id	sid	tid	token	lemma	pos
ejpam-5911	1	1	european	european	PROPN
ejpam-5911	1	2	journal	journal	PROPN
ejpam-5911	1	3	of	of	ADP
ejpam-5911	1	4	pure	pure	ADJ
ejpam-5911	1	5	and	and	CCONJ
ejpam-5911	1	6	applied	applied	ADJ
ejpam-5911	1	7	mathematics	mathematic	NOUN
ejpam-5911	1	8	2025	2025	NUM
ejpam-5911	1	9	,	,	PUNCT
ejpam-5911	1	10	vol	vol	NOUN
ejpam-5911	1	11	.	.	PROPN
ejpam-5911	1	12	18	18	NUM
ejpam-5911	1	13	,	,	PUNCT
ejpam-5911	1	14	issue	issue	NOUN
ejpam-5911	1	15	2	2	NUM
ejpam-5911	1	16	,	,	PUNCT
ejpam-5911	1	17	article	article	NOUN
ejpam-5911	1	18	number	number	NOUN
ejpam-5911	1	19	5911	5911	NUM
ejpam-5911	1	20	issn	issn	PROPN
ejpam-5911	1	21	1307	1307	NUM
ejpam-5911	1	22	-	-	SYM
ejpam-5911	1	23	5543	5543	NUM
ejpam-5911	1	24	–	–	PUNCT
ejpam-5911	1	25	ejpam.com	ejpam.com	X
ejpam-5911	1	26	published	publish	VERB
ejpam-5911	1	27	by	by	ADP
ejpam-5911	1	28	new	new	PROPN
ejpam-5911	1	29	york	york	PROPN
ejpam-5911	1	30	business	business	NOUN
ejpam-5911	1	31	global	global	VERB
ejpam-5911	1	32	some	some	DET
ejpam-5911	1	33	characterizations	characterization	NOUN
ejpam-5911	1	34	of	of	ADP
ejpam-5911	1	35	(	(	PUNCT
ejpam-5911	1	36	r	r	NOUN
ejpam-5911	1	37	,	,	PUNCT
ejpam-5911	1	38	s)-fuzzy	s)-fuzzy	ADJ
ejpam-5911	1	39	b	b	X
ejpam-5911	1	40	-	-	PUNCT
ejpam-5911	1	41	open	open	ADJ
ejpam-5911	1	42	sets	set	NOUN
ejpam-5911	1	43	with	with	ADP
ejpam-5911	1	44	applications	application	NOUN
ejpam-5911	1	45	in	in	ADP
ejpam-5911	1	46	double	double	ADJ
ejpam-5911	1	47	fuzzy	fuzzy	ADJ
ejpam-5911	1	48	topological	topological	ADJ
ejpam-5911	1	49	spaces	space	NOUN
ejpam-5911	1	50	islam	islam	PROPN
ejpam-5911	1	51	m.	m.	PROPN
ejpam-5911	1	52	taha1,∗	taha1,∗	NOUN
ejpam-5911	1	53	,	,	PUNCT
ejpam-5911	1	54	jawaher	jawaher	PROPN
ejpam-5911	1	55	al	al	PROPN
ejpam-5911	1	56	-	-	PUNCT
ejpam-5911	1	57	mufarrij2	mufarrij2	PROPN
ejpam-5911	1	58	,	,	PUNCT
ejpam-5911	1	59	osama	osama	PROPN
ejpam-5911	1	60	m.	m.	NOUN
ejpam-5911	1	61	taha1	taha1	NOUN
ejpam-5911	1	62	1	1	NUM
ejpam-5911	1	63	department	department	NOUN
ejpam-5911	1	64	of	of	ADP
ejpam-5911	1	65	mathematics	mathematic	NOUN
ejpam-5911	1	66	,	,	PUNCT
ejpam-5911	1	67	faculty	faculty	NOUN
ejpam-5911	1	68	of	of	ADP
ejpam-5911	1	69	science	science	NOUN
ejpam-5911	1	70	,	,	PUNCT
ejpam-5911	1	71	sohag	sohag	NOUN
ejpam-5911	1	72	university	university	NOUN
ejpam-5911	1	73	,	,	PUNCT
ejpam-5911	1	74	sohag	sohag	NOUN
ejpam-5911	1	75	,	,	PUNCT
ejpam-5911	1	76	egypt	egypt	PROPN
ejpam-5911	1	77	2	2	NUM
ejpam-5911	1	78	department	department	NOUN
ejpam-5911	1	79	of	of	ADP
ejpam-5911	1	80	mathematics	mathematic	NOUN
ejpam-5911	1	81	,	,	PUNCT
ejpam-5911	1	82	women	woman	NOUN
ejpam-5911	1	83	section	section	NOUN
ejpam-5911	1	84	,	,	PUNCT
ejpam-5911	1	85	king	king	PROPN
ejpam-5911	1	86	saud	saud	PROPN
ejpam-5911	1	87	university	university	PROPN
ejpam-5911	1	88	,	,	PUNCT
ejpam-5911	1	89	riyadh	riyadh	PROPN
ejpam-5911	1	90	12372	12372	NUM
ejpam-5911	1	91	,	,	PUNCT
ejpam-5911	1	92	saudi	saudi	PROPN
ejpam-5911	1	93	arabia	arabia	PROPN
ejpam-5911	1	94	abstract	abstract	NOUN
ejpam-5911	1	95	.	.	PUNCT
ejpam-5911	2	1	in	in	ADP
ejpam-5911	2	2	this	this	DET
ejpam-5911	2	3	paper	paper	NOUN
ejpam-5911	2	4	,	,	PUNCT
ejpam-5911	2	5	we	we	PRON
ejpam-5911	2	6	displayed	display	VERB
ejpam-5911	2	7	and	and	CCONJ
ejpam-5911	2	8	characterized	characterize	VERB
ejpam-5911	2	9	a	a	DET
ejpam-5911	2	10	novel	novel	ADJ
ejpam-5911	2	11	class	class	NOUN
ejpam-5911	2	12	of	of	ADP
ejpam-5911	2	13	fuzzy	fuzzy	ADJ
ejpam-5911	2	14	open	open	ADJ
ejpam-5911	2	15	sets	set	NOUN
ejpam-5911	2	16	(	(	PUNCT
ejpam-5911	2	17	f	f	X
ejpam-5911	2	18	-	-	PUNCT
ejpam-5911	2	19	open	open	ADJ
ejpam-5911	2	20	sets	set	NOUN
ejpam-5911	2	21	)	)	PUNCT
ejpam-5911	2	22	in	in	ADP
ejpam-5911	2	23	double	double	ADJ
ejpam-5911	2	24	fuzzy	fuzzy	ADJ
ejpam-5911	2	25	topological	topological	ADJ
ejpam-5911	2	26	spaces	space	NOUN
ejpam-5911	2	27	(	(	PUNCT
ejpam-5911	2	28	dft	dft	PROPN
ejpam-5911	2	29	ss	ss	PROPN
ejpam-5911	2	30	)	)	PUNCT
ejpam-5911	2	31	based	base	VERB
ejpam-5911	2	32	on	on	ADP
ejpam-5911	2	33	šostak	šostak	NOUN
ejpam-5911	2	34	,	,	PUNCT
ejpam-5911	2	35	s	s	PART
ejpam-5911	2	36	sense	sense	NOUN
ejpam-5911	2	37	,	,	PUNCT
ejpam-5911	2	38	called	call	VERB
ejpam-5911	2	39	(	(	PUNCT
ejpam-5911	2	40	r	r	NOUN
ejpam-5911	2	41	,	,	PUNCT
ejpam-5911	2	42	s)-fuzzy	s)-fuzzy	PRON
ejpam-5911	2	43	bopen	bopen	VERB
ejpam-5911	2	44	sets	set	NOUN
ejpam-5911	2	45	(	(	PUNCT
ejpam-5911	2	46	(	(	PUNCT
ejpam-5911	2	47	r	r	NOUN
ejpam-5911	2	48	,	,	PUNCT
ejpam-5911	2	49	s)-f	s)-f	NOUN
ejpam-5911	2	50	-	-	PUNCT
ejpam-5911	2	51	b	b	NOUN
ejpam-5911	2	52	-	-	PUNCT
ejpam-5911	2	53	open	open	ADJ
ejpam-5911	2	54	sets	set	NOUN
ejpam-5911	2	55	)	)	PUNCT
ejpam-5911	2	56	.	.	PUNCT
ejpam-5911	3	1	this	this	DET
ejpam-5911	3	2	class	class	NOUN
ejpam-5911	3	3	is	be	AUX
ejpam-5911	3	4	contained	contain	VERB
ejpam-5911	3	5	in	in	ADP
ejpam-5911	3	6	the	the	DET
ejpam-5911	3	7	class	class	NOUN
ejpam-5911	3	8	of	of	ADP
ejpam-5911	3	9	(	(	PUNCT
ejpam-5911	3	10	r	r	NOUN
ejpam-5911	3	11	,	,	PUNCT
ejpam-5911	3	12	s)-f	s)-f	NOUN
ejpam-5911	3	13	-	-	PUNCT
ejpam-5911	3	14	β	β	NOUN
ejpam-5911	3	15	-	-	ADJ
ejpam-5911	3	16	open	open	ADJ
ejpam-5911	3	17	sets	set	NOUN
ejpam-5911	3	18	and	and	CCONJ
ejpam-5911	3	19	contains	contain	VERB
ejpam-5911	3	20	all	all	DET
ejpam-5911	3	21	(	(	PUNCT
ejpam-5911	3	22	r	r	NOUN
ejpam-5911	3	23	,	,	PUNCT
ejpam-5911	3	24	s)-f	s)-f	NOUN
ejpam-5911	3	25	-	-	PUNCT
ejpam-5911	3	26	α	α	NOUN
ejpam-5911	3	27	-	-	ADJ
ejpam-5911	3	28	open	open	ADJ
ejpam-5911	3	29	sets	set	NOUN
ejpam-5911	3	30	,	,	PUNCT
ejpam-5911	3	31	(	(	PUNCT
ejpam-5911	3	32	r	r	NOUN
ejpam-5911	3	33	,	,	PUNCT
ejpam-5911	3	34	s)-f	s)-f	NOUN
ejpam-5911	3	35	-	-	PUNCT
ejpam-5911	3	36	pre	pre	ADJ
ejpam-5911	3	37	-	-	ADJ
ejpam-5911	3	38	open	open	ADJ
ejpam-5911	3	39	sets	set	NOUN
ejpam-5911	3	40	,	,	PUNCT
ejpam-5911	3	41	and	and	CCONJ
ejpam-5911	3	42	(	(	PUNCT
ejpam-5911	3	43	r	r	NOUN
ejpam-5911	3	44	,	,	PUNCT
ejpam-5911	3	45	s)-f	s)-f	NOUN
ejpam-5911	3	46	-	-	PUNCT
ejpam-5911	3	47	semi	semi	ADJ
ejpam-5911	3	48	-	-	ADJ
ejpam-5911	3	49	open	open	ADJ
ejpam-5911	3	50	sets	set	NOUN
ejpam-5911	3	51	.	.	PUNCT
ejpam-5911	4	1	next	next	ADV
ejpam-5911	4	2	,	,	PUNCT
ejpam-5911	4	3	we	we	PRON
ejpam-5911	4	4	explored	explore	VERB
ejpam-5911	4	5	and	and	CCONJ
ejpam-5911	4	6	studied	study	VERB
ejpam-5911	4	7	the	the	DET
ejpam-5911	4	8	notion	notion	NOUN
ejpam-5911	4	9	of	of	ADP
ejpam-5911	4	10	df	df	PROPN
ejpam-5911	4	11	-	-	PUNCT
ejpam-5911	4	12	b	b	NOUN
ejpam-5911	4	13	-	-	PUNCT
ejpam-5911	4	14	continuity	continuity	NOUN
ejpam-5911	4	15	between	between	ADP
ejpam-5911	4	16	dft	dft	PROPN
ejpam-5911	4	17	ss	ss	PROPN
ejpam-5911	4	18	(	(	PUNCT
ejpam-5911	4	19	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	4	20	)	)	PUNCT
ejpam-5911	4	21	and	and	CCONJ
ejpam-5911	4	22	(	(	PUNCT
ejpam-5911	4	23	z	z	NOUN
ejpam-5911	4	24	,	,	PUNCT
ejpam-5911	4	25	𭟋	𭟋	NOUN
ejpam-5911	4	26	,	,	PUNCT
ejpam-5911	4	27	𭟋∗	𭟋∗	NOUN
ejpam-5911	4	28	)	)	PUNCT
ejpam-5911	4	29	.	.	PUNCT
ejpam-5911	5	1	we	we	PRON
ejpam-5911	5	2	also	also	ADV
ejpam-5911	5	3	defined	define	VERB
ejpam-5911	5	4	and	and	CCONJ
ejpam-5911	5	5	discussed	discuss	VERB
ejpam-5911	5	6	the	the	DET
ejpam-5911	5	7	notions	notion	NOUN
ejpam-5911	5	8	of	of	ADP
ejpam-5911	5	9	df	df	NOUN
ejpam-5911	5	10	-	-	PUNCT
ejpam-5911	5	11	almost	almost	ADV
ejpam-5911	5	12	b	b	NOUN
ejpam-5911	5	13	-	-	PUNCT
ejpam-5911	5	14	continuity	continuity	NOUN
ejpam-5911	5	15	and	and	CCONJ
ejpam-5911	5	16	df	df	NOUN
ejpam-5911	5	17	-	-	PUNCT
ejpam-5911	5	18	weakly	weakly	ADJ
ejpam-5911	5	19	b	b	NOUN
ejpam-5911	5	20	-	-	PUNCT
ejpam-5911	5	21	continuity	continuity	NOUN
ejpam-5911	5	22	,	,	PUNCT
ejpam-5911	5	23	which	which	PRON
ejpam-5911	5	24	are	be	AUX
ejpam-5911	5	25	weaker	weak	ADJ
ejpam-5911	5	26	forms	form	NOUN
ejpam-5911	5	27	of	of	ADP
ejpam-5911	5	28	df	df	PROPN
ejpam-5911	5	29	-	-	PUNCT
ejpam-5911	5	30	b	b	NOUN
ejpam-5911	5	31	-	-	PUNCT
ejpam-5911	5	32	continuity	continuity	NOUN
ejpam-5911	5	33	.	.	PUNCT
ejpam-5911	6	1	thereafter	thereafter	ADV
ejpam-5911	6	2	,	,	PUNCT
ejpam-5911	6	3	we	we	PRON
ejpam-5911	6	4	presented	present	VERB
ejpam-5911	6	5	and	and	CCONJ
ejpam-5911	6	6	investigated	investigate	VERB
ejpam-5911	6	7	novel	novel	NOUN
ejpam-5911	6	8	dfmappings	dfmapping	NOUN
ejpam-5911	6	9	via	via	ADP
ejpam-5911	6	10	(	(	PUNCT
ejpam-5911	6	11	r	r	NOUN
ejpam-5911	6	12	,	,	PUNCT
ejpam-5911	6	13	s)-f	s)-f	NOUN
ejpam-5911	6	14	-	-	PUNCT
ejpam-5911	6	15	b	b	NOUN
ejpam-5911	6	16	-	-	PUNCT
ejpam-5911	6	17	open	open	ADJ
ejpam-5911	6	18	and	and	CCONJ
ejpam-5911	6	19	(	(	PUNCT
ejpam-5911	6	20	r	r	NOUN
ejpam-5911	6	21	,	,	PUNCT
ejpam-5911	6	22	s)-f	s)-f	NOUN
ejpam-5911	6	23	-	-	PUNCT
ejpam-5911	6	24	b	b	NOUN
ejpam-5911	6	25	-	-	PUNCT
ejpam-5911	6	26	closed	closed	ADJ
ejpam-5911	6	27	sets	set	NOUN
ejpam-5911	6	28	.	.	PUNCT
ejpam-5911	7	1	finally	finally	ADV
ejpam-5911	7	2	,	,	PUNCT
ejpam-5911	7	3	we	we	PRON
ejpam-5911	7	4	introduced	introduce	VERB
ejpam-5911	7	5	some	some	DET
ejpam-5911	7	6	novel	novel	ADJ
ejpam-5911	7	7	types	type	NOUN
ejpam-5911	7	8	of	of	ADP
ejpam-5911	7	9	df	df	NOUN
ejpam-5911	7	10	-	-	PUNCT
ejpam-5911	7	11	separation	separation	NOUN
ejpam-5911	7	12	axioms	axiom	NOUN
ejpam-5911	7	13	,	,	PUNCT
ejpam-5911	7	14	called	call	VERB
ejpam-5911	7	15	(	(	PUNCT
ejpam-5911	7	16	r	r	NOUN
ejpam-5911	7	17	,	,	PUNCT
ejpam-5911	7	18	s)-f	s)-f	NOUN
ejpam-5911	7	19	-	-	PUNCT
ejpam-5911	7	20	b	b	NOUN
ejpam-5911	7	21	-	-	PUNCT
ejpam-5911	7	22	regular	regular	ADJ
ejpam-5911	7	23	and	and	CCONJ
ejpam-5911	7	24	(	(	PUNCT
ejpam-5911	7	25	r	r	NOUN
ejpam-5911	7	26	,	,	PUNCT
ejpam-5911	7	27	s)-f	s)-f	NOUN
ejpam-5911	7	28	-	-	PUNCT
ejpam-5911	7	29	b	b	NOUN
ejpam-5911	7	30	-	-	PUNCT
ejpam-5911	7	31	normal	normal	ADJ
ejpam-5911	7	32	spaces	space	NOUN
ejpam-5911	7	33	,	,	PUNCT
ejpam-5911	7	34	and	and	CCONJ
ejpam-5911	7	35	studied	study	VERB
ejpam-5911	7	36	some	some	DET
ejpam-5911	7	37	properties	property	NOUN
ejpam-5911	7	38	of	of	ADP
ejpam-5911	7	39	them	they	PRON
ejpam-5911	7	40	.	.	PUNCT
ejpam-5911	8	1	2020	2020	NUM
ejpam-5911	8	2	mathematics	mathematic	NOUN
ejpam-5911	8	3	subject	subject	NOUN
ejpam-5911	8	4	classifications	classification	NOUN
ejpam-5911	8	5	:	:	PUNCT
ejpam-5911	8	6	54a05	54a05	NUM
ejpam-5911	8	7	,	,	PUNCT
ejpam-5911	8	8	54a40	54a40	NUM
ejpam-5911	8	9	,	,	PUNCT
ejpam-5911	8	10	54c05	54c05	NUM
ejpam-5911	8	11	,	,	PUNCT
ejpam-5911	8	12	54c08	54c08	NUM
ejpam-5911	8	13	,	,	PUNCT
ejpam-5911	8	14	54d15	54d15	PRON
ejpam-5911	8	15	key	key	ADJ
ejpam-5911	8	16	words	word	NOUN
ejpam-5911	8	17	and	and	CCONJ
ejpam-5911	8	18	phrases	phrase	NOUN
ejpam-5911	8	19	:	:	PUNCT
ejpam-5911	8	20	df	df	NOUN
ejpam-5911	8	21	-	-	PUNCT
ejpam-5911	8	22	topology	topology	NOUN
ejpam-5911	8	23	,	,	PUNCT
ejpam-5911	8	24	(	(	PUNCT
ejpam-5911	8	25	r	r	NOUN
ejpam-5911	8	26	,	,	PUNCT
ejpam-5911	8	27	s)-f	s)-f	NOUN
ejpam-5911	8	28	-	-	PUNCT
ejpam-5911	8	29	b	b	NOUN
ejpam-5911	8	30	-	-	PUNCT
ejpam-5911	8	31	open	open	ADJ
ejpam-5911	8	32	set	set	NOUN
ejpam-5911	8	33	,	,	PUNCT
ejpam-5911	8	34	df	df	PROPN
ejpam-5911	8	35	-	-	PUNCT
ejpam-5911	8	36	b	b	NOUN
ejpam-5911	8	37	-	-	PUNCT
ejpam-5911	8	38	closure	closure	NOUN
ejpam-5911	8	39	operator	operator	NOUN
ejpam-5911	8	40	,	,	PUNCT
ejpam-5911	8	41	df	df	NOUN
ejpam-5911	8	42	-	-	PUNCT
ejpam-5911	8	43	bcontinuity	bcontinuity	NOUN
ejpam-5911	8	44	,	,	PUNCT
ejpam-5911	8	45	df	df	PROPN
ejpam-5911	8	46	-	-	PUNCT
ejpam-5911	8	47	b	b	NOUN
ejpam-5911	8	48	-	-	PUNCT
ejpam-5911	8	49	irresoluteness	irresoluteness	NOUN
ejpam-5911	8	50	,	,	PUNCT
ejpam-5911	8	51	df	df	PROPN
ejpam-5911	8	52	-	-	PUNCT
ejpam-5911	8	53	b	b	NOUN
ejpam-5911	8	54	-	-	PUNCT
ejpam-5911	8	55	openness	openness	NOUN
ejpam-5911	8	56	,	,	PUNCT
ejpam-5911	8	57	df	df	PROPN
ejpam-5911	8	58	-	-	PUNCT
ejpam-5911	8	59	b	b	NOUN
ejpam-5911	8	60	-	-	PUNCT
ejpam-5911	8	61	closeness	closeness	NOUN
ejpam-5911	8	62	,	,	PUNCT
ejpam-5911	8	63	(	(	PUNCT
ejpam-5911	8	64	r	r	NOUN
ejpam-5911	8	65	,	,	PUNCT
ejpam-5911	8	66	s)-f	s)-f	NOUN
ejpam-5911	8	67	-	-	PUNCT
ejpam-5911	8	68	b	b	NOUN
ejpam-5911	8	69	-	-	PUNCT
ejpam-5911	8	70	normal	normal	ADJ
ejpam-5911	8	71	space	space	NOUN
ejpam-5911	8	72	,	,	PUNCT
ejpam-5911	8	73	(	(	PUNCT
ejpam-5911	8	74	r	r	NOUN
ejpam-5911	8	75	,	,	PUNCT
ejpam-5911	8	76	s)-fb	s)-fb	NOUN
ejpam-5911	8	77	-	-	PUNCT
ejpam-5911	8	78	regular	regular	ADJ
ejpam-5911	8	79	space	space	NOUN
ejpam-5911	8	80	1	1	NUM
ejpam-5911	8	81	.	.	PUNCT
ejpam-5911	8	82	introduction	introduction	NOUN
ejpam-5911	8	83	the	the	DET
ejpam-5911	8	84	concept	concept	NOUN
ejpam-5911	8	85	of	of	ADP
ejpam-5911	8	86	a	a	DET
ejpam-5911	8	87	fuzzy	fuzzy	ADJ
ejpam-5911	8	88	set	set	NOUN
ejpam-5911	8	89	(	(	PUNCT
ejpam-5911	8	90	f	f	NOUN
ejpam-5911	8	91	-	-	PUNCT
ejpam-5911	8	92	set	set	NOUN
ejpam-5911	8	93	)	)	PUNCT
ejpam-5911	8	94	of	of	ADP
ejpam-5911	8	95	a	a	DET
ejpam-5911	8	96	nonempty	nonempty	ADV
ejpam-5911	8	97	set	set	VERB
ejpam-5911	8	98	g	g	NOUN
ejpam-5911	8	99	is	be	AUX
ejpam-5911	8	100	a	a	DET
ejpam-5911	8	101	mapping	mapping	NOUN
ejpam-5911	8	102	m	m	NOUN
ejpam-5911	8	103	:	:	PUNCT
ejpam-5911	8	104	g	g	X
ejpam-5911	8	105	→	→	SYM
ejpam-5911	8	106	i	i	PROPN
ejpam-5911	8	107	(	(	PUNCT
ejpam-5911	8	108	where	where	SCONJ
ejpam-5911	8	109	i	i	PRON
ejpam-5911	8	110	=	=	PUNCT
ejpam-5911	9	1	[	[	X
ejpam-5911	9	2	0	0	NUM
ejpam-5911	9	3	,	,	PUNCT
ejpam-5911	9	4	1	1	NUM
ejpam-5911	9	5	]	]	NUM
ejpam-5911	9	6	)	)	PUNCT
ejpam-5911	9	7	.	.	PUNCT
ejpam-5911	10	1	this	this	DET
ejpam-5911	10	2	concept	concept	NOUN
ejpam-5911	10	3	was	be	AUX
ejpam-5911	10	4	first	first	ADV
ejpam-5911	10	5	defined	define	VERB
ejpam-5911	10	6	in	in	ADP
ejpam-5911	10	7	1965	1965	NUM
ejpam-5911	10	8	by	by	ADP
ejpam-5911	10	9	zadeh	zadeh	PROPN
ejpam-5911	11	1	[	[	X
ejpam-5911	11	2	1	1	NUM
ejpam-5911	11	3	]	]	PUNCT
ejpam-5911	11	4	.	.	PUNCT
ejpam-5911	12	1	the	the	DET
ejpam-5911	12	2	concept	concept	NOUN
ejpam-5911	12	3	of	of	ADP
ejpam-5911	12	4	an	an	DET
ejpam-5911	12	5	f	f	NOUN
ejpam-5911	12	6	-	-	PUNCT
ejpam-5911	12	7	topology	topology	NOUN
ejpam-5911	12	8	was	be	AUX
ejpam-5911	12	9	presented	present	VERB
ejpam-5911	12	10	in	in	ADP
ejpam-5911	12	11	1968	1968	NUM
ejpam-5911	12	12	by	by	ADP
ejpam-5911	12	13	the	the	DET
ejpam-5911	12	14	author	author	NOUN
ejpam-5911	12	15	of	of	ADP
ejpam-5911	12	16	[	[	X
ejpam-5911	12	17	2	2	NUM
ejpam-5911	12	18	]	]	PUNCT
ejpam-5911	12	19	.	.	PUNCT
ejpam-5911	13	1	several	several	ADJ
ejpam-5911	13	2	authors	author	NOUN
ejpam-5911	13	3	have	have	AUX
ejpam-5911	13	4	successfully	successfully	ADV
ejpam-5911	13	5	generalized	generalize	VERB
ejpam-5911	13	6	the	the	DET
ejpam-5911	13	7	theory	theory	NOUN
ejpam-5911	13	8	of	of	ADP
ejpam-5911	13	9	general	general	ADJ
ejpam-5911	13	10	topology	topology	NOUN
ejpam-5911	13	11	to	to	ADP
ejpam-5911	13	12	the	the	DET
ejpam-5911	13	13	fuzzy	fuzzy	ADJ
ejpam-5911	13	14	setting	setting	NOUN
ejpam-5911	13	15	with	with	ADP
ejpam-5911	13	16	crisp	crisp	ADJ
ejpam-5911	13	17	methods	method	NOUN
ejpam-5911	13	18	.	.	PUNCT
ejpam-5911	14	1	according	accord	VERB
ejpam-5911	14	2	to	to	ADP
ejpam-5911	14	3	šostak	šostak	NOUN
ejpam-5911	14	4	[	[	X
ejpam-5911	14	5	3	3	NUM
ejpam-5911	14	6	]	]	PUNCT
ejpam-5911	14	7	,	,	PUNCT
ejpam-5911	14	8	the	the	DET
ejpam-5911	14	9	notion	notion	NOUN
ejpam-5911	14	10	of	of	ADP
ejpam-5911	14	11	an	an	DET
ejpam-5911	14	12	f	f	NOUN
ejpam-5911	14	13	-	-	PUNCT
ejpam-5911	14	14	topology	topology	NOUN
ejpam-5911	14	15	being	be	AUX
ejpam-5911	14	16	a	a	DET
ejpam-5911	14	17	crisp	crisp	ADJ
ejpam-5911	14	18	subclass	subclass	NOUN
ejpam-5911	14	19	of	of	ADP
ejpam-5911	14	20	the	the	DET
ejpam-5911	14	21	class	class	NOUN
ejpam-5911	14	22	of	of	ADP
ejpam-5911	14	23	f	f	NOUN
ejpam-5911	14	24	-	-	PUNCT
ejpam-5911	14	25	sets	set	NOUN
ejpam-5911	14	26	and	and	CCONJ
ejpam-5911	14	27	fuzziness	fuzziness	NOUN
ejpam-5911	14	28	in	in	ADP
ejpam-5911	14	29	the	the	DET
ejpam-5911	14	30	notion	notion	NOUN
ejpam-5911	14	31	of	of	ADP
ejpam-5911	14	32	openness	openness	NOUN
ejpam-5911	14	33	of	of	ADP
ejpam-5911	14	34	an	an	DET
ejpam-5911	14	35	f	f	NOUN
ejpam-5911	14	36	-	-	PUNCT
ejpam-5911	14	37	set	set	NOUN
ejpam-5911	14	38	have	have	AUX
ejpam-5911	14	39	not	not	PART
ejpam-5911	14	40	been	be	AUX
ejpam-5911	14	41	considered	consider	VERB
ejpam-5911	14	42	,	,	PUNCT
ejpam-5911	14	43	which	which	PRON
ejpam-5911	14	44	seems	seem	VERB
ejpam-5911	14	45	to	to	PART
ejpam-5911	14	46	be	be	AUX
ejpam-5911	14	47	a	a	DET
ejpam-5911	14	48	drawback	drawback	NOUN
ejpam-5911	14	49	in	in	ADP
ejpam-5911	14	50	the	the	DET
ejpam-5911	14	51	process	process	NOUN
ejpam-5911	14	52	of	of	ADP
ejpam-5911	14	53	fuzzification	fuzzification	NOUN
ejpam-5911	14	54	of	of	ADP
ejpam-5911	14	55	a	a	DET
ejpam-5911	14	56	topological	topological	ADJ
ejpam-5911	14	57	space	space	NOUN
ejpam-5911	14	58	.	.	PUNCT
ejpam-5911	15	1	thus	thus	ADV
ejpam-5911	15	2	,	,	PUNCT
ejpam-5911	15	3	the	the	DET
ejpam-5911	15	4	author	author	NOUN
ejpam-5911	15	5	of	of	ADP
ejpam-5911	15	6	[	[	X
ejpam-5911	15	7	3	3	NUM
ejpam-5911	15	8	]	]	PUNCT
ejpam-5911	15	9	introduced	introduce	VERB
ejpam-5911	15	10	a	a	DET
ejpam-5911	15	11	novel	novel	ADJ
ejpam-5911	15	12	definition	definition	NOUN
ejpam-5911	15	13	of	of	ADP
ejpam-5911	15	14	an	an	DET
ejpam-5911	15	15	f	f	NOUN
ejpam-5911	15	16	-	-	PUNCT
ejpam-5911	15	17	topology	topology	NOUN
ejpam-5911	15	18	as	as	ADP
ejpam-5911	15	19	the	the	DET
ejpam-5911	15	20	concept	concept	NOUN
ejpam-5911	15	21	of	of	ADP
ejpam-5911	15	22	openness	openness	NOUN
ejpam-5911	15	23	∗corresponding	∗corresponde	VERB
ejpam-5911	15	24	author	author	NOUN
ejpam-5911	15	25	.	.	PUNCT
ejpam-5911	16	1	doi	doi	NOUN
ejpam-5911	16	2	:	:	PUNCT
ejpam-5911	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5911	https://doi.org/10.29020/nybg.ejpam.v18i2.5911	DET
ejpam-5911	16	4	email	email	NOUN
ejpam-5911	16	5	addresses	address	VERB
ejpam-5911	16	6	:	:	PUNCT
ejpam-5911	16	7	imtaha2010@yahoo.com	imtaha2010@yahoo.com	X
ejpam-5911	16	8	(	(	PUNCT
ejpam-5911	16	9	i.	i.	PROPN
ejpam-5911	16	10	m.	m.	PROPN
ejpam-5911	16	11	taha	taha	PROPN
ejpam-5911	16	12	)	)	PUNCT
ejpam-5911	16	13	,	,	PUNCT
ejpam-5911	16	14	jmufarij@ksu.edu.sa	jmufarij@ksu.edu.sa	PROPN
ejpam-5911	16	15	(	(	PUNCT
ejpam-5911	16	16	j.	j.	PROPN
ejpam-5911	16	17	al	al	PROPN
ejpam-5911	16	18	-	-	PUNCT
ejpam-5911	16	19	mufarrij	mufarrij	PROPN
ejpam-5911	16	20	)	)	PUNCT
ejpam-5911	16	21	,	,	PUNCT
ejpam-5911	16	22	osama.taha2015@yahoo.com	osama.taha2015@yahoo.com	NUM
ejpam-5911	16	23	(	(	PUNCT
ejpam-5911	16	24	o.	o.	PROPN
ejpam-5911	16	25	m.	m.	PROPN
ejpam-5911	16	26	taha	taha	PROPN
ejpam-5911	16	27	)	)	PUNCT
ejpam-5911	16	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5911	17	1	1	1	NUM
ejpam-5911	17	2	copyright	copyright	NOUN
ejpam-5911	17	3	:	:	PUNCT
ejpam-5911	17	4	©	©	PROPN
ejpam-5911	17	5	2025	2025	NUM
ejpam-5911	17	6	the	the	DET
ejpam-5911	17	7	author(s	author(s	NOUN
ejpam-5911	17	8	)	)	PUNCT
ejpam-5911	17	9	.	.	PUNCT
ejpam-5911	18	1	(	(	PUNCT
ejpam-5911	18	2	cc	cc	NOUN
ejpam-5911	18	3	by	by	ADP
ejpam-5911	18	4	-	-	PUNCT
ejpam-5911	18	5	nc	nc	PROPN
ejpam-5911	18	6	4.0	4.0	NUM
ejpam-5911	18	7	)	)	PUNCT
ejpam-5911	18	8	i.	i.	PROPN
ejpam-5911	18	9	m.	m.	PROPN
ejpam-5911	18	10	taha	taha	PROPN
ejpam-5911	18	11	,	,	PUNCT
ejpam-5911	18	12	j.	j.	PROPN
ejpam-5911	18	13	al	al	PROPN
ejpam-5911	18	14	-	-	PUNCT
ejpam-5911	18	15	mufarrij	mufarrij	PROPN
ejpam-5911	18	16	,	,	PUNCT
ejpam-5911	18	17	o.	o.	PROPN
ejpam-5911	18	18	m.	m.	PROPN
ejpam-5911	18	19	taha	taha	PROPN
ejpam-5911	18	20	/	/	PUNCT
ejpam-5911	18	21	eur	eur	PROPN
ejpam-5911	18	22	.	.	PUNCT
ejpam-5911	19	1	j.	j.	PROPN
ejpam-5911	19	2	pure	pure	PROPN
ejpam-5911	19	3	appl	appl	PROPN
ejpam-5911	19	4	.	.	PROPN
ejpam-5911	19	5	math	math	PROPN
ejpam-5911	19	6	,	,	PUNCT
ejpam-5911	19	7	18	18	NUM
ejpam-5911	19	8	(	(	PUNCT
ejpam-5911	19	9	2	2	NUM
ejpam-5911	19	10	)	)	PUNCT
ejpam-5911	19	11	(	(	PUNCT
ejpam-5911	19	12	2025	2025	NUM
ejpam-5911	19	13	)	)	PUNCT
ejpam-5911	19	14	,	,	PUNCT
ejpam-5911	19	15	5911	5911	NUM
ejpam-5911	19	16	2	2	NUM
ejpam-5911	19	17	of	of	ADP
ejpam-5911	19	18	27	27	NUM
ejpam-5911	19	19	of	of	ADP
ejpam-5911	19	20	f	f	NOUN
ejpam-5911	19	21	-	-	PUNCT
ejpam-5911	19	22	sets	set	NOUN
ejpam-5911	19	23	.	.	PUNCT
ejpam-5911	20	1	it	it	PRON
ejpam-5911	20	2	is	be	AUX
ejpam-5911	20	3	an	an	DET
ejpam-5911	20	4	extension	extension	NOUN
ejpam-5911	20	5	of	of	ADP
ejpam-5911	20	6	an	an	DET
ejpam-5911	20	7	f	f	NOUN
ejpam-5911	20	8	-	-	PUNCT
ejpam-5911	20	9	topology	topology	NOUN
ejpam-5911	20	10	introduced	introduce	VERB
ejpam-5911	20	11	by	by	ADP
ejpam-5911	20	12	chang	chang	PROPN
ejpam-5911	21	1	[	[	X
ejpam-5911	21	2	2	2	NUM
ejpam-5911	21	3	]	]	PUNCT
ejpam-5911	21	4	.	.	PUNCT
ejpam-5911	22	1	also	also	ADV
ejpam-5911	22	2	,	,	PUNCT
ejpam-5911	22	3	many	many	ADJ
ejpam-5911	22	4	researchers	researcher	NOUN
ejpam-5911	22	5	(	(	PUNCT
ejpam-5911	22	6	ramadan	ramadan	PROPN
ejpam-5911	22	7	[	[	X
ejpam-5911	22	8	4	4	NUM
ejpam-5911	22	9	]	]	PUNCT
ejpam-5911	22	10	,	,	PUNCT
ejpam-5911	22	11	chattopadhyay	chattopadhyay	PROPN
ejpam-5911	22	12	et	et	PROPN
ejpam-5911	22	13	.	.	PUNCT
ejpam-5911	23	1	al	al	PROPN
ejpam-5911	23	2	.	.	PUNCT
ejpam-5911	24	1	[	[	X
ejpam-5911	24	2	5	5	NUM
ejpam-5911	24	3	]	]	PUNCT
ejpam-5911	24	4	,	,	PUNCT
ejpam-5911	24	5	el	el	PROPN
ejpam-5911	24	6	gayyar	gayyar	PROPN
ejpam-5911	24	7	et	et	PROPN
ejpam-5911	24	8	.	.	PUNCT
ejpam-5911	25	1	al	al	PROPN
ejpam-5911	25	2	.	.	PUNCT
ejpam-5911	26	1	[	[	X
ejpam-5911	26	2	6	6	NUM
ejpam-5911	26	3	]	]	PUNCT
ejpam-5911	26	4	,	,	PUNCT
ejpam-5911	26	5	höhle	höhle	ADJ
ejpam-5911	26	6	and	and	CCONJ
ejpam-5911	26	7	šostak	šostak	ADJ
ejpam-5911	26	8	[	[	X
ejpam-5911	26	9	7	7	NUM
ejpam-5911	26	10	]	]	PUNCT
ejpam-5911	26	11	,	,	PUNCT
ejpam-5911	26	12	ramadan	ramadan	PROPN
ejpam-5911	26	13	et	et	PROPN
ejpam-5911	26	14	.	.	PUNCT
ejpam-5911	27	1	al	al	PROPN
ejpam-5911	27	2	.	.	PUNCT
ejpam-5911	28	1	[	[	X
ejpam-5911	28	2	8	8	NUM
ejpam-5911	28	3	]	]	PUNCT
ejpam-5911	28	4	,	,	PUNCT
ejpam-5911	28	5	kim	kim	PROPN
ejpam-5911	28	6	et	et	PROPN
ejpam-5911	28	7	.	.	PUNCT
ejpam-5911	29	1	al	al	PROPN
ejpam-5911	29	2	.	.	PUNCT
ejpam-5911	30	1	[	[	X
ejpam-5911	30	2	9	9	NUM
ejpam-5911	30	3	]	]	PUNCT
ejpam-5911	30	4	,	,	PUNCT
ejpam-5911	30	5	abbas	abbas	PROPN
ejpam-5911	31	1	[	[	X
ejpam-5911	31	2	10	10	NUM
ejpam-5911	31	3	,	,	PUNCT
ejpam-5911	31	4	11	11	NUM
ejpam-5911	31	5	]	]	PUNCT
ejpam-5911	31	6	,	,	PUNCT
ejpam-5911	31	7	kim	kim	PROPN
ejpam-5911	31	8	and	and	CCONJ
ejpam-5911	31	9	abbas	abbas	PROPN
ejpam-5911	32	1	[	[	X
ejpam-5911	32	2	12	12	NUM
ejpam-5911	32	3	]	]	PUNCT
ejpam-5911	32	4	,	,	PUNCT
ejpam-5911	32	5	aygun	aygun	NOUN
ejpam-5911	32	6	and	and	CCONJ
ejpam-5911	32	7	abbas	abbas	NOUN
ejpam-5911	33	1	[	[	X
ejpam-5911	33	2	13	13	NUM
ejpam-5911	33	3	,	,	PUNCT
ejpam-5911	33	4	14	14	NUM
ejpam-5911	33	5	]	]	PUNCT
ejpam-5911	33	6	,	,	PUNCT
ejpam-5911	33	7	li	li	PROPN
ejpam-5911	33	8	and	and	CCONJ
ejpam-5911	33	9	shi	shi	PROPN
ejpam-5911	34	1	[	[	X
ejpam-5911	34	2	15	15	NUM
ejpam-5911	34	3	,	,	PUNCT
ejpam-5911	34	4	16	16	NUM
ejpam-5911	34	5	]	]	PUNCT
ejpam-5911	34	6	,	,	PUNCT
ejpam-5911	34	7	shi	shi	PROPN
ejpam-5911	34	8	and	and	CCONJ
ejpam-5911	34	9	li	li	PROPN
ejpam-5911	35	1	[	[	X
ejpam-5911	35	2	17	17	NUM
ejpam-5911	35	3	]	]	PUNCT
ejpam-5911	35	4	,	,	PUNCT
ejpam-5911	35	5	fang	fang	X
ejpam-5911	35	6	and	and	CCONJ
ejpam-5911	35	7	guo	guo	PROPN
ejpam-5911	36	1	[	[	X
ejpam-5911	36	2	18	18	NUM
ejpam-5911	36	3	]	]	PUNCT
ejpam-5911	36	4	,	,	PUNCT
ejpam-5911	36	5	el	el	PROPN
ejpam-5911	36	6	-	-	PUNCT
ejpam-5911	36	7	dardery	dardery	NOUN
ejpam-5911	36	8	et	et	NOUN
ejpam-5911	36	9	.	.	PUNCT
ejpam-5911	37	1	al	al	PROPN
ejpam-5911	37	2	.	.	PUNCT
ejpam-5911	38	1	[	[	X
ejpam-5911	38	2	19	19	NUM
ejpam-5911	38	3	]	]	PUNCT
ejpam-5911	38	4	,	,	PUNCT
ejpam-5911	38	5	kalaivani	kalaivani	PROPN
ejpam-5911	38	6	and	and	CCONJ
ejpam-5911	38	7	roopkumar	roopkumar	PROPN
ejpam-5911	38	8	[	[	X
ejpam-5911	38	9	20	20	NUM
ejpam-5911	38	10	]	]	PUNCT
ejpam-5911	38	11	,	,	PUNCT
ejpam-5911	38	12	solovyov	solovyov	NOUN
ejpam-5911	38	13	[	[	X
ejpam-5911	38	14	21	21	NUM
ejpam-5911	38	15	]	]	PUNCT
ejpam-5911	38	16	,	,	PUNCT
ejpam-5911	38	17	minana	minana	PROPN
ejpam-5911	38	18	and	and	CCONJ
ejpam-5911	38	19	šostak	šostak	VERB
ejpam-5911	38	20	[	[	X
ejpam-5911	38	21	22	22	NUM
ejpam-5911	38	22	]	]	PUNCT
ejpam-5911	38	23	)	)	PUNCT
ejpam-5911	38	24	have	have	AUX
ejpam-5911	38	25	redefined	redefine	VERB
ejpam-5911	38	26	the	the	DET
ejpam-5911	38	27	same	same	ADJ
ejpam-5911	38	28	notion	notion	NOUN
ejpam-5911	38	29	and	and	CCONJ
ejpam-5911	38	30	studied	study	VERB
ejpam-5911	38	31	ft	ft	AUX
ejpam-5911	38	32	ss	ss	ADV
ejpam-5911	38	33	being	be	AUX
ejpam-5911	38	34	unaware	unaware	ADJ
ejpam-5911	38	35	of	of	ADP
ejpam-5911	38	36	šostak	šostak	NOUN
ejpam-5911	38	37	,	,	PUNCT
ejpam-5911	38	38	s	s	PART
ejpam-5911	38	39	work	work	NOUN
ejpam-5911	38	40	.	.	PUNCT
ejpam-5911	39	1	the	the	DET
ejpam-5911	39	2	notion	notion	NOUN
ejpam-5911	39	3	of	of	ADP
ejpam-5911	39	4	an	an	DET
ejpam-5911	39	5	intuitionistic	intuitionistic	ADJ
ejpam-5911	39	6	f	f	NOUN
ejpam-5911	39	7	-	-	PUNCT
ejpam-5911	39	8	set	set	NOUN
ejpam-5911	39	9	was	be	AUX
ejpam-5911	39	10	defined	define	VERB
ejpam-5911	39	11	by	by	ADP
ejpam-5911	39	12	atanassov	atanassov	NOUN
ejpam-5911	39	13	[	[	X
ejpam-5911	39	14	23	23	NUM
ejpam-5911	39	15	,	,	PUNCT
ejpam-5911	39	16	24	24	NUM
ejpam-5911	39	17	]	]	PUNCT
ejpam-5911	39	18	,	,	PUNCT
ejpam-5911	39	19	which	which	PRON
ejpam-5911	39	20	is	be	AUX
ejpam-5911	39	21	a	a	DET
ejpam-5911	39	22	generalization	generalization	NOUN
ejpam-5911	39	23	of	of	ADP
ejpam-5911	39	24	an	an	DET
ejpam-5911	39	25	f	f	NOUN
ejpam-5911	39	26	-	-	PUNCT
ejpam-5911	39	27	set	set	VERB
ejpam-5911	39	28	[	[	X
ejpam-5911	39	29	1	1	NUM
ejpam-5911	39	30	]	]	PUNCT
ejpam-5911	39	31	.	.	PUNCT
ejpam-5911	40	1	coker	coker	NOUN
ejpam-5911	41	1	[	[	X
ejpam-5911	41	2	25	25	NUM
ejpam-5911	41	3	,	,	PUNCT
ejpam-5911	41	4	26	26	NUM
ejpam-5911	41	5	]	]	PUNCT
ejpam-5911	41	6	presented	present	VERB
ejpam-5911	41	7	the	the	DET
ejpam-5911	41	8	notion	notion	NOUN
ejpam-5911	41	9	of	of	ADP
ejpam-5911	41	10	an	an	DET
ejpam-5911	41	11	intuitionistic	intuitionistic	ADJ
ejpam-5911	41	12	f	f	NOUN
ejpam-5911	41	13	-	-	PUNCT
ejpam-5911	41	14	topology	topology	NOUN
ejpam-5911	41	15	based	base	VERB
ejpam-5911	41	16	on	on	ADP
ejpam-5911	41	17	chang	chang	PROPN
ejpam-5911	41	18	,	,	PUNCT
ejpam-5911	41	19	s	s	PART
ejpam-5911	41	20	sense	sense	NOUN
ejpam-5911	41	21	[	[	X
ejpam-5911	41	22	2	2	NUM
ejpam-5911	41	23	]	]	PUNCT
ejpam-5911	41	24	.	.	PUNCT
ejpam-5911	42	1	after	after	ADP
ejpam-5911	42	2	that	that	PRON
ejpam-5911	42	3	,	,	PUNCT
ejpam-5911	42	4	the	the	DET
ejpam-5911	42	5	notion	notion	NOUN
ejpam-5911	42	6	of	of	ADP
ejpam-5911	42	7	an	an	DET
ejpam-5911	42	8	intuitionistic	intuitionistic	ADJ
ejpam-5911	42	9	ftopology	ftopology	NOUN
ejpam-5911	42	10	based	base	VERB
ejpam-5911	42	11	on	on	ADP
ejpam-5911	42	12	šostak	šostak	NOUN
ejpam-5911	42	13	,	,	PUNCT
ejpam-5911	42	14	s	s	PART
ejpam-5911	42	15	sense	sense	NOUN
ejpam-5911	43	1	[	[	X
ejpam-5911	43	2	3	3	NUM
ejpam-5911	43	3	]	]	PUNCT
ejpam-5911	43	4	was	be	AUX
ejpam-5911	43	5	introduced	introduce	VERB
ejpam-5911	43	6	by	by	ADP
ejpam-5911	43	7	the	the	DET
ejpam-5911	43	8	authors	author	NOUN
ejpam-5911	43	9	of	of	ADP
ejpam-5911	43	10	[	[	X
ejpam-5911	43	11	27	27	NUM
ejpam-5911	43	12	,	,	PUNCT
ejpam-5911	43	13	28	28	NUM
ejpam-5911	43	14	]	]	PUNCT
ejpam-5911	43	15	.	.	PUNCT
ejpam-5911	44	1	the	the	DET
ejpam-5911	44	2	name	name	NOUN
ejpam-5911	44	3	(	(	PUNCT
ejpam-5911	44	4	intuitionistic	intuitionistic	ADJ
ejpam-5911	44	5	)	)	PUNCT
ejpam-5911	44	6	was	be	AUX
ejpam-5911	44	7	replaced	replace	VERB
ejpam-5911	44	8	with	with	ADP
ejpam-5911	44	9	the	the	DET
ejpam-5911	44	10	name	name	NOUN
ejpam-5911	44	11	(	(	PUNCT
ejpam-5911	44	12	double	double	ADJ
ejpam-5911	44	13	)	)	PUNCT
ejpam-5911	44	14	by	by	ADP
ejpam-5911	44	15	garcia	garcia	PROPN
ejpam-5911	44	16	and	and	CCONJ
ejpam-5911	44	17	rodabaugh	rodabaugh	ADJ
ejpam-5911	44	18	[	[	X
ejpam-5911	44	19	29	29	NUM
ejpam-5911	44	20	]	]	PUNCT
ejpam-5911	44	21	.	.	PUNCT
ejpam-5911	45	1	in	in	ADP
ejpam-5911	45	2	addition	addition	NOUN
ejpam-5911	45	3	,	,	PUNCT
ejpam-5911	45	4	the	the	DET
ejpam-5911	45	5	notions	notion	NOUN
ejpam-5911	45	6	of	of	ADP
ejpam-5911	45	7	(	(	PUNCT
ejpam-5911	45	8	r	r	NOUN
ejpam-5911	45	9	,	,	PUNCT
ejpam-5911	45	10	s)-f	s)-f	NOUN
ejpam-5911	45	11	-	-	PUNCT
ejpam-5911	45	12	semi	semi	ADV
ejpam-5911	45	13	-	-	ADJ
ejpam-5911	45	14	open	open	ADJ
ejpam-5911	45	15	,	,	PUNCT
ejpam-5911	45	16	(	(	PUNCT
ejpam-5911	45	17	r	r	NOUN
ejpam-5911	45	18	,	,	PUNCT
ejpam-5911	45	19	s)-f	s)-f	NOUN
ejpam-5911	45	20	-	-	PUNCT
ejpam-5911	45	21	pre	pre	NOUN
ejpam-5911	45	22	-	-	ADJ
ejpam-5911	45	23	open	open	ADJ
ejpam-5911	45	24	,	,	PUNCT
ejpam-5911	45	25	and	and	CCONJ
ejpam-5911	45	26	(	(	PUNCT
ejpam-5911	45	27	r	r	NOUN
ejpam-5911	45	28	,	,	PUNCT
ejpam-5911	45	29	s)-f	s)-f	NOUN
ejpam-5911	45	30	-	-	PUNCT
ejpam-5911	45	31	α	α	NOUN
ejpam-5911	45	32	-	-	ADJ
ejpam-5911	45	33	open	open	ADJ
ejpam-5911	45	34	sets	set	NOUN
ejpam-5911	45	35	were	be	AUX
ejpam-5911	45	36	introduced	introduce	VERB
ejpam-5911	45	37	by	by	ADP
ejpam-5911	45	38	the	the	DET
ejpam-5911	45	39	authors	author	NOUN
ejpam-5911	45	40	of	of	ADP
ejpam-5911	45	41	[	[	X
ejpam-5911	45	42	30	30	NUM
ejpam-5911	45	43	,	,	PUNCT
ejpam-5911	45	44	31	31	NUM
ejpam-5911	45	45	]	]	PUNCT
ejpam-5911	45	46	based	base	VERB
ejpam-5911	45	47	on	on	ADP
ejpam-5911	45	48	šostak	šostak	NOUN
ejpam-5911	45	49	,	,	PUNCT
ejpam-5911	45	50	s	s	PART
ejpam-5911	45	51	sense	sense	NOUN
ejpam-5911	45	52	[	[	X
ejpam-5911	45	53	3	3	NUM
ejpam-5911	45	54	]	]	PUNCT
ejpam-5911	45	55	.	.	PUNCT
ejpam-5911	46	1	also	also	ADV
ejpam-5911	46	2	,	,	PUNCT
ejpam-5911	46	3	lots	lot	NOUN
ejpam-5911	46	4	of	of	ADP
ejpam-5911	46	5	creative	creative	ADJ
ejpam-5911	46	6	studies	study	NOUN
ejpam-5911	46	7	about	about	ADP
ejpam-5911	46	8	the	the	DET
ejpam-5911	46	9	theories	theory	NOUN
ejpam-5911	46	10	of	of	ADP
ejpam-5911	46	11	an	an	DET
ejpam-5911	46	12	intuitionistic	intuitionistic	ADJ
ejpam-5911	46	13	f	f	NOUN
ejpam-5911	46	14	-	-	PUNCT
ejpam-5911	46	15	set	set	NOUN
ejpam-5911	46	16	have	have	AUX
ejpam-5911	46	17	been	be	AUX
ejpam-5911	46	18	considered	consider	VERB
ejpam-5911	46	19	by	by	ADP
ejpam-5911	46	20	several	several	ADJ
ejpam-5911	46	21	researchers	researcher	NOUN
ejpam-5911	46	22	;	;	PUNCT
ejpam-5911	46	23	see	see	VERB
ejpam-5911	46	24	[	[	X
ejpam-5911	46	25	32–39	32–39	NUM
ejpam-5911	46	26	]	]	PUNCT
ejpam-5911	46	27	.	.	PUNCT
ejpam-5911	47	1	the	the	DET
ejpam-5911	47	2	layout	layout	NOUN
ejpam-5911	47	3	of	of	ADP
ejpam-5911	47	4	this	this	DET
ejpam-5911	47	5	study	study	NOUN
ejpam-5911	47	6	is	be	AUX
ejpam-5911	47	7	as	as	SCONJ
ejpam-5911	47	8	follows	follow	VERB
ejpam-5911	47	9	.	.	PUNCT
ejpam-5911	48	1	•	•	NOUN
ejpam-5911	48	2	in	in	ADP
ejpam-5911	48	3	section	section	NOUN
ejpam-5911	48	4	3	3	NUM
ejpam-5911	48	5	,	,	PUNCT
ejpam-5911	48	6	we	we	PRON
ejpam-5911	48	7	present	present	VERB
ejpam-5911	48	8	and	and	CCONJ
ejpam-5911	48	9	investigate	investigate	VERB
ejpam-5911	48	10	a	a	DET
ejpam-5911	48	11	novel	novel	ADJ
ejpam-5911	48	12	class	class	NOUN
ejpam-5911	48	13	of	of	ADP
ejpam-5911	48	14	f	f	NOUN
ejpam-5911	48	15	-	-	PUNCT
ejpam-5911	48	16	open	open	ADJ
ejpam-5911	48	17	sets	set	NOUN
ejpam-5911	48	18	in	in	ADP
ejpam-5911	48	19	dft	dft	PROPN
ejpam-5911	48	20	ss	ss	PROPN
ejpam-5911	48	21	based	base	VERB
ejpam-5911	48	22	on	on	ADP
ejpam-5911	48	23	šostak	šostak	NOUN
ejpam-5911	48	24	,	,	PUNCT
ejpam-5911	48	25	s	s	PART
ejpam-5911	48	26	sense	sense	NOUN
ejpam-5911	49	1	[	[	X
ejpam-5911	49	2	3	3	NUM
ejpam-5911	49	3	]	]	PUNCT
ejpam-5911	49	4	,	,	PUNCT
ejpam-5911	49	5	called	call	VERB
ejpam-5911	49	6	(	(	PUNCT
ejpam-5911	49	7	r	r	NOUN
ejpam-5911	49	8	,	,	PUNCT
ejpam-5911	49	9	s)-f	s)-f	NOUN
ejpam-5911	49	10	-	-	PUNCT
ejpam-5911	49	11	b	b	NOUN
ejpam-5911	49	12	-	-	PUNCT
ejpam-5911	49	13	open	open	ADJ
ejpam-5911	49	14	sets	set	NOUN
ejpam-5911	49	15	.	.	PUNCT
ejpam-5911	50	1	furthermore	furthermore	ADV
ejpam-5911	50	2	,	,	PUNCT
ejpam-5911	50	3	we	we	PRON
ejpam-5911	50	4	define	define	VERB
ejpam-5911	50	5	and	and	CCONJ
ejpam-5911	50	6	discuss	discuss	VERB
ejpam-5911	50	7	the	the	DET
ejpam-5911	50	8	notions	notion	NOUN
ejpam-5911	50	9	of	of	ADP
ejpam-5911	50	10	df	df	PROPN
ejpam-5911	50	11	-	-	PUNCT
ejpam-5911	50	12	b	b	NOUN
ejpam-5911	50	13	-	-	PUNCT
ejpam-5911	50	14	closure	closure	NOUN
ejpam-5911	50	15	operators	operator	NOUN
ejpam-5911	50	16	and	and	CCONJ
ejpam-5911	50	17	df	df	PROPN
ejpam-5911	50	18	-	-	PUNCT
ejpam-5911	50	19	b	b	NOUN
ejpam-5911	50	20	-	-	PUNCT
ejpam-5911	50	21	interior	interior	ADJ
ejpam-5911	50	22	operators	operator	NOUN
ejpam-5911	50	23	.	.	PUNCT
ejpam-5911	51	1	•	•	NUM
ejpam-5911	51	2	in	in	ADP
ejpam-5911	51	3	section	section	NOUN
ejpam-5911	51	4	4	4	NUM
ejpam-5911	51	5	,	,	PUNCT
ejpam-5911	51	6	we	we	PRON
ejpam-5911	51	7	introduce	introduce	VERB
ejpam-5911	51	8	and	and	CCONJ
ejpam-5911	51	9	discuss	discuss	VERB
ejpam-5911	51	10	the	the	DET
ejpam-5911	51	11	concept	concept	NOUN
ejpam-5911	51	12	of	of	ADP
ejpam-5911	51	13	df	df	PROPN
ejpam-5911	51	14	-	-	PUNCT
ejpam-5911	51	15	b	b	NOUN
ejpam-5911	51	16	-	-	PUNCT
ejpam-5911	51	17	continuity	continuity	NOUN
ejpam-5911	51	18	between	between	ADP
ejpam-5911	51	19	dft	dft	PROPN
ejpam-5911	51	20	ss	ss	PROPN
ejpam-5911	51	21	(	(	PUNCT
ejpam-5911	51	22	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	51	23	)	)	PUNCT
ejpam-5911	51	24	and	and	CCONJ
ejpam-5911	51	25	(	(	PUNCT
ejpam-5911	51	26	z	z	NOUN
ejpam-5911	51	27	,	,	PUNCT
ejpam-5911	51	28	𭟋	𭟋	NOUN
ejpam-5911	51	29	,	,	PUNCT
ejpam-5911	51	30	𭟋∗	𭟋∗	NOUN
ejpam-5911	51	31	)	)	PUNCT
ejpam-5911	51	32	.	.	PUNCT
ejpam-5911	52	1	in	in	ADP
ejpam-5911	52	2	addition	addition	NOUN
ejpam-5911	52	3	,	,	PUNCT
ejpam-5911	52	4	we	we	PRON
ejpam-5911	52	5	display	display	VERB
ejpam-5911	52	6	and	and	CCONJ
ejpam-5911	52	7	characterize	characterize	VERB
ejpam-5911	52	8	the	the	DET
ejpam-5911	52	9	concepts	concept	NOUN
ejpam-5911	52	10	of	of	ADP
ejpam-5911	52	11	df	df	NOUN
ejpam-5911	52	12	-	-	PUNCT
ejpam-5911	52	13	weakly	weakly	ADJ
ejpam-5911	52	14	b	b	NOUN
ejpam-5911	52	15	-	-	PUNCT
ejpam-5911	52	16	continuity	continuity	NOUN
ejpam-5911	52	17	and	and	CCONJ
ejpam-5911	52	18	df	df	NOUN
ejpam-5911	52	19	-	-	PUNCT
ejpam-5911	52	20	almost	almost	ADV
ejpam-5911	52	21	b	b	NOUN
ejpam-5911	52	22	-	-	PUNCT
ejpam-5911	52	23	continuity	continuity	NOUN
ejpam-5911	52	24	,	,	PUNCT
ejpam-5911	52	25	which	which	PRON
ejpam-5911	52	26	are	be	AUX
ejpam-5911	52	27	weaker	weak	ADJ
ejpam-5911	52	28	forms	form	NOUN
ejpam-5911	52	29	of	of	ADP
ejpam-5911	52	30	df	df	NOUN
ejpam-5911	52	31	-	-	PUNCT
ejpam-5911	52	32	bcontinuity	bcontinuity	NOUN
ejpam-5911	52	33	.	.	PUNCT
ejpam-5911	53	1	•	•	NUM
ejpam-5911	53	2	in	in	ADP
ejpam-5911	53	3	section	section	NOUN
ejpam-5911	53	4	5	5	NUM
ejpam-5911	53	5	,	,	PUNCT
ejpam-5911	53	6	we	we	PRON
ejpam-5911	53	7	explore	explore	VERB
ejpam-5911	53	8	and	and	CCONJ
ejpam-5911	53	9	characterize	characterize	VERB
ejpam-5911	53	10	some	some	DET
ejpam-5911	53	11	novel	novel	ADJ
ejpam-5911	53	12	df	df	NOUN
ejpam-5911	53	13	-	-	PUNCT
ejpam-5911	53	14	mappings	mapping	NOUN
ejpam-5911	53	15	using	use	VERB
ejpam-5911	53	16	(	(	PUNCT
ejpam-5911	53	17	r	r	NOUN
ejpam-5911	53	18	,	,	PUNCT
ejpam-5911	53	19	s)-f	s)-f	NOUN
ejpam-5911	53	20	-	-	PUNCT
ejpam-5911	53	21	bopen	bopen	NOUN
ejpam-5911	53	22	and	and	CCONJ
ejpam-5911	53	23	(	(	PUNCT
ejpam-5911	53	24	r	r	NOUN
ejpam-5911	53	25	,	,	PUNCT
ejpam-5911	53	26	s)-f	s)-f	NOUN
ejpam-5911	53	27	-	-	PUNCT
ejpam-5911	53	28	b	b	NOUN
ejpam-5911	53	29	-	-	PUNCT
ejpam-5911	53	30	closed	closed	ADJ
ejpam-5911	53	31	sets	set	NOUN
ejpam-5911	53	32	.	.	PUNCT
ejpam-5911	54	1	we	we	PRON
ejpam-5911	54	2	also	also	ADV
ejpam-5911	54	3	introduce	introduce	VERB
ejpam-5911	54	4	novel	novel	ADJ
ejpam-5911	54	5	types	type	NOUN
ejpam-5911	54	6	of	of	ADP
ejpam-5911	54	7	df	df	NOUN
ejpam-5911	54	8	-	-	PUNCT
ejpam-5911	54	9	separation	separation	NOUN
ejpam-5911	54	10	axioms	axiom	NOUN
ejpam-5911	54	11	,	,	PUNCT
ejpam-5911	54	12	called	call	VERB
ejpam-5911	54	13	(	(	PUNCT
ejpam-5911	54	14	r	r	NOUN
ejpam-5911	54	15	,	,	PUNCT
ejpam-5911	54	16	s)-f	s)-f	NOUN
ejpam-5911	54	17	-	-	PUNCT
ejpam-5911	54	18	b	b	NOUN
ejpam-5911	54	19	-	-	PUNCT
ejpam-5911	54	20	regular	regular	ADJ
ejpam-5911	54	21	and	and	CCONJ
ejpam-5911	54	22	(	(	PUNCT
ejpam-5911	54	23	r	r	NOUN
ejpam-5911	54	24	,	,	PUNCT
ejpam-5911	54	25	s)-f	s)-f	NOUN
ejpam-5911	54	26	-	-	PUNCT
ejpam-5911	54	27	b	b	NOUN
ejpam-5911	54	28	-	-	PUNCT
ejpam-5911	54	29	normal	normal	ADJ
ejpam-5911	54	30	spaces	space	NOUN
ejpam-5911	54	31	,	,	PUNCT
ejpam-5911	54	32	and	and	CCONJ
ejpam-5911	54	33	discuss	discuss	VERB
ejpam-5911	54	34	some	some	DET
ejpam-5911	54	35	properties	property	NOUN
ejpam-5911	54	36	of	of	ADP
ejpam-5911	54	37	them	they	PRON
ejpam-5911	54	38	.	.	PUNCT
ejpam-5911	55	1	•	•	NUM
ejpam-5911	55	2	in	in	ADP
ejpam-5911	55	3	section	section	NOUN
ejpam-5911	55	4	6	6	NUM
ejpam-5911	55	5	,	,	PUNCT
ejpam-5911	55	6	we	we	PRON
ejpam-5911	55	7	close	close	VERB
ejpam-5911	55	8	this	this	DET
ejpam-5911	55	9	paper	paper	NOUN
ejpam-5911	55	10	with	with	ADP
ejpam-5911	55	11	conclusions	conclusion	NOUN
ejpam-5911	55	12	and	and	CCONJ
ejpam-5911	55	13	proposed	propose	VERB
ejpam-5911	55	14	future	future	ADJ
ejpam-5911	55	15	papers	paper	NOUN
ejpam-5911	55	16	.	.	PUNCT
ejpam-5911	56	1	2	2	X
ejpam-5911	56	2	.	.	X
ejpam-5911	56	3	preliminaries	preliminary	NOUN
ejpam-5911	56	4	in	in	ADP
ejpam-5911	56	5	this	this	DET
ejpam-5911	56	6	study	study	NOUN
ejpam-5911	56	7	,	,	PUNCT
ejpam-5911	56	8	nonempty	nonempty	NOUN
ejpam-5911	56	9	sets	set	NOUN
ejpam-5911	56	10	will	will	AUX
ejpam-5911	56	11	be	be	AUX
ejpam-5911	56	12	denoted	denote	VERB
ejpam-5911	56	13	by	by	ADP
ejpam-5911	56	14	g	g	PROPN
ejpam-5911	56	15	,	,	PUNCT
ejpam-5911	56	16	z	z	NOUN
ejpam-5911	56	17	,	,	PUNCT
ejpam-5911	56	18	q	q	NOUN
ejpam-5911	56	19	,	,	PUNCT
ejpam-5911	56	20	etc	etc	X
ejpam-5911	56	21	.	.	X
ejpam-5911	57	1	on	on	ADP
ejpam-5911	57	2	g	g	PROPN
ejpam-5911	57	3	,	,	PUNCT
ejpam-5911	57	4	ig	ig	PROPN
ejpam-5911	57	5	is	be	AUX
ejpam-5911	57	6	the	the	DET
ejpam-5911	57	7	class	class	NOUN
ejpam-5911	57	8	of	of	ADP
ejpam-5911	57	9	all	all	DET
ejpam-5911	57	10	f	f	NOUN
ejpam-5911	57	11	-	-	PUNCT
ejpam-5911	57	12	sets	set	NOUN
ejpam-5911	57	13	.	.	PUNCT
ejpam-5911	58	1	for	for	ADP
ejpam-5911	58	2	any	any	DET
ejpam-5911	58	3	f	f	NOUN
ejpam-5911	58	4	-	-	PUNCT
ejpam-5911	58	5	set	set	VERB
ejpam-5911	58	6	m	m	NOUN
ejpam-5911	58	7	∈	∈	PROPN
ejpam-5911	58	8	ig	ig	PROPN
ejpam-5911	58	9	,	,	PUNCT
ejpam-5911	58	10	mc(g	mc(g	AUX
ejpam-5911	58	11	)	)	PUNCT
ejpam-5911	58	12	=	=	SYM
ejpam-5911	58	13	1	1	NUM
ejpam-5911	58	14	−m(g	−m(g	ADJ
ejpam-5911	58	15	)	)	PUNCT
ejpam-5911	58	16	,	,	PUNCT
ejpam-5911	58	17	for	for	ADP
ejpam-5911	58	18	each	each	DET
ejpam-5911	58	19	g	g	PROPN
ejpam-5911	58	20	∈	∈	PROPN
ejpam-5911	58	21	g.	g.	NOUN
ejpam-5911	58	22	also	also	ADV
ejpam-5911	58	23	,	,	PUNCT
ejpam-5911	58	24	for	for	ADP
ejpam-5911	58	25	θ	θ	PROPN
ejpam-5911	58	26	∈	∈	PROPN
ejpam-5911	58	27	i	i	PRON
ejpam-5911	58	28	,	,	PUNCT
ejpam-5911	58	29	θ(g	θ(g	ADJ
ejpam-5911	58	30	)	)	PUNCT
ejpam-5911	58	31	=	=	SYM
ejpam-5911	58	32	θ	θ	NOUN
ejpam-5911	58	33	,	,	PUNCT
ejpam-5911	58	34	for	for	ADP
ejpam-5911	58	35	each	each	DET
ejpam-5911	58	36	g	g	PROPN
ejpam-5911	58	37	∈	∈	PROPN
ejpam-5911	58	38	g.	g.	NOUN
ejpam-5911	58	39	an	an	DET
ejpam-5911	58	40	f	f	NOUN
ejpam-5911	58	41	-	-	PUNCT
ejpam-5911	58	42	point	point	NOUN
ejpam-5911	58	43	gθ	gθ	NOUN
ejpam-5911	58	44	on	on	ADP
ejpam-5911	58	45	g	g	PROPN
ejpam-5911	58	46	is	be	AUX
ejpam-5911	58	47	an	an	DET
ejpam-5911	58	48	f	f	NOUN
ejpam-5911	58	49	-	-	PUNCT
ejpam-5911	58	50	set	set	NOUN
ejpam-5911	58	51	,	,	PUNCT
ejpam-5911	58	52	and	and	CCONJ
ejpam-5911	58	53	is	be	AUX
ejpam-5911	58	54	defined	define	VERB
ejpam-5911	58	55	as	as	SCONJ
ejpam-5911	58	56	follows	follow	VERB
ejpam-5911	58	57	:	:	PUNCT
ejpam-5911	58	58	gθ(v	gθ(v	NUM
ejpam-5911	58	59	)	)	PUNCT
ejpam-5911	59	1	=	=	SYM
ejpam-5911	59	2	θ	θ	NOUN
ejpam-5911	59	3	if	if	SCONJ
ejpam-5911	59	4	v	v	NOUN
ejpam-5911	59	5	=	=	SYM
ejpam-5911	59	6	g	g	NOUN
ejpam-5911	59	7	,	,	PUNCT
ejpam-5911	59	8	and	and	CCONJ
ejpam-5911	59	9	gθ(v	gθ(v	NUM
ejpam-5911	59	10	)	)	PUNCT
ejpam-5911	59	11	=	=	SYM
ejpam-5911	59	12	0	0	NUM
ejpam-5911	59	13	for	for	ADP
ejpam-5911	59	14	any	any	DET
ejpam-5911	59	15	v	v	NOUN
ejpam-5911	59	16	∈	∈	PRON
ejpam-5911	59	17	g−	g−	PROPN
ejpam-5911	59	18	{	{	PUNCT
ejpam-5911	59	19	g	g	NOUN
ejpam-5911	59	20	}	}	PUNCT
ejpam-5911	59	21	.	.	PUNCT
ejpam-5911	60	1	moreover	moreover	ADV
ejpam-5911	60	2	,	,	PUNCT
ejpam-5911	60	3	we	we	PRON
ejpam-5911	60	4	say	say	VERB
ejpam-5911	60	5	that	that	SCONJ
ejpam-5911	60	6	gθ	gθ	PROPN
ejpam-5911	60	7	belongs	belong	VERB
ejpam-5911	60	8	to	to	ADP
ejpam-5911	60	9	m	m	PROPN
ejpam-5911	60	10	∈	∈	PROPN
ejpam-5911	60	11	ig	ig	PROPN
ejpam-5911	60	12	(	(	PUNCT
ejpam-5911	60	13	gθ	gθ	PROPN
ejpam-5911	60	14	∈	∈	PROPN
ejpam-5911	60	15	m	m	PROPN
ejpam-5911	60	16	)	)	PUNCT
ejpam-5911	60	17	,	,	PUNCT
ejpam-5911	60	18	if	if	SCONJ
ejpam-5911	60	19	i.	i.	PROPN
ejpam-5911	60	20	m.	m.	PROPN
ejpam-5911	60	21	taha	taha	PROPN
ejpam-5911	60	22	,	,	PUNCT
ejpam-5911	60	23	j.	j.	PROPN
ejpam-5911	60	24	al	al	PROPN
ejpam-5911	60	25	-	-	PUNCT
ejpam-5911	60	26	mufarrij	mufarrij	PROPN
ejpam-5911	60	27	,	,	PUNCT
ejpam-5911	60	28	o.	o.	PROPN
ejpam-5911	60	29	m.	m.	PROPN
ejpam-5911	60	30	taha	taha	PROPN
ejpam-5911	60	31	/	/	PUNCT
ejpam-5911	60	32	eur	eur	PROPN
ejpam-5911	60	33	.	.	PUNCT
ejpam-5911	61	1	j.	j.	PROPN
ejpam-5911	61	2	pure	pure	PROPN
ejpam-5911	61	3	appl	appl	PROPN
ejpam-5911	61	4	.	.	PROPN
ejpam-5911	61	5	math	math	PROPN
ejpam-5911	61	6	,	,	PUNCT
ejpam-5911	61	7	18	18	NUM
ejpam-5911	61	8	(	(	PUNCT
ejpam-5911	61	9	2	2	NUM
ejpam-5911	61	10	)	)	PUNCT
ejpam-5911	61	11	(	(	PUNCT
ejpam-5911	61	12	2025	2025	NUM
ejpam-5911	61	13	)	)	PUNCT
ejpam-5911	61	14	,	,	PUNCT
ejpam-5911	61	15	5911	5911	NUM
ejpam-5911	61	16	3	3	NUM
ejpam-5911	61	17	of	of	ADP
ejpam-5911	61	18	27	27	NUM
ejpam-5911	61	19	θ	θ	PROPN
ejpam-5911	61	20	≤	≤	PROPN
ejpam-5911	61	21	m(g	m(g	PROPN
ejpam-5911	61	22	)	)	PUNCT
ejpam-5911	61	23	.	.	PUNCT
ejpam-5911	62	1	on	on	ADP
ejpam-5911	62	2	g	g	NOUN
ejpam-5911	62	3	,	,	PUNCT
ejpam-5911	62	4	pθ(g	pθ(g	ADJ
ejpam-5911	62	5	)	)	PUNCT
ejpam-5911	62	6	is	be	AUX
ejpam-5911	62	7	the	the	DET
ejpam-5911	62	8	class	class	NOUN
ejpam-5911	62	9	of	of	ADP
ejpam-5911	62	10	all	all	DET
ejpam-5911	62	11	f	f	NOUN
ejpam-5911	62	12	-	-	PUNCT
ejpam-5911	62	13	points	point	NOUN
ejpam-5911	62	14	.	.	PUNCT
ejpam-5911	63	1	on	on	ADP
ejpam-5911	63	2	g	g	PROPN
ejpam-5911	63	3	,	,	PUNCT
ejpam-5911	63	4	an	an	DET
ejpam-5911	63	5	f	f	NOUN
ejpam-5911	63	6	-	-	PUNCT
ejpam-5911	63	7	set	set	VERB
ejpam-5911	63	8	m	m	NOUN
ejpam-5911	63	9	∈	∈	NOUN
ejpam-5911	63	10	ig	ig	PROPN
ejpam-5911	63	11	is	be	AUX
ejpam-5911	63	12	a	a	DET
ejpam-5911	63	13	quasi	quasi	NOUN
ejpam-5911	63	14	-	-	NOUN
ejpam-5911	63	15	coincident	coincident	ADJ
ejpam-5911	63	16	with	with	ADP
ejpam-5911	63	17	n	n	DET
ejpam-5911	63	18	∈	∈	NOUN
ejpam-5911	63	19	ig	ig	PROPN
ejpam-5911	63	20	(	(	PUNCT
ejpam-5911	63	21	m	m	PROPN
ejpam-5911	63	22	q	q	PROPN
ejpam-5911	63	23	n	n	PROPN
ejpam-5911	63	24	)	)	PUNCT
ejpam-5911	63	25	,	,	PUNCT
ejpam-5911	63	26	if	if	SCONJ
ejpam-5911	63	27	there	there	PRON
ejpam-5911	63	28	is	be	VERB
ejpam-5911	63	29	g	g	PROPN
ejpam-5911	63	30	∈	∈	PROPN
ejpam-5911	63	31	g	g	NOUN
ejpam-5911	63	32	,	,	PUNCT
ejpam-5911	63	33	with	with	ADP
ejpam-5911	63	34	m(g	m(g	NOUN
ejpam-5911	63	35	)	)	PUNCT
ejpam-5911	64	1	+	+	NOUN
ejpam-5911	64	2	n	n	X
ejpam-5911	64	3	(	(	PUNCT
ejpam-5911	64	4	g	g	NOUN
ejpam-5911	64	5	)	)	PUNCT
ejpam-5911	64	6	>	>	X
ejpam-5911	65	1	1	1	X
ejpam-5911	65	2	.	.	PUNCT
ejpam-5911	65	3	otherwise	otherwise	ADV
ejpam-5911	65	4	,	,	PUNCT
ejpam-5911	65	5	m	m	VERB
ejpam-5911	65	6	is	be	AUX
ejpam-5911	65	7	not	not	PART
ejpam-5911	65	8	a	a	DET
ejpam-5911	65	9	quasi	quasi	NOUN
ejpam-5911	65	10	-	-	NOUN
ejpam-5911	65	11	coincident	coincident	ADJ
ejpam-5911	65	12	with	with	ADP
ejpam-5911	65	13	n	n	PROPN
ejpam-5911	65	14	(	(	PUNCT
ejpam-5911	65	15	m	m	PROPN
ejpam-5911	65	16	q	q	PROPN
ejpam-5911	65	17	n	n	PROPN
ejpam-5911	65	18	)	)	PUNCT
ejpam-5911	65	19	.	.	PUNCT
ejpam-5911	66	1	lemma	lemma	PROPN
ejpam-5911	66	2	1	1	NUM
ejpam-5911	66	3	.	.	PUNCT
ejpam-5911	67	1	[	[	X
ejpam-5911	67	2	40	40	NUM
ejpam-5911	67	3	]	]	PUNCT
ejpam-5911	67	4	let	let	VERB
ejpam-5911	67	5	m	m	PRON
ejpam-5911	67	6	,	,	PUNCT
ejpam-5911	67	7	n	n	PROPN
ejpam-5911	67	8	∈	∈	PROPN
ejpam-5911	67	9	ig	ig	PROPN
ejpam-5911	67	10	.	.	PUNCT
ejpam-5911	68	1	thus	thus	ADV
ejpam-5911	68	2	,	,	PUNCT
ejpam-5911	68	3	(	(	PUNCT
ejpam-5911	68	4	i	i	NOUN
ejpam-5911	68	5	)	)	PUNCT
ejpam-5911	68	6	m	m	VERB
ejpam-5911	68	7	q	q	NOUN
ejpam-5911	68	8	n	n	PRON
ejpam-5911	68	9	iff	iff	VERB
ejpam-5911	68	10	there	there	PRON
ejpam-5911	68	11	is	be	VERB
ejpam-5911	68	12	gθ	gθ	PROPN
ejpam-5911	68	13	∈	∈	NOUN
ejpam-5911	68	14	m	m	NOUN
ejpam-5911	68	15	such	such	ADJ
ejpam-5911	68	16	that	that	SCONJ
ejpam-5911	68	17	gθ	gθ	VERB
ejpam-5911	68	18	q	q	PROPN
ejpam-5911	68	19	n	n	PROPN
ejpam-5911	68	20	,	,	PUNCT
ejpam-5911	68	21	(	(	PUNCT
ejpam-5911	68	22	ii	ii	NOUN
ejpam-5911	68	23	)	)	PUNCT
ejpam-5911	68	24	m∧n	m∧n	NOUN
ejpam-5911	69	1	=	=	SYM
ejpam-5911	69	2	̸	̸	NUM
ejpam-5911	69	3	0	0	PUNCT
ejpam-5911	70	1	if	if	SCONJ
ejpam-5911	70	2	m	m	VERB
ejpam-5911	70	3	q	q	NOUN
ejpam-5911	70	4	n	n	ADJ
ejpam-5911	70	5	,	,	PUNCT
ejpam-5911	70	6	(	(	PUNCT
ejpam-5911	70	7	iii	iii	X
ejpam-5911	70	8	)	)	PUNCT
ejpam-5911	70	9	m	m	PROPN
ejpam-5911	70	10	q	q	NOUN
ejpam-5911	70	11	n	n	INTJ
ejpam-5911	70	12	iff	iff	VERB
ejpam-5911	70	13	m	m	VERB
ejpam-5911	70	14	≤	≤	NOUN
ejpam-5911	71	1	n	n	PROPN
ejpam-5911	71	2	c	c	NOUN
ejpam-5911	71	3	,	,	PUNCT
ejpam-5911	71	4	(	(	PUNCT
ejpam-5911	71	5	iv	iv	X
ejpam-5911	71	6	)	)	PUNCT
ejpam-5911	71	7	m	m	VERB
ejpam-5911	71	8	≤	≤	NOUN
ejpam-5911	72	1	n	n	PRON
ejpam-5911	72	2	iff	iff	PROPN
ejpam-5911	72	3	gθ	gθ	PROPN
ejpam-5911	72	4	∈	∈	PROPN
ejpam-5911	72	5	m	m	PROPN
ejpam-5911	72	6	implies	imply	VERB
ejpam-5911	72	7	gθ	gθ	PROPN
ejpam-5911	72	8	∈	∈	PROPN
ejpam-5911	72	9	n	n	PRON
ejpam-5911	72	10	iff	iff	PROPN
ejpam-5911	72	11	gθ	gθ	PROPN
ejpam-5911	72	12	q	q	PROPN
ejpam-5911	72	13	m	m	PROPN
ejpam-5911	72	14	implies	imply	VERB
ejpam-5911	72	15	gθ	gθ	PROPN
ejpam-5911	72	16	q	q	PROPN
ejpam-5911	72	17	n	n	PROPN
ejpam-5911	72	18	,	,	PUNCT
ejpam-5911	72	19	(	(	PUNCT
ejpam-5911	72	20	v	v	NOUN
ejpam-5911	72	21	)	)	PUNCT
ejpam-5911	72	22	gθ	gθ	PROPN
ejpam-5911	72	23	q	q	PROPN
ejpam-5911	72	24	∨	∨	PROPN
ejpam-5911	72	25	i∈γmi	i∈γmi	PROPN
ejpam-5911	72	26	iff	iff	PROPN
ejpam-5911	72	27	there	there	PRON
ejpam-5911	72	28	is	be	VERB
ejpam-5911	72	29	i	i	PROPN
ejpam-5911	72	30	◦	◦	NOUN
ejpam-5911	72	31	∈	∈	PROPN
ejpam-5911	72	32	γ	γ	NOUN
ejpam-5911	72	33	such	such	ADJ
ejpam-5911	72	34	that	that	SCONJ
ejpam-5911	72	35	gθ	gθ	PROPN
ejpam-5911	72	36	q	q	PROPN
ejpam-5911	72	37	mi	mi	PROPN
ejpam-5911	72	38	◦	◦	NOUN
ejpam-5911	72	39	.	.	PUNCT
ejpam-5911	73	1	definition	definition	NOUN
ejpam-5911	73	2	1	1	NUM
ejpam-5911	73	3	.	.	PUNCT
ejpam-5911	74	1	[	[	X
ejpam-5911	74	2	27	27	NUM
ejpam-5911	74	3	,	,	PUNCT
ejpam-5911	74	4	35	35	NUM
ejpam-5911	74	5	,	,	PUNCT
ejpam-5911	74	6	38	38	NUM
ejpam-5911	74	7	]	]	PUNCT
ejpam-5911	74	8	a	a	DET
ejpam-5911	74	9	double	double	ADJ
ejpam-5911	74	10	fuzzy	fuzzy	ADJ
ejpam-5911	74	11	topology	topology	NOUN
ejpam-5911	74	12	(	(	PUNCT
ejpam-5911	74	13	dft	dft	PROPN
ejpam-5911	74	14	)	)	PUNCT
ejpam-5911	74	15	on	on	ADP
ejpam-5911	74	16	g	g	PROPN
ejpam-5911	74	17	is	be	AUX
ejpam-5911	74	18	a	a	DET
ejpam-5911	74	19	pair	pair	NOUN
ejpam-5911	74	20	(	(	PUNCT
ejpam-5911	74	21	ℑ,ℑ∗	ℑ,ℑ∗	NOUN
ejpam-5911	74	22	)	)	PUNCT
ejpam-5911	74	23	of	of	ADP
ejpam-5911	74	24	the	the	DET
ejpam-5911	74	25	mappings	mapping	NOUN
ejpam-5911	74	26	ℑ,ℑ∗	ℑ,ℑ∗	NUM
ejpam-5911	74	27	:	:	PUNCT
ejpam-5911	75	1	ig	ig	PROPN
ejpam-5911	75	2	−→	−→	PROPN
ejpam-5911	76	1	i	i	PRON
ejpam-5911	76	2	,	,	PUNCT
ejpam-5911	76	3	which	which	PRON
ejpam-5911	76	4	satisfy	satisfy	VERB
ejpam-5911	76	5	the	the	DET
ejpam-5911	76	6	following	follow	VERB
ejpam-5911	76	7	conditions	condition	NOUN
ejpam-5911	76	8	:	:	PUNCT
ejpam-5911	76	9	(	(	PUNCT
ejpam-5911	76	10	i	i	NOUN
ejpam-5911	76	11	)	)	PUNCT
ejpam-5911	76	12	ℑ(m	ℑ(m	NUM
ejpam-5911	76	13	)	)	PUNCT
ejpam-5911	76	14	+	+	CCONJ
ejpam-5911	76	15	ℑ∗(m	ℑ∗(m	NOUN
ejpam-5911	76	16	)	)	PUNCT
ejpam-5911	76	17	≤	≤	NUM
ejpam-5911	76	18	1	1	NUM
ejpam-5911	76	19	,	,	PUNCT
ejpam-5911	76	20	∀	∀	VERB
ejpam-5911	76	21	m	m	NOUN
ejpam-5911	76	22	∈	∈	NOUN
ejpam-5911	76	23	ig	ig	PROPN
ejpam-5911	76	24	.	.	PUNCT
ejpam-5911	76	25	(	(	PUNCT
ejpam-5911	76	26	ii	ii	NOUN
ejpam-5911	76	27	)	)	PUNCT
ejpam-5911	76	28	ℑ(m∧n	ℑ(m∧n	PUNCT
ejpam-5911	76	29	)	)	PUNCT
ejpam-5911	76	30	≥	≥	NOUN
ejpam-5911	76	31	ℑ(m	ℑ(m	NUM
ejpam-5911	76	32	)	)	PUNCT
ejpam-5911	76	33	∧	∧	PROPN
ejpam-5911	76	34	ℑ(n	ℑ(n	PART
ejpam-5911	76	35	)	)	PUNCT
ejpam-5911	76	36	and	and	CCONJ
ejpam-5911	76	37	ℑ∗(m∧n	ℑ∗(m∧n	NOUN
ejpam-5911	76	38	)	)	PUNCT
ejpam-5911	76	39	≤	≤	NOUN
ejpam-5911	76	40	ℑ∗(m	ℑ∗(m	NOUN
ejpam-5911	76	41	)	)	PUNCT
ejpam-5911	76	42	∨	∨	NUM
ejpam-5911	76	43	ℑ∗(n	ℑ∗(n	NOUN
ejpam-5911	76	44	)	)	PUNCT
ejpam-5911	76	45	,	,	PUNCT
ejpam-5911	76	46	∀	∀	X
ejpam-5911	76	47	m	m	NOUN
ejpam-5911	76	48	,	,	PUNCT
ejpam-5911	76	49	n	n	PROPN
ejpam-5911	76	50	∈	∈	PROPN
ejpam-5911	76	51	ig	ig	PROPN
ejpam-5911	76	52	.	.	PUNCT
ejpam-5911	77	1	(	(	PUNCT
ejpam-5911	77	2	iii	iii	X
ejpam-5911	77	3	)	)	PUNCT
ejpam-5911	77	4	ℑ	ℑ	PROPN
ejpam-5911	77	5	(	(	PUNCT
ejpam-5911	77	6	∨	∨	NUM
ejpam-5911	77	7	i∈γmi	i∈γmi	PROPN
ejpam-5911	77	8	)	)	PUNCT
ejpam-5911	77	9	≥	≥	NOUN
ejpam-5911	77	10	∧	∧	PROPN
ejpam-5911	77	11	i∈γℑ(mi	i∈γℑ(mi	PROPN
ejpam-5911	77	12	)	)	PUNCT
ejpam-5911	77	13	and	and	CCONJ
ejpam-5911	77	14	ℑ∗	ℑ∗	NUM
ejpam-5911	77	15	(	(	PUNCT
ejpam-5911	77	16	∨	∨	NUM
ejpam-5911	77	17	i∈γmi	i∈γmi	PROPN
ejpam-5911	77	18	)	)	PUNCT
ejpam-5911	77	19	≤	≤	NOUN
ejpam-5911	77	20	∨	∨	NUM
ejpam-5911	77	21	i∈γℑ∗(mi	i∈γℑ∗(mi	NOUN
ejpam-5911	77	22	)	)	PUNCT
ejpam-5911	77	23	,	,	PUNCT
ejpam-5911	77	24	∀	∀	X
ejpam-5911	77	25	{	{	PUNCT
ejpam-5911	77	26	mi}i∈γ	mi}i∈γ	NUM
ejpam-5911	77	27	⊂	⊂	PROPN
ejpam-5911	77	28	ig	ig	PROPN
ejpam-5911	77	29	.	.	PUNCT
ejpam-5911	78	1	thus	thus	ADV
ejpam-5911	78	2	,	,	PUNCT
ejpam-5911	78	3	(	(	PUNCT
ejpam-5911	78	4	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	78	5	)	)	PUNCT
ejpam-5911	78	6	is	be	AUX
ejpam-5911	78	7	said	say	VERB
ejpam-5911	78	8	to	to	PART
ejpam-5911	78	9	be	be	AUX
ejpam-5911	78	10	an	an	DET
ejpam-5911	78	11	dft	dft	NOUN
ejpam-5911	78	12	s	s	VERB
ejpam-5911	78	13	based	base	VERB
ejpam-5911	78	14	on	on	ADP
ejpam-5911	78	15	šostak	šostak	NOUN
ejpam-5911	78	16	,	,	PUNCT
ejpam-5911	78	17	s	s	PART
ejpam-5911	78	18	sense	sense	NOUN
ejpam-5911	78	19	[	[	X
ejpam-5911	78	20	3	3	NUM
ejpam-5911	78	21	]	]	PUNCT
ejpam-5911	78	22	.	.	PUNCT
ejpam-5911	79	1	definition	definition	NOUN
ejpam-5911	79	2	2	2	NUM
ejpam-5911	79	3	.	.	PUNCT
ejpam-5911	80	1	[	[	X
ejpam-5911	80	2	28	28	NUM
ejpam-5911	80	3	,	,	PUNCT
ejpam-5911	80	4	30	30	NUM
ejpam-5911	80	5	,	,	PUNCT
ejpam-5911	80	6	35	35	NUM
ejpam-5911	80	7	]	]	PUNCT
ejpam-5911	80	8	in	in	ADP
ejpam-5911	80	9	an	an	DET
ejpam-5911	80	10	dft	dft	PROPN
ejpam-5911	80	11	s	s	X
ejpam-5911	80	12	(	(	PUNCT
ejpam-5911	80	13	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	80	14	)	)	PUNCT
ejpam-5911	80	15	,	,	PUNCT
ejpam-5911	80	16	for	for	ADP
ejpam-5911	80	17	each	each	DET
ejpam-5911	80	18	m	m	PROPN
ejpam-5911	80	19	∈	∈	PROPN
ejpam-5911	80	20	ig	ig	PROPN
ejpam-5911	80	21	,	,	PUNCT
ejpam-5911	80	22	r	r	NOUN
ejpam-5911	80	23	∈	∈	PROPN
ejpam-5911	80	24	i	i	NOUN
ejpam-5911	80	25	◦	◦	NOUN
ejpam-5911	80	26	,	,	PUNCT
ejpam-5911	80	27	and	and	CCONJ
ejpam-5911	80	28	s	s	PROPN
ejpam-5911	80	29	∈	∈	PROPN
ejpam-5911	80	30	i1	i1	PROPN
ejpam-5911	80	31	(	(	PUNCT
ejpam-5911	80	32	where	where	SCONJ
ejpam-5911	80	33	i	i	PRON
ejpam-5911	80	34	◦	◦	VERB
ejpam-5911	80	35	=	=	SYM
ejpam-5911	80	36	(	(	PUNCT
ejpam-5911	80	37	0	0	NUM
ejpam-5911	80	38	,	,	PUNCT
ejpam-5911	80	39	1	1	NUM
ejpam-5911	80	40	]	]	PUNCT
ejpam-5911	80	41	and	and	CCONJ
ejpam-5911	80	42	i1	i1	PROPN
ejpam-5911	80	43	=	=	PUNCT
ejpam-5911	81	1	[	[	X
ejpam-5911	81	2	0	0	NUM
ejpam-5911	81	3	,	,	PUNCT
ejpam-5911	81	4	1	1	NUM
ejpam-5911	81	5	)	)	PUNCT
ejpam-5911	81	6	)	)	PUNCT
ejpam-5911	81	7	,	,	PUNCT
ejpam-5911	81	8	we	we	PRON
ejpam-5911	81	9	define	define	VERB
ejpam-5911	81	10	df	df	PROPN
ejpam-5911	81	11	-	-	PUNCT
ejpam-5911	81	12	operators	operator	NOUN
ejpam-5911	81	13	cℑ∗	cℑ∗	NOUN
ejpam-5911	81	14	and	and	CCONJ
ejpam-5911	81	15	iℑ∗	iℑ∗	NOUN
ejpam-5911	81	16	:	:	PUNCT
ejpam-5911	81	17	ig×i	ig×i	NOUN
ejpam-5911	81	18	◦	◦	NOUN
ejpam-5911	81	19	×i1	×i1	NOUN
ejpam-5911	81	20	→	→	PUNCT
ejpam-5911	81	21	ig	ig	PROPN
ejpam-5911	81	22	as	as	SCONJ
ejpam-5911	81	23	follows	follow	VERB
ejpam-5911	81	24	:	:	PUNCT
ejpam-5911	81	25	cℑ∗(m	cℑ∗(m	VERB
ejpam-5911	81	26	,	,	PUNCT
ejpam-5911	81	27	r	r	NOUN
ejpam-5911	81	28	,	,	PUNCT
ejpam-5911	81	29	s	s	NOUN
ejpam-5911	81	30	)	)	PUNCT
ejpam-5911	81	31	=	=	SYM
ejpam-5911	81	32	∧	∧	NOUN
ejpam-5911	81	33	{	{	PUNCT
ejpam-5911	81	34	n	n	NOUN
ejpam-5911	81	35	∈	∈	NOUN
ejpam-5911	81	36	ig	ig	PROPN
ejpam-5911	81	37	:	:	PUNCT
ejpam-5911	81	38	m	m	VERB
ejpam-5911	81	39	≤	≤	ADJ
ejpam-5911	81	40	n	n	PRON
ejpam-5911	81	41	,	,	PUNCT
ejpam-5911	81	42	ℑ(n	ℑ(n	PROPN
ejpam-5911	81	43	c	c	NOUN
ejpam-5911	81	44	)	)	PUNCT
ejpam-5911	81	45	≥	≥	NOUN
ejpam-5911	81	46	r,ℑ∗(n	r,ℑ∗(n	NOUN
ejpam-5911	81	47	c	c	NOUN
ejpam-5911	81	48	)	)	PUNCT
ejpam-5911	81	49	≤	≤	NOUN
ejpam-5911	82	1	s	s	PART
ejpam-5911	82	2	}	}	PUNCT
ejpam-5911	82	3	.	.	PUNCT
ejpam-5911	83	1	iℑ∗(m	iℑ∗(m	PROPN
ejpam-5911	83	2	,	,	PUNCT
ejpam-5911	83	3	r	r	NOUN
ejpam-5911	83	4	,	,	PUNCT
ejpam-5911	83	5	s	s	PART
ejpam-5911	83	6	)	)	PUNCT
ejpam-5911	83	7	=	=	SYM
ejpam-5911	83	8	∨	∨	X
ejpam-5911	83	9	{	{	PUNCT
ejpam-5911	83	10	n	n	NOUN
ejpam-5911	83	11	∈	∈	NOUN
ejpam-5911	83	12	ig	ig	PROPN
ejpam-5911	83	13	:	:	PUNCT
ejpam-5911	83	14	n	n	PRON
ejpam-5911	83	15	≤	≤	NUM
ejpam-5911	83	16	m	m	NOUN
ejpam-5911	83	17	,	,	PUNCT
ejpam-5911	83	18	ℑ(n	ℑ(n	PART
ejpam-5911	83	19	)	)	PUNCT
ejpam-5911	83	20	≥	≥	NOUN
ejpam-5911	83	21	r,ℑ∗(n	r,ℑ∗(n	NOUN
ejpam-5911	83	22	)	)	PUNCT
ejpam-5911	83	23	≤	≤	NUM
ejpam-5911	83	24	s	s	PART
ejpam-5911	83	25	}	}	PUNCT
ejpam-5911	83	26	.	.	PUNCT
ejpam-5911	84	1	i.	i.	PROPN
ejpam-5911	84	2	m.	m.	PROPN
ejpam-5911	84	3	taha	taha	PROPN
ejpam-5911	84	4	,	,	PUNCT
ejpam-5911	84	5	j.	j.	PROPN
ejpam-5911	84	6	al	al	PROPN
ejpam-5911	84	7	-	-	PUNCT
ejpam-5911	84	8	mufarrij	mufarrij	PROPN
ejpam-5911	84	9	,	,	PUNCT
ejpam-5911	84	10	o.	o.	PROPN
ejpam-5911	84	11	m.	m.	PROPN
ejpam-5911	84	12	taha	taha	PROPN
ejpam-5911	84	13	/	/	PUNCT
ejpam-5911	84	14	eur	eur	PROPN
ejpam-5911	84	15	.	.	PUNCT
ejpam-5911	85	1	j.	j.	PROPN
ejpam-5911	85	2	pure	pure	PROPN
ejpam-5911	85	3	appl	appl	PROPN
ejpam-5911	85	4	.	.	PROPN
ejpam-5911	85	5	math	math	PROPN
ejpam-5911	85	6	,	,	PUNCT
ejpam-5911	85	7	18	18	NUM
ejpam-5911	85	8	(	(	PUNCT
ejpam-5911	85	9	2	2	NUM
ejpam-5911	85	10	)	)	PUNCT
ejpam-5911	85	11	(	(	PUNCT
ejpam-5911	85	12	2025	2025	NUM
ejpam-5911	85	13	)	)	PUNCT
ejpam-5911	85	14	,	,	PUNCT
ejpam-5911	85	15	5911	5911	NUM
ejpam-5911	85	16	4	4	NUM
ejpam-5911	85	17	of	of	ADP
ejpam-5911	85	18	27	27	NUM
ejpam-5911	85	19	definition	definition	NOUN
ejpam-5911	85	20	3	3	NUM
ejpam-5911	85	21	.	.	PUNCT
ejpam-5911	86	1	[	[	X
ejpam-5911	86	2	30	30	NUM
ejpam-5911	86	3	,	,	PUNCT
ejpam-5911	86	4	31	31	NUM
ejpam-5911	86	5	,	,	PUNCT
ejpam-5911	86	6	35	35	NUM
ejpam-5911	86	7	]	]	PUNCT
ejpam-5911	86	8	let	let	VERB
ejpam-5911	86	9	(	(	PUNCT
ejpam-5911	86	10	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	86	11	)	)	PUNCT
ejpam-5911	86	12	be	be	VERB
ejpam-5911	86	13	an	an	DET
ejpam-5911	86	14	dft	dft	NOUN
ejpam-5911	86	15	s	s	PROPN
ejpam-5911	86	16	,	,	PUNCT
ejpam-5911	86	17	r	r	NOUN
ejpam-5911	86	18	∈	∈	PROPN
ejpam-5911	86	19	i	i	NOUN
ejpam-5911	86	20	◦	◦	NOUN
ejpam-5911	86	21	,	,	PUNCT
ejpam-5911	86	22	and	and	CCONJ
ejpam-5911	86	23	s	s	PROPN
ejpam-5911	86	24	∈	∈	PROPN
ejpam-5911	86	25	i1	i1	PROPN
ejpam-5911	86	26	.	.	PUNCT
ejpam-5911	87	1	an	an	DET
ejpam-5911	87	2	fset	fset	NOUN
ejpam-5911	87	3	m	m	PROPN
ejpam-5911	87	4	∈	∈	NOUN
ejpam-5911	87	5	ig	ig	PROPN
ejpam-5911	87	6	is	be	AUX
ejpam-5911	87	7	said	say	VERB
ejpam-5911	87	8	to	to	PART
ejpam-5911	87	9	be	be	AUX
ejpam-5911	87	10	(	(	PUNCT
ejpam-5911	87	11	r	r	NOUN
ejpam-5911	87	12	,	,	PUNCT
ejpam-5911	87	13	s)-f	s)-f	NOUN
ejpam-5911	87	14	-	-	PUNCT
ejpam-5911	87	15	regularly	regularly	ADV
ejpam-5911	87	16	-	-	PUNCT
ejpam-5911	87	17	open	open	ADJ
ejpam-5911	87	18	(	(	PUNCT
ejpam-5911	87	19	resp	resp	NOUN
ejpam-5911	87	20	.	.	PUNCT
ejpam-5911	88	1	(	(	PUNCT
ejpam-5911	88	2	r	r	NOUN
ejpam-5911	88	3	,	,	PUNCT
ejpam-5911	88	4	s)-f	s)-f	NOUN
ejpam-5911	88	5	-	-	PUNCT
ejpam-5911	88	6	pre	pre	NOUN
ejpam-5911	88	7	-	-	ADJ
ejpam-5911	88	8	open	open	ADJ
ejpam-5911	88	9	,	,	PUNCT
ejpam-5911	88	10	(	(	PUNCT
ejpam-5911	88	11	r	r	NOUN
ejpam-5911	88	12	,	,	PUNCT
ejpam-5911	88	13	s)-f	s)-f	NOUN
ejpam-5911	88	14	-	-	PUNCT
ejpam-5911	88	15	semiopen	semiopen	ADJ
ejpam-5911	88	16	,	,	PUNCT
ejpam-5911	88	17	(	(	PUNCT
ejpam-5911	88	18	r	r	NOUN
ejpam-5911	88	19	,	,	PUNCT
ejpam-5911	88	20	s)-f	s)-f	NOUN
ejpam-5911	88	21	-	-	PUNCT
ejpam-5911	88	22	β	β	NOUN
ejpam-5911	88	23	-	-	ADJ
ejpam-5911	88	24	open	open	ADJ
ejpam-5911	88	25	,	,	PUNCT
ejpam-5911	88	26	and	and	CCONJ
ejpam-5911	88	27	(	(	PUNCT
ejpam-5911	88	28	r	r	NOUN
ejpam-5911	88	29	,	,	PUNCT
ejpam-5911	88	30	s)-f	s)-f	NOUN
ejpam-5911	88	31	-	-	PUNCT
ejpam-5911	88	32	α	α	NOUN
ejpam-5911	88	33	-	-	NOUN
ejpam-5911	88	34	open	open	ADJ
ejpam-5911	88	35	)	)	PUNCT
ejpam-5911	88	36	if	if	SCONJ
ejpam-5911	88	37	m	m	NOUN
ejpam-5911	88	38	=	=	SYM
ejpam-5911	88	39	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	88	40	,	,	PUNCT
ejpam-5911	88	41	r	r	NOUN
ejpam-5911	88	42	,	,	PUNCT
ejpam-5911	88	43	s	s	PART
ejpam-5911	88	44	)	)	PUNCT
ejpam-5911	88	45	,	,	PUNCT
ejpam-5911	88	46	r	r	NOUN
ejpam-5911	88	47	,	,	PUNCT
ejpam-5911	88	48	s	s	PART
ejpam-5911	88	49	)	)	PUNCT
ejpam-5911	88	50	(	(	PUNCT
ejpam-5911	88	51	resp	resp	NOUN
ejpam-5911	88	52	.	.	PUNCT
ejpam-5911	89	1	m	m	VERB
ejpam-5911	89	2	≤	≤	ADJ
ejpam-5911	89	3	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	89	4	,	,	PUNCT
ejpam-5911	89	5	r	r	NOUN
ejpam-5911	89	6	,	,	PUNCT
ejpam-5911	89	7	s	s	PART
ejpam-5911	89	8	)	)	PUNCT
ejpam-5911	89	9	,	,	PUNCT
ejpam-5911	89	10	r	r	NOUN
ejpam-5911	89	11	,	,	PUNCT
ejpam-5911	89	12	s),m	s),m	ADJ
ejpam-5911	89	13	≤	≤	NOUN
ejpam-5911	89	14	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	PROPN
ejpam-5911	89	15	,	,	PUNCT
ejpam-5911	89	16	r	r	NOUN
ejpam-5911	89	17	,	,	PUNCT
ejpam-5911	89	18	s	s	PART
ejpam-5911	89	19	)	)	PUNCT
ejpam-5911	89	20	,	,	PUNCT
ejpam-5911	89	21	r	r	NOUN
ejpam-5911	89	22	,	,	PUNCT
ejpam-5911	89	23	s),m	s),m	ADJ
ejpam-5911	89	24	≤	≤	ADJ
ejpam-5911	89	25	cℑ∗(iℑ∗(cℑ∗(m	cℑ∗(iℑ∗(cℑ∗(m	NOUN
ejpam-5911	89	26	,	,	PUNCT
ejpam-5911	89	27	r	r	NOUN
ejpam-5911	89	28	,	,	PUNCT
ejpam-5911	89	29	s	s	PART
ejpam-5911	89	30	)	)	PUNCT
ejpam-5911	89	31	,	,	PUNCT
ejpam-5911	89	32	r	r	NOUN
ejpam-5911	89	33	,	,	PUNCT
ejpam-5911	89	34	s	s	PART
ejpam-5911	89	35	)	)	PUNCT
ejpam-5911	89	36	,	,	PUNCT
ejpam-5911	89	37	r	r	NOUN
ejpam-5911	89	38	,	,	PUNCT
ejpam-5911	89	39	s	s	NOUN
ejpam-5911	89	40	)	)	PUNCT
ejpam-5911	89	41	,	,	PUNCT
ejpam-5911	89	42	and	and	CCONJ
ejpam-5911	89	43	m	m	PRON
ejpam-5911	89	44	≤	≤	NOUN
ejpam-5911	89	45	iℑ∗(cℑ∗(iℑ∗(m	iℑ∗(cℑ∗(iℑ∗(m	NOUN
ejpam-5911	89	46	,	,	PUNCT
ejpam-5911	89	47	r	r	NOUN
ejpam-5911	89	48	,	,	PUNCT
ejpam-5911	89	49	s	s	PART
ejpam-5911	89	50	)	)	PUNCT
ejpam-5911	89	51	,	,	PUNCT
ejpam-5911	89	52	r	r	NOUN
ejpam-5911	89	53	,	,	PUNCT
ejpam-5911	89	54	s	s	PART
ejpam-5911	89	55	)	)	PUNCT
ejpam-5911	89	56	,	,	PUNCT
ejpam-5911	89	57	r	r	NOUN
ejpam-5911	89	58	,	,	PUNCT
ejpam-5911	89	59	s	s	NOUN
ejpam-5911	89	60	)	)	PUNCT
ejpam-5911	89	61	)	)	PUNCT
ejpam-5911	89	62	.	.	PUNCT
ejpam-5911	90	1	definition	definition	NOUN
ejpam-5911	90	2	4	4	NUM
ejpam-5911	90	3	.	.	PUNCT
ejpam-5911	91	1	[	[	X
ejpam-5911	91	2	28	28	NUM
ejpam-5911	91	3	,	,	PUNCT
ejpam-5911	91	4	35	35	NUM
ejpam-5911	91	5	,	,	PUNCT
ejpam-5911	91	6	38	38	NUM
ejpam-5911	91	7	]	]	PUNCT
ejpam-5911	92	1	an	an	DET
ejpam-5911	92	2	f	f	X
ejpam-5911	92	3	-	-	PUNCT
ejpam-5911	92	4	mapping	mapping	NOUN
ejpam-5911	92	5	p	p	NOUN
ejpam-5911	92	6	:	:	PUNCT
ejpam-5911	92	7	(	(	PUNCT
ejpam-5911	92	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	92	9	)	)	PUNCT
ejpam-5911	92	10	−→	−→	NOUN
ejpam-5911	92	11	(	(	PUNCT
ejpam-5911	92	12	z	z	NOUN
ejpam-5911	92	13	,	,	PUNCT
ejpam-5911	92	14	𭟋	𭟋	NOUN
ejpam-5911	92	15	,	,	PUNCT
ejpam-5911	92	16	𭟋∗	𭟋∗	NOUN
ejpam-5911	92	17	)	)	PUNCT
ejpam-5911	92	18	is	be	AUX
ejpam-5911	92	19	said	say	VERB
ejpam-5911	92	20	to	to	PART
ejpam-5911	92	21	be	be	AUX
ejpam-5911	92	22	(	(	PUNCT
ejpam-5911	92	23	i	i	NOUN
ejpam-5911	92	24	)	)	PUNCT
ejpam-5911	92	25	df	df	NOUN
ejpam-5911	92	26	-	-	PUNCT
ejpam-5911	92	27	continuous	continuous	ADJ
ejpam-5911	92	28	if	if	SCONJ
ejpam-5911	92	29	ℑ(p−1(n	ℑ(p−1(n	NOUN
ejpam-5911	92	30	)	)	PUNCT
ejpam-5911	92	31	)	)	PUNCT
ejpam-5911	92	32	≥	≥	NOUN
ejpam-5911	92	33	𭟋(n	𭟋(n	PROPN
ejpam-5911	92	34	)	)	PUNCT
ejpam-5911	92	35	and	and	CCONJ
ejpam-5911	92	36	ℑ∗(p−1(n	ℑ∗(p−1(n	NOUN
ejpam-5911	92	37	)	)	PUNCT
ejpam-5911	92	38	)	)	PUNCT
ejpam-5911	93	1	≤	≤	NUM
ejpam-5911	93	2	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	93	3	)	)	PUNCT
ejpam-5911	93	4	,	,	PUNCT
ejpam-5911	93	5	∀	∀	X
ejpam-5911	93	6	n	n	PRON
ejpam-5911	93	7	∈	∈	NOUN
ejpam-5911	93	8	iz	iz	INTJ
ejpam-5911	93	9	;	;	PUNCT
ejpam-5911	93	10	(	(	PUNCT
ejpam-5911	93	11	ii	ii	NOUN
ejpam-5911	93	12	)	)	PUNCT
ejpam-5911	93	13	df	df	NOUN
ejpam-5911	93	14	-	-	PUNCT
ejpam-5911	93	15	open	open	ADJ
ejpam-5911	93	16	if	if	SCONJ
ejpam-5911	93	17	𭟋(p(m	𭟋(p(m	NOUN
ejpam-5911	93	18	)	)	PUNCT
ejpam-5911	93	19	)	)	PUNCT
ejpam-5911	93	20	≥	≥	NOUN
ejpam-5911	93	21	ℑ(m	ℑ(m	NUM
ejpam-5911	93	22	)	)	PUNCT
ejpam-5911	93	23	and	and	CCONJ
ejpam-5911	93	24	𭟋∗(p(m	𭟋∗(p(m	X
ejpam-5911	93	25	)	)	PUNCT
ejpam-5911	93	26	)	)	PUNCT
ejpam-5911	94	1	≤	≤	NUM
ejpam-5911	94	2	ℑ∗(m	ℑ∗(m	NOUN
ejpam-5911	94	3	)	)	PUNCT
ejpam-5911	94	4	,	,	PUNCT
ejpam-5911	94	5	∀	∀	PUNCT
ejpam-5911	94	6	m	m	VERB
ejpam-5911	94	7	∈	∈	NOUN
ejpam-5911	94	8	ig	ig	PROPN
ejpam-5911	94	9	;	;	PUNCT
ejpam-5911	94	10	(	(	PUNCT
ejpam-5911	94	11	iii	iii	X
ejpam-5911	94	12	)	)	PUNCT
ejpam-5911	94	13	df	df	NOUN
ejpam-5911	94	14	-	-	PUNCT
ejpam-5911	94	15	closed	closed	ADJ
ejpam-5911	94	16	if	if	SCONJ
ejpam-5911	94	17	𭟋((p(m))c	𭟋((p(m))c	NUM
ejpam-5911	94	18	)	)	PUNCT
ejpam-5911	94	19	≥	≥	NOUN
ejpam-5911	94	20	ℑ(mc	ℑ(mc	VERB
ejpam-5911	94	21	)	)	PUNCT
ejpam-5911	94	22	and	and	CCONJ
ejpam-5911	94	23	𭟋∗((p(m))c	𭟋∗((p(m))c	PROPN
ejpam-5911	94	24	)	)	PUNCT
ejpam-5911	94	25	≤	≤	NOUN
ejpam-5911	94	26	ℑ∗(mc	ℑ∗(mc	VERB
ejpam-5911	94	27	)	)	PUNCT
ejpam-5911	94	28	,	,	PUNCT
ejpam-5911	94	29	∀	∀	PUNCT
ejpam-5911	95	1	m	m	VERB
ejpam-5911	95	2	∈	∈	NOUN
ejpam-5911	95	3	ig	ig	PROPN
ejpam-5911	95	4	.	.	PUNCT
ejpam-5911	95	5	definition	definition	NOUN
ejpam-5911	95	6	5	5	NUM
ejpam-5911	95	7	.	.	PUNCT
ejpam-5911	96	1	[	[	X
ejpam-5911	96	2	30	30	NUM
ejpam-5911	96	3	,	,	PUNCT
ejpam-5911	96	4	31	31	NUM
ejpam-5911	96	5	,	,	PUNCT
ejpam-5911	96	6	35	35	NUM
ejpam-5911	96	7	]	]	PUNCT
ejpam-5911	96	8	let	let	VERB
ejpam-5911	96	9	(	(	PUNCT
ejpam-5911	96	10	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	96	11	)	)	PUNCT
ejpam-5911	96	12	and	and	CCONJ
ejpam-5911	96	13	(	(	PUNCT
ejpam-5911	96	14	z	z	NOUN
ejpam-5911	96	15	,	,	PUNCT
ejpam-5911	96	16	𭟋	𭟋	NOUN
ejpam-5911	96	17	,	,	PUNCT
ejpam-5911	96	18	𭟋∗	𭟋∗	NOUN
ejpam-5911	96	19	)	)	PUNCT
ejpam-5911	96	20	be	be	AUX
ejpam-5911	96	21	dft	dft	PROPN
ejpam-5911	96	22	ss	ss	PROPN
ejpam-5911	96	23	,	,	PUNCT
ejpam-5911	96	24	r	r	NOUN
ejpam-5911	96	25	∈	∈	PROPN
ejpam-5911	97	1	i	i	NOUN
ejpam-5911	97	2	◦	◦	NOUN
ejpam-5911	97	3	,	,	PUNCT
ejpam-5911	97	4	and	and	CCONJ
ejpam-5911	97	5	s	s	PROPN
ejpam-5911	97	6	∈	∈	PROPN
ejpam-5911	97	7	i1	i1	PROPN
ejpam-5911	97	8	.	.	PUNCT
ejpam-5911	98	1	an	an	DET
ejpam-5911	98	2	f	f	X
ejpam-5911	98	3	-	-	PUNCT
ejpam-5911	98	4	mapping	mapping	NOUN
ejpam-5911	98	5	p	p	NOUN
ejpam-5911	98	6	:	:	PUNCT
ejpam-5911	98	7	ig	ig	PROPN
ejpam-5911	98	8	−→	−→	NOUN
ejpam-5911	98	9	iz	iz	INTJ
ejpam-5911	98	10	is	be	AUX
ejpam-5911	98	11	said	say	VERB
ejpam-5911	98	12	to	to	PART
ejpam-5911	98	13	be	be	AUX
ejpam-5911	98	14	df	df	PROPN
ejpam-5911	98	15	-	-	PUNCT
ejpam-5911	98	16	α	α	NOUN
ejpam-5911	98	17	-	-	ADJ
ejpam-5911	98	18	continuous	continuous	ADJ
ejpam-5911	98	19	(	(	PUNCT
ejpam-5911	98	20	resp	resp	NOUN
ejpam-5911	98	21	.	.	PUNCT
ejpam-5911	99	1	df	df	PROPN
ejpam-5911	99	2	-	-	PUNCT
ejpam-5911	99	3	pre	pre	NOUN
ejpam-5911	99	4	-	-	ADJ
ejpam-5911	99	5	continuous	continuous	ADJ
ejpam-5911	99	6	,	,	PUNCT
ejpam-5911	99	7	df	df	NOUN
ejpam-5911	99	8	-	-	PUNCT
ejpam-5911	99	9	semi	semi	ADV
ejpam-5911	99	10	-	-	ADJ
ejpam-5911	99	11	continuous	continuous	ADJ
ejpam-5911	99	12	,	,	PUNCT
ejpam-5911	99	13	and	and	CCONJ
ejpam-5911	99	14	df	df	PROPN
ejpam-5911	99	15	-	-	PUNCT
ejpam-5911	99	16	β	β	NOUN
ejpam-5911	99	17	-	-	ADJ
ejpam-5911	99	18	continuous	continuous	ADJ
ejpam-5911	99	19	)	)	PUNCT
ejpam-5911	99	20	if	if	SCONJ
ejpam-5911	99	21	p−1(n	p−1(n	NOUN
ejpam-5911	99	22	)	)	PUNCT
ejpam-5911	99	23	is	be	AUX
ejpam-5911	99	24	an	an	DET
ejpam-5911	99	25	(	(	PUNCT
ejpam-5911	99	26	r	r	NOUN
ejpam-5911	99	27	,	,	PUNCT
ejpam-5911	99	28	s)-f	s)-f	NOUN
ejpam-5911	99	29	-	-	PUNCT
ejpam-5911	99	30	α	α	NOUN
ejpam-5911	99	31	-	-	ADJ
ejpam-5911	99	32	open	open	ADJ
ejpam-5911	99	33	set	set	NOUN
ejpam-5911	99	34	(	(	PUNCT
ejpam-5911	99	35	resp	resp	NOUN
ejpam-5911	99	36	.	.	PUNCT
ejpam-5911	100	1	(	(	PUNCT
ejpam-5911	100	2	r	r	NOUN
ejpam-5911	100	3	,	,	PUNCT
ejpam-5911	100	4	s)-f	s)-f	NOUN
ejpam-5911	100	5	-	-	PUNCT
ejpam-5911	100	6	pre	pre	ADJ
ejpam-5911	100	7	-	-	ADJ
ejpam-5911	100	8	open	open	ADJ
ejpam-5911	100	9	set	set	NOUN
ejpam-5911	100	10	,	,	PUNCT
ejpam-5911	100	11	(	(	PUNCT
ejpam-5911	100	12	r	r	NOUN
ejpam-5911	100	13	,	,	PUNCT
ejpam-5911	100	14	s)-f	s)-f	NOUN
ejpam-5911	100	15	-	-	PUNCT
ejpam-5911	100	16	semi	semi	ADJ
ejpam-5911	100	17	-	-	ADJ
ejpam-5911	100	18	open	open	ADJ
ejpam-5911	100	19	set	set	NOUN
ejpam-5911	100	20	,	,	PUNCT
ejpam-5911	100	21	and	and	CCONJ
ejpam-5911	100	22	(	(	PUNCT
ejpam-5911	100	23	r	r	NOUN
ejpam-5911	100	24	,	,	PUNCT
ejpam-5911	100	25	s)-f	s)-f	NOUN
ejpam-5911	100	26	-	-	PUNCT
ejpam-5911	100	27	β	β	NOUN
ejpam-5911	100	28	-	-	ADJ
ejpam-5911	100	29	open	open	ADJ
ejpam-5911	100	30	set	set	NOUN
ejpam-5911	100	31	)	)	PUNCT
ejpam-5911	100	32	,	,	PUNCT
ejpam-5911	100	33	for	for	ADP
ejpam-5911	100	34	every	every	DET
ejpam-5911	100	35	n	n	NOUN
ejpam-5911	100	36	∈	∈	NOUN
ejpam-5911	100	37	iz	iz	INTJ
ejpam-5911	100	38	with	with	ADP
ejpam-5911	100	39	𭟋(n	𭟋(n	PROPN
ejpam-5911	100	40	)	)	PUNCT
ejpam-5911	101	1	≥	≥	PROPN
ejpam-5911	101	2	r	r	NOUN
ejpam-5911	101	3	and	and	CCONJ
ejpam-5911	101	4	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	101	5	)	)	PUNCT
ejpam-5911	101	6	≤	≤	PUNCT
ejpam-5911	101	7	s.	s.	PROPN
ejpam-5911	101	8	some	some	DET
ejpam-5911	101	9	basic	basic	ADJ
ejpam-5911	101	10	notations	notation	NOUN
ejpam-5911	101	11	and	and	CCONJ
ejpam-5911	101	12	results	result	NOUN
ejpam-5911	101	13	that	that	PRON
ejpam-5911	101	14	we	we	PRON
ejpam-5911	101	15	need	need	VERB
ejpam-5911	101	16	in	in	ADP
ejpam-5911	101	17	the	the	DET
ejpam-5911	101	18	sequel	sequel	NOUN
ejpam-5911	101	19	are	be	AUX
ejpam-5911	101	20	found	find	VERB
ejpam-5911	101	21	in	in	ADP
ejpam-5911	101	22	[	[	X
ejpam-5911	101	23	27	27	NUM
ejpam-5911	101	24	,	,	PUNCT
ejpam-5911	101	25	28	28	NUM
ejpam-5911	101	26	,	,	PUNCT
ejpam-5911	101	27	30	30	NUM
ejpam-5911	101	28	,	,	PUNCT
ejpam-5911	101	29	31	31	NUM
ejpam-5911	101	30	,	,	PUNCT
ejpam-5911	101	31	35	35	NUM
ejpam-5911	101	32	,	,	PUNCT
ejpam-5911	101	33	36	36	NUM
ejpam-5911	101	34	]	]	PUNCT
ejpam-5911	101	35	.	.	PUNCT
ejpam-5911	102	1	3	3	X
ejpam-5911	102	2	.	.	X
ejpam-5911	102	3	on	on	ADP
ejpam-5911	102	4	(	(	PUNCT
ejpam-5911	102	5	r	r	NOUN
ejpam-5911	102	6	,	,	PUNCT
ejpam-5911	102	7	s)-fuzzy	s)-fuzzy	ADJ
ejpam-5911	102	8	b	b	X
ejpam-5911	102	9	-	-	PUNCT
ejpam-5911	102	10	open	open	ADJ
ejpam-5911	102	11	and	and	CCONJ
ejpam-5911	102	12	b	b	X
ejpam-5911	102	13	-	-	PUNCT
ejpam-5911	102	14	closed	closed	ADJ
ejpam-5911	102	15	sets	set	NOUN
ejpam-5911	102	16	here	here	ADV
ejpam-5911	102	17	,	,	PUNCT
ejpam-5911	102	18	we	we	PRON
ejpam-5911	102	19	present	present	VERB
ejpam-5911	102	20	and	and	CCONJ
ejpam-5911	102	21	study	study	VERB
ejpam-5911	102	22	a	a	DET
ejpam-5911	102	23	new	new	ADJ
ejpam-5911	102	24	class	class	NOUN
ejpam-5911	102	25	of	of	ADP
ejpam-5911	102	26	f	f	NOUN
ejpam-5911	102	27	-	-	PUNCT
ejpam-5911	102	28	open	open	ADJ
ejpam-5911	102	29	sets	set	NOUN
ejpam-5911	102	30	,	,	PUNCT
ejpam-5911	102	31	called	call	VERB
ejpam-5911	102	32	(	(	PUNCT
ejpam-5911	102	33	r	r	NOUN
ejpam-5911	102	34	,	,	PUNCT
ejpam-5911	102	35	s)-f	s)-f	NOUN
ejpam-5911	102	36	-	-	PUNCT
ejpam-5911	102	37	b	b	NOUN
ejpam-5911	102	38	-	-	PUNCT
ejpam-5911	102	39	open	open	ADJ
ejpam-5911	102	40	sets	set	NOUN
ejpam-5911	102	41	in	in	ADP
ejpam-5911	102	42	dft	dft	PROPN
ejpam-5911	102	43	s	s	PROPN
ejpam-5911	102	44	(	(	PUNCT
ejpam-5911	102	45	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	102	46	)	)	PUNCT
ejpam-5911	102	47	based	base	VERB
ejpam-5911	102	48	on	on	ADP
ejpam-5911	102	49	šostak	šostak	NOUN
ejpam-5911	102	50	,	,	PUNCT
ejpam-5911	102	51	s	s	PART
ejpam-5911	102	52	sense	sense	NOUN
ejpam-5911	102	53	[	[	X
ejpam-5911	102	54	3	3	NUM
ejpam-5911	102	55	]	]	PUNCT
ejpam-5911	102	56	.	.	PUNCT
ejpam-5911	103	1	also	also	ADV
ejpam-5911	103	2	,	,	PUNCT
ejpam-5911	103	3	we	we	PRON
ejpam-5911	103	4	explore	explore	VERB
ejpam-5911	103	5	and	and	CCONJ
ejpam-5911	103	6	investigate	investigate	VERB
ejpam-5911	103	7	the	the	DET
ejpam-5911	103	8	concepts	concept	NOUN
ejpam-5911	103	9	of	of	ADP
ejpam-5911	103	10	df	df	PROPN
ejpam-5911	103	11	-	-	PUNCT
ejpam-5911	103	12	b	b	NOUN
ejpam-5911	103	13	-	-	PUNCT
ejpam-5911	103	14	interior	interior	ADJ
ejpam-5911	103	15	operators	operator	NOUN
ejpam-5911	103	16	and	and	CCONJ
ejpam-5911	103	17	df	df	PROPN
ejpam-5911	103	18	-	-	PUNCT
ejpam-5911	103	19	b	b	NOUN
ejpam-5911	103	20	-	-	PUNCT
ejpam-5911	103	21	closure	closure	NOUN
ejpam-5911	103	22	operators	operator	NOUN
ejpam-5911	103	23	.	.	PUNCT
ejpam-5911	104	1	definition	definition	NOUN
ejpam-5911	104	2	6	6	NUM
ejpam-5911	104	3	.	.	PUNCT
ejpam-5911	105	1	let	let	AUX
ejpam-5911	105	2	(	(	PUNCT
ejpam-5911	105	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	105	4	)	)	PUNCT
ejpam-5911	105	5	be	be	VERB
ejpam-5911	105	6	an	an	DET
ejpam-5911	105	7	dft	dft	NOUN
ejpam-5911	105	8	s	s	PROPN
ejpam-5911	105	9	,	,	PUNCT
ejpam-5911	105	10	r	r	NOUN
ejpam-5911	105	11	∈	∈	PROPN
ejpam-5911	106	1	i	i	NOUN
ejpam-5911	106	2	◦	◦	NOUN
ejpam-5911	106	3	,	,	PUNCT
ejpam-5911	106	4	and	and	CCONJ
ejpam-5911	106	5	s	s	PROPN
ejpam-5911	106	6	∈	∈	PROPN
ejpam-5911	106	7	i1	i1	PROPN
ejpam-5911	106	8	.	.	PUNCT
ejpam-5911	107	1	an	an	DET
ejpam-5911	107	2	f	f	X
ejpam-5911	107	3	-	-	PUNCT
ejpam-5911	107	4	set	set	VERB
ejpam-5911	107	5	m	m	NOUN
ejpam-5911	107	6	∈	∈	NOUN
ejpam-5911	107	7	ig	ig	PROPN
ejpam-5911	107	8	is	be	AUX
ejpam-5911	107	9	said	say	VERB
ejpam-5911	107	10	to	to	PART
ejpam-5911	107	11	be	be	AUX
ejpam-5911	107	12	an	an	DET
ejpam-5911	107	13	(	(	PUNCT
ejpam-5911	107	14	r	r	NOUN
ejpam-5911	107	15	,	,	PUNCT
ejpam-5911	107	16	s)-f	s)-f	NOUN
ejpam-5911	107	17	-	-	PUNCT
ejpam-5911	107	18	b	b	NOUN
ejpam-5911	107	19	-	-	PUNCT
ejpam-5911	107	20	open	open	ADJ
ejpam-5911	107	21	set	set	NOUN
ejpam-5911	107	22	if	if	SCONJ
ejpam-5911	107	23	m	m	NOUN
ejpam-5911	107	24	≤	≤	VERB
ejpam-5911	107	25	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	ADJ
ejpam-5911	107	26	,	,	PUNCT
ejpam-5911	107	27	r	r	NOUN
ejpam-5911	107	28	,	,	PUNCT
ejpam-5911	107	29	s	s	PART
ejpam-5911	107	30	)	)	PUNCT
ejpam-5911	107	31	,	,	PUNCT
ejpam-5911	107	32	r	r	NOUN
ejpam-5911	107	33	,	,	PUNCT
ejpam-5911	107	34	s	s	PART
ejpam-5911	107	35	)	)	PUNCT
ejpam-5911	107	36	∨	∨	NUM
ejpam-5911	107	37	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	107	38	,	,	PUNCT
ejpam-5911	107	39	r	r	NOUN
ejpam-5911	107	40	,	,	PUNCT
ejpam-5911	107	41	s	s	PART
ejpam-5911	107	42	)	)	PUNCT
ejpam-5911	107	43	,	,	PUNCT
ejpam-5911	107	44	r	r	NOUN
ejpam-5911	107	45	,	,	PUNCT
ejpam-5911	107	46	s	s	PART
ejpam-5911	107	47	)	)	PUNCT
ejpam-5911	107	48	.	.	PUNCT
ejpam-5911	108	1	definition	definition	NOUN
ejpam-5911	108	2	7	7	NUM
ejpam-5911	108	3	.	.	PUNCT
ejpam-5911	109	1	let	let	AUX
ejpam-5911	109	2	(	(	PUNCT
ejpam-5911	109	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	109	4	)	)	PUNCT
ejpam-5911	109	5	be	be	VERB
ejpam-5911	109	6	an	an	DET
ejpam-5911	109	7	dft	dft	NOUN
ejpam-5911	109	8	s	s	PROPN
ejpam-5911	109	9	,	,	PUNCT
ejpam-5911	109	10	r	r	NOUN
ejpam-5911	109	11	∈	∈	PROPN
ejpam-5911	110	1	i	i	NOUN
ejpam-5911	110	2	◦	◦	NOUN
ejpam-5911	110	3	,	,	PUNCT
ejpam-5911	110	4	and	and	CCONJ
ejpam-5911	110	5	s	s	PROPN
ejpam-5911	110	6	∈	∈	PROPN
ejpam-5911	110	7	i1	i1	PROPN
ejpam-5911	110	8	.	.	PUNCT
ejpam-5911	111	1	an	an	DET
ejpam-5911	111	2	f	f	X
ejpam-5911	111	3	-	-	PUNCT
ejpam-5911	111	4	set	set	VERB
ejpam-5911	111	5	m	m	NOUN
ejpam-5911	111	6	∈	∈	NOUN
ejpam-5911	111	7	ig	ig	PROPN
ejpam-5911	111	8	is	be	AUX
ejpam-5911	111	9	said	say	VERB
ejpam-5911	111	10	to	to	PART
ejpam-5911	111	11	be	be	AUX
ejpam-5911	111	12	an	an	DET
ejpam-5911	111	13	(	(	PUNCT
ejpam-5911	111	14	r	r	NOUN
ejpam-5911	111	15	,	,	PUNCT
ejpam-5911	111	16	s)-f	s)-f	NOUN
ejpam-5911	111	17	-	-	PUNCT
ejpam-5911	111	18	b	b	NOUN
ejpam-5911	111	19	-	-	PUNCT
ejpam-5911	111	20	closed	closed	ADJ
ejpam-5911	111	21	set	set	NOUN
ejpam-5911	111	22	if	if	SCONJ
ejpam-5911	111	23	m	m	NOUN
ejpam-5911	111	24	≥	≥	VERB
ejpam-5911	111	25	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	ADJ
ejpam-5911	111	26	,	,	PUNCT
ejpam-5911	111	27	r	r	NOUN
ejpam-5911	111	28	,	,	PUNCT
ejpam-5911	111	29	s	s	PART
ejpam-5911	111	30	)	)	PUNCT
ejpam-5911	111	31	,	,	PUNCT
ejpam-5911	111	32	r	r	NOUN
ejpam-5911	111	33	,	,	PUNCT
ejpam-5911	111	34	s	s	NOUN
ejpam-5911	111	35	)	)	PUNCT
ejpam-5911	111	36	∧	∧	NOUN
ejpam-5911	111	37	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	111	38	,	,	PUNCT
ejpam-5911	111	39	r	r	NOUN
ejpam-5911	111	40	,	,	PUNCT
ejpam-5911	111	41	s	s	PART
ejpam-5911	111	42	)	)	PUNCT
ejpam-5911	111	43	,	,	PUNCT
ejpam-5911	111	44	r	r	NOUN
ejpam-5911	111	45	,	,	PUNCT
ejpam-5911	111	46	s	s	PART
ejpam-5911	111	47	)	)	PUNCT
ejpam-5911	111	48	.	.	PUNCT
ejpam-5911	112	1	remark	remark	PROPN
ejpam-5911	112	2	1	1	NUM
ejpam-5911	112	3	.	.	PUNCT
ejpam-5911	113	1	the	the	DET
ejpam-5911	113	2	complement	complement	NOUN
ejpam-5911	113	3	of	of	ADP
ejpam-5911	113	4	(	(	PUNCT
ejpam-5911	113	5	r	r	NOUN
ejpam-5911	113	6	,	,	PUNCT
ejpam-5911	113	7	s)-f	s)-f	NOUN
ejpam-5911	113	8	-	-	PUNCT
ejpam-5911	113	9	b	b	NOUN
ejpam-5911	113	10	-	-	PUNCT
ejpam-5911	113	11	open	open	ADJ
ejpam-5911	113	12	sets	set	NOUN
ejpam-5911	113	13	(	(	PUNCT
ejpam-5911	113	14	resp	resp	NOUN
ejpam-5911	113	15	.	.	PUNCT
ejpam-5911	114	1	(	(	PUNCT
ejpam-5911	114	2	r	r	NOUN
ejpam-5911	114	3	,	,	PUNCT
ejpam-5911	114	4	s)-f	s)-f	NOUN
ejpam-5911	114	5	-	-	PUNCT
ejpam-5911	114	6	b	b	NOUN
ejpam-5911	114	7	-	-	PUNCT
ejpam-5911	114	8	closed	close	VERB
ejpam-5911	114	9	sets	set	NOUN
ejpam-5911	114	10	)	)	PUNCT
ejpam-5911	114	11	are	be	AUX
ejpam-5911	114	12	(	(	PUNCT
ejpam-5911	114	13	r	r	NOUN
ejpam-5911	114	14	,	,	PUNCT
ejpam-5911	114	15	s)-f	s)-f	NOUN
ejpam-5911	114	16	-	-	PUNCT
ejpam-5911	114	17	b	b	NOUN
ejpam-5911	114	18	-	-	PUNCT
ejpam-5911	114	19	closed	closed	ADJ
ejpam-5911	114	20	sets	set	NOUN
ejpam-5911	114	21	(	(	PUNCT
ejpam-5911	114	22	resp	resp	NOUN
ejpam-5911	114	23	.	.	PUNCT
ejpam-5911	115	1	(	(	PUNCT
ejpam-5911	115	2	r	r	NOUN
ejpam-5911	115	3	,	,	PUNCT
ejpam-5911	115	4	s)-f	s)-f	NOUN
ejpam-5911	115	5	-	-	PUNCT
ejpam-5911	115	6	b	b	NOUN
ejpam-5911	115	7	-	-	PUNCT
ejpam-5911	115	8	open	open	ADJ
ejpam-5911	115	9	sets	set	NOUN
ejpam-5911	115	10	)	)	PUNCT
ejpam-5911	115	11	.	.	PUNCT
ejpam-5911	116	1	i.	i.	PROPN
ejpam-5911	116	2	m.	m.	PROPN
ejpam-5911	116	3	taha	taha	PROPN
ejpam-5911	116	4	,	,	PUNCT
ejpam-5911	116	5	j.	j.	PROPN
ejpam-5911	116	6	al	al	PROPN
ejpam-5911	116	7	-	-	PUNCT
ejpam-5911	116	8	mufarrij	mufarrij	PROPN
ejpam-5911	116	9	,	,	PUNCT
ejpam-5911	116	10	o.	o.	PROPN
ejpam-5911	116	11	m.	m.	PROPN
ejpam-5911	116	12	taha	taha	PROPN
ejpam-5911	116	13	/	/	PUNCT
ejpam-5911	116	14	eur	eur	PROPN
ejpam-5911	116	15	.	.	PUNCT
ejpam-5911	117	1	j.	j.	PROPN
ejpam-5911	117	2	pure	pure	PROPN
ejpam-5911	117	3	appl	appl	PROPN
ejpam-5911	117	4	.	.	PROPN
ejpam-5911	117	5	math	math	PROPN
ejpam-5911	117	6	,	,	PUNCT
ejpam-5911	117	7	18	18	NUM
ejpam-5911	117	8	(	(	PUNCT
ejpam-5911	117	9	2	2	NUM
ejpam-5911	117	10	)	)	PUNCT
ejpam-5911	117	11	(	(	PUNCT
ejpam-5911	117	12	2025	2025	NUM
ejpam-5911	117	13	)	)	PUNCT
ejpam-5911	117	14	,	,	PUNCT
ejpam-5911	117	15	5911	5911	NUM
ejpam-5911	117	16	5	5	NUM
ejpam-5911	117	17	of	of	ADP
ejpam-5911	117	18	27	27	NUM
ejpam-5911	117	19	proposition	proposition	NOUN
ejpam-5911	117	20	1	1	NUM
ejpam-5911	117	21	.	.	PUNCT
ejpam-5911	118	1	in	in	ADP
ejpam-5911	118	2	an	an	DET
ejpam-5911	118	3	dft	dft	NOUN
ejpam-5911	118	4	s	s	X
ejpam-5911	118	5	(	(	PUNCT
ejpam-5911	118	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	118	7	)	)	PUNCT
ejpam-5911	118	8	,	,	PUNCT
ejpam-5911	118	9	for	for	ADP
ejpam-5911	118	10	each	each	DET
ejpam-5911	118	11	m	m	PROPN
ejpam-5911	118	12	∈	∈	PROPN
ejpam-5911	118	13	ig	ig	PROPN
ejpam-5911	118	14	,	,	PUNCT
ejpam-5911	118	15	r	r	NOUN
ejpam-5911	118	16	∈	∈	PROPN
ejpam-5911	118	17	i	i	NOUN
ejpam-5911	118	18	◦	◦	NOUN
ejpam-5911	118	19	,	,	PUNCT
ejpam-5911	118	20	and	and	CCONJ
ejpam-5911	118	21	s	s	PROPN
ejpam-5911	118	22	∈	∈	PROPN
ejpam-5911	118	23	i1	i1	PROPN
ejpam-5911	118	24	,	,	PUNCT
ejpam-5911	118	25	then	then	ADV
ejpam-5911	118	26	(	(	PUNCT
ejpam-5911	118	27	i	i	NOUN
ejpam-5911	118	28	)	)	PUNCT
ejpam-5911	118	29	every	every	DET
ejpam-5911	118	30	(	(	PUNCT
ejpam-5911	118	31	r	r	NOUN
ejpam-5911	118	32	,	,	PUNCT
ejpam-5911	118	33	s)-f	s)-f	NOUN
ejpam-5911	118	34	-	-	PUNCT
ejpam-5911	118	35	pre	pre	ADJ
ejpam-5911	118	36	-	-	ADJ
ejpam-5911	118	37	open	open	ADJ
ejpam-5911	118	38	set	set	NOUN
ejpam-5911	118	39	is	be	AUX
ejpam-5911	118	40	(	(	PUNCT
ejpam-5911	118	41	r	r	NOUN
ejpam-5911	118	42	,	,	PUNCT
ejpam-5911	118	43	s)-f	s)-f	NOUN
ejpam-5911	118	44	-	-	PUNCT
ejpam-5911	118	45	b	b	NOUN
ejpam-5911	118	46	-	-	PUNCT
ejpam-5911	118	47	open	open	ADJ
ejpam-5911	118	48	;	;	PUNCT
ejpam-5911	118	49	(	(	PUNCT
ejpam-5911	118	50	ii	ii	NOUN
ejpam-5911	118	51	)	)	PUNCT
ejpam-5911	118	52	every	every	DET
ejpam-5911	118	53	(	(	PUNCT
ejpam-5911	118	54	r	r	NOUN
ejpam-5911	118	55	,	,	PUNCT
ejpam-5911	118	56	s)-f	s)-f	NOUN
ejpam-5911	118	57	-	-	PUNCT
ejpam-5911	118	58	b	b	NOUN
ejpam-5911	118	59	-	-	PUNCT
ejpam-5911	118	60	open	open	ADJ
ejpam-5911	118	61	set	set	NOUN
ejpam-5911	118	62	is	be	AUX
ejpam-5911	118	63	(	(	PUNCT
ejpam-5911	118	64	r	r	NOUN
ejpam-5911	118	65	,	,	PUNCT
ejpam-5911	118	66	s)-f	s)-f	NOUN
ejpam-5911	118	67	-	-	PUNCT
ejpam-5911	118	68	β	β	NOUN
ejpam-5911	118	69	-	-	ADJ
ejpam-5911	118	70	open	open	ADJ
ejpam-5911	118	71	;	;	PUNCT
ejpam-5911	118	72	(	(	PUNCT
ejpam-5911	118	73	iii	iii	X
ejpam-5911	118	74	)	)	PUNCT
ejpam-5911	118	75	every	every	DET
ejpam-5911	118	76	(	(	PUNCT
ejpam-5911	118	77	r	r	NOUN
ejpam-5911	118	78	,	,	PUNCT
ejpam-5911	118	79	s)-f	s)-f	NOUN
ejpam-5911	118	80	-	-	PUNCT
ejpam-5911	118	81	semi	semi	ADJ
ejpam-5911	118	82	-	-	ADJ
ejpam-5911	118	83	open	open	ADJ
ejpam-5911	118	84	set	set	NOUN
ejpam-5911	118	85	is	be	AUX
ejpam-5911	118	86	(	(	PUNCT
ejpam-5911	118	87	r	r	NOUN
ejpam-5911	118	88	,	,	PUNCT
ejpam-5911	118	89	s)-f	s)-f	NOUN
ejpam-5911	118	90	-	-	PUNCT
ejpam-5911	118	91	b	b	NOUN
ejpam-5911	118	92	-	-	PUNCT
ejpam-5911	118	93	open	open	ADJ
ejpam-5911	118	94	.	.	PUNCT
ejpam-5911	119	1	proof	proof	NOUN
ejpam-5911	119	2	.	.	PUNCT
ejpam-5911	120	1	(	(	PUNCT
ejpam-5911	120	2	i	i	NOUN
ejpam-5911	120	3	)	)	PUNCT
ejpam-5911	120	4	if	if	SCONJ
ejpam-5911	120	5	m	m	NOUN
ejpam-5911	120	6	is	be	AUX
ejpam-5911	120	7	an	an	DET
ejpam-5911	120	8	(	(	PUNCT
ejpam-5911	120	9	r	r	NOUN
ejpam-5911	120	10	,	,	PUNCT
ejpam-5911	120	11	s)-f	s)-f	NOUN
ejpam-5911	120	12	-	-	PUNCT
ejpam-5911	120	13	pre	pre	ADJ
ejpam-5911	120	14	-	-	ADJ
ejpam-5911	120	15	open	open	ADJ
ejpam-5911	120	16	set	set	NOUN
ejpam-5911	120	17	,	,	PUNCT
ejpam-5911	120	18	then	then	ADV
ejpam-5911	120	19	m	m	VERB
ejpam-5911	120	20	≤	≤	NOUN
ejpam-5911	120	21	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	120	22	,	,	PUNCT
ejpam-5911	120	23	r	r	NOUN
ejpam-5911	120	24	,	,	PUNCT
ejpam-5911	120	25	s	s	PART
ejpam-5911	120	26	)	)	PUNCT
ejpam-5911	120	27	,	,	PUNCT
ejpam-5911	120	28	r	r	NOUN
ejpam-5911	120	29	,	,	PUNCT
ejpam-5911	120	30	s	s	NOUN
ejpam-5911	120	31	)	)	PUNCT
ejpam-5911	120	32	≤	≤	NOUN
ejpam-5911	121	1	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	121	2	,	,	PUNCT
ejpam-5911	121	3	r	r	NOUN
ejpam-5911	121	4	,	,	PUNCT
ejpam-5911	121	5	s	s	PART
ejpam-5911	121	6	)	)	PUNCT
ejpam-5911	121	7	,	,	PUNCT
ejpam-5911	121	8	r	r	NOUN
ejpam-5911	121	9	,	,	PUNCT
ejpam-5911	121	10	s	s	PART
ejpam-5911	121	11	)	)	PUNCT
ejpam-5911	121	12	∨	∨	NOUN
ejpam-5911	121	13	iℑ∗(m	iℑ∗(m	NOUN
ejpam-5911	121	14	,	,	PUNCT
ejpam-5911	121	15	r	r	NOUN
ejpam-5911	121	16	,	,	PUNCT
ejpam-5911	121	17	s	s	NOUN
ejpam-5911	121	18	)	)	PUNCT
ejpam-5911	121	19	≤	≤	NOUN
ejpam-5911	121	20	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	121	21	,	,	PUNCT
ejpam-5911	121	22	r	r	NOUN
ejpam-5911	121	23	,	,	PUNCT
ejpam-5911	121	24	s	s	PART
ejpam-5911	121	25	)	)	PUNCT
ejpam-5911	121	26	,	,	PUNCT
ejpam-5911	121	27	r	r	NOUN
ejpam-5911	121	28	,	,	PUNCT
ejpam-5911	121	29	s	s	PART
ejpam-5911	121	30	)	)	PUNCT
ejpam-5911	121	31	∨	∨	NOUN
ejpam-5911	121	32	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	PROPN
ejpam-5911	121	33	,	,	PUNCT
ejpam-5911	121	34	r	r	NOUN
ejpam-5911	121	35	,	,	PUNCT
ejpam-5911	121	36	s	s	PART
ejpam-5911	121	37	)	)	PUNCT
ejpam-5911	121	38	,	,	PUNCT
ejpam-5911	121	39	r	r	NOUN
ejpam-5911	121	40	,	,	PUNCT
ejpam-5911	121	41	s	s	NOUN
ejpam-5911	121	42	)	)	PUNCT
ejpam-5911	121	43	.	.	PUNCT
ejpam-5911	122	1	thus	thus	ADV
ejpam-5911	122	2	,	,	PUNCT
ejpam-5911	122	3	m	m	VERB
ejpam-5911	122	4	is	be	AUX
ejpam-5911	122	5	(	(	PUNCT
ejpam-5911	122	6	r	r	NOUN
ejpam-5911	122	7	,	,	PUNCT
ejpam-5911	122	8	s)-f	s)-f	NOUN
ejpam-5911	122	9	-	-	PUNCT
ejpam-5911	122	10	b	b	NOUN
ejpam-5911	122	11	-	-	PUNCT
ejpam-5911	122	12	open	open	ADJ
ejpam-5911	122	13	.	.	PUNCT
ejpam-5911	123	1	(	(	PUNCT
ejpam-5911	123	2	ii	ii	NOUN
ejpam-5911	123	3	)	)	PUNCT
ejpam-5911	123	4	if	if	SCONJ
ejpam-5911	123	5	m	m	NOUN
ejpam-5911	123	6	is	be	AUX
ejpam-5911	123	7	an	an	DET
ejpam-5911	123	8	(	(	PUNCT
ejpam-5911	123	9	r	r	NOUN
ejpam-5911	123	10	,	,	PUNCT
ejpam-5911	123	11	s)-f	s)-f	NOUN
ejpam-5911	123	12	-	-	PUNCT
ejpam-5911	123	13	b	b	NOUN
ejpam-5911	123	14	-	-	PUNCT
ejpam-5911	123	15	open	open	ADJ
ejpam-5911	123	16	set	set	NOUN
ejpam-5911	123	17	,	,	PUNCT
ejpam-5911	123	18	then	then	ADV
ejpam-5911	123	19	m	m	VERB
ejpam-5911	123	20	≤	≤	ADJ
ejpam-5911	123	21	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	ADJ
ejpam-5911	123	22	,	,	PUNCT
ejpam-5911	123	23	r	r	NOUN
ejpam-5911	123	24	,	,	PUNCT
ejpam-5911	123	25	s	s	PART
ejpam-5911	123	26	)	)	PUNCT
ejpam-5911	123	27	,	,	PUNCT
ejpam-5911	123	28	r	r	NOUN
ejpam-5911	123	29	,	,	PUNCT
ejpam-5911	123	30	s	s	PART
ejpam-5911	123	31	)	)	PUNCT
ejpam-5911	123	32	∨	∨	NUM
ejpam-5911	123	33	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	123	34	,	,	PUNCT
ejpam-5911	123	35	r	r	NOUN
ejpam-5911	123	36	,	,	PUNCT
ejpam-5911	123	37	s	s	PART
ejpam-5911	123	38	)	)	PUNCT
ejpam-5911	123	39	,	,	PUNCT
ejpam-5911	123	40	r	r	NOUN
ejpam-5911	123	41	,	,	PUNCT
ejpam-5911	123	42	s	s	NOUN
ejpam-5911	123	43	)	)	PUNCT
ejpam-5911	123	44	≤	≤	NOUN
ejpam-5911	124	1	cℑ∗(iℑ∗(cℑ∗(m	cℑ∗(iℑ∗(cℑ∗(m	NOUN
ejpam-5911	124	2	,	,	PUNCT
ejpam-5911	124	3	r	r	NOUN
ejpam-5911	124	4	,	,	PUNCT
ejpam-5911	124	5	s	s	PART
ejpam-5911	124	6	)	)	PUNCT
ejpam-5911	124	7	,	,	PUNCT
ejpam-5911	124	8	r	r	NOUN
ejpam-5911	124	9	,	,	PUNCT
ejpam-5911	124	10	s	s	PART
ejpam-5911	124	11	)	)	PUNCT
ejpam-5911	124	12	,	,	PUNCT
ejpam-5911	124	13	r	r	NOUN
ejpam-5911	124	14	,	,	PUNCT
ejpam-5911	124	15	s	s	PART
ejpam-5911	124	16	)	)	PUNCT
ejpam-5911	124	17	∨	∨	NUM
ejpam-5911	124	18	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	124	19	,	,	PUNCT
ejpam-5911	124	20	r	r	NOUN
ejpam-5911	124	21	,	,	PUNCT
ejpam-5911	124	22	s	s	PART
ejpam-5911	124	23	)	)	PUNCT
ejpam-5911	124	24	,	,	PUNCT
ejpam-5911	124	25	r	r	NOUN
ejpam-5911	124	26	,	,	PUNCT
ejpam-5911	124	27	s	s	NOUN
ejpam-5911	124	28	)	)	PUNCT
ejpam-5911	124	29	≤	≤	NOUN
ejpam-5911	125	1	cℑ∗(iℑ∗(cℑ∗(m	cℑ∗(iℑ∗(cℑ∗(m	NOUN
ejpam-5911	125	2	,	,	PUNCT
ejpam-5911	125	3	r	r	NOUN
ejpam-5911	125	4	,	,	PUNCT
ejpam-5911	125	5	s	s	PART
ejpam-5911	125	6	)	)	PUNCT
ejpam-5911	125	7	,	,	PUNCT
ejpam-5911	125	8	r	r	NOUN
ejpam-5911	125	9	,	,	PUNCT
ejpam-5911	125	10	s	s	PART
ejpam-5911	125	11	)	)	PUNCT
ejpam-5911	125	12	,	,	PUNCT
ejpam-5911	125	13	r	r	NOUN
ejpam-5911	125	14	,	,	PUNCT
ejpam-5911	125	15	s	s	NOUN
ejpam-5911	125	16	)	)	PUNCT
ejpam-5911	125	17	.	.	PUNCT
ejpam-5911	126	1	thus	thus	ADV
ejpam-5911	126	2	,	,	PUNCT
ejpam-5911	126	3	m	m	VERB
ejpam-5911	126	4	is	be	AUX
ejpam-5911	126	5	(	(	PUNCT
ejpam-5911	126	6	r	r	NOUN
ejpam-5911	126	7	,	,	PUNCT
ejpam-5911	126	8	s)-f	s)-f	NOUN
ejpam-5911	126	9	-	-	PUNCT
ejpam-5911	126	10	β	β	NOUN
ejpam-5911	126	11	-	-	ADJ
ejpam-5911	126	12	open	open	ADJ
ejpam-5911	126	13	.	.	PUNCT
ejpam-5911	127	1	(	(	PUNCT
ejpam-5911	127	2	iii	iii	X
ejpam-5911	127	3	)	)	PUNCT
ejpam-5911	127	4	if	if	SCONJ
ejpam-5911	127	5	m	m	NOUN
ejpam-5911	127	6	is	be	AUX
ejpam-5911	127	7	an	an	DET
ejpam-5911	127	8	(	(	PUNCT
ejpam-5911	127	9	r	r	NOUN
ejpam-5911	127	10	,	,	PUNCT
ejpam-5911	127	11	s)-f	s)-f	NOUN
ejpam-5911	127	12	-	-	PUNCT
ejpam-5911	127	13	semi	semi	ADJ
ejpam-5911	127	14	-	-	ADJ
ejpam-5911	127	15	open	open	ADJ
ejpam-5911	127	16	set	set	NOUN
ejpam-5911	127	17	,	,	PUNCT
ejpam-5911	127	18	then	then	ADV
ejpam-5911	127	19	m	m	VERB
ejpam-5911	127	20	≤	≤	ADJ
ejpam-5911	127	21	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	ADJ
ejpam-5911	127	22	,	,	PUNCT
ejpam-5911	127	23	r	r	NOUN
ejpam-5911	127	24	,	,	PUNCT
ejpam-5911	127	25	s	s	PART
ejpam-5911	127	26	)	)	PUNCT
ejpam-5911	127	27	,	,	PUNCT
ejpam-5911	127	28	r	r	NOUN
ejpam-5911	127	29	,	,	PUNCT
ejpam-5911	127	30	s	s	NOUN
ejpam-5911	127	31	)	)	PUNCT
ejpam-5911	127	32	≤	≤	NOUN
ejpam-5911	128	1	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	PROPN
ejpam-5911	128	2	,	,	PUNCT
ejpam-5911	128	3	r	r	NOUN
ejpam-5911	128	4	,	,	PUNCT
ejpam-5911	128	5	s	s	PART
ejpam-5911	128	6	)	)	PUNCT
ejpam-5911	128	7	,	,	PUNCT
ejpam-5911	128	8	r	r	NOUN
ejpam-5911	128	9	,	,	PUNCT
ejpam-5911	128	10	s	s	PART
ejpam-5911	128	11	)	)	PUNCT
ejpam-5911	128	12	∨	∨	NOUN
ejpam-5911	128	13	iℑ∗(m	iℑ∗(m	NOUN
ejpam-5911	128	14	,	,	PUNCT
ejpam-5911	128	15	r	r	NOUN
ejpam-5911	128	16	,	,	PUNCT
ejpam-5911	128	17	s	s	NOUN
ejpam-5911	128	18	)	)	PUNCT
ejpam-5911	128	19	≤	≤	NOUN
ejpam-5911	129	1	cℑ∗(iℑ∗(m	cℑ∗(iℑ∗(m	PROPN
ejpam-5911	129	2	,	,	PUNCT
ejpam-5911	129	3	r	r	NOUN
ejpam-5911	129	4	,	,	PUNCT
ejpam-5911	129	5	s	s	PART
ejpam-5911	129	6	)	)	PUNCT
ejpam-5911	129	7	,	,	PUNCT
ejpam-5911	129	8	r	r	NOUN
ejpam-5911	129	9	,	,	PUNCT
ejpam-5911	129	10	s	s	PART
ejpam-5911	129	11	)	)	PUNCT
ejpam-5911	129	12	∨	∨	NUM
ejpam-5911	129	13	iℑ∗(cℑ∗(m	iℑ∗(cℑ∗(m	PROPN
ejpam-5911	129	14	,	,	PUNCT
ejpam-5911	129	15	r	r	NOUN
ejpam-5911	129	16	,	,	PUNCT
ejpam-5911	129	17	s	s	PART
ejpam-5911	129	18	)	)	PUNCT
ejpam-5911	129	19	,	,	PUNCT
ejpam-5911	129	20	r	r	NOUN
ejpam-5911	129	21	,	,	PUNCT
ejpam-5911	129	22	s	s	NOUN
ejpam-5911	129	23	)	)	PUNCT
ejpam-5911	129	24	.	.	PUNCT
ejpam-5911	130	1	thus	thus	ADV
ejpam-5911	130	2	,	,	PUNCT
ejpam-5911	130	3	m	m	VERB
ejpam-5911	130	4	is	be	AUX
ejpam-5911	130	5	(	(	PUNCT
ejpam-5911	130	6	r	r	NOUN
ejpam-5911	130	7	,	,	PUNCT
ejpam-5911	130	8	s)-f	s)-f	NOUN
ejpam-5911	130	9	-	-	PUNCT
ejpam-5911	130	10	b	b	NOUN
ejpam-5911	130	11	-	-	PUNCT
ejpam-5911	130	12	open	open	ADJ
ejpam-5911	130	13	.	.	PUNCT
ejpam-5911	131	1	remark	remark	NOUN
ejpam-5911	131	2	2	2	NUM
ejpam-5911	131	3	.	.	PUNCT
ejpam-5911	131	4	from	from	ADP
ejpam-5911	131	5	the	the	DET
ejpam-5911	131	6	previous	previous	ADJ
ejpam-5911	131	7	discussions	discussion	NOUN
ejpam-5911	131	8	and	and	CCONJ
ejpam-5911	131	9	definitions	definition	NOUN
ejpam-5911	131	10	,	,	PUNCT
ejpam-5911	131	11	we	we	PRON
ejpam-5911	131	12	have	have	VERB
ejpam-5911	131	13	the	the	DET
ejpam-5911	131	14	following	follow	VERB
ejpam-5911	131	15	diagram	diagram	NOUN
ejpam-5911	131	16	.	.	PUNCT
ejpam-5911	132	1	(	(	PUNCT
ejpam-5911	132	2	r	r	NOUN
ejpam-5911	132	3	,	,	PUNCT
ejpam-5911	132	4	s)-f	s)-f	NOUN
ejpam-5911	132	5	-	-	PUNCT
ejpam-5911	132	6	pre	pre	ADJ
ejpam-5911	132	7	-	-	ADJ
ejpam-5911	132	8	open	open	ADJ
ejpam-5911	132	9	set	set	ADJ
ejpam-5911	132	10	↗	↗	PROPN
ejpam-5911	132	11	↓	↓	NOUN
ejpam-5911	132	12	(	(	PUNCT
ejpam-5911	132	13	r	r	NOUN
ejpam-5911	132	14	,	,	PUNCT
ejpam-5911	132	15	s)-f	s)-f	NOUN
ejpam-5911	132	16	-	-	PUNCT
ejpam-5911	132	17	α	α	NOUN
ejpam-5911	132	18	-	-	ADJ
ejpam-5911	132	19	open	open	ADJ
ejpam-5911	132	20	set	set	VERB
ejpam-5911	132	21	−→	−→	NOUN
ejpam-5911	132	22	(	(	PUNCT
ejpam-5911	132	23	r	r	NOUN
ejpam-5911	132	24	,	,	PUNCT
ejpam-5911	132	25	s)-f	s)-f	NOUN
ejpam-5911	132	26	-	-	PUNCT
ejpam-5911	132	27	b	b	NOUN
ejpam-5911	132	28	-	-	PUNCT
ejpam-5911	132	29	open	open	ADJ
ejpam-5911	132	30	set	set	VERB
ejpam-5911	132	31	−→	−→	NOUN
ejpam-5911	132	32	(	(	PUNCT
ejpam-5911	132	33	r	r	NOUN
ejpam-5911	132	34	,	,	PUNCT
ejpam-5911	132	35	s)-f	s)-f	NOUN
ejpam-5911	132	36	-	-	PUNCT
ejpam-5911	132	37	β	β	NOUN
ejpam-5911	132	38	-	-	ADJ
ejpam-5911	132	39	open	open	ADJ
ejpam-5911	132	40	set	set	NOUN
ejpam-5911	132	41	↘	↘	PROPN
ejpam-5911	132	42	↑	↑	NOUN
ejpam-5911	132	43	(	(	PUNCT
ejpam-5911	132	44	r	r	NOUN
ejpam-5911	132	45	,	,	PUNCT
ejpam-5911	132	46	s)-f	s)-f	NOUN
ejpam-5911	132	47	-	-	PUNCT
ejpam-5911	132	48	semi	semi	ADJ
ejpam-5911	132	49	-	-	ADJ
ejpam-5911	132	50	open	open	ADJ
ejpam-5911	132	51	set	set	VERB
ejpam-5911	132	52	i.	i.	PROPN
ejpam-5911	132	53	m.	m.	PROPN
ejpam-5911	132	54	taha	taha	PROPN
ejpam-5911	132	55	,	,	PUNCT
ejpam-5911	132	56	j.	j.	PROPN
ejpam-5911	132	57	al	al	PROPN
ejpam-5911	132	58	-	-	PUNCT
ejpam-5911	132	59	mufarrij	mufarrij	PROPN
ejpam-5911	132	60	,	,	PUNCT
ejpam-5911	132	61	o.	o.	PROPN
ejpam-5911	132	62	m.	m.	PROPN
ejpam-5911	132	63	taha	taha	PROPN
ejpam-5911	132	64	/	/	PUNCT
ejpam-5911	132	65	eur	eur	PROPN
ejpam-5911	132	66	.	.	PUNCT
ejpam-5911	133	1	j.	j.	PROPN
ejpam-5911	133	2	pure	pure	PROPN
ejpam-5911	133	3	appl	appl	PROPN
ejpam-5911	133	4	.	.	PROPN
ejpam-5911	133	5	math	math	PROPN
ejpam-5911	133	6	,	,	PUNCT
ejpam-5911	133	7	18	18	NUM
ejpam-5911	133	8	(	(	PUNCT
ejpam-5911	133	9	2	2	NUM
ejpam-5911	133	10	)	)	PUNCT
ejpam-5911	133	11	(	(	PUNCT
ejpam-5911	133	12	2025	2025	NUM
ejpam-5911	133	13	)	)	PUNCT
ejpam-5911	133	14	,	,	PUNCT
ejpam-5911	133	15	5911	5911	NUM
ejpam-5911	133	16	6	6	NUM
ejpam-5911	133	17	of	of	ADP
ejpam-5911	133	18	27	27	NUM
ejpam-5911	133	19	remark	remark	NOUN
ejpam-5911	133	20	3	3	NUM
ejpam-5911	133	21	.	.	PUNCT
ejpam-5911	134	1	the	the	DET
ejpam-5911	134	2	converse	converse	NOUN
ejpam-5911	134	3	of	of	ADP
ejpam-5911	134	4	the	the	DET
ejpam-5911	134	5	above	above	ADJ
ejpam-5911	134	6	diagram	diagram	NOUN
ejpam-5911	134	7	fails	fail	VERB
ejpam-5911	134	8	as	as	ADP
ejpam-5911	134	9	examples	example	NOUN
ejpam-5911	134	10	1	1	NUM
ejpam-5911	134	11	,	,	PUNCT
ejpam-5911	134	12	2	2	NUM
ejpam-5911	134	13	,	,	PUNCT
ejpam-5911	134	14	and	and	CCONJ
ejpam-5911	134	15	3	3	NUM
ejpam-5911	134	16	will	will	AUX
ejpam-5911	134	17	show	show	VERB
ejpam-5911	134	18	.	.	PUNCT
ejpam-5911	135	1	example	example	NOUN
ejpam-5911	136	1	1	1	NUM
ejpam-5911	136	2	.	.	PUNCT
ejpam-5911	136	3	let	let	VERB
ejpam-5911	136	4	g	g	PROPN
ejpam-5911	136	5	=	=	SYM
ejpam-5911	136	6	{	{	PUNCT
ejpam-5911	136	7	g1	g1	PROPN
ejpam-5911	136	8	,	,	PUNCT
ejpam-5911	136	9	g2	g2	PROPN
ejpam-5911	136	10	}	}	PUNCT
ejpam-5911	136	11	and	and	CCONJ
ejpam-5911	136	12	define	define	VERB
ejpam-5911	136	13	m	m	PROPN
ejpam-5911	136	14	,	,	PUNCT
ejpam-5911	136	15	n	n	CCONJ
ejpam-5911	136	16	,	,	PUNCT
ejpam-5911	136	17	u	u	PROPN
ejpam-5911	136	18	∈	∈	PROPN
ejpam-5911	136	19	ig	ig	PROPN
ejpam-5911	136	20	as	as	SCONJ
ejpam-5911	136	21	follows	follow	VERB
ejpam-5911	136	22	:	:	PUNCT
ejpam-5911	136	23	m	m	VERB
ejpam-5911	136	24	=	=	PUNCT
ejpam-5911	136	25	{	{	PUNCT
ejpam-5911	136	26	g1	g1	PROPN
ejpam-5911	136	27	0.4	0.4	NUM
ejpam-5911	136	28	,	,	PUNCT
ejpam-5911	136	29	g2	g2	PROPN
ejpam-5911	136	30	0.3	0.3	NUM
ejpam-5911	136	31	}	}	PUNCT
ejpam-5911	136	32	,	,	PUNCT
ejpam-5911	136	33	n	n	NOUN
ejpam-5911	136	34	=	=	PRON
ejpam-5911	136	35	{	{	PUNCT
ejpam-5911	136	36	g1	g1	PROPN
ejpam-5911	136	37	0.2	0.2	NUM
ejpam-5911	136	38	,	,	PUNCT
ejpam-5911	136	39	g2	g2	PROPN
ejpam-5911	136	40	0.6	0.6	NUM
ejpam-5911	136	41	}	}	PUNCT
ejpam-5911	136	42	,	,	PUNCT
ejpam-5911	136	43	u	u	NOUN
ejpam-5911	136	44	=	=	PUNCT
ejpam-5911	136	45	{	{	PUNCT
ejpam-5911	136	46	g1	g1	PROPN
ejpam-5911	136	47	0.5	0.5	NUM
ejpam-5911	136	48	,	,	PUNCT
ejpam-5911	136	49	g2	g2	PROPN
ejpam-5911	136	50	0.7	0.7	NUM
ejpam-5911	136	51	}	}	PUNCT
ejpam-5911	136	52	.	.	PUNCT
ejpam-5911	137	1	define	define	VERB
ejpam-5911	137	2	ℑ,ℑ∗	ℑ,ℑ∗	NOUN
ejpam-5911	137	3	:	:	PUNCT
ejpam-5911	137	4	ig	ig	PROPN
ejpam-5911	137	5	−→	−→	NOUN
ejpam-5911	138	1	i	i	PRON
ejpam-5911	138	2	as	as	SCONJ
ejpam-5911	138	3	follows	follow	VERB
ejpam-5911	138	4	:	:	PUNCT
ejpam-5911	138	5	ℑ(v	ℑ(v	X
ejpam-5911	138	6	)	)	PUNCT
ejpam-5911	138	7	=	=	SYM
ejpam-5911	138	8			NUM
ejpam-5911	138	9	1	1	NUM
ejpam-5911	138	10	,	,	PUNCT
ejpam-5911	138	11	if	if	SCONJ
ejpam-5911	138	12	v	v	ADP
ejpam-5911	138	13	∈	∈	NOUN
ejpam-5911	138	14	{	{	PUNCT
ejpam-5911	138	15	1	1	NUM
ejpam-5911	138	16	,	,	PUNCT
ejpam-5911	138	17	0	0	NUM
ejpam-5911	138	18	}	}	PUNCT
ejpam-5911	138	19	,	,	PUNCT
ejpam-5911	138	20	1	1	NUM
ejpam-5911	138	21	4	4	NUM
ejpam-5911	138	22	,	,	PUNCT
ejpam-5911	138	23	if	if	SCONJ
ejpam-5911	138	24	v	v	VERB
ejpam-5911	138	25	=	=	SYM
ejpam-5911	138	26	n	n	NOUN
ejpam-5911	138	27	,	,	PUNCT
ejpam-5911	138	28	1	1	NUM
ejpam-5911	138	29	2	2	NUM
ejpam-5911	138	30	,	,	PUNCT
ejpam-5911	138	31	if	if	SCONJ
ejpam-5911	138	32	v	v	ADP
ejpam-5911	138	33	=	=	SYM
ejpam-5911	138	34	m	m	NOUN
ejpam-5911	138	35	,	,	PUNCT
ejpam-5911	138	36	1	1	NUM
ejpam-5911	138	37	4	4	NUM
ejpam-5911	138	38	,	,	PUNCT
ejpam-5911	138	39	if	if	SCONJ
ejpam-5911	138	40	v	v	VERB
ejpam-5911	138	41	=	=	SYM
ejpam-5911	138	42	n	n	PRON
ejpam-5911	138	43	∧m	∧m	PROPN
ejpam-5911	138	44	,	,	PUNCT
ejpam-5911	138	45	1	1	NUM
ejpam-5911	138	46	2	2	NUM
ejpam-5911	138	47	,	,	PUNCT
ejpam-5911	138	48	if	if	SCONJ
ejpam-5911	138	49	v	v	VERB
ejpam-5911	138	50	=	=	SYM
ejpam-5911	138	51	n	n	PRON
ejpam-5911	138	52	∨m	∨m	NOUN
ejpam-5911	138	53	,	,	PUNCT
ejpam-5911	138	54	0	0	NUM
ejpam-5911	138	55	,	,	PUNCT
ejpam-5911	138	56	otherwise	otherwise	ADV
ejpam-5911	138	57	,	,	PUNCT
ejpam-5911	138	58	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	138	59	)	)	PUNCT
ejpam-5911	138	60	=	=	PUNCT
ejpam-5911	139	1			NOUN
ejpam-5911	139	2	0	0	NUM
ejpam-5911	139	3	,	,	PUNCT
ejpam-5911	139	4	if	if	SCONJ
ejpam-5911	139	5	v	v	ADP
ejpam-5911	139	6	∈	∈	NOUN
ejpam-5911	139	7	{	{	PUNCT
ejpam-5911	139	8	1	1	NUM
ejpam-5911	139	9	,	,	PUNCT
ejpam-5911	139	10	0	0	NUM
ejpam-5911	139	11	}	}	PUNCT
ejpam-5911	139	12	,	,	PUNCT
ejpam-5911	139	13	1	1	NUM
ejpam-5911	139	14	4	4	NUM
ejpam-5911	139	15	,	,	PUNCT
ejpam-5911	139	16	if	if	SCONJ
ejpam-5911	139	17	v	v	VERB
ejpam-5911	139	18	=	=	SYM
ejpam-5911	139	19	n	n	NOUN
ejpam-5911	139	20	,	,	PUNCT
ejpam-5911	139	21	1	1	NUM
ejpam-5911	139	22	2	2	NUM
ejpam-5911	139	23	,	,	PUNCT
ejpam-5911	139	24	if	if	SCONJ
ejpam-5911	139	25	v	v	ADP
ejpam-5911	139	26	=	=	SYM
ejpam-5911	139	27	m	m	NOUN
ejpam-5911	139	28	,	,	PUNCT
ejpam-5911	139	29	1	1	NUM
ejpam-5911	139	30	2	2	NUM
ejpam-5911	139	31	,	,	PUNCT
ejpam-5911	139	32	if	if	SCONJ
ejpam-5911	139	33	v	v	VERB
ejpam-5911	139	34	=	=	SYM
ejpam-5911	139	35	n	n	PRON
ejpam-5911	139	36	∧m	∧m	PROPN
ejpam-5911	139	37	,	,	PUNCT
ejpam-5911	139	38	1	1	NUM
ejpam-5911	139	39	4	4	NUM
ejpam-5911	139	40	,	,	PUNCT
ejpam-5911	139	41	if	if	SCONJ
ejpam-5911	139	42	v	v	VERB
ejpam-5911	139	43	=	=	SYM
ejpam-5911	139	44	n	n	PRON
ejpam-5911	139	45	∨m	∨m	NOUN
ejpam-5911	139	46	,	,	PUNCT
ejpam-5911	139	47	1	1	NUM
ejpam-5911	139	48	,	,	PUNCT
ejpam-5911	139	49	otherwise	otherwise	ADV
ejpam-5911	139	50	.	.	PUNCT
ejpam-5911	140	1	thus	thus	ADV
ejpam-5911	140	2	,	,	PUNCT
ejpam-5911	140	3	u	u	NOUN
ejpam-5911	140	4	is	be	AUX
ejpam-5911	140	5	an	an	DET
ejpam-5911	140	6	(	(	PUNCT
ejpam-5911	140	7	14	14	NUM
ejpam-5911	140	8	,	,	PUNCT
ejpam-5911	140	9	1	1	NUM
ejpam-5911	140	10	2)-f	2)-f	NUM
ejpam-5911	140	11	-	-	PUNCT
ejpam-5911	140	12	b	b	NOUN
ejpam-5911	140	13	-	-	PUNCT
ejpam-5911	140	14	open	open	ADJ
ejpam-5911	140	15	set	set	NOUN
ejpam-5911	140	16	,	,	PUNCT
ejpam-5911	140	17	but	but	CCONJ
ejpam-5911	140	18	it	it	PRON
ejpam-5911	140	19	is	be	AUX
ejpam-5911	140	20	neither	neither	CCONJ
ejpam-5911	140	21	(	(	PUNCT
ejpam-5911	140	22	14	14	NUM
ejpam-5911	140	23	,	,	PUNCT
ejpam-5911	140	24	1	1	NUM
ejpam-5911	140	25	2)-f	2)-f	NUM
ejpam-5911	140	26	-	-	PUNCT
ejpam-5911	140	27	pre	pre	NOUN
ejpam-5911	140	28	-	-	ADJ
ejpam-5911	140	29	open	open	ADJ
ejpam-5911	140	30	nor	nor	CCONJ
ejpam-5911	140	31	(	(	PUNCT
ejpam-5911	140	32	14	14	NUM
ejpam-5911	140	33	,	,	PUNCT
ejpam-5911	140	34	1	1	NUM
ejpam-5911	140	35	2)-f	2)-f	NUM
ejpam-5911	140	36	-	-	PUNCT
ejpam-5911	140	37	αopen	αopen	NOUN
ejpam-5911	140	38	.	.	PUNCT
ejpam-5911	140	39	example	example	NOUN
ejpam-5911	141	1	2	2	NUM
ejpam-5911	141	2	.	.	PUNCT
ejpam-5911	141	3	let	let	VERB
ejpam-5911	141	4	g	g	NOUN
ejpam-5911	141	5	=	=	SYM
ejpam-5911	141	6	{	{	PUNCT
ejpam-5911	141	7	g1	g1	PROPN
ejpam-5911	141	8	,	,	PUNCT
ejpam-5911	141	9	g2	g2	PROPN
ejpam-5911	141	10	}	}	PUNCT
ejpam-5911	141	11	and	and	CCONJ
ejpam-5911	141	12	define	define	VERB
ejpam-5911	141	13	m	m	PROPN
ejpam-5911	141	14	,	,	PUNCT
ejpam-5911	141	15	n	n	CCONJ
ejpam-5911	141	16	,	,	PUNCT
ejpam-5911	141	17	u	u	PROPN
ejpam-5911	141	18	∈	∈	PROPN
ejpam-5911	141	19	ig	ig	PROPN
ejpam-5911	141	20	as	as	SCONJ
ejpam-5911	141	21	follows	follow	VERB
ejpam-5911	141	22	:	:	PUNCT
ejpam-5911	141	23	m	m	VERB
ejpam-5911	141	24	=	=	PUNCT
ejpam-5911	141	25	{	{	PUNCT
ejpam-5911	141	26	g1	g1	PROPN
ejpam-5911	141	27	0.3	0.3	NUM
ejpam-5911	141	28	,	,	PUNCT
ejpam-5911	141	29	g2	g2	PROPN
ejpam-5911	141	30	0.2	0.2	NUM
ejpam-5911	141	31	}	}	PUNCT
ejpam-5911	141	32	,	,	PUNCT
ejpam-5911	141	33	n	n	NOUN
ejpam-5911	141	34	=	=	PRON
ejpam-5911	141	35	{	{	PUNCT
ejpam-5911	141	36	g1	g1	PROPN
ejpam-5911	141	37	0.7	0.7	NUM
ejpam-5911	141	38	,	,	PUNCT
ejpam-5911	141	39	g2	g2	PROPN
ejpam-5911	141	40	0.8	0.8	NUM
ejpam-5911	141	41	}	}	PUNCT
ejpam-5911	141	42	,	,	PUNCT
ejpam-5911	141	43	u	u	NOUN
ejpam-5911	141	44	=	=	PUNCT
ejpam-5911	141	45	{	{	PUNCT
ejpam-5911	141	46	g1	g1	PROPN
ejpam-5911	141	47	0.5	0.5	NUM
ejpam-5911	141	48	,	,	PUNCT
ejpam-5911	141	49	g2	g2	PROPN
ejpam-5911	141	50	0.4	0.4	NUM
ejpam-5911	141	51	}	}	PUNCT
ejpam-5911	141	52	.	.	PUNCT
ejpam-5911	142	1	define	define	VERB
ejpam-5911	142	2	ℑ,ℑ∗	ℑ,ℑ∗	NOUN
ejpam-5911	142	3	:	:	PUNCT
ejpam-5911	142	4	ig	ig	PROPN
ejpam-5911	142	5	−→	−→	NOUN
ejpam-5911	143	1	i	i	PRON
ejpam-5911	143	2	as	as	SCONJ
ejpam-5911	143	3	follows	follow	VERB
ejpam-5911	143	4	:	:	PUNCT
ejpam-5911	143	5	ℑ(v	ℑ(v	X
ejpam-5911	143	6	)	)	PUNCT
ejpam-5911	143	7	=	=	PUNCT
ejpam-5911	143	8			NOUN
ejpam-5911	143	9	1	1	NUM
ejpam-5911	143	10	,	,	PUNCT
ejpam-5911	143	11	if	if	SCONJ
ejpam-5911	143	12	v	v	ADP
ejpam-5911	143	13	∈	∈	NOUN
ejpam-5911	143	14	{	{	PUNCT
ejpam-5911	143	15	1	1	NUM
ejpam-5911	143	16	,	,	PUNCT
ejpam-5911	143	17	0	0	NUM
ejpam-5911	143	18	}	}	PUNCT
ejpam-5911	143	19	,	,	PUNCT
ejpam-5911	143	20	1	1	NUM
ejpam-5911	143	21	3	3	NUM
ejpam-5911	143	22	,	,	PUNCT
ejpam-5911	143	23	if	if	SCONJ
ejpam-5911	143	24	v	v	ADP
ejpam-5911	143	25	=	=	SYM
ejpam-5911	143	26	m	m	NOUN
ejpam-5911	143	27	,	,	PUNCT
ejpam-5911	143	28	1	1	NUM
ejpam-5911	143	29	2	2	NUM
ejpam-5911	143	30	,	,	PUNCT
ejpam-5911	143	31	if	if	SCONJ
ejpam-5911	143	32	v	v	VERB
ejpam-5911	143	33	=	=	SYM
ejpam-5911	143	34	n	n	NOUN
ejpam-5911	143	35	,	,	PUNCT
ejpam-5911	143	36	0	0	NUM
ejpam-5911	143	37	,	,	PUNCT
ejpam-5911	143	38	otherwise	otherwise	ADV
ejpam-5911	143	39	,	,	PUNCT
ejpam-5911	143	40	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	143	41	)	)	PUNCT
ejpam-5911	143	42	=	=	PUNCT
ejpam-5911	144	1			NOUN
ejpam-5911	144	2	0	0	NUM
ejpam-5911	144	3	,	,	PUNCT
ejpam-5911	144	4	if	if	SCONJ
ejpam-5911	144	5	v	v	ADP
ejpam-5911	144	6	∈	∈	NOUN
ejpam-5911	144	7	{	{	PUNCT
ejpam-5911	144	8	1	1	NUM
ejpam-5911	144	9	,	,	PUNCT
ejpam-5911	144	10	0	0	NUM
ejpam-5911	144	11	}	}	PUNCT
ejpam-5911	144	12	,	,	PUNCT
ejpam-5911	144	13	1	1	NUM
ejpam-5911	144	14	2	2	NUM
ejpam-5911	144	15	,	,	PUNCT
ejpam-5911	144	16	if	if	SCONJ
ejpam-5911	144	17	v	v	ADP
ejpam-5911	144	18	=	=	SYM
ejpam-5911	144	19	m	m	NOUN
ejpam-5911	144	20	,	,	PUNCT
ejpam-5911	144	21	1	1	NUM
ejpam-5911	144	22	3	3	NUM
ejpam-5911	144	23	,	,	PUNCT
ejpam-5911	144	24	if	if	SCONJ
ejpam-5911	144	25	v	v	VERB
ejpam-5911	144	26	=	=	SYM
ejpam-5911	144	27	n	n	NOUN
ejpam-5911	144	28	,	,	PUNCT
ejpam-5911	144	29	1	1	NUM
ejpam-5911	144	30	,	,	PUNCT
ejpam-5911	144	31	otherwise	otherwise	ADV
ejpam-5911	144	32	.	.	PUNCT
ejpam-5911	145	1	thus	thus	ADV
ejpam-5911	145	2	,	,	PUNCT
ejpam-5911	145	3	u	u	NOUN
ejpam-5911	145	4	is	be	AUX
ejpam-5911	145	5	an	an	DET
ejpam-5911	145	6	(	(	PUNCT
ejpam-5911	145	7	13	13	NUM
ejpam-5911	145	8	,	,	PUNCT
ejpam-5911	145	9	1	1	NUM
ejpam-5911	145	10	2)-f	2)-f	NUM
ejpam-5911	145	11	-	-	PUNCT
ejpam-5911	145	12	b	b	NOUN
ejpam-5911	145	13	-	-	PUNCT
ejpam-5911	145	14	open	open	ADJ
ejpam-5911	145	15	set	set	NOUN
ejpam-5911	145	16	,	,	PUNCT
ejpam-5911	145	17	but	but	CCONJ
ejpam-5911	145	18	it	it	PRON
ejpam-5911	145	19	is	be	AUX
ejpam-5911	145	20	not	not	PART
ejpam-5911	145	21	(	(	PUNCT
ejpam-5911	145	22	13	13	NUM
ejpam-5911	145	23	,	,	PUNCT
ejpam-5911	145	24	1	1	NUM
ejpam-5911	145	25	2)-f	2)-f	NUM
ejpam-5911	145	26	-	-	PUNCT
ejpam-5911	145	27	semi	semi	ADV
ejpam-5911	145	28	-	-	ADJ
ejpam-5911	145	29	open	open	ADJ
ejpam-5911	145	30	.	.	PUNCT
ejpam-5911	146	1	example	example	NOUN
ejpam-5911	147	1	3	3	X
ejpam-5911	147	2	.	.	PUNCT
ejpam-5911	147	3	let	let	VERB
ejpam-5911	147	4	g	g	PROPN
ejpam-5911	147	5	=	=	SYM
ejpam-5911	147	6	{	{	PUNCT
ejpam-5911	147	7	g1	g1	PROPN
ejpam-5911	147	8	,	,	PUNCT
ejpam-5911	147	9	g2	g2	PROPN
ejpam-5911	147	10	}	}	PUNCT
ejpam-5911	147	11	and	and	CCONJ
ejpam-5911	147	12	define	define	VERB
ejpam-5911	147	13	m	m	PROPN
ejpam-5911	147	14	,	,	PUNCT
ejpam-5911	147	15	u	u	PROPN
ejpam-5911	147	16	∈	∈	PROPN
ejpam-5911	147	17	ig	ig	PROPN
ejpam-5911	147	18	as	as	SCONJ
ejpam-5911	147	19	follows	follow	VERB
ejpam-5911	147	20	:	:	PUNCT
ejpam-5911	147	21	m	m	VERB
ejpam-5911	147	22	=	=	PUNCT
ejpam-5911	147	23	{	{	PUNCT
ejpam-5911	147	24	g1	g1	PROPN
ejpam-5911	147	25	0.5	0.5	NUM
ejpam-5911	147	26	,	,	PUNCT
ejpam-5911	147	27	g2	g2	PROPN
ejpam-5911	147	28	0.4	0.4	NUM
ejpam-5911	147	29	}	}	PUNCT
ejpam-5911	147	30	,	,	PUNCT
ejpam-5911	147	31	u	u	NOUN
ejpam-5911	147	32	=	=	PUNCT
ejpam-5911	147	33	{	{	PUNCT
ejpam-5911	147	34	g1	g1	PROPN
ejpam-5911	147	35	0.4	0.4	NUM
ejpam-5911	147	36	,	,	PUNCT
ejpam-5911	147	37	g2	g2	PROPN
ejpam-5911	147	38	0.5	0.5	NUM
ejpam-5911	147	39	}	}	PUNCT
ejpam-5911	147	40	.	.	PUNCT
ejpam-5911	148	1	define	define	VERB
ejpam-5911	148	2	ℑ,ℑ∗	ℑ,ℑ∗	NOUN
ejpam-5911	148	3	:	:	PUNCT
ejpam-5911	149	1	i	i	PRON
ejpam-5911	149	2	m	m	VERB
ejpam-5911	149	3	−→	−→	ADJ
ejpam-5911	149	4	i	i	PRON
ejpam-5911	149	5	as	as	SCONJ
ejpam-5911	149	6	follows	follow	VERB
ejpam-5911	149	7	:	:	PUNCT
ejpam-5911	149	8	ℑ(v	ℑ(v	X
ejpam-5911	149	9	)	)	PUNCT
ejpam-5911	149	10	=	=	SYM
ejpam-5911	150	1			NOUN
ejpam-5911	150	2	1	1	NUM
ejpam-5911	150	3	,	,	PUNCT
ejpam-5911	150	4	if	if	SCONJ
ejpam-5911	150	5	v	v	ADP
ejpam-5911	150	6	∈	∈	NOUN
ejpam-5911	150	7	{	{	PUNCT
ejpam-5911	150	8	1	1	NUM
ejpam-5911	150	9	,	,	PUNCT
ejpam-5911	150	10	0	0	NUM
ejpam-5911	150	11	}	}	PUNCT
ejpam-5911	150	12	,	,	PUNCT
ejpam-5911	150	13	1	1	NUM
ejpam-5911	150	14	2	2	NUM
ejpam-5911	150	15	,	,	PUNCT
ejpam-5911	150	16	if	if	SCONJ
ejpam-5911	150	17	v	v	ADP
ejpam-5911	150	18	=	=	NOUN
ejpam-5911	150	19	m	m	PROPN
ejpam-5911	150	20	,	,	PUNCT
ejpam-5911	150	21	0	0	NUM
ejpam-5911	150	22	,	,	PUNCT
ejpam-5911	150	23	otherwise	otherwise	ADV
ejpam-5911	150	24	,	,	PUNCT
ejpam-5911	150	25	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	150	26	)	)	PUNCT
ejpam-5911	151	1	=	=	SYM
ejpam-5911	152	1			NOUN
ejpam-5911	152	2	0	0	NUM
ejpam-5911	152	3	,	,	PUNCT
ejpam-5911	152	4	if	if	SCONJ
ejpam-5911	152	5	v	v	ADP
ejpam-5911	152	6	∈	∈	NOUN
ejpam-5911	152	7	{	{	PUNCT
ejpam-5911	152	8	1	1	NUM
ejpam-5911	152	9	,	,	PUNCT
ejpam-5911	152	10	0	0	NUM
ejpam-5911	152	11	}	}	PUNCT
ejpam-5911	152	12	,	,	PUNCT
ejpam-5911	152	13	1	1	NUM
ejpam-5911	152	14	2	2	NUM
ejpam-5911	152	15	,	,	PUNCT
ejpam-5911	152	16	if	if	SCONJ
ejpam-5911	152	17	v	v	ADP
ejpam-5911	152	18	=	=	NOUN
ejpam-5911	152	19	m	m	PROPN
ejpam-5911	152	20	,	,	PUNCT
ejpam-5911	152	21	1	1	NUM
ejpam-5911	152	22	,	,	PUNCT
ejpam-5911	152	23	otherwise	otherwise	ADV
ejpam-5911	152	24	.	.	PUNCT
ejpam-5911	153	1	thus	thus	ADV
ejpam-5911	153	2	,	,	PUNCT
ejpam-5911	153	3	u	u	NOUN
ejpam-5911	153	4	is	be	AUX
ejpam-5911	153	5	an	an	DET
ejpam-5911	153	6	(	(	PUNCT
ejpam-5911	153	7	13	13	NUM
ejpam-5911	153	8	,	,	PUNCT
ejpam-5911	153	9	1	1	NUM
ejpam-5911	153	10	2)-f	2)-f	NUM
ejpam-5911	153	11	-	-	PUNCT
ejpam-5911	153	12	β	β	NOUN
ejpam-5911	153	13	-	-	ADJ
ejpam-5911	153	14	open	open	ADJ
ejpam-5911	153	15	set	set	NOUN
ejpam-5911	153	16	,	,	PUNCT
ejpam-5911	153	17	but	but	CCONJ
ejpam-5911	153	18	it	it	PRON
ejpam-5911	153	19	is	be	AUX
ejpam-5911	153	20	not	not	PART
ejpam-5911	153	21	(	(	PUNCT
ejpam-5911	153	22	13	13	NUM
ejpam-5911	153	23	,	,	PUNCT
ejpam-5911	153	24	1	1	NUM
ejpam-5911	153	25	2)-f	2)-f	NUM
ejpam-5911	153	26	-	-	PUNCT
ejpam-5911	153	27	b	b	NOUN
ejpam-5911	153	28	-	-	PUNCT
ejpam-5911	153	29	open	open	ADJ
ejpam-5911	153	30	.	.	PUNCT
ejpam-5911	154	1	i.	i.	PROPN
ejpam-5911	154	2	m.	m.	PROPN
ejpam-5911	154	3	taha	taha	PROPN
ejpam-5911	154	4	,	,	PUNCT
ejpam-5911	154	5	j.	j.	PROPN
ejpam-5911	154	6	al	al	PROPN
ejpam-5911	154	7	-	-	PUNCT
ejpam-5911	154	8	mufarrij	mufarrij	PROPN
ejpam-5911	154	9	,	,	PUNCT
ejpam-5911	154	10	o.	o.	PROPN
ejpam-5911	154	11	m.	m.	PROPN
ejpam-5911	154	12	taha	taha	PROPN
ejpam-5911	154	13	/	/	PUNCT
ejpam-5911	154	14	eur	eur	PROPN
ejpam-5911	154	15	.	.	PUNCT
ejpam-5911	155	1	j.	j.	PROPN
ejpam-5911	155	2	pure	pure	PROPN
ejpam-5911	155	3	appl	appl	PROPN
ejpam-5911	155	4	.	.	PROPN
ejpam-5911	155	5	math	math	PROPN
ejpam-5911	155	6	,	,	PUNCT
ejpam-5911	155	7	18	18	NUM
ejpam-5911	155	8	(	(	PUNCT
ejpam-5911	155	9	2	2	NUM
ejpam-5911	155	10	)	)	PUNCT
ejpam-5911	155	11	(	(	PUNCT
ejpam-5911	155	12	2025	2025	NUM
ejpam-5911	155	13	)	)	PUNCT
ejpam-5911	155	14	,	,	PUNCT
ejpam-5911	155	15	5911	5911	NUM
ejpam-5911	155	16	7	7	NUM
ejpam-5911	155	17	of	of	ADP
ejpam-5911	155	18	27	27	NUM
ejpam-5911	155	19	corollary	corollary	ADJ
ejpam-5911	155	20	1	1	NUM
ejpam-5911	155	21	.	.	PUNCT
ejpam-5911	156	1	in	in	ADP
ejpam-5911	156	2	an	an	DET
ejpam-5911	156	3	dft	dft	NOUN
ejpam-5911	156	4	s	s	X
ejpam-5911	156	5	(	(	PUNCT
ejpam-5911	156	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	156	7	)	)	PUNCT
ejpam-5911	156	8	,	,	PUNCT
ejpam-5911	156	9	r	r	NOUN
ejpam-5911	156	10	∈	∈	PROPN
ejpam-5911	156	11	i	i	X
ejpam-5911	156	12	◦	◦	NOUN
ejpam-5911	156	13	,	,	PUNCT
ejpam-5911	156	14	and	and	CCONJ
ejpam-5911	156	15	s	s	PROPN
ejpam-5911	156	16	∈	∈	PROPN
ejpam-5911	156	17	i1	i1	PROPN
ejpam-5911	156	18	,	,	PUNCT
ejpam-5911	156	19	we	we	PRON
ejpam-5911	156	20	have	have	VERB
ejpam-5911	156	21	the	the	DET
ejpam-5911	156	22	following	follow	VERB
ejpam-5911	156	23	properties	property	NOUN
ejpam-5911	156	24	:	:	PUNCT
ejpam-5911	156	25	(	(	PUNCT
ejpam-5911	156	26	i	i	NOUN
ejpam-5911	156	27	)	)	PUNCT
ejpam-5911	156	28	the	the	DET
ejpam-5911	156	29	union	union	NOUN
ejpam-5911	156	30	of	of	ADP
ejpam-5911	156	31	(	(	PUNCT
ejpam-5911	156	32	r	r	NOUN
ejpam-5911	156	33	,	,	PUNCT
ejpam-5911	156	34	s)-f	s)-f	NOUN
ejpam-5911	156	35	-	-	PUNCT
ejpam-5911	156	36	b	b	NOUN
ejpam-5911	156	37	-	-	PUNCT
ejpam-5911	156	38	open	open	ADJ
ejpam-5911	156	39	sets	set	NOUN
ejpam-5911	156	40	is	be	AUX
ejpam-5911	156	41	(	(	PUNCT
ejpam-5911	156	42	r	r	NOUN
ejpam-5911	156	43	,	,	PUNCT
ejpam-5911	156	44	s)-f	s)-f	NOUN
ejpam-5911	156	45	-	-	PUNCT
ejpam-5911	156	46	b	b	NOUN
ejpam-5911	156	47	-	-	PUNCT
ejpam-5911	156	48	open	open	ADJ
ejpam-5911	156	49	;	;	PUNCT
ejpam-5911	156	50	(	(	PUNCT
ejpam-5911	156	51	ii	ii	NOUN
ejpam-5911	156	52	)	)	PUNCT
ejpam-5911	156	53	the	the	DET
ejpam-5911	156	54	intersection	intersection	NOUN
ejpam-5911	156	55	of	of	ADP
ejpam-5911	156	56	(	(	PUNCT
ejpam-5911	156	57	r	r	NOUN
ejpam-5911	156	58	,	,	PUNCT
ejpam-5911	156	59	s)-f	s)-f	NOUN
ejpam-5911	156	60	-	-	PUNCT
ejpam-5911	156	61	b	b	NOUN
ejpam-5911	156	62	-	-	PUNCT
ejpam-5911	156	63	closed	closed	ADJ
ejpam-5911	156	64	sets	set	NOUN
ejpam-5911	156	65	is	be	AUX
ejpam-5911	156	66	(	(	PUNCT
ejpam-5911	156	67	r	r	NOUN
ejpam-5911	156	68	,	,	PUNCT
ejpam-5911	156	69	s)-f	s)-f	NOUN
ejpam-5911	156	70	-	-	PUNCT
ejpam-5911	156	71	b	b	NOUN
ejpam-5911	156	72	-	-	PUNCT
ejpam-5911	156	73	closed	closed	ADJ
ejpam-5911	156	74	.	.	PUNCT
ejpam-5911	157	1	proof	proof	NOUN
ejpam-5911	157	2	.	.	PUNCT
ejpam-5911	158	1	this	this	PRON
ejpam-5911	158	2	is	be	AUX
ejpam-5911	158	3	easily	easily	ADV
ejpam-5911	158	4	proved	prove	VERB
ejpam-5911	158	5	by	by	ADP
ejpam-5911	158	6	definitions	definition	NOUN
ejpam-5911	158	7	6	6	NUM
ejpam-5911	158	8	and	and	CCONJ
ejpam-5911	158	9	7	7	NUM
ejpam-5911	158	10	.	.	PUNCT
ejpam-5911	158	11	corollary	corollary	ADJ
ejpam-5911	158	12	2	2	NUM
ejpam-5911	158	13	.	.	PUNCT
ejpam-5911	159	1	in	in	ADP
ejpam-5911	159	2	an	an	DET
ejpam-5911	159	3	dft	dft	NOUN
ejpam-5911	159	4	s	s	X
ejpam-5911	159	5	(	(	PUNCT
ejpam-5911	159	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	159	7	)	)	PUNCT
ejpam-5911	159	8	,	,	PUNCT
ejpam-5911	159	9	for	for	ADP
ejpam-5911	159	10	each	each	DET
ejpam-5911	159	11	(	(	PUNCT
ejpam-5911	159	12	r	r	NOUN
ejpam-5911	159	13	,	,	PUNCT
ejpam-5911	159	14	s)-f	s)-f	NOUN
ejpam-5911	159	15	-	-	PUNCT
ejpam-5911	159	16	b	b	NOUN
ejpam-5911	159	17	-	-	PUNCT
ejpam-5911	159	18	closed	closed	ADJ
ejpam-5911	159	19	set	set	NOUN
ejpam-5911	159	20	m	m	NOUN
ejpam-5911	159	21	∈	∈	PROPN
ejpam-5911	159	22	ig	ig	PROPN
ejpam-5911	159	23	:	:	PUNCT
ejpam-5911	159	24	(	(	PUNCT
ejpam-5911	159	25	i	i	NOUN
ejpam-5911	159	26	)	)	PUNCT
ejpam-5911	159	27	if	if	SCONJ
ejpam-5911	159	28	m	m	NOUN
ejpam-5911	159	29	is	be	AUX
ejpam-5911	159	30	(	(	PUNCT
ejpam-5911	159	31	r	r	NOUN
ejpam-5911	159	32	,	,	PUNCT
ejpam-5911	159	33	s)-f	s)-f	NOUN
ejpam-5911	159	34	-	-	PUNCT
ejpam-5911	159	35	regularly	regularly	ADV
ejpam-5911	159	36	-	-	PUNCT
ejpam-5911	159	37	open	open	ADJ
ejpam-5911	159	38	,	,	PUNCT
ejpam-5911	159	39	then	then	ADV
ejpam-5911	159	40	m	m	NOUN
ejpam-5911	159	41	is	be	AUX
ejpam-5911	159	42	(	(	PUNCT
ejpam-5911	159	43	r	r	NOUN
ejpam-5911	159	44	,	,	PUNCT
ejpam-5911	159	45	s)-f	s)-f	NOUN
ejpam-5911	159	46	-	-	PUNCT
ejpam-5911	159	47	pre	pre	NOUN
ejpam-5911	159	48	-	-	ADJ
ejpam-5911	159	49	closed	closed	ADJ
ejpam-5911	159	50	.	.	PUNCT
ejpam-5911	160	1	(	(	PUNCT
ejpam-5911	160	2	ii	ii	NOUN
ejpam-5911	160	3	)	)	PUNCT
ejpam-5911	160	4	if	if	SCONJ
ejpam-5911	160	5	m	m	NOUN
ejpam-5911	160	6	is	be	AUX
ejpam-5911	160	7	(	(	PUNCT
ejpam-5911	160	8	r	r	NOUN
ejpam-5911	160	9	,	,	PUNCT
ejpam-5911	160	10	s)-f	s)-f	NOUN
ejpam-5911	160	11	-	-	PUNCT
ejpam-5911	160	12	regularly	regularly	ADV
ejpam-5911	160	13	-	-	PUNCT
ejpam-5911	160	14	closed	closed	ADJ
ejpam-5911	160	15	,	,	PUNCT
ejpam-5911	160	16	then	then	ADV
ejpam-5911	160	17	m	m	NOUN
ejpam-5911	160	18	is	be	AUX
ejpam-5911	160	19	(	(	PUNCT
ejpam-5911	160	20	r	r	NOUN
ejpam-5911	160	21	,	,	PUNCT
ejpam-5911	160	22	s)-f	s)-f	NOUN
ejpam-5911	160	23	-	-	PUNCT
ejpam-5911	160	24	semi	semi	ADV
ejpam-5911	160	25	-	-	ADJ
ejpam-5911	160	26	closed	closed	ADJ
ejpam-5911	160	27	.	.	PUNCT
ejpam-5911	161	1	(	(	PUNCT
ejpam-5911	161	2	iii	iii	X
ejpam-5911	161	3	)	)	PUNCT
ejpam-5911	161	4	if	if	SCONJ
ejpam-5911	161	5	iℑ∗(m	iℑ∗(m	NOUN
ejpam-5911	161	6	,	,	PUNCT
ejpam-5911	161	7	r	r	NOUN
ejpam-5911	161	8	,	,	PUNCT
ejpam-5911	161	9	s	s	PART
ejpam-5911	161	10	)	)	PUNCT
ejpam-5911	161	11	=	=	SYM
ejpam-5911	161	12	0	0	NUM
ejpam-5911	161	13	,	,	PUNCT
ejpam-5911	161	14	then	then	ADV
ejpam-5911	161	15	m	m	VERB
ejpam-5911	161	16	is	be	AUX
ejpam-5911	161	17	(	(	PUNCT
ejpam-5911	161	18	r	r	NOUN
ejpam-5911	161	19	,	,	PUNCT
ejpam-5911	161	20	s)-f	s)-f	NOUN
ejpam-5911	161	21	-	-	PUNCT
ejpam-5911	161	22	semi	semi	ADV
ejpam-5911	161	23	-	-	ADJ
ejpam-5911	161	24	closed	closed	ADJ
ejpam-5911	161	25	.	.	PUNCT
ejpam-5911	162	1	(	(	PUNCT
ejpam-5911	162	2	iv	iv	X
ejpam-5911	162	3	)	)	PUNCT
ejpam-5911	162	4	if	if	SCONJ
ejpam-5911	162	5	cℑ∗(m	cℑ∗(m	VERB
ejpam-5911	162	6	,	,	PUNCT
ejpam-5911	162	7	r	r	NOUN
ejpam-5911	162	8	,	,	PUNCT
ejpam-5911	162	9	s	s	PART
ejpam-5911	162	10	)	)	PUNCT
ejpam-5911	162	11	=	=	SYM
ejpam-5911	162	12	0	0	NUM
ejpam-5911	163	1	,	,	PUNCT
ejpam-5911	163	2	then	then	ADV
ejpam-5911	163	3	m	m	VERB
ejpam-5911	163	4	is	be	AUX
ejpam-5911	163	5	(	(	PUNCT
ejpam-5911	163	6	r	r	NOUN
ejpam-5911	163	7	,	,	PUNCT
ejpam-5911	163	8	s)-f	s)-f	NOUN
ejpam-5911	163	9	-	-	PUNCT
ejpam-5911	163	10	pre	pre	NOUN
ejpam-5911	163	11	-	-	ADJ
ejpam-5911	163	12	closed	closed	ADJ
ejpam-5911	163	13	.	.	PUNCT
ejpam-5911	164	1	proof	proof	NOUN
ejpam-5911	164	2	.	.	PUNCT
ejpam-5911	165	1	the	the	DET
ejpam-5911	165	2	proof	proof	NOUN
ejpam-5911	165	3	follows	follow	VERB
ejpam-5911	165	4	by	by	ADP
ejpam-5911	165	5	definitions	definition	NOUN
ejpam-5911	165	6	3	3	NUM
ejpam-5911	165	7	and	and	CCONJ
ejpam-5911	165	8	7	7	NUM
ejpam-5911	165	9	.	.	PUNCT
ejpam-5911	165	10	corollary	corollary	ADJ
ejpam-5911	165	11	3	3	X
ejpam-5911	165	12	.	.	PUNCT
ejpam-5911	166	1	in	in	ADP
ejpam-5911	166	2	an	an	DET
ejpam-5911	166	3	dft	dft	NOUN
ejpam-5911	166	4	s	s	X
ejpam-5911	166	5	(	(	PUNCT
ejpam-5911	166	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	166	7	)	)	PUNCT
ejpam-5911	166	8	,	,	PUNCT
ejpam-5911	166	9	for	for	ADP
ejpam-5911	166	10	each	each	PRON
ejpam-5911	166	11	(	(	PUNCT
ejpam-5911	166	12	r	r	NOUN
ejpam-5911	166	13	,	,	PUNCT
ejpam-5911	166	14	s)-f	s)-f	NOUN
ejpam-5911	166	15	-	-	PUNCT
ejpam-5911	166	16	b	b	NOUN
ejpam-5911	166	17	-	-	PUNCT
ejpam-5911	166	18	open	open	ADJ
ejpam-5911	166	19	set	set	VERB
ejpam-5911	166	20	n	n	CCONJ
ejpam-5911	166	21	∈	∈	PROPN
ejpam-5911	166	22	ig	ig	PROPN
ejpam-5911	166	23	:	:	PUNCT
ejpam-5911	166	24	(	(	PUNCT
ejpam-5911	166	25	i	i	NOUN
ejpam-5911	166	26	)	)	PUNCT
ejpam-5911	166	27	if	if	SCONJ
ejpam-5911	166	28	n	n	PRON
ejpam-5911	166	29	is	be	AUX
ejpam-5911	166	30	(	(	PUNCT
ejpam-5911	166	31	r	r	NOUN
ejpam-5911	166	32	,	,	PUNCT
ejpam-5911	166	33	s)-f	s)-f	NOUN
ejpam-5911	166	34	-	-	PUNCT
ejpam-5911	166	35	regularly	regularly	ADV
ejpam-5911	166	36	-	-	PUNCT
ejpam-5911	166	37	open	open	ADJ
ejpam-5911	166	38	,	,	PUNCT
ejpam-5911	166	39	then	then	ADV
ejpam-5911	166	40	n	n	X
ejpam-5911	166	41	is	be	AUX
ejpam-5911	166	42	(	(	PUNCT
ejpam-5911	166	43	r	r	NOUN
ejpam-5911	166	44	,	,	PUNCT
ejpam-5911	166	45	s)-f	s)-f	NOUN
ejpam-5911	166	46	-	-	PUNCT
ejpam-5911	166	47	semi	semi	ADV
ejpam-5911	166	48	-	-	ADJ
ejpam-5911	166	49	open	open	ADJ
ejpam-5911	166	50	.	.	PUNCT
ejpam-5911	167	1	(	(	PUNCT
ejpam-5911	167	2	ii	ii	NOUN
ejpam-5911	167	3	)	)	PUNCT
ejpam-5911	167	4	if	if	SCONJ
ejpam-5911	167	5	n	n	PRON
ejpam-5911	167	6	is	be	AUX
ejpam-5911	167	7	(	(	PUNCT
ejpam-5911	167	8	r	r	NOUN
ejpam-5911	167	9	,	,	PUNCT
ejpam-5911	167	10	s)-f	s)-f	NOUN
ejpam-5911	167	11	-	-	PUNCT
ejpam-5911	167	12	regularly	regularly	ADV
ejpam-5911	167	13	-	-	PUNCT
ejpam-5911	167	14	closed	closed	ADJ
ejpam-5911	167	15	,	,	PUNCT
ejpam-5911	167	16	then	then	ADV
ejpam-5911	167	17	n	n	X
ejpam-5911	167	18	is	be	AUX
ejpam-5911	167	19	(	(	PUNCT
ejpam-5911	167	20	r	r	NOUN
ejpam-5911	167	21	,	,	PUNCT
ejpam-5911	167	22	s)-f	s)-f	NOUN
ejpam-5911	167	23	-	-	PUNCT
ejpam-5911	167	24	pre	pre	NOUN
ejpam-5911	167	25	-	-	ADJ
ejpam-5911	167	26	open	open	ADJ
ejpam-5911	167	27	.	.	PUNCT
ejpam-5911	168	1	(	(	PUNCT
ejpam-5911	168	2	iii	iii	X
ejpam-5911	168	3	)	)	PUNCT
ejpam-5911	168	4	if	if	SCONJ
ejpam-5911	168	5	iℑ∗(n	iℑ∗(n	NOUN
ejpam-5911	168	6	,	,	PUNCT
ejpam-5911	168	7	r	r	NOUN
ejpam-5911	168	8	,	,	PUNCT
ejpam-5911	168	9	s	s	PART
ejpam-5911	168	10	)	)	PUNCT
ejpam-5911	168	11	=	=	SYM
ejpam-5911	168	12	0	0	NUM
ejpam-5911	168	13	,	,	PUNCT
ejpam-5911	168	14	then	then	ADV
ejpam-5911	168	15	n	n	X
ejpam-5911	168	16	is	be	AUX
ejpam-5911	168	17	(	(	PUNCT
ejpam-5911	168	18	r	r	NOUN
ejpam-5911	168	19	,	,	PUNCT
ejpam-5911	168	20	s)-f	s)-f	NOUN
ejpam-5911	168	21	-	-	PUNCT
ejpam-5911	168	22	pre	pre	NOUN
ejpam-5911	168	23	-	-	ADJ
ejpam-5911	168	24	open	open	ADJ
ejpam-5911	168	25	.	.	PUNCT
ejpam-5911	169	1	(	(	PUNCT
ejpam-5911	169	2	iv	iv	X
ejpam-5911	169	3	)	)	PUNCT
ejpam-5911	169	4	if	if	SCONJ
ejpam-5911	169	5	cℑ∗(n	cℑ∗(n	NOUN
ejpam-5911	169	6	,	,	PUNCT
ejpam-5911	169	7	r	r	NOUN
ejpam-5911	169	8	,	,	PUNCT
ejpam-5911	169	9	s	s	PART
ejpam-5911	169	10	)	)	PUNCT
ejpam-5911	169	11	=	=	SYM
ejpam-5911	169	12	0	0	NUM
ejpam-5911	169	13	,	,	PUNCT
ejpam-5911	169	14	then	then	ADV
ejpam-5911	169	15	n	n	X
ejpam-5911	169	16	is	be	AUX
ejpam-5911	169	17	(	(	PUNCT
ejpam-5911	169	18	r	r	NOUN
ejpam-5911	169	19	,	,	PUNCT
ejpam-5911	169	20	s)-f	s)-f	NOUN
ejpam-5911	169	21	-	-	PUNCT
ejpam-5911	169	22	semi	semi	ADV
ejpam-5911	169	23	-	-	ADJ
ejpam-5911	169	24	open	open	ADJ
ejpam-5911	169	25	.	.	PUNCT
ejpam-5911	170	1	proof	proof	NOUN
ejpam-5911	170	2	.	.	PUNCT
ejpam-5911	171	1	the	the	DET
ejpam-5911	171	2	proof	proof	NOUN
ejpam-5911	171	3	follows	follow	VERB
ejpam-5911	171	4	by	by	ADP
ejpam-5911	171	5	definitions	definition	NOUN
ejpam-5911	171	6	3	3	NUM
ejpam-5911	171	7	and	and	CCONJ
ejpam-5911	171	8	6	6	NUM
ejpam-5911	171	9	.	.	X
ejpam-5911	171	10	definition	definition	NOUN
ejpam-5911	171	11	8	8	NUM
ejpam-5911	171	12	.	.	PUNCT
ejpam-5911	172	1	in	in	ADP
ejpam-5911	172	2	an	an	DET
ejpam-5911	172	3	dft	dft	NOUN
ejpam-5911	172	4	s	s	X
ejpam-5911	172	5	(	(	PUNCT
ejpam-5911	172	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	172	7	)	)	PUNCT
ejpam-5911	172	8	,	,	PUNCT
ejpam-5911	172	9	for	for	ADP
ejpam-5911	172	10	each	each	DET
ejpam-5911	172	11	m	m	PROPN
ejpam-5911	172	12	∈	∈	PROPN
ejpam-5911	172	13	ig	ig	PROPN
ejpam-5911	172	14	,	,	PUNCT
ejpam-5911	172	15	r	r	NOUN
ejpam-5911	172	16	∈	∈	PROPN
ejpam-5911	172	17	i	i	NOUN
ejpam-5911	172	18	◦	◦	NOUN
ejpam-5911	172	19	,	,	PUNCT
ejpam-5911	172	20	and	and	CCONJ
ejpam-5911	172	21	s	s	PROPN
ejpam-5911	172	22	∈	∈	PROPN
ejpam-5911	172	23	i1	i1	PROPN
ejpam-5911	172	24	,	,	PUNCT
ejpam-5911	172	25	we	we	PRON
ejpam-5911	172	26	define	define	VERB
ejpam-5911	172	27	an	an	DET
ejpam-5911	172	28	df	df	PROPN
ejpam-5911	172	29	-	-	PUNCT
ejpam-5911	172	30	b	b	NOUN
ejpam-5911	172	31	-	-	PUNCT
ejpam-5911	172	32	closure	closure	NOUN
ejpam-5911	172	33	operator	operator	NOUN
ejpam-5911	172	34	bcℑ∗	bcℑ∗	NOUN
ejpam-5911	172	35	:	:	PUNCT
ejpam-5911	172	36	ig	ig	INTJ
ejpam-5911	172	37	×	×	INTJ
ejpam-5911	173	1	i	i	PRON
ejpam-5911	173	2	◦	◦	VERB
ejpam-5911	173	3	×	×	PROPN
ejpam-5911	173	4	i1	i1	PROPN
ejpam-5911	173	5	−→	−→	NOUN
ejpam-5911	173	6	ig	ig	PROPN
ejpam-5911	173	7	as	as	SCONJ
ejpam-5911	173	8	follows	follow	VERB
ejpam-5911	173	9	:	:	PUNCT
ejpam-5911	173	10	bcℑ∗(m	bcℑ∗(m	NOUN
ejpam-5911	173	11	,	,	PUNCT
ejpam-5911	173	12	r	r	NOUN
ejpam-5911	173	13	,	,	PUNCT
ejpam-5911	173	14	s	s	NOUN
ejpam-5911	173	15	)	)	PUNCT
ejpam-5911	173	16	=	=	SYM
ejpam-5911	173	17	∧	∧	NOUN
ejpam-5911	173	18	{	{	PUNCT
ejpam-5911	173	19	n	n	NOUN
ejpam-5911	173	20	∈	∈	NOUN
ejpam-5911	174	1	ig	ig	PROPN
ejpam-5911	174	2	:	:	PUNCT
ejpam-5911	174	3	m	m	VERB
ejpam-5911	174	4	≤	≤	ADJ
ejpam-5911	174	5	n	n	PRON
ejpam-5911	174	6	,	,	PUNCT
ejpam-5911	174	7	n	n	X
ejpam-5911	174	8	is	be	AUX
ejpam-5911	174	9	(	(	PUNCT
ejpam-5911	174	10	r	r	NOUN
ejpam-5911	174	11	,	,	PUNCT
ejpam-5911	174	12	s)-f	s)-f	NOUN
ejpam-5911	174	13	-	-	PUNCT
ejpam-5911	174	14	b	b	NOUN
ejpam-5911	174	15	-	-	PUNCT
ejpam-5911	174	16	closed	closed	ADJ
ejpam-5911	174	17	}	}	PUNCT
ejpam-5911	174	18	.	.	PUNCT
ejpam-5911	175	1	proposition	proposition	NOUN
ejpam-5911	175	2	2	2	NUM
ejpam-5911	175	3	.	.	PUNCT
ejpam-5911	176	1	in	in	ADP
ejpam-5911	176	2	an	an	DET
ejpam-5911	176	3	dft	dft	NOUN
ejpam-5911	176	4	s	s	X
ejpam-5911	176	5	(	(	PUNCT
ejpam-5911	176	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	176	7	)	)	PUNCT
ejpam-5911	176	8	,	,	PUNCT
ejpam-5911	176	9	for	for	ADP
ejpam-5911	176	10	each	each	DET
ejpam-5911	176	11	m	m	PROPN
ejpam-5911	176	12	∈	∈	PROPN
ejpam-5911	176	13	ig	ig	PROPN
ejpam-5911	176	14	,	,	PUNCT
ejpam-5911	176	15	r	r	NOUN
ejpam-5911	176	16	∈	∈	PROPN
ejpam-5911	176	17	i	i	NOUN
ejpam-5911	176	18	◦	◦	NOUN
ejpam-5911	176	19	,	,	PUNCT
ejpam-5911	176	20	and	and	CCONJ
ejpam-5911	176	21	s	s	PROPN
ejpam-5911	176	22	∈	∈	PROPN
ejpam-5911	176	23	i1	i1	PROPN
ejpam-5911	176	24	.	.	PUNCT
ejpam-5911	177	1	an	an	DET
ejpam-5911	177	2	f	f	X
ejpam-5911	177	3	-	-	PUNCT
ejpam-5911	177	4	set	set	VERB
ejpam-5911	177	5	m	m	NOUN
ejpam-5911	177	6	is	be	AUX
ejpam-5911	177	7	(	(	PUNCT
ejpam-5911	177	8	r	r	NOUN
ejpam-5911	177	9	,	,	PUNCT
ejpam-5911	177	10	s)-f	s)-f	NOUN
ejpam-5911	177	11	-	-	PUNCT
ejpam-5911	177	12	b	b	NOUN
ejpam-5911	177	13	-	-	PUNCT
ejpam-5911	177	14	closed	closed	ADJ
ejpam-5911	177	15	iff	iff	PROPN
ejpam-5911	177	16	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	177	17	,	,	PUNCT
ejpam-5911	177	18	r	r	PROPN
ejpam-5911	177	19	,	,	PUNCT
ejpam-5911	177	20	s	s	NOUN
ejpam-5911	177	21	)	)	PUNCT
ejpam-5911	177	22	=	=	VERB
ejpam-5911	177	23	m.	m.	NOUN
ejpam-5911	177	24	proof	proof	NOUN
ejpam-5911	177	25	.	.	PUNCT
ejpam-5911	178	1	this	this	PRON
ejpam-5911	178	2	is	be	AUX
ejpam-5911	178	3	easily	easily	ADV
ejpam-5911	178	4	proved	prove	VERB
ejpam-5911	178	5	from	from	ADP
ejpam-5911	178	6	definition	definition	NOUN
ejpam-5911	178	7	8	8	NUM
ejpam-5911	178	8	.	.	PUNCT
ejpam-5911	178	9	i.	i.	PROPN
ejpam-5911	178	10	m.	m.	PROPN
ejpam-5911	178	11	taha	taha	PROPN
ejpam-5911	178	12	,	,	PUNCT
ejpam-5911	178	13	j.	j.	PROPN
ejpam-5911	178	14	al	al	PROPN
ejpam-5911	178	15	-	-	PUNCT
ejpam-5911	178	16	mufarrij	mufarrij	PROPN
ejpam-5911	178	17	,	,	PUNCT
ejpam-5911	178	18	o.	o.	PROPN
ejpam-5911	178	19	m.	m.	PROPN
ejpam-5911	178	20	taha	taha	PROPN
ejpam-5911	178	21	/	/	PUNCT
ejpam-5911	178	22	eur	eur	PROPN
ejpam-5911	178	23	.	.	PUNCT
ejpam-5911	179	1	j.	j.	PROPN
ejpam-5911	179	2	pure	pure	PROPN
ejpam-5911	179	3	appl	appl	PROPN
ejpam-5911	179	4	.	.	PROPN
ejpam-5911	179	5	math	math	PROPN
ejpam-5911	179	6	,	,	PUNCT
ejpam-5911	179	7	18	18	NUM
ejpam-5911	179	8	(	(	PUNCT
ejpam-5911	179	9	2	2	NUM
ejpam-5911	179	10	)	)	PUNCT
ejpam-5911	179	11	(	(	PUNCT
ejpam-5911	179	12	2025	2025	NUM
ejpam-5911	179	13	)	)	PUNCT
ejpam-5911	179	14	,	,	PUNCT
ejpam-5911	179	15	5911	5911	NUM
ejpam-5911	179	16	8	8	NUM
ejpam-5911	179	17	of	of	ADP
ejpam-5911	179	18	27	27	NUM
ejpam-5911	179	19	theorem	theorem	NOUN
ejpam-5911	179	20	1	1	NUM
ejpam-5911	179	21	.	.	PUNCT
ejpam-5911	180	1	in	in	ADP
ejpam-5911	180	2	an	an	DET
ejpam-5911	180	3	dft	dft	NOUN
ejpam-5911	180	4	s	s	X
ejpam-5911	180	5	(	(	PUNCT
ejpam-5911	180	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	180	7	)	)	PUNCT
ejpam-5911	180	8	,	,	PUNCT
ejpam-5911	180	9	for	for	ADP
ejpam-5911	180	10	each	each	DET
ejpam-5911	180	11	m	m	NOUN
ejpam-5911	180	12	,	,	PUNCT
ejpam-5911	180	13	n	n	PROPN
ejpam-5911	180	14	∈	∈	PROPN
ejpam-5911	180	15	ig	ig	PROPN
ejpam-5911	180	16	,	,	PUNCT
ejpam-5911	180	17	r	r	NOUN
ejpam-5911	180	18	∈	∈	PROPN
ejpam-5911	180	19	i	i	NOUN
ejpam-5911	180	20	◦	◦	NOUN
ejpam-5911	180	21	,	,	PUNCT
ejpam-5911	180	22	and	and	CCONJ
ejpam-5911	180	23	s	s	PROPN
ejpam-5911	180	24	∈	∈	PROPN
ejpam-5911	180	25	i1	i1	PROPN
ejpam-5911	180	26	.	.	PUNCT
ejpam-5911	181	1	an	an	DET
ejpam-5911	181	2	df	df	NOUN
ejpam-5911	181	3	-	-	PUNCT
ejpam-5911	181	4	operator	operator	NOUN
ejpam-5911	181	5	bcℑ∗	bcℑ∗	NOUN
ejpam-5911	181	6	:	:	PUNCT
ejpam-5911	181	7	ig	ig	INTJ
ejpam-5911	181	8	×	×	INTJ
ejpam-5911	182	1	i	i	PRON
ejpam-5911	182	2	◦	◦	VERB
ejpam-5911	182	3	×	×	PROPN
ejpam-5911	182	4	i1	i1	PROPN
ejpam-5911	182	5	−→	−→	NOUN
ejpam-5911	182	6	ig	ig	PROPN
ejpam-5911	182	7	satisfies	satisfy	VERB
ejpam-5911	182	8	the	the	DET
ejpam-5911	182	9	following	follow	VERB
ejpam-5911	182	10	properties	property	NOUN
ejpam-5911	182	11	.	.	PUNCT
ejpam-5911	183	1	(	(	PUNCT
ejpam-5911	183	2	i	i	NOUN
ejpam-5911	183	3	)	)	PUNCT
ejpam-5911	183	4	bcℑ∗(0	bcℑ∗(0	NOUN
ejpam-5911	183	5	,	,	PUNCT
ejpam-5911	183	6	r	r	NOUN
ejpam-5911	183	7	,	,	PUNCT
ejpam-5911	183	8	s	s	PART
ejpam-5911	183	9	)	)	PUNCT
ejpam-5911	183	10	=	=	SYM
ejpam-5911	183	11	0	0	X
ejpam-5911	183	12	.	.	PUNCT
ejpam-5911	183	13	(	(	PUNCT
ejpam-5911	183	14	ii	ii	NOUN
ejpam-5911	183	15	)	)	PUNCT
ejpam-5911	183	16	m	m	VERB
ejpam-5911	183	17	≤	≤	NUM
ejpam-5911	183	18	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	183	19	,	,	PUNCT
ejpam-5911	183	20	r	r	NOUN
ejpam-5911	183	21	,	,	PUNCT
ejpam-5911	183	22	s	s	NOUN
ejpam-5911	183	23	)	)	PUNCT
ejpam-5911	183	24	≤	≤	NOUN
ejpam-5911	183	25	cℑ∗(m	cℑ∗(m	VERB
ejpam-5911	183	26	,	,	PUNCT
ejpam-5911	183	27	r	r	NOUN
ejpam-5911	183	28	,	,	PUNCT
ejpam-5911	183	29	s	s	NOUN
ejpam-5911	183	30	)	)	PUNCT
ejpam-5911	183	31	.	.	PUNCT
ejpam-5911	184	1	(	(	PUNCT
ejpam-5911	184	2	iii	iii	X
ejpam-5911	184	3	)	)	PUNCT
ejpam-5911	184	4	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	184	5	,	,	PUNCT
ejpam-5911	184	6	r	r	NOUN
ejpam-5911	184	7	,	,	PUNCT
ejpam-5911	184	8	s	s	NOUN
ejpam-5911	184	9	)	)	PUNCT
ejpam-5911	184	10	≤	≤	NUM
ejpam-5911	184	11	bcℑ∗(n	bcℑ∗(n	NUM
ejpam-5911	184	12	,	,	PUNCT
ejpam-5911	184	13	r	r	NOUN
ejpam-5911	184	14	,	,	PUNCT
ejpam-5911	184	15	s	s	PART
ejpam-5911	184	16	)	)	PUNCT
ejpam-5911	184	17	if	if	SCONJ
ejpam-5911	184	18	m	m	VERB
ejpam-5911	184	19	≤	≤	VERB
ejpam-5911	184	20	n	n	ADV
ejpam-5911	184	21	.	.	PUNCT
ejpam-5911	185	1	(	(	PUNCT
ejpam-5911	185	2	iv	iv	X
ejpam-5911	185	3	)	)	PUNCT
ejpam-5911	185	4	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	185	5	,	,	PUNCT
ejpam-5911	185	6	r	r	NOUN
ejpam-5911	185	7	,	,	PUNCT
ejpam-5911	185	8	s	s	PART
ejpam-5911	185	9	)	)	PUNCT
ejpam-5911	185	10	,	,	PUNCT
ejpam-5911	185	11	r	r	NOUN
ejpam-5911	185	12	,	,	PUNCT
ejpam-5911	185	13	s	s	NOUN
ejpam-5911	185	14	)	)	PUNCT
ejpam-5911	185	15	=	=	SYM
ejpam-5911	185	16	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	185	17	,	,	PUNCT
ejpam-5911	185	18	r	r	NOUN
ejpam-5911	185	19	,	,	PUNCT
ejpam-5911	185	20	s	s	NOUN
ejpam-5911	185	21	)	)	PUNCT
ejpam-5911	185	22	.	.	PUNCT
ejpam-5911	186	1	(	(	PUNCT
ejpam-5911	186	2	v	v	NOUN
ejpam-5911	186	3	)	)	PUNCT
ejpam-5911	186	4	bcℑ∗(m∨n	bcℑ∗(m∨n	PROPN
ejpam-5911	186	5	,	,	PUNCT
ejpam-5911	186	6	r	r	NOUN
ejpam-5911	186	7	,	,	PUNCT
ejpam-5911	186	8	s	s	PART
ejpam-5911	186	9	)	)	PUNCT
ejpam-5911	186	10	≥	≥	NOUN
ejpam-5911	186	11	bcℑ∗(m	bcℑ∗(m	NOUN
ejpam-5911	186	12	,	,	PUNCT
ejpam-5911	186	13	r	r	NOUN
ejpam-5911	186	14	,	,	PUNCT
ejpam-5911	186	15	s	s	PART
ejpam-5911	186	16	)	)	PUNCT
ejpam-5911	186	17	∨	∨	NUM
ejpam-5911	186	18	bcℑ∗(n	bcℑ∗(n	PROPN
ejpam-5911	186	19	,	,	PUNCT
ejpam-5911	186	20	r	r	PROPN
ejpam-5911	186	21	,	,	PUNCT
ejpam-5911	186	22	s	s	NOUN
ejpam-5911	186	23	)	)	PUNCT
ejpam-5911	186	24	.	.	PUNCT
ejpam-5911	187	1	(	(	PUNCT
ejpam-5911	187	2	vi	vi	NOUN
ejpam-5911	187	3	)	)	PUNCT
ejpam-5911	187	4	bcℑ∗(cℑ∗(m	bcℑ∗(cℑ∗(m	NOUN
ejpam-5911	187	5	,	,	PUNCT
ejpam-5911	187	6	r	r	NOUN
ejpam-5911	187	7	,	,	PUNCT
ejpam-5911	187	8	s	s	PART
ejpam-5911	187	9	)	)	PUNCT
ejpam-5911	187	10	,	,	PUNCT
ejpam-5911	187	11	r	r	NOUN
ejpam-5911	187	12	,	,	PUNCT
ejpam-5911	187	13	s	s	PART
ejpam-5911	187	14	)	)	PUNCT
ejpam-5911	187	15	=	=	SYM
ejpam-5911	188	1	cℑ∗(m	cℑ∗(m	VERB
ejpam-5911	188	2	,	,	PUNCT
ejpam-5911	188	3	r	r	NOUN
ejpam-5911	188	4	,	,	PUNCT
ejpam-5911	188	5	s	s	NOUN
ejpam-5911	188	6	)	)	PUNCT
ejpam-5911	188	7	.	.	PUNCT
ejpam-5911	189	1	proof	proof	NOUN
ejpam-5911	189	2	.	.	PUNCT
ejpam-5911	190	1	(	(	PUNCT
ejpam-5911	190	2	i	i	NOUN
ejpam-5911	190	3	)	)	PUNCT
ejpam-5911	190	4	,	,	PUNCT
ejpam-5911	190	5	(	(	PUNCT
ejpam-5911	190	6	ii	ii	NOUN
ejpam-5911	190	7	)	)	PUNCT
ejpam-5911	190	8	,	,	PUNCT
ejpam-5911	190	9	and	and	CCONJ
ejpam-5911	190	10	(	(	PUNCT
ejpam-5911	190	11	iii	iii	X
ejpam-5911	190	12	)	)	PUNCT
ejpam-5911	190	13	are	be	AUX
ejpam-5911	190	14	easily	easily	ADV
ejpam-5911	190	15	proved	prove	VERB
ejpam-5911	190	16	by	by	ADP
ejpam-5911	190	17	definition	definition	NOUN
ejpam-5911	190	18	8	8	NUM
ejpam-5911	190	19	.	.	PUNCT
ejpam-5911	191	1	(	(	PUNCT
ejpam-5911	191	2	iv	iv	X
ejpam-5911	191	3	)	)	PUNCT
ejpam-5911	191	4	from	from	ADP
ejpam-5911	191	5	(	(	PUNCT
ejpam-5911	191	6	ii	ii	NOUN
ejpam-5911	191	7	)	)	PUNCT
ejpam-5911	191	8	and	and	CCONJ
ejpam-5911	191	9	(	(	PUNCT
ejpam-5911	191	10	iii	iii	NOUN
ejpam-5911	191	11	)	)	PUNCT
ejpam-5911	191	12	,	,	PUNCT
ejpam-5911	191	13	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	191	14	,	,	PUNCT
ejpam-5911	191	15	r	r	NOUN
ejpam-5911	191	16	,	,	PUNCT
ejpam-5911	191	17	s	s	NOUN
ejpam-5911	191	18	)	)	PUNCT
ejpam-5911	191	19	≤	≤	NUM
ejpam-5911	191	20	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	NOUN
ejpam-5911	191	21	,	,	PUNCT
ejpam-5911	191	22	r	r	NOUN
ejpam-5911	191	23	,	,	PUNCT
ejpam-5911	191	24	s	s	PART
ejpam-5911	191	25	)	)	PUNCT
ejpam-5911	191	26	,	,	PUNCT
ejpam-5911	191	27	r	r	NOUN
ejpam-5911	191	28	,	,	PUNCT
ejpam-5911	191	29	s	s	NOUN
ejpam-5911	191	30	)	)	PUNCT
ejpam-5911	191	31	.	.	PUNCT
ejpam-5911	192	1	now	now	ADV
ejpam-5911	192	2	,	,	PUNCT
ejpam-5911	192	3	we	we	PRON
ejpam-5911	192	4	show	show	VERB
ejpam-5911	192	5	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	192	6	,	,	PUNCT
ejpam-5911	192	7	r	r	NOUN
ejpam-5911	192	8	,	,	PUNCT
ejpam-5911	192	9	s	s	PART
ejpam-5911	192	10	)	)	PUNCT
ejpam-5911	192	11	≥	≥	NOUN
ejpam-5911	192	12	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	192	13	,	,	PUNCT
ejpam-5911	192	14	r	r	NOUN
ejpam-5911	192	15	,	,	PUNCT
ejpam-5911	192	16	s	s	PART
ejpam-5911	192	17	)	)	PUNCT
ejpam-5911	192	18	,	,	PUNCT
ejpam-5911	192	19	r	r	NOUN
ejpam-5911	192	20	,	,	PUNCT
ejpam-5911	192	21	s	s	NOUN
ejpam-5911	192	22	)	)	PUNCT
ejpam-5911	192	23	.	.	PUNCT
ejpam-5911	193	1	if	if	SCONJ
ejpam-5911	193	2	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	193	3	,	,	PUNCT
ejpam-5911	193	4	r	r	PROPN
ejpam-5911	193	5	,	,	PUNCT
ejpam-5911	193	6	s	s	PART
ejpam-5911	193	7	)	)	PUNCT
ejpam-5911	193	8	does	do	AUX
ejpam-5911	193	9	not	not	PART
ejpam-5911	193	10	contain	contain	VERB
ejpam-5911	193	11	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	NUM
ejpam-5911	193	12	,	,	PUNCT
ejpam-5911	193	13	r	r	NOUN
ejpam-5911	193	14	,	,	PUNCT
ejpam-5911	193	15	s	s	PART
ejpam-5911	193	16	)	)	PUNCT
ejpam-5911	193	17	,	,	PUNCT
ejpam-5911	193	18	r	r	NOUN
ejpam-5911	193	19	,	,	PUNCT
ejpam-5911	193	20	s	s	PART
ejpam-5911	193	21	)	)	PUNCT
ejpam-5911	193	22	,	,	PUNCT
ejpam-5911	193	23	there	there	PRON
ejpam-5911	193	24	is	be	VERB
ejpam-5911	193	25	g	g	PROPN
ejpam-5911	193	26	∈	∈	PROPN
ejpam-5911	193	27	g	g	NOUN
ejpam-5911	193	28	and	and	CCONJ
ejpam-5911	193	29	θ	θ	PROPN
ejpam-5911	193	30	∈	∈	PROPN
ejpam-5911	193	31	(	(	PUNCT
ejpam-5911	193	32	0	0	NUM
ejpam-5911	193	33	,	,	PUNCT
ejpam-5911	193	34	1	1	NUM
ejpam-5911	193	35	)	)	PUNCT
ejpam-5911	193	36	with	with	ADP
ejpam-5911	193	37	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	193	38	,	,	PUNCT
ejpam-5911	193	39	r	r	NOUN
ejpam-5911	193	40	,	,	PUNCT
ejpam-5911	193	41	s)(g	s)(g	NUM
ejpam-5911	193	42	)	)	PUNCT
ejpam-5911	193	43	<	<	X
ejpam-5911	193	44	θ	θ	X
ejpam-5911	193	45	<	<	X
ejpam-5911	193	46	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	193	47	,	,	PUNCT
ejpam-5911	193	48	r	r	NOUN
ejpam-5911	193	49	,	,	PUNCT
ejpam-5911	193	50	s	s	PART
ejpam-5911	193	51	)	)	PUNCT
ejpam-5911	193	52	,	,	PUNCT
ejpam-5911	193	53	r	r	NOUN
ejpam-5911	193	54	,	,	PUNCT
ejpam-5911	193	55	s)(g	s)(g	NUM
ejpam-5911	193	56	)	)	PUNCT
ejpam-5911	193	57	.	.	PUNCT
ejpam-5911	194	1	(	(	PUNCT
ejpam-5911	194	2	g	g	NOUN
ejpam-5911	194	3	)	)	PUNCT
ejpam-5911	194	4	since	since	SCONJ
ejpam-5911	194	5	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	194	6	,	,	PUNCT
ejpam-5911	194	7	r	r	NOUN
ejpam-5911	194	8	,	,	PUNCT
ejpam-5911	194	9	s)(g	s)(g	NUM
ejpam-5911	194	10	)	)	PUNCT
ejpam-5911	194	11	<	<	X
ejpam-5911	194	12	θ	θ	X
ejpam-5911	194	13	,	,	PUNCT
ejpam-5911	194	14	by	by	ADP
ejpam-5911	194	15	definition	definition	NOUN
ejpam-5911	194	16	8	8	NUM
ejpam-5911	194	17	,	,	PUNCT
ejpam-5911	194	18	there	there	PRON
ejpam-5911	194	19	is	be	VERB
ejpam-5911	194	20	u	u	PROPN
ejpam-5911	194	21	∈	∈	PROPN
ejpam-5911	194	22	ig	ig	PROPN
ejpam-5911	194	23	as	as	ADP
ejpam-5911	194	24	an	an	DET
ejpam-5911	194	25	(	(	PUNCT
ejpam-5911	194	26	r	r	NOUN
ejpam-5911	194	27	,	,	PUNCT
ejpam-5911	194	28	s)-f	s)-f	NOUN
ejpam-5911	194	29	-	-	PUNCT
ejpam-5911	194	30	b	b	NOUN
ejpam-5911	194	31	-	-	PUNCT
ejpam-5911	194	32	closed	closed	ADJ
ejpam-5911	194	33	set	set	NOUN
ejpam-5911	194	34	and	and	CCONJ
ejpam-5911	194	35	m	m	NOUN
ejpam-5911	194	36	≤	≤	NOUN
ejpam-5911	194	37	u	u	NOUN
ejpam-5911	194	38	with	with	ADP
ejpam-5911	194	39	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	194	40	,	,	PUNCT
ejpam-5911	194	41	r	r	NOUN
ejpam-5911	194	42	,	,	PUNCT
ejpam-5911	194	43	s)(g	s)(g	NUM
ejpam-5911	194	44	)	)	PUNCT
ejpam-5911	194	45	≤	≤	NOUN
ejpam-5911	195	1	u(g	u(g	ADP
ejpam-5911	195	2	)	)	PUNCT
ejpam-5911	195	3	<	<	X
ejpam-5911	195	4	θ	θ	X
ejpam-5911	195	5	.	.	PUNCT
ejpam-5911	196	1	since	since	SCONJ
ejpam-5911	196	2	m	m	PROPN
ejpam-5911	196	3	≤	≤	NUM
ejpam-5911	196	4	u	u	NOUN
ejpam-5911	196	5	,	,	PUNCT
ejpam-5911	196	6	then	then	ADV
ejpam-5911	196	7	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	196	8	,	,	PUNCT
ejpam-5911	196	9	r	r	NOUN
ejpam-5911	196	10	,	,	PUNCT
ejpam-5911	196	11	s	s	NOUN
ejpam-5911	196	12	)	)	PUNCT
ejpam-5911	196	13	≤	≤	NUM
ejpam-5911	196	14	u	u	NOUN
ejpam-5911	196	15	.	.	PUNCT
ejpam-5911	197	1	again	again	ADV
ejpam-5911	197	2	,	,	PUNCT
ejpam-5911	197	3	by	by	ADP
ejpam-5911	197	4	the	the	DET
ejpam-5911	197	5	definition	definition	NOUN
ejpam-5911	197	6	of	of	ADP
ejpam-5911	197	7	bcℑ∗	bcℑ∗	NOUN
ejpam-5911	197	8	,	,	PUNCT
ejpam-5911	197	9	then	then	ADV
ejpam-5911	197	10	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	197	11	,	,	PUNCT
ejpam-5911	197	12	r	r	NOUN
ejpam-5911	197	13	,	,	PUNCT
ejpam-5911	197	14	s	s	PART
ejpam-5911	197	15	)	)	PUNCT
ejpam-5911	197	16	,	,	PUNCT
ejpam-5911	197	17	r	r	NOUN
ejpam-5911	197	18	,	,	PUNCT
ejpam-5911	197	19	s	s	NOUN
ejpam-5911	197	20	)	)	PUNCT
ejpam-5911	197	21	≤	≤	NUM
ejpam-5911	197	22	u	u	NOUN
ejpam-5911	197	23	.	.	PUNCT
ejpam-5911	198	1	hence	hence	ADV
ejpam-5911	198	2	,	,	PUNCT
ejpam-5911	198	3	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	198	4	,	,	PUNCT
ejpam-5911	198	5	r	r	NOUN
ejpam-5911	198	6	,	,	PUNCT
ejpam-5911	198	7	s	s	PART
ejpam-5911	198	8	)	)	PUNCT
ejpam-5911	198	9	,	,	PUNCT
ejpam-5911	198	10	r	r	NOUN
ejpam-5911	198	11	,	,	PUNCT
ejpam-5911	198	12	s)(g	s)(g	NUM
ejpam-5911	198	13	)	)	PUNCT
ejpam-5911	198	14	≤	≤	NOUN
ejpam-5911	199	1	u(g	u(g	ADP
ejpam-5911	199	2	)	)	PUNCT
ejpam-5911	199	3	<	<	X
ejpam-5911	199	4	θ	θ	PROPN
ejpam-5911	199	5	,	,	PUNCT
ejpam-5911	199	6	which	which	PRON
ejpam-5911	199	7	is	be	AUX
ejpam-5911	199	8	a	a	DET
ejpam-5911	199	9	contradiction	contradiction	NOUN
ejpam-5911	199	10	for	for	ADP
ejpam-5911	199	11	(	(	PUNCT
ejpam-5911	199	12	g	g	NOUN
ejpam-5911	199	13	)	)	PUNCT
ejpam-5911	199	14	.	.	PUNCT
ejpam-5911	200	1	thus	thus	ADV
ejpam-5911	200	2	,	,	PUNCT
ejpam-5911	200	3	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	200	4	,	,	PUNCT
ejpam-5911	200	5	r	r	NOUN
ejpam-5911	200	6	,	,	PUNCT
ejpam-5911	200	7	s	s	PART
ejpam-5911	200	8	)	)	PUNCT
ejpam-5911	200	9	≥	≥	NOUN
ejpam-5911	200	10	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	200	11	,	,	PUNCT
ejpam-5911	200	12	r	r	NOUN
ejpam-5911	200	13	,	,	PUNCT
ejpam-5911	200	14	s	s	PART
ejpam-5911	200	15	)	)	PUNCT
ejpam-5911	200	16	,	,	PUNCT
ejpam-5911	200	17	r	r	NOUN
ejpam-5911	200	18	,	,	PUNCT
ejpam-5911	200	19	s	s	PART
ejpam-5911	200	20	)	)	PUNCT
ejpam-5911	200	21	.	.	PUNCT
ejpam-5911	201	1	therefore	therefore	ADV
ejpam-5911	201	2	,	,	PUNCT
ejpam-5911	201	3	bcℑ∗(bcℑ∗(m	bcℑ∗(bcℑ∗(m	PROPN
ejpam-5911	201	4	,	,	PUNCT
ejpam-5911	201	5	r	r	NOUN
ejpam-5911	201	6	,	,	PUNCT
ejpam-5911	201	7	s	s	PART
ejpam-5911	201	8	)	)	PUNCT
ejpam-5911	201	9	,	,	PUNCT
ejpam-5911	201	10	r	r	NOUN
ejpam-5911	201	11	,	,	PUNCT
ejpam-5911	201	12	s	s	NOUN
ejpam-5911	201	13	)	)	PUNCT
ejpam-5911	201	14	=	=	SYM
ejpam-5911	201	15	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	201	16	,	,	PUNCT
ejpam-5911	201	17	r	r	NOUN
ejpam-5911	201	18	,	,	PUNCT
ejpam-5911	201	19	s	s	NOUN
ejpam-5911	201	20	)	)	PUNCT
ejpam-5911	201	21	.	.	PUNCT
ejpam-5911	202	1	(	(	PUNCT
ejpam-5911	202	2	v	v	NOUN
ejpam-5911	202	3	)	)	PUNCT
ejpam-5911	202	4	since	since	SCONJ
ejpam-5911	202	5	m	m	PROPN
ejpam-5911	202	6	≤	≤	ADJ
ejpam-5911	202	7	m∨n	m∨n	PROPN
ejpam-5911	202	8	and	and	CCONJ
ejpam-5911	202	9	n	n	PRON
ejpam-5911	202	10	≤	≤	NOUN
ejpam-5911	202	11	m∨n	m∨n	PROPN
ejpam-5911	202	12	,	,	PUNCT
ejpam-5911	202	13	hence	hence	ADV
ejpam-5911	202	14	by	by	ADP
ejpam-5911	202	15	(	(	PUNCT
ejpam-5911	202	16	iii	iii	NOUN
ejpam-5911	202	17	)	)	PUNCT
ejpam-5911	202	18	,	,	PUNCT
ejpam-5911	202	19	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	202	20	,	,	PUNCT
ejpam-5911	202	21	r	r	NOUN
ejpam-5911	202	22	,	,	PUNCT
ejpam-5911	202	23	s	s	NOUN
ejpam-5911	202	24	)	)	PUNCT
ejpam-5911	202	25	≤	≤	NOUN
ejpam-5911	202	26	bcℑ∗(m∨	bcℑ∗(m∨	PROPN
ejpam-5911	202	27	n	n	NOUN
ejpam-5911	202	28	,	,	PUNCT
ejpam-5911	202	29	r	r	NOUN
ejpam-5911	202	30	,	,	PUNCT
ejpam-5911	202	31	s	s	PART
ejpam-5911	202	32	)	)	PUNCT
ejpam-5911	202	33	and	and	CCONJ
ejpam-5911	202	34	bcℑ∗(n	bcℑ∗(n	PROPN
ejpam-5911	202	35	,	,	PUNCT
ejpam-5911	202	36	r	r	NOUN
ejpam-5911	202	37	,	,	PUNCT
ejpam-5911	202	38	s	s	NOUN
ejpam-5911	202	39	)	)	PUNCT
ejpam-5911	202	40	≤	≤	NUM
ejpam-5911	202	41	bcℑ∗(m∨n	bcℑ∗(m∨n	PUNCT
ejpam-5911	202	42	,	,	PUNCT
ejpam-5911	202	43	r	r	NOUN
ejpam-5911	202	44	,	,	PUNCT
ejpam-5911	202	45	s	s	NOUN
ejpam-5911	202	46	)	)	PUNCT
ejpam-5911	202	47	.	.	PUNCT
ejpam-5911	203	1	thus	thus	ADV
ejpam-5911	203	2	,	,	PUNCT
ejpam-5911	203	3	bcℑ∗(m∨n	bcℑ∗(m∨n	PROPN
ejpam-5911	203	4	,	,	PUNCT
ejpam-5911	203	5	r	r	NOUN
ejpam-5911	203	6	,	,	PUNCT
ejpam-5911	203	7	s	s	PART
ejpam-5911	203	8	)	)	PUNCT
ejpam-5911	203	9	≥	≥	NOUN
ejpam-5911	203	10	bcℑ∗(m	bcℑ∗(m	NOUN
ejpam-5911	203	11	,	,	PUNCT
ejpam-5911	203	12	r	r	NOUN
ejpam-5911	203	13	,	,	PUNCT
ejpam-5911	203	14	s)∨	s)∨	PROPN
ejpam-5911	203	15	bcℑ∗(n	bcℑ∗(n	PROPN
ejpam-5911	203	16	,	,	PUNCT
ejpam-5911	203	17	r	r	PROPN
ejpam-5911	203	18	,	,	PUNCT
ejpam-5911	203	19	s	s	NOUN
ejpam-5911	203	20	)	)	PUNCT
ejpam-5911	203	21	.	.	PUNCT
ejpam-5911	204	1	(	(	PUNCT
ejpam-5911	204	2	vi	vi	NOUN
ejpam-5911	204	3	)	)	PUNCT
ejpam-5911	204	4	from	from	ADP
ejpam-5911	204	5	proposition	proposition	NOUN
ejpam-5911	204	6	2	2	NUM
ejpam-5911	204	7	and	and	CCONJ
ejpam-5911	204	8	the	the	DET
ejpam-5911	204	9	fact	fact	NOUN
ejpam-5911	204	10	that	that	SCONJ
ejpam-5911	204	11	cℑ∗(m	cℑ∗(m	NOUN
ejpam-5911	204	12	,	,	PUNCT
ejpam-5911	204	13	r	r	NOUN
ejpam-5911	204	14	,	,	PUNCT
ejpam-5911	204	15	s	s	PART
ejpam-5911	204	16	)	)	PUNCT
ejpam-5911	204	17	is	be	AUX
ejpam-5911	204	18	an	an	DET
ejpam-5911	204	19	(	(	PUNCT
ejpam-5911	204	20	r	r	NOUN
ejpam-5911	204	21	,	,	PUNCT
ejpam-5911	204	22	s)-f	s)-f	NOUN
ejpam-5911	204	23	-	-	PUNCT
ejpam-5911	204	24	b	b	NOUN
ejpam-5911	204	25	-	-	PUNCT
ejpam-5911	204	26	closed	closed	ADJ
ejpam-5911	204	27	set	set	NOUN
ejpam-5911	204	28	,	,	PUNCT
ejpam-5911	204	29	then	then	ADV
ejpam-5911	204	30	bcℑ∗(cℑ∗(m	bcℑ∗(cℑ∗(m	ADJ
ejpam-5911	204	31	,	,	PUNCT
ejpam-5911	204	32	r	r	NOUN
ejpam-5911	204	33	,	,	PUNCT
ejpam-5911	204	34	s	s	PART
ejpam-5911	204	35	)	)	PUNCT
ejpam-5911	204	36	,	,	PUNCT
ejpam-5911	204	37	r	r	NOUN
ejpam-5911	204	38	,	,	PUNCT
ejpam-5911	204	39	s	s	PART
ejpam-5911	204	40	)	)	PUNCT
ejpam-5911	204	41	=	=	SYM
ejpam-5911	205	1	cℑ∗(m	cℑ∗(m	VERB
ejpam-5911	205	2	,	,	PUNCT
ejpam-5911	205	3	r	r	NOUN
ejpam-5911	205	4	,	,	PUNCT
ejpam-5911	205	5	s	s	PART
ejpam-5911	205	6	)	)	PUNCT
ejpam-5911	205	7	.	.	PUNCT
ejpam-5911	206	1	definition	definition	NOUN
ejpam-5911	206	2	9	9	NUM
ejpam-5911	206	3	.	.	PUNCT
ejpam-5911	207	1	in	in	ADP
ejpam-5911	207	2	an	an	DET
ejpam-5911	207	3	dft	dft	NOUN
ejpam-5911	207	4	s	s	X
ejpam-5911	207	5	(	(	PUNCT
ejpam-5911	207	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	207	7	)	)	PUNCT
ejpam-5911	207	8	,	,	PUNCT
ejpam-5911	207	9	for	for	ADP
ejpam-5911	207	10	each	each	DET
ejpam-5911	207	11	m	m	PROPN
ejpam-5911	207	12	∈	∈	PROPN
ejpam-5911	207	13	ig	ig	PROPN
ejpam-5911	207	14	,	,	PUNCT
ejpam-5911	207	15	r	r	NOUN
ejpam-5911	207	16	∈	∈	PROPN
ejpam-5911	207	17	i	i	NOUN
ejpam-5911	207	18	◦	◦	NOUN
ejpam-5911	207	19	,	,	PUNCT
ejpam-5911	207	20	and	and	CCONJ
ejpam-5911	207	21	s	s	PROPN
ejpam-5911	207	22	∈	∈	PROPN
ejpam-5911	207	23	i1	i1	PROPN
ejpam-5911	207	24	,	,	PUNCT
ejpam-5911	207	25	we	we	PRON
ejpam-5911	207	26	define	define	VERB
ejpam-5911	207	27	an	an	DET
ejpam-5911	207	28	df	df	PROPN
ejpam-5911	207	29	-	-	PUNCT
ejpam-5911	207	30	b	b	NOUN
ejpam-5911	207	31	-	-	PUNCT
ejpam-5911	207	32	interior	interior	ADJ
ejpam-5911	207	33	operator	operator	NOUN
ejpam-5911	207	34	biℑ∗	biℑ∗	NOUN
ejpam-5911	207	35	:	:	PUNCT
ejpam-5911	207	36	ig	ig	INTJ
ejpam-5911	207	37	×	×	INTJ
ejpam-5911	207	38	i	i	PRON
ejpam-5911	207	39	◦	◦	VERB
ejpam-5911	207	40	×	×	PROPN
ejpam-5911	207	41	i1	i1	PROPN
ejpam-5911	207	42	−→	−→	NOUN
ejpam-5911	207	43	ig	ig	PROPN
ejpam-5911	207	44	as	as	SCONJ
ejpam-5911	207	45	follows	follow	VERB
ejpam-5911	207	46	:	:	PUNCT
ejpam-5911	207	47	biℑ∗(m	biℑ∗(m	NOUN
ejpam-5911	207	48	,	,	PUNCT
ejpam-5911	207	49	r	r	NOUN
ejpam-5911	207	50	,	,	PUNCT
ejpam-5911	207	51	s	s	PART
ejpam-5911	207	52	)	)	PUNCT
ejpam-5911	207	53	=	=	SYM
ejpam-5911	207	54	∨	∨	X
ejpam-5911	207	55	{	{	PUNCT
ejpam-5911	207	56	n	n	NOUN
ejpam-5911	207	57	∈	∈	NOUN
ejpam-5911	207	58	ig	ig	PROPN
ejpam-5911	207	59	:	:	PUNCT
ejpam-5911	207	60	n	n	PRON
ejpam-5911	207	61	≤	≤	NUM
ejpam-5911	207	62	m	m	PROPN
ejpam-5911	207	63	,	,	PUNCT
ejpam-5911	207	64	n	n	X
ejpam-5911	207	65	is	be	AUX
ejpam-5911	207	66	(	(	PUNCT
ejpam-5911	207	67	r	r	NOUN
ejpam-5911	207	68	,	,	PUNCT
ejpam-5911	207	69	s)-f	s)-f	NOUN
ejpam-5911	207	70	-	-	PUNCT
ejpam-5911	207	71	b	b	NOUN
ejpam-5911	207	72	-	-	PUNCT
ejpam-5911	207	73	open	open	ADJ
ejpam-5911	207	74	}	}	PUNCT
ejpam-5911	207	75	.	.	PUNCT
ejpam-5911	208	1	proposition	proposition	NOUN
ejpam-5911	208	2	3	3	X
ejpam-5911	208	3	.	.	PUNCT
ejpam-5911	209	1	let	let	AUX
ejpam-5911	209	2	(	(	PUNCT
ejpam-5911	209	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	209	4	)	)	PUNCT
ejpam-5911	209	5	be	be	VERB
ejpam-5911	209	6	an	an	DET
ejpam-5911	209	7	dft	dft	NOUN
ejpam-5911	209	8	s	s	PROPN
ejpam-5911	209	9	,	,	PUNCT
ejpam-5911	209	10	m	m	PROPN
ejpam-5911	209	11	∈	∈	PROPN
ejpam-5911	209	12	ig	ig	PROPN
ejpam-5911	209	13	,	,	PUNCT
ejpam-5911	209	14	r	r	NOUN
ejpam-5911	209	15	∈	∈	PROPN
ejpam-5911	210	1	i	i	NOUN
ejpam-5911	210	2	◦	◦	NOUN
ejpam-5911	210	3	,	,	PUNCT
ejpam-5911	210	4	and	and	CCONJ
ejpam-5911	210	5	s	s	PROPN
ejpam-5911	210	6	∈	∈	PROPN
ejpam-5911	210	7	i1	i1	PROPN
ejpam-5911	210	8	.	.	PUNCT
ejpam-5911	211	1	then	then	ADV
ejpam-5911	211	2	(	(	PUNCT
ejpam-5911	211	3	i	i	NOUN
ejpam-5911	211	4	)	)	PUNCT
ejpam-5911	211	5	bcℑ∗(mc	bcℑ∗(mc	PROPN
ejpam-5911	211	6	,	,	PUNCT
ejpam-5911	211	7	r	r	NOUN
ejpam-5911	211	8	,	,	PUNCT
ejpam-5911	211	9	s	s	NOUN
ejpam-5911	211	10	)	)	PUNCT
ejpam-5911	211	11	=	=	SYM
ejpam-5911	211	12	(	(	PUNCT
ejpam-5911	211	13	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	211	14	,	,	PUNCT
ejpam-5911	211	15	r	r	NOUN
ejpam-5911	211	16	,	,	PUNCT
ejpam-5911	211	17	s))c	s))c	NOUN
ejpam-5911	211	18	;	;	PUNCT
ejpam-5911	211	19	i.	i.	PROPN
ejpam-5911	211	20	m.	m.	PROPN
ejpam-5911	211	21	taha	taha	PROPN
ejpam-5911	211	22	,	,	PUNCT
ejpam-5911	211	23	j.	j.	PROPN
ejpam-5911	211	24	al	al	PROPN
ejpam-5911	211	25	-	-	PUNCT
ejpam-5911	211	26	mufarrij	mufarrij	PROPN
ejpam-5911	211	27	,	,	PUNCT
ejpam-5911	211	28	o.	o.	PROPN
ejpam-5911	211	29	m.	m.	PROPN
ejpam-5911	211	30	taha	taha	PROPN
ejpam-5911	211	31	/	/	PUNCT
ejpam-5911	211	32	eur	eur	PROPN
ejpam-5911	211	33	.	.	PUNCT
ejpam-5911	212	1	j.	j.	PROPN
ejpam-5911	212	2	pure	pure	PROPN
ejpam-5911	212	3	appl	appl	PROPN
ejpam-5911	212	4	.	.	PROPN
ejpam-5911	212	5	math	math	PROPN
ejpam-5911	212	6	,	,	PUNCT
ejpam-5911	212	7	18	18	NUM
ejpam-5911	212	8	(	(	PUNCT
ejpam-5911	212	9	2	2	NUM
ejpam-5911	212	10	)	)	PUNCT
ejpam-5911	212	11	(	(	PUNCT
ejpam-5911	212	12	2025	2025	NUM
ejpam-5911	212	13	)	)	PUNCT
ejpam-5911	212	14	,	,	PUNCT
ejpam-5911	212	15	5911	5911	NUM
ejpam-5911	212	16	9	9	NUM
ejpam-5911	212	17	of	of	ADP
ejpam-5911	212	18	27	27	NUM
ejpam-5911	212	19	(	(	PUNCT
ejpam-5911	212	20	ii	ii	NOUN
ejpam-5911	212	21	)	)	PUNCT
ejpam-5911	212	22	biℑ∗(mc	biℑ∗(mc	PROPN
ejpam-5911	212	23	,	,	PUNCT
ejpam-5911	212	24	r	r	NOUN
ejpam-5911	212	25	,	,	PUNCT
ejpam-5911	212	26	s	s	NOUN
ejpam-5911	212	27	)	)	PUNCT
ejpam-5911	212	28	=	=	SYM
ejpam-5911	212	29	(	(	PUNCT
ejpam-5911	212	30	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	212	31	,	,	PUNCT
ejpam-5911	212	32	r	r	NOUN
ejpam-5911	212	33	,	,	PUNCT
ejpam-5911	212	34	s))c	s))c	NOUN
ejpam-5911	212	35	.	.	PUNCT
ejpam-5911	213	1	proof	proof	NOUN
ejpam-5911	213	2	.	.	PUNCT
ejpam-5911	214	1	(	(	PUNCT
ejpam-5911	214	2	i	i	NOUN
ejpam-5911	214	3	)	)	PUNCT
ejpam-5911	214	4	for	for	ADP
ejpam-5911	214	5	eachm	eachm	PROPN
ejpam-5911	214	6	∈	∈	PROPN
ejpam-5911	214	7	ig	ig	PROPN
ejpam-5911	214	8	,	,	PUNCT
ejpam-5911	214	9	we	we	PRON
ejpam-5911	214	10	have	have	AUX
ejpam-5911	214	11	bcℑ∗(mc	bcℑ∗(mc	VERB
ejpam-5911	214	12	,	,	PUNCT
ejpam-5911	214	13	r	r	NOUN
ejpam-5911	214	14	,	,	PUNCT
ejpam-5911	214	15	s	s	NOUN
ejpam-5911	214	16	)	)	PUNCT
ejpam-5911	214	17	=	=	SYM
ejpam-5911	214	18	∧	∧	NOUN
ejpam-5911	214	19	{	{	PUNCT
ejpam-5911	214	20	n	n	NOUN
ejpam-5911	214	21	∈	∈	NOUN
ejpam-5911	214	22	ig	ig	PROPN
ejpam-5911	214	23	:	:	PUNCT
ejpam-5911	214	24	mc	mc	PROPN
ejpam-5911	214	25	≤	≤	PROPN
ejpam-5911	214	26	n	n	CCONJ
ejpam-5911	214	27	,	,	PUNCT
ejpam-5911	214	28	n	n	X
ejpam-5911	214	29	is	be	AUX
ejpam-5911	214	30	(	(	PUNCT
ejpam-5911	214	31	r	r	NOUN
ejpam-5911	214	32	,	,	PUNCT
ejpam-5911	214	33	s)-f	s)-f	NOUN
ejpam-5911	214	34	-	-	PUNCT
ejpam-5911	214	35	b	b	NOUN
ejpam-5911	214	36	-	-	PUNCT
ejpam-5911	214	37	closed	closed	ADJ
ejpam-5911	214	38	}	}	PUNCT
ejpam-5911	214	39	=	=	SYM
ejpam-5911	214	40	[	[	PUNCT
ejpam-5911	214	41	∨	∨	X
ejpam-5911	214	42	{	{	PUNCT
ejpam-5911	214	43	n	n	PROPN
ejpam-5911	214	44	c	c	NOUN
ejpam-5911	214	45	∈	∈	NOUN
ejpam-5911	214	46	ig	ig	PROPN
ejpam-5911	214	47	:	:	PUNCT
ejpam-5911	214	48	n	n	PROPN
ejpam-5911	214	49	c	c	X
ejpam-5911	214	50	≤	≤	NUM
ejpam-5911	214	51	m	m	PROPN
ejpam-5911	214	52	,	,	PUNCT
ejpam-5911	214	53	n	n	PROPN
ejpam-5911	214	54	c	c	NOUN
ejpam-5911	214	55	is	be	AUX
ejpam-5911	214	56	(	(	PUNCT
ejpam-5911	214	57	r	r	NOUN
ejpam-5911	214	58	,	,	PUNCT
ejpam-5911	214	59	s)-f	s)-f	NOUN
ejpam-5911	214	60	-	-	PUNCT
ejpam-5911	214	61	b	b	NOUN
ejpam-5911	214	62	-	-	PUNCT
ejpam-5911	214	63	open}]c	open}]c	ADJ
ejpam-5911	214	64	=	=	SYM
ejpam-5911	214	65	(	(	PUNCT
ejpam-5911	214	66	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	214	67	,	,	PUNCT
ejpam-5911	214	68	r	r	NOUN
ejpam-5911	214	69	,	,	PUNCT
ejpam-5911	214	70	s))c	s))c	NOUN
ejpam-5911	214	71	.	.	PUNCT
ejpam-5911	215	1	(	(	PUNCT
ejpam-5911	215	2	ii	ii	X
ejpam-5911	215	3	)	)	PUNCT
ejpam-5911	215	4	this	this	PRON
ejpam-5911	215	5	is	be	AUX
ejpam-5911	215	6	similar	similar	ADJ
ejpam-5911	215	7	to	to	ADP
ejpam-5911	215	8	that	that	PRON
ejpam-5911	215	9	of	of	ADP
ejpam-5911	215	10	(	(	PUNCT
ejpam-5911	215	11	i	i	NOUN
ejpam-5911	215	12	)	)	PUNCT
ejpam-5911	215	13	.	.	PUNCT
ejpam-5911	216	1	proposition	proposition	NOUN
ejpam-5911	216	2	4	4	NUM
ejpam-5911	216	3	.	.	PUNCT
ejpam-5911	217	1	in	in	ADP
ejpam-5911	217	2	an	an	DET
ejpam-5911	217	3	dft	dft	NOUN
ejpam-5911	217	4	s	s	X
ejpam-5911	217	5	(	(	PUNCT
ejpam-5911	217	6	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	217	7	)	)	PUNCT
ejpam-5911	217	8	,	,	PUNCT
ejpam-5911	217	9	for	for	ADP
ejpam-5911	217	10	each	each	DET
ejpam-5911	217	11	m	m	PROPN
ejpam-5911	217	12	∈	∈	PROPN
ejpam-5911	217	13	ig	ig	PROPN
ejpam-5911	217	14	,	,	PUNCT
ejpam-5911	217	15	r	r	NOUN
ejpam-5911	217	16	∈	∈	PROPN
ejpam-5911	217	17	i	i	NOUN
ejpam-5911	217	18	◦	◦	NOUN
ejpam-5911	217	19	,	,	PUNCT
ejpam-5911	217	20	and	and	CCONJ
ejpam-5911	217	21	s	s	PROPN
ejpam-5911	217	22	∈	∈	PROPN
ejpam-5911	217	23	i1	i1	PROPN
ejpam-5911	217	24	.	.	PUNCT
ejpam-5911	218	1	an	an	DET
ejpam-5911	218	2	f	f	X
ejpam-5911	218	3	-	-	PUNCT
ejpam-5911	218	4	set	set	VERB
ejpam-5911	218	5	m	m	NOUN
ejpam-5911	218	6	is	be	AUX
ejpam-5911	218	7	(	(	PUNCT
ejpam-5911	218	8	r	r	NOUN
ejpam-5911	218	9	,	,	PUNCT
ejpam-5911	218	10	s)-f	s)-f	NOUN
ejpam-5911	218	11	-	-	PUNCT
ejpam-5911	218	12	b	b	NOUN
ejpam-5911	218	13	-	-	PUNCT
ejpam-5911	218	14	open	open	ADJ
ejpam-5911	218	15	iff	iff	PROPN
ejpam-5911	218	16	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	218	17	,	,	PUNCT
ejpam-5911	218	18	r	r	NOUN
ejpam-5911	218	19	,	,	PUNCT
ejpam-5911	218	20	s	s	NOUN
ejpam-5911	218	21	)	)	PUNCT
ejpam-5911	218	22	=	=	VERB
ejpam-5911	218	23	m.	m.	NOUN
ejpam-5911	218	24	proof	proof	NOUN
ejpam-5911	218	25	.	.	PUNCT
ejpam-5911	219	1	this	this	PRON
ejpam-5911	219	2	is	be	AUX
ejpam-5911	219	3	easily	easily	ADV
ejpam-5911	219	4	proved	prove	VERB
ejpam-5911	219	5	from	from	ADP
ejpam-5911	219	6	definition	definition	NOUN
ejpam-5911	219	7	9	9	NUM
ejpam-5911	219	8	.	.	PUNCT
ejpam-5911	219	9	theorem	theorem	NOUN
ejpam-5911	219	10	2	2	NUM
ejpam-5911	219	11	.	.	PUNCT
ejpam-5911	219	12	in	in	ADP
ejpam-5911	219	13	an	an	DET
ejpam-5911	219	14	dft	dft	NOUN
ejpam-5911	219	15	s	s	X
ejpam-5911	219	16	(	(	PUNCT
ejpam-5911	219	17	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	219	18	)	)	PUNCT
ejpam-5911	219	19	,	,	PUNCT
ejpam-5911	219	20	for	for	ADP
ejpam-5911	219	21	each	each	DET
ejpam-5911	219	22	m	m	NOUN
ejpam-5911	219	23	,	,	PUNCT
ejpam-5911	219	24	n	n	PROPN
ejpam-5911	219	25	∈	∈	PROPN
ejpam-5911	219	26	ig	ig	PROPN
ejpam-5911	219	27	,	,	PUNCT
ejpam-5911	219	28	r	r	NOUN
ejpam-5911	219	29	∈	∈	PROPN
ejpam-5911	219	30	i	i	NOUN
ejpam-5911	219	31	◦	◦	NOUN
ejpam-5911	219	32	,	,	PUNCT
ejpam-5911	219	33	and	and	CCONJ
ejpam-5911	219	34	s	s	PROPN
ejpam-5911	219	35	∈	∈	PROPN
ejpam-5911	219	36	i1	i1	PROPN
ejpam-5911	219	37	.	.	PUNCT
ejpam-5911	220	1	an	an	DET
ejpam-5911	220	2	df	df	NOUN
ejpam-5911	220	3	-	-	PUNCT
ejpam-5911	220	4	operator	operator	NOUN
ejpam-5911	220	5	biℑ∗	biℑ∗	NOUN
ejpam-5911	220	6	:	:	PUNCT
ejpam-5911	220	7	ig	ig	PROPN
ejpam-5911	220	8	×	×	INTJ
ejpam-5911	221	1	i	i	PRON
ejpam-5911	221	2	◦	◦	VERB
ejpam-5911	221	3	×	×	PROPN
ejpam-5911	221	4	i1	i1	PROPN
ejpam-5911	221	5	−→	−→	NOUN
ejpam-5911	221	6	ig	ig	PROPN
ejpam-5911	221	7	satisfies	satisfy	VERB
ejpam-5911	221	8	the	the	DET
ejpam-5911	221	9	following	follow	VERB
ejpam-5911	221	10	properties	property	NOUN
ejpam-5911	221	11	.	.	PUNCT
ejpam-5911	222	1	(	(	PUNCT
ejpam-5911	222	2	i	i	NOUN
ejpam-5911	222	3	)	)	PUNCT
ejpam-5911	222	4	biℑ∗(1	biℑ∗(1	NOUN
ejpam-5911	222	5	,	,	PUNCT
ejpam-5911	222	6	r	r	NOUN
ejpam-5911	222	7	,	,	PUNCT
ejpam-5911	222	8	s	s	PART
ejpam-5911	222	9	)	)	PUNCT
ejpam-5911	222	10	=	=	SYM
ejpam-5911	222	11	1	1	X
ejpam-5911	222	12	.	.	PUNCT
ejpam-5911	222	13	(	(	PUNCT
ejpam-5911	222	14	ii	ii	NOUN
ejpam-5911	222	15	)	)	PUNCT
ejpam-5911	222	16	iℑ∗(m	iℑ∗(m	PROPN
ejpam-5911	222	17	,	,	PUNCT
ejpam-5911	222	18	r	r	NOUN
ejpam-5911	222	19	,	,	PUNCT
ejpam-5911	222	20	s	s	NOUN
ejpam-5911	222	21	)	)	PUNCT
ejpam-5911	222	22	≤	≤	NOUN
ejpam-5911	222	23	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	222	24	,	,	PUNCT
ejpam-5911	222	25	r	r	NOUN
ejpam-5911	222	26	,	,	PUNCT
ejpam-5911	222	27	s	s	NOUN
ejpam-5911	222	28	)	)	PUNCT
ejpam-5911	222	29	≤	≤	ADJ
ejpam-5911	222	30	m.	m.	NOUN
ejpam-5911	222	31	(	(	PUNCT
ejpam-5911	222	32	iii	iii	NOUN
ejpam-5911	222	33	)	)	PUNCT
ejpam-5911	222	34	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	222	35	,	,	PUNCT
ejpam-5911	222	36	r	r	NOUN
ejpam-5911	222	37	,	,	PUNCT
ejpam-5911	222	38	s	s	NOUN
ejpam-5911	222	39	)	)	PUNCT
ejpam-5911	222	40	≤	≤	NOUN
ejpam-5911	222	41	biℑ∗(n	biℑ∗(n	PROPN
ejpam-5911	222	42	,	,	PUNCT
ejpam-5911	222	43	r	r	NOUN
ejpam-5911	222	44	,	,	PUNCT
ejpam-5911	222	45	s	s	PART
ejpam-5911	222	46	)	)	PUNCT
ejpam-5911	222	47	if	if	SCONJ
ejpam-5911	222	48	m	m	VERB
ejpam-5911	222	49	≤	≤	VERB
ejpam-5911	222	50	n	n	ADV
ejpam-5911	222	51	.	.	PUNCT
ejpam-5911	223	1	(	(	PUNCT
ejpam-5911	223	2	iv	iv	X
ejpam-5911	223	3	)	)	PUNCT
ejpam-5911	223	4	biℑ∗(biℑ∗(m	biℑ∗(biℑ∗(m	PROPN
ejpam-5911	223	5	,	,	PUNCT
ejpam-5911	223	6	r	r	NOUN
ejpam-5911	223	7	,	,	PUNCT
ejpam-5911	223	8	s	s	PART
ejpam-5911	223	9	)	)	PUNCT
ejpam-5911	223	10	,	,	PUNCT
ejpam-5911	223	11	r	r	NOUN
ejpam-5911	223	12	,	,	PUNCT
ejpam-5911	223	13	s	s	NOUN
ejpam-5911	223	14	)	)	PUNCT
ejpam-5911	223	15	=	=	SYM
ejpam-5911	223	16	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	223	17	,	,	PUNCT
ejpam-5911	223	18	r	r	NOUN
ejpam-5911	223	19	,	,	PUNCT
ejpam-5911	223	20	s	s	NOUN
ejpam-5911	223	21	)	)	PUNCT
ejpam-5911	223	22	.	.	PUNCT
ejpam-5911	224	1	(	(	PUNCT
ejpam-5911	224	2	v	v	NOUN
ejpam-5911	224	3	)	)	PUNCT
ejpam-5911	224	4	biℑ∗(m	biℑ∗(m	PROPN
ejpam-5911	224	5	,	,	PUNCT
ejpam-5911	224	6	r	r	NOUN
ejpam-5911	224	7	,	,	PUNCT
ejpam-5911	224	8	s	s	NOUN
ejpam-5911	224	9	)	)	PUNCT
ejpam-5911	224	10	∧	∧	NOUN
ejpam-5911	224	11	biℑ∗(n	biℑ∗(n	PROPN
ejpam-5911	224	12	,	,	PUNCT
ejpam-5911	224	13	r	r	NOUN
ejpam-5911	224	14	,	,	PUNCT
ejpam-5911	224	15	s	s	PART
ejpam-5911	224	16	)	)	PUNCT
ejpam-5911	224	17	≥	≥	NOUN
ejpam-5911	224	18	biℑ∗(m∧n	biℑ∗(m∧n	NOUN
ejpam-5911	224	19	,	,	PUNCT
ejpam-5911	224	20	r	r	NOUN
ejpam-5911	224	21	,	,	PUNCT
ejpam-5911	224	22	s	s	NOUN
ejpam-5911	224	23	)	)	PUNCT
ejpam-5911	224	24	.	.	PUNCT
ejpam-5911	225	1	proof	proof	NOUN
ejpam-5911	225	2	.	.	PUNCT
ejpam-5911	226	1	the	the	DET
ejpam-5911	226	2	proof	proof	NOUN
ejpam-5911	226	3	is	be	AUX
ejpam-5911	226	4	similar	similar	ADJ
ejpam-5911	226	5	to	to	ADP
ejpam-5911	226	6	that	that	PRON
ejpam-5911	226	7	of	of	ADP
ejpam-5911	226	8	theorem	theorem	NOUN
ejpam-5911	226	9	1	1	NUM
ejpam-5911	226	10	.	.	NOUN
ejpam-5911	226	11	4	4	NUM
ejpam-5911	226	12	.	.	X
ejpam-5911	226	13	on	on	ADP
ejpam-5911	226	14	double	double	ADJ
ejpam-5911	226	15	fuzzy	fuzzy	ADJ
ejpam-5911	226	16	b	b	NOUN
ejpam-5911	226	17	-	-	PUNCT
ejpam-5911	226	18	continuity	continuity	NOUN
ejpam-5911	226	19	and	and	CCONJ
ejpam-5911	226	20	b	b	NOUN
ejpam-5911	226	21	-	-	PUNCT
ejpam-5911	226	22	irresoluteness	irresoluteness	NOUN
ejpam-5911	226	23	here	here	ADV
ejpam-5911	226	24	,	,	PUNCT
ejpam-5911	226	25	we	we	PRON
ejpam-5911	226	26	display	display	VERB
ejpam-5911	226	27	and	and	CCONJ
ejpam-5911	226	28	discuss	discuss	VERB
ejpam-5911	226	29	the	the	DET
ejpam-5911	226	30	concept	concept	NOUN
ejpam-5911	226	31	of	of	ADP
ejpam-5911	226	32	df	df	PROPN
ejpam-5911	226	33	-	-	PUNCT
ejpam-5911	226	34	b	b	NOUN
ejpam-5911	226	35	-	-	PUNCT
ejpam-5911	226	36	continuity	continuity	NOUN
ejpam-5911	226	37	between	between	ADP
ejpam-5911	226	38	dft	dft	PROPN
ejpam-5911	226	39	ss	ss	PROPN
ejpam-5911	226	40	based	base	VERB
ejpam-5911	226	41	on	on	ADP
ejpam-5911	226	42	šostak	šostak	NOUN
ejpam-5911	226	43	,	,	PUNCT
ejpam-5911	226	44	s	s	PART
ejpam-5911	226	45	sense	sense	NOUN
ejpam-5911	226	46	[	[	X
ejpam-5911	226	47	3	3	NUM
ejpam-5911	226	48	]	]	PUNCT
ejpam-5911	226	49	.	.	PUNCT
ejpam-5911	227	1	moreover	moreover	ADV
ejpam-5911	227	2	,	,	PUNCT
ejpam-5911	227	3	we	we	PRON
ejpam-5911	227	4	present	present	VERB
ejpam-5911	227	5	and	and	CCONJ
ejpam-5911	227	6	study	study	VERB
ejpam-5911	227	7	the	the	DET
ejpam-5911	227	8	notions	notion	NOUN
ejpam-5911	227	9	of	of	ADP
ejpam-5911	227	10	df	df	NOUN
ejpam-5911	227	11	-	-	PUNCT
ejpam-5911	227	12	almost	almost	ADV
ejpam-5911	227	13	b	b	NOUN
ejpam-5911	227	14	-	-	PUNCT
ejpam-5911	227	15	continuity	continuity	NOUN
ejpam-5911	227	16	and	and	CCONJ
ejpam-5911	227	17	df	df	NOUN
ejpam-5911	227	18	-	-	PUNCT
ejpam-5911	227	19	weakly	weakly	ADJ
ejpam-5911	227	20	b	b	NOUN
ejpam-5911	227	21	-	-	PUNCT
ejpam-5911	227	22	continuity	continuity	NOUN
ejpam-5911	227	23	.	.	PUNCT
ejpam-5911	228	1	definition	definition	NOUN
ejpam-5911	228	2	10	10	NUM
ejpam-5911	228	3	.	.	PUNCT
ejpam-5911	229	1	an	an	DET
ejpam-5911	229	2	f	f	X
ejpam-5911	229	3	-	-	PUNCT
ejpam-5911	229	4	mapping	mapping	NOUN
ejpam-5911	229	5	p	p	NOUN
ejpam-5911	229	6	:	:	PUNCT
ejpam-5911	229	7	(	(	PUNCT
ejpam-5911	229	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	229	9	)	)	PUNCT
ejpam-5911	230	1	−→	−→	NOUN
ejpam-5911	230	2	(	(	PUNCT
ejpam-5911	230	3	z	z	NOUN
ejpam-5911	230	4	,	,	PUNCT
ejpam-5911	230	5	𭟋	𭟋	NOUN
ejpam-5911	230	6	,	,	PUNCT
ejpam-5911	230	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	230	8	)	)	PUNCT
ejpam-5911	230	9	is	be	AUX
ejpam-5911	230	10	called	call	VERB
ejpam-5911	230	11	df	df	PROPN
ejpam-5911	230	12	-	-	PUNCT
ejpam-5911	230	13	b	b	NOUN
ejpam-5911	230	14	-	-	PUNCT
ejpam-5911	230	15	continuous	continuous	ADJ
ejpam-5911	230	16	if	if	SCONJ
ejpam-5911	230	17	p−1(n	p−1(n	NOUN
ejpam-5911	230	18	)	)	PUNCT
ejpam-5911	230	19	is	be	AUX
ejpam-5911	230	20	an	an	DET
ejpam-5911	230	21	(	(	PUNCT
ejpam-5911	230	22	r	r	NOUN
ejpam-5911	230	23	,	,	PUNCT
ejpam-5911	230	24	s)-f	s)-f	NOUN
ejpam-5911	230	25	-	-	PUNCT
ejpam-5911	230	26	b	b	NOUN
ejpam-5911	230	27	-	-	PUNCT
ejpam-5911	230	28	open	open	ADJ
ejpam-5911	230	29	set	set	NOUN
ejpam-5911	230	30	,	,	PUNCT
ejpam-5911	230	31	for	for	ADP
ejpam-5911	230	32	each	each	DET
ejpam-5911	230	33	n	n	PRON
ejpam-5911	230	34	∈	∈	NOUN
ejpam-5911	231	1	iz	iz	INTJ
ejpam-5911	231	2	with	with	ADP
ejpam-5911	231	3	𭟋(n	𭟋(n	PROPN
ejpam-5911	231	4	)	)	PUNCT
ejpam-5911	231	5	≥	≥	PROPN
ejpam-5911	231	6	r	r	NOUN
ejpam-5911	231	7	and	and	CCONJ
ejpam-5911	231	8	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	231	9	)	)	PUNCT
ejpam-5911	231	10	≤	≤	NUM
ejpam-5911	231	11	s.	s.	PROPN
ejpam-5911	231	12	i.	i.	PROPN
ejpam-5911	231	13	m.	m.	PROPN
ejpam-5911	231	14	taha	taha	PROPN
ejpam-5911	231	15	,	,	PUNCT
ejpam-5911	231	16	j.	j.	PROPN
ejpam-5911	231	17	al	al	PROPN
ejpam-5911	231	18	-	-	PUNCT
ejpam-5911	231	19	mufarrij	mufarrij	PROPN
ejpam-5911	231	20	,	,	PUNCT
ejpam-5911	231	21	o.	o.	PROPN
ejpam-5911	231	22	m.	m.	PROPN
ejpam-5911	231	23	taha	taha	PROPN
ejpam-5911	231	24	/	/	PUNCT
ejpam-5911	231	25	eur	eur	PROPN
ejpam-5911	231	26	.	.	PUNCT
ejpam-5911	232	1	j.	j.	PROPN
ejpam-5911	232	2	pure	pure	PROPN
ejpam-5911	232	3	appl	appl	PROPN
ejpam-5911	232	4	.	.	PROPN
ejpam-5911	232	5	math	math	PROPN
ejpam-5911	232	6	,	,	PUNCT
ejpam-5911	232	7	18	18	NUM
ejpam-5911	232	8	(	(	PUNCT
ejpam-5911	232	9	2	2	NUM
ejpam-5911	232	10	)	)	PUNCT
ejpam-5911	232	11	(	(	PUNCT
ejpam-5911	232	12	2025	2025	NUM
ejpam-5911	232	13	)	)	PUNCT
ejpam-5911	232	14	,	,	PUNCT
ejpam-5911	232	15	5911	5911	NUM
ejpam-5911	232	16	10	10	NUM
ejpam-5911	232	17	of	of	ADP
ejpam-5911	232	18	27	27	NUM
ejpam-5911	232	19	remark	remark	NOUN
ejpam-5911	232	20	4	4	NUM
ejpam-5911	232	21	.	.	PUNCT
ejpam-5911	233	1	from	from	ADP
ejpam-5911	233	2	the	the	DET
ejpam-5911	233	3	previous	previous	ADJ
ejpam-5911	233	4	definitions	definition	NOUN
ejpam-5911	233	5	,	,	PUNCT
ejpam-5911	233	6	we	we	PRON
ejpam-5911	233	7	have	have	VERB
ejpam-5911	233	8	the	the	DET
ejpam-5911	233	9	following	follow	VERB
ejpam-5911	233	10	diagram	diagram	NOUN
ejpam-5911	233	11	.	.	PUNCT
ejpam-5911	234	1	df	df	PROPN
ejpam-5911	234	2	-	-	PUNCT
ejpam-5911	234	3	pre	pre	NOUN
ejpam-5911	234	4	-	-	NOUN
ejpam-5911	234	5	continuity	continuity	ADJ
ejpam-5911	234	6	↗	↗	PROPN
ejpam-5911	234	7	↓	↓	NOUN
ejpam-5911	234	8	df	df	PROPN
ejpam-5911	234	9	-	-	PUNCT
ejpam-5911	234	10	α	α	NOUN
ejpam-5911	234	11	-	-	PUNCT
ejpam-5911	234	12	continuity	continuity	NOUN
ejpam-5911	234	13	−→	−→	NOUN
ejpam-5911	234	14	df	df	PROPN
ejpam-5911	234	15	-	-	PUNCT
ejpam-5911	234	16	b	b	NOUN
ejpam-5911	234	17	-	-	PUNCT
ejpam-5911	234	18	continuity	continuity	NOUN
ejpam-5911	234	19	−→	−→	NOUN
ejpam-5911	234	20	df	df	NOUN
ejpam-5911	234	21	-	-	PUNCT
ejpam-5911	234	22	β	β	NOUN
ejpam-5911	234	23	-	-	PUNCT
ejpam-5911	234	24	continuity	continuity	NOUN
ejpam-5911	234	25	↘	↘	PROPN
ejpam-5911	234	26	↑	↑	PROPN
ejpam-5911	234	27	df	df	PROPN
ejpam-5911	234	28	-	-	PUNCT
ejpam-5911	234	29	semi	semi	ADJ
ejpam-5911	234	30	-	-	ADJ
ejpam-5911	234	31	continuity	continuity	ADJ
ejpam-5911	234	32	remark	remark	NOUN
ejpam-5911	234	33	5	5	NUM
ejpam-5911	234	34	.	.	PUNCT
ejpam-5911	235	1	the	the	DET
ejpam-5911	235	2	converse	converse	NOUN
ejpam-5911	235	3	of	of	ADP
ejpam-5911	235	4	the	the	DET
ejpam-5911	235	5	above	above	ADJ
ejpam-5911	235	6	diagram	diagram	NOUN
ejpam-5911	235	7	fails	fail	VERB
ejpam-5911	235	8	as	as	ADP
ejpam-5911	235	9	examples	example	NOUN
ejpam-5911	235	10	4	4	NUM
ejpam-5911	235	11	,	,	PUNCT
ejpam-5911	235	12	5	5	NUM
ejpam-5911	235	13	,	,	PUNCT
ejpam-5911	235	14	and	and	CCONJ
ejpam-5911	235	15	6	6	NUM
ejpam-5911	235	16	will	will	AUX
ejpam-5911	235	17	show	show	VERB
ejpam-5911	235	18	.	.	PUNCT
ejpam-5911	236	1	example	example	NOUN
ejpam-5911	237	1	4	4	X
ejpam-5911	237	2	.	.	PUNCT
ejpam-5911	237	3	let	let	VERB
ejpam-5911	237	4	g	g	NOUN
ejpam-5911	237	5	=	=	SYM
ejpam-5911	237	6	{	{	PUNCT
ejpam-5911	237	7	g1	g1	PROPN
ejpam-5911	237	8	,	,	PUNCT
ejpam-5911	237	9	g2	g2	PROPN
ejpam-5911	237	10	}	}	PUNCT
ejpam-5911	237	11	and	and	CCONJ
ejpam-5911	237	12	define	define	VERB
ejpam-5911	237	13	m	m	PROPN
ejpam-5911	237	14	,	,	PUNCT
ejpam-5911	237	15	n	n	CCONJ
ejpam-5911	237	16	,	,	PUNCT
ejpam-5911	237	17	u	u	PROPN
ejpam-5911	237	18	∈	∈	PROPN
ejpam-5911	237	19	ig	ig	PROPN
ejpam-5911	237	20	as	as	SCONJ
ejpam-5911	237	21	follows	follow	VERB
ejpam-5911	237	22	:	:	PUNCT
ejpam-5911	237	23	m	m	VERB
ejpam-5911	237	24	=	=	PUNCT
ejpam-5911	237	25	{	{	PUNCT
ejpam-5911	237	26	g1	g1	PROPN
ejpam-5911	237	27	0.4	0.4	NUM
ejpam-5911	237	28	,	,	PUNCT
ejpam-5911	237	29	g2	g2	PROPN
ejpam-5911	237	30	0.3	0.3	NUM
ejpam-5911	237	31	}	}	PUNCT
ejpam-5911	237	32	,	,	PUNCT
ejpam-5911	237	33	n	n	NOUN
ejpam-5911	237	34	=	=	PRON
ejpam-5911	237	35	{	{	PUNCT
ejpam-5911	237	36	g1	g1	PROPN
ejpam-5911	237	37	0.2	0.2	NUM
ejpam-5911	237	38	,	,	PUNCT
ejpam-5911	237	39	g2	g2	PROPN
ejpam-5911	237	40	0.6	0.6	NUM
ejpam-5911	237	41	}	}	PUNCT
ejpam-5911	237	42	,	,	PUNCT
ejpam-5911	237	43	u	u	NOUN
ejpam-5911	237	44	=	=	PUNCT
ejpam-5911	237	45	{	{	PUNCT
ejpam-5911	237	46	g1	g1	PROPN
ejpam-5911	237	47	0.5	0.5	NUM
ejpam-5911	237	48	,	,	PUNCT
ejpam-5911	237	49	g2	g2	PROPN
ejpam-5911	237	50	0.7	0.7	NUM
ejpam-5911	237	51	}	}	PUNCT
ejpam-5911	237	52	.	.	PUNCT
ejpam-5911	238	1	define	define	VERB
ejpam-5911	238	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	238	3	,	,	PUNCT
ejpam-5911	238	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	238	5	:	:	PUNCT
ejpam-5911	238	6	ig	ig	PROPN
ejpam-5911	238	7	−→	−→	NOUN
ejpam-5911	239	1	i	i	PRON
ejpam-5911	239	2	as	as	SCONJ
ejpam-5911	239	3	follows	follow	VERB
ejpam-5911	239	4	:	:	PUNCT
ejpam-5911	239	5	ℑ(v	ℑ(v	X
ejpam-5911	239	6	)	)	PUNCT
ejpam-5911	239	7	=	=	SYM
ejpam-5911	239	8			NUM
ejpam-5911	239	9	1	1	NUM
ejpam-5911	239	10	,	,	PUNCT
ejpam-5911	239	11	if	if	SCONJ
ejpam-5911	239	12	v	v	ADP
ejpam-5911	239	13	∈	∈	NOUN
ejpam-5911	239	14	{	{	PUNCT
ejpam-5911	239	15	1	1	NUM
ejpam-5911	239	16	,	,	PUNCT
ejpam-5911	239	17	0	0	NUM
ejpam-5911	239	18	}	}	PUNCT
ejpam-5911	239	19	,	,	PUNCT
ejpam-5911	239	20	1	1	NUM
ejpam-5911	239	21	4	4	NUM
ejpam-5911	239	22	,	,	PUNCT
ejpam-5911	239	23	if	if	SCONJ
ejpam-5911	239	24	v	v	VERB
ejpam-5911	239	25	=	=	SYM
ejpam-5911	239	26	n	n	NOUN
ejpam-5911	239	27	,	,	PUNCT
ejpam-5911	239	28	1	1	NUM
ejpam-5911	239	29	2	2	NUM
ejpam-5911	239	30	,	,	PUNCT
ejpam-5911	239	31	if	if	SCONJ
ejpam-5911	239	32	v	v	ADP
ejpam-5911	239	33	=	=	SYM
ejpam-5911	239	34	m	m	NOUN
ejpam-5911	239	35	,	,	PUNCT
ejpam-5911	239	36	1	1	NUM
ejpam-5911	239	37	4	4	NUM
ejpam-5911	239	38	,	,	PUNCT
ejpam-5911	239	39	if	if	SCONJ
ejpam-5911	239	40	v	v	VERB
ejpam-5911	239	41	=	=	SYM
ejpam-5911	239	42	n	n	PRON
ejpam-5911	239	43	∧m	∧m	PROPN
ejpam-5911	239	44	,	,	PUNCT
ejpam-5911	239	45	1	1	NUM
ejpam-5911	239	46	2	2	NUM
ejpam-5911	239	47	,	,	PUNCT
ejpam-5911	239	48	if	if	SCONJ
ejpam-5911	239	49	v	v	VERB
ejpam-5911	239	50	=	=	SYM
ejpam-5911	239	51	n	n	PRON
ejpam-5911	239	52	∨m	∨m	NOUN
ejpam-5911	239	53	,	,	PUNCT
ejpam-5911	239	54	0	0	NUM
ejpam-5911	239	55	,	,	PUNCT
ejpam-5911	239	56	otherwise	otherwise	ADV
ejpam-5911	239	57	,	,	PUNCT
ejpam-5911	239	58	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	239	59	)	)	PUNCT
ejpam-5911	239	60	=	=	PUNCT
ejpam-5911	240	1			NOUN
ejpam-5911	240	2	0	0	NUM
ejpam-5911	240	3	,	,	PUNCT
ejpam-5911	240	4	if	if	SCONJ
ejpam-5911	240	5	v	v	ADP
ejpam-5911	240	6	∈	∈	NOUN
ejpam-5911	240	7	{	{	PUNCT
ejpam-5911	240	8	1	1	NUM
ejpam-5911	240	9	,	,	PUNCT
ejpam-5911	240	10	0	0	NUM
ejpam-5911	240	11	}	}	PUNCT
ejpam-5911	240	12	,	,	PUNCT
ejpam-5911	240	13	1	1	NUM
ejpam-5911	240	14	4	4	NUM
ejpam-5911	240	15	,	,	PUNCT
ejpam-5911	240	16	if	if	SCONJ
ejpam-5911	240	17	v	v	VERB
ejpam-5911	240	18	=	=	SYM
ejpam-5911	240	19	n	n	NOUN
ejpam-5911	240	20	,	,	PUNCT
ejpam-5911	240	21	1	1	NUM
ejpam-5911	240	22	2	2	NUM
ejpam-5911	240	23	,	,	PUNCT
ejpam-5911	240	24	if	if	SCONJ
ejpam-5911	240	25	v	v	ADP
ejpam-5911	240	26	=	=	SYM
ejpam-5911	240	27	m	m	NOUN
ejpam-5911	240	28	,	,	PUNCT
ejpam-5911	240	29	1	1	NUM
ejpam-5911	240	30	2	2	NUM
ejpam-5911	240	31	,	,	PUNCT
ejpam-5911	240	32	if	if	SCONJ
ejpam-5911	240	33	v	v	VERB
ejpam-5911	240	34	=	=	SYM
ejpam-5911	240	35	n	n	PRON
ejpam-5911	240	36	∧m	∧m	PROPN
ejpam-5911	240	37	,	,	PUNCT
ejpam-5911	240	38	1	1	NUM
ejpam-5911	240	39	4	4	NUM
ejpam-5911	240	40	,	,	PUNCT
ejpam-5911	240	41	if	if	SCONJ
ejpam-5911	240	42	v	v	VERB
ejpam-5911	240	43	=	=	SYM
ejpam-5911	240	44	n	n	PRON
ejpam-5911	240	45	∨m	∨m	NOUN
ejpam-5911	240	46	,	,	PUNCT
ejpam-5911	240	47	1	1	NUM
ejpam-5911	240	48	,	,	PUNCT
ejpam-5911	240	49	otherwise	otherwise	ADV
ejpam-5911	240	50	,	,	PUNCT
ejpam-5911	240	51	𭟋(v	𭟋(v	NOUN
ejpam-5911	240	52	)	)	PUNCT
ejpam-5911	240	53	=	=	SYM
ejpam-5911	241	1			NOUN
ejpam-5911	241	2	1	1	NUM
ejpam-5911	241	3	,	,	PUNCT
ejpam-5911	241	4	if	if	SCONJ
ejpam-5911	241	5	v	v	ADP
ejpam-5911	241	6	∈	∈	NOUN
ejpam-5911	241	7	{	{	PUNCT
ejpam-5911	241	8	1	1	NUM
ejpam-5911	241	9	,	,	PUNCT
ejpam-5911	241	10	0	0	NUM
ejpam-5911	241	11	}	}	PUNCT
ejpam-5911	241	12	,	,	PUNCT
ejpam-5911	241	13	1	1	NUM
ejpam-5911	241	14	4	4	NUM
ejpam-5911	241	15	,	,	PUNCT
ejpam-5911	241	16	if	if	SCONJ
ejpam-5911	241	17	v	v	ADP
ejpam-5911	241	18	=	=	SYM
ejpam-5911	241	19	u	u	NOUN
ejpam-5911	241	20	,	,	PUNCT
ejpam-5911	241	21	0	0	NUM
ejpam-5911	241	22	,	,	PUNCT
ejpam-5911	241	23	otherwise	otherwise	ADV
ejpam-5911	241	24	,	,	PUNCT
ejpam-5911	241	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	241	26	)	)	PUNCT
ejpam-5911	242	1	=	=	PUNCT
ejpam-5911	243	1			NOUN
ejpam-5911	243	2	0	0	NUM
ejpam-5911	243	3	,	,	PUNCT
ejpam-5911	243	4	if	if	SCONJ
ejpam-5911	243	5	v	v	ADP
ejpam-5911	243	6	∈	∈	NOUN
ejpam-5911	243	7	{	{	PUNCT
ejpam-5911	243	8	1	1	NUM
ejpam-5911	243	9	,	,	PUNCT
ejpam-5911	243	10	0	0	NUM
ejpam-5911	243	11	}	}	PUNCT
ejpam-5911	243	12	,	,	PUNCT
ejpam-5911	243	13	1	1	NUM
ejpam-5911	243	14	2	2	NUM
ejpam-5911	243	15	,	,	PUNCT
ejpam-5911	243	16	if	if	SCONJ
ejpam-5911	243	17	v	v	ADP
ejpam-5911	243	18	=	=	SYM
ejpam-5911	243	19	u	u	NOUN
ejpam-5911	243	20	,	,	PUNCT
ejpam-5911	243	21	1	1	NUM
ejpam-5911	243	22	,	,	PUNCT
ejpam-5911	243	23	otherwise	otherwise	ADV
ejpam-5911	243	24	.	.	PUNCT
ejpam-5911	244	1	thus	thus	ADV
ejpam-5911	244	2	,	,	PUNCT
ejpam-5911	244	3	the	the	DET
ejpam-5911	244	4	identity	identity	NOUN
ejpam-5911	244	5	f	f	NOUN
ejpam-5911	244	6	-	-	PUNCT
ejpam-5911	244	7	mapping	mapping	NOUN
ejpam-5911	244	8	p	p	NOUN
ejpam-5911	244	9	:	:	PUNCT
ejpam-5911	244	10	(	(	PUNCT
ejpam-5911	244	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	244	12	)	)	PUNCT
ejpam-5911	244	13	−→	−→	NOUN
ejpam-5911	244	14	(	(	PUNCT
ejpam-5911	244	15	g	g	NOUN
ejpam-5911	244	16	,	,	PUNCT
ejpam-5911	244	17	𭟋	𭟋	NOUN
ejpam-5911	244	18	,	,	PUNCT
ejpam-5911	244	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	244	20	)	)	PUNCT
ejpam-5911	244	21	is	be	AUX
ejpam-5911	244	22	df	df	PROPN
ejpam-5911	244	23	-	-	PUNCT
ejpam-5911	244	24	b	b	NOUN
ejpam-5911	244	25	-	-	PUNCT
ejpam-5911	244	26	continuous	continuous	ADJ
ejpam-5911	244	27	,	,	PUNCT
ejpam-5911	244	28	but	but	CCONJ
ejpam-5911	244	29	it	it	PRON
ejpam-5911	244	30	is	be	AUX
ejpam-5911	244	31	neither	neither	CCONJ
ejpam-5911	244	32	df	df	NOUN
ejpam-5911	244	33	-	-	PUNCT
ejpam-5911	244	34	pre	pre	NOUN
ejpam-5911	244	35	-	-	ADJ
ejpam-5911	244	36	continuous	continuous	ADJ
ejpam-5911	244	37	nor	nor	CCONJ
ejpam-5911	244	38	df	df	NOUN
ejpam-5911	244	39	-	-	PUNCT
ejpam-5911	244	40	α	α	NOUN
ejpam-5911	244	41	-	-	ADJ
ejpam-5911	244	42	continuous	continuous	ADJ
ejpam-5911	244	43	.	.	PUNCT
ejpam-5911	244	44	example	example	NOUN
ejpam-5911	245	1	5	5	NUM
ejpam-5911	245	2	.	.	PUNCT
ejpam-5911	245	3	let	let	VERB
ejpam-5911	245	4	g	g	NOUN
ejpam-5911	245	5	=	=	SYM
ejpam-5911	245	6	{	{	PUNCT
ejpam-5911	245	7	g1	g1	PROPN
ejpam-5911	245	8	,	,	PUNCT
ejpam-5911	245	9	g2	g2	PROPN
ejpam-5911	245	10	}	}	PUNCT
ejpam-5911	245	11	and	and	CCONJ
ejpam-5911	245	12	define	define	VERB
ejpam-5911	245	13	m	m	PROPN
ejpam-5911	245	14	,	,	PUNCT
ejpam-5911	245	15	n	n	CCONJ
ejpam-5911	245	16	,	,	PUNCT
ejpam-5911	245	17	u	u	PROPN
ejpam-5911	245	18	∈	∈	PROPN
ejpam-5911	245	19	ig	ig	PROPN
ejpam-5911	245	20	as	as	SCONJ
ejpam-5911	245	21	follows	follow	VERB
ejpam-5911	245	22	:	:	PUNCT
ejpam-5911	245	23	m	m	VERB
ejpam-5911	245	24	=	=	PUNCT
ejpam-5911	245	25	{	{	PUNCT
ejpam-5911	245	26	g1	g1	PROPN
ejpam-5911	245	27	0.3	0.3	NUM
ejpam-5911	245	28	,	,	PUNCT
ejpam-5911	245	29	g2	g2	PROPN
ejpam-5911	245	30	0.2	0.2	NUM
ejpam-5911	245	31	}	}	PUNCT
ejpam-5911	245	32	,	,	PUNCT
ejpam-5911	245	33	n	n	NOUN
ejpam-5911	245	34	=	=	PRON
ejpam-5911	245	35	{	{	PUNCT
ejpam-5911	245	36	g1	g1	PROPN
ejpam-5911	245	37	0.7	0.7	NUM
ejpam-5911	245	38	,	,	PUNCT
ejpam-5911	245	39	g2	g2	PROPN
ejpam-5911	245	40	0.8	0.8	NUM
ejpam-5911	245	41	}	}	PUNCT
ejpam-5911	245	42	,	,	PUNCT
ejpam-5911	245	43	u	u	NOUN
ejpam-5911	245	44	=	=	PUNCT
ejpam-5911	245	45	{	{	PUNCT
ejpam-5911	245	46	g1	g1	PROPN
ejpam-5911	245	47	0.5	0.5	NUM
ejpam-5911	245	48	,	,	PUNCT
ejpam-5911	245	49	g2	g2	PROPN
ejpam-5911	245	50	0.4	0.4	NUM
ejpam-5911	245	51	}	}	PUNCT
ejpam-5911	245	52	.	.	PUNCT
ejpam-5911	246	1	define	define	VERB
ejpam-5911	246	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	246	3	,	,	PUNCT
ejpam-5911	246	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	246	5	:	:	PUNCT
ejpam-5911	246	6	ig	ig	PROPN
ejpam-5911	246	7	−→	−→	NOUN
ejpam-5911	247	1	i	i	PRON
ejpam-5911	247	2	as	as	SCONJ
ejpam-5911	247	3	follows	follow	VERB
ejpam-5911	247	4	:	:	PUNCT
ejpam-5911	247	5	ℑ(v	ℑ(v	X
ejpam-5911	247	6	)	)	PUNCT
ejpam-5911	247	7	=	=	PUNCT
ejpam-5911	247	8			NOUN
ejpam-5911	247	9	1	1	NUM
ejpam-5911	247	10	,	,	PUNCT
ejpam-5911	247	11	if	if	SCONJ
ejpam-5911	247	12	v	v	ADP
ejpam-5911	247	13	∈	∈	NOUN
ejpam-5911	247	14	{	{	PUNCT
ejpam-5911	247	15	1	1	NUM
ejpam-5911	247	16	,	,	PUNCT
ejpam-5911	247	17	0	0	NUM
ejpam-5911	247	18	}	}	PUNCT
ejpam-5911	247	19	,	,	PUNCT
ejpam-5911	247	20	1	1	NUM
ejpam-5911	247	21	3	3	NUM
ejpam-5911	247	22	,	,	PUNCT
ejpam-5911	247	23	if	if	SCONJ
ejpam-5911	247	24	v	v	ADP
ejpam-5911	247	25	=	=	SYM
ejpam-5911	247	26	m	m	NOUN
ejpam-5911	247	27	,	,	PUNCT
ejpam-5911	247	28	1	1	NUM
ejpam-5911	247	29	2	2	NUM
ejpam-5911	247	30	,	,	PUNCT
ejpam-5911	247	31	if	if	SCONJ
ejpam-5911	247	32	v	v	VERB
ejpam-5911	247	33	=	=	SYM
ejpam-5911	247	34	n	n	NOUN
ejpam-5911	247	35	,	,	PUNCT
ejpam-5911	247	36	0	0	NUM
ejpam-5911	247	37	,	,	PUNCT
ejpam-5911	247	38	otherwise	otherwise	ADV
ejpam-5911	247	39	,	,	PUNCT
ejpam-5911	247	40	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	247	41	)	)	PUNCT
ejpam-5911	247	42	=	=	PUNCT
ejpam-5911	248	1			NOUN
ejpam-5911	248	2	0	0	NUM
ejpam-5911	248	3	,	,	PUNCT
ejpam-5911	248	4	if	if	SCONJ
ejpam-5911	248	5	v	v	ADP
ejpam-5911	248	6	∈	∈	NOUN
ejpam-5911	248	7	{	{	PUNCT
ejpam-5911	248	8	1	1	NUM
ejpam-5911	248	9	,	,	PUNCT
ejpam-5911	248	10	0	0	NUM
ejpam-5911	248	11	}	}	PUNCT
ejpam-5911	248	12	,	,	PUNCT
ejpam-5911	248	13	1	1	NUM
ejpam-5911	248	14	2	2	NUM
ejpam-5911	248	15	,	,	PUNCT
ejpam-5911	248	16	if	if	SCONJ
ejpam-5911	248	17	v	v	ADP
ejpam-5911	248	18	=	=	SYM
ejpam-5911	248	19	m	m	NOUN
ejpam-5911	248	20	,	,	PUNCT
ejpam-5911	248	21	1	1	NUM
ejpam-5911	248	22	3	3	NUM
ejpam-5911	248	23	,	,	PUNCT
ejpam-5911	248	24	if	if	SCONJ
ejpam-5911	248	25	v	v	VERB
ejpam-5911	248	26	=	=	SYM
ejpam-5911	248	27	n	n	NOUN
ejpam-5911	248	28	,	,	PUNCT
ejpam-5911	248	29	1	1	NUM
ejpam-5911	248	30	,	,	PUNCT
ejpam-5911	248	31	otherwise	otherwise	ADV
ejpam-5911	248	32	,	,	PUNCT
ejpam-5911	248	33	i.	i.	PROPN
ejpam-5911	248	34	m.	m.	PROPN
ejpam-5911	248	35	taha	taha	PROPN
ejpam-5911	248	36	,	,	PUNCT
ejpam-5911	248	37	j.	j.	PROPN
ejpam-5911	248	38	al	al	PROPN
ejpam-5911	248	39	-	-	PUNCT
ejpam-5911	248	40	mufarrij	mufarrij	PROPN
ejpam-5911	248	41	,	,	PUNCT
ejpam-5911	248	42	o.	o.	PROPN
ejpam-5911	248	43	m.	m.	PROPN
ejpam-5911	248	44	taha	taha	PROPN
ejpam-5911	248	45	/	/	PUNCT
ejpam-5911	248	46	eur	eur	PROPN
ejpam-5911	248	47	.	.	PUNCT
ejpam-5911	249	1	j.	j.	PROPN
ejpam-5911	249	2	pure	pure	PROPN
ejpam-5911	249	3	appl	appl	PROPN
ejpam-5911	249	4	.	.	PROPN
ejpam-5911	249	5	math	math	PROPN
ejpam-5911	249	6	,	,	PUNCT
ejpam-5911	249	7	18	18	NUM
ejpam-5911	249	8	(	(	PUNCT
ejpam-5911	249	9	2	2	NUM
ejpam-5911	249	10	)	)	PUNCT
ejpam-5911	249	11	(	(	PUNCT
ejpam-5911	249	12	2025	2025	NUM
ejpam-5911	249	13	)	)	PUNCT
ejpam-5911	249	14	,	,	PUNCT
ejpam-5911	249	15	5911	5911	NUM
ejpam-5911	249	16	11	11	NUM
ejpam-5911	249	17	of	of	ADP
ejpam-5911	249	18	27	27	NUM
ejpam-5911	249	19	𭟋(v	𭟋(v	NOUN
ejpam-5911	249	20	)	)	PUNCT
ejpam-5911	249	21	=	=	SYM
ejpam-5911	250	1			NOUN
ejpam-5911	250	2	1	1	NUM
ejpam-5911	250	3	,	,	PUNCT
ejpam-5911	250	4	if	if	SCONJ
ejpam-5911	250	5	v	v	ADP
ejpam-5911	250	6	∈	∈	NOUN
ejpam-5911	250	7	{	{	PUNCT
ejpam-5911	250	8	1	1	NUM
ejpam-5911	250	9	,	,	PUNCT
ejpam-5911	250	10	0	0	NUM
ejpam-5911	250	11	}	}	PUNCT
ejpam-5911	250	12	,	,	PUNCT
ejpam-5911	250	13	1	1	NUM
ejpam-5911	250	14	3	3	NUM
ejpam-5911	250	15	,	,	PUNCT
ejpam-5911	250	16	if	if	SCONJ
ejpam-5911	250	17	v	v	ADP
ejpam-5911	250	18	=	=	SYM
ejpam-5911	250	19	u	u	NOUN
ejpam-5911	250	20	,	,	PUNCT
ejpam-5911	250	21	0	0	NUM
ejpam-5911	250	22	,	,	PUNCT
ejpam-5911	250	23	otherwise	otherwise	ADV
ejpam-5911	250	24	,	,	PUNCT
ejpam-5911	250	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	250	26	)	)	PUNCT
ejpam-5911	251	1	=	=	PUNCT
ejpam-5911	252	1			NOUN
ejpam-5911	252	2	0	0	NUM
ejpam-5911	252	3	,	,	PUNCT
ejpam-5911	252	4	if	if	SCONJ
ejpam-5911	252	5	v	v	ADP
ejpam-5911	252	6	∈	∈	NOUN
ejpam-5911	252	7	{	{	PUNCT
ejpam-5911	252	8	1	1	NUM
ejpam-5911	252	9	,	,	PUNCT
ejpam-5911	252	10	0	0	NUM
ejpam-5911	252	11	}	}	PUNCT
ejpam-5911	252	12	,	,	PUNCT
ejpam-5911	252	13	1	1	NUM
ejpam-5911	252	14	2	2	NUM
ejpam-5911	252	15	,	,	PUNCT
ejpam-5911	252	16	if	if	SCONJ
ejpam-5911	252	17	v	v	ADP
ejpam-5911	252	18	=	=	SYM
ejpam-5911	252	19	u	u	NOUN
ejpam-5911	252	20	,	,	PUNCT
ejpam-5911	252	21	1	1	NUM
ejpam-5911	252	22	,	,	PUNCT
ejpam-5911	252	23	otherwise	otherwise	ADV
ejpam-5911	252	24	.	.	PUNCT
ejpam-5911	253	1	thus	thus	ADV
ejpam-5911	253	2	,	,	PUNCT
ejpam-5911	253	3	the	the	DET
ejpam-5911	253	4	identity	identity	NOUN
ejpam-5911	253	5	f	f	NOUN
ejpam-5911	253	6	-	-	PUNCT
ejpam-5911	253	7	mapping	mapping	NOUN
ejpam-5911	253	8	p	p	NOUN
ejpam-5911	253	9	:	:	PUNCT
ejpam-5911	253	10	(	(	PUNCT
ejpam-5911	253	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	253	12	)	)	PUNCT
ejpam-5911	253	13	−→	−→	NOUN
ejpam-5911	253	14	(	(	PUNCT
ejpam-5911	253	15	g	g	NOUN
ejpam-5911	253	16	,	,	PUNCT
ejpam-5911	253	17	𭟋	𭟋	NOUN
ejpam-5911	253	18	,	,	PUNCT
ejpam-5911	253	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	253	20	)	)	PUNCT
ejpam-5911	253	21	is	be	AUX
ejpam-5911	253	22	df	df	PROPN
ejpam-5911	253	23	-	-	PUNCT
ejpam-5911	253	24	b	b	NOUN
ejpam-5911	253	25	-	-	PUNCT
ejpam-5911	253	26	continuous	continuous	ADJ
ejpam-5911	253	27	,	,	PUNCT
ejpam-5911	253	28	but	but	CCONJ
ejpam-5911	253	29	it	it	PRON
ejpam-5911	253	30	is	be	AUX
ejpam-5911	253	31	not	not	PART
ejpam-5911	253	32	df	df	NOUN
ejpam-5911	253	33	-	-	PUNCT
ejpam-5911	253	34	semi	semi	ADV
ejpam-5911	253	35	-	-	ADJ
ejpam-5911	253	36	continuous	continuous	ADJ
ejpam-5911	253	37	.	.	PUNCT
ejpam-5911	253	38	example	example	NOUN
ejpam-5911	254	1	6	6	NUM
ejpam-5911	254	2	.	.	PUNCT
ejpam-5911	255	1	let	let	VERB
ejpam-5911	255	2	g	g	PROPN
ejpam-5911	255	3	=	=	SYM
ejpam-5911	255	4	{	{	PUNCT
ejpam-5911	255	5	g1	g1	PROPN
ejpam-5911	255	6	,	,	PUNCT
ejpam-5911	255	7	g2	g2	PROPN
ejpam-5911	255	8	}	}	PUNCT
ejpam-5911	255	9	and	and	CCONJ
ejpam-5911	255	10	define	define	VERB
ejpam-5911	255	11	m	m	PROPN
ejpam-5911	255	12	,	,	PUNCT
ejpam-5911	255	13	u	u	PROPN
ejpam-5911	255	14	∈	∈	PROPN
ejpam-5911	255	15	ig	ig	PROPN
ejpam-5911	255	16	as	as	SCONJ
ejpam-5911	255	17	follows	follow	VERB
ejpam-5911	255	18	:	:	PUNCT
ejpam-5911	255	19	m	m	VERB
ejpam-5911	255	20	=	=	PUNCT
ejpam-5911	255	21	{	{	PUNCT
ejpam-5911	255	22	g1	g1	PROPN
ejpam-5911	255	23	0.5	0.5	NUM
ejpam-5911	255	24	,	,	PUNCT
ejpam-5911	255	25	g2	g2	PROPN
ejpam-5911	255	26	0.4	0.4	NUM
ejpam-5911	255	27	}	}	PUNCT
ejpam-5911	255	28	,	,	PUNCT
ejpam-5911	255	29	u	u	NOUN
ejpam-5911	255	30	=	=	PUNCT
ejpam-5911	255	31	{	{	PUNCT
ejpam-5911	255	32	g1	g1	PROPN
ejpam-5911	255	33	0.4	0.4	NUM
ejpam-5911	255	34	,	,	PUNCT
ejpam-5911	255	35	g2	g2	PROPN
ejpam-5911	255	36	0.5	0.5	NUM
ejpam-5911	255	37	}	}	PUNCT
ejpam-5911	255	38	.	.	PUNCT
ejpam-5911	256	1	define	define	VERB
ejpam-5911	256	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	256	3	,	,	PUNCT
ejpam-5911	256	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	256	5	:	:	PUNCT
ejpam-5911	256	6	ig	ig	PROPN
ejpam-5911	256	7	−→	−→	NOUN
ejpam-5911	257	1	i	i	PRON
ejpam-5911	257	2	as	as	SCONJ
ejpam-5911	257	3	follows	follow	VERB
ejpam-5911	257	4	:	:	PUNCT
ejpam-5911	257	5	ℑ(v	ℑ(v	X
ejpam-5911	257	6	)	)	PUNCT
ejpam-5911	257	7	=	=	SYM
ejpam-5911	258	1			NOUN
ejpam-5911	258	2	1	1	NUM
ejpam-5911	258	3	,	,	PUNCT
ejpam-5911	258	4	if	if	SCONJ
ejpam-5911	258	5	v	v	ADP
ejpam-5911	258	6	∈	∈	NOUN
ejpam-5911	258	7	{	{	PUNCT
ejpam-5911	258	8	1	1	NUM
ejpam-5911	258	9	,	,	PUNCT
ejpam-5911	258	10	0	0	NUM
ejpam-5911	258	11	}	}	PUNCT
ejpam-5911	258	12	,	,	PUNCT
ejpam-5911	258	13	1	1	NUM
ejpam-5911	258	14	2	2	NUM
ejpam-5911	258	15	,	,	PUNCT
ejpam-5911	258	16	if	if	SCONJ
ejpam-5911	258	17	v	v	ADP
ejpam-5911	258	18	=	=	NOUN
ejpam-5911	258	19	m	m	PROPN
ejpam-5911	258	20	,	,	PUNCT
ejpam-5911	258	21	0	0	NUM
ejpam-5911	258	22	,	,	PUNCT
ejpam-5911	258	23	otherwise	otherwise	ADV
ejpam-5911	258	24	,	,	PUNCT
ejpam-5911	258	25	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	258	26	)	)	PUNCT
ejpam-5911	259	1	=	=	SYM
ejpam-5911	260	1			NOUN
ejpam-5911	260	2	0	0	NUM
ejpam-5911	260	3	,	,	PUNCT
ejpam-5911	260	4	if	if	SCONJ
ejpam-5911	260	5	v	v	ADP
ejpam-5911	260	6	∈	∈	NOUN
ejpam-5911	260	7	{	{	PUNCT
ejpam-5911	260	8	1	1	NUM
ejpam-5911	260	9	,	,	PUNCT
ejpam-5911	260	10	0	0	NUM
ejpam-5911	260	11	}	}	PUNCT
ejpam-5911	260	12	,	,	PUNCT
ejpam-5911	260	13	1	1	NUM
ejpam-5911	260	14	2	2	NUM
ejpam-5911	260	15	,	,	PUNCT
ejpam-5911	260	16	if	if	SCONJ
ejpam-5911	260	17	v	v	ADP
ejpam-5911	260	18	=	=	NOUN
ejpam-5911	260	19	m	m	PROPN
ejpam-5911	260	20	,	,	PUNCT
ejpam-5911	260	21	1	1	NUM
ejpam-5911	260	22	,	,	PUNCT
ejpam-5911	260	23	otherwise	otherwise	ADV
ejpam-5911	260	24	,	,	PUNCT
ejpam-5911	260	25	𭟋(v	𭟋(v	NOUN
ejpam-5911	260	26	)	)	PUNCT
ejpam-5911	260	27	=	=	SYM
ejpam-5911	261	1			NOUN
ejpam-5911	261	2	1	1	NUM
ejpam-5911	261	3	,	,	PUNCT
ejpam-5911	261	4	if	if	SCONJ
ejpam-5911	261	5	v	v	ADP
ejpam-5911	261	6	∈	∈	NOUN
ejpam-5911	261	7	{	{	PUNCT
ejpam-5911	261	8	1	1	NUM
ejpam-5911	261	9	,	,	PUNCT
ejpam-5911	261	10	0	0	NUM
ejpam-5911	261	11	}	}	PUNCT
ejpam-5911	261	12	,	,	PUNCT
ejpam-5911	261	13	1	1	NUM
ejpam-5911	261	14	3	3	NUM
ejpam-5911	261	15	,	,	PUNCT
ejpam-5911	261	16	if	if	SCONJ
ejpam-5911	261	17	v	v	ADP
ejpam-5911	261	18	=	=	SYM
ejpam-5911	261	19	u	u	NOUN
ejpam-5911	261	20	,	,	PUNCT
ejpam-5911	261	21	0	0	NUM
ejpam-5911	261	22	,	,	PUNCT
ejpam-5911	261	23	otherwise	otherwise	ADV
ejpam-5911	261	24	,	,	PUNCT
ejpam-5911	261	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	261	26	)	)	PUNCT
ejpam-5911	262	1	=	=	PUNCT
ejpam-5911	263	1			NOUN
ejpam-5911	263	2	0	0	NUM
ejpam-5911	263	3	,	,	PUNCT
ejpam-5911	263	4	if	if	SCONJ
ejpam-5911	263	5	v	v	ADP
ejpam-5911	263	6	∈	∈	NOUN
ejpam-5911	263	7	{	{	PUNCT
ejpam-5911	263	8	1	1	NUM
ejpam-5911	263	9	,	,	PUNCT
ejpam-5911	263	10	0	0	NUM
ejpam-5911	263	11	}	}	PUNCT
ejpam-5911	263	12	,	,	PUNCT
ejpam-5911	263	13	1	1	NUM
ejpam-5911	263	14	2	2	NUM
ejpam-5911	263	15	,	,	PUNCT
ejpam-5911	263	16	if	if	SCONJ
ejpam-5911	263	17	v	v	ADP
ejpam-5911	263	18	=	=	SYM
ejpam-5911	263	19	u	u	NOUN
ejpam-5911	263	20	,	,	PUNCT
ejpam-5911	263	21	1	1	NUM
ejpam-5911	263	22	,	,	PUNCT
ejpam-5911	263	23	otherwise	otherwise	ADV
ejpam-5911	263	24	.	.	PUNCT
ejpam-5911	264	1	thus	thus	ADV
ejpam-5911	264	2	,	,	PUNCT
ejpam-5911	264	3	the	the	DET
ejpam-5911	264	4	identity	identity	NOUN
ejpam-5911	264	5	f	f	NOUN
ejpam-5911	264	6	-	-	PUNCT
ejpam-5911	264	7	mapping	mapping	NOUN
ejpam-5911	264	8	p	p	NOUN
ejpam-5911	264	9	:	:	PUNCT
ejpam-5911	264	10	(	(	PUNCT
ejpam-5911	264	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	264	12	)	)	PUNCT
ejpam-5911	264	13	−→	−→	NOUN
ejpam-5911	264	14	(	(	PUNCT
ejpam-5911	264	15	g	g	NOUN
ejpam-5911	264	16	,	,	PUNCT
ejpam-5911	264	17	𭟋	𭟋	NOUN
ejpam-5911	264	18	,	,	PUNCT
ejpam-5911	264	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	264	20	)	)	PUNCT
ejpam-5911	264	21	is	be	AUX
ejpam-5911	264	22	df	df	PROPN
ejpam-5911	264	23	-	-	PUNCT
ejpam-5911	264	24	β	β	NOUN
ejpam-5911	264	25	-	-	ADJ
ejpam-5911	264	26	continuous	continuous	ADJ
ejpam-5911	264	27	,	,	PUNCT
ejpam-5911	264	28	but	but	CCONJ
ejpam-5911	264	29	it	it	PRON
ejpam-5911	264	30	is	be	AUX
ejpam-5911	264	31	not	not	PART
ejpam-5911	264	32	df	df	NOUN
ejpam-5911	264	33	-	-	PUNCT
ejpam-5911	264	34	b	b	NOUN
ejpam-5911	264	35	-	-	PUNCT
ejpam-5911	264	36	continuous	continuous	ADJ
ejpam-5911	264	37	.	.	PUNCT
ejpam-5911	265	1	theorem	theorem	NOUN
ejpam-5911	265	2	3	3	NUM
ejpam-5911	265	3	.	.	PUNCT
ejpam-5911	266	1	an	an	DET
ejpam-5911	266	2	f	f	NOUN
ejpam-5911	266	3	-	-	PUNCT
ejpam-5911	266	4	mapping	mapping	NOUN
ejpam-5911	266	5	p	p	NOUN
ejpam-5911	266	6	:	:	PUNCT
ejpam-5911	266	7	(	(	PUNCT
ejpam-5911	266	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	266	9	)	)	PUNCT
ejpam-5911	267	1	−→	−→	NOUN
ejpam-5911	267	2	(	(	PUNCT
ejpam-5911	267	3	z	z	NOUN
ejpam-5911	267	4	,	,	PUNCT
ejpam-5911	267	5	𭟋	𭟋	NOUN
ejpam-5911	267	6	,	,	PUNCT
ejpam-5911	267	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	267	8	)	)	PUNCT
ejpam-5911	267	9	is	be	AUX
ejpam-5911	267	10	df	df	PROPN
ejpam-5911	267	11	-	-	PUNCT
ejpam-5911	267	12	b	b	NOUN
ejpam-5911	267	13	-	-	PUNCT
ejpam-5911	267	14	continuous	continuous	ADJ
ejpam-5911	267	15	iff	iff	NOUN
ejpam-5911	267	16	for	for	ADP
ejpam-5911	267	17	any	any	DET
ejpam-5911	267	18	gθ	gθ	PROPN
ejpam-5911	267	19	∈	∈	PROPN
ejpam-5911	267	20	pθ(g	pθ(g	NOUN
ejpam-5911	267	21	)	)	PUNCT
ejpam-5911	267	22	and	and	CCONJ
ejpam-5911	267	23	any	any	DET
ejpam-5911	267	24	n	n	NOUN
ejpam-5911	267	25	∈	∈	NOUN
ejpam-5911	267	26	iz	iz	INTJ
ejpam-5911	267	27	with	with	ADP
ejpam-5911	267	28	𭟋(n	𭟋(n	PROPN
ejpam-5911	267	29	)	)	PUNCT
ejpam-5911	268	1	≥	≥	PROPN
ejpam-5911	269	1	r	r	NOUN
ejpam-5911	269	2	and	and	CCONJ
ejpam-5911	269	3	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	269	4	)	)	PUNCT
ejpam-5911	269	5	≤	≤	NUM
ejpam-5911	269	6	s	s	AUX
ejpam-5911	269	7	containing	contain	VERB
ejpam-5911	269	8	p(gθ	p(gθ	PROPN
ejpam-5911	269	9	)	)	PUNCT
ejpam-5911	269	10	,	,	PUNCT
ejpam-5911	269	11	there	there	PRON
ejpam-5911	269	12	is	be	VERB
ejpam-5911	269	13	m	m	PROPN
ejpam-5911	269	14	∈	∈	NOUN
ejpam-5911	269	15	ig	ig	PROPN
ejpam-5911	269	16	that	that	PRON
ejpam-5911	269	17	is	be	AUX
ejpam-5911	269	18	(	(	PUNCT
ejpam-5911	269	19	r	r	NOUN
ejpam-5911	269	20	,	,	PUNCT
ejpam-5911	269	21	s)-f	s)-f	NOUN
ejpam-5911	269	22	-	-	PUNCT
ejpam-5911	269	23	b	b	NOUN
ejpam-5911	269	24	-	-	PUNCT
ejpam-5911	269	25	open	open	ADJ
ejpam-5911	269	26	containing	contain	VERB
ejpam-5911	269	27	gθ	gθ	NOUN
ejpam-5911	269	28	with	with	ADP
ejpam-5911	269	29	p(m	p(m	NOUN
ejpam-5911	269	30	)	)	PUNCT
ejpam-5911	269	31	≤	≤	NOUN
ejpam-5911	269	32	n	n	NOUN
ejpam-5911	269	33	.	.	PUNCT
ejpam-5911	270	1	proof	proof	NOUN
ejpam-5911	270	2	.	.	PUNCT
ejpam-5911	271	1	(	(	PUNCT
ejpam-5911	271	2	⇒	⇒	PROPN
ejpam-5911	271	3	)	)	PUNCT
ejpam-5911	271	4	let	let	VERB
ejpam-5911	271	5	gθ	gθ	PROPN
ejpam-5911	271	6	∈	∈	PROPN
ejpam-5911	271	7	pθ(g	pθ(g	NOUN
ejpam-5911	271	8	)	)	PUNCT
ejpam-5911	271	9	and	and	CCONJ
ejpam-5911	271	10	n	n	PRON
ejpam-5911	271	11	∈	∈	NOUN
ejpam-5911	271	12	iz	iz	INTJ
ejpam-5911	271	13	with	with	ADP
ejpam-5911	271	14	𭟋(n	𭟋(n	PROPN
ejpam-5911	271	15	)	)	PUNCT
ejpam-5911	271	16	≥	≥	PROPN
ejpam-5911	271	17	r	r	NOUN
ejpam-5911	271	18	and	and	CCONJ
ejpam-5911	271	19	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	271	20	)	)	PUNCT
ejpam-5911	271	21	≤	≤	NUM
ejpam-5911	271	22	s	s	AUX
ejpam-5911	271	23	containing	contain	VERB
ejpam-5911	271	24	p(gθ	p(gθ	PROPN
ejpam-5911	271	25	)	)	PUNCT
ejpam-5911	271	26	,	,	PUNCT
ejpam-5911	271	27	and	and	CCONJ
ejpam-5911	271	28	then	then	ADV
ejpam-5911	271	29	p−1(n	p−1(n	ADV
ejpam-5911	271	30	)	)	PUNCT
ejpam-5911	271	31	≤	≤	NUM
ejpam-5911	271	32	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	271	33	)	)	PUNCT
ejpam-5911	271	34	,	,	PUNCT
ejpam-5911	271	35	r	r	NOUN
ejpam-5911	271	36	,	,	PUNCT
ejpam-5911	271	37	s	s	NOUN
ejpam-5911	271	38	)	)	PUNCT
ejpam-5911	271	39	.	.	PUNCT
ejpam-5911	272	1	since	since	SCONJ
ejpam-5911	272	2	gθ	gθ	PROPN
ejpam-5911	272	3	∈	∈	PROPN
ejpam-5911	272	4	p−1(n	p−1(n	PROPN
ejpam-5911	272	5	)	)	PUNCT
ejpam-5911	272	6	,	,	PUNCT
ejpam-5911	272	7	then	then	ADV
ejpam-5911	272	8	we	we	PRON
ejpam-5911	272	9	obtain	obtain	VERB
ejpam-5911	272	10	gθ	gθ	NOUN
ejpam-5911	272	11	∈	∈	NOUN
ejpam-5911	272	12	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	272	13	)	)	PUNCT
ejpam-5911	272	14	,	,	PUNCT
ejpam-5911	272	15	r	r	NOUN
ejpam-5911	272	16	,	,	PUNCT
ejpam-5911	272	17	s	s	PART
ejpam-5911	272	18	)	)	PUNCT
ejpam-5911	272	19	=	=	SYM
ejpam-5911	272	20	m	m	PROPN
ejpam-5911	272	21	(	(	PUNCT
ejpam-5911	272	22	say	say	INTJ
ejpam-5911	272	23	)	)	PUNCT
ejpam-5911	272	24	.	.	PUNCT
ejpam-5911	273	1	hence	hence	ADV
ejpam-5911	273	2	,	,	PUNCT
ejpam-5911	273	3	m	m	PROPN
ejpam-5911	273	4	∈	∈	NOUN
ejpam-5911	273	5	ig	ig	PROPN
ejpam-5911	273	6	is	be	AUX
ejpam-5911	273	7	(	(	PUNCT
ejpam-5911	273	8	r	r	NOUN
ejpam-5911	273	9	,	,	PUNCT
ejpam-5911	273	10	s)-f	s)-f	NOUN
ejpam-5911	273	11	-	-	PUNCT
ejpam-5911	273	12	b	b	NOUN
ejpam-5911	273	13	-	-	PUNCT
ejpam-5911	273	14	open	open	ADJ
ejpam-5911	273	15	containing	contain	VERB
ejpam-5911	273	16	gθ	gθ	NOUN
ejpam-5911	273	17	with	with	ADP
ejpam-5911	273	18	p(m	p(m	NOUN
ejpam-5911	273	19	)	)	PUNCT
ejpam-5911	273	20	≤	≤	NOUN
ejpam-5911	273	21	n	n	NOUN
ejpam-5911	273	22	.	.	PUNCT
ejpam-5911	274	1	(	(	PUNCT
ejpam-5911	274	2	⇐	⇐	NOUN
ejpam-5911	274	3	)	)	PUNCT
ejpam-5911	274	4	let	let	VERB
ejpam-5911	274	5	gθ	gθ	PROPN
ejpam-5911	274	6	∈	∈	PROPN
ejpam-5911	274	7	pθ(g	pθ(g	NOUN
ejpam-5911	274	8	)	)	PUNCT
ejpam-5911	274	9	and	and	CCONJ
ejpam-5911	274	10	n	n	PRON
ejpam-5911	274	11	∈	∈	NOUN
ejpam-5911	274	12	iz	iz	INTJ
ejpam-5911	274	13	with	with	ADP
ejpam-5911	274	14	𭟋(n	𭟋(n	PROPN
ejpam-5911	274	15	)	)	PUNCT
ejpam-5911	275	1	≥	≥	PROPN
ejpam-5911	275	2	r	r	NOUN
ejpam-5911	275	3	and	and	CCONJ
ejpam-5911	275	4	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	275	5	)	)	PUNCT
ejpam-5911	275	6	≤	≤	NUM
ejpam-5911	275	7	s	s	AUX
ejpam-5911	275	8	containing	contain	VERB
ejpam-5911	275	9	p(gθ	p(gθ	PROPN
ejpam-5911	275	10	)	)	PUNCT
ejpam-5911	275	11	.	.	PUNCT
ejpam-5911	276	1	according	accord	VERB
ejpam-5911	276	2	to	to	ADP
ejpam-5911	276	3	the	the	DET
ejpam-5911	276	4	assumption	assumption	NOUN
ejpam-5911	276	5	there	there	PRON
ejpam-5911	276	6	is	be	VERB
ejpam-5911	276	7	m	m	NOUN
ejpam-5911	276	8	∈	∈	NOUN
ejpam-5911	276	9	ig	ig	PROPN
ejpam-5911	276	10	that	that	PRON
ejpam-5911	276	11	is	be	AUX
ejpam-5911	276	12	(	(	PUNCT
ejpam-5911	276	13	r	r	NOUN
ejpam-5911	276	14	,	,	PUNCT
ejpam-5911	276	15	s)-f	s)-f	NOUN
ejpam-5911	276	16	-	-	PUNCT
ejpam-5911	276	17	b	b	NOUN
ejpam-5911	276	18	-	-	PUNCT
ejpam-5911	276	19	open	open	ADJ
ejpam-5911	276	20	containing	contain	VERB
ejpam-5911	276	21	gθ	gθ	NOUN
ejpam-5911	276	22	with	with	ADP
ejpam-5911	276	23	p(m	p(m	NOUN
ejpam-5911	276	24	)	)	PUNCT
ejpam-5911	276	25	≤	≤	NOUN
ejpam-5911	276	26	n	n	NOUN
ejpam-5911	276	27	.	.	PUNCT
ejpam-5911	277	1	hence	hence	ADV
ejpam-5911	277	2	,	,	PUNCT
ejpam-5911	277	3	gθ	gθ	PROPN
ejpam-5911	277	4	∈	∈	PROPN
ejpam-5911	277	5	m	m	NOUN
ejpam-5911	277	6	≤	≤	NOUN
ejpam-5911	277	7	p−1(n	p−1(n	NOUN
ejpam-5911	277	8	)	)	PUNCT
ejpam-5911	277	9	and	and	CCONJ
ejpam-5911	277	10	gθ	gθ	PROPN
ejpam-5911	277	11	∈	∈	PROPN
ejpam-5911	277	12	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	277	13	)	)	PUNCT
ejpam-5911	277	14	,	,	PUNCT
ejpam-5911	277	15	r	r	NOUN
ejpam-5911	277	16	,	,	PUNCT
ejpam-5911	277	17	s	s	NOUN
ejpam-5911	277	18	)	)	PUNCT
ejpam-5911	277	19	.	.	PUNCT
ejpam-5911	278	1	thus	thus	ADV
ejpam-5911	278	2	,	,	PUNCT
ejpam-5911	278	3	p−1(n	p−1(n	NOUN
ejpam-5911	278	4	)	)	PUNCT
ejpam-5911	278	5	≤	≤	NUM
ejpam-5911	278	6	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	278	7	)	)	PUNCT
ejpam-5911	278	8	,	,	PUNCT
ejpam-5911	278	9	r	r	NOUN
ejpam-5911	278	10	,	,	PUNCT
ejpam-5911	278	11	s	s	PART
ejpam-5911	278	12	)	)	PUNCT
ejpam-5911	278	13	,	,	PUNCT
ejpam-5911	278	14	so	so	ADV
ejpam-5911	278	15	p−1(n	p−1(n	VERB
ejpam-5911	278	16	)	)	PUNCT
ejpam-5911	278	17	is	be	AUX
ejpam-5911	278	18	an	an	DET
ejpam-5911	278	19	(	(	PUNCT
ejpam-5911	278	20	r	r	NOUN
ejpam-5911	278	21	,	,	PUNCT
ejpam-5911	278	22	s)-f	s)-f	NOUN
ejpam-5911	278	23	-	-	PUNCT
ejpam-5911	278	24	b	b	NOUN
ejpam-5911	278	25	-	-	PUNCT
ejpam-5911	278	26	open	open	ADJ
ejpam-5911	278	27	set	set	NOUN
ejpam-5911	278	28	.	.	PUNCT
ejpam-5911	279	1	then	then	ADV
ejpam-5911	279	2	,	,	PUNCT
ejpam-5911	279	3	p	p	NOUN
ejpam-5911	279	4	is	be	AUX
ejpam-5911	279	5	df	df	PROPN
ejpam-5911	279	6	-	-	PUNCT
ejpam-5911	279	7	b	b	NOUN
ejpam-5911	279	8	-	-	PUNCT
ejpam-5911	279	9	continuous	continuous	ADJ
ejpam-5911	279	10	.	.	PUNCT
ejpam-5911	280	1	theorem	theorem	NOUN
ejpam-5911	280	2	4	4	NUM
ejpam-5911	280	3	.	.	PUNCT
ejpam-5911	281	1	let	let	VERB
ejpam-5911	281	2	p	p	NOUN
ejpam-5911	281	3	:	:	PUNCT
ejpam-5911	281	4	(	(	PUNCT
ejpam-5911	281	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	281	6	)	)	PUNCT
ejpam-5911	282	1	−→	−→	NOUN
ejpam-5911	282	2	(	(	PUNCT
ejpam-5911	282	3	z	z	NOUN
ejpam-5911	282	4	,	,	PUNCT
ejpam-5911	282	5	𭟋	𭟋	NOUN
ejpam-5911	282	6	,	,	PUNCT
ejpam-5911	282	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	282	8	)	)	PUNCT
ejpam-5911	282	9	be	be	AUX
ejpam-5911	282	10	an	an	DET
ejpam-5911	282	11	f	f	NOUN
ejpam-5911	282	12	-	-	PUNCT
ejpam-5911	282	13	mapping	mapping	NOUN
ejpam-5911	282	14	,	,	PUNCT
ejpam-5911	282	15	r	r	NOUN
ejpam-5911	282	16	∈	∈	PROPN
ejpam-5911	283	1	i	i	NOUN
ejpam-5911	283	2	◦	◦	NOUN
ejpam-5911	283	3	,	,	PUNCT
ejpam-5911	283	4	and	and	CCONJ
ejpam-5911	283	5	s	s	PROPN
ejpam-5911	283	6	∈	∈	PROPN
ejpam-5911	283	7	i1	i1	PROPN
ejpam-5911	283	8	.	.	PUNCT
ejpam-5911	284	1	then	then	ADV
ejpam-5911	284	2	the	the	DET
ejpam-5911	284	3	following	follow	VERB
ejpam-5911	284	4	statements	statement	NOUN
ejpam-5911	284	5	are	be	AUX
ejpam-5911	284	6	equivalent	equivalent	ADJ
ejpam-5911	284	7	for	for	ADP
ejpam-5911	284	8	every	every	DET
ejpam-5911	284	9	m	m	NOUN
ejpam-5911	284	10	∈	∈	NOUN
ejpam-5911	284	11	ig	ig	PROPN
ejpam-5911	284	12	and	and	CCONJ
ejpam-5911	284	13	n	n	PRON
ejpam-5911	284	14	∈	∈	PROPN
ejpam-5911	285	1	iz	iz	INTJ
ejpam-5911	285	2	:	:	PUNCT
ejpam-5911	285	3	(	(	PUNCT
ejpam-5911	285	4	i	i	NOUN
ejpam-5911	285	5	)	)	PUNCT
ejpam-5911	285	6	p	p	NOUN
ejpam-5911	285	7	is	be	AUX
ejpam-5911	285	8	df	df	PROPN
ejpam-5911	285	9	-	-	PUNCT
ejpam-5911	285	10	b	b	NOUN
ejpam-5911	285	11	-	-	PUNCT
ejpam-5911	285	12	continuous	continuous	ADJ
ejpam-5911	285	13	.	.	PUNCT
ejpam-5911	286	1	i.	i.	PROPN
ejpam-5911	286	2	m.	m.	PROPN
ejpam-5911	286	3	taha	taha	PROPN
ejpam-5911	286	4	,	,	PUNCT
ejpam-5911	286	5	j.	j.	PROPN
ejpam-5911	286	6	al	al	PROPN
ejpam-5911	286	7	-	-	PUNCT
ejpam-5911	286	8	mufarrij	mufarrij	PROPN
ejpam-5911	286	9	,	,	PUNCT
ejpam-5911	286	10	o.	o.	PROPN
ejpam-5911	286	11	m.	m.	PROPN
ejpam-5911	286	12	taha	taha	PROPN
ejpam-5911	286	13	/	/	PUNCT
ejpam-5911	286	14	eur	eur	PROPN
ejpam-5911	286	15	.	.	PUNCT
ejpam-5911	287	1	j.	j.	PROPN
ejpam-5911	287	2	pure	pure	PROPN
ejpam-5911	287	3	appl	appl	PROPN
ejpam-5911	287	4	.	.	PROPN
ejpam-5911	287	5	math	math	PROPN
ejpam-5911	287	6	,	,	PUNCT
ejpam-5911	287	7	18	18	NUM
ejpam-5911	287	8	(	(	PUNCT
ejpam-5911	287	9	2	2	NUM
ejpam-5911	287	10	)	)	PUNCT
ejpam-5911	287	11	(	(	PUNCT
ejpam-5911	287	12	2025	2025	NUM
ejpam-5911	287	13	)	)	PUNCT
ejpam-5911	287	14	,	,	PUNCT
ejpam-5911	287	15	5911	5911	NUM
ejpam-5911	287	16	12	12	NUM
ejpam-5911	287	17	of	of	ADP
ejpam-5911	287	18	27	27	NUM
ejpam-5911	287	19	(	(	PUNCT
ejpam-5911	287	20	ii	ii	NOUN
ejpam-5911	287	21	)	)	PUNCT
ejpam-5911	287	22	p−1(n	p−1(n	PROPN
ejpam-5911	287	23	)	)	PUNCT
ejpam-5911	287	24	is	be	AUX
ejpam-5911	287	25	(	(	PUNCT
ejpam-5911	287	26	r	r	NOUN
ejpam-5911	287	27	,	,	PUNCT
ejpam-5911	287	28	s)-f	s)-f	NOUN
ejpam-5911	287	29	-	-	PUNCT
ejpam-5911	287	30	b	b	NOUN
ejpam-5911	287	31	-	-	PUNCT
ejpam-5911	287	32	closed	closed	ADJ
ejpam-5911	287	33	,	,	PUNCT
ejpam-5911	287	34	for	for	ADP
ejpam-5911	287	35	every	every	DET
ejpam-5911	287	36	n	n	NOUN
ejpam-5911	287	37	∈	∈	NOUN
ejpam-5911	287	38	iz	iz	INTJ
ejpam-5911	287	39	with	with	ADP
ejpam-5911	287	40	𭟋(n	𭟋(n	PROPN
ejpam-5911	287	41	c	c	PROPN
ejpam-5911	287	42	)	)	PUNCT
ejpam-5911	287	43	≥	≥	NOUN
ejpam-5911	287	44	r	r	NOUN
ejpam-5911	287	45	and	and	CCONJ
ejpam-5911	287	46	𭟋∗(n	𭟋∗(n	PROPN
ejpam-5911	287	47	c	c	NOUN
ejpam-5911	287	48	)	)	PUNCT
ejpam-5911	287	49	≤	≤	PROPN
ejpam-5911	287	50	s.	s.	PROPN
ejpam-5911	287	51	(	(	PUNCT
ejpam-5911	287	52	iii	iii	NOUN
ejpam-5911	287	53	)	)	PUNCT
ejpam-5911	287	54	p(bcℑ∗(m	p(bcℑ∗(m	NUM
ejpam-5911	287	55	,	,	PUNCT
ejpam-5911	287	56	r	r	NOUN
ejpam-5911	287	57	,	,	PUNCT
ejpam-5911	287	58	s	s	NOUN
ejpam-5911	287	59	)	)	PUNCT
ejpam-5911	287	60	)	)	PUNCT
ejpam-5911	287	61	≤	≤	NOUN
ejpam-5911	287	62	c𭟋∗(p(m	c𭟋∗(p(m	NOUN
ejpam-5911	287	63	)	)	PUNCT
ejpam-5911	287	64	,	,	PUNCT
ejpam-5911	287	65	r	r	NOUN
ejpam-5911	287	66	,	,	PUNCT
ejpam-5911	287	67	s	s	NOUN
ejpam-5911	287	68	)	)	PUNCT
ejpam-5911	287	69	.	.	PUNCT
ejpam-5911	288	1	(	(	PUNCT
ejpam-5911	288	2	iv	iv	X
ejpam-5911	288	3	)	)	PUNCT
ejpam-5911	288	4	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	288	5	)	)	PUNCT
ejpam-5911	288	6	,	,	PUNCT
ejpam-5911	288	7	r	r	NOUN
ejpam-5911	288	8	,	,	PUNCT
ejpam-5911	288	9	s	s	NOUN
ejpam-5911	288	10	)	)	PUNCT
ejpam-5911	288	11	≤	≤	PUNCT
ejpam-5911	289	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	289	2	,	,	PUNCT
ejpam-5911	289	3	r	r	NOUN
ejpam-5911	289	4	,	,	PUNCT
ejpam-5911	289	5	s	s	NOUN
ejpam-5911	289	6	)	)	PUNCT
ejpam-5911	289	7	)	)	PUNCT
ejpam-5911	289	8	.	.	PUNCT
ejpam-5911	290	1	(	(	PUNCT
ejpam-5911	290	2	v	v	NOUN
ejpam-5911	290	3	)	)	PUNCT
ejpam-5911	290	4	p−1(i𭟋∗(n	p−1(i𭟋∗(n	ADJ
ejpam-5911	290	5	,	,	PUNCT
ejpam-5911	290	6	r	r	NOUN
ejpam-5911	290	7	,	,	PUNCT
ejpam-5911	290	8	s	s	NOUN
ejpam-5911	290	9	)	)	PUNCT
ejpam-5911	290	10	)	)	PUNCT
ejpam-5911	291	1	≤	≤	NUM
ejpam-5911	291	2	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	291	3	)	)	PUNCT
ejpam-5911	291	4	,	,	PUNCT
ejpam-5911	291	5	r	r	NOUN
ejpam-5911	291	6	,	,	PUNCT
ejpam-5911	291	7	s	s	NOUN
ejpam-5911	291	8	)	)	PUNCT
ejpam-5911	291	9	.	.	PUNCT
ejpam-5911	292	1	proof	proof	NOUN
ejpam-5911	292	2	.	.	PUNCT
ejpam-5911	293	1	(	(	PUNCT
ejpam-5911	293	2	i	i	NOUN
ejpam-5911	293	3	)	)	PUNCT
ejpam-5911	293	4	⇔	⇔	PROPN
ejpam-5911	293	5	(	(	PUNCT
ejpam-5911	293	6	ii	ii	PROPN
ejpam-5911	293	7	)	)	PUNCT
ejpam-5911	293	8	the	the	DET
ejpam-5911	293	9	proof	proof	NOUN
ejpam-5911	293	10	follows	follow	VERB
ejpam-5911	293	11	by	by	ADP
ejpam-5911	293	12	p−1(n	p−1(n	NOUN
ejpam-5911	293	13	c	c	NOUN
ejpam-5911	293	14	)	)	PUNCT
ejpam-5911	293	15	=	=	SYM
ejpam-5911	293	16	(	(	PUNCT
ejpam-5911	293	17	p−1(n	p−1(n	NOUN
ejpam-5911	293	18	)	)	PUNCT
ejpam-5911	293	19	)	)	PUNCT
ejpam-5911	294	1	c	c	NOUN
ejpam-5911	294	2	and	and	CCONJ
ejpam-5911	294	3	definition	definition	NOUN
ejpam-5911	294	4	10	10	NUM
ejpam-5911	294	5	.	.	PUNCT
ejpam-5911	295	1	(	(	PUNCT
ejpam-5911	295	2	ii	ii	NOUN
ejpam-5911	295	3	)	)	PUNCT
ejpam-5911	295	4	⇒	⇒	NOUN
ejpam-5911	295	5	(	(	PUNCT
ejpam-5911	295	6	iii	iii	X
ejpam-5911	295	7	)	)	PUNCT
ejpam-5911	295	8	let	let	VERB
ejpam-5911	295	9	m	m	PROPN
ejpam-5911	295	10	∈	∈	VERB
ejpam-5911	295	11	ig	ig	PROPN
ejpam-5911	295	12	.	.	PUNCT
ejpam-5911	296	1	by	by	ADP
ejpam-5911	296	2	(	(	PUNCT
ejpam-5911	296	3	ii	ii	NOUN
ejpam-5911	296	4	)	)	PUNCT
ejpam-5911	296	5	,	,	PUNCT
ejpam-5911	296	6	we	we	PRON
ejpam-5911	296	7	have	have	VERB
ejpam-5911	296	8	p−1(c𭟋∗(p(m	p−1(c𭟋∗(p(m	PROPN
ejpam-5911	296	9	)	)	PUNCT
ejpam-5911	296	10	,	,	PUNCT
ejpam-5911	296	11	r	r	NOUN
ejpam-5911	296	12	,	,	PUNCT
ejpam-5911	296	13	s	s	NOUN
ejpam-5911	296	14	)	)	PUNCT
ejpam-5911	296	15	)	)	PUNCT
ejpam-5911	297	1	is	be	AUX
ejpam-5911	297	2	(	(	PUNCT
ejpam-5911	297	3	r	r	NOUN
ejpam-5911	297	4	,	,	PUNCT
ejpam-5911	297	5	s)-f	s)-f	NOUN
ejpam-5911	297	6	-	-	PUNCT
ejpam-5911	297	7	b	b	NOUN
ejpam-5911	297	8	-	-	PUNCT
ejpam-5911	297	9	closed	closed	ADJ
ejpam-5911	297	10	.	.	PUNCT
ejpam-5911	298	1	thus	thus	ADV
ejpam-5911	298	2	,	,	PUNCT
ejpam-5911	298	3	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	298	4	,	,	PUNCT
ejpam-5911	298	5	r	r	NOUN
ejpam-5911	298	6	,	,	PUNCT
ejpam-5911	298	7	s	s	NOUN
ejpam-5911	298	8	)	)	PUNCT
ejpam-5911	298	9	≤	≤	NUM
ejpam-5911	298	10	bcℑ∗(p−1(p(m	bcℑ∗(p−1(p(m	NOUN
ejpam-5911	298	11	)	)	PUNCT
ejpam-5911	298	12	)	)	PUNCT
ejpam-5911	298	13	,	,	PUNCT
ejpam-5911	298	14	r	r	NOUN
ejpam-5911	298	15	,	,	PUNCT
ejpam-5911	298	16	s	s	NOUN
ejpam-5911	298	17	)	)	PUNCT
ejpam-5911	298	18	≤	≤	NUM
ejpam-5911	298	19	bcℑ∗(p−1(c𭟋∗(p(m	bcℑ∗(p−1(c𭟋∗(p(m	NOUN
ejpam-5911	298	20	)	)	PUNCT
ejpam-5911	298	21	,	,	PUNCT
ejpam-5911	298	22	r	r	NOUN
ejpam-5911	298	23	,	,	PUNCT
ejpam-5911	298	24	s	s	NOUN
ejpam-5911	298	25	)	)	PUNCT
ejpam-5911	298	26	)	)	PUNCT
ejpam-5911	298	27	,	,	PUNCT
ejpam-5911	298	28	r	r	NOUN
ejpam-5911	298	29	,	,	PUNCT
ejpam-5911	298	30	s	s	NOUN
ejpam-5911	298	31	)	)	PUNCT
ejpam-5911	298	32	=	=	SYM
ejpam-5911	298	33	p−1(c𭟋∗(p(m	p−1(c𭟋∗(p(m	PROPN
ejpam-5911	298	34	)	)	PUNCT
ejpam-5911	298	35	,	,	PUNCT
ejpam-5911	298	36	r	r	NOUN
ejpam-5911	298	37	,	,	PUNCT
ejpam-5911	298	38	s	s	NOUN
ejpam-5911	298	39	)	)	PUNCT
ejpam-5911	298	40	)	)	PUNCT
ejpam-5911	298	41	.	.	PUNCT
ejpam-5911	299	1	therefore	therefore	ADV
ejpam-5911	299	2	,	,	PUNCT
ejpam-5911	299	3	p(bcℑ∗(m	p(bcℑ∗(m	NUM
ejpam-5911	299	4	,	,	PUNCT
ejpam-5911	299	5	r	r	NOUN
ejpam-5911	299	6	,	,	PUNCT
ejpam-5911	299	7	s	s	NOUN
ejpam-5911	299	8	)	)	PUNCT
ejpam-5911	299	9	)	)	PUNCT
ejpam-5911	299	10	≤	≤	NOUN
ejpam-5911	299	11	c𭟋∗(p(m	c𭟋∗(p(m	NOUN
ejpam-5911	299	12	)	)	PUNCT
ejpam-5911	299	13	,	,	PUNCT
ejpam-5911	299	14	r	r	NOUN
ejpam-5911	299	15	,	,	PUNCT
ejpam-5911	299	16	s	s	NOUN
ejpam-5911	299	17	)	)	PUNCT
ejpam-5911	299	18	.	.	PUNCT
ejpam-5911	300	1	(	(	PUNCT
ejpam-5911	300	2	iii	iii	X
ejpam-5911	300	3	)	)	PUNCT
ejpam-5911	300	4	⇒	⇒	NOUN
ejpam-5911	300	5	(	(	PUNCT
ejpam-5911	300	6	iv	iv	X
ejpam-5911	300	7	)	)	PUNCT
ejpam-5911	300	8	let	let	VERB
ejpam-5911	300	9	n	n	PRON
ejpam-5911	300	10	∈	∈	NOUN
ejpam-5911	300	11	iz	iz	INTJ
ejpam-5911	300	12	.	.	PUNCT
ejpam-5911	301	1	by	by	ADP
ejpam-5911	301	2	(	(	PUNCT
ejpam-5911	301	3	iii	iii	NOUN
ejpam-5911	301	4	)	)	PUNCT
ejpam-5911	301	5	,	,	PUNCT
ejpam-5911	301	6	p(bcℑ∗(p−1(n	p(bcℑ∗(p−1(n	NOUN
ejpam-5911	301	7	)	)	PUNCT
ejpam-5911	301	8	,	,	PUNCT
ejpam-5911	301	9	r	r	NOUN
ejpam-5911	301	10	,	,	PUNCT
ejpam-5911	301	11	s	s	NOUN
ejpam-5911	301	12	)	)	PUNCT
ejpam-5911	301	13	)	)	PUNCT
ejpam-5911	301	14	≤	≤	NOUN
ejpam-5911	301	15	c𭟋∗(p(p−1(n	c𭟋∗(p(p−1(n	NOUN
ejpam-5911	301	16	)	)	PUNCT
ejpam-5911	301	17	)	)	PUNCT
ejpam-5911	301	18	,	,	PUNCT
ejpam-5911	301	19	r	r	NOUN
ejpam-5911	301	20	,	,	PUNCT
ejpam-5911	301	21	s	s	NOUN
ejpam-5911	301	22	)	)	PUNCT
ejpam-5911	301	23	≤	≤	NUM
ejpam-5911	301	24	c𭟋∗(n	c𭟋∗(n	NOUN
ejpam-5911	301	25	,	,	PUNCT
ejpam-5911	301	26	r	r	NOUN
ejpam-5911	301	27	,	,	PUNCT
ejpam-5911	301	28	s	s	NOUN
ejpam-5911	301	29	)	)	PUNCT
ejpam-5911	301	30	.	.	PUNCT
ejpam-5911	302	1	thus	thus	ADV
ejpam-5911	302	2	,	,	PUNCT
ejpam-5911	302	3	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	302	4	)	)	PUNCT
ejpam-5911	302	5	,	,	PUNCT
ejpam-5911	302	6	r	r	NOUN
ejpam-5911	302	7	,	,	PUNCT
ejpam-5911	302	8	s	s	NOUN
ejpam-5911	302	9	)	)	PUNCT
ejpam-5911	302	10	≤	≤	NOUN
ejpam-5911	302	11	p−1(p(bcℑ∗(p−1(n	p−1(p(bcℑ∗(p−1(n	NOUN
ejpam-5911	302	12	)	)	PUNCT
ejpam-5911	302	13	,	,	PUNCT
ejpam-5911	302	14	r	r	NOUN
ejpam-5911	302	15	,	,	PUNCT
ejpam-5911	302	16	s	s	NOUN
ejpam-5911	302	17	)	)	PUNCT
ejpam-5911	302	18	)	)	PUNCT
ejpam-5911	302	19	)	)	PUNCT
ejpam-5911	302	20	≤	≤	PUNCT
ejpam-5911	303	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	303	2	,	,	PUNCT
ejpam-5911	303	3	r	r	NOUN
ejpam-5911	303	4	,	,	PUNCT
ejpam-5911	303	5	s	s	NOUN
ejpam-5911	303	6	)	)	PUNCT
ejpam-5911	303	7	)	)	PUNCT
ejpam-5911	303	8	.	.	PUNCT
ejpam-5911	304	1	(	(	PUNCT
ejpam-5911	304	2	iv	iv	X
ejpam-5911	304	3	)	)	PUNCT
ejpam-5911	304	4	⇔	⇔	X
ejpam-5911	304	5	(	(	PUNCT
ejpam-5911	304	6	v	v	NOUN
ejpam-5911	304	7	)	)	PUNCT
ejpam-5911	304	8	the	the	DET
ejpam-5911	304	9	proof	proof	NOUN
ejpam-5911	304	10	follows	follow	VERB
ejpam-5911	304	11	by	by	ADP
ejpam-5911	304	12	p−1(n	p−1(n	NOUN
ejpam-5911	304	13	c	c	NOUN
ejpam-5911	304	14	)	)	PUNCT
ejpam-5911	304	15	=	=	SYM
ejpam-5911	304	16	(	(	PUNCT
ejpam-5911	304	17	p−1(n	p−1(n	NOUN
ejpam-5911	304	18	)	)	PUNCT
ejpam-5911	304	19	)	)	PUNCT
ejpam-5911	305	1	c	c	NOUN
ejpam-5911	305	2	and	and	CCONJ
ejpam-5911	305	3	proposition	proposition	NOUN
ejpam-5911	305	4	3	3	NUM
ejpam-5911	305	5	.	.	PUNCT
ejpam-5911	305	6	(	(	PUNCT
ejpam-5911	305	7	v	v	NOUN
ejpam-5911	305	8	)	)	PUNCT
ejpam-5911	305	9	⇒	⇒	NOUN
ejpam-5911	305	10	(	(	PUNCT
ejpam-5911	305	11	i	i	NOUN
ejpam-5911	305	12	)	)	PUNCT
ejpam-5911	305	13	let	let	VERB
ejpam-5911	305	14	n	n	PRON
ejpam-5911	305	15	∈	∈	VERB
ejpam-5911	305	16	iz	iz	INTJ
ejpam-5911	305	17	with	with	ADP
ejpam-5911	305	18	𭟋(n	𭟋(n	PROPN
ejpam-5911	305	19	)	)	PUNCT
ejpam-5911	305	20	≥	≥	PROPN
ejpam-5911	306	1	r	r	NOUN
ejpam-5911	306	2	and	and	CCONJ
ejpam-5911	306	3	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	306	4	)	)	PUNCT
ejpam-5911	306	5	≤	≤	NOUN
ejpam-5911	306	6	s.	s.	PROPN
ejpam-5911	306	7	by	by	ADP
ejpam-5911	306	8	(	(	PUNCT
ejpam-5911	306	9	v	v	NOUN
ejpam-5911	306	10	)	)	PUNCT
ejpam-5911	306	11	,	,	PUNCT
ejpam-5911	306	12	we	we	PRON
ejpam-5911	306	13	obtain	obtain	VERB
ejpam-5911	306	14	p−1(n	p−1(n	NOUN
ejpam-5911	306	15	)	)	PUNCT
ejpam-5911	307	1	=	=	VERB
ejpam-5911	307	2	p−1(i𭟋∗(n	p−1(i𭟋∗(n	ADJ
ejpam-5911	307	3	,	,	PUNCT
ejpam-5911	307	4	r	r	NOUN
ejpam-5911	307	5	,	,	PUNCT
ejpam-5911	307	6	s	s	NOUN
ejpam-5911	307	7	)	)	PUNCT
ejpam-5911	307	8	)	)	PUNCT
ejpam-5911	308	1	≤	≤	NUM
ejpam-5911	308	2	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	308	3	)	)	PUNCT
ejpam-5911	308	4	,	,	PUNCT
ejpam-5911	308	5	r	r	NOUN
ejpam-5911	308	6	,	,	PUNCT
ejpam-5911	308	7	s	s	NOUN
ejpam-5911	308	8	)	)	PUNCT
ejpam-5911	308	9	≤	≤	NOUN
ejpam-5911	308	10	p−1(n	p−1(n	NOUN
ejpam-5911	308	11	)	)	PUNCT
ejpam-5911	308	12	.	.	PUNCT
ejpam-5911	309	1	then	then	ADV
ejpam-5911	309	2	,	,	PUNCT
ejpam-5911	309	3	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	309	4	)	)	PUNCT
ejpam-5911	309	5	,	,	PUNCT
ejpam-5911	309	6	r	r	NOUN
ejpam-5911	309	7	,	,	PUNCT
ejpam-5911	309	8	s	s	NOUN
ejpam-5911	309	9	)	)	PUNCT
ejpam-5911	309	10	=	=	SYM
ejpam-5911	309	11	p−1(n	p−1(n	NOUN
ejpam-5911	309	12	)	)	PUNCT
ejpam-5911	309	13	.	.	PUNCT
ejpam-5911	310	1	thus	thus	ADV
ejpam-5911	310	2	,	,	PUNCT
ejpam-5911	310	3	p−1(n	p−1(n	NOUN
ejpam-5911	310	4	)	)	PUNCT
ejpam-5911	310	5	is	be	AUX
ejpam-5911	310	6	(	(	PUNCT
ejpam-5911	310	7	r	r	NOUN
ejpam-5911	310	8	,	,	PUNCT
ejpam-5911	310	9	s)-f	s)-f	NOUN
ejpam-5911	310	10	-	-	PUNCT
ejpam-5911	310	11	b	b	NOUN
ejpam-5911	310	12	-	-	PUNCT
ejpam-5911	310	13	open	open	ADJ
ejpam-5911	310	14	,	,	PUNCT
ejpam-5911	310	15	so	so	CCONJ
ejpam-5911	310	16	p	p	PROPN
ejpam-5911	310	17	is	be	AUX
ejpam-5911	310	18	df	df	PROPN
ejpam-5911	310	19	-	-	PUNCT
ejpam-5911	310	20	b	b	NOUN
ejpam-5911	310	21	-	-	PUNCT
ejpam-5911	310	22	continuous	continuous	ADJ
ejpam-5911	310	23	.	.	PUNCT
ejpam-5911	311	1	definition	definition	NOUN
ejpam-5911	311	2	11	11	NUM
ejpam-5911	311	3	.	.	PUNCT
ejpam-5911	312	1	an	an	DET
ejpam-5911	312	2	f	f	X
ejpam-5911	312	3	-	-	PUNCT
ejpam-5911	312	4	mapping	mapping	NOUN
ejpam-5911	312	5	p	p	NOUN
ejpam-5911	312	6	:	:	PUNCT
ejpam-5911	312	7	(	(	PUNCT
ejpam-5911	312	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	312	9	)	)	PUNCT
ejpam-5911	313	1	−→	−→	NOUN
ejpam-5911	313	2	(	(	PUNCT
ejpam-5911	313	3	z	z	NOUN
ejpam-5911	313	4	,	,	PUNCT
ejpam-5911	313	5	𭟋	𭟋	NOUN
ejpam-5911	313	6	,	,	PUNCT
ejpam-5911	313	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	313	8	)	)	PUNCT
ejpam-5911	313	9	is	be	AUX
ejpam-5911	313	10	called	call	VERB
ejpam-5911	313	11	df	df	PROPN
ejpam-5911	313	12	-	-	PUNCT
ejpam-5911	313	13	b	b	NOUN
ejpam-5911	313	14	-	-	PUNCT
ejpam-5911	313	15	irresolute	irresolute	ADJ
ejpam-5911	313	16	if	if	SCONJ
ejpam-5911	313	17	p−1(n	p−1(n	NOUN
ejpam-5911	313	18	)	)	PUNCT
ejpam-5911	313	19	is	be	AUX
ejpam-5911	313	20	an	an	DET
ejpam-5911	313	21	(	(	PUNCT
ejpam-5911	313	22	r	r	NOUN
ejpam-5911	313	23	,	,	PUNCT
ejpam-5911	313	24	s)-f	s)-f	NOUN
ejpam-5911	313	25	-	-	PUNCT
ejpam-5911	313	26	b	b	NOUN
ejpam-5911	313	27	-	-	PUNCT
ejpam-5911	313	28	open	open	ADJ
ejpam-5911	313	29	set	set	NOUN
ejpam-5911	313	30	,	,	PUNCT
ejpam-5911	313	31	for	for	ADP
ejpam-5911	313	32	every	every	DET
ejpam-5911	313	33	(	(	PUNCT
ejpam-5911	313	34	r	r	NOUN
ejpam-5911	313	35	,	,	PUNCT
ejpam-5911	313	36	s)-f	s)-f	NOUN
ejpam-5911	313	37	-	-	PUNCT
ejpam-5911	313	38	b	b	NOUN
ejpam-5911	313	39	-	-	PUNCT
ejpam-5911	313	40	open	open	ADJ
ejpam-5911	313	41	set	set	NOUN
ejpam-5911	313	42	n	n	CCONJ
ejpam-5911	313	43	∈	∈	NOUN
ejpam-5911	314	1	iz	iz	INTJ
ejpam-5911	314	2	.	.	PUNCT
ejpam-5911	315	1	lemma	lemma	PROPN
ejpam-5911	315	2	2	2	NUM
ejpam-5911	315	3	.	.	X
ejpam-5911	316	1	every	every	DET
ejpam-5911	316	2	df	df	PROPN
ejpam-5911	316	3	-	-	PUNCT
ejpam-5911	316	4	b	b	NOUN
ejpam-5911	316	5	-	-	PUNCT
ejpam-5911	316	6	irresolute	irresolute	ADJ
ejpam-5911	316	7	mapping	mapping	NOUN
ejpam-5911	316	8	is	be	AUX
ejpam-5911	316	9	df	df	PROPN
ejpam-5911	316	10	-	-	PUNCT
ejpam-5911	316	11	b	b	NOUN
ejpam-5911	316	12	-	-	PUNCT
ejpam-5911	316	13	continuous	continuous	ADJ
ejpam-5911	316	14	.	.	PUNCT
ejpam-5911	317	1	proof	proof	NOUN
ejpam-5911	317	2	.	.	PUNCT
ejpam-5911	318	1	the	the	DET
ejpam-5911	318	2	proof	proof	NOUN
ejpam-5911	318	3	follows	follow	VERB
ejpam-5911	318	4	by	by	ADP
ejpam-5911	318	5	definitions	definition	NOUN
ejpam-5911	318	6	10	10	NUM
ejpam-5911	318	7	and	and	CCONJ
ejpam-5911	318	8	11	11	NUM
ejpam-5911	318	9	.	.	PUNCT
ejpam-5911	319	1	remark	remark	NOUN
ejpam-5911	319	2	6	6	NUM
ejpam-5911	319	3	.	.	PUNCT
ejpam-5911	320	1	the	the	DET
ejpam-5911	320	2	converse	converse	NOUN
ejpam-5911	320	3	of	of	ADP
ejpam-5911	320	4	lemma	lemma	PROPN
ejpam-5911	320	5	2	2	NUM
ejpam-5911	320	6	fails	fail	VERB
ejpam-5911	320	7	as	as	ADP
ejpam-5911	320	8	example	example	NOUN
ejpam-5911	320	9	7	7	NUM
ejpam-5911	320	10	will	will	AUX
ejpam-5911	320	11	show	show	VERB
ejpam-5911	320	12	.	.	PUNCT
ejpam-5911	321	1	example	example	NOUN
ejpam-5911	322	1	7	7	NUM
ejpam-5911	322	2	.	.	PUNCT
ejpam-5911	323	1	let	let	VERB
ejpam-5911	323	2	g	g	NOUN
ejpam-5911	323	3	=	=	SYM
ejpam-5911	323	4	{	{	PUNCT
ejpam-5911	323	5	g1	g1	PROPN
ejpam-5911	323	6	,	,	PUNCT
ejpam-5911	323	7	g2	g2	PROPN
ejpam-5911	323	8	}	}	PUNCT
ejpam-5911	323	9	and	and	CCONJ
ejpam-5911	323	10	define	define	VERB
ejpam-5911	323	11	m	m	NOUN
ejpam-5911	323	12	,	,	PUNCT
ejpam-5911	323	13	n	n	PROPN
ejpam-5911	323	14	∈	∈	PROPN
ejpam-5911	323	15	ig	ig	PROPN
ejpam-5911	323	16	as	as	SCONJ
ejpam-5911	323	17	follows	follow	VERB
ejpam-5911	323	18	:	:	PUNCT
ejpam-5911	323	19	m	m	VERB
ejpam-5911	323	20	=	=	PUNCT
ejpam-5911	323	21	{	{	PUNCT
ejpam-5911	323	22	g1	g1	PROPN
ejpam-5911	323	23	0.5	0.5	NUM
ejpam-5911	323	24	,	,	PUNCT
ejpam-5911	323	25	g2	g2	PROPN
ejpam-5911	323	26	0.5	0.5	NUM
ejpam-5911	323	27	}	}	PUNCT
ejpam-5911	323	28	,	,	PUNCT
ejpam-5911	323	29	n	n	NOUN
ejpam-5911	323	30	=	=	PRON
ejpam-5911	323	31	{	{	PUNCT
ejpam-5911	323	32	g1	g1	PROPN
ejpam-5911	323	33	0.5	0.5	NUM
ejpam-5911	323	34	,	,	PUNCT
ejpam-5911	323	35	g2	g2	PROPN
ejpam-5911	323	36	0.4	0.4	NUM
ejpam-5911	323	37	}	}	PUNCT
ejpam-5911	323	38	.	.	PUNCT
ejpam-5911	324	1	define	define	VERB
ejpam-5911	324	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	324	3	,	,	PUNCT
ejpam-5911	324	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	324	5	:	:	PUNCT
ejpam-5911	324	6	ig	ig	PROPN
ejpam-5911	324	7	−→	−→	NOUN
ejpam-5911	325	1	i	i	PRON
ejpam-5911	325	2	as	as	SCONJ
ejpam-5911	325	3	follows	follow	VERB
ejpam-5911	325	4	:	:	PUNCT
ejpam-5911	325	5	ℑ(v	ℑ(v	X
ejpam-5911	325	6	)	)	PUNCT
ejpam-5911	325	7	=	=	SYM
ejpam-5911	326	1			NOUN
ejpam-5911	326	2	1	1	NUM
ejpam-5911	326	3	,	,	PUNCT
ejpam-5911	326	4	if	if	SCONJ
ejpam-5911	326	5	v	v	ADP
ejpam-5911	326	6	∈	∈	NOUN
ejpam-5911	326	7	{	{	PUNCT
ejpam-5911	326	8	1	1	NUM
ejpam-5911	326	9	,	,	PUNCT
ejpam-5911	326	10	0	0	NUM
ejpam-5911	326	11	}	}	PUNCT
ejpam-5911	326	12	,	,	PUNCT
ejpam-5911	326	13	1	1	NUM
ejpam-5911	326	14	2	2	NUM
ejpam-5911	326	15	,	,	PUNCT
ejpam-5911	326	16	if	if	SCONJ
ejpam-5911	326	17	v	v	VERB
ejpam-5911	326	18	=	=	SYM
ejpam-5911	326	19	n	n	NOUN
ejpam-5911	326	20	,	,	PUNCT
ejpam-5911	326	21	0	0	NUM
ejpam-5911	326	22	,	,	PUNCT
ejpam-5911	326	23	otherwise	otherwise	ADV
ejpam-5911	326	24	,	,	PUNCT
ejpam-5911	326	25	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	326	26	)	)	PUNCT
ejpam-5911	327	1	=	=	SYM
ejpam-5911	328	1			NOUN
ejpam-5911	328	2	0	0	NUM
ejpam-5911	328	3	,	,	PUNCT
ejpam-5911	328	4	if	if	SCONJ
ejpam-5911	328	5	v	v	ADP
ejpam-5911	328	6	∈	∈	NOUN
ejpam-5911	328	7	{	{	PUNCT
ejpam-5911	328	8	1	1	NUM
ejpam-5911	328	9	,	,	PUNCT
ejpam-5911	328	10	0	0	NUM
ejpam-5911	328	11	}	}	PUNCT
ejpam-5911	328	12	,	,	PUNCT
ejpam-5911	328	13	1	1	NUM
ejpam-5911	328	14	2	2	NUM
ejpam-5911	328	15	,	,	PUNCT
ejpam-5911	328	16	if	if	SCONJ
ejpam-5911	328	17	v	v	VERB
ejpam-5911	328	18	=	=	SYM
ejpam-5911	328	19	n	n	NOUN
ejpam-5911	328	20	,	,	PUNCT
ejpam-5911	328	21	1	1	NUM
ejpam-5911	328	22	,	,	PUNCT
ejpam-5911	328	23	otherwise	otherwise	ADV
ejpam-5911	328	24	,	,	PUNCT
ejpam-5911	328	25	i.	i.	PROPN
ejpam-5911	328	26	m.	m.	PROPN
ejpam-5911	328	27	taha	taha	PROPN
ejpam-5911	328	28	,	,	PUNCT
ejpam-5911	328	29	j.	j.	PROPN
ejpam-5911	328	30	al	al	PROPN
ejpam-5911	328	31	-	-	PUNCT
ejpam-5911	328	32	mufarrij	mufarrij	PROPN
ejpam-5911	328	33	,	,	PUNCT
ejpam-5911	328	34	o.	o.	PROPN
ejpam-5911	328	35	m.	m.	PROPN
ejpam-5911	328	36	taha	taha	PROPN
ejpam-5911	328	37	/	/	PUNCT
ejpam-5911	328	38	eur	eur	PROPN
ejpam-5911	328	39	.	.	PUNCT
ejpam-5911	329	1	j.	j.	PROPN
ejpam-5911	329	2	pure	pure	PROPN
ejpam-5911	329	3	appl	appl	PROPN
ejpam-5911	329	4	.	.	PROPN
ejpam-5911	329	5	math	math	PROPN
ejpam-5911	329	6	,	,	PUNCT
ejpam-5911	329	7	18	18	NUM
ejpam-5911	329	8	(	(	PUNCT
ejpam-5911	329	9	2	2	NUM
ejpam-5911	329	10	)	)	PUNCT
ejpam-5911	329	11	(	(	PUNCT
ejpam-5911	329	12	2025	2025	NUM
ejpam-5911	329	13	)	)	PUNCT
ejpam-5911	329	14	,	,	PUNCT
ejpam-5911	329	15	5911	5911	NUM
ejpam-5911	329	16	13	13	NUM
ejpam-5911	329	17	of	of	ADP
ejpam-5911	329	18	27	27	NUM
ejpam-5911	329	19	𭟋(v	𭟋(v	NOUN
ejpam-5911	329	20	)	)	PUNCT
ejpam-5911	329	21	=	=	SYM
ejpam-5911	330	1			NOUN
ejpam-5911	330	2	1	1	NUM
ejpam-5911	330	3	,	,	PUNCT
ejpam-5911	330	4	if	if	SCONJ
ejpam-5911	330	5	v	v	ADP
ejpam-5911	330	6	∈	∈	NOUN
ejpam-5911	330	7	{	{	PUNCT
ejpam-5911	330	8	1	1	NUM
ejpam-5911	330	9	,	,	PUNCT
ejpam-5911	330	10	0	0	NUM
ejpam-5911	330	11	}	}	PUNCT
ejpam-5911	330	12	,	,	PUNCT
ejpam-5911	330	13	1	1	NUM
ejpam-5911	330	14	3	3	NUM
ejpam-5911	330	15	,	,	PUNCT
ejpam-5911	330	16	if	if	SCONJ
ejpam-5911	330	17	v	v	ADP
ejpam-5911	330	18	=	=	NOUN
ejpam-5911	330	19	m	m	PROPN
ejpam-5911	330	20	,	,	PUNCT
ejpam-5911	330	21	0	0	NUM
ejpam-5911	330	22	,	,	PUNCT
ejpam-5911	330	23	otherwise	otherwise	ADV
ejpam-5911	330	24	,	,	PUNCT
ejpam-5911	330	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	330	26	)	)	PUNCT
ejpam-5911	331	1	=	=	PUNCT
ejpam-5911	332	1			NOUN
ejpam-5911	332	2	0	0	NUM
ejpam-5911	332	3	,	,	PUNCT
ejpam-5911	332	4	if	if	SCONJ
ejpam-5911	332	5	v	v	ADP
ejpam-5911	332	6	∈	∈	NOUN
ejpam-5911	332	7	{	{	PUNCT
ejpam-5911	332	8	1	1	NUM
ejpam-5911	332	9	,	,	PUNCT
ejpam-5911	332	10	0	0	NUM
ejpam-5911	332	11	}	}	PUNCT
ejpam-5911	332	12	,	,	PUNCT
ejpam-5911	332	13	1	1	NUM
ejpam-5911	332	14	2	2	NUM
ejpam-5911	332	15	,	,	PUNCT
ejpam-5911	332	16	if	if	SCONJ
ejpam-5911	332	17	v	v	ADP
ejpam-5911	332	18	=	=	NOUN
ejpam-5911	332	19	m	m	PROPN
ejpam-5911	332	20	,	,	PUNCT
ejpam-5911	332	21	1	1	NUM
ejpam-5911	332	22	,	,	PUNCT
ejpam-5911	332	23	otherwise	otherwise	ADV
ejpam-5911	332	24	.	.	PUNCT
ejpam-5911	333	1	thus	thus	ADV
ejpam-5911	333	2	,	,	PUNCT
ejpam-5911	333	3	the	the	DET
ejpam-5911	333	4	identity	identity	NOUN
ejpam-5911	333	5	f	f	NOUN
ejpam-5911	333	6	-	-	PUNCT
ejpam-5911	333	7	mapping	mapping	NOUN
ejpam-5911	333	8	p	p	NOUN
ejpam-5911	333	9	:	:	PUNCT
ejpam-5911	333	10	(	(	PUNCT
ejpam-5911	333	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	333	12	)	)	PUNCT
ejpam-5911	333	13	−→	−→	NOUN
ejpam-5911	333	14	(	(	PUNCT
ejpam-5911	333	15	g	g	NOUN
ejpam-5911	333	16	,	,	PUNCT
ejpam-5911	333	17	𭟋	𭟋	NOUN
ejpam-5911	333	18	,	,	PUNCT
ejpam-5911	333	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	333	20	)	)	PUNCT
ejpam-5911	333	21	is	be	AUX
ejpam-5911	333	22	df	df	PROPN
ejpam-5911	333	23	-	-	PUNCT
ejpam-5911	333	24	b	b	NOUN
ejpam-5911	333	25	-	-	PUNCT
ejpam-5911	333	26	continuous	continuous	ADJ
ejpam-5911	333	27	,	,	PUNCT
ejpam-5911	333	28	but	but	CCONJ
ejpam-5911	333	29	it	it	PRON
ejpam-5911	333	30	is	be	AUX
ejpam-5911	333	31	not	not	PART
ejpam-5911	333	32	df	df	PROPN
ejpam-5911	333	33	-	-	PUNCT
ejpam-5911	333	34	b	b	NOUN
ejpam-5911	333	35	-	-	PUNCT
ejpam-5911	333	36	irresolute	irresolute	ADJ
ejpam-5911	333	37	.	.	PUNCT
ejpam-5911	334	1	theorem	theorem	NOUN
ejpam-5911	334	2	5	5	NUM
ejpam-5911	334	3	.	.	PUNCT
ejpam-5911	335	1	let	let	VERB
ejpam-5911	335	2	p	p	NOUN
ejpam-5911	335	3	:	:	PUNCT
ejpam-5911	335	4	(	(	PUNCT
ejpam-5911	335	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	335	6	)	)	PUNCT
ejpam-5911	336	1	−→	−→	NOUN
ejpam-5911	336	2	(	(	PUNCT
ejpam-5911	336	3	z	z	NOUN
ejpam-5911	336	4	,	,	PUNCT
ejpam-5911	336	5	𭟋	𭟋	NOUN
ejpam-5911	336	6	,	,	PUNCT
ejpam-5911	336	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	336	8	)	)	PUNCT
ejpam-5911	336	9	be	be	AUX
ejpam-5911	336	10	an	an	DET
ejpam-5911	336	11	f	f	NOUN
ejpam-5911	336	12	-	-	PUNCT
ejpam-5911	336	13	mapping	mapping	NOUN
ejpam-5911	336	14	,	,	PUNCT
ejpam-5911	336	15	r	r	NOUN
ejpam-5911	336	16	∈	∈	PROPN
ejpam-5911	337	1	i	i	NOUN
ejpam-5911	337	2	◦	◦	NOUN
ejpam-5911	337	3	,	,	PUNCT
ejpam-5911	337	4	and	and	CCONJ
ejpam-5911	337	5	s	s	PROPN
ejpam-5911	337	6	∈	∈	PROPN
ejpam-5911	337	7	i1	i1	PROPN
ejpam-5911	337	8	.	.	PUNCT
ejpam-5911	338	1	then	then	ADV
ejpam-5911	338	2	the	the	DET
ejpam-5911	338	3	following	follow	VERB
ejpam-5911	338	4	statements	statement	NOUN
ejpam-5911	338	5	are	be	AUX
ejpam-5911	338	6	equivalent	equivalent	ADJ
ejpam-5911	338	7	for	for	ADP
ejpam-5911	338	8	every	every	DET
ejpam-5911	338	9	m	m	NOUN
ejpam-5911	338	10	∈	∈	NOUN
ejpam-5911	338	11	ig	ig	PROPN
ejpam-5911	338	12	and	and	CCONJ
ejpam-5911	338	13	n	n	PRON
ejpam-5911	338	14	∈	∈	PROPN
ejpam-5911	339	1	iz	iz	INTJ
ejpam-5911	339	2	:	:	PUNCT
ejpam-5911	339	3	(	(	PUNCT
ejpam-5911	339	4	i	i	NOUN
ejpam-5911	339	5	)	)	PUNCT
ejpam-5911	339	6	p	p	NOUN
ejpam-5911	339	7	is	be	AUX
ejpam-5911	339	8	df	df	PROPN
ejpam-5911	339	9	-	-	PUNCT
ejpam-5911	339	10	b	b	NOUN
ejpam-5911	339	11	-	-	PUNCT
ejpam-5911	339	12	irresolute	irresolute	NOUN
ejpam-5911	339	13	.	.	PUNCT
ejpam-5911	340	1	(	(	PUNCT
ejpam-5911	340	2	ii	ii	NOUN
ejpam-5911	340	3	)	)	PUNCT
ejpam-5911	340	4	p−1(n	p−1(n	PROPN
ejpam-5911	340	5	)	)	PUNCT
ejpam-5911	340	6	is	be	AUX
ejpam-5911	340	7	(	(	PUNCT
ejpam-5911	340	8	r	r	NOUN
ejpam-5911	340	9	,	,	PUNCT
ejpam-5911	340	10	s)-f	s)-f	NOUN
ejpam-5911	340	11	-	-	PUNCT
ejpam-5911	340	12	b	b	NOUN
ejpam-5911	340	13	-	-	PUNCT
ejpam-5911	340	14	closed	closed	ADJ
ejpam-5911	340	15	,	,	PUNCT
ejpam-5911	340	16	for	for	SCONJ
ejpam-5911	340	17	every	every	DET
ejpam-5911	340	18	n	n	NOUN
ejpam-5911	340	19	is	be	AUX
ejpam-5911	340	20	(	(	PUNCT
ejpam-5911	340	21	r	r	NOUN
ejpam-5911	340	22	,	,	PUNCT
ejpam-5911	340	23	s)-f	s)-f	NOUN
ejpam-5911	340	24	-	-	PUNCT
ejpam-5911	340	25	b	b	NOUN
ejpam-5911	340	26	-	-	PUNCT
ejpam-5911	340	27	closed	closed	ADJ
ejpam-5911	340	28	.	.	PUNCT
ejpam-5911	341	1	(	(	PUNCT
ejpam-5911	341	2	iii	iii	NOUN
ejpam-5911	341	3	)	)	PUNCT
ejpam-5911	341	4	p(bcℑ∗(m	p(bcℑ∗(m	NUM
ejpam-5911	341	5	,	,	PUNCT
ejpam-5911	341	6	r	r	NOUN
ejpam-5911	341	7	,	,	PUNCT
ejpam-5911	341	8	s	s	NOUN
ejpam-5911	341	9	)	)	PUNCT
ejpam-5911	341	10	)	)	PUNCT
ejpam-5911	341	11	≤	≤	NUM
ejpam-5911	341	12	bc𭟋∗(p(m	bc𭟋∗(p(m	NOUN
ejpam-5911	341	13	)	)	PUNCT
ejpam-5911	341	14	,	,	PUNCT
ejpam-5911	341	15	r	r	NOUN
ejpam-5911	341	16	,	,	PUNCT
ejpam-5911	341	17	s	s	NOUN
ejpam-5911	341	18	)	)	PUNCT
ejpam-5911	341	19	.	.	PUNCT
ejpam-5911	342	1	(	(	PUNCT
ejpam-5911	342	2	iv	iv	X
ejpam-5911	342	3	)	)	PUNCT
ejpam-5911	342	4	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	342	5	)	)	PUNCT
ejpam-5911	342	6	,	,	PUNCT
ejpam-5911	342	7	r	r	NOUN
ejpam-5911	342	8	,	,	PUNCT
ejpam-5911	342	9	s	s	NOUN
ejpam-5911	342	10	)	)	PUNCT
ejpam-5911	343	1	≤	≤	NOUN
ejpam-5911	343	2	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	PROPN
ejpam-5911	343	3	,	,	PUNCT
ejpam-5911	343	4	r	r	NOUN
ejpam-5911	343	5	,	,	PUNCT
ejpam-5911	343	6	s	s	NOUN
ejpam-5911	343	7	)	)	PUNCT
ejpam-5911	343	8	)	)	PUNCT
ejpam-5911	343	9	.	.	PUNCT
ejpam-5911	344	1	(	(	PUNCT
ejpam-5911	344	2	v	v	X
ejpam-5911	344	3	)	)	PUNCT
ejpam-5911	344	4	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	NOUN
ejpam-5911	344	5	,	,	PUNCT
ejpam-5911	344	6	r	r	NOUN
ejpam-5911	344	7	,	,	PUNCT
ejpam-5911	344	8	s	s	NOUN
ejpam-5911	344	9	)	)	PUNCT
ejpam-5911	344	10	)	)	PUNCT
ejpam-5911	345	1	≤	≤	NUM
ejpam-5911	345	2	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	345	3	)	)	PUNCT
ejpam-5911	345	4	,	,	PUNCT
ejpam-5911	345	5	r	r	NOUN
ejpam-5911	345	6	,	,	PUNCT
ejpam-5911	345	7	s	s	NOUN
ejpam-5911	345	8	)	)	PUNCT
ejpam-5911	345	9	.	.	PUNCT
ejpam-5911	346	1	proof	proof	NOUN
ejpam-5911	346	2	.	.	PUNCT
ejpam-5911	347	1	(	(	PUNCT
ejpam-5911	347	2	i	i	NOUN
ejpam-5911	347	3	)	)	PUNCT
ejpam-5911	347	4	⇔	⇔	PROPN
ejpam-5911	347	5	(	(	PUNCT
ejpam-5911	347	6	ii	ii	PROPN
ejpam-5911	347	7	)	)	PUNCT
ejpam-5911	347	8	the	the	DET
ejpam-5911	347	9	proof	proof	NOUN
ejpam-5911	347	10	follows	follow	VERB
ejpam-5911	347	11	by	by	ADP
ejpam-5911	347	12	p−1(n	p−1(n	NOUN
ejpam-5911	347	13	c	c	NOUN
ejpam-5911	347	14	)	)	PUNCT
ejpam-5911	347	15	=	=	SYM
ejpam-5911	347	16	(	(	PUNCT
ejpam-5911	347	17	p−1(n	p−1(n	NOUN
ejpam-5911	347	18	)	)	PUNCT
ejpam-5911	347	19	)	)	PUNCT
ejpam-5911	348	1	c	c	NOUN
ejpam-5911	348	2	and	and	CCONJ
ejpam-5911	348	3	definition	definition	NOUN
ejpam-5911	348	4	11	11	NUM
ejpam-5911	348	5	.	.	PUNCT
ejpam-5911	349	1	(	(	PUNCT
ejpam-5911	349	2	ii	ii	NOUN
ejpam-5911	349	3	)	)	PUNCT
ejpam-5911	349	4	⇒	⇒	NOUN
ejpam-5911	349	5	(	(	PUNCT
ejpam-5911	349	6	iii	iii	X
ejpam-5911	349	7	)	)	PUNCT
ejpam-5911	349	8	let	let	VERB
ejpam-5911	349	9	m	m	PROPN
ejpam-5911	349	10	∈	∈	VERB
ejpam-5911	349	11	ig	ig	PROPN
ejpam-5911	349	12	.	.	PUNCT
ejpam-5911	350	1	by	by	ADP
ejpam-5911	350	2	(	(	PUNCT
ejpam-5911	350	3	ii	ii	NOUN
ejpam-5911	350	4	)	)	PUNCT
ejpam-5911	350	5	,	,	PUNCT
ejpam-5911	350	6	we	we	PRON
ejpam-5911	350	7	have	have	VERB
ejpam-5911	350	8	p−1(bc𭟋∗(p(m	p−1(bc𭟋∗(p(m	NOUN
ejpam-5911	350	9	)	)	PUNCT
ejpam-5911	350	10	,	,	PUNCT
ejpam-5911	350	11	r	r	NOUN
ejpam-5911	350	12	,	,	PUNCT
ejpam-5911	350	13	s	s	NOUN
ejpam-5911	350	14	)	)	PUNCT
ejpam-5911	350	15	)	)	PUNCT
ejpam-5911	351	1	is	be	AUX
ejpam-5911	351	2	(	(	PUNCT
ejpam-5911	351	3	r	r	NOUN
ejpam-5911	351	4	,	,	PUNCT
ejpam-5911	351	5	s)-f	s)-f	NOUN
ejpam-5911	351	6	-	-	PUNCT
ejpam-5911	351	7	b	b	NOUN
ejpam-5911	351	8	-	-	PUNCT
ejpam-5911	351	9	closed	closed	ADJ
ejpam-5911	351	10	.	.	PUNCT
ejpam-5911	352	1	thus	thus	ADV
ejpam-5911	352	2	,	,	PUNCT
ejpam-5911	352	3	bcℑ∗(m	bcℑ∗(m	PROPN
ejpam-5911	352	4	,	,	PUNCT
ejpam-5911	352	5	r	r	NOUN
ejpam-5911	352	6	,	,	PUNCT
ejpam-5911	352	7	s	s	NOUN
ejpam-5911	352	8	)	)	PUNCT
ejpam-5911	352	9	≤	≤	NUM
ejpam-5911	352	10	bcℑ∗(p−1(p(m	bcℑ∗(p−1(p(m	NOUN
ejpam-5911	352	11	)	)	PUNCT
ejpam-5911	352	12	)	)	PUNCT
ejpam-5911	352	13	,	,	PUNCT
ejpam-5911	352	14	r	r	NOUN
ejpam-5911	352	15	,	,	PUNCT
ejpam-5911	352	16	s	s	NOUN
ejpam-5911	352	17	)	)	PUNCT
ejpam-5911	352	18	≤	≤	NUM
ejpam-5911	352	19	bcℑ∗(p−1(bc𭟋∗(p(m	bcℑ∗(p−1(bc𭟋∗(p(m	NOUN
ejpam-5911	352	20	)	)	PUNCT
ejpam-5911	352	21	,	,	PUNCT
ejpam-5911	352	22	r	r	NOUN
ejpam-5911	352	23	,	,	PUNCT
ejpam-5911	352	24	s	s	NOUN
ejpam-5911	352	25	)	)	PUNCT
ejpam-5911	352	26	)	)	PUNCT
ejpam-5911	352	27	,	,	PUNCT
ejpam-5911	353	1	r	r	NOUN
ejpam-5911	353	2	,	,	PUNCT
ejpam-5911	353	3	s	s	NOUN
ejpam-5911	353	4	)	)	PUNCT
ejpam-5911	353	5	=	=	SYM
ejpam-5911	353	6	p−1(bc𭟋∗(p(m	p−1(bc𭟋∗(p(m	X
ejpam-5911	353	7	)	)	PUNCT
ejpam-5911	353	8	,	,	PUNCT
ejpam-5911	353	9	r	r	NOUN
ejpam-5911	353	10	,	,	PUNCT
ejpam-5911	353	11	s	s	NOUN
ejpam-5911	353	12	)	)	PUNCT
ejpam-5911	353	13	)	)	PUNCT
ejpam-5911	353	14	.	.	PUNCT
ejpam-5911	354	1	therefore	therefore	ADV
ejpam-5911	354	2	,	,	PUNCT
ejpam-5911	354	3	p(bcℑ∗(m	p(bcℑ∗(m	NUM
ejpam-5911	354	4	,	,	PUNCT
ejpam-5911	354	5	r	r	NOUN
ejpam-5911	354	6	,	,	PUNCT
ejpam-5911	354	7	s	s	NOUN
ejpam-5911	354	8	)	)	PUNCT
ejpam-5911	354	9	)	)	PUNCT
ejpam-5911	354	10	≤	≤	NUM
ejpam-5911	354	11	bc𭟋∗(p(m	bc𭟋∗(p(m	NOUN
ejpam-5911	354	12	)	)	PUNCT
ejpam-5911	354	13	,	,	PUNCT
ejpam-5911	354	14	r	r	NOUN
ejpam-5911	354	15	,	,	PUNCT
ejpam-5911	354	16	s	s	NOUN
ejpam-5911	354	17	)	)	PUNCT
ejpam-5911	354	18	.	.	PUNCT
ejpam-5911	355	1	(	(	PUNCT
ejpam-5911	355	2	iii	iii	X
ejpam-5911	355	3	)	)	PUNCT
ejpam-5911	355	4	⇒	⇒	NOUN
ejpam-5911	355	5	(	(	PUNCT
ejpam-5911	355	6	iv	iv	X
ejpam-5911	355	7	)	)	PUNCT
ejpam-5911	355	8	let	let	VERB
ejpam-5911	355	9	n	n	PRON
ejpam-5911	355	10	∈	∈	NOUN
ejpam-5911	355	11	iz	iz	INTJ
ejpam-5911	355	12	.	.	PUNCT
ejpam-5911	356	1	by	by	ADP
ejpam-5911	356	2	(	(	PUNCT
ejpam-5911	356	3	iii	iii	NOUN
ejpam-5911	356	4	)	)	PUNCT
ejpam-5911	356	5	,	,	PUNCT
ejpam-5911	356	6	p(bcℑ∗(p−1(n	p(bcℑ∗(p−1(n	NOUN
ejpam-5911	356	7	)	)	PUNCT
ejpam-5911	356	8	,	,	PUNCT
ejpam-5911	356	9	r	r	NOUN
ejpam-5911	356	10	,	,	PUNCT
ejpam-5911	356	11	s	s	NOUN
ejpam-5911	356	12	)	)	PUNCT
ejpam-5911	356	13	)	)	PUNCT
ejpam-5911	356	14	≤	≤	NUM
ejpam-5911	356	15	bc𭟋∗(p(p−1(n	bc𭟋∗(p(p−1(n	NOUN
ejpam-5911	356	16	)	)	PUNCT
ejpam-5911	356	17	)	)	PUNCT
ejpam-5911	356	18	,	,	PUNCT
ejpam-5911	356	19	r	r	NOUN
ejpam-5911	356	20	,	,	PUNCT
ejpam-5911	356	21	s	s	NOUN
ejpam-5911	356	22	)	)	PUNCT
ejpam-5911	356	23	≤	≤	NOUN
ejpam-5911	356	24	bc𭟋∗(n	bc𭟋∗(n	VERB
ejpam-5911	356	25	,	,	PUNCT
ejpam-5911	356	26	r	r	NOUN
ejpam-5911	356	27	,	,	PUNCT
ejpam-5911	356	28	s	s	NOUN
ejpam-5911	356	29	)	)	PUNCT
ejpam-5911	356	30	.	.	PUNCT
ejpam-5911	357	1	thus	thus	ADV
ejpam-5911	357	2	,	,	PUNCT
ejpam-5911	357	3	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	357	4	)	)	PUNCT
ejpam-5911	357	5	,	,	PUNCT
ejpam-5911	357	6	r	r	NOUN
ejpam-5911	357	7	,	,	PUNCT
ejpam-5911	357	8	s	s	NOUN
ejpam-5911	357	9	)	)	PUNCT
ejpam-5911	357	10	≤	≤	NOUN
ejpam-5911	357	11	p−1(p(bcℑ∗(p−1(n	p−1(p(bcℑ∗(p−1(n	NOUN
ejpam-5911	357	12	)	)	PUNCT
ejpam-5911	357	13	,	,	PUNCT
ejpam-5911	357	14	r	r	NOUN
ejpam-5911	357	15	,	,	PUNCT
ejpam-5911	357	16	s	s	NOUN
ejpam-5911	357	17	)	)	PUNCT
ejpam-5911	357	18	)	)	PUNCT
ejpam-5911	357	19	)	)	PUNCT
ejpam-5911	358	1	≤	≤	NUM
ejpam-5911	359	1	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	PROPN
ejpam-5911	359	2	,	,	PUNCT
ejpam-5911	359	3	r	r	NOUN
ejpam-5911	359	4	,	,	PUNCT
ejpam-5911	359	5	s	s	NOUN
ejpam-5911	359	6	)	)	PUNCT
ejpam-5911	359	7	)	)	PUNCT
ejpam-5911	359	8	.	.	PUNCT
ejpam-5911	360	1	(	(	PUNCT
ejpam-5911	360	2	iv	iv	X
ejpam-5911	360	3	)	)	PUNCT
ejpam-5911	360	4	⇔	⇔	X
ejpam-5911	360	5	(	(	PUNCT
ejpam-5911	360	6	v	v	NOUN
ejpam-5911	360	7	)	)	PUNCT
ejpam-5911	360	8	the	the	DET
ejpam-5911	360	9	proof	proof	NOUN
ejpam-5911	360	10	follows	follow	VERB
ejpam-5911	360	11	by	by	ADP
ejpam-5911	360	12	p−1(n	p−1(n	NOUN
ejpam-5911	360	13	c	c	NOUN
ejpam-5911	360	14	)	)	PUNCT
ejpam-5911	360	15	=	=	SYM
ejpam-5911	360	16	(	(	PUNCT
ejpam-5911	360	17	p−1(n	p−1(n	NOUN
ejpam-5911	360	18	)	)	PUNCT
ejpam-5911	360	19	)	)	PUNCT
ejpam-5911	361	1	c	c	NOUN
ejpam-5911	361	2	and	and	CCONJ
ejpam-5911	361	3	proposition	proposition	NOUN
ejpam-5911	361	4	3	3	NUM
ejpam-5911	361	5	.	.	PUNCT
ejpam-5911	361	6	(	(	PUNCT
ejpam-5911	361	7	v	v	NOUN
ejpam-5911	361	8	)	)	PUNCT
ejpam-5911	361	9	⇒	⇒	NOUN
ejpam-5911	361	10	(	(	PUNCT
ejpam-5911	361	11	i	i	NOUN
ejpam-5911	361	12	)	)	PUNCT
ejpam-5911	361	13	let	let	VERB
ejpam-5911	361	14	n	n	PRON
ejpam-5911	361	15	∈	∈	PROPN
ejpam-5911	361	16	iz	iz	INTJ
ejpam-5911	361	17	be	be	AUX
ejpam-5911	361	18	an	an	DET
ejpam-5911	361	19	(	(	PUNCT
ejpam-5911	361	20	r	r	NOUN
ejpam-5911	361	21	,	,	PUNCT
ejpam-5911	361	22	s)-f	s)-f	NOUN
ejpam-5911	361	23	-	-	PUNCT
ejpam-5911	361	24	b	b	NOUN
ejpam-5911	361	25	-	-	PUNCT
ejpam-5911	361	26	open	open	ADJ
ejpam-5911	361	27	set	set	NOUN
ejpam-5911	361	28	.	.	PUNCT
ejpam-5911	362	1	by	by	ADP
ejpam-5911	362	2	(	(	PUNCT
ejpam-5911	362	3	v	v	NOUN
ejpam-5911	362	4	)	)	PUNCT
ejpam-5911	362	5	,	,	PUNCT
ejpam-5911	362	6	p−1(n	p−1(n	ADV
ejpam-5911	362	7	)	)	PUNCT
ejpam-5911	363	1	=	=	PUNCT
ejpam-5911	363	2	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	NOUN
ejpam-5911	363	3	,	,	PUNCT
ejpam-5911	363	4	r	r	NOUN
ejpam-5911	363	5	,	,	PUNCT
ejpam-5911	363	6	s	s	NOUN
ejpam-5911	363	7	)	)	PUNCT
ejpam-5911	363	8	)	)	PUNCT
ejpam-5911	364	1	≤	≤	NUM
ejpam-5911	364	2	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	364	3	)	)	PUNCT
ejpam-5911	364	4	,	,	PUNCT
ejpam-5911	364	5	r	r	NOUN
ejpam-5911	364	6	,	,	PUNCT
ejpam-5911	364	7	s	s	NOUN
ejpam-5911	364	8	)	)	PUNCT
ejpam-5911	364	9	≤	≤	NOUN
ejpam-5911	364	10	p−1(n	p−1(n	NOUN
ejpam-5911	364	11	)	)	PUNCT
ejpam-5911	364	12	.	.	PUNCT
ejpam-5911	365	1	thus	thus	ADV
ejpam-5911	365	2	,	,	PUNCT
ejpam-5911	365	3	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	365	4	)	)	PUNCT
ejpam-5911	365	5	,	,	PUNCT
ejpam-5911	365	6	r	r	NOUN
ejpam-5911	365	7	,	,	PUNCT
ejpam-5911	365	8	s	s	NOUN
ejpam-5911	365	9	)	)	PUNCT
ejpam-5911	365	10	=	=	SYM
ejpam-5911	365	11	p−1(n	p−1(n	NOUN
ejpam-5911	365	12	)	)	PUNCT
ejpam-5911	365	13	.	.	PUNCT
ejpam-5911	366	1	therefore	therefore	ADV
ejpam-5911	366	2	,	,	PUNCT
ejpam-5911	366	3	p−1(n	p−1(n	PROPN
ejpam-5911	366	4	)	)	PUNCT
ejpam-5911	366	5	is	be	AUX
ejpam-5911	366	6	(	(	PUNCT
ejpam-5911	366	7	r	r	NOUN
ejpam-5911	366	8	,	,	PUNCT
ejpam-5911	366	9	s)-f	s)-f	NOUN
ejpam-5911	366	10	-	-	PUNCT
ejpam-5911	366	11	b	b	NOUN
ejpam-5911	366	12	-	-	PUNCT
ejpam-5911	366	13	open	open	ADJ
ejpam-5911	366	14	,	,	PUNCT
ejpam-5911	366	15	so	so	CCONJ
ejpam-5911	366	16	p	p	PROPN
ejpam-5911	366	17	is	be	AUX
ejpam-5911	366	18	df	df	NOUN
ejpam-5911	366	19	-	-	PUNCT
ejpam-5911	366	20	birresolute	birresolute	NOUN
ejpam-5911	366	21	.	.	PUNCT
ejpam-5911	367	1	i.	i.	PROPN
ejpam-5911	367	2	m.	m.	PROPN
ejpam-5911	367	3	taha	taha	PROPN
ejpam-5911	367	4	,	,	PUNCT
ejpam-5911	367	5	j.	j.	PROPN
ejpam-5911	367	6	al	al	PROPN
ejpam-5911	367	7	-	-	PUNCT
ejpam-5911	367	8	mufarrij	mufarrij	PROPN
ejpam-5911	367	9	,	,	PUNCT
ejpam-5911	367	10	o.	o.	PROPN
ejpam-5911	367	11	m.	m.	PROPN
ejpam-5911	367	12	taha	taha	PROPN
ejpam-5911	367	13	/	/	PUNCT
ejpam-5911	367	14	eur	eur	PROPN
ejpam-5911	367	15	.	.	PUNCT
ejpam-5911	368	1	j.	j.	PROPN
ejpam-5911	368	2	pure	pure	PROPN
ejpam-5911	368	3	appl	appl	PROPN
ejpam-5911	368	4	.	.	PROPN
ejpam-5911	368	5	math	math	PROPN
ejpam-5911	368	6	,	,	PUNCT
ejpam-5911	368	7	18	18	NUM
ejpam-5911	368	8	(	(	PUNCT
ejpam-5911	368	9	2	2	NUM
ejpam-5911	368	10	)	)	PUNCT
ejpam-5911	368	11	(	(	PUNCT
ejpam-5911	368	12	2025	2025	NUM
ejpam-5911	368	13	)	)	PUNCT
ejpam-5911	368	14	,	,	PUNCT
ejpam-5911	368	15	5911	5911	NUM
ejpam-5911	368	16	14	14	NUM
ejpam-5911	368	17	of	of	ADP
ejpam-5911	368	18	27	27	NUM
ejpam-5911	368	19	proposition	proposition	NOUN
ejpam-5911	368	20	5	5	NUM
ejpam-5911	368	21	.	.	PUNCT
ejpam-5911	369	1	let	let	VERB
ejpam-5911	369	2	(	(	PUNCT
ejpam-5911	369	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	369	4	)	)	PUNCT
ejpam-5911	369	5	,	,	PUNCT
ejpam-5911	369	6	(	(	PUNCT
ejpam-5911	369	7	q	q	X
ejpam-5911	369	8	,	,	PUNCT
ejpam-5911	369	9	η	η	NOUN
ejpam-5911	369	10	,	,	PUNCT
ejpam-5911	369	11	η∗	η∗	NOUN
ejpam-5911	369	12	)	)	PUNCT
ejpam-5911	369	13	and	and	CCONJ
ejpam-5911	369	14	(	(	PUNCT
ejpam-5911	369	15	z	z	NOUN
ejpam-5911	369	16	,	,	PUNCT
ejpam-5911	369	17	𭟋	𭟋	NOUN
ejpam-5911	369	18	,	,	PUNCT
ejpam-5911	369	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	369	20	)	)	PUNCT
ejpam-5911	369	21	bedft	bedft	NOUN
ejpam-5911	369	22	ss	ss	PROPN
ejpam-5911	369	23	,	,	PUNCT
ejpam-5911	369	24	and	and	CCONJ
ejpam-5911	369	25	p	p	X
ejpam-5911	369	26	:	:	PUNCT
ejpam-5911	369	27	(	(	PUNCT
ejpam-5911	369	28	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	369	29	)	)	PUNCT
ejpam-5911	370	1	−→	−→	NOUN
ejpam-5911	370	2	(	(	PUNCT
ejpam-5911	370	3	q	q	NOUN
ejpam-5911	370	4	,	,	PUNCT
ejpam-5911	370	5	η	η	NOUN
ejpam-5911	370	6	,	,	PUNCT
ejpam-5911	370	7	η∗	η∗	PROPN
ejpam-5911	370	8	)	)	PUNCT
ejpam-5911	370	9	,	,	PUNCT
ejpam-5911	370	10	y	y	PROPN
ejpam-5911	370	11	:	:	PUNCT
ejpam-5911	370	12	(	(	PUNCT
ejpam-5911	370	13	q	q	X
ejpam-5911	370	14	,	,	PUNCT
ejpam-5911	370	15	η	η	NOUN
ejpam-5911	370	16	,	,	PUNCT
ejpam-5911	370	17	η∗	η∗	NOUN
ejpam-5911	370	18	)	)	PUNCT
ejpam-5911	370	19	−→	−→	NOUN
ejpam-5911	370	20	(	(	PUNCT
ejpam-5911	370	21	z	z	NOUN
ejpam-5911	370	22	,	,	PUNCT
ejpam-5911	370	23	𭟋	𭟋	NOUN
ejpam-5911	370	24	,	,	PUNCT
ejpam-5911	370	25	𭟋∗	𭟋∗	NOUN
ejpam-5911	370	26	)	)	PUNCT
ejpam-5911	370	27	be	be	VERB
ejpam-5911	370	28	two	two	NUM
ejpam-5911	370	29	f	f	NOUN
ejpam-5911	370	30	-	-	PUNCT
ejpam-5911	370	31	mappings	mapping	NOUN
ejpam-5911	370	32	.	.	PUNCT
ejpam-5911	371	1	then	then	ADV
ejpam-5911	371	2	the	the	DET
ejpam-5911	371	3	composition	composition	NOUN
ejpam-5911	371	4	y	y	PROPN
ejpam-5911	371	5	◦	◦	NOUN
ejpam-5911	371	6	p	p	NOUN
ejpam-5911	371	7	is	be	AUX
ejpam-5911	371	8	df	df	PROPN
ejpam-5911	371	9	-	-	PUNCT
ejpam-5911	371	10	b	b	NOUN
ejpam-5911	371	11	-	-	PUNCT
ejpam-5911	371	12	irresolute	irresolute	ADJ
ejpam-5911	371	13	(	(	PUNCT
ejpam-5911	371	14	resp	resp	NOUN
ejpam-5911	371	15	.	.	PUNCT
ejpam-5911	372	1	df	df	PROPN
ejpam-5911	372	2	-	-	PUNCT
ejpam-5911	372	3	b	b	NOUN
ejpam-5911	372	4	-	-	PUNCT
ejpam-5911	372	5	continuous	continuous	ADJ
ejpam-5911	372	6	)	)	PUNCT
ejpam-5911	372	7	if	if	SCONJ
ejpam-5911	372	8	p	p	NOUN
ejpam-5911	372	9	is	be	AUX
ejpam-5911	372	10	df	df	PROPN
ejpam-5911	372	11	-	-	PUNCT
ejpam-5911	372	12	b	b	NOUN
ejpam-5911	372	13	-	-	PUNCT
ejpam-5911	372	14	irresolute	irresolute	ADJ
ejpam-5911	372	15	and	and	CCONJ
ejpam-5911	372	16	y	y	PROPN
ejpam-5911	372	17	is	be	AUX
ejpam-5911	372	18	df	df	PROPN
ejpam-5911	372	19	-	-	PUNCT
ejpam-5911	372	20	b	b	NOUN
ejpam-5911	372	21	-	-	PUNCT
ejpam-5911	372	22	irresolute	irresolute	ADJ
ejpam-5911	372	23	(	(	PUNCT
ejpam-5911	372	24	resp	resp	NOUN
ejpam-5911	372	25	.	.	PUNCT
ejpam-5911	373	1	df	df	PROPN
ejpam-5911	373	2	-	-	PUNCT
ejpam-5911	373	3	b	b	NOUN
ejpam-5911	373	4	-	-	PUNCT
ejpam-5911	373	5	continuous	continuous	ADJ
ejpam-5911	373	6	)	)	PUNCT
ejpam-5911	373	7	.	.	PUNCT
ejpam-5911	374	1	proof	proof	NOUN
ejpam-5911	374	2	.	.	PUNCT
ejpam-5911	375	1	the	the	DET
ejpam-5911	375	2	proof	proof	NOUN
ejpam-5911	375	3	follows	follow	VERB
ejpam-5911	375	4	from	from	ADP
ejpam-5911	375	5	definitions	definition	NOUN
ejpam-5911	375	6	10	10	NUM
ejpam-5911	375	7	and	and	CCONJ
ejpam-5911	375	8	11	11	NUM
ejpam-5911	375	9	.	.	PUNCT
ejpam-5911	376	1	definition	definition	NOUN
ejpam-5911	376	2	12	12	NUM
ejpam-5911	376	3	.	.	PUNCT
ejpam-5911	377	1	an	an	DET
ejpam-5911	377	2	f	f	X
ejpam-5911	377	3	-	-	PUNCT
ejpam-5911	377	4	mapping	mapping	NOUN
ejpam-5911	377	5	p	p	NOUN
ejpam-5911	377	6	:	:	PUNCT
ejpam-5911	377	7	(	(	PUNCT
ejpam-5911	377	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	377	9	)	)	PUNCT
ejpam-5911	378	1	−→	−→	NOUN
ejpam-5911	378	2	(	(	PUNCT
ejpam-5911	378	3	z	z	NOUN
ejpam-5911	378	4	,	,	PUNCT
ejpam-5911	378	5	𭟋	𭟋	NOUN
ejpam-5911	378	6	,	,	PUNCT
ejpam-5911	378	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	378	8	)	)	PUNCT
ejpam-5911	378	9	is	be	AUX
ejpam-5911	378	10	called	call	VERB
ejpam-5911	378	11	df	df	NOUN
ejpam-5911	378	12	-	-	PUNCT
ejpam-5911	378	13	almost	almost	ADV
ejpam-5911	378	14	bcontinuous	bcontinuous	ADJ
ejpam-5911	378	15	if	if	SCONJ
ejpam-5911	378	16	p−1(n	p−1(n	NOUN
ejpam-5911	378	17	)	)	PUNCT
ejpam-5911	378	18	≤	≤	NOUN
ejpam-5911	378	19	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	378	20	,	,	PUNCT
ejpam-5911	378	21	r	r	NOUN
ejpam-5911	378	22	,	,	PUNCT
ejpam-5911	378	23	s	s	PART
ejpam-5911	378	24	)	)	PUNCT
ejpam-5911	378	25	,	,	PUNCT
ejpam-5911	378	26	r	r	NOUN
ejpam-5911	378	27	,	,	PUNCT
ejpam-5911	378	28	s	s	NOUN
ejpam-5911	378	29	)	)	PUNCT
ejpam-5911	378	30	)	)	PUNCT
ejpam-5911	378	31	,	,	PUNCT
ejpam-5911	378	32	r	r	NOUN
ejpam-5911	378	33	,	,	PUNCT
ejpam-5911	378	34	s	s	PART
ejpam-5911	378	35	)	)	PUNCT
ejpam-5911	378	36	,	,	PUNCT
ejpam-5911	378	37	for	for	ADP
ejpam-5911	378	38	every	every	DET
ejpam-5911	378	39	n	n	NOUN
ejpam-5911	378	40	∈	∈	NOUN
ejpam-5911	378	41	iz	iz	INTJ
ejpam-5911	378	42	with	with	ADP
ejpam-5911	378	43	𭟋(n	𭟋(n	PROPN
ejpam-5911	378	44	)	)	PUNCT
ejpam-5911	378	45	≥	≥	PROPN
ejpam-5911	378	46	r	r	NOUN
ejpam-5911	378	47	and	and	CCONJ
ejpam-5911	378	48	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	378	49	)	)	PUNCT
ejpam-5911	378	50	≤	≤	NOUN
ejpam-5911	379	1	s.	s.	PROPN
ejpam-5911	379	2	lemma	lemma	PROPN
ejpam-5911	380	1	3	3	X
ejpam-5911	380	2	.	.	PUNCT
ejpam-5911	381	1	every	every	DET
ejpam-5911	381	2	df	df	PROPN
ejpam-5911	381	3	-	-	PUNCT
ejpam-5911	381	4	b	b	NOUN
ejpam-5911	381	5	-	-	PUNCT
ejpam-5911	381	6	continuous	continuous	ADJ
ejpam-5911	381	7	mapping	mapping	NOUN
ejpam-5911	381	8	is	be	AUX
ejpam-5911	381	9	df	df	NOUN
ejpam-5911	381	10	-	-	PUNCT
ejpam-5911	381	11	almost	almost	ADV
ejpam-5911	381	12	b	b	NOUN
ejpam-5911	381	13	-	-	PUNCT
ejpam-5911	381	14	continuous	continuous	ADJ
ejpam-5911	381	15	.	.	PUNCT
ejpam-5911	382	1	proof	proof	NOUN
ejpam-5911	382	2	.	.	PUNCT
ejpam-5911	383	1	the	the	DET
ejpam-5911	383	2	proof	proof	NOUN
ejpam-5911	383	3	follows	follow	VERB
ejpam-5911	383	4	by	by	ADP
ejpam-5911	383	5	definitions	definition	NOUN
ejpam-5911	383	6	10	10	NUM
ejpam-5911	383	7	and	and	CCONJ
ejpam-5911	383	8	12	12	NUM
ejpam-5911	383	9	.	.	PUNCT
ejpam-5911	384	1	remark	remark	PROPN
ejpam-5911	384	2	7	7	NUM
ejpam-5911	384	3	.	.	PUNCT
ejpam-5911	385	1	the	the	DET
ejpam-5911	385	2	converse	converse	NOUN
ejpam-5911	385	3	of	of	ADP
ejpam-5911	385	4	lemma	lemma	PROPN
ejpam-5911	385	5	3	3	NUM
ejpam-5911	385	6	fails	fail	VERB
ejpam-5911	385	7	as	as	ADP
ejpam-5911	385	8	example	example	NOUN
ejpam-5911	385	9	8	8	NUM
ejpam-5911	385	10	will	will	AUX
ejpam-5911	385	11	show	show	VERB
ejpam-5911	385	12	.	.	PUNCT
ejpam-5911	386	1	example	example	NOUN
ejpam-5911	386	2	8	8	NUM
ejpam-5911	386	3	.	.	PUNCT
ejpam-5911	387	1	let	let	VERB
ejpam-5911	387	2	g	g	PROPN
ejpam-5911	387	3	=	=	SYM
ejpam-5911	387	4	{	{	PUNCT
ejpam-5911	387	5	g1	g1	PROPN
ejpam-5911	387	6	,	,	PUNCT
ejpam-5911	387	7	g2	g2	PROPN
ejpam-5911	387	8	,	,	PUNCT
ejpam-5911	387	9	g3	g3	PROPN
ejpam-5911	387	10	}	}	PUNCT
ejpam-5911	387	11	and	and	CCONJ
ejpam-5911	387	12	define	define	VERB
ejpam-5911	387	13	m	m	PROPN
ejpam-5911	387	14	,	,	PUNCT
ejpam-5911	387	15	n	n	CCONJ
ejpam-5911	387	16	,	,	PUNCT
ejpam-5911	387	17	u	u	PROPN
ejpam-5911	387	18	∈	∈	PROPN
ejpam-5911	387	19	ig	ig	PROPN
ejpam-5911	387	20	as	as	SCONJ
ejpam-5911	387	21	follows	follow	VERB
ejpam-5911	387	22	:	:	PUNCT
ejpam-5911	387	23	m	m	VERB
ejpam-5911	387	24	=	=	PUNCT
ejpam-5911	387	25	{	{	PUNCT
ejpam-5911	387	26	g1	g1	PROPN
ejpam-5911	387	27	0.4	0.4	NUM
ejpam-5911	387	28	,	,	PUNCT
ejpam-5911	387	29	g2	g2	PROPN
ejpam-5911	387	30	0.2	0.2	NUM
ejpam-5911	387	31	,	,	PUNCT
ejpam-5911	387	32	g3	g3	PROPN
ejpam-5911	387	33	0.4	0.4	NUM
ejpam-5911	387	34	}	}	PUNCT
ejpam-5911	387	35	,	,	PUNCT
ejpam-5911	387	36	n	n	NOUN
ejpam-5911	387	37	=	=	PRON
ejpam-5911	387	38	{	{	PUNCT
ejpam-5911	387	39	g1	g1	PROPN
ejpam-5911	387	40	0.5	0.5	NUM
ejpam-5911	387	41	,	,	PUNCT
ejpam-5911	387	42	g2	g2	PROPN
ejpam-5911	387	43	0.5	0.5	NUM
ejpam-5911	387	44	,	,	PUNCT
ejpam-5911	387	45	g3	g3	NOUN
ejpam-5911	387	46	0.4	0.4	NUM
ejpam-5911	387	47	}	}	PUNCT
ejpam-5911	387	48	,	,	PUNCT
ejpam-5911	387	49	u	u	NOUN
ejpam-5911	387	50	=	=	PUNCT
ejpam-5911	387	51	{	{	PUNCT
ejpam-5911	387	52	g1	g1	PROPN
ejpam-5911	387	53	0.3	0.3	NUM
ejpam-5911	387	54	,	,	PUNCT
ejpam-5911	387	55	g2	g2	PROPN
ejpam-5911	387	56	0.2	0.2	NUM
ejpam-5911	387	57	,	,	PUNCT
ejpam-5911	387	58	g3	g3	X
ejpam-5911	387	59	0.6	0.6	NUM
ejpam-5911	387	60	}	}	PUNCT
ejpam-5911	387	61	.	.	PUNCT
ejpam-5911	388	1	define	define	VERB
ejpam-5911	388	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	388	3	,	,	PUNCT
ejpam-5911	388	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	388	5	:	:	PUNCT
ejpam-5911	388	6	ig	ig	PROPN
ejpam-5911	388	7	−→	−→	NOUN
ejpam-5911	389	1	i	i	PRON
ejpam-5911	389	2	as	as	SCONJ
ejpam-5911	389	3	follows	follow	VERB
ejpam-5911	389	4	:	:	PUNCT
ejpam-5911	389	5	ℑ(v	ℑ(v	X
ejpam-5911	389	6	)	)	PUNCT
ejpam-5911	389	7	=	=	PUNCT
ejpam-5911	389	8			NOUN
ejpam-5911	389	9	1	1	NUM
ejpam-5911	389	10	,	,	PUNCT
ejpam-5911	389	11	if	if	SCONJ
ejpam-5911	389	12	v	v	ADP
ejpam-5911	389	13	∈	∈	PROPN
ejpam-5911	389	14	{	{	PUNCT
ejpam-5911	389	15	0	0	NUM
ejpam-5911	389	16	,	,	PUNCT
ejpam-5911	389	17	1	1	NUM
ejpam-5911	389	18	}	}	PUNCT
ejpam-5911	389	19	,	,	PUNCT
ejpam-5911	389	20	2	2	NUM
ejpam-5911	389	21	3	3	NUM
ejpam-5911	389	22	,	,	PUNCT
ejpam-5911	389	23	if	if	SCONJ
ejpam-5911	389	24	v	v	ADP
ejpam-5911	389	25	=	=	SYM
ejpam-5911	389	26	m	m	NOUN
ejpam-5911	389	27	,	,	PUNCT
ejpam-5911	389	28	1	1	NUM
ejpam-5911	389	29	2	2	NUM
ejpam-5911	389	30	,	,	PUNCT
ejpam-5911	389	31	if	if	SCONJ
ejpam-5911	389	32	v	v	VERB
ejpam-5911	389	33	=	=	SYM
ejpam-5911	389	34	n	n	NOUN
ejpam-5911	389	35	,	,	PUNCT
ejpam-5911	389	36	0	0	NUM
ejpam-5911	389	37	,	,	PUNCT
ejpam-5911	389	38	otherwise	otherwise	ADV
ejpam-5911	389	39	,	,	PUNCT
ejpam-5911	389	40	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	389	41	)	)	PUNCT
ejpam-5911	389	42	=	=	PUNCT
ejpam-5911	390	1			NOUN
ejpam-5911	390	2	0	0	NUM
ejpam-5911	390	3	,	,	PUNCT
ejpam-5911	390	4	if	if	SCONJ
ejpam-5911	390	5	v	v	ADP
ejpam-5911	390	6	∈	∈	PROPN
ejpam-5911	390	7	{	{	PUNCT
ejpam-5911	390	8	0	0	NUM
ejpam-5911	390	9	,	,	PUNCT
ejpam-5911	390	10	1	1	NUM
ejpam-5911	390	11	}	}	PUNCT
ejpam-5911	390	12	,	,	PUNCT
ejpam-5911	390	13	1	1	NUM
ejpam-5911	390	14	3	3	NUM
ejpam-5911	390	15	,	,	PUNCT
ejpam-5911	390	16	if	if	SCONJ
ejpam-5911	390	17	v	v	ADP
ejpam-5911	390	18	=	=	SYM
ejpam-5911	390	19	m	m	NOUN
ejpam-5911	390	20	,	,	PUNCT
ejpam-5911	390	21	1	1	NUM
ejpam-5911	390	22	3	3	NUM
ejpam-5911	390	23	,	,	PUNCT
ejpam-5911	390	24	if	if	SCONJ
ejpam-5911	390	25	v	v	VERB
ejpam-5911	390	26	=	=	SYM
ejpam-5911	390	27	n	n	NOUN
ejpam-5911	390	28	,	,	PUNCT
ejpam-5911	390	29	1	1	NUM
ejpam-5911	390	30	,	,	PUNCT
ejpam-5911	390	31	otherwise	otherwise	ADV
ejpam-5911	390	32	,	,	PUNCT
ejpam-5911	390	33	𭟋(v	𭟋(v	NOUN
ejpam-5911	390	34	)	)	PUNCT
ejpam-5911	390	35	=	=	SYM
ejpam-5911	391	1			NOUN
ejpam-5911	391	2	1	1	NUM
ejpam-5911	391	3	,	,	PUNCT
ejpam-5911	391	4	if	if	SCONJ
ejpam-5911	391	5	v	v	ADP
ejpam-5911	391	6	∈	∈	PROPN
ejpam-5911	391	7	{	{	PUNCT
ejpam-5911	391	8	0	0	NUM
ejpam-5911	391	9	,	,	PUNCT
ejpam-5911	391	10	1	1	NUM
ejpam-5911	391	11	}	}	PUNCT
ejpam-5911	391	12	,	,	PUNCT
ejpam-5911	391	13	1	1	NUM
ejpam-5911	391	14	2	2	NUM
ejpam-5911	391	15	,	,	PUNCT
ejpam-5911	391	16	if	if	SCONJ
ejpam-5911	391	17	v	v	ADP
ejpam-5911	391	18	=	=	SYM
ejpam-5911	391	19	u	u	NOUN
ejpam-5911	391	20	,	,	PUNCT
ejpam-5911	391	21	0	0	NUM
ejpam-5911	391	22	,	,	PUNCT
ejpam-5911	391	23	otherwise	otherwise	ADV
ejpam-5911	391	24	.	.	PUNCT
ejpam-5911	392	1	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	392	2	)	)	PUNCT
ejpam-5911	393	1	=	=	PUNCT
ejpam-5911	394	1			NOUN
ejpam-5911	394	2	0	0	NUM
ejpam-5911	394	3	,	,	PUNCT
ejpam-5911	394	4	if	if	SCONJ
ejpam-5911	394	5	v	v	ADP
ejpam-5911	394	6	∈	∈	PROPN
ejpam-5911	394	7	{	{	PUNCT
ejpam-5911	394	8	0	0	NUM
ejpam-5911	394	9	,	,	PUNCT
ejpam-5911	394	10	1	1	NUM
ejpam-5911	394	11	}	}	PUNCT
ejpam-5911	394	12	,	,	PUNCT
ejpam-5911	394	13	1	1	NUM
ejpam-5911	394	14	3	3	NUM
ejpam-5911	394	15	,	,	PUNCT
ejpam-5911	394	16	if	if	SCONJ
ejpam-5911	394	17	v	v	ADP
ejpam-5911	394	18	=	=	SYM
ejpam-5911	394	19	u	u	NOUN
ejpam-5911	394	20	,	,	PUNCT
ejpam-5911	394	21	1	1	NUM
ejpam-5911	394	22	,	,	PUNCT
ejpam-5911	394	23	otherwise	otherwise	ADV
ejpam-5911	394	24	.	.	PUNCT
ejpam-5911	395	1	thus	thus	ADV
ejpam-5911	395	2	,	,	PUNCT
ejpam-5911	395	3	the	the	DET
ejpam-5911	395	4	identity	identity	NOUN
ejpam-5911	395	5	f	f	NOUN
ejpam-5911	395	6	-	-	PUNCT
ejpam-5911	395	7	mapping	mapping	NOUN
ejpam-5911	395	8	p	p	NOUN
ejpam-5911	395	9	:	:	PUNCT
ejpam-5911	395	10	(	(	PUNCT
ejpam-5911	395	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	395	12	)	)	PUNCT
ejpam-5911	395	13	−→	−→	NOUN
ejpam-5911	395	14	(	(	PUNCT
ejpam-5911	395	15	g	g	NOUN
ejpam-5911	395	16	,	,	PUNCT
ejpam-5911	395	17	𭟋	𭟋	NOUN
ejpam-5911	395	18	,	,	PUNCT
ejpam-5911	395	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	395	20	)	)	PUNCT
ejpam-5911	395	21	is	be	AUX
ejpam-5911	395	22	df	df	NOUN
ejpam-5911	395	23	-	-	PUNCT
ejpam-5911	395	24	almost	almost	ADV
ejpam-5911	395	25	b	b	NOUN
ejpam-5911	395	26	-	-	ADJ
ejpam-5911	395	27	continuous	continuous	ADJ
ejpam-5911	395	28	,	,	PUNCT
ejpam-5911	395	29	but	but	CCONJ
ejpam-5911	395	30	it	it	PRON
ejpam-5911	395	31	is	be	AUX
ejpam-5911	395	32	not	not	PART
ejpam-5911	395	33	df	df	NOUN
ejpam-5911	395	34	-	-	PUNCT
ejpam-5911	395	35	b	b	NOUN
ejpam-5911	395	36	-	-	PUNCT
ejpam-5911	395	37	continuous	continuous	ADJ
ejpam-5911	395	38	.	.	PUNCT
ejpam-5911	396	1	theorem	theorem	NOUN
ejpam-5911	396	2	6	6	NUM
ejpam-5911	396	3	.	.	PUNCT
ejpam-5911	397	1	an	an	DET
ejpam-5911	397	2	f	f	NOUN
ejpam-5911	397	3	-	-	PUNCT
ejpam-5911	397	4	mapping	mapping	NOUN
ejpam-5911	397	5	p	p	NOUN
ejpam-5911	397	6	:	:	PUNCT
ejpam-5911	397	7	(	(	PUNCT
ejpam-5911	397	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	397	9	)	)	PUNCT
ejpam-5911	398	1	−→	−→	NOUN
ejpam-5911	398	2	(	(	PUNCT
ejpam-5911	398	3	z	z	NOUN
ejpam-5911	398	4	,	,	PUNCT
ejpam-5911	398	5	𭟋	𭟋	NOUN
ejpam-5911	398	6	,	,	PUNCT
ejpam-5911	398	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	398	8	)	)	PUNCT
ejpam-5911	398	9	is	be	AUX
ejpam-5911	398	10	df	df	NOUN
ejpam-5911	398	11	-	-	PUNCT
ejpam-5911	398	12	almost	almost	ADV
ejpam-5911	398	13	b	b	NOUN
ejpam-5911	398	14	-	-	PUNCT
ejpam-5911	398	15	continuous	continuous	ADJ
ejpam-5911	398	16	iff	iff	PROPN
ejpam-5911	398	17	for	for	ADP
ejpam-5911	398	18	any	any	DET
ejpam-5911	398	19	gθ	gθ	PROPN
ejpam-5911	398	20	∈	∈	PROPN
ejpam-5911	398	21	pθ(g	pθ(g	NOUN
ejpam-5911	398	22	)	)	PUNCT
ejpam-5911	398	23	and	and	CCONJ
ejpam-5911	398	24	any	any	DET
ejpam-5911	398	25	n	n	NOUN
ejpam-5911	398	26	∈	∈	NOUN
ejpam-5911	398	27	iz	iz	INTJ
ejpam-5911	398	28	with	with	ADP
ejpam-5911	398	29	𭟋(n	𭟋(n	PROPN
ejpam-5911	398	30	)	)	PUNCT
ejpam-5911	398	31	≥	≥	PROPN
ejpam-5911	398	32	r	r	NOUN
ejpam-5911	398	33	and	and	CCONJ
ejpam-5911	398	34	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	398	35	)	)	PUNCT
ejpam-5911	398	36	≤	≤	NUM
ejpam-5911	398	37	s	s	AUX
ejpam-5911	398	38	containing	contain	VERB
ejpam-5911	398	39	p(gθ	p(gθ	PROPN
ejpam-5911	398	40	)	)	PUNCT
ejpam-5911	398	41	,	,	PUNCT
ejpam-5911	398	42	there	there	PRON
ejpam-5911	398	43	is	be	VERB
ejpam-5911	398	44	m	m	PROPN
ejpam-5911	398	45	∈	∈	NOUN
ejpam-5911	398	46	ig	ig	PROPN
ejpam-5911	398	47	that	that	PRON
ejpam-5911	398	48	is	be	AUX
ejpam-5911	398	49	(	(	PUNCT
ejpam-5911	398	50	r	r	NOUN
ejpam-5911	398	51	,	,	PUNCT
ejpam-5911	398	52	s)-f	s)-f	NOUN
ejpam-5911	398	53	-	-	PUNCT
ejpam-5911	398	54	b	b	NOUN
ejpam-5911	398	55	-	-	PUNCT
ejpam-5911	398	56	open	open	ADJ
ejpam-5911	398	57	containing	contain	VERB
ejpam-5911	398	58	gθ	gθ	NOUN
ejpam-5911	398	59	with	with	ADP
ejpam-5911	398	60	p(m	p(m	NOUN
ejpam-5911	398	61	)	)	PUNCT
ejpam-5911	398	62	≤	≤	NOUN
ejpam-5911	398	63	i𭟋∗(c𭟋∗(n	i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	398	64	,	,	PUNCT
ejpam-5911	398	65	r	r	NOUN
ejpam-5911	398	66	,	,	PUNCT
ejpam-5911	398	67	s	s	PART
ejpam-5911	398	68	)	)	PUNCT
ejpam-5911	398	69	,	,	PUNCT
ejpam-5911	398	70	r	r	NOUN
ejpam-5911	398	71	,	,	PUNCT
ejpam-5911	398	72	s	s	NOUN
ejpam-5911	398	73	)	)	PUNCT
ejpam-5911	398	74	.	.	PUNCT
ejpam-5911	399	1	i.	i.	PROPN
ejpam-5911	399	2	m.	m.	PROPN
ejpam-5911	399	3	taha	taha	PROPN
ejpam-5911	399	4	,	,	PUNCT
ejpam-5911	399	5	j.	j.	PROPN
ejpam-5911	399	6	al	al	PROPN
ejpam-5911	399	7	-	-	PUNCT
ejpam-5911	399	8	mufarrij	mufarrij	PROPN
ejpam-5911	399	9	,	,	PUNCT
ejpam-5911	399	10	o.	o.	PROPN
ejpam-5911	399	11	m.	m.	PROPN
ejpam-5911	399	12	taha	taha	PROPN
ejpam-5911	399	13	/	/	PUNCT
ejpam-5911	399	14	eur	eur	PROPN
ejpam-5911	399	15	.	.	PUNCT
ejpam-5911	400	1	j.	j.	PROPN
ejpam-5911	400	2	pure	pure	PROPN
ejpam-5911	400	3	appl	appl	PROPN
ejpam-5911	400	4	.	.	PROPN
ejpam-5911	400	5	math	math	PROPN
ejpam-5911	400	6	,	,	PUNCT
ejpam-5911	400	7	18	18	NUM
ejpam-5911	400	8	(	(	PUNCT
ejpam-5911	400	9	2	2	NUM
ejpam-5911	400	10	)	)	PUNCT
ejpam-5911	400	11	(	(	PUNCT
ejpam-5911	400	12	2025	2025	NUM
ejpam-5911	400	13	)	)	PUNCT
ejpam-5911	400	14	,	,	PUNCT
ejpam-5911	400	15	5911	5911	NUM
ejpam-5911	400	16	15	15	NUM
ejpam-5911	400	17	of	of	ADP
ejpam-5911	400	18	27	27	NUM
ejpam-5911	400	19	proof	proof	NOUN
ejpam-5911	400	20	.	.	PUNCT
ejpam-5911	401	1	(	(	PUNCT
ejpam-5911	401	2	⇒	⇒	PROPN
ejpam-5911	401	3	)	)	PUNCT
ejpam-5911	401	4	let	let	VERB
ejpam-5911	401	5	gθ	gθ	PROPN
ejpam-5911	401	6	∈	∈	PROPN
ejpam-5911	401	7	pθ(g	pθ(g	NOUN
ejpam-5911	401	8	)	)	PUNCT
ejpam-5911	401	9	and	and	CCONJ
ejpam-5911	401	10	n	n	PRON
ejpam-5911	401	11	∈	∈	NOUN
ejpam-5911	401	12	iz	iz	INTJ
ejpam-5911	401	13	with	with	ADP
ejpam-5911	401	14	𭟋(n	𭟋(n	PROPN
ejpam-5911	401	15	)	)	PUNCT
ejpam-5911	401	16	≥	≥	PROPN
ejpam-5911	401	17	r	r	NOUN
ejpam-5911	401	18	and	and	CCONJ
ejpam-5911	401	19	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	401	20	)	)	PUNCT
ejpam-5911	401	21	≤	≤	NUM
ejpam-5911	401	22	s	s	AUX
ejpam-5911	401	23	containing	contain	VERB
ejpam-5911	401	24	p(gθ	p(gθ	PROPN
ejpam-5911	401	25	)	)	PUNCT
ejpam-5911	401	26	,	,	PUNCT
ejpam-5911	401	27	and	and	CCONJ
ejpam-5911	401	28	then	then	ADV
ejpam-5911	401	29	p−1(n	p−1(n	PROPN
ejpam-5911	401	30	)	)	PUNCT
ejpam-5911	401	31	≤	≤	NOUN
ejpam-5911	401	32	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	401	33	,	,	PUNCT
ejpam-5911	401	34	r	r	NOUN
ejpam-5911	401	35	,	,	PUNCT
ejpam-5911	401	36	s	s	PART
ejpam-5911	401	37	)	)	PUNCT
ejpam-5911	401	38	,	,	PUNCT
ejpam-5911	401	39	r	r	NOUN
ejpam-5911	401	40	,	,	PUNCT
ejpam-5911	401	41	s	s	NOUN
ejpam-5911	401	42	)	)	PUNCT
ejpam-5911	401	43	)	)	PUNCT
ejpam-5911	401	44	,	,	PUNCT
ejpam-5911	401	45	r	r	NOUN
ejpam-5911	401	46	,	,	PUNCT
ejpam-5911	401	47	s	s	NOUN
ejpam-5911	401	48	)	)	PUNCT
ejpam-5911	401	49	.	.	PUNCT
ejpam-5911	402	1	since	since	SCONJ
ejpam-5911	402	2	gθ	gθ	PROPN
ejpam-5911	402	3	∈	∈	PROPN
ejpam-5911	402	4	p−1(n	p−1(n	NOUN
ejpam-5911	402	5	)	)	PUNCT
ejpam-5911	402	6	,	,	PUNCT
ejpam-5911	402	7	then	then	ADV
ejpam-5911	402	8	gθ	gθ	PROPN
ejpam-5911	402	9	∈	∈	PROPN
ejpam-5911	402	10	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	PROPN
ejpam-5911	402	11	,	,	PUNCT
ejpam-5911	402	12	r	r	NOUN
ejpam-5911	402	13	,	,	PUNCT
ejpam-5911	402	14	s	s	PART
ejpam-5911	402	15	)	)	PUNCT
ejpam-5911	402	16	,	,	PUNCT
ejpam-5911	402	17	r	r	NOUN
ejpam-5911	402	18	,	,	PUNCT
ejpam-5911	402	19	s	s	NOUN
ejpam-5911	402	20	)	)	PUNCT
ejpam-5911	402	21	)	)	PUNCT
ejpam-5911	402	22	,	,	PUNCT
ejpam-5911	402	23	r	r	NOUN
ejpam-5911	402	24	,	,	PUNCT
ejpam-5911	402	25	s	s	PART
ejpam-5911	402	26	)	)	PUNCT
ejpam-5911	402	27	=	=	SYM
ejpam-5911	402	28	m	m	PROPN
ejpam-5911	402	29	(	(	PUNCT
ejpam-5911	402	30	say	say	INTJ
ejpam-5911	402	31	)	)	PUNCT
ejpam-5911	402	32	.	.	PUNCT
ejpam-5911	403	1	therefore	therefore	ADV
ejpam-5911	403	2	,	,	PUNCT
ejpam-5911	403	3	m	m	PROPN
ejpam-5911	403	4	∈	∈	NOUN
ejpam-5911	403	5	ig	ig	PROPN
ejpam-5911	403	6	is	be	AUX
ejpam-5911	403	7	(	(	PUNCT
ejpam-5911	403	8	r	r	NOUN
ejpam-5911	403	9	,	,	PUNCT
ejpam-5911	403	10	s)-f	s)-f	NOUN
ejpam-5911	403	11	-	-	PUNCT
ejpam-5911	403	12	b	b	NOUN
ejpam-5911	403	13	-	-	PUNCT
ejpam-5911	403	14	open	open	ADJ
ejpam-5911	403	15	containing	contain	VERB
ejpam-5911	403	16	gθ	gθ	NOUN
ejpam-5911	403	17	with	with	ADP
ejpam-5911	403	18	p(m	p(m	NOUN
ejpam-5911	403	19	)	)	PUNCT
ejpam-5911	403	20	≤	≤	NOUN
ejpam-5911	403	21	i𭟋∗(c𭟋∗(n	i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	403	22	,	,	PUNCT
ejpam-5911	403	23	r	r	NOUN
ejpam-5911	403	24	,	,	PUNCT
ejpam-5911	403	25	s	s	PART
ejpam-5911	403	26	)	)	PUNCT
ejpam-5911	403	27	,	,	PUNCT
ejpam-5911	403	28	r	r	NOUN
ejpam-5911	403	29	,	,	PUNCT
ejpam-5911	403	30	s	s	NOUN
ejpam-5911	403	31	)	)	PUNCT
ejpam-5911	403	32	.	.	PUNCT
ejpam-5911	404	1	(	(	PUNCT
ejpam-5911	404	2	⇐	⇐	NOUN
ejpam-5911	404	3	)	)	PUNCT
ejpam-5911	404	4	let	let	VERB
ejpam-5911	404	5	gθ	gθ	PROPN
ejpam-5911	404	6	∈	∈	PROPN
ejpam-5911	404	7	pθ(g	pθ(g	NOUN
ejpam-5911	404	8	)	)	PUNCT
ejpam-5911	404	9	and	and	CCONJ
ejpam-5911	404	10	n	n	PRON
ejpam-5911	404	11	∈	∈	NOUN
ejpam-5911	404	12	iz	iz	INTJ
ejpam-5911	404	13	with	with	ADP
ejpam-5911	404	14	𭟋(n	𭟋(n	PROPN
ejpam-5911	404	15	)	)	PUNCT
ejpam-5911	405	1	≥	≥	PROPN
ejpam-5911	405	2	r	r	NOUN
ejpam-5911	405	3	and	and	CCONJ
ejpam-5911	405	4	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	405	5	)	)	PUNCT
ejpam-5911	405	6	≤	≤	NUM
ejpam-5911	405	7	s	s	VERB
ejpam-5911	405	8	such	such	ADJ
ejpam-5911	405	9	that	that	SCONJ
ejpam-5911	405	10	gθ	gθ	PROPN
ejpam-5911	405	11	∈	∈	PROPN
ejpam-5911	405	12	p−1(n	p−1(n	NOUN
ejpam-5911	405	13	)	)	PUNCT
ejpam-5911	405	14	.	.	PUNCT
ejpam-5911	406	1	according	accord	VERB
ejpam-5911	406	2	to	to	ADP
ejpam-5911	406	3	the	the	DET
ejpam-5911	406	4	assumption	assumption	NOUN
ejpam-5911	406	5	there	there	PRON
ejpam-5911	406	6	is	be	VERB
ejpam-5911	406	7	m	m	NOUN
ejpam-5911	406	8	∈	∈	NOUN
ejpam-5911	406	9	ig	ig	PROPN
ejpam-5911	406	10	that	that	PRON
ejpam-5911	406	11	is	be	AUX
ejpam-5911	406	12	(	(	PUNCT
ejpam-5911	406	13	r	r	NOUN
ejpam-5911	406	14	,	,	PUNCT
ejpam-5911	406	15	s)-f	s)-f	NOUN
ejpam-5911	406	16	-	-	PUNCT
ejpam-5911	406	17	b	b	NOUN
ejpam-5911	406	18	-	-	PUNCT
ejpam-5911	406	19	open	open	ADJ
ejpam-5911	406	20	containing	contain	VERB
ejpam-5911	406	21	gθ	gθ	NOUN
ejpam-5911	406	22	with	with	ADP
ejpam-5911	406	23	p(m	p(m	NOUN
ejpam-5911	406	24	)	)	PUNCT
ejpam-5911	406	25	≤	≤	NOUN
ejpam-5911	406	26	i𭟋∗(c𭟋∗(n	i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	406	27	,	,	PUNCT
ejpam-5911	406	28	r	r	NOUN
ejpam-5911	406	29	,	,	PUNCT
ejpam-5911	406	30	s	s	PART
ejpam-5911	406	31	)	)	PUNCT
ejpam-5911	406	32	,	,	PUNCT
ejpam-5911	406	33	r	r	NOUN
ejpam-5911	406	34	,	,	PUNCT
ejpam-5911	406	35	s	s	NOUN
ejpam-5911	406	36	)	)	PUNCT
ejpam-5911	406	37	.	.	PUNCT
ejpam-5911	407	1	hence	hence	ADV
ejpam-5911	407	2	,	,	PUNCT
ejpam-5911	407	3	gθ	gθ	PROPN
ejpam-5911	407	4	∈	∈	PROPN
ejpam-5911	407	5	m	m	NOUN
ejpam-5911	407	6	≤	≤	ADJ
ejpam-5911	407	7	p−1(i𭟋∗(c𭟋∗(n	p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	407	8	,	,	PUNCT
ejpam-5911	407	9	r	r	NOUN
ejpam-5911	407	10	,	,	PUNCT
ejpam-5911	407	11	s	s	PART
ejpam-5911	407	12	)	)	PUNCT
ejpam-5911	407	13	,	,	PUNCT
ejpam-5911	407	14	r	r	NOUN
ejpam-5911	407	15	,	,	PUNCT
ejpam-5911	407	16	s	s	NOUN
ejpam-5911	407	17	)	)	PUNCT
ejpam-5911	407	18	)	)	PUNCT
ejpam-5911	407	19	and	and	CCONJ
ejpam-5911	407	20	gθ	gθ	PROPN
ejpam-5911	407	21	∈	∈	PROPN
ejpam-5911	407	22	biℑ(p−1(i𭟋∗(c𭟋∗(n	biℑ(p−1(i𭟋∗(c𭟋∗(n	PROPN
ejpam-5911	407	23	,	,	PUNCT
ejpam-5911	407	24	r	r	NOUN
ejpam-5911	407	25	,	,	PUNCT
ejpam-5911	407	26	s	s	PART
ejpam-5911	407	27	)	)	PUNCT
ejpam-5911	407	28	,	,	PUNCT
ejpam-5911	407	29	r	r	NOUN
ejpam-5911	407	30	,	,	PUNCT
ejpam-5911	407	31	s	s	NOUN
ejpam-5911	407	32	)	)	PUNCT
ejpam-5911	407	33	)	)	PUNCT
ejpam-5911	407	34	,	,	PUNCT
ejpam-5911	407	35	r	r	NOUN
ejpam-5911	407	36	,	,	PUNCT
ejpam-5911	407	37	s	s	NOUN
ejpam-5911	407	38	)	)	PUNCT
ejpam-5911	407	39	.	.	PUNCT
ejpam-5911	408	1	thus	thus	ADV
ejpam-5911	408	2	,	,	PUNCT
ejpam-5911	408	3	p−1(n	p−1(n	ADV
ejpam-5911	408	4	)	)	PUNCT
ejpam-5911	408	5	≤	≤	NOUN
ejpam-5911	408	6	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	408	7	,	,	PUNCT
ejpam-5911	408	8	r	r	NOUN
ejpam-5911	408	9	,	,	PUNCT
ejpam-5911	408	10	s	s	PART
ejpam-5911	408	11	)	)	PUNCT
ejpam-5911	408	12	,	,	PUNCT
ejpam-5911	408	13	r	r	NOUN
ejpam-5911	408	14	,	,	PUNCT
ejpam-5911	408	15	s	s	NOUN
ejpam-5911	408	16	)	)	PUNCT
ejpam-5911	408	17	)	)	PUNCT
ejpam-5911	408	18	,	,	PUNCT
ejpam-5911	408	19	r	r	NOUN
ejpam-5911	408	20	,	,	PUNCT
ejpam-5911	408	21	s	s	PART
ejpam-5911	408	22	)	)	PUNCT
ejpam-5911	408	23	.	.	PUNCT
ejpam-5911	409	1	therefore	therefore	ADV
ejpam-5911	409	2	,	,	PUNCT
ejpam-5911	409	3	p	p	NOUN
ejpam-5911	409	4	is	be	AUX
ejpam-5911	409	5	df	df	NOUN
ejpam-5911	409	6	-	-	PUNCT
ejpam-5911	409	7	almost	almost	ADV
ejpam-5911	409	8	bcontinuous	bcontinuous	ADJ
ejpam-5911	409	9	.	.	PUNCT
ejpam-5911	410	1	theorem	theorem	VERB
ejpam-5911	410	2	7	7	NUM
ejpam-5911	410	3	.	.	PUNCT
ejpam-5911	411	1	let	let	VERB
ejpam-5911	411	2	p	p	NOUN
ejpam-5911	411	3	:	:	PUNCT
ejpam-5911	411	4	(	(	PUNCT
ejpam-5911	411	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	411	6	)	)	PUNCT
ejpam-5911	412	1	−→	−→	NOUN
ejpam-5911	412	2	(	(	PUNCT
ejpam-5911	412	3	z	z	NOUN
ejpam-5911	412	4	,	,	PUNCT
ejpam-5911	412	5	𭟋	𭟋	NOUN
ejpam-5911	412	6	,	,	PUNCT
ejpam-5911	412	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	412	8	)	)	PUNCT
ejpam-5911	412	9	be	be	AUX
ejpam-5911	412	10	an	an	DET
ejpam-5911	412	11	f	f	NOUN
ejpam-5911	412	12	-	-	PUNCT
ejpam-5911	412	13	mapping	mapping	NOUN
ejpam-5911	412	14	.	.	PUNCT
ejpam-5911	413	1	then	then	ADV
ejpam-5911	413	2	the	the	DET
ejpam-5911	413	3	following	follow	VERB
ejpam-5911	413	4	statements	statement	NOUN
ejpam-5911	413	5	are	be	AUX
ejpam-5911	413	6	equivalent	equivalent	ADJ
ejpam-5911	413	7	:	:	PUNCT
ejpam-5911	413	8	(	(	PUNCT
ejpam-5911	413	9	i	i	NOUN
ejpam-5911	413	10	)	)	PUNCT
ejpam-5911	413	11	p	p	NOUN
ejpam-5911	413	12	is	be	AUX
ejpam-5911	413	13	df	df	NOUN
ejpam-5911	413	14	-	-	PUNCT
ejpam-5911	413	15	almost	almost	ADV
ejpam-5911	413	16	b	b	NOUN
ejpam-5911	413	17	-	-	ADJ
ejpam-5911	413	18	continuous	continuous	ADJ
ejpam-5911	413	19	.	.	PUNCT
ejpam-5911	414	1	(	(	PUNCT
ejpam-5911	414	2	ii	ii	NOUN
ejpam-5911	414	3	)	)	PUNCT
ejpam-5911	414	4	p−1(n	p−1(n	PROPN
ejpam-5911	414	5	)	)	PUNCT
ejpam-5911	414	6	is	be	AUX
ejpam-5911	414	7	(	(	PUNCT
ejpam-5911	414	8	r	r	NOUN
ejpam-5911	414	9	,	,	PUNCT
ejpam-5911	414	10	s)-f	s)-f	NOUN
ejpam-5911	414	11	-	-	PUNCT
ejpam-5911	414	12	b	b	NOUN
ejpam-5911	414	13	-	-	PUNCT
ejpam-5911	414	14	open	open	ADJ
ejpam-5911	414	15	,	,	PUNCT
ejpam-5911	414	16	for	for	ADP
ejpam-5911	414	17	every	every	DET
ejpam-5911	414	18	(	(	PUNCT
ejpam-5911	414	19	r	r	NOUN
ejpam-5911	414	20	,	,	PUNCT
ejpam-5911	414	21	s)-f	s)-f	NOUN
ejpam-5911	414	22	-	-	PUNCT
ejpam-5911	414	23	regularly	regularly	ADV
ejpam-5911	414	24	open	open	ADJ
ejpam-5911	414	25	set	set	VERB
ejpam-5911	415	1	n	n	PRON
ejpam-5911	415	2	∈	∈	NOUN
ejpam-5911	416	1	iz	iz	INTJ
ejpam-5911	416	2	.	.	PUNCT
ejpam-5911	417	1	(	(	PUNCT
ejpam-5911	417	2	iii	iii	X
ejpam-5911	417	3	)	)	PUNCT
ejpam-5911	417	4	p−1(n	p−1(n	NOUN
ejpam-5911	417	5	)	)	PUNCT
ejpam-5911	417	6	is	be	AUX
ejpam-5911	417	7	(	(	PUNCT
ejpam-5911	417	8	r	r	NOUN
ejpam-5911	417	9	,	,	PUNCT
ejpam-5911	417	10	s)-f	s)-f	NOUN
ejpam-5911	417	11	-	-	PUNCT
ejpam-5911	417	12	b	b	NOUN
ejpam-5911	417	13	-	-	PUNCT
ejpam-5911	417	14	closed	closed	ADJ
ejpam-5911	417	15	,	,	PUNCT
ejpam-5911	417	16	for	for	SCONJ
ejpam-5911	417	17	every	every	DET
ejpam-5911	417	18	(	(	PUNCT
ejpam-5911	417	19	r	r	NOUN
ejpam-5911	417	20	,	,	PUNCT
ejpam-5911	417	21	s)-f	s)-f	NOUN
ejpam-5911	417	22	-	-	PUNCT
ejpam-5911	417	23	regularly	regularly	ADV
ejpam-5911	417	24	closed	closed	ADJ
ejpam-5911	417	25	set	set	VERB
ejpam-5911	417	26	n	n	PRON
ejpam-5911	417	27	∈	∈	NOUN
ejpam-5911	417	28	iz	iz	INTJ
ejpam-5911	417	29	.	.	PUNCT
ejpam-5911	418	1	(	(	PUNCT
ejpam-5911	418	2	iv	iv	X
ejpam-5911	418	3	)	)	PUNCT
ejpam-5911	418	4	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	418	5	)	)	PUNCT
ejpam-5911	418	6	,	,	PUNCT
ejpam-5911	418	7	r	r	NOUN
ejpam-5911	418	8	,	,	PUNCT
ejpam-5911	418	9	s	s	NOUN
ejpam-5911	418	10	)	)	PUNCT
ejpam-5911	418	11	≤	≤	PUNCT
ejpam-5911	419	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	419	2	,	,	PUNCT
ejpam-5911	419	3	r	r	NOUN
ejpam-5911	419	4	,	,	PUNCT
ejpam-5911	419	5	s	s	NOUN
ejpam-5911	419	6	)	)	PUNCT
ejpam-5911	419	7	)	)	PUNCT
ejpam-5911	419	8	,	,	PUNCT
ejpam-5911	419	9	for	for	ADP
ejpam-5911	419	10	every	every	DET
ejpam-5911	419	11	(	(	PUNCT
ejpam-5911	419	12	r	r	NOUN
ejpam-5911	419	13	,	,	PUNCT
ejpam-5911	419	14	s)-f	s)-f	NOUN
ejpam-5911	419	15	-	-	PUNCT
ejpam-5911	419	16	b	b	NOUN
ejpam-5911	419	17	-	-	PUNCT
ejpam-5911	419	18	open	open	ADJ
ejpam-5911	419	19	set	set	NOUN
ejpam-5911	419	20	n	n	CCONJ
ejpam-5911	419	21	∈	∈	NOUN
ejpam-5911	419	22	iz	iz	INTJ
ejpam-5911	419	23	.	.	PUNCT
ejpam-5911	420	1	(	(	PUNCT
ejpam-5911	420	2	v	v	NOUN
ejpam-5911	420	3	)	)	PUNCT
ejpam-5911	420	4	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	420	5	)	)	PUNCT
ejpam-5911	420	6	,	,	PUNCT
ejpam-5911	420	7	r	r	NOUN
ejpam-5911	420	8	,	,	PUNCT
ejpam-5911	420	9	s	s	NOUN
ejpam-5911	420	10	)	)	PUNCT
ejpam-5911	420	11	≤	≤	PUNCT
ejpam-5911	421	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	421	2	,	,	PUNCT
ejpam-5911	421	3	r	r	NOUN
ejpam-5911	421	4	,	,	PUNCT
ejpam-5911	421	5	s	s	NOUN
ejpam-5911	421	6	)	)	PUNCT
ejpam-5911	421	7	)	)	PUNCT
ejpam-5911	421	8	,	,	PUNCT
ejpam-5911	421	9	for	for	ADP
ejpam-5911	421	10	every	every	DET
ejpam-5911	421	11	(	(	PUNCT
ejpam-5911	421	12	r	r	NOUN
ejpam-5911	421	13	,	,	PUNCT
ejpam-5911	421	14	s)-f	s)-f	NOUN
ejpam-5911	421	15	-	-	PUNCT
ejpam-5911	421	16	semi	semi	ADJ
ejpam-5911	421	17	-	-	ADJ
ejpam-5911	421	18	open	open	ADJ
ejpam-5911	421	19	set	set	ADJ
ejpam-5911	421	20	n	n	CCONJ
ejpam-5911	421	21	∈	∈	NOUN
ejpam-5911	421	22	iz	iz	INTJ
ejpam-5911	421	23	.	.	PUNCT
ejpam-5911	422	1	proof	proof	NOUN
ejpam-5911	422	2	.	.	PUNCT
ejpam-5911	423	1	(	(	PUNCT
ejpam-5911	423	2	i	i	NOUN
ejpam-5911	423	3	)	)	PUNCT
ejpam-5911	423	4	⇒	⇒	PROPN
ejpam-5911	423	5	(	(	PUNCT
ejpam-5911	423	6	ii	ii	NOUN
ejpam-5911	423	7	)	)	PUNCT
ejpam-5911	423	8	let	let	VERB
ejpam-5911	423	9	gθ	gθ	PROPN
ejpam-5911	423	10	∈	∈	PROPN
ejpam-5911	423	11	pθ(g	pθ(g	NOUN
ejpam-5911	423	12	)	)	PUNCT
ejpam-5911	423	13	and	and	CCONJ
ejpam-5911	423	14	n	n	PRON
ejpam-5911	423	15	∈	∈	NOUN
ejpam-5911	423	16	iz	iz	INTJ
ejpam-5911	423	17	be	be	AUX
ejpam-5911	423	18	an	an	DET
ejpam-5911	423	19	(	(	PUNCT
ejpam-5911	423	20	r	r	NOUN
ejpam-5911	423	21	,	,	PUNCT
ejpam-5911	423	22	s)-f	s)-f	NOUN
ejpam-5911	423	23	-	-	PUNCT
ejpam-5911	423	24	regularly	regularly	ADV
ejpam-5911	423	25	open	open	ADJ
ejpam-5911	423	26	set	set	VERB
ejpam-5911	423	27	with	with	ADP
ejpam-5911	423	28	gθ	gθ	PROPN
ejpam-5911	423	29	∈	∈	PROPN
ejpam-5911	423	30	p−1(n	p−1(n	NOUN
ejpam-5911	423	31	)	)	PUNCT
ejpam-5911	423	32	.	.	PUNCT
ejpam-5911	424	1	hence	hence	ADV
ejpam-5911	424	2	,	,	PUNCT
ejpam-5911	424	3	by	by	ADP
ejpam-5911	424	4	(	(	PUNCT
ejpam-5911	424	5	i	i	NOUN
ejpam-5911	424	6	)	)	PUNCT
ejpam-5911	424	7	,	,	PUNCT
ejpam-5911	424	8	there	there	PRON
ejpam-5911	424	9	is	be	VERB
ejpam-5911	424	10	m	m	PROPN
ejpam-5911	424	11	∈	∈	NOUN
ejpam-5911	424	12	ig	ig	PROPN
ejpam-5911	424	13	that	that	PRON
ejpam-5911	424	14	is	be	AUX
ejpam-5911	424	15	(	(	PUNCT
ejpam-5911	424	16	r	r	NOUN
ejpam-5911	424	17	,	,	PUNCT
ejpam-5911	424	18	s)-f	s)-f	NOUN
ejpam-5911	424	19	-	-	PUNCT
ejpam-5911	424	20	b	b	NOUN
ejpam-5911	424	21	-	-	PUNCT
ejpam-5911	424	22	open	open	ADJ
ejpam-5911	424	23	with	with	ADP
ejpam-5911	424	24	gθ	gθ	PROPN
ejpam-5911	424	25	∈	∈	PROPN
ejpam-5911	424	26	m	m	NOUN
ejpam-5911	424	27	and	and	CCONJ
ejpam-5911	424	28	p(m	p(m	NOUN
ejpam-5911	424	29	)	)	PUNCT
ejpam-5911	424	30	≤	≤	NOUN
ejpam-5911	424	31	i𭟋∗(c𭟋∗(n	i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	424	32	,	,	PUNCT
ejpam-5911	424	33	r	r	NOUN
ejpam-5911	424	34	,	,	PUNCT
ejpam-5911	424	35	s	s	PART
ejpam-5911	424	36	)	)	PUNCT
ejpam-5911	424	37	,	,	PUNCT
ejpam-5911	424	38	r	r	NOUN
ejpam-5911	424	39	,	,	PUNCT
ejpam-5911	424	40	s	s	NOUN
ejpam-5911	424	41	)	)	PUNCT
ejpam-5911	424	42	.	.	PUNCT
ejpam-5911	425	1	thus	thus	ADV
ejpam-5911	425	2	,	,	PUNCT
ejpam-5911	425	3	m	m	VERB
ejpam-5911	425	4	≤	≤	ADJ
ejpam-5911	425	5	p−1(i𭟋∗(c𭟋∗(n	p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	425	6	,	,	PUNCT
ejpam-5911	425	7	r	r	NOUN
ejpam-5911	425	8	,	,	PUNCT
ejpam-5911	425	9	s	s	PART
ejpam-5911	425	10	)	)	PUNCT
ejpam-5911	425	11	,	,	PUNCT
ejpam-5911	425	12	r	r	NOUN
ejpam-5911	425	13	,	,	PUNCT
ejpam-5911	425	14	s	s	NOUN
ejpam-5911	425	15	)	)	PUNCT
ejpam-5911	425	16	)	)	PUNCT
ejpam-5911	426	1	=	=	SYM
ejpam-5911	426	2	p−1(n	p−1(n	PROPN
ejpam-5911	426	3	)	)	PUNCT
ejpam-5911	426	4	and	and	CCONJ
ejpam-5911	426	5	gθ	gθ	PROPN
ejpam-5911	426	6	∈	∈	PROPN
ejpam-5911	426	7	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	426	8	)	)	PUNCT
ejpam-5911	426	9	,	,	PUNCT
ejpam-5911	426	10	r	r	NOUN
ejpam-5911	426	11	,	,	PUNCT
ejpam-5911	426	12	s	s	PART
ejpam-5911	426	13	)	)	PUNCT
ejpam-5911	426	14	.	.	PUNCT
ejpam-5911	427	1	therefore	therefore	ADV
ejpam-5911	427	2	,	,	PUNCT
ejpam-5911	427	3	p−1(n	p−1(n	ADV
ejpam-5911	427	4	)	)	PUNCT
ejpam-5911	427	5	≤	≤	NUM
ejpam-5911	427	6	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	427	7	)	)	PUNCT
ejpam-5911	427	8	,	,	PUNCT
ejpam-5911	427	9	r	r	NOUN
ejpam-5911	427	10	,	,	PUNCT
ejpam-5911	427	11	s	s	PART
ejpam-5911	427	12	)	)	PUNCT
ejpam-5911	427	13	,	,	PUNCT
ejpam-5911	427	14	so	so	ADV
ejpam-5911	427	15	p−1(n	p−1(n	VERB
ejpam-5911	427	16	)	)	PUNCT
ejpam-5911	427	17	is	be	AUX
ejpam-5911	427	18	(	(	PUNCT
ejpam-5911	427	19	r	r	NOUN
ejpam-5911	427	20	,	,	PUNCT
ejpam-5911	427	21	s)-f	s)-f	NOUN
ejpam-5911	427	22	-	-	PUNCT
ejpam-5911	427	23	bopen	bopen	NOUN
ejpam-5911	427	24	.	.	PUNCT
ejpam-5911	428	1	(	(	PUNCT
ejpam-5911	428	2	ii	ii	NOUN
ejpam-5911	428	3	)	)	PUNCT
ejpam-5911	428	4	⇒	⇒	NOUN
ejpam-5911	428	5	(	(	PUNCT
ejpam-5911	428	6	iii	iii	X
ejpam-5911	428	7	)	)	PUNCT
ejpam-5911	428	8	if	if	SCONJ
ejpam-5911	428	9	n	n	NUM
ejpam-5911	428	10	∈	∈	NOUN
ejpam-5911	429	1	iz	iz	INTJ
ejpam-5911	429	2	is	be	AUX
ejpam-5911	429	3	(	(	PUNCT
ejpam-5911	429	4	r	r	NOUN
ejpam-5911	429	5	,	,	PUNCT
ejpam-5911	429	6	s)-f	s)-f	NOUN
ejpam-5911	429	7	-	-	PUNCT
ejpam-5911	429	8	regularly	regularly	ADV
ejpam-5911	429	9	closed	close	VERB
ejpam-5911	429	10	,	,	PUNCT
ejpam-5911	429	11	then	then	ADV
ejpam-5911	429	12	by	by	ADP
ejpam-5911	429	13	(	(	PUNCT
ejpam-5911	429	14	ii	ii	NOUN
ejpam-5911	429	15	)	)	PUNCT
ejpam-5911	429	16	,	,	PUNCT
ejpam-5911	429	17	p−1(n	p−1(n	PROPN
ejpam-5911	429	18	c	c	NOUN
ejpam-5911	429	19	)	)	PUNCT
ejpam-5911	429	20	=	=	SYM
ejpam-5911	429	21	(	(	PUNCT
ejpam-5911	429	22	p−1(n	p−1(n	PROPN
ejpam-5911	429	23	)	)	PUNCT
ejpam-5911	429	24	)	)	PUNCT
ejpam-5911	430	1	c	c	NOUN
ejpam-5911	430	2	is	be	AUX
ejpam-5911	430	3	(	(	PUNCT
ejpam-5911	430	4	r	r	NOUN
ejpam-5911	430	5	,	,	PUNCT
ejpam-5911	430	6	s)-f	s)-f	NOUN
ejpam-5911	430	7	-	-	PUNCT
ejpam-5911	430	8	b	b	NOUN
ejpam-5911	430	9	-	-	PUNCT
ejpam-5911	430	10	open	open	ADJ
ejpam-5911	430	11	.	.	PUNCT
ejpam-5911	431	1	thus	thus	ADV
ejpam-5911	431	2	,	,	PUNCT
ejpam-5911	431	3	p−1(n	p−1(n	NOUN
ejpam-5911	431	4	)	)	PUNCT
ejpam-5911	431	5	is	be	AUX
ejpam-5911	431	6	(	(	PUNCT
ejpam-5911	431	7	r	r	NOUN
ejpam-5911	431	8	,	,	PUNCT
ejpam-5911	431	9	s)-f	s)-f	NOUN
ejpam-5911	431	10	-	-	PUNCT
ejpam-5911	431	11	b	b	NOUN
ejpam-5911	431	12	-	-	PUNCT
ejpam-5911	431	13	closed	closed	ADJ
ejpam-5911	431	14	.	.	PUNCT
ejpam-5911	432	1	(	(	PUNCT
ejpam-5911	432	2	iii	iii	X
ejpam-5911	432	3	)	)	PUNCT
ejpam-5911	432	4	⇒	⇒	NOUN
ejpam-5911	432	5	(	(	PUNCT
ejpam-5911	432	6	iv	iv	X
ejpam-5911	432	7	)	)	PUNCT
ejpam-5911	432	8	if	if	SCONJ
ejpam-5911	432	9	n	n	PRON
ejpam-5911	432	10	∈	∈	NOUN
ejpam-5911	433	1	iz	iz	INTJ
ejpam-5911	433	2	is	be	AUX
ejpam-5911	433	3	(	(	PUNCT
ejpam-5911	433	4	r	r	NOUN
ejpam-5911	433	5	,	,	PUNCT
ejpam-5911	433	6	s)-f	s)-f	NOUN
ejpam-5911	433	7	-	-	PUNCT
ejpam-5911	433	8	b	b	NOUN
ejpam-5911	433	9	-	-	PUNCT
ejpam-5911	433	10	open	open	ADJ
ejpam-5911	433	11	and	and	CCONJ
ejpam-5911	433	12	since	since	SCONJ
ejpam-5911	433	13	c𭟋∗(n	c𭟋∗(n	NOUN
ejpam-5911	433	14	,	,	PUNCT
ejpam-5911	433	15	r	r	NOUN
ejpam-5911	433	16	,	,	PUNCT
ejpam-5911	433	17	s	s	PART
ejpam-5911	433	18	)	)	PUNCT
ejpam-5911	433	19	is	be	AUX
ejpam-5911	433	20	(	(	PUNCT
ejpam-5911	433	21	r	r	NOUN
ejpam-5911	433	22	,	,	PUNCT
ejpam-5911	433	23	s)-f	s)-f	NOUN
ejpam-5911	433	24	-	-	PUNCT
ejpam-5911	433	25	regularly	regularly	ADV
ejpam-5911	433	26	closed	close	VERB
ejpam-5911	433	27	,	,	PUNCT
ejpam-5911	433	28	then	then	ADV
ejpam-5911	433	29	by	by	ADP
ejpam-5911	433	30	(	(	PUNCT
ejpam-5911	433	31	iii	iii	NOUN
ejpam-5911	433	32	)	)	PUNCT
ejpam-5911	433	33	,	,	PUNCT
ejpam-5911	433	34	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	433	35	,	,	PUNCT
ejpam-5911	433	36	r	r	NOUN
ejpam-5911	433	37	,	,	PUNCT
ejpam-5911	433	38	s	s	NOUN
ejpam-5911	433	39	)	)	PUNCT
ejpam-5911	433	40	)	)	PUNCT
ejpam-5911	434	1	is	be	AUX
ejpam-5911	434	2	(	(	PUNCT
ejpam-5911	434	3	r	r	NOUN
ejpam-5911	434	4	,	,	PUNCT
ejpam-5911	434	5	s)-f	s)-f	NOUN
ejpam-5911	434	6	-	-	PUNCT
ejpam-5911	434	7	b	b	NOUN
ejpam-5911	434	8	-	-	PUNCT
ejpam-5911	434	9	closed	closed	ADJ
ejpam-5911	434	10	.	.	PUNCT
ejpam-5911	435	1	since	since	SCONJ
ejpam-5911	435	2	p−1(n	p−1(n	NOUN
ejpam-5911	435	3	)	)	PUNCT
ejpam-5911	435	4	≤	≤	PUNCT
ejpam-5911	436	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	436	2	,	,	PUNCT
ejpam-5911	436	3	r	r	NOUN
ejpam-5911	436	4	,	,	PUNCT
ejpam-5911	436	5	s	s	NOUN
ejpam-5911	436	6	)	)	PUNCT
ejpam-5911	436	7	)	)	PUNCT
ejpam-5911	436	8	,	,	PUNCT
ejpam-5911	436	9	hence	hence	ADV
ejpam-5911	436	10	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NUM
ejpam-5911	436	11	)	)	PUNCT
ejpam-5911	436	12	,	,	PUNCT
ejpam-5911	436	13	r	r	NOUN
ejpam-5911	436	14	,	,	PUNCT
ejpam-5911	436	15	s	s	NOUN
ejpam-5911	436	16	)	)	PUNCT
ejpam-5911	436	17	≤	≤	PUNCT
ejpam-5911	437	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	437	2	,	,	PUNCT
ejpam-5911	437	3	r	r	NOUN
ejpam-5911	437	4	,	,	PUNCT
ejpam-5911	437	5	s	s	NOUN
ejpam-5911	437	6	)	)	PUNCT
ejpam-5911	437	7	)	)	PUNCT
ejpam-5911	437	8	.	.	PUNCT
ejpam-5911	438	1	i.	i.	PROPN
ejpam-5911	438	2	m.	m.	PROPN
ejpam-5911	438	3	taha	taha	PROPN
ejpam-5911	438	4	,	,	PUNCT
ejpam-5911	438	5	j.	j.	PROPN
ejpam-5911	438	6	al	al	PROPN
ejpam-5911	438	7	-	-	PUNCT
ejpam-5911	438	8	mufarrij	mufarrij	PROPN
ejpam-5911	438	9	,	,	PUNCT
ejpam-5911	438	10	o.	o.	PROPN
ejpam-5911	438	11	m.	m.	PROPN
ejpam-5911	438	12	taha	taha	PROPN
ejpam-5911	438	13	/	/	PUNCT
ejpam-5911	438	14	eur	eur	PROPN
ejpam-5911	438	15	.	.	PUNCT
ejpam-5911	439	1	j.	j.	PROPN
ejpam-5911	439	2	pure	pure	PROPN
ejpam-5911	439	3	appl	appl	PROPN
ejpam-5911	439	4	.	.	PROPN
ejpam-5911	439	5	math	math	PROPN
ejpam-5911	439	6	,	,	PUNCT
ejpam-5911	439	7	18	18	NUM
ejpam-5911	439	8	(	(	PUNCT
ejpam-5911	439	9	2	2	NUM
ejpam-5911	439	10	)	)	PUNCT
ejpam-5911	439	11	(	(	PUNCT
ejpam-5911	439	12	2025	2025	NUM
ejpam-5911	439	13	)	)	PUNCT
ejpam-5911	439	14	,	,	PUNCT
ejpam-5911	439	15	5911	5911	NUM
ejpam-5911	439	16	16	16	NUM
ejpam-5911	439	17	of	of	ADP
ejpam-5911	439	18	27	27	NUM
ejpam-5911	439	19	(	(	PUNCT
ejpam-5911	439	20	iv	iv	NOUN
ejpam-5911	439	21	)	)	PUNCT
ejpam-5911	439	22	⇒	⇒	NOUN
ejpam-5911	439	23	(	(	PUNCT
ejpam-5911	439	24	v	v	NOUN
ejpam-5911	439	25	)	)	PUNCT
ejpam-5911	439	26	the	the	DET
ejpam-5911	439	27	proof	proof	NOUN
ejpam-5911	439	28	follows	follow	VERB
ejpam-5911	439	29	from	from	ADP
ejpam-5911	439	30	the	the	DET
ejpam-5911	439	31	fact	fact	NOUN
ejpam-5911	439	32	that	that	SCONJ
ejpam-5911	439	33	any	any	DET
ejpam-5911	439	34	(	(	PUNCT
ejpam-5911	439	35	r	r	NOUN
ejpam-5911	439	36	,	,	PUNCT
ejpam-5911	439	37	s)-f	s)-f	NOUN
ejpam-5911	439	38	-	-	PUNCT
ejpam-5911	439	39	semi	semi	ADJ
ejpam-5911	439	40	-	-	ADJ
ejpam-5911	439	41	open	open	ADJ
ejpam-5911	439	42	set	set	NOUN
ejpam-5911	439	43	is	be	AUX
ejpam-5911	439	44	(	(	PUNCT
ejpam-5911	439	45	r	r	NOUN
ejpam-5911	439	46	,	,	PUNCT
ejpam-5911	439	47	s)-fb	s)-fb	NOUN
ejpam-5911	439	48	-	-	PUNCT
ejpam-5911	439	49	open	open	ADJ
ejpam-5911	439	50	.	.	PUNCT
ejpam-5911	440	1	(	(	PUNCT
ejpam-5911	440	2	v	v	NOUN
ejpam-5911	440	3	)	)	PUNCT
ejpam-5911	440	4	⇒	⇒	NOUN
ejpam-5911	440	5	(	(	PUNCT
ejpam-5911	440	6	iii	iii	X
ejpam-5911	440	7	)	)	PUNCT
ejpam-5911	440	8	if	if	SCONJ
ejpam-5911	440	9	n	n	NUM
ejpam-5911	440	10	∈	∈	NOUN
ejpam-5911	441	1	iz	iz	INTJ
ejpam-5911	441	2	is	be	AUX
ejpam-5911	441	3	(	(	PUNCT
ejpam-5911	441	4	r	r	NOUN
ejpam-5911	441	5	,	,	PUNCT
ejpam-5911	441	6	s)-f	s)-f	NOUN
ejpam-5911	441	7	-	-	PUNCT
ejpam-5911	441	8	regularly	regularly	ADV
ejpam-5911	441	9	closed	closed	ADJ
ejpam-5911	441	10	,	,	PUNCT
ejpam-5911	441	11	then	then	ADV
ejpam-5911	441	12	n	n	X
ejpam-5911	441	13	is	be	AUX
ejpam-5911	441	14	(	(	PUNCT
ejpam-5911	441	15	r	r	NOUN
ejpam-5911	441	16	,	,	PUNCT
ejpam-5911	441	17	s)-f	s)-f	NOUN
ejpam-5911	441	18	-	-	PUNCT
ejpam-5911	441	19	semi	semi	ADV
ejpam-5911	441	20	-	-	ADJ
ejpam-5911	441	21	open	open	ADJ
ejpam-5911	441	22	.	.	PUNCT
ejpam-5911	442	1	by	by	ADP
ejpam-5911	442	2	(	(	PUNCT
ejpam-5911	442	3	v	v	NOUN
ejpam-5911	442	4	)	)	PUNCT
ejpam-5911	442	5	,	,	PUNCT
ejpam-5911	442	6	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NUM
ejpam-5911	442	7	)	)	PUNCT
ejpam-5911	442	8	,	,	PUNCT
ejpam-5911	442	9	r	r	NOUN
ejpam-5911	442	10	,	,	PUNCT
ejpam-5911	442	11	s	s	NOUN
ejpam-5911	442	12	)	)	PUNCT
ejpam-5911	442	13	≤	≤	PUNCT
ejpam-5911	443	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	443	2	,	,	PUNCT
ejpam-5911	443	3	r	r	NOUN
ejpam-5911	443	4	,	,	PUNCT
ejpam-5911	443	5	s	s	NOUN
ejpam-5911	443	6	)	)	PUNCT
ejpam-5911	443	7	)	)	PUNCT
ejpam-5911	444	1	=	=	SYM
ejpam-5911	444	2	p−1(n	p−1(n	NOUN
ejpam-5911	444	3	)	)	PUNCT
ejpam-5911	444	4	.	.	PUNCT
ejpam-5911	445	1	hence	hence	ADV
ejpam-5911	445	2	,	,	PUNCT
ejpam-5911	445	3	p−1(n	p−1(n	PROPN
ejpam-5911	445	4	)	)	PUNCT
ejpam-5911	445	5	is	be	AUX
ejpam-5911	445	6	(	(	PUNCT
ejpam-5911	445	7	r	r	NOUN
ejpam-5911	445	8	,	,	PUNCT
ejpam-5911	445	9	s)-f	s)-f	NOUN
ejpam-5911	445	10	-	-	PUNCT
ejpam-5911	445	11	b	b	NOUN
ejpam-5911	445	12	-	-	PUNCT
ejpam-5911	445	13	closed	closed	ADJ
ejpam-5911	445	14	.	.	PUNCT
ejpam-5911	446	1	(	(	PUNCT
ejpam-5911	446	2	iii	iii	X
ejpam-5911	446	3	)	)	PUNCT
ejpam-5911	446	4	⇒	⇒	NOUN
ejpam-5911	446	5	(	(	PUNCT
ejpam-5911	446	6	i	i	NOUN
ejpam-5911	446	7	)	)	PUNCT
ejpam-5911	447	1	if	if	SCONJ
ejpam-5911	447	2	gθ	gθ	PROPN
ejpam-5911	447	3	∈	∈	PROPN
ejpam-5911	447	4	pθ(g	pθ(g	NOUN
ejpam-5911	447	5	)	)	PUNCT
ejpam-5911	447	6	and	and	CCONJ
ejpam-5911	447	7	n	n	PRON
ejpam-5911	447	8	∈	∈	NOUN
ejpam-5911	447	9	iz	iz	INTJ
ejpam-5911	447	10	with	with	ADP
ejpam-5911	447	11	𭟋(n	𭟋(n	PROPN
ejpam-5911	447	12	)	)	PUNCT
ejpam-5911	447	13	≥	≥	PROPN
ejpam-5911	447	14	r	r	NOUN
ejpam-5911	447	15	and	and	CCONJ
ejpam-5911	447	16	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	447	17	)	)	PUNCT
ejpam-5911	447	18	≤	≤	NUM
ejpam-5911	447	19	s	s	VERB
ejpam-5911	447	20	such	such	ADJ
ejpam-5911	447	21	that	that	SCONJ
ejpam-5911	447	22	gθ	gθ	PROPN
ejpam-5911	447	23	∈	∈	PROPN
ejpam-5911	447	24	p−1(n	p−1(n	NOUN
ejpam-5911	447	25	)	)	PUNCT
ejpam-5911	447	26	,	,	PUNCT
ejpam-5911	447	27	and	and	CCONJ
ejpam-5911	447	28	then	then	ADV
ejpam-5911	447	29	gθ	gθ	PROPN
ejpam-5911	447	30	∈	∈	PROPN
ejpam-5911	447	31	p−1(i𭟋∗(c𭟋∗(n	p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	447	32	,	,	PUNCT
ejpam-5911	447	33	r	r	NOUN
ejpam-5911	447	34	,	,	PUNCT
ejpam-5911	447	35	s	s	PART
ejpam-5911	447	36	)	)	PUNCT
ejpam-5911	447	37	,	,	PUNCT
ejpam-5911	447	38	r	r	NOUN
ejpam-5911	447	39	,	,	PUNCT
ejpam-5911	447	40	s	s	NOUN
ejpam-5911	447	41	)	)	PUNCT
ejpam-5911	447	42	)	)	PUNCT
ejpam-5911	447	43	.	.	PUNCT
ejpam-5911	448	1	since	since	SCONJ
ejpam-5911	448	2	[	[	X
ejpam-5911	448	3	i𭟋∗(c𭟋∗(n	i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	448	4	,	,	PUNCT
ejpam-5911	448	5	r	r	NOUN
ejpam-5911	448	6	,	,	PUNCT
ejpam-5911	448	7	s	s	PART
ejpam-5911	448	8	)	)	PUNCT
ejpam-5911	448	9	,	,	PUNCT
ejpam-5911	448	10	r	r	NOUN
ejpam-5911	448	11	,	,	PUNCT
ejpam-5911	448	12	s)]c	s)]c	NOUN
ejpam-5911	448	13	is	be	AUX
ejpam-5911	448	14	(	(	PUNCT
ejpam-5911	448	15	r	r	NOUN
ejpam-5911	448	16	,	,	PUNCT
ejpam-5911	448	17	s)f	s)f	NOUN
ejpam-5911	448	18	-	-	PUNCT
ejpam-5911	448	19	regularly	regularly	ADV
ejpam-5911	448	20	closed	close	VERB
ejpam-5911	448	21	,	,	PUNCT
ejpam-5911	448	22	then	then	ADV
ejpam-5911	448	23	by	by	ADP
ejpam-5911	448	24	(	(	PUNCT
ejpam-5911	448	25	iii	iii	NOUN
ejpam-5911	448	26	)	)	PUNCT
ejpam-5911	448	27	,	,	PUNCT
ejpam-5911	448	28	we	we	PRON
ejpam-5911	448	29	have	have	VERB
ejpam-5911	448	30	p−1([i𭟋∗(c𭟋∗(n	p−1([i𭟋∗(c𭟋∗(n	PROPN
ejpam-5911	448	31	,	,	PUNCT
ejpam-5911	448	32	r	r	NOUN
ejpam-5911	448	33	,	,	PUNCT
ejpam-5911	448	34	s	s	PART
ejpam-5911	448	35	)	)	PUNCT
ejpam-5911	448	36	,	,	PUNCT
ejpam-5911	448	37	r	r	NOUN
ejpam-5911	448	38	,	,	PUNCT
ejpam-5911	448	39	s)]c	s)]c	NOUN
ejpam-5911	448	40	)	)	PUNCT
ejpam-5911	448	41	is	be	AUX
ejpam-5911	448	42	(	(	PUNCT
ejpam-5911	448	43	r	r	NOUN
ejpam-5911	448	44	,	,	PUNCT
ejpam-5911	448	45	s)-f	s)-f	NOUN
ejpam-5911	448	46	-	-	PUNCT
ejpam-5911	448	47	b	b	NOUN
ejpam-5911	448	48	-	-	PUNCT
ejpam-5911	448	49	closed	closed	ADJ
ejpam-5911	448	50	.	.	PUNCT
ejpam-5911	449	1	hence	hence	ADV
ejpam-5911	449	2	,	,	PUNCT
ejpam-5911	449	3	p−1(i𭟋∗(c𭟋∗(n	p−1(i𭟋∗(c𭟋∗(n	PROPN
ejpam-5911	449	4	)	)	PUNCT
ejpam-5911	449	5	,	,	PUNCT
ejpam-5911	449	6	r	r	NOUN
ejpam-5911	449	7	,	,	PUNCT
ejpam-5911	449	8	s	s	NOUN
ejpam-5911	449	9	)	)	PUNCT
ejpam-5911	449	10	)	)	PUNCT
ejpam-5911	449	11	is	be	AUX
ejpam-5911	449	12	(	(	PUNCT
ejpam-5911	449	13	r	r	NOUN
ejpam-5911	449	14	,	,	PUNCT
ejpam-5911	449	15	s)-f	s)-f	NOUN
ejpam-5911	449	16	-	-	PUNCT
ejpam-5911	449	17	b	b	NOUN
ejpam-5911	449	18	-	-	PUNCT
ejpam-5911	449	19	open	open	ADJ
ejpam-5911	449	20	and	and	CCONJ
ejpam-5911	449	21	gθ	gθ	PROPN
ejpam-5911	449	22	∈	∈	PROPN
ejpam-5911	449	23	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	449	24	,	,	PUNCT
ejpam-5911	449	25	r	r	NOUN
ejpam-5911	449	26	,	,	PUNCT
ejpam-5911	449	27	s	s	PART
ejpam-5911	449	28	)	)	PUNCT
ejpam-5911	449	29	,	,	PUNCT
ejpam-5911	449	30	r	r	NOUN
ejpam-5911	449	31	,	,	PUNCT
ejpam-5911	449	32	s	s	NOUN
ejpam-5911	449	33	)	)	PUNCT
ejpam-5911	449	34	)	)	PUNCT
ejpam-5911	449	35	,	,	PUNCT
ejpam-5911	449	36	r	r	NOUN
ejpam-5911	449	37	,	,	PUNCT
ejpam-5911	449	38	s	s	NOUN
ejpam-5911	449	39	)	)	PUNCT
ejpam-5911	449	40	.	.	PUNCT
ejpam-5911	450	1	thus	thus	ADV
ejpam-5911	450	2	,	,	PUNCT
ejpam-5911	450	3	p−1(n	p−1(n	ADV
ejpam-5911	450	4	)	)	PUNCT
ejpam-5911	450	5	≤	≤	NOUN
ejpam-5911	450	6	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	biℑ∗(p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	450	7	,	,	PUNCT
ejpam-5911	450	8	r	r	NOUN
ejpam-5911	450	9	,	,	PUNCT
ejpam-5911	450	10	s	s	PART
ejpam-5911	450	11	)	)	PUNCT
ejpam-5911	450	12	,	,	PUNCT
ejpam-5911	450	13	r	r	NOUN
ejpam-5911	450	14	,	,	PUNCT
ejpam-5911	450	15	s	s	NOUN
ejpam-5911	450	16	)	)	PUNCT
ejpam-5911	450	17	)	)	PUNCT
ejpam-5911	450	18	,	,	PUNCT
ejpam-5911	450	19	r	r	NOUN
ejpam-5911	450	20	,	,	PUNCT
ejpam-5911	450	21	s	s	PART
ejpam-5911	450	22	)	)	PUNCT
ejpam-5911	450	23	.	.	PUNCT
ejpam-5911	451	1	therefore	therefore	ADV
ejpam-5911	451	2	,	,	PUNCT
ejpam-5911	451	3	p	p	NOUN
ejpam-5911	451	4	is	be	AUX
ejpam-5911	451	5	df	df	NOUN
ejpam-5911	451	6	-	-	PUNCT
ejpam-5911	451	7	almost	almost	ADV
ejpam-5911	451	8	b	b	NOUN
ejpam-5911	451	9	-	-	PUNCT
ejpam-5911	451	10	continuous	continuous	ADJ
ejpam-5911	451	11	.	.	PUNCT
ejpam-5911	452	1	definition	definition	NOUN
ejpam-5911	452	2	13	13	NUM
ejpam-5911	452	3	.	.	PUNCT
ejpam-5911	453	1	an	an	DET
ejpam-5911	453	2	f	f	X
ejpam-5911	453	3	-	-	PUNCT
ejpam-5911	453	4	mapping	mapping	NOUN
ejpam-5911	453	5	p	p	NOUN
ejpam-5911	453	6	:	:	PUNCT
ejpam-5911	453	7	(	(	PUNCT
ejpam-5911	453	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	453	9	)	)	PUNCT
ejpam-5911	454	1	−→	−→	NOUN
ejpam-5911	454	2	(	(	PUNCT
ejpam-5911	454	3	z	z	NOUN
ejpam-5911	454	4	,	,	PUNCT
ejpam-5911	454	5	𭟋	𭟋	NOUN
ejpam-5911	454	6	,	,	PUNCT
ejpam-5911	454	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	454	8	)	)	PUNCT
ejpam-5911	454	9	is	be	AUX
ejpam-5911	454	10	called	call	VERB
ejpam-5911	454	11	df	df	NOUN
ejpam-5911	454	12	-	-	PUNCT
ejpam-5911	454	13	weakly	weakly	ADV
ejpam-5911	454	14	bcontinuous	bcontinuous	ADJ
ejpam-5911	454	15	if	if	SCONJ
ejpam-5911	454	16	p−1(n	p−1(n	NOUN
ejpam-5911	454	17	)	)	PUNCT
ejpam-5911	454	18	≤	≤	NUM
ejpam-5911	454	19	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	SYM
ejpam-5911	454	20	,	,	PUNCT
ejpam-5911	454	21	r	r	NOUN
ejpam-5911	454	22	,	,	PUNCT
ejpam-5911	454	23	s	s	NOUN
ejpam-5911	454	24	)	)	PUNCT
ejpam-5911	454	25	)	)	PUNCT
ejpam-5911	454	26	,	,	PUNCT
ejpam-5911	454	27	r	r	NOUN
ejpam-5911	454	28	,	,	PUNCT
ejpam-5911	454	29	s	s	PART
ejpam-5911	454	30	)	)	PUNCT
ejpam-5911	454	31	,	,	PUNCT
ejpam-5911	454	32	for	for	ADP
ejpam-5911	454	33	every	every	DET
ejpam-5911	454	34	n	n	NOUN
ejpam-5911	454	35	∈	∈	NOUN
ejpam-5911	454	36	iz	iz	INTJ
ejpam-5911	454	37	with	with	ADP
ejpam-5911	454	38	𭟋(n	𭟋(n	PROPN
ejpam-5911	454	39	)	)	PUNCT
ejpam-5911	454	40	≥	≥	PROPN
ejpam-5911	454	41	r	r	NOUN
ejpam-5911	454	42	and	and	CCONJ
ejpam-5911	454	43	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	454	44	)	)	PUNCT
ejpam-5911	454	45	≤	≤	NUM
ejpam-5911	454	46	s.	s.	PROPN
ejpam-5911	454	47	lemma	lemma	PROPN
ejpam-5911	455	1	4	4	X
ejpam-5911	455	2	.	.	PUNCT
ejpam-5911	456	1	every	every	DET
ejpam-5911	456	2	df	df	PROPN
ejpam-5911	456	3	-	-	PUNCT
ejpam-5911	456	4	b	b	NOUN
ejpam-5911	456	5	-	-	PUNCT
ejpam-5911	456	6	continuous	continuous	ADJ
ejpam-5911	456	7	mapping	mapping	NOUN
ejpam-5911	456	8	is	be	AUX
ejpam-5911	456	9	df	df	NOUN
ejpam-5911	456	10	-	-	PUNCT
ejpam-5911	456	11	weakly	weakly	ADJ
ejpam-5911	456	12	b	b	NOUN
ejpam-5911	456	13	-	-	PUNCT
ejpam-5911	456	14	continuous	continuous	ADJ
ejpam-5911	456	15	.	.	PUNCT
ejpam-5911	457	1	proof	proof	NOUN
ejpam-5911	457	2	.	.	PUNCT
ejpam-5911	458	1	the	the	DET
ejpam-5911	458	2	proof	proof	NOUN
ejpam-5911	458	3	follows	follow	VERB
ejpam-5911	458	4	by	by	ADP
ejpam-5911	458	5	definitions	definition	NOUN
ejpam-5911	458	6	10	10	NUM
ejpam-5911	458	7	and	and	CCONJ
ejpam-5911	458	8	13	13	NUM
ejpam-5911	458	9	.	.	PUNCT
ejpam-5911	458	10	remark	remark	PROPN
ejpam-5911	458	11	8	8	NUM
ejpam-5911	458	12	.	.	PUNCT
ejpam-5911	459	1	the	the	DET
ejpam-5911	459	2	converse	converse	NOUN
ejpam-5911	459	3	of	of	ADP
ejpam-5911	459	4	lemma	lemma	PROPN
ejpam-5911	459	5	4	4	NUM
ejpam-5911	459	6	fails	fail	VERB
ejpam-5911	459	7	as	as	ADP
ejpam-5911	459	8	example	example	NOUN
ejpam-5911	459	9	9	9	NUM
ejpam-5911	459	10	will	will	AUX
ejpam-5911	459	11	show	show	VERB
ejpam-5911	459	12	.	.	PUNCT
ejpam-5911	460	1	example	example	NOUN
ejpam-5911	461	1	9	9	NUM
ejpam-5911	461	2	.	.	PUNCT
ejpam-5911	462	1	let	let	VERB
ejpam-5911	462	2	g	g	NOUN
ejpam-5911	462	3	=	=	SYM
ejpam-5911	462	4	{	{	PUNCT
ejpam-5911	462	5	g1	g1	PROPN
ejpam-5911	462	6	,	,	PUNCT
ejpam-5911	462	7	g2	g2	PROPN
ejpam-5911	462	8	,	,	PUNCT
ejpam-5911	462	9	g3	g3	PROPN
ejpam-5911	462	10	}	}	PUNCT
ejpam-5911	462	11	and	and	CCONJ
ejpam-5911	462	12	define	define	VERB
ejpam-5911	462	13	m	m	PROPN
ejpam-5911	462	14	,	,	PUNCT
ejpam-5911	462	15	n	n	CCONJ
ejpam-5911	462	16	,	,	PUNCT
ejpam-5911	462	17	u	u	PROPN
ejpam-5911	462	18	∈	∈	PROPN
ejpam-5911	462	19	ig	ig	PROPN
ejpam-5911	462	20	as	as	SCONJ
ejpam-5911	462	21	follows	follow	VERB
ejpam-5911	462	22	:	:	PUNCT
ejpam-5911	462	23	m	m	VERB
ejpam-5911	462	24	=	=	PUNCT
ejpam-5911	462	25	{	{	PUNCT
ejpam-5911	462	26	g1	g1	PROPN
ejpam-5911	462	27	0.4	0.4	NUM
ejpam-5911	462	28	,	,	PUNCT
ejpam-5911	462	29	g2	g2	PROPN
ejpam-5911	462	30	0.2	0.2	NUM
ejpam-5911	462	31	,	,	PUNCT
ejpam-5911	462	32	g3	g3	PROPN
ejpam-5911	462	33	0.4	0.4	NUM
ejpam-5911	462	34	}	}	PUNCT
ejpam-5911	462	35	,	,	PUNCT
ejpam-5911	462	36	n	n	NOUN
ejpam-5911	462	37	=	=	PRON
ejpam-5911	462	38	{	{	PUNCT
ejpam-5911	462	39	g1	g1	PROPN
ejpam-5911	462	40	0.5	0.5	NUM
ejpam-5911	462	41	,	,	PUNCT
ejpam-5911	462	42	g2	g2	PROPN
ejpam-5911	462	43	0.5	0.5	NUM
ejpam-5911	462	44	,	,	PUNCT
ejpam-5911	462	45	g3	g3	NOUN
ejpam-5911	462	46	0.4	0.4	NUM
ejpam-5911	462	47	}	}	PUNCT
ejpam-5911	462	48	,	,	PUNCT
ejpam-5911	462	49	u	u	NOUN
ejpam-5911	462	50	=	=	PUNCT
ejpam-5911	462	51	{	{	PUNCT
ejpam-5911	462	52	g1	g1	PROPN
ejpam-5911	462	53	0.3	0.3	NUM
ejpam-5911	462	54	,	,	PUNCT
ejpam-5911	462	55	g2	g2	PROPN
ejpam-5911	462	56	0.2	0.2	NUM
ejpam-5911	462	57	,	,	PUNCT
ejpam-5911	462	58	g3	g3	X
ejpam-5911	462	59	0.6	0.6	NUM
ejpam-5911	462	60	}	}	PUNCT
ejpam-5911	462	61	.	.	PUNCT
ejpam-5911	463	1	define	define	VERB
ejpam-5911	463	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	463	3	,	,	PUNCT
ejpam-5911	463	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	463	5	:	:	PUNCT
ejpam-5911	463	6	ig	ig	PROPN
ejpam-5911	463	7	−→	−→	NOUN
ejpam-5911	464	1	i	i	PRON
ejpam-5911	464	2	as	as	SCONJ
ejpam-5911	464	3	follows	follow	VERB
ejpam-5911	464	4	:	:	PUNCT
ejpam-5911	464	5	ℑ(v	ℑ(v	X
ejpam-5911	464	6	)	)	PUNCT
ejpam-5911	464	7	=	=	PUNCT
ejpam-5911	464	8			NOUN
ejpam-5911	464	9	1	1	NUM
ejpam-5911	464	10	,	,	PUNCT
ejpam-5911	464	11	if	if	SCONJ
ejpam-5911	464	12	v	v	ADP
ejpam-5911	464	13	∈	∈	NOUN
ejpam-5911	464	14	{	{	PUNCT
ejpam-5911	464	15	1	1	NUM
ejpam-5911	464	16	,	,	PUNCT
ejpam-5911	464	17	0	0	NUM
ejpam-5911	464	18	}	}	PUNCT
ejpam-5911	464	19	,	,	PUNCT
ejpam-5911	464	20	1	1	NUM
ejpam-5911	464	21	3	3	NUM
ejpam-5911	464	22	,	,	PUNCT
ejpam-5911	464	23	if	if	SCONJ
ejpam-5911	464	24	v	v	ADP
ejpam-5911	464	25	=	=	SYM
ejpam-5911	464	26	m	m	NOUN
ejpam-5911	464	27	,	,	PUNCT
ejpam-5911	464	28	1	1	NUM
ejpam-5911	464	29	2	2	NUM
ejpam-5911	464	30	,	,	PUNCT
ejpam-5911	464	31	if	if	SCONJ
ejpam-5911	464	32	v	v	VERB
ejpam-5911	464	33	=	=	SYM
ejpam-5911	464	34	n	n	NOUN
ejpam-5911	464	35	,	,	PUNCT
ejpam-5911	464	36	0	0	NUM
ejpam-5911	464	37	,	,	PUNCT
ejpam-5911	464	38	otherwise	otherwise	ADV
ejpam-5911	464	39	,	,	PUNCT
ejpam-5911	464	40	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	464	41	)	)	PUNCT
ejpam-5911	464	42	=	=	PUNCT
ejpam-5911	465	1			NOUN
ejpam-5911	465	2	0	0	NUM
ejpam-5911	465	3	,	,	PUNCT
ejpam-5911	465	4	if	if	SCONJ
ejpam-5911	465	5	v	v	ADP
ejpam-5911	465	6	∈	∈	NOUN
ejpam-5911	465	7	{	{	PUNCT
ejpam-5911	465	8	1	1	NUM
ejpam-5911	465	9	,	,	PUNCT
ejpam-5911	465	10	0	0	NUM
ejpam-5911	465	11	}	}	PUNCT
ejpam-5911	465	12	,	,	PUNCT
ejpam-5911	465	13	1	1	NUM
ejpam-5911	465	14	3	3	NUM
ejpam-5911	465	15	,	,	PUNCT
ejpam-5911	465	16	if	if	SCONJ
ejpam-5911	465	17	v	v	ADP
ejpam-5911	465	18	=	=	SYM
ejpam-5911	465	19	m	m	NOUN
ejpam-5911	465	20	,	,	PUNCT
ejpam-5911	465	21	1	1	NUM
ejpam-5911	465	22	2	2	NUM
ejpam-5911	465	23	,	,	PUNCT
ejpam-5911	465	24	if	if	SCONJ
ejpam-5911	465	25	v	v	VERB
ejpam-5911	465	26	=	=	SYM
ejpam-5911	465	27	n	n	NOUN
ejpam-5911	465	28	,	,	PUNCT
ejpam-5911	465	29	1	1	NUM
ejpam-5911	465	30	,	,	PUNCT
ejpam-5911	465	31	otherwise	otherwise	ADV
ejpam-5911	465	32	,	,	PUNCT
ejpam-5911	465	33	𭟋(v	𭟋(v	NOUN
ejpam-5911	465	34	)	)	PUNCT
ejpam-5911	465	35	=	=	SYM
ejpam-5911	466	1			NOUN
ejpam-5911	466	2	1	1	NUM
ejpam-5911	466	3	,	,	PUNCT
ejpam-5911	466	4	if	if	SCONJ
ejpam-5911	466	5	v	v	ADP
ejpam-5911	466	6	∈	∈	NOUN
ejpam-5911	466	7	{	{	PUNCT
ejpam-5911	466	8	1	1	NUM
ejpam-5911	466	9	,	,	PUNCT
ejpam-5911	466	10	0	0	NUM
ejpam-5911	466	11	}	}	PUNCT
ejpam-5911	466	12	,	,	PUNCT
ejpam-5911	466	13	1	1	NUM
ejpam-5911	466	14	3	3	NUM
ejpam-5911	466	15	,	,	PUNCT
ejpam-5911	466	16	if	if	SCONJ
ejpam-5911	466	17	v	v	ADP
ejpam-5911	466	18	=	=	SYM
ejpam-5911	466	19	u	u	NOUN
ejpam-5911	466	20	,	,	PUNCT
ejpam-5911	466	21	0	0	NUM
ejpam-5911	466	22	,	,	PUNCT
ejpam-5911	466	23	otherwise	otherwise	ADV
ejpam-5911	466	24	,	,	PUNCT
ejpam-5911	466	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	466	26	)	)	PUNCT
ejpam-5911	467	1	=	=	PUNCT
ejpam-5911	468	1			NOUN
ejpam-5911	468	2	0	0	NUM
ejpam-5911	468	3	,	,	PUNCT
ejpam-5911	468	4	if	if	SCONJ
ejpam-5911	468	5	v	v	ADP
ejpam-5911	468	6	∈	∈	NOUN
ejpam-5911	468	7	{	{	PUNCT
ejpam-5911	468	8	1	1	NUM
ejpam-5911	468	9	,	,	PUNCT
ejpam-5911	468	10	0	0	NUM
ejpam-5911	468	11	}	}	PUNCT
ejpam-5911	468	12	,	,	PUNCT
ejpam-5911	468	13	1	1	NUM
ejpam-5911	468	14	2	2	NUM
ejpam-5911	468	15	,	,	PUNCT
ejpam-5911	468	16	if	if	SCONJ
ejpam-5911	468	17	v	v	ADP
ejpam-5911	468	18	=	=	SYM
ejpam-5911	468	19	u	u	NOUN
ejpam-5911	468	20	,	,	PUNCT
ejpam-5911	468	21	1	1	NUM
ejpam-5911	468	22	,	,	PUNCT
ejpam-5911	468	23	otherwise	otherwise	ADV
ejpam-5911	468	24	.	.	PUNCT
ejpam-5911	469	1	thus	thus	ADV
ejpam-5911	469	2	,	,	PUNCT
ejpam-5911	469	3	the	the	DET
ejpam-5911	469	4	identity	identity	NOUN
ejpam-5911	469	5	f	f	NOUN
ejpam-5911	469	6	-	-	PUNCT
ejpam-5911	469	7	mapping	mapping	NOUN
ejpam-5911	469	8	p	p	NOUN
ejpam-5911	469	9	:	:	PUNCT
ejpam-5911	469	10	(	(	PUNCT
ejpam-5911	469	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	469	12	)	)	PUNCT
ejpam-5911	469	13	−→	−→	NOUN
ejpam-5911	469	14	(	(	PUNCT
ejpam-5911	469	15	g	g	NOUN
ejpam-5911	469	16	,	,	PUNCT
ejpam-5911	469	17	𭟋	𭟋	NOUN
ejpam-5911	469	18	,	,	PUNCT
ejpam-5911	469	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	469	20	)	)	PUNCT
ejpam-5911	469	21	isdf	isdf	NOUN
ejpam-5911	469	22	-	-	PUNCT
ejpam-5911	469	23	weakly	weakly	ADJ
ejpam-5911	469	24	b	b	NOUN
ejpam-5911	469	25	-	-	ADJ
ejpam-5911	469	26	continuous	continuous	ADJ
ejpam-5911	469	27	,	,	PUNCT
ejpam-5911	469	28	but	but	CCONJ
ejpam-5911	469	29	it	it	PRON
ejpam-5911	469	30	is	be	AUX
ejpam-5911	469	31	not	not	PART
ejpam-5911	469	32	df	df	NOUN
ejpam-5911	469	33	-	-	PUNCT
ejpam-5911	469	34	b	b	NOUN
ejpam-5911	469	35	-	-	PUNCT
ejpam-5911	469	36	continuous	continuous	ADJ
ejpam-5911	469	37	.	.	PUNCT
ejpam-5911	470	1	i.	i.	PROPN
ejpam-5911	470	2	m.	m.	PROPN
ejpam-5911	470	3	taha	taha	PROPN
ejpam-5911	470	4	,	,	PUNCT
ejpam-5911	470	5	j.	j.	PROPN
ejpam-5911	470	6	al	al	PROPN
ejpam-5911	470	7	-	-	PUNCT
ejpam-5911	470	8	mufarrij	mufarrij	PROPN
ejpam-5911	470	9	,	,	PUNCT
ejpam-5911	470	10	o.	o.	PROPN
ejpam-5911	470	11	m.	m.	PROPN
ejpam-5911	470	12	taha	taha	PROPN
ejpam-5911	470	13	/	/	PUNCT
ejpam-5911	470	14	eur	eur	PROPN
ejpam-5911	470	15	.	.	PUNCT
ejpam-5911	471	1	j.	j.	PROPN
ejpam-5911	471	2	pure	pure	PROPN
ejpam-5911	471	3	appl	appl	PROPN
ejpam-5911	471	4	.	.	PROPN
ejpam-5911	471	5	math	math	PROPN
ejpam-5911	471	6	,	,	PUNCT
ejpam-5911	471	7	18	18	NUM
ejpam-5911	471	8	(	(	PUNCT
ejpam-5911	471	9	2	2	NUM
ejpam-5911	471	10	)	)	PUNCT
ejpam-5911	471	11	(	(	PUNCT
ejpam-5911	471	12	2025	2025	NUM
ejpam-5911	471	13	)	)	PUNCT
ejpam-5911	471	14	,	,	PUNCT
ejpam-5911	471	15	5911	5911	NUM
ejpam-5911	471	16	17	17	NUM
ejpam-5911	471	17	of	of	ADP
ejpam-5911	471	18	27	27	NUM
ejpam-5911	471	19	theorem	theorem	NOUN
ejpam-5911	471	20	8	8	NUM
ejpam-5911	471	21	.	.	PUNCT
ejpam-5911	472	1	an	an	DET
ejpam-5911	472	2	f	f	X
ejpam-5911	472	3	-	-	PUNCT
ejpam-5911	472	4	mapping	mapping	NOUN
ejpam-5911	472	5	p	p	NOUN
ejpam-5911	472	6	:	:	PUNCT
ejpam-5911	472	7	(	(	PUNCT
ejpam-5911	472	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	472	9	)	)	PUNCT
ejpam-5911	473	1	−→	−→	NOUN
ejpam-5911	473	2	(	(	PUNCT
ejpam-5911	473	3	z	z	NOUN
ejpam-5911	473	4	,	,	PUNCT
ejpam-5911	473	5	𭟋	𭟋	NOUN
ejpam-5911	473	6	,	,	PUNCT
ejpam-5911	473	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	473	8	)	)	PUNCT
ejpam-5911	473	9	is	be	AUX
ejpam-5911	473	10	df	df	NOUN
ejpam-5911	473	11	-	-	PUNCT
ejpam-5911	473	12	weakly	weakly	ADJ
ejpam-5911	473	13	b	b	NOUN
ejpam-5911	473	14	-	-	PUNCT
ejpam-5911	473	15	continuous	continuous	ADJ
ejpam-5911	473	16	iff	iff	PROPN
ejpam-5911	473	17	for	for	ADP
ejpam-5911	473	18	any	any	DET
ejpam-5911	473	19	gθ	gθ	PROPN
ejpam-5911	473	20	∈	∈	PROPN
ejpam-5911	473	21	pθ(g	pθ(g	NOUN
ejpam-5911	473	22	)	)	PUNCT
ejpam-5911	473	23	and	and	CCONJ
ejpam-5911	473	24	any	any	DET
ejpam-5911	473	25	n	n	NOUN
ejpam-5911	473	26	∈	∈	NOUN
ejpam-5911	473	27	iz	iz	INTJ
ejpam-5911	473	28	with	with	ADP
ejpam-5911	473	29	𭟋(n	𭟋(n	PROPN
ejpam-5911	473	30	)	)	PUNCT
ejpam-5911	474	1	≥	≥	PROPN
ejpam-5911	475	1	r	r	NOUN
ejpam-5911	475	2	and	and	CCONJ
ejpam-5911	475	3	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	475	4	)	)	PUNCT
ejpam-5911	475	5	≤	≤	NUM
ejpam-5911	475	6	s	s	AUX
ejpam-5911	475	7	containing	contain	VERB
ejpam-5911	475	8	p(gθ	p(gθ	PROPN
ejpam-5911	475	9	)	)	PUNCT
ejpam-5911	475	10	,	,	PUNCT
ejpam-5911	475	11	there	there	PRON
ejpam-5911	475	12	is	be	VERB
ejpam-5911	475	13	m	m	PROPN
ejpam-5911	475	14	∈	∈	NOUN
ejpam-5911	475	15	ig	ig	PROPN
ejpam-5911	475	16	that	that	PRON
ejpam-5911	475	17	is	be	AUX
ejpam-5911	475	18	(	(	PUNCT
ejpam-5911	475	19	r	r	NOUN
ejpam-5911	475	20	,	,	PUNCT
ejpam-5911	475	21	s)-f	s)-f	NOUN
ejpam-5911	475	22	-	-	PUNCT
ejpam-5911	475	23	b	b	NOUN
ejpam-5911	475	24	-	-	PUNCT
ejpam-5911	475	25	open	open	ADJ
ejpam-5911	475	26	containing	contain	VERB
ejpam-5911	475	27	gθ	gθ	NOUN
ejpam-5911	475	28	with	with	ADP
ejpam-5911	475	29	p(m	p(m	NOUN
ejpam-5911	475	30	)	)	PUNCT
ejpam-5911	475	31	≤	≤	NOUN
ejpam-5911	475	32	c𭟋∗(n	c𭟋∗(n	NOUN
ejpam-5911	475	33	,	,	PUNCT
ejpam-5911	475	34	r	r	NOUN
ejpam-5911	475	35	,	,	PUNCT
ejpam-5911	475	36	s	s	NOUN
ejpam-5911	475	37	)	)	PUNCT
ejpam-5911	475	38	.	.	PUNCT
ejpam-5911	476	1	proof	proof	NOUN
ejpam-5911	476	2	.	.	PUNCT
ejpam-5911	477	1	(	(	PUNCT
ejpam-5911	477	2	⇒	⇒	PROPN
ejpam-5911	477	3	)	)	PUNCT
ejpam-5911	477	4	let	let	VERB
ejpam-5911	477	5	gθ	gθ	PROPN
ejpam-5911	477	6	∈	∈	PROPN
ejpam-5911	477	7	pθ(g	pθ(g	NOUN
ejpam-5911	477	8	)	)	PUNCT
ejpam-5911	477	9	and	and	CCONJ
ejpam-5911	477	10	n	n	PRON
ejpam-5911	477	11	∈	∈	NOUN
ejpam-5911	477	12	iz	iz	INTJ
ejpam-5911	477	13	with	with	ADP
ejpam-5911	477	14	𭟋(n	𭟋(n	PROPN
ejpam-5911	477	15	)	)	PUNCT
ejpam-5911	477	16	≥	≥	PROPN
ejpam-5911	477	17	r	r	NOUN
ejpam-5911	477	18	and	and	CCONJ
ejpam-5911	477	19	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	477	20	)	)	PUNCT
ejpam-5911	477	21	≤	≤	NUM
ejpam-5911	477	22	s	s	AUX
ejpam-5911	477	23	containing	contain	VERB
ejpam-5911	477	24	p(gθ	p(gθ	PROPN
ejpam-5911	477	25	)	)	PUNCT
ejpam-5911	477	26	,	,	PUNCT
ejpam-5911	477	27	and	and	CCONJ
ejpam-5911	477	28	then	then	ADV
ejpam-5911	477	29	p−1(n	p−1(n	PROPN
ejpam-5911	477	30	)	)	PUNCT
ejpam-5911	477	31	≤	≤	NUM
ejpam-5911	477	32	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	SYM
ejpam-5911	477	33	,	,	PUNCT
ejpam-5911	477	34	r	r	NOUN
ejpam-5911	477	35	,	,	PUNCT
ejpam-5911	477	36	s	s	NOUN
ejpam-5911	477	37	)	)	PUNCT
ejpam-5911	477	38	)	)	PUNCT
ejpam-5911	477	39	,	,	PUNCT
ejpam-5911	477	40	r	r	NOUN
ejpam-5911	477	41	,	,	PUNCT
ejpam-5911	477	42	s	s	NOUN
ejpam-5911	477	43	)	)	PUNCT
ejpam-5911	477	44	.	.	PUNCT
ejpam-5911	478	1	since	since	SCONJ
ejpam-5911	478	2	gθ	gθ	PROPN
ejpam-5911	478	3	∈	∈	PROPN
ejpam-5911	478	4	p−1(n	p−1(n	NOUN
ejpam-5911	478	5	)	)	PUNCT
ejpam-5911	478	6	,	,	PUNCT
ejpam-5911	478	7	then	then	ADV
ejpam-5911	478	8	gθ	gθ	PROPN
ejpam-5911	478	9	∈	∈	PROPN
ejpam-5911	478	10	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	X
ejpam-5911	478	11	,	,	PUNCT
ejpam-5911	478	12	r	r	NOUN
ejpam-5911	478	13	,	,	PUNCT
ejpam-5911	478	14	s	s	NOUN
ejpam-5911	478	15	)	)	PUNCT
ejpam-5911	478	16	)	)	PUNCT
ejpam-5911	478	17	,	,	PUNCT
ejpam-5911	478	18	r	r	NOUN
ejpam-5911	478	19	,	,	PUNCT
ejpam-5911	478	20	s	s	PART
ejpam-5911	478	21	)	)	PUNCT
ejpam-5911	478	22	=	=	SYM
ejpam-5911	478	23	m	m	PROPN
ejpam-5911	478	24	(	(	PUNCT
ejpam-5911	478	25	say	say	INTJ
ejpam-5911	478	26	)	)	PUNCT
ejpam-5911	478	27	.	.	PUNCT
ejpam-5911	479	1	hence	hence	ADV
ejpam-5911	479	2	,	,	PUNCT
ejpam-5911	479	3	m	m	PROPN
ejpam-5911	479	4	∈	∈	NOUN
ejpam-5911	479	5	ig	ig	PROPN
ejpam-5911	479	6	is	be	AUX
ejpam-5911	479	7	(	(	PUNCT
ejpam-5911	479	8	r	r	NOUN
ejpam-5911	479	9	,	,	PUNCT
ejpam-5911	479	10	s)-f	s)-f	NOUN
ejpam-5911	479	11	-	-	PUNCT
ejpam-5911	479	12	b	b	NOUN
ejpam-5911	479	13	-	-	PUNCT
ejpam-5911	479	14	open	open	ADJ
ejpam-5911	479	15	containing	contain	VERB
ejpam-5911	479	16	gθ	gθ	NOUN
ejpam-5911	479	17	with	with	ADP
ejpam-5911	479	18	p(m	p(m	NOUN
ejpam-5911	479	19	)	)	PUNCT
ejpam-5911	479	20	≤	≤	NOUN
ejpam-5911	479	21	c𭟋∗(n	c𭟋∗(n	NOUN
ejpam-5911	479	22	,	,	PUNCT
ejpam-5911	479	23	r	r	NOUN
ejpam-5911	479	24	,	,	PUNCT
ejpam-5911	479	25	s	s	NOUN
ejpam-5911	479	26	)	)	PUNCT
ejpam-5911	479	27	.	.	PUNCT
ejpam-5911	480	1	(	(	PUNCT
ejpam-5911	480	2	⇐	⇐	NOUN
ejpam-5911	480	3	)	)	PUNCT
ejpam-5911	480	4	let	let	VERB
ejpam-5911	480	5	gθ	gθ	PROPN
ejpam-5911	480	6	∈	∈	PROPN
ejpam-5911	480	7	pθ(g	pθ(g	NOUN
ejpam-5911	480	8	)	)	PUNCT
ejpam-5911	480	9	and	and	CCONJ
ejpam-5911	480	10	n	n	PRON
ejpam-5911	480	11	∈	∈	NOUN
ejpam-5911	480	12	iz	iz	INTJ
ejpam-5911	480	13	with	with	ADP
ejpam-5911	480	14	𭟋(n	𭟋(n	PROPN
ejpam-5911	480	15	)	)	PUNCT
ejpam-5911	481	1	≥	≥	PROPN
ejpam-5911	481	2	r	r	NOUN
ejpam-5911	481	3	and	and	CCONJ
ejpam-5911	481	4	𭟋∗(n	𭟋∗(n	ADJ
ejpam-5911	481	5	)	)	PUNCT
ejpam-5911	481	6	≤	≤	NUM
ejpam-5911	481	7	s	s	VERB
ejpam-5911	481	8	such	such	ADJ
ejpam-5911	481	9	that	that	SCONJ
ejpam-5911	481	10	gθ	gθ	PROPN
ejpam-5911	481	11	∈	∈	PROPN
ejpam-5911	481	12	p−1(n	p−1(n	NOUN
ejpam-5911	481	13	)	)	PUNCT
ejpam-5911	481	14	.	.	PUNCT
ejpam-5911	482	1	according	accord	VERB
ejpam-5911	482	2	to	to	ADP
ejpam-5911	482	3	the	the	DET
ejpam-5911	482	4	assumption	assumption	NOUN
ejpam-5911	482	5	there	there	PRON
ejpam-5911	482	6	is	be	VERB
ejpam-5911	482	7	m	m	NOUN
ejpam-5911	482	8	∈	∈	NOUN
ejpam-5911	482	9	ig	ig	PROPN
ejpam-5911	482	10	that	that	PRON
ejpam-5911	482	11	is	be	AUX
ejpam-5911	482	12	(	(	PUNCT
ejpam-5911	482	13	r	r	NOUN
ejpam-5911	482	14	,	,	PUNCT
ejpam-5911	482	15	s)-f	s)-f	NOUN
ejpam-5911	482	16	-	-	PUNCT
ejpam-5911	482	17	b	b	NOUN
ejpam-5911	482	18	-	-	PUNCT
ejpam-5911	482	19	open	open	ADJ
ejpam-5911	482	20	containing	contain	VERB
ejpam-5911	482	21	gθ	gθ	NOUN
ejpam-5911	482	22	with	with	ADP
ejpam-5911	482	23	p(m	p(m	NOUN
ejpam-5911	482	24	)	)	PUNCT
ejpam-5911	482	25	≤	≤	NOUN
ejpam-5911	482	26	c𭟋∗(n	c𭟋∗(n	NOUN
ejpam-5911	482	27	,	,	PUNCT
ejpam-5911	482	28	r	r	NOUN
ejpam-5911	482	29	,	,	PUNCT
ejpam-5911	482	30	s	s	NOUN
ejpam-5911	482	31	)	)	PUNCT
ejpam-5911	482	32	.	.	PUNCT
ejpam-5911	483	1	hence	hence	ADV
ejpam-5911	483	2	,	,	PUNCT
ejpam-5911	483	3	gθ	gθ	PROPN
ejpam-5911	483	4	∈	∈	PROPN
ejpam-5911	483	5	m	m	VERB
ejpam-5911	483	6	≤	≤	ADJ
ejpam-5911	483	7	p−1(c𭟋∗(n	p−1(c𭟋∗(n	ADV
ejpam-5911	483	8	,	,	PUNCT
ejpam-5911	483	9	r	r	NOUN
ejpam-5911	483	10	,	,	PUNCT
ejpam-5911	483	11	s	s	NOUN
ejpam-5911	483	12	)	)	PUNCT
ejpam-5911	483	13	)	)	PUNCT
ejpam-5911	483	14	and	and	CCONJ
ejpam-5911	483	15	gθ	gθ	PROPN
ejpam-5911	483	16	∈	∈	PROPN
ejpam-5911	483	17	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	X
ejpam-5911	483	18	,	,	PUNCT
ejpam-5911	483	19	r	r	NOUN
ejpam-5911	483	20	,	,	PUNCT
ejpam-5911	483	21	s	s	NOUN
ejpam-5911	483	22	)	)	PUNCT
ejpam-5911	483	23	)	)	PUNCT
ejpam-5911	483	24	,	,	PUNCT
ejpam-5911	483	25	r	r	NOUN
ejpam-5911	483	26	,	,	PUNCT
ejpam-5911	483	27	s	s	NOUN
ejpam-5911	483	28	)	)	PUNCT
ejpam-5911	483	29	.	.	PUNCT
ejpam-5911	484	1	thus	thus	ADV
ejpam-5911	484	2	,	,	PUNCT
ejpam-5911	484	3	p−1(n	p−1(n	NOUN
ejpam-5911	484	4	)	)	PUNCT
ejpam-5911	484	5	≤	≤	NUM
ejpam-5911	484	6	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	SYM
ejpam-5911	484	7	,	,	PUNCT
ejpam-5911	484	8	r	r	NOUN
ejpam-5911	484	9	,	,	PUNCT
ejpam-5911	484	10	s	s	NOUN
ejpam-5911	484	11	)	)	PUNCT
ejpam-5911	484	12	)	)	PUNCT
ejpam-5911	484	13	,	,	PUNCT
ejpam-5911	484	14	r	r	NOUN
ejpam-5911	484	15	,	,	PUNCT
ejpam-5911	484	16	s	s	PART
ejpam-5911	484	17	)	)	PUNCT
ejpam-5911	484	18	.	.	PUNCT
ejpam-5911	485	1	therefore	therefore	ADV
ejpam-5911	485	2	,	,	PUNCT
ejpam-5911	485	3	p	p	NOUN
ejpam-5911	485	4	is	be	AUX
ejpam-5911	485	5	df	df	NOUN
ejpam-5911	485	6	-	-	PUNCT
ejpam-5911	485	7	weakly	weakly	ADJ
ejpam-5911	485	8	b	b	NOUN
ejpam-5911	485	9	-	-	PUNCT
ejpam-5911	485	10	continuous	continuous	ADJ
ejpam-5911	485	11	.	.	PUNCT
ejpam-5911	486	1	theorem	theorem	NOUN
ejpam-5911	486	2	9	9	NUM
ejpam-5911	486	3	.	.	PUNCT
ejpam-5911	487	1	let	let	VERB
ejpam-5911	487	2	p	p	NOUN
ejpam-5911	487	3	:	:	PUNCT
ejpam-5911	487	4	(	(	PUNCT
ejpam-5911	487	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	487	6	)	)	PUNCT
ejpam-5911	488	1	−→	−→	NOUN
ejpam-5911	488	2	(	(	PUNCT
ejpam-5911	488	3	z	z	NOUN
ejpam-5911	488	4	,	,	PUNCT
ejpam-5911	488	5	𭟋	𭟋	NOUN
ejpam-5911	488	6	,	,	PUNCT
ejpam-5911	488	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	488	8	)	)	PUNCT
ejpam-5911	488	9	be	be	AUX
ejpam-5911	488	10	an	an	DET
ejpam-5911	488	11	f	f	NOUN
ejpam-5911	488	12	-	-	PUNCT
ejpam-5911	488	13	mapping	mapping	NOUN
ejpam-5911	488	14	.	.	PUNCT
ejpam-5911	489	1	then	then	ADV
ejpam-5911	489	2	the	the	DET
ejpam-5911	489	3	following	follow	VERB
ejpam-5911	489	4	statements	statement	NOUN
ejpam-5911	489	5	are	be	AUX
ejpam-5911	489	6	equivalent	equivalent	ADJ
ejpam-5911	489	7	:	:	PUNCT
ejpam-5911	489	8	(	(	PUNCT
ejpam-5911	489	9	i	i	NOUN
ejpam-5911	489	10	)	)	PUNCT
ejpam-5911	489	11	p	p	NOUN
ejpam-5911	489	12	is	be	AUX
ejpam-5911	489	13	df	df	NOUN
ejpam-5911	489	14	-	-	PUNCT
ejpam-5911	489	15	weakly	weakly	ADJ
ejpam-5911	489	16	b	b	NOUN
ejpam-5911	489	17	-	-	PUNCT
ejpam-5911	489	18	continuous	continuous	ADJ
ejpam-5911	489	19	.	.	PUNCT
ejpam-5911	490	1	(	(	PUNCT
ejpam-5911	490	2	ii	ii	PROPN
ejpam-5911	490	3	)	)	PUNCT
ejpam-5911	490	4	p−1(n	p−1(n	PROPN
ejpam-5911	490	5	)	)	PUNCT
ejpam-5911	490	6	≥	≥	NUM
ejpam-5911	491	1	bcℑ∗(p−1(i𭟋∗(n	bcℑ∗(p−1(i𭟋∗(n	NOUN
ejpam-5911	491	2	,	,	PUNCT
ejpam-5911	491	3	r	r	NOUN
ejpam-5911	491	4	,	,	PUNCT
ejpam-5911	491	5	s	s	NOUN
ejpam-5911	491	6	)	)	PUNCT
ejpam-5911	491	7	)	)	PUNCT
ejpam-5911	491	8	,	,	PUNCT
ejpam-5911	491	9	r	r	NOUN
ejpam-5911	491	10	,	,	PUNCT
ejpam-5911	491	11	s	s	PART
ejpam-5911	491	12	)	)	PUNCT
ejpam-5911	491	13	,	,	PUNCT
ejpam-5911	491	14	if	if	SCONJ
ejpam-5911	491	15	n	n	PRON
ejpam-5911	491	16	∈	∈	NOUN
ejpam-5911	491	17	iz	iz	INTJ
ejpam-5911	491	18	with	with	ADP
ejpam-5911	491	19	𭟋(n	𭟋(n	PROPN
ejpam-5911	491	20	c	c	PROPN
ejpam-5911	491	21	)	)	PUNCT
ejpam-5911	491	22	≥	≥	NOUN
ejpam-5911	491	23	r	r	NOUN
ejpam-5911	491	24	and	and	CCONJ
ejpam-5911	491	25	𭟋∗(n	𭟋∗(n	PROPN
ejpam-5911	491	26	c	c	NOUN
ejpam-5911	491	27	)	)	PUNCT
ejpam-5911	491	28	≤	≤	PROPN
ejpam-5911	491	29	s.	s.	PROPN
ejpam-5911	491	30	(	(	PUNCT
ejpam-5911	491	31	iii	iii	NOUN
ejpam-5911	491	32	)	)	PUNCT
ejpam-5911	491	33	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	PROPN
ejpam-5911	491	34	,	,	PUNCT
ejpam-5911	491	35	r	r	NOUN
ejpam-5911	491	36	,	,	PUNCT
ejpam-5911	491	37	s	s	NOUN
ejpam-5911	491	38	)	)	PUNCT
ejpam-5911	491	39	)	)	PUNCT
ejpam-5911	491	40	,	,	PUNCT
ejpam-5911	491	41	r	r	NOUN
ejpam-5911	491	42	,	,	PUNCT
ejpam-5911	491	43	s	s	PART
ejpam-5911	491	44	)	)	PUNCT
ejpam-5911	491	45	≥	≥	NOUN
ejpam-5911	491	46	p−1(i𭟋∗(n	p−1(i𭟋∗(n	VERB
ejpam-5911	491	47	,	,	PUNCT
ejpam-5911	491	48	r	r	NOUN
ejpam-5911	491	49	,	,	PUNCT
ejpam-5911	491	50	s	s	NOUN
ejpam-5911	491	51	)	)	PUNCT
ejpam-5911	491	52	)	)	PUNCT
ejpam-5911	491	53	.	.	PUNCT
ejpam-5911	492	1	(	(	PUNCT
ejpam-5911	492	2	iv	iv	X
ejpam-5911	492	3	)	)	PUNCT
ejpam-5911	492	4	bcℑ∗(p−1(i𭟋∗(n	bcℑ∗(p−1(i𭟋∗(n	NOUN
ejpam-5911	492	5	,	,	PUNCT
ejpam-5911	492	6	r	r	NOUN
ejpam-5911	492	7	,	,	PUNCT
ejpam-5911	492	8	s	s	NOUN
ejpam-5911	492	9	)	)	PUNCT
ejpam-5911	492	10	)	)	PUNCT
ejpam-5911	492	11	,	,	PUNCT
ejpam-5911	492	12	r	r	NOUN
ejpam-5911	492	13	,	,	PUNCT
ejpam-5911	492	14	s	s	NOUN
ejpam-5911	492	15	)	)	PUNCT
ejpam-5911	492	16	≤	≤	PUNCT
ejpam-5911	493	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	493	2	,	,	PUNCT
ejpam-5911	493	3	r	r	NOUN
ejpam-5911	493	4	,	,	PUNCT
ejpam-5911	493	5	s	s	NOUN
ejpam-5911	493	6	)	)	PUNCT
ejpam-5911	493	7	)	)	PUNCT
ejpam-5911	493	8	.	.	PUNCT
ejpam-5911	494	1	proof	proof	NOUN
ejpam-5911	494	2	.	.	PUNCT
ejpam-5911	495	1	(	(	PUNCT
ejpam-5911	495	2	i	i	NOUN
ejpam-5911	495	3	)	)	PUNCT
ejpam-5911	495	4	⇔	⇔	PROPN
ejpam-5911	495	5	(	(	PUNCT
ejpam-5911	495	6	ii	ii	PROPN
ejpam-5911	495	7	)	)	PUNCT
ejpam-5911	495	8	the	the	DET
ejpam-5911	495	9	proof	proof	NOUN
ejpam-5911	495	10	follows	follow	VERB
ejpam-5911	495	11	by	by	ADP
ejpam-5911	495	12	proposition	proposition	NOUN
ejpam-5911	495	13	3	3	NUM
ejpam-5911	495	14	and	and	CCONJ
ejpam-5911	495	15	definition	definition	NOUN
ejpam-5911	495	16	13	13	NUM
ejpam-5911	495	17	.	.	PUNCT
ejpam-5911	496	1	(	(	PUNCT
ejpam-5911	496	2	ii	ii	NOUN
ejpam-5911	496	3	)	)	PUNCT
ejpam-5911	496	4	⇒	⇒	NOUN
ejpam-5911	496	5	(	(	PUNCT
ejpam-5911	496	6	iii	iii	X
ejpam-5911	496	7	)	)	PUNCT
ejpam-5911	496	8	let	let	VERB
ejpam-5911	496	9	n	n	PRON
ejpam-5911	496	10	∈	∈	NOUN
ejpam-5911	497	1	iz	iz	INTJ
ejpam-5911	497	2	.	.	PUNCT
ejpam-5911	498	1	hence	hence	ADV
ejpam-5911	498	2	by	by	ADP
ejpam-5911	498	3	(	(	PUNCT
ejpam-5911	498	4	ii	ii	NOUN
ejpam-5911	498	5	)	)	PUNCT
ejpam-5911	498	6	,	,	PUNCT
ejpam-5911	498	7	bcℑ∗(p−1(i𭟋∗(c𭟋∗(n	bcℑ∗(p−1(i𭟋∗(c𭟋∗(n	NOUN
ejpam-5911	498	8	c	c	PROPN
ejpam-5911	498	9	,	,	PUNCT
ejpam-5911	498	10	r	r	NOUN
ejpam-5911	498	11	,	,	PUNCT
ejpam-5911	498	12	s	s	PART
ejpam-5911	498	13	)	)	PUNCT
ejpam-5911	498	14	,	,	PUNCT
ejpam-5911	498	15	r	r	NOUN
ejpam-5911	498	16	,	,	PUNCT
ejpam-5911	498	17	s	s	NOUN
ejpam-5911	498	18	)	)	PUNCT
ejpam-5911	498	19	)	)	PUNCT
ejpam-5911	498	20	,	,	PUNCT
ejpam-5911	498	21	r	r	NOUN
ejpam-5911	498	22	,	,	PUNCT
ejpam-5911	498	23	s	s	NOUN
ejpam-5911	498	24	)	)	PUNCT
ejpam-5911	498	25	≤	≤	PUNCT
ejpam-5911	499	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	499	2	c	c	X
ejpam-5911	499	3	,	,	PUNCT
ejpam-5911	499	4	r	r	NOUN
ejpam-5911	499	5	,	,	PUNCT
ejpam-5911	499	6	s	s	NOUN
ejpam-5911	499	7	)	)	PUNCT
ejpam-5911	499	8	)	)	PUNCT
ejpam-5911	499	9	.	.	PUNCT
ejpam-5911	500	1	thus	thus	ADV
ejpam-5911	500	2	,	,	PUNCT
ejpam-5911	500	3	p−1(i𭟋∗(n	p−1(i𭟋∗(n	ADJ
ejpam-5911	500	4	,	,	PUNCT
ejpam-5911	500	5	r	r	NOUN
ejpam-5911	500	6	,	,	PUNCT
ejpam-5911	500	7	s	s	NOUN
ejpam-5911	500	8	)	)	PUNCT
ejpam-5911	500	9	)	)	PUNCT
ejpam-5911	501	1	≤	≤	NUM
ejpam-5911	501	2	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	SYM
ejpam-5911	501	3	,	,	PUNCT
ejpam-5911	501	4	r	r	NOUN
ejpam-5911	501	5	,	,	PUNCT
ejpam-5911	501	6	s	s	NOUN
ejpam-5911	501	7	)	)	PUNCT
ejpam-5911	501	8	)	)	PUNCT
ejpam-5911	501	9	,	,	PUNCT
ejpam-5911	501	10	r	r	NOUN
ejpam-5911	501	11	,	,	PUNCT
ejpam-5911	501	12	s	s	NOUN
ejpam-5911	501	13	)	)	PUNCT
ejpam-5911	501	14	.	.	PUNCT
ejpam-5911	502	1	(	(	PUNCT
ejpam-5911	502	2	iii	iii	X
ejpam-5911	502	3	)	)	PUNCT
ejpam-5911	502	4	⇔	⇔	X
ejpam-5911	502	5	(	(	PUNCT
ejpam-5911	502	6	iv	iv	X
ejpam-5911	502	7	)	)	PUNCT
ejpam-5911	502	8	the	the	DET
ejpam-5911	502	9	proof	proof	NOUN
ejpam-5911	502	10	follows	follow	VERB
ejpam-5911	502	11	from	from	ADP
ejpam-5911	502	12	proposition	proposition	NOUN
ejpam-5911	502	13	3	3	NUM
ejpam-5911	502	14	.	.	PUNCT
ejpam-5911	502	15	(	(	PUNCT
ejpam-5911	502	16	iv)⇒	iv)⇒	X
ejpam-5911	502	17	(	(	PUNCT
ejpam-5911	502	18	i	i	NOUN
ejpam-5911	502	19	)	)	PUNCT
ejpam-5911	502	20	letn	letn	VERB
ejpam-5911	502	21	∈	∈	PROPN
ejpam-5911	502	22	iz	iz	INTJ
ejpam-5911	502	23	with𭟋(n	with𭟋(n	NOUN
ejpam-5911	502	24	)	)	PUNCT
ejpam-5911	502	25	≥	≥	PROPN
ejpam-5911	502	26	r	r	NOUN
ejpam-5911	502	27	and𭟋∗(n	and𭟋∗(n	PROPN
ejpam-5911	502	28	)	)	PUNCT
ejpam-5911	502	29	≤	≤	PUNCT
ejpam-5911	503	1	s.	s.	PROPN
ejpam-5911	503	2	hence	hence	ADV
ejpam-5911	503	3	by	by	ADP
ejpam-5911	503	4	(	(	PUNCT
ejpam-5911	503	5	iv	iv	NOUN
ejpam-5911	503	6	)	)	PUNCT
ejpam-5911	503	7	,	,	PUNCT
ejpam-5911	503	8	bcℑ∗(p−1(i𭟋∗(n	bcℑ∗(p−1(i𭟋∗(n	NOUN
ejpam-5911	503	9	c	c	X
ejpam-5911	503	10	,	,	PUNCT
ejpam-5911	503	11	r	r	NOUN
ejpam-5911	503	12	,	,	PUNCT
ejpam-5911	503	13	s	s	NOUN
ejpam-5911	503	14	)	)	PUNCT
ejpam-5911	503	15	)	)	PUNCT
ejpam-5911	503	16	,	,	PUNCT
ejpam-5911	503	17	r	r	NOUN
ejpam-5911	503	18	,	,	PUNCT
ejpam-5911	503	19	s	s	NOUN
ejpam-5911	503	20	)	)	PUNCT
ejpam-5911	503	21	≤	≤	PUNCT
ejpam-5911	504	1	p−1(c𭟋∗(n	p−1(c𭟋∗(n	CCONJ
ejpam-5911	504	2	c	c	X
ejpam-5911	504	3	,	,	PUNCT
ejpam-5911	504	4	r	r	NOUN
ejpam-5911	504	5	,	,	PUNCT
ejpam-5911	504	6	s	s	NOUN
ejpam-5911	504	7	)	)	PUNCT
ejpam-5911	504	8	)	)	PUNCT
ejpam-5911	505	1	=	=	PRON
ejpam-5911	505	2	p−1(n	p−1(n	NOUN
ejpam-5911	505	3	c	c	NOUN
ejpam-5911	505	4	)	)	PUNCT
ejpam-5911	505	5	.	.	PUNCT
ejpam-5911	506	1	thus	thus	ADV
ejpam-5911	506	2	,	,	PUNCT
ejpam-5911	506	3	p−1(n	p−1(n	NOUN
ejpam-5911	506	4	)	)	PUNCT
ejpam-5911	506	5	≤	≤	NUM
ejpam-5911	506	6	biℑ∗(p−1(c𭟋∗(n	biℑ∗(p−1(c𭟋∗(n	SYM
ejpam-5911	506	7	,	,	PUNCT
ejpam-5911	506	8	r	r	NOUN
ejpam-5911	506	9	,	,	PUNCT
ejpam-5911	506	10	s	s	NOUN
ejpam-5911	506	11	)	)	PUNCT
ejpam-5911	506	12	)	)	PUNCT
ejpam-5911	506	13	,	,	PUNCT
ejpam-5911	506	14	r	r	NOUN
ejpam-5911	506	15	,	,	PUNCT
ejpam-5911	506	16	s	s	PART
ejpam-5911	506	17	)	)	PUNCT
ejpam-5911	506	18	,	,	PUNCT
ejpam-5911	506	19	so	so	ADV
ejpam-5911	506	20	p	p	NOUN
ejpam-5911	506	21	is	be	AUX
ejpam-5911	506	22	dfweakly	dfweakly	ADJ
ejpam-5911	506	23	b	b	NOUN
ejpam-5911	506	24	-	-	PUNCT
ejpam-5911	506	25	continuous	continuous	ADJ
ejpam-5911	506	26	.	.	PUNCT
ejpam-5911	507	1	lemma	lemma	PROPN
ejpam-5911	507	2	5	5	NUM
ejpam-5911	507	3	.	.	PUNCT
ejpam-5911	508	1	every	every	DET
ejpam-5911	508	2	df	df	PROPN
ejpam-5911	508	3	-	-	PUNCT
ejpam-5911	508	4	almost	almost	ADV
ejpam-5911	508	5	b	b	NOUN
ejpam-5911	508	6	-	-	PUNCT
ejpam-5911	508	7	continuous	continuous	ADJ
ejpam-5911	508	8	mapping	mapping	NOUN
ejpam-5911	508	9	is	be	AUX
ejpam-5911	508	10	df	df	NOUN
ejpam-5911	508	11	-	-	PUNCT
ejpam-5911	508	12	weakly	weakly	ADJ
ejpam-5911	508	13	b	b	NOUN
ejpam-5911	508	14	-	-	PUNCT
ejpam-5911	508	15	continuous	continuous	ADJ
ejpam-5911	508	16	.	.	PUNCT
ejpam-5911	509	1	i.	i.	PROPN
ejpam-5911	509	2	m.	m.	PROPN
ejpam-5911	509	3	taha	taha	PROPN
ejpam-5911	509	4	,	,	PUNCT
ejpam-5911	509	5	j.	j.	PROPN
ejpam-5911	509	6	al	al	PROPN
ejpam-5911	509	7	-	-	PUNCT
ejpam-5911	509	8	mufarrij	mufarrij	PROPN
ejpam-5911	509	9	,	,	PUNCT
ejpam-5911	509	10	o.	o.	PROPN
ejpam-5911	509	11	m.	m.	PROPN
ejpam-5911	509	12	taha	taha	PROPN
ejpam-5911	509	13	/	/	PUNCT
ejpam-5911	509	14	eur	eur	PROPN
ejpam-5911	509	15	.	.	PUNCT
ejpam-5911	510	1	j.	j.	PROPN
ejpam-5911	510	2	pure	pure	PROPN
ejpam-5911	510	3	appl	appl	PROPN
ejpam-5911	510	4	.	.	PROPN
ejpam-5911	510	5	math	math	PROPN
ejpam-5911	510	6	,	,	PUNCT
ejpam-5911	510	7	18	18	NUM
ejpam-5911	510	8	(	(	PUNCT
ejpam-5911	510	9	2	2	NUM
ejpam-5911	510	10	)	)	PUNCT
ejpam-5911	510	11	(	(	PUNCT
ejpam-5911	510	12	2025	2025	NUM
ejpam-5911	510	13	)	)	PUNCT
ejpam-5911	510	14	,	,	PUNCT
ejpam-5911	510	15	5911	5911	NUM
ejpam-5911	510	16	18	18	NUM
ejpam-5911	510	17	of	of	ADP
ejpam-5911	510	18	27	27	NUM
ejpam-5911	510	19	proof	proof	NOUN
ejpam-5911	510	20	.	.	PUNCT
ejpam-5911	511	1	the	the	DET
ejpam-5911	511	2	proof	proof	NOUN
ejpam-5911	511	3	follows	follow	VERB
ejpam-5911	511	4	by	by	ADP
ejpam-5911	511	5	definitions	definition	NOUN
ejpam-5911	511	6	12	12	NUM
ejpam-5911	511	7	and	and	CCONJ
ejpam-5911	511	8	13	13	NUM
ejpam-5911	511	9	.	.	PUNCT
ejpam-5911	511	10	remark	remark	NOUN
ejpam-5911	511	11	9	9	NUM
ejpam-5911	511	12	.	.	PUNCT
ejpam-5911	512	1	the	the	DET
ejpam-5911	512	2	converse	converse	NOUN
ejpam-5911	512	3	of	of	ADP
ejpam-5911	512	4	lemma	lemma	PROPN
ejpam-5911	512	5	5	5	NUM
ejpam-5911	512	6	fails	fail	VERB
ejpam-5911	512	7	as	as	ADP
ejpam-5911	512	8	example	example	NOUN
ejpam-5911	512	9	10	10	NUM
ejpam-5911	512	10	will	will	AUX
ejpam-5911	512	11	show	show	VERB
ejpam-5911	512	12	.	.	PUNCT
ejpam-5911	513	1	example	example	NOUN
ejpam-5911	514	1	10	10	NUM
ejpam-5911	514	2	.	.	PUNCT
ejpam-5911	515	1	letg	letg	PROPN
ejpam-5911	515	2	=	=	SYM
ejpam-5911	515	3	{	{	PUNCT
ejpam-5911	515	4	g1	g1	PROPN
ejpam-5911	515	5	,	,	PUNCT
ejpam-5911	515	6	g2	g2	PROPN
ejpam-5911	515	7	,	,	PUNCT
ejpam-5911	515	8	g3	g3	PROPN
ejpam-5911	515	9	}	}	PUNCT
ejpam-5911	515	10	and	and	CCONJ
ejpam-5911	515	11	definem	definem	PROPN
ejpam-5911	515	12	,	,	PUNCT
ejpam-5911	515	13	n	n	NOUN
ejpam-5911	515	14	,	,	PUNCT
ejpam-5911	515	15	u	u	PROPN
ejpam-5911	515	16	∈	∈	PROPN
ejpam-5911	515	17	ig	ig	PROPN
ejpam-5911	515	18	as	as	SCONJ
ejpam-5911	515	19	follows	follow	VERB
ejpam-5911	515	20	:	:	PUNCT
ejpam-5911	515	21	m	m	VERB
ejpam-5911	515	22	=	=	PUNCT
ejpam-5911	515	23	{	{	PUNCT
ejpam-5911	515	24	g1	g1	PROPN
ejpam-5911	515	25	0.6	0.6	NUM
ejpam-5911	515	26	,	,	PUNCT
ejpam-5911	515	27	g2	g2	PROPN
ejpam-5911	515	28	0.2	0.2	NUM
ejpam-5911	515	29	,	,	PUNCT
ejpam-5911	515	30	g3	g3	PROPN
ejpam-5911	515	31	0.4	0.4	NUM
ejpam-5911	515	32	}	}	PUNCT
ejpam-5911	515	33	,	,	PUNCT
ejpam-5911	515	34	n	n	NOUN
ejpam-5911	515	35	=	=	PRON
ejpam-5911	515	36	{	{	PUNCT
ejpam-5911	515	37	g1	g1	PROPN
ejpam-5911	515	38	0.3	0.3	NUM
ejpam-5911	515	39	,	,	PUNCT
ejpam-5911	515	40	g2	g2	PROPN
ejpam-5911	515	41	0.2	0.2	NUM
ejpam-5911	515	42	,	,	PUNCT
ejpam-5911	515	43	g3	g3	PROPN
ejpam-5911	515	44	0.5	0.5	NUM
ejpam-5911	515	45	}	}	PUNCT
ejpam-5911	515	46	,	,	PUNCT
ejpam-5911	515	47	u	u	NOUN
ejpam-5911	515	48	=	=	PUNCT
ejpam-5911	515	49	{	{	PUNCT
ejpam-5911	515	50	g1	g1	PROPN
ejpam-5911	515	51	0.3	0.3	NUM
ejpam-5911	515	52	,	,	PUNCT
ejpam-5911	515	53	g2	g2	PROPN
ejpam-5911	515	54	0.2	0.2	NUM
ejpam-5911	515	55	,	,	PUNCT
ejpam-5911	515	56	g3	g3	PROPN
ejpam-5911	515	57	0.4	0.4	NUM
ejpam-5911	515	58	}	}	PUNCT
ejpam-5911	515	59	.	.	PUNCT
ejpam-5911	516	1	define	define	VERB
ejpam-5911	516	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	516	3	,	,	PUNCT
ejpam-5911	516	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	516	5	:	:	PUNCT
ejpam-5911	516	6	ig	ig	PROPN
ejpam-5911	516	7	−→	−→	NOUN
ejpam-5911	517	1	i	i	PRON
ejpam-5911	517	2	as	as	SCONJ
ejpam-5911	517	3	follows	follow	VERB
ejpam-5911	517	4	:	:	PUNCT
ejpam-5911	517	5	ℑ(v	ℑ(v	X
ejpam-5911	517	6	)	)	PUNCT
ejpam-5911	517	7	=	=	PUNCT
ejpam-5911	517	8			NOUN
ejpam-5911	517	9	1	1	NUM
ejpam-5911	517	10	,	,	PUNCT
ejpam-5911	517	11	if	if	SCONJ
ejpam-5911	517	12	v	v	ADP
ejpam-5911	517	13	∈	∈	NOUN
ejpam-5911	517	14	{	{	PUNCT
ejpam-5911	517	15	1	1	NUM
ejpam-5911	517	16	,	,	PUNCT
ejpam-5911	517	17	0	0	NUM
ejpam-5911	517	18	}	}	PUNCT
ejpam-5911	517	19	,	,	PUNCT
ejpam-5911	517	20	1	1	NUM
ejpam-5911	517	21	4	4	NUM
ejpam-5911	517	22	,	,	PUNCT
ejpam-5911	517	23	if	if	SCONJ
ejpam-5911	517	24	v	v	ADP
ejpam-5911	517	25	=	=	SYM
ejpam-5911	517	26	m	m	NOUN
ejpam-5911	517	27	,	,	PUNCT
ejpam-5911	517	28	1	1	NUM
ejpam-5911	517	29	2	2	NUM
ejpam-5911	517	30	,	,	PUNCT
ejpam-5911	517	31	if	if	SCONJ
ejpam-5911	517	32	v	v	ADP
ejpam-5911	517	33	=	=	SYM
ejpam-5911	517	34	u	u	NOUN
ejpam-5911	517	35	,	,	PUNCT
ejpam-5911	517	36	0	0	NUM
ejpam-5911	517	37	,	,	PUNCT
ejpam-5911	517	38	otherwise	otherwise	ADV
ejpam-5911	517	39	,	,	PUNCT
ejpam-5911	517	40	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	517	41	)	)	PUNCT
ejpam-5911	517	42	=	=	PUNCT
ejpam-5911	518	1			NOUN
ejpam-5911	518	2	0	0	NUM
ejpam-5911	518	3	,	,	PUNCT
ejpam-5911	518	4	if	if	SCONJ
ejpam-5911	518	5	v	v	ADP
ejpam-5911	518	6	∈	∈	NOUN
ejpam-5911	518	7	{	{	PUNCT
ejpam-5911	518	8	1	1	NUM
ejpam-5911	518	9	,	,	PUNCT
ejpam-5911	518	10	0	0	NUM
ejpam-5911	518	11	}	}	PUNCT
ejpam-5911	518	12	,	,	PUNCT
ejpam-5911	518	13	1	1	NUM
ejpam-5911	518	14	4	4	NUM
ejpam-5911	518	15	,	,	PUNCT
ejpam-5911	518	16	if	if	SCONJ
ejpam-5911	518	17	v	v	ADP
ejpam-5911	518	18	=	=	SYM
ejpam-5911	518	19	m	m	NOUN
ejpam-5911	518	20	,	,	PUNCT
ejpam-5911	518	21	1	1	NUM
ejpam-5911	518	22	2	2	NUM
ejpam-5911	518	23	,	,	PUNCT
ejpam-5911	518	24	if	if	SCONJ
ejpam-5911	518	25	v	v	ADP
ejpam-5911	518	26	=	=	SYM
ejpam-5911	518	27	u	u	NOUN
ejpam-5911	518	28	,	,	PUNCT
ejpam-5911	518	29	1	1	NUM
ejpam-5911	518	30	,	,	PUNCT
ejpam-5911	518	31	otherwise	otherwise	ADV
ejpam-5911	518	32	,	,	PUNCT
ejpam-5911	518	33	𭟋(v	𭟋(v	NOUN
ejpam-5911	518	34	)	)	PUNCT
ejpam-5911	518	35	=	=	SYM
ejpam-5911	519	1			NOUN
ejpam-5911	519	2	1	1	NUM
ejpam-5911	519	3	,	,	PUNCT
ejpam-5911	519	4	if	if	SCONJ
ejpam-5911	519	5	v	v	ADP
ejpam-5911	519	6	∈	∈	NOUN
ejpam-5911	519	7	{	{	PUNCT
ejpam-5911	519	8	1	1	NUM
ejpam-5911	519	9	,	,	PUNCT
ejpam-5911	519	10	0	0	NUM
ejpam-5911	519	11	}	}	PUNCT
ejpam-5911	519	12	,	,	PUNCT
ejpam-5911	519	13	1	1	NUM
ejpam-5911	519	14	4	4	NUM
ejpam-5911	519	15	,	,	PUNCT
ejpam-5911	519	16	if	if	SCONJ
ejpam-5911	519	17	v	v	VERB
ejpam-5911	519	18	=	=	SYM
ejpam-5911	519	19	n	n	NOUN
ejpam-5911	519	20	,	,	PUNCT
ejpam-5911	519	21	0	0	NUM
ejpam-5911	519	22	,	,	PUNCT
ejpam-5911	519	23	otherwise	otherwise	ADV
ejpam-5911	519	24	,	,	PUNCT
ejpam-5911	519	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	519	26	)	)	PUNCT
ejpam-5911	520	1	=	=	PUNCT
ejpam-5911	521	1			NOUN
ejpam-5911	521	2	0	0	NUM
ejpam-5911	521	3	,	,	PUNCT
ejpam-5911	521	4	if	if	SCONJ
ejpam-5911	521	5	v	v	ADP
ejpam-5911	521	6	∈	∈	NOUN
ejpam-5911	521	7	{	{	PUNCT
ejpam-5911	521	8	1	1	NUM
ejpam-5911	521	9	,	,	PUNCT
ejpam-5911	521	10	0	0	NUM
ejpam-5911	521	11	}	}	PUNCT
ejpam-5911	521	12	,	,	PUNCT
ejpam-5911	521	13	1	1	NUM
ejpam-5911	521	14	2	2	NUM
ejpam-5911	521	15	,	,	PUNCT
ejpam-5911	521	16	if	if	SCONJ
ejpam-5911	521	17	v	v	VERB
ejpam-5911	521	18	=	=	SYM
ejpam-5911	521	19	n	n	NOUN
ejpam-5911	521	20	,	,	PUNCT
ejpam-5911	521	21	1	1	NUM
ejpam-5911	521	22	,	,	PUNCT
ejpam-5911	521	23	otherwise	otherwise	ADV
ejpam-5911	521	24	.	.	PUNCT
ejpam-5911	522	1	thus	thus	ADV
ejpam-5911	522	2	,	,	PUNCT
ejpam-5911	522	3	the	the	DET
ejpam-5911	522	4	identity	identity	NOUN
ejpam-5911	522	5	f	f	NOUN
ejpam-5911	522	6	-	-	PUNCT
ejpam-5911	522	7	mapping	mapping	NOUN
ejpam-5911	522	8	p	p	NOUN
ejpam-5911	522	9	:	:	PUNCT
ejpam-5911	522	10	(	(	PUNCT
ejpam-5911	522	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	522	12	)	)	PUNCT
ejpam-5911	522	13	−→	−→	NOUN
ejpam-5911	522	14	(	(	PUNCT
ejpam-5911	522	15	g	g	NOUN
ejpam-5911	522	16	,	,	PUNCT
ejpam-5911	522	17	𭟋	𭟋	NOUN
ejpam-5911	522	18	,	,	PUNCT
ejpam-5911	522	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	522	20	)	)	PUNCT
ejpam-5911	522	21	isdf	isdf	NOUN
ejpam-5911	522	22	-	-	PUNCT
ejpam-5911	522	23	weakly	weakly	ADJ
ejpam-5911	522	24	b	b	NOUN
ejpam-5911	522	25	-	-	ADJ
ejpam-5911	522	26	continuous	continuous	ADJ
ejpam-5911	522	27	,	,	PUNCT
ejpam-5911	522	28	but	but	CCONJ
ejpam-5911	522	29	it	it	PRON
ejpam-5911	522	30	is	be	AUX
ejpam-5911	522	31	not	not	PART
ejpam-5911	522	32	df	df	NOUN
ejpam-5911	522	33	-	-	PUNCT
ejpam-5911	522	34	almost	almost	ADV
ejpam-5911	522	35	b	b	NOUN
ejpam-5911	522	36	-	-	PUNCT
ejpam-5911	522	37	continuous	continuous	ADJ
ejpam-5911	522	38	.	.	PUNCT
ejpam-5911	523	1	remark	remark	NOUN
ejpam-5911	523	2	10	10	NUM
ejpam-5911	523	3	.	.	PUNCT
ejpam-5911	524	1	from	from	ADP
ejpam-5911	524	2	the	the	DET
ejpam-5911	524	3	previous	previous	ADJ
ejpam-5911	524	4	discussions	discussion	NOUN
ejpam-5911	524	5	and	and	CCONJ
ejpam-5911	524	6	definitions	definition	NOUN
ejpam-5911	524	7	,	,	PUNCT
ejpam-5911	524	8	we	we	PRON
ejpam-5911	524	9	have	have	VERB
ejpam-5911	524	10	the	the	DET
ejpam-5911	524	11	following	follow	VERB
ejpam-5911	524	12	diagram	diagram	NOUN
ejpam-5911	524	13	.	.	PUNCT
ejpam-5911	525	1	df	df	PROPN
ejpam-5911	525	2	-	-	PUNCT
ejpam-5911	525	3	b	b	NOUN
ejpam-5911	525	4	-	-	PUNCT
ejpam-5911	525	5	continuity	continuity	NOUN
ejpam-5911	525	6	−→	−→	NOUN
ejpam-5911	525	7	df	df	NOUN
ejpam-5911	525	8	-	-	PUNCT
ejpam-5911	525	9	almost	almost	ADV
ejpam-5911	525	10	b	b	NOUN
ejpam-5911	525	11	-	-	PUNCT
ejpam-5911	525	12	continuity	continuity	NOUN
ejpam-5911	525	13	−→	−→	NOUN
ejpam-5911	525	14	df	df	NOUN
ejpam-5911	525	15	-	-	PUNCT
ejpam-5911	525	16	weakly	weakly	ADJ
ejpam-5911	525	17	b	b	NOUN
ejpam-5911	525	18	-	-	PUNCT
ejpam-5911	525	19	continuity	continuity	NOUN
ejpam-5911	525	20	proposition	proposition	NOUN
ejpam-5911	525	21	6	6	NUM
ejpam-5911	525	22	.	.	PUNCT
ejpam-5911	526	1	let	let	VERB
ejpam-5911	526	2	(	(	PUNCT
ejpam-5911	526	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	526	4	)	)	PUNCT
ejpam-5911	526	5	,	,	PUNCT
ejpam-5911	526	6	(	(	PUNCT
ejpam-5911	526	7	q	q	X
ejpam-5911	526	8	,	,	PUNCT
ejpam-5911	526	9	η	η	NOUN
ejpam-5911	526	10	,	,	PUNCT
ejpam-5911	526	11	η∗	η∗	NOUN
ejpam-5911	526	12	)	)	PUNCT
ejpam-5911	526	13	and	and	CCONJ
ejpam-5911	526	14	(	(	PUNCT
ejpam-5911	526	15	z	z	NOUN
ejpam-5911	526	16	,	,	PUNCT
ejpam-5911	526	17	𭟋	𭟋	NOUN
ejpam-5911	526	18	,	,	PUNCT
ejpam-5911	526	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	526	20	)	)	PUNCT
ejpam-5911	526	21	bedft	bedft	NOUN
ejpam-5911	526	22	ss	ss	PROPN
ejpam-5911	526	23	,	,	PUNCT
ejpam-5911	526	24	and	and	CCONJ
ejpam-5911	526	25	p	p	X
ejpam-5911	526	26	:	:	PUNCT
ejpam-5911	526	27	(	(	PUNCT
ejpam-5911	526	28	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	526	29	)	)	PUNCT
ejpam-5911	527	1	−→	−→	NOUN
ejpam-5911	527	2	(	(	PUNCT
ejpam-5911	527	3	q	q	NOUN
ejpam-5911	527	4	,	,	PUNCT
ejpam-5911	527	5	η	η	NOUN
ejpam-5911	527	6	,	,	PUNCT
ejpam-5911	527	7	η∗	η∗	PROPN
ejpam-5911	527	8	)	)	PUNCT
ejpam-5911	527	9	,	,	PUNCT
ejpam-5911	527	10	y	y	PROPN
ejpam-5911	527	11	:	:	PUNCT
ejpam-5911	527	12	(	(	PUNCT
ejpam-5911	527	13	q	q	X
ejpam-5911	527	14	,	,	PUNCT
ejpam-5911	527	15	η	η	NOUN
ejpam-5911	527	16	,	,	PUNCT
ejpam-5911	527	17	η∗	η∗	NOUN
ejpam-5911	527	18	)	)	PUNCT
ejpam-5911	527	19	−→	−→	NOUN
ejpam-5911	527	20	(	(	PUNCT
ejpam-5911	527	21	z	z	NOUN
ejpam-5911	527	22	,	,	PUNCT
ejpam-5911	527	23	𭟋	𭟋	NOUN
ejpam-5911	527	24	,	,	PUNCT
ejpam-5911	527	25	𭟋∗	𭟋∗	NOUN
ejpam-5911	527	26	)	)	PUNCT
ejpam-5911	527	27	be	be	VERB
ejpam-5911	527	28	two	two	NUM
ejpam-5911	527	29	f	f	NOUN
ejpam-5911	527	30	-	-	PUNCT
ejpam-5911	527	31	mappings	mapping	NOUN
ejpam-5911	527	32	.	.	PUNCT
ejpam-5911	528	1	then	then	ADV
ejpam-5911	528	2	the	the	DET
ejpam-5911	528	3	composition	composition	NOUN
ejpam-5911	528	4	y	y	PROPN
ejpam-5911	528	5	◦	◦	NOUN
ejpam-5911	528	6	p	p	NOUN
ejpam-5911	528	7	is	be	AUX
ejpam-5911	528	8	df	df	NOUN
ejpam-5911	528	9	-	-	PUNCT
ejpam-5911	528	10	almost	almost	ADV
ejpam-5911	528	11	b	b	NOUN
ejpam-5911	528	12	-	-	ADJ
ejpam-5911	528	13	continuous	continuous	ADJ
ejpam-5911	528	14	if	if	SCONJ
ejpam-5911	528	15	p	p	NOUN
ejpam-5911	528	16	is	be	AUX
ejpam-5911	528	17	df	df	PROPN
ejpam-5911	528	18	-	-	PUNCT
ejpam-5911	528	19	b	b	NOUN
ejpam-5911	528	20	-	-	PUNCT
ejpam-5911	528	21	irresolute	irresolute	ADJ
ejpam-5911	528	22	(	(	PUNCT
ejpam-5911	528	23	resp	resp	NOUN
ejpam-5911	528	24	.	.	PUNCT
ejpam-5911	529	1	df	df	PROPN
ejpam-5911	529	2	-	-	PUNCT
ejpam-5911	529	3	b	b	NOUN
ejpam-5911	529	4	-	-	PUNCT
ejpam-5911	529	5	continuous	continuous	ADJ
ejpam-5911	529	6	)	)	PUNCT
ejpam-5911	529	7	and	and	CCONJ
ejpam-5911	529	8	y	y	PROPN
ejpam-5911	529	9	is	be	AUX
ejpam-5911	529	10	dfalmost	dfalmost	NOUN
ejpam-5911	529	11	b	b	NOUN
ejpam-5911	529	12	-	-	PUNCT
ejpam-5911	529	13	continuous	continuous	ADJ
ejpam-5911	529	14	(	(	PUNCT
ejpam-5911	529	15	resp	resp	NOUN
ejpam-5911	529	16	.	.	PUNCT
ejpam-5911	530	1	df	df	NOUN
ejpam-5911	530	2	-	-	PUNCT
ejpam-5911	530	3	continuous	continuous	ADJ
ejpam-5911	530	4	)	)	PUNCT
ejpam-5911	530	5	.	.	PUNCT
ejpam-5911	531	1	proof	proof	NOUN
ejpam-5911	531	2	.	.	PUNCT
ejpam-5911	532	1	the	the	DET
ejpam-5911	532	2	proof	proof	NOUN
ejpam-5911	532	3	follows	follow	VERB
ejpam-5911	532	4	by	by	ADP
ejpam-5911	532	5	the	the	DET
ejpam-5911	532	6	previous	previous	ADJ
ejpam-5911	532	7	definitions	definition	NOUN
ejpam-5911	532	8	.	.	PUNCT
ejpam-5911	533	1	5	5	X
ejpam-5911	533	2	.	.	X
ejpam-5911	534	1	some	some	DET
ejpam-5911	534	2	applications	application	NOUN
ejpam-5911	534	3	here	here	ADV
ejpam-5911	534	4	,	,	PUNCT
ejpam-5911	534	5	we	we	PRON
ejpam-5911	534	6	present	present	VERB
ejpam-5911	534	7	and	and	CCONJ
ejpam-5911	534	8	study	study	VERB
ejpam-5911	534	9	some	some	DET
ejpam-5911	534	10	new	new	ADJ
ejpam-5911	534	11	df	df	NOUN
ejpam-5911	534	12	-	-	PUNCT
ejpam-5911	534	13	mappings	mapping	NOUN
ejpam-5911	534	14	between	between	ADP
ejpam-5911	534	15	dft	dft	PROPN
ejpam-5911	534	16	ss	ss	PROPN
ejpam-5911	534	17	(	(	PUNCT
ejpam-5911	534	18	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	534	19	)	)	PUNCT
ejpam-5911	534	20	and	and	CCONJ
ejpam-5911	534	21	(	(	PUNCT
ejpam-5911	534	22	z	z	NOUN
ejpam-5911	534	23	,	,	PUNCT
ejpam-5911	534	24	𭟋	𭟋	NOUN
ejpam-5911	534	25	,	,	PUNCT
ejpam-5911	534	26	𭟋∗	𭟋∗	NOUN
ejpam-5911	534	27	)	)	PUNCT
ejpam-5911	534	28	based	base	VERB
ejpam-5911	534	29	on	on	ADP
ejpam-5911	534	30	šostak	šostak	NOUN
ejpam-5911	534	31	,	,	PUNCT
ejpam-5911	534	32	s	s	PART
ejpam-5911	534	33	sense	sense	NOUN
ejpam-5911	534	34	[	[	X
ejpam-5911	534	35	3	3	NUM
ejpam-5911	534	36	]	]	PUNCT
ejpam-5911	534	37	.	.	PUNCT
ejpam-5911	535	1	next	next	ADV
ejpam-5911	535	2	,	,	PUNCT
ejpam-5911	535	3	we	we	PRON
ejpam-5911	535	4	introduce	introduce	VERB
ejpam-5911	535	5	and	and	CCONJ
ejpam-5911	535	6	discuss	discuss	VERB
ejpam-5911	535	7	new	new	ADJ
ejpam-5911	535	8	types	type	NOUN
ejpam-5911	535	9	of	of	ADP
ejpam-5911	535	10	dfseparation	dfseparation	NOUN
ejpam-5911	535	11	axioms	axiom	NOUN
ejpam-5911	535	12	via	via	ADP
ejpam-5911	535	13	(	(	PUNCT
ejpam-5911	535	14	r	r	NOUN
ejpam-5911	535	15	,	,	PUNCT
ejpam-5911	535	16	s)-f	s)-f	NOUN
ejpam-5911	535	17	-	-	PUNCT
ejpam-5911	535	18	b	b	NOUN
ejpam-5911	535	19	-	-	PUNCT
ejpam-5911	535	20	closed	close	VERB
ejpam-5911	535	21	sets	set	NOUN
ejpam-5911	535	22	,	,	PUNCT
ejpam-5911	535	23	called	call	VERB
ejpam-5911	535	24	(	(	PUNCT
ejpam-5911	535	25	r	r	NOUN
ejpam-5911	535	26	,	,	PUNCT
ejpam-5911	535	27	s)-f	s)-f	NOUN
ejpam-5911	535	28	-	-	PUNCT
ejpam-5911	535	29	b	b	NOUN
ejpam-5911	535	30	-	-	PUNCT
ejpam-5911	535	31	regular	regular	ADJ
ejpam-5911	535	32	and	and	CCONJ
ejpam-5911	535	33	(	(	PUNCT
ejpam-5911	535	34	r	r	NOUN
ejpam-5911	535	35	,	,	PUNCT
ejpam-5911	535	36	s)-f	s)-f	NOUN
ejpam-5911	535	37	-	-	PUNCT
ejpam-5911	535	38	b	b	NOUN
ejpam-5911	535	39	-	-	PUNCT
ejpam-5911	535	40	normal	normal	ADJ
ejpam-5911	535	41	spaces	space	NOUN
ejpam-5911	535	42	.	.	PUNCT
ejpam-5911	536	1	i.	i.	PROPN
ejpam-5911	536	2	m.	m.	PROPN
ejpam-5911	536	3	taha	taha	PROPN
ejpam-5911	536	4	,	,	PUNCT
ejpam-5911	536	5	j.	j.	PROPN
ejpam-5911	536	6	al	al	PROPN
ejpam-5911	536	7	-	-	PUNCT
ejpam-5911	536	8	mufarrij	mufarrij	PROPN
ejpam-5911	536	9	,	,	PUNCT
ejpam-5911	536	10	o.	o.	PROPN
ejpam-5911	536	11	m.	m.	PROPN
ejpam-5911	536	12	taha	taha	PROPN
ejpam-5911	536	13	/	/	PUNCT
ejpam-5911	536	14	eur	eur	PROPN
ejpam-5911	536	15	.	.	PUNCT
ejpam-5911	537	1	j.	j.	PROPN
ejpam-5911	537	2	pure	pure	PROPN
ejpam-5911	537	3	appl	appl	PROPN
ejpam-5911	537	4	.	.	PROPN
ejpam-5911	537	5	math	math	PROPN
ejpam-5911	537	6	,	,	PUNCT
ejpam-5911	537	7	18	18	NUM
ejpam-5911	537	8	(	(	PUNCT
ejpam-5911	537	9	2	2	NUM
ejpam-5911	537	10	)	)	PUNCT
ejpam-5911	537	11	(	(	PUNCT
ejpam-5911	537	12	2025	2025	NUM
ejpam-5911	537	13	)	)	PUNCT
ejpam-5911	537	14	,	,	PUNCT
ejpam-5911	537	15	5911	5911	NUM
ejpam-5911	537	16	19	19	NUM
ejpam-5911	537	17	of	of	ADP
ejpam-5911	537	18	27	27	NUM
ejpam-5911	537	19	definition	definition	NOUN
ejpam-5911	537	20	14	14	NUM
ejpam-5911	537	21	.	.	PUNCT
ejpam-5911	538	1	an	an	DET
ejpam-5911	538	2	f	f	X
ejpam-5911	538	3	-	-	PUNCT
ejpam-5911	538	4	mapping	mapping	NOUN
ejpam-5911	538	5	p	p	NOUN
ejpam-5911	538	6	:	:	PUNCT
ejpam-5911	538	7	(	(	PUNCT
ejpam-5911	538	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	538	9	)	)	PUNCT
ejpam-5911	539	1	−→	−→	NOUN
ejpam-5911	539	2	(	(	PUNCT
ejpam-5911	539	3	z	z	NOUN
ejpam-5911	539	4	,	,	PUNCT
ejpam-5911	539	5	𭟋	𭟋	NOUN
ejpam-5911	539	6	,	,	PUNCT
ejpam-5911	539	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	539	8	)	)	PUNCT
ejpam-5911	539	9	is	be	AUX
ejpam-5911	539	10	called	call	VERB
ejpam-5911	539	11	df	df	PROPN
ejpam-5911	539	12	-	-	PUNCT
ejpam-5911	539	13	b	b	NOUN
ejpam-5911	539	14	-	-	PUNCT
ejpam-5911	539	15	open	open	ADJ
ejpam-5911	539	16	if	if	SCONJ
ejpam-5911	539	17	p(m	p(m	NOUN
ejpam-5911	539	18	)	)	PUNCT
ejpam-5911	539	19	is	be	AUX
ejpam-5911	539	20	an	an	DET
ejpam-5911	539	21	(	(	PUNCT
ejpam-5911	539	22	r	r	NOUN
ejpam-5911	539	23	,	,	PUNCT
ejpam-5911	539	24	s)-f	s)-f	NOUN
ejpam-5911	539	25	-	-	PUNCT
ejpam-5911	539	26	b	b	NOUN
ejpam-5911	539	27	-	-	PUNCT
ejpam-5911	539	28	open	open	ADJ
ejpam-5911	539	29	set	set	NOUN
ejpam-5911	539	30	,	,	PUNCT
ejpam-5911	539	31	for	for	SCONJ
ejpam-5911	539	32	each	each	DET
ejpam-5911	539	33	m	m	NOUN
ejpam-5911	539	34	∈	∈	NOUN
ejpam-5911	539	35	ig	ig	PROPN
ejpam-5911	539	36	with	with	ADP
ejpam-5911	539	37	ℑ(m	ℑ(m	NOUN
ejpam-5911	539	38	)	)	PUNCT
ejpam-5911	539	39	≥	≥	NOUN
ejpam-5911	539	40	r	r	NOUN
ejpam-5911	539	41	and	and	CCONJ
ejpam-5911	539	42	ℑ∗(m	ℑ∗(m	NOUN
ejpam-5911	539	43	)	)	PUNCT
ejpam-5911	539	44	≤	≤	NUM
ejpam-5911	539	45	s.	s.	PROPN
ejpam-5911	539	46	definition	definition	NOUN
ejpam-5911	539	47	15	15	NUM
ejpam-5911	539	48	.	.	PUNCT
ejpam-5911	540	1	an	an	DET
ejpam-5911	540	2	f	f	X
ejpam-5911	540	3	-	-	PUNCT
ejpam-5911	540	4	mapping	mapping	NOUN
ejpam-5911	540	5	p	p	NOUN
ejpam-5911	540	6	:	:	PUNCT
ejpam-5911	540	7	(	(	PUNCT
ejpam-5911	540	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	540	9	)	)	PUNCT
ejpam-5911	541	1	−→	−→	NOUN
ejpam-5911	541	2	(	(	PUNCT
ejpam-5911	541	3	z	z	NOUN
ejpam-5911	541	4	,	,	PUNCT
ejpam-5911	541	5	𭟋	𭟋	NOUN
ejpam-5911	541	6	,	,	PUNCT
ejpam-5911	541	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	541	8	)	)	PUNCT
ejpam-5911	541	9	is	be	AUX
ejpam-5911	541	10	called	call	VERB
ejpam-5911	541	11	df	df	PROPN
ejpam-5911	541	12	-	-	PUNCT
ejpam-5911	541	13	b	b	NOUN
ejpam-5911	541	14	-	-	PUNCT
ejpam-5911	541	15	irresolute	irresolute	ADJ
ejpam-5911	541	16	open	open	ADJ
ejpam-5911	541	17	if	if	SCONJ
ejpam-5911	541	18	p(m	p(m	NOUN
ejpam-5911	541	19	)	)	PUNCT
ejpam-5911	541	20	is	be	AUX
ejpam-5911	541	21	an	an	DET
ejpam-5911	541	22	(	(	PUNCT
ejpam-5911	541	23	r	r	NOUN
ejpam-5911	541	24	,	,	PUNCT
ejpam-5911	541	25	s)-f	s)-f	NOUN
ejpam-5911	541	26	-	-	PUNCT
ejpam-5911	541	27	b	b	NOUN
ejpam-5911	541	28	-	-	PUNCT
ejpam-5911	541	29	open	open	ADJ
ejpam-5911	541	30	set	set	NOUN
ejpam-5911	541	31	,	,	PUNCT
ejpam-5911	541	32	for	for	ADP
ejpam-5911	541	33	each	each	PRON
ejpam-5911	541	34	(	(	PUNCT
ejpam-5911	541	35	r	r	NOUN
ejpam-5911	541	36	,	,	PUNCT
ejpam-5911	541	37	s)-f	s)-f	NOUN
ejpam-5911	541	38	-	-	PUNCT
ejpam-5911	541	39	b	b	NOUN
ejpam-5911	541	40	-	-	PUNCT
ejpam-5911	541	41	open	open	ADJ
ejpam-5911	541	42	set	set	NOUN
ejpam-5911	542	1	m	m	PROPN
ejpam-5911	542	2	∈	∈	PROPN
ejpam-5911	542	3	ig	ig	PROPN
ejpam-5911	542	4	.	.	PUNCT
ejpam-5911	542	5	lemma	lemma	PROPN
ejpam-5911	542	6	6	6	NUM
ejpam-5911	542	7	.	.	PUNCT
ejpam-5911	543	1	each	each	DET
ejpam-5911	543	2	df	df	PROPN
ejpam-5911	543	3	-	-	PUNCT
ejpam-5911	543	4	b	b	NOUN
ejpam-5911	543	5	-	-	PUNCT
ejpam-5911	543	6	irresolute	irresolute	ADJ
ejpam-5911	543	7	open	open	ADJ
ejpam-5911	543	8	mapping	mapping	NOUN
ejpam-5911	543	9	is	be	AUX
ejpam-5911	543	10	df	df	PROPN
ejpam-5911	543	11	-	-	PUNCT
ejpam-5911	543	12	b	b	NOUN
ejpam-5911	543	13	-	-	PUNCT
ejpam-5911	543	14	open	open	ADJ
ejpam-5911	543	15	.	.	PUNCT
ejpam-5911	544	1	proof	proof	NOUN
ejpam-5911	544	2	.	.	PUNCT
ejpam-5911	545	1	the	the	DET
ejpam-5911	545	2	proof	proof	NOUN
ejpam-5911	545	3	follows	follow	VERB
ejpam-5911	545	4	from	from	ADP
ejpam-5911	545	5	definitions	definition	NOUN
ejpam-5911	545	6	14	14	NUM
ejpam-5911	545	7	and	and	CCONJ
ejpam-5911	545	8	15	15	NUM
ejpam-5911	545	9	.	.	PUNCT
ejpam-5911	545	10	remark	remark	NOUN
ejpam-5911	545	11	11	11	NUM
ejpam-5911	545	12	.	.	PUNCT
ejpam-5911	546	1	the	the	DET
ejpam-5911	546	2	converse	converse	NOUN
ejpam-5911	546	3	of	of	ADP
ejpam-5911	546	4	lemma	lemma	PROPN
ejpam-5911	546	5	6	6	NUM
ejpam-5911	546	6	fails	fail	VERB
ejpam-5911	546	7	as	as	ADP
ejpam-5911	546	8	example	example	NOUN
ejpam-5911	546	9	11	11	NUM
ejpam-5911	546	10	will	will	AUX
ejpam-5911	546	11	show	show	VERB
ejpam-5911	546	12	.	.	PUNCT
ejpam-5911	547	1	example	example	NOUN
ejpam-5911	547	2	11	11	NUM
ejpam-5911	547	3	.	.	PUNCT
ejpam-5911	548	1	let	let	VERB
ejpam-5911	548	2	g	g	PROPN
ejpam-5911	548	3	=	=	SYM
ejpam-5911	548	4	{	{	PUNCT
ejpam-5911	548	5	g1	g1	PROPN
ejpam-5911	548	6	,	,	PUNCT
ejpam-5911	548	7	g2	g2	PROPN
ejpam-5911	548	8	}	}	PUNCT
ejpam-5911	548	9	and	and	CCONJ
ejpam-5911	548	10	define	define	VERB
ejpam-5911	548	11	m	m	NOUN
ejpam-5911	548	12	,	,	PUNCT
ejpam-5911	548	13	n	n	PROPN
ejpam-5911	548	14	∈	∈	PROPN
ejpam-5911	548	15	ig	ig	PROPN
ejpam-5911	548	16	as	as	SCONJ
ejpam-5911	548	17	follows	follow	VERB
ejpam-5911	548	18	:	:	PUNCT
ejpam-5911	548	19	m	m	VERB
ejpam-5911	548	20	=	=	PUNCT
ejpam-5911	548	21	{	{	PUNCT
ejpam-5911	548	22	g1	g1	PROPN
ejpam-5911	548	23	0.5	0.5	NUM
ejpam-5911	548	24	,	,	PUNCT
ejpam-5911	548	25	g2	g2	PROPN
ejpam-5911	548	26	0.5	0.5	NUM
ejpam-5911	548	27	}	}	PUNCT
ejpam-5911	548	28	,	,	PUNCT
ejpam-5911	548	29	n	n	NOUN
ejpam-5911	548	30	=	=	PRON
ejpam-5911	548	31	{	{	PUNCT
ejpam-5911	548	32	g1	g1	PROPN
ejpam-5911	548	33	0.5	0.5	NUM
ejpam-5911	548	34	,	,	PUNCT
ejpam-5911	548	35	g2	g2	PROPN
ejpam-5911	548	36	0.4	0.4	NUM
ejpam-5911	548	37	}	}	PUNCT
ejpam-5911	548	38	.	.	PUNCT
ejpam-5911	549	1	define	define	VERB
ejpam-5911	549	2	ℑ,ℑ∗,𭟋	ℑ,ℑ∗,𭟋	NOUN
ejpam-5911	549	3	,	,	PUNCT
ejpam-5911	549	4	𭟋∗	𭟋∗	NOUN
ejpam-5911	549	5	:	:	PUNCT
ejpam-5911	549	6	ig	ig	PROPN
ejpam-5911	549	7	−→	−→	NOUN
ejpam-5911	550	1	i	i	PRON
ejpam-5911	550	2	as	as	SCONJ
ejpam-5911	550	3	follows	follow	VERB
ejpam-5911	550	4	:	:	PUNCT
ejpam-5911	550	5	ℑ(v	ℑ(v	X
ejpam-5911	550	6	)	)	PUNCT
ejpam-5911	550	7	=	=	SYM
ejpam-5911	551	1			NOUN
ejpam-5911	551	2	1	1	NUM
ejpam-5911	551	3	,	,	PUNCT
ejpam-5911	551	4	if	if	SCONJ
ejpam-5911	551	5	v	v	ADP
ejpam-5911	551	6	∈	∈	NOUN
ejpam-5911	551	7	{	{	PUNCT
ejpam-5911	551	8	1	1	NUM
ejpam-5911	551	9	,	,	PUNCT
ejpam-5911	551	10	0	0	NUM
ejpam-5911	551	11	}	}	PUNCT
ejpam-5911	551	12	,	,	PUNCT
ejpam-5911	551	13	1	1	NUM
ejpam-5911	551	14	5	5	NUM
ejpam-5911	551	15	,	,	PUNCT
ejpam-5911	551	16	if	if	SCONJ
ejpam-5911	551	17	v	v	ADP
ejpam-5911	551	18	=	=	NOUN
ejpam-5911	551	19	m	m	PROPN
ejpam-5911	551	20	,	,	PUNCT
ejpam-5911	551	21	0	0	NUM
ejpam-5911	551	22	,	,	PUNCT
ejpam-5911	551	23	otherwise	otherwise	ADV
ejpam-5911	551	24	,	,	PUNCT
ejpam-5911	551	25	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	551	26	)	)	PUNCT
ejpam-5911	552	1	=	=	SYM
ejpam-5911	553	1			NOUN
ejpam-5911	553	2	0	0	NUM
ejpam-5911	553	3	,	,	PUNCT
ejpam-5911	553	4	if	if	SCONJ
ejpam-5911	553	5	v	v	ADP
ejpam-5911	553	6	∈	∈	NOUN
ejpam-5911	553	7	{	{	PUNCT
ejpam-5911	553	8	1	1	NUM
ejpam-5911	553	9	,	,	PUNCT
ejpam-5911	553	10	0	0	NUM
ejpam-5911	553	11	}	}	PUNCT
ejpam-5911	553	12	,	,	PUNCT
ejpam-5911	553	13	1	1	NUM
ejpam-5911	553	14	5	5	NUM
ejpam-5911	553	15	,	,	PUNCT
ejpam-5911	553	16	if	if	SCONJ
ejpam-5911	553	17	v	v	ADP
ejpam-5911	553	18	=	=	NOUN
ejpam-5911	553	19	m	m	PROPN
ejpam-5911	553	20	,	,	PUNCT
ejpam-5911	553	21	1	1	NUM
ejpam-5911	553	22	,	,	PUNCT
ejpam-5911	553	23	otherwise	otherwise	ADV
ejpam-5911	553	24	,	,	PUNCT
ejpam-5911	553	25	𭟋(v	𭟋(v	NOUN
ejpam-5911	553	26	)	)	PUNCT
ejpam-5911	553	27	=	=	SYM
ejpam-5911	554	1			NOUN
ejpam-5911	554	2	1	1	NUM
ejpam-5911	554	3	,	,	PUNCT
ejpam-5911	554	4	if	if	SCONJ
ejpam-5911	554	5	v	v	ADP
ejpam-5911	554	6	∈	∈	NOUN
ejpam-5911	554	7	{	{	PUNCT
ejpam-5911	554	8	1	1	NUM
ejpam-5911	554	9	,	,	PUNCT
ejpam-5911	554	10	0	0	NUM
ejpam-5911	554	11	}	}	PUNCT
ejpam-5911	554	12	,	,	PUNCT
ejpam-5911	554	13	1	1	NUM
ejpam-5911	554	14	5	5	NUM
ejpam-5911	554	15	,	,	PUNCT
ejpam-5911	554	16	if	if	SCONJ
ejpam-5911	554	17	v	v	VERB
ejpam-5911	554	18	=	=	SYM
ejpam-5911	554	19	n	n	NOUN
ejpam-5911	554	20	,	,	PUNCT
ejpam-5911	554	21	0	0	NUM
ejpam-5911	554	22	,	,	PUNCT
ejpam-5911	554	23	otherwise	otherwise	ADV
ejpam-5911	554	24	,	,	PUNCT
ejpam-5911	554	25	𭟋∗(v	𭟋∗(v	PROPN
ejpam-5911	554	26	)	)	PUNCT
ejpam-5911	555	1	=	=	PUNCT
ejpam-5911	556	1			NOUN
ejpam-5911	556	2	0	0	NUM
ejpam-5911	556	3	,	,	PUNCT
ejpam-5911	556	4	if	if	SCONJ
ejpam-5911	556	5	v	v	ADP
ejpam-5911	556	6	∈	∈	NOUN
ejpam-5911	556	7	{	{	PUNCT
ejpam-5911	556	8	1	1	NUM
ejpam-5911	556	9	,	,	PUNCT
ejpam-5911	556	10	0	0	NUM
ejpam-5911	556	11	}	}	PUNCT
ejpam-5911	556	12	,	,	PUNCT
ejpam-5911	556	13	1	1	NUM
ejpam-5911	556	14	5	5	NUM
ejpam-5911	556	15	,	,	PUNCT
ejpam-5911	556	16	if	if	SCONJ
ejpam-5911	556	17	v	v	VERB
ejpam-5911	556	18	=	=	SYM
ejpam-5911	556	19	n	n	NOUN
ejpam-5911	556	20	,	,	PUNCT
ejpam-5911	556	21	1	1	NUM
ejpam-5911	556	22	,	,	PUNCT
ejpam-5911	556	23	otherwise	otherwise	ADV
ejpam-5911	556	24	.	.	PUNCT
ejpam-5911	557	1	thus	thus	ADV
ejpam-5911	557	2	,	,	PUNCT
ejpam-5911	557	3	the	the	DET
ejpam-5911	557	4	identity	identity	NOUN
ejpam-5911	557	5	f	f	NOUN
ejpam-5911	557	6	-	-	PUNCT
ejpam-5911	557	7	mapping	mapping	NOUN
ejpam-5911	557	8	p	p	NOUN
ejpam-5911	557	9	:	:	PUNCT
ejpam-5911	557	10	(	(	PUNCT
ejpam-5911	557	11	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	557	12	)	)	PUNCT
ejpam-5911	557	13	−→	−→	NOUN
ejpam-5911	557	14	(	(	PUNCT
ejpam-5911	557	15	g	g	NOUN
ejpam-5911	557	16	,	,	PUNCT
ejpam-5911	557	17	𭟋	𭟋	NOUN
ejpam-5911	557	18	,	,	PUNCT
ejpam-5911	557	19	𭟋∗	𭟋∗	NOUN
ejpam-5911	557	20	)	)	PUNCT
ejpam-5911	557	21	is	be	AUX
ejpam-5911	557	22	df	df	PROPN
ejpam-5911	557	23	-	-	PUNCT
ejpam-5911	557	24	b	b	NOUN
ejpam-5911	557	25	-	-	PUNCT
ejpam-5911	557	26	open	open	ADJ
ejpam-5911	557	27	,	,	PUNCT
ejpam-5911	557	28	but	but	CCONJ
ejpam-5911	557	29	it	it	PRON
ejpam-5911	557	30	is	be	AUX
ejpam-5911	557	31	not	not	PART
ejpam-5911	557	32	df	df	PROPN
ejpam-5911	557	33	-	-	PUNCT
ejpam-5911	557	34	b	b	NOUN
ejpam-5911	557	35	-	-	PUNCT
ejpam-5911	557	36	irresolute	irresolute	ADJ
ejpam-5911	557	37	open	open	ADJ
ejpam-5911	557	38	.	.	PUNCT
ejpam-5911	558	1	theorem	theorem	ADJ
ejpam-5911	558	2	10	10	NUM
ejpam-5911	558	3	.	.	PUNCT
ejpam-5911	559	1	let	let	VERB
ejpam-5911	559	2	p	p	NOUN
ejpam-5911	559	3	:	:	PUNCT
ejpam-5911	559	4	(	(	PUNCT
ejpam-5911	559	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	559	6	)	)	PUNCT
ejpam-5911	560	1	−→	−→	NOUN
ejpam-5911	560	2	(	(	PUNCT
ejpam-5911	560	3	z	z	NOUN
ejpam-5911	560	4	,	,	PUNCT
ejpam-5911	560	5	𭟋	𭟋	NOUN
ejpam-5911	560	6	,	,	PUNCT
ejpam-5911	560	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	560	8	)	)	PUNCT
ejpam-5911	560	9	be	be	AUX
ejpam-5911	560	10	an	an	DET
ejpam-5911	560	11	f	f	NOUN
ejpam-5911	560	12	-	-	PUNCT
ejpam-5911	560	13	mapping	mapping	NOUN
ejpam-5911	560	14	.	.	PUNCT
ejpam-5911	561	1	then	then	ADV
ejpam-5911	561	2	the	the	DET
ejpam-5911	561	3	following	follow	VERB
ejpam-5911	561	4	statements	statement	NOUN
ejpam-5911	561	5	are	be	AUX
ejpam-5911	561	6	equivalent	equivalent	ADJ
ejpam-5911	561	7	for	for	ADP
ejpam-5911	561	8	every	every	DET
ejpam-5911	561	9	m	m	NOUN
ejpam-5911	561	10	∈	∈	NOUN
ejpam-5911	561	11	ig	ig	PROPN
ejpam-5911	561	12	and	and	CCONJ
ejpam-5911	561	13	n	n	PRON
ejpam-5911	561	14	∈	∈	PROPN
ejpam-5911	562	1	iz	iz	INTJ
ejpam-5911	562	2	:	:	PUNCT
ejpam-5911	562	3	(	(	PUNCT
ejpam-5911	562	4	i	i	NOUN
ejpam-5911	562	5	)	)	PUNCT
ejpam-5911	562	6	p	p	NOUN
ejpam-5911	562	7	is	be	AUX
ejpam-5911	562	8	df	df	PROPN
ejpam-5911	562	9	-	-	PUNCT
ejpam-5911	562	10	b	b	NOUN
ejpam-5911	562	11	-	-	PUNCT
ejpam-5911	562	12	open	open	ADJ
ejpam-5911	562	13	.	.	PUNCT
ejpam-5911	563	1	(	(	PUNCT
ejpam-5911	563	2	ii	ii	NOUN
ejpam-5911	563	3	)	)	PUNCT
ejpam-5911	563	4	p(iℑ∗(m	p(iℑ∗(m	PROPN
ejpam-5911	563	5	,	,	PUNCT
ejpam-5911	563	6	r	r	NOUN
ejpam-5911	563	7	,	,	PUNCT
ejpam-5911	563	8	s	s	NOUN
ejpam-5911	563	9	)	)	PUNCT
ejpam-5911	563	10	)	)	PUNCT
ejpam-5911	563	11	≤	≤	NUM
ejpam-5911	564	1	bi𭟋∗(p(m	bi𭟋∗(p(m	NOUN
ejpam-5911	564	2	)	)	PUNCT
ejpam-5911	564	3	,	,	PUNCT
ejpam-5911	564	4	r	r	NOUN
ejpam-5911	564	5	,	,	PUNCT
ejpam-5911	564	6	s	s	NOUN
ejpam-5911	564	7	)	)	PUNCT
ejpam-5911	564	8	.	.	PUNCT
ejpam-5911	565	1	(	(	PUNCT
ejpam-5911	565	2	iii	iii	X
ejpam-5911	565	3	)	)	PUNCT
ejpam-5911	565	4	iℑ∗(p−1(n	iℑ∗(p−1(n	NOUN
ejpam-5911	565	5	)	)	PUNCT
ejpam-5911	566	1	,	,	PUNCT
ejpam-5911	566	2	r	r	NOUN
ejpam-5911	566	3	,	,	PUNCT
ejpam-5911	566	4	s	s	NOUN
ejpam-5911	566	5	)	)	PUNCT
ejpam-5911	566	6	≤	≤	NOUN
ejpam-5911	567	1	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	X
ejpam-5911	567	2	,	,	PUNCT
ejpam-5911	567	3	r	r	NOUN
ejpam-5911	567	4	,	,	PUNCT
ejpam-5911	567	5	s	s	NOUN
ejpam-5911	567	6	)	)	PUNCT
ejpam-5911	567	7	)	)	PUNCT
ejpam-5911	567	8	.	.	PUNCT
ejpam-5911	568	1	(	(	PUNCT
ejpam-5911	568	2	iv	iv	X
ejpam-5911	568	3	)	)	PUNCT
ejpam-5911	568	4	for	for	ADP
ejpam-5911	568	5	every	every	DET
ejpam-5911	568	6	n	n	NOUN
ejpam-5911	568	7	and	and	CCONJ
ejpam-5911	568	8	every	every	DET
ejpam-5911	568	9	m	m	NOUN
ejpam-5911	568	10	with	with	ADP
ejpam-5911	568	11	ℑ(mc	ℑ(mc	ADJ
ejpam-5911	568	12	)	)	PUNCT
ejpam-5911	568	13	≥	≥	NOUN
ejpam-5911	568	14	r	r	NOUN
ejpam-5911	568	15	,	,	PUNCT
ejpam-5911	568	16	ℑ∗(mc	ℑ∗(mc	X
ejpam-5911	568	17	)	)	PUNCT
ejpam-5911	568	18	≤	≤	PROPN
ejpam-5911	568	19	s	s	NOUN
ejpam-5911	568	20	and	and	CCONJ
ejpam-5911	568	21	p−1(n	p−1(n	NOUN
ejpam-5911	568	22	)	)	PUNCT
ejpam-5911	568	23	≤	≤	NUM
ejpam-5911	568	24	m	m	ADP
ejpam-5911	568	25	,	,	PUNCT
ejpam-5911	568	26	there	there	PRON
ejpam-5911	568	27	is	be	VERB
ejpam-5911	568	28	u	u	PROPN
ejpam-5911	568	29	∈	∈	PROPN
ejpam-5911	568	30	iz	iz	INTJ
ejpam-5911	568	31	is	be	AUX
ejpam-5911	568	32	(	(	PUNCT
ejpam-5911	568	33	r	r	NOUN
ejpam-5911	568	34	,	,	PUNCT
ejpam-5911	568	35	s)-f	s)-f	NOUN
ejpam-5911	568	36	-	-	PUNCT
ejpam-5911	568	37	b	b	NOUN
ejpam-5911	568	38	-	-	PUNCT
ejpam-5911	568	39	closed	closed	ADJ
ejpam-5911	568	40	with	with	ADP
ejpam-5911	568	41	n	n	DET
ejpam-5911	568	42	≤	≤	NOUN
ejpam-5911	568	43	u	u	NOUN
ejpam-5911	568	44	and	and	CCONJ
ejpam-5911	568	45	p−1(u	p−1(u	NOUN
ejpam-5911	568	46	)	)	PUNCT
ejpam-5911	568	47	≤	≤	NUM
ejpam-5911	568	48	m.	m.	NOUN
ejpam-5911	568	49	i.	i.	PROPN
ejpam-5911	568	50	m.	m.	PROPN
ejpam-5911	568	51	taha	taha	PROPN
ejpam-5911	568	52	,	,	PUNCT
ejpam-5911	568	53	j.	j.	PROPN
ejpam-5911	568	54	al	al	PROPN
ejpam-5911	568	55	-	-	PUNCT
ejpam-5911	568	56	mufarrij	mufarrij	PROPN
ejpam-5911	568	57	,	,	PUNCT
ejpam-5911	568	58	o.	o.	PROPN
ejpam-5911	568	59	m.	m.	PROPN
ejpam-5911	568	60	taha	taha	PROPN
ejpam-5911	568	61	/	/	PUNCT
ejpam-5911	568	62	eur	eur	PROPN
ejpam-5911	568	63	.	.	PUNCT
ejpam-5911	569	1	j.	j.	PROPN
ejpam-5911	569	2	pure	pure	PROPN
ejpam-5911	569	3	appl	appl	PROPN
ejpam-5911	569	4	.	.	PROPN
ejpam-5911	569	5	math	math	PROPN
ejpam-5911	569	6	,	,	PUNCT
ejpam-5911	569	7	18	18	NUM
ejpam-5911	569	8	(	(	PUNCT
ejpam-5911	569	9	2	2	NUM
ejpam-5911	569	10	)	)	PUNCT
ejpam-5911	569	11	(	(	PUNCT
ejpam-5911	569	12	2025	2025	NUM
ejpam-5911	569	13	)	)	PUNCT
ejpam-5911	569	14	,	,	PUNCT
ejpam-5911	569	15	5911	5911	NUM
ejpam-5911	569	16	20	20	NUM
ejpam-5911	569	17	of	of	ADP
ejpam-5911	569	18	27	27	NUM
ejpam-5911	569	19	proof	proof	NOUN
ejpam-5911	569	20	.	.	PUNCT
ejpam-5911	570	1	(	(	PUNCT
ejpam-5911	570	2	i	i	NOUN
ejpam-5911	570	3	)	)	PUNCT
ejpam-5911	570	4	⇒	⇒	PROPN
ejpam-5911	570	5	(	(	PUNCT
ejpam-5911	570	6	ii	ii	NOUN
ejpam-5911	570	7	)	)	PUNCT
ejpam-5911	570	8	since	since	SCONJ
ejpam-5911	570	9	p(iℑ∗(m	p(iℑ∗(m	PROPN
ejpam-5911	570	10	,	,	PUNCT
ejpam-5911	570	11	r	r	NOUN
ejpam-5911	570	12	,	,	PUNCT
ejpam-5911	570	13	s	s	NOUN
ejpam-5911	570	14	)	)	PUNCT
ejpam-5911	570	15	)	)	PUNCT
ejpam-5911	570	16	≤	≤	NUM
ejpam-5911	570	17	p(m	p(m	NOUN
ejpam-5911	570	18	)	)	PUNCT
ejpam-5911	570	19	,	,	PUNCT
ejpam-5911	570	20	hence	hence	ADV
ejpam-5911	570	21	by	by	ADP
ejpam-5911	570	22	(	(	PUNCT
ejpam-5911	570	23	i	i	NOUN
ejpam-5911	570	24	)	)	PUNCT
ejpam-5911	570	25	,	,	PUNCT
ejpam-5911	570	26	p(iℑ∗(m	p(iℑ∗(m	PROPN
ejpam-5911	570	27	,	,	PUNCT
ejpam-5911	570	28	r	r	NOUN
ejpam-5911	570	29	,	,	PUNCT
ejpam-5911	570	30	s	s	NOUN
ejpam-5911	570	31	)	)	PUNCT
ejpam-5911	570	32	)	)	PUNCT
ejpam-5911	570	33	is	be	AUX
ejpam-5911	570	34	(	(	PUNCT
ejpam-5911	570	35	r	r	NOUN
ejpam-5911	570	36	,	,	PUNCT
ejpam-5911	570	37	s)f	s)f	NUM
ejpam-5911	570	38	-	-	PUNCT
ejpam-5911	570	39	b	b	NOUN
ejpam-5911	570	40	-	-	PUNCT
ejpam-5911	570	41	open	open	ADJ
ejpam-5911	570	42	.	.	PUNCT
ejpam-5911	571	1	thus	thus	ADV
ejpam-5911	571	2	,	,	PUNCT
ejpam-5911	571	3	p(iℑ∗(m	p(iℑ∗(m	PROPN
ejpam-5911	571	4	,	,	PUNCT
ejpam-5911	571	5	r	r	NOUN
ejpam-5911	571	6	,	,	PUNCT
ejpam-5911	571	7	s	s	NOUN
ejpam-5911	571	8	)	)	PUNCT
ejpam-5911	571	9	)	)	PUNCT
ejpam-5911	571	10	≤	≤	NUM
ejpam-5911	572	1	bi𭟋∗(p(m	bi𭟋∗(p(m	NOUN
ejpam-5911	572	2	)	)	PUNCT
ejpam-5911	572	3	,	,	PUNCT
ejpam-5911	572	4	r	r	NOUN
ejpam-5911	572	5	,	,	PUNCT
ejpam-5911	572	6	s	s	NOUN
ejpam-5911	572	7	)	)	PUNCT
ejpam-5911	572	8	.	.	PUNCT
ejpam-5911	573	1	(	(	PUNCT
ejpam-5911	573	2	ii)⇒	ii)⇒	X
ejpam-5911	573	3	(	(	PUNCT
ejpam-5911	573	4	iii	iii	NOUN
ejpam-5911	573	5	)	)	PUNCT
ejpam-5911	573	6	setm	setm	NOUN
ejpam-5911	573	7	=	=	SYM
ejpam-5911	573	8	p−1(n	p−1(n	NOUN
ejpam-5911	573	9	)	)	PUNCT
ejpam-5911	573	10	,	,	PUNCT
ejpam-5911	573	11	hence	hence	ADV
ejpam-5911	573	12	by	by	ADP
ejpam-5911	573	13	(	(	PUNCT
ejpam-5911	573	14	ii	ii	NOUN
ejpam-5911	573	15	)	)	PUNCT
ejpam-5911	573	16	,	,	PUNCT
ejpam-5911	573	17	p(iℑ∗(p−1(n	p(iℑ∗(p−1(n	NOUN
ejpam-5911	573	18	)	)	PUNCT
ejpam-5911	573	19	,	,	PUNCT
ejpam-5911	573	20	r	r	NOUN
ejpam-5911	573	21	,	,	PUNCT
ejpam-5911	573	22	s	s	NOUN
ejpam-5911	573	23	)	)	PUNCT
ejpam-5911	573	24	)	)	PUNCT
ejpam-5911	574	1	≤	≤	NUM
ejpam-5911	574	2	bi𭟋∗(p(p−1(n	bi𭟋∗(p(p−1(n	NOUN
ejpam-5911	574	3	)	)	PUNCT
ejpam-5911	574	4	)	)	PUNCT
ejpam-5911	574	5	,	,	PUNCT
ejpam-5911	574	6	r	r	NOUN
ejpam-5911	574	7	,	,	PUNCT
ejpam-5911	574	8	s	s	NOUN
ejpam-5911	574	9	)	)	PUNCT
ejpam-5911	574	10	≤	≤	NOUN
ejpam-5911	574	11	bi𭟋∗(n	bi𭟋∗(n	NOUN
ejpam-5911	574	12	,	,	PUNCT
ejpam-5911	574	13	r	r	NOUN
ejpam-5911	574	14	,	,	PUNCT
ejpam-5911	574	15	s	s	NOUN
ejpam-5911	574	16	)	)	PUNCT
ejpam-5911	574	17	.	.	PUNCT
ejpam-5911	575	1	thus	thus	ADV
ejpam-5911	575	2	,	,	PUNCT
ejpam-5911	575	3	iℑ∗(p−1(n	iℑ∗(p−1(n	NOUN
ejpam-5911	575	4	)	)	PUNCT
ejpam-5911	575	5	,	,	PUNCT
ejpam-5911	575	6	r	r	NOUN
ejpam-5911	575	7	,	,	PUNCT
ejpam-5911	575	8	s	s	NOUN
ejpam-5911	575	9	)	)	PUNCT
ejpam-5911	575	10	≤	≤	NOUN
ejpam-5911	575	11	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	X
ejpam-5911	575	12	,	,	PUNCT
ejpam-5911	575	13	r	r	NOUN
ejpam-5911	575	14	,	,	PUNCT
ejpam-5911	575	15	s	s	NOUN
ejpam-5911	575	16	)	)	PUNCT
ejpam-5911	575	17	)	)	PUNCT
ejpam-5911	575	18	.	.	PUNCT
ejpam-5911	576	1	(	(	PUNCT
ejpam-5911	576	2	iii	iii	X
ejpam-5911	576	3	)	)	PUNCT
ejpam-5911	576	4	⇒	⇒	NOUN
ejpam-5911	576	5	(	(	PUNCT
ejpam-5911	576	6	iv	iv	X
ejpam-5911	576	7	)	)	PUNCT
ejpam-5911	576	8	let	let	VERB
ejpam-5911	576	9	n	n	PRON
ejpam-5911	576	10	∈	∈	VERB
ejpam-5911	577	1	iz	iz	INTJ
ejpam-5911	577	2	and	and	CCONJ
ejpam-5911	577	3	m	m	PROPN
ejpam-5911	577	4	∈	∈	NOUN
ejpam-5911	577	5	ig	ig	PROPN
ejpam-5911	577	6	with	with	ADP
ejpam-5911	577	7	ℑ(mc	ℑ(mc	ADJ
ejpam-5911	577	8	)	)	PUNCT
ejpam-5911	577	9	≥	≥	NOUN
ejpam-5911	577	10	r	r	NOUN
ejpam-5911	577	11	and	and	CCONJ
ejpam-5911	577	12	ℑ∗(mc	ℑ∗(mc	PROPN
ejpam-5911	577	13	)	)	PUNCT
ejpam-5911	577	14	≤	≤	NUM
ejpam-5911	577	15	s	s	VERB
ejpam-5911	577	16	such	such	ADJ
ejpam-5911	577	17	that	that	DET
ejpam-5911	577	18	p−1(n	p−1(n	NOUN
ejpam-5911	577	19	)	)	PUNCT
ejpam-5911	577	20	≤	≤	NUM
ejpam-5911	577	21	m.	m.	NOUN
ejpam-5911	577	22	since	since	SCONJ
ejpam-5911	577	23	mc	mc	PROPN
ejpam-5911	577	24	≤	≤	PROPN
ejpam-5911	577	25	p−1(n	p−1(n	PROPN
ejpam-5911	577	26	c	c	PROPN
ejpam-5911	577	27	)	)	PUNCT
ejpam-5911	577	28	,	,	PUNCT
ejpam-5911	577	29	mc	mc	PROPN
ejpam-5911	577	30	=	=	PROPN
ejpam-5911	577	31	iℑ∗(mc	iℑ∗(mc	PROPN
ejpam-5911	577	32	,	,	PUNCT
ejpam-5911	577	33	r	r	NOUN
ejpam-5911	577	34	,	,	PUNCT
ejpam-5911	577	35	s	s	NOUN
ejpam-5911	577	36	)	)	PUNCT
ejpam-5911	577	37	≤	≤	NUM
ejpam-5911	577	38	iℑ∗(p−1(n	iℑ∗(p−1(n	NUM
ejpam-5911	577	39	c	c	NOUN
ejpam-5911	577	40	)	)	PUNCT
ejpam-5911	577	41	,	,	PUNCT
ejpam-5911	577	42	r	r	NOUN
ejpam-5911	577	43	,	,	PUNCT
ejpam-5911	577	44	s	s	NOUN
ejpam-5911	577	45	)	)	PUNCT
ejpam-5911	577	46	.	.	PUNCT
ejpam-5911	578	1	hence	hence	ADV
ejpam-5911	578	2	by	by	ADP
ejpam-5911	578	3	(	(	PUNCT
ejpam-5911	578	4	iii	iii	NOUN
ejpam-5911	578	5	)	)	PUNCT
ejpam-5911	578	6	,	,	PUNCT
ejpam-5911	578	7	mc	mc	PROPN
ejpam-5911	578	8	≤	≤	NUM
ejpam-5911	578	9	iℑ∗(p−1(n	iℑ∗(p−1(n	PRON
ejpam-5911	578	10	c	c	NOUN
ejpam-5911	578	11	)	)	PUNCT
ejpam-5911	578	12	,	,	PUNCT
ejpam-5911	578	13	r	r	NOUN
ejpam-5911	578	14	,	,	PUNCT
ejpam-5911	578	15	s	s	NOUN
ejpam-5911	578	16	)	)	PUNCT
ejpam-5911	578	17	≤	≤	PUNCT
ejpam-5911	578	18	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	ADP
ejpam-5911	578	19	c	c	NOUN
ejpam-5911	578	20	,	,	PUNCT
ejpam-5911	578	21	r	r	NOUN
ejpam-5911	578	22	,	,	PUNCT
ejpam-5911	578	23	s	s	NOUN
ejpam-5911	578	24	)	)	PUNCT
ejpam-5911	578	25	)	)	PUNCT
ejpam-5911	578	26	.	.	PUNCT
ejpam-5911	579	1	then	then	ADV
ejpam-5911	579	2	,	,	PUNCT
ejpam-5911	579	3	we	we	PRON
ejpam-5911	579	4	have	have	VERB
ejpam-5911	579	5	m	m	PRON
ejpam-5911	579	6	≥	≥	NOUN
ejpam-5911	579	7	(	(	PUNCT
ejpam-5911	579	8	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	PROPN
ejpam-5911	579	9	c	c	PROPN
ejpam-5911	579	10	,	,	PUNCT
ejpam-5911	579	11	r	r	NOUN
ejpam-5911	579	12	,	,	PUNCT
ejpam-5911	579	13	s)))c	s)))c	ADJ
ejpam-5911	579	14	=	=	SYM
ejpam-5911	579	15	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	PROPN
ejpam-5911	579	16	,	,	PUNCT
ejpam-5911	579	17	r	r	NOUN
ejpam-5911	579	18	,	,	PUNCT
ejpam-5911	579	19	s	s	NOUN
ejpam-5911	579	20	)	)	PUNCT
ejpam-5911	579	21	)	)	PUNCT
ejpam-5911	579	22	.	.	PUNCT
ejpam-5911	580	1	thus	thus	ADV
ejpam-5911	580	2	,	,	PUNCT
ejpam-5911	580	3	bc𭟋∗(n	bc𭟋∗(n	NOUN
ejpam-5911	580	4	,	,	PUNCT
ejpam-5911	580	5	r	r	NOUN
ejpam-5911	580	6	,	,	PUNCT
ejpam-5911	580	7	s	s	PART
ejpam-5911	580	8	)	)	PUNCT
ejpam-5911	580	9	∈	∈	NOUN
ejpam-5911	580	10	iz	iz	VERB
ejpam-5911	580	11	is	be	AUX
ejpam-5911	580	12	(	(	PUNCT
ejpam-5911	580	13	r	r	NOUN
ejpam-5911	580	14	,	,	PUNCT
ejpam-5911	580	15	s)-f	s)-f	NOUN
ejpam-5911	580	16	-	-	PUNCT
ejpam-5911	580	17	b	b	NOUN
ejpam-5911	580	18	-	-	PUNCT
ejpam-5911	580	19	closed	close	VERB
ejpam-5911	580	20	withn	withn	NOUN
ejpam-5911	580	21	≤	≤	NOUN
ejpam-5911	580	22	bc𭟋∗(n	bc𭟋∗(n	X
ejpam-5911	580	23	,	,	PUNCT
ejpam-5911	580	24	r	r	NOUN
ejpam-5911	580	25	,	,	PUNCT
ejpam-5911	580	26	s	s	PART
ejpam-5911	580	27	)	)	PUNCT
ejpam-5911	580	28	and	and	CCONJ
ejpam-5911	580	29	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	PROPN
ejpam-5911	580	30	,	,	PUNCT
ejpam-5911	580	31	r	r	NOUN
ejpam-5911	580	32	,	,	PUNCT
ejpam-5911	580	33	s	s	NOUN
ejpam-5911	580	34	)	)	PUNCT
ejpam-5911	580	35	)	)	PUNCT
ejpam-5911	580	36	≤	≤	NUM
ejpam-5911	580	37	m.	m.	NOUN
ejpam-5911	580	38	(	(	PUNCT
ejpam-5911	580	39	iv	iv	X
ejpam-5911	580	40	)	)	PUNCT
ejpam-5911	580	41	⇒	⇒	NOUN
ejpam-5911	580	42	(	(	PUNCT
ejpam-5911	580	43	i	i	NOUN
ejpam-5911	580	44	)	)	PUNCT
ejpam-5911	580	45	let	let	VERB
ejpam-5911	580	46	v	v	NUM
ejpam-5911	580	47	∈	∈	VERB
ejpam-5911	580	48	ig	ig	PROPN
ejpam-5911	580	49	with	with	ADP
ejpam-5911	580	50	ℑ(v	ℑ(v	NOUN
ejpam-5911	580	51	)	)	PUNCT
ejpam-5911	580	52	≥	≥	NOUN
ejpam-5911	580	53	r	r	NOUN
ejpam-5911	580	54	and	and	CCONJ
ejpam-5911	580	55	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	580	56	)	)	PUNCT
ejpam-5911	580	57	≤	≤	NUM
ejpam-5911	580	58	s.	s.	PROPN
ejpam-5911	580	59	set	set	VERB
ejpam-5911	580	60	n	n	NOUN
ejpam-5911	580	61	=	=	SYM
ejpam-5911	580	62	(	(	PUNCT
ejpam-5911	580	63	p(v))c	p(v))c	PROPN
ejpam-5911	580	64	and	and	CCONJ
ejpam-5911	580	65	m	m	PROPN
ejpam-5911	580	66	=	=	ADJ
ejpam-5911	580	67	vc	vc	PROPN
ejpam-5911	580	68	,	,	PUNCT
ejpam-5911	580	69	then	then	ADV
ejpam-5911	580	70	p−1(n	p−1(n	ADV
ejpam-5911	580	71	)	)	PUNCT
ejpam-5911	580	72	=	=	PUNCT
ejpam-5911	580	73	p−1((p(v))c	p−1((p(v))c	X
ejpam-5911	580	74	)	)	PUNCT
ejpam-5911	580	75	≤	≤	NUM
ejpam-5911	580	76	m.	m.	NOUN
ejpam-5911	580	77	hence	hence	ADV
ejpam-5911	580	78	by	by	ADP
ejpam-5911	580	79	(	(	PUNCT
ejpam-5911	580	80	iv	iv	X
ejpam-5911	580	81	)	)	PUNCT
ejpam-5911	580	82	,	,	PUNCT
ejpam-5911	580	83	there	there	PRON
ejpam-5911	580	84	is	be	VERB
ejpam-5911	580	85	u	u	PROPN
ejpam-5911	580	86	∈	∈	PROPN
ejpam-5911	580	87	iz	iz	INTJ
ejpam-5911	580	88	is	be	AUX
ejpam-5911	580	89	(	(	PUNCT
ejpam-5911	580	90	r	r	NOUN
ejpam-5911	580	91	,	,	PUNCT
ejpam-5911	580	92	s)-f	s)-f	NOUN
ejpam-5911	580	93	-	-	PUNCT
ejpam-5911	580	94	b	b	NOUN
ejpam-5911	580	95	-	-	PUNCT
ejpam-5911	580	96	closed	closed	ADJ
ejpam-5911	580	97	with	with	ADP
ejpam-5911	580	98	n	n	DET
ejpam-5911	580	99	≤	≤	NOUN
ejpam-5911	580	100	u	u	NOUN
ejpam-5911	580	101	and	and	CCONJ
ejpam-5911	580	102	p−1(u	p−1(u	NOUN
ejpam-5911	580	103	)	)	PUNCT
ejpam-5911	581	1	≤	≤	NUM
ejpam-5911	582	1	m	m	NOUN
ejpam-5911	582	2	=	=	SYM
ejpam-5911	582	3	vc	vc	PROPN
ejpam-5911	582	4	.	.	PUNCT
ejpam-5911	582	5	thus	thus	ADV
ejpam-5911	582	6	,	,	PUNCT
ejpam-5911	582	7	p(v	p(v	NOUN
ejpam-5911	582	8	)	)	PUNCT
ejpam-5911	582	9	≤	≤	NUM
ejpam-5911	582	10	p(p−1(uc	p(p−1(uc	NOUN
ejpam-5911	582	11	)	)	PUNCT
ejpam-5911	582	12	)	)	PUNCT
ejpam-5911	582	13	≤	≤	PUNCT
ejpam-5911	583	1	uc	uc	PROPN
ejpam-5911	583	2	.	.	PUNCT
ejpam-5911	584	1	on	on	ADP
ejpam-5911	584	2	the	the	DET
ejpam-5911	584	3	other	other	ADJ
ejpam-5911	584	4	hand	hand	NOUN
ejpam-5911	584	5	,	,	PUNCT
ejpam-5911	584	6	since	since	SCONJ
ejpam-5911	584	7	n	n	ADP
ejpam-5911	584	8	≤	≤	NOUN
ejpam-5911	584	9	u	u	NOUN
ejpam-5911	584	10	,	,	PUNCT
ejpam-5911	584	11	p(v	p(v	NOUN
ejpam-5911	584	12	)	)	PUNCT
ejpam-5911	584	13	=	=	SYM
ejpam-5911	584	14	n	n	PROPN
ejpam-5911	584	15	c	c	X
ejpam-5911	584	16	≥	≥	X
ejpam-5911	584	17	uc	uc	PROPN
ejpam-5911	584	18	.	.	PROPN
ejpam-5911	584	19	hence	hence	ADV
ejpam-5911	584	20	,	,	PUNCT
ejpam-5911	584	21	p(v	p(v	NOUN
ejpam-5911	584	22	)	)	PUNCT
ejpam-5911	584	23	=	=	SYM
ejpam-5911	585	1	uc	uc	PROPN
ejpam-5911	585	2	,	,	PUNCT
ejpam-5911	585	3	so	so	SCONJ
ejpam-5911	585	4	p(v	p(v	NOUN
ejpam-5911	585	5	)	)	PUNCT
ejpam-5911	585	6	is	be	AUX
ejpam-5911	585	7	an	an	DET
ejpam-5911	585	8	(	(	PUNCT
ejpam-5911	585	9	r	r	NOUN
ejpam-5911	585	10	,	,	PUNCT
ejpam-5911	585	11	s)-f	s)-f	NOUN
ejpam-5911	585	12	-	-	PUNCT
ejpam-5911	585	13	b	b	NOUN
ejpam-5911	585	14	-	-	PUNCT
ejpam-5911	585	15	open	open	ADJ
ejpam-5911	585	16	set	set	NOUN
ejpam-5911	585	17	.	.	PUNCT
ejpam-5911	586	1	therefore	therefore	ADV
ejpam-5911	586	2	,	,	PUNCT
ejpam-5911	586	3	p	p	PRON
ejpam-5911	586	4	is	be	AUX
ejpam-5911	586	5	df	df	PROPN
ejpam-5911	586	6	-	-	PUNCT
ejpam-5911	586	7	b	b	NOUN
ejpam-5911	586	8	-	-	PUNCT
ejpam-5911	586	9	open	open	ADJ
ejpam-5911	586	10	.	.	PUNCT
ejpam-5911	587	1	theorem	theorem	VERB
ejpam-5911	587	2	11	11	NUM
ejpam-5911	587	3	.	.	PUNCT
ejpam-5911	588	1	let	let	VERB
ejpam-5911	588	2	p	p	NOUN
ejpam-5911	588	3	:	:	PUNCT
ejpam-5911	588	4	(	(	PUNCT
ejpam-5911	588	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	588	6	)	)	PUNCT
ejpam-5911	589	1	−→	−→	NOUN
ejpam-5911	589	2	(	(	PUNCT
ejpam-5911	589	3	z	z	NOUN
ejpam-5911	589	4	,	,	PUNCT
ejpam-5911	589	5	𭟋	𭟋	NOUN
ejpam-5911	589	6	,	,	PUNCT
ejpam-5911	589	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	589	8	)	)	PUNCT
ejpam-5911	589	9	be	be	AUX
ejpam-5911	589	10	an	an	DET
ejpam-5911	589	11	f	f	NOUN
ejpam-5911	589	12	-	-	PUNCT
ejpam-5911	589	13	mapping	mapping	NOUN
ejpam-5911	589	14	.	.	PUNCT
ejpam-5911	590	1	then	then	ADV
ejpam-5911	590	2	the	the	DET
ejpam-5911	590	3	following	follow	VERB
ejpam-5911	590	4	statements	statement	NOUN
ejpam-5911	590	5	are	be	AUX
ejpam-5911	590	6	equivalent	equivalent	ADJ
ejpam-5911	590	7	for	for	ADP
ejpam-5911	590	8	every	every	DET
ejpam-5911	590	9	m	m	NOUN
ejpam-5911	590	10	∈	∈	NOUN
ejpam-5911	590	11	ig	ig	PROPN
ejpam-5911	590	12	and	and	CCONJ
ejpam-5911	590	13	n	n	PRON
ejpam-5911	590	14	∈	∈	PROPN
ejpam-5911	591	1	iz	iz	INTJ
ejpam-5911	591	2	:	:	PUNCT
ejpam-5911	591	3	(	(	PUNCT
ejpam-5911	591	4	i	i	NOUN
ejpam-5911	591	5	)	)	PUNCT
ejpam-5911	591	6	p	p	NOUN
ejpam-5911	591	7	is	be	AUX
ejpam-5911	591	8	df	df	PROPN
ejpam-5911	591	9	-	-	PUNCT
ejpam-5911	591	10	b	b	NOUN
ejpam-5911	591	11	-	-	PUNCT
ejpam-5911	591	12	irresolute	irresolute	ADJ
ejpam-5911	591	13	open	open	ADJ
ejpam-5911	591	14	.	.	PUNCT
ejpam-5911	592	1	(	(	PUNCT
ejpam-5911	592	2	ii	ii	NOUN
ejpam-5911	592	3	)	)	PUNCT
ejpam-5911	592	4	p(biℑ∗(m	p(biℑ∗(m	PUNCT
ejpam-5911	592	5	,	,	PUNCT
ejpam-5911	592	6	r	r	NOUN
ejpam-5911	592	7	,	,	PUNCT
ejpam-5911	592	8	s	s	NOUN
ejpam-5911	592	9	)	)	PUNCT
ejpam-5911	592	10	)	)	PUNCT
ejpam-5911	592	11	≤	≤	NUM
ejpam-5911	593	1	bi𭟋∗(p(m	bi𭟋∗(p(m	NOUN
ejpam-5911	593	2	)	)	PUNCT
ejpam-5911	593	3	,	,	PUNCT
ejpam-5911	593	4	r	r	NOUN
ejpam-5911	593	5	,	,	PUNCT
ejpam-5911	593	6	s	s	NOUN
ejpam-5911	593	7	)	)	PUNCT
ejpam-5911	593	8	.	.	PUNCT
ejpam-5911	594	1	(	(	PUNCT
ejpam-5911	594	2	iii	iii	X
ejpam-5911	594	3	)	)	PUNCT
ejpam-5911	594	4	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	594	5	)	)	PUNCT
ejpam-5911	594	6	,	,	PUNCT
ejpam-5911	594	7	r	r	NOUN
ejpam-5911	594	8	,	,	PUNCT
ejpam-5911	594	9	s	s	NOUN
ejpam-5911	594	10	)	)	PUNCT
ejpam-5911	594	11	≤	≤	NOUN
ejpam-5911	595	1	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	X
ejpam-5911	595	2	,	,	PUNCT
ejpam-5911	595	3	r	r	NOUN
ejpam-5911	595	4	,	,	PUNCT
ejpam-5911	595	5	s	s	NOUN
ejpam-5911	595	6	)	)	PUNCT
ejpam-5911	595	7	)	)	PUNCT
ejpam-5911	595	8	.	.	PUNCT
ejpam-5911	596	1	(	(	PUNCT
ejpam-5911	596	2	iv	iv	X
ejpam-5911	596	3	)	)	PUNCT
ejpam-5911	596	4	for	for	ADP
ejpam-5911	596	5	every	every	DET
ejpam-5911	596	6	n	n	NOUN
ejpam-5911	596	7	and	and	CCONJ
ejpam-5911	596	8	every	every	DET
ejpam-5911	596	9	m	m	NOUN
ejpam-5911	596	10	is	be	AUX
ejpam-5911	596	11	an	an	DET
ejpam-5911	596	12	(	(	PUNCT
ejpam-5911	596	13	r	r	NOUN
ejpam-5911	596	14	,	,	PUNCT
ejpam-5911	596	15	s)-f	s)-f	NOUN
ejpam-5911	596	16	-	-	PUNCT
ejpam-5911	596	17	b	b	NOUN
ejpam-5911	596	18	-	-	PUNCT
ejpam-5911	596	19	closed	closed	ADJ
ejpam-5911	596	20	set	set	NOUN
ejpam-5911	596	21	with	with	ADP
ejpam-5911	596	22	p−1(n	p−1(n	NOUN
ejpam-5911	596	23	)	)	PUNCT
ejpam-5911	596	24	≤	≤	NUM
ejpam-5911	596	25	m	m	ADP
ejpam-5911	596	26	,	,	PUNCT
ejpam-5911	596	27	there	there	PRON
ejpam-5911	596	28	is	be	VERB
ejpam-5911	596	29	u	u	PROPN
ejpam-5911	596	30	∈	∈	PROPN
ejpam-5911	596	31	iz	iz	INTJ
ejpam-5911	596	32	is	be	AUX
ejpam-5911	596	33	(	(	PUNCT
ejpam-5911	596	34	r	r	NOUN
ejpam-5911	596	35	,	,	PUNCT
ejpam-5911	596	36	s)-f	s)-f	NOUN
ejpam-5911	596	37	-	-	PUNCT
ejpam-5911	596	38	b	b	NOUN
ejpam-5911	596	39	-	-	PUNCT
ejpam-5911	596	40	closed	closed	ADJ
ejpam-5911	596	41	with	with	ADP
ejpam-5911	596	42	n	n	DET
ejpam-5911	596	43	≤	≤	NOUN
ejpam-5911	596	44	u	u	NOUN
ejpam-5911	596	45	and	and	CCONJ
ejpam-5911	596	46	p−1(u	p−1(u	NOUN
ejpam-5911	596	47	)	)	PUNCT
ejpam-5911	596	48	≤	≤	NUM
ejpam-5911	596	49	m.	m.	NOUN
ejpam-5911	596	50	proof	proof	NOUN
ejpam-5911	596	51	.	.	PUNCT
ejpam-5911	597	1	the	the	DET
ejpam-5911	597	2	proof	proof	NOUN
ejpam-5911	597	3	is	be	AUX
ejpam-5911	597	4	similar	similar	ADJ
ejpam-5911	597	5	to	to	ADP
ejpam-5911	597	6	that	that	PRON
ejpam-5911	597	7	of	of	ADP
ejpam-5911	597	8	theorem	theorem	ADJ
ejpam-5911	597	9	10	10	NUM
ejpam-5911	597	10	.	.	PUNCT
ejpam-5911	598	1	definition	definition	NOUN
ejpam-5911	598	2	16	16	NUM
ejpam-5911	598	3	.	.	PUNCT
ejpam-5911	599	1	an	an	DET
ejpam-5911	599	2	f	f	X
ejpam-5911	599	3	-	-	PUNCT
ejpam-5911	599	4	mapping	mapping	NOUN
ejpam-5911	599	5	p	p	NOUN
ejpam-5911	599	6	:	:	PUNCT
ejpam-5911	599	7	(	(	PUNCT
ejpam-5911	599	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	599	9	)	)	PUNCT
ejpam-5911	600	1	−→	−→	NOUN
ejpam-5911	600	2	(	(	PUNCT
ejpam-5911	600	3	z	z	NOUN
ejpam-5911	600	4	,	,	PUNCT
ejpam-5911	600	5	𭟋	𭟋	NOUN
ejpam-5911	600	6	,	,	PUNCT
ejpam-5911	600	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	600	8	)	)	PUNCT
ejpam-5911	600	9	is	be	AUX
ejpam-5911	600	10	called	call	VERB
ejpam-5911	600	11	df	df	PROPN
ejpam-5911	600	12	-	-	PUNCT
ejpam-5911	600	13	b	b	NOUN
ejpam-5911	600	14	-	-	PUNCT
ejpam-5911	600	15	closed	closed	ADJ
ejpam-5911	600	16	if	if	SCONJ
ejpam-5911	600	17	p(m	p(m	NOUN
ejpam-5911	600	18	)	)	PUNCT
ejpam-5911	600	19	is	be	AUX
ejpam-5911	600	20	an	an	DET
ejpam-5911	600	21	(	(	PUNCT
ejpam-5911	600	22	r	r	NOUN
ejpam-5911	600	23	,	,	PUNCT
ejpam-5911	600	24	s)-f	s)-f	NOUN
ejpam-5911	600	25	-	-	PUNCT
ejpam-5911	600	26	b	b	NOUN
ejpam-5911	600	27	-	-	PUNCT
ejpam-5911	600	28	closed	closed	ADJ
ejpam-5911	600	29	set	set	NOUN
ejpam-5911	600	30	,	,	PUNCT
ejpam-5911	600	31	for	for	ADP
ejpam-5911	600	32	each	each	DET
ejpam-5911	600	33	m	m	NOUN
ejpam-5911	600	34	∈	∈	NOUN
ejpam-5911	600	35	ig	ig	PROPN
ejpam-5911	600	36	with	with	ADP
ejpam-5911	600	37	ℑ(mc	ℑ(mc	ADJ
ejpam-5911	600	38	)	)	PUNCT
ejpam-5911	600	39	≥	≥	NOUN
ejpam-5911	600	40	r	r	NOUN
ejpam-5911	600	41	and	and	CCONJ
ejpam-5911	600	42	ℑ∗(mc	ℑ∗(mc	NOUN
ejpam-5911	600	43	)	)	PUNCT
ejpam-5911	600	44	≤	≤	NUM
ejpam-5911	600	45	s.	s.	PROPN
ejpam-5911	600	46	definition	definition	NOUN
ejpam-5911	600	47	17	17	NUM
ejpam-5911	600	48	.	.	PUNCT
ejpam-5911	601	1	an	an	DET
ejpam-5911	601	2	f	f	X
ejpam-5911	601	3	-	-	PUNCT
ejpam-5911	601	4	mapping	mapping	NOUN
ejpam-5911	601	5	p	p	NOUN
ejpam-5911	601	6	:	:	PUNCT
ejpam-5911	601	7	(	(	PUNCT
ejpam-5911	601	8	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	601	9	)	)	PUNCT
ejpam-5911	602	1	−→	−→	NOUN
ejpam-5911	602	2	(	(	PUNCT
ejpam-5911	602	3	z	z	NOUN
ejpam-5911	602	4	,	,	PUNCT
ejpam-5911	602	5	𭟋	𭟋	NOUN
ejpam-5911	602	6	,	,	PUNCT
ejpam-5911	602	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	602	8	)	)	PUNCT
ejpam-5911	602	9	is	be	AUX
ejpam-5911	602	10	called	call	VERB
ejpam-5911	602	11	df	df	PROPN
ejpam-5911	602	12	-	-	PUNCT
ejpam-5911	602	13	b	b	NOUN
ejpam-5911	602	14	-	-	PUNCT
ejpam-5911	602	15	irresolute	irresolute	ADJ
ejpam-5911	602	16	closed	closed	ADJ
ejpam-5911	602	17	if	if	SCONJ
ejpam-5911	602	18	p(m	p(m	NOUN
ejpam-5911	602	19	)	)	PUNCT
ejpam-5911	602	20	is	be	AUX
ejpam-5911	602	21	an	an	DET
ejpam-5911	602	22	(	(	PUNCT
ejpam-5911	602	23	r	r	NOUN
ejpam-5911	602	24	,	,	PUNCT
ejpam-5911	602	25	s)-f	s)-f	NOUN
ejpam-5911	602	26	-	-	PUNCT
ejpam-5911	602	27	b	b	NOUN
ejpam-5911	602	28	-	-	PUNCT
ejpam-5911	602	29	closed	closed	ADJ
ejpam-5911	602	30	set	set	NOUN
ejpam-5911	602	31	,	,	PUNCT
ejpam-5911	602	32	for	for	ADP
ejpam-5911	602	33	each	each	DET
ejpam-5911	602	34	(	(	PUNCT
ejpam-5911	602	35	r	r	NOUN
ejpam-5911	602	36	,	,	PUNCT
ejpam-5911	602	37	s)-f	s)-f	NOUN
ejpam-5911	602	38	-	-	PUNCT
ejpam-5911	602	39	b	b	NOUN
ejpam-5911	602	40	-	-	PUNCT
ejpam-5911	602	41	closed	closed	ADJ
ejpam-5911	602	42	set	set	NOUN
ejpam-5911	602	43	m	m	PROPN
ejpam-5911	602	44	∈	∈	PROPN
ejpam-5911	602	45	ig	ig	PROPN
ejpam-5911	602	46	.	.	PROPN
ejpam-5911	602	47	i.	i.	PROPN
ejpam-5911	602	48	m.	m.	PROPN
ejpam-5911	602	49	taha	taha	PROPN
ejpam-5911	602	50	,	,	PUNCT
ejpam-5911	602	51	j.	j.	PROPN
ejpam-5911	602	52	al	al	PROPN
ejpam-5911	602	53	-	-	PUNCT
ejpam-5911	602	54	mufarrij	mufarrij	PROPN
ejpam-5911	602	55	,	,	PUNCT
ejpam-5911	602	56	o.	o.	PROPN
ejpam-5911	602	57	m.	m.	PROPN
ejpam-5911	602	58	taha	taha	PROPN
ejpam-5911	602	59	/	/	PUNCT
ejpam-5911	602	60	eur	eur	PROPN
ejpam-5911	602	61	.	.	PUNCT
ejpam-5911	603	1	j.	j.	PROPN
ejpam-5911	603	2	pure	pure	PROPN
ejpam-5911	603	3	appl	appl	PROPN
ejpam-5911	603	4	.	.	PROPN
ejpam-5911	603	5	math	math	PROPN
ejpam-5911	603	6	,	,	PUNCT
ejpam-5911	603	7	18	18	NUM
ejpam-5911	603	8	(	(	PUNCT
ejpam-5911	603	9	2	2	NUM
ejpam-5911	603	10	)	)	PUNCT
ejpam-5911	603	11	(	(	PUNCT
ejpam-5911	603	12	2025	2025	NUM
ejpam-5911	603	13	)	)	PUNCT
ejpam-5911	603	14	,	,	PUNCT
ejpam-5911	603	15	5911	5911	NUM
ejpam-5911	603	16	21	21	NUM
ejpam-5911	603	17	of	of	ADP
ejpam-5911	603	18	27	27	NUM
ejpam-5911	603	19	lemma	lemma	PROPN
ejpam-5911	603	20	7	7	NUM
ejpam-5911	603	21	.	.	PUNCT
ejpam-5911	604	1	each	each	DET
ejpam-5911	604	2	df	df	PROPN
ejpam-5911	604	3	-	-	PUNCT
ejpam-5911	604	4	b	b	NOUN
ejpam-5911	604	5	-	-	PUNCT
ejpam-5911	604	6	irresolute	irresolute	ADJ
ejpam-5911	604	7	closed	closed	ADJ
ejpam-5911	604	8	mapping	mapping	NOUN
ejpam-5911	604	9	is	be	AUX
ejpam-5911	604	10	df	df	PROPN
ejpam-5911	604	11	-	-	PUNCT
ejpam-5911	604	12	b	b	NOUN
ejpam-5911	604	13	-	-	PUNCT
ejpam-5911	604	14	closed	closed	ADJ
ejpam-5911	604	15	.	.	PUNCT
ejpam-5911	605	1	proof	proof	NOUN
ejpam-5911	605	2	.	.	PUNCT
ejpam-5911	606	1	the	the	DET
ejpam-5911	606	2	proof	proof	NOUN
ejpam-5911	606	3	follows	follow	VERB
ejpam-5911	606	4	from	from	ADP
ejpam-5911	606	5	definitions	definition	NOUN
ejpam-5911	606	6	16	16	NUM
ejpam-5911	606	7	and	and	CCONJ
ejpam-5911	606	8	17	17	NUM
ejpam-5911	606	9	.	.	PUNCT
ejpam-5911	607	1	theorem	theorem	NOUN
ejpam-5911	607	2	12	12	NUM
ejpam-5911	607	3	.	.	PUNCT
ejpam-5911	608	1	let	let	VERB
ejpam-5911	608	2	p	p	NOUN
ejpam-5911	608	3	:	:	PUNCT
ejpam-5911	608	4	(	(	PUNCT
ejpam-5911	608	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	608	6	)	)	PUNCT
ejpam-5911	609	1	−→	−→	NOUN
ejpam-5911	609	2	(	(	PUNCT
ejpam-5911	609	3	z	z	NOUN
ejpam-5911	609	4	,	,	PUNCT
ejpam-5911	609	5	𭟋	𭟋	NOUN
ejpam-5911	609	6	,	,	PUNCT
ejpam-5911	609	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	609	8	)	)	PUNCT
ejpam-5911	609	9	be	be	AUX
ejpam-5911	609	10	an	an	DET
ejpam-5911	609	11	f	f	NOUN
ejpam-5911	609	12	-	-	PUNCT
ejpam-5911	609	13	mapping	mapping	NOUN
ejpam-5911	609	14	.	.	PUNCT
ejpam-5911	610	1	then	then	ADV
ejpam-5911	610	2	the	the	DET
ejpam-5911	610	3	following	follow	VERB
ejpam-5911	610	4	statements	statement	NOUN
ejpam-5911	610	5	are	be	AUX
ejpam-5911	610	6	equivalent	equivalent	ADJ
ejpam-5911	610	7	for	for	ADP
ejpam-5911	610	8	every	every	DET
ejpam-5911	610	9	m	m	NOUN
ejpam-5911	610	10	∈	∈	NOUN
ejpam-5911	610	11	ig	ig	PROPN
ejpam-5911	610	12	and	and	CCONJ
ejpam-5911	610	13	n	n	PRON
ejpam-5911	610	14	∈	∈	PROPN
ejpam-5911	611	1	iz	iz	INTJ
ejpam-5911	611	2	:	:	PUNCT
ejpam-5911	611	3	(	(	PUNCT
ejpam-5911	611	4	i	i	NOUN
ejpam-5911	611	5	)	)	PUNCT
ejpam-5911	611	6	p	p	NOUN
ejpam-5911	611	7	is	be	AUX
ejpam-5911	611	8	df	df	PROPN
ejpam-5911	611	9	-	-	PUNCT
ejpam-5911	611	10	b	b	NOUN
ejpam-5911	611	11	-	-	PUNCT
ejpam-5911	611	12	closed	closed	ADJ
ejpam-5911	611	13	.	.	PUNCT
ejpam-5911	612	1	(	(	PUNCT
ejpam-5911	612	2	ii	ii	NOUN
ejpam-5911	612	3	)	)	PUNCT
ejpam-5911	612	4	bc𭟋∗(p(m	bc𭟋∗(p(m	NOUN
ejpam-5911	612	5	)	)	PUNCT
ejpam-5911	612	6	,	,	PUNCT
ejpam-5911	612	7	r	r	NOUN
ejpam-5911	612	8	,	,	PUNCT
ejpam-5911	612	9	s	s	NOUN
ejpam-5911	612	10	)	)	PUNCT
ejpam-5911	612	11	≤	≤	NOUN
ejpam-5911	612	12	p(cℑ∗(m	p(cℑ∗(m	NUM
ejpam-5911	612	13	,	,	PUNCT
ejpam-5911	612	14	r	r	NOUN
ejpam-5911	612	15	,	,	PUNCT
ejpam-5911	612	16	s	s	NOUN
ejpam-5911	612	17	)	)	PUNCT
ejpam-5911	612	18	)	)	PUNCT
ejpam-5911	612	19	.	.	PUNCT
ejpam-5911	613	1	(	(	PUNCT
ejpam-5911	613	2	iii	iii	X
ejpam-5911	613	3	)	)	PUNCT
ejpam-5911	613	4	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	PROPN
ejpam-5911	613	5	,	,	PUNCT
ejpam-5911	613	6	r	r	NOUN
ejpam-5911	613	7	,	,	PUNCT
ejpam-5911	613	8	s	s	NOUN
ejpam-5911	613	9	)	)	PUNCT
ejpam-5911	613	10	)	)	PUNCT
ejpam-5911	613	11	≤	≤	NUM
ejpam-5911	613	12	cℑ∗(p−1(n	cℑ∗(p−1(n	NOUN
ejpam-5911	613	13	)	)	PUNCT
ejpam-5911	613	14	,	,	PUNCT
ejpam-5911	613	15	r	r	NOUN
ejpam-5911	613	16	,	,	PUNCT
ejpam-5911	613	17	s	s	NOUN
ejpam-5911	613	18	)	)	PUNCT
ejpam-5911	613	19	.	.	PUNCT
ejpam-5911	614	1	(	(	PUNCT
ejpam-5911	614	2	iv	iv	X
ejpam-5911	614	3	)	)	PUNCT
ejpam-5911	614	4	for	for	ADP
ejpam-5911	614	5	every	every	DET
ejpam-5911	614	6	n	n	NOUN
ejpam-5911	614	7	and	and	CCONJ
ejpam-5911	614	8	every	every	DET
ejpam-5911	614	9	m	m	NOUN
ejpam-5911	614	10	with	with	ADP
ejpam-5911	614	11	ℑ(m	ℑ(m	NOUN
ejpam-5911	614	12	)	)	PUNCT
ejpam-5911	614	13	≥	≥	NOUN
ejpam-5911	614	14	r	r	NOUN
ejpam-5911	614	15	,	,	PUNCT
ejpam-5911	614	16	ℑ∗(m	ℑ∗(m	PROPN
ejpam-5911	614	17	)	)	PUNCT
ejpam-5911	614	18	≤	≤	NOUN
ejpam-5911	614	19	s	s	NOUN
ejpam-5911	614	20	and	and	CCONJ
ejpam-5911	614	21	p−1(n	p−1(n	NOUN
ejpam-5911	614	22	)	)	PUNCT
ejpam-5911	615	1	≤	≤	NUM
ejpam-5911	615	2	m	m	ADP
ejpam-5911	615	3	,	,	PUNCT
ejpam-5911	615	4	there	there	PRON
ejpam-5911	615	5	is	be	VERB
ejpam-5911	615	6	u	u	PROPN
ejpam-5911	615	7	∈	∈	PROPN
ejpam-5911	615	8	iz	iz	INTJ
ejpam-5911	615	9	is	be	AUX
ejpam-5911	615	10	(	(	PUNCT
ejpam-5911	615	11	r	r	NOUN
ejpam-5911	615	12	,	,	PUNCT
ejpam-5911	615	13	s)-f	s)-f	NOUN
ejpam-5911	615	14	-	-	PUNCT
ejpam-5911	615	15	b	b	NOUN
ejpam-5911	615	16	-	-	PUNCT
ejpam-5911	615	17	open	open	ADJ
ejpam-5911	615	18	with	with	ADP
ejpam-5911	615	19	n	n	DET
ejpam-5911	615	20	≤	≤	NOUN
ejpam-5911	615	21	u	u	NOUN
ejpam-5911	615	22	and	and	CCONJ
ejpam-5911	615	23	p−1(u	p−1(u	NOUN
ejpam-5911	615	24	)	)	PUNCT
ejpam-5911	615	25	≤	≤	NUM
ejpam-5911	615	26	m.	m.	NOUN
ejpam-5911	615	27	proof	proof	NOUN
ejpam-5911	615	28	.	.	PUNCT
ejpam-5911	616	1	the	the	DET
ejpam-5911	616	2	proof	proof	NOUN
ejpam-5911	616	3	is	be	AUX
ejpam-5911	616	4	similar	similar	ADJ
ejpam-5911	616	5	to	to	ADP
ejpam-5911	616	6	that	that	PRON
ejpam-5911	616	7	of	of	ADP
ejpam-5911	616	8	theorem	theorem	ADJ
ejpam-5911	616	9	10	10	NUM
ejpam-5911	616	10	.	.	PUNCT
ejpam-5911	617	1	theorem	theorem	VERB
ejpam-5911	617	2	13	13	NUM
ejpam-5911	617	3	.	.	PUNCT
ejpam-5911	618	1	let	let	VERB
ejpam-5911	618	2	p	p	NOUN
ejpam-5911	618	3	:	:	PUNCT
ejpam-5911	618	4	(	(	PUNCT
ejpam-5911	618	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	618	6	)	)	PUNCT
ejpam-5911	619	1	−→	−→	NOUN
ejpam-5911	619	2	(	(	PUNCT
ejpam-5911	619	3	z	z	NOUN
ejpam-5911	619	4	,	,	PUNCT
ejpam-5911	619	5	𭟋	𭟋	NOUN
ejpam-5911	619	6	,	,	PUNCT
ejpam-5911	619	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	619	8	)	)	PUNCT
ejpam-5911	619	9	be	be	AUX
ejpam-5911	619	10	an	an	DET
ejpam-5911	619	11	f	f	NOUN
ejpam-5911	619	12	-	-	PUNCT
ejpam-5911	619	13	mapping	mapping	NOUN
ejpam-5911	619	14	.	.	PUNCT
ejpam-5911	620	1	then	then	ADV
ejpam-5911	620	2	the	the	DET
ejpam-5911	620	3	following	follow	VERB
ejpam-5911	620	4	statements	statement	NOUN
ejpam-5911	620	5	are	be	AUX
ejpam-5911	620	6	equivalent	equivalent	ADJ
ejpam-5911	620	7	for	for	ADP
ejpam-5911	620	8	every	every	DET
ejpam-5911	620	9	m	m	NOUN
ejpam-5911	620	10	∈	∈	NOUN
ejpam-5911	620	11	ig	ig	PROPN
ejpam-5911	620	12	and	and	CCONJ
ejpam-5911	620	13	n	n	PRON
ejpam-5911	620	14	∈	∈	PROPN
ejpam-5911	621	1	iz	iz	INTJ
ejpam-5911	621	2	:	:	PUNCT
ejpam-5911	621	3	(	(	PUNCT
ejpam-5911	621	4	i	i	NOUN
ejpam-5911	621	5	)	)	PUNCT
ejpam-5911	621	6	p	p	NOUN
ejpam-5911	621	7	is	be	AUX
ejpam-5911	621	8	df	df	PROPN
ejpam-5911	621	9	-	-	PUNCT
ejpam-5911	621	10	b	b	NOUN
ejpam-5911	621	11	-	-	PUNCT
ejpam-5911	621	12	irresolute	irresolute	ADJ
ejpam-5911	621	13	closed	close	VERB
ejpam-5911	621	14	.	.	PUNCT
ejpam-5911	622	1	(	(	PUNCT
ejpam-5911	622	2	ii	ii	NOUN
ejpam-5911	622	3	)	)	PUNCT
ejpam-5911	622	4	bc𭟋∗(p(m	bc𭟋∗(p(m	NOUN
ejpam-5911	622	5	)	)	PUNCT
ejpam-5911	622	6	,	,	PUNCT
ejpam-5911	622	7	r	r	NOUN
ejpam-5911	622	8	,	,	PUNCT
ejpam-5911	622	9	s	s	NOUN
ejpam-5911	622	10	)	)	PUNCT
ejpam-5911	622	11	≤	≤	NOUN
ejpam-5911	622	12	p(bcℑ∗(m	p(bcℑ∗(m	PUNCT
ejpam-5911	622	13	,	,	PUNCT
ejpam-5911	622	14	r	r	NOUN
ejpam-5911	622	15	,	,	PUNCT
ejpam-5911	622	16	s	s	NOUN
ejpam-5911	622	17	)	)	PUNCT
ejpam-5911	622	18	)	)	PUNCT
ejpam-5911	622	19	.	.	PUNCT
ejpam-5911	623	1	(	(	PUNCT
ejpam-5911	623	2	iii	iii	X
ejpam-5911	623	3	)	)	PUNCT
ejpam-5911	623	4	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	PROPN
ejpam-5911	623	5	,	,	PUNCT
ejpam-5911	623	6	r	r	NOUN
ejpam-5911	623	7	,	,	PUNCT
ejpam-5911	623	8	s	s	NOUN
ejpam-5911	623	9	)	)	PUNCT
ejpam-5911	623	10	)	)	PUNCT
ejpam-5911	623	11	≤	≤	NOUN
ejpam-5911	623	12	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	623	13	)	)	PUNCT
ejpam-5911	623	14	,	,	PUNCT
ejpam-5911	623	15	r	r	NOUN
ejpam-5911	623	16	,	,	PUNCT
ejpam-5911	623	17	s	s	NOUN
ejpam-5911	623	18	)	)	PUNCT
ejpam-5911	623	19	.	.	PUNCT
ejpam-5911	624	1	(	(	PUNCT
ejpam-5911	624	2	iv	iv	X
ejpam-5911	624	3	)	)	PUNCT
ejpam-5911	624	4	for	for	ADP
ejpam-5911	624	5	every	every	DET
ejpam-5911	624	6	n	n	NOUN
ejpam-5911	624	7	and	and	CCONJ
ejpam-5911	624	8	every	every	DET
ejpam-5911	624	9	m	m	NOUN
ejpam-5911	624	10	is	be	AUX
ejpam-5911	624	11	an	an	DET
ejpam-5911	624	12	(	(	PUNCT
ejpam-5911	624	13	r	r	NOUN
ejpam-5911	624	14	,	,	PUNCT
ejpam-5911	624	15	s)-f	s)-f	NOUN
ejpam-5911	624	16	-	-	PUNCT
ejpam-5911	624	17	b	b	NOUN
ejpam-5911	624	18	-	-	PUNCT
ejpam-5911	624	19	open	open	ADJ
ejpam-5911	624	20	set	set	NOUN
ejpam-5911	624	21	with	with	ADP
ejpam-5911	624	22	p−1(n	p−1(n	NOUN
ejpam-5911	624	23	)	)	PUNCT
ejpam-5911	624	24	≤	≤	NUM
ejpam-5911	624	25	m	m	ADP
ejpam-5911	624	26	,	,	PUNCT
ejpam-5911	624	27	there	there	PRON
ejpam-5911	624	28	is	be	VERB
ejpam-5911	624	29	u	u	PROPN
ejpam-5911	624	30	∈	∈	PROPN
ejpam-5911	624	31	iz	iz	INTJ
ejpam-5911	624	32	is	be	AUX
ejpam-5911	624	33	(	(	PUNCT
ejpam-5911	624	34	r	r	NOUN
ejpam-5911	624	35	,	,	PUNCT
ejpam-5911	624	36	s)-f	s)-f	NOUN
ejpam-5911	624	37	-	-	PUNCT
ejpam-5911	624	38	b	b	NOUN
ejpam-5911	624	39	-	-	PUNCT
ejpam-5911	624	40	open	open	ADJ
ejpam-5911	624	41	with	with	ADP
ejpam-5911	624	42	n	n	DET
ejpam-5911	624	43	≤	≤	NOUN
ejpam-5911	624	44	u	u	NOUN
ejpam-5911	624	45	and	and	CCONJ
ejpam-5911	624	46	p−1(u	p−1(u	NOUN
ejpam-5911	624	47	)	)	PUNCT
ejpam-5911	624	48	≤	≤	NUM
ejpam-5911	624	49	m.	m.	NOUN
ejpam-5911	624	50	proof	proof	NOUN
ejpam-5911	624	51	.	.	PUNCT
ejpam-5911	625	1	the	the	DET
ejpam-5911	625	2	proof	proof	NOUN
ejpam-5911	625	3	is	be	AUX
ejpam-5911	625	4	similar	similar	ADJ
ejpam-5911	625	5	to	to	ADP
ejpam-5911	625	6	that	that	PRON
ejpam-5911	625	7	of	of	ADP
ejpam-5911	625	8	theorem	theorem	ADJ
ejpam-5911	625	9	10	10	NUM
ejpam-5911	625	10	.	.	PUNCT
ejpam-5911	626	1	proposition	proposition	NOUN
ejpam-5911	626	2	7	7	NUM
ejpam-5911	626	3	.	.	PUNCT
ejpam-5911	627	1	let	let	VERB
ejpam-5911	627	2	p	p	NOUN
ejpam-5911	627	3	:	:	PUNCT
ejpam-5911	627	4	(	(	PUNCT
ejpam-5911	627	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	627	6	)	)	PUNCT
ejpam-5911	628	1	−→	−→	NOUN
ejpam-5911	628	2	(	(	PUNCT
ejpam-5911	628	3	z	z	NOUN
ejpam-5911	628	4	,	,	PUNCT
ejpam-5911	628	5	𭟋	𭟋	NOUN
ejpam-5911	628	6	,	,	PUNCT
ejpam-5911	628	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	628	8	)	)	PUNCT
ejpam-5911	628	9	be	be	AUX
ejpam-5911	628	10	a	a	DET
ejpam-5911	628	11	bijective	bijective	ADJ
ejpam-5911	628	12	f	f	X
ejpam-5911	628	13	-	-	PUNCT
ejpam-5911	628	14	mapping	mapping	NOUN
ejpam-5911	628	15	,	,	PUNCT
ejpam-5911	628	16	then	then	ADV
ejpam-5911	628	17	p	p	NOUN
ejpam-5911	628	18	is	be	AUX
ejpam-5911	628	19	df	df	PROPN
ejpam-5911	628	20	-	-	PUNCT
ejpam-5911	628	21	b	b	NOUN
ejpam-5911	628	22	-	-	PUNCT
ejpam-5911	628	23	irresolute	irresolute	ADJ
ejpam-5911	628	24	open	open	ADJ
ejpam-5911	628	25	iff	iff	PROPN
ejpam-5911	628	26	p	p	PROPN
ejpam-5911	628	27	is	be	AUX
ejpam-5911	628	28	df	df	PROPN
ejpam-5911	628	29	-	-	PUNCT
ejpam-5911	628	30	b	b	NOUN
ejpam-5911	628	31	-	-	PUNCT
ejpam-5911	628	32	irresolute	irresolute	ADJ
ejpam-5911	628	33	closed	closed	ADJ
ejpam-5911	628	34	.	.	PUNCT
ejpam-5911	629	1	proof	proof	NOUN
ejpam-5911	629	2	.	.	PUNCT
ejpam-5911	630	1	the	the	DET
ejpam-5911	630	2	proof	proof	NOUN
ejpam-5911	630	3	follows	follow	VERB
ejpam-5911	630	4	from	from	ADP
ejpam-5911	630	5	:	:	PUNCT
ejpam-5911	630	6	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	NOUN
ejpam-5911	630	7	,	,	PUNCT
ejpam-5911	630	8	r	r	NOUN
ejpam-5911	630	9	,	,	PUNCT
ejpam-5911	630	10	s	s	NOUN
ejpam-5911	630	11	)	)	PUNCT
ejpam-5911	630	12	)	)	PUNCT
ejpam-5911	630	13	≤	≤	NOUN
ejpam-5911	630	14	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	630	15	)	)	PUNCT
ejpam-5911	630	16	,	,	PUNCT
ejpam-5911	630	17	r	r	NOUN
ejpam-5911	630	18	,	,	PUNCT
ejpam-5911	630	19	s	s	PART
ejpam-5911	630	20	)	)	PUNCT
ejpam-5911	630	21	⇐	⇐	ADJ
ejpam-5911	630	22	⇒	⇒	NOUN
ejpam-5911	630	23	p−1(bi𭟋∗(n	p−1(bi𭟋∗(n	VERB
ejpam-5911	630	24	c	c	NOUN
ejpam-5911	630	25	,	,	PUNCT
ejpam-5911	630	26	r	r	NOUN
ejpam-5911	630	27	,	,	PUNCT
ejpam-5911	630	28	s	s	NOUN
ejpam-5911	630	29	)	)	PUNCT
ejpam-5911	630	30	)	)	PUNCT
ejpam-5911	631	1	≤	≤	NUM
ejpam-5911	632	1	biℑ∗(p−1(n	biℑ∗(p−1(n	NUM
ejpam-5911	632	2	c	c	NOUN
ejpam-5911	632	3	)	)	PUNCT
ejpam-5911	632	4	,	,	PUNCT
ejpam-5911	632	5	r	r	NOUN
ejpam-5911	632	6	,	,	PUNCT
ejpam-5911	632	7	s	s	PART
ejpam-5911	632	8	)	)	PUNCT
ejpam-5911	632	9	.	.	PUNCT
ejpam-5911	633	1	definition	definition	NOUN
ejpam-5911	633	2	18	18	NUM
ejpam-5911	633	3	.	.	PUNCT
ejpam-5911	634	1	a	a	DET
ejpam-5911	634	2	bijective	bijective	ADJ
ejpam-5911	634	3	f	f	X
ejpam-5911	634	4	-	-	PUNCT
ejpam-5911	634	5	mapping	mapping	NOUN
ejpam-5911	634	6	p	p	NOUN
ejpam-5911	634	7	:	:	PUNCT
ejpam-5911	634	8	(	(	PUNCT
ejpam-5911	634	9	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	634	10	)	)	PUNCT
ejpam-5911	635	1	−→	−→	NOUN
ejpam-5911	635	2	(	(	PUNCT
ejpam-5911	635	3	z	z	NOUN
ejpam-5911	635	4	,	,	PUNCT
ejpam-5911	635	5	𭟋	𭟋	NOUN
ejpam-5911	635	6	,	,	PUNCT
ejpam-5911	635	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	635	8	)	)	PUNCT
ejpam-5911	635	9	is	be	AUX
ejpam-5911	635	10	called	call	VERB
ejpam-5911	635	11	df	df	PROPN
ejpam-5911	635	12	-	-	PUNCT
ejpam-5911	635	13	birresolute	birresolute	NOUN
ejpam-5911	635	14	homeomorphism	homeomorphism	PROPN
ejpam-5911	635	15	if	if	SCONJ
ejpam-5911	635	16	p	p	PROPN
ejpam-5911	635	17	and	and	CCONJ
ejpam-5911	635	18	p−1	p−1	PROPN
ejpam-5911	635	19	are	be	AUX
ejpam-5911	635	20	df	df	PROPN
ejpam-5911	635	21	-	-	PUNCT
ejpam-5911	635	22	b	b	NOUN
ejpam-5911	635	23	-	-	PUNCT
ejpam-5911	635	24	irresolute	irresolute	ADJ
ejpam-5911	635	25	.	.	PUNCT
ejpam-5911	636	1	i.	i.	PROPN
ejpam-5911	636	2	m.	m.	PROPN
ejpam-5911	636	3	taha	taha	PROPN
ejpam-5911	636	4	,	,	PUNCT
ejpam-5911	636	5	j.	j.	PROPN
ejpam-5911	636	6	al	al	PROPN
ejpam-5911	636	7	-	-	PUNCT
ejpam-5911	636	8	mufarrij	mufarrij	PROPN
ejpam-5911	636	9	,	,	PUNCT
ejpam-5911	636	10	o.	o.	PROPN
ejpam-5911	636	11	m.	m.	PROPN
ejpam-5911	636	12	taha	taha	PROPN
ejpam-5911	636	13	/	/	PUNCT
ejpam-5911	636	14	eur	eur	PROPN
ejpam-5911	636	15	.	.	PUNCT
ejpam-5911	637	1	j.	j.	PROPN
ejpam-5911	637	2	pure	pure	PROPN
ejpam-5911	637	3	appl	appl	PROPN
ejpam-5911	637	4	.	.	PROPN
ejpam-5911	637	5	math	math	PROPN
ejpam-5911	637	6	,	,	PUNCT
ejpam-5911	637	7	18	18	NUM
ejpam-5911	637	8	(	(	PUNCT
ejpam-5911	637	9	2	2	NUM
ejpam-5911	637	10	)	)	PUNCT
ejpam-5911	637	11	(	(	PUNCT
ejpam-5911	637	12	2025	2025	NUM
ejpam-5911	637	13	)	)	PUNCT
ejpam-5911	637	14	,	,	PUNCT
ejpam-5911	637	15	5911	5911	NUM
ejpam-5911	637	16	22	22	NUM
ejpam-5911	637	17	of	of	ADP
ejpam-5911	637	18	27	27	NUM
ejpam-5911	637	19	the	the	DET
ejpam-5911	637	20	proof	proof	NOUN
ejpam-5911	637	21	of	of	ADP
ejpam-5911	637	22	the	the	DET
ejpam-5911	637	23	following	follow	VERB
ejpam-5911	637	24	corollary	corollary	NOUN
ejpam-5911	637	25	is	be	AUX
ejpam-5911	637	26	easy	easy	ADJ
ejpam-5911	637	27	and	and	CCONJ
ejpam-5911	637	28	so	so	ADV
ejpam-5911	637	29	is	be	AUX
ejpam-5911	637	30	omitted	omit	VERB
ejpam-5911	637	31	.	.	PUNCT
ejpam-5911	638	1	corollary	corollary	ADJ
ejpam-5911	638	2	4	4	NUM
ejpam-5911	638	3	.	.	PUNCT
ejpam-5911	639	1	let	let	VERB
ejpam-5911	639	2	p	p	NOUN
ejpam-5911	639	3	:	:	PUNCT
ejpam-5911	639	4	(	(	PUNCT
ejpam-5911	639	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	639	6	)	)	PUNCT
ejpam-5911	640	1	−→	−→	NOUN
ejpam-5911	640	2	(	(	PUNCT
ejpam-5911	640	3	z	z	NOUN
ejpam-5911	640	4	,	,	PUNCT
ejpam-5911	640	5	𭟋	𭟋	NOUN
ejpam-5911	640	6	,	,	PUNCT
ejpam-5911	640	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	640	8	)	)	PUNCT
ejpam-5911	640	9	be	be	AUX
ejpam-5911	640	10	a	a	DET
ejpam-5911	640	11	bijective	bijective	ADJ
ejpam-5911	640	12	f	f	NOUN
ejpam-5911	640	13	-	-	PUNCT
ejpam-5911	640	14	mapping	mapping	NOUN
ejpam-5911	640	15	.	.	PUNCT
ejpam-5911	641	1	then	then	ADV
ejpam-5911	641	2	the	the	DET
ejpam-5911	641	3	following	follow	VERB
ejpam-5911	641	4	statements	statement	NOUN
ejpam-5911	641	5	are	be	AUX
ejpam-5911	641	6	equivalent	equivalent	ADJ
ejpam-5911	641	7	for	for	ADP
ejpam-5911	641	8	every	every	DET
ejpam-5911	641	9	m	m	NOUN
ejpam-5911	641	10	∈	∈	NOUN
ejpam-5911	641	11	ig	ig	PROPN
ejpam-5911	641	12	and	and	CCONJ
ejpam-5911	641	13	n	n	PRON
ejpam-5911	641	14	∈	∈	PROPN
ejpam-5911	642	1	iz	iz	INTJ
ejpam-5911	642	2	:	:	PUNCT
ejpam-5911	642	3	(	(	PUNCT
ejpam-5911	642	4	i	i	NOUN
ejpam-5911	642	5	)	)	PUNCT
ejpam-5911	642	6	p	p	NOUN
ejpam-5911	642	7	is	be	AUX
ejpam-5911	642	8	df	df	PROPN
ejpam-5911	642	9	-	-	PUNCT
ejpam-5911	642	10	b	b	NOUN
ejpam-5911	642	11	-	-	PUNCT
ejpam-5911	642	12	irresolute	irresolute	ADJ
ejpam-5911	642	13	homeomorphism	homeomorphism	NOUN
ejpam-5911	642	14	.	.	PUNCT
ejpam-5911	643	1	(	(	PUNCT
ejpam-5911	643	2	ii	ii	NOUN
ejpam-5911	643	3	)	)	PUNCT
ejpam-5911	643	4	p	p	NOUN
ejpam-5911	643	5	is	be	AUX
ejpam-5911	643	6	df	df	PROPN
ejpam-5911	643	7	-	-	PUNCT
ejpam-5911	643	8	b	b	NOUN
ejpam-5911	643	9	-	-	PUNCT
ejpam-5911	643	10	irresolute	irresolute	ADJ
ejpam-5911	643	11	closed	closed	ADJ
ejpam-5911	643	12	and	and	CCONJ
ejpam-5911	643	13	df	df	PROPN
ejpam-5911	643	14	-	-	PUNCT
ejpam-5911	643	15	b	b	NOUN
ejpam-5911	643	16	-	-	PUNCT
ejpam-5911	643	17	irresolute	irresolute	NOUN
ejpam-5911	643	18	.	.	PUNCT
ejpam-5911	644	1	(	(	PUNCT
ejpam-5911	644	2	iii	iii	X
ejpam-5911	644	3	)	)	PUNCT
ejpam-5911	644	4	p	p	NOUN
ejpam-5911	644	5	is	be	AUX
ejpam-5911	644	6	df	df	PROPN
ejpam-5911	644	7	-	-	PUNCT
ejpam-5911	644	8	b	b	NOUN
ejpam-5911	644	9	-	-	PUNCT
ejpam-5911	644	10	irresolute	irresolute	ADJ
ejpam-5911	644	11	open	open	ADJ
ejpam-5911	644	12	and	and	CCONJ
ejpam-5911	644	13	df	df	PROPN
ejpam-5911	644	14	-	-	PUNCT
ejpam-5911	644	15	b	b	NOUN
ejpam-5911	644	16	-	-	PUNCT
ejpam-5911	644	17	irresolute	irresolute	NOUN
ejpam-5911	644	18	.	.	PUNCT
ejpam-5911	645	1	(	(	PUNCT
ejpam-5911	645	2	iv	iv	X
ejpam-5911	645	3	)	)	PUNCT
ejpam-5911	645	4	p(biℑ∗(m	p(biℑ∗(m	PUNCT
ejpam-5911	645	5	,	,	PUNCT
ejpam-5911	645	6	r	r	NOUN
ejpam-5911	645	7	,	,	PUNCT
ejpam-5911	645	8	s	s	NOUN
ejpam-5911	645	9	)	)	PUNCT
ejpam-5911	645	10	)	)	PUNCT
ejpam-5911	646	1	=	=	PUNCT
ejpam-5911	646	2	bi𭟋∗(p(m	bi𭟋∗(p(m	NOUN
ejpam-5911	646	3	)	)	PUNCT
ejpam-5911	646	4	,	,	PUNCT
ejpam-5911	646	5	r	r	NOUN
ejpam-5911	646	6	,	,	PUNCT
ejpam-5911	646	7	s	s	NOUN
ejpam-5911	646	8	)	)	PUNCT
ejpam-5911	646	9	.	.	PUNCT
ejpam-5911	647	1	(	(	PUNCT
ejpam-5911	647	2	v	v	NOUN
ejpam-5911	647	3	)	)	PUNCT
ejpam-5911	647	4	p(bcℑ∗(m	p(bcℑ∗(m	PUNCT
ejpam-5911	647	5	,	,	PUNCT
ejpam-5911	647	6	r	r	NOUN
ejpam-5911	647	7	,	,	PUNCT
ejpam-5911	647	8	s	s	NOUN
ejpam-5911	647	9	)	)	PUNCT
ejpam-5911	647	10	)	)	PUNCT
ejpam-5911	648	1	=	=	SYM
ejpam-5911	648	2	bc𭟋∗(p(m	bc𭟋∗(p(m	NOUN
ejpam-5911	648	3	)	)	PUNCT
ejpam-5911	648	4	,	,	PUNCT
ejpam-5911	648	5	r	r	NOUN
ejpam-5911	648	6	,	,	PUNCT
ejpam-5911	648	7	s	s	NOUN
ejpam-5911	648	8	)	)	PUNCT
ejpam-5911	648	9	.	.	PUNCT
ejpam-5911	649	1	(	(	PUNCT
ejpam-5911	649	2	vi	vi	NOUN
ejpam-5911	649	3	)	)	PUNCT
ejpam-5911	649	4	biℑ∗(p−1(n	biℑ∗(p−1(n	NOUN
ejpam-5911	649	5	)	)	PUNCT
ejpam-5911	649	6	,	,	PUNCT
ejpam-5911	649	7	r	r	NOUN
ejpam-5911	649	8	,	,	PUNCT
ejpam-5911	649	9	s	s	PART
ejpam-5911	649	10	)	)	PUNCT
ejpam-5911	650	1	=	=	VERB
ejpam-5911	650	2	p−1(b𭟋∗(n	p−1(b𭟋∗(n	NOUN
ejpam-5911	650	3	,	,	PUNCT
ejpam-5911	650	4	r	r	NOUN
ejpam-5911	650	5	,	,	PUNCT
ejpam-5911	650	6	s	s	NOUN
ejpam-5911	650	7	)	)	PUNCT
ejpam-5911	650	8	)	)	PUNCT
ejpam-5911	650	9	.	.	PUNCT
ejpam-5911	651	1	(	(	PUNCT
ejpam-5911	651	2	vii	vii	PROPN
ejpam-5911	651	3	)	)	PUNCT
ejpam-5911	651	4	bcℑ∗(p−1(n	bcℑ∗(p−1(n	NOUN
ejpam-5911	651	5	)	)	PUNCT
ejpam-5911	651	6	,	,	PUNCT
ejpam-5911	651	7	r	r	NOUN
ejpam-5911	651	8	,	,	PUNCT
ejpam-5911	651	9	s	s	NOUN
ejpam-5911	651	10	)	)	PUNCT
ejpam-5911	652	1	=	=	SYM
ejpam-5911	652	2	p−1(bc𭟋∗(n	p−1(bc𭟋∗(n	NOUN
ejpam-5911	652	3	,	,	PUNCT
ejpam-5911	652	4	r	r	NOUN
ejpam-5911	652	5	,	,	PUNCT
ejpam-5911	652	6	s	s	NOUN
ejpam-5911	652	7	)	)	PUNCT
ejpam-5911	652	8	)	)	PUNCT
ejpam-5911	652	9	.	.	PUNCT
ejpam-5911	653	1	definition	definition	NOUN
ejpam-5911	653	2	19	19	NUM
ejpam-5911	653	3	.	.	PUNCT
ejpam-5911	654	1	let	let	VERB
ejpam-5911	654	2	gθ	gθ	PROPN
ejpam-5911	654	3	∈	∈	PROPN
ejpam-5911	654	4	pθ(g	pθ(g	NOUN
ejpam-5911	654	5	)	)	PUNCT
ejpam-5911	654	6	,	,	PUNCT
ejpam-5911	654	7	m	m	PROPN
ejpam-5911	654	8	∈	∈	PROPN
ejpam-5911	654	9	ig	ig	PROPN
ejpam-5911	654	10	,	,	PUNCT
ejpam-5911	654	11	r	r	NOUN
ejpam-5911	654	12	∈	∈	PROPN
ejpam-5911	654	13	i	i	NOUN
ejpam-5911	654	14	◦	◦	NOUN
ejpam-5911	654	15	,	,	PUNCT
ejpam-5911	654	16	and	and	CCONJ
ejpam-5911	654	17	s	s	PROPN
ejpam-5911	654	18	∈	∈	PROPN
ejpam-5911	654	19	i1	i1	PROPN
ejpam-5911	654	20	.	.	PUNCT
ejpam-5911	655	1	an	an	DET
ejpam-5911	655	2	dft	dft	PROPN
ejpam-5911	655	3	s	s	X
ejpam-5911	655	4	(	(	PUNCT
ejpam-5911	655	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	655	6	)	)	PUNCT
ejpam-5911	655	7	is	be	AUX
ejpam-5911	655	8	called	call	VERB
ejpam-5911	655	9	an	an	DET
ejpam-5911	655	10	(	(	PUNCT
ejpam-5911	655	11	r	r	NOUN
ejpam-5911	655	12	,	,	PUNCT
ejpam-5911	655	13	s)-f	s)-f	NOUN
ejpam-5911	655	14	-	-	PUNCT
ejpam-5911	655	15	b	b	NOUN
ejpam-5911	655	16	-	-	PUNCT
ejpam-5911	655	17	regular	regular	ADJ
ejpam-5911	655	18	space	space	NOUN
ejpam-5911	655	19	if	if	SCONJ
ejpam-5911	655	20	gθ	gθ	VERB
ejpam-5911	655	21	q	q	PROPN
ejpam-5911	655	22	m	m	VERB
ejpam-5911	655	23	for	for	ADP
ejpam-5911	655	24	each	each	DET
ejpam-5911	655	25	(	(	PUNCT
ejpam-5911	655	26	r	r	NOUN
ejpam-5911	655	27	,	,	PUNCT
ejpam-5911	655	28	s)-f	s)-f	NOUN
ejpam-5911	655	29	-	-	PUNCT
ejpam-5911	655	30	b	b	NOUN
ejpam-5911	655	31	-	-	PUNCT
ejpam-5911	655	32	closed	close	VERB
ejpam-5911	655	33	set	set	NOUN
ejpam-5911	655	34	m	m	NOUN
ejpam-5911	655	35	,	,	PUNCT
ejpam-5911	655	36	there	there	PRON
ejpam-5911	655	37	is	be	VERB
ejpam-5911	655	38	ui	ui	PROPN
ejpam-5911	655	39	∈	∈	PROPN
ejpam-5911	655	40	ig	ig	PROPN
ejpam-5911	655	41	with	with	ADP
ejpam-5911	655	42	ℑ(ui	ℑ(ui	PROPN
ejpam-5911	655	43	)	)	PUNCT
ejpam-5911	655	44	≥	≥	PROPN
ejpam-5911	655	45	r	r	NOUN
ejpam-5911	655	46	and	and	CCONJ
ejpam-5911	655	47	ℑ∗(ui	ℑ∗(ui	NOUN
ejpam-5911	655	48	)	)	PUNCT
ejpam-5911	656	1	≤	≤	NUM
ejpam-5911	656	2	s	s	VERB
ejpam-5911	656	3	for	for	ADP
ejpam-5911	656	4	i	i	PROPN
ejpam-5911	656	5	=	=	SYM
ejpam-5911	656	6	1	1	NUM
ejpam-5911	656	7	,	,	PUNCT
ejpam-5911	656	8	2	2	NUM
ejpam-5911	656	9	,	,	PUNCT
ejpam-5911	656	10	such	such	ADJ
ejpam-5911	656	11	that	that	SCONJ
ejpam-5911	656	12	gθ	gθ	PROPN
ejpam-5911	656	13	∈	∈	PROPN
ejpam-5911	656	14	u1	u1	NOUN
ejpam-5911	656	15	,	,	PUNCT
ejpam-5911	656	16	m	m	NOUN
ejpam-5911	656	17	≤	≤	NOUN
ejpam-5911	656	18	u2	u2	NOUN
ejpam-5911	656	19	,	,	PUNCT
ejpam-5911	656	20	and	and	CCONJ
ejpam-5911	656	21	u1	u1	VERB
ejpam-5911	656	22	q	q	PROPN
ejpam-5911	656	23	u2	u2	PROPN
ejpam-5911	656	24	.	.	PUNCT
ejpam-5911	657	1	definition	definition	NOUN
ejpam-5911	657	2	20	20	NUM
ejpam-5911	657	3	.	.	PUNCT
ejpam-5911	658	1	let	let	VERB
ejpam-5911	658	2	m	m	PRON
ejpam-5911	658	3	,	,	PUNCT
ejpam-5911	658	4	n	n	PROPN
ejpam-5911	658	5	∈	∈	PROPN
ejpam-5911	658	6	ig	ig	PROPN
ejpam-5911	658	7	,	,	PUNCT
ejpam-5911	658	8	r	r	NOUN
ejpam-5911	658	9	∈	∈	PROPN
ejpam-5911	658	10	i	i	NOUN
ejpam-5911	658	11	◦	◦	NOUN
ejpam-5911	658	12	,	,	PUNCT
ejpam-5911	658	13	and	and	CCONJ
ejpam-5911	658	14	s	s	PROPN
ejpam-5911	658	15	∈	∈	PROPN
ejpam-5911	658	16	i1	i1	PROPN
ejpam-5911	658	17	.	.	PUNCT
ejpam-5911	659	1	an	an	DET
ejpam-5911	659	2	dft	dft	PROPN
ejpam-5911	659	3	s	s	X
ejpam-5911	659	4	(	(	PUNCT
ejpam-5911	659	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	659	6	)	)	PUNCT
ejpam-5911	659	7	is	be	AUX
ejpam-5911	659	8	called	call	VERB
ejpam-5911	659	9	an	an	DET
ejpam-5911	659	10	(	(	PUNCT
ejpam-5911	659	11	r	r	NOUN
ejpam-5911	659	12	,	,	PUNCT
ejpam-5911	659	13	s)-f	s)-f	NOUN
ejpam-5911	659	14	-	-	PUNCT
ejpam-5911	659	15	b	b	NOUN
ejpam-5911	659	16	-	-	PUNCT
ejpam-5911	659	17	normal	normal	ADJ
ejpam-5911	659	18	space	space	NOUN
ejpam-5911	659	19	if	if	SCONJ
ejpam-5911	659	20	m	m	VERB
ejpam-5911	659	21	q	q	NOUN
ejpam-5911	659	22	n	n	PROPN
ejpam-5911	659	23	for	for	ADP
ejpam-5911	659	24	each	each	DET
ejpam-5911	659	25	(	(	PUNCT
ejpam-5911	659	26	r	r	NOUN
ejpam-5911	659	27	,	,	PUNCT
ejpam-5911	659	28	s)-f	s)-f	NOUN
ejpam-5911	659	29	-	-	PUNCT
ejpam-5911	659	30	b	b	NOUN
ejpam-5911	659	31	-	-	PUNCT
ejpam-5911	659	32	closed	close	VERB
ejpam-5911	659	33	sets	set	NOUN
ejpam-5911	659	34	m	m	VERB
ejpam-5911	659	35	and	and	CCONJ
ejpam-5911	659	36	n	n	CCONJ
ejpam-5911	659	37	,	,	PUNCT
ejpam-5911	659	38	there	there	PRON
ejpam-5911	659	39	is	be	VERB
ejpam-5911	659	40	ui	ui	PROPN
ejpam-5911	659	41	∈	∈	PROPN
ejpam-5911	659	42	ig	ig	PROPN
ejpam-5911	659	43	with	with	ADP
ejpam-5911	659	44	ℑ(ui	ℑ(ui	PROPN
ejpam-5911	659	45	)	)	PUNCT
ejpam-5911	659	46	≥	≥	PROPN
ejpam-5911	659	47	r	r	NOUN
ejpam-5911	659	48	and	and	CCONJ
ejpam-5911	659	49	ℑ∗(ui	ℑ∗(ui	NOUN
ejpam-5911	659	50	)	)	PUNCT
ejpam-5911	660	1	≤	≤	NUM
ejpam-5911	660	2	s	s	VERB
ejpam-5911	660	3	for	for	ADP
ejpam-5911	660	4	i	i	PROPN
ejpam-5911	660	5	=	=	SYM
ejpam-5911	660	6	1	1	NUM
ejpam-5911	660	7	,	,	PUNCT
ejpam-5911	660	8	2	2	NUM
ejpam-5911	660	9	,	,	PUNCT
ejpam-5911	660	10	such	such	ADJ
ejpam-5911	660	11	that	that	SCONJ
ejpam-5911	660	12	m	m	VERB
ejpam-5911	660	13	≤	≤	NUM
ejpam-5911	660	14	u1	u1	NOUN
ejpam-5911	660	15	,	,	PUNCT
ejpam-5911	660	16	n	n	CCONJ
ejpam-5911	660	17	≤	≤	NOUN
ejpam-5911	660	18	u2	u2	NOUN
ejpam-5911	660	19	,	,	PUNCT
ejpam-5911	660	20	and	and	CCONJ
ejpam-5911	660	21	u1	u1	PROPN
ejpam-5911	660	22	q	q	PROPN
ejpam-5911	660	23	u2	u2	PROPN
ejpam-5911	660	24	.	.	PUNCT
ejpam-5911	660	25	theorem	theorem	PROPN
ejpam-5911	660	26	14	14	NUM
ejpam-5911	660	27	.	.	PUNCT
ejpam-5911	661	1	let	let	AUX
ejpam-5911	661	2	(	(	PUNCT
ejpam-5911	661	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	661	4	)	)	PUNCT
ejpam-5911	661	5	be	be	VERB
ejpam-5911	661	6	an	an	DET
ejpam-5911	661	7	dft	dft	NOUN
ejpam-5911	661	8	s	s	NOUN
ejpam-5911	661	9	,	,	PUNCT
ejpam-5911	661	10	gθ	gθ	PROPN
ejpam-5911	661	11	∈	∈	PROPN
ejpam-5911	661	12	pθ(g	pθ(g	NOUN
ejpam-5911	661	13	)	)	PUNCT
ejpam-5911	661	14	,	,	PUNCT
ejpam-5911	661	15	and	and	CCONJ
ejpam-5911	661	16	m	m	PROPN
ejpam-5911	661	17	∈	∈	PROPN
ejpam-5911	661	18	ig	ig	PROPN
ejpam-5911	661	19	.	.	PUNCT
ejpam-5911	662	1	then	then	ADV
ejpam-5911	662	2	the	the	DET
ejpam-5911	662	3	following	follow	VERB
ejpam-5911	662	4	statements	statement	NOUN
ejpam-5911	662	5	are	be	AUX
ejpam-5911	662	6	equivalent	equivalent	ADJ
ejpam-5911	662	7	:	:	PUNCT
ejpam-5911	662	8	(	(	PUNCT
ejpam-5911	662	9	i	i	NOUN
ejpam-5911	662	10	)	)	PUNCT
ejpam-5911	662	11	(	(	PUNCT
ejpam-5911	662	12	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	662	13	)	)	PUNCT
ejpam-5911	662	14	is	be	AUX
ejpam-5911	662	15	an	an	DET
ejpam-5911	662	16	(	(	PUNCT
ejpam-5911	662	17	r	r	NOUN
ejpam-5911	662	18	,	,	PUNCT
ejpam-5911	662	19	s)-f	s)-f	NOUN
ejpam-5911	662	20	-	-	PUNCT
ejpam-5911	662	21	b	b	NOUN
ejpam-5911	662	22	-	-	PUNCT
ejpam-5911	662	23	regular	regular	ADJ
ejpam-5911	662	24	space	space	NOUN
ejpam-5911	662	25	.	.	PUNCT
ejpam-5911	663	1	(	(	PUNCT
ejpam-5911	663	2	ii	ii	NOUN
ejpam-5911	663	3	)	)	PUNCT
ejpam-5911	663	4	if	if	SCONJ
ejpam-5911	663	5	gθ	gθ	PROPN
ejpam-5911	663	6	∈	∈	PROPN
ejpam-5911	663	7	m	m	VERB
ejpam-5911	663	8	for	for	ADP
ejpam-5911	663	9	every	every	DET
ejpam-5911	663	10	(	(	PUNCT
ejpam-5911	663	11	r	r	NOUN
ejpam-5911	663	12	,	,	PUNCT
ejpam-5911	663	13	s)-f	s)-f	NOUN
ejpam-5911	663	14	-	-	PUNCT
ejpam-5911	663	15	b	b	NOUN
ejpam-5911	663	16	-	-	PUNCT
ejpam-5911	663	17	open	open	ADJ
ejpam-5911	663	18	set	set	NOUN
ejpam-5911	663	19	m	m	NOUN
ejpam-5911	663	20	,	,	PUNCT
ejpam-5911	663	21	there	there	PRON
ejpam-5911	663	22	is	be	VERB
ejpam-5911	663	23	n	n	DET
ejpam-5911	663	24	∈	∈	NOUN
ejpam-5911	663	25	ig	ig	PROPN
ejpam-5911	663	26	with	with	ADP
ejpam-5911	663	27	ℑ(n	ℑ(n	PRON
ejpam-5911	663	28	)	)	PUNCT
ejpam-5911	663	29	≥	≥	PROPN
ejpam-5911	663	30	r	r	NOUN
ejpam-5911	663	31	,	,	PUNCT
ejpam-5911	663	32	ℑ∗(n	ℑ∗(n	NOUN
ejpam-5911	663	33	)	)	PUNCT
ejpam-5911	663	34	≤	≤	PROPN
ejpam-5911	663	35	s	s	PART
ejpam-5911	663	36	,	,	PUNCT
ejpam-5911	663	37	and	and	CCONJ
ejpam-5911	663	38	gθ	gθ	PROPN
ejpam-5911	663	39	∈	∈	PROPN
ejpam-5911	663	40	n	n	CCONJ
ejpam-5911	663	41	≤	≤	NOUN
ejpam-5911	663	42	cℑ∗(n	cℑ∗(n	NOUN
ejpam-5911	663	43	,	,	PUNCT
ejpam-5911	663	44	r	r	NOUN
ejpam-5911	663	45	,	,	PUNCT
ejpam-5911	663	46	s	s	NOUN
ejpam-5911	663	47	)	)	PUNCT
ejpam-5911	663	48	≤	≤	ADJ
ejpam-5911	663	49	m.	m.	NOUN
ejpam-5911	663	50	(	(	PUNCT
ejpam-5911	663	51	iii	iii	NOUN
ejpam-5911	663	52	)	)	PUNCT
ejpam-5911	663	53	if	if	SCONJ
ejpam-5911	663	54	gθ	gθ	PROPN
ejpam-5911	663	55	q	q	PROPN
ejpam-5911	663	56	m	m	VERB
ejpam-5911	663	57	for	for	ADP
ejpam-5911	663	58	each	each	DET
ejpam-5911	663	59	(	(	PUNCT
ejpam-5911	663	60	r	r	NOUN
ejpam-5911	663	61	,	,	PUNCT
ejpam-5911	663	62	s)-f	s)-f	NOUN
ejpam-5911	663	63	-	-	PUNCT
ejpam-5911	663	64	b	b	NOUN
ejpam-5911	663	65	-	-	PUNCT
ejpam-5911	663	66	closed	close	VERB
ejpam-5911	663	67	set	set	NOUN
ejpam-5911	663	68	m	m	NOUN
ejpam-5911	663	69	,	,	PUNCT
ejpam-5911	663	70	there	there	PRON
ejpam-5911	663	71	is	be	VERB
ejpam-5911	663	72	oi	oi	PROPN
ejpam-5911	663	73	∈	∈	PROPN
ejpam-5911	663	74	ig	ig	PROPN
ejpam-5911	663	75	with	with	ADP
ejpam-5911	663	76	ℑ(oi	ℑ(oi	NOUN
ejpam-5911	663	77	)	)	PUNCT
ejpam-5911	663	78	≥	≥	NOUN
ejpam-5911	663	79	r	r	NOUN
ejpam-5911	663	80	and	and	CCONJ
ejpam-5911	663	81	ℑ∗(oi	ℑ∗(oi	NOUN
ejpam-5911	663	82	)	)	PUNCT
ejpam-5911	663	83	≤	≤	NUM
ejpam-5911	663	84	s	s	VERB
ejpam-5911	663	85	for	for	ADP
ejpam-5911	663	86	i	i	PROPN
ejpam-5911	663	87	=	=	SYM
ejpam-5911	663	88	1	1	NUM
ejpam-5911	663	89	,	,	PUNCT
ejpam-5911	663	90	2	2	NUM
ejpam-5911	663	91	,	,	PUNCT
ejpam-5911	663	92	such	such	ADJ
ejpam-5911	663	93	that	that	SCONJ
ejpam-5911	663	94	gθ	gθ	PROPN
ejpam-5911	663	95	∈	∈	PROPN
ejpam-5911	663	96	o1	o1	PROPN
ejpam-5911	663	97	,	,	PUNCT
ejpam-5911	663	98	m	m	VERB
ejpam-5911	663	99	≤	≤	ADJ
ejpam-5911	663	100	o2	o2	ADJ
ejpam-5911	663	101	,	,	PUNCT
ejpam-5911	663	102	and	and	CCONJ
ejpam-5911	663	103	cℑ∗(o1	cℑ∗(o1	PROPN
ejpam-5911	663	104	,	,	PUNCT
ejpam-5911	663	105	r	r	NOUN
ejpam-5911	663	106	,	,	PUNCT
ejpam-5911	663	107	s	s	NOUN
ejpam-5911	663	108	)	)	PUNCT
ejpam-5911	663	109	q	q	NOUN
ejpam-5911	663	110	cℑ∗(o2	cℑ∗(o2	NOUN
ejpam-5911	663	111	,	,	PUNCT
ejpam-5911	663	112	r	r	NOUN
ejpam-5911	663	113	,	,	PUNCT
ejpam-5911	663	114	s	s	NOUN
ejpam-5911	663	115	)	)	PUNCT
ejpam-5911	663	116	.	.	PUNCT
ejpam-5911	664	1	i.	i.	PROPN
ejpam-5911	664	2	m.	m.	PROPN
ejpam-5911	664	3	taha	taha	PROPN
ejpam-5911	664	4	,	,	PUNCT
ejpam-5911	664	5	j.	j.	PROPN
ejpam-5911	664	6	al	al	PROPN
ejpam-5911	664	7	-	-	PUNCT
ejpam-5911	664	8	mufarrij	mufarrij	PROPN
ejpam-5911	664	9	,	,	PUNCT
ejpam-5911	664	10	o.	o.	PROPN
ejpam-5911	664	11	m.	m.	PROPN
ejpam-5911	664	12	taha	taha	PROPN
ejpam-5911	664	13	/	/	PUNCT
ejpam-5911	664	14	eur	eur	PROPN
ejpam-5911	664	15	.	.	PUNCT
ejpam-5911	665	1	j.	j.	PROPN
ejpam-5911	665	2	pure	pure	PROPN
ejpam-5911	665	3	appl	appl	PROPN
ejpam-5911	665	4	.	.	PROPN
ejpam-5911	665	5	math	math	PROPN
ejpam-5911	665	6	,	,	PUNCT
ejpam-5911	665	7	18	18	NUM
ejpam-5911	665	8	(	(	PUNCT
ejpam-5911	665	9	2	2	NUM
ejpam-5911	665	10	)	)	PUNCT
ejpam-5911	665	11	(	(	PUNCT
ejpam-5911	665	12	2025	2025	NUM
ejpam-5911	665	13	)	)	PUNCT
ejpam-5911	665	14	,	,	PUNCT
ejpam-5911	665	15	5911	5911	NUM
ejpam-5911	665	16	23	23	NUM
ejpam-5911	665	17	of	of	ADP
ejpam-5911	665	18	27	27	NUM
ejpam-5911	665	19	proof	proof	NOUN
ejpam-5911	665	20	.	.	PUNCT
ejpam-5911	666	1	(	(	PUNCT
ejpam-5911	666	2	i	i	NOUN
ejpam-5911	666	3	)	)	PUNCT
ejpam-5911	666	4	⇒	⇒	PROPN
ejpam-5911	666	5	(	(	PUNCT
ejpam-5911	666	6	ii	ii	NOUN
ejpam-5911	666	7	)	)	PUNCT
ejpam-5911	666	8	let	let	VERB
ejpam-5911	666	9	gθ	gθ	PROPN
ejpam-5911	666	10	∈	∈	VERB
ejpam-5911	666	11	m	m	PROPN
ejpam-5911	666	12	for	for	ADP
ejpam-5911	666	13	every	every	DET
ejpam-5911	666	14	(	(	PUNCT
ejpam-5911	666	15	r	r	NOUN
ejpam-5911	666	16	,	,	PUNCT
ejpam-5911	666	17	s)-f	s)-f	NOUN
ejpam-5911	666	18	-	-	PUNCT
ejpam-5911	666	19	b	b	NOUN
ejpam-5911	666	20	-	-	PUNCT
ejpam-5911	666	21	open	open	ADJ
ejpam-5911	666	22	set	set	NOUN
ejpam-5911	666	23	m	m	PROPN
ejpam-5911	666	24	,	,	PUNCT
ejpam-5911	666	25	then	then	ADV
ejpam-5911	666	26	gθ	gθ	PROPN
ejpam-5911	666	27	q	q	PROPN
ejpam-5911	666	28	mc	mc	PROPN
ejpam-5911	666	29	.	.	PROPN
ejpam-5911	667	1	since	since	SCONJ
ejpam-5911	667	2	(	(	PUNCT
ejpam-5911	667	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	667	4	)	)	PUNCT
ejpam-5911	667	5	is	be	AUX
ejpam-5911	667	6	(	(	PUNCT
ejpam-5911	667	7	r	r	NOUN
ejpam-5911	667	8	,	,	PUNCT
ejpam-5911	667	9	s)-f	s)-f	NOUN
ejpam-5911	667	10	-	-	PUNCT
ejpam-5911	667	11	b	b	NOUN
ejpam-5911	667	12	-	-	PUNCT
ejpam-5911	667	13	regular	regular	ADJ
ejpam-5911	667	14	,	,	PUNCT
ejpam-5911	667	15	then	then	ADV
ejpam-5911	667	16	there	there	PRON
ejpam-5911	667	17	is	be	VERB
ejpam-5911	667	18	n	n	PRON
ejpam-5911	667	19	,	,	PUNCT
ejpam-5911	667	20	o	o	PROPN
ejpam-5911	667	21	∈	∈	PROPN
ejpam-5911	667	22	ig	ig	PROPN
ejpam-5911	667	23	with	with	ADP
ejpam-5911	667	24	ℑ(n	ℑ(n	PRON
ejpam-5911	667	25	)	)	PUNCT
ejpam-5911	667	26	≥	≥	PROPN
ejpam-5911	667	27	r	r	NOUN
ejpam-5911	667	28	,	,	PUNCT
ejpam-5911	667	29	ℑ∗(n	ℑ∗(n	NOUN
ejpam-5911	667	30	)	)	PUNCT
ejpam-5911	667	31	≤	≤	PROPN
ejpam-5911	667	32	s	s	PROPN
ejpam-5911	667	33	,	,	PUNCT
ejpam-5911	667	34	ℑ(o	ℑ(o	NOUN
ejpam-5911	667	35	)	)	PUNCT
ejpam-5911	667	36	≥	≥	NOUN
ejpam-5911	667	37	r	r	NOUN
ejpam-5911	667	38	,	,	PUNCT
ejpam-5911	667	39	and	and	CCONJ
ejpam-5911	667	40	ℑ∗(o	ℑ∗(o	NOUN
ejpam-5911	667	41	)	)	PUNCT
ejpam-5911	667	42	≤	≤	NUM
ejpam-5911	667	43	s	s	NOUN
ejpam-5911	667	44	,	,	PUNCT
ejpam-5911	668	1	such	such	ADJ
ejpam-5911	668	2	that	that	SCONJ
ejpam-5911	668	3	gθ	gθ	PROPN
ejpam-5911	668	4	∈	∈	PROPN
ejpam-5911	668	5	n	n	PROPN
ejpam-5911	668	6	,	,	PUNCT
ejpam-5911	668	7	mc	mc	PROPN
ejpam-5911	668	8	≤	≤	NUM
ejpam-5911	668	9	o	o	NOUN
ejpam-5911	668	10	,	,	PUNCT
ejpam-5911	668	11	and	and	CCONJ
ejpam-5911	668	12	n	n	PRON
ejpam-5911	668	13	q	q	PROPN
ejpam-5911	669	1	o.	o.	PROPN
ejpam-5911	669	2	thus	thus	ADV
ejpam-5911	669	3	,	,	PUNCT
ejpam-5911	669	4	gθ	gθ	PROPN
ejpam-5911	669	5	∈	∈	PROPN
ejpam-5911	669	6	n	n	CCONJ
ejpam-5911	669	7	≤	≤	X
ejpam-5911	669	8	oc	oc	ADP
ejpam-5911	669	9	≤	≤	NUM
ejpam-5911	669	10	m	m	PROPN
ejpam-5911	669	11	,	,	PUNCT
ejpam-5911	669	12	so	so	ADV
ejpam-5911	669	13	gθ	gθ	PROPN
ejpam-5911	669	14	∈	∈	PROPN
ejpam-5911	669	15	n	n	CCONJ
ejpam-5911	669	16	≤	≤	NOUN
ejpam-5911	669	17	cℑ∗(n	cℑ∗(n	NOUN
ejpam-5911	669	18	,	,	PUNCT
ejpam-5911	669	19	r	r	NOUN
ejpam-5911	669	20	,	,	PUNCT
ejpam-5911	669	21	s	s	NOUN
ejpam-5911	669	22	)	)	PUNCT
ejpam-5911	669	23	≤	≤	ADJ
ejpam-5911	669	24	m.	m.	NOUN
ejpam-5911	669	25	(	(	PUNCT
ejpam-5911	669	26	ii	ii	NOUN
ejpam-5911	669	27	)	)	PUNCT
ejpam-5911	669	28	⇒	⇒	NOUN
ejpam-5911	669	29	(	(	PUNCT
ejpam-5911	669	30	iii	iii	X
ejpam-5911	669	31	)	)	PUNCT
ejpam-5911	669	32	let	let	VERB
ejpam-5911	669	33	gθ	gθ	PROPN
ejpam-5911	669	34	q	q	VERB
ejpam-5911	669	35	m	m	VERB
ejpam-5911	669	36	for	for	ADP
ejpam-5911	669	37	each	each	PRON
ejpam-5911	669	38	(	(	PUNCT
ejpam-5911	669	39	r	r	NOUN
ejpam-5911	669	40	,	,	PUNCT
ejpam-5911	669	41	s)-f	s)-f	NOUN
ejpam-5911	669	42	-	-	PUNCT
ejpam-5911	669	43	b	b	NOUN
ejpam-5911	669	44	-	-	PUNCT
ejpam-5911	669	45	closed	close	VERB
ejpam-5911	669	46	set	set	NOUN
ejpam-5911	669	47	m	m	PROPN
ejpam-5911	669	48	,	,	PUNCT
ejpam-5911	669	49	then	then	ADV
ejpam-5911	669	50	gθ	gθ	PROPN
ejpam-5911	669	51	∈	∈	PROPN
ejpam-5911	669	52	mc	mc	PROPN
ejpam-5911	669	53	.	.	PUNCT
ejpam-5911	670	1	by	by	ADP
ejpam-5911	670	2	(	(	PUNCT
ejpam-5911	670	3	ii	ii	NOUN
ejpam-5911	670	4	)	)	PUNCT
ejpam-5911	670	5	,	,	PUNCT
ejpam-5911	670	6	there	there	PRON
ejpam-5911	670	7	is	be	VERB
ejpam-5911	670	8	o	o	PROPN
ejpam-5911	670	9	∈	∈	PROPN
ejpam-5911	670	10	ig	ig	PROPN
ejpam-5911	670	11	with	with	ADP
ejpam-5911	670	12	ℑ(o	ℑ(o	NOUN
ejpam-5911	670	13	)	)	PUNCT
ejpam-5911	670	14	≥	≥	NOUN
ejpam-5911	670	15	r	r	NOUN
ejpam-5911	670	16	,	,	PUNCT
ejpam-5911	670	17	ℑ∗(o	ℑ∗(o	NOUN
ejpam-5911	670	18	)	)	PUNCT
ejpam-5911	670	19	≤	≤	NOUN
ejpam-5911	670	20	s	s	NOUN
ejpam-5911	670	21	and	and	CCONJ
ejpam-5911	670	22	gθ	gθ	PROPN
ejpam-5911	670	23	∈	∈	PROPN
ejpam-5911	670	24	o	o	NOUN
ejpam-5911	670	25	≤	≤	X
ejpam-5911	670	26	cℑ∗(o	cℑ∗(o	NOUN
ejpam-5911	670	27	,	,	PUNCT
ejpam-5911	670	28	r	r	NOUN
ejpam-5911	670	29	,	,	PUNCT
ejpam-5911	670	30	s	s	NOUN
ejpam-5911	670	31	)	)	PUNCT
ejpam-5911	670	32	≤	≤	NUM
ejpam-5911	670	33	mc	mc	PROPN
ejpam-5911	670	34	.	.	PUNCT
ejpam-5911	671	1	since	since	SCONJ
ejpam-5911	671	2	ℑ(o	ℑ(o	NOUN
ejpam-5911	671	3	)	)	PUNCT
ejpam-5911	671	4	≥	≥	NOUN
ejpam-5911	671	5	r	r	NOUN
ejpam-5911	671	6	and	and	CCONJ
ejpam-5911	671	7	ℑ∗(o	ℑ∗(o	NOUN
ejpam-5911	671	8	)	)	PUNCT
ejpam-5911	671	9	≤	≤	NOUN
ejpam-5911	671	10	s	s	PROPN
ejpam-5911	671	11	,	,	PUNCT
ejpam-5911	671	12	theno	theno	VERB
ejpam-5911	671	13	is	be	AUX
ejpam-5911	671	14	an	an	DET
ejpam-5911	671	15	(	(	PUNCT
ejpam-5911	671	16	r	r	NOUN
ejpam-5911	671	17	,	,	PUNCT
ejpam-5911	671	18	s)-f	s)-f	NOUN
ejpam-5911	671	19	-	-	PUNCT
ejpam-5911	671	20	b	b	NOUN
ejpam-5911	671	21	-	-	PUNCT
ejpam-5911	671	22	open	open	ADJ
ejpam-5911	671	23	set	set	NOUN
ejpam-5911	671	24	and	and	CCONJ
ejpam-5911	671	25	gθ	gθ	PROPN
ejpam-5911	671	26	∈	∈	PROPN
ejpam-5911	671	27	o.	o.	NOUN
ejpam-5911	671	28	again	again	ADV
ejpam-5911	671	29	,	,	PUNCT
ejpam-5911	671	30	by	by	ADP
ejpam-5911	671	31	(	(	PUNCT
ejpam-5911	671	32	ii	ii	NOUN
ejpam-5911	671	33	)	)	PUNCT
ejpam-5911	671	34	,	,	PUNCT
ejpam-5911	671	35	there	there	PRON
ejpam-5911	671	36	is	be	VERB
ejpam-5911	671	37	v	v	ADP
ejpam-5911	671	38	∈	∈	NOUN
ejpam-5911	671	39	ig	ig	PROPN
ejpam-5911	671	40	with	with	ADP
ejpam-5911	671	41	ℑ(v	ℑ(v	NOUN
ejpam-5911	671	42	)	)	PUNCT
ejpam-5911	671	43	≥	≥	NOUN
ejpam-5911	671	44	r	r	NOUN
ejpam-5911	671	45	,	,	PUNCT
ejpam-5911	671	46	ℑ∗(v	ℑ∗(v	NOUN
ejpam-5911	671	47	)	)	PUNCT
ejpam-5911	671	48	≤	≤	NOUN
ejpam-5911	671	49	s	s	PART
ejpam-5911	671	50	,	,	PUNCT
ejpam-5911	671	51	and	and	CCONJ
ejpam-5911	671	52	gθ	gθ	PROPN
ejpam-5911	671	53	∈	∈	PROPN
ejpam-5911	671	54	v	v	ADJ
ejpam-5911	671	55	≤	≤	NUM
ejpam-5911	671	56	cℑ∗(v	cℑ∗(v	NOUN
ejpam-5911	671	57	,	,	PUNCT
ejpam-5911	671	58	r	r	NOUN
ejpam-5911	671	59	,	,	PUNCT
ejpam-5911	671	60	s	s	NOUN
ejpam-5911	671	61	)	)	PUNCT
ejpam-5911	671	62	≤	≤	NUM
ejpam-5911	671	63	o	o	NOUN
ejpam-5911	671	64	≤	≤	X
ejpam-5911	671	65	cℑ∗(o	cℑ∗(o	NOUN
ejpam-5911	671	66	,	,	PUNCT
ejpam-5911	671	67	r	r	NOUN
ejpam-5911	671	68	,	,	PUNCT
ejpam-5911	671	69	s	s	NOUN
ejpam-5911	671	70	)	)	PUNCT
ejpam-5911	671	71	≤	≤	PROPN
ejpam-5911	671	72	mc	mc	PROPN
ejpam-5911	671	73	.	.	PROPN
ejpam-5911	672	1	hence	hence	ADV
ejpam-5911	672	2	,	,	PUNCT
ejpam-5911	672	3	m	m	VERB
ejpam-5911	672	4	≤	≤	NOUN
ejpam-5911	672	5	(	(	PUNCT
ejpam-5911	672	6	cℑ∗(o	cℑ∗(o	NOUN
ejpam-5911	672	7	,	,	PUNCT
ejpam-5911	672	8	r	r	NOUN
ejpam-5911	672	9	,	,	PUNCT
ejpam-5911	672	10	s))c	s))c	NOUN
ejpam-5911	672	11	=	=	SYM
ejpam-5911	672	12	iℑ∗(oc	iℑ∗(oc	PROPN
ejpam-5911	672	13	,	,	PUNCT
ejpam-5911	672	14	r	r	NOUN
ejpam-5911	672	15	,	,	PUNCT
ejpam-5911	672	16	s	s	NOUN
ejpam-5911	672	17	)	)	PUNCT
ejpam-5911	672	18	≤	≤	NUM
ejpam-5911	672	19	oc	oc	NOUN
ejpam-5911	672	20	.	.	PUNCT
ejpam-5911	673	1	set	set	VERB
ejpam-5911	673	2	u	u	NOUN
ejpam-5911	673	3	=	=	NOUN
ejpam-5911	673	4	iℑ∗(oc	iℑ∗(oc	PROPN
ejpam-5911	673	5	,	,	PUNCT
ejpam-5911	673	6	r	r	NOUN
ejpam-5911	673	7	,	,	PUNCT
ejpam-5911	673	8	s	s	PART
ejpam-5911	673	9	)	)	PUNCT
ejpam-5911	673	10	,	,	PUNCT
ejpam-5911	673	11	thus	thus	ADV
ejpam-5911	673	12	ℑ(u	ℑ(u	ADJ
ejpam-5911	673	13	)	)	PUNCT
ejpam-5911	673	14	≥	≥	NOUN
ejpam-5911	673	15	r	r	NOUN
ejpam-5911	673	16	and	and	CCONJ
ejpam-5911	673	17	ℑ∗(u	ℑ∗(u	NOUN
ejpam-5911	673	18	)	)	PUNCT
ejpam-5911	673	19	≤	≤	NOUN
ejpam-5911	674	1	s.	s.	PROPN
ejpam-5911	674	2	then	then	ADV
ejpam-5911	674	3	,	,	PUNCT
ejpam-5911	674	4	cℑ∗(u	cℑ∗(u	PROPN
ejpam-5911	674	5	,	,	PUNCT
ejpam-5911	674	6	r	r	NOUN
ejpam-5911	674	7	,	,	PUNCT
ejpam-5911	674	8	s	s	NOUN
ejpam-5911	674	9	)	)	PUNCT
ejpam-5911	674	10	≤	≤	NOUN
ejpam-5911	674	11	oc	oc	ADP
ejpam-5911	674	12	≤	≤	PROPN
ejpam-5911	674	13	(	(	PUNCT
ejpam-5911	674	14	cℑ∗(v	cℑ∗(v	NOUN
ejpam-5911	674	15	,	,	PUNCT
ejpam-5911	674	16	r	r	NOUN
ejpam-5911	674	17	,	,	PUNCT
ejpam-5911	674	18	s))c	s))c	NOUN
ejpam-5911	674	19	.	.	PUNCT
ejpam-5911	675	1	therefore	therefore	ADV
ejpam-5911	675	2	,	,	PUNCT
ejpam-5911	675	3	cℑ∗(u	cℑ∗(u	PROPN
ejpam-5911	675	4	,	,	PUNCT
ejpam-5911	675	5	r	r	NOUN
ejpam-5911	675	6	,	,	PUNCT
ejpam-5911	675	7	s	s	NOUN
ejpam-5911	675	8	)	)	PUNCT
ejpam-5911	675	9	q	q	NOUN
ejpam-5911	675	10	cℑ∗(v	cℑ∗(v	NOUN
ejpam-5911	675	11	,	,	PUNCT
ejpam-5911	675	12	r	r	NOUN
ejpam-5911	675	13	,	,	PUNCT
ejpam-5911	675	14	s	s	NOUN
ejpam-5911	675	15	)	)	PUNCT
ejpam-5911	675	16	.	.	PUNCT
ejpam-5911	676	1	(	(	PUNCT
ejpam-5911	676	2	iii	iii	X
ejpam-5911	676	3	)	)	PUNCT
ejpam-5911	676	4	⇒	⇒	NOUN
ejpam-5911	676	5	(	(	PUNCT
ejpam-5911	676	6	i	i	NOUN
ejpam-5911	676	7	)	)	PUNCT
ejpam-5911	676	8	this	this	PRON
ejpam-5911	676	9	is	be	AUX
ejpam-5911	676	10	easily	easily	ADV
ejpam-5911	676	11	proved	prove	VERB
ejpam-5911	676	12	by	by	ADP
ejpam-5911	676	13	definition	definition	NOUN
ejpam-5911	676	14	19	19	NUM
ejpam-5911	676	15	.	.	PUNCT
ejpam-5911	676	16	theorem	theorem	VERB
ejpam-5911	676	17	15	15	NUM
ejpam-5911	676	18	.	.	PUNCT
ejpam-5911	677	1	let	let	AUX
ejpam-5911	677	2	(	(	PUNCT
ejpam-5911	677	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	677	4	)	)	PUNCT
ejpam-5911	677	5	be	be	VERB
ejpam-5911	677	6	an	an	DET
ejpam-5911	677	7	dft	dft	PROPN
ejpam-5911	677	8	s	s	PROPN
ejpam-5911	677	9	,	,	PUNCT
ejpam-5911	677	10	m	m	PROPN
ejpam-5911	677	11	,	,	PUNCT
ejpam-5911	677	12	n	n	PROPN
ejpam-5911	677	13	∈	∈	PROPN
ejpam-5911	677	14	ig	ig	PROPN
ejpam-5911	677	15	.	.	PUNCT
ejpam-5911	678	1	then	then	ADV
ejpam-5911	678	2	the	the	DET
ejpam-5911	678	3	following	follow	VERB
ejpam-5911	678	4	statements	statement	NOUN
ejpam-5911	678	5	are	be	AUX
ejpam-5911	678	6	equivalent	equivalent	ADJ
ejpam-5911	678	7	:	:	PUNCT
ejpam-5911	678	8	(	(	PUNCT
ejpam-5911	678	9	i	i	NOUN
ejpam-5911	678	10	)	)	PUNCT
ejpam-5911	678	11	(	(	PUNCT
ejpam-5911	678	12	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	678	13	)	)	PUNCT
ejpam-5911	678	14	is	be	AUX
ejpam-5911	678	15	an	an	DET
ejpam-5911	678	16	(	(	PUNCT
ejpam-5911	678	17	r	r	NOUN
ejpam-5911	678	18	,	,	PUNCT
ejpam-5911	678	19	s)-f	s)-f	NOUN
ejpam-5911	678	20	-	-	PUNCT
ejpam-5911	678	21	b	b	NOUN
ejpam-5911	678	22	-	-	PUNCT
ejpam-5911	678	23	normal	normal	ADJ
ejpam-5911	678	24	space	space	NOUN
ejpam-5911	678	25	.	.	PUNCT
ejpam-5911	679	1	(	(	PUNCT
ejpam-5911	679	2	ii	ii	NOUN
ejpam-5911	679	3	)	)	PUNCT
ejpam-5911	679	4	if	if	SCONJ
ejpam-5911	679	5	n	n	PRON
ejpam-5911	679	6	≤	≤	X
ejpam-5911	679	7	m	m	VERB
ejpam-5911	679	8	for	for	ADP
ejpam-5911	679	9	every	every	DET
ejpam-5911	679	10	(	(	PUNCT
ejpam-5911	679	11	r	r	NOUN
ejpam-5911	679	12	,	,	PUNCT
ejpam-5911	679	13	s)-f	s)-f	NOUN
ejpam-5911	679	14	-	-	PUNCT
ejpam-5911	679	15	b	b	NOUN
ejpam-5911	679	16	-	-	PUNCT
ejpam-5911	679	17	closed	closed	ADJ
ejpam-5911	679	18	set	set	NOUN
ejpam-5911	679	19	n	n	NOUN
ejpam-5911	680	1	and	and	CCONJ
ejpam-5911	681	1	(	(	PUNCT
ejpam-5911	681	2	r	r	NOUN
ejpam-5911	681	3	,	,	PUNCT
ejpam-5911	681	4	s)-f	s)-f	NOUN
ejpam-5911	681	5	-	-	PUNCT
ejpam-5911	681	6	b	b	NOUN
ejpam-5911	681	7	-	-	PUNCT
ejpam-5911	681	8	open	open	ADJ
ejpam-5911	681	9	set	set	NOUN
ejpam-5911	681	10	m	m	NOUN
ejpam-5911	681	11	,	,	PUNCT
ejpam-5911	681	12	there	there	PRON
ejpam-5911	681	13	is	be	VERB
ejpam-5911	681	14	o	o	PROPN
ejpam-5911	681	15	∈	∈	PROPN
ejpam-5911	681	16	ig	ig	PROPN
ejpam-5911	681	17	with	with	ADP
ejpam-5911	681	18	ℑ(o	ℑ(o	NOUN
ejpam-5911	681	19	)	)	PUNCT
ejpam-5911	681	20	≥	≥	NOUN
ejpam-5911	681	21	r	r	NOUN
ejpam-5911	681	22	,	,	PUNCT
ejpam-5911	681	23	ℑ∗(o	ℑ∗(o	NOUN
ejpam-5911	681	24	)	)	PUNCT
ejpam-5911	681	25	≤	≤	NOUN
ejpam-5911	681	26	s	s	PROPN
ejpam-5911	681	27	,	,	PUNCT
ejpam-5911	681	28	and	and	CCONJ
ejpam-5911	681	29	n	n	PRON
ejpam-5911	681	30	≤	≤	NOUN
ejpam-5911	681	31	o	o	X
ejpam-5911	681	32	≤	≤	X
ejpam-5911	681	33	cℑ∗(o	cℑ∗(o	NOUN
ejpam-5911	681	34	,	,	PUNCT
ejpam-5911	681	35	r	r	NOUN
ejpam-5911	681	36	,	,	PUNCT
ejpam-5911	681	37	s	s	NOUN
ejpam-5911	681	38	)	)	PUNCT
ejpam-5911	681	39	≤	≤	ADJ
ejpam-5911	681	40	m.	m.	NOUN
ejpam-5911	681	41	(	(	PUNCT
ejpam-5911	681	42	iii	iii	NOUN
ejpam-5911	681	43	)	)	PUNCT
ejpam-5911	681	44	if	if	SCONJ
ejpam-5911	681	45	m	m	VERB
ejpam-5911	681	46	q	q	VERB
ejpam-5911	681	47	n	n	PROPN
ejpam-5911	681	48	for	for	ADP
ejpam-5911	681	49	each	each	DET
ejpam-5911	681	50	(	(	PUNCT
ejpam-5911	681	51	r	r	NOUN
ejpam-5911	681	52	,	,	PUNCT
ejpam-5911	681	53	s)-f	s)-f	NOUN
ejpam-5911	681	54	-	-	PUNCT
ejpam-5911	681	55	b	b	NOUN
ejpam-5911	681	56	-	-	PUNCT
ejpam-5911	681	57	closed	close	VERB
ejpam-5911	681	58	sets	set	NOUN
ejpam-5911	681	59	m	m	VERB
ejpam-5911	681	60	and	and	CCONJ
ejpam-5911	681	61	n	n	CCONJ
ejpam-5911	681	62	,	,	PUNCT
ejpam-5911	681	63	there	there	PRON
ejpam-5911	681	64	is	be	VERB
ejpam-5911	681	65	oi	oi	PROPN
ejpam-5911	681	66	∈	∈	PROPN
ejpam-5911	681	67	ig	ig	PROPN
ejpam-5911	681	68	with	with	ADP
ejpam-5911	681	69	ℑ(oi	ℑ(oi	NOUN
ejpam-5911	681	70	)	)	PUNCT
ejpam-5911	681	71	≥	≥	NOUN
ejpam-5911	681	72	r	r	NOUN
ejpam-5911	681	73	,	,	PUNCT
ejpam-5911	681	74	ℑ∗(oi	ℑ∗(oi	NOUN
ejpam-5911	681	75	)	)	PUNCT
ejpam-5911	681	76	≤	≤	NUM
ejpam-5911	681	77	s	s	VERB
ejpam-5911	681	78	for	for	ADP
ejpam-5911	681	79	i	i	PROPN
ejpam-5911	681	80	=	=	SYM
ejpam-5911	681	81	1	1	NUM
ejpam-5911	681	82	,	,	PUNCT
ejpam-5911	681	83	2	2	NUM
ejpam-5911	681	84	,	,	PUNCT
ejpam-5911	681	85	such	such	ADJ
ejpam-5911	681	86	that	that	SCONJ
ejpam-5911	681	87	m	m	VERB
ejpam-5911	681	88	≤	≤	ADJ
ejpam-5911	681	89	o1	o1	NOUN
ejpam-5911	681	90	,	,	PUNCT
ejpam-5911	681	91	n	n	CCONJ
ejpam-5911	681	92	≤	≤	NOUN
ejpam-5911	681	93	o2	o2	PROPN
ejpam-5911	681	94	,	,	PUNCT
ejpam-5911	681	95	and	and	CCONJ
ejpam-5911	681	96	cℑ∗(o1	cℑ∗(o1	PROPN
ejpam-5911	681	97	,	,	PUNCT
ejpam-5911	681	98	r	r	NOUN
ejpam-5911	681	99	,	,	PUNCT
ejpam-5911	681	100	s	s	NOUN
ejpam-5911	681	101	)	)	PUNCT
ejpam-5911	681	102	q	q	NOUN
ejpam-5911	681	103	cℑ∗(o2	cℑ∗(o2	NOUN
ejpam-5911	681	104	,	,	PUNCT
ejpam-5911	681	105	r	r	NOUN
ejpam-5911	681	106	,	,	PUNCT
ejpam-5911	681	107	s	s	NOUN
ejpam-5911	681	108	)	)	PUNCT
ejpam-5911	681	109	.	.	PUNCT
ejpam-5911	682	1	proof	proof	NOUN
ejpam-5911	682	2	.	.	PUNCT
ejpam-5911	683	1	the	the	DET
ejpam-5911	683	2	proof	proof	NOUN
ejpam-5911	683	3	is	be	AUX
ejpam-5911	683	4	similar	similar	ADJ
ejpam-5911	683	5	to	to	ADP
ejpam-5911	683	6	that	that	PRON
ejpam-5911	683	7	of	of	ADP
ejpam-5911	683	8	theorem	theorem	ADJ
ejpam-5911	683	9	14	14	NUM
ejpam-5911	683	10	.	.	PUNCT
ejpam-5911	684	1	theorem	theorem	VERB
ejpam-5911	684	2	16	16	NUM
ejpam-5911	684	3	.	.	PUNCT
ejpam-5911	685	1	let	let	VERB
ejpam-5911	685	2	p	p	NOUN
ejpam-5911	685	3	:	:	PUNCT
ejpam-5911	685	4	(	(	PUNCT
ejpam-5911	685	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	685	6	)	)	PUNCT
ejpam-5911	686	1	−→	−→	NOUN
ejpam-5911	686	2	(	(	PUNCT
ejpam-5911	686	3	z	z	NOUN
ejpam-5911	686	4	,	,	PUNCT
ejpam-5911	686	5	𭟋	𭟋	NOUN
ejpam-5911	686	6	,	,	PUNCT
ejpam-5911	686	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	686	8	)	)	PUNCT
ejpam-5911	686	9	be	be	AUX
ejpam-5911	686	10	a	a	DET
ejpam-5911	686	11	bijective	bijective	ADJ
ejpam-5911	686	12	df	df	PROPN
ejpam-5911	686	13	-	-	PUNCT
ejpam-5911	686	14	b	b	NOUN
ejpam-5911	686	15	-	-	PUNCT
ejpam-5911	686	16	irresolute	irresolute	ADJ
ejpam-5911	686	17	and	and	CCONJ
ejpam-5911	686	18	dfopen	dfopen	VERB
ejpam-5911	686	19	mapping	mapping	NOUN
ejpam-5911	686	20	.	.	PUNCT
ejpam-5911	687	1	if	if	SCONJ
ejpam-5911	687	2	(	(	PUNCT
ejpam-5911	687	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	687	4	)	)	PUNCT
ejpam-5911	687	5	is	be	AUX
ejpam-5911	687	6	an	an	DET
ejpam-5911	687	7	(	(	PUNCT
ejpam-5911	687	8	r	r	NOUN
ejpam-5911	687	9	,	,	PUNCT
ejpam-5911	687	10	s)-f	s)-f	NOUN
ejpam-5911	687	11	-	-	PUNCT
ejpam-5911	687	12	b	b	NOUN
ejpam-5911	687	13	-	-	PUNCT
ejpam-5911	687	14	regular	regular	ADJ
ejpam-5911	687	15	space	space	NOUN
ejpam-5911	687	16	(	(	PUNCT
ejpam-5911	687	17	resp	resp	NOUN
ejpam-5911	687	18	.	.	PUNCT
ejpam-5911	688	1	(	(	PUNCT
ejpam-5911	688	2	r	r	NOUN
ejpam-5911	688	3	,	,	PUNCT
ejpam-5911	688	4	s)-f	s)-f	NOUN
ejpam-5911	688	5	-	-	PUNCT
ejpam-5911	688	6	b	b	NOUN
ejpam-5911	688	7	-	-	PUNCT
ejpam-5911	688	8	normal	normal	ADJ
ejpam-5911	688	9	space	space	NOUN
ejpam-5911	688	10	)	)	PUNCT
ejpam-5911	688	11	,	,	PUNCT
ejpam-5911	688	12	then	then	ADV
ejpam-5911	688	13	(	(	PUNCT
ejpam-5911	688	14	z	z	NOUN
ejpam-5911	688	15	,	,	PUNCT
ejpam-5911	688	16	𭟋	𭟋	NOUN
ejpam-5911	688	17	,	,	PUNCT
ejpam-5911	688	18	𭟋∗	𭟋∗	NOUN
ejpam-5911	688	19	)	)	PUNCT
ejpam-5911	688	20	is	be	AUX
ejpam-5911	688	21	an	an	DET
ejpam-5911	688	22	(	(	PUNCT
ejpam-5911	688	23	r	r	NOUN
ejpam-5911	688	24	,	,	PUNCT
ejpam-5911	688	25	s)-f	s)-f	NOUN
ejpam-5911	688	26	-	-	PUNCT
ejpam-5911	688	27	b	b	NOUN
ejpam-5911	688	28	-	-	PUNCT
ejpam-5911	688	29	regular	regular	ADJ
ejpam-5911	688	30	space	space	NOUN
ejpam-5911	688	31	(	(	PUNCT
ejpam-5911	688	32	resp	resp	NOUN
ejpam-5911	688	33	.	.	PUNCT
ejpam-5911	689	1	(	(	PUNCT
ejpam-5911	689	2	r	r	NOUN
ejpam-5911	689	3	,	,	PUNCT
ejpam-5911	689	4	s)-f	s)-f	NOUN
ejpam-5911	689	5	-	-	PUNCT
ejpam-5911	689	6	b	b	NOUN
ejpam-5911	689	7	-	-	PUNCT
ejpam-5911	689	8	normal	normal	ADJ
ejpam-5911	689	9	space	space	NOUN
ejpam-5911	689	10	)	)	PUNCT
ejpam-5911	689	11	.	.	PUNCT
ejpam-5911	690	1	proof	proof	NOUN
ejpam-5911	690	2	.	.	PUNCT
ejpam-5911	691	1	if	if	SCONJ
ejpam-5911	691	2	zθ	zθ	PRON
ejpam-5911	691	3	q	q	X
ejpam-5911	691	4	n	n	PROPN
ejpam-5911	691	5	for	for	ADP
ejpam-5911	691	6	every	every	DET
ejpam-5911	691	7	(	(	PUNCT
ejpam-5911	691	8	r	r	NOUN
ejpam-5911	691	9	,	,	PUNCT
ejpam-5911	691	10	s)-f	s)-f	NOUN
ejpam-5911	691	11	-	-	PUNCT
ejpam-5911	691	12	b	b	NOUN
ejpam-5911	691	13	-	-	PUNCT
ejpam-5911	691	14	closed	closed	ADJ
ejpam-5911	691	15	set	set	NOUN
ejpam-5911	691	16	n	n	CCONJ
ejpam-5911	691	17	∈	∈	NOUN
ejpam-5911	692	1	iz	iz	INTJ
ejpam-5911	693	1	and	and	CCONJ
ejpam-5911	693	2	p	p	NOUN
ejpam-5911	693	3	is	be	AUX
ejpam-5911	693	4	df	df	PROPN
ejpam-5911	693	5	-	-	PUNCT
ejpam-5911	693	6	b	b	NOUN
ejpam-5911	693	7	-	-	PUNCT
ejpam-5911	693	8	irresolute	irresolute	ADJ
ejpam-5911	693	9	,	,	PUNCT
ejpam-5911	693	10	then	then	ADV
ejpam-5911	693	11	p−1(n	p−1(n	PROPN
ejpam-5911	693	12	)	)	PUNCT
ejpam-5911	693	13	is	be	AUX
ejpam-5911	693	14	an	an	DET
ejpam-5911	693	15	(	(	PUNCT
ejpam-5911	693	16	r	r	NOUN
ejpam-5911	693	17	,	,	PUNCT
ejpam-5911	693	18	s)-f	s)-f	NOUN
ejpam-5911	693	19	-	-	PUNCT
ejpam-5911	693	20	b	b	NOUN
ejpam-5911	693	21	-	-	PUNCT
ejpam-5911	693	22	closed	closed	ADJ
ejpam-5911	693	23	set	set	NOUN
ejpam-5911	693	24	.	.	PUNCT
ejpam-5911	694	1	set	set	VERB
ejpam-5911	694	2	zθ	zθ	NOUN
ejpam-5911	694	3	=	=	SYM
ejpam-5911	694	4	p(gθ	p(gθ	PROPN
ejpam-5911	694	5	)	)	PUNCT
ejpam-5911	694	6	,	,	PUNCT
ejpam-5911	694	7	and	and	CCONJ
ejpam-5911	694	8	then	then	ADV
ejpam-5911	694	9	gθ	gθ	PROPN
ejpam-5911	694	10	q	q	PROPN
ejpam-5911	694	11	p−1(n	p−1(n	PROPN
ejpam-5911	694	12	)	)	PUNCT
ejpam-5911	694	13	.	.	PUNCT
ejpam-5911	695	1	since	since	SCONJ
ejpam-5911	695	2	(	(	PUNCT
ejpam-5911	695	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	695	4	)	)	PUNCT
ejpam-5911	695	5	is	be	AUX
ejpam-5911	695	6	(	(	PUNCT
ejpam-5911	695	7	r	r	NOUN
ejpam-5911	695	8	,	,	PUNCT
ejpam-5911	695	9	s)-f	s)-f	NOUN
ejpam-5911	695	10	-	-	PUNCT
ejpam-5911	695	11	b	b	NOUN
ejpam-5911	695	12	-	-	PUNCT
ejpam-5911	695	13	regular	regular	ADJ
ejpam-5911	695	14	,	,	PUNCT
ejpam-5911	695	15	there	there	PRON
ejpam-5911	695	16	is	be	VERB
ejpam-5911	695	17	o1	o1	NOUN
ejpam-5911	695	18	,	,	PUNCT
ejpam-5911	695	19	o2	o2	PROPN
ejpam-5911	695	20	∈	∈	PROPN
ejpam-5911	695	21	ig	ig	PROPN
ejpam-5911	695	22	with	with	ADP
ejpam-5911	695	23	ℑ(o1	ℑ(o1	PROPN
ejpam-5911	695	24	)	)	PUNCT
ejpam-5911	695	25	≥	≥	NOUN
ejpam-5911	695	26	r	r	NOUN
ejpam-5911	695	27	,	,	PUNCT
ejpam-5911	695	28	ℑ∗(o1	ℑ∗(o1	NOUN
ejpam-5911	695	29	)	)	PUNCT
ejpam-5911	695	30	≤	≤	PROPN
ejpam-5911	696	1	s	s	PROPN
ejpam-5911	696	2	,	,	PUNCT
ejpam-5911	696	3	ℑ(o2	ℑ(o2	NOUN
ejpam-5911	696	4	)	)	PUNCT
ejpam-5911	696	5	≥	≥	NOUN
ejpam-5911	696	6	r	r	NOUN
ejpam-5911	696	7	,	,	PUNCT
ejpam-5911	696	8	and	and	CCONJ
ejpam-5911	696	9	ℑ∗(o2	ℑ∗(o2	NOUN
ejpam-5911	696	10	)	)	PUNCT
ejpam-5911	697	1	≤	≤	NUM
ejpam-5911	697	2	s	s	VERB
ejpam-5911	697	3	such	such	ADJ
ejpam-5911	697	4	that	that	SCONJ
ejpam-5911	697	5	gθ	gθ	PROPN
ejpam-5911	697	6	∈	∈	PROPN
ejpam-5911	697	7	o1	o1	PROPN
ejpam-5911	697	8	,	,	PUNCT
ejpam-5911	697	9	p−1(n	p−1(n	PROPN
ejpam-5911	697	10	)	)	PUNCT
ejpam-5911	697	11	≤	≤	PROPN
ejpam-5911	697	12	o2	o2	PROPN
ejpam-5911	697	13	,	,	PUNCT
ejpam-5911	697	14	and	and	CCONJ
ejpam-5911	697	15	o1	o1	PROPN
ejpam-5911	697	16	q	q	PROPN
ejpam-5911	697	17	o2	o2	PROPN
ejpam-5911	697	18	.	.	PUNCT
ejpam-5911	698	1	since	since	SCONJ
ejpam-5911	698	2	p	p	NOUN
ejpam-5911	698	3	is	be	AUX
ejpam-5911	698	4	a	a	DET
ejpam-5911	698	5	bijective	bijective	ADJ
ejpam-5911	698	6	df	df	NOUN
ejpam-5911	698	7	-	-	PUNCT
ejpam-5911	698	8	open	open	ADJ
ejpam-5911	698	9	mapping	mapping	NOUN
ejpam-5911	698	10	,	,	PUNCT
ejpam-5911	698	11	hence	hence	ADV
ejpam-5911	698	12	zθ	zθ	NOUN
ejpam-5911	698	13	∈	∈	PROPN
ejpam-5911	698	14	p(o1	p(o1	NOUN
ejpam-5911	698	15	)	)	PUNCT
ejpam-5911	698	16	,	,	PUNCT
ejpam-5911	698	17	n	n	PROPN
ejpam-5911	698	18	=	=	SYM
ejpam-5911	698	19	p(p−1(n	p(p−1(n	PROPN
ejpam-5911	698	20	)	)	PUNCT
ejpam-5911	698	21	)	)	PUNCT
ejpam-5911	698	22	≤	≤	NUM
ejpam-5911	698	23	p(o2	p(o2	NOUN
ejpam-5911	698	24	)	)	PUNCT
ejpam-5911	698	25	,	,	PUNCT
ejpam-5911	698	26	and	and	CCONJ
ejpam-5911	698	27	p(o1	p(o1	NOUN
ejpam-5911	698	28	)	)	PUNCT
ejpam-5911	698	29	q	q	NOUN
ejpam-5911	698	30	p(o2	p(o2	NOUN
ejpam-5911	698	31	)	)	PUNCT
ejpam-5911	698	32	.	.	PUNCT
ejpam-5911	699	1	therefore	therefore	ADV
ejpam-5911	699	2	,	,	PUNCT
ejpam-5911	699	3	(	(	PUNCT
ejpam-5911	699	4	z	z	NOUN
ejpam-5911	699	5	,	,	PUNCT
ejpam-5911	699	6	𭟋	𭟋	NOUN
ejpam-5911	699	7	,	,	PUNCT
ejpam-5911	699	8	𭟋∗	𭟋∗	NOUN
ejpam-5911	699	9	)	)	PUNCT
ejpam-5911	699	10	is	be	AUX
ejpam-5911	699	11	an	an	DET
ejpam-5911	699	12	(	(	PUNCT
ejpam-5911	699	13	r	r	NOUN
ejpam-5911	699	14	,	,	PUNCT
ejpam-5911	699	15	s)-f	s)-f	NOUN
ejpam-5911	699	16	-	-	PUNCT
ejpam-5911	699	17	b	b	NOUN
ejpam-5911	699	18	-	-	PUNCT
ejpam-5911	699	19	regular	regular	ADJ
ejpam-5911	699	20	space	space	NOUN
ejpam-5911	699	21	.	.	PUNCT
ejpam-5911	700	1	the	the	DET
ejpam-5911	700	2	other	other	ADJ
ejpam-5911	700	3	case	case	NOUN
ejpam-5911	700	4	also	also	ADV
ejpam-5911	700	5	follows	follow	VERB
ejpam-5911	700	6	similar	similar	ADJ
ejpam-5911	700	7	lines	line	NOUN
ejpam-5911	700	8	.	.	PUNCT
ejpam-5911	701	1	theorem	theorem	NOUN
ejpam-5911	701	2	17	17	NUM
ejpam-5911	701	3	.	.	PUNCT
ejpam-5911	702	1	let	let	VERB
ejpam-5911	702	2	p	p	NOUN
ejpam-5911	702	3	:	:	PUNCT
ejpam-5911	702	4	(	(	PUNCT
ejpam-5911	702	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	702	6	)	)	PUNCT
ejpam-5911	703	1	−→	−→	NOUN
ejpam-5911	703	2	(	(	PUNCT
ejpam-5911	703	3	z	z	NOUN
ejpam-5911	703	4	,	,	PUNCT
ejpam-5911	703	5	𭟋	𭟋	NOUN
ejpam-5911	703	6	,	,	PUNCT
ejpam-5911	703	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	703	8	)	)	PUNCT
ejpam-5911	703	9	be	be	AUX
ejpam-5911	703	10	an	an	DET
ejpam-5911	703	11	injective	injective	ADJ
ejpam-5911	703	12	df	df	NOUN
ejpam-5911	703	13	-	-	PUNCT
ejpam-5911	703	14	continuous	continuous	ADJ
ejpam-5911	703	15	and	and	CCONJ
ejpam-5911	703	16	dfb	dfb	PROPN
ejpam-5911	703	17	-	-	PUNCT
ejpam-5911	703	18	irresolute	irresolute	ADJ
ejpam-5911	703	19	closed	closed	ADJ
ejpam-5911	703	20	mapping	mapping	NOUN
ejpam-5911	703	21	.	.	PUNCT
ejpam-5911	704	1	if	if	SCONJ
ejpam-5911	704	2	(	(	PUNCT
ejpam-5911	704	3	z	z	NOUN
ejpam-5911	704	4	,	,	PUNCT
ejpam-5911	704	5	𭟋	𭟋	NOUN
ejpam-5911	704	6	,	,	PUNCT
ejpam-5911	704	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	704	8	)	)	PUNCT
ejpam-5911	704	9	is	be	AUX
ejpam-5911	704	10	an	an	DET
ejpam-5911	704	11	(	(	PUNCT
ejpam-5911	704	12	r	r	NOUN
ejpam-5911	704	13	,	,	PUNCT
ejpam-5911	704	14	s)-f	s)-f	NOUN
ejpam-5911	704	15	-	-	PUNCT
ejpam-5911	704	16	b	b	NOUN
ejpam-5911	704	17	-	-	PUNCT
ejpam-5911	704	18	regular	regular	ADJ
ejpam-5911	704	19	space	space	NOUN
ejpam-5911	704	20	(	(	PUNCT
ejpam-5911	704	21	resp	resp	NOUN
ejpam-5911	704	22	.	.	PUNCT
ejpam-5911	705	1	(	(	PUNCT
ejpam-5911	705	2	r	r	NOUN
ejpam-5911	705	3	,	,	PUNCT
ejpam-5911	705	4	s)-fb	s)-fb	ADJ
ejpam-5911	705	5	-	-	PUNCT
ejpam-5911	705	6	normal	normal	ADJ
ejpam-5911	705	7	space	space	NOUN
ejpam-5911	705	8	)	)	PUNCT
ejpam-5911	705	9	,	,	PUNCT
ejpam-5911	705	10	then	then	ADV
ejpam-5911	705	11	(	(	PUNCT
ejpam-5911	705	12	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	705	13	)	)	PUNCT
ejpam-5911	705	14	is	be	AUX
ejpam-5911	705	15	an	an	DET
ejpam-5911	705	16	(	(	PUNCT
ejpam-5911	705	17	r	r	NOUN
ejpam-5911	705	18	,	,	PUNCT
ejpam-5911	705	19	s)-f	s)-f	NOUN
ejpam-5911	705	20	-	-	PUNCT
ejpam-5911	705	21	b	b	NOUN
ejpam-5911	705	22	-	-	PUNCT
ejpam-5911	705	23	regular	regular	ADJ
ejpam-5911	705	24	space	space	NOUN
ejpam-5911	705	25	(	(	PUNCT
ejpam-5911	705	26	resp	resp	NOUN
ejpam-5911	705	27	.	.	PUNCT
ejpam-5911	706	1	(	(	PUNCT
ejpam-5911	706	2	r	r	NOUN
ejpam-5911	706	3	,	,	PUNCT
ejpam-5911	706	4	s)-f	s)-f	NOUN
ejpam-5911	706	5	-	-	PUNCT
ejpam-5911	706	6	b	b	NOUN
ejpam-5911	706	7	-	-	PUNCT
ejpam-5911	706	8	normal	normal	ADJ
ejpam-5911	706	9	space	space	NOUN
ejpam-5911	706	10	)	)	PUNCT
ejpam-5911	706	11	.	.	PUNCT
ejpam-5911	707	1	i.	i.	PROPN
ejpam-5911	707	2	m.	m.	PROPN
ejpam-5911	707	3	taha	taha	PROPN
ejpam-5911	707	4	,	,	PUNCT
ejpam-5911	707	5	j.	j.	PROPN
ejpam-5911	707	6	al	al	PROPN
ejpam-5911	707	7	-	-	PUNCT
ejpam-5911	707	8	mufarrij	mufarrij	PROPN
ejpam-5911	707	9	,	,	PUNCT
ejpam-5911	707	10	o.	o.	PROPN
ejpam-5911	707	11	m.	m.	PROPN
ejpam-5911	707	12	taha	taha	PROPN
ejpam-5911	707	13	/	/	PUNCT
ejpam-5911	707	14	eur	eur	PROPN
ejpam-5911	707	15	.	.	PUNCT
ejpam-5911	708	1	j.	j.	PROPN
ejpam-5911	708	2	pure	pure	PROPN
ejpam-5911	708	3	appl	appl	PROPN
ejpam-5911	708	4	.	.	PROPN
ejpam-5911	708	5	math	math	PROPN
ejpam-5911	708	6	,	,	PUNCT
ejpam-5911	708	7	18	18	NUM
ejpam-5911	708	8	(	(	PUNCT
ejpam-5911	708	9	2	2	NUM
ejpam-5911	708	10	)	)	PUNCT
ejpam-5911	708	11	(	(	PUNCT
ejpam-5911	708	12	2025	2025	NUM
ejpam-5911	708	13	)	)	PUNCT
ejpam-5911	708	14	,	,	PUNCT
ejpam-5911	708	15	5911	5911	NUM
ejpam-5911	708	16	24	24	NUM
ejpam-5911	708	17	of	of	ADP
ejpam-5911	708	18	27	27	NUM
ejpam-5911	708	19	proof	proof	NOUN
ejpam-5911	708	20	.	.	PUNCT
ejpam-5911	709	1	if	if	SCONJ
ejpam-5911	709	2	gθ	gθ	PROPN
ejpam-5911	709	3	q	q	PROPN
ejpam-5911	709	4	m	m	VERB
ejpam-5911	709	5	for	for	ADP
ejpam-5911	709	6	each	each	DET
ejpam-5911	709	7	(	(	PUNCT
ejpam-5911	709	8	r	r	NOUN
ejpam-5911	709	9	,	,	PUNCT
ejpam-5911	709	10	s)-f	s)-f	NOUN
ejpam-5911	709	11	-	-	PUNCT
ejpam-5911	709	12	b	b	NOUN
ejpam-5911	709	13	-	-	PUNCT
ejpam-5911	709	14	closed	closed	ADJ
ejpam-5911	709	15	set	set	NOUN
ejpam-5911	709	16	m	m	NOUN
ejpam-5911	709	17	∈	∈	PROPN
ejpam-5911	709	18	ig	ig	PROPN
ejpam-5911	709	19	and	and	CCONJ
ejpam-5911	709	20	p	p	NOUN
ejpam-5911	709	21	is	be	AUX
ejpam-5911	709	22	injective	injective	ADJ
ejpam-5911	709	23	dfb	dfb	PROPN
ejpam-5911	709	24	-	-	PUNCT
ejpam-5911	709	25	irresolute	irresolute	NOUN
ejpam-5911	709	26	closed	closed	ADJ
ejpam-5911	709	27	,	,	PUNCT
ejpam-5911	709	28	hence	hence	ADV
ejpam-5911	709	29	p(m	p(m	NOUN
ejpam-5911	709	30	)	)	PUNCT
ejpam-5911	709	31	is	be	AUX
ejpam-5911	709	32	an	an	DET
ejpam-5911	709	33	(	(	PUNCT
ejpam-5911	709	34	r	r	NOUN
ejpam-5911	709	35	,	,	PUNCT
ejpam-5911	709	36	s)-f	s)-f	NOUN
ejpam-5911	709	37	-	-	PUNCT
ejpam-5911	709	38	b	b	NOUN
ejpam-5911	709	39	-	-	PUNCT
ejpam-5911	709	40	closed	closed	ADJ
ejpam-5911	709	41	set	set	NOUN
ejpam-5911	709	42	and	and	CCONJ
ejpam-5911	709	43	p(gθ	p(gθ	NOUN
ejpam-5911	709	44	)	)	PUNCT
ejpam-5911	709	45	q	q	NOUN
ejpam-5911	709	46	p(m	p(m	NOUN
ejpam-5911	709	47	)	)	PUNCT
ejpam-5911	709	48	.	.	PUNCT
ejpam-5911	710	1	since	since	SCONJ
ejpam-5911	710	2	(	(	PUNCT
ejpam-5911	710	3	z	z	NOUN
ejpam-5911	710	4	,	,	PUNCT
ejpam-5911	710	5	𭟋	𭟋	NOUN
ejpam-5911	710	6	,	,	PUNCT
ejpam-5911	710	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	710	8	)	)	PUNCT
ejpam-5911	710	9	is	be	AUX
ejpam-5911	710	10	(	(	PUNCT
ejpam-5911	710	11	r	r	NOUN
ejpam-5911	710	12	,	,	PUNCT
ejpam-5911	710	13	s)-f	s)-f	NOUN
ejpam-5911	710	14	-	-	PUNCT
ejpam-5911	710	15	b	b	NOUN
ejpam-5911	710	16	-	-	PUNCT
ejpam-5911	710	17	regular	regular	ADJ
ejpam-5911	710	18	,	,	PUNCT
ejpam-5911	710	19	there	there	PRON
ejpam-5911	710	20	is	be	VERB
ejpam-5911	710	21	o1,o2	o1,o2	PROPN
ejpam-5911	710	22	∈	∈	PROPN
ejpam-5911	710	23	iz	iz	ADP
ejpam-5911	710	24	with	with	ADP
ejpam-5911	710	25	𭟋(o1	𭟋(o1	NOUN
ejpam-5911	710	26	)	)	PUNCT
ejpam-5911	710	27	≥	≥	NOUN
ejpam-5911	710	28	r	r	NOUN
ejpam-5911	710	29	,	,	PUNCT
ejpam-5911	710	30	𭟋∗(o1	𭟋∗(o1	PROPN
ejpam-5911	710	31	)	)	PUNCT
ejpam-5911	710	32	≤	≤	PROPN
ejpam-5911	711	1	s	s	PROPN
ejpam-5911	711	2	,	,	PUNCT
ejpam-5911	711	3	𭟋(o2	𭟋(o2	NOUN
ejpam-5911	711	4	)	)	PUNCT
ejpam-5911	711	5	≥	≥	NOUN
ejpam-5911	711	6	r	r	NOUN
ejpam-5911	711	7	,	,	PUNCT
ejpam-5911	711	8	and	and	CCONJ
ejpam-5911	711	9	𭟋∗(o2	𭟋∗(o2	ADJ
ejpam-5911	711	10	)	)	PUNCT
ejpam-5911	712	1	≤	≤	NOUN
ejpam-5911	712	2	s	s	VERB
ejpam-5911	712	3	such	such	ADJ
ejpam-5911	712	4	that	that	SCONJ
ejpam-5911	712	5	p(gθ	p(gθ	PROPN
ejpam-5911	712	6	)	)	PUNCT
ejpam-5911	712	7	∈	∈	PROPN
ejpam-5911	712	8	o1	o1	NOUN
ejpam-5911	712	9	,	,	PUNCT
ejpam-5911	712	10	p(m	p(m	NOUN
ejpam-5911	712	11	)	)	PUNCT
ejpam-5911	712	12	≤	≤	NOUN
ejpam-5911	712	13	o2	o2	PROPN
ejpam-5911	712	14	,	,	PUNCT
ejpam-5911	712	15	and	and	CCONJ
ejpam-5911	712	16	o1	o1	PROPN
ejpam-5911	712	17	q	q	PROPN
ejpam-5911	712	18	o2	o2	PROPN
ejpam-5911	712	19	.	.	PUNCT
ejpam-5911	713	1	since	since	SCONJ
ejpam-5911	713	2	p	p	NOUN
ejpam-5911	713	3	is	be	AUX
ejpam-5911	713	4	an	an	DET
ejpam-5911	713	5	df	df	NOUN
ejpam-5911	713	6	-	-	PUNCT
ejpam-5911	713	7	continuous	continuous	ADJ
ejpam-5911	713	8	mapping	mapping	NOUN
ejpam-5911	713	9	,	,	PUNCT
ejpam-5911	713	10	then	then	ADV
ejpam-5911	713	11	gθ	gθ	PROPN
ejpam-5911	713	12	∈	∈	PROPN
ejpam-5911	713	13	p−1(o1	p−1(o1	PROPN
ejpam-5911	713	14	)	)	PUNCT
ejpam-5911	713	15	and	and	CCONJ
ejpam-5911	713	16	m	m	PRON
ejpam-5911	713	17	≤	≤	NUM
ejpam-5911	713	18	p−1(o2	p−1(o2	NOUN
ejpam-5911	713	19	)	)	PUNCT
ejpam-5911	713	20	with	with	ADP
ejpam-5911	713	21	ℑ(p−1(o1	ℑ(p−1(o1	PROPN
ejpam-5911	713	22	)	)	PUNCT
ejpam-5911	713	23	)	)	PUNCT
ejpam-5911	713	24	≥	≥	PROPN
ejpam-5911	713	25	r	r	NOUN
ejpam-5911	713	26	,	,	PUNCT
ejpam-5911	713	27	ℑ∗(p−1(o1	ℑ∗(p−1(o1	PROPN
ejpam-5911	713	28	)	)	PUNCT
ejpam-5911	713	29	)	)	PUNCT
ejpam-5911	714	1	≤	≤	PROPN
ejpam-5911	714	2	s	s	X
ejpam-5911	714	3	,	,	PUNCT
ejpam-5911	714	4	ℑ(p−1(o2	ℑ(p−1(o2	PROPN
ejpam-5911	714	5	)	)	PUNCT
ejpam-5911	714	6	)	)	PUNCT
ejpam-5911	714	7	≥	≥	PROPN
ejpam-5911	714	8	r	r	NOUN
ejpam-5911	714	9	,	,	PUNCT
ejpam-5911	714	10	ℑ∗(p−1(o2	ℑ∗(p−1(o2	NOUN
ejpam-5911	714	11	)	)	PUNCT
ejpam-5911	714	12	)	)	PUNCT
ejpam-5911	715	1	≤	≤	PROPN
ejpam-5911	715	2	s	s	PROPN
ejpam-5911	715	3	,	,	PUNCT
ejpam-5911	715	4	and	and	CCONJ
ejpam-5911	715	5	p−1(o1	p−1(o1	NOUN
ejpam-5911	715	6	)	)	PUNCT
ejpam-5911	715	7	q	q	NOUN
ejpam-5911	715	8	p−1(o2	p−1(o2	NOUN
ejpam-5911	715	9	)	)	PUNCT
ejpam-5911	715	10	.	.	PUNCT
ejpam-5911	716	1	hence	hence	ADV
ejpam-5911	716	2	,	,	PUNCT
ejpam-5911	716	3	(	(	PUNCT
ejpam-5911	716	4	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	716	5	)	)	PUNCT
ejpam-5911	716	6	is	be	AUX
ejpam-5911	716	7	an	an	DET
ejpam-5911	716	8	(	(	PUNCT
ejpam-5911	716	9	r	r	NOUN
ejpam-5911	716	10	,	,	PUNCT
ejpam-5911	716	11	s)-f	s)-f	NOUN
ejpam-5911	716	12	-	-	PUNCT
ejpam-5911	716	13	b	b	NOUN
ejpam-5911	716	14	-	-	PUNCT
ejpam-5911	716	15	regular	regular	ADJ
ejpam-5911	716	16	space	space	NOUN
ejpam-5911	716	17	.	.	PUNCT
ejpam-5911	717	1	the	the	DET
ejpam-5911	717	2	other	other	ADJ
ejpam-5911	717	3	case	case	NOUN
ejpam-5911	717	4	also	also	ADV
ejpam-5911	717	5	follows	follow	VERB
ejpam-5911	717	6	similar	similar	ADJ
ejpam-5911	717	7	lines	line	NOUN
ejpam-5911	717	8	.	.	PUNCT
ejpam-5911	718	1	theorem	theorem	NOUN
ejpam-5911	718	2	18	18	NUM
ejpam-5911	718	3	.	.	PUNCT
ejpam-5911	719	1	let	let	VERB
ejpam-5911	719	2	p	p	NOUN
ejpam-5911	719	3	:	:	PUNCT
ejpam-5911	719	4	(	(	PUNCT
ejpam-5911	719	5	g,ℑ,ℑ∗	g,ℑ,ℑ∗	NOUN
ejpam-5911	719	6	)	)	PUNCT
ejpam-5911	720	1	−→	−→	NOUN
ejpam-5911	720	2	(	(	PUNCT
ejpam-5911	720	3	z	z	NOUN
ejpam-5911	720	4	,	,	PUNCT
ejpam-5911	720	5	𭟋	𭟋	NOUN
ejpam-5911	720	6	,	,	PUNCT
ejpam-5911	720	7	𭟋∗	𭟋∗	NOUN
ejpam-5911	720	8	)	)	PUNCT
ejpam-5911	720	9	be	be	AUX
ejpam-5911	720	10	a	a	DET
ejpam-5911	720	11	surjective	surjective	ADJ
ejpam-5911	720	12	df	df	PROPN
ejpam-5911	720	13	-	-	PUNCT
ejpam-5911	720	14	b	b	NOUN
ejpam-5911	720	15	-	-	PUNCT
ejpam-5911	720	16	irresolute	irresolute	ADJ
ejpam-5911	720	17	,	,	PUNCT
ejpam-5911	720	18	dfopen	dfopen	NOUN
ejpam-5911	720	19	,	,	PUNCT
ejpam-5911	720	20	and	and	CCONJ
ejpam-5911	720	21	df	df	NOUN
ejpam-5911	720	22	-	-	PUNCT
ejpam-5911	720	23	closed	close	VERB
ejpam-5911	720	24	mapping	mapping	NOUN
ejpam-5911	720	25	.	.	PUNCT
ejpam-5911	721	1	if	if	SCONJ
ejpam-5911	721	2	(	(	PUNCT
ejpam-5911	721	3	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	721	4	)	)	PUNCT
ejpam-5911	721	5	is	be	AUX
ejpam-5911	721	6	an	an	DET
ejpam-5911	721	7	(	(	PUNCT
ejpam-5911	721	8	r	r	NOUN
ejpam-5911	721	9	,	,	PUNCT
ejpam-5911	721	10	s)-f	s)-f	NOUN
ejpam-5911	721	11	-	-	PUNCT
ejpam-5911	721	12	b	b	NOUN
ejpam-5911	721	13	-	-	PUNCT
ejpam-5911	721	14	regular	regular	ADJ
ejpam-5911	721	15	space	space	NOUN
ejpam-5911	721	16	(	(	PUNCT
ejpam-5911	721	17	resp	resp	NOUN
ejpam-5911	721	18	.	.	PUNCT
ejpam-5911	722	1	(	(	PUNCT
ejpam-5911	722	2	r	r	NOUN
ejpam-5911	722	3	,	,	PUNCT
ejpam-5911	722	4	s)f	s)f	NUM
ejpam-5911	722	5	-	-	PUNCT
ejpam-5911	722	6	b	b	X
ejpam-5911	722	7	-	-	PUNCT
ejpam-5911	722	8	normal	normal	ADJ
ejpam-5911	722	9	space	space	NOUN
ejpam-5911	722	10	)	)	PUNCT
ejpam-5911	722	11	,	,	PUNCT
ejpam-5911	722	12	then	then	ADV
ejpam-5911	722	13	(	(	PUNCT
ejpam-5911	722	14	z	z	NOUN
ejpam-5911	722	15	,	,	PUNCT
ejpam-5911	722	16	𭟋	𭟋	NOUN
ejpam-5911	722	17	,	,	PUNCT
ejpam-5911	722	18	𭟋∗	𭟋∗	NOUN
ejpam-5911	722	19	)	)	PUNCT
ejpam-5911	722	20	is	be	AUX
ejpam-5911	722	21	an	an	DET
ejpam-5911	722	22	(	(	PUNCT
ejpam-5911	722	23	r	r	NOUN
ejpam-5911	722	24	,	,	PUNCT
ejpam-5911	722	25	s)-f	s)-f	NOUN
ejpam-5911	722	26	-	-	PUNCT
ejpam-5911	722	27	b	b	NOUN
ejpam-5911	722	28	-	-	PUNCT
ejpam-5911	722	29	regular	regular	ADJ
ejpam-5911	722	30	space	space	NOUN
ejpam-5911	722	31	(	(	PUNCT
ejpam-5911	722	32	resp	resp	NOUN
ejpam-5911	722	33	.	.	PUNCT
ejpam-5911	723	1	(	(	PUNCT
ejpam-5911	723	2	r	r	NOUN
ejpam-5911	723	3	,	,	PUNCT
ejpam-5911	723	4	s)-f	s)-f	NOUN
ejpam-5911	723	5	-	-	PUNCT
ejpam-5911	723	6	b	b	NOUN
ejpam-5911	723	7	-	-	PUNCT
ejpam-5911	723	8	normal	normal	ADJ
ejpam-5911	723	9	space	space	NOUN
ejpam-5911	723	10	)	)	PUNCT
ejpam-5911	723	11	.	.	PUNCT
ejpam-5911	724	1	proof	proof	NOUN
ejpam-5911	724	2	.	.	PUNCT
ejpam-5911	725	1	the	the	DET
ejpam-5911	725	2	proof	proof	NOUN
ejpam-5911	725	3	is	be	AUX
ejpam-5911	725	4	similar	similar	ADJ
ejpam-5911	725	5	to	to	ADP
ejpam-5911	725	6	that	that	PRON
ejpam-5911	725	7	of	of	ADP
ejpam-5911	725	8	theorem	theorem	NOUN
ejpam-5911	725	9	16	16	NUM
ejpam-5911	725	10	.	.	NOUN
ejpam-5911	726	1	6	6	NUM
ejpam-5911	726	2	.	.	PUNCT
ejpam-5911	726	3	conclusions	conclusion	NOUN
ejpam-5911	726	4	in	in	ADP
ejpam-5911	726	5	the	the	DET
ejpam-5911	726	6	present	present	ADJ
ejpam-5911	726	7	paper	paper	NOUN
ejpam-5911	726	8	,	,	PUNCT
ejpam-5911	726	9	a	a	DET
ejpam-5911	726	10	novel	novel	ADJ
ejpam-5911	726	11	class	class	NOUN
ejpam-5911	726	12	of	of	ADP
ejpam-5911	726	13	generalized	generalized	ADJ
ejpam-5911	726	14	f	f	NOUN
ejpam-5911	726	15	-	-	PUNCT
ejpam-5911	726	16	open	open	ADJ
ejpam-5911	726	17	sets	set	NOUN
ejpam-5911	726	18	,	,	PUNCT
ejpam-5911	726	19	called	call	VERB
ejpam-5911	726	20	(	(	PUNCT
ejpam-5911	726	21	r	r	NOUN
ejpam-5911	726	22	,	,	PUNCT
ejpam-5911	726	23	s)-f	s)-f	NOUN
ejpam-5911	726	24	-	-	PUNCT
ejpam-5911	726	25	b	b	NOUN
ejpam-5911	726	26	-	-	PUNCT
ejpam-5911	726	27	open	open	ADJ
ejpam-5911	726	28	sets	set	NOUN
ejpam-5911	726	29	,	,	PUNCT
ejpam-5911	726	30	has	have	AUX
ejpam-5911	726	31	been	be	AUX
ejpam-5911	726	32	introduced	introduce	VERB
ejpam-5911	726	33	in	in	ADP
ejpam-5911	726	34	dft	dft	PROPN
ejpam-5911	726	35	s	s	VERB
ejpam-5911	726	36	based	base	VERB
ejpam-5911	726	37	on	on	ADP
ejpam-5911	726	38	šostak	šostak	NOUN
ejpam-5911	726	39	,	,	PUNCT
ejpam-5911	726	40	s	s	PART
ejpam-5911	726	41	sense	sense	NOUN
ejpam-5911	726	42	[	[	X
ejpam-5911	726	43	3	3	NUM
ejpam-5911	726	44	]	]	PUNCT
ejpam-5911	726	45	.	.	PUNCT
ejpam-5911	727	1	furthermore	furthermore	ADV
ejpam-5911	727	2	,	,	PUNCT
ejpam-5911	727	3	some	some	DET
ejpam-5911	727	4	characterizations	characterization	NOUN
ejpam-5911	727	5	of	of	ADP
ejpam-5911	727	6	(	(	PUNCT
ejpam-5911	727	7	r	r	NOUN
ejpam-5911	727	8	,	,	PUNCT
ejpam-5911	727	9	s)-f	s)-f	NOUN
ejpam-5911	727	10	-	-	PUNCT
ejpam-5911	727	11	b	b	NOUN
ejpam-5911	727	12	-	-	PUNCT
ejpam-5911	727	13	open	open	ADJ
ejpam-5911	727	14	sets	set	NOUN
ejpam-5911	727	15	along	along	ADP
ejpam-5911	727	16	with	with	ADP
ejpam-5911	727	17	their	their	PRON
ejpam-5911	727	18	mutual	mutual	ADJ
ejpam-5911	727	19	relationships	relationship	NOUN
ejpam-5911	727	20	have	have	AUX
ejpam-5911	727	21	been	be	AUX
ejpam-5911	727	22	discussed	discuss	VERB
ejpam-5911	727	23	.	.	PUNCT
ejpam-5911	728	1	in	in	ADP
ejpam-5911	728	2	addition	addition	NOUN
ejpam-5911	728	3	,	,	PUNCT
ejpam-5911	728	4	the	the	DET
ejpam-5911	728	5	notions	notion	NOUN
ejpam-5911	728	6	of	of	ADP
ejpam-5911	728	7	df	df	PROPN
ejpam-5911	728	8	-	-	PUNCT
ejpam-5911	728	9	b	b	NOUN
ejpam-5911	728	10	-	-	PUNCT
ejpam-5911	728	11	closure	closure	NOUN
ejpam-5911	728	12	operators	operator	NOUN
ejpam-5911	728	13	and	and	CCONJ
ejpam-5911	728	14	df	df	PROPN
ejpam-5911	728	15	-	-	PUNCT
ejpam-5911	728	16	b	b	NOUN
ejpam-5911	728	17	-	-	ADJ
ejpam-5911	728	18	interior	interior	ADJ
ejpam-5911	728	19	operators	operator	NOUN
ejpam-5911	728	20	have	have	AUX
ejpam-5911	728	21	been	be	AUX
ejpam-5911	728	22	presented	present	VERB
ejpam-5911	728	23	and	and	CCONJ
ejpam-5911	728	24	investigated	investigate	VERB
ejpam-5911	728	25	.	.	PUNCT
ejpam-5911	729	1	thereafter	thereafter	ADV
ejpam-5911	729	2	,	,	PUNCT
ejpam-5911	729	3	the	the	DET
ejpam-5911	729	4	notion	notion	NOUN
ejpam-5911	729	5	of	of	ADP
ejpam-5911	729	6	df	df	PROPN
ejpam-5911	729	7	-	-	PUNCT
ejpam-5911	729	8	b	b	NOUN
ejpam-5911	729	9	-	-	PUNCT
ejpam-5911	729	10	continuity	continuity	NOUN
ejpam-5911	729	11	between	between	ADP
ejpam-5911	729	12	dft	dft	PROPN
ejpam-5911	729	13	ss	ss	PROPN
ejpam-5911	729	14	(	(	PUNCT
ejpam-5911	729	15	g,ℑ,ℑ∗	g,ℑ,ℑ∗	PROPN
ejpam-5911	729	16	)	)	PUNCT
ejpam-5911	729	17	and	and	CCONJ
ejpam-5911	729	18	(	(	PUNCT
ejpam-5911	729	19	z	z	NOUN
ejpam-5911	729	20	,	,	PUNCT
ejpam-5911	729	21	𭟋	𭟋	NOUN
ejpam-5911	729	22	,	,	PUNCT
ejpam-5911	729	23	𭟋∗	𭟋∗	NOUN
ejpam-5911	729	24	)	)	PUNCT
ejpam-5911	729	25	has	have	AUX
ejpam-5911	729	26	been	be	AUX
ejpam-5911	729	27	defined	define	VERB
ejpam-5911	729	28	and	and	CCONJ
ejpam-5911	729	29	discussed	discuss	VERB
ejpam-5911	729	30	.	.	PUNCT
ejpam-5911	730	1	moreover	moreover	ADV
ejpam-5911	730	2	,	,	PUNCT
ejpam-5911	730	3	the	the	DET
ejpam-5911	730	4	concepts	concept	NOUN
ejpam-5911	730	5	of	of	ADP
ejpam-5911	730	6	df	df	PROPN
ejpam-5911	730	7	-	-	PUNCT
ejpam-5911	730	8	almost	almost	ADV
ejpam-5911	730	9	b	b	NOUN
ejpam-5911	730	10	-	-	PUNCT
ejpam-5911	730	11	continuity	continuity	NOUN
ejpam-5911	730	12	and	and	CCONJ
ejpam-5911	730	13	df	df	NOUN
ejpam-5911	730	14	-	-	PUNCT
ejpam-5911	730	15	weakly	weakly	ADJ
ejpam-5911	730	16	b	b	NOUN
ejpam-5911	730	17	-	-	PUNCT
ejpam-5911	730	18	continuity	continuity	NOUN
ejpam-5911	730	19	,	,	PUNCT
ejpam-5911	730	20	which	which	PRON
ejpam-5911	730	21	are	be	AUX
ejpam-5911	730	22	weaker	weak	ADJ
ejpam-5911	730	23	forms	form	NOUN
ejpam-5911	730	24	of	of	ADP
ejpam-5911	730	25	dfb	dfb	NOUN
ejpam-5911	730	26	-	-	PUNCT
ejpam-5911	730	27	continuity	continuity	NOUN
ejpam-5911	730	28	,	,	PUNCT
ejpam-5911	730	29	have	have	AUX
ejpam-5911	730	30	been	be	AUX
ejpam-5911	730	31	explored	explore	VERB
ejpam-5911	730	32	and	and	CCONJ
ejpam-5911	730	33	characterized	characterize	VERB
ejpam-5911	730	34	.	.	PUNCT
ejpam-5911	731	1	after	after	ADP
ejpam-5911	731	2	that	that	PRON
ejpam-5911	731	3	,	,	PUNCT
ejpam-5911	731	4	some	some	DET
ejpam-5911	731	5	new	new	ADJ
ejpam-5911	731	6	df	df	NOUN
ejpam-5911	731	7	-	-	PUNCT
ejpam-5911	731	8	mappings	mapping	NOUN
ejpam-5911	731	9	using	use	VERB
ejpam-5911	731	10	(	(	PUNCT
ejpam-5911	731	11	r	r	NOUN
ejpam-5911	731	12	,	,	PUNCT
ejpam-5911	731	13	s)-f	s)-f	NOUN
ejpam-5911	731	14	-	-	PUNCT
ejpam-5911	731	15	b	b	NOUN
ejpam-5911	731	16	-	-	PUNCT
ejpam-5911	731	17	closed	closed	ADJ
ejpam-5911	731	18	sets	set	NOUN
ejpam-5911	731	19	and	and	CCONJ
ejpam-5911	731	20	(	(	PUNCT
ejpam-5911	731	21	r	r	NOUN
ejpam-5911	731	22	,	,	PUNCT
ejpam-5911	731	23	s)-f	s)-f	NOUN
ejpam-5911	731	24	-	-	PUNCT
ejpam-5911	731	25	b	b	NOUN
ejpam-5911	731	26	-	-	PUNCT
ejpam-5911	731	27	open	open	ADJ
ejpam-5911	731	28	sets	set	NOUN
ejpam-5911	731	29	have	have	AUX
ejpam-5911	731	30	been	be	AUX
ejpam-5911	731	31	defined	define	VERB
ejpam-5911	731	32	and	and	CCONJ
ejpam-5911	731	33	studied	study	VERB
ejpam-5911	731	34	.	.	PUNCT
ejpam-5911	732	1	lastly	lastly	ADV
ejpam-5911	732	2	,	,	PUNCT
ejpam-5911	732	3	we	we	PRON
ejpam-5911	732	4	introduced	introduce	VERB
ejpam-5911	732	5	new	new	ADJ
ejpam-5911	732	6	types	type	NOUN
ejpam-5911	732	7	of	of	ADP
ejpam-5911	732	8	df	df	NOUN
ejpam-5911	732	9	-	-	PUNCT
ejpam-5911	732	10	separation	separation	NOUN
ejpam-5911	732	11	axioms	axiom	NOUN
ejpam-5911	732	12	using	use	VERB
ejpam-5911	732	13	(	(	PUNCT
ejpam-5911	732	14	r	r	NOUN
ejpam-5911	732	15	,	,	PUNCT
ejpam-5911	732	16	s)-f	s)-f	NOUN
ejpam-5911	732	17	-	-	PUNCT
ejpam-5911	732	18	b	b	NOUN
ejpam-5911	732	19	-	-	PUNCT
ejpam-5911	732	20	closed	closed	ADJ
ejpam-5911	732	21	sets	set	NOUN
ejpam-5911	732	22	,	,	PUNCT
ejpam-5911	732	23	and	and	CCONJ
ejpam-5911	732	24	some	some	DET
ejpam-5911	732	25	properties	property	NOUN
ejpam-5911	732	26	have	have	AUX
ejpam-5911	732	27	been	be	AUX
ejpam-5911	732	28	specified	specify	VERB
ejpam-5911	732	29	.	.	PUNCT
ejpam-5911	733	1	in	in	ADP
ejpam-5911	733	2	upcoming	upcoming	ADJ
ejpam-5911	733	3	works	work	NOUN
ejpam-5911	733	4	might	might	AUX
ejpam-5911	733	5	look	look	VERB
ejpam-5911	733	6	into	into	ADP
ejpam-5911	733	7	the	the	DET
ejpam-5911	733	8	following	follow	VERB
ejpam-5911	733	9	topics	topic	NOUN
ejpam-5911	733	10	:	:	PUNCT
ejpam-5911	733	11	(	(	PUNCT
ejpam-5911	733	12	i	i	NOUN
ejpam-5911	733	13	)	)	PUNCT
ejpam-5911	733	14	defining	define	VERB
ejpam-5911	733	15	upper	upper	ADJ
ejpam-5911	733	16	(	(	PUNCT
ejpam-5911	733	17	lower	low	ADJ
ejpam-5911	733	18	)	)	PUNCT
ejpam-5911	733	19	b	b	X
ejpam-5911	733	20	-	-	PUNCT
ejpam-5911	733	21	continuous	continuous	ADJ
ejpam-5911	733	22	df	df	NOUN
ejpam-5911	733	23	-	-	PUNCT
ejpam-5911	733	24	multifunctions	multifunction	NOUN
ejpam-5911	733	25	and	and	CCONJ
ejpam-5911	733	26	(	(	PUNCT
ejpam-5911	733	27	r	r	NOUN
ejpam-5911	733	28	,	,	PUNCT
ejpam-5911	733	29	s)-f	s)-f	NOUN
ejpam-5911	733	30	-	-	PUNCT
ejpam-5911	733	31	b	b	NOUN
ejpam-5911	733	32	-	-	PUNCT
ejpam-5911	733	33	connected	connect	VERB
ejpam-5911	733	34	sets	set	NOUN
ejpam-5911	733	35	;	;	PUNCT
ejpam-5911	733	36	(	(	PUNCT
ejpam-5911	733	37	ii	ii	NOUN
ejpam-5911	733	38	)	)	PUNCT
ejpam-5911	733	39	introducing	introduce	VERB
ejpam-5911	733	40	these	these	DET
ejpam-5911	733	41	novel	novel	ADJ
ejpam-5911	733	42	notions	notion	NOUN
ejpam-5911	733	43	given	give	VERB
ejpam-5911	733	44	here	here	ADV
ejpam-5911	733	45	in	in	ADP
ejpam-5911	733	46	the	the	DET
ejpam-5911	733	47	frame	frame	NOUN
ejpam-5911	733	48	of	of	ADP
ejpam-5911	733	49	fuzzy	fuzzy	ADJ
ejpam-5911	733	50	ideals	ideal	NOUN
ejpam-5911	733	51	as	as	SCONJ
ejpam-5911	733	52	defined	define	VERB
ejpam-5911	733	53	in	in	ADP
ejpam-5911	733	54	[	[	X
ejpam-5911	733	55	41–43	41–43	NUM
ejpam-5911	733	56	]	]	X
ejpam-5911	733	57	;	;	PUNCT
ejpam-5911	733	58	and	and	CCONJ
ejpam-5911	733	59	(	(	PUNCT
ejpam-5911	733	60	iii	iii	NOUN
ejpam-5911	733	61	)	)	PUNCT
ejpam-5911	733	62	extending	extend	VERB
ejpam-5911	733	63	these	these	DET
ejpam-5911	733	64	novel	novel	ADJ
ejpam-5911	733	65	notions	notion	NOUN
ejpam-5911	733	66	given	give	VERB
ejpam-5911	733	67	here	here	ADV
ejpam-5911	733	68	in	in	ADP
ejpam-5911	733	69	the	the	DET
ejpam-5911	733	70	frame	frame	NOUN
ejpam-5911	733	71	of	of	ADP
ejpam-5911	733	72	fuzzy	fuzzy	ADJ
ejpam-5911	733	73	soft	soft	ADJ
ejpam-5911	733	74	topological	topological	ADJ
ejpam-5911	733	75	(	(	PUNCT
ejpam-5911	733	76	r	r	NOUN
ejpam-5911	733	77	-	-	PUNCT
ejpam-5911	733	78	minimal	minimal	ADJ
ejpam-5911	733	79	)	)	PUNCT
ejpam-5911	733	80	spaces	space	NOUN
ejpam-5911	733	81	as	as	SCONJ
ejpam-5911	733	82	defined	define	VERB
ejpam-5911	733	83	in	in	ADP
ejpam-5911	733	84	[	[	X
ejpam-5911	733	85	44–46	44–46	NOUN
ejpam-5911	733	86	]	]	PUNCT
ejpam-5911	733	87	.	.	PUNCT
ejpam-5911	734	1	acknowledgements	acknowledgement	NOUN
ejpam-5911	734	2	we	we	PRON
ejpam-5911	734	3	would	would	AUX
ejpam-5911	734	4	like	like	VERB
ejpam-5911	734	5	to	to	PART
ejpam-5911	734	6	thank	thank	VERB
ejpam-5911	734	7	the	the	DET
ejpam-5911	734	8	reviewers	reviewer	NOUN
ejpam-5911	734	9	and	and	CCONJ
ejpam-5911	734	10	editors	editor	NOUN
ejpam-5911	734	11	whose	whose	DET
ejpam-5911	734	12	constructive	constructive	ADJ
ejpam-5911	734	13	comments	comment	NOUN
ejpam-5911	734	14	and	and	CCONJ
ejpam-5911	734	15	suggestions	suggestion	NOUN
ejpam-5911	734	16	helped	help	VERB
ejpam-5911	734	17	to	to	PART
ejpam-5911	734	18	improve	improve	VERB
ejpam-5911	734	19	this	this	DET
ejpam-5911	734	20	paper	paper	NOUN
ejpam-5911	734	21	.	.	PUNCT
ejpam-5911	735	1	i.	i.	PROPN
ejpam-5911	735	2	m.	m.	PROPN
ejpam-5911	735	3	taha	taha	PROPN
ejpam-5911	735	4	,	,	PUNCT
ejpam-5911	735	5	j.	j.	PROPN
ejpam-5911	735	6	al	al	PROPN
ejpam-5911	735	7	-	-	PUNCT
ejpam-5911	735	8	mufarrij	mufarrij	PROPN
ejpam-5911	735	9	,	,	PUNCT
ejpam-5911	735	10	o.	o.	PROPN
ejpam-5911	735	11	m.	m.	PROPN
ejpam-5911	735	12	taha	taha	PROPN
ejpam-5911	735	13	/	/	PUNCT
ejpam-5911	735	14	eur	eur	PROPN
ejpam-5911	735	15	.	.	PUNCT
ejpam-5911	736	1	j.	j.	PROPN
ejpam-5911	736	2	pure	pure	PROPN
ejpam-5911	736	3	appl	appl	PROPN
ejpam-5911	736	4	.	.	PROPN
ejpam-5911	736	5	math	math	PROPN
ejpam-5911	736	6	,	,	PUNCT
ejpam-5911	736	7	18	18	NUM
ejpam-5911	736	8	(	(	PUNCT
ejpam-5911	736	9	2	2	NUM
ejpam-5911	736	10	)	)	PUNCT
ejpam-5911	736	11	(	(	PUNCT
ejpam-5911	736	12	2025	2025	NUM
ejpam-5911	736	13	)	)	PUNCT
ejpam-5911	736	14	,	,	PUNCT
ejpam-5911	736	15	5911	5911	NUM
ejpam-5911	736	16	25	25	NUM
ejpam-5911	736	17	of	of	ADP
ejpam-5911	736	18	27	27	NUM
ejpam-5911	736	19	references	reference	NOUN
ejpam-5911	736	20	[	[	X
ejpam-5911	736	21	1	1	NUM
ejpam-5911	736	22	]	]	PUNCT
ejpam-5911	736	23	l.	l.	PROPN
ejpam-5911	736	24	a.	a.	PROPN
ejpam-5911	736	25	zadeh	zadeh	PROPN
ejpam-5911	736	26	.	.	PUNCT
ejpam-5911	737	1	fuzzy	fuzzy	ADJ
ejpam-5911	737	2	sets	set	NOUN
ejpam-5911	737	3	.	.	PUNCT
ejpam-5911	738	1	inform	inform	NOUN
ejpam-5911	738	2	.	.	PUNCT
ejpam-5911	739	1	control	control	NOUN
ejpam-5911	739	2	,	,	PUNCT
ejpam-5911	739	3	8:338–353	8:338–353	NUM
ejpam-5911	739	4	,	,	PUNCT
ejpam-5911	739	5	1965	1965	NUM
ejpam-5911	739	6	.	.	PUNCT
ejpam-5911	740	1	[	[	X
ejpam-5911	740	2	2	2	NUM
ejpam-5911	740	3	]	]	PUNCT
ejpam-5911	740	4	c.	c.	PROPN
ejpam-5911	740	5	l.	l.	PROPN
ejpam-5911	740	6	chang	chang	PROPN
ejpam-5911	740	7	.	.	PUNCT
ejpam-5911	741	1	fuzzy	fuzzy	ADJ
ejpam-5911	741	2	topological	topological	ADJ
ejpam-5911	741	3	spaces	space	NOUN
ejpam-5911	741	4	.	.	PUNCT
ejpam-5911	742	1	j.	j.	PROPN
ejpam-5911	742	2	math	math	PROPN
ejpam-5911	742	3	.	.	PUNCT
ejpam-5911	743	1	anal	anal	PROPN
ejpam-5911	743	2	.	.	PUNCT
ejpam-5911	744	1	appl	appl	PROPN
ejpam-5911	744	2	.	.	PROPN
ejpam-5911	744	3	,	,	PUNCT
ejpam-5911	745	1	24:182–190	24:182–190	NUM
ejpam-5911	745	2	,	,	PUNCT
ejpam-5911	745	3	1968	1968	NUM
ejpam-5911	745	4	.	.	PUNCT
ejpam-5911	746	1	[	[	X
ejpam-5911	746	2	3	3	NUM
ejpam-5911	746	3	]	]	PUNCT
ejpam-5911	746	4	a.	a.	NOUN
ejpam-5911	746	5	p.	p.	NOUN
ejpam-5911	746	6	šostak	šostak	NOUN
ejpam-5911	746	7	.	.	PUNCT
ejpam-5911	747	1	on	on	ADP
ejpam-5911	747	2	a	a	DET
ejpam-5911	747	3	fuzzy	fuzzy	ADJ
ejpam-5911	747	4	topological	topological	ADJ
ejpam-5911	747	5	structure	structure	NOUN
ejpam-5911	747	6	.	.	PUNCT
ejpam-5911	748	1	in	in	ADP
ejpam-5911	748	2	in	in	ADP
ejpam-5911	748	3	:	:	PUNCT
ejpam-5911	748	4	proceedings	proceeding	NOUN
ejpam-5911	748	5	of	of	ADP
ejpam-5911	748	6	the	the	DET
ejpam-5911	748	7	13th	13th	NOUN
ejpam-5911	748	8	winter	winter	NOUN
ejpam-5911	748	9	school	school	NOUN
ejpam-5911	748	10	on	on	ADP
ejpam-5911	748	11	abstract	abstract	ADJ
ejpam-5911	748	12	analysis	analysis	NOUN
ejpam-5911	748	13	,	,	PUNCT
ejpam-5911	748	14	section	section	NOUN
ejpam-5911	748	15	of	of	ADP
ejpam-5911	748	16	topology	topology	NOUN
ejpam-5911	748	17	,	,	PUNCT
ejpam-5911	748	18	palermo	palermo	NOUN
ejpam-5911	748	19	:	:	PUNCT
ejpam-5911	748	20	circolo	circolo	PROPN
ejpam-5911	748	21	matematico	matematico	NOUN
ejpam-5911	748	22	di	di	X
ejpam-5911	748	23	palermo	palermo	NOUN
ejpam-5911	748	24	,	,	PUNCT
ejpam-5911	748	25	pages	page	NOUN
ejpam-5911	748	26	89–103	89–103	PROPN
ejpam-5911	748	27	,	,	PUNCT
ejpam-5911	748	28	1985	1985	NUM
ejpam-5911	748	29	.	.	PUNCT
ejpam-5911	749	1	[	[	X
ejpam-5911	749	2	4	4	NUM
ejpam-5911	749	3	]	]	PUNCT
ejpam-5911	749	4	a.	a.	NOUN
ejpam-5911	749	5	a.	a.	PROPN
ejpam-5911	749	6	ramadan	ramadan	PROPN
ejpam-5911	749	7	.	.	PUNCT
ejpam-5911	750	1	smooth	smooth	ADJ
ejpam-5911	750	2	topological	topological	ADJ
ejpam-5911	750	3	spaces	space	NOUN
ejpam-5911	750	4	.	.	PUNCT
ejpam-5911	751	1	fuzzy	fuzzy	ADJ
ejpam-5911	751	2	set	set	PROPN
ejpam-5911	751	3	.	.	PUNCT
ejpam-5911	752	1	syst	syst	PROPN
ejpam-5911	752	2	.	.	PROPN
ejpam-5911	752	3	,	,	PUNCT
ejpam-5911	752	4	48:371–375	48:371–375	PROPN
ejpam-5911	752	5	,	,	PUNCT
ejpam-5911	752	6	1992	1992	NUM
ejpam-5911	752	7	.	.	PUNCT
ejpam-5911	753	1	[	[	X
ejpam-5911	753	2	5	5	X
ejpam-5911	753	3	]	]	PUNCT
ejpam-5911	753	4	k.	k.	PROPN
ejpam-5911	753	5	c.	c.	PROPN
ejpam-5911	753	6	chattopadhyay	chattopadhyay	PROPN
ejpam-5911	753	7	and	and	CCONJ
ejpam-5911	753	8	s.	s.	PROPN
ejpam-5911	753	9	k.	k.	PROPN
ejpam-5911	753	10	samanta	samanta	PROPN
ejpam-5911	753	11	.	.	PUNCT
ejpam-5911	753	12	fuzzy	fuzzy	ADJ
ejpam-5911	753	13	topology	topology	NOUN
ejpam-5911	753	14	:	:	PUNCT
ejpam-5911	753	15	fuzzy	fuzzy	ADJ
ejpam-5911	753	16	closure	closure	NOUN
ejpam-5911	753	17	operator	operator	NOUN
ejpam-5911	753	18	,	,	PUNCT
ejpam-5911	753	19	fuzzy	fuzzy	ADJ
ejpam-5911	753	20	compactness	compactness	NOUN
ejpam-5911	753	21	and	and	CCONJ
ejpam-5911	753	22	fuzzy	fuzzy	ADJ
ejpam-5911	753	23	connectedness	connectedness	NOUN
ejpam-5911	753	24	.	.	PUNCT
ejpam-5911	754	1	fuzzy	fuzzy	ADJ
ejpam-5911	754	2	set	set	PROPN
ejpam-5911	754	3	.	.	PUNCT
ejpam-5911	755	1	syst	syst	PROPN
ejpam-5911	755	2	.	.	PROPN
ejpam-5911	755	3	,	,	PUNCT
ejpam-5911	755	4	54(2):207–212	54(2):207–212	PROPN
ejpam-5911	755	5	,	,	PUNCT
ejpam-5911	755	6	1993	1993	NUM
ejpam-5911	755	7	.	.	PUNCT
ejpam-5911	756	1	[	[	X
ejpam-5911	756	2	6	6	NUM
ejpam-5911	756	3	]	]	PUNCT
ejpam-5911	756	4	m.	m.	NOUN
ejpam-5911	756	5	k.	k.	PROPN
ejpam-5911	757	1	el	el	PROPN
ejpam-5911	757	2	-	-	PUNCT
ejpam-5911	757	3	gayyar	gayyar	PROPN
ejpam-5911	757	4	,	,	PUNCT
ejpam-5911	757	5	e.	e.	PROPN
ejpam-5911	757	6	e.	e.	PROPN
ejpam-5911	757	7	kerre	kerre	PROPN
ejpam-5911	757	8	,	,	PUNCT
ejpam-5911	757	9	and	and	CCONJ
ejpam-5911	757	10	a.	a.	NOUN
ejpam-5911	757	11	a.	a.	PROPN
ejpam-5911	757	12	ramadan	ramadan	PROPN
ejpam-5911	757	13	.	.	PUNCT
ejpam-5911	758	1	almost	almost	ADV
ejpam-5911	758	2	compactness	compactness	NOUN
ejpam-5911	758	3	and	and	CCONJ
ejpam-5911	758	4	near	near	ADJ
ejpam-5911	758	5	compactness	compactness	NOUN
ejpam-5911	758	6	in	in	ADP
ejpam-5911	758	7	smooth	smooth	ADJ
ejpam-5911	758	8	topological	topological	ADJ
ejpam-5911	758	9	spaces	space	NOUN
ejpam-5911	758	10	.	.	PUNCT
ejpam-5911	759	1	mathematics	mathematic	NOUN
ejpam-5911	759	2	,	,	PUNCT
ejpam-5911	759	3	62(2):193–202	62(2):193–202	PROPN
ejpam-5911	759	4	,	,	PUNCT
ejpam-5911	759	5	1994	1994	NUM
ejpam-5911	759	6	.	.	PUNCT
ejpam-5911	760	1	[	[	X
ejpam-5911	760	2	7	7	X
ejpam-5911	760	3	]	]	X
ejpam-5911	760	4	u.	u.	NOUN
ejpam-5911	760	5	höhle	höhle	PROPN
ejpam-5911	760	6	and	and	CCONJ
ejpam-5911	760	7	a.	a.	NOUN
ejpam-5911	760	8	p.	p.	NOUN
ejpam-5911	760	9	šostak	šostak	NOUN
ejpam-5911	760	10	.	.	PUNCT
ejpam-5911	761	1	a	a	DET
ejpam-5911	761	2	general	general	ADJ
ejpam-5911	761	3	theory	theory	NOUN
ejpam-5911	761	4	of	of	ADP
ejpam-5911	761	5	fuzzy	fuzzy	ADJ
ejpam-5911	761	6	topological	topological	ADJ
ejpam-5911	761	7	spaces	space	NOUN
ejpam-5911	761	8	.	.	PUNCT
ejpam-5911	762	1	fuzzy	fuzzy	ADJ
ejpam-5911	762	2	set	set	PROPN
ejpam-5911	762	3	.	.	PUNCT
ejpam-5911	763	1	syst	syst	PROPN
ejpam-5911	763	2	.	.	PUNCT
ejpam-5911	763	3	,	,	PUNCT
ejpam-5911	764	1	73:131–149	73:131–149	NUM
ejpam-5911	764	2	,	,	PUNCT
ejpam-5911	764	3	1995	1995	NUM
ejpam-5911	764	4	.	.	PUNCT
ejpam-5911	765	1	[	[	X
ejpam-5911	765	2	8	8	NUM
ejpam-5911	765	3	]	]	PUNCT
ejpam-5911	765	4	a.	a.	NOUN
ejpam-5911	765	5	a.	a.	PROPN
ejpam-5911	765	6	ramadan	ramadan	PROPN
ejpam-5911	765	7	,	,	PUNCT
ejpam-5911	765	8	s.	s.	PROPN
ejpam-5911	765	9	e.	e.	PROPN
ejpam-5911	765	10	abbas	abbas	PROPN
ejpam-5911	765	11	,	,	PUNCT
ejpam-5911	765	12	and	and	CCONJ
ejpam-5911	766	1	y.	y.	PROPN
ejpam-5911	766	2	c.	c.	PROPN
ejpam-5911	766	3	kim	kim	PROPN
ejpam-5911	766	4	.	.	PUNCT
ejpam-5911	767	1	fuzzy	fuzzy	ADJ
ejpam-5911	767	2	irresolute	irresolute	ADJ
ejpam-5911	767	3	mappings	mapping	NOUN
ejpam-5911	767	4	in	in	ADP
ejpam-5911	767	5	smooth	smooth	ADJ
ejpam-5911	767	6	fuzzy	fuzzy	ADJ
ejpam-5911	767	7	topological	topological	ADJ
ejpam-5911	767	8	spaces	space	NOUN
ejpam-5911	767	9	.	.	PUNCT
ejpam-5911	768	1	j.	j.	PROPN
ejpam-5911	768	2	fuzzy	fuzzy	PROPN
ejpam-5911	768	3	math	math	PROPN
ejpam-5911	768	4	.	.	PUNCT
ejpam-5911	768	5	,	,	PUNCT
ejpam-5911	768	6	9(4):865–877	9(4):865–877	PROPN
ejpam-5911	768	7	,	,	PUNCT
ejpam-5911	768	8	2001	2001	NUM
ejpam-5911	768	9	.	.	PUNCT
ejpam-5911	769	1	[	[	X
ejpam-5911	769	2	9	9	NUM
ejpam-5911	769	3	]	]	X
ejpam-5911	769	4	y.	y.	PROPN
ejpam-5911	769	5	c.	c.	PROPN
ejpam-5911	769	6	kim	kim	PROPN
ejpam-5911	769	7	,	,	PUNCT
ejpam-5911	769	8	a.	a.	PROPN
ejpam-5911	769	9	a.	a.	PROPN
ejpam-5911	769	10	ramadan	ramadan	PROPN
ejpam-5911	769	11	,	,	PUNCT
ejpam-5911	769	12	and	and	CCONJ
ejpam-5911	769	13	s.	s.	PROPN
ejpam-5911	769	14	e.	e.	PROPN
ejpam-5911	769	15	abbas	abbas	PROPN
ejpam-5911	769	16	.	.	PUNCT
ejpam-5911	770	1	weaker	weak	ADJ
ejpam-5911	770	2	forms	form	NOUN
ejpam-5911	770	3	of	of	ADP
ejpam-5911	770	4	continuity	continuity	NOUN
ejpam-5911	770	5	in	in	ADP
ejpam-5911	770	6	šostak	šostak	NOUN
ejpam-5911	770	7	’s	’s	PART
ejpam-5911	770	8	fuzzy	fuzzy	ADJ
ejpam-5911	770	9	topology	topology	NOUN
ejpam-5911	770	10	.	.	PUNCT
ejpam-5911	771	1	indian	indian	PROPN
ejpam-5911	771	2	j.	j.	PROPN
ejpam-5911	771	3	pure	pure	PROPN
ejpam-5911	771	4	appl	appl	PROPN
ejpam-5911	771	5	.	.	PUNCT
ejpam-5911	771	6	math	math	PROPN
ejpam-5911	771	7	.	.	PUNCT
ejpam-5911	772	1	,	,	PUNCT
ejpam-5911	772	2	34(2):311–333	34(2):311–333	ADV
ejpam-5911	772	3	,	,	PUNCT
ejpam-5911	772	4	2003	2003	NUM
ejpam-5911	772	5	.	.	PUNCT
ejpam-5911	773	1	[	[	X
ejpam-5911	773	2	10	10	NUM
ejpam-5911	773	3	]	]	PUNCT
ejpam-5911	773	4	s.	s.	PROPN
ejpam-5911	773	5	e.	e.	PROPN
ejpam-5911	773	6	abbas	abbas	PROPN
ejpam-5911	773	7	.	.	PUNCT
ejpam-5911	774	1	fuzzy	fuzzy	ADJ
ejpam-5911	774	2	super	super	ADJ
ejpam-5911	774	3	irresolute	irresolute	ADJ
ejpam-5911	774	4	functions	function	NOUN
ejpam-5911	774	5	.	.	PUNCT
ejpam-5911	775	1	inter	inter	PROPN
ejpam-5911	775	2	.	.	PUNCT
ejpam-5911	776	1	j.	j.	PROPN
ejpam-5911	776	2	math	math	PROPN
ejpam-5911	776	3	.	.	PUNCT
ejpam-5911	777	1	mathematical	mathematical	PROPN
ejpam-5911	777	2	sci	sci	PROPN
ejpam-5911	777	3	.	.	PROPN
ejpam-5911	777	4	,	,	PUNCT
ejpam-5911	777	5	42:2689–2700	42:2689–2700	PROPN
ejpam-5911	777	6	,	,	PUNCT
ejpam-5911	777	7	2003	2003	NUM
ejpam-5911	777	8	.	.	PUNCT
ejpam-5911	778	1	[	[	X
ejpam-5911	778	2	11	11	NUM
ejpam-5911	778	3	]	]	PUNCT
ejpam-5911	778	4	s.	s.	PROPN
ejpam-5911	778	5	e.	e.	PROPN
ejpam-5911	778	6	abbas	abbas	PROPN
ejpam-5911	778	7	.	.	PUNCT
ejpam-5911	779	1	fuzzy	fuzzy	ADJ
ejpam-5911	779	2	β	β	X
ejpam-5911	779	3	-	-	PUNCT
ejpam-5911	779	4	irresolute	irresolute	ADJ
ejpam-5911	779	5	functions	function	NOUN
ejpam-5911	779	6	.	.	PUNCT
ejpam-5911	780	1	appl	appl	PROPN
ejpam-5911	780	2	.	.	PROPN
ejpam-5911	780	3	math	math	PROPN
ejpam-5911	780	4	.	.	PUNCT
ejpam-5911	781	1	comp	comp	PROPN
ejpam-5911	781	2	.	.	PUNCT
ejpam-5911	781	3	,	,	PUNCT
ejpam-5911	781	4	157:369–380	157:369–380	NUM
ejpam-5911	781	5	,	,	PUNCT
ejpam-5911	781	6	2004	2004	NUM
ejpam-5911	781	7	.	.	PUNCT
ejpam-5911	782	1	[	[	X
ejpam-5911	782	2	12	12	NUM
ejpam-5911	782	3	]	]	X
ejpam-5911	782	4	y.	y.	PROPN
ejpam-5911	782	5	c.	c.	PROPN
ejpam-5911	782	6	kim	kim	PROPN
ejpam-5911	782	7	and	and	CCONJ
ejpam-5911	782	8	s.	s.	PROPN
ejpam-5911	782	9	e.	e.	PROPN
ejpam-5911	782	10	abbas	abbas	PROPN
ejpam-5911	782	11	.	.	PUNCT
ejpam-5911	783	1	on	on	ADP
ejpam-5911	783	2	several	several	ADJ
ejpam-5911	783	3	types	type	NOUN
ejpam-5911	783	4	of	of	ADP
ejpam-5911	783	5	r	r	NOUN
ejpam-5911	783	6	-	-	PUNCT
ejpam-5911	783	7	fuzzy	fuzzy	ADJ
ejpam-5911	783	8	compactness	compactness	NOUN
ejpam-5911	783	9	.	.	PUNCT
ejpam-5911	784	1	j.	j.	PROPN
ejpam-5911	784	2	fuzzy	fuzzy	PROPN
ejpam-5911	784	3	math	math	PROPN
ejpam-5911	784	4	.	.	PUNCT
ejpam-5911	784	5	,	,	PUNCT
ejpam-5911	784	6	12(4):827–844	12(4):827–844	NUM
ejpam-5911	784	7	,	,	PUNCT
ejpam-5911	784	8	2004	2004	NUM
ejpam-5911	784	9	.	.	PUNCT
ejpam-5911	785	1	[	[	X
ejpam-5911	785	2	13	13	NUM
ejpam-5911	785	3	]	]	X
ejpam-5911	785	4	h.	h.	NOUN
ejpam-5911	785	5	aygün	aygün	PROPN
ejpam-5911	785	6	and	and	CCONJ
ejpam-5911	785	7	s.	s.	PROPN
ejpam-5911	785	8	e.	e.	PROPN
ejpam-5911	785	9	abbas	abbas	PROPN
ejpam-5911	785	10	.	.	PUNCT
ejpam-5911	786	1	on	on	ADP
ejpam-5911	786	2	characterization	characterization	NOUN
ejpam-5911	786	3	of	of	ADP
ejpam-5911	786	4	some	some	DET
ejpam-5911	786	5	covering	cover	VERB
ejpam-5911	786	6	properties	property	NOUN
ejpam-5911	786	7	in	in	ADP
ejpam-5911	786	8	l	l	ADJ
ejpam-5911	786	9	-	-	ADJ
ejpam-5911	786	10	fuzzy	fuzzy	ADJ
ejpam-5911	786	11	topological	topological	ADJ
ejpam-5911	786	12	spaces	space	NOUN
ejpam-5911	786	13	in	in	ADP
ejpam-5911	786	14	šostak	šostak	ADJ
ejpam-5911	786	15	sense	sense	NOUN
ejpam-5911	786	16	.	.	PUNCT
ejpam-5911	787	1	inform	inform	NOUN
ejpam-5911	787	2	.	.	PUNCT
ejpam-5911	788	1	sciences	science	NOUN
ejpam-5911	788	2	,	,	PUNCT
ejpam-5911	788	3	165:221–233	165:221–233	NUM
ejpam-5911	788	4	,	,	PUNCT
ejpam-5911	788	5	2004	2004	NUM
ejpam-5911	788	6	.	.	PUNCT
ejpam-5911	789	1	[	[	X
ejpam-5911	789	2	14	14	NUM
ejpam-5911	789	3	]	]	X
ejpam-5911	789	4	h.	h.	PROPN
ejpam-5911	789	5	aygün	aygün	PROPN
ejpam-5911	789	6	and	and	CCONJ
ejpam-5911	789	7	s.	s.	PROPN
ejpam-5911	789	8	e.	e.	PROPN
ejpam-5911	789	9	abbas	abbas	PROPN
ejpam-5911	789	10	.	.	PUNCT
ejpam-5911	790	1	some	some	DET
ejpam-5911	790	2	good	good	ADJ
ejpam-5911	790	3	extensions	extension	NOUN
ejpam-5911	790	4	of	of	ADP
ejpam-5911	790	5	compactness	compactness	NOUN
ejpam-5911	790	6	in	in	ADP
ejpam-5911	790	7	šostak	šostak	NOUN
ejpam-5911	790	8	’s	’s	PART
ejpam-5911	790	9	l	l	ADJ
ejpam-5911	790	10	-	-	ADJ
ejpam-5911	790	11	fuzzy	fuzzy	ADJ
ejpam-5911	790	12	topology	topology	NOUN
ejpam-5911	790	13	.	.	PUNCT
ejpam-5911	791	1	hacett	hacett	PROPN
ejpam-5911	791	2	.	.	PUNCT
ejpam-5911	792	1	j.	j.	PROPN
ejpam-5911	792	2	math	math	PROPN
ejpam-5911	792	3	.	.	PUNCT
ejpam-5911	793	1	stat	stat	PROPN
ejpam-5911	793	2	.	.	PUNCT
ejpam-5911	793	3	,	,	PUNCT
ejpam-5911	794	1	36(2):115–125	36(2):115–125	PROPN
ejpam-5911	794	2	,	,	PUNCT
ejpam-5911	794	3	2007	2007	NUM
ejpam-5911	794	4	.	.	PUNCT
ejpam-5911	795	1	[	[	X
ejpam-5911	795	2	15	15	NUM
ejpam-5911	795	3	]	]	X
ejpam-5911	795	4	h.	h.	PROPN
ejpam-5911	795	5	y.	y.	PROPN
ejpam-5911	795	6	li	li	PROPN
ejpam-5911	795	7	and	and	CCONJ
ejpam-5911	795	8	f.	f.	PROPN
ejpam-5911	795	9	g	g	PROPN
ejpam-5911	795	10	shi	shi	PROPN
ejpam-5911	795	11	.	.	PUNCT
ejpam-5911	796	1	some	some	DET
ejpam-5911	796	2	separation	separation	NOUN
ejpam-5911	796	3	axioms	axiom	VERB
ejpam-5911	796	4	in	in	ADP
ejpam-5911	796	5	i	i	NOUN
ejpam-5911	796	6	-	-	PUNCT
ejpam-5911	796	7	fuzzy	fuzzy	ADJ
ejpam-5911	796	8	topological	topological	ADJ
ejpam-5911	796	9	spaces	space	NOUN
ejpam-5911	796	10	.	.	PUNCT
ejpam-5911	797	1	fuzzy	fuzzy	ADJ
ejpam-5911	797	2	set	set	PROPN
ejpam-5911	797	3	.	.	PUNCT
ejpam-5911	798	1	syst	syst	PROPN
ejpam-5911	798	2	.	.	PUNCT
ejpam-5911	798	3	,	,	PUNCT
ejpam-5911	798	4	159:573–587	159:573–587	NUM
ejpam-5911	798	5	,	,	PUNCT
ejpam-5911	798	6	2008	2008	NUM
ejpam-5911	798	7	.	.	PUNCT
ejpam-5911	799	1	[	[	X
ejpam-5911	799	2	16	16	NUM
ejpam-5911	799	3	]	]	PUNCT
ejpam-5911	799	4	h.	h.	PROPN
ejpam-5911	799	5	y.	y.	PROPN
ejpam-5911	799	6	li	li	PROPN
ejpam-5911	799	7	and	and	CCONJ
ejpam-5911	799	8	f.	f.	PROPN
ejpam-5911	799	9	g.	g.	PROPN
ejpam-5911	799	10	shi	shi	PROPN
ejpam-5911	799	11	.	.	PUNCT
ejpam-5911	800	1	measures	measure	NOUN
ejpam-5911	800	2	of	of	ADP
ejpam-5911	800	3	fuzzy	fuzzy	ADJ
ejpam-5911	800	4	compactness	compactness	NOUN
ejpam-5911	800	5	in	in	ADP
ejpam-5911	800	6	l	l	ADJ
ejpam-5911	800	7	-	-	ADJ
ejpam-5911	800	8	fuzzy	fuzzy	ADJ
ejpam-5911	800	9	topological	topological	ADJ
ejpam-5911	800	10	spaces	space	NOUN
ejpam-5911	800	11	.	.	PUNCT
ejpam-5911	801	1	comput	comput	NOUN
ejpam-5911	801	2	.	.	PUNCT
ejpam-5911	802	1	math	math	NOUN
ejpam-5911	802	2	.	.	PUNCT
ejpam-5911	803	1	appl	appl	PROPN
ejpam-5911	803	2	.	.	PROPN
ejpam-5911	803	3	,	,	PUNCT
ejpam-5911	804	1	59:941–947	59:941–947	PROPN
ejpam-5911	804	2	,	,	PUNCT
ejpam-5911	804	3	2010	2010	NUM
ejpam-5911	804	4	.	.	PUNCT
ejpam-5911	805	1	[	[	X
ejpam-5911	805	2	17	17	NUM
ejpam-5911	805	3	]	]	X
ejpam-5911	805	4	f.	f.	PROPN
ejpam-5911	805	5	g.	g.	PROPN
ejpam-5911	805	6	shi	shi	PROPN
ejpam-5911	805	7	and	and	CCONJ
ejpam-5911	806	1	r.	r.	PROPN
ejpam-5911	806	2	x.	x.	PROPN
ejpam-5911	806	3	li	li	PROPN
ejpam-5911	806	4	.	.	PROPN
ejpam-5911	806	5	compactness	compactness	NOUN
ejpam-5911	806	6	in	in	ADP
ejpam-5911	806	7	l	l	ADJ
ejpam-5911	806	8	-	-	ADJ
ejpam-5911	806	9	fuzzy	fuzzy	ADJ
ejpam-5911	806	10	topological	topological	ADJ
ejpam-5911	806	11	spaces	space	NOUN
ejpam-5911	806	12	.	.	PUNCT
ejpam-5911	807	1	hacet	hacet	PROPN
ejpam-5911	807	2	.	.	PUNCT
ejpam-5911	808	1	j.	j.	PROPN
ejpam-5911	808	2	math	math	PROPN
ejpam-5911	808	3	.	.	PUNCT
ejpam-5911	809	1	stat	stat	PROPN
ejpam-5911	809	2	.	.	PUNCT
ejpam-5911	809	3	,	,	PUNCT
ejpam-5911	809	4	40(6):767–774	40(6):767–774	NOUN
ejpam-5911	809	5	,	,	PUNCT
ejpam-5911	809	6	2011	2011	NUM
ejpam-5911	809	7	.	.	PUNCT
ejpam-5911	810	1	[	[	X
ejpam-5911	810	2	18	18	NUM
ejpam-5911	810	3	]	]	X
ejpam-5911	810	4	j.	j.	PROPN
ejpam-5911	810	5	fang	fang	PROPN
ejpam-5911	810	6	and	and	CCONJ
ejpam-5911	810	7	y.	y.	PROPN
ejpam-5911	810	8	guo	guo	PROPN
ejpam-5911	810	9	.	.	PUNCT
ejpam-5911	811	1	quasi	quasi	ADJ
ejpam-5911	811	2	-	-	ADJ
ejpam-5911	811	3	coincident	coincident	ADJ
ejpam-5911	811	4	neighborhood	neighborhood	NOUN
ejpam-5911	811	5	structure	structure	NOUN
ejpam-5911	811	6	of	of	ADP
ejpam-5911	811	7	relative	relative	ADJ
ejpam-5911	811	8	i	i	NOUN
ejpam-5911	811	9	-	-	PUNCT
ejpam-5911	811	10	fuzzy	fuzzy	ADJ
ejpam-5911	811	11	topology	topology	NOUN
ejpam-5911	811	12	and	and	CCONJ
ejpam-5911	811	13	its	its	PRON
ejpam-5911	811	14	applications	application	NOUN
ejpam-5911	811	15	.	.	PUNCT
ejpam-5911	812	1	fuzzy	fuzzy	ADJ
ejpam-5911	812	2	set	set	PROPN
ejpam-5911	812	3	.	.	PUNCT
ejpam-5911	813	1	syst	syst	PROPN
ejpam-5911	813	2	.	.	PROPN
ejpam-5911	813	3	,	,	PUNCT
ejpam-5911	813	4	190:105–117	190:105–117	NUM
ejpam-5911	813	5	,	,	PUNCT
ejpam-5911	813	6	2012	2012	NUM
ejpam-5911	813	7	.	.	PUNCT
ejpam-5911	814	1	[	[	X
ejpam-5911	814	2	19	19	NUM
ejpam-5911	814	3	]	]	PUNCT
ejpam-5911	814	4	m.	m.	NOUN
ejpam-5911	814	5	el	el	PROPN
ejpam-5911	814	6	-	-	NOUN
ejpam-5911	814	7	dardery	dardery	PROPN
ejpam-5911	814	8	,	,	PUNCT
ejpam-5911	814	9	a.	a.	PROPN
ejpam-5911	814	10	a.	a.	PROPN
ejpam-5911	814	11	ramadan	ramadan	PROPN
ejpam-5911	814	12	,	,	PUNCT
ejpam-5911	814	13	and	and	CCONJ
ejpam-5911	814	14	y.	y.	PROPN
ejpam-5911	814	15	c.	c.	PROPN
ejpam-5911	814	16	kim	kim	PROPN
ejpam-5911	814	17	.	.	PUNCT
ejpam-5911	815	1	l	l	ADJ
ejpam-5911	815	2	-	-	ADJ
ejpam-5911	815	3	fuzzy	fuzzy	ADJ
ejpam-5911	815	4	topogenous	topogenous	ADJ
ejpam-5911	815	5	orders	order	NOUN
ejpam-5911	815	6	and	and	CCONJ
ejpam-5911	815	7	l	l	ADJ
ejpam-5911	815	8	-	-	ADJ
ejpam-5911	815	9	fuzzy	fuzzy	ADJ
ejpam-5911	815	10	topologies	topology	NOUN
ejpam-5911	815	11	.	.	PUNCT
ejpam-5911	816	1	j.	j.	PROPN
ejpam-5911	816	2	intell	intell	PROPN
ejpam-5911	816	3	.	.	PUNCT
ejpam-5911	817	1	fuzzy	fuzzy	ADJ
ejpam-5911	817	2	syst	syst	PROPN
ejpam-5911	817	3	.	.	PROPN
ejpam-5911	817	4	,	,	PUNCT
ejpam-5911	817	5	24(4):685–691	24(4):685–691	PROPN
ejpam-5911	817	6	,	,	PUNCT
ejpam-5911	817	7	2013	2013	NUM
ejpam-5911	817	8	.	.	PUNCT
ejpam-5911	818	1	[	[	X
ejpam-5911	818	2	20	20	NUM
ejpam-5911	818	3	]	]	X
ejpam-5911	818	4	c.	c.	PROPN
ejpam-5911	818	5	kalaivani	kalaivani	PROPN
ejpam-5911	818	6	and	and	CCONJ
ejpam-5911	818	7	r.	r.	PROPN
ejpam-5911	818	8	roopkumar	roopkumar	PROPN
ejpam-5911	818	9	.	.	PUNCT
ejpam-5911	819	1	fuzzy	fuzzy	ADJ
ejpam-5911	819	2	perfect	perfect	ADJ
ejpam-5911	819	3	mappings	mapping	NOUN
ejpam-5911	819	4	and	and	CCONJ
ejpam-5911	819	5	q	q	NOUN
ejpam-5911	819	6	-	-	NOUN
ejpam-5911	819	7	compactness	compactness	NOUN
ejpam-5911	819	8	in	in	ADP
ejpam-5911	819	9	smooth	smooth	ADJ
ejpam-5911	819	10	fuzzy	fuzzy	ADJ
ejpam-5911	819	11	topological	topological	ADJ
ejpam-5911	819	12	spaces	space	NOUN
ejpam-5911	819	13	.	.	PUNCT
ejpam-5911	820	1	fuzzy	fuzzy	ADJ
ejpam-5911	820	2	inform	inform	NOUN
ejpam-5911	820	3	.	.	PUNCT
ejpam-5911	821	1	eng	eng	PROPN
ejpam-5911	821	2	.	.	PROPN
ejpam-5911	821	3	,	,	PUNCT
ejpam-5911	821	4	6(1):115–131	6(1):115–131	NUM
ejpam-5911	821	5	,	,	PUNCT
ejpam-5911	821	6	2014	2014	NUM
ejpam-5911	821	7	.	.	PUNCT
ejpam-5911	822	1	[	[	X
ejpam-5911	822	2	21	21	NUM
ejpam-5911	822	3	]	]	PUNCT
ejpam-5911	822	4	s.	s.	PROPN
ejpam-5911	822	5	a.	a.	NOUN
ejpam-5911	822	6	solovyov	solovyov	PROPN
ejpam-5911	822	7	.	.	PUNCT
ejpam-5911	823	1	on	on	ADP
ejpam-5911	823	2	fuzzification	fuzzification	NOUN
ejpam-5911	823	3	of	of	ADP
ejpam-5911	823	4	topological	topological	ADJ
ejpam-5911	823	5	categories	category	NOUN
ejpam-5911	823	6	.	.	PUNCT
ejpam-5911	824	1	fuzzy	fuzzy	ADJ
ejpam-5911	824	2	set	set	PROPN
ejpam-5911	824	3	.	.	PUNCT
ejpam-5911	825	1	syst	syst	PROPN
ejpam-5911	825	2	.	.	PROPN
ejpam-5911	825	3	,	,	PUNCT
ejpam-5911	825	4	238:1–25	238:1–25	NUM
ejpam-5911	825	5	,	,	PUNCT
ejpam-5911	825	6	2014	2014	NUM
ejpam-5911	825	7	.	.	PUNCT
ejpam-5911	826	1	[	[	X
ejpam-5911	826	2	22	22	NUM
ejpam-5911	826	3	]	]	PUNCT
ejpam-5911	826	4	j.	j.	PROPN
ejpam-5911	826	5	j.	j.	PROPN
ejpam-5911	826	6	minana	minana	PROPN
ejpam-5911	826	7	and	and	CCONJ
ejpam-5911	826	8	a.	a.	NOUN
ejpam-5911	826	9	p.	p.	PROPN
ejpam-5911	826	10	šostak	šostak	NOUN
ejpam-5911	826	11	.	.	PUNCT
ejpam-5911	827	1	fuzzifying	fuzzifye	VERB
ejpam-5911	827	2	topology	topology	NOUN
ejpam-5911	827	3	induced	induce	VERB
ejpam-5911	827	4	by	by	ADP
ejpam-5911	827	5	a	a	DET
ejpam-5911	827	6	strong	strong	ADJ
ejpam-5911	827	7	fuzzy	fuzzy	ADJ
ejpam-5911	827	8	metric	metric	ADJ
ejpam-5911	827	9	.	.	PUNCT
ejpam-5911	827	10	fuzzy	fuzzy	ADJ
ejpam-5911	827	11	set	set	PROPN
ejpam-5911	827	12	.	.	PUNCT
ejpam-5911	828	1	syst	syst	PROPN
ejpam-5911	828	2	.	.	PROPN
ejpam-5911	828	3	,	,	PUNCT
ejpam-5911	828	4	300:24–39	300:24–39	NUM
ejpam-5911	828	5	,	,	PUNCT
ejpam-5911	828	6	2016	2016	NUM
ejpam-5911	828	7	.	.	PUNCT
ejpam-5911	829	1	i.	i.	PROPN
ejpam-5911	829	2	m.	m.	PROPN
ejpam-5911	829	3	taha	taha	PROPN
ejpam-5911	829	4	,	,	PUNCT
ejpam-5911	829	5	j.	j.	PROPN
ejpam-5911	829	6	al	al	PROPN
ejpam-5911	829	7	-	-	PUNCT
ejpam-5911	829	8	mufarrij	mufarrij	PROPN
ejpam-5911	829	9	,	,	PUNCT
ejpam-5911	829	10	o.	o.	PROPN
ejpam-5911	829	11	m.	m.	PROPN
ejpam-5911	829	12	taha	taha	PROPN
ejpam-5911	829	13	/	/	PUNCT
ejpam-5911	829	14	eur	eur	PROPN
ejpam-5911	829	15	.	.	PUNCT
ejpam-5911	830	1	j.	j.	PROPN
ejpam-5911	830	2	pure	pure	PROPN
ejpam-5911	830	3	appl	appl	PROPN
ejpam-5911	830	4	.	.	PROPN
ejpam-5911	830	5	math	math	PROPN
ejpam-5911	830	6	,	,	PUNCT
ejpam-5911	830	7	18	18	NUM
ejpam-5911	830	8	(	(	PUNCT
ejpam-5911	830	9	2	2	NUM
ejpam-5911	830	10	)	)	PUNCT
ejpam-5911	830	11	(	(	PUNCT
ejpam-5911	830	12	2025	2025	NUM
ejpam-5911	830	13	)	)	PUNCT
ejpam-5911	830	14	,	,	PUNCT
ejpam-5911	830	15	5911	5911	NUM
ejpam-5911	830	16	26	26	NUM
ejpam-5911	830	17	of	of	ADP
ejpam-5911	830	18	27	27	NUM
ejpam-5911	830	19	[	[	X
ejpam-5911	830	20	23	23	NUM
ejpam-5911	830	21	]	]	PUNCT
ejpam-5911	830	22	k.	k.	PROPN
ejpam-5911	830	23	atanassov	atanassov	PROPN
ejpam-5911	830	24	.	.	PUNCT
ejpam-5911	831	1	intuitionistic	intuitionistic	ADJ
ejpam-5911	831	2	fuzzy	fuzzy	ADJ
ejpam-5911	831	3	sets	set	NOUN
ejpam-5911	831	4	.	.	PUNCT
ejpam-5911	832	1	fuzzy	fuzzy	ADJ
ejpam-5911	832	2	sets	set	NOUN
ejpam-5911	832	3	syst	syst	PROPN
ejpam-5911	832	4	.	.	PUNCT
ejpam-5911	832	5	,	,	PUNCT
ejpam-5911	832	6	20:87–96	20:87–96	NUM
ejpam-5911	832	7	,	,	PUNCT
ejpam-5911	832	8	1986	1986	NUM
ejpam-5911	832	9	.	.	PUNCT
ejpam-5911	833	1	[	[	X
ejpam-5911	833	2	24	24	NUM
ejpam-5911	833	3	]	]	PUNCT
ejpam-5911	833	4	k.	k.	PROPN
ejpam-5911	833	5	atanassov	atanassov	PROPN
ejpam-5911	833	6	.	.	PUNCT
ejpam-5911	834	1	new	new	ADJ
ejpam-5911	834	2	operators	operator	NOUN
ejpam-5911	834	3	defined	define	VERB
ejpam-5911	834	4	over	over	ADP
ejpam-5911	834	5	the	the	DET
ejpam-5911	834	6	intuitionistic	intuitionistic	ADJ
ejpam-5911	834	7	fuzzy	fuzzy	ADJ
ejpam-5911	834	8	sets	set	NOUN
ejpam-5911	834	9	.	.	PUNCT
ejpam-5911	835	1	fuzzy	fuzzy	ADJ
ejpam-5911	835	2	sets	set	NOUN
ejpam-5911	835	3	syst	syst	PROPN
ejpam-5911	835	4	.	.	PUNCT
ejpam-5911	835	5	,	,	PUNCT
ejpam-5911	835	6	61:131–142	61:131–142	PROPN
ejpam-5911	835	7	,	,	PUNCT
ejpam-5911	835	8	1993	1993	NUM
ejpam-5911	835	9	.	.	PUNCT
ejpam-5911	836	1	[	[	X
ejpam-5911	836	2	25	25	NUM
ejpam-5911	836	3	]	]	X
ejpam-5911	836	4	d.	d.	PROPN
ejpam-5911	836	5	coker	coker	PROPN
ejpam-5911	836	6	.	.	PUNCT
ejpam-5911	837	1	an	an	DET
ejpam-5911	837	2	introduction	introduction	NOUN
ejpam-5911	837	3	to	to	ADP
ejpam-5911	837	4	fuzzy	fuzzy	ADJ
ejpam-5911	837	5	subspaces	subspace	NOUN
ejpam-5911	837	6	in	in	ADP
ejpam-5911	837	7	intuitionistic	intuitionistic	ADJ
ejpam-5911	837	8	fuzzy	fuzzy	ADJ
ejpam-5911	837	9	topological	topological	ADJ
ejpam-5911	837	10	spaces	space	NOUN
ejpam-5911	837	11	.	.	PUNCT
ejpam-5911	838	1	j.	j.	PROPN
ejpam-5911	838	2	fuzzy	fuzzy	PROPN
ejpam-5911	838	3	math	math	PROPN
ejpam-5911	838	4	.	.	PUNCT
ejpam-5911	838	5	,	,	PUNCT
ejpam-5911	838	6	4:749–764	4:749–764	NOUN
ejpam-5911	838	7	,	,	PUNCT
ejpam-5911	838	8	1996	1996	NUM
ejpam-5911	838	9	.	.	PUNCT
ejpam-5911	839	1	[	[	X
ejpam-5911	839	2	26	26	NUM
ejpam-5911	839	3	]	]	X
ejpam-5911	839	4	d.	d.	PROPN
ejpam-5911	839	5	coker	coker	PROPN
ejpam-5911	839	6	.	.	PUNCT
ejpam-5911	840	1	an	an	DET
ejpam-5911	840	2	introduction	introduction	NOUN
ejpam-5911	840	3	to	to	ADP
ejpam-5911	840	4	intuitionistic	intuitionistic	ADJ
ejpam-5911	840	5	fuzzy	fuzzy	ADJ
ejpam-5911	840	6	topological	topological	ADJ
ejpam-5911	840	7	spaces	space	NOUN
ejpam-5911	840	8	.	.	PUNCT
ejpam-5911	841	1	fuzzy	fuzzy	ADJ
ejpam-5911	841	2	sets	set	NOUN
ejpam-5911	841	3	syst	syst	PROPN
ejpam-5911	841	4	.	.	PUNCT
ejpam-5911	841	5	,	,	PUNCT
ejpam-5911	841	6	88:81–89	88:81–89	NUM
ejpam-5911	841	7	,	,	PUNCT
ejpam-5911	841	8	1997	1997	NUM
ejpam-5911	841	9	.	.	PUNCT
ejpam-5911	842	1	[	[	X
ejpam-5911	842	2	27	27	NUM
ejpam-5911	842	3	]	]	PUNCT
ejpam-5911	842	4	m.	m.	NOUN
ejpam-5911	842	5	demirci	demirci	PROPN
ejpam-5911	842	6	and	and	CCONJ
ejpam-5911	842	7	d.	d.	PROPN
ejpam-5911	842	8	coker	coker	PROPN
ejpam-5911	842	9	.	.	PUNCT
ejpam-5911	843	1	an	an	DET
ejpam-5911	843	2	introduction	introduction	NOUN
ejpam-5911	843	3	to	to	ADP
ejpam-5911	843	4	intuitionistic	intuitionistic	ADJ
ejpam-5911	843	5	fuzzy	fuzzy	ADJ
ejpam-5911	843	6	topological	topological	ADJ
ejpam-5911	843	7	spaces	space	NOUN
ejpam-5911	843	8	in	in	ADP
ejpam-5911	843	9	šostak	šostak	NOUN
ejpam-5911	843	10	’s	’s	PART
ejpam-5911	843	11	sense	sense	NOUN
ejpam-5911	843	12	.	.	PUNCT
ejpam-5911	844	1	busefal	busefal	PROPN
ejpam-5911	844	2	,	,	PUNCT
ejpam-5911	844	3	67:67–76	67:67–76	NUM
ejpam-5911	844	4	,	,	PUNCT
ejpam-5911	844	5	1996	1996	NUM
ejpam-5911	844	6	.	.	PUNCT
ejpam-5911	845	1	[	[	X
ejpam-5911	845	2	28	28	NUM
ejpam-5911	845	3	]	]	X
ejpam-5911	845	4	s.	s.	PROPN
ejpam-5911	845	5	k.	k.	PROPN
ejpam-5911	845	6	samanta	samanta	PROPN
ejpam-5911	845	7	and	and	CCONJ
ejpam-5911	845	8	t.	t.	PROPN
ejpam-5911	845	9	k.	k.	PROPN
ejpam-5911	845	10	mondal	mondal	PROPN
ejpam-5911	845	11	.	.	PUNCT
ejpam-5911	846	1	intuitionistic	intuitionistic	ADJ
ejpam-5911	846	2	gradation	gradation	NOUN
ejpam-5911	846	3	of	of	ADP
ejpam-5911	846	4	openness	openness	NOUN
ejpam-5911	846	5	:	:	PUNCT
ejpam-5911	846	6	intuitionistic	intuitionistic	ADJ
ejpam-5911	846	7	fuzzy	fuzzy	ADJ
ejpam-5911	846	8	topology	topology	NOUN
ejpam-5911	846	9	.	.	PUNCT
ejpam-5911	847	1	busefal	busefal	PROPN
ejpam-5911	847	2	,	,	PUNCT
ejpam-5911	847	3	73:8–17	73:8–17	NUM
ejpam-5911	847	4	,	,	PUNCT
ejpam-5911	847	5	1997	1997	NUM
ejpam-5911	847	6	.	.	PUNCT
ejpam-5911	848	1	[	[	X
ejpam-5911	848	2	29	29	NUM
ejpam-5911	848	3	]	]	PUNCT
ejpam-5911	848	4	j.	j.	PROPN
ejpam-5911	848	5	g.	g.	PROPN
ejpam-5911	848	6	garcia	garcia	PROPN
ejpam-5911	848	7	and	and	CCONJ
ejpam-5911	848	8	s.	s.	PROPN
ejpam-5911	848	9	e.	e.	PROPN
ejpam-5911	848	10	rodabaugh	rodabaugh	PROPN
ejpam-5911	848	11	.	.	PUNCT
ejpam-5911	849	1	ordertheoretic	ordertheoretic	ADJ
ejpam-5911	849	2	,	,	PUNCT
ejpam-5911	849	3	topological	topological	ADJ
ejpam-5911	849	4	,	,	PUNCT
ejpam-5911	849	5	categorical	categorical	ADJ
ejpam-5911	849	6	redundancies	redundancy	NOUN
ejpam-5911	849	7	of	of	ADP
ejpam-5911	849	8	interval	interval	NOUN
ejpam-5911	849	9	-	-	PUNCT
ejpam-5911	849	10	valued	value	VERB
ejpam-5911	849	11	sets	set	NOUN
ejpam-5911	849	12	,	,	PUNCT
ejpam-5911	849	13	grey	grey	NOUN
ejpam-5911	849	14	sets	set	NOUN
ejpam-5911	849	15	,	,	PUNCT
ejpam-5911	849	16	vague	vague	ADJ
ejpam-5911	849	17	sets	set	NOUN
ejpam-5911	849	18	,	,	PUNCT
ejpam-5911	849	19	intervalvalued	intervalvalue	VERB
ejpam-5911	849	20	;	;	PUNCT
ejpam-5911	849	21	intuitionistic	intuitionistic	ADJ
ejpam-5911	849	22	sets	set	NOUN
ejpam-5911	849	23	,	,	PUNCT
ejpam-5911	849	24	intuitionistic	intuitionistic	ADJ
ejpam-5911	849	25	fuzzy	fuzzy	ADJ
ejpam-5911	849	26	sets	set	NOUN
ejpam-5911	849	27	and	and	CCONJ
ejpam-5911	849	28	topologies	topology	NOUN
ejpam-5911	849	29	.	.	PUNCT
ejpam-5911	850	1	fuzzy	fuzzy	ADJ
ejpam-5911	850	2	sets	set	NOUN
ejpam-5911	850	3	syst	syst	PROPN
ejpam-5911	850	4	.	.	PUNCT
ejpam-5911	850	5	,	,	PUNCT
ejpam-5911	850	6	156(3):445–484	156(3):445–484	NUM
ejpam-5911	850	7	,	,	PUNCT
ejpam-5911	850	8	2005	2005	NUM
ejpam-5911	850	9	.	.	PUNCT
ejpam-5911	851	1	[	[	X
ejpam-5911	851	2	30	30	NUM
ejpam-5911	851	3	]	]	PUNCT
ejpam-5911	851	4	e.	e.	PROPN
ejpam-5911	851	5	p.	p.	PROPN
ejpam-5911	851	6	lee	lee	PROPN
ejpam-5911	851	7	.	.	PROPN
ejpam-5911	852	1	semiopen	semiopen	VERB
ejpam-5911	852	2	sets	set	NOUN
ejpam-5911	852	3	on	on	ADP
ejpam-5911	852	4	intuitionistic	intuitionistic	ADJ
ejpam-5911	852	5	fuzzy	fuzzy	ADJ
ejpam-5911	852	6	topological	topological	ADJ
ejpam-5911	852	7	spaces	space	NOUN
ejpam-5911	852	8	in	in	ADP
ejpam-5911	852	9	šostak	šostak	NOUN
ejpam-5911	852	10	’s	’s	PART
ejpam-5911	852	11	sense	sense	NOUN
ejpam-5911	852	12	.	.	PUNCT
ejpam-5911	853	1	int	int	NOUN
ejpam-5911	853	2	.	.	PUNCT
ejpam-5911	854	1	j.	j.	PROPN
ejpam-5911	854	2	fuzzy	fuzzy	ADJ
ejpam-5911	854	3	logic	logic	PROPN
ejpam-5911	854	4	intel	intel	PROPN
ejpam-5911	854	5	.	.	PUNCT
ejpam-5911	855	1	sys	sys	PROPN
ejpam-5911	855	2	.	.	PROPN
ejpam-5911	855	3	,	,	PUNCT
ejpam-5911	855	4	14:234–238	14:234–238	NUM
ejpam-5911	855	5	,	,	PUNCT
ejpam-5911	855	6	2004	2004	NUM
ejpam-5911	855	7	.	.	PUNCT
ejpam-5911	856	1	[	[	X
ejpam-5911	856	2	31	31	NUM
ejpam-5911	856	3	]	]	PUNCT
ejpam-5911	856	4	e.	e.	PROPN
ejpam-5911	856	5	p.	p.	PROPN
ejpam-5911	856	6	lee	lee	PROPN
ejpam-5911	857	1	and	and	CCONJ
ejpam-5911	858	1	j.	j.	PROPN
ejpam-5911	858	2	i.	i.	PROPN
ejpam-5911	858	3	kim	kim	PROPN
ejpam-5911	858	4	.	.	PUNCT
ejpam-5911	859	1	fuzzy	fuzzy	ADJ
ejpam-5911	859	2	strongly	strongly	ADV
ejpam-5911	859	3	(	(	PUNCT
ejpam-5911	859	4	r	r	NOUN
ejpam-5911	859	5	,	,	PUNCT
ejpam-5911	859	6	s)-preopen	s)-preopen	ADJ
ejpam-5911	859	7	and	and	CCONJ
ejpam-5911	859	8	preclosed	preclose	VERB
ejpam-5911	859	9	mappings	mapping	NOUN
ejpam-5911	859	10	.	.	PUNCT
ejpam-5911	860	1	commun	commun	PROPN
ejpam-5911	860	2	.	.	PUNCT
ejpam-5911	861	1	korean	korean	ADJ
ejpam-5911	861	2	math	math	PROPN
ejpam-5911	861	3	.	.	PUNCT
ejpam-5911	862	1	soc	soc	PROPN
ejpam-5911	862	2	.	.	PUNCT
ejpam-5911	862	3	,	,	PUNCT
ejpam-5911	862	4	26(4):661–667	26(4):661–667	NUM
ejpam-5911	862	5	,	,	PUNCT
ejpam-5911	862	6	2011	2011	NUM
ejpam-5911	862	7	.	.	PUNCT
ejpam-5911	863	1	[	[	X
ejpam-5911	863	2	32	32	NUM
ejpam-5911	863	3	]	]	PUNCT
ejpam-5911	863	4	m.	m.	NOUN
ejpam-5911	863	5	s.	s.	PROPN
ejpam-5911	863	6	k.	k.	PROPN
ejpam-5911	863	7	samanta	samanta	PROPN
ejpam-5911	863	8	and	and	CCONJ
ejpam-5911	863	9	t.	t.	PROPN
ejpam-5911	863	10	k.	k.	PROPN
ejpam-5911	863	11	mondal	mondal	PROPN
ejpam-5911	863	12	.	.	PUNCT
ejpam-5911	864	1	on	on	ADP
ejpam-5911	864	2	intuitionistic	intuitionistic	ADJ
ejpam-5911	864	3	gradation	gradation	NOUN
ejpam-5911	864	4	of	of	ADP
ejpam-5911	864	5	openness	openness	NOUN
ejpam-5911	864	6	.	.	PUNCT
ejpam-5911	865	1	fuzzy	fuzzy	ADJ
ejpam-5911	865	2	sets	set	NOUN
ejpam-5911	865	3	syst	syst	PROPN
ejpam-5911	865	4	.	.	PUNCT
ejpam-5911	865	5	,	,	PUNCT
ejpam-5911	865	6	131:323–336	131:323–336	NUM
ejpam-5911	865	7	,	,	PUNCT
ejpam-5911	865	8	2002	2002	NUM
ejpam-5911	865	9	.	.	PUNCT
ejpam-5911	866	1	[	[	X
ejpam-5911	866	2	33	33	NUM
ejpam-5911	866	3	]	]	PUNCT
ejpam-5911	866	4	s.	s.	PROPN
ejpam-5911	866	5	e.	e.	PROPN
ejpam-5911	866	6	abbas	abbas	PROPN
ejpam-5911	866	7	.	.	PUNCT
ejpam-5911	867	1	(	(	PUNCT
ejpam-5911	867	2	r	r	NOUN
ejpam-5911	867	3	,	,	PUNCT
ejpam-5911	867	4	s)-generalized	s)-generalized	ADJ
ejpam-5911	867	5	intuitionistic	intuitionistic	ADJ
ejpam-5911	867	6	fuzzy	fuzzy	ADJ
ejpam-5911	867	7	closed	closed	ADJ
ejpam-5911	867	8	sets	set	NOUN
ejpam-5911	867	9	.	.	PUNCT
ejpam-5911	868	1	j.	j.	PROPN
ejpam-5911	868	2	egyptian	egyptian	PROPN
ejpam-5911	868	3	math	math	PROPN
ejpam-5911	868	4	.	.	PUNCT
ejpam-5911	869	1	soc	soc	PROPN
ejpam-5911	869	2	.	.	PUNCT
ejpam-5911	869	3	,	,	PUNCT
ejpam-5911	869	4	14:331–351	14:331–351	PROPN
ejpam-5911	869	5	,	,	PUNCT
ejpam-5911	869	6	2006	2006	NUM
ejpam-5911	869	7	.	.	PUNCT
ejpam-5911	870	1	[	[	X
ejpam-5911	870	2	34	34	NUM
ejpam-5911	870	3	]	]	X
ejpam-5911	870	4	s.	s.	PROPN
ejpam-5911	870	5	e.	e.	PROPN
ejpam-5911	870	6	abbas	abbas	PROPN
ejpam-5911	870	7	and	and	CCONJ
ejpam-5911	870	8	b.	b.	PROPN
ejpam-5911	870	9	krsteska	krsteska	PROPN
ejpam-5911	870	10	.	.	PUNCT
ejpam-5911	871	1	some	some	DET
ejpam-5911	871	2	properties	property	NOUN
ejpam-5911	871	3	of	of	ADP
ejpam-5911	871	4	intuitionistic	intuitionistic	ADJ
ejpam-5911	871	5	(	(	PUNCT
ejpam-5911	871	6	r	r	NOUN
ejpam-5911	871	7	,	,	PUNCT
ejpam-5911	871	8	s)-t0	s)-t0	ADJ
ejpam-5911	871	9	and	and	CCONJ
ejpam-5911	871	10	(	(	PUNCT
ejpam-5911	871	11	r	r	NOUN
ejpam-5911	871	12	,	,	PUNCT
ejpam-5911	871	13	s)-t1	s)-t1	NOUN
ejpam-5911	871	14	spaces	space	NOUN
ejpam-5911	871	15	.	.	PUNCT
ejpam-5911	872	1	int	int	NOUN
ejpam-5911	872	2	.	.	PUNCT
ejpam-5911	873	1	j.	j.	PROPN
ejpam-5911	873	2	math	math	PROPN
ejpam-5911	873	3	.	.	PUNCT
ejpam-5911	874	1	math	math	NOUN
ejpam-5911	874	2	.	.	PUNCT
ejpam-5911	875	1	sci	sci	PROPN
ejpam-5911	875	2	.	.	PROPN
ejpam-5911	875	3	,	,	PUNCT
ejpam-5911	875	4	2008:1–11	2008:1–11	NUM
ejpam-5911	875	5	,	,	PUNCT
ejpam-5911	875	6	2008	2008	NUM
ejpam-5911	875	7	.	.	PUNCT
ejpam-5911	876	1	[	[	X
ejpam-5911	876	2	35	35	NUM
ejpam-5911	876	3	]	]	PUNCT
ejpam-5911	876	4	a.	a.	NOUN
ejpam-5911	876	5	m.	m.	NOUN
ejpam-5911	876	6	zahran	zahran	PROPN
ejpam-5911	876	7	,	,	PUNCT
ejpam-5911	876	8	m.	m.	NOUN
ejpam-5911	876	9	a.	a.	PROPN
ejpam-5911	876	10	abd	abd	PROPN
ejpam-5911	876	11	-	-	PUNCT
ejpam-5911	876	12	allah	allah	PROPN
ejpam-5911	876	13	,	,	PUNCT
ejpam-5911	876	14	and	and	CCONJ
ejpam-5911	876	15	a.	a.	NOUN
ejpam-5911	876	16	ghareeb	ghareeb	NOUN
ejpam-5911	876	17	.	.	PUNCT
ejpam-5911	877	1	several	several	ADJ
ejpam-5911	877	2	types	type	NOUN
ejpam-5911	877	3	of	of	ADP
ejpam-5911	877	4	double	double	ADJ
ejpam-5911	877	5	fuzzy	fuzzy	ADJ
ejpam-5911	877	6	irresolute	irresolute	ADJ
ejpam-5911	877	7	functions	function	NOUN
ejpam-5911	877	8	.	.	PUNCT
ejpam-5911	878	1	int	int	NOUN
ejpam-5911	878	2	.	.	PUNCT
ejpam-5911	879	1	j.	j.	PROPN
ejpam-5911	879	2	comput	comput	PROPN
ejpam-5911	879	3	.	.	PUNCT
ejpam-5911	880	1	cognition	cognition	NOUN
ejpam-5911	880	2	,	,	PUNCT
ejpam-5911	880	3	8(2):19–23	8(2):19–23	NUM
ejpam-5911	880	4	,	,	PUNCT
ejpam-5911	880	5	2010	2010	NUM
ejpam-5911	880	6	.	.	PUNCT
ejpam-5911	881	1	[	[	X
ejpam-5911	881	2	36	36	NUM
ejpam-5911	881	3	]	]	X
ejpam-5911	881	4	f.	f.	PROPN
ejpam-5911	881	5	m.	m.	PROPN
ejpam-5911	881	6	mohammed	mohammed	PROPN
ejpam-5911	881	7	,	,	PUNCT
ejpam-5911	881	8	m.	m.	NOUN
ejpam-5911	881	9	s.	s.	PROPN
ejpam-5911	881	10	m.	m.	PROPN
ejpam-5911	881	11	noorani	noorani	PROPN
ejpam-5911	881	12	,	,	PUNCT
ejpam-5911	881	13	and	and	CCONJ
ejpam-5911	881	14	a.	a.	NOUN
ejpam-5911	881	15	ghareeb	ghareeb	NOUN
ejpam-5911	881	16	.	.	PUNCT
ejpam-5911	882	1	several	several	ADJ
ejpam-5911	882	2	notions	notion	NOUN
ejpam-5911	882	3	of	of	ADP
ejpam-5911	882	4	generalized	generalized	ADJ
ejpam-5911	882	5	semi	semi	NOUN
ejpam-5911	882	6	-	-	NOUN
ejpam-5911	882	7	compactness	compactness	NOUN
ejpam-5911	882	8	in	in	ADP
ejpam-5911	882	9	double	double	ADJ
ejpam-5911	882	10	fuzzy	fuzzy	ADJ
ejpam-5911	882	11	topological	topological	ADJ
ejpam-5911	882	12	spaces	space	NOUN
ejpam-5911	882	13	.	.	PUNCT
ejpam-5911	883	1	int	int	NOUN
ejpam-5911	883	2	.	.	PUNCT
ejpam-5911	884	1	j.	j.	PROPN
ejpam-5911	884	2	pure	pure	PROPN
ejpam-5911	884	3	appl	appl	PROPN
ejpam-5911	884	4	.	.	PUNCT
ejpam-5911	884	5	math	math	PROPN
ejpam-5911	884	6	.	.	PUNCT
ejpam-5911	884	7	,	,	PUNCT
ejpam-5911	884	8	109(2):153–175	109(2):153–175	NUM
ejpam-5911	884	9	,	,	PUNCT
ejpam-5911	884	10	2016	2016	NUM
ejpam-5911	884	11	.	.	PUNCT
ejpam-5911	885	1	[	[	X
ejpam-5911	885	2	37	37	NUM
ejpam-5911	885	3	]	]	X
ejpam-5911	885	4	e.	e.	PROPN
ejpam-5911	885	5	el	el	PROPN
ejpam-5911	885	6	-	-	PUNCT
ejpam-5911	885	7	sanousy	sanousy	PROPN
ejpam-5911	885	8	and	and	CCONJ
ejpam-5911	885	9	a.	a.	PROPN
ejpam-5911	885	10	atef	atef	PROPN
ejpam-5911	885	11	.	.	PUNCT
ejpam-5911	886	1	(	(	PUNCT
ejpam-5911	886	2	r	r	NOUN
ejpam-5911	886	3	,	,	PUNCT
ejpam-5911	886	4	s)-fuzzy	s)-fuzzy	PUNCT
ejpam-5911	886	5	g∗p	g∗p	NUM
ejpam-5911	886	6	-	-	PUNCT
ejpam-5911	886	7	closed	close	VERB
ejpam-5911	886	8	sets	set	NOUN
ejpam-5911	886	9	and	and	CCONJ
ejpam-5911	886	10	its	its	PRON
ejpam-5911	886	11	applications	application	NOUN
ejpam-5911	886	12	.	.	PUNCT
ejpam-5911	887	1	appl	appl	PROPN
ejpam-5911	887	2	.	.	PROPN
ejpam-5911	888	1	math	math	PROPN
ejpam-5911	888	2	.	.	PUNCT
ejpam-5911	889	1	inf	inf	PROPN
ejpam-5911	889	2	.	.	PUNCT
ejpam-5911	890	1	sci	sci	PROPN
ejpam-5911	890	2	.	.	PROPN
ejpam-5911	890	3	,	,	PUNCT
ejpam-5911	890	4	16(1):17–24	16(1):17–24	NUM
ejpam-5911	890	5	,	,	PUNCT
ejpam-5911	890	6	2022	2022	NUM
ejpam-5911	890	7	.	.	PUNCT
ejpam-5911	891	1	[	[	X
ejpam-5911	891	2	38	38	NUM
ejpam-5911	891	3	]	]	PUNCT
ejpam-5911	891	4	i.	i.	PROPN
ejpam-5911	891	5	m.	m.	PROPN
ejpam-5911	891	6	taha	taha	PROPN
ejpam-5911	891	7	.	.	PUNCT
ejpam-5911	892	1	some	some	DET
ejpam-5911	892	2	properties	property	NOUN
ejpam-5911	892	3	of	of	ADP
ejpam-5911	892	4	(	(	PUNCT
ejpam-5911	892	5	r	r	NOUN
ejpam-5911	892	6	,	,	PUNCT
ejpam-5911	892	7	s)-generalized	s)-generalized	ADJ
ejpam-5911	892	8	fuzzy	fuzzy	ADJ
ejpam-5911	892	9	semi	semi	ADJ
ejpam-5911	892	10	-	-	ADJ
ejpam-5911	892	11	closed	closed	ADJ
ejpam-5911	892	12	sets	set	NOUN
ejpam-5911	892	13	and	and	CCONJ
ejpam-5911	892	14	some	some	DET
ejpam-5911	892	15	applications	application	NOUN
ejpam-5911	892	16	.	.	PUNCT
ejpam-5911	893	1	j.	j.	PROPN
ejpam-5911	893	2	math	math	PROPN
ejpam-5911	893	3	.	.	PUNCT
ejpam-5911	894	1	comput	comput	NOUN
ejpam-5911	894	2	.	.	PUNCT
ejpam-5911	895	1	sci	sci	PROPN
ejpam-5911	895	2	.	.	PROPN
ejpam-5911	895	3	,	,	PUNCT
ejpam-5911	895	4	27(2):164–175	27(2):164–175	PROPN
ejpam-5911	895	5	,	,	PUNCT
ejpam-5911	895	6	2022	2022	NUM
ejpam-5911	895	7	.	.	PUNCT
ejpam-5911	896	1	[	[	X
ejpam-5911	896	2	39	39	NUM
ejpam-5911	896	3	]	]	PUNCT
ejpam-5911	896	4	f.	f.	PROPN
ejpam-5911	896	5	alsharari	alsharari	PROPN
ejpam-5911	896	6	,	,	PUNCT
ejpam-5911	896	7	o.	o.	PROPN
ejpam-5911	896	8	m.	m.	PROPN
ejpam-5911	896	9	taha	taha	PROPN
ejpam-5911	896	10	,	,	PUNCT
ejpam-5911	896	11	and	and	CCONJ
ejpam-5911	896	12	i.	i.	PROPN
ejpam-5911	896	13	m.	m.	PROPN
ejpam-5911	896	14	taha	taha	PROPN
ejpam-5911	896	15	.	.	PUNCT
ejpam-5911	897	1	some	some	DET
ejpam-5911	897	2	new	new	ADJ
ejpam-5911	897	3	types	type	NOUN
ejpam-5911	897	4	of	of	ADP
ejpam-5911	897	5	fuzzy	fuzzy	ADJ
ejpam-5911	897	6	closed	closed	ADJ
ejpam-5911	897	7	sets	set	NOUN
ejpam-5911	897	8	,	,	PUNCT
ejpam-5911	897	9	separation	separation	NOUN
ejpam-5911	897	10	axioms	axiom	NOUN
ejpam-5911	897	11	,	,	PUNCT
ejpam-5911	897	12	and	and	CCONJ
ejpam-5911	897	13	compactness	compactness	NOUN
ejpam-5911	897	14	via	via	ADP
ejpam-5911	897	15	double	double	ADJ
ejpam-5911	897	16	fuzzy	fuzzy	ADJ
ejpam-5911	897	17	topologies	topology	NOUN
ejpam-5911	897	18	.	.	PUNCT
ejpam-5911	898	1	eur	eur	PROPN
ejpam-5911	898	2	.	.	PUNCT
ejpam-5911	899	1	j.	j.	PROPN
ejpam-5911	899	2	pure	pure	PROPN
ejpam-5911	899	3	appl	appl	PROPN
ejpam-5911	899	4	.	.	PUNCT
ejpam-5911	899	5	math	math	PROPN
ejpam-5911	899	6	.	.	PUNCT
ejpam-5911	899	7	,	,	PUNCT
ejpam-5911	899	8	17(4):4093–4111	17(4):4093–4111	NUM
ejpam-5911	899	9	,	,	PUNCT
ejpam-5911	899	10	2024	2024	NUM
ejpam-5911	899	11	.	.	PUNCT
ejpam-5911	900	1	[	[	X
ejpam-5911	900	2	40	40	NUM
ejpam-5911	900	3	]	]	PUNCT
ejpam-5911	900	4	a.	a.	NOUN
ejpam-5911	900	5	kandil	kandil	PROPN
ejpam-5911	900	6	and	and	CCONJ
ejpam-5911	900	7	m.	m.	PROPN
ejpam-5911	900	8	e.	e.	PROPN
ejpam-5911	900	9	el	el	PROPN
ejpam-5911	900	10	-	-	PROPN
ejpam-5911	900	11	shafei	shafei	PROPN
ejpam-5911	900	12	.	.	PUNCT
ejpam-5911	901	1	regularity	regularity	NOUN
ejpam-5911	901	2	axioms	axiom	NOUN
ejpam-5911	901	3	in	in	ADP
ejpam-5911	901	4	fuzzy	fuzzy	ADJ
ejpam-5911	901	5	topological	topological	ADJ
ejpam-5911	901	6	spaces	space	NOUN
ejpam-5911	901	7	and	and	CCONJ
ejpam-5911	901	8	fri	fri	NOUN
ejpam-5911	901	9	-	-	NOUN
ejpam-5911	901	10	proximities	proximity	NOUN
ejpam-5911	901	11	.	.	PUNCT
ejpam-5911	902	1	fuzzy	fuzzy	ADJ
ejpam-5911	902	2	set	set	PROPN
ejpam-5911	902	3	.	.	PUNCT
ejpam-5911	903	1	syst	syst	PROPN
ejpam-5911	903	2	.	.	PUNCT
ejpam-5911	903	3	,	,	PUNCT
ejpam-5911	904	1	27:217–231	27:217–231	NUM
ejpam-5911	904	2	,	,	PUNCT
ejpam-5911	904	3	1988	1988	NUM
ejpam-5911	904	4	.	.	PUNCT
ejpam-5911	905	1	[	[	X
ejpam-5911	905	2	41	41	NUM
ejpam-5911	905	3	]	]	X
ejpam-5911	905	4	i.	i.	PROPN
ejpam-5911	905	5	m.	m.	PROPN
ejpam-5911	905	6	taha	taha	PROPN
ejpam-5911	905	7	.	.	PUNCT
ejpam-5911	906	1	on	on	ADP
ejpam-5911	906	2	r	r	NOUN
ejpam-5911	906	3	-	-	PUNCT
ejpam-5911	906	4	fuzzy	fuzzy	ADJ
ejpam-5911	906	5	ℓ-open	ℓ-open	NOUN
ejpam-5911	906	6	sets	set	NOUN
ejpam-5911	906	7	and	and	CCONJ
ejpam-5911	906	8	continuity	continuity	NOUN
ejpam-5911	906	9	of	of	ADP
ejpam-5911	906	10	fuzzy	fuzzy	ADJ
ejpam-5911	906	11	multifunctions	multifunction	NOUN
ejpam-5911	906	12	via	via	ADP
ejpam-5911	906	13	fuzzy	fuzzy	ADJ
ejpam-5911	906	14	ideals	ideal	NOUN
ejpam-5911	906	15	.	.	PUNCT
ejpam-5911	907	1	j.	j.	PROPN
ejpam-5911	907	2	math	math	PROPN
ejpam-5911	907	3	.	.	PUNCT
ejpam-5911	908	1	comput	comput	NOUN
ejpam-5911	908	2	.	.	PUNCT
ejpam-5911	909	1	sci	sci	PROPN
ejpam-5911	909	2	.	.	PROPN
ejpam-5911	909	3	,	,	PUNCT
ejpam-5911	909	4	10(6):2613–2633	10(6):2613–2633	NUM
ejpam-5911	909	5	,	,	PUNCT
ejpam-5911	909	6	2020	2020	NUM
ejpam-5911	909	7	.	.	PUNCT
ejpam-5911	910	1	[	[	X
ejpam-5911	910	2	42	42	NUM
ejpam-5911	910	3	]	]	PUNCT
ejpam-5911	910	4	i.	i.	PROPN
ejpam-5911	910	5	m.	m.	PROPN
ejpam-5911	910	6	taha	taha	PROPN
ejpam-5911	910	7	.	.	PUNCT
ejpam-5911	911	1	on	on	ADP
ejpam-5911	911	2	r	r	NOUN
ejpam-5911	911	3	-	-	PUNCT
ejpam-5911	911	4	generalized	generalize	VERB
ejpam-5911	911	5	fuzzy	fuzzy	ADJ
ejpam-5911	911	6	ℓ-closed	ℓ-close	VERB
ejpam-5911	911	7	sets	set	NOUN
ejpam-5911	911	8	:	:	PUNCT
ejpam-5911	911	9	properties	property	NOUN
ejpam-5911	911	10	and	and	CCONJ
ejpam-5911	911	11	applications	application	NOUN
ejpam-5911	911	12	.	.	PUNCT
ejpam-5911	912	1	j.	j.	PROPN
ejpam-5911	912	2	math	math	PROPN
ejpam-5911	912	3	.	.	PUNCT
ejpam-5911	912	4	,	,	PUNCT
ejpam-5911	912	5	page	page	NOUN
ejpam-5911	912	6	4483481	4483481	NUM
ejpam-5911	912	7	,	,	PUNCT
ejpam-5911	912	8	2021	2021	NUM
ejpam-5911	912	9	.	.	PUNCT
ejpam-5911	913	1	[	[	X
ejpam-5911	913	2	43	43	NUM
ejpam-5911	913	3	]	]	X
ejpam-5911	913	4	i.	i.	PROPN
ejpam-5911	913	5	m.	m.	PROPN
ejpam-5911	913	6	taha	taha	PROPN
ejpam-5911	913	7	.	.	PUNCT
ejpam-5911	914	1	r	r	X
ejpam-5911	914	2	-	-	PUNCT
ejpam-5911	914	3	fuzzy	fuzzy	ADJ
ejpam-5911	914	4	δ-ℓ-open	δ-ℓ-open	NOUN
ejpam-5911	914	5	sets	set	NOUN
ejpam-5911	914	6	and	and	CCONJ
ejpam-5911	914	7	fuzzy	fuzzy	ADJ
ejpam-5911	914	8	upper	upper	ADJ
ejpam-5911	914	9	(	(	PUNCT
ejpam-5911	914	10	lower	low	ADJ
ejpam-5911	914	11	)	)	PUNCT
ejpam-5911	914	12	δ-ℓ-continuity	δ-ℓ-continuity	NOUN
ejpam-5911	914	13	via	via	ADP
ejpam-5911	914	14	fuzzy	fuzzy	ADJ
ejpam-5911	914	15	i.	i.	PROPN
ejpam-5911	914	16	m.	m.	PROPN
ejpam-5911	914	17	taha	taha	PROPN
ejpam-5911	914	18	,	,	PUNCT
ejpam-5911	914	19	j.	j.	PROPN
ejpam-5911	914	20	al	al	PROPN
ejpam-5911	914	21	-	-	PUNCT
ejpam-5911	914	22	mufarrij	mufarrij	PROPN
ejpam-5911	914	23	,	,	PUNCT
ejpam-5911	914	24	o.	o.	PROPN
ejpam-5911	914	25	m.	m.	PROPN
ejpam-5911	914	26	taha	taha	PROPN
ejpam-5911	914	27	/	/	PUNCT
ejpam-5911	914	28	eur	eur	PROPN
ejpam-5911	914	29	.	.	PUNCT
ejpam-5911	915	1	j.	j.	PROPN
ejpam-5911	915	2	pure	pure	PROPN
ejpam-5911	915	3	appl	appl	PROPN
ejpam-5911	915	4	.	.	PROPN
ejpam-5911	915	5	math	math	PROPN
ejpam-5911	915	6	,	,	PUNCT
ejpam-5911	915	7	18	18	NUM
ejpam-5911	915	8	(	(	PUNCT
ejpam-5911	915	9	2	2	NUM
ejpam-5911	915	10	)	)	PUNCT
ejpam-5911	915	11	(	(	PUNCT
ejpam-5911	915	12	2025	2025	NUM
ejpam-5911	915	13	)	)	PUNCT
ejpam-5911	915	14	,	,	PUNCT
ejpam-5911	915	15	5911	5911	NUM
ejpam-5911	915	16	27	27	NUM
ejpam-5911	915	17	of	of	ADP
ejpam-5911	915	18	27	27	NUM
ejpam-5911	915	19	idealization	idealization	NOUN
ejpam-5911	915	20	.	.	PUNCT
ejpam-5911	916	1	j.	j.	PROPN
ejpam-5911	916	2	math	math	PROPN
ejpam-5911	916	3	.	.	PUNCT
ejpam-5911	917	1	comput	comput	NOUN
ejpam-5911	917	2	.	.	PUNCT
ejpam-5911	918	1	sci	sci	PROPN
ejpam-5911	918	2	.	.	PROPN
ejpam-5911	918	3	,	,	PUNCT
ejpam-5911	918	4	25(1):1–9	25(1):1–9	NUM
ejpam-5911	918	5	,	,	PUNCT
ejpam-5911	918	6	2022	2022	NUM
ejpam-5911	918	7	.	.	PUNCT
ejpam-5911	919	1	[	[	X
ejpam-5911	919	2	44	44	NUM
ejpam-5911	919	3	]	]	PUNCT
ejpam-5911	919	4	i.	i.	PROPN
ejpam-5911	919	5	m.	m.	PROPN
ejpam-5911	919	6	taha	taha	PROPN
ejpam-5911	919	7	.	.	PUNCT
ejpam-5911	920	1	some	some	DET
ejpam-5911	920	2	new	new	ADJ
ejpam-5911	920	3	separation	separation	NOUN
ejpam-5911	920	4	axioms	axiom	VERB
ejpam-5911	920	5	in	in	ADP
ejpam-5911	920	6	fuzzy	fuzzy	ADJ
ejpam-5911	920	7	soft	soft	ADJ
ejpam-5911	920	8	topological	topological	ADJ
ejpam-5911	920	9	spaces	space	NOUN
ejpam-5911	920	10	.	.	PUNCT
ejpam-5911	921	1	filomat	filomat	PROPN
ejpam-5911	921	2	,	,	PUNCT
ejpam-5911	921	3	35:1775–1783	35:1775–1783	PROPN
ejpam-5911	921	4	,	,	PUNCT
ejpam-5911	921	5	2021	2021	NUM
ejpam-5911	921	6	.	.	PUNCT
ejpam-5911	922	1	[	[	X
ejpam-5911	922	2	45	45	NUM
ejpam-5911	922	3	]	]	PUNCT
ejpam-5911	922	4	i.	i.	PROPN
ejpam-5911	922	5	m.	m.	PROPN
ejpam-5911	922	6	taha	taha	PROPN
ejpam-5911	922	7	.	.	PUNCT
ejpam-5911	922	8	compactness	compactness	NOUN
ejpam-5911	922	9	on	on	ADP
ejpam-5911	922	10	fuzzy	fuzzy	ADJ
ejpam-5911	922	11	soft	soft	ADJ
ejpam-5911	922	12	r	r	NOUN
ejpam-5911	922	13	-	-	PUNCT
ejpam-5911	922	14	minimal	minimal	ADJ
ejpam-5911	922	15	spaces	space	NOUN
ejpam-5911	922	16	.	.	PUNCT
ejpam-5911	923	1	int	int	NOUN
ejpam-5911	923	2	.	.	PUNCT
ejpam-5911	924	1	j.	j.	PROPN
ejpam-5911	924	2	fuzzy	fuzzy	PROPN
ejpam-5911	924	3	logic	logic	PROPN
ejpam-5911	924	4	intell	intell	PROPN
ejpam-5911	924	5	.	.	PUNCT
ejpam-5911	925	1	syst	syst	PROPN
ejpam-5911	925	2	.	.	PROPN
ejpam-5911	925	3	,	,	PUNCT
ejpam-5911	925	4	21:251–258	21:251–258	PROPN
ejpam-5911	925	5	,	,	PUNCT
ejpam-5911	925	6	2021	2021	NUM
ejpam-5911	925	7	.	.	PUNCT
ejpam-5911	926	1	[	[	X
ejpam-5911	926	2	46	46	NUM
ejpam-5911	926	3	]	]	X
ejpam-5911	926	4	i.	i.	PROPN
ejpam-5911	926	5	m.	m.	PROPN
ejpam-5911	926	6	taha	taha	PROPN
ejpam-5911	926	7	.	.	PUNCT
ejpam-5911	927	1	some	some	DET
ejpam-5911	927	2	new	new	ADJ
ejpam-5911	927	3	results	result	NOUN
ejpam-5911	927	4	on	on	ADP
ejpam-5911	927	5	fuzzy	fuzzy	ADJ
ejpam-5911	927	6	soft	soft	ADJ
ejpam-5911	927	7	r	r	NOUN
ejpam-5911	927	8	-	-	PUNCT
ejpam-5911	927	9	minimal	minimal	ADJ
ejpam-5911	927	10	spaces	space	NOUN
ejpam-5911	927	11	.	.	PUNCT
ejpam-5911	928	1	aims	aim	VERB
ejpam-5911	928	2	mathematics	mathematic	NOUN
ejpam-5911	928	3	,	,	PUNCT
ejpam-5911	928	4	7:12458–12470	7:12458–12470	NUM
ejpam-5911	928	5	,	,	PUNCT
ejpam-5911	928	6	2022	2022	NUM
ejpam-5911	928	7	.	.	PUNCT