id	sid	tid	token	lemma	pos
cana-1585	1	1	communications	communication	NOUN
cana-1585	1	2	on	on	ADP
cana-1585	1	3	applied	apply	VERB
cana-1585	1	4	nonlinear	nonlinear	ADJ
cana-1585	1	5	analysis	analysis	NOUN
cana-1585	1	6	issn	issn	NOUN
cana-1585	1	7	:	:	PUNCT
cana-1585	1	8	1074	1074	NUM
cana-1585	1	9	-	-	PUNCT
cana-1585	1	10	133x	133x	NUM
cana-1585	1	11	vol	vol	NOUN
cana-1585	1	12	31	31	NUM
cana-1585	1	13	no	no	NOUN
cana-1585	1	14	.	.	PUNCT
cana-1585	2	1	8s	8s	PROPN
cana-1585	2	2	(	(	PUNCT
cana-1585	2	3	2024	2024	NUM
cana-1585	2	4	)	)	PUNCT
cana-1585	2	5	740	740	NUM
cana-1585	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	2	7	on	on	ADP
cana-1585	2	8	δgα	δgα	NOUN
cana-1585	2	9	closure	closure	NOUN
cana-1585	2	10	and	and	CCONJ
cana-1585	2	11	δgα	δgα	PROPN
cana-1585	2	12	interior	interior	PROPN
cana-1585	2	13	s	s	PART
cana-1585	2	14	in	in	ADP
cana-1585	2	15	tss	tss	PROPN
cana-1585	2	16	m.	m.	PROPN
cana-1585	2	17	madhesan1	madhesan1	PROPN
cana-1585	2	18	,	,	PUNCT
cana-1585	2	19	v.e	v.e	PROPN
cana-1585	2	20	.	.	PROPN
cana-1585	2	21	sasikala2	sasikala2	PROPN
cana-1585	2	22	,	,	PUNCT
cana-1585	2	23	*	*	PROPN
cana-1585	2	24	1research	1research	NUM
cana-1585	2	25	scholar	scholar	NOUN
cana-1585	2	26	,	,	PUNCT
cana-1585	2	27	vels	vels	PROPN
cana-1585	2	28	institute	institute	PROPN
cana-1585	2	29	of	of	ADP
cana-1585	2	30	science	science	PROPN
cana-1585	2	31	technology	technology	NOUN
cana-1585	2	32	and	and	CCONJ
cana-1585	2	33	advanced	advanced	ADJ
cana-1585	2	34	studies	study	NOUN
cana-1585	2	35	,	,	PUNCT
cana-1585	2	36	chennai	chennai	PROPN
cana-1585	2	37	,	,	PUNCT
cana-1585	2	38	tamil	tamil	PROPN
cana-1585	2	39	nadu	nadu	PROPN
cana-1585	2	40	,	,	PUNCT
cana-1585	2	41	india	india	PROPN
cana-1585	2	42	.	.	PUNCT
cana-1585	3	1	2,*research	2,*research	NUM
cana-1585	3	2	supervisor	supervisor	NOUN
cana-1585	3	3	,	,	PUNCT
cana-1585	3	4	assistant	assistant	NOUN
cana-1585	3	5	professor	professor	NOUN
cana-1585	3	6	,	,	PUNCT
cana-1585	3	7	vels	vels	PROPN
cana-1585	3	8	institute	institute	PROPN
cana-1585	3	9	of	of	ADP
cana-1585	3	10	science	science	PROPN
cana-1585	3	11	technology	technology	NOUN
cana-1585	3	12	and	and	CCONJ
cana-1585	3	13	advanced	advanced	ADJ
cana-1585	3	14	studies	study	NOUN
cana-1585	3	15	,	,	PUNCT
cana-1585	3	16	chennai	chennai	PROPN
cana-1585	3	17	,	,	PUNCT
cana-1585	3	18	tamil	tamil	PROPN
cana-1585	3	19	nadu	nadu	PROPN
cana-1585	3	20	,	,	PUNCT
cana-1585	3	21	india	india	PROPN
cana-1585	3	22	2	2	NUM
cana-1585	3	23	,	,	PUNCT
cana-1585	3	24	*	*	PUNCT
cana-1585	3	25	corresponding	correspond	VERB
cana-1585	3	26	author	author	NOUN
cana-1585	3	27	:	:	PUNCT
cana-1585	3	28	sasikala.sbs@velsuniv.ac.in	sasikala.sbs@velsuniv.ac.in	PROPN
cana-1585	3	29	article	article	NOUN
cana-1585	3	30	history	history	NOUN
cana-1585	3	31	:	:	PUNCT
cana-1585	3	32	received	receive	VERB
cana-1585	3	33	:	:	PUNCT
cana-1585	3	34	21	21	NUM
cana-1585	3	35	-	-	PUNCT
cana-1585	3	36	04	04	NUM
cana-1585	3	37	-	-	PUNCT
cana-1585	3	38	2024	2024	NUM
cana-1585	3	39	revised	revise	VERB
cana-1585	3	40	:	:	PUNCT
cana-1585	3	41	11	11	NUM
cana-1585	3	42	-	-	SYM
cana-1585	3	43	06	06	NUM
cana-1585	3	44	-	-	PUNCT
cana-1585	3	45	2024	2024	NUM
cana-1585	3	46	accepted	accept	VERB
cana-1585	3	47	:	:	PUNCT
cana-1585	3	48	24	24	NUM
cana-1585	3	49	-	-	PUNCT
cana-1585	3	50	06	06	NUM
cana-1585	3	51	-	-	PUNCT
cana-1585	3	52	2024	2024	NUM
cana-1585	3	53	abstract	abstract	NOUN
cana-1585	3	54	:	:	PUNCT
cana-1585	3	55	the	the	DET
cana-1585	3	56	purpose	purpose	NOUN
cana-1585	3	57	of	of	ADP
cana-1585	3	58	this	this	DET
cana-1585	3	59	research	research	NOUN
cana-1585	3	60	article	article	NOUN
cana-1585	3	61	is	be	AUX
cana-1585	3	62	to	to	PART
cana-1585	3	63	explain	explain	VERB
cana-1585	3	64	the	the	DET
cana-1585	3	65	new	new	ADJ
cana-1585	3	66	notions	notion	NOUN
cana-1585	3	67	of	of	ADP
cana-1585	3	68	δgα	δgα	NOUN
cana-1585	3	69	derived	derive	VERB
cana-1585	3	70	,	,	PUNCT
cana-1585	3	71	δgαclosure	δgαclosure	NOUN
cana-1585	3	72	,	,	PUNCT
cana-1585	3	73	δgα	δgα	NOUN
cana-1585	3	74	-	-	PUNCT
cana-1585	3	75	interior	interior	ADJ
cana-1585	3	76	,	,	PUNCT
cana-1585	3	77	δgα	δgα	NOUN
cana-1585	3	78	-	-	PUNCT
cana-1585	3	79	nbd	nbd	PROPN
cana-1585	3	80	.	.	PROPN
cana-1585	3	81	,	,	PUNCT
cana-1585	3	82	and	and	CCONJ
cana-1585	3	83	moreover	moreover	ADV
cana-1585	3	84	,	,	PUNCT
cana-1585	3	85	the	the	DET
cana-1585	3	86	connections	connection	NOUN
cana-1585	3	87	among	among	ADP
cana-1585	3	88	them	they	PRON
cana-1585	3	89	are	be	AUX
cana-1585	3	90	identified	identify	VERB
cana-1585	3	91	.	.	PUNCT
cana-1585	4	1	keywords	keyword	NOUN
cana-1585	4	2	:	:	PUNCT
cana-1585	4	3	δgα	δgα	NOUN
cana-1585	4	4	-	-	PUNCT
cana-1585	4	5	o	o	NOUN
cana-1585	4	6	,	,	PUNCT
cana-1585	4	7	δgα	δgα	NOUN
cana-1585	4	8	-	-	PUNCT
cana-1585	4	9	closure	closure	NOUN
cana-1585	4	10	,	,	PUNCT
cana-1585	4	11	δgα	δgα	NOUN
cana-1585	4	12	-	-	PUNCT
cana-1585	4	13	interior	interior	ADJ
cana-1585	4	14	,	,	PUNCT
cana-1585	4	15	δgα	δgα	NOUN
cana-1585	4	16	-	-	PUNCT
cana-1585	4	17	nbd	nbd	PROPN
cana-1585	4	18	.	.	PROPN
cana-1585	4	19	,	,	PUNCT
cana-1585	4	20	δgα	δgα	NOUN
cana-1585	4	21	-	-	PUNCT
cana-1585	4	22	derived	derive	VERB
cana-1585	4	23	,	,	PUNCT
cana-1585	4	24	δgα	δgα	NOUN
cana-1585	4	25	-	-	PUNCT
cana-1585	4	26	border	border	NOUN
cana-1585	4	27	,	,	PUNCT
cana-1585	4	28	δgαfrontier	δgαfrontier	ADV
cana-1585	4	29	,	,	PUNCT
cana-1585	4	30	δgα	δgα	NOUN
cana-1585	4	31	-	-	PUNCT
cana-1585	4	32	exterior	exterior	ADJ
cana-1585	4	33	and	and	CCONJ
cana-1585	4	34	δgα	δgα	NOUN
cana-1585	4	35	-	-	PUNCT
cana-1585	4	36	saturated	saturate	VERB
cana-1585	4	37	.	.	PUNCT
cana-1585	5	1	1	1	X
cana-1585	5	2	.	.	X
cana-1585	5	3	introduction	introduction	NOUN
cana-1585	5	4	in	in	ADP
cana-1585	5	5	many	many	ADJ
cana-1585	5	6	application	application	NOUN
cana-1585	5	7	domains	domain	NOUN
cana-1585	5	8	,	,	PUNCT
cana-1585	5	9	like	like	ADP
cana-1585	5	10	data	data	NOUN
cana-1585	5	11	mining	mining	NOUN
cana-1585	5	12	,	,	PUNCT
cana-1585	5	13	the	the	DET
cana-1585	5	14	significance	significance	NOUN
cana-1585	5	15	of	of	ADP
cana-1585	5	16	general	general	ADJ
cana-1585	5	17	tss	tss	PROPN
cana-1585	5	18	is	be	AUX
cana-1585	5	19	growing	grow	VERB
cana-1585	5	20	quickly	quickly	ADV
cana-1585	5	21	[	[	X
cana-1585	5	22	13	13	NUM
cana-1585	5	23	]	]	PUNCT
cana-1585	5	24	.	.	PUNCT
cana-1585	6	1	mathematizing	mathematize	VERB
cana-1585	6	2	both	both	CCONJ
cana-1585	6	3	quantitative	quantitative	ADJ
cana-1585	6	4	and	and	CCONJ
cana-1585	6	5	qualitative	qualitative	ADJ
cana-1585	6	6	data	datum	NOUN
cana-1585	6	7	is	be	AUX
cana-1585	6	8	possible	possible	ADJ
cana-1585	6	9	with	with	ADP
cana-1585	6	10	topological	topological	ADJ
cana-1585	6	11	structures	structure	NOUN
cana-1585	6	12	on	on	ADP
cana-1585	6	13	the	the	DET
cana-1585	6	14	data	data	NOUN
cana-1585	6	15	collection	collection	NOUN
cana-1585	6	16	serving	serve	VERB
cana-1585	6	17	as	as	ADP
cana-1585	6	18	appropriate	appropriate	ADJ
cana-1585	6	19	mathematical	mathematical	ADJ
cana-1585	6	20	models	model	NOUN
cana-1585	6	21	.	.	PUNCT
cana-1585	7	1	nowadays	nowadays	ADV
cana-1585	7	2	,	,	PUNCT
cana-1585	7	3	a	a	DET
cana-1585	7	4	large	large	ADJ
cana-1585	7	5	number	number	NOUN
cana-1585	7	6	of	of	ADP
cana-1585	7	7	topologists	topologist	NOUN
cana-1585	7	8	worldwide	worldwide	ADV
cana-1585	7	9	are	be	AUX
cana-1585	7	10	studying	study	VERB
cana-1585	7	11	generalized	generalize	VERB
cana-1585	7	12	os	os	NOUN
cana-1585	7	13	because	because	SCONJ
cana-1585	7	14	they	they	PRON
cana-1585	7	15	are	be	AUX
cana-1585	7	16	crucial	crucial	ADJ
cana-1585	7	17	to	to	ADP
cana-1585	7	18	general	general	ADJ
cana-1585	7	19	topology	topology	NOUN
cana-1585	7	20	.	.	PUNCT
cana-1585	8	1	a	a	DET
cana-1585	8	2	widely	widely	ADV
cana-1585	8	3	recognized	recognize	VERB
cana-1585	8	4	concept	concept	NOUN
cana-1585	8	5	that	that	PRON
cana-1585	8	6	serves	serve	VERB
cana-1585	8	7	as	as	ADP
cana-1585	8	8	a	a	DET
cana-1585	8	9	source	source	NOUN
cana-1585	8	10	of	of	ADP
cana-1585	8	11	inspiration	inspiration	NOUN
cana-1585	8	12	is	be	AUX
cana-1585	8	13	the	the	DET
cana-1585	8	14	idea	idea	NOUN
cana-1585	8	15	of	of	ADP
cana-1585	8	16	αδ	αδ	ADP
cana-1585	8	17	-	-	PUNCT
cana-1585	8	18	o	o	NOUN
cana-1585	9	1	[	[	X
cana-1585	9	2	12	12	NUM
cana-1585	9	3	]	]	PUNCT
cana-1585	9	4	,	,	PUNCT
cana-1585	9	5	which	which	PRON
cana-1585	9	6	was	be	AUX
cana-1585	9	7	first	first	ADV
cana-1585	9	8	presented	present	VERB
cana-1585	9	9	by	by	ADP
cana-1585	9	10	r.	r.	PROPN
cana-1585	9	11	devi	devi	PROPN
cana-1585	9	12	et	et	PROPN
cana-1585	9	13	al	al	PROPN
cana-1585	9	14	.	.	PROPN
cana-1585	9	15	,	,	PUNCT
cana-1585	9	16	we	we	PRON
cana-1585	9	17	shall	shall	AUX
cana-1585	9	18	carry	carry	VERB
cana-1585	9	19	out	out	ADP
cana-1585	9	20	the	the	DET
cana-1585	9	21	analysis	analysis	NOUN
cana-1585	9	22	of	of	ADP
cana-1585	9	23	related	related	ADJ
cana-1585	9	24	functions	function	NOUN
cana-1585	9	25	with	with	ADP
cana-1585	9	26	αδ	αδ	ADP
cana-1585	9	27	-	-	PUNCT
cana-1585	9	28	o	o	NOUN
cana-1585	9	29	and	and	CCONJ
cana-1585	9	30	αδc	αδc	NOUN
cana-1585	9	31	s	s	X
cana-1585	9	32	in	in	ADP
cana-1585	9	33	this	this	DET
cana-1585	9	34	research	research	NOUN
cana-1585	9	35	.	.	PUNCT
cana-1585	10	1	we	we	PRON
cana-1585	10	2	present	present	VERB
cana-1585	10	3	and	and	CCONJ
cana-1585	10	4	define	define	VERB
cana-1585	10	5	the	the	DET
cana-1585	10	6	terms	term	NOUN
cana-1585	10	7	"	"	PUNCT
cana-1585	10	8	αδ	αδ	ADP
cana-1585	10	9	-	-	PUNCT
cana-1585	10	10	d	d	NOUN
cana-1585	10	11	,	,	PUNCT
cana-1585	10	12	"	"	PUNCT
cana-1585	10	13	"	"	PUNCT
cana-1585	10	14	αδ	αδ	ADP
cana-1585	10	15	-	-	PUNCT
cana-1585	10	16	exterior	exterior	NOUN
cana-1585	10	17	,	,	PUNCT
cana-1585	10	18	"	"	PUNCT
cana-1585	10	19	as	as	ADV
cana-1585	10	20	well	well	ADV
cana-1585	10	21	as	as	ADP
cana-1585	10	22	deduce	deduce	VERB
cana-1585	10	23	their	their	PRON
cana-1585	10	24	relationship	relationship	NOUN
cana-1585	10	25	.	.	PUNCT
cana-1585	11	1	furthermore	furthermore	ADV
cana-1585	11	2	,	,	PUNCT
cana-1585	11	3	we	we	PRON
cana-1585	11	4	present	present	VERB
cana-1585	11	5	a	a	DET
cana-1585	11	6	brand	brand	NOUN
cana-1585	11	7	-	-	PUNCT
cana-1585	11	8	new	new	ADJ
cana-1585	11	9	function	function	NOUN
cana-1585	11	10	known	know	VERB
cana-1585	11	11	as	as	ADP
cana-1585	11	12	αδ	αδ	ADP
cana-1585	11	13	-	-	PUNCT
cana-1585	11	14	totally	totally	ADV
cana-1585	11	15	-	-	PUNCT
cana-1585	11	16	continuous	continuous	ADJ
cana-1585	11	17	functions	function	NOUN
cana-1585	11	18	.	.	PUNCT
cana-1585	12	1	additionally	additionally	ADV
cana-1585	12	2	,	,	PUNCT
cana-1585	12	3	as	as	ADV
cana-1585	12	4	delineated	delineated	ADJ
cana-1585	12	5	and	and	CCONJ
cana-1585	12	6	examined	examine	VERB
cana-1585	12	7	in	in	ADP
cana-1585	12	8	these	these	DET
cana-1585	12	9	works	work	NOUN
cana-1585	12	10	by	by	ADP
cana-1585	12	11	d.	d.	PROPN
cana-1585	12	12	sivaraj	sivaraj	PROPN
cana-1585	12	13	et	et	PROPN
cana-1585	12	14	al	al	PROPN
cana-1585	12	15	.	.	PROPN
cana-1585	12	16	,	,	PUNCT
cana-1585	13	1	[	[	X
cana-1585	13	2	1	1	NUM
cana-1585	13	3	-	-	SYM
cana-1585	13	4	4	4	NUM
cana-1585	13	5	]	]	PUNCT
cana-1585	13	6	,	,	PUNCT
cana-1585	13	7	a	a	DET
cana-1585	13	8	study	study	NOUN
cana-1585	13	9	on	on	ADP
cana-1585	13	10	beta	beta	ADJ
cana-1585	13	11	generalized	generalize	VERB
cana-1585	13	12	c	c	NOUN
cana-1585	13	13	s	s	X
cana-1585	13	14	in	in	ADP
cana-1585	13	15	ts	ts	ADP
cana-1585	13	16	,	,	PUNCT
cana-1585	13	17	soft	soft	ADJ
cana-1585	13	18	α	α	NOUN
cana-1585	13	19	–	–	PUNCT
cana-1585	13	20	o	o	NOUN
cana-1585	13	21	s	s	NOUN
cana-1585	13	22	,	,	PUNCT
cana-1585	13	23	[	[	X
cana-1585	13	24	19–25	19–25	NUM
cana-1585	13	25	]	]	PUNCT
cana-1585	13	26	on	on	ADP
cana-1585	13	27	soft	soft	ADJ
cana-1585	13	28	regular	regular	ADJ
cana-1585	13	29	star	star	NOUN
cana-1585	13	30	generalized	generalize	VERB
cana-1585	13	31	star	star	NOUN
cana-1585	13	32	c	c	PROPN
cana-1585	13	33	s	s	PROPN
cana-1585	13	34	in	in	ADP
cana-1585	13	35	soft	soft	ADJ
cana-1585	13	36	tss	tss	NOUN
cana-1585	13	37	and	and	CCONJ
cana-1585	13	38	[	[	X
cana-1585	13	39	5	5	NUM
cana-1585	13	40	-	-	SYM
cana-1585	13	41	10	10	NUM
cana-1585	13	42	]	]	PUNCT
cana-1585	13	43	semi	semi	NOUN
cana-1585	13	44	-	-	NOUN
cana-1585	13	45	closure	closure	ADJ
cana-1585	13	46	,	,	PUNCT
cana-1585	13	47	a	a	DET
cana-1585	13	48	note	note	NOUN
cana-1585	13	49	on	on	ADP
cana-1585	13	50	soft	soft	ADJ
cana-1585	13	51	g	g	NOUN
cana-1585	13	52	-	-	PUNCT
cana-1585	13	53	c	c	NOUN
cana-1585	13	54	s	s	PROPN
cana-1585	13	55	hildebrand	hildebrand	PROPN
cana-1585	13	56	s.	s.	PROPN
cana-1585	13	57	k.	k.	PROPN
cana-1585	13	58	et	et	PROPN
cana-1585	14	1	al	al	PROPN
cana-1585	14	2	.	.	PROPN
cana-1585	14	3	,	,	PUNCT
cana-1585	14	4	regarding	regard	VERB
cana-1585	14	5	very	very	ADV
cana-1585	14	6	αδ	αδ	ADP
cana-1585	14	7	super	super	PROPN
cana-1585	14	8	irresolute	irresolute	ADJ
cana-1585	14	9	functions	function	NOUN
cana-1585	14	10	in	in	ADP
cana-1585	14	11	tss	tss	PROPN
cana-1585	14	12	,	,	PUNCT
cana-1585	14	13	benchalli	benchalli	PROPN
cana-1585	14	14	s	s	PART
cana-1585	14	15	et	et	NOUN
cana-1585	14	16	al	al	PROPN
cana-1585	14	17	.	.	PROPN
cana-1585	14	18	,	,	PUNCT
cana-1585	14	19	on	on	ADP
cana-1585	14	20	rw	rw	NOUN
cana-1585	14	21	-	-	PUNCT
cana-1585	14	22	c	c	NOUN
cana-1585	14	23	s	s	NOUN
cana-1585	14	24	in	in	ADP
cana-1585	14	25	tss	tss	NOUN
cana-1585	14	26	,	,	PUNCT
cana-1585	14	27	[	[	X
cana-1585	14	28	11–12	11–12	NUM
cana-1585	14	29	]	]	X
cana-1585	14	30	v.	v.	CCONJ
cana-1585	14	31	kokilavani	kokilavani	PROPN
cana-1585	14	32	et	et	PROPN
cana-1585	14	33	al	al	PROPN
cana-1585	14	34	.	.	PROPN
cana-1585	14	35	,	,	PUNCT
cana-1585	14	36	the	the	DET
cana-1585	14	37	αδkernal	αδkernal	NOUN
cana-1585	14	38	and	and	CCONJ
cana-1585	14	39	αδ	αδ	NOUN
cana-1585	14	40	-	-	PUNCT
cana-1585	14	41	closure	closure	NOUN
cana-1585	14	42	via	via	ADP
cana-1585	14	43	αδ	αδ	ADP
cana-1585	14	44	-	-	PUNCT
cana-1585	14	45	o	o	NOUN
cana-1585	14	46	s	s	PROPN
cana-1585	14	47	in	in	ADP
cana-1585	14	48	tss	tss	NOUN
cana-1585	14	49	,	,	PUNCT
cana-1585	14	50	d	d	PROPN
cana-1585	14	51	–	–	PUNCT
cana-1585	14	52	αδ	αδ	ADP
cana-1585	14	53	-s	-s	PROPN
cana-1585	14	54	and	and	CCONJ
cana-1585	14	55	related	related	ADJ
cana-1585	14	56	separation	separation	NOUN
cana-1585	14	57	axioms	axiom	NOUN
cana-1585	14	58	in	in	ADP
cana-1585	14	59	tss	tss	NOUN
cana-1585	14	60	,	,	PUNCT
cana-1585	14	61	[	[	X
cana-1585	14	62	15–18	15–18	NUM
cana-1585	14	63	]	]	X
cana-1585	14	64	davis	davis	PROPN
cana-1585	14	65	a.	a.	PROPN
cana-1585	14	66	s.	s.	PROPN
cana-1585	14	67	,	,	PUNCT
cana-1585	14	68	in	in	ADP
cana-1585	14	69	addition	addition	NOUN
cana-1585	14	70	,	,	PUNCT
cana-1585	14	71	the	the	DET
cana-1585	14	72	fundamental	fundamental	ADJ
cana-1585	14	73	characteristics	characteristic	NOUN
cana-1585	14	74	of	of	ADP
cana-1585	14	75	these	these	DET
cana-1585	14	76	functions	function	NOUN
cana-1585	14	77	as	as	ADV
cana-1585	14	78	well	well	ADV
cana-1585	14	79	as	as	ADP
cana-1585	14	80	ts	ts	ADP
cana-1585	14	81	preservation	preservation	NOUN
cana-1585	14	82	theorems	theorem	NOUN
cana-1585	14	83	are	be	AUX
cana-1585	14	84	presented	present	VERB
cana-1585	14	85	and	and	CCONJ
cana-1585	14	86	examined	examine	VERB
cana-1585	14	87	.	.	PUNCT
cana-1585	15	1	2	2	X
cana-1585	15	2	.	.	X
cana-1585	15	3	preliminaries	preliminary	NOUN
cana-1585	15	4	let	let	VERB
cana-1585	15	5	x	x	PRON
cana-1585	15	6	be	be	AUX
cana-1585	15	7	a	a	DET
cana-1585	15	8	ts	ts	NOUN
cana-1585	15	9	and	and	CCONJ
cana-1585	15	10	a	a	DET
cana-1585	15	11	be	be	NOUN
cana-1585	15	12	x	x	NOUN
cana-1585	15	13	's	's	PART
cana-1585	15	14	subset	subset	NOUN
cana-1585	15	15	.	.	PUNCT
cana-1585	16	1	a	a	DET
cana-1585	16	2	's	's	PART
cana-1585	16	3	interior	interior	ADJ
cana-1585	16	4	and	and	CCONJ
cana-1585	16	5	closure	closure	NOUN
cana-1585	16	6	are	be	AUX
cana-1585	16	7	represented	represent	VERB
cana-1585	16	8	,	,	PUNCT
cana-1585	16	9	respectively	respectively	ADV
cana-1585	16	10	,	,	PUNCT
cana-1585	16	11	by	by	ADP
cana-1585	16	12	the	the	DET
cana-1585	16	13	symbols	symbol	NOUN
cana-1585	16	14	cl(a	cl(a	X
cana-1585	16	15	)	)	PUNCT
cana-1585	16	16	and	and	CCONJ
cana-1585	16	17	int(a	int(a	PROPN
cana-1585	16	18	)	)	PUNCT
cana-1585	16	19	.	.	PUNCT
cana-1585	17	1	definition	definition	NOUN
cana-1585	17	2	2.1	2.1	NUM
cana-1585	17	3	:	:	PUNCT
cana-1585	17	4	a	a	DET
cana-1585	17	5	sub	sub	NOUN
cana-1585	17	6	a	a	PRON
cana-1585	17	7	of	of	ADP
cana-1585	17	8	a	a	DET
cana-1585	17	9	space	space	NOUN
cana-1585	17	10	(	(	PUNCT
cana-1585	17	11	x	x	X
cana-1585	17	12	,	,	PUNCT
cana-1585	17	13			PROPN
cana-1585	17	14	)	)	PUNCT
cana-1585	17	15	is	be	AUX
cana-1585	17	16	called	call	VERB
cana-1585	17	17	(	(	PUNCT
cana-1585	17	18	1	1	NUM
cana-1585	17	19	)	)	PUNCT
cana-1585	17	20	regular	regular	ADJ
cana-1585	17	21	-	-	PUNCT
cana-1585	17	22	o	o	NOUN
cana-1585	18	1	[	[	X
cana-1585	18	2	15	15	NUM
cana-1585	18	3	]	]	X
cana-1585	18	4	if	if	SCONJ
cana-1585	18	5	a	a	PRON
cana-1585	18	6	=	=	X
cana-1585	18	7	int(cl(a	int(cl(a	PROPN
cana-1585	18	8	)	)	PUNCT
cana-1585	18	9	)	)	PUNCT
cana-1585	18	10	.	.	PUNCT
cana-1585	19	1	(	(	PUNCT
cana-1585	19	2	2	2	X
cana-1585	19	3	)	)	PUNCT
cana-1585	19	4	semi	semi	NOUN
cana-1585	19	5	-	-	NOUN
cana-1585	19	6	o	o	NOUN
cana-1585	20	1	[	[	X
cana-1585	20	2	15	15	NUM
cana-1585	20	3	]	]	X
cana-1585	20	4	if	if	SCONJ
cana-1585	20	5	a	a	DET
cana-1585	20	6	⊆	⊆	NUM
cana-1585	20	7	cl(int(a	cl(int(a	NOUN
cana-1585	20	8	)	)	PUNCT
cana-1585	20	9	)	)	PUNCT
cana-1585	20	10	.	.	PUNCT
cana-1585	21	1	(	(	PUNCT
cana-1585	21	2	3	3	X
cana-1585	21	3	)	)	PUNCT
cana-1585	21	4	α	α	NOUN
cana-1585	21	5	-	-	NOUN
cana-1585	21	6	o	o	X
cana-1585	22	1	[	[	X
cana-1585	22	2	2	2	X
cana-1585	22	3	]	]	X
cana-1585	22	4	if	if	SCONJ
cana-1585	22	5	a	a	DET
cana-1585	22	6	⊆	⊆	NUM
cana-1585	22	7	int(cl(int(a	int(cl(int(a	NOUN
cana-1585	22	8	)	)	PUNCT
cana-1585	22	9	)	)	PUNCT
cana-1585	22	10	)	)	PUNCT
cana-1585	22	11	.	.	PUNCT
cana-1585	23	1	communications	communication	NOUN
cana-1585	23	2	on	on	ADP
cana-1585	23	3	applied	apply	VERB
cana-1585	23	4	nonlinear	nonlinear	ADJ
cana-1585	23	5	analysis	analysis	NOUN
cana-1585	23	6	issn	issn	NOUN
cana-1585	23	7	:	:	PUNCT
cana-1585	23	8	1074	1074	NUM
cana-1585	23	9	-	-	PUNCT
cana-1585	23	10	133x	133x	NUM
cana-1585	23	11	vol	vol	NOUN
cana-1585	23	12	31	31	NUM
cana-1585	23	13	no	no	NOUN
cana-1585	23	14	.	.	PUNCT
cana-1585	24	1	8s	8s	PROPN
cana-1585	24	2	(	(	PUNCT
cana-1585	24	3	2024	2024	NUM
cana-1585	24	4	)	)	PUNCT
cana-1585	24	5	741	741	NUM
cana-1585	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	24	7	(	(	PUNCT
cana-1585	24	8	4	4	X
cana-1585	24	9	)	)	PUNCT
cana-1585	24	10	δ	δ	NOUN
cana-1585	24	11	-	-	PUNCT
cana-1585	24	12	semi	semi	NOUN
cana-1585	24	13	-	-	NOUN
cana-1585	24	14	o	o	NOUN
cana-1585	25	1	[	[	X
cana-1585	25	2	12	12	NUM
cana-1585	25	3	]	]	PUNCT
cana-1585	25	4	a	a	DET
cana-1585	25	5	⊆	⊆	NUM
cana-1585	25	6	cl(int	cl(int	PROPN
cana-1585	25	7	δ	δ	PROPN
cana-1585	25	8	(	(	PUNCT
cana-1585	25	9	a	a	NOUN
cana-1585	25	10	)	)	PUNCT
cana-1585	25	11	)	)	PUNCT
cana-1585	25	12	.	.	PUNCT
cana-1585	26	1	levine	levine	PROPN
cana-1585	26	2	's	's	PART
cana-1585	26	3	g	g	PROPN
cana-1585	26	4	-	-	PUNCT
cana-1585	26	5	cs	cs	PROPN
cana-1585	26	6	have	have	AUX
cana-1585	26	7	been	be	AUX
cana-1585	26	8	compared	compare	VERB
cana-1585	26	9	to	to	ADP
cana-1585	26	10	other	other	ADJ
cana-1585	26	11	generalized	generalized	ADJ
cana-1585	26	12	closure	closure	NOUN
cana-1585	26	13	operators	operator	NOUN
cana-1585	26	14	or	or	CCONJ
cana-1585	26	15	classes	class	NOUN
cana-1585	26	16	of	of	ADP
cana-1585	26	17	generalized	generalize	VERB
cana-1585	26	18	-	-	PUNCT
cana-1585	26	19	o	o	NOUN
cana-1585	26	20	s	s	NOUN
cana-1585	26	21	to	to	PART
cana-1585	26	22	generate	generate	VERB
cana-1585	26	23	a	a	DET
cana-1585	26	24	variety	variety	NOUN
cana-1585	26	25	of	of	ADP
cana-1585	26	26	ideas	idea	NOUN
cana-1585	26	27	.	.	PUNCT
cana-1585	27	1	a	a	DET
cana-1585	27	2	useful	useful	ADJ
cana-1585	27	3	tool	tool	NOUN
cana-1585	27	4	for	for	ADP
cana-1585	27	5	characterizing	characterize	VERB
cana-1585	27	6	tss	tss	NOUN
cana-1585	27	7	is	be	AUX
cana-1585	27	8	the	the	DET
cana-1585	27	9	generalize	generalize	VERB
cana-1585	27	10	-	-	PUNCT
cana-1585	27	11	c.	c.	NOUN
cana-1585	27	12	the	the	DET
cana-1585	27	13	union	union	NOUN
cana-1585	27	14	of	of	ADP
cana-1585	27	15	all	all	DET
cana-1585	27	16	regular	regular	ADJ
cana-1585	27	17	os	os	NOUN
cana-1585	27	18	of	of	ADP
cana-1585	27	19	x	x	PUNCT
cana-1585	27	20	contained	contain	VERB
cana-1585	27	21	in	in	ADP
cana-1585	27	22	a	a	PRON
cana-1585	27	23	is	be	AUX
cana-1585	27	24	the	the	DET
cana-1585	27	25	δ	δ	PROPN
cana-1585	27	26	-	-	NOUN
cana-1585	27	27	interior	interior	ADJ
cana-1585	27	28	[	[	X
cana-1585	27	29	10	10	NUM
cana-1585	27	30	]	]	PUNCT
cana-1585	27	31	of	of	ADP
cana-1585	27	32	a	a	DET
cana-1585	27	33	sub	sub	NOUN
cana-1585	27	34	a	a	PRON
cana-1585	27	35	of	of	ADP
cana-1585	27	36	x	x	PRON
cana-1585	27	37	,	,	PUNCT
cana-1585	27	38	and	and	CCONJ
cana-1585	27	39	it	it	PRON
cana-1585	27	40	is	be	AUX
cana-1585	27	41	represented	represent	VERB
cana-1585	27	42	by	by	ADP
cana-1585	27	43	intδ(a	intδ(a	NOUN
cana-1585	27	44	)	)	PUNCT
cana-1585	27	45	.	.	PUNCT
cana-1585	28	1	if	if	SCONJ
cana-1585	28	2	a	a	DET
cana-1585	28	3	=	=	NOUN
cana-1585	28	4	intδ(a	intδ(a	NOUN
cana-1585	28	5	)	)	PUNCT
cana-1585	28	6	,	,	PUNCT
cana-1585	28	7	then	then	ADV
cana-1585	28	8	the	the	DET
cana-1585	28	9	sub	sub	NOUN
cana-1585	28	10	a	a	PRON
cana-1585	28	11	is	be	AUX
cana-1585	28	12	referred	refer	VERB
cana-1585	28	13	to	to	ADP
cana-1585	28	14	as	as	ADP
cana-1585	28	15	δ	δ	PROPN
cana-1585	28	16	-	-	PROPN
cana-1585	28	17	o	o	X
cana-1585	29	1	[	[	X
cana-1585	29	2	10	10	NUM
cana-1585	29	3	]	]	PUNCT
cana-1585	29	4	.	.	PUNCT
cana-1585	30	1	that	that	PRON
cana-1585	30	2	is	be	AUX
cana-1585	30	3	,	,	PUNCT
cana-1585	30	4	if	if	SCONJ
cana-1585	30	5	an	an	PRON
cana-1585	30	6	is	be	AUX
cana-1585	30	7	the	the	DET
cana-1585	30	8	union	union	NOUN
cana-1585	30	9	of	of	ADP
cana-1585	30	10	regular	regular	ADJ
cana-1585	30	11	-	-	PUNCT
cana-1585	30	12	o	o	NOUN
cana-1585	30	13	s	s	NOUN
cana-1585	30	14	,	,	PUNCT
cana-1585	30	15	then	then	ADV
cana-1585	30	16	it	it	PRON
cana-1585	30	17	is	be	AUX
cana-1585	30	18	δ	δ	PROPN
cana-1585	30	19	-	-	PROPN
cana-1585	30	20	o.	o.	PROPN
cana-1585	30	21	a	a	DET
cana-1585	30	22	δ	δ	PROPN
cana-1585	30	23	-	-	PUNCT
cana-1585	30	24	c	c	PROPN
cana-1585	30	25	is	be	AUX
cana-1585	30	26	the	the	DET
cana-1585	30	27	complement	complement	NOUN
cana-1585	30	28	of	of	ADP
cana-1585	30	29	a	a	DET
cana-1585	30	30	δ	δ	PROPN
cana-1585	30	31	-	-	PUNCT
cana-1585	30	32	o.	o.	ADJ
cana-1585	30	33	detailed	detailed	ADJ
cana-1585	30	34	study	study	NOUN
cana-1585	30	35	in	in	ADP
cana-1585	30	36	this	this	DET
cana-1585	30	37	regard	regard	NOUN
cana-1585	30	38	by	by	ADP
cana-1585	30	39	many	many	ADJ
cana-1585	30	40	investigators	investigator	NOUN
cana-1585	30	41	has	have	AUX
cana-1585	30	42	enriched	enrich	VERB
cana-1585	30	43	the	the	DET
cana-1585	30	44	field	field	NOUN
cana-1585	30	45	of	of	ADP
cana-1585	30	46	generalized	generalized	ADJ
cana-1585	30	47	c	c	NOUN
cana-1585	30	48	s	s	NOUN
cana-1585	30	49	to	to	ADP
cana-1585	30	50	a	a	DET
cana-1585	30	51	considerable	considerable	ADJ
cana-1585	30	52	extent	extent	NOUN
cana-1585	30	53	.	.	PUNCT
cana-1585	31	1	nbd	nbd	PROPN
cana-1585	31	2	.	.	PROPN
cana-1585	31	3	is	be	AUX
cana-1585	31	4	one	one	NUM
cana-1585	31	5	of	of	ADP
cana-1585	31	6	the	the	DET
cana-1585	31	7	core	core	NOUN
cana-1585	31	8	concepts	concept	NOUN
cana-1585	31	9	of	of	ADP
cana-1585	31	10	topology	topology	NOUN
cana-1585	31	11	.	.	PUNCT
cana-1585	32	1	nbd	nbd	PROPN
cana-1585	32	2	.	.	PROPN
cana-1585	33	1	in	in	ADP
cana-1585	33	2	topology	topology	NOUN
cana-1585	33	3	have	have	VERB
cana-1585	33	4	significant	significant	ADJ
cana-1585	33	5	role	role	NOUN
cana-1585	33	6	in	in	ADP
cana-1585	33	7	the	the	DET
cana-1585	33	8	applications	application	NOUN
cana-1585	33	9	of	of	ADP
cana-1585	33	10	mathematics	mathematic	NOUN
cana-1585	33	11	.	.	PUNCT
cana-1585	34	1	3	3	X
cana-1585	34	2	.	.	X
cana-1585	34	3	δgα	δgα	PROPN
cana-1585	34	4	−closure	−closure	PROPN
cana-1585	34	5	(	(	PUNCT
cana-1585	34	6	δgα	δgα	PROPN
cana-1585	34	7	−cl	−cl	PROPN
cana-1585	34	8	)	)	PUNCT
cana-1585	34	9	and	and	CCONJ
cana-1585	34	10	δgα	δgα	PROPN
cana-1585	34	11	−interior	−interior	PROPN
cana-1585	34	12	(	(	PUNCT
cana-1585	34	13	δgα	δgα	NOUN
cana-1585	34	14	−int	−int	NOUN
cana-1585	34	15	)	)	PUNCT
cana-1585	34	16	in	in	ADP
cana-1585	34	17	tss	tss	NOUN
cana-1585	34	18	in	in	ADP
cana-1585	34	19	this	this	DET
cana-1585	34	20	paper	paper	NOUN
cana-1585	34	21	we	we	PRON
cana-1585	34	22	establish	establish	VERB
cana-1585	34	23	the	the	DET
cana-1585	34	24	notion	notion	NOUN
cana-1585	34	25	of	of	ADP
cana-1585	34	26	δgα	δgα	NOUN
cana-1585	34	27	−	−	PROPN
cana-1585	34	28	closure	closure	NOUN
cana-1585	34	29	,	,	PUNCT
cana-1585	34	30	δgα	δgα	NOUN
cana-1585	34	31	−	−	PROPN
cana-1585	34	32	interior	interior	PROPN
cana-1585	34	33	in	in	ADP
cana-1585	34	34	the	the	DET
cana-1585	34	35	tss	tss	NOUN
cana-1585	34	36	.	.	PUNCT
cana-1585	35	1	definition	definition	NOUN
cana-1585	35	2	3.1	3.1	NUM
cana-1585	35	3	.	.	PUNCT
cana-1585	36	1	a	a	DET
cana-1585	36	2	subset	subset	NOUN
cana-1585	36	3	m	m	VERB
cana-1585	36	4	of	of	ADP
cana-1585	36	5	a	a	DET
cana-1585	36	6	ts	ts	NOUN
cana-1585	36	7	x	x	AUX
cana-1585	36	8	is	be	AUX
cana-1585	36	9	called	call	VERB
cana-1585	36	10	a	a	DET
cana-1585	36	11	δgα	δgα	NOUN
cana-1585	36	12	-o	-o	INTJ
cana-1585	36	13	(	(	PUNCT
cana-1585	36	14	briefly	briefly	ADV
cana-1585	36	15	,	,	PUNCT
cana-1585	36	16	δgα	δgα	NOUN
cana-1585	36	17	-	-	PUNCT
cana-1585	36	18	o	o	NOUN
cana-1585	36	19	)	)	PUNCT
cana-1585	36	20	if	if	SCONJ
cana-1585	36	21	mc	mc	PROPN
cana-1585	36	22	is	be	AUX
cana-1585	36	23	δgα	δgα	NOUN
cana-1585	37	1	-c	-c	PUNCT
cana-1585	37	2	.	.	PUNCT
cana-1585	38	1	the	the	DET
cana-1585	38	2	family	family	NOUN
cana-1585	38	3	of	of	ADP
cana-1585	38	4	all	all	DET
cana-1585	38	5	δgα	δgα	NOUN
cana-1585	39	1	o	o	NOUN
cana-1585	39	2	s	s	VERB
cana-1585	39	3	in	in	ADP
cana-1585	39	4	a	a	DET
cana-1585	39	5	ts	ts	NOUN
cana-1585	39	6	x	x	VERB
cana-1585	39	7	is	be	AUX
cana-1585	39	8	represented	represent	VERB
cana-1585	39	9	by	by	ADP
cana-1585	39	10	δgα	δgα	NOUN
cana-1585	39	11	-	-	PUNCT
cana-1585	39	12	o(x	o(x	PROPN
cana-1585	39	13	)	)	PUNCT
cana-1585	39	14	.	.	PUNCT
cana-1585	40	1	example	example	NOUN
cana-1585	40	2	3.2	3.2	NUM
cana-1585	40	3	.	.	PUNCT
cana-1585	41	1	let	let	VERB
cana-1585	41	2	x=	x=	PUNCT
cana-1585	41	3	{	{	PUNCT
cana-1585	41	4	e	e	NOUN
cana-1585	41	5	,	,	PUNCT
cana-1585	41	6	f	f	PROPN
cana-1585	41	7	,	,	PUNCT
cana-1585	41	8	g	g	PROPN
cana-1585	41	9	,	,	PUNCT
cana-1585	41	10	h	h	NOUN
cana-1585	41	11	}	}	PUNCT
cana-1585	41	12	,	,	PUNCT
cana-1585	41	13	τ	τ	X
cana-1585	41	14	=	=	PUNCT
cana-1585	41	15	{	{	PUNCT
cana-1585	41	16	x	x	PROPN
cana-1585	41	17	,	,	PUNCT
cana-1585	41	18	φ	φ	PROPN
cana-1585	41	19	,	,	PUNCT
cana-1585	41	20	{	{	PUNCT
cana-1585	41	21	e	e	NOUN
cana-1585	41	22	}	}	PUNCT
cana-1585	41	23	,	,	PUNCT
cana-1585	41	24	{	{	PUNCT
cana-1585	41	25	f	f	X
cana-1585	41	26	}	}	PUNCT
cana-1585	41	27	,	,	PUNCT
cana-1585	41	28	{	{	PUNCT
cana-1585	41	29	e	e	NOUN
cana-1585	41	30	,	,	PUNCT
cana-1585	41	31	f	f	PROPN
cana-1585	41	32	}	}	PUNCT
cana-1585	41	33	,	,	PUNCT
cana-1585	41	34	{	{	PUNCT
cana-1585	41	35	e	e	NOUN
cana-1585	41	36	,	,	PUNCT
cana-1585	41	37	g	g	NOUN
cana-1585	41	38	}	}	PUNCT
cana-1585	41	39	,	,	PUNCT
cana-1585	41	40	{	{	PUNCT
cana-1585	41	41	e	e	NOUN
cana-1585	41	42	,	,	PUNCT
cana-1585	41	43	h	h	NOUN
cana-1585	41	44	}	}	PUNCT
cana-1585	41	45	,	,	PUNCT
cana-1585	41	46	{	{	PUNCT
cana-1585	41	47	e	e	NOUN
cana-1585	41	48	,	,	PUNCT
cana-1585	41	49	f	f	X
cana-1585	41	50	,	,	PUNCT
cana-1585	41	51	g	g	NOUN
cana-1585	41	52	}	}	PUNCT
cana-1585	41	53	,	,	PUNCT
cana-1585	41	54	{	{	PUNCT
cana-1585	41	55	e	e	NOUN
cana-1585	41	56	,	,	PUNCT
cana-1585	41	57	f	f	PROPN
cana-1585	41	58	,	,	PUNCT
cana-1585	41	59	h	h	NOUN
cana-1585	41	60	}	}	PUNCT
cana-1585	41	61	,	,	PUNCT
cana-1585	41	62	{	{	PUNCT
cana-1585	41	63	e	e	NOUN
cana-1585	41	64	,	,	PUNCT
cana-1585	41	65	g	g	PROPN
cana-1585	41	66	,	,	PUNCT
cana-1585	41	67	h	h	NOUN
cana-1585	41	68	}	}	PUNCT
cana-1585	41	69	}	}	PUNCT
cana-1585	41	70	then	then	ADV
cana-1585	41	71	the	the	DET
cana-1585	41	72	δgα	δgα	NOUN
cana-1585	41	73	c	c	PROPN
cana-1585	41	74	s	s	PRON
cana-1585	41	75	are	be	AUX
cana-1585	41	76	{	{	PUNCT
cana-1585	41	77	x	x	X
cana-1585	41	78	,	,	PUNCT
cana-1585	41	79	φ	φ	PROPN
cana-1585	41	80	,	,	PUNCT
cana-1585	41	81	{	{	PUNCT
cana-1585	41	82	e	e	NOUN
cana-1585	41	83	}	}	PUNCT
cana-1585	41	84	,	,	PUNCT
cana-1585	41	85	{	{	PUNCT
cana-1585	41	86	f	f	X
cana-1585	41	87	}	}	PUNCT
cana-1585	41	88	,	,	PUNCT
cana-1585	41	89	{	{	PUNCT
cana-1585	41	90	g	g	NOUN
cana-1585	41	91	}	}	PUNCT
cana-1585	41	92	,	,	PUNCT
cana-1585	41	93	{	{	PUNCT
cana-1585	41	94	e	e	NOUN
cana-1585	41	95	,	,	PUNCT
cana-1585	41	96	f	f	X
cana-1585	41	97	,	,	PUNCT
cana-1585	41	98	g	g	NOUN
cana-1585	41	99	}	}	PUNCT
cana-1585	41	100	}	}	PUNCT
cana-1585	41	101	and	and	CCONJ
cana-1585	41	102	δgα	δgα	NOUN
cana-1585	41	103	-o	-o	X
cana-1585	41	104	s	s	VERB
cana-1585	41	105	are	be	AUX
cana-1585	41	106	{	{	PUNCT
cana-1585	41	107	x	x	NOUN
cana-1585	41	108	,	,	PUNCT
cana-1585	41	109	𝜑	𝜑	PROPN
cana-1585	41	110	,	,	PUNCT
cana-1585	41	111	{	{	PUNCT
cana-1585	41	112	f	f	X
cana-1585	41	113	,	,	PUNCT
cana-1585	41	114	g	g	PROPN
cana-1585	41	115	,	,	PUNCT
cana-1585	41	116	h	h	NOUN
cana-1585	41	117	}	}	PUNCT
cana-1585	41	118	,	,	PUNCT
cana-1585	41	119	{	{	PUNCT
cana-1585	41	120	e	e	NOUN
cana-1585	41	121	,	,	PUNCT
cana-1585	41	122	g	g	PROPN
cana-1585	41	123	,	,	PUNCT
cana-1585	41	124	h},{e	h},{e	PROPN
cana-1585	41	125	,	,	PUNCT
cana-1585	41	126	f	f	X
cana-1585	41	127	,	,	PUNCT
cana-1585	41	128	h	h	NOUN
cana-1585	41	129	}	}	PUNCT
cana-1585	41	130	{	{	PUNCT
cana-1585	41	131	h	h	NOUN
cana-1585	41	132	}	}	PUNCT
cana-1585	41	133	}	}	PUNCT
cana-1585	41	134	.	.	PUNCT
cana-1585	42	1	definition	definition	NOUN
cana-1585	42	2	3.3	3.3	NUM
cana-1585	42	3	.	.	PUNCT
cana-1585	43	1	the	the	DET
cana-1585	43	2	δgα	δgα	NOUN
cana-1585	43	3	−	−	PROPN
cana-1585	43	4	cl	cl	NOUN
cana-1585	43	5	of	of	ADP
cana-1585	43	6	a	a	DET
cana-1585	43	7	subset	subset	NOUN
cana-1585	43	8	a	a	PRON
cana-1585	43	9	of	of	ADP
cana-1585	43	10	(	(	PUNCT
cana-1585	43	11	x	x	NOUN
cana-1585	43	12	,	,	PUNCT
cana-1585	43	13			PROPN
cana-1585	43	14	)	)	PUNCT
cana-1585	43	15	is	be	AUX
cana-1585	43	16	denoted	denote	VERB
cana-1585	43	17	by	by	ADP
cana-1585	43	18	δgα−	δgα−	PROPN
cana-1585	43	19	cl(a	cl(a	NUM
cana-1585	43	20	)	)	PUNCT
cana-1585	43	21	and	and	CCONJ
cana-1585	43	22	is	be	AUX
cana-1585	43	23	defined	define	VERB
cana-1585	43	24	as	as	ADP
cana-1585	43	25	the	the	DET
cana-1585	43	26	intersection	intersection	NOUN
cana-1585	43	27	of	of	ADP
cana-1585	43	28	all	all	DET
cana-1585	43	29	δgα	δgα	NOUN
cana-1585	43	30	−	−	PROPN
cana-1585	43	31	c	c	PROPN
cana-1585	43	32	s	s	AUX
cana-1585	43	33	containing	contain	VERB
cana-1585	43	34	a	a	PRON
cana-1585	43	35	and	and	CCONJ
cana-1585	43	36	is	be	AUX
cana-1585	43	37	denoted	denote	VERB
cana-1585	43	38	by	by	ADP
cana-1585	43	39	δgα	δgα	NOUN
cana-1585	43	40	-	-	PUNCT
cana-1585	43	41	cl(a	cl(a	NUM
cana-1585	43	42	)	)	PUNCT
cana-1585	43	43	.	.	PUNCT
cana-1585	44	1	δgα	δgα	NOUN
cana-1585	44	2	-	-	PUNCT
cana-1585	44	3	cl(a	cl(a	X
cana-1585	44	4	)	)	PUNCT
cana-1585	44	5	is	be	AUX
cana-1585	44	6	the	the	DET
cana-1585	44	7	smallest	small	ADJ
cana-1585	44	8	δgα	δgα	NOUN
cana-1585	44	9	-	-	PUNCT
cana-1585	44	10	c	c	PROPN
cana-1585	44	11	containing	contain	VERB
cana-1585	44	12	a.	a.	NOUN
cana-1585	44	13	therefore	therefore	ADV
cana-1585	44	14	,	,	PUNCT
cana-1585	44	15	δgα	δgα	PROPN
cana-1585	44	16	−	−	PROPN
cana-1585	44	17	cl(a)=	cl(a)=	PROPN
cana-1585	44	18	{	{	PUNCT
cana-1585	44	19	m	m	PROPN
cana-1585	44	20			ADJ
cana-1585	44	21	x	x	NOUN
cana-1585	44	22	:	:	PUNCT
cana-1585	44	23	a	a	PROPN
cana-1585	44	24	m	m	PROPN
cana-1585	44	25	and	and	CCONJ
cana-1585	44	26	m	m	PROPN
cana-1585	44	27	is	be	AUX
cana-1585	44	28	δgα	δgα	NOUN
cana-1585	45	1	−	−	PROPN
cana-1585	45	2	c	c	X
cana-1585	45	3	}	}	PUNCT
cana-1585	45	4	.	.	PUNCT
cana-1585	46	1	definition	definition	NOUN
cana-1585	46	2	3.4	3.4	NUM
cana-1585	46	3	.	.	PUNCT
cana-1585	47	1	the	the	DET
cana-1585	47	2	δgα	δgα	NOUN
cana-1585	47	3	−	−	PROPN
cana-1585	47	4	int	int	NOUN
cana-1585	47	5	of	of	ADP
cana-1585	47	6	subset	subset	NOUN
cana-1585	47	7	a	a	PRON
cana-1585	47	8	of	of	ADP
cana-1585	47	9	(	(	PUNCT
cana-1585	47	10	x	x	NOUN
cana-1585	47	11	,	,	PUNCT
cana-1585	47	12			PROPN
cana-1585	47	13	)	)	PUNCT
cana-1585	47	14	is	be	AUX
cana-1585	47	15	denoted	denote	VERB
cana-1585	47	16	by	by	ADP
cana-1585	47	17	δgα	δgα	PROPN
cana-1585	47	18	−int(a	−int(a	PROPN
cana-1585	47	19	)	)	PUNCT
cana-1585	47	20	and	and	CCONJ
cana-1585	47	21	is	be	AUX
cana-1585	47	22	defined	define	VERB
cana-1585	47	23	as	as	ADP
cana-1585	47	24	the	the	DET
cana-1585	47	25	union	union	NOUN
cana-1585	47	26	of	of	ADP
cana-1585	47	27	all	all	DET
cana-1585	47	28	δgα	δgα	NOUN
cana-1585	47	29	−	−	NOUN
cana-1585	47	30	o	o	INTJ
cana-1585	47	31	contained	contain	VERB
cana-1585	47	32	in	in	ADP
cana-1585	47	33	a	a	PRON
cana-1585	47	34	and	and	CCONJ
cana-1585	47	35	is	be	AUX
cana-1585	47	36	denoted	denote	VERB
cana-1585	47	37	by	by	ADP
cana-1585	47	38	δgα	δgα	NOUN
cana-1585	47	39	-	-	PUNCT
cana-1585	47	40	int(a	int(a	NOUN
cana-1585	47	41	)	)	PUNCT
cana-1585	47	42	.	.	PUNCT
cana-1585	48	1	δgα	δgα	NOUN
cana-1585	48	2	-	-	PUNCT
cana-1585	48	3	int(a	int(a	NOUN
cana-1585	48	4	)	)	PUNCT
cana-1585	48	5	is	be	AUX
cana-1585	48	6	the	the	DET
cana-1585	48	7	largest	large	ADJ
cana-1585	48	8	δgα	δgα	NOUN
cana-1585	48	9	o	o	NOUN
cana-1585	48	10	sub	sub	NOUN
cana-1585	48	11	of	of	ADP
cana-1585	48	12	a.	a.	NOUN
cana-1585	48	13	therefore	therefore	ADV
cana-1585	48	14	,	,	PUNCT
cana-1585	48	15	δgα	δgα	NOUN
cana-1585	48	16	-	-	PUNCT
cana-1585	48	17	int(a	int(a	NOUN
cana-1585	48	18	)	)	PUNCT
cana-1585	49	1	=	=	NOUN
cana-1585	49	2			NOUN
cana-1585	49	3	{	{	PUNCT
cana-1585	49	4	n	n	CCONJ
cana-1585	49	5			PROPN
cana-1585	49	6	x	x	NOUN
cana-1585	49	7	:	:	PUNCT
cana-1585	49	8	n	n	PRON
cana-1585	49	9			PROPN
cana-1585	49	10	a	a	PRON
cana-1585	49	11	and	and	CCONJ
cana-1585	49	12	n	n	PROPN
cana-1585	49	13	is	be	AUX
cana-1585	49	14	δgα	δgα	NOUN
cana-1585	49	15	−	−	PROPN
cana-1585	49	16	o	o	NOUN
cana-1585	49	17	}	}	PUNCT
cana-1585	49	18	.	.	PUNCT
cana-1585	50	1	remark	remark	PROPN
cana-1585	50	2	3.5	3.5	NUM
cana-1585	50	3	.	.	PUNCT
cana-1585	51	1	(	(	PUNCT
cana-1585	51	2	i	i	NOUN
cana-1585	51	3	)	)	PUNCT
cana-1585	51	4	.	.	PUNCT
cana-1585	52	1	every	every	DET
cana-1585	52	2	o	o	NOUN
cana-1585	52	3	is	be	AUX
cana-1585	52	4	δgα	δgα	NOUN
cana-1585	52	5	-o	-o	PUNCT
cana-1585	52	6	.	.	PUNCT
cana-1585	53	1	(	(	PUNCT
cana-1585	53	2	ii	ii	NOUN
cana-1585	53	3	)	)	PUNCT
cana-1585	53	4	.	.	PUNCT
cana-1585	54	1	finite	finite	PROPN
cana-1585	54	2	intersection	intersection	NOUN
cana-1585	54	3	of	of	ADP
cana-1585	54	4	δgα	δgα	NOUN
cana-1585	54	5	-	-	PUNCT
cana-1585	54	6	o	o	NOUN
cana-1585	54	7	s	s	NOUN
cana-1585	54	8	need	need	NOUN
cana-1585	54	9	not	not	PART
cana-1585	54	10	be	be	AUX
cana-1585	54	11	δgα	δgα	NOUN
cana-1585	54	12	-	-	PUNCT
cana-1585	54	13	o.	o.	INTJ
cana-1585	54	14	(	(	PUNCT
cana-1585	54	15	iii	iii	NOUN
cana-1585	54	16	)	)	PUNCT
cana-1585	54	17	.	.	PUNCT
cana-1585	55	1	finite	finite	PROPN
cana-1585	55	2	union	union	PROPN
cana-1585	55	3	of	of	ADP
cana-1585	55	4	δgα	δgα	NOUN
cana-1585	55	5	-	-	PUNCT
cana-1585	55	6	o	o	NOUN
cana-1585	55	7	s	s	NOUN
cana-1585	55	8	need	need	NOUN
cana-1585	55	9	not	not	PART
cana-1585	55	10	be	be	AUX
cana-1585	55	11	δgα	δgα	NOUN
cana-1585	55	12	-	-	PUNCT
cana-1585	55	13	o.	o.	NOUN
cana-1585	55	14	theorem	theorem	VERB
cana-1585	55	15	3.6	3.6	NUM
cana-1585	55	16	.	.	PUNCT
cana-1585	56	1	a	a	DET
cana-1585	56	2	subset	subset	NOUN
cana-1585	56	3	m	m	NOUN
cana-1585	56	4	of	of	ADP
cana-1585	56	5	a	a	DET
cana-1585	56	6	space	space	NOUN
cana-1585	56	7	z	z	NOUN
cana-1585	56	8	is	be	AUX
cana-1585	56	9	δgα	δgα	NOUN
cana-1585	56	10	-o	-o	PUNCT
cana-1585	56	11	⟺	⟺	PROPN
cana-1585	56	12	f⊆	f⊆	PROPN
cana-1585	56	13	αint(m	αint(m	PROPN
cana-1585	56	14	)	)	PUNCT
cana-1585	56	15	whenever	whenever	SCONJ
cana-1585	56	16	f⊆m	f⊆m	PROPN
cana-1585	56	17	where	where	SCONJ
cana-1585	56	18	f	f	PROPN
cana-1585	56	19	is	be	AUX
cana-1585	56	20	δ	δ	PROPN
cana-1585	56	21	-	-	PUNCT
cana-1585	56	22	c.	c.	PROPN
cana-1585	56	23	proof	proof	NOUN
cana-1585	56	24	:	:	PUNCT
cana-1585	56	25	let	let	VERB
cana-1585	56	26	m	m	PRON
cana-1585	56	27	be	be	AUX
cana-1585	56	28	a	a	DET
cana-1585	56	29	δgα	δgα	NOUN
cana-1585	56	30	-o	-o	PRON
cana-1585	56	31	subset	subset	VERB
cana-1585	56	32	of	of	ADP
cana-1585	56	33	x	x	PUNCT
cana-1585	56	34	and	and	CCONJ
cana-1585	56	35	suppose	suppose	VERB
cana-1585	56	36	f⊆	f⊆	PROPN
cana-1585	56	37	m	m	VERB
cana-1585	56	38	where	where	SCONJ
cana-1585	56	39	f	f	PROPN
cana-1585	56	40	is	be	AUX
cana-1585	56	41	δ	δ	PROPN
cana-1585	56	42	-	-	PROPN
cana-1585	56	43	c.	c.	PROPN
cana-1585	56	44	then	then	ADV
cana-1585	56	45	z	z	PROPN
cana-1585	56	46	-	-	PUNCT
cana-1585	56	47	m	m	PROPN
cana-1585	56	48	is	be	AUX
cana-1585	56	49	δgα	δgα	NOUN
cana-1585	56	50	-	-	PUNCT
cana-1585	56	51	c	c	PROPN
cana-1585	56	52	and	and	CCONJ
cana-1585	56	53	zm	zm	PROPN
cana-1585	56	54	⊆	⊆	PROPN
cana-1585	56	55	z	z	PROPN
cana-1585	56	56	-	-	PUNCT
cana-1585	56	57	f	f	PROPN
cana-1585	56	58	where	where	SCONJ
cana-1585	56	59	z	z	NOUN
cana-1585	56	60	-	-	PUNCT
cana-1585	56	61	f	f	PROPN
cana-1585	56	62	is	be	AUX
cana-1585	56	63	δ	δ	PROPN
cana-1585	56	64	-	-	NOUN
cana-1585	56	65	o	o	PROPN
cana-1585	56	66	in	in	ADP
cana-1585	56	67	z.	z.	PROPN
cana-1585	56	68	by	by	ADP
cana-1585	56	69	definition	definition	NOUN
cana-1585	56	70	of	of	ADP
cana-1585	56	71	δgα	δgα	PROPN
cana-1585	56	72	-c	-c	PROPN
cana-1585	56	73	,	,	PUNCT
cana-1585	56	74	αcl(z	αcl(z	NOUN
cana-1585	56	75	-	-	PUNCT
cana-1585	56	76	m)⊆	m)⊆	PROPN
cana-1585	56	77	z	z	PROPN
cana-1585	56	78	-	-	PROPN
cana-1585	56	79	f.	f.	PROPN
cana-1585	56	80	since	since	SCONJ
cana-1585	56	81	αcl	αcl	NOUN
cana-1585	56	82	(	(	PUNCT
cana-1585	56	83	z	z	NOUN
cana-1585	56	84	m	m	VERB
cana-1585	56	85	)	)	PUNCT
cana-1585	57	1	=	=	SYM
cana-1585	57	2	z	z	NOUN
cana-1585	57	3	αint(m	αint(m	PROPN
cana-1585	57	4	)	)	PUNCT
cana-1585	57	5	,	,	PUNCT
cana-1585	57	6	then	then	ADV
cana-1585	57	7	z	z	PROPN
cana-1585	57	8	αint(m	αint(m	PROPN
cana-1585	57	9	)	)	PUNCT
cana-1585	57	10	⊆	⊆	PROPN
cana-1585	57	11	z	z	PROPN
cana-1585	57	12	f.	f.	PROPN
cana-1585	57	13	therefore	therefore	ADV
cana-1585	57	14	f	f	PROPN
cana-1585	57	15	⊆	⊆	NUM
cana-1585	57	16	α	α	PRON
cana-1585	57	17	int(m	int(m	PROPN
cana-1585	57	18	)	)	PUNCT
cana-1585	57	19	.	.	PUNCT
cana-1585	58	1	conversely	conversely	ADV
cana-1585	58	2	,	,	PUNCT
cana-1585	58	3	let	let	VERB
cana-1585	58	4	f	f	PROPN
cana-1585	58	5	⊆	⊆	NUM
cana-1585	58	6	α	α	DET
cana-1585	58	7	int(m	int(m	PROPN
cana-1585	58	8	)	)	PUNCT
cana-1585	58	9	be	be	AUX
cana-1585	58	10	true	true	ADJ
cana-1585	58	11	whenever	whenever	SCONJ
cana-1585	58	12	f	f	PROPN
cana-1585	58	13	⊆	⊆	NUM
cana-1585	58	14	m	m	NOUN
cana-1585	58	15	and	and	CCONJ
cana-1585	58	16	f	f	PROPN
cana-1585	58	17	is	be	AUX
cana-1585	58	18	δ	δ	PROPN
cana-1585	58	19	-	-	PUNCT
cana-1585	58	20	c	c	PROPN
cana-1585	58	21	in	in	ADP
cana-1585	58	22	z	z	PROPN
cana-1585	58	23	,	,	PUNCT
cana-1585	59	1	then	then	ADV
cana-1585	59	2	z	z	NOUN
cana-1585	59	3	α	α	NOUN
cana-1585	59	4	int(m	int(m	PROPN
cana-1585	59	5	)	)	PUNCT
cana-1585	59	6	⊆z	⊆z	ADP
cana-1585	59	7	f.	f.	PROPN
cana-1585	59	8	that	that	ADV
cana-1585	59	9	is	be	AUX
cana-1585	59	10	,	,	PUNCT
cana-1585	59	11	αcl(z	αcl(z	PROPN
cana-1585	59	12	m	m	NOUN
cana-1585	59	13	)	)	PUNCT
cana-1585	60	1	⊆	⊆	NUM
cana-1585	60	2	z	z	PROPN
cana-1585	60	3	f.	f.	PROPN
cana-1585	61	1	thus	thus	ADV
cana-1585	61	2	z	z	PROPN
cana-1585	61	3	m	m	VERB
cana-1585	61	4	is	be	AUX
cana-1585	61	5	δgα	δgα	NOUN
cana-1585	61	6	–	–	PUNCT
cana-1585	61	7	c	c	NOUN
cana-1585	61	8	and	and	CCONJ
cana-1585	61	9	m	m	PROPN
cana-1585	61	10	is	be	AUX
cana-1585	61	11	δgα	δgα	PROPN
cana-1585	61	12	-o	-o	PRON
cana-1585	61	13	.	.	PUNCT
cana-1585	62	1	theorem	theorem	VERB
cana-1585	62	2	3.7	3.7	NUM
cana-1585	62	3	.	.	PUNCT
cana-1585	63	1	if	if	SCONJ
cana-1585	63	2	f	f	PROPN
cana-1585	63	3	is	be	AUX
cana-1585	63	4	δgα	δgα	NOUN
cana-1585	63	5	-	-	PUNCT
cana-1585	63	6	o	o	NOUN
cana-1585	63	7	sub	sub	NOUN
cana-1585	63	8	of	of	ADP
cana-1585	63	9	a	a	DET
cana-1585	63	10	space	space	NOUN
cana-1585	63	11	z	z	NOUN
cana-1585	63	12	whereas	whereas	SCONJ
cana-1585	63	13	αint(f	αint(f	NOUN
cana-1585	63	14	)	)	PUNCT
cana-1585	63	15	⊆g⊆f	⊆g⊆f	NOUN
cana-1585	63	16	,	,	PUNCT
cana-1585	63	17	then	then	ADV
cana-1585	63	18	v	v	NOUN
cana-1585	63	19	is	be	AUX
cana-1585	63	20	δgα	δgα	NOUN
cana-1585	63	21	-o	-o	PUNCT
cana-1585	63	22	.	.	PUNCT
cana-1585	64	1	proof	proof	NOUN
cana-1585	64	2	:	:	PUNCT
cana-1585	64	3	from	from	ADP
cana-1585	64	4	the	the	DET
cana-1585	64	5	definition	definition	NOUN
cana-1585	64	6	3.1	3.1	NUM
cana-1585	64	7	and	and	CCONJ
cana-1585	64	8	δgα	δgα	NOUN
cana-1585	64	9	–	–	PUNCT
cana-1585	64	10	c.	c.	PROPN
cana-1585	64	11	theorem	theorem	VERB
cana-1585	64	12	3.8	3.8	NUM
cana-1585	64	13	.	.	PUNCT
cana-1585	65	1	if	if	SCONJ
cana-1585	65	2	s	s	NOUN
cana-1585	65	3	is	be	AUX
cana-1585	65	4	any	any	DET
cana-1585	65	5	δgα	δgα	NOUN
cana-1585	65	6	-o	-o	INTJ
cana-1585	65	7	sub	sub	NOUN
cana-1585	65	8	of	of	ADP
cana-1585	65	9	a	a	DET
cana-1585	65	10	space	space	NOUN
cana-1585	65	11	x	x	PUNCT
cana-1585	65	12	whereas	whereas	SCONJ
cana-1585	65	13	αint(s	αint(	NOUN
cana-1585	65	14	)	)	PUNCT
cana-1585	65	15	⊆n	⊆n	ADJ
cana-1585	65	16	,	,	PUNCT
cana-1585	65	17	then	then	ADV
cana-1585	65	18	s⋂n	s⋂n	NOUN
cana-1585	65	19	is	be	AUX
cana-1585	65	20	δgα	δgα	NOUN
cana-1585	65	21	-o	-o	PUNCT
cana-1585	65	22	.	.	PUNCT
cana-1585	66	1	communications	communication	NOUN
cana-1585	66	2	on	on	ADP
cana-1585	66	3	applied	apply	VERB
cana-1585	66	4	nonlinear	nonlinear	ADJ
cana-1585	66	5	analysis	analysis	NOUN
cana-1585	66	6	issn	issn	NOUN
cana-1585	66	7	:	:	PUNCT
cana-1585	66	8	1074	1074	NUM
cana-1585	66	9	-	-	PUNCT
cana-1585	66	10	133x	133x	NUM
cana-1585	66	11	vol	vol	NOUN
cana-1585	66	12	31	31	NUM
cana-1585	66	13	no	no	NOUN
cana-1585	66	14	.	.	PUNCT
cana-1585	67	1	8s	8s	PROPN
cana-1585	67	2	(	(	PUNCT
cana-1585	67	3	2024	2024	NUM
cana-1585	67	4	)	)	PUNCT
cana-1585	67	5	742	742	NUM
cana-1585	67	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	67	7	proof	proof	NOUN
cana-1585	67	8	:	:	PUNCT
cana-1585	67	9	let	let	VERB
cana-1585	67	10	s	s	PRON
cana-1585	67	11	be	be	AUX
cana-1585	67	12	any	any	DET
cana-1585	67	13	δgα	δgα	NOUN
cana-1585	67	14	-	-	PUNCT
cana-1585	67	15	o	o	NOUN
cana-1585	67	16	sub	sub	NOUN
cana-1585	67	17	of	of	ADP
cana-1585	67	18	x	x	X
cana-1585	67	19	and	and	CCONJ
cana-1585	67	20	αint(s	αint(s	NUM
cana-1585	67	21	)	)	PUNCT
cana-1585	68	1	⊆	⊆	NUM
cana-1585	68	2	n	n	CCONJ
cana-1585	68	3	,	,	PUNCT
cana-1585	68	4	then	then	ADV
cana-1585	68	5	s	s	VERB
cana-1585	68	6	⋂	⋂	PROPN
cana-1585	68	7	αint(s	αint(s	NOUN
cana-1585	68	8	)	)	PUNCT
cana-1585	68	9	⊆	⊆	NUM
cana-1585	68	10	s	s	VERB
cana-1585	68	11	⋂	⋂	PROPN
cana-1585	68	12	n	n	ADV
cana-1585	68	13	⊆	⊆	NUM
cana-1585	68	14	s.	s.	NOUN
cana-1585	68	15	since	since	SCONJ
cana-1585	68	16	αint(s	αint(s	PROPN
cana-1585	68	17	)	)	PUNCT
cana-1585	68	18	⊆	⊆	NUM
cana-1585	68	19	s	s	NOUN
cana-1585	68	20	,	,	PUNCT
cana-1585	68	21	then	then	ADV
cana-1585	68	22	αint(s	αint(s	PROPN
cana-1585	68	23	)	)	PUNCT
cana-1585	68	24	⊆	⊆	NUM
cana-1585	68	25	s	s	VERB
cana-1585	68	26	⋂	⋂	PROPN
cana-1585	68	27	n	n	ADV
cana-1585	68	28	⊆	⊆	NUM
cana-1585	68	29	s	s	NOUN
cana-1585	68	30	and	and	CCONJ
cana-1585	68	31	from	from	ADP
cana-1585	68	32	theorem	theorem	ADJ
cana-1585	68	33	3.5	3.5	NUM
cana-1585	68	34	,	,	PUNCT
cana-1585	68	35	s	s	VERB
cana-1585	68	36	⋂	⋂	PROPN
cana-1585	68	37	n	n	PROPN
cana-1585	68	38	is	be	AUX
cana-1585	68	39	δgα	δgα	NOUN
cana-1585	68	40	-	-	PUNCT
cana-1585	68	41	o	o	NOUN
cana-1585	68	42	in	in	ADP
cana-1585	68	43	x.	x.	PROPN
cana-1585	68	44	theorem	theorem	VERB
cana-1585	68	45	3.9	3.9	NUM
cana-1585	68	46	.	.	PUNCT
cana-1585	69	1	let	let	VERB
cana-1585	69	2	m	m	PRON
cana-1585	69	3	be	be	AUX
cana-1585	69	4	any	any	DET
cana-1585	69	5	δgα	δgα	NOUN
cana-1585	69	6	-	-	PUNCT
cana-1585	69	7	c	c	NOUN
cana-1585	69	8	subset	subset	NOUN
cana-1585	69	9	.	.	PUNCT
cana-1585	70	1	then	then	ADV
cana-1585	70	2	αcl(m)-m	αcl(m)-m	PROPN
cana-1585	70	3	is	be	AUX
cana-1585	70	4	δgα	δgα	NOUN
cana-1585	70	5	-o	-o	PUNCT
cana-1585	70	6	.	.	PUNCT
cana-1585	71	1	proof	proof	NOUN
cana-1585	71	2	:	:	PUNCT
cana-1585	71	3	let	let	VERB
cana-1585	71	4	m	m	PRON
cana-1585	71	5	be	be	AUX
cana-1585	71	6	a	a	DET
cana-1585	71	7	δgα	δgα	NOUN
cana-1585	71	8	-	-	PUNCT
cana-1585	71	9	c	c	PROPN
cana-1585	71	10	and	and	CCONJ
cana-1585	71	11	f	f	PROPN
cana-1585	71	12	be	be	AUX
cana-1585	71	13	a	a	DET
cana-1585	71	14	δ	δ	PROPN
cana-1585	71	15	-	-	PUNCT
cana-1585	71	16	c	c	NOUN
cana-1585	71	17	in	in	ADP
cana-1585	71	18	x	x	SYM
cana-1585	71	19	whereas	whereas	SCONJ
cana-1585	71	20	f	f	PROPN
cana-1585	71	21	⊆	⊆	NUM
cana-1585	71	22	αcl(m	αcl(m	PROPN
cana-1585	71	23	)	)	PUNCT
cana-1585	71	24	–	–	PUNCT
cana-1585	71	25	m	m	PROPN
cana-1585	71	26	,	,	PUNCT
cana-1585	71	27	then	then	ADV
cana-1585	71	28	by	by	ADP
cana-1585	71	29	theorem	theorem	NOUN
cana-1585	71	30	m	m	AUX
cana-1585	71	31	be	be	AUX
cana-1585	71	32	a	a	DET
cana-1585	71	33	δgα	δgα	NOUN
cana-1585	71	34	-c	-c	PRON
cana-1585	71	35	sub	sub	NOUN
cana-1585	71	36	of	of	ADP
cana-1585	71	37	a	a	DET
cana-1585	71	38	space	space	NOUN
cana-1585	71	39	x	x	NOUN
cana-1585	71	40	,	,	PUNCT
cana-1585	71	41	then	then	ADV
cana-1585	71	42	αcl(m)-m	αcl(m)-m	PROPN
cana-1585	71	43	contains	contain	VERB
cana-1585	71	44	no	no	DET
cana-1585	71	45	non	non	ADJ
cana-1585	71	46	empty	empty	ADJ
cana-1585	71	47	δ	δ	PROPN
cana-1585	71	48	-	-	PROPN
cana-1585	71	49	c	c	PROPN
cana-1585	71	50	.	.	PUNCT
cana-1585	71	51	,	,	PUNCT
cana-1585	71	52	f	f	X
cana-1585	71	53	=	=	NOUN
cana-1585	71	54	∅	∅	NOUN
cana-1585	71	55	and	and	CCONJ
cana-1585	71	56	hence	hence	ADV
cana-1585	71	57	f	f	PROPN
cana-1585	71	58	⊆αint(αcl(m	⊆αint(αcl(m	PROPN
cana-1585	71	59	)	)	PUNCT
cana-1585	71	60	m	m	PROPN
cana-1585	71	61	)	)	PUNCT
cana-1585	71	62	.	.	PUNCT
cana-1585	72	1	therefore	therefore	ADV
cana-1585	72	2	,	,	PUNCT
cana-1585	72	3	by	by	ADP
cana-1585	72	4	theorem	theorem	NOUN
cana-1585	72	5	3.4	3.4	NUM
cana-1585	72	6	,	,	PUNCT
cana-1585	72	7	αcl(m	αcl(m	PROPN
cana-1585	72	8	)	)	PUNCT
cana-1585	72	9	m	m	VERB
cana-1585	72	10	is	be	AUX
cana-1585	72	11	δgα	δgα	PROPN
cana-1585	72	12	-o	-o	PUNCT
cana-1585	72	13	in	in	ADP
cana-1585	72	14	x.	x.	PROPN
cana-1585	72	15	lemma	lemma	PROPN
cana-1585	72	16	3.10	3.10	NUM
cana-1585	72	17	.	.	PUNCT
cana-1585	73	1	let	let	VERB
cana-1585	73	2	y	y	PRON
cana-1585	73	3	be	be	AUX
cana-1585	73	4	a	a	DET
cana-1585	73	5	δgα	δgα	NOUN
cana-1585	73	6	-	-	PUNCT
cana-1585	73	7	subspace	subspace	NOUN
cana-1585	73	8	of	of	ADP
cana-1585	73	9	x.	x.	NOUN
cana-1585	73	10	if	if	SCONJ
cana-1585	73	11	u	u	PROPN
cana-1585	73	12	is	be	AUX
cana-1585	73	13	δgα	δgα	NOUN
cana-1585	73	14	o	o	PROPN
cana-1585	73	15	in	in	ADP
cana-1585	73	16	y	y	PROPN
cana-1585	73	17	and	and	CCONJ
cana-1585	73	18	y	y	PROPN
cana-1585	73	19	is	be	AUX
cana-1585	73	20	δgα	δgα	PROPN
cana-1585	73	21	o	o	NOUN
cana-1585	73	22	,	,	PUNCT
cana-1585	73	23	then	then	ADV
cana-1585	73	24	u	u	NOUN
cana-1585	73	25	is	be	AUX
cana-1585	73	26	δgα	δgα	NOUN
cana-1585	73	27	-	-	PUNCT
cana-1585	73	28	o.	o.	ADJ
cana-1585	73	29	proof	proof	NOUN
cana-1585	73	30	:	:	PUNCT
cana-1585	73	31	given	give	VERB
cana-1585	73	32	u	u	NOUN
cana-1585	73	33	is	be	AUX
cana-1585	73	34	δgα	δgα	NOUN
cana-1585	73	35	o	o	PROPN
cana-1585	73	36	in	in	ADP
cana-1585	73	37	y	y	PROPN
cana-1585	73	38	,	,	PUNCT
cana-1585	73	39	u	u	NOUN
cana-1585	73	40	=	=	PROPN
cana-1585	73	41	y	y	PROPN
cana-1585	73	42	⋂	⋂	PROPN
cana-1585	73	43	g	g	NOUN
cana-1585	73	44	for	for	ADP
cana-1585	73	45	some	some	DET
cana-1585	73	46	g	g	PROPN
cana-1585	73	47	δgα	δgα	NOUN
cana-1585	73	48	o	o	PROPN
cana-1585	73	49	in	in	ADP
cana-1585	73	50	x.	x.	PROPN
cana-1585	73	51	but	but	CCONJ
cana-1585	73	52	y	y	PROPN
cana-1585	73	53	and	and	CCONJ
cana-1585	73	54	g	g	PROPN
cana-1585	73	55	are	be	AUX
cana-1585	73	56	both	both	PRON
cana-1585	73	57	δgα	δgα	NOUN
cana-1585	73	58	o	o	INTJ
cana-1585	73	59	in	in	ADP
cana-1585	73	60	x	x	PROPN
cana-1585	73	61	so	so	ADV
cana-1585	73	62	y	y	PROPN
cana-1585	73	63	⋂g	⋂g	PROPN
cana-1585	73	64	is	be	AUX
cana-1585	73	65	also	also	ADV
cana-1585	73	66	δgα	δgα	NOUN
cana-1585	73	67	o	o	PROPN
cana-1585	73	68	in	in	ADP
cana-1585	73	69	x.	x.	PROPN
cana-1585	73	70	theorem	theorem	VERB
cana-1585	73	71	3.11	3.11	NUM
cana-1585	73	72	.	.	PUNCT
cana-1585	74	1	assume	assume	VERB
cana-1585	74	2	that	that	SCONJ
cana-1585	74	3	m	m	PROPN
cana-1585	74	4	and	and	CCONJ
cana-1585	74	5	n	n	ADV
cana-1585	74	6	be	be	VERB
cana-1585	74	7	any	any	DET
cana-1585	74	8	two	two	NUM
cana-1585	74	9	subs	sub	NOUN
cana-1585	74	10	of	of	ADP
cana-1585	74	11	a	a	DET
cana-1585	74	12	ts	ts	NOUN
cana-1585	74	13	.	.	PUNCT
cana-1585	75	1	then	then	ADV
cana-1585	75	2	the	the	DET
cana-1585	75	3	succeeding	succeed	VERB
cana-1585	75	4	properties	property	NOUN
cana-1585	75	5	hold	hold	VERB
cana-1585	75	6	.	.	PUNCT
cana-1585	76	1	1	1	X
cana-1585	76	2	.	.	X
cana-1585	76	3	e	e	NOUN
cana-1585	76	4	is	be	AUX
cana-1585	76	5	δgα	δgα	NOUN
cana-1585	76	6	−	−	PROPN
cana-1585	76	7	c	c	PROPN
cana-1585	76	8	iff	iff	PROPN
cana-1585	76	9	δgα	δgα	PROPN
cana-1585	76	10	−	−	PROPN
cana-1585	76	11	cl(e	cl(e	NUM
cana-1585	76	12	)	)	PUNCT
cana-1585	77	1	=	=	SYM
cana-1585	77	2	e.	e.	PROPN
cana-1585	77	3	2	2	PROPN
cana-1585	77	4	.	.	PUNCT
cana-1585	77	5	δgα	δgα	NOUN
cana-1585	77	6	−	−	PROPN
cana-1585	77	7	cl(e	cl(e	NUM
cana-1585	77	8	)	)	PUNCT
cana-1585	77	9	is	be	AUX
cana-1585	77	10	the	the	DET
cana-1585	77	11	smallest	small	ADJ
cana-1585	77	12	δgα	δgα	NOUN
cana-1585	77	13	−	−	PROPN
cana-1585	77	14	c	c	NOUN
cana-1585	77	15	sub	sub	NOUN
cana-1585	77	16	of	of	ADP
cana-1585	77	17	x	x	PUNCT
cana-1585	77	18	containing	contain	VERB
cana-1585	77	19	e.	e.	PROPN
cana-1585	77	20	3	3	PROPN
cana-1585	77	21	.	.	PROPN
cana-1585	77	22	δgα	δgα	NOUN
cana-1585	77	23	−	−	PROPN
cana-1585	77	24	cl	cl	NOUN
cana-1585	77	25	(	(	PUNCT
cana-1585	77	26			NOUN
cana-1585	77	27	)	)	PUNCT
cana-1585	77	28	is	be	AUX
cana-1585	77	29	empty	empty	ADJ
cana-1585	77	30	,	,	PUNCT
cana-1585	77	31	δgα	δgα	NOUN
cana-1585	77	32	−	−	PROPN
cana-1585	77	33	cl	cl	NOUN
cana-1585	77	34	(	(	PUNCT
cana-1585	77	35	x)=	x)=	X
cana-1585	77	36	x.	x.	NOUN
cana-1585	77	37	4	4	X
cana-1585	77	38	.	.	X
cana-1585	77	39	δgα	δgα	NOUN
cana-1585	77	40	−	−	PROPN
cana-1585	77	41	cl(e	cl(e	NUM
cana-1585	77	42	)	)	PUNCT
cana-1585	77	43	is	be	AUX
cana-1585	77	44	a	a	DET
cana-1585	77	45	δgα	δgα	NOUN
cana-1585	77	46	−	−	PROPN
cana-1585	77	47	c	c	PROPN
cana-1585	77	48	in	in	ADP
cana-1585	77	49	(	(	PUNCT
cana-1585	77	50	x	x	NOUN
cana-1585	77	51	,	,	PUNCT
cana-1585	77	52			PROPN
cana-1585	77	53	)	)	PUNCT
cana-1585	77	54	.	.	PUNCT
cana-1585	78	1	5	5	X
cana-1585	78	2	.	.	X
cana-1585	79	1	if	if	SCONJ
cana-1585	79	2	e	e	PROPN
cana-1585	79	3			PROPN
cana-1585	79	4	f	f	X
cana-1585	79	5	,	,	PUNCT
cana-1585	79	6	then	then	ADV
cana-1585	79	7	δgα	δgα	NOUN
cana-1585	79	8	−	−	PROPN
cana-1585	79	9	cl(e	cl(e	NOUN
cana-1585	79	10	)	)	PUNCT
cana-1585	79	11			PROPN
cana-1585	79	12	δgα	δgα	PROPN
cana-1585	79	13	−	−	PROPN
cana-1585	79	14	cl(f	cl(f	PROPN
cana-1585	79	15	)	)	PUNCT
cana-1585	79	16	6	6	NUM
cana-1585	79	17	.	.	X
cana-1585	80	1	δgα	δgα	NOUN
cana-1585	80	2	−	−	PROPN
cana-1585	80	3	cl	cl	INTJ
cana-1585	80	4	(	(	PUNCT
cana-1585	80	5	e	e	NOUN
cana-1585	80	6	f	f	NOUN
cana-1585	80	7	)	)	PUNCT
cana-1585	80	8	=	=	SYM
cana-1585	80	9	δgα	δgα	NOUN
cana-1585	80	10	−	−	PROPN
cana-1585	80	11	cl(e	cl(e	NOUN
cana-1585	80	12	)	)	PUNCT
cana-1585	80	13			NOUN
cana-1585	80	14	δgα	δgα	PROPN
cana-1585	80	15	−	−	PROPN
cana-1585	80	16	cl(f	cl(f	PROPN
cana-1585	80	17	)	)	PUNCT
cana-1585	80	18	.	.	PUNCT
cana-1585	81	1	7	7	X
cana-1585	81	2	.	.	X
cana-1585	81	3	δgα	δgα	NOUN
cana-1585	81	4	−	−	PROPN
cana-1585	81	5	cl	cl	INTJ
cana-1585	81	6	(	(	PUNCT
cana-1585	81	7	e	e	NOUN
cana-1585	81	8	f	f	NOUN
cana-1585	81	9	)	)	PUNCT
cana-1585	81	10	=	=	SYM
cana-1585	81	11	δgα	δgα	NOUN
cana-1585	81	12	−	−	PROPN
cana-1585	81	13	cl(e	cl(e	NOUN
cana-1585	81	14	)	)	PUNCT
cana-1585	81	15			PUNCT
cana-1585	81	16	δgα	δgα	NOUN
cana-1585	81	17	−	−	PROPN
cana-1585	81	18	cl(f	cl(f	PROPN
cana-1585	81	19	)	)	PUNCT
cana-1585	81	20	.	.	PUNCT
cana-1585	82	1	8	8	X
cana-1585	82	2	.	.	X
cana-1585	82	3	δgα	δgα	NOUN
cana-1585	82	4	−	−	PROPN
cana-1585	82	5	cl	cl	PROPN
cana-1585	82	6	(	(	PUNCT
cana-1585	82	7	δgα	δgα	NOUN
cana-1585	82	8	−	−	PROPN
cana-1585	82	9	cl(e	cl(e	NOUN
cana-1585	82	10	)	)	PUNCT
cana-1585	82	11	)	)	PUNCT
cana-1585	83	1	=	=	SYM
cana-1585	83	2	δgα	δgα	PROPN
cana-1585	83	3	−	−	PROPN
cana-1585	83	4	cl(f	cl(f	PROPN
cana-1585	83	5	)	)	PUNCT
cana-1585	83	6	.	.	PUNCT
cana-1585	84	1	proof	proof	NOUN
cana-1585	84	2	:	:	PUNCT
cana-1585	84	3	1	1	X
cana-1585	84	4	.	.	X
cana-1585	84	5	for	for	ADP
cana-1585	84	6	any	any	DET
cana-1585	84	7	sub	sub	NOUN
cana-1585	84	8	e	e	NOUN
cana-1585	84	9	of	of	ADP
cana-1585	84	10	x	x	PRON
cana-1585	84	11	we	we	PRON
cana-1585	84	12	have	have	VERB
cana-1585	84	13	e	e	NOUN
cana-1585	84	14			PROPN
cana-1585	84	15	δgα	δgα	PROPN
cana-1585	84	16	−	−	PROPN
cana-1585	84	17	cl(e	cl(e	NUM
cana-1585	84	18	)	)	PUNCT
cana-1585	84	19	.	.	PUNCT
cana-1585	85	1	assume	assume	VERB
cana-1585	85	2	that	that	SCONJ
cana-1585	85	3	e	e	PRON
cana-1585	85	4	is	be	AUX
cana-1585	85	5	a	a	DET
cana-1585	85	6	δgα	δgα	NOUN
cana-1585	85	7	−	−	PROPN
cana-1585	85	8	c	c	PROPN
cana-1585	85	9	in	in	ADP
cana-1585	85	10	(	(	PUNCT
cana-1585	85	11	x	x	NOUN
cana-1585	85	12	,	,	PUNCT
cana-1585	85	13			PROPN
cana-1585	85	14	)	)	PUNCT
cana-1585	85	15	.	.	PUNCT
cana-1585	86	1	but	but	CCONJ
cana-1585	86	2	e	e	X
cana-1585	86	3			PROPN
cana-1585	86	4	e.	e.	PROPN
cana-1585	86	5	also	also	ADV
cana-1585	86	6	e	e	VERB
cana-1585	86	7	{h	{h	NOUN
cana-1585	86	8			PROPN
cana-1585	86	9	x	x	NOUN
cana-1585	86	10	:	:	PUNCT
cana-1585	86	11	e	e	PROPN
cana-1585	86	12			PROPN
cana-1585	86	13	h	h	PROPN
cana-1585	86	14	and	and	CCONJ
cana-1585	86	15	e	e	PROPN
cana-1585	86	16	is	be	AUX
cana-1585	86	17	δgα	δgα	NOUN
cana-1585	86	18	−	−	PROPN
cana-1585	86	19	c	c	X
cana-1585	86	20	}	}	PUNCT
cana-1585	86	21	,	,	PUNCT
cana-1585	86	22	it	it	PRON
cana-1585	86	23	gives	give	VERB
cana-1585	86	24	e	e	NOUN
cana-1585	86	25	=	=	PRON
cana-1585	86	26			X
cana-1585	86	27	{	{	PUNCT
cana-1585	86	28	h	h	NOUN
cana-1585	86	29			PROPN
cana-1585	86	30	x	x	X
cana-1585	86	31	:	:	PUNCT
cana-1585	86	32	e	e	PROPN
cana-1585	86	33			PROPN
cana-1585	86	34	h	h	PROPN
cana-1585	86	35	and	and	CCONJ
cana-1585	86	36	h	h	NOUN
cana-1585	86	37	is	be	AUX
cana-1585	86	38	δgα	δgα	PROPN
cana-1585	86	39	−c}	−c}	PROPN
cana-1585	86	40	e.	e.	PROPN
cana-1585	87	1	then	then	ADV
cana-1585	87	2	δgα	δgα	PROPN
cana-1585	87	3	−	−	PROPN
cana-1585	87	4	cl(e	cl(e	NOUN
cana-1585	87	5	)	)	PUNCT
cana-1585	87	6			PROPN
cana-1585	87	7	e.	e.	PROPN
cana-1585	87	8	so	so	ADV
cana-1585	87	9			ADJ
cana-1585	87	10	=	=	SYM
cana-1585	87	11	δgα	δgα	NOUN
cana-1585	87	12	−cl(e	−cl(e	NOUN
cana-1585	87	13	)	)	PUNCT
cana-1585	87	14	.	.	PUNCT
cana-1585	88	1	2	2	X
cana-1585	88	2	.	.	X
cana-1585	88	3	beginning	begin	VERB
cana-1585	88	4	the	the	DET
cana-1585	88	5	definition	definition	NOUN
cana-1585	88	6	of	of	ADP
cana-1585	88	7	δgα	δgα	NOUN
cana-1585	88	8	−	−	PROPN
cana-1585	88	9	cl	cl	PROPN
cana-1585	88	10	,	,	PUNCT
cana-1585	88	11	δgα	δgα	NOUN
cana-1585	88	12	−	−	PROPN
cana-1585	88	13	cl(e	cl(e	NUM
cana-1585	88	14	)	)	PUNCT
cana-1585	88	15	is	be	AUX
cana-1585	88	16	c.	c.	NOUN
cana-1585	88	17	suppose	suppose	VERB
cana-1585	88	18	if	if	SCONJ
cana-1585	88	19	f	f	PROPN
cana-1585	88	20	is	be	AUX
cana-1585	88	21	any	any	DET
cana-1585	88	22	δgα	δgα	NOUN
cana-1585	89	1	−	−	PROPN
cana-1585	89	2	c	c	PROPN
cana-1585	89	3	then	then	ADV
cana-1585	89	4	δgα	δgα	PROPN
cana-1585	89	5	−	−	PROPN
cana-1585	89	6	cl(e	cl(e	NOUN
cana-1585	89	7	)	)	PUNCT
cana-1585	89	8			PROPN
cana-1585	89	9	f.	f.	PROPN
cana-1585	89	10	hence	hence	ADV
cana-1585	89	11	δgα	δgα	NOUN
cana-1585	89	12	−	−	PROPN
cana-1585	89	13	cl(e	cl(e	NUM
cana-1585	89	14	)	)	PUNCT
cana-1585	89	15	is	be	AUX
cana-1585	89	16	the	the	DET
cana-1585	89	17	smallest	small	ADJ
cana-1585	89	18	δgα	δgα	NOUN
cana-1585	89	19	−	−	PROPN
cana-1585	89	20	c	c	PROPN
cana-1585	89	21	in	in	ADP
cana-1585	89	22	(	(	PUNCT
cana-1585	89	23	x	x	NOUN
cana-1585	89	24	,	,	PUNCT
cana-1585	89	25			PROPN
cana-1585	89	26	)	)	PUNCT
cana-1585	89	27	containing	contain	VERB
cana-1585	89	28	.	.	ADV
cana-1585	89	29	3	3	NUM
cana-1585	89	30	.	.	PUNCT
cana-1585	90	1	proof	proof	NOUN
cana-1585	90	2	is	be	AUX
cana-1585	90	3	obvious	obvious	ADJ
cana-1585	90	4	from	from	ADP
cana-1585	90	5	the	the	DET
cana-1585	90	6	definition	definition	NOUN
cana-1585	90	7	.	.	PUNCT
cana-1585	91	1	4	4	X
cana-1585	91	2	.	.	X
cana-1585	91	3	proof	proof	NOUN
cana-1585	91	4	is	be	AUX
cana-1585	91	5	apparent	apparent	ADJ
cana-1585	91	6	from	from	ADP
cana-1585	91	7	the	the	DET
cana-1585	91	8	definition	definition	NOUN
cana-1585	91	9	.	.	PUNCT
cana-1585	92	1	5	5	X
cana-1585	92	2	.	.	X
cana-1585	93	1	if	if	SCONJ
cana-1585	93	2	e	e	PROPN
cana-1585	93	3			PROPN
cana-1585	93	4	f	f	PROPN
cana-1585	93	5	then	then	ADV
cana-1585	93	6	e	e	PROPN
cana-1585	93	7			PROPN
cana-1585	93	8	δgα	δgα	PROPN
cana-1585	93	9	−	−	PROPN
cana-1585	93	10	cl(f	cl(f	PROPN
cana-1585	93	11	)	)	PUNCT
cana-1585	93	12	because	because	SCONJ
cana-1585	93	13	f	f	PROPN
cana-1585	93	14			PROPN
cana-1585	93	15	δgα	δgα	PROPN
cana-1585	93	16	−	−	PROPN
cana-1585	93	17	cl(f	cl(f	PROPN
cana-1585	93	18	)	)	PUNCT
cana-1585	93	19	for	for	ADP
cana-1585	93	20	all	all	DET
cana-1585	93	21	f.	f.	PROPN
cana-1585	93	22	hence	hence	ADV
cana-1585	93	23	δgα	δgα	PROPN
cana-1585	93	24	−	−	PROPN
cana-1585	93	25	cl(f	cl(f	PROPN
cana-1585	93	26	)	)	PUNCT
cana-1585	93	27	is	be	AUX
cana-1585	93	28	the	the	DET
cana-1585	93	29	δgα	δgα	NOUN
cana-1585	93	30	−	−	PROPN
cana-1585	93	31	c	c	PROPN
cana-1585	93	32	containing	contain	VERB
cana-1585	93	33	e.	e.	PROPN
cana-1585	93	34	but	but	CCONJ
cana-1585	93	35	δgα	δgα	NOUN
cana-1585	93	36	−cl(e	−cl(e	NOUN
cana-1585	93	37	)	)	PUNCT
cana-1585	93	38	is	be	AUX
cana-1585	93	39	smallest	small	ADJ
cana-1585	93	40	δgα	δgα	NOUN
cana-1585	93	41	−	−	PROPN
cana-1585	93	42	c	c	PROPN
cana-1585	93	43	containing	contain	VERB
cana-1585	93	44	e.	e.	PROPN
cana-1585	94	1	so	so	PROPN
cana-1585	94	2	δgα	δgα	PROPN
cana-1585	94	3	−	−	PROPN
cana-1585	94	4	cl(e	cl(e	NOUN
cana-1585	94	5	)	)	PUNCT
cana-1585	94	6			PROPN
cana-1585	94	7	δgα	δgα	PROPN
cana-1585	94	8	−	−	PROPN
cana-1585	94	9	cl(f	cl(f	PROPN
cana-1585	94	10	)	)	PUNCT
cana-1585	94	11	.	.	PUNCT
cana-1585	95	1	6	6	X
cana-1585	95	2	.	.	X
cana-1585	96	1	we	we	PRON
cana-1585	96	2	know	know	VERB
cana-1585	96	3	the	the	DET
cana-1585	96	4	result	result	NOUN
cana-1585	96	5	e	e	NOUN
cana-1585	96	6			PROPN
cana-1585	96	7	(	(	PUNCT
cana-1585	96	8	e	e	NOUN
cana-1585	96	9	f	f	NOUN
cana-1585	96	10	)	)	PUNCT
cana-1585	96	11	and	and	CCONJ
cana-1585	96	12	n	n	CCONJ
cana-1585	96	13			PROPN
cana-1585	96	14	e	e	PROPN
cana-1585	96	15			NOUN
cana-1585	96	16	f	f	PROPN
cana-1585	96	17	,	,	PUNCT
cana-1585	96	18	from	from	ADP
cana-1585	96	19	the	the	DET
cana-1585	96	20	above	above	ADJ
cana-1585	96	21	result	result	NOUN
cana-1585	96	22	,	,	PUNCT
cana-1585	96	23	δgα	δgα	NOUN
cana-1585	96	24	−	−	PROPN
cana-1585	96	25	cl(e	cl(e	NOUN
cana-1585	96	26	)	)	PUNCT
cana-1585	96	27			PROPN
cana-1585	96	28	δgα	δgα	NOUN
cana-1585	96	29	−	−	PROPN
cana-1585	96	30	cl	cl	NOUN
cana-1585	96	31	(	(	PUNCT
cana-1585	96	32	e	e	NOUN
cana-1585	96	33	f	f	NOUN
cana-1585	96	34	)	)	PUNCT
cana-1585	96	35	also	also	ADV
cana-1585	96	36	δgα	δgα	PROPN
cana-1585	96	37	−	−	PROPN
cana-1585	96	38	cl(f	cl(f	PROPN
cana-1585	96	39	)	)	PUNCT
cana-1585	97	1			PROPN
cana-1585	97	2	δgα	δgα	PROPN
cana-1585	97	3	−	−	PROPN
cana-1585	97	4	cl	cl	NOUN
cana-1585	97	5	(	(	PUNCT
cana-1585	97	6	e	e	NOUN
cana-1585	97	7	f	f	NOUN
cana-1585	97	8	)	)	PUNCT
cana-1585	97	9	and	and	CCONJ
cana-1585	97	10	δgα	δgα	PROPN
cana-1585	97	11	−	−	PROPN
cana-1585	97	12	cl(f	cl(f	PROPN
cana-1585	97	13	)	)	PUNCT
cana-1585	97	14			PROPN
cana-1585	97	15	δgα	δgα	PROPN
cana-1585	98	1	−	−	PROPN
cana-1585	99	1	cl	cl	INTJ
cana-1585	99	2	(	(	PUNCT
cana-1585	99	3			ADJ
cana-1585	99	4	f	f	NOUN
cana-1585	99	5	)	)	PUNCT
cana-1585	99	6	.	.	PUNCT
cana-1585	100	1	so	so	ADV
cana-1585	100	2	δgα	δgα	NOUN
cana-1585	100	3	−	−	PROPN
cana-1585	100	4	cl(e	cl(e	NOUN
cana-1585	100	5	)	)	PUNCT
cana-1585	100	6			NOUN
cana-1585	100	7	δgα	δgα	PROPN
cana-1585	100	8	−	−	PROPN
cana-1585	100	9	cl(f	cl(f	PROPN
cana-1585	100	10	)	)	PUNCT
cana-1585	100	11			PROPN
cana-1585	100	12	δgα	δgα	PROPN
cana-1585	100	13	−	−	PROPN
cana-1585	100	14	cl	cl	NOUN
cana-1585	100	15	(	(	PUNCT
cana-1585	100	16	e	e	PROPN
cana-1585	100	17			NOUN
cana-1585	100	18	f	f	PROPN
cana-1585	100	19	)	)	PUNCT
cana-1585	100	20	.	.	PUNCT
cana-1585	101	1	but	but	CCONJ
cana-1585	101	2	δgα	δgα	NOUN
cana-1585	101	3	−	−	PROPN
cana-1585	101	4	cl(e	cl(e	NUM
cana-1585	101	5	)	)	PUNCT
cana-1585	101	6	is	be	AUX
cana-1585	101	7	δgα	δgα	NOUN
cana-1585	101	8	−	−	PROPN
cana-1585	101	9	c	c	PROPN
cana-1585	101	10	containing	contain	VERB
cana-1585	101	11	e	e	NOUN
cana-1585	101	12	and	and	CCONJ
cana-1585	101	13	δgα	δgα	PROPN
cana-1585	101	14	−	−	PROPN
cana-1585	101	15	cl(f	cl(f	PROPN
cana-1585	101	16	)	)	PUNCT
cana-1585	101	17	is	be	AUX
cana-1585	101	18	δgα	δgα	NOUN
cana-1585	101	19	−	−	PROPN
cana-1585	101	20	c	c	PROPN
cana-1585	101	21	containing	contain	VERB
cana-1585	101	22	f.	f.	PROPN
cana-1585	101	23	hence	hence	ADV
cana-1585	101	24	δgα	δgα	NOUN
cana-1585	101	25	−	−	PROPN
cana-1585	101	26	cl(e	cl(e	NOUN
cana-1585	101	27	)	)	PUNCT
cana-1585	101	28			NOUN
cana-1585	101	29	δgα	δgα	NOUN
cana-1585	101	30	−	−	PROPN
cana-1585	101	31	cl(e	cl(e	NUM
cana-1585	101	32	)	)	PUNCT
cana-1585	101	33	is	be	AUX
cana-1585	101	34	δgα	δgα	NOUN
cana-1585	101	35	−	−	PROPN
cana-1585	101	36	c	c	PROPN
cana-1585	101	37	containing	contain	VERB
cana-1585	101	38	e	e	PROPN
cana-1585	101	39			PROPN
cana-1585	101	40	f.	f.	PROPN
cana-1585	101	41	here	here	ADV
cana-1585	101	42	δgα	δgα	PROPN
cana-1585	102	1	−	−	PROPN
cana-1585	102	2	cl	cl	NOUN
cana-1585	102	3	(	(	PUNCT
cana-1585	102	4	e	e	PROPN
cana-1585	102	5			NOUN
cana-1585	102	6	f	f	PROPN
cana-1585	102	7	)	)	PUNCT
cana-1585	102	8	is	be	AUX
cana-1585	102	9	communications	communication	NOUN
cana-1585	102	10	on	on	ADP
cana-1585	102	11	applied	apply	VERB
cana-1585	102	12	nonlinear	nonlinear	ADJ
cana-1585	102	13	analysis	analysis	NOUN
cana-1585	102	14	issn	issn	NOUN
cana-1585	102	15	:	:	PUNCT
cana-1585	102	16	1074	1074	NUM
cana-1585	102	17	-	-	PUNCT
cana-1585	102	18	133x	133x	NUM
cana-1585	102	19	vol	vol	NOUN
cana-1585	102	20	31	31	NUM
cana-1585	102	21	no	no	NOUN
cana-1585	102	22	.	.	PUNCT
cana-1585	103	1	8s	8s	PROPN
cana-1585	103	2	(	(	PUNCT
cana-1585	103	3	2024	2024	NUM
cana-1585	103	4	)	)	PUNCT
cana-1585	103	5	743	743	NUM
cana-1585	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	103	7	δgα	δgα	NOUN
cana-1585	103	8	−	−	PROPN
cana-1585	103	9	c	c	PROPN
cana-1585	103	10	containing	contain	VERB
cana-1585	103	11	(	(	PUNCT
cana-1585	103	12	e	e	PROPN
cana-1585	103	13			NOUN
cana-1585	103	14	f	f	PROPN
cana-1585	103	15	)	)	PUNCT
cana-1585	103	16	.	.	PUNCT
cana-1585	104	1	therefore	therefore	ADV
cana-1585	104	2	δgα	δgα	PROPN
cana-1585	104	3	−	−	PROPN
cana-1585	104	4	cl	cl	INTJ
cana-1585	104	5	(	(	PUNCT
cana-1585	104	6			ADJ
cana-1585	104	7	)	)	PUNCT
cana-1585	104	8			NOUN
cana-1585	104	9	δgα	δgα	PROPN
cana-1585	104	10	−	−	PROPN
cana-1585	104	11	cl(f	cl(f	PROPN
cana-1585	104	12	)	)	PUNCT
cana-1585	104	13			PROPN
cana-1585	104	14	δgα	δgα	NOUN
cana-1585	104	15	−	−	PROPN
cana-1585	104	16	cl(e	cl(e	PROPN
cana-1585	104	17			NOUN
cana-1585	104	18	f	f	PROPN
cana-1585	104	19	)	)	PUNCT
cana-1585	104	20	.	.	PUNCT
cana-1585	105	1	therefore	therefore	ADV
cana-1585	105	2	we	we	PRON
cana-1585	105	3	get	get	VERB
cana-1585	105	4	δgα	δgα	NOUN
cana-1585	105	5	−	−	PROPN
cana-1585	105	6	cl(e	cl(e	PROPN
cana-1585	105	7			NOUN
cana-1585	106	1	f	f	NOUN
cana-1585	106	2	)	)	PUNCT
cana-1585	106	3	=	=	SYM
cana-1585	106	4	δgα	δgα	NOUN
cana-1585	106	5	−	−	PROPN
cana-1585	106	6	cl(e	cl(e	NOUN
cana-1585	106	7	)	)	PUNCT
cana-1585	106	8			NOUN
cana-1585	106	9	δgα	δgα	PROPN
cana-1585	106	10	−	−	PROPN
cana-1585	106	11	cl(f	cl(f	PROPN
cana-1585	106	12	)	)	PUNCT
cana-1585	106	13	.	.	PUNCT
cana-1585	107	1	7	7	X
cana-1585	107	2	.	.	X
cana-1585	107	3	we	we	PRON
cana-1585	107	4	know	know	VERB
cana-1585	107	5	that	that	SCONJ
cana-1585	107	6	(	(	PUNCT
cana-1585	107	7	e	e	X
cana-1585	107	8			X
cana-1585	107	9	f	f	NOUN
cana-1585	107	10	)	)	PUNCT
cana-1585	107	11			PROPN
cana-1585	107	12	e	e	PROPN
cana-1585	107	13	and	and	CCONJ
cana-1585	107	14	(	(	PUNCT
cana-1585	107	15	e	e	X
cana-1585	107	16			X
cana-1585	107	17	f	f	X
cana-1585	107	18	)	)	PUNCT
cana-1585	107	19			PROPN
cana-1585	107	20	f.	f.	PROPN
cana-1585	107	21	by	by	ADP
cana-1585	107	22	(	(	PUNCT
cana-1585	107	23	v	v	NOUN
cana-1585	107	24	)	)	PUNCT
cana-1585	107	25	δgα	δgα	NOUN
cana-1585	107	26	−	−	PROPN
cana-1585	107	27	cl(e	cl(e	NOUN
cana-1585	107	28			ADJ
cana-1585	107	29	f	f	NOUN
cana-1585	107	30	)	)	PUNCT
cana-1585	107	31			PROPN
cana-1585	107	32	δgα	δgα	NOUN
cana-1585	107	33	−	−	PROPN
cana-1585	107	34	cl(e	cl(e	NUM
cana-1585	107	35	)	)	PUNCT
cana-1585	107	36	and	and	CCONJ
cana-1585	108	1	δgα	δgα	NOUN
cana-1585	108	2	−	−	PROPN
cana-1585	108	3	cl(e	cl(e	NOUN
cana-1585	108	4			ADJ
cana-1585	108	5	f	f	NOUN
cana-1585	108	6	)	)	PUNCT
cana-1585	108	7			PROPN
cana-1585	108	8	δgα	δgα	NOUN
cana-1585	108	9	−	−	PROPN
cana-1585	108	10	cl(e	cl(e	NOUN
cana-1585	108	11	)	)	PUNCT
cana-1585	108	12			PUNCT
cana-1585	108	13	δgα	δgα	NOUN
cana-1585	108	14	−	−	PROPN
cana-1585	108	15	cl(f	cl(f	PROPN
cana-1585	108	16	)	)	PUNCT
cana-1585	108	17	.	.	PUNCT
cana-1585	109	1	8	8	X
cana-1585	109	2	.	.	X
cana-1585	109	3	δgα	δgα	NOUN
cana-1585	109	4	−	−	PROPN
cana-1585	109	5	cl(e	cl(e	NUM
cana-1585	109	6	)	)	PUNCT
cana-1585	109	7	is	be	AUX
cana-1585	109	8	a	a	DET
cana-1585	109	9	δgα	δgα	NOUN
cana-1585	109	10	c	c	X
cana-1585	109	11	in	in	ADP
cana-1585	109	12	(	(	PUNCT
cana-1585	109	13	x	x	NOUN
cana-1585	109	14	,	,	PUNCT
cana-1585	109	15			PROPN
cana-1585	109	16	)	)	PUNCT
cana-1585	109	17	.	.	PUNCT
cana-1585	110	1	let	let	VERB
cana-1585	110	2	then	then	ADV
cana-1585	110	3	k	k	PROPN
cana-1585	110	4	is	be	AUX
cana-1585	110	5	δgα	δgα	PROPN
cana-1585	110	6	-c	-c	PUNCT
cana-1585	110	7	δgα	δgα	NOUN
cana-1585	110	8	−	−	PROPN
cana-1585	110	9	cl(e	cl(e	NUM
cana-1585	110	10	)	)	PUNCT
cana-1585	110	11	=	=	SYM
cana-1585	111	1	k	k	NOUN
cana-1585	111	2	,	,	PUNCT
cana-1585	111	3	in	in	ADP
cana-1585	111	4	(	(	PUNCT
cana-1585	111	5	x	x	NOUN
cana-1585	111	6	,	,	PUNCT
cana-1585	111	7			PROPN
cana-1585	111	8	)	)	PUNCT
cana-1585	111	9	.	.	PUNCT
cana-1585	112	1	using	use	VERB
cana-1585	112	2	(	(	PUNCT
cana-1585	112	3	i	i	NOUN
cana-1585	112	4	)	)	PUNCT
cana-1585	112	5	δgα	δgα	NOUN
cana-1585	112	6	−	−	PROPN
cana-1585	112	7	cl(k	cl(k	NOUN
cana-1585	112	8	)	)	PUNCT
cana-1585	113	1	=	=	SYM
cana-1585	113	2	k	k	NOUN
cana-1585	113	3	,	,	PUNCT
cana-1585	113	4	which	which	PRON
cana-1585	113	5	gives	give	VERB
cana-1585	113	6	δgα	δgα	NOUN
cana-1585	113	7	−	−	PROPN
cana-1585	113	8	cl	cl	NOUN
cana-1585	113	9	(	(	PUNCT
cana-1585	113	10	δgα	δgα	NOUN
cana-1585	113	11	−	−	PROPN
cana-1585	113	12	cl(e	cl(e	NOUN
cana-1585	113	13	)	)	PUNCT
cana-1585	113	14	)	)	PUNCT
cana-1585	114	1	=	=	SYM
cana-1585	114	2	δgα	δgα	NOUN
cana-1585	114	3	−	−	PROPN
cana-1585	114	4	cl(e	cl(e	NUM
cana-1585	114	5	)	)	PUNCT
cana-1585	114	6	.	.	PUNCT
cana-1585	115	1	remark	remark	PROPN
cana-1585	115	2	3.12	3.12	NUM
cana-1585	115	3	.	.	PUNCT
cana-1585	116	1	for	for	ADP
cana-1585	116	2	any	any	DET
cana-1585	116	3	sub	sub	NOUN
cana-1585	116	4	a	a	DET
cana-1585	116	5			PROPN
cana-1585	116	6	x	x	SYM
cana-1585	116	7	,	,	PUNCT
cana-1585	116	8	1	1	NUM
cana-1585	116	9	.	.	X
cana-1585	116	10	δgα	δgα	PROPN
cana-1585	116	11	−int(e	−int(e	PROPN
cana-1585	116	12	)	)	PUNCT
cana-1585	116	13	is	be	AUX
cana-1585	116	14	the	the	DET
cana-1585	116	15	largest	large	ADJ
cana-1585	116	16	δgα	δgα	NOUN
cana-1585	116	17	−	−	PROPN
cana-1585	116	18	o	o	PROPN
cana-1585	117	1	⊆	⊆	NUM
cana-1585	117	2	e.	e.	PROPN
cana-1585	117	3	2	2	NUM
cana-1585	117	4	.	.	PUNCT
cana-1585	118	1	a	a	PRON
cana-1585	118	2	is	be	AUX
cana-1585	118	3	δgα	δgα	NOUN
cana-1585	118	4	−	−	PROPN
cana-1585	118	5	o	o	PROPN
cana-1585	118	6	,	,	PUNCT
cana-1585	118	7	iff	iff	PROPN
cana-1585	118	8	δgα	δgα	PROPN
cana-1585	118	9	−int(a	−int(a	PROPN
cana-1585	118	10	)	)	PUNCT
cana-1585	118	11	=	=	SYM
cana-1585	119	1	a.	a.	NOUN
cana-1585	119	2	3	3	NUM
cana-1585	119	3	.	.	PUNCT
cana-1585	119	4	δgα	δgα	NOUN
cana-1585	119	5	−	−	PROPN
cana-1585	119	6	int(x	int(x	PROPN
cana-1585	119	7	)	)	PUNCT
cana-1585	119	8	=	=	PUNCT
cana-1585	119	9	x.	x.	NOUN
cana-1585	120	1	4	4	X
cana-1585	120	2	.	.	X
cana-1585	120	3	δgα	δgα	NOUN
cana-1585	120	4	−	−	PROPN
cana-1585	120	5	int(	int(	PROPN
cana-1585	120	6	)	)	PUNCT
cana-1585	120	7	=	=	PUNCT
cana-1585	120	8	.	.	X
cana-1585	120	9	4	4	NUM
cana-1585	120	10	.	.	X
cana-1585	120	11	δgα	δgα	PROPN
cana-1585	120	12	nbd	nbd	PROPN
cana-1585	120	13	in	in	ADP
cana-1585	120	14	tss	tss	PROPN
cana-1585	120	15	:	:	PUNCT
cana-1585	120	16	in	in	ADP
cana-1585	120	17	this	this	DET
cana-1585	120	18	paper	paper	NOUN
cana-1585	120	19	we	we	PRON
cana-1585	120	20	establish	establish	VERB
cana-1585	120	21	the	the	DET
cana-1585	120	22	notion	notion	NOUN
cana-1585	120	23	of	of	ADP
cana-1585	120	24	δgα	δgα	PROPN
cana-1585	120	25	−	−	PROPN
cana-1585	120	26	nbd	nbd	PROPN
cana-1585	120	27	.	.	PUNCT
cana-1585	121	1	in	in	ADP
cana-1585	121	2	the	the	DET
cana-1585	121	3	tss	tss	NOUN
cana-1585	121	4	.	.	PUNCT
cana-1585	122	1	definition	definition	NOUN
cana-1585	122	2	4.1	4.1	NUM
cana-1585	122	3	.	.	PUNCT
cana-1585	123	1	let	let	VERB
cana-1585	123	2	n	n	PRON
cana-1585	123	3	be	be	AUX
cana-1585	123	4	a	a	DET
cana-1585	123	5	sub	sub	NOUN
cana-1585	123	6	of	of	ADP
cana-1585	123	7	ts	ts	X
cana-1585	123	8	(	(	PUNCT
cana-1585	123	9	x	x	X
cana-1585	123	10	,	,	PUNCT
cana-1585	123	11			PROPN
cana-1585	123	12	)	)	PUNCT
cana-1585	123	13	,	,	PUNCT
cana-1585	123	14	then	then	ADV
cana-1585	123	15	n	n	PRON
cana-1585	123	16	is	be	AUX
cana-1585	123	17	said	say	VERB
cana-1585	123	18	to	to	PART
cana-1585	123	19	be	be	AUX
cana-1585	123	20	δgα	δgα	PROPN
cana-1585	123	21	−	−	PROPN
cana-1585	123	22	nbd	nbd	PROPN
cana-1585	123	23	.	.	PUNCT
cana-1585	124	1	of	of	ADP
cana-1585	124	2	point	point	NOUN
cana-1585	124	3	x	x	PROPN
cana-1585	124	4	x	x	PUNCT
cana-1585	124	5	if	if	SCONJ
cana-1585	124	6	there	there	PRON
cana-1585	124	7	exist	exist	VERB
cana-1585	124	8	a	a	DET
cana-1585	124	9	δgα	δgα	NOUN
cana-1585	124	10	−	−	PROPN
cana-1585	124	11	o	o	INTJ
cana-1585	124	12	(	(	PUNCT
cana-1585	124	13	g	g	NOUN
cana-1585	124	14	)	)	PUNCT
cana-1585	124	15	where	where	SCONJ
cana-1585	124	16	as	as	ADP
cana-1585	124	17	xg	xg	PROPN
cana-1585	124	18			PROPN
cana-1585	124	19	n.	n.	PROPN
cana-1585	124	20	the	the	DET
cana-1585	124	21	group	group	NOUN
cana-1585	124	22	of	of	ADP
cana-1585	124	23	all	all	DET
cana-1585	124	24	δgα	δgα	NOUN
cana-1585	124	25	−	−	PROPN
cana-1585	124	26	nbd	nbd	PROPN
cana-1585	124	27	.	.	PROPN
cana-1585	125	1	of	of	ADP
cana-1585	125	2	an	an	DET
cana-1585	125	3	element	element	NOUN
cana-1585	125	4	x	x	NOUN
cana-1585	125	5	x	x	PRON
cana-1585	125	6	called	call	VERB
cana-1585	125	7	δgα	δgα	NOUN
cana-1585	125	8	−	−	PROPN
cana-1585	125	9	nbd	nbd	PROPN
cana-1585	125	10	.	.	PUNCT
cana-1585	126	1	of	of	ADP
cana-1585	126	2	x	x	PUNCT
cana-1585	126	3	and	and	CCONJ
cana-1585	126	4	is	be	AUX
cana-1585	126	5	signified	signify	VERB
cana-1585	126	6	by	by	ADP
cana-1585	126	7	δgα	δgα	NOUN
cana-1585	126	8	−(x	−(x	NOUN
cana-1585	126	9	)	)	PUNCT
cana-1585	126	10	.	.	PUNCT
cana-1585	127	1	example	example	NOUN
cana-1585	128	1	4.2	4.2	NUM
cana-1585	128	2	.	.	PUNCT
cana-1585	129	1	let	let	VERB
cana-1585	129	2	x=	x=	PUNCT
cana-1585	129	3	{	{	PUNCT
cana-1585	129	4	e	e	NOUN
cana-1585	129	5	,	,	PUNCT
cana-1585	129	6	f	f	PROPN
cana-1585	129	7	,	,	PUNCT
cana-1585	129	8	g	g	PROPN
cana-1585	129	9	,	,	PUNCT
cana-1585	129	10	h	h	NOUN
cana-1585	129	11	}	}	PUNCT
cana-1585	129	12	,	,	PUNCT
cana-1585	129	13	τ	τ	X
cana-1585	129	14	=	=	PUNCT
cana-1585	129	15	{	{	PUNCT
cana-1585	129	16	x	x	PROPN
cana-1585	129	17	,	,	PUNCT
cana-1585	129	18	φ	φ	PROPN
cana-1585	129	19	,	,	PUNCT
cana-1585	129	20	{	{	PUNCT
cana-1585	129	21	e	e	NOUN
cana-1585	129	22	}	}	PUNCT
cana-1585	129	23	,	,	PUNCT
cana-1585	129	24	{	{	PUNCT
cana-1585	129	25	f	f	X
cana-1585	129	26	}	}	PUNCT
cana-1585	129	27	,	,	PUNCT
cana-1585	129	28	{	{	PUNCT
cana-1585	129	29	e	e	NOUN
cana-1585	129	30	,	,	PUNCT
cana-1585	129	31	f	f	PROPN
cana-1585	129	32	}	}	PUNCT
cana-1585	129	33	,	,	PUNCT
cana-1585	129	34	{	{	PUNCT
cana-1585	129	35	e	e	NOUN
cana-1585	129	36	,	,	PUNCT
cana-1585	129	37	g	g	NOUN
cana-1585	129	38	}	}	PUNCT
cana-1585	129	39	,	,	PUNCT
cana-1585	129	40	{	{	PUNCT
cana-1585	129	41	e	e	NOUN
cana-1585	129	42	,	,	PUNCT
cana-1585	129	43	h	h	NOUN
cana-1585	129	44	}	}	PUNCT
cana-1585	129	45	,	,	PUNCT
cana-1585	129	46	{	{	PUNCT
cana-1585	129	47	e	e	NOUN
cana-1585	129	48	,	,	PUNCT
cana-1585	129	49	f	f	X
cana-1585	129	50	,	,	PUNCT
cana-1585	129	51	g	g	NOUN
cana-1585	129	52	}	}	PUNCT
cana-1585	129	53	,	,	PUNCT
cana-1585	129	54	{	{	PUNCT
cana-1585	129	55	e	e	NOUN
cana-1585	129	56	,	,	PUNCT
cana-1585	129	57	f	f	X
cana-1585	129	58	,	,	PUNCT
cana-1585	129	59	d	d	NOUN
cana-1585	129	60	}	}	PUNCT
cana-1585	129	61	,	,	PUNCT
cana-1585	129	62	{	{	PUNCT
cana-1585	129	63	e	e	NOUN
cana-1585	129	64	,	,	PUNCT
cana-1585	129	65	g	g	PROPN
cana-1585	129	66	,	,	PUNCT
cana-1585	129	67	h	h	NOUN
cana-1585	129	68	}	}	PUNCT
cana-1585	129	69	}	}	PUNCT
cana-1585	129	70	then	then	ADV
cana-1585	129	71	the	the	DET
cana-1585	129	72	δgα	δgα	NOUN
cana-1585	129	73	c	c	PROPN
cana-1585	129	74	s	s	PRON
cana-1585	129	75	are	be	AUX
cana-1585	129	76	{	{	PUNCT
cana-1585	129	77	x	x	X
cana-1585	129	78	,	,	PUNCT
cana-1585	129	79	φ	φ	PROPN
cana-1585	129	80	,	,	PUNCT
cana-1585	129	81	{	{	PUNCT
cana-1585	129	82	e	e	NOUN
cana-1585	129	83	}	}	PUNCT
cana-1585	129	84	,	,	PUNCT
cana-1585	129	85	{	{	PUNCT
cana-1585	129	86	f	f	X
cana-1585	129	87	}	}	PUNCT
cana-1585	129	88	,	,	PUNCT
cana-1585	129	89	{	{	PUNCT
cana-1585	129	90	g	g	NOUN
cana-1585	129	91	}	}	PUNCT
cana-1585	129	92	,	,	PUNCT
cana-1585	129	93	{	{	PUNCT
cana-1585	129	94	e	e	NOUN
cana-1585	129	95	,	,	PUNCT
cana-1585	129	96	f	f	X
cana-1585	129	97	,	,	PUNCT
cana-1585	129	98	g	g	NOUN
cana-1585	129	99	}	}	PUNCT
cana-1585	129	100	}	}	PUNCT
cana-1585	129	101	and	and	CCONJ
cana-1585	129	102	δgα	δgα	PROPN
cana-1585	129	103	o	o	X
cana-1585	129	104	s	s	VERB
cana-1585	129	105	are	be	AUX
cana-1585	129	106	{	{	PUNCT
cana-1585	129	107	x	x	NOUN
cana-1585	129	108	,	,	PUNCT
cana-1585	129	109	𝜑	𝜑	PROPN
cana-1585	129	110	,	,	PUNCT
cana-1585	129	111	{	{	PUNCT
cana-1585	129	112	f	f	X
cana-1585	129	113	,	,	PUNCT
cana-1585	129	114	g	g	PROPN
cana-1585	129	115	,	,	PUNCT
cana-1585	129	116	h	h	NOUN
cana-1585	129	117	}	}	PUNCT
cana-1585	129	118	,	,	PUNCT
cana-1585	129	119	{	{	PUNCT
cana-1585	129	120	e	e	NOUN
cana-1585	129	121	,	,	PUNCT
cana-1585	129	122	g	g	PROPN
cana-1585	129	123	,	,	PUNCT
cana-1585	129	124	h},{e	h},{e	PROPN
cana-1585	129	125	,	,	PUNCT
cana-1585	129	126	f	f	X
cana-1585	129	127	,	,	PUNCT
cana-1585	129	128	h	h	NOUN
cana-1585	129	129	}	}	PUNCT
cana-1585	129	130	{	{	PUNCT
cana-1585	129	131	h	h	NOUN
cana-1585	129	132	}	}	PUNCT
cana-1585	129	133	}	}	PUNCT
cana-1585	129	134	.	.	PUNCT
cana-1585	130	1	let	let	VERB
cana-1585	130	2	b	b	PROPN
cana-1585	130	3	x	x	PRON
cana-1585	130	4	,	,	PUNCT
cana-1585	130	5	if	if	SCONJ
cana-1585	130	6	there	there	PRON
cana-1585	130	7	exist	exist	VERB
cana-1585	130	8	a	a	DET
cana-1585	130	9	δgα	δgα	NOUN
cana-1585	130	10	−	−	NOUN
cana-1585	130	11	o	o	INTJ
cana-1585	130	12	g	g	PROPN
cana-1585	130	13	whereas	whereas	SCONJ
cana-1585	130	14	fg	fg	PROPN
cana-1585	130	15			PROPN
cana-1585	130	16	n	n	CCONJ
cana-1585	130	17	,	,	PUNCT
cana-1585	130	18	then	then	ADV
cana-1585	130	19	δgα	δgα	PROPN
cana-1585	130	20	-	-	PUNCT
cana-1585	130	21	nbd	nbd	PROPN
cana-1585	130	22	.	.	PUNCT
cana-1585	131	1	of	of	ADP
cana-1585	131	2	an	an	DET
cana-1585	131	3	element	element	NOUN
cana-1585	131	4	b	b	PROPN
cana-1585	131	5	x	x	PRON
cana-1585	131	6	,	,	PUNCT
cana-1585	131	7	that	that	PRON
cana-1585	131	8	is	be	AUX
cana-1585	131	9	δgα	δgα	NOUN
cana-1585	131	10	−(f	−(f	NOUN
cana-1585	131	11	)	)	PUNCT
cana-1585	132	1	=	=	NOUN
cana-1585	132	2	{	{	PUNCT
cana-1585	132	3	x	x	NOUN
cana-1585	132	4	,	,	PUNCT
cana-1585	132	5	𝜑	𝜑	PROPN
cana-1585	132	6	,	,	PUNCT
cana-1585	132	7	{	{	PUNCT
cana-1585	132	8	f	f	X
cana-1585	132	9	,	,	PUNCT
cana-1585	132	10	g	g	PROPN
cana-1585	132	11	,	,	PUNCT
cana-1585	132	12	h	h	NOUN
cana-1585	132	13	}	}	PUNCT
cana-1585	132	14	,	,	PUNCT
cana-1585	132	15	{	{	PUNCT
cana-1585	132	16	e	e	NOUN
cana-1585	132	17	,	,	PUNCT
cana-1585	132	18	f	f	PROPN
cana-1585	132	19	,	,	PUNCT
cana-1585	132	20	h	h	NOUN
cana-1585	132	21	}	}	PUNCT
cana-1585	132	22	}	}	PUNCT
cana-1585	132	23	.	.	PUNCT
cana-1585	133	1	theorem	theorem	VERB
cana-1585	133	2	4.3	4.3	NUM
cana-1585	133	3	.	.	PUNCT
cana-1585	134	1	a	a	DET
cana-1585	134	2	sub	sub	NOUN
cana-1585	134	3	p	p	NOUN
cana-1585	134	4	of	of	ADP
cana-1585	134	5	(	(	PUNCT
cana-1585	134	6	x	x	NOUN
cana-1585	134	7	,	,	PUNCT
cana-1585	134	8			PROPN
cana-1585	134	9	)	)	PUNCT
cana-1585	134	10	is	be	AUX
cana-1585	134	11	δgα	δgα	NOUN
cana-1585	134	12	−	−	PROPN
cana-1585	134	13	c	c	PROPN
cana-1585	134	14	and	and	CCONJ
cana-1585	134	15	p	p	PROPN
cana-1585	134	16	δgα	δgα	NOUN
cana-1585	134	17	−	−	PROPN
cana-1585	134	18	cl(p	cl(p	NOUN
cana-1585	134	19	)	)	PUNCT
cana-1585	134	20	iff	iff	PROPN
cana-1585	134	21	y	y	PROPN
cana-1585	134	22			PROPN
cana-1585	134	23	p	p	NOUN
cana-1585	134	24	is	be	AUX
cana-1585	134	25	not	not	PART
cana-1585	134	26	empty	empty	ADJ
cana-1585	134	27	for	for	ADP
cana-1585	134	28	any	any	DET
cana-1585	134	29	δgα	δgα	NOUN
cana-1585	134	30	−	−	PROPN
cana-1585	134	31	nbd	nbd	PROPN
cana-1585	134	32	.	.	PUNCT
cana-1585	135	1	y	y	PROPN
cana-1585	135	2	of	of	ADP
cana-1585	135	3	p	p	NOUN
cana-1585	135	4	in	in	ADP
cana-1585	135	5	(	(	PUNCT
cana-1585	135	6	x	x	NOUN
cana-1585	135	7	,	,	PUNCT
cana-1585	135	8			PROPN
cana-1585	135	9	)	)	PUNCT
cana-1585	135	10	.	.	PUNCT
cana-1585	136	1	proof	proof	NOUN
cana-1585	136	2	:	:	PUNCT
cana-1585	136	3	assume	assume	VERB
cana-1585	136	4	p	p	NOUN
cana-1585	136	5	is	be	AUX
cana-1585	136	6	not	not	PART
cana-1585	136	7	an	an	DET
cana-1585	136	8	element	element	NOUN
cana-1585	136	9	of	of	ADP
cana-1585	136	10	δgα	δgα	NOUN
cana-1585	136	11	−	−	PROPN
cana-1585	136	12	cl(p	cl(p	NOUN
cana-1585	136	13	)	)	PUNCT
cana-1585	136	14	.	.	PUNCT
cana-1585	137	1	then	then	ADV
cana-1585	137	2	there	there	PRON
cana-1585	137	3	exits	exit	VERB
cana-1585	137	4	δgα	δgα	NOUN
cana-1585	137	5	−c	−c	NOUN
cana-1585	137	6	e	e	PROPN
cana-1585	137	7	of	of	ADP
cana-1585	137	8	x	x	PRON
cana-1585	137	9	whereas	whereas	SCONJ
cana-1585	137	10	p	p	PROPN
cana-1585	137	11			PROPN
cana-1585	137	12	e	e	PROPN
cana-1585	137	13	and	and	CCONJ
cana-1585	137	14	p	p	NOUN
cana-1585	137	15	is	be	AUX
cana-1585	137	16	not	not	PART
cana-1585	137	17	an	an	DET
cana-1585	137	18	element	element	NOUN
cana-1585	137	19	of	of	ADP
cana-1585	137	20	e.	e.	PROPN
cana-1585	137	21	hence	hence	ADV
cana-1585	137	22	p(x	p(x	VERB
cana-1585	137	23	\	\	NOUN
cana-1585	137	24	e	e	NOUN
cana-1585	137	25	)	)	PUNCT
cana-1585	137	26	is	be	AUX
cana-1585	137	27	δgα	δgα	NOUN
cana-1585	137	28	−	−	PROPN
cana-1585	137	29	o	o	INTJ
cana-1585	137	30	in	in	ADP
cana-1585	137	31	x.	x.	PROPN
cana-1585	137	32	but	but	CCONJ
cana-1585	137	33	p	p	NOUN
cana-1585	137	34	(	(	PUNCT
cana-1585	137	35	x	x	SYM
cana-1585	137	36	\	\	PROPN
cana-1585	137	37	e	e	X
cana-1585	137	38	)	)	PUNCT
cana-1585	137	39	is	be	AUX
cana-1585	137	40	empty	empty	ADJ
cana-1585	137	41	.	.	PUNCT
cana-1585	138	1	this	this	PRON
cana-1585	138	2	is	be	AUX
cana-1585	138	3	a	a	DET
cana-1585	138	4	contradiction	contradiction	NOUN
cana-1585	138	5	.	.	PUNCT
cana-1585	139	1	thus	thus	ADV
cana-1585	139	2	p	p	VERB
cana-1585	139	3	δgα	δgα	NOUN
cana-1585	139	4	−	−	PROPN
cana-1585	139	5	cl(p	cl(p	NOUN
cana-1585	139	6	)	)	PUNCT
cana-1585	139	7	.	.	PUNCT
cana-1585	140	1	conversely	conversely	ADV
cana-1585	140	2	assume	assume	VERB
cana-1585	140	3	that	that	SCONJ
cana-1585	140	4	there	there	PRON
cana-1585	140	5	is	be	VERB
cana-1585	140	6	a	a	DET
cana-1585	140	7	δgα	δgα	NOUN
cana-1585	140	8	−	−	PROPN
cana-1585	140	9	nbd	nbd	PROPN
cana-1585	140	10	.	.	PUNCT
cana-1585	141	1	y	y	PROPN
cana-1585	141	2	of	of	ADP
cana-1585	141	3	a	a	DET
cana-1585	141	4	pt	pt	PROPN
cana-1585	141	5	.	.	PROPN
cana-1585	141	6	p	p	PROPN
cana-1585	141	7	x	x	SYM
cana-1585	141	8	where	where	SCONJ
cana-1585	141	9	as	as	SCONJ
cana-1585	141	10	y	y	PROPN
cana-1585	141	11			PUNCT
cana-1585	141	12	p	p	NOUN
cana-1585	141	13	is	be	AUX
cana-1585	141	14	empty	empty	ADJ
cana-1585	141	15	.	.	PUNCT
cana-1585	142	1	then	then	ADV
cana-1585	142	2	there	there	PRON
cana-1585	142	3	is	be	VERB
cana-1585	142	4	a	a	DET
cana-1585	142	5	δgα	δgα	NOUN
cana-1585	142	6	−	−	NOUN
cana-1585	142	7	o	o	NOUN
cana-1585	142	8	e	e	NOUN
cana-1585	142	9	of	of	ADP
cana-1585	142	10	x	x	SYM
cana-1585	142	11	whereas	whereas	SCONJ
cana-1585	142	12	p	p	PROPN
cana-1585	142	13	e	e	NOUN
cana-1585	142	14			PROPN
cana-1585	142	15	y.	y.	PROPN
cana-1585	142	16	hence	hence	ADV
cana-1585	142	17	e	e	NOUN
cana-1585	142	18			PUNCT
cana-1585	142	19	p	p	NOUN
cana-1585	142	20	is	be	AUX
cana-1585	142	21	empty	empty	ADJ
cana-1585	142	22	,	,	PUNCT
cana-1585	142	23	p(x	p(x	X
cana-1585	142	24	/	/	SYM
cana-1585	142	25	e	e	NOUN
cana-1585	142	26	)	)	PUNCT
cana-1585	142	27	.	.	PUNCT
cana-1585	143	1	so	so	ADV
cana-1585	143	2	δgα	δgα	PROPN
cana-1585	143	3	−	−	PROPN
cana-1585	143	4	(x	(x	PUNCT
cana-1585	143	5	\	\	X
cana-1585	144	1	e	e	X
cana-1585	144	2	)	)	PUNCT
cana-1585	144	3	and	and	CCONJ
cana-1585	144	4	p	p	NOUN
cana-1585	144	5	is	be	AUX
cana-1585	144	6	not	not	PART
cana-1585	144	7	an	an	DET
cana-1585	144	8	element	element	NOUN
cana-1585	144	9	of	of	ADP
cana-1585	144	10	δgα	δgα	NOUN
cana-1585	144	11	−	−	PROPN
cana-1585	144	12	cl(p	cl(p	NOUN
cana-1585	144	13	)	)	PUNCT
cana-1585	144	14	.	.	PUNCT
cana-1585	145	1	this	this	PRON
cana-1585	145	2	is	be	AUX
cana-1585	145	3	a	a	DET
cana-1585	145	4	contradiction	contradiction	NOUN
cana-1585	145	5	to	to	PART
cana-1585	145	6	p	p	VERB
cana-1585	145	7	δgα	δgα	NOUN
cana-1585	145	8	−	−	PROPN
cana-1585	145	9	cl(p	cl(p	NOUN
cana-1585	145	10	)	)	PUNCT
cana-1585	145	11	.	.	PUNCT
cana-1585	146	1	thus	thus	ADV
cana-1585	146	2	,	,	PUNCT
cana-1585	146	3	the	the	DET
cana-1585	146	4	intersection	intersection	NOUN
cana-1585	146	5	of	of	ADP
cana-1585	146	6	y	y	PROPN
cana-1585	146	7	and	and	CCONJ
cana-1585	146	8	p	p	NOUN
cana-1585	146	9	is	be	AUX
cana-1585	146	10	not	not	PART
cana-1585	146	11	empty	empty	ADJ
cana-1585	146	12	.	.	PUNCT
cana-1585	147	1	theorem	theorem	VERB
cana-1585	147	2	4.4	4.4	NUM
cana-1585	147	3	.	.	PUNCT
cana-1585	148	1	if	if	SCONJ
cana-1585	148	2	b	b	PROPN
cana-1585	148	3	is	be	AUX
cana-1585	148	4	δgα	δgα	NOUN
cana-1585	149	1	−	−	PROPN
cana-1585	149	2	o	o	INTJ
cana-1585	149	3	then	then	ADV
cana-1585	149	4	it	it	PRON
cana-1585	149	5	is	be	AUX
cana-1585	149	6	δgα	δgα	PROPN
cana-1585	149	7	−	−	PROPN
cana-1585	149	8	nbd	nbd	PROPN
cana-1585	149	9	.	.	PROPN
cana-1585	150	1	of	of	ADP
cana-1585	150	2	each	each	PRON
cana-1585	150	3	of	of	ADP
cana-1585	150	4	its	its	PRON
cana-1585	150	5	pts	pt	NOUN
cana-1585	150	6	.	.	PUNCT
cana-1585	151	1	proof	proof	NOUN
cana-1585	151	2	:	:	PUNCT
cana-1585	151	3	consider	consider	VERB
cana-1585	151	4	a	a	DET
cana-1585	151	5	δgα	δgα	NOUN
cana-1585	151	6	−	−	PROPN
cana-1585	151	7	o	o	PROPN
cana-1585	151	8	of	of	ADP
cana-1585	151	9	(	(	PUNCT
cana-1585	151	10	x,	x,	PROPN
cana-1585	151	11	)	)	PUNCT
cana-1585	151	12	.	.	PUNCT
cana-1585	152	1	then	then	ADV
cana-1585	152	2	by	by	ADP
cana-1585	152	3	definition	definition	NOUN
cana-1585	152	4	for	for	ADP
cana-1585	152	5	all	all	PRON
cana-1585	152	6	bb	bb	PROPN
cana-1585	152	7	,	,	PUNCT
cana-1585	152	8	b	b	PROPN
cana-1585	152	9			PROPN
cana-1585	152	10	.	.	PROPN
cana-1585	153	1	so	so	ADV
cana-1585	153	2	m	m	VERB
cana-1585	153	3	is	be	AUX
cana-1585	153	4	δgα	δgα	PROPN
cana-1585	153	5	−	−	PROPN
cana-1585	153	6	nbd	nbd	PROPN
cana-1585	153	7	.	.	PROPN
cana-1585	154	1	of	of	ADP
cana-1585	154	2	each	each	PRON
cana-1585	154	3	of	of	ADP
cana-1585	154	4	its	its	PRON
cana-1585	154	5	pts	pt	NOUN
cana-1585	154	6	.	.	PUNCT
cana-1585	154	7	theorem	theorem	VERB
cana-1585	154	8	4.5	4.5	NUM
cana-1585	154	9	.	.	PUNCT
cana-1585	155	1	if	if	SCONJ
cana-1585	155	2	b	b	VERB
cana-1585	155	3	x	x	AUX
cana-1585	155	4	is	be	AUX
cana-1585	155	5	a	a	DET
cana-1585	155	6	δgα	δgα	NOUN
cana-1585	155	7	−	−	PROPN
cana-1585	155	8	c	c	PROPN
cana-1585	155	9	,	,	PUNCT
cana-1585	155	10	bbc	bbc	PROPN
cana-1585	155	11	,	,	PUNCT
cana-1585	155	12	then	then	ADV
cana-1585	155	13	there	there	PRON
cana-1585	155	14	is	be	VERB
cana-1585	155	15	a	a	DET
cana-1585	155	16	δgα	δgα	NOUN
cana-1585	155	17	−	−	PROPN
cana-1585	155	18	nbd	nbd	PROPN
cana-1585	155	19	.	.	PUNCT
cana-1585	156	1	m	m	PROPN
cana-1585	156	2	of	of	ADP
cana-1585	156	3	b	b	NOUN
cana-1585	156	4	whereas	whereas	SCONJ
cana-1585	156	5	m	m	AUX
cana-1585	156	6	b	b	VERB
cana-1585	157	1	=	=	NOUN
cana-1585	157	2			NOUN
cana-1585	157	3	.	.	PUNCT
cana-1585	158	1	communications	communication	NOUN
cana-1585	158	2	on	on	ADP
cana-1585	158	3	applied	apply	VERB
cana-1585	158	4	nonlinear	nonlinear	ADJ
cana-1585	158	5	analysis	analysis	NOUN
cana-1585	158	6	issn	issn	NOUN
cana-1585	158	7	:	:	PUNCT
cana-1585	158	8	1074	1074	NUM
cana-1585	158	9	-	-	PUNCT
cana-1585	158	10	133x	133x	NUM
cana-1585	158	11	vol	vol	NOUN
cana-1585	158	12	31	31	NUM
cana-1585	158	13	no	no	NOUN
cana-1585	158	14	.	.	PUNCT
cana-1585	159	1	8s	8s	PROPN
cana-1585	159	2	(	(	PUNCT
cana-1585	159	3	2024	2024	NUM
cana-1585	159	4	)	)	PUNCT
cana-1585	159	5	744	744	NUM
cana-1585	159	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	159	7	proof	proof	NOUN
cana-1585	159	8	:	:	PUNCT
cana-1585	159	9	assume	assume	VERB
cana-1585	159	10	that	that	SCONJ
cana-1585	159	11	b	b	PROPN
cana-1585	159	12	is	be	AUX
cana-1585	159	13	a	a	DET
cana-1585	159	14	δgα	δgα	NOUN
cana-1585	159	15	−	−	PROPN
cana-1585	160	1	c	c	X
cana-1585	160	2	,	,	PUNCT
cana-1585	160	3	then	then	ADV
cana-1585	160	4	bc	bc	PROPN
cana-1585	160	5	is	be	AUX
cana-1585	160	6	δgα	δgα	NOUN
cana-1585	160	7	−	−	PROPN
cana-1585	161	1	o.	o.	INTJ
cana-1585	161	2	by	by	ADP
cana-1585	161	3	definition	definition	NOUN
cana-1585	161	4	bc	bc	PROPN
cana-1585	161	5	is	be	AUX
cana-1585	161	6	δgα	δgα	PROPN
cana-1585	161	7	−	−	PROPN
cana-1585	161	8	nbd	nbd	PROPN
cana-1585	161	9	.	.	PROPN
cana-1585	162	1	of	of	ADP
cana-1585	162	2	each	each	PRON
cana-1585	162	3	of	of	ADP
cana-1585	162	4	its	its	PRON
cana-1585	162	5	points	point	NOUN
cana-1585	162	6	.	.	PUNCT
cana-1585	163	1	let	let	VERB
cana-1585	163	2	us	we	PRON
cana-1585	163	3	assume	assume	VERB
cana-1585	163	4	that	that	SCONJ
cana-1585	163	5	bc	bc	VERB
cana-1585	163	6	then	then	ADV
cana-1585	163	7	there	there	PRON
cana-1585	163	8	is	be	VERB
cana-1585	163	9	a	a	DET
cana-1585	163	10	δgα	δgα	NOUN
cana-1585	164	1	−	−	NOUN
cana-1585	164	2	o	o	INTJ
cana-1585	164	3	m	m	VERB
cana-1585	164	4	whereas	whereas	SCONJ
cana-1585	164	5	bm	bm	SYM
cana-1585	164	6			PROPN
cana-1585	164	7	bc	bc	PROPN
cana-1585	164	8	.	.	PUNCT
cana-1585	165	1	so	so	ADV
cana-1585	165	2	m	m	AUX
cana-1585	165	3			PROPN
cana-1585	165	4	b	b	X
cana-1585	165	5	=	=	NOUN
cana-1585	165	6	.	.	X
cana-1585	165	7	theorem	theorem	VERB
cana-1585	165	8	4.6	4.6	NUM
cana-1585	165	9	.	.	PUNCT
cana-1585	166	1	if	if	SCONJ
cana-1585	166	2	x	x	PRON
cana-1585	166	3	is	be	AUX
cana-1585	166	4	an	an	DET
cana-1585	166	5	element	element	NOUN
cana-1585	166	6	in	in	ADP
cana-1585	166	7	the	the	DET
cana-1585	166	8	ts	ts	X
cana-1585	166	9	(	(	PUNCT
cana-1585	166	10	x	x	X
cana-1585	166	11	,	,	PUNCT
cana-1585	166	12			PROPN
cana-1585	166	13	)	)	PUNCT
cana-1585	166	14	then	then	ADV
cana-1585	166	15	1	1	X
cana-1585	166	16	.	.	X
cana-1585	166	17	δgα	δgα	NOUN
cana-1585	166	18	−	−	PROPN
cana-1585	166	19	n(x	n(x	PROPN
cana-1585	166	20	)	)	PUNCT
cana-1585	166	21	is	be	AUX
cana-1585	166	22	non	non	X
cana-1585	166	23	empty	empty	ADJ
cana-1585	166	24	.	.	PUNCT
cana-1585	167	1	2	2	X
cana-1585	167	2	.	.	X
cana-1585	168	1	if	if	SCONJ
cana-1585	168	2	a	a	DET
cana-1585	168	3	sub	sub	NOUN
cana-1585	168	4	b	b	PROPN
cana-1585	168	5	δgα	δgα	PROPN
cana-1585	168	6	−	−	PROPN
cana-1585	168	7	n(x	n(x	PROPN
cana-1585	168	8	)	)	PUNCT
cana-1585	168	9	then	then	ADV
cana-1585	168	10	xb	xb	PUNCT
cana-1585	168	11	.	.	PUNCT
cana-1585	168	12	proof	proof	NOUN
cana-1585	168	13	:	:	PUNCT
cana-1585	168	14	(	(	PUNCT
cana-1585	168	15	1	1	X
cana-1585	168	16	)	)	PUNCT
cana-1585	168	17	since	since	SCONJ
cana-1585	168	18	x	x	PUNCT
cana-1585	168	19			PROPN
cana-1585	168	20	δgα	δgα	NOUN
cana-1585	168	21	−	−	PROPN
cana-1585	168	22	n(x	n(x	PROPN
cana-1585	168	23	)	)	PUNCT
cana-1585	168	24	and	and	CCONJ
cana-1585	168	25	δgα	δgα	NOUN
cana-1585	168	26	-	-	PUNCT
cana-1585	168	27	n(x	n(x	X
cana-1585	168	28	)	)	PUNCT
cana-1585	168	29	is	be	AUX
cana-1585	168	30	not	not	PART
cana-1585	168	31	empty	empty	ADJ
cana-1585	168	32	.	.	PUNCT
cana-1585	169	1	(	(	PUNCT
cana-1585	169	2	2	2	X
cana-1585	169	3	)	)	PUNCT
cana-1585	169	4	assume	assume	VERB
cana-1585	169	5	that	that	SCONJ
cana-1585	169	6	b	b	PROPN
cana-1585	169	7	δgα	δgα	PROPN
cana-1585	169	8	−	−	PROPN
cana-1585	169	9	n(x	n(x	PROPN
cana-1585	169	10	)	)	PUNCT
cana-1585	169	11	,	,	PUNCT
cana-1585	169	12	then	then	ADV
cana-1585	169	13	there	there	PRON
cana-1585	169	14	is	be	VERB
cana-1585	169	15	a	a	DET
cana-1585	169	16	δgα	δgα	NOUN
cana-1585	170	1	−	−	NOUN
cana-1585	170	2	o	o	INTJ
cana-1585	170	3	m	m	VERB
cana-1585	170	4	whereas	whereas	SCONJ
cana-1585	170	5	xm	xm	NOUN
cana-1585	170	6			PROPN
cana-1585	170	7	.	.	NOUN
cana-1585	170	8	hence	hence	ADV
cana-1585	170	9	x.	x.	PROPN
cana-1585	170	10	theorem	theorem	VERB
cana-1585	170	11	4.7	4.7	NUM
cana-1585	170	12	.	.	PUNCT
cana-1585	171	1	if	if	SCONJ
cana-1585	171	2	a	a	DET
cana-1585	171	3	sub	sub	NOUN
cana-1585	171	4	b	b	PROPN
cana-1585	171	5	δgα	δgα	PROPN
cana-1585	171	6	−	−	PROPN
cana-1585	171	7	n(x	n(x	PROPN
cana-1585	171	8	)	)	PUNCT
cana-1585	171	9	and	and	CCONJ
cana-1585	171	10	b	b	NOUN
cana-1585	171	11			PROPN
cana-1585	171	12			PROPN
cana-1585	171	13	,	,	PUNCT
cana-1585	171	14	then	then	ADV
cana-1585	171	15	a	a	PROPN
cana-1585	171	16	δgα	δgα	NOUN
cana-1585	171	17	−	−	PROPN
cana-1585	171	18	n(x	n(x	PROPN
cana-1585	171	19	)	)	PUNCT
cana-1585	171	20	.	.	PUNCT
cana-1585	172	1	proof	proof	NOUN
cana-1585	172	2	:	:	PUNCT
cana-1585	172	3	assume	assume	VERB
cana-1585	172	4	that	that	SCONJ
cana-1585	172	5	b	b	PROPN
cana-1585	172	6	δgα	δgα	PROPN
cana-1585	172	7	−	−	PROPN
cana-1585	172	8	n(x	n(x	PROPN
cana-1585	172	9	)	)	PUNCT
cana-1585	172	10	,	,	PUNCT
cana-1585	172	11	then	then	ADV
cana-1585	172	12	there	there	PRON
cana-1585	172	13	is	be	VERB
cana-1585	172	14	a	a	DET
cana-1585	172	15	δgα	δgα	NOUN
cana-1585	173	1	−	−	NOUN
cana-1585	173	2	o	o	INTJ
cana-1585	173	3	u	u	NOUN
cana-1585	173	4	whereas	whereas	SCONJ
cana-1585	173	5	xu	xu	PROPN
cana-1585	173	6			PROPN
cana-1585	173	7	b.	b.	PROPN
cana-1585	173	8	given	give	VERB
cana-1585	173	9	b	b	PROPN
cana-1585	173	10			PROPN
cana-1585	173	11	a	a	PROPN
cana-1585	173	12	,	,	PUNCT
cana-1585	173	13	then	then	ADV
cana-1585	173	14	xu	xu	PUNCT
cana-1585	174	1			PROPN
cana-1585	174	2	.	.	PROPN
cana-1585	174	3	hence	hence	ADV
cana-1585	174	4	a	a	PROPN
cana-1585	174	5	δgα	δgα	NOUN
cana-1585	174	6	−	−	PROPN
cana-1585	174	7	n(x	n(x	PROPN
cana-1585	174	8	)	)	PUNCT
cana-1585	174	9	.	.	PUNCT
cana-1585	175	1	theorem	theorem	NOUN
cana-1585	175	2	4.8	4.8	NUM
cana-1585	175	3	.	.	PUNCT
cana-1585	176	1	let	let	AUX
cana-1585	176	2	(	(	PUNCT
cana-1585	176	3	x	x	NOUN
cana-1585	176	4	,	,	PUNCT
cana-1585	176	5			PROPN
cana-1585	176	6	)	)	PUNCT
cana-1585	176	7	be	be	VERB
cana-1585	176	8	a	a	DET
cana-1585	176	9	ts	ts	NOUN
cana-1585	176	10	.	.	PUNCT
cana-1585	177	1	if	if	SCONJ
cana-1585	177	2	n	n	PRON
cana-1585	177	3	is	be	AUX
cana-1585	177	4	a	a	DET
cana-1585	177	5	nbd	nbd	PROPN
cana-1585	177	6	.	.	PUNCT
cana-1585	177	7	of	of	ADP
cana-1585	177	8	t	t	PROPN
cana-1585	177	9			PROPN
cana-1585	177	10	x	x	SYM
cana-1585	177	11	,	,	PUNCT
cana-1585	177	12	then	then	ADV
cana-1585	177	13	n	n	PRON
cana-1585	177	14	is	be	AUX
cana-1585	177	15	a	a	DET
cana-1585	177	16	δgα	δgα	NOUN
cana-1585	177	17	−	−	PROPN
cana-1585	177	18	nbd	nbd	PROPN
cana-1585	177	19	.	.	PUNCT
cana-1585	178	1	of	of	ADP
cana-1585	178	2	x.	x.	NOUN
cana-1585	178	3	proof	proof	PROPN
cana-1585	178	4	:	:	PUNCT
cana-1585	178	5	assume	assume	VERB
cana-1585	178	6	that	that	SCONJ
cana-1585	178	7	n	n	PRON
cana-1585	178	8	is	be	AUX
cana-1585	178	9	a	a	DET
cana-1585	178	10	nbd	nbd	PROPN
cana-1585	178	11	.	.	PUNCT
cana-1585	178	12	of	of	ADP
cana-1585	178	13	t	t	PROPN
cana-1585	178	14			PROPN
cana-1585	178	15	x.	x.	NOUN
cana-1585	178	16	by	by	ADP
cana-1585	178	17	definition	definition	NOUN
cana-1585	178	18	there	there	PRON
cana-1585	178	19	exist	exist	VERB
cana-1585	178	20	an	an	DET
cana-1585	178	21	o	o	NOUN
cana-1585	178	22	h	h	NOUN
cana-1585	178	23	whereas	whereas	SCONJ
cana-1585	178	24	t	t	PROPN
cana-1585	178	25	f	f	NOUN
cana-1585	178	26			PROPN
cana-1585	178	27	n.	n.	NOUN
cana-1585	179	1	but	but	CCONJ
cana-1585	179	2	we	we	PRON
cana-1585	179	3	know	know	VERB
cana-1585	179	4	that	that	SCONJ
cana-1585	179	5	all	all	DET
cana-1585	179	6	o	o	VERB
cana-1585	179	7	s	s	VERB
cana-1585	179	8	are	be	AUX
cana-1585	179	9	δgα	δgα	NOUN
cana-1585	180	1	−	−	NOUN
cana-1585	180	2	o	o	INTJ
cana-1585	180	3	whereas	whereas	SCONJ
cana-1585	180	4	t	t	PROPN
cana-1585	180	5	f	f	PROPN
cana-1585	180	6			PROPN
cana-1585	180	7	n.	n.	PROPN
cana-1585	180	8	thus	thus	ADV
cana-1585	180	9	,	,	PUNCT
cana-1585	180	10	n	n	X
cana-1585	180	11	is	be	AUX
cana-1585	180	12	δgα	δgα	PROPN
cana-1585	180	13	−	−	PROPN
cana-1585	180	14	nbd	nbd	PROPN
cana-1585	180	15	.	.	PUNCT
cana-1585	181	1	of	of	ADP
cana-1585	181	2	x.	x.	NOUN
cana-1585	181	3	5	5	NUM
cana-1585	181	4	.	.	NOUN
cana-1585	181	5	δgα	δgα	NOUN
cana-1585	181	6	-	-	PUNCT
cana-1585	181	7	derived	derive	VERB
cana-1585	181	8	in	in	ADP
cana-1585	181	9	this	this	DET
cana-1585	181	10	paper	paper	NOUN
cana-1585	181	11	we	we	PRON
cana-1585	181	12	establish	establish	VERB
cana-1585	181	13	the	the	DET
cana-1585	181	14	notion	notion	NOUN
cana-1585	181	15	of	of	ADP
cana-1585	181	16	δgα	δgα	NOUN
cana-1585	181	17	−	−	PROPN
cana-1585	181	18	derived	derive	VERB
cana-1585	181	19	in	in	ADP
cana-1585	181	20	tss	tss	PROPN
cana-1585	181	21	.	.	PUNCT
cana-1585	182	1	definition	definition	NOUN
cana-1585	182	2	5.1	5.1	NUM
cana-1585	182	3	:	:	PUNCT
cana-1585	182	4	if	if	SCONJ
cana-1585	182	5	m	m	NOUN
cana-1585	182	6	is	be	AUX
cana-1585	182	7	a	a	DET
cana-1585	182	8	sub	sub	NOUN
cana-1585	182	9	of	of	ADP
cana-1585	182	10	a	a	DET
cana-1585	182	11	ts	ts	X
cana-1585	182	12	(	(	PUNCT
cana-1585	182	13	x	x	NOUN
cana-1585	182	14	,	,	PUNCT
cana-1585	182	15			PROPN
cana-1585	182	16	)	)	PUNCT
cana-1585	182	17	,	,	PUNCT
cana-1585	182	18	then	then	ADV
cana-1585	182	19	a	a	DET
cana-1585	182	20	pt	pt	PROPN
cana-1585	182	21	.	.	PROPN
cana-1585	182	22	p	p	PROPN
cana-1585	182	23	x	x	VERB
cana-1585	182	24	is	be	AUX
cana-1585	182	25	called	call	VERB
cana-1585	182	26	an	an	DET
cana-1585	182	27	δgα	δgα	NOUN
cana-1585	182	28	−	−	NOUN
cana-1585	182	29	limit	limit	NOUN
cana-1585	182	30	point	point	NOUN
cana-1585	182	31	of	of	ADP
cana-1585	182	32	a	a	DET
cana-1585	182	33	m	m	NOUN
cana-1585	182	34	x	x	PUNCT
cana-1585	182	35	if	if	SCONJ
cana-1585	182	36	every	every	DET
cana-1585	182	37	δgα	δgα	NOUN
cana-1585	182	38	-	-	PUNCT
cana-1585	182	39	o	o	NOUN
cana-1585	182	40	s	s	NOUN
cana-1585	182	41	x	x	SYM
cana-1585	182	42	containing	contain	VERB
cana-1585	182	43	p	p	PRON
cana-1585	182	44	,	,	PUNCT
cana-1585	182	45	contains	contain	VERB
cana-1585	182	46	a	a	DET
cana-1585	182	47	pt	pt	NOUN
cana-1585	182	48	.	.	PROPN
cana-1585	182	49	of	of	ADP
cana-1585	182	50	m	m	PROPN
cana-1585	182	51	other	other	ADJ
cana-1585	182	52	than	than	ADP
cana-1585	182	53	p.	p.	VERB
cana-1585	182	54	the	the	DET
cana-1585	182	55	set	set	NOUN
cana-1585	182	56	of	of	ADP
cana-1585	182	57	all	all	DET
cana-1585	182	58	δgα	δgα	NOUN
cana-1585	182	59	−	−	PROPN
cana-1585	182	60	limit	limit	PROPN
cana-1585	182	61	pt	pt	NOUN
cana-1585	182	62	.	.	PROPN
cana-1585	182	63	of	of	ADP
cana-1585	182	64	m	m	PROPN
cana-1585	182	65	is	be	AUX
cana-1585	182	66	called	call	VERB
cana-1585	182	67	an	an	DET
cana-1585	182	68	δgα	δgα	NOUN
cana-1585	182	69	-	-	PUNCT
cana-1585	182	70	derived	derive	VERB
cana-1585	182	71	set	set	NOUN
cana-1585	182	72	of	of	ADP
cana-1585	182	73	m	m	PRON
cana-1585	182	74	and	and	CCONJ
cana-1585	182	75	is	be	AUX
cana-1585	182	76	signified	signify	VERB
cana-1585	182	77	by	by	ADP
cana-1585	182	78	δgα	δgα	NOUN
cana-1585	182	79	-	-	PUNCT
cana-1585	182	80	d(m	d(m	PROPN
cana-1585	182	81	)	)	PUNCT
cana-1585	182	82	.	.	PUNCT
cana-1585	183	1	theorem	theorem	VERB
cana-1585	183	2	5.2	5.2	NUM
cana-1585	183	3	:	:	PUNCT
cana-1585	183	4	the	the	DET
cana-1585	183	5	following	follow	VERB
cana-1585	183	6	five	five	NUM
cana-1585	183	7	results	result	NOUN
cana-1585	183	8	are	be	AUX
cana-1585	183	9	true	true	ADJ
cana-1585	183	10	.	.	PUNCT
cana-1585	184	1	if	if	SCONJ
cana-1585	184	2	m	m	PROPN
cana-1585	184	3	and	and	CCONJ
cana-1585	184	4	s	s	VERB
cana-1585	184	5	are	be	AUX
cana-1585	184	6	two	two	NUM
cana-1585	184	7	subs	sub	NOUN
cana-1585	184	8	of	of	ADP
cana-1585	184	9	a	a	DET
cana-1585	184	10	ts	ts	X
cana-1585	184	11	(	(	PUNCT
cana-1585	184	12	x	x	NOUN
cana-1585	184	13	,	,	PUNCT
cana-1585	184	14			PROPN
cana-1585	184	15	)	)	PUNCT
cana-1585	184	16	.	.	PUNCT
cana-1585	185	1	(	(	PUNCT
cana-1585	185	2	i	i	NOUN
cana-1585	185	3	)	)	PUNCT
cana-1585	185	4	.	.	PUNCT
cana-1585	186	1	if	if	SCONJ
cana-1585	186	2	m	m	PROPN
cana-1585	186	3			PROPN
cana-1585	186	4	s	s	PROPN
cana-1585	186	5	,	,	PUNCT
cana-1585	186	6	then	then	ADV
cana-1585	186	7	δgα	δgα	NOUN
cana-1585	186	8	-	-	PUNCT
cana-1585	186	9	d(m	d(m	NOUN
cana-1585	186	10	)	)	PUNCT
cana-1585	186	11			PROPN
cana-1585	186	12	δgα	δgα	NOUN
cana-1585	186	13	-	-	PUNCT
cana-1585	186	14	d(s	d(s	PROPN
cana-1585	186	15	)	)	PUNCT
cana-1585	186	16	.	.	PUNCT
cana-1585	187	1	(	(	PUNCT
cana-1585	187	2	ii	ii	X
cana-1585	187	3	)	)	PUNCT
cana-1585	187	4	m	m	VERB
cana-1585	187	5	is	be	AUX
cana-1585	187	6	an	an	DET
cana-1585	187	7	δgα	δgα	NOUN
cana-1585	187	8	-	-	PUNCT
cana-1585	187	9	c	c	NOUN
cana-1585	187	10	if	if	SCONJ
cana-1585	188	1	and	and	CCONJ
cana-1585	188	2	only	only	ADV
cana-1585	188	3	if	if	SCONJ
cana-1585	188	4	it	it	PRON
cana-1585	188	5	contains	contain	VERB
cana-1585	188	6	each	each	PRON
cana-1585	188	7	of	of	ADP
cana-1585	188	8	its	its	PRON
cana-1585	188	9	δgα	δgα	NOUN
cana-1585	188	10	-	-	PUNCT
cana-1585	188	11	limit	limit	NOUN
cana-1585	188	12	point	point	NOUN
cana-1585	188	13	.	.	PUNCT
cana-1585	189	1	(	(	PUNCT
cana-1585	189	2	iii	iii	NOUN
cana-1585	189	3	)	)	PUNCT
cana-1585	189	4	.	.	PUNCT
cana-1585	190	1	δgα	δgα	NOUN
cana-1585	190	2	-	-	PUNCT
cana-1585	190	3	cl(m	cl(m	NOUN
cana-1585	190	4	)	)	PUNCT
cana-1585	191	1	=	=	PUNCT
cana-1585	191	2	m	m	NOUN
cana-1585	191	3	∪	∪	VERB
cana-1585	191	4	δgα	δgα	NOUN
cana-1585	191	5	-	-	PUNCT
cana-1585	191	6	d(m	d(m	NOUN
cana-1585	191	7	)	)	PUNCT
cana-1585	191	8	.	.	PUNCT
cana-1585	192	1	(	(	PUNCT
cana-1585	192	2	iv	iv	X
cana-1585	192	3	)	)	PUNCT
cana-1585	192	4	.	.	PUNCT
cana-1585	193	1	δgα	δgα	NOUN
cana-1585	193	2	-	-	PUNCT
cana-1585	193	3	d(m∪s	d(m∪s	PROPN
cana-1585	193	4	)	)	PUNCT
cana-1585	193	5	⊇	⊇	PROPN
cana-1585	193	6	δgα	δgα	NOUN
cana-1585	193	7	-	-	PUNCT
cana-1585	193	8	d(m	d(m	NOUN
cana-1585	193	9	)	)	PUNCT
cana-1585	193	10	∪	∪	VERB
cana-1585	193	11	δgα	δgα	NOUN
cana-1585	193	12	-	-	PUNCT
cana-1585	193	13	d(s	d(s	PROPN
cana-1585	193	14	)	)	PUNCT
cana-1585	193	15	.	.	PUNCT
cana-1585	194	1	(	(	PUNCT
cana-1585	194	2	v	v	NOUN
cana-1585	194	3	)	)	PUNCT
cana-1585	194	4	.	.	PUNCT
cana-1585	195	1	δgα	δgα	NOUN
cana-1585	195	2	-	-	PUNCT
cana-1585	195	3	d(m⋂s	d(m⋂s	PROPN
cana-1585	195	4	)	)	PUNCT
cana-1585	195	5	⊆	⊆	NUM
cana-1585	195	6	δgα	δgα	NOUN
cana-1585	195	7	-	-	PUNCT
cana-1585	195	8	d(m	d(m	NOUN
cana-1585	195	9	)	)	PUNCT
cana-1585	195	10	⋂	⋂	PROPN
cana-1585	195	11	δgα	δgα	NOUN
cana-1585	195	12	-	-	PUNCT
cana-1585	195	13	d(s	d(s	PROPN
cana-1585	195	14	)	)	PUNCT
cana-1585	195	15	.	.	PUNCT
cana-1585	196	1	proof	proof	NOUN
cana-1585	196	2	:	:	PUNCT
cana-1585	196	3	(	(	PUNCT
cana-1585	196	4	i	i	NOUN
cana-1585	196	5	)	)	PUNCT
cana-1585	196	6	by	by	ADP
cana-1585	196	7	definition	definition	NOUN
cana-1585	196	8	5.1	5.1	NUM
cana-1585	196	9	,	,	PUNCT
cana-1585	196	10	we	we	PRON
cana-1585	196	11	have	have	VERB
cana-1585	196	12	p	p	NOUN
cana-1585	196	13	δgα	δgα	NOUN
cana-1585	196	14	-	-	PUNCT
cana-1585	196	15	d(m	d(m	NOUN
cana-1585	196	16	)	)	PUNCT
cana-1585	197	1	if	if	SCONJ
cana-1585	197	2	and	and	CCONJ
cana-1585	197	3	only	only	ADV
cana-1585	197	4	if	if	SCONJ
cana-1585	197	5	e	e	PROPN
cana-1585	197	6	⋂	⋂	PROPN
cana-1585	197	7	(	(	PUNCT
cana-1585	197	8	m-{p})≠	m-{p})≠	PROPN
cana-1585	197	9	φ	φ	PROPN
cana-1585	197	10	,	,	PUNCT
cana-1585	197	11	for	for	ADP
cana-1585	197	12	every	every	DET
cana-1585	197	13	δgα	δgα	NOUN
cana-1585	197	14	-	-	PUNCT
cana-1585	197	15	o	o	NOUN
cana-1585	197	16	e	e	NOUN
cana-1585	197	17	containing	contain	VERB
cana-1585	197	18	p.	p.	NOUN
cana-1585	197	19	but	but	CCONJ
cana-1585	197	20	,	,	PUNCT
cana-1585	197	21	m⊆s	m⊆s	PROPN
cana-1585	197	22	,	,	PUNCT
cana-1585	197	23	then	then	ADV
cana-1585	197	24	e	e	PROPN
cana-1585	197	25	⋂	⋂	PROPN
cana-1585	197	26	(	(	PUNCT
cana-1585	197	27	s-{p})≠	s-{p})≠	PROPN
cana-1585	197	28	φ	φ	NUM
cana-1585	197	29	,	,	PUNCT
cana-1585	197	30	for	for	ADP
cana-1585	197	31	every	every	DET
cana-1585	197	32	δgα	δgα	NOUN
cana-1585	197	33	-	-	PUNCT
cana-1585	197	34	o	o	NOUN
cana-1585	197	35	e	e	NOUN
cana-1585	197	36	containing	contain	VERB
cana-1585	197	37	p.	p.	NOUN
cana-1585	197	38	hence	hence	ADV
cana-1585	197	39	pδgαd(s	pδgαd(s	PUNCT
cana-1585	197	40	)	)	PUNCT
cana-1585	197	41	.	.	PUNCT
cana-1585	198	1	therefore	therefore	ADV
cana-1585	198	2	,	,	PUNCT
cana-1585	198	3	δgα	δgα	NOUN
cana-1585	198	4	-	-	PUNCT
cana-1585	198	5	d(m	d(m	NOUN
cana-1585	198	6	)	)	PUNCT
cana-1585	198	7			PROPN
cana-1585	198	8	δgα	δgα	NOUN
cana-1585	198	9	-	-	PUNCT
cana-1585	198	10	d(s	d(s	PROPN
cana-1585	198	11	)	)	PUNCT
cana-1585	198	12	.	.	PUNCT
cana-1585	199	1	(	(	PUNCT
cana-1585	199	2	ii	ii	NOUN
cana-1585	199	3	)	)	PUNCT
cana-1585	199	4	.	.	PUNCT
cana-1585	200	1	let	let	VERB
cana-1585	200	2	m	m	PRON
cana-1585	200	3	be	be	AUX
cana-1585	200	4	an	an	DET
cana-1585	200	5	δgα	δgα	NOUN
cana-1585	200	6	-	-	PUNCT
cana-1585	200	7	c	c	PROPN
cana-1585	200	8	and	and	CCONJ
cana-1585	200	9	pm	pm	PROPN
cana-1585	200	10	then	then	ADV
cana-1585	200	11	p	p	X
cana-1585	200	12			PROPN
cana-1585	200	13	(	(	PUNCT
cana-1585	200	14	x	x	NOUN
cana-1585	200	15	-	-	NOUN
cana-1585	200	16	m	m	VERB
cana-1585	200	17	)	)	PUNCT
cana-1585	200	18	which	which	PRON
cana-1585	200	19	is	be	AUX
cana-1585	200	20	an	an	DET
cana-1585	200	21	δgα	δgα	NOUN
cana-1585	200	22	-	-	PUNCT
cana-1585	200	23	o	o	NOUN
cana-1585	200	24	,	,	PUNCT
cana-1585	200	25	hence	hence	ADV
cana-1585	200	26	there	there	PRON
cana-1585	200	27	exist	exist	VERB
cana-1585	200	28	an	an	DET
cana-1585	200	29	δgα	δgα	NOUN
cana-1585	200	30	-	-	PUNCT
cana-1585	200	31	o	o	X
cana-1585	200	32	(	(	PUNCT
cana-1585	200	33	xm	xm	PROPN
cana-1585	200	34	)	)	PUNCT
cana-1585	200	35	whereas	whereas	SCONJ
cana-1585	200	36	(	(	PUNCT
cana-1585	200	37	x	x	X
cana-1585	200	38	-	-	NOUN
cana-1585	200	39	m	m	NOUN
cana-1585	200	40	)	)	PUNCT
cana-1585	200	41	⋂	⋂	PROPN
cana-1585	200	42	m	m	PROPN
cana-1585	200	43	=	=	SYM
cana-1585	200	44	φ	φ	PROPN
cana-1585	200	45	.	.	PUNCT
cana-1585	201	1	so	so	ADV
cana-1585	201	2	p	p	X
cana-1585	201	3			NUM
cana-1585	201	4	δgα	δgα	NOUN
cana-1585	201	5	-	-	PUNCT
cana-1585	201	6	d(m	d(m	NOUN
cana-1585	201	7	)	)	PUNCT
cana-1585	201	8	,	,	PUNCT
cana-1585	201	9	therefore	therefore	ADV
cana-1585	201	10	,	,	PUNCT
cana-1585	201	11	δgα	δgα	NOUN
cana-1585	201	12	-	-	PUNCT
cana-1585	201	13	d(m	d(m	NOUN
cana-1585	201	14	)	)	PUNCT
cana-1585	202	1	⊆	⊆	NUM
cana-1585	202	2	m.	m.	NOUN
cana-1585	202	3	conversely	conversely	ADV
cana-1585	202	4	,	,	PUNCT
cana-1585	202	5	suppose	suppose	VERB
cana-1585	202	6	that	that	SCONJ
cana-1585	202	7	δgα	δgα	NOUN
cana-1585	202	8	-	-	PUNCT
cana-1585	202	9	d(m	d(m	NOUN
cana-1585	202	10	)	)	PUNCT
cana-1585	202	11	⊆	⊆	NUM
cana-1585	202	12	m	m	NOUN
cana-1585	202	13	and	and	CCONJ
cana-1585	202	14	pm	pm	PROPN
cana-1585	202	15	.	.	PUNCT
cana-1585	203	1	then	then	ADV
cana-1585	203	2	pδgα	pδgα	NOUN
cana-1585	203	3	-	-	PUNCT
cana-1585	203	4	d(m	d(m	NOUN
cana-1585	203	5	)	)	PUNCT
cana-1585	203	6	,	,	PUNCT
cana-1585	203	7	hence	hence	ADV
cana-1585	203	8	there	there	PRON
cana-1585	203	9	exist	exist	VERB
cana-1585	203	10	communications	communication	NOUN
cana-1585	203	11	on	on	ADP
cana-1585	203	12	applied	apply	VERB
cana-1585	203	13	nonlinear	nonlinear	ADJ
cana-1585	203	14	analysis	analysis	NOUN
cana-1585	203	15	issn	issn	NOUN
cana-1585	203	16	:	:	PUNCT
cana-1585	203	17	1074	1074	NUM
cana-1585	203	18	-	-	PUNCT
cana-1585	203	19	133x	133x	NUM
cana-1585	203	20	vol	vol	NOUN
cana-1585	203	21	31	31	NUM
cana-1585	203	22	no	no	NOUN
cana-1585	203	23	.	.	PUNCT
cana-1585	204	1	8s	8s	PROPN
cana-1585	204	2	(	(	PUNCT
cana-1585	204	3	2024	2024	NUM
cana-1585	204	4	)	)	PUNCT
cana-1585	204	5	745	745	NUM
cana-1585	204	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	204	7	an	an	DET
cana-1585	204	8	δgα	δgα	NOUN
cana-1585	204	9	-	-	PUNCT
cana-1585	204	10	o	o	NOUN
cana-1585	204	11	e	e	NOUN
cana-1585	204	12	containing	contain	VERB
cana-1585	204	13	p	p	NOUN
cana-1585	204	14	whereas	whereas	SCONJ
cana-1585	204	15	e	e	PROPN
cana-1585	204	16	⋂	⋂	PROPN
cana-1585	204	17	m	m	PROPN
cana-1585	204	18	=	=	NOUN
cana-1585	204	19	φ	φ	PROPN
cana-1585	204	20	and	and	CCONJ
cana-1585	204	21	hence	hence	ADV
cana-1585	204	22	x	x	NOUN
cana-1585	204	23	-	-	PUNCT
cana-1585	204	24	m	m	NOUN
cana-1585	204	25	=	=	PUNCT
cana-1585	204	26	up	up	ADP
cana-1585	204	27			NOUN
cana-1585	204	28			NUM
cana-1585	204	29			PROPN
cana-1585	204	30			PROPN
cana-1585	204	31	is	be	AUX
cana-1585	204	32	δgα	δgα	NOUN
cana-1585	204	33	-	-	PUNCT
cana-1585	204	34	o	o	NOUN
cana-1585	204	35	}	}	PUNCT
cana-1585	204	36	.	.	PUNCT
cana-1585	205	1	therefore	therefore	ADV
cana-1585	205	2	,	,	PUNCT
cana-1585	205	3	m	m	VERB
cana-1585	205	4	is	be	AUX
cana-1585	205	5	δgαc	δgαc	ADJ
cana-1585	205	6	.	.	PUNCT
cana-1585	206	1	(	(	PUNCT
cana-1585	206	2	iii	iii	NOUN
cana-1585	206	3	)	)	PUNCT
cana-1585	206	4	.	.	PUNCT
cana-1585	207	1	since	since	SCONJ
cana-1585	207	2	δgα	δgα	NOUN
cana-1585	207	3	-	-	PUNCT
cana-1585	207	4	d(m	d(m	NOUN
cana-1585	207	5	)	)	PUNCT
cana-1585	207	6	⊆	⊆	NUM
cana-1585	207	7	δgα	δgα	NOUN
cana-1585	207	8	-	-	PUNCT
cana-1585	207	9	cl(m	cl(m	NOUN
cana-1585	207	10	)	)	PUNCT
cana-1585	207	11	and	and	CCONJ
cana-1585	207	12	m	m	PROPN
cana-1585	207	13	⊆	⊆	NUM
cana-1585	207	14	δgα	δgα	NOUN
cana-1585	207	15	-	-	PUNCT
cana-1585	207	16	cl(m	cl(m	NOUN
cana-1585	207	17	)	)	PUNCT
cana-1585	207	18	.	.	PUNCT
cana-1585	208	1	δgα	δgα	NOUN
cana-1585	208	2	-	-	PUNCT
cana-1585	208	3	d(m	d(m	PROPN
cana-1585	208	4	)	)	PUNCT
cana-1585	209	1	∪	∪	ADP
cana-1585	209	2	m	m	PROPN
cana-1585	209	3	⊆	⊆	NUM
cana-1585	209	4	δgα	δgα	NOUN
cana-1585	209	5	-	-	PUNCT
cana-1585	209	6	cl(m	cl(m	NOUN
cana-1585	209	7	)	)	PUNCT
cana-1585	209	8	.	.	PUNCT
cana-1585	210	1	conversely	conversely	ADV
cana-1585	210	2	,	,	PUNCT
cana-1585	210	3	suppose	suppose	VERB
cana-1585	210	4	that	that	SCONJ
cana-1585	210	5	p	p	PROPN
cana-1585	210	6	δgα	δgα	NOUN
cana-1585	210	7	-	-	PUNCT
cana-1585	210	8	d(m	d(m	NOUN
cana-1585	210	9	)	)	PUNCT
cana-1585	210	10	∪	∪	VERB
cana-1585	210	11	m.	m.	NOUN
cana-1585	210	12	then	then	ADV
cana-1585	210	13	p	p	PROPN
cana-1585	210	14	δgα	δgα	NOUN
cana-1585	210	15	-	-	PUNCT
cana-1585	210	16	d(m	d(m	NOUN
cana-1585	210	17	)	)	PUNCT
cana-1585	210	18	,	,	PUNCT
cana-1585	210	19	p	p	PROPN
cana-1585	210	20	m	m	VERB
cana-1585	210	21	and	and	CCONJ
cana-1585	210	22	hence	hence	ADV
cana-1585	210	23	there	there	PRON
cana-1585	210	24	exist	exist	VERB
cana-1585	210	25	an	an	DET
cana-1585	210	26	δgα	δgα	NOUN
cana-1585	210	27	-	-	PUNCT
cana-1585	210	28	o	o	NOUN
cana-1585	210	29	e	e	NOUN
cana-1585	210	30	containing	contain	VERB
cana-1585	210	31	p	p	NOUN
cana-1585	210	32	whereas	whereas	SCONJ
cana-1585	210	33	e⋂m	e⋂m	PROPN
cana-1585	210	34	=	=	SYM
cana-1585	210	35	φ	φ	PROPN
cana-1585	210	36	.	.	PUNCT
cana-1585	211	1	thus	thus	ADV
cana-1585	211	2	p	p	X
cana-1585	211	3			NUM
cana-1585	211	4	δgα	δgα	NOUN
cana-1585	211	5	-	-	PUNCT
cana-1585	211	6	cl(m	cl(m	NOUN
cana-1585	211	7	)	)	PUNCT
cana-1585	211	8	)	)	PUNCT
cana-1585	211	9	.	.	PUNCT
cana-1585	212	1	δgα	δgα	NOUN
cana-1585	212	2	-	-	PUNCT
cana-1585	212	3	cl(m	cl(m	NOUN
cana-1585	212	4	)	)	PUNCT
cana-1585	212	5	⊆	⊆	NUM
cana-1585	212	6	δgα	δgα	NOUN
cana-1585	212	7	-	-	PUNCT
cana-1585	212	8	d(m	d(m	NOUN
cana-1585	212	9	)	)	PUNCT
cana-1585	212	10	∪	∪	ADP
cana-1585	212	11	m	m	PROPN
cana-1585	212	12	,	,	PUNCT
cana-1585	212	13	therefore	therefore	ADV
cana-1585	212	14	,	,	PUNCT
cana-1585	212	15	δgα	δgα	NOUN
cana-1585	212	16	-	-	PUNCT
cana-1585	212	17	cl(m	cl(m	NOUN
cana-1585	212	18	)	)	PUNCT
cana-1585	212	19	=	=	SYM
cana-1585	212	20	δgα	δgα	NOUN
cana-1585	212	21	-	-	PUNCT
cana-1585	212	22	d(m	d(m	NOUN
cana-1585	212	23	)	)	PUNCT
cana-1585	212	24	∪m	∪m	NUM
cana-1585	212	25	.	.	PUNCT
cana-1585	212	26	(	(	PUNCT
cana-1585	212	27	iv	iv	X
cana-1585	212	28	)	)	PUNCT
cana-1585	212	29	.	.	PUNCT
cana-1585	213	1	since	since	SCONJ
cana-1585	213	2	m	m	PROPN
cana-1585	213	3	⊆	⊆	NUM
cana-1585	213	4	m	m	NOUN
cana-1585	213	5	∪	∪	NOUN
cana-1585	213	6	s	s	PRON
cana-1585	213	7	and	and	CCONJ
cana-1585	213	8	s	s	VERB
cana-1585	213	9	⊆	⊆	NUM
cana-1585	213	10	m	m	NOUN
cana-1585	213	11	∪	∪	ADJ
cana-1585	213	12	s.	s.	PROPN
cana-1585	213	13	we	we	PRON
cana-1585	213	14	have	have	VERB
cana-1585	213	15	,	,	PUNCT
cana-1585	213	16	δgα	δgα	NOUN
cana-1585	213	17	-	-	PUNCT
cana-1585	213	18	d(m	d(m	NOUN
cana-1585	213	19	)	)	PUNCT
cana-1585	213	20	⊆	⊆	NUM
cana-1585	213	21	δgα	δgα	NOUN
cana-1585	213	22	-	-	PUNCT
cana-1585	213	23	d(m∪s	d(m∪	NOUN
cana-1585	213	24	)	)	PUNCT
cana-1585	213	25	and	and	CCONJ
cana-1585	213	26	δgα	δgα	NOUN
cana-1585	213	27	-	-	PUNCT
cana-1585	213	28	d(s	d(s	PROPN
cana-1585	213	29	)	)	PUNCT
cana-1585	213	30	⊆	⊆	NUM
cana-1585	213	31	δgαd(m∪s	δgαd(m∪	NOUN
cana-1585	213	32	)	)	PUNCT
cana-1585	213	33	.	.	PUNCT
cana-1585	214	1	therefore	therefore	ADV
cana-1585	214	2	,	,	PUNCT
cana-1585	214	3	δgα	δgα	NOUN
cana-1585	214	4	-	-	PUNCT
cana-1585	214	5	d(m	d(m	NOUN
cana-1585	214	6	)	)	PUNCT
cana-1585	214	7	∪	∪	VERB
cana-1585	214	8	δgα	δgα	NOUN
cana-1585	214	9	-	-	PUNCT
cana-1585	214	10	d(s	d(s	PROPN
cana-1585	214	11	)	)	PUNCT
cana-1585	215	1	⊆	⊆	NUM
cana-1585	215	2	δgα	δgα	NOUN
cana-1585	215	3	-	-	PUNCT
cana-1585	215	4	d(m∪s	d(m∪s	PROPN
cana-1585	215	5	)	)	PUNCT
cana-1585	215	6	.	.	PUNCT
cana-1585	216	1	(	(	PUNCT
cana-1585	216	2	v	v	NOUN
cana-1585	216	3	)	)	PUNCT
cana-1585	216	4	.	.	PUNCT
cana-1585	217	1	since	since	SCONJ
cana-1585	217	2	m	m	PROPN
cana-1585	217	3	⊇	⊇	PROPN
cana-1585	217	4	m	m	PROPN
cana-1585	217	5	⋂	⋂	PROPN
cana-1585	217	6	s	s	PART
cana-1585	217	7	and	and	CCONJ
cana-1585	217	8	s	s	PROPN
cana-1585	217	9	⊇	⊇	PROPN
cana-1585	217	10	m⋂s	m⋂s	PROPN
cana-1585	217	11	.	.	PUNCT
cana-1585	218	1	we	we	PRON
cana-1585	218	2	have	have	VERB
cana-1585	218	3	,	,	PUNCT
cana-1585	218	4	δgα	δgα	NOUN
cana-1585	218	5	-	-	PUNCT
cana-1585	218	6	d(m	d(m	PROPN
cana-1585	218	7	)	)	PUNCT
cana-1585	218	8	⊇	⊇	PROPN
cana-1585	218	9	δgα	δgα	NOUN
cana-1585	218	10	-	-	PUNCT
cana-1585	218	11	d(m⋂s	d(m⋂s	NOUN
cana-1585	218	12	)	)	PUNCT
cana-1585	218	13	and	and	CCONJ
cana-1585	218	14	δgα	δgα	NOUN
cana-1585	218	15	-	-	PUNCT
cana-1585	218	16	d(s	d(s	PROPN
cana-1585	218	17	)	)	PUNCT
cana-1585	218	18	⊇	⊇	PROPN
cana-1585	218	19	δgαd(m⋂s	δgαd(m⋂s	PROPN
cana-1585	218	20	)	)	PUNCT
cana-1585	218	21	.	.	PUNCT
cana-1585	219	1	therefore	therefore	ADV
cana-1585	219	2	,	,	PUNCT
cana-1585	219	3	δgα	δgα	NOUN
cana-1585	219	4	-	-	PUNCT
cana-1585	219	5	d(m	d(m	NOUN
cana-1585	219	6	)	)	PUNCT
cana-1585	220	1	⋂	⋂	PROPN
cana-1585	220	2	δgα	δgα	NOUN
cana-1585	220	3	-	-	PUNCT
cana-1585	220	4	d(s	d(s	PROPN
cana-1585	220	5	)	)	PUNCT
cana-1585	220	6	⊇	⊇	PROPN
cana-1585	220	7	δgα	δgα	NOUN
cana-1585	220	8	-	-	PUNCT
cana-1585	220	9	d(m⋂s	d(m⋂s	PROPN
cana-1585	220	10	)	)	PUNCT
cana-1585	220	11	.	.	PUNCT
cana-1585	221	1	6	6	X
cana-1585	221	2	.	.	X
cana-1585	221	3	conclusion	conclusion	NOUN
cana-1585	221	4	in	in	ADP
cana-1585	221	5	this	this	DET
cana-1585	221	6	study	study	NOUN
cana-1585	221	7	,	,	PUNCT
cana-1585	221	8	different	different	ADJ
cana-1585	221	9	idea	idea	NOUN
cana-1585	221	10	of	of	ADP
cana-1585	221	11	closure	closure	NOUN
cana-1585	221	12	and	and	CCONJ
cana-1585	221	13	interior	interior	ADJ
cana-1585	221	14	sets	set	NOUN
cana-1585	221	15	namely	namely	ADV
cana-1585	221	16	,	,	PUNCT
cana-1585	221	17	δgα	δgα	NOUN
cana-1585	221	18	-	-	PUNCT
cana-1585	221	19	closure	closure	NOUN
cana-1585	221	20	,	,	PUNCT
cana-1585	221	21	δgα	δgα	NOUN
cana-1585	221	22	-	-	PUNCT
cana-1585	221	23	interior	interior	PROPN
cana-1585	221	24	was	be	AUX
cana-1585	221	25	established	establish	VERB
cana-1585	221	26	and	and	CCONJ
cana-1585	221	27	also	also	ADV
cana-1585	221	28	discussed	discuss	VERB
cana-1585	221	29	about	about	ADP
cana-1585	221	30	δgα	δgα	NOUN
cana-1585	221	31	-	-	PUNCT
cana-1585	221	32	nbd	nbd	PROPN
cana-1585	221	33	,	,	PUNCT
cana-1585	221	34	δgα	δgα	NOUN
cana-1585	221	35	-	-	PUNCT
cana-1585	221	36	derived	derive	VERB
cana-1585	221	37	sets	set	NOUN
cana-1585	221	38	and	and	CCONJ
cana-1585	221	39	also	also	ADV
cana-1585	221	40	about	about	ADP
cana-1585	221	41	their	their	PRON
cana-1585	221	42	properties	property	NOUN
cana-1585	221	43	in	in	ADP
cana-1585	221	44	topological	topological	ADJ
cana-1585	221	45	spaces	space	NOUN
cana-1585	221	46	.	.	PUNCT
cana-1585	222	1	references	reference	NOUN
cana-1585	222	2	[	[	X
cana-1585	222	3	1	1	NUM
cana-1585	222	4	]	]	X
cana-1585	222	5	sivaraj	sivaraj	X
cana-1585	222	6	,	,	PUNCT
cana-1585	222	7	d.	d.	PROPN
cana-1585	222	8	,	,	PUNCT
cana-1585	222	9	&	&	CCONJ
cana-1585	222	10	sasikala	sasikala	PROPN
cana-1585	222	11	,	,	PUNCT
cana-1585	222	12	v.	v.	PROPN
cana-1585	222	13	e.	e.	PROPN
cana-1585	222	14	(	(	PUNCT
cana-1585	222	15	2016	2016	NUM
cana-1585	222	16	)	)	PUNCT
cana-1585	222	17	.	.	PUNCT
cana-1585	223	1	a	a	DET
cana-1585	223	2	study	study	NOUN
cana-1585	223	3	on	on	ADP
cana-1585	223	4	soft	soft	ADJ
cana-1585	223	5	α	α	NOUN
cana-1585	223	6	–	–	PUNCT
cana-1585	223	7	o	o	NOUN
cana-1585	223	8	sets	set	NOUN
cana-1585	223	9	.	.	PUNCT
cana-1585	224	1	iosr	iosr	ADJ
cana-1585	224	2	journal	journal	PROPN
cana-1585	224	3	of	of	ADP
cana-1585	224	4	mathematics	mathematic	NOUN
cana-1585	224	5	,	,	PUNCT
cana-1585	224	6	12(5	12(5	NUM
cana-1585	224	7	)	)	PUNCT
cana-1585	224	8	,	,	PUNCT
cana-1585	224	9	70	70	NUM
cana-1585	224	10	-	-	SYM
cana-1585	224	11	74	74	NUM
cana-1585	224	12	.	.	PUNCT
cana-1585	225	1	[	[	X
cana-1585	225	2	2	2	NUM
cana-1585	225	3	]	]	X
cana-1585	225	4	kavitha	kavitha	PROPN
cana-1585	225	5	,	,	PUNCT
cana-1585	225	6	v.	v.	PROPN
cana-1585	225	7	,	,	PUNCT
cana-1585	225	8	&	&	CCONJ
cana-1585	225	9	sasikala	sasikala	PROPN
cana-1585	225	10	,	,	PUNCT
cana-1585	225	11	v.	v.	PROPN
cana-1585	225	12	e.	e.	PROPN
cana-1585	225	13	(	(	PUNCT
cana-1585	225	14	2022	2022	NUM
cana-1585	225	15	)	)	PUNCT
cana-1585	225	16	.	.	PUNCT
cana-1585	226	1	beta	beta	ADJ
cana-1585	226	2	generalized	generalize	VERB
cana-1585	226	3	closed	close	VERB
cana-1585	226	4	sets	set	NOUN
cana-1585	226	5	in	in	ADP
cana-1585	226	6	topological	topological	ADJ
cana-1585	226	7	spaces	space	NOUN
cana-1585	226	8	.	.	PUNCT
cana-1585	227	1	journal	journal	NOUN
cana-1585	227	2	of	of	ADP
cana-1585	227	3	algebraic	algebraic	PROPN
cana-1585	227	4	statistics	statistic	NOUN
cana-1585	227	5	,	,	PUNCT
cana-1585	227	6	13(3	13(3	NUM
cana-1585	227	7	)	)	PUNCT
cana-1585	227	8	,	,	PUNCT
cana-1585	227	9	891	891	NUM
cana-1585	227	10	-	-	SYM
cana-1585	227	11	898	898	NUM
cana-1585	227	12	.	.	PUNCT
cana-1585	228	1	[	[	X
cana-1585	228	2	3	3	NUM
cana-1585	228	3	]	]	SYM
cana-1585	228	4	sasikala	sasikala	NOUN
cana-1585	228	5	,	,	PUNCT
cana-1585	228	6	v.	v.	PROPN
cana-1585	228	7	e.	e.	PROPN
cana-1585	228	8	,	,	PUNCT
cana-1585	228	9	sivaraj	sivaraj	PROPN
cana-1585	228	10	,	,	PUNCT
cana-1585	228	11	d.	d.	PROPN
cana-1585	228	12	,	,	PUNCT
cana-1585	228	13	&	&	CCONJ
cana-1585	228	14	thirumalaisamy	thirumalaisamy	PROPN
cana-1585	228	15	,	,	PUNCT
cana-1585	228	16	r.	r.	PROPN
cana-1585	228	17	(	(	PUNCT
cana-1585	228	18	2018	2018	NUM
cana-1585	228	19	)	)	PUNCT
cana-1585	228	20	.	.	PUNCT
cana-1585	229	1	note	note	VERB
cana-1585	229	2	on	on	ADP
cana-1585	229	3	soft	soft	ADJ
cana-1585	229	4	g	g	NOUN
cana-1585	229	5	-	-	PUNCT
cana-1585	229	6	closed	close	VERB
cana-1585	229	7	sets	set	NOUN
cana-1585	229	8	.	.	PUNCT
cana-1585	230	1	journal	journal	NOUN
cana-1585	230	2	of	of	ADP
cana-1585	230	3	advanced	advanced	ADJ
cana-1585	230	4	research	research	NOUN
cana-1585	230	5	in	in	ADP
cana-1585	230	6	dynamical	dynamical	ADJ
cana-1585	230	7	and	and	CCONJ
cana-1585	230	8	control	control	NOUN
cana-1585	230	9	systems	system	NOUN
cana-1585	230	10	,	,	PUNCT
cana-1585	230	11	10(7	10(7	NUM
cana-1585	230	12	)	)	PUNCT
cana-1585	230	13	,	,	PUNCT
cana-1585	230	14	2129	2129	NUM
cana-1585	230	15	-	-	SYM
cana-1585	230	16	2134	2134	NUM
cana-1585	230	17	.	.	PUNCT
cana-1585	231	1	[	[	X
cana-1585	231	2	4	4	NUM
cana-1585	231	3	]	]	SYM
cana-1585	231	4	sasikala	sasikala	NOUN
cana-1585	231	5	,	,	PUNCT
cana-1585	231	6	v.	v.	PROPN
cana-1585	231	7	e.	e.	PROPN
cana-1585	231	8	,	,	PUNCT
cana-1585	231	9	sivaraj	sivaraj	PROPN
cana-1585	231	10	,	,	PUNCT
cana-1585	231	11	d.	d.	PROPN
cana-1585	231	12	,	,	PUNCT
cana-1585	231	13	thirumalaisamy	thirumalaisamy	PROPN
cana-1585	231	14	,	,	PUNCT
cana-1585	231	15	r.	r.	PROPN
cana-1585	231	16	,	,	PUNCT
cana-1585	231	17	&	&	CCONJ
cana-1585	231	18	venkatesan	venkatesan	PROPN
cana-1585	231	19	,	,	PUNCT
cana-1585	231	20	s.	s.	PROPN
cana-1585	231	21	j.	j.	PROPN
cana-1585	231	22	(	(	PUNCT
cana-1585	231	23	2018	2018	NUM
cana-1585	231	24	)	)	PUNCT
cana-1585	231	25	.	.	PUNCT
cana-1585	232	1	on	on	ADP
cana-1585	232	2	soft	soft	ADJ
cana-1585	232	3	regular	regular	ADJ
cana-1585	232	4	star	star	NOUN
cana-1585	232	5	generalized	generalize	VERB
cana-1585	232	6	star	star	NOUN
cana-1585	232	7	closed	close	VERB
cana-1585	232	8	sets	set	NOUN
cana-1585	232	9	in	in	ADP
cana-1585	232	10	soft	soft	ADJ
cana-1585	232	11	topological	topological	ADJ
cana-1585	232	12	spaces	space	NOUN
cana-1585	232	13	.	.	PUNCT
cana-1585	233	1	journal	journal	NOUN
cana-1585	233	2	of	of	ADP
cana-1585	233	3	advanced	advanced	ADJ
cana-1585	233	4	research	research	NOUN
cana-1585	233	5	in	in	ADP
cana-1585	233	6	dynamical	dynamical	ADJ
cana-1585	233	7	and	and	CCONJ
cana-1585	233	8	control	control	NOUN
cana-1585	233	9	systems	system	NOUN
cana-1585	233	10	,	,	PUNCT
cana-1585	233	11	10(7	10(7	NUM
cana-1585	233	12	)	)	PUNCT
cana-1585	233	13	,	,	PUNCT
cana-1585	233	14	21352142	21352142	NUM
cana-1585	233	15	.	.	PUNCT
cana-1585	234	1	[	[	X
cana-1585	234	2	5	5	NUM
cana-1585	234	3	]	]	PUNCT
cana-1585	234	4	crossley	crossley	NOUN
cana-1585	234	5	,	,	PUNCT
cana-1585	234	6	s.	s.	PROPN
cana-1585	234	7	g.	g.	PROPN
cana-1585	234	8	,	,	PUNCT
cana-1585	234	9	&	&	CCONJ
cana-1585	234	10	hildebrand	hildebrand	PROPN
cana-1585	234	11	,	,	PUNCT
cana-1585	234	12	s.	s.	PROPN
cana-1585	234	13	k.	k.	PROPN
cana-1585	234	14	(	(	PUNCT
cana-1585	234	15	1971	1971	NUM
cana-1585	234	16	)	)	PUNCT
cana-1585	234	17	.	.	PUNCT
cana-1585	235	1	semi	semi	ADJ
cana-1585	235	2	-	-	NOUN
cana-1585	235	3	closure	closure	ADJ
cana-1585	235	4	.	.	PUNCT
cana-1585	236	1	texas	texas	PROPN
cana-1585	236	2	journal	journal	PROPN
cana-1585	236	3	of	of	ADP
cana-1585	236	4	science	science	PROPN
cana-1585	236	5	,	,	PUNCT
cana-1585	236	6	22	22	NUM
cana-1585	236	7	,	,	PUNCT
cana-1585	236	8	99	99	NUM
cana-1585	236	9	-	-	SYM
cana-1585	236	10	112	112	NUM
cana-1585	236	11	.	.	PUNCT
cana-1585	237	1	[	[	X
cana-1585	237	2	6	6	NUM
cana-1585	237	3	]	]	PUNCT
cana-1585	237	4	crossley	crossley	NOUN
cana-1585	237	5	,	,	PUNCT
cana-1585	237	6	s.	s.	PROPN
cana-1585	237	7	g.	g.	PROPN
cana-1585	237	8	,	,	PUNCT
cana-1585	237	9	&	&	CCONJ
cana-1585	237	10	hildebrand	hildebrand	PROPN
cana-1585	237	11	,	,	PUNCT
cana-1585	237	12	s.	s.	PROPN
cana-1585	237	13	k.	k.	PROPN
cana-1585	237	14	(	(	PUNCT
cana-1585	237	15	1972	1972	NUM
cana-1585	237	16	)	)	PUNCT
cana-1585	237	17	.	.	PUNCT
cana-1585	238	1	semi	semi	ADJ
cana-1585	238	2	topological	topological	ADJ
cana-1585	238	3	properties	property	NOUN
cana-1585	238	4	.	.	PUNCT
cana-1585	239	1	fundamenta	fundamenta	PROPN
cana-1585	239	2	mathematicae	mathematicae	PROPN
cana-1585	239	3	,	,	PUNCT
cana-1585	239	4	74	74	NUM
cana-1585	239	5	,	,	PUNCT
cana-1585	239	6	233	233	NUM
cana-1585	239	7	-	-	SYM
cana-1585	239	8	254	254	NUM
cana-1585	239	9	.	.	PUNCT
cana-1585	240	1	[	[	X
cana-1585	240	2	7	7	NUM
cana-1585	240	3	]	]	SYM
cana-1585	240	4	devi	devi	PROPN
cana-1585	240	5	,	,	PUNCT
cana-1585	240	6	r.	r.	PROPN
cana-1585	240	7	,	,	PUNCT
cana-1585	240	8	kokilavani	kokilavani	PROPN
cana-1585	240	9	,	,	PUNCT
cana-1585	240	10	v.	v.	ADV
cana-1585	240	11	,	,	PUNCT
cana-1585	240	12	&	&	CCONJ
cana-1585	240	13	basker	basker	PROPN
cana-1585	240	14	,	,	PUNCT
cana-1585	240	15	p.	p.	PROPN
cana-1585	240	16	(	(	PUNCT
cana-1585	240	17	2012	2012	NUM
cana-1585	240	18	)	)	PUNCT
cana-1585	240	19	.	.	PUNCT
cana-1585	241	1	on	on	ADP
cana-1585	241	2	strongly	strongly	ADV
cana-1585	241	3	αδ	αδ	ADP
cana-1585	241	4	super	super	ADJ
cana-1585	241	5	irresolute	irresolute	ADJ
cana-1585	241	6	functions	function	NOUN
cana-1585	241	7	in	in	ADP
cana-1585	241	8	topological	topological	ADJ
cana-1585	241	9	spaces	space	NOUN
cana-1585	241	10	.	.	PUNCT
cana-1585	242	1	international	international	ADJ
cana-1585	242	2	journal	journal	PROPN
cana-1585	242	3	of	of	ADP
cana-1585	242	4	computer	computer	NOUN
cana-1585	242	5	applications	application	NOUN
cana-1585	242	6	,	,	PUNCT
cana-1585	242	7	40(17	40(17	NUM
cana-1585	242	8	)	)	PUNCT
cana-1585	242	9	,	,	PUNCT
cana-1585	242	10	38	38	NUM
cana-1585	242	11	-	-	SYM
cana-1585	242	12	42	42	NUM
cana-1585	242	13	.	.	PUNCT
cana-1585	243	1	[	[	X
cana-1585	243	2	8	8	NUM
cana-1585	243	3	]	]	PUNCT
cana-1585	243	4	benchalli	benchalli	NOUN
cana-1585	243	5	,	,	PUNCT
cana-1585	243	6	s.	s.	PROPN
cana-1585	243	7	,	,	PUNCT
cana-1585	243	8	&	&	CCONJ
cana-1585	243	9	wali	wali	PROPN
cana-1585	243	10	,	,	PUNCT
cana-1585	243	11	r.	r.	PROPN
cana-1585	243	12	s.	s.	PROPN
cana-1585	243	13	(	(	PUNCT
cana-1585	243	14	2007	2007	NUM
cana-1585	243	15	)	)	PUNCT
cana-1585	243	16	.	.	PUNCT
cana-1585	244	1	on	on	ADP
cana-1585	244	2	rw	rw	NOUN
cana-1585	244	3	-	-	PUNCT
cana-1585	244	4	closed	close	VERB
cana-1585	244	5	sets	set	NOUN
cana-1585	244	6	in	in	ADP
cana-1585	244	7	topological	topological	ADJ
cana-1585	244	8	spaces	space	NOUN
cana-1585	244	9	.	.	PUNCT
cana-1585	245	1	bulletin	bulletin	NOUN
cana-1585	245	2	of	of	ADP
cana-1585	245	3	the	the	DET
cana-1585	245	4	malaysian	malaysian	PROPN
cana-1585	245	5	mathematical	mathematical	PROPN
cana-1585	245	6	sciences	sciences	PROPN
cana-1585	245	7	society	society	NOUN
cana-1585	245	8	,	,	PUNCT
cana-1585	245	9	30(2	30(2	NUM
cana-1585	245	10	)	)	PUNCT
cana-1585	245	11	,	,	PUNCT
cana-1585	245	12	99	99	NUM
cana-1585	245	13	-	-	SYM
cana-1585	245	14	110	110	NUM
cana-1585	245	15	.	.	PUNCT
cana-1585	246	1	[	[	X
cana-1585	246	2	9	9	NUM
cana-1585	246	3	]	]	PUNCT
cana-1585	246	4	benchalli	benchalli	NOUN
cana-1585	246	5	,	,	PUNCT
cana-1585	246	6	s.	s.	PROPN
cana-1585	246	7	s.	s.	PROPN
cana-1585	246	8	,	,	PUNCT
cana-1585	246	9	patil	patil	PROPN
cana-1585	246	10	,	,	PUNCT
cana-1585	246	11	p.	p.	PROPN
cana-1585	246	12	g.	g.	PROPN
cana-1585	246	13	,	,	PUNCT
cana-1585	246	14	&	&	CCONJ
cana-1585	246	15	rayanagauda	rayanagauda	NOUN
cana-1585	246	16	,	,	PUNCT
cana-1585	246	17	d.	d.	PROPN
cana-1585	246	18	(	(	PUNCT
cana-1585	246	19	2009	2009	NUM
cana-1585	246	20	)	)	PUNCT
cana-1585	246	21	.	.	PUNCT
cana-1585	247	1	wα	wα	NOUN
cana-1585	247	2	-	-	PUNCT
cana-1585	247	3	closed	close	VERB
cana-1585	247	4	sets	set	NOUN
cana-1585	247	5	in	in	ADP
cana-1585	247	6	topological	topological	ADJ
cana-1585	247	7	spaces	space	NOUN
cana-1585	247	8	.	.	PUNCT
cana-1585	248	1	the	the	DET
cana-1585	248	2	global	global	ADJ
cana-1585	248	3	journal	journal	NOUN
cana-1585	248	4	of	of	ADP
cana-1585	248	5	applied	apply	VERB
cana-1585	248	6	mathematics	mathematic	NOUN
cana-1585	248	7	and	and	CCONJ
cana-1585	248	8	mathematical	mathematical	ADJ
cana-1585	248	9	sciences	science	NOUN
cana-1585	248	10	,	,	PUNCT
cana-1585	248	11	2(1	2(1	NUM
cana-1585	248	12	-	-	SYM
cana-1585	248	13	2	2	NUM
cana-1585	248	14	)	)	PUNCT
cana-1585	248	15	,	,	PUNCT
cana-1585	248	16	53	53	NUM
cana-1585	248	17	-	-	SYM
cana-1585	248	18	63	63	NUM
cana-1585	248	19	.	.	PUNCT
cana-1585	249	1	[	[	X
cana-1585	249	2	10	10	NUM
cana-1585	249	3	]	]	X
cana-1585	249	4	kokilavani	kokilavani	NOUN
cana-1585	249	5	,	,	PUNCT
cana-1585	249	6	v.	v.	ADV
cana-1585	249	7	,	,	PUNCT
cana-1585	249	8	&	&	CCONJ
cana-1585	249	9	basker	basker	PROPN
cana-1585	249	10	,	,	PUNCT
cana-1585	249	11	p.	p.	PROPN
cana-1585	249	12	(	(	PUNCT
cana-1585	249	13	2012	2012	NUM
cana-1585	249	14	)	)	PUNCT
cana-1585	249	15	.	.	PUNCT
cana-1585	250	1	on	on	ADP
cana-1585	250	2	sober	sober	NOUN
cana-1585	250	3	-	-	PUNCT
cana-1585	250	4	mx	mx	NOUN
cana-1585	250	5	αδ	αδ	PART
cana-1585	250	6	r0	r0	VERB
cana-1585	250	7	spaces	space	NOUN
cana-1585	250	8	in	in	ADP
cana-1585	250	9	m	m	NOUN
cana-1585	250	10	-	-	NOUN
cana-1585	250	11	structures	structure	NOUN
cana-1585	250	12	.	.	PUNCT
cana-1585	251	1	international	international	ADJ
cana-1585	251	2	journal	journal	NOUN
cana-1585	251	3	of	of	ADP
cana-1585	251	4	scientific	scientific	ADJ
cana-1585	251	5	research	research	NOUN
cana-1585	251	6	publications	publication	NOUN
cana-1585	251	7	,	,	PUNCT
cana-1585	251	8	2(3	2(3	NUM
cana-1585	251	9	)	)	PUNCT
cana-1585	251	10	,	,	PUNCT
cana-1585	251	11	1	1	NUM
cana-1585	251	12	-	-	SYM
cana-1585	251	13	4	4	NUM
cana-1585	251	14	.	.	PUNCT
cana-1585	252	1	[	[	X
cana-1585	252	2	11	11	NUM
cana-1585	252	3	]	]	PUNCT
cana-1585	252	4	benchalli	benchalli	NOUN
cana-1585	252	5	,	,	PUNCT
cana-1585	252	6	s.	s.	PROPN
cana-1585	252	7	s.	s.	PROPN
cana-1585	252	8	,	,	PUNCT
cana-1585	252	9	&	&	CCONJ
cana-1585	252	10	patil	patil	PROPN
cana-1585	252	11	,	,	PUNCT
cana-1585	252	12	p.	p.	NOUN
cana-1585	252	13	g.	g.	PROPN
cana-1585	252	14	(	(	PUNCT
cana-1585	252	15	2010	2010	NUM
cana-1585	252	16	)	)	PUNCT
cana-1585	252	17	.	.	PUNCT
cana-1585	253	1	some	some	DET
cana-1585	253	2	new	new	ADJ
cana-1585	253	3	continuous	continuous	ADJ
cana-1585	253	4	maps	map	NOUN
cana-1585	253	5	in	in	ADP
cana-1585	253	6	topological	topological	ADJ
cana-1585	253	7	spaces	space	NOUN
cana-1585	253	8	.	.	PUNCT
cana-1585	254	1	journal	journal	NOUN
cana-1585	254	2	of	of	ADP
cana-1585	254	3	advanced	advanced	ADJ
cana-1585	254	4	topics	topic	NOUN
cana-1585	254	5	in	in	ADP
cana-1585	254	6	topology	topology	NOUN
cana-1585	254	7	,	,	PUNCT
cana-1585	254	8	1(2	1(2	NUM
cana-1585	254	9	)	)	PUNCT
cana-1585	254	10	.	.	PUNCT
cana-1585	255	1	[	[	X
cana-1585	255	2	12	12	NUM
cana-1585	255	3	]	]	X
cana-1585	255	4	kokilavani	kokilavani	NOUN
cana-1585	255	5	,	,	PUNCT
cana-1585	255	6	v.	v.	ADV
cana-1585	255	7	,	,	PUNCT
cana-1585	255	8	&	&	CCONJ
cana-1585	255	9	basker	basker	PROPN
cana-1585	255	10	,	,	PUNCT
cana-1585	255	11	p.	p.	PROPN
cana-1585	255	12	(	(	PUNCT
cana-1585	255	13	2012	2012	NUM
cana-1585	255	14	)	)	PUNCT
cana-1585	255	15	.	.	PUNCT
cana-1585	256	1	the	the	DET
cana-1585	256	2	αδ	αδ	PROPN
cana-1585	256	3	-	-	PUNCT
cana-1585	256	4	kernel	kernel	PROPN
cana-1585	256	5	and	and	CCONJ
cana-1585	256	6	αδ	αδ	NOUN
cana-1585	256	7	-	-	PUNCT
cana-1585	256	8	closure	closure	NOUN
cana-1585	256	9	via	via	ADP
cana-1585	256	10	αδ	αδ	ADV
cana-1585	256	11	-	-	PUNCT
cana-1585	256	12	open	open	ADJ
cana-1585	256	13	sets	set	NOUN
cana-1585	256	14	in	in	ADP
cana-1585	256	15	topological	topological	ADJ
cana-1585	256	16	spaces	space	NOUN
cana-1585	256	17	.	.	PUNCT
cana-1585	257	1	international	international	ADJ
cana-1585	257	2	journal	journal	PROPN
cana-1585	257	3	of	of	ADP
cana-1585	257	4	mathematics	mathematics	PROPN
cana-1585	257	5	archive	archive	NOUN
cana-1585	257	6	,	,	PUNCT
cana-1585	257	7	3(3	3(3	NUM
cana-1585	257	8	)	)	PUNCT
cana-1585	257	9	,	,	PUNCT
cana-1585	257	10	1	1	NUM
cana-1585	257	11	-	-	SYM
cana-1585	257	12	4	4	NUM
cana-1585	257	13	.	.	PUNCT
cana-1585	258	1	[	[	X
cana-1585	258	2	13	13	NUM
cana-1585	258	3	]	]	X
cana-1585	258	4	kokilavani	kokilavani	NOUN
cana-1585	258	5	,	,	PUNCT
cana-1585	258	6	v.	v.	ADV
cana-1585	258	7	,	,	PUNCT
cana-1585	258	8	&	&	CCONJ
cana-1585	258	9	basker	basker	PROPN
cana-1585	258	10	,	,	PUNCT
cana-1585	258	11	p.	p.	PROPN
cana-1585	258	12	(	(	PUNCT
cana-1585	258	13	2012	2012	NUM
cana-1585	258	14	)	)	PUNCT
cana-1585	258	15	.	.	PUNCT
cana-1585	259	1	d	d	X
cana-1585	259	2	-	-	PUNCT
cana-1585	259	3	αδ	αδ	ADP
cana-1585	259	4	-	-	PUNCT
cana-1585	259	5	sets	set	NOUN
cana-1585	259	6	and	and	CCONJ
cana-1585	259	7	associated	associated	ADJ
cana-1585	259	8	separation	separation	NOUN
cana-1585	259	9	axioms	axiom	NOUN
cana-1585	259	10	in	in	ADP
cana-1585	259	11	topological	topological	ADJ
cana-1585	259	12	spaces	space	NOUN
cana-1585	259	13	.	.	PUNCT
cana-1585	260	1	elixir	elixir	NOUN
cana-1585	260	2	discrete	discrete	NOUN
cana-1585	260	3	mathematics	mathematic	NOUN
cana-1585	260	4	,	,	PUNCT
cana-1585	260	5	46	46	NUM
cana-1585	260	6	,	,	PUNCT
cana-1585	260	7	8207	8207	NUM
cana-1585	260	8	-	-	SYM
cana-1585	260	9	8210	8210	NUM
cana-1585	260	10	.	.	PUNCT
cana-1585	261	1	[	[	X
cana-1585	261	2	14	14	NUM
cana-1585	261	3	]	]	X
cana-1585	261	4	maki	maki	NOUN
cana-1585	261	5	,	,	PUNCT
cana-1585	261	6	h.	h.	PROPN
cana-1585	261	7	(	(	PUNCT
cana-1585	261	8	1996	1996	NUM
cana-1585	261	9	)	)	PUNCT
cana-1585	261	10	.	.	PUNCT
cana-1585	262	1	on	on	ADP
cana-1585	262	2	generalizing	generalize	VERB
cana-1585	262	3	semi	semi	ADJ
cana-1585	262	4	-	-	ADJ
cana-1585	262	5	open	open	ADJ
cana-1585	262	6	sets	set	NOUN
cana-1585	262	7	and	and	CCONJ
cana-1585	262	8	pre	pre	ADJ
cana-1585	262	9	-	-	ADJ
cana-1585	262	10	open	open	ADJ
cana-1585	262	11	sets	set	NOUN
cana-1585	262	12	.	.	PUNCT
cana-1585	263	1	in	in	ADP
cana-1585	263	2	meeting	meet	VERB
cana-1585	263	3	on	on	ADP
cana-1585	263	4	topological	topological	ADJ
cana-1585	263	5	spaces	space	NOUN
cana-1585	263	6	theory	theory	NOUN
cana-1585	263	7	and	and	CCONJ
cana-1585	263	8	its	its	PRON
cana-1585	263	9	application	application	NOUN
cana-1585	263	10	(	(	PUNCT
cana-1585	263	11	pp	pp	ADJ
cana-1585	263	12	.	.	PUNCT
cana-1585	263	13	13	13	NUM
cana-1585	263	14	-	-	SYM
cana-1585	263	15	18	18	NUM
cana-1585	263	16	)	)	PUNCT
cana-1585	263	17	.	.	PUNCT
cana-1585	264	1	communications	communication	NOUN
cana-1585	264	2	on	on	ADP
cana-1585	264	3	applied	apply	VERB
cana-1585	264	4	nonlinear	nonlinear	ADJ
cana-1585	264	5	analysis	analysis	NOUN
cana-1585	264	6	issn	issn	NOUN
cana-1585	264	7	:	:	PUNCT
cana-1585	264	8	1074	1074	NUM
cana-1585	264	9	-	-	PUNCT
cana-1585	264	10	133x	133x	NUM
cana-1585	264	11	vol	vol	NOUN
cana-1585	264	12	31	31	NUM
cana-1585	264	13	no	no	NOUN
cana-1585	264	14	.	.	PUNCT
cana-1585	265	1	8s	8s	PROPN
cana-1585	265	2	(	(	PUNCT
cana-1585	265	3	2024	2024	NUM
cana-1585	265	4	)	)	PUNCT
cana-1585	265	5	746	746	NUM
cana-1585	265	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1585	266	1	[	[	X
cana-1585	266	2	15	15	NUM
cana-1585	266	3	]	]	X
cana-1585	266	4	davis	davis	PROPN
cana-1585	266	5	,	,	PUNCT
cana-1585	266	6	a.	a.	PROPN
cana-1585	266	7	s.	s.	PROPN
cana-1585	266	8	(	(	PUNCT
cana-1585	266	9	1961	1961	NUM
cana-1585	266	10	)	)	PUNCT
cana-1585	266	11	.	.	PUNCT
cana-1585	267	1	indexed	index	VERB
cana-1585	267	2	system	system	NOUN
cana-1585	267	3	of	of	ADP
cana-1585	267	4	neighborhoods	neighborhood	NOUN
cana-1585	267	5	for	for	ADP
cana-1585	267	6	general	general	ADJ
cana-1585	267	7	topology	topology	NOUN
cana-1585	267	8	.	.	PUNCT
cana-1585	268	1	american	american	PROPN
cana-1585	268	2	mathematical	mathematical	PROPN
cana-1585	268	3	society	society	NOUN
cana-1585	268	4	,	,	PUNCT
cana-1585	268	5	68(9	68(9	NOUN
cana-1585	268	6	)	)	PUNCT
cana-1585	268	7	,	,	PUNCT
cana-1585	268	8	886	886	NUM
cana-1585	268	9	-	-	SYM
cana-1585	268	10	893	893	NUM
cana-1585	268	11	.	.	PUNCT
cana-1585	269	1	[	[	X
cana-1585	269	2	16	16	NUM
cana-1585	269	3	]	]	X
cana-1585	269	4	bhattacharya	bhattacharya	NOUN
cana-1585	269	5	,	,	PUNCT
cana-1585	269	6	p.	p.	NOUN
cana-1585	269	7	,	,	PUNCT
cana-1585	269	8	&	&	CCONJ
cana-1585	269	9	lahiri	lahiri	PROPN
cana-1585	269	10	,	,	PUNCT
cana-1585	269	11	b.	b.	PROPN
cana-1585	269	12	k.	k.	PROPN
cana-1585	269	13	(	(	PUNCT
cana-1585	269	14	1987	1987	NUM
cana-1585	269	15	)	)	PUNCT
cana-1585	269	16	.	.	PUNCT
cana-1585	270	1	semi	semi	ADJ
cana-1585	270	2	-	-	ADJ
cana-1585	270	3	generalized	generalized	ADJ
cana-1585	270	4	closed	closed	ADJ
cana-1585	270	5	sets	set	NOUN
cana-1585	270	6	in	in	ADP
cana-1585	270	7	topology	topology	NOUN
cana-1585	270	8	.	.	PUNCT
cana-1585	271	1	indian	indian	PROPN
cana-1585	271	2	journal	journal	PROPN
cana-1585	271	3	of	of	ADP
cana-1585	271	4	mathematics	mathematic	NOUN
cana-1585	271	5	,	,	PUNCT
cana-1585	271	6	29(3	29(3	NUM
cana-1585	271	7	)	)	PUNCT
cana-1585	271	8	,	,	PUNCT
cana-1585	271	9	375	375	NUM
cana-1585	271	10	-	-	SYM
cana-1585	271	11	382	382	NUM
cana-1585	271	12	.	.	PUNCT
cana-1585	272	1	[	[	X
cana-1585	272	2	17	17	NUM
cana-1585	272	3	]	]	X
cana-1585	272	4	al	al	PROPN
cana-1585	272	5	-	-	PUNCT
cana-1585	272	6	swidi	swidi	PROPN
cana-1585	272	7	,	,	PUNCT
cana-1585	272	8	a.	a.	PROPN
cana-1585	272	9	l.	l.	PROPN
cana-1585	272	10	,	,	PUNCT
cana-1585	272	11	&	&	CCONJ
cana-1585	272	12	mohammed	mohammed	PROPN
cana-1585	272	13	,	,	PUNCT
cana-1585	272	14	b.	b.	PROPN
cana-1585	272	15	(	(	PUNCT
cana-1585	272	16	2012	2012	NUM
cana-1585	272	17	)	)	PUNCT
cana-1585	272	18	.	.	PUNCT
cana-1585	273	1	separation	separation	NOUN
cana-1585	273	2	axioms	axiom	VERB
cana-1585	273	3	via	via	ADP
cana-1585	273	4	kernel	kernel	PROPN
cana-1585	273	5	in	in	ADP
cana-1585	273	6	topological	topological	ADJ
cana-1585	273	7	spaces	space	NOUN
cana-1585	273	8	.	.	PUNCT
cana-1585	274	1	archive	archive	PROPN
cana-1585	274	2	des	des	PROPN
cana-1585	274	3	sciences	sciences	PROPN
cana-1585	274	4	,	,	PUNCT
cana-1585	274	5	65(7	65(7	NUM
cana-1585	274	6	)	)	PUNCT
cana-1585	274	7	,	,	PUNCT
cana-1585	274	8	41	41	NUM
cana-1585	274	9	-	-	SYM
cana-1585	274	10	48	48	NUM
cana-1585	274	11	.	.	PUNCT
cana-1585	275	1	[	[	X
cana-1585	275	2	18	18	NUM
cana-1585	275	3	]	]	PUNCT
cana-1585	275	4	bhattacharya	bhattacharya	NOUN
cana-1585	275	5	,	,	PUNCT
cana-1585	275	6	p.	p.	NOUN
cana-1585	275	7	,	,	PUNCT
cana-1585	275	8	&	&	CCONJ
cana-1585	275	9	lahiri	lahiri	PROPN
cana-1585	275	10	,	,	PUNCT
cana-1585	275	11	b.	b.	PROPN
cana-1585	275	12	k.	k.	PROPN
cana-1585	275	13	(	(	PUNCT
cana-1585	275	14	1987	1987	NUM
cana-1585	275	15	)	)	PUNCT
cana-1585	275	16	.	.	PUNCT
cana-1585	276	1	semi	semi	ADJ
cana-1585	276	2	-	-	ADJ
cana-1585	276	3	generalized	generalized	ADJ
cana-1585	276	4	closed	closed	ADJ
cana-1585	276	5	sets	set	NOUN
cana-1585	276	6	in	in	ADP
cana-1585	276	7	topology	topology	NOUN
cana-1585	276	8	.	.	PUNCT
cana-1585	277	1	indian	indian	PROPN
cana-1585	277	2	journal	journal	PROPN
cana-1585	277	3	of	of	ADP
cana-1585	277	4	mathematics	mathematic	NOUN
cana-1585	277	5	,	,	PUNCT
cana-1585	277	6	29(3	29(3	NUM
cana-1585	277	7	)	)	PUNCT
cana-1585	277	8	,	,	PUNCT
cana-1585	277	9	375	375	NUM
cana-1585	277	10	-	-	SYM
cana-1585	277	11	382	382	NUM
cana-1585	277	12	.	.	PUNCT
cana-1585	278	1	[	[	X
cana-1585	278	2	19	19	NUM
cana-1585	278	3	]	]	PUNCT
cana-1585	278	4	levine	levine	PROPN
cana-1585	278	5	,	,	PUNCT
cana-1585	278	6	n.	n.	PROPN
cana-1585	278	7	(	(	PUNCT
cana-1585	278	8	1970	1970	NUM
cana-1585	278	9	)	)	PUNCT
cana-1585	278	10	.	.	PUNCT
cana-1585	279	1	generalized	generalize	VERB
cana-1585	279	2	closed	close	VERB
cana-1585	279	3	sets	set	NOUN
cana-1585	279	4	in	in	ADP
cana-1585	279	5	topology	topology	NOUN
cana-1585	279	6	.	.	PUNCT
cana-1585	280	1	rendiconti	rendiconti	VERB
cana-1585	280	2	del	del	PROPN
cana-1585	280	3	circolo	circolo	PROPN
cana-1585	280	4	matematico	matematico	NOUN
cana-1585	280	5	di	di	NOUN
cana-1585	280	6	palermo	palermo	NOUN
cana-1585	280	7	,	,	PUNCT
cana-1585	280	8	19	19	NUM
cana-1585	280	9	,	,	PUNCT
cana-1585	280	10	89	89	NUM
cana-1585	280	11	-	-	SYM
cana-1585	280	12	96	96	NUM
cana-1585	280	13	.	.	PUNCT
cana-1585	281	1	[	[	X
cana-1585	281	2	20	20	NUM
cana-1585	281	3	]	]	SYM
cana-1585	281	4	mandal	mandal	PROPN
cana-1585	281	5	,	,	PUNCT
cana-1585	281	6	d.	d.	PROPN
cana-1585	281	7	,	,	PUNCT
cana-1585	281	8	&	&	CCONJ
cana-1585	281	9	mukherjee	mukherjee	PROPN
cana-1585	281	10	,	,	PUNCT
cana-1585	281	11	m.	m.	NOUN
cana-1585	281	12	n.	n.	PROPN
cana-1585	281	13	(	(	PUNCT
cana-1585	281	14	2007	2007	NUM
cana-1585	281	15	)	)	PUNCT
cana-1585	281	16	.	.	PUNCT
cana-1585	282	1	on	on	ADP
cana-1585	282	2	a	a	DET
cana-1585	282	3	type	type	NOUN
cana-1585	282	4	of	of	ADP
cana-1585	282	5	generalized	generalized	ADJ
cana-1585	282	6	closed	closed	ADJ
cana-1585	282	7	sets	set	NOUN
cana-1585	282	8	.	.	PUNCT
cana-1585	283	1	sociedade	sociedade	PROPN
cana-1585	283	2	paranaense	paranaense	PROPN
cana-1585	283	3	de	de	PROPN
cana-1585	283	4	matemática	matemática	PROPN
cana-1585	283	5	,	,	PUNCT
cana-1585	283	6	30(1	30(1	NUM
cana-1585	283	7	)	)	PUNCT
cana-1585	283	8	,	,	PUNCT
cana-1585	283	9	67	67	NUM
cana-1585	283	10	-	-	SYM
cana-1585	283	11	76	76	NUM
cana-1585	283	12	.	.	PUNCT
cana-1585	284	1	[	[	X
cana-1585	284	2	21	21	NUM
cana-1585	284	3	]	]	PUNCT
cana-1585	284	4	ganguly	ganguly	PROPN
cana-1585	284	5	,	,	PUNCT
cana-1585	284	6	g.	g.	PROPN
cana-1585	284	7	a.	a.	PROPN
cana-1585	284	8	,	,	PUNCT
cana-1585	284	9	&	&	CCONJ
cana-1585	284	10	chandel	chandel	PROPN
cana-1585	284	11	,	,	PUNCT
cana-1585	284	12	r.	r.	PROPN
cana-1585	284	13	s.	s.	PROPN
cana-1585	284	14	(	(	PUNCT
cana-1585	284	15	1987	1987	NUM
cana-1585	284	16	)	)	PUNCT
cana-1585	284	17	.	.	PUNCT
cana-1585	285	1	some	some	DET
cana-1585	285	2	results	result	NOUN
cana-1585	285	3	on	on	ADP
cana-1585	285	4	general	general	ADJ
cana-1585	285	5	topology	topology	NOUN
cana-1585	285	6	.	.	PUNCT
cana-1585	286	1	journal	journal	PROPN
cana-1585	286	2	of	of	ADP
cana-1585	286	3	the	the	DET
cana-1585	286	4	indian	indian	PROPN
cana-1585	286	5	academy	academy	PROPN
cana-1585	286	6	of	of	ADP
cana-1585	286	7	mathematics	mathematics	PROPN
cana-1585	286	8	,	,	PUNCT
cana-1585	286	9	9(2	9(2	NUM
cana-1585	286	10	)	)	PUNCT
cana-1585	286	11	,	,	PUNCT
cana-1585	286	12	87	87	NUM
cana-1585	286	13	-	-	SYM
cana-1585	286	14	91	91	NUM
cana-1585	286	15	.	.	PUNCT
cana-1585	287	1	[	[	X
cana-1585	287	2	22	22	NUM
cana-1585	287	3	]	]	PUNCT
cana-1585	287	4	ganster	ganster	NOUN
cana-1585	287	5	,	,	PUNCT
cana-1585	287	6	m.	m.	NOUN
cana-1585	287	7	,	,	PUNCT
cana-1585	287	8	jafari	jafari	PROPN
cana-1585	287	9	,	,	PUNCT
cana-1585	287	10	s.	s.	PROPN
cana-1585	287	11	,	,	PUNCT
cana-1585	287	12	&	&	CCONJ
cana-1585	287	13	navalagi	navalagi	PROPN
cana-1585	287	14	,	,	PUNCT
cana-1585	287	15	g.	g.	PROPN
cana-1585	287	16	b.	b.	PROPN
cana-1585	287	17	(	(	PUNCT
cana-1585	287	18	2002	2002	NUM
cana-1585	287	19	)	)	PUNCT
cana-1585	287	20	.	.	PUNCT
cana-1585	288	1	on	on	ADP
cana-1585	288	2	semi	semi	ADJ
cana-1585	288	3	-	-	ADJ
cana-1585	288	4	g	g	NOUN
cana-1585	288	5	-	-	PUNCT
cana-1585	288	6	regular	regular	ADJ
cana-1585	288	7	and	and	CCONJ
cana-1585	288	8	semi	semi	ADJ
cana-1585	288	9	-	-	ADJ
cana-1585	288	10	g	g	NOUN
cana-1585	288	11	-	-	PUNCT
cana-1585	288	12	normal	normal	ADJ
cana-1585	288	13	spaces	space	NOUN
cana-1585	288	14	.	.	PUNCT
cana-1585	289	1	demonstratio	demonstratio	PROPN
cana-1585	289	2	mathematica	mathematica	PROPN
cana-1585	289	3	,	,	PUNCT
cana-1585	289	4	35(2	35(2	NUM
cana-1585	289	5	)	)	PUNCT
cana-1585	289	6	,	,	PUNCT
cana-1585	289	7	415	415	NUM
cana-1585	289	8	-	-	SYM
cana-1585	289	9	421	421	NUM
cana-1585	289	10	.	.	PUNCT
cana-1585	290	1	[	[	X
cana-1585	290	2	23	23	NUM
cana-1585	290	3	]	]	X
cana-1585	290	4	maki	maki	PROPN
cana-1585	290	5	,	,	PUNCT
cana-1585	290	6	h.	h.	PROPN
cana-1585	290	7	,	,	PUNCT
cana-1585	290	8	devi	devi	PROPN
cana-1585	290	9	,	,	PUNCT
cana-1585	290	10	r.	r.	PROPN
cana-1585	290	11	,	,	PUNCT
cana-1585	290	12	&	&	CCONJ
cana-1585	290	13	balachandran	balachandran	PROPN
cana-1585	290	14	,	,	PUNCT
cana-1585	290	15	k.	k.	PROPN
cana-1585	290	16	(	(	PUNCT
cana-1585	290	17	1994	1994	NUM
cana-1585	290	18	)	)	PUNCT
cana-1585	290	19	.	.	PUNCT
cana-1585	291	1	associated	associated	ADJ
cana-1585	291	2	topologies	topology	NOUN
cana-1585	291	3	of	of	ADP
cana-1585	291	4	generalized	generalized	ADJ
cana-1585	291	5	α	α	NOUN
cana-1585	291	6	-	-	PUNCT
cana-1585	291	7	closed	closed	ADJ
cana-1585	291	8	sets	set	NOUN
cana-1585	291	9	and	and	CCONJ
cana-1585	291	10	α	α	X
cana-1585	291	11	-	-	ADJ
cana-1585	291	12	generalized	generalize	VERB
cana-1585	291	13	closed	closed	ADJ
cana-1585	291	14	sets	set	NOUN
cana-1585	291	15	.	.	PUNCT
cana-1585	292	1	memoirs	memoir	NOUN
cana-1585	292	2	of	of	ADP
cana-1585	292	3	the	the	DET
cana-1585	292	4	faculty	faculty	NOUN
cana-1585	292	5	of	of	ADP
cana-1585	292	6	science	science	NOUN
cana-1585	292	7	,	,	PUNCT
cana-1585	292	8	kochi	kochi	PROPN
cana-1585	292	9	university	university	PROPN
cana-1585	292	10	,	,	PUNCT
cana-1585	292	11	series	series	NOUN
cana-1585	292	12	a	a	PRON
cana-1585	292	13	:	:	PUNCT
cana-1585	292	14	mathematics	mathematic	NOUN
cana-1585	292	15	,	,	PUNCT
cana-1585	292	16	15	15	NUM
cana-1585	292	17	,	,	PUNCT
cana-1585	292	18	51	51	NUM
cana-1585	292	19	-	-	SYM
cana-1585	292	20	63	63	NUM
cana-1585	292	21	.	.	PUNCT
cana-1585	293	1	[	[	X
cana-1585	293	2	24	24	NUM
cana-1585	293	3	]	]	SYM
cana-1585	293	4	malghan	malghan	PROPN
cana-1585	293	5	,	,	PUNCT
cana-1585	293	6	s.	s.	PROPN
cana-1585	293	7	r.	r.	PROPN
cana-1585	293	8	(	(	PUNCT
cana-1585	293	9	1982	1982	NUM
cana-1585	293	10	)	)	PUNCT
cana-1585	293	11	.	.	PUNCT
cana-1585	294	1	generalized	generalize	VERB
cana-1585	294	2	closed	closed	ADJ
cana-1585	294	3	maps	map	NOUN
cana-1585	294	4	.	.	PUNCT
cana-1585	295	1	journal	journal	PROPN
cana-1585	295	2	of	of	ADP
cana-1585	295	3	karnatak	karnatak	PROPN
cana-1585	295	4	university	university	PROPN
cana-1585	295	5	,	,	PUNCT
cana-1585	295	6	science	science	NOUN
cana-1585	295	7	,	,	PUNCT
cana-1585	295	8	27	27	NUM
cana-1585	295	9	,	,	PUNCT
cana-1585	295	10	82	82	NUM
cana-1585	295	11	-	-	SYM
cana-1585	295	12	88	88	NUM
cana-1585	295	13	.	.	PUNCT
cana-1585	296	1	[	[	X
cana-1585	296	2	25	25	NUM
cana-1585	296	3	]	]	PUNCT
cana-1585	296	4	njastad	njastad	NOUN
cana-1585	296	5	,	,	PUNCT
cana-1585	296	6	o.	o.	PROPN
cana-1585	296	7	(	(	PUNCT
cana-1585	296	8	1965	1965	NUM
cana-1585	296	9	)	)	PUNCT
cana-1585	296	10	.	.	PUNCT
cana-1585	297	1	on	on	ADP
cana-1585	297	2	some	some	DET
cana-1585	297	3	classes	class	NOUN
cana-1585	297	4	of	of	ADP
cana-1585	297	5	nearly	nearly	ADV
cana-1585	297	6	open	open	ADJ
cana-1585	297	7	sets	set	NOUN
cana-1585	297	8	.	.	PUNCT
cana-1585	298	1	pacific	pacific	PROPN
cana-1585	298	2	journal	journal	PROPN
cana-1585	298	3	of	of	ADP
cana-1585	298	4	mathematics	mathematic	NOUN
cana-1585	298	5	,	,	PUNCT
cana-1585	298	6	15	15	NUM
cana-1585	298	7	,	,	PUNCT
cana-1585	298	8	961	961	NUM
cana-1585	298	9	-	-	SYM
cana-1585	298	10	970	970	NUM
cana-1585	298	11	.	.	PUNCT