id	sid	tid	token	lemma	pos
ejpam-5782	1	1	european	european	PROPN
ejpam-5782	1	2	journal	journal	PROPN
ejpam-5782	1	3	of	of	ADP
ejpam-5782	1	4	pure	pure	ADJ
ejpam-5782	1	5	and	and	CCONJ
ejpam-5782	1	6	applied	applied	ADJ
ejpam-5782	1	7	mathematics	mathematic	NOUN
ejpam-5782	1	8	2025	2025	NUM
ejpam-5782	1	9	,	,	PUNCT
ejpam-5782	1	10	vol	vol	NOUN
ejpam-5782	1	11	.	.	PROPN
ejpam-5782	1	12	18	18	NUM
ejpam-5782	1	13	,	,	PUNCT
ejpam-5782	1	14	issue	issue	NOUN
ejpam-5782	1	15	2	2	NUM
ejpam-5782	1	16	,	,	PUNCT
ejpam-5782	1	17	article	article	NOUN
ejpam-5782	1	18	number	number	NOUN
ejpam-5782	1	19	5782	5782	NUM
ejpam-5782	1	20	issn	issn	VERB
ejpam-5782	1	21	1307	1307	NUM
ejpam-5782	1	22	-	-	SYM
ejpam-5782	1	23	5543	5543	NUM
ejpam-5782	1	24	–	–	PUNCT
ejpam-5782	1	25	ejpam.com	ejpam.com	X
ejpam-5782	1	26	published	publish	VERB
ejpam-5782	1	27	by	by	ADP
ejpam-5782	1	28	new	new	PROPN
ejpam-5782	1	29	york	york	PROPN
ejpam-5782	1	30	business	business	PROPN
ejpam-5782	1	31	global	global	PROPN
ejpam-5782	1	32	an	an	DET
ejpam-5782	1	33	introduction	introduction	NOUN
ejpam-5782	1	34	to	to	ADP
ejpam-5782	1	35	mixed	mixed	ADJ
ejpam-5782	1	36	h	h	NOUN
ejpam-5782	1	37	(	(	PUNCT
ejpam-5782	1	38	θ(µ	θ(µ	PROPN
ejpam-5782	1	39	,	,	PUNCT
ejpam-5782	1	40	ν	ν	NOUN
ejpam-5782	1	41	)	)	PUNCT
ejpam-5782	1	42	)	)	PUNCT
ejpam-5782	2	1	-open	-open	NOUN
ejpam-5782	2	2	sets	set	NOUN
ejpam-5782	2	3	generated	generate	VERB
ejpam-5782	2	4	by	by	ADP
ejpam-5782	2	5	hereditary	hereditary	ADJ
ejpam-5782	2	6	classes	class	NOUN
ejpam-5782	2	7	in	in	ADP
ejpam-5782	2	8	generalized	generalized	ADJ
ejpam-5782	2	9	topological	topological	ADJ
ejpam-5782	2	10	spaces	space	NOUN
ejpam-5782	2	11	fahad	fahad	PROPN
ejpam-5782	2	12	alsharari1,∗	alsharari1,∗	PROPN
ejpam-5782	2	13	,	,	PUNCT
ejpam-5782	2	14	abdo	abdo	PROPN
ejpam-5782	2	15	qahis2	qahis2	PROPN
ejpam-5782	2	16	1	1	NUM
ejpam-5782	2	17	department	department	NOUN
ejpam-5782	2	18	of	of	ADP
ejpam-5782	2	19	mathematics	mathematic	NOUN
ejpam-5782	2	20	,	,	PUNCT
ejpam-5782	2	21	college	college	NOUN
ejpam-5782	2	22	of	of	ADP
ejpam-5782	2	23	science	science	NOUN
ejpam-5782	2	24	,	,	PUNCT
ejpam-5782	2	25	jouf	jouf	PROPN
ejpam-5782	2	26	university	university	PROPN
ejpam-5782	2	27	,	,	PUNCT
ejpam-5782	2	28	sakaka	sakaka	NOUN
ejpam-5782	2	29	72311	72311	NUM
ejpam-5782	2	30	,	,	PUNCT
ejpam-5782	2	31	saudi	saudi	PROPN
ejpam-5782	2	32	arabia	arabia	PROPN
ejpam-5782	2	33	2	2	NUM
ejpam-5782	2	34	department	department	NOUN
ejpam-5782	2	35	of	of	ADP
ejpam-5782	2	36	mathematics	mathematic	NOUN
ejpam-5782	2	37	,	,	PUNCT
ejpam-5782	2	38	college	college	NOUN
ejpam-5782	2	39	of	of	ADP
ejpam-5782	2	40	science	science	NOUN
ejpam-5782	2	41	and	and	CCONJ
ejpam-5782	2	42	arts	art	NOUN
ejpam-5782	2	43	,	,	PUNCT
ejpam-5782	2	44	najran	najran	ADJ
ejpam-5782	2	45	university	university	NOUN
ejpam-5782	2	46	,	,	PUNCT
ejpam-5782	2	47	najran	najran	NOUN
ejpam-5782	2	48	,	,	PUNCT
ejpam-5782	2	49	saudi	saudi	PROPN
ejpam-5782	2	50	arabia	arabia	PROPN
ejpam-5782	2	51	abstract	abstract	NOUN
ejpam-5782	2	52	.	.	PUNCT
ejpam-5782	3	1	in	in	ADP
ejpam-5782	3	2	[	[	X
ejpam-5782	3	3	1	1	NUM
ejpam-5782	3	4	]	]	PUNCT
ejpam-5782	3	5	,	,	PUNCT
ejpam-5782	3	6	kim	kim	PROPN
ejpam-5782	3	7	and	and	CCONJ
ejpam-5782	3	8	min	min	PROPN
ejpam-5782	3	9	introduced	introduce	VERB
ejpam-5782	3	10	the	the	DET
ejpam-5782	3	11	operation	operation	NOUN
ejpam-5782	3	12	γ∗	γ∗	NOUN
ejpam-5782	3	13	and	and	CCONJ
ejpam-5782	3	14	h(θ)-open	h(θ)-open	PROPN
ejpam-5782	3	15	sets	set	NOUN
ejpam-5782	3	16	within	within	ADP
ejpam-5782	3	17	the	the	DET
ejpam-5782	3	18	context	context	NOUN
ejpam-5782	3	19	of	of	ADP
ejpam-5782	3	20	generalized	generalized	ADJ
ejpam-5782	3	21	topological	topological	ADJ
ejpam-5782	3	22	spaces	space	NOUN
ejpam-5782	3	23	,	,	PUNCT
ejpam-5782	3	24	utilizing	utilize	VERB
ejpam-5782	3	25	a	a	DET
ejpam-5782	3	26	hereditary	hereditary	ADJ
ejpam-5782	3	27	class	class	NOUN
ejpam-5782	3	28	h.	h.	NOUN
ejpam-5782	3	29	in	in	ADP
ejpam-5782	3	30	this	this	DET
ejpam-5782	3	31	study	study	NOUN
ejpam-5782	3	32	,	,	PUNCT
ejpam-5782	3	33	we	we	PRON
ejpam-5782	3	34	extend	extend	VERB
ejpam-5782	3	35	these	these	DET
ejpam-5782	3	36	concepts	concept	NOUN
ejpam-5782	3	37	by	by	ADP
ejpam-5782	3	38	employing	employ	VERB
ejpam-5782	3	39	two	two	NUM
ejpam-5782	3	40	generalized	generalized	ADJ
ejpam-5782	3	41	topologies	topology	NOUN
ejpam-5782	3	42	,	,	PUNCT
ejpam-5782	3	43	µ	µ	NOUN
ejpam-5782	3	44	and	and	CCONJ
ejpam-5782	3	45	ν	ν	NOUN
ejpam-5782	3	46	,	,	PUNCT
ejpam-5782	3	47	along	along	ADP
ejpam-5782	3	48	with	with	ADP
ejpam-5782	3	49	a	a	DET
ejpam-5782	3	50	hereditary	hereditary	ADJ
ejpam-5782	3	51	class	class	NOUN
ejpam-5782	3	52	h.	h.	PROPN
ejpam-5782	3	53	specifically	specifically	ADV
ejpam-5782	3	54	,	,	PUNCT
ejpam-5782	3	55	we	we	PRON
ejpam-5782	3	56	introduce	introduce	VERB
ejpam-5782	3	57	and	and	CCONJ
ejpam-5782	3	58	investigate	investigate	VERB
ejpam-5782	3	59	the	the	DET
ejpam-5782	3	60	mixed	mixed	ADJ
ejpam-5782	3	61	operation	operation	NOUN
ejpam-5782	3	62	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	3	63	,	,	PUNCT
ejpam-5782	3	64	ν	ν	NOUN
ejpam-5782	3	65	)	)	PUNCT
ejpam-5782	3	66	(	(	PUNCT
ejpam-5782	3	67	denoted	denote	VERB
ejpam-5782	3	68	briefly	briefly	ADV
ejpam-5782	3	69	as	as	ADP
ejpam-5782	3	70	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	3	71	,	,	PUNCT
ejpam-5782	3	72	ν	ν	NOUN
ejpam-5782	3	73	)	)	PUNCT
ejpam-5782	3	74	)	)	PUNCT
ejpam-5782	3	75	and	and	CCONJ
ejpam-5782	3	76	the	the	DET
ejpam-5782	3	77	mixed	mix	VERB
ejpam-5782	3	78	h(θ(µ	h(θ(µ	PROPN
ejpam-5782	3	79	,	,	PUNCT
ejpam-5782	3	80	ν))-open	ν))-open	ADJ
ejpam-5782	3	81	sets	set	NOUN
ejpam-5782	3	82	(	(	PUNCT
ejpam-5782	3	83	denoted	denote	VERB
ejpam-5782	3	84	as	as	ADP
ejpam-5782	3	85	h(θ(µ	h(θ(µ	NUM
ejpam-5782	3	86	,	,	PUNCT
ejpam-5782	3	87	ν))-open	ν))-open	ADJ
ejpam-5782	3	88	sets	set	NOUN
ejpam-5782	3	89	)	)	PUNCT
ejpam-5782	3	90	.	.	PUNCT
ejpam-5782	4	1	we	we	PRON
ejpam-5782	4	2	explore	explore	VERB
ejpam-5782	4	3	the	the	DET
ejpam-5782	4	4	interrelationships	interrelationship	NOUN
ejpam-5782	4	5	between	between	ADP
ejpam-5782	4	6	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	4	7	,	,	PUNCT
ejpam-5782	4	8	ν	ν	NOUN
ejpam-5782	4	9	)	)	PUNCT
ejpam-5782	4	10	,	,	PUNCT
ejpam-5782	4	11	γ∗	γ∗	NOUN
ejpam-5782	4	12	,	,	PUNCT
ejpam-5782	4	13	and	and	CCONJ
ejpam-5782	4	14	the	the	DET
ejpam-5782	4	15	µ-closure	µ-closure	NOUN
ejpam-5782	4	16	,	,	PUNCT
ejpam-5782	4	17	as	as	ADV
ejpam-5782	4	18	well	well	ADV
ejpam-5782	4	19	as	as	ADP
ejpam-5782	4	20	the	the	DET
ejpam-5782	4	21	connections	connection	NOUN
ejpam-5782	4	22	between	between	ADP
ejpam-5782	4	23	h(θ(µ	h(θ(µ	PROPN
ejpam-5782	4	24	,	,	PUNCT
ejpam-5782	4	25	ν))-open	ν))-open	ADJ
ejpam-5782	4	26	sets	set	NOUN
ejpam-5782	4	27	,	,	PUNCT
ejpam-5782	4	28	θ(µ	θ(µ	PROPN
ejpam-5782	4	29	,	,	PUNCT
ejpam-5782	4	30	ν)-open	ν)-open	PUNCT
ejpam-5782	4	31	sets	set	NOUN
ejpam-5782	4	32	,	,	PUNCT
ejpam-5782	4	33	and	and	CCONJ
ejpam-5782	4	34	µ-open	µ-open	NOUN
ejpam-5782	4	35	sets	set	NOUN
ejpam-5782	4	36	.	.	PUNCT
ejpam-5782	5	1	additionally	additionally	ADV
ejpam-5782	5	2	,	,	PUNCT
ejpam-5782	5	3	we	we	PRON
ejpam-5782	5	4	define	define	VERB
ejpam-5782	5	5	the	the	DET
ejpam-5782	5	6	concepts	concept	NOUN
ejpam-5782	5	7	of	of	ADP
ejpam-5782	5	8	hr(µ	hr(µ	NOUN
ejpam-5782	5	9	,	,	PUNCT
ejpam-5782	5	10	ν)-regular	ν)-regular	PUNCT
ejpam-5782	5	11	open	open	ADJ
ejpam-5782	5	12	sets	set	NOUN
ejpam-5782	5	13	and	and	CCONJ
ejpam-5782	5	14	h(µ	h(µ	PROPN
ejpam-5782	5	15	,	,	PUNCT
ejpam-5782	5	16	ν)-regular	ν)-regular	PUNCT
ejpam-5782	5	17	open	open	ADJ
ejpam-5782	5	18	sets	set	NOUN
ejpam-5782	5	19	.	.	PUNCT
ejpam-5782	6	1	finally	finally	ADV
ejpam-5782	6	2	,	,	PUNCT
ejpam-5782	6	3	we	we	PRON
ejpam-5782	6	4	examine	examine	VERB
ejpam-5782	6	5	properties	property	NOUN
ejpam-5782	6	6	and	and	CCONJ
ejpam-5782	6	7	characterizations	characterization	NOUN
ejpam-5782	6	8	of	of	ADP
ejpam-5782	6	9	h(θ(µ	h(θ(µ	PROPN
ejpam-5782	6	10	,	,	PUNCT
ejpam-5782	6	11	ν))-open	ν))-open	ADJ
ejpam-5782	6	12	sets	set	NOUN
ejpam-5782	6	13	in	in	ADP
ejpam-5782	6	14	terms	term	NOUN
ejpam-5782	6	15	of	of	ADP
ejpam-5782	6	16	hr(µ	hr(µ	NOUN
ejpam-5782	6	17	,	,	PUNCT
ejpam-5782	6	18	ν)-regular	ν)-regular	PUNCT
ejpam-5782	6	19	open	open	ADJ
ejpam-5782	6	20	sets	set	NOUN
ejpam-5782	6	21	and	and	CCONJ
ejpam-5782	6	22	h(µ	h(µ	PROPN
ejpam-5782	6	23	,	,	PUNCT
ejpam-5782	6	24	ν)-regular	ν)-regular	PUNCT
ejpam-5782	6	25	open	open	ADJ
ejpam-5782	6	26	sets	set	NOUN
ejpam-5782	6	27	.	.	PUNCT
ejpam-5782	7	1	2020	2020	NUM
ejpam-5782	7	2	mathematics	mathematic	NOUN
ejpam-5782	7	3	subject	subject	NOUN
ejpam-5782	7	4	classifications	classification	NOUN
ejpam-5782	7	5	:	:	PUNCT
ejpam-5782	7	6	54a05	54a05	NUM
ejpam-5782	7	7	,	,	PUNCT
ejpam-5782	7	8	54c08s	54c08s	PRON
ejpam-5782	7	9	key	key	ADJ
ejpam-5782	7	10	words	word	NOUN
ejpam-5782	7	11	and	and	CCONJ
ejpam-5782	7	12	phrases	phrase	NOUN
ejpam-5782	7	13	:	:	PUNCT
ejpam-5782	7	14	hereditary	hereditary	ADJ
ejpam-5782	7	15	classes	class	NOUN
ejpam-5782	7	16	h	h	NOUN
ejpam-5782	7	17	,	,	PUNCT
ejpam-5782	7	18	mixed	mixed	ADJ
ejpam-5782	7	19	operation	operation	NOUN
ejpam-5782	7	20	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	7	21	,	,	PUNCT
ejpam-5782	7	22	ν	ν	NOUN
ejpam-5782	7	23	)	)	PUNCT
ejpam-5782	7	24	,	,	PUNCT
ejpam-5782	7	25	mixed	mixed	ADJ
ejpam-5782	7	26	h	h	NOUN
ejpam-5782	7	27	(	(	PUNCT
ejpam-5782	7	28	θ(µ	θ(µ	PROPN
ejpam-5782	7	29	,	,	PUNCT
ejpam-5782	7	30	ν	ν	NOUN
ejpam-5782	7	31	)	)	PUNCT
ejpam-5782	7	32	)	)	PUNCT
ejpam-5782	7	33	open	open	ADJ
ejpam-5782	7	34	sets	set	NOUN
ejpam-5782	7	35	,	,	PUNCT
ejpam-5782	7	36	hr(µ	hr(µ	NOUN
ejpam-5782	7	37	,	,	PUNCT
ejpam-5782	7	38	ν)-regular	ν)-regular	PUNCT
ejpam-5782	7	39	open	open	ADJ
ejpam-5782	7	40	sets	set	NOUN
ejpam-5782	7	41	,	,	PUNCT
ejpam-5782	7	42	h(µ	h(µ	PROPN
ejpam-5782	7	43	,	,	PUNCT
ejpam-5782	7	44	ν)-regular	ν)-regular	ADJ
ejpam-5782	7	45	1	1	NUM
ejpam-5782	7	46	.	.	PUNCT
ejpam-5782	8	1	introduction	introduction	NOUN
ejpam-5782	8	2	á.	á.	PROPN
ejpam-5782	8	3	császár	császár	PROPN
ejpam-5782	8	4	formulated	formulate	VERB
ejpam-5782	8	5	the	the	DET
ejpam-5782	8	6	idea	idea	NOUN
ejpam-5782	8	7	of	of	ADP
ejpam-5782	8	8	generalized	generalized	ADJ
ejpam-5782	8	9	topology	topology	NOUN
ejpam-5782	8	10	and	and	CCONJ
ejpam-5782	8	11	generalized	generalize	VERB
ejpam-5782	8	12	open	open	ADJ
ejpam-5782	8	13	sets	set	NOUN
ejpam-5782	8	14	in	in	ADP
ejpam-5782	8	15	[	[	X
ejpam-5782	8	16	2	2	NUM
ejpam-5782	8	17	]	]	PUNCT
ejpam-5782	8	18	,	,	PUNCT
ejpam-5782	8	19	along	along	ADP
ejpam-5782	8	20	with	with	ADP
ejpam-5782	8	21	the	the	DET
ejpam-5782	8	22	notion	notion	NOUN
ejpam-5782	8	23	of	of	ADP
ejpam-5782	8	24	θ	θ	ADJ
ejpam-5782	8	25	-	-	ADJ
ejpam-5782	8	26	open	open	ADJ
ejpam-5782	8	27	sets	set	NOUN
ejpam-5782	8	28	and	and	CCONJ
ejpam-5782	8	29	their	their	PRON
ejpam-5782	8	30	properties	property	NOUN
ejpam-5782	8	31	.	.	PUNCT
ejpam-5782	9	1	for	for	ADP
ejpam-5782	9	2	further	further	ADJ
ejpam-5782	9	3	details	detail	NOUN
ejpam-5782	9	4	,	,	PUNCT
ejpam-5782	9	5	one	one	PRON
ejpam-5782	9	6	can	can	AUX
ejpam-5782	9	7	refer	refer	VERB
ejpam-5782	9	8	to	to	ADP
ejpam-5782	9	9	[	[	X
ejpam-5782	9	10	3–5	3–5	NOUN
ejpam-5782	9	11	]	]	PUNCT
ejpam-5782	9	12	.	.	PUNCT
ejpam-5782	10	1	in	in	ADP
ejpam-5782	10	2	[	[	X
ejpam-5782	10	3	6	6	NUM
ejpam-5782	10	4	]	]	PUNCT
ejpam-5782	10	5	,	,	PUNCT
ejpam-5782	10	6	he	he	PRON
ejpam-5782	10	7	also	also	ADV
ejpam-5782	10	8	introduced	introduce	VERB
ejpam-5782	10	9	the	the	DET
ejpam-5782	10	10	concept	concept	NOUN
ejpam-5782	10	11	of	of	ADP
ejpam-5782	10	12	hereditary	hereditary	ADJ
ejpam-5782	10	13	classes	class	NOUN
ejpam-5782	10	14	in	in	ADP
ejpam-5782	10	15	generalized	generalized	ADJ
ejpam-5782	10	16	topological	topological	ADJ
ejpam-5782	10	17	spaces	space	NOUN
ejpam-5782	10	18	.	.	PUNCT
ejpam-5782	11	1	specifically	specifically	ADV
ejpam-5782	11	2	,	,	PUNCT
ejpam-5782	11	3	a	a	DET
ejpam-5782	11	4	subset	subset	ADJ
ejpam-5782	11	5	h	h	NOUN
ejpam-5782	11	6	⊆	⊆	NUM
ejpam-5782	11	7	p(x	p(x	PROPN
ejpam-5782	11	8	)	)	PUNCT
ejpam-5782	11	9	(	(	PUNCT
ejpam-5782	11	10	where	where	SCONJ
ejpam-5782	11	11	p(x	p(x	NOUN
ejpam-5782	11	12	)	)	PUNCT
ejpam-5782	11	13	denotes	denote	VERB
ejpam-5782	11	14	the	the	DET
ejpam-5782	11	15	power	power	NOUN
ejpam-5782	11	16	set	set	NOUN
ejpam-5782	11	17	of	of	ADP
ejpam-5782	11	18	a	a	DET
ejpam-5782	11	19	non	non	ADJ
ejpam-5782	11	20	-	-	ADJ
ejpam-5782	11	21	empty	empty	ADJ
ejpam-5782	11	22	set	set	NOUN
ejpam-5782	11	23	x	x	NOUN
ejpam-5782	11	24	)	)	PUNCT
ejpam-5782	11	25	is	be	AUX
ejpam-5782	11	26	termed	term	VERB
ejpam-5782	11	27	a	a	DET
ejpam-5782	11	28	hereditary	hereditary	ADJ
ejpam-5782	11	29	class	class	NOUN
ejpam-5782	11	30	on	on	ADP
ejpam-5782	11	31	x	x	SYM
ejpam-5782	11	32	if	if	SCONJ
ejpam-5782	11	33	it	it	PRON
ejpam-5782	11	34	satisfies	satisfy	VERB
ejpam-5782	11	35	the	the	DET
ejpam-5782	11	36	condition	condition	NOUN
ejpam-5782	11	37	that	that	SCONJ
ejpam-5782	11	38	for	for	ADP
ejpam-5782	11	39	any	any	DET
ejpam-5782	11	40	a	a	DET
ejpam-5782	11	41	⊆	⊆	NUM
ejpam-5782	11	42	b	b	NOUN
ejpam-5782	11	43	and	and	CCONJ
ejpam-5782	11	44	b	b	PROPN
ejpam-5782	11	45	∈	∈	PROPN
ejpam-5782	11	46	h	h	NOUN
ejpam-5782	11	47	,	,	PUNCT
ejpam-5782	11	48	it	it	PRON
ejpam-5782	11	49	follows	follow	VERB
ejpam-5782	11	50	that	that	SCONJ
ejpam-5782	11	51	a	a	DET
ejpam-5782	11	52	∈	∈	PROPN
ejpam-5782	11	53	h.	h.	NOUN
ejpam-5782	11	54	building	building	NOUN
ejpam-5782	11	55	on	on	ADP
ejpam-5782	11	56	these	these	DET
ejpam-5782	11	57	foundations	foundation	NOUN
ejpam-5782	11	58	of	of	ADP
ejpam-5782	11	59	generalized	generalized	ADJ
ejpam-5782	11	60	topology	topology	NOUN
ejpam-5782	11	61	and	and	CCONJ
ejpam-5782	11	62	hereditary	hereditary	ADJ
ejpam-5782	11	63	classes	class	NOUN
ejpam-5782	11	64	,	,	PUNCT
ejpam-5782	11	65	authors	author	NOUN
ejpam-5782	11	66	in	in	ADP
ejpam-5782	11	67	[	[	X
ejpam-5782	11	68	1	1	NUM
ejpam-5782	11	69	]	]	PUNCT
ejpam-5782	11	70	introduced	introduce	VERB
ejpam-5782	11	71	the	the	DET
ejpam-5782	11	72	concepts	concept	NOUN
ejpam-5782	11	73	of	of	ADP
ejpam-5782	11	74	h(θ)-open	h(θ)-open	NOUN
ejpam-5782	11	75	sets	set	NOUN
ejpam-5782	11	76	and	and	CCONJ
ejpam-5782	11	77	the	the	DET
ejpam-5782	11	78	operator	operator	NOUN
ejpam-5782	11	79	γ∗.	γ∗.	ADV
ejpam-5782	11	80	∗corresponding	∗corresponde	VERB
ejpam-5782	11	81	author	author	NOUN
ejpam-5782	11	82	.	.	PUNCT
ejpam-5782	12	1	doi	doi	NOUN
ejpam-5782	12	2	:	:	PUNCT
ejpam-5782	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5782	https://doi.org/10.29020/nybg.ejpam.v18i2.5782	NOUN
ejpam-5782	12	4	email	email	NOUN
ejpam-5782	12	5	addresses	address	NOUN
ejpam-5782	12	6	:	:	PUNCT
ejpam-5782	12	7	f.alsharari@ju.edu.sa	f.alsharari@ju.edu.sa	PROPN
ejpam-5782	12	8	(	(	PUNCT
ejpam-5782	12	9	f.	f.	PROPN
ejpam-5782	12	10	alsharari	alsharari	PROPN
ejpam-5782	12	11	)	)	PUNCT
ejpam-5782	12	12	,	,	PUNCT
ejpam-5782	12	13	cahis82@gmail.com	cahis82@gmail.com	X
ejpam-5782	12	14	(	(	PUNCT
ejpam-5782	12	15	a.	a.	NOUN
ejpam-5782	12	16	qahis	qahis	PROPN
ejpam-5782	12	17	)	)	PUNCT
ejpam-5782	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5782	13	1	1	1	NUM
ejpam-5782	13	2	copyright	copyright	NOUN
ejpam-5782	13	3	:	:	PUNCT
ejpam-5782	13	4	©	©	PROPN
ejpam-5782	13	5	2025	2025	NUM
ejpam-5782	13	6	the	the	DET
ejpam-5782	13	7	author(s	author(s	NOUN
ejpam-5782	13	8	)	)	PUNCT
ejpam-5782	13	9	.	.	PUNCT
ejpam-5782	14	1	(	(	PUNCT
ejpam-5782	14	2	cc	cc	NOUN
ejpam-5782	14	3	by	by	ADP
ejpam-5782	14	4	-	-	PUNCT
ejpam-5782	14	5	nc	nc	PROPN
ejpam-5782	14	6	4.0	4.0	NUM
ejpam-5782	14	7	)	)	PUNCT
ejpam-5782	14	8	f.	f.	PROPN
ejpam-5782	14	9	alsharari	alsharari	PROPN
ejpam-5782	14	10	,	,	PUNCT
ejpam-5782	14	11	a.	a.	PROPN
ejpam-5782	14	12	qahis	qahis	PROPN
ejpam-5782	14	13	/	/	SYM
ejpam-5782	14	14	eur	eur	PROPN
ejpam-5782	14	15	.	.	PUNCT
ejpam-5782	15	1	j.	j.	PROPN
ejpam-5782	15	2	pure	pure	PROPN
ejpam-5782	15	3	appl	appl	PROPN
ejpam-5782	15	4	.	.	PROPN
ejpam-5782	15	5	math	math	PROPN
ejpam-5782	15	6	,	,	PUNCT
ejpam-5782	15	7	18	18	NUM
ejpam-5782	15	8	(	(	PUNCT
ejpam-5782	15	9	2	2	NUM
ejpam-5782	15	10	)	)	PUNCT
ejpam-5782	15	11	(	(	PUNCT
ejpam-5782	15	12	2025	2025	NUM
ejpam-5782	15	13	)	)	PUNCT
ejpam-5782	15	14	,	,	PUNCT
ejpam-5782	15	15	5782	5782	NUM
ejpam-5782	15	16	2	2	NUM
ejpam-5782	15	17	of	of	ADP
ejpam-5782	15	18	10	10	NUM
ejpam-5782	15	19	in	in	ADP
ejpam-5782	15	20	this	this	DET
ejpam-5782	15	21	study	study	NOUN
ejpam-5782	16	1	,	,	PUNCT
ejpam-5782	16	2	we	we	PRON
ejpam-5782	16	3	extend	extend	VERB
ejpam-5782	16	4	these	these	DET
ejpam-5782	16	5	ideas	idea	NOUN
ejpam-5782	16	6	by	by	ADP
ejpam-5782	16	7	examining	examine	VERB
ejpam-5782	16	8	two	two	NUM
ejpam-5782	16	9	generalized	generalized	ADJ
ejpam-5782	16	10	topologies	topology	NOUN
ejpam-5782	16	11	,	,	PUNCT
ejpam-5782	16	12	denoted	denote	VERB
ejpam-5782	16	13	as	as	ADP
ejpam-5782	16	14	µ	µ	NOUN
ejpam-5782	16	15	and	and	CCONJ
ejpam-5782	16	16	ν	ν	NOUN
ejpam-5782	16	17	,	,	PUNCT
ejpam-5782	16	18	within	within	ADP
ejpam-5782	16	19	the	the	DET
ejpam-5782	16	20	framework	framework	NOUN
ejpam-5782	16	21	of	of	ADP
ejpam-5782	16	22	a	a	DET
ejpam-5782	16	23	hereditary	hereditary	ADJ
ejpam-5782	16	24	class	class	NOUN
ejpam-5782	16	25	h.	h.	NOUN
ejpam-5782	16	26	we	we	PRON
ejpam-5782	16	27	introduce	introduce	VERB
ejpam-5782	16	28	and	and	CCONJ
ejpam-5782	16	29	investigate	investigate	VERB
ejpam-5782	16	30	the	the	DET
ejpam-5782	16	31	concepts	concept	NOUN
ejpam-5782	16	32	of	of	ADP
ejpam-5782	16	33	the	the	DET
ejpam-5782	16	34	mixed	mixed	ADJ
ejpam-5782	16	35	operator	operator	NOUN
ejpam-5782	16	36	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	16	37	,	,	PUNCT
ejpam-5782	16	38	ν	ν	NOUN
ejpam-5782	16	39	)	)	PUNCT
ejpam-5782	16	40	(	(	PUNCT
ejpam-5782	16	41	denoted	denote	VERB
ejpam-5782	16	42	briefly	briefly	ADV
ejpam-5782	16	43	as	as	ADP
ejpam-5782	16	44	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	16	45	,	,	PUNCT
ejpam-5782	16	46	ν	ν	NOUN
ejpam-5782	16	47	)	)	PUNCT
ejpam-5782	16	48	)	)	PUNCT
ejpam-5782	16	49	and	and	CCONJ
ejpam-5782	16	50	mixed	mix	VERB
ejpam-5782	16	51	h(θ(µ	h(θ(µ	VERB
ejpam-5782	16	52	,	,	PUNCT
ejpam-5782	16	53	ν))open	ν))open	ADJ
ejpam-5782	16	54	sets	set	NOUN
ejpam-5782	16	55	(	(	PUNCT
ejpam-5782	16	56	referred	refer	VERB
ejpam-5782	16	57	to	to	ADP
ejpam-5782	16	58	as	as	ADP
ejpam-5782	16	59	h(θ(µ	h(θ(µ	VERB
ejpam-5782	16	60	,	,	PUNCT
ejpam-5782	16	61	ν))-open	ν))-open	ADJ
ejpam-5782	16	62	sets	set	NOUN
ejpam-5782	16	63	)	)	PUNCT
ejpam-5782	16	64	.	.	PUNCT
ejpam-5782	17	1	our	our	PRON
ejpam-5782	17	2	exploration	exploration	NOUN
ejpam-5782	17	3	includes	include	VERB
ejpam-5782	17	4	a	a	DET
ejpam-5782	17	5	detailed	detailed	ADJ
ejpam-5782	17	6	study	study	NOUN
ejpam-5782	17	7	of	of	ADP
ejpam-5782	17	8	their	their	PRON
ejpam-5782	17	9	properties	property	NOUN
ejpam-5782	17	10	and	and	CCONJ
ejpam-5782	17	11	the	the	DET
ejpam-5782	17	12	relationships	relationship	NOUN
ejpam-5782	17	13	between	between	ADP
ejpam-5782	17	14	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	17	15	,	,	PUNCT
ejpam-5782	17	16	ν	ν	NOUN
ejpam-5782	17	17	)	)	PUNCT
ejpam-5782	17	18	,	,	PUNCT
ejpam-5782	17	19	the	the	DET
ejpam-5782	17	20	operator	operator	NOUN
ejpam-5782	17	21	γ∗	γ∗	NOUN
ejpam-5782	17	22	,	,	PUNCT
ejpam-5782	17	23	and	and	CCONJ
ejpam-5782	17	24	the	the	DET
ejpam-5782	17	25	µclosure	µclosure	NOUN
ejpam-5782	17	26	.	.	PUNCT
ejpam-5782	18	1	in	in	ADP
ejpam-5782	18	2	addition	addition	NOUN
ejpam-5782	18	3	,	,	PUNCT
ejpam-5782	18	4	we	we	PRON
ejpam-5782	18	5	examine	examine	VERB
ejpam-5782	18	6	the	the	DET
ejpam-5782	18	7	interconnections	interconnection	NOUN
ejpam-5782	18	8	between	between	ADP
ejpam-5782	18	9	sets	set	NOUN
ejpam-5782	18	10	that	that	PRON
ejpam-5782	18	11	are	be	AUX
ejpam-5782	18	12	h(θ(µ	h(θ(µ	VERB
ejpam-5782	18	13	,	,	PUNCT
ejpam-5782	18	14	ν))open	ν))open	NOUN
ejpam-5782	18	15	,	,	PUNCT
ejpam-5782	18	16	θ(µ	θ(µ	PROPN
ejpam-5782	18	17	,	,	PUNCT
ejpam-5782	18	18	ν)-open	ν)-open	NOUN
ejpam-5782	18	19	,	,	PUNCT
ejpam-5782	18	20	and	and	CCONJ
ejpam-5782	18	21	µ-open	µ-open	VERB
ejpam-5782	18	22	.	.	PUNCT
ejpam-5782	19	1	we	we	PRON
ejpam-5782	19	2	also	also	ADV
ejpam-5782	19	3	present	present	VERB
ejpam-5782	19	4	various	various	ADJ
ejpam-5782	19	5	properties	property	NOUN
ejpam-5782	19	6	and	and	CCONJ
ejpam-5782	19	7	characterizations	characterization	NOUN
ejpam-5782	19	8	of	of	ADP
ejpam-5782	19	9	these	these	DET
ejpam-5782	19	10	concepts	concept	NOUN
ejpam-5782	19	11	in	in	ADP
ejpam-5782	19	12	terms	term	NOUN
ejpam-5782	19	13	of	of	ADP
ejpam-5782	19	14	hr(µ	hr(µ	NOUN
ejpam-5782	19	15	,	,	PUNCT
ejpam-5782	19	16	ν)-regular	ν)-regular	PUNCT
ejpam-5782	19	17	open	open	ADJ
ejpam-5782	19	18	sets	set	NOUN
ejpam-5782	19	19	and	and	CCONJ
ejpam-5782	19	20	h(µ	h(µ	PROPN
ejpam-5782	19	21	,	,	PUNCT
ejpam-5782	19	22	ν)-regular	ν)-regular	ADJ
ejpam-5782	19	23	sets	set	NOUN
ejpam-5782	19	24	.	.	PUNCT
ejpam-5782	20	1	2	2	X
ejpam-5782	20	2	.	.	X
ejpam-5782	20	3	preliminaries	preliminary	NOUN
ejpam-5782	20	4	let	let	VERB
ejpam-5782	20	5	x	x	PUNCT
ejpam-5782	20	6	̸=	̸=	PROPN
ejpam-5782	20	7	∅	∅	NOUN
ejpam-5782	20	8	and	and	CCONJ
ejpam-5782	20	9	let	let	VERB
ejpam-5782	20	10	p(x	p(x	PROPN
ejpam-5782	20	11	)	)	PUNCT
ejpam-5782	20	12	be	be	AUX
ejpam-5782	20	13	its	its	PRON
ejpam-5782	20	14	power	power	NOUN
ejpam-5782	20	15	set	set	NOUN
ejpam-5782	20	16	.	.	PUNCT
ejpam-5782	21	1	a	a	DET
ejpam-5782	21	2	family	family	NOUN
ejpam-5782	21	3	µ	µ	ADJ
ejpam-5782	21	4	⊆	⊆	NUM
ejpam-5782	21	5	p(x	p(x	NOUN
ejpam-5782	21	6	)	)	PUNCT
ejpam-5782	21	7	is	be	AUX
ejpam-5782	21	8	called	call	VERB
ejpam-5782	21	9	a	a	DET
ejpam-5782	21	10	generalized	generalized	ADJ
ejpam-5782	21	11	topology	topology	NOUN
ejpam-5782	21	12	(	(	PUNCT
ejpam-5782	21	13	gt	gt	PROPN
ejpam-5782	21	14	)	)	PUNCT
ejpam-5782	21	15	on	on	ADP
ejpam-5782	21	16	x	x	SYM
ejpam-5782	21	17	if	if	SCONJ
ejpam-5782	21	18	:	:	PUNCT
ejpam-5782	21	19	∅	∅	NOUN
ejpam-5782	21	20	∈	∈	NOUN
ejpam-5782	21	21	µ,⋃	µ,⋃	DET
ejpam-5782	21	22	i∈i	i∈i	ADJ
ejpam-5782	21	23	ui	ui	PROPN
ejpam-5782	21	24	∈	∈	PROPN
ejpam-5782	21	25	µ	µ	PROPN
ejpam-5782	21	26	for	for	ADP
ejpam-5782	21	27	any	any	DET
ejpam-5782	21	28	collection	collection	NOUN
ejpam-5782	21	29	{	{	PUNCT
ejpam-5782	21	30	ui}i∈i	ui}i∈i	NUM
ejpam-5782	21	31	⊆	⊆	NUM
ejpam-5782	21	32	µ.	µ.	NOUN
ejpam-5782	21	33	this	this	DET
ejpam-5782	21	34	concept	concept	NOUN
ejpam-5782	21	35	was	be	AUX
ejpam-5782	21	36	first	first	ADV
ejpam-5782	21	37	introduced	introduce	VERB
ejpam-5782	21	38	by	by	ADP
ejpam-5782	21	39	á.	á.	PROPN
ejpam-5782	21	40	császár	császár	PROPN
ejpam-5782	21	41	in	in	ADP
ejpam-5782	21	42	[	[	X
ejpam-5782	21	43	2	2	NUM
ejpam-5782	21	44	]	]	PUNCT
ejpam-5782	21	45	.	.	PUNCT
ejpam-5782	22	1	a	a	DET
ejpam-5782	22	2	pair	pair	NOUN
ejpam-5782	22	3	(	(	PUNCT
ejpam-5782	22	4	x,µ	x,µ	NOUN
ejpam-5782	22	5	)	)	PUNCT
ejpam-5782	22	6	is	be	AUX
ejpam-5782	22	7	then	then	ADV
ejpam-5782	22	8	referred	refer	VERB
ejpam-5782	22	9	to	to	ADP
ejpam-5782	22	10	as	as	ADP
ejpam-5782	22	11	a	a	DET
ejpam-5782	22	12	generalized	generalized	ADJ
ejpam-5782	22	13	topological	topological	ADJ
ejpam-5782	22	14	space	space	NOUN
ejpam-5782	22	15	(	(	PUNCT
ejpam-5782	22	16	gts	gts	NOUN
ejpam-5782	22	17	)	)	PUNCT
ejpam-5782	22	18	on	on	ADP
ejpam-5782	22	19	x.	x.	NOUN
ejpam-5782	22	20	the	the	DET
ejpam-5782	22	21	elements	element	NOUN
ejpam-5782	22	22	of	of	ADP
ejpam-5782	22	23	µ	µ	NOUN
ejpam-5782	22	24	are	be	AUX
ejpam-5782	22	25	called	call	VERB
ejpam-5782	22	26	µ-open	µ-open	NOUN
ejpam-5782	22	27	sets	set	NOUN
ejpam-5782	22	28	,	,	PUNCT
ejpam-5782	22	29	while	while	SCONJ
ejpam-5782	22	30	their	their	PRON
ejpam-5782	22	31	complements	complement	NOUN
ejpam-5782	22	32	are	be	AUX
ejpam-5782	22	33	called	call	VERB
ejpam-5782	22	34	µ-closed	µ-close	VERB
ejpam-5782	22	35	sets	set	NOUN
ejpam-5782	22	36	.	.	PUNCT
ejpam-5782	23	1	the	the	DET
ejpam-5782	23	2	union	union	NOUN
ejpam-5782	23	3	of	of	ADP
ejpam-5782	23	4	all	all	DET
ejpam-5782	23	5	elements	element	NOUN
ejpam-5782	23	6	of	of	ADP
ejpam-5782	23	7	µ	µ	NOUN
ejpam-5782	23	8	is	be	AUX
ejpam-5782	23	9	denoted	denote	VERB
ejpam-5782	23	10	by	by	ADP
ejpam-5782	23	11	mµ	mµ	INTJ
ejpam-5782	23	12	,	,	PUNCT
ejpam-5782	23	13	as	as	SCONJ
ejpam-5782	23	14	stated	state	VERB
ejpam-5782	23	15	in	in	ADP
ejpam-5782	23	16	[	[	X
ejpam-5782	23	17	7	7	NUM
ejpam-5782	23	18	]	]	PUNCT
ejpam-5782	23	19	.	.	PUNCT
ejpam-5782	24	1	a	a	DET
ejpam-5782	24	2	gts	gts	NOUN
ejpam-5782	24	3	(	(	PUNCT
ejpam-5782	24	4	x,µ	x,µ	NOUN
ejpam-5782	24	5	)	)	PUNCT
ejpam-5782	24	6	is	be	AUX
ejpam-5782	24	7	is	be	AUX
ejpam-5782	24	8	said	say	VERB
ejpam-5782	24	9	to	to	PART
ejpam-5782	24	10	be	be	AUX
ejpam-5782	24	11	strong	strong	ADJ
ejpam-5782	24	12	[	[	X
ejpam-5782	24	13	8	8	NUM
ejpam-5782	24	14	]	]	X
ejpam-5782	24	15	if	if	SCONJ
ejpam-5782	24	16	x	x	PROPN
ejpam-5782	24	17	∈	∈	PROPN
ejpam-5782	24	18	µ.	µ.	NOUN
ejpam-5782	24	19	for	for	ADP
ejpam-5782	24	20	a	a	DET
ejpam-5782	24	21	subset	subset	NOUN
ejpam-5782	24	22	a	a	PRON
ejpam-5782	24	23	of	of	ADP
ejpam-5782	24	24	a	a	DET
ejpam-5782	24	25	gts	gts	NOUN
ejpam-5782	24	26	(	(	PUNCT
ejpam-5782	24	27	x,µ	x,µ	NOUN
ejpam-5782	24	28	)	)	PUNCT
ejpam-5782	24	29	,	,	PUNCT
ejpam-5782	24	30	the	the	DET
ejpam-5782	24	31	µ-closure	µ-closure	NOUN
ejpam-5782	24	32	of	of	ADP
ejpam-5782	24	33	a	a	PRON
ejpam-5782	24	34	,	,	PUNCT
ejpam-5782	24	35	denoted	denote	VERB
ejpam-5782	24	36	cµ(a	cµ(a	PROPN
ejpam-5782	24	37	)	)	PUNCT
ejpam-5782	24	38	,	,	PUNCT
ejpam-5782	24	39	is	be	AUX
ejpam-5782	24	40	defined	define	VERB
ejpam-5782	24	41	as	as	ADP
ejpam-5782	24	42	the	the	DET
ejpam-5782	24	43	intersection	intersection	NOUN
ejpam-5782	24	44	of	of	ADP
ejpam-5782	24	45	all	all	DET
ejpam-5782	24	46	µ-closed	µ-close	VERB
ejpam-5782	24	47	sets	set	NOUN
ejpam-5782	24	48	that	that	PRON
ejpam-5782	24	49	contain	contain	VERB
ejpam-5782	24	50	a.	a.	NOUN
ejpam-5782	24	51	the	the	DET
ejpam-5782	24	52	µ-interior	µ-interior	NOUN
ejpam-5782	24	53	of	of	ADP
ejpam-5782	24	54	a	a	PRON
ejpam-5782	24	55	,	,	PUNCT
ejpam-5782	24	56	denoted	denote	VERB
ejpam-5782	24	57	iµ(a	iµ(a	PROPN
ejpam-5782	24	58	)	)	PUNCT
ejpam-5782	24	59	,	,	PUNCT
ejpam-5782	24	60	is	be	AUX
ejpam-5782	24	61	the	the	DET
ejpam-5782	24	62	union	union	NOUN
ejpam-5782	24	63	of	of	ADP
ejpam-5782	24	64	all	all	DET
ejpam-5782	24	65	µ-open	µ-open	PROPN
ejpam-5782	24	66	sets	set	NOUN
ejpam-5782	24	67	that	that	PRON
ejpam-5782	24	68	are	be	AUX
ejpam-5782	24	69	contained	contain	VERB
ejpam-5782	24	70	within	within	ADP
ejpam-5782	24	71	a	a	DET
ejpam-5782	24	72	(	(	PUNCT
ejpam-5782	24	73	see	see	PROPN
ejpam-5782	24	74	[	[	X
ejpam-5782	24	75	2	2	NUM
ejpam-5782	24	76	,	,	PUNCT
ejpam-5782	24	77	7	7	NUM
ejpam-5782	24	78	]	]	NUM
ejpam-5782	24	79	)	)	PUNCT
ejpam-5782	24	80	.	.	PUNCT
ejpam-5782	25	1	now	now	ADV
ejpam-5782	25	2	,	,	PUNCT
ejpam-5782	25	3	considering	consider	VERB
ejpam-5782	25	4	a	a	DET
ejpam-5782	25	5	hereditary	hereditary	ADJ
ejpam-5782	25	6	class	class	NOUN
ejpam-5782	25	7	h	h	NOUN
ejpam-5782	25	8	,	,	PUNCT
ejpam-5782	25	9	an	an	DET
ejpam-5782	25	10	operator	operator	NOUN
ejpam-5782	25	11	(	(	PUNCT
ejpam-5782	25	12	)	)	PUNCT
ejpam-5782	25	13	∗	∗	NOUN
ejpam-5782	25	14	:	:	PUNCT
ejpam-5782	25	15	p(x	p(x	PROPN
ejpam-5782	25	16	)	)	PUNCT
ejpam-5782	25	17	→	→	SYM
ejpam-5782	25	18	p(x	p(x	PROPN
ejpam-5782	25	19	)	)	PUNCT
ejpam-5782	25	20	was	be	AUX
ejpam-5782	25	21	introduced	introduce	VERB
ejpam-5782	25	22	in	in	ADP
ejpam-5782	25	23	[	[	X
ejpam-5782	25	24	3	3	NUM
ejpam-5782	25	25	]	]	PUNCT
ejpam-5782	25	26	.	.	PUNCT
ejpam-5782	26	1	specifically	specifically	ADV
ejpam-5782	26	2	,	,	PUNCT
ejpam-5782	26	3	c∗	c∗	NOUN
ejpam-5782	26	4	:	:	PUNCT
ejpam-5782	26	5	p(x	p(x	PROPN
ejpam-5782	26	6	)	)	PUNCT
ejpam-5782	26	7	→	→	SYM
ejpam-5782	26	8	p(x	p(x	PROPN
ejpam-5782	26	9	)	)	PUNCT
ejpam-5782	26	10	is	be	AUX
ejpam-5782	26	11	defined	define	VERB
ejpam-5782	26	12	using	use	VERB
ejpam-5782	26	13	(	(	PUNCT
ejpam-5782	26	14	)	)	PUNCT
ejpam-5782	26	15	∗	∗	NOUN
ejpam-5782	26	16	by	by	ADP
ejpam-5782	26	17	c∗(a	c∗(a	PROPN
ejpam-5782	26	18	)	)	PUNCT
ejpam-5782	26	19	=	=	NOUN
ejpam-5782	27	1	a	a	DET
ejpam-5782	27	2	∪	∪	ADJ
ejpam-5782	27	3	a∗	a∗	NOUN
ejpam-5782	27	4	,	,	PUNCT
ejpam-5782	27	5	where	where	SCONJ
ejpam-5782	27	6	a∗	a∗	NOUN
ejpam-5782	27	7	=	=	SYM
ejpam-5782	27	8	{	{	PUNCT
ejpam-5782	27	9	x	x	SYM
ejpam-5782	27	10	∈	∈	PROPN
ejpam-5782	27	11	x	x	PUNCT
ejpam-5782	27	12	|	|	ADV
ejpam-5782	27	13	a	a	DET
ejpam-5782	27	14	∩	∩	NOUN
ejpam-5782	27	15	m	m	NOUN
ejpam-5782	27	16	/∈	/∈	NOUN
ejpam-5782	27	17	h	h	NOUN
ejpam-5782	27	18	,	,	PUNCT
ejpam-5782	27	19	∀m	∀m	PROPN
ejpam-5782	27	20	∈	∈	PROPN
ejpam-5782	27	21	µ	µ	NOUN
ejpam-5782	27	22	,	,	PUNCT
ejpam-5782	27	23	x	x	SYM
ejpam-5782	27	24	∈	∈	PROPN
ejpam-5782	27	25	m	m	NOUN
ejpam-5782	27	26	}	}	PUNCT
ejpam-5782	27	27	.	.	PUNCT
ejpam-5782	28	1	here	here	ADV
ejpam-5782	28	2	,	,	PUNCT
ejpam-5782	28	3	x	x	PROPN
ejpam-5782	28	4	/∈	/∈	PUNCT
ejpam-5782	28	5	a∗	a∗	PROPN
ejpam-5782	28	6	if	if	SCONJ
ejpam-5782	28	7	and	and	CCONJ
ejpam-5782	28	8	only	only	ADV
ejpam-5782	28	9	if	if	SCONJ
ejpam-5782	28	10	there	there	PRON
ejpam-5782	28	11	exists	exist	VERB
ejpam-5782	28	12	m	m	VERB
ejpam-5782	28	13	∈	∈	PROPN
ejpam-5782	28	14	µ	µ	PRON
ejpam-5782	28	15	such	such	ADJ
ejpam-5782	28	16	that	that	SCONJ
ejpam-5782	28	17	x	x	SYM
ejpam-5782	28	18	∈	∈	PROPN
ejpam-5782	28	19	m	m	NOUN
ejpam-5782	28	20	and	and	CCONJ
ejpam-5782	28	21	m	m	PROPN
ejpam-5782	28	22	∩a	∩a	PROPN
ejpam-5782	28	23	∈	∈	PROPN
ejpam-5782	28	24	h.	h.	PROPN
ejpam-5782	28	25	recalling	recall	VERB
ejpam-5782	28	26	definitions	definition	NOUN
ejpam-5782	28	27	and	and	CCONJ
ejpam-5782	28	28	notations	notation	NOUN
ejpam-5782	28	29	from	from	ADP
ejpam-5782	28	30	[	[	X
ejpam-5782	28	31	3	3	NUM
ejpam-5782	28	32	]	]	PUNCT
ejpam-5782	28	33	,	,	PUNCT
ejpam-5782	28	34	let	let	VERB
ejpam-5782	28	35	µ	µ	X
ejpam-5782	28	36	be	be	AUX
ejpam-5782	28	37	a	a	DET
ejpam-5782	28	38	gt	gt	PROPN
ejpam-5782	28	39	on	on	ADP
ejpam-5782	28	40	x	x	PUNCT
ejpam-5782	28	41	and	and	CCONJ
ejpam-5782	28	42	p(x	p(x	PROPN
ejpam-5782	28	43	)	)	PUNCT
ejpam-5782	28	44	be	be	VERB
ejpam-5782	28	45	the	the	DET
ejpam-5782	28	46	power	power	NOUN
ejpam-5782	28	47	set	set	NOUN
ejpam-5782	28	48	of	of	ADP
ejpam-5782	28	49	x.	x.	NOUN
ejpam-5782	28	50	a	a	DET
ejpam-5782	28	51	collection	collection	NOUN
ejpam-5782	28	52	θ	θ	PROPN
ejpam-5782	28	53	⊆	⊆	NUM
ejpam-5782	28	54	p(x	p(x	PROPN
ejpam-5782	28	55	)	)	PUNCT
ejpam-5782	28	56	is	be	AUX
ejpam-5782	28	57	defined	define	VERB
ejpam-5782	28	58	as	as	SCONJ
ejpam-5782	28	59	follows	follow	VERB
ejpam-5782	28	60	:	:	PUNCT
ejpam-5782	28	61	a	a	DET
ejpam-5782	28	62	∈	∈	ADJ
ejpam-5782	28	63	θ	θ	NOUN
ejpam-5782	28	64	if	if	SCONJ
ejpam-5782	28	65	for	for	ADP
ejpam-5782	28	66	each	each	DET
ejpam-5782	28	67	x	x	SYM
ejpam-5782	28	68	∈	∈	PROPN
ejpam-5782	28	69	a	a	PRON
ejpam-5782	28	70	,	,	PUNCT
ejpam-5782	28	71	there	there	PRON
ejpam-5782	28	72	exists	exist	VERB
ejpam-5782	28	73	m	m	VERB
ejpam-5782	28	74	∈	∈	PROPN
ejpam-5782	28	75	µ	µ	X
ejpam-5782	28	76	containing	contain	VERB
ejpam-5782	28	77	x	x	PUNCT
ejpam-5782	28	78	such	such	ADJ
ejpam-5782	28	79	that	that	SCONJ
ejpam-5782	28	80	m	m	PROPN
ejpam-5782	28	81	⊆	⊆	NUM
ejpam-5782	28	82	cµ(m	cµ(m	NOUN
ejpam-5782	28	83	)	)	PUNCT
ejpam-5782	28	84	⊆	⊆	NUM
ejpam-5782	28	85	a.	a.	NOUN
ejpam-5782	28	86	the	the	DET
ejpam-5782	28	87	family	family	NOUN
ejpam-5782	28	88	θ	θ	PROPN
ejpam-5782	28	89	is	be	AUX
ejpam-5782	28	90	a	a	DET
ejpam-5782	28	91	gt	gt	PROPN
ejpam-5782	28	92	on	on	ADP
ejpam-5782	28	93	x	x	PUNCT
ejpam-5782	28	94	included	include	VERB
ejpam-5782	28	95	in	in	ADP
ejpam-5782	28	96	µ	µ	NUM
ejpam-5782	28	97	,	,	PUNCT
ejpam-5782	28	98	and	and	CCONJ
ejpam-5782	28	99	the	the	DET
ejpam-5782	28	100	elements	element	NOUN
ejpam-5782	28	101	of	of	ADP
ejpam-5782	28	102	θ	θ	PROPN
ejpam-5782	28	103	are	be	AUX
ejpam-5782	28	104	θ(µ)-open	θ(µ)-open	PROPN
ejpam-5782	28	105	sets	set	NOUN
ejpam-5782	28	106	,	,	PUNCT
ejpam-5782	28	107	with	with	ADP
ejpam-5782	28	108	complements	complement	NOUN
ejpam-5782	28	109	called	call	VERB
ejpam-5782	28	110	θ(µ)-closed	θ(µ)-close	VERB
ejpam-5782	28	111	sets	set	NOUN
ejpam-5782	28	112	.	.	PUNCT
ejpam-5782	29	1	for	for	ADP
ejpam-5782	29	2	a	a	DET
ejpam-5782	29	3	⊆	⊆	NUM
ejpam-5782	29	4	x	x	NOUN
ejpam-5782	29	5	,	,	PUNCT
ejpam-5782	29	6	the	the	DET
ejpam-5782	29	7	operation	operation	NOUN
ejpam-5782	29	8	γθ	γθ	NOUN
ejpam-5782	29	9	:	:	PUNCT
ejpam-5782	29	10	p(x	p(x	PROPN
ejpam-5782	29	11	)	)	PUNCT
ejpam-5782	29	12	→	→	SYM
ejpam-5782	29	13	p(x	p(x	PROPN
ejpam-5782	29	14	)	)	PUNCT
ejpam-5782	29	15	is	be	AUX
ejpam-5782	29	16	defined	define	VERB
ejpam-5782	29	17	in	in	ADP
ejpam-5782	29	18	[	[	X
ejpam-5782	29	19	3	3	NUM
ejpam-5782	29	20	]	]	PUNCT
ejpam-5782	29	21	,	,	PUNCT
ejpam-5782	29	22	by	by	ADP
ejpam-5782	29	23	γθ(a	γθ(a	NUM
ejpam-5782	29	24	)	)	PUNCT
ejpam-5782	30	1	=	=	PRON
ejpam-5782	30	2	{	{	PUNCT
ejpam-5782	30	3	x	x	PUNCT
ejpam-5782	30	4	∈	∈	PROPN
ejpam-5782	30	5	x	x	X
ejpam-5782	30	6	|	|	NOUN
ejpam-5782	30	7	cµ(m	cµ(m	NOUN
ejpam-5782	30	8	)	)	PUNCT
ejpam-5782	30	9	∩a	∩a	PROPN
ejpam-5782	30	10	̸=	̸=	PROPN
ejpam-5782	30	11	∅	∅	NOUN
ejpam-5782	30	12	,	,	PUNCT
ejpam-5782	30	13	∀m	∀m	PROPN
ejpam-5782	30	14	∈	∈	PROPN
ejpam-5782	30	15	µ	µ	NOUN
ejpam-5782	30	16	,	,	PUNCT
ejpam-5782	30	17	x	x	SYM
ejpam-5782	30	18	∈	∈	PROPN
ejpam-5782	30	19	m	m	NOUN
ejpam-5782	30	20	}	}	PUNCT
ejpam-5782	30	21	.	.	PUNCT
ejpam-5782	31	1	kim	kim	PROPN
ejpam-5782	31	2	and	and	CCONJ
ejpam-5782	31	3	min	min	PROPN
ejpam-5782	31	4	in	in	ADP
ejpam-5782	31	5	[	[	X
ejpam-5782	31	6	5	5	NUM
ejpam-5782	31	7	]	]	PUNCT
ejpam-5782	31	8	,	,	PUNCT
ejpam-5782	31	9	extended	extend	VERB
ejpam-5782	31	10	the	the	DET
ejpam-5782	31	11	study	study	NOUN
ejpam-5782	31	12	to	to	ADP
ejpam-5782	31	13	θ	θ	NOUN
ejpam-5782	31	14	-	-	VERB
ejpam-5782	31	15	open	open	ADJ
ejpam-5782	31	16	using	use	VERB
ejpam-5782	31	17	a	a	DET
ejpam-5782	31	18	hereditary	hereditary	ADJ
ejpam-5782	31	19	class	class	NOUN
ejpam-5782	31	20	h	h	NOUN
ejpam-5782	31	21	:	:	PUNCT
ejpam-5782	31	22	a	a	DET
ejpam-5782	31	23	collection	collection	NOUN
ejpam-5782	31	24	h(θ	h(θ	PROPN
ejpam-5782	31	25	)	)	PUNCT
ejpam-5782	31	26	⊆	⊆	NUM
ejpam-5782	31	27	p(x	p(x	NOUN
ejpam-5782	31	28	)	)	PUNCT
ejpam-5782	31	29	is	be	AUX
ejpam-5782	31	30	defined	define	VERB
ejpam-5782	31	31	such	such	ADJ
ejpam-5782	31	32	that	that	SCONJ
ejpam-5782	31	33	a	a	DET
ejpam-5782	31	34	∈	∈	PROPN
ejpam-5782	31	35	h(θ	h(θ	PROPN
ejpam-5782	31	36	)	)	PUNCT
ejpam-5782	31	37	if	if	SCONJ
ejpam-5782	31	38	for	for	SCONJ
ejpam-5782	31	39	each	each	DET
ejpam-5782	31	40	x	x	SYM
ejpam-5782	31	41	∈	∈	PROPN
ejpam-5782	31	42	a	a	PRON
ejpam-5782	31	43	,	,	PUNCT
ejpam-5782	31	44	there	there	PRON
ejpam-5782	31	45	exists	exist	VERB
ejpam-5782	31	46	m	m	VERB
ejpam-5782	31	47	∈	∈	PROPN
ejpam-5782	31	48	µ	µ	X
ejpam-5782	31	49	containing	contain	VERB
ejpam-5782	31	50	x	x	PUNCT
ejpam-5782	31	51	with	with	ADP
ejpam-5782	31	52	m	m	PROPN
ejpam-5782	31	53	⊆	⊆	NUM
ejpam-5782	31	54	c∗µ(m	c∗µ(m	NOUN
ejpam-5782	31	55	)	)	PUNCT
ejpam-5782	31	56	⊆	⊆	NUM
ejpam-5782	31	57	a.	a.	NOUN
ejpam-5782	31	58	the	the	DET
ejpam-5782	31	59	family	family	NOUN
ejpam-5782	31	60	h(θ	h(θ	PROPN
ejpam-5782	31	61	)	)	PUNCT
ejpam-5782	31	62	is	be	AUX
ejpam-5782	31	63	a	a	DET
ejpam-5782	31	64	gt	gt	PROPN
ejpam-5782	31	65	on	on	ADP
ejpam-5782	31	66	x	x	PUNCT
ejpam-5782	31	67	included	include	VERB
ejpam-5782	31	68	in	in	ADP
ejpam-5782	31	69	µ	µ	NUM
ejpam-5782	31	70	,	,	PUNCT
ejpam-5782	31	71	with	with	ADP
ejpam-5782	31	72	elements	element	NOUN
ejpam-5782	31	73	termed	term	VERB
ejpam-5782	31	74	h(θ)-open	h(θ)-open	NOUN
ejpam-5782	31	75	sets	set	NOUN
ejpam-5782	31	76	and	and	CCONJ
ejpam-5782	31	77	their	their	PRON
ejpam-5782	31	78	complements	complement	NOUN
ejpam-5782	31	79	h(θ)-closed	h(θ)-close	VERB
ejpam-5782	31	80	sets	set	NOUN
ejpam-5782	31	81	.	.	PUNCT
ejpam-5782	32	1	additionally	additionally	ADV
ejpam-5782	32	2	,	,	PUNCT
ejpam-5782	32	3	the	the	DET
ejpam-5782	32	4	operation	operation	NOUN
ejpam-5782	32	5	γ∗	γ∗	NOUN
ejpam-5782	32	6	:	:	PUNCT
ejpam-5782	32	7	p(x	p(x	PROPN
ejpam-5782	32	8	)	)	PUNCT
ejpam-5782	32	9	→	→	SYM
ejpam-5782	32	10	p(x	p(x	PROPN
ejpam-5782	32	11	)	)	PUNCT
ejpam-5782	32	12	is	be	AUX
ejpam-5782	32	13	defined	define	VERB
ejpam-5782	32	14	in	in	ADP
ejpam-5782	32	15	[	[	X
ejpam-5782	32	16	5	5	NUM
ejpam-5782	32	17	]	]	PUNCT
ejpam-5782	32	18	as	as	ADP
ejpam-5782	32	19	γ∗(a	γ∗(a	NOUN
ejpam-5782	32	20	)	)	PUNCT
ejpam-5782	32	21	=	=	PRON
ejpam-5782	33	1	{	{	PUNCT
ejpam-5782	33	2	x	x	PUNCT
ejpam-5782	33	3	∈	∈	PROPN
ejpam-5782	33	4	x	x	X
ejpam-5782	33	5	|	|	ADV
ejpam-5782	33	6	c∗µ(m	c∗µ(m	NOUN
ejpam-5782	33	7	)	)	PUNCT
ejpam-5782	33	8	∩a	∩a	PROPN
ejpam-5782	33	9	̸=	̸=	PROPN
ejpam-5782	33	10	∅,∀m	∅,∀m	ADP
ejpam-5782	33	11	∈	∈	PROPN
ejpam-5782	33	12	µ	µ	NOUN
ejpam-5782	33	13	,	,	PUNCT
ejpam-5782	33	14	x	x	SYM
ejpam-5782	33	15	∈	∈	PROPN
ejpam-5782	33	16	m	m	NOUN
ejpam-5782	33	17	}	}	PUNCT
ejpam-5782	33	18	.	.	PUNCT
ejpam-5782	34	1	in	in	ADP
ejpam-5782	34	2	[	[	X
ejpam-5782	34	3	4	4	NUM
ejpam-5782	34	4	]	]	PUNCT
ejpam-5782	34	5	,	,	PUNCT
ejpam-5782	34	6	á.	á.	PROPN
ejpam-5782	34	7	császár	császár	PROPN
ejpam-5782	34	8	and	and	CCONJ
ejpam-5782	34	9	makai	makai	PROPN
ejpam-5782	34	10	jr	jr	PROPN
ejpam-5782	34	11	.	.	PROPN
ejpam-5782	34	12	introduced	introduce	VERB
ejpam-5782	34	13	θ(ν1	θ(ν1	NOUN
ejpam-5782	34	14	,	,	PUNCT
ejpam-5782	34	15	ν2)-open	ν2)-open	ADJ
ejpam-5782	34	16	sets	set	NOUN
ejpam-5782	34	17	as	as	ADP
ejpam-5782	34	18	a	a	DET
ejpam-5782	34	19	means	means	NOUN
ejpam-5782	34	20	of	of	ADP
ejpam-5782	34	21	combining	combine	VERB
ejpam-5782	34	22	two	two	NUM
ejpam-5782	34	23	generalized	generalized	ADJ
ejpam-5782	34	24	topologies	topology	NOUN
ejpam-5782	34	25	(	(	PUNCT
ejpam-5782	34	26	gts	gts	NOUN
ejpam-5782	34	27	)	)	PUNCT
ejpam-5782	34	28	,	,	PUNCT
ejpam-5782	34	29	ν1	ν1	NOUN
ejpam-5782	34	30	and	and	CCONJ
ejpam-5782	34	31	ν2	ν2	NOUN
ejpam-5782	34	32	,	,	PUNCT
ejpam-5782	34	33	on	on	ADP
ejpam-5782	34	34	a	a	DET
ejpam-5782	34	35	set	set	NOUN
ejpam-5782	34	36	x.	x.	NOUN
ejpam-5782	34	37	a	a	DET
ejpam-5782	34	38	subset	subset	VERB
ejpam-5782	34	39	a	a	DET
ejpam-5782	34	40	⊆	⊆	NUM
ejpam-5782	34	41	x	x	PUNCT
ejpam-5782	34	42	belongs	belong	VERB
ejpam-5782	34	43	to	to	ADP
ejpam-5782	34	44	f.	f.	PROPN
ejpam-5782	34	45	alsharari	alsharari	PROPN
ejpam-5782	34	46	,	,	PUNCT
ejpam-5782	34	47	a.	a.	PROPN
ejpam-5782	34	48	qahis	qahis	PROPN
ejpam-5782	34	49	/	/	SYM
ejpam-5782	34	50	eur	eur	PROPN
ejpam-5782	34	51	.	.	PUNCT
ejpam-5782	35	1	j.	j.	PROPN
ejpam-5782	35	2	pure	pure	PROPN
ejpam-5782	35	3	appl	appl	PROPN
ejpam-5782	35	4	.	.	PROPN
ejpam-5782	35	5	math	math	PROPN
ejpam-5782	35	6	,	,	PUNCT
ejpam-5782	35	7	18	18	NUM
ejpam-5782	35	8	(	(	PUNCT
ejpam-5782	35	9	2	2	NUM
ejpam-5782	35	10	)	)	PUNCT
ejpam-5782	35	11	(	(	PUNCT
ejpam-5782	35	12	2025	2025	NUM
ejpam-5782	35	13	)	)	PUNCT
ejpam-5782	35	14	,	,	PUNCT
ejpam-5782	35	15	5782	5782	NUM
ejpam-5782	35	16	3	3	NUM
ejpam-5782	35	17	of	of	ADP
ejpam-5782	35	18	10	10	NUM
ejpam-5782	35	19	θ(ν1	θ(ν1	NOUN
ejpam-5782	35	20	,	,	PUNCT
ejpam-5782	35	21	ν2	ν2	NOUN
ejpam-5782	35	22	)	)	PUNCT
ejpam-5782	35	23	if	if	SCONJ
ejpam-5782	35	24	,	,	PUNCT
ejpam-5782	35	25	for	for	ADP
ejpam-5782	35	26	every	every	DET
ejpam-5782	35	27	x	x	PROPN
ejpam-5782	35	28	∈	∈	PROPN
ejpam-5782	35	29	a	a	PRON
ejpam-5782	35	30	,	,	PUNCT
ejpam-5782	35	31	there	there	PRON
ejpam-5782	35	32	exists	exist	VERB
ejpam-5782	35	33	m	m	PROPN
ejpam-5782	35	34	∈	∈	NOUN
ejpam-5782	35	35	ν1	ν1	NOUN
ejpam-5782	35	36	such	such	ADJ
ejpam-5782	35	37	that	that	SCONJ
ejpam-5782	35	38	x	x	SYM
ejpam-5782	35	39	∈	∈	PROPN
ejpam-5782	35	40	m	m	VERB
ejpam-5782	35	41	⊆	⊆	NUM
ejpam-5782	35	42	cν2(m	cν2(m	NOUN
ejpam-5782	35	43	)	)	PUNCT
ejpam-5782	35	44	⊆	⊆	NUM
ejpam-5782	35	45	a.	a.	NOUN
ejpam-5782	35	46	moreover	moreover	ADV
ejpam-5782	35	47	,	,	PUNCT
ejpam-5782	35	48	the	the	DET
ejpam-5782	35	49	family	family	NOUN
ejpam-5782	35	50	θ(ν1	θ(ν1	NOUN
ejpam-5782	35	51	,	,	PUNCT
ejpam-5782	35	52	ν2	ν2	NOUN
ejpam-5782	35	53	)	)	PUNCT
ejpam-5782	35	54	itself	itself	PRON
ejpam-5782	35	55	forms	form	VERB
ejpam-5782	35	56	a	a	DET
ejpam-5782	35	57	gt	gt	PROPN
ejpam-5782	35	58	contained	contain	VERB
ejpam-5782	35	59	within	within	ADP
ejpam-5782	35	60	ν1	ν1	NOUN
ejpam-5782	35	61	on	on	ADP
ejpam-5782	35	62	x.	x.	NOUN
ejpam-5782	35	63	the	the	DET
ejpam-5782	35	64	sets	set	NOUN
ejpam-5782	35	65	in	in	ADP
ejpam-5782	35	66	θ(ν1	θ(ν1	NOUN
ejpam-5782	35	67	,	,	PUNCT
ejpam-5782	35	68	ν2	ν2	NOUN
ejpam-5782	35	69	)	)	PUNCT
ejpam-5782	35	70	are	be	AUX
ejpam-5782	35	71	called	call	VERB
ejpam-5782	35	72	θ(ν1	θ(ν1	NOUN
ejpam-5782	35	73	,	,	PUNCT
ejpam-5782	35	74	ν2)-open	ν2)-open	ADJ
ejpam-5782	35	75	sets	set	NOUN
ejpam-5782	35	76	,	,	PUNCT
ejpam-5782	35	77	while	while	SCONJ
ejpam-5782	35	78	their	their	PRON
ejpam-5782	35	79	complements	complement	NOUN
ejpam-5782	35	80	are	be	AUX
ejpam-5782	35	81	referred	refer	VERB
ejpam-5782	35	82	to	to	ADP
ejpam-5782	35	83	as	as	ADP
ejpam-5782	35	84	θ(ν1	θ(ν1	NOUN
ejpam-5782	35	85	,	,	PUNCT
ejpam-5782	35	86	ν2)closed	ν2)close	VERB
ejpam-5782	35	87	sets	set	NOUN
ejpam-5782	35	88	.	.	PUNCT
ejpam-5782	36	1	subsequently	subsequently	ADV
ejpam-5782	36	2	,	,	PUNCT
ejpam-5782	36	3	in	in	ADP
ejpam-5782	36	4	[	[	PUNCT
ejpam-5782	36	5	9	9	NUM
ejpam-5782	36	6	]	]	PUNCT
ejpam-5782	36	7	,	,	PUNCT
ejpam-5782	36	8	abdo	abdo	PROPN
ejpam-5782	36	9	qahis	qahis	PROPN
ejpam-5782	36	10	and	and	CCONJ
ejpam-5782	36	11	awn	awn	PROPN
ejpam-5782	36	12	alqahtani	alqahtani	PROPN
ejpam-5782	36	13	introduced	introduce	VERB
ejpam-5782	36	14	a	a	DET
ejpam-5782	36	15	modification	modification	NOUN
ejpam-5782	36	16	of	of	ADP
ejpam-5782	36	17	this	this	DET
ejpam-5782	36	18	concept	concept	NOUN
ejpam-5782	36	19	,	,	PUNCT
ejpam-5782	36	20	defining	define	VERB
ejpam-5782	36	21	the	the	DET
ejpam-5782	36	22	class	class	NOUN
ejpam-5782	36	23	of	of	ADP
ejpam-5782	36	24	θ̃(ν1	θ̃(ν1	PROPN
ejpam-5782	36	25	,	,	PUNCT
ejpam-5782	36	26	ν2)-open	ν2)-open	ADJ
ejpam-5782	36	27	sets	set	NOUN
ejpam-5782	36	28	.	.	PUNCT
ejpam-5782	37	1	a	a	DET
ejpam-5782	37	2	subset	subset	NOUN
ejpam-5782	37	3	a	a	DET
ejpam-5782	37	4	⊆	⊆	NUM
ejpam-5782	37	5	x	x	SYM
ejpam-5782	37	6	is	be	AUX
ejpam-5782	37	7	said	say	VERB
ejpam-5782	37	8	to	to	PART
ejpam-5782	37	9	be	be	AUX
ejpam-5782	37	10	mixed	mix	VERB
ejpam-5782	37	11	θ̃(ν1	θ̃(ν1	NOUN
ejpam-5782	37	12	,	,	PUNCT
ejpam-5782	37	13	ν2)-open	ν2)-open	ADJ
ejpam-5782	37	14	(	(	PUNCT
ejpam-5782	37	15	or	or	CCONJ
ejpam-5782	37	16	simply	simply	ADV
ejpam-5782	37	17	θ̃(ν1	θ̃(ν1	PROPN
ejpam-5782	37	18	,	,	PUNCT
ejpam-5782	37	19	ν2)-open	ν2)-open	ADJ
ejpam-5782	37	20	)	)	PUNCT
ejpam-5782	37	21	if	if	SCONJ
ejpam-5782	37	22	,	,	PUNCT
ejpam-5782	37	23	for	for	ADP
ejpam-5782	37	24	every	every	DET
ejpam-5782	37	25	x	x	PROPN
ejpam-5782	37	26	∈	∈	PROPN
ejpam-5782	37	27	a	a	PRON
ejpam-5782	37	28	,	,	PUNCT
ejpam-5782	37	29	there	there	PRON
ejpam-5782	37	30	exists	exist	VERB
ejpam-5782	37	31	m	m	PROPN
ejpam-5782	37	32	∈	∈	NOUN
ejpam-5782	37	33	ν1	ν1	NOUN
ejpam-5782	38	1	such	such	ADJ
ejpam-5782	38	2	that	that	SCONJ
ejpam-5782	38	3	x	x	SYM
ejpam-5782	38	4	∈	∈	PROPN
ejpam-5782	38	5	m	m	NOUN
ejpam-5782	38	6	and	and	CCONJ
ejpam-5782	38	7	m	m	PROPN
ejpam-5782	38	8	⊆	⊆	NUM
ejpam-5782	38	9	cν2(m	cν2(m	NOUN
ejpam-5782	38	10	)	)	PUNCT
ejpam-5782	38	11	∩mν1	∩mν1	NOUN
ejpam-5782	38	12	⊆	⊆	NUM
ejpam-5782	38	13	a.	a.	NOUN
ejpam-5782	38	14	in	in	ADP
ejpam-5782	38	15	conclusion	conclusion	NOUN
ejpam-5782	38	16	of	of	ADP
ejpam-5782	38	17	this	this	DET
ejpam-5782	38	18	section	section	NOUN
ejpam-5782	38	19	,	,	PUNCT
ejpam-5782	38	20	we	we	PRON
ejpam-5782	38	21	review	review	VERB
ejpam-5782	38	22	the	the	DET
ejpam-5782	38	23	following	follow	VERB
ejpam-5782	38	24	important	important	ADJ
ejpam-5782	38	25	facts	fact	NOUN
ejpam-5782	38	26	due	due	ADP
ejpam-5782	38	27	to	to	ADP
ejpam-5782	38	28	their	their	PRON
ejpam-5782	38	29	significance	significance	NOUN
ejpam-5782	38	30	to	to	ADP
ejpam-5782	38	31	the	the	DET
ejpam-5782	38	32	content	content	NOUN
ejpam-5782	38	33	of	of	ADP
ejpam-5782	38	34	our	our	PRON
ejpam-5782	38	35	paper	paper	NOUN
ejpam-5782	38	36	.	.	PUNCT
ejpam-5782	39	1	theorem	theorem	NOUN
ejpam-5782	39	2	1	1	NUM
ejpam-5782	39	3	.	.	PUNCT
ejpam-5782	40	1	[	[	X
ejpam-5782	40	2	6	6	NUM
ejpam-5782	40	3	]	]	PUNCT
ejpam-5782	40	4	let	let	VERB
ejpam-5782	40	5	µ	µ	X
ejpam-5782	40	6	be	be	AUX
ejpam-5782	40	7	a	a	DET
ejpam-5782	40	8	gts	gts	NOUN
ejpam-5782	40	9	on	on	ADP
ejpam-5782	40	10	x	x	PUNCT
ejpam-5782	40	11	and	and	CCONJ
ejpam-5782	40	12	h	h	DET
ejpam-5782	40	13	a	a	DET
ejpam-5782	40	14	hereditary	hereditary	ADJ
ejpam-5782	40	15	class	class	NOUN
ejpam-5782	40	16	on	on	ADP
ejpam-5782	40	17	x.	x.	NOUN
ejpam-5782	40	18	then	then	ADV
ejpam-5782	40	19	a∗	a∗	PROPN
ejpam-5782	40	20	⊆	⊆	NUM
ejpam-5782	40	21	c∗µ(a	c∗µ(a	PROPN
ejpam-5782	40	22	)	)	PUNCT
ejpam-5782	40	23	⊆	⊆	NUM
ejpam-5782	40	24	cµ(a	cµ(a	NUM
ejpam-5782	40	25	)	)	PUNCT
ejpam-5782	40	26	for	for	ADP
ejpam-5782	40	27	any	any	DET
ejpam-5782	40	28	a	a	DET
ejpam-5782	40	29	⊆	⊆	NUM
ejpam-5782	40	30	x.	x.	NOUN
ejpam-5782	40	31	in	in	ADP
ejpam-5782	40	32	[	[	X
ejpam-5782	40	33	10	10	NUM
ejpam-5782	40	34	]	]	PUNCT
ejpam-5782	40	35	,	,	PUNCT
ejpam-5782	40	36	the	the	DET
ejpam-5782	40	37	authors	author	NOUN
ejpam-5782	40	38	introduced	introduce	VERB
ejpam-5782	40	39	the	the	DET
ejpam-5782	40	40	operator	operator	NOUN
ejpam-5782	40	41	i∗	i∗	NOUN
ejpam-5782	40	42	:	:	PUNCT
ejpam-5782	40	43	p(x	p(x	PROPN
ejpam-5782	40	44	)	)	PUNCT
ejpam-5782	40	45	→	→	SYM
ejpam-5782	40	46	p(x	p(x	PROPN
ejpam-5782	40	47	)	)	PUNCT
ejpam-5782	40	48	,	,	PUNCT
ejpam-5782	40	49	defined	define	VERB
ejpam-5782	40	50	by	by	ADP
ejpam-5782	40	51	i∗(a	i∗(a	PROPN
ejpam-5782	40	52	)	)	PUNCT
ejpam-5782	40	53	=	=	PUNCT
ejpam-5782	41	1	x	x	SYM
ejpam-5782	41	2	\	\	PROPN
ejpam-5782	41	3	c∗(x	c∗(x	NOUN
ejpam-5782	41	4	\a	\a	ADJ
ejpam-5782	41	5	)	)	PUNCT
ejpam-5782	41	6	for	for	ADP
ejpam-5782	41	7	a	a	DET
ejpam-5782	41	8	⊆	⊆	NUM
ejpam-5782	41	9	x.	x.	NOUN
ejpam-5782	41	10	theorem	theorem	NOUN
ejpam-5782	41	11	2	2	NUM
ejpam-5782	41	12	.	.	PUNCT
ejpam-5782	42	1	[	[	X
ejpam-5782	42	2	10	10	NUM
ejpam-5782	42	3	]	]	PUNCT
ejpam-5782	42	4	let	let	VERB
ejpam-5782	42	5	µ	µ	X
ejpam-5782	42	6	be	be	AUX
ejpam-5782	42	7	a	a	DET
ejpam-5782	42	8	gt	gt	PROPN
ejpam-5782	42	9	on	on	ADP
ejpam-5782	42	10	x	x	PUNCT
ejpam-5782	42	11	and	and	CCONJ
ejpam-5782	42	12	h	h	DET
ejpam-5782	42	13	a	a	DET
ejpam-5782	42	14	hereditary	hereditary	ADJ
ejpam-5782	42	15	class	class	NOUN
ejpam-5782	42	16	.	.	PUNCT
ejpam-5782	43	1	then	then	ADV
ejpam-5782	43	2	for	for	ADP
ejpam-5782	43	3	a	a	DET
ejpam-5782	43	4	⊆	⊆	NUM
ejpam-5782	43	5	x	x	SYM
ejpam-5782	43	6	,	,	PUNCT
ejpam-5782	43	7	(	(	PUNCT
ejpam-5782	43	8	i	i	NOUN
ejpam-5782	43	9	)	)	PUNCT
ejpam-5782	43	10	c∗µ(a	c∗µ(a	PROPN
ejpam-5782	43	11	)	)	PUNCT
ejpam-5782	43	12	=	=	PUNCT
ejpam-5782	43	13	x	x	SYM
ejpam-5782	43	14	\	\	PROPN
ejpam-5782	43	15	i∗µ(x	i∗µ(x	PROPN
ejpam-5782	43	16	\a	\a	ADJ
ejpam-5782	43	17	)	)	PUNCT
ejpam-5782	43	18	.	.	PUNCT
ejpam-5782	44	1	(	(	PUNCT
ejpam-5782	44	2	ii	ii	NOUN
ejpam-5782	44	3	)	)	PUNCT
ejpam-5782	44	4	iµ(a	iµ(a	ADJ
ejpam-5782	44	5	)	)	PUNCT
ejpam-5782	45	1	⊆	⊆	NUM
ejpam-5782	45	2	i∗µ(a	i∗µ(a	PROPN
ejpam-5782	45	3	)	)	PUNCT
ejpam-5782	45	4	⊆	⊆	NUM
ejpam-5782	45	5	a.	a.	NOUN
ejpam-5782	45	6	lemma	lemma	PROPN
ejpam-5782	45	7	1	1	X
ejpam-5782	45	8	.	.	PUNCT
ejpam-5782	46	1	[	[	X
ejpam-5782	46	2	11	11	NUM
ejpam-5782	46	3	]	]	PUNCT
ejpam-5782	46	4	let	let	VERB
ejpam-5782	46	5	µ	µ	NOUN
ejpam-5782	46	6	and	and	CCONJ
ejpam-5782	46	7	ν	ν	PROPN
ejpam-5782	46	8	be	be	AUX
ejpam-5782	46	9	two	two	NUM
ejpam-5782	46	10	gts	gts	NOUN
ejpam-5782	46	11	on	on	ADP
ejpam-5782	46	12	a	a	DET
ejpam-5782	46	13	nonempty	nonempty	ADV
ejpam-5782	46	14	set	set	VERB
ejpam-5782	46	15	x	x	PUNCT
ejpam-5782	46	16	and	and	CCONJ
ejpam-5782	46	17	a	a	DET
ejpam-5782	46	18	⊆	⊆	NUM
ejpam-5782	46	19	x.	x.	NOUN
ejpam-5782	46	20	then	then	ADV
ejpam-5782	46	21	the	the	DET
ejpam-5782	46	22	following	follow	VERB
ejpam-5782	46	23	statements	statement	NOUN
ejpam-5782	46	24	hold	hold	VERB
ejpam-5782	46	25	:	:	PUNCT
ejpam-5782	46	26	(	(	PUNCT
ejpam-5782	46	27	i	i	NOUN
ejpam-5782	46	28	)	)	PUNCT
ejpam-5782	46	29	x	x	SYM
ejpam-5782	46	30	∈	∈	PROPN
ejpam-5782	46	31	iθ(µ,ν)(a	iθ(µ,ν)(a	PROPN
ejpam-5782	46	32	)	)	PUNCT
ejpam-5782	47	1	if	if	SCONJ
ejpam-5782	47	2	and	and	CCONJ
ejpam-5782	47	3	only	only	ADV
ejpam-5782	47	4	if	if	SCONJ
ejpam-5782	47	5	there	there	PRON
ejpam-5782	47	6	exists	exist	VERB
ejpam-5782	47	7	a	a	DET
ejpam-5782	47	8	µ-open	µ-open	NOUN
ejpam-5782	47	9	set	set	VERB
ejpam-5782	47	10	m	m	AUX
ejpam-5782	47	11	containing	contain	VERB
ejpam-5782	47	12	x	x	PUNCT
ejpam-5782	47	13	such	such	ADJ
ejpam-5782	47	14	that	that	SCONJ
ejpam-5782	47	15	m	m	PROPN
ejpam-5782	47	16	⊆	⊆	NUM
ejpam-5782	47	17	cν(m	cν(m	NOUN
ejpam-5782	47	18	)	)	PUNCT
ejpam-5782	47	19	⊆	⊆	NUM
ejpam-5782	47	20	a.	a.	NOUN
ejpam-5782	47	21	(	(	PUNCT
ejpam-5782	47	22	ii	ii	NOUN
ejpam-5782	47	23	)	)	PUNCT
ejpam-5782	47	24	if	if	SCONJ
ejpam-5782	47	25	a	a	PRON
ejpam-5782	47	26	is	be	AUX
ejpam-5782	47	27	ν	ν	NOUN
ejpam-5782	47	28	-	-	ADJ
ejpam-5782	47	29	open	open	ADJ
ejpam-5782	47	30	in	in	ADP
ejpam-5782	47	31	x	x	NOUN
ejpam-5782	47	32	,	,	PUNCT
ejpam-5782	47	33	then	then	ADV
ejpam-5782	47	34	γθ(µ,ν)(a	γθ(µ,ν)(a	NUM
ejpam-5782	47	35	)	)	PUNCT
ejpam-5782	47	36	=	=	SYM
ejpam-5782	47	37	cµ(a	cµ(a	ADJ
ejpam-5782	47	38	)	)	PUNCT
ejpam-5782	47	39	.	.	PUNCT
ejpam-5782	48	1	definition	definition	NOUN
ejpam-5782	48	2	1	1	NUM
ejpam-5782	48	3	.	.	PUNCT
ejpam-5782	49	1	[	[	X
ejpam-5782	49	2	1	1	X
ejpam-5782	49	3	]	]	PUNCT
ejpam-5782	49	4	let	let	VERB
ejpam-5782	49	5	µ	µ	X
ejpam-5782	49	6	be	be	AUX
ejpam-5782	49	7	gt	gt	PROPN
ejpam-5782	49	8	on	on	ADP
ejpam-5782	49	9	a	a	DET
ejpam-5782	49	10	nonempty	nonempty	ADV
ejpam-5782	49	11	set	set	VERB
ejpam-5782	49	12	x	x	NOUN
ejpam-5782	49	13	,	,	PUNCT
ejpam-5782	49	14	and	and	CCONJ
ejpam-5782	49	15	h	h	DET
ejpam-5782	49	16	a	a	DET
ejpam-5782	49	17	hereditary	hereditary	ADJ
ejpam-5782	49	18	class	class	NOUN
ejpam-5782	49	19	on	on	ADP
ejpam-5782	49	20	x.	x.	NOUN
ejpam-5782	49	21	then	then	ADV
ejpam-5782	49	22	(	(	PUNCT
ejpam-5782	49	23	x,µ	x,µ	NOUN
ejpam-5782	49	24	)	)	PUNCT
ejpam-5782	49	25	is	be	AUX
ejpam-5782	49	26	h	h	NOUN
ejpam-5782	49	27	-	-	PUNCT
ejpam-5782	49	28	regular	regular	ADJ
ejpam-5782	49	29	if	if	SCONJ
ejpam-5782	49	30	and	and	CCONJ
ejpam-5782	49	31	only	only	ADV
ejpam-5782	49	32	if	if	SCONJ
ejpam-5782	49	33	for	for	ADP
ejpam-5782	49	34	every	every	DET
ejpam-5782	49	35	x	x	SYM
ejpam-5782	49	36	∈	∈	PROPN
ejpam-5782	49	37	x	x	X
ejpam-5782	49	38	and	and	CCONJ
ejpam-5782	49	39	every	every	DET
ejpam-5782	49	40	µ-open	µ-open	NOUN
ejpam-5782	49	41	set	set	VERB
ejpam-5782	49	42	u	u	PRON
ejpam-5782	49	43	containing	contain	VERB
ejpam-5782	49	44	x	x	PRON
ejpam-5782	49	45	,	,	PUNCT
ejpam-5782	49	46	there	there	PRON
ejpam-5782	49	47	exists	exist	VERB
ejpam-5782	49	48	a	a	DET
ejpam-5782	49	49	µ-open	µ-open	NOUN
ejpam-5782	49	50	set	set	VERB
ejpam-5782	49	51	v	v	NOUN
ejpam-5782	49	52	containing	contain	VERB
ejpam-5782	49	53	x	x	PUNCT
ejpam-5782	49	54	such	such	ADJ
ejpam-5782	49	55	that	that	SCONJ
ejpam-5782	49	56	x	x	SYM
ejpam-5782	49	57	∈	∈	NOUN
ejpam-5782	49	58	v	v	ADP
ejpam-5782	49	59	⊆	⊆	NUM
ejpam-5782	49	60	c∗(v	c∗(v	PROPN
ejpam-5782	49	61	)	)	PUNCT
ejpam-5782	49	62	⊆	⊆	NUM
ejpam-5782	49	63	u	u	NOUN
ejpam-5782	49	64	.	.	PUNCT
ejpam-5782	50	1	theorem	theorem	NOUN
ejpam-5782	50	2	3	3	NUM
ejpam-5782	50	3	.	.	PUNCT
ejpam-5782	51	1	[	[	X
ejpam-5782	51	2	11	11	NUM
ejpam-5782	51	3	]	]	PUNCT
ejpam-5782	51	4	let	let	VERB
ejpam-5782	51	5	µ	µ	NOUN
ejpam-5782	51	6	and	and	CCONJ
ejpam-5782	51	7	ν	ν	PROPN
ejpam-5782	51	8	be	be	AUX
ejpam-5782	51	9	measures	measure	NOUN
ejpam-5782	51	10	on	on	ADP
ejpam-5782	51	11	a	a	DET
ejpam-5782	51	12	nonempty	nonempty	ADV
ejpam-5782	51	13	set	set	VERB
ejpam-5782	51	14	x.	x.	NOUN
ejpam-5782	51	15	then	then	ADV
ejpam-5782	51	16	x	x	X
ejpam-5782	51	17	is	be	AUX
ejpam-5782	51	18	(	(	PUNCT
ejpam-5782	51	19	µ	µ	NOUN
ejpam-5782	51	20	,	,	PUNCT
ejpam-5782	51	21	ν)-regular	ν)-regular	ADJ
ejpam-5782	51	22	if	if	SCONJ
ejpam-5782	51	23	and	and	CCONJ
ejpam-5782	51	24	only	only	ADV
ejpam-5782	51	25	if	if	SCONJ
ejpam-5782	51	26	for	for	ADP
ejpam-5782	51	27	every	every	DET
ejpam-5782	51	28	x	x	SYM
ejpam-5782	51	29	∈	∈	PROPN
ejpam-5782	51	30	x	x	X
ejpam-5782	51	31	and	and	CCONJ
ejpam-5782	51	32	every	every	DET
ejpam-5782	51	33	µ-open	µ-open	NOUN
ejpam-5782	51	34	set	set	VERB
ejpam-5782	51	35	u	u	PRON
ejpam-5782	51	36	containing	contain	VERB
ejpam-5782	51	37	x	x	PRON
ejpam-5782	51	38	,	,	PUNCT
ejpam-5782	51	39	there	there	PRON
ejpam-5782	51	40	exists	exist	VERB
ejpam-5782	51	41	a	a	DET
ejpam-5782	51	42	µ-open	µ-open	NOUN
ejpam-5782	51	43	set	set	VERB
ejpam-5782	51	44	v	v	NOUN
ejpam-5782	51	45	containing	contain	VERB
ejpam-5782	51	46	x	x	PUNCT
ejpam-5782	51	47	such	such	ADJ
ejpam-5782	51	48	that	that	SCONJ
ejpam-5782	51	49	x	x	SYM
ejpam-5782	51	50	∈	∈	NOUN
ejpam-5782	51	51	v	v	ADP
ejpam-5782	51	52	⊆	⊆	NUM
ejpam-5782	51	53	cν(v	cν(v	X
ejpam-5782	51	54	)	)	PUNCT
ejpam-5782	51	55	⊆	⊆	NUM
ejpam-5782	51	56	u	u	NOUN
ejpam-5782	51	57	.	.	PUNCT
ejpam-5782	52	1	3	3	X
ejpam-5782	52	2	.	.	X
ejpam-5782	52	3	properties	property	NOUN
ejpam-5782	52	4	of	of	ADP
ejpam-5782	52	5	the	the	DET
ejpam-5782	52	6	mixed	mixed	ADJ
ejpam-5782	52	7	operator	operator	NOUN
ejpam-5782	52	8	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	52	9	,	,	PUNCT
ejpam-5782	52	10	ν	ν	NOUN
ejpam-5782	52	11	)	)	PUNCT
ejpam-5782	52	12	in	in	ADP
ejpam-5782	52	13	[	[	X
ejpam-5782	52	14	4	4	NUM
ejpam-5782	52	15	]	]	PUNCT
ejpam-5782	52	16	,	,	PUNCT
ejpam-5782	52	17	császár	császár	PROPN
ejpam-5782	52	18	and	and	CCONJ
ejpam-5782	52	19	makai	makai	PROPN
ejpam-5782	52	20	jr	jr	PROPN
ejpam-5782	52	21	introduced	introduce	VERB
ejpam-5782	52	22	an	an	DET
ejpam-5782	52	23	operation	operation	NOUN
ejpam-5782	52	24	γθ(µ,ν	γθ(µ,ν	NOUN
ejpam-5782	52	25	)	)	PUNCT
ejpam-5782	52	26	:	:	PUNCT
ejpam-5782	52	27	p(x	p(x	PROPN
ejpam-5782	52	28	)	)	PUNCT
ejpam-5782	52	29	→	→	SYM
ejpam-5782	52	30	p(x	p(x	PROPN
ejpam-5782	52	31	)	)	PUNCT
ejpam-5782	52	32	,	,	PUNCT
ejpam-5782	52	33	utilizing	utilize	VERB
ejpam-5782	52	34	two	two	NUM
ejpam-5782	52	35	generalized	generalized	ADJ
ejpam-5782	52	36	topologies	topology	NOUN
ejpam-5782	52	37	µ	µ	VERB
ejpam-5782	52	38	and	and	CCONJ
ejpam-5782	52	39	ν	ν	NOUN
ejpam-5782	52	40	on	on	ADP
ejpam-5782	52	41	x.	x.	NOUN
ejpam-5782	52	42	according	accord	VERB
ejpam-5782	52	43	to	to	ADP
ejpam-5782	52	44	their	their	PRON
ejpam-5782	52	45	definition	definition	NOUN
ejpam-5782	52	46	,	,	PUNCT
ejpam-5782	52	47	x	x	PROPN
ejpam-5782	52	48	∈	∈	PROPN
ejpam-5782	52	49	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	52	50	)	)	PUNCT
ejpam-5782	53	1	if	if	SCONJ
ejpam-5782	53	2	and	and	CCONJ
ejpam-5782	53	3	only	only	ADV
ejpam-5782	53	4	if	if	SCONJ
ejpam-5782	53	5	cν(m	cν(m	NOUN
ejpam-5782	53	6	)	)	PUNCT
ejpam-5782	53	7	∩	∩	NOUN
ejpam-5782	53	8	a	a	DET
ejpam-5782	53	9	̸=	̸=	PROPN
ejpam-5782	53	10	∅	∅	NOUN
ejpam-5782	53	11	for	for	ADP
ejpam-5782	53	12	every	every	DET
ejpam-5782	53	13	µ-open	µ-open	NOUN
ejpam-5782	53	14	set	set	VERB
ejpam-5782	53	15	m	m	AUX
ejpam-5782	53	16	containing	contain	VERB
ejpam-5782	53	17	x.	x.	NOUN
ejpam-5782	53	18	if	if	SCONJ
ejpam-5782	53	19	x	x	X
ejpam-5782	53	20	/∈	/∈	PUNCT
ejpam-5782	53	21	mµ	mµ	INTJ
ejpam-5782	53	22	,	,	PUNCT
ejpam-5782	53	23	then	then	ADV
ejpam-5782	53	24	by	by	ADP
ejpam-5782	53	25	definition	definition	NOUN
ejpam-5782	53	26	x	x	X
ejpam-5782	53	27	∈	∈	PROPN
ejpam-5782	53	28	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	53	29	)	)	PUNCT
ejpam-5782	53	30	.	.	PUNCT
ejpam-5782	54	1	additionally	additionally	ADV
ejpam-5782	54	2	,	,	PUNCT
ejpam-5782	54	3	x	x	PROPN
ejpam-5782	54	4	/∈	/∈	PUNCT
ejpam-5782	54	5	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	54	6	)	)	PUNCT
ejpam-5782	55	1	if	if	SCONJ
ejpam-5782	55	2	and	and	CCONJ
ejpam-5782	55	3	only	only	ADV
ejpam-5782	55	4	if	if	SCONJ
ejpam-5782	55	5	there	there	PRON
ejpam-5782	55	6	exists	exist	VERB
ejpam-5782	55	7	m	m	PROPN
ejpam-5782	55	8	∈	∈	PROPN
ejpam-5782	55	9	µ	µ	X
ejpam-5782	55	10	with	with	ADP
ejpam-5782	55	11	x	x	SYM
ejpam-5782	55	12	∈	∈	NOUN
ejpam-5782	55	13	m	m	VERB
ejpam-5782	55	14	such	such	ADJ
ejpam-5782	55	15	that	that	PRON
ejpam-5782	55	16	cν(m	cν(m	PUNCT
ejpam-5782	55	17	)	)	PUNCT
ejpam-5782	56	1	∩a	∩a	PROPN
ejpam-5782	56	2	=	=	PUNCT
ejpam-5782	57	1	∅.	∅.	PROPN
ejpam-5782	57	2	f.	f.	PROPN
ejpam-5782	57	3	alsharari	alsharari	PROPN
ejpam-5782	57	4	,	,	PUNCT
ejpam-5782	57	5	a.	a.	PROPN
ejpam-5782	57	6	qahis	qahis	PROPN
ejpam-5782	57	7	/	/	SYM
ejpam-5782	57	8	eur	eur	PROPN
ejpam-5782	57	9	.	.	PUNCT
ejpam-5782	58	1	j.	j.	PROPN
ejpam-5782	58	2	pure	pure	PROPN
ejpam-5782	58	3	appl	appl	PROPN
ejpam-5782	58	4	.	.	PROPN
ejpam-5782	58	5	math	math	PROPN
ejpam-5782	58	6	,	,	PUNCT
ejpam-5782	58	7	18	18	NUM
ejpam-5782	58	8	(	(	PUNCT
ejpam-5782	58	9	2	2	NUM
ejpam-5782	58	10	)	)	PUNCT
ejpam-5782	58	11	(	(	PUNCT
ejpam-5782	58	12	2025	2025	NUM
ejpam-5782	58	13	)	)	PUNCT
ejpam-5782	58	14	,	,	PUNCT
ejpam-5782	58	15	5782	5782	NUM
ejpam-5782	58	16	4	4	NUM
ejpam-5782	58	17	of	of	ADP
ejpam-5782	58	18	10	10	NUM
ejpam-5782	58	19	definition	definition	NOUN
ejpam-5782	58	20	2	2	NUM
ejpam-5782	58	21	.	.	PUNCT
ejpam-5782	59	1	let	let	VERB
ejpam-5782	59	2	µ	µ	NOUN
ejpam-5782	59	3	and	and	CCONJ
ejpam-5782	59	4	ν	ν	PROPN
ejpam-5782	59	5	be	be	AUX
ejpam-5782	59	6	two	two	NUM
ejpam-5782	59	7	gt	gt	NOUN
ejpam-5782	59	8	’s	’s	NOUN
ejpam-5782	59	9	on	on	ADP
ejpam-5782	59	10	a	a	DET
ejpam-5782	59	11	nonempty	nonempty	ADV
ejpam-5782	59	12	set	set	VERB
ejpam-5782	59	13	x	x	NOUN
ejpam-5782	59	14	,	,	PUNCT
ejpam-5782	59	15	and	and	CCONJ
ejpam-5782	59	16	h	h	DET
ejpam-5782	59	17	a	a	DET
ejpam-5782	59	18	hereditary	hereditary	ADJ
ejpam-5782	59	19	class	class	NOUN
ejpam-5782	59	20	on	on	ADP
ejpam-5782	59	21	x.	x.	PROPN
ejpam-5782	59	22	an	an	DET
ejpam-5782	59	23	operation	operation	NOUN
ejpam-5782	59	24	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	59	25	,	,	PUNCT
ejpam-5782	59	26	ν	ν	NOUN
ejpam-5782	59	27	)	)	PUNCT
ejpam-5782	59	28	:	:	PUNCT
ejpam-5782	59	29	p(x	p(x	PROPN
ejpam-5782	59	30	)	)	PUNCT
ejpam-5782	59	31	→	→	SYM
ejpam-5782	59	32	p(x	p(x	PROPN
ejpam-5782	59	33	)	)	PUNCT
ejpam-5782	59	34	is	be	AUX
ejpam-5782	59	35	defined	define	VERB
ejpam-5782	59	36	as	as	SCONJ
ejpam-5782	59	37	follows	follow	VERB
ejpam-5782	59	38	:	:	PUNCT
ejpam-5782	59	39	for	for	ADP
ejpam-5782	59	40	every	every	DET
ejpam-5782	59	41	a	a	DET
ejpam-5782	59	42	⊆	⊆	NUM
ejpam-5782	59	43	x	x	SYM
ejpam-5782	59	44	,	,	PUNCT
ejpam-5782	59	45	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	59	46	,	,	PUNCT
ejpam-5782	59	47	ν)(a	ν)(a	NUM
ejpam-5782	59	48	)	)	PUNCT
ejpam-5782	60	1	=	=	PRON
ejpam-5782	60	2	{	{	PUNCT
ejpam-5782	60	3	x	x	PUNCT
ejpam-5782	60	4	∈	∈	NOUN
ejpam-5782	60	5	x	x	X
ejpam-5782	60	6	:	:	PUNCT
ejpam-5782	60	7	c∗ν(m	c∗ν(m	X
ejpam-5782	60	8	)	)	PUNCT
ejpam-5782	60	9	∩a	∩a	PROPN
ejpam-5782	60	10	̸=	̸=	PROPN
ejpam-5782	60	11	∅	∅	NOUN
ejpam-5782	60	12	,	,	PUNCT
ejpam-5782	60	13	∀m	∀m	PROPN
ejpam-5782	60	14	∈	∈	PROPN
ejpam-5782	60	15	µ	µ	NOUN
ejpam-5782	60	16	and	and	CCONJ
ejpam-5782	60	17	x	x	SYM
ejpam-5782	60	18	∈	∈	PROPN
ejpam-5782	60	19	m	m	NOUN
ejpam-5782	60	20	}	}	PUNCT
ejpam-5782	60	21	.	.	PUNCT
ejpam-5782	61	1	if	if	SCONJ
ejpam-5782	61	2	x	x	X
ejpam-5782	61	3	/∈	/∈	VERB
ejpam-5782	61	4	mµ	mµ	INTJ
ejpam-5782	61	5	,	,	PUNCT
ejpam-5782	61	6	then	then	ADV
ejpam-5782	61	7	by	by	ADP
ejpam-5782	61	8	definition	definition	NOUN
ejpam-5782	61	9	x	x	X
ejpam-5782	61	10	∈	∈	PROPN
ejpam-5782	61	11	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	61	12	,	,	PUNCT
ejpam-5782	61	13	ν)(a	ν)(a	NOUN
ejpam-5782	61	14	)	)	PUNCT
ejpam-5782	61	15	.	.	PUNCT
ejpam-5782	62	1	according	accord	VERB
ejpam-5782	62	2	to	to	ADP
ejpam-5782	62	3	definition	definition	NOUN
ejpam-5782	62	4	2	2	NUM
ejpam-5782	62	5	,	,	PUNCT
ejpam-5782	62	6	x	x	PROPN
ejpam-5782	62	7	/∈	/∈	PROPN
ejpam-5782	62	8	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	62	9	,	,	PUNCT
ejpam-5782	62	10	ν)(a	ν)(a	NOUN
ejpam-5782	62	11	)	)	PUNCT
ejpam-5782	62	12	if	if	SCONJ
ejpam-5782	62	13	and	and	CCONJ
ejpam-5782	62	14	only	only	ADV
ejpam-5782	62	15	if	if	SCONJ
ejpam-5782	62	16	there	there	PRON
ejpam-5782	62	17	exists	exist	VERB
ejpam-5782	62	18	m	m	PROPN
ejpam-5782	62	19	∈	∈	PROPN
ejpam-5782	62	20	µ	µ	NOUN
ejpam-5782	62	21	and	and	CCONJ
ejpam-5782	62	22	x	x	SYM
ejpam-5782	62	23	∈	∈	PROPN
ejpam-5782	62	24	m	m	VERB
ejpam-5782	62	25	such	such	ADJ
ejpam-5782	62	26	that	that	SCONJ
ejpam-5782	62	27	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	62	28	)	)	PUNCT
ejpam-5782	63	1	∩a	∩a	PROPN
ejpam-5782	64	1	=	=	PUNCT
ejpam-5782	64	2	∅.	∅.	VERB
ejpam-5782	64	3	the	the	DET
ejpam-5782	64	4	following	follow	VERB
ejpam-5782	64	5	is	be	AUX
ejpam-5782	64	6	an	an	DET
ejpam-5782	64	7	immediate	immediate	ADJ
ejpam-5782	64	8	consequence	consequence	NOUN
ejpam-5782	64	9	that	that	PRON
ejpam-5782	64	10	can	can	AUX
ejpam-5782	64	11	be	be	AUX
ejpam-5782	64	12	obviously	obviously	ADV
ejpam-5782	64	13	obtained	obtain	VERB
ejpam-5782	64	14	.	.	PUNCT
ejpam-5782	65	1	corollary	corollary	ADJ
ejpam-5782	65	2	1	1	NUM
ejpam-5782	65	3	.	.	PUNCT
ejpam-5782	66	1	let	let	VERB
ejpam-5782	66	2	µ	µ	NOUN
ejpam-5782	66	3	and	and	CCONJ
ejpam-5782	66	4	ν	ν	PROPN
ejpam-5782	66	5	be	be	AUX
ejpam-5782	66	6	two	two	NUM
ejpam-5782	66	7	gt	gt	NOUN
ejpam-5782	66	8	’s	’s	NOUN
ejpam-5782	66	9	on	on	ADP
ejpam-5782	66	10	a	a	DET
ejpam-5782	66	11	nonempty	nonempty	ADV
ejpam-5782	66	12	set	set	VERB
ejpam-5782	66	13	x	x	PUNCT
ejpam-5782	66	14	such	such	ADJ
ejpam-5782	66	15	that	that	SCONJ
ejpam-5782	66	16	µ	µ	NOUN
ejpam-5782	66	17	=	=	SYM
ejpam-5782	66	18	ν	ν	NOUN
ejpam-5782	66	19	,	,	PUNCT
ejpam-5782	66	20	and	and	CCONJ
ejpam-5782	66	21	let	let	VERB
ejpam-5782	66	22	h	h	NOUN
ejpam-5782	66	23	be	be	AUX
ejpam-5782	66	24	a	a	DET
ejpam-5782	66	25	hereditary	hereditary	ADJ
ejpam-5782	66	26	class	class	NOUN
ejpam-5782	66	27	on	on	ADP
ejpam-5782	66	28	x.	x.	NOUN
ejpam-5782	66	29	for	for	ADP
ejpam-5782	66	30	any	any	DET
ejpam-5782	66	31	a	a	DET
ejpam-5782	66	32	⊆	⊆	NUM
ejpam-5782	66	33	x	x	NOUN
ejpam-5782	66	34	,	,	PUNCT
ejpam-5782	66	35	the	the	DET
ejpam-5782	66	36	following	following	ADJ
ejpam-5782	66	37	statements	statement	NOUN
ejpam-5782	66	38	hold	hold	VERB
ejpam-5782	66	39	:	:	PUNCT
ejpam-5782	66	40	(	(	PUNCT
ejpam-5782	66	41	i	i	NOUN
ejpam-5782	66	42	)	)	PUNCT
ejpam-5782	66	43	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	66	44	,	,	PUNCT
ejpam-5782	66	45	ν)(a	ν)(a	NUM
ejpam-5782	66	46	)	)	PUNCT
ejpam-5782	66	47	=	=	SYM
ejpam-5782	67	1	γ∗(a	γ∗(a	NOUN
ejpam-5782	67	2	)	)	PUNCT
ejpam-5782	67	3	.	.	PUNCT
ejpam-5782	68	1	(	(	PUNCT
ejpam-5782	68	2	ii	ii	NOUN
ejpam-5782	68	3	)	)	PUNCT
ejpam-5782	68	4	if	if	SCONJ
ejpam-5782	68	5	h	h	NOUN
ejpam-5782	68	6	=	=	NOUN
ejpam-5782	68	7	{	{	PUNCT
ejpam-5782	68	8	∅	∅	NOUN
ejpam-5782	68	9	}	}	PUNCT
ejpam-5782	68	10	,	,	PUNCT
ejpam-5782	68	11	then	then	ADV
ejpam-5782	68	12	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	68	13	,	,	PUNCT
ejpam-5782	68	14	ν)(a	ν)(a	NUM
ejpam-5782	68	15	)	)	PUNCT
ejpam-5782	68	16	=	=	SYM
ejpam-5782	68	17	γ∗(a	γ∗(a	NOUN
ejpam-5782	68	18	)	)	PUNCT
ejpam-5782	68	19	=	=	PUNCT
ejpam-5782	68	20	γθ(a	γθ(a	NUM
ejpam-5782	68	21	)	)	PUNCT
ejpam-5782	68	22	.	.	PUNCT
ejpam-5782	69	1	theorem	theorem	ADJ
ejpam-5782	69	2	4	4	NUM
ejpam-5782	69	3	.	.	PUNCT
ejpam-5782	69	4	let	let	VERB
ejpam-5782	69	5	µ	µ	NOUN
ejpam-5782	69	6	and	and	CCONJ
ejpam-5782	69	7	ν	ν	PROPN
ejpam-5782	69	8	be	be	AUX
ejpam-5782	69	9	two	two	NUM
ejpam-5782	69	10	gt	gt	NOUN
ejpam-5782	69	11	’s	’s	NOUN
ejpam-5782	69	12	on	on	ADP
ejpam-5782	69	13	a	a	DET
ejpam-5782	69	14	nonempty	nonempty	ADV
ejpam-5782	69	15	set	set	VERB
ejpam-5782	69	16	x	x	NOUN
ejpam-5782	69	17	,	,	PUNCT
ejpam-5782	69	18	and	and	CCONJ
ejpam-5782	69	19	let	let	VERB
ejpam-5782	69	20	h	h	NOUN
ejpam-5782	69	21	be	be	AUX
ejpam-5782	69	22	a	a	DET
ejpam-5782	69	23	hereditary	hereditary	ADJ
ejpam-5782	69	24	class	class	NOUN
ejpam-5782	69	25	on	on	ADP
ejpam-5782	69	26	x.	x.	NOUN
ejpam-5782	69	27	then	then	ADV
ejpam-5782	69	28	for	for	ADP
ejpam-5782	69	29	any	any	DET
ejpam-5782	69	30	a	a	DET
ejpam-5782	69	31	⊆	⊆	NUM
ejpam-5782	69	32	x	x	SYM
ejpam-5782	69	33	,	,	PUNCT
ejpam-5782	69	34	we	we	PRON
ejpam-5782	69	35	have	have	VERB
ejpam-5782	69	36	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	69	37	,	,	PUNCT
ejpam-5782	69	38	ν)(a	ν)(a	NUM
ejpam-5782	69	39	)	)	PUNCT
ejpam-5782	69	40	⊆	⊆	NUM
ejpam-5782	69	41	γθ(µ,ν)(a	γθ(µ,ν)(a	NUM
ejpam-5782	69	42	)	)	PUNCT
ejpam-5782	69	43	.	.	PUNCT
ejpam-5782	70	1	proof	proof	NOUN
ejpam-5782	70	2	.	.	PUNCT
ejpam-5782	71	1	let	let	VERB
ejpam-5782	71	2	x	x	SYM
ejpam-5782	71	3	∈	∈	PROPN
ejpam-5782	71	4	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	71	5	,	,	PUNCT
ejpam-5782	71	6	ν)(a	ν)(a	NOUN
ejpam-5782	71	7	)	)	PUNCT
ejpam-5782	71	8	.	.	PUNCT
ejpam-5782	72	1	for	for	ADP
ejpam-5782	72	2	each	each	DET
ejpam-5782	72	3	µ-open	µ-open	NOUN
ejpam-5782	72	4	set	set	VERB
ejpam-5782	72	5	m	m	VERB
ejpam-5782	72	6	containing	contain	VERB
ejpam-5782	72	7	x	x	SYM
ejpam-5782	72	8	,	,	PUNCT
ejpam-5782	72	9	we	we	PRON
ejpam-5782	72	10	have	have	VERB
ejpam-5782	72	11	c∗ν(m)∩a	c∗ν(m)∩a	NOUN
ejpam-5782	72	12	̸=	̸=	PROPN
ejpam-5782	72	13	∅.	∅.	ADV
ejpam-5782	72	14	since	since	SCONJ
ejpam-5782	72	15	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	72	16	)	)	PUNCT
ejpam-5782	72	17	⊆	⊆	NUM
ejpam-5782	72	18	cν(m	cν(m	NOUN
ejpam-5782	72	19	)	)	PUNCT
ejpam-5782	72	20	,	,	PUNCT
ejpam-5782	72	21	it	it	PRON
ejpam-5782	72	22	follows	follow	VERB
ejpam-5782	72	23	that	that	SCONJ
ejpam-5782	72	24	cν(m)∩a	cν(m)∩a	PROPN
ejpam-5782	72	25	̸=	̸=	PROPN
ejpam-5782	72	26	∅.	∅.	VERB
ejpam-5782	72	27	therefore	therefore	ADV
ejpam-5782	72	28	,	,	PUNCT
ejpam-5782	72	29	x	x	PROPN
ejpam-5782	72	30	∈	∈	PROPN
ejpam-5782	72	31	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	72	32	)	)	PUNCT
ejpam-5782	72	33	,	,	PUNCT
ejpam-5782	72	34	and	and	CCONJ
ejpam-5782	72	35	so	so	ADV
ejpam-5782	72	36	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	72	37	,	,	PUNCT
ejpam-5782	72	38	ν)(a	ν)(a	NUM
ejpam-5782	72	39	)	)	PUNCT
ejpam-5782	72	40	⊆	⊆	NUM
ejpam-5782	72	41	γθ(µ,ν)(a	γθ(µ,ν)(a	NUM
ejpam-5782	72	42	)	)	PUNCT
ejpam-5782	72	43	.	.	PUNCT
ejpam-5782	73	1	the	the	DET
ejpam-5782	73	2	following	follow	VERB
ejpam-5782	73	3	example	example	NOUN
ejpam-5782	73	4	demonstrates	demonstrate	VERB
ejpam-5782	73	5	that	that	SCONJ
ejpam-5782	73	6	,	,	PUNCT
ejpam-5782	73	7	in	in	ADP
ejpam-5782	73	8	general	general	ADJ
ejpam-5782	73	9	,	,	PUNCT
ejpam-5782	73	10	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	73	11	,	,	PUNCT
ejpam-5782	73	12	ν)(a	ν)(a	NUM
ejpam-5782	73	13	)	)	PUNCT
ejpam-5782	73	14	̸=	̸=	NOUN
ejpam-5782	73	15	γθ(µ	γθ(µ	NOUN
ejpam-5782	73	16	,	,	PUNCT
ejpam-5782	73	17	ν)(a	ν)(a	NOUN
ejpam-5782	73	18	)	)	PUNCT
ejpam-5782	73	19	.	.	PUNCT
ejpam-5782	74	1	example	example	NOUN
ejpam-5782	75	1	1	1	X
ejpam-5782	75	2	.	.	PUNCT
ejpam-5782	75	3	let	let	VERB
ejpam-5782	75	4	x	x	PUNCT
ejpam-5782	75	5	=	=	PRON
ejpam-5782	75	6	{	{	PUNCT
ejpam-5782	75	7	a	a	PRON
ejpam-5782	75	8	,	,	PUNCT
ejpam-5782	75	9	b	b	NOUN
ejpam-5782	75	10	,	,	PUNCT
ejpam-5782	75	11	c	c	NOUN
ejpam-5782	75	12	,	,	PUNCT
ejpam-5782	75	13	d	d	NOUN
ejpam-5782	75	14	}	}	PUNCT
ejpam-5782	75	15	.	.	PUNCT
ejpam-5782	76	1	consider	consider	VERB
ejpam-5782	76	2	two	two	NUM
ejpam-5782	76	3	generalized	generalized	ADJ
ejpam-5782	76	4	topologies	topology	NOUN
ejpam-5782	76	5	:	:	PUNCT
ejpam-5782	76	6	µ	µ	X
ejpam-5782	76	7	=	=	SYM
ejpam-5782	76	8	{	{	PUNCT
ejpam-5782	76	9	∅	∅	NOUN
ejpam-5782	76	10	,	,	PUNCT
ejpam-5782	76	11	{	{	PUNCT
ejpam-5782	76	12	b	b	NOUN
ejpam-5782	76	13	,	,	PUNCT
ejpam-5782	76	14	d	d	NOUN
ejpam-5782	76	15	}	}	PUNCT
ejpam-5782	76	16	}	}	PUNCT
ejpam-5782	76	17	and	and	CCONJ
ejpam-5782	76	18	ν	ν	X
ejpam-5782	76	19	=	=	SYM
ejpam-5782	76	20	{	{	PUNCT
ejpam-5782	76	21	∅	∅	NOUN
ejpam-5782	76	22	,	,	PUNCT
ejpam-5782	76	23	{	{	PUNCT
ejpam-5782	76	24	a	a	DET
ejpam-5782	76	25	,	,	PUNCT
ejpam-5782	76	26	b	b	NOUN
ejpam-5782	76	27	}	}	PUNCT
ejpam-5782	76	28	,	,	PUNCT
ejpam-5782	76	29	{	{	PUNCT
ejpam-5782	76	30	b	b	X
ejpam-5782	76	31	,	,	PUNCT
ejpam-5782	76	32	c	c	NOUN
ejpam-5782	76	33	}	}	PUNCT
ejpam-5782	76	34	,	,	PUNCT
ejpam-5782	76	35	{	{	PUNCT
ejpam-5782	76	36	a	a	PRON
ejpam-5782	76	37	,	,	PUNCT
ejpam-5782	76	38	b	b	NOUN
ejpam-5782	76	39	,	,	PUNCT
ejpam-5782	76	40	c	c	NOUN
ejpam-5782	76	41	}	}	PUNCT
ejpam-5782	76	42	}	}	PUNCT
ejpam-5782	76	43	,	,	PUNCT
ejpam-5782	76	44	and	and	CCONJ
ejpam-5782	76	45	a	a	DET
ejpam-5782	76	46	hereditary	hereditary	ADJ
ejpam-5782	76	47	class	class	NOUN
ejpam-5782	76	48	h	h	NOUN
ejpam-5782	76	49	=	=	PRON
ejpam-5782	76	50	{	{	PUNCT
ejpam-5782	76	51	∅	∅	NOUN
ejpam-5782	76	52	,	,	PUNCT
ejpam-5782	76	53	{	{	PUNCT
ejpam-5782	76	54	b	b	NOUN
ejpam-5782	76	55	}	}	PUNCT
ejpam-5782	76	56	}	}	PUNCT
ejpam-5782	76	57	on	on	ADP
ejpam-5782	76	58	x.	x.	NOUN
ejpam-5782	76	59	for	for	ADP
ejpam-5782	76	60	a	a	DET
ejpam-5782	76	61	set	set	NOUN
ejpam-5782	76	62	a	a	X
ejpam-5782	76	63	=	=	X
ejpam-5782	76	64	{	{	PUNCT
ejpam-5782	76	65	a	a	X
ejpam-5782	76	66	,	,	PUNCT
ejpam-5782	76	67	c	c	NOUN
ejpam-5782	76	68	}	}	PUNCT
ejpam-5782	76	69	,	,	PUNCT
ejpam-5782	76	70	we	we	PRON
ejpam-5782	76	71	have	have	VERB
ejpam-5782	76	72	cν({b	cν({b	ADJ
ejpam-5782	76	73	,	,	PUNCT
ejpam-5782	76	74	d	d	NOUN
ejpam-5782	76	75	}	}	PUNCT
ejpam-5782	76	76	)	)	PUNCT
ejpam-5782	77	1	=	=	SYM
ejpam-5782	77	2	x	x	X
ejpam-5782	77	3	,	,	PUNCT
ejpam-5782	77	4	mµ	mµ	ADP
ejpam-5782	77	5	=	=	SYM
ejpam-5782	77	6	{	{	PUNCT
ejpam-5782	77	7	b	b	NOUN
ejpam-5782	77	8	,	,	PUNCT
ejpam-5782	77	9	d	d	NOUN
ejpam-5782	77	10	}	}	PUNCT
ejpam-5782	77	11	,	,	PUNCT
ejpam-5782	77	12	and	and	CCONJ
ejpam-5782	77	13	cν({b	cν({b	ADJ
ejpam-5782	77	14	,	,	PUNCT
ejpam-5782	77	15	d	d	NOUN
ejpam-5782	77	16	}	}	PUNCT
ejpam-5782	77	17	)	)	PUNCT
ejpam-5782	77	18	∩	∩	NOUN
ejpam-5782	77	19	a	a	DET
ejpam-5782	77	20	̸=	̸=	PROPN
ejpam-5782	77	21	∅.	∅.	ADV
ejpam-5782	77	22	thus	thus	ADV
ejpam-5782	77	23	,	,	PUNCT
ejpam-5782	77	24	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	77	25	)	)	PUNCT
ejpam-5782	77	26	=	=	PUNCT
ejpam-5782	78	1	x.	x.	NOUN
ejpam-5782	78	2	since	since	SCONJ
ejpam-5782	78	3	mµ	mµ	VERB
ejpam-5782	78	4	=	=	SYM
ejpam-5782	78	5	{	{	PUNCT
ejpam-5782	78	6	b	b	NOUN
ejpam-5782	78	7	,	,	PUNCT
ejpam-5782	78	8	d	d	NOUN
ejpam-5782	78	9	}	}	PUNCT
ejpam-5782	78	10	,	,	PUNCT
ejpam-5782	78	11	it	it	PRON
ejpam-5782	78	12	is	be	AUX
ejpam-5782	78	13	clear	clear	ADJ
ejpam-5782	78	14	that	that	SCONJ
ejpam-5782	78	15	a	a	X
ejpam-5782	78	16	,	,	PUNCT
ejpam-5782	78	17	c	c	PROPN
ejpam-5782	78	18	∈	∈	PROPN
ejpam-5782	78	19	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	78	20	,	,	PUNCT
ejpam-5782	78	21	ν)(a	ν)(a	NOUN
ejpam-5782	78	22	)	)	PUNCT
ejpam-5782	78	23	.	.	PUNCT
ejpam-5782	79	1	noting	note	VERB
ejpam-5782	79	2	that	that	SCONJ
ejpam-5782	79	3	{	{	PUNCT
ejpam-5782	79	4	b	b	X
ejpam-5782	79	5	,	,	PUNCT
ejpam-5782	79	6	d}∗(h	d}∗(h	PROPN
ejpam-5782	79	7	,	,	PUNCT
ejpam-5782	79	8	ν	ν	NOUN
ejpam-5782	79	9	)	)	PUNCT
ejpam-5782	79	10	=	=	SYM
ejpam-5782	79	11	{	{	PUNCT
ejpam-5782	79	12	d	d	NOUN
ejpam-5782	79	13	}	}	PUNCT
ejpam-5782	79	14	,	,	PUNCT
ejpam-5782	79	15	we	we	PRON
ejpam-5782	79	16	find	find	VERB
ejpam-5782	79	17	c∗ν({b	c∗ν({b	ADJ
ejpam-5782	79	18	,	,	PUNCT
ejpam-5782	79	19	d	d	NOUN
ejpam-5782	79	20	}	}	PUNCT
ejpam-5782	79	21	)	)	PUNCT
ejpam-5782	79	22	∩	∩	NOUN
ejpam-5782	79	23	a	a	DET
ejpam-5782	79	24	=	=	SYM
ejpam-5782	79	25	∅	∅	NOUN
ejpam-5782	79	26	,	,	PUNCT
ejpam-5782	79	27	hence	hence	ADV
ejpam-5782	79	28	b	b	NOUN
ejpam-5782	79	29	,	,	PUNCT
ejpam-5782	79	30	d	d	PROPN
ejpam-5782	79	31	/∈	/∈	PROPN
ejpam-5782	79	32	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	79	33	,	,	PUNCT
ejpam-5782	79	34	ν)(a	ν)(a	NOUN
ejpam-5782	79	35	)	)	PUNCT
ejpam-5782	79	36	.	.	PUNCT
ejpam-5782	80	1	therefore	therefore	ADV
ejpam-5782	80	2	,	,	PUNCT
ejpam-5782	80	3	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	80	4	,	,	PUNCT
ejpam-5782	80	5	ν)(a	ν)(a	NUM
ejpam-5782	80	6	)	)	PUNCT
ejpam-5782	80	7	=	=	PRON
ejpam-5782	80	8	{	{	PUNCT
ejpam-5782	80	9	a	a	X
ejpam-5782	80	10	,	,	PUNCT
ejpam-5782	80	11	c	c	NOUN
ejpam-5782	80	12	}	}	PUNCT
ejpam-5782	80	13	and	and	CCONJ
ejpam-5782	80	14	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	80	15	,	,	PUNCT
ejpam-5782	80	16	ν)(a	ν)(a	NUM
ejpam-5782	80	17	)	)	PUNCT
ejpam-5782	80	18	⊂	⊂	PROPN
ejpam-5782	80	19	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	80	20	)	)	PUNCT
ejpam-5782	80	21	.	.	PUNCT
ejpam-5782	81	1	corollary	corollary	ADJ
ejpam-5782	81	2	2	2	NUM
ejpam-5782	81	3	.	.	PUNCT
ejpam-5782	82	1	let	let	VERB
ejpam-5782	82	2	µ	µ	NOUN
ejpam-5782	82	3	and	and	CCONJ
ejpam-5782	82	4	ν	ν	PROPN
ejpam-5782	82	5	be	be	AUX
ejpam-5782	82	6	two	two	NUM
ejpam-5782	82	7	gt	gt	NOUN
ejpam-5782	82	8	’s	’s	NOUN
ejpam-5782	82	9	on	on	ADP
ejpam-5782	82	10	a	a	DET
ejpam-5782	82	11	nonempty	nonempty	ADV
ejpam-5782	82	12	set	set	VERB
ejpam-5782	82	13	x	x	PUNCT
ejpam-5782	82	14	and	and	CCONJ
ejpam-5782	82	15	let	let	VERB
ejpam-5782	82	16	h	h	NOUN
ejpam-5782	82	17	be	be	AUX
ejpam-5782	82	18	a	a	DET
ejpam-5782	82	19	hereditary	hereditary	ADJ
ejpam-5782	82	20	class	class	NOUN
ejpam-5782	82	21	on	on	ADP
ejpam-5782	82	22	x.	x.	NOUN
ejpam-5782	82	23	if	if	SCONJ
ejpam-5782	82	24	h	h	PRON
ejpam-5782	82	25	=	=	NOUN
ejpam-5782	82	26	{	{	PUNCT
ejpam-5782	82	27	∅	∅	NOUN
ejpam-5782	82	28	}	}	PUNCT
ejpam-5782	82	29	,	,	PUNCT
ejpam-5782	82	30	then	then	ADV
ejpam-5782	82	31	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	82	32	,	,	PUNCT
ejpam-5782	82	33	ν)(a	ν)(a	NUM
ejpam-5782	82	34	)	)	PUNCT
ejpam-5782	82	35	=	=	SYM
ejpam-5782	82	36	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	82	37	)	)	PUNCT
ejpam-5782	82	38	for	for	ADP
ejpam-5782	82	39	any	any	DET
ejpam-5782	82	40	a	a	DET
ejpam-5782	82	41	⊆	⊆	NUM
ejpam-5782	82	42	x.	x.	NOUN
ejpam-5782	82	43	theorem	theorem	NOUN
ejpam-5782	82	44	5	5	NUM
ejpam-5782	82	45	.	.	PUNCT
ejpam-5782	83	1	let	let	VERB
ejpam-5782	83	2	µ	µ	NOUN
ejpam-5782	83	3	and	and	CCONJ
ejpam-5782	83	4	ν	ν	PROPN
ejpam-5782	83	5	be	be	AUX
ejpam-5782	83	6	two	two	NUM
ejpam-5782	83	7	gt	gt	NOUN
ejpam-5782	83	8	’s	’s	NOUN
ejpam-5782	83	9	on	on	ADP
ejpam-5782	83	10	a	a	DET
ejpam-5782	83	11	nonempty	nonempty	ADV
ejpam-5782	83	12	set	set	VERB
ejpam-5782	83	13	x	x	NOUN
ejpam-5782	83	14	,	,	PUNCT
ejpam-5782	83	15	and	and	CCONJ
ejpam-5782	83	16	let	let	VERB
ejpam-5782	83	17	h	h	NOUN
ejpam-5782	83	18	be	be	AUX
ejpam-5782	83	19	a	a	DET
ejpam-5782	83	20	hereditary	hereditary	ADJ
ejpam-5782	83	21	class	class	NOUN
ejpam-5782	83	22	on	on	ADP
ejpam-5782	83	23	x.	x.	NOUN
ejpam-5782	83	24	for	for	ADP
ejpam-5782	83	25	any	any	DET
ejpam-5782	83	26	subsets	subset	NOUN
ejpam-5782	83	27	a	a	PRON
ejpam-5782	83	28	and	and	CCONJ
ejpam-5782	83	29	b	b	NOUN
ejpam-5782	83	30	of	of	ADP
ejpam-5782	83	31	x	x	PRON
ejpam-5782	83	32	,	,	PUNCT
ejpam-5782	83	33	the	the	DET
ejpam-5782	83	34	following	follow	VERB
ejpam-5782	83	35	properties	property	NOUN
ejpam-5782	83	36	hold	hold	VERB
ejpam-5782	83	37	:	:	PUNCT
ejpam-5782	83	38	(	(	PUNCT
ejpam-5782	83	39	i	i	NOUN
ejpam-5782	83	40	)	)	PUNCT
ejpam-5782	83	41	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	83	42	,	,	PUNCT
ejpam-5782	83	43	ν)(∅	ν)(∅	NOUN
ejpam-5782	83	44	)	)	PUNCT
ejpam-5782	83	45	=	=	SYM
ejpam-5782	83	46	∅.	∅.	PRON
ejpam-5782	83	47	(	(	PUNCT
ejpam-5782	83	48	ii	ii	NOUN
ejpam-5782	83	49	)	)	PUNCT
ejpam-5782	83	50	if	if	SCONJ
ejpam-5782	83	51	a	a	DET
ejpam-5782	83	52	⊆	⊆	NUM
ejpam-5782	83	53	b	b	NOUN
ejpam-5782	83	54	,	,	PUNCT
ejpam-5782	83	55	then	then	ADV
ejpam-5782	83	56	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	83	57	,	,	PUNCT
ejpam-5782	83	58	ν)(a	ν)(a	NUM
ejpam-5782	83	59	)	)	PUNCT
ejpam-5782	83	60	⊆	⊆	NUM
ejpam-5782	83	61	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	83	62	,	,	PUNCT
ejpam-5782	83	63	ν)(b	ν)(b	PROPN
ejpam-5782	83	64	)	)	PUNCT
ejpam-5782	83	65	.	.	PUNCT
ejpam-5782	84	1	(	(	PUNCT
ejpam-5782	84	2	iii	iii	X
ejpam-5782	84	3	)	)	PUNCT
ejpam-5782	84	4	a	a	DET
ejpam-5782	84	5	⊆	⊆	NUM
ejpam-5782	84	6	cµ(a	cµ(a	NUM
ejpam-5782	84	7	)	)	PUNCT
ejpam-5782	84	8	⊆	⊆	NUM
ejpam-5782	84	9	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	84	10	,	,	PUNCT
ejpam-5782	84	11	ν)(a	ν)(a	NOUN
ejpam-5782	84	12	)	)	PUNCT
ejpam-5782	84	13	.	.	PUNCT
ejpam-5782	85	1	proof	proof	NOUN
ejpam-5782	85	2	.	.	PUNCT
ejpam-5782	86	1	(	(	PUNCT
ejpam-5782	86	2	1	1	X
ejpam-5782	86	3	)	)	PUNCT
ejpam-5782	86	4	and	and	CCONJ
ejpam-5782	86	5	(	(	PUNCT
ejpam-5782	86	6	2	2	X
ejpam-5782	86	7	)	)	PUNCT
ejpam-5782	86	8	are	be	AUX
ejpam-5782	86	9	obvious	obvious	ADJ
ejpam-5782	86	10	.	.	PUNCT
ejpam-5782	87	1	(	(	PUNCT
ejpam-5782	87	2	3	3	X
ejpam-5782	87	3	)	)	PUNCT
ejpam-5782	87	4	for	for	ADP
ejpam-5782	87	5	x	x	PROPN
ejpam-5782	87	6	∈	∈	PROPN
ejpam-5782	87	7	cµ(a	cµ(a	PROPN
ejpam-5782	87	8	)	)	PUNCT
ejpam-5782	87	9	and	and	CCONJ
ejpam-5782	87	10	any	any	DET
ejpam-5782	87	11	µ-open	µ-open	NOUN
ejpam-5782	87	12	set	set	VERB
ejpam-5782	87	13	m	m	VERB
ejpam-5782	87	14	containing	contain	VERB
ejpam-5782	87	15	x	x	SYM
ejpam-5782	87	16	,	,	PUNCT
ejpam-5782	87	17	we	we	PRON
ejpam-5782	87	18	have	have	VERB
ejpam-5782	87	19	m	m	NOUN
ejpam-5782	87	20	∩	∩	NOUN
ejpam-5782	87	21	a	a	DET
ejpam-5782	87	22	̸=	̸=	PROPN
ejpam-5782	87	23	∅.	∅.	ADV
ejpam-5782	87	24	consequently	consequently	ADV
ejpam-5782	87	25	,	,	PUNCT
ejpam-5782	87	26	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	87	27	)	)	PUNCT
ejpam-5782	88	1	∩a	∩a	PROPN
ejpam-5782	88	2	̸=	̸=	PROPN
ejpam-5782	88	3	∅.	∅.	VERB
ejpam-5782	88	4	therefore	therefore	ADV
ejpam-5782	88	5	,	,	PUNCT
ejpam-5782	88	6	x	x	PROPN
ejpam-5782	88	7	∈	∈	PROPN
ejpam-5782	88	8	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	88	9	,	,	PUNCT
ejpam-5782	88	10	ν)(a	ν)(a	NUM
ejpam-5782	88	11	)	)	PUNCT
ejpam-5782	88	12	,	,	PUNCT
ejpam-5782	88	13	implying	imply	VERB
ejpam-5782	88	14	that	that	SCONJ
ejpam-5782	88	15	cµ(a	cµ(a	PROPN
ejpam-5782	88	16	)	)	PUNCT
ejpam-5782	88	17	⊆	⊆	NUM
ejpam-5782	88	18	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	88	19	,	,	PUNCT
ejpam-5782	88	20	ν)(a	ν)(a	PROPN
ejpam-5782	88	21	)	)	PUNCT
ejpam-5782	88	22	.	.	PUNCT
ejpam-5782	89	1	the	the	DET
ejpam-5782	89	2	following	follow	VERB
ejpam-5782	89	3	example	example	NOUN
ejpam-5782	89	4	shows	show	VERB
ejpam-5782	89	5	that	that	SCONJ
ejpam-5782	89	6	,	,	PUNCT
ejpam-5782	89	7	in	in	ADP
ejpam-5782	89	8	general	general	ADJ
ejpam-5782	89	9	,	,	PUNCT
ejpam-5782	89	10	cµ(a	cµ(a	ADJ
ejpam-5782	89	11	)	)	PUNCT
ejpam-5782	89	12	̸=	̸=	PROPN
ejpam-5782	89	13	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	89	14	,	,	PUNCT
ejpam-5782	89	15	ν)(a	ν)(a	PROPN
ejpam-5782	89	16	)	)	PUNCT
ejpam-5782	89	17	.	.	PUNCT
ejpam-5782	90	1	f.	f.	PROPN
ejpam-5782	90	2	alsharari	alsharari	PROPN
ejpam-5782	90	3	,	,	PUNCT
ejpam-5782	90	4	a.	a.	PROPN
ejpam-5782	90	5	qahis	qahis	PROPN
ejpam-5782	90	6	/	/	SYM
ejpam-5782	90	7	eur	eur	PROPN
ejpam-5782	90	8	.	.	PUNCT
ejpam-5782	91	1	j.	j.	PROPN
ejpam-5782	91	2	pure	pure	PROPN
ejpam-5782	91	3	appl	appl	PROPN
ejpam-5782	91	4	.	.	PROPN
ejpam-5782	91	5	math	math	PROPN
ejpam-5782	91	6	,	,	PUNCT
ejpam-5782	91	7	18	18	NUM
ejpam-5782	91	8	(	(	PUNCT
ejpam-5782	91	9	2	2	NUM
ejpam-5782	91	10	)	)	PUNCT
ejpam-5782	91	11	(	(	PUNCT
ejpam-5782	91	12	2025	2025	NUM
ejpam-5782	91	13	)	)	PUNCT
ejpam-5782	91	14	,	,	PUNCT
ejpam-5782	91	15	5782	5782	NUM
ejpam-5782	91	16	5	5	NUM
ejpam-5782	91	17	of	of	ADP
ejpam-5782	91	18	10	10	NUM
ejpam-5782	91	19	example	example	NOUN
ejpam-5782	92	1	2	2	NUM
ejpam-5782	92	2	.	.	PUNCT
ejpam-5782	93	1	let	let	VERB
ejpam-5782	93	2	x	x	PUNCT
ejpam-5782	93	3	=	=	PRON
ejpam-5782	93	4	{	{	PUNCT
ejpam-5782	93	5	a	a	PRON
ejpam-5782	93	6	,	,	PUNCT
ejpam-5782	93	7	b	b	NOUN
ejpam-5782	93	8	,	,	PUNCT
ejpam-5782	93	9	c	c	NOUN
ejpam-5782	93	10	,	,	PUNCT
ejpam-5782	93	11	d	d	NOUN
ejpam-5782	93	12	}	}	PUNCT
ejpam-5782	93	13	.	.	PUNCT
ejpam-5782	94	1	consider	consider	VERB
ejpam-5782	94	2	two	two	NUM
ejpam-5782	94	3	generalized	generalized	ADJ
ejpam-5782	94	4	topologies	topology	NOUN
ejpam-5782	94	5	:	:	PUNCT
ejpam-5782	94	6	µ	µ	X
ejpam-5782	94	7	=	=	SYM
ejpam-5782	94	8	{	{	PUNCT
ejpam-5782	94	9	∅	∅	NOUN
ejpam-5782	94	10	,	,	PUNCT
ejpam-5782	94	11	{	{	PUNCT
ejpam-5782	94	12	a	a	X
ejpam-5782	94	13	}	}	PUNCT
ejpam-5782	94	14	}	}	PUNCT
ejpam-5782	94	15	,	,	PUNCT
ejpam-5782	94	16	ν	ν	X
ejpam-5782	94	17	=	=	PRON
ejpam-5782	94	18	{	{	PUNCT
ejpam-5782	94	19	∅	∅	NOUN
ejpam-5782	94	20	,	,	PUNCT
ejpam-5782	94	21	{	{	PUNCT
ejpam-5782	94	22	a	a	DET
ejpam-5782	94	23	,	,	PUNCT
ejpam-5782	94	24	b	b	NOUN
ejpam-5782	94	25	}	}	PUNCT
ejpam-5782	94	26	,	,	PUNCT
ejpam-5782	94	27	{	{	PUNCT
ejpam-5782	94	28	b	b	X
ejpam-5782	94	29	,	,	PUNCT
ejpam-5782	94	30	c	c	NOUN
ejpam-5782	94	31	}	}	PUNCT
ejpam-5782	94	32	,	,	PUNCT
ejpam-5782	94	33	{	{	PUNCT
ejpam-5782	94	34	a	a	PRON
ejpam-5782	94	35	,	,	PUNCT
ejpam-5782	94	36	b	b	NOUN
ejpam-5782	94	37	,	,	PUNCT
ejpam-5782	94	38	c	c	NOUN
ejpam-5782	94	39	}	}	PUNCT
ejpam-5782	94	40	}	}	PUNCT
ejpam-5782	94	41	on	on	ADP
ejpam-5782	94	42	x	x	NOUN
ejpam-5782	94	43	,	,	PUNCT
ejpam-5782	94	44	and	and	CCONJ
ejpam-5782	94	45	a	a	DET
ejpam-5782	94	46	hereditary	hereditary	ADJ
ejpam-5782	94	47	class	class	NOUN
ejpam-5782	94	48	h	h	NOUN
ejpam-5782	94	49	=	=	PRON
ejpam-5782	94	50	{	{	PUNCT
ejpam-5782	94	51	∅	∅	NOUN
ejpam-5782	94	52	,	,	PUNCT
ejpam-5782	94	53	{	{	PUNCT
ejpam-5782	94	54	b	b	NOUN
ejpam-5782	94	55	}	}	PUNCT
ejpam-5782	94	56	}	}	PUNCT
ejpam-5782	94	57	.	.	PUNCT
ejpam-5782	95	1	for	for	ADP
ejpam-5782	95	2	a	a	DET
ejpam-5782	95	3	set	set	NOUN
ejpam-5782	95	4	a	a	PRON
ejpam-5782	95	5	=	=	SYM
ejpam-5782	95	6	{	{	PUNCT
ejpam-5782	95	7	b	b	PROPN
ejpam-5782	95	8	,	,	PUNCT
ejpam-5782	95	9	c	c	NOUN
ejpam-5782	95	10	,	,	PUNCT
ejpam-5782	95	11	d	d	NOUN
ejpam-5782	95	12	}	}	PUNCT
ejpam-5782	95	13	,	,	PUNCT
ejpam-5782	95	14	since	since	SCONJ
ejpam-5782	95	15	a	a	PRON
ejpam-5782	95	16	is	be	AUX
ejpam-5782	95	17	µ-closed	µ-close	VERB
ejpam-5782	95	18	,	,	PUNCT
ejpam-5782	95	19	cµ(a	cµ(a	ADJ
ejpam-5782	95	20	)	)	PUNCT
ejpam-5782	96	1	=	=	SYM
ejpam-5782	96	2	a.	a.	NOUN
ejpam-5782	96	3	given	give	VERB
ejpam-5782	96	4	mµ	mµ	ADP
ejpam-5782	96	5	=	=	PUNCT
ejpam-5782	96	6	{	{	PUNCT
ejpam-5782	96	7	a	a	NOUN
ejpam-5782	96	8	}	}	PUNCT
ejpam-5782	96	9	,	,	PUNCT
ejpam-5782	96	10	it	it	PRON
ejpam-5782	96	11	follows	follow	VERB
ejpam-5782	96	12	by	by	ADP
ejpam-5782	96	13	the	the	DET
ejpam-5782	96	14	definition	definition	NOUN
ejpam-5782	96	15	of	of	ADP
ejpam-5782	96	16	the	the	DET
ejpam-5782	96	17	operator	operator	NOUN
ejpam-5782	96	18	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	96	19	,	,	PUNCT
ejpam-5782	96	20	ν	ν	NOUN
ejpam-5782	96	21	)	)	PUNCT
ejpam-5782	96	22	that	that	PRON
ejpam-5782	96	23	x	x	SYM
ejpam-5782	96	24	−mµ	−mµ	PROPN
ejpam-5782	96	25	=	=	SYM
ejpam-5782	96	26	{	{	PUNCT
ejpam-5782	96	27	b	b	PROPN
ejpam-5782	96	28	,	,	PUNCT
ejpam-5782	96	29	c	c	NOUN
ejpam-5782	96	30	,	,	PUNCT
ejpam-5782	96	31	d	d	NOUN
ejpam-5782	96	32	}	}	PUNCT
ejpam-5782	96	33	⊆	⊆	NUM
ejpam-5782	96	34	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	96	35	,	,	PUNCT
ejpam-5782	96	36	ν)(a	ν)(a	PROPN
ejpam-5782	96	37	)	)	PUNCT
ejpam-5782	96	38	.	.	PUNCT
ejpam-5782	97	1	next	next	ADV
ejpam-5782	97	2	,	,	PUNCT
ejpam-5782	97	3	we	we	PRON
ejpam-5782	97	4	show	show	VERB
ejpam-5782	97	5	that	that	SCONJ
ejpam-5782	97	6	a	a	DET
ejpam-5782	97	7	∈	∈	PROPN
ejpam-5782	97	8	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	97	9	,	,	PUNCT
ejpam-5782	97	10	ν)(a	ν)(a	NOUN
ejpam-5782	97	11	)	)	PUNCT
ejpam-5782	97	12	.	.	PUNCT
ejpam-5782	98	1	since	since	SCONJ
ejpam-5782	98	2	m	m	PROPN
ejpam-5782	98	3	=	=	X
ejpam-5782	98	4	{	{	PUNCT
ejpam-5782	98	5	a	a	DET
ejpam-5782	98	6	}	}	PUNCT
ejpam-5782	98	7	∈	∈	PROPN
ejpam-5782	98	8	µ	µ	X
ejpam-5782	98	9	and	and	CCONJ
ejpam-5782	98	10	{	{	PUNCT
ejpam-5782	98	11	a}∗(h	a}∗(h	ADV
ejpam-5782	98	12	,	,	PUNCT
ejpam-5782	98	13	ν	ν	NOUN
ejpam-5782	98	14	)	)	PUNCT
ejpam-5782	98	15	=	=	SYM
ejpam-5782	98	16	{	{	PUNCT
ejpam-5782	98	17	a	a	X
ejpam-5782	98	18	,	,	PUNCT
ejpam-5782	98	19	d	d	NOUN
ejpam-5782	98	20	}	}	PUNCT
ejpam-5782	98	21	,	,	PUNCT
ejpam-5782	98	22	we	we	PRON
ejpam-5782	98	23	have	have	VERB
ejpam-5782	98	24	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	98	25	)	)	PUNCT
ejpam-5782	98	26	∩	∩	NOUN
ejpam-5782	98	27	a	a	DET
ejpam-5782	98	28	̸=	̸=	PROPN
ejpam-5782	98	29	∅.	∅.	ADV
ejpam-5782	98	30	thus	thus	ADV
ejpam-5782	98	31	,	,	PUNCT
ejpam-5782	98	32	a	a	DET
ejpam-5782	98	33	∈	∈	PROPN
ejpam-5782	98	34	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	98	35	,	,	PUNCT
ejpam-5782	98	36	ν)(a	ν)(a	NUM
ejpam-5782	98	37	)	)	PUNCT
ejpam-5782	98	38	,	,	PUNCT
ejpam-5782	98	39	implying	imply	VERB
ejpam-5782	98	40	cµ(a	cµ(a	PROPN
ejpam-5782	98	41	)	)	PUNCT
ejpam-5782	99	1	⊂	⊂	PROPN
ejpam-5782	99	2	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	99	3	,	,	PUNCT
ejpam-5782	99	4	ν)(a	ν)(a	NUM
ejpam-5782	99	5	)	)	PUNCT
ejpam-5782	99	6	=	=	PUNCT
ejpam-5782	100	1	x.	x.	NOUN
ejpam-5782	100	2	thus	thus	ADV
ejpam-5782	100	3	cµ(a	cµ(a	ADJ
ejpam-5782	100	4	)	)	PUNCT
ejpam-5782	100	5	̸=	̸=	PROPN
ejpam-5782	100	6	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	100	7	,	,	PUNCT
ejpam-5782	100	8	ν)(a	ν)(a	PROPN
ejpam-5782	100	9	)	)	PUNCT
ejpam-5782	100	10	.	.	PUNCT
ejpam-5782	101	1	the	the	DET
ejpam-5782	101	2	following	follow	VERB
ejpam-5782	101	3	corollary	corollary	NOUN
ejpam-5782	101	4	follows	follow	VERB
ejpam-5782	101	5	immediately	immediately	ADV
ejpam-5782	101	6	from	from	ADP
ejpam-5782	101	7	theorem	theorem	ADJ
ejpam-5782	101	8	5(iii	5(iii	NUM
ejpam-5782	101	9	)	)	PUNCT
ejpam-5782	101	10	,	,	PUNCT
ejpam-5782	101	11	and	and	CCONJ
ejpam-5782	101	12	theorem	theorem	VERB
ejpam-5782	101	13	1	1	NUM
ejpam-5782	101	14	.	.	PUNCT
ejpam-5782	101	15	corollary	corollary	ADJ
ejpam-5782	101	16	3	3	NUM
ejpam-5782	101	17	.	.	PUNCT
ejpam-5782	102	1	let	let	VERB
ejpam-5782	102	2	µ	µ	NOUN
ejpam-5782	102	3	and	and	CCONJ
ejpam-5782	102	4	ν	ν	PROPN
ejpam-5782	102	5	be	be	AUX
ejpam-5782	102	6	two	two	NUM
ejpam-5782	102	7	gt	gt	NOUN
ejpam-5782	102	8	’s	’s	NOUN
ejpam-5782	102	9	on	on	ADP
ejpam-5782	102	10	a	a	DET
ejpam-5782	102	11	nonempty	nonempty	ADV
ejpam-5782	102	12	set	set	VERB
ejpam-5782	102	13	x	x	NOUN
ejpam-5782	102	14	,	,	PUNCT
ejpam-5782	102	15	and	and	CCONJ
ejpam-5782	102	16	h	h	DET
ejpam-5782	102	17	a	a	DET
ejpam-5782	102	18	hereditary	hereditary	ADJ
ejpam-5782	102	19	class	class	NOUN
ejpam-5782	102	20	on	on	ADP
ejpam-5782	102	21	x.	x.	NOUN
ejpam-5782	102	22	for	for	ADP
ejpam-5782	102	23	a	a	DET
ejpam-5782	102	24	⊆	⊆	NUM
ejpam-5782	102	25	x	x	NOUN
ejpam-5782	102	26	,	,	PUNCT
ejpam-5782	102	27	a∗	a∗	PROPN
ejpam-5782	102	28	⊆	⊆	NUM
ejpam-5782	102	29	c∗µ(a	c∗µ(a	PROPN
ejpam-5782	102	30	)	)	PUNCT
ejpam-5782	102	31	⊆	⊆	NUM
ejpam-5782	102	32	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	102	33	,	,	PUNCT
ejpam-5782	102	34	ν)(a	ν)(a	NOUN
ejpam-5782	102	35	)	)	PUNCT
ejpam-5782	102	36	.	.	PUNCT
ejpam-5782	103	1	theorem	theorem	VERB
ejpam-5782	103	2	6	6	NUM
ejpam-5782	103	3	.	.	PUNCT
ejpam-5782	104	1	let	let	VERB
ejpam-5782	104	2	µ	µ	NOUN
ejpam-5782	104	3	and	and	CCONJ
ejpam-5782	104	4	ν	ν	PROPN
ejpam-5782	104	5	be	be	AUX
ejpam-5782	104	6	two	two	NUM
ejpam-5782	104	7	gt	gt	NOUN
ejpam-5782	104	8	’s	’s	NOUN
ejpam-5782	104	9	on	on	ADP
ejpam-5782	104	10	a	a	DET
ejpam-5782	104	11	nonempty	nonempty	ADJ
ejpam-5782	104	12	set	set	VERB
ejpam-5782	104	13	x	x	SYM
ejpam-5782	104	14	,	,	PUNCT
ejpam-5782	104	15	h	h	PROPN
ejpam-5782	104	16	a	a	DET
ejpam-5782	104	17	hereditary	hereditary	ADJ
ejpam-5782	104	18	class	class	NOUN
ejpam-5782	104	19	on	on	ADP
ejpam-5782	104	20	x	x	NOUN
ejpam-5782	104	21	,	,	PUNCT
ejpam-5782	104	22	and	and	CCONJ
ejpam-5782	104	23	a	a	DET
ejpam-5782	104	24	⊆	⊆	NUM
ejpam-5782	104	25	x.	x.	NOUN
ejpam-5782	104	26	then	then	ADV
ejpam-5782	104	27	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	104	28	,	,	PUNCT
ejpam-5782	104	29	ν)(a	ν)(a	NUM
ejpam-5782	104	30	)	)	PUNCT
ejpam-5782	105	1	is	be	AUX
ejpam-5782	105	2	µ-closed	µ-close	VERB
ejpam-5782	105	3	.	.	PUNCT
ejpam-5782	106	1	proof	proof	NOUN
ejpam-5782	106	2	.	.	PUNCT
ejpam-5782	107	1	let	let	VERB
ejpam-5782	107	2	x	x	SYM
ejpam-5782	107	3	∈	∈	PROPN
ejpam-5782	107	4	x	x	X
ejpam-5782	107	5	−	−	PROPN
ejpam-5782	107	6	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	107	7	,	,	PUNCT
ejpam-5782	107	8	ν)(a	ν)(a	PROPN
ejpam-5782	107	9	)	)	PUNCT
ejpam-5782	107	10	.	.	PUNCT
ejpam-5782	108	1	this	this	PRON
ejpam-5782	108	2	means	mean	VERB
ejpam-5782	108	3	there	there	PRON
ejpam-5782	108	4	exists	exist	VERB
ejpam-5782	108	5	mx	mx	PROPN
ejpam-5782	108	6	∈	∈	PROPN
ejpam-5782	108	7	µ	µ	PRON
ejpam-5782	108	8	such	such	ADJ
ejpam-5782	108	9	that	that	DET
ejpam-5782	108	10	c∗ν(mx	c∗ν(mx	PROPN
ejpam-5782	108	11	)	)	PUNCT
ejpam-5782	108	12	∩	∩	NOUN
ejpam-5782	108	13	a	a	DET
ejpam-5782	108	14	=	=	SYM
ejpam-5782	108	15	∅.	∅.	NOUN
ejpam-5782	108	16	since	since	SCONJ
ejpam-5782	108	17	mx	mx	PROPN
ejpam-5782	108	18	⊆	⊆	NUM
ejpam-5782	108	19	c∗ν(mx	c∗ν(mx	NOUN
ejpam-5782	108	20	)	)	PUNCT
ejpam-5782	108	21	,	,	PUNCT
ejpam-5782	108	22	it	it	PRON
ejpam-5782	108	23	follows	follow	VERB
ejpam-5782	108	24	that	that	SCONJ
ejpam-5782	108	25	mx	mx	PROPN
ejpam-5782	108	26	∩	∩	PROPN
ejpam-5782	108	27	a	a	DET
ejpam-5782	108	28	=	=	SYM
ejpam-5782	108	29	∅.	∅.	VERB
ejpam-5782	108	30	therefore	therefore	ADV
ejpam-5782	108	31	,	,	PUNCT
ejpam-5782	108	32	every	every	DET
ejpam-5782	108	33	y	y	PROPN
ejpam-5782	108	34	∈	∈	PROPN
ejpam-5782	108	35	mx	mx	PROPN
ejpam-5782	108	36	implies	imply	VERB
ejpam-5782	108	37	y	y	PROPN
ejpam-5782	108	38	∈	∈	PROPN
ejpam-5782	108	39	x	x	X
ejpam-5782	108	40	−	−	PROPN
ejpam-5782	108	41	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	108	42	,	,	PUNCT
ejpam-5782	108	43	ν)(a	ν)(a	NUM
ejpam-5782	108	44	)	)	PUNCT
ejpam-5782	108	45	,	,	PUNCT
ejpam-5782	108	46	implying	imply	VERB
ejpam-5782	108	47	x	x	X
ejpam-5782	108	48	−	−	PROPN
ejpam-5782	108	49	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	108	50	,	,	PUNCT
ejpam-5782	108	51	ν)(a	ν)(a	NUM
ejpam-5782	108	52	)	)	PUNCT
ejpam-5782	108	53	=	=	SYM
ejpam-5782	108	54	⋃	⋃	NOUN
ejpam-5782	108	55	x∈x−γ∗(µ,ν)(a)mx	x∈x−γ∗(µ,ν)(a)mx	NOUN
ejpam-5782	108	56	.	.	PUNCT
ejpam-5782	109	1	thus	thus	ADV
ejpam-5782	109	2	,	,	PUNCT
ejpam-5782	109	3	x	x	PROPN
ejpam-5782	109	4	−	−	PROPN
ejpam-5782	109	5	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	109	6	,	,	PUNCT
ejpam-5782	109	7	ν)(a	ν)(a	NUM
ejpam-5782	109	8	)	)	PUNCT
ejpam-5782	109	9	is	be	AUX
ejpam-5782	109	10	µ-open	µ-open	NOUN
ejpam-5782	109	11	,	,	PUNCT
ejpam-5782	109	12	hence	hence	ADV
ejpam-5782	109	13	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	109	14	,	,	PUNCT
ejpam-5782	109	15	ν)(a	ν)(a	NUM
ejpam-5782	109	16	)	)	PUNCT
ejpam-5782	109	17	is	be	AUX
ejpam-5782	109	18	µ-closed	µ-close	VERB
ejpam-5782	109	19	.	.	PUNCT
ejpam-5782	110	1	theorem	theorem	ADJ
ejpam-5782	110	2	7	7	NUM
ejpam-5782	110	3	.	.	PUNCT
ejpam-5782	110	4	let	let	VERB
ejpam-5782	110	5	µ	µ	NOUN
ejpam-5782	110	6	and	and	CCONJ
ejpam-5782	110	7	ν	ν	PROPN
ejpam-5782	110	8	be	be	AUX
ejpam-5782	110	9	two	two	NUM
ejpam-5782	110	10	gt	gt	NOUN
ejpam-5782	110	11	’s	’s	NOUN
ejpam-5782	110	12	on	on	ADP
ejpam-5782	110	13	a	a	DET
ejpam-5782	110	14	nonempty	nonempty	ADV
ejpam-5782	110	15	set	set	VERB
ejpam-5782	110	16	x	x	NOUN
ejpam-5782	110	17	,	,	PUNCT
ejpam-5782	110	18	and	and	CCONJ
ejpam-5782	110	19	h	h	DET
ejpam-5782	110	20	a	a	DET
ejpam-5782	110	21	hereditary	hereditary	ADJ
ejpam-5782	110	22	class	class	NOUN
ejpam-5782	110	23	on	on	ADP
ejpam-5782	110	24	x.	x.	NOUN
ejpam-5782	110	25	if	if	SCONJ
ejpam-5782	110	26	a	a	PRON
ejpam-5782	110	27	is	be	AUX
ejpam-5782	110	28	ν	ν	NOUN
ejpam-5782	110	29	-	-	ADJ
ejpam-5782	110	30	open	open	ADJ
ejpam-5782	110	31	in	in	ADP
ejpam-5782	110	32	x	x	NOUN
ejpam-5782	110	33	,	,	PUNCT
ejpam-5782	110	34	then	then	ADV
ejpam-5782	110	35	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	110	36	,	,	PUNCT
ejpam-5782	110	37	ν)(a	ν)(a	NUM
ejpam-5782	110	38	)	)	PUNCT
ejpam-5782	110	39	=	=	SYM
ejpam-5782	110	40	cµ(a	cµ(a	ADJ
ejpam-5782	110	41	)	)	PUNCT
ejpam-5782	110	42	.	.	PUNCT
ejpam-5782	111	1	proof	proof	NOUN
ejpam-5782	111	2	.	.	PUNCT
ejpam-5782	112	1	from	from	ADP
ejpam-5782	112	2	(	(	PUNCT
ejpam-5782	112	3	iii	iii	NOUN
ejpam-5782	112	4	)	)	PUNCT
ejpam-5782	112	5	of	of	ADP
ejpam-5782	112	6	theorem	theorem	NOUN
ejpam-5782	112	7	5	5	NUM
ejpam-5782	112	8	,	,	PUNCT
ejpam-5782	112	9	we	we	PRON
ejpam-5782	112	10	have	have	VERB
ejpam-5782	112	11	cµ(a	cµ(a	PROPN
ejpam-5782	112	12	)	)	PUNCT
ejpam-5782	112	13	⊆	⊆	NUM
ejpam-5782	112	14	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	112	15	,	,	PUNCT
ejpam-5782	112	16	ν)(a	ν)(a	NOUN
ejpam-5782	112	17	)	)	PUNCT
ejpam-5782	112	18	.	.	PUNCT
ejpam-5782	113	1	for	for	ADP
ejpam-5782	113	2	the	the	DET
ejpam-5782	113	3	converse	converse	NOUN
ejpam-5782	113	4	inclusion	inclusion	NOUN
ejpam-5782	113	5	,	,	PUNCT
ejpam-5782	113	6	suppose	suppose	VERB
ejpam-5782	113	7	x	x	X
ejpam-5782	113	8	∈	∈	PROPN
ejpam-5782	113	9	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	113	10	,	,	PUNCT
ejpam-5782	113	11	ν)(a	ν)(a	NOUN
ejpam-5782	113	12	)	)	PUNCT
ejpam-5782	113	13	.	.	PUNCT
ejpam-5782	114	1	for	for	ADP
ejpam-5782	114	2	each	each	DET
ejpam-5782	114	3	m	m	PROPN
ejpam-5782	114	4	∈	∈	PROPN
ejpam-5782	114	5	µ	µ	PRON
ejpam-5782	114	6	such	such	ADJ
ejpam-5782	114	7	that	that	SCONJ
ejpam-5782	114	8	x	x	SYM
ejpam-5782	114	9	∈	∈	PROPN
ejpam-5782	114	10	m	m	NOUN
ejpam-5782	114	11	and	and	CCONJ
ejpam-5782	114	12	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	114	13	)	)	PUNCT
ejpam-5782	114	14	∩	∩	NOUN
ejpam-5782	114	15	a	a	DET
ejpam-5782	114	16	̸=	̸=	PROPN
ejpam-5782	114	17	∅.	∅.	NOUN
ejpam-5782	114	18	since	since	SCONJ
ejpam-5782	114	19	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	114	20	)	)	PUNCT
ejpam-5782	114	21	⊆	⊆	NUM
ejpam-5782	114	22	cν(m	cν(m	NOUN
ejpam-5782	114	23	)	)	PUNCT
ejpam-5782	114	24	,	,	PUNCT
ejpam-5782	114	25	it	it	PRON
ejpam-5782	114	26	follows	follow	VERB
ejpam-5782	114	27	that	that	SCONJ
ejpam-5782	114	28	cν(m	cν(m	NOUN
ejpam-5782	114	29	)	)	PUNCT
ejpam-5782	114	30	∩	∩	NOUN
ejpam-5782	114	31	a	a	DET
ejpam-5782	114	32	̸=	̸=	PROPN
ejpam-5782	114	33	∅.	∅.	ADV
ejpam-5782	114	34	thus	thus	ADV
ejpam-5782	114	35	,	,	PUNCT
ejpam-5782	114	36	there	there	PRON
ejpam-5782	114	37	exists	exist	VERB
ejpam-5782	114	38	y	y	PROPN
ejpam-5782	114	39	∈	∈	PROPN
ejpam-5782	114	40	cν(m	cν(m	NOUN
ejpam-5782	114	41	)	)	PUNCT
ejpam-5782	114	42	∩	∩	ADJ
ejpam-5782	114	43	a.	a.	NOUN
ejpam-5782	114	44	since	since	SCONJ
ejpam-5782	114	45	a	a	PRON
ejpam-5782	114	46	is	be	AUX
ejpam-5782	114	47	ν	ν	NOUN
ejpam-5782	114	48	-	-	ADJ
ejpam-5782	114	49	open	open	ADJ
ejpam-5782	114	50	and	and	CCONJ
ejpam-5782	114	51	contains	contain	VERB
ejpam-5782	114	52	y	y	PROPN
ejpam-5782	114	53	,	,	PUNCT
ejpam-5782	114	54	we	we	PRON
ejpam-5782	114	55	have	have	VERB
ejpam-5782	114	56	m	m	NOUN
ejpam-5782	114	57	∩	∩	NOUN
ejpam-5782	114	58	a	a	DET
ejpam-5782	114	59	̸=	̸=	PROPN
ejpam-5782	114	60	∅	∅	NOUN
ejpam-5782	114	61	,	,	PUNCT
ejpam-5782	114	62	implying	imply	VERB
ejpam-5782	114	63	x	x	X
ejpam-5782	114	64	∈	∈	PROPN
ejpam-5782	114	65	cµ(a	cµ(a	NOUN
ejpam-5782	114	66	)	)	PUNCT
ejpam-5782	114	67	.	.	PUNCT
ejpam-5782	115	1	therefore	therefore	ADV
ejpam-5782	115	2	,	,	PUNCT
ejpam-5782	115	3	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	115	4	,	,	PUNCT
ejpam-5782	115	5	ν)(a	ν)(a	NUM
ejpam-5782	115	6	)	)	PUNCT
ejpam-5782	115	7	⊆	⊆	NUM
ejpam-5782	115	8	cµ(a	cµ(a	NUM
ejpam-5782	115	9	)	)	PUNCT
ejpam-5782	115	10	.	.	PUNCT
ejpam-5782	116	1	combining	combine	VERB
ejpam-5782	116	2	this	this	PRON
ejpam-5782	116	3	with	with	ADP
ejpam-5782	116	4	the	the	DET
ejpam-5782	116	5	earlier	early	ADJ
ejpam-5782	116	6	inclusion	inclusion	NOUN
ejpam-5782	116	7	,	,	PUNCT
ejpam-5782	116	8	we	we	PRON
ejpam-5782	116	9	conclude	conclude	VERB
ejpam-5782	116	10	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	116	11	,	,	PUNCT
ejpam-5782	116	12	ν)(a	ν)(a	NUM
ejpam-5782	116	13	)	)	PUNCT
ejpam-5782	116	14	=	=	SYM
ejpam-5782	116	15	cµ(a	cµ(a	ADJ
ejpam-5782	116	16	)	)	PUNCT
ejpam-5782	116	17	.	.	PUNCT
ejpam-5782	117	1	the	the	DET
ejpam-5782	117	2	following	follow	VERB
ejpam-5782	117	3	corollary	corollary	NOUN
ejpam-5782	117	4	follows	follow	VERB
ejpam-5782	117	5	from	from	ADP
ejpam-5782	117	6	lemma	lemma	PROPN
ejpam-5782	117	7	1(ii	1(ii	NUM
ejpam-5782	117	8	)	)	PUNCT
ejpam-5782	117	9	and	and	CCONJ
ejpam-5782	117	10	theorem	theorem	VERB
ejpam-5782	117	11	7	7	NUM
ejpam-5782	117	12	.	.	PUNCT
ejpam-5782	117	13	corollary	corollary	ADJ
ejpam-5782	117	14	4	4	NUM
ejpam-5782	117	15	.	.	PUNCT
ejpam-5782	118	1	let	let	VERB
ejpam-5782	118	2	µ	µ	NOUN
ejpam-5782	118	3	and	and	CCONJ
ejpam-5782	118	4	ν	ν	PROPN
ejpam-5782	118	5	be	be	AUX
ejpam-5782	118	6	two	two	NUM
ejpam-5782	118	7	gt	gt	NOUN
ejpam-5782	118	8	’s	’s	NOUN
ejpam-5782	118	9	on	on	ADP
ejpam-5782	118	10	a	a	DET
ejpam-5782	118	11	nonempty	nonempty	ADJ
ejpam-5782	118	12	set	set	VERB
ejpam-5782	118	13	x	x	SYM
ejpam-5782	118	14	,	,	PUNCT
ejpam-5782	118	15	h	h	PROPN
ejpam-5782	118	16	a	a	DET
ejpam-5782	118	17	hereditary	hereditary	ADJ
ejpam-5782	118	18	class	class	NOUN
ejpam-5782	118	19	on	on	ADP
ejpam-5782	118	20	x	x	NOUN
ejpam-5782	118	21	,	,	PUNCT
ejpam-5782	118	22	and	and	CCONJ
ejpam-5782	118	23	a	a	DET
ejpam-5782	118	24	⊆	⊆	NUM
ejpam-5782	118	25	x.	x.	NOUN
ejpam-5782	118	26	if	if	SCONJ
ejpam-5782	118	27	a	a	DET
ejpam-5782	118	28	∈	∈	PROPN
ejpam-5782	118	29	ν	ν	NOUN
ejpam-5782	118	30	,	,	PUNCT
ejpam-5782	118	31	then	then	ADV
ejpam-5782	118	32	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	118	33	,	,	PUNCT
ejpam-5782	118	34	ν)(a	ν)(a	NUM
ejpam-5782	118	35	)	)	PUNCT
ejpam-5782	118	36	=	=	SYM
ejpam-5782	119	1	cµ(a	cµ(a	ADJ
ejpam-5782	119	2	)	)	PUNCT
ejpam-5782	119	3	=	=	SYM
ejpam-5782	119	4	γθ(µ,ν)(a	γθ(µ,ν)(a	PROPN
ejpam-5782	119	5	)	)	PUNCT
ejpam-5782	119	6	.	.	PUNCT
ejpam-5782	120	1	4	4	X
ejpam-5782	120	2	.	.	X
ejpam-5782	120	3	h	h	NOUN
ejpam-5782	120	4	(	(	PUNCT
ejpam-5782	120	5	θ(µ	θ(µ	PROPN
ejpam-5782	120	6	,	,	PUNCT
ejpam-5782	120	7	ν	ν	NOUN
ejpam-5782	120	8	)	)	PUNCT
ejpam-5782	120	9	)	)	PUNCT
ejpam-5782	120	10	-open	-open	NOUN
ejpam-5782	120	11	sets	set	NOUN
ejpam-5782	120	12	definition	definition	NOUN
ejpam-5782	120	13	3	3	X
ejpam-5782	120	14	.	.	PUNCT
ejpam-5782	120	15	let	let	VERB
ejpam-5782	120	16	µ	µ	NOUN
ejpam-5782	120	17	and	and	CCONJ
ejpam-5782	120	18	ν	ν	PROPN
ejpam-5782	120	19	be	be	AUX
ejpam-5782	120	20	two	two	NUM
ejpam-5782	120	21	gt	gt	NOUN
ejpam-5782	120	22	’s	’s	NOUN
ejpam-5782	120	23	on	on	ADP
ejpam-5782	120	24	a	a	DET
ejpam-5782	120	25	nonempty	nonempty	ADV
ejpam-5782	120	26	set	set	VERB
ejpam-5782	120	27	x	x	NOUN
ejpam-5782	120	28	,	,	PUNCT
ejpam-5782	120	29	and	and	CCONJ
ejpam-5782	120	30	let	let	VERB
ejpam-5782	120	31	h	h	NOUN
ejpam-5782	120	32	be	be	AUX
ejpam-5782	120	33	a	a	DET
ejpam-5782	120	34	hereditary	hereditary	ADJ
ejpam-5782	120	35	class	class	NOUN
ejpam-5782	120	36	on	on	ADP
ejpam-5782	120	37	x.	x.	NOUN
ejpam-5782	120	38	we	we	PRON
ejpam-5782	120	39	define	define	VERB
ejpam-5782	120	40	the	the	DET
ejpam-5782	120	41	collection	collection	NOUN
ejpam-5782	120	42	h	h	NOUN
ejpam-5782	120	43	(	(	PUNCT
ejpam-5782	120	44	θ(µ	θ(µ	PROPN
ejpam-5782	120	45	,	,	PUNCT
ejpam-5782	120	46	ν	ν	NOUN
ejpam-5782	120	47	)	)	PUNCT
ejpam-5782	120	48	)	)	PUNCT
ejpam-5782	121	1	⊆	⊆	NUM
ejpam-5782	121	2	p(x	p(x	NOUN
ejpam-5782	121	3	)	)	PUNCT
ejpam-5782	121	4	such	such	ADJ
ejpam-5782	121	5	that	that	SCONJ
ejpam-5782	121	6	a	a	DET
ejpam-5782	121	7	∈	∈	PROPN
ejpam-5782	121	8	h	h	NOUN
ejpam-5782	121	9	(	(	PUNCT
ejpam-5782	121	10	θ(µ	θ(µ	PROPN
ejpam-5782	121	11	,	,	PUNCT
ejpam-5782	121	12	ν	ν	NOUN
ejpam-5782	121	13	)	)	PUNCT
ejpam-5782	121	14	)	)	PUNCT
ejpam-5782	122	1	if	if	SCONJ
ejpam-5782	122	2	and	and	CCONJ
ejpam-5782	122	3	only	only	ADV
ejpam-5782	122	4	if	if	SCONJ
ejpam-5782	122	5	for	for	ADP
ejpam-5782	122	6	each	each	DET
ejpam-5782	122	7	x	x	SYM
ejpam-5782	122	8	∈	∈	PROPN
ejpam-5782	122	9	a	a	PRON
ejpam-5782	122	10	,	,	PUNCT
ejpam-5782	122	11	there	there	PRON
ejpam-5782	122	12	exists	exist	VERB
ejpam-5782	122	13	m	m	PROPN
ejpam-5782	122	14	∈	∈	PROPN
ejpam-5782	122	15	µ	µ	PRON
ejpam-5782	122	16	such	such	ADJ
ejpam-5782	122	17	that	that	SCONJ
ejpam-5782	122	18	x	x	SYM
ejpam-5782	122	19	∈	∈	PROPN
ejpam-5782	122	20	m	m	VERB
ejpam-5782	122	21	⊆	⊆	NUM
ejpam-5782	122	22	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	122	23	)	)	PUNCT
ejpam-5782	122	24	⊆	⊆	NUM
ejpam-5782	122	25	a.	a.	NOUN
ejpam-5782	122	26	the	the	DET
ejpam-5782	122	27	elements	element	NOUN
ejpam-5782	122	28	ofh	ofh	X
ejpam-5782	122	29	(	(	PUNCT
ejpam-5782	122	30	θ(µ	θ(µ	PROPN
ejpam-5782	122	31	,	,	PUNCT
ejpam-5782	122	32	ν	ν	NOUN
ejpam-5782	122	33	)	)	PUNCT
ejpam-5782	122	34	)	)	PUNCT
ejpam-5782	122	35	are	be	AUX
ejpam-5782	122	36	called	call	VERB
ejpam-5782	122	37	mixedh	mixedh	NOUN
ejpam-5782	122	38	(	(	PUNCT
ejpam-5782	122	39	θ(µ	θ(µ	PROPN
ejpam-5782	122	40	,	,	PUNCT
ejpam-5782	122	41	ν	ν	NOUN
ejpam-5782	122	42	)	)	PUNCT
ejpam-5782	122	43	)	)	PUNCT
ejpam-5782	122	44	-open	-open	NOUN
ejpam-5782	122	45	(	(	PUNCT
ejpam-5782	122	46	briefly	briefly	ADV
ejpam-5782	122	47	,	,	PUNCT
ejpam-5782	122	48	h	h	NOUN
ejpam-5782	122	49	(	(	PUNCT
ejpam-5782	122	50	θ(µ	θ(µ	PROPN
ejpam-5782	122	51	,	,	PUNCT
ejpam-5782	122	52	ν	ν	NOUN
ejpam-5782	122	53	)	)	PUNCT
ejpam-5782	122	54	)	)	PUNCT
ejpam-5782	122	55	-open	-open	NOUN
ejpam-5782	122	56	)	)	PUNCT
ejpam-5782	122	57	,	,	PUNCT
ejpam-5782	122	58	and	and	CCONJ
ejpam-5782	122	59	their	their	PRON
ejpam-5782	122	60	complements	complement	NOUN
ejpam-5782	122	61	are	be	AUX
ejpam-5782	122	62	called	call	VERB
ejpam-5782	122	63	mixed	mixed	ADJ
ejpam-5782	122	64	h	h	NOUN
ejpam-5782	122	65	(	(	PUNCT
ejpam-5782	122	66	θ(µ	θ(µ	PROPN
ejpam-5782	122	67	,	,	PUNCT
ejpam-5782	122	68	ν	ν	NOUN
ejpam-5782	122	69	)	)	PUNCT
ejpam-5782	122	70	)	)	PUNCT
ejpam-5782	123	1	-closed	-close	VERB
ejpam-5782	123	2	(	(	PUNCT
ejpam-5782	123	3	briefly	briefly	ADV
ejpam-5782	123	4	,	,	PUNCT
ejpam-5782	123	5	h	h	NOUN
ejpam-5782	123	6	(	(	PUNCT
ejpam-5782	123	7	θ(µ	θ(µ	PROPN
ejpam-5782	123	8	,	,	PUNCT
ejpam-5782	123	9	ν	ν	NOUN
ejpam-5782	123	10	)	)	PUNCT
ejpam-5782	123	11	)	)	PUNCT
ejpam-5782	123	12	-closed	-close	VERB
ejpam-5782	123	13	)	)	PUNCT
ejpam-5782	123	14	.	.	PUNCT
ejpam-5782	124	1	f.	f.	PROPN
ejpam-5782	124	2	alsharari	alsharari	PROPN
ejpam-5782	124	3	,	,	PUNCT
ejpam-5782	124	4	a.	a.	PROPN
ejpam-5782	124	5	qahis	qahis	PROPN
ejpam-5782	124	6	/	/	SYM
ejpam-5782	124	7	eur	eur	PROPN
ejpam-5782	124	8	.	.	PUNCT
ejpam-5782	125	1	j.	j.	PROPN
ejpam-5782	125	2	pure	pure	PROPN
ejpam-5782	125	3	appl	appl	PROPN
ejpam-5782	125	4	.	.	PROPN
ejpam-5782	125	5	math	math	PROPN
ejpam-5782	125	6	,	,	PUNCT
ejpam-5782	125	7	18	18	NUM
ejpam-5782	125	8	(	(	PUNCT
ejpam-5782	125	9	2	2	NUM
ejpam-5782	125	10	)	)	PUNCT
ejpam-5782	125	11	(	(	PUNCT
ejpam-5782	125	12	2025	2025	NUM
ejpam-5782	125	13	)	)	PUNCT
ejpam-5782	125	14	,	,	PUNCT
ejpam-5782	125	15	5782	5782	NUM
ejpam-5782	125	16	6	6	NUM
ejpam-5782	125	17	of	of	ADP
ejpam-5782	125	18	10	10	NUM
ejpam-5782	125	19	remark	remark	NOUN
ejpam-5782	125	20	1	1	NUM
ejpam-5782	125	21	.	.	PUNCT
ejpam-5782	125	22	consider	consider	VERB
ejpam-5782	125	23	µ	µ	NOUN
ejpam-5782	125	24	and	and	CCONJ
ejpam-5782	125	25	ν	ν	NOUN
ejpam-5782	125	26	to	to	PART
ejpam-5782	125	27	be	be	AUX
ejpam-5782	125	28	two	two	NUM
ejpam-5782	125	29	gt	gt	NOUN
ejpam-5782	125	30	’s	’s	NOUN
ejpam-5782	125	31	on	on	ADP
ejpam-5782	125	32	a	a	DET
ejpam-5782	125	33	nonempty	nonempty	ADV
ejpam-5782	125	34	set	set	VERB
ejpam-5782	125	35	x	x	NOUN
ejpam-5782	125	36	,	,	PUNCT
ejpam-5782	125	37	and	and	CCONJ
ejpam-5782	125	38	let	let	VERB
ejpam-5782	125	39	h	h	NOUN
ejpam-5782	125	40	be	be	AUX
ejpam-5782	125	41	a	a	DET
ejpam-5782	125	42	hereditary	hereditary	ADJ
ejpam-5782	125	43	class	class	NOUN
ejpam-5782	125	44	on	on	ADP
ejpam-5782	125	45	x.	x.	NOUN
ejpam-5782	125	46	if	if	SCONJ
ejpam-5782	125	47	µ	µ	X
ejpam-5782	125	48	=	=	SYM
ejpam-5782	125	49	ν	ν	NOUN
ejpam-5782	125	50	,	,	PUNCT
ejpam-5782	125	51	then	then	ADV
ejpam-5782	125	52	h	h	PROPN
ejpam-5782	125	53	(	(	PUNCT
ejpam-5782	125	54	θ(µ	θ(µ	PROPN
ejpam-5782	125	55	,	,	PUNCT
ejpam-5782	125	56	ν	ν	NOUN
ejpam-5782	125	57	)	)	PUNCT
ejpam-5782	125	58	)	)	PUNCT
ejpam-5782	126	1	=	=	SYM
ejpam-5782	126	2	h(θ	h(θ	PROPN
ejpam-5782	126	3	)	)	PUNCT
ejpam-5782	126	4	.	.	PUNCT
ejpam-5782	127	1	theorem	theorem	ADJ
ejpam-5782	127	2	8	8	NUM
ejpam-5782	127	3	.	.	PUNCT
ejpam-5782	128	1	let	let	VERB
ejpam-5782	128	2	µ	µ	NOUN
ejpam-5782	128	3	and	and	CCONJ
ejpam-5782	128	4	ν	ν	PROPN
ejpam-5782	128	5	be	be	AUX
ejpam-5782	128	6	two	two	NUM
ejpam-5782	128	7	gt	gt	NOUN
ejpam-5782	128	8	’s	’s	NOUN
ejpam-5782	128	9	on	on	ADP
ejpam-5782	128	10	a	a	DET
ejpam-5782	128	11	nonempty	nonempty	ADV
ejpam-5782	128	12	set	set	VERB
ejpam-5782	128	13	x	x	NOUN
ejpam-5782	128	14	,	,	PUNCT
ejpam-5782	128	15	and	and	CCONJ
ejpam-5782	128	16	let	let	VERB
ejpam-5782	128	17	h	h	NOUN
ejpam-5782	128	18	be	be	AUX
ejpam-5782	128	19	a	a	DET
ejpam-5782	128	20	hereditary	hereditary	ADJ
ejpam-5782	128	21	class	class	NOUN
ejpam-5782	128	22	on	on	ADP
ejpam-5782	128	23	x.	x.	NOUN
ejpam-5782	128	24	then	then	ADV
ejpam-5782	128	25	θ(µ	θ(µ	PROPN
ejpam-5782	128	26	,	,	PUNCT
ejpam-5782	128	27	ν	ν	NOUN
ejpam-5782	128	28	)	)	PUNCT
ejpam-5782	128	29	⊆	⊆	NUM
ejpam-5782	128	30	h	h	NOUN
ejpam-5782	128	31	(	(	PUNCT
ejpam-5782	128	32	θ(µ	θ(µ	PROPN
ejpam-5782	128	33	,	,	PUNCT
ejpam-5782	128	34	ν	ν	NOUN
ejpam-5782	128	35	)	)	PUNCT
ejpam-5782	128	36	)	)	PUNCT
ejpam-5782	129	1	⊆	⊆	NUM
ejpam-5782	129	2	µ.	µ.	NOUN
ejpam-5782	129	3	proof	proof	NOUN
ejpam-5782	129	4	.	.	PUNCT
ejpam-5782	130	1	to	to	PART
ejpam-5782	130	2	show	show	VERB
ejpam-5782	130	3	that	that	SCONJ
ejpam-5782	130	4	θ(µ	θ(µ	NOUN
ejpam-5782	130	5	,	,	PUNCT
ejpam-5782	130	6	ν	ν	NOUN
ejpam-5782	130	7	)	)	PUNCT
ejpam-5782	130	8	⊆	⊆	NUM
ejpam-5782	130	9	h	h	NOUN
ejpam-5782	130	10	(	(	PUNCT
ejpam-5782	130	11	θ(µ	θ(µ	PROPN
ejpam-5782	130	12	,	,	PUNCT
ejpam-5782	130	13	ν	ν	NOUN
ejpam-5782	130	14	)	)	PUNCT
ejpam-5782	130	15	)	)	PUNCT
ejpam-5782	130	16	,	,	PUNCT
ejpam-5782	130	17	let	let	VERB
ejpam-5782	130	18	a	a	DET
ejpam-5782	130	19	∈	∈	NOUN
ejpam-5782	130	20	θ(µ	θ(µ	NOUN
ejpam-5782	130	21	,	,	PUNCT
ejpam-5782	130	22	ν	ν	NOUN
ejpam-5782	130	23	)	)	PUNCT
ejpam-5782	130	24	and	and	CCONJ
ejpam-5782	130	25	x	x	PUNCT
ejpam-5782	130	26	∈	∈	NOUN
ejpam-5782	130	27	a.	a.	NOUN
ejpam-5782	130	28	then	then	ADV
ejpam-5782	130	29	there	there	PRON
ejpam-5782	130	30	exists	exist	VERB
ejpam-5782	130	31	m	m	PROPN
ejpam-5782	130	32	∈	∈	PROPN
ejpam-5782	130	33	µ	µ	PRON
ejpam-5782	130	34	such	such	ADJ
ejpam-5782	130	35	that	that	SCONJ
ejpam-5782	130	36	x	x	SYM
ejpam-5782	130	37	∈	∈	PROPN
ejpam-5782	130	38	m	m	VERB
ejpam-5782	130	39	⊆	⊆	NUM
ejpam-5782	130	40	cν(m	cν(m	NOUN
ejpam-5782	130	41	)	)	PUNCT
ejpam-5782	130	42	⊆	⊆	NUM
ejpam-5782	130	43	a.	a.	NOUN
ejpam-5782	130	44	since	since	SCONJ
ejpam-5782	130	45	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	130	46	)	)	PUNCT
ejpam-5782	130	47	⊆	⊆	NUM
ejpam-5782	130	48	cν(m	cν(m	NOUN
ejpam-5782	130	49	)	)	PUNCT
ejpam-5782	130	50	,	,	PUNCT
ejpam-5782	130	51	we	we	PRON
ejpam-5782	130	52	have	have	VERB
ejpam-5782	130	53	x	x	PROPN
ejpam-5782	130	54	∈	∈	NOUN
ejpam-5782	130	55	m	m	NOUN
ejpam-5782	130	56	⊆	⊆	NUM
ejpam-5782	130	57	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	130	58	)	)	PUNCT
ejpam-5782	130	59	⊆	⊆	NUM
ejpam-5782	130	60	a.	a.	NOUN
ejpam-5782	130	61	therefore	therefore	ADV
ejpam-5782	130	62	,	,	PUNCT
ejpam-5782	130	63	a	a	PRON
ejpam-5782	130	64	is	be	AUX
ejpam-5782	130	65	an	an	DET
ejpam-5782	130	66	h	h	NOUN
ejpam-5782	130	67	(	(	PUNCT
ejpam-5782	130	68	θ(µ	θ(µ	PROPN
ejpam-5782	130	69	,	,	PUNCT
ejpam-5782	130	70	ν	ν	NOUN
ejpam-5782	130	71	)	)	PUNCT
ejpam-5782	130	72	)	)	PUNCT
ejpam-5782	131	1	-open	-open	NOUN
ejpam-5782	131	2	set	set	NOUN
ejpam-5782	131	3	.	.	PUNCT
ejpam-5782	132	1	next	next	ADV
ejpam-5782	132	2	,	,	PUNCT
ejpam-5782	132	3	to	to	PART
ejpam-5782	132	4	show	show	VERB
ejpam-5782	132	5	that	that	SCONJ
ejpam-5782	132	6	h	h	NOUN
ejpam-5782	132	7	(	(	PUNCT
ejpam-5782	132	8	θ(µ	θ(µ	PROPN
ejpam-5782	132	9	,	,	PUNCT
ejpam-5782	132	10	ν	ν	NOUN
ejpam-5782	132	11	)	)	PUNCT
ejpam-5782	132	12	)	)	PUNCT
ejpam-5782	133	1	⊆	⊆	NUM
ejpam-5782	133	2	µ	µ	NUM
ejpam-5782	133	3	,	,	PUNCT
ejpam-5782	133	4	suppose	suppose	VERB
ejpam-5782	133	5	a	a	DET
ejpam-5782	133	6	∈	∈	PROPN
ejpam-5782	133	7	h	h	NOUN
ejpam-5782	133	8	(	(	PUNCT
ejpam-5782	133	9	θ(µ	θ(µ	PROPN
ejpam-5782	133	10	,	,	PUNCT
ejpam-5782	133	11	ν	ν	NOUN
ejpam-5782	133	12	)	)	PUNCT
ejpam-5782	133	13	)	)	PUNCT
ejpam-5782	133	14	and	and	CCONJ
ejpam-5782	133	15	let	let	VERB
ejpam-5782	133	16	x	x	PUNCT
ejpam-5782	133	17	∈	∈	NOUN
ejpam-5782	133	18	a.	a.	NOUN
ejpam-5782	133	19	then	then	ADV
ejpam-5782	133	20	there	there	PRON
ejpam-5782	133	21	exists	exist	VERB
ejpam-5782	133	22	a	a	DET
ejpam-5782	133	23	µ-open	µ-open	NOUN
ejpam-5782	133	24	set	set	VERB
ejpam-5782	133	25	mx	mx	PROPN
ejpam-5782	133	26	such	such	ADJ
ejpam-5782	133	27	that	that	SCONJ
ejpam-5782	133	28	x	x	SYM
ejpam-5782	133	29	∈	∈	PROPN
ejpam-5782	133	30	mx	mx	PROPN
ejpam-5782	133	31	⊆	⊆	NUM
ejpam-5782	133	32	c∗ν(mx	c∗ν(mx	PROPN
ejpam-5782	133	33	)	)	PUNCT
ejpam-5782	133	34	⊆	⊆	NUM
ejpam-5782	133	35	a.	a.	NOUN
ejpam-5782	133	36	therefore	therefore	ADV
ejpam-5782	133	37	,	,	PUNCT
ejpam-5782	133	38	a	a	DET
ejpam-5782	133	39	=	=	X
ejpam-5782	133	40	⋃	⋃	PROPN
ejpam-5782	133	41	x∈amx	x∈amx	PROPN
ejpam-5782	133	42	∈	∈	PROPN
ejpam-5782	133	43	µ.	µ.	NOUN
ejpam-5782	133	44	remark	remark	NOUN
ejpam-5782	133	45	2	2	NUM
ejpam-5782	133	46	.	.	PUNCT
ejpam-5782	133	47	based	base	VERB
ejpam-5782	133	48	on	on	ADP
ejpam-5782	133	49	theorem	theorem	NOUN
ejpam-5782	133	50	8	8	NUM
ejpam-5782	133	51	,	,	PUNCT
ejpam-5782	133	52	we	we	PRON
ejpam-5782	133	53	can	can	AUX
ejpam-5782	133	54	illustrate	illustrate	VERB
ejpam-5782	133	55	the	the	DET
ejpam-5782	133	56	following	follow	VERB
ejpam-5782	133	57	diagram	diagram	NOUN
ejpam-5782	133	58	.	.	PUNCT
ejpam-5782	134	1	the	the	DET
ejpam-5782	134	2	following	follow	VERB
ejpam-5782	134	3	example	example	NOUN
ejpam-5782	134	4	demonstrates	demonstrate	VERB
ejpam-5782	134	5	that	that	SCONJ
ejpam-5782	134	6	the	the	DET
ejpam-5782	134	7	above	above	ADJ
ejpam-5782	134	8	implications	implication	NOUN
ejpam-5782	134	9	are	be	AUX
ejpam-5782	134	10	not	not	PART
ejpam-5782	134	11	reversible	reversible	ADJ
ejpam-5782	134	12	in	in	ADP
ejpam-5782	134	13	general	general	ADJ
ejpam-5782	134	14	.	.	PUNCT
ejpam-5782	135	1	example	example	NOUN
ejpam-5782	136	1	3	3	X
ejpam-5782	136	2	.	.	PUNCT
ejpam-5782	136	3	let	let	VERB
ejpam-5782	136	4	x	x	PUNCT
ejpam-5782	136	5	=	=	PRON
ejpam-5782	136	6	{	{	PUNCT
ejpam-5782	136	7	a	a	PRON
ejpam-5782	136	8	,	,	PUNCT
ejpam-5782	136	9	b	b	NOUN
ejpam-5782	136	10	,	,	PUNCT
ejpam-5782	136	11	c	c	NOUN
ejpam-5782	136	12	,	,	PUNCT
ejpam-5782	136	13	d	d	NOUN
ejpam-5782	136	14	}	}	PUNCT
ejpam-5782	136	15	.	.	PUNCT
ejpam-5782	137	1	consider	consider	VERB
ejpam-5782	137	2	two	two	NUM
ejpam-5782	137	3	generalized	generalized	ADJ
ejpam-5782	137	4	topologies	topology	NOUN
ejpam-5782	137	5	µ	µ	X
ejpam-5782	137	6	=	=	SYM
ejpam-5782	137	7	{	{	PUNCT
ejpam-5782	137	8	∅	∅	NOUN
ejpam-5782	137	9	,	,	PUNCT
ejpam-5782	137	10	{	{	PUNCT
ejpam-5782	137	11	a	a	DET
ejpam-5782	137	12	,	,	PUNCT
ejpam-5782	137	13	b	b	NOUN
ejpam-5782	137	14	}	}	PUNCT
ejpam-5782	137	15	,	,	PUNCT
ejpam-5782	137	16	{	{	PUNCT
ejpam-5782	137	17	b	b	X
ejpam-5782	137	18	,	,	PUNCT
ejpam-5782	137	19	c	c	NOUN
ejpam-5782	137	20	}	}	PUNCT
ejpam-5782	137	21	,	,	PUNCT
ejpam-5782	137	22	{	{	PUNCT
ejpam-5782	137	23	a	a	PRON
ejpam-5782	137	24	,	,	PUNCT
ejpam-5782	137	25	b	b	NOUN
ejpam-5782	137	26	,	,	PUNCT
ejpam-5782	137	27	c	c	NOUN
ejpam-5782	137	28	}	}	PUNCT
ejpam-5782	137	29	}	}	PUNCT
ejpam-5782	137	30	and	and	CCONJ
ejpam-5782	137	31	ν	ν	X
ejpam-5782	137	32	=	=	SYM
ejpam-5782	137	33	{	{	PUNCT
ejpam-5782	137	34	∅	∅	NOUN
ejpam-5782	137	35	,	,	PUNCT
ejpam-5782	137	36	{	{	PUNCT
ejpam-5782	137	37	b	b	NOUN
ejpam-5782	137	38	,	,	PUNCT
ejpam-5782	137	39	d	d	NOUN
ejpam-5782	137	40	}	}	PUNCT
ejpam-5782	137	41	}	}	PUNCT
ejpam-5782	137	42	and	and	CCONJ
ejpam-5782	137	43	a	a	DET
ejpam-5782	137	44	hereditary	hereditary	ADJ
ejpam-5782	137	45	class	class	NOUN
ejpam-5782	137	46	h	h	NOUN
ejpam-5782	137	47	=	=	NOUN
ejpam-5782	137	48	{	{	PUNCT
ejpam-5782	137	49	∅	∅	NOUN
ejpam-5782	137	50	,	,	PUNCT
ejpam-5782	137	51	{	{	PUNCT
ejpam-5782	137	52	b	b	NOUN
ejpam-5782	137	53	}	}	PUNCT
ejpam-5782	137	54	}	}	PUNCT
ejpam-5782	137	55	.	.	PUNCT
ejpam-5782	138	1	note	note	VERB
ejpam-5782	138	2	that	that	SCONJ
ejpam-5782	138	3	:	:	PUNCT
ejpam-5782	138	4	(	(	PUNCT
ejpam-5782	138	5	i	i	NOUN
ejpam-5782	138	6	)	)	PUNCT
ejpam-5782	138	7	for	for	ADP
ejpam-5782	138	8	a	a	DET
ejpam-5782	138	9	set	set	NOUN
ejpam-5782	138	10	a	a	X
ejpam-5782	138	11	=	=	X
ejpam-5782	138	12	{	{	PUNCT
ejpam-5782	138	13	a	a	PROPN
ejpam-5782	138	14	,	,	PUNCT
ejpam-5782	138	15	b	b	NOUN
ejpam-5782	138	16	,	,	PUNCT
ejpam-5782	138	17	c	c	NOUN
ejpam-5782	138	18	}	}	PUNCT
ejpam-5782	138	19	,	,	PUNCT
ejpam-5782	138	20	we	we	PRON
ejpam-5782	138	21	have	have	VERB
ejpam-5782	138	22	ma	ma	PROPN
ejpam-5782	138	23	=	=	PUNCT
ejpam-5782	138	24	mb	mb	PROPN
ejpam-5782	138	25	=	=	PUNCT
ejpam-5782	138	26	{	{	PUNCT
ejpam-5782	138	27	a	a	PRON
ejpam-5782	138	28	,	,	PUNCT
ejpam-5782	138	29	b	b	NOUN
ejpam-5782	138	30	}	}	PUNCT
ejpam-5782	138	31	∈	∈	PROPN
ejpam-5782	138	32	µ	µ	X
ejpam-5782	138	33	and	and	CCONJ
ejpam-5782	138	34	mc	mc	PROPN
ejpam-5782	138	35	=	=	PUNCT
ejpam-5782	138	36	{	{	PUNCT
ejpam-5782	138	37	b	b	PROPN
ejpam-5782	138	38	,	,	PUNCT
ejpam-5782	138	39	c	c	NOUN
ejpam-5782	138	40	}	}	PUNCT
ejpam-5782	138	41	∈	∈	PROPN
ejpam-5782	138	42	µ.	µ.	NOUN
ejpam-5782	138	43	then	then	ADV
ejpam-5782	138	44	m∗	m∗	VERB
ejpam-5782	138	45	a	a	DET
ejpam-5782	138	46	(	(	PUNCT
ejpam-5782	138	47	h	h	NOUN
ejpam-5782	138	48	,	,	PUNCT
ejpam-5782	138	49	ν	ν	NOUN
ejpam-5782	138	50	)	)	PUNCT
ejpam-5782	139	1	=	=	SYM
ejpam-5782	139	2	m∗	m∗	PROPN
ejpam-5782	139	3	b	b	SYM
ejpam-5782	139	4	(	(	PUNCT
ejpam-5782	139	5	h	h	NOUN
ejpam-5782	139	6	,	,	PUNCT
ejpam-5782	139	7	ν	ν	NOUN
ejpam-5782	139	8	)	)	PUNCT
ejpam-5782	139	9	=	=	SYM
ejpam-5782	139	10	m⋆	m⋆	X
ejpam-5782	139	11	c	c	NOUN
ejpam-5782	139	12	(	(	PUNCT
ejpam-5782	139	13	h	h	NOUN
ejpam-5782	139	14	,	,	PUNCT
ejpam-5782	139	15	ν	ν	NOUN
ejpam-5782	139	16	)	)	PUNCT
ejpam-5782	139	17	=	=	SYM
ejpam-5782	139	18	{	{	PUNCT
ejpam-5782	139	19	a	a	X
ejpam-5782	139	20	,	,	PUNCT
ejpam-5782	139	21	c	c	NOUN
ejpam-5782	139	22	}	}	PUNCT
ejpam-5782	139	23	and	and	CCONJ
ejpam-5782	139	24	c∗v(ma	c∗v(ma	PROPN
ejpam-5782	139	25	)	)	PUNCT
ejpam-5782	140	1	=	=	SYM
ejpam-5782	140	2	c∗v(mb	c∗v(mb	NOUN
ejpam-5782	140	3	)	)	PUNCT
ejpam-5782	140	4	=	=	SYM
ejpam-5782	140	5	c∗v(mc	c∗v(mc	X
ejpam-5782	140	6	)	)	PUNCT
ejpam-5782	140	7	=	=	PRON
ejpam-5782	140	8	{	{	PUNCT
ejpam-5782	140	9	a	a	PRON
ejpam-5782	140	10	,	,	PUNCT
ejpam-5782	140	11	b	b	NOUN
ejpam-5782	140	12	,	,	PUNCT
ejpam-5782	140	13	c	c	NOUN
ejpam-5782	140	14	}	}	PUNCT
ejpam-5782	140	15	⊆	⊆	NUM
ejpam-5782	140	16	a	a	DET
ejpam-5782	140	17	;	;	PUNCT
ejpam-5782	140	18	(	(	PUNCT
ejpam-5782	140	19	ii	ii	NOUN
ejpam-5782	140	20	)	)	PUNCT
ejpam-5782	140	21	since	since	SCONJ
ejpam-5782	140	22	cν({a	cν({a	ADJ
ejpam-5782	140	23	,	,	PUNCT
ejpam-5782	140	24	b	b	NOUN
ejpam-5782	140	25	}	}	PUNCT
ejpam-5782	140	26	)	)	PUNCT
ejpam-5782	140	27	=	=	PUNCT
ejpam-5782	141	1	cν({b	cν({b	X
ejpam-5782	141	2	,	,	PUNCT
ejpam-5782	141	3	c	c	NOUN
ejpam-5782	141	4	}	}	PUNCT
ejpam-5782	141	5	)	)	PUNCT
ejpam-5782	141	6	=	=	SYM
ejpam-5782	142	1	cν({a	cν({a	ADJ
ejpam-5782	142	2	,	,	PUNCT
ejpam-5782	142	3	b	b	NOUN
ejpam-5782	142	4	,	,	PUNCT
ejpam-5782	142	5	c	c	NOUN
ejpam-5782	142	6	}	}	PUNCT
ejpam-5782	142	7	)	)	PUNCT
ejpam-5782	142	8	=	=	PUNCT
ejpam-5782	143	1	x	x	X
ejpam-5782	143	2	⊈	⊈	PROPN
ejpam-5782	143	3	a	a	DET
ejpam-5782	143	4	,	,	PUNCT
ejpam-5782	143	5	then	then	ADV
ejpam-5782	143	6	θ(µ	θ(µ	PROPN
ejpam-5782	143	7	,	,	PUNCT
ejpam-5782	143	8	ν	ν	NOUN
ejpam-5782	143	9	)	)	PUNCT
ejpam-5782	143	10	=	=	SYM
ejpam-5782	143	11	{	{	PUNCT
ejpam-5782	143	12	∅	∅	NOUN
ejpam-5782	143	13	}	}	PUNCT
ejpam-5782	143	14	.	.	PUNCT
ejpam-5782	144	1	(	(	PUNCT
ejpam-5782	144	2	iii	iii	NOUN
ejpam-5782	144	3	)	)	PUNCT
ejpam-5782	144	4	from	from	ADP
ejpam-5782	144	5	(	(	PUNCT
ejpam-5782	144	6	1	1	NUM
ejpam-5782	144	7	)	)	PUNCT
ejpam-5782	144	8	and	and	CCONJ
ejpam-5782	144	9	(	(	PUNCT
ejpam-5782	144	10	2	2	NUM
ejpam-5782	144	11	)	)	PUNCT
ejpam-5782	144	12	,	,	PUNCT
ejpam-5782	144	13	we	we	PRON
ejpam-5782	144	14	show	show	VERB
ejpam-5782	144	15	that	that	SCONJ
ejpam-5782	144	16	the	the	DET
ejpam-5782	144	17	set	set	NOUN
ejpam-5782	144	18	a	a	NOUN
ejpam-5782	144	19	is	be	AUX
ejpam-5782	144	20	h	h	NOUN
ejpam-5782	144	21	(	(	PUNCT
ejpam-5782	144	22	θ(µ	θ(µ	PROPN
ejpam-5782	144	23	,	,	PUNCT
ejpam-5782	144	24	ν	ν	NOUN
ejpam-5782	144	25	)	)	PUNCT
ejpam-5782	144	26	)	)	PUNCT
ejpam-5782	145	1	-open	-open	NOUN
ejpam-5782	146	1	but	but	CCONJ
ejpam-5782	146	2	it	it	PRON
ejpam-5782	146	3	is	be	AUX
ejpam-5782	146	4	not	not	PART
ejpam-5782	146	5	θ(µ	θ(µ	NOUN
ejpam-5782	146	6	,	,	PUNCT
ejpam-5782	146	7	ν)-open	ν)-open	NOUN
ejpam-5782	146	8	.	.	PUNCT
ejpam-5782	147	1	also	also	ADV
ejpam-5782	147	2	,	,	PUNCT
ejpam-5782	147	3	it	it	PRON
ejpam-5782	147	4	is	be	AUX
ejpam-5782	147	5	easy	easy	ADJ
ejpam-5782	147	6	to	to	PART
ejpam-5782	147	7	check	check	VERB
ejpam-5782	147	8	that	that	DET
ejpam-5782	147	9	b	b	NOUN
ejpam-5782	147	10	=	=	PRON
ejpam-5782	147	11	{	{	PUNCT
ejpam-5782	147	12	a	a	PROPN
ejpam-5782	147	13	,	,	PUNCT
ejpam-5782	147	14	b	b	NOUN
ejpam-5782	147	15	}	}	PUNCT
ejpam-5782	147	16	is	be	AUX
ejpam-5782	147	17	µ-open	µ-open	NOUN
ejpam-5782	147	18	but	but	CCONJ
ejpam-5782	147	19	it	it	PRON
ejpam-5782	147	20	is	be	AUX
ejpam-5782	147	21	not	not	PART
ejpam-5782	147	22	h	h	NOUN
ejpam-5782	147	23	(	(	PUNCT
ejpam-5782	147	24	θ(µ	θ(µ	PROPN
ejpam-5782	147	25	,	,	PUNCT
ejpam-5782	147	26	ν	ν	NOUN
ejpam-5782	147	27	)	)	PUNCT
ejpam-5782	147	28	)	)	PUNCT
ejpam-5782	148	1	-open	-open	NOUN
ejpam-5782	148	2	.	.	PUNCT
ejpam-5782	149	1	theorem	theorem	NOUN
ejpam-5782	149	2	9	9	NUM
ejpam-5782	149	3	.	.	PUNCT
ejpam-5782	150	1	let	let	VERB
ejpam-5782	150	2	µ	µ	NOUN
ejpam-5782	150	3	and	and	CCONJ
ejpam-5782	150	4	ν	ν	PROPN
ejpam-5782	150	5	be	be	AUX
ejpam-5782	150	6	two	two	NUM
ejpam-5782	150	7	gts	gts	NOUN
ejpam-5782	150	8	on	on	ADP
ejpam-5782	150	9	a	a	DET
ejpam-5782	150	10	nonempty	nonempty	ADV
ejpam-5782	150	11	set	set	VERB
ejpam-5782	150	12	x	x	NOUN
ejpam-5782	150	13	,	,	PUNCT
ejpam-5782	150	14	and	and	CCONJ
ejpam-5782	150	15	h	h	NOUN
ejpam-5782	150	16	be	be	VERB
ejpam-5782	150	17	a	a	DET
ejpam-5782	150	18	hereditary	hereditary	ADJ
ejpam-5782	150	19	class	class	NOUN
ejpam-5782	150	20	on	on	ADP
ejpam-5782	150	21	x.	x.	NOUN
ejpam-5782	150	22	then	then	ADV
ejpam-5782	150	23	the	the	DET
ejpam-5782	150	24	family	family	NOUN
ejpam-5782	150	25	h	h	NOUN
ejpam-5782	150	26	(	(	PUNCT
ejpam-5782	150	27	θ(µ	θ(µ	PROPN
ejpam-5782	150	28	,	,	PUNCT
ejpam-5782	150	29	ν	ν	NOUN
ejpam-5782	150	30	)	)	PUNCT
ejpam-5782	150	31	)	)	PUNCT
ejpam-5782	150	32	is	be	AUX
ejpam-5782	150	33	a	a	DET
ejpam-5782	150	34	gt	gt	PROPN
ejpam-5782	150	35	contained	contain	VERB
ejpam-5782	150	36	in	in	ADP
ejpam-5782	150	37	µ	µ	NOUN
ejpam-5782	150	38	on	on	ADP
ejpam-5782	150	39	x.	x.	NOUN
ejpam-5782	150	40	proof	proof	NOUN
ejpam-5782	150	41	.	.	PUNCT
ejpam-5782	151	1	firstly	firstly	ADV
ejpam-5782	151	2	,	,	PUNCT
ejpam-5782	151	3	∅	∅	NOUN
ejpam-5782	151	4	∈	∈	PROPN
ejpam-5782	151	5	h	h	NOUN
ejpam-5782	151	6	(	(	PUNCT
ejpam-5782	151	7	θ(µ	θ(µ	PROPN
ejpam-5782	151	8	,	,	PUNCT
ejpam-5782	151	9	ν	ν	NOUN
ejpam-5782	151	10	)	)	PUNCT
ejpam-5782	151	11	)	)	PUNCT
ejpam-5782	151	12	is	be	AUX
ejpam-5782	151	13	obvious	obvious	ADJ
ejpam-5782	151	14	.	.	PUNCT
ejpam-5782	152	1	now	now	ADV
ejpam-5782	152	2	,	,	PUNCT
ejpam-5782	152	3	let	let	VERB
ejpam-5782	152	4	{	{	PUNCT
ejpam-5782	152	5	aα	aα	NOUN
ejpam-5782	152	6	⊆	⊆	NUM
ejpam-5782	152	7	x	x	X
ejpam-5782	152	8	:	:	PUNCT
ejpam-5782	152	9	aα	aα	NOUN
ejpam-5782	152	10	∈	∈	PROPN
ejpam-5782	152	11	h	h	NOUN
ejpam-5782	152	12	(	(	PUNCT
ejpam-5782	152	13	θ(µ	θ(µ	PROPN
ejpam-5782	152	14	,	,	PUNCT
ejpam-5782	152	15	ν	ν	NOUN
ejpam-5782	152	16	)	)	PUNCT
ejpam-5782	152	17	)	)	PUNCT
ejpam-5782	152	18	}	}	PUNCT
ejpam-5782	152	19	for	for	ADP
ejpam-5782	152	20	α	α	PRON
ejpam-5782	152	21	∈	∈	PROPN
ejpam-5782	152	22	λ	λ	PROPN
ejpam-5782	152	23	.	.	PUNCT
ejpam-5782	152	24	consider	consider	VERB
ejpam-5782	152	25	x	x	X
ejpam-5782	152	26	∈	∈	PROPN
ejpam-5782	152	27	∪αaα	∪αaα	PROPN
ejpam-5782	152	28	.	.	PUNCT
ejpam-5782	153	1	then	then	ADV
ejpam-5782	153	2	there	there	PRON
ejpam-5782	153	3	exists	exist	VERB
ejpam-5782	153	4	some	some	DET
ejpam-5782	153	5	α0	α0	PROPN
ejpam-5782	153	6	∈	∈	PROPN
ejpam-5782	153	7	λ	λ	NOUN
ejpam-5782	153	8	such	such	ADJ
ejpam-5782	153	9	that	that	PRON
ejpam-5782	153	10	for	for	ADP
ejpam-5782	153	11	some	some	DET
ejpam-5782	153	12	µ-open	µ-open	NOUN
ejpam-5782	153	13	set	set	VERB
ejpam-5782	153	14	m	m	AUX
ejpam-5782	153	15	containing	contain	VERB
ejpam-5782	153	16	x	x	SYM
ejpam-5782	153	17	,	,	PUNCT
ejpam-5782	153	18	we	we	PRON
ejpam-5782	153	19	have	have	VERB
ejpam-5782	153	20	m	m	NOUN
ejpam-5782	153	21	⊆	⊆	NUM
ejpam-5782	153	22	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	153	23	)	)	PUNCT
ejpam-5782	153	24	⊆	⊆	NUM
ejpam-5782	153	25	aα0	aα0	NOUN
ejpam-5782	153	26	.	.	PUNCT
ejpam-5782	154	1	this	this	PRON
ejpam-5782	154	2	implies	imply	VERB
ejpam-5782	154	3	there	there	PRON
ejpam-5782	154	4	exists	exist	VERB
ejpam-5782	154	5	x	x	X
ejpam-5782	154	6	∈	∈	PROPN
ejpam-5782	154	7	m	m	NOUN
ejpam-5782	154	8	∈	∈	NOUN
ejpam-5782	154	9	µ	µ	PRON
ejpam-5782	154	10	such	such	ADJ
ejpam-5782	154	11	that	that	SCONJ
ejpam-5782	154	12	m	m	PROPN
ejpam-5782	154	13	⊆	⊆	NUM
ejpam-5782	154	14	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	154	15	)	)	PUNCT
ejpam-5782	154	16	⊆	⊆	NUM
ejpam-5782	154	17	∪αaα	∪αaα	ADJ
ejpam-5782	154	18	and	and	CCONJ
ejpam-5782	154	19	so	so	ADV
ejpam-5782	154	20	∪αaα	∪αaα	ADV
ejpam-5782	154	21	∈	∈	PROPN
ejpam-5782	154	22	h	h	NOUN
ejpam-5782	154	23	(	(	PUNCT
ejpam-5782	154	24	θ(µ	θ(µ	PROPN
ejpam-5782	154	25	,	,	PUNCT
ejpam-5782	154	26	ν	ν	NOUN
ejpam-5782	154	27	)	)	PUNCT
ejpam-5782	154	28	)	)	PUNCT
ejpam-5782	154	29	.	.	PUNCT
ejpam-5782	155	1	theorem	theorem	ADJ
ejpam-5782	155	2	10	10	NUM
ejpam-5782	155	3	.	.	PUNCT
ejpam-5782	156	1	let	let	VERB
ejpam-5782	156	2	µ	µ	NOUN
ejpam-5782	156	3	and	and	CCONJ
ejpam-5782	156	4	ν	ν	PROPN
ejpam-5782	156	5	be	be	AUX
ejpam-5782	156	6	two	two	NUM
ejpam-5782	156	7	gt	gt	NOUN
ejpam-5782	156	8	’s	’s	NOUN
ejpam-5782	156	9	on	on	ADP
ejpam-5782	156	10	a	a	DET
ejpam-5782	156	11	nonempty	nonempty	ADJ
ejpam-5782	156	12	set	set	VERB
ejpam-5782	156	13	x	x	SYM
ejpam-5782	156	14	,	,	PUNCT
ejpam-5782	156	15	h	h	PROPN
ejpam-5782	156	16	a	a	DET
ejpam-5782	156	17	hereditary	hereditary	ADJ
ejpam-5782	156	18	class	class	NOUN
ejpam-5782	156	19	on	on	ADP
ejpam-5782	156	20	x	x	NOUN
ejpam-5782	156	21	,	,	PUNCT
ejpam-5782	156	22	and	and	CCONJ
ejpam-5782	156	23	a	a	DET
ejpam-5782	156	24	⊆	⊆	NUM
ejpam-5782	156	25	x.	x.	NOUN
ejpam-5782	156	26	then	then	ADV
ejpam-5782	156	27	,	,	PUNCT
ejpam-5782	156	28	a	a	PRON
ejpam-5782	156	29	is	be	AUX
ejpam-5782	156	30	h(θ(µ	h(θ(µ	VERB
ejpam-5782	156	31	,	,	PUNCT
ejpam-5782	156	32	ν))-closed	ν))-close	VERB
ejpam-5782	156	33	if	if	SCONJ
ejpam-5782	156	34	and	and	CCONJ
ejpam-5782	156	35	only	only	ADV
ejpam-5782	157	1	if	if	SCONJ
ejpam-5782	157	2	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	157	3	,	,	PUNCT
ejpam-5782	157	4	ν)(a	ν)(a	NUM
ejpam-5782	157	5	)	)	PUNCT
ejpam-5782	157	6	=	=	SYM
ejpam-5782	157	7	a.	a.	PROPN
ejpam-5782	157	8	f.	f.	PROPN
ejpam-5782	157	9	alsharari	alsharari	PROPN
ejpam-5782	157	10	,	,	PUNCT
ejpam-5782	157	11	a.	a.	PROPN
ejpam-5782	157	12	qahis	qahis	PROPN
ejpam-5782	157	13	/	/	SYM
ejpam-5782	157	14	eur	eur	PROPN
ejpam-5782	157	15	.	.	PUNCT
ejpam-5782	158	1	j.	j.	PROPN
ejpam-5782	158	2	pure	pure	PROPN
ejpam-5782	158	3	appl	appl	PROPN
ejpam-5782	158	4	.	.	PROPN
ejpam-5782	158	5	math	math	PROPN
ejpam-5782	158	6	,	,	PUNCT
ejpam-5782	158	7	18	18	NUM
ejpam-5782	158	8	(	(	PUNCT
ejpam-5782	158	9	2	2	NUM
ejpam-5782	158	10	)	)	PUNCT
ejpam-5782	158	11	(	(	PUNCT
ejpam-5782	158	12	2025	2025	NUM
ejpam-5782	158	13	)	)	PUNCT
ejpam-5782	158	14	,	,	PUNCT
ejpam-5782	158	15	5782	5782	NUM
ejpam-5782	158	16	7	7	NUM
ejpam-5782	158	17	of	of	ADP
ejpam-5782	158	18	10	10	NUM
ejpam-5782	158	19	proof	proof	NOUN
ejpam-5782	158	20	.	.	PUNCT
ejpam-5782	159	1	let	let	VERB
ejpam-5782	159	2	a	a	DET
ejpam-5782	159	3	be	be	AUX
ejpam-5782	159	4	h	h	NOUN
ejpam-5782	159	5	(	(	PUNCT
ejpam-5782	159	6	θ(µ	θ(µ	PROPN
ejpam-5782	159	7	,	,	PUNCT
ejpam-5782	159	8	ν	ν	NOUN
ejpam-5782	159	9	)	)	PUNCT
ejpam-5782	159	10	)	)	PUNCT
ejpam-5782	160	1	-closed	-close	VERB
ejpam-5782	160	2	in	in	ADP
ejpam-5782	160	3	x.	x.	NOUN
ejpam-5782	160	4	since	since	SCONJ
ejpam-5782	160	5	x−a	x−a	PROPN
ejpam-5782	160	6	∈	∈	PROPN
ejpam-5782	160	7	h	h	NOUN
ejpam-5782	160	8	(	(	PUNCT
ejpam-5782	160	9	θ(µ	θ(µ	PROPN
ejpam-5782	160	10	,	,	PUNCT
ejpam-5782	160	11	ν	ν	NOUN
ejpam-5782	160	12	)	)	PUNCT
ejpam-5782	160	13	)	)	PUNCT
ejpam-5782	160	14	,	,	PUNCT
ejpam-5782	160	15	for	for	ADP
ejpam-5782	160	16	each	each	DET
ejpam-5782	160	17	x	x	SYM
ejpam-5782	160	18	∈	∈	PROPN
ejpam-5782	160	19	x−a	x−a	PROPN
ejpam-5782	160	20	,	,	PUNCT
ejpam-5782	160	21	there	there	PRON
ejpam-5782	160	22	exists	exist	VERB
ejpam-5782	160	23	m	m	PROPN
ejpam-5782	160	24	∈	∈	PROPN
ejpam-5782	160	25	µ	µ	PRON
ejpam-5782	160	26	such	such	ADJ
ejpam-5782	160	27	that	that	SCONJ
ejpam-5782	160	28	x	x	SYM
ejpam-5782	160	29	∈	∈	PROPN
ejpam-5782	160	30	m	m	VERB
ejpam-5782	160	31	⊆	⊆	NUM
ejpam-5782	160	32	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	160	33	)	)	PUNCT
ejpam-5782	160	34	⊆	⊆	NUM
ejpam-5782	160	35	x	x	SYM
ejpam-5782	160	36	−	−	NOUN
ejpam-5782	160	37	a.	a.	NOUN
ejpam-5782	160	38	thus	thus	ADV
ejpam-5782	160	39	,	,	PUNCT
ejpam-5782	160	40	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	160	41	)	)	PUNCT
ejpam-5782	160	42	∩	∩	NOUN
ejpam-5782	160	43	a	a	DET
ejpam-5782	160	44	=	=	SYM
ejpam-5782	160	45	∅	∅	NOUN
ejpam-5782	160	46	,	,	PUNCT
ejpam-5782	160	47	implying	imply	VERB
ejpam-5782	160	48	x	x	X
ejpam-5782	160	49	/∈	/∈	PROPN
ejpam-5782	160	50	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	160	51	,	,	PUNCT
ejpam-5782	160	52	ν)(a	ν)(a	NOUN
ejpam-5782	160	53	)	)	PUNCT
ejpam-5782	160	54	.	.	PUNCT
ejpam-5782	161	1	therefore	therefore	ADV
ejpam-5782	161	2	,	,	PUNCT
ejpam-5782	161	3	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	161	4	,	,	PUNCT
ejpam-5782	161	5	ν)(a	ν)(a	NUM
ejpam-5782	161	6	)	)	PUNCT
ejpam-5782	161	7	⊆	⊆	NUM
ejpam-5782	161	8	a	a	PRON
ejpam-5782	161	9	,	,	PUNCT
ejpam-5782	161	10	implying	imply	VERB
ejpam-5782	161	11	that	that	SCONJ
ejpam-5782	161	12	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	161	13	,	,	PUNCT
ejpam-5782	161	14	ν)(a	ν)(a	NUM
ejpam-5782	161	15	)	)	PUNCT
ejpam-5782	161	16	=	=	SYM
ejpam-5782	161	17	a.	a.	NOUN
ejpam-5782	161	18	for	for	ADP
ejpam-5782	161	19	the	the	DET
ejpam-5782	161	20	reverse	reverse	ADJ
ejpam-5782	161	21	inclusion	inclusion	NOUN
ejpam-5782	161	22	,	,	PUNCT
ejpam-5782	161	23	suppose	suppose	VERB
ejpam-5782	161	24	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	161	25	,	,	PUNCT
ejpam-5782	161	26	ν)(a	ν)(a	NUM
ejpam-5782	161	27	)	)	PUNCT
ejpam-5782	161	28	=	=	PUNCT
ejpam-5782	162	1	a	a	PRON
ejpam-5782	163	1	and	and	CCONJ
ejpam-5782	163	2	let	let	VERB
ejpam-5782	163	3	x	x	X
ejpam-5782	163	4	∈	∈	NOUN
ejpam-5782	163	5	x−a	x−a	NOUN
ejpam-5782	164	1	=	=	SYM
ejpam-5782	164	2	x−γ∗(µ	x−γ∗(µ	PROPN
ejpam-5782	164	3	,	,	PUNCT
ejpam-5782	164	4	ν)(a	ν)(a	NOUN
ejpam-5782	164	5	)	)	PUNCT
ejpam-5782	164	6	.	.	PUNCT
ejpam-5782	165	1	then	then	ADV
ejpam-5782	165	2	there	there	PRON
ejpam-5782	165	3	exists	exist	VERB
ejpam-5782	165	4	m	m	PROPN
ejpam-5782	165	5	∈	∈	PROPN
ejpam-5782	165	6	µ	µ	PRON
ejpam-5782	165	7	such	such	ADJ
ejpam-5782	165	8	that	that	SCONJ
ejpam-5782	165	9	x	x	SYM
ejpam-5782	165	10	∈	∈	PROPN
ejpam-5782	165	11	m	m	NOUN
ejpam-5782	165	12	and	and	CCONJ
ejpam-5782	165	13	c∗ν(m)∩a	c∗ν(m)∩a	NOUN
ejpam-5782	165	14	=	=	PUNCT
ejpam-5782	165	15	∅.	∅.	VERB
ejpam-5782	165	16	hence	hence	ADV
ejpam-5782	165	17	,	,	PUNCT
ejpam-5782	165	18	x	x	PUNCT
ejpam-5782	165	19	∈	∈	PROPN
ejpam-5782	165	20	m	m	VERB
ejpam-5782	165	21	⊆	⊆	NUM
ejpam-5782	165	22	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	165	23	)	)	PUNCT
ejpam-5782	165	24	⊆	⊆	NUM
ejpam-5782	165	25	x	x	SYM
ejpam-5782	165	26	−a	−a	NOUN
ejpam-5782	165	27	,	,	PUNCT
ejpam-5782	165	28	showing	show	VERB
ejpam-5782	165	29	that	that	SCONJ
ejpam-5782	165	30	x	x	SYM
ejpam-5782	165	31	−a	−a	NOUN
ejpam-5782	165	32	is	be	AUX
ejpam-5782	165	33	h	h	NOUN
ejpam-5782	165	34	(	(	PUNCT
ejpam-5782	165	35	θ(µ	θ(µ	PROPN
ejpam-5782	165	36	,	,	PUNCT
ejpam-5782	165	37	ν	ν	NOUN
ejpam-5782	165	38	)	)	PUNCT
ejpam-5782	165	39	)	)	PUNCT
ejpam-5782	166	1	-open	-open	NOUN
ejpam-5782	166	2	.	.	PUNCT
ejpam-5782	167	1	therefore	therefore	ADV
ejpam-5782	167	2	,	,	PUNCT
ejpam-5782	167	3	a	a	PRON
ejpam-5782	167	4	is	be	AUX
ejpam-5782	167	5	h	h	NOUN
ejpam-5782	167	6	(	(	PUNCT
ejpam-5782	167	7	θ(µ	θ(µ	PROPN
ejpam-5782	167	8	,	,	PUNCT
ejpam-5782	167	9	ν	ν	NOUN
ejpam-5782	167	10	)	)	PUNCT
ejpam-5782	167	11	)	)	PUNCT
ejpam-5782	168	1	-closed	-close	VERB
ejpam-5782	168	2	.	.	PUNCT
ejpam-5782	169	1	from	from	ADP
ejpam-5782	169	2	theorem	theorem	ADJ
ejpam-5782	169	3	10	10	NUM
ejpam-5782	169	4	and	and	CCONJ
ejpam-5782	169	5	theorem	theorem	VERB
ejpam-5782	169	6	7	7	NUM
ejpam-5782	169	7	,	,	PUNCT
ejpam-5782	169	8	the	the	DET
ejpam-5782	169	9	following	follow	VERB
ejpam-5782	169	10	corollary	corollary	NOUN
ejpam-5782	169	11	is	be	AUX
ejpam-5782	169	12	directly	directly	ADV
ejpam-5782	169	13	obtained	obtain	VERB
ejpam-5782	169	14	.	.	PUNCT
ejpam-5782	170	1	corollary	corollary	ADJ
ejpam-5782	170	2	5	5	NUM
ejpam-5782	170	3	.	.	PUNCT
ejpam-5782	171	1	let	let	VERB
ejpam-5782	171	2	µ	µ	NOUN
ejpam-5782	171	3	and	and	CCONJ
ejpam-5782	171	4	ν	ν	PROPN
ejpam-5782	171	5	be	be	AUX
ejpam-5782	171	6	two	two	NUM
ejpam-5782	171	7	gt	gt	NOUN
ejpam-5782	171	8	’s	’s	NOUN
ejpam-5782	171	9	on	on	ADP
ejpam-5782	171	10	a	a	DET
ejpam-5782	171	11	nonempty	nonempty	ADJ
ejpam-5782	171	12	set	set	VERB
ejpam-5782	171	13	x	x	SYM
ejpam-5782	171	14	,	,	PUNCT
ejpam-5782	171	15	h	h	PROPN
ejpam-5782	171	16	a	a	DET
ejpam-5782	171	17	hereditary	hereditary	ADJ
ejpam-5782	171	18	class	class	NOUN
ejpam-5782	171	19	on	on	ADP
ejpam-5782	171	20	x	x	NOUN
ejpam-5782	171	21	,	,	PUNCT
ejpam-5782	171	22	and	and	CCONJ
ejpam-5782	171	23	a	a	DET
ejpam-5782	171	24	⊆	⊆	NUM
ejpam-5782	171	25	x	x	SYM
ejpam-5782	171	26	be	be	AUX
ejpam-5782	171	27	h	h	NOUN
ejpam-5782	171	28	(	(	PUNCT
ejpam-5782	171	29	θ(µ	θ(µ	PROPN
ejpam-5782	171	30	,	,	PUNCT
ejpam-5782	171	31	ν	ν	NOUN
ejpam-5782	171	32	)	)	PUNCT
ejpam-5782	171	33	)	)	PUNCT
ejpam-5782	172	1	-closed	-close	VERB
ejpam-5782	172	2	.	.	PUNCT
ejpam-5782	173	1	if	if	SCONJ
ejpam-5782	173	2	a	a	DET
ejpam-5782	173	3	∈	∈	PROPN
ejpam-5782	173	4	ν	ν	NOUN
ejpam-5782	173	5	,	,	PUNCT
ejpam-5782	173	6	then	then	ADV
ejpam-5782	173	7	a	a	PRON
ejpam-5782	173	8	is	be	AUX
ejpam-5782	173	9	µ-closed	µ-close	VERB
ejpam-5782	173	10	.	.	PUNCT
ejpam-5782	174	1	definition	definition	NOUN
ejpam-5782	174	2	4	4	NUM
ejpam-5782	174	3	.	.	PUNCT
ejpam-5782	175	1	let	let	VERB
ejpam-5782	175	2	µ	µ	NOUN
ejpam-5782	175	3	and	and	CCONJ
ejpam-5782	175	4	ν	ν	PROPN
ejpam-5782	175	5	be	be	AUX
ejpam-5782	175	6	two	two	NUM
ejpam-5782	175	7	gt	gt	NOUN
ejpam-5782	175	8	’s	’s	NOUN
ejpam-5782	175	9	on	on	ADP
ejpam-5782	175	10	a	a	DET
ejpam-5782	175	11	nonempty	nonempty	ADV
ejpam-5782	175	12	set	set	VERB
ejpam-5782	175	13	x	x	NOUN
ejpam-5782	175	14	,	,	PUNCT
ejpam-5782	175	15	and	and	CCONJ
ejpam-5782	176	1	h	h	DET
ejpam-5782	176	2	a	a	DET
ejpam-5782	176	3	hereditary	hereditary	ADJ
ejpam-5782	176	4	class	class	NOUN
ejpam-5782	176	5	on	on	ADP
ejpam-5782	176	6	x.	x.	NOUN
ejpam-5782	176	7	the	the	DET
ejpam-5782	176	8	h	h	NOUN
ejpam-5782	176	9	(	(	PUNCT
ejpam-5782	176	10	θ(µ	θ(µ	PROPN
ejpam-5782	176	11	,	,	PUNCT
ejpam-5782	176	12	ν	ν	NOUN
ejpam-5782	176	13	)	)	PUNCT
ejpam-5782	176	14	)	)	PUNCT
ejpam-5782	176	15	-closure	-closure	NOUN
ejpam-5782	176	16	of	of	ADP
ejpam-5782	176	17	a	a	DET
ejpam-5782	176	18	⊆	⊆	NUM
ejpam-5782	176	19	x	x	NOUN
ejpam-5782	176	20	,	,	PUNCT
ejpam-5782	176	21	denoted	denote	VERB
ejpam-5782	176	22	by	by	ADP
ejpam-5782	176	23	chθ(µ,ν)(a	chθ(µ,ν)(a	PROPN
ejpam-5782	176	24	)	)	PUNCT
ejpam-5782	176	25	,	,	PUNCT
ejpam-5782	176	26	is	be	AUX
ejpam-5782	176	27	the	the	DET
ejpam-5782	176	28	intersection	intersection	NOUN
ejpam-5782	176	29	of	of	ADP
ejpam-5782	176	30	all	all	DET
ejpam-5782	176	31	h	h	NOUN
ejpam-5782	176	32	(	(	PUNCT
ejpam-5782	176	33	θ(µ	θ(µ	PROPN
ejpam-5782	176	34	,	,	PUNCT
ejpam-5782	176	35	ν	ν	NOUN
ejpam-5782	176	36	)	)	PUNCT
ejpam-5782	176	37	)	)	PUNCT
ejpam-5782	177	1	-closed	-close	VERB
ejpam-5782	177	2	sets	set	NOUN
ejpam-5782	177	3	containing	contain	VERB
ejpam-5782	177	4	a.	a.	NOUN
ejpam-5782	177	5	the	the	DET
ejpam-5782	177	6	h	h	NOUN
ejpam-5782	177	7	(	(	PUNCT
ejpam-5782	177	8	θ(µ	θ(µ	PROPN
ejpam-5782	177	9	,	,	PUNCT
ejpam-5782	177	10	ν	ν	NOUN
ejpam-5782	177	11	)	)	PUNCT
ejpam-5782	177	12	)	)	PUNCT
ejpam-5782	178	1	-interior	-interior	NOUN
ejpam-5782	178	2	of	of	ADP
ejpam-5782	178	3	a	a	PRON
ejpam-5782	178	4	,	,	PUNCT
ejpam-5782	178	5	denoted	denote	VERB
ejpam-5782	178	6	by	by	ADP
ejpam-5782	178	7	ih(θ(µ,ν))(a	ih(θ(µ,ν))(a	PROPN
ejpam-5782	178	8	)	)	PUNCT
ejpam-5782	178	9	,	,	PUNCT
ejpam-5782	178	10	is	be	AUX
ejpam-5782	178	11	the	the	DET
ejpam-5782	178	12	union	union	NOUN
ejpam-5782	178	13	of	of	ADP
ejpam-5782	178	14	all	all	DET
ejpam-5782	178	15	h	h	NOUN
ejpam-5782	178	16	(	(	PUNCT
ejpam-5782	178	17	θ(µ	θ(µ	PROPN
ejpam-5782	178	18	,	,	PUNCT
ejpam-5782	178	19	ν	ν	NOUN
ejpam-5782	178	20	)	)	PUNCT
ejpam-5782	178	21	)	)	PUNCT
ejpam-5782	178	22	-open	-open	NOUN
ejpam-5782	178	23	sets	set	NOUN
ejpam-5782	178	24	contained	contain	VERB
ejpam-5782	178	25	in	in	ADP
ejpam-5782	178	26	a.	a.	NOUN
ejpam-5782	178	27	theorem	theorem	NOUN
ejpam-5782	178	28	11	11	NUM
ejpam-5782	178	29	.	.	PUNCT
ejpam-5782	179	1	let	let	VERB
ejpam-5782	179	2	µ	µ	NOUN
ejpam-5782	179	3	and	and	CCONJ
ejpam-5782	179	4	ν	ν	PROPN
ejpam-5782	179	5	be	be	AUX
ejpam-5782	179	6	two	two	NUM
ejpam-5782	179	7	gt	gt	NOUN
ejpam-5782	179	8	’s	’s	NOUN
ejpam-5782	179	9	on	on	ADP
ejpam-5782	179	10	a	a	DET
ejpam-5782	179	11	nonempty	nonempty	ADV
ejpam-5782	179	12	set	set	VERB
ejpam-5782	179	13	x	x	NOUN
ejpam-5782	179	14	,	,	PUNCT
ejpam-5782	179	15	and	and	CCONJ
ejpam-5782	179	16	let	let	VERB
ejpam-5782	179	17	h	h	NOUN
ejpam-5782	179	18	be	be	AUX
ejpam-5782	179	19	a	a	DET
ejpam-5782	179	20	hereditary	hereditary	ADJ
ejpam-5782	179	21	class	class	NOUN
ejpam-5782	179	22	on	on	ADP
ejpam-5782	179	23	x.	x.	PROPN
ejpam-5782	179	24	then	then	ADV
ejpam-5782	179	25	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	179	26	,	,	PUNCT
ejpam-5782	179	27	ν)(a	ν)(a	NUM
ejpam-5782	179	28	)	)	PUNCT
ejpam-5782	180	1	⊆	⊆	NUM
ejpam-5782	180	2	chθ(µ,ν)(a	chθ(µ,ν)(a	PROPN
ejpam-5782	180	3	)	)	PUNCT
ejpam-5782	180	4	.	.	PUNCT
ejpam-5782	181	1	proof	proof	NOUN
ejpam-5782	181	2	.	.	PUNCT
ejpam-5782	182	1	let	let	VERB
ejpam-5782	182	2	x	x	X
ejpam-5782	182	3	/∈	/∈	PUNCT
ejpam-5782	182	4	chθ(µ,ν)(a	chθ(µ,ν)(a	PROPN
ejpam-5782	182	5	)	)	PUNCT
ejpam-5782	182	6	.	.	PUNCT
ejpam-5782	183	1	then	then	ADV
ejpam-5782	183	2	there	there	PRON
ejpam-5782	183	3	exists	exist	VERB
ejpam-5782	183	4	an	an	DET
ejpam-5782	183	5	h	h	NOUN
ejpam-5782	183	6	(	(	PUNCT
ejpam-5782	183	7	θ(µ	θ(µ	PROPN
ejpam-5782	183	8	,	,	PUNCT
ejpam-5782	183	9	ν	ν	NOUN
ejpam-5782	183	10	)	)	PUNCT
ejpam-5782	183	11	)	)	PUNCT
ejpam-5782	184	1	-open	-open	VERB
ejpam-5782	184	2	set	set	VERB
ejpam-5782	184	3	w	w	NOUN
ejpam-5782	184	4	containing	contain	VERB
ejpam-5782	184	5	x	x	PUNCT
ejpam-5782	184	6	such	such	ADJ
ejpam-5782	184	7	that	that	SCONJ
ejpam-5782	184	8	w	w	PROPN
ejpam-5782	184	9	∩	∩	NOUN
ejpam-5782	184	10	a	a	DET
ejpam-5782	184	11	=	=	SYM
ejpam-5782	184	12	∅.	∅.	NOUN
ejpam-5782	184	13	since	since	SCONJ
ejpam-5782	184	14	w	w	PROPN
ejpam-5782	184	15	∈	∈	PROPN
ejpam-5782	184	16	h	h	NOUN
ejpam-5782	184	17	(	(	PUNCT
ejpam-5782	184	18	θ(µ	θ(µ	PROPN
ejpam-5782	184	19	,	,	PUNCT
ejpam-5782	184	20	ν	ν	NOUN
ejpam-5782	184	21	)	)	PUNCT
ejpam-5782	184	22	)	)	PUNCT
ejpam-5782	184	23	,	,	PUNCT
ejpam-5782	184	24	there	there	PRON
ejpam-5782	184	25	exists	exist	VERB
ejpam-5782	184	26	m	m	VERB
ejpam-5782	184	27	∈	∈	PROPN
ejpam-5782	184	28	µ	µ	X
ejpam-5782	184	29	containing	contain	VERB
ejpam-5782	184	30	x	x	PUNCT
ejpam-5782	184	31	such	such	ADJ
ejpam-5782	184	32	that	that	SCONJ
ejpam-5782	184	33	x	x	SYM
ejpam-5782	184	34	∈	∈	PROPN
ejpam-5782	184	35	m	m	VERB
ejpam-5782	184	36	⊆	⊆	NUM
ejpam-5782	184	37	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	184	38	)	)	PUNCT
ejpam-5782	184	39	⊆	⊆	NUM
ejpam-5782	184	40	w	w	ADP
ejpam-5782	184	41	⊆	⊆	NUM
ejpam-5782	184	42	x	x	SYM
ejpam-5782	184	43	−	−	NOUN
ejpam-5782	184	44	a.	a.	NOUN
ejpam-5782	184	45	this	this	PRON
ejpam-5782	184	46	implies	imply	VERB
ejpam-5782	184	47	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	184	48	)	)	PUNCT
ejpam-5782	184	49	∩	∩	NOUN
ejpam-5782	184	50	a	a	DET
ejpam-5782	184	51	=	=	NOUN
ejpam-5782	184	52	∅	∅	NOUN
ejpam-5782	184	53	and	and	CCONJ
ejpam-5782	184	54	hence	hence	ADV
ejpam-5782	184	55	x	x	PROPN
ejpam-5782	184	56	/∈	/∈	PROPN
ejpam-5782	184	57	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	184	58	,	,	PUNCT
ejpam-5782	184	59	ν)(a	ν)(a	NOUN
ejpam-5782	184	60	)	)	PUNCT
ejpam-5782	184	61	.	.	PUNCT
ejpam-5782	185	1	therefore	therefore	ADV
ejpam-5782	185	2	,	,	PUNCT
ejpam-5782	185	3	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	185	4	,	,	PUNCT
ejpam-5782	185	5	ν)(a	ν)(a	NUM
ejpam-5782	185	6	)	)	PUNCT
ejpam-5782	185	7	⊆	⊆	NUM
ejpam-5782	185	8	chθ(µ,ν)(a	chθ(µ,ν)(a	PROPN
ejpam-5782	185	9	)	)	PUNCT
ejpam-5782	185	10	.	.	PUNCT
ejpam-5782	186	1	definition	definition	NOUN
ejpam-5782	186	2	5	5	NUM
ejpam-5782	186	3	.	.	PUNCT
ejpam-5782	187	1	let	let	VERB
ejpam-5782	187	2	µ	µ	NOUN
ejpam-5782	187	3	and	and	CCONJ
ejpam-5782	187	4	ν	ν	PROPN
ejpam-5782	187	5	be	be	AUX
ejpam-5782	187	6	two	two	NUM
ejpam-5782	187	7	gts	gts	NOUN
ejpam-5782	187	8	on	on	ADP
ejpam-5782	187	9	a	a	DET
ejpam-5782	187	10	nonempty	nonempty	ADV
ejpam-5782	187	11	set	set	VERB
ejpam-5782	187	12	x	x	NOUN
ejpam-5782	187	13	,	,	PUNCT
ejpam-5782	187	14	and	and	CCONJ
ejpam-5782	187	15	let	let	VERB
ejpam-5782	187	16	h	h	NOUN
ejpam-5782	187	17	be	be	AUX
ejpam-5782	187	18	a	a	DET
ejpam-5782	187	19	hereditary	hereditary	ADJ
ejpam-5782	187	20	class	class	NOUN
ejpam-5782	187	21	on	on	ADP
ejpam-5782	187	22	x.	x.	PROPN
ejpam-5782	187	23	a	a	DET
ejpam-5782	187	24	subset	subset	VERB
ejpam-5782	187	25	a	a	DET
ejpam-5782	187	26	⊆	⊆	NUM
ejpam-5782	187	27	x	x	NUM
ejpam-5782	187	28	is	be	AUX
ejpam-5782	187	29	called	call	VERB
ejpam-5782	187	30	h(µ	h(µ	PROPN
ejpam-5782	187	31	,	,	PUNCT
ejpam-5782	187	32	ν)-regular	ν)-regular	PUNCT
ejpam-5782	187	33	open	open	ADJ
ejpam-5782	187	34	(	(	PUNCT
ejpam-5782	187	35	briefly	briefly	ADV
ejpam-5782	187	36	,	,	PUNCT
ejpam-5782	187	37	hr(µ	hr(µ	NOUN
ejpam-5782	187	38	,	,	PUNCT
ejpam-5782	187	39	ν)-open	ν)-open	PUNCT
ejpam-5782	187	40	)	)	PUNCT
ejpam-5782	187	41	if	if	SCONJ
ejpam-5782	187	42	a	a	PRON
ejpam-5782	187	43	=	=	NOUN
ejpam-5782	187	44	iµ(c	iµ(c	NOUN
ejpam-5782	187	45	∗	∗	PROPN
ejpam-5782	187	46	ν(a	ν(a	PROPN
ejpam-5782	187	47	)	)	PUNCT
ejpam-5782	187	48	)	)	PUNCT
ejpam-5782	187	49	.	.	PUNCT
ejpam-5782	188	1	similarly	similarly	ADV
ejpam-5782	188	2	,	,	PUNCT
ejpam-5782	188	3	a	a	PRON
ejpam-5782	188	4	is	be	AUX
ejpam-5782	188	5	called	call	VERB
ejpam-5782	188	6	h(µ	h(µ	PROPN
ejpam-5782	188	7	,	,	PUNCT
ejpam-5782	188	8	ν)-regular	ν)-regular	PUNCT
ejpam-5782	188	9	closed	close	VERB
ejpam-5782	188	10	(	(	PUNCT
ejpam-5782	188	11	briefly	briefly	ADV
ejpam-5782	188	12	,	,	PUNCT
ejpam-5782	188	13	hr(µ	hr(µ	PROPN
ejpam-5782	188	14	,	,	PUNCT
ejpam-5782	188	15	ν)-closed	ν)-close	VERB
ejpam-5782	188	16	)	)	PUNCT
ejpam-5782	188	17	if	if	SCONJ
ejpam-5782	188	18	cµ(i	cµ(i	VERB
ejpam-5782	188	19	∗	∗	NOUN
ejpam-5782	188	20	ν(a	ν(a	PROPN
ejpam-5782	188	21	)	)	PUNCT
ejpam-5782	188	22	)	)	PUNCT
ejpam-5782	189	1	=	=	SYM
ejpam-5782	189	2	a.	a.	NOUN
ejpam-5782	189	3	theorem	theorem	NOUN
ejpam-5782	189	4	12	12	NUM
ejpam-5782	189	5	.	.	PUNCT
ejpam-5782	190	1	let	let	VERB
ejpam-5782	190	2	µ	µ	NOUN
ejpam-5782	190	3	and	and	CCONJ
ejpam-5782	190	4	ν	ν	PROPN
ejpam-5782	190	5	be	be	AUX
ejpam-5782	190	6	two	two	NUM
ejpam-5782	190	7	gts	gts	NOUN
ejpam-5782	190	8	on	on	ADP
ejpam-5782	190	9	a	a	DET
ejpam-5782	190	10	nonempty	nonempty	ADV
ejpam-5782	190	11	set	set	VERB
ejpam-5782	190	12	x	x	SYM
ejpam-5782	190	13	,	,	PUNCT
ejpam-5782	190	14	h	h	PROPN
ejpam-5782	190	15	a	a	DET
ejpam-5782	190	16	hereditary	hereditary	ADJ
ejpam-5782	190	17	class	class	NOUN
ejpam-5782	190	18	on	on	ADP
ejpam-5782	190	19	x	x	NOUN
ejpam-5782	190	20	,	,	PUNCT
ejpam-5782	190	21	and	and	CCONJ
ejpam-5782	190	22	a	a	DET
ejpam-5782	190	23	⊆	⊆	NUM
ejpam-5782	190	24	x.	x.	NOUN
ejpam-5782	190	25	if	if	SCONJ
ejpam-5782	190	26	a	a	DET
ejpam-5782	190	27	∈	∈	PROPN
ejpam-5782	190	28	h	h	NOUN
ejpam-5782	190	29	(	(	PUNCT
ejpam-5782	190	30	θ(µ	θ(µ	PROPN
ejpam-5782	190	31	,	,	PUNCT
ejpam-5782	190	32	ν	ν	NOUN
ejpam-5782	190	33	)	)	PUNCT
ejpam-5782	190	34	)	)	PUNCT
ejpam-5782	191	1	and	and	CCONJ
ejpam-5782	191	2	x	x	PUNCT
ejpam-5782	191	3	∈	∈	PROPN
ejpam-5782	191	4	a	a	PRON
ejpam-5782	191	5	,	,	PUNCT
ejpam-5782	191	6	then	then	ADV
ejpam-5782	191	7	there	there	PRON
ejpam-5782	191	8	exists	exist	VERB
ejpam-5782	191	9	a	a	DET
ejpam-5782	191	10	hr(µ	hr(µ	NOUN
ejpam-5782	191	11	,	,	PUNCT
ejpam-5782	191	12	ν)-open	ν)-open	PUNCT
ejpam-5782	191	13	set	set	VERB
ejpam-5782	191	14	u	u	PRON
ejpam-5782	191	15	such	such	ADJ
ejpam-5782	191	16	that	that	SCONJ
ejpam-5782	191	17	x	x	SYM
ejpam-5782	191	18	∈	∈	PROPN
ejpam-5782	191	19	u	u	NOUN
ejpam-5782	191	20	⊆	⊆	NUM
ejpam-5782	191	21	c∗ν(u	c∗ν(u	PROPN
ejpam-5782	191	22	)	)	PUNCT
ejpam-5782	191	23	⊆	⊆	NUM
ejpam-5782	191	24	a.	a.	NOUN
ejpam-5782	191	25	proof	proof	NOUN
ejpam-5782	191	26	.	.	PUNCT
ejpam-5782	192	1	since	since	SCONJ
ejpam-5782	192	2	a	a	DET
ejpam-5782	192	3	∈	∈	PROPN
ejpam-5782	192	4	h	h	NOUN
ejpam-5782	192	5	(	(	PUNCT
ejpam-5782	192	6	θ(µ	θ(µ	PROPN
ejpam-5782	192	7	,	,	PUNCT
ejpam-5782	192	8	ν	ν	NOUN
ejpam-5782	192	9	)	)	PUNCT
ejpam-5782	192	10	)	)	PUNCT
ejpam-5782	192	11	and	and	CCONJ
ejpam-5782	192	12	x	x	PUNCT
ejpam-5782	192	13	∈	∈	PROPN
ejpam-5782	192	14	a	a	X
ejpam-5782	192	15	,	,	PUNCT
ejpam-5782	192	16	there	there	PRON
ejpam-5782	192	17	exists	exist	VERB
ejpam-5782	192	18	a	a	DET
ejpam-5782	192	19	µ-open	µ-open	NOUN
ejpam-5782	192	20	set	set	VERB
ejpam-5782	192	21	m	m	VERB
ejpam-5782	192	22	such	such	ADJ
ejpam-5782	192	23	that	that	SCONJ
ejpam-5782	192	24	x	x	SYM
ejpam-5782	192	25	∈	∈	PROPN
ejpam-5782	192	26	m	m	VERB
ejpam-5782	192	27	⊆	⊆	NUM
ejpam-5782	192	28	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	192	29	)	)	PUNCT
ejpam-5782	192	30	⊆	⊆	NUM
ejpam-5782	192	31	a.	a.	NOUN
ejpam-5782	192	32	define	define	NOUN
ejpam-5782	192	33	u	u	NOUN
ejpam-5782	192	34	=	=	X
ejpam-5782	192	35	iµ	iµ	PROPN
ejpam-5782	192	36	(	(	PUNCT
ejpam-5782	192	37	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	192	38	)	)	PUNCT
ejpam-5782	192	39	)	)	PUNCT
ejpam-5782	192	40	.	.	PUNCT
ejpam-5782	193	1	then	then	ADV
ejpam-5782	193	2	u	u	PROPN
ejpam-5782	193	3	is	be	AUX
ejpam-5782	193	4	hr(µ	hr(µ	NOUN
ejpam-5782	193	5	,	,	PUNCT
ejpam-5782	193	6	ν)-open	ν)-open	VERB
ejpam-5782	193	7	,	,	PUNCT
ejpam-5782	193	8	m	m	VERB
ejpam-5782	193	9	⊆	⊆	NUM
ejpam-5782	193	10	u	u	NOUN
ejpam-5782	193	11	,	,	PUNCT
ejpam-5782	193	12	and	and	CCONJ
ejpam-5782	193	13	c∗ν(u	c∗ν(u	PROPN
ejpam-5782	193	14	)	)	PUNCT
ejpam-5782	194	1	=	=	SYM
ejpam-5782	194	2	c∗ν	c∗ν	PROPN
ejpam-5782	194	3	(	(	PUNCT
ejpam-5782	194	4	iµ	iµ	PROPN
ejpam-5782	194	5	(	(	PUNCT
ejpam-5782	194	6	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	194	7	)	)	PUNCT
ejpam-5782	194	8	)	)	PUNCT
ejpam-5782	194	9	)	)	PUNCT
ejpam-5782	195	1	⊆	⊆	NUM
ejpam-5782	195	2	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	195	3	)	)	PUNCT
ejpam-5782	195	4	.	.	PUNCT
ejpam-5782	196	1	this	this	PRON
ejpam-5782	196	2	implies	imply	VERB
ejpam-5782	196	3	x	x	X
ejpam-5782	196	4	∈	∈	PROPN
ejpam-5782	196	5	m	m	VERB
ejpam-5782	196	6	⊆	⊆	NUM
ejpam-5782	196	7	u	u	NOUN
ejpam-5782	196	8	⊆	⊆	NUM
ejpam-5782	196	9	c∗ν(u	c∗ν(u	PROPN
ejpam-5782	196	10	)	)	PUNCT
ejpam-5782	196	11	⊆	⊆	NUM
ejpam-5782	196	12	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	196	13	)	)	PUNCT
ejpam-5782	196	14	⊆	⊆	NUM
ejpam-5782	196	15	a.	a.	NOUN
ejpam-5782	196	16	thus	thus	ADV
ejpam-5782	196	17	,	,	PUNCT
ejpam-5782	196	18	we	we	PRON
ejpam-5782	196	19	have	have	VERB
ejpam-5782	196	20	x	x	X
ejpam-5782	196	21	∈	∈	PROPN
ejpam-5782	196	22	u	u	NOUN
ejpam-5782	196	23	⊆	⊆	NUM
ejpam-5782	196	24	c∗ν(u	c∗ν(u	PROPN
ejpam-5782	196	25	)	)	PUNCT
ejpam-5782	196	26	⊆	⊆	NUM
ejpam-5782	196	27	a	a	PRON
ejpam-5782	196	28	for	for	ADP
ejpam-5782	196	29	some	some	DET
ejpam-5782	196	30	hr(µ	hr(µ	NOUN
ejpam-5782	196	31	,	,	PUNCT
ejpam-5782	196	32	ν)-open	ν)-open	PUNCT
ejpam-5782	196	33	set	set	VERB
ejpam-5782	196	34	u	u	NOUN
ejpam-5782	196	35	.	.	PUNCT
ejpam-5782	197	1	since	since	SCONJ
ejpam-5782	197	2	everyh(µ	everyh(µ	PROPN
ejpam-5782	197	3	,	,	PUNCT
ejpam-5782	197	4	ν)-regular	ν)-regular	PUNCT
ejpam-5782	197	5	open	open	ADJ
ejpam-5782	197	6	set	set	NOUN
ejpam-5782	197	7	is	be	AUX
ejpam-5782	197	8	µ-open	µ-open	PROPN
ejpam-5782	197	9	inx	inx	PROPN
ejpam-5782	197	10	,	,	PUNCT
ejpam-5782	197	11	the	the	DET
ejpam-5782	197	12	following	follow	VERB
ejpam-5782	197	13	corollary	corollary	NOUN
ejpam-5782	197	14	is	be	AUX
ejpam-5782	197	15	evidently	evidently	ADV
ejpam-5782	197	16	obtained	obtain	VERB
ejpam-5782	197	17	.	.	PUNCT
ejpam-5782	198	1	corollary	corollary	ADJ
ejpam-5782	198	2	6	6	NUM
ejpam-5782	198	3	.	.	PUNCT
ejpam-5782	199	1	let	let	VERB
ejpam-5782	199	2	µ	µ	NOUN
ejpam-5782	199	3	and	and	CCONJ
ejpam-5782	199	4	ν	ν	PROPN
ejpam-5782	199	5	be	be	AUX
ejpam-5782	199	6	two	two	NUM
ejpam-5782	199	7	gt	gt	NOUN
ejpam-5782	199	8	’s	’s	NOUN
ejpam-5782	199	9	on	on	ADP
ejpam-5782	199	10	a	a	DET
ejpam-5782	199	11	nonempty	nonempty	ADJ
ejpam-5782	199	12	set	set	VERB
ejpam-5782	199	13	x	x	SYM
ejpam-5782	199	14	,	,	PUNCT
ejpam-5782	199	15	h	h	PROPN
ejpam-5782	199	16	a	a	DET
ejpam-5782	199	17	hereditary	hereditary	ADJ
ejpam-5782	199	18	class	class	NOUN
ejpam-5782	199	19	on	on	ADP
ejpam-5782	199	20	x	x	NOUN
ejpam-5782	199	21	,	,	PUNCT
ejpam-5782	199	22	and	and	CCONJ
ejpam-5782	199	23	a	a	DET
ejpam-5782	199	24	⊆	⊆	NUM
ejpam-5782	199	25	x.	x.	NOUN
ejpam-5782	199	26	then	then	ADV
ejpam-5782	199	27	,	,	PUNCT
ejpam-5782	199	28	a	a	DET
ejpam-5782	199	29	∈	∈	PROPN
ejpam-5782	199	30	h	h	NOUN
ejpam-5782	199	31	(	(	PUNCT
ejpam-5782	199	32	θ(µ	θ(µ	PROPN
ejpam-5782	199	33	,	,	PUNCT
ejpam-5782	199	34	ν	ν	NOUN
ejpam-5782	199	35	)	)	PUNCT
ejpam-5782	199	36	)	)	PUNCT
ejpam-5782	200	1	and	and	CCONJ
ejpam-5782	200	2	x	x	PUNCT
ejpam-5782	200	3	∈	∈	PROPN
ejpam-5782	200	4	a	a	DET
ejpam-5782	200	5	if	if	NOUN
ejpam-5782	201	1	and	and	CCONJ
ejpam-5782	201	2	only	only	ADV
ejpam-5782	201	3	if	if	SCONJ
ejpam-5782	201	4	there	there	PRON
ejpam-5782	201	5	exists	exist	VERB
ejpam-5782	201	6	a	a	DET
ejpam-5782	201	7	hr(µ	hr(µ	NOUN
ejpam-5782	201	8	,	,	PUNCT
ejpam-5782	201	9	ν)-open	ν)-open	PUNCT
ejpam-5782	201	10	set	set	VERB
ejpam-5782	201	11	u	u	PRON
ejpam-5782	201	12	such	such	ADJ
ejpam-5782	201	13	that	that	SCONJ
ejpam-5782	201	14	x	x	SYM
ejpam-5782	201	15	∈	∈	PROPN
ejpam-5782	201	16	u	u	NOUN
ejpam-5782	201	17	⊆	⊆	NUM
ejpam-5782	201	18	c∗ν(u	c∗ν(u	PROPN
ejpam-5782	201	19	)	)	PUNCT
ejpam-5782	201	20	⊆	⊆	NUM
ejpam-5782	201	21	a.	a.	PROPN
ejpam-5782	201	22	f.	f.	PROPN
ejpam-5782	201	23	alsharari	alsharari	PROPN
ejpam-5782	201	24	,	,	PUNCT
ejpam-5782	201	25	a.	a.	PROPN
ejpam-5782	201	26	qahis	qahis	PROPN
ejpam-5782	201	27	/	/	SYM
ejpam-5782	201	28	eur	eur	PROPN
ejpam-5782	201	29	.	.	PUNCT
ejpam-5782	202	1	j.	j.	PROPN
ejpam-5782	202	2	pure	pure	PROPN
ejpam-5782	202	3	appl	appl	PROPN
ejpam-5782	202	4	.	.	PROPN
ejpam-5782	202	5	math	math	PROPN
ejpam-5782	202	6	,	,	PUNCT
ejpam-5782	202	7	18	18	NUM
ejpam-5782	202	8	(	(	PUNCT
ejpam-5782	202	9	2	2	NUM
ejpam-5782	202	10	)	)	PUNCT
ejpam-5782	202	11	(	(	PUNCT
ejpam-5782	202	12	2025	2025	NUM
ejpam-5782	202	13	)	)	PUNCT
ejpam-5782	202	14	,	,	PUNCT
ejpam-5782	202	15	5782	5782	NUM
ejpam-5782	202	16	8	8	NUM
ejpam-5782	202	17	of	of	ADP
ejpam-5782	202	18	10	10	NUM
ejpam-5782	202	19	definition	definition	NOUN
ejpam-5782	202	20	6	6	NUM
ejpam-5782	202	21	.	.	PUNCT
ejpam-5782	203	1	let	let	VERB
ejpam-5782	203	2	µ	µ	NOUN
ejpam-5782	203	3	and	and	CCONJ
ejpam-5782	203	4	ν	ν	PROPN
ejpam-5782	203	5	be	be	AUX
ejpam-5782	203	6	two	two	NUM
ejpam-5782	203	7	gt	gt	NOUN
ejpam-5782	203	8	’s	’s	NOUN
ejpam-5782	203	9	on	on	ADP
ejpam-5782	203	10	a	a	DET
ejpam-5782	203	11	nonempty	nonempty	ADV
ejpam-5782	203	12	set	set	VERB
ejpam-5782	203	13	x	x	NOUN
ejpam-5782	203	14	,	,	PUNCT
ejpam-5782	203	15	and	and	CCONJ
ejpam-5782	203	16	let	let	VERB
ejpam-5782	203	17	h	h	NOUN
ejpam-5782	203	18	be	be	AUX
ejpam-5782	203	19	a	a	DET
ejpam-5782	203	20	hereditary	hereditary	ADJ
ejpam-5782	203	21	class	class	NOUN
ejpam-5782	203	22	on	on	ADP
ejpam-5782	203	23	x.	x.	NOUN
ejpam-5782	203	24	a	a	DET
ejpam-5782	203	25	set	set	NOUN
ejpam-5782	203	26	x	x	PUNCT
ejpam-5782	203	27	is	be	AUX
ejpam-5782	203	28	said	say	VERB
ejpam-5782	203	29	to	to	PART
ejpam-5782	203	30	be	be	AUX
ejpam-5782	203	31	h(µ	h(µ	ADJ
ejpam-5782	203	32	,	,	PUNCT
ejpam-5782	203	33	ν)-regular	ν)-regular	PUNCT
ejpam-5782	203	34	(	(	PUNCT
ejpam-5782	203	35	or	or	CCONJ
ejpam-5782	203	36	simply	simply	ADV
ejpam-5782	203	37	h(µ	h(µ	ADJ
ejpam-5782	203	38	,	,	PUNCT
ejpam-5782	203	39	ν)-regular	ν)-regular	ADJ
ejpam-5782	203	40	)	)	PUNCT
ejpam-5782	203	41	if	if	SCONJ
ejpam-5782	203	42	for	for	ADP
ejpam-5782	203	43	every	every	DET
ejpam-5782	203	44	x	x	SYM
ejpam-5782	203	45	∈	∈	PROPN
ejpam-5782	203	46	x	x	X
ejpam-5782	203	47	and	and	CCONJ
ejpam-5782	203	48	every	every	DET
ejpam-5782	203	49	µ-closed	µ-close	VERB
ejpam-5782	203	50	set	set	VERB
ejpam-5782	203	51	f	f	PROPN
ejpam-5782	203	52	with	with	ADP
ejpam-5782	203	53	x	x	PROPN
ejpam-5782	203	54	/∈	/∈	PROPN
ejpam-5782	203	55	f	f	PROPN
ejpam-5782	203	56	,	,	PUNCT
ejpam-5782	203	57	there	there	PRON
ejpam-5782	203	58	exist	exist	VERB
ejpam-5782	203	59	sets	set	VERB
ejpam-5782	203	60	u	u	PROPN
ejpam-5782	203	61	∈	∈	PROPN
ejpam-5782	203	62	µ	µ	PROPN
ejpam-5782	203	63	,	,	PUNCT
ejpam-5782	203	64	v	v	PROPN
ejpam-5782	203	65	∈	∈	PROPN
ejpam-5782	203	66	ν∗	ν∗	NOUN
ejpam-5782	203	67	such	such	ADJ
ejpam-5782	203	68	that	that	PRON
ejpam-5782	203	69	:	:	PUNCT
ejpam-5782	203	70	x	x	X
ejpam-5782	203	71	∈	∈	PROPN
ejpam-5782	203	72	u	u	PROPN
ejpam-5782	203	73	,	,	PUNCT
ejpam-5782	203	74	f	f	PROPN
ejpam-5782	203	75	⊆	⊆	NUM
ejpam-5782	203	76	v	v	NOUN
ejpam-5782	203	77	,	,	PUNCT
ejpam-5782	203	78	and	and	CCONJ
ejpam-5782	203	79	u	u	NOUN
ejpam-5782	203	80	∩	∩	NOUN
ejpam-5782	203	81	v	v	NOUN
ejpam-5782	203	82	=	=	PUNCT
ejpam-5782	203	83	∅.	∅.	NOUN
ejpam-5782	203	84	theorem	theorem	VERB
ejpam-5782	203	85	13	13	NUM
ejpam-5782	203	86	.	.	PUNCT
ejpam-5782	204	1	let	let	VERB
ejpam-5782	204	2	µ	µ	NOUN
ejpam-5782	204	3	and	and	CCONJ
ejpam-5782	204	4	ν	ν	PROPN
ejpam-5782	204	5	be	be	AUX
ejpam-5782	204	6	gt	gt	INTJ
ejpam-5782	204	7	’s	’s	NOUN
ejpam-5782	204	8	on	on	ADP
ejpam-5782	204	9	a	a	DET
ejpam-5782	204	10	nonempty	nonempty	ADV
ejpam-5782	204	11	set	set	VERB
ejpam-5782	204	12	x	x	NOUN
ejpam-5782	204	13	,	,	PUNCT
ejpam-5782	204	14	and	and	CCONJ
ejpam-5782	204	15	h	h	DET
ejpam-5782	204	16	a	a	DET
ejpam-5782	204	17	hereditary	hereditary	ADJ
ejpam-5782	204	18	class	class	NOUN
ejpam-5782	204	19	on	on	ADP
ejpam-5782	204	20	x.	x.	NOUN
ejpam-5782	204	21	then	then	ADV
ejpam-5782	204	22	x	x	X
ejpam-5782	204	23	is	be	AUX
ejpam-5782	204	24	h(µ	h(µ	ADJ
ejpam-5782	204	25	,	,	PUNCT
ejpam-5782	204	26	ν)-regular	ν)-regular	ADJ
ejpam-5782	204	27	if	if	SCONJ
ejpam-5782	204	28	and	and	CCONJ
ejpam-5782	204	29	only	only	ADV
ejpam-5782	204	30	if	if	SCONJ
ejpam-5782	204	31	for	for	ADP
ejpam-5782	204	32	every	every	DET
ejpam-5782	204	33	x	x	SYM
ejpam-5782	204	34	∈	∈	PROPN
ejpam-5782	204	35	x	x	X
ejpam-5782	204	36	and	and	CCONJ
ejpam-5782	204	37	every	every	DET
ejpam-5782	204	38	µ-open	µ-open	NOUN
ejpam-5782	204	39	set	set	VERB
ejpam-5782	204	40	u	u	PRON
ejpam-5782	204	41	containing	contain	VERB
ejpam-5782	204	42	x	x	PRON
ejpam-5782	204	43	,	,	PUNCT
ejpam-5782	204	44	there	there	PRON
ejpam-5782	204	45	exists	exist	VERB
ejpam-5782	204	46	a	a	DET
ejpam-5782	204	47	µ-open	µ-open	NOUN
ejpam-5782	204	48	set	set	VERB
ejpam-5782	204	49	v	v	NOUN
ejpam-5782	204	50	containing	contain	VERB
ejpam-5782	204	51	x	x	PUNCT
ejpam-5782	204	52	such	such	ADJ
ejpam-5782	204	53	that	that	SCONJ
ejpam-5782	204	54	x	x	SYM
ejpam-5782	204	55	∈	∈	NOUN
ejpam-5782	204	56	v	v	ADP
ejpam-5782	204	57	⊆	⊆	NUM
ejpam-5782	204	58	c∗ν(v	c∗ν(v	X
ejpam-5782	204	59	)	)	PUNCT
ejpam-5782	204	60	⊆	⊆	NUM
ejpam-5782	204	61	u	u	NOUN
ejpam-5782	204	62	.	.	PUNCT
ejpam-5782	205	1	proof	proof	NOUN
ejpam-5782	205	2	.	.	PUNCT
ejpam-5782	206	1	assume	assume	VERB
ejpam-5782	206	2	x	x	PUNCT
ejpam-5782	206	3	is	be	AUX
ejpam-5782	206	4	h(µ	h(µ	ADJ
ejpam-5782	206	5	,	,	PUNCT
ejpam-5782	206	6	ν)-regular	ν)-regular	ADJ
ejpam-5782	206	7	.	.	PUNCT
ejpam-5782	207	1	for	for	SCONJ
ejpam-5782	207	2	x	x	SYM
ejpam-5782	207	3	∈	∈	PROPN
ejpam-5782	207	4	x	x	X
ejpam-5782	207	5	and	and	CCONJ
ejpam-5782	207	6	a	a	DET
ejpam-5782	207	7	µ-open	µ-open	NOUN
ejpam-5782	207	8	set	set	VERB
ejpam-5782	207	9	u	u	PRON
ejpam-5782	207	10	containing	contain	VERB
ejpam-5782	207	11	x	x	X
ejpam-5782	207	12	,	,	PUNCT
ejpam-5782	207	13	there	there	PRON
ejpam-5782	207	14	exist	exist	VERB
ejpam-5782	207	15	disjoint	disjoint	NOUN
ejpam-5782	207	16	sets	set	NOUN
ejpam-5782	207	17	v	v	ADP
ejpam-5782	207	18	∈	∈	PROPN
ejpam-5782	207	19	µ	µ	PRON
ejpam-5782	207	20	andw	andw	NOUN
ejpam-5782	207	21	∈	∈	PROPN
ejpam-5782	207	22	ν∗	ν∗	VERB
ejpam-5782	207	23	such	such	ADJ
ejpam-5782	207	24	that	that	SCONJ
ejpam-5782	207	25	x	x	SYM
ejpam-5782	207	26	∈	∈	PROPN
ejpam-5782	207	27	v	v	NOUN
ejpam-5782	207	28	,	,	PUNCT
ejpam-5782	207	29	(	(	PUNCT
ejpam-5782	207	30	x−u	x−u	NOUN
ejpam-5782	207	31	)	)	PUNCT
ejpam-5782	207	32	⊆	⊆	NUM
ejpam-5782	207	33	w	w	NOUN
ejpam-5782	207	34	.	.	PUNCT
ejpam-5782	208	1	since	since	SCONJ
ejpam-5782	208	2	v	v	NUM
ejpam-5782	208	3	⊆	⊆	NUM
ejpam-5782	208	4	x−w	x−w	PROPN
ejpam-5782	208	5	and	and	CCONJ
ejpam-5782	208	6	x−w	x−w	PROPN
ejpam-5782	208	7	is	be	AUX
ejpam-5782	208	8	ν∗-closed	ν∗-close	VERB
ejpam-5782	208	9	,	,	PUNCT
ejpam-5782	208	10	we	we	PRON
ejpam-5782	208	11	have	have	AUX
ejpam-5782	208	12	c∗ν(v	c∗ν(v	VERB
ejpam-5782	208	13	)	)	PUNCT
ejpam-5782	209	1	⊆	⊆	NUM
ejpam-5782	209	2	x−w	x−w	PROPN
ejpam-5782	209	3	.	.	PUNCT
ejpam-5782	210	1	this	this	PRON
ejpam-5782	210	2	implies	imply	VERB
ejpam-5782	210	3	c∗ν(v	c∗ν(v	NOUN
ejpam-5782	210	4	)	)	PUNCT
ejpam-5782	210	5	∩(x−u	∩(x−u	NOUN
ejpam-5782	210	6	)	)	PUNCT
ejpam-5782	210	7	⊆	⊆	NUM
ejpam-5782	210	8	c∗ν(v	c∗ν(v	NOUN
ejpam-5782	210	9	)	)	PUNCT
ejpam-5782	210	10	∩w	∩w	NOUN
ejpam-5782	210	11	=	=	VERB
ejpam-5782	210	12	∅	∅	NOUN
ejpam-5782	210	13	,	,	PUNCT
ejpam-5782	210	14	hence	hence	ADV
ejpam-5782	210	15	x	x	ADP
ejpam-5782	210	16	∈	∈	NOUN
ejpam-5782	210	17	v	v	ADP
ejpam-5782	210	18	⊆	⊆	NUM
ejpam-5782	210	19	c∗ν(v	c∗ν(v	X
ejpam-5782	210	20	)	)	PUNCT
ejpam-5782	210	21	⊆	⊆	NUM
ejpam-5782	210	22	u	u	NOUN
ejpam-5782	210	23	.	.	PUNCT
ejpam-5782	211	1	conversely	conversely	ADV
ejpam-5782	211	2	,	,	PUNCT
ejpam-5782	211	3	suppose	suppose	VERB
ejpam-5782	211	4	f	f	PROPN
ejpam-5782	211	5	is	be	AUX
ejpam-5782	211	6	a	a	DET
ejpam-5782	211	7	µ-closed	µ-close	VERB
ejpam-5782	211	8	set	set	NOUN
ejpam-5782	211	9	and	and	CCONJ
ejpam-5782	211	10	x	x	SYM
ejpam-5782	211	11	/∈	/∈	PROPN
ejpam-5782	211	12	f	f	PROPN
ejpam-5782	211	13	for	for	ADP
ejpam-5782	211	14	x	x	PROPN
ejpam-5782	211	15	∈	∈	PROPN
ejpam-5782	211	16	x.	x.	NOUN
ejpam-5782	211	17	since	since	SCONJ
ejpam-5782	211	18	x	x	PROPN
ejpam-5782	211	19	−f	−f	PROPN
ejpam-5782	211	20	is	be	AUX
ejpam-5782	211	21	a	a	DET
ejpam-5782	211	22	µ-open	µ-open	NOUN
ejpam-5782	211	23	set	set	NOUN
ejpam-5782	211	24	containing	contain	VERB
ejpam-5782	211	25	x	x	X
ejpam-5782	211	26	,	,	PUNCT
ejpam-5782	211	27	by	by	ADP
ejpam-5782	211	28	hypothesis	hypothesis	NOUN
ejpam-5782	211	29	,	,	PUNCT
ejpam-5782	211	30	there	there	PRON
ejpam-5782	211	31	exists	exist	VERB
ejpam-5782	211	32	a	a	DET
ejpam-5782	211	33	µ-open	µ-open	NOUN
ejpam-5782	211	34	set	set	VERB
ejpam-5782	211	35	v	v	NOUN
ejpam-5782	211	36	containing	contain	VERB
ejpam-5782	211	37	x	x	PUNCT
ejpam-5782	211	38	such	such	ADJ
ejpam-5782	211	39	that	that	SCONJ
ejpam-5782	211	40	x	x	SYM
ejpam-5782	211	41	∈	∈	PROPN
ejpam-5782	211	42	v	v	NOUN
ejpam-5782	211	43	,	,	PUNCT
ejpam-5782	211	44	v	v	ADP
ejpam-5782	211	45	⊆	⊆	NUM
ejpam-5782	211	46	c∗ν(v	c∗ν(v	X
ejpam-5782	211	47	)	)	PUNCT
ejpam-5782	212	1	⊆	⊆	NUM
ejpam-5782	212	2	x	x	SYM
ejpam-5782	212	3	−	−	PROPN
ejpam-5782	212	4	f	f	PROPN
ejpam-5782	212	5	,	,	PUNCT
ejpam-5782	212	6	c∗ν(v	c∗ν(v	PROPN
ejpam-5782	212	7	)	)	PUNCT
ejpam-5782	212	8	∩	∩	NOUN
ejpam-5782	212	9	f	f	NOUN
ejpam-5782	212	10	=	=	SYM
ejpam-5782	212	11	∅	∅	NOUN
ejpam-5782	212	12	,	,	PUNCT
ejpam-5782	212	13	and	and	CCONJ
ejpam-5782	212	14	f	f	PROPN
ejpam-5782	212	15	⊆	⊆	NUM
ejpam-5782	212	16	x	x	SYM
ejpam-5782	212	17	−	−	PROPN
ejpam-5782	212	18	c∗ν(v	c∗ν(v	NOUN
ejpam-5782	212	19	)	)	PUNCT
ejpam-5782	212	20	.	.	PUNCT
ejpam-5782	213	1	as	as	ADP
ejpam-5782	213	2	x	x	SYM
ejpam-5782	213	3	−	−	NOUN
ejpam-5782	213	4	c∗ν(v	c∗ν(v	NUM
ejpam-5782	213	5	)	)	PUNCT
ejpam-5782	213	6	∈	∈	PROPN
ejpam-5782	213	7	ν∗	ν∗	NOUN
ejpam-5782	213	8	and	and	CCONJ
ejpam-5782	213	9	v	v	ADP
ejpam-5782	213	10	∩	∩	NOUN
ejpam-5782	213	11	(	(	PUNCT
ejpam-5782	213	12	x	x	SYM
ejpam-5782	213	13	−	−	PROPN
ejpam-5782	213	14	c∗ν(v	c∗ν(v	PROPN
ejpam-5782	213	15	)	)	PUNCT
ejpam-5782	213	16	)	)	PUNCT
ejpam-5782	214	1	=	=	NOUN
ejpam-5782	214	2	∅	∅	NOUN
ejpam-5782	214	3	,	,	PUNCT
ejpam-5782	214	4	it	it	PRON
ejpam-5782	214	5	follows	follow	VERB
ejpam-5782	214	6	that	that	SCONJ
ejpam-5782	214	7	x	x	PRON
ejpam-5782	214	8	is	be	AUX
ejpam-5782	214	9	h(µ	h(µ	ADJ
ejpam-5782	214	10	,	,	PUNCT
ejpam-5782	214	11	ν)-regular	ν)-regular	ADJ
ejpam-5782	214	12	.	.	PUNCT
ejpam-5782	215	1	remark	remark	PROPN
ejpam-5782	215	2	3	3	NUM
ejpam-5782	215	3	.	.	PUNCT
ejpam-5782	216	1	let	let	VERB
ejpam-5782	216	2	µ	µ	NOUN
ejpam-5782	216	3	and	and	CCONJ
ejpam-5782	216	4	ν	ν	PROPN
ejpam-5782	216	5	be	be	AUX
ejpam-5782	216	6	two	two	NUM
ejpam-5782	216	7	gt	gt	NOUN
ejpam-5782	216	8	’s	’s	NOUN
ejpam-5782	216	9	on	on	ADP
ejpam-5782	216	10	a	a	DET
ejpam-5782	216	11	nonempty	nonempty	ADV
ejpam-5782	216	12	set	set	VERB
ejpam-5782	216	13	x	x	NOUN
ejpam-5782	216	14	,	,	PUNCT
ejpam-5782	216	15	and	and	CCONJ
ejpam-5782	216	16	let	let	VERB
ejpam-5782	216	17	h	h	NOUN
ejpam-5782	216	18	be	be	AUX
ejpam-5782	216	19	a	a	DET
ejpam-5782	216	20	hereditary	hereditary	ADJ
ejpam-5782	216	21	class	class	NOUN
ejpam-5782	216	22	on	on	ADP
ejpam-5782	216	23	x	x	SYM
ejpam-5782	216	24	such	such	ADJ
ejpam-5782	216	25	that	that	SCONJ
ejpam-5782	216	26	µ	µ	NOUN
ejpam-5782	216	27	=	=	SYM
ejpam-5782	216	28	ν	ν	NOUN
ejpam-5782	216	29	.	.	PUNCT
ejpam-5782	217	1	if	if	SCONJ
ejpam-5782	217	2	x	x	PRON
ejpam-5782	217	3	is	be	AUX
ejpam-5782	217	4	h(µ	h(µ	ADJ
ejpam-5782	217	5	,	,	PUNCT
ejpam-5782	217	6	ν)-regular	ν)-regular	ADJ
ejpam-5782	217	7	,	,	PUNCT
ejpam-5782	217	8	then	then	ADV
ejpam-5782	217	9	x	x	PUNCT
ejpam-5782	217	10	is	be	AUX
ejpam-5782	217	11	also	also	ADV
ejpam-5782	217	12	h	h	NOUN
ejpam-5782	217	13	-	-	PUNCT
ejpam-5782	217	14	regular	regular	ADJ
ejpam-5782	217	15	.	.	PUNCT
ejpam-5782	218	1	proposition	proposition	NOUN
ejpam-5782	218	2	1	1	NUM
ejpam-5782	218	3	.	.	PUNCT
ejpam-5782	219	1	let	let	VERB
ejpam-5782	219	2	µ	µ	NOUN
ejpam-5782	219	3	and	and	CCONJ
ejpam-5782	219	4	ν	ν	PROPN
ejpam-5782	219	5	be	be	AUX
ejpam-5782	219	6	two	two	NUM
ejpam-5782	219	7	gt	gt	NOUN
ejpam-5782	219	8	’s	’s	NOUN
ejpam-5782	219	9	on	on	ADP
ejpam-5782	219	10	a	a	DET
ejpam-5782	219	11	nonempty	nonempty	ADV
ejpam-5782	219	12	set	set	VERB
ejpam-5782	219	13	x	x	NOUN
ejpam-5782	219	14	,	,	PUNCT
ejpam-5782	219	15	and	and	CCONJ
ejpam-5782	219	16	h	h	DET
ejpam-5782	219	17	a	a	DET
ejpam-5782	219	18	hereditary	hereditary	ADJ
ejpam-5782	219	19	class	class	NOUN
ejpam-5782	219	20	on	on	ADP
ejpam-5782	219	21	x.	x.	NOUN
ejpam-5782	219	22	if	if	SCONJ
ejpam-5782	219	23	x	x	PRON
ejpam-5782	219	24	is	be	AUX
ejpam-5782	219	25	(	(	PUNCT
ejpam-5782	219	26	µ	µ	NOUN
ejpam-5782	219	27	,	,	PUNCT
ejpam-5782	219	28	ν)-regular	ν)-regular	ADJ
ejpam-5782	219	29	,	,	PUNCT
ejpam-5782	219	30	then	then	ADV
ejpam-5782	219	31	x	x	PUNCT
ejpam-5782	219	32	is	be	AUX
ejpam-5782	219	33	h(µ	h(µ	ADJ
ejpam-5782	219	34	,	,	PUNCT
ejpam-5782	219	35	ν)-regular	ν)-regular	ADJ
ejpam-5782	219	36	.	.	PUNCT
ejpam-5782	220	1	proof	proof	NOUN
ejpam-5782	220	2	.	.	PUNCT
ejpam-5782	221	1	let	let	VERB
ejpam-5782	221	2	x	x	PRON
ejpam-5782	221	3	be	be	AUX
ejpam-5782	221	4	(	(	PUNCT
ejpam-5782	221	5	µ	µ	NOUN
ejpam-5782	221	6	,	,	PUNCT
ejpam-5782	221	7	ν)-regular	ν)-regular	ADJ
ejpam-5782	221	8	.	.	PUNCT
ejpam-5782	222	1	consider	consider	VERB
ejpam-5782	222	2	x	x	X
ejpam-5782	222	3	∈	∈	PROPN
ejpam-5782	222	4	x	x	X
ejpam-5782	222	5	and	and	CCONJ
ejpam-5782	222	6	an	an	DET
ejpam-5782	222	7	µ-closed	µ-close	VERB
ejpam-5782	222	8	set	set	NOUN
ejpam-5782	222	9	f	f	PROPN
ejpam-5782	222	10	such	such	ADJ
ejpam-5782	222	11	that	that	PRON
ejpam-5782	222	12	x	x	X
ejpam-5782	222	13	/∈	/∈	PROPN
ejpam-5782	223	1	f	f	PROPN
ejpam-5782	223	2	.	.	PUNCT
ejpam-5782	224	1	then	then	ADV
ejpam-5782	224	2	x	x	X
ejpam-5782	224	3	−	−	PROPN
ejpam-5782	224	4	f	f	PROPN
ejpam-5782	224	5	is	be	AUX
ejpam-5782	224	6	a	a	DET
ejpam-5782	224	7	µ-open	µ-open	NOUN
ejpam-5782	224	8	set	set	NOUN
ejpam-5782	224	9	containing	contain	VERB
ejpam-5782	224	10	x.	x.	NOUN
ejpam-5782	224	11	by	by	ADP
ejpam-5782	224	12	theorem	theorem	NOUN
ejpam-5782	224	13	3	3	NUM
ejpam-5782	224	14	,	,	PUNCT
ejpam-5782	224	15	there	there	PRON
ejpam-5782	224	16	exists	exist	VERB
ejpam-5782	224	17	a	a	DET
ejpam-5782	224	18	µ-open	µ-open	NOUN
ejpam-5782	224	19	set	set	VERB
ejpam-5782	224	20	v	v	NOUN
ejpam-5782	224	21	containing	contain	VERB
ejpam-5782	224	22	x	x	PUNCT
ejpam-5782	224	23	such	such	ADJ
ejpam-5782	224	24	that	that	SCONJ
ejpam-5782	224	25	x	x	SYM
ejpam-5782	224	26	∈	∈	NOUN
ejpam-5782	224	27	v	v	ADP
ejpam-5782	224	28	⊆	⊆	NUM
ejpam-5782	224	29	cν(v	cν(v	X
ejpam-5782	224	30	)	)	PUNCT
ejpam-5782	225	1	⊆	⊆	NUM
ejpam-5782	225	2	x	x	SYM
ejpam-5782	225	3	−	−	PROPN
ejpam-5782	225	4	f.	f.	NOUN
ejpam-5782	225	5	since	since	SCONJ
ejpam-5782	225	6	c∗ν(v	c∗ν(v	PROPN
ejpam-5782	225	7	)	)	PUNCT
ejpam-5782	226	1	⊆	⊆	NUM
ejpam-5782	226	2	cν(v	cν(v	NUM
ejpam-5782	226	3	)	)	PUNCT
ejpam-5782	226	4	,	,	PUNCT
ejpam-5782	226	5	it	it	PRON
ejpam-5782	226	6	follows	follow	VERB
ejpam-5782	226	7	that	that	SCONJ
ejpam-5782	226	8	x	x	SYM
ejpam-5782	227	1	∈	∈	NOUN
ejpam-5782	227	2	v	v	ADP
ejpam-5782	227	3	⊆	⊆	NUM
ejpam-5782	227	4	c∗ν(v	c∗ν(v	X
ejpam-5782	227	5	)	)	PUNCT
ejpam-5782	228	1	⊆	⊆	NUM
ejpam-5782	228	2	x	x	SYM
ejpam-5782	228	3	−	−	PROPN
ejpam-5782	228	4	f.	f.	PROPN
ejpam-5782	228	5	by	by	ADP
ejpam-5782	228	6	theorem	theorem	PROPN
ejpam-5782	228	7	13	13	NUM
ejpam-5782	228	8	,	,	PUNCT
ejpam-5782	228	9	x	x	X
ejpam-5782	228	10	is	be	AUX
ejpam-5782	228	11	h(µ	h(µ	ADJ
ejpam-5782	228	12	,	,	PUNCT
ejpam-5782	228	13	ν)-regular	ν)-regular	ADJ
ejpam-5782	228	14	.	.	PUNCT
ejpam-5782	229	1	theorem	theorem	VERB
ejpam-5782	229	2	14	14	NUM
ejpam-5782	229	3	.	.	PUNCT
ejpam-5782	230	1	let	let	VERB
ejpam-5782	230	2	µ	µ	NOUN
ejpam-5782	230	3	and	and	CCONJ
ejpam-5782	230	4	ν	ν	PROPN
ejpam-5782	230	5	be	be	AUX
ejpam-5782	230	6	two	two	NUM
ejpam-5782	230	7	gt	gt	NOUN
ejpam-5782	230	8	’s	’s	NOUN
ejpam-5782	230	9	on	on	ADP
ejpam-5782	230	10	a	a	DET
ejpam-5782	230	11	nonempty	nonempty	ADV
ejpam-5782	230	12	set	set	VERB
ejpam-5782	230	13	x	x	NOUN
ejpam-5782	230	14	,	,	PUNCT
ejpam-5782	230	15	and	and	CCONJ
ejpam-5782	230	16	let	let	VERB
ejpam-5782	230	17	h	h	NOUN
ejpam-5782	230	18	be	be	AUX
ejpam-5782	230	19	a	a	DET
ejpam-5782	230	20	hereditary	hereditary	ADJ
ejpam-5782	230	21	class	class	NOUN
ejpam-5782	230	22	on	on	ADP
ejpam-5782	230	23	x.	x.	NOUN
ejpam-5782	230	24	if	if	SCONJ
ejpam-5782	230	25	x	x	PRON
ejpam-5782	230	26	is	be	AUX
ejpam-5782	230	27	h(µ	h(µ	ADJ
ejpam-5782	230	28	,	,	PUNCT
ejpam-5782	230	29	ν)-regular	ν)-regular	ADJ
ejpam-5782	230	30	,	,	PUNCT
ejpam-5782	230	31	then	then	ADV
ejpam-5782	230	32	the	the	DET
ejpam-5782	230	33	following	follow	VERB
ejpam-5782	230	34	hold	hold	NOUN
ejpam-5782	230	35	:	:	PUNCT
ejpam-5782	230	36	(	(	PUNCT
ejpam-5782	230	37	i	i	NOUN
ejpam-5782	230	38	)	)	PUNCT
ejpam-5782	230	39	for	for	ADP
ejpam-5782	230	40	any	any	DET
ejpam-5782	230	41	a	a	DET
ejpam-5782	230	42	⊆	⊆	NUM
ejpam-5782	230	43	x	x	SYM
ejpam-5782	230	44	,	,	PUNCT
ejpam-5782	230	45	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	230	46	,	,	PUNCT
ejpam-5782	230	47	ν)(a	ν)(a	NUM
ejpam-5782	230	48	)	)	PUNCT
ejpam-5782	230	49	=	=	SYM
ejpam-5782	230	50	cµ(a	cµ(a	ADJ
ejpam-5782	230	51	)	)	PUNCT
ejpam-5782	230	52	.	.	PUNCT
ejpam-5782	231	1	(	(	PUNCT
ejpam-5782	231	2	ii	ii	NOUN
ejpam-5782	231	3	)	)	PUNCT
ejpam-5782	231	4	every	every	DET
ejpam-5782	231	5	µ-open	µ-open	NOUN
ejpam-5782	231	6	set	set	VERB
ejpam-5782	231	7	is	be	AUX
ejpam-5782	231	8	h(θ(µ	h(θ(µ	VERB
ejpam-5782	231	9	,	,	PUNCT
ejpam-5782	231	10	ν))-open	ν))-open	NOUN
ejpam-5782	231	11	.	.	PUNCT
ejpam-5782	232	1	f.	f.	PROPN
ejpam-5782	232	2	alsharari	alsharari	PROPN
ejpam-5782	232	3	,	,	PUNCT
ejpam-5782	232	4	a.	a.	PROPN
ejpam-5782	232	5	qahis	qahis	PROPN
ejpam-5782	232	6	/	/	SYM
ejpam-5782	232	7	eur	eur	PROPN
ejpam-5782	232	8	.	.	PUNCT
ejpam-5782	233	1	j.	j.	PROPN
ejpam-5782	233	2	pure	pure	PROPN
ejpam-5782	233	3	appl	appl	PROPN
ejpam-5782	233	4	.	.	PROPN
ejpam-5782	233	5	math	math	PROPN
ejpam-5782	233	6	,	,	PUNCT
ejpam-5782	233	7	18	18	NUM
ejpam-5782	233	8	(	(	PUNCT
ejpam-5782	233	9	2	2	NUM
ejpam-5782	233	10	)	)	PUNCT
ejpam-5782	233	11	(	(	PUNCT
ejpam-5782	233	12	2025	2025	NUM
ejpam-5782	233	13	)	)	PUNCT
ejpam-5782	233	14	,	,	PUNCT
ejpam-5782	233	15	5782	5782	NUM
ejpam-5782	233	16	9	9	NUM
ejpam-5782	233	17	of	of	ADP
ejpam-5782	233	18	10	10	NUM
ejpam-5782	233	19	proof	proof	NOUN
ejpam-5782	233	20	.	.	PUNCT
ejpam-5782	234	1	(	(	PUNCT
ejpam-5782	234	2	1	1	X
ejpam-5782	234	3	)	)	PUNCT
ejpam-5782	234	4	by	by	ADP
ejpam-5782	234	5	theorem	theorem	ADJ
ejpam-5782	234	6	5(iii	5(iii	NUM
ejpam-5782	234	7	)	)	PUNCT
ejpam-5782	234	8	,	,	PUNCT
ejpam-5782	234	9	we	we	PRON
ejpam-5782	234	10	have	have	VERB
ejpam-5782	234	11	cµ(a	cµ(a	PROPN
ejpam-5782	234	12	)	)	PUNCT
ejpam-5782	234	13	⊆	⊆	NUM
ejpam-5782	234	14	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	234	15	,	,	PUNCT
ejpam-5782	234	16	ν)(a	ν)(a	NOUN
ejpam-5782	234	17	)	)	PUNCT
ejpam-5782	234	18	.	.	PUNCT
ejpam-5782	235	1	to	to	PART
ejpam-5782	235	2	show	show	VERB
ejpam-5782	235	3	the	the	DET
ejpam-5782	235	4	reverse	reverse	ADJ
ejpam-5782	235	5	inclusion	inclusion	NOUN
ejpam-5782	235	6	,	,	PUNCT
ejpam-5782	235	7	let	let	VERB
ejpam-5782	235	8	x	x	X
ejpam-5782	235	9	∈	∈	PROPN
ejpam-5782	235	10	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	235	11	,	,	PUNCT
ejpam-5782	235	12	ν)(a	ν)(a	NUM
ejpam-5782	235	13	)	)	PUNCT
ejpam-5782	235	14	and	and	CCONJ
ejpam-5782	235	15	let	let	VERB
ejpam-5782	235	16	u	u	PRON
ejpam-5782	235	17	be	be	AUX
ejpam-5782	235	18	any	any	DET
ejpam-5782	235	19	µ-open	µ-open	NOUN
ejpam-5782	235	20	set	set	VERB
ejpam-5782	235	21	containing	contain	VERB
ejpam-5782	235	22	x.	x.	NOUN
ejpam-5782	235	23	fromh(µ	fromh(µ	PROPN
ejpam-5782	235	24	,	,	PUNCT
ejpam-5782	235	25	ν)-regularity	ν)-regularity	NOUN
ejpam-5782	235	26	,	,	PUNCT
ejpam-5782	235	27	there	there	PRON
ejpam-5782	235	28	exists	exist	VERB
ejpam-5782	235	29	a	a	DET
ejpam-5782	235	30	µ-open	µ-open	NOUN
ejpam-5782	235	31	set	set	VERB
ejpam-5782	235	32	v	v	ADP
ejpam-5782	235	33	such	such	ADJ
ejpam-5782	235	34	that	that	SCONJ
ejpam-5782	235	35	x	x	SYM
ejpam-5782	235	36	∈	∈	NOUN
ejpam-5782	235	37	v	v	ADP
ejpam-5782	235	38	⊆	⊆	NUM
ejpam-5782	235	39	c∗ν(v	c∗ν(v	X
ejpam-5782	235	40	)	)	PUNCT
ejpam-5782	235	41	⊆	⊆	NUM
ejpam-5782	235	42	u	u	NOUN
ejpam-5782	235	43	.	.	PUNCT
ejpam-5782	236	1	since	since	SCONJ
ejpam-5782	236	2	x	x	PROPN
ejpam-5782	236	3	∈	∈	PROPN
ejpam-5782	236	4	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	236	5	,	,	PUNCT
ejpam-5782	236	6	ν)(a	ν)(a	NUM
ejpam-5782	236	7	)	)	PUNCT
ejpam-5782	236	8	,	,	PUNCT
ejpam-5782	236	9	it	it	PRON
ejpam-5782	236	10	follows	follow	VERB
ejpam-5782	236	11	that	that	SCONJ
ejpam-5782	236	12	c∗ν(v	c∗ν(v	VERB
ejpam-5782	236	13	)	)	PUNCT
ejpam-5782	237	1	∩a	∩a	PROPN
ejpam-5782	237	2	̸=	̸=	PROPN
ejpam-5782	237	3	∅.	∅.	ADV
ejpam-5782	237	4	thus	thus	ADV
ejpam-5782	237	5	,	,	PUNCT
ejpam-5782	237	6	u	u	NOUN
ejpam-5782	237	7	∩a	∩a	PROPN
ejpam-5782	237	8	̸=	̸=	PROPN
ejpam-5782	237	9	∅	∅	NOUN
ejpam-5782	237	10	,	,	PUNCT
ejpam-5782	237	11	implying	imply	VERB
ejpam-5782	237	12	x	x	X
ejpam-5782	237	13	∈	∈	PROPN
ejpam-5782	237	14	cµ(a	cµ(a	NOUN
ejpam-5782	237	15	)	)	PUNCT
ejpam-5782	237	16	.	.	PUNCT
ejpam-5782	238	1	(	(	PUNCT
ejpam-5782	238	2	2	2	X
ejpam-5782	238	3	)	)	PUNCT
ejpam-5782	238	4	let	let	VERB
ejpam-5782	238	5	m	m	PRON
ejpam-5782	238	6	be	be	AUX
ejpam-5782	238	7	a	a	DET
ejpam-5782	238	8	µ-open	µ-open	NOUN
ejpam-5782	238	9	set	set	NOUN
ejpam-5782	238	10	.	.	PUNCT
ejpam-5782	239	1	from	from	ADP
ejpam-5782	239	2	(	(	PUNCT
ejpam-5782	239	3	1	1	NUM
ejpam-5782	239	4	)	)	PUNCT
ejpam-5782	239	5	,	,	PUNCT
ejpam-5782	239	6	we	we	PRON
ejpam-5782	239	7	have	have	VERB
ejpam-5782	239	8	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	239	9	,	,	PUNCT
ejpam-5782	239	10	ν)(x−m	ν)(x−m	NOUN
ejpam-5782	239	11	)	)	PUNCT
ejpam-5782	239	12	=	=	SYM
ejpam-5782	239	13	cµ(x−m	cµ(x−m	NOUN
ejpam-5782	239	14	)	)	PUNCT
ejpam-5782	239	15	=	=	SYM
ejpam-5782	239	16	x−m	x−m	PROPN
ejpam-5782	239	17	.	.	PUNCT
ejpam-5782	240	1	by	by	ADP
ejpam-5782	240	2	theorem	theorem	NOUN
ejpam-5782	240	3	10	10	NUM
ejpam-5782	240	4	,	,	PUNCT
ejpam-5782	240	5	x	x	PRON
ejpam-5782	240	6	−m	−m	NOUN
ejpam-5782	240	7	is	be	AUX
ejpam-5782	240	8	h(θ(µ	h(θ(µ	VERB
ejpam-5782	240	9	,	,	PUNCT
ejpam-5782	240	10	ν))-closed	ν))-close	VERB
ejpam-5782	240	11	,	,	PUNCT
ejpam-5782	240	12	which	which	PRON
ejpam-5782	240	13	means	mean	VERB
ejpam-5782	240	14	m	m	NOUN
ejpam-5782	240	15	is	be	AUX
ejpam-5782	240	16	h(θ(µ	h(θ(µ	VERB
ejpam-5782	240	17	,	,	PUNCT
ejpam-5782	240	18	ν))-open	ν))-open	ADJ
ejpam-5782	240	19	.	.	PUNCT
ejpam-5782	241	1	the	the	DET
ejpam-5782	241	2	next	next	ADJ
ejpam-5782	241	3	result	result	NOUN
ejpam-5782	241	4	follows	follow	VERB
ejpam-5782	241	5	from	from	ADP
ejpam-5782	241	6	theorem	theorem	ADJ
ejpam-5782	241	7	8	8	NUM
ejpam-5782	241	8	and	and	CCONJ
ejpam-5782	241	9	theorem	theorem	VERB
ejpam-5782	241	10	14(ii	14(ii	NUM
ejpam-5782	241	11	)	)	PUNCT
ejpam-5782	241	12	.	.	PUNCT
ejpam-5782	242	1	corollary	corollary	ADJ
ejpam-5782	242	2	7	7	NUM
ejpam-5782	242	3	.	.	PUNCT
ejpam-5782	243	1	let	let	VERB
ejpam-5782	243	2	µ	µ	NOUN
ejpam-5782	243	3	and	and	CCONJ
ejpam-5782	243	4	ν	ν	PROPN
ejpam-5782	243	5	be	be	AUX
ejpam-5782	243	6	two	two	NUM
ejpam-5782	243	7	gt	gt	NOUN
ejpam-5782	243	8	’s	’s	NOUN
ejpam-5782	243	9	on	on	ADP
ejpam-5782	243	10	a	a	DET
ejpam-5782	243	11	nonempty	nonempty	ADV
ejpam-5782	243	12	set	set	VERB
ejpam-5782	243	13	x	x	NOUN
ejpam-5782	243	14	,	,	PUNCT
ejpam-5782	243	15	and	and	CCONJ
ejpam-5782	243	16	let	let	VERB
ejpam-5782	243	17	h	h	NOUN
ejpam-5782	243	18	be	be	AUX
ejpam-5782	243	19	a	a	DET
ejpam-5782	243	20	hereditary	hereditary	ADJ
ejpam-5782	243	21	class	class	NOUN
ejpam-5782	243	22	on	on	ADP
ejpam-5782	243	23	x.	x.	NOUN
ejpam-5782	243	24	if	if	SCONJ
ejpam-5782	243	25	x	x	PRON
ejpam-5782	243	26	is	be	AUX
ejpam-5782	243	27	h(µ	h(µ	ADJ
ejpam-5782	243	28	,	,	PUNCT
ejpam-5782	243	29	ν)-regular	ν)-regular	ADJ
ejpam-5782	243	30	,	,	PUNCT
ejpam-5782	243	31	then	then	ADV
ejpam-5782	243	32	µ	µ	X
ejpam-5782	243	33	=	=	SYM
ejpam-5782	243	34	h(θ(µ	h(θ(µ	PROPN
ejpam-5782	243	35	,	,	PUNCT
ejpam-5782	243	36	ν	ν	NOUN
ejpam-5782	243	37	)	)	PUNCT
ejpam-5782	243	38	)	)	PUNCT
ejpam-5782	243	39	.	.	PUNCT
ejpam-5782	244	1	definition	definition	NOUN
ejpam-5782	244	2	7	7	NUM
ejpam-5782	244	3	.	.	PUNCT
ejpam-5782	245	1	let	let	VERB
ejpam-5782	245	2	µ	µ	NOUN
ejpam-5782	245	3	and	and	CCONJ
ejpam-5782	245	4	ν	ν	PROPN
ejpam-5782	245	5	be	be	AUX
ejpam-5782	245	6	two	two	NUM
ejpam-5782	245	7	gt	gt	NOUN
ejpam-5782	245	8	’s	’s	NOUN
ejpam-5782	245	9	on	on	ADP
ejpam-5782	245	10	a	a	DET
ejpam-5782	245	11	nonempty	nonempty	ADV
ejpam-5782	245	12	set	set	VERB
ejpam-5782	245	13	x	x	NOUN
ejpam-5782	245	14	,	,	PUNCT
ejpam-5782	245	15	and	and	CCONJ
ejpam-5782	245	16	let	let	VERB
ejpam-5782	245	17	h	h	NOUN
ejpam-5782	245	18	be	be	AUX
ejpam-5782	245	19	a	a	DET
ejpam-5782	245	20	hereditary	hereditary	ADJ
ejpam-5782	245	21	class	class	NOUN
ejpam-5782	245	22	on	on	ADP
ejpam-5782	245	23	x.	x.	NOUN
ejpam-5782	245	24	we	we	PRON
ejpam-5782	245	25	define	define	VERB
ejpam-5782	245	26	the	the	DET
ejpam-5782	245	27	following	follow	VERB
ejpam-5782	245	28	notions	notion	NOUN
ejpam-5782	245	29	:	:	PUNCT
ejpam-5782	245	30	ℓh(θ(µ,ν))(a	ℓh(θ(µ,ν))(a	NOUN
ejpam-5782	245	31	)	)	PUNCT
ejpam-5782	245	32	=	=	PRON
ejpam-5782	246	1	{	{	PUNCT
ejpam-5782	246	2	x	x	PUNCT
ejpam-5782	246	3	∈	∈	NOUN
ejpam-5782	246	4	x	x	X
ejpam-5782	246	5	:	:	PUNCT
ejpam-5782	246	6	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	246	7	)	)	PUNCT
ejpam-5782	246	8	⊆	⊆	NUM
ejpam-5782	246	9	a	a	PRON
ejpam-5782	246	10	for	for	ADP
ejpam-5782	246	11	some	some	DET
ejpam-5782	246	12	µ-open	µ-open	NOUN
ejpam-5782	246	13	set	set	VERB
ejpam-5782	246	14	m	m	AUX
ejpam-5782	246	15	containing	contain	VERB
ejpam-5782	246	16	x	x	X
ejpam-5782	246	17	}	}	PUNCT
ejpam-5782	246	18	.	.	PUNCT
ejpam-5782	247	1	ℓθ(µ,ν))(a	ℓθ(µ,ν))(a	NOUN
ejpam-5782	247	2	)	)	PUNCT
ejpam-5782	247	3	=	=	PRON
ejpam-5782	248	1	{	{	PUNCT
ejpam-5782	248	2	x	x	PUNCT
ejpam-5782	248	3	∈	∈	PROPN
ejpam-5782	248	4	x	x	X
ejpam-5782	248	5	:	:	PUNCT
ejpam-5782	248	6	cν(m	cν(m	X
ejpam-5782	248	7	)	)	PUNCT
ejpam-5782	248	8	⊆	⊆	NUM
ejpam-5782	248	9	a	a	PRON
ejpam-5782	248	10	for	for	ADP
ejpam-5782	248	11	some	some	DET
ejpam-5782	248	12	µ-open	µ-open	NOUN
ejpam-5782	248	13	set	set	VERB
ejpam-5782	248	14	m	m	AUX
ejpam-5782	248	15	containing	contain	VERB
ejpam-5782	248	16	x	x	X
ejpam-5782	248	17	}	}	PUNCT
ejpam-5782	248	18	.	.	PUNCT
ejpam-5782	249	1	ℓh(θ)(a	ℓh(θ)(a	NUM
ejpam-5782	249	2	)	)	PUNCT
ejpam-5782	250	1	=	=	PRON
ejpam-5782	250	2	{	{	PUNCT
ejpam-5782	250	3	x	x	PUNCT
ejpam-5782	250	4	∈	∈	PROPN
ejpam-5782	250	5	x	x	X
ejpam-5782	250	6	:	:	PUNCT
ejpam-5782	250	7	c∗µ(m	c∗µ(m	NOUN
ejpam-5782	250	8	)	)	PUNCT
ejpam-5782	250	9	⊆	⊆	NUM
ejpam-5782	250	10	a	a	PRON
ejpam-5782	250	11	for	for	ADP
ejpam-5782	250	12	some	some	DET
ejpam-5782	250	13	µ-open	µ-open	NOUN
ejpam-5782	250	14	set	set	VERB
ejpam-5782	250	15	m	m	AUX
ejpam-5782	250	16	containing	contain	VERB
ejpam-5782	250	17	x	x	X
ejpam-5782	250	18	}	}	PUNCT
ejpam-5782	250	19	.	.	PUNCT
ejpam-5782	251	1	proposition	proposition	NOUN
ejpam-5782	251	2	2	2	NUM
ejpam-5782	251	3	.	.	X
ejpam-5782	252	1	for	for	ADP
ejpam-5782	252	2	any	any	DET
ejpam-5782	252	3	two	two	NUM
ejpam-5782	252	4	gt	gt	PROPN
ejpam-5782	252	5	’s	’s	PART
ejpam-5782	252	6	ν1	ν1	NOUN
ejpam-5782	252	7	and	and	CCONJ
ejpam-5782	252	8	ν2	ν2	NOUN
ejpam-5782	252	9	on	on	ADP
ejpam-5782	252	10	a	a	DET
ejpam-5782	252	11	nonempty	nonempty	ADV
ejpam-5782	252	12	set	set	VERB
ejpam-5782	252	13	x	x	NOUN
ejpam-5782	252	14	,	,	PUNCT
ejpam-5782	252	15	we	we	PRON
ejpam-5782	252	16	have	have	VERB
ejpam-5782	252	17	ℓθ(ν1,ν2)(a	ℓθ(ν1,ν2)(a	NOUN
ejpam-5782	252	18	)	)	PUNCT
ejpam-5782	253	1	⊆	⊆	NUM
ejpam-5782	253	2	ℓh(θ(µ,ν))(a	ℓh(θ(µ,ν))(a	NOUN
ejpam-5782	253	3	)	)	PUNCT
ejpam-5782	253	4	for	for	ADP
ejpam-5782	253	5	any	any	DET
ejpam-5782	253	6	a	a	DET
ejpam-5782	253	7	⊆	⊆	NUM
ejpam-5782	253	8	x.	x.	NOUN
ejpam-5782	253	9	proof	proof	NOUN
ejpam-5782	253	10	.	.	PUNCT
ejpam-5782	254	1	let	let	VERB
ejpam-5782	254	2	x	x	SYM
ejpam-5782	254	3	∈	∈	PROPN
ejpam-5782	254	4	ℓθ(µ,ν)(a	ℓθ(µ,ν)(a	PROPN
ejpam-5782	254	5	)	)	PUNCT
ejpam-5782	254	6	.	.	PUNCT
ejpam-5782	255	1	then	then	ADV
ejpam-5782	255	2	there	there	PRON
ejpam-5782	255	3	exists	exist	VERB
ejpam-5782	255	4	a	a	DET
ejpam-5782	255	5	µ-open	µ-open	NOUN
ejpam-5782	255	6	set	set	VERB
ejpam-5782	255	7	m	m	AUX
ejpam-5782	255	8	containing	contain	VERB
ejpam-5782	255	9	x	x	PUNCT
ejpam-5782	255	10	such	such	ADJ
ejpam-5782	255	11	that	that	PRON
ejpam-5782	255	12	cν(m	cν(m	NOUN
ejpam-5782	255	13	)	)	PUNCT
ejpam-5782	255	14	⊆	⊆	NUM
ejpam-5782	255	15	a.	a.	NOUN
ejpam-5782	255	16	since	since	SCONJ
ejpam-5782	255	17	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	255	18	)	)	PUNCT
ejpam-5782	255	19	⊆	⊆	NUM
ejpam-5782	255	20	cν(m	cν(m	NOUN
ejpam-5782	255	21	)	)	PUNCT
ejpam-5782	255	22	,	,	PUNCT
ejpam-5782	255	23	it	it	PRON
ejpam-5782	255	24	follows	follow	VERB
ejpam-5782	255	25	that	that	SCONJ
ejpam-5782	255	26	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	255	27	)	)	PUNCT
ejpam-5782	255	28	⊆	⊆	NUM
ejpam-5782	255	29	a.	a.	NOUN
ejpam-5782	255	30	therefore	therefore	ADV
ejpam-5782	255	31	,	,	PUNCT
ejpam-5782	255	32	x	x	PROPN
ejpam-5782	255	33	∈	∈	PROPN
ejpam-5782	255	34	ℓh(θ(µ,ν))(a	ℓh(θ(µ,ν))(a	NOUN
ejpam-5782	255	35	)	)	PUNCT
ejpam-5782	255	36	.	.	PUNCT
ejpam-5782	256	1	remark	remark	PROPN
ejpam-5782	256	2	4	4	NUM
ejpam-5782	256	3	.	.	PUNCT
ejpam-5782	257	1	let	let	VERB
ejpam-5782	257	2	µ	µ	NOUN
ejpam-5782	257	3	and	and	CCONJ
ejpam-5782	257	4	ν	ν	PROPN
ejpam-5782	257	5	be	be	AUX
ejpam-5782	257	6	two	two	NUM
ejpam-5782	257	7	gts	gts	NOUN
ejpam-5782	257	8	on	on	ADP
ejpam-5782	257	9	a	a	DET
ejpam-5782	257	10	nonempty	nonempty	ADV
ejpam-5782	257	11	set	set	VERB
ejpam-5782	257	12	x	x	NOUN
ejpam-5782	257	13	,	,	PUNCT
ejpam-5782	257	14	and	and	CCONJ
ejpam-5782	257	15	let	let	VERB
ejpam-5782	257	16	a	a	DET
ejpam-5782	257	17	⊆	⊆	NUM
ejpam-5782	257	18	x.	x.	NOUN
ejpam-5782	257	19	if	if	SCONJ
ejpam-5782	257	20	µ	µ	X
ejpam-5782	257	21	=	=	SYM
ejpam-5782	257	22	ν	ν	NOUN
ejpam-5782	257	23	,	,	PUNCT
ejpam-5782	257	24	then	then	ADV
ejpam-5782	257	25	ℓh(θ(µ,ν))(a	ℓh(θ(µ,ν))(a	NOUN
ejpam-5782	257	26	)	)	PUNCT
ejpam-5782	257	27	=	=	PUNCT
ejpam-5782	258	1	ℓh(θ)(a	ℓh(θ)(a	NUM
ejpam-5782	258	2	)	)	PUNCT
ejpam-5782	258	3	.	.	PUNCT
ejpam-5782	259	1	theorem	theorem	VERB
ejpam-5782	259	2	15	15	NUM
ejpam-5782	259	3	.	.	PUNCT
ejpam-5782	260	1	let	let	VERB
ejpam-5782	260	2	ν1	ν1	NOUN
ejpam-5782	260	3	and	and	CCONJ
ejpam-5782	260	4	ν2	ν2	NOUN
ejpam-5782	260	5	be	be	AUX
ejpam-5782	260	6	two	two	NUM
ejpam-5782	260	7	gt	gt	NOUN
ejpam-5782	260	8	’s	’s	NOUN
ejpam-5782	260	9	on	on	ADP
ejpam-5782	260	10	a	a	DET
ejpam-5782	260	11	nonempty	nonempty	ADV
ejpam-5782	260	12	set	set	VERB
ejpam-5782	260	13	x	x	PUNCT
ejpam-5782	260	14	and	and	CCONJ
ejpam-5782	260	15	a	a	DET
ejpam-5782	260	16	⊆	⊆	NUM
ejpam-5782	260	17	x.	x.	NOUN
ejpam-5782	260	18	then	then	ADV
ejpam-5782	260	19	the	the	DET
ejpam-5782	260	20	following	follow	VERB
ejpam-5782	260	21	properties	property	NOUN
ejpam-5782	260	22	hold	hold	VERB
ejpam-5782	260	23	:	:	PUNCT
ejpam-5782	260	24	(	(	PUNCT
ejpam-5782	260	25	i	i	NOUN
ejpam-5782	260	26	)	)	PUNCT
ejpam-5782	260	27	ih(θ(µ,ν)(a	ih(θ(µ,ν)(a	NUM
ejpam-5782	260	28	)	)	PUNCT
ejpam-5782	260	29	=	=	PUNCT
ejpam-5782	261	1	x	x	PUNCT
ejpam-5782	261	2	−	−	PUNCT
ejpam-5782	261	3	ch(θ(µ,ν)(x	ch(θ(µ,ν)(x	PROPN
ejpam-5782	261	4	−a	−a	NOUN
ejpam-5782	261	5	)	)	PUNCT
ejpam-5782	261	6	and	and	CCONJ
ejpam-5782	261	7	ch(θ(µ,ν)(a	ch(θ(µ,ν)(a	NOUN
ejpam-5782	261	8	)	)	PUNCT
ejpam-5782	262	1	=	=	PUNCT
ejpam-5782	262	2	x	x	PUNCT
ejpam-5782	262	3	−	−	PUNCT
ejpam-5782	262	4	ih(θ(µ,ν)(x	ih(θ(µ,ν)(x	PROPN
ejpam-5782	262	5	−a	−a	NOUN
ejpam-5782	262	6	)	)	PUNCT
ejpam-5782	262	7	.	.	PUNCT
ejpam-5782	263	1	(	(	PUNCT
ejpam-5782	263	2	ii	ii	NOUN
ejpam-5782	263	3	)	)	PUNCT
ejpam-5782	263	4	ℓh(θ(µ,ν)(a	ℓh(θ(µ,ν)(a	NOUN
ejpam-5782	263	5	)	)	PUNCT
ejpam-5782	263	6	=	=	PUNCT
ejpam-5782	264	1	x	x	X
ejpam-5782	264	2	−	−	PROPN
ejpam-5782	264	3	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	264	4	,	,	PUNCT
ejpam-5782	264	5	ν)(x	ν)(x	NOUN
ejpam-5782	264	6	−a	−a	NOUN
ejpam-5782	264	7	)	)	PUNCT
ejpam-5782	264	8	and	and	CCONJ
ejpam-5782	264	9	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	264	10	,	,	PUNCT
ejpam-5782	264	11	ν)(a	ν)(a	NUM
ejpam-5782	264	12	)	)	PUNCT
ejpam-5782	265	1	=	=	PUNCT
ejpam-5782	266	1	x	x	X
ejpam-5782	266	2	−	−	PROPN
ejpam-5782	266	3	ℓh(θ(µ,ν)(x	ℓh(θ(µ,ν)(x	PROPN
ejpam-5782	266	4	−a	−a	NOUN
ejpam-5782	266	5	)	)	PUNCT
ejpam-5782	266	6	.	.	PUNCT
ejpam-5782	267	1	proof	proof	NOUN
ejpam-5782	267	2	.	.	PUNCT
ejpam-5782	268	1	the	the	DET
ejpam-5782	268	2	proof	proof	NOUN
ejpam-5782	268	3	is	be	AUX
ejpam-5782	268	4	obvious	obvious	ADJ
ejpam-5782	268	5	.	.	PUNCT
ejpam-5782	269	1	the	the	DET
ejpam-5782	269	2	following	follow	VERB
ejpam-5782	269	3	corollary	corollary	NOUN
ejpam-5782	269	4	comes	come	VERB
ejpam-5782	269	5	directly	directly	ADV
ejpam-5782	269	6	from	from	ADP
ejpam-5782	269	7	definition	definition	NOUN
ejpam-5782	269	8	4	4	NUM
ejpam-5782	269	9	and	and	CCONJ
ejpam-5782	269	10	definition	definition	NOUN
ejpam-5782	269	11	7	7	NUM
ejpam-5782	269	12	.	.	PUNCT
ejpam-5782	269	13	corollary	corollary	ADJ
ejpam-5782	269	14	8	8	NUM
ejpam-5782	269	15	.	.	PUNCT
ejpam-5782	270	1	let	let	VERB
ejpam-5782	270	2	µ	µ	NOUN
ejpam-5782	270	3	and	and	CCONJ
ejpam-5782	270	4	ν	ν	PROPN
ejpam-5782	270	5	be	be	AUX
ejpam-5782	270	6	two	two	NUM
ejpam-5782	270	7	gts	gts	NOUN
ejpam-5782	270	8	on	on	ADP
ejpam-5782	270	9	a	a	DET
ejpam-5782	270	10	nonempty	nonempty	ADV
ejpam-5782	270	11	set	set	VERB
ejpam-5782	270	12	x	x	PUNCT
ejpam-5782	270	13	and	and	CCONJ
ejpam-5782	270	14	a	a	DET
ejpam-5782	270	15	⊆	⊆	NUM
ejpam-5782	270	16	x.	x.	NOUN
ejpam-5782	270	17	then	then	ADV
ejpam-5782	270	18	ih(θ(µ,ν))(a	ih(θ(µ,ν))(a	PROPN
ejpam-5782	270	19	)	)	PUNCT
ejpam-5782	271	1	if	if	SCONJ
ejpam-5782	271	2	and	and	CCONJ
ejpam-5782	271	3	only	only	ADV
ejpam-5782	271	4	if	if	SCONJ
ejpam-5782	271	5	there	there	PRON
ejpam-5782	271	6	exists	exist	VERB
ejpam-5782	271	7	a	a	DET
ejpam-5782	271	8	µ-open	µ-open	NOUN
ejpam-5782	271	9	set	set	VERB
ejpam-5782	271	10	m	m	AUX
ejpam-5782	271	11	containing	contain	VERB
ejpam-5782	271	12	x	x	PUNCT
ejpam-5782	271	13	such	such	ADJ
ejpam-5782	271	14	that	that	SCONJ
ejpam-5782	271	15	m	m	VERB
ejpam-5782	271	16	⊆	⊆	NUM
ejpam-5782	271	17	c∗ν(m	c∗ν(m	NOUN
ejpam-5782	271	18	)	)	PUNCT
ejpam-5782	271	19	⊆	⊆	NUM
ejpam-5782	271	20	a.	a.	PROPN
ejpam-5782	271	21	f.	f.	PROPN
ejpam-5782	271	22	alsharari	alsharari	PROPN
ejpam-5782	271	23	,	,	PUNCT
ejpam-5782	271	24	a.	a.	PROPN
ejpam-5782	271	25	qahis	qahis	PROPN
ejpam-5782	271	26	/	/	SYM
ejpam-5782	271	27	eur	eur	PROPN
ejpam-5782	271	28	.	.	PUNCT
ejpam-5782	272	1	j.	j.	PROPN
ejpam-5782	272	2	pure	pure	PROPN
ejpam-5782	272	3	appl	appl	PROPN
ejpam-5782	272	4	.	.	PROPN
ejpam-5782	272	5	math	math	PROPN
ejpam-5782	272	6	,	,	PUNCT
ejpam-5782	272	7	18	18	NUM
ejpam-5782	272	8	(	(	PUNCT
ejpam-5782	272	9	2	2	NUM
ejpam-5782	272	10	)	)	PUNCT
ejpam-5782	272	11	(	(	PUNCT
ejpam-5782	272	12	2025	2025	NUM
ejpam-5782	272	13	)	)	PUNCT
ejpam-5782	272	14	,	,	PUNCT
ejpam-5782	272	15	5782	5782	NUM
ejpam-5782	272	16	10	10	NUM
ejpam-5782	272	17	of	of	ADP
ejpam-5782	272	18	10	10	NUM
ejpam-5782	272	19	5	5	NUM
ejpam-5782	272	20	.	.	PUNCT
ejpam-5782	272	21	conclusion	conclusion	NOUN
ejpam-5782	272	22	this	this	DET
ejpam-5782	272	23	study	study	NOUN
ejpam-5782	272	24	aimed	aim	VERB
ejpam-5782	272	25	to	to	PART
ejpam-5782	272	26	introduce	introduce	VERB
ejpam-5782	272	27	and	and	CCONJ
ejpam-5782	272	28	examine	examine	VERB
ejpam-5782	272	29	the	the	DET
ejpam-5782	272	30	operation	operation	NOUN
ejpam-5782	272	31	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	272	32	,	,	PUNCT
ejpam-5782	272	33	ν	ν	NOUN
ejpam-5782	272	34	)	)	PUNCT
ejpam-5782	272	35	and	and	CCONJ
ejpam-5782	272	36	h	h	NOUN
ejpam-5782	272	37	(	(	PUNCT
ejpam-5782	272	38	θ(µ	θ(µ	PROPN
ejpam-5782	272	39	,	,	PUNCT
ejpam-5782	272	40	ν	ν	NOUN
ejpam-5782	272	41	)	)	PUNCT
ejpam-5782	272	42	)	)	PUNCT
ejpam-5782	272	43	open	open	ADJ
ejpam-5782	272	44	sets	set	NOUN
ejpam-5782	272	45	within	within	ADP
ejpam-5782	272	46	generalized	generalized	ADJ
ejpam-5782	272	47	topological	topological	ADJ
ejpam-5782	272	48	spaces	space	NOUN
ejpam-5782	272	49	.	.	PUNCT
ejpam-5782	273	1	several	several	ADJ
ejpam-5782	273	2	significant	significant	ADJ
ejpam-5782	273	3	results	result	NOUN
ejpam-5782	273	4	regarding	regard	VERB
ejpam-5782	273	5	these	these	DET
ejpam-5782	273	6	concepts	concept	NOUN
ejpam-5782	273	7	were	be	AUX
ejpam-5782	273	8	established	establish	VERB
ejpam-5782	273	9	.	.	PUNCT
ejpam-5782	274	1	we	we	PRON
ejpam-5782	274	2	thoroughly	thoroughly	ADV
ejpam-5782	274	3	investigated	investigate	VERB
ejpam-5782	274	4	the	the	DET
ejpam-5782	274	5	relationships	relationship	NOUN
ejpam-5782	274	6	among	among	ADP
ejpam-5782	274	7	γ∗(µ	γ∗(µ	PROPN
ejpam-5782	274	8	,	,	PUNCT
ejpam-5782	274	9	ν	ν	NOUN
ejpam-5782	274	10	)	)	PUNCT
ejpam-5782	274	11	,	,	PUNCT
ejpam-5782	274	12	γ∗	γ∗	NOUN
ejpam-5782	274	13	,	,	PUNCT
ejpam-5782	274	14	and	and	CCONJ
ejpam-5782	274	15	the	the	DET
ejpam-5782	274	16	µ-closure	µ-closure	NOUN
ejpam-5782	274	17	,	,	PUNCT
ejpam-5782	274	18	as	as	ADV
ejpam-5782	274	19	well	well	ADV
ejpam-5782	274	20	as	as	ADP
ejpam-5782	274	21	those	those	PRON
ejpam-5782	274	22	among	among	ADP
ejpam-5782	274	23	h	h	NOUN
ejpam-5782	274	24	(	(	PUNCT
ejpam-5782	274	25	θ(µ	θ(µ	PROPN
ejpam-5782	274	26	,	,	PUNCT
ejpam-5782	274	27	ν	ν	NOUN
ejpam-5782	274	28	)	)	PUNCT
ejpam-5782	274	29	)	)	PUNCT
ejpam-5782	274	30	-open	-open	NOUN
ejpam-5782	274	31	sets	set	NOUN
ejpam-5782	274	32	,	,	PUNCT
ejpam-5782	274	33	θ(µ	θ(µ	PROPN
ejpam-5782	274	34	,	,	PUNCT
ejpam-5782	274	35	ν)-open	ν)-open	PUNCT
ejpam-5782	274	36	sets	set	NOUN
ejpam-5782	274	37	,	,	PUNCT
ejpam-5782	274	38	and	and	CCONJ
ejpam-5782	274	39	µ-open	µ-open	NOUN
ejpam-5782	274	40	sets	set	NOUN
ejpam-5782	274	41	.	.	PUNCT
ejpam-5782	275	1	finally	finally	ADV
ejpam-5782	275	2	,	,	PUNCT
ejpam-5782	275	3	we	we	PRON
ejpam-5782	275	4	have	have	AUX
ejpam-5782	275	5	derived	derive	VERB
ejpam-5782	275	6	various	various	ADJ
ejpam-5782	275	7	properties	property	NOUN
ejpam-5782	275	8	and	and	CCONJ
ejpam-5782	275	9	characterizations	characterization	NOUN
ejpam-5782	275	10	of	of	ADP
ejpam-5782	275	11	h	h	NOUN
ejpam-5782	275	12	(	(	PUNCT
ejpam-5782	275	13	θ(µ	θ(µ	PROPN
ejpam-5782	275	14	,	,	PUNCT
ejpam-5782	275	15	ν	ν	NOUN
ejpam-5782	275	16	)	)	PUNCT
ejpam-5782	275	17	)	)	PUNCT
ejpam-5782	276	1	-open	-open	NOUN
ejpam-5782	276	2	sets	set	NOUN
ejpam-5782	276	3	in	in	ADP
ejpam-5782	276	4	terms	term	NOUN
ejpam-5782	276	5	of	of	ADP
ejpam-5782	276	6	the	the	DET
ejpam-5782	276	7	concept	concept	NOUN
ejpam-5782	276	8	of	of	ADP
ejpam-5782	276	9	h(µ	h(µ	PROPN
ejpam-5782	276	10	,	,	PUNCT
ejpam-5782	276	11	ν)-regularity	ν)-regularity	NOUN
ejpam-5782	276	12	.	.	PUNCT
ejpam-5782	277	1	acknowledgements	acknowledgement	NOUN
ejpam-5782	277	2	we	we	PRON
ejpam-5782	277	3	would	would	AUX
ejpam-5782	277	4	like	like	VERB
ejpam-5782	277	5	to	to	PART
ejpam-5782	277	6	thank	thank	VERB
ejpam-5782	277	7	the	the	DET
ejpam-5782	277	8	reviewers	reviewer	NOUN
ejpam-5782	277	9	for	for	ADP
ejpam-5782	277	10	taking	take	VERB
ejpam-5782	277	11	the	the	DET
ejpam-5782	277	12	time	time	NOUN
ejpam-5782	277	13	and	and	CCONJ
ejpam-5782	277	14	effort	effort	NOUN
ejpam-5782	277	15	necessary	necessary	ADJ
ejpam-5782	277	16	to	to	PART
ejpam-5782	277	17	review	review	VERB
ejpam-5782	277	18	the	the	DET
ejpam-5782	277	19	manuscript	manuscript	NOUN
ejpam-5782	277	20	.	.	PUNCT
ejpam-5782	278	1	we	we	PRON
ejpam-5782	278	2	sincerely	sincerely	ADV
ejpam-5782	278	3	appreciate	appreciate	VERB
ejpam-5782	278	4	all	all	DET
ejpam-5782	278	5	valuable	valuable	ADJ
ejpam-5782	278	6	comments	comment	NOUN
ejpam-5782	278	7	,	,	PUNCT
ejpam-5782	278	8	careful	careful	ADJ
ejpam-5782	278	9	reading	reading	NOUN
ejpam-5782	278	10	and	and	CCONJ
ejpam-5782	278	11	suggestions	suggestion	NOUN
ejpam-5782	278	12	that	that	PRON
ejpam-5782	278	13	lead	lead	VERB
ejpam-5782	278	14	to	to	PART
ejpam-5782	278	15	improve	improve	VERB
ejpam-5782	278	16	the	the	DET
ejpam-5782	278	17	quality	quality	NOUN
ejpam-5782	278	18	of	of	ADP
ejpam-5782	278	19	this	this	DET
ejpam-5782	278	20	manuscript	manuscript	NOUN
ejpam-5782	278	21	.	.	PUNCT
ejpam-5782	279	1	references	reference	NOUN
ejpam-5782	279	2	[	[	X
ejpam-5782	279	3	1	1	NUM
ejpam-5782	279	4	]	]	PUNCT
ejpam-5782	279	5	young	young	ADJ
ejpam-5782	279	6	key	key	ADJ
ejpam-5782	279	7	kim	kim	PROPN
ejpam-5782	279	8	and	and	CCONJ
ejpam-5782	279	9	wonkeun	wonkeun	PROPN
ejpam-5782	279	10	min	min	PROPN
ejpam-5782	279	11	.	.	PUNCT
ejpam-5782	280	1	h(θ)-open	h(θ)-open	NOUN
ejpam-5782	280	2	sets	set	NOUN
ejpam-5782	280	3	induced	induce	VERB
ejpam-5782	280	4	by	by	ADP
ejpam-5782	280	5	hereditary	hereditary	ADJ
ejpam-5782	280	6	classes	class	NOUN
ejpam-5782	280	7	on	on	ADP
ejpam-5782	280	8	generalized	generalized	ADJ
ejpam-5782	280	9	topological	topological	ADJ
ejpam-5782	280	10	spaces	space	NOUN
ejpam-5782	280	11	.	.	PUNCT
ejpam-5782	281	1	international	international	ADJ
ejpam-5782	281	2	journal	journal	NOUN
ejpam-5782	281	3	of	of	ADP
ejpam-5782	281	4	pure	pure	ADJ
ejpam-5782	281	5	and	and	CCONJ
ejpam-5782	281	6	applied	applied	ADJ
ejpam-5782	281	7	mathematics	mathematic	NOUN
ejpam-5782	281	8	,	,	PUNCT
ejpam-5782	281	9	93:307–315	93:307–315	PROPN
ejpam-5782	281	10	,	,	PUNCT
ejpam-5782	281	11	may	may	AUX
ejpam-5782	281	12	2014	2014	NUM
ejpam-5782	281	13	.	.	PUNCT
ejpam-5782	282	1	[	[	X
ejpam-5782	282	2	2	2	X
ejpam-5782	282	3	]	]	PUNCT
ejpam-5782	282	4	akos	akos	NOUN
ejpam-5782	282	5	császár	császár	PROPN
ejpam-5782	282	6	.	.	PUNCT
ejpam-5782	283	1	generalized	generalize	VERB
ejpam-5782	283	2	topology	topology	NOUN
ejpam-5782	283	3	,	,	PUNCT
ejpam-5782	283	4	generized	generize	VERB
ejpam-5782	283	5	continuity	continuity	NOUN
ejpam-5782	283	6	.	.	PUNCT
ejpam-5782	284	1	acta	acta	PROPN
ejpam-5782	284	2	mathematica	mathematica	PROPN
ejpam-5782	284	3	hungarica	hungarica	PROPN
ejpam-5782	284	4	,	,	PUNCT
ejpam-5782	284	5	96:351–357	96:351–357	PROPN
ejpam-5782	284	6	,	,	PUNCT
ejpam-5782	284	7	2002	2002	NUM
ejpam-5782	284	8	.	.	PUNCT
ejpam-5782	285	1	[	[	X
ejpam-5782	285	2	3	3	X
ejpam-5782	285	3	]	]	PUNCT
ejpam-5782	285	4	á	á	NOUN
ejpam-5782	285	5	császár	császár	NOUN
ejpam-5782	285	6	.	.	PUNCT
ejpam-5782	286	1	δ	δ	PROPN
ejpam-5782	286	2	-	-	PUNCT
ejpam-5782	286	3	and	and	CCONJ
ejpam-5782	286	4	θ	θ	NOUN
ejpam-5782	286	5	-	-	PUNCT
ejpam-5782	286	6	modifications	modification	NOUN
ejpam-5782	286	7	of	of	ADP
ejpam-5782	286	8	generalized	generalized	ADJ
ejpam-5782	286	9	topologies	topology	NOUN
ejpam-5782	286	10	.	.	PUNCT
ejpam-5782	287	1	acta	acta	PROPN
ejpam-5782	287	2	mathematica	mathematica	PROPN
ejpam-5782	287	3	hungarica	hungarica	PROPN
ejpam-5782	287	4	,	,	PUNCT
ejpam-5782	287	5	120(3):275–279	120(3):275–279	NUM
ejpam-5782	287	6	,	,	PUNCT
ejpam-5782	287	7	2008	2008	NUM
ejpam-5782	287	8	.	.	PUNCT
ejpam-5782	288	1	[	[	X
ejpam-5782	288	2	4	4	X
ejpam-5782	288	3	]	]	PUNCT
ejpam-5782	288	4	á	á	NOUN
ejpam-5782	288	5	császár	császár	NOUN
ejpam-5782	288	6	and	and	CCONJ
ejpam-5782	288	7	e	e	PROPN
ejpam-5782	288	8	makai	makai	PROPN
ejpam-5782	288	9	jr	jr	PROPN
ejpam-5782	288	10	.	.	PROPN
ejpam-5782	288	11	further	further	ADJ
ejpam-5782	288	12	remarks	remark	NOUN
ejpam-5782	288	13	on	on	ADP
ejpam-5782	288	14	δ	δ	PROPN
ejpam-5782	288	15	-	-	PUNCT
ejpam-5782	288	16	and	and	CCONJ
ejpam-5782	288	17	θ	θ	NOUN
ejpam-5782	288	18	-	-	NOUN
ejpam-5782	288	19	modifications	modification	NOUN
ejpam-5782	288	20	.	.	PUNCT
ejpam-5782	289	1	acta	acta	PROPN
ejpam-5782	289	2	mathematica	mathematica	PROPN
ejpam-5782	289	3	hungarica	hungarica	PROPN
ejpam-5782	289	4	,	,	PUNCT
ejpam-5782	289	5	123(3):223–228	123(3):223–228	NUM
ejpam-5782	289	6	,	,	PUNCT
ejpam-5782	289	7	2009	2009	NUM
ejpam-5782	289	8	.	.	PUNCT
ejpam-5782	290	1	[	[	X
ejpam-5782	290	2	5	5	NUM
ejpam-5782	290	3	]	]	PUNCT
ejpam-5782	290	4	ugur	ugur	ADJ
ejpam-5782	290	5	sengul	sengul	NOUN
ejpam-5782	290	6	.	.	PUNCT
ejpam-5782	291	1	more	more	ADV
ejpam-5782	291	2	on	on	ADP
ejpam-5782	291	3	δand	δand	NOUN
ejpam-5782	291	4	θ	θ	NOUN
ejpam-5782	291	5	-	-	NOUN
ejpam-5782	291	6	modifications	modification	NOUN
ejpam-5782	291	7	.	.	PUNCT
ejpam-5782	292	1	creative	creative	ADJ
ejpam-5782	292	2	mathematics	mathematic	NOUN
ejpam-5782	292	3	and	and	CCONJ
ejpam-5782	292	4	informatics	informatic	NOUN
ejpam-5782	292	5	,	,	PUNCT
ejpam-5782	292	6	30(1):89–96	30(1):89–96	NUM
ejpam-5782	292	7	,	,	PUNCT
ejpam-5782	292	8	02	02	NUM
ejpam-5782	292	9	2021	2021	NUM
ejpam-5782	292	10	.	.	PUNCT
ejpam-5782	293	1	[	[	X
ejpam-5782	293	2	6	6	NUM
ejpam-5782	293	3	]	]	PUNCT
ejpam-5782	293	4	ákos	ákos	PROPN
ejpam-5782	293	5	császár	császár	NOUN
ejpam-5782	293	6	.	.	PUNCT
ejpam-5782	294	1	modification	modification	NOUN
ejpam-5782	294	2	of	of	ADP
ejpam-5782	294	3	generalized	generalized	ADJ
ejpam-5782	294	4	topologies	topology	NOUN
ejpam-5782	294	5	via	via	ADP
ejpam-5782	294	6	hereditary	hereditary	ADJ
ejpam-5782	294	7	classes	class	NOUN
ejpam-5782	294	8	.	.	PUNCT
ejpam-5782	295	1	acta	acta	PROPN
ejpam-5782	295	2	mathematica	mathematica	PROPN
ejpam-5782	295	3	hungarica	hungarica	PROPN
ejpam-5782	295	4	,	,	PUNCT
ejpam-5782	295	5	115(1	115(1	NUM
ejpam-5782	295	6	-	-	SYM
ejpam-5782	295	7	2):29–36	2):29–36	NUM
ejpam-5782	295	8	,	,	PUNCT
ejpam-5782	295	9	2007	2007	NUM
ejpam-5782	295	10	.	.	PUNCT
ejpam-5782	296	1	[	[	X
ejpam-5782	296	2	7	7	X
ejpam-5782	296	3	]	]	X
ejpam-5782	296	4	akos	akos	NOUN
ejpam-5782	296	5	császár	császár	PROPN
ejpam-5782	296	6	.	.	PUNCT
ejpam-5782	297	1	generalized	generalize	VERB
ejpam-5782	297	2	open	open	ADJ
ejpam-5782	297	3	sets	set	NOUN
ejpam-5782	297	4	in	in	ADP
ejpam-5782	297	5	generalized	generalized	ADJ
ejpam-5782	297	6	topologies	topology	NOUN
ejpam-5782	297	7	.	.	PUNCT
ejpam-5782	298	1	acta	acta	PROPN
ejpam-5782	298	2	mathematica	mathematica	PROPN
ejpam-5782	298	3	hungarica	hungarica	PROPN
ejpam-5782	298	4	,	,	PUNCT
ejpam-5782	298	5	106	106	NUM
ejpam-5782	298	6	,	,	PUNCT
ejpam-5782	298	7	2005	2005	NUM
ejpam-5782	298	8	.	.	PUNCT
ejpam-5782	299	1	[	[	X
ejpam-5782	299	2	8	8	NUM
ejpam-5782	299	3	]	]	PUNCT
ejpam-5782	299	4	á	á	NOUN
ejpam-5782	299	5	császár	császár	NOUN
ejpam-5782	299	6	.	.	PUNCT
ejpam-5782	300	1	extremally	extremally	ADV
ejpam-5782	300	2	disconnected	disconnect	VERB
ejpam-5782	300	3	generalized	generalized	ADJ
ejpam-5782	300	4	topologies	topology	NOUN
ejpam-5782	300	5	.	.	PUNCT
ejpam-5782	301	1	in	in	ADP
ejpam-5782	301	2	annales	annales	PROPN
ejpam-5782	301	3	univ	univ	PROPN
ejpam-5782	301	4	.	.	PUNCT
ejpam-5782	302	1	sci	sci	PROPN
ejpam-5782	302	2	.	.	PUNCT
ejpam-5782	302	3	budapest	budapest	PROPN
ejpam-5782	302	4	,	,	PUNCT
ejpam-5782	302	5	volume	volume	NOUN
ejpam-5782	302	6	47	47	NUM
ejpam-5782	302	7	,	,	PUNCT
ejpam-5782	302	8	pages	page	NOUN
ejpam-5782	302	9	151–161	151–161	NUM
ejpam-5782	302	10	,	,	PUNCT
ejpam-5782	302	11	2004	2004	NUM
ejpam-5782	302	12	.	.	PUNCT
ejpam-5782	303	1	[	[	X
ejpam-5782	303	2	9	9	NUM
ejpam-5782	303	3	]	]	X
ejpam-5782	303	4	abdo	abdo	PROPN
ejpam-5782	303	5	qahis	qahis	PROPN
ejpam-5782	303	6	and	and	CCONJ
ejpam-5782	303	7	awn	awn	VERB
ejpam-5782	303	8	alqahtani	alqahtani	PROPN
ejpam-5782	303	9	.	.	PUNCT
ejpam-5782	304	1	modifications	modification	NOUN
ejpam-5782	304	2	to	to	ADP
ejpam-5782	304	3	mixed	mixed	ADJ
ejpam-5782	304	4	θ	θ	PROPN
ejpam-5782	304	5	(	(	PUNCT
ejpam-5782	304	6	ν1	ν1	NOUN
ejpam-5782	304	7	,	,	PUNCT
ejpam-5782	304	8	ν2)-open	ν2)-open	ADJ
ejpam-5782	304	9	sets	set	NOUN
ejpam-5782	304	10	ingeneralized	ingeneralize	VERB
ejpam-5782	304	11	topological	topological	ADJ
ejpam-5782	304	12	spaces	space	NOUN
ejpam-5782	304	13	.	.	PUNCT
ejpam-5782	305	1	european	european	ADJ
ejpam-5782	305	2	journal	journal	PROPN
ejpam-5782	305	3	of	of	ADP
ejpam-5782	305	4	pure	pure	ADJ
ejpam-5782	305	5	and	and	CCONJ
ejpam-5782	305	6	applied	applied	ADJ
ejpam-5782	305	7	mathematics	mathematic	NOUN
ejpam-5782	305	8	,	,	PUNCT
ejpam-5782	305	9	17(4):3610–3621	17(4):3610–3621	NUM
ejpam-5782	305	10	,	,	PUNCT
ejpam-5782	305	11	2024	2024	NUM
ejpam-5782	305	12	.	.	PUNCT
ejpam-5782	306	1	[	[	X
ejpam-5782	306	2	10	10	NUM
ejpam-5782	306	3	]	]	X
ejpam-5782	306	4	young	young	ADJ
ejpam-5782	306	5	key	key	ADJ
ejpam-5782	306	6	kim	kim	PROPN
ejpam-5782	306	7	and	and	CCONJ
ejpam-5782	306	8	won	win	VERB
ejpam-5782	306	9	keun	keun	PROPN
ejpam-5782	306	10	min	min	PROPN
ejpam-5782	306	11	.	.	PROPN
ejpam-5782	306	12	on	on	ADP
ejpam-5782	306	13	operations	operation	NOUN
ejpam-5782	306	14	induced	induce	VERB
ejpam-5782	306	15	by	by	ADP
ejpam-5782	306	16	hereditary	hereditary	ADJ
ejpam-5782	306	17	classes	class	NOUN
ejpam-5782	306	18	on	on	ADP
ejpam-5782	306	19	generalized	generalized	ADJ
ejpam-5782	306	20	topological	topological	ADJ
ejpam-5782	306	21	spaces	space	NOUN
ejpam-5782	306	22	.	.	PUNCT
ejpam-5782	307	1	acta	acta	PROPN
ejpam-5782	307	2	mathematica	mathematica	PROPN
ejpam-5782	307	3	hungarica	hungarica	PROPN
ejpam-5782	307	4	,	,	PUNCT
ejpam-5782	307	5	137(1):130–138	137(1):130–138	NUM
ejpam-5782	307	6	,	,	PUNCT
ejpam-5782	307	7	2012	2012	NUM
ejpam-5782	307	8	.	.	PUNCT
ejpam-5782	308	1	[	[	X
ejpam-5782	308	2	11	11	NUM
ejpam-5782	308	3	]	]	PUNCT
ejpam-5782	308	4	won	win	VERB
ejpam-5782	308	5	keun	keun	PROPN
ejpam-5782	308	6	min	min	PROPN
ejpam-5782	308	7	.	.	PROPN
ejpam-5782	308	8	mixed	mixed	ADJ
ejpam-5782	308	9	weak	weak	ADJ
ejpam-5782	308	10	continuity	continuity	NOUN
ejpam-5782	308	11	on	on	ADP
ejpam-5782	308	12	generalized	generalized	ADJ
ejpam-5782	308	13	topological	topological	ADJ
ejpam-5782	308	14	spaces	space	NOUN
ejpam-5782	308	15	.	.	PUNCT
ejpam-5782	309	1	acta	acta	PROPN
ejpam-5782	309	2	mathematica	mathematica	PROPN
ejpam-5782	309	3	hungarica	hungarica	PROPN
ejpam-5782	309	4	,	,	PUNCT
ejpam-5782	309	5	132(4):339–347	132(4):339–347	NUM
ejpam-5782	309	6	,	,	PUNCT
ejpam-5782	309	7	2011	2011	NUM
ejpam-5782	309	8	.	.	PUNCT