id	sid	tid	token	lemma	pos
cana-5707	1	1	communications	communication	NOUN
cana-5707	1	2	on	on	ADP
cana-5707	1	3	applied	apply	VERB
cana-5707	1	4	nonlinear	nonlinear	ADJ
cana-5707	1	5	analysis	analysis	NOUN
cana-5707	1	6	issn	issn	NOUN
cana-5707	1	7	:	:	PUNCT
cana-5707	1	8	1074	1074	NUM
cana-5707	1	9	-	-	PUNCT
cana-5707	1	10	133x	133x	NUM
cana-5707	1	11	vol	vol	VERB
cana-5707	1	12	32	32	NUM
cana-5707	1	13	no	no	NOUN
cana-5707	1	14	.	.	PUNCT
cana-5707	2	1	10s	10	NOUN
cana-5707	2	2	(	(	PUNCT
cana-5707	2	3	2025	2025	NUM
cana-5707	2	4	)	)	PUNCT
cana-5707	2	5	2662	2662	NUM
cana-5707	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5707	2	7	decomposition	decomposition	NOUN
cana-5707	2	8	of	of	ADP
cana-5707	2	9	(	(	PUNCT
cana-5707	2	10	ψαhb	ψαhb	PROPN
cana-5707	2	11	,	,	PUNCT
cana-5707	2	12	δ)-continuity	δ)-continuity	PROPN
cana-5707	2	13	r.	r.	PROPN
cana-5707	2	14	ramesh	ramesh	PROPN
cana-5707	2	15	∗	∗	PROPN
cana-5707	2	16	,	,	PUNCT
cana-5707	2	17	t.	t.	PROPN
cana-5707	2	18	muthukumar	muthukumar	PROPN
cana-5707	2	19	,	,	PUNCT
cana-5707	2	20	k.	k.	PROPN
cana-5707	2	21	kalaiselvi	kalaiselvi	PROPN
cana-5707	2	22	and	and	CCONJ
cana-5707	2	23	l.	l.	PROPN
cana-5707	2	24	senthil	senthil	PROPN
cana-5707	2	25	kumar	kumar	PROPN
cana-5707	2	26	department	department	PROPN
cana-5707	2	27	of	of	ADP
cana-5707	2	28	mathematics	mathematics	PROPN
cana-5707	2	29	,	,	PUNCT
cana-5707	2	30	dr	dr	PROPN
cana-5707	2	31	.	.	PROPN
cana-5707	2	32	mahalingam	mahalingam	PROPN
cana-5707	2	33	college	college	PROPN
cana-5707	2	34	of	of	ADP
cana-5707	2	35	engineering	engineering	NOUN
cana-5707	2	36	and	and	CCONJ
cana-5707	2	37	technology	technology	NOUN
cana-5707	2	38	,	,	PUNCT
cana-5707	2	39	pollachi	pollachi	PROPN
cana-5707	2	40	,	,	PUNCT
cana-5707	2	41	tamil	tamil	PROPN
cana-5707	2	42	nadu	nadu	PROPN
cana-5707	2	43	,	,	PUNCT
cana-5707	2	44	india	india	PROPN
cana-5707	2	45	.	.	PUNCT
cana-5707	3	1	∗e	∗e	NOUN
cana-5707	3	2	-	-	PUNCT
cana-5707	3	3	mail	mail	NOUN
cana-5707	3	4	:	:	PUNCT
cana-5707	3	5	rameshwaran141@gmail.com	rameshwaran141@gmail.com	X
cana-5707	4	1	article	article	NOUN
cana-5707	4	2	history	history	NOUN
cana-5707	4	3	:	:	PUNCT
cana-5707	4	4	received	receive	VERB
cana-5707	4	5	:	:	PUNCT
cana-5707	4	6	12	12	NUM
cana-5707	4	7	-	-	SYM
cana-5707	4	8	01	01	NUM
cana-5707	4	9	-	-	PUNCT
cana-5707	4	10	2025	2025	NUM
cana-5707	4	11	revised	revise	VERB
cana-5707	4	12	:	:	PUNCT
cana-5707	4	13	15	15	NUM
cana-5707	4	14	-	-	NUM
cana-5707	4	15	02	02	NUM
cana-5707	4	16	-	-	PUNCT
cana-5707	4	17	2025	2025	NUM
cana-5707	4	18	accepted	accept	VERB
cana-5707	4	19	:	:	PUNCT
cana-5707	4	20	01	01	NUM
cana-5707	4	21	-	-	SYM
cana-5707	4	22	03	03	NUM
cana-5707	4	23	-	-	PUNCT
cana-5707	4	24	2025	2025	NUM
cana-5707	4	25	abstract	abstract	NOUN
cana-5707	4	26	:	:	PUNCT
cana-5707	4	27	in	in	ADP
cana-5707	4	28	this	this	DET
cana-5707	4	29	article	article	NOUN
cana-5707	4	30	,	,	PUNCT
cana-5707	4	31	we	we	PRON
cana-5707	4	32	explore	explore	VERB
cana-5707	4	33	and	and	CCONJ
cana-5707	4	34	introduce	introduce	VERB
cana-5707	4	35	the	the	DET
cana-5707	4	36	variety	variety	NOUN
cana-5707	4	37	of	of	ADP
cana-5707	4	38	open	open	ADJ
cana-5707	4	39	sets	set	NOUN
cana-5707	4	40	in	in	ADP
cana-5707	4	41	h	h	NOUN
cana-5707	4	42	-	-	PUNCT
cana-5707	4	43	gts	gts	NOUN
cana-5707	4	44	.	.	PUNCT
cana-5707	5	1	additionally	additionally	ADV
cana-5707	5	2	,	,	PUNCT
cana-5707	5	3	we	we	PRON
cana-5707	5	4	get	get	VERB
cana-5707	5	5	the	the	DET
cana-5707	5	6	decomposition	decomposition	NOUN
cana-5707	5	7	of	of	ADP
cana-5707	5	8	(	(	PUNCT
cana-5707	5	9	ψαhb	ψαhb	INTJ
cana-5707	5	10	,	,	PUNCT
cana-5707	5	11	δ)-c	δ)-c	NOUN
cana-5707	5	12	.	.	PUNCT
cana-5707	6	1	keywords	keyword	NOUN
cana-5707	6	2	:	:	PUNCT
cana-5707	6	3	hereditary	hereditary	ADJ
cana-5707	6	4	generalized	generalize	VERB
cana-5707	6	5	topology	topology	NOUN
cana-5707	6	6	,	,	PUNCT
cana-5707	6	7	α	α	PROPN
cana-5707	6	8	-	-	PUNCT
cana-5707	6	9	hb	hb	NOUN
cana-5707	6	10	-	-	PUNCT
cana-5707	6	11	open	open	ADJ
cana-5707	6	12	,	,	PUNCT
cana-5707	6	13	π	π	PROPN
cana-5707	6	14	-	-	PUNCT
cana-5707	6	15	hb	hb	X
cana-5707	6	16	-	-	PUNCT
cana-5707	6	17	open	open	ADJ
cana-5707	6	18	and	and	CCONJ
cana-5707	6	19	π	π	ADJ
cana-5707	6	20	-	-	PUNCT
cana-5707	6	21	hbopen	hbopen	ADJ
cana-5707	6	22	sets	set	NOUN
cana-5707	6	23	.	.	PUNCT
cana-5707	7	1	1	1	X
cana-5707	7	2	.	.	X
cana-5707	7	3	introduction	introduction	NOUN
cana-5707	7	4	let	let	VERB
cana-5707	7	5	z	z	PRON
cana-5707	7	6	be	be	AUX
cana-5707	7	7	a	a	DET
cana-5707	7	8	nonempty	nonempty	ADV
cana-5707	7	9	set	set	VERB
cana-5707	7	10	and	and	CCONJ
cana-5707	7	11	ϑ	ϑ	X
cana-5707	7	12	be	be	AUX
cana-5707	7	13	a	a	DET
cana-5707	7	14	collection	collection	NOUN
cana-5707	7	15	from	from	ADP
cana-5707	7	16	the	the	DET
cana-5707	7	17	subsets	subset	NOUN
cana-5707	7	18	of	of	ADP
cana-5707	7	19	z.	z.	PROPN
cana-5707	7	20	then	then	ADV
cana-5707	7	21	ϑ	ϑ	PROPN
cana-5707	7	22	is	be	AUX
cana-5707	7	23	called	call	VERB
cana-5707	7	24	a	a	DET
cana-5707	7	25	generalized	generalized	ADJ
cana-5707	7	26	topology	topology	NOUN
cana-5707	7	27	(	(	PUNCT
cana-5707	7	28	briefly	briefly	NOUN
cana-5707	7	29	gt	gt	PROPN
cana-5707	7	30	)	)	PUNCT
cana-5707	8	1	[	[	X
cana-5707	8	2	1	1	NUM
cana-5707	8	3	]	]	PUNCT
cana-5707	8	4	,	,	PUNCT
cana-5707	8	5	iff	iff	PROPN
cana-5707	8	6	∅∈ϑ	∅∈ϑ	PROPN
cana-5707	8	7	and	and	CCONJ
cana-5707	8	8	union	union	NOUN
cana-5707	8	9	of	of	ADP
cana-5707	8	10	open	open	ADJ
cana-5707	8	11	sets	set	NOUN
cana-5707	8	12	of	of	ADP
cana-5707	8	13	ϑ	ϑ	NOUN
cana-5707	8	14	is	be	AUX
cana-5707	8	15	open	open	ADJ
cana-5707	8	16	in	in	ADP
cana-5707	8	17	ϑ.	ϑ.	NOUN
cana-5707	8	18	the	the	DET
cana-5707	8	19	closure	closure	NOUN
cana-5707	8	20	of	of	ADP
cana-5707	8	21	a	a	DET
cana-5707	8	22	subset	subset	NOUN
cana-5707	8	23	b	b	NOUN
cana-5707	8	24	of	of	ADP
cana-5707	8	25	z	z	PROPN
cana-5707	8	26	,	,	PUNCT
cana-5707	8	27	denoted	denote	VERB
cana-5707	8	28	by	by	ADP
cana-5707	8	29	cϑ(b	cϑ(b	NOUN
cana-5707	8	30	)	)	PUNCT
cana-5707	8	31	is	be	AUX
cana-5707	8	32	the	the	DET
cana-5707	8	33	smallest	small	ADJ
cana-5707	8	34	ϑ	ϑ	X
cana-5707	8	35	closed	closed	ADJ
cana-5707	8	36	sets	set	NOUN
cana-5707	8	37	containing	contain	VERB
cana-5707	8	38	b	b	PROPN
cana-5707	8	39	and	and	CCONJ
cana-5707	8	40	the	the	DET
cana-5707	8	41	interior	interior	ADJ
cana-5707	8	42	(	(	PUNCT
cana-5707	8	43	resp	resp	NOUN
cana-5707	8	44	.	.	PUNCT
cana-5707	9	1	ϑ-σ	ϑ-σ	NOUN
cana-5707	9	2	-	-	PUNCT
cana-5707	9	3	interior	interior	NOUN
cana-5707	9	4	)	)	PUNCT
cana-5707	9	5	of	of	ADP
cana-5707	9	6	b	b	NOUN
cana-5707	9	7	,	,	PUNCT
cana-5707	9	8	denoted	denote	VERB
cana-5707	9	9	by	by	ADP
cana-5707	9	10	iϑ(b	iϑ(b	NOUN
cana-5707	9	11	)	)	PUNCT
cana-5707	9	12	(	(	PUNCT
cana-5707	9	13	resp	resp	NOUN
cana-5707	9	14	.	.	PUNCT
cana-5707	9	15	iσ(b	iσ(b	NOUN
cana-5707	9	16	)	)	PUNCT
cana-5707	9	17	)	)	PUNCT
cana-5707	9	18	is	be	AUX
cana-5707	9	19	the	the	DET
cana-5707	9	20	largest	large	ADJ
cana-5707	9	21	ϑ-open	ϑ-open	ADJ
cana-5707	9	22	(	(	PUNCT
cana-5707	9	23	resp	resp	NOUN
cana-5707	9	24	.	.	PUNCT
cana-5707	9	25	ϑ-σ	ϑ-σ	NOUN
cana-5707	9	26	-	-	PUNCT
cana-5707	9	27	open	open	ADJ
cana-5707	9	28	)	)	PUNCT
cana-5707	9	29	sets	set	NOUN
cana-5707	9	30	contained	contain	VERB
cana-5707	9	31	in	in	ADP
cana-5707	9	32	b.	b.	PROPN
cana-5707	9	33	definition	definition	NOUN
cana-5707	9	34	1.1	1.1	NUM
cana-5707	9	35	.	.	PUNCT
cana-5707	10	1	a	a	DET
cana-5707	10	2	subset	subset	NOUN
cana-5707	10	3	b⊂z	b⊂z	NOUN
cana-5707	10	4	is	be	AUX
cana-5707	10	5	called	call	VERB
cana-5707	10	6	1	1	NUM
cana-5707	10	7	.	.	PUNCT
cana-5707	10	8	ϑ-α	ϑ-α	ADJ
cana-5707	10	9	-	-	ADJ
cana-5707	10	10	open	open	ADJ
cana-5707	10	11	[	[	X
cana-5707	10	12	2	2	NUM
cana-5707	10	13	]	]	PUNCT
cana-5707	10	14	,	,	PUNCT
cana-5707	10	15	if	if	SCONJ
cana-5707	10	16	b⊂iϑcϑiϑ(b	b⊂iϑcϑiϑ(b	ADJ
cana-5707	10	17	)	)	PUNCT
cana-5707	10	18	.	.	PUNCT
cana-5707	11	1	2	2	X
cana-5707	11	2	.	.	X
cana-5707	11	3	ϑ-σ	ϑ-σ	NOUN
cana-5707	11	4	-	-	PUNCT
cana-5707	11	5	open	open	VERB
cana-5707	11	6	[	[	X
cana-5707	11	7	2	2	NUM
cana-5707	11	8	]	]	PUNCT
cana-5707	11	9	,	,	PUNCT
cana-5707	11	10	if	if	SCONJ
cana-5707	11	11	b⊂cϑiϑ(b	b⊂cϑiϑ(b	PROPN
cana-5707	11	12	)	)	PUNCT
cana-5707	11	13	.	.	PUNCT
cana-5707	12	1	3	3	X
cana-5707	12	2	.	.	X
cana-5707	12	3	ϑ-π	ϑ-π	VERB
cana-5707	12	4	-	-	PUNCT
cana-5707	12	5	open	open	ADJ
cana-5707	12	6	[	[	X
cana-5707	12	7	2	2	NUM
cana-5707	12	8	]	]	PUNCT
cana-5707	12	9	,	,	PUNCT
cana-5707	12	10	if	if	SCONJ
cana-5707	12	11	b⊂iϑcϑ(b	b⊂iϑcϑ(b	PROPN
cana-5707	12	12	)	)	PUNCT
cana-5707	12	13	.	.	PUNCT
cana-5707	13	1	4	4	X
cana-5707	13	2	.	.	X
cana-5707	13	3	ϑ-β	ϑ-β	NOUN
cana-5707	13	4	-	-	ADJ
cana-5707	13	5	open	open	ADJ
cana-5707	13	6	[	[	X
cana-5707	13	7	2	2	NUM
cana-5707	13	8	]	]	PUNCT
cana-5707	13	9	,	,	PUNCT
cana-5707	13	10	if	if	SCONJ
cana-5707	13	11	b⊂cϑiϑcϑ(b	b⊂cϑiϑcϑ(b	NOUN
cana-5707	13	12	)	)	PUNCT
cana-5707	13	13	.	.	PUNCT
cana-5707	14	1	5	5	X
cana-5707	14	2	.	.	X
cana-5707	14	3	ϑ-b	ϑ-b	NOUN
cana-5707	14	4	-	-	PUNCT
cana-5707	14	5	open	open	ADJ
cana-5707	14	6	[	[	X
cana-5707	14	7	14	14	NUM
cana-5707	14	8	]	]	PUNCT
cana-5707	14	9	,	,	PUNCT
cana-5707	14	10	if	if	SCONJ
cana-5707	14	11	b⊂cϑiϑ(b)∪iϑcϑ(b	b⊂cϑiϑ(b)∪iϑcϑ(b	VERB
cana-5707	14	12	)	)	PUNCT
cana-5707	14	13	.	.	PUNCT
cana-5707	15	1	definition	definition	NOUN
cana-5707	15	2	1.2	1.2	NUM
cana-5707	15	3	.	.	PUNCT
cana-5707	16	1	a	a	DET
cana-5707	16	2	collection	collection	NOUN
cana-5707	16	3	h	h	NOUN
cana-5707	16	4	of	of	ADP
cana-5707	16	5	subsets	subset	NOUN
cana-5707	16	6	of	of	ADP
cana-5707	16	7	z	z	PROPN
cana-5707	16	8	is	be	AUX
cana-5707	16	9	called	call	VERB
cana-5707	16	10	as	as	ADP
cana-5707	16	11	a	a	DET
cana-5707	16	12	hereditary	hereditary	ADJ
cana-5707	16	13	class	class	NOUN
cana-5707	17	1	[	[	X
cana-5707	17	2	3	3	NUM
cana-5707	17	3	]	]	PUNCT
cana-5707	17	4	,	,	PUNCT
cana-5707	17	5	if	if	SCONJ
cana-5707	17	6	b∈h	b∈h	NOUN
cana-5707	17	7	and	and	CCONJ
cana-5707	17	8	v⊂b	v⊂b	NOUN
cana-5707	17	9	,	,	PUNCT
cana-5707	17	10	then	then	ADV
cana-5707	17	11	v∈h	v∈h	NOUN
cana-5707	17	12	.	.	PUNCT
cana-5707	18	1	definition	definition	NOUN
cana-5707	18	2	1.3	1.3	NUM
cana-5707	18	3	.	.	PUNCT
cana-5707	19	1	for	for	ADP
cana-5707	19	2	a	a	DET
cana-5707	19	3	hereditary	hereditary	ADJ
cana-5707	19	4	class	class	NOUN
cana-5707	19	5	h	h	NOUN
cana-5707	19	6	on	on	ADP
cana-5707	19	7	band	band	NOUN
cana-5707	19	8	b⊂z	b⊂z	NOUN
cana-5707	19	9	,	,	PUNCT
cana-5707	19	10	we	we	PRON
cana-5707	19	11	define	define	VERB
cana-5707	19	12	b∗(h	b∗(h	PROPN
cana-5707	19	13	,	,	PUNCT
cana-5707	19	14	ϑ	ϑ	NOUN
cana-5707	19	15	)	)	PUNCT
cana-5707	19	16	=	=	SYM
cana-5707	19	17	{	{	PUNCT
cana-5707	19	18	a	a	PRON
cana-5707	19	19	∈	∈	PROPN
cana-5707	19	20	z	z	NOUN
cana-5707	19	21	:	:	PUNCT
cana-5707	19	22	b	b	NUM
cana-5707	19	23	∩	∩	ADJ
cana-5707	19	24	v	v	ADP
cana-5707	19	25	∈/	∈/	PROPN
cana-5707	19	26	h	h	NOUN
cana-5707	19	27	for	for	ADP
cana-5707	19	28	all	all	DET
cana-5707	19	29	v∈ϑ	v∈ϑ	NOUN
cana-5707	19	30	such	such	ADJ
cana-5707	19	31	that	that	SCONJ
cana-5707	19	32	a	a	DET
cana-5707	19	33	∈	∈	PROPN
cana-5707	19	34	v	v	NOUN
cana-5707	19	35	}	}	PUNCT
cana-5707	19	36	[	[	X
cana-5707	19	37	3	3	NUM
cana-5707	19	38	]	]	PUNCT
cana-5707	19	39	.	.	PUNCT
cana-5707	20	1	definition	definition	NOUN
cana-5707	20	2	1.4	1.4	NUM
cana-5707	20	3	.	.	PUNCT
cana-5707	21	1	a	a	DET
cana-5707	21	2	subset	subset	NOUN
cana-5707	21	3	b	b	X
cana-5707	21	4	⊂	⊂	PROPN
cana-5707	21	5	z	z	PROPN
cana-5707	21	6	is	be	AUX
cana-5707	21	7	called	call	VERB
cana-5707	21	8	1	1	NUM
cana-5707	21	9	.	.	PUNCT
cana-5707	21	10	αho	αho	NOUN
cana-5707	21	11	p	p	X
cana-5707	21	12	en	en	PROPN
cana-5707	21	13	[	[	X
cana-5707	21	14	3	3	NUM
cana-5707	21	15	]	]	PUNCT
cana-5707	21	16	,	,	PUNCT
cana-5707	21	17	if	if	SCONJ
cana-5707	21	18	b	b	PROPN
cana-5707	21	19	⊆	⊆	NUM
cana-5707	21	20	iϑcϑ	iϑcϑ	NOUN
cana-5707	21	21	∗	∗	NOUN
cana-5707	21	22	iϑ(b	iϑ(b	NUM
cana-5707	21	23	)	)	PUNCT
cana-5707	21	24	,	,	PUNCT
cana-5707	21	25	2	2	X
cana-5707	21	26	.	.	PUNCT
cana-5707	21	27	σ	σ	PROPN
cana-5707	21	28	-	-	PUNCT
cana-5707	21	29	h	h	NOUN
cana-5707	21	30	-	-	PUNCT
cana-5707	21	31	o	o	NOUN
cana-5707	21	32	pen	pen	NOUN
cana-5707	22	1	[	[	X
cana-5707	22	2	3	3	NUM
cana-5707	22	3	]	]	PUNCT
cana-5707	22	4	,	,	PUNCT
cana-5707	22	5	if	if	SCONJ
cana-5707	22	6	b	b	PROPN
cana-5707	22	7	⊆	⊆	NUM
cana-5707	22	8	cϑ	cϑ	NOUN
cana-5707	22	9	∗	∗	NOUN
cana-5707	22	10	iϑ(b	iϑ(b	NUM
cana-5707	22	11	)	)	PUNCT
cana-5707	22	12	,	,	PUNCT
cana-5707	22	13	3	3	X
cana-5707	22	14	.	.	X
cana-5707	23	1	π	π	PROPN
cana-5707	23	2	-	-	PUNCT
cana-5707	23	3	ho	ho	ADJ
cana-5707	23	4	p	p	X
cana-5707	23	5	en	en	X
cana-5707	23	6	[	[	X
cana-5707	23	7	3	3	NUM
cana-5707	23	8	]	]	PUNCT
cana-5707	23	9	,	,	PUNCT
cana-5707	23	10	if	if	SCONJ
cana-5707	23	11	b	b	PROPN
cana-5707	23	12	⊆	⊆	NUM
cana-5707	23	13	iϑcϑ	iϑcϑ	NOUN
cana-5707	23	14	∗	∗	NOUN
cana-5707	23	15	(	(	PUNCT
cana-5707	23	16	b	b	NOUN
cana-5707	23	17	)	)	PUNCT
cana-5707	23	18	,	,	PUNCT
cana-5707	23	19	4	4	NUM
cana-5707	23	20	.	.	X
cana-5707	23	21	β	β	X
cana-5707	23	22	-	-	PUNCT
cana-5707	23	23	ho	ho	INTJ
cana-5707	23	24	p	p	X
cana-5707	23	25	en	en	X
cana-5707	23	26	[	[	X
cana-5707	23	27	3	3	NUM
cana-5707	23	28	]	]	PUNCT
cana-5707	23	29	,	,	PUNCT
cana-5707	23	30	if	if	SCONJ
cana-5707	23	31	b	b	PROPN
cana-5707	23	32	⊆	⊆	NUM
cana-5707	23	33	cϑiϑcϑ	cϑiϑcϑ	NOUN
cana-5707	23	34	∗	∗	NOUN
cana-5707	23	35	(	(	PUNCT
cana-5707	23	36	b	b	NOUN
cana-5707	23	37	)	)	PUNCT
cana-5707	23	38	,	,	PUNCT
cana-5707	23	39	5	5	X
cana-5707	23	40	.	.	PUNCT
cana-5707	23	41	ϑ∗	ϑ∗	PROPN
cana-5707	23	42	c	c	PROPN
cana-5707	23	43	losed	losed	PROPN
cana-5707	24	1	[	[	X
cana-5707	24	2	3	3	NUM
cana-5707	24	3	]	]	PUNCT
cana-5707	24	4	,	,	PUNCT
cana-5707	24	5	if	if	SCONJ
cana-5707	24	6	cϑ	cϑ	ADV
cana-5707	24	7	∗	∗	NOUN
cana-5707	24	8	(	(	PUNCT
cana-5707	24	9	b	b	NOUN
cana-5707	24	10	)	)	PUNCT
cana-5707	25	1	⊂	⊂	PROPN
cana-5707	25	2	b.	b.	PROPN
cana-5707	26	1	6	6	NUM
cana-5707	26	2	.	.	X
cana-5707	26	3	b	b	X
cana-5707	26	4	-	-	PUNCT
cana-5707	26	5	ho	ho	NOUN
cana-5707	26	6	p	p	X
cana-5707	26	7	e	e	PROPN
cana-5707	26	8	n	n	CCONJ
cana-5707	26	9	[	[	X
cana-5707	26	10	8	8	NUM
cana-5707	26	11	]	]	PUNCT
cana-5707	26	12	,	,	PUNCT
cana-5707	26	13	if	if	SCONJ
cana-5707	26	14	b⊆	b⊆	PROPN
cana-5707	26	15	iϑcϑ	iϑcϑ	PROPN
cana-5707	26	16	∗	∗	X
cana-5707	26	17	(	(	PUNCT
cana-5707	26	18	b	b	NOUN
cana-5707	26	19	)	)	PUNCT
cana-5707	26	20	∪	∪	ADP
cana-5707	26	21	cϑ	cϑ	NOUN
cana-5707	26	22	∗	∗	NOUN
cana-5707	26	23	iϑ(b	iϑ(b	X
cana-5707	26	24	)	)	PUNCT
cana-5707	26	25	7	7	NUM
cana-5707	26	26	.	.	PUNCT
cana-5707	26	27	σϑ∗	σϑ∗	PROPN
cana-5707	26	28	c	c	PROPN
cana-5707	26	29	losed	losed	PROPN
cana-5707	27	1	[	[	X
cana-5707	27	2	5	5	NUM
cana-5707	27	3	]	]	PUNCT
cana-5707	27	4	,	,	PUNCT
cana-5707	27	5	if	if	SCONJ
cana-5707	27	6	bσ	bσ	NOUN
cana-5707	27	7	∗⊆b	∗⊆b	VERB
cana-5707	27	8	definition	definition	NOUN
cana-5707	27	9	1.5	1.5	NUM
cana-5707	27	10	.	.	PUNCT
cana-5707	28	1	a	a	DET
cana-5707	28	2	subset	subset	NOUN
cana-5707	28	3	b	b	X
cana-5707	28	4	⊂	⊂	PROPN
cana-5707	28	5	z	z	PROPN
cana-5707	28	6	is	be	AUX
cana-5707	28	7	said	say	VERB
cana-5707	28	8	to	to	PART
cana-5707	28	9	be	be	AUX
cana-5707	28	10	1	1	NUM
cana-5707	28	11	.	.	PUNCT
cana-5707	29	1	α	α	X
cana-5707	29	2	-	-	PUNCT
cana-5707	29	3	hσ	hσ	NOUN
cana-5707	29	4	-	-	NOUN
cana-5707	29	5	o	o	NOUN
cana-5707	29	6	p	p	X
cana-5707	29	7	en	en	X
cana-5707	30	1	[	[	X
cana-5707	30	2	11	11	NUM
cana-5707	30	3	]	]	PUNCT
cana-5707	30	4	,	,	PUNCT
cana-5707	30	5	if	if	SCONJ
cana-5707	30	6	b⊆iϑcσ	b⊆iϑcσ	NOUN
cana-5707	30	7	∗	∗	NOUN
cana-5707	30	8	iϑ(b	iϑ(b	NUM
cana-5707	30	9	)	)	PUNCT
cana-5707	30	10	,	,	PUNCT
cana-5707	30	11	2	2	X
cana-5707	30	12	.	.	X
cana-5707	30	13	σ	σ	PROPN
cana-5707	30	14	-	-	PUNCT
cana-5707	30	15	hσ	hσ	NOUN
cana-5707	30	16	-	-	NOUN
cana-5707	30	17	o	o	NOUN
cana-5707	30	18	p	p	X
cana-5707	30	19	e	e	PROPN
cana-5707	30	20	n	n	CCONJ
cana-5707	30	21	[	[	X
cana-5707	30	22	11	11	NUM
cana-5707	30	23	]	]	PUNCT
cana-5707	30	24	,	,	PUNCT
cana-5707	30	25	if	if	SCONJ
cana-5707	30	26	b⊆cσ	b⊆cσ	NOUN
cana-5707	30	27	∗	∗	NOUN
cana-5707	30	28	iϑ(b	iϑ(b	NUM
cana-5707	30	29	)	)	PUNCT
cana-5707	30	30	,	,	PUNCT
cana-5707	30	31	3	3	X
cana-5707	30	32	.	.	X
cana-5707	30	33	π	π	PROPN
cana-5707	30	34	-	-	PUNCT
cana-5707	30	35	hσo	hσo	NOUN
cana-5707	30	36	p	p	NOUN
cana-5707	30	37	e	e	PROPN
cana-5707	30	38	n	n	CCONJ
cana-5707	30	39	[	[	X
cana-5707	30	40	11	11	NUM
cana-5707	30	41	]	]	PUNCT
cana-5707	30	42	,	,	PUNCT
cana-5707	30	43	if	if	SCONJ
cana-5707	30	44	b⊆iϑcσ	b⊆iϑcσ	NOUN
cana-5707	30	45	∗	∗	NOUN
cana-5707	30	46	(	(	PUNCT
cana-5707	30	47	b	b	NOUN
cana-5707	30	48	)	)	PUNCT
cana-5707	30	49	,	,	PUNCT
cana-5707	30	50	4	4	NUM
cana-5707	30	51	.	.	X
cana-5707	30	52	β	β	X
cana-5707	30	53	-	-	PUNCT
cana-5707	30	54	hσ	hσ	NOUN
cana-5707	30	55	-	-	NOUN
cana-5707	30	56	o	o	NOUN
cana-5707	30	57	p	p	X
cana-5707	30	58	en	en	X
cana-5707	30	59	[	[	X
cana-5707	30	60	11	11	NUM
cana-5707	30	61	]	]	PUNCT
cana-5707	30	62	,	,	PUNCT
cana-5707	30	63	if	if	SCONJ
cana-5707	30	64	b⊆cϑiϑcσ	b⊆cϑiϑcσ	NOUN
cana-5707	30	65	∗	∗	NOUN
cana-5707	30	66	(	(	PUNCT
cana-5707	30	67	b	b	NOUN
cana-5707	30	68	)	)	PUNCT
cana-5707	30	69	.	.	PUNCT
cana-5707	31	1	5	5	NUM
cana-5707	31	2	.	.	X
cana-5707	31	3	b	b	X
cana-5707	31	4	-	-	PUNCT
cana-5707	31	5	hσ	hσ	NOUN
cana-5707	31	6	-	-	NOUN
cana-5707	31	7	o	o	NOUN
cana-5707	31	8	p	p	X
cana-5707	31	9	e	e	PROPN
cana-5707	31	10	n	n	CCONJ
cana-5707	31	11	[	[	X
cana-5707	31	12	10	10	NUM
cana-5707	31	13	]	]	PUNCT
cana-5707	31	14	,	,	PUNCT
cana-5707	31	15	if	if	SCONJ
cana-5707	31	16	b⊆iϑcσ	b⊆iϑcσ	NOUN
cana-5707	31	17	∗	∗	NOUN
cana-5707	31	18	(	(	PUNCT
cana-5707	31	19	b)∪cσ	b)∪cσ	ADJ
cana-5707	31	20	∗	∗	NOUN
cana-5707	31	21	iϑ(b	iϑ(b	NUM
cana-5707	31	22	)	)	PUNCT
cana-5707	31	23	.	.	PUNCT
cana-5707	32	1	definition	definition	NOUN
cana-5707	32	2	1.6	1.6	NUM
cana-5707	32	3	.	.	PUNCT
cana-5707	33	1	consider	consider	VERB
cana-5707	33	2	b	b	NOUN
cana-5707	33	3	be	be	AUX
cana-5707	33	4	a	a	DET
cana-5707	33	5	subset	subset	NOUN
cana-5707	33	6	of	of	ADP
cana-5707	33	7	h	h	NOUN
cana-5707	33	8	-	-	PUNCT
cana-5707	33	9	gts	gts	NOUN
cana-5707	33	10	(	(	PUNCT
cana-5707	33	11	z	z	NOUN
cana-5707	33	12	,	,	PUNCT
cana-5707	33	13	ϑ	ϑ	X
cana-5707	33	14	,	,	PUNCT
cana-5707	33	15	h	h	NOUN
cana-5707	33	16	)	)	PUNCT
cana-5707	33	17	.	.	PUNCT
cana-5707	34	1	then	then	ADV
cana-5707	34	2	bb	bb	PROPN
cana-5707	34	3	∗(h	∗(h	PROPN
cana-5707	34	4	,	,	PUNCT
cana-5707	34	5	ϑ)={z∈z	ϑ)={z∈z	NOUN
cana-5707	34	6	:	:	PUNCT
cana-5707	34	7	b∩v∈/h	b∩v∈/h	VERB
cana-5707	34	8	for	for	ADP
cana-5707	34	9	all	all	DET
cana-5707	34	10	v∈ϑ-b	v∈ϑ-b	NOUN
cana-5707	34	11	-	-	PUNCT
cana-5707	34	12	open	open	ADJ
cana-5707	34	13	such	such	ADJ
cana-5707	34	14	that	that	DET
cana-5707	34	15	z∈v	z∈v	NOUN
cana-5707	34	16	}	}	PUNCT
cana-5707	34	17	.	.	PUNCT
cana-5707	35	1	consider	consider	VERB
cana-5707	35	2	(	(	PUNCT
cana-5707	35	3	z	z	NOUN
cana-5707	35	4	,	,	PUNCT
cana-5707	35	5	ϑ	ϑ	X
cana-5707	35	6	,	,	PUNCT
cana-5707	35	7	h	h	NOUN
cana-5707	35	8	)	)	PUNCT
cana-5707	35	9	be	be	VERB
cana-5707	35	10	a	a	DET
cana-5707	35	11	hereditary	hereditary	ADJ
cana-5707	35	12	generalized	generalized	ADJ
cana-5707	35	13	topological	topological	ADJ
cana-5707	35	14	space	space	NOUN
cana-5707	35	15	.	.	PUNCT
cana-5707	36	1	for	for	ADP
cana-5707	36	2	b⊂z	b⊂z	NOUN
cana-5707	36	3	,	,	PUNCT
cana-5707	36	4	define	define	VERB
cana-5707	36	5	cb	cb	PROPN
cana-5707	36	6	∗(b)=b	∗(b)=b	PROPN
cana-5707	36	7	∪bb	∪bb	PROPN
cana-5707	36	8	∗(h	∗(h	PROPN
cana-5707	36	9	,	,	PUNCT
cana-5707	36	10	ϑ	ϑ	NOUN
cana-5707	36	11	)	)	PUNCT
cana-5707	36	12	and	and	CCONJ
cana-5707	36	13	cb	cb	PROPN
cana-5707	36	14	∗(b	∗(b	PROPN
cana-5707	36	15	)	)	PUNCT
cana-5707	36	16	is	be	AUX
cana-5707	36	17	enlarging	enlarge	VERB
cana-5707	36	18	,	,	PUNCT
cana-5707	36	19	monotone	monotone	ADJ
cana-5707	36	20	and	and	CCONJ
cana-5707	36	21	idempotent	idempotent	NOUN
cana-5707	36	22	.	.	PUNCT
cana-5707	37	1	communications	communication	NOUN
cana-5707	37	2	on	on	ADP
cana-5707	37	3	applied	apply	VERB
cana-5707	37	4	nonlinear	nonlinear	ADJ
cana-5707	37	5	analysis	analysis	NOUN
cana-5707	37	6	issn	issn	NOUN
cana-5707	37	7	:	:	PUNCT
cana-5707	37	8	1074	1074	NUM
cana-5707	37	9	-	-	PUNCT
cana-5707	37	10	133x	133x	NUM
cana-5707	37	11	vol	vol	VERB
cana-5707	37	12	32	32	NUM
cana-5707	37	13	no	no	NOUN
cana-5707	37	14	.	.	PUNCT
cana-5707	38	1	10s	10	NOUN
cana-5707	38	2	(	(	PUNCT
cana-5707	38	3	2025	2025	NUM
cana-5707	38	4	)	)	PUNCT
cana-5707	38	5	2663	2663	NUM
cana-5707	38	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5707	38	7	definition	definition	NOUN
cana-5707	38	8	1.7	1.7	NUM
cana-5707	38	9	.	.	PUNCT
cana-5707	39	1	[	[	X
cana-5707	39	2	12	12	NUM
cana-5707	39	3	]	]	PUNCT
cana-5707	39	4	a	a	DET
cana-5707	39	5	subset	subset	NOUN
cana-5707	39	6	b	b	X
cana-5707	39	7	⊂	⊂	PROPN
cana-5707	39	8	z	z	PROPN
cana-5707	39	9	is	be	AUX
cana-5707	39	10	called	call	VERB
cana-5707	39	11	1	1	NUM
cana-5707	39	12	.	.	PUNCT
cana-5707	39	13	∆hψo	∆hψo	PROPN
cana-5707	39	14	pen	pen	NOUN
cana-5707	39	15	,	,	PUNCT
cana-5707	39	16	if	if	SCONJ
cana-5707	39	17	b⊆iσcσ	b⊆iσcσ	VERB
cana-5707	39	18	∗	∗	NOUN
cana-5707	39	19	iσ(b	iσ(b	NOUN
cana-5707	39	20	)	)	PUNCT
cana-5707	39	21	.	.	PUNCT
cana-5707	40	1	2	2	X
cana-5707	40	2	.	.	X
cana-5707	40	3	σ	σ	NOUN
cana-5707	40	4	-	-	PUNCT
cana-5707	40	5	hψ	hψ	ADP
cana-5707	40	6	-	-	NOUN
cana-5707	40	7	o	o	NOUN
cana-5707	40	8	p	p	X
cana-5707	40	9	en	en	INTJ
cana-5707	40	10	,	,	PUNCT
cana-5707	40	11	if	if	SCONJ
cana-5707	40	12	b⊆cσ	b⊆cσ	NOUN
cana-5707	40	13	∗	∗	NOUN
cana-5707	40	14	iσ(b	iσ(b	NOUN
cana-5707	40	15	)	)	PUNCT
cana-5707	40	16	.	.	PUNCT
cana-5707	41	1	3	3	X
cana-5707	41	2	.	.	X
cana-5707	41	3	φ	φ	PROPN
cana-5707	41	4	-	-	PUNCT
cana-5707	41	5	hψ	hψ	ADP
cana-5707	41	6	-	-	NOUN
cana-5707	41	7	o	o	NOUN
cana-5707	41	8	p	p	X
cana-5707	41	9	en	en	INTJ
cana-5707	41	10	,	,	PUNCT
cana-5707	41	11	if	if	SCONJ
cana-5707	41	12	b⊆iσcσ	b⊆iσcσ	VERB
cana-5707	41	13	∗	∗	NOUN
cana-5707	41	14	(	(	PUNCT
cana-5707	41	15	b	b	NOUN
cana-5707	41	16	)	)	PUNCT
cana-5707	41	17	.	.	PUNCT
cana-5707	42	1	4	4	X
cana-5707	42	2	.	.	X
cana-5707	42	3	ω	ω	NUM
cana-5707	42	4	-	-	PUNCT
cana-5707	42	5	hψ	hψ	ADP
cana-5707	42	6	-	-	NOUN
cana-5707	42	7	o	o	NOUN
cana-5707	42	8	p	p	X
cana-5707	42	9	en	en	INTJ
cana-5707	42	10	,	,	PUNCT
cana-5707	42	11	if	if	SCONJ
cana-5707	42	12	b⊆cϑiσcσ	b⊆cϑiσcσ	VERB
cana-5707	42	13	∗	∗	NOUN
cana-5707	42	14	(	(	PUNCT
cana-5707	42	15	b	b	NOUN
cana-5707	42	16	)	)	PUNCT
cana-5707	42	17	.	.	PUNCT
cana-5707	43	1	5	5	NUM
cana-5707	43	2	.	.	X
cana-5707	43	3	b	b	X
cana-5707	43	4	-	-	PUNCT
cana-5707	43	5	hψ	hψ	NOUN
cana-5707	43	6	-	-	NOUN
cana-5707	43	7	o	o	NOUN
cana-5707	43	8	p	p	X
cana-5707	43	9	e	e	PROPN
cana-5707	43	10	n	n	CCONJ
cana-5707	43	11	,	,	PUNCT
cana-5707	43	12	if	if	SCONJ
cana-5707	43	13	b⊆cσ	b⊆cσ	NOUN
cana-5707	43	14	∗	∗	VERB
cana-5707	43	15	iσ∪iσcσ	iσ∪iσcσ	VERB
cana-5707	43	16	∗	∗	NOUN
cana-5707	43	17	(	(	PUNCT
cana-5707	43	18	b	b	NOUN
cana-5707	43	19	)	)	PUNCT
cana-5707	43	20	.	.	PUNCT
cana-5707	44	1	definition	definition	NOUN
cana-5707	44	2	1.8	1.8	NUM
cana-5707	44	3	.	.	PUNCT
cana-5707	45	1	[	[	X
cana-5707	45	2	13	13	NUM
cana-5707	45	3	]	]	PUNCT
cana-5707	45	4	a	a	DET
cana-5707	45	5	subset	subset	NOUN
cana-5707	45	6	b	b	NOUN
cana-5707	45	7	of	of	ADP
cana-5707	45	8	a	a	DET
cana-5707	45	9	h	h	NOUN
cana-5707	45	10	gt	gt	NOUN
cana-5707	45	11	s	s	X
cana-5707	46	1	(	(	PUNCT
cana-5707	46	2	z	z	NOUN
cana-5707	46	3	,	,	PUNCT
cana-5707	46	4	ϑ	ϑ	X
cana-5707	46	5	,	,	PUNCT
cana-5707	46	6	h	h	NOUN
cana-5707	46	7	)	)	PUNCT
cana-5707	46	8	is	be	AUX
cana-5707	46	9	called	call	VERB
cana-5707	46	10	as	as	ADP
cana-5707	46	11	1	1	NUM
cana-5707	46	12	.	.	PUNCT
cana-5707	47	1	α	α	X
cana-5707	47	2	-	-	PUNCT
cana-5707	47	3	hb	hb	NOUN
cana-5707	47	4	-	-	PUNCT
cana-5707	47	5	open	open	ADJ
cana-5707	47	6	,	,	PUNCT
cana-5707	47	7	if	if	SCONJ
cana-5707	47	8	b⊆iϑcb∗iϑ(b	b⊆iϑcb∗iϑ(b	PROPN
cana-5707	47	9	)	)	PUNCT
cana-5707	47	10	2	2	NUM
cana-5707	47	11	.	.	X
cana-5707	47	12	σ	σ	PROPN
cana-5707	47	13	-	-	PUNCT
cana-5707	47	14	hb	hb	PROPN
cana-5707	47	15	-	-	PUNCT
cana-5707	47	16	open	open	ADJ
cana-5707	47	17	,	,	PUNCT
cana-5707	47	18	if	if	SCONJ
cana-5707	47	19	b⊆cb∗iϑ(b	b⊆cb∗iϑ(b	VERB
cana-5707	47	20	)	)	PUNCT
cana-5707	47	21	3	3	NUM
cana-5707	47	22	.	.	X
cana-5707	48	1	π	π	PROPN
cana-5707	48	2	-	-	PUNCT
cana-5707	48	3	hb	hb	X
cana-5707	48	4	-	-	PUNCT
cana-5707	48	5	open	open	ADJ
cana-5707	48	6	,	,	PUNCT
cana-5707	48	7	if	if	SCONJ
cana-5707	48	8	b⊆iϑcb∗(b	b⊆iϑcb∗(b	PROPN
cana-5707	48	9	)	)	PUNCT
cana-5707	48	10	4	4	NUM
cana-5707	48	11	.	.	X
cana-5707	48	12	β	β	X
cana-5707	48	13	-	-	PUNCT
cana-5707	48	14	hb	hb	NOUN
cana-5707	48	15	-	-	PUNCT
cana-5707	48	16	open	open	ADJ
cana-5707	48	17	,	,	PUNCT
cana-5707	48	18	if	if	SCONJ
cana-5707	48	19	b⊆cϑiϑcb∗(b	b⊆cϑiϑcb∗(b	VERB
cana-5707	48	20	)	)	PUNCT
cana-5707	48	21	5	5	NUM
cana-5707	48	22	.	.	X
cana-5707	48	23	b	b	X
cana-5707	48	24	-	-	PUNCT
cana-5707	48	25	hb	hb	NOUN
cana-5707	48	26	-	-	PUNCT
cana-5707	48	27	open	open	ADJ
cana-5707	48	28	,	,	PUNCT
cana-5707	48	29	if	if	SCONJ
cana-5707	48	30	a⊆iϑcb∗(a)∪cb∗iϑ(a	a⊆iϑcb∗(a)∪cb∗iϑ(a	NOUN
cana-5707	48	31	)	)	PUNCT
cana-5707	48	32	.	.	PUNCT
cana-5707	49	1	2	2	X
cana-5707	49	2	.	.	X
cana-5707	49	3	generalized	generalize	VERB
cana-5707	49	4	ψhb	ψhb	PROPN
cana-5707	49	5	-open	-open	PROPN
cana-5707	49	6	sets	set	NOUN
cana-5707	49	7	definition	definition	NOUN
cana-5707	49	8	2.1	2.1	NUM
cana-5707	49	9	.	.	PUNCT
cana-5707	50	1	a	a	DET
cana-5707	50	2	subset	subset	NOUN
cana-5707	50	3	b	b	NOUN
cana-5707	50	4	of	of	ADP
cana-5707	50	5	a	a	DET
cana-5707	50	6	h	h	NOUN
cana-5707	50	7	gt	gt	NOUN
cana-5707	50	8	s	s	X
cana-5707	50	9	(	(	PUNCT
cana-5707	50	10	z	z	NOUN
cana-5707	50	11	,	,	PUNCT
cana-5707	50	12	ϑ	ϑ	X
cana-5707	50	13	,	,	PUNCT
cana-5707	50	14	h	h	NOUN
cana-5707	50	15	)	)	PUNCT
cana-5707	50	16	is	be	AUX
cana-5707	50	17	called	call	VERB
cana-5707	50	18	as	as	ADP
cana-5707	50	19	1	1	NUM
cana-5707	50	20	.	.	PUNCT
cana-5707	50	21	ψα	ψα	ADP
cana-5707	50	22	-	-	PUNCT
cana-5707	50	23	hb	hb	NOUN
cana-5707	50	24	-open	-open	NOUN
cana-5707	50	25	,	,	PUNCT
cana-5707	50	26	if	if	SCONJ
cana-5707	50	27	b	b	PROPN
cana-5707	50	28	⊆	⊆	NUM
cana-5707	50	29	iσcb	iσcb	ADJ
cana-5707	50	30	∗iσ(b	∗iσ(b	PROPN
cana-5707	50	31	)	)	PUNCT
cana-5707	50	32	2	2	NUM
cana-5707	50	33	.	.	X
cana-5707	50	34	ψσ	ψσ	ADJ
cana-5707	50	35	-	-	PUNCT
cana-5707	50	36	hb	hb	NOUN
cana-5707	50	37	-open	-open	NOUN
cana-5707	50	38	,	,	PUNCT
cana-5707	50	39	if	if	SCONJ
cana-5707	50	40	b	b	PROPN
cana-5707	50	41	⊆	⊆	NUM
cana-5707	50	42	cb	cb	PROPN
cana-5707	50	43	∗iσ(b	∗iσ(b	PROPN
cana-5707	50	44	)	)	PUNCT
cana-5707	50	45	3	3	NUM
cana-5707	50	46	.	.	X
cana-5707	50	47	ψπ	ψπ	PROPN
cana-5707	50	48	-	-	PUNCT
cana-5707	50	49	hb	hb	NOUN
cana-5707	50	50	-open	-open	PROPN
cana-5707	50	51	,	,	PUNCT
cana-5707	50	52	if	if	SCONJ
cana-5707	50	53	b	b	PROPN
cana-5707	50	54	⊆	⊆	NUM
cana-5707	50	55	iσcb	iσcb	ADJ
cana-5707	50	56	∗(b	∗(b	NOUN
cana-5707	50	57	)	)	PUNCT
cana-5707	50	58	4	4	NUM
cana-5707	50	59	.	.	PUNCT
cana-5707	51	1	ψβ	ψβ	NOUN
cana-5707	51	2	-	-	PUNCT
cana-5707	51	3	hb	hb	PROPN
cana-5707	51	4	-open	-open	PROPN
cana-5707	51	5	,	,	PUNCT
cana-5707	51	6	if	if	SCONJ
cana-5707	51	7	b	b	PROPN
cana-5707	51	8	⊆	⊆	NUM
cana-5707	51	9	cϑiσcb	cϑiσcb	ADJ
cana-5707	51	10	∗(b	∗(b	PROPN
cana-5707	51	11	)	)	PUNCT
cana-5707	51	12	5	5	NUM
cana-5707	51	13	.	.	X
cana-5707	52	1	ψb	ψb	ADJ
cana-5707	52	2	-	-	PUNCT
cana-5707	52	3	hb	hb	NOUN
cana-5707	52	4	-open	-open	NOUN
cana-5707	52	5	,	,	PUNCT
cana-5707	52	6	if	if	SCONJ
cana-5707	52	7	b	b	PROPN
cana-5707	52	8	⊆	⊆	NUM
cana-5707	52	9	iσcb	iσcb	ADJ
cana-5707	52	10	∗(b	∗(b	NOUN
cana-5707	52	11	)	)	PUNCT
cana-5707	52	12	∪	∪	PROPN
cana-5707	52	13	cb	cb	PROPN
cana-5707	52	14	∗iσ(b	∗iσ(b	PROPN
cana-5707	52	15	)	)	PUNCT
cana-5707	52	16	.	.	PUNCT
cana-5707	53	1	the	the	DET
cana-5707	53	2	sets	set	NOUN
cana-5707	53	3	ψα	ψα	ADP
cana-5707	53	4	-	-	PUNCT
cana-5707	53	5	hb	hb	NOUN
cana-5707	53	6	-	-	PUNCT
cana-5707	53	7	open	open	ADJ
cana-5707	53	8	(	(	PUNCT
cana-5707	53	9	resp	resp	NOUN
cana-5707	53	10	.	.	PUNCT
cana-5707	54	1	ψσ	ψσ	ADP
cana-5707	54	2	-	-	PUNCT
cana-5707	54	3	hb	hb	NOUN
cana-5707	54	4	-	-	PUNCT
cana-5707	54	5	open	open	ADJ
cana-5707	54	6	,	,	PUNCT
cana-5707	54	7	ψπ	ψπ	ADJ
cana-5707	54	8	-	-	PUNCT
cana-5707	54	9	hb	hb	NOUN
cana-5707	54	10	-	-	PUNCT
cana-5707	54	11	open	open	ADJ
cana-5707	54	12	,	,	PUNCT
cana-5707	54	13	ψβ	ψβ	PROPN
cana-5707	54	14	-	-	PUNCT
cana-5707	54	15	hb	hb	PROPN
cana-5707	54	16	-	-	PUNCT
cana-5707	54	17	open	open	ADJ
cana-5707	54	18	,	,	PUNCT
cana-5707	54	19	ψb	ψb	ADJ
cana-5707	54	20	-	-	PUNCT
cana-5707	54	21	hb	hb	NOUN
cana-5707	54	22	-	-	PUNCT
cana-5707	54	23	open	open	ADJ
cana-5707	54	24	,	,	PUNCT
cana-5707	54	25	ϑ-pen	ϑ-pen	NOUN
cana-5707	54	26	)	)	PUNCT
cana-5707	54	27	denoted	denote	VERB
cana-5707	54	28	by	by	ADP
cana-5707	54	29	ψα	ψα	NOUN
cana-5707	54	30	-	-	PUNCT
cana-5707	54	31	hbo(z	hbo(z	NOUN
cana-5707	54	32	)	)	PUNCT
cana-5707	54	33	(	(	PUNCT
cana-5707	54	34	resp	resp	NOUN
cana-5707	54	35	.	.	PUNCT
cana-5707	55	1	ψσ	ψσ	VERB
cana-5707	55	2	-	-	PUNCT
cana-5707	55	3	hbo(z	hbo(z	NUM
cana-5707	55	4	)	)	PUNCT
cana-5707	55	5	,	,	PUNCT
cana-5707	55	6	ψπ	ψπ	PROPN
cana-5707	55	7	-	-	PUNCT
cana-5707	55	8	hbo(z	hbo(z	NUM
cana-5707	55	9	)	)	PUNCT
cana-5707	55	10	,	,	PUNCT
cana-5707	55	11	ψβ	ψβ	PROPN
cana-5707	55	12	-	-	PUNCT
cana-5707	55	13	hbo(z	hbo(z	PROPN
cana-5707	55	14	)	)	PUNCT
cana-5707	55	15	,	,	PUNCT
cana-5707	55	16	ψb	ψb	PROPN
cana-5707	55	17	-	-	PUNCT
cana-5707	55	18	hbo(z	hbo(z	NUM
cana-5707	55	19	)	)	PUNCT
cana-5707	55	20	,	,	PUNCT
cana-5707	55	21	ϑo(z	ϑo(z	NOUN
cana-5707	55	22	)	)	PUNCT
cana-5707	55	23	)	)	PUNCT
cana-5707	55	24	.	.	PUNCT
cana-5707	56	1	theorem	theorem	VERB
cana-5707	56	2	2.2	2.2	NUM
cana-5707	56	3	.	.	PUNCT
cana-5707	57	1	in	in	ADP
cana-5707	57	2	h	h	PROPN
cana-5707	57	3	gt	gt	PROPN
cana-5707	57	4	s	s	X
cana-5707	57	5	(	(	PUNCT
cana-5707	57	6	z	z	NOUN
cana-5707	57	7	,	,	PUNCT
cana-5707	57	8	ϑ	ϑ	X
cana-5707	57	9	,	,	PUNCT
cana-5707	57	10	h	h	NOUN
cana-5707	57	11	)	)	PUNCT
cana-5707	57	12	:	:	PUNCT
cana-5707	57	13	1	1	X
cana-5707	57	14	.	.	X
cana-5707	57	15	any	any	DET
cana-5707	57	16	ϑo(z	ϑo(z	NOUN
cana-5707	57	17	)	)	PUNCT
cana-5707	57	18	set	set	NOUN
cana-5707	57	19	is	be	AUX
cana-5707	57	20	ψα	ψα	ADP
cana-5707	57	21	-	-	PUNCT
cana-5707	57	22	hbo(z	hbo(z	NUM
cana-5707	57	23	)	)	PUNCT
cana-5707	57	24	.	.	PUNCT
cana-5707	58	1	2	2	X
cana-5707	58	2	.	.	X
cana-5707	58	3	any	any	DET
cana-5707	58	4	ϑo(z	ϑo(z	NOUN
cana-5707	58	5	)	)	PUNCT
cana-5707	58	6	set	set	NOUN
cana-5707	58	7	is	be	AUX
cana-5707	58	8	ψσ	ψσ	ADJ
cana-5707	58	9	-	-	PUNCT
cana-5707	58	10	hbo(z	hbo(z	NUM
cana-5707	58	11	)	)	PUNCT
cana-5707	58	12	.	.	PUNCT
cana-5707	59	1	3	3	X
cana-5707	59	2	.	.	X
cana-5707	60	1	any	any	DET
cana-5707	60	2	ϑo(z	ϑo(z	NOUN
cana-5707	60	3	)	)	PUNCT
cana-5707	60	4	set	set	NOUN
cana-5707	60	5	is	be	AUX
cana-5707	60	6	ψπ	ψπ	NOUN
cana-5707	60	7	-	-	PUNCT
cana-5707	60	8	hbo(z	hbo(z	NUM
cana-5707	60	9	)	)	PUNCT
cana-5707	60	10	.	.	PUNCT
cana-5707	61	1	4	4	X
cana-5707	61	2	.	.	X
cana-5707	62	1	any	any	DET
cana-5707	62	2	ϑo(z	ϑo(z	NOUN
cana-5707	62	3	)	)	PUNCT
cana-5707	62	4	set	set	NOUN
cana-5707	62	5	is	be	AUX
cana-5707	62	6	ψβ	ψβ	PROPN
cana-5707	62	7	-	-	PUNCT
cana-5707	62	8	hbo(z	hbo(z	PROPN
cana-5707	62	9	)	)	PUNCT
cana-5707	62	10	.	.	PUNCT
cana-5707	63	1	5	5	X
cana-5707	63	2	.	.	X
cana-5707	64	1	any	any	DET
cana-5707	64	2	ϑo(z	ϑo(z	NOUN
cana-5707	64	3	)	)	PUNCT
cana-5707	64	4	set	set	NOUN
cana-5707	64	5	is	be	AUX
cana-5707	64	6	ψb	ψb	NOUN
cana-5707	64	7	-	-	PUNCT
cana-5707	64	8	hbo(z	hbo(z	NUM
cana-5707	64	9	)	)	PUNCT
cana-5707	64	10	.	.	PUNCT
cana-5707	65	1	proof	proof	NOUN
cana-5707	65	2	.	.	PUNCT
cana-5707	66	1	(	(	PUNCT
cana-5707	66	2	1	1	NUM
cana-5707	66	3	)	)	PUNCT
cana-5707	66	4	.	.	PUNCT
cana-5707	67	1	consider	consider	VERB
cana-5707	67	2	a	a	DET
cana-5707	67	3	subset	subset	NOUN
cana-5707	67	4	b	b	NOUN
cana-5707	67	5	of	of	ADP
cana-5707	67	6	h	h	PROPN
cana-5707	67	7	-gt	-gt	X
cana-5707	67	8	s	s	X
cana-5707	67	9	(	(	PUNCT
cana-5707	67	10	z	z	NOUN
cana-5707	67	11	,	,	PUNCT
cana-5707	67	12	ϑ	ϑ	X
cana-5707	67	13	,	,	PUNCT
cana-5707	67	14	h	h	NOUN
cana-5707	67	15	)	)	PUNCT
cana-5707	67	16	is	be	AUX
cana-5707	67	17	ϑo(z	ϑo(z	NOUN
cana-5707	67	18	)	)	PUNCT
cana-5707	67	19	.	.	PUNCT
cana-5707	68	1	then	then	ADV
cana-5707	68	2	b⊆iϑ(b)⊆iϑ	b⊆iϑ(b)⊆iϑ	PUNCT
cana-5707	68	3	∗(b)⊆iϑcb	∗(b)⊆iϑcb	ADP
cana-5707	68	4	∗iϑ(b)⊆iσcb	∗iϑ(b)⊆iσcb	NUM
cana-5707	68	5	∗iσ(b	∗iσ(b	PROPN
cana-5707	68	6	)	)	PUNCT
cana-5707	68	7	.	.	PUNCT
cana-5707	69	1	hence	hence	ADV
cana-5707	69	2	b	b	NOUN
cana-5707	69	3	is	be	AUX
cana-5707	69	4	ψα	ψα	ADP
cana-5707	69	5	-	-	PUNCT
cana-5707	69	6	hbo(z	hbo(z	NUM
cana-5707	69	7	)	)	PUNCT
cana-5707	69	8	.	.	PUNCT
cana-5707	70	1	(	(	PUNCT
cana-5707	70	2	2	2	NUM
cana-5707	70	3	)	)	PUNCT
cana-5707	70	4	.	.	PUNCT
cana-5707	71	1	consider	consider	VERB
cana-5707	71	2	a	a	DET
cana-5707	71	3	subset	subset	NOUN
cana-5707	71	4	b	b	NOUN
cana-5707	71	5	of	of	ADP
cana-5707	71	6	h	h	NOUN
cana-5707	71	7	-	-	PUNCT
cana-5707	71	8	gts	gts	NOUN
cana-5707	71	9	(	(	PUNCT
cana-5707	71	10	z	z	NOUN
cana-5707	71	11	,	,	PUNCT
cana-5707	71	12	ϑ	ϑ	X
cana-5707	71	13	,	,	PUNCT
cana-5707	71	14	h	h	NOUN
cana-5707	71	15	)	)	PUNCT
cana-5707	71	16	is	be	AUX
cana-5707	71	17	ϑo(z	ϑo(z	NOUN
cana-5707	71	18	)	)	PUNCT
cana-5707	71	19	.	.	PUNCT
cana-5707	72	1	then	then	ADV
cana-5707	72	2	,	,	PUNCT
cana-5707	72	3	b⊆iϑ(b)⊆cb	b⊆iϑ(b)⊆cb	PROPN
cana-5707	72	4	∗iϑ(b)⊆cb	∗iϑ(b)⊆cb	PROPN
cana-5707	72	5	∗iσ(b	∗iσ(b	PROPN
cana-5707	72	6	)	)	PUNCT
cana-5707	72	7	.	.	PUNCT
cana-5707	73	1	hence	hence	ADV
cana-5707	73	2	b	b	PROPN
cana-5707	73	3	is	be	AUX
cana-5707	73	4	ψσ	ψσ	ADJ
cana-5707	73	5	-	-	PUNCT
cana-5707	73	6	hbo(z	hbo(z	NUM
cana-5707	73	7	)	)	PUNCT
cana-5707	73	8	.	.	PUNCT
cana-5707	74	1	(	(	PUNCT
cana-5707	74	2	3	3	NUM
cana-5707	74	3	)	)	PUNCT
cana-5707	74	4	.	.	PUNCT
cana-5707	75	1	consider	consider	VERB
cana-5707	75	2	a	a	DET
cana-5707	75	3	subset	subset	NOUN
cana-5707	75	4	b	b	NOUN
cana-5707	75	5	of	of	ADP
cana-5707	75	6	h	h	NOUN
cana-5707	75	7	-	-	PUNCT
cana-5707	75	8	gts	gts	NOUN
cana-5707	75	9	(	(	PUNCT
cana-5707	75	10	z	z	NOUN
cana-5707	75	11	,	,	PUNCT
cana-5707	75	12	ϑ	ϑ	X
cana-5707	75	13	,	,	PUNCT
cana-5707	75	14	h	h	NOUN
cana-5707	75	15	)	)	PUNCT
cana-5707	75	16	is	be	AUX
cana-5707	75	17	ϑo(z	ϑo(z	NOUN
cana-5707	75	18	)	)	PUNCT
cana-5707	75	19	.	.	PUNCT
cana-5707	76	1	then	then	ADV
cana-5707	76	2	,	,	PUNCT
cana-5707	76	3	b⊆iϑ(b)⊆iϑ	b⊆iϑ(b)⊆iϑ	PUNCT
cana-5707	76	4	cb	cb	PROPN
cana-5707	76	5	∗(b)⊆	∗(b)⊆	PROPN
cana-5707	76	6	iσ	iσ	PROPN
cana-5707	76	7	cb	cb	PROPN
cana-5707	76	8	∗(b	∗(b	PROPN
cana-5707	76	9	)	)	PUNCT
cana-5707	76	10	.	.	PUNCT
cana-5707	77	1	hence	hence	ADV
cana-5707	77	2	b	b	NOUN
cana-5707	77	3	is	be	AUX
cana-5707	77	4	ψπ	ψπ	ADJ
cana-5707	77	5	-	-	PUNCT
cana-5707	77	6	hbo(z	hbo(z	NUM
cana-5707	77	7	)	)	PUNCT
cana-5707	77	8	.	.	PUNCT
cana-5707	78	1	(	(	PUNCT
cana-5707	78	2	4	4	NUM
cana-5707	78	3	)	)	PUNCT
cana-5707	78	4	.	.	PUNCT
cana-5707	79	1	consider	consider	VERB
cana-5707	79	2	a	a	DET
cana-5707	79	3	subset	subset	NOUN
cana-5707	79	4	b	b	NOUN
cana-5707	79	5	of	of	ADP
cana-5707	79	6	h	h	NOUN
cana-5707	79	7	-	-	PUNCT
cana-5707	79	8	gts	gts	NOUN
cana-5707	79	9	(	(	PUNCT
cana-5707	79	10	z	z	NOUN
cana-5707	79	11	,	,	PUNCT
cana-5707	79	12	ϑ	ϑ	X
cana-5707	79	13	,	,	PUNCT
cana-5707	79	14	h	h	NOUN
cana-5707	79	15	)	)	PUNCT
cana-5707	79	16	is	be	AUX
cana-5707	79	17	ϑo(z	ϑo(z	NOUN
cana-5707	79	18	)	)	PUNCT
cana-5707	79	19	.	.	PUNCT
cana-5707	80	1	then	then	ADV
cana-5707	80	2	,	,	PUNCT
cana-5707	80	3	b⊆iϑ(b)⊆cϑiϑ	b⊆iϑ(b)⊆cϑiϑ	PROPN
cana-5707	80	4	cb	cb	PROPN
cana-5707	80	5	∗(b)⊆cϑiσcb	∗(b)⊆cϑiσcb	ADV
cana-5707	80	6	∗(b	∗(b	PROPN
cana-5707	80	7	)	)	PUNCT
cana-5707	80	8	.	.	PUNCT
cana-5707	81	1	hence	hence	ADV
cana-5707	81	2	b	b	PROPN
cana-5707	81	3	is	be	AUX
cana-5707	81	4	ψβ	ψβ	PROPN
cana-5707	81	5	-	-	PUNCT
cana-5707	81	6	hbo(z	hbo(z	PROPN
cana-5707	81	7	)	)	PUNCT
cana-5707	81	8	.	.	PUNCT
cana-5707	82	1	(	(	PUNCT
cana-5707	82	2	5	5	NUM
cana-5707	82	3	)	)	PUNCT
cana-5707	82	4	.	.	PUNCT
cana-5707	83	1	consider	consider	VERB
cana-5707	83	2	a	a	DET
cana-5707	83	3	subset	subset	NOUN
cana-5707	83	4	b	b	NOUN
cana-5707	83	5	of	of	ADP
cana-5707	83	6	h	h	NOUN
cana-5707	83	7	-	-	PUNCT
cana-5707	83	8	gts	gts	NOUN
cana-5707	83	9	(	(	PUNCT
cana-5707	83	10	z	z	NOUN
cana-5707	83	11	,	,	PUNCT
cana-5707	83	12	ϑ	ϑ	X
cana-5707	83	13	,	,	PUNCT
cana-5707	83	14	h	h	NOUN
cana-5707	83	15	)	)	PUNCT
cana-5707	83	16	is	be	AUX
cana-5707	83	17	ϑo(z	ϑo(z	NOUN
cana-5707	83	18	)	)	PUNCT
cana-5707	83	19	.	.	PUNCT
cana-5707	84	1	then	then	ADV
cana-5707	84	2	,	,	PUNCT
cana-5707	84	3	b⊆iϑ(b)⊆iϑc∗(b)⊆iϑ	b⊆iϑ(b)⊆iϑc∗(b)⊆iϑ	PROPN
cana-5707	84	4	cb	cb	PROPN
cana-5707	84	5	∗(b)∪cb	∗(b)∪cb	PROPN
cana-5707	84	6	∗iϑ(b)⊆iσcb	∗iϑ(b)⊆iσcb	NUM
cana-5707	84	7	∗(b)∪cb	∗(b)∪cb	X
cana-5707	84	8	∗iσ(b	∗iσ(b	PROPN
cana-5707	84	9	)	)	PUNCT
cana-5707	84	10	.	.	PUNCT
cana-5707	85	1	hence	hence	ADV
cana-5707	85	2	,	,	PUNCT
cana-5707	85	3	b	b	PROPN
cana-5707	85	4	is	be	AUX
cana-5707	85	5	ψb	ψb	ADV
cana-5707	85	6	-	-	PUNCT
cana-5707	85	7	hbo(z	hbo(z	NUM
cana-5707	85	8	)	)	PUNCT
cana-5707	85	9	.	.	PUNCT
cana-5707	86	1	theorem	theorem	VERB
cana-5707	86	2	2.3	2.3	NUM
cana-5707	86	3	.	.	PUNCT
cana-5707	87	1	in	in	ADP
cana-5707	87	2	h	h	PROPN
cana-5707	87	3	gt	gt	PROPN
cana-5707	87	4	s	s	X
cana-5707	87	5	(	(	PUNCT
cana-5707	87	6	z	z	NOUN
cana-5707	87	7	,	,	PUNCT
cana-5707	87	8	ϑ	ϑ	X
cana-5707	87	9	,	,	PUNCT
cana-5707	87	10	h	h	NOUN
cana-5707	87	11	):	):	PUNCT
cana-5707	87	12	1	1	NUM
cana-5707	87	13	.	.	X
cana-5707	88	1	any	any	DET
cana-5707	88	2	α	α	NOUN
cana-5707	88	3	-	-	PUNCT
cana-5707	88	4	hbo(z	hbo(z	NUM
cana-5707	88	5	)	)	PUNCT
cana-5707	88	6	is	be	AUX
cana-5707	88	7	ψα	ψα	ADP
cana-5707	88	8	-	-	PUNCT
cana-5707	88	9	hbo(z	hbo(z	NUM
cana-5707	88	10	)	)	PUNCT
cana-5707	88	11	.	.	PUNCT
cana-5707	89	1	2	2	X
cana-5707	89	2	.	.	X
cana-5707	89	3	any	any	DET
cana-5707	89	4	σ	σ	PROPN
cana-5707	89	5	-	-	PUNCT
cana-5707	89	6	hbo(z	hbo(z	PROPN
cana-5707	89	7	)	)	PUNCT
cana-5707	89	8	is	be	AUX
cana-5707	89	9	ψσ	ψσ	ADJ
cana-5707	89	10	-	-	PUNCT
cana-5707	89	11	hbo(z	hbo(z	NUM
cana-5707	89	12	)	)	PUNCT
cana-5707	89	13	.	.	PUNCT
cana-5707	90	1	3	3	X
cana-5707	90	2	.	.	X
cana-5707	90	3	any	any	PRON
cana-5707	90	4	π	π	PROPN
cana-5707	90	5	-	-	PUNCT
cana-5707	90	6	hbo(z	hbo(z	PROPN
cana-5707	90	7	)	)	PUNCT
cana-5707	90	8	is	be	AUX
cana-5707	90	9	ψπ	ψπ	NOUN
cana-5707	90	10	-	-	PUNCT
cana-5707	90	11	hbo(z	hbo(z	NUM
cana-5707	90	12	)	)	PUNCT
cana-5707	90	13	.	.	PUNCT
cana-5707	91	1	4	4	X
cana-5707	91	2	.	.	X
cana-5707	91	3	any	any	DET
cana-5707	91	4	β	β	NOUN
cana-5707	91	5	-	-	PUNCT
cana-5707	91	6	hbo(z	hbo(z	NUM
cana-5707	91	7	)	)	PUNCT
cana-5707	91	8	is	be	AUX
cana-5707	91	9	ψβ	ψβ	PROPN
cana-5707	91	10	-	-	PUNCT
cana-5707	91	11	hbo(z	hbo(z	PROPN
cana-5707	91	12	)	)	PUNCT
cana-5707	91	13	.	.	PUNCT
cana-5707	92	1	5	5	X
cana-5707	92	2	.	.	X
cana-5707	92	3	any	any	DET
cana-5707	92	4	b	b	X
cana-5707	92	5	-	-	PUNCT
cana-5707	92	6	hbo(z	hbo(z	NUM
cana-5707	92	7	)	)	PUNCT
cana-5707	92	8	is	be	AUX
cana-5707	92	9	ψb	ψb	NOUN
cana-5707	92	10	-	-	PUNCT
cana-5707	92	11	hbo(z	hbo(z	NUM
cana-5707	92	12	)	)	PUNCT
cana-5707	92	13	.	.	PUNCT
cana-5707	93	1	proof	proof	NOUN
cana-5707	93	2	.	.	PUNCT
cana-5707	94	1	1	1	X
cana-5707	94	2	.	.	X
cana-5707	94	3	consider	consider	VERB
cana-5707	94	4	b	b	NOUN
cana-5707	94	5	be	be	AUX
cana-5707	94	6	α	α	X
cana-5707	94	7	-	-	PUNCT
cana-5707	94	8	hbo(z	hbo(z	NUM
cana-5707	94	9	)	)	PUNCT
cana-5707	94	10	.	.	PUNCT
cana-5707	95	1	then	then	ADV
cana-5707	95	2	we	we	PRON
cana-5707	95	3	have	have	VERB
cana-5707	95	4	,	,	PUNCT
cana-5707	95	5	b⊆iϑcb	b⊆iϑcb	NOUN
cana-5707	95	6	∗iϑ(b)⊆iσcb	∗iϑ(b)⊆iσcb	NUM
cana-5707	95	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	95	8	)	)	PUNCT
cana-5707	95	9	.	.	PUNCT
cana-5707	96	1	hence	hence	ADV
cana-5707	96	2	ψα	ψα	ADP
cana-5707	96	3	-	-	PUNCT
cana-5707	96	4	hbo(z	hbo(z	NUM
cana-5707	96	5	)	)	PUNCT
cana-5707	96	6	.	.	PUNCT
cana-5707	97	1	2	2	X
cana-5707	97	2	.	.	X
cana-5707	97	3	consider	consider	VERB
cana-5707	97	4	b	b	NOUN
cana-5707	97	5	be	be	AUX
cana-5707	97	6	σ	σ	PROPN
cana-5707	97	7	-	-	PUNCT
cana-5707	97	8	hbo(z	hbo(z	PROPN
cana-5707	97	9	)	)	PUNCT
cana-5707	97	10	.	.	PUNCT
cana-5707	98	1	then	then	ADV
cana-5707	98	2	we	we	PRON
cana-5707	98	3	have	have	VERB
cana-5707	98	4	,	,	PUNCT
cana-5707	98	5	b⊆cb	b⊆cb	PROPN
cana-5707	98	6	∗iϑ(b)⊆	∗iϑ(b)⊆	PROPN
cana-5707	98	7	cb	cb	PROPN
cana-5707	98	8	∗iσ(b	∗iσ(b	PROPN
cana-5707	98	9	)	)	PUNCT
cana-5707	98	10	.	.	PUNCT
cana-5707	99	1	hence	hence	ADV
cana-5707	99	2	ψσ	ψσ	NOUN
cana-5707	99	3	-	-	PUNCT
cana-5707	99	4	hbo(z	hbo(z	NUM
cana-5707	99	5	)	)	PUNCT
cana-5707	99	6	.	.	PUNCT
cana-5707	100	1	3	3	X
cana-5707	100	2	.	.	X
cana-5707	100	3	consider	consider	VERB
cana-5707	100	4	b	b	NOUN
cana-5707	100	5	be	be	AUX
cana-5707	100	6	π	π	X
cana-5707	100	7	-	-	PUNCT
cana-5707	100	8	hbo(z	hbo(z	NUM
cana-5707	100	9	)	)	PUNCT
cana-5707	100	10	.	.	PUNCT
cana-5707	101	1	then	then	ADV
cana-5707	101	2	we	we	PRON
cana-5707	101	3	have	have	VERB
cana-5707	101	4	,	,	PUNCT
cana-5707	101	5	b⊆iϑcb	b⊆iϑcb	NOUN
cana-5707	101	6	∗(b	∗(b	PROPN
cana-5707	101	7	)	)	PUNCT
cana-5707	101	8	⊆	⊆	NUM
cana-5707	101	9	iσcb	iσcb	ADJ
cana-5707	101	10	∗	∗	NOUN
cana-5707	101	11	(	(	PUNCT
cana-5707	101	12	b	b	NOUN
cana-5707	101	13	)	)	PUNCT
cana-5707	101	14	.	.	PUNCT
cana-5707	102	1	hence	hence	ADV
cana-5707	102	2	ψπ	ψπ	PROPN
cana-5707	102	3	-	-	PUNCT
cana-5707	102	4	hbo(z	hbo(z	NUM
cana-5707	102	5	)	)	PUNCT
cana-5707	102	6	.	.	PUNCT
cana-5707	103	1	4	4	X
cana-5707	103	2	.	.	X
cana-5707	103	3	consider	consider	VERB
cana-5707	103	4	b	b	NOUN
cana-5707	103	5	be	be	AUX
cana-5707	103	6	β	β	X
cana-5707	103	7	-	-	PUNCT
cana-5707	103	8	hbo(z	hbo(z	NUM
cana-5707	103	9	)	)	PUNCT
cana-5707	103	10	.	.	PUNCT
cana-5707	104	1	then	then	ADV
cana-5707	104	2	we	we	PRON
cana-5707	104	3	have	have	VERB
cana-5707	104	4	,	,	PUNCT
cana-5707	104	5	b⊆	b⊆	PROPN
cana-5707	104	6	cϑiϑcb	cϑiϑcb	NOUN
cana-5707	104	7	∗(b	∗(b	PROPN
cana-5707	104	8	)	)	PUNCT
cana-5707	104	9	⊆	⊆	NUM
cana-5707	104	10	cϑiσcb	cϑiσcb	NOUN
cana-5707	104	11	∗	∗	X
cana-5707	104	12	(	(	PUNCT
cana-5707	104	13	b	b	NOUN
cana-5707	104	14	)	)	PUNCT
cana-5707	104	15	.	.	PUNCT
cana-5707	105	1	hence	hence	ADV
cana-5707	105	2	ψβ	ψβ	PROPN
cana-5707	105	3	-	-	PUNCT
cana-5707	105	4	hbo(z	hbo(z	PROPN
cana-5707	105	5	)	)	PUNCT
cana-5707	105	6	.	.	PUNCT
cana-5707	106	1	5	5	X
cana-5707	106	2	.	.	X
cana-5707	106	3	consider	consider	VERB
cana-5707	106	4	b	b	NOUN
cana-5707	106	5	be	be	AUX
cana-5707	106	6	b	b	NOUN
cana-5707	106	7	-	-	PUNCT
cana-5707	106	8	hbo(z	hbo(z	NUM
cana-5707	106	9	)	)	PUNCT
cana-5707	106	10	.	.	PUNCT
cana-5707	107	1	then	then	ADV
cana-5707	107	2	we	we	PRON
cana-5707	107	3	have	have	VERB
cana-5707	107	4	,	,	PUNCT
cana-5707	107	5	b	b	PROPN
cana-5707	107	6	⊆	⊆	NUM
cana-5707	107	7	iϑcb	iϑcb	ADJ
cana-5707	107	8	∗(b	∗(b	PROPN
cana-5707	107	9	)	)	PUNCT
cana-5707	107	10	∪	∪	PROPN
cana-5707	107	11	cb	cb	PROPN
cana-5707	107	12	∗iϑ(b	∗iϑ(b	PROPN
cana-5707	107	13	)	)	PUNCT
cana-5707	107	14	⊆	⊆	NUM
cana-5707	107	15	iσcb	iσcb	ADJ
cana-5707	107	16	∗(b	∗(b	NOUN
cana-5707	107	17	)	)	PUNCT
cana-5707	107	18	∪	∪	PROPN
cana-5707	107	19	cb	cb	PROPN
cana-5707	107	20	∗iσ(b	∗iσ(b	PROPN
cana-5707	107	21	)	)	PUNCT
cana-5707	107	22	.	.	PUNCT
cana-5707	108	1	hence	hence	ADV
cana-5707	108	2	ψb	ψb	ADV
cana-5707	108	3	-	-	PUNCT
cana-5707	108	4	hbo(z	hbo(z	NUM
cana-5707	108	5	)	)	PUNCT
cana-5707	108	6	.	.	PUNCT
cana-5707	109	1	theorem	theorem	VERB
cana-5707	109	2	2.4	2.4	NUM
cana-5707	109	3	.	.	PUNCT
cana-5707	110	1	in	in	ADP
cana-5707	110	2	h	h	PROPN
cana-5707	110	3	gt	gt	PROPN
cana-5707	110	4	s	s	X
cana-5707	110	5	(	(	PUNCT
cana-5707	110	6	z	z	NOUN
cana-5707	110	7	,	,	PUNCT
cana-5707	110	8	ϑ	ϑ	X
cana-5707	110	9	,	,	PUNCT
cana-5707	110	10	h	h	NOUN
cana-5707	110	11	):	):	PUNCT
cana-5707	110	12	1	1	NUM
cana-5707	110	13	.	.	X
cana-5707	111	1	any	any	DET
cana-5707	111	2	ψα	ψα	NOUN
cana-5707	111	3	-	-	PUNCT
cana-5707	111	4	hbo(z	hbo(z	NOUN
cana-5707	111	5	)	)	PUNCT
cana-5707	111	6	is	be	AUX
cana-5707	111	7	∆-ho(z	∆-ho(z	NOUN
cana-5707	111	8	)	)	PUNCT
cana-5707	111	9	.	.	PUNCT
cana-5707	112	1	2	2	X
cana-5707	112	2	.	.	X
cana-5707	112	3	any	any	DET
cana-5707	112	4	ψσ	ψσ	NOUN
cana-5707	112	5	-	-	PUNCT
cana-5707	112	6	hbo(z	hbo(z	NOUN
cana-5707	112	7	)	)	PUNCT
cana-5707	112	8	is	be	AUX
cana-5707	112	9	σ	σ	NOUN
cana-5707	112	10	-	-	PUNCT
cana-5707	112	11	ho(z	ho(z	NUM
cana-5707	112	12	)	)	PUNCT
cana-5707	112	13	.	.	PUNCT
cana-5707	113	1	3	3	X
cana-5707	113	2	.	.	X
cana-5707	114	1	any	any	DET
cana-5707	114	2	ψπ	ψπ	NOUN
cana-5707	114	3	-	-	PUNCT
cana-5707	114	4	hbo(z	hbo(z	NOUN
cana-5707	114	5	)	)	PUNCT
cana-5707	114	6	is	be	AUX
cana-5707	114	7	φ	φ	NOUN
cana-5707	114	8	-	-	PUNCT
cana-5707	114	9	ho(z	ho(z	NUM
cana-5707	114	10	)	)	PUNCT
cana-5707	114	11	.	.	PUNCT
cana-5707	115	1	communications	communication	NOUN
cana-5707	115	2	on	on	ADP
cana-5707	115	3	applied	apply	VERB
cana-5707	115	4	nonlinear	nonlinear	ADJ
cana-5707	115	5	analysis	analysis	NOUN
cana-5707	115	6	issn	issn	NOUN
cana-5707	115	7	:	:	PUNCT
cana-5707	115	8	1074	1074	NUM
cana-5707	115	9	-	-	PUNCT
cana-5707	115	10	133x	133x	NUM
cana-5707	115	11	vol	vol	VERB
cana-5707	115	12	32	32	NUM
cana-5707	115	13	no	no	NOUN
cana-5707	115	14	.	.	PUNCT
cana-5707	116	1	10s	10	NOUN
cana-5707	116	2	(	(	PUNCT
cana-5707	116	3	2025	2025	NUM
cana-5707	116	4	)	)	PUNCT
cana-5707	116	5	2664	2664	NUM
cana-5707	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5707	116	7	4	4	NUM
cana-5707	116	8	.	.	X
cana-5707	117	1	any	any	DET
cana-5707	117	2	ψβ	ψβ	PROPN
cana-5707	117	3	-	-	PUNCT
cana-5707	117	4	hbo(z	hbo(z	PROPN
cana-5707	117	5	)	)	PUNCT
cana-5707	117	6	is	be	AUX
cana-5707	117	7	ω	ω	NUM
cana-5707	117	8	bo(z	bo(z	ADP
cana-5707	117	9	)	)	PUNCT
cana-5707	117	10	.	.	PUNCT
cana-5707	118	1	5	5	X
cana-5707	118	2	.	.	X
cana-5707	118	3	any	any	DET
cana-5707	118	4	ψb	ψb	ADV
cana-5707	118	5	hbo(z	hbo(z	NUM
cana-5707	118	6	)	)	PUNCT
cana-5707	118	7	is	be	AUX
cana-5707	118	8	b	b	NOUN
cana-5707	118	9	-hbo(z	-hbo(z	PROPN
cana-5707	118	10	)	)	PUNCT
cana-5707	118	11	.	.	PUNCT
cana-5707	119	1	proof	proof	NOUN
cana-5707	119	2	.	.	PUNCT
cana-5707	120	1	1	1	X
cana-5707	120	2	.	.	X
cana-5707	120	3	consider	consider	VERB
cana-5707	120	4	b	b	NOUN
cana-5707	120	5	be	be	AUX
cana-5707	120	6	ψα	ψα	ADP
cana-5707	120	7	-	-	PUNCT
cana-5707	120	8	hbo(z	hbo(z	NUM
cana-5707	120	9	)	)	PUNCT
cana-5707	120	10	.	.	PUNCT
cana-5707	121	1	then	then	ADV
cana-5707	121	2	we	we	PRON
cana-5707	121	3	have	have	VERB
cana-5707	121	4	,	,	PUNCT
cana-5707	121	5	b⊆iσcb	b⊆iσcb	ADJ
cana-5707	121	6	∗iσ(b	∗iσ(b	PROPN
cana-5707	121	7	)	)	PUNCT
cana-5707	122	1	⊆	⊆	NUM
cana-5707	122	2	iσcσ	iσcσ	NOUN
cana-5707	122	3	∗	∗	NOUN
cana-5707	122	4	iσ(b	iσ(b	NOUN
cana-5707	122	5	)	)	PUNCT
cana-5707	122	6	.	.	PUNCT
cana-5707	123	1	hence	hence	ADV
cana-5707	123	2	∆-ho(z	∆-ho(z	NOUN
cana-5707	123	3	)	)	PUNCT
cana-5707	123	4	.	.	PUNCT
cana-5707	124	1	2	2	X
cana-5707	124	2	.	.	X
cana-5707	124	3	consider	consider	VERB
cana-5707	124	4	b	b	NOUN
cana-5707	124	5	be	be	AUX
cana-5707	124	6	ψσ	ψσ	ADJ
cana-5707	124	7	-	-	PUNCT
cana-5707	124	8	hbo(z	hbo(z	NUM
cana-5707	124	9	)	)	PUNCT
cana-5707	124	10	.	.	PUNCT
cana-5707	125	1	then	then	ADV
cana-5707	125	2	we	we	PRON
cana-5707	125	3	have	have	AUX
cana-5707	125	4	,	,	PUNCT
cana-5707	125	5	b⊆cb	b⊆cb	PROPN
cana-5707	125	6	∗iσ(b)⊆cσ	∗iσ(b)⊆cσ	ADJ
cana-5707	125	7	∗	∗	NOUN
cana-5707	125	8	iσ(b	iσ(b	NOUN
cana-5707	125	9	)	)	PUNCT
cana-5707	125	10	.	.	PUNCT
cana-5707	126	1	hence	hence	ADV
cana-5707	126	2	σ	σ	PROPN
cana-5707	126	3	-	-	PUNCT
cana-5707	126	4	ho(z	ho(z	NUM
cana-5707	126	5	)	)	PUNCT
cana-5707	126	6	.	.	PUNCT
cana-5707	127	1	3	3	X
cana-5707	127	2	.	.	X
cana-5707	127	3	consider	consider	VERB
cana-5707	127	4	b	b	NOUN
cana-5707	127	5	be	be	AUX
cana-5707	127	6	ψπ	ψπ	NOUN
cana-5707	127	7	-	-	PUNCT
cana-5707	127	8	hbo(z	hbo(z	NUM
cana-5707	127	9	)	)	PUNCT
cana-5707	127	10	.	.	PUNCT
cana-5707	128	1	then	then	ADV
cana-5707	128	2	we	we	PRON
cana-5707	128	3	have	have	VERB
cana-5707	128	4	,	,	PUNCT
cana-5707	128	5	b⊆iσcb	b⊆iσcb	X
cana-5707	128	6	∗(b)⊆iσcσ	∗(b)⊆iσcσ	VERB
cana-5707	128	7	∗	∗	NOUN
cana-5707	128	8	(	(	PUNCT
cana-5707	128	9	b	b	NOUN
cana-5707	128	10	)	)	PUNCT
cana-5707	128	11	.	.	PUNCT
cana-5707	129	1	hence	hence	ADV
cana-5707	129	2	b	b	PROPN
cana-5707	129	3	is	be	AUX
cana-5707	129	4	φ	φ	NUM
cana-5707	129	5	-	-	PUNCT
cana-5707	129	6	ho(z	ho(z	NUM
cana-5707	129	7	)	)	PUNCT
cana-5707	129	8	.	.	PUNCT
cana-5707	130	1	4	4	X
cana-5707	130	2	.	.	X
cana-5707	130	3	consider	consider	VERB
cana-5707	130	4	b	b	NOUN
cana-5707	130	5	be	be	AUX
cana-5707	130	6	ψβ	ψβ	PROPN
cana-5707	130	7	-	-	PUNCT
cana-5707	130	8	hbo(z	hbo(z	PROPN
cana-5707	130	9	)	)	PUNCT
cana-5707	130	10	.	.	PUNCT
cana-5707	131	1	then	then	ADV
cana-5707	131	2	we	we	PRON
cana-5707	131	3	have	have	AUX
cana-5707	131	4	,	,	PUNCT
cana-5707	131	5	b⊆cσiσcb	b⊆cσiσcb	VERB
cana-5707	131	6	∗(b)⊆cσiσcσ	∗(b)⊆cσiσcσ	PROPN
cana-5707	131	7	∗	∗	NOUN
cana-5707	131	8	(	(	PUNCT
cana-5707	131	9	b	b	NOUN
cana-5707	131	10	)	)	PUNCT
cana-5707	131	11	.	.	PUNCT
cana-5707	132	1	hence	hence	ADV
cana-5707	132	2	b	b	PROPN
cana-5707	132	3	is	be	AUX
cana-5707	132	4	ω	ω	NUM
cana-5707	132	5	hbo(z	hbo(z	NUM
cana-5707	132	6	)	)	PUNCT
cana-5707	132	7	.	.	PUNCT
cana-5707	133	1	5	5	X
cana-5707	133	2	.	.	X
cana-5707	133	3	consider	consider	VERB
cana-5707	133	4	b	b	NOUN
cana-5707	133	5	be	be	AUX
cana-5707	133	6	ψb	ψb	ADV
cana-5707	133	7	hbo(z	hbo(z	NUM
cana-5707	133	8	)	)	PUNCT
cana-5707	133	9	.	.	PUNCT
cana-5707	134	1	then	then	ADV
cana-5707	134	2	we	we	PRON
cana-5707	134	3	have	have	VERB
cana-5707	134	4	,	,	PUNCT
cana-5707	134	5	b	b	PROPN
cana-5707	134	6	⊆	⊆	NUM
cana-5707	134	7	iσc∗(b	iσc∗(b	NOUN
cana-5707	134	8	)	)	PUNCT
cana-5707	134	9	∪	∪	NOUN
cana-5707	134	10	cb	cb	PROPN
cana-5707	134	11	∗iσ(b)⊆	∗iσ(b)⊆	PROPN
cana-5707	134	12	iσcσ	iσcσ	PROPN
cana-5707	134	13	∗	∗	NOUN
cana-5707	134	14	(	(	PUNCT
cana-5707	134	15	b	b	NOUN
cana-5707	134	16	)	)	PUNCT
cana-5707	134	17	∪	∪	NOUN
cana-5707	134	18	cσ	cσ	ADP
cana-5707	134	19	∗	∗	NOUN
cana-5707	134	20	iσ(b	iσ(b	NOUN
cana-5707	134	21	)	)	PUNCT
cana-5707	134	22	.	.	PUNCT
cana-5707	135	1	hence	hence	ADV
cana-5707	135	2	b	b	PROPN
cana-5707	135	3	is	be	AUX
cana-5707	135	4	b	b	NOUN
cana-5707	135	5	hbo(z	hbo(z	NUM
cana-5707	135	6	)	)	PUNCT
cana-5707	135	7	.	.	PUNCT
cana-5707	136	1	theorem	theorem	VERB
cana-5707	136	2	2.5	2.5	NUM
cana-5707	136	3	.	.	PUNCT
cana-5707	137	1	if	if	SCONJ
cana-5707	137	2	b	b	NOUN
cana-5707	137	3	is	be	AUX
cana-5707	137	4	ψα	ψα	ADP
cana-5707	137	5	hbo(z	hbo(z	NUM
cana-5707	137	6	)	)	PUNCT
cana-5707	137	7	,	,	PUNCT
cana-5707	137	8	then	then	ADV
cana-5707	137	9	it	it	PRON
cana-5707	137	10	is	be	AUX
cana-5707	137	11	α(σ	α(σ	ADJ
cana-5707	137	12	)	)	PUNCT
cana-5707	137	13	-open	-open	NOUN
cana-5707	137	14	.	.	PUNCT
cana-5707	138	1	proof	proof	NOUN
cana-5707	138	2	.	.	PUNCT
cana-5707	139	1	consider	consider	VERB
cana-5707	139	2	a	a	DET
cana-5707	139	3	subset	subset	NOUN
cana-5707	139	4	b	b	NOUN
cana-5707	139	5	of	of	ADP
cana-5707	139	6	h	h	NOUN
cana-5707	139	7	-	-	PUNCT
cana-5707	139	8	gts	gts	NOUN
cana-5707	139	9	(	(	PUNCT
cana-5707	139	10	z	z	NOUN
cana-5707	139	11	,	,	PUNCT
cana-5707	139	12	ϑ	ϑ	X
cana-5707	139	13	,	,	PUNCT
cana-5707	139	14	h	h	NOUN
cana-5707	139	15	)	)	PUNCT
cana-5707	139	16	is	be	AUX
cana-5707	139	17	ψα	ψα	ADP
cana-5707	139	18	-	-	PUNCT
cana-5707	139	19	hbo(z	hbo(z	NUM
cana-5707	139	20	)	)	PUNCT
cana-5707	139	21	.	.	PUNCT
cana-5707	140	1	then	then	ADV
cana-5707	140	2	,	,	PUNCT
cana-5707	140	3	b⊆iσcb	b⊆iσcb	X
cana-5707	140	4	∗iσ(b)⊆iσcσ	∗iσ(b)⊆iσcσ	NUM
cana-5707	140	5	∗	∗	NOUN
cana-5707	140	6	iσ(b	iσ(b	NOUN
cana-5707	140	7	)	)	PUNCT
cana-5707	140	8	⊆	⊆	NUM
cana-5707	140	9	iσcσiσ(b	iσcσiσ(b	NUM
cana-5707	140	10	)	)	PUNCT
cana-5707	140	11	.	.	PUNCT
cana-5707	141	1	hence	hence	ADV
cana-5707	141	2	b	b	PROPN
cana-5707	141	3	is	be	AUX
cana-5707	141	4	α(σ	α(σ	VERB
cana-5707	141	5	)	)	PUNCT
cana-5707	141	6	-open	-open	NOUN
cana-5707	141	7	.	.	PUNCT
cana-5707	142	1	theorem	theorem	VERB
cana-5707	142	2	2.6	2.6	NUM
cana-5707	142	3	.	.	PUNCT
cana-5707	143	1	if	if	SCONJ
cana-5707	143	2	b	b	PROPN
cana-5707	143	3	is	be	AUX
cana-5707	143	4	ψσ	ψσ	ADJ
cana-5707	143	5	-	-	PUNCT
cana-5707	143	6	hbo(z	hbo(z	NUM
cana-5707	143	7	)	)	PUNCT
cana-5707	143	8	,	,	PUNCT
cana-5707	143	9	then	then	ADV
cana-5707	143	10	it	it	PRON
cana-5707	143	11	is	be	AUX
cana-5707	143	12	σ(σ	σ(σ	PROPN
cana-5707	143	13	)	)	PUNCT
cana-5707	143	14	-open	-open	PROPN
cana-5707	143	15	.	.	PUNCT
cana-5707	144	1	proof	proof	NOUN
cana-5707	144	2	.	.	PUNCT
cana-5707	145	1	consider	consider	VERB
cana-5707	145	2	a	a	DET
cana-5707	145	3	subset	subset	NOUN
cana-5707	145	4	b	b	NOUN
cana-5707	145	5	of	of	ADP
cana-5707	145	6	h	h	NOUN
cana-5707	145	7	-	-	PUNCT
cana-5707	145	8	gt	gt	PROPN
cana-5707	145	9	s	s	X
cana-5707	145	10	(	(	PUNCT
cana-5707	145	11	z	z	NOUN
cana-5707	145	12	,	,	PUNCT
cana-5707	145	13	ϑ	ϑ	X
cana-5707	145	14	,	,	PUNCT
cana-5707	145	15	h	h	NOUN
cana-5707	145	16	)	)	PUNCT
cana-5707	145	17	is	be	AUX
cana-5707	145	18	ψσ	ψσ	ADJ
cana-5707	145	19	-	-	PUNCT
cana-5707	145	20	hbo(z	hbo(z	NUM
cana-5707	145	21	)	)	PUNCT
cana-5707	145	22	.	.	PUNCT
cana-5707	146	1	then	then	ADV
cana-5707	146	2	,	,	PUNCT
cana-5707	146	3	b⊆cb	b⊆cb	ADP
cana-5707	146	4	∗iσ(b)⊆cσ	∗iσ(b)⊆cσ	ADJ
cana-5707	146	5	∗	∗	NOUN
cana-5707	146	6	iσ(b	iσ(b	NOUN
cana-5707	146	7	)	)	PUNCT
cana-5707	146	8	⊆	⊆	NUM
cana-5707	146	9	cσiσ(b	cσiσ(b	NOUN
cana-5707	146	10	)	)	PUNCT
cana-5707	146	11	.	.	PUNCT
cana-5707	147	1	hence	hence	ADV
cana-5707	147	2	b	b	PROPN
cana-5707	147	3	is	be	AUX
cana-5707	147	4	σ(σ	σ(σ	PROPN
cana-5707	147	5	)	)	PUNCT
cana-5707	147	6	-open	-open	PROPN
cana-5707	147	7	.	.	PUNCT
cana-5707	148	1	theorem	theorem	VERB
cana-5707	148	2	2.7	2.7	NUM
cana-5707	148	3	.	.	PUNCT
cana-5707	149	1	if	if	SCONJ
cana-5707	149	2	b	b	NOUN
cana-5707	149	3	is	be	AUX
cana-5707	149	4	ψπ	ψπ	NOUN
cana-5707	149	5	-	-	PUNCT
cana-5707	149	6	hbo(z	hbo(z	NUM
cana-5707	149	7	)	)	PUNCT
cana-5707	149	8	,	,	PUNCT
cana-5707	149	9	then	then	ADV
cana-5707	149	10	it	it	PRON
cana-5707	149	11	is	be	AUX
cana-5707	149	12	π(σ	π(σ	ADV
cana-5707	149	13	)	)	PUNCT
cana-5707	149	14	-open	-open	NOUN
cana-5707	149	15	.	.	PUNCT
cana-5707	150	1	proof	proof	NOUN
cana-5707	150	2	.	.	PUNCT
cana-5707	151	1	consider	consider	VERB
cana-5707	151	2	a	a	DET
cana-5707	151	3	subset	subset	NOUN
cana-5707	151	4	b	b	NOUN
cana-5707	151	5	of	of	ADP
cana-5707	151	6	h	h	NOUN
cana-5707	151	7	-	-	PUNCT
cana-5707	151	8	gts	gts	NOUN
cana-5707	151	9	(	(	PUNCT
cana-5707	151	10	z	z	NOUN
cana-5707	151	11	,	,	PUNCT
cana-5707	151	12	ϑ	ϑ	X
cana-5707	151	13	,	,	PUNCT
cana-5707	151	14	h	h	NOUN
cana-5707	151	15	)	)	PUNCT
cana-5707	151	16	is	be	AUX
cana-5707	151	17	ψπ	ψπ	NOUN
cana-5707	151	18	-	-	PUNCT
cana-5707	151	19	hbo(z	hbo(z	NUM
cana-5707	151	20	)	)	PUNCT
cana-5707	151	21	.	.	PUNCT
cana-5707	152	1	then	then	ADV
cana-5707	152	2	,	,	PUNCT
cana-5707	152	3	b⊆iσ	b⊆iσ	PROPN
cana-5707	152	4	cb	cb	PROPN
cana-5707	152	5	∗(b	∗(b	PROPN
cana-5707	152	6	)	)	PUNCT
cana-5707	152	7	⊆	⊆	NUM
cana-5707	152	8	iσ	iσ	NOUN
cana-5707	152	9	cσ	cσ	ADP
cana-5707	152	10	∗	∗	NOUN
cana-5707	152	11	(	(	PUNCT
cana-5707	152	12	b	b	NOUN
cana-5707	152	13	)	)	PUNCT
cana-5707	152	14	⊆iσcσ(b	⊆iσcσ(b	NOUN
cana-5707	152	15	)	)	PUNCT
cana-5707	152	16	.	.	PUNCT
cana-5707	153	1	hence	hence	ADV
cana-5707	153	2	b	b	PROPN
cana-5707	153	3	is	be	AUX
cana-5707	153	4	π(σ	π(σ	ADV
cana-5707	153	5	)	)	PUNCT
cana-5707	153	6	-open	-open	NOUN
cana-5707	153	7	.	.	PUNCT
cana-5707	154	1	theorem	theorem	VERB
cana-5707	154	2	2.8	2.8	NUM
cana-5707	154	3	.	.	PUNCT
cana-5707	155	1	in	in	ADP
cana-5707	155	2	h	h	PROPN
cana-5707	155	3	-gt	-gt	X
cana-5707	155	4	s	s	X
cana-5707	155	5	(	(	PUNCT
cana-5707	155	6	z	z	NOUN
cana-5707	155	7	,	,	PUNCT
cana-5707	155	8	ϑ	ϑ	X
cana-5707	155	9	,	,	PUNCT
cana-5707	155	10	h	h	NOUN
cana-5707	155	11	)	)	PUNCT
cana-5707	155	12	,	,	PUNCT
cana-5707	155	13	any	any	DET
cana-5707	155	14	ψα	ψα	NOUN
cana-5707	155	15	-	-	PUNCT
cana-5707	155	16	hbo(z	hbo(z	NOUN
cana-5707	155	17	)	)	PUNCT
cana-5707	155	18	is	be	AUX
cana-5707	155	19	ψσ	ψσ	ADJ
cana-5707	155	20	-	-	PUNCT
cana-5707	155	21	hbo(z	hbo(z	NUM
cana-5707	155	22	)	)	PUNCT
cana-5707	155	23	.	.	PUNCT
cana-5707	156	1	proof	proof	NOUN
cana-5707	156	2	.	.	PUNCT
cana-5707	157	1	consider	consider	VERB
cana-5707	157	2	a	a	DET
cana-5707	157	3	subset	subset	NOUN
cana-5707	157	4	b	b	NOUN
cana-5707	157	5	of	of	ADP
cana-5707	157	6	h	h	PROPN
cana-5707	157	7	-gts	-gts	PROPN
cana-5707	157	8	(	(	PUNCT
cana-5707	157	9	z	z	NOUN
cana-5707	157	10	,	,	PUNCT
cana-5707	157	11	ϑ	ϑ	X
cana-5707	157	12	,	,	PUNCT
cana-5707	157	13	h	h	NOUN
cana-5707	157	14	)	)	PUNCT
cana-5707	157	15	is	be	AUX
cana-5707	157	16	ψα	ψα	ADP
cana-5707	157	17	-	-	PUNCT
cana-5707	157	18	hbo(z	hbo(z	NUM
cana-5707	157	19	)	)	PUNCT
cana-5707	157	20	.	.	PUNCT
cana-5707	158	1	then	then	ADV
cana-5707	158	2	,	,	PUNCT
cana-5707	158	3	b⊆iσ	b⊆iσ	PROPN
cana-5707	158	4	cb	cb	PROPN
cana-5707	158	5	∗iσ(b)⊆	∗iσ(b)⊆	PROPN
cana-5707	158	6	cb	cb	PROPN
cana-5707	158	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	158	8	)	)	PUNCT
cana-5707	158	9	.	.	PUNCT
cana-5707	159	1	hence	hence	ADV
cana-5707	159	2	ψσ	ψσ	ADP
cana-5707	159	3	hbo(z	hbo(z	NUM
cana-5707	159	4	)	)	PUNCT
cana-5707	159	5	.	.	PUNCT
cana-5707	160	1	theorem	theorem	VERB
cana-5707	160	2	2.9	2.9	NUM
cana-5707	160	3	.	.	PUNCT
cana-5707	161	1	in	in	ADP
cana-5707	161	2	h	h	NOUN
cana-5707	161	3	-	-	PUNCT
cana-5707	161	4	gts	gts	NOUN
cana-5707	161	5	(	(	PUNCT
cana-5707	161	6	z	z	NOUN
cana-5707	161	7	,	,	PUNCT
cana-5707	161	8	ϑ	ϑ	X
cana-5707	161	9	,	,	PUNCT
cana-5707	161	10	h	h	NOUN
cana-5707	161	11	)	)	PUNCT
cana-5707	161	12	,	,	PUNCT
cana-5707	161	13	any	any	PRON
cana-5707	161	14	ψα	ψα	ADP
cana-5707	161	15	hbo(z	hbo(z	NUM
cana-5707	161	16	)	)	PUNCT
cana-5707	161	17	is	be	AUX
cana-5707	161	18	ψπ	ψπ	ADP
cana-5707	161	19	hbo(z	hbo(z	NUM
cana-5707	161	20	)	)	PUNCT
cana-5707	161	21	.	.	PUNCT
cana-5707	162	1	proof	proof	NOUN
cana-5707	162	2	.	.	PUNCT
cana-5707	163	1	consider	consider	VERB
cana-5707	163	2	a	a	DET
cana-5707	163	3	subset	subset	NOUN
cana-5707	163	4	b	b	NOUN
cana-5707	163	5	of	of	ADP
cana-5707	163	6	h	h	NOUN
cana-5707	163	7	-	-	PUNCT
cana-5707	163	8	gts	gts	NOUN
cana-5707	163	9	(	(	PUNCT
cana-5707	163	10	z	z	NOUN
cana-5707	163	11	,	,	PUNCT
cana-5707	163	12	ϑ	ϑ	X
cana-5707	163	13	,	,	PUNCT
cana-5707	163	14	h	h	NOUN
cana-5707	163	15	)	)	PUNCT
cana-5707	163	16	is	be	AUX
cana-5707	163	17	ψα	ψα	ADP
cana-5707	163	18	-	-	PUNCT
cana-5707	163	19	hbo(z	hbo(z	NUM
cana-5707	163	20	)	)	PUNCT
cana-5707	163	21	.	.	PUNCT
cana-5707	164	1	then	then	ADV
cana-5707	164	2	,	,	PUNCT
cana-5707	164	3	b⊆iσ	b⊆iσ	PROPN
cana-5707	164	4	cb	cb	PROPN
cana-5707	164	5	∗iσ(b)⊆	∗iσ(b)⊆	PROPN
cana-5707	164	6	iσc∗(b	iσc∗(b	NOUN
cana-5707	164	7	)	)	PUNCT
cana-5707	164	8	.	.	PUNCT
cana-5707	165	1	hence	hence	ADV
cana-5707	165	2	ψπhbo(z	ψπhbo(z	NUM
cana-5707	165	3	)	)	PUNCT
cana-5707	165	4	.	.	PUNCT
cana-5707	166	1	theorem	theorem	VERB
cana-5707	166	2	2.10	2.10	NUM
cana-5707	166	3	.	.	PUNCT
cana-5707	167	1	a	a	DET
cana-5707	167	2	subset	subset	NOUN
cana-5707	167	3	b	b	NOUN
cana-5707	167	4	of	of	ADP
cana-5707	167	5	a	a	DET
cana-5707	167	6	h	h	NOUN
cana-5707	167	7	-	-	PUNCT
cana-5707	167	8	gt	gt	NOUN
cana-5707	167	9	s	s	X
cana-5707	167	10	(	(	PUNCT
cana-5707	167	11	z	z	NOUN
cana-5707	167	12	,	,	PUNCT
cana-5707	167	13	ϑ	ϑ	X
cana-5707	167	14	,	,	PUNCT
cana-5707	167	15	h	h	NOUN
cana-5707	167	16	)	)	PUNCT
cana-5707	167	17	,	,	PUNCT
cana-5707	167	18	the	the	DET
cana-5707	167	19	following	follow	VERB
cana-5707	167	20	results	result	NOUN
cana-5707	167	21	are	be	AUX
cana-5707	167	22	equivalent	equivalent	ADJ
cana-5707	167	23	.	.	PUNCT
cana-5707	168	1	1	1	X
cana-5707	168	2	.	.	X
cana-5707	168	3	ψα	ψα	NOUN
cana-5707	168	4	-	-	PUNCT
cana-5707	168	5	hbo(z	hbo(z	NOUN
cana-5707	168	6	)	)	PUNCT
cana-5707	168	7	2	2	NUM
cana-5707	168	8	.	.	X
cana-5707	168	9	ψσhbo(z	ψσhbo(z	NOUN
cana-5707	168	10	)	)	PUNCT
cana-5707	168	11	and	and	CCONJ
cana-5707	168	12	ψπ	ψπ	NOUN
cana-5707	168	13	-	-	PUNCT
cana-5707	168	14	hbo(z	hbo(z	NUM
cana-5707	168	15	)	)	PUNCT
cana-5707	168	16	.	.	PUNCT
cana-5707	169	1	proof	proof	NOUN
cana-5707	169	2	.	.	PUNCT
cana-5707	170	1	(	(	PUNCT
cana-5707	170	2	1)⇒(2	1)⇒(2	NUM
cana-5707	170	3	)	)	PUNCT
cana-5707	170	4	.	.	PUNCT
cana-5707	171	1	consider	consider	VERB
cana-5707	171	2	b	b	NOUN
cana-5707	171	3	is	be	AUX
cana-5707	171	4	ψα	ψα	ADP
cana-5707	171	5	-	-	PUNCT
cana-5707	171	6	hbo(z	hbo(z	NUM
cana-5707	171	7	)	)	PUNCT
cana-5707	171	8	.	.	PUNCT
cana-5707	172	1	then	then	ADV
cana-5707	172	2	by	by	ADP
cana-5707	172	3	theorem	theorem	ADJ
cana-5707	172	4	2.8	2.8	NUM
cana-5707	172	5	and	and	CCONJ
cana-5707	172	6	2.9	2.9	NUM
cana-5707	172	7	,	,	PUNCT
cana-5707	172	8	ψσ	ψσ	NOUN
cana-5707	172	9	-	-	PUNCT
cana-5707	172	10	hbo(z	hbo(z	NUM
cana-5707	172	11	)	)	PUNCT
cana-5707	172	12	and	and	CCONJ
cana-5707	172	13	ψπ	ψπ	NOUN
cana-5707	172	14	-	-	PUNCT
cana-5707	172	15	hbo(z	hbo(z	NUM
cana-5707	172	16	)	)	PUNCT
cana-5707	172	17	.	.	PUNCT
cana-5707	173	1	(	(	PUNCT
cana-5707	173	2	2	2	X
cana-5707	173	3	)	)	PUNCT
cana-5707	173	4	⇒	⇒	NOUN
cana-5707	173	5	(	(	PUNCT
cana-5707	173	6	1	1	NUM
cana-5707	173	7	)	)	PUNCT
cana-5707	173	8	.	.	PUNCT
cana-5707	174	1	consider	consider	VERB
cana-5707	174	2	b	b	NOUN
cana-5707	174	3	is	be	AUX
cana-5707	174	4	both	both	PRON
cana-5707	174	5	ψσ	ψσ	ADJ
cana-5707	174	6	-	-	PUNCT
cana-5707	174	7	hbo(z	hbo(z	NUM
cana-5707	174	8	)	)	PUNCT
cana-5707	174	9	and	and	CCONJ
cana-5707	174	10	ψπ	ψπ	NOUN
cana-5707	174	11	-	-	PUNCT
cana-5707	174	12	hbo(z	hbo(z	NUM
cana-5707	174	13	)	)	PUNCT
cana-5707	174	14	.	.	PUNCT
cana-5707	175	1	then	then	ADV
cana-5707	175	2	b⊆iσ	b⊆iσ	PROPN
cana-5707	175	3	cb	cb	PROPN
cana-5707	175	4	∗(b	∗(b	PROPN
cana-5707	175	5	)	)	PUNCT
cana-5707	175	6	⊆	⊆	NUM
cana-5707	175	7	iσ	iσ	ADP
cana-5707	175	8	cb	cb	PROPN
cana-5707	175	9	∗	∗	PROPN
cana-5707	175	10	cb	cb	PROPN
cana-5707	175	11	∗iσ(b	∗iσ(b	PROPN
cana-5707	175	12	)	)	PUNCT
cana-5707	175	13	⊆	⊆	NUM
cana-5707	175	14	iσ	iσ	ADP
cana-5707	175	15	cb	cb	PROPN
cana-5707	175	16	∗iσ(b	∗iσ(b	PROPN
cana-5707	175	17	)	)	PUNCT
cana-5707	175	18	.	.	PUNCT
cana-5707	176	1	hence	hence	ADV
cana-5707	176	2	ψα	ψα	ADP
cana-5707	176	3	-	-	PUNCT
cana-5707	176	4	hbo(z	hbo(z	NUM
cana-5707	176	5	)	)	PUNCT
cana-5707	176	6	.	.	PUNCT
cana-5707	177	1	example	example	NOUN
cana-5707	177	2	2.11	2.11	NUM
cana-5707	177	3	.	.	PUNCT
cana-5707	178	1	consider	consider	VERB
cana-5707	178	2	z={z1	z={z1	NOUN
cana-5707	178	3	,	,	PUNCT
cana-5707	178	4	z2	z2	PROPN
cana-5707	178	5	,	,	PUNCT
cana-5707	178	6	z3	z3	PROPN
cana-5707	178	7	,	,	PUNCT
cana-5707	178	8	z4	z4	PROPN
cana-5707	178	9	,	,	PUNCT
cana-5707	178	10	z5	z5	PROPN
cana-5707	178	11	}	}	PUNCT
cana-5707	178	12	,	,	PUNCT
cana-5707	178	13	ϑ={∅	ϑ={∅	PROPN
cana-5707	178	14	,	,	PUNCT
cana-5707	178	15	{	{	PUNCT
cana-5707	178	16	z1	z1	NOUN
cana-5707	178	17	}	}	PUNCT
cana-5707	178	18	,	,	PUNCT
cana-5707	178	19	{	{	PUNCT
cana-5707	178	20	z2	z2	NOUN
cana-5707	178	21	}	}	PUNCT
cana-5707	178	22	,	,	PUNCT
cana-5707	178	23	{	{	PUNCT
cana-5707	178	24	z3	z3	NOUN
cana-5707	178	25	}	}	PUNCT
cana-5707	178	26	,	,	PUNCT
cana-5707	178	27	{	{	PUNCT
cana-5707	178	28	z1	z1	NOUN
cana-5707	178	29	,	,	PUNCT
cana-5707	178	30	z2	z2	PROPN
cana-5707	178	31	}	}	PUNCT
cana-5707	178	32	,	,	PUNCT
cana-5707	178	33	{	{	PUNCT
cana-5707	178	34	z1	z1	NOUN
cana-5707	178	35	,	,	PUNCT
cana-5707	178	36	z3	z3	PROPN
cana-5707	178	37	}	}	PUNCT
cana-5707	178	38	,	,	PUNCT
cana-5707	178	39	{	{	PUNCT
cana-5707	178	40	z2	z2	NOUN
cana-5707	178	41	,	,	PUNCT
cana-5707	178	42	z3	z3	PROPN
cana-5707	178	43	}	}	PUNCT
cana-5707	178	44	,	,	PUNCT
cana-5707	178	45	{	{	PUNCT
cana-5707	178	46	z1	z1	NOUN
cana-5707	178	47	,	,	PUNCT
cana-5707	178	48	z2	z2	PROPN
cana-5707	178	49	,	,	PUNCT
cana-5707	178	50	z3	z3	PROPN
cana-5707	178	51	}	}	PUNCT
cana-5707	178	52	,	,	PUNCT
cana-5707	178	53	{	{	PUNCT
cana-5707	178	54	z1	z1	NOUN
cana-5707	178	55	,	,	PUNCT
cana-5707	178	56	z3	z3	PROPN
cana-5707	178	57	,	,	PUNCT
cana-5707	178	58	z4	z4	PROPN
cana-5707	178	59	}	}	PUNCT
cana-5707	178	60	,	,	PUNCT
cana-5707	178	61	{	{	PUNCT
cana-5707	178	62	z1	z1	NOUN
cana-5707	178	63	,	,	PUNCT
cana-5707	178	64	z2	z2	PROPN
cana-5707	178	65	,	,	PUNCT
cana-5707	178	66	z3	z3	PROPN
cana-5707	178	67	}	}	PUNCT
cana-5707	178	68	,	,	PUNCT
cana-5707	178	69	{	{	PUNCT
cana-5707	178	70	z1	z1	NOUN
cana-5707	178	71	,	,	PUNCT
cana-5707	178	72	z2	z2	PROPN
cana-5707	178	73	,	,	PUNCT
cana-5707	178	74	z3	z3	PROPN
cana-5707	178	75	,	,	PUNCT
cana-5707	178	76	z4	z4	PROPN
cana-5707	178	77	}	}	PUNCT
cana-5707	178	78	}	}	PUNCT
cana-5707	178	79	,	,	PUNCT
cana-5707	178	80	h={∅	h={∅	PROPN
cana-5707	178	81	,	,	PUNCT
cana-5707	178	82	{	{	PUNCT
cana-5707	178	83	z1	z1	NOUN
cana-5707	178	84	}	}	PUNCT
cana-5707	178	85	}	}	PUNCT
cana-5707	178	86	.	.	PUNCT
cana-5707	179	1	then	then	ADV
cana-5707	179	2	b	b	X
cana-5707	179	3	=	=	SYM
cana-5707	179	4	{	{	PUNCT
cana-5707	179	5	z1	z1	PROPN
cana-5707	179	6	}	}	PUNCT
cana-5707	179	7	,	,	PUNCT
cana-5707	179	8	{	{	PUNCT
cana-5707	179	9	z5	z5	NOUN
cana-5707	179	10	}	}	PUNCT
cana-5707	179	11	}	}	PUNCT
cana-5707	179	12	is	be	AUX
cana-5707	179	13	ψσ	ψσ	ADJ
cana-5707	179	14	-	-	PUNCT
cana-5707	179	15	hbo(z	hbo(z	NUM
cana-5707	179	16	)	)	PUNCT
cana-5707	179	17	but	but	CCONJ
cana-5707	179	18	not	not	PART
cana-5707	179	19	ψα	ψα	VERB
cana-5707	179	20	-	-	PUNCT
cana-5707	179	21	hbo(z	hbo(z	NUM
cana-5707	179	22	)	)	PUNCT
cana-5707	179	23	.	.	PUNCT
cana-5707	180	1	example	example	NOUN
cana-5707	181	1	2.12	2.12	NUM
cana-5707	181	2	.	.	PUNCT
cana-5707	182	1	consider	consider	VERB
cana-5707	182	2	z={z1	z={z1	NOUN
cana-5707	182	3	,	,	PUNCT
cana-5707	182	4	z2	z2	PROPN
cana-5707	182	5	,	,	PUNCT
cana-5707	182	6	z3	z3	PROPN
cana-5707	182	7	,	,	PUNCT
cana-5707	182	8	z4	z4	PROPN
cana-5707	182	9	}	}	PUNCT
cana-5707	182	10	,	,	PUNCT
cana-5707	182	11	ϑ={∅	ϑ={∅	PROPN
cana-5707	182	12	,	,	PUNCT
cana-5707	182	13	{	{	PUNCT
cana-5707	182	14	z1	z1	NOUN
cana-5707	182	15	,	,	PUNCT
cana-5707	182	16	z3	z3	PROPN
cana-5707	182	17	}	}	PUNCT
cana-5707	182	18	,	,	PUNCT
cana-5707	182	19	{	{	PUNCT
cana-5707	182	20	z4	z4	X
cana-5707	182	21	}	}	PUNCT
cana-5707	182	22	,	,	PUNCT
cana-5707	182	23	{	{	PUNCT
cana-5707	182	24	z1	z1	NOUN
cana-5707	182	25	,	,	PUNCT
cana-5707	182	26	z3	z3	PROPN
cana-5707	182	27	,	,	PUNCT
cana-5707	182	28	z4	z4	PROPN
cana-5707	182	29	}	}	PUNCT
cana-5707	182	30	,	,	PUNCT
cana-5707	182	31	z	z	NOUN
cana-5707	182	32	}	}	PUNCT
cana-5707	182	33	h={∅	h={∅	PROPN
cana-5707	182	34	,	,	PUNCT
cana-5707	182	35	{	{	PUNCT
cana-5707	182	36	z3	z3	NOUN
cana-5707	182	37	}	}	PUNCT
cana-5707	182	38	}	}	PUNCT
cana-5707	182	39	.	.	PUNCT
cana-5707	183	1	then	then	ADV
cana-5707	183	2	b={z1	b={z1	PROPN
cana-5707	183	3	,	,	PUNCT
cana-5707	183	4	z2	z2	PROPN
cana-5707	183	5	,	,	PUNCT
cana-5707	183	6	z4	z4	PROPN
cana-5707	183	7	}	}	PUNCT
cana-5707	183	8	is	be	AUX
cana-5707	183	9	ψπ	ψπ	ADJ
cana-5707	183	10	-	-	PUNCT
cana-5707	183	11	hbo(z	hbo(z	NUM
cana-5707	183	12	)	)	PUNCT
cana-5707	183	13	but	but	CCONJ
cana-5707	183	14	not	not	PART
cana-5707	183	15	ψα	ψα	VERB
cana-5707	183	16	-	-	PUNCT
cana-5707	183	17	hbo(z	hbo(z	NUM
cana-5707	183	18	)	)	PUNCT
cana-5707	183	19	.	.	PUNCT
cana-5707	184	1	remark	remark	PROPN
cana-5707	184	2	2.13	2.13	NUM
cana-5707	184	3	.	.	PUNCT
cana-5707	185	1	the	the	DET
cana-5707	185	2	notions	notion	NOUN
cana-5707	185	3	of	of	ADP
cana-5707	185	4	ψσ	ψσ	ADP
cana-5707	185	5	hbo(z	hbo(z	NUM
cana-5707	185	6	)	)	PUNCT
cana-5707	185	7	and	and	CCONJ
cana-5707	185	8	ψπ	ψπ	NOUN
cana-5707	185	9	-	-	PUNCT
cana-5707	185	10	hbo(z	hbo(z	NUM
cana-5707	185	11	)	)	PUNCT
cana-5707	185	12	are	be	AUX
cana-5707	185	13	independent	independent	ADJ
cana-5707	185	14	.	.	PUNCT
cana-5707	185	15	example	example	NOUN
cana-5707	185	16	2.14	2.14	NUM
cana-5707	185	17	.	.	PUNCT
cana-5707	186	1	consider	consider	VERB
cana-5707	186	2	z	z	NOUN
cana-5707	186	3	=	=	SYM
cana-5707	186	4	{	{	PUNCT
cana-5707	186	5	z1	z1	PROPN
cana-5707	186	6	,	,	PUNCT
cana-5707	186	7	z2	z2	PROPN
cana-5707	186	8	,	,	PUNCT
cana-5707	186	9	z3	z3	PROPN
cana-5707	186	10	,	,	PUNCT
cana-5707	186	11	z4	z4	PROPN
cana-5707	186	12	,	,	PUNCT
cana-5707	186	13	z5	z5	PROPN
cana-5707	186	14	}	}	PUNCT
cana-5707	186	15	,	,	PUNCT
cana-5707	186	16	ϑ	ϑ	X
cana-5707	186	17	=	=	X
cana-5707	186	18	{	{	PUNCT
cana-5707	186	19	∅	∅	NOUN
cana-5707	186	20	,	,	PUNCT
cana-5707	186	21	{	{	PUNCT
cana-5707	186	22	z1	z1	NOUN
cana-5707	186	23	}	}	PUNCT
cana-5707	186	24	,	,	PUNCT
cana-5707	186	25	{	{	PUNCT
cana-5707	186	26	z2	z2	NOUN
cana-5707	186	27	}	}	PUNCT
cana-5707	186	28	,	,	PUNCT
cana-5707	186	29	{	{	PUNCT
cana-5707	186	30	z3	z3	NOUN
cana-5707	186	31	}	}	PUNCT
cana-5707	186	32	,	,	PUNCT
cana-5707	186	33	{	{	PUNCT
cana-5707	186	34	z1	z1	NOUN
cana-5707	186	35	,	,	PUNCT
cana-5707	186	36	z2	z2	PROPN
cana-5707	186	37	}	}	PUNCT
cana-5707	186	38	,	,	PUNCT
cana-5707	186	39	{	{	PUNCT
cana-5707	186	40	z1	z1	NOUN
cana-5707	186	41	,	,	PUNCT
cana-5707	186	42	z3	z3	PROPN
cana-5707	186	43	}	}	PUNCT
cana-5707	186	44	,	,	PUNCT
cana-5707	186	45	{	{	PUNCT
cana-5707	186	46	z2	z2	NOUN
cana-5707	186	47	,	,	PUNCT
cana-5707	186	48	z3	z3	PROPN
cana-5707	186	49	}	}	PUNCT
cana-5707	186	50	,	,	PUNCT
cana-5707	186	51	{	{	PUNCT
cana-5707	186	52	z1	z1	NOUN
cana-5707	186	53	,	,	PUNCT
cana-5707	186	54	z2	z2	PROPN
cana-5707	186	55	,	,	PUNCT
cana-5707	186	56	z3	z3	PROPN
cana-5707	186	57	}	}	PUNCT
cana-5707	186	58	,	,	PUNCT
cana-5707	186	59	{	{	PUNCT
cana-5707	186	60	z1	z1	NOUN
cana-5707	186	61	,	,	PUNCT
cana-5707	186	62	z3	z3	PROPN
cana-5707	186	63	,	,	PUNCT
cana-5707	186	64	z4	z4	PROPN
cana-5707	186	65	}	}	PUNCT
cana-5707	186	66	,	,	PUNCT
cana-5707	186	67	{	{	PUNCT
cana-5707	186	68	z2	z2	NOUN
cana-5707	186	69	,	,	PUNCT
cana-5707	186	70	z3	z3	PROPN
cana-5707	186	71	,	,	PUNCT
cana-5707	186	72	z4	z4	PROPN
cana-5707	186	73	}	}	PUNCT
cana-5707	186	74	,	,	PUNCT
cana-5707	186	75	{	{	PUNCT
cana-5707	186	76	z1	z1	NOUN
cana-5707	186	77	,	,	PUNCT
cana-5707	186	78	z2	z2	PROPN
cana-5707	186	79	,	,	PUNCT
cana-5707	186	80	z3	z3	PROPN
cana-5707	186	81	,	,	PUNCT
cana-5707	186	82	z4	z4	PROPN
cana-5707	186	83	}	}	PUNCT
cana-5707	186	84	}	}	PUNCT
cana-5707	186	85	,	,	PUNCT
cana-5707	186	86	h	h	NOUN
cana-5707	186	87	=	=	PRON
cana-5707	186	88	{	{	PUNCT
cana-5707	186	89	∅	∅	NOUN
cana-5707	186	90	,	,	PUNCT
cana-5707	186	91	{	{	PUNCT
cana-5707	186	92	z1	z1	NOUN
cana-5707	186	93	}	}	PUNCT
cana-5707	186	94	}	}	PUNCT
cana-5707	186	95	.	.	PUNCT
cana-5707	187	1	then	then	ADV
cana-5707	187	2	b	b	X
cana-5707	187	3	=	=	SYM
cana-5707	187	4	{	{	PUNCT
cana-5707	187	5	z1	z1	PROPN
cana-5707	187	6	,	,	PUNCT
cana-5707	187	7	z3	z3	PROPN
cana-5707	187	8	}	}	PUNCT
cana-5707	187	9	is	be	AUX
cana-5707	187	10	ψσ	ψσ	ADJ
cana-5707	187	11	-	-	PUNCT
cana-5707	187	12	hbo(z	hbo(z	NUM
cana-5707	187	13	)	)	PUNCT
cana-5707	187	14	but	but	CCONJ
cana-5707	187	15	not	not	PART
cana-5707	187	16	ψπ	ψπ	VERB
cana-5707	187	17	-	-	PUNCT
cana-5707	187	18	hbo(z	hbo(z	NUM
cana-5707	187	19	)	)	PUNCT
cana-5707	187	20	.	.	PUNCT
cana-5707	188	1	example	example	NOUN
cana-5707	188	2	2.15	2.15	NUM
cana-5707	188	3	.	.	PUNCT
cana-5707	189	1	consider	consider	VERB
cana-5707	189	2	z	z	NOUN
cana-5707	189	3	=	=	SYM
cana-5707	189	4	{	{	PUNCT
cana-5707	189	5	z1	z1	PROPN
cana-5707	189	6	,	,	PUNCT
cana-5707	189	7	z2	z2	PROPN
cana-5707	189	8	,	,	PUNCT
cana-5707	189	9	z3	z3	PROPN
cana-5707	189	10	,	,	PUNCT
cana-5707	189	11	z4	z4	PROPN
cana-5707	189	12	}	}	PUNCT
cana-5707	189	13	ϑ	ϑ	X
cana-5707	189	14	=	=	PUNCT
cana-5707	189	15	{	{	PUNCT
cana-5707	189	16	∅	∅	NOUN
cana-5707	189	17	,	,	PUNCT
cana-5707	189	18	{	{	PUNCT
cana-5707	189	19	z1	z1	NOUN
cana-5707	189	20	,	,	PUNCT
cana-5707	189	21	z3	z3	PROPN
cana-5707	189	22	}	}	PUNCT
cana-5707	189	23	,	,	PUNCT
cana-5707	189	24	{	{	PUNCT
cana-5707	189	25	z4	z4	X
cana-5707	189	26	}	}	PUNCT
cana-5707	189	27	,	,	PUNCT
cana-5707	189	28	{	{	PUNCT
cana-5707	189	29	z1	z1	NOUN
cana-5707	189	30	,	,	PUNCT
cana-5707	189	31	z3	z3	PROPN
cana-5707	189	32	,	,	PUNCT
cana-5707	189	33	z4	z4	PROPN
cana-5707	189	34	}	}	PUNCT
cana-5707	189	35	,	,	PUNCT
cana-5707	189	36	z	z	NOUN
cana-5707	189	37	}	}	PUNCT
cana-5707	189	38	,	,	PUNCT
cana-5707	189	39	h	h	NOUN
cana-5707	189	40	=	=	PRON
cana-5707	189	41	{	{	PUNCT
cana-5707	189	42	∅	∅	NOUN
cana-5707	189	43	,	,	PUNCT
cana-5707	189	44	{	{	PUNCT
cana-5707	189	45	z3	z3	NOUN
cana-5707	189	46	}	}	PUNCT
cana-5707	189	47	}	}	PUNCT
cana-5707	189	48	.	.	PUNCT
cana-5707	190	1	then	then	ADV
cana-5707	190	2	b	b	X
cana-5707	190	3	=	=	SYM
cana-5707	190	4	{	{	PUNCT
cana-5707	190	5	z1	z1	PROPN
cana-5707	190	6	,	,	PUNCT
cana-5707	190	7	z3	z3	PROPN
cana-5707	190	8	,	,	PUNCT
cana-5707	190	9	z4	z4	PROPN
cana-5707	190	10	}	}	PUNCT
cana-5707	190	11	is	be	AUX
cana-5707	190	12	ψπ	ψπ	ADJ
cana-5707	190	13	-	-	PUNCT
cana-5707	190	14	hbo(z	hbo(z	NUM
cana-5707	190	15	)	)	PUNCT
cana-5707	190	16	but	but	CCONJ
cana-5707	190	17	not	not	PART
cana-5707	190	18	ψσ	ψσ	VERB
cana-5707	190	19	-	-	PUNCT
cana-5707	190	20	hbo(z	hbo(z	NUM
cana-5707	190	21	)	)	PUNCT
cana-5707	190	22	.	.	PUNCT
cana-5707	191	1	theorem	theorem	VERB
cana-5707	191	2	2.16	2.16	NUM
cana-5707	191	3	.	.	PUNCT
cana-5707	192	1	any	any	DET
cana-5707	192	2	ψπ	ψπ	NOUN
cana-5707	192	3	-	-	PUNCT
cana-5707	192	4	hbo(z	hbo(z	NOUN
cana-5707	192	5	)	)	PUNCT
cana-5707	192	6	set	set	NOUN
cana-5707	192	7	is	be	AUX
cana-5707	192	8	ψβ	ψβ	PROPN
cana-5707	192	9	-	-	PUNCT
cana-5707	192	10	hbo(z	hbo(z	PROPN
cana-5707	192	11	)	)	PUNCT
cana-5707	192	12	set	set	NOUN
cana-5707	192	13	.	.	PUNCT
cana-5707	193	1	proof	proof	NOUN
cana-5707	193	2	.	.	PUNCT
cana-5707	194	1	consider	consider	VERB
cana-5707	194	2	a	a	DET
cana-5707	194	3	subset	subset	NOUN
cana-5707	194	4	b	b	NOUN
cana-5707	194	5	of	of	ADP
cana-5707	194	6	h	h	NOUN
cana-5707	194	7	-	-	PUNCT
cana-5707	194	8	gts	gts	NOUN
cana-5707	194	9	(	(	PUNCT
cana-5707	194	10	z	z	NOUN
cana-5707	194	11	,	,	PUNCT
cana-5707	194	12	ϑ	ϑ	X
cana-5707	194	13	,	,	PUNCT
cana-5707	194	14	h	h	NOUN
cana-5707	194	15	)	)	PUNCT
cana-5707	194	16	is	be	AUX
cana-5707	194	17	ψπ	ψπ	NOUN
cana-5707	194	18	-	-	PUNCT
cana-5707	194	19	hbo(z	hbo(z	NUM
cana-5707	194	20	)	)	PUNCT
cana-5707	194	21	.	.	PUNCT
cana-5707	195	1	then	then	ADV
cana-5707	195	2	b⊆iσcb	b⊆iσcb	NOUN
cana-5707	195	3	∗(b)⊆cϑiσcb	∗(b)⊆cϑiσcb	ADV
cana-5707	195	4	∗(b	∗(b	PROPN
cana-5707	195	5	)	)	PUNCT
cana-5707	195	6	.	.	PUNCT
cana-5707	196	1	hence	hence	ADV
cana-5707	196	2	b	b	PROPN
cana-5707	196	3	is	be	AUX
cana-5707	196	4	ψβhbo(z	ψβhbo(z	NOUN
cana-5707	196	5	)	)	PUNCT
cana-5707	196	6	.	.	PUNCT
cana-5707	197	1	theorem	theorem	VERB
cana-5707	197	2	2.17	2.17	NUM
cana-5707	197	3	.	.	PUNCT
cana-5707	198	1	any	any	DET
cana-5707	198	2	ψα	ψα	NOUN
cana-5707	198	3	-	-	PUNCT
cana-5707	198	4	hbo(z	hbo(z	NOUN
cana-5707	198	5	)	)	PUNCT
cana-5707	198	6	set	set	NOUN
cana-5707	198	7	is	be	AUX
cana-5707	198	8	ψβ	ψβ	PROPN
cana-5707	198	9	-	-	PUNCT
cana-5707	198	10	hbo(z	hbo(z	PROPN
cana-5707	198	11	)	)	PUNCT
cana-5707	198	12	set	set	NOUN
cana-5707	198	13	.	.	PUNCT
cana-5707	199	1	communications	communication	NOUN
cana-5707	199	2	on	on	ADP
cana-5707	199	3	applied	apply	VERB
cana-5707	199	4	nonlinear	nonlinear	ADJ
cana-5707	199	5	analysis	analysis	NOUN
cana-5707	199	6	issn	issn	NOUN
cana-5707	199	7	:	:	PUNCT
cana-5707	199	8	1074	1074	NUM
cana-5707	199	9	-	-	PUNCT
cana-5707	199	10	133x	133x	NUM
cana-5707	199	11	vol	vol	VERB
cana-5707	199	12	32	32	NUM
cana-5707	199	13	no	no	NOUN
cana-5707	199	14	.	.	PUNCT
cana-5707	200	1	10s	10	NOUN
cana-5707	200	2	(	(	PUNCT
cana-5707	200	3	2025	2025	NUM
cana-5707	200	4	)	)	PUNCT
cana-5707	200	5	2665	2665	NUM
cana-5707	200	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5707	200	7	proof	proof	NOUN
cana-5707	200	8	.	.	PUNCT
cana-5707	201	1	consider	consider	VERB
cana-5707	201	2	a	a	DET
cana-5707	201	3	subset	subset	NOUN
cana-5707	201	4	b	b	NOUN
cana-5707	201	5	of	of	ADP
cana-5707	201	6	h	h	NOUN
cana-5707	201	7	-	-	PUNCT
cana-5707	201	8	gts	gts	NOUN
cana-5707	201	9	(	(	PUNCT
cana-5707	201	10	z	z	NOUN
cana-5707	201	11	,	,	PUNCT
cana-5707	201	12	ϑ	ϑ	X
cana-5707	201	13	,	,	PUNCT
cana-5707	201	14	h	h	NOUN
cana-5707	201	15	)	)	PUNCT
cana-5707	201	16	is	be	AUX
cana-5707	201	17	ψα	ψα	ADP
cana-5707	201	18	-	-	PUNCT
cana-5707	201	19	hbo(z	hbo(z	NUM
cana-5707	201	20	)	)	PUNCT
cana-5707	201	21	.	.	PUNCT
cana-5707	202	1	then	then	ADV
cana-5707	202	2	b⊆iσcb	b⊆iσcb	NOUN
cana-5707	202	3	∗iσ(b)⊆iσc∗(b	∗iσ(b)⊆iσc∗(b	NUM
cana-5707	202	4	)	)	PUNCT
cana-5707	202	5	⊆cϑiσcb	⊆cϑiσcb	ADJ
cana-5707	202	6	∗(b	∗(b	PROPN
cana-5707	202	7	)	)	PUNCT
cana-5707	202	8	.	.	PUNCT
cana-5707	203	1	hence	hence	ADV
cana-5707	203	2	b	b	PROPN
cana-5707	203	3	is	be	AUX
cana-5707	203	4	ψβ	ψβ	PROPN
cana-5707	203	5	-	-	PUNCT
cana-5707	203	6	hbo(z	hbo(z	PROPN
cana-5707	203	7	)	)	PUNCT
cana-5707	203	8	.	.	PUNCT
cana-5707	204	1	theorem	theorem	VERB
cana-5707	204	2	2.18	2.18	NUM
cana-5707	204	3	.	.	PUNCT
cana-5707	205	1	any	any	DET
cana-5707	205	2	ψσ	ψσ	NOUN
cana-5707	205	3	-	-	PUNCT
cana-5707	205	4	hbo(z	hbo(z	NOUN
cana-5707	205	5	)	)	PUNCT
cana-5707	205	6	set	set	NOUN
cana-5707	205	7	is	be	AUX
cana-5707	205	8	ψβ	ψβ	PROPN
cana-5707	205	9	-	-	PUNCT
cana-5707	205	10	hbo(z	hbo(z	PROPN
cana-5707	205	11	)	)	PUNCT
cana-5707	205	12	set	set	NOUN
cana-5707	205	13	.	.	PUNCT
cana-5707	206	1	proof	proof	NOUN
cana-5707	206	2	.	.	PUNCT
cana-5707	207	1	consider	consider	VERB
cana-5707	207	2	a	a	DET
cana-5707	207	3	subset	subset	NOUN
cana-5707	207	4	b	b	NOUN
cana-5707	207	5	of	of	ADP
cana-5707	207	6	h	h	NOUN
cana-5707	207	7	-	-	PUNCT
cana-5707	207	8	gts	gts	NOUN
cana-5707	207	9	(	(	PUNCT
cana-5707	207	10	z	z	NOUN
cana-5707	207	11	,	,	PUNCT
cana-5707	207	12	ϑ	ϑ	X
cana-5707	207	13	,	,	PUNCT
cana-5707	207	14	h	h	NOUN
cana-5707	207	15	)	)	PUNCT
cana-5707	207	16	is	be	AUX
cana-5707	207	17	ψσ	ψσ	ADJ
cana-5707	207	18	-	-	PUNCT
cana-5707	207	19	hbo(z	hbo(z	NUM
cana-5707	207	20	)	)	PUNCT
cana-5707	207	21	.	.	PUNCT
cana-5707	208	1	then	then	ADV
cana-5707	208	2	b⊆cb	b⊆cb	PROPN
cana-5707	208	3	∗iσ(b)⊆cϑ	∗iσ(b)⊆cϑ	PROPN
cana-5707	208	4	∗	∗	NOUN
cana-5707	208	5	iσ(b)⊆cϑiσ(b)⊆cϑiσcb	iσ(b)⊆cϑiσ(b)⊆cϑiσcb	CCONJ
cana-5707	208	6	∗(b	∗(b	NOUN
cana-5707	208	7	)	)	PUNCT
cana-5707	208	8	.	.	PUNCT
cana-5707	209	1	hence	hence	ADV
cana-5707	209	2	b	b	PROPN
cana-5707	209	3	is	be	AUX
cana-5707	209	4	ψβ	ψβ	PROPN
cana-5707	209	5	-	-	PUNCT
cana-5707	209	6	hbo(z	hbo(z	PROPN
cana-5707	209	7	)	)	PUNCT
cana-5707	209	8	.	.	PUNCT
cana-5707	210	1	theorem	theorem	VERB
cana-5707	210	2	2.19	2.19	NUM
cana-5707	210	3	.	.	PUNCT
cana-5707	211	1	any	any	DET
cana-5707	211	2	ψσ	ψσ	ADP
cana-5707	211	3	hbo(z	hbo(z	NUM
cana-5707	211	4	)	)	PUNCT
cana-5707	211	5	set	set	NOUN
cana-5707	211	6	is	be	AUX
cana-5707	211	7	ψb	ψb	ADV
cana-5707	211	8	hbo(z	hbo(z	NUM
cana-5707	211	9	)	)	PUNCT
cana-5707	211	10	set	set	NOUN
cana-5707	211	11	.	.	PUNCT
cana-5707	212	1	proof	proof	NOUN
cana-5707	212	2	.	.	PUNCT
cana-5707	213	1	consider	consider	VERB
cana-5707	213	2	a	a	DET
cana-5707	213	3	subset	subset	NOUN
cana-5707	213	4	b	b	NOUN
cana-5707	213	5	of	of	ADP
cana-5707	213	6	h	h	NOUN
cana-5707	213	7	-	-	PUNCT
cana-5707	213	8	gts	gts	NOUN
cana-5707	213	9	(	(	PUNCT
cana-5707	213	10	z	z	NOUN
cana-5707	213	11	,	,	PUNCT
cana-5707	213	12	ϑ	ϑ	X
cana-5707	213	13	,	,	PUNCT
cana-5707	213	14	h	h	NOUN
cana-5707	213	15	)	)	PUNCT
cana-5707	213	16	is	be	AUX
cana-5707	213	17	ψσ	ψσ	ADJ
cana-5707	213	18	-	-	PUNCT
cana-5707	213	19	hbo(z	hbo(z	NUM
cana-5707	213	20	)	)	PUNCT
cana-5707	213	21	.	.	PUNCT
cana-5707	214	1	then	then	ADV
cana-5707	214	2	b⊆cb	b⊆cb	ADP
cana-5707	214	3	∗iσ(b	∗iσ(b	PROPN
cana-5707	214	4	)	)	PUNCT
cana-5707	214	5	⊆	⊆	NUM
cana-5707	214	6	cb	cb	PROPN
cana-5707	214	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	214	8	)	)	PUNCT
cana-5707	214	9	∪	∪	VERB
cana-5707	214	10	iσcb	iσcb	ADJ
cana-5707	214	11	∗(b	∗(b	PROPN
cana-5707	214	12	)	)	PUNCT
cana-5707	214	13	.	.	PUNCT
cana-5707	215	1	hence	hence	ADV
cana-5707	215	2	b	b	X
cana-5707	215	3	is	be	AUX
cana-5707	215	4	ψb	ψb	ADV
cana-5707	215	5	-	-	PUNCT
cana-5707	215	6	hbo(z	hbo(z	NUM
cana-5707	215	7	)	)	PUNCT
cana-5707	215	8	.	.	PUNCT
cana-5707	216	1	theorem	theorem	VERB
cana-5707	216	2	2.20	2.20	NUM
cana-5707	216	3	.	.	PUNCT
cana-5707	217	1	any	any	DET
cana-5707	217	2	ψπ	ψπ	NOUN
cana-5707	217	3	-	-	PUNCT
cana-5707	217	4	hbo(z	hbo(z	NOUN
cana-5707	217	5	)	)	PUNCT
cana-5707	217	6	set	set	NOUN
cana-5707	217	7	is	be	AUX
cana-5707	217	8	ψb	ψb	ADV
cana-5707	217	9	-	-	PUNCT
cana-5707	217	10	hbo(z	hbo(z	NOUN
cana-5707	217	11	)	)	PUNCT
cana-5707	217	12	set	set	NOUN
cana-5707	217	13	.	.	PUNCT
cana-5707	218	1	proof	proof	NOUN
cana-5707	218	2	.	.	PUNCT
cana-5707	219	1	consider	consider	VERB
cana-5707	219	2	a	a	DET
cana-5707	219	3	subset	subset	NOUN
cana-5707	219	4	b	b	NOUN
cana-5707	219	5	of	of	ADP
cana-5707	219	6	h	h	NOUN
cana-5707	219	7	-	-	PUNCT
cana-5707	219	8	gts	gts	NOUN
cana-5707	219	9	(	(	PUNCT
cana-5707	219	10	z	z	NOUN
cana-5707	219	11	,	,	PUNCT
cana-5707	219	12	ϑ	ϑ	X
cana-5707	219	13	,	,	PUNCT
cana-5707	219	14	h	h	NOUN
cana-5707	219	15	)	)	PUNCT
cana-5707	219	16	is	be	AUX
cana-5707	219	17	ψπ	ψπ	NOUN
cana-5707	219	18	-	-	PUNCT
cana-5707	219	19	hbo(z	hbo(z	NUM
cana-5707	219	20	)	)	PUNCT
cana-5707	219	21	.	.	PUNCT
cana-5707	220	1	then	then	ADV
cana-5707	220	2	b⊆iσcb	b⊆iσcb	ADV
cana-5707	220	3	∗(b)⊆cb	∗(b)⊆cb	PUNCT
cana-5707	220	4	∗iσ(b)∪iσcb	∗iσ(b)∪iσcb	PROPN
cana-5707	220	5	∗(b	∗(b	PROPN
cana-5707	220	6	)	)	PUNCT
cana-5707	220	7	.	.	PUNCT
cana-5707	221	1	hence	hence	ADV
cana-5707	221	2	b	b	X
cana-5707	221	3	is	be	AUX
cana-5707	221	4	ψb	ψb	ADV
cana-5707	221	5	-	-	PUNCT
cana-5707	221	6	hbo(z	hbo(z	NUM
cana-5707	221	7	)	)	PUNCT
cana-5707	221	8	.	.	PUNCT
cana-5707	222	1	theorem	theorem	VERB
cana-5707	222	2	2.21	2.21	NUM
cana-5707	222	3	.	.	PUNCT
cana-5707	223	1	if	if	SCONJ
cana-5707	223	2	b⊂z	b⊂z	NOUN
cana-5707	223	3	is	be	AUX
cana-5707	223	4	both	both	PRON
cana-5707	223	5	ψb	ψb	NOUN
cana-5707	223	6	-	-	PUNCT
cana-5707	223	7	hbo(z	hbo(z	NUM
cana-5707	223	8	)	)	PUNCT
cana-5707	223	9	and	and	CCONJ
cana-5707	223	10	ϑ-σ	ϑ-σ	NOUN
cana-5707	223	11	-	-	PUNCT
cana-5707	223	12	open	open	ADJ
cana-5707	223	13	,	,	PUNCT
cana-5707	223	14	then	then	ADV
cana-5707	223	15	it	it	PRON
cana-5707	223	16	is	be	AUX
cana-5707	223	17	ψβ	ψβ	PROPN
cana-5707	223	18	-	-	PUNCT
cana-5707	223	19	hbo(z	hbo(z	PROPN
cana-5707	223	20	)	)	PUNCT
cana-5707	223	21	.	.	PUNCT
cana-5707	224	1	proof	proof	NOUN
cana-5707	224	2	.	.	PUNCT
cana-5707	225	1	let	let	VERB
cana-5707	225	2	b	b	NOUN
cana-5707	225	3	is	be	AUX
cana-5707	225	4	both	both	PRON
cana-5707	225	5	ψb	ψb	NOUN
cana-5707	225	6	-	-	PUNCT
cana-5707	225	7	hbo(z	hbo(z	NUM
cana-5707	225	8	)	)	PUNCT
cana-5707	225	9	and	and	CCONJ
cana-5707	225	10	ϑ-σ	ϑ-σ	NOUN
cana-5707	225	11	-	-	PUNCT
cana-5707	225	12	open	open	ADJ
cana-5707	225	13	.	.	PUNCT
cana-5707	226	1	now	now	ADV
cana-5707	226	2	b⊆iσcb	b⊆iσcb	ADJ
cana-5707	226	3	∗(b	∗(b	PROPN
cana-5707	226	4	)	)	PUNCT
cana-5707	226	5	∪	∪	PROPN
cana-5707	226	6	cb	cb	PROPN
cana-5707	226	7	∗iσ(b)⊆cb	∗iσ(b)⊆cb	PROPN
cana-5707	226	8	∗(b	∗(b	PROPN
cana-5707	226	9	)	)	PUNCT
cana-5707	226	10	and	and	CCONJ
cana-5707	226	11	cϑiϑ(b	cϑiϑ(b	VERB
cana-5707	226	12	)	)	PUNCT
cana-5707	226	13	⊆	⊆	NUM
cana-5707	226	14	cϑiσ(b	cϑiσ(b	NOUN
cana-5707	226	15	)	)	PUNCT
cana-5707	226	16	⊆	⊆	NUM
cana-5707	226	17	cϑiσcb	cϑiσcb	PROPN
cana-5707	226	18	∗(b	∗(b	PROPN
cana-5707	226	19	)	)	PUNCT
cana-5707	226	20	.	.	PUNCT
cana-5707	227	1	hence	hence	ADV
cana-5707	227	2	b	b	PROPN
cana-5707	227	3	is	be	AUX
cana-5707	227	4	ψβ	ψβ	PROPN
cana-5707	227	5	-	-	PUNCT
cana-5707	227	6	hbo(z	hbo(z	PROPN
cana-5707	227	7	)	)	PUNCT
cana-5707	227	8	.	.	PUNCT
cana-5707	228	1	theorem	theorem	VERB
cana-5707	228	2	2.22	2.22	NUM
cana-5707	228	3	.	.	PUNCT
cana-5707	229	1	if	if	SCONJ
cana-5707	229	2	b⊂z	b⊂z	NOUN
cana-5707	229	3	is	be	AUX
cana-5707	229	4	both	both	PRON
cana-5707	229	5	ψb	ψb	NOUN
cana-5707	229	6	-	-	PUNCT
cana-5707	229	7	hbo(z	hbo(z	NUM
cana-5707	229	8	)	)	PUNCT
cana-5707	229	9	and	and	CCONJ
cana-5707	229	10	ϑ-σ	ϑ-σ	NOUN
cana-5707	229	11	-	-	PUNCT
cana-5707	229	12	open	open	ADJ
cana-5707	229	13	,	,	PUNCT
cana-5707	229	14	then	then	ADV
cana-5707	229	15	it	it	PRON
cana-5707	229	16	is	be	AUX
cana-5707	229	17	ϑ-β	ϑ-β	NOUN
cana-5707	229	18	-	-	ADJ
cana-5707	229	19	open	open	ADJ
cana-5707	229	20	.	.	PUNCT
cana-5707	230	1	proof	proof	NOUN
cana-5707	230	2	.	.	PUNCT
cana-5707	231	1	let	let	VERB
cana-5707	231	2	b	b	NOUN
cana-5707	231	3	is	be	AUX
cana-5707	231	4	both	both	PRON
cana-5707	231	5	ψb	ψb	NOUN
cana-5707	231	6	-	-	PUNCT
cana-5707	231	7	hbo(z	hbo(z	NUM
cana-5707	231	8	)	)	PUNCT
cana-5707	231	9	and	and	CCONJ
cana-5707	231	10	ϑ-σ	ϑ-σ	NOUN
cana-5707	231	11	-	-	PUNCT
cana-5707	231	12	open	open	ADJ
cana-5707	231	13	.	.	PUNCT
cana-5707	232	1	then	then	ADV
cana-5707	232	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	232	3	∗(b	∗(b	PROPN
cana-5707	232	4	)	)	PUNCT
cana-5707	232	5	∪	∪	PROPN
cana-5707	232	6	cb	cb	PROPN
cana-5707	232	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	232	8	)	)	PUNCT
cana-5707	232	9	and	and	CCONJ
cana-5707	232	10	b⊆cϑiϑ(b	b⊆cϑiϑ(b	PROPN
cana-5707	232	11	)	)	PUNCT
cana-5707	232	12	.	.	PUNCT
cana-5707	233	1	now	now	ADV
cana-5707	233	2	b⊆iϑcb	b⊆iϑcb	NOUN
cana-5707	233	3	∗(b	∗(b	PROPN
cana-5707	233	4	)	)	PUNCT
cana-5707	233	5	∪cb	∪cb	PROPN
cana-5707	233	6	∗iϑ(b)⊆cb	∗iϑ(b)⊆cb	PUNCT
cana-5707	233	7	∗(b	∗(b	PROPN
cana-5707	233	8	)	)	PUNCT
cana-5707	233	9	,	,	PUNCT
cana-5707	233	10	which	which	PRON
cana-5707	233	11	implies	imply	VERB
cana-5707	233	12	cϑiϑ(b)⊆cϑiϑcb	cϑiϑ(b)⊆cϑiϑcb	PROPN
cana-5707	233	13	∗(b)⊆cϑiϑcb	∗(b)⊆cϑiϑcb	PROPN
cana-5707	233	14	∗	∗	NOUN
cana-5707	233	15	(	(	PUNCT
cana-5707	233	16	b)⊆cϑiϑcϑ(b	b)⊆cϑiϑcϑ(b	ADJ
cana-5707	233	17	)	)	PUNCT
cana-5707	233	18	so	so	ADV
cana-5707	233	19	b⊆cϑiϑ(b)⊆cϑiϑcϑ(b	b⊆cϑiϑ(b)⊆cϑiϑcϑ(b	ADJ
cana-5707	233	20	)	)	PUNCT
cana-5707	233	21	.	.	PUNCT
cana-5707	234	1	hence	hence	ADV
cana-5707	234	2	b	b	PROPN
cana-5707	234	3	is	be	AUX
cana-5707	234	4	ϑ	ϑ	X
cana-5707	234	5	β	β	X
cana-5707	234	6	-open	-open	PROPN
cana-5707	234	7	.	.	PUNCT
cana-5707	235	1	theorem	theorem	VERB
cana-5707	235	2	2.23	2.23	NUM
cana-5707	235	3	.	.	PUNCT
cana-5707	236	1	if	if	SCONJ
cana-5707	236	2	b	b	PROPN
cana-5707	236	3	⊂	⊂	PROPN
cana-5707	236	4	z	z	PROPN
cana-5707	236	5	is	be	AUX
cana-5707	236	6	both	both	PRON
cana-5707	236	7	ψb	ψb	NOUN
cana-5707	236	8	-	-	PUNCT
cana-5707	236	9	hbo(z	hbo(z	NUM
cana-5707	236	10	)	)	PUNCT
cana-5707	236	11	and	and	CCONJ
cana-5707	236	12	ϑ∗	ϑ∗	PROPN
cana-5707	236	13	-closed	-close	VERB
cana-5707	236	14	,	,	PUNCT
cana-5707	236	15	then	then	ADV
cana-5707	236	16	it	it	PRON
cana-5707	236	17	is	be	AUX
cana-5707	236	18	ψσ	ψσ	ADJ
cana-5707	236	19	-	-	PUNCT
cana-5707	236	20	hbo(z	hbo(z	NUM
cana-5707	236	21	)	)	PUNCT
cana-5707	236	22	.	.	PUNCT
cana-5707	237	1	proof	proof	NOUN
cana-5707	237	2	.	.	PUNCT
cana-5707	238	1	let	let	VERB
cana-5707	238	2	b	b	NOUN
cana-5707	238	3	is	be	AUX
cana-5707	238	4	both	both	PRON
cana-5707	238	5	ψb	ψb	NOUN
cana-5707	238	6	-	-	PUNCT
cana-5707	238	7	hbo(z	hbo(z	NUM
cana-5707	238	8	)	)	PUNCT
cana-5707	238	9	and	and	CCONJ
cana-5707	238	10	ϑ∗-closed	ϑ∗-close	VERB
cana-5707	238	11	.	.	PUNCT
cana-5707	239	1	then	then	ADV
cana-5707	239	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	239	3	∗(b	∗(b	PROPN
cana-5707	239	4	)	)	PUNCT
cana-5707	239	5	∪	∪	PROPN
cana-5707	239	6	cb	cb	PROPN
cana-5707	239	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	239	8	)	)	PUNCT
cana-5707	239	9	and	and	CCONJ
cana-5707	239	10	c∗(b)⊆b	c∗(b)⊆b	PROPN
cana-5707	239	11	.	.	PUNCT
cana-5707	240	1	now	now	ADV
cana-5707	240	2	b⊆iσcb	b⊆iσcb	ADV
cana-5707	240	3	∗(b)∪	∗(b)∪	NOUN
cana-5707	240	4	cb	cb	PROPN
cana-5707	240	5	∗iσ(b)⊆cb	∗iσ(b)⊆cb	PROPN
cana-5707	240	6	∗iσ(b)∪iσ(b)=cb	∗iσ(b)∪iσ(b)=cb	PROPN
cana-5707	240	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	240	8	)	)	PUNCT
cana-5707	240	9	.	.	PUNCT
cana-5707	241	1	hence	hence	ADV
cana-5707	241	2	b	b	PROPN
cana-5707	241	3	is	be	AUX
cana-5707	241	4	ψσ	ψσ	ADJ
cana-5707	241	5	-	-	PUNCT
cana-5707	241	6	hbo(z	hbo(z	NUM
cana-5707	241	7	)	)	PUNCT
cana-5707	241	8	.	.	PUNCT
cana-5707	242	1	theorem	theorem	VERB
cana-5707	242	2	2.24	2.24	NUM
cana-5707	242	3	.	.	PUNCT
cana-5707	243	1	if	if	SCONJ
cana-5707	243	2	b⊂z	b⊂z	NOUN
cana-5707	243	3	is	be	AUX
cana-5707	243	4	both	both	PRON
cana-5707	243	5	ψb	ψb	NOUN
cana-5707	243	6	-	-	PUNCT
cana-5707	243	7	hbo(z	hbo(z	NUM
cana-5707	243	8	)	)	PUNCT
cana-5707	243	9	and	and	CCONJ
cana-5707	243	10	ϑ∗-closed	ϑ∗-close	VERB
cana-5707	243	11	,	,	PUNCT
cana-5707	243	12	then	then	ADV
cana-5707	243	13	it	it	PRON
cana-5707	243	14	is	be	AUX
cana-5707	243	15	σ(σ)-open	σ(σ)-open	PROPN
cana-5707	243	16	.	.	PUNCT
cana-5707	244	1	proof	proof	NOUN
cana-5707	244	2	.	.	PUNCT
cana-5707	245	1	let	let	VERB
cana-5707	245	2	b	b	NOUN
cana-5707	245	3	is	be	AUX
cana-5707	245	4	both	both	PRON
cana-5707	245	5	ψb	ψb	NOUN
cana-5707	245	6	-	-	PUNCT
cana-5707	245	7	hbo(z	hbo(z	NUM
cana-5707	245	8	)	)	PUNCT
cana-5707	245	9	and	and	CCONJ
cana-5707	245	10	ϑ∗-closed	ϑ∗-close	VERB
cana-5707	245	11	.	.	PUNCT
cana-5707	246	1	then	then	ADV
cana-5707	246	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	246	3	∗(b	∗(b	PROPN
cana-5707	246	4	)	)	PUNCT
cana-5707	246	5	∪	∪	PROPN
cana-5707	246	6	cb	cb	PROPN
cana-5707	246	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	246	8	)	)	PUNCT
cana-5707	246	9	and	and	CCONJ
cana-5707	246	10	cb	cb	PROPN
cana-5707	246	11	∗(b)⊆b	∗(b)⊆b	PROPN
cana-5707	246	12	.	.	PUNCT
cana-5707	247	1	now	now	ADV
cana-5707	247	2	b⊆iσcb	b⊆iσcb	INTJ
cana-5707	247	3	∗(b)∪cb	∗(b)∪cb	PUNCT
cana-5707	248	1	∗iσ(b)⊆cb	∗iσ(b)⊆cb	PROPN
cana-5707	248	2	∗iσ(b)∪iσ(b)⊆cb	∗iσ(b)∪iσ(b)⊆cb	PROPN
cana-5707	248	3	∗iσ(b)⊆cb	∗iσ(b)⊆cb	PROPN
cana-5707	248	4	∗	∗	NOUN
cana-5707	248	5	iσ(b)⊆cσiσ(b	iσ(b)⊆cσiσ(b	PROPN
cana-5707	248	6	)	)	PUNCT
cana-5707	248	7	.	.	PUNCT
cana-5707	249	1	hence	hence	ADV
cana-5707	249	2	b	b	PROPN
cana-5707	249	3	is	be	AUX
cana-5707	249	4	σ(σ)-open	σ(σ)-open	PROPN
cana-5707	249	5	.	.	PUNCT
cana-5707	250	1	theorem	theorem	VERB
cana-5707	250	2	2.25	2.25	NUM
cana-5707	250	3	.	.	PUNCT
cana-5707	251	1	if	if	SCONJ
cana-5707	251	2	b⊂z	b⊂z	NOUN
cana-5707	251	3	is	be	AUX
cana-5707	251	4	both	both	PRON
cana-5707	251	5	ψb	ψb	NOUN
cana-5707	251	6	-	-	PUNCT
cana-5707	251	7	hbo(z	hbo(z	NUM
cana-5707	251	8	)	)	PUNCT
cana-5707	251	9	and	and	CCONJ
cana-5707	251	10	bϑ∗-closed	bϑ∗-close	VERB
cana-5707	251	11	,	,	PUNCT
cana-5707	251	12	then	then	ADV
cana-5707	251	13	it	it	PRON
cana-5707	251	14	is	be	AUX
cana-5707	251	15	ψσ	ψσ	ADJ
cana-5707	251	16	-	-	PUNCT
cana-5707	251	17	hbo(z	hbo(z	NUM
cana-5707	251	18	)	)	PUNCT
cana-5707	251	19	.	.	PUNCT
cana-5707	252	1	proof	proof	NOUN
cana-5707	252	2	.	.	PUNCT
cana-5707	253	1	let	let	VERB
cana-5707	253	2	b	b	NOUN
cana-5707	253	3	is	be	AUX
cana-5707	253	4	both	both	PRON
cana-5707	253	5	ψb	ψb	NOUN
cana-5707	253	6	-	-	PUNCT
cana-5707	253	7	hbo(z	hbo(z	NUM
cana-5707	253	8	)	)	PUNCT
cana-5707	253	9	and	and	CCONJ
cana-5707	253	10	bϑ∗-closed	bϑ∗-close	VERB
cana-5707	253	11	.	.	PUNCT
cana-5707	254	1	then	then	ADV
cana-5707	254	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	254	3	∗(b	∗(b	PROPN
cana-5707	254	4	)	)	PUNCT
cana-5707	254	5	∪	∪	PROPN
cana-5707	254	6	cb	cb	PROPN
cana-5707	254	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	254	8	)	)	PUNCT
cana-5707	254	9	and	and	CCONJ
cana-5707	254	10	cb	cb	PROPN
cana-5707	254	11	∗(b	∗(b	PROPN
cana-5707	254	12	)	)	PUNCT
cana-5707	254	13	⊆	⊆	NUM
cana-5707	254	14	b.	b.	NOUN
cana-5707	254	15	now	now	ADV
cana-5707	254	16	b	b	PROPN
cana-5707	254	17	⊆	⊆	NUM
cana-5707	254	18	iσcb	iσcb	ADJ
cana-5707	254	19	∗(b	∗(b	NOUN
cana-5707	254	20	)	)	PUNCT
cana-5707	254	21	∪	∪	PROPN
cana-5707	254	22	cb	cb	PROPN
cana-5707	254	23	∗iσ(b	∗iσ(b	PROPN
cana-5707	254	24	)	)	PUNCT
cana-5707	254	25	⊆	⊆	NUM
cana-5707	254	26	cb	cb	PROPN
cana-5707	254	27	∗iσ(b	∗iσ(b	PROPN
cana-5707	254	28	)	)	PUNCT
cana-5707	254	29	∪	∪	ADP
cana-5707	254	30	iσ(b	iσ(b	NOUN
cana-5707	254	31	)	)	PUNCT
cana-5707	254	32	=	=	SYM
cana-5707	254	33	cb	cb	PROPN
cana-5707	254	34	∗iσ(b	∗iσ(b	PROPN
cana-5707	254	35	)	)	PUNCT
cana-5707	254	36	.	.	PUNCT
cana-5707	255	1	hence	hence	ADV
cana-5707	255	2	b	b	PROPN
cana-5707	255	3	is	be	AUX
cana-5707	255	4	ψσ	ψσ	ADJ
cana-5707	255	5	-	-	PUNCT
cana-5707	255	6	hbo(z	hbo(z	NUM
cana-5707	255	7	)	)	PUNCT
cana-5707	255	8	.	.	PUNCT
cana-5707	256	1	theorem	theorem	VERB
cana-5707	256	2	2.26	2.26	NUM
cana-5707	256	3	.	.	PUNCT
cana-5707	257	1	if	if	SCONJ
cana-5707	257	2	b⊂z	b⊂z	NOUN
cana-5707	257	3	is	be	AUX
cana-5707	257	4	both	both	PRON
cana-5707	257	5	ψb	ψb	NOUN
cana-5707	257	6	-	-	PUNCT
cana-5707	257	7	hbo(z	hbo(z	NUM
cana-5707	257	8	)	)	PUNCT
cana-5707	257	9	and	and	CCONJ
cana-5707	257	10	bϑ∗-closed	bϑ∗-close	VERB
cana-5707	257	11	,	,	PUNCT
cana-5707	257	12	then	then	ADV
cana-5707	257	13	it	it	PRON
cana-5707	257	14	is	be	AUX
cana-5707	257	15	σ(σ)-open	σ(σ)-open	PROPN
cana-5707	257	16	.	.	PUNCT
cana-5707	258	1	proof	proof	NOUN
cana-5707	258	2	.	.	PUNCT
cana-5707	259	1	let	let	VERB
cana-5707	259	2	b	b	NOUN
cana-5707	259	3	is	be	AUX
cana-5707	259	4	both	both	PRON
cana-5707	259	5	ψb	ψb	NOUN
cana-5707	259	6	-	-	PUNCT
cana-5707	259	7	hbo(z	hbo(z	NUM
cana-5707	259	8	)	)	PUNCT
cana-5707	259	9	and	and	CCONJ
cana-5707	259	10	bϑ∗-closed	bϑ∗-close	VERB
cana-5707	259	11	.	.	PUNCT
cana-5707	260	1	then	then	ADV
cana-5707	260	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	260	3	∗(b	∗(b	PROPN
cana-5707	260	4	)	)	PUNCT
cana-5707	260	5	∪	∪	PROPN
cana-5707	260	6	cb	cb	PROPN
cana-5707	260	7	∗iσ(b	∗iσ(b	PROPN
cana-5707	260	8	)	)	PUNCT
cana-5707	260	9	and	and	CCONJ
cana-5707	260	10	cb	cb	PROPN
cana-5707	260	11	∗(b)⊆b	∗(b)⊆b	PROPN
cana-5707	260	12	.	.	PUNCT
cana-5707	261	1	now	now	ADV
cana-5707	261	2	b⊆iσcb	b⊆iσcb	INTJ
cana-5707	261	3	∗(b)∪cb	∗(b)∪cb	PUNCT
cana-5707	262	1	∗iσ(b)⊆cb	∗iσ(b)⊆cb	PROPN
cana-5707	262	2	∗iσ(b)∪iσ(b)⊆cb	∗iσ(b)∪iσ(b)⊆cb	PROPN
cana-5707	262	3	∗iσ(b)⊆cb	∗iσ(b)⊆cb	PROPN
cana-5707	262	4	∗	∗	NOUN
cana-5707	262	5	iσ(b)⊆cσiσ(b	iσ(b)⊆cσiσ(b	PROPN
cana-5707	262	6	)	)	PUNCT
cana-5707	262	7	.	.	PUNCT
cana-5707	263	1	hence	hence	ADV
cana-5707	263	2	b	b	PROPN
cana-5707	263	3	is	be	AUX
cana-5707	263	4	σ(σ)-open	σ(σ)-open	PROPN
cana-5707	263	5	.	.	PUNCT
cana-5707	264	1	theorem	theorem	VERB
cana-5707	264	2	2.27	2.27	NUM
cana-5707	264	3	.	.	PUNCT
cana-5707	265	1	if	if	SCONJ
cana-5707	265	2	b⊂z	b⊂z	NOUN
cana-5707	265	3	is	be	AUX
cana-5707	265	4	ψb	ψb	ADV
cana-5707	265	5	-	-	PUNCT
cana-5707	265	6	hbo(z	hbo(z	NOUN
cana-5707	265	7	)	)	PUNCT
cana-5707	265	8	such	such	ADJ
cana-5707	265	9	that	that	SCONJ
cana-5707	265	10	iσ(b)=∅	iσ(b)=∅	PROPN
cana-5707	265	11	,	,	PUNCT
cana-5707	265	12	then	then	ADV
cana-5707	265	13	it	it	PRON
cana-5707	265	14	is	be	AUX
cana-5707	265	15	ψπ	ψπ	NOUN
cana-5707	265	16	-	-	PUNCT
cana-5707	265	17	hbo(z	hbo(z	NUM
cana-5707	265	18	)	)	PUNCT
cana-5707	265	19	.	.	PUNCT
cana-5707	266	1	proof	proof	NOUN
cana-5707	266	2	.	.	PUNCT
cana-5707	267	1	let	let	VERB
cana-5707	267	2	b	b	X
cana-5707	267	3	be	be	AUX
cana-5707	267	4	a	a	DET
cana-5707	267	5	ψb	ψb	NOUN
cana-5707	267	6	-	-	PUNCT
cana-5707	267	7	hbo(z	hbo(z	NOUN
cana-5707	267	8	)	)	PUNCT
cana-5707	267	9	and	and	CCONJ
cana-5707	267	10	iσ(b)=∅.	iσ(b)=∅.	PUNCT
cana-5707	267	11	then	then	ADV
cana-5707	267	12	b⊆iσcb	b⊆iσcb	ADJ
cana-5707	267	13	∗(b)∪cb	∗(b)∪cb	PROPN
cana-5707	267	14	∗iσ(b)=iσcb	∗iσ(b)=iσcb	PROPN
cana-5707	267	15	∗(b	∗(b	PROPN
cana-5707	267	16	)	)	PUNCT
cana-5707	267	17	.	.	PUNCT
cana-5707	268	1	hence	hence	ADV
cana-5707	268	2	b	b	NOUN
cana-5707	268	3	is	be	AUX
cana-5707	268	4	ψπ	ψπ	ADJ
cana-5707	268	5	-	-	PUNCT
cana-5707	268	6	hbo(z	hbo(z	NUM
cana-5707	268	7	)	)	PUNCT
cana-5707	268	8	.	.	PUNCT
cana-5707	269	1	theorem	theorem	VERB
cana-5707	269	2	2.28	2.28	NUM
cana-5707	269	3	.	.	PUNCT
cana-5707	270	1	if	if	SCONJ
cana-5707	270	2	b⊂z	b⊂z	NOUN
cana-5707	270	3	is	be	AUX
cana-5707	270	4	both	both	PRON
cana-5707	270	5	ψπ	ψπ	NOUN
cana-5707	270	6	-	-	PUNCT
cana-5707	270	7	hbo(z	hbo(z	NUM
cana-5707	270	8	)	)	PUNCT
cana-5707	270	9	and	and	CCONJ
cana-5707	270	10	ϑ∗	ϑ∗	PROPN
cana-5707	270	11	-closed	-close	VERB
cana-5707	270	12	,	,	PUNCT
cana-5707	270	13	then	then	ADV
cana-5707	270	14	it	it	PRON
cana-5707	270	15	is	be	AUX
cana-5707	270	16	σ(σ	σ(σ	PROPN
cana-5707	270	17	)	)	PUNCT
cana-5707	270	18	open	open	ADJ
cana-5707	270	19	.	.	PUNCT
cana-5707	271	1	proof	proof	NOUN
cana-5707	271	2	.	.	PUNCT
cana-5707	272	1	let	let	VERB
cana-5707	272	2	b	b	NOUN
cana-5707	272	3	is	be	AUX
cana-5707	272	4	both	both	PRON
cana-5707	272	5	ψπ	ψπ	NOUN
cana-5707	272	6	-	-	PUNCT
cana-5707	272	7	hbo(z	hbo(z	NUM
cana-5707	272	8	)	)	PUNCT
cana-5707	272	9	and	and	CCONJ
cana-5707	272	10	ϑ∗-closed	ϑ∗-close	VERB
cana-5707	272	11	.	.	PUNCT
cana-5707	273	1	then	then	ADV
cana-5707	273	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	273	3	∗(b	∗(b	PROPN
cana-5707	273	4	)	)	PUNCT
cana-5707	273	5	and	and	CCONJ
cana-5707	273	6	cb	cb	PROPN
cana-5707	273	7	∗(b)⊆b	∗(b)⊆b	PROPN
cana-5707	273	8	.	.	PUNCT
cana-5707	274	1	now	now	ADV
cana-5707	274	2	b⊆iσcb	b⊆iσcb	ADJ
cana-5707	274	3	∗(b)⊆iσ(b	∗(b)⊆iσ(b	PROPN
cana-5707	274	4	)	)	PUNCT
cana-5707	274	5	.	.	PUNCT
cana-5707	275	1	hence	hence	ADV
cana-5707	275	2	b	b	NOUN
cana-5707	275	3	is	be	AUX
cana-5707	275	4	ϑ-σ	ϑ-σ	NOUN
cana-5707	275	5	-	-	PUNCT
cana-5707	275	6	open	open	ADJ
cana-5707	275	7	.	.	PUNCT
cana-5707	276	1	theorem	theorem	VERB
cana-5707	276	2	2.29	2.29	NUM
cana-5707	276	3	.	.	PUNCT
cana-5707	277	1	if	if	SCONJ
cana-5707	277	2	b⊂z	b⊂z	NOUN
cana-5707	277	3	is	be	AUX
cana-5707	277	4	both	both	PRON
cana-5707	277	5	ψπ	ψπ	NOUN
cana-5707	277	6	-	-	PUNCT
cana-5707	277	7	hbo(z	hbo(z	NUM
cana-5707	277	8	)	)	PUNCT
cana-5707	277	9	and	and	CCONJ
cana-5707	277	10	bϑ∗-closed	bϑ∗-close	VERB
cana-5707	277	11	,	,	PUNCT
cana-5707	277	12	then	then	ADV
cana-5707	277	13	it	it	PRON
cana-5707	277	14	is	be	AUX
cana-5707	277	15	σ(σ	σ(σ	PROPN
cana-5707	277	16	)	)	PUNCT
cana-5707	277	17	open	open	ADJ
cana-5707	277	18	.	.	PUNCT
cana-5707	278	1	proof	proof	NOUN
cana-5707	278	2	.	.	PUNCT
cana-5707	279	1	let	let	VERB
cana-5707	279	2	b	b	NOUN
cana-5707	279	3	is	be	AUX
cana-5707	279	4	both	both	PRON
cana-5707	279	5	ψπ	ψπ	NOUN
cana-5707	279	6	-	-	PUNCT
cana-5707	279	7	hbo(z	hbo(z	NUM
cana-5707	279	8	)	)	PUNCT
cana-5707	279	9	and	and	CCONJ
cana-5707	279	10	bϑ∗-closed	bϑ∗-close	VERB
cana-5707	279	11	.	.	PUNCT
cana-5707	280	1	then	then	ADV
cana-5707	280	2	b⊆iσcb	b⊆iσcb	PROPN
cana-5707	280	3	∗(b	∗(b	PROPN
cana-5707	280	4	)	)	PUNCT
cana-5707	280	5	and	and	CCONJ
cana-5707	280	6	cb	cb	PROPN
cana-5707	280	7	∗(b)⊆b	∗(b)⊆b	PROPN
cana-5707	280	8	.	.	PUNCT
cana-5707	281	1	now	now	PROPN
cana-5707	281	2	b⊆	b⊆	PROPN
cana-5707	281	3	iσcb	iσcb	ADJ
cana-5707	281	4	∗(b)⊆iσ(b	∗(b)⊆iσ(b	PROPN
cana-5707	281	5	)	)	PUNCT
cana-5707	281	6	.	.	PUNCT
cana-5707	282	1	hence	hence	ADV
cana-5707	282	2	b	b	NOUN
cana-5707	282	3	is	be	AUX
cana-5707	282	4	ϑ-σ	ϑ-σ	NOUN
cana-5707	282	5	-	-	PUNCT
cana-5707	282	6	open	open	ADJ
cana-5707	282	7	.	.	PUNCT
cana-5707	283	1	3	3	X
cana-5707	283	2	.	.	X
cana-5707	283	3	decomposition	decomposition	NOUN
cana-5707	283	4	of	of	ADP
cana-5707	283	5	(	(	PUNCT
cana-5707	283	6	ψαhb	ψαhb	PROPN
cana-5707	283	7	,	,	PUNCT
cana-5707	283	8	δ	δ	PROPN
cana-5707	283	9	)	)	PUNCT
cana-5707	283	10	-continuity	-continuity	PROPN
cana-5707	283	11	definition	definition	NOUN
cana-5707	283	12	3.1	3.1	NUM
cana-5707	283	13	.	.	PUNCT
cana-5707	284	1	a	a	DET
cana-5707	284	2	map	map	NOUN
cana-5707	284	3	j:(z	j:(z	NOUN
cana-5707	284	4	,	,	PUNCT
cana-5707	284	5	ϑ	ϑ	NOUN
cana-5707	284	6	,	,	PUNCT
cana-5707	284	7	h)→	h)→	NUM
cana-5707	284	8	(	(	PUNCT
cana-5707	284	9	w	w	PROPN
cana-5707	284	10	,	,	PUNCT
cana-5707	284	11	δ	δ	PROPN
cana-5707	284	12	)	)	PUNCT
cana-5707	284	13	is	be	AUX
cana-5707	284	14	(	(	PUNCT
cana-5707	284	15	ψαhb	ψαhb	ADJ
cana-5707	284	16	,	,	PUNCT
cana-5707	284	17	δ	δ	PROPN
cana-5707	284	18	)	)	PUNCT
cana-5707	284	19	-continuous	-continuous	ADJ
cana-5707	284	20	(	(	PUNCT
cana-5707	284	21	(	(	PUNCT
cana-5707	284	22	ψαhb	ψαhb	ADJ
cana-5707	284	23	,	,	PUNCT
cana-5707	284	24	ϑ)-c	ϑ)-c	INTJ
cana-5707	284	25	)	)	PUNCT
cana-5707	284	26	,	,	PUNCT
cana-5707	284	27	if	if	SCONJ
cana-5707	284	28	j−1(v	j−1(v	PROPN
cana-5707	284	29	)	)	PUNCT
cana-5707	284	30	is	be	AUX
cana-5707	284	31	ψα	ψα	ADP
cana-5707	284	32	-	-	PUNCT
cana-5707	284	33	hbo(z	hbo(z	NOUN
cana-5707	284	34	)	)	PUNCT
cana-5707	284	35	for	for	ADP
cana-5707	284	36	each	each	DET
cana-5707	284	37	δo(z	δo(z	NOUN
cana-5707	284	38	)	)	PUNCT
cana-5707	284	39	set	set	VERB
cana-5707	284	40	v	v	NOUN
cana-5707	284	41	in	in	ADP
cana-5707	284	42	(	(	PUNCT
cana-5707	284	43	w	w	PROPN
cana-5707	284	44	,	,	PUNCT
cana-5707	284	45	δ	δ	PROPN
cana-5707	284	46	)	)	PUNCT
cana-5707	284	47	.	.	PUNCT
cana-5707	285	1	communications	communication	NOUN
cana-5707	285	2	on	on	ADP
cana-5707	285	3	applied	apply	VERB
cana-5707	285	4	nonlinear	nonlinear	ADJ
cana-5707	285	5	analysis	analysis	NOUN
cana-5707	285	6	issn	issn	NOUN
cana-5707	285	7	:	:	PUNCT
cana-5707	285	8	1074	1074	NUM
cana-5707	285	9	-	-	PUNCT
cana-5707	285	10	133x	133x	NUM
cana-5707	285	11	vol	vol	VERB
cana-5707	285	12	32	32	NUM
cana-5707	285	13	no	no	NOUN
cana-5707	285	14	.	.	PUNCT
cana-5707	286	1	10s	10	NOUN
cana-5707	286	2	(	(	PUNCT
cana-5707	286	3	2025	2025	NUM
cana-5707	286	4	)	)	PUNCT
cana-5707	286	5	2666	2666	NUM
cana-5707	286	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5707	286	7	definition	definition	NOUN
cana-5707	286	8	3.2	3.2	NUM
cana-5707	286	9	.	.	PUNCT
cana-5707	287	1	a	a	DET
cana-5707	287	2	map	map	NOUN
cana-5707	287	3	j	j	NOUN
cana-5707	287	4	:	:	PUNCT
cana-5707	287	5	(	(	PUNCT
cana-5707	287	6	z	z	NOUN
cana-5707	287	7	,	,	PUNCT
cana-5707	287	8	ϑ	ϑ	X
cana-5707	287	9	,	,	PUNCT
cana-5707	287	10	h)→	h)→	NUM
cana-5707	287	11	(	(	PUNCT
cana-5707	287	12	w	w	PROPN
cana-5707	287	13	,	,	PUNCT
cana-5707	287	14	δ	δ	PROPN
cana-5707	287	15	)	)	PUNCT
cana-5707	287	16	is	be	AUX
cana-5707	287	17	(	(	PUNCT
cana-5707	287	18	ψσhb	ψσhb	NOUN
cana-5707	287	19	,	,	PUNCT
cana-5707	287	20	δ	δ	PROPN
cana-5707	287	21	)	)	PUNCT
cana-5707	287	22	-continuous	-continuous	ADJ
cana-5707	287	23	(	(	PUNCT
cana-5707	287	24	(	(	PUNCT
cana-5707	287	25	ψσhb	ψσhb	NOUN
cana-5707	287	26	,	,	PUNCT
cana-5707	287	27	ϑ	ϑ	NOUN
cana-5707	287	28	)	)	PUNCT
cana-5707	287	29	-c	-c	NUM
cana-5707	287	30	)	)	PUNCT
cana-5707	287	31	,	,	PUNCT
cana-5707	287	32	if	if	SCONJ
cana-5707	287	33	j−1(v	j−1(v	PROPN
cana-5707	287	34	)	)	PUNCT
cana-5707	287	35	is	be	AUX
cana-5707	287	36	ψσ	ψσ	ADJ
cana-5707	287	37	-	-	PUNCT
cana-5707	287	38	hbo(z	hbo(z	NUM
cana-5707	287	39	)	)	PUNCT
cana-5707	287	40	for	for	ADP
cana-5707	287	41	each	each	DET
cana-5707	287	42	δo(z	δo(z	NOUN
cana-5707	287	43	)	)	PUNCT
cana-5707	287	44	set	set	VERB
cana-5707	287	45	v	v	NOUN
cana-5707	287	46	in	in	ADP
cana-5707	287	47	(	(	PUNCT
cana-5707	287	48	w	w	PROPN
cana-5707	287	49	,	,	PUNCT
cana-5707	287	50	δ	δ	PROPN
cana-5707	287	51	)	)	PUNCT
cana-5707	287	52	.	.	PUNCT
cana-5707	288	1	definition	definition	NOUN
cana-5707	288	2	3.3	3.3	NUM
cana-5707	288	3	.	.	PUNCT
cana-5707	289	1	a	a	DET
cana-5707	289	2	map	map	NOUN
cana-5707	289	3	j	j	NOUN
cana-5707	289	4	:	:	PUNCT
cana-5707	289	5	(	(	PUNCT
cana-5707	289	6	z	z	NOUN
cana-5707	289	7	,	,	PUNCT
cana-5707	289	8	ϑ	ϑ	X
cana-5707	289	9	,	,	PUNCT
cana-5707	289	10	h)→	h)→	NUM
cana-5707	289	11	(	(	PUNCT
cana-5707	289	12	w	w	PROPN
cana-5707	289	13	,	,	PUNCT
cana-5707	289	14	δ	δ	PROPN
cana-5707	289	15	)	)	PUNCT
cana-5707	289	16	is	be	AUX
cana-5707	289	17	(	(	PUNCT
cana-5707	289	18	ψπhb	ψπhb	NOUN
cana-5707	289	19	,	,	PUNCT
cana-5707	289	20	δ)-continuous	δ)-continuous	ADJ
cana-5707	289	21	(	(	PUNCT
cana-5707	289	22	(	(	PUNCT
cana-5707	289	23	ψπhb	ψπhb	NOUN
cana-5707	289	24	,	,	PUNCT
cana-5707	289	25	ϑ	ϑ	NOUN
cana-5707	289	26	)	)	PUNCT
cana-5707	289	27	-c	-c	NUM
cana-5707	289	28	)	)	PUNCT
cana-5707	289	29	,	,	PUNCT
cana-5707	289	30	if	if	SCONJ
cana-5707	289	31	j−1(v	j−1(v	PROPN
cana-5707	289	32	)	)	PUNCT
cana-5707	289	33	is	be	AUX
cana-5707	289	34	ψπ	ψπ	ADJ
cana-5707	289	35	-	-	PUNCT
cana-5707	289	36	hbo(z	hbo(z	NOUN
cana-5707	289	37	)	)	PUNCT
cana-5707	289	38	for	for	ADP
cana-5707	289	39	each	each	DET
cana-5707	289	40	δo(z	δo(z	NOUN
cana-5707	289	41	)	)	PUNCT
cana-5707	289	42	set	set	VERB
cana-5707	289	43	v	v	NOUN
cana-5707	289	44	in	in	ADP
cana-5707	289	45	(	(	PUNCT
cana-5707	289	46	w	w	PROPN
cana-5707	289	47	,	,	PUNCT
cana-5707	289	48	δ	δ	PROPN
cana-5707	289	49	)	)	PUNCT
cana-5707	289	50	.	.	PUNCT
cana-5707	290	1	theorem	theorem	VERB
cana-5707	290	2	3.4	3.4	NUM
cana-5707	290	3	.	.	PUNCT
cana-5707	291	1	for	for	ADP
cana-5707	291	2	a	a	DET
cana-5707	291	3	map	map	NOUN
cana-5707	291	4	j	j	NOUN
cana-5707	291	5	:	:	PUNCT
cana-5707	291	6	(	(	PUNCT
cana-5707	291	7	z	z	NOUN
cana-5707	291	8	,	,	PUNCT
cana-5707	291	9	ϑ	ϑ	X
cana-5707	291	10	,	,	PUNCT
cana-5707	291	11	h	h	NOUN
cana-5707	291	12	)	)	PUNCT
cana-5707	291	13	→	→	SYM
cana-5707	291	14	(	(	PUNCT
cana-5707	291	15	w	w	PROPN
cana-5707	291	16	,	,	PUNCT
cana-5707	291	17	δ	δ	PROPN
cana-5707	291	18	,	,	PUNCT
cana-5707	291	19	the	the	DET
cana-5707	291	20	following	follow	VERB
cana-5707	291	21	results	result	NOUN
cana-5707	291	22	are	be	AUX
cana-5707	291	23	equivalent	equivalent	ADJ
cana-5707	291	24	.	.	PUNCT
cana-5707	292	1	1	1	X
cana-5707	292	2	.	.	X
cana-5707	292	3	j	j	PROPN
cana-5707	292	4	is	be	AUX
cana-5707	292	5	(	(	PUNCT
cana-5707	292	6	ψαhb	ψαhb	ADJ
cana-5707	292	7	,	,	PUNCT
cana-5707	292	8	ϑ	ϑ	NOUN
cana-5707	292	9	)	)	PUNCT
cana-5707	292	10	c.	c.	NOUN
cana-5707	292	11	2	2	NUM
cana-5707	292	12	.	.	PUNCT
cana-5707	293	1	j	j	PROPN
cana-5707	293	2	is	be	AUX
cana-5707	293	3	(	(	PUNCT
cana-5707	293	4	ψσhb	ψσhb	NOUN
cana-5707	293	5	,	,	PUNCT
cana-5707	293	6	ϑ	ϑ	NOUN
cana-5707	293	7	)	)	PUNCT
cana-5707	293	8	c	c	NOUN
cana-5707	293	9	and	and	CCONJ
cana-5707	293	10	(	(	PUNCT
cana-5707	293	11	ψπhb	ψπhb	NOUN
cana-5707	293	12	,	,	PUNCT
cana-5707	293	13	ϑ	ϑ	NOUN
cana-5707	293	14	)	)	PUNCT
cana-5707	293	15	c.	c.	NOUN
cana-5707	293	16	proof	proof	NOUN
cana-5707	293	17	.	.	PUNCT
cana-5707	294	1	proof	proof	NOUN
cana-5707	294	2	is	be	AUX
cana-5707	294	3	trivial	trivial	ADJ
cana-5707	294	4	from	from	ADP
cana-5707	294	5	theorem	theorem	ADJ
cana-5707	294	6	2.14	2.14	NUM
cana-5707	294	7	.	.	PUNCT
cana-5707	295	1	4	4	NUM
cana-5707	295	2	.	.	X
cana-5707	295	3	conclusion	conclusion	NOUN
cana-5707	295	4	in	in	ADP
cana-5707	295	5	this	this	DET
cana-5707	295	6	paper	paper	NOUN
cana-5707	295	7	,	,	PUNCT
cana-5707	295	8	we	we	PRON
cana-5707	295	9	introduced	introduce	VERB
cana-5707	295	10	ψα	ψα	ADP
cana-5707	295	11	hbo(z	hbo(z	NUM
cana-5707	295	12	)	)	PUNCT
cana-5707	295	13	,	,	PUNCT
cana-5707	295	14	ψσ	ψσ	ADP
cana-5707	295	15	hbo(z	hbo(z	NUM
cana-5707	295	16	)	)	PUNCT
cana-5707	295	17	,	,	PUNCT
cana-5707	295	18	ψπ	ψπ	ADP
cana-5707	295	19	hbo(z	hbo(z	NUM
cana-5707	295	20	)	)	PUNCT
cana-5707	295	21	,	,	PUNCT
cana-5707	295	22	ψβ	ψβ	NOUN
cana-5707	295	23	hbo(z	hbo(z	NUM
cana-5707	295	24	)	)	PUNCT
cana-5707	295	25	,	,	PUNCT
cana-5707	295	26	and	and	CCONJ
cana-5707	295	27	ψb	ψb	ADV
cana-5707	295	28	hbo(z	hbo(z	NUM
cana-5707	295	29	)	)	PUNCT
cana-5707	295	30	sets	set	NOUN
cana-5707	295	31	and	and	CCONJ
cana-5707	295	32	obtained	obtain	VERB
cana-5707	295	33	decomposition	decomposition	NOUN
cana-5707	295	34	of	of	ADP
cana-5707	295	35	(	(	PUNCT
cana-5707	295	36	ψαhb	ψαhb	INTJ
cana-5707	295	37	,	,	PUNCT
cana-5707	295	38	ϑ	ϑ	NOUN
cana-5707	295	39	)	)	PUNCT
cana-5707	295	40	c.	c.	NOUN
cana-5707	295	41	in	in	ADP
cana-5707	295	42	future	future	ADJ
cana-5707	295	43	work	work	NOUN
cana-5707	295	44	we	we	PRON
cana-5707	295	45	will	will	AUX
cana-5707	295	46	introduce	introduce	VERB
cana-5707	295	47	new	new	ADJ
cana-5707	295	48	types	type	NOUN
cana-5707	295	49	of	of	ADP
cana-5707	295	50	generalized	generalized	ADJ
cana-5707	295	51	open	open	ADJ
cana-5707	295	52	sets	set	NOUN
cana-5707	295	53	related	relate	VERB
cana-5707	295	54	to	to	ADP
cana-5707	295	55	these	these	DET
cana-5707	295	56	sets	set	NOUN
cana-5707	295	57	and	and	CCONJ
cana-5707	295	58	obtain	obtain	VERB
cana-5707	295	59	new	new	ADJ
cana-5707	295	60	decomposition	decomposition	NOUN
cana-5707	295	61	of	of	ADP
cana-5707	295	62	(	(	PUNCT
cana-5707	295	63	ϑ	ϑ	X
cana-5707	295	64	,	,	PUNCT
cana-5707	295	65	δ	δ	PROPN
cana-5707	295	66	)	)	PUNCT
cana-5707	295	67	c.	c.	PROPN
cana-5707	295	68	references	reference	NOUN
cana-5707	295	69	1	1	NUM
cana-5707	295	70	.	.	PUNCT
cana-5707	296	1	csaszar	csaszar	PROPN
cana-5707	296	2	,	,	PUNCT
cana-5707	296	3	generalized	generalized	ADJ
cana-5707	296	4	topology	topology	NOUN
cana-5707	296	5	generalized	generalize	VERB
cana-5707	296	6	continuity	continuity	NOUN
cana-5707	296	7	acta	acta	PROPN
cana-5707	296	8	mathematica	mathematica	PROPN
cana-5707	296	9	hungarica	hungarica	PROPN
cana-5707	296	10	96	96	NUM
cana-5707	296	11	(	(	PUNCT
cana-5707	296	12	2002	2002	NUM
cana-5707	296	13	)	)	PUNCT
cana-5707	296	14	,	,	PUNCT
cana-5707	296	15	351	351	NUM
cana-5707	296	16	-	-	SYM
cana-5707	296	17	357	357	NUM
cana-5707	296	18	.	.	NOUN
cana-5707	297	1	2	2	NUM
cana-5707	297	2	.	.	X
cana-5707	297	3	csaszar	csaszar	PROPN
cana-5707	297	4	,	,	PUNCT
cana-5707	297	5	generalized	generalize	VERB
cana-5707	297	6	open	open	ADJ
cana-5707	297	7	sets	set	NOUN
cana-5707	297	8	in	in	ADP
cana-5707	297	9	generalized	generalized	ADJ
cana-5707	297	10	topologies	topology	NOUN
cana-5707	297	11	acta	acta	PROPN
cana-5707	297	12	mathematica	mathematica	PROPN
cana-5707	297	13	hungarica	hungarica	PROPN
cana-5707	297	14	106	106	NUM
cana-5707	297	15	(	(	PUNCT
cana-5707	297	16	2005	2005	NUM
cana-5707	297	17	)	)	PUNCT
cana-5707	297	18	,	,	PUNCT
cana-5707	297	19	53	53	NUM
cana-5707	297	20	-	-	SYM
cana-5707	297	21	56	56	NUM
cana-5707	297	22	.	.	NOUN
cana-5707	298	1	3	3	NUM
cana-5707	298	2	.	.	X
cana-5707	298	3	csaszar	csaszar	PROPN
cana-5707	298	4	,	,	PUNCT
cana-5707	298	5	modification	modification	NOUN
cana-5707	298	6	of	of	ADP
cana-5707	298	7	generalized	generalized	ADJ
cana-5707	298	8	topologies	topology	NOUN
cana-5707	298	9	via	via	ADP
cana-5707	298	10	hereditary	hereditary	ADJ
cana-5707	298	11	classes	class	NOUN
cana-5707	298	12	acta	acta	PROPN
cana-5707	298	13	mathematica	mathematica	PROPN
cana-5707	298	14	hungarica	hungarica	PROPN
cana-5707	298	15	115(2007	115(2007	NUM
cana-5707	298	16	)	)	PUNCT
cana-5707	298	17	,	,	PUNCT
cana-5707	298	18	29	29	NUM
cana-5707	298	19	-	-	SYM
cana-5707	298	20	36	36	NUM
cana-5707	298	21	.	.	PUNCT
cana-5707	299	1	4	4	NUM
cana-5707	299	2	.	.	X
cana-5707	299	3	w.	w.	PROPN
cana-5707	299	4	k.	k.	PROPN
cana-5707	299	5	min	min	PROPN
cana-5707	299	6	,	,	PUNCT
cana-5707	299	7	generalized	generalized	ADJ
cana-5707	299	8	continuity	continuity	NOUN
cana-5707	299	9	maps	map	NOUN
cana-5707	299	10	defined	define	VERB
cana-5707	299	11	by	by	ADP
cana-5707	299	12	generalized	generalized	ADJ
cana-5707	299	13	open	open	ADJ
cana-5707	299	14	sets	set	NOUN
cana-5707	299	15	on	on	ADP
cana-5707	299	16	generalized	generalized	ADJ
cana-5707	299	17	topological	topological	ADJ
cana-5707	299	18	spaces	space	NOUN
cana-5707	299	19	acta	acta	PROPN
cana-5707	299	20	mathematica	mathematica	PROPN
cana-5707	299	21	hungarica	hungarica	PROPN
cana-5707	299	22	128(4	128(4	NUM
cana-5707	299	23	)	)	PUNCT
cana-5707	299	24	(	(	PUNCT
cana-5707	299	25	2010)pp	2010)pp	NUM
cana-5707	299	26	299	299	NUM
cana-5707	299	27	-	-	SYM
cana-5707	299	28	306	306	NUM
cana-5707	299	29	.	.	PUNCT
cana-5707	300	1	5	5	NUM
cana-5707	300	2	.	.	PUNCT
cana-5707	300	3	m.	m.	NOUN
cana-5707	300	4	rajamani	rajamani	PROPN
cana-5707	300	5	,	,	PUNCT
cana-5707	300	6	v.	v.	ADP
cana-5707	300	7	inthumathi	inthumathi	ADV
cana-5707	300	8	and	and	CCONJ
cana-5707	300	9	r.	r.	PROPN
cana-5707	300	10	ramesh	ramesh	PROPN
cana-5707	300	11	,	,	PUNCT
cana-5707	300	12	some	some	DET
cana-5707	300	13	new	new	ADJ
cana-5707	300	14	generalized	generalized	ADJ
cana-5707	300	15	topologies	topology	NOUN
cana-5707	300	16	via	via	ADP
cana-5707	300	17	hereditary	hereditary	ADJ
cana-5707	300	18	classes	class	NOUN
cana-5707	300	19	bol	bol	NOUN
cana-5707	300	20	.	.	PUNCT
cana-5707	301	1	soc	soc	PROPN
cana-5707	301	2	.	.	PUNCT
cana-5707	302	1	paran	paran	PROPN
cana-5707	302	2	.	.	PUNCT
cana-5707	303	1	mat	mat	PROPN
cana-5707	303	2	.	.	NOUN
cana-5707	304	1	30(2)(2012	30(2)(2012	NUM
cana-5707	304	2	)	)	PUNCT
cana-5707	304	3	,	,	PUNCT
cana-5707	304	4	71	71	NUM
cana-5707	304	5	-	-	SYM
cana-5707	304	6	77	77	NUM
cana-5707	304	7	.	.	PUNCT
cana-5707	305	1	6	6	NUM
cana-5707	305	2	.	.	PUNCT
cana-5707	305	3	m.	m.	NOUN
cana-5707	305	4	rajamani	rajamani	PROPN
cana-5707	305	5	,	,	PUNCT
cana-5707	305	6	v.	v.	ADP
cana-5707	305	7	inthumathi	inthumathi	ADV
cana-5707	305	8	and	and	CCONJ
cana-5707	305	9	r.	r.	PROPN
cana-5707	305	10	ramesh	ramesh	PROPN
cana-5707	305	11	,	,	PUNCT
cana-5707	305	12	a	a	DET
cana-5707	305	13	decomposition	decomposition	NOUN
cana-5707	305	14	of	of	ADP
cana-5707	305	15	(	(	PUNCT
cana-5707	305	16	µ	µ	X
cana-5707	305	17	,	,	PUNCT
cana-5707	305	18	λ	λ	NOUN
cana-5707	305	19	)	)	PUNCT
cana-5707	305	20	continuity	continuity	NOUN
cana-5707	305	21	in	in	ADP
cana-5707	305	22	generalized	generalized	ADJ
cana-5707	305	23	topological	topological	ADJ
cana-5707	305	24	spaces	space	NOUN
cana-5707	305	25	,	,	PUNCT
cana-5707	305	26	jordan	jordan	PROPN
cana-5707	305	27	journal	journal	PROPN
cana-5707	305	28	of	of	ADP
cana-5707	305	29	mathematics	mathematics	PROPN
cana-5707	305	30	and	and	CCONJ
cana-5707	305	31	statistics	statistic	NOUN
cana-5707	305	32	,	,	PUNCT
cana-5707	305	33	6(1)(2013	6(1)(2013	NUM
cana-5707	305	34	)	)	PUNCT
cana-5707	305	35	,	,	PUNCT
cana-5707	305	36	15	15	NUM
cana-5707	305	37	27	27	NUM
cana-5707	305	38	.	.	PUNCT
cana-5707	306	1	7	7	X
cana-5707	306	2	.	.	PUNCT
cana-5707	306	3	a.	a.	PROPN
cana-5707	306	4	al	al	PROPN
cana-5707	306	5	-	-	PUNCT
cana-5707	306	6	omari	omari	PROPN
cana-5707	306	7	,	,	PUNCT
cana-5707	306	8	m.	m.	NOUN
cana-5707	306	9	rajamani	rajamani	PROPN
cana-5707	306	10	and	and	CCONJ
cana-5707	306	11	r.	r.	PROPN
cana-5707	306	12	ramesh	ramesh	PROPN
cana-5707	306	13	,	,	PUNCT
cana-5707	306	14	aexpansion	aexpansion	NOUN
cana-5707	306	15	continuous	continuous	ADJ
cana-5707	306	16	maps	map	NOUN
cana-5707	306	17	and	and	CCONJ
cana-5707	306	18	(	(	PUNCT
cana-5707	306	19	a	a	PRON
cana-5707	306	20	,	,	PUNCT
cana-5707	306	21	b)-weakly	b)-weakly	ADV
cana-5707	306	22	continuous	continuous	ADJ
cana-5707	306	23	maps	map	NOUN
cana-5707	306	24	in	in	ADP
cana-5707	306	25	hereditary	hereditary	ADJ
cana-5707	306	26	generalized	generalized	ADJ
cana-5707	306	27	topological	topological	ADJ
cana-5707	306	28	spaces	space	NOUN
cana-5707	306	29	,	,	PUNCT
cana-5707	306	30	scientific	scientific	ADJ
cana-5707	306	31	studies	study	NOUN
cana-5707	306	32	and	and	CCONJ
cana-5707	306	33	research	research	NOUN
cana-5707	306	34	,	,	PUNCT
cana-5707	306	35	23(2	23(2	NUM
cana-5707	306	36	)	)	PUNCT
cana-5707	306	37	(	(	PUNCT
cana-5707	306	38	2013	2013	NUM
cana-5707	306	39	)	)	PUNCT
cana-5707	306	40	,	,	PUNCT
cana-5707	306	41	13	13	NUM
cana-5707	306	42	-	-	SYM
cana-5707	306	43	22	22	NUM
cana-5707	306	44	.	.	PUNCT
cana-5707	307	1	8	8	NUM
cana-5707	307	2	.	.	X
cana-5707	307	3	r.	r.	PROPN
cana-5707	307	4	ramesh	ramesh	PROPN
cana-5707	307	5	and	and	CCONJ
cana-5707	307	6	r.	r.	PROPN
cana-5707	307	7	mariappan	mariappan	PROPN
cana-5707	307	8	generalized	generalize	VERB
cana-5707	307	9	open	open	ADJ
cana-5707	307	10	sets	set	NOUN
cana-5707	307	11	in	in	ADP
cana-5707	307	12	hereditary	hereditary	ADJ
cana-5707	307	13	generalized	generalized	ADJ
cana-5707	307	14	topological	topological	ADJ
cana-5707	307	15	spaces	space	NOUN
cana-5707	307	16	,	,	PUNCT
cana-5707	307	17	j.	j.	PROPN
cana-5707	307	18	math	math	PROPN
cana-5707	307	19	.	.	PUNCT
cana-5707	308	1	comput	comput	NOUN
cana-5707	308	2	.	.	PUNCT
cana-5707	309	1	sci	sci	PROPN
cana-5707	309	2	.	.	PROPN
cana-5707	309	3	,	,	PUNCT
cana-5707	309	4	5(2	5(2	NUM
cana-5707	309	5	)	)	PUNCT
cana-5707	309	6	(	(	PUNCT
cana-5707	309	7	2015	2015	NUM
cana-5707	309	8	)	)	PUNCT
cana-5707	309	9	,	,	PUNCT
cana-5707	309	10	149	149	NUM
cana-5707	309	11	-	-	SYM
cana-5707	309	12	159	159	NUM
cana-5707	309	13	.	.	PUNCT
cana-5707	310	1	9	9	NUM
cana-5707	310	2	.	.	X
cana-5707	310	3	r.	r.	PROPN
cana-5707	310	4	ramesh	ramesh	PROPN
cana-5707	310	5	,	,	PUNCT
cana-5707	310	6	decomposition	decomposition	NOUN
cana-5707	310	7	of	of	ADP
cana-5707	310	8	(	(	PUNCT
cana-5707	310	9	κµ∗	κµ∗	NOUN
cana-5707	310	10	,	,	PUNCT
cana-5707	310	11	λ)-continuity	λ)-continuity	NOUN
cana-5707	310	12	,	,	PUNCT
cana-5707	310	13	journal	journal	NOUN
cana-5707	310	14	of	of	ADP
cana-5707	310	15	xi’an	xi’an	PROPN
cana-5707	310	16	university	university	PROPN
cana-5707	310	17	of	of	ADP
cana-5707	310	18	architecture	architecture	NOUN
cana-5707	310	19	and	and	CCONJ
cana-5707	310	20	technology	technology	NOUN
cana-5707	310	21	,	,	PUNCT
cana-5707	310	22	11(vi	11(vi	NUM
cana-5707	310	23	)	)	PUNCT
cana-5707	310	24	,	,	PUNCT
cana-5707	310	25	(	(	PUNCT
cana-5707	310	26	2020	2020	NUM
cana-5707	310	27	)	)	PUNCT
cana-5707	310	28	,	,	PUNCT
cana-5707	310	29	2095	2095	NUM
cana-5707	310	30	-	-	SYM
cana-5707	310	31	2101	2101	NUM
cana-5707	310	32	.	.	PUNCT
cana-5707	311	1	10	10	NUM
cana-5707	311	2	.	.	PUNCT
cana-5707	311	3	r.	r.	PROPN
cana-5707	311	4	ramesh	ramesh	PROPN
cana-5707	311	5	and	and	CCONJ
cana-5707	311	6	ahmad	ahmad	PROPN
cana-5707	311	7	al	al	PROPN
cana-5707	311	8	-	-	PUNCT
cana-5707	311	9	omari	omari	PROPN
cana-5707	311	10	,	,	PUNCT
cana-5707	311	11	b	b	X
cana-5707	311	12	-	-	PUNCT
cana-5707	311	13	hσ	hσ	NOUN
cana-5707	311	14	-	-	ADJ
cana-5707	311	15	open	open	ADJ
cana-5707	311	16	sets	set	NOUN
cana-5707	311	17	in	in	ADP
cana-5707	311	18	hgts	hgts	NOUN
cana-5707	311	19	,	,	PUNCT
cana-5707	311	20	poincare	poincare	PROPN
cana-5707	311	21	journal	journal	PROPN
cana-5707	311	22	of	of	ADP
cana-5707	311	23	analysis	analysis	NOUN
cana-5707	311	24	and	and	CCONJ
cana-5707	311	25	applications	application	NOUN
cana-5707	311	26	9(1	9(1	NUM
cana-5707	311	27	)	)	PUNCT
cana-5707	311	28	(	(	PUNCT
cana-5707	311	29	2022	2022	NUM
cana-5707	311	30	)	)	PUNCT
cana-5707	311	31	,	,	PUNCT
cana-5707	311	32	31	31	NUM
cana-5707	311	33	-	-	SYM
cana-5707	311	34	40	40	NUM
cana-5707	311	35	.	.	PUNCT
cana-5707	312	1	11	11	NUM
cana-5707	312	2	.	.	PUNCT
cana-5707	313	1	r.	r.	PROPN
cana-5707	313	2	ramesh	ramesh	PROPN
cana-5707	313	3	and	and	CCONJ
cana-5707	313	4	ahmad	ahmad	PROPN
cana-5707	313	5	al	al	PROPN
cana-5707	313	6	-	-	PUNCT
cana-5707	313	7	omari	omari	PROPN
cana-5707	313	8	,	,	PUNCT
cana-5707	313	9	decomposition	decomposition	NOUN
cana-5707	313	10	of	of	ADP
cana-5707	313	11	(	(	PUNCT
cana-5707	313	12	α	α	NOUN
cana-5707	313	13	-	-	PUNCT
cana-5707	313	14	hσ	hσ	NOUN
cana-5707	313	15	,	,	PUNCT
cana-5707	313	16	λ	λ	NOUN
cana-5707	313	17	)	)	PUNCT
cana-5707	313	18	-continuity	-continuity	PROPN
cana-5707	313	19	,	,	PUNCT
cana-5707	313	20	poincare	poincare	PROPN
cana-5707	313	21	journal	journal	PROPN
cana-5707	313	22	of	of	ADP
cana-5707	313	23	analysis	analysis	NOUN
cana-5707	313	24	and	and	CCONJ
cana-5707	313	25	applications	application	NOUN
cana-5707	313	26	10(1	10(1	NUM
cana-5707	313	27	)	)	PUNCT
cana-5707	313	28	(	(	PUNCT
cana-5707	313	29	2023	2023	NUM
cana-5707	313	30	)	)	PUNCT
cana-5707	313	31	,	,	PUNCT
cana-5707	313	32	155	155	NUM
cana-5707	313	33	-	-	SYM
cana-5707	313	34	163	163	NUM
cana-5707	313	35	.	.	PUNCT
cana-5707	313	36	12	12	NUM
cana-5707	313	37	.	.	PUNCT
cana-5707	313	38	r.	r.	PROPN
cana-5707	313	39	ramesh	ramesh	PROPN
cana-5707	313	40	,	,	PUNCT
cana-5707	313	41	l.	l.	PROPN
cana-5707	313	42	senthil	senthil	PROPN
cana-5707	313	43	kumar	kumar	PROPN
cana-5707	313	44	and	and	CCONJ
cana-5707	313	45	t.	t.	PROPN
cana-5707	313	46	muthukumar	muthukumar	PROPN
cana-5707	313	47	,	,	PUNCT
cana-5707	313	48	b	b	X
cana-5707	313	49	-	-	PUNCT
cana-5707	313	50	hψ	hψ	NOUN
cana-5707	313	51	-open	-open	ADJ
cana-5707	313	52	sets	set	NOUN
cana-5707	313	53	in	in	ADP
cana-5707	313	54	hgts	hgts	NOUN
cana-5707	313	55	,	,	PUNCT
cana-5707	313	56	indian	indian	ADJ
cana-5707	313	57	journal	journal	NOUN
cana-5707	313	58	of	of	ADP
cana-5707	313	59	natural	natural	ADJ
cana-5707	313	60	sceince	sceince	NOUN
cana-5707	313	61	.	.	PUNCT
cana-5707	314	1	13	13	NUM
cana-5707	314	2	.	.	PUNCT
cana-5707	314	3	r.	r.	PROPN
cana-5707	314	4	ramesh	ramesh	PROPN
cana-5707	314	5	and	and	CCONJ
cana-5707	314	6	r.	r.	PROPN
cana-5707	314	7	uma	uma	PROPN
cana-5707	314	8	,	,	PUNCT
cana-5707	314	9	decomposition	decomposition	NOUN
cana-5707	314	10	of	of	ADP
cana-5707	314	11	(	(	PUNCT
cana-5707	314	12	αhb	αhb	PROPN
cana-5707	314	13	,	,	PUNCT
cana-5707	314	14	ϑ	ϑ	NOUN
cana-5707	314	15	)	)	PUNCT
cana-5707	314	16	-continuity	-continuity	PROPN
cana-5707	314	17	,	,	PUNCT
cana-5707	314	18	indian	indian	ADJ
cana-5707	314	19	journal	journal	NOUN
cana-5707	314	20	of	of	ADP
cana-5707	314	21	natural	natural	ADJ
cana-5707	314	22	science	science	NOUN
cana-5707	314	23	.	.	PUNCT
cana-5707	315	1	14	14	NUM
cana-5707	315	2	.	.	PUNCT
cana-5707	316	1	m.s	m.s	PROPN
cana-5707	316	2	.	.	PROPN
cana-5707	316	3	sarsak	sarsak	PROPN
cana-5707	316	4	,	,	PUNCT
cana-5707	316	5	on	on	ADP
cana-5707	316	6	some	some	DET
cana-5707	316	7	properties	property	NOUN
cana-5707	316	8	of	of	ADP
cana-5707	316	9	generalized	generalized	ADJ
cana-5707	316	10	open	open	ADJ
cana-5707	316	11	sets	set	NOUN
cana-5707	316	12	in	in	ADP
cana-5707	316	13	generalized	generalized	ADJ
cana-5707	316	14	topological	topological	ADJ
cana-5707	316	15	spaces	space	NOUN
cana-5707	316	16	,	,	PUNCT
cana-5707	316	17	demonstratio	demonstratio	PROPN
cana-5707	316	18	math	math	PROPN
cana-5707	316	19	.	.	PUNCT
cana-5707	317	1	(	(	PUNCT
cana-5707	317	2	2013	2013	NUM
cana-5707	317	3	)	)	PUNCT
cana-5707	317	4	.	.	PUNCT