id	sid	tid	token	lemma	pos
ejpam-5573	1	1	european	european	PROPN
ejpam-5573	1	2	journal	journal	PROPN
ejpam-5573	1	3	of	of	ADP
ejpam-5573	1	4	pure	pure	ADJ
ejpam-5573	1	5	and	and	CCONJ
ejpam-5573	1	6	applied	apply	VERB
ejpam-5573	1	7	mathematics	mathematic	NOUN
ejpam-5573	1	8	vol	vol	NOUN
ejpam-5573	1	9	.	.	PROPN
ejpam-5573	2	1	17	17	NUM
ejpam-5573	2	2	,	,	PUNCT
ejpam-5573	2	3	no	no	INTJ
ejpam-5573	2	4	.	.	NOUN
ejpam-5573	2	5	4	4	NUM
ejpam-5573	2	6	,	,	PUNCT
ejpam-5573	2	7	2024	2024	NUM
ejpam-5573	2	8	,	,	PUNCT
ejpam-5573	2	9	4093	4093	NUM
ejpam-5573	2	10	-	-	PUNCT
ejpam-5573	2	11	4111	4111	NUM
ejpam-5573	2	12	issn	issn	PROPN
ejpam-5573	2	13	1307	1307	NUM
ejpam-5573	2	14	-	-	SYM
ejpam-5573	2	15	5543	5543	NUM
ejpam-5573	2	16	–	–	PUNCT
ejpam-5573	2	17	ejpam.com	ejpam.com	X
ejpam-5573	2	18	published	publish	VERB
ejpam-5573	2	19	by	by	ADP
ejpam-5573	2	20	new	new	PROPN
ejpam-5573	2	21	york	york	PROPN
ejpam-5573	2	22	business	business	PROPN
ejpam-5573	2	23	global	global	VERB
ejpam-5573	2	24	some	some	DET
ejpam-5573	2	25	new	new	ADJ
ejpam-5573	2	26	types	type	NOUN
ejpam-5573	2	27	of	of	ADP
ejpam-5573	2	28	fuzzy	fuzzy	ADJ
ejpam-5573	2	29	closed	closed	ADJ
ejpam-5573	2	30	sets	set	NOUN
ejpam-5573	2	31	,	,	PUNCT
ejpam-5573	2	32	separation	separation	NOUN
ejpam-5573	2	33	axioms	axiom	NOUN
ejpam-5573	2	34	,	,	PUNCT
ejpam-5573	2	35	and	and	CCONJ
ejpam-5573	2	36	compactness	compactness	NOUN
ejpam-5573	2	37	via	via	ADP
ejpam-5573	2	38	double	double	ADJ
ejpam-5573	2	39	fuzzy	fuzzy	ADJ
ejpam-5573	2	40	topologies	topology	NOUN
ejpam-5573	2	41	fahad	fahad	ADJ
ejpam-5573	2	42	alsharari1	alsharari1	PROPN
ejpam-5573	2	43	,	,	PUNCT
ejpam-5573	2	44	osama	osama	PROPN
ejpam-5573	2	45	m.	m.	NOUN
ejpam-5573	2	46	taha2	taha2	PROPN
ejpam-5573	2	47	,	,	PUNCT
ejpam-5573	2	48	islam	islam	PROPN
ejpam-5573	2	49	m.	m.	PROPN
ejpam-5573	2	50	taha2,3,∗	taha2,3,∗	PROPN
ejpam-5573	2	51	1	1	NUM
ejpam-5573	2	52	department	department	NOUN
ejpam-5573	2	53	of	of	ADP
ejpam-5573	2	54	mathematics	mathematic	NOUN
ejpam-5573	2	55	,	,	PUNCT
ejpam-5573	2	56	college	college	NOUN
ejpam-5573	2	57	of	of	ADP
ejpam-5573	2	58	science	science	NOUN
ejpam-5573	2	59	,	,	PUNCT
ejpam-5573	2	60	jouf	jouf	PROPN
ejpam-5573	2	61	university	university	PROPN
ejpam-5573	2	62	,	,	PUNCT
ejpam-5573	2	63	sakaka	sakaka	PROPN
ejpam-5573	2	64	,	,	PUNCT
ejpam-5573	2	65	saudi	saudi	PROPN
ejpam-5573	2	66	arabia	arabia	PROPN
ejpam-5573	2	67	2	2	NUM
ejpam-5573	2	68	department	department	NOUN
ejpam-5573	2	69	of	of	ADP
ejpam-5573	2	70	mathematics	mathematic	NOUN
ejpam-5573	2	71	,	,	PUNCT
ejpam-5573	2	72	faculty	faculty	NOUN
ejpam-5573	2	73	of	of	ADP
ejpam-5573	2	74	science	science	NOUN
ejpam-5573	2	75	,	,	PUNCT
ejpam-5573	2	76	sohag	sohag	NOUN
ejpam-5573	2	77	university	university	NOUN
ejpam-5573	2	78	,	,	PUNCT
ejpam-5573	2	79	sohag	sohag	NOUN
ejpam-5573	2	80	,	,	PUNCT
ejpam-5573	2	81	egypt	egypt	PROPN
ejpam-5573	2	82	3	3	NUM
ejpam-5573	2	83	department	department	NOUN
ejpam-5573	2	84	of	of	ADP
ejpam-5573	2	85	basic	basic	ADJ
ejpam-5573	2	86	sciences	science	NOUN
ejpam-5573	2	87	,	,	PUNCT
ejpam-5573	2	88	higher	high	ADJ
ejpam-5573	2	89	institute	institute	NOUN
ejpam-5573	2	90	of	of	ADP
ejpam-5573	2	91	engineering	engineering	NOUN
ejpam-5573	2	92	and	and	CCONJ
ejpam-5573	2	93	technology	technology	NOUN
ejpam-5573	2	94	,	,	PUNCT
ejpam-5573	2	95	egypt	egypt	PROPN
ejpam-5573	2	96	abstract	abstract	PROPN
ejpam-5573	2	97	.	.	PUNCT
ejpam-5573	3	1	in	in	ADP
ejpam-5573	3	2	this	this	DET
ejpam-5573	3	3	article	article	NOUN
ejpam-5573	3	4	,	,	PUNCT
ejpam-5573	3	5	we	we	PRON
ejpam-5573	3	6	first	first	ADV
ejpam-5573	3	7	defined	define	VERB
ejpam-5573	3	8	a	a	DET
ejpam-5573	3	9	stronger	strong	ADJ
ejpam-5573	3	10	form	form	NOUN
ejpam-5573	3	11	of	of	ADP
ejpam-5573	3	12	(	(	PUNCT
ejpam-5573	3	13	r	r	NOUN
ejpam-5573	3	14	,	,	PUNCT
ejpam-5573	3	15	s)-generalized	s)-generalized	ADJ
ejpam-5573	3	16	fuzzy	fuzzy	ADJ
ejpam-5573	3	17	semi	semi	ADJ
ejpam-5573	3	18	-	-	ADJ
ejpam-5573	3	19	closed	closed	ADJ
ejpam-5573	3	20	sets	set	NOUN
ejpam-5573	3	21	⟨briefly	⟨briefly	VERB
ejpam-5573	3	22	,	,	PUNCT
ejpam-5573	3	23	(	(	PUNCT
ejpam-5573	3	24	r	r	NOUN
ejpam-5573	3	25	,	,	PUNCT
ejpam-5573	3	26	s)-gfsc	s)-gfsc	PROPN
ejpam-5573	4	1	sets⟩	sets⟩	PROPN
ejpam-5573	4	2	called	call	VERB
ejpam-5573	4	3	(	(	PUNCT
ejpam-5573	4	4	r	r	NOUN
ejpam-5573	4	5	,	,	PUNCT
ejpam-5573	4	6	s)−	s)−	PROPN
ejpam-5573	5	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	5	2	sets	set	VERB
ejpam-5573	5	3	and	and	CCONJ
ejpam-5573	5	4	investigated	investigate	VERB
ejpam-5573	5	5	some	some	PRON
ejpam-5573	5	6	of	of	ADP
ejpam-5573	5	7	its	its	PRON
ejpam-5573	5	8	features	feature	NOUN
ejpam-5573	5	9	.	.	PUNCT
ejpam-5573	6	1	moreover	moreover	ADV
ejpam-5573	6	2	,	,	PUNCT
ejpam-5573	6	3	we	we	PRON
ejpam-5573	6	4	showed	show	VERB
ejpam-5573	6	5	that	that	SCONJ
ejpam-5573	6	6	(	(	PUNCT
ejpam-5573	6	7	r	r	NOUN
ejpam-5573	6	8	,	,	PUNCT
ejpam-5573	6	9	s)−fsc	s)−fsc	X
ejpam-5573	6	10	set⇒	set⇒	PROPN
ejpam-5573	6	11	(	(	PUNCT
ejpam-5573	6	12	r	r	NOUN
ejpam-5573	6	13	,	,	PUNCT
ejpam-5573	6	14	s)−	s)−	PROPN
ejpam-5573	7	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	7	2	set⇒	set⇒	PROPN
ejpam-5573	7	3	(	(	PUNCT
ejpam-5573	7	4	r	r	NOUN
ejpam-5573	7	5	,	,	PUNCT
ejpam-5573	7	6	s)−	s)−	PROPN
ejpam-5573	7	7	gfsc	gfsc	PROPN
ejpam-5573	7	8	set	set	VERB
ejpam-5573	7	9	,	,	PUNCT
ejpam-5573	7	10	but	but	CCONJ
ejpam-5573	7	11	the	the	DET
ejpam-5573	7	12	converse	converse	NOUN
ejpam-5573	7	13	may	may	AUX
ejpam-5573	7	14	not	not	PART
ejpam-5573	7	15	be	be	AUX
ejpam-5573	7	16	true	true	ADJ
ejpam-5573	7	17	.	.	PUNCT
ejpam-5573	8	1	in	in	ADP
ejpam-5573	8	2	addition	addition	NOUN
ejpam-5573	8	3	,	,	PUNCT
ejpam-5573	8	4	we	we	PRON
ejpam-5573	8	5	explored	explore	VERB
ejpam-5573	8	6	novel	novel	ADJ
ejpam-5573	8	7	types	type	NOUN
ejpam-5573	8	8	of	of	ADP
ejpam-5573	8	9	fuzzy	fuzzy	ADJ
ejpam-5573	8	10	generalized	generalized	ADJ
ejpam-5573	8	11	mappings	mapping	NOUN
ejpam-5573	8	12	between	between	ADP
ejpam-5573	8	13	double	double	ADJ
ejpam-5573	8	14	fuzzy	fuzzy	ADJ
ejpam-5573	8	15	topological	topological	ADJ
ejpam-5573	8	16	spaces	space	NOUN
ejpam-5573	8	17	(	(	PUNCT
ejpam-5573	8	18	u	u	NOUN
ejpam-5573	8	19	,	,	PUNCT
ejpam-5573	8	20	τ	τ	PROPN
ejpam-5573	8	21	,	,	PUNCT
ejpam-5573	8	22	τ∗	τ∗	PROPN
ejpam-5573	8	23	)	)	PUNCT
ejpam-5573	8	24	and	and	CCONJ
ejpam-5573	8	25	(	(	PUNCT
ejpam-5573	8	26	v	v	NOUN
ejpam-5573	8	27	,	,	PUNCT
ejpam-5573	8	28	η	η	NOUN
ejpam-5573	8	29	,	,	PUNCT
ejpam-5573	8	30	η∗	η∗	NOUN
ejpam-5573	8	31	)	)	PUNCT
ejpam-5573	8	32	,	,	PUNCT
ejpam-5573	8	33	and	and	CCONJ
ejpam-5573	8	34	the	the	DET
ejpam-5573	8	35	relationships	relationship	NOUN
ejpam-5573	8	36	between	between	ADP
ejpam-5573	8	37	these	these	DET
ejpam-5573	8	38	classes	class	NOUN
ejpam-5573	8	39	of	of	ADP
ejpam-5573	8	40	mappings	mapping	NOUN
ejpam-5573	8	41	were	be	AUX
ejpam-5573	8	42	examined	examine	VERB
ejpam-5573	8	43	with	with	ADP
ejpam-5573	8	44	the	the	DET
ejpam-5573	8	45	help	help	NOUN
ejpam-5573	8	46	of	of	ADP
ejpam-5573	8	47	some	some	DET
ejpam-5573	8	48	illustrative	illustrative	ADJ
ejpam-5573	8	49	examples	example	NOUN
ejpam-5573	8	50	.	.	PUNCT
ejpam-5573	9	1	thereafter	thereafter	ADV
ejpam-5573	9	2	,	,	PUNCT
ejpam-5573	9	3	we	we	PRON
ejpam-5573	9	4	introduced	introduce	VERB
ejpam-5573	9	5	novel	novel	ADJ
ejpam-5573	9	6	types	type	NOUN
ejpam-5573	9	7	of	of	ADP
ejpam-5573	9	8	higher	high	ADJ
ejpam-5573	9	9	separation	separation	NOUN
ejpam-5573	9	10	axioms	axiom	NOUN
ejpam-5573	9	11	called	call	VERB
ejpam-5573	9	12	(	(	PUNCT
ejpam-5573	9	13	r	r	NOUN
ejpam-5573	9	14	,	,	PUNCT
ejpam-5573	9	15	s)-gfs	s)-gf	NOUN
ejpam-5573	9	16	-	-	PUNCT
ejpam-5573	9	17	regular	regular	ADJ
ejpam-5573	9	18	and	and	CCONJ
ejpam-5573	9	19	(	(	PUNCT
ejpam-5573	9	20	r	r	NOUN
ejpam-5573	9	21	,	,	PUNCT
ejpam-5573	9	22	s)-gfs	s)-gf	NOUN
ejpam-5573	9	23	-	-	PUNCT
ejpam-5573	9	24	normal	normal	ADJ
ejpam-5573	9	25	spaces	space	NOUN
ejpam-5573	9	26	with	with	ADP
ejpam-5573	9	27	the	the	DET
ejpam-5573	9	28	help	help	NOUN
ejpam-5573	9	29	of	of	ADP
ejpam-5573	9	30	(	(	PUNCT
ejpam-5573	9	31	r	r	NOUN
ejpam-5573	9	32	,	,	PUNCT
ejpam-5573	9	33	s)-gfsc	s)-gfsc	NOUN
ejpam-5573	9	34	sets	set	VERB
ejpam-5573	9	35	and	and	CCONJ
ejpam-5573	9	36	discussed	discuss	VERB
ejpam-5573	9	37	some	some	DET
ejpam-5573	9	38	topological	topological	ADJ
ejpam-5573	9	39	properties	property	NOUN
ejpam-5573	9	40	of	of	ADP
ejpam-5573	9	41	them	they	PRON
ejpam-5573	9	42	.	.	PUNCT
ejpam-5573	10	1	finally	finally	ADV
ejpam-5573	10	2	,	,	PUNCT
ejpam-5573	10	3	some	some	DET
ejpam-5573	10	4	novel	novel	ADJ
ejpam-5573	10	5	types	type	NOUN
ejpam-5573	10	6	of	of	ADP
ejpam-5573	10	7	compactness	compactness	NOUN
ejpam-5573	10	8	via	via	ADP
ejpam-5573	10	9	(	(	PUNCT
ejpam-5573	10	10	r	r	NOUN
ejpam-5573	10	11	,	,	PUNCT
ejpam-5573	10	12	s)-gfso	s)-gfso	NOUN
ejpam-5573	10	13	sets	set	NOUN
ejpam-5573	10	14	were	be	AUX
ejpam-5573	10	15	defined	define	VERB
ejpam-5573	10	16	and	and	CCONJ
ejpam-5573	10	17	the	the	DET
ejpam-5573	10	18	relationships	relationship	NOUN
ejpam-5573	10	19	between	between	ADP
ejpam-5573	10	20	them	they	PRON
ejpam-5573	10	21	were	be	AUX
ejpam-5573	10	22	introduced	introduce	VERB
ejpam-5573	10	23	.	.	PUNCT
ejpam-5573	11	1	2020	2020	NUM
ejpam-5573	11	2	mathematics	mathematics	PROPN
ejpam-5573	11	3	subject	subject	NOUN
ejpam-5573	11	4	classifications	classification	NOUN
ejpam-5573	11	5	:	:	PUNCT
ejpam-5573	11	6	03e72	03e72	NUM
ejpam-5573	11	7	,	,	PUNCT
ejpam-5573	11	8	54a05	54a05	NUM
ejpam-5573	11	9	,	,	PUNCT
ejpam-5573	11	10	54a40	54a40	NUM
ejpam-5573	11	11	,	,	PUNCT
ejpam-5573	11	12	54c08	54c08	NUM
ejpam-5573	11	13	,	,	PUNCT
ejpam-5573	11	14	54d15	54d15	PRON
ejpam-5573	11	15	key	key	ADJ
ejpam-5573	11	16	words	word	NOUN
ejpam-5573	11	17	and	and	CCONJ
ejpam-5573	11	18	phrases	phrase	NOUN
ejpam-5573	11	19	:	:	PUNCT
ejpam-5573	11	20	intuitionistic	intuitionistic	ADJ
ejpam-5573	11	21	fuzzy	fuzzy	ADJ
ejpam-5573	11	22	set	set	NOUN
ejpam-5573	11	23	,	,	PUNCT
ejpam-5573	11	24	double	double	ADJ
ejpam-5573	11	25	fuzzy	fuzzy	ADJ
ejpam-5573	11	26	topology	topology	NOUN
ejpam-5573	11	27	,	,	PUNCT
ejpam-5573	11	28	(	(	PUNCT
ejpam-5573	11	29	r	r	NOUN
ejpam-5573	11	30	,	,	PUNCT
ejpam-5573	11	31	s	s	NOUN
ejpam-5573	11	32	)	)	PUNCT
ejpam-5573	11	33	−	−	PROPN
ejpam-5573	11	34	gfsc	gfsc	PROPN
ejpam-5573	11	35	set	set	PROPN
ejpam-5573	11	36	,	,	PUNCT
ejpam-5573	11	37	(	(	PUNCT
ejpam-5573	11	38	r	r	NOUN
ejpam-5573	11	39	,	,	PUNCT
ejpam-5573	11	40	s)−	s)−	PROPN
ejpam-5573	12	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	12	2	set	set	NOUN
ejpam-5573	12	3	,	,	PUNCT
ejpam-5573	12	4	continuity	continuity	NOUN
ejpam-5573	12	5	,	,	PUNCT
ejpam-5573	12	6	(	(	PUNCT
ejpam-5573	12	7	r	r	NOUN
ejpam-5573	12	8	,	,	PUNCT
ejpam-5573	12	9	s)-gfs	s)-gf	NOUN
ejpam-5573	12	10	-	-	PUNCT
ejpam-5573	12	11	regular	regular	ADJ
ejpam-5573	12	12	space	space	NOUN
ejpam-5573	12	13	,	,	PUNCT
ejpam-5573	12	14	(	(	PUNCT
ejpam-5573	12	15	r	r	NOUN
ejpam-5573	12	16	,	,	PUNCT
ejpam-5573	12	17	s)-gfs	s)-gf	NOUN
ejpam-5573	12	18	-	-	PUNCT
ejpam-5573	12	19	normal	normal	ADJ
ejpam-5573	12	20	space	space	NOUN
ejpam-5573	12	21	,	,	PUNCT
ejpam-5573	12	22	compactness	compactness	NOUN
ejpam-5573	12	23	1	1	NUM
ejpam-5573	12	24	.	.	PUNCT
ejpam-5573	12	25	introduction	introduction	NOUN
ejpam-5573	12	26	and	and	CCONJ
ejpam-5573	12	27	preliminaries	preliminary	NOUN
ejpam-5573	12	28	the	the	DET
ejpam-5573	12	29	theory	theory	NOUN
ejpam-5573	12	30	of	of	ADP
ejpam-5573	12	31	fuzzy	fuzzy	ADJ
ejpam-5573	12	32	set	set	NOUN
ejpam-5573	12	33	was	be	AUX
ejpam-5573	12	34	first	first	ADV
ejpam-5573	12	35	presented	present	VERB
ejpam-5573	12	36	by	by	ADP
ejpam-5573	12	37	zadeh	zadeh	PROPN
ejpam-5573	12	38	[	[	X
ejpam-5573	12	39	46	46	NUM
ejpam-5573	12	40	]	]	PUNCT
ejpam-5573	12	41	.	.	PUNCT
ejpam-5573	13	1	since	since	SCONJ
ejpam-5573	13	2	then	then	ADV
ejpam-5573	13	3	it	it	PRON
ejpam-5573	13	4	has	have	AUX
ejpam-5573	13	5	been	be	AUX
ejpam-5573	13	6	improved	improve	VERB
ejpam-5573	13	7	and	and	CCONJ
ejpam-5573	13	8	applied	apply	VERB
ejpam-5573	13	9	in	in	ADP
ejpam-5573	13	10	most	most	ADJ
ejpam-5573	13	11	all	all	DET
ejpam-5573	13	12	the	the	DET
ejpam-5573	13	13	branches	branch	NOUN
ejpam-5573	13	14	of	of	ADP
ejpam-5573	13	15	technology	technology	NOUN
ejpam-5573	13	16	and	and	CCONJ
ejpam-5573	13	17	science	science	NOUN
ejpam-5573	13	18	,	,	PUNCT
ejpam-5573	13	19	where	where	SCONJ
ejpam-5573	13	20	theory	theory	NOUN
ejpam-5573	13	21	of	of	ADP
ejpam-5573	13	22	sets	set	NOUN
ejpam-5573	13	23	and	and	CCONJ
ejpam-5573	13	24	mathematical	mathematical	ADJ
ejpam-5573	13	25	logic	logic	NOUN
ejpam-5573	13	26	play	play	VERB
ejpam-5573	13	27	an	an	DET
ejpam-5573	13	28	important	important	ADJ
ejpam-5573	13	29	role	role	NOUN
ejpam-5573	13	30	.	.	PUNCT
ejpam-5573	14	1	also	also	ADV
ejpam-5573	14	2	,	,	PUNCT
ejpam-5573	14	3	many	many	ADJ
ejpam-5573	14	4	applications	application	NOUN
ejpam-5573	14	5	of	of	ADP
ejpam-5573	14	6	these	these	DET
ejpam-5573	14	7	theory	theory	NOUN
ejpam-5573	14	8	contributed	contribute	VERB
ejpam-5573	14	9	to	to	ADP
ejpam-5573	14	10	solving	solve	VERB
ejpam-5573	14	11	several	several	ADJ
ejpam-5573	14	12	practical	practical	ADJ
ejpam-5573	14	13	problems	problem	NOUN
ejpam-5573	14	14	in	in	ADP
ejpam-5573	14	15	mathematics	mathematic	NOUN
ejpam-5573	14	16	,	,	PUNCT
ejpam-5573	14	17	social	social	ADJ
ejpam-5573	14	18	science	science	NOUN
ejpam-5573	14	19	,	,	PUNCT
ejpam-5573	14	20	engineering	engineering	NOUN
ejpam-5573	14	21	,	,	PUNCT
ejpam-5573	14	22	economics	economic	NOUN
ejpam-5573	14	23	,	,	PUNCT
ejpam-5573	14	24	etc	etc	X
ejpam-5573	14	25	.	.	X
ejpam-5573	14	26	in	in	ADP
ejpam-5573	14	27	recent	recent	ADJ
ejpam-5573	14	28	years	year	NOUN
ejpam-5573	14	29	,	,	PUNCT
ejpam-5573	14	30	many	many	ADJ
ejpam-5573	14	31	authors	author	NOUN
ejpam-5573	14	32	have	have	AUX
ejpam-5573	14	33	contributed	contribute	VERB
ejpam-5573	14	34	to	to	ADP
ejpam-5573	14	35	fuzzy	fuzzy	ADJ
ejpam-5573	14	36	sets	set	NOUN
ejpam-5573	14	37	theory	theory	NOUN
ejpam-5573	14	38	in	in	ADP
ejpam-5573	14	39	the	the	DET
ejpam-5573	14	40	different	different	ADJ
ejpam-5573	14	41	directions	direction	NOUN
ejpam-5573	14	42	in	in	ADP
ejpam-5573	14	43	mathematics	mathematic	NOUN
ejpam-5573	14	44	such	such	ADJ
ejpam-5573	14	45	as	as	ADP
ejpam-5573	14	46	geometry	geometry	NOUN
ejpam-5573	14	47	,	,	PUNCT
ejpam-5573	14	48	topology	topology	NOUN
ejpam-5573	14	49	,	,	PUNCT
ejpam-5573	14	50	algebra	algebra	NOUN
ejpam-5573	14	51	,	,	PUNCT
ejpam-5573	14	52	operation	operation	NOUN
ejpam-5573	14	53	research	research	NOUN
ejpam-5573	14	54	,	,	PUNCT
ejpam-5573	14	55	see	see	VERB
ejpam-5573	14	56	[	[	X
ejpam-5573	14	57	31	31	NUM
ejpam-5573	14	58	,	,	PUNCT
ejpam-5573	14	59	48	48	NUM
ejpam-5573	14	60	]	]	PUNCT
ejpam-5573	14	61	.	.	PUNCT
ejpam-5573	15	1	the	the	DET
ejpam-5573	15	2	notion	notion	NOUN
ejpam-5573	15	3	of	of	ADP
ejpam-5573	15	4	fuzzy	fuzzy	ADJ
ejpam-5573	15	5	sets	set	NOUN
ejpam-5573	15	6	was	be	AUX
ejpam-5573	15	7	used	use	VERB
ejpam-5573	15	8	to	to	PART
ejpam-5573	15	9	introduce	introduce	VERB
ejpam-5573	15	10	fuzzy	fuzzy	ADJ
ejpam-5573	15	11	topological	topological	ADJ
ejpam-5573	15	12	spaces	space	NOUN
ejpam-5573	15	13	in	in	ADP
ejpam-5573	15	14	[	[	X
ejpam-5573	15	15	15	15	NUM
ejpam-5573	15	16	]	]	PUNCT
ejpam-5573	15	17	.	.	PUNCT
ejpam-5573	16	1	the	the	DET
ejpam-5573	16	2	study	study	NOUN
ejpam-5573	16	3	in	in	ADP
ejpam-5573	16	4	[	[	X
ejpam-5573	16	5	15	15	NUM
ejpam-5573	16	6	]	]	PUNCT
ejpam-5573	16	7	was	be	AUX
ejpam-5573	16	8	particularly	particularly	ADV
ejpam-5573	16	9	important	important	ADJ
ejpam-5573	16	10	in	in	ADP
ejpam-5573	16	11	the	the	DET
ejpam-5573	16	12	development	development	NOUN
ejpam-5573	16	13	of	of	ADP
ejpam-5573	16	14	the	the	DET
ejpam-5573	16	15	field	field	NOUN
ejpam-5573	16	16	of	of	ADP
ejpam-5573	16	17	fuzzy	fuzzy	ADJ
ejpam-5573	16	18	topology	topology	NOUN
ejpam-5573	16	19	,	,	PUNCT
ejpam-5573	16	20	see	see	VERB
ejpam-5573	16	21	[	[	X
ejpam-5573	16	22	3	3	NUM
ejpam-5573	16	23	,	,	PUNCT
ejpam-5573	16	24	14	14	NUM
ejpam-5573	16	25	,	,	PUNCT
ejpam-5573	16	26	16	16	NUM
ejpam-5573	16	27	,	,	PUNCT
ejpam-5573	16	28	19	19	NUM
ejpam-5573	16	29	,	,	PUNCT
ejpam-5573	16	30	26	26	NUM
ejpam-5573	16	31	,	,	PUNCT
ejpam-5573	16	32	27	27	NUM
ejpam-5573	16	33	]	]	PUNCT
ejpam-5573	16	34	.	.	PUNCT
ejpam-5573	17	1	the	the	DET
ejpam-5573	17	2	authors	author	NOUN
ejpam-5573	17	3	of	of	ADP
ejpam-5573	17	4	[	[	X
ejpam-5573	17	5	4–10	4–10	NOUN
ejpam-5573	17	6	,	,	PUNCT
ejpam-5573	17	7	21	21	NUM
ejpam-5573	17	8	,	,	PUNCT
ejpam-5573	17	9	28	28	NUM
ejpam-5573	17	10	,	,	PUNCT
ejpam-5573	17	11	36	36	NUM
ejpam-5573	17	12	,	,	PUNCT
ejpam-5573	17	13	39	39	NUM
ejpam-5573	17	14	]	]	PUNCT
ejpam-5573	17	15	∗corresponding	∗corresponde	VERB
ejpam-5573	17	16	author	author	NOUN
ejpam-5573	17	17	.	.	PUNCT
ejpam-5573	18	1	doi	doi	NOUN
ejpam-5573	18	2	:	:	PUNCT
ejpam-5573	18	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5573	https://doi.org/10.29020/nybg.ejpam.v17i4.5573	NOUN
ejpam-5573	18	4	email	email	NOUN
ejpam-5573	18	5	addresses	address	NOUN
ejpam-5573	18	6	:	:	PUNCT
ejpam-5573	18	7	f.alsharari@ju.edu.sa	f.alsharari@ju.edu.sa	PROPN
ejpam-5573	18	8	(	(	PUNCT
ejpam-5573	18	9	f.	f.	PROPN
ejpam-5573	18	10	alsharari	alsharari	PROPN
ejpam-5573	18	11	)	)	PUNCT
ejpam-5573	18	12	,	,	PUNCT
ejpam-5573	18	13	osama.taha2015@yahoo.com	osama.taha2015@yahoo.com	NUM
ejpam-5573	18	14	(	(	PUNCT
ejpam-5573	18	15	o.	o.	PROPN
ejpam-5573	18	16	m.	m.	PROPN
ejpam-5573	18	17	taha	taha	PROPN
ejpam-5573	18	18	)	)	PUNCT
ejpam-5573	18	19	,	,	PUNCT
ejpam-5573	18	20	imtaha2010@yahoo.com	imtaha2010@yahoo.com	X
ejpam-5573	18	21	(	(	PUNCT
ejpam-5573	18	22	i.	i.	PROPN
ejpam-5573	18	23	m.	m.	PROPN
ejpam-5573	18	24	taha	taha	PROPN
ejpam-5573	18	25	)	)	PUNCT
ejpam-5573	18	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5573	18	27	4093	4093	NUM
ejpam-5573	18	28	copyright	copyright	NOUN
ejpam-5573	18	29	:	:	PUNCT
ejpam-5573	18	30	©	©	PROPN
ejpam-5573	18	31	2024	2024	NUM
ejpam-5573	18	32	the	the	DET
ejpam-5573	18	33	author(s	author(s	NOUN
ejpam-5573	18	34	)	)	PUNCT
ejpam-5573	18	35	.	.	PUNCT
ejpam-5573	19	1	(	(	PUNCT
ejpam-5573	19	2	cc	cc	NOUN
ejpam-5573	19	3	by	by	ADP
ejpam-5573	19	4	-	-	PUNCT
ejpam-5573	19	5	nc	nc	PROPN
ejpam-5573	19	6	4.0	4.0	NUM
ejpam-5573	19	7	)	)	PUNCT
ejpam-5573	19	8	f.	f.	PROPN
ejpam-5573	19	9	alsharari	alsharari	PROPN
ejpam-5573	19	10	,	,	PUNCT
ejpam-5573	19	11	o.	o.	PROPN
ejpam-5573	19	12	m.	m.	PROPN
ejpam-5573	19	13	taha	taha	PROPN
ejpam-5573	19	14	,	,	PUNCT
ejpam-5573	19	15	i.	i.	PROPN
ejpam-5573	19	16	m.	m.	PROPN
ejpam-5573	19	17	taha	taha	PROPN
ejpam-5573	19	18	/	/	PUNCT
ejpam-5573	19	19	eur	eur	PROPN
ejpam-5573	19	20	.	.	PUNCT
ejpam-5573	20	1	j.	j.	PROPN
ejpam-5573	20	2	pure	pure	PROPN
ejpam-5573	20	3	appl	appl	PROPN
ejpam-5573	20	4	.	.	PROPN
ejpam-5573	20	5	math	math	PROPN
ejpam-5573	20	6	,	,	PUNCT
ejpam-5573	20	7	17	17	NUM
ejpam-5573	20	8	(	(	PUNCT
ejpam-5573	20	9	4	4	NUM
ejpam-5573	20	10	)	)	PUNCT
ejpam-5573	20	11	(	(	PUNCT
ejpam-5573	20	12	2024	2024	NUM
ejpam-5573	20	13	)	)	PUNCT
ejpam-5573	20	14	,	,	PUNCT
ejpam-5573	20	15	4093	4093	NUM
ejpam-5573	20	16	-	-	SYM
ejpam-5573	20	17	4111	4111	NUM
ejpam-5573	20	18	4094	4094	NUM
ejpam-5573	20	19	studied	study	VERB
ejpam-5573	20	20	topological	topological	ADJ
ejpam-5573	20	21	structures	structure	NOUN
ejpam-5573	20	22	inspired	inspire	VERB
ejpam-5573	20	23	by	by	ADP
ejpam-5573	20	24	the	the	DET
ejpam-5573	20	25	hybridizations	hybridization	NOUN
ejpam-5573	20	26	of	of	ADP
ejpam-5573	20	27	soft	soft	ADJ
ejpam-5573	20	28	sets	set	NOUN
ejpam-5573	20	29	[	[	X
ejpam-5573	20	30	33	33	NUM
ejpam-5573	20	31	]	]	PUNCT
ejpam-5573	20	32	with	with	ADP
ejpam-5573	20	33	fuzzy	fuzzy	ADJ
ejpam-5573	20	34	sets	set	NOUN
ejpam-5573	20	35	[	[	X
ejpam-5573	20	36	46	46	NUM
ejpam-5573	20	37	]	]	PUNCT
ejpam-5573	20	38	and	and	CCONJ
ejpam-5573	20	39	rough	rough	ADJ
ejpam-5573	20	40	sets	set	NOUN
ejpam-5573	20	41	[	[	X
ejpam-5573	20	42	24	24	NUM
ejpam-5573	20	43	]	]	PUNCT
ejpam-5573	20	44	.	.	PUNCT
ejpam-5573	21	1	the	the	DET
ejpam-5573	21	2	concept	concept	NOUN
ejpam-5573	21	3	of	of	ADP
ejpam-5573	21	4	an	an	DET
ejpam-5573	21	5	intuitionistic	intuitionistic	ADJ
ejpam-5573	21	6	fuzzy	fuzzy	ADJ
ejpam-5573	21	7	set	set	NOUN
ejpam-5573	21	8	was	be	AUX
ejpam-5573	21	9	initiated	initiate	VERB
ejpam-5573	21	10	by	by	ADP
ejpam-5573	21	11	atanassov	atanassov	NOUN
ejpam-5573	21	12	[	[	X
ejpam-5573	21	13	11	11	NUM
ejpam-5573	21	14	,	,	PUNCT
ejpam-5573	21	15	12	12	NUM
ejpam-5573	21	16	]	]	PUNCT
ejpam-5573	21	17	,	,	PUNCT
ejpam-5573	21	18	which	which	PRON
ejpam-5573	21	19	is	be	AUX
ejpam-5573	21	20	a	a	DET
ejpam-5573	21	21	generalization	generalization	NOUN
ejpam-5573	21	22	of	of	ADP
ejpam-5573	21	23	a	a	DET
ejpam-5573	21	24	fuzzy	fuzzy	ADJ
ejpam-5573	21	25	set	set	NOUN
ejpam-5573	21	26	.	.	PUNCT
ejpam-5573	22	1	coker	coker	NOUN
ejpam-5573	23	1	[	[	X
ejpam-5573	23	2	17	17	NUM
ejpam-5573	23	3	,	,	PUNCT
ejpam-5573	23	4	18	18	NUM
ejpam-5573	23	5	]	]	PUNCT
ejpam-5573	23	6	introduced	introduce	VERB
ejpam-5573	23	7	the	the	DET
ejpam-5573	23	8	concept	concept	NOUN
ejpam-5573	23	9	of	of	ADP
ejpam-5573	23	10	an	an	DET
ejpam-5573	23	11	intuitionistic	intuitionistic	ADJ
ejpam-5573	23	12	fuzzy	fuzzy	ADJ
ejpam-5573	23	13	topological	topological	ADJ
ejpam-5573	23	14	space	space	NOUN
ejpam-5573	23	15	based	base	VERB
ejpam-5573	23	16	on	on	ADP
ejpam-5573	23	17	the	the	DET
ejpam-5573	23	18	sense	sense	NOUN
ejpam-5573	23	19	of	of	ADP
ejpam-5573	23	20	chang	chang	PROPN
ejpam-5573	24	1	[	[	X
ejpam-5573	24	2	15	15	NUM
ejpam-5573	24	3	]	]	PUNCT
ejpam-5573	24	4	.	.	PUNCT
ejpam-5573	25	1	later	later	ADV
ejpam-5573	25	2	,	,	PUNCT
ejpam-5573	25	3	samanta	samanta	PROPN
ejpam-5573	25	4	and	and	CCONJ
ejpam-5573	25	5	mondal	mondal	PROPN
ejpam-5573	25	6	[	[	X
ejpam-5573	25	7	34	34	NUM
ejpam-5573	25	8	,	,	PUNCT
ejpam-5573	25	9	35	35	NUM
ejpam-5573	25	10	]	]	PUNCT
ejpam-5573	25	11	gave	give	VERB
ejpam-5573	25	12	the	the	DET
ejpam-5573	25	13	definition	definition	NOUN
ejpam-5573	25	14	of	of	ADP
ejpam-5573	25	15	an	an	DET
ejpam-5573	25	16	intuitionistic	intuitionistic	ADJ
ejpam-5573	25	17	fuzzy	fuzzy	ADJ
ejpam-5573	25	18	topological	topological	ADJ
ejpam-5573	25	19	space	space	NOUN
ejpam-5573	25	20	based	base	VERB
ejpam-5573	25	21	on	on	ADP
ejpam-5573	25	22	the	the	DET
ejpam-5573	25	23	sense	sense	NOUN
ejpam-5573	25	24	of	of	ADP
ejpam-5573	25	25	šostak	šostak	NOUN
ejpam-5573	25	26	[	[	X
ejpam-5573	25	27	45	45	NUM
ejpam-5573	25	28	]	]	PUNCT
ejpam-5573	25	29	.	.	PUNCT
ejpam-5573	26	1	the	the	DET
ejpam-5573	26	2	name	name	NOUN
ejpam-5573	26	3	(	(	PUNCT
ejpam-5573	26	4	intuitionistic	intuitionistic	ADJ
ejpam-5573	26	5	)	)	PUNCT
ejpam-5573	26	6	was	be	AUX
ejpam-5573	26	7	replaced	replace	VERB
ejpam-5573	26	8	with	with	ADP
ejpam-5573	26	9	the	the	DET
ejpam-5573	26	10	name	name	NOUN
ejpam-5573	26	11	(	(	PUNCT
ejpam-5573	26	12	double	double	ADJ
ejpam-5573	26	13	)	)	PUNCT
ejpam-5573	26	14	by	by	ADP
ejpam-5573	26	15	garcia	garcia	PROPN
ejpam-5573	26	16	and	and	CCONJ
ejpam-5573	26	17	rodabaugh	rodabaugh	ADJ
ejpam-5573	26	18	[	[	X
ejpam-5573	26	19	25	25	NUM
ejpam-5573	26	20	]	]	PUNCT
ejpam-5573	26	21	.	.	PUNCT
ejpam-5573	27	1	the	the	DET
ejpam-5573	27	2	concept	concept	NOUN
ejpam-5573	27	3	of	of	ADP
ejpam-5573	27	4	(	(	PUNCT
ejpam-5573	27	5	r	r	NOUN
ejpam-5573	27	6	,	,	PUNCT
ejpam-5573	27	7	s	s	NOUN
ejpam-5573	27	8	)	)	PUNCT
ejpam-5573	27	9	−	−	NOUN
ejpam-5573	27	10	gfc	gfc	NOUN
ejpam-5573	27	11	sets	set	NOUN
ejpam-5573	27	12	was	be	AUX
ejpam-5573	27	13	introduced	introduce	VERB
ejpam-5573	27	14	and	and	CCONJ
ejpam-5573	27	15	investigated	investigate	VERB
ejpam-5573	27	16	by	by	ADP
ejpam-5573	27	17	abbas	abbas	PROPN
ejpam-5573	28	1	[	[	X
ejpam-5573	28	2	1	1	NUM
ejpam-5573	28	3	]	]	PUNCT
ejpam-5573	28	4	.	.	PUNCT
ejpam-5573	29	1	thereafter	thereafter	ADV
ejpam-5573	29	2	,	,	PUNCT
ejpam-5573	29	3	the	the	DET
ejpam-5573	29	4	concept	concept	NOUN
ejpam-5573	29	5	of	of	ADP
ejpam-5573	29	6	(	(	PUNCT
ejpam-5573	29	7	r	r	NOUN
ejpam-5573	29	8	,	,	PUNCT
ejpam-5573	29	9	s	s	NOUN
ejpam-5573	29	10	)	)	PUNCT
ejpam-5573	29	11	−	−	NOUN
ejpam-5573	29	12	sgfc	sgfc	NOUN
ejpam-5573	29	13	sets	set	NOUN
ejpam-5573	29	14	was	be	AUX
ejpam-5573	29	15	introduced	introduce	VERB
ejpam-5573	29	16	by	by	ADP
ejpam-5573	29	17	zahran	zahran	PROPN
ejpam-5573	29	18	et	et	PROPN
ejpam-5573	29	19	al	al	PROPN
ejpam-5573	29	20	.	.	PUNCT
ejpam-5573	30	1	[	[	X
ejpam-5573	30	2	47	47	NUM
ejpam-5573	30	3	]	]	PUNCT
ejpam-5573	30	4	on	on	ADP
ejpam-5573	30	5	double	double	ADJ
ejpam-5573	30	6	fuzzy	fuzzy	ADJ
ejpam-5573	30	7	topological	topological	ADJ
ejpam-5573	30	8	space	space	NOUN
ejpam-5573	30	9	based	base	VERB
ejpam-5573	30	10	on	on	ADP
ejpam-5573	30	11	the	the	DET
ejpam-5573	30	12	sense	sense	NOUN
ejpam-5573	30	13	of	of	ADP
ejpam-5573	30	14	šostak	šostak	NOUN
ejpam-5573	30	15	.	.	PUNCT
ejpam-5573	31	1	also	also	ADV
ejpam-5573	31	2	,	,	PUNCT
ejpam-5573	31	3	taha	taha	PROPN
ejpam-5573	32	1	[	[	X
ejpam-5573	32	2	42	42	NUM
ejpam-5573	32	3	]	]	PUNCT
ejpam-5573	32	4	defined	define	VERB
ejpam-5573	32	5	the	the	DET
ejpam-5573	32	6	concept	concept	NOUN
ejpam-5573	32	7	of	of	ADP
ejpam-5573	32	8	(	(	PUNCT
ejpam-5573	32	9	r	r	NOUN
ejpam-5573	32	10	,	,	PUNCT
ejpam-5573	32	11	s)−gfsc	s)−gfsc	PROPN
ejpam-5573	32	12	sets	set	NOUN
ejpam-5573	32	13	and	and	CCONJ
ejpam-5573	32	14	some	some	DET
ejpam-5573	32	15	characterizations	characterization	NOUN
ejpam-5573	32	16	were	be	AUX
ejpam-5573	32	17	given	give	VERB
ejpam-5573	32	18	.	.	PUNCT
ejpam-5573	33	1	so	so	ADV
ejpam-5573	33	2	far	far	ADV
ejpam-5573	33	3	,	,	PUNCT
ejpam-5573	33	4	lots	lot	NOUN
ejpam-5573	33	5	of	of	ADP
ejpam-5573	33	6	spectacular	spectacular	ADJ
ejpam-5573	33	7	and	and	CCONJ
ejpam-5573	33	8	creative	creative	ADJ
ejpam-5573	33	9	studies	study	NOUN
ejpam-5573	33	10	about	about	ADP
ejpam-5573	33	11	the	the	DET
ejpam-5573	33	12	theories	theory	NOUN
ejpam-5573	33	13	of	of	ADP
ejpam-5573	33	14	an	an	DET
ejpam-5573	33	15	intuitionistic	intuitionistic	ADJ
ejpam-5573	33	16	fuzzy	fuzzy	ADJ
ejpam-5573	33	17	set	set	NOUN
ejpam-5573	33	18	have	have	AUX
ejpam-5573	33	19	been	be	AUX
ejpam-5573	33	20	considered	consider	VERB
ejpam-5573	33	21	by	by	ADP
ejpam-5573	33	22	some	some	DET
ejpam-5573	33	23	scholars	scholar	NOUN
ejpam-5573	33	24	,	,	PUNCT
ejpam-5573	33	25	see	see	VERB
ejpam-5573	33	26	e.	e.	PROPN
ejpam-5573	33	27	g.	g.	PROPN
ejpam-5573	34	1	[	[	X
ejpam-5573	34	2	2	2	NUM
ejpam-5573	34	3	,	,	PUNCT
ejpam-5573	34	4	13	13	NUM
ejpam-5573	34	5	,	,	PUNCT
ejpam-5573	34	6	20	20	NUM
ejpam-5573	34	7	,	,	PUNCT
ejpam-5573	34	8	22	22	NUM
ejpam-5573	34	9	,	,	PUNCT
ejpam-5573	34	10	23	23	NUM
ejpam-5573	34	11	]	]	PUNCT
ejpam-5573	34	12	.	.	PUNCT
ejpam-5573	35	1	the	the	DET
ejpam-5573	35	2	organization	organization	NOUN
ejpam-5573	35	3	of	of	ADP
ejpam-5573	35	4	this	this	DET
ejpam-5573	35	5	article	article	NOUN
ejpam-5573	35	6	is	be	AUX
ejpam-5573	35	7	as	as	SCONJ
ejpam-5573	35	8	follows	follow	VERB
ejpam-5573	35	9	:	:	PUNCT
ejpam-5573	35	10	•	•	NOUN
ejpam-5573	35	11	in	in	ADP
ejpam-5573	35	12	section	section	NOUN
ejpam-5573	35	13	2	2	NUM
ejpam-5573	35	14	,	,	PUNCT
ejpam-5573	35	15	as	as	ADP
ejpam-5573	35	16	a	a	DET
ejpam-5573	35	17	stronger	strong	ADJ
ejpam-5573	35	18	form	form	NOUN
ejpam-5573	35	19	of	of	ADP
ejpam-5573	35	20	(	(	PUNCT
ejpam-5573	35	21	r	r	NOUN
ejpam-5573	35	22	,	,	PUNCT
ejpam-5573	35	23	s)−	s)−	PROPN
ejpam-5573	35	24	gfsc	gfsc	PROPN
ejpam-5573	35	25	sets	set	VERB
ejpam-5573	35	26	[	[	X
ejpam-5573	35	27	42	42	NUM
ejpam-5573	35	28	]	]	PUNCT
ejpam-5573	35	29	,	,	PUNCT
ejpam-5573	35	30	the	the	DET
ejpam-5573	35	31	notion	notion	NOUN
ejpam-5573	35	32	of	of	ADP
ejpam-5573	35	33	(	(	PUNCT
ejpam-5573	35	34	r	r	NOUN
ejpam-5573	35	35	,	,	PUNCT
ejpam-5573	35	36	s)−	s)−	PROPN
ejpam-5573	36	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	36	2	sets	set	NOUN
ejpam-5573	36	3	is	be	AUX
ejpam-5573	36	4	introduced	introduce	VERB
ejpam-5573	36	5	and	and	CCONJ
ejpam-5573	36	6	some	some	DET
ejpam-5573	36	7	properties	property	NOUN
ejpam-5573	36	8	are	be	AUX
ejpam-5573	36	9	investigated	investigate	VERB
ejpam-5573	36	10	.	.	PUNCT
ejpam-5573	37	1	moreover	moreover	ADV
ejpam-5573	37	2	,	,	PUNCT
ejpam-5573	37	3	we	we	PRON
ejpam-5573	37	4	introduce	introduce	VERB
ejpam-5573	37	5	new	new	ADJ
ejpam-5573	37	6	types	type	NOUN
ejpam-5573	37	7	of	of	ADP
ejpam-5573	37	8	fuzzy	fuzzy	ADJ
ejpam-5573	37	9	mappings	mapping	NOUN
ejpam-5573	37	10	between	between	ADP
ejpam-5573	37	11	double	double	ADJ
ejpam-5573	37	12	fuzzy	fuzzy	ADJ
ejpam-5573	37	13	topological	topological	ADJ
ejpam-5573	37	14	spaces	space	NOUN
ejpam-5573	37	15	and	and	CCONJ
ejpam-5573	37	16	relationships	relationship	NOUN
ejpam-5573	37	17	are	be	AUX
ejpam-5573	37	18	obtained	obtain	VERB
ejpam-5573	37	19	.	.	PUNCT
ejpam-5573	37	20	•	•	NUM
ejpam-5573	37	21	in	in	ADP
ejpam-5573	37	22	section	section	NOUN
ejpam-5573	37	23	3	3	NUM
ejpam-5573	37	24	,	,	PUNCT
ejpam-5573	37	25	we	we	PRON
ejpam-5573	37	26	define	define	VERB
ejpam-5573	37	27	new	new	ADJ
ejpam-5573	37	28	types	type	NOUN
ejpam-5573	37	29	of	of	ADP
ejpam-5573	37	30	fuzzy	fuzzy	ADJ
ejpam-5573	37	31	separation	separation	NOUN
ejpam-5573	37	32	axioms	axiom	NOUN
ejpam-5573	37	33	with	with	ADP
ejpam-5573	37	34	the	the	DET
ejpam-5573	37	35	help	help	NOUN
ejpam-5573	37	36	of	of	ADP
ejpam-5573	37	37	(	(	PUNCT
ejpam-5573	37	38	r	r	NOUN
ejpam-5573	37	39	,	,	PUNCT
ejpam-5573	37	40	s)−	s)−	PROPN
ejpam-5573	37	41	gfsc	gfsc	PROPN
ejpam-5573	37	42	sets	set	VERB
ejpam-5573	37	43	and	and	CCONJ
ejpam-5573	37	44	establish	establish	VERB
ejpam-5573	37	45	some	some	PRON
ejpam-5573	37	46	of	of	ADP
ejpam-5573	37	47	their	their	PRON
ejpam-5573	37	48	properties	property	NOUN
ejpam-5573	37	49	.	.	PUNCT
ejpam-5573	38	1	•	•	NUM
ejpam-5573	38	2	in	in	ADP
ejpam-5573	38	3	section	section	NOUN
ejpam-5573	38	4	4	4	NUM
ejpam-5573	38	5	,	,	PUNCT
ejpam-5573	38	6	some	some	DET
ejpam-5573	38	7	new	new	ADJ
ejpam-5573	38	8	types	type	NOUN
ejpam-5573	38	9	of	of	ADP
ejpam-5573	38	10	compactness	compactness	NOUN
ejpam-5573	38	11	in	in	ADP
ejpam-5573	38	12	double	double	ADJ
ejpam-5573	38	13	fuzzy	fuzzy	ADJ
ejpam-5573	38	14	topological	topological	ADJ
ejpam-5573	38	15	spaces	space	NOUN
ejpam-5573	38	16	are	be	AUX
ejpam-5573	38	17	defined	define	VERB
ejpam-5573	38	18	and	and	CCONJ
ejpam-5573	38	19	the	the	DET
ejpam-5573	38	20	relationships	relationship	NOUN
ejpam-5573	38	21	between	between	ADP
ejpam-5573	38	22	them	they	PRON
ejpam-5573	38	23	are	be	AUX
ejpam-5573	38	24	specified	specify	VERB
ejpam-5573	38	25	.	.	PUNCT
ejpam-5573	39	1	•	•	NUM
ejpam-5573	39	2	in	in	ADP
ejpam-5573	39	3	the	the	DET
ejpam-5573	39	4	end	end	NOUN
ejpam-5573	39	5	,	,	PUNCT
ejpam-5573	39	6	we	we	PRON
ejpam-5573	39	7	give	give	VERB
ejpam-5573	39	8	some	some	DET
ejpam-5573	39	9	conclusions	conclusion	NOUN
ejpam-5573	39	10	and	and	CCONJ
ejpam-5573	39	11	make	make	VERB
ejpam-5573	39	12	a	a	DET
ejpam-5573	39	13	plan	plan	NOUN
ejpam-5573	39	14	for	for	ADP
ejpam-5573	39	15	future	future	ADJ
ejpam-5573	39	16	works	work	NOUN
ejpam-5573	39	17	in	in	ADP
ejpam-5573	39	18	section	section	NOUN
ejpam-5573	39	19	5	5	NUM
ejpam-5573	39	20	.	.	PUNCT
ejpam-5573	40	1	throughout	throughout	ADP
ejpam-5573	40	2	this	this	DET
ejpam-5573	40	3	article	article	NOUN
ejpam-5573	40	4	,	,	PUNCT
ejpam-5573	40	5	nonempty	nonempty	NOUN
ejpam-5573	40	6	sets	set	NOUN
ejpam-5573	40	7	will	will	AUX
ejpam-5573	40	8	be	be	AUX
ejpam-5573	40	9	denoted	denote	VERB
ejpam-5573	40	10	by	by	ADP
ejpam-5573	40	11	v	v	NUM
ejpam-5573	40	12	,	,	PUNCT
ejpam-5573	40	13	u	u	NOUN
ejpam-5573	40	14	,	,	PUNCT
ejpam-5573	40	15	etc	etc	X
ejpam-5573	40	16	.	.	X
ejpam-5573	41	1	the	the	DET
ejpam-5573	41	2	family	family	NOUN
ejpam-5573	41	3	of	of	ADP
ejpam-5573	41	4	all	all	DET
ejpam-5573	41	5	fuzzy	fuzzy	ADJ
ejpam-5573	41	6	sets	set	NOUN
ejpam-5573	41	7	on	on	ADP
ejpam-5573	41	8	u	u	NOUN
ejpam-5573	41	9	is	be	AUX
ejpam-5573	41	10	denoted	denote	VERB
ejpam-5573	41	11	by	by	ADP
ejpam-5573	41	12	iu	iu	ADV
ejpam-5573	41	13	,	,	PUNCT
ejpam-5573	41	14	and	and	CCONJ
ejpam-5573	41	15	for	for	ADP
ejpam-5573	41	16	µ	µ	NOUN
ejpam-5573	41	17	∈	∈	PROPN
ejpam-5573	41	18	iu	iu	X
ejpam-5573	41	19	,	,	PUNCT
ejpam-5573	41	20	µc(u	µc(u	ADJ
ejpam-5573	41	21	)	)	PUNCT
ejpam-5573	41	22	=	=	SYM
ejpam-5573	41	23	1−	1−	NUM
ejpam-5573	41	24	µ(u	µ(u	NOUN
ejpam-5573	41	25	)	)	PUNCT
ejpam-5573	41	26	,	,	PUNCT
ejpam-5573	41	27	for	for	ADP
ejpam-5573	41	28	all	all	PRON
ejpam-5573	41	29	u	u	PRON
ejpam-5573	41	30	∈	∈	PROPN
ejpam-5573	41	31	u	u	NOUN
ejpam-5573	41	32	(	(	PUNCT
ejpam-5573	41	33	where	where	SCONJ
ejpam-5573	41	34	i	i	PRON
ejpam-5573	41	35	=	=	PUNCT
ejpam-5573	42	1	[	[	X
ejpam-5573	42	2	0	0	NUM
ejpam-5573	42	3	,	,	PUNCT
ejpam-5573	42	4	1	1	NUM
ejpam-5573	42	5	]	]	PUNCT
ejpam-5573	42	6	,	,	PUNCT
ejpam-5573	42	7	i1	i1	PROPN
ejpam-5573	42	8	=	=	PUNCT
ejpam-5573	43	1	[	[	X
ejpam-5573	43	2	0	0	NUM
ejpam-5573	43	3	,	,	PUNCT
ejpam-5573	43	4	1	1	NUM
ejpam-5573	43	5	)	)	PUNCT
ejpam-5573	43	6	,	,	PUNCT
ejpam-5573	43	7	and	and	CCONJ
ejpam-5573	43	8	i	i	PRON
ejpam-5573	43	9	◦	◦	NOUN
ejpam-5573	43	10	=	=	SYM
ejpam-5573	43	11	(	(	PUNCT
ejpam-5573	43	12	0	0	NUM
ejpam-5573	43	13	,	,	PUNCT
ejpam-5573	43	14	1	1	NUM
ejpam-5573	43	15	]	]	NUM
ejpam-5573	43	16	)	)	PUNCT
ejpam-5573	43	17	.	.	PUNCT
ejpam-5573	44	1	also	also	ADV
ejpam-5573	44	2	,	,	PUNCT
ejpam-5573	44	3	for	for	ADP
ejpam-5573	44	4	t	t	PROPN
ejpam-5573	44	5	∈	∈	PROPN
ejpam-5573	44	6	i	i	PRON
ejpam-5573	44	7	,	,	PUNCT
ejpam-5573	44	8	t(u	t(u	PROPN
ejpam-5573	44	9	)	)	PUNCT
ejpam-5573	44	10	=	=	SYM
ejpam-5573	44	11	t	t	PROPN
ejpam-5573	44	12	,	,	PUNCT
ejpam-5573	44	13	for	for	ADP
ejpam-5573	44	14	all	all	DET
ejpam-5573	44	15	u	u	PROPN
ejpam-5573	44	16	∈	∈	PROPN
ejpam-5573	44	17	u.	u.	VERB
ejpam-5573	44	18	a	a	DET
ejpam-5573	44	19	fuzzy	fuzzy	ADJ
ejpam-5573	44	20	point	point	NOUN
ejpam-5573	44	21	ut	ut	PROPN
ejpam-5573	44	22	on	on	ADP
ejpam-5573	44	23	u	u	PROPN
ejpam-5573	44	24	is	be	AUX
ejpam-5573	44	25	a	a	DET
ejpam-5573	44	26	fuzzy	fuzzy	ADJ
ejpam-5573	44	27	set	set	NOUN
ejpam-5573	44	28	,	,	PUNCT
ejpam-5573	44	29	defined	define	VERB
ejpam-5573	44	30	as	as	SCONJ
ejpam-5573	44	31	follows	follow	VERB
ejpam-5573	44	32	:	:	PUNCT
ejpam-5573	44	33	ut(k	ut(k	SYM
ejpam-5573	44	34	)	)	PUNCT
ejpam-5573	45	1	=	=	SYM
ejpam-5573	45	2	t	t	NOUN
ejpam-5573	45	3	if	if	SCONJ
ejpam-5573	45	4	k	k	PROPN
ejpam-5573	45	5	=	=	SYM
ejpam-5573	45	6	u	u	PROPN
ejpam-5573	45	7	,	,	PUNCT
ejpam-5573	45	8	and	and	CCONJ
ejpam-5573	45	9	ut(k	ut(k	SYM
ejpam-5573	45	10	)	)	PUNCT
ejpam-5573	45	11	=	=	SYM
ejpam-5573	45	12	0	0	NUM
ejpam-5573	45	13	for	for	ADP
ejpam-5573	45	14	all	all	DET
ejpam-5573	45	15	k	k	PROPN
ejpam-5573	45	16	∈	∈	PROPN
ejpam-5573	45	17	u	u	NOUN
ejpam-5573	45	18	−	−	PROPN
ejpam-5573	45	19	{	{	PUNCT
ejpam-5573	45	20	u	u	NOUN
ejpam-5573	45	21	}	}	PUNCT
ejpam-5573	45	22	.	.	PUNCT
ejpam-5573	46	1	ut	ut	PROPN
ejpam-5573	46	2	is	be	AUX
ejpam-5573	46	3	said	say	VERB
ejpam-5573	46	4	to	to	PART
ejpam-5573	46	5	belong	belong	VERB
ejpam-5573	46	6	to	to	ADP
ejpam-5573	46	7	a	a	DET
ejpam-5573	46	8	fuzzy	fuzzy	ADJ
ejpam-5573	46	9	set	set	VERB
ejpam-5573	46	10	µ	µ	NOUN
ejpam-5573	46	11	,	,	PUNCT
ejpam-5573	46	12	denoted	denote	VERB
ejpam-5573	46	13	by	by	ADP
ejpam-5573	46	14	ut	ut	PROPN
ejpam-5573	46	15	∈	∈	PROPN
ejpam-5573	46	16	µ	µ	PROPN
ejpam-5573	46	17	,	,	PUNCT
ejpam-5573	46	18	if	if	SCONJ
ejpam-5573	46	19	t	t	PROPN
ejpam-5573	46	20	≤	≤	NUM
ejpam-5573	46	21	µ(u	µ(u	NOUN
ejpam-5573	46	22	)	)	PUNCT
ejpam-5573	46	23	.	.	PUNCT
ejpam-5573	47	1	the	the	DET
ejpam-5573	47	2	family	family	NOUN
ejpam-5573	47	3	of	of	ADP
ejpam-5573	47	4	all	all	DET
ejpam-5573	47	5	fuzzy	fuzzy	ADJ
ejpam-5573	47	6	points	point	NOUN
ejpam-5573	47	7	on	on	ADP
ejpam-5573	47	8	u	u	NOUN
ejpam-5573	47	9	is	be	AUX
ejpam-5573	47	10	denoted	denote	VERB
ejpam-5573	47	11	by	by	ADP
ejpam-5573	47	12	pt(u	pt(u	NOUN
ejpam-5573	47	13	)	)	PUNCT
ejpam-5573	47	14	.	.	PUNCT
ejpam-5573	48	1	a	a	DET
ejpam-5573	48	2	fuzzy	fuzzy	ADJ
ejpam-5573	48	3	set	set	NOUN
ejpam-5573	48	4	µ	µ	NOUN
ejpam-5573	48	5	is	be	AUX
ejpam-5573	48	6	a	a	DET
ejpam-5573	48	7	quasi	quasi	NOUN
ejpam-5573	48	8	-	-	NOUN
ejpam-5573	48	9	coincident	coincident	ADJ
ejpam-5573	48	10	with	with	ADP
ejpam-5573	48	11	λ	λ	NOUN
ejpam-5573	48	12	,	,	PUNCT
ejpam-5573	48	13	denoted	denote	VERB
ejpam-5573	48	14	by	by	ADP
ejpam-5573	48	15	µqλ	µqλ	NOUN
ejpam-5573	48	16	,	,	PUNCT
ejpam-5573	48	17	if	if	SCONJ
ejpam-5573	48	18	there	there	PRON
ejpam-5573	48	19	is	be	VERB
ejpam-5573	48	20	u	u	PROPN
ejpam-5573	48	21	∈	∈	PROPN
ejpam-5573	48	22	u	u	NOUN
ejpam-5573	48	23	,	,	PUNCT
ejpam-5573	48	24	such	such	ADJ
ejpam-5573	48	25	that	that	SCONJ
ejpam-5573	48	26	µ(u	µ(u	NOUN
ejpam-5573	48	27	)	)	PUNCT
ejpam-5573	49	1	+	+	SYM
ejpam-5573	49	2	λ(u	λ(u	X
ejpam-5573	49	3	)	)	PUNCT
ejpam-5573	49	4	>	>	X
ejpam-5573	50	1	1	1	NUM
ejpam-5573	50	2	,	,	PUNCT
ejpam-5573	50	3	if	if	SCONJ
ejpam-5573	50	4	µ	µ	NOUN
ejpam-5573	50	5	is	be	AUX
ejpam-5573	50	6	not	not	PART
ejpam-5573	50	7	quasi	quasi	ADJ
ejpam-5573	50	8	-	-	NOUN
ejpam-5573	50	9	coincident	coincident	ADJ
ejpam-5573	50	10	with	with	ADP
ejpam-5573	50	11	λ	λ	NOUN
ejpam-5573	50	12	,	,	PUNCT
ejpam-5573	50	13	we	we	PRON
ejpam-5573	50	14	denote	denote	VERB
ejpam-5573	50	15	µqλ	µqλ	NOUN
ejpam-5573	50	16	.	.	PUNCT
ejpam-5573	51	1	the	the	DET
ejpam-5573	51	2	following	follow	VERB
ejpam-5573	51	3	results	result	NOUN
ejpam-5573	51	4	and	and	CCONJ
ejpam-5573	51	5	notions	notion	NOUN
ejpam-5573	51	6	will	will	AUX
ejpam-5573	51	7	be	be	AUX
ejpam-5573	51	8	used	use	VERB
ejpam-5573	51	9	in	in	ADP
ejpam-5573	51	10	the	the	DET
ejpam-5573	51	11	next	next	ADJ
ejpam-5573	51	12	sections	section	NOUN
ejpam-5573	51	13	:	:	PUNCT
ejpam-5573	51	14	f.	f.	PROPN
ejpam-5573	51	15	alsharari	alsharari	PROPN
ejpam-5573	51	16	,	,	PUNCT
ejpam-5573	51	17	o.	o.	PROPN
ejpam-5573	51	18	m.	m.	PROPN
ejpam-5573	51	19	taha	taha	PROPN
ejpam-5573	51	20	,	,	PUNCT
ejpam-5573	51	21	i.	i.	PROPN
ejpam-5573	51	22	m.	m.	PROPN
ejpam-5573	51	23	taha	taha	PROPN
ejpam-5573	51	24	/	/	PUNCT
ejpam-5573	51	25	eur	eur	PROPN
ejpam-5573	51	26	.	.	PUNCT
ejpam-5573	52	1	j.	j.	PROPN
ejpam-5573	52	2	pure	pure	PROPN
ejpam-5573	52	3	appl	appl	PROPN
ejpam-5573	52	4	.	.	PROPN
ejpam-5573	52	5	math	math	PROPN
ejpam-5573	52	6	,	,	PUNCT
ejpam-5573	52	7	17	17	NUM
ejpam-5573	52	8	(	(	PUNCT
ejpam-5573	52	9	4	4	NUM
ejpam-5573	52	10	)	)	PUNCT
ejpam-5573	52	11	(	(	PUNCT
ejpam-5573	52	12	2024	2024	NUM
ejpam-5573	52	13	)	)	PUNCT
ejpam-5573	52	14	,	,	PUNCT
ejpam-5573	52	15	4093	4093	NUM
ejpam-5573	52	16	-	-	SYM
ejpam-5573	52	17	4111	4111	NUM
ejpam-5573	52	18	4095	4095	NUM
ejpam-5573	52	19	lemma	lemma	PROPN
ejpam-5573	52	20	1	1	NUM
ejpam-5573	52	21	.	.	PUNCT
ejpam-5573	53	1	[	[	X
ejpam-5573	53	2	27	27	NUM
ejpam-5573	53	3	]	]	PUNCT
ejpam-5573	53	4	let	let	VERB
ejpam-5573	53	5	u	u	PRON
ejpam-5573	53	6	be	be	AUX
ejpam-5573	53	7	a	a	DET
ejpam-5573	53	8	nonempty	nonempty	ADV
ejpam-5573	53	9	set	set	VERB
ejpam-5573	53	10	and	and	CCONJ
ejpam-5573	53	11	ν	ν	NOUN
ejpam-5573	53	12	,	,	PUNCT
ejpam-5573	53	13	µ	µ	X
ejpam-5573	53	14	∈	∈	NOUN
ejpam-5573	53	15	iu	iu	ADV
ejpam-5573	53	16	.	.	PUNCT
ejpam-5573	54	1	then	then	ADV
ejpam-5573	54	2	,	,	PUNCT
ejpam-5573	54	3	(	(	PUNCT
ejpam-5573	54	4	i	i	NOUN
ejpam-5573	54	5	)	)	PUNCT
ejpam-5573	54	6	νqµ	νqµ	NOUN
ejpam-5573	54	7	iff	iff	PROPN
ejpam-5573	54	8	there	there	PRON
ejpam-5573	54	9	is	be	VERB
ejpam-5573	54	10	ut	ut	PROPN
ejpam-5573	54	11	∈	∈	PROPN
ejpam-5573	54	12	ν	ν	NOUN
ejpam-5573	54	13	such	such	ADJ
ejpam-5573	54	14	that	that	DET
ejpam-5573	54	15	utqµ	utqµ	NOUN
ejpam-5573	54	16	,	,	PUNCT
ejpam-5573	54	17	(	(	PUNCT
ejpam-5573	54	18	ii	ii	NOUN
ejpam-5573	54	19	)	)	PUNCT
ejpam-5573	54	20	ν	ν	PROPN
ejpam-5573	54	21	∧	∧	PROPN
ejpam-5573	54	22	µ	µ	DET
ejpam-5573	54	23	̸=	̸=	PROPN
ejpam-5573	54	24	0	0	PUNCT
ejpam-5573	54	25	if	if	SCONJ
ejpam-5573	54	26	νqµ	νqµ	NOUN
ejpam-5573	54	27	,	,	PUNCT
ejpam-5573	54	28	(	(	PUNCT
ejpam-5573	54	29	iii	iii	X
ejpam-5573	54	30	)	)	PUNCT
ejpam-5573	54	31	νqµ	νqµ	NOUN
ejpam-5573	54	32	iff	iff	PROPN
ejpam-5573	54	33	ν	ν	PROPN
ejpam-5573	54	34	≤	≤	NUM
ejpam-5573	54	35	µc	µc	ADP
ejpam-5573	54	36	,	,	PUNCT
ejpam-5573	54	37	(	(	PUNCT
ejpam-5573	54	38	iv	iv	X
ejpam-5573	54	39	)	)	PUNCT
ejpam-5573	54	40	µ	µ	PROPN
ejpam-5573	54	41	≤	≤	NUM
ejpam-5573	54	42	ν	ν	ADP
ejpam-5573	54	43	iff	iff	PROPN
ejpam-5573	54	44	ut	ut	PROPN
ejpam-5573	54	45	∈	∈	PROPN
ejpam-5573	54	46	µ	µ	X
ejpam-5573	54	47	implies	imply	VERB
ejpam-5573	54	48	ut	ut	PROPN
ejpam-5573	54	49	∈	∈	PROPN
ejpam-5573	54	50	ν	ν	NOUN
ejpam-5573	54	51	iff	iff	PROPN
ejpam-5573	54	52	utqµ	utqµ	PROPN
ejpam-5573	54	53	implies	imply	VERB
ejpam-5573	54	54	utqν	utqν	PROPN
ejpam-5573	54	55	iff	iff	PROPN
ejpam-5573	54	56	utqν	utqν	PROPN
ejpam-5573	54	57	implies	imply	VERB
ejpam-5573	54	58	utqµ	utqµ	ADJ
ejpam-5573	54	59	,	,	PUNCT
ejpam-5573	54	60	(	(	PUNCT
ejpam-5573	54	61	v	v	NOUN
ejpam-5573	54	62	)	)	PUNCT
ejpam-5573	54	63	utq	utq	ADJ
ejpam-5573	54	64	∨	∨	NUM
ejpam-5573	54	65	δ∈∆	δ∈∆	PROPN
ejpam-5573	54	66	νδ	νδ	PROPN
ejpam-5573	54	67	iff	iff	NOUN
ejpam-5573	54	68	there	there	PRON
ejpam-5573	54	69	is	be	VERB
ejpam-5573	54	70	δ0	δ0	NOUN
ejpam-5573	54	71	∈	∈	NOUN
ejpam-5573	54	72	∆	∆	PROPN
ejpam-5573	55	1	such	such	ADJ
ejpam-5573	55	2	that	that	DET
ejpam-5573	55	3	utqνδ0	utqνδ0	NOUN
ejpam-5573	55	4	.	.	PUNCT
ejpam-5573	56	1	definition	definition	NOUN
ejpam-5573	56	2	1	1	NUM
ejpam-5573	56	3	.	.	PUNCT
ejpam-5573	57	1	[	[	X
ejpam-5573	57	2	35	35	NUM
ejpam-5573	57	3	,	,	PUNCT
ejpam-5573	57	4	47	47	NUM
ejpam-5573	57	5	]	]	PUNCT
ejpam-5573	57	6	a	a	DET
ejpam-5573	57	7	double	double	ADJ
ejpam-5573	57	8	fuzzy	fuzzy	ADJ
ejpam-5573	57	9	topology	topology	NOUN
ejpam-5573	57	10	on	on	ADP
ejpam-5573	57	11	u	u	PROPN
ejpam-5573	57	12	is	be	AUX
ejpam-5573	57	13	a	a	DET
ejpam-5573	57	14	pair	pair	NOUN
ejpam-5573	57	15	(	(	PUNCT
ejpam-5573	57	16	η	η	NOUN
ejpam-5573	57	17	,	,	PUNCT
ejpam-5573	57	18	η∗	η∗	PROPN
ejpam-5573	57	19	)	)	PUNCT
ejpam-5573	57	20	of	of	ADP
ejpam-5573	57	21	the	the	DET
ejpam-5573	57	22	mappings	mapping	NOUN
ejpam-5573	57	23	η	η	PROPN
ejpam-5573	57	24	,	,	PUNCT
ejpam-5573	57	25	η∗	η∗	NOUN
ejpam-5573	57	26	:	:	PUNCT
ejpam-5573	57	27	iu	iu	ADP
ejpam-5573	57	28	→	→	SYM
ejpam-5573	57	29	i	i	PROPN
ejpam-5573	57	30	,	,	PUNCT
ejpam-5573	57	31	which	which	PRON
ejpam-5573	57	32	satisfy	satisfy	VERB
ejpam-5573	57	33	the	the	DET
ejpam-5573	57	34	following	following	ADJ
ejpam-5573	57	35	conditions	condition	NOUN
ejpam-5573	57	36	.	.	PUNCT
ejpam-5573	58	1	(	(	PUNCT
ejpam-5573	58	2	i	i	NOUN
ejpam-5573	58	3	)	)	PUNCT
ejpam-5573	58	4	η(ν	η(ν	PROPN
ejpam-5573	58	5	)	)	PUNCT
ejpam-5573	58	6	+	+	SYM
ejpam-5573	58	7	η∗(ν	η∗(ν	SYM
ejpam-5573	58	8	)	)	PUNCT
ejpam-5573	58	9	≤	≤	NUM
ejpam-5573	58	10	1	1	NUM
ejpam-5573	58	11	,	,	PUNCT
ejpam-5573	58	12	for	for	ADP
ejpam-5573	58	13	each	each	DET
ejpam-5573	58	14	ν	ν	NOUN
ejpam-5573	58	15	∈	∈	PROPN
ejpam-5573	58	16	iu	iu	ADP
ejpam-5573	58	17	.	.	PUNCT
ejpam-5573	59	1	(	(	PUNCT
ejpam-5573	59	2	ii	ii	NOUN
ejpam-5573	59	3	)	)	PUNCT
ejpam-5573	59	4	η(ν1	η(ν1	NOUN
ejpam-5573	59	5	∧	∧	PROPN
ejpam-5573	59	6	ν2	ν2	PROPN
ejpam-5573	59	7	)	)	PUNCT
ejpam-5573	59	8	≥	≥	NOUN
ejpam-5573	59	9	η(ν1	η(ν1	NOUN
ejpam-5573	59	10	)	)	PUNCT
ejpam-5573	59	11	∧	∧	NOUN
ejpam-5573	59	12	η(ν2	η(ν2	NOUN
ejpam-5573	59	13	)	)	PUNCT
ejpam-5573	59	14	and	and	CCONJ
ejpam-5573	59	15	η∗(ν1	η∗(ν1	PROPN
ejpam-5573	59	16	∧	∧	PROPN
ejpam-5573	59	17	ν2	ν2	NOUN
ejpam-5573	59	18	)	)	PUNCT
ejpam-5573	59	19	≤	≤	NOUN
ejpam-5573	59	20	η∗(ν1	η∗(ν1	PROPN
ejpam-5573	59	21	)	)	PUNCT
ejpam-5573	59	22	∨	∨	PROPN
ejpam-5573	59	23	η∗(ν2	η∗(ν2	PROPN
ejpam-5573	59	24	)	)	PUNCT
ejpam-5573	59	25	,	,	PUNCT
ejpam-5573	59	26	for	for	ADP
ejpam-5573	59	27	each	each	DET
ejpam-5573	59	28	ν1	ν1	NOUN
ejpam-5573	59	29	,	,	PUNCT
ejpam-5573	59	30	ν2	ν2	NOUN
ejpam-5573	59	31	∈	∈	PROPN
ejpam-5573	59	32	iu	iu	ADV
ejpam-5573	59	33	.	.	PUNCT
ejpam-5573	60	1	(	(	PUNCT
ejpam-5573	60	2	iii	iii	X
ejpam-5573	60	3	)	)	PUNCT
ejpam-5573	60	4	η	η	PROPN
ejpam-5573	60	5	(	(	PUNCT
ejpam-5573	60	6	∨	∨	NUM
ejpam-5573	60	7	δ∈∆	δ∈∆	PROPN
ejpam-5573	60	8	νδ	νδ	NOUN
ejpam-5573	60	9	)	)	PUNCT
ejpam-5573	60	10	≥	≥	NOUN
ejpam-5573	60	11	∧	∧	PROPN
ejpam-5573	60	12	δ∈∆	δ∈∆	PROPN
ejpam-5573	60	13	η(νδ	η(νδ	PROPN
ejpam-5573	60	14	)	)	PUNCT
ejpam-5573	60	15	and	and	CCONJ
ejpam-5573	60	16	η∗	η∗	PROPN
ejpam-5573	60	17	(	(	PUNCT
ejpam-5573	60	18	∨	∨	NUM
ejpam-5573	60	19	δ∈∆	δ∈∆	PROPN
ejpam-5573	60	20	νδ	νδ	NOUN
ejpam-5573	60	21	)	)	PUNCT
ejpam-5573	60	22	≤	≤	NOUN
ejpam-5573	60	23	∨	∨	NUM
ejpam-5573	60	24	δ∈∆	δ∈∆	PROPN
ejpam-5573	60	25	η∗(νδ	η∗(νδ	NOUN
ejpam-5573	60	26	)	)	PUNCT
ejpam-5573	60	27	,	,	PUNCT
ejpam-5573	60	28	for	for	SCONJ
ejpam-5573	60	29	each	each	PRON
ejpam-5573	60	30	{	{	PUNCT
ejpam-5573	60	31	νδ}δ∈∆	νδ}δ∈∆	X
ejpam-5573	60	32	⊂	⊂	PROPN
ejpam-5573	60	33	iu	iu	ADV
ejpam-5573	60	34	.	.	PUNCT
ejpam-5573	61	1	the	the	DET
ejpam-5573	61	2	triplet	triplet	NOUN
ejpam-5573	61	3	(	(	PUNCT
ejpam-5573	61	4	u	u	NOUN
ejpam-5573	61	5	,	,	PUNCT
ejpam-5573	61	6	η	η	PROPN
ejpam-5573	61	7	,	,	PUNCT
ejpam-5573	61	8	η∗	η∗	NOUN
ejpam-5573	61	9	)	)	PUNCT
ejpam-5573	61	10	is	be	AUX
ejpam-5573	61	11	said	say	VERB
ejpam-5573	61	12	to	to	PART
ejpam-5573	61	13	be	be	AUX
ejpam-5573	61	14	a	a	DET
ejpam-5573	61	15	double	double	ADJ
ejpam-5573	61	16	fuzzy	fuzzy	ADJ
ejpam-5573	61	17	topological	topological	ADJ
ejpam-5573	61	18	space	space	NOUN
ejpam-5573	61	19	⟨briefly	⟨briefly	ADV
ejpam-5573	61	20	,	,	PUNCT
ejpam-5573	61	21	dfts⟩	dfts⟩	VERB
ejpam-5573	61	22	in	in	ADP
ejpam-5573	61	23	the	the	DET
ejpam-5573	61	24	sense	sense	NOUN
ejpam-5573	61	25	of	of	ADP
ejpam-5573	61	26	šostak	šostak	NOUN
ejpam-5573	61	27	.	.	PUNCT
ejpam-5573	62	1	η∗(ν	η∗(ν	NOUN
ejpam-5573	62	2	)	)	PUNCT
ejpam-5573	62	3	and	and	CCONJ
ejpam-5573	62	4	η(ν	η(ν	PROPN
ejpam-5573	62	5	)	)	PUNCT
ejpam-5573	62	6	may	may	AUX
ejpam-5573	62	7	be	be	AUX
ejpam-5573	62	8	interpreted	interpret	VERB
ejpam-5573	62	9	as	as	ADP
ejpam-5573	62	10	gradation	gradation	NOUN
ejpam-5573	62	11	of	of	ADP
ejpam-5573	62	12	nonopenness	nonopenness	NOUN
ejpam-5573	62	13	and	and	CCONJ
ejpam-5573	62	14	openness	openness	NOUN
ejpam-5573	62	15	for	for	ADP
ejpam-5573	62	16	ν	ν	NOUN
ejpam-5573	62	17	∈	∈	PROPN
ejpam-5573	62	18	iu	iu	X
ejpam-5573	62	19	,	,	PUNCT
ejpam-5573	62	20	respectively	respectively	ADV
ejpam-5573	62	21	.	.	PUNCT
ejpam-5573	63	1	in	in	ADP
ejpam-5573	63	2	a	a	DET
ejpam-5573	63	3	dfts	dft	NOUN
ejpam-5573	63	4	(	(	PUNCT
ejpam-5573	63	5	u	u	NOUN
ejpam-5573	63	6	,	,	PUNCT
ejpam-5573	63	7	η	η	PROPN
ejpam-5573	63	8	,	,	PUNCT
ejpam-5573	63	9	η∗	η∗	PROPN
ejpam-5573	63	10	)	)	PUNCT
ejpam-5573	63	11	,	,	PUNCT
ejpam-5573	63	12	the	the	DET
ejpam-5573	63	13	interior	interior	NOUN
ejpam-5573	63	14	of	of	ADP
ejpam-5573	63	15	ν	ν	X
ejpam-5573	63	16	∈	∈	PROPN
ejpam-5573	63	17	iu	iu	ADP
ejpam-5573	63	18	,	,	PUNCT
ejpam-5573	63	19	the	the	DET
ejpam-5573	63	20	closure	closure	NOUN
ejpam-5573	63	21	of	of	ADP
ejpam-5573	63	22	ν	ν	X
ejpam-5573	63	23	∈	∈	PROPN
ejpam-5573	63	24	iu	iu	ADP
ejpam-5573	63	25	,	,	PUNCT
ejpam-5573	63	26	the	the	DET
ejpam-5573	63	27	semi	semi	NOUN
ejpam-5573	63	28	-	-	NOUN
ejpam-5573	63	29	closure	closure	NOUN
ejpam-5573	63	30	of	of	ADP
ejpam-5573	63	31	ν	ν	X
ejpam-5573	63	32	∈	∈	PROPN
ejpam-5573	63	33	iu	iu	ADP
ejpam-5573	63	34	and	and	CCONJ
ejpam-5573	63	35	the	the	DET
ejpam-5573	63	36	semi	semi	ADJ
ejpam-5573	63	37	-	-	ADJ
ejpam-5573	63	38	interior	interior	ADJ
ejpam-5573	63	39	of	of	ADP
ejpam-5573	63	40	ν	ν	X
ejpam-5573	63	41	∈	∈	PROPN
ejpam-5573	63	42	iu	iu	ADP
ejpam-5573	63	43	will	will	AUX
ejpam-5573	63	44	be	be	AUX
ejpam-5573	63	45	denoted	denote	VERB
ejpam-5573	63	46	by	by	ADP
ejpam-5573	63	47	iη	iη	NOUN
ejpam-5573	63	48	,	,	PUNCT
ejpam-5573	63	49	η∗(ν	η∗(ν	NOUN
ejpam-5573	63	50	,	,	PUNCT
ejpam-5573	63	51	r	r	NOUN
ejpam-5573	63	52	,	,	PUNCT
ejpam-5573	63	53	s	s	PART
ejpam-5573	63	54	)	)	PUNCT
ejpam-5573	63	55	,	,	PUNCT
ejpam-5573	63	56	cη	cη	INTJ
ejpam-5573	63	57	,	,	PUNCT
ejpam-5573	63	58	η∗(ν	η∗(ν	NOUN
ejpam-5573	63	59	,	,	PUNCT
ejpam-5573	63	60	r	r	NOUN
ejpam-5573	63	61	,	,	PUNCT
ejpam-5573	63	62	s	s	PART
ejpam-5573	63	63	)	)	PUNCT
ejpam-5573	63	64	,	,	PUNCT
ejpam-5573	63	65	scη	scη	NOUN
ejpam-5573	63	66	,	,	PUNCT
ejpam-5573	63	67	η∗(ν	η∗(ν	NOUN
ejpam-5573	63	68	,	,	PUNCT
ejpam-5573	63	69	r	r	NOUN
ejpam-5573	63	70	,	,	PUNCT
ejpam-5573	63	71	s	s	PART
ejpam-5573	63	72	)	)	PUNCT
ejpam-5573	63	73	and	and	CCONJ
ejpam-5573	63	74	siη	siη	PROPN
ejpam-5573	63	75	,	,	PUNCT
ejpam-5573	63	76	η∗(ν	η∗(ν	NOUN
ejpam-5573	63	77	,	,	PUNCT
ejpam-5573	63	78	r	r	NOUN
ejpam-5573	63	79	,	,	PUNCT
ejpam-5573	63	80	s	s	PART
ejpam-5573	63	81	)	)	PUNCT
ejpam-5573	63	82	,	,	PUNCT
ejpam-5573	63	83	respectively	respectively	ADV
ejpam-5573	63	84	[	[	X
ejpam-5573	63	85	20	20	NUM
ejpam-5573	63	86	,	,	PUNCT
ejpam-5573	63	87	29	29	NUM
ejpam-5573	63	88	,	,	PUNCT
ejpam-5573	63	89	34	34	NUM
ejpam-5573	63	90	]	]	PUNCT
ejpam-5573	63	91	.	.	PUNCT
ejpam-5573	64	1	definition	definition	NOUN
ejpam-5573	64	2	2	2	NUM
ejpam-5573	64	3	.	.	PUNCT
ejpam-5573	65	1	[	[	X
ejpam-5573	65	2	29	29	NUM
ejpam-5573	65	3	,	,	PUNCT
ejpam-5573	65	4	30	30	NUM
ejpam-5573	65	5	]	]	PUNCT
ejpam-5573	65	6	let	let	VERB
ejpam-5573	65	7	(	(	PUNCT
ejpam-5573	65	8	u	u	NOUN
ejpam-5573	65	9	,	,	PUNCT
ejpam-5573	65	10	η	η	PROPN
ejpam-5573	65	11	,	,	PUNCT
ejpam-5573	65	12	η∗	η∗	NOUN
ejpam-5573	65	13	)	)	PUNCT
ejpam-5573	65	14	be	be	VERB
ejpam-5573	65	15	a	a	DET
ejpam-5573	65	16	dfts	dft	NOUN
ejpam-5573	65	17	,	,	PUNCT
ejpam-5573	65	18	ν	ν	X
ejpam-5573	65	19	∈	∈	NOUN
ejpam-5573	65	20	iu	iu	ADV
ejpam-5573	65	21	,	,	PUNCT
ejpam-5573	65	22	r	r	NOUN
ejpam-5573	65	23	∈	∈	PROPN
ejpam-5573	65	24	i	i	NOUN
ejpam-5573	65	25	◦	◦	NOUN
ejpam-5573	65	26	,	,	PUNCT
ejpam-5573	65	27	and	and	CCONJ
ejpam-5573	65	28	s	s	PROPN
ejpam-5573	65	29	∈	∈	PROPN
ejpam-5573	65	30	i1	i1	PROPN
ejpam-5573	65	31	,	,	PUNCT
ejpam-5573	65	32	then	then	ADV
ejpam-5573	65	33	we	we	PRON
ejpam-5573	65	34	have	have	VERB
ejpam-5573	65	35	(	(	PUNCT
ejpam-5573	65	36	i	i	NOUN
ejpam-5573	65	37	)	)	PUNCT
ejpam-5573	65	38	ν	ν	NOUN
ejpam-5573	65	39	is	be	AUX
ejpam-5573	65	40	called	call	VERB
ejpam-5573	65	41	an	an	DET
ejpam-5573	65	42	(	(	PUNCT
ejpam-5573	65	43	r	r	NOUN
ejpam-5573	65	44	,	,	PUNCT
ejpam-5573	65	45	s)-fsc	s)-fsc	NOUN
ejpam-5573	65	46	⟨resp	⟨resp	PROPN
ejpam-5573	65	47	.	.	PROPN
ejpam-5573	65	48	,	,	PUNCT
ejpam-5573	65	49	(	(	PUNCT
ejpam-5573	65	50	r	r	NOUN
ejpam-5573	65	51	,	,	PUNCT
ejpam-5573	65	52	s)-fpc	s)-fpc	NOUN
ejpam-5573	65	53	and	and	CCONJ
ejpam-5573	65	54	(	(	PUNCT
ejpam-5573	65	55	r	r	NOUN
ejpam-5573	65	56	,	,	PUNCT
ejpam-5573	65	57	s)-frc⟩	s)-frc⟩	ADV
ejpam-5573	65	58	set	set	VERB
ejpam-5573	65	59	if	if	SCONJ
ejpam-5573	65	60	ν	ν	PROPN
ejpam-5573	65	61	≥	≥	NUM
ejpam-5573	65	62	iη	iη	NOUN
ejpam-5573	65	63	,	,	PUNCT
ejpam-5573	65	64	η∗(cη	η∗(cη	NOUN
ejpam-5573	65	65	,	,	PUNCT
ejpam-5573	65	66	η∗	η∗	NOUN
ejpam-5573	65	67	(	(	PUNCT
ejpam-5573	65	68	ν	ν	NOUN
ejpam-5573	65	69	,	,	PUNCT
ejpam-5573	65	70	r	r	NOUN
ejpam-5573	65	71	,	,	PUNCT
ejpam-5573	65	72	s	s	PART
ejpam-5573	65	73	)	)	PUNCT
ejpam-5573	65	74	,	,	PUNCT
ejpam-5573	65	75	r	r	NOUN
ejpam-5573	65	76	,	,	PUNCT
ejpam-5573	65	77	s	s	NOUN
ejpam-5573	65	78	)	)	PUNCT
ejpam-5573	65	79	⟨resp	⟨resp	PROPN
ejpam-5573	65	80	.	.	PROPN
ejpam-5573	65	81	,	,	PUNCT
ejpam-5573	65	82	ν	ν	X
ejpam-5573	65	83	≥	≥	NOUN
ejpam-5573	65	84	cη	cη	ADP
ejpam-5573	65	85	,	,	PUNCT
ejpam-5573	65	86	η∗(iη	η∗(iη	PROPN
ejpam-5573	65	87	,	,	PUNCT
ejpam-5573	65	88	η∗	η∗	NOUN
ejpam-5573	65	89	(	(	PUNCT
ejpam-5573	65	90	ν	ν	NOUN
ejpam-5573	65	91	,	,	PUNCT
ejpam-5573	65	92	r	r	NOUN
ejpam-5573	65	93	,	,	PUNCT
ejpam-5573	65	94	s	s	PART
ejpam-5573	65	95	)	)	PUNCT
ejpam-5573	65	96	,	,	PUNCT
ejpam-5573	65	97	r	r	NOUN
ejpam-5573	65	98	,	,	PUNCT
ejpam-5573	65	99	s	s	PART
ejpam-5573	65	100	)	)	PUNCT
ejpam-5573	65	101	and	and	CCONJ
ejpam-5573	65	102	ν	ν	X
ejpam-5573	65	103	=	=	SYM
ejpam-5573	65	104	cη	cη	PROPN
ejpam-5573	65	105	,	,	PUNCT
ejpam-5573	65	106	η∗(iη	η∗(iη	PROPN
ejpam-5573	65	107	,	,	PUNCT
ejpam-5573	65	108	η∗	η∗	NOUN
ejpam-5573	65	109	(	(	PUNCT
ejpam-5573	65	110	ν	ν	NOUN
ejpam-5573	65	111	,	,	PUNCT
ejpam-5573	65	112	r	r	NOUN
ejpam-5573	65	113	,	,	PUNCT
ejpam-5573	65	114	s	s	PART
ejpam-5573	65	115	)	)	PUNCT
ejpam-5573	65	116	,	,	PUNCT
ejpam-5573	65	117	r	r	NOUN
ejpam-5573	65	118	,	,	PUNCT
ejpam-5573	65	119	s)⟩.	s)⟩.	NOUN
ejpam-5573	65	120	(	(	PUNCT
ejpam-5573	65	121	ii	ii	NOUN
ejpam-5573	65	122	)	)	PUNCT
ejpam-5573	65	123	ν	ν	NOUN
ejpam-5573	65	124	is	be	AUX
ejpam-5573	65	125	called	call	VERB
ejpam-5573	65	126	an	an	DET
ejpam-5573	65	127	(	(	PUNCT
ejpam-5573	65	128	r	r	NOUN
ejpam-5573	65	129	,	,	PUNCT
ejpam-5573	65	130	s)-fso	s)-fso	VERB
ejpam-5573	65	131	⟨resp	⟨resp	PROPN
ejpam-5573	65	132	.	.	PROPN
ejpam-5573	65	133	,	,	PUNCT
ejpam-5573	65	134	(	(	PUNCT
ejpam-5573	65	135	r	r	NOUN
ejpam-5573	65	136	,	,	PUNCT
ejpam-5573	65	137	s)-fpo	s)-fpo	NOUN
ejpam-5573	65	138	and	and	CCONJ
ejpam-5573	65	139	(	(	PUNCT
ejpam-5573	65	140	r	r	NOUN
ejpam-5573	65	141	,	,	PUNCT
ejpam-5573	65	142	s)-fro⟩	s)-fro⟩	PROPN
ejpam-5573	65	143	set	set	VERB
ejpam-5573	65	144	if	if	SCONJ
ejpam-5573	65	145	ν	ν	NOUN
ejpam-5573	65	146	≤	≤	X
ejpam-5573	65	147	cη	cη	ADP
ejpam-5573	65	148	,	,	PUNCT
ejpam-5573	65	149	η∗(iη	η∗(iη	PROPN
ejpam-5573	65	150	,	,	PUNCT
ejpam-5573	65	151	η∗	η∗	NOUN
ejpam-5573	65	152	(	(	PUNCT
ejpam-5573	65	153	ν	ν	NOUN
ejpam-5573	65	154	,	,	PUNCT
ejpam-5573	65	155	r	r	NOUN
ejpam-5573	65	156	,	,	PUNCT
ejpam-5573	65	157	s	s	PART
ejpam-5573	65	158	)	)	PUNCT
ejpam-5573	65	159	,	,	PUNCT
ejpam-5573	65	160	r	r	NOUN
ejpam-5573	65	161	,	,	PUNCT
ejpam-5573	65	162	s	s	NOUN
ejpam-5573	65	163	)	)	PUNCT
ejpam-5573	65	164	⟨resp	⟨resp	PROPN
ejpam-5573	65	165	.	.	PROPN
ejpam-5573	65	166	,	,	PUNCT
ejpam-5573	65	167	ν	ν	PROPN
ejpam-5573	65	168	≤	≤	NUM
ejpam-5573	65	169	iη	iη	NOUN
ejpam-5573	65	170	,	,	PUNCT
ejpam-5573	65	171	η∗(cη	η∗(cη	NOUN
ejpam-5573	65	172	,	,	PUNCT
ejpam-5573	65	173	η∗	η∗	NOUN
ejpam-5573	65	174	(	(	PUNCT
ejpam-5573	65	175	ν	ν	NOUN
ejpam-5573	65	176	,	,	PUNCT
ejpam-5573	65	177	r	r	NOUN
ejpam-5573	65	178	,	,	PUNCT
ejpam-5573	65	179	s	s	PART
ejpam-5573	65	180	)	)	PUNCT
ejpam-5573	65	181	,	,	PUNCT
ejpam-5573	65	182	r	r	NOUN
ejpam-5573	65	183	,	,	PUNCT
ejpam-5573	65	184	s	s	PART
ejpam-5573	65	185	)	)	PUNCT
ejpam-5573	65	186	and	and	CCONJ
ejpam-5573	65	187	ν	ν	X
ejpam-5573	65	188	=	=	SYM
ejpam-5573	65	189	iη	iη	NOUN
ejpam-5573	65	190	,	,	PUNCT
ejpam-5573	65	191	η∗(cη	η∗(cη	NOUN
ejpam-5573	65	192	,	,	PUNCT
ejpam-5573	65	193	η∗	η∗	NOUN
ejpam-5573	65	194	(	(	PUNCT
ejpam-5573	65	195	ν	ν	NOUN
ejpam-5573	65	196	,	,	PUNCT
ejpam-5573	65	197	r	r	NOUN
ejpam-5573	65	198	,	,	PUNCT
ejpam-5573	65	199	s	s	PART
ejpam-5573	65	200	)	)	PUNCT
ejpam-5573	65	201	,	,	PUNCT
ejpam-5573	65	202	r	r	NOUN
ejpam-5573	65	203	,	,	PUNCT
ejpam-5573	65	204	s)⟩.	s)⟩.	ADJ
ejpam-5573	65	205	definition	definition	NOUN
ejpam-5573	65	206	3	3	NUM
ejpam-5573	65	207	.	.	PUNCT
ejpam-5573	66	1	[	[	X
ejpam-5573	66	2	1	1	NUM
ejpam-5573	66	3	,	,	PUNCT
ejpam-5573	66	4	42	42	NUM
ejpam-5573	66	5	,	,	PUNCT
ejpam-5573	66	6	47	47	NUM
ejpam-5573	66	7	]	]	PUNCT
ejpam-5573	66	8	let	let	AUX
ejpam-5573	66	9	(	(	PUNCT
ejpam-5573	66	10	u	u	NOUN
ejpam-5573	66	11	,	,	PUNCT
ejpam-5573	66	12	η	η	PROPN
ejpam-5573	66	13	,	,	PUNCT
ejpam-5573	66	14	η∗	η∗	NOUN
ejpam-5573	66	15	)	)	PUNCT
ejpam-5573	66	16	be	be	VERB
ejpam-5573	66	17	a	a	DET
ejpam-5573	66	18	dfts	dft	NOUN
ejpam-5573	66	19	,	,	PUNCT
ejpam-5573	66	20	µ	µ	NOUN
ejpam-5573	66	21	,	,	PUNCT
ejpam-5573	66	22	ν	ν	X
ejpam-5573	66	23	∈	∈	NOUN
ejpam-5573	66	24	iu	iu	ADV
ejpam-5573	66	25	,	,	PUNCT
ejpam-5573	66	26	r	r	NOUN
ejpam-5573	66	27	∈	∈	PROPN
ejpam-5573	66	28	i	i	NOUN
ejpam-5573	66	29	◦	◦	NOUN
ejpam-5573	66	30	,	,	PUNCT
ejpam-5573	66	31	and	and	CCONJ
ejpam-5573	66	32	s	s	PROPN
ejpam-5573	66	33	∈	∈	PROPN
ejpam-5573	66	34	i1	i1	PROPN
ejpam-5573	66	35	,	,	PUNCT
ejpam-5573	66	36	then	then	ADV
ejpam-5573	66	37	we	we	PRON
ejpam-5573	66	38	have	have	VERB
ejpam-5573	66	39	(	(	PUNCT
ejpam-5573	66	40	i	i	NOUN
ejpam-5573	66	41	)	)	PUNCT
ejpam-5573	66	42	µ	µ	PROPN
ejpam-5573	66	43	is	be	AUX
ejpam-5573	66	44	called	call	VERB
ejpam-5573	66	45	an	an	DET
ejpam-5573	66	46	(	(	PUNCT
ejpam-5573	66	47	r	r	NOUN
ejpam-5573	66	48	,	,	PUNCT
ejpam-5573	66	49	s)-generalized	s)-generalized	ADJ
ejpam-5573	66	50	fuzzy	fuzzy	ADJ
ejpam-5573	66	51	closed	close	VERB
ejpam-5573	66	52	⟨briefly	⟨briefly	ADV
ejpam-5573	66	53	,	,	PUNCT
ejpam-5573	66	54	(	(	PUNCT
ejpam-5573	66	55	r	r	NOUN
ejpam-5573	66	56	,	,	PUNCT
ejpam-5573	66	57	s)-gfc⟩	s)-gfc⟩	ADP
ejpam-5573	66	58	set	set	NOUN
ejpam-5573	66	59	if	if	SCONJ
ejpam-5573	66	60	cη	cη	PROPN
ejpam-5573	66	61	,	,	PUNCT
ejpam-5573	66	62	η∗(µ	η∗(µ	PROPN
ejpam-5573	66	63	,	,	PUNCT
ejpam-5573	66	64	r	r	NOUN
ejpam-5573	66	65	,	,	PUNCT
ejpam-5573	66	66	s	s	NOUN
ejpam-5573	66	67	)	)	PUNCT
ejpam-5573	66	68	≤	≤	NUM
ejpam-5573	66	69	ν	ν	NOUN
ejpam-5573	66	70	whenever	whenever	SCONJ
ejpam-5573	66	71	µ	µ	PRON
ejpam-5573	66	72	≤	≤	NUM
ejpam-5573	66	73	ν	ν	NOUN
ejpam-5573	66	74	and	and	CCONJ
ejpam-5573	66	75	η(ν	η(ν	PROPN
ejpam-5573	66	76	)	)	PUNCT
ejpam-5573	66	77	≥	≥	NOUN
ejpam-5573	66	78	r	r	NOUN
ejpam-5573	66	79	,	,	PUNCT
ejpam-5573	66	80	η∗(ν	η∗(ν	NOUN
ejpam-5573	66	81	)	)	PUNCT
ejpam-5573	66	82	≤	≤	NOUN
ejpam-5573	67	1	s.	s.	PROPN
ejpam-5573	67	2	f.	f.	PROPN
ejpam-5573	67	3	alsharari	alsharari	PROPN
ejpam-5573	67	4	,	,	PUNCT
ejpam-5573	67	5	o.	o.	PROPN
ejpam-5573	67	6	m.	m.	PROPN
ejpam-5573	67	7	taha	taha	PROPN
ejpam-5573	67	8	,	,	PUNCT
ejpam-5573	67	9	i.	i.	PROPN
ejpam-5573	67	10	m.	m.	PROPN
ejpam-5573	67	11	taha	taha	PROPN
ejpam-5573	67	12	/	/	PUNCT
ejpam-5573	67	13	eur	eur	PROPN
ejpam-5573	67	14	.	.	PUNCT
ejpam-5573	68	1	j.	j.	PROPN
ejpam-5573	68	2	pure	pure	PROPN
ejpam-5573	68	3	appl	appl	PROPN
ejpam-5573	68	4	.	.	PROPN
ejpam-5573	68	5	math	math	PROPN
ejpam-5573	68	6	,	,	PUNCT
ejpam-5573	68	7	17	17	NUM
ejpam-5573	68	8	(	(	PUNCT
ejpam-5573	68	9	4	4	NUM
ejpam-5573	68	10	)	)	PUNCT
ejpam-5573	68	11	(	(	PUNCT
ejpam-5573	68	12	2024	2024	NUM
ejpam-5573	68	13	)	)	PUNCT
ejpam-5573	68	14	,	,	PUNCT
ejpam-5573	68	15	4093	4093	NUM
ejpam-5573	68	16	-	-	SYM
ejpam-5573	68	17	4111	4111	NUM
ejpam-5573	68	18	4096	4096	NUM
ejpam-5573	68	19	(	(	PUNCT
ejpam-5573	68	20	ii	ii	NOUN
ejpam-5573	68	21	)	)	PUNCT
ejpam-5573	68	22	µ	µ	PROPN
ejpam-5573	68	23	is	be	AUX
ejpam-5573	68	24	called	call	VERB
ejpam-5573	68	25	an	an	DET
ejpam-5573	68	26	(	(	PUNCT
ejpam-5573	68	27	r	r	NOUN
ejpam-5573	68	28	,	,	PUNCT
ejpam-5573	68	29	s)-semi	s)-semi	PUNCT
ejpam-5573	68	30	generalized	generalize	VERB
ejpam-5573	68	31	fuzzy	fuzzy	ADJ
ejpam-5573	68	32	closed	close	VERB
ejpam-5573	68	33	⟨briefly	⟨briefly	ADV
ejpam-5573	68	34	,	,	PUNCT
ejpam-5573	68	35	(	(	PUNCT
ejpam-5573	68	36	r	r	NOUN
ejpam-5573	68	37	,	,	PUNCT
ejpam-5573	68	38	s)-sgfc⟩	s)-sgfc⟩	NOUN
ejpam-5573	68	39	set	set	VERB
ejpam-5573	68	40	if	if	SCONJ
ejpam-5573	68	41	scη	scη	PROPN
ejpam-5573	68	42	,	,	PUNCT
ejpam-5573	68	43	η∗(µ	η∗(µ	PROPN
ejpam-5573	68	44	,	,	PUNCT
ejpam-5573	68	45	r	r	NOUN
ejpam-5573	68	46	,	,	PUNCT
ejpam-5573	68	47	s	s	NOUN
ejpam-5573	68	48	)	)	PUNCT
ejpam-5573	68	49	≤	≤	NUM
ejpam-5573	68	50	ν	ν	NOUN
ejpam-5573	68	51	whenever	whenever	SCONJ
ejpam-5573	68	52	µ	µ	PRON
ejpam-5573	68	53	≤	≤	NUM
ejpam-5573	68	54	ν	ν	NOUN
ejpam-5573	68	55	and	and	CCONJ
ejpam-5573	68	56	ν	ν	PROPN
ejpam-5573	68	57	is	be	AUX
ejpam-5573	68	58	(	(	PUNCT
ejpam-5573	68	59	r	r	NOUN
ejpam-5573	68	60	,	,	PUNCT
ejpam-5573	68	61	s)-fso	s)-fso	VERB
ejpam-5573	68	62	set	set	NOUN
ejpam-5573	68	63	.	.	PUNCT
ejpam-5573	69	1	(	(	PUNCT
ejpam-5573	69	2	iii	iii	X
ejpam-5573	69	3	)	)	PUNCT
ejpam-5573	69	4	µ	µ	PROPN
ejpam-5573	69	5	is	be	AUX
ejpam-5573	69	6	called	call	VERB
ejpam-5573	69	7	an	an	DET
ejpam-5573	69	8	(	(	PUNCT
ejpam-5573	69	9	r	r	NOUN
ejpam-5573	69	10	,	,	PUNCT
ejpam-5573	69	11	s)-generalized	s)-generalized	ADJ
ejpam-5573	69	12	fuzzy	fuzzy	ADJ
ejpam-5573	69	13	semi	semi	ADJ
ejpam-5573	69	14	-	-	ADJ
ejpam-5573	69	15	closed	closed	ADJ
ejpam-5573	69	16	⟨briefly	⟨briefly	NOUN
ejpam-5573	69	17	,	,	PUNCT
ejpam-5573	69	18	(	(	PUNCT
ejpam-5573	69	19	r	r	NOUN
ejpam-5573	69	20	,	,	PUNCT
ejpam-5573	69	21	s)-gfsc⟩	s)-gfsc⟩	NOUN
ejpam-5573	69	22	set	set	VERB
ejpam-5573	69	23	if	if	SCONJ
ejpam-5573	69	24	scη	scη	PROPN
ejpam-5573	69	25	,	,	PUNCT
ejpam-5573	69	26	η∗(µ	η∗(µ	PROPN
ejpam-5573	69	27	,	,	PUNCT
ejpam-5573	69	28	r	r	NOUN
ejpam-5573	69	29	,	,	PUNCT
ejpam-5573	69	30	s	s	NOUN
ejpam-5573	69	31	)	)	PUNCT
ejpam-5573	69	32	≤	≤	NUM
ejpam-5573	69	33	ν	ν	NOUN
ejpam-5573	69	34	whenever	whenever	SCONJ
ejpam-5573	69	35	µ	µ	PRON
ejpam-5573	69	36	≤	≤	NUM
ejpam-5573	69	37	ν	ν	NOUN
ejpam-5573	69	38	and	and	CCONJ
ejpam-5573	69	39	η(ν	η(ν	PROPN
ejpam-5573	69	40	)	)	PUNCT
ejpam-5573	69	41	≥	≥	NOUN
ejpam-5573	69	42	r	r	NOUN
ejpam-5573	69	43	,	,	PUNCT
ejpam-5573	69	44	η∗(ν	η∗(ν	NOUN
ejpam-5573	69	45	)	)	PUNCT
ejpam-5573	69	46	≤	≤	NOUN
ejpam-5573	69	47	s.	s.	PROPN
ejpam-5573	69	48	definition	definition	NOUN
ejpam-5573	69	49	4	4	NUM
ejpam-5573	69	50	.	.	PUNCT
ejpam-5573	70	1	[	[	X
ejpam-5573	70	2	34	34	NUM
ejpam-5573	70	3	,	,	PUNCT
ejpam-5573	70	4	47	47	NUM
ejpam-5573	70	5	]	]	PUNCT
ejpam-5573	70	6	let	let	AUX
ejpam-5573	70	7	h	h	NOUN
ejpam-5573	70	8	:	:	PUNCT
ejpam-5573	70	9	(	(	PUNCT
ejpam-5573	70	10	u	u	NOUN
ejpam-5573	70	11	,	,	PUNCT
ejpam-5573	70	12	τ	τ	X
ejpam-5573	70	13	,	,	PUNCT
ejpam-5573	70	14	τ∗)→	τ∗)→	PROPN
ejpam-5573	70	15	(	(	PUNCT
ejpam-5573	70	16	v	v	PROPN
ejpam-5573	70	17	,	,	PUNCT
ejpam-5573	70	18	η	η	NOUN
ejpam-5573	70	19	,	,	PUNCT
ejpam-5573	70	20	η∗	η∗	NOUN
ejpam-5573	70	21	)	)	PUNCT
ejpam-5573	70	22	be	be	VERB
ejpam-5573	70	23	a	a	DET
ejpam-5573	70	24	mapping	mapping	NOUN
ejpam-5573	70	25	,	,	PUNCT
ejpam-5573	70	26	then	then	ADV
ejpam-5573	70	27	h	h	NOUN
ejpam-5573	70	28	is	be	AUX
ejpam-5573	70	29	said	say	VERB
ejpam-5573	70	30	to	to	PART
ejpam-5573	70	31	be	be	AUX
ejpam-5573	70	32	(	(	PUNCT
ejpam-5573	70	33	i	i	NOUN
ejpam-5573	70	34	)	)	PUNCT
ejpam-5573	70	35	df	df	NOUN
ejpam-5573	70	36	-	-	PUNCT
ejpam-5573	70	37	continuous	continuous	ADJ
ejpam-5573	70	38	if	if	SCONJ
ejpam-5573	70	39	τ(h−1(λ	τ(h−1(λ	PROPN
ejpam-5573	70	40	)	)	PUNCT
ejpam-5573	70	41	)	)	PUNCT
ejpam-5573	70	42	≥	≥	PRON
ejpam-5573	70	43	η(λ	η(λ	NOUN
ejpam-5573	70	44	)	)	PUNCT
ejpam-5573	70	45	and	and	CCONJ
ejpam-5573	70	46	τ∗(h−1(λ	τ∗(h−1(λ	NOUN
ejpam-5573	70	47	)	)	PUNCT
ejpam-5573	70	48	)	)	PUNCT
ejpam-5573	70	49	≤	≤	NUM
ejpam-5573	70	50	η∗(λ	η∗(λ	NOUN
ejpam-5573	70	51	)	)	PUNCT
ejpam-5573	70	52	for	for	ADP
ejpam-5573	70	53	each	each	DET
ejpam-5573	70	54	λ	λ	PROPN
ejpam-5573	70	55	∈	∈	PROPN
ejpam-5573	70	56	iv	iv	X
ejpam-5573	70	57	.	.	PUNCT
ejpam-5573	71	1	(	(	PUNCT
ejpam-5573	71	2	ii	ii	NOUN
ejpam-5573	71	3	)	)	PUNCT
ejpam-5573	71	4	df	df	NOUN
ejpam-5573	71	5	-	-	PUNCT
ejpam-5573	71	6	open	open	ADJ
ejpam-5573	71	7	if	if	SCONJ
ejpam-5573	71	8	η(h(ν	η(h(ν	PROPN
ejpam-5573	71	9	)	)	PUNCT
ejpam-5573	71	10	)	)	PUNCT
ejpam-5573	71	11	≥	≥	NOUN
ejpam-5573	71	12	τ(ν	τ(ν	NOUN
ejpam-5573	71	13	)	)	PUNCT
ejpam-5573	71	14	and	and	CCONJ
ejpam-5573	71	15	η∗(h(ν	η∗(h(ν	NOUN
ejpam-5573	71	16	)	)	PUNCT
ejpam-5573	71	17	)	)	PUNCT
ejpam-5573	71	18	≤	≤	NUM
ejpam-5573	71	19	τ∗(ν	τ∗(ν	PROPN
ejpam-5573	71	20	)	)	PUNCT
ejpam-5573	71	21	for	for	ADP
ejpam-5573	71	22	each	each	DET
ejpam-5573	71	23	ν	ν	NOUN
ejpam-5573	71	24	∈	∈	PROPN
ejpam-5573	71	25	iu	iu	ADP
ejpam-5573	71	26	.	.	PUNCT
ejpam-5573	72	1	(	(	PUNCT
ejpam-5573	72	2	iii	iii	X
ejpam-5573	72	3	)	)	PUNCT
ejpam-5573	72	4	df	df	NOUN
ejpam-5573	72	5	-	-	PUNCT
ejpam-5573	72	6	closed	closed	ADJ
ejpam-5573	72	7	if	if	SCONJ
ejpam-5573	72	8	η(hc(ν	η(hc(ν	NOUN
ejpam-5573	72	9	)	)	PUNCT
ejpam-5573	72	10	)	)	PUNCT
ejpam-5573	72	11	≥	≥	NOUN
ejpam-5573	72	12	τ(νc	τ(νc	NUM
ejpam-5573	72	13	)	)	PUNCT
ejpam-5573	72	14	and	and	CCONJ
ejpam-5573	72	15	η∗(hc(ν	η∗(hc(ν	NUM
ejpam-5573	72	16	)	)	PUNCT
ejpam-5573	72	17	)	)	PUNCT
ejpam-5573	73	1	≤	≤	NOUN
ejpam-5573	73	2	τ∗(µc	τ∗(µc	NOUN
ejpam-5573	73	3	)	)	PUNCT
ejpam-5573	73	4	for	for	ADP
ejpam-5573	73	5	each	each	DET
ejpam-5573	73	6	ν	ν	NOUN
ejpam-5573	73	7	∈	∈	PROPN
ejpam-5573	73	8	iu	iu	X
ejpam-5573	73	9	.	.	PUNCT
ejpam-5573	74	1	definition	definition	NOUN
ejpam-5573	74	2	5	5	NUM
ejpam-5573	74	3	.	.	PUNCT
ejpam-5573	75	1	[	[	X
ejpam-5573	75	2	1	1	NUM
ejpam-5573	75	3	,	,	PUNCT
ejpam-5573	75	4	29	29	NUM
ejpam-5573	75	5	,	,	PUNCT
ejpam-5573	75	6	42	42	NUM
ejpam-5573	75	7	]	]	PUNCT
ejpam-5573	75	8	let	let	VERB
ejpam-5573	75	9	h	h	NOUN
ejpam-5573	75	10	:	:	PUNCT
ejpam-5573	75	11	(	(	PUNCT
ejpam-5573	75	12	u	u	NOUN
ejpam-5573	75	13	,	,	PUNCT
ejpam-5573	75	14	τ	τ	X
ejpam-5573	75	15	,	,	PUNCT
ejpam-5573	75	16	τ∗)→	τ∗)→	PROPN
ejpam-5573	75	17	(	(	PUNCT
ejpam-5573	75	18	v	v	PROPN
ejpam-5573	75	19	,	,	PUNCT
ejpam-5573	75	20	η	η	NOUN
ejpam-5573	75	21	,	,	PUNCT
ejpam-5573	75	22	η∗	η∗	NOUN
ejpam-5573	75	23	)	)	PUNCT
ejpam-5573	75	24	be	be	VERB
ejpam-5573	75	25	a	a	DET
ejpam-5573	75	26	mapping	mapping	NOUN
ejpam-5573	75	27	,	,	PUNCT
ejpam-5573	75	28	r	r	NOUN
ejpam-5573	75	29	∈	∈	PROPN
ejpam-5573	75	30	i	i	NOUN
ejpam-5573	75	31	◦	◦	NOUN
ejpam-5573	75	32	,	,	PUNCT
ejpam-5573	75	33	and	and	CCONJ
ejpam-5573	75	34	s	s	PROPN
ejpam-5573	75	35	∈	∈	PROPN
ejpam-5573	75	36	i1	i1	PROPN
ejpam-5573	75	37	,	,	PUNCT
ejpam-5573	75	38	then	then	ADV
ejpam-5573	75	39	h	h	PROPN
ejpam-5573	75	40	is	be	AUX
ejpam-5573	75	41	said	say	VERB
ejpam-5573	75	42	to	to	PART
ejpam-5573	75	43	be	be	AUX
ejpam-5573	75	44	(	(	PUNCT
ejpam-5573	75	45	i	i	NOUN
ejpam-5573	75	46	)	)	PUNCT
ejpam-5573	75	47	dfs	dfs	ADJ
ejpam-5573	75	48	-	-	PUNCT
ejpam-5573	75	49	continuous	continuous	ADJ
ejpam-5573	75	50	⟨resp	⟨resp	PROPN
ejpam-5573	75	51	.	.	PROPN
ejpam-5573	75	52	,	,	PUNCT
ejpam-5573	75	53	dfgs	dfgs	NOUN
ejpam-5573	75	54	-	-	PUNCT
ejpam-5573	75	55	continuous	continuous	ADJ
ejpam-5573	75	56	and	and	CCONJ
ejpam-5573	75	57	dfg	dfg	NOUN
ejpam-5573	75	58	-	-	PUNCT
ejpam-5573	75	59	continuous⟩	continuous⟩	NOUN
ejpam-5573	75	60	if	if	SCONJ
ejpam-5573	75	61	h−1(µ	h−1(µ	NOUN
ejpam-5573	75	62	)	)	PUNCT
ejpam-5573	75	63	is	be	AUX
ejpam-5573	75	64	(	(	PUNCT
ejpam-5573	75	65	r	r	NOUN
ejpam-5573	75	66	,	,	PUNCT
ejpam-5573	75	67	s)fso	s)fso	PROPN
ejpam-5573	75	68	⟨resp	⟨resp	PROPN
ejpam-5573	75	69	.	.	PROPN
ejpam-5573	75	70	,	,	PUNCT
ejpam-5573	75	71	(	(	PUNCT
ejpam-5573	75	72	r	r	NOUN
ejpam-5573	75	73	,	,	PUNCT
ejpam-5573	75	74	s)-gfso	s)-gfso	VERB
ejpam-5573	75	75	and	and	CCONJ
ejpam-5573	75	76	(	(	PUNCT
ejpam-5573	75	77	r	r	NOUN
ejpam-5573	75	78	,	,	PUNCT
ejpam-5573	75	79	s)-gfo⟩	s)-gfo⟩	NUM
ejpam-5573	75	80	set	set	NOUN
ejpam-5573	75	81	for	for	ADP
ejpam-5573	75	82	each	each	DET
ejpam-5573	75	83	µ	µ	PRON
ejpam-5573	75	84	∈	∈	NOUN
ejpam-5573	75	85	iv	iv	NUM
ejpam-5573	75	86	with	with	ADP
ejpam-5573	75	87	η(µ	η(µ	PROPN
ejpam-5573	75	88	)	)	PUNCT
ejpam-5573	75	89	≥	≥	PROPN
ejpam-5573	75	90	r	r	NOUN
ejpam-5573	75	91	,	,	PUNCT
ejpam-5573	75	92	η∗(µ	η∗(µ	PROPN
ejpam-5573	75	93	)	)	PUNCT
ejpam-5573	75	94	≤	≤	PROPN
ejpam-5573	76	1	s.	s.	PROPN
ejpam-5573	76	2	(	(	PUNCT
ejpam-5573	76	3	ii	ii	PROPN
ejpam-5573	76	4	)	)	PUNCT
ejpam-5573	76	5	dfgs	dfgs	NOUN
ejpam-5573	76	6	-	-	PUNCT
ejpam-5573	76	7	irresolute	irresolute	PROPN
ejpam-5573	76	8	⟨resp	⟨resp	PROPN
ejpam-5573	76	9	.	.	PROPN
ejpam-5573	76	10	,	,	PUNCT
ejpam-5573	76	11	df	df	PROPN
ejpam-5573	76	12	-	-	PUNCT
ejpam-5573	76	13	irresolute⟩	irresolute⟩	PROPN
ejpam-5573	76	14	if	if	SCONJ
ejpam-5573	76	15	h−1(µ	h−1(µ	NOUN
ejpam-5573	76	16	)	)	PUNCT
ejpam-5573	76	17	is	be	AUX
ejpam-5573	76	18	(	(	PUNCT
ejpam-5573	76	19	r	r	NOUN
ejpam-5573	76	20	,	,	PUNCT
ejpam-5573	76	21	s)-gfso	s)-gfso	VERB
ejpam-5573	76	22	⟨resp	⟨resp	PROPN
ejpam-5573	76	23	.	.	PROPN
ejpam-5573	76	24	,	,	PUNCT
ejpam-5573	76	25	(	(	PUNCT
ejpam-5573	76	26	r	r	NOUN
ejpam-5573	76	27	,	,	PUNCT
ejpam-5573	76	28	s)-fso⟩	s)-fso⟩	NOUN
ejpam-5573	76	29	set	set	VERB
ejpam-5573	76	30	for	for	ADP
ejpam-5573	76	31	each	each	DET
ejpam-5573	76	32	µ	µ	PROPN
ejpam-5573	76	33	∈	∈	NOUN
ejpam-5573	76	34	iv	iv	X
ejpam-5573	76	35	is	be	AUX
ejpam-5573	76	36	(	(	PUNCT
ejpam-5573	76	37	r	r	NOUN
ejpam-5573	76	38	,	,	PUNCT
ejpam-5573	76	39	s)-gfso	s)-gfso	VERB
ejpam-5573	76	40	⟨resp	⟨resp	PROPN
ejpam-5573	76	41	.	.	PROPN
ejpam-5573	76	42	,	,	PUNCT
ejpam-5573	76	43	(	(	PUNCT
ejpam-5573	76	44	r	r	NOUN
ejpam-5573	76	45	,	,	PUNCT
ejpam-5573	76	46	s)-fso⟩	s)-fso⟩	NOUN
ejpam-5573	76	47	set	set	NOUN
ejpam-5573	76	48	.	.	PUNCT
ejpam-5573	77	1	(	(	PUNCT
ejpam-5573	77	2	iii	iii	X
ejpam-5573	77	3	)	)	PUNCT
ejpam-5573	77	4	dfs	dfs	ADJ
ejpam-5573	77	5	-	-	PUNCT
ejpam-5573	77	6	open	open	ADJ
ejpam-5573	77	7	⟨resp	⟨resp	PROPN
ejpam-5573	77	8	.	.	PROPN
ejpam-5573	77	9	,	,	PUNCT
ejpam-5573	77	10	dfgs	dfgs	NOUN
ejpam-5573	77	11	-	-	PUNCT
ejpam-5573	77	12	open	open	ADJ
ejpam-5573	77	13	and	and	CCONJ
ejpam-5573	77	14	dfg	dfg	NOUN
ejpam-5573	77	15	-	-	PUNCT
ejpam-5573	77	16	open⟩	open⟩	NOUN
ejpam-5573	77	17	if	if	SCONJ
ejpam-5573	77	18	h(ν	h(ν	PRON
ejpam-5573	77	19	)	)	PUNCT
ejpam-5573	77	20	is	be	AUX
ejpam-5573	77	21	(	(	PUNCT
ejpam-5573	77	22	r	r	NOUN
ejpam-5573	77	23	,	,	PUNCT
ejpam-5573	77	24	s)-fso	s)-fso	VERB
ejpam-5573	77	25	⟨resp	⟨resp	PROPN
ejpam-5573	77	26	.	.	PROPN
ejpam-5573	77	27	,	,	PUNCT
ejpam-5573	77	28	(	(	PUNCT
ejpam-5573	77	29	r	r	NOUN
ejpam-5573	77	30	,	,	PUNCT
ejpam-5573	77	31	s)gfso	s)gfso	NOUN
ejpam-5573	77	32	and	and	CCONJ
ejpam-5573	77	33	(	(	PUNCT
ejpam-5573	77	34	r	r	NOUN
ejpam-5573	77	35	,	,	PUNCT
ejpam-5573	77	36	s)-gfo⟩	s)-gfo⟩	NUM
ejpam-5573	77	37	set	set	NOUN
ejpam-5573	77	38	for	for	ADP
ejpam-5573	77	39	each	each	DET
ejpam-5573	77	40	ν	ν	NOUN
ejpam-5573	77	41	∈	∈	NOUN
ejpam-5573	77	42	iu	iu	ADV
ejpam-5573	77	43	with	with	ADP
ejpam-5573	77	44	τ(ν	τ(ν	NOUN
ejpam-5573	77	45	)	)	PUNCT
ejpam-5573	77	46	≥	≥	NOUN
ejpam-5573	77	47	r	r	NOUN
ejpam-5573	77	48	,	,	PUNCT
ejpam-5573	77	49	τ∗(ν	τ∗(ν	PROPN
ejpam-5573	77	50	)	)	PUNCT
ejpam-5573	77	51	≤	≤	ADJ
ejpam-5573	77	52	s.	s.	PROPN
ejpam-5573	77	53	(	(	PUNCT
ejpam-5573	77	54	iv	iv	X
ejpam-5573	77	55	)	)	PUNCT
ejpam-5573	77	56	dfs	dfs	ADJ
ejpam-5573	77	57	-	-	PUNCT
ejpam-5573	77	58	closed	closed	ADJ
ejpam-5573	77	59	⟨resp	⟨resp	PROPN
ejpam-5573	77	60	.	.	PROPN
ejpam-5573	77	61	,	,	PUNCT
ejpam-5573	77	62	dfgs	dfgs	NOUN
ejpam-5573	77	63	-	-	PUNCT
ejpam-5573	77	64	closed	close	VERB
ejpam-5573	77	65	and	and	CCONJ
ejpam-5573	77	66	dfg	dfg	NOUN
ejpam-5573	77	67	-	-	PUNCT
ejpam-5573	77	68	closed⟩	closed⟩	PROPN
ejpam-5573	77	69	if	if	SCONJ
ejpam-5573	77	70	h(ν	h(ν	NOUN
ejpam-5573	77	71	)	)	PUNCT
ejpam-5573	77	72	is	be	AUX
ejpam-5573	77	73	(	(	PUNCT
ejpam-5573	77	74	r	r	NOUN
ejpam-5573	77	75	,	,	PUNCT
ejpam-5573	77	76	s)-fsc	s)-fsc	NOUN
ejpam-5573	77	77	⟨resp	⟨resp	PROPN
ejpam-5573	77	78	.	.	PROPN
ejpam-5573	77	79	,	,	PUNCT
ejpam-5573	77	80	(	(	PUNCT
ejpam-5573	77	81	r	r	NOUN
ejpam-5573	77	82	,	,	PUNCT
ejpam-5573	77	83	s)-gfsc	s)-gfsc	PUNCT
ejpam-5573	77	84	and	and	CCONJ
ejpam-5573	77	85	(	(	PUNCT
ejpam-5573	77	86	r	r	NOUN
ejpam-5573	77	87	,	,	PUNCT
ejpam-5573	77	88	s)-gfc⟩	s)-gfc⟩	ADP
ejpam-5573	77	89	set	set	NOUN
ejpam-5573	77	90	for	for	ADP
ejpam-5573	77	91	each	each	DET
ejpam-5573	77	92	ν	ν	NOUN
ejpam-5573	77	93	∈	∈	PROPN
ejpam-5573	77	94	iu	iu	ADP
ejpam-5573	77	95	with	with	ADP
ejpam-5573	77	96	τ(νc	τ(νc	PROPN
ejpam-5573	77	97	)	)	PUNCT
ejpam-5573	77	98	≥	≥	NOUN
ejpam-5573	77	99	r	r	NOUN
ejpam-5573	77	100	,	,	PUNCT
ejpam-5573	77	101	τ∗(νc	τ∗(νc	PROPN
ejpam-5573	77	102	)	)	PUNCT
ejpam-5573	77	103	≤	≤	PUNCT
ejpam-5573	77	104	s.	s.	PROPN
ejpam-5573	77	105	the	the	DET
ejpam-5573	77	106	basic	basic	ADJ
ejpam-5573	77	107	results	result	NOUN
ejpam-5573	77	108	and	and	CCONJ
ejpam-5573	77	109	notions	notion	NOUN
ejpam-5573	77	110	that	that	SCONJ
ejpam-5573	77	111	we	we	PRON
ejpam-5573	77	112	need	need	VERB
ejpam-5573	77	113	in	in	ADP
ejpam-5573	77	114	the	the	DET
ejpam-5573	77	115	next	next	ADJ
ejpam-5573	77	116	sections	section	NOUN
ejpam-5573	77	117	are	be	AUX
ejpam-5573	77	118	found	find	VERB
ejpam-5573	77	119	in	in	ADP
ejpam-5573	77	120	[	[	X
ejpam-5573	77	121	1	1	NUM
ejpam-5573	77	122	,	,	PUNCT
ejpam-5573	77	123	32	32	NUM
ejpam-5573	77	124	,	,	PUNCT
ejpam-5573	77	125	42	42	NUM
ejpam-5573	77	126	–	–	SYM
ejpam-5573	77	127	44	44	NUM
ejpam-5573	77	128	,	,	PUNCT
ejpam-5573	77	129	47	47	NUM
ejpam-5573	77	130	]	]	PUNCT
ejpam-5573	77	131	.	.	PUNCT
ejpam-5573	78	1	2	2	X
ejpam-5573	78	2	.	.	X
ejpam-5573	78	3	a	a	DET
ejpam-5573	78	4	stronger	strong	ADJ
ejpam-5573	78	5	novel	novel	ADJ
ejpam-5573	78	6	form	form	NOUN
ejpam-5573	78	7	of	of	ADP
ejpam-5573	78	8	(	(	PUNCT
ejpam-5573	78	9	r	r	NOUN
ejpam-5573	78	10	,	,	PUNCT
ejpam-5573	78	11	s)−	s)−	PROPN
ejpam-5573	78	12	gfsc	gfsc	PROPN
ejpam-5573	78	13	sets	set	VERB
ejpam-5573	78	14	here	here	ADV
ejpam-5573	78	15	,	,	PUNCT
ejpam-5573	78	16	we	we	PRON
ejpam-5573	78	17	introduce	introduce	VERB
ejpam-5573	78	18	and	and	CCONJ
ejpam-5573	78	19	study	study	VERB
ejpam-5573	78	20	a	a	DET
ejpam-5573	78	21	stronger	strong	ADJ
ejpam-5573	78	22	form	form	NOUN
ejpam-5573	78	23	of	of	ADP
ejpam-5573	78	24	(	(	PUNCT
ejpam-5573	78	25	r	r	NOUN
ejpam-5573	78	26	,	,	PUNCT
ejpam-5573	78	27	s)−	s)−	PROPN
ejpam-5573	78	28	gfsc	gfsc	PROPN
ejpam-5573	78	29	sets	set	VERB
ejpam-5573	78	30	called	call	VERB
ejpam-5573	78	31	(	(	PUNCT
ejpam-5573	78	32	r	r	NOUN
ejpam-5573	78	33	,	,	PUNCT
ejpam-5573	78	34	s)−	s)−	PROPN
ejpam-5573	79	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	79	2	sets	set	VERB
ejpam-5573	79	3	.	.	PUNCT
ejpam-5573	80	1	also	also	ADV
ejpam-5573	80	2	,	,	PUNCT
ejpam-5573	80	3	we	we	PRON
ejpam-5573	80	4	show	show	VERB
ejpam-5573	80	5	that	that	SCONJ
ejpam-5573	80	6	(	(	PUNCT
ejpam-5573	80	7	r	r	NOUN
ejpam-5573	80	8	,	,	PUNCT
ejpam-5573	80	9	s)−	s)−	PROPN
ejpam-5573	80	10	fsc	fsc	PROPN
ejpam-5573	80	11	set	set	VERB
ejpam-5573	80	12	[	[	X
ejpam-5573	80	13	29	29	NUM
ejpam-5573	80	14	]	]	PUNCT
ejpam-5573	80	15	⇒	⇒	NOUN
ejpam-5573	80	16	(	(	PUNCT
ejpam-5573	80	17	r	r	NOUN
ejpam-5573	80	18	,	,	PUNCT
ejpam-5573	80	19	s)−	s)−	PROPN
ejpam-5573	81	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	81	2	set	set	VERB
ejpam-5573	81	3	⇒	⇒	NOUN
ejpam-5573	81	4	(	(	PUNCT
ejpam-5573	81	5	r	r	NOUN
ejpam-5573	81	6	,	,	PUNCT
ejpam-5573	81	7	s)−	s)−	PROPN
ejpam-5573	81	8	gfsc	gfsc	PROPN
ejpam-5573	81	9	set	set	VERB
ejpam-5573	82	1	[	[	X
ejpam-5573	82	2	42	42	NUM
ejpam-5573	82	3	]	]	PUNCT
ejpam-5573	82	4	,	,	PUNCT
ejpam-5573	82	5	but	but	CCONJ
ejpam-5573	82	6	the	the	DET
ejpam-5573	82	7	converse	converse	NOUN
ejpam-5573	82	8	may	may	AUX
ejpam-5573	82	9	not	not	PART
ejpam-5573	82	10	be	be	AUX
ejpam-5573	82	11	true	true	ADJ
ejpam-5573	82	12	.	.	PUNCT
ejpam-5573	83	1	after	after	ADP
ejpam-5573	83	2	that	that	PRON
ejpam-5573	83	3	,	,	PUNCT
ejpam-5573	83	4	we	we	PRON
ejpam-5573	83	5	introduce	introduce	VERB
ejpam-5573	83	6	new	new	ADJ
ejpam-5573	83	7	types	type	NOUN
ejpam-5573	83	8	of	of	ADP
ejpam-5573	83	9	fuzzy	fuzzy	ADJ
ejpam-5573	83	10	mappings	mapping	NOUN
ejpam-5573	83	11	between	between	ADP
ejpam-5573	83	12	double	double	ADJ
ejpam-5573	83	13	fuzzy	fuzzy	ADJ
ejpam-5573	83	14	topological	topological	ADJ
ejpam-5573	83	15	spaces	space	NOUN
ejpam-5573	83	16	and	and	CCONJ
ejpam-5573	83	17	relationships	relationship	NOUN
ejpam-5573	83	18	are	be	AUX
ejpam-5573	83	19	obtained	obtain	VERB
ejpam-5573	83	20	.	.	PUNCT
ejpam-5573	84	1	f.	f.	PROPN
ejpam-5573	84	2	alsharari	alsharari	PROPN
ejpam-5573	84	3	,	,	PUNCT
ejpam-5573	84	4	o.	o.	PROPN
ejpam-5573	84	5	m.	m.	PROPN
ejpam-5573	84	6	taha	taha	PROPN
ejpam-5573	84	7	,	,	PUNCT
ejpam-5573	84	8	i.	i.	PROPN
ejpam-5573	84	9	m.	m.	PROPN
ejpam-5573	84	10	taha	taha	PROPN
ejpam-5573	84	11	/	/	PUNCT
ejpam-5573	84	12	eur	eur	PROPN
ejpam-5573	84	13	.	.	PUNCT
ejpam-5573	85	1	j.	j.	PROPN
ejpam-5573	85	2	pure	pure	PROPN
ejpam-5573	85	3	appl	appl	PROPN
ejpam-5573	85	4	.	.	PROPN
ejpam-5573	85	5	math	math	PROPN
ejpam-5573	85	6	,	,	PUNCT
ejpam-5573	85	7	17	17	NUM
ejpam-5573	85	8	(	(	PUNCT
ejpam-5573	85	9	4	4	NUM
ejpam-5573	85	10	)	)	PUNCT
ejpam-5573	85	11	(	(	PUNCT
ejpam-5573	85	12	2024	2024	NUM
ejpam-5573	85	13	)	)	PUNCT
ejpam-5573	85	14	,	,	PUNCT
ejpam-5573	85	15	4093	4093	NUM
ejpam-5573	85	16	-	-	SYM
ejpam-5573	85	17	4111	4111	NUM
ejpam-5573	85	18	4097	4097	NUM
ejpam-5573	85	19	definition	definition	NOUN
ejpam-5573	85	20	6	6	NUM
ejpam-5573	85	21	.	.	PUNCT
ejpam-5573	86	1	let	let	VERB
ejpam-5573	86	2	(	(	PUNCT
ejpam-5573	86	3	v	v	NOUN
ejpam-5573	86	4	,	,	PUNCT
ejpam-5573	86	5	η	η	NOUN
ejpam-5573	86	6	,	,	PUNCT
ejpam-5573	86	7	η∗	η∗	NOUN
ejpam-5573	86	8	)	)	PUNCT
ejpam-5573	86	9	be	be	VERB
ejpam-5573	86	10	a	a	DET
ejpam-5573	86	11	dfts	dft	NOUN
ejpam-5573	86	12	,	,	PUNCT
ejpam-5573	86	13	ν	ν	NOUN
ejpam-5573	86	14	,	,	PUNCT
ejpam-5573	86	15	ρ	ρ	PROPN
ejpam-5573	86	16	∈	∈	PROPN
ejpam-5573	86	17	iv	iv	X
ejpam-5573	86	18	,	,	PUNCT
ejpam-5573	86	19	r	r	NOUN
ejpam-5573	86	20	∈	∈	PROPN
ejpam-5573	86	21	i	i	NOUN
ejpam-5573	86	22	◦	◦	NOUN
ejpam-5573	86	23	,	,	PUNCT
ejpam-5573	86	24	and	and	CCONJ
ejpam-5573	86	25	s	s	PROPN
ejpam-5573	86	26	∈	∈	PROPN
ejpam-5573	86	27	i1	i1	PROPN
ejpam-5573	86	28	,	,	PUNCT
ejpam-5573	86	29	then	then	ADV
ejpam-5573	86	30	we	we	PRON
ejpam-5573	86	31	have	have	VERB
ejpam-5573	86	32	:	:	PUNCT
ejpam-5573	86	33	(	(	PUNCT
ejpam-5573	86	34	i	i	NOUN
ejpam-5573	86	35	)	)	PUNCT
ejpam-5573	86	36	ρ	ρ	PROPN
ejpam-5573	86	37	is	be	AUX
ejpam-5573	86	38	called	call	VERB
ejpam-5573	86	39	an	an	DET
ejpam-5573	86	40	(	(	PUNCT
ejpam-5573	86	41	r	r	NOUN
ejpam-5573	86	42	,	,	PUNCT
ejpam-5573	86	43	s)-strongly	s)-strongly	ADV
ejpam-5573	86	44	generalized	generalize	VERB
ejpam-5573	86	45	fuzzy	fuzzy	ADJ
ejpam-5573	86	46	semi	semi	ADJ
ejpam-5573	86	47	-	-	ADJ
ejpam-5573	86	48	closed	closed	ADJ
ejpam-5573	86	49	⟨briefly	⟨briefly	NOUN
ejpam-5573	86	50	,	,	PUNCT
ejpam-5573	86	51	(	(	PUNCT
ejpam-5573	86	52	r	r	NOUN
ejpam-5573	86	53	,	,	PUNCT
ejpam-5573	86	54	s)−	s)−	PROPN
ejpam-5573	86	55	g⊖fsc⟩	g⊖fsc⟩	NOUN
ejpam-5573	86	56	if	if	SCONJ
ejpam-5573	86	57	scη	scη	PROPN
ejpam-5573	86	58	,	,	PUNCT
ejpam-5573	86	59	η∗(ρ	η∗(ρ	PROPN
ejpam-5573	86	60	,	,	PUNCT
ejpam-5573	86	61	r	r	NOUN
ejpam-5573	86	62	,	,	PUNCT
ejpam-5573	86	63	s	s	NOUN
ejpam-5573	86	64	)	)	PUNCT
ejpam-5573	86	65	≤	≤	NUM
ejpam-5573	86	66	ν	ν	NOUN
ejpam-5573	86	67	whenever	whenever	SCONJ
ejpam-5573	86	68	ρ	ρ	NOUN
ejpam-5573	86	69	≤	≤	NUM
ejpam-5573	86	70	ν	ν	NOUN
ejpam-5573	86	71	and	and	CCONJ
ejpam-5573	86	72	ν	ν	PROPN
ejpam-5573	86	73	is	be	AUX
ejpam-5573	86	74	(	(	PUNCT
ejpam-5573	86	75	r	r	NOUN
ejpam-5573	86	76	,	,	PUNCT
ejpam-5573	86	77	s)−	s)−	PROPN
ejpam-5573	86	78	gfo	gfo	PROPN
ejpam-5573	86	79	set	set	PROPN
ejpam-5573	86	80	,	,	PUNCT
ejpam-5573	86	81	(	(	PUNCT
ejpam-5573	86	82	ii	ii	NOUN
ejpam-5573	86	83	)	)	PUNCT
ejpam-5573	86	84	ρ	ρ	PROPN
ejpam-5573	86	85	is	be	AUX
ejpam-5573	86	86	called	call	VERB
ejpam-5573	86	87	an	an	DET
ejpam-5573	86	88	(	(	PUNCT
ejpam-5573	86	89	r	r	NOUN
ejpam-5573	86	90	,	,	PUNCT
ejpam-5573	86	91	s)-strongly∗	s)-strongly∗	NOUN
ejpam-5573	86	92	generalized	generalize	VERB
ejpam-5573	86	93	fuzzy	fuzzy	ADJ
ejpam-5573	86	94	semi	semi	ADJ
ejpam-5573	86	95	-	-	ADJ
ejpam-5573	86	96	closed	closed	ADJ
ejpam-5573	86	97	⟨briefly	⟨briefly	NOUN
ejpam-5573	86	98	,	,	PUNCT
ejpam-5573	86	99	(	(	PUNCT
ejpam-5573	86	100	r	r	NOUN
ejpam-5573	86	101	,	,	PUNCT
ejpam-5573	86	102	s)−	s)−	PROPN
ejpam-5573	86	103	g⊛fsc⟩	g⊛fsc⟩	VERB
ejpam-5573	86	104	if	if	SCONJ
ejpam-5573	86	105	scη	scη	NOUN
ejpam-5573	86	106	,	,	PUNCT
ejpam-5573	86	107	η∗(ρ	η∗(ρ	PROPN
ejpam-5573	86	108	,	,	PUNCT
ejpam-5573	86	109	r	r	NOUN
ejpam-5573	86	110	,	,	PUNCT
ejpam-5573	86	111	s	s	NOUN
ejpam-5573	86	112	)	)	PUNCT
ejpam-5573	86	113	≤	≤	NUM
ejpam-5573	86	114	ν	ν	NOUN
ejpam-5573	86	115	whenever	whenever	SCONJ
ejpam-5573	86	116	ρ	ρ	NOUN
ejpam-5573	86	117	≤	≤	NUM
ejpam-5573	86	118	ν	ν	NOUN
ejpam-5573	86	119	and	and	CCONJ
ejpam-5573	86	120	ν	ν	PROPN
ejpam-5573	86	121	is	be	AUX
ejpam-5573	86	122	(	(	PUNCT
ejpam-5573	86	123	r	r	NOUN
ejpam-5573	86	124	,	,	PUNCT
ejpam-5573	86	125	s)−	s)−	PROPN
ejpam-5573	86	126	gfso	gfso	NOUN
ejpam-5573	86	127	set	set	VERB
ejpam-5573	86	128	.	.	PUNCT
ejpam-5573	87	1	remark	remark	PROPN
ejpam-5573	87	2	1	1	NUM
ejpam-5573	87	3	.	.	PUNCT
ejpam-5573	88	1	(	(	PUNCT
ejpam-5573	88	2	i	i	NOUN
ejpam-5573	88	3	)	)	PUNCT
ejpam-5573	88	4	a	a	DET
ejpam-5573	88	5	fuzzy	fuzzy	ADJ
ejpam-5573	88	6	set	set	VERB
ejpam-5573	88	7	ρ	ρ	PROPN
ejpam-5573	88	8	∈	∈	NOUN
ejpam-5573	88	9	iv	iv	X
ejpam-5573	88	10	is	be	AUX
ejpam-5573	88	11	(	(	PUNCT
ejpam-5573	88	12	r	r	NOUN
ejpam-5573	88	13	,	,	PUNCT
ejpam-5573	88	14	s)−	s)−	PROPN
ejpam-5573	88	15	g⊖fso	g⊖fso	PROPN
ejpam-5573	88	16	if	if	SCONJ
ejpam-5573	88	17	ρc	ρc	PRON
ejpam-5573	88	18	is	be	AUX
ejpam-5573	88	19	(	(	PUNCT
ejpam-5573	88	20	r	r	NOUN
ejpam-5573	88	21	,	,	PUNCT
ejpam-5573	88	22	s)−	s)−	PROPN
ejpam-5573	88	23	g⊖fsc	g⊖fsc	PROPN
ejpam-5573	88	24	set	set	VERB
ejpam-5573	88	25	.	.	PUNCT
ejpam-5573	89	1	(	(	PUNCT
ejpam-5573	89	2	ii	ii	NOUN
ejpam-5573	89	3	)	)	PUNCT
ejpam-5573	89	4	a	a	DET
ejpam-5573	89	5	fuzzy	fuzzy	ADJ
ejpam-5573	89	6	set	set	VERB
ejpam-5573	89	7	ρ	ρ	PROPN
ejpam-5573	89	8	∈	∈	NOUN
ejpam-5573	89	9	iv	iv	X
ejpam-5573	89	10	is	be	AUX
ejpam-5573	89	11	(	(	PUNCT
ejpam-5573	89	12	r	r	NOUN
ejpam-5573	89	13	,	,	PUNCT
ejpam-5573	89	14	s)−	s)−	PROPN
ejpam-5573	89	15	g⊛fso	g⊛fso	PROPN
ejpam-5573	90	1	if	if	SCONJ
ejpam-5573	90	2	ρc	ρc	PRON
ejpam-5573	90	3	is	be	AUX
ejpam-5573	90	4	(	(	PUNCT
ejpam-5573	90	5	r	r	NOUN
ejpam-5573	90	6	,	,	PUNCT
ejpam-5573	90	7	s)−	s)−	PROPN
ejpam-5573	91	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	91	2	set	set	VERB
ejpam-5573	91	3	.	.	PUNCT
ejpam-5573	92	1	remark	remark	PROPN
ejpam-5573	92	2	2	2	NUM
ejpam-5573	92	3	.	.	PUNCT
ejpam-5573	92	4	from	from	ADP
ejpam-5573	92	5	the	the	DET
ejpam-5573	92	6	previous	previous	ADJ
ejpam-5573	92	7	definition	definition	NOUN
ejpam-5573	93	1	,	,	PUNCT
ejpam-5573	93	2	we	we	PRON
ejpam-5573	93	3	can	can	AUX
ejpam-5573	93	4	summarize	summarize	VERB
ejpam-5573	93	5	the	the	DET
ejpam-5573	93	6	relationships	relationship	NOUN
ejpam-5573	93	7	among	among	ADP
ejpam-5573	93	8	different	different	ADJ
ejpam-5573	93	9	types	type	NOUN
ejpam-5573	93	10	of	of	ADP
ejpam-5573	93	11	fuzzy	fuzzy	ADJ
ejpam-5573	93	12	closed	closed	ADJ
ejpam-5573	93	13	subsets	subset	NOUN
ejpam-5573	93	14	as	as	ADP
ejpam-5573	93	15	in	in	ADP
ejpam-5573	93	16	the	the	DET
ejpam-5573	93	17	next	next	ADJ
ejpam-5573	93	18	diagram	diagram	NOUN
ejpam-5573	93	19	.	.	PUNCT
ejpam-5573	94	1	(	(	PUNCT
ejpam-5573	94	2	r	r	NOUN
ejpam-5573	94	3	,	,	PUNCT
ejpam-5573	94	4	s)−	s)−	PROPN
ejpam-5573	94	5	fsc	fsc	PROPN
ejpam-5573	94	6	→	→	PUNCT
ejpam-5573	94	7	(	(	PUNCT
ejpam-5573	94	8	r	r	NOUN
ejpam-5573	94	9	,	,	PUNCT
ejpam-5573	94	10	s)−	s)−	PROPN
ejpam-5573	95	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	95	2	↓	↓	PROPN
ejpam-5573	95	3	↓	↓	PROPN
ejpam-5573	95	4	(	(	PUNCT
ejpam-5573	95	5	r	r	NOUN
ejpam-5573	95	6	,	,	PUNCT
ejpam-5573	95	7	s)−	s)−	NOUN
ejpam-5573	95	8	sgfc	sgfc	NOUN
ejpam-5573	95	9	(	(	PUNCT
ejpam-5573	95	10	r	r	NOUN
ejpam-5573	95	11	,	,	PUNCT
ejpam-5573	95	12	s)−	s)−	PROPN
ejpam-5573	95	13	g⊖fsc	g⊖fsc	PROPN
ejpam-5573	95	14	↓	↓	PROPN
ejpam-5573	95	15	↓	↓	PROPN
ejpam-5573	95	16	(	(	PUNCT
ejpam-5573	95	17	r	r	NOUN
ejpam-5573	95	18	,	,	PUNCT
ejpam-5573	95	19	s)−	s)−	PROPN
ejpam-5573	95	20	gfsc	gfsc	PROPN
ejpam-5573	95	21	remark	remark	VERB
ejpam-5573	95	22	3	3	NUM
ejpam-5573	95	23	.	.	PUNCT
ejpam-5573	96	1	the	the	DET
ejpam-5573	96	2	converses	converse	NOUN
ejpam-5573	96	3	of	of	ADP
ejpam-5573	96	4	the	the	DET
ejpam-5573	96	5	above	above	ADJ
ejpam-5573	96	6	implications	implication	NOUN
ejpam-5573	96	7	may	may	AUX
ejpam-5573	96	8	not	not	PART
ejpam-5573	96	9	be	be	AUX
ejpam-5573	96	10	true	true	ADJ
ejpam-5573	96	11	,	,	PUNCT
ejpam-5573	96	12	as	as	SCONJ
ejpam-5573	96	13	shown	show	VERB
ejpam-5573	96	14	by	by	ADP
ejpam-5573	96	15	examples	example	NOUN
ejpam-5573	96	16	1	1	NUM
ejpam-5573	96	17	,	,	PUNCT
ejpam-5573	96	18	2	2	NUM
ejpam-5573	96	19	,	,	PUNCT
ejpam-5573	96	20	3	3	NUM
ejpam-5573	96	21	and	and	CCONJ
ejpam-5573	96	22	4	4	NUM
ejpam-5573	96	23	.	.	NOUN
ejpam-5573	96	24	example	example	NOUN
ejpam-5573	97	1	1	1	NUM
ejpam-5573	97	2	.	.	PUNCT
ejpam-5573	98	1	let	let	VERB
ejpam-5573	98	2	v	v	VERB
ejpam-5573	98	3	=	=	SYM
ejpam-5573	98	4	{	{	PUNCT
ejpam-5573	98	5	v1	v1	PROPN
ejpam-5573	98	6	,	,	PUNCT
ejpam-5573	98	7	v2	v2	PROPN
ejpam-5573	98	8	,	,	PUNCT
ejpam-5573	98	9	v3	v3	PROPN
ejpam-5573	98	10	,	,	PUNCT
ejpam-5573	98	11	v4	v4	PROPN
ejpam-5573	98	12	}	}	PUNCT
ejpam-5573	98	13	and	and	CCONJ
ejpam-5573	98	14	ρ	ρ	NOUN
ejpam-5573	98	15	,	,	PUNCT
ejpam-5573	98	16	ν	ν	PROPN
ejpam-5573	98	17	∈	∈	NOUN
ejpam-5573	98	18	iv	iv	NUM
ejpam-5573	98	19	defined	define	VERB
ejpam-5573	98	20	as	as	SCONJ
ejpam-5573	98	21	follows	follow	VERB
ejpam-5573	98	22	:	:	PUNCT
ejpam-5573	98	23	ρ	ρ	PROPN
ejpam-5573	98	24	=	=	PUNCT
ejpam-5573	98	25	{	{	PUNCT
ejpam-5573	98	26	v1	v1	PROPN
ejpam-5573	98	27	1.0	1.0	NUM
ejpam-5573	98	28	,	,	PUNCT
ejpam-5573	98	29	v2	v2	PROPN
ejpam-5573	98	30	1.0	1.0	NUM
ejpam-5573	98	31	,	,	PUNCT
ejpam-5573	98	32	v3	v3	PROPN
ejpam-5573	98	33	1.0	1.0	NUM
ejpam-5573	98	34	,	,	PUNCT
ejpam-5573	98	35	v4	v4	VERB
ejpam-5573	98	36	0.0	0.0	NUM
ejpam-5573	98	37	}	}	PUNCT
ejpam-5573	98	38	and	and	CCONJ
ejpam-5573	98	39	ν	ν	X
ejpam-5573	98	40	=	=	X
ejpam-5573	98	41	{	{	PUNCT
ejpam-5573	98	42	v1	v1	PROPN
ejpam-5573	98	43	0.0	0.0	NUM
ejpam-5573	98	44	,	,	PUNCT
ejpam-5573	98	45	v2	v2	PROPN
ejpam-5573	98	46	0.0	0.0	NUM
ejpam-5573	98	47	,	,	PUNCT
ejpam-5573	98	48	v3	v3	PROPN
ejpam-5573	98	49	1.0	1.0	NUM
ejpam-5573	98	50	,	,	PUNCT
ejpam-5573	98	51	v4	v4	PROPN
ejpam-5573	98	52	1.0	1.0	NUM
ejpam-5573	98	53	}	}	PUNCT
ejpam-5573	98	54	.	.	PUNCT
ejpam-5573	99	1	also	also	ADV
ejpam-5573	99	2	,	,	PUNCT
ejpam-5573	99	3	(	(	PUNCT
ejpam-5573	99	4	η	η	PROPN
ejpam-5573	99	5	,	,	PUNCT
ejpam-5573	99	6	η	η	PROPN
ejpam-5573	99	7	∗	∗	NOUN
ejpam-5573	99	8	)	)	PUNCT
ejpam-5573	99	9	defined	define	VERB
ejpam-5573	99	10	on	on	ADP
ejpam-5573	99	11	v	v	NOUN
ejpam-5573	99	12	as	as	SCONJ
ejpam-5573	99	13	follows	follow	VERB
ejpam-5573	99	14	:	:	PUNCT
ejpam-5573	99	15	η(µ	η(µ	PROPN
ejpam-5573	99	16	)	)	PUNCT
ejpam-5573	100	1	=	=	SYM
ejpam-5573	100	2			NOUN
ejpam-5573	100	3	1	1	NUM
ejpam-5573	100	4	,	,	PUNCT
ejpam-5573	100	5	if	if	SCONJ
ejpam-5573	100	6	µ	µ	X
ejpam-5573	100	7	∈	∈	X
ejpam-5573	100	8	{	{	PUNCT
ejpam-5573	100	9	0	0	NUM
ejpam-5573	100	10	,	,	PUNCT
ejpam-5573	100	11	1	1	NUM
ejpam-5573	100	12	}	}	PUNCT
ejpam-5573	100	13	,	,	PUNCT
ejpam-5573	100	14	1	1	NUM
ejpam-5573	100	15	2	2	NUM
ejpam-5573	100	16	,	,	PUNCT
ejpam-5573	100	17	if	if	SCONJ
ejpam-5573	100	18	µ	µ	X
ejpam-5573	100	19	=	=	SYM
ejpam-5573	100	20	ν	ν	NOUN
ejpam-5573	100	21	,	,	PUNCT
ejpam-5573	100	22	0	0	NUM
ejpam-5573	100	23	,	,	PUNCT
ejpam-5573	100	24	otherwise	otherwise	ADV
ejpam-5573	100	25	,	,	PUNCT
ejpam-5573	100	26	η∗(µ	η∗(µ	PROPN
ejpam-5573	100	27	)	)	PUNCT
ejpam-5573	100	28	=	=	SYM
ejpam-5573	101	1			NOUN
ejpam-5573	101	2	0	0	NUM
ejpam-5573	101	3	,	,	PUNCT
ejpam-5573	101	4	if	if	SCONJ
ejpam-5573	101	5	µ	µ	X
ejpam-5573	101	6	∈	∈	X
ejpam-5573	101	7	{	{	PUNCT
ejpam-5573	101	8	0	0	NUM
ejpam-5573	101	9	,	,	PUNCT
ejpam-5573	101	10	1	1	NUM
ejpam-5573	101	11	}	}	PUNCT
ejpam-5573	101	12	,	,	PUNCT
ejpam-5573	101	13	1	1	NUM
ejpam-5573	101	14	2	2	NUM
ejpam-5573	101	15	,	,	PUNCT
ejpam-5573	101	16	if	if	SCONJ
ejpam-5573	101	17	µ	µ	X
ejpam-5573	101	18	=	=	SYM
ejpam-5573	101	19	ν	ν	NOUN
ejpam-5573	101	20	,	,	PUNCT
ejpam-5573	101	21	1	1	NUM
ejpam-5573	101	22	,	,	PUNCT
ejpam-5573	101	23	otherwise	otherwise	ADV
ejpam-5573	101	24	.	.	PUNCT
ejpam-5573	102	1	thus	thus	ADV
ejpam-5573	102	2	,	,	PUNCT
ejpam-5573	102	3	ρ	ρ	PROPN
ejpam-5573	102	4	is	be	AUX
ejpam-5573	102	5	(	(	PUNCT
ejpam-5573	102	6	12	12	NUM
ejpam-5573	102	7	,	,	PUNCT
ejpam-5573	102	8	1	1	NUM
ejpam-5573	102	9	2)−	2)−	NUM
ejpam-5573	102	10	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	102	11	set	set	VERB
ejpam-5573	102	12	,	,	PUNCT
ejpam-5573	102	13	but	but	CCONJ
ejpam-5573	102	14	it	it	PRON
ejpam-5573	102	15	is	be	AUX
ejpam-5573	102	16	not	not	PART
ejpam-5573	102	17	(	(	PUNCT
ejpam-5573	102	18	12	12	NUM
ejpam-5573	102	19	,	,	PUNCT
ejpam-5573	102	20	1	1	NUM
ejpam-5573	102	21	2)−	2)−	NUM
ejpam-5573	102	22	fsc	fsc	PROPN
ejpam-5573	102	23	set	set	PROPN
ejpam-5573	102	24	.	.	PUNCT
ejpam-5573	102	25	example	example	NOUN
ejpam-5573	103	1	2	2	NUM
ejpam-5573	103	2	.	.	PUNCT
ejpam-5573	103	3	let	let	VERB
ejpam-5573	103	4	v	v	VERB
ejpam-5573	103	5	=	=	SYM
ejpam-5573	103	6	{	{	PUNCT
ejpam-5573	103	7	v1	v1	PROPN
ejpam-5573	103	8	,	,	PUNCT
ejpam-5573	103	9	v2	v2	PROPN
ejpam-5573	103	10	,	,	PUNCT
ejpam-5573	103	11	v3	v3	PROPN
ejpam-5573	103	12	,	,	PUNCT
ejpam-5573	103	13	v4	v4	PROPN
ejpam-5573	103	14	}	}	PUNCT
ejpam-5573	103	15	and	and	CCONJ
ejpam-5573	103	16	ρ	ρ	NOUN
ejpam-5573	103	17	,	,	PUNCT
ejpam-5573	103	18	λ1	λ1	ADJ
ejpam-5573	103	19	,	,	PUNCT
ejpam-5573	103	20	λ2	λ2	NOUN
ejpam-5573	103	21	,	,	PUNCT
ejpam-5573	103	22	λ3	λ3	PROPN
ejpam-5573	103	23	∈	∈	PROPN
ejpam-5573	103	24	iv	iv	NUM
ejpam-5573	103	25	defined	define	VERB
ejpam-5573	103	26	as	as	SCONJ
ejpam-5573	103	27	follows	follow	VERB
ejpam-5573	103	28	:	:	PUNCT
ejpam-5573	103	29	ρ	ρ	PROPN
ejpam-5573	103	30	=	=	PUNCT
ejpam-5573	103	31	{	{	PUNCT
ejpam-5573	103	32	v1	v1	PROPN
ejpam-5573	103	33	1.0	1.0	NUM
ejpam-5573	103	34	,	,	PUNCT
ejpam-5573	103	35	v2	v2	PROPN
ejpam-5573	103	36	0.0	0.0	NUM
ejpam-5573	103	37	,	,	PUNCT
ejpam-5573	103	38	v3	v3	PROPN
ejpam-5573	103	39	1.0	1.0	NUM
ejpam-5573	103	40	,	,	PUNCT
ejpam-5573	103	41	v4	v4	PROPN
ejpam-5573	103	42	0.0	0.0	NUM
ejpam-5573	103	43	}	}	PUNCT
ejpam-5573	103	44	,	,	PUNCT
ejpam-5573	103	45	λ1	λ1	PROPN
ejpam-5573	103	46	=	=	SYM
ejpam-5573	103	47	{	{	PUNCT
ejpam-5573	103	48	v1	v1	PROPN
ejpam-5573	103	49	0.0	0.0	NUM
ejpam-5573	103	50	,	,	PUNCT
ejpam-5573	103	51	v2	v2	PROPN
ejpam-5573	103	52	1.0	1.0	NUM
ejpam-5573	103	53	,	,	PUNCT
ejpam-5573	103	54	v3	v3	PROPN
ejpam-5573	103	55	1.0	1.0	NUM
ejpam-5573	103	56	,	,	PUNCT
ejpam-5573	103	57	v4	v4	PROPN
ejpam-5573	103	58	1.0	1.0	NUM
ejpam-5573	103	59	}	}	PUNCT
ejpam-5573	103	60	,	,	PUNCT
ejpam-5573	103	61	λ2	λ2	NOUN
ejpam-5573	103	62	=	=	PUNCT
ejpam-5573	103	63	{	{	PUNCT
ejpam-5573	103	64	v1	v1	PROPN
ejpam-5573	103	65	0.0	0.0	NUM
ejpam-5573	103	66	,	,	PUNCT
ejpam-5573	103	67	v2	v2	PROPN
ejpam-5573	103	68	1.0	1.0	NUM
ejpam-5573	103	69	,	,	PUNCT
ejpam-5573	103	70	v3	v3	PROPN
ejpam-5573	103	71	1.0	1.0	NUM
ejpam-5573	103	72	,	,	PUNCT
ejpam-5573	103	73	v4	v4	VERB
ejpam-5573	103	74	0.0	0.0	NUM
ejpam-5573	103	75	}	}	PUNCT
ejpam-5573	103	76	and	and	CCONJ
ejpam-5573	103	77	λ3	λ3	PROPN
ejpam-5573	103	78	=	=	SYM
ejpam-5573	103	79	{	{	PUNCT
ejpam-5573	103	80	v1	v1	PROPN
ejpam-5573	103	81	0.0	0.0	NUM
ejpam-5573	103	82	,	,	PUNCT
ejpam-5573	103	83	v2	v2	PROPN
ejpam-5573	103	84	0.0	0.0	NUM
ejpam-5573	103	85	,	,	PUNCT
ejpam-5573	103	86	v3	v3	PROPN
ejpam-5573	103	87	1.0	1.0	NUM
ejpam-5573	103	88	,	,	PUNCT
ejpam-5573	103	89	v4	v4	PROPN
ejpam-5573	103	90	0.0	0.0	NUM
ejpam-5573	103	91	}	}	PUNCT
ejpam-5573	103	92	.	.	PUNCT
ejpam-5573	104	1	also	also	ADV
ejpam-5573	104	2	,	,	PUNCT
ejpam-5573	104	3	(	(	PUNCT
ejpam-5573	104	4	η	η	NOUN
ejpam-5573	104	5	,	,	PUNCT
ejpam-5573	104	6	η∗	η∗	NOUN
ejpam-5573	104	7	)	)	PUNCT
ejpam-5573	104	8	defined	define	VERB
ejpam-5573	104	9	on	on	ADP
ejpam-5573	104	10	v	v	NOUN
ejpam-5573	104	11	as	as	SCONJ
ejpam-5573	104	12	follows	follow	VERB
ejpam-5573	104	13	:	:	PUNCT
ejpam-5573	104	14	η(µ	η(µ	PROPN
ejpam-5573	104	15	)	)	PUNCT
ejpam-5573	105	1	=	=	SYM
ejpam-5573	105	2			NOUN
ejpam-5573	105	3	1	1	NUM
ejpam-5573	105	4	,	,	PUNCT
ejpam-5573	105	5	if	if	SCONJ
ejpam-5573	105	6	µ	µ	X
ejpam-5573	105	7	∈	∈	X
ejpam-5573	105	8	{	{	PUNCT
ejpam-5573	105	9	0	0	NUM
ejpam-5573	105	10	,	,	PUNCT
ejpam-5573	105	11	1	1	NUM
ejpam-5573	105	12	}	}	PUNCT
ejpam-5573	105	13	,	,	PUNCT
ejpam-5573	105	14	1	1	NUM
ejpam-5573	105	15	4	4	NUM
ejpam-5573	105	16	,	,	PUNCT
ejpam-5573	105	17	if	if	SCONJ
ejpam-5573	105	18	µ	µ	X
ejpam-5573	105	19	∈	∈	PROPN
ejpam-5573	105	20	{	{	PUNCT
ejpam-5573	105	21	λ1	λ1	ADJ
ejpam-5573	105	22	,	,	PUNCT
ejpam-5573	105	23	λ2	λ2	NOUN
ejpam-5573	105	24	,	,	PUNCT
ejpam-5573	105	25	λ3	λ3	PROPN
ejpam-5573	105	26	}	}	PUNCT
ejpam-5573	105	27	,	,	PUNCT
ejpam-5573	105	28	0	0	NUM
ejpam-5573	105	29	,	,	PUNCT
ejpam-5573	105	30	otherwise	otherwise	ADV
ejpam-5573	105	31	,	,	PUNCT
ejpam-5573	105	32	η∗(µ	η∗(µ	PROPN
ejpam-5573	105	33	)	)	PUNCT
ejpam-5573	105	34	=	=	SYM
ejpam-5573	106	1			NOUN
ejpam-5573	106	2	0	0	NUM
ejpam-5573	106	3	,	,	PUNCT
ejpam-5573	106	4	if	if	SCONJ
ejpam-5573	106	5	µ	µ	X
ejpam-5573	106	6	∈	∈	X
ejpam-5573	106	7	{	{	PUNCT
ejpam-5573	106	8	0	0	NUM
ejpam-5573	106	9	,	,	PUNCT
ejpam-5573	106	10	1	1	NUM
ejpam-5573	106	11	}	}	PUNCT
ejpam-5573	106	12	,	,	PUNCT
ejpam-5573	106	13	1	1	NUM
ejpam-5573	106	14	4	4	NUM
ejpam-5573	106	15	,	,	PUNCT
ejpam-5573	106	16	if	if	SCONJ
ejpam-5573	106	17	µ	µ	X
ejpam-5573	106	18	∈	∈	PROPN
ejpam-5573	106	19	{	{	PUNCT
ejpam-5573	106	20	λ1	λ1	ADJ
ejpam-5573	106	21	,	,	PUNCT
ejpam-5573	106	22	λ2	λ2	NOUN
ejpam-5573	106	23	,	,	PUNCT
ejpam-5573	106	24	λ3	λ3	PROPN
ejpam-5573	106	25	}	}	PUNCT
ejpam-5573	106	26	,	,	PUNCT
ejpam-5573	106	27	1	1	NUM
ejpam-5573	106	28	,	,	PUNCT
ejpam-5573	106	29	otherwise	otherwise	ADV
ejpam-5573	106	30	.	.	PUNCT
ejpam-5573	107	1	thus	thus	ADV
ejpam-5573	107	2	,	,	PUNCT
ejpam-5573	107	3	ρ	ρ	PROPN
ejpam-5573	107	4	is	be	AUX
ejpam-5573	107	5	(	(	PUNCT
ejpam-5573	107	6	14	14	NUM
ejpam-5573	107	7	,	,	PUNCT
ejpam-5573	107	8	1	1	NUM
ejpam-5573	107	9	4)−	4)−	PROPN
ejpam-5573	107	10	g⊖fsc	g⊖fsc	PROPN
ejpam-5573	107	11	set	set	NOUN
ejpam-5573	107	12	,	,	PUNCT
ejpam-5573	107	13	but	but	CCONJ
ejpam-5573	107	14	it	it	PRON
ejpam-5573	107	15	is	be	AUX
ejpam-5573	107	16	not	not	PART
ejpam-5573	107	17	(	(	PUNCT
ejpam-5573	107	18	14	14	NUM
ejpam-5573	107	19	,	,	PUNCT
ejpam-5573	107	20	1	1	NUM
ejpam-5573	107	21	4)−	4)−	PROPN
ejpam-5573	107	22	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	107	23	set	set	VERB
ejpam-5573	107	24	.	.	PUNCT
ejpam-5573	108	1	f.	f.	PROPN
ejpam-5573	108	2	alsharari	alsharari	PROPN
ejpam-5573	108	3	,	,	PUNCT
ejpam-5573	108	4	o.	o.	PROPN
ejpam-5573	108	5	m.	m.	PROPN
ejpam-5573	108	6	taha	taha	PROPN
ejpam-5573	108	7	,	,	PUNCT
ejpam-5573	108	8	i.	i.	PROPN
ejpam-5573	108	9	m.	m.	PROPN
ejpam-5573	108	10	taha	taha	PROPN
ejpam-5573	108	11	/	/	PUNCT
ejpam-5573	108	12	eur	eur	PROPN
ejpam-5573	108	13	.	.	PUNCT
ejpam-5573	109	1	j.	j.	PROPN
ejpam-5573	109	2	pure	pure	PROPN
ejpam-5573	109	3	appl	appl	PROPN
ejpam-5573	109	4	.	.	PROPN
ejpam-5573	109	5	math	math	PROPN
ejpam-5573	109	6	,	,	PUNCT
ejpam-5573	109	7	17	17	NUM
ejpam-5573	109	8	(	(	PUNCT
ejpam-5573	109	9	4	4	NUM
ejpam-5573	109	10	)	)	PUNCT
ejpam-5573	109	11	(	(	PUNCT
ejpam-5573	109	12	2024	2024	NUM
ejpam-5573	109	13	)	)	PUNCT
ejpam-5573	109	14	,	,	PUNCT
ejpam-5573	109	15	4093	4093	NUM
ejpam-5573	109	16	-	-	SYM
ejpam-5573	109	17	4111	4111	NUM
ejpam-5573	109	18	4098	4098	NUM
ejpam-5573	109	19	example	example	NOUN
ejpam-5573	109	20	3	3	X
ejpam-5573	109	21	.	.	PUNCT
ejpam-5573	110	1	let	let	VERB
ejpam-5573	110	2	v	v	VERB
ejpam-5573	110	3	=	=	SYM
ejpam-5573	110	4	{	{	PUNCT
ejpam-5573	110	5	v1	v1	PROPN
ejpam-5573	110	6	,	,	PUNCT
ejpam-5573	110	7	v2	v2	PROPN
ejpam-5573	110	8	,	,	PUNCT
ejpam-5573	110	9	v3	v3	PROPN
ejpam-5573	110	10	}	}	PUNCT
ejpam-5573	110	11	and	and	CCONJ
ejpam-5573	110	12	ν,µ1	ν,µ1	PROPN
ejpam-5573	110	13	,	,	PUNCT
ejpam-5573	110	14	µ2	µ2	PROPN
ejpam-5573	110	15	∈	∈	PROPN
ejpam-5573	110	16	iv	iv	NUM
ejpam-5573	110	17	defined	define	VERB
ejpam-5573	110	18	as	as	SCONJ
ejpam-5573	110	19	follows	follow	VERB
ejpam-5573	110	20	:	:	PUNCT
ejpam-5573	110	21	ν	ν	X
ejpam-5573	110	22	=	=	PRON
ejpam-5573	110	23	{	{	PUNCT
ejpam-5573	110	24	v1	v1	PROPN
ejpam-5573	110	25	1.0	1.0	NUM
ejpam-5573	110	26	,	,	PUNCT
ejpam-5573	110	27	v2	v2	PROPN
ejpam-5573	110	28	0.0	0.0	NUM
ejpam-5573	110	29	,	,	PUNCT
ejpam-5573	110	30	v3	v3	PROPN
ejpam-5573	110	31	0.0	0.0	NUM
ejpam-5573	110	32	}	}	PUNCT
ejpam-5573	110	33	,	,	PUNCT
ejpam-5573	110	34	µ1	µ1	PROPN
ejpam-5573	110	35	=	=	SYM
ejpam-5573	110	36	{	{	PUNCT
ejpam-5573	110	37	v1	v1	PROPN
ejpam-5573	110	38	0.0	0.0	NUM
ejpam-5573	110	39	,	,	PUNCT
ejpam-5573	110	40	v2	v2	PROPN
ejpam-5573	110	41	0.0	0.0	NUM
ejpam-5573	110	42	,	,	PUNCT
ejpam-5573	110	43	v3	v3	PROPN
ejpam-5573	110	44	1.0	1.0	NUM
ejpam-5573	110	45	}	}	PUNCT
ejpam-5573	110	46	and	and	CCONJ
ejpam-5573	110	47	µ2	µ2	PROPN
ejpam-5573	110	48	=	=	PUNCT
ejpam-5573	110	49	{	{	PUNCT
ejpam-5573	110	50	v1	v1	PROPN
ejpam-5573	110	51	1.0	1.0	NUM
ejpam-5573	110	52	,	,	PUNCT
ejpam-5573	110	53	v2	v2	PROPN
ejpam-5573	110	54	1.0	1.0	NUM
ejpam-5573	110	55	,	,	PUNCT
ejpam-5573	110	56	v3	v3	PROPN
ejpam-5573	110	57	0.0	0.0	NUM
ejpam-5573	110	58	}	}	PUNCT
ejpam-5573	110	59	.	.	PUNCT
ejpam-5573	111	1	also	also	ADV
ejpam-5573	111	2	,	,	PUNCT
ejpam-5573	111	3	(	(	PUNCT
ejpam-5573	111	4	η	η	PROPN
ejpam-5573	111	5	,	,	PUNCT
ejpam-5573	111	6	η	η	PROPN
ejpam-5573	111	7	∗	∗	NOUN
ejpam-5573	111	8	)	)	PUNCT
ejpam-5573	111	9	defined	define	VERB
ejpam-5573	111	10	on	on	ADP
ejpam-5573	111	11	v	v	NOUN
ejpam-5573	111	12	as	as	SCONJ
ejpam-5573	111	13	follows	follow	VERB
ejpam-5573	111	14	:	:	PUNCT
ejpam-5573	111	15	η(µ	η(µ	PROPN
ejpam-5573	111	16	)	)	PUNCT
ejpam-5573	112	1	=	=	SYM
ejpam-5573	112	2			NOUN
ejpam-5573	112	3	1	1	NUM
ejpam-5573	112	4	,	,	PUNCT
ejpam-5573	112	5	if	if	SCONJ
ejpam-5573	112	6	µ	µ	X
ejpam-5573	112	7	∈	∈	X
ejpam-5573	112	8	{	{	PUNCT
ejpam-5573	112	9	0	0	NUM
ejpam-5573	112	10	,	,	PUNCT
ejpam-5573	112	11	1	1	NUM
ejpam-5573	112	12	}	}	PUNCT
ejpam-5573	112	13	,	,	PUNCT
ejpam-5573	112	14	1	1	NUM
ejpam-5573	112	15	2	2	NUM
ejpam-5573	112	16	,	,	PUNCT
ejpam-5573	112	17	if	if	SCONJ
ejpam-5573	112	18	µ	µ	X
ejpam-5573	112	19	∈	∈	X
ejpam-5573	112	20	{	{	PUNCT
ejpam-5573	112	21	µ1	µ1	PROPN
ejpam-5573	112	22	,	,	PUNCT
ejpam-5573	112	23	µ2	µ2	PROPN
ejpam-5573	112	24	}	}	PUNCT
ejpam-5573	112	25	,	,	PUNCT
ejpam-5573	112	26	0	0	NUM
ejpam-5573	112	27	,	,	PUNCT
ejpam-5573	112	28	otherwise	otherwise	ADV
ejpam-5573	112	29	,	,	PUNCT
ejpam-5573	112	30	η∗(µ	η∗(µ	PROPN
ejpam-5573	112	31	)	)	PUNCT
ejpam-5573	112	32	=	=	SYM
ejpam-5573	113	1			NOUN
ejpam-5573	113	2	0	0	NUM
ejpam-5573	113	3	,	,	PUNCT
ejpam-5573	113	4	if	if	SCONJ
ejpam-5573	113	5	µ	µ	X
ejpam-5573	113	6	∈	∈	X
ejpam-5573	113	7	{	{	PUNCT
ejpam-5573	113	8	0	0	NUM
ejpam-5573	113	9	,	,	PUNCT
ejpam-5573	113	10	1	1	NUM
ejpam-5573	113	11	}	}	PUNCT
ejpam-5573	113	12	,	,	PUNCT
ejpam-5573	113	13	1	1	NUM
ejpam-5573	113	14	2	2	NUM
ejpam-5573	113	15	,	,	PUNCT
ejpam-5573	113	16	if	if	SCONJ
ejpam-5573	113	17	µ	µ	X
ejpam-5573	113	18	∈	∈	X
ejpam-5573	113	19	{	{	PUNCT
ejpam-5573	113	20	µ1	µ1	PROPN
ejpam-5573	113	21	,	,	PUNCT
ejpam-5573	113	22	µ2	µ2	PROPN
ejpam-5573	113	23	}	}	PUNCT
ejpam-5573	113	24	,	,	PUNCT
ejpam-5573	113	25	1	1	NUM
ejpam-5573	113	26	,	,	PUNCT
ejpam-5573	113	27	otherwise	otherwise	ADV
ejpam-5573	113	28	.	.	PUNCT
ejpam-5573	114	1	thus	thus	ADV
ejpam-5573	114	2	,	,	PUNCT
ejpam-5573	114	3	ν	ν	NOUN
ejpam-5573	114	4	is	be	AUX
ejpam-5573	114	5	(	(	PUNCT
ejpam-5573	114	6	12	12	NUM
ejpam-5573	114	7	,	,	PUNCT
ejpam-5573	114	8	1	1	NUM
ejpam-5573	114	9	2)−	2)−	NUM
ejpam-5573	114	10	sgfc	sgfc	NOUN
ejpam-5573	114	11	set	set	NOUN
ejpam-5573	114	12	,	,	PUNCT
ejpam-5573	114	13	but	but	CCONJ
ejpam-5573	114	14	it	it	PRON
ejpam-5573	114	15	is	be	AUX
ejpam-5573	114	16	not	not	PART
ejpam-5573	114	17	(	(	PUNCT
ejpam-5573	114	18	12	12	NUM
ejpam-5573	114	19	,	,	PUNCT
ejpam-5573	114	20	1	1	NUM
ejpam-5573	114	21	2)−	2)−	NUM
ejpam-5573	114	22	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	114	23	set	set	VERB
ejpam-5573	114	24	.	.	PUNCT
ejpam-5573	114	25	example	example	NOUN
ejpam-5573	115	1	4	4	X
ejpam-5573	115	2	.	.	PUNCT
ejpam-5573	115	3	let	let	VERB
ejpam-5573	115	4	v	v	VERB
ejpam-5573	115	5	=	=	SYM
ejpam-5573	115	6	{	{	PUNCT
ejpam-5573	115	7	v1	v1	PROPN
ejpam-5573	115	8	,	,	PUNCT
ejpam-5573	115	9	v2	v2	PROPN
ejpam-5573	115	10	,	,	PUNCT
ejpam-5573	115	11	v3	v3	PROPN
ejpam-5573	115	12	}	}	PUNCT
ejpam-5573	115	13	and	and	CCONJ
ejpam-5573	115	14	ν	ν	NOUN
ejpam-5573	115	15	,	,	PUNCT
ejpam-5573	115	16	µ1	µ1	PROPN
ejpam-5573	115	17	,	,	PUNCT
ejpam-5573	115	18	µ2	µ2	PROPN
ejpam-5573	115	19	∈	∈	PROPN
ejpam-5573	115	20	iv	iv	NUM
ejpam-5573	115	21	defined	define	VERB
ejpam-5573	115	22	as	as	SCONJ
ejpam-5573	115	23	follows	follow	VERB
ejpam-5573	115	24	:	:	PUNCT
ejpam-5573	115	25	ν	ν	X
ejpam-5573	115	26	=	=	PRON
ejpam-5573	115	27	{	{	PUNCT
ejpam-5573	115	28	v1	v1	PROPN
ejpam-5573	115	29	1.0	1.0	NUM
ejpam-5573	115	30	,	,	PUNCT
ejpam-5573	115	31	v2	v2	PROPN
ejpam-5573	115	32	0.0	0.0	NUM
ejpam-5573	115	33	,	,	PUNCT
ejpam-5573	115	34	v3	v3	PROPN
ejpam-5573	115	35	1.0	1.0	NUM
ejpam-5573	115	36	}	}	PUNCT
ejpam-5573	115	37	,	,	PUNCT
ejpam-5573	115	38	µ1	µ1	PROPN
ejpam-5573	115	39	=	=	SYM
ejpam-5573	115	40	{	{	PUNCT
ejpam-5573	115	41	v1	v1	PROPN
ejpam-5573	115	42	1.0	1.0	NUM
ejpam-5573	115	43	,	,	PUNCT
ejpam-5573	115	44	v2	v2	PROPN
ejpam-5573	115	45	0.0	0.0	NUM
ejpam-5573	115	46	,	,	PUNCT
ejpam-5573	115	47	v3	v3	PROPN
ejpam-5573	115	48	0.0	0.0	NUM
ejpam-5573	115	49	}	}	PUNCT
ejpam-5573	115	50	and	and	CCONJ
ejpam-5573	115	51	µ2	µ2	PROPN
ejpam-5573	115	52	=	=	PUNCT
ejpam-5573	115	53	{	{	PUNCT
ejpam-5573	115	54	v1	v1	PROPN
ejpam-5573	115	55	1.0	1.0	NUM
ejpam-5573	115	56	,	,	PUNCT
ejpam-5573	115	57	v2	v2	PROPN
ejpam-5573	115	58	1.0	1.0	NUM
ejpam-5573	115	59	,	,	PUNCT
ejpam-5573	115	60	v3	v3	PROPN
ejpam-5573	115	61	0.0	0.0	NUM
ejpam-5573	115	62	}	}	PUNCT
ejpam-5573	115	63	.	.	PUNCT
ejpam-5573	116	1	also	also	ADV
ejpam-5573	116	2	,	,	PUNCT
ejpam-5573	116	3	(	(	PUNCT
ejpam-5573	116	4	η	η	PROPN
ejpam-5573	116	5	,	,	PUNCT
ejpam-5573	116	6	η	η	PROPN
ejpam-5573	116	7	∗	∗	NOUN
ejpam-5573	116	8	)	)	PUNCT
ejpam-5573	116	9	defined	define	VERB
ejpam-5573	116	10	on	on	ADP
ejpam-5573	116	11	v	v	NOUN
ejpam-5573	116	12	as	as	SCONJ
ejpam-5573	116	13	follows	follow	VERB
ejpam-5573	116	14	:	:	PUNCT
ejpam-5573	116	15	η(µ	η(µ	PROPN
ejpam-5573	116	16	)	)	PUNCT
ejpam-5573	117	1	=	=	SYM
ejpam-5573	117	2			NOUN
ejpam-5573	117	3	1	1	NUM
ejpam-5573	117	4	,	,	PUNCT
ejpam-5573	117	5	if	if	SCONJ
ejpam-5573	117	6	µ	µ	X
ejpam-5573	117	7	∈	∈	X
ejpam-5573	117	8	{	{	PUNCT
ejpam-5573	117	9	0	0	NUM
ejpam-5573	117	10	,	,	PUNCT
ejpam-5573	117	11	1	1	NUM
ejpam-5573	117	12	}	}	PUNCT
ejpam-5573	117	13	,	,	PUNCT
ejpam-5573	117	14	1	1	NUM
ejpam-5573	117	15	3	3	NUM
ejpam-5573	117	16	,	,	PUNCT
ejpam-5573	117	17	if	if	SCONJ
ejpam-5573	117	18	µ	µ	X
ejpam-5573	117	19	∈	∈	X
ejpam-5573	117	20	{	{	PUNCT
ejpam-5573	117	21	µ1	µ1	PROPN
ejpam-5573	117	22	,	,	PUNCT
ejpam-5573	117	23	µ2	µ2	PROPN
ejpam-5573	117	24	}	}	PUNCT
ejpam-5573	117	25	,	,	PUNCT
ejpam-5573	117	26	0	0	NUM
ejpam-5573	117	27	,	,	PUNCT
ejpam-5573	117	28	otherwise	otherwise	ADV
ejpam-5573	117	29	,	,	PUNCT
ejpam-5573	117	30	η∗(µ	η∗(µ	PROPN
ejpam-5573	117	31	)	)	PUNCT
ejpam-5573	117	32	=	=	SYM
ejpam-5573	118	1			NOUN
ejpam-5573	118	2	0	0	NUM
ejpam-5573	118	3	,	,	PUNCT
ejpam-5573	118	4	if	if	SCONJ
ejpam-5573	118	5	µ	µ	X
ejpam-5573	118	6	∈	∈	X
ejpam-5573	118	7	{	{	PUNCT
ejpam-5573	118	8	0	0	NUM
ejpam-5573	118	9	,	,	PUNCT
ejpam-5573	118	10	1	1	NUM
ejpam-5573	118	11	}	}	PUNCT
ejpam-5573	118	12	,	,	PUNCT
ejpam-5573	118	13	1	1	NUM
ejpam-5573	118	14	3	3	NUM
ejpam-5573	118	15	,	,	PUNCT
ejpam-5573	118	16	if	if	SCONJ
ejpam-5573	118	17	µ	µ	X
ejpam-5573	118	18	∈	∈	X
ejpam-5573	118	19	{	{	PUNCT
ejpam-5573	118	20	µ1	µ1	PROPN
ejpam-5573	118	21	,	,	PUNCT
ejpam-5573	118	22	µ2	µ2	PROPN
ejpam-5573	118	23	}	}	PUNCT
ejpam-5573	118	24	,	,	PUNCT
ejpam-5573	118	25	1	1	NUM
ejpam-5573	118	26	,	,	PUNCT
ejpam-5573	118	27	otherwise	otherwise	ADV
ejpam-5573	118	28	.	.	PUNCT
ejpam-5573	119	1	thus	thus	ADV
ejpam-5573	119	2	,	,	PUNCT
ejpam-5573	119	3	ν	ν	NOUN
ejpam-5573	119	4	is	be	AUX
ejpam-5573	119	5	(	(	PUNCT
ejpam-5573	119	6	13	13	NUM
ejpam-5573	119	7	,	,	PUNCT
ejpam-5573	119	8	1	1	NUM
ejpam-5573	119	9	3)−	3)−	NUM
ejpam-5573	119	10	gfsc	gfsc	PROPN
ejpam-5573	119	11	set	set	VERB
ejpam-5573	119	12	,	,	PUNCT
ejpam-5573	119	13	but	but	CCONJ
ejpam-5573	119	14	it	it	PRON
ejpam-5573	119	15	is	be	AUX
ejpam-5573	119	16	not	not	PART
ejpam-5573	119	17	(	(	PUNCT
ejpam-5573	119	18	13	13	NUM
ejpam-5573	119	19	,	,	PUNCT
ejpam-5573	119	20	1	1	NUM
ejpam-5573	119	21	3)−	3)−	NUM
ejpam-5573	119	22	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	119	23	set	set	VERB
ejpam-5573	119	24	.	.	PUNCT
ejpam-5573	120	1	remark	remark	PROPN
ejpam-5573	120	2	4	4	NUM
ejpam-5573	120	3	.	.	PUNCT
ejpam-5573	121	1	in	in	ADP
ejpam-5573	121	2	general	general	ADJ
ejpam-5573	121	3	,	,	PUNCT
ejpam-5573	121	4	(	(	PUNCT
ejpam-5573	121	5	r	r	NOUN
ejpam-5573	121	6	,	,	PUNCT
ejpam-5573	121	7	s)−gfc	s)−gfc	PRON
ejpam-5573	121	8	sets	set	VERB
ejpam-5573	121	9	[	[	X
ejpam-5573	121	10	1	1	NUM
ejpam-5573	121	11	]	]	PUNCT
ejpam-5573	121	12	and	and	CCONJ
ejpam-5573	121	13	(	(	PUNCT
ejpam-5573	121	14	r	r	NOUN
ejpam-5573	121	15	,	,	PUNCT
ejpam-5573	121	16	s)−g⊛fsc	s)−g⊛fsc	ADJ
ejpam-5573	121	17	sets	set	NOUN
ejpam-5573	121	18	are	be	AUX
ejpam-5573	121	19	independent	independent	ADJ
ejpam-5573	121	20	concepts	concept	NOUN
ejpam-5573	121	21	,	,	PUNCT
ejpam-5573	121	22	as	as	SCONJ
ejpam-5573	121	23	shown	show	VERB
ejpam-5573	121	24	by	by	ADP
ejpam-5573	121	25	example	example	NOUN
ejpam-5573	121	26	5	5	NUM
ejpam-5573	121	27	.	.	PUNCT
ejpam-5573	121	28	example	example	NOUN
ejpam-5573	122	1	5	5	NUM
ejpam-5573	122	2	.	.	PUNCT
ejpam-5573	123	1	let	let	VERB
ejpam-5573	123	2	v	v	VERB
ejpam-5573	123	3	=	=	SYM
ejpam-5573	123	4	{	{	PUNCT
ejpam-5573	123	5	v1	v1	PROPN
ejpam-5573	123	6	,	,	PUNCT
ejpam-5573	123	7	v2	v2	PROPN
ejpam-5573	123	8	,	,	PUNCT
ejpam-5573	123	9	v3	v3	PROPN
ejpam-5573	123	10	,	,	PUNCT
ejpam-5573	123	11	v4	v4	PROPN
ejpam-5573	123	12	}	}	PUNCT
ejpam-5573	123	13	and	and	CCONJ
ejpam-5573	123	14	ρ	ρ	NOUN
ejpam-5573	123	15	,	,	PUNCT
ejpam-5573	123	16	ν	ν	NOUN
ejpam-5573	123	17	,	,	PUNCT
ejpam-5573	123	18	µ1	µ1	PROPN
ejpam-5573	123	19	,	,	PUNCT
ejpam-5573	123	20	µ2	µ2	PROPN
ejpam-5573	123	21	∈	∈	PROPN
ejpam-5573	123	22	iv	iv	NUM
ejpam-5573	123	23	defined	define	VERB
ejpam-5573	123	24	as	as	SCONJ
ejpam-5573	123	25	follows	follow	VERB
ejpam-5573	123	26	:	:	PUNCT
ejpam-5573	123	27	ρ	ρ	PROPN
ejpam-5573	123	28	=	=	PUNCT
ejpam-5573	123	29	{	{	PUNCT
ejpam-5573	123	30	v1	v1	PROPN
ejpam-5573	123	31	0.0	0.0	NUM
ejpam-5573	123	32	,	,	PUNCT
ejpam-5573	123	33	v2	v2	PROPN
ejpam-5573	123	34	1.0	1.0	NUM
ejpam-5573	123	35	,	,	PUNCT
ejpam-5573	123	36	v3	v3	PROPN
ejpam-5573	123	37	0.0	0.0	NUM
ejpam-5573	123	38	,	,	PUNCT
ejpam-5573	123	39	v4	v4	PROPN
ejpam-5573	123	40	0.0	0.0	NUM
ejpam-5573	123	41	}	}	PUNCT
ejpam-5573	123	42	,	,	PUNCT
ejpam-5573	123	43	ν	ν	X
ejpam-5573	123	44	=	=	PRON
ejpam-5573	123	45	{	{	PUNCT
ejpam-5573	123	46	v1	v1	PROPN
ejpam-5573	123	47	1.0	1.0	NUM
ejpam-5573	123	48	,	,	PUNCT
ejpam-5573	123	49	v2	v2	PROPN
ejpam-5573	123	50	1.0	1.0	NUM
ejpam-5573	123	51	,	,	PUNCT
ejpam-5573	123	52	v3	v3	PROPN
ejpam-5573	123	53	0.0	0.0	NUM
ejpam-5573	123	54	,	,	PUNCT
ejpam-5573	123	55	v4	v4	PROPN
ejpam-5573	123	56	1.0	1.0	NUM
ejpam-5573	123	57	}	}	PUNCT
ejpam-5573	123	58	,	,	PUNCT
ejpam-5573	123	59	µ1	µ1	PROPN
ejpam-5573	123	60	=	=	SYM
ejpam-5573	123	61	{	{	PUNCT
ejpam-5573	123	62	v1	v1	PROPN
ejpam-5573	123	63	1.0	1.0	NUM
ejpam-5573	123	64	,	,	PUNCT
ejpam-5573	123	65	v2	v2	PROPN
ejpam-5573	123	66	0.0	0.0	NUM
ejpam-5573	123	67	,	,	PUNCT
ejpam-5573	123	68	v3	v3	PROPN
ejpam-5573	123	69	0.0	0.0	NUM
ejpam-5573	123	70	,	,	PUNCT
ejpam-5573	123	71	v4	v4	PROPN
ejpam-5573	123	72	0.0	0.0	NUM
ejpam-5573	123	73	}	}	PUNCT
ejpam-5573	123	74	and	and	CCONJ
ejpam-5573	123	75	µ2	µ2	PROPN
ejpam-5573	123	76	=	=	PUNCT
ejpam-5573	123	77	{	{	PUNCT
ejpam-5573	123	78	v1	v1	PROPN
ejpam-5573	123	79	1.0	1.0	NUM
ejpam-5573	123	80	,	,	PUNCT
ejpam-5573	123	81	v2	v2	PROPN
ejpam-5573	123	82	1.0	1.0	NUM
ejpam-5573	123	83	,	,	PUNCT
ejpam-5573	123	84	v3	v3	PROPN
ejpam-5573	123	85	0.0	0.0	NUM
ejpam-5573	123	86	,	,	PUNCT
ejpam-5573	123	87	v4	v4	PROPN
ejpam-5573	123	88	0.0	0.0	NUM
ejpam-5573	123	89	}	}	PUNCT
ejpam-5573	123	90	.	.	PUNCT
ejpam-5573	124	1	also	also	ADV
ejpam-5573	124	2	,	,	PUNCT
ejpam-5573	124	3	(	(	PUNCT
ejpam-5573	124	4	η	η	NOUN
ejpam-5573	124	5	,	,	PUNCT
ejpam-5573	124	6	η∗	η∗	NOUN
ejpam-5573	124	7	)	)	PUNCT
ejpam-5573	124	8	defined	define	VERB
ejpam-5573	124	9	on	on	ADP
ejpam-5573	124	10	v	v	NOUN
ejpam-5573	124	11	as	as	SCONJ
ejpam-5573	124	12	follows	follow	VERB
ejpam-5573	124	13	:	:	PUNCT
ejpam-5573	124	14	η(µ	η(µ	PROPN
ejpam-5573	124	15	)	)	PUNCT
ejpam-5573	125	1	=	=	SYM
ejpam-5573	125	2			NOUN
ejpam-5573	125	3	1	1	NUM
ejpam-5573	125	4	,	,	PUNCT
ejpam-5573	125	5	if	if	SCONJ
ejpam-5573	125	6	µ	µ	X
ejpam-5573	125	7	∈	∈	X
ejpam-5573	125	8	{	{	PUNCT
ejpam-5573	125	9	0	0	NUM
ejpam-5573	125	10	,	,	PUNCT
ejpam-5573	125	11	1	1	NUM
ejpam-5573	125	12	}	}	PUNCT
ejpam-5573	125	13	,	,	PUNCT
ejpam-5573	125	14	1	1	NUM
ejpam-5573	125	15	2	2	NUM
ejpam-5573	125	16	,	,	PUNCT
ejpam-5573	125	17	if	if	SCONJ
ejpam-5573	125	18	µ	µ	X
ejpam-5573	125	19	∈	∈	X
ejpam-5573	125	20	{	{	PUNCT
ejpam-5573	125	21	µ1	µ1	PROPN
ejpam-5573	125	22	,	,	PUNCT
ejpam-5573	125	23	µ2	µ2	PROPN
ejpam-5573	125	24	}	}	PUNCT
ejpam-5573	125	25	,	,	PUNCT
ejpam-5573	125	26	0	0	NUM
ejpam-5573	125	27	,	,	PUNCT
ejpam-5573	125	28	otherwise	otherwise	ADV
ejpam-5573	125	29	,	,	PUNCT
ejpam-5573	125	30	η∗(µ	η∗(µ	PROPN
ejpam-5573	125	31	)	)	PUNCT
ejpam-5573	125	32	=	=	SYM
ejpam-5573	126	1			NOUN
ejpam-5573	126	2	0	0	NUM
ejpam-5573	126	3	,	,	PUNCT
ejpam-5573	126	4	if	if	SCONJ
ejpam-5573	126	5	µ	µ	X
ejpam-5573	126	6	∈	∈	X
ejpam-5573	126	7	{	{	PUNCT
ejpam-5573	126	8	0	0	NUM
ejpam-5573	126	9	,	,	PUNCT
ejpam-5573	126	10	1	1	NUM
ejpam-5573	126	11	}	}	PUNCT
ejpam-5573	126	12	,	,	PUNCT
ejpam-5573	126	13	1	1	NUM
ejpam-5573	126	14	2	2	NUM
ejpam-5573	126	15	,	,	PUNCT
ejpam-5573	126	16	if	if	SCONJ
ejpam-5573	126	17	µ	µ	X
ejpam-5573	126	18	∈	∈	X
ejpam-5573	126	19	{	{	PUNCT
ejpam-5573	126	20	µ1	µ1	PROPN
ejpam-5573	126	21	,	,	PUNCT
ejpam-5573	126	22	µ2	µ2	PROPN
ejpam-5573	126	23	}	}	PUNCT
ejpam-5573	126	24	,	,	PUNCT
ejpam-5573	126	25	1	1	NUM
ejpam-5573	126	26	,	,	PUNCT
ejpam-5573	126	27	otherwise	otherwise	ADV
ejpam-5573	126	28	.	.	PUNCT
ejpam-5573	127	1	thus	thus	ADV
ejpam-5573	127	2	,	,	PUNCT
ejpam-5573	127	3	ρ	ρ	PROPN
ejpam-5573	127	4	is	be	AUX
ejpam-5573	127	5	(	(	PUNCT
ejpam-5573	127	6	12	12	NUM
ejpam-5573	127	7	,	,	PUNCT
ejpam-5573	127	8	1	1	NUM
ejpam-5573	127	9	2)−	2)−	NUM
ejpam-5573	127	10	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	127	11	set	set	VERB
ejpam-5573	127	12	,	,	PUNCT
ejpam-5573	127	13	but	but	CCONJ
ejpam-5573	127	14	it	it	PRON
ejpam-5573	127	15	is	be	AUX
ejpam-5573	127	16	not	not	PART
ejpam-5573	127	17	(	(	PUNCT
ejpam-5573	127	18	12	12	NUM
ejpam-5573	127	19	,	,	PUNCT
ejpam-5573	127	20	1	1	NUM
ejpam-5573	127	21	2)−	2)−	NUM
ejpam-5573	127	22	gfc	gfc	NOUN
ejpam-5573	127	23	set	set	NOUN
ejpam-5573	127	24	.	.	PUNCT
ejpam-5573	128	1	also	also	ADV
ejpam-5573	128	2	,	,	PUNCT
ejpam-5573	128	3	ν	ν	NOUN
ejpam-5573	128	4	is	be	AUX
ejpam-5573	128	5	(	(	PUNCT
ejpam-5573	128	6	12	12	NUM
ejpam-5573	128	7	,	,	PUNCT
ejpam-5573	128	8	1	1	NUM
ejpam-5573	128	9	2)−	2)−	NUM
ejpam-5573	128	10	gfc	gfc	NOUN
ejpam-5573	128	11	set	set	NOUN
ejpam-5573	128	12	,	,	PUNCT
ejpam-5573	128	13	but	but	CCONJ
ejpam-5573	128	14	it	it	PRON
ejpam-5573	128	15	is	be	AUX
ejpam-5573	128	16	not	not	PART
ejpam-5573	128	17	(	(	PUNCT
ejpam-5573	128	18	12	12	NUM
ejpam-5573	128	19	,	,	PUNCT
ejpam-5573	128	20	1	1	NUM
ejpam-5573	128	21	2)−	2)−	NUM
ejpam-5573	128	22	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	128	23	set	set	VERB
ejpam-5573	128	24	.	.	PUNCT
ejpam-5573	129	1	remark	remark	PROPN
ejpam-5573	129	2	5	5	NUM
ejpam-5573	129	3	.	.	PUNCT
ejpam-5573	130	1	in	in	ADP
ejpam-5573	130	2	general	general	ADJ
ejpam-5573	130	3	,	,	PUNCT
ejpam-5573	130	4	any	any	DET
ejpam-5573	130	5	intersection	intersection	NOUN
ejpam-5573	130	6	of	of	ADP
ejpam-5573	130	7	(	(	PUNCT
ejpam-5573	130	8	r	r	NOUN
ejpam-5573	130	9	,	,	PUNCT
ejpam-5573	130	10	s	s	NOUN
ejpam-5573	130	11	)	)	PUNCT
ejpam-5573	130	12	−	−	PROPN
ejpam-5573	131	1	g⊛fso	g⊛fso	PROPN
ejpam-5573	131	2	sets	set	NOUN
ejpam-5573	131	3	is	be	AUX
ejpam-5573	131	4	not	not	PART
ejpam-5573	131	5	(	(	PUNCT
ejpam-5573	131	6	r	r	NOUN
ejpam-5573	131	7	,	,	PUNCT
ejpam-5573	131	8	s	s	NOUN
ejpam-5573	131	9	)	)	PUNCT
ejpam-5573	131	10	−	−	PROPN
ejpam-5573	132	1	g⊛fso	g⊛fso	PROPN
ejpam-5573	132	2	,	,	PUNCT
ejpam-5573	132	3	and	and	CCONJ
ejpam-5573	132	4	any	any	DET
ejpam-5573	132	5	union	union	NOUN
ejpam-5573	132	6	of	of	ADP
ejpam-5573	132	7	(	(	PUNCT
ejpam-5573	132	8	r	r	NOUN
ejpam-5573	132	9	,	,	PUNCT
ejpam-5573	132	10	s)−	s)−	PROPN
ejpam-5573	133	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	133	2	sets	set	NOUN
ejpam-5573	133	3	is	be	AUX
ejpam-5573	133	4	not	not	PART
ejpam-5573	133	5	(	(	PUNCT
ejpam-5573	133	6	r	r	NOUN
ejpam-5573	133	7	,	,	PUNCT
ejpam-5573	133	8	s)−	s)−	PROPN
ejpam-5573	134	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	134	2	,	,	PUNCT
ejpam-5573	134	3	as	as	SCONJ
ejpam-5573	134	4	shown	show	VERB
ejpam-5573	134	5	by	by	ADP
ejpam-5573	134	6	example	example	NOUN
ejpam-5573	134	7	6	6	NUM
ejpam-5573	134	8	.	.	PUNCT
ejpam-5573	134	9	example	example	NOUN
ejpam-5573	134	10	6	6	NUM
ejpam-5573	134	11	.	.	PUNCT
ejpam-5573	135	1	let	let	VERB
ejpam-5573	135	2	v	v	VERB
ejpam-5573	135	3	=	=	SYM
ejpam-5573	135	4	{	{	PUNCT
ejpam-5573	135	5	v1	v1	PROPN
ejpam-5573	135	6	,	,	PUNCT
ejpam-5573	135	7	v2	v2	PROPN
ejpam-5573	135	8	,	,	PUNCT
ejpam-5573	135	9	v3	v3	PROPN
ejpam-5573	135	10	,	,	PUNCT
ejpam-5573	135	11	v4	v4	NOUN
ejpam-5573	135	12	}	}	PUNCT
ejpam-5573	135	13	and	and	CCONJ
ejpam-5573	135	14	ν	ν	PROPN
ejpam-5573	135	15	,	,	PUNCT
ejpam-5573	135	16	ρ	ρ	PROPN
ejpam-5573	135	17	,	,	PUNCT
ejpam-5573	135	18	µ1	µ1	PROPN
ejpam-5573	135	19	,	,	PUNCT
ejpam-5573	135	20	µ2	µ2	PROPN
ejpam-5573	135	21	,	,	PUNCT
ejpam-5573	135	22	µ3	µ3	NOUN
ejpam-5573	135	23	∈	∈	NOUN
ejpam-5573	135	24	iv	iv	NUM
ejpam-5573	135	25	defined	define	VERB
ejpam-5573	135	26	as	as	SCONJ
ejpam-5573	135	27	follows	follow	VERB
ejpam-5573	135	28	:	:	PUNCT
ejpam-5573	135	29	ν	ν	X
ejpam-5573	135	30	=	=	PRON
ejpam-5573	135	31	{	{	PUNCT
ejpam-5573	135	32	v1	v1	PROPN
ejpam-5573	135	33	1.0	1.0	NUM
ejpam-5573	135	34	,	,	PUNCT
ejpam-5573	135	35	v2	v2	PROPN
ejpam-5573	135	36	0.0	0.0	NUM
ejpam-5573	135	37	,	,	PUNCT
ejpam-5573	135	38	v3	v3	PROPN
ejpam-5573	135	39	1.0	1.0	NUM
ejpam-5573	135	40	,	,	PUNCT
ejpam-5573	135	41	v4	v4	VERB
ejpam-5573	135	42	1.0	1.0	NUM
ejpam-5573	135	43	}	}	PUNCT
ejpam-5573	135	44	,	,	PUNCT
ejpam-5573	135	45	ρ	ρ	PROPN
ejpam-5573	135	46	=	=	PUNCT
ejpam-5573	135	47	{	{	PUNCT
ejpam-5573	135	48	v1	v1	PROPN
ejpam-5573	135	49	0.0	0.0	NUM
ejpam-5573	135	50	,	,	PUNCT
ejpam-5573	135	51	v2	v2	PROPN
ejpam-5573	135	52	1.0	1.0	NUM
ejpam-5573	135	53	,	,	PUNCT
ejpam-5573	135	54	v3	v3	PROPN
ejpam-5573	135	55	1.0	1.0	NUM
ejpam-5573	135	56	,	,	PUNCT
ejpam-5573	135	57	v4	v4	PROPN
ejpam-5573	135	58	1.0	1.0	NUM
ejpam-5573	135	59	}	}	PUNCT
ejpam-5573	135	60	,	,	PUNCT
ejpam-5573	135	61	µ1	µ1	PROPN
ejpam-5573	135	62	=	=	SYM
ejpam-5573	135	63	{	{	PUNCT
ejpam-5573	135	64	v1	v1	PROPN
ejpam-5573	135	65	1.0	1.0	NUM
ejpam-5573	135	66	,	,	PUNCT
ejpam-5573	135	67	v2	v2	PROPN
ejpam-5573	135	68	0.0	0.0	NUM
ejpam-5573	135	69	,	,	PUNCT
ejpam-5573	135	70	v3	v3	PROPN
ejpam-5573	135	71	0.0	0.0	NUM
ejpam-5573	135	72	,	,	PUNCT
ejpam-5573	135	73	v4	v4	PROPN
ejpam-5573	135	74	0.0	0.0	NUM
ejpam-5573	135	75	}	}	PUNCT
ejpam-5573	135	76	,	,	PUNCT
ejpam-5573	135	77	µ2	µ2	PROPN
ejpam-5573	135	78	=	=	PUNCT
ejpam-5573	135	79	{	{	PUNCT
ejpam-5573	135	80	v1	v1	PROPN
ejpam-5573	135	81	0.0	0.0	NUM
ejpam-5573	135	82	,	,	PUNCT
ejpam-5573	135	83	v2	v2	PROPN
ejpam-5573	135	84	1.0	1.0	NUM
ejpam-5573	135	85	,	,	PUNCT
ejpam-5573	135	86	v3	v3	PROPN
ejpam-5573	135	87	0.0	0.0	NUM
ejpam-5573	135	88	,	,	PUNCT
ejpam-5573	135	89	v4	v4	PROPN
ejpam-5573	135	90	0.0	0.0	NUM
ejpam-5573	135	91	}	}	PUNCT
ejpam-5573	135	92	and	and	CCONJ
ejpam-5573	135	93	µ3	µ3	NOUN
ejpam-5573	136	1	=	=	SYM
ejpam-5573	136	2	{	{	PUNCT
ejpam-5573	136	3	v1	v1	PROPN
ejpam-5573	136	4	1.0	1.0	NUM
ejpam-5573	136	5	,	,	PUNCT
ejpam-5573	136	6	v2	v2	PROPN
ejpam-5573	136	7	1.0	1.0	NUM
ejpam-5573	136	8	,	,	PUNCT
ejpam-5573	136	9	v3	v3	PROPN
ejpam-5573	136	10	0.0	0.0	NUM
ejpam-5573	136	11	,	,	PUNCT
ejpam-5573	136	12	v4	v4	PROPN
ejpam-5573	136	13	0.0	0.0	NUM
ejpam-5573	136	14	}	}	PUNCT
ejpam-5573	136	15	.	.	PUNCT
ejpam-5573	137	1	also	also	ADV
ejpam-5573	137	2	,	,	PUNCT
ejpam-5573	137	3	(	(	PUNCT
ejpam-5573	137	4	η	η	PROPN
ejpam-5573	137	5	,	,	PUNCT
ejpam-5573	137	6	η	η	PROPN
ejpam-5573	137	7	∗	∗	NOUN
ejpam-5573	137	8	)	)	PUNCT
ejpam-5573	137	9	defined	define	VERB
ejpam-5573	137	10	on	on	ADP
ejpam-5573	137	11	v	v	NOUN
ejpam-5573	137	12	as	as	SCONJ
ejpam-5573	137	13	follows	follow	VERB
ejpam-5573	137	14	:	:	PUNCT
ejpam-5573	137	15	η(µ	η(µ	PROPN
ejpam-5573	137	16	)	)	PUNCT
ejpam-5573	138	1	=	=	SYM
ejpam-5573	138	2			NOUN
ejpam-5573	138	3	1	1	NUM
ejpam-5573	138	4	,	,	PUNCT
ejpam-5573	138	5	if	if	SCONJ
ejpam-5573	138	6	µ	µ	X
ejpam-5573	138	7	∈	∈	X
ejpam-5573	138	8	{	{	PUNCT
ejpam-5573	138	9	0	0	NUM
ejpam-5573	138	10	,	,	PUNCT
ejpam-5573	138	11	1	1	NUM
ejpam-5573	138	12	}	}	PUNCT
ejpam-5573	138	13	,	,	PUNCT
ejpam-5573	138	14	1	1	NUM
ejpam-5573	138	15	3	3	NUM
ejpam-5573	138	16	,	,	PUNCT
ejpam-5573	138	17	if	if	SCONJ
ejpam-5573	138	18	µ	µ	X
ejpam-5573	138	19	∈	∈	X
ejpam-5573	138	20	{	{	PUNCT
ejpam-5573	138	21	µ1	µ1	PROPN
ejpam-5573	138	22	,	,	PUNCT
ejpam-5573	138	23	µ2	µ2	NOUN
ejpam-5573	138	24	,	,	PUNCT
ejpam-5573	138	25	µ3	µ3	NUM
ejpam-5573	138	26	}	}	PUNCT
ejpam-5573	138	27	,	,	PUNCT
ejpam-5573	138	28	0	0	NUM
ejpam-5573	138	29	,	,	PUNCT
ejpam-5573	138	30	otherwise	otherwise	ADV
ejpam-5573	138	31	,	,	PUNCT
ejpam-5573	138	32	η∗(µ	η∗(µ	PROPN
ejpam-5573	138	33	)	)	PUNCT
ejpam-5573	138	34	=	=	SYM
ejpam-5573	139	1			NOUN
ejpam-5573	139	2	0	0	NUM
ejpam-5573	139	3	,	,	PUNCT
ejpam-5573	139	4	if	if	SCONJ
ejpam-5573	139	5	µ	µ	X
ejpam-5573	139	6	∈	∈	X
ejpam-5573	139	7	{	{	PUNCT
ejpam-5573	139	8	0	0	NUM
ejpam-5573	139	9	,	,	PUNCT
ejpam-5573	139	10	1	1	NUM
ejpam-5573	139	11	}	}	PUNCT
ejpam-5573	139	12	,	,	PUNCT
ejpam-5573	139	13	1	1	NUM
ejpam-5573	139	14	3	3	NUM
ejpam-5573	139	15	,	,	PUNCT
ejpam-5573	139	16	if	if	SCONJ
ejpam-5573	139	17	µ	µ	X
ejpam-5573	139	18	∈	∈	X
ejpam-5573	139	19	{	{	PUNCT
ejpam-5573	139	20	µ1	µ1	PROPN
ejpam-5573	139	21	,	,	PUNCT
ejpam-5573	139	22	µ2	µ2	NOUN
ejpam-5573	139	23	,	,	PUNCT
ejpam-5573	139	24	µ3	µ3	NUM
ejpam-5573	139	25	}	}	PUNCT
ejpam-5573	139	26	,	,	PUNCT
ejpam-5573	139	27	1	1	NUM
ejpam-5573	139	28	,	,	PUNCT
ejpam-5573	139	29	otherwise	otherwise	ADV
ejpam-5573	139	30	.	.	PUNCT
ejpam-5573	140	1	thus	thus	ADV
ejpam-5573	140	2	,	,	PUNCT
ejpam-5573	140	3	µ1	µ1	PROPN
ejpam-5573	140	4	and	and	CCONJ
ejpam-5573	140	5	µ2	µ2	PROPN
ejpam-5573	140	6	are	be	AUX
ejpam-5573	140	7	(	(	PUNCT
ejpam-5573	140	8	13	13	NUM
ejpam-5573	140	9	,	,	PUNCT
ejpam-5573	140	10	1	1	NUM
ejpam-5573	140	11	3)−	3)−	NUM
ejpam-5573	140	12	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	140	13	sets	set	VERB
ejpam-5573	140	14	,	,	PUNCT
ejpam-5573	140	15	but	but	CCONJ
ejpam-5573	140	16	µ1	µ1	NOUN
ejpam-5573	140	17	∨µ2	∨µ2	NOUN
ejpam-5573	140	18	is	be	AUX
ejpam-5573	140	19	not	not	PART
ejpam-5573	140	20	(	(	PUNCT
ejpam-5573	140	21	13	13	NUM
ejpam-5573	140	22	,	,	PUNCT
ejpam-5573	140	23	1	1	NUM
ejpam-5573	140	24	3)−	3)−	PROPN
ejpam-5573	140	25	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	140	26	.	.	PUNCT
ejpam-5573	141	1	also	also	ADV
ejpam-5573	141	2	,	,	PUNCT
ejpam-5573	141	3	ρ	ρ	PROPN
ejpam-5573	141	4	and	and	CCONJ
ejpam-5573	141	5	ν	ν	NOUN
ejpam-5573	141	6	are	be	AUX
ejpam-5573	141	7	(	(	PUNCT
ejpam-5573	141	8	13	13	NUM
ejpam-5573	141	9	,	,	PUNCT
ejpam-5573	141	10	1	1	NUM
ejpam-5573	141	11	3)−	3)−	NUM
ejpam-5573	141	12	g⊛fso	g⊛fso	PROPN
ejpam-5573	141	13	sets	set	VERB
ejpam-5573	141	14	,	,	PUNCT
ejpam-5573	141	15	but	but	CCONJ
ejpam-5573	141	16	ρ	ρ	NUM
ejpam-5573	141	17	∧	∧	PROPN
ejpam-5573	141	18	ν	ν	NOUN
ejpam-5573	141	19	is	be	AUX
ejpam-5573	141	20	not	not	PART
ejpam-5573	141	21	(	(	PUNCT
ejpam-5573	141	22	13	13	NUM
ejpam-5573	141	23	,	,	PUNCT
ejpam-5573	141	24	1	1	NUM
ejpam-5573	141	25	3)−	3)−	PROPN
ejpam-5573	141	26	g⊛fso	g⊛fso	PROPN
ejpam-5573	141	27	.	.	PUNCT
ejpam-5573	142	1	f.	f.	PROPN
ejpam-5573	142	2	alsharari	alsharari	PROPN
ejpam-5573	142	3	,	,	PUNCT
ejpam-5573	142	4	o.	o.	PROPN
ejpam-5573	142	5	m.	m.	PROPN
ejpam-5573	142	6	taha	taha	PROPN
ejpam-5573	142	7	,	,	PUNCT
ejpam-5573	142	8	i.	i.	PROPN
ejpam-5573	142	9	m.	m.	PROPN
ejpam-5573	142	10	taha	taha	PROPN
ejpam-5573	142	11	/	/	PUNCT
ejpam-5573	142	12	eur	eur	PROPN
ejpam-5573	142	13	.	.	PUNCT
ejpam-5573	143	1	j.	j.	PROPN
ejpam-5573	143	2	pure	pure	PROPN
ejpam-5573	143	3	appl	appl	PROPN
ejpam-5573	143	4	.	.	PROPN
ejpam-5573	143	5	math	math	PROPN
ejpam-5573	143	6	,	,	PUNCT
ejpam-5573	143	7	17	17	NUM
ejpam-5573	143	8	(	(	PUNCT
ejpam-5573	143	9	4	4	NUM
ejpam-5573	143	10	)	)	PUNCT
ejpam-5573	143	11	(	(	PUNCT
ejpam-5573	143	12	2024	2024	NUM
ejpam-5573	143	13	)	)	PUNCT
ejpam-5573	143	14	,	,	PUNCT
ejpam-5573	143	15	4093	4093	NUM
ejpam-5573	143	16	-	-	SYM
ejpam-5573	143	17	4111	4111	NUM
ejpam-5573	143	18	4099	4099	NUM
ejpam-5573	143	19	theorem	theorem	NOUN
ejpam-5573	143	20	1	1	NUM
ejpam-5573	143	21	.	.	PUNCT
ejpam-5573	144	1	let	let	VERB
ejpam-5573	144	2	(	(	PUNCT
ejpam-5573	144	3	v	v	NOUN
ejpam-5573	144	4	,	,	PUNCT
ejpam-5573	144	5	η	η	NOUN
ejpam-5573	144	6	,	,	PUNCT
ejpam-5573	144	7	η∗	η∗	NOUN
ejpam-5573	144	8	)	)	PUNCT
ejpam-5573	144	9	be	be	AUX
ejpam-5573	144	10	a	a	DET
ejpam-5573	144	11	dfts	dft	NOUN
ejpam-5573	144	12	,	,	PUNCT
ejpam-5573	144	13	µ	µ	NOUN
ejpam-5573	144	14	,	,	PUNCT
ejpam-5573	145	1	λ	λ	PROPN
ejpam-5573	145	2	∈	∈	NOUN
ejpam-5573	145	3	iv	iv	X
ejpam-5573	145	4	,	,	PUNCT
ejpam-5573	145	5	r	r	NOUN
ejpam-5573	145	6	∈	∈	PROPN
ejpam-5573	145	7	i	i	NOUN
ejpam-5573	145	8	◦	◦	NOUN
ejpam-5573	145	9	,	,	PUNCT
ejpam-5573	145	10	and	and	CCONJ
ejpam-5573	145	11	s	s	PROPN
ejpam-5573	145	12	∈	∈	PROPN
ejpam-5573	145	13	i1	i1	PROPN
ejpam-5573	145	14	,	,	PUNCT
ejpam-5573	145	15	then	then	ADV
ejpam-5573	145	16	λ	λ	PROPN
ejpam-5573	145	17	is	be	AUX
ejpam-5573	145	18	(	(	PUNCT
ejpam-5573	145	19	r	r	NOUN
ejpam-5573	145	20	,	,	PUNCT
ejpam-5573	145	21	s)−g⊛fsc	s)−g⊛fsc	PROPN
ejpam-5573	145	22	set	set	VERB
ejpam-5573	145	23	iff	iff	PROPN
ejpam-5573	145	24	every	every	DET
ejpam-5573	145	25	µ	µ	NOUN
ejpam-5573	145	26	is	be	AUX
ejpam-5573	145	27	(	(	PUNCT
ejpam-5573	145	28	r	r	NOUN
ejpam-5573	145	29	,	,	PUNCT
ejpam-5573	145	30	s	s	NOUN
ejpam-5573	145	31	)	)	PUNCT
ejpam-5573	145	32	−	−	NOUN
ejpam-5573	145	33	gfso	gfso	NOUN
ejpam-5573	145	34	set	set	VERB
ejpam-5573	145	35	and	and	CCONJ
ejpam-5573	145	36	λ	λ	X
ejpam-5573	145	37	≤	≤	NOUN
ejpam-5573	145	38	µ	µ	NUM
ejpam-5573	145	39	,	,	PUNCT
ejpam-5573	145	40	there	there	PRON
ejpam-5573	145	41	is	be	VERB
ejpam-5573	145	42	ρ	ρ	NOUN
ejpam-5573	145	43	is	be	AUX
ejpam-5573	145	44	(	(	PUNCT
ejpam-5573	145	45	r	r	NOUN
ejpam-5573	145	46	,	,	PUNCT
ejpam-5573	145	47	s	s	NOUN
ejpam-5573	145	48	)	)	PUNCT
ejpam-5573	145	49	−	−	PROPN
ejpam-5573	145	50	fsc	fsc	PROPN
ejpam-5573	145	51	set	set	PROPN
ejpam-5573	145	52	,	,	PUNCT
ejpam-5573	145	53	such	such	ADJ
ejpam-5573	145	54	that	that	SCONJ
ejpam-5573	145	55	λ	λ	PROPN
ejpam-5573	145	56	≤	≤	NOUN
ejpam-5573	145	57	ρ	ρ	PROPN
ejpam-5573	145	58	≤	≤	PROPN
ejpam-5573	145	59	µ.	µ.	NOUN
ejpam-5573	145	60	proof	proof	NOUN
ejpam-5573	145	61	.	.	PUNCT
ejpam-5573	146	1	(	(	PUNCT
ejpam-5573	146	2	⇒	⇒	NOUN
ejpam-5573	146	3	)	)	PUNCT
ejpam-5573	146	4	let	let	VERB
ejpam-5573	146	5	λ	λ	NOUN
ejpam-5573	146	6	be	be	AUX
ejpam-5573	146	7	an	an	DET
ejpam-5573	146	8	(	(	PUNCT
ejpam-5573	146	9	r	r	NOUN
ejpam-5573	146	10	,	,	PUNCT
ejpam-5573	146	11	s	s	NOUN
ejpam-5573	146	12	)	)	PUNCT
ejpam-5573	146	13	−	−	PROPN
ejpam-5573	147	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	147	2	,	,	PUNCT
ejpam-5573	147	3	λ	λ	PROPN
ejpam-5573	147	4	≤	≤	NOUN
ejpam-5573	147	5	µ	µ	X
ejpam-5573	147	6	and	and	CCONJ
ejpam-5573	147	7	µ	µ	PRON
ejpam-5573	147	8	be	be	AUX
ejpam-5573	147	9	an	an	DET
ejpam-5573	147	10	(	(	PUNCT
ejpam-5573	147	11	r	r	NOUN
ejpam-5573	147	12	,	,	PUNCT
ejpam-5573	147	13	s	s	NOUN
ejpam-5573	147	14	)	)	PUNCT
ejpam-5573	147	15	−	−	PROPN
ejpam-5573	147	16	gfso	gfso	NOUN
ejpam-5573	147	17	set	set	NOUN
ejpam-5573	147	18	,	,	PUNCT
ejpam-5573	147	19	then	then	ADV
ejpam-5573	147	20	scη	scη	PROPN
ejpam-5573	147	21	,	,	PUNCT
ejpam-5573	147	22	η∗(λ	η∗(λ	PROPN
ejpam-5573	147	23	,	,	PUNCT
ejpam-5573	147	24	r	r	NOUN
ejpam-5573	147	25	,	,	PUNCT
ejpam-5573	147	26	s	s	NOUN
ejpam-5573	147	27	)	)	PUNCT
ejpam-5573	147	28	≤	≤	NUM
ejpam-5573	147	29	µ.	µ.	NOUN
ejpam-5573	147	30	put	put	VERB
ejpam-5573	147	31	ρ	ρ	PROPN
ejpam-5573	147	32	=	=	SYM
ejpam-5573	147	33	scη	scη	PROPN
ejpam-5573	147	34	,	,	PUNCT
ejpam-5573	147	35	η∗(λ	η∗(λ	PROPN
ejpam-5573	147	36	,	,	PUNCT
ejpam-5573	147	37	r	r	NOUN
ejpam-5573	147	38	,	,	PUNCT
ejpam-5573	147	39	s	s	PART
ejpam-5573	147	40	)	)	PUNCT
ejpam-5573	147	41	,	,	PUNCT
ejpam-5573	147	42	there	there	PRON
ejpam-5573	147	43	is	be	VERB
ejpam-5573	147	44	ρ	ρ	NOUN
ejpam-5573	147	45	is	be	AUX
ejpam-5573	147	46	(	(	PUNCT
ejpam-5573	147	47	r	r	NOUN
ejpam-5573	147	48	,	,	PUNCT
ejpam-5573	147	49	s)−fsc	s)−fsc	PRON
ejpam-5573	147	50	set	set	VERB
ejpam-5573	147	51	such	such	ADJ
ejpam-5573	147	52	that	that	SCONJ
ejpam-5573	147	53	λ	λ	PROPN
ejpam-5573	147	54	≤	≤	NOUN
ejpam-5573	147	55	ρ	ρ	PROPN
ejpam-5573	147	56	≤	≤	PROPN
ejpam-5573	147	57	µ.	µ.	NOUN
ejpam-5573	147	58	(	(	PUNCT
ejpam-5573	147	59	⇐	⇐	ADJ
ejpam-5573	147	60	)	)	PUNCT
ejpam-5573	147	61	assume	assume	VERB
ejpam-5573	147	62	that	that	SCONJ
ejpam-5573	147	63	λ	λ	PROPN
ejpam-5573	147	64	≤	≤	NOUN
ejpam-5573	147	65	µ	µ	NOUN
ejpam-5573	147	66	and	and	CCONJ
ejpam-5573	147	67	µ	µ	NOUN
ejpam-5573	147	68	is	be	AUX
ejpam-5573	147	69	(	(	PUNCT
ejpam-5573	147	70	r	r	NOUN
ejpam-5573	147	71	,	,	PUNCT
ejpam-5573	147	72	s	s	NOUN
ejpam-5573	147	73	)	)	PUNCT
ejpam-5573	147	74	−	−	PROPN
ejpam-5573	147	75	gfso	gfso	NOUN
ejpam-5573	147	76	set	set	NOUN
ejpam-5573	147	77	,	,	PUNCT
ejpam-5573	147	78	then	then	ADV
ejpam-5573	147	79	by	by	ADP
ejpam-5573	147	80	hypothesis	hypothesis	NOUN
ejpam-5573	147	81	,	,	PUNCT
ejpam-5573	147	82	there	there	PRON
ejpam-5573	147	83	is	be	VERB
ejpam-5573	147	84	ρ	ρ	NOUN
ejpam-5573	147	85	is	be	AUX
ejpam-5573	147	86	(	(	PUNCT
ejpam-5573	147	87	r	r	NOUN
ejpam-5573	147	88	,	,	PUNCT
ejpam-5573	147	89	s)−	s)−	PROPN
ejpam-5573	147	90	fsc	fsc	PROPN
ejpam-5573	147	91	set	set	VERB
ejpam-5573	147	92	such	such	ADJ
ejpam-5573	147	93	that	that	SCONJ
ejpam-5573	147	94	λ	λ	PROPN
ejpam-5573	147	95	≤	≤	NOUN
ejpam-5573	147	96	ρ	ρ	PROPN
ejpam-5573	147	97	≤	≤	PROPN
ejpam-5573	147	98	µ	µ	NUM
ejpam-5573	147	99	,	,	PUNCT
ejpam-5573	147	100	therefore	therefore	ADV
ejpam-5573	147	101	,	,	PUNCT
ejpam-5573	147	102	scη	scη	PROPN
ejpam-5573	147	103	,	,	PUNCT
ejpam-5573	147	104	η∗(λ	η∗(λ	PROPN
ejpam-5573	147	105	,	,	PUNCT
ejpam-5573	147	106	r	r	NOUN
ejpam-5573	147	107	,	,	PUNCT
ejpam-5573	147	108	s	s	NOUN
ejpam-5573	147	109	)	)	PUNCT
ejpam-5573	147	110	≤	≤	NUM
ejpam-5573	147	111	µ.	µ.	NOUN
ejpam-5573	148	1	so	so	ADV
ejpam-5573	148	2	,	,	PUNCT
ejpam-5573	148	3	λ	λ	PROPN
ejpam-5573	148	4	is	be	AUX
ejpam-5573	148	5	(	(	PUNCT
ejpam-5573	148	6	r	r	NOUN
ejpam-5573	148	7	,	,	PUNCT
ejpam-5573	148	8	s)−	s)−	PROPN
ejpam-5573	149	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	149	2	set	set	VERB
ejpam-5573	149	3	.	.	PUNCT
ejpam-5573	150	1	proposition	proposition	NOUN
ejpam-5573	150	2	1	1	NUM
ejpam-5573	150	3	.	.	PUNCT
ejpam-5573	151	1	let	let	VERB
ejpam-5573	151	2	(	(	PUNCT
ejpam-5573	151	3	v	v	NOUN
ejpam-5573	151	4	,	,	PUNCT
ejpam-5573	151	5	η	η	NOUN
ejpam-5573	151	6	,	,	PUNCT
ejpam-5573	151	7	η∗	η∗	NOUN
ejpam-5573	151	8	)	)	PUNCT
ejpam-5573	151	9	be	be	VERB
ejpam-5573	151	10	a	a	DET
ejpam-5573	151	11	dfts	dft	NOUN
ejpam-5573	151	12	,	,	PUNCT
ejpam-5573	151	13	µ	µ	NOUN
ejpam-5573	151	14	,	,	PUNCT
ejpam-5573	151	15	λ	λ	PROPN
ejpam-5573	151	16	∈	∈	NOUN
ejpam-5573	151	17	iv	iv	X
ejpam-5573	151	18	,	,	PUNCT
ejpam-5573	151	19	r	r	NOUN
ejpam-5573	151	20	∈	∈	PROPN
ejpam-5573	152	1	i	i	NOUN
ejpam-5573	152	2	◦	◦	NOUN
ejpam-5573	152	3	,	,	PUNCT
ejpam-5573	152	4	and	and	CCONJ
ejpam-5573	152	5	s	s	PROPN
ejpam-5573	152	6	∈	∈	PROPN
ejpam-5573	152	7	i1	i1	PROPN
ejpam-5573	152	8	,	,	PUNCT
ejpam-5573	152	9	then	then	ADV
ejpam-5573	152	10	the	the	DET
ejpam-5573	152	11	following	follow	VERB
ejpam-5573	152	12	properties	property	NOUN
ejpam-5573	152	13	holds	hold	VERB
ejpam-5573	152	14	.	.	PUNCT
ejpam-5573	153	1	(	(	PUNCT
ejpam-5573	153	2	i	i	NOUN
ejpam-5573	153	3	)	)	PUNCT
ejpam-5573	153	4	if	if	SCONJ
ejpam-5573	153	5	λ	λ	NOUN
ejpam-5573	153	6	is	be	AUX
ejpam-5573	153	7	(	(	PUNCT
ejpam-5573	153	8	r	r	NOUN
ejpam-5573	153	9	,	,	PUNCT
ejpam-5573	153	10	s)−	s)−	PROPN
ejpam-5573	154	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	154	2	and	and	CCONJ
ejpam-5573	154	3	λ	λ	PROPN
ejpam-5573	154	4	≤	≤	PROPN
ejpam-5573	154	5	µ	µ	PRON
ejpam-5573	154	6	≤	≤	NUM
ejpam-5573	154	7	scη	scη	NOUN
ejpam-5573	154	8	,	,	PUNCT
ejpam-5573	154	9	η∗(λ	η∗(λ	PROPN
ejpam-5573	154	10	,	,	PUNCT
ejpam-5573	154	11	r	r	NOUN
ejpam-5573	154	12	,	,	PUNCT
ejpam-5573	154	13	s	s	PART
ejpam-5573	154	14	)	)	PUNCT
ejpam-5573	154	15	,	,	PUNCT
ejpam-5573	154	16	then	then	ADV
ejpam-5573	154	17	µ	µ	X
ejpam-5573	154	18	is	be	AUX
ejpam-5573	154	19	(	(	PUNCT
ejpam-5573	154	20	r	r	NOUN
ejpam-5573	154	21	,	,	PUNCT
ejpam-5573	154	22	s)−	s)−	PROPN
ejpam-5573	155	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	155	2	set	set	VERB
ejpam-5573	155	3	.	.	PUNCT
ejpam-5573	156	1	(	(	PUNCT
ejpam-5573	156	2	ii	ii	NOUN
ejpam-5573	156	3	)	)	PUNCT
ejpam-5573	156	4	if	if	SCONJ
ejpam-5573	156	5	λ	λ	X
ejpam-5573	156	6	is	be	AUX
ejpam-5573	156	7	(	(	PUNCT
ejpam-5573	156	8	r	r	NOUN
ejpam-5573	156	9	,	,	PUNCT
ejpam-5573	156	10	s)−	s)−	PROPN
ejpam-5573	156	11	g⊛fso	g⊛fso	PROPN
ejpam-5573	156	12	and	and	CCONJ
ejpam-5573	156	13	siη	siη	PROPN
ejpam-5573	156	14	,	,	PUNCT
ejpam-5573	156	15	η∗(λ	η∗(λ	PROPN
ejpam-5573	156	16	,	,	PUNCT
ejpam-5573	156	17	r	r	NOUN
ejpam-5573	156	18	,	,	PUNCT
ejpam-5573	156	19	s	s	NOUN
ejpam-5573	156	20	)	)	PUNCT
ejpam-5573	156	21	≤	≤	NUM
ejpam-5573	156	22	µ	µ	PRON
ejpam-5573	156	23	≤	≤	NUM
ejpam-5573	156	24	λ	λ	PROPN
ejpam-5573	156	25	,	,	PUNCT
ejpam-5573	156	26	then	then	ADV
ejpam-5573	156	27	µ	µ	NOUN
ejpam-5573	156	28	is	be	AUX
ejpam-5573	156	29	(	(	PUNCT
ejpam-5573	156	30	r	r	NOUN
ejpam-5573	156	31	,	,	PUNCT
ejpam-5573	156	32	s)−	s)−	PROPN
ejpam-5573	156	33	g⊛fso	g⊛fso	PROPN
ejpam-5573	156	34	set	set	VERB
ejpam-5573	156	35	.	.	PUNCT
ejpam-5573	157	1	(	(	PUNCT
ejpam-5573	157	2	iii	iii	X
ejpam-5573	157	3	)	)	PUNCT
ejpam-5573	157	4	if	if	SCONJ
ejpam-5573	157	5	one	one	NUM
ejpam-5573	157	6	of	of	ADP
ejpam-5573	157	7	the	the	DET
ejpam-5573	157	8	following	follow	VERB
ejpam-5573	157	9	two	two	NUM
ejpam-5573	157	10	cases	case	NOUN
ejpam-5573	157	11	holds	hold	VERB
ejpam-5573	157	12	:	:	PUNCT
ejpam-5573	157	13	(	(	PUNCT
ejpam-5573	157	14	a	a	X
ejpam-5573	157	15	)	)	PUNCT
ejpam-5573	157	16	λ	λ	NOUN
ejpam-5573	157	17	is	be	AUX
ejpam-5573	157	18	(	(	PUNCT
ejpam-5573	157	19	r	r	NOUN
ejpam-5573	157	20	,	,	PUNCT
ejpam-5573	157	21	s)−	s)−	PROPN
ejpam-5573	158	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	158	2	and	and	CCONJ
ejpam-5573	158	3	(	(	PUNCT
ejpam-5573	158	4	r	r	NOUN
ejpam-5573	158	5	,	,	PUNCT
ejpam-5573	158	6	s)−	s)−	PROPN
ejpam-5573	158	7	gfso	gfso	NOUN
ejpam-5573	158	8	.	.	PUNCT
ejpam-5573	159	1	(	(	PUNCT
ejpam-5573	159	2	b	b	X
ejpam-5573	159	3	)	)	PUNCT
ejpam-5573	159	4	λ	λ	NOUN
ejpam-5573	159	5	is	be	AUX
ejpam-5573	159	6	(	(	PUNCT
ejpam-5573	159	7	r	r	NOUN
ejpam-5573	159	8	,	,	PUNCT
ejpam-5573	159	9	s)−	s)−	PROPN
ejpam-5573	159	10	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	159	11	and	and	CCONJ
ejpam-5573	159	12	η(λ	η(λ	ADJ
ejpam-5573	159	13	)	)	PUNCT
ejpam-5573	159	14	≥	≥	NOUN
ejpam-5573	159	15	r	r	NOUN
ejpam-5573	159	16	,	,	PUNCT
ejpam-5573	159	17	η∗(λ	η∗(λ	PROPN
ejpam-5573	159	18	)	)	PUNCT
ejpam-5573	159	19	≤	≤	PUNCT
ejpam-5573	159	20	s.	s.	PROPN
ejpam-5573	160	1	then	then	ADV
ejpam-5573	160	2	,	,	PUNCT
ejpam-5573	160	3	λ	λ	PROPN
ejpam-5573	160	4	is	be	AUX
ejpam-5573	160	5	(	(	PUNCT
ejpam-5573	160	6	r	r	NOUN
ejpam-5573	160	7	,	,	PUNCT
ejpam-5573	160	8	s)−	s)−	PROPN
ejpam-5573	160	9	fsc	fsc	PROPN
ejpam-5573	160	10	set	set	PROPN
ejpam-5573	160	11	.	.	PUNCT
ejpam-5573	161	1	proof	proof	NOUN
ejpam-5573	161	2	.	.	PUNCT
ejpam-5573	162	1	(	(	PUNCT
ejpam-5573	162	2	i	i	NOUN
ejpam-5573	162	3	)	)	PUNCT
ejpam-5573	162	4	let	let	VERB
ejpam-5573	162	5	ν	ν	NOUN
ejpam-5573	162	6	be	be	AUX
ejpam-5573	162	7	an	an	DET
ejpam-5573	162	8	(	(	PUNCT
ejpam-5573	162	9	r	r	NOUN
ejpam-5573	162	10	,	,	PUNCT
ejpam-5573	162	11	s)−	s)−	PROPN
ejpam-5573	162	12	gfso	gfso	NOUN
ejpam-5573	162	13	set	set	VERB
ejpam-5573	162	14	and	and	CCONJ
ejpam-5573	162	15	µ	µ	PRON
ejpam-5573	162	16	≤	≤	NOUN
ejpam-5573	162	17	ν	ν	NOUN
ejpam-5573	162	18	,	,	PUNCT
ejpam-5573	162	19	then	then	ADV
ejpam-5573	162	20	λ	λ	X
ejpam-5573	162	21	≤	≤	NOUN
ejpam-5573	162	22	ν	ν	NOUN
ejpam-5573	162	23	.	.	PUNCT
ejpam-5573	163	1	since	since	SCONJ
ejpam-5573	163	2	λ	λ	PROPN
ejpam-5573	163	3	is	be	AUX
ejpam-5573	163	4	(	(	PUNCT
ejpam-5573	163	5	r	r	NOUN
ejpam-5573	163	6	,	,	PUNCT
ejpam-5573	163	7	s)−	s)−	PROPN
ejpam-5573	164	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	164	2	set	set	VERB
ejpam-5573	164	3	,	,	PUNCT
ejpam-5573	164	4	hence	hence	ADV
ejpam-5573	164	5	scη	scη	PROPN
ejpam-5573	164	6	,	,	PUNCT
ejpam-5573	164	7	η∗(λ	η∗(λ	PROPN
ejpam-5573	164	8	,	,	PUNCT
ejpam-5573	164	9	r	r	NOUN
ejpam-5573	164	10	,	,	PUNCT
ejpam-5573	164	11	s	s	NOUN
ejpam-5573	164	12	)	)	PUNCT
ejpam-5573	164	13	≤	≤	NUM
ejpam-5573	164	14	ν	ν	NOUN
ejpam-5573	164	15	,	,	PUNCT
ejpam-5573	164	16	but	but	CCONJ
ejpam-5573	164	17	µ	µ	PRON
ejpam-5573	164	18	≤	≤	NUM
ejpam-5573	164	19	scη	scη	NOUN
ejpam-5573	164	20	,	,	PUNCT
ejpam-5573	164	21	η∗(λ	η∗(λ	PROPN
ejpam-5573	164	22	,	,	PUNCT
ejpam-5573	164	23	r	r	NOUN
ejpam-5573	164	24	,	,	PUNCT
ejpam-5573	164	25	s	s	NOUN
ejpam-5573	164	26	)	)	PUNCT
ejpam-5573	164	27	.	.	PUNCT
ejpam-5573	165	1	then	then	ADV
ejpam-5573	165	2	,	,	PUNCT
ejpam-5573	165	3	scη	scη	PROPN
ejpam-5573	165	4	,	,	PUNCT
ejpam-5573	165	5	η∗(µ	η∗(µ	PROPN
ejpam-5573	165	6	,	,	PUNCT
ejpam-5573	165	7	r	r	NOUN
ejpam-5573	165	8	,	,	PUNCT
ejpam-5573	165	9	s	s	NOUN
ejpam-5573	165	10	)	)	PUNCT
ejpam-5573	165	11	≤	≤	NUM
ejpam-5573	165	12	ν	ν	NOUN
ejpam-5573	165	13	.	.	PUNCT
ejpam-5573	166	1	so	so	ADV
ejpam-5573	166	2	,	,	PUNCT
ejpam-5573	166	3	µ	µ	X
ejpam-5573	166	4	is	be	AUX
ejpam-5573	166	5	(	(	PUNCT
ejpam-5573	166	6	r	r	NOUN
ejpam-5573	166	7	,	,	PUNCT
ejpam-5573	166	8	s)−	s)−	PROPN
ejpam-5573	167	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	167	2	set	set	VERB
ejpam-5573	167	3	.	.	PUNCT
ejpam-5573	168	1	(	(	PUNCT
ejpam-5573	168	2	ii	ii	NOUN
ejpam-5573	168	3	)	)	PUNCT
ejpam-5573	168	4	and	and	CCONJ
ejpam-5573	168	5	(	(	PUNCT
ejpam-5573	168	6	iii	iii	X
ejpam-5573	168	7	)	)	PUNCT
ejpam-5573	168	8	are	be	AUX
ejpam-5573	168	9	easily	easily	ADV
ejpam-5573	168	10	proved	prove	VERB
ejpam-5573	168	11	by	by	ADP
ejpam-5573	168	12	a	a	DET
ejpam-5573	168	13	similar	similar	ADJ
ejpam-5573	168	14	way	way	NOUN
ejpam-5573	168	15	.	.	PUNCT
ejpam-5573	169	1	theorem	theorem	NOUN
ejpam-5573	169	2	2	2	NUM
ejpam-5573	169	3	.	.	X
ejpam-5573	170	1	let	let	VERB
ejpam-5573	170	2	(	(	PUNCT
ejpam-5573	170	3	v	v	NOUN
ejpam-5573	170	4	,	,	PUNCT
ejpam-5573	170	5	η	η	NOUN
ejpam-5573	170	6	,	,	PUNCT
ejpam-5573	170	7	η∗	η∗	NOUN
ejpam-5573	170	8	)	)	PUNCT
ejpam-5573	170	9	be	be	AUX
ejpam-5573	170	10	a	a	DET
ejpam-5573	170	11	dfts	dft	NOUN
ejpam-5573	170	12	,	,	PUNCT
ejpam-5573	170	13	ν	ν	X
ejpam-5573	170	14	∈	∈	PROPN
ejpam-5573	170	15	iv	iv	X
ejpam-5573	170	16	,	,	PUNCT
ejpam-5573	170	17	s	s	PROPN
ejpam-5573	170	18	∈	∈	PROPN
ejpam-5573	170	19	i1	i1	NOUN
ejpam-5573	170	20	,	,	PUNCT
ejpam-5573	170	21	and	and	CCONJ
ejpam-5573	171	1	r	r	NOUN
ejpam-5573	171	2	∈	∈	PROPN
ejpam-5573	172	1	i	i	PRON
ejpam-5573	172	2	◦	◦	NOUN
ejpam-5573	172	3	,	,	PUNCT
ejpam-5573	172	4	then	then	ADV
ejpam-5573	172	5	the	the	DET
ejpam-5573	172	6	following	following	ADJ
ejpam-5573	172	7	statements	statement	NOUN
ejpam-5573	172	8	are	be	AUX
ejpam-5573	172	9	equivalent	equivalent	ADJ
ejpam-5573	172	10	.	.	PUNCT
ejpam-5573	173	1	(	(	PUNCT
ejpam-5573	173	2	i	i	NOUN
ejpam-5573	173	3	)	)	PUNCT
ejpam-5573	173	4	ν	ν	NOUN
ejpam-5573	173	5	is	be	AUX
ejpam-5573	173	6	(	(	PUNCT
ejpam-5573	173	7	r	r	NOUN
ejpam-5573	173	8	,	,	PUNCT
ejpam-5573	173	9	s)−	s)−	PROPN
ejpam-5573	173	10	fro	fro	NOUN
ejpam-5573	173	11	set	set	NOUN
ejpam-5573	173	12	.	.	PUNCT
ejpam-5573	174	1	(	(	PUNCT
ejpam-5573	174	2	ii	ii	NOUN
ejpam-5573	174	3	)	)	PUNCT
ejpam-5573	174	4	ν	ν	NOUN
ejpam-5573	174	5	is	be	AUX
ejpam-5573	174	6	(	(	PUNCT
ejpam-5573	174	7	r	r	NOUN
ejpam-5573	174	8	,	,	PUNCT
ejpam-5573	174	9	s)−	s)−	PROPN
ejpam-5573	175	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	175	2	set	set	VERB
ejpam-5573	175	3	and	and	CCONJ
ejpam-5573	175	4	η(ν	η(ν	PROPN
ejpam-5573	175	5	)	)	PUNCT
ejpam-5573	175	6	≥	≥	NOUN
ejpam-5573	175	7	r	r	NOUN
ejpam-5573	175	8	,	,	PUNCT
ejpam-5573	175	9	η∗(ν	η∗(ν	NOUN
ejpam-5573	175	10	)	)	PUNCT
ejpam-5573	175	11	≤	≤	NOUN
ejpam-5573	175	12	s.	s.	PROPN
ejpam-5573	175	13	proof	proof	PROPN
ejpam-5573	175	14	.	.	PUNCT
ejpam-5573	176	1	(	(	PUNCT
ejpam-5573	176	2	i	i	NOUN
ejpam-5573	176	3	)	)	PUNCT
ejpam-5573	176	4	⇒	⇒	PROPN
ejpam-5573	176	5	(	(	PUNCT
ejpam-5573	176	6	ii	ii	NOUN
ejpam-5573	176	7	)	)	PUNCT
ejpam-5573	176	8	let	let	VERB
ejpam-5573	176	9	µ	µ	X
ejpam-5573	176	10	∈	∈	NOUN
ejpam-5573	176	11	iv	iv	X
ejpam-5573	176	12	be	be	AUX
ejpam-5573	176	13	an	an	DET
ejpam-5573	176	14	(	(	PUNCT
ejpam-5573	176	15	r	r	NOUN
ejpam-5573	176	16	,	,	PUNCT
ejpam-5573	176	17	s)−	s)−	PROPN
ejpam-5573	176	18	gfso	gfso	NOUN
ejpam-5573	176	19	set	set	VERB
ejpam-5573	176	20	and	and	CCONJ
ejpam-5573	176	21	ν	ν	PROPN
ejpam-5573	176	22	≤	≤	NUM
ejpam-5573	176	23	µ.	µ.	NOUN
ejpam-5573	176	24	since	since	SCONJ
ejpam-5573	176	25	ν	ν	PROPN
ejpam-5573	176	26	is	be	AUX
ejpam-5573	176	27	(	(	PUNCT
ejpam-5573	176	28	r	r	NOUN
ejpam-5573	176	29	,	,	PUNCT
ejpam-5573	176	30	s)−	s)−	PROPN
ejpam-5573	176	31	fro	fro	NOUN
ejpam-5573	176	32	set	set	NOUN
ejpam-5573	176	33	,	,	PUNCT
ejpam-5573	176	34	then	then	ADV
ejpam-5573	176	35	ν	ν	X
ejpam-5573	176	36	∨	∨	NUM
ejpam-5573	176	37	iη	iη	NOUN
ejpam-5573	176	38	,	,	PUNCT
ejpam-5573	176	39	η∗(cη	η∗(cη	NOUN
ejpam-5573	176	40	,	,	PUNCT
ejpam-5573	176	41	η∗(ν	η∗(ν	NOUN
ejpam-5573	176	42	,	,	PUNCT
ejpam-5573	176	43	r	r	NOUN
ejpam-5573	176	44	,	,	PUNCT
ejpam-5573	176	45	s	s	PART
ejpam-5573	176	46	)	)	PUNCT
ejpam-5573	176	47	,	,	PUNCT
ejpam-5573	176	48	r	r	NOUN
ejpam-5573	176	49	,	,	PUNCT
ejpam-5573	176	50	s	s	NOUN
ejpam-5573	176	51	)	)	PUNCT
ejpam-5573	176	52	=	=	SYM
ejpam-5573	176	53	ν	ν	PROPN
ejpam-5573	176	54	≤	≤	NUM
ejpam-5573	176	55	µ.	µ.	NOUN
ejpam-5573	176	56	so	so	ADV
ejpam-5573	176	57	,	,	PUNCT
ejpam-5573	176	58	scη	scη	NOUN
ejpam-5573	176	59	,	,	PUNCT
ejpam-5573	176	60	η∗(ν	η∗(ν	NOUN
ejpam-5573	176	61	,	,	PUNCT
ejpam-5573	176	62	r	r	NOUN
ejpam-5573	176	63	,	,	PUNCT
ejpam-5573	176	64	s	s	NOUN
ejpam-5573	176	65	)	)	PUNCT
ejpam-5573	176	66	≤	≤	NOUN
ejpam-5573	176	67	µ	µ	NUM
ejpam-5573	176	68	,	,	PUNCT
ejpam-5573	176	69	and	and	CCONJ
ejpam-5573	176	70	hence	hence	ADV
ejpam-5573	176	71	ν	ν	X
ejpam-5573	176	72	is	be	AUX
ejpam-5573	176	73	(	(	PUNCT
ejpam-5573	176	74	r	r	NOUN
ejpam-5573	176	75	,	,	PUNCT
ejpam-5573	176	76	s)−	s)−	PROPN
ejpam-5573	177	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	177	2	set	set	VERB
ejpam-5573	177	3	.	.	PUNCT
ejpam-5573	178	1	(	(	PUNCT
ejpam-5573	178	2	ii	ii	NOUN
ejpam-5573	178	3	)	)	PUNCT
ejpam-5573	178	4	⇒	⇒	NOUN
ejpam-5573	178	5	(	(	PUNCT
ejpam-5573	178	6	i	i	NOUN
ejpam-5573	178	7	)	)	PUNCT
ejpam-5573	178	8	since	since	SCONJ
ejpam-5573	178	9	ν	ν	PROPN
ejpam-5573	178	10	is	be	AUX
ejpam-5573	178	11	(	(	PUNCT
ejpam-5573	178	12	r	r	NOUN
ejpam-5573	178	13	,	,	PUNCT
ejpam-5573	178	14	s	s	NOUN
ejpam-5573	178	15	)	)	PUNCT
ejpam-5573	178	16	−	−	PROPN
ejpam-5573	179	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	179	2	set	set	VERB
ejpam-5573	179	3	and	and	CCONJ
ejpam-5573	179	4	η(ν	η(ν	PROPN
ejpam-5573	179	5	)	)	PUNCT
ejpam-5573	179	6	≥	≥	NOUN
ejpam-5573	179	7	r	r	NOUN
ejpam-5573	179	8	,	,	PUNCT
ejpam-5573	179	9	η∗(ν	η∗(ν	NOUN
ejpam-5573	179	10	)	)	PUNCT
ejpam-5573	179	11	≤	≤	NOUN
ejpam-5573	180	1	s	s	PROPN
ejpam-5573	180	2	,	,	PUNCT
ejpam-5573	180	3	then	then	ADV
ejpam-5573	180	4	by	by	ADP
ejpam-5573	180	5	proposition	proposition	NOUN
ejpam-5573	180	6	1(iii	1(iii	NUM
ejpam-5573	180	7	)	)	PUNCT
ejpam-5573	180	8	,	,	PUNCT
ejpam-5573	180	9	ν	ν	PROPN
ejpam-5573	180	10	is	be	AUX
ejpam-5573	180	11	(	(	PUNCT
ejpam-5573	180	12	r	r	NOUN
ejpam-5573	180	13	,	,	PUNCT
ejpam-5573	180	14	s)−	s)−	PROPN
ejpam-5573	180	15	fsc	fsc	PROPN
ejpam-5573	180	16	set	set	PROPN
ejpam-5573	180	17	.	.	PUNCT
ejpam-5573	181	1	but	but	CCONJ
ejpam-5573	181	2	,	,	PUNCT
ejpam-5573	181	3	ν	ν	PROPN
ejpam-5573	181	4	is	be	AUX
ejpam-5573	181	5	(	(	PUNCT
ejpam-5573	181	6	r	r	NOUN
ejpam-5573	181	7	,	,	PUNCT
ejpam-5573	181	8	s)−	s)−	PROPN
ejpam-5573	181	9	fpo	fpo	PROPN
ejpam-5573	181	10	set	set	PROPN
ejpam-5573	181	11	.	.	PUNCT
ejpam-5573	182	1	therefore	therefore	ADV
ejpam-5573	182	2	,	,	PUNCT
ejpam-5573	182	3	ν	ν	PROPN
ejpam-5573	182	4	is	be	AUX
ejpam-5573	182	5	(	(	PUNCT
ejpam-5573	182	6	r	r	NOUN
ejpam-5573	182	7	,	,	PUNCT
ejpam-5573	182	8	s)−	s)−	PROPN
ejpam-5573	182	9	fro	fro	NOUN
ejpam-5573	182	10	set	set	NOUN
ejpam-5573	182	11	.	.	PUNCT
ejpam-5573	183	1	f.	f.	PROPN
ejpam-5573	183	2	alsharari	alsharari	PROPN
ejpam-5573	183	3	,	,	PUNCT
ejpam-5573	183	4	o.	o.	PROPN
ejpam-5573	183	5	m.	m.	PROPN
ejpam-5573	183	6	taha	taha	PROPN
ejpam-5573	183	7	,	,	PUNCT
ejpam-5573	183	8	i.	i.	PROPN
ejpam-5573	183	9	m.	m.	PROPN
ejpam-5573	183	10	taha	taha	PROPN
ejpam-5573	183	11	/	/	PUNCT
ejpam-5573	183	12	eur	eur	PROPN
ejpam-5573	183	13	.	.	PUNCT
ejpam-5573	184	1	j.	j.	PROPN
ejpam-5573	184	2	pure	pure	PROPN
ejpam-5573	184	3	appl	appl	PROPN
ejpam-5573	184	4	.	.	PROPN
ejpam-5573	184	5	math	math	PROPN
ejpam-5573	184	6	,	,	PUNCT
ejpam-5573	184	7	17	17	NUM
ejpam-5573	184	8	(	(	PUNCT
ejpam-5573	184	9	4	4	NUM
ejpam-5573	184	10	)	)	PUNCT
ejpam-5573	184	11	(	(	PUNCT
ejpam-5573	184	12	2024	2024	NUM
ejpam-5573	184	13	)	)	PUNCT
ejpam-5573	184	14	,	,	PUNCT
ejpam-5573	184	15	4093	4093	NUM
ejpam-5573	184	16	-	-	SYM
ejpam-5573	184	17	4111	4111	NUM
ejpam-5573	184	18	4100	4100	NUM
ejpam-5573	184	19	theorem	theorem	NOUN
ejpam-5573	184	20	3	3	X
ejpam-5573	184	21	.	.	PUNCT
ejpam-5573	185	1	let	let	ADJ
ejpam-5573	185	2	(	(	PUNCT
ejpam-5573	185	3	v	v	NOUN
ejpam-5573	185	4	,	,	PUNCT
ejpam-5573	185	5	η	η	NOUN
ejpam-5573	185	6	,	,	PUNCT
ejpam-5573	185	7	η∗	η∗	NOUN
ejpam-5573	185	8	)	)	PUNCT
ejpam-5573	185	9	be	be	VERB
ejpam-5573	185	10	a	a	DET
ejpam-5573	185	11	dfts	dft	NOUN
ejpam-5573	185	12	,	,	PUNCT
ejpam-5573	185	13	ρ	ρ	PROPN
ejpam-5573	185	14	,	,	PUNCT
ejpam-5573	185	15	µ	µ	NOUN
ejpam-5573	185	16	,	,	PUNCT
ejpam-5573	185	17	ν	ν	X
ejpam-5573	185	18	∈	∈	PROPN
ejpam-5573	185	19	iv	iv	X
ejpam-5573	185	20	,	,	PUNCT
ejpam-5573	185	21	s	s	PROPN
ejpam-5573	185	22	∈	∈	PROPN
ejpam-5573	185	23	i1	i1	NOUN
ejpam-5573	185	24	,	,	PUNCT
ejpam-5573	185	25	and	and	CCONJ
ejpam-5573	185	26	r	r	NOUN
ejpam-5573	185	27	∈	∈	PROPN
ejpam-5573	185	28	i	i	PRON
ejpam-5573	185	29	◦	◦	NOUN
ejpam-5573	185	30	,	,	PUNCT
ejpam-5573	185	31	then	then	ADV
ejpam-5573	185	32	the	the	DET
ejpam-5573	185	33	following	following	ADJ
ejpam-5573	185	34	statements	statement	NOUN
ejpam-5573	185	35	are	be	AUX
ejpam-5573	185	36	equivalent	equivalent	ADJ
ejpam-5573	185	37	.	.	PUNCT
ejpam-5573	186	1	(	(	PUNCT
ejpam-5573	186	2	i	i	NOUN
ejpam-5573	186	3	)	)	PUNCT
ejpam-5573	186	4	ν	ν	NOUN
ejpam-5573	186	5	is	be	AUX
ejpam-5573	186	6	(	(	PUNCT
ejpam-5573	186	7	r	r	NOUN
ejpam-5573	186	8	,	,	PUNCT
ejpam-5573	186	9	s)−	s)−	PROPN
ejpam-5573	186	10	g⊛fso	g⊛fso	PROPN
ejpam-5573	186	11	set	set	VERB
ejpam-5573	186	12	.	.	PUNCT
ejpam-5573	187	1	(	(	PUNCT
ejpam-5573	187	2	ii	ii	NOUN
ejpam-5573	187	3	)	)	PUNCT
ejpam-5573	187	4	for	for	ADP
ejpam-5573	187	5	any	any	DET
ejpam-5573	187	6	µ	µ	NOUN
ejpam-5573	187	7	is	be	AUX
ejpam-5573	187	8	(	(	PUNCT
ejpam-5573	187	9	r	r	NOUN
ejpam-5573	187	10	,	,	PUNCT
ejpam-5573	187	11	s)−	s)−	PROPN
ejpam-5573	187	12	gfsc	gfsc	PROPN
ejpam-5573	187	13	set	set	VERB
ejpam-5573	187	14	and	and	CCONJ
ejpam-5573	187	15	µ	µ	PRON
ejpam-5573	187	16	≤	≤	NUM
ejpam-5573	187	17	ν	ν	NOUN
ejpam-5573	187	18	,	,	PUNCT
ejpam-5573	187	19	then	then	ADV
ejpam-5573	187	20	µ	µ	PROPN
ejpam-5573	187	21	≤	≤	NUM
ejpam-5573	187	22	siη	siη	NOUN
ejpam-5573	187	23	,	,	PUNCT
ejpam-5573	187	24	η∗(ν	η∗(ν	NOUN
ejpam-5573	187	25	,	,	PUNCT
ejpam-5573	187	26	r	r	NOUN
ejpam-5573	187	27	,	,	PUNCT
ejpam-5573	187	28	s	s	NOUN
ejpam-5573	187	29	)	)	PUNCT
ejpam-5573	187	30	.	.	PUNCT
ejpam-5573	188	1	(	(	PUNCT
ejpam-5573	188	2	iii	iii	X
ejpam-5573	188	3	)	)	PUNCT
ejpam-5573	188	4	for	for	ADP
ejpam-5573	188	5	any	any	DET
ejpam-5573	188	6	µ	µ	NOUN
ejpam-5573	188	7	is	be	AUX
ejpam-5573	188	8	(	(	PUNCT
ejpam-5573	188	9	r	r	NOUN
ejpam-5573	188	10	,	,	PUNCT
ejpam-5573	188	11	s	s	NOUN
ejpam-5573	188	12	)	)	PUNCT
ejpam-5573	188	13	−	−	PROPN
ejpam-5573	188	14	gfsc	gfsc	PROPN
ejpam-5573	188	15	set	set	VERB
ejpam-5573	188	16	and	and	CCONJ
ejpam-5573	188	17	µ	µ	PRON
ejpam-5573	188	18	≤	≤	NOUN
ejpam-5573	188	19	ν	ν	NOUN
ejpam-5573	188	20	,	,	PUNCT
ejpam-5573	188	21	there	there	PRON
ejpam-5573	188	22	is	be	VERB
ejpam-5573	188	23	ρ	ρ	NOUN
ejpam-5573	188	24	is	be	AUX
ejpam-5573	188	25	(	(	PUNCT
ejpam-5573	188	26	r	r	NOUN
ejpam-5573	188	27	,	,	PUNCT
ejpam-5573	188	28	s	s	NOUN
ejpam-5573	188	29	)	)	PUNCT
ejpam-5573	188	30	−	−	NOUN
ejpam-5573	188	31	fso	fso	NOUN
ejpam-5573	188	32	set	set	VERB
ejpam-5573	188	33	such	such	ADJ
ejpam-5573	188	34	that	that	SCONJ
ejpam-5573	188	35	µ	µ	PROPN
ejpam-5573	188	36	≤	≤	NUM
ejpam-5573	188	37	ρ	ρ	PROPN
ejpam-5573	188	38	≤	≤	ADJ
ejpam-5573	188	39	ν	ν	NOUN
ejpam-5573	188	40	.	.	PUNCT
ejpam-5573	189	1	proof	proof	NOUN
ejpam-5573	189	2	.	.	PUNCT
ejpam-5573	190	1	(	(	PUNCT
ejpam-5573	190	2	i	i	NOUN
ejpam-5573	190	3	)	)	PUNCT
ejpam-5573	190	4	⇒	⇒	PROPN
ejpam-5573	190	5	(	(	PUNCT
ejpam-5573	190	6	ii	ii	NOUN
ejpam-5573	190	7	)	)	PUNCT
ejpam-5573	190	8	let	let	VERB
ejpam-5573	190	9	µ	µ	X
ejpam-5573	190	10	be	be	AUX
ejpam-5573	190	11	an	an	DET
ejpam-5573	190	12	(	(	PUNCT
ejpam-5573	190	13	r	r	NOUN
ejpam-5573	190	14	,	,	PUNCT
ejpam-5573	190	15	s	s	NOUN
ejpam-5573	190	16	)	)	PUNCT
ejpam-5573	190	17	−	−	PROPN
ejpam-5573	190	18	gfsc	gfsc	PROPN
ejpam-5573	190	19	set	set	VERB
ejpam-5573	190	20	and	and	CCONJ
ejpam-5573	190	21	µ	µ	PRON
ejpam-5573	190	22	≤	≤	NOUN
ejpam-5573	190	23	ν	ν	NOUN
ejpam-5573	190	24	.	.	PUNCT
ejpam-5573	191	1	then	then	ADV
ejpam-5573	191	2	,	,	PUNCT
ejpam-5573	191	3	νc	νc	X
ejpam-5573	191	4	≤	≤	NUM
ejpam-5573	191	5	µc	µc	ADP
ejpam-5573	191	6	,	,	PUNCT
ejpam-5573	191	7	which	which	PRON
ejpam-5573	191	8	is	be	AUX
ejpam-5573	191	9	(	(	PUNCT
ejpam-5573	191	10	r	r	NOUN
ejpam-5573	191	11	,	,	PUNCT
ejpam-5573	191	12	s	s	NOUN
ejpam-5573	191	13	)	)	PUNCT
ejpam-5573	191	14	−	−	PROPN
ejpam-5573	191	15	gfso	gfso	NOUN
ejpam-5573	191	16	set	set	NOUN
ejpam-5573	191	17	.	.	PUNCT
ejpam-5573	192	1	hence	hence	ADV
ejpam-5573	192	2	,	,	PUNCT
ejpam-5573	192	3	scη	scη	PROPN
ejpam-5573	192	4	,	,	PUNCT
ejpam-5573	192	5	η∗(ν	η∗(ν	PROPN
ejpam-5573	192	6	c	c	NOUN
ejpam-5573	192	7	,	,	PUNCT
ejpam-5573	192	8	r	r	NOUN
ejpam-5573	192	9	,	,	PUNCT
ejpam-5573	192	10	s	s	NOUN
ejpam-5573	192	11	)	)	PUNCT
ejpam-5573	192	12	≤	≤	NUM
ejpam-5573	192	13	µc	µc	AUX
ejpam-5573	192	14	implies	imply	VERB
ejpam-5573	192	15	µ	µ	PRON
ejpam-5573	192	16	≤	≤	NOUN
ejpam-5573	192	17	(	(	PUNCT
ejpam-5573	192	18	scη	scη	VERB
ejpam-5573	192	19	,	,	PUNCT
ejpam-5573	192	20	η∗(ν	η∗(ν	PROPN
ejpam-5573	192	21	c	c	NOUN
ejpam-5573	192	22	,	,	PUNCT
ejpam-5573	192	23	r	r	NOUN
ejpam-5573	192	24	,	,	PUNCT
ejpam-5573	192	25	s))c	s))c	NOUN
ejpam-5573	192	26	.	.	PUNCT
ejpam-5573	193	1	then	then	ADV
ejpam-5573	193	2	,	,	PUNCT
ejpam-5573	193	3	µ	µ	ADJ
ejpam-5573	193	4	≤	≤	NUM
ejpam-5573	193	5	siη	siη	NOUN
ejpam-5573	193	6	,	,	PUNCT
ejpam-5573	193	7	η∗(ν	η∗(ν	NOUN
ejpam-5573	193	8	,	,	PUNCT
ejpam-5573	193	9	r	r	NOUN
ejpam-5573	193	10	,	,	PUNCT
ejpam-5573	193	11	s	s	NOUN
ejpam-5573	193	12	)	)	PUNCT
ejpam-5573	193	13	.	.	PUNCT
ejpam-5573	194	1	(	(	PUNCT
ejpam-5573	194	2	ii	ii	NOUN
ejpam-5573	194	3	)	)	PUNCT
ejpam-5573	194	4	⇒	⇒	NOUN
ejpam-5573	194	5	(	(	PUNCT
ejpam-5573	194	6	iii	iii	X
ejpam-5573	194	7	)	)	PUNCT
ejpam-5573	194	8	let	let	VERB
ejpam-5573	194	9	µ	µ	X
ejpam-5573	194	10	be	be	AUX
ejpam-5573	194	11	an	an	DET
ejpam-5573	194	12	(	(	PUNCT
ejpam-5573	194	13	r	r	NOUN
ejpam-5573	194	14	,	,	PUNCT
ejpam-5573	194	15	s	s	NOUN
ejpam-5573	194	16	)	)	PUNCT
ejpam-5573	194	17	−	−	PROPN
ejpam-5573	194	18	gfsc	gfsc	PROPN
ejpam-5573	194	19	set	set	VERB
ejpam-5573	194	20	and	and	CCONJ
ejpam-5573	194	21	µ	µ	PRON
ejpam-5573	194	22	≤	≤	NOUN
ejpam-5573	194	23	ν	ν	NOUN
ejpam-5573	194	24	.	.	PUNCT
ejpam-5573	195	1	then	then	ADV
ejpam-5573	195	2	,	,	PUNCT
ejpam-5573	195	3	by	by	ADP
ejpam-5573	195	4	hypothesis	hypothesis	NOUN
ejpam-5573	195	5	µ	µ	PROPN
ejpam-5573	195	6	≤	≤	NUM
ejpam-5573	195	7	siη	siη	NOUN
ejpam-5573	195	8	,	,	PUNCT
ejpam-5573	195	9	η∗(ν	η∗(ν	NOUN
ejpam-5573	195	10	,	,	PUNCT
ejpam-5573	195	11	r	r	NOUN
ejpam-5573	195	12	,	,	PUNCT
ejpam-5573	195	13	s	s	PART
ejpam-5573	195	14	)	)	PUNCT
ejpam-5573	195	15	.	.	PUNCT
ejpam-5573	196	1	put	put	VERB
ejpam-5573	196	2	siη	siη	NOUN
ejpam-5573	196	3	,	,	PUNCT
ejpam-5573	196	4	η∗(ν	η∗(ν	NOUN
ejpam-5573	196	5	,	,	PUNCT
ejpam-5573	196	6	r	r	NOUN
ejpam-5573	196	7	,	,	PUNCT
ejpam-5573	196	8	s	s	NOUN
ejpam-5573	196	9	)	)	PUNCT
ejpam-5573	196	10	=	=	SYM
ejpam-5573	196	11	ρ	ρ	PROPN
ejpam-5573	196	12	.	.	PUNCT
ejpam-5573	197	1	hence	hence	ADV
ejpam-5573	197	2	,	,	PUNCT
ejpam-5573	197	3	µ	µ	PROPN
ejpam-5573	197	4	≤	≤	NOUN
ejpam-5573	197	5	ρ	ρ	PROPN
ejpam-5573	197	6	≤	≤	NOUN
ejpam-5573	197	7	ν	ν	X
ejpam-5573	197	8	.	.	PUNCT
ejpam-5573	197	9	(	(	PUNCT
ejpam-5573	197	10	iii	iii	X
ejpam-5573	197	11	)	)	PUNCT
ejpam-5573	197	12	⇒	⇒	NOUN
ejpam-5573	197	13	(	(	PUNCT
ejpam-5573	197	14	i	i	NOUN
ejpam-5573	197	15	)	)	PUNCT
ejpam-5573	197	16	let	let	VERB
ejpam-5573	197	17	µ	µ	X
ejpam-5573	197	18	be	be	AUX
ejpam-5573	197	19	an	an	DET
ejpam-5573	197	20	(	(	PUNCT
ejpam-5573	197	21	r	r	NOUN
ejpam-5573	197	22	,	,	PUNCT
ejpam-5573	197	23	s)−	s)−	PROPN
ejpam-5573	197	24	gfso	gfso	NOUN
ejpam-5573	197	25	set	set	VERB
ejpam-5573	197	26	and	and	CCONJ
ejpam-5573	197	27	νc	νc	X
ejpam-5573	197	28	≤	≤	NUM
ejpam-5573	197	29	µ.	µ.	NOUN
ejpam-5573	197	30	then	then	ADV
ejpam-5573	197	31	,	,	PUNCT
ejpam-5573	197	32	µc	µc	ADV
ejpam-5573	197	33	≤	≤	ADJ
ejpam-5573	197	34	ν	ν	NOUN
ejpam-5573	197	35	and	and	CCONJ
ejpam-5573	197	36	by	by	ADP
ejpam-5573	197	37	hypothesis	hypothesis	NOUN
ejpam-5573	197	38	,	,	PUNCT
ejpam-5573	197	39	there	there	PRON
ejpam-5573	197	40	is	be	VERB
ejpam-5573	197	41	ρ	ρ	NOUN
ejpam-5573	197	42	is	be	AUX
ejpam-5573	197	43	(	(	PUNCT
ejpam-5573	197	44	r	r	NOUN
ejpam-5573	197	45	,	,	PUNCT
ejpam-5573	197	46	s	s	NOUN
ejpam-5573	197	47	)	)	PUNCT
ejpam-5573	197	48	−	−	NOUN
ejpam-5573	197	49	fso	fso	NOUN
ejpam-5573	197	50	set	set	VERB
ejpam-5573	197	51	such	such	ADJ
ejpam-5573	197	52	that	that	SCONJ
ejpam-5573	197	53	µc	µc	ADP
ejpam-5573	197	54	≤	≤	PROPN
ejpam-5573	197	55	ρ	ρ	PROPN
ejpam-5573	197	56	≤	≤	ADJ
ejpam-5573	197	57	ν	ν	NOUN
ejpam-5573	197	58	,	,	PUNCT
ejpam-5573	197	59	that	that	ADV
ejpam-5573	197	60	is	is	ADV
ejpam-5573	197	61	,	,	PUNCT
ejpam-5573	197	62	νc	νc	X
ejpam-5573	197	63	≤	≤	NUM
ejpam-5573	197	64	ρc	ρc	VERB
ejpam-5573	197	65	≤	≤	NUM
ejpam-5573	197	66	µ.	µ.	NOUN
ejpam-5573	197	67	therefore	therefore	ADV
ejpam-5573	197	68	,	,	PUNCT
ejpam-5573	197	69	by	by	ADP
ejpam-5573	197	70	theorem	theorem	NOUN
ejpam-5573	197	71	1	1	NUM
ejpam-5573	197	72	,	,	PUNCT
ejpam-5573	197	73	νc	νc	X
ejpam-5573	197	74	is	be	AUX
ejpam-5573	197	75	(	(	PUNCT
ejpam-5573	197	76	r	r	NOUN
ejpam-5573	197	77	,	,	PUNCT
ejpam-5573	197	78	s)−	s)−	PROPN
ejpam-5573	198	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	198	2	set	set	VERB
ejpam-5573	198	3	.	.	PUNCT
ejpam-5573	199	1	hence	hence	ADV
ejpam-5573	199	2	,	,	PUNCT
ejpam-5573	199	3	ν	ν	PROPN
ejpam-5573	199	4	is	be	AUX
ejpam-5573	199	5	(	(	PUNCT
ejpam-5573	199	6	r	r	NOUN
ejpam-5573	199	7	,	,	PUNCT
ejpam-5573	199	8	s)−	s)−	PROPN
ejpam-5573	199	9	g⊛fso	g⊛fso	PROPN
ejpam-5573	199	10	set	set	VERB
ejpam-5573	199	11	.	.	PUNCT
ejpam-5573	200	1	definition	definition	NOUN
ejpam-5573	200	2	7	7	NUM
ejpam-5573	200	3	.	.	PUNCT
ejpam-5573	201	1	let	let	VERB
ejpam-5573	201	2	h	h	NOUN
ejpam-5573	201	3	:	:	PUNCT
ejpam-5573	201	4	(	(	PUNCT
ejpam-5573	201	5	u	u	NOUN
ejpam-5573	201	6	,	,	PUNCT
ejpam-5573	201	7	τ	τ	X
ejpam-5573	201	8	,	,	PUNCT
ejpam-5573	201	9	τ∗)→	τ∗)→	PROPN
ejpam-5573	201	10	(	(	PUNCT
ejpam-5573	201	11	v	v	PROPN
ejpam-5573	201	12	,	,	PUNCT
ejpam-5573	201	13	η	η	NOUN
ejpam-5573	201	14	,	,	PUNCT
ejpam-5573	201	15	η∗	η∗	NOUN
ejpam-5573	201	16	)	)	PUNCT
ejpam-5573	201	17	be	be	VERB
ejpam-5573	201	18	a	a	DET
ejpam-5573	201	19	mapping	mapping	NOUN
ejpam-5573	201	20	,	,	PUNCT
ejpam-5573	201	21	then	then	ADV
ejpam-5573	201	22	h	h	NOUN
ejpam-5573	201	23	is	be	AUX
ejpam-5573	201	24	said	say	VERB
ejpam-5573	201	25	to	to	PART
ejpam-5573	201	26	be	be	AUX
ejpam-5573	201	27	(	(	PUNCT
ejpam-5573	201	28	i	i	NOUN
ejpam-5573	201	29	)	)	PUNCT
ejpam-5573	201	30	strongly∗	strongly∗	NOUN
ejpam-5573	201	31	double	double	ADJ
ejpam-5573	201	32	fuzzy	fuzzy	ADJ
ejpam-5573	201	33	generalized	generalized	ADJ
ejpam-5573	201	34	semi	semi	ADJ
ejpam-5573	201	35	-	-	ADJ
ejpam-5573	201	36	continuous	continuous	ADJ
ejpam-5573	201	37	⟨briefly	⟨briefly	NOUN
ejpam-5573	201	38	,	,	PUNCT
ejpam-5573	201	39	s∗dfgs	s∗dfgs	NOUN
ejpam-5573	201	40	-	-	PUNCT
ejpam-5573	201	41	continuous⟩	continuous⟩	NOUN
ejpam-5573	201	42	if	if	SCONJ
ejpam-5573	201	43	h−1(ν	h−1(ν	PROPN
ejpam-5573	201	44	)	)	PUNCT
ejpam-5573	201	45	is	be	AUX
ejpam-5573	201	46	(	(	PUNCT
ejpam-5573	201	47	r	r	NOUN
ejpam-5573	201	48	,	,	PUNCT
ejpam-5573	201	49	s)−	s)−	PROPN
ejpam-5573	201	50	g⊛fso	g⊛fso	PROPN
ejpam-5573	201	51	set	set	VERB
ejpam-5573	201	52	for	for	ADP
ejpam-5573	201	53	each	each	DET
ejpam-5573	201	54	ν	ν	NOUN
ejpam-5573	201	55	∈	∈	PROPN
ejpam-5573	201	56	iv	iv	X
ejpam-5573	201	57	and	and	CCONJ
ejpam-5573	201	58	η(ν	η(ν	PROPN
ejpam-5573	201	59	)	)	PUNCT
ejpam-5573	201	60	≥	≥	NOUN
ejpam-5573	201	61	r	r	NOUN
ejpam-5573	201	62	,	,	PUNCT
ejpam-5573	201	63	η∗(ν	η∗(ν	NOUN
ejpam-5573	201	64	)	)	PUNCT
ejpam-5573	201	65	≤	≤	NUM
ejpam-5573	201	66	s	s	PART
ejpam-5573	201	67	.	.	PUNCT
ejpam-5573	202	1	(	(	PUNCT
ejpam-5573	202	2	ii	ii	NOUN
ejpam-5573	202	3	)	)	PUNCT
ejpam-5573	202	4	s∗dfgs	s∗dfgs	NOUN
ejpam-5573	202	5	-	-	PUNCT
ejpam-5573	202	6	irresolute	irresolute	ADJ
ejpam-5573	202	7	if	if	SCONJ
ejpam-5573	202	8	h−1(ν	h−1(ν	PROPN
ejpam-5573	202	9	)	)	PUNCT
ejpam-5573	202	10	is	be	AUX
ejpam-5573	202	11	(	(	PUNCT
ejpam-5573	202	12	r	r	NOUN
ejpam-5573	202	13	,	,	PUNCT
ejpam-5573	202	14	s)−	s)−	PROPN
ejpam-5573	202	15	g⊛fso	g⊛fso	PROPN
ejpam-5573	202	16	set	set	VERB
ejpam-5573	202	17	for	for	ADP
ejpam-5573	202	18	each	each	DET
ejpam-5573	202	19	ν	ν	NOUN
ejpam-5573	202	20	∈	∈	NOUN
ejpam-5573	202	21	iv	iv	X
ejpam-5573	202	22	is	be	AUX
ejpam-5573	202	23	(	(	PUNCT
ejpam-5573	202	24	r	r	NOUN
ejpam-5573	202	25	,	,	PUNCT
ejpam-5573	202	26	s)−	s)−	PROPN
ejpam-5573	202	27	g⊛fso	g⊛fso	PROPN
ejpam-5573	202	28	set	set	VERB
ejpam-5573	202	29	.	.	PUNCT
ejpam-5573	203	1	(	(	PUNCT
ejpam-5573	203	2	iii	iii	NOUN
ejpam-5573	203	3	)	)	PUNCT
ejpam-5573	203	4	s∗dfgs	s∗dfgs	NOUN
ejpam-5573	203	5	-	-	PUNCT
ejpam-5573	203	6	open	open	ADJ
ejpam-5573	203	7	if	if	SCONJ
ejpam-5573	203	8	h(ρ	h(ρ	NOUN
ejpam-5573	203	9	)	)	PUNCT
ejpam-5573	203	10	is	be	AUX
ejpam-5573	203	11	(	(	PUNCT
ejpam-5573	203	12	r	r	NOUN
ejpam-5573	203	13	,	,	PUNCT
ejpam-5573	203	14	s)−g⊛fso	s)−g⊛fso	NOUN
ejpam-5573	203	15	set	set	NOUN
ejpam-5573	203	16	for	for	ADP
ejpam-5573	203	17	each	each	DET
ejpam-5573	203	18	ρ	ρ	NOUN
ejpam-5573	203	19	∈	∈	PROPN
ejpam-5573	203	20	iu	iu	ADP
ejpam-5573	203	21	and	and	CCONJ
ejpam-5573	203	22	τ(ρ	τ(ρ	PROPN
ejpam-5573	203	23	)	)	PUNCT
ejpam-5573	203	24	≥	≥	PROPN
ejpam-5573	203	25	r	r	NOUN
ejpam-5573	203	26	,	,	PUNCT
ejpam-5573	203	27	τ∗(ρ	τ∗(ρ	NUM
ejpam-5573	203	28	)	)	PUNCT
ejpam-5573	203	29	≤	≤	NUM
ejpam-5573	203	30	s	s	PART
ejpam-5573	203	31	.	.	PUNCT
ejpam-5573	204	1	(	(	PUNCT
ejpam-5573	204	2	iv	iv	X
ejpam-5573	204	3	)	)	PUNCT
ejpam-5573	204	4	s∗dfgs	s∗dfgs	NOUN
ejpam-5573	204	5	-	-	PUNCT
ejpam-5573	204	6	closed	close	VERB
ejpam-5573	204	7	if	if	SCONJ
ejpam-5573	204	8	h(ρ	h(ρ	NOUN
ejpam-5573	204	9	)	)	PUNCT
ejpam-5573	204	10	is	be	AUX
ejpam-5573	204	11	(	(	PUNCT
ejpam-5573	204	12	r	r	NOUN
ejpam-5573	204	13	,	,	PUNCT
ejpam-5573	205	1	s)−	s)−	PROPN
ejpam-5573	206	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	206	2	set	set	VERB
ejpam-5573	206	3	for	for	ADP
ejpam-5573	206	4	ρ	ρ	PROPN
ejpam-5573	206	5	∈	∈	PROPN
ejpam-5573	206	6	iu	iu	ADV
ejpam-5573	206	7	and	and	CCONJ
ejpam-5573	206	8	τ(ρc	τ(ρc	VERB
ejpam-5573	206	9	)	)	PUNCT
ejpam-5573	206	10	≥	≥	NOUN
ejpam-5573	206	11	r	r	NOUN
ejpam-5573	206	12	,	,	PUNCT
ejpam-5573	206	13	τ∗(ρc	τ∗(ρc	NOUN
ejpam-5573	206	14	)	)	PUNCT
ejpam-5573	207	1	≤	≤	PROPN
ejpam-5573	208	1	s	s	PART
ejpam-5573	208	2	.	.	PUNCT
ejpam-5573	209	1	remark	remark	PROPN
ejpam-5573	209	2	6	6	NUM
ejpam-5573	209	3	.	.	PUNCT
ejpam-5573	210	1	from	from	ADP
ejpam-5573	210	2	the	the	DET
ejpam-5573	210	3	previous	previous	ADJ
ejpam-5573	210	4	definitions	definition	NOUN
ejpam-5573	210	5	,	,	PUNCT
ejpam-5573	210	6	we	we	PRON
ejpam-5573	210	7	can	can	AUX
ejpam-5573	210	8	summarize	summarize	VERB
ejpam-5573	210	9	the	the	DET
ejpam-5573	210	10	relationships	relationship	NOUN
ejpam-5573	210	11	among	among	ADP
ejpam-5573	210	12	different	different	ADJ
ejpam-5573	210	13	types	type	NOUN
ejpam-5573	210	14	of	of	ADP
ejpam-5573	210	15	df	df	NOUN
ejpam-5573	210	16	-	-	PUNCT
ejpam-5573	210	17	continuity	continuity	NOUN
ejpam-5573	210	18	as	as	ADP
ejpam-5573	210	19	in	in	ADP
ejpam-5573	210	20	the	the	DET
ejpam-5573	210	21	next	next	ADJ
ejpam-5573	210	22	diagram	diagram	NOUN
ejpam-5573	210	23	.	.	PUNCT
ejpam-5573	211	1	df	df	PROPN
ejpam-5573	211	2	−	−	PROPN
ejpam-5573	211	3	continuity	continuity	NOUN
ejpam-5573	211	4	↙	↙	PROPN
ejpam-5573	212	1	↘	↘	PROPN
ejpam-5573	212	2	dfg	dfg	PROPN
ejpam-5573	212	3	−	−	PROPN
ejpam-5573	212	4	continuity	continuity	NOUN
ejpam-5573	212	5	dfs	dfs	NOUN
ejpam-5573	212	6	−	−	PROPN
ejpam-5573	212	7	continuity	continuity	NOUN
ejpam-5573	212	8	↓	↓	NOUN
ejpam-5573	212	9	↓	↓	NOUN
ejpam-5573	212	10	dfgs	dfg	VERB
ejpam-5573	212	11	−	−	PROPN
ejpam-5573	212	12	continuity	continuity	NOUN
ejpam-5573	212	13	←−	←−	NUM
ejpam-5573	212	14	s∗dfgs	s∗dfg	VERB
ejpam-5573	212	15	−	−	NOUN
ejpam-5573	212	16	continuity	continuity	NOUN
ejpam-5573	212	17	f.	f.	PROPN
ejpam-5573	212	18	alsharari	alsharari	PROPN
ejpam-5573	212	19	,	,	PUNCT
ejpam-5573	212	20	o.	o.	PROPN
ejpam-5573	212	21	m.	m.	PROPN
ejpam-5573	212	22	taha	taha	PROPN
ejpam-5573	212	23	,	,	PUNCT
ejpam-5573	212	24	i.	i.	PROPN
ejpam-5573	212	25	m.	m.	PROPN
ejpam-5573	212	26	taha	taha	PROPN
ejpam-5573	212	27	/	/	PUNCT
ejpam-5573	212	28	eur	eur	PROPN
ejpam-5573	212	29	.	.	PUNCT
ejpam-5573	213	1	j.	j.	PROPN
ejpam-5573	213	2	pure	pure	PROPN
ejpam-5573	213	3	appl	appl	PROPN
ejpam-5573	213	4	.	.	PROPN
ejpam-5573	213	5	math	math	PROPN
ejpam-5573	213	6	,	,	PUNCT
ejpam-5573	213	7	17	17	NUM
ejpam-5573	213	8	(	(	PUNCT
ejpam-5573	213	9	4	4	NUM
ejpam-5573	213	10	)	)	PUNCT
ejpam-5573	213	11	(	(	PUNCT
ejpam-5573	213	12	2024	2024	NUM
ejpam-5573	213	13	)	)	PUNCT
ejpam-5573	213	14	,	,	PUNCT
ejpam-5573	213	15	4093	4093	NUM
ejpam-5573	213	16	-	-	SYM
ejpam-5573	213	17	4111	4111	NUM
ejpam-5573	213	18	4101	4101	NUM
ejpam-5573	213	19	remark	remark	NOUN
ejpam-5573	213	20	7	7	NUM
ejpam-5573	213	21	.	.	PUNCT
ejpam-5573	214	1	the	the	DET
ejpam-5573	214	2	converses	converse	NOUN
ejpam-5573	214	3	of	of	ADP
ejpam-5573	214	4	the	the	DET
ejpam-5573	214	5	above	above	ADJ
ejpam-5573	214	6	implications	implication	NOUN
ejpam-5573	214	7	may	may	AUX
ejpam-5573	214	8	not	not	PART
ejpam-5573	214	9	be	be	AUX
ejpam-5573	214	10	true	true	ADJ
ejpam-5573	214	11	,	,	PUNCT
ejpam-5573	214	12	as	as	SCONJ
ejpam-5573	214	13	shown	show	VERB
ejpam-5573	214	14	by	by	ADP
ejpam-5573	214	15	examples	example	NOUN
ejpam-5573	214	16	7	7	NUM
ejpam-5573	214	17	and	and	CCONJ
ejpam-5573	214	18	8	8	NUM
ejpam-5573	214	19	.	.	NOUN
ejpam-5573	214	20	example	example	NOUN
ejpam-5573	215	1	7	7	NUM
ejpam-5573	215	2	.	.	PUNCT
ejpam-5573	216	1	let	let	VERB
ejpam-5573	216	2	v	v	VERB
ejpam-5573	216	3	=	=	SYM
ejpam-5573	216	4	{	{	PUNCT
ejpam-5573	216	5	v1	v1	PROPN
ejpam-5573	216	6	,	,	PUNCT
ejpam-5573	216	7	v2	v2	PROPN
ejpam-5573	216	8	,	,	PUNCT
ejpam-5573	216	9	v3	v3	PROPN
ejpam-5573	216	10	,	,	PUNCT
ejpam-5573	216	11	v4	v4	PROPN
ejpam-5573	216	12	}	}	PUNCT
ejpam-5573	216	13	and	and	CCONJ
ejpam-5573	216	14	ρ	ρ	NOUN
ejpam-5573	216	15	,	,	PUNCT
ejpam-5573	216	16	ν	ν	PROPN
ejpam-5573	216	17	∈	∈	NOUN
ejpam-5573	216	18	iv	iv	NUM
ejpam-5573	216	19	defined	define	VERB
ejpam-5573	216	20	as	as	SCONJ
ejpam-5573	216	21	follows	follow	VERB
ejpam-5573	216	22	:	:	PUNCT
ejpam-5573	216	23	ρ	ρ	PROPN
ejpam-5573	216	24	=	=	PUNCT
ejpam-5573	216	25	{	{	PUNCT
ejpam-5573	216	26	v1	v1	PROPN
ejpam-5573	216	27	0.0	0.0	NUM
ejpam-5573	216	28	,	,	PUNCT
ejpam-5573	216	29	v2	v2	PROPN
ejpam-5573	216	30	0.0	0.0	NUM
ejpam-5573	216	31	,	,	PUNCT
ejpam-5573	216	32	v3	v3	PROPN
ejpam-5573	216	33	1.0	1.0	NUM
ejpam-5573	216	34	,	,	PUNCT
ejpam-5573	216	35	v4	v4	VERB
ejpam-5573	216	36	1.0	1.0	NUM
ejpam-5573	216	37	}	}	PUNCT
ejpam-5573	216	38	and	and	CCONJ
ejpam-5573	216	39	ν	ν	X
ejpam-5573	216	40	=	=	X
ejpam-5573	216	41	{	{	PUNCT
ejpam-5573	216	42	v1	v1	PROPN
ejpam-5573	216	43	0.0	0.0	NUM
ejpam-5573	216	44	,	,	PUNCT
ejpam-5573	216	45	v2	v2	PROPN
ejpam-5573	216	46	0.0	0.0	NUM
ejpam-5573	216	47	,	,	PUNCT
ejpam-5573	216	48	v3	v3	PROPN
ejpam-5573	216	49	0.0	0.0	NUM
ejpam-5573	216	50	,	,	PUNCT
ejpam-5573	216	51	v4	v4	PROPN
ejpam-5573	216	52	1.0	1.0	NUM
ejpam-5573	216	53	}	}	PUNCT
ejpam-5573	216	54	.	.	PUNCT
ejpam-5573	217	1	define	define	VERB
ejpam-5573	217	2	η	η	PROPN
ejpam-5573	217	3	,	,	PUNCT
ejpam-5573	217	4	η∗	η∗	PROPN
ejpam-5573	217	5	,	,	PUNCT
ejpam-5573	217	6	τ	τ	X
ejpam-5573	217	7	,	,	PUNCT
ejpam-5573	217	8	τ∗	τ∗	NOUN
ejpam-5573	217	9	:	:	PUNCT
ejpam-5573	217	10	iv	iv	NUM
ejpam-5573	218	1	−→	−→	NOUN
ejpam-5573	218	2	i	i	PRON
ejpam-5573	218	3	as	as	SCONJ
ejpam-5573	218	4	follows	follow	VERB
ejpam-5573	218	5	:	:	PUNCT
ejpam-5573	218	6	η(µ	η(µ	PROPN
ejpam-5573	218	7	)	)	PUNCT
ejpam-5573	219	1	=	=	SYM
ejpam-5573	219	2			NOUN
ejpam-5573	219	3	1	1	NUM
ejpam-5573	219	4	,	,	PUNCT
ejpam-5573	219	5	if	if	SCONJ
ejpam-5573	219	6	µ	µ	X
ejpam-5573	219	7	∈	∈	X
ejpam-5573	219	8	{	{	PUNCT
ejpam-5573	219	9	0	0	NUM
ejpam-5573	219	10	,	,	PUNCT
ejpam-5573	219	11	1	1	NUM
ejpam-5573	219	12	}	}	PUNCT
ejpam-5573	219	13	,	,	PUNCT
ejpam-5573	219	14	1	1	NUM
ejpam-5573	219	15	2	2	NUM
ejpam-5573	219	16	,	,	PUNCT
ejpam-5573	219	17	if	if	SCONJ
ejpam-5573	219	18	µ	µ	X
ejpam-5573	219	19	=	=	SYM
ejpam-5573	219	20	ρ	ρ	PROPN
ejpam-5573	219	21	,	,	PUNCT
ejpam-5573	219	22	0	0	NUM
ejpam-5573	219	23	,	,	PUNCT
ejpam-5573	219	24	otherwise	otherwise	ADV
ejpam-5573	219	25	,	,	PUNCT
ejpam-5573	219	26	η∗(µ	η∗(µ	PROPN
ejpam-5573	219	27	)	)	PUNCT
ejpam-5573	219	28	=	=	SYM
ejpam-5573	220	1			NOUN
ejpam-5573	220	2	0	0	NUM
ejpam-5573	220	3	,	,	PUNCT
ejpam-5573	220	4	if	if	SCONJ
ejpam-5573	220	5	µ	µ	X
ejpam-5573	220	6	∈	∈	X
ejpam-5573	220	7	{	{	PUNCT
ejpam-5573	220	8	0	0	NUM
ejpam-5573	220	9	,	,	PUNCT
ejpam-5573	220	10	1	1	NUM
ejpam-5573	220	11	}	}	PUNCT
ejpam-5573	220	12	,	,	PUNCT
ejpam-5573	220	13	1	1	NUM
ejpam-5573	220	14	2	2	NUM
ejpam-5573	220	15	,	,	PUNCT
ejpam-5573	220	16	if	if	SCONJ
ejpam-5573	220	17	µ	µ	X
ejpam-5573	220	18	=	=	SYM
ejpam-5573	220	19	ρ	ρ	PROPN
ejpam-5573	220	20	,	,	PUNCT
ejpam-5573	220	21	1	1	NUM
ejpam-5573	220	22	,	,	PUNCT
ejpam-5573	220	23	otherwise	otherwise	ADV
ejpam-5573	220	24	,	,	PUNCT
ejpam-5573	220	25	τ(µ	τ(µ	PROPN
ejpam-5573	220	26	)	)	PUNCT
ejpam-5573	221	1	=	=	SYM
ejpam-5573	221	2			NOUN
ejpam-5573	221	3	1	1	NUM
ejpam-5573	221	4	,	,	PUNCT
ejpam-5573	221	5	if	if	SCONJ
ejpam-5573	221	6	µ	µ	X
ejpam-5573	221	7	∈	∈	X
ejpam-5573	221	8	{	{	PUNCT
ejpam-5573	221	9	0	0	NUM
ejpam-5573	221	10	,	,	PUNCT
ejpam-5573	221	11	1	1	NUM
ejpam-5573	221	12	}	}	PUNCT
ejpam-5573	221	13	,	,	PUNCT
ejpam-5573	221	14	1	1	NUM
ejpam-5573	221	15	2	2	NUM
ejpam-5573	221	16	,	,	PUNCT
ejpam-5573	221	17	if	if	SCONJ
ejpam-5573	221	18	µ	µ	X
ejpam-5573	221	19	=	=	SYM
ejpam-5573	221	20	ν	ν	NOUN
ejpam-5573	221	21	,	,	PUNCT
ejpam-5573	221	22	0	0	NUM
ejpam-5573	221	23	,	,	PUNCT
ejpam-5573	221	24	otherwise	otherwise	ADV
ejpam-5573	221	25	,	,	PUNCT
ejpam-5573	221	26	τ∗(µ	τ∗(µ	PROPN
ejpam-5573	221	27	)	)	PUNCT
ejpam-5573	221	28	=	=	SYM
ejpam-5573	222	1			NOUN
ejpam-5573	222	2	0	0	NUM
ejpam-5573	222	3	,	,	PUNCT
ejpam-5573	222	4	if	if	SCONJ
ejpam-5573	222	5	µ	µ	X
ejpam-5573	222	6	∈	∈	X
ejpam-5573	222	7	{	{	PUNCT
ejpam-5573	222	8	0	0	NUM
ejpam-5573	222	9	,	,	PUNCT
ejpam-5573	222	10	1	1	NUM
ejpam-5573	222	11	}	}	PUNCT
ejpam-5573	222	12	,	,	PUNCT
ejpam-5573	222	13	1	1	NUM
ejpam-5573	222	14	2	2	NUM
ejpam-5573	222	15	,	,	PUNCT
ejpam-5573	222	16	if	if	SCONJ
ejpam-5573	222	17	µ	µ	X
ejpam-5573	222	18	=	=	SYM
ejpam-5573	222	19	ν	ν	NOUN
ejpam-5573	222	20	,	,	PUNCT
ejpam-5573	222	21	1	1	NUM
ejpam-5573	222	22	,	,	PUNCT
ejpam-5573	222	23	otherwise	otherwise	ADV
ejpam-5573	222	24	.	.	PUNCT
ejpam-5573	223	1	thus	thus	ADV
ejpam-5573	223	2	,	,	PUNCT
ejpam-5573	223	3	the	the	DET
ejpam-5573	223	4	identity	identity	NOUN
ejpam-5573	223	5	mapping	mapping	NOUN
ejpam-5573	223	6	idv	idv	NOUN
ejpam-5573	223	7	:	:	PUNCT
ejpam-5573	223	8	(	(	PUNCT
ejpam-5573	223	9	v	v	NOUN
ejpam-5573	223	10	,	,	PUNCT
ejpam-5573	223	11	η	η	NOUN
ejpam-5573	223	12	,	,	PUNCT
ejpam-5573	223	13	η∗	η∗	NOUN
ejpam-5573	223	14	)	)	PUNCT
ejpam-5573	223	15	→	→	SYM
ejpam-5573	223	16	(	(	PUNCT
ejpam-5573	223	17	v	v	NOUN
ejpam-5573	223	18	,	,	PUNCT
ejpam-5573	223	19	τ	τ	PROPN
ejpam-5573	223	20	,	,	PUNCT
ejpam-5573	223	21	τ∗	τ∗	NOUN
ejpam-5573	223	22	)	)	PUNCT
ejpam-5573	223	23	is	be	AUX
ejpam-5573	223	24	s∗dfgs	s∗dfg	VERB
ejpam-5573	223	25	-	-	PUNCT
ejpam-5573	223	26	continuous	continuous	ADJ
ejpam-5573	223	27	,	,	PUNCT
ejpam-5573	223	28	but	but	CCONJ
ejpam-5573	223	29	it	it	PRON
ejpam-5573	223	30	is	be	AUX
ejpam-5573	223	31	not	not	PART
ejpam-5573	223	32	dfs	dfs	ADJ
ejpam-5573	223	33	-	-	PUNCT
ejpam-5573	223	34	continuous	continuous	ADJ
ejpam-5573	223	35	.	.	PUNCT
ejpam-5573	223	36	example	example	NOUN
ejpam-5573	223	37	8	8	NUM
ejpam-5573	223	38	.	.	PUNCT
ejpam-5573	224	1	let	let	VERB
ejpam-5573	224	2	v	v	VERB
ejpam-5573	224	3	=	=	SYM
ejpam-5573	224	4	{	{	PUNCT
ejpam-5573	224	5	v1	v1	PROPN
ejpam-5573	224	6	,	,	PUNCT
ejpam-5573	224	7	v2	v2	PROPN
ejpam-5573	224	8	,	,	PUNCT
ejpam-5573	224	9	v3	v3	PROPN
ejpam-5573	224	10	}	}	PUNCT
ejpam-5573	224	11	and	and	CCONJ
ejpam-5573	224	12	µ1	µ1	PROPN
ejpam-5573	224	13	,	,	PUNCT
ejpam-5573	224	14	µ2	µ2	PROPN
ejpam-5573	224	15	,	,	PUNCT
ejpam-5573	224	16	µ3	µ3	NOUN
ejpam-5573	224	17	∈	∈	NOUN
ejpam-5573	224	18	iv	iv	NUM
ejpam-5573	224	19	defined	define	VERB
ejpam-5573	224	20	as	as	SCONJ
ejpam-5573	224	21	follows	follow	VERB
ejpam-5573	224	22	:	:	PUNCT
ejpam-5573	224	23	µ1	µ1	PROPN
ejpam-5573	224	24	=	=	NOUN
ejpam-5573	224	25	{	{	PUNCT
ejpam-5573	224	26	v1	v1	PROPN
ejpam-5573	224	27	0.0	0.0	NUM
ejpam-5573	224	28	,	,	PUNCT
ejpam-5573	224	29	v2	v2	PROPN
ejpam-5573	224	30	0.0	0.0	NUM
ejpam-5573	224	31	,	,	PUNCT
ejpam-5573	224	32	v3	v3	PROPN
ejpam-5573	224	33	1.0	1.0	NUM
ejpam-5573	224	34	}	}	PUNCT
ejpam-5573	224	35	,	,	PUNCT
ejpam-5573	224	36	µ2	µ2	PROPN
ejpam-5573	224	37	=	=	PUNCT
ejpam-5573	224	38	{	{	PUNCT
ejpam-5573	224	39	v1	v1	PROPN
ejpam-5573	224	40	1.0	1.0	NUM
ejpam-5573	224	41	,	,	PUNCT
ejpam-5573	224	42	v2	v2	PROPN
ejpam-5573	224	43	1.0	1.0	NUM
ejpam-5573	224	44	,	,	PUNCT
ejpam-5573	224	45	v3	v3	PROPN
ejpam-5573	224	46	0.0	0.0	NUM
ejpam-5573	224	47	}	}	PUNCT
ejpam-5573	224	48	and	and	CCONJ
ejpam-5573	224	49	µ3	µ3	NOUN
ejpam-5573	224	50	=	=	SYM
ejpam-5573	224	51	{	{	PUNCT
ejpam-5573	224	52	v1	v1	PROPN
ejpam-5573	224	53	0.0	0.0	NUM
ejpam-5573	224	54	,	,	PUNCT
ejpam-5573	224	55	v2	v2	PROPN
ejpam-5573	224	56	1.0	1.0	NUM
ejpam-5573	224	57	,	,	PUNCT
ejpam-5573	224	58	v3	v3	PROPN
ejpam-5573	224	59	1.0	1.0	NUM
ejpam-5573	224	60	}	}	PUNCT
ejpam-5573	224	61	.	.	PUNCT
ejpam-5573	225	1	define	define	VERB
ejpam-5573	225	2	η	η	PROPN
ejpam-5573	225	3	,	,	PUNCT
ejpam-5573	225	4	η∗	η∗	PROPN
ejpam-5573	225	5	,	,	PUNCT
ejpam-5573	225	6	τ	τ	X
ejpam-5573	225	7	,	,	PUNCT
ejpam-5573	225	8	τ∗	τ∗	NOUN
ejpam-5573	225	9	:	:	PUNCT
ejpam-5573	225	10	iv	iv	NUM
ejpam-5573	226	1	−→	−→	NOUN
ejpam-5573	226	2	i	i	PRON
ejpam-5573	226	3	as	as	SCONJ
ejpam-5573	226	4	follows	follow	VERB
ejpam-5573	226	5	:	:	PUNCT
ejpam-5573	226	6	η(µ	η(µ	PROPN
ejpam-5573	226	7	)	)	PUNCT
ejpam-5573	227	1	=	=	SYM
ejpam-5573	227	2			NOUN
ejpam-5573	227	3	1	1	NUM
ejpam-5573	227	4	,	,	PUNCT
ejpam-5573	227	5	if	if	SCONJ
ejpam-5573	227	6	µ	µ	X
ejpam-5573	227	7	∈	∈	X
ejpam-5573	227	8	{	{	PUNCT
ejpam-5573	227	9	0	0	NUM
ejpam-5573	227	10	,	,	PUNCT
ejpam-5573	227	11	1	1	NUM
ejpam-5573	227	12	}	}	PUNCT
ejpam-5573	227	13	,	,	PUNCT
ejpam-5573	227	14	1	1	NUM
ejpam-5573	227	15	2	2	NUM
ejpam-5573	227	16	,	,	PUNCT
ejpam-5573	227	17	if	if	SCONJ
ejpam-5573	227	18	µ	µ	X
ejpam-5573	227	19	∈	∈	X
ejpam-5573	227	20	{	{	PUNCT
ejpam-5573	227	21	µ1	µ1	PROPN
ejpam-5573	227	22	,	,	PUNCT
ejpam-5573	227	23	µ2	µ2	PROPN
ejpam-5573	227	24	}	}	PUNCT
ejpam-5573	227	25	,	,	PUNCT
ejpam-5573	227	26	0	0	NUM
ejpam-5573	227	27	,	,	PUNCT
ejpam-5573	227	28	otherwise	otherwise	ADV
ejpam-5573	227	29	,	,	PUNCT
ejpam-5573	227	30	η∗(µ	η∗(µ	PROPN
ejpam-5573	227	31	)	)	PUNCT
ejpam-5573	227	32	=	=	SYM
ejpam-5573	228	1			NOUN
ejpam-5573	228	2	0	0	NUM
ejpam-5573	228	3	,	,	PUNCT
ejpam-5573	228	4	if	if	SCONJ
ejpam-5573	228	5	µ	µ	X
ejpam-5573	228	6	∈	∈	X
ejpam-5573	228	7	{	{	PUNCT
ejpam-5573	228	8	0	0	NUM
ejpam-5573	228	9	,	,	PUNCT
ejpam-5573	228	10	1	1	NUM
ejpam-5573	228	11	}	}	PUNCT
ejpam-5573	228	12	,	,	PUNCT
ejpam-5573	228	13	1	1	NUM
ejpam-5573	228	14	2	2	NUM
ejpam-5573	228	15	,	,	PUNCT
ejpam-5573	228	16	if	if	SCONJ
ejpam-5573	228	17	µ	µ	X
ejpam-5573	228	18	∈	∈	X
ejpam-5573	228	19	{	{	PUNCT
ejpam-5573	228	20	µ1	µ1	PROPN
ejpam-5573	228	21	,	,	PUNCT
ejpam-5573	228	22	µ2	µ2	PROPN
ejpam-5573	228	23	}	}	PUNCT
ejpam-5573	228	24	,	,	PUNCT
ejpam-5573	228	25	1	1	NUM
ejpam-5573	228	26	,	,	PUNCT
ejpam-5573	228	27	otherwise	otherwise	ADV
ejpam-5573	228	28	,	,	PUNCT
ejpam-5573	228	29	τ(µ	τ(µ	PROPN
ejpam-5573	228	30	)	)	PUNCT
ejpam-5573	229	1	=	=	SYM
ejpam-5573	229	2			NOUN
ejpam-5573	229	3	1	1	NUM
ejpam-5573	229	4	,	,	PUNCT
ejpam-5573	229	5	if	if	SCONJ
ejpam-5573	229	6	µ	µ	X
ejpam-5573	229	7	∈	∈	X
ejpam-5573	229	8	{	{	PUNCT
ejpam-5573	229	9	0	0	NUM
ejpam-5573	229	10	,	,	PUNCT
ejpam-5573	229	11	1	1	NUM
ejpam-5573	229	12	}	}	PUNCT
ejpam-5573	229	13	,	,	PUNCT
ejpam-5573	229	14	1	1	NUM
ejpam-5573	229	15	2	2	NUM
ejpam-5573	229	16	,	,	PUNCT
ejpam-5573	229	17	if	if	SCONJ
ejpam-5573	229	18	µ	µ	X
ejpam-5573	229	19	=	=	SYM
ejpam-5573	229	20	µ3	µ3	NOUN
ejpam-5573	229	21	,	,	PUNCT
ejpam-5573	229	22	0	0	NUM
ejpam-5573	229	23	,	,	PUNCT
ejpam-5573	229	24	otherwise	otherwise	ADV
ejpam-5573	229	25	,	,	PUNCT
ejpam-5573	229	26	τ∗(µ	τ∗(µ	PROPN
ejpam-5573	229	27	)	)	PUNCT
ejpam-5573	229	28	=	=	SYM
ejpam-5573	230	1			NOUN
ejpam-5573	230	2	0	0	NUM
ejpam-5573	230	3	,	,	PUNCT
ejpam-5573	230	4	if	if	SCONJ
ejpam-5573	230	5	µ	µ	X
ejpam-5573	230	6	∈	∈	X
ejpam-5573	230	7	{	{	PUNCT
ejpam-5573	230	8	0	0	NUM
ejpam-5573	230	9	,	,	PUNCT
ejpam-5573	230	10	1	1	NUM
ejpam-5573	230	11	}	}	PUNCT
ejpam-5573	230	12	,	,	PUNCT
ejpam-5573	230	13	1	1	NUM
ejpam-5573	230	14	2	2	NUM
ejpam-5573	230	15	,	,	PUNCT
ejpam-5573	230	16	if	if	SCONJ
ejpam-5573	230	17	µ	µ	X
ejpam-5573	230	18	=	=	SYM
ejpam-5573	230	19	µ3	µ3	NOUN
ejpam-5573	230	20	,	,	PUNCT
ejpam-5573	230	21	1	1	NUM
ejpam-5573	230	22	,	,	PUNCT
ejpam-5573	230	23	otherwise	otherwise	ADV
ejpam-5573	230	24	.	.	PUNCT
ejpam-5573	231	1	thus	thus	ADV
ejpam-5573	231	2	,	,	PUNCT
ejpam-5573	231	3	the	the	DET
ejpam-5573	231	4	identity	identity	NOUN
ejpam-5573	231	5	mapping	mapping	NOUN
ejpam-5573	231	6	idv	idv	NOUN
ejpam-5573	231	7	:	:	PUNCT
ejpam-5573	231	8	(	(	PUNCT
ejpam-5573	231	9	v	v	NOUN
ejpam-5573	231	10	,	,	PUNCT
ejpam-5573	231	11	η	η	NOUN
ejpam-5573	231	12	,	,	PUNCT
ejpam-5573	231	13	η∗)→	η∗)→	PROPN
ejpam-5573	231	14	(	(	PUNCT
ejpam-5573	231	15	v	v	PROPN
ejpam-5573	231	16	,	,	PUNCT
ejpam-5573	231	17	τ	τ	PROPN
ejpam-5573	231	18	,	,	PUNCT
ejpam-5573	231	19	τ∗	τ∗	NOUN
ejpam-5573	231	20	)	)	PUNCT
ejpam-5573	231	21	is	be	AUX
ejpam-5573	231	22	dfgs	dfgs	NOUN
ejpam-5573	231	23	-	-	PUNCT
ejpam-5573	231	24	continuous	continuous	ADJ
ejpam-5573	231	25	,	,	PUNCT
ejpam-5573	231	26	but	but	CCONJ
ejpam-5573	231	27	it	it	PRON
ejpam-5573	231	28	is	be	AUX
ejpam-5573	231	29	not	not	PART
ejpam-5573	231	30	s∗dfgs	s∗dfg	VERB
ejpam-5573	231	31	-	-	PUNCT
ejpam-5573	231	32	continuous	continuous	ADJ
ejpam-5573	231	33	.	.	PUNCT
ejpam-5573	232	1	lemma	lemma	PROPN
ejpam-5573	232	2	2	2	NUM
ejpam-5573	232	3	.	.	PUNCT
ejpam-5573	233	1	every	every	DET
ejpam-5573	233	2	s∗dfgs	s∗dfg	VERB
ejpam-5573	233	3	-	-	PUNCT
ejpam-5573	233	4	irresolute	irresolute	ADJ
ejpam-5573	233	5	mapping	mapping	NOUN
ejpam-5573	233	6	is	be	AUX
ejpam-5573	233	7	s∗dfgs	s∗dfgs	ADJ
ejpam-5573	233	8	-	-	PUNCT
ejpam-5573	233	9	continuous	continuous	ADJ
ejpam-5573	233	10	.	.	PUNCT
ejpam-5573	234	1	remark	remark	PROPN
ejpam-5573	234	2	8	8	NUM
ejpam-5573	234	3	.	.	PUNCT
ejpam-5573	235	1	the	the	DET
ejpam-5573	235	2	converse	converse	NOUN
ejpam-5573	235	3	of	of	ADP
ejpam-5573	235	4	lemma	lemma	PROPN
ejpam-5573	235	5	2	2	NUM
ejpam-5573	235	6	may	may	AUX
ejpam-5573	235	7	not	not	PART
ejpam-5573	235	8	be	be	AUX
ejpam-5573	235	9	true	true	ADJ
ejpam-5573	235	10	,	,	PUNCT
ejpam-5573	235	11	as	as	SCONJ
ejpam-5573	235	12	shown	show	VERB
ejpam-5573	235	13	by	by	ADP
ejpam-5573	235	14	example	example	NOUN
ejpam-5573	235	15	9	9	NUM
ejpam-5573	235	16	.	.	PUNCT
ejpam-5573	235	17	example	example	NOUN
ejpam-5573	236	1	9	9	NUM
ejpam-5573	236	2	.	.	PUNCT
ejpam-5573	237	1	let	let	VERB
ejpam-5573	237	2	v	v	VERB
ejpam-5573	237	3	=	=	SYM
ejpam-5573	237	4	{	{	PUNCT
ejpam-5573	237	5	v1	v1	NOUN
ejpam-5573	237	6	,	,	PUNCT
ejpam-5573	237	7	v2	v2	PROPN
ejpam-5573	237	8	}	}	PUNCT
ejpam-5573	237	9	.	.	PUNCT
ejpam-5573	238	1	define	define	VERB
ejpam-5573	238	2	η	η	PROPN
ejpam-5573	238	3	,	,	PUNCT
ejpam-5573	238	4	η∗	η∗	PROPN
ejpam-5573	238	5	,	,	PUNCT
ejpam-5573	238	6	τ	τ	X
ejpam-5573	238	7	,	,	PUNCT
ejpam-5573	238	8	τ∗	τ∗	NOUN
ejpam-5573	238	9	:	:	PUNCT
ejpam-5573	238	10	iv	iv	NUM
ejpam-5573	239	1	−→	−→	NOUN
ejpam-5573	239	2	i	i	PRON
ejpam-5573	239	3	as	as	SCONJ
ejpam-5573	239	4	follows	follow	VERB
ejpam-5573	239	5	:	:	PUNCT
ejpam-5573	239	6	η(ρ	η(ρ	X
ejpam-5573	239	7	)	)	PUNCT
ejpam-5573	240	1	=	=	PUNCT
ejpam-5573	240	2			NOUN
ejpam-5573	240	3	1	1	NUM
ejpam-5573	240	4	,	,	PUNCT
ejpam-5573	240	5	if	if	SCONJ
ejpam-5573	240	6	ρ	ρ	PROPN
ejpam-5573	240	7	∈	∈	PROPN
ejpam-5573	240	8	{	{	PUNCT
ejpam-5573	240	9	0	0	NUM
ejpam-5573	240	10	,	,	PUNCT
ejpam-5573	240	11	1	1	NUM
ejpam-5573	240	12	}	}	PUNCT
ejpam-5573	240	13	,	,	PUNCT
ejpam-5573	240	14	1	1	NUM
ejpam-5573	240	15	2	2	NUM
ejpam-5573	240	16	,	,	PUNCT
ejpam-5573	240	17	if	if	SCONJ
ejpam-5573	240	18	ρ	ρ	PROPN
ejpam-5573	240	19	∈	∈	PROPN
ejpam-5573	240	20	{	{	PUNCT
ejpam-5573	240	21	0.1	0.1	NUM
ejpam-5573	240	22	,	,	PUNCT
ejpam-5573	240	23	0.3	0.3	NUM
ejpam-5573	240	24	}	}	PUNCT
ejpam-5573	240	25	,	,	PUNCT
ejpam-5573	240	26	0	0	NUM
ejpam-5573	240	27	,	,	PUNCT
ejpam-5573	240	28	otherwise	otherwise	ADV
ejpam-5573	240	29	,	,	PUNCT
ejpam-5573	240	30	η∗(ρ	η∗(ρ	PROPN
ejpam-5573	240	31	)	)	PUNCT
ejpam-5573	240	32	=	=	SYM
ejpam-5573	241	1			NOUN
ejpam-5573	241	2	0	0	NUM
ejpam-5573	241	3	,	,	PUNCT
ejpam-5573	241	4	if	if	SCONJ
ejpam-5573	241	5	ρ	ρ	PROPN
ejpam-5573	241	6	∈	∈	PROPN
ejpam-5573	241	7	{	{	PUNCT
ejpam-5573	241	8	0	0	NUM
ejpam-5573	241	9	,	,	PUNCT
ejpam-5573	241	10	1	1	NUM
ejpam-5573	241	11	}	}	PUNCT
ejpam-5573	241	12	,	,	PUNCT
ejpam-5573	241	13	1	1	NUM
ejpam-5573	241	14	2	2	NUM
ejpam-5573	241	15	,	,	PUNCT
ejpam-5573	241	16	if	if	SCONJ
ejpam-5573	241	17	ρ	ρ	PROPN
ejpam-5573	241	18	∈	∈	PROPN
ejpam-5573	241	19	{	{	PUNCT
ejpam-5573	241	20	0.1	0.1	NUM
ejpam-5573	241	21	,	,	PUNCT
ejpam-5573	241	22	0.3	0.3	NUM
ejpam-5573	241	23	}	}	PUNCT
ejpam-5573	241	24	,	,	PUNCT
ejpam-5573	241	25	1	1	NUM
ejpam-5573	241	26	,	,	PUNCT
ejpam-5573	241	27	otherwise	otherwise	ADV
ejpam-5573	241	28	,	,	PUNCT
ejpam-5573	241	29	f.	f.	PROPN
ejpam-5573	241	30	alsharari	alsharari	PROPN
ejpam-5573	241	31	,	,	PUNCT
ejpam-5573	241	32	o.	o.	PROPN
ejpam-5573	241	33	m.	m.	PROPN
ejpam-5573	241	34	taha	taha	PROPN
ejpam-5573	241	35	,	,	PUNCT
ejpam-5573	241	36	i.	i.	PROPN
ejpam-5573	241	37	m.	m.	PROPN
ejpam-5573	241	38	taha	taha	PROPN
ejpam-5573	241	39	/	/	PUNCT
ejpam-5573	241	40	eur	eur	PROPN
ejpam-5573	241	41	.	.	PUNCT
ejpam-5573	242	1	j.	j.	PROPN
ejpam-5573	242	2	pure	pure	PROPN
ejpam-5573	242	3	appl	appl	PROPN
ejpam-5573	242	4	.	.	PROPN
ejpam-5573	242	5	math	math	PROPN
ejpam-5573	242	6	,	,	PUNCT
ejpam-5573	242	7	17	17	NUM
ejpam-5573	242	8	(	(	PUNCT
ejpam-5573	242	9	4	4	NUM
ejpam-5573	242	10	)	)	PUNCT
ejpam-5573	242	11	(	(	PUNCT
ejpam-5573	242	12	2024	2024	NUM
ejpam-5573	242	13	)	)	PUNCT
ejpam-5573	242	14	,	,	PUNCT
ejpam-5573	242	15	4093	4093	NUM
ejpam-5573	242	16	-	-	SYM
ejpam-5573	242	17	4111	4111	NUM
ejpam-5573	242	18	4102	4102	NUM
ejpam-5573	242	19	τ(ρ	τ(ρ	NOUN
ejpam-5573	242	20	)	)	PUNCT
ejpam-5573	243	1	=	=	PUNCT
ejpam-5573	244	1			NOUN
ejpam-5573	244	2	1	1	NUM
ejpam-5573	244	3	,	,	PUNCT
ejpam-5573	244	4	if	if	SCONJ
ejpam-5573	244	5	ρ	ρ	PROPN
ejpam-5573	244	6	∈	∈	PROPN
ejpam-5573	244	7	{	{	PUNCT
ejpam-5573	244	8	0	0	NUM
ejpam-5573	244	9	,	,	PUNCT
ejpam-5573	244	10	1	1	NUM
ejpam-5573	244	11	}	}	PUNCT
ejpam-5573	244	12	,	,	PUNCT
ejpam-5573	244	13	1	1	NUM
ejpam-5573	244	14	2	2	NUM
ejpam-5573	244	15	,	,	PUNCT
ejpam-5573	244	16	if	if	SCONJ
ejpam-5573	244	17	ρ	ρ	PROPN
ejpam-5573	244	18	=	=	SYM
ejpam-5573	244	19	0.1	0.1	NUM
ejpam-5573	244	20	,	,	PUNCT
ejpam-5573	244	21	0	0	NUM
ejpam-5573	244	22	,	,	PUNCT
ejpam-5573	244	23	otherwise	otherwise	ADV
ejpam-5573	244	24	,	,	PUNCT
ejpam-5573	244	25	τ∗(ρ	τ∗(ρ	NUM
ejpam-5573	244	26	)	)	PUNCT
ejpam-5573	245	1	=	=	SYM
ejpam-5573	246	1			NOUN
ejpam-5573	246	2	0	0	NUM
ejpam-5573	246	3	,	,	PUNCT
ejpam-5573	246	4	if	if	SCONJ
ejpam-5573	246	5	ρ	ρ	PROPN
ejpam-5573	246	6	∈	∈	PROPN
ejpam-5573	246	7	{	{	PUNCT
ejpam-5573	246	8	0	0	NUM
ejpam-5573	246	9	,	,	PUNCT
ejpam-5573	246	10	1	1	NUM
ejpam-5573	246	11	}	}	PUNCT
ejpam-5573	246	12	,	,	PUNCT
ejpam-5573	246	13	1	1	NUM
ejpam-5573	246	14	2	2	NUM
ejpam-5573	246	15	,	,	PUNCT
ejpam-5573	246	16	if	if	SCONJ
ejpam-5573	246	17	ρ	ρ	PROPN
ejpam-5573	246	18	=	=	SYM
ejpam-5573	246	19	0.1	0.1	NUM
ejpam-5573	246	20	,	,	PUNCT
ejpam-5573	246	21	1	1	NUM
ejpam-5573	246	22	,	,	PUNCT
ejpam-5573	246	23	otherwise	otherwise	ADV
ejpam-5573	246	24	.	.	PUNCT
ejpam-5573	247	1	thus	thus	ADV
ejpam-5573	247	2	,	,	PUNCT
ejpam-5573	247	3	the	the	DET
ejpam-5573	247	4	identity	identity	NOUN
ejpam-5573	247	5	mapping	mapping	NOUN
ejpam-5573	247	6	idv	idv	NOUN
ejpam-5573	247	7	:	:	PUNCT
ejpam-5573	247	8	(	(	PUNCT
ejpam-5573	247	9	v	v	NOUN
ejpam-5573	247	10	,	,	PUNCT
ejpam-5573	247	11	η	η	NOUN
ejpam-5573	247	12	,	,	PUNCT
ejpam-5573	247	13	η∗	η∗	NOUN
ejpam-5573	247	14	)	)	PUNCT
ejpam-5573	247	15	→	→	SYM
ejpam-5573	247	16	(	(	PUNCT
ejpam-5573	247	17	v	v	NOUN
ejpam-5573	247	18	,	,	PUNCT
ejpam-5573	247	19	τ	τ	PROPN
ejpam-5573	247	20	,	,	PUNCT
ejpam-5573	247	21	τ∗	τ∗	NOUN
ejpam-5573	247	22	)	)	PUNCT
ejpam-5573	247	23	is	be	AUX
ejpam-5573	247	24	s∗dfgs	s∗dfg	VERB
ejpam-5573	247	25	-	-	PUNCT
ejpam-5573	247	26	continuous	continuous	ADJ
ejpam-5573	247	27	,	,	PUNCT
ejpam-5573	247	28	but	but	CCONJ
ejpam-5573	247	29	it	it	PRON
ejpam-5573	247	30	is	be	AUX
ejpam-5573	247	31	not	not	PART
ejpam-5573	247	32	s∗dfgs	s∗dfg	VERB
ejpam-5573	247	33	-	-	PUNCT
ejpam-5573	247	34	irresolute	irresolute	ADJ
ejpam-5573	247	35	.	.	PUNCT
ejpam-5573	248	1	3	3	X
ejpam-5573	248	2	.	.	X
ejpam-5573	249	1	some	some	DET
ejpam-5573	249	2	novel	novel	ADJ
ejpam-5573	249	3	higher	high	ADJ
ejpam-5573	249	4	separation	separation	NOUN
ejpam-5573	249	5	axioms	axiom	NOUN
ejpam-5573	249	6	here	here	ADV
ejpam-5573	249	7	,	,	PUNCT
ejpam-5573	249	8	we	we	PRON
ejpam-5573	249	9	are	be	AUX
ejpam-5573	249	10	going	go	VERB
ejpam-5573	249	11	to	to	PART
ejpam-5573	249	12	give	give	VERB
ejpam-5573	249	13	the	the	DET
ejpam-5573	249	14	definitions	definition	NOUN
ejpam-5573	249	15	of	of	ADP
ejpam-5573	249	16	two	two	NUM
ejpam-5573	249	17	types	type	NOUN
ejpam-5573	249	18	of	of	ADP
ejpam-5573	249	19	higher	high	ADJ
ejpam-5573	249	20	fuzzy	fuzzy	ADJ
ejpam-5573	249	21	separation	separation	NOUN
ejpam-5573	249	22	axioms	axiom	NOUN
ejpam-5573	249	23	with	with	ADP
ejpam-5573	249	24	the	the	DET
ejpam-5573	249	25	help	help	NOUN
ejpam-5573	249	26	of	of	ADP
ejpam-5573	249	27	(	(	PUNCT
ejpam-5573	249	28	r	r	NOUN
ejpam-5573	249	29	,	,	PUNCT
ejpam-5573	249	30	s)−	s)−	PROPN
ejpam-5573	249	31	gfsc	gfsc	PROPN
ejpam-5573	249	32	sets	set	VERB
ejpam-5573	249	33	[	[	X
ejpam-5573	249	34	42	42	NUM
ejpam-5573	249	35	]	]	PUNCT
ejpam-5573	249	36	called	call	VERB
ejpam-5573	249	37	(	(	PUNCT
ejpam-5573	249	38	r	r	NOUN
ejpam-5573	249	39	,	,	PUNCT
ejpam-5573	249	40	s)-gfs	s)-gf	NOUN
ejpam-5573	249	41	-	-	PUNCT
ejpam-5573	249	42	regular	regular	ADJ
ejpam-5573	249	43	⟨resp	⟨resp	NOUN
ejpam-5573	249	44	.	.	PROPN
ejpam-5573	249	45	,	,	PUNCT
ejpam-5573	249	46	(	(	PUNCT
ejpam-5573	249	47	r	r	NOUN
ejpam-5573	249	48	,	,	PUNCT
ejpam-5573	249	49	s)-gfs	s)-gf	NOUN
ejpam-5573	249	50	-	-	PUNCT
ejpam-5573	249	51	normal⟩	normal⟩	ADJ
ejpam-5573	249	52	spaces	space	NOUN
ejpam-5573	249	53	and	and	CCONJ
ejpam-5573	249	54	establish	establish	VERB
ejpam-5573	249	55	some	some	PRON
ejpam-5573	249	56	of	of	ADP
ejpam-5573	249	57	their	their	PRON
ejpam-5573	249	58	properties	property	NOUN
ejpam-5573	249	59	.	.	PUNCT
ejpam-5573	250	1	definition	definition	NOUN
ejpam-5573	250	2	8	8	NUM
ejpam-5573	250	3	.	.	PUNCT
ejpam-5573	251	1	a	a	DET
ejpam-5573	251	2	dfts	dft	NOUN
ejpam-5573	251	3	(	(	PUNCT
ejpam-5573	251	4	u	u	NOUN
ejpam-5573	251	5	,	,	PUNCT
ejpam-5573	251	6	η	η	PROPN
ejpam-5573	251	7	,	,	PUNCT
ejpam-5573	251	8	η∗	η∗	NOUN
ejpam-5573	251	9	)	)	PUNCT
ejpam-5573	251	10	is	be	AUX
ejpam-5573	251	11	said	say	VERB
ejpam-5573	251	12	to	to	PART
ejpam-5573	251	13	be	be	AUX
ejpam-5573	251	14	(	(	PUNCT
ejpam-5573	251	15	i	i	NOUN
ejpam-5573	251	16	)	)	PUNCT
ejpam-5573	251	17	(	(	PUNCT
ejpam-5573	251	18	r	r	NOUN
ejpam-5573	251	19	,	,	PUNCT
ejpam-5573	251	20	s)-gfs	s)-gf	NOUN
ejpam-5573	251	21	-	-	PUNCT
ejpam-5573	251	22	regular	regular	ADJ
ejpam-5573	251	23	iff	iff	PROPN
ejpam-5573	251	24	utqµ	utqµ	NOUN
ejpam-5573	251	25	for	for	ADP
ejpam-5573	251	26	each	each	DET
ejpam-5573	251	27	µ	µ	PROPN
ejpam-5573	251	28	∈	∈	NOUN
ejpam-5573	251	29	iu	iu	ADV
ejpam-5573	251	30	is	be	AUX
ejpam-5573	251	31	(	(	PUNCT
ejpam-5573	251	32	r	r	NOUN
ejpam-5573	251	33	,	,	PUNCT
ejpam-5573	251	34	s)−	s)−	PROPN
ejpam-5573	251	35	gfsc	gfsc	PROPN
ejpam-5573	251	36	set	set	PROPN
ejpam-5573	251	37	implies	imply	VERB
ejpam-5573	251	38	that	that	SCONJ
ejpam-5573	251	39	,	,	PUNCT
ejpam-5573	251	40	there	there	PRON
ejpam-5573	251	41	is	be	VERB
ejpam-5573	251	42	νδ	νδ	ADJ
ejpam-5573	251	43	∈	∈	PROPN
ejpam-5573	251	44	iu	iu	ADP
ejpam-5573	251	45	with	with	ADP
ejpam-5573	251	46	η(νδ	η(νδ	NUM
ejpam-5573	251	47	)	)	PUNCT
ejpam-5573	251	48	≥	≥	NOUN
ejpam-5573	251	49	r	r	NOUN
ejpam-5573	251	50	,	,	PUNCT
ejpam-5573	251	51	η∗(νδ	η∗(νδ	NOUN
ejpam-5573	251	52	)	)	PUNCT
ejpam-5573	251	53	≤	≤	NUM
ejpam-5573	251	54	s	s	VERB
ejpam-5573	251	55	for	for	ADP
ejpam-5573	251	56	δ	δ	PROPN
ejpam-5573	251	57	∈	∈	PROPN
ejpam-5573	251	58	{	{	PUNCT
ejpam-5573	251	59	1	1	NUM
ejpam-5573	251	60	,	,	PUNCT
ejpam-5573	251	61	2	2	NUM
ejpam-5573	251	62	}	}	PUNCT
ejpam-5573	251	63	,	,	PUNCT
ejpam-5573	251	64	such	such	ADJ
ejpam-5573	251	65	that	that	SCONJ
ejpam-5573	251	66	ut	ut	PROPN
ejpam-5573	251	67	∈	∈	PROPN
ejpam-5573	251	68	ν1	ν1	NOUN
ejpam-5573	251	69	,	,	PUNCT
ejpam-5573	251	70	µ	µ	NOUN
ejpam-5573	251	71	≤	≤	NOUN
ejpam-5573	251	72	ν2	ν2	NOUN
ejpam-5573	251	73	and	and	CCONJ
ejpam-5573	251	74	ν1qν2	ν1qν2	NOUN
ejpam-5573	251	75	.	.	PUNCT
ejpam-5573	252	1	(	(	PUNCT
ejpam-5573	252	2	ii	ii	NOUN
ejpam-5573	252	3	)	)	PUNCT
ejpam-5573	252	4	(	(	PUNCT
ejpam-5573	252	5	r	r	NOUN
ejpam-5573	252	6	,	,	PUNCT
ejpam-5573	252	7	s)-gfs	s)-gf	NOUN
ejpam-5573	252	8	-	-	PUNCT
ejpam-5573	252	9	normal	normal	ADJ
ejpam-5573	252	10	iff	iff	PROPN
ejpam-5573	252	11	µ1qµ2	µ1qµ2	NOUN
ejpam-5573	252	12	for	for	ADP
ejpam-5573	252	13	each	each	DET
ejpam-5573	252	14	(	(	PUNCT
ejpam-5573	252	15	r	r	NOUN
ejpam-5573	252	16	,	,	PUNCT
ejpam-5573	252	17	s)−gfsc	s)−gfsc	PRON
ejpam-5573	252	18	sets	set	VERB
ejpam-5573	252	19	µδ	µδ	ADP
ejpam-5573	252	20	∈	∈	NOUN
ejpam-5573	252	21	iu	iu	ADP
ejpam-5573	252	22	for	for	ADP
ejpam-5573	252	23	δ	δ	PROPN
ejpam-5573	252	24	∈	∈	PROPN
ejpam-5573	252	25	{	{	PUNCT
ejpam-5573	252	26	1	1	NUM
ejpam-5573	252	27	,	,	PUNCT
ejpam-5573	252	28	2	2	NUM
ejpam-5573	252	29	}	}	PUNCT
ejpam-5573	252	30	implies	imply	VERB
ejpam-5573	252	31	that	that	SCONJ
ejpam-5573	252	32	,	,	PUNCT
ejpam-5573	252	33	there	there	PRON
ejpam-5573	252	34	is	be	VERB
ejpam-5573	252	35	νδ	νδ	ADJ
ejpam-5573	252	36	∈	∈	PROPN
ejpam-5573	252	37	iu	iu	ADP
ejpam-5573	252	38	with	with	ADP
ejpam-5573	252	39	η(νδ	η(νδ	NUM
ejpam-5573	252	40	)	)	PUNCT
ejpam-5573	252	41	≥	≥	NOUN
ejpam-5573	252	42	r	r	NOUN
ejpam-5573	252	43	and	and	CCONJ
ejpam-5573	252	44	η∗(νδ	η∗(νδ	NOUN
ejpam-5573	252	45	)	)	PUNCT
ejpam-5573	252	46	≤	≤	NOUN
ejpam-5573	252	47	s	s	NOUN
ejpam-5573	252	48	,	,	PUNCT
ejpam-5573	252	49	such	such	ADJ
ejpam-5573	252	50	that	that	SCONJ
ejpam-5573	252	51	µδ	µδ	VERB
ejpam-5573	252	52	≤	≤	NUM
ejpam-5573	252	53	νδ	νδ	NOUN
ejpam-5573	252	54	and	and	CCONJ
ejpam-5573	252	55	ν1qν2	ν1qν2	NOUN
ejpam-5573	252	56	.	.	PUNCT
ejpam-5573	253	1	theorem	theorem	VERB
ejpam-5573	253	2	4	4	NUM
ejpam-5573	253	3	.	.	PUNCT
ejpam-5573	254	1	let	let	AUX
ejpam-5573	254	2	(	(	PUNCT
ejpam-5573	254	3	u	u	NOUN
ejpam-5573	254	4	,	,	PUNCT
ejpam-5573	254	5	η	η	PROPN
ejpam-5573	254	6	,	,	PUNCT
ejpam-5573	254	7	η∗	η∗	NOUN
ejpam-5573	254	8	)	)	PUNCT
ejpam-5573	254	9	be	be	VERB
ejpam-5573	254	10	a	a	DET
ejpam-5573	254	11	dfts	dft	NOUN
ejpam-5573	254	12	,	,	PUNCT
ejpam-5573	254	13	r	r	NOUN
ejpam-5573	254	14	∈	∈	PROPN
ejpam-5573	254	15	i	i	NOUN
ejpam-5573	254	16	◦	◦	NOUN
ejpam-5573	254	17	,	,	PUNCT
ejpam-5573	254	18	and	and	CCONJ
ejpam-5573	254	19	s	s	PROPN
ejpam-5573	254	20	∈	∈	PROPN
ejpam-5573	254	21	i1	i1	PROPN
ejpam-5573	254	22	,	,	PUNCT
ejpam-5573	254	23	then	then	ADV
ejpam-5573	254	24	the	the	DET
ejpam-5573	254	25	following	following	ADJ
ejpam-5573	254	26	statements	statement	NOUN
ejpam-5573	254	27	are	be	AUX
ejpam-5573	254	28	equivalent	equivalent	ADJ
ejpam-5573	254	29	.	.	PUNCT
ejpam-5573	255	1	(	(	PUNCT
ejpam-5573	255	2	i	i	NOUN
ejpam-5573	255	3	)	)	PUNCT
ejpam-5573	255	4	(	(	PUNCT
ejpam-5573	255	5	u	u	NOUN
ejpam-5573	255	6	,	,	PUNCT
ejpam-5573	255	7	η	η	PROPN
ejpam-5573	255	8	,	,	PUNCT
ejpam-5573	255	9	η∗	η∗	NOUN
ejpam-5573	255	10	)	)	PUNCT
ejpam-5573	255	11	is	be	AUX
ejpam-5573	255	12	(	(	PUNCT
ejpam-5573	255	13	r	r	NOUN
ejpam-5573	255	14	,	,	PUNCT
ejpam-5573	255	15	s)-gfs	s)-gf	NOUN
ejpam-5573	255	16	-	-	PUNCT
ejpam-5573	255	17	regular	regular	ADJ
ejpam-5573	255	18	space	space	NOUN
ejpam-5573	255	19	.	.	PUNCT
ejpam-5573	256	1	(	(	PUNCT
ejpam-5573	256	2	ii	ii	NOUN
ejpam-5573	256	3	)	)	PUNCT
ejpam-5573	256	4	if	if	SCONJ
ejpam-5573	256	5	ut	ut	PROPN
ejpam-5573	256	6	∈	∈	PROPN
ejpam-5573	256	7	λ	λ	PROPN
ejpam-5573	256	8	for	for	ADP
ejpam-5573	256	9	each	each	DET
ejpam-5573	256	10	λ	λ	PROPN
ejpam-5573	256	11	∈	∈	PROPN
ejpam-5573	256	12	iu	iu	ADV
ejpam-5573	256	13	is	be	AUX
ejpam-5573	256	14	(	(	PUNCT
ejpam-5573	256	15	r	r	NOUN
ejpam-5573	256	16	,	,	PUNCT
ejpam-5573	256	17	s	s	NOUN
ejpam-5573	256	18	)	)	PUNCT
ejpam-5573	256	19	−	−	NOUN
ejpam-5573	256	20	gfso	gfso	NOUN
ejpam-5573	256	21	,	,	PUNCT
ejpam-5573	256	22	there	there	PRON
ejpam-5573	256	23	is	be	VERB
ejpam-5573	256	24	µ	µ	PRON
ejpam-5573	256	25	∈	∈	NOUN
ejpam-5573	256	26	iu	iu	ADV
ejpam-5573	256	27	with	with	ADP
ejpam-5573	256	28	η(µ	η(µ	PROPN
ejpam-5573	256	29	)	)	PUNCT
ejpam-5573	256	30	≥	≥	NOUN
ejpam-5573	256	31	r	r	NOUN
ejpam-5573	256	32	and	and	CCONJ
ejpam-5573	256	33	η∗(µ	η∗(µ	PROPN
ejpam-5573	256	34	)	)	PUNCT
ejpam-5573	256	35	≤	≤	NOUN
ejpam-5573	257	1	s	s	NOUN
ejpam-5573	257	2	,	,	PUNCT
ejpam-5573	257	3	such	such	ADJ
ejpam-5573	257	4	that	that	SCONJ
ejpam-5573	257	5	ut	ut	PROPN
ejpam-5573	257	6	∈	∈	PROPN
ejpam-5573	257	7	µ	µ	PROPN
ejpam-5573	257	8	≤	≤	X
ejpam-5573	257	9	cη	cη	ADP
ejpam-5573	257	10	,	,	PUNCT
ejpam-5573	257	11	η∗(µ	η∗(µ	PROPN
ejpam-5573	257	12	,	,	PUNCT
ejpam-5573	257	13	r	r	NOUN
ejpam-5573	257	14	,	,	PUNCT
ejpam-5573	257	15	s	s	NOUN
ejpam-5573	257	16	)	)	PUNCT
ejpam-5573	257	17	≤	≤	NUM
ejpam-5573	257	18	λ	λ	PROPN
ejpam-5573	257	19	.	.	PUNCT
ejpam-5573	257	20	(	(	PUNCT
ejpam-5573	257	21	iii	iii	X
ejpam-5573	257	22	)	)	PUNCT
ejpam-5573	257	23	if	if	SCONJ
ejpam-5573	257	24	utqλ	utqλ	VERB
ejpam-5573	257	25	for	for	ADP
ejpam-5573	257	26	each	each	DET
ejpam-5573	257	27	λ	λ	PROPN
ejpam-5573	257	28	∈	∈	PROPN
ejpam-5573	257	29	iu	iu	ADV
ejpam-5573	257	30	is	be	AUX
ejpam-5573	257	31	(	(	PUNCT
ejpam-5573	257	32	r	r	NOUN
ejpam-5573	257	33	,	,	PUNCT
ejpam-5573	257	34	s)−gfsc	s)−gfsc	PROPN
ejpam-5573	257	35	,	,	PUNCT
ejpam-5573	257	36	there	there	PRON
ejpam-5573	257	37	is	be	VERB
ejpam-5573	257	38	µδ	µδ	PRON
ejpam-5573	257	39	∈	∈	NOUN
ejpam-5573	257	40	iu	iu	ADP
ejpam-5573	257	41	with	with	ADP
ejpam-5573	257	42	η(µδ	η(µδ	PROPN
ejpam-5573	257	43	)	)	PUNCT
ejpam-5573	257	44	≥	≥	NOUN
ejpam-5573	257	45	r	r	NOUN
ejpam-5573	257	46	,	,	PUNCT
ejpam-5573	257	47	η∗(µδ	η∗(µδ	PROPN
ejpam-5573	257	48	)	)	PUNCT
ejpam-5573	257	49	≤	≤	NOUN
ejpam-5573	257	50	s	s	PART
ejpam-5573	257	51	for	for	ADP
ejpam-5573	257	52	δ	δ	PROPN
ejpam-5573	257	53	∈	∈	PROPN
ejpam-5573	257	54	{	{	PUNCT
ejpam-5573	257	55	1	1	NUM
ejpam-5573	257	56	,	,	PUNCT
ejpam-5573	257	57	2	2	NUM
ejpam-5573	257	58	}	}	PUNCT
ejpam-5573	257	59	,	,	PUNCT
ejpam-5573	257	60	such	such	ADJ
ejpam-5573	257	61	that	that	SCONJ
ejpam-5573	257	62	ut	ut	PROPN
ejpam-5573	257	63	∈	∈	PROPN
ejpam-5573	257	64	µ1	µ1	PROPN
ejpam-5573	257	65	,	,	PUNCT
ejpam-5573	257	66	λ	λ	PROPN
ejpam-5573	257	67	≤	≤	X
ejpam-5573	257	68	µ2	µ2	PROPN
ejpam-5573	257	69	and	and	CCONJ
ejpam-5573	257	70	cη	cη	NOUN
ejpam-5573	257	71	,	,	PUNCT
ejpam-5573	257	72	η∗(µ1	η∗(µ1	NOUN
ejpam-5573	257	73	,	,	PUNCT
ejpam-5573	257	74	r	r	NOUN
ejpam-5573	257	75	,	,	PUNCT
ejpam-5573	257	76	s)qcη	s)qcη	PROPN
ejpam-5573	257	77	,	,	PUNCT
ejpam-5573	257	78	η∗(µ2	η∗(µ2	PROPN
ejpam-5573	257	79	,	,	PUNCT
ejpam-5573	257	80	r	r	NOUN
ejpam-5573	257	81	,	,	PUNCT
ejpam-5573	257	82	s	s	NOUN
ejpam-5573	257	83	)	)	PUNCT
ejpam-5573	257	84	.	.	PUNCT
ejpam-5573	258	1	proof	proof	NOUN
ejpam-5573	258	2	.	.	PUNCT
ejpam-5573	259	1	(	(	PUNCT
ejpam-5573	259	2	i)⇒	i)⇒	PROPN
ejpam-5573	259	3	(	(	PUNCT
ejpam-5573	259	4	ii	ii	NOUN
ejpam-5573	259	5	)	)	PUNCT
ejpam-5573	259	6	let	let	VERB
ejpam-5573	259	7	ut	ut	PROPN
ejpam-5573	259	8	∈	∈	PROPN
ejpam-5573	259	9	λ	λ	PROPN
ejpam-5573	259	10	for	for	ADP
ejpam-5573	259	11	each	each	DET
ejpam-5573	259	12	λ	λ	PROPN
ejpam-5573	259	13	∈	∈	PROPN
ejpam-5573	259	14	iu	iu	ADV
ejpam-5573	259	15	is	be	AUX
ejpam-5573	259	16	an	an	DET
ejpam-5573	259	17	(	(	PUNCT
ejpam-5573	259	18	r	r	NOUN
ejpam-5573	259	19	,	,	PUNCT
ejpam-5573	259	20	s)−gfso	s)−gfso	PROPN
ejpam-5573	259	21	,	,	PUNCT
ejpam-5573	259	22	then	then	ADV
ejpam-5573	259	23	utqλ	utqλ	PROPN
ejpam-5573	259	24	c	c	PROPN
ejpam-5573	259	25	for	for	ADP
ejpam-5573	259	26	(	(	PUNCT
ejpam-5573	259	27	r	r	NOUN
ejpam-5573	259	28	,	,	PUNCT
ejpam-5573	259	29	s)−gfsc	s)−gfsc	PROPN
ejpam-5573	259	30	set	set	VERB
ejpam-5573	259	31	λc	λc	INTJ
ejpam-5573	259	32	.	.	PUNCT
ejpam-5573	260	1	since	since	SCONJ
ejpam-5573	260	2	(	(	PUNCT
ejpam-5573	260	3	u	u	NOUN
ejpam-5573	260	4	,	,	PUNCT
ejpam-5573	260	5	η	η	PROPN
ejpam-5573	260	6	,	,	PUNCT
ejpam-5573	260	7	η∗	η∗	NOUN
ejpam-5573	260	8	)	)	PUNCT
ejpam-5573	260	9	is	be	AUX
ejpam-5573	260	10	(	(	PUNCT
ejpam-5573	260	11	r	r	NOUN
ejpam-5573	260	12	,	,	PUNCT
ejpam-5573	260	13	s)-gfs	s)-gf	NOUN
ejpam-5573	260	14	-	-	PUNCT
ejpam-5573	260	15	regular	regular	ADJ
ejpam-5573	260	16	,	,	PUNCT
ejpam-5573	260	17	there	there	PRON
ejpam-5573	260	18	is	be	VERB
ejpam-5573	260	19	µ	µ	NUM
ejpam-5573	260	20	,	,	PUNCT
ejpam-5573	260	21	ν	ν	X
ejpam-5573	260	22	∈	∈	NOUN
ejpam-5573	260	23	iu	iu	ADV
ejpam-5573	260	24	with	with	ADP
ejpam-5573	260	25	η(µ	η(µ	PROPN
ejpam-5573	260	26	)	)	PUNCT
ejpam-5573	260	27	≥	≥	PROPN
ejpam-5573	260	28	r	r	NOUN
ejpam-5573	260	29	,	,	PUNCT
ejpam-5573	260	30	η∗(µ	η∗(µ	PROPN
ejpam-5573	260	31	)	)	PUNCT
ejpam-5573	260	32	≤	≤	PROPN
ejpam-5573	260	33	s	s	PROPN
ejpam-5573	260	34	and	and	CCONJ
ejpam-5573	260	35	η(ν	η(ν	PROPN
ejpam-5573	260	36	)	)	PUNCT
ejpam-5573	260	37	≥	≥	NOUN
ejpam-5573	260	38	r	r	NOUN
ejpam-5573	260	39	,	,	PUNCT
ejpam-5573	260	40	η∗(ν	η∗(ν	NOUN
ejpam-5573	260	41	)	)	PUNCT
ejpam-5573	260	42	≤	≤	NOUN
ejpam-5573	260	43	s	s	VERB
ejpam-5573	260	44	such	such	ADJ
ejpam-5573	260	45	that	that	SCONJ
ejpam-5573	260	46	ut	ut	PROPN
ejpam-5573	260	47	∈	∈	PROPN
ejpam-5573	260	48	µ	µ	PROPN
ejpam-5573	260	49	,	,	PUNCT
ejpam-5573	260	50	λc	λc	NOUN
ejpam-5573	260	51	≤	≤	X
ejpam-5573	260	52	ν	ν	NOUN
ejpam-5573	260	53	and	and	CCONJ
ejpam-5573	260	54	µqν	µqν	PROPN
ejpam-5573	260	55	.	.	PUNCT
ejpam-5573	261	1	it	it	PRON
ejpam-5573	261	2	implies	imply	VERB
ejpam-5573	261	3	ut	ut	PROPN
ejpam-5573	261	4	∈	∈	PROPN
ejpam-5573	261	5	µ	µ	PRON
ejpam-5573	261	6	≤	≤	NUM
ejpam-5573	261	7	νc	νc	X
ejpam-5573	261	8	≤	≤	PROPN
ejpam-5573	261	9	λ	λ	PROPN
ejpam-5573	261	10	.	.	PUNCT
ejpam-5573	262	1	since	since	SCONJ
ejpam-5573	262	2	η(ν	η(ν	PROPN
ejpam-5573	262	3	)	)	PUNCT
ejpam-5573	262	4	≥	≥	NOUN
ejpam-5573	262	5	r	r	NOUN
ejpam-5573	262	6	and	and	CCONJ
ejpam-5573	262	7	η∗(ν	η∗(ν	NOUN
ejpam-5573	262	8	)	)	PUNCT
ejpam-5573	262	9	≤	≤	NOUN
ejpam-5573	262	10	s	s	PROPN
ejpam-5573	262	11	,	,	PUNCT
ejpam-5573	262	12	ut	ut	PROPN
ejpam-5573	262	13	∈	∈	PROPN
ejpam-5573	262	14	µ	µ	PROPN
ejpam-5573	262	15	≤	≤	X
ejpam-5573	262	16	cη	cη	ADP
ejpam-5573	262	17	,	,	PUNCT
ejpam-5573	262	18	η∗(µ	η∗(µ	PROPN
ejpam-5573	262	19	,	,	PUNCT
ejpam-5573	262	20	r	r	NOUN
ejpam-5573	262	21	,	,	PUNCT
ejpam-5573	262	22	s	s	NOUN
ejpam-5573	262	23	)	)	PUNCT
ejpam-5573	262	24	≤	≤	NUM
ejpam-5573	262	25	λ	λ	PROPN
ejpam-5573	262	26	.	.	PUNCT
ejpam-5573	263	1	(	(	PUNCT
ejpam-5573	263	2	ii)⇒	ii)⇒	X
ejpam-5573	263	3	(	(	PUNCT
ejpam-5573	263	4	iii	iii	NOUN
ejpam-5573	263	5	)	)	PUNCT
ejpam-5573	263	6	let	let	VERB
ejpam-5573	263	7	utqλ	utqλ	PRON
ejpam-5573	263	8	for	for	ADP
ejpam-5573	263	9	each	each	DET
ejpam-5573	263	10	λ	λ	PROPN
ejpam-5573	263	11	∈	∈	PROPN
ejpam-5573	263	12	iu	iu	ADV
ejpam-5573	263	13	is	be	AUX
ejpam-5573	263	14	an	an	DET
ejpam-5573	263	15	(	(	PUNCT
ejpam-5573	263	16	r	r	NOUN
ejpam-5573	263	17	,	,	PUNCT
ejpam-5573	263	18	s)−gfsc	s)−gfsc	PROPN
ejpam-5573	263	19	,	,	PUNCT
ejpam-5573	263	20	then	then	ADV
ejpam-5573	263	21	ut	ut	PROPN
ejpam-5573	263	22	∈	∈	PROPN
ejpam-5573	263	23	λc	λc	X
ejpam-5573	263	24	for	for	ADP
ejpam-5573	263	25	(	(	PUNCT
ejpam-5573	263	26	r	r	NOUN
ejpam-5573	263	27	,	,	PUNCT
ejpam-5573	263	28	s)−gfso	s)−gfso	PROPN
ejpam-5573	263	29	set	set	VERB
ejpam-5573	263	30	λc	λc	INTJ
ejpam-5573	263	31	.	.	PUNCT
ejpam-5573	264	1	by	by	ADP
ejpam-5573	264	2	(	(	PUNCT
ejpam-5573	264	3	ii	ii	NOUN
ejpam-5573	264	4	)	)	PUNCT
ejpam-5573	264	5	,	,	PUNCT
ejpam-5573	264	6	there	there	PRON
ejpam-5573	264	7	is	be	VERB
ejpam-5573	264	8	µ	µ	PRON
ejpam-5573	264	9	∈	∈	NOUN
ejpam-5573	264	10	iu	iu	ADV
ejpam-5573	264	11	with	with	ADP
ejpam-5573	264	12	η(µ	η(µ	PROPN
ejpam-5573	264	13	)	)	PUNCT
ejpam-5573	264	14	≥	≥	PROPN
ejpam-5573	264	15	r	r	NOUN
ejpam-5573	264	16	,	,	PUNCT
ejpam-5573	264	17	η∗(µ	η∗(µ	PROPN
ejpam-5573	264	18	)	)	PUNCT
ejpam-5573	264	19	≤	≤	PROPN
ejpam-5573	264	20	s	s	VERB
ejpam-5573	264	21	such	such	ADJ
ejpam-5573	265	1	that	that	SCONJ
ejpam-5573	265	2	ut	ut	PROPN
ejpam-5573	265	3	∈	∈	PROPN
ejpam-5573	265	4	µ	µ	PROPN
ejpam-5573	265	5	≤	≤	X
ejpam-5573	265	6	cη	cη	ADP
ejpam-5573	265	7	,	,	PUNCT
ejpam-5573	265	8	η∗(µ	η∗(µ	PROPN
ejpam-5573	265	9	,	,	PUNCT
ejpam-5573	265	10	r	r	NOUN
ejpam-5573	265	11	,	,	PUNCT
ejpam-5573	265	12	s	s	NOUN
ejpam-5573	265	13	)	)	PUNCT
ejpam-5573	265	14	≤	≤	NUM
ejpam-5573	265	15	λc	λc	NOUN
ejpam-5573	265	16	.	.	PUNCT
ejpam-5573	266	1	since	since	SCONJ
ejpam-5573	266	2	η(µ	η(µ	PROPN
ejpam-5573	266	3	)	)	PUNCT
ejpam-5573	266	4	≥	≥	NOUN
ejpam-5573	266	5	r	r	NOUN
ejpam-5573	266	6	and	and	CCONJ
ejpam-5573	266	7	η∗(µ	η∗(µ	PROPN
ejpam-5573	266	8	)	)	PUNCT
ejpam-5573	266	9	≤	≤	PROPN
ejpam-5573	267	1	s	s	PROPN
ejpam-5573	267	2	,	,	PUNCT
ejpam-5573	267	3	then	then	ADV
ejpam-5573	267	4	µ	µ	X
ejpam-5573	267	5	is	be	AUX
ejpam-5573	267	6	(	(	PUNCT
ejpam-5573	267	7	r	r	NOUN
ejpam-5573	267	8	,	,	PUNCT
ejpam-5573	267	9	s	s	NOUN
ejpam-5573	267	10	)	)	PUNCT
ejpam-5573	267	11	−	−	NOUN
ejpam-5573	267	12	gfso	gfso	NOUN
ejpam-5573	267	13	and	and	CCONJ
ejpam-5573	267	14	ut	ut	PROPN
ejpam-5573	267	15	∈	∈	PROPN
ejpam-5573	267	16	µ.	µ.	NOUN
ejpam-5573	267	17	again	again	ADV
ejpam-5573	267	18	,	,	PUNCT
ejpam-5573	267	19	by	by	ADP
ejpam-5573	267	20	(	(	PUNCT
ejpam-5573	267	21	ii	ii	NOUN
ejpam-5573	267	22	)	)	PUNCT
ejpam-5573	267	23	,	,	PUNCT
ejpam-5573	267	24	there	there	PRON
ejpam-5573	267	25	is	be	VERB
ejpam-5573	267	26	µ1	µ1	NOUN
ejpam-5573	267	27	∈	∈	NOUN
ejpam-5573	267	28	iu	iu	ADP
ejpam-5573	267	29	with	with	ADP
ejpam-5573	267	30	η(µ1	η(µ1	NOUN
ejpam-5573	267	31	)	)	PUNCT
ejpam-5573	267	32	≥	≥	PROPN
ejpam-5573	267	33	r	r	NOUN
ejpam-5573	267	34	,	,	PUNCT
ejpam-5573	267	35	η∗(µ1	η∗(µ1	NOUN
ejpam-5573	267	36	)	)	PUNCT
ejpam-5573	267	37	≤	≤	NUM
ejpam-5573	267	38	s	s	VERB
ejpam-5573	267	39	such	such	ADJ
ejpam-5573	267	40	that	that	SCONJ
ejpam-5573	267	41	ut	ut	PROPN
ejpam-5573	267	42	∈	∈	PROPN
ejpam-5573	267	43	µ1	µ1	PROPN
ejpam-5573	267	44	≤	≤	PUNCT
ejpam-5573	267	45	cη	cη	ADP
ejpam-5573	267	46	,	,	PUNCT
ejpam-5573	267	47	η∗(µ1	η∗(µ1	NOUN
ejpam-5573	267	48	,	,	PUNCT
ejpam-5573	267	49	r	r	NOUN
ejpam-5573	267	50	,	,	PUNCT
ejpam-5573	267	51	s	s	NOUN
ejpam-5573	267	52	)	)	PUNCT
ejpam-5573	267	53	≤	≤	NUM
ejpam-5573	267	54	µ	µ	X
ejpam-5573	267	55	≤	≤	NOUN
ejpam-5573	267	56	cη	cη	ADP
ejpam-5573	267	57	,	,	PUNCT
ejpam-5573	267	58	η∗(µ	η∗(µ	PROPN
ejpam-5573	267	59	,	,	PUNCT
ejpam-5573	267	60	r	r	NOUN
ejpam-5573	267	61	,	,	PUNCT
ejpam-5573	267	62	s	s	NOUN
ejpam-5573	267	63	)	)	PUNCT
ejpam-5573	267	64	≤	≤	NUM
ejpam-5573	267	65	λc	λc	NOUN
ejpam-5573	267	66	.	.	PUNCT
ejpam-5573	267	67	f.	f.	PROPN
ejpam-5573	267	68	alsharari	alsharari	PROPN
ejpam-5573	267	69	,	,	PUNCT
ejpam-5573	267	70	o.	o.	PROPN
ejpam-5573	267	71	m.	m.	PROPN
ejpam-5573	267	72	taha	taha	PROPN
ejpam-5573	267	73	,	,	PUNCT
ejpam-5573	267	74	i.	i.	PROPN
ejpam-5573	267	75	m.	m.	PROPN
ejpam-5573	267	76	taha	taha	PROPN
ejpam-5573	267	77	/	/	PUNCT
ejpam-5573	267	78	eur	eur	PROPN
ejpam-5573	267	79	.	.	PUNCT
ejpam-5573	268	1	j.	j.	PROPN
ejpam-5573	268	2	pure	pure	PROPN
ejpam-5573	268	3	appl	appl	PROPN
ejpam-5573	268	4	.	.	PROPN
ejpam-5573	268	5	math	math	PROPN
ejpam-5573	268	6	,	,	PUNCT
ejpam-5573	268	7	17	17	NUM
ejpam-5573	268	8	(	(	PUNCT
ejpam-5573	268	9	4	4	NUM
ejpam-5573	268	10	)	)	PUNCT
ejpam-5573	268	11	(	(	PUNCT
ejpam-5573	268	12	2024	2024	NUM
ejpam-5573	268	13	)	)	PUNCT
ejpam-5573	268	14	,	,	PUNCT
ejpam-5573	268	15	4093	4093	NUM
ejpam-5573	268	16	-	-	SYM
ejpam-5573	268	17	4111	4111	NUM
ejpam-5573	268	18	4103	4103	NUM
ejpam-5573	268	19	it	it	PRON
ejpam-5573	268	20	implies	imply	VERB
ejpam-5573	268	21	λ	λ	X
ejpam-5573	268	22	≤	≤	X
ejpam-5573	268	23	(	(	PUNCT
ejpam-5573	268	24	cη	cη	INTJ
ejpam-5573	268	25	,	,	PUNCT
ejpam-5573	268	26	η∗(µ	η∗(µ	PROPN
ejpam-5573	268	27	,	,	PUNCT
ejpam-5573	268	28	r	r	NOUN
ejpam-5573	268	29	,	,	PUNCT
ejpam-5573	268	30	s	s	NOUN
ejpam-5573	268	31	)	)	PUNCT
ejpam-5573	268	32	)	)	PUNCT
ejpam-5573	269	1	c	c	NOUN
ejpam-5573	270	1	=	=	SYM
ejpam-5573	270	2	iη	iη	PROPN
ejpam-5573	270	3	,	,	PUNCT
ejpam-5573	270	4	η∗(µ	η∗(µ	PROPN
ejpam-5573	270	5	c	c	X
ejpam-5573	270	6	,	,	PUNCT
ejpam-5573	270	7	r	r	NOUN
ejpam-5573	270	8	,	,	PUNCT
ejpam-5573	270	9	s	s	NOUN
ejpam-5573	270	10	)	)	PUNCT
ejpam-5573	270	11	≤	≤	NUM
ejpam-5573	270	12	µc	µc	PROPN
ejpam-5573	270	13	.	.	PROPN
ejpam-5573	270	14	put	put	VERB
ejpam-5573	270	15	µ2	µ2	PROPN
ejpam-5573	270	16	=	=	SYM
ejpam-5573	270	17	iη	iη	PROPN
ejpam-5573	270	18	,	,	PUNCT
ejpam-5573	270	19	η∗(µ	η∗(µ	PROPN
ejpam-5573	270	20	c	c	X
ejpam-5573	270	21	,	,	PUNCT
ejpam-5573	270	22	r	r	NOUN
ejpam-5573	270	23	,	,	PUNCT
ejpam-5573	270	24	s	s	PART
ejpam-5573	270	25	)	)	PUNCT
ejpam-5573	270	26	,	,	PUNCT
ejpam-5573	270	27	then	then	ADV
ejpam-5573	270	28	η(µ2	η(µ2	NOUN
ejpam-5573	270	29	)	)	PUNCT
ejpam-5573	270	30	≥	≥	NOUN
ejpam-5573	270	31	r	r	NOUN
ejpam-5573	270	32	,	,	PUNCT
ejpam-5573	270	33	η∗(µ2	η∗(µ2	PROPN
ejpam-5573	270	34	)	)	PUNCT
ejpam-5573	270	35	≤	≤	NOUN
ejpam-5573	270	36	s.	s.	PROPN
ejpam-5573	271	1	so	so	ADV
ejpam-5573	271	2	,	,	PUNCT
ejpam-5573	271	3	cη	cη	INTJ
ejpam-5573	271	4	,	,	PUNCT
ejpam-5573	271	5	η∗(µ2	η∗(µ2	PROPN
ejpam-5573	271	6	,	,	PUNCT
ejpam-5573	271	7	r	r	NOUN
ejpam-5573	271	8	,	,	PUNCT
ejpam-5573	271	9	s	s	NOUN
ejpam-5573	271	10	)	)	PUNCT
ejpam-5573	271	11	≤	≤	NUM
ejpam-5573	271	12	µc	µc	ADP
ejpam-5573	271	13	≤	≤	NOUN
ejpam-5573	271	14	(	(	PUNCT
ejpam-5573	271	15	cη	cη	INTJ
ejpam-5573	271	16	,	,	PUNCT
ejpam-5573	271	17	η∗(µ1	η∗(µ1	NOUN
ejpam-5573	271	18	,	,	PUNCT
ejpam-5573	271	19	r	r	NOUN
ejpam-5573	271	20	,	,	PUNCT
ejpam-5573	271	21	s	s	NOUN
ejpam-5573	271	22	)	)	PUNCT
ejpam-5573	271	23	)	)	PUNCT
ejpam-5573	272	1	c	c	X
ejpam-5573	272	2	,	,	PUNCT
ejpam-5573	272	3	that	that	ADV
ejpam-5573	272	4	is	is	ADV
ejpam-5573	272	5	,	,	PUNCT
ejpam-5573	272	6	cη	cη	INTJ
ejpam-5573	272	7	,	,	PUNCT
ejpam-5573	272	8	η∗(µ1	η∗(µ1	NOUN
ejpam-5573	272	9	,	,	PUNCT
ejpam-5573	272	10	r	r	NOUN
ejpam-5573	272	11	,	,	PUNCT
ejpam-5573	272	12	s)qcη	s)qcη	PROPN
ejpam-5573	272	13	,	,	PUNCT
ejpam-5573	272	14	η∗(µ2	η∗(µ2	PROPN
ejpam-5573	272	15	,	,	PUNCT
ejpam-5573	272	16	r	r	NOUN
ejpam-5573	272	17	,	,	PUNCT
ejpam-5573	272	18	s	s	NOUN
ejpam-5573	272	19	)	)	PUNCT
ejpam-5573	272	20	.	.	PUNCT
ejpam-5573	273	1	(	(	PUNCT
ejpam-5573	273	2	iii	iii	X
ejpam-5573	273	3	)	)	PUNCT
ejpam-5573	273	4	⇒	⇒	NOUN
ejpam-5573	273	5	(	(	PUNCT
ejpam-5573	273	6	i	i	NOUN
ejpam-5573	273	7	)	)	PUNCT
ejpam-5573	273	8	it	it	PRON
ejpam-5573	273	9	is	be	AUX
ejpam-5573	273	10	trivial	trivial	ADJ
ejpam-5573	273	11	.	.	PUNCT
ejpam-5573	274	1	in	in	ADP
ejpam-5573	274	2	a	a	DET
ejpam-5573	274	3	similar	similar	ADJ
ejpam-5573	274	4	way	way	NOUN
ejpam-5573	274	5	,	,	PUNCT
ejpam-5573	274	6	we	we	PRON
ejpam-5573	274	7	can	can	AUX
ejpam-5573	274	8	prove	prove	VERB
ejpam-5573	274	9	theorem	theorem	ADJ
ejpam-5573	274	10	5	5	NUM
ejpam-5573	274	11	.	.	PUNCT
ejpam-5573	274	12	theorem	theorem	NOUN
ejpam-5573	274	13	5	5	NUM
ejpam-5573	274	14	.	.	PUNCT
ejpam-5573	275	1	let	let	VERB
ejpam-5573	275	2	(	(	PUNCT
ejpam-5573	275	3	u	u	NOUN
ejpam-5573	275	4	,	,	PUNCT
ejpam-5573	275	5	η	η	PROPN
ejpam-5573	275	6	,	,	PUNCT
ejpam-5573	275	7	η∗	η∗	NOUN
ejpam-5573	275	8	)	)	PUNCT
ejpam-5573	275	9	be	be	VERB
ejpam-5573	275	10	a	a	DET
ejpam-5573	275	11	dfts	dft	NOUN
ejpam-5573	275	12	,	,	PUNCT
ejpam-5573	275	13	r	r	NOUN
ejpam-5573	275	14	∈	∈	PROPN
ejpam-5573	276	1	i	i	NOUN
ejpam-5573	276	2	◦	◦	NOUN
ejpam-5573	276	3	,	,	PUNCT
ejpam-5573	276	4	and	and	CCONJ
ejpam-5573	276	5	s	s	PROPN
ejpam-5573	276	6	∈	∈	PROPN
ejpam-5573	276	7	i1	i1	PROPN
ejpam-5573	276	8	,	,	PUNCT
ejpam-5573	276	9	then	then	ADV
ejpam-5573	276	10	the	the	DET
ejpam-5573	276	11	following	following	ADJ
ejpam-5573	276	12	statements	statement	NOUN
ejpam-5573	276	13	are	be	AUX
ejpam-5573	276	14	equivalent	equivalent	ADJ
ejpam-5573	276	15	.	.	PUNCT
ejpam-5573	277	1	(	(	PUNCT
ejpam-5573	277	2	i	i	NOUN
ejpam-5573	277	3	)	)	PUNCT
ejpam-5573	277	4	(	(	PUNCT
ejpam-5573	277	5	u	u	NOUN
ejpam-5573	277	6	,	,	PUNCT
ejpam-5573	277	7	η	η	PROPN
ejpam-5573	277	8	,	,	PUNCT
ejpam-5573	277	9	η∗	η∗	NOUN
ejpam-5573	277	10	)	)	PUNCT
ejpam-5573	277	11	is	be	AUX
ejpam-5573	277	12	(	(	PUNCT
ejpam-5573	277	13	r	r	NOUN
ejpam-5573	277	14	,	,	PUNCT
ejpam-5573	277	15	s)-gfs	s)-gf	NOUN
ejpam-5573	277	16	-	-	PUNCT
ejpam-5573	277	17	normal	normal	ADJ
ejpam-5573	277	18	space	space	NOUN
ejpam-5573	277	19	.	.	PUNCT
ejpam-5573	278	1	(	(	PUNCT
ejpam-5573	278	2	ii	ii	NOUN
ejpam-5573	278	3	)	)	PUNCT
ejpam-5573	278	4	if	if	SCONJ
ejpam-5573	278	5	ν	ν	NOUN
ejpam-5573	278	6	≤	≤	X
ejpam-5573	278	7	λ	λ	PROPN
ejpam-5573	278	8	for	for	ADP
ejpam-5573	278	9	each	each	DET
ejpam-5573	278	10	ν	ν	NOUN
ejpam-5573	278	11	∈	∈	PROPN
ejpam-5573	278	12	iu	iu	ADV
ejpam-5573	278	13	is	be	AUX
ejpam-5573	278	14	(	(	PUNCT
ejpam-5573	278	15	r	r	NOUN
ejpam-5573	278	16	,	,	PUNCT
ejpam-5573	278	17	s	s	NOUN
ejpam-5573	278	18	)	)	PUNCT
ejpam-5573	278	19	−	−	PROPN
ejpam-5573	278	20	gfsc	gfsc	PROPN
ejpam-5573	278	21	and	and	CCONJ
ejpam-5573	278	22	λ	λ	PROPN
ejpam-5573	278	23	∈	∈	PROPN
ejpam-5573	278	24	iu	iu	ADV
ejpam-5573	278	25	is	be	AUX
ejpam-5573	278	26	(	(	PUNCT
ejpam-5573	278	27	r	r	NOUN
ejpam-5573	278	28	,	,	PUNCT
ejpam-5573	278	29	s	s	NOUN
ejpam-5573	278	30	)	)	PUNCT
ejpam-5573	278	31	−	−	NOUN
ejpam-5573	278	32	gfso	gfso	NOUN
ejpam-5573	278	33	set	set	NOUN
ejpam-5573	278	34	,	,	PUNCT
ejpam-5573	278	35	there	there	PRON
ejpam-5573	278	36	is	be	VERB
ejpam-5573	278	37	µ	µ	PRON
ejpam-5573	278	38	∈	∈	NOUN
ejpam-5573	278	39	iu	iu	ADV
ejpam-5573	278	40	with	with	ADP
ejpam-5573	278	41	η(µ	η(µ	PROPN
ejpam-5573	278	42	)	)	PUNCT
ejpam-5573	278	43	≥	≥	NOUN
ejpam-5573	278	44	r	r	NOUN
ejpam-5573	278	45	and	and	CCONJ
ejpam-5573	278	46	η∗(µ	η∗(µ	PROPN
ejpam-5573	278	47	)	)	PUNCT
ejpam-5573	278	48	≤	≤	NOUN
ejpam-5573	279	1	s	s	PROPN
ejpam-5573	279	2	,	,	PUNCT
ejpam-5573	279	3	such	such	ADJ
ejpam-5573	279	4	that	that	SCONJ
ejpam-5573	279	5	ν	ν	PROPN
ejpam-5573	279	6	≤	≤	X
ejpam-5573	279	7	µ	µ	X
ejpam-5573	279	8	≤	≤	NOUN
ejpam-5573	279	9	cη	cη	ADP
ejpam-5573	279	10	,	,	PUNCT
ejpam-5573	279	11	η∗(µ	η∗(µ	PROPN
ejpam-5573	279	12	,	,	PUNCT
ejpam-5573	279	13	r	r	NOUN
ejpam-5573	279	14	,	,	PUNCT
ejpam-5573	279	15	s	s	NOUN
ejpam-5573	279	16	)	)	PUNCT
ejpam-5573	279	17	≤	≤	NUM
ejpam-5573	279	18	λ	λ	PROPN
ejpam-5573	279	19	.	.	PUNCT
ejpam-5573	279	20	(	(	PUNCT
ejpam-5573	279	21	iii	iii	X
ejpam-5573	279	22	)	)	PUNCT
ejpam-5573	279	23	if	if	SCONJ
ejpam-5573	279	24	λ1qλ2	λ1qλ2	NOUN
ejpam-5573	279	25	for	for	ADP
ejpam-5573	279	26	each	each	PRON
ejpam-5573	279	27	(	(	PUNCT
ejpam-5573	279	28	r	r	NOUN
ejpam-5573	279	29	,	,	PUNCT
ejpam-5573	279	30	s	s	NOUN
ejpam-5573	279	31	)	)	PUNCT
ejpam-5573	279	32	−	−	PROPN
ejpam-5573	279	33	gfsc	gfsc	PROPN
ejpam-5573	279	34	sets	set	VERB
ejpam-5573	279	35	λδ	λδ	PRON
ejpam-5573	279	36	∈	∈	PROPN
ejpam-5573	279	37	iu	iu	ADV
ejpam-5573	279	38	for	for	ADP
ejpam-5573	279	39	δ	δ	PROPN
ejpam-5573	279	40	∈	∈	PROPN
ejpam-5573	279	41	{	{	PUNCT
ejpam-5573	279	42	1	1	NUM
ejpam-5573	279	43	,	,	PUNCT
ejpam-5573	279	44	2	2	NUM
ejpam-5573	279	45	}	}	PUNCT
ejpam-5573	279	46	,	,	PUNCT
ejpam-5573	279	47	there	there	PRON
ejpam-5573	279	48	is	be	VERB
ejpam-5573	279	49	µδ	µδ	PRON
ejpam-5573	279	50	∈	∈	NOUN
ejpam-5573	279	51	iu	iu	ADP
ejpam-5573	279	52	with	with	ADP
ejpam-5573	279	53	η(µδ	η(µδ	PROPN
ejpam-5573	279	54	)	)	PUNCT
ejpam-5573	279	55	≥	≥	NOUN
ejpam-5573	279	56	r	r	NOUN
ejpam-5573	279	57	and	and	CCONJ
ejpam-5573	279	58	η∗(µδ	η∗(µδ	PROPN
ejpam-5573	279	59	)	)	PUNCT
ejpam-5573	279	60	≤	≤	NOUN
ejpam-5573	280	1	s	s	PROPN
ejpam-5573	280	2	,	,	PUNCT
ejpam-5573	280	3	such	such	ADJ
ejpam-5573	280	4	that	that	SCONJ
ejpam-5573	280	5	λδ	λδ	DET
ejpam-5573	280	6	≤	≤	ADJ
ejpam-5573	280	7	µδ	µδ	NOUN
ejpam-5573	280	8	and	and	CCONJ
ejpam-5573	280	9	cη	cη	INTJ
ejpam-5573	280	10	,	,	PUNCT
ejpam-5573	280	11	η∗(µ1	η∗(µ1	NOUN
ejpam-5573	280	12	,	,	PUNCT
ejpam-5573	280	13	r	r	NOUN
ejpam-5573	280	14	,	,	PUNCT
ejpam-5573	280	15	s)qcη	s)qcη	PROPN
ejpam-5573	280	16	,	,	PUNCT
ejpam-5573	280	17	η∗(µ2	η∗(µ2	PROPN
ejpam-5573	280	18	,	,	PUNCT
ejpam-5573	280	19	r	r	NOUN
ejpam-5573	280	20	,	,	PUNCT
ejpam-5573	280	21	s	s	PART
ejpam-5573	280	22	)	)	PUNCT
ejpam-5573	280	23	.	.	PUNCT
ejpam-5573	281	1	theorem	theorem	VERB
ejpam-5573	281	2	6	6	NUM
ejpam-5573	281	3	.	.	PUNCT
ejpam-5573	282	1	if	if	SCONJ
ejpam-5573	282	2	h	h	NOUN
ejpam-5573	282	3	:	:	PUNCT
ejpam-5573	282	4	(	(	PUNCT
ejpam-5573	282	5	u	u	NOUN
ejpam-5573	282	6	,	,	PUNCT
ejpam-5573	282	7	τ	τ	PROPN
ejpam-5573	282	8	,	,	PUNCT
ejpam-5573	282	9	τ∗	τ∗	NOUN
ejpam-5573	282	10	)	)	PUNCT
ejpam-5573	282	11	→	→	SYM
ejpam-5573	282	12	(	(	PUNCT
ejpam-5573	282	13	v	v	PROPN
ejpam-5573	282	14	,	,	PUNCT
ejpam-5573	282	15	η	η	NOUN
ejpam-5573	282	16	,	,	PUNCT
ejpam-5573	282	17	η∗	η∗	NOUN
ejpam-5573	282	18	)	)	PUNCT
ejpam-5573	282	19	is	be	AUX
ejpam-5573	282	20	df	df	NOUN
ejpam-5573	282	21	-	-	PUNCT
ejpam-5573	282	22	irresolute	irresolute	ADJ
ejpam-5573	282	23	,	,	PUNCT
ejpam-5573	282	24	df	df	NOUN
ejpam-5573	282	25	-	-	PUNCT
ejpam-5573	282	26	open	open	ADJ
ejpam-5573	282	27	and	and	CCONJ
ejpam-5573	282	28	bijective	bijective	ADJ
ejpam-5573	282	29	map	map	NOUN
ejpam-5573	282	30	,	,	PUNCT
ejpam-5573	282	31	and	and	CCONJ
ejpam-5573	282	32	(	(	PUNCT
ejpam-5573	282	33	u	u	NOUN
ejpam-5573	282	34	,	,	PUNCT
ejpam-5573	282	35	τ	τ	PROPN
ejpam-5573	282	36	,	,	PUNCT
ejpam-5573	282	37	τ∗	τ∗	PROPN
ejpam-5573	282	38	)	)	PUNCT
ejpam-5573	282	39	is	be	AUX
ejpam-5573	282	40	(	(	PUNCT
ejpam-5573	282	41	r	r	NOUN
ejpam-5573	282	42	,	,	PUNCT
ejpam-5573	282	43	s)-gfs	s)-gf	NOUN
ejpam-5573	282	44	-	-	PUNCT
ejpam-5573	282	45	regular	regular	ADJ
ejpam-5573	282	46	⟨resp	⟨resp	NOUN
ejpam-5573	282	47	.	.	PROPN
ejpam-5573	282	48	,	,	PUNCT
ejpam-5573	282	49	(	(	PUNCT
ejpam-5573	282	50	r	r	NOUN
ejpam-5573	282	51	,	,	PUNCT
ejpam-5573	282	52	s)-gfs	s)-gfs	NOUN
ejpam-5573	282	53	-	-	PUNCT
ejpam-5573	282	54	normal⟩	normal⟩	ADJ
ejpam-5573	282	55	space	space	NOUN
ejpam-5573	282	56	,	,	PUNCT
ejpam-5573	282	57	then	then	ADV
ejpam-5573	282	58	(	(	PUNCT
ejpam-5573	282	59	v	v	NOUN
ejpam-5573	282	60	,	,	PUNCT
ejpam-5573	282	61	η	η	NOUN
ejpam-5573	282	62	,	,	PUNCT
ejpam-5573	282	63	η∗	η∗	NOUN
ejpam-5573	282	64	)	)	PUNCT
ejpam-5573	282	65	is	be	AUX
ejpam-5573	282	66	(	(	PUNCT
ejpam-5573	282	67	r	r	NOUN
ejpam-5573	282	68	,	,	PUNCT
ejpam-5573	282	69	s)gfs	s)gfs	NOUN
ejpam-5573	282	70	-	-	ADJ
ejpam-5573	282	71	regular	regular	ADJ
ejpam-5573	282	72	⟨resp	⟨resp	NOUN
ejpam-5573	282	73	.	.	PROPN
ejpam-5573	282	74	,	,	PUNCT
ejpam-5573	282	75	(	(	PUNCT
ejpam-5573	282	76	r	r	NOUN
ejpam-5573	282	77	,	,	PUNCT
ejpam-5573	282	78	s)-gfs	s)-gfs	NOUN
ejpam-5573	282	79	-	-	PUNCT
ejpam-5573	282	80	normal⟩	normal⟩	ADJ
ejpam-5573	282	81	space	space	NOUN
ejpam-5573	282	82	.	.	PUNCT
ejpam-5573	283	1	proof	proof	NOUN
ejpam-5573	283	2	.	.	PUNCT
ejpam-5573	284	1	let	let	VERB
ejpam-5573	284	2	vtqµ	vtqµ	NOUN
ejpam-5573	284	3	for	for	ADP
ejpam-5573	284	4	each	each	DET
ejpam-5573	284	5	µ	µ	PROPN
ejpam-5573	284	6	∈	∈	NOUN
ejpam-5573	284	7	iv	iv	X
ejpam-5573	284	8	is	be	AUX
ejpam-5573	284	9	(	(	PUNCT
ejpam-5573	284	10	r	r	NOUN
ejpam-5573	284	11	,	,	PUNCT
ejpam-5573	284	12	s	s	NOUN
ejpam-5573	284	13	)	)	PUNCT
ejpam-5573	284	14	−	−	PROPN
ejpam-5573	285	1	gfsc	gfsc	PROPN
ejpam-5573	285	2	.	.	PUNCT
ejpam-5573	286	1	since	since	SCONJ
ejpam-5573	286	2	h	h	PROPN
ejpam-5573	286	3	is	be	AUX
ejpam-5573	286	4	df	df	NOUN
ejpam-5573	286	5	-	-	PUNCT
ejpam-5573	286	6	irresolute	irresolute	ADJ
ejpam-5573	286	7	,	,	PUNCT
ejpam-5573	286	8	df	df	NOUN
ejpam-5573	286	9	-	-	PUNCT
ejpam-5573	286	10	open	open	ADJ
ejpam-5573	286	11	and	and	CCONJ
ejpam-5573	286	12	bijective	bijective	ADJ
ejpam-5573	286	13	map	map	NOUN
ejpam-5573	286	14	,	,	PUNCT
ejpam-5573	286	15	then	then	ADV
ejpam-5573	286	16	by	by	ADP
ejpam-5573	286	17	theorem	theorem	NOUN
ejpam-5573	286	18	4.11	4.11	NUM
ejpam-5573	286	19	[	[	X
ejpam-5573	286	20	42	42	NUM
ejpam-5573	286	21	]	]	PUNCT
ejpam-5573	286	22	,	,	PUNCT
ejpam-5573	286	23	h	h	PROPN
ejpam-5573	286	24	is	be	AUX
ejpam-5573	286	25	dfgs	dfgs	NOUN
ejpam-5573	286	26	-	-	PUNCT
ejpam-5573	286	27	irresolute	irresolute	ADJ
ejpam-5573	286	28	.	.	PUNCT
ejpam-5573	287	1	hence	hence	ADV
ejpam-5573	287	2	,	,	PUNCT
ejpam-5573	287	3	h−1(µ	h−1(µ	PROPN
ejpam-5573	287	4	)	)	PUNCT
ejpam-5573	287	5	is	be	AUX
ejpam-5573	287	6	(	(	PUNCT
ejpam-5573	287	7	r	r	NOUN
ejpam-5573	287	8	,	,	PUNCT
ejpam-5573	287	9	s)−	s)−	PROPN
ejpam-5573	287	10	gfsc	gfsc	PROPN
ejpam-5573	287	11	set	set	PROPN
ejpam-5573	287	12	.	.	PUNCT
ejpam-5573	288	1	put	put	VERB
ejpam-5573	288	2	vt	vt	PROPN
ejpam-5573	288	3	=	=	PROPN
ejpam-5573	288	4	h(ut	h(ut	PROPN
ejpam-5573	288	5	)	)	PUNCT
ejpam-5573	288	6	.	.	PUNCT
ejpam-5573	289	1	then	then	ADV
ejpam-5573	289	2	,	,	PUNCT
ejpam-5573	289	3	utqh	utqh	PROPN
ejpam-5573	289	4	−1(µ	−1(µ	NOUN
ejpam-5573	289	5	)	)	PUNCT
ejpam-5573	289	6	.	.	PUNCT
ejpam-5573	290	1	since	since	SCONJ
ejpam-5573	290	2	(	(	PUNCT
ejpam-5573	290	3	u	u	NOUN
ejpam-5573	290	4	,	,	PUNCT
ejpam-5573	290	5	τ	τ	PROPN
ejpam-5573	290	6	,	,	PUNCT
ejpam-5573	290	7	τ∗	τ∗	PROPN
ejpam-5573	290	8	)	)	PUNCT
ejpam-5573	290	9	is	be	AUX
ejpam-5573	290	10	(	(	PUNCT
ejpam-5573	290	11	r	r	NOUN
ejpam-5573	290	12	,	,	PUNCT
ejpam-5573	290	13	s)-gfs	s)-gf	NOUN
ejpam-5573	290	14	-	-	PUNCT
ejpam-5573	290	15	regular	regular	ADJ
ejpam-5573	290	16	,	,	PUNCT
ejpam-5573	290	17	there	there	PRON
ejpam-5573	290	18	is	be	VERB
ejpam-5573	290	19	µδ	µδ	PRON
ejpam-5573	290	20	∈	∈	NOUN
ejpam-5573	290	21	iu	iu	ADP
ejpam-5573	290	22	with	with	ADP
ejpam-5573	290	23	τ(µδ	τ(µδ	NUM
ejpam-5573	290	24	)	)	PUNCT
ejpam-5573	290	25	≥	≥	NOUN
ejpam-5573	290	26	r	r	NOUN
ejpam-5573	290	27	,	,	PUNCT
ejpam-5573	290	28	τ∗(µδ	τ∗(µδ	NOUN
ejpam-5573	290	29	)	)	PUNCT
ejpam-5573	290	30	≤	≤	PROPN
ejpam-5573	290	31	s	s	PART
ejpam-5573	290	32	and	and	CCONJ
ejpam-5573	290	33	δ	δ	PROPN
ejpam-5573	290	34	∈	∈	PROPN
ejpam-5573	290	35	{	{	PUNCT
ejpam-5573	290	36	1	1	NUM
ejpam-5573	290	37	,	,	PUNCT
ejpam-5573	290	38	2	2	NUM
ejpam-5573	290	39	}	}	PUNCT
ejpam-5573	290	40	such	such	ADJ
ejpam-5573	290	41	that	that	SCONJ
ejpam-5573	290	42	ut	ut	PROPN
ejpam-5573	290	43	∈	∈	PROPN
ejpam-5573	290	44	µ1	µ1	PROPN
ejpam-5573	290	45	,	,	PUNCT
ejpam-5573	290	46	h	h	NOUN
ejpam-5573	290	47	−1(µ	−1(µ	NOUN
ejpam-5573	290	48	)	)	PUNCT
ejpam-5573	290	49	≤	≤	NOUN
ejpam-5573	290	50	µ2	µ2	NOUN
ejpam-5573	290	51	and	and	CCONJ
ejpam-5573	290	52	µ1qµ2	µ1qµ2	NOUN
ejpam-5573	290	53	.	.	PUNCT
ejpam-5573	291	1	since	since	SCONJ
ejpam-5573	291	2	h	h	NOUN
ejpam-5573	291	3	is	be	AUX
ejpam-5573	291	4	df	df	NOUN
ejpam-5573	291	5	-	-	PUNCT
ejpam-5573	291	6	open	open	ADJ
ejpam-5573	291	7	and	and	CCONJ
ejpam-5573	291	8	bijective	bijective	ADJ
ejpam-5573	291	9	map	map	NOUN
ejpam-5573	291	10	,	,	PUNCT
ejpam-5573	291	11	we	we	PRON
ejpam-5573	291	12	have	have	VERB
ejpam-5573	291	13	vt	vt	PROPN
ejpam-5573	291	14	∈	∈	PROPN
ejpam-5573	291	15	h(µ1	h(µ1	NOUN
ejpam-5573	291	16	)	)	PUNCT
ejpam-5573	291	17	,	,	PUNCT
ejpam-5573	291	18	µ	µ	X
ejpam-5573	291	19	=	=	SYM
ejpam-5573	291	20	h(h−1(µ	h(h−1(µ	PROPN
ejpam-5573	291	21	)	)	PUNCT
ejpam-5573	291	22	)	)	PUNCT
ejpam-5573	291	23	≤	≤	NOUN
ejpam-5573	292	1	h(µ2	h(µ2	X
ejpam-5573	292	2	)	)	PUNCT
ejpam-5573	292	3	,	,	PUNCT
ejpam-5573	292	4	h(µ1)qh(µ2	h(µ1)qh(µ2	PROPN
ejpam-5573	292	5	)	)	PUNCT
ejpam-5573	292	6	.	.	PUNCT
ejpam-5573	293	1	hence	hence	ADV
ejpam-5573	293	2	,	,	PUNCT
ejpam-5573	293	3	(	(	PUNCT
ejpam-5573	293	4	v	v	NOUN
ejpam-5573	293	5	,	,	PUNCT
ejpam-5573	293	6	η	η	NOUN
ejpam-5573	293	7	,	,	PUNCT
ejpam-5573	293	8	η∗	η∗	NOUN
ejpam-5573	293	9	)	)	PUNCT
ejpam-5573	293	10	is	be	AUX
ejpam-5573	293	11	(	(	PUNCT
ejpam-5573	293	12	r	r	NOUN
ejpam-5573	293	13	,	,	PUNCT
ejpam-5573	293	14	s)-gfs	s)-gf	NOUN
ejpam-5573	293	15	-	-	PUNCT
ejpam-5573	293	16	regular	regular	ADJ
ejpam-5573	293	17	space	space	NOUN
ejpam-5573	293	18	.	.	PUNCT
ejpam-5573	294	1	the	the	DET
ejpam-5573	294	2	other	other	ADJ
ejpam-5573	294	3	case	case	NOUN
ejpam-5573	294	4	follows	follow	VERB
ejpam-5573	294	5	similar	similar	ADJ
ejpam-5573	294	6	lines	line	NOUN
ejpam-5573	294	7	.	.	PUNCT
ejpam-5573	295	1	theorem	theorem	VERB
ejpam-5573	295	2	7	7	NUM
ejpam-5573	295	3	.	.	PUNCT
ejpam-5573	296	1	if	if	SCONJ
ejpam-5573	296	2	h	h	NOUN
ejpam-5573	296	3	:	:	PUNCT
ejpam-5573	296	4	(	(	PUNCT
ejpam-5573	296	5	u	u	NOUN
ejpam-5573	296	6	,	,	PUNCT
ejpam-5573	296	7	τ	τ	PROPN
ejpam-5573	296	8	,	,	PUNCT
ejpam-5573	296	9	τ∗	τ∗	NOUN
ejpam-5573	296	10	)	)	PUNCT
ejpam-5573	296	11	→	→	SYM
ejpam-5573	296	12	(	(	PUNCT
ejpam-5573	296	13	v	v	PROPN
ejpam-5573	296	14	,	,	PUNCT
ejpam-5573	296	15	η	η	NOUN
ejpam-5573	296	16	,	,	PUNCT
ejpam-5573	296	17	η∗	η∗	NOUN
ejpam-5573	296	18	)	)	PUNCT
ejpam-5573	296	19	is	be	AUX
ejpam-5573	296	20	df	df	NOUN
ejpam-5573	296	21	-	-	PUNCT
ejpam-5573	296	22	continuous	continuous	ADJ
ejpam-5573	296	23	,	,	PUNCT
ejpam-5573	296	24	dfgs	dfgs	NOUN
ejpam-5573	296	25	-	-	PUNCT
ejpam-5573	296	26	irresolute	irresolute	VERB
ejpam-5573	296	27	closed	closed	ADJ
ejpam-5573	296	28	and	and	CCONJ
ejpam-5573	296	29	injective	injective	ADJ
ejpam-5573	296	30	map	map	NOUN
ejpam-5573	296	31	,	,	PUNCT
ejpam-5573	296	32	and	and	CCONJ
ejpam-5573	296	33	(	(	PUNCT
ejpam-5573	296	34	v	v	NOUN
ejpam-5573	296	35	,	,	PUNCT
ejpam-5573	296	36	η	η	NOUN
ejpam-5573	296	37	,	,	PUNCT
ejpam-5573	296	38	η∗	η∗	NOUN
ejpam-5573	296	39	)	)	PUNCT
ejpam-5573	296	40	is	be	AUX
ejpam-5573	296	41	(	(	PUNCT
ejpam-5573	296	42	r	r	NOUN
ejpam-5573	296	43	,	,	PUNCT
ejpam-5573	296	44	s)-gfs	s)-gf	NOUN
ejpam-5573	296	45	-	-	PUNCT
ejpam-5573	296	46	regular	regular	ADJ
ejpam-5573	296	47	⟨resp	⟨resp	NOUN
ejpam-5573	296	48	.	.	PROPN
ejpam-5573	296	49	,	,	PUNCT
ejpam-5573	296	50	(	(	PUNCT
ejpam-5573	296	51	r	r	NOUN
ejpam-5573	296	52	,	,	PUNCT
ejpam-5573	296	53	s)-gfs	s)-gf	NOUN
ejpam-5573	296	54	-	-	PUNCT
ejpam-5573	296	55	normal⟩	normal⟩	ADJ
ejpam-5573	296	56	,	,	PUNCT
ejpam-5573	296	57	then	then	ADV
ejpam-5573	296	58	(	(	PUNCT
ejpam-5573	296	59	u	u	NOUN
ejpam-5573	296	60	,	,	PUNCT
ejpam-5573	296	61	τ	τ	PROPN
ejpam-5573	296	62	,	,	PUNCT
ejpam-5573	296	63	τ∗	τ∗	PROPN
ejpam-5573	296	64	)	)	PUNCT
ejpam-5573	296	65	is	be	AUX
ejpam-5573	296	66	(	(	PUNCT
ejpam-5573	296	67	r	r	NOUN
ejpam-5573	296	68	,	,	PUNCT
ejpam-5573	296	69	s)-gfs	s)-gf	NOUN
ejpam-5573	296	70	-	-	PUNCT
ejpam-5573	296	71	regular	regular	ADJ
ejpam-5573	296	72	⟨resp	⟨resp	NOUN
ejpam-5573	296	73	.	.	PROPN
ejpam-5573	296	74	,	,	PUNCT
ejpam-5573	296	75	(	(	PUNCT
ejpam-5573	296	76	r	r	NOUN
ejpam-5573	296	77	,	,	PUNCT
ejpam-5573	296	78	s)-gfs	s)-gfs	NOUN
ejpam-5573	296	79	-	-	PUNCT
ejpam-5573	296	80	normal⟩.	normal⟩.	NOUN
ejpam-5573	296	81	proof	proof	NOUN
ejpam-5573	296	82	.	.	PUNCT
ejpam-5573	297	1	let	let	VERB
ejpam-5573	297	2	utqλ	utqλ	PRON
ejpam-5573	297	3	for	for	ADP
ejpam-5573	297	4	each	each	DET
ejpam-5573	297	5	λ	λ	PROPN
ejpam-5573	297	6	∈	∈	PROPN
ejpam-5573	297	7	iu	iu	ADV
ejpam-5573	297	8	is	be	AUX
ejpam-5573	297	9	(	(	PUNCT
ejpam-5573	297	10	r	r	NOUN
ejpam-5573	297	11	,	,	PUNCT
ejpam-5573	297	12	s	s	NOUN
ejpam-5573	297	13	)	)	PUNCT
ejpam-5573	297	14	−	−	PROPN
ejpam-5573	298	1	gfsc	gfsc	PROPN
ejpam-5573	298	2	.	.	PUNCT
ejpam-5573	299	1	since	since	SCONJ
ejpam-5573	299	2	h	h	PROPN
ejpam-5573	299	3	is	be	AUX
ejpam-5573	299	4	dfgs	dfgs	NOUN
ejpam-5573	299	5	-	-	PUNCT
ejpam-5573	299	6	irresolute	irresolute	NOUN
ejpam-5573	299	7	closed	closed	ADJ
ejpam-5573	299	8	,	,	PUNCT
ejpam-5573	299	9	h(λ	h(λ	PROPN
ejpam-5573	299	10	)	)	PUNCT
ejpam-5573	299	11	is	be	AUX
ejpam-5573	299	12	(	(	PUNCT
ejpam-5573	299	13	r	r	NOUN
ejpam-5573	299	14	,	,	PUNCT
ejpam-5573	299	15	s	s	NOUN
ejpam-5573	299	16	)	)	PUNCT
ejpam-5573	299	17	−	−	PROPN
ejpam-5573	299	18	gfsc	gfsc	PROPN
ejpam-5573	299	19	.	.	PUNCT
ejpam-5573	300	1	since	since	SCONJ
ejpam-5573	300	2	h	h	NOUN
ejpam-5573	300	3	is	be	AUX
ejpam-5573	300	4	injective	injective	ADJ
ejpam-5573	300	5	,	,	PUNCT
ejpam-5573	300	6	utqλ	utqλ	PROPN
ejpam-5573	300	7	implies	imply	VERB
ejpam-5573	300	8	h(ut)qh(λ	h(ut)qh(λ	PROPN
ejpam-5573	300	9	)	)	PUNCT
ejpam-5573	300	10	.	.	PUNCT
ejpam-5573	301	1	since	since	SCONJ
ejpam-5573	301	2	(	(	PUNCT
ejpam-5573	301	3	v	v	PROPN
ejpam-5573	301	4	,	,	PUNCT
ejpam-5573	301	5	η	η	NOUN
ejpam-5573	301	6	,	,	PUNCT
ejpam-5573	301	7	η∗	η∗	NOUN
ejpam-5573	301	8	)	)	PUNCT
ejpam-5573	301	9	is	be	AUX
ejpam-5573	301	10	(	(	PUNCT
ejpam-5573	301	11	r	r	NOUN
ejpam-5573	301	12	,	,	PUNCT
ejpam-5573	301	13	s)-gfs	s)-gf	NOUN
ejpam-5573	301	14	-	-	PUNCT
ejpam-5573	301	15	regular	regular	ADJ
ejpam-5573	301	16	,	,	PUNCT
ejpam-5573	301	17	there	there	PRON
ejpam-5573	301	18	is	be	VERB
ejpam-5573	301	19	µδ	µδ	PRON
ejpam-5573	301	20	∈	∈	NOUN
ejpam-5573	301	21	iu	iu	ADP
ejpam-5573	301	22	with	with	ADP
ejpam-5573	301	23	η(µδ	η(µδ	PROPN
ejpam-5573	301	24	)	)	PUNCT
ejpam-5573	301	25	≥	≥	NOUN
ejpam-5573	301	26	r	r	NOUN
ejpam-5573	301	27	,	,	PUNCT
ejpam-5573	301	28	η∗(µδ	η∗(µδ	PROPN
ejpam-5573	301	29	)	)	PUNCT
ejpam-5573	301	30	≤	≤	PROPN
ejpam-5573	301	31	s	s	PART
ejpam-5573	301	32	and	and	CCONJ
ejpam-5573	301	33	δ	δ	PROPN
ejpam-5573	301	34	∈	∈	PROPN
ejpam-5573	301	35	{	{	PUNCT
ejpam-5573	301	36	1	1	NUM
ejpam-5573	301	37	,	,	PUNCT
ejpam-5573	301	38	2	2	NUM
ejpam-5573	301	39	}	}	PUNCT
ejpam-5573	301	40	such	such	ADJ
ejpam-5573	301	41	that	that	SCONJ
ejpam-5573	301	42	h(ut	h(ut	PROPN
ejpam-5573	301	43	)	)	PUNCT
ejpam-5573	301	44	∈	∈	PROPN
ejpam-5573	301	45	µ1	µ1	PROPN
ejpam-5573	301	46	,	,	PUNCT
ejpam-5573	301	47	h(λ	h(λ	PROPN
ejpam-5573	301	48	)	)	PUNCT
ejpam-5573	301	49	≤	≤	NOUN
ejpam-5573	301	50	µ2	µ2	NOUN
ejpam-5573	301	51	and	and	CCONJ
ejpam-5573	301	52	µ1qµ2	µ1qµ2	NOUN
ejpam-5573	301	53	.	.	PUNCT
ejpam-5573	302	1	since	since	SCONJ
ejpam-5573	302	2	h	h	NOUN
ejpam-5573	302	3	is	be	AUX
ejpam-5573	302	4	df	df	NOUN
ejpam-5573	302	5	-	-	PUNCT
ejpam-5573	302	6	continuous	continuous	ADJ
ejpam-5573	302	7	,	,	PUNCT
ejpam-5573	302	8	ut	ut	PROPN
ejpam-5573	302	9	∈	∈	PROPN
ejpam-5573	302	10	h−1(µ1	h−1(µ1	PROPN
ejpam-5573	302	11	)	)	PUNCT
ejpam-5573	302	12	,	,	PUNCT
ejpam-5573	302	13	λ	λ	X
ejpam-5573	302	14	≤	≤	ADJ
ejpam-5573	302	15	h−1(µ2	h−1(µ2	ADV
ejpam-5573	302	16	)	)	PUNCT
ejpam-5573	302	17	with	with	ADP
ejpam-5573	302	18	η(h−1(µδ	η(h−1(µδ	NOUN
ejpam-5573	302	19	)	)	PUNCT
ejpam-5573	302	20	)	)	PUNCT
ejpam-5573	302	21	≥	≥	PROPN
ejpam-5573	302	22	r	r	NOUN
ejpam-5573	302	23	,	,	PUNCT
ejpam-5573	302	24	η∗(h−1(µδ	η∗(h−1(µδ	NOUN
ejpam-5573	302	25	)	)	PUNCT
ejpam-5573	302	26	)	)	PUNCT
ejpam-5573	303	1	≤	≤	PROPN
ejpam-5573	303	2	s	s	PART
ejpam-5573	303	3	and	and	CCONJ
ejpam-5573	303	4	δ	δ	PROPN
ejpam-5573	303	5	∈	∈	PROPN
ejpam-5573	303	6	{	{	PUNCT
ejpam-5573	303	7	1	1	NUM
ejpam-5573	303	8	,	,	PUNCT
ejpam-5573	303	9	2	2	NUM
ejpam-5573	303	10	}	}	PUNCT
ejpam-5573	303	11	and	and	CCONJ
ejpam-5573	303	12	h−1(µ1)qh	h−1(µ1)qh	NUM
ejpam-5573	303	13	−1(µ2	−1(µ2	NOUN
ejpam-5573	303	14	)	)	PUNCT
ejpam-5573	303	15	.	.	PUNCT
ejpam-5573	304	1	hence	hence	ADV
ejpam-5573	304	2	,	,	PUNCT
ejpam-5573	304	3	(	(	PUNCT
ejpam-5573	304	4	u	u	NOUN
ejpam-5573	304	5	,	,	PUNCT
ejpam-5573	304	6	τ	τ	PROPN
ejpam-5573	304	7	,	,	PUNCT
ejpam-5573	304	8	τ∗	τ∗	PROPN
ejpam-5573	304	9	)	)	PUNCT
ejpam-5573	304	10	is	be	AUX
ejpam-5573	304	11	(	(	PUNCT
ejpam-5573	304	12	r	r	NOUN
ejpam-5573	304	13	,	,	PUNCT
ejpam-5573	304	14	s)-gfs	s)-gf	NOUN
ejpam-5573	304	15	-	-	PUNCT
ejpam-5573	304	16	regular	regular	ADJ
ejpam-5573	304	17	.	.	PUNCT
ejpam-5573	305	1	the	the	DET
ejpam-5573	305	2	other	other	ADJ
ejpam-5573	305	3	case	case	NOUN
ejpam-5573	305	4	follows	follow	VERB
ejpam-5573	305	5	similar	similar	ADJ
ejpam-5573	305	6	lines	line	NOUN
ejpam-5573	305	7	.	.	PUNCT
ejpam-5573	306	1	f.	f.	PROPN
ejpam-5573	306	2	alsharari	alsharari	PROPN
ejpam-5573	306	3	,	,	PUNCT
ejpam-5573	306	4	o.	o.	PROPN
ejpam-5573	306	5	m.	m.	PROPN
ejpam-5573	306	6	taha	taha	PROPN
ejpam-5573	306	7	,	,	PUNCT
ejpam-5573	306	8	i.	i.	PROPN
ejpam-5573	306	9	m.	m.	PROPN
ejpam-5573	306	10	taha	taha	PROPN
ejpam-5573	306	11	/	/	PUNCT
ejpam-5573	306	12	eur	eur	PROPN
ejpam-5573	306	13	.	.	PUNCT
ejpam-5573	307	1	j.	j.	PROPN
ejpam-5573	307	2	pure	pure	PROPN
ejpam-5573	307	3	appl	appl	PROPN
ejpam-5573	307	4	.	.	PROPN
ejpam-5573	307	5	math	math	PROPN
ejpam-5573	307	6	,	,	PUNCT
ejpam-5573	307	7	17	17	NUM
ejpam-5573	307	8	(	(	PUNCT
ejpam-5573	307	9	4	4	NUM
ejpam-5573	307	10	)	)	PUNCT
ejpam-5573	307	11	(	(	PUNCT
ejpam-5573	307	12	2024	2024	NUM
ejpam-5573	307	13	)	)	PUNCT
ejpam-5573	307	14	,	,	PUNCT
ejpam-5573	307	15	4093	4093	NUM
ejpam-5573	307	16	-	-	SYM
ejpam-5573	307	17	4111	4111	NUM
ejpam-5573	307	18	4104	4104	NUM
ejpam-5573	307	19	theorem	theorem	VERB
ejpam-5573	307	20	8	8	NUM
ejpam-5573	307	21	.	.	PUNCT
ejpam-5573	308	1	if	if	SCONJ
ejpam-5573	308	2	h	h	NOUN
ejpam-5573	308	3	:	:	PUNCT
ejpam-5573	308	4	(	(	PUNCT
ejpam-5573	308	5	u	u	NOUN
ejpam-5573	308	6	,	,	PUNCT
ejpam-5573	308	7	τ	τ	PROPN
ejpam-5573	308	8	,	,	PUNCT
ejpam-5573	308	9	τ∗	τ∗	NOUN
ejpam-5573	308	10	)	)	PUNCT
ejpam-5573	308	11	→	→	SYM
ejpam-5573	308	12	(	(	PUNCT
ejpam-5573	308	13	v	v	PROPN
ejpam-5573	308	14	,	,	PUNCT
ejpam-5573	308	15	η	η	NOUN
ejpam-5573	308	16	,	,	PUNCT
ejpam-5573	308	17	η∗	η∗	NOUN
ejpam-5573	308	18	)	)	PUNCT
ejpam-5573	308	19	is	be	AUX
ejpam-5573	308	20	dfgs	dfgs	NOUN
ejpam-5573	308	21	-	-	PUNCT
ejpam-5573	308	22	irresolute	irresolute	ADJ
ejpam-5573	308	23	,	,	PUNCT
ejpam-5573	308	24	df	df	NOUN
ejpam-5573	308	25	-	-	PUNCT
ejpam-5573	308	26	open	open	ADJ
ejpam-5573	308	27	,	,	PUNCT
ejpam-5573	308	28	df	df	NOUN
ejpam-5573	308	29	-	-	PUNCT
ejpam-5573	308	30	closed	close	VERB
ejpam-5573	308	31	and	and	CCONJ
ejpam-5573	308	32	surjective	surjective	ADJ
ejpam-5573	308	33	map	map	NOUN
ejpam-5573	308	34	,	,	PUNCT
ejpam-5573	308	35	and	and	CCONJ
ejpam-5573	308	36	(	(	PUNCT
ejpam-5573	308	37	u	u	NOUN
ejpam-5573	308	38	,	,	PUNCT
ejpam-5573	308	39	τ	τ	PROPN
ejpam-5573	308	40	,	,	PUNCT
ejpam-5573	308	41	τ∗	τ∗	PROPN
ejpam-5573	308	42	)	)	PUNCT
ejpam-5573	308	43	is	be	AUX
ejpam-5573	308	44	(	(	PUNCT
ejpam-5573	308	45	r	r	NOUN
ejpam-5573	308	46	,	,	PUNCT
ejpam-5573	308	47	s)-gfs	s)-gf	NOUN
ejpam-5573	308	48	-	-	PUNCT
ejpam-5573	308	49	regular	regular	ADJ
ejpam-5573	308	50	⟨resp	⟨resp	NOUN
ejpam-5573	308	51	.	.	PROPN
ejpam-5573	308	52	,	,	PUNCT
ejpam-5573	308	53	(	(	PUNCT
ejpam-5573	308	54	r	r	NOUN
ejpam-5573	308	55	,	,	PUNCT
ejpam-5573	308	56	s)-gfs	s)-gf	NOUN
ejpam-5573	308	57	-	-	PUNCT
ejpam-5573	308	58	normal⟩	normal⟩	ADJ
ejpam-5573	308	59	,	,	PUNCT
ejpam-5573	308	60	then	then	ADV
ejpam-5573	308	61	(	(	PUNCT
ejpam-5573	308	62	v	v	NOUN
ejpam-5573	308	63	,	,	PUNCT
ejpam-5573	308	64	η	η	NOUN
ejpam-5573	308	65	,	,	PUNCT
ejpam-5573	308	66	η∗	η∗	NOUN
ejpam-5573	308	67	)	)	PUNCT
ejpam-5573	308	68	is	be	AUX
ejpam-5573	308	69	(	(	PUNCT
ejpam-5573	308	70	r	r	NOUN
ejpam-5573	308	71	,	,	PUNCT
ejpam-5573	308	72	s)-gfs	s)-gf	NOUN
ejpam-5573	308	73	-	-	PUNCT
ejpam-5573	308	74	regular	regular	ADJ
ejpam-5573	308	75	⟨resp	⟨resp	NOUN
ejpam-5573	308	76	.	.	PROPN
ejpam-5573	308	77	,	,	PUNCT
ejpam-5573	308	78	(	(	PUNCT
ejpam-5573	308	79	r	r	NOUN
ejpam-5573	308	80	,	,	PUNCT
ejpam-5573	308	81	s)-gfs	s)-gfs	NOUN
ejpam-5573	308	82	-	-	PUNCT
ejpam-5573	308	83	normal⟩.	normal⟩.	NOUN
ejpam-5573	308	84	proof	proof	NOUN
ejpam-5573	308	85	.	.	PUNCT
ejpam-5573	309	1	let	let	VERB
ejpam-5573	309	2	vt	vt	PROPN
ejpam-5573	309	3	∈	∈	PROPN
ejpam-5573	309	4	µ	µ	PROPN
ejpam-5573	309	5	for	for	ADP
ejpam-5573	309	6	each	each	DET
ejpam-5573	309	7	µ	µ	PROPN
ejpam-5573	309	8	∈	∈	NOUN
ejpam-5573	309	9	iv	iv	X
ejpam-5573	309	10	is	be	AUX
ejpam-5573	309	11	(	(	PUNCT
ejpam-5573	309	12	r	r	NOUN
ejpam-5573	309	13	,	,	PUNCT
ejpam-5573	309	14	s	s	NOUN
ejpam-5573	309	15	)	)	PUNCT
ejpam-5573	309	16	−	−	NOUN
ejpam-5573	309	17	gfso	gfso	NOUN
ejpam-5573	309	18	.	.	PUNCT
ejpam-5573	310	1	since	since	SCONJ
ejpam-5573	310	2	h	h	PROPN
ejpam-5573	310	3	is	be	AUX
ejpam-5573	310	4	dfgs	dfgs	NOUN
ejpam-5573	310	5	-	-	PUNCT
ejpam-5573	310	6	irresolute	irresolute	ADJ
ejpam-5573	310	7	and	and	CCONJ
ejpam-5573	310	8	surjective	surjective	ADJ
ejpam-5573	310	9	then	then	ADV
ejpam-5573	310	10	,	,	PUNCT
ejpam-5573	310	11	there	there	PRON
ejpam-5573	310	12	is	be	VERB
ejpam-5573	310	13	u	u	PROPN
ejpam-5573	310	14	∈	∈	PROPN
ejpam-5573	310	15	h−1({v	h−1({v	NOUN
ejpam-5573	310	16	}	}	PUNCT
ejpam-5573	310	17	)	)	PUNCT
ejpam-5573	310	18	such	such	ADJ
ejpam-5573	310	19	that	that	SCONJ
ejpam-5573	310	20	ut	ut	PROPN
ejpam-5573	310	21	∈	∈	PROPN
ejpam-5573	310	22	h−1(µ	h−1(µ	PROPN
ejpam-5573	310	23	)	)	PUNCT
ejpam-5573	310	24	with	with	ADP
ejpam-5573	310	25	(	(	PUNCT
ejpam-5573	310	26	r	r	NOUN
ejpam-5573	310	27	,	,	PUNCT
ejpam-5573	310	28	s)−	s)−	PROPN
ejpam-5573	310	29	gfso	gfso	NOUN
ejpam-5573	310	30	set	set	VERB
ejpam-5573	310	31	h−1(µ	h−1(µ	PROPN
ejpam-5573	310	32	)	)	PUNCT
ejpam-5573	310	33	.	.	PUNCT
ejpam-5573	311	1	since	since	SCONJ
ejpam-5573	311	2	(	(	PUNCT
ejpam-5573	311	3	u	u	NOUN
ejpam-5573	311	4	,	,	PUNCT
ejpam-5573	311	5	τ	τ	PROPN
ejpam-5573	311	6	,	,	PUNCT
ejpam-5573	311	7	τ∗	τ∗	PROPN
ejpam-5573	311	8	)	)	PUNCT
ejpam-5573	311	9	is	be	AUX
ejpam-5573	311	10	(	(	PUNCT
ejpam-5573	311	11	r	r	NOUN
ejpam-5573	311	12	,	,	PUNCT
ejpam-5573	311	13	s)-gfs	s)-gf	NOUN
ejpam-5573	311	14	-	-	PUNCT
ejpam-5573	311	15	regular	regular	ADJ
ejpam-5573	311	16	,	,	PUNCT
ejpam-5573	311	17	by	by	ADP
ejpam-5573	311	18	theorem	theorem	NOUN
ejpam-5573	311	19	4	4	NUM
ejpam-5573	311	20	,	,	PUNCT
ejpam-5573	311	21	there	there	PRON
ejpam-5573	311	22	is	be	VERB
ejpam-5573	311	23	ν	ν	PRON
ejpam-5573	311	24	∈	∈	NOUN
ejpam-5573	311	25	iu	iu	ADV
ejpam-5573	311	26	with	with	ADP
ejpam-5573	311	27	τ(ν	τ(ν	NOUN
ejpam-5573	311	28	)	)	PUNCT
ejpam-5573	311	29	≥	≥	NOUN
ejpam-5573	311	30	r	r	NOUN
ejpam-5573	311	31	,	,	PUNCT
ejpam-5573	311	32	τ∗(ν	τ∗(ν	ADJ
ejpam-5573	311	33	)	)	PUNCT
ejpam-5573	311	34	≤	≤	NOUN
ejpam-5573	311	35	s	s	VERB
ejpam-5573	311	36	such	such	ADJ
ejpam-5573	311	37	that	that	SCONJ
ejpam-5573	311	38	ut	ut	PROPN
ejpam-5573	311	39	∈	∈	PROPN
ejpam-5573	311	40	ν	ν	NOUN
ejpam-5573	311	41	≤	≤	NUM
ejpam-5573	311	42	cτ	cτ	ADP
ejpam-5573	311	43	,	,	PUNCT
ejpam-5573	311	44	τ∗(ν	τ∗(ν	PROPN
ejpam-5573	311	45	,	,	PUNCT
ejpam-5573	311	46	r	r	NOUN
ejpam-5573	311	47	,	,	PUNCT
ejpam-5573	311	48	s	s	NOUN
ejpam-5573	311	49	)	)	PUNCT
ejpam-5573	311	50	≤	≤	NUM
ejpam-5573	311	51	h−1(µ	h−1(µ	PROPN
ejpam-5573	311	52	)	)	PUNCT
ejpam-5573	311	53	.	.	PUNCT
ejpam-5573	312	1	it	it	PRON
ejpam-5573	312	2	implies	imply	VERB
ejpam-5573	312	3	vt	vt	PROPN
ejpam-5573	312	4	∈	∈	PROPN
ejpam-5573	312	5	h(ν	h(ν	PROPN
ejpam-5573	312	6	)	)	PUNCT
ejpam-5573	312	7	≤	≤	NOUN
ejpam-5573	312	8	h(cτ	h(cτ	PROPN
ejpam-5573	312	9	,	,	PUNCT
ejpam-5573	312	10	τ∗(ν	τ∗(ν	PROPN
ejpam-5573	312	11	,	,	PUNCT
ejpam-5573	312	12	r	r	NOUN
ejpam-5573	312	13	,	,	PUNCT
ejpam-5573	312	14	s	s	NOUN
ejpam-5573	312	15	)	)	PUNCT
ejpam-5573	312	16	)	)	PUNCT
ejpam-5573	312	17	≤	≤	NUM
ejpam-5573	312	18	µ.	µ.	NOUN
ejpam-5573	312	19	since	since	SCONJ
ejpam-5573	312	20	h	h	PROPN
ejpam-5573	312	21	isdf	isdf	ADJ
ejpam-5573	312	22	-	-	PUNCT
ejpam-5573	312	23	open	open	ADJ
ejpam-5573	312	24	anddf	anddf	NOUN
ejpam-5573	312	25	-	-	PUNCT
ejpam-5573	312	26	closed	closed	ADJ
ejpam-5573	312	27	,	,	PUNCT
ejpam-5573	312	28	then	then	ADV
ejpam-5573	312	29	η(h(ν	η(h(ν	PROPN
ejpam-5573	312	30	)	)	PUNCT
ejpam-5573	312	31	)	)	PUNCT
ejpam-5573	312	32	≥	≥	PROPN
ejpam-5573	312	33	r	r	NOUN
ejpam-5573	312	34	,	,	PUNCT
ejpam-5573	312	35	η∗(h(ν	η∗(h(ν	NOUN
ejpam-5573	312	36	)	)	PUNCT
ejpam-5573	312	37	)	)	PUNCT
ejpam-5573	312	38	≤	≤	PROPN
ejpam-5573	312	39	s	s	VERB
ejpam-5573	312	40	and	and	CCONJ
ejpam-5573	312	41	η(hc(cτ	η(hc(cτ	ADJ
ejpam-5573	312	42	,	,	PUNCT
ejpam-5573	312	43	τ∗(ν	τ∗(ν	PROPN
ejpam-5573	312	44	,	,	PUNCT
ejpam-5573	312	45	r	r	NOUN
ejpam-5573	312	46	,	,	PUNCT
ejpam-5573	312	47	s	s	NOUN
ejpam-5573	312	48	)	)	PUNCT
ejpam-5573	312	49	)	)	PUNCT
ejpam-5573	312	50	)	)	PUNCT
ejpam-5573	312	51	≥	≥	PROPN
ejpam-5573	312	52	r.	r.	PROPN
ejpam-5573	312	53	hence	hence	ADV
ejpam-5573	312	54	,	,	PUNCT
ejpam-5573	312	55	vt	vt	PROPN
ejpam-5573	312	56	∈	∈	PROPN
ejpam-5573	312	57	h(ν	h(ν	PROPN
ejpam-5573	312	58	)	)	PUNCT
ejpam-5573	312	59	≤	≤	NOUN
ejpam-5573	312	60	cη	cη	ADP
ejpam-5573	312	61	,	,	PUNCT
ejpam-5573	312	62	η∗(h(ν	η∗(h(ν	NOUN
ejpam-5573	312	63	)	)	PUNCT
ejpam-5573	312	64	,	,	PUNCT
ejpam-5573	312	65	r	r	NOUN
ejpam-5573	312	66	,	,	PUNCT
ejpam-5573	312	67	s	s	NOUN
ejpam-5573	312	68	)	)	PUNCT
ejpam-5573	312	69	≤	≤	NOUN
ejpam-5573	312	70	cη	cη	ADP
ejpam-5573	312	71	,	,	PUNCT
ejpam-5573	312	72	η∗(h(cτ	η∗(h(cτ	NOUN
ejpam-5573	312	73	,	,	PUNCT
ejpam-5573	312	74	τ∗(ν	τ∗(ν	PROPN
ejpam-5573	312	75	,	,	PUNCT
ejpam-5573	312	76	r	r	NOUN
ejpam-5573	312	77	,	,	PUNCT
ejpam-5573	312	78	s	s	NOUN
ejpam-5573	312	79	)	)	PUNCT
ejpam-5573	312	80	)	)	PUNCT
ejpam-5573	312	81	,	,	PUNCT
ejpam-5573	312	82	r	r	NOUN
ejpam-5573	312	83	,	,	PUNCT
ejpam-5573	312	84	s	s	NOUN
ejpam-5573	312	85	)	)	PUNCT
ejpam-5573	312	86	≤	≤	NUM
ejpam-5573	312	87	µ.	µ.	NOUN
ejpam-5573	312	88	thus	thus	ADV
ejpam-5573	312	89	,	,	PUNCT
ejpam-5573	312	90	(	(	PUNCT
ejpam-5573	312	91	v	v	NOUN
ejpam-5573	312	92	,	,	PUNCT
ejpam-5573	312	93	η	η	NOUN
ejpam-5573	312	94	,	,	PUNCT
ejpam-5573	312	95	η∗	η∗	NOUN
ejpam-5573	312	96	)	)	PUNCT
ejpam-5573	312	97	is	be	AUX
ejpam-5573	312	98	(	(	PUNCT
ejpam-5573	312	99	r	r	NOUN
ejpam-5573	312	100	,	,	PUNCT
ejpam-5573	312	101	s)-gfs	s)-gf	NOUN
ejpam-5573	312	102	-	-	PUNCT
ejpam-5573	312	103	regular	regular	ADJ
ejpam-5573	312	104	.	.	PUNCT
ejpam-5573	313	1	the	the	DET
ejpam-5573	313	2	other	other	ADJ
ejpam-5573	313	3	case	case	NOUN
ejpam-5573	313	4	follows	follow	VERB
ejpam-5573	313	5	similar	similar	ADJ
ejpam-5573	313	6	lines	line	NOUN
ejpam-5573	313	7	.	.	PUNCT
ejpam-5573	314	1	4	4	X
ejpam-5573	314	2	.	.	NOUN
ejpam-5573	314	3	novel	novel	ADJ
ejpam-5573	314	4	types	type	NOUN
ejpam-5573	314	5	of	of	ADP
ejpam-5573	314	6	compactness	compactness	NOUN
ejpam-5573	314	7	here	here	ADV
ejpam-5573	314	8	,	,	PUNCT
ejpam-5573	314	9	several	several	ADJ
ejpam-5573	314	10	types	type	NOUN
ejpam-5573	314	11	of	of	ADP
ejpam-5573	314	12	compactness	compactness	NOUN
ejpam-5573	314	13	in	in	ADP
ejpam-5573	314	14	double	double	ADJ
ejpam-5573	314	15	fuzzy	fuzzy	ADJ
ejpam-5573	314	16	topological	topological	ADJ
ejpam-5573	314	17	spaces	space	NOUN
ejpam-5573	314	18	were	be	AUX
ejpam-5573	314	19	introduced	introduce	VERB
ejpam-5573	314	20	and	and	CCONJ
ejpam-5573	314	21	the	the	DET
ejpam-5573	314	22	relationships	relationship	NOUN
ejpam-5573	314	23	between	between	ADP
ejpam-5573	314	24	them	they	PRON
ejpam-5573	314	25	were	be	AUX
ejpam-5573	314	26	studied	study	VERB
ejpam-5573	314	27	.	.	PUNCT
ejpam-5573	315	1	definition	definition	NOUN
ejpam-5573	315	2	9	9	NUM
ejpam-5573	315	3	.	.	PUNCT
ejpam-5573	316	1	let	let	VERB
ejpam-5573	316	2	(	(	PUNCT
ejpam-5573	316	3	u	u	NOUN
ejpam-5573	316	4	,	,	PUNCT
ejpam-5573	316	5	η	η	PROPN
ejpam-5573	316	6	,	,	PUNCT
ejpam-5573	316	7	η∗	η∗	NOUN
ejpam-5573	316	8	)	)	PUNCT
ejpam-5573	316	9	be	be	VERB
ejpam-5573	316	10	a	a	DET
ejpam-5573	316	11	dfts	dft	NOUN
ejpam-5573	316	12	,	,	PUNCT
ejpam-5573	316	13	r	r	NOUN
ejpam-5573	316	14	∈	∈	PROPN
ejpam-5573	317	1	i	i	NOUN
ejpam-5573	317	2	◦	◦	NOUN
ejpam-5573	317	3	,	,	PUNCT
ejpam-5573	317	4	and	and	CCONJ
ejpam-5573	317	5	s	s	PROPN
ejpam-5573	317	6	∈	∈	PROPN
ejpam-5573	317	7	i1	i1	PROPN
ejpam-5573	317	8	,	,	PUNCT
ejpam-5573	317	9	then	then	ADV
ejpam-5573	317	10	µ	µ	X
ejpam-5573	317	11	∈	∈	NOUN
ejpam-5573	317	12	iu	iu	ADV
ejpam-5573	317	13	is	be	AUX
ejpam-5573	317	14	called	call	VERB
ejpam-5573	317	15	an	an	DET
ejpam-5573	317	16	(	(	PUNCT
ejpam-5573	317	17	r	r	NOUN
ejpam-5573	317	18	,	,	PUNCT
ejpam-5573	317	19	s)-fuzzy	s)-fuzzy	PRON
ejpam-5573	317	20	compact	compact	ADJ
ejpam-5573	317	21	iff	iff	PROPN
ejpam-5573	317	22	for	for	ADP
ejpam-5573	317	23	each	each	DET
ejpam-5573	317	24	family	family	NOUN
ejpam-5573	317	25	{	{	PUNCT
ejpam-5573	317	26	λj	λj	PROPN
ejpam-5573	317	27	∈	∈	PROPN
ejpam-5573	317	28	iu	iu	SCONJ
ejpam-5573	317	29	|	|	ADV
ejpam-5573	317	30	η(λj	η(λj	NOUN
ejpam-5573	317	31	)	)	PUNCT
ejpam-5573	317	32	≥	≥	NOUN
ejpam-5573	317	33	r	r	NOUN
ejpam-5573	317	34	and	and	CCONJ
ejpam-5573	317	35	η∗(λj	η∗(λj	NOUN
ejpam-5573	317	36	)	)	PUNCT
ejpam-5573	317	37	≤	≤	NOUN
ejpam-5573	317	38	s}j∈𭟋	s}j∈𭟋	NOUN
ejpam-5573	317	39	,	,	PUNCT
ejpam-5573	317	40	such	such	ADJ
ejpam-5573	317	41	that	that	SCONJ
ejpam-5573	317	42	µ	µ	PRON
ejpam-5573	317	43	≤	≤	NUM
ejpam-5573	317	44	∨	∨	NUM
ejpam-5573	317	45	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	317	46	λj	λj	INTJ
ejpam-5573	317	47	,	,	PUNCT
ejpam-5573	317	48	there	there	PRON
ejpam-5573	317	49	is	be	VERB
ejpam-5573	317	50	a	a	DET
ejpam-5573	317	51	finite	finite	NOUN
ejpam-5573	317	52	subset	subset	NOUN
ejpam-5573	317	53	𭟋	𭟋	ADP
ejpam-5573	317	54	◦	◦	NOUN
ejpam-5573	317	55	of	of	ADP
ejpam-5573	317	56	𭟋	𭟋	NOUN
ejpam-5573	317	57	,	,	PUNCT
ejpam-5573	317	58	such	such	ADJ
ejpam-5573	317	59	that	that	SCONJ
ejpam-5573	317	60	µ	µ	PRON
ejpam-5573	317	61	≤	≤	NUM
ejpam-5573	317	62	∨	∨	NUM
ejpam-5573	317	63	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	317	64	◦	◦	NOUN
ejpam-5573	317	65	λj	λj	X
ejpam-5573	317	66	.	.	PUNCT
ejpam-5573	318	1	definition	definition	NOUN
ejpam-5573	318	2	10	10	NUM
ejpam-5573	318	3	.	.	PUNCT
ejpam-5573	319	1	let	let	VERB
ejpam-5573	319	2	(	(	PUNCT
ejpam-5573	319	3	u	u	NOUN
ejpam-5573	319	4	,	,	PUNCT
ejpam-5573	319	5	η	η	PROPN
ejpam-5573	319	6	,	,	PUNCT
ejpam-5573	319	7	η∗	η∗	NOUN
ejpam-5573	319	8	)	)	PUNCT
ejpam-5573	319	9	be	be	VERB
ejpam-5573	319	10	a	a	DET
ejpam-5573	319	11	dfts	dft	NOUN
ejpam-5573	319	12	,	,	PUNCT
ejpam-5573	319	13	r	r	NOUN
ejpam-5573	319	14	∈	∈	PROPN
ejpam-5573	320	1	i	i	NOUN
ejpam-5573	320	2	◦	◦	NOUN
ejpam-5573	320	3	,	,	PUNCT
ejpam-5573	320	4	and	and	CCONJ
ejpam-5573	320	5	s	s	PROPN
ejpam-5573	320	6	∈	∈	PROPN
ejpam-5573	320	7	i1	i1	PROPN
ejpam-5573	320	8	,	,	PUNCT
ejpam-5573	321	1	then	then	ADV
ejpam-5573	321	2	µ	µ	X
ejpam-5573	321	3	∈	∈	NOUN
ejpam-5573	321	4	iu	iu	ADV
ejpam-5573	321	5	is	be	AUX
ejpam-5573	321	6	called	call	VERB
ejpam-5573	321	7	an	an	DET
ejpam-5573	321	8	(	(	PUNCT
ejpam-5573	321	9	r	r	NOUN
ejpam-5573	321	10	,	,	PUNCT
ejpam-5573	321	11	s)-fuzzy	s)-fuzzy	ADJ
ejpam-5573	321	12	gs	gs	ADJ
ejpam-5573	321	13	-	-	PUNCT
ejpam-5573	321	14	compact	compact	ADJ
ejpam-5573	321	15	iff	iff	NOUN
ejpam-5573	321	16	for	for	ADP
ejpam-5573	321	17	each	each	DET
ejpam-5573	321	18	family	family	NOUN
ejpam-5573	321	19	{	{	PUNCT
ejpam-5573	321	20	λj	λj	PROPN
ejpam-5573	321	21	∈	∈	PROPN
ejpam-5573	321	22	iu	iu	ADV
ejpam-5573	321	23	|	|	ADV
ejpam-5573	321	24	λj	λj	PROPN
ejpam-5573	321	25	is	be	AUX
ejpam-5573	321	26	(	(	PUNCT
ejpam-5573	321	27	r	r	NOUN
ejpam-5573	321	28	,	,	PUNCT
ejpam-5573	321	29	s	s	NOUN
ejpam-5573	321	30	)	)	PUNCT
ejpam-5573	321	31	−	−	PROPN
ejpam-5573	321	32	gfso}j∈𭟋	gfso}j∈𭟋	PROPN
ejpam-5573	321	33	,	,	PUNCT
ejpam-5573	321	34	such	such	ADJ
ejpam-5573	321	35	that	that	SCONJ
ejpam-5573	321	36	µ	µ	PRON
ejpam-5573	321	37	≤	≤	NUM
ejpam-5573	321	38	∨	∨	NUM
ejpam-5573	321	39	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	321	40	λj	λj	INTJ
ejpam-5573	321	41	,	,	PUNCT
ejpam-5573	321	42	there	there	PRON
ejpam-5573	321	43	is	be	VERB
ejpam-5573	321	44	a	a	DET
ejpam-5573	321	45	finite	finite	NOUN
ejpam-5573	321	46	subset	subset	NOUN
ejpam-5573	321	47	𭟋	𭟋	ADP
ejpam-5573	321	48	◦	◦	NOUN
ejpam-5573	321	49	of	of	ADP
ejpam-5573	321	50	𭟋	𭟋	NOUN
ejpam-5573	321	51	,	,	PUNCT
ejpam-5573	321	52	such	such	ADJ
ejpam-5573	321	53	that	that	SCONJ
ejpam-5573	321	54	µ	µ	PRON
ejpam-5573	321	55	≤	≤	NUM
ejpam-5573	321	56	∨	∨	NUM
ejpam-5573	321	57	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	321	58	◦	◦	NOUN
ejpam-5573	321	59	λj	λj	X
ejpam-5573	321	60	.	.	PUNCT
ejpam-5573	322	1	lemma	lemma	PROPN
ejpam-5573	322	2	3	3	X
ejpam-5573	322	3	.	.	PUNCT
ejpam-5573	323	1	let	let	AUX
ejpam-5573	323	2	(	(	PUNCT
ejpam-5573	323	3	u	u	NOUN
ejpam-5573	323	4	,	,	PUNCT
ejpam-5573	323	5	η	η	PROPN
ejpam-5573	323	6	,	,	PUNCT
ejpam-5573	323	7	η∗	η∗	NOUN
ejpam-5573	323	8	)	)	PUNCT
ejpam-5573	323	9	be	be	VERB
ejpam-5573	323	10	a	a	DET
ejpam-5573	323	11	dfts	dft	NOUN
ejpam-5573	323	12	,	,	PUNCT
ejpam-5573	323	13	r	r	NOUN
ejpam-5573	323	14	∈	∈	PROPN
ejpam-5573	323	15	i	i	NOUN
ejpam-5573	323	16	◦	◦	NOUN
ejpam-5573	323	17	,	,	PUNCT
ejpam-5573	323	18	and	and	CCONJ
ejpam-5573	323	19	s	s	PROPN
ejpam-5573	323	20	∈	∈	PROPN
ejpam-5573	323	21	i1	i1	PROPN
ejpam-5573	323	22	.	.	PUNCT
ejpam-5573	324	1	if	if	SCONJ
ejpam-5573	324	2	µ	µ	PRON
ejpam-5573	324	3	∈	∈	NOUN
ejpam-5573	324	4	iu	iu	ADV
ejpam-5573	324	5	is	be	AUX
ejpam-5573	324	6	(	(	PUNCT
ejpam-5573	324	7	r	r	NOUN
ejpam-5573	324	8	,	,	PUNCT
ejpam-5573	324	9	s)-fuzzy	s)-fuzzy	NOUN
ejpam-5573	324	10	gscompact	gscompact	ADJ
ejpam-5573	324	11	,	,	PUNCT
ejpam-5573	324	12	then	then	ADV
ejpam-5573	324	13	µ	µ	X
ejpam-5573	324	14	is	be	AUX
ejpam-5573	324	15	(	(	PUNCT
ejpam-5573	324	16	r	r	NOUN
ejpam-5573	324	17	,	,	PUNCT
ejpam-5573	324	18	s)-fuzzy	s)-fuzzy	NOUN
ejpam-5573	324	19	compact	compact	ADJ
ejpam-5573	324	20	.	.	PUNCT
ejpam-5573	325	1	proof	proof	NOUN
ejpam-5573	325	2	.	.	PUNCT
ejpam-5573	326	1	follows	follow	VERB
ejpam-5573	326	2	from	from	ADP
ejpam-5573	326	3	definitions	definition	NOUN
ejpam-5573	326	4	9	9	NUM
ejpam-5573	326	5	and	and	CCONJ
ejpam-5573	326	6	10	10	NUM
ejpam-5573	326	7	.	.	PUNCT
ejpam-5573	327	1	theorem	theorem	NOUN
ejpam-5573	327	2	9	9	NUM
ejpam-5573	327	3	.	.	PUNCT
ejpam-5573	328	1	let	let	VERB
ejpam-5573	328	2	h	h	NOUN
ejpam-5573	328	3	:	:	PUNCT
ejpam-5573	328	4	(	(	PUNCT
ejpam-5573	328	5	u	u	NOUN
ejpam-5573	328	6	,	,	PUNCT
ejpam-5573	328	7	τ	τ	PROPN
ejpam-5573	328	8	,	,	PUNCT
ejpam-5573	328	9	τ∗	τ∗	NOUN
ejpam-5573	328	10	)	)	PUNCT
ejpam-5573	328	11	→	→	SYM
ejpam-5573	328	12	(	(	PUNCT
ejpam-5573	328	13	v	v	PROPN
ejpam-5573	328	14	,	,	PUNCT
ejpam-5573	328	15	η	η	NOUN
ejpam-5573	328	16	,	,	PUNCT
ejpam-5573	328	17	η∗	η∗	NOUN
ejpam-5573	328	18	)	)	PUNCT
ejpam-5573	328	19	be	be	VERB
ejpam-5573	328	20	a	a	DET
ejpam-5573	328	21	dfgs	dfgs	NOUN
ejpam-5573	328	22	-	-	PUNCT
ejpam-5573	328	23	continuous	continuous	ADJ
ejpam-5573	328	24	mapping	mapping	NOUN
ejpam-5573	328	25	,	,	PUNCT
ejpam-5573	328	26	r	r	NOUN
ejpam-5573	328	27	∈	∈	PROPN
ejpam-5573	329	1	i	i	NOUN
ejpam-5573	329	2	◦	◦	NOUN
ejpam-5573	329	3	,	,	PUNCT
ejpam-5573	329	4	and	and	CCONJ
ejpam-5573	329	5	s	s	PROPN
ejpam-5573	329	6	∈	∈	PROPN
ejpam-5573	329	7	i1	i1	PROPN
ejpam-5573	329	8	.	.	PUNCT
ejpam-5573	330	1	if	if	SCONJ
ejpam-5573	330	2	µ	µ	PRON
ejpam-5573	330	3	∈	∈	NOUN
ejpam-5573	330	4	iu	iu	ADV
ejpam-5573	330	5	is	be	AUX
ejpam-5573	330	6	(	(	PUNCT
ejpam-5573	330	7	r	r	NOUN
ejpam-5573	330	8	,	,	PUNCT
ejpam-5573	330	9	s)-fuzzy	s)-fuzzy	ADJ
ejpam-5573	330	10	gs	gs	ADJ
ejpam-5573	330	11	-	-	PUNCT
ejpam-5573	330	12	compact	compact	ADJ
ejpam-5573	330	13	,	,	PUNCT
ejpam-5573	330	14	then	then	ADV
ejpam-5573	330	15	h(µ	h(µ	PROPN
ejpam-5573	330	16	)	)	PUNCT
ejpam-5573	330	17	is	be	AUX
ejpam-5573	330	18	(	(	PUNCT
ejpam-5573	330	19	r	r	NOUN
ejpam-5573	330	20	,	,	PUNCT
ejpam-5573	330	21	s)-fuzzy	s)-fuzzy	NOUN
ejpam-5573	330	22	compact	compact	ADJ
ejpam-5573	330	23	.	.	PUNCT
ejpam-5573	331	1	proof	proof	NOUN
ejpam-5573	331	2	.	.	PUNCT
ejpam-5573	332	1	let	let	VERB
ejpam-5573	332	2	{	{	PUNCT
ejpam-5573	332	3	λj	λj	PROPN
ejpam-5573	332	4	∈	∈	PROPN
ejpam-5573	332	5	iv	iv	NUM
ejpam-5573	332	6	|	|	ADV
ejpam-5573	332	7	η(λj	η(λj	NOUN
ejpam-5573	332	8	)	)	PUNCT
ejpam-5573	332	9	≥	≥	NOUN
ejpam-5573	332	10	r	r	NOUN
ejpam-5573	332	11	and	and	CCONJ
ejpam-5573	332	12	η∗(λj	η∗(λj	NOUN
ejpam-5573	332	13	)	)	PUNCT
ejpam-5573	332	14	≤	≤	NUM
ejpam-5573	332	15	s}j∈𭟋	s}j∈𭟋	NOUN
ejpam-5573	332	16	with	with	ADP
ejpam-5573	332	17	h(µ	h(µ	NOUN
ejpam-5573	332	18	)	)	PUNCT
ejpam-5573	332	19	≤	≤	NUM
ejpam-5573	332	20	∨	∨	NUM
ejpam-5573	332	21	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	332	22	λj	λj	INTJ
ejpam-5573	332	23	,	,	PUNCT
ejpam-5573	332	24	then	then	ADV
ejpam-5573	332	25	{	{	PUNCT
ejpam-5573	332	26	h−1(λj	h−1(λj	NOUN
ejpam-5573	332	27	)	)	PUNCT
ejpam-5573	332	28	∈	∈	NOUN
ejpam-5573	332	29	iu	iu	ADP
ejpam-5573	332	30	|	|	ADV
ejpam-5573	332	31	h−1(λj	h−1(λj	NOUN
ejpam-5573	332	32	)	)	PUNCT
ejpam-5573	332	33	is	be	AUX
ejpam-5573	332	34	(	(	PUNCT
ejpam-5573	332	35	r	r	NOUN
ejpam-5573	332	36	,	,	PUNCT
ejpam-5573	332	37	s	s	NOUN
ejpam-5573	332	38	)	)	PUNCT
ejpam-5573	332	39	−	−	PROPN
ejpam-5573	332	40	gfso	gfso	NOUN
ejpam-5573	332	41	}	}	PUNCT
ejpam-5573	332	42	(	(	PUNCT
ejpam-5573	332	43	by	by	ADP
ejpam-5573	332	44	h	h	NOUN
ejpam-5573	332	45	is	be	AUX
ejpam-5573	332	46	dfgs	dfgs	NOUN
ejpam-5573	332	47	-	-	PUNCT
ejpam-5573	332	48	continuous	continuous	ADJ
ejpam-5573	332	49	)	)	PUNCT
ejpam-5573	332	50	,	,	PUNCT
ejpam-5573	332	51	such	such	ADJ
ejpam-5573	332	52	that	that	SCONJ
ejpam-5573	332	53	µ	µ	PRON
ejpam-5573	332	54	≤∨	≤∨	NOUN
ejpam-5573	332	55	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	332	56	h−1(λj	h−1(λj	NOUN
ejpam-5573	332	57	)	)	PUNCT
ejpam-5573	332	58	.	.	PUNCT
ejpam-5573	333	1	since	since	SCONJ
ejpam-5573	333	2	µ	µ	NOUN
ejpam-5573	333	3	is	be	AUX
ejpam-5573	333	4	(	(	PUNCT
ejpam-5573	333	5	r	r	NOUN
ejpam-5573	333	6	,	,	PUNCT
ejpam-5573	333	7	s)-fuzzy	s)-fuzzy	ADJ
ejpam-5573	333	8	gs	gs	ADJ
ejpam-5573	333	9	-	-	PUNCT
ejpam-5573	333	10	compact	compact	ADJ
ejpam-5573	333	11	,	,	PUNCT
ejpam-5573	333	12	there	there	PRON
ejpam-5573	333	13	is	be	VERB
ejpam-5573	333	14	a	a	DET
ejpam-5573	333	15	finite	finite	NOUN
ejpam-5573	333	16	subset	subset	NOUN
ejpam-5573	333	17	𭟋	𭟋	ADP
ejpam-5573	333	18	◦	◦	NOUN
ejpam-5573	333	19	of	of	ADP
ejpam-5573	333	20	𭟋	𭟋	NOUN
ejpam-5573	333	21	,	,	PUNCT
ejpam-5573	333	22	such	such	ADJ
ejpam-5573	333	23	that	that	SCONJ
ejpam-5573	333	24	µ	µ	PRON
ejpam-5573	333	25	≤	≤	NUM
ejpam-5573	333	26	∨	∨	NUM
ejpam-5573	333	27	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	333	28	◦	◦	NOUN
ejpam-5573	333	29	h−1(λj	h−1(λj	NOUN
ejpam-5573	333	30	)	)	PUNCT
ejpam-5573	333	31	.	.	PUNCT
ejpam-5573	334	1	thus	thus	ADV
ejpam-5573	334	2	,	,	PUNCT
ejpam-5573	334	3	h(µ	h(µ	PROPN
ejpam-5573	334	4	)	)	PUNCT
ejpam-5573	334	5	≤	≤	NUM
ejpam-5573	334	6	∨	∨	NUM
ejpam-5573	334	7	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	334	8	◦	◦	NOUN
ejpam-5573	334	9	λj	λj	X
ejpam-5573	334	10	.	.	PUNCT
ejpam-5573	335	1	hence	hence	ADV
ejpam-5573	335	2	,	,	PUNCT
ejpam-5573	335	3	the	the	DET
ejpam-5573	335	4	proof	proof	NOUN
ejpam-5573	335	5	is	be	AUX
ejpam-5573	335	6	completed	complete	VERB
ejpam-5573	335	7	.	.	PUNCT
ejpam-5573	336	1	definition	definition	NOUN
ejpam-5573	336	2	11	11	NUM
ejpam-5573	336	3	.	.	PUNCT
ejpam-5573	337	1	let	let	VERB
ejpam-5573	337	2	(	(	PUNCT
ejpam-5573	337	3	u	u	NOUN
ejpam-5573	337	4	,	,	PUNCT
ejpam-5573	337	5	η	η	PROPN
ejpam-5573	337	6	,	,	PUNCT
ejpam-5573	337	7	η∗	η∗	NOUN
ejpam-5573	337	8	)	)	PUNCT
ejpam-5573	337	9	be	be	VERB
ejpam-5573	337	10	a	a	DET
ejpam-5573	337	11	dfts	dft	NOUN
ejpam-5573	337	12	,	,	PUNCT
ejpam-5573	337	13	r	r	NOUN
ejpam-5573	337	14	∈	∈	PROPN
ejpam-5573	338	1	i	i	NOUN
ejpam-5573	338	2	◦	◦	NOUN
ejpam-5573	338	3	,	,	PUNCT
ejpam-5573	338	4	and	and	CCONJ
ejpam-5573	338	5	s	s	PROPN
ejpam-5573	338	6	∈	∈	PROPN
ejpam-5573	338	7	i1	i1	PROPN
ejpam-5573	338	8	,	,	PUNCT
ejpam-5573	338	9	then	then	ADV
ejpam-5573	338	10	µ	µ	X
ejpam-5573	338	11	∈	∈	NOUN
ejpam-5573	338	12	iu	iu	ADV
ejpam-5573	338	13	is	be	AUX
ejpam-5573	338	14	called	call	VERB
ejpam-5573	338	15	an	an	DET
ejpam-5573	338	16	(	(	PUNCT
ejpam-5573	338	17	r	r	NOUN
ejpam-5573	338	18	,	,	PUNCT
ejpam-5573	338	19	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	338	20	almost	almost	ADV
ejpam-5573	338	21	compact	compact	ADJ
ejpam-5573	338	22	iff	iff	NOUN
ejpam-5573	338	23	for	for	ADP
ejpam-5573	338	24	each	each	DET
ejpam-5573	338	25	family	family	NOUN
ejpam-5573	338	26	{	{	PUNCT
ejpam-5573	338	27	λj	λj	PROPN
ejpam-5573	338	28	∈	∈	PROPN
ejpam-5573	338	29	iu	iu	SCONJ
ejpam-5573	338	30	|	|	ADV
ejpam-5573	338	31	η(λj	η(λj	NOUN
ejpam-5573	338	32	)	)	PUNCT
ejpam-5573	338	33	≥	≥	NOUN
ejpam-5573	338	34	r	r	NOUN
ejpam-5573	338	35	and	and	CCONJ
ejpam-5573	338	36	η∗(λj	η∗(λj	NOUN
ejpam-5573	338	37	)	)	PUNCT
ejpam-5573	338	38	≤	≤	NOUN
ejpam-5573	338	39	s}j∈𭟋	s}j∈𭟋	NOUN
ejpam-5573	338	40	,	,	PUNCT
ejpam-5573	338	41	such	such	ADJ
ejpam-5573	338	42	that	that	SCONJ
ejpam-5573	338	43	µ	µ	PRON
ejpam-5573	338	44	≤	≤	NUM
ejpam-5573	338	45	∨	∨	NUM
ejpam-5573	338	46	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	338	47	λj	λj	INTJ
ejpam-5573	338	48	,	,	PUNCT
ejpam-5573	338	49	there	there	PRON
ejpam-5573	338	50	is	be	VERB
ejpam-5573	338	51	a	a	DET
ejpam-5573	338	52	finite	finite	NOUN
ejpam-5573	338	53	subset	subset	NOUN
ejpam-5573	338	54	𭟋	𭟋	ADP
ejpam-5573	338	55	◦	◦	NOUN
ejpam-5573	338	56	of	of	ADP
ejpam-5573	338	57	𭟋	𭟋	NOUN
ejpam-5573	338	58	,	,	PUNCT
ejpam-5573	338	59	such	such	ADJ
ejpam-5573	338	60	that	that	SCONJ
ejpam-5573	338	61	µ	µ	PRON
ejpam-5573	338	62	≤	≤	NUM
ejpam-5573	338	63	∨	∨	NUM
ejpam-5573	338	64	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	338	65	◦	◦	NOUN
ejpam-5573	338	66	cη	cη	ADP
ejpam-5573	338	67	,	,	PUNCT
ejpam-5573	338	68	η∗(λj	η∗(λj	NOUN
ejpam-5573	338	69	,	,	PUNCT
ejpam-5573	338	70	r	r	NOUN
ejpam-5573	338	71	,	,	PUNCT
ejpam-5573	338	72	s	s	NOUN
ejpam-5573	338	73	)	)	PUNCT
ejpam-5573	338	74	.	.	PUNCT
ejpam-5573	339	1	f.	f.	PROPN
ejpam-5573	339	2	alsharari	alsharari	PROPN
ejpam-5573	339	3	,	,	PUNCT
ejpam-5573	339	4	o.	o.	PROPN
ejpam-5573	339	5	m.	m.	PROPN
ejpam-5573	339	6	taha	taha	PROPN
ejpam-5573	339	7	,	,	PUNCT
ejpam-5573	339	8	i.	i.	PROPN
ejpam-5573	339	9	m.	m.	PROPN
ejpam-5573	339	10	taha	taha	PROPN
ejpam-5573	339	11	/	/	PUNCT
ejpam-5573	339	12	eur	eur	PROPN
ejpam-5573	339	13	.	.	PUNCT
ejpam-5573	340	1	j.	j.	PROPN
ejpam-5573	340	2	pure	pure	PROPN
ejpam-5573	340	3	appl	appl	PROPN
ejpam-5573	340	4	.	.	PROPN
ejpam-5573	340	5	math	math	PROPN
ejpam-5573	340	6	,	,	PUNCT
ejpam-5573	340	7	17	17	NUM
ejpam-5573	340	8	(	(	PUNCT
ejpam-5573	340	9	4	4	NUM
ejpam-5573	340	10	)	)	PUNCT
ejpam-5573	340	11	(	(	PUNCT
ejpam-5573	340	12	2024	2024	NUM
ejpam-5573	340	13	)	)	PUNCT
ejpam-5573	340	14	,	,	PUNCT
ejpam-5573	340	15	4093	4093	NUM
ejpam-5573	340	16	-	-	SYM
ejpam-5573	340	17	4111	4111	NUM
ejpam-5573	340	18	4105	4105	NUM
ejpam-5573	340	19	definition	definition	NOUN
ejpam-5573	340	20	12	12	NUM
ejpam-5573	340	21	.	.	PUNCT
ejpam-5573	341	1	let	let	VERB
ejpam-5573	341	2	(	(	PUNCT
ejpam-5573	341	3	u	u	NOUN
ejpam-5573	341	4	,	,	PUNCT
ejpam-5573	341	5	η	η	PROPN
ejpam-5573	341	6	,	,	PUNCT
ejpam-5573	341	7	η∗	η∗	NOUN
ejpam-5573	341	8	)	)	PUNCT
ejpam-5573	341	9	be	be	VERB
ejpam-5573	341	10	a	a	DET
ejpam-5573	341	11	dfts	dft	NOUN
ejpam-5573	341	12	,	,	PUNCT
ejpam-5573	341	13	r	r	NOUN
ejpam-5573	341	14	∈	∈	PROPN
ejpam-5573	342	1	i	i	NOUN
ejpam-5573	342	2	◦	◦	NOUN
ejpam-5573	342	3	,	,	PUNCT
ejpam-5573	342	4	and	and	CCONJ
ejpam-5573	342	5	s	s	PROPN
ejpam-5573	342	6	∈	∈	PROPN
ejpam-5573	342	7	i1	i1	PROPN
ejpam-5573	342	8	,	,	PUNCT
ejpam-5573	343	1	then	then	ADV
ejpam-5573	343	2	µ	µ	X
ejpam-5573	343	3	∈	∈	NOUN
ejpam-5573	343	4	iu	iu	ADV
ejpam-5573	343	5	is	be	AUX
ejpam-5573	343	6	called	call	VERB
ejpam-5573	343	7	an	an	DET
ejpam-5573	343	8	(	(	PUNCT
ejpam-5573	343	9	r	r	NOUN
ejpam-5573	343	10	,	,	PUNCT
ejpam-5573	343	11	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	343	12	almost	almost	ADV
ejpam-5573	343	13	gs	gs	ADJ
ejpam-5573	343	14	-	-	PUNCT
ejpam-5573	343	15	compact	compact	ADJ
ejpam-5573	343	16	iff	iff	NOUN
ejpam-5573	343	17	for	for	ADP
ejpam-5573	343	18	each	each	DET
ejpam-5573	343	19	family	family	NOUN
ejpam-5573	343	20	{	{	PUNCT
ejpam-5573	343	21	λj	λj	PROPN
ejpam-5573	343	22	∈	∈	PROPN
ejpam-5573	343	23	iu	iu	ADV
ejpam-5573	343	24	|	|	ADV
ejpam-5573	343	25	λj	λj	PROPN
ejpam-5573	343	26	is	be	AUX
ejpam-5573	343	27	(	(	PUNCT
ejpam-5573	343	28	r	r	NOUN
ejpam-5573	343	29	,	,	PUNCT
ejpam-5573	343	30	s)−	s)−	PROPN
ejpam-5573	343	31	gfso}j∈𭟋	gfso}j∈𭟋	PROPN
ejpam-5573	343	32	,	,	PUNCT
ejpam-5573	343	33	such	such	ADJ
ejpam-5573	343	34	that	that	SCONJ
ejpam-5573	343	35	µ	µ	PRON
ejpam-5573	343	36	≤	≤	NUM
ejpam-5573	343	37	∨	∨	NUM
ejpam-5573	343	38	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	343	39	λj	λj	INTJ
ejpam-5573	343	40	,	,	PUNCT
ejpam-5573	343	41	there	there	PRON
ejpam-5573	343	42	is	be	VERB
ejpam-5573	343	43	a	a	DET
ejpam-5573	343	44	finite	finite	NOUN
ejpam-5573	343	45	subset	subset	NOUN
ejpam-5573	343	46	𭟋	𭟋	ADP
ejpam-5573	343	47	◦	◦	NOUN
ejpam-5573	343	48	of	of	ADP
ejpam-5573	343	49	𭟋	𭟋	NOUN
ejpam-5573	343	50	,	,	PUNCT
ejpam-5573	343	51	such	such	ADJ
ejpam-5573	343	52	that	that	SCONJ
ejpam-5573	343	53	µ	µ	PRON
ejpam-5573	343	54	≤	≤	NUM
ejpam-5573	343	55	∨	∨	NUM
ejpam-5573	343	56	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	343	57	◦	◦	NOUN
ejpam-5573	343	58	cη	cη	ADP
ejpam-5573	343	59	,	,	PUNCT
ejpam-5573	343	60	η∗(λj	η∗(λj	NOUN
ejpam-5573	343	61	,	,	PUNCT
ejpam-5573	343	62	r	r	NOUN
ejpam-5573	343	63	,	,	PUNCT
ejpam-5573	343	64	s	s	PART
ejpam-5573	343	65	)	)	PUNCT
ejpam-5573	343	66	.	.	PUNCT
ejpam-5573	344	1	lemma	lemma	PROPN
ejpam-5573	344	2	4	4	X
ejpam-5573	344	3	.	.	PUNCT
ejpam-5573	345	1	let	let	AUX
ejpam-5573	345	2	(	(	PUNCT
ejpam-5573	345	3	u	u	NOUN
ejpam-5573	345	4	,	,	PUNCT
ejpam-5573	345	5	η	η	PROPN
ejpam-5573	345	6	,	,	PUNCT
ejpam-5573	345	7	η∗	η∗	NOUN
ejpam-5573	345	8	)	)	PUNCT
ejpam-5573	345	9	be	be	VERB
ejpam-5573	345	10	a	a	DET
ejpam-5573	345	11	dfts	dft	NOUN
ejpam-5573	345	12	,	,	PUNCT
ejpam-5573	345	13	r	r	NOUN
ejpam-5573	345	14	∈	∈	PROPN
ejpam-5573	345	15	i	i	NOUN
ejpam-5573	345	16	◦	◦	NOUN
ejpam-5573	345	17	,	,	PUNCT
ejpam-5573	345	18	and	and	CCONJ
ejpam-5573	345	19	s	s	PROPN
ejpam-5573	345	20	∈	∈	PROPN
ejpam-5573	345	21	i1	i1	PROPN
ejpam-5573	345	22	.	.	PUNCT
ejpam-5573	346	1	if	if	SCONJ
ejpam-5573	346	2	µ	µ	PRON
ejpam-5573	346	3	∈	∈	NOUN
ejpam-5573	346	4	iu	iu	ADV
ejpam-5573	346	5	is	be	AUX
ejpam-5573	346	6	(	(	PUNCT
ejpam-5573	346	7	r	r	NOUN
ejpam-5573	346	8	,	,	PUNCT
ejpam-5573	346	9	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	346	10	almost	almost	ADV
ejpam-5573	346	11	gs	gs	ADJ
ejpam-5573	346	12	-	-	PUNCT
ejpam-5573	346	13	compact	compact	ADJ
ejpam-5573	346	14	,	,	PUNCT
ejpam-5573	346	15	then	then	ADV
ejpam-5573	346	16	µ	µ	X
ejpam-5573	346	17	is	be	AUX
ejpam-5573	346	18	(	(	PUNCT
ejpam-5573	346	19	r	r	NOUN
ejpam-5573	346	20	,	,	PUNCT
ejpam-5573	346	21	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	346	22	almost	almost	ADV
ejpam-5573	346	23	compact	compact	ADJ
ejpam-5573	346	24	.	.	PUNCT
ejpam-5573	347	1	proof	proof	NOUN
ejpam-5573	347	2	.	.	PUNCT
ejpam-5573	348	1	follows	follow	VERB
ejpam-5573	348	2	from	from	ADP
ejpam-5573	348	3	definitions	definition	NOUN
ejpam-5573	348	4	11	11	NUM
ejpam-5573	348	5	and	and	CCONJ
ejpam-5573	348	6	12	12	NUM
ejpam-5573	348	7	.	.	PUNCT
ejpam-5573	349	1	lemma	lemma	PROPN
ejpam-5573	349	2	5	5	X
ejpam-5573	349	3	.	.	PUNCT
ejpam-5573	350	1	let	let	VERB
ejpam-5573	350	2	(	(	PUNCT
ejpam-5573	350	3	u	u	NOUN
ejpam-5573	350	4	,	,	PUNCT
ejpam-5573	350	5	η	η	PROPN
ejpam-5573	350	6	,	,	PUNCT
ejpam-5573	350	7	η∗	η∗	NOUN
ejpam-5573	350	8	)	)	PUNCT
ejpam-5573	350	9	be	be	VERB
ejpam-5573	350	10	a	a	DET
ejpam-5573	350	11	dfts	dft	NOUN
ejpam-5573	350	12	,	,	PUNCT
ejpam-5573	350	13	r	r	NOUN
ejpam-5573	350	14	∈	∈	PROPN
ejpam-5573	351	1	i	i	NOUN
ejpam-5573	351	2	◦	◦	NOUN
ejpam-5573	351	3	,	,	PUNCT
ejpam-5573	351	4	and	and	CCONJ
ejpam-5573	351	5	s	s	PROPN
ejpam-5573	351	6	∈	∈	PROPN
ejpam-5573	351	7	i1	i1	PROPN
ejpam-5573	351	8	.	.	PUNCT
ejpam-5573	352	1	if	if	SCONJ
ejpam-5573	352	2	µ	µ	PRON
ejpam-5573	352	3	∈	∈	NOUN
ejpam-5573	352	4	iu	iu	ADV
ejpam-5573	352	5	is	be	AUX
ejpam-5573	352	6	(	(	PUNCT
ejpam-5573	352	7	r	r	NOUN
ejpam-5573	352	8	,	,	PUNCT
ejpam-5573	352	9	s)-fuzzy	s)-fuzzy	NOUN
ejpam-5573	352	10	compact	compact	ADJ
ejpam-5573	352	11	(	(	PUNCT
ejpam-5573	352	12	resp	resp	NOUN
ejpam-5573	352	13	.	.	PUNCT
ejpam-5573	352	14	,	,	PUNCT
ejpam-5573	352	15	gs	gs	NOUN
ejpam-5573	352	16	-	-	PUNCT
ejpam-5573	352	17	compact	compact	ADJ
ejpam-5573	352	18	)	)	PUNCT
ejpam-5573	352	19	,	,	PUNCT
ejpam-5573	352	20	then	then	ADV
ejpam-5573	352	21	µ	µ	X
ejpam-5573	352	22	is	be	AUX
ejpam-5573	352	23	(	(	PUNCT
ejpam-5573	352	24	r	r	NOUN
ejpam-5573	352	25	,	,	PUNCT
ejpam-5573	352	26	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	352	27	almost	almost	ADV
ejpam-5573	352	28	compact	compact	ADJ
ejpam-5573	352	29	(	(	PUNCT
ejpam-5573	352	30	resp	resp	NOUN
ejpam-5573	352	31	.	.	PUNCT
ejpam-5573	352	32	,	,	PUNCT
ejpam-5573	352	33	almost	almost	ADV
ejpam-5573	352	34	gs	gs	ADJ
ejpam-5573	352	35	-	-	PUNCT
ejpam-5573	352	36	compact	compact	ADJ
ejpam-5573	352	37	)	)	PUNCT
ejpam-5573	352	38	.	.	PUNCT
ejpam-5573	353	1	proof	proof	NOUN
ejpam-5573	353	2	.	.	PUNCT
ejpam-5573	354	1	follows	follow	VERB
ejpam-5573	354	2	from	from	ADP
ejpam-5573	354	3	definitions	definition	NOUN
ejpam-5573	354	4	9	9	NUM
ejpam-5573	354	5	,	,	PUNCT
ejpam-5573	354	6	10	10	NUM
ejpam-5573	354	7	,	,	PUNCT
ejpam-5573	354	8	11	11	NUM
ejpam-5573	354	9	and	and	CCONJ
ejpam-5573	354	10	12	12	NUM
ejpam-5573	354	11	.	.	PUNCT
ejpam-5573	355	1	remark	remark	NOUN
ejpam-5573	355	2	9	9	NUM
ejpam-5573	355	3	.	.	PUNCT
ejpam-5573	356	1	the	the	DET
ejpam-5573	356	2	converse	converse	NOUN
ejpam-5573	356	3	of	of	ADP
ejpam-5573	356	4	lemma	lemma	PROPN
ejpam-5573	356	5	5	5	NUM
ejpam-5573	356	6	may	may	AUX
ejpam-5573	356	7	not	not	PART
ejpam-5573	356	8	be	be	AUX
ejpam-5573	356	9	true	true	ADJ
ejpam-5573	356	10	,	,	PUNCT
ejpam-5573	356	11	as	as	SCONJ
ejpam-5573	356	12	shown	show	VERB
ejpam-5573	356	13	by	by	ADP
ejpam-5573	356	14	example	example	NOUN
ejpam-5573	356	15	10	10	NUM
ejpam-5573	356	16	.	.	PUNCT
ejpam-5573	356	17	example	example	NOUN
ejpam-5573	357	1	10	10	NUM
ejpam-5573	357	2	.	.	PUNCT
ejpam-5573	358	1	let	let	VERB
ejpam-5573	358	2	v	v	VERB
ejpam-5573	358	3	=	=	SYM
ejpam-5573	358	4	i	i	PROPN
ejpam-5573	358	5	,	,	PUNCT
ejpam-5573	358	6	k	k	PROPN
ejpam-5573	358	7	∈	∈	PROPN
ejpam-5573	358	8	n	n	PRON
ejpam-5573	358	9	−	−	PROPN
ejpam-5573	358	10	{	{	PUNCT
ejpam-5573	358	11	1	1	NUM
ejpam-5573	358	12	}	}	PUNCT
ejpam-5573	358	13	,	,	PUNCT
ejpam-5573	358	14	and	and	CCONJ
ejpam-5573	358	15	ρ	ρ	NOUN
ejpam-5573	358	16	,	,	PUNCT
ejpam-5573	358	17	λk	λk	PROPN
ejpam-5573	358	18	∈	∈	NOUN
ejpam-5573	358	19	iv	iv	NUM
ejpam-5573	358	20	defined	define	VERB
ejpam-5573	358	21	as	as	SCONJ
ejpam-5573	358	22	follows	follow	VERB
ejpam-5573	358	23	:	:	PUNCT
ejpam-5573	358	24	ρ(v	ρ(v	X
ejpam-5573	358	25	)	)	PUNCT
ejpam-5573	359	1	=	=	NOUN
ejpam-5573	359	2	{	{	PUNCT
ejpam-5573	359	3	1	1	NUM
ejpam-5573	359	4	,	,	PUNCT
ejpam-5573	359	5	if	if	SCONJ
ejpam-5573	359	6	v	v	NOUN
ejpam-5573	359	7	=	=	SYM
ejpam-5573	359	8	0	0	NUM
ejpam-5573	359	9	,	,	PUNCT
ejpam-5573	359	10	1	1	NUM
ejpam-5573	359	11	2	2	NUM
ejpam-5573	359	12	,	,	PUNCT
ejpam-5573	359	13	otherwise	otherwise	ADV
ejpam-5573	359	14	,	,	PUNCT
ejpam-5573	359	15	λk(v	λk(v	PUNCT
ejpam-5573	359	16	)	)	PUNCT
ejpam-5573	360	1	=	=	PUNCT
ejpam-5573	360	2			NOUN
ejpam-5573	360	3	0.8	0.8	NUM
ejpam-5573	360	4	,	,	PUNCT
ejpam-5573	360	5	if	if	SCONJ
ejpam-5573	360	6	v	v	NOUN
ejpam-5573	360	7	=	=	SYM
ejpam-5573	360	8	0	0	NUM
ejpam-5573	360	9	,	,	PUNCT
ejpam-5573	360	10	kv	kv	PROPN
ejpam-5573	360	11	,	,	PUNCT
ejpam-5573	360	12	if	if	SCONJ
ejpam-5573	360	13	0	0	NUM
ejpam-5573	360	14	<	<	X
ejpam-5573	360	15	v	v	X
ejpam-5573	360	16	≤	≤	NUM
ejpam-5573	360	17	1	1	NUM
ejpam-5573	360	18	k	k	NOUN
ejpam-5573	360	19	,	,	PUNCT
ejpam-5573	360	20	1	1	NUM
ejpam-5573	360	21	,	,	PUNCT
ejpam-5573	360	22	if	if	SCONJ
ejpam-5573	360	23	1	1	NUM
ejpam-5573	360	24	k	k	NOUN
ejpam-5573	360	25	<	<	X
ejpam-5573	360	26	v	v	X
ejpam-5573	360	27	≤	≤	NUM
ejpam-5573	360	28	1	1	NUM
ejpam-5573	360	29	.	.	PUNCT
ejpam-5573	361	1	also	also	ADV
ejpam-5573	361	2	,	,	PUNCT
ejpam-5573	361	3	(	(	PUNCT
ejpam-5573	361	4	η	η	NOUN
ejpam-5573	361	5	,	,	PUNCT
ejpam-5573	361	6	η∗	η∗	NOUN
ejpam-5573	361	7	)	)	PUNCT
ejpam-5573	361	8	defined	define	VERB
ejpam-5573	361	9	on	on	ADP
ejpam-5573	361	10	v	v	NOUN
ejpam-5573	361	11	as	as	SCONJ
ejpam-5573	361	12	follows	follow	VERB
ejpam-5573	361	13	:	:	PUNCT
ejpam-5573	361	14	η(µ	η(µ	PROPN
ejpam-5573	361	15	)	)	PUNCT
ejpam-5573	362	1	=	=	PUNCT
ejpam-5573	362	2			NOUN
ejpam-5573	362	3	1	1	NUM
ejpam-5573	362	4	,	,	PUNCT
ejpam-5573	362	5	if	if	SCONJ
ejpam-5573	362	6	µ	µ	X
ejpam-5573	362	7	∈	∈	X
ejpam-5573	362	8	{	{	PUNCT
ejpam-5573	362	9	0	0	NUM
ejpam-5573	362	10	,	,	PUNCT
ejpam-5573	362	11	1	1	NUM
ejpam-5573	362	12	}	}	PUNCT
ejpam-5573	362	13	,	,	PUNCT
ejpam-5573	362	14	2	2	NUM
ejpam-5573	362	15	3	3	NUM
ejpam-5573	362	16	,	,	PUNCT
ejpam-5573	362	17	if	if	SCONJ
ejpam-5573	362	18	µ	µ	PRON
ejpam-5573	362	19	≤	≤	NOUN
ejpam-5573	362	20	ρ	ρ	PROPN
ejpam-5573	362	21	,	,	PUNCT
ejpam-5573	362	22	k	k	PROPN
ejpam-5573	362	23	k+1	k+1	X
ejpam-5573	362	24	,	,	PUNCT
ejpam-5573	362	25	if	if	SCONJ
ejpam-5573	362	26	µ	µ	PRON
ejpam-5573	362	27	≤	≤	X
ejpam-5573	362	28	λk	λk	ADP
ejpam-5573	362	29	,	,	PUNCT
ejpam-5573	362	30	0	0	NUM
ejpam-5573	362	31	,	,	PUNCT
ejpam-5573	362	32	otherwise	otherwise	ADV
ejpam-5573	362	33	,	,	PUNCT
ejpam-5573	362	34	η∗(µ	η∗(µ	PROPN
ejpam-5573	362	35	)	)	PUNCT
ejpam-5573	362	36	=	=	PUNCT
ejpam-5573	363	1			NOUN
ejpam-5573	363	2	0	0	NUM
ejpam-5573	363	3	,	,	PUNCT
ejpam-5573	363	4	if	if	SCONJ
ejpam-5573	363	5	µ	µ	X
ejpam-5573	363	6	∈	∈	X
ejpam-5573	363	7	{	{	PUNCT
ejpam-5573	363	8	0	0	NUM
ejpam-5573	363	9	,	,	PUNCT
ejpam-5573	363	10	1	1	NUM
ejpam-5573	363	11	}	}	PUNCT
ejpam-5573	363	12	,	,	PUNCT
ejpam-5573	363	13	1	1	NUM
ejpam-5573	363	14	3	3	NUM
ejpam-5573	363	15	,	,	PUNCT
ejpam-5573	363	16	if	if	SCONJ
ejpam-5573	363	17	µ	µ	PRON
ejpam-5573	363	18	≤	≤	NUM
ejpam-5573	363	19	ρ	ρ	NUM
ejpam-5573	363	20	,	,	PUNCT
ejpam-5573	363	21	1	1	NUM
ejpam-5573	363	22	k+1	k+1	NOUN
ejpam-5573	363	23	,	,	PUNCT
ejpam-5573	363	24	if	if	SCONJ
ejpam-5573	363	25	µ	µ	PRON
ejpam-5573	363	26	≤	≤	X
ejpam-5573	363	27	λk	λk	ADP
ejpam-5573	363	28	,	,	PUNCT
ejpam-5573	363	29	1	1	NUM
ejpam-5573	363	30	,	,	PUNCT
ejpam-5573	363	31	otherwise	otherwise	ADV
ejpam-5573	363	32	.	.	PUNCT
ejpam-5573	364	1	thus	thus	ADV
ejpam-5573	364	2	,	,	PUNCT
ejpam-5573	364	3	v	v	NOUN
ejpam-5573	364	4	is	be	AUX
ejpam-5573	364	5	(	(	PUNCT
ejpam-5573	364	6	12	12	NUM
ejpam-5573	364	7	,	,	PUNCT
ejpam-5573	364	8	1	1	NUM
ejpam-5573	364	9	2)-fuzzy	2)-fuzzy	NUM
ejpam-5573	364	10	almost	almost	ADV
ejpam-5573	364	11	compact	compact	ADJ
ejpam-5573	364	12	,	,	PUNCT
ejpam-5573	364	13	but	but	CCONJ
ejpam-5573	364	14	it	it	PRON
ejpam-5573	364	15	is	be	AUX
ejpam-5573	364	16	not	not	PART
ejpam-5573	364	17	(	(	PUNCT
ejpam-5573	364	18	12	12	NUM
ejpam-5573	364	19	,	,	PUNCT
ejpam-5573	364	20	1	1	NUM
ejpam-5573	364	21	2)-fuzzy	2)-fuzzy	NUM
ejpam-5573	364	22	compact	compact	ADJ
ejpam-5573	364	23	.	.	PUNCT
ejpam-5573	365	1	theorem	theorem	ADJ
ejpam-5573	365	2	10	10	NUM
ejpam-5573	365	3	.	.	PUNCT
ejpam-5573	366	1	let	let	VERB
ejpam-5573	366	2	h	h	NOUN
ejpam-5573	366	3	:	:	PUNCT
ejpam-5573	366	4	(	(	PUNCT
ejpam-5573	366	5	u	u	NOUN
ejpam-5573	366	6	,	,	PUNCT
ejpam-5573	366	7	τ	τ	PROPN
ejpam-5573	366	8	,	,	PUNCT
ejpam-5573	366	9	τ∗	τ∗	NOUN
ejpam-5573	366	10	)	)	PUNCT
ejpam-5573	366	11	→	→	SYM
ejpam-5573	366	12	(	(	PUNCT
ejpam-5573	366	13	v	v	PROPN
ejpam-5573	366	14	,	,	PUNCT
ejpam-5573	366	15	η	η	NOUN
ejpam-5573	366	16	,	,	PUNCT
ejpam-5573	366	17	η∗	η∗	NOUN
ejpam-5573	366	18	)	)	PUNCT
ejpam-5573	366	19	be	be	VERB
ejpam-5573	366	20	a	a	DET
ejpam-5573	366	21	df	df	NOUN
ejpam-5573	366	22	-	-	PUNCT
ejpam-5573	366	23	continuous	continuous	ADJ
ejpam-5573	366	24	mapping	mapping	NOUN
ejpam-5573	366	25	,	,	PUNCT
ejpam-5573	366	26	r	r	NOUN
ejpam-5573	366	27	∈	∈	PROPN
ejpam-5573	367	1	i	i	NOUN
ejpam-5573	367	2	◦	◦	NOUN
ejpam-5573	367	3	,	,	PUNCT
ejpam-5573	367	4	and	and	CCONJ
ejpam-5573	367	5	s	s	PROPN
ejpam-5573	367	6	∈	∈	PROPN
ejpam-5573	367	7	i1	i1	PROPN
ejpam-5573	367	8	.	.	PUNCT
ejpam-5573	368	1	if	if	SCONJ
ejpam-5573	368	2	µ	µ	PRON
ejpam-5573	368	3	∈	∈	NOUN
ejpam-5573	368	4	iu	iu	ADV
ejpam-5573	368	5	is	be	AUX
ejpam-5573	368	6	(	(	PUNCT
ejpam-5573	368	7	r	r	NOUN
ejpam-5573	368	8	,	,	PUNCT
ejpam-5573	368	9	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	368	10	almost	almost	ADV
ejpam-5573	368	11	gs	gs	ADJ
ejpam-5573	368	12	-	-	PUNCT
ejpam-5573	368	13	compact	compact	ADJ
ejpam-5573	368	14	,	,	PUNCT
ejpam-5573	368	15	then	then	ADV
ejpam-5573	368	16	h(µ	h(µ	PROPN
ejpam-5573	368	17	)	)	PUNCT
ejpam-5573	368	18	is	be	AUX
ejpam-5573	368	19	(	(	PUNCT
ejpam-5573	368	20	r	r	NOUN
ejpam-5573	368	21	,	,	PUNCT
ejpam-5573	368	22	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	368	23	almost	almost	ADV
ejpam-5573	368	24	compact	compact	ADJ
ejpam-5573	368	25	.	.	PUNCT
ejpam-5573	369	1	proof	proof	NOUN
ejpam-5573	369	2	.	.	PUNCT
ejpam-5573	370	1	let	let	VERB
ejpam-5573	370	2	{	{	PUNCT
ejpam-5573	370	3	λj	λj	PROPN
ejpam-5573	370	4	∈	∈	PROPN
ejpam-5573	370	5	iv	iv	NUM
ejpam-5573	370	6	|	|	ADV
ejpam-5573	370	7	η(λj	η(λj	NOUN
ejpam-5573	370	8	)	)	PUNCT
ejpam-5573	370	9	≥	≥	NOUN
ejpam-5573	370	10	r	r	NOUN
ejpam-5573	370	11	and	and	CCONJ
ejpam-5573	370	12	η∗(λj	η∗(λj	NOUN
ejpam-5573	370	13	)	)	PUNCT
ejpam-5573	370	14	≤	≤	NUM
ejpam-5573	370	15	s}j∈𭟋	s}j∈𭟋	NOUN
ejpam-5573	370	16	with	with	ADP
ejpam-5573	370	17	h(µ	h(µ	NOUN
ejpam-5573	370	18	)	)	PUNCT
ejpam-5573	370	19	≤	≤	NUM
ejpam-5573	370	20	∨	∨	NUM
ejpam-5573	370	21	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	370	22	λj	λj	INTJ
ejpam-5573	370	23	,	,	PUNCT
ejpam-5573	370	24	then	then	ADV
ejpam-5573	370	25	{	{	PUNCT
ejpam-5573	370	26	h−1(λj	h−1(λj	NOUN
ejpam-5573	370	27	)	)	PUNCT
ejpam-5573	370	28	∈	∈	NOUN
ejpam-5573	370	29	iu	iu	ADP
ejpam-5573	370	30	|	|	ADV
ejpam-5573	370	31	h−1(λj	h−1(λj	NOUN
ejpam-5573	370	32	)	)	PUNCT
ejpam-5573	370	33	is	be	AUX
ejpam-5573	370	34	(	(	PUNCT
ejpam-5573	370	35	r	r	NOUN
ejpam-5573	370	36	,	,	PUNCT
ejpam-5573	370	37	s	s	NOUN
ejpam-5573	370	38	)	)	PUNCT
ejpam-5573	370	39	−	−	PROPN
ejpam-5573	370	40	gfso	gfso	NOUN
ejpam-5573	370	41	}	}	PUNCT
ejpam-5573	370	42	(	(	PUNCT
ejpam-5573	370	43	by	by	ADP
ejpam-5573	370	44	h	h	NOUN
ejpam-5573	370	45	is	be	AUX
ejpam-5573	370	46	dfgs	dfgs	NOUN
ejpam-5573	370	47	-	-	PUNCT
ejpam-5573	370	48	continuous	continuous	ADJ
ejpam-5573	370	49	)	)	PUNCT
ejpam-5573	370	50	,	,	PUNCT
ejpam-5573	370	51	such	such	ADJ
ejpam-5573	370	52	that	that	SCONJ
ejpam-5573	370	53	µ	µ	PRON
ejpam-5573	370	54	≤∨	≤∨	NOUN
ejpam-5573	370	55	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	370	56	h−1(λj	h−1(λj	NOUN
ejpam-5573	370	57	)	)	PUNCT
ejpam-5573	370	58	.	.	PUNCT
ejpam-5573	371	1	since	since	SCONJ
ejpam-5573	371	2	µ	µ	NOUN
ejpam-5573	371	3	is	be	AUX
ejpam-5573	371	4	(	(	PUNCT
ejpam-5573	371	5	r	r	NOUN
ejpam-5573	371	6	,	,	PUNCT
ejpam-5573	371	7	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	371	8	almost	almost	ADV
ejpam-5573	371	9	gs	gs	ADJ
ejpam-5573	371	10	-	-	PUNCT
ejpam-5573	371	11	compact	compact	ADJ
ejpam-5573	371	12	,	,	PUNCT
ejpam-5573	371	13	there	there	PRON
ejpam-5573	371	14	is	be	VERB
ejpam-5573	371	15	a	a	DET
ejpam-5573	371	16	finite	finite	NOUN
ejpam-5573	371	17	subset	subset	NOUN
ejpam-5573	371	18	𭟋	𭟋	ADP
ejpam-5573	371	19	◦	◦	NOUN
ejpam-5573	371	20	of	of	ADP
ejpam-5573	371	21	𭟋	𭟋	NOUN
ejpam-5573	371	22	,	,	PUNCT
ejpam-5573	371	23	such	such	ADJ
ejpam-5573	371	24	that	that	SCONJ
ejpam-5573	371	25	µ	µ	PRON
ejpam-5573	371	26	≤	≤	NUM
ejpam-5573	371	27	∨	∨	NUM
ejpam-5573	371	28	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	371	29	◦	◦	PROPN
ejpam-5573	371	30	cτ	cτ	PROPN
ejpam-5573	371	31	,	,	PUNCT
ejpam-5573	371	32	τ∗(h	τ∗(h	PROPN
ejpam-5573	371	33	−1(λj	−1(λj	NOUN
ejpam-5573	371	34	)	)	PUNCT
ejpam-5573	371	35	,	,	PUNCT
ejpam-5573	371	36	r	r	NOUN
ejpam-5573	371	37	,	,	PUNCT
ejpam-5573	371	38	s	s	NOUN
ejpam-5573	371	39	)	)	PUNCT
ejpam-5573	371	40	.	.	PUNCT
ejpam-5573	372	1	since	since	SCONJ
ejpam-5573	372	2	h	h	PROPN
ejpam-5573	372	3	is	be	AUX
ejpam-5573	372	4	df	df	NOUN
ejpam-5573	372	5	-	-	PUNCT
ejpam-5573	372	6	continuous	continuous	ADJ
ejpam-5573	372	7	mapping	mapping	NOUN
ejpam-5573	372	8	,	,	PUNCT
ejpam-5573	372	9	it	it	PRON
ejpam-5573	372	10	follows	follow	VERB
ejpam-5573	372	11	µ	µ	NOUN
ejpam-5573	372	12	≤	≤	NUM
ejpam-5573	372	13	∨	∨	NUM
ejpam-5573	372	14	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	372	15	◦	◦	PROPN
ejpam-5573	372	16	cτ	cτ	PROPN
ejpam-5573	372	17	,	,	PUNCT
ejpam-5573	372	18	τ∗(h	τ∗(h	PROPN
ejpam-5573	372	19	−1(λj	−1(λj	NOUN
ejpam-5573	372	20	)	)	PUNCT
ejpam-5573	372	21	,	,	PUNCT
ejpam-5573	372	22	r	r	NOUN
ejpam-5573	372	23	,	,	PUNCT
ejpam-5573	372	24	s	s	PART
ejpam-5573	372	25	)	)	PUNCT
ejpam-5573	372	26	f.	f.	PROPN
ejpam-5573	372	27	alsharari	alsharari	PROPN
ejpam-5573	372	28	,	,	PUNCT
ejpam-5573	372	29	o.	o.	PROPN
ejpam-5573	372	30	m.	m.	PROPN
ejpam-5573	372	31	taha	taha	PROPN
ejpam-5573	372	32	,	,	PUNCT
ejpam-5573	372	33	i.	i.	PROPN
ejpam-5573	372	34	m.	m.	PROPN
ejpam-5573	372	35	taha	taha	PROPN
ejpam-5573	372	36	/	/	PUNCT
ejpam-5573	372	37	eur	eur	PROPN
ejpam-5573	372	38	.	.	PUNCT
ejpam-5573	373	1	j.	j.	PROPN
ejpam-5573	373	2	pure	pure	PROPN
ejpam-5573	373	3	appl	appl	PROPN
ejpam-5573	373	4	.	.	PROPN
ejpam-5573	373	5	math	math	PROPN
ejpam-5573	373	6	,	,	PUNCT
ejpam-5573	373	7	17	17	NUM
ejpam-5573	373	8	(	(	PUNCT
ejpam-5573	373	9	4	4	NUM
ejpam-5573	373	10	)	)	PUNCT
ejpam-5573	373	11	(	(	PUNCT
ejpam-5573	373	12	2024	2024	NUM
ejpam-5573	373	13	)	)	PUNCT
ejpam-5573	373	14	,	,	PUNCT
ejpam-5573	373	15	4093	4093	NUM
ejpam-5573	373	16	-	-	SYM
ejpam-5573	373	17	4111	4111	NUM
ejpam-5573	373	18	4106	4106	NUM
ejpam-5573	373	19	≤	≤	NUM
ejpam-5573	373	20	∨	∨	NUM
ejpam-5573	373	21	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	373	22	◦	◦	NOUN
ejpam-5573	373	23	h−1(cη	h−1(cη	PROPN
ejpam-5573	373	24	,	,	PUNCT
ejpam-5573	373	25	η∗(λj	η∗(λj	NOUN
ejpam-5573	373	26	,	,	PUNCT
ejpam-5573	373	27	r	r	NOUN
ejpam-5573	373	28	,	,	PUNCT
ejpam-5573	373	29	s	s	NOUN
ejpam-5573	373	30	)	)	PUNCT
ejpam-5573	373	31	)	)	PUNCT
ejpam-5573	374	1	=	=	SYM
ejpam-5573	374	2	h−1	h−1	PROPN
ejpam-5573	374	3	(	(	PUNCT
ejpam-5573	374	4	∨	∨	NUM
ejpam-5573	374	5	j∈𭟋	j∈𭟋	PROPN
ejpam-5573	374	6	◦	◦	PROPN
ejpam-5573	374	7	cη	cη	ADP
ejpam-5573	374	8	,	,	PUNCT
ejpam-5573	374	9	η∗(λj	η∗(λj	NOUN
ejpam-5573	374	10	,	,	PUNCT
ejpam-5573	374	11	r	r	NOUN
ejpam-5573	374	12	,	,	PUNCT
ejpam-5573	374	13	s	s	NOUN
ejpam-5573	374	14	)	)	PUNCT
ejpam-5573	374	15	)	)	PUNCT
ejpam-5573	374	16	.	.	PUNCT
ejpam-5573	375	1	thus	thus	ADV
ejpam-5573	375	2	,	,	PUNCT
ejpam-5573	375	3	h(µ	h(µ	PROPN
ejpam-5573	375	4	)	)	PUNCT
ejpam-5573	375	5	≤	≤	NUM
ejpam-5573	375	6	∨	∨	NUM
ejpam-5573	375	7	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	375	8	◦	◦	NOUN
ejpam-5573	375	9	cη	cη	ADP
ejpam-5573	375	10	,	,	PUNCT
ejpam-5573	375	11	η∗(λj	η∗(λj	NOUN
ejpam-5573	375	12	,	,	PUNCT
ejpam-5573	375	13	r	r	NOUN
ejpam-5573	375	14	,	,	PUNCT
ejpam-5573	375	15	s	s	NOUN
ejpam-5573	375	16	)	)	PUNCT
ejpam-5573	375	17	.	.	PUNCT
ejpam-5573	376	1	hence	hence	ADV
ejpam-5573	376	2	,	,	PUNCT
ejpam-5573	376	3	the	the	DET
ejpam-5573	376	4	proof	proof	NOUN
ejpam-5573	376	5	is	be	AUX
ejpam-5573	376	6	completed	complete	VERB
ejpam-5573	376	7	.	.	PUNCT
ejpam-5573	377	1	definition	definition	NOUN
ejpam-5573	377	2	13	13	NUM
ejpam-5573	377	3	.	.	PUNCT
ejpam-5573	378	1	let	let	VERB
ejpam-5573	378	2	(	(	PUNCT
ejpam-5573	378	3	u	u	NOUN
ejpam-5573	378	4	,	,	PUNCT
ejpam-5573	378	5	η	η	PROPN
ejpam-5573	378	6	,	,	PUNCT
ejpam-5573	378	7	η∗	η∗	NOUN
ejpam-5573	378	8	)	)	PUNCT
ejpam-5573	378	9	be	be	VERB
ejpam-5573	378	10	a	a	DET
ejpam-5573	378	11	dfts	dft	NOUN
ejpam-5573	378	12	,	,	PUNCT
ejpam-5573	378	13	r	r	NOUN
ejpam-5573	378	14	∈	∈	PROPN
ejpam-5573	379	1	i	i	NOUN
ejpam-5573	379	2	◦	◦	NOUN
ejpam-5573	379	3	,	,	PUNCT
ejpam-5573	379	4	and	and	CCONJ
ejpam-5573	379	5	s	s	PROPN
ejpam-5573	379	6	∈	∈	PROPN
ejpam-5573	379	7	i1	i1	PROPN
ejpam-5573	379	8	,	,	PUNCT
ejpam-5573	379	9	then	then	ADV
ejpam-5573	379	10	µ	µ	X
ejpam-5573	379	11	∈	∈	NOUN
ejpam-5573	379	12	iu	iu	ADV
ejpam-5573	379	13	is	be	AUX
ejpam-5573	379	14	called	call	VERB
ejpam-5573	379	15	an	an	DET
ejpam-5573	379	16	(	(	PUNCT
ejpam-5573	379	17	r	r	NOUN
ejpam-5573	379	18	,	,	PUNCT
ejpam-5573	379	19	s)fuzzy	s)fuzzy	X
ejpam-5573	379	20	nearly	nearly	ADV
ejpam-5573	379	21	compact	compact	ADJ
ejpam-5573	379	22	iff	iff	NOUN
ejpam-5573	379	23	for	for	ADP
ejpam-5573	379	24	each	each	DET
ejpam-5573	379	25	family	family	NOUN
ejpam-5573	379	26	{	{	PUNCT
ejpam-5573	379	27	λj	λj	PROPN
ejpam-5573	379	28	∈	∈	PROPN
ejpam-5573	379	29	iu	iu	SCONJ
ejpam-5573	379	30	|	|	ADV
ejpam-5573	379	31	η(λj	η(λj	NOUN
ejpam-5573	379	32	)	)	PUNCT
ejpam-5573	379	33	≥	≥	NOUN
ejpam-5573	379	34	r	r	NOUN
ejpam-5573	379	35	and	and	CCONJ
ejpam-5573	379	36	η∗(λj	η∗(λj	NOUN
ejpam-5573	379	37	)	)	PUNCT
ejpam-5573	379	38	≤	≤	NOUN
ejpam-5573	379	39	s}j∈𭟋	s}j∈𭟋	NOUN
ejpam-5573	379	40	,	,	PUNCT
ejpam-5573	379	41	such	such	ADJ
ejpam-5573	379	42	that	that	SCONJ
ejpam-5573	379	43	µ	µ	PRON
ejpam-5573	379	44	≤	≤	NUM
ejpam-5573	379	45	∨	∨	NUM
ejpam-5573	379	46	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	379	47	λj	λj	INTJ
ejpam-5573	379	48	,	,	PUNCT
ejpam-5573	379	49	there	there	PRON
ejpam-5573	379	50	is	be	VERB
ejpam-5573	379	51	a	a	DET
ejpam-5573	379	52	finite	finite	NOUN
ejpam-5573	379	53	subset	subset	NOUN
ejpam-5573	379	54	𭟋	𭟋	ADP
ejpam-5573	379	55	◦	◦	NOUN
ejpam-5573	379	56	of	of	ADP
ejpam-5573	379	57	𭟋	𭟋	NOUN
ejpam-5573	379	58	,	,	PUNCT
ejpam-5573	379	59	such	such	ADJ
ejpam-5573	379	60	that	that	SCONJ
ejpam-5573	379	61	µ	µ	PRON
ejpam-5573	379	62	≤	≤	NUM
ejpam-5573	379	63	∨	∨	NUM
ejpam-5573	379	64	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	379	65	◦	◦	NOUN
ejpam-5573	379	66	iη	iη	NOUN
ejpam-5573	379	67	,	,	PUNCT
ejpam-5573	379	68	η∗(cη	η∗(cη	NOUN
ejpam-5573	379	69	,	,	PUNCT
ejpam-5573	379	70	η∗(λj	η∗(λj	NOUN
ejpam-5573	379	71	,	,	PUNCT
ejpam-5573	379	72	r	r	NOUN
ejpam-5573	379	73	,	,	PUNCT
ejpam-5573	379	74	s	s	PART
ejpam-5573	379	75	)	)	PUNCT
ejpam-5573	379	76	,	,	PUNCT
ejpam-5573	379	77	r	r	NOUN
ejpam-5573	379	78	,	,	PUNCT
ejpam-5573	379	79	s	s	PART
ejpam-5573	379	80	)	)	PUNCT
ejpam-5573	379	81	.	.	PUNCT
ejpam-5573	380	1	definition	definition	NOUN
ejpam-5573	380	2	14	14	NUM
ejpam-5573	380	3	.	.	PUNCT
ejpam-5573	381	1	let	let	VERB
ejpam-5573	381	2	(	(	PUNCT
ejpam-5573	381	3	u	u	NOUN
ejpam-5573	381	4	,	,	PUNCT
ejpam-5573	381	5	η	η	PROPN
ejpam-5573	381	6	,	,	PUNCT
ejpam-5573	381	7	η∗	η∗	NOUN
ejpam-5573	381	8	)	)	PUNCT
ejpam-5573	381	9	be	be	VERB
ejpam-5573	381	10	a	a	DET
ejpam-5573	381	11	dfts	dft	NOUN
ejpam-5573	381	12	,	,	PUNCT
ejpam-5573	381	13	r	r	NOUN
ejpam-5573	381	14	∈	∈	PROPN
ejpam-5573	382	1	i	i	NOUN
ejpam-5573	382	2	◦	◦	NOUN
ejpam-5573	382	3	,	,	PUNCT
ejpam-5573	382	4	and	and	CCONJ
ejpam-5573	382	5	s	s	PROPN
ejpam-5573	382	6	∈	∈	PROPN
ejpam-5573	382	7	i1	i1	PROPN
ejpam-5573	382	8	,	,	PUNCT
ejpam-5573	383	1	then	then	ADV
ejpam-5573	383	2	µ	µ	X
ejpam-5573	383	3	∈	∈	NOUN
ejpam-5573	383	4	iu	iu	ADV
ejpam-5573	383	5	is	be	AUX
ejpam-5573	383	6	called	call	VERB
ejpam-5573	383	7	an	an	DET
ejpam-5573	383	8	(	(	PUNCT
ejpam-5573	383	9	r	r	NOUN
ejpam-5573	383	10	,	,	PUNCT
ejpam-5573	383	11	s)fuzzy	s)fuzzy	PROPN
ejpam-5573	383	12	nearly	nearly	ADV
ejpam-5573	383	13	gs	gs	ADJ
ejpam-5573	383	14	-	-	PUNCT
ejpam-5573	383	15	compact	compact	ADJ
ejpam-5573	383	16	iff	iff	NOUN
ejpam-5573	383	17	for	for	ADP
ejpam-5573	383	18	each	each	DET
ejpam-5573	383	19	family	family	NOUN
ejpam-5573	383	20	{	{	PUNCT
ejpam-5573	383	21	λj	λj	PROPN
ejpam-5573	383	22	∈	∈	PROPN
ejpam-5573	383	23	iu	iu	ADV
ejpam-5573	383	24	|	|	ADV
ejpam-5573	383	25	λj	λj	PROPN
ejpam-5573	383	26	is	be	AUX
ejpam-5573	383	27	(	(	PUNCT
ejpam-5573	383	28	r	r	NOUN
ejpam-5573	383	29	,	,	PUNCT
ejpam-5573	383	30	s	s	NOUN
ejpam-5573	383	31	)	)	PUNCT
ejpam-5573	383	32	−	−	PROPN
ejpam-5573	383	33	gfso}j∈𭟋	gfso}j∈𭟋	PROPN
ejpam-5573	383	34	,	,	PUNCT
ejpam-5573	383	35	such	such	ADJ
ejpam-5573	383	36	that	that	SCONJ
ejpam-5573	383	37	µ	µ	PRON
ejpam-5573	383	38	≤	≤	NUM
ejpam-5573	383	39	∨	∨	NUM
ejpam-5573	383	40	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	383	41	λj	λj	INTJ
ejpam-5573	383	42	,	,	PUNCT
ejpam-5573	383	43	there	there	PRON
ejpam-5573	383	44	is	be	VERB
ejpam-5573	383	45	a	a	DET
ejpam-5573	383	46	finite	finite	NOUN
ejpam-5573	383	47	subset	subset	NOUN
ejpam-5573	383	48	𭟋	𭟋	ADP
ejpam-5573	383	49	◦	◦	NOUN
ejpam-5573	383	50	of	of	ADP
ejpam-5573	383	51	𭟋	𭟋	NOUN
ejpam-5573	383	52	,	,	PUNCT
ejpam-5573	383	53	such	such	ADJ
ejpam-5573	383	54	that	that	SCONJ
ejpam-5573	383	55	µ	µ	PRON
ejpam-5573	383	56	≤	≤	NUM
ejpam-5573	383	57	∨	∨	NUM
ejpam-5573	383	58	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	383	59	◦	◦	NOUN
ejpam-5573	383	60	iη	iη	NOUN
ejpam-5573	383	61	,	,	PUNCT
ejpam-5573	383	62	η∗(cη	η∗(cη	NOUN
ejpam-5573	383	63	,	,	PUNCT
ejpam-5573	383	64	η∗(λj	η∗(λj	NOUN
ejpam-5573	383	65	,	,	PUNCT
ejpam-5573	383	66	r	r	NOUN
ejpam-5573	383	67	,	,	PUNCT
ejpam-5573	383	68	s	s	PART
ejpam-5573	383	69	)	)	PUNCT
ejpam-5573	383	70	,	,	PUNCT
ejpam-5573	383	71	r	r	NOUN
ejpam-5573	383	72	,	,	PUNCT
ejpam-5573	383	73	s	s	PART
ejpam-5573	383	74	)	)	PUNCT
ejpam-5573	383	75	.	.	PUNCT
ejpam-5573	384	1	lemma	lemma	PROPN
ejpam-5573	384	2	6	6	NUM
ejpam-5573	384	3	.	.	PUNCT
ejpam-5573	385	1	let	let	VERB
ejpam-5573	385	2	(	(	PUNCT
ejpam-5573	385	3	u	u	NOUN
ejpam-5573	385	4	,	,	PUNCT
ejpam-5573	385	5	η	η	PROPN
ejpam-5573	385	6	,	,	PUNCT
ejpam-5573	385	7	η∗	η∗	NOUN
ejpam-5573	385	8	)	)	PUNCT
ejpam-5573	385	9	be	be	VERB
ejpam-5573	385	10	a	a	DET
ejpam-5573	385	11	dfts	dft	NOUN
ejpam-5573	385	12	,	,	PUNCT
ejpam-5573	385	13	r	r	NOUN
ejpam-5573	385	14	∈	∈	PROPN
ejpam-5573	386	1	i	i	NOUN
ejpam-5573	386	2	◦	◦	NOUN
ejpam-5573	386	3	,	,	PUNCT
ejpam-5573	386	4	and	and	CCONJ
ejpam-5573	386	5	s	s	PROPN
ejpam-5573	386	6	∈	∈	PROPN
ejpam-5573	386	7	i1	i1	PROPN
ejpam-5573	386	8	.	.	PUNCT
ejpam-5573	387	1	if	if	SCONJ
ejpam-5573	387	2	µ	µ	PRON
ejpam-5573	387	3	∈	∈	NOUN
ejpam-5573	387	4	iu	iu	ADV
ejpam-5573	387	5	is	be	AUX
ejpam-5573	387	6	(	(	PUNCT
ejpam-5573	387	7	r	r	NOUN
ejpam-5573	387	8	,	,	PUNCT
ejpam-5573	387	9	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	387	10	nearly	nearly	ADV
ejpam-5573	387	11	gs	gs	ADJ
ejpam-5573	387	12	-	-	ADJ
ejpam-5573	387	13	compact	compact	ADJ
ejpam-5573	387	14	,	,	PUNCT
ejpam-5573	387	15	then	then	ADV
ejpam-5573	387	16	µ	µ	X
ejpam-5573	387	17	is	be	AUX
ejpam-5573	387	18	(	(	PUNCT
ejpam-5573	387	19	r	r	NOUN
ejpam-5573	387	20	,	,	PUNCT
ejpam-5573	387	21	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	387	22	nearly	nearly	ADV
ejpam-5573	387	23	compact	compact	ADJ
ejpam-5573	387	24	.	.	PUNCT
ejpam-5573	388	1	proof	proof	NOUN
ejpam-5573	388	2	.	.	PUNCT
ejpam-5573	389	1	follows	follow	VERB
ejpam-5573	389	2	from	from	ADP
ejpam-5573	389	3	definitions	definition	NOUN
ejpam-5573	389	4	13	13	NUM
ejpam-5573	389	5	and	and	CCONJ
ejpam-5573	389	6	14	14	NUM
ejpam-5573	389	7	.	.	PUNCT
ejpam-5573	390	1	lemma	lemma	PROPN
ejpam-5573	390	2	7	7	X
ejpam-5573	390	3	.	.	PUNCT
ejpam-5573	391	1	let	let	VERB
ejpam-5573	391	2	(	(	PUNCT
ejpam-5573	391	3	u	u	NOUN
ejpam-5573	391	4	,	,	PUNCT
ejpam-5573	391	5	η	η	PROPN
ejpam-5573	391	6	,	,	PUNCT
ejpam-5573	391	7	η∗	η∗	NOUN
ejpam-5573	391	8	)	)	PUNCT
ejpam-5573	391	9	be	be	VERB
ejpam-5573	391	10	a	a	DET
ejpam-5573	391	11	dfts	dft	NOUN
ejpam-5573	391	12	,	,	PUNCT
ejpam-5573	391	13	r	r	NOUN
ejpam-5573	391	14	∈	∈	PROPN
ejpam-5573	392	1	i	i	NOUN
ejpam-5573	392	2	◦	◦	NOUN
ejpam-5573	392	3	,	,	PUNCT
ejpam-5573	392	4	and	and	CCONJ
ejpam-5573	392	5	s	s	PROPN
ejpam-5573	392	6	∈	∈	PROPN
ejpam-5573	392	7	i1	i1	PROPN
ejpam-5573	392	8	.	.	PUNCT
ejpam-5573	393	1	if	if	SCONJ
ejpam-5573	393	2	µ	µ	PRON
ejpam-5573	393	3	∈	∈	NOUN
ejpam-5573	393	4	iu	iu	ADV
ejpam-5573	393	5	is	be	AUX
ejpam-5573	393	6	(	(	PUNCT
ejpam-5573	393	7	r	r	NOUN
ejpam-5573	393	8	,	,	PUNCT
ejpam-5573	393	9	s)-fuzzy	s)-fuzzy	NOUN
ejpam-5573	393	10	compact	compact	ADJ
ejpam-5573	393	11	(	(	PUNCT
ejpam-5573	393	12	resp	resp	NOUN
ejpam-5573	393	13	.	.	PUNCT
ejpam-5573	393	14	,	,	PUNCT
ejpam-5573	393	15	gs	gs	NOUN
ejpam-5573	393	16	-	-	PUNCT
ejpam-5573	393	17	compact	compact	ADJ
ejpam-5573	393	18	)	)	PUNCT
ejpam-5573	393	19	,	,	PUNCT
ejpam-5573	393	20	then	then	ADV
ejpam-5573	393	21	µ	µ	X
ejpam-5573	393	22	is	be	AUX
ejpam-5573	393	23	(	(	PUNCT
ejpam-5573	393	24	r	r	NOUN
ejpam-5573	393	25	,	,	PUNCT
ejpam-5573	393	26	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	393	27	nearly	nearly	ADV
ejpam-5573	393	28	compact	compact	ADJ
ejpam-5573	393	29	(	(	PUNCT
ejpam-5573	393	30	resp	resp	NOUN
ejpam-5573	393	31	.	.	PUNCT
ejpam-5573	393	32	,	,	PUNCT
ejpam-5573	393	33	nearly	nearly	ADV
ejpam-5573	393	34	gs	gs	ADJ
ejpam-5573	393	35	-	-	PUNCT
ejpam-5573	393	36	compact	compact	ADJ
ejpam-5573	393	37	)	)	PUNCT
ejpam-5573	393	38	.	.	PUNCT
ejpam-5573	394	1	proof	proof	NOUN
ejpam-5573	394	2	.	.	PUNCT
ejpam-5573	395	1	follows	follow	VERB
ejpam-5573	395	2	from	from	ADP
ejpam-5573	395	3	definitions	definition	NOUN
ejpam-5573	395	4	9	9	NUM
ejpam-5573	395	5	,	,	PUNCT
ejpam-5573	395	6	10	10	NUM
ejpam-5573	395	7	,	,	PUNCT
ejpam-5573	395	8	13	13	NUM
ejpam-5573	395	9	and	and	CCONJ
ejpam-5573	395	10	14	14	NUM
ejpam-5573	395	11	.	.	PUNCT
ejpam-5573	396	1	remark	remark	PROPN
ejpam-5573	396	2	10	10	NUM
ejpam-5573	396	3	.	.	PUNCT
ejpam-5573	397	1	the	the	DET
ejpam-5573	397	2	converse	converse	NOUN
ejpam-5573	397	3	of	of	ADP
ejpam-5573	397	4	lemma	lemma	PROPN
ejpam-5573	397	5	7	7	NUM
ejpam-5573	397	6	may	may	AUX
ejpam-5573	397	7	not	not	PART
ejpam-5573	397	8	be	be	AUX
ejpam-5573	397	9	true	true	ADJ
ejpam-5573	397	10	,	,	PUNCT
ejpam-5573	397	11	as	as	SCONJ
ejpam-5573	397	12	shown	show	VERB
ejpam-5573	397	13	by	by	ADP
ejpam-5573	397	14	example	example	NOUN
ejpam-5573	397	15	11	11	NUM
ejpam-5573	397	16	.	.	PUNCT
ejpam-5573	397	17	example	example	NOUN
ejpam-5573	398	1	11	11	NUM
ejpam-5573	398	2	.	.	PUNCT
ejpam-5573	399	1	let	let	VERB
ejpam-5573	399	2	v	v	VERB
ejpam-5573	399	3	=	=	PUNCT
ejpam-5573	399	4	i	i	PROPN
ejpam-5573	399	5	,	,	PUNCT
ejpam-5573	399	6	0	0	PUNCT
ejpam-5573	399	7	<	<	X
ejpam-5573	399	8	k	k	X
ejpam-5573	399	9	<	<	X
ejpam-5573	399	10	1	1	NUM
ejpam-5573	399	11	,	,	PUNCT
ejpam-5573	399	12	and	and	CCONJ
ejpam-5573	399	13	ν	ν	NOUN
ejpam-5573	399	14	,	,	PUNCT
ejpam-5573	399	15	ρ	ρ	PROPN
ejpam-5573	399	16	,	,	PUNCT
ejpam-5573	399	17	λk	λk	PROPN
ejpam-5573	399	18	∈	∈	NOUN
ejpam-5573	400	1	iv	iv	NUM
ejpam-5573	400	2	defined	define	VERB
ejpam-5573	400	3	as	as	SCONJ
ejpam-5573	400	4	follows	follow	VERB
ejpam-5573	400	5	:	:	PUNCT
ejpam-5573	400	6	ν(v	ν(v	NUM
ejpam-5573	400	7	)	)	PUNCT
ejpam-5573	401	1	=	=	PRON
ejpam-5573	401	2	{	{	PUNCT
ejpam-5573	401	3	1	1	NUM
ejpam-5573	401	4	2	2	NUM
ejpam-5573	401	5	,	,	PUNCT
ejpam-5573	401	6	if	if	SCONJ
ejpam-5573	401	7	0	0	NUM
ejpam-5573	401	8	≤	≤	NUM
ejpam-5573	401	9	v	v	ADP
ejpam-5573	401	10	<	<	X
ejpam-5573	401	11	1	1	NUM
ejpam-5573	401	12	,	,	PUNCT
ejpam-5573	401	13	1	1	NUM
ejpam-5573	401	14	,	,	PUNCT
ejpam-5573	401	15	if	if	SCONJ
ejpam-5573	401	16	v	v	ADP
ejpam-5573	401	17	=	=	SYM
ejpam-5573	401	18	1	1	NUM
ejpam-5573	401	19	,	,	PUNCT
ejpam-5573	401	20	ρ(v	ρ(v	X
ejpam-5573	401	21	)	)	PUNCT
ejpam-5573	401	22	=	=	NOUN
ejpam-5573	401	23	{	{	PUNCT
ejpam-5573	401	24	1	1	NUM
ejpam-5573	401	25	,	,	PUNCT
ejpam-5573	401	26	if	if	SCONJ
ejpam-5573	401	27	v	v	NOUN
ejpam-5573	401	28	=	=	SYM
ejpam-5573	401	29	0	0	NUM
ejpam-5573	401	30	,	,	PUNCT
ejpam-5573	401	31	1	1	NUM
ejpam-5573	401	32	2	2	NUM
ejpam-5573	401	33	,	,	PUNCT
ejpam-5573	401	34	if	if	SCONJ
ejpam-5573	401	35	0	0	NUM
ejpam-5573	401	36	<	<	X
ejpam-5573	401	37	v	v	X
ejpam-5573	401	38	≤	≤	NUM
ejpam-5573	401	39	1	1	NUM
ejpam-5573	401	40	,	,	PUNCT
ejpam-5573	401	41	λk(v	λk(v	PUNCT
ejpam-5573	401	42	)	)	PUNCT
ejpam-5573	401	43	=	=	PRON
ejpam-5573	401	44	{	{	PUNCT
ejpam-5573	401	45	v	v	NOUN
ejpam-5573	401	46	k	k	X
ejpam-5573	401	47	,	,	PUNCT
ejpam-5573	401	48	if	if	SCONJ
ejpam-5573	401	49	0	0	NUM
ejpam-5573	401	50	≤	≤	NUM
ejpam-5573	401	51	v	v	NOUN
ejpam-5573	401	52	≤	≤	NUM
ejpam-5573	402	1	k	k	NOUN
ejpam-5573	402	2	,	,	PUNCT
ejpam-5573	402	3	1−v	1−v	NUM
ejpam-5573	402	4	1−k	1−k	NUM
ejpam-5573	402	5	,	,	PUNCT
ejpam-5573	402	6	if	if	SCONJ
ejpam-5573	402	7	k	k	PROPN
ejpam-5573	402	8	<	<	X
ejpam-5573	402	9	v	v	X
ejpam-5573	402	10	≤	≤	NUM
ejpam-5573	402	11	1	1	NUM
ejpam-5573	402	12	.	.	PUNCT
ejpam-5573	403	1	also	also	ADV
ejpam-5573	403	2	,	,	PUNCT
ejpam-5573	403	3	(	(	PUNCT
ejpam-5573	403	4	η	η	NOUN
ejpam-5573	403	5	,	,	PUNCT
ejpam-5573	403	6	η∗	η∗	NOUN
ejpam-5573	403	7	)	)	PUNCT
ejpam-5573	403	8	defined	define	VERB
ejpam-5573	403	9	on	on	ADP
ejpam-5573	403	10	v	v	NOUN
ejpam-5573	403	11	as	as	SCONJ
ejpam-5573	403	12	follows	follow	VERB
ejpam-5573	403	13	:	:	PUNCT
ejpam-5573	403	14	η(µ	η(µ	PROPN
ejpam-5573	403	15	)	)	PUNCT
ejpam-5573	404	1	=	=	SYM
ejpam-5573	404	2			NOUN
ejpam-5573	404	3	1	1	NUM
ejpam-5573	404	4	,	,	PUNCT
ejpam-5573	404	5	if	if	SCONJ
ejpam-5573	404	6	µ	µ	X
ejpam-5573	404	7	∈	∈	NOUN
ejpam-5573	404	8	{	{	PUNCT
ejpam-5573	404	9	ν	ν	NOUN
ejpam-5573	404	10	,	,	PUNCT
ejpam-5573	404	11	ρ	ρ	PROPN
ejpam-5573	404	12	,	,	PUNCT
ejpam-5573	404	13	0	0	NUM
ejpam-5573	404	14	,	,	PUNCT
ejpam-5573	404	15	1	1	NUM
ejpam-5573	404	16	}	}	PUNCT
ejpam-5573	404	17	,	,	PUNCT
ejpam-5573	404	18	max({1−	max({1−	PROPN
ejpam-5573	404	19	k	k	NOUN
ejpam-5573	404	20	,	,	PUNCT
ejpam-5573	404	21	k	k	NOUN
ejpam-5573	404	22	}	}	PUNCT
ejpam-5573	404	23	)	)	PUNCT
ejpam-5573	404	24	,	,	PUNCT
ejpam-5573	404	25	if	if	SCONJ
ejpam-5573	404	26	µ	µ	X
ejpam-5573	404	27	=	=	X
ejpam-5573	404	28	λk	λk	PROPN
ejpam-5573	404	29	,	,	PUNCT
ejpam-5573	404	30	0	0	NUM
ejpam-5573	404	31	,	,	PUNCT
ejpam-5573	404	32	otherwise	otherwise	ADV
ejpam-5573	404	33	,	,	PUNCT
ejpam-5573	404	34	η∗(µ	η∗(µ	PROPN
ejpam-5573	404	35	)	)	PUNCT
ejpam-5573	404	36	=	=	SYM
ejpam-5573	405	1			NOUN
ejpam-5573	405	2	0	0	NUM
ejpam-5573	405	3	,	,	PUNCT
ejpam-5573	405	4	if	if	SCONJ
ejpam-5573	405	5	µ	µ	X
ejpam-5573	405	6	∈	∈	NOUN
ejpam-5573	405	7	{	{	PUNCT
ejpam-5573	405	8	ν	ν	NOUN
ejpam-5573	405	9	,	,	PUNCT
ejpam-5573	405	10	ρ	ρ	PROPN
ejpam-5573	405	11	,	,	PUNCT
ejpam-5573	405	12	0	0	NUM
ejpam-5573	405	13	,	,	PUNCT
ejpam-5573	405	14	1	1	NUM
ejpam-5573	405	15	}	}	PUNCT
ejpam-5573	405	16	,	,	PUNCT
ejpam-5573	405	17	min({k	min({k	PROPN
ejpam-5573	405	18	,	,	PUNCT
ejpam-5573	405	19	1−	1−	NUM
ejpam-5573	405	20	k	k	NOUN
ejpam-5573	405	21	}	}	PUNCT
ejpam-5573	405	22	)	)	PUNCT
ejpam-5573	405	23	,	,	PUNCT
ejpam-5573	405	24	if	if	SCONJ
ejpam-5573	405	25	µ	µ	X
ejpam-5573	405	26	=	=	SYM
ejpam-5573	405	27	λk	λk	X
ejpam-5573	405	28	,	,	PUNCT
ejpam-5573	405	29	1	1	NUM
ejpam-5573	405	30	,	,	PUNCT
ejpam-5573	405	31	otherwise	otherwise	ADV
ejpam-5573	405	32	.	.	PUNCT
ejpam-5573	406	1	thus	thus	ADV
ejpam-5573	406	2	,	,	PUNCT
ejpam-5573	406	3	v	v	NOUN
ejpam-5573	406	4	is	be	AUX
ejpam-5573	406	5	(	(	PUNCT
ejpam-5573	406	6	12	12	NUM
ejpam-5573	406	7	,	,	PUNCT
ejpam-5573	406	8	1	1	NUM
ejpam-5573	406	9	2)-fuzzy	2)-fuzzy	NUM
ejpam-5573	406	10	nearly	nearly	ADV
ejpam-5573	406	11	compact	compact	ADJ
ejpam-5573	406	12	,	,	PUNCT
ejpam-5573	406	13	but	but	CCONJ
ejpam-5573	406	14	it	it	PRON
ejpam-5573	406	15	is	be	AUX
ejpam-5573	406	16	not	not	PART
ejpam-5573	406	17	(	(	PUNCT
ejpam-5573	406	18	12	12	NUM
ejpam-5573	406	19	,	,	PUNCT
ejpam-5573	406	20	1	1	NUM
ejpam-5573	406	21	2)-fuzzy	2)-fuzzy	NUM
ejpam-5573	406	22	compact	compact	ADJ
ejpam-5573	406	23	.	.	PUNCT
ejpam-5573	407	1	f.	f.	PROPN
ejpam-5573	407	2	alsharari	alsharari	PROPN
ejpam-5573	407	3	,	,	PUNCT
ejpam-5573	407	4	o.	o.	PROPN
ejpam-5573	407	5	m.	m.	PROPN
ejpam-5573	407	6	taha	taha	PROPN
ejpam-5573	407	7	,	,	PUNCT
ejpam-5573	407	8	i.	i.	PROPN
ejpam-5573	407	9	m.	m.	PROPN
ejpam-5573	407	10	taha	taha	PROPN
ejpam-5573	407	11	/	/	PUNCT
ejpam-5573	407	12	eur	eur	PROPN
ejpam-5573	407	13	.	.	PUNCT
ejpam-5573	408	1	j.	j.	PROPN
ejpam-5573	408	2	pure	pure	PROPN
ejpam-5573	408	3	appl	appl	PROPN
ejpam-5573	408	4	.	.	PROPN
ejpam-5573	408	5	math	math	PROPN
ejpam-5573	408	6	,	,	PUNCT
ejpam-5573	408	7	17	17	NUM
ejpam-5573	408	8	(	(	PUNCT
ejpam-5573	408	9	4	4	NUM
ejpam-5573	408	10	)	)	PUNCT
ejpam-5573	408	11	(	(	PUNCT
ejpam-5573	408	12	2024	2024	NUM
ejpam-5573	408	13	)	)	PUNCT
ejpam-5573	408	14	,	,	PUNCT
ejpam-5573	408	15	4093	4093	NUM
ejpam-5573	408	16	-	-	SYM
ejpam-5573	408	17	4111	4111	NUM
ejpam-5573	408	18	4107	4107	NUM
ejpam-5573	408	19	theorem	theorem	VERB
ejpam-5573	408	20	11	11	NUM
ejpam-5573	408	21	.	.	PUNCT
ejpam-5573	409	1	let	let	VERB
ejpam-5573	409	2	h	h	NOUN
ejpam-5573	409	3	:	:	PUNCT
ejpam-5573	409	4	(	(	PUNCT
ejpam-5573	409	5	u	u	NOUN
ejpam-5573	409	6	,	,	PUNCT
ejpam-5573	409	7	τ	τ	X
ejpam-5573	409	8	,	,	PUNCT
ejpam-5573	409	9	τ∗)→	τ∗)→	PROPN
ejpam-5573	409	10	(	(	PUNCT
ejpam-5573	409	11	v	v	PROPN
ejpam-5573	409	12	,	,	PUNCT
ejpam-5573	409	13	η	η	NOUN
ejpam-5573	409	14	,	,	PUNCT
ejpam-5573	409	15	η∗	η∗	NOUN
ejpam-5573	409	16	)	)	PUNCT
ejpam-5573	409	17	be	be	VERB
ejpam-5573	409	18	a	a	DET
ejpam-5573	409	19	df	df	NOUN
ejpam-5573	409	20	-	-	PUNCT
ejpam-5573	409	21	continuous	continuous	ADJ
ejpam-5573	409	22	and	and	CCONJ
ejpam-5573	409	23	df	df	NOUN
ejpam-5573	409	24	-	-	PUNCT
ejpam-5573	409	25	open	open	ADJ
ejpam-5573	409	26	mapping	mapping	NOUN
ejpam-5573	409	27	,	,	PUNCT
ejpam-5573	409	28	r	r	NOUN
ejpam-5573	409	29	∈	∈	PROPN
ejpam-5573	410	1	i	i	NOUN
ejpam-5573	410	2	◦	◦	NOUN
ejpam-5573	410	3	,	,	PUNCT
ejpam-5573	410	4	and	and	CCONJ
ejpam-5573	410	5	s	s	PROPN
ejpam-5573	410	6	∈	∈	PROPN
ejpam-5573	410	7	i1	i1	PROPN
ejpam-5573	410	8	.	.	PUNCT
ejpam-5573	411	1	if	if	SCONJ
ejpam-5573	411	2	µ	µ	PRON
ejpam-5573	411	3	∈	∈	NOUN
ejpam-5573	411	4	iu	iu	ADV
ejpam-5573	411	5	is	be	AUX
ejpam-5573	411	6	(	(	PUNCT
ejpam-5573	411	7	r	r	NOUN
ejpam-5573	411	8	,	,	PUNCT
ejpam-5573	411	9	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	411	10	nearly	nearly	ADV
ejpam-5573	411	11	gs	gs	ADJ
ejpam-5573	411	12	-	-	ADJ
ejpam-5573	411	13	compact	compact	ADJ
ejpam-5573	411	14	,	,	PUNCT
ejpam-5573	411	15	h(µ	h(µ	PROPN
ejpam-5573	411	16	)	)	PUNCT
ejpam-5573	411	17	is	be	AUX
ejpam-5573	411	18	(	(	PUNCT
ejpam-5573	411	19	r	r	NOUN
ejpam-5573	411	20	,	,	PUNCT
ejpam-5573	411	21	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	411	22	nearly	nearly	ADV
ejpam-5573	411	23	compact	compact	ADJ
ejpam-5573	411	24	.	.	PUNCT
ejpam-5573	412	1	proof	proof	NOUN
ejpam-5573	412	2	.	.	PUNCT
ejpam-5573	413	1	let	let	VERB
ejpam-5573	413	2	{	{	PUNCT
ejpam-5573	413	3	λj	λj	PROPN
ejpam-5573	413	4	∈	∈	PROPN
ejpam-5573	413	5	iv	iv	NUM
ejpam-5573	413	6	|	|	ADV
ejpam-5573	413	7	η(λj	η(λj	NOUN
ejpam-5573	413	8	)	)	PUNCT
ejpam-5573	413	9	≥	≥	NOUN
ejpam-5573	413	10	r	r	NOUN
ejpam-5573	413	11	and	and	CCONJ
ejpam-5573	413	12	η∗(λj	η∗(λj	NOUN
ejpam-5573	413	13	)	)	PUNCT
ejpam-5573	413	14	≤	≤	NUM
ejpam-5573	413	15	s}j∈𭟋	s}j∈𭟋	NOUN
ejpam-5573	413	16	with	with	ADP
ejpam-5573	413	17	h(µ	h(µ	NOUN
ejpam-5573	413	18	)	)	PUNCT
ejpam-5573	413	19	≤	≤	NUM
ejpam-5573	413	20	∨	∨	NUM
ejpam-5573	413	21	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	413	22	λj	λj	INTJ
ejpam-5573	413	23	,	,	PUNCT
ejpam-5573	413	24	then	then	ADV
ejpam-5573	413	25	{	{	PUNCT
ejpam-5573	413	26	h−1(λj	h−1(λj	NOUN
ejpam-5573	413	27	)	)	PUNCT
ejpam-5573	413	28	∈	∈	NOUN
ejpam-5573	413	29	iu	iu	ADP
ejpam-5573	413	30	|	|	ADV
ejpam-5573	413	31	h−1(λj	h−1(λj	NOUN
ejpam-5573	413	32	)	)	PUNCT
ejpam-5573	413	33	is	be	AUX
ejpam-5573	413	34	(	(	PUNCT
ejpam-5573	413	35	r	r	NOUN
ejpam-5573	413	36	,	,	PUNCT
ejpam-5573	413	37	s	s	NOUN
ejpam-5573	413	38	)	)	PUNCT
ejpam-5573	413	39	−	−	PROPN
ejpam-5573	413	40	gfso	gfso	NOUN
ejpam-5573	413	41	}	}	PUNCT
ejpam-5573	413	42	(	(	PUNCT
ejpam-5573	413	43	by	by	ADP
ejpam-5573	413	44	h	h	NOUN
ejpam-5573	413	45	is	be	AUX
ejpam-5573	413	46	dfgs	dfgs	NOUN
ejpam-5573	413	47	-	-	PUNCT
ejpam-5573	413	48	continuous	continuous	ADJ
ejpam-5573	413	49	)	)	PUNCT
ejpam-5573	413	50	,	,	PUNCT
ejpam-5573	413	51	such	such	ADJ
ejpam-5573	413	52	that	that	SCONJ
ejpam-5573	413	53	µ	µ	PRON
ejpam-5573	413	54	≤∨	≤∨	NOUN
ejpam-5573	413	55	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	413	56	h−1(λj	h−1(λj	NOUN
ejpam-5573	413	57	)	)	PUNCT
ejpam-5573	413	58	.	.	PUNCT
ejpam-5573	414	1	since	since	SCONJ
ejpam-5573	414	2	µ	µ	NOUN
ejpam-5573	414	3	is	be	AUX
ejpam-5573	414	4	(	(	PUNCT
ejpam-5573	414	5	r	r	NOUN
ejpam-5573	414	6	,	,	PUNCT
ejpam-5573	414	7	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	414	8	nearly	nearly	ADV
ejpam-5573	414	9	gs	gs	ADJ
ejpam-5573	414	10	-	-	ADJ
ejpam-5573	414	11	compact	compact	ADJ
ejpam-5573	414	12	,	,	PUNCT
ejpam-5573	414	13	there	there	PRON
ejpam-5573	414	14	is	be	VERB
ejpam-5573	414	15	a	a	DET
ejpam-5573	414	16	finite	finite	NOUN
ejpam-5573	414	17	subset	subset	NOUN
ejpam-5573	414	18	𭟋	𭟋	ADP
ejpam-5573	414	19	◦	◦	NOUN
ejpam-5573	414	20	of	of	ADP
ejpam-5573	414	21	𭟋	𭟋	NOUN
ejpam-5573	414	22	,	,	PUNCT
ejpam-5573	414	23	such	such	ADJ
ejpam-5573	414	24	that	that	SCONJ
ejpam-5573	414	25	µ	µ	PRON
ejpam-5573	414	26	≤	≤	NUM
ejpam-5573	414	27	∨	∨	NUM
ejpam-5573	414	28	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	414	29	◦	◦	NOUN
ejpam-5573	414	30	iτ	iτ	NOUN
ejpam-5573	414	31	,	,	PUNCT
ejpam-5573	414	32	τ∗(cτ	τ∗(cτ	PROPN
ejpam-5573	414	33	,	,	PUNCT
ejpam-5573	414	34	τ∗(h	τ∗(h	PROPN
ejpam-5573	414	35	−1(λj	−1(λj	NOUN
ejpam-5573	414	36	)	)	PUNCT
ejpam-5573	414	37	,	,	PUNCT
ejpam-5573	414	38	r	r	NOUN
ejpam-5573	414	39	,	,	PUNCT
ejpam-5573	414	40	s	s	PART
ejpam-5573	414	41	)	)	PUNCT
ejpam-5573	414	42	,	,	PUNCT
ejpam-5573	414	43	r	r	NOUN
ejpam-5573	414	44	,	,	PUNCT
ejpam-5573	414	45	s	s	NOUN
ejpam-5573	414	46	)	)	PUNCT
ejpam-5573	414	47	.	.	PUNCT
ejpam-5573	415	1	since	since	SCONJ
ejpam-5573	415	2	h	h	PROPN
ejpam-5573	415	3	is	be	AUX
ejpam-5573	415	4	df	df	NOUN
ejpam-5573	415	5	-	-	PUNCT
ejpam-5573	415	6	continuous	continuous	ADJ
ejpam-5573	415	7	and	and	CCONJ
ejpam-5573	415	8	df	df	NOUN
ejpam-5573	415	9	-	-	PUNCT
ejpam-5573	415	10	open	open	ADJ
ejpam-5573	415	11	,	,	PUNCT
ejpam-5573	415	12	it	it	PRON
ejpam-5573	415	13	follows	follow	VERB
ejpam-5573	415	14	h(µ	h(µ	PROPN
ejpam-5573	415	15	)	)	PUNCT
ejpam-5573	415	16	≤	≤	NUM
ejpam-5573	415	17	∨	∨	NUM
ejpam-5573	415	18	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	415	19	◦	◦	NOUN
ejpam-5573	415	20	h(iτ	h(iτ	PROPN
ejpam-5573	415	21	,	,	PUNCT
ejpam-5573	415	22	τ∗(cτ	τ∗(cτ	PROPN
ejpam-5573	415	23	,	,	PUNCT
ejpam-5573	415	24	τ∗(h	τ∗(h	PROPN
ejpam-5573	415	25	−1(λj	−1(λj	NOUN
ejpam-5573	415	26	)	)	PUNCT
ejpam-5573	415	27	,	,	PUNCT
ejpam-5573	415	28	r	r	NOUN
ejpam-5573	415	29	,	,	PUNCT
ejpam-5573	415	30	s	s	PART
ejpam-5573	415	31	)	)	PUNCT
ejpam-5573	415	32	,	,	PUNCT
ejpam-5573	415	33	r	r	NOUN
ejpam-5573	415	34	,	,	PUNCT
ejpam-5573	415	35	s	s	NOUN
ejpam-5573	415	36	)	)	PUNCT
ejpam-5573	415	37	)	)	PUNCT
ejpam-5573	415	38	≤	≤	NUM
ejpam-5573	415	39	∨	∨	NUM
ejpam-5573	415	40	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	415	41	◦	◦	NOUN
ejpam-5573	415	42	iη	iη	NOUN
ejpam-5573	415	43	,	,	PUNCT
ejpam-5573	415	44	η∗(h(cτ	η∗(h(cτ	NOUN
ejpam-5573	415	45	,	,	PUNCT
ejpam-5573	415	46	τ∗(h	τ∗(h	PROPN
ejpam-5573	415	47	−1(λj	−1(λj	NOUN
ejpam-5573	415	48	)	)	PUNCT
ejpam-5573	415	49	,	,	PUNCT
ejpam-5573	415	50	r	r	NOUN
ejpam-5573	415	51	,	,	PUNCT
ejpam-5573	415	52	s	s	NOUN
ejpam-5573	415	53	)	)	PUNCT
ejpam-5573	415	54	)	)	PUNCT
ejpam-5573	415	55	,	,	PUNCT
ejpam-5573	415	56	r	r	NOUN
ejpam-5573	415	57	,	,	PUNCT
ejpam-5573	415	58	s	s	NOUN
ejpam-5573	415	59	)	)	PUNCT
ejpam-5573	415	60	≤	≤	NUM
ejpam-5573	415	61	∨	∨	NUM
ejpam-5573	415	62	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	415	63	◦	◦	NOUN
ejpam-5573	415	64	iη	iη	NOUN
ejpam-5573	415	65	,	,	PUNCT
ejpam-5573	415	66	η∗(h(h	η∗(h(h	ADV
ejpam-5573	415	67	−1(cη	−1(cη	ADJ
ejpam-5573	415	68	,	,	PUNCT
ejpam-5573	415	69	η∗(λj	η∗(λj	NOUN
ejpam-5573	415	70	,	,	PUNCT
ejpam-5573	415	71	r	r	NOUN
ejpam-5573	415	72	,	,	PUNCT
ejpam-5573	415	73	s	s	NOUN
ejpam-5573	415	74	)	)	PUNCT
ejpam-5573	415	75	)	)	PUNCT
ejpam-5573	415	76	)	)	PUNCT
ejpam-5573	415	77	,	,	PUNCT
ejpam-5573	415	78	r	r	NOUN
ejpam-5573	415	79	,	,	PUNCT
ejpam-5573	415	80	s	s	NOUN
ejpam-5573	415	81	)	)	PUNCT
ejpam-5573	415	82	≤	≤	NUM
ejpam-5573	415	83	∨	∨	NUM
ejpam-5573	415	84	j∈𭟋	j∈𭟋	NOUN
ejpam-5573	415	85	◦	◦	NOUN
ejpam-5573	415	86	iη	iη	NOUN
ejpam-5573	415	87	,	,	PUNCT
ejpam-5573	415	88	η∗(cη	η∗(cη	NOUN
ejpam-5573	415	89	,	,	PUNCT
ejpam-5573	415	90	η∗(λj	η∗(λj	NOUN
ejpam-5573	415	91	,	,	PUNCT
ejpam-5573	415	92	r	r	NOUN
ejpam-5573	415	93	,	,	PUNCT
ejpam-5573	415	94	s	s	PART
ejpam-5573	415	95	)	)	PUNCT
ejpam-5573	415	96	,	,	PUNCT
ejpam-5573	415	97	r	r	NOUN
ejpam-5573	415	98	,	,	PUNCT
ejpam-5573	415	99	s	s	NOUN
ejpam-5573	415	100	)	)	PUNCT
ejpam-5573	415	101	.	.	PUNCT
ejpam-5573	416	1	hence	hence	ADV
ejpam-5573	416	2	,	,	PUNCT
ejpam-5573	416	3	the	the	DET
ejpam-5573	416	4	proof	proof	NOUN
ejpam-5573	416	5	is	be	AUX
ejpam-5573	416	6	completed	complete	VERB
ejpam-5573	416	7	.	.	PUNCT
ejpam-5573	417	1	lemma	lemma	PROPN
ejpam-5573	417	2	8	8	NUM
ejpam-5573	417	3	.	.	PUNCT
ejpam-5573	418	1	let	let	VERB
ejpam-5573	418	2	(	(	PUNCT
ejpam-5573	418	3	u	u	NOUN
ejpam-5573	418	4	,	,	PUNCT
ejpam-5573	418	5	η	η	PROPN
ejpam-5573	418	6	,	,	PUNCT
ejpam-5573	418	7	η∗	η∗	NOUN
ejpam-5573	418	8	)	)	PUNCT
ejpam-5573	418	9	be	be	VERB
ejpam-5573	418	10	a	a	DET
ejpam-5573	418	11	dfts	dft	NOUN
ejpam-5573	418	12	,	,	PUNCT
ejpam-5573	418	13	r	r	NOUN
ejpam-5573	418	14	∈	∈	PROPN
ejpam-5573	419	1	i	i	NOUN
ejpam-5573	419	2	◦	◦	NOUN
ejpam-5573	419	3	,	,	PUNCT
ejpam-5573	419	4	and	and	CCONJ
ejpam-5573	419	5	s	s	PROPN
ejpam-5573	419	6	∈	∈	PROPN
ejpam-5573	419	7	i1	i1	PROPN
ejpam-5573	419	8	.	.	PUNCT
ejpam-5573	420	1	if	if	SCONJ
ejpam-5573	420	2	µ	µ	PRON
ejpam-5573	420	3	∈	∈	NOUN
ejpam-5573	420	4	iu	iu	ADV
ejpam-5573	420	5	is	be	AUX
ejpam-5573	420	6	(	(	PUNCT
ejpam-5573	420	7	r	r	NOUN
ejpam-5573	420	8	,	,	PUNCT
ejpam-5573	420	9	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	420	10	soft	soft	ADJ
ejpam-5573	420	11	nearly	nearly	ADV
ejpam-5573	420	12	gs	gs	NOUN
ejpam-5573	420	13	-	-	ADJ
ejpam-5573	420	14	compact	compact	ADJ
ejpam-5573	420	15	(	(	PUNCT
ejpam-5573	420	16	resp	resp	NOUN
ejpam-5573	420	17	.	.	PUNCT
ejpam-5573	420	18	,	,	PUNCT
ejpam-5573	420	19	nearly	nearly	ADV
ejpam-5573	420	20	compact	compact	ADJ
ejpam-5573	420	21	)	)	PUNCT
ejpam-5573	420	22	,	,	PUNCT
ejpam-5573	420	23	then	then	ADV
ejpam-5573	420	24	µ	µ	X
ejpam-5573	420	25	is	be	AUX
ejpam-5573	420	26	(	(	PUNCT
ejpam-5573	420	27	r	r	NOUN
ejpam-5573	420	28	,	,	PUNCT
ejpam-5573	420	29	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	420	30	soft	soft	ADJ
ejpam-5573	420	31	almost	almost	ADV
ejpam-5573	420	32	gs	gs	ADJ
ejpam-5573	420	33	-	-	ADJ
ejpam-5573	420	34	compact	compact	ADJ
ejpam-5573	420	35	(	(	PUNCT
ejpam-5573	420	36	resp	resp	NOUN
ejpam-5573	420	37	.	.	PUNCT
ejpam-5573	420	38	,	,	PUNCT
ejpam-5573	420	39	almost	almost	ADV
ejpam-5573	420	40	compact	compact	ADJ
ejpam-5573	420	41	)	)	PUNCT
ejpam-5573	420	42	.	.	PUNCT
ejpam-5573	421	1	proof	proof	NOUN
ejpam-5573	421	2	.	.	PUNCT
ejpam-5573	422	1	follows	follow	VERB
ejpam-5573	422	2	from	from	ADP
ejpam-5573	422	3	definitions	definition	NOUN
ejpam-5573	422	4	11	11	NUM
ejpam-5573	422	5	,	,	PUNCT
ejpam-5573	422	6	12	12	NUM
ejpam-5573	422	7	,	,	PUNCT
ejpam-5573	422	8	13	13	NUM
ejpam-5573	422	9	and	and	CCONJ
ejpam-5573	422	10	14	14	NUM
ejpam-5573	422	11	.	.	PUNCT
ejpam-5573	423	1	remark	remark	NOUN
ejpam-5573	423	2	11	11	NUM
ejpam-5573	423	3	.	.	PUNCT
ejpam-5573	424	1	we	we	PRON
ejpam-5573	424	2	can	can	AUX
ejpam-5573	424	3	summarize	summarize	VERB
ejpam-5573	424	4	the	the	DET
ejpam-5573	424	5	relationships	relationship	NOUN
ejpam-5573	424	6	among	among	ADP
ejpam-5573	424	7	different	different	ADJ
ejpam-5573	424	8	types	type	NOUN
ejpam-5573	424	9	of	of	ADP
ejpam-5573	424	10	fuzzy	fuzzy	ADJ
ejpam-5573	424	11	compactness	compactness	NOUN
ejpam-5573	424	12	as	as	ADP
ejpam-5573	424	13	in	in	ADP
ejpam-5573	424	14	the	the	DET
ejpam-5573	424	15	next	next	ADJ
ejpam-5573	424	16	diagram	diagram	NOUN
ejpam-5573	424	17	.	.	PUNCT
ejpam-5573	425	1	gs	gs	NOUN
ejpam-5573	425	2	-	-	PUNCT
ejpam-5573	425	3	compactness	compactness	NOUN
ejpam-5573	425	4	→	→	PUNCT
ejpam-5573	425	5	compactness	compactness	NOUN
ejpam-5573	425	6	↓	↓	NOUN
ejpam-5573	425	7	↓	↓	PROPN
ejpam-5573	425	8	nearly	nearly	ADV
ejpam-5573	425	9	gs	gs	NOUN
ejpam-5573	425	10	-	-	PUNCT
ejpam-5573	425	11	compactness	compactness	NOUN
ejpam-5573	425	12	→	→	PUNCT
ejpam-5573	425	13	nearly	nearly	ADV
ejpam-5573	425	14	compactness	compactness	NOUN
ejpam-5573	425	15	↓	↓	NOUN
ejpam-5573	425	16	↓	↓	PROPN
ejpam-5573	425	17	almost	almost	ADV
ejpam-5573	425	18	gs	gs	NOUN
ejpam-5573	425	19	-	-	PUNCT
ejpam-5573	425	20	compactness	compactness	NOUN
ejpam-5573	425	21	→	→	ADP
ejpam-5573	425	22	almost	almost	ADV
ejpam-5573	425	23	compactness	compactness	NOUN
ejpam-5573	425	24	references	reference	NOUN
ejpam-5573	425	25	4108	4108	NUM
ejpam-5573	425	26	5	5	NUM
ejpam-5573	425	27	.	.	PUNCT
ejpam-5573	426	1	conclusion	conclusion	NOUN
ejpam-5573	426	2	and	and	CCONJ
ejpam-5573	426	3	future	future	ADJ
ejpam-5573	426	4	work	work	NOUN
ejpam-5573	426	5	in	in	ADP
ejpam-5573	426	6	this	this	DET
ejpam-5573	426	7	article	article	NOUN
ejpam-5573	427	1	,	,	PUNCT
ejpam-5573	427	2	we	we	PRON
ejpam-5573	427	3	have	have	AUX
ejpam-5573	427	4	introduced	introduce	VERB
ejpam-5573	427	5	a	a	DET
ejpam-5573	427	6	novel	novel	ADJ
ejpam-5573	427	7	class	class	NOUN
ejpam-5573	427	8	of	of	ADP
ejpam-5573	427	9	generalizations	generalization	NOUN
ejpam-5573	427	10	of	of	ADP
ejpam-5573	427	11	fuzzy	fuzzy	ADJ
ejpam-5573	427	12	closed	closed	ADJ
ejpam-5573	427	13	subsets	subset	NOUN
ejpam-5573	427	14	called	call	VERB
ejpam-5573	427	15	“	"	PUNCT
ejpam-5573	427	16	(	(	PUNCT
ejpam-5573	427	17	r	r	NOUN
ejpam-5573	427	18	,	,	PUNCT
ejpam-5573	427	19	s)−g⊛fsc	s)−g⊛fsc	ADJ
ejpam-5573	427	20	sets	set	NOUN
ejpam-5573	427	21	”	"	PUNCT
ejpam-5573	427	22	via	via	ADP
ejpam-5573	427	23	double	double	ADJ
ejpam-5573	427	24	fuzzy	fuzzy	ADJ
ejpam-5573	427	25	topologies	topology	NOUN
ejpam-5573	427	26	and	and	CCONJ
ejpam-5573	427	27	some	some	DET
ejpam-5573	427	28	characterizations	characterization	NOUN
ejpam-5573	427	29	have	have	AUX
ejpam-5573	427	30	been	be	AUX
ejpam-5573	427	31	discussed	discuss	VERB
ejpam-5573	427	32	.	.	PUNCT
ejpam-5573	428	1	moreover	moreover	ADV
ejpam-5573	428	2	,	,	PUNCT
ejpam-5573	428	3	we	we	PRON
ejpam-5573	428	4	have	have	AUX
ejpam-5573	428	5	defined	define	VERB
ejpam-5573	428	6	novel	novel	ADJ
ejpam-5573	428	7	types	type	NOUN
ejpam-5573	428	8	of	of	ADP
ejpam-5573	428	9	fuzzy	fuzzy	ADJ
ejpam-5573	428	10	mappings	mapping	NOUN
ejpam-5573	428	11	and	and	CCONJ
ejpam-5573	428	12	the	the	DET
ejpam-5573	428	13	relationship	relationship	NOUN
ejpam-5573	428	14	between	between	ADP
ejpam-5573	428	15	these	these	DET
ejpam-5573	428	16	mappings	mapping	NOUN
ejpam-5573	428	17	have	have	AUX
ejpam-5573	428	18	been	be	AUX
ejpam-5573	428	19	introduced	introduce	VERB
ejpam-5573	428	20	with	with	ADP
ejpam-5573	428	21	the	the	DET
ejpam-5573	428	22	help	help	NOUN
ejpam-5573	428	23	of	of	ADP
ejpam-5573	428	24	some	some	DET
ejpam-5573	428	25	problems	problem	NOUN
ejpam-5573	428	26	.	.	PUNCT
ejpam-5573	429	1	also	also	ADV
ejpam-5573	429	2	,	,	PUNCT
ejpam-5573	429	3	we	we	PRON
ejpam-5573	429	4	have	have	AUX
ejpam-5573	429	5	shown	show	VERB
ejpam-5573	429	6	that	that	SCONJ
ejpam-5573	429	7	(	(	PUNCT
ejpam-5573	429	8	r	r	NOUN
ejpam-5573	429	9	,	,	PUNCT
ejpam-5573	429	10	s)−	s)−	PROPN
ejpam-5573	429	11	fsc	fsc	PROPN
ejpam-5573	429	12	⇒	⇒	PROPN
ejpam-5573	429	13	(	(	PUNCT
ejpam-5573	429	14	r	r	NOUN
ejpam-5573	429	15	,	,	PUNCT
ejpam-5573	429	16	s)−	s)−	PROPN
ejpam-5573	430	1	g⊛fsc	g⊛fsc	PROPN
ejpam-5573	430	2	⇓	⇓	PROPN
ejpam-5573	430	3	⇓	⇓	PROPN
ejpam-5573	430	4	(	(	PUNCT
ejpam-5573	430	5	r	r	NOUN
ejpam-5573	430	6	,	,	PUNCT
ejpam-5573	430	7	s)−	s)−	NOUN
ejpam-5573	430	8	sgfc	sgfc	NOUN
ejpam-5573	430	9	(	(	PUNCT
ejpam-5573	430	10	r	r	NOUN
ejpam-5573	430	11	,	,	PUNCT
ejpam-5573	430	12	s)−	s)−	PROPN
ejpam-5573	430	13	g⊖fsc	g⊖fsc	PROPN
ejpam-5573	430	14	⇓	⇓	PROPN
ejpam-5573	430	15	⇓	⇓	PROPN
ejpam-5573	430	16	(	(	PUNCT
ejpam-5573	430	17	r	r	NOUN
ejpam-5573	430	18	,	,	PUNCT
ejpam-5573	430	19	s)−	s)−	PROPN
ejpam-5573	430	20	gfsc	gfsc	PROPN
ejpam-5573	430	21	but	but	CCONJ
ejpam-5573	430	22	in	in	ADP
ejpam-5573	430	23	general	general	ADJ
ejpam-5573	430	24	,	,	PUNCT
ejpam-5573	430	25	the	the	DET
ejpam-5573	430	26	converses	converse	NOUN
ejpam-5573	430	27	of	of	ADP
ejpam-5573	430	28	the	the	DET
ejpam-5573	430	29	above	above	ADJ
ejpam-5573	430	30	implications	implication	NOUN
ejpam-5573	430	31	may	may	AUX
ejpam-5573	430	32	not	not	PART
ejpam-5573	430	33	be	be	AUX
ejpam-5573	430	34	true	true	ADJ
ejpam-5573	430	35	.	.	PUNCT
ejpam-5573	431	1	thereafter	thereafter	ADV
ejpam-5573	431	2	,	,	PUNCT
ejpam-5573	431	3	“	"	PUNCT
ejpam-5573	431	4	(	(	PUNCT
ejpam-5573	431	5	r	r	NOUN
ejpam-5573	431	6	,	,	PUNCT
ejpam-5573	431	7	s)-gfs	s)-gfs	NOUN
ejpam-5573	431	8	-	-	PUNCT
ejpam-5573	431	9	regular	regular	ADJ
ejpam-5573	431	10	”	"	PUNCT
ejpam-5573	431	11	and	and	CCONJ
ejpam-5573	431	12	“	"	PUNCT
ejpam-5573	431	13	(	(	PUNCT
ejpam-5573	431	14	r	r	NOUN
ejpam-5573	431	15	,	,	PUNCT
ejpam-5573	431	16	s)-gfs	s)-gf	NOUN
ejpam-5573	431	17	-	-	PUNCT
ejpam-5573	431	18	normal	normal	ADJ
ejpam-5573	431	19	”	"	PUNCT
ejpam-5573	431	20	spaces	space	NOUN
ejpam-5573	431	21	have	have	AUX
ejpam-5573	431	22	been	be	AUX
ejpam-5573	431	23	defined	define	VERB
ejpam-5573	431	24	as	as	ADP
ejpam-5573	431	25	two	two	NUM
ejpam-5573	431	26	new	new	ADJ
ejpam-5573	431	27	notions	notion	NOUN
ejpam-5573	431	28	of	of	ADP
ejpam-5573	431	29	higher	high	ADJ
ejpam-5573	431	30	fuzzy	fuzzy	ADJ
ejpam-5573	431	31	separation	separation	NOUN
ejpam-5573	431	32	axioms	axiom	NOUN
ejpam-5573	431	33	and	and	CCONJ
ejpam-5573	431	34	some	some	DET
ejpam-5573	431	35	characterizations	characterization	NOUN
ejpam-5573	431	36	of	of	ADP
ejpam-5573	431	37	these	these	DET
ejpam-5573	431	38	separation	separation	NOUN
ejpam-5573	431	39	axioms	axiom	NOUN
ejpam-5573	431	40	have	have	AUX
ejpam-5573	431	41	been	be	AUX
ejpam-5573	431	42	obtained	obtain	VERB
ejpam-5573	431	43	.	.	PUNCT
ejpam-5573	432	1	in	in	ADP
ejpam-5573	432	2	the	the	DET
ejpam-5573	432	3	end	end	NOUN
ejpam-5573	432	4	,	,	PUNCT
ejpam-5573	432	5	several	several	ADJ
ejpam-5573	432	6	novel	novel	ADJ
ejpam-5573	432	7	types	type	NOUN
ejpam-5573	432	8	of	of	ADP
ejpam-5573	432	9	fuzzy	fuzzy	ADJ
ejpam-5573	432	10	compactness	compactness	NOUN
ejpam-5573	432	11	in	in	ADP
ejpam-5573	432	12	the	the	DET
ejpam-5573	432	13	frame	frame	NOUN
ejpam-5573	432	14	of	of	ADP
ejpam-5573	432	15	double	double	ADJ
ejpam-5573	432	16	fuzzy	fuzzy	ADJ
ejpam-5573	432	17	topologies	topology	NOUN
ejpam-5573	432	18	have	have	AUX
ejpam-5573	432	19	been	be	AUX
ejpam-5573	432	20	introduced	introduce	VERB
ejpam-5573	432	21	and	and	CCONJ
ejpam-5573	432	22	some	some	DET
ejpam-5573	432	23	properties	property	NOUN
ejpam-5573	432	24	have	have	AUX
ejpam-5573	432	25	been	be	AUX
ejpam-5573	432	26	given	give	VERB
ejpam-5573	432	27	.	.	PUNCT
ejpam-5573	433	1	also	also	ADV
ejpam-5573	433	2	,	,	PUNCT
ejpam-5573	433	3	the	the	DET
ejpam-5573	433	4	relationship	relationship	NOUN
ejpam-5573	433	5	between	between	ADP
ejpam-5573	433	6	them	they	PRON
ejpam-5573	433	7	have	have	AUX
ejpam-5573	433	8	been	be	AUX
ejpam-5573	433	9	explored	explore	VERB
ejpam-5573	433	10	.	.	PUNCT
ejpam-5573	434	1	in	in	ADP
ejpam-5573	434	2	the	the	DET
ejpam-5573	434	3	upcoming	upcoming	ADJ
ejpam-5573	434	4	papers	paper	NOUN
ejpam-5573	434	5	,	,	PUNCT
ejpam-5573	434	6	we	we	PRON
ejpam-5573	434	7	shall	shall	AUX
ejpam-5573	434	8	discuss	discuss	VERB
ejpam-5573	434	9	the	the	DET
ejpam-5573	434	10	concepts	concept	NOUN
ejpam-5573	434	11	given	give	VERB
ejpam-5573	434	12	here	here	ADV
ejpam-5573	434	13	in	in	ADP
ejpam-5573	434	14	the	the	DET
ejpam-5573	434	15	frames	frame	NOUN
ejpam-5573	434	16	of	of	ADP
ejpam-5573	434	17	a	a	DET
ejpam-5573	434	18	fuzzy	fuzzy	ADJ
ejpam-5573	434	19	idealization	idealization	NOUN
ejpam-5573	434	20	[	[	X
ejpam-5573	434	21	38	38	NUM
ejpam-5573	434	22	,	,	PUNCT
ejpam-5573	434	23	40	40	NUM
ejpam-5573	434	24	]	]	PUNCT
ejpam-5573	434	25	and	and	CCONJ
ejpam-5573	434	26	fuzzy	fuzzy	ADJ
ejpam-5573	434	27	soft	soft	ADJ
ejpam-5573	434	28	r	r	NOUN
ejpam-5573	434	29	-	-	PUNCT
ejpam-5573	434	30	minimal	minimal	ADJ
ejpam-5573	434	31	structures	structure	NOUN
ejpam-5573	434	32	[	[	X
ejpam-5573	434	33	37	37	NUM
ejpam-5573	434	34	,	,	PUNCT
ejpam-5573	434	35	41	41	NUM
ejpam-5573	434	36	]	]	PUNCT
ejpam-5573	434	37	.	.	PUNCT
ejpam-5573	435	1	moreover	moreover	ADV
ejpam-5573	435	2	,	,	PUNCT
ejpam-5573	435	3	we	we	PRON
ejpam-5573	435	4	will	will	AUX
ejpam-5573	435	5	study	study	VERB
ejpam-5573	435	6	the	the	DET
ejpam-5573	435	7	main	main	ADJ
ejpam-5573	435	8	properties	property	NOUN
ejpam-5573	435	9	of	of	ADP
ejpam-5573	435	10	classical	classical	ADJ
ejpam-5573	435	11	compactness	compactness	NOUN
ejpam-5573	435	12	in	in	ADP
ejpam-5573	435	13	the	the	DET
ejpam-5573	435	14	frame	frame	NOUN
ejpam-5573	435	15	of	of	ADP
ejpam-5573	435	16	double	double	ADJ
ejpam-5573	435	17	fuzzy	fuzzy	ADJ
ejpam-5573	435	18	topologies	topology	NOUN
ejpam-5573	435	19	.	.	PUNCT
ejpam-5573	436	1	acknowledgements	acknowledgement	NOUN
ejpam-5573	436	2	we	we	PRON
ejpam-5573	436	3	would	would	AUX
ejpam-5573	436	4	like	like	VERB
ejpam-5573	436	5	to	to	PART
ejpam-5573	436	6	thank	thank	VERB
ejpam-5573	436	7	the	the	DET
ejpam-5573	436	8	reviewers	reviewer	NOUN
ejpam-5573	436	9	and	and	CCONJ
ejpam-5573	436	10	editors	editor	NOUN
ejpam-5573	436	11	whose	whose	DET
ejpam-5573	436	12	constructive	constructive	ADJ
ejpam-5573	436	13	comments	comment	NOUN
ejpam-5573	436	14	and	and	CCONJ
ejpam-5573	436	15	suggestions	suggestion	NOUN
ejpam-5573	436	16	helped	help	VERB
ejpam-5573	436	17	to	to	PART
ejpam-5573	436	18	improve	improve	VERB
ejpam-5573	436	19	this	this	DET
ejpam-5573	436	20	paper	paper	NOUN
ejpam-5573	436	21	.	.	PUNCT
ejpam-5573	437	1	references	reference	NOUN
ejpam-5573	437	2	[	[	X
ejpam-5573	437	3	1	1	X
ejpam-5573	437	4	]	]	PUNCT
ejpam-5573	437	5	s.	s.	PROPN
ejpam-5573	437	6	e.	e.	PROPN
ejpam-5573	437	7	abbas	abbas	PROPN
ejpam-5573	437	8	.	.	PUNCT
ejpam-5573	438	1	(	(	PUNCT
ejpam-5573	438	2	r	r	NOUN
ejpam-5573	438	3	,	,	PUNCT
ejpam-5573	438	4	s)-generalized	s)-generalized	ADJ
ejpam-5573	438	5	intuitionistic	intuitionistic	ADJ
ejpam-5573	438	6	fuzzy	fuzzy	ADJ
ejpam-5573	438	7	closed	closed	ADJ
ejpam-5573	438	8	sets	set	NOUN
ejpam-5573	438	9	.	.	PUNCT
ejpam-5573	439	1	j.	j.	PROPN
ejpam-5573	439	2	egyptian	egyptian	PROPN
ejpam-5573	439	3	math	math	PROPN
ejpam-5573	439	4	.	.	PUNCT
ejpam-5573	440	1	soc	soc	PROPN
ejpam-5573	440	2	.	.	PUNCT
ejpam-5573	440	3	,	,	PUNCT
ejpam-5573	440	4	14:331–351	14:331–351	PROPN
ejpam-5573	440	5	,	,	PUNCT
ejpam-5573	440	6	2006	2006	NUM
ejpam-5573	440	7	.	.	PUNCT
ejpam-5573	441	1	[	[	X
ejpam-5573	441	2	2	2	X
ejpam-5573	441	3	]	]	PUNCT
ejpam-5573	441	4	s.	s.	PROPN
ejpam-5573	441	5	e.	e.	PROPN
ejpam-5573	441	6	abbas	abbas	PROPN
ejpam-5573	441	7	and	and	CCONJ
ejpam-5573	441	8	b.	b.	PROPN
ejpam-5573	441	9	krsteska	krsteska	PROPN
ejpam-5573	441	10	.	.	PUNCT
ejpam-5573	442	1	some	some	DET
ejpam-5573	442	2	properties	property	NOUN
ejpam-5573	442	3	of	of	ADP
ejpam-5573	442	4	intuitionistic	intuitionistic	ADJ
ejpam-5573	442	5	(	(	PUNCT
ejpam-5573	442	6	r	r	NOUN
ejpam-5573	442	7	,	,	PUNCT
ejpam-5573	442	8	s)-t0	s)-t0	ADJ
ejpam-5573	442	9	and	and	CCONJ
ejpam-5573	442	10	(	(	PUNCT
ejpam-5573	442	11	r	r	NOUN
ejpam-5573	442	12	,	,	PUNCT
ejpam-5573	442	13	s)-t1	s)-t1	NOUN
ejpam-5573	442	14	spaces	space	NOUN
ejpam-5573	442	15	.	.	PUNCT
ejpam-5573	443	1	int	int	NOUN
ejpam-5573	443	2	.	.	PUNCT
ejpam-5573	444	1	j.	j.	PROPN
ejpam-5573	444	2	math	math	PROPN
ejpam-5573	444	3	.	.	PUNCT
ejpam-5573	445	1	math	math	NOUN
ejpam-5573	445	2	.	.	PUNCT
ejpam-5573	446	1	sci	sci	PROPN
ejpam-5573	446	2	.	.	PROPN
ejpam-5573	446	3	,	,	PUNCT
ejpam-5573	446	4	pages	page	NOUN
ejpam-5573	446	5	1–11	1–11	PROPN
ejpam-5573	446	6	,	,	PUNCT
ejpam-5573	446	7	2008	2008	NUM
ejpam-5573	446	8	.	.	PUNCT
ejpam-5573	447	1	[	[	X
ejpam-5573	447	2	3	3	X
ejpam-5573	447	3	]	]	X
ejpam-5573	447	4	r.	r.	PROPN
ejpam-5573	447	5	abu	abu	PROPN
ejpam-5573	447	6	-	-	PUNCT
ejpam-5573	447	7	gdairi	gdairi	PROPN
ejpam-5573	447	8	,	,	PUNCT
ejpam-5573	447	9	a.	a.	NOUN
ejpam-5573	447	10	a.	a.	NOUN
ejpam-5573	447	11	nasef	nasef	PROPN
ejpam-5573	447	12	,	,	PUNCT
ejpam-5573	447	13	m.	m.	NOUN
ejpam-5573	447	14	a.	a.	PROPN
ejpam-5573	447	15	el	el	PROPN
ejpam-5573	447	16	-	-	PROPN
ejpam-5573	447	17	gayar	gayar	NOUN
ejpam-5573	447	18	,	,	PUNCT
ejpam-5573	447	19	and	and	CCONJ
ejpam-5573	447	20	m.	m.	PROPN
ejpam-5573	447	21	k.	k.	PROPN
ejpam-5573	448	1	el	el	PROPN
ejpam-5573	448	2	-	-	PROPN
ejpam-5573	448	3	bably	bably	ADV
ejpam-5573	448	4	.	.	PUNCT
ejpam-5573	449	1	on	on	ADP
ejpam-5573	449	2	fuzzy	fuzzy	ADJ
ejpam-5573	449	3	point	point	NOUN
ejpam-5573	449	4	applications	application	NOUN
ejpam-5573	449	5	of	of	ADP
ejpam-5573	449	6	fuzzy	fuzzy	ADJ
ejpam-5573	449	7	topological	topological	ADJ
ejpam-5573	449	8	spaces	space	NOUN
ejpam-5573	449	9	.	.	PUNCT
ejpam-5573	450	1	int	int	NOUN
ejpam-5573	450	2	.	.	PUNCT
ejpam-5573	451	1	j.	j.	PROPN
ejpam-5573	451	2	fuzzy	fuzzy	PROPN
ejpam-5573	451	3	logic	logic	PROPN
ejpam-5573	451	4	intell	intell	PROPN
ejpam-5573	451	5	.	.	PUNCT
ejpam-5573	452	1	syst	syst	PROPN
ejpam-5573	452	2	.	.	PROPN
ejpam-5573	452	3	,	,	PUNCT
ejpam-5573	452	4	23(2):162	23(2):162	NUM
ejpam-5573	452	5	–	–	PUNCT
ejpam-5573	452	6	172	172	NUM
ejpam-5573	452	7	,	,	PUNCT
ejpam-5573	452	8	2023	2023	NUM
ejpam-5573	452	9	.	.	PUNCT
ejpam-5573	453	1	references	reference	NOUN
ejpam-5573	453	2	4109	4109	NUM
ejpam-5573	454	1	[	[	X
ejpam-5573	454	2	4	4	X
ejpam-5573	454	3	]	]	PUNCT
ejpam-5573	454	4	t.	t.	PROPN
ejpam-5573	454	5	m.	m.	PROPN
ejpam-5573	454	6	al	al	PROPN
ejpam-5573	454	7	-	-	PUNCT
ejpam-5573	454	8	shami	shami	PROPN
ejpam-5573	454	9	and	and	CCONJ
ejpam-5573	454	10	m.	m.	PROPN
ejpam-5573	454	11	e.	e.	PROPN
ejpam-5573	454	12	el	el	PROPN
ejpam-5573	454	13	-	-	PROPN
ejpam-5573	454	14	shafei	shafei	PROPN
ejpam-5573	454	15	.	.	PUNCT
ejpam-5573	455	1	on	on	ADP
ejpam-5573	455	2	supra	supra	PROPN
ejpam-5573	455	3	soft	soft	ADJ
ejpam-5573	455	4	topological	topological	ADJ
ejpam-5573	455	5	ordered	order	VERB
ejpam-5573	455	6	spaces	space	NOUN
ejpam-5573	455	7	.	.	PUNCT
ejpam-5573	456	1	arab	arab	PROPN
ejpam-5573	456	2	j.	j.	PROPN
ejpam-5573	456	3	basic	basic	PROPN
ejpam-5573	456	4	appl	appl	PROPN
ejpam-5573	456	5	.	.	PUNCT
ejpam-5573	457	1	sci	sci	PROPN
ejpam-5573	457	2	.	.	PROPN
ejpam-5573	457	3	,	,	PUNCT
ejpam-5573	457	4	26(1):433–445	26(1):433–445	PROPN
ejpam-5573	457	5	,	,	PUNCT
ejpam-5573	457	6	2019	2019	NUM
ejpam-5573	457	7	.	.	PUNCT
ejpam-5573	458	1	[	[	X
ejpam-5573	458	2	5	5	X
ejpam-5573	458	3	]	]	PUNCT
ejpam-5573	458	4	t.	t.	PROPN
ejpam-5573	458	5	m.	m.	PROPN
ejpam-5573	458	6	al	al	PROPN
ejpam-5573	458	7	-	-	PUNCT
ejpam-5573	458	8	shami	shami	PROPN
ejpam-5573	458	9	and	and	CCONJ
ejpam-5573	458	10	l.	l.	PROPN
ejpam-5573	458	11	d.	d.	PROPN
ejpam-5573	458	12	r.	r.	PROPN
ejpam-5573	458	13	kočinac	kočinac	PROPN
ejpam-5573	458	14	.	.	PUNCT
ejpam-5573	459	1	nearly	nearly	ADV
ejpam-5573	459	2	soft	soft	ADJ
ejpam-5573	459	3	menger	menger	NOUN
ejpam-5573	459	4	spaces	space	NOUN
ejpam-5573	459	5	.	.	PUNCT
ejpam-5573	460	1	j.	j.	PROPN
ejpam-5573	460	2	math	math	PROPN
ejpam-5573	460	3	.	.	PUNCT
ejpam-5573	460	4	,	,	PUNCT
ejpam-5573	460	5	2020:1–9	2020:1–9	NUM
ejpam-5573	460	6	,	,	PUNCT
ejpam-5573	460	7	2020	2020	NUM
ejpam-5573	460	8	.	.	PUNCT
ejpam-5573	461	1	[	[	X
ejpam-5573	461	2	6	6	NUM
ejpam-5573	461	3	]	]	PUNCT
ejpam-5573	461	4	t.	t.	PROPN
ejpam-5573	461	5	m.	m.	PROPN
ejpam-5573	461	6	al	al	PROPN
ejpam-5573	461	7	-	-	PUNCT
ejpam-5573	461	8	shami	shami	PROPN
ejpam-5573	461	9	and	and	CCONJ
ejpam-5573	461	10	a.	a.	NOUN
ejpam-5573	461	11	mhemdi	mhemdi	PROPN
ejpam-5573	461	12	.	.	PUNCT
ejpam-5573	462	1	a	a	DET
ejpam-5573	462	2	weak	weak	ADJ
ejpam-5573	462	3	form	form	NOUN
ejpam-5573	462	4	of	of	ADP
ejpam-5573	462	5	soft	soft	ADJ
ejpam-5573	462	6	α	α	NOUN
ejpam-5573	462	7	-	-	ADJ
ejpam-5573	462	8	open	open	ADJ
ejpam-5573	462	9	sets	set	NOUN
ejpam-5573	462	10	and	and	CCONJ
ejpam-5573	462	11	its	its	PRON
ejpam-5573	462	12	applications	application	NOUN
ejpam-5573	462	13	via	via	ADP
ejpam-5573	462	14	soft	soft	ADJ
ejpam-5573	462	15	topologies	topology	NOUN
ejpam-5573	462	16	.	.	PUNCT
ejpam-5573	463	1	aims	aim	VERB
ejpam-5573	463	2	math	math	NOUN
ejpam-5573	463	3	.	.	PUNCT
ejpam-5573	463	4	,	,	PUNCT
ejpam-5573	463	5	8(3):11373–11396	8(3):11373–11396	NUM
ejpam-5573	463	6	,	,	PUNCT
ejpam-5573	463	7	2023	2023	NUM
ejpam-5573	463	8	.	.	PUNCT
ejpam-5573	464	1	[	[	X
ejpam-5573	464	2	7	7	X
ejpam-5573	464	3	]	]	PUNCT
ejpam-5573	464	4	t.	t.	PROPN
ejpam-5573	464	5	m.	m.	PROPN
ejpam-5573	464	6	al	al	PROPN
ejpam-5573	464	7	-	-	PUNCT
ejpam-5573	464	8	shami	shami	PROPN
ejpam-5573	464	9	,	,	PUNCT
ejpam-5573	464	10	a.	a.	NOUN
ejpam-5573	464	11	mhemdi	mhemdi	PROPN
ejpam-5573	464	12	,	,	PUNCT
ejpam-5573	464	13	r.	r.	PROPN
ejpam-5573	464	14	abu	abu	PROPN
ejpam-5573	464	15	-	-	PUNCT
ejpam-5573	464	16	gdairi	gdairi	PROPN
ejpam-5573	464	17	,	,	PUNCT
ejpam-5573	464	18	and	and	CCONJ
ejpam-5573	464	19	m.	m.	PROPN
ejpam-5573	464	20	e.	e.	PROPN
ejpam-5573	464	21	el	el	PROPN
ejpam-5573	464	22	-	-	PROPN
ejpam-5573	464	23	shafei	shafei	PROPN
ejpam-5573	464	24	.	.	PUNCT
ejpam-5573	465	1	compactness	compactness	NOUN
ejpam-5573	465	2	and	and	CCONJ
ejpam-5573	465	3	connectedness	connectedness	NOUN
ejpam-5573	465	4	via	via	ADP
ejpam-5573	465	5	the	the	DET
ejpam-5573	465	6	class	class	NOUN
ejpam-5573	465	7	of	of	ADP
ejpam-5573	465	8	soft	soft	ADJ
ejpam-5573	465	9	somewhat	somewhat	ADV
ejpam-5573	465	10	open	open	ADJ
ejpam-5573	465	11	sets	set	NOUN
ejpam-5573	465	12	.	.	PUNCT
ejpam-5573	466	1	aims	aim	VERB
ejpam-5573	466	2	math	math	NOUN
ejpam-5573	466	3	.	.	PUNCT
ejpam-5573	467	1	,	,	PUNCT
ejpam-5573	467	2	8(1):815–840	8(1):815–840	NUM
ejpam-5573	467	3	,	,	PUNCT
ejpam-5573	467	4	2023	2023	NUM
ejpam-5573	467	5	.	.	PUNCT
ejpam-5573	468	1	[	[	X
ejpam-5573	468	2	8	8	NUM
ejpam-5573	468	3	]	]	PUNCT
ejpam-5573	468	4	t.	t.	PROPN
ejpam-5573	468	5	m.	m.	PROPN
ejpam-5573	468	6	al	al	PROPN
ejpam-5573	468	7	-	-	PUNCT
ejpam-5573	468	8	shami	shami	PROPN
ejpam-5573	468	9	,	,	PUNCT
ejpam-5573	468	10	a.	a.	NOUN
ejpam-5573	468	11	mhemdi	mhemdi	PROPN
ejpam-5573	468	12	,	,	PUNCT
ejpam-5573	468	13	and	and	CCONJ
ejpam-5573	468	14	r.	r.	PROPN
ejpam-5573	468	15	abu	abu	PROPN
ejpam-5573	468	16	-	-	PUNCT
ejpam-5573	468	17	gdairid	gdairid	PROPN
ejpam-5573	468	18	.	.	PUNCT
ejpam-5573	469	1	a	a	DET
ejpam-5573	469	2	novel	novel	ADJ
ejpam-5573	469	3	framework	framework	NOUN
ejpam-5573	469	4	for	for	ADP
ejpam-5573	469	5	generalizations	generalization	NOUN
ejpam-5573	469	6	of	of	ADP
ejpam-5573	469	7	soft	soft	ADJ
ejpam-5573	469	8	open	open	ADJ
ejpam-5573	469	9	sets	set	NOUN
ejpam-5573	469	10	and	and	CCONJ
ejpam-5573	469	11	its	its	PRON
ejpam-5573	469	12	applications	application	NOUN
ejpam-5573	469	13	via	via	ADP
ejpam-5573	469	14	soft	soft	ADJ
ejpam-5573	469	15	topologies	topology	NOUN
ejpam-5573	469	16	.	.	PUNCT
ejpam-5573	470	1	mathematics	mathematic	NOUN
ejpam-5573	470	2	,	,	PUNCT
ejpam-5573	470	3	11:1–16	11:1–16	NUM
ejpam-5573	470	4	,	,	PUNCT
ejpam-5573	470	5	2023	2023	NUM
ejpam-5573	470	6	.	.	PUNCT
ejpam-5573	471	1	[	[	X
ejpam-5573	471	2	9	9	NUM
ejpam-5573	471	3	]	]	PUNCT
ejpam-5573	471	4	m.	m.	NOUN
ejpam-5573	471	5	i.	i.	PROPN
ejpam-5573	471	6	ali	ali	PROPN
ejpam-5573	471	7	,	,	PUNCT
ejpam-5573	471	8	m.	m.	PROPN
ejpam-5573	471	9	k.	k.	PROPN
ejpam-5573	471	10	el	el	PROPN
ejpam-5573	471	11	-	-	PROPN
ejpam-5573	471	12	bably	bably	ADV
ejpam-5573	471	13	,	,	PUNCT
ejpam-5573	471	14	and	and	CCONJ
ejpam-5573	471	15	e.	e.	PROPN
ejpam-5573	471	16	a.	a.	PROPN
ejpam-5573	471	17	abo	abo	PROPN
ejpam-5573	471	18	-	-	PUNCT
ejpam-5573	471	19	tabl	tabl	NOUN
ejpam-5573	471	20	.	.	PUNCT
ejpam-5573	472	1	topological	topological	ADJ
ejpam-5573	472	2	approach	approach	NOUN
ejpam-5573	472	3	to	to	ADP
ejpam-5573	472	4	generalized	generalize	VERB
ejpam-5573	472	5	soft	soft	ADJ
ejpam-5573	472	6	rough	rough	ADJ
ejpam-5573	472	7	sets	set	NOUN
ejpam-5573	472	8	via	via	ADP
ejpam-5573	472	9	near	near	ADJ
ejpam-5573	472	10	concepts	concept	NOUN
ejpam-5573	472	11	.	.	PUNCT
ejpam-5573	473	1	soft	soft	ADJ
ejpam-5573	473	2	computing	computing	NOUN
ejpam-5573	473	3	,	,	PUNCT
ejpam-5573	473	4	26:499–509	26:499–509	NOUN
ejpam-5573	473	5	,	,	PUNCT
ejpam-5573	473	6	2022	2022	NUM
ejpam-5573	473	7	.	.	PUNCT
ejpam-5573	474	1	[	[	X
ejpam-5573	474	2	10	10	NUM
ejpam-5573	474	3	]	]	X
ejpam-5573	474	4	i.	i.	NOUN
ejpam-5573	474	5	alshammari	alshammari	PROPN
ejpam-5573	474	6	and	and	CCONJ
ejpam-5573	474	7	i.	i.	PROPN
ejpam-5573	474	8	m.	m.	PROPN
ejpam-5573	474	9	taha	taha	PROPN
ejpam-5573	474	10	.	.	PUNCT
ejpam-5573	475	1	on	on	ADP
ejpam-5573	475	2	fuzzy	fuzzy	ADJ
ejpam-5573	475	3	soft	soft	ADJ
ejpam-5573	475	4	β	β	NOUN
ejpam-5573	475	5	-	-	NOUN
ejpam-5573	475	6	continuity	continuity	NOUN
ejpam-5573	475	7	and	and	CCONJ
ejpam-5573	475	8	β	β	NOUN
ejpam-5573	475	9	-	-	NOUN
ejpam-5573	475	10	irresoluteness	irresoluteness	NOUN
ejpam-5573	475	11	:	:	PUNCT
ejpam-5573	475	12	some	some	DET
ejpam-5573	475	13	new	new	ADJ
ejpam-5573	475	14	results	result	NOUN
ejpam-5573	475	15	.	.	PUNCT
ejpam-5573	476	1	aims	aim	VERB
ejpam-5573	476	2	math	math	NOUN
ejpam-5573	476	3	.	.	PUNCT
ejpam-5573	476	4	,	,	PUNCT
ejpam-5573	476	5	9(5):11304–11319	9(5):11304–11319	PROPN
ejpam-5573	476	6	,	,	PUNCT
ejpam-5573	476	7	2024	2024	NUM
ejpam-5573	476	8	.	.	PUNCT
ejpam-5573	477	1	[	[	X
ejpam-5573	477	2	11	11	NUM
ejpam-5573	477	3	]	]	PUNCT
ejpam-5573	477	4	k.	k.	PROPN
ejpam-5573	477	5	atanassov	atanassov	PROPN
ejpam-5573	477	6	.	.	PUNCT
ejpam-5573	478	1	intuitionistic	intuitionistic	ADJ
ejpam-5573	478	2	fuzzy	fuzzy	ADJ
ejpam-5573	478	3	sets	set	NOUN
ejpam-5573	478	4	.	.	PUNCT
ejpam-5573	479	1	fuzzy	fuzzy	ADJ
ejpam-5573	479	2	sets	set	NOUN
ejpam-5573	479	3	syst	syst	PROPN
ejpam-5573	479	4	.	.	PUNCT
ejpam-5573	479	5	,	,	PUNCT
ejpam-5573	479	6	20:87–96	20:87–96	NUM
ejpam-5573	479	7	,	,	PUNCT
ejpam-5573	479	8	1986	1986	NUM
ejpam-5573	479	9	.	.	PUNCT
ejpam-5573	480	1	[	[	X
ejpam-5573	480	2	12	12	NUM
ejpam-5573	480	3	]	]	PUNCT
ejpam-5573	480	4	k.	k.	PROPN
ejpam-5573	480	5	atanassov	atanassov	PROPN
ejpam-5573	480	6	.	.	PUNCT
ejpam-5573	481	1	new	new	ADJ
ejpam-5573	481	2	operators	operator	NOUN
ejpam-5573	481	3	defined	define	VERB
ejpam-5573	481	4	over	over	ADP
ejpam-5573	481	5	the	the	DET
ejpam-5573	481	6	intuitionistic	intuitionistic	ADJ
ejpam-5573	481	7	fuzzy	fuzzy	ADJ
ejpam-5573	481	8	sets	set	NOUN
ejpam-5573	481	9	.	.	PUNCT
ejpam-5573	482	1	fuzzy	fuzzy	ADJ
ejpam-5573	482	2	sets	set	NOUN
ejpam-5573	482	3	syst	syst	PROPN
ejpam-5573	482	4	.	.	PUNCT
ejpam-5573	482	5	,	,	PUNCT
ejpam-5573	482	6	61:131–142	61:131–142	PROPN
ejpam-5573	482	7	,	,	PUNCT
ejpam-5573	482	8	1993	1993	NUM
ejpam-5573	482	9	.	.	PUNCT
ejpam-5573	483	1	[	[	X
ejpam-5573	483	2	13	13	NUM
ejpam-5573	483	3	]	]	PUNCT
ejpam-5573	483	4	j.	j.	PROPN
ejpam-5573	483	5	p.	p.	PROPN
ejpam-5573	483	6	bajpai	bajpai	PROPN
ejpam-5573	483	7	and	and	CCONJ
ejpam-5573	483	8	s.	s.	PROPN
ejpam-5573	483	9	s.	s.	PROPN
ejpam-5573	483	10	thakur	thakur	PROPN
ejpam-5573	483	11	.	.	PUNCT
ejpam-5573	484	1	intuitionistic	intuitionistic	ADJ
ejpam-5573	484	2	fuzzy	fuzzy	ADJ
ejpam-5573	484	3	sgp	sgp	NOUN
ejpam-5573	484	4	-	-	PUNCT
ejpam-5573	484	5	closed	close	VERB
ejpam-5573	484	6	set	set	NOUN
ejpam-5573	484	7	.	.	PUNCT
ejpam-5573	485	1	int	int	NOUN
ejpam-5573	485	2	.	.	PUNCT
ejpam-5573	486	1	j.	j.	PROPN
ejpam-5573	486	2	latest	late	ADJ
ejpam-5573	486	3	trends	trend	NOUN
ejpam-5573	486	4	eng	eng	PROPN
ejpam-5573	486	5	.	.	PROPN
ejpam-5573	486	6	technol	technol	PROPN
ejpam-5573	486	7	.	.	PROPN
ejpam-5573	486	8	,	,	PUNCT
ejpam-5573	486	9	8(1):636–642	8(1):636–642	NUM
ejpam-5573	486	10	,	,	PUNCT
ejpam-5573	486	11	2017	2017	NUM
ejpam-5573	486	12	.	.	PUNCT
ejpam-5573	487	1	[	[	X
ejpam-5573	487	2	14	14	NUM
ejpam-5573	487	3	]	]	X
ejpam-5573	487	4	g.	g.	PROPN
ejpam-5573	487	5	balasubramanian	balasubramanian	PROPN
ejpam-5573	487	6	and	and	CCONJ
ejpam-5573	487	7	p.	p.	PROPN
ejpam-5573	487	8	sundaram	sundaram	PROPN
ejpam-5573	487	9	.	.	PUNCT
ejpam-5573	488	1	on	on	ADP
ejpam-5573	488	2	some	some	DET
ejpam-5573	488	3	generalizations	generalization	NOUN
ejpam-5573	488	4	of	of	ADP
ejpam-5573	488	5	fuzzy	fuzzy	ADJ
ejpam-5573	488	6	continuous	continuous	ADJ
ejpam-5573	488	7	functions	function	NOUN
ejpam-5573	488	8	.	.	PUNCT
ejpam-5573	489	1	fuzzy	fuzzy	ADJ
ejpam-5573	489	2	set	set	PROPN
ejpam-5573	489	3	.	.	PUNCT
ejpam-5573	490	1	syst	syst	PROPN
ejpam-5573	490	2	.	.	PROPN
ejpam-5573	490	3	,	,	PUNCT
ejpam-5573	490	4	86:93–100	86:93–100	NUM
ejpam-5573	490	5	,	,	PUNCT
ejpam-5573	490	6	1997	1997	NUM
ejpam-5573	490	7	.	.	PUNCT
ejpam-5573	491	1	[	[	X
ejpam-5573	491	2	15	15	NUM
ejpam-5573	491	3	]	]	X
ejpam-5573	491	4	c.	c.	PROPN
ejpam-5573	491	5	l.	l.	PROPN
ejpam-5573	491	6	chang	chang	PROPN
ejpam-5573	491	7	.	.	PUNCT
ejpam-5573	492	1	fuzzy	fuzzy	ADJ
ejpam-5573	492	2	topological	topological	ADJ
ejpam-5573	492	3	spaces	space	NOUN
ejpam-5573	492	4	.	.	PUNCT
ejpam-5573	493	1	j.	j.	PROPN
ejpam-5573	493	2	math	math	PROPN
ejpam-5573	493	3	.	.	PUNCT
ejpam-5573	494	1	anal	anal	PROPN
ejpam-5573	494	2	.	.	PUNCT
ejpam-5573	495	1	appl	appl	PROPN
ejpam-5573	495	2	.	.	PROPN
ejpam-5573	495	3	,	,	PUNCT
ejpam-5573	496	1	24:182–190	24:182–190	NUM
ejpam-5573	496	2	,	,	PUNCT
ejpam-5573	496	3	1968	1968	NUM
ejpam-5573	496	4	.	.	PUNCT
ejpam-5573	497	1	[	[	X
ejpam-5573	497	2	16	16	NUM
ejpam-5573	497	3	]	]	PUNCT
ejpam-5573	497	4	p.	p.	NOUN
ejpam-5573	497	5	g.	g.	PROPN
ejpam-5573	497	6	chetty	chetty	PROPN
ejpam-5573	497	7	.	.	PUNCT
ejpam-5573	498	1	generalized	generalize	VERB
ejpam-5573	498	2	fuzzy	fuzzy	ADJ
ejpam-5573	498	3	topology	topology	NOUN
ejpam-5573	498	4	.	.	PUNCT
ejpam-5573	499	1	ital	ital	PROPN
ejpam-5573	499	2	.	.	PUNCT
ejpam-5573	500	1	j.	j.	PROPN
ejpam-5573	500	2	pure	pure	PROPN
ejpam-5573	500	3	appl	appl	PROPN
ejpam-5573	500	4	.	.	PUNCT
ejpam-5573	500	5	math	math	PROPN
ejpam-5573	500	6	.	.	PUNCT
ejpam-5573	500	7	,	,	PUNCT
ejpam-5573	501	1	24:91–96	24:91–96	NUM
ejpam-5573	501	2	,	,	PUNCT
ejpam-5573	501	3	2008	2008	NUM
ejpam-5573	501	4	.	.	PUNCT
ejpam-5573	502	1	[	[	X
ejpam-5573	502	2	17	17	NUM
ejpam-5573	502	3	]	]	X
ejpam-5573	502	4	d.	d.	PROPN
ejpam-5573	502	5	coker	coker	PROPN
ejpam-5573	502	6	.	.	PUNCT
ejpam-5573	503	1	an	an	DET
ejpam-5573	503	2	introduction	introduction	NOUN
ejpam-5573	503	3	to	to	ADP
ejpam-5573	503	4	fuzzy	fuzzy	ADJ
ejpam-5573	503	5	subspaces	subspace	NOUN
ejpam-5573	503	6	in	in	ADP
ejpam-5573	503	7	intuitionistic	intuitionistic	ADJ
ejpam-5573	503	8	fuzzy	fuzzy	ADJ
ejpam-5573	503	9	topological	topological	ADJ
ejpam-5573	503	10	spaces	space	NOUN
ejpam-5573	503	11	.	.	PUNCT
ejpam-5573	504	1	j.	j.	PROPN
ejpam-5573	504	2	fuzzy	fuzzy	PROPN
ejpam-5573	504	3	math	math	PROPN
ejpam-5573	504	4	.	.	PUNCT
ejpam-5573	504	5	,	,	PUNCT
ejpam-5573	504	6	4:749–764	4:749–764	NOUN
ejpam-5573	504	7	,	,	PUNCT
ejpam-5573	504	8	1996	1996	NUM
ejpam-5573	504	9	.	.	PUNCT
ejpam-5573	505	1	[	[	X
ejpam-5573	505	2	18	18	NUM
ejpam-5573	505	3	]	]	X
ejpam-5573	505	4	d.	d.	PROPN
ejpam-5573	505	5	coker	coker	PROPN
ejpam-5573	505	6	.	.	PUNCT
ejpam-5573	506	1	an	an	DET
ejpam-5573	506	2	introduction	introduction	NOUN
ejpam-5573	506	3	to	to	ADP
ejpam-5573	506	4	intuitionistic	intuitionistic	ADJ
ejpam-5573	506	5	fuzzy	fuzzy	ADJ
ejpam-5573	506	6	topological	topological	ADJ
ejpam-5573	506	7	spaces	space	NOUN
ejpam-5573	506	8	.	.	PUNCT
ejpam-5573	507	1	fuzzy	fuzzy	ADJ
ejpam-5573	507	2	sets	set	NOUN
ejpam-5573	507	3	syst	syst	PROPN
ejpam-5573	507	4	.	.	PUNCT
ejpam-5573	507	5	,	,	PUNCT
ejpam-5573	507	6	88:81–89	88:81–89	NUM
ejpam-5573	507	7	,	,	PUNCT
ejpam-5573	507	8	1997	1997	NUM
ejpam-5573	507	9	.	.	PUNCT
ejpam-5573	508	1	[	[	X
ejpam-5573	508	2	19	19	NUM
ejpam-5573	508	3	]	]	PUNCT
ejpam-5573	508	4	b.	b.	PROPN
ejpam-5573	508	5	das	das	PROPN
ejpam-5573	508	6	,	,	PUNCT
ejpam-5573	508	7	j.	j.	PROPN
ejpam-5573	508	8	chakraborty	chakraborty	PROPN
ejpam-5573	508	9	,	,	PUNCT
ejpam-5573	508	10	g.	g.	PROPN
ejpam-5573	508	11	paul	paul	PROPN
ejpam-5573	508	12	,	,	PUNCT
ejpam-5573	508	13	and	and	CCONJ
ejpam-5573	508	14	b.	b.	PROPN
ejpam-5573	508	15	bhattacharya	bhattacharya	PROPN
ejpam-5573	508	16	.	.	PUNCT
ejpam-5573	509	1	a	a	DET
ejpam-5573	509	2	new	new	ADJ
ejpam-5573	509	3	approach	approach	NOUN
ejpam-5573	509	4	for	for	ADP
ejpam-5573	509	5	some	some	DET
ejpam-5573	509	6	applications	application	NOUN
ejpam-5573	509	7	of	of	ADP
ejpam-5573	509	8	generalized	generalized	ADJ
ejpam-5573	509	9	fuzzy	fuzzy	ADJ
ejpam-5573	509	10	closed	close	VERB
ejpam-5573	509	11	sets	set	NOUN
ejpam-5573	509	12	.	.	PUNCT
ejpam-5573	510	1	comp	comp	NOUN
ejpam-5573	510	2	.	.	PUNCT
ejpam-5573	511	1	appl	appl	PROPN
ejpam-5573	511	2	.	.	PROPN
ejpam-5573	511	3	math	math	PROPN
ejpam-5573	511	4	.	.	PUNCT
ejpam-5573	511	5	,	,	PUNCT
ejpam-5573	511	6	40:1–14	40:1–14	PROPN
ejpam-5573	511	7	,	,	PUNCT
ejpam-5573	511	8	2021	2021	NUM
ejpam-5573	511	9	.	.	PUNCT
ejpam-5573	512	1	[	[	X
ejpam-5573	512	2	20	20	NUM
ejpam-5573	512	3	]	]	PUNCT
ejpam-5573	512	4	m.	m.	NOUN
ejpam-5573	512	5	demirci	demirci	PROPN
ejpam-5573	512	6	and	and	CCONJ
ejpam-5573	512	7	d.	d.	PROPN
ejpam-5573	512	8	coker	coker	PROPN
ejpam-5573	512	9	.	.	PUNCT
ejpam-5573	513	1	an	an	DET
ejpam-5573	513	2	introduction	introduction	NOUN
ejpam-5573	513	3	to	to	ADP
ejpam-5573	513	4	intuitionistic	intuitionistic	ADJ
ejpam-5573	513	5	fuzzy	fuzzy	ADJ
ejpam-5573	513	6	topological	topological	ADJ
ejpam-5573	513	7	spaces	space	NOUN
ejpam-5573	513	8	in	in	ADP
ejpam-5573	513	9	šostaks	šostak	NOUN
ejpam-5573	513	10	sense	sense	NOUN
ejpam-5573	513	11	.	.	PUNCT
ejpam-5573	514	1	busefal	busefal	PROPN
ejpam-5573	514	2	,	,	PUNCT
ejpam-5573	514	3	67:67–76	67:67–76	NUM
ejpam-5573	514	4	,	,	PUNCT
ejpam-5573	514	5	1996	1996	NUM
ejpam-5573	514	6	.	.	PUNCT
ejpam-5573	515	1	references	reference	NOUN
ejpam-5573	515	2	4110	4110	PROPN
ejpam-5573	516	1	[	[	X
ejpam-5573	516	2	21	21	NUM
ejpam-5573	516	3	]	]	PUNCT
ejpam-5573	516	4	m.	m.	PROPN
ejpam-5573	516	5	k.	k.	PROPN
ejpam-5573	517	1	el	el	PROPN
ejpam-5573	517	2	-	-	PROPN
ejpam-5573	517	3	bably	bably	PROPN
ejpam-5573	517	4	and	and	CCONJ
ejpam-5573	517	5	a.	a.	NOUN
ejpam-5573	517	6	a.	a.	PROPN
ejpam-5573	517	7	el	el	PROPN
ejpam-5573	517	8	atik	atik	PROPN
ejpam-5573	517	9	.	.	PUNCT
ejpam-5573	518	1	soft	soft	ADJ
ejpam-5573	518	2	β	β	NOUN
ejpam-5573	518	3	-	-	ADJ
ejpam-5573	518	4	rough	rough	ADJ
ejpam-5573	518	5	sets	set	NOUN
ejpam-5573	518	6	and	and	CCONJ
ejpam-5573	518	7	its	its	PRON
ejpam-5573	518	8	application	application	NOUN
ejpam-5573	518	9	to	to	PART
ejpam-5573	518	10	determine	determine	VERB
ejpam-5573	518	11	covid-19	covid-19	PROPN
ejpam-5573	518	12	.	.	PROPN
ejpam-5573	518	13	turk	turk	PROPN
ejpam-5573	518	14	.	.	PUNCT
ejpam-5573	519	1	j.	j.	PROPN
ejpam-5573	519	2	math	math	PROPN
ejpam-5573	519	3	.	.	PUNCT
ejpam-5573	519	4	,	,	PUNCT
ejpam-5573	519	5	45(3):1133–1148	45(3):1133–1148	NUM
ejpam-5573	519	6	,	,	PUNCT
ejpam-5573	519	7	2021	2021	NUM
ejpam-5573	519	8	.	.	PUNCT
ejpam-5573	520	1	[	[	X
ejpam-5573	520	2	22	22	NUM
ejpam-5573	520	3	]	]	X
ejpam-5573	520	4	e.	e.	PROPN
ejpam-5573	520	5	el	el	PROPN
ejpam-5573	520	6	-	-	PUNCT
ejpam-5573	520	7	sanousy	sanousy	PROPN
ejpam-5573	520	8	.	.	PUNCT
ejpam-5573	521	1	(	(	PUNCT
ejpam-5573	521	2	r	r	NOUN
ejpam-5573	521	3	,	,	PUNCT
ejpam-5573	521	4	s)-(τ1,2	s)-(τ1,2	PROPN
ejpam-5573	521	5	,	,	PUNCT
ejpam-5573	521	6	τ	τ	PROPN
ejpam-5573	521	7	∗	∗	NOUN
ejpam-5573	521	8	1,2)-θ	1,2)-θ	PROPN
ejpam-5573	521	9	-	-	PUNCT
ejpam-5573	521	10	generalized	generalize	VERB
ejpam-5573	521	11	double	double	ADJ
ejpam-5573	521	12	fuzzy	fuzzy	ADJ
ejpam-5573	521	13	closed	close	VERB
ejpam-5573	521	14	sets	set	NOUN
ejpam-5573	521	15	in	in	ADP
ejpam-5573	521	16	bitopological	bitopological	ADJ
ejpam-5573	521	17	spaces	space	NOUN
ejpam-5573	521	18	.	.	PUNCT
ejpam-5573	522	1	j.	j.	PROPN
ejpam-5573	522	2	egyptian	egyptian	PROPN
ejpam-5573	522	3	math	math	PROPN
ejpam-5573	522	4	.	.	PUNCT
ejpam-5573	523	1	soc	soc	PROPN
ejpam-5573	523	2	.	.	PUNCT
ejpam-5573	523	3	,	,	PUNCT
ejpam-5573	523	4	24:574–581	24:574–581	NUM
ejpam-5573	523	5	,	,	PUNCT
ejpam-5573	523	6	2016	2016	NUM
ejpam-5573	523	7	.	.	PUNCT
ejpam-5573	524	1	[	[	X
ejpam-5573	524	2	23	23	NUM
ejpam-5573	524	3	]	]	X
ejpam-5573	524	4	e.	e.	PROPN
ejpam-5573	524	5	el	el	PROPN
ejpam-5573	524	6	-	-	PUNCT
ejpam-5573	524	7	sanousy	sanousy	PROPN
ejpam-5573	524	8	and	and	CCONJ
ejpam-5573	524	9	a.	a.	PROPN
ejpam-5573	524	10	atef	atef	PROPN
ejpam-5573	524	11	.	.	PUNCT
ejpam-5573	525	1	(	(	PUNCT
ejpam-5573	525	2	r	r	NOUN
ejpam-5573	525	3	,	,	PUNCT
ejpam-5573	525	4	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5573	525	5	g∗p	g∗p	NUM
ejpam-5573	525	6	-	-	PUNCT
ejpam-5573	525	7	closed	close	VERB
ejpam-5573	525	8	sets	set	NOUN
ejpam-5573	525	9	and	and	CCONJ
ejpam-5573	525	10	its	its	PRON
ejpam-5573	525	11	applications	application	NOUN
ejpam-5573	525	12	.	.	PUNCT
ejpam-5573	526	1	appl	appl	PROPN
ejpam-5573	526	2	.	.	PROPN
ejpam-5573	527	1	math	math	PROPN
ejpam-5573	527	2	.	.	PUNCT
ejpam-5573	528	1	inf	inf	PROPN
ejpam-5573	528	2	.	.	PUNCT
ejpam-5573	529	1	sci	sci	PROPN
ejpam-5573	529	2	.	.	PROPN
ejpam-5573	529	3	,	,	PUNCT
ejpam-5573	529	4	16(1):17–24	16(1):17–24	NUM
ejpam-5573	529	5	,	,	PUNCT
ejpam-5573	529	6	2022	2022	NUM
ejpam-5573	529	7	.	.	PUNCT
ejpam-5573	530	1	[	[	X
ejpam-5573	530	2	24	24	NUM
ejpam-5573	530	3	]	]	X
ejpam-5573	530	4	f.	f.	PROPN
ejpam-5573	530	5	feng	feng	PROPN
ejpam-5573	530	6	,	,	PUNCT
ejpam-5573	530	7	x.	x.	PROPN
ejpam-5573	530	8	liu	liu	PROPN
ejpam-5573	530	9	,	,	PUNCT
ejpam-5573	530	10	v.	v.	PROPN
ejpam-5573	530	11	l.	l.	PROPN
ejpam-5573	530	12	fotea	fotea	PROPN
ejpam-5573	530	13	,	,	PUNCT
ejpam-5573	530	14	and	and	CCONJ
ejpam-5573	530	15	y.	y.	PROPN
ejpam-5573	530	16	b.	b.	PROPN
ejpam-5573	530	17	jun	jun	PROPN
ejpam-5573	530	18	.	.	PROPN
ejpam-5573	530	19	soft	soft	ADJ
ejpam-5573	530	20	sets	set	NOUN
ejpam-5573	530	21	and	and	CCONJ
ejpam-5573	530	22	soft	soft	ADJ
ejpam-5573	530	23	rough	rough	ADJ
ejpam-5573	530	24	sets	set	NOUN
ejpam-5573	530	25	.	.	PUNCT
ejpam-5573	531	1	info	info	NOUN
ejpam-5573	531	2	.	.	PUNCT
ejpam-5573	532	1	sciences	science	NOUN
ejpam-5573	532	2	,	,	PUNCT
ejpam-5573	532	3	181(6):1125–1137	181(6):1125–1137	NUM
ejpam-5573	532	4	,	,	PUNCT
ejpam-5573	532	5	2011	2011	NUM
ejpam-5573	532	6	.	.	PUNCT
ejpam-5573	533	1	[	[	X
ejpam-5573	533	2	25	25	NUM
ejpam-5573	533	3	]	]	PUNCT
ejpam-5573	533	4	j.	j.	PROPN
ejpam-5573	533	5	g.	g.	PROPN
ejpam-5573	533	6	garcia	garcia	PROPN
ejpam-5573	533	7	and	and	CCONJ
ejpam-5573	533	8	s.	s.	PROPN
ejpam-5573	533	9	e.	e.	PROPN
ejpam-5573	533	10	rodabaugh	rodabaugh	PROPN
ejpam-5573	533	11	.	.	PUNCT
ejpam-5573	534	1	ordertheoretic	ordertheoretic	ADJ
ejpam-5573	534	2	,	,	PUNCT
ejpam-5573	534	3	topological	topological	ADJ
ejpam-5573	534	4	,	,	PUNCT
ejpam-5573	534	5	categorical	categorical	ADJ
ejpam-5573	534	6	redundancies	redundancy	NOUN
ejpam-5573	534	7	of	of	ADP
ejpam-5573	534	8	interval	interval	NOUN
ejpam-5573	534	9	-	-	PUNCT
ejpam-5573	534	10	valued	value	VERB
ejpam-5573	534	11	sets	set	NOUN
ejpam-5573	534	12	,	,	PUNCT
ejpam-5573	534	13	grey	grey	NOUN
ejpam-5573	534	14	sets	set	NOUN
ejpam-5573	534	15	,	,	PUNCT
ejpam-5573	534	16	vague	vague	ADJ
ejpam-5573	534	17	sets	set	NOUN
ejpam-5573	534	18	,	,	PUNCT
ejpam-5573	534	19	intervalvalued	intervalvalue	VERB
ejpam-5573	534	20	;	;	PUNCT
ejpam-5573	534	21	intuitionistic	intuitionistic	ADJ
ejpam-5573	534	22	sets	set	NOUN
ejpam-5573	534	23	,	,	PUNCT
ejpam-5573	534	24	intuitionistic	intuitionistic	ADJ
ejpam-5573	534	25	fuzzy	fuzzy	ADJ
ejpam-5573	534	26	sets	set	NOUN
ejpam-5573	534	27	and	and	CCONJ
ejpam-5573	534	28	topologies	topology	NOUN
ejpam-5573	534	29	.	.	PUNCT
ejpam-5573	535	1	fuzzy	fuzzy	ADJ
ejpam-5573	535	2	sets	set	NOUN
ejpam-5573	535	3	syst	syst	PROPN
ejpam-5573	535	4	.	.	PUNCT
ejpam-5573	535	5	,	,	PUNCT
ejpam-5573	535	6	156(3):445–484	156(3):445–484	NUM
ejpam-5573	535	7	,	,	PUNCT
ejpam-5573	535	8	2005	2005	NUM
ejpam-5573	535	9	.	.	PUNCT
ejpam-5573	536	1	[	[	X
ejpam-5573	536	2	26	26	NUM
ejpam-5573	536	3	]	]	PUNCT
ejpam-5573	536	4	a.	a.	NOUN
ejpam-5573	536	5	kandil	kandil	PROPN
ejpam-5573	536	6	and	and	CCONJ
ejpam-5573	536	7	a.	a.	NOUN
ejpam-5573	536	8	m.	m.	PROPN
ejpam-5573	537	1	el	el	PROPN
ejpam-5573	537	2	-	-	PROPN
ejpam-5573	537	3	etriby	etriby	PROPN
ejpam-5573	537	4	.	.	PUNCT
ejpam-5573	538	1	on	on	ADP
ejpam-5573	538	2	separation	separation	NOUN
ejpam-5573	538	3	axioms	axiom	NOUN
ejpam-5573	538	4	in	in	ADP
ejpam-5573	538	5	fuzzy	fuzzy	ADJ
ejpam-5573	538	6	topological	topological	ADJ
ejpam-5573	538	7	spaces	space	NOUN
ejpam-5573	538	8	.	.	PUNCT
ejpam-5573	539	1	tamkang	tamkang	PROPN
ejpam-5573	539	2	j.	j.	PROPN
ejpam-5573	539	3	math	math	PROPN
ejpam-5573	539	4	.	.	PROPN
ejpam-5573	539	5	,	,	PUNCT
ejpam-5573	539	6	18:49–59	18:49–59	NUM
ejpam-5573	539	7	,	,	PUNCT
ejpam-5573	539	8	1987	1987	NUM
ejpam-5573	539	9	.	.	PUNCT
ejpam-5573	540	1	[	[	X
ejpam-5573	540	2	27	27	NUM
ejpam-5573	540	3	]	]	SYM
ejpam-5573	540	4	a.	a.	NOUN
ejpam-5573	540	5	kandil	kandil	PROPN
ejpam-5573	540	6	and	and	CCONJ
ejpam-5573	540	7	m.	m.	PROPN
ejpam-5573	540	8	e.	e.	PROPN
ejpam-5573	540	9	el	el	PROPN
ejpam-5573	540	10	-	-	PROPN
ejpam-5573	540	11	shafei	shafei	PROPN
ejpam-5573	540	12	.	.	PUNCT
ejpam-5573	541	1	regularity	regularity	NOUN
ejpam-5573	541	2	axioms	axiom	NOUN
ejpam-5573	541	3	in	in	ADP
ejpam-5573	541	4	fuzzy	fuzzy	ADJ
ejpam-5573	541	5	topological	topological	ADJ
ejpam-5573	541	6	spaces	space	NOUN
ejpam-5573	541	7	and	and	CCONJ
ejpam-5573	541	8	fri	fri	NOUN
ejpam-5573	541	9	-	-	NOUN
ejpam-5573	541	10	proximities	proximity	NOUN
ejpam-5573	541	11	.	.	PUNCT
ejpam-5573	542	1	fuzzy	fuzzy	ADJ
ejpam-5573	542	2	set	set	PROPN
ejpam-5573	542	3	.	.	PUNCT
ejpam-5573	543	1	syst	syst	PROPN
ejpam-5573	543	2	.	.	PUNCT
ejpam-5573	543	3	,	,	PUNCT
ejpam-5573	544	1	27:217–231	27:217–231	NUM
ejpam-5573	544	2	,	,	PUNCT
ejpam-5573	544	3	1988	1988	NUM
ejpam-5573	544	4	.	.	PUNCT
ejpam-5573	545	1	[	[	X
ejpam-5573	545	2	28	28	NUM
ejpam-5573	545	3	]	]	X
ejpam-5573	545	4	s.	s.	PROPN
ejpam-5573	545	5	kaur	kaur	PROPN
ejpam-5573	545	6	,	,	PUNCT
ejpam-5573	545	7	t.	t.	PROPN
ejpam-5573	545	8	m.	m.	PROPN
ejpam-5573	545	9	al	al	PROPN
ejpam-5573	545	10	-	-	PUNCT
ejpam-5573	545	11	shami	shami	PROPN
ejpam-5573	545	12	,	,	PUNCT
ejpam-5573	545	13	a.	a.	NOUN
ejpam-5573	545	14	ozkan	ozkan	PROPN
ejpam-5573	545	15	,	,	PUNCT
ejpam-5573	545	16	and	and	CCONJ
ejpam-5573	545	17	m.	m.	PROPN
ejpam-5573	545	18	hosny	hosny	PROPN
ejpam-5573	545	19	.	.	PUNCT
ejpam-5573	546	1	a	a	DET
ejpam-5573	546	2	new	new	ADJ
ejpam-5573	546	3	approach	approach	NOUN
ejpam-5573	546	4	to	to	ADP
ejpam-5573	546	5	soft	soft	ADJ
ejpam-5573	546	6	continuity	continuity	NOUN
ejpam-5573	546	7	.	.	PUNCT
ejpam-5573	547	1	mathematics	mathematic	NOUN
ejpam-5573	547	2	,	,	PUNCT
ejpam-5573	547	3	11:1–11	11:1–11	NUM
ejpam-5573	547	4	,	,	PUNCT
ejpam-5573	547	5	2023	2023	NUM
ejpam-5573	547	6	.	.	PUNCT
ejpam-5573	548	1	[	[	X
ejpam-5573	548	2	29	29	NUM
ejpam-5573	548	3	]	]	PUNCT
ejpam-5573	548	4	e.	e.	PROPN
ejpam-5573	548	5	p.	p.	PROPN
ejpam-5573	548	6	lee	lee	PROPN
ejpam-5573	548	7	.	.	PROPN
ejpam-5573	549	1	semiopen	semiopen	VERB
ejpam-5573	549	2	sets	set	NOUN
ejpam-5573	549	3	on	on	ADP
ejpam-5573	549	4	intuitionistic	intuitionistic	ADJ
ejpam-5573	549	5	fuzzy	fuzzy	ADJ
ejpam-5573	549	6	topological	topological	ADJ
ejpam-5573	549	7	spaces	space	NOUN
ejpam-5573	549	8	in	in	ADP
ejpam-5573	549	9	šostaks	šostak	NOUN
ejpam-5573	549	10	sense	sense	NOUN
ejpam-5573	549	11	.	.	PUNCT
ejpam-5573	550	1	int	int	NOUN
ejpam-5573	550	2	.	.	PUNCT
ejpam-5573	551	1	j.	j.	PROPN
ejpam-5573	551	2	fuzzy	fuzzy	ADJ
ejpam-5573	551	3	logic	logic	PROPN
ejpam-5573	551	4	intel	intel	PROPN
ejpam-5573	551	5	.	.	PUNCT
ejpam-5573	552	1	sys	sys	PROPN
ejpam-5573	552	2	.	.	PROPN
ejpam-5573	552	3	,	,	PUNCT
ejpam-5573	552	4	14:234–238	14:234–238	NUM
ejpam-5573	552	5	,	,	PUNCT
ejpam-5573	552	6	2004	2004	NUM
ejpam-5573	552	7	.	.	PUNCT
ejpam-5573	553	1	[	[	X
ejpam-5573	553	2	30	30	NUM
ejpam-5573	553	3	]	]	PUNCT
ejpam-5573	553	4	e.	e.	PROPN
ejpam-5573	553	5	p.	p.	PROPN
ejpam-5573	553	6	lee	lee	PROPN
ejpam-5573	554	1	and	and	CCONJ
ejpam-5573	555	1	j.	j.	PROPN
ejpam-5573	555	2	i.	i.	PROPN
ejpam-5573	555	3	kim	kim	PROPN
ejpam-5573	555	4	.	.	PUNCT
ejpam-5573	556	1	fuzzy	fuzzy	ADJ
ejpam-5573	556	2	strongly	strongly	ADV
ejpam-5573	556	3	(	(	PUNCT
ejpam-5573	556	4	r	r	NOUN
ejpam-5573	556	5	,	,	PUNCT
ejpam-5573	556	6	s)-preopen	s)-preopen	ADJ
ejpam-5573	556	7	and	and	CCONJ
ejpam-5573	556	8	preclosed	preclose	VERB
ejpam-5573	556	9	mappings	mapping	NOUN
ejpam-5573	556	10	.	.	PUNCT
ejpam-5573	557	1	commun	commun	PROPN
ejpam-5573	557	2	.	.	PUNCT
ejpam-5573	558	1	korean	korean	ADJ
ejpam-5573	558	2	math	math	PROPN
ejpam-5573	558	3	.	.	PUNCT
ejpam-5573	559	1	soc	soc	PROPN
ejpam-5573	559	2	.	.	PUNCT
ejpam-5573	559	3	,	,	PUNCT
ejpam-5573	559	4	26(4):661–667	26(4):661–667	NUM
ejpam-5573	559	5	,	,	PUNCT
ejpam-5573	559	6	2011	2011	NUM
ejpam-5573	559	7	.	.	PUNCT
ejpam-5573	560	1	[	[	X
ejpam-5573	560	2	31	31	NUM
ejpam-5573	560	3	]	]	PUNCT
ejpam-5573	560	4	h.	h.	PROPN
ejpam-5573	560	5	x.	x.	PROPN
ejpam-5573	560	6	li	li	PROPN
ejpam-5573	560	7	and	and	CCONJ
ejpam-5573	560	8	v.	v.	ADP
ejpam-5573	560	9	c.	c.	PROPN
ejpam-5573	560	10	yen	yen	PROPN
ejpam-5573	560	11	.	.	PUNCT
ejpam-5573	561	1	fuzzy	fuzzy	ADJ
ejpam-5573	561	2	sets	set	NOUN
ejpam-5573	561	3	and	and	CCONJ
ejpam-5573	561	4	fuzzy	fuzzy	ADJ
ejpam-5573	561	5	decision	decision	NOUN
ejpam-5573	561	6	making	making	NOUN
ejpam-5573	561	7	.	.	PUNCT
ejpam-5573	562	1	crc	crc	PROPN
ejpam-5573	562	2	press	press	PROPN
ejpam-5573	562	3	,	,	PUNCT
ejpam-5573	562	4	london	london	PROPN
ejpam-5573	562	5	,	,	PUNCT
ejpam-5573	562	6	1995	1995	NUM
ejpam-5573	562	7	.	.	PUNCT
ejpam-5573	563	1	[	[	X
ejpam-5573	563	2	32	32	NUM
ejpam-5573	563	3	]	]	PUNCT
ejpam-5573	563	4	f.	f.	PROPN
ejpam-5573	563	5	m.	m.	PROPN
ejpam-5573	563	6	mohammed	mohammed	PROPN
ejpam-5573	563	7	,	,	PUNCT
ejpam-5573	563	8	m.	m.	NOUN
ejpam-5573	563	9	s.	s.	PROPN
ejpam-5573	563	10	m.	m.	PROPN
ejpam-5573	563	11	noorani	noorani	PROPN
ejpam-5573	563	12	,	,	PUNCT
ejpam-5573	563	13	and	and	CCONJ
ejpam-5573	563	14	a.	a.	NOUN
ejpam-5573	563	15	ghareeb	ghareeb	NOUN
ejpam-5573	563	16	.	.	PUNCT
ejpam-5573	564	1	several	several	ADJ
ejpam-5573	564	2	notions	notion	NOUN
ejpam-5573	564	3	of	of	ADP
ejpam-5573	564	4	generalized	generalized	ADJ
ejpam-5573	564	5	semi	semi	NOUN
ejpam-5573	564	6	-	-	NOUN
ejpam-5573	564	7	compactness	compactness	NOUN
ejpam-5573	564	8	in	in	ADP
ejpam-5573	564	9	double	double	ADJ
ejpam-5573	564	10	fuzzy	fuzzy	ADJ
ejpam-5573	564	11	topological	topological	ADJ
ejpam-5573	564	12	spaces	space	NOUN
ejpam-5573	564	13	.	.	PUNCT
ejpam-5573	565	1	int	int	NOUN
ejpam-5573	565	2	.	.	PUNCT
ejpam-5573	566	1	j.	j.	PROPN
ejpam-5573	566	2	pure	pure	PROPN
ejpam-5573	566	3	appl	appl	PROPN
ejpam-5573	566	4	.	.	PUNCT
ejpam-5573	566	5	math	math	PROPN
ejpam-5573	566	6	.	.	PUNCT
ejpam-5573	566	7	,	,	PUNCT
ejpam-5573	566	8	109(2):153–175	109(2):153–175	NUM
ejpam-5573	566	9	,	,	PUNCT
ejpam-5573	566	10	2016	2016	NUM
ejpam-5573	566	11	.	.	PUNCT
ejpam-5573	567	1	[	[	X
ejpam-5573	567	2	33	33	NUM
ejpam-5573	567	3	]	]	X
ejpam-5573	567	4	d.	d.	PROPN
ejpam-5573	567	5	molodtsov	molodtsov	PROPN
ejpam-5573	567	6	.	.	PUNCT
ejpam-5573	568	1	soft	soft	ADJ
ejpam-5573	568	2	set	set	NOUN
ejpam-5573	568	3	theory	theory	NOUN
ejpam-5573	568	4	-	-	PUNCT
ejpam-5573	568	5	first	first	ADJ
ejpam-5573	568	6	results	result	NOUN
ejpam-5573	568	7	.	.	PUNCT
ejpam-5573	569	1	comput	comput	NOUN
ejpam-5573	569	2	.	.	PUNCT
ejpam-5573	570	1	math	math	NOUN
ejpam-5573	570	2	.	.	PUNCT
ejpam-5573	571	1	appl	appl	PROPN
ejpam-5573	571	2	.	.	PROPN
ejpam-5573	571	3	,	,	PUNCT
ejpam-5573	571	4	37:19–31	37:19–31	PROPN
ejpam-5573	571	5	,	,	PUNCT
ejpam-5573	571	6	1999	1999	NUM
ejpam-5573	571	7	.	.	PUNCT
ejpam-5573	572	1	[	[	X
ejpam-5573	572	2	34	34	NUM
ejpam-5573	572	3	]	]	PUNCT
ejpam-5573	572	4	m.	m.	NOUN
ejpam-5573	572	5	s.	s.	PROPN
ejpam-5573	572	6	k.	k.	PROPN
ejpam-5573	572	7	samanta	samanta	PROPN
ejpam-5573	572	8	and	and	CCONJ
ejpam-5573	572	9	t.	t.	PROPN
ejpam-5573	572	10	k.	k.	PROPN
ejpam-5573	572	11	mondal	mondal	PROPN
ejpam-5573	572	12	.	.	PUNCT
ejpam-5573	573	1	on	on	ADP
ejpam-5573	573	2	intuitionistic	intuitionistic	ADJ
ejpam-5573	573	3	gradation	gradation	NOUN
ejpam-5573	573	4	of	of	ADP
ejpam-5573	573	5	openness	openness	NOUN
ejpam-5573	573	6	.	.	PUNCT
ejpam-5573	574	1	fuzzy	fuzzy	ADJ
ejpam-5573	574	2	sets	set	NOUN
ejpam-5573	574	3	syst	syst	PROPN
ejpam-5573	574	4	.	.	PUNCT
ejpam-5573	574	5	,	,	PUNCT
ejpam-5573	574	6	131:323–336	131:323–336	NUM
ejpam-5573	574	7	,	,	PUNCT
ejpam-5573	574	8	2002	2002	NUM
ejpam-5573	574	9	.	.	PUNCT
ejpam-5573	575	1	[	[	X
ejpam-5573	575	2	35	35	NUM
ejpam-5573	575	3	]	]	PUNCT
ejpam-5573	575	4	s.	s.	PROPN
ejpam-5573	575	5	k.	k.	PROPN
ejpam-5573	575	6	samanta	samanta	PROPN
ejpam-5573	575	7	and	and	CCONJ
ejpam-5573	575	8	t.	t.	PROPN
ejpam-5573	575	9	k.	k.	PROPN
ejpam-5573	575	10	mondal	mondal	PROPN
ejpam-5573	575	11	.	.	PUNCT
ejpam-5573	576	1	intuitionistic	intuitionistic	ADJ
ejpam-5573	576	2	gradation	gradation	NOUN
ejpam-5573	576	3	of	of	ADP
ejpam-5573	576	4	openness	openness	NOUN
ejpam-5573	576	5	:	:	PUNCT
ejpam-5573	576	6	intuitionistic	intuitionistic	ADJ
ejpam-5573	576	7	fuzzy	fuzzy	ADJ
ejpam-5573	576	8	topology	topology	NOUN
ejpam-5573	576	9	.	.	PUNCT
ejpam-5573	577	1	busefal	busefal	PROPN
ejpam-5573	577	2	,	,	PUNCT
ejpam-5573	577	3	73:8–17	73:8–17	NUM
ejpam-5573	577	4	,	,	PUNCT
ejpam-5573	577	5	1997	1997	NUM
ejpam-5573	577	6	.	.	PUNCT
ejpam-5573	578	1	[	[	X
ejpam-5573	578	2	36	36	NUM
ejpam-5573	578	3	]	]	X
ejpam-5573	578	4	i.	i.	PROPN
ejpam-5573	578	5	m.	m.	PROPN
ejpam-5573	578	6	taha	taha	PROPN
ejpam-5573	578	7	.	.	PUNCT
ejpam-5573	579	1	a	a	DET
ejpam-5573	579	2	new	new	ADJ
ejpam-5573	579	3	approach	approach	NOUN
ejpam-5573	579	4	to	to	ADP
ejpam-5573	579	5	separation	separation	NOUN
ejpam-5573	579	6	and	and	CCONJ
ejpam-5573	579	7	regularity	regularity	NOUN
ejpam-5573	579	8	axioms	axiom	NOUN
ejpam-5573	579	9	via	via	ADP
ejpam-5573	579	10	fuzzy	fuzzy	ADJ
ejpam-5573	579	11	soft	soft	ADJ
ejpam-5573	579	12	sets	set	NOUN
ejpam-5573	579	13	.	.	PUNCT
ejpam-5573	580	1	ann	ann	PROPN
ejpam-5573	580	2	.	.	PUNCT
ejpam-5573	580	3	fuzzy	fuzzy	ADJ
ejpam-5573	580	4	math	math	NOUN
ejpam-5573	580	5	.	.	PUNCT
ejpam-5573	581	1	inform	inform	NOUN
ejpam-5573	581	2	.	.	PUNCT
ejpam-5573	581	3	,	,	PUNCT
ejpam-5573	581	4	20(2):115–123	20(2):115–123	PROPN
ejpam-5573	581	5	,	,	PUNCT
ejpam-5573	581	6	2020	2020	NUM
ejpam-5573	581	7	.	.	PUNCT
ejpam-5573	582	1	references	reference	NOUN
ejpam-5573	582	2	4111	4111	NUM
ejpam-5573	583	1	[	[	X
ejpam-5573	583	2	37	37	NUM
ejpam-5573	583	3	]	]	PUNCT
ejpam-5573	583	4	i.	i.	PROPN
ejpam-5573	583	5	m.	m.	PROPN
ejpam-5573	583	6	taha	taha	PROPN
ejpam-5573	583	7	.	.	PUNCT
ejpam-5573	584	1	compactness	compactness	NOUN
ejpam-5573	584	2	on	on	ADP
ejpam-5573	584	3	fuzzy	fuzzy	ADJ
ejpam-5573	584	4	soft	soft	ADJ
ejpam-5573	584	5	r	r	NOUN
ejpam-5573	584	6	-	-	PUNCT
ejpam-5573	584	7	minimal	minimal	ADJ
ejpam-5573	584	8	spaces	space	NOUN
ejpam-5573	584	9	.	.	PUNCT
ejpam-5573	585	1	int	int	NOUN
ejpam-5573	585	2	.	.	PUNCT
ejpam-5573	586	1	j.	j.	PROPN
ejpam-5573	586	2	fuzzy	fuzzy	PROPN
ejpam-5573	586	3	logic	logic	PROPN
ejpam-5573	586	4	intell	intell	PROPN
ejpam-5573	586	5	.	.	PUNCT
ejpam-5573	587	1	syst	syst	PROPN
ejpam-5573	587	2	.	.	PROPN
ejpam-5573	587	3	,	,	PUNCT
ejpam-5573	587	4	21(3):251–258	21(3):251–258	PROPN
ejpam-5573	587	5	,	,	PUNCT
ejpam-5573	587	6	2021	2021	NUM
ejpam-5573	587	7	.	.	PUNCT
ejpam-5573	588	1	[	[	X
ejpam-5573	588	2	38	38	NUM
ejpam-5573	588	3	]	]	PUNCT
ejpam-5573	588	4	i.	i.	PROPN
ejpam-5573	588	5	m.	m.	PROPN
ejpam-5573	588	6	taha	taha	PROPN
ejpam-5573	588	7	.	.	PUNCT
ejpam-5573	589	1	on	on	ADP
ejpam-5573	589	2	r	r	NOUN
ejpam-5573	589	3	-	-	PUNCT
ejpam-5573	589	4	generalized	generalize	VERB
ejpam-5573	589	5	fuzzy	fuzzy	ADJ
ejpam-5573	589	6	ℓ-closed	ℓ-close	VERB
ejpam-5573	589	7	sets	set	NOUN
ejpam-5573	589	8	:	:	PUNCT
ejpam-5573	589	9	properties	property	NOUN
ejpam-5573	589	10	and	and	CCONJ
ejpam-5573	589	11	applications	application	NOUN
ejpam-5573	589	12	.	.	PUNCT
ejpam-5573	590	1	j.	j.	PROPN
ejpam-5573	590	2	math	math	PROPN
ejpam-5573	590	3	.	.	PUNCT
ejpam-5573	590	4	,	,	PUNCT
ejpam-5573	590	5	2021:1–8	2021:1–8	PROPN
ejpam-5573	590	6	,	,	PUNCT
ejpam-5573	590	7	2021	2021	NUM
ejpam-5573	590	8	.	.	PUNCT
ejpam-5573	591	1	[	[	X
ejpam-5573	591	2	39	39	NUM
ejpam-5573	591	3	]	]	PUNCT
ejpam-5573	591	4	i.	i.	PROPN
ejpam-5573	591	5	m.	m.	PROPN
ejpam-5573	591	6	taha	taha	PROPN
ejpam-5573	591	7	.	.	PUNCT
ejpam-5573	592	1	some	some	DET
ejpam-5573	592	2	new	new	ADJ
ejpam-5573	592	3	separation	separation	NOUN
ejpam-5573	592	4	axioms	axiom	VERB
ejpam-5573	592	5	in	in	ADP
ejpam-5573	592	6	fuzzy	fuzzy	ADJ
ejpam-5573	592	7	soft	soft	ADJ
ejpam-5573	592	8	topological	topological	ADJ
ejpam-5573	592	9	spaces	space	NOUN
ejpam-5573	592	10	.	.	PUNCT
ejpam-5573	593	1	filomat	filomat	NOUN
ejpam-5573	593	2	,	,	PUNCT
ejpam-5573	593	3	35(6):1775–1783	35(6):1775–1783	NOUN
ejpam-5573	593	4	,	,	PUNCT
ejpam-5573	593	5	2021	2021	NUM
ejpam-5573	593	6	.	.	PUNCT
ejpam-5573	594	1	[	[	X
ejpam-5573	594	2	40	40	NUM
ejpam-5573	594	3	]	]	PUNCT
ejpam-5573	594	4	i.	i.	PROPN
ejpam-5573	594	5	m.	m.	PROPN
ejpam-5573	594	6	taha	taha	PROPN
ejpam-5573	594	7	.	.	PUNCT
ejpam-5573	595	1	r	r	X
ejpam-5573	595	2	-	-	PUNCT
ejpam-5573	595	3	fuzzy	fuzzy	ADJ
ejpam-5573	595	4	δ-ℓ-open	δ-ℓ-open	NOUN
ejpam-5573	595	5	sets	set	NOUN
ejpam-5573	595	6	and	and	CCONJ
ejpam-5573	595	7	fuzzy	fuzzy	ADJ
ejpam-5573	595	8	upper	upper	ADJ
ejpam-5573	595	9	(	(	PUNCT
ejpam-5573	595	10	lower	low	ADJ
ejpam-5573	595	11	)	)	PUNCT
ejpam-5573	595	12	δ-ℓ-continuity	δ-ℓ-continuity	NOUN
ejpam-5573	595	13	via	via	ADP
ejpam-5573	595	14	fuzzy	fuzzy	ADJ
ejpam-5573	595	15	idealization	idealization	NOUN
ejpam-5573	595	16	.	.	PUNCT
ejpam-5573	596	1	j.	j.	PROPN
ejpam-5573	596	2	math	math	PROPN
ejpam-5573	596	3	.	.	PUNCT
ejpam-5573	597	1	comput	comput	NOUN
ejpam-5573	597	2	.	.	PUNCT
ejpam-5573	598	1	sci	sci	PROPN
ejpam-5573	598	2	.	.	PROPN
ejpam-5573	598	3	,	,	PUNCT
ejpam-5573	598	4	25(1):1–9	25(1):1–9	NUM
ejpam-5573	598	5	,	,	PUNCT
ejpam-5573	598	6	2022	2022	NUM
ejpam-5573	598	7	.	.	PUNCT
ejpam-5573	599	1	[	[	X
ejpam-5573	599	2	41	41	NUM
ejpam-5573	599	3	]	]	X
ejpam-5573	599	4	i.	i.	PROPN
ejpam-5573	599	5	m.	m.	PROPN
ejpam-5573	599	6	taha	taha	PROPN
ejpam-5573	599	7	.	.	PUNCT
ejpam-5573	600	1	some	some	DET
ejpam-5573	600	2	new	new	ADJ
ejpam-5573	600	3	results	result	NOUN
ejpam-5573	600	4	on	on	ADP
ejpam-5573	600	5	fuzzy	fuzzy	ADJ
ejpam-5573	600	6	soft	soft	ADJ
ejpam-5573	600	7	r	r	NOUN
ejpam-5573	600	8	-	-	PUNCT
ejpam-5573	600	9	minimal	minimal	ADJ
ejpam-5573	600	10	spaces	space	NOUN
ejpam-5573	600	11	.	.	PUNCT
ejpam-5573	601	1	aims	aim	VERB
ejpam-5573	601	2	math	math	NOUN
ejpam-5573	601	3	.	.	PUNCT
ejpam-5573	601	4	,	,	PUNCT
ejpam-5573	602	1	7(7):12458–12470	7(7):12458–12470	PROPN
ejpam-5573	602	2	,	,	PUNCT
ejpam-5573	602	3	2022	2022	NUM
ejpam-5573	602	4	.	.	PUNCT
ejpam-5573	603	1	[	[	X
ejpam-5573	603	2	42	42	NUM
ejpam-5573	603	3	]	]	X
ejpam-5573	603	4	i.	i.	PROPN
ejpam-5573	603	5	m.	m.	PROPN
ejpam-5573	603	6	taha	taha	PROPN
ejpam-5573	603	7	.	.	PUNCT
ejpam-5573	604	1	some	some	DET
ejpam-5573	604	2	properties	property	NOUN
ejpam-5573	604	3	of	of	ADP
ejpam-5573	604	4	(	(	PUNCT
ejpam-5573	604	5	r	r	NOUN
ejpam-5573	604	6	,	,	PUNCT
ejpam-5573	604	7	s)-generalized	s)-generalized	ADJ
ejpam-5573	604	8	fuzzy	fuzzy	ADJ
ejpam-5573	604	9	semi	semi	ADJ
ejpam-5573	604	10	-	-	ADJ
ejpam-5573	604	11	closed	closed	ADJ
ejpam-5573	604	12	sets	set	NOUN
ejpam-5573	604	13	and	and	CCONJ
ejpam-5573	604	14	some	some	DET
ejpam-5573	604	15	applications	application	NOUN
ejpam-5573	604	16	.	.	PUNCT
ejpam-5573	605	1	j.	j.	PROPN
ejpam-5573	605	2	math	math	PROPN
ejpam-5573	605	3	.	.	PUNCT
ejpam-5573	606	1	comput	comput	NOUN
ejpam-5573	606	2	.	.	PUNCT
ejpam-5573	607	1	sci	sci	PROPN
ejpam-5573	607	2	.	.	PROPN
ejpam-5573	607	3	,	,	PUNCT
ejpam-5573	607	4	27(2):164–175	27(2):164–175	PROPN
ejpam-5573	607	5	,	,	PUNCT
ejpam-5573	607	6	2022	2022	NUM
ejpam-5573	607	7	.	.	PUNCT
ejpam-5573	608	1	[	[	X
ejpam-5573	608	2	43	43	NUM
ejpam-5573	608	3	]	]	PUNCT
ejpam-5573	608	4	s.	s.	PROPN
ejpam-5573	608	5	s.	s.	PROPN
ejpam-5573	608	6	thakur	thakur	PROPN
ejpam-5573	608	7	and	and	CCONJ
ejpam-5573	608	8	j.	j.	PROPN
ejpam-5573	608	9	p.	p.	PROPN
ejpam-5573	608	10	bajpai	bajpai	PROPN
ejpam-5573	608	11	.	.	PUNCT
ejpam-5573	609	1	intuitionistic	intuitionistic	ADJ
ejpam-5573	609	2	fuzzy	fuzzy	ADJ
ejpam-5573	609	3	sg	sg	NOUN
ejpam-5573	609	4	-	-	PUNCT
ejpam-5573	609	5	continuous	continuous	ADJ
ejpam-5573	609	6	mappings	mapping	NOUN
ejpam-5573	609	7	.	.	PUNCT
ejpam-5573	610	1	int	int	NOUN
ejpam-5573	610	2	.	.	PUNCT
ejpam-5573	611	1	j.	j.	PROPN
ejpam-5573	611	2	appl	appl	PROPN
ejpam-5573	611	3	.	.	PROPN
ejpam-5573	611	4	math	math	PROPN
ejpam-5573	611	5	.	.	PUNCT
ejpam-5573	612	1	anal	anal	PROPN
ejpam-5573	612	2	.	.	PUNCT
ejpam-5573	612	3	appl	appl	PROPN
ejpam-5573	612	4	.	.	PROPN
ejpam-5573	612	5	,	,	PUNCT
ejpam-5573	612	6	5(1):45–51	5(1):45–51	NUM
ejpam-5573	612	7	,	,	PUNCT
ejpam-5573	612	8	2010	2010	NUM
ejpam-5573	612	9	.	.	PUNCT
ejpam-5573	613	1	[	[	X
ejpam-5573	613	2	44	44	NUM
ejpam-5573	613	3	]	]	PUNCT
ejpam-5573	613	4	s.	s.	PROPN
ejpam-5573	613	5	s.	s.	PROPN
ejpam-5573	613	6	thakur	thakur	PROPN
ejpam-5573	613	7	and	and	CCONJ
ejpam-5573	613	8	j.	j.	PROPN
ejpam-5573	613	9	p.	p.	PROPN
ejpam-5573	613	10	bajpai	bajpai	PROPN
ejpam-5573	613	11	.	.	PUNCT
ejpam-5573	614	1	semi	semi	ADJ
ejpam-5573	614	2	generalized	generalize	VERB
ejpam-5573	614	3	closed	closed	ADJ
ejpam-5573	614	4	sets	set	NOUN
ejpam-5573	614	5	in	in	ADP
ejpam-5573	614	6	intuitionistic	intuitionistic	ADJ
ejpam-5573	614	7	fuzzy	fuzzy	ADJ
ejpam-5573	614	8	topology	topology	NOUN
ejpam-5573	614	9	.	.	PUNCT
ejpam-5573	615	1	int	int	NOUN
ejpam-5573	615	2	.	.	PUNCT
ejpam-5573	616	1	rev	rev	PROPN
ejpam-5573	616	2	.	.	PROPN
ejpam-5573	616	3	fuzzy	fuzzy	ADJ
ejpam-5573	616	4	math	math	NOUN
ejpam-5573	616	5	.	.	PUNCT
ejpam-5573	616	6	,	,	PUNCT
ejpam-5573	616	7	6(2):69–76	6(2):69–76	NUM
ejpam-5573	616	8	,	,	PUNCT
ejpam-5573	616	9	2011	2011	NUM
ejpam-5573	616	10	.	.	PUNCT
ejpam-5573	617	1	[	[	X
ejpam-5573	617	2	45	45	NUM
ejpam-5573	617	3	]	]	PUNCT
ejpam-5573	617	4	a.	a.	NOUN
ejpam-5573	617	5	p.	p.	NOUN
ejpam-5573	617	6	šostak	šostak	NOUN
ejpam-5573	617	7	.	.	PUNCT
ejpam-5573	618	1	on	on	ADP
ejpam-5573	618	2	a	a	DET
ejpam-5573	618	3	fuzzy	fuzzy	ADJ
ejpam-5573	618	4	topological	topological	ADJ
ejpam-5573	618	5	structure	structure	NOUN
ejpam-5573	618	6	.	.	PUNCT
ejpam-5573	619	1	in	in	ADP
ejpam-5573	619	2	in	in	ADP
ejpam-5573	619	3	:	:	PUNCT
ejpam-5573	619	4	proceedings	proceeding	NOUN
ejpam-5573	619	5	of	of	ADP
ejpam-5573	619	6	the	the	DET
ejpam-5573	619	7	13th	13th	NOUN
ejpam-5573	619	8	winter	winter	NOUN
ejpam-5573	619	9	school	school	NOUN
ejpam-5573	619	10	on	on	ADP
ejpam-5573	619	11	abstract	abstract	ADJ
ejpam-5573	619	12	analysis	analysis	NOUN
ejpam-5573	619	13	,	,	PUNCT
ejpam-5573	619	14	section	section	NOUN
ejpam-5573	619	15	of	of	ADP
ejpam-5573	619	16	topology	topology	NOUN
ejpam-5573	619	17	,	,	PUNCT
ejpam-5573	619	18	palermo	palermo	NOUN
ejpam-5573	619	19	:	:	PUNCT
ejpam-5573	619	20	circolo	circolo	PROPN
ejpam-5573	619	21	matematico	matematico	NOUN
ejpam-5573	619	22	di	di	X
ejpam-5573	619	23	palermo	palermo	NOUN
ejpam-5573	619	24	,	,	PUNCT
ejpam-5573	619	25	pages	page	NOUN
ejpam-5573	619	26	89–103	89–103	PROPN
ejpam-5573	619	27	,	,	PUNCT
ejpam-5573	619	28	1985	1985	NUM
ejpam-5573	619	29	.	.	PUNCT
ejpam-5573	620	1	[	[	X
ejpam-5573	620	2	46	46	NUM
ejpam-5573	620	3	]	]	X
ejpam-5573	620	4	l.	l.	PROPN
ejpam-5573	620	5	a.	a.	PROPN
ejpam-5573	620	6	zadeh	zadeh	PROPN
ejpam-5573	620	7	.	.	PUNCT
ejpam-5573	620	8	fuzzy	fuzzy	ADJ
ejpam-5573	620	9	sets	set	NOUN
ejpam-5573	620	10	.	.	PUNCT
ejpam-5573	621	1	inform	inform	NOUN
ejpam-5573	621	2	.	.	PUNCT
ejpam-5573	622	1	control	control	NOUN
ejpam-5573	622	2	,	,	PUNCT
ejpam-5573	622	3	8:338–353	8:338–353	NUM
ejpam-5573	622	4	,	,	PUNCT
ejpam-5573	622	5	1965	1965	NUM
ejpam-5573	622	6	.	.	PUNCT
ejpam-5573	623	1	[	[	X
ejpam-5573	623	2	47	47	NUM
ejpam-5573	623	3	]	]	PUNCT
ejpam-5573	623	4	a.	a.	NOUN
ejpam-5573	623	5	m.	m.	NOUN
ejpam-5573	623	6	zahran	zahran	PROPN
ejpam-5573	623	7	,	,	PUNCT
ejpam-5573	623	8	m.	m.	NOUN
ejpam-5573	623	9	a.	a.	PROPN
ejpam-5573	623	10	abd	abd	PROPN
ejpam-5573	623	11	-	-	PUNCT
ejpam-5573	623	12	allah	allah	PROPN
ejpam-5573	623	13	,	,	PUNCT
ejpam-5573	623	14	and	and	CCONJ
ejpam-5573	623	15	a.	a.	NOUN
ejpam-5573	623	16	ghareeb	ghareeb	NOUN
ejpam-5573	623	17	.	.	PUNCT
ejpam-5573	624	1	several	several	ADJ
ejpam-5573	624	2	types	type	NOUN
ejpam-5573	624	3	of	of	ADP
ejpam-5573	624	4	double	double	ADJ
ejpam-5573	624	5	fuzzy	fuzzy	ADJ
ejpam-5573	624	6	irresolute	irresolute	ADJ
ejpam-5573	624	7	functions	function	NOUN
ejpam-5573	624	8	.	.	PUNCT
ejpam-5573	625	1	int	int	NOUN
ejpam-5573	625	2	.	.	PUNCT
ejpam-5573	626	1	j.	j.	PROPN
ejpam-5573	626	2	comput	comput	PROPN
ejpam-5573	626	3	.	.	PUNCT
ejpam-5573	627	1	cognition	cognition	NOUN
ejpam-5573	627	2	,	,	PUNCT
ejpam-5573	627	3	8:19–23	8:19–23	NUM
ejpam-5573	627	4	,	,	PUNCT
ejpam-5573	627	5	2011	2011	NUM
ejpam-5573	627	6	.	.	PUNCT
ejpam-5573	628	1	[	[	X
ejpam-5573	628	2	48	48	NUM
ejpam-5573	628	3	]	]	PUNCT
ejpam-5573	628	4	h.	h.	PROPN
ejpam-5573	628	5	j.	j.	PROPN
ejpam-5573	628	6	zimmermann	zimmermann	PROPN
ejpam-5573	628	7	.	.	PUNCT
ejpam-5573	629	1	fuzzy	fuzzy	ADJ
ejpam-5573	629	2	set	set	VERB
ejpam-5573	629	3	theory	theory	NOUN
ejpam-5573	629	4	and	and	CCONJ
ejpam-5573	629	5	its	its	PRON
ejpam-5573	629	6	applications	application	NOUN
ejpam-5573	629	7	.	.	PUNCT
ejpam-5573	630	1	kluwer	kluwer	PROPN
ejpam-5573	630	2	acad	acad	PROPN
ejpam-5573	630	3	.	.	PUNCT
ejpam-5573	631	1	publ	publ	PROPN
ejpam-5573	631	2	.	.	PROPN
ejpam-5573	631	3	,	,	PUNCT
ejpam-5573	631	4	boston	boston	PROPN
ejpam-5573	631	5	,	,	PUNCT
ejpam-5573	631	6	1991	1991	NUM
ejpam-5573	631	7	.	.	PUNCT