	6	−→	−→	NOUN
ejpam-4624	265	7	ix	ix	PROPN
ejpam-4624	265	8	be	be	AUX
ejpam-4624	265	9	a	a	DET
ejpam-4624	265	10	function	function	NOUN
ejpam-4624	265	11	satisfy	satisfy	VERB
ejpam-4624	265	12	the	the	DET
ejpam-4624	265	13	conditions	condition	NOUN
ejpam-4624	265	14	(	(	PUNCT
ejpam-4624	265	15	1	1	NUM
ejpam-4624	265	16	-	-	SYM
ejpam-4624	265	17	5	5	NUM
ejpam-4624	265	18	)	)	PUNCT
ejpam-4624	265	19	in	in	ADP
ejpam-4624	265	20	proposition	proposition	NOUN
ejpam-4624	265	21	2.6	2.6	NUM
ejpam-4624	265	22	such	such	ADJ
ejpam-4624	265	23	that	that	DET
ejpam-4624	265	24	t	t	PROPN
ejpam-4624	265	25	,	,	PUNCT
ejpam-4624	265	26	t	t	PROPN
ejpam-4624	265	27	∗	∗	NOUN
ejpam-4624	265	28	:	:	PUNCT
ejpam-4624	265	29	ix	ix	PROPN
ejpam-4624	265	30	→	→	PUNCT
ejpam-4624	265	31	i	i	PRON
ejpam-4624	265	32	be	be	VERB
ejpam-4624	265	33	a	a	DET
ejpam-4624	265	34	function	function	NOUN
ejpam-4624	265	35	defined	define	VERB
ejpam-4624	265	36	by	by	ADP
ejpam-4624	265	37	:	:	PUNCT
ejpam-4624	265	38	t	t	PROPN
ejpam-4624	265	39	(	(	PUNCT
ejpam-4624	265	40	ρ	ρ	NOUN
ejpam-4624	265	41	)	)	PUNCT
ejpam-4624	265	42	=	=	SYM
ejpam-4624	265	43	∨	∨	X
ejpam-4624	265	44	{	{	PUNCT
ejpam-4624	265	45	r	r	NOUN
ejpam-4624	265	46	∈	∈	PROPN
ejpam-4624	265	47	i|δct	i|δct	NOUN
ejpam-4624	265	48	,	,	PUNCT
ejpam-4624	265	49	t	t	NOUN
ejpam-4624	265	50	∗(ρ	∗(ρ	NOUN
ejpam-4624	265	51	,	,	PUNCT
ejpam-4624	265	52	r	r	NOUN
ejpam-4624	265	53	,	,	PUNCT
ejpam-4624	265	54	s	s	NOUN
ejpam-4624	265	55	)	)	PUNCT
ejpam-4624	265	56	=	=	SYM
ejpam-4624	265	57	ρ	ρ	PROPN
ejpam-4624	265	58	}	}	PUNCT
ejpam-4624	265	59	and	and	CCONJ
ejpam-4624	265	60	t	t	NOUN
ejpam-4624	265	61	∗(ρ	∗(ρ	NOUN
ejpam-4624	265	62	)	)	PUNCT
ejpam-4624	266	1	=	=	SYM
ejpam-4624	266	2	∧	∧	NOUN
ejpam-4624	266	3	{	{	PUNCT
ejpam-4624	266	4	s	s	NOUN
ejpam-4624	266	5	∈	∈	NOUN
ejpam-4624	266	6	i|δct	i|δct	NOUN
ejpam-4624	266	7	,	,	PUNCT
ejpam-4624	266	8	t	t	NOUN
ejpam-4624	266	9	∗(ρ	∗(ρ	NOUN
ejpam-4624	266	10	,	,	PUNCT
ejpam-4624	266	11	r	r	NOUN
ejpam-4624	266	12	,	,	PUNCT
ejpam-4624	266	13	s	s	PART
ejpam-4624	266	14	)	)	PUNCT
ejpam-4624	266	15	=	=	SYM
ejpam-4624	266	16	ρ	ρ	PROPN
ejpam-4624	266	17	}	}	PUNCT
ejpam-4624	266	18	.	.	PUNCT
ejpam-4624	267	1	then	then	ADV
ejpam-4624	267	2	ζ	ζ	X
ejpam-4624	267	3	=	=	SYM
ejpam-4624	267	4	(	(	PUNCT
ejpam-4624	267	5	t	t	PROPN
ejpam-4624	267	6	,	,	PUNCT
ejpam-4624	267	7	t	t	PROPN
ejpam-4624	267	8	∗	∗	NOUN
ejpam-4624	267	9	)	)	PUNCT
ejpam-4624	267	10	is	be	AUX
ejpam-4624	267	11	a	a	DET
ejpam-4624	267	12	double	double	ADJ
ejpam-4624	267	13	fuzzy	fuzzy	ADJ
ejpam-4624	267	14	family	family	NOUN
ejpam-4624	267	15	of	of	ADP
ejpam-4624	267	16	closed	closed	ADJ
ejpam-4624	267	17	sets	set	NOUN
ejpam-4624	267	18	in	in	ADP
ejpam-4624	267	19	x.	x.	NOUN
ejpam-4624	267	20	proof	proof	NOUN
ejpam-4624	267	21	.	.	PUNCT
ejpam-4624	268	1	similar	similar	ADJ
ejpam-4624	268	2	to	to	ADP
ejpam-4624	268	3	proposition	proposition	VERB
ejpam-4624	268	4	2.15	2.15	NUM
ejpam-4624	268	5	3	3	NUM
ejpam-4624	268	6	.	.	PUNCT
ejpam-4624	269	1	(	(	PUNCT
ejpam-4624	269	2	r	r	NOUN
ejpam-4624	269	3	,	,	PUNCT
ejpam-4624	269	4	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	269	5	δ	δ	ADJ
ejpam-4624	269	6	-	-	PUNCT
ejpam-4624	269	7	continuous	continuous	ADJ
ejpam-4624	269	8	functions	function	NOUN
ejpam-4624	269	9	definition	definition	NOUN
ejpam-4624	269	10	3.1	3.1	NUM
ejpam-4624	269	11	.	.	PUNCT
ejpam-4624	270	1	a	a	DET
ejpam-4624	270	2	function	function	NOUN
ejpam-4624	270	3	f	f	NOUN
ejpam-4624	270	4	from	from	ADP
ejpam-4624	270	5	an	an	DET
ejpam-4624	270	6	dfts	dft	NOUN
ejpam-4624	270	7	(	(	PUNCT
ejpam-4624	270	8	x	x	X
ejpam-4624	270	9	,	,	PUNCT
ejpam-4624	270	10	t1	t1	PROPN
ejpam-4624	270	11	,	,	PUNCT
ejpam-4624	270	12	t	t	PROPN
ejpam-4624	270	13	∗	∗	X
ejpam-4624	270	14	1	1	NUM
ejpam-4624	270	15	)	)	PUNCT
ejpam-4624	270	16	into	into	ADP
ejpam-4624	270	17	an	an	DET
ejpam-4624	270	18	dfts	dft	NOUN
ejpam-4624	270	19	(	(	PUNCT
ejpam-4624	270	20	y	y	PROPN
ejpam-4624	270	21	,	,	PUNCT
ejpam-4624	270	22	t2	t2	PROPN
ejpam-4624	270	23	,	,	PUNCT
ejpam-4624	270	24	t	t	PROPN
ejpam-4624	270	25	∗	∗	X
ejpam-4624	270	26	2	2	NUM
ejpam-4624	270	27	)	)	PUNCT
ejpam-4624	270	28	is	be	AUX
ejpam-4624	270	29	said	say	VERB
ejpam-4624	270	30	to	to	PART
ejpam-4624	270	31	be	be	AUX
ejpam-4624	270	32	double	double	ADJ
ejpam-4624	270	33	fuzzy	fuzzy	ADJ
ejpam-4624	270	34	δ	δ	NOUN
ejpam-4624	270	35	-	-	NOUN
ejpam-4624	270	36	continuous	continuous	ADJ
ejpam-4624	270	37	at	at	ADP
ejpam-4624	270	38	a	a	DET
ejpam-4624	270	39	double	double	ADJ
ejpam-4624	270	40	fuzzy	fuzzy	ADJ
ejpam-4624	270	41	point	point	NOUN
ejpam-4624	270	42	xα	xα	INTJ
ejpam-4624	270	43	,	,	PUNCT
ejpam-4624	270	44	β	β	X
ejpam-4624	270	45	in	in	ADP
ejpam-4624	270	46	x	x	SYM
ejpam-4624	270	47	,	,	PUNCT
ejpam-4624	270	48	if	if	SCONJ
ejpam-4624	270	49	f−1(υ	f−1(υ	PROPN
ejpam-4624	270	50	)	)	PUNCT
ejpam-4624	270	51	is	be	AUX
ejpam-4624	270	52	a	a	DET
ejpam-4624	270	53	(	(	PUNCT
ejpam-4624	270	54	r	r	NOUN
ejpam-4624	270	55	,	,	PUNCT
ejpam-4624	270	56	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	270	57	δ	δ	PROPN
ejpam-4624	270	58	-	-	PUNCT
ejpam-4624	270	59	open	open	ADJ
ejpam-4624	270	60	set	set	NOUN
ejpam-4624	270	61	,	,	PUNCT
ejpam-4624	270	62	for	for	ADP
ejpam-4624	270	63	each	each	DET
ejpam-4624	270	64	r	r	NOUN
ejpam-4624	270	65	∈	∈	PROPN
ejpam-4624	270	66	i0	i0	PROPN
ejpam-4624	270	67	,	,	PUNCT
ejpam-4624	270	68	s	s	PROPN
ejpam-4624	270	69	∈	∈	PROPN
ejpam-4624	270	70	i1	i1	PROPN
ejpam-4624	270	71	,	,	PUNCT
ejpam-4624	270	72	and	and	CCONJ
ejpam-4624	270	73	υ	υ	NOUN
ejpam-4624	270	74	is	be	AUX
ejpam-4624	270	75	a	a	DET
ejpam-4624	270	76	(	(	PUNCT
ejpam-4624	270	77	r	r	NOUN
ejpam-4624	270	78	,	,	PUNCT
ejpam-4624	270	79	s)-fro	s)-fro	NOUN
ejpam-4624	270	80	set	set	VERB
ejpam-4624	270	81	in	in	ADP
ejpam-4624	270	82	iy	iy	PROPN
ejpam-4624	270	83	such	such	ADJ
ejpam-4624	270	84	that	that	PRON
ejpam-4624	270	85	t2(υ	t2(υ	NOUN
ejpam-4624	270	86	)	)	PUNCT
ejpam-4624	270	87	≥	≥	NOUN
ejpam-4624	270	88	r	r	NOUN
ejpam-4624	270	89	and	and	CCONJ
ejpam-4624	270	90	t	t	PROPN
ejpam-4624	270	91	∗	∗	X
ejpam-4624	270	92	2	2	NUM
ejpam-4624	270	93	(	(	PUNCT
ejpam-4624	270	94	υ	υ	NOUN
ejpam-4624	270	95	)	)	PUNCT
ejpam-4624	270	96	≤	≤	NOUN
ejpam-4624	270	97	s.	s.	PROPN
ejpam-4624	270	98	i.e	i.e	X
ejpam-4624	270	99	for	for	ADP
ejpam-4624	270	100	each	each	DET
ejpam-4624	270	101	double	double	ADJ
ejpam-4624	270	102	fuzzy	fuzzy	ADJ
ejpam-4624	270	103	point	point	NOUN
ejpam-4624	270	104	xαinx	xαinx	NOUN
ejpam-4624	270	105	and	and	CCONJ
ejpam-4624	270	106	for	for	SCONJ
ejpam-4624	270	107	any	any	DET
ejpam-4624	270	108	(	(	PUNCT
ejpam-4624	270	109	r	r	NOUN
ejpam-4624	270	110	,	,	PUNCT
ejpam-4624	270	111	s)-fro	s)-fro	NOUN
ejpam-4624	270	112	set	set	VERB
ejpam-4624	270	113	q	q	ADJ
ejpam-4624	270	114	-	-	PUNCT
ejpam-4624	270	115	neighborhood	neighborhood	NOUN
ejpam-4624	270	116	γ	γ	NOUN
ejpam-4624	270	117	of	of	ADP
ejpam-4624	270	118	f(xα	f(xα	PROPN
ejpam-4624	270	119	)	)	PUNCT
ejpam-4624	270	120	in	in	ADP
ejpam-4624	270	121	iy	iy	PROPN
ejpam-4624	270	122	,	,	PUNCT
ejpam-4624	270	123	there	there	PRON
ejpam-4624	270	124	exists	exist	VERB
ejpam-4624	270	125	a	a	DET
ejpam-4624	270	126	(	(	PUNCT
ejpam-4624	270	127	r	r	NOUN
ejpam-4624	270	128	,	,	PUNCT
ejpam-4624	270	129	s)-fro	s)-fro	NOUN
ejpam-4624	270	130	set	set	VERB
ejpam-4624	270	131	q	q	NOUN
ejpam-4624	270	132	-	-	PUNCT
ejpam-4624	270	133	neighborhood	neighborhood	NOUN
ejpam-4624	270	134	β	β	NOUN
ejpam-4624	270	135	of	of	ADP
ejpam-4624	270	136	xα	xα	INTJ
ejpam-4624	270	137	such	such	ADJ
ejpam-4624	270	138	that	that	DET
ejpam-4624	270	139	f(β	f(β	NOUN
ejpam-4624	270	140	)	)	PUNCT
ejpam-4624	270	141	≤	≤	NOUN
ejpam-4624	270	142	γ	γ	X
ejpam-4624	270	143	.	.	PUNCT
ejpam-4624	271	1	theorem	theorem	VERB
ejpam-4624	271	2	3.2	3.2	NUM
ejpam-4624	271	3	.	.	PUNCT
ejpam-4624	272	1	let	let	VERB
ejpam-4624	272	2	f	f	PRON
ejpam-4624	272	3	be	be	AUX
ejpam-4624	272	4	a	a	DET
ejpam-4624	272	5	function	function	NOUN
ejpam-4624	272	6	from	from	ADP
ejpam-4624	272	7	an	an	DET
ejpam-4624	272	8	dfts	dft	NOUN
ejpam-4624	272	9	(	(	PUNCT
ejpam-4624	272	10	x	x	X
ejpam-4624	272	11	,	,	PUNCT
ejpam-4624	272	12	t1	t1	PROPN
ejpam-4624	272	13	,	,	PUNCT
ejpam-4624	272	14	t	t	PROPN
ejpam-4624	272	15	∗	∗	X
ejpam-4624	272	16	1	1	NUM
ejpam-4624	272	17	)	)	PUNCT
ejpam-4624	272	18	into	into	ADP
ejpam-4624	272	19	an	an	DET
ejpam-4624	272	20	dfts	dft	NOUN
ejpam-4624	272	21	(	(	PUNCT
ejpam-4624	272	22	y	y	PROPN
ejpam-4624	272	23	,	,	PUNCT
ejpam-4624	272	24	t2	t2	PROPN
ejpam-4624	272	25	,	,	PUNCT
ejpam-4624	272	26	t	t	PROPN
ejpam-4624	272	27	∗	∗	X
ejpam-4624	272	28	2	2	NUM
ejpam-4624	272	29	)	)	PUNCT
ejpam-4624	272	30	.	.	PUNCT
ejpam-4624	273	1	then	then	ADV
ejpam-4624	273	2	the	the	DET
ejpam-4624	273	3	following	follow	VERB
ejpam-4624	273	4	two	two	NUM
ejpam-4624	273	5	conditions	condition	NOUN
ejpam-4624	273	6	are	be	AUX
ejpam-4624	273	7	equivalent	equivalent	ADJ
ejpam-4624	273	8	w.	w.	PROPN
ejpam-4624	273	9	f.	f.	PROPN
ejpam-4624	273	10	al	al	PROPN
ejpam-4624	273	11	-	-	PUNCT
ejpam-4624	273	12	omeri	omeri	ADJ
ejpam-4624	273	13	/	/	SYM
ejpam-4624	273	14	eur	eur	PROPN
ejpam-4624	273	15	.	.	PUNCT
ejpam-4624	274	1	j.	j.	PROPN
ejpam-4624	274	2	pure	pure	PROPN
ejpam-4624	274	3	appl	appl	PROPN
ejpam-4624	274	4	.	.	PROPN
ejpam-4624	274	5	math	math	PROPN
ejpam-4624	274	6	,	,	PUNCT
ejpam-4624	274	7	18	18	NUM
ejpam-4624	274	8	(	(	PUNCT
ejpam-4624	274	9	2	2	NUM
ejpam-4624	274	10	)	)	PUNCT
ejpam-4624	274	11	(	(	PUNCT
ejpam-4624	274	12	2025	2025	NUM
ejpam-4624	274	13	)	)	PUNCT
ejpam-4624	274	14	,	,	PUNCT
ejpam-4624	274	15	4624	4624	NUM
ejpam-4624	274	16	11	11	NUM
ejpam-4624	274	17	of	of	ADP
ejpam-4624	274	18	15	15	NUM
ejpam-4624	274	19	(	(	PUNCT
ejpam-4624	274	20	i	i	NOUN
ejpam-4624	274	21	)	)	PUNCT
ejpam-4624	275	1	f	f	PROPN
ejpam-4624	275	2	is	be	AUX
ejpam-4624	275	3	double	double	ADJ
ejpam-4624	275	4	fuzzy	fuzzy	ADJ
ejpam-4624	275	5	δ	δ	NOUN
ejpam-4624	275	6	-	-	ADJ
ejpam-4624	275	7	continuous	continuous	ADJ
ejpam-4624	275	8	,	,	PUNCT
ejpam-4624	275	9	(	(	PUNCT
ejpam-4624	275	10	ii	ii	NOUN
ejpam-4624	275	11	)	)	PUNCT
ejpam-4624	275	12	for	for	ADP
ejpam-4624	275	13	each	each	DET
ejpam-4624	275	14	double	double	ADJ
ejpam-4624	275	15	fuzzy	fuzzy	ADJ
ejpam-4624	275	16	point	point	NOUN
ejpam-4624	275	17	xi	xi	INTJ
ejpam-4624	275	18	in	in	ADP
ejpam-4624	275	19	x	x	PRON
ejpam-4624	275	20	and	and	CCONJ
ejpam-4624	275	21	each	each	DET
ejpam-4624	275	22	(	(	PUNCT
ejpam-4624	275	23	r	r	NOUN
ejpam-4624	275	24	,	,	PUNCT
ejpam-4624	275	25	s)-fro	s)-fro	NOUN
ejpam-4624	275	26	set	set	VERB
ejpam-4624	275	27	ρ	ρ	NOUN
ejpam-4624	275	28	containing	contain	VERB
ejpam-4624	275	29	f(xi	f(xi	PROPN
ejpam-4624	275	30	)	)	PUNCT
ejpam-4624	275	31	,	,	PUNCT
ejpam-4624	275	32	there	there	PRON
ejpam-4624	275	33	exists	exist	VERB
ejpam-4624	275	34	a	a	DET
ejpam-4624	275	35	(	(	PUNCT
ejpam-4624	275	36	r	r	NOUN
ejpam-4624	275	37	,	,	PUNCT
ejpam-4624	275	38	s)-fro	s)-fro	NOUN
ejpam-4624	275	39	set	set	VERB
ejpam-4624	275	40	ϕ	ϕ	NOUN
ejpam-4624	275	41	containing	contain	VERB
ejpam-4624	275	42	xi	xi	ADP
ejpam-4624	275	43	where	where	SCONJ
ejpam-4624	275	44	r	r	NOUN
ejpam-4624	275	45	∈	∈	PROPN
ejpam-4624	275	46	i0	i0	PROPN
ejpam-4624	275	47	,	,	PUNCT
ejpam-4624	275	48	s	s	PROPN
ejpam-4624	275	49	∈	∈	PROPN
ejpam-4624	275	50	i1	i1	PROPN
ejpam-4624	275	51	such	such	ADJ
ejpam-4624	275	52	that	that	SCONJ
ejpam-4624	275	53	f(ϕ	f(ϕ	PROPN
ejpam-4624	275	54	)	)	PUNCT
ejpam-4624	275	55	≤	≤	NOUN
ejpam-4624	275	56	ρ	ρ	NOUN
ejpam-4624	275	57	.	.	PUNCT
ejpam-4624	276	1	proof	proof	NOUN
ejpam-4624	276	2	.	.	PUNCT
ejpam-4624	277	1	(	(	PUNCT
ejpam-4624	277	2	1	1	X
ejpam-4624	277	3	)	)	PUNCT
ejpam-4624	277	4	⇒	⇒	NOUN
ejpam-4624	277	5	(	(	PUNCT
ejpam-4624	277	6	2	2	X
ejpam-4624	277	7	)	)	PUNCT
ejpam-4624	277	8	let	let	VERB
ejpam-4624	277	9	xi	xi	PRON
ejpam-4624	277	10	be	be	AUX
ejpam-4624	277	11	a	a	DET
ejpam-4624	277	12	fuzzy	fuzzy	ADJ
ejpam-4624	277	13	point	point	NOUN
ejpam-4624	277	14	in	in	ADP
ejpam-4624	277	15	(	(	PUNCT
ejpam-4624	277	16	x	x	NOUN
ejpam-4624	277	17	,	,	PUNCT
ejpam-4624	277	18	t1	t1	PROPN
ejpam-4624	277	19	,	,	PUNCT
ejpam-4624	277	20	t	t	PROPN
ejpam-4624	277	21	∗	∗	X
ejpam-4624	277	22	1	1	NUM
ejpam-4624	277	23	)	)	PUNCT
ejpam-4624	277	24	and	and	CCONJ
ejpam-4624	277	25	ρ	ρ	PROPN
ejpam-4624	277	26	be	be	AUX
ejpam-4624	277	27	a	a	DET
ejpam-4624	277	28	(	(	PUNCT
ejpam-4624	277	29	r	r	NOUN
ejpam-4624	277	30	,	,	PUNCT
ejpam-4624	277	31	s)-fro	s)-fro	NOUN
ejpam-4624	277	32	set	set	NOUN
ejpam-4624	277	33	containing	contain	VERB
ejpam-4624	277	34	f(xi	f(xi	PROPN
ejpam-4624	277	35	)	)	PUNCT
ejpam-4624	277	36	,	,	PUNCT
ejpam-4624	277	37	where	where	SCONJ
ejpam-4624	277	38	r	r	PROPN
ejpam-4624	277	39	∈	∈	PROPN
ejpam-4624	277	40	i0	i0	PROPN
ejpam-4624	277	41	,	,	PUNCT
ejpam-4624	277	42	s	s	PROPN
ejpam-4624	277	43	∈	∈	PROPN
ejpam-4624	277	44	i1	i1	PROPN
ejpam-4624	277	45	.	.	PUNCT
ejpam-4624	278	1	since	since	SCONJ
ejpam-4624	278	2	every	every	DET
ejpam-4624	278	3	(	(	PUNCT
ejpam-4624	278	4	r	r	NOUN
ejpam-4624	278	5	,	,	PUNCT
ejpam-4624	278	6	s)-fro	s)-fro	NOUN
ejpam-4624	278	7	set	set	NOUN
ejpam-4624	278	8	is	be	AUX
ejpam-4624	278	9	a	a	DET
ejpam-4624	278	10	fuzzy	fuzzy	ADJ
ejpam-4624	278	11	open	open	ADJ
ejpam-4624	278	12	set	set	NOUN
ejpam-4624	278	13	,	,	PUNCT
ejpam-4624	278	14	it	it	PRON
ejpam-4624	278	15	follows	follow	VERB
ejpam-4624	278	16	from	from	ADP
ejpam-4624	278	17	(	(	PUNCT
ejpam-4624	278	18	1	1	NUM
ejpam-4624	278	19	)	)	PUNCT
ejpam-4624	278	20	that	that	SCONJ
ejpam-4624	278	21	there	there	PRON
ejpam-4624	278	22	exists	exist	VERB
ejpam-4624	278	23	a	a	DET
ejpam-4624	278	24	double	double	ADJ
ejpam-4624	278	25	fuzzy	fuzzy	ADJ
ejpam-4624	278	26	open	open	ADJ
ejpam-4624	278	27	nbd	nbd	PROPN
ejpam-4624	278	28	ϕ	ϕ	PROPN
ejpam-4624	278	29	of	of	ADP
ejpam-4624	278	30	xi	xi	INTJ
ejpam-4624	278	31	such	such	ADJ
ejpam-4624	278	32	that	that	PRON
ejpam-4624	278	33	,	,	PUNCT
ejpam-4624	278	34	f(it1,t	f(it1,t	PROPN
ejpam-4624	278	35	∗	∗	NOUN
ejpam-4624	278	36	1	1	NUM
ejpam-4624	278	37	(	(	PUNCT
ejpam-4624	278	38	ct1,t	ct1,t	NOUN
ejpam-4624	278	39	∗	∗	VERB
ejpam-4624	278	40	1	1	NUM
ejpam-4624	278	41	(	(	PUNCT
ejpam-4624	278	42	ϕ	ϕ	NOUN
ejpam-4624	278	43	,	,	PUNCT
ejpam-4624	278	44	r	r	NOUN
ejpam-4624	278	45	,	,	PUNCT
ejpam-4624	278	46	s	s	NOUN
ejpam-4624	278	47	)	)	PUNCT
ejpam-4624	278	48	)	)	PUNCT
ejpam-4624	278	49	)	)	PUNCT
ejpam-4624	279	1	≤	≤	ADV
ejpam-4624	279	2	it2,t	it2,t	PROPN
ejpam-4624	279	3	∗	∗	NOUN
ejpam-4624	279	4	2	2	NUM
ejpam-4624	279	5	(	(	PUNCT
ejpam-4624	279	6	ct2,t	ct2,t	PROPN
ejpam-4624	279	7	∗	∗	NOUN
ejpam-4624	279	8	2	2	NUM
ejpam-4624	279	9	(	(	PUNCT
ejpam-4624	279	10	ρ	ρ	PROPN
ejpam-4624	279	11	,	,	PUNCT
ejpam-4624	279	12	r	r	NOUN
ejpam-4624	279	13	,	,	PUNCT
ejpam-4624	279	14	s	s	NOUN
ejpam-4624	279	15	)	)	PUNCT
ejpam-4624	279	16	)	)	PUNCT
ejpam-4624	280	1	=	=	SYM
ejpam-4624	280	2	ρ	ρ	X
ejpam-4624	280	3	.	.	PUNCT
ejpam-4624	281	1	taking	take	VERB
ejpam-4624	281	2	it1,t	it1,t	PROPN
ejpam-4624	281	3	∗	∗	NOUN
ejpam-4624	281	4	1	1	NUM
ejpam-4624	281	5	(	(	PUNCT
ejpam-4624	281	6	ct1,t	ct1,t	NOUN
ejpam-4624	281	7	∗	∗	VERB
ejpam-4624	281	8	1	1	NUM
ejpam-4624	281	9	(	(	PUNCT
ejpam-4624	281	10	ϕ1	ϕ1	NOUN
ejpam-4624	281	11	,	,	PUNCT
ejpam-4624	281	12	r	r	NOUN
ejpam-4624	281	13	,	,	PUNCT
ejpam-4624	281	14	s	s	NOUN
ejpam-4624	281	15	)	)	PUNCT
ejpam-4624	281	16	)	)	PUNCT
ejpam-4624	281	17	)	)	PUNCT
ejpam-4624	282	1	=	=	SYM
ejpam-4624	282	2	ϕ	ϕ	X
ejpam-4624	282	3	(	(	PUNCT
ejpam-4624	282	4	being	be	AUX
ejpam-4624	282	5	a	a	DET
ejpam-4624	282	6	(	(	PUNCT
ejpam-4624	282	7	r	r	NOUN
ejpam-4624	282	8	,	,	PUNCT
ejpam-4624	282	9	s)-fro	s)-fro	NOUN
ejpam-4624	282	10	set	set	NOUN
ejpam-4624	282	11	containing	contain	VERB
ejpam-4624	282	12	xi	xi	PROPN
ejpam-4624	282	13	,	,	PUNCT
ejpam-4624	282	14	we	we	PRON
ejpam-4624	282	15	obtain	obtain	VERB
ejpam-4624	282	16	(	(	PUNCT
ejpam-4624	282	17	2	2	NUM
ejpam-4624	282	18	)	)	PUNCT
ejpam-4624	282	19	.	.	PUNCT
ejpam-4624	283	1	(	(	PUNCT
ejpam-4624	283	2	2	2	X
ejpam-4624	283	3	)	)	PUNCT
ejpam-4624	283	4	⇒	⇒	NOUN
ejpam-4624	283	5	(	(	PUNCT
ejpam-4624	283	6	1	1	X
ejpam-4624	283	7	)	)	PUNCT
ejpam-4624	283	8	let	let	VERB
ejpam-4624	283	9	xi	xi	PRON
ejpam-4624	283	10	be	be	AUX
ejpam-4624	283	11	a	a	DET
ejpam-4624	283	12	double	double	ADJ
ejpam-4624	283	13	point	point	NOUN
ejpam-4624	283	14	of	of	ADP
ejpam-4624	283	15	x	x	PUNCT
ejpam-4624	283	16	and	and	CCONJ
ejpam-4624	283	17	ρ	ρ	PROPN
ejpam-4624	283	18	be	be	AUX
ejpam-4624	283	19	a	a	DET
ejpam-4624	283	20	double	double	ADJ
ejpam-4624	283	21	fuzzy	fuzzy	ADJ
ejpam-4624	283	22	open	open	ADJ
ejpam-4624	283	23	nbd	nbd	PROPN
ejpam-4624	283	24	containing	contain	VERB
ejpam-4624	283	25	f(xi	f(xi	PROPN
ejpam-4624	283	26	)	)	PUNCT
ejpam-4624	283	27	.	.	PUNCT
ejpam-4624	284	1	then	then	ADV
ejpam-4624	284	2	it2,t	it2,t	NOUN
ejpam-4624	284	3	∗	∗	NOUN
ejpam-4624	284	4	2	2	NUM
ejpam-4624	284	5	(	(	PUNCT
ejpam-4624	284	6	ct2,t	ct2,t	PROPN
ejpam-4624	284	7	∗	∗	NOUN
ejpam-4624	284	8	2	2	NUM
ejpam-4624	284	9	(	(	PUNCT
ejpam-4624	284	10	ρ	ρ	PROPN
ejpam-4624	284	11	,	,	PUNCT
ejpam-4624	284	12	r	r	NOUN
ejpam-4624	284	13	,	,	PUNCT
ejpam-4624	284	14	s	s	NOUN
ejpam-4624	284	15	)	)	PUNCT
ejpam-4624	284	16	)	)	PUNCT
ejpam-4624	284	17	is	be	AUX
ejpam-4624	284	18	a	a	DET
ejpam-4624	284	19	(	(	PUNCT
ejpam-4624	284	20	r	r	NOUN
ejpam-4624	284	21	,	,	PUNCT
ejpam-4624	284	22	s)-fro	s)-fro	NOUN
ejpam-4624	284	23	set	set	NOUN
ejpam-4624	284	24	containing	contain	VERB
ejpam-4624	284	25	f(xi	f(xi	PROPN
ejpam-4624	284	26	)	)	PUNCT
ejpam-4624	284	27	and	and	CCONJ
ejpam-4624	284	28	ρ	ρ	NOUN
ejpam-4624	284	29	≤	≤	ADJ
ejpam-4624	284	30	it2,t	it2,t	PROPN
ejpam-4624	284	31	∗	∗	NOUN
ejpam-4624	284	32	2	2	NUM
ejpam-4624	284	33	(	(	PUNCT
ejpam-4624	284	34	ct2,t	ct2,t	PROPN
ejpam-4624	284	35	∗	∗	NOUN
ejpam-4624	284	36	2	2	NUM
ejpam-4624	284	37	(	(	PUNCT
ejpam-4624	284	38	ρ	ρ	PROPN
ejpam-4624	284	39	,	,	PUNCT
ejpam-4624	284	40	r	r	NOUN
ejpam-4624	284	41	,	,	PUNCT
ejpam-4624	284	42	s	s	NOUN
ejpam-4624	284	43	)	)	PUNCT
ejpam-4624	284	44	)	)	PUNCT
ejpam-4624	284	45	.	.	PUNCT
ejpam-4624	285	1	by	by	ADP
ejpam-4624	285	2	(	(	PUNCT
ejpam-4624	285	3	2	2	NUM
ejpam-4624	285	4	)	)	PUNCT
ejpam-4624	285	5	,	,	PUNCT
ejpam-4624	285	6	there	there	PRON
ejpam-4624	285	7	is	be	VERB
ejpam-4624	285	8	a	a	DET
ejpam-4624	285	9	(	(	PUNCT
ejpam-4624	285	10	r	r	NOUN
ejpam-4624	285	11	,	,	PUNCT
ejpam-4624	285	12	s)-fro	s)-fro	NOUN
ejpam-4624	285	13	set	set	VERB
ejpam-4624	285	14	ϕ	ϕ	NOUN
ejpam-4624	285	15	containing	contain	VERB
ejpam-4624	285	16	xi	xi	ADP
ejpam-4624	285	17	such	such	ADJ
ejpam-4624	285	18	that	that	SCONJ
ejpam-4624	285	19	f(ϕ	f(ϕ	PROPN
ejpam-4624	285	20	)	)	PUNCT
ejpam-4624	285	21	≤	≤	NOUN
ejpam-4624	285	22	it2,t	it2,t	PROPN
ejpam-4624	285	23	∗	∗	NOUN
ejpam-4624	285	24	2	2	NUM
ejpam-4624	285	25	(	(	PUNCT
ejpam-4624	285	26	ct2,t	ct2,t	PROPN
ejpam-4624	285	27	∗	∗	NOUN
ejpam-4624	285	28	2	2	NUM
ejpam-4624	285	29	(	(	PUNCT
ejpam-4624	285	30	ρ	ρ	PROPN
ejpam-4624	285	31	,	,	PUNCT
ejpam-4624	285	32	r	r	NOUN
ejpam-4624	285	33	,	,	PUNCT
ejpam-4624	285	34	s	s	NOUN
ejpam-4624	285	35	)	)	PUNCT
ejpam-4624	285	36	)	)	PUNCT
ejpam-4624	285	37	(	(	PUNCT
ejpam-4624	285	38	i.e.	i.e.	X
ejpam-4624	285	39	,	,	PUNCT
ejpam-4624	285	40	since	since	SCONJ
ejpam-4624	285	41	a	a	DET
ejpam-4624	285	42	(	(	PUNCT
ejpam-4624	285	43	r	r	NOUN
ejpam-4624	285	44	,	,	PUNCT
ejpam-4624	285	45	s)-fro	s)-fro	NOUN
ejpam-4624	285	46	set	set	NOUN
ejpam-4624	285	47	is	be	AUX
ejpam-4624	285	48	a	a	DET
ejpam-4624	285	49	double	double	ADJ
ejpam-4624	285	50	fuzzy	fuzzy	ADJ
ejpam-4624	285	51	open	open	ADJ
ejpam-4624	285	52	set	set	NOUN
ejpam-4624	285	53	)	)	PUNCT
ejpam-4624	285	54	and	and	CCONJ
ejpam-4624	285	55	it1,t	it1,t	PROPN
ejpam-4624	285	56	∗	∗	NOUN
ejpam-4624	285	57	1	1	NUM
ejpam-4624	285	58	(	(	PUNCT
ejpam-4624	285	59	ct1,t	ct1,t	NOUN
ejpam-4624	285	60	∗	∗	VERB
ejpam-4624	285	61	1	1	NUM
ejpam-4624	285	62	(	(	PUNCT
ejpam-4624	285	63	ϕ	ϕ	NOUN
ejpam-4624	285	64	,	,	PUNCT
ejpam-4624	285	65	r	r	NOUN
ejpam-4624	285	66	,	,	PUNCT
ejpam-4624	285	67	s	s	NOUN
ejpam-4624	285	68	)	)	PUNCT
ejpam-4624	285	69	)	)	PUNCT
ejpam-4624	286	1	=	=	PUNCT
ejpam-4624	286	2	ϕ	ϕ	NOUN
ejpam-4624	286	3	there	there	PRON
ejpam-4624	286	4	is	be	VERB
ejpam-4624	286	5	a	a	DET
ejpam-4624	286	6	double	double	ADJ
ejpam-4624	286	7	fuzzy	fuzzy	ADJ
ejpam-4624	286	8	open	open	ADJ
ejpam-4624	286	9	set	set	NOUN
ejpam-4624	286	10	ϕ	ϕ	NOUN
ejpam-4624	286	11	containing	contain	VERB
ejpam-4624	286	12	xi	xi	ADP
ejpam-4624	286	13	such	such	ADJ
ejpam-4624	286	14	that	that	PRON
ejpam-4624	286	15	,	,	PUNCT
ejpam-4624	286	16	f(it1,t	f(it1,t	PROPN
ejpam-4624	286	17	∗	∗	NOUN
ejpam-4624	286	18	1	1	NUM
ejpam-4624	286	19	(	(	PUNCT
ejpam-4624	286	20	ct1,t	ct1,t	NOUN
ejpam-4624	286	21	∗	∗	VERB
ejpam-4624	286	22	1	1	NUM
ejpam-4624	286	23	(	(	PUNCT
ejpam-4624	286	24	ϕ	ϕ	NOUN
ejpam-4624	286	25	,	,	PUNCT
ejpam-4624	286	26	r	r	NOUN
ejpam-4624	286	27	,	,	PUNCT
ejpam-4624	286	28	s	s	NOUN
ejpam-4624	286	29	)	)	PUNCT
ejpam-4624	286	30	)	)	PUNCT
ejpam-4624	286	31	)	)	PUNCT
ejpam-4624	286	32	≤	≤	ADV
ejpam-4624	286	33	it2,t	it2,t	PROPN
ejpam-4624	286	34	∗	∗	NOUN
ejpam-4624	286	35	2	2	NUM
ejpam-4624	286	36	(	(	PUNCT
ejpam-4624	286	37	ct2,t	ct2,t	PROPN
ejpam-4624	286	38	∗	∗	NOUN
ejpam-4624	286	39	2	2	NUM
ejpam-4624	286	40	(	(	PUNCT
ejpam-4624	286	41	ρ	ρ	PROPN
ejpam-4624	286	42	,	,	PUNCT
ejpam-4624	286	43	r	r	NOUN
ejpam-4624	286	44	,	,	PUNCT
ejpam-4624	286	45	s	s	NOUN
ejpam-4624	286	46	)	)	PUNCT
ejpam-4624	286	47	)	)	PUNCT
ejpam-4624	286	48	.	.	PUNCT
ejpam-4624	287	1	theorem	theorem	VERB
ejpam-4624	287	2	3.3	3.3	NUM
ejpam-4624	287	3	.	.	PUNCT
ejpam-4624	288	1	for	for	ADP
ejpam-4624	288	2	a	a	DET
ejpam-4624	288	3	function	function	NOUN
ejpam-4624	288	4	f	f	NOUN
ejpam-4624	288	5	:	:	PUNCT
ejpam-4624	288	6	(	(	PUNCT
ejpam-4624	288	7	x	x	X
ejpam-4624	288	8	,	,	PUNCT
ejpam-4624	288	9	t1	t1	PROPN
ejpam-4624	288	10	,	,	PUNCT
ejpam-4624	288	11	t	t	PROPN
ejpam-4624	288	12	∗	∗	X
ejpam-4624	288	13	1	1	NUM
ejpam-4624	288	14	)	)	PUNCT
ejpam-4624	288	15	−→	−→	NOUN
ejpam-4624	288	16	(	(	PUNCT
ejpam-4624	288	17	y	y	PROPN
ejpam-4624	288	18	,	,	PUNCT
ejpam-4624	288	19	t2	t2	PROPN
ejpam-4624	288	20	,	,	PUNCT
ejpam-4624	288	21	t	t	PROPN
ejpam-4624	288	22	∗	∗	X
ejpam-4624	288	23	2	2	NUM
ejpam-4624	288	24	)	)	PUNCT
ejpam-4624	288	25	.	.	PUNCT
ejpam-4624	289	1	the	the	DET
ejpam-4624	289	2	following	follow	VERB
ejpam-4624	289	3	statements	statement	NOUN
ejpam-4624	289	4	are	be	AUX
ejpam-4624	289	5	equivalent	equivalent	ADJ
ejpam-4624	289	6	:	:	PUNCT
ejpam-4624	289	7	(	(	PUNCT
ejpam-4624	289	8	i	i	NOUN
ejpam-4624	289	9	)	)	PUNCT
ejpam-4624	289	10	f	f	PROPN
ejpam-4624	289	11	is	be	AUX
ejpam-4624	289	12	double	double	ADJ
ejpam-4624	289	13	fuzzy	fuzzy	ADJ
ejpam-4624	290	1	δ	δ	NOUN
ejpam-4624	290	2	-	-	ADJ
ejpam-4624	290	3	continuous	continuous	ADJ
ejpam-4624	290	4	,	,	PUNCT
ejpam-4624	290	5	(	(	PUNCT
ejpam-4624	290	6	ii	ii	NOUN
ejpam-4624	290	7	)	)	PUNCT
ejpam-4624	290	8	f(δct1,t	f(δct1,t	PROPN
ejpam-4624	290	9	∗	∗	NOUN
ejpam-4624	290	10	1	1	NUM
ejpam-4624	290	11	(	(	PUNCT
ejpam-4624	290	12	ρ	ρ	PROPN
ejpam-4624	290	13	,	,	PUNCT
ejpam-4624	290	14	r	r	NOUN
ejpam-4624	290	15	,	,	PUNCT
ejpam-4624	290	16	s	s	NOUN
ejpam-4624	290	17	)	)	PUNCT
ejpam-4624	290	18	)	)	PUNCT
ejpam-4624	290	19	≤	≤	NUM
ejpam-4624	290	20	δct2,t	δct2,t	NOUN
ejpam-4624	290	21	∗	∗	NOUN
ejpam-4624	290	22	2	2	NUM
ejpam-4624	290	23	(	(	PUNCT
ejpam-4624	290	24	f(ρ	f(ρ	NOUN
ejpam-4624	290	25	)	)	PUNCT
ejpam-4624	290	26	,	,	PUNCT
ejpam-4624	290	27	r	r	NOUN
ejpam-4624	290	28	,	,	PUNCT
ejpam-4624	290	29	s	s	PART
ejpam-4624	290	30	)	)	PUNCT
ejpam-4624	290	31	,	,	PUNCT
ejpam-4624	290	32	for	for	ADP
ejpam-4624	290	33	each	each	DET
ejpam-4624	290	34	r	r	NOUN
ejpam-4624	290	35	∈	∈	PROPN
ejpam-4624	290	36	i0	i0	PROPN
ejpam-4624	290	37	,	,	PUNCT
ejpam-4624	290	38	s	s	PROPN
ejpam-4624	290	39	∈	∈	PROPN
ejpam-4624	290	40	i1	i1	NOUN
ejpam-4624	290	41	,	,	PUNCT
ejpam-4624	290	42	and	and	CCONJ
ejpam-4624	290	43	ρ	ρ	PROPN
ejpam-4624	290	44	∈	∈	PROPN
ejpam-4624	290	45	ix	ix	X
ejpam-4624	290	46	.	.	PUNCT
ejpam-4624	291	1	(	(	PUNCT
ejpam-4624	291	2	iii	iii	X
ejpam-4624	291	3	)	)	PUNCT
ejpam-4624	291	4	δct2,t	δct2,t	NOUN
ejpam-4624	291	5	∗	∗	NOUN
ejpam-4624	291	6	2	2	NUM
ejpam-4624	291	7	(	(	PUNCT
ejpam-4624	291	8	f(ϕ)−1	f(ϕ)−1	PROPN
ejpam-4624	291	9	,	,	PUNCT
ejpam-4624	291	10	r	r	NOUN
ejpam-4624	291	11	,	,	PUNCT
ejpam-4624	291	12	s	s	NOUN
ejpam-4624	291	13	)	)	PUNCT
ejpam-4624	291	14	≤	≤	NUM
ejpam-4624	292	1	f−1(δct1,t	f−1(δct1,t	PROPN
ejpam-4624	292	2	∗	∗	NOUN
ejpam-4624	292	3	1	1	NUM
ejpam-4624	292	4	(	(	PUNCT
ejpam-4624	292	5	ϕ	ϕ	NOUN
ejpam-4624	292	6	,	,	PUNCT
ejpam-4624	292	7	r	r	NOUN
ejpam-4624	292	8	,	,	PUNCT
ejpam-4624	292	9	s	s	NOUN
ejpam-4624	292	10	)	)	PUNCT
ejpam-4624	292	11	)	)	PUNCT
ejpam-4624	292	12	,	,	PUNCT
ejpam-4624	292	13	for	for	ADP
ejpam-4624	292	14	each	each	DET
ejpam-4624	292	15	r	r	NOUN
ejpam-4624	292	16	∈	∈	PROPN
ejpam-4624	292	17	i0	i0	PROPN
ejpam-4624	292	18	,	,	PUNCT
ejpam-4624	292	19	s	s	PROPN
ejpam-4624	292	20	∈	∈	PROPN
ejpam-4624	292	21	i1	i1	PROPN
ejpam-4624	292	22	,	,	PUNCT
ejpam-4624	292	23	and	and	CCONJ
ejpam-4624	292	24	ϕ	ϕ	PROPN
ejpam-4624	292	25	∈	∈	PROPN
ejpam-4624	292	26	iy	iy	PROPN
ejpam-4624	292	27	.	.	PUNCT
ejpam-4624	293	1	(	(	PUNCT
ejpam-4624	293	2	iv	iv	X
ejpam-4624	293	3	)	)	PUNCT
ejpam-4624	293	4	for	for	ADP
ejpam-4624	293	5	every	every	DET
ejpam-4624	293	6	(	(	PUNCT
ejpam-4624	293	7	r	r	NOUN
ejpam-4624	293	8	,	,	PUNCT
ejpam-4624	293	9	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	293	10	δ	δ	PROPN
ejpam-4624	293	11	-	-	PUNCT
ejpam-4624	293	12	closed	close	VERB
ejpam-4624	293	13	set	set	ADJ
ejpam-4624	293	14	ϕ	ϕ	NOUN
ejpam-4624	293	15	in	in	ADP
ejpam-4624	293	16	iy	iy	PROPN
ejpam-4624	293	17	,	,	PUNCT
ejpam-4624	293	18	r	r	PROPN
ejpam-4624	293	19	∈	∈	PROPN
ejpam-4624	293	20	i0	i0	PROPN
ejpam-4624	293	21	,	,	PUNCT
ejpam-4624	293	22	s	s	PROPN
ejpam-4624	293	23	∈	∈	PROPN
ejpam-4624	293	24	i1	i1	PROPN
ejpam-4624	293	25	,	,	PUNCT
ejpam-4624	293	26	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	293	27	)	)	PUNCT
ejpam-4624	293	28	is	be	AUX
ejpam-4624	293	29	(	(	PUNCT
ejpam-4624	293	30	r	r	NOUN
ejpam-4624	293	31	,	,	PUNCT
ejpam-4624	293	32	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	293	33	δ	δ	PROPN
ejpam-4624	293	34	-	-	PUNCT
ejpam-4624	293	35	closed	close	VERB
ejpam-4624	293	36	set	set	NOUN
ejpam-4624	293	37	in	in	ADP
ejpam-4624	293	38	ix	ix	PROPN
ejpam-4624	293	39	.	.	PUNCT
ejpam-4624	294	1	(	(	PUNCT
ejpam-4624	294	2	v	v	NOUN
ejpam-4624	294	3	)	)	PUNCT
ejpam-4624	294	4	for	for	ADP
ejpam-4624	294	5	every	every	DET
ejpam-4624	294	6	(	(	PUNCT
ejpam-4624	294	7	r	r	NOUN
ejpam-4624	294	8	,	,	PUNCT
ejpam-4624	294	9	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	294	10	δ	δ	PROPN
ejpam-4624	294	11	-	-	ADJ
ejpam-4624	294	12	open	open	ADJ
ejpam-4624	294	13	set	set	VERB
ejpam-4624	294	14	ϕ	ϕ	PROPN
ejpam-4624	294	15	in	in	ADP
ejpam-4624	294	16	iy	iy	PROPN
ejpam-4624	294	17	,	,	PUNCT
ejpam-4624	294	18	r	r	PROPN
ejpam-4624	294	19	∈	∈	PROPN
ejpam-4624	294	20	i0	i0	PROPN
ejpam-4624	294	21	,	,	PUNCT
ejpam-4624	294	22	s	s	PROPN
ejpam-4624	294	23	∈	∈	PROPN
ejpam-4624	294	24	i1	i1	PROPN
ejpam-4624	294	25	,	,	PUNCT
ejpam-4624	294	26	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	294	27	)	)	PUNCT
ejpam-4624	294	28	is	be	AUX
ejpam-4624	294	29	(	(	PUNCT
ejpam-4624	294	30	r	r	NOUN
ejpam-4624	294	31	,	,	PUNCT
ejpam-4624	294	32	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	294	33	δ	δ	PROPN
ejpam-4624	294	34	-	-	PUNCT
ejpam-4624	294	35	open	open	ADJ
ejpam-4624	294	36	set	set	NOUN
ejpam-4624	294	37	in	in	ADP
ejpam-4624	294	38	ix	ix	PROPN
ejpam-4624	294	39	.	.	PUNCT
ejpam-4624	295	1	proof	proof	NOUN
ejpam-4624	295	2	.	.	PUNCT
ejpam-4624	296	1	(	(	PUNCT
ejpam-4624	296	2	1	1	X
ejpam-4624	296	3	)	)	PUNCT
ejpam-4624	296	4	⇒	⇒	NOUN
ejpam-4624	296	5	(	(	PUNCT
ejpam-4624	296	6	2	2	X
ejpam-4624	296	7	)	)	PUNCT
ejpam-4624	296	8	let	let	VERB
ejpam-4624	296	9	ρ	ρ	PROPN
ejpam-4624	296	10	∈	∈	PROPN
ejpam-4624	296	11	ix	ix	X
ejpam-4624	296	12	,	,	PUNCT
ejpam-4624	296	13	xα	xα	ADP
ejpam-4624	296	14	∈	∈	PROPN
ejpam-4624	296	15	δct	δct	NOUN
ejpam-4624	296	16	,	,	PUNCT
ejpam-4624	296	17	t	t	NOUN
ejpam-4624	296	18	∗(ρ	∗(ρ	NOUN
ejpam-4624	296	19	,	,	PUNCT
ejpam-4624	296	20	r	r	NOUN
ejpam-4624	296	21	,	,	PUNCT
ejpam-4624	296	22	s	s	PART
ejpam-4624	296	23	)	)	PUNCT
ejpam-4624	296	24	and	and	CCONJ
ejpam-4624	296	25	γ	γ	X
ejpam-4624	296	26	be	be	AUX
ejpam-4624	296	27	a	a	DET
ejpam-4624	296	28	(	(	PUNCT
ejpam-4624	296	29	r	r	NOUN
ejpam-4624	296	30	,	,	PUNCT
ejpam-4624	296	31	s)-regular	s)-regular	ADJ
ejpam-4624	296	32	open	open	ADJ
ejpam-4624	296	33	q	q	NOUN
ejpam-4624	296	34	-	-	PUNCT
ejpam-4624	296	35	neighborhood	neighborhood	NOUN
ejpam-4624	296	36	of	of	ADP
ejpam-4624	296	37	f(xα	f(xα	PROPN
ejpam-4624	296	38	)	)	PUNCT
ejpam-4624	296	39	.	.	PUNCT
ejpam-4624	297	1	then	then	ADV
ejpam-4624	297	2	there	there	PRON
ejpam-4624	297	3	exists	exist	VERB
ejpam-4624	297	4	a	a	DET
ejpam-4624	297	5	(	(	PUNCT
ejpam-4624	297	6	r	r	NOUN
ejpam-4624	297	7	,	,	PUNCT
ejpam-4624	297	8	s)-regular	s)-regular	ADJ
ejpam-4624	297	9	open	open	ADJ
ejpam-4624	297	10	q	q	ADJ
ejpam-4624	297	11	-	-	PUNCT
ejpam-4624	297	12	neighborhood	neighborhood	NOUN
ejpam-4624	297	13	β	β	NOUN
ejpam-4624	297	14	of	of	ADP
ejpam-4624	297	15	xα	xα	INTJ
ejpam-4624	297	16	such	such	ADJ
ejpam-4624	297	17	that	that	DET
ejpam-4624	297	18	f(γ	f(γ	NOUN
ejpam-4624	297	19	)	)	PUNCT
ejpam-4624	297	20	≤	≤	NOUN
ejpam-4624	297	21	β	β	X
ejpam-4624	297	22	.	.	PUNCT
ejpam-4624	298	1	since	since	SCONJ
ejpam-4624	298	2	xα	xα	INTJ
ejpam-4624	298	3	∈	∈	PROPN
ejpam-4624	298	4	δct	δct	NOUN
ejpam-4624	298	5	,	,	PUNCT
ejpam-4624	298	6	t	t	NOUN
ejpam-4624	298	7	∗(ρ	∗(ρ	NOUN
ejpam-4624	298	8	,	,	PUNCT
ejpam-4624	298	9	r	r	NOUN
ejpam-4624	298	10	,	,	PUNCT
ejpam-4624	298	11	s	s	PART
ejpam-4624	298	12	)	)	PUNCT
ejpam-4624	298	13	,	,	PUNCT
ejpam-4624	298	14	we	we	PRON
ejpam-4624	298	15	have	have	VERB
ejpam-4624	298	16	βqρ	βqρ	NOUN
ejpam-4624	298	17	.	.	PUNCT
ejpam-4624	299	1	then	then	ADV
ejpam-4624	299	2	f(β)qf(ρ	f(β)qf(ρ	NOUN
ejpam-4624	299	3	)	)	PUNCT
ejpam-4624	299	4	.	.	PUNCT
ejpam-4624	300	1	thus	thus	ADV
ejpam-4624	300	2	γqf(ρ	γqf(ρ	X
ejpam-4624	300	3	)	)	PUNCT
ejpam-4624	300	4	and	and	CCONJ
ejpam-4624	300	5	hence	hence	ADV
ejpam-4624	300	6	f(xα	f(xα	PROPN
ejpam-4624	300	7	)	)	PUNCT
ejpam-4624	300	8	∈	∈	NOUN
ejpam-4624	300	9	δct	δct	NOUN
ejpam-4624	300	10	,	,	PUNCT
ejpam-4624	300	11	t	t	NOUN
ejpam-4624	300	12	∗(f(ρ	∗(f(ρ	NOUN
ejpam-4624	300	13	)	)	PUNCT
ejpam-4624	300	14	,	,	PUNCT
ejpam-4624	300	15	r	r	NOUN
ejpam-4624	300	16	,	,	PUNCT
ejpam-4624	300	17	s	s	NOUN
ejpam-4624	300	18	)	)	PUNCT
ejpam-4624	300	19	.	.	PUNCT
ejpam-4624	301	1	so	so	ADV
ejpam-4624	301	2	f(δct	f(δct	ADV
ejpam-4624	301	3	,	,	PUNCT
ejpam-4624	301	4	t	t	NOUN
ejpam-4624	301	5	∗(ρ	∗(ρ	NOUN
ejpam-4624	301	6	,	,	PUNCT
ejpam-4624	301	7	r	r	NOUN
ejpam-4624	301	8	,	,	PUNCT
ejpam-4624	301	9	s	s	NOUN
ejpam-4624	301	10	)	)	PUNCT
ejpam-4624	301	11	)	)	PUNCT
ejpam-4624	301	12	≤	≤	NUM
ejpam-4624	301	13	δct	δct	NOUN
ejpam-4624	301	14	,	,	PUNCT
ejpam-4624	301	15	t	t	NOUN
ejpam-4624	301	16	∗(f(ρ	∗(f(ρ	NOUN
ejpam-4624	301	17	)	)	PUNCT
ejpam-4624	301	18	,	,	PUNCT
ejpam-4624	301	19	r	r	NOUN
ejpam-4624	301	20	,	,	PUNCT
ejpam-4624	301	21	s	s	NOUN
ejpam-4624	301	22	)	)	PUNCT
ejpam-4624	301	23	.	.	PUNCT
ejpam-4624	302	1	(	(	PUNCT
ejpam-4624	302	2	2	2	X
ejpam-4624	302	3	)	)	PUNCT
ejpam-4624	302	4	⇒	⇒	NOUN
ejpam-4624	302	5	(	(	PUNCT
ejpam-4624	302	6	3	3	X
ejpam-4624	302	7	)	)	PUNCT
ejpam-4624	302	8	let	let	VERB
ejpam-4624	302	9	ϕ	ϕ	PROPN
ejpam-4624	302	10	∈	∈	PROPN
ejpam-4624	302	11	iy	iy	PROPN
ejpam-4624	302	12	.	.	PUNCT
ejpam-4624	303	1	by	by	ADP
ejpam-4624	303	2	using	use	VERB
ejpam-4624	303	3	(	(	PUNCT
ejpam-4624	303	4	2	2	NUM
ejpam-4624	303	5	)	)	PUNCT
ejpam-4624	303	6	,	,	PUNCT
ejpam-4624	303	7	f(δct1,t	f(δct1,t	PROPN
ejpam-4624	303	8	∗	∗	NOUN
ejpam-4624	303	9	1	1	NUM
ejpam-4624	303	10	(	(	PUNCT
ejpam-4624	303	11	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	303	12	)	)	PUNCT
ejpam-4624	303	13	,	,	PUNCT
ejpam-4624	303	14	r	r	NOUN
ejpam-4624	303	15	,	,	PUNCT
ejpam-4624	303	16	s	s	NOUN
ejpam-4624	303	17	)	)	PUNCT
ejpam-4624	303	18	)	)	PUNCT
ejpam-4624	303	19	≤	≤	NUM
ejpam-4624	303	20	δct1,t	δct1,t	NOUN
ejpam-4624	303	21	∗	∗	VERB
ejpam-4624	303	22	1	1	NUM
ejpam-4624	303	23	(	(	PUNCT
ejpam-4624	303	24	f(f−1(ϕ	f(f−1(ϕ	PROPN
ejpam-4624	303	25	)	)	PUNCT
ejpam-4624	303	26	)	)	PUNCT
ejpam-4624	303	27	,	,	PUNCT
ejpam-4624	303	28	r	r	NOUN
ejpam-4624	303	29	,	,	PUNCT
ejpam-4624	303	30	s	s	NOUN
ejpam-4624	303	31	)	)	PUNCT
ejpam-4624	303	32	≤	≤	NOUN
ejpam-4624	303	33	δct2,t	δct2,t	NOUN
ejpam-4624	303	34	∗	∗	NOUN
ejpam-4624	303	35	2	2	NUM
ejpam-4624	303	36	(	(	PUNCT
ejpam-4624	303	37	ϕ	ϕ	NOUN
ejpam-4624	303	38	,	,	PUNCT
ejpam-4624	303	39	r	r	NOUN
ejpam-4624	303	40	,	,	PUNCT
ejpam-4624	303	41	s	s	NOUN
ejpam-4624	303	42	)	)	PUNCT
ejpam-4624	303	43	.	.	PUNCT
ejpam-4624	304	1	hence	hence	ADV
ejpam-4624	304	2	,	,	PUNCT
ejpam-4624	304	3	δct1,t	δct1,t	NOUN
ejpam-4624	304	4	∗	∗	VERB
ejpam-4624	304	5	1	1	NUM
ejpam-4624	304	6	(	(	PUNCT
ejpam-4624	304	7	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	304	8	)	)	PUNCT
ejpam-4624	304	9	,	,	PUNCT
ejpam-4624	304	10	r	r	NOUN
ejpam-4624	304	11	,	,	PUNCT
ejpam-4624	304	12	s	s	NOUN
ejpam-4624	304	13	)	)	PUNCT
ejpam-4624	304	14	≤	≤	PUNCT
ejpam-4624	305	1	f−1(δct2,t	f−1(δct2,t	PROPN
ejpam-4624	305	2	∗	∗	X
ejpam-4624	305	3	2	2	NUM
ejpam-4624	305	4	(	(	PUNCT
ejpam-4624	305	5	ϕ	ϕ	NOUN
ejpam-4624	305	6	,	,	PUNCT
ejpam-4624	305	7	r	r	NOUN
ejpam-4624	305	8	,	,	PUNCT
ejpam-4624	305	9	s	s	NOUN
ejpam-4624	305	10	)	)	PUNCT
ejpam-4624	305	11	)	)	PUNCT
ejpam-4624	305	12	.	.	PUNCT
ejpam-4624	306	1	w.	w.	PROPN
ejpam-4624	306	2	f.	f.	PROPN
ejpam-4624	306	3	al	al	PROPN
ejpam-4624	306	4	-	-	PUNCT
ejpam-4624	306	5	omeri	omeri	ADJ
ejpam-4624	306	6	/	/	SYM
ejpam-4624	306	7	eur	eur	PROPN
ejpam-4624	306	8	.	.	PUNCT
ejpam-4624	307	1	j.	j.	PROPN
ejpam-4624	307	2	pure	pure	PROPN
ejpam-4624	307	3	appl	appl	PROPN
ejpam-4624	307	4	.	.	PROPN
ejpam-4624	307	5	math	math	PROPN
ejpam-4624	307	6	,	,	PUNCT
ejpam-4624	307	7	18	18	NUM
ejpam-4624	307	8	(	(	PUNCT
ejpam-4624	307	9	2	2	NUM
ejpam-4624	307	10	)	)	PUNCT
ejpam-4624	307	11	(	(	PUNCT
ejpam-4624	307	12	2025	2025	NUM
ejpam-4624	307	13	)	)	PUNCT
ejpam-4624	307	14	,	,	PUNCT
ejpam-4624	307	15	4624	4624	NUM
ejpam-4624	307	16	12	12	NUM
ejpam-4624	307	17	of	of	ADP
ejpam-4624	307	18	15	15	NUM
ejpam-4624	307	19	(	(	PUNCT
ejpam-4624	307	20	3	3	NUM
ejpam-4624	307	21	)	)	PUNCT
ejpam-4624	307	22	⇒	⇒	NOUN
ejpam-4624	307	23	(	(	PUNCT
ejpam-4624	307	24	4	4	X
ejpam-4624	307	25	)	)	PUNCT
ejpam-4624	307	26	we	we	PRON
ejpam-4624	307	27	have	have	VERB
ejpam-4624	307	28	ϕ	ϕ	NOUN
ejpam-4624	307	29	=	=	NOUN
ejpam-4624	307	30	δct2,t	δct2,t	NOUN
ejpam-4624	307	31	∗	∗	NOUN
ejpam-4624	307	32	2	2	NUM
ejpam-4624	307	33	(	(	PUNCT
ejpam-4624	307	34	ϕ	ϕ	NOUN
ejpam-4624	307	35	,	,	PUNCT
ejpam-4624	307	36	r	r	NOUN
ejpam-4624	307	37	,	,	PUNCT
ejpam-4624	307	38	s	s	NOUN
ejpam-4624	307	39	)	)	PUNCT
ejpam-4624	307	40	.	.	PUNCT
ejpam-4624	308	1	now	now	ADV
ejpam-4624	308	2	by	by	ADP
ejpam-4624	308	3	(	(	PUNCT
ejpam-4624	308	4	3	3	NUM
ejpam-4624	308	5	)	)	PUNCT
ejpam-4624	308	6	,	,	PUNCT
ejpam-4624	308	7	δct1,t	δct1,t	NOUN
ejpam-4624	308	8	∗	∗	VERB
ejpam-4624	308	9	1	1	NUM
ejpam-4624	308	10	(	(	PUNCT
ejpam-4624	308	11	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	308	12	)	)	PUNCT
ejpam-4624	308	13	,	,	PUNCT
ejpam-4624	308	14	r	r	NOUN
ejpam-4624	308	15	,	,	PUNCT
ejpam-4624	308	16	s	s	NOUN
ejpam-4624	308	17	)	)	PUNCT
ejpam-4624	308	18	≤	≤	PUNCT
ejpam-4624	309	1	f−1(δct2,t	f−1(δct2,t	PROPN
ejpam-4624	309	2	∗	∗	X
ejpam-4624	309	3	2	2	NUM
ejpam-4624	309	4	(	(	PUNCT
ejpam-4624	309	5	ϕ	ϕ	NOUN
ejpam-4624	309	6	,	,	PUNCT
ejpam-4624	309	7	r	r	NOUN
ejpam-4624	309	8	,	,	PUNCT
ejpam-4624	309	9	s	s	NOUN
ejpam-4624	309	10	)	)	PUNCT
ejpam-4624	309	11	)	)	PUNCT
ejpam-4624	310	1	=	=	PUNCT
ejpam-4624	310	2	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	310	3	)	)	PUNCT
ejpam-4624	310	4	.	.	PUNCT
ejpam-4624	311	1	therefore	therefore	ADV
ejpam-4624	311	2	,	,	PUNCT
ejpam-4624	311	3	δct1,t	δct1,t	NOUN
ejpam-4624	311	4	∗	∗	VERB
ejpam-4624	311	5	1	1	NUM
ejpam-4624	311	6	(	(	PUNCT
ejpam-4624	311	7	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	311	8	)	)	PUNCT
ejpam-4624	311	9	,	,	PUNCT
ejpam-4624	311	10	r	r	NOUN
ejpam-4624	311	11	,	,	PUNCT
ejpam-4624	311	12	s	s	NOUN
ejpam-4624	311	13	)	)	PUNCT
ejpam-4624	311	14	=	=	PUNCT
ejpam-4624	311	15	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	311	16	)	)	PUNCT
ejpam-4624	311	17	.	.	PUNCT
ejpam-4624	312	1	hence	hence	ADV
ejpam-4624	312	2	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	312	3	)	)	PUNCT
ejpam-4624	312	4	is	be	AUX
ejpam-4624	312	5	a	a	DET
ejpam-4624	312	6	(	(	PUNCT
ejpam-4624	312	7	r	r	NOUN
ejpam-4624	312	8	,	,	PUNCT
ejpam-4624	312	9	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	312	10	δ	δ	PROPN
ejpam-4624	312	11	-	-	PUNCT
ejpam-4624	312	12	closed	closed	ADJ
ejpam-4624	312	13	.	.	PUNCT
ejpam-4624	313	1	(	(	PUNCT
ejpam-4624	313	2	4	4	X
ejpam-4624	313	3	)	)	PUNCT
ejpam-4624	313	4	⇒	⇒	NOUN
ejpam-4624	313	5	(	(	PUNCT
ejpam-4624	313	6	5	5	X
ejpam-4624	313	7	)	)	PUNCT
ejpam-4624	313	8	let	let	VERB
ejpam-4624	313	9	ϕ	ϕ	PROPN
ejpam-4624	313	10	∈	∈	PROPN
ejpam-4624	313	11	iy	iy	PROPN
ejpam-4624	313	12	,	,	PUNCT
ejpam-4624	313	13	and	and	CCONJ
ejpam-4624	313	14	ϕ	ϕ	NOUN
ejpam-4624	313	15	be	be	AUX
ejpam-4624	313	16	a	a	DET
ejpam-4624	313	17	(	(	PUNCT
ejpam-4624	313	18	r	r	NOUN
ejpam-4624	313	19	,	,	PUNCT
ejpam-4624	313	20	s)-fuzzy	s)-fuzzy	ADV
ejpam-4624	313	21	δ	δ	NOUN
ejpam-4624	313	22	-	-	NOUN
ejpam-4624	313	23	open	open	ADJ
ejpam-4624	313	24	.	.	PUNCT
ejpam-4624	314	1	then	then	ADV
ejpam-4624	314	2	,	,	PUNCT
ejpam-4624	314	3	1	1	NUM
ejpam-4624	314	4	−	−	PROPN
ejpam-4624	314	5	ϕ	ϕ	NOUN
ejpam-4624	314	6	is	be	AUX
ejpam-4624	314	7	a	a	DET
ejpam-4624	314	8	(	(	PUNCT
ejpam-4624	314	9	r	r	NOUN
ejpam-4624	314	10	,	,	PUNCT
ejpam-4624	314	11	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	314	12	δ	δ	PROPN
ejpam-4624	314	13	-	-	PUNCT
ejpam-4624	314	14	closed	close	VERB
ejpam-4624	314	15	in	in	ADP
ejpam-4624	314	16	iy	iy	PROPN
ejpam-4624	314	17	.	.	PUNCT
ejpam-4624	315	1	by	by	ADP
ejpam-4624	315	2	(	(	PUNCT
ejpam-4624	315	3	4	4	NUM
ejpam-4624	315	4	)	)	PUNCT
ejpam-4624	315	5	,	,	PUNCT
ejpam-4624	315	6	f−1(1	f−1(1	ADP
ejpam-4624	315	7	−	−	PROPN
ejpam-4624	315	8	ϕ	ϕ	NOUN
ejpam-4624	315	9	)	)	PUNCT
ejpam-4624	315	10	is	be	AUX
ejpam-4624	315	11	a	a	DET
ejpam-4624	315	12	(	(	PUNCT
ejpam-4624	315	13	r	r	NOUN
ejpam-4624	315	14	,	,	PUNCT
ejpam-4624	315	15	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	315	16	δ	δ	PROPN
ejpam-4624	315	17	-	-	PUNCT
ejpam-4624	315	18	closed	close	VERB
ejpam-4624	315	19	in	in	ADP
ejpam-4624	315	20	ix	ix	PROPN
ejpam-4624	315	21	.	.	PUNCT
ejpam-4624	316	1	since	since	SCONJ
ejpam-4624	316	2	f−1(1	f−1(1	VERB
ejpam-4624	316	3	−	−	PROPN
ejpam-4624	316	4	ϕ	ϕ	NOUN
ejpam-4624	316	5	)	)	PUNCT
ejpam-4624	316	6	=	=	SYM
ejpam-4624	316	7	1−	1−	NUM
ejpam-4624	316	8	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	316	9	)	)	PUNCT
ejpam-4624	316	10	,	,	PUNCT
ejpam-4624	316	11	f−1(ϕ	f−1(ϕ	ADV
ejpam-4624	316	12	)	)	PUNCT
ejpam-4624	316	13	is	be	AUX
ejpam-4624	316	14	(	(	PUNCT
ejpam-4624	316	15	r	r	NOUN
ejpam-4624	316	16	,	,	PUNCT
ejpam-4624	316	17	s)-fuzzy	s)-fuzzy	ADV
ejpam-4624	316	18	δ	δ	PROPN
ejpam-4624	316	19	-	-	PUNCT
ejpam-4624	316	20	open	open	ADJ
ejpam-4624	316	21	in	in	ADP
ejpam-4624	316	22	ix	ix	PROPN
ejpam-4624	316	23	.	.	PUNCT
ejpam-4624	317	1	(	(	PUNCT
ejpam-4624	317	2	5	5	X
ejpam-4624	317	3	)	)	PUNCT
ejpam-4624	317	4	⇒	⇒	NOUN
ejpam-4624	317	5	(	(	PUNCT
ejpam-4624	317	6	1	1	X
ejpam-4624	317	7	)	)	PUNCT
ejpam-4624	317	8	the	the	DET
ejpam-4624	317	9	proof	proof	NOUN
ejpam-4624	317	10	is	be	AUX
ejpam-4624	317	11	clear	clear	ADJ
ejpam-4624	317	12	.	.	PUNCT
ejpam-4624	318	1	theorem	theorem	VERB
ejpam-4624	318	2	3.4	3.4	NUM
ejpam-4624	318	3	.	.	PUNCT
ejpam-4624	319	1	for	for	ADP
ejpam-4624	319	2	a	a	DET
ejpam-4624	319	3	function	function	NOUN
ejpam-4624	319	4	f	f	NOUN
ejpam-4624	319	5	:	:	PUNCT
ejpam-4624	319	6	(	(	PUNCT
ejpam-4624	319	7	x	x	NOUN
ejpam-4624	319	8	,	,	PUNCT
ejpam-4624	319	9	τ1	τ1	PROPN
ejpam-4624	319	10	,	,	PUNCT
ejpam-4624	319	11	τ	τ	PROPN
ejpam-4624	319	12	∗	∗	X
ejpam-4624	319	13	1	1	NUM
ejpam-4624	319	14	)	)	PUNCT
ejpam-4624	319	15	→	→	SYM
ejpam-4624	319	16	(	(	PUNCT
ejpam-4624	319	17	y	y	PROPN
ejpam-4624	319	18	,	,	PUNCT
ejpam-4624	319	19	τ2	τ2	PROPN
ejpam-4624	319	20	,	,	PUNCT
ejpam-4624	319	21	τ	τ	PROPN
ejpam-4624	319	22	∗	∗	NOUN
ejpam-4624	319	23	2	2	NUM
ejpam-4624	319	24	)	)	PUNCT
ejpam-4624	319	25	.	.	PUNCT
ejpam-4624	320	1	the	the	DET
ejpam-4624	320	2	following	follow	VERB
ejpam-4624	320	3	statements	statement	NOUN
ejpam-4624	320	4	are	be	AUX
ejpam-4624	320	5	equivalent	equivalent	ADJ
ejpam-4624	320	6	:	:	PUNCT
ejpam-4624	320	7	(	(	PUNCT
ejpam-4624	320	8	i	i	NOUN
ejpam-4624	320	9	)	)	PUNCT
ejpam-4624	320	10	f	f	PROPN
ejpam-4624	320	11	is	be	AUX
ejpam-4624	320	12	double	double	ADJ
ejpam-4624	320	13	fuzzy	fuzzy	ADJ
ejpam-4624	320	14	δ	δ	NOUN
ejpam-4624	320	15	-	-	ADJ
ejpam-4624	320	16	continuous	continuous	ADJ
ejpam-4624	320	17	function	function	NOUN
ejpam-4624	320	18	,	,	PUNCT
ejpam-4624	320	19	(	(	PUNCT
ejpam-4624	320	20	ii	ii	NOUN
ejpam-4624	320	21	)	)	PUNCT
ejpam-4624	320	22	f−1(µ	f−1(µ	PROPN
ejpam-4624	320	23	)	)	PUNCT
ejpam-4624	320	24	is	be	AUX
ejpam-4624	320	25	an	an	DET
ejpam-4624	320	26	(	(	PUNCT
ejpam-4624	320	27	r0	r0	NOUN
ejpam-4624	320	28	,	,	PUNCT
ejpam-4624	320	29	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	320	30	δ	δ	NOUN
ejpam-4624	320	31	-	-	PUNCT
ejpam-4624	320	32	closed	close	VERB
ejpam-4624	320	33	set	set	NOUN
ejpam-4624	320	34	in	in	ADP
ejpam-4624	320	35	ix	ix	ADP
ejpam-4624	320	36	for	for	ADP
ejpam-4624	320	37	each	each	DET
ejpam-4624	320	38	µ	µ	PROPN
ejpam-4624	320	39	∈	∈	PROPN
ejpam-4624	320	40	iy	iy	PROPN
ejpam-4624	320	41	,	,	PUNCT
ejpam-4624	320	42	r0	r0	PROPN
ejpam-4624	320	43	∈	∈	PROPN
ejpam-4624	320	44	i0	i0	PROPN
ejpam-4624	320	45	,	,	PUNCT
ejpam-4624	320	46	s1	s1	PROPN
ejpam-4624	320	47	∈	∈	PROPN
ejpam-4624	320	48	i1	i1	PROPN
ejpam-4624	320	49	,	,	PUNCT
ejpam-4624	320	50	(	(	PUNCT
ejpam-4624	320	51	iii	iii	NOUN
ejpam-4624	320	52	)	)	PUNCT
ejpam-4624	320	53	f−1(µ	f−1(µ	PROPN
ejpam-4624	320	54	)	)	PUNCT
ejpam-4624	320	55	is	be	AUX
ejpam-4624	320	56	an	an	DET
ejpam-4624	320	57	(	(	PUNCT
ejpam-4624	320	58	r0	r0	NOUN
ejpam-4624	320	59	,	,	PUNCT
ejpam-4624	320	60	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	320	61	δ	δ	NOUN
ejpam-4624	320	62	-	-	ADJ
ejpam-4624	320	63	open	open	ADJ
ejpam-4624	320	64	set	set	NOUN
ejpam-4624	320	65	in	in	ADP
ejpam-4624	320	66	ix	ix	ADP
ejpam-4624	320	67	for	for	ADP
ejpam-4624	320	68	each	each	DET
ejpam-4624	320	69	µ	µ	PROPN
ejpam-4624	320	70	∈	∈	PROPN
ejpam-4624	320	71	iy	iy	PROPN
ejpam-4624	320	72	,	,	PUNCT
ejpam-4624	320	73	r0	r0	PROPN
ejpam-4624	320	74	∈	∈	PROPN
ejpam-4624	320	75	i0	i0	PROPN
ejpam-4624	320	76	,	,	PUNCT
ejpam-4624	320	77	s1	s1	PROPN
ejpam-4624	320	78	∈	∈	PROPN
ejpam-4624	320	79	i1	i1	PROPN
ejpam-4624	320	80	.	.	PUNCT
ejpam-4624	321	1	proof	proof	NOUN
ejpam-4624	321	2	.	.	PUNCT
ejpam-4624	322	1	(	(	PUNCT
ejpam-4624	322	2	1	1	X
ejpam-4624	322	3	)	)	PUNCT
ejpam-4624	322	4	⇒	⇒	NOUN
ejpam-4624	322	5	(	(	PUNCT
ejpam-4624	322	6	2	2	X
ejpam-4624	322	7	)	)	PUNCT
ejpam-4624	322	8	let	let	VERB
ejpam-4624	322	9	µ	µ	X
ejpam-4624	322	10	be	be	AUX
ejpam-4624	322	11	an	an	DET
ejpam-4624	322	12	(	(	PUNCT
ejpam-4624	322	13	r0	r0	NOUN
ejpam-4624	322	14	,	,	PUNCT
ejpam-4624	322	15	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	322	16	δ	δ	NOUN
ejpam-4624	322	17	-	-	PUNCT
ejpam-4624	322	18	closed	close	VERB
ejpam-4624	322	19	set	set	NOUN
ejpam-4624	322	20	in	in	ADP
ejpam-4624	322	21	ix	ix	ADP
ejpam-4624	322	22	for	for	ADP
ejpam-4624	322	23	each	each	DET
ejpam-4624	322	24	µ	µ	PROPN
ejpam-4624	322	25	∈	∈	PROPN
ejpam-4624	322	26	iy	iy	PROPN
ejpam-4624	322	27	,	,	PUNCT
ejpam-4624	322	28	r0	r0	PROPN
ejpam-4624	322	29	∈	∈	PROPN
ejpam-4624	322	30	i0	i0	PROPN
ejpam-4624	322	31	,	,	PUNCT
ejpam-4624	322	32	s1	s1	PROPN
ejpam-4624	322	33	∈	∈	PROPN
ejpam-4624	322	34	i1	i1	PROPN
ejpam-4624	322	35	.	.	PUNCT
ejpam-4624	323	1	then	then	ADV
ejpam-4624	323	2	µ	µ	X
ejpam-4624	323	3	=	=	SYM
ejpam-4624	323	4	δct1,t	δct1,t	NOUN
ejpam-4624	323	5	∗	∗	NOUN
ejpam-4624	323	6	1	1	NUM
ejpam-4624	323	7	(	(	PUNCT
ejpam-4624	323	8	µ	µ	NOUN
ejpam-4624	323	9	,	,	PUNCT
ejpam-4624	323	10	r0	r0	NOUN
ejpam-4624	323	11	,	,	PUNCT
ejpam-4624	323	12	s1	s1	NOUN
ejpam-4624	323	13	)	)	PUNCT
ejpam-4624	323	14	.	.	PUNCT
ejpam-4624	324	1	but	but	CCONJ
ejpam-4624	324	2	,	,	PUNCT
ejpam-4624	324	3	by	by	ADP
ejpam-4624	324	4	theorem	theorem	NOUN
ejpam-4624	324	5	3.3	3.3	NUM
ejpam-4624	324	6	we	we	PRON
ejpam-4624	324	7	have	have	VERB
ejpam-4624	324	8	δct1,t	δct1,t	NOUN
ejpam-4624	324	9	∗	∗	NOUN
ejpam-4624	324	10	1	1	NUM
ejpam-4624	324	11	(	(	PUNCT
ejpam-4624	324	12	f−1(µ	f−1(µ	PROPN
ejpam-4624	324	13	)	)	PUNCT
ejpam-4624	324	14	,	,	PUNCT
ejpam-4624	324	15	r0	r0	NOUN
ejpam-4624	324	16	,	,	PUNCT
ejpam-4624	324	17	s1	s1	NOUN
ejpam-4624	324	18	)	)	PUNCT
ejpam-4624	324	19	≤	≤	PUNCT
ejpam-4624	324	20	f−1(δct1,t	f−1(δct1,t	PROPN
ejpam-4624	324	21	∗	∗	NOUN
ejpam-4624	324	22	1	1	NUM
ejpam-4624	324	23	(	(	PUNCT
ejpam-4624	324	24	µ	µ	NOUN
ejpam-4624	324	25	,	,	PUNCT
ejpam-4624	324	26	r0	r0	NOUN
ejpam-4624	324	27	,	,	PUNCT
ejpam-4624	324	28	s1	s1	NOUN
ejpam-4624	324	29	)	)	PUNCT
ejpam-4624	324	30	)	)	PUNCT
ejpam-4624	325	1	=	=	SYM
ejpam-4624	325	2	f−1(µ	f−1(µ	PROPN
ejpam-4624	325	3	)	)	PUNCT
ejpam-4624	325	4	.	.	PUNCT
ejpam-4624	326	1	hence	hence	ADV
ejpam-4624	326	2	f−1(µ)=	f−1(µ)=	ADJ
ejpam-4624	326	3	δct1,t	δct1,t	NOUN
ejpam-4624	326	4	∗	∗	NOUN
ejpam-4624	326	5	1	1	NUM
ejpam-4624	326	6	(	(	PUNCT
ejpam-4624	326	7	µ	µ	NOUN
ejpam-4624	326	8	,	,	PUNCT
ejpam-4624	326	9	r0	r0	NOUN
ejpam-4624	326	10	,	,	PUNCT
ejpam-4624	326	11	s1	s1	NOUN
ejpam-4624	326	12	)	)	PUNCT
ejpam-4624	326	13	.	.	PUNCT
ejpam-4624	327	1	so	so	ADV
ejpam-4624	327	2	we	we	PRON
ejpam-4624	327	3	get	get	VERB
ejpam-4624	327	4	,	,	PUNCT
ejpam-4624	327	5	f−1(µ	f−1(µ	PROPN
ejpam-4624	327	6	)	)	PUNCT
ejpam-4624	327	7	is	be	AUX
ejpam-4624	327	8	an	an	DET
ejpam-4624	327	9	(	(	PUNCT
ejpam-4624	327	10	r0	r0	NOUN
ejpam-4624	327	11	,	,	PUNCT
ejpam-4624	327	12	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	327	13	δ	δ	NOUN
ejpam-4624	327	14	-	-	PUNCT
ejpam-4624	327	15	closed	close	VERB
ejpam-4624	327	16	set	set	NOUN
ejpam-4624	327	17	in	in	ADP
ejpam-4624	327	18	ix	ix	PROPN
ejpam-4624	327	19	.	.	PUNCT
ejpam-4624	328	1	(	(	PUNCT
ejpam-4624	328	2	2	2	X
ejpam-4624	328	3	)	)	PUNCT
ejpam-4624	328	4	⇒	⇒	NOUN
ejpam-4624	328	5	(	(	PUNCT
ejpam-4624	328	6	3	3	X
ejpam-4624	328	7	)	)	PUNCT
ejpam-4624	328	8	trivial	trivial	ADJ
ejpam-4624	328	9	by	by	ADP
ejpam-4624	328	10	taking	take	VERB
ejpam-4624	328	11	the	the	DET
ejpam-4624	328	12	complement	complement	NOUN
ejpam-4624	328	13	of	of	ADP
ejpam-4624	328	14	(	(	PUNCT
ejpam-4624	328	15	r0	r0	NOUN
ejpam-4624	328	16	,	,	PUNCT
ejpam-4624	328	17	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	328	18	δ	δ	NOUN
ejpam-4624	328	19	-	-	PUNCT
ejpam-4624	328	20	closed	close	VERB
ejpam-4624	328	21	set	set	NOUN
ejpam-4624	328	22	to	to	PART
ejpam-4624	328	23	be	be	AUX
ejpam-4624	328	24	an	an	DET
ejpam-4624	328	25	(	(	PUNCT
ejpam-4624	328	26	r0	r0	NOUN
ejpam-4624	328	27	,	,	PUNCT
ejpam-4624	328	28	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	328	29	δ	δ	NOUN
ejpam-4624	328	30	-	-	ADJ
ejpam-4624	328	31	open	open	ADJ
ejpam-4624	328	32	set	set	NOUN
ejpam-4624	328	33	.	.	PUNCT
ejpam-4624	329	1	(	(	PUNCT
ejpam-4624	329	2	3	3	X
ejpam-4624	329	3	)	)	PUNCT
ejpam-4624	329	4	⇒	⇒	NOUN
ejpam-4624	329	5	(	(	PUNCT
ejpam-4624	329	6	1	1	X
ejpam-4624	329	7	)	)	PUNCT
ejpam-4624	329	8	let	let	VERB
ejpam-4624	329	9	x(α	x(α	PROPN
ejpam-4624	329	10	,	,	PUNCT
ejpam-4624	329	11	β	β	X
ejpam-4624	329	12	)	)	PUNCT
ejpam-4624	329	13	be	be	VERB
ejpam-4624	329	14	a	a	DET
ejpam-4624	329	15	fuzzy	fuzzy	ADJ
ejpam-4624	329	16	point	point	NOUN
ejpam-4624	329	17	in	in	ADP
ejpam-4624	329	18	ix	ix	ADV
ejpam-4624	329	19	and	and	CCONJ
ejpam-4624	329	20	let	let	VERB
ejpam-4624	329	21	γ	γ	NOUN
ejpam-4624	329	22	be	be	AUX
ejpam-4624	329	23	an	an	DET
ejpam-4624	329	24	(	(	PUNCT
ejpam-4624	329	25	r0	r0	NOUN
ejpam-4624	329	26	,	,	PUNCT
ejpam-4624	329	27	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	329	28	regular	regular	ADJ
ejpam-4624	329	29	-	-	PUNCT
ejpam-4624	329	30	open	open	ADJ
ejpam-4624	329	31	qneighborhood	qneighborhood	NOUN
ejpam-4624	329	32	of	of	ADP
ejpam-4624	329	33	f(x(α	f(x(α	PROPN
ejpam-4624	329	34	,	,	PUNCT
ejpam-4624	329	35	β	β	NOUN
ejpam-4624	329	36	)	)	PUNCT
ejpam-4624	329	37	)	)	PUNCT
ejpam-4624	329	38	for	for	ADP
ejpam-4624	329	39	each	each	DET
ejpam-4624	329	40	γ	γ	PROPN
ejpam-4624	329	41	∈	∈	PROPN
ejpam-4624	329	42	i	i	PRON
ejpam-4624	329	43	,	,	PUNCT
ejpam-4624	329	44	r0	r0	PROPN
ejpam-4624	329	45	∈	∈	PROPN
ejpam-4624	329	46	i0	i0	PROPN
ejpam-4624	329	47	,	,	PUNCT
ejpam-4624	329	48	s1	s1	PROPN
ejpam-4624	329	49	∈	∈	PROPN
ejpam-4624	329	50	i1	i1	PROPN
ejpam-4624	329	51	.	.	PUNCT
ejpam-4624	330	1	but	but	CCONJ
ejpam-4624	330	2	,	,	PUNCT
ejpam-4624	330	3	γ	γ	PROPN
ejpam-4624	330	4	is	be	AUX
ejpam-4624	330	5	an	an	DET
ejpam-4624	330	6	(	(	PUNCT
ejpam-4624	330	7	r0	r0	NOUN
ejpam-4624	330	8	,	,	PUNCT
ejpam-4624	330	9	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	330	10	δ	δ	NOUN
ejpam-4624	330	11	-	-	ADJ
ejpam-4624	330	12	open	open	ADJ
ejpam-4624	330	13	set	set	NOUN
ejpam-4624	330	14	in	in	ADP
ejpam-4624	330	15	iy	iy	PROPN
ejpam-4624	330	16	and	and	CCONJ
ejpam-4624	330	17	by	by	ADP
ejpam-4624	330	18	hypothesis	hypothesis	NOUN
ejpam-4624	330	19	,	,	PUNCT
ejpam-4624	330	20	f−1(γ	f−1(γ	NOUN
ejpam-4624	330	21	)	)	PUNCT
ejpam-4624	330	22	is	be	AUX
ejpam-4624	330	23	an	an	DET
ejpam-4624	330	24	(	(	PUNCT
ejpam-4624	330	25	r0	r0	NOUN
ejpam-4624	330	26	,	,	PUNCT
ejpam-4624	330	27	s1)-fuzzy	s1)-fuzzy	PROPN
ejpam-4624	330	28	δ	δ	NOUN
ejpam-4624	330	29	-	-	ADJ
ejpam-4624	330	30	open	open	ADJ
ejpam-4624	330	31	set	set	NOUN
ejpam-4624	330	32	in	in	ADP
ejpam-4624	330	33	ix	ix	PROPN
ejpam-4624	330	34	.	.	PUNCT
ejpam-4624	331	1	since	since	SCONJ
ejpam-4624	331	2	x(α	x(α	PROPN
ejpam-4624	331	3	,	,	PUNCT
ejpam-4624	331	4	β	β	X
ejpam-4624	331	5	)	)	PUNCT
ejpam-4624	331	6	q	q	PROPN
ejpam-4624	331	7	f−1(γ	f−1(γ	NOUN
ejpam-4624	331	8	)	)	PUNCT
ejpam-4624	331	9	so	so	SCONJ
ejpam-4624	331	10	we	we	PRON
ejpam-4624	331	11	get	get	VERB
ejpam-4624	331	12	,	,	PUNCT
ejpam-4624	331	13	f−1(γ	f−1(γ	NOUN
ejpam-4624	331	14	)	)	PUNCT
ejpam-4624	332	1	is	be	AUX
ejpam-4624	332	2	(	(	PUNCT
ejpam-4624	332	3	r0	r0	NOUN
ejpam-4624	332	4	,	,	PUNCT
ejpam-4624	332	5	s1)fuzzy	s1)fuzzy	PROPN
ejpam-4624	332	6	δ	δ	PROPN
ejpam-4624	332	7	-	-	PUNCT
ejpam-4624	332	8	neighborhood	neighborhood	NOUN
ejpam-4624	332	9	of	of	ADP
ejpam-4624	332	10	x(α	x(α	PROPN
ejpam-4624	332	11	,	,	PUNCT
ejpam-4624	332	12	β	β	NOUN
ejpam-4624	332	13	)	)	PUNCT
ejpam-4624	332	14	.	.	PUNCT
ejpam-4624	333	1	therefore	therefore	ADV
ejpam-4624	333	2	,	,	PUNCT
ejpam-4624	333	3	there	there	PRON
ejpam-4624	333	4	exists	exist	VERB
ejpam-4624	333	5	an	an	DET
ejpam-4624	333	6	(	(	PUNCT
ejpam-4624	333	7	r0	r0	NOUN
ejpam-4624	333	8	,	,	PUNCT
ejpam-4624	333	9	s1)fuzzy	s1)fuzzy	ADJ
ejpam-4624	333	10	regular	regular	ADJ
ejpam-4624	333	11	-	-	PUNCT
ejpam-4624	333	12	neighborhood	neighborhood	NOUN
ejpam-4624	333	13	of	of	ADP
ejpam-4624	333	14	µ	µ	NOUN
ejpam-4624	333	15	of	of	ADP
ejpam-4624	333	16	x(α	x(α	PROPN
ejpam-4624	333	17	,	,	PUNCT
ejpam-4624	333	18	β)such	β)such	PUNCT
ejpam-4624	333	19	that	that	PRON
ejpam-4624	333	20	µ≤	µ≤	PROPN
ejpam-4624	333	21	f−1(γ	f−1(γ	PROPN
ejpam-4624	333	22	,	,	PUNCT
ejpam-4624	333	23	r0	r0	NOUN
ejpam-4624	333	24	,	,	PUNCT
ejpam-4624	333	25	s1	s1	PROPN
ejpam-4624	333	26	)	)	PUNCT
ejpam-4624	333	27	.	.	PUNCT
ejpam-4624	334	1	hence	hence	ADV
ejpam-4624	334	2	,	,	PUNCT
ejpam-4624	334	3	f(µ	f(µ	NUM
ejpam-4624	334	4	)	)	PUNCT
ejpam-4624	334	5	≤	≤	NUM
ejpam-4624	334	6	γ	γ	PROPN
ejpam-4624	334	7	.	.	PUNCT
ejpam-4624	334	8	theorem	theorem	VERB
ejpam-4624	334	9	3.5	3.5	NUM
ejpam-4624	334	10	.	.	PUNCT
ejpam-4624	335	1	let	let	AUX
ejpam-4624	335	2	f	f	NOUN
ejpam-4624	335	3	:	:	PUNCT
ejpam-4624	335	4	(	(	PUNCT
ejpam-4624	335	5	x	x	X
ejpam-4624	335	6	,	,	PUNCT
ejpam-4624	335	7	τx	τx	NOUN
ejpam-4624	335	8	,	,	PUNCT
ejpam-4624	335	9	τx∗	τx∗	ADJ
ejpam-4624	335	10	)	)	PUNCT
ejpam-4624	335	11	→	→	SYM
ejpam-4624	335	12	(	(	PUNCT
ejpam-4624	335	13	y	y	PROPN
ejpam-4624	335	14	,	,	PUNCT
ejpam-4624	335	15	τy	τy	X
ejpam-4624	335	16	,	,	PUNCT
ejpam-4624	335	17	τy∗	τy∗	ADV
ejpam-4624	335	18	)	)	PUNCT
ejpam-4624	335	19	be	be	AUX
ejpam-4624	335	20	a	a	DET
ejpam-4624	335	21	bijection	bijection	ADJ
ejpam-4624	335	22	function	function	NOUN
ejpam-4624	335	23	.	.	PUNCT
ejpam-4624	336	1	then	then	ADV
ejpam-4624	336	2	the	the	DET
ejpam-4624	336	3	following	follow	VERB
ejpam-4624	336	4	statements	statement	NOUN
ejpam-4624	336	5	are	be	AUX
ejpam-4624	336	6	equivalent	equivalent	ADJ
ejpam-4624	336	7	:	:	PUNCT
ejpam-4624	336	8	(	(	PUNCT
ejpam-4624	336	9	i	i	NOUN
ejpam-4624	336	10	)	)	PUNCT
ejpam-4624	336	11	f	f	PROPN
ejpam-4624	336	12	is	be	AUX
ejpam-4624	336	13	double	double	ADJ
ejpam-4624	336	14	fuzzy	fuzzy	ADJ
ejpam-4624	336	15	δ	δ	NOUN
ejpam-4624	336	16	-	-	ADJ
ejpam-4624	336	17	continuous	continuous	ADJ
ejpam-4624	336	18	function	function	NOUN
ejpam-4624	336	19	,	,	PUNCT
ejpam-4624	336	20	(	(	PUNCT
ejpam-4624	336	21	ii	ii	NOUN
ejpam-4624	336	22	)	)	PUNCT
ejpam-4624	336	23	δiτx	δiτx	NOUN
ejpam-4624	336	24	,	,	PUNCT
ejpam-4624	336	25	τx∗(λ	τx∗(λ	PROPN
ejpam-4624	336	26	,	,	PUNCT
ejpam-4624	336	27	r0	r0	NOUN
ejpam-4624	336	28	,	,	PUNCT
ejpam-4624	336	29	s1)=f(δiτx	s1)=f(δiτx	NOUN
ejpam-4624	336	30	,	,	PUNCT
ejpam-4624	336	31	τx∗(λ	τx∗(λ	PROPN
ejpam-4624	336	32	,	,	PUNCT
ejpam-4624	336	33	r0	r0	NOUN
ejpam-4624	336	34	,	,	PUNCT
ejpam-4624	336	35	s1	s1	NOUN
ejpam-4624	336	36	)	)	PUNCT
ejpam-4624	336	37	)	)	PUNCT
ejpam-4624	336	38	for	for	ADP
ejpam-4624	336	39	each	each	DET
ejpam-4624	336	40	(	(	PUNCT
ejpam-4624	336	41	r0	r0	NOUN
ejpam-4624	336	42	,	,	PUNCT
ejpam-4624	336	43	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	336	44	set	set	NOUN
ejpam-4624	336	45	λ	λ	PROPN
ejpam-4624	336	46	in	in	ADP
ejpam-4624	336	47	ix	ix	PROPN
ejpam-4624	336	48	,	,	PUNCT
ejpam-4624	336	49	r0	r0	PROPN
ejpam-4624	336	50	∈	∈	PROPN
ejpam-4624	336	51	i0	i0	PROPN
ejpam-4624	336	52	,	,	PUNCT
ejpam-4624	336	53	s1	s1	PROPN
ejpam-4624	336	54	∈	∈	PROPN
ejpam-4624	336	55	i1	i1	PROPN
ejpam-4624	336	56	.	.	PUNCT
ejpam-4624	337	1	proof	proof	NOUN
ejpam-4624	337	2	.	.	PUNCT
ejpam-4624	338	1	(	(	PUNCT
ejpam-4624	338	2	1	1	X
ejpam-4624	338	3	)	)	PUNCT
ejpam-4624	338	4	⇒	⇒	NOUN
ejpam-4624	338	5	(	(	PUNCT
ejpam-4624	338	6	2	2	X
ejpam-4624	338	7	)	)	PUNCT
ejpam-4624	338	8	let	let	VERB
ejpam-4624	338	9	λ	λ	NOUN
ejpam-4624	338	10	be	be	AUX
ejpam-4624	338	11	an	an	DET
ejpam-4624	338	12	(	(	PUNCT
ejpam-4624	338	13	r0	r0	NOUN
ejpam-4624	338	14	,	,	PUNCT
ejpam-4624	338	15	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	338	16	set	set	VERB
ejpam-4624	338	17	in	in	ADP
ejpam-4624	338	18	ix	ix	PROPN
ejpam-4624	338	19	,	,	PUNCT
ejpam-4624	338	20	r0	r0	PROPN
ejpam-4624	338	21	∈	∈	PROPN
ejpam-4624	338	22	i0	i0	PROPN
ejpam-4624	338	23	,	,	PUNCT
ejpam-4624	338	24	s1	s1	PROPN
ejpam-4624	338	25	∈	∈	PROPN
ejpam-4624	338	26	i1	i1	PROPN
ejpam-4624	338	27	.	.	PUNCT
ejpam-4624	339	1	then	then	ADV
ejpam-4624	339	2	f(λ	f(λ	PROPN
ejpam-4624	339	3	)	)	PUNCT
ejpam-4624	339	4	(	(	PUNCT
ejpam-4624	339	5	r0	r0	NOUN
ejpam-4624	339	6	,	,	PUNCT
ejpam-4624	339	7	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	339	8	set	set	NOUN
ejpam-4624	339	9	λ	λ	PROPN
ejpam-4624	339	10	in	in	ADP
ejpam-4624	339	11	iy	iy	PROPN
ejpam-4624	339	12	.	.	PUNCT
ejpam-4624	340	1	but	but	CCONJ
ejpam-4624	340	2	,	,	PUNCT
ejpam-4624	340	3	f	f	PROPN
ejpam-4624	340	4	is	be	AUX
ejpam-4624	340	5	oneto	oneto	NOUN
ejpam-4624	340	6	-	-	PUNCT
ejpam-4624	340	7	one	one	NUM
ejpam-4624	340	8	,	,	PUNCT
ejpam-4624	340	9	then	then	ADV
ejpam-4624	340	10	f−1(δiτx	f−1(δiτx	VERB
ejpam-4624	340	11	,	,	PUNCT
ejpam-4624	340	12	τx∗(f(λ	τx∗(f(λ	NUM
ejpam-4624	340	13	)	)	PUNCT
ejpam-4624	340	14	,	,	PUNCT
ejpam-4624	340	15	r0	r0	NOUN
ejpam-4624	340	16	,	,	PUNCT
ejpam-4624	340	17	s1	s1	NOUN
ejpam-4624	340	18	)	)	PUNCT
ejpam-4624	340	19	≤	≤	NUM
ejpam-4624	340	20	δiτy	δiτy	NOUN
ejpam-4624	340	21	,	,	PUNCT
ejpam-4624	340	22	τy∗(f	τy∗(f	PRON
ejpam-4624	340	23	−	−	PROPN
ejpam-4624	340	24	1(f(λ	1(f(λ	NUM
ejpam-4624	340	25	)	)	PUNCT
ejpam-4624	340	26	)	)	PUNCT
ejpam-4624	340	27	,	,	PUNCT
ejpam-4624	340	28	r0	r0	NOUN
ejpam-4624	340	29	,	,	PUNCT
ejpam-4624	340	30	s1	s1	NOUN
ejpam-4624	340	31	)	)	PUNCT
ejpam-4624	340	32	=	=	SYM
ejpam-4624	340	33	δiτx	δiτx	NOUN
ejpam-4624	340	34	,	,	PUNCT
ejpam-4624	340	35	τx∗(λ	τx∗(λ	PROPN
ejpam-4624	340	36	,	,	PUNCT
ejpam-4624	340	37	r0	r0	NOUN
ejpam-4624	340	38	,	,	PUNCT
ejpam-4624	340	39	s1	s1	PROPN
ejpam-4624	340	40	)	)	PUNCT
ejpam-4624	340	41	.	.	PUNCT
ejpam-4624	341	1	since	since	SCONJ
ejpam-4624	341	2	f	f	PROPN
ejpam-4624	341	3	is	be	AUX
ejpam-4624	341	4	onto	onto	ADP
ejpam-4624	341	5	,	,	PUNCT
ejpam-4624	341	6	so	so	ADV
ejpam-4624	341	7	w.	w.	PROPN
ejpam-4624	341	8	f.	f.	PROPN
ejpam-4624	341	9	al	al	PROPN
ejpam-4624	341	10	-	-	PUNCT
ejpam-4624	341	11	omeri	omeri	ADJ
ejpam-4624	341	12	/	/	SYM
ejpam-4624	341	13	eur	eur	PROPN
ejpam-4624	341	14	.	.	PUNCT
ejpam-4624	342	1	j.	j.	PROPN
ejpam-4624	342	2	pure	pure	PROPN
ejpam-4624	342	3	appl	appl	PROPN
ejpam-4624	342	4	.	.	PROPN
ejpam-4624	342	5	math	math	PROPN
ejpam-4624	342	6	,	,	PUNCT
ejpam-4624	342	7	18	18	NUM
ejpam-4624	342	8	(	(	PUNCT
ejpam-4624	342	9	2	2	NUM
ejpam-4624	342	10	)	)	PUNCT
ejpam-4624	342	11	(	(	PUNCT
ejpam-4624	342	12	2025	2025	NUM
ejpam-4624	342	13	)	)	PUNCT
ejpam-4624	342	14	,	,	PUNCT
ejpam-4624	342	15	4624	4624	NUM
ejpam-4624	342	16	13	13	NUM
ejpam-4624	342	17	of	of	ADP
ejpam-4624	342	18	15	15	NUM
ejpam-4624	342	19	δiτx	δiτx	NOUN
ejpam-4624	342	20	,	,	PUNCT
ejpam-4624	342	21	τx∗(f(λ	τx∗(f(λ	ADJ
ejpam-4624	342	22	)	)	PUNCT
ejpam-4624	342	23	,	,	PUNCT
ejpam-4624	342	24	r0	r0	NOUN
ejpam-4624	342	25	,	,	PUNCT
ejpam-4624	342	26	s1	s1	NOUN
ejpam-4624	342	27	)	)	PUNCT
ejpam-4624	342	28	=	=	SYM
ejpam-4624	342	29	f(f−1(iτy	f(f−1(iτy	NOUN
ejpam-4624	342	30	,	,	PUNCT
ejpam-4624	342	31	τy∗(f(λ	τy∗(f(λ	ADJ
ejpam-4624	342	32	)	)	PUNCT
ejpam-4624	342	33	,	,	PUNCT
ejpam-4624	342	34	r0	r0	NOUN
ejpam-4624	342	35	,	,	PUNCT
ejpam-4624	342	36	s1	s1	NOUN
ejpam-4624	342	37	)	)	PUNCT
ejpam-4624	342	38	)	)	PUNCT
ejpam-4624	342	39	)	)	PUNCT
ejpam-4624	343	1	≤	≤	NUM
ejpam-4624	343	2	f(iτx	f(iτx	NOUN
ejpam-4624	343	3	,	,	PUNCT
ejpam-4624	343	4	τx∗(λ	τx∗(λ	PROPN
ejpam-4624	343	5	,	,	PUNCT
ejpam-4624	343	6	r0	r0	NOUN
ejpam-4624	343	7	,	,	PUNCT
ejpam-4624	343	8	s1	s1	PROPN
ejpam-4624	343	9	)	)	PUNCT
ejpam-4624	343	10	.	.	PUNCT
ejpam-4624	344	1	(	(	PUNCT
ejpam-4624	344	2	2	2	X
ejpam-4624	344	3	)	)	PUNCT
ejpam-4624	344	4	⇒	⇒	NOUN
ejpam-4624	344	5	(	(	PUNCT
ejpam-4624	344	6	1	1	X
ejpam-4624	344	7	)	)	PUNCT
ejpam-4624	344	8	let	let	VERB
ejpam-4624	344	9	λ	λ	NOUN
ejpam-4624	344	10	be	be	AUX
ejpam-4624	344	11	an	an	DET
ejpam-4624	344	12	(	(	PUNCT
ejpam-4624	344	13	r0	r0	NOUN
ejpam-4624	344	14	,	,	PUNCT
ejpam-4624	344	15	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	344	16	set	set	VERB
ejpam-4624	344	17	in	in	ADP
ejpam-4624	344	18	iy	iy	PROPN
ejpam-4624	344	19	,	,	PUNCT
ejpam-4624	344	20	r0	r0	PROPN
ejpam-4624	344	21	∈	∈	PROPN
ejpam-4624	344	22	i0	i0	PROPN
ejpam-4624	344	23	,	,	PUNCT
ejpam-4624	344	24	s1	s1	PROPN
ejpam-4624	344	25	∈	∈	PROPN
ejpam-4624	344	26	i1	i1	PROPN
ejpam-4624	344	27	.	.	PUNCT
ejpam-4624	345	1	then	then	ADV
ejpam-4624	345	2	f−1(λ	f−1(λ	PROPN
ejpam-4624	345	3	)	)	PUNCT
ejpam-4624	345	4	is	be	AUX
ejpam-4624	345	5	an	an	DET
ejpam-4624	345	6	(	(	PUNCT
ejpam-4624	345	7	r0	r0	NOUN
ejpam-4624	345	8	,	,	PUNCT
ejpam-4624	345	9	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	345	10	set	set	NOUN
ejpam-4624	345	11	λ	λ	PROPN
ejpam-4624	345	12	in	in	ADP
ejpam-4624	345	13	iy	iy	PROPN
ejpam-4624	345	14	.	.	PUNCT
ejpam-4624	346	1	but	but	CCONJ
ejpam-4624	346	2	by	by	ADP
ejpam-4624	346	3	hypothesis	hypothesis	NOUN
ejpam-4624	346	4	,	,	PUNCT
ejpam-4624	346	5	δiτy	δiτy	VERB
ejpam-4624	346	6	,	,	PUNCT
ejpam-4624	346	7	τy∗	τy∗	PROPN
ejpam-4624	346	8	(	(	PUNCT
ejpam-4624	346	9	λ	λ	PROPN
ejpam-4624	346	10	,	,	PUNCT
ejpam-4624	346	11	r0	r0	NOUN
ejpam-4624	346	12	,	,	PUNCT
ejpam-4624	346	13	s1	s1	NOUN
ejpam-4624	346	14	)	)	PUNCT
ejpam-4624	346	15	=	=	SYM
ejpam-4624	346	16	δiτx	δiτx	NOUN
ejpam-4624	346	17	,	,	PUNCT
ejpam-4624	347	1	τx∗(f(f	τx∗(f(f	PROPN
ejpam-4624	347	2	−	−	PROPN
ejpam-4624	347	3	1(λ	1(λ	NUM
ejpam-4624	347	4	,	,	PUNCT
ejpam-4624	347	5	r0	r0	NOUN
ejpam-4624	347	6	,	,	PUNCT
ejpam-4624	347	7	s1	s1	NOUN
ejpam-4624	347	8	)	)	PUNCT
ejpam-4624	347	9	≤	≤	NUM
ejpam-4624	347	10	f(δiτy	f(δiτy	NOUN
ejpam-4624	347	11	,	,	PUNCT
ejpam-4624	347	12	τy∗(f	τy∗(f	ADJ
ejpam-4624	347	13	−1(λ	−1(λ	NOUN
ejpam-4624	347	14	)	)	PUNCT
ejpam-4624	347	15	,	,	PUNCT
ejpam-4624	347	16	r0	r0	NOUN
ejpam-4624	347	17	,	,	PUNCT
ejpam-4624	347	18	s1	s1	NOUN
ejpam-4624	347	19	)	)	PUNCT
ejpam-4624	347	20	)	)	PUNCT
ejpam-4624	347	21	)	)	PUNCT
ejpam-4624	348	1	for	for	ADP
ejpam-4624	348	2	each	each	DET
ejpam-4624	348	3	(	(	PUNCT
ejpam-4624	348	4	r0	r0	NOUN
ejpam-4624	348	5	,	,	PUNCT
ejpam-4624	348	6	s1)-fuzzy	s1)-fuzzy	X
ejpam-4624	348	7	set	set	NOUN
ejpam-4624	348	8	λ	λ	PROPN
ejpam-4624	348	9	in	in	ADP
ejpam-4624	348	10	ix	ix	PROPN
ejpam-4624	348	11	,	,	PUNCT
ejpam-4624	348	12	r0	r0	PROPN
ejpam-4624	348	13	∈	∈	PROPN
ejpam-4624	348	14	i0	i0	PROPN
ejpam-4624	348	15	,	,	PUNCT
ejpam-4624	348	16	s1	s1	PROPN
ejpam-4624	348	17	∈	∈	PROPN
ejpam-4624	348	18	i1	i1	PROPN
ejpam-4624	348	19	.	.	PUNCT
ejpam-4624	349	1	but	but	CCONJ
ejpam-4624	349	2	f	f	PROPN
ejpam-4624	349	3	is	be	AUX
ejpam-4624	349	4	one	one	NUM
ejpam-4624	349	5	-to	-to	ADJ
ejpam-4624	349	6	-	-	PUNCT
ejpam-4624	349	7	one	one	NUM
ejpam-4624	349	8	function	function	NOUN
ejpam-4624	349	9	,	,	PUNCT
ejpam-4624	349	10	then	then	ADV
ejpam-4624	349	11	f−1(δiτy	f−1(δiτy	NUM
ejpam-4624	349	12	,	,	PUNCT
ejpam-4624	349	13	τy∗(λ	τy∗(λ	NOUN
ejpam-4624	349	14	,	,	PUNCT
ejpam-4624	349	15	r0	r0	NOUN
ejpam-4624	349	16	,	,	PUNCT
ejpam-4624	349	17	s1	s1	NOUN
ejpam-4624	349	18	)	)	PUNCT
ejpam-4624	349	19	≤	≤	NOUN
ejpam-4624	349	20	f−1(f(δiτx	f−1(f(δiτx	PROPN
ejpam-4624	349	21	,	,	PUNCT
ejpam-4624	349	22	τx∗(f	τx∗(f	PRON
ejpam-4624	349	23	−1(λ	−1(λ	NOUN
ejpam-4624	349	24	)	)	PUNCT
ejpam-4624	349	25	,	,	PUNCT
ejpam-4624	349	26	r0	r0	NOUN
ejpam-4624	349	27	,	,	PUNCT
ejpam-4624	349	28	s1	s1	NOUN
ejpam-4624	349	29	)	)	PUNCT
ejpam-4624	349	30	)	)	PUNCT
ejpam-4624	349	31	)	)	PUNCT
ejpam-4624	350	1	=	=	PUNCT
ejpam-4624	350	2	δiτy	δiτy	NOUN
ejpam-4624	350	3	,	,	PUNCT
ejpam-4624	350	4	τy∗(f	τy∗(f	ADJ
ejpam-4624	350	5	−1(λ	−1(λ	NOUN
ejpam-4624	350	6	)	)	PUNCT
ejpam-4624	350	7	,	,	PUNCT
ejpam-4624	350	8	r0	r0	NOUN
ejpam-4624	350	9	,	,	PUNCT
ejpam-4624	350	10	s1	s1	NOUN
ejpam-4624	350	11	)	)	PUNCT
ejpam-4624	350	12	hence	hence	ADV
ejpam-4624	350	13	by	by	ADP
ejpam-4624	350	14	theorem	theorem	ADJ
ejpam-4624	350	15	3.3	3.3	NUM
ejpam-4624	350	16	,	,	PUNCT
ejpam-4624	350	17	f	f	PROPN
ejpam-4624	350	18	is	be	AUX
ejpam-4624	350	19	double	double	ADJ
ejpam-4624	350	20	fuzzy	fuzzy	ADJ
ejpam-4624	350	21	δ	δ	NOUN
ejpam-4624	350	22	-	-	ADJ
ejpam-4624	350	23	continuous	continuous	ADJ
ejpam-4624	350	24	function	function	NOUN
ejpam-4624	350	25	.	.	PUNCT
ejpam-4624	351	1	remark	remark	NOUN
ejpam-4624	351	2	3.6	3.6	NUM
ejpam-4624	351	3	.	.	PUNCT
ejpam-4624	352	1	the	the	DET
ejpam-4624	352	2	concepts	concept	NOUN
ejpam-4624	352	3	of	of	ADP
ejpam-4624	352	4	a	a	DET
ejpam-4624	352	5	(	(	PUNCT
ejpam-4624	352	6	r	r	NOUN
ejpam-4624	352	7	,	,	PUNCT
ejpam-4624	352	8	s)-fuzzy	s)-fuzzy	ADV
ejpam-4624	352	9	δ	δ	PROPN
ejpam-4624	352	10	-	-	ADJ
ejpam-4624	352	11	continuous	continuous	ADJ
ejpam-4624	352	12	and	and	CCONJ
ejpam-4624	352	13	a	a	DET
ejpam-4624	352	14	(	(	PUNCT
ejpam-4624	352	15	r	r	NOUN
ejpam-4624	352	16	,	,	PUNCT
ejpam-4624	352	17	s)-fuzzy	s)-fuzzy	NOUN
ejpam-4624	352	18	-	-	ADJ
ejpam-4624	352	19	continuous	continuous	ADJ
ejpam-4624	352	20	are	be	AUX
ejpam-4624	352	21	independent	independent	ADJ
ejpam-4624	352	22	to	to	ADP
ejpam-4624	352	23	each	each	DET
ejpam-4624	352	24	other	other	ADJ
ejpam-4624	352	25	for	for	ADP
ejpam-4624	352	26	each	each	DET
ejpam-4624	352	27	r	r	NOUN
ejpam-4624	352	28	∈	∈	PROPN
ejpam-4624	352	29	i0	i0	PROPN
ejpam-4624	352	30	,	,	PUNCT
ejpam-4624	352	31	s	s	PROPN
ejpam-4624	352	32	∈	∈	PROPN
ejpam-4624	352	33	i1	i1	PROPN
ejpam-4624	352	34	.	.	PUNCT
ejpam-4624	353	1	example	example	NOUN
ejpam-4624	353	2	3.7	3.7	NUM
ejpam-4624	353	3	.	.	PUNCT
ejpam-4624	354	1	let	let	VERB
ejpam-4624	354	2	x	x	PUNCT
ejpam-4624	354	3	=	=	PUNCT
ejpam-4624	355	1	[	[	X
ejpam-4624	355	2	0	0	NUM
ejpam-4624	355	3	,	,	PUNCT
ejpam-4624	355	4	1	1	NUM
ejpam-4624	355	5	]	]	PUNCT
ejpam-4624	355	6	and	and	CCONJ
ejpam-4624	355	7	f	f	X
ejpam-4624	355	8	:	:	PUNCT
ejpam-4624	355	9	(	(	PUNCT
ejpam-4624	355	10	x	x	X
ejpam-4624	355	11	,	,	PUNCT
ejpam-4624	355	12	t1	t1	PROPN
ejpam-4624	355	13	,	,	PUNCT
ejpam-4624	355	14	t	t	PROPN
ejpam-4624	355	15	∗	∗	X
ejpam-4624	355	16	1	1	NUM
ejpam-4624	355	17	)	)	PUNCT
ejpam-4624	355	18	→	→	SYM
ejpam-4624	355	19	(	(	PUNCT
ejpam-4624	355	20	x	x	X
ejpam-4624	355	21	,	,	PUNCT
ejpam-4624	355	22	t2	t2	NOUN
ejpam-4624	355	23	,	,	PUNCT
ejpam-4624	355	24	t	t	PROPN
ejpam-4624	355	25	∗	∗	X
ejpam-4624	355	26	2	2	NUM
ejpam-4624	355	27	)	)	PUNCT
ejpam-4624	355	28	be	be	AUX
ejpam-4624	355	29	the	the	DET
ejpam-4624	355	30	identity	identity	NOUN
ejpam-4624	355	31	function	function	NOUN
ejpam-4624	355	32	(	(	PUNCT
ejpam-4624	355	33	1)define	1)define	NUM
ejpam-4624	355	34	ρ1	ρ1	NOUN
ejpam-4624	355	35	and	and	CCONJ
ejpam-4624	355	36	β1	β1	NOUN
ejpam-4624	355	37	as	as	SCONJ
ejpam-4624	355	38	follows	follow	VERB
ejpam-4624	355	39	:	:	PUNCT
ejpam-4624	355	40	ρ1(0	ρ1(0	NOUN
ejpam-4624	355	41	)	)	PUNCT
ejpam-4624	355	42	=	=	SYM
ejpam-4624	355	43	0.3	0.3	NUM
ejpam-4624	355	44	,	,	PUNCT
ejpam-4624	355	45	ρ1(1	ρ1(1	NOUN
ejpam-4624	355	46	)	)	PUNCT
ejpam-4624	355	47	=	=	NOUN
ejpam-4624	355	48	0.7	0.7	NUM
ejpam-4624	355	49	,	,	PUNCT
ejpam-4624	355	50	β1(0	β1(0	PROPN
ejpam-4624	355	51	)	)	PUNCT
ejpam-4624	355	52	=	=	SYM
ejpam-4624	355	53	0.8	0.8	NUM
ejpam-4624	355	54	,	,	PUNCT
ejpam-4624	355	55	β1(1	β1(1	NUM
ejpam-4624	355	56	)	)	PUNCT
ejpam-4624	355	57	=	=	SYM
ejpam-4624	355	58	0.2	0.2	NUM
ejpam-4624	355	59	,	,	PUNCT
ejpam-4624	355	60	and	and	CCONJ
ejpam-4624	355	61	the	the	DET
ejpam-4624	355	62	two	two	NUM
ejpam-4624	355	63	spaces	space	NOUN
ejpam-4624	355	64	(	(	PUNCT
ejpam-4624	355	65	t1	t1	NOUN
ejpam-4624	355	66	,	,	PUNCT
ejpam-4624	355	67	t	t	PROPN
ejpam-4624	355	68	∗	∗	X
ejpam-4624	355	69	1	1	NUM
ejpam-4624	355	70	)	)	PUNCT
ejpam-4624	355	71	and	and	CCONJ
ejpam-4624	355	72	(	(	PUNCT
ejpam-4624	355	73	t2	t2	PROPN
ejpam-4624	355	74	,	,	PUNCT
ejpam-4624	355	75	t	t	PROPN
ejpam-4624	355	76	∗	∗	X
ejpam-4624	355	77	2	2	NUM
ejpam-4624	355	78	)	)	PUNCT
ejpam-4624	355	79	are	be	AUX
ejpam-4624	355	80	define	define	ADJ
ejpam-4624	355	81	as	as	SCONJ
ejpam-4624	355	82	follows	follow	VERB
ejpam-4624	355	83	:	:	PUNCT
ejpam-4624	355	84	t1(ρ	t1(ρ	X
ejpam-4624	355	85	)	)	PUNCT
ejpam-4624	355	86	=	=	PUNCT
ejpam-4624	356	1			PROPN
ejpam-4624	356	2	1	1	NUM
ejpam-4624	356	3	,	,	PUNCT
ejpam-4624	356	4	if	if	SCONJ
ejpam-4624	356	5	ρ	ρ	PROPN
ejpam-4624	356	6	∈	∈	PROPN
ejpam-4624	356	7	{	{	PUNCT
ejpam-4624	356	8	0	0	NUM
ejpam-4624	356	9	,	,	PUNCT
ejpam-4624	356	10	1	1	NUM
ejpam-4624	356	11	}	}	PUNCT
ejpam-4624	356	12	,	,	PUNCT
ejpam-4624	356	13	1	1	NUM
ejpam-4624	356	14	3	3	NUM
ejpam-4624	356	15	,	,	PUNCT
ejpam-4624	356	16	if	if	SCONJ
ejpam-4624	356	17	ρ	ρ	PROPN
ejpam-4624	356	18	=	=	SYM
ejpam-4624	356	19	ρ1	ρ1	PROPN
ejpam-4624	356	20	,	,	PUNCT
ejpam-4624	356	21	0	0	NUM
ejpam-4624	356	22	,	,	PUNCT
ejpam-4624	356	23	otherwise	otherwise	ADV
ejpam-4624	356	24	.	.	PUNCT
ejpam-4624	357	1	t	t	PROPN
ejpam-4624	357	2	∗	∗	NOUN
ejpam-4624	357	3	1	1	NUM
ejpam-4624	357	4	(	(	PUNCT
ejpam-4624	357	5	ρ	ρ	NOUN
ejpam-4624	357	6	)	)	PUNCT
ejpam-4624	357	7	=	=	PUNCT
ejpam-4624	358	1			PROPN
ejpam-4624	358	2	0	0	NUM
ejpam-4624	358	3	,	,	PUNCT
ejpam-4624	358	4	if	if	SCONJ
ejpam-4624	358	5	ρ	ρ	PROPN
ejpam-4624	358	6	∈	∈	PROPN
ejpam-4624	358	7	{	{	PUNCT
ejpam-4624	358	8	0	0	NUM
ejpam-4624	358	9	,	,	PUNCT
ejpam-4624	358	10	1	1	NUM
ejpam-4624	358	11	}	}	PUNCT
ejpam-4624	358	12	,	,	PUNCT
ejpam-4624	358	13	2	2	NUM
ejpam-4624	358	14	3	3	NUM
ejpam-4624	358	15	,	,	PUNCT
ejpam-4624	358	16	if	if	SCONJ
ejpam-4624	358	17	ρ	ρ	PROPN
ejpam-4624	358	18	=	=	SYM
ejpam-4624	358	19	ρ1	ρ1	PROPN
ejpam-4624	358	20	,	,	PUNCT
ejpam-4624	358	21	1	1	NUM
ejpam-4624	358	22	,	,	PUNCT
ejpam-4624	358	23	otherwise	otherwise	ADV
ejpam-4624	358	24	.	.	PUNCT
ejpam-4624	359	1	and	and	CCONJ
ejpam-4624	359	2	t2(ρ	t2(ρ	NUM
ejpam-4624	359	3	)	)	PUNCT
ejpam-4624	359	4	=	=	PUNCT
ejpam-4624	359	5			NUM
ejpam-4624	359	6	1	1	NUM
ejpam-4624	359	7	,	,	PUNCT
ejpam-4624	359	8	if	if	SCONJ
ejpam-4624	359	9	ρ	ρ	PROPN
ejpam-4624	359	10	∈	∈	PROPN
ejpam-4624	359	11	{	{	PUNCT
ejpam-4624	359	12	0	0	NUM
ejpam-4624	359	13	,	,	PUNCT
ejpam-4624	359	14	1	1	NUM
ejpam-4624	359	15	}	}	PUNCT
ejpam-4624	359	16	,	,	PUNCT
ejpam-4624	359	17	1	1	NUM
ejpam-4624	359	18	3	3	NUM
ejpam-4624	359	19	,	,	PUNCT
ejpam-4624	359	20	if	if	SCONJ
ejpam-4624	359	21	ρ	ρ	PROPN
ejpam-4624	359	22	=	=	SYM
ejpam-4624	359	23	ρ1	ρ1	PROPN
ejpam-4624	359	24	,	,	PUNCT
ejpam-4624	359	25	8	8	NUM
ejpam-4624	359	26	10	10	NUM
ejpam-4624	359	27	,	,	PUNCT
ejpam-4624	359	28	if	if	SCONJ
ejpam-4624	359	29	ρ	ρ	PROPN
ejpam-4624	359	30	=	=	SYM
ejpam-4624	359	31	β1	β1	PROPN
ejpam-4624	359	32	,	,	PUNCT
ejpam-4624	359	33	0	0	NUM
ejpam-4624	359	34	,	,	PUNCT
ejpam-4624	359	35	otherwise	otherwise	ADV
ejpam-4624	359	36	.	.	PUNCT
ejpam-4624	360	1	t	t	PROPN
ejpam-4624	360	2	∗	∗	NOUN
ejpam-4624	360	3	2	2	NUM
ejpam-4624	360	4	(	(	PUNCT
ejpam-4624	360	5	ρ	ρ	NOUN
ejpam-4624	360	6	)	)	PUNCT
ejpam-4624	360	7	=	=	SYM
ejpam-4624	360	8			X
ejpam-4624	360	9	0	0	NUM
ejpam-4624	360	10	,	,	PUNCT
ejpam-4624	360	11	if	if	SCONJ
ejpam-4624	360	12	ρ	ρ	PROPN
ejpam-4624	360	13	∈	∈	PROPN
ejpam-4624	360	14	{	{	PUNCT
ejpam-4624	360	15	0	0	NUM
ejpam-4624	360	16	,	,	PUNCT
ejpam-4624	360	17	1	1	NUM
ejpam-4624	360	18	}	}	SYM
ejpam-4624	360	19	2	2	NUM
ejpam-4624	360	20	3	3	NUM
ejpam-4624	360	21	,	,	PUNCT
ejpam-4624	360	22	if	if	SCONJ
ejpam-4624	360	23	ρ	ρ	PROPN
ejpam-4624	360	24	=	=	SYM
ejpam-4624	360	25	ρ1	ρ1	NOUN
ejpam-4624	360	26	,	,	PUNCT
ejpam-4624	360	27	2	2	NUM
ejpam-4624	360	28	10	10	NUM
ejpam-4624	360	29	,	,	PUNCT
ejpam-4624	360	30	if	if	SCONJ
ejpam-4624	360	31	ρ	ρ	PROPN
ejpam-4624	360	32	=	=	SYM
ejpam-4624	360	33	β1	β1	PROPN
ejpam-4624	360	34	,	,	PUNCT
ejpam-4624	360	35	1	1	NUM
ejpam-4624	360	36	,	,	PUNCT
ejpam-4624	360	37	otherwise	otherwise	ADV
ejpam-4624	360	38	.	.	PUNCT
ejpam-4624	361	1	then	then	ADV
ejpam-4624	361	2	,	,	PUNCT
ejpam-4624	361	3	f	f	PROPN
ejpam-4624	361	4	is	be	AUX
ejpam-4624	361	5	double	double	ADJ
ejpam-4624	361	6	fuzzy	fuzzy	ADJ
ejpam-4624	361	7	δ	δ	NOUN
ejpam-4624	361	8	-	-	ADJ
ejpam-4624	361	9	continuous	continuous	ADJ
ejpam-4624	361	10	function	function	NOUN
ejpam-4624	361	11	but	but	CCONJ
ejpam-4624	361	12	not	not	PART
ejpam-4624	361	13	double	double	ADJ
ejpam-4624	361	14	fuzzy	fuzzy	ADJ
ejpam-4624	361	15	continuous	continuous	ADJ
ejpam-4624	361	16	function	function	NOUN
ejpam-4624	361	17	.	.	PUNCT
ejpam-4624	362	1	(	(	PUNCT
ejpam-4624	362	2	2)define	2)define	NUM
ejpam-4624	362	3	ρ1	ρ1	NOUN
ejpam-4624	362	4	and	and	CCONJ
ejpam-4624	362	5	β1	β1	NOUN
ejpam-4624	362	6	as	as	SCONJ
ejpam-4624	362	7	follows	follow	VERB
ejpam-4624	362	8	:	:	PUNCT
ejpam-4624	362	9	ρ1(0	ρ1(0	NOUN
ejpam-4624	362	10	)	)	PUNCT
ejpam-4624	362	11	=	=	SYM
ejpam-4624	363	1	0.3	0.3	NUM
ejpam-4624	363	2	,	,	PUNCT
ejpam-4624	363	3	ρ1(1	ρ1(1	NOUN
ejpam-4624	363	4	)	)	PUNCT
ejpam-4624	363	5	=	=	NOUN
ejpam-4624	363	6	0.7	0.7	NUM
ejpam-4624	363	7	,	,	PUNCT
ejpam-4624	363	8	β1(0	β1(0	PROPN
ejpam-4624	363	9	)	)	PUNCT
ejpam-4624	363	10	=	=	SYM
ejpam-4624	363	11	0.5	0.5	NUM
ejpam-4624	363	12	,	,	PUNCT
ejpam-4624	363	13	β1(1	β1(1	NUM
ejpam-4624	363	14	)	)	PUNCT
ejpam-4624	363	15	=	=	SYM
ejpam-4624	363	16	0.5	0.5	NUM
ejpam-4624	363	17	,	,	PUNCT
ejpam-4624	363	18	and	and	CCONJ
ejpam-4624	363	19	the	the	DET
ejpam-4624	363	20	two	two	NUM
ejpam-4624	363	21	spaces	space	NOUN
ejpam-4624	363	22	(	(	PUNCT
ejpam-4624	363	23	t1	t1	NOUN
ejpam-4624	363	24	,	,	PUNCT
ejpam-4624	363	25	t	t	PROPN
ejpam-4624	363	26	∗	∗	X
ejpam-4624	363	27	1	1	NUM
ejpam-4624	363	28	)	)	PUNCT
ejpam-4624	363	29	and	and	CCONJ
ejpam-4624	363	30	(	(	PUNCT
ejpam-4624	363	31	t2	t2	PROPN
ejpam-4624	363	32	,	,	PUNCT
ejpam-4624	363	33	t	t	PROPN
ejpam-4624	363	34	∗	∗	X
ejpam-4624	363	35	2	2	NUM
ejpam-4624	363	36	)	)	PUNCT
ejpam-4624	363	37	are	be	AUX
ejpam-4624	363	38	defined	define	VERB
ejpam-4624	363	39	as	as	SCONJ
ejpam-4624	363	40	follows	follow	VERB
ejpam-4624	363	41	:	:	PUNCT
ejpam-4624	363	42	t1(ρ	t1(ρ	X
ejpam-4624	363	43	)	)	PUNCT
ejpam-4624	363	44	=	=	SYM
ejpam-4624	364	1			NUM
ejpam-4624	364	2	1	1	NUM
ejpam-4624	364	3	,	,	PUNCT
ejpam-4624	364	4	if	if	SCONJ
ejpam-4624	364	5	ρ	ρ	PROPN
ejpam-4624	364	6	∈	∈	PROPN
ejpam-4624	364	7	{	{	PUNCT
ejpam-4624	364	8	0	0	NUM
ejpam-4624	364	9	,	,	PUNCT
ejpam-4624	364	10	1	1	NUM
ejpam-4624	364	11	}	}	PUNCT
ejpam-4624	364	12	,	,	PUNCT
ejpam-4624	364	13	1	1	NUM
ejpam-4624	364	14	3	3	NUM
ejpam-4624	364	15	,	,	PUNCT
ejpam-4624	364	16	if	if	SCONJ
ejpam-4624	364	17	ρ	ρ	PROPN
ejpam-4624	364	18	=	=	SYM
ejpam-4624	364	19	ρ1	ρ1	PROPN
ejpam-4624	364	20	,	,	PUNCT
ejpam-4624	364	21	1	1	NUM
ejpam-4624	364	22	2	2	NUM
ejpam-4624	364	23	,	,	PUNCT
ejpam-4624	364	24	if	if	SCONJ
ejpam-4624	364	25	ρ	ρ	PROPN
ejpam-4624	364	26	=	=	SYM
ejpam-4624	364	27	β1	β1	PROPN
ejpam-4624	364	28	,	,	PUNCT
ejpam-4624	364	29	0	0	NUM
ejpam-4624	364	30	,	,	PUNCT
ejpam-4624	364	31	otherwise	otherwise	ADV
ejpam-4624	364	32	.	.	PUNCT
ejpam-4624	365	1	t	t	PROPN
ejpam-4624	365	2	∗	∗	NOUN
ejpam-4624	365	3	1	1	NUM
ejpam-4624	365	4	(	(	PUNCT
ejpam-4624	365	5	ρ	ρ	NOUN
ejpam-4624	365	6	)	)	PUNCT
ejpam-4624	365	7	=	=	SYM
ejpam-4624	365	8			X
ejpam-4624	365	9	0	0	NUM
ejpam-4624	365	10	,	,	PUNCT
ejpam-4624	365	11	if	if	SCONJ
ejpam-4624	365	12	ρ	ρ	PROPN
ejpam-4624	365	13	∈	∈	PROPN
ejpam-4624	365	14	{	{	PUNCT
ejpam-4624	365	15	0	0	NUM
ejpam-4624	365	16	,	,	PUNCT
ejpam-4624	365	17	1	1	NUM
ejpam-4624	365	18	}	}	PUNCT
ejpam-4624	365	19	,	,	PUNCT
ejpam-4624	365	20	2	2	NUM
ejpam-4624	365	21	3	3	NUM
ejpam-4624	365	22	,	,	PUNCT
ejpam-4624	365	23	if	if	SCONJ
ejpam-4624	365	24	ρ	ρ	PROPN
ejpam-4624	365	25	=	=	SYM
ejpam-4624	365	26	ρ1	ρ1	PROPN
ejpam-4624	365	27	,	,	PUNCT
ejpam-4624	365	28	1	1	NUM
ejpam-4624	365	29	2	2	NUM
ejpam-4624	365	30	,	,	PUNCT
ejpam-4624	365	31	if	if	SCONJ
ejpam-4624	365	32	ρ	ρ	PROPN
ejpam-4624	365	33	=	=	SYM
ejpam-4624	365	34	β1	β1	PROPN
ejpam-4624	365	35	,	,	PUNCT
ejpam-4624	365	36	1	1	NUM
ejpam-4624	365	37	,	,	PUNCT
ejpam-4624	365	38	otherwise	otherwise	ADV
ejpam-4624	365	39	.	.	PUNCT
ejpam-4624	366	1	w.	w.	PROPN
ejpam-4624	366	2	f.	f.	PROPN
ejpam-4624	366	3	al	al	PROPN
ejpam-4624	366	4	-	-	PUNCT
ejpam-4624	366	5	omeri	omeri	ADJ
ejpam-4624	366	6	/	/	SYM
ejpam-4624	366	7	eur	eur	PROPN
ejpam-4624	366	8	.	.	PUNCT
ejpam-4624	367	1	j.	j.	PROPN
ejpam-4624	367	2	pure	pure	PROPN
ejpam-4624	367	3	appl	appl	PROPN
ejpam-4624	367	4	.	.	PROPN
ejpam-4624	367	5	math	math	PROPN
ejpam-4624	367	6	,	,	PUNCT
ejpam-4624	367	7	18	18	NUM
ejpam-4624	367	8	(	(	PUNCT
ejpam-4624	367	9	2	2	NUM
ejpam-4624	367	10	)	)	PUNCT
ejpam-4624	367	11	(	(	PUNCT
ejpam-4624	367	12	2025	2025	NUM
ejpam-4624	367	13	)	)	PUNCT
ejpam-4624	367	14	,	,	PUNCT
ejpam-4624	367	15	4624	4624	NUM
ejpam-4624	367	16	14	14	NUM
ejpam-4624	367	17	of	of	ADP
ejpam-4624	367	18	15	15	NUM
ejpam-4624	367	19	and	and	CCONJ
ejpam-4624	367	20	t2(ρ	t2(ρ	NOUN
ejpam-4624	367	21	)	)	PUNCT
ejpam-4624	367	22	=	=	PUNCT
ejpam-4624	368	1			PROPN
ejpam-4624	368	2	1	1	NUM
ejpam-4624	368	3	,	,	PUNCT
ejpam-4624	368	4	if	if	SCONJ
ejpam-4624	368	5	ρ	ρ	PROPN
ejpam-4624	368	6	∈	∈	PROPN
ejpam-4624	368	7	{	{	PUNCT
ejpam-4624	368	8	0	0	NUM
ejpam-4624	368	9	,	,	PUNCT
ejpam-4624	368	10	1	1	NUM
ejpam-4624	368	11	}	}	PUNCT
ejpam-4624	368	12	,	,	PUNCT
ejpam-4624	368	13	1	1	NUM
ejpam-4624	368	14	3	3	NUM
ejpam-4624	368	15	,	,	PUNCT
ejpam-4624	368	16	if	if	SCONJ
ejpam-4624	368	17	ρ	ρ	PROPN
ejpam-4624	368	18	=	=	SYM
ejpam-4624	368	19	ρ1	ρ1	PROPN
ejpam-4624	368	20	,	,	PUNCT
ejpam-4624	368	21	0	0	NUM
ejpam-4624	368	22	,	,	PUNCT
ejpam-4624	368	23	otherwise	otherwise	ADV
ejpam-4624	368	24	.	.	PUNCT
ejpam-4624	369	1	t	t	PROPN
ejpam-4624	369	2	∗	∗	NOUN
ejpam-4624	369	3	2	2	NUM
ejpam-4624	369	4	(	(	PUNCT
ejpam-4624	369	5	ρ	ρ	NOUN
ejpam-4624	369	6	)	)	PUNCT
ejpam-4624	369	7	=	=	PUNCT
ejpam-4624	370	1			PROPN
ejpam-4624	370	2	0	0	NUM
ejpam-4624	370	3	,	,	PUNCT
ejpam-4624	370	4	if	if	SCONJ
ejpam-4624	370	5	ρ	ρ	PROPN
ejpam-4624	370	6	∈	∈	PROPN
ejpam-4624	370	7	{	{	PUNCT
ejpam-4624	370	8	0	0	NUM
ejpam-4624	370	9	,	,	PUNCT
ejpam-4624	370	10	1	1	NUM
ejpam-4624	370	11	}	}	SYM
ejpam-4624	370	12	2	2	NUM
ejpam-4624	370	13	3	3	NUM
ejpam-4624	370	14	,	,	PUNCT
ejpam-4624	370	15	if	if	SCONJ
ejpam-4624	370	16	ρ	ρ	PROPN
ejpam-4624	370	17	=	=	SYM
ejpam-4624	370	18	ρ1	ρ1	PROPN
ejpam-4624	370	19	,	,	PUNCT
ejpam-4624	370	20	1	1	NUM
ejpam-4624	370	21	,	,	PUNCT
ejpam-4624	370	22	otherwise	otherwise	ADV
ejpam-4624	370	23	.	.	PUNCT
ejpam-4624	371	1	then	then	ADV
ejpam-4624	371	2	,	,	PUNCT
ejpam-4624	371	3	f	f	PROPN
ejpam-4624	371	4	is	be	AUX
ejpam-4624	371	5	double	double	ADJ
ejpam-4624	371	6	fuzzy	fuzzy	ADJ
ejpam-4624	371	7	continuous	continuous	ADJ
ejpam-4624	371	8	function	function	NOUN
ejpam-4624	371	9	but	but	CCONJ
ejpam-4624	371	10	not	not	PART
ejpam-4624	371	11	double	double	ADJ
ejpam-4624	371	12	fuzzy	fuzzy	ADJ
ejpam-4624	371	13	δ	δ	NOUN
ejpam-4624	371	14	-	-	ADJ
ejpam-4624	371	15	continuous	continuous	ADJ
ejpam-4624	371	16	function	function	NOUN
ejpam-4624	371	17	.	.	PUNCT
ejpam-4624	372	1	theorem	theorem	VERB
ejpam-4624	372	2	3.8	3.8	NUM
ejpam-4624	372	3	.	.	PUNCT
ejpam-4624	373	1	let	let	VERB
ejpam-4624	373	2	(	(	PUNCT
ejpam-4624	373	3	x	x	NOUN
ejpam-4624	373	4	,	,	PUNCT
ejpam-4624	373	5	t1	t1	PROPN
ejpam-4624	373	6	,	,	PUNCT
ejpam-4624	373	7	t	t	PROPN
ejpam-4624	373	8	∗	∗	NOUN
ejpam-4624	373	9	1	1	NUM
ejpam-4624	373	10	)	)	PUNCT
ejpam-4624	373	11	,	,	PUNCT
ejpam-4624	373	12	(	(	PUNCT
ejpam-4624	373	13	y	y	NOUN
ejpam-4624	373	14	,	,	PUNCT
ejpam-4624	373	15	t2	t2	PROPN
ejpam-4624	373	16	,	,	PUNCT
ejpam-4624	373	17	t	t	PROPN
ejpam-4624	373	18	∗	∗	X
ejpam-4624	373	19	2	2	NUM
ejpam-4624	373	20	)	)	PUNCT
ejpam-4624	373	21	and	and	CCONJ
ejpam-4624	373	22	(	(	PUNCT
ejpam-4624	373	23	z	z	PROPN
ejpam-4624	373	24	,	,	PUNCT
ejpam-4624	373	25	t3	t3	PROPN
ejpam-4624	373	26	,	,	PUNCT
ejpam-4624	373	27	t	t	PROPN
ejpam-4624	373	28	∗	∗	X
ejpam-4624	373	29	3	3	NUM
ejpam-4624	373	30	)	)	PUNCT
ejpam-4624	373	31	be	be	AUX
ejpam-4624	373	32	an	an	DET
ejpam-4624	373	33	dftss	dftss	NOUN
ejpam-4624	373	34	.	.	PUNCT
ejpam-4624	374	1	for	for	ADP
ejpam-4624	374	2	the	the	DET
ejpam-4624	374	3	functions	function	NOUN
ejpam-4624	374	4	f	f	X
ejpam-4624	374	5	:	:	PUNCT
ejpam-4624	374	6	(	(	PUNCT
ejpam-4624	374	7	x	x	X
ejpam-4624	374	8	,	,	PUNCT
ejpam-4624	374	9	t1	t1	PROPN
ejpam-4624	374	10	,	,	PUNCT
ejpam-4624	374	11	t	t	PROPN
ejpam-4624	374	12	∗	∗	X
ejpam-4624	374	13	1	1	NUM
ejpam-4624	374	14	)	)	PUNCT
ejpam-4624	374	15	→	→	SYM
ejpam-4624	374	16	(	(	PUNCT
ejpam-4624	374	17	y	y	PROPN
ejpam-4624	374	18	,	,	PUNCT
ejpam-4624	374	19	t2	t2	PROPN
ejpam-4624	374	20	,	,	PUNCT
ejpam-4624	374	21	t	t	PROPN
ejpam-4624	374	22	∗	∗	X
ejpam-4624	374	23	2	2	NUM
ejpam-4624	374	24	)	)	PUNCT
ejpam-4624	374	25	and	and	CCONJ
ejpam-4624	374	26	g	g	NOUN
ejpam-4624	374	27	:	:	PUNCT
ejpam-4624	374	28	(	(	PUNCT
ejpam-4624	374	29	x	x	X
ejpam-4624	374	30	,	,	PUNCT
ejpam-4624	374	31	t1	t1	PROPN
ejpam-4624	374	32	,	,	PUNCT
ejpam-4624	374	33	t	t	PROPN
ejpam-4624	374	34	∗	∗	X
ejpam-4624	374	35	1	1	NUM
ejpam-4624	374	36	)	)	PUNCT
ejpam-4624	374	37	→	→	SYM
ejpam-4624	374	38	(	(	PUNCT
ejpam-4624	374	39	z	z	PROPN
ejpam-4624	374	40	,	,	PUNCT
ejpam-4624	374	41	t3	t3	PROPN
ejpam-4624	374	42	,	,	PUNCT
ejpam-4624	374	43	t	t	PROPN
ejpam-4624	374	44	∗	∗	NOUN
ejpam-4624	374	45	3	3	NUM
ejpam-4624	374	46	)	)	PUNCT
ejpam-4624	374	47	.	.	PUNCT
ejpam-4624	375	1	if	if	SCONJ
ejpam-4624	375	2	f	f	PROPN
ejpam-4624	375	3	and	and	CCONJ
ejpam-4624	375	4	g	g	PROPN
ejpam-4624	375	5	are	be	AUX
ejpam-4624	375	6	(	(	PUNCT
ejpam-4624	375	7	r	r	NOUN
ejpam-4624	375	8	,	,	PUNCT
ejpam-4624	375	9	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	375	10	δ	δ	ADJ
ejpam-4624	375	11	-	-	PUNCT
ejpam-4624	375	12	continuous	continuous	ADJ
ejpam-4624	375	13	functions	function	NOUN
ejpam-4624	375	14	,	,	PUNCT
ejpam-4624	375	15	then	then	ADV
ejpam-4624	375	16	g	g	PROPN
ejpam-4624	375	17	◦	◦	PROPN
ejpam-4624	375	18	f	f	X
ejpam-4624	375	19	(	(	PUNCT
ejpam-4624	375	20	r	r	NOUN
ejpam-4624	375	21	,	,	PUNCT
ejpam-4624	375	22	s)-fuzzy	s)-fuzzy	ADV
ejpam-4624	375	23	δ	δ	PROPN
ejpam-4624	375	24	-	-	PUNCT
ejpam-4624	375	25	continuous	continuous	ADJ
ejpam-4624	375	26	.	.	PUNCT
ejpam-4624	376	1	proof	proof	NOUN
ejpam-4624	376	2	.	.	PUNCT
ejpam-4624	377	1	straightforward	straightforward	ADJ
ejpam-4624	377	2	.	.	PUNCT
ejpam-4624	378	1	corollary	corollary	ADJ
ejpam-4624	378	2	3.9	3.9	NUM
ejpam-4624	378	3	.	.	PUNCT
ejpam-4624	379	1	let	let	VERB
ejpam-4624	379	2	f	f	NOUN
ejpam-4624	379	3	:	:	PUNCT
ejpam-4624	379	4	(	(	PUNCT
ejpam-4624	379	5	x	x	X
ejpam-4624	379	6	,	,	PUNCT
ejpam-4624	379	7	t1	t1	PROPN
ejpam-4624	379	8	,	,	PUNCT
ejpam-4624	379	9	t	t	PROPN
ejpam-4624	379	10	∗	∗	X
ejpam-4624	379	11	1	1	NUM
ejpam-4624	379	12	)	)	PUNCT
ejpam-4624	379	13	→	→	SYM
ejpam-4624	379	14	(	(	PUNCT
ejpam-4624	379	15	y	y	PROPN
ejpam-4624	379	16	,	,	PUNCT
ejpam-4624	379	17	t2	t2	PROPN
ejpam-4624	379	18	,	,	PUNCT
ejpam-4624	379	19	t	t	PROPN
ejpam-4624	379	20	∗	∗	X
ejpam-4624	379	21	2	2	NUM
ejpam-4624	379	22	)	)	PUNCT
ejpam-4624	379	23	be	be	AUX
ejpam-4624	379	24	double	double	ADV
ejpam-4624	379	25	fuzzy	fuzzy	ADJ
ejpam-4624	379	26	regular	regular	ADJ
ejpam-4624	379	27	δ	δ	NOUN
ejpam-4624	379	28	-	-	ADJ
ejpam-4624	379	29	continuous	continuous	ADJ
ejpam-4624	379	30	function	function	NOUN
ejpam-4624	379	31	,	,	PUNCT
ejpam-4624	379	32	then	then	ADV
ejpam-4624	379	33	δct1,t	δct1,t	NOUN
ejpam-4624	379	34	∗	∗	VERB
ejpam-4624	379	35	1	1	NUM
ejpam-4624	379	36	(	(	PUNCT
ejpam-4624	379	37	f(ϕ)−1	f(ϕ)−1	PROPN
ejpam-4624	379	38	,	,	PUNCT
ejpam-4624	379	39	r	r	NOUN
ejpam-4624	379	40	,	,	PUNCT
ejpam-4624	379	41	s	s	NOUN
ejpam-4624	379	42	)	)	PUNCT
ejpam-4624	379	43	≤	≤	PUNCT
ejpam-4624	380	1	f−1(δct2,t	f−1(δct2,t	PROPN
ejpam-4624	380	2	∗	∗	X
ejpam-4624	380	3	2	2	NUM
ejpam-4624	380	4	(	(	PUNCT
ejpam-4624	380	5	ϕ	ϕ	NOUN
ejpam-4624	380	6	,	,	PUNCT
ejpam-4624	380	7	r	r	NOUN
ejpam-4624	380	8	,	,	PUNCT
ejpam-4624	380	9	s	s	NOUN
ejpam-4624	380	10	)	)	PUNCT
ejpam-4624	380	11	)	)	PUNCT
ejpam-4624	380	12	,	,	PUNCT
ejpam-4624	380	13	for	for	ADP
ejpam-4624	380	14	each	each	DET
ejpam-4624	380	15	t2(ϕ	t2(ϕ	NOUN
ejpam-4624	380	16	)	)	PUNCT
ejpam-4624	380	17	≥	≥	NOUN
ejpam-4624	380	18	r	r	NOUN
ejpam-4624	380	19	,	,	PUNCT
ejpam-4624	380	20	t	t	PROPN
ejpam-4624	380	21	∗	∗	X
ejpam-4624	380	22	2	2	NUM
ejpam-4624	380	23	(	(	PUNCT
ejpam-4624	380	24	ϕ	ϕ	NOUN
ejpam-4624	380	25	)	)	PUNCT
ejpam-4624	380	26	≤	≤	NOUN
ejpam-4624	380	27	s	s	PART
ejpam-4624	380	28	,	,	PUNCT
ejpam-4624	380	29	and	and	CCONJ
ejpam-4624	380	30	r	r	NOUN
ejpam-4624	380	31	∈	∈	PROPN
ejpam-4624	380	32	i0	i0	PROPN
ejpam-4624	380	33	,	,	PUNCT
ejpam-4624	380	34	s	s	PROPN
ejpam-4624	380	35	∈	∈	PROPN
ejpam-4624	380	36	i1	i1	PROPN
ejpam-4624	380	37	.	.	PUNCT
ejpam-4624	381	1	4	4	X
ejpam-4624	381	2	.	.	X
ejpam-4624	381	3	conclusion	conclusion	VERB
ejpam-4624	381	4	the	the	DET
ejpam-4624	381	5	main	main	ADJ
ejpam-4624	381	6	purpose	purpose	NOUN
ejpam-4624	381	7	of	of	ADP
ejpam-4624	381	8	this	this	DET
ejpam-4624	381	9	paper	paper	NOUN
ejpam-4624	381	10	is	be	AUX
ejpam-4624	381	11	to	to	PART
ejpam-4624	381	12	introduce	introduce	VERB
ejpam-4624	381	13	a	a	DET
ejpam-4624	381	14	new	new	ADJ
ejpam-4624	381	15	concept	concept	NOUN
ejpam-4624	381	16	in	in	ADP
ejpam-4624	381	17	double	double	ADJ
ejpam-4624	381	18	fuzzy	fuzzy	ADJ
ejpam-4624	381	19	set	set	NOUN
ejpam-4624	381	20	theory	theory	NOUN
ejpam-4624	381	21	,	,	PUNCT
ejpam-4624	381	22	namely	namely	ADV
ejpam-4624	381	23	a	a	DET
ejpam-4624	381	24	(	(	PUNCT
ejpam-4624	381	25	r	r	NOUN
ejpam-4624	381	26	,	,	PUNCT
ejpam-4624	381	27	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	381	28	δ	δ	PROPN
ejpam-4624	381	29	-	-	PUNCT
ejpam-4624	381	30	closed	close	VERB
ejpam-4624	381	31	sets	set	NOUN
ejpam-4624	381	32	and	and	CCONJ
ejpam-4624	381	33	a	a	DET
ejpam-4624	381	34	double	double	ADJ
ejpam-4624	381	35	fuzzy	fuzzy	ADJ
ejpam-4624	381	36	δ	δ	NOUN
ejpam-4624	381	37	-	-	ADJ
ejpam-4624	381	38	continuous	continuous	ADJ
ejpam-4624	381	39	functions	function	NOUN
ejpam-4624	381	40	.	.	PUNCT
ejpam-4624	382	1	on	on	ADP
ejpam-4624	382	2	the	the	DET
ejpam-4624	382	3	other	other	ADJ
ejpam-4624	382	4	hand	hand	NOUN
ejpam-4624	382	5	,	,	PUNCT
ejpam-4624	382	6	the	the	DET
ejpam-4624	382	7	double	double	ADJ
ejpam-4624	382	8	fuzzy	fuzzy	ADJ
ejpam-4624	382	9	topology	topology	NOUN
ejpam-4624	382	10	on	on	ADP
ejpam-4624	382	11	a	a	DET
ejpam-4624	382	12	double	double	ADJ
ejpam-4624	382	13	fuzzy	fuzzy	ADJ
ejpam-4624	382	14	set	set	NOUN
ejpam-4624	382	15	is	be	AUX
ejpam-4624	382	16	a	a	DET
ejpam-4624	382	17	kind	kind	NOUN
ejpam-4624	382	18	of	of	ADP
ejpam-4624	382	19	abstract	abstract	ADJ
ejpam-4624	382	20	theory	theory	NOUN
ejpam-4624	382	21	of	of	ADP
ejpam-4624	382	22	mathematics	mathematic	NOUN
ejpam-4624	382	23	.	.	PUNCT
ejpam-4624	383	1	first	first	ADV
ejpam-4624	383	2	,	,	PUNCT
ejpam-4624	383	3	we	we	PRON
ejpam-4624	383	4	present	present	VERB
ejpam-4624	383	5	and	and	CCONJ
ejpam-4624	383	6	study	study	VERB
ejpam-4624	383	7	a	a	DET
ejpam-4624	383	8	(	(	PUNCT
ejpam-4624	383	9	r	r	NOUN
ejpam-4624	383	10	,	,	PUNCT
ejpam-4624	383	11	s)-fuzzy	s)-fuzzy	ADJ
ejpam-4624	383	12	δ	δ	PROPN
ejpam-4624	383	13	-	-	PUNCT
ejpam-4624	383	14	closed	close	VERB
ejpam-4624	383	15	sets	set	NOUN
ejpam-4624	383	16	and	and	CCONJ
ejpam-4624	383	17	double	double	ADJ
ejpam-4624	383	18	fuzzy	fuzzy	ADJ
ejpam-4624	383	19	δ	δ	NOUN
ejpam-4624	383	20	-	-	NOUN
ejpam-4624	383	21	continuity	continuity	NOUN
ejpam-4624	383	22	from	from	ADP
ejpam-4624	383	23	a	a	DET
ejpam-4624	383	24	double	double	ADJ
ejpam-4624	383	25	fuzzy	fuzzy	ADJ
ejpam-4624	383	26	topological	topological	ADJ
ejpam-4624	383	27	space	space	NOUN
ejpam-4624	383	28	on	on	ADP
ejpam-4624	383	29	a	a	DET
ejpam-4624	383	30	double	double	ADJ
ejpam-4624	383	31	fuzzy	fuzzy	NOUN
ejpam-4624	383	32	set	set	VERB
ejpam-4624	383	33	into	into	ADP
ejpam-4624	383	34	another	another	PRON
ejpam-4624	383	35	.	.	PUNCT
ejpam-4624	384	1	then	then	ADV
ejpam-4624	384	2	,	,	PUNCT
ejpam-4624	384	3	we	we	PRON
ejpam-4624	384	4	present	present	VERB
ejpam-4624	384	5	the	the	DET
ejpam-4624	384	6	relationships	relationship	NOUN
ejpam-4624	384	7	between	between	ADP
ejpam-4624	384	8	types	type	NOUN
ejpam-4624	384	9	of	of	ADP
ejpam-4624	384	10	double	double	ADJ
ejpam-4624	384	11	fuzzy	fuzzy	ADJ
ejpam-4624	384	12	δ	δ	NOUN
ejpam-4624	384	13	-	-	PUNCT
ejpam-4624	384	14	continuity	continuity	NOUN
ejpam-4624	384	15	functions	function	NOUN
ejpam-4624	384	16	.	.	PUNCT
ejpam-4624	385	1	references	reference	NOUN
ejpam-4624	385	2	[	[	X
ejpam-4624	385	3	1	1	NUM
ejpam-4624	385	4	]	]	PUNCT
ejpam-4624	385	5	l.	l.	PROPN
ejpam-4624	385	6	a.	a.	PROPN
ejpam-4624	385	7	zadeh	zadeh	PROPN
ejpam-4624	385	8	.	.	PUNCT
ejpam-4624	386	1	fuzzy	fuzzy	ADJ
ejpam-4624	386	2	sets	set	NOUN
ejpam-4624	386	3	.	.	PUNCT
ejpam-4624	387	1	information	information	NOUN
ejpam-4624	387	2	and	and	CCONJ
ejpam-4624	387	3	control	control	NOUN
ejpam-4624	387	4	,	,	PUNCT
ejpam-4624	387	5	8(3):338–353	8(3):338–353	NUM
ejpam-4624	387	6	,	,	PUNCT
ejpam-4624	387	7	1965	1965	NUM
ejpam-4624	387	8	.	.	PUNCT
ejpam-4624	388	1	[	[	X
ejpam-4624	388	2	2	2	NUM
ejpam-4624	388	3	]	]	PUNCT
ejpam-4624	388	4	c.	c.	PROPN
ejpam-4624	388	5	l.	l.	PROPN
ejpam-4624	388	6	chang	chang	PROPN
ejpam-4624	388	7	.	.	PUNCT
ejpam-4624	389	1	fuzzy	fuzzy	ADJ
ejpam-4624	389	2	topological	topological	ADJ
ejpam-4624	389	3	spaces	space	NOUN
ejpam-4624	389	4	.	.	PUNCT
ejpam-4624	390	1	journal	journal	PROPN
ejpam-4624	390	2	of	of	ADP
ejpam-4624	390	3	mathematical	mathematical	ADJ
ejpam-4624	390	4	analysis	analysis	NOUN
ejpam-4624	390	5	and	and	CCONJ
ejpam-4624	390	6	applications	application	NOUN
ejpam-4624	390	7	,	,	PUNCT
ejpam-4624	390	8	24(1):182–190	24(1):182–190	NUM
ejpam-4624	390	9	,	,	PUNCT
ejpam-4624	390	10	1968	1968	NUM
ejpam-4624	390	11	.	.	PUNCT
ejpam-4624	391	1	[	[	X
ejpam-4624	391	2	3	3	X
ejpam-4624	391	3	]	]	X
ejpam-4624	391	4	d.	d.	PROPN
ejpam-4624	391	5	coker	coker	PROPN
ejpam-4624	391	6	.	.	PUNCT
ejpam-4624	392	1	an	an	DET
ejpam-4624	392	2	introduction	introduction	NOUN
ejpam-4624	392	3	to	to	ADP
ejpam-4624	392	4	fuzzy	fuzzy	ADJ
ejpam-4624	392	5	subspaces	subspace	NOUN
ejpam-4624	392	6	in	in	ADP
ejpam-4624	392	7	intuitionistic	intuitionistic	ADJ
ejpam-4624	392	8	fuzzy	fuzzy	ADJ
ejpam-4624	392	9	topological	topological	ADJ
ejpam-4624	392	10	spaces	space	NOUN
ejpam-4624	392	11	.	.	PUNCT
ejpam-4624	393	1	journal	journal	NOUN
ejpam-4624	393	2	of	of	ADP
ejpam-4624	393	3	fuzzy	fuzzy	ADJ
ejpam-4624	393	4	mathematics	mathematic	NOUN
ejpam-4624	393	5	,	,	PUNCT
ejpam-4624	393	6	4(4):749–764	4(4):749–764	NUM
ejpam-4624	393	7	,	,	PUNCT
ejpam-4624	393	8	1996	1996	NUM
ejpam-4624	393	9	.	.	PUNCT
ejpam-4624	394	1	[	[	X
ejpam-4624	394	2	4	4	NUM
ejpam-4624	394	3	]	]	X
ejpam-4624	394	4	d.	d.	PROPN
ejpam-4624	394	5	čoker	čoker	PROPN
ejpam-4624	394	6	.	.	PUNCT
ejpam-4624	395	1	an	an	DET
ejpam-4624	395	2	introduction	introduction	NOUN
ejpam-4624	395	3	to	to	ADP
ejpam-4624	395	4	intuitionistic	intuitionistic	ADJ
ejpam-4624	395	5	fuzzy	fuzzy	ADJ
ejpam-4624	395	6	topological	topological	ADJ
ejpam-4624	395	7	spaces	space	NOUN
ejpam-4624	395	8	.	.	PUNCT
ejpam-4624	396	1	fuzzy	fuzzy	ADJ
ejpam-4624	396	2	sets	set	NOUN
ejpam-4624	396	3	and	and	CCONJ
ejpam-4624	396	4	systems	system	NOUN
ejpam-4624	396	5	,	,	PUNCT
ejpam-4624	396	6	88(1):81–89	88(1):81–89	NUM
ejpam-4624	396	7	,	,	PUNCT
ejpam-4624	396	8	1997	1997	NUM
ejpam-4624	396	9	.	.	PUNCT
ejpam-4624	397	1	[	[	X
ejpam-4624	397	2	5	5	NUM
ejpam-4624	397	3	]	]	PUNCT
ejpam-4624	397	4	m.	m.	NOUN
ejpam-4624	397	5	demirci	demirci	PROPN
ejpam-4624	397	6	and	and	CCONJ
ejpam-4624	397	7	d.	d.	PROPN
ejpam-4624	397	8	čoker	čoker	PROPN
ejpam-4624	397	9	.	.	PUNCT
ejpam-4624	398	1	an	an	DET
ejpam-4624	398	2	introduction	introduction	NOUN
ejpam-4624	398	3	to	to	ADP
ejpam-4624	398	4	intuitionistic	intuitionistic	ADJ
ejpam-4624	398	5	fuzzy	fuzzy	ADJ
ejpam-4624	398	6	topological	topological	ADJ
ejpam-4624	398	7	spaces	space	NOUN
ejpam-4624	398	8	in	in	ADP
ejpam-4624	398	9	šostak	šostak	NOUN
ejpam-4624	398	10	’s	’s	PART
ejpam-4624	398	11	sense	sense	NOUN
ejpam-4624	398	12	.	.	PUNCT
ejpam-4624	399	1	busefal	busefal	PROPN
ejpam-4624	399	2	,	,	PUNCT
ejpam-4624	399	3	67:67–76	67:67–76	NUM
ejpam-4624	399	4	,	,	PUNCT
ejpam-4624	399	5	1996	1996	NUM
ejpam-4624	399	6	.	.	PUNCT
ejpam-4624	400	1	[	[	X
ejpam-4624	400	2	6	6	NUM
ejpam-4624	400	3	]	]	PUNCT
ejpam-4624	400	4	t.	t.	PROPN
ejpam-4624	400	5	k.	k.	PROPN
ejpam-4624	400	6	mondal	mondal	PROPN
ejpam-4624	400	7	and	and	CCONJ
ejpam-4624	400	8	s.	s.	PROPN
ejpam-4624	400	9	k.	k.	PROPN
ejpam-4624	400	10	samanta	samanta	PROPN
ejpam-4624	400	11	.	.	PUNCT
ejpam-4624	401	1	on	on	ADP
ejpam-4624	401	2	intuitionistic	intuitionistic	ADJ
ejpam-4624	401	3	gradation	gradation	NOUN
ejpam-4624	401	4	of	of	ADP
ejpam-4624	401	5	openness	openness	NOUN
ejpam-4624	401	6	.	.	PUNCT
ejpam-4624	402	1	fuzzy	fuzzy	ADJ
ejpam-4624	402	2	sets	set	NOUN
ejpam-4624	402	3	and	and	CCONJ
ejpam-4624	402	4	systems	system	NOUN
ejpam-4624	402	5	,	,	PUNCT
ejpam-4624	402	6	131(3):323–336	131(3):323–336	PROPN
ejpam-4624	402	7	,	,	PUNCT
ejpam-4624	402	8	2002	2002	NUM
ejpam-4624	402	9	.	.	PUNCT
ejpam-4624	403	1	[	[	X
ejpam-4624	403	2	7	7	X
ejpam-4624	403	3	]	]	X
ejpam-4624	403	4	j.	j.	PROPN
ejpam-4624	403	5	gutiérrez	gutiérrez	PROPN
ejpam-4624	403	6	garcía	garcía	PROPN
ejpam-4624	403	7	and	and	CCONJ
ejpam-4624	403	8	s.	s.	PROPN
ejpam-4624	403	9	e.	e.	PROPN
ejpam-4624	403	10	rodabaugh	rodabaugh	PROPN
ejpam-4624	403	11	.	.	PUNCT
ejpam-4624	404	1	order	order	NOUN
ejpam-4624	404	2	-	-	PUNCT
ejpam-4624	404	3	theoretic	theoretic	ADJ
ejpam-4624	404	4	,	,	PUNCT
ejpam-4624	404	5	topological	topological	ADJ
ejpam-4624	404	6	,	,	PUNCT
ejpam-4624	404	7	categorical	categorical	ADJ
ejpam-4624	404	8	redundancies	redundancy	NOUN
ejpam-4624	404	9	of	of	ADP
ejpam-4624	404	10	interval	interval	NOUN
ejpam-4624	404	11	-	-	PUNCT
ejpam-4624	404	12	valued	value	VERB
ejpam-4624	404	13	sets	set	NOUN
ejpam-4624	404	14	,	,	PUNCT
ejpam-4624	404	15	grey	grey	NOUN
ejpam-4624	404	16	sets	set	NOUN
ejpam-4624	404	17	,	,	PUNCT
ejpam-4624	404	18	vague	vague	ADJ
ejpam-4624	404	19	sets	set	NOUN
ejpam-4624	404	20	,	,	PUNCT
ejpam-4624	404	21	interval	interval	NOUN
ejpam-4624	404	22	-	-	PUNCT
ejpam-4624	404	23	valued	value	VERB
ejpam-4624	404	24	intuitionistic	intuitionistic	ADJ
ejpam-4624	404	25	sets	set	NOUN
ejpam-4624	404	26	,	,	PUNCT
ejpam-4624	404	27	intuitionistic	intuitionistic	ADJ
ejpam-4624	404	28	fuzzy	fuzzy	ADJ
ejpam-4624	404	29	sets	set	NOUN
ejpam-4624	404	30	and	and	CCONJ
ejpam-4624	404	31	topologies	topology	NOUN
ejpam-4624	404	32	.	.	PUNCT
ejpam-4624	405	1	fuzzy	fuzzy	ADJ
ejpam-4624	405	2	sets	set	NOUN
ejpam-4624	405	3	and	and	CCONJ
ejpam-4624	405	4	systems	system	NOUN
ejpam-4624	405	5	,	,	PUNCT
ejpam-4624	405	6	156(3):445–484	156(3):445–484	NUM
ejpam-4624	405	7	,	,	PUNCT
ejpam-4624	405	8	2005	2005	NUM
ejpam-4624	405	9	.	.	PUNCT
ejpam-4624	406	1	[	[	X
ejpam-4624	406	2	8	8	NUM
ejpam-4624	406	3	]	]	PUNCT
ejpam-4624	406	4	a.	a.	NOUN
ejpam-4624	406	5	ghareeb	ghareeb	NOUN
ejpam-4624	406	6	.	.	PUNCT
ejpam-4624	407	1	normality	normality	NOUN
ejpam-4624	407	2	of	of	ADP
ejpam-4624	407	3	double	double	ADJ
ejpam-4624	407	4	fuzzy	fuzzy	ADJ
ejpam-4624	407	5	topological	topological	ADJ
ejpam-4624	407	6	spaces	space	NOUN
ejpam-4624	407	7	.	.	PUNCT
ejpam-4624	408	1	applied	apply	VERB
ejpam-4624	408	2	mathematics	mathematics	NOUN
ejpam-4624	408	3	letters	letter	NOUN
ejpam-4624	408	4	,	,	PUNCT
ejpam-4624	408	5	24(4):533–540	24(4):533–540	NUM
ejpam-4624	408	6	,	,	PUNCT
ejpam-4624	408	7	2011	2011	NUM
ejpam-4624	408	8	.	.	PUNCT
ejpam-4624	409	1	w.	w.	PROPN
ejpam-4624	409	2	f.	f.	PROPN
ejpam-4624	409	3	al	al	PROPN
ejpam-4624	409	4	-	-	PUNCT
ejpam-4624	409	5	omeri	omeri	ADJ
ejpam-4624	409	6	/	/	SYM
ejpam-4624	409	7	eur	eur	PROPN
ejpam-4624	409	8	.	.	PUNCT
ejpam-4624	410	1	j.	j.	PROPN
ejpam-4624	410	2	pure	pure	PROPN
ejpam-4624	410	3	appl	appl	PROPN
ejpam-4624	410	4	.	.	PROPN
ejpam-4624	410	5	math	math	PROPN
ejpam-4624	410	6	,	,	PUNCT
ejpam-4624	410	7	18	18	NUM
ejpam-4624	410	8	(	(	PUNCT
ejpam-4624	410	9	2	2	NUM
ejpam-4624	410	10	)	)	PUNCT
ejpam-4624	410	11	(	(	PUNCT
ejpam-4624	410	12	2025	2025	NUM
ejpam-4624	410	13	)	)	PUNCT
ejpam-4624	410	14	,	,	PUNCT
ejpam-4624	410	15	4624	4624	NUM
ejpam-4624	410	16	15	15	NUM
ejpam-4624	410	17	of	of	ADP
ejpam-4624	410	18	15	15	NUM
ejpam-4624	410	19	[	[	SYM
ejpam-4624	410	20	9	9	NUM
ejpam-4624	410	21	]	]	PUNCT
ejpam-4624	410	22	hariwan	hariwan	PROPN
ejpam-4624	410	23	z.	z.	PROPN
ejpam-4624	410	24	ibrahim	ibrahim	PROPN
ejpam-4624	410	25	,	,	PUNCT
ejpam-4624	410	26	tareq	tareq	PROPN
ejpam-4624	410	27	m.	m.	PROPN
ejpam-4624	410	28	al	al	PROPN
ejpam-4624	410	29	-	-	PUNCT
ejpam-4624	410	30	shami	shami	PROPN
ejpam-4624	410	31	,	,	PUNCT
ejpam-4624	410	32	and	and	CCONJ
ejpam-4624	410	33	o.	o.	PROPN
ejpam-4624	410	34	g.	g.	PROPN
ejpam-4624	410	35	elbarbary	elbarbary	PROPN
ejpam-4624	410	36	.	.	PUNCT
ejpam-4624	411	1	(	(	PUNCT
ejpam-4624	411	2	3	3	NUM
ejpam-4624	411	3	,	,	PUNCT
ejpam-4624	411	4	2)-fuzzy	2)-fuzzy	NUM
ejpam-4624	411	5	sets	set	NOUN
ejpam-4624	411	6	and	and	CCONJ
ejpam-4624	411	7	their	their	PRON
ejpam-4624	411	8	applications	application	NOUN
ejpam-4624	411	9	to	to	ADP
ejpam-4624	411	10	topology	topology	NOUN
ejpam-4624	411	11	and	and	CCONJ
ejpam-4624	411	12	optimal	optimal	ADJ
ejpam-4624	411	13	choices	choice	NOUN
ejpam-4624	411	14	.	.	PUNCT
ejpam-4624	412	1	computational	computational	ADJ
ejpam-4624	412	2	intelligence	intelligence	NOUN
ejpam-4624	412	3	and	and	CCONJ
ejpam-4624	412	4	neuroscience	neuroscience	NOUN
ejpam-4624	412	5	,	,	PUNCT
ejpam-4624	412	6	2021:1272264	2021:1272264	NUM
ejpam-4624	412	7	,	,	PUNCT
ejpam-4624	412	8	2021	2021	NUM
ejpam-4624	412	9	.	.	PUNCT
ejpam-4624	413	1	[	[	X
ejpam-4624	413	2	10	10	NUM
ejpam-4624	413	3	]	]	X
ejpam-4624	413	4	tareq	tareq	PROPN
ejpam-4624	413	5	m.	m.	PROPN
ejpam-4624	413	6	al	al	PROPN
ejpam-4624	413	7	-	-	PUNCT
ejpam-4624	413	8	shami	shami	PROPN
ejpam-4624	413	9	.	.	PUNCT
ejpam-4624	414	1	(	(	PUNCT
ejpam-4624	414	2	2	2	NUM
ejpam-4624	414	3	,	,	PUNCT
ejpam-4624	414	4	1)-fuzzy	1)-fuzzy	NUM
ejpam-4624	414	5	sets	set	NOUN
ejpam-4624	414	6	:	:	PUNCT
ejpam-4624	414	7	properties	property	NOUN
ejpam-4624	414	8	,	,	PUNCT
ejpam-4624	414	9	weighted	weight	VERB
ejpam-4624	414	10	aggregated	aggregate	VERB
ejpam-4624	414	11	operators	operator	NOUN
ejpam-4624	414	12	and	and	CCONJ
ejpam-4624	414	13	their	their	PRON
ejpam-4624	414	14	applications	application	NOUN
ejpam-4624	414	15	to	to	ADP
ejpam-4624	414	16	multi	multi	ADJ
ejpam-4624	414	17	-	-	NOUN
ejpam-4624	414	18	criteria	criterion	NOUN
ejpam-4624	414	19	decision	decision	NOUN
ejpam-4624	414	20	-	-	PUNCT
ejpam-4624	414	21	making	make	VERB
ejpam-4624	414	22	methods	method	NOUN
ejpam-4624	414	23	.	.	PUNCT
ejpam-4624	415	1	complex	complex	ADJ
ejpam-4624	415	2	&	&	CCONJ
ejpam-4624	415	3	intelligent	intelligent	ADJ
ejpam-4624	415	4	systems	system	NOUN
ejpam-4624	415	5	,	,	PUNCT
ejpam-4624	415	6	9(2):1687–1705	9(2):1687–1705	NUM
ejpam-4624	415	7	,	,	PUNCT
ejpam-4624	415	8	2023	2023	NUM
ejpam-4624	415	9	.	.	PUNCT
ejpam-4624	416	1	[	[	X
ejpam-4624	416	2	11	11	NUM
ejpam-4624	416	3	]	]	PUNCT
ejpam-4624	416	4	wadei	wadei	VERB
ejpam-4624	416	5	f.	f.	PROPN
ejpam-4624	416	6	al	al	PROPN
ejpam-4624	416	7	-	-	PUNCT
ejpam-4624	416	8	omeri	omeri	PROPN
ejpam-4624	416	9	.	.	PUNCT
ejpam-4624	417	1	on	on	ADP
ejpam-4624	417	2	mixed	mixed	ADJ
ejpam-4624	417	3	b	b	NOUN
ejpam-4624	417	4	-	-	PUNCT
ejpam-4624	417	5	fuzzy	fuzzy	ADJ
ejpam-4624	417	6	topological	topological	ADJ
ejpam-4624	417	7	spaces	space	NOUN
ejpam-4624	417	8	.	.	PUNCT
ejpam-4624	418	1	international	international	ADJ
ejpam-4624	418	2	journal	journal	NOUN
ejpam-4624	418	3	of	of	ADP
ejpam-4624	418	4	fuzzy	fuzzy	ADJ
ejpam-4624	418	5	logic	logic	NOUN
ejpam-4624	418	6	and	and	CCONJ
ejpam-4624	418	7	intelligent	intelligent	ADJ
ejpam-4624	418	8	systems	system	NOUN
ejpam-4624	418	9	,	,	PUNCT
ejpam-4624	418	10	20(3):242–246	20(3):242–246	NUM
ejpam-4624	418	11	,	,	PUNCT
ejpam-4624	418	12	2020	2020	NUM
ejpam-4624	418	13	.	.	PUNCT
ejpam-4624	419	1	[	[	X
ejpam-4624	419	2	12	12	NUM
ejpam-4624	419	3	]	]	X
ejpam-4624	419	4	wadei	wadei	VERB
ejpam-4624	419	5	f.	f.	PROPN
ejpam-4624	419	6	al	al	PROPN
ejpam-4624	419	7	-	-	PUNCT
ejpam-4624	419	8	omeri	omeri	PROPN
ejpam-4624	419	9	.	.	PUNCT
ejpam-4624	420	1	on	on	ADP
ejpam-4624	420	2	almost	almost	ADV
ejpam-4624	420	3	e	e	NOUN
ejpam-4624	420	4	-	-	ADJ
ejpam-4624	420	5	i	i	NOUN
ejpam-4624	420	6	-	-	PUNCT
ejpam-4624	420	7	continuous	continuous	ADJ
ejpam-4624	420	8	functions	function	NOUN
ejpam-4624	420	9	.	.	PUNCT
ejpam-4624	421	1	demonstratio	demonstratio	PROPN
ejpam-4624	421	2	mathematica	mathematica	PROPN
ejpam-4624	421	3	,	,	PUNCT
ejpam-4624	421	4	54(1):168–177	54(1):168–177	PROPN
ejpam-4624	421	5	,	,	PUNCT
ejpam-4624	421	6	2021	2021	NUM
ejpam-4624	421	7	.	.	PUNCT
ejpam-4624	422	1	[	[	X
ejpam-4624	422	2	13	13	NUM
ejpam-4624	422	3	]	]	PUNCT
ejpam-4624	422	4	wadei	wadei	VERB
ejpam-4624	422	5	f.	f.	PROPN
ejpam-4624	422	6	al	al	PROPN
ejpam-4624	422	7	-	-	PUNCT
ejpam-4624	422	8	omeri	omeri	ADJ
ejpam-4624	422	9	,	,	PUNCT
ejpam-4624	422	10	o.	o.	PROPN
ejpam-4624	422	11	h.	h.	PROPN
ejpam-4624	422	12	khalil	khalil	PROPN
ejpam-4624	422	13	,	,	PUNCT
ejpam-4624	422	14	and	and	CCONJ
ejpam-4624	422	15	a.	a.	NOUN
ejpam-4624	422	16	ghareeb	ghareeb	PROPN
ejpam-4624	422	17	.	.	PUNCT
ejpam-4624	422	18	degree	degree	NOUN
ejpam-4624	422	19	of	of	ADP
ejpam-4624	422	20	(	(	PUNCT
ejpam-4624	422	21	l	l	NOUN
ejpam-4624	422	22	,	,	PUNCT
ejpam-4624	422	23	m)-fuzzy	m)-fuzzy	VERB
ejpam-4624	422	24	semiprecontinuous	semiprecontinuous	ADJ
ejpam-4624	422	25	and	and	CCONJ
ejpam-4624	422	26	(	(	PUNCT
ejpam-4624	422	27	l	l	NOUN
ejpam-4624	422	28	,	,	PUNCT
ejpam-4624	422	29	m)-fuzzy	m)-fuzzy	ADJ
ejpam-4624	422	30	semi	semi	ADJ
ejpam-4624	422	31	-	-	ADJ
ejpam-4624	422	32	preirresolute	preirresolute	ADJ
ejpam-4624	422	33	functions	function	NOUN
ejpam-4624	422	34	.	.	PUNCT
ejpam-4624	423	1	demonstratio	demonstratio	PROPN
ejpam-4624	423	2	mathematica	mathematica	PROPN
ejpam-4624	423	3	,	,	PUNCT
ejpam-4624	423	4	51(1):182–197	51(1):182–197	PROPN
ejpam-4624	423	5	,	,	PUNCT
ejpam-4624	423	6	2018	2018	NUM
ejpam-4624	423	7	.	.	PUNCT
ejpam-4624	424	1	[	[	X
ejpam-4624	424	2	14	14	NUM
ejpam-4624	424	3	]	]	PUNCT
ejpam-4624	424	4	m.	m.	NOUN
ejpam-4624	424	5	a.	a.	PROPN
ejpam-4624	424	6	abd	abd	PROPN
ejpam-4624	424	7	-	-	PUNCT
ejpam-4624	424	8	allah	allah	PROPN
ejpam-4624	424	9	,	,	PUNCT
ejpam-4624	424	10	k.	k.	PROPN
ejpam-4624	424	11	el	el	PROPN
ejpam-4624	424	12	-	-	PUNCT
ejpam-4624	424	13	saady	saady	NOUN
ejpam-4624	424	14	,	,	PUNCT
ejpam-4624	424	15	and	and	CCONJ
ejpam-4624	424	16	a.	a.	NOUN
ejpam-4624	424	17	ghareeb	ghareeb	NOUN
ejpam-4624	424	18	.	.	PUNCT
ejpam-4624	425	1	(	(	PUNCT
ejpam-4624	425	2	r	r	NOUN
ejpam-4624	425	3	,	,	PUNCT
ejpam-4624	425	4	s)-fuzzy	s)-fuzzy	ADP
ejpam-4624	425	5	f	f	PROPN
ejpam-4624	425	6	-open	-open	PROPN
ejpam-4624	425	7	sets	set	NOUN
ejpam-4624	425	8	and	and	CCONJ
ejpam-4624	425	9	(	(	PUNCT
ejpam-4624	425	10	r	r	NOUN
ejpam-4624	425	11	,	,	PUNCT
ejpam-4624	425	12	s)fuzzy	s)fuzzy	PROPN
ejpam-4624	425	13	f	f	PROPN
ejpam-4624	426	1	-closed	-close	VERB
ejpam-4624	426	2	spaces	space	NOUN
ejpam-4624	426	3	.	.	PUNCT
ejpam-4624	427	1	chaos	chaos	NOUN
ejpam-4624	427	2	,	,	PUNCT
ejpam-4624	427	3	solitons	soliton	NOUN
ejpam-4624	427	4	&	&	CCONJ
ejpam-4624	427	5	fractals	fractal	NOUN
ejpam-4624	427	6	,	,	PUNCT
ejpam-4624	427	7	42(2):649–656	42(2):649–656	NUM
ejpam-4624	427	8	,	,	PUNCT
ejpam-4624	427	9	2009	2009	NUM
ejpam-4624	427	10	.	.	PUNCT
ejpam-4624	428	1	[	[	X
ejpam-4624	428	2	15	15	NUM
ejpam-4624	428	3	]	]	X
ejpam-4624	428	4	tareq	tareq	PROPN
ejpam-4624	428	5	m.	m.	PROPN
ejpam-4624	428	6	al	al	PROPN
ejpam-4624	428	7	-	-	PUNCT
ejpam-4624	428	8	shami	shami	PROPN
ejpam-4624	428	9	,	,	PUNCT
ejpam-4624	428	10	josé	josé	PROPN
ejpam-4624	428	11	carlos	carlos	PROPN
ejpam-4624	428	12	r.	r.	PROPN
ejpam-4624	428	13	alcantud	alcantud	PROPN
ejpam-4624	428	14	,	,	PUNCT
ejpam-4624	428	15	and	and	CCONJ
ejpam-4624	428	16	abdelwaheb	abdelwaheb	PROPN
ejpam-4624	428	17	mhemdi	mhemdi	PROPN
ejpam-4624	428	18	.	.	PUNCT
ejpam-4624	429	1	new	new	ADJ
ejpam-4624	429	2	generalization	generalization	NOUN
ejpam-4624	429	3	of	of	ADP
ejpam-4624	429	4	fuzzy	fuzzy	ADJ
ejpam-4624	429	5	soft	soft	ADJ
ejpam-4624	429	6	sets	set	NOUN
ejpam-4624	429	7	:	:	PUNCT
ejpam-4624	429	8	(	(	PUNCT
ejpam-4624	429	9	a	a	PRON
ejpam-4624	429	10	,	,	PUNCT
ejpam-4624	429	11	b)-fuzzy	b)-fuzzy	PUNCT
ejpam-4624	429	12	soft	soft	ADJ
ejpam-4624	429	13	sets	set	NOUN
ejpam-4624	429	14	.	.	PUNCT
ejpam-4624	430	1	aims	aim	VERB
ejpam-4624	430	2	mathematics	mathematic	NOUN
ejpam-4624	430	3	,	,	PUNCT
ejpam-4624	430	4	8(2):2995–3025	8(2):2995–3025	NUM
ejpam-4624	430	5	,	,	PUNCT
ejpam-4624	430	6	2023	2023	NUM
ejpam-4624	430	7	.	.	PUNCT
ejpam-4624	431	1	[	[	X
ejpam-4624	431	2	16	16	NUM
ejpam-4624	431	3	]	]	PUNCT
ejpam-4624	431	4	s.	s.	PROPN
ejpam-4624	431	5	e.	e.	PROPN
ejpam-4624	431	6	abbas	abbas	PROPN
ejpam-4624	431	7	and	and	CCONJ
ejpam-4624	431	8	e.	e.	PROPN
ejpam-4624	431	9	el	el	PROPN
ejpam-4624	431	10	-	-	PUNCT
ejpam-4624	431	11	sanousy	sanousy	PROPN
ejpam-4624	431	12	.	.	PUNCT
ejpam-4624	432	1	several	several	ADJ
ejpam-4624	432	2	types	type	NOUN
ejpam-4624	432	3	of	of	ADP
ejpam-4624	432	4	double	double	ADJ
ejpam-4624	432	5	fuzzy	fuzzy	ADJ
ejpam-4624	432	6	semiclosed	semiclose	VERB
ejpam-4624	432	7	sets	set	NOUN
ejpam-4624	432	8	.	.	PUNCT
ejpam-4624	433	1	journal	journal	NOUN
ejpam-4624	433	2	of	of	ADP
ejpam-4624	433	3	fuzzy	fuzzy	ADJ
ejpam-4624	433	4	mathematics	mathematic	NOUN
ejpam-4624	433	5	,	,	PUNCT
ejpam-4624	433	6	20(1):89–102	20(1):89–102	NUM
ejpam-4624	433	7	,	,	PUNCT
ejpam-4624	433	8	2012	2012	NUM
ejpam-4624	433	9	.	.	PUNCT
ejpam-4624	434	1	[	[	X
ejpam-4624	434	2	17	17	NUM
ejpam-4624	434	3	]	]	PUNCT
ejpam-4624	434	4	a.	a.	NOUN
ejpam-4624	434	5	ghareeb	ghareeb	NOUN
ejpam-4624	434	6	.	.	PUNCT
ejpam-4624	435	1	weak	weak	ADJ
ejpam-4624	435	2	forms	form	NOUN
ejpam-4624	435	3	of	of	ADP
ejpam-4624	435	4	continuity	continuity	NOUN
ejpam-4624	435	5	in	in	ADP
ejpam-4624	435	6	i	i	PRON
ejpam-4624	435	7	-	-	PUNCT
ejpam-4624	435	8	double	double	ADJ
ejpam-4624	435	9	gradation	gradation	NOUN
ejpam-4624	435	10	fuzzy	fuzzy	ADJ
ejpam-4624	435	11	topological	topological	ADJ
ejpam-4624	435	12	spaces	space	NOUN
ejpam-4624	435	13	.	.	PUNCT
ejpam-4624	436	1	springerplus	springerplus	PROPN
ejpam-4624	436	2	,	,	PUNCT
ejpam-4624	436	3	1(1):47	1(1):47	NUM
ejpam-4624	436	4	,	,	PUNCT
ejpam-4624	436	5	2012	2012	NUM
ejpam-4624	436	6	.	.	PUNCT