id	sid	tid	token	lemma	pos
ejpam-6541	1	1	european	european	PROPN
ejpam-6541	1	2	journal	journal	PROPN
ejpam-6541	1	3	of	of	ADP
ejpam-6541	1	4	pure	pure	ADJ
ejpam-6541	1	5	and	and	CCONJ
ejpam-6541	1	6	applied	applied	ADJ
ejpam-6541	1	7	mathematics	mathematic	NOUN
ejpam-6541	1	8	2025	2025	NUM
ejpam-6541	1	9	,	,	PUNCT
ejpam-6541	1	10	vol	vol	NOUN
ejpam-6541	1	11	.	.	PROPN
ejpam-6541	1	12	18	18	NUM
ejpam-6541	1	13	,	,	PUNCT
ejpam-6541	1	14	issue	issue	NOUN
ejpam-6541	1	15	4	4	NUM
ejpam-6541	1	16	,	,	PUNCT
ejpam-6541	1	17	article	article	NOUN
ejpam-6541	1	18	number	number	NOUN
ejpam-6541	1	19	6541	6541	NUM
ejpam-6541	1	20	issn	issn	VERB
ejpam-6541	1	21	1307	1307	NUM
ejpam-6541	1	22	-	-	SYM
ejpam-6541	1	23	5543	5543	NUM
ejpam-6541	1	24	–	–	PUNCT
ejpam-6541	1	25	ejpam.com	ejpam.com	X
ejpam-6541	1	26	published	publish	VERB
ejpam-6541	1	27	by	by	ADP
ejpam-6541	1	28	new	new	PROPN
ejpam-6541	1	29	york	york	PROPN
ejpam-6541	1	30	business	business	PROPN
ejpam-6541	1	31	global	global	ADJ
ejpam-6541	1	32	completeness	completeness	NOUN
ejpam-6541	1	33	and	and	CCONJ
ejpam-6541	1	34	compactness	compactness	NOUN
ejpam-6541	1	35	on	on	ADP
ejpam-6541	1	36	hesitant	hesitant	ADJ
ejpam-6541	1	37	fuzzy	fuzzy	ADJ
ejpam-6541	1	38	normed	normed	PROPN
ejpam-6541	1	39	linear	linear	PROPN
ejpam-6541	1	40	spaces	space	NOUN
ejpam-6541	1	41	krishnamoorthy	krishnamoorthy	PROPN
ejpam-6541	1	42	kavitha1	kavitha1	PROPN
ejpam-6541	1	43	,	,	PUNCT
ejpam-6541	1	44	prakasam	prakasam	NOUN
ejpam-6541	1	45	muralikrishna2,∗	muralikrishna2,∗	VERB
ejpam-6541	1	46	1	1	NUM
ejpam-6541	1	47	pg	pg	NOUN
ejpam-6541	1	48	and	and	CCONJ
ejpam-6541	1	49	research	research	PROPN
ejpam-6541	1	50	department	department	PROPN
ejpam-6541	1	51	of	of	ADP
ejpam-6541	1	52	mathematics	mathematic	NOUN
ejpam-6541	1	53	,	,	PUNCT
ejpam-6541	1	54	muthurangam	muthurangam	NOUN
ejpam-6541	1	55	government	government	NOUN
ejpam-6541	1	56	arts	arts	PROPN
ejpam-6541	1	57	college	college	PROPN
ejpam-6541	1	58	(	(	PUNCT
ejpam-6541	1	59	autonomous	autonomous	ADJ
ejpam-6541	1	60	)	)	PUNCT
ejpam-6541	1	61	(	(	PUNCT
ejpam-6541	1	62	affiliated	affiliate	VERB
ejpam-6541	1	63	to	to	PART
ejpam-6541	1	64	thiruvalluvar	thiruvalluvar	NOUN
ejpam-6541	1	65	university	university	NOUN
ejpam-6541	1	66	,	,	PUNCT
ejpam-6541	1	67	serkkadu	serkkadu	ADJ
ejpam-6541	1	68	,	,	PUNCT
ejpam-6541	1	69	vellore	vellore	NOUN
ejpam-6541	1	70	)	)	PUNCT
ejpam-6541	1	71	,	,	PUNCT
ejpam-6541	1	72	vellore-632002	vellore-632002	NOUN
ejpam-6541	1	73	,	,	PUNCT
ejpam-6541	1	74	tamil	tamil	PROPN
ejpam-6541	1	75	nadu	nadu	NOUN
ejpam-6541	1	76	,	,	PUNCT
ejpam-6541	1	77	india	india	PROPN
ejpam-6541	1	78	2	2	NUM
ejpam-6541	1	79	pg	pg	NOUN
ejpam-6541	1	80	and	and	CCONJ
ejpam-6541	1	81	research	research	PROPN
ejpam-6541	1	82	department	department	PROPN
ejpam-6541	1	83	of	of	ADP
ejpam-6541	1	84	mathematics	mathematic	NOUN
ejpam-6541	1	85	,	,	PUNCT
ejpam-6541	1	86	muthurangam	muthurangam	NOUN
ejpam-6541	1	87	government	government	NOUN
ejpam-6541	1	88	arts	arts	PROPN
ejpam-6541	1	89	college	college	PROPN
ejpam-6541	1	90	(	(	PUNCT
ejpam-6541	1	91	autonomous	autonomous	ADJ
ejpam-6541	1	92	)	)	PUNCT
ejpam-6541	1	93	(	(	PUNCT
ejpam-6541	1	94	affiliated	affiliate	VERB
ejpam-6541	1	95	to	to	PART
ejpam-6541	1	96	thiruvalluvar	thiruvalluvar	NOUN
ejpam-6541	1	97	university	university	NOUN
ejpam-6541	1	98	,	,	PUNCT
ejpam-6541	1	99	serkkadu	serkkadu	ADJ
ejpam-6541	1	100	,	,	PUNCT
ejpam-6541	1	101	vellore	vellore	NOUN
ejpam-6541	1	102	)	)	PUNCT
ejpam-6541	1	103	,	,	PUNCT
ejpam-6541	1	104	vellore-632002	vellore-632002	NOUN
ejpam-6541	1	105	,	,	PUNCT
ejpam-6541	1	106	tamil	tamil	PROPN
ejpam-6541	1	107	nadu	nadu	NOUN
ejpam-6541	1	108	,	,	PUNCT
ejpam-6541	1	109	india	india	PROPN
ejpam-6541	1	110	abstract	abstract	NOUN
ejpam-6541	1	111	.	.	PUNCT
ejpam-6541	2	1	in	in	ADP
ejpam-6541	2	2	this	this	DET
ejpam-6541	2	3	work	work	NOUN
ejpam-6541	2	4	,	,	PUNCT
ejpam-6541	2	5	we	we	PRON
ejpam-6541	2	6	examine	examine	VERB
ejpam-6541	2	7	the	the	DET
ejpam-6541	2	8	properties	property	NOUN
ejpam-6541	2	9	of	of	ADP
ejpam-6541	2	10	completeness	completeness	NOUN
ejpam-6541	2	11	and	and	CCONJ
ejpam-6541	2	12	compactness	compactness	NOUN
ejpam-6541	2	13	on	on	ADP
ejpam-6541	2	14	hesitant	hesitant	ADJ
ejpam-6541	2	15	fuzzy	fuzzy	ADJ
ejpam-6541	2	16	normed	norme	VERB
ejpam-6541	2	17	linear	linear	ADJ
ejpam-6541	2	18	space	space	NOUN
ejpam-6541	2	19	,	,	PUNCT
ejpam-6541	2	20	also	also	ADV
ejpam-6541	2	21	address	address	VERB
ejpam-6541	2	22	the	the	DET
ejpam-6541	2	23	same	same	ADJ
ejpam-6541	2	24	properties	property	NOUN
ejpam-6541	2	25	on	on	ADP
ejpam-6541	2	26	intuitionistic	intuitionistic	ADJ
ejpam-6541	2	27	hesitant	hesitant	ADJ
ejpam-6541	2	28	fuzzy	fuzzy	ADJ
ejpam-6541	2	29	normed	norme	VERB
ejpam-6541	2	30	linear	linear	ADJ
ejpam-6541	2	31	space	space	NOUN
ejpam-6541	2	32	in	in	ADP
ejpam-6541	2	33	finite	finite	ADJ
ejpam-6541	2	34	dimension	dimension	NOUN
ejpam-6541	2	35	using	use	VERB
ejpam-6541	2	36	definitions	definition	NOUN
ejpam-6541	2	37	,	,	PUNCT
ejpam-6541	2	38	lemmas	lemmas	ADJ
ejpam-6541	2	39	,	,	PUNCT
ejpam-6541	2	40	and	and	CCONJ
ejpam-6541	2	41	theorems	theorem	NOUN
ejpam-6541	2	42	.	.	PUNCT
ejpam-6541	3	1	we	we	PRON
ejpam-6541	3	2	also	also	ADV
ejpam-6541	3	3	investigate	investigate	VERB
ejpam-6541	3	4	the	the	DET
ejpam-6541	3	5	continuity	continuity	NOUN
ejpam-6541	3	6	of	of	ADP
ejpam-6541	3	7	underlying	underlie	VERB
ejpam-6541	3	8	t	t	NOUN
ejpam-6541	3	9	-	-	PUNCT
ejpam-6541	3	10	norms	norm	NOUN
ejpam-6541	3	11	and	and	CCONJ
ejpam-6541	3	12	co	co	NOUN
ejpam-6541	3	13	-	-	ADJ
ejpam-6541	3	14	t	t	NOUN
ejpam-6541	3	15	-	-	PUNCT
ejpam-6541	3	16	norm	norm	NOUN
ejpam-6541	3	17	on	on	ADP
ejpam-6541	3	18	finite	finite	ADJ
ejpam-6541	3	19	-	-	ADJ
ejpam-6541	3	20	dimensional	dimensional	ADJ
ejpam-6541	3	21	intuitionistic	intuitionistic	ADJ
ejpam-6541	3	22	hesitant	hesitant	ADJ
ejpam-6541	3	23	fuzzy	fuzzy	ADJ
ejpam-6541	3	24	normed	norme	VERB
ejpam-6541	3	25	linear	linear	ADJ
ejpam-6541	3	26	space	space	NOUN
ejpam-6541	3	27	.	.	PUNCT
ejpam-6541	4	1	2020	2020	NUM
ejpam-6541	4	2	mathematics	mathematic	NOUN
ejpam-6541	4	3	subject	subject	NOUN
ejpam-6541	4	4	classifications	classification	NOUN
ejpam-6541	4	5	:	:	PUNCT
ejpam-6541	4	6	00a05	00a05	NUM
ejpam-6541	4	7	,	,	PUNCT
ejpam-6541	4	8	00a22	00a22	NOUN
ejpam-6541	4	9	key	key	ADJ
ejpam-6541	4	10	words	word	NOUN
ejpam-6541	4	11	and	and	CCONJ
ejpam-6541	4	12	phrases	phrase	NOUN
ejpam-6541	4	13	:	:	PUNCT
ejpam-6541	4	14	hesitant	hesitant	ADJ
ejpam-6541	4	15	fuzzy	fuzzy	ADJ
ejpam-6541	4	16	,	,	PUNCT
ejpam-6541	4	17	intuitionistic	intuitionistic	ADJ
ejpam-6541	4	18	hesitant	hesitant	ADJ
ejpam-6541	4	19	fuzzy	fuzzy	ADJ
ejpam-6541	4	20	,	,	PUNCT
ejpam-6541	4	21	normed	normed	ADJ
ejpam-6541	4	22	linear	linear	ADJ
ejpam-6541	4	23	space	space	NOUN
ejpam-6541	4	24	1	1	NUM
ejpam-6541	4	25	.	.	PUNCT
ejpam-6541	4	26	introduction	introduction	NOUN
ejpam-6541	4	27	in	in	ADP
ejpam-6541	4	28	1965	1965	NUM
ejpam-6541	4	29	,	,	PUNCT
ejpam-6541	4	30	zadeh	zadeh	PROPN
ejpam-6541	5	1	[	[	X
ejpam-6541	5	2	1	1	NUM
ejpam-6541	5	3	]	]	PUNCT
ejpam-6541	5	4	invented	invent	VERB
ejpam-6541	5	5	fuzzy	fuzzy	ADJ
ejpam-6541	5	6	set	set	NOUN
ejpam-6541	5	7	theory	theory	NOUN
ejpam-6541	5	8	.	.	PUNCT
ejpam-6541	6	1	the	the	DET
ejpam-6541	6	2	search	search	NOUN
ejpam-6541	6	3	for	for	ADP
ejpam-6541	6	4	fuzzy	fuzzy	ADJ
ejpam-6541	6	5	equivalents	equivalent	NOUN
ejpam-6541	6	6	of	of	ADP
ejpam-6541	6	7	classical	classical	ADJ
ejpam-6541	6	8	theories	theory	NOUN
ejpam-6541	6	9	has	have	AUX
ejpam-6541	6	10	been	be	AUX
ejpam-6541	6	11	intense	intense	ADJ
ejpam-6541	6	12	since	since	SCONJ
ejpam-6541	6	13	zadeh	zadeh	PROPN
ejpam-6541	6	14	’s	’s	PART
ejpam-6541	6	15	groundbreaking	groundbreake	VERB
ejpam-6541	6	16	work	work	NOUN
ejpam-6541	6	17	.	.	PUNCT
ejpam-6541	7	1	additionally	additionally	ADV
ejpam-6541	7	2	,	,	PUNCT
ejpam-6541	7	3	other	other	ADJ
ejpam-6541	7	4	areas	area	NOUN
ejpam-6541	7	5	,	,	PUNCT
ejpam-6541	7	6	fuzzy	fuzzy	ADJ
ejpam-6541	7	7	metric	metric	ADJ
ejpam-6541	7	8	spaces	space	NOUN
ejpam-6541	7	9	along	along	ADP
ejpam-6541	7	10	with	with	ADP
ejpam-6541	7	11	fuzzy	fuzzy	ADJ
ejpam-6541	7	12	normed	norme	VERB
ejpam-6541	7	13	linear	linear	PROPN
ejpam-6541	7	14	spaces	space	NOUN
ejpam-6541	7	15	have	have	AUX
ejpam-6541	7	16	seen	see	VERB
ejpam-6541	7	17	advancements	advancement	NOUN
ejpam-6541	7	18	,	,	PUNCT
ejpam-6541	7	19	in	in	ADP
ejpam-6541	7	20	[	[	X
ejpam-6541	7	21	[	[	X
ejpam-6541	7	22	2],[3	2],[3	NUM
ejpam-6541	7	23	]	]	X
ejpam-6541	7	24	]	]	X
ejpam-6541	7	25	two	two	NUM
ejpam-6541	7	26	kinds	kind	NOUN
ejpam-6541	7	27	of	of	ADP
ejpam-6541	7	28	fuzzy	fuzzy	ADJ
ejpam-6541	7	29	bounded	bound	VERB
ejpam-6541	7	30	linear	linear	PROPN
ejpam-6541	7	31	operators	operator	NOUN
ejpam-6541	7	32	—	—	PUNCT
ejpam-6541	7	33	strong	strong	ADJ
ejpam-6541	7	34	and	and	CCONJ
ejpam-6541	7	35	weak	weak	ADJ
ejpam-6541	7	36	—	—	PUNCT
ejpam-6541	7	37	are	be	AUX
ejpam-6541	7	38	developed	develop	VERB
ejpam-6541	7	39	in	in	ADP
ejpam-6541	7	40	this	this	DET
ejpam-6541	7	41	study	study	NOUN
ejpam-6541	7	42	,	,	PUNCT
ejpam-6541	7	43	along	along	ADP
ejpam-6541	7	44	with	with	ADP
ejpam-6541	7	45	the	the	DET
ejpam-6541	7	46	concept	concept	NOUN
ejpam-6541	7	47	regarding	regard	VERB
ejpam-6541	7	48	boundedness	boundedness	NOUN
ejpam-6541	7	49	of	of	ADP
ejpam-6541	7	50	a	a	DET
ejpam-6541	7	51	linear	linear	ADJ
ejpam-6541	7	52	operator	operator	NOUN
ejpam-6541	7	53	out	out	ADP
ejpam-6541	7	54	of	of	ADP
ejpam-6541	7	55	one	one	NUM
ejpam-6541	7	56	fuzzy	fuzzy	ADV
ejpam-6541	7	57	normed	norme	VERB
ejpam-6541	7	58	linear	linear	ADJ
ejpam-6541	7	59	space	space	NOUN
ejpam-6541	7	60	to	to	ADP
ejpam-6541	7	61	another	another	DET
ejpam-6541	7	62	fuzzy	fuzzy	ADJ
ejpam-6541	7	63	normed	norme	VERB
ejpam-6541	7	64	linear	linear	ADJ
ejpam-6541	7	65	space	space	NOUN
ejpam-6541	7	66	.	.	PUNCT
ejpam-6541	8	1	a	a	DET
ejpam-6541	8	2	relationship	relationship	NOUN
ejpam-6541	8	3	between	between	ADP
ejpam-6541	8	4	fuzzy	fuzzy	ADJ
ejpam-6541	8	5	boundedness	boundedness	NOUN
ejpam-6541	8	6	and	and	CCONJ
ejpam-6541	8	7	fuzzy	fuzzy	ADJ
ejpam-6541	8	8	continuity	continuity	NOUN
ejpam-6541	8	9	is	be	AUX
ejpam-6541	8	10	examined	examine	VERB
ejpam-6541	8	11	.	.	PUNCT
ejpam-6541	9	1	the	the	DET
ejpam-6541	9	2	concepts	concept	NOUN
ejpam-6541	9	3	of	of	ADP
ejpam-6541	9	4	fuzzy	fuzzy	ADJ
ejpam-6541	9	5	dual	dual	ADJ
ejpam-6541	9	6	spaces	space	NOUN
ejpam-6541	9	7	and	and	CCONJ
ejpam-6541	9	8	fuzzy	fuzzy	ADJ
ejpam-6541	9	9	bounded	bound	VERB
ejpam-6541	9	10	linear	linear	ADJ
ejpam-6541	9	11	functionals	functional	NOUN
ejpam-6541	9	12	are	be	AUX
ejpam-6541	9	13	defined	define	VERB
ejpam-6541	9	14	,	,	PUNCT
ejpam-6541	9	15	establish	establish	VERB
ejpam-6541	9	16	uniform	uniform	ADJ
ejpam-6541	9	17	boundedness	boundedness	PROPN
ejpam-6541	9	18	principle	principle	NOUN
ejpam-6541	9	19	,	,	PUNCT
ejpam-6541	9	20	closed	closed	ADJ
ejpam-6541	9	21	graph	graph	NOUN
ejpam-6541	9	22	,	,	PUNCT
ejpam-6541	9	23	open	open	ADJ
ejpam-6541	9	24	mapping	mapping	NOUN
ejpam-6541	9	25	and	and	CCONJ
ejpam-6541	9	26	the	the	DET
ejpam-6541	9	27	hahn	hahn	NOUN
ejpam-6541	9	28	-	-	PUNCT
ejpam-6541	9	29	banach	banach	NOUN
ejpam-6541	9	30	theorem	theorem	VERB
ejpam-6541	9	31	,	,	PUNCT
ejpam-6541	9	32	in	in	ADP
ejpam-6541	9	33	[	[	X
ejpam-6541	9	34	4	4	X
ejpam-6541	9	35	]	]	X
ejpam-6541	9	36	a	a	DET
ejpam-6541	9	37	fuzzy	fuzzy	ADJ
ejpam-6541	9	38	normed	norme	VERB
ejpam-6541	9	39	linear	linear	ADJ
ejpam-6541	9	40	space	space	NOUN
ejpam-6541	9	41	,	,	PUNCT
ejpam-6541	9	42	the	the	DET
ejpam-6541	9	43	terms	term	NOUN
ejpam-6541	9	44	”	"	PUNCT
ejpam-6541	9	45	strongly	strongly	ADV
ejpam-6541	9	46	and	and	CCONJ
ejpam-6541	9	47	weakly	weakly	ADJ
ejpam-6541	9	48	fuzzy	fuzzy	ADJ
ejpam-6541	9	49	convergent	convergent	NOUN
ejpam-6541	9	50	sequence	sequence	NOUN
ejpam-6541	9	51	,	,	PUNCT
ejpam-6541	9	52	”	"	PUNCT
ejpam-6541	9	53	are	be	AUX
ejpam-6541	9	54	defined	define	VERB
ejpam-6541	9	55	over	over	ADP
ejpam-6541	9	56	this	this	DET
ejpam-6541	9	57	study	study	NOUN
ejpam-6541	9	58	.	.	PUNCT
ejpam-6541	10	1	fixed	fix	VERB
ejpam-6541	10	2	point	point	NOUN
ejpam-6541	10	3	theorems	theorem	NOUN
ejpam-6541	10	4	for	for	ADP
ejpam-6541	10	5	fuzzy	fuzzy	ADJ
ejpam-6541	10	6	non	non	ADJ
ejpam-6541	10	7	-	-	ADJ
ejpam-6541	10	8	expansive	expansive	ADJ
ejpam-6541	10	9	mappings	mapping	NOUN
ejpam-6541	10	10	are	be	AUX
ejpam-6541	10	11	established	establish	VERB
ejpam-6541	10	12	,	,	PUNCT
ejpam-6541	10	13	along	along	ADP
ejpam-6541	10	14	with	with	ADP
ejpam-6541	10	15	the	the	DET
ejpam-6541	10	16	notions	notion	NOUN
ejpam-6541	10	17	of	of	ADP
ejpam-6541	10	18	uniformly	uniformly	ADV
ejpam-6541	10	19	convex	convex	NOUN
ejpam-6541	10	20	fuzzy	fuzzy	ADJ
ejpam-6541	10	21	normed	norme	VERB
ejpam-6541	10	22	linear	linear	ADJ
ejpam-6541	10	23	space	space	NOUN
ejpam-6541	10	24	,	,	PUNCT
ejpam-6541	10	25	fuzzy	fuzzy	ADJ
ejpam-6541	10	26	normal	normal	ADJ
ejpam-6541	10	27	structure	structure	NOUN
ejpam-6541	10	28	,	,	PUNCT
ejpam-6541	10	29	∗corresponding	∗corresponde	VERB
ejpam-6541	10	30	author	author	NOUN
ejpam-6541	10	31	.	.	PUNCT
ejpam-6541	11	1	doi	doi	NOUN
ejpam-6541	11	2	:	:	PUNCT
ejpam-6541	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6541	https://doi.org/10.29020/nybg.ejpam.v18i4.6541	NUM
ejpam-6541	11	4	email	email	NOUN
ejpam-6541	11	5	addresses	address	NOUN
ejpam-6541	11	6	:	:	PUNCT
ejpam-6541	11	7	kavithamths@gmail.com	kavithamths@gmail.com	X
ejpam-6541	11	8	(	(	PUNCT
ejpam-6541	11	9	k.	k.	PROPN
ejpam-6541	11	10	kavitha	kavitha	PROPN
ejpam-6541	11	11	)	)	PUNCT
ejpam-6541	11	12	,	,	PUNCT
ejpam-6541	11	13	pmkrishna@rocketmail.com	pmkrishna@rocketmail.com	X
ejpam-6541	12	1	(	(	PUNCT
ejpam-6541	12	2	p.	p.	NOUN
ejpam-6541	12	3	muralikrishna	muralikrishna	PROPN
ejpam-6541	12	4	)	)	PUNCT
ejpam-6541	12	5	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6541	13	1	1	1	NUM
ejpam-6541	13	2	copyright	copyright	NOUN
ejpam-6541	13	3	:	:	PUNCT
ejpam-6541	13	4	©	©	PROPN
ejpam-6541	13	5	2025	2025	NUM
ejpam-6541	13	6	the	the	DET
ejpam-6541	13	7	author(s	author(s	NOUN
ejpam-6541	13	8	)	)	PUNCT
ejpam-6541	13	9	.	.	PUNCT
ejpam-6541	14	1	(	(	PUNCT
ejpam-6541	14	2	cc	cc	NOUN
ejpam-6541	14	3	by	by	ADP
ejpam-6541	14	4	-	-	PUNCT
ejpam-6541	14	5	nc	nc	PROPN
ejpam-6541	14	6	4.0	4.0	NUM
ejpam-6541	14	7	)	)	PUNCT
ejpam-6541	14	8	k.	k.	PROPN
ejpam-6541	14	9	kavitha	kavitha	PROPN
ejpam-6541	14	10	,	,	PUNCT
ejpam-6541	14	11	p.	p.	PROPN
ejpam-6541	14	12	muralikrishna	muralikrishna	PROPN
ejpam-6541	14	13	/	/	SYM
ejpam-6541	14	14	eur	eur	PROPN
ejpam-6541	14	15	.	.	PUNCT
ejpam-6541	15	1	j.	j.	PROPN
ejpam-6541	15	2	pure	pure	PROPN
ejpam-6541	15	3	appl	appl	PROPN
ejpam-6541	15	4	.	.	PROPN
ejpam-6541	15	5	math	math	PROPN
ejpam-6541	15	6	,	,	PUNCT
ejpam-6541	15	7	18	18	NUM
ejpam-6541	15	8	(	(	PUNCT
ejpam-6541	15	9	4	4	NUM
ejpam-6541	15	10	)	)	PUNCT
ejpam-6541	15	11	(	(	PUNCT
ejpam-6541	15	12	2025	2025	NUM
ejpam-6541	15	13	)	)	PUNCT
ejpam-6541	15	14	,	,	PUNCT
ejpam-6541	15	15	6541	6541	NUM
ejpam-6541	15	16	2	2	NUM
ejpam-6541	15	17	of	of	ADP
ejpam-6541	15	18	14	14	NUM
ejpam-6541	15	19	and	and	CCONJ
ejpam-6541	15	20	fuzzy	fuzzy	ADJ
ejpam-6541	15	21	non	non	ADJ
ejpam-6541	15	22	-	-	ADJ
ejpam-6541	15	23	expansive	expansive	ADJ
ejpam-6541	15	24	mapping	mapping	NOUN
ejpam-6541	15	25	.	.	PUNCT
ejpam-6541	16	1	in	in	ADP
ejpam-6541	16	2	[	[	X
ejpam-6541	16	3	5	5	NUM
ejpam-6541	16	4	]	]	PUNCT
ejpam-6541	16	5	an	an	DET
ejpam-6541	16	6	introduction	introduction	NOUN
ejpam-6541	16	7	to	to	ADP
ejpam-6541	16	8	fuzzy	fuzzy	ADJ
ejpam-6541	16	9	normed	norme	VERB
ejpam-6541	16	10	linear	linear	ADJ
ejpam-6541	16	11	space	space	NOUN
ejpam-6541	16	12	is	be	AUX
ejpam-6541	16	13	given	give	VERB
ejpam-6541	16	14	.	.	PUNCT
ejpam-6541	17	1	it	it	PRON
ejpam-6541	17	2	has	have	AUX
ejpam-6541	17	3	been	be	AUX
ejpam-6541	17	4	demonstrated	demonstrate	VERB
ejpam-6541	17	5	that	that	SCONJ
ejpam-6541	17	6	fuzzy	fuzzy	ADJ
ejpam-6541	17	7	norms	norm	NOUN
ejpam-6541	17	8	are	be	AUX
ejpam-6541	17	9	equivalent	equivalent	ADJ
ejpam-6541	17	10	up	up	ADP
ejpam-6541	17	11	to	to	ADP
ejpam-6541	17	12	fuzzy	fuzzy	ADJ
ejpam-6541	17	13	equivalency	equivalency	NOUN
ejpam-6541	17	14	in	in	ADP
ejpam-6541	17	15	a	a	DET
ejpam-6541	17	16	finite	finite	ADJ
ejpam-6541	17	17	dimensional	dimensional	ADJ
ejpam-6541	17	18	fuzzy	fuzzy	ADJ
ejpam-6541	17	19	normed	norme	VERB
ejpam-6541	17	20	linear	linear	ADJ
ejpam-6541	17	21	space	space	NOUN
ejpam-6541	17	22	.	.	PUNCT
ejpam-6541	18	1	it	it	PRON
ejpam-6541	18	2	is	be	AUX
ejpam-6541	18	3	demonstrated	demonstrate	VERB
ejpam-6541	18	4	that	that	SCONJ
ejpam-6541	18	5	fuzzy	fuzzy	ADJ
ejpam-6541	18	6	subspaces	subspace	NOUN
ejpam-6541	18	7	of	of	ADP
ejpam-6541	18	8	a	a	DET
ejpam-6541	18	9	fuzzy	fuzzy	ADJ
ejpam-6541	18	10	normed	norme	VERB
ejpam-6541	18	11	linear	linear	ADJ
ejpam-6541	18	12	space	space	NOUN
ejpam-6541	18	13	among	among	ADP
ejpam-6541	18	14	finite	finite	ADJ
ejpam-6541	18	15	dimensions	dimension	NOUN
ejpam-6541	18	16	must	must	AUX
ejpam-6541	18	17	be	be	AUX
ejpam-6541	18	18	full	full	ADJ
ejpam-6541	18	19	fuzzy	fuzzy	ADJ
ejpam-6541	18	20	normed	normed	ADJ
ejpam-6541	18	21	linear	linear	PROPN
ejpam-6541	18	22	spaces	space	NOUN
ejpam-6541	18	23	,	,	PUNCT
ejpam-6541	18	24	[	[	X
ejpam-6541	18	25	6	6	NUM
ejpam-6541	18	26	]	]	PUNCT
ejpam-6541	18	27	present	present	VERB
ejpam-6541	18	28	the	the	DET
ejpam-6541	18	29	idea	idea	NOUN
ejpam-6541	18	30	of	of	ADP
ejpam-6541	18	31	a	a	DET
ejpam-6541	18	32	fuzzy	fuzzy	ADJ
ejpam-6541	18	33	metric	metric	ADJ
ejpam-6541	18	34	space	space	NOUN
ejpam-6541	18	35	in	in	ADP
ejpam-6541	18	36	this	this	DET
ejpam-6541	18	37	study	study	NOUN
ejpam-6541	18	38	.	.	PUNCT
ejpam-6541	19	1	in	in	ADP
ejpam-6541	19	2	a	a	DET
ejpam-6541	19	3	fuzzy	fuzzy	ADJ
ejpam-6541	19	4	metric	metric	ADJ
ejpam-6541	19	5	space	space	NOUN
ejpam-6541	19	6	,	,	PUNCT
ejpam-6541	19	7	the	the	DET
ejpam-6541	19	8	separation	separation	NOUN
ejpam-6541	19	9	among	among	ADP
ejpam-6541	19	10	two	two	NUM
ejpam-6541	19	11	points	point	NOUN
ejpam-6541	19	12	,	,	PUNCT
ejpam-6541	19	13	is	be	AUX
ejpam-6541	19	14	a	a	DET
ejpam-6541	19	15	normal	normal	ADJ
ejpam-6541	19	16	,	,	PUNCT
ejpam-6541	19	17	convex	convex	PROPN
ejpam-6541	19	18	,	,	PUNCT
ejpam-6541	19	19	upper	upper	ADJ
ejpam-6541	19	20	semicontinuous	semicontinuous	NOUN
ejpam-6541	19	21	,	,	PUNCT
ejpam-6541	19	22	non	non	ADJ
ejpam-6541	19	23	-	-	ADJ
ejpam-6541	19	24	negative	negative	ADJ
ejpam-6541	19	25	fuzzy	fuzzy	ADJ
ejpam-6541	19	26	number	number	NOUN
ejpam-6541	19	27	.	.	PUNCT
ejpam-6541	20	1	a	a	DET
ejpam-6541	20	2	few	few	ADJ
ejpam-6541	20	3	fixed	fix	VERB
ejpam-6541	20	4	point	point	NOUN
ejpam-6541	20	5	theorems	theorem	NOUN
ejpam-6541	20	6	are	be	AUX
ejpam-6541	20	7	proved	prove	VERB
ejpam-6541	20	8	and	and	CCONJ
ejpam-6541	20	9	the	the	DET
ejpam-6541	20	10	properties	property	NOUN
ejpam-6541	20	11	of	of	ADP
ejpam-6541	20	12	fuzzy	fuzzy	ADJ
ejpam-6541	20	13	metric	metric	ADJ
ejpam-6541	20	14	spaces	space	NOUN
ejpam-6541	20	15	are	be	AUX
ejpam-6541	20	16	examined	examine	VERB
ejpam-6541	20	17	.	.	PUNCT
ejpam-6541	21	1	in	in	ADP
ejpam-6541	21	2	[	[	X
ejpam-6541	21	3	7	7	X
ejpam-6541	21	4	]	]	PUNCT
ejpam-6541	21	5	a	a	DET
ejpam-6541	21	6	few	few	ADJ
ejpam-6541	21	7	fuzzy	fuzzy	ADJ
ejpam-6541	21	8	topological	topological	ADJ
ejpam-6541	21	9	vector	vector	NOUN
ejpam-6541	21	10	space	space	NOUN
ejpam-6541	21	11	properties	property	NOUN
ejpam-6541	21	12	are	be	AUX
ejpam-6541	21	13	examined	examine	VERB
ejpam-6541	21	14	.	.	PUNCT
ejpam-6541	22	1	additionally	additionally	ADV
ejpam-6541	22	2	,	,	PUNCT
ejpam-6541	22	3	for	for	ADP
ejpam-6541	22	4	a	a	DET
ejpam-6541	22	5	fuzzy	fuzzy	ADJ
ejpam-6541	22	6	linear	linear	NOUN
ejpam-6541	22	7	topology	topology	NOUN
ejpam-6541	22	8	,	,	PUNCT
ejpam-6541	22	9	necessary	necessary	ADJ
ejpam-6541	22	10	and	and	CCONJ
ejpam-6541	22	11	sufficient	sufficient	ADJ
ejpam-6541	22	12	criteria	criterion	NOUN
ejpam-6541	22	13	are	be	AUX
ejpam-6541	22	14	shown	show	VERB
ejpam-6541	22	15	for	for	SCONJ
ejpam-6541	22	16	a	a	DET
ejpam-6541	22	17	family	family	NOUN
ejpam-6541	22	18	of	of	ADP
ejpam-6541	22	19	fuzzy	fuzzy	ADJ
ejpam-6541	22	20	sets	set	NOUN
ejpam-6541	22	21	in	in	ADP
ejpam-6541	22	22	vector	vector	NOUN
ejpam-6541	22	23	space	space	NOUN
ejpam-6541	22	24	e	e	NOUN
ejpam-6541	22	25	to	to	PART
ejpam-6541	22	26	be	be	AUX
ejpam-6541	22	27	the	the	DET
ejpam-6541	22	28	family	family	NOUN
ejpam-6541	22	29	of	of	ADP
ejpam-6541	22	30	all	all	DET
ejpam-6541	22	31	neighborhoods	neighborhood	NOUN
ejpam-6541	22	32	of	of	ADP
ejpam-6541	22	33	zero.as	zero.as	PRON
ejpam-6541	22	34	a	a	DET
ejpam-6541	22	35	generalized	generalize	VERB
ejpam-6541	22	36	fuzzy	fuzzy	ADJ
ejpam-6541	22	37	set	set	NOUN
ejpam-6541	22	38	,	,	PUNCT
ejpam-6541	22	39	atanassov	atanassov	VERB
ejpam-6541	22	40	[	[	X
ejpam-6541	22	41	8	8	NUM
ejpam-6541	22	42	]	]	PUNCT
ejpam-6541	22	43	developed	develop	VERB
ejpam-6541	22	44	the	the	DET
ejpam-6541	22	45	idea	idea	NOUN
ejpam-6541	22	46	of	of	ADP
ejpam-6541	22	47	intuitionistic	intuitionistic	ADJ
ejpam-6541	22	48	fuzzy	fuzzy	ADJ
ejpam-6541	22	49	sets	set	NOUN
ejpam-6541	22	50	.	.	PUNCT
ejpam-6541	23	1	originating	originate	VERB
ejpam-6541	23	2	the	the	DET
ejpam-6541	23	3	concept	concept	NOUN
ejpam-6541	23	4	of	of	ADP
ejpam-6541	23	5	intuitionistic	intuitionistic	ADJ
ejpam-6541	23	6	fuzzy	fuzzy	ADJ
ejpam-6541	23	7	metric	metric	ADJ
ejpam-6541	23	8	space	space	NOUN
ejpam-6541	23	9	was	be	AUX
ejpam-6541	23	10	j.h	j.h	PROPN
ejpam-6541	23	11	.	.	PROPN
ejpam-6541	23	12	park	park	NOUN
ejpam-6541	24	1	[	[	X
ejpam-6541	24	2	9	9	NUM
ejpam-6541	24	3	]	]	PUNCT
ejpam-6541	24	4	and	and	CCONJ
ejpam-6541	24	5	researched	research	VERB
ejpam-6541	24	6	a	a	DET
ejpam-6541	24	7	few	few	ADJ
ejpam-6541	24	8	fundamental	fundamental	ADJ
ejpam-6541	24	9	characteristics	characteristic	NOUN
ejpam-6541	24	10	.	.	PUNCT
ejpam-6541	25	1	however	however	ADV
ejpam-6541	25	2	,	,	PUNCT
ejpam-6541	25	3	a	a	DET
ejpam-6541	25	4	significant	significant	ADJ
ejpam-6541	25	5	addition	addition	NOUN
ejpam-6541	25	6	to	to	ADP
ejpam-6541	25	7	intuitionistic	intuitionistic	ADJ
ejpam-6541	25	8	fuzzy	fuzzy	ADJ
ejpam-6541	25	9	topological	topological	ADJ
ejpam-6541	25	10	spaces	space	NOUN
ejpam-6541	25	11	is	be	AUX
ejpam-6541	25	12	made	make	VERB
ejpam-6541	25	13	by	by	ADP
ejpam-6541	25	14	saadati	saadati	ADJ
ejpam-6541	25	15	park	park	NOUN
ejpam-6541	26	1	[	[	X
ejpam-6541	26	2	9	9	NUM
ejpam-6541	26	3	]	]	PUNCT
ejpam-6541	26	4	.	.	PUNCT
ejpam-6541	27	1	they	they	PRON
ejpam-6541	27	2	have	have	AUX
ejpam-6541	27	3	also	also	ADV
ejpam-6541	27	4	examined	examine	VERB
ejpam-6541	27	5	certain	certain	ADJ
ejpam-6541	27	6	fundamental	fundamental	ADJ
ejpam-6541	27	7	characteristics	characteristic	NOUN
ejpam-6541	27	8	in	in	ADP
ejpam-6541	27	9	intuitionistic	intuitionistic	ADJ
ejpam-6541	27	10	fuzzy	fuzzy	ADJ
ejpam-6541	27	11	normed	norme	VERB
ejpam-6541	27	12	linear	linear	PROPN
ejpam-6541	27	13	spaces	space	NOUN
ejpam-6541	27	14	and	and	CCONJ
ejpam-6541	27	15	introduced	introduce	VERB
ejpam-6541	27	16	the	the	DET
ejpam-6541	27	17	idea	idea	NOUN
ejpam-6541	27	18	of	of	ADP
ejpam-6541	27	19	such	such	ADJ
ejpam-6541	27	20	spaces	space	NOUN
ejpam-6541	27	21	.	.	PUNCT
ejpam-6541	28	1	many	many	ADJ
ejpam-6541	28	2	studies	study	NOUN
ejpam-6541	28	3	have	have	AUX
ejpam-6541	28	4	been	be	AUX
ejpam-6541	28	5	conducted	conduct	VERB
ejpam-6541	28	6	on	on	ADP
ejpam-6541	28	7	intuitive	intuitive	ADJ
ejpam-6541	28	8	fuzzy	fuzzy	ADJ
ejpam-6541	28	9	sets	set	NOUN
ejpam-6541	28	10	,	,	PUNCT
ejpam-6541	28	11	including	include	VERB
ejpam-6541	28	12	those	those	PRON
ejpam-6541	28	13	by	by	ADP
ejpam-6541	28	14	t.k	t.k	PROPN
ejpam-6541	28	15	.	.	PROPN
ejpam-6541	28	16	mandal	mandal	PROPN
ejpam-6541	28	17	and	and	CCONJ
ejpam-6541	28	18	s.k	s.k	PROPN
ejpam-6541	28	19	.	.	PROPN
ejpam-6541	28	20	samanta	samanta	PROPN
ejpam-6541	28	21	[	[	X
ejpam-6541	28	22	10],[11].[12	10],[11].[12	NUM
ejpam-6541	28	23	]	]	X
ejpam-6541	28	24	n.	n.	NOUN
ejpam-6541	28	25	thillaigovindan	thillaigovindan	PROPN
ejpam-6541	28	26	et	et	PROPN
ejpam-6541	29	1	al	al	PROPN
ejpam-6541	29	2	.	.	PROPN
ejpam-6541	30	1	vijayabalaji	vijayabalaji	PROPN
ejpam-6541	30	2	et	et	PROPN
ejpam-6541	30	3	al	al	PROPN
ejpam-6541	30	4	.	.	PUNCT
ejpam-6541	31	1	[	[	X
ejpam-6541	31	2	13	13	NUM
ejpam-6541	31	3	]	]	PUNCT
ejpam-6541	31	4	recently	recently	ADV
ejpam-6541	31	5	obtained	obtain	VERB
ejpam-6541	31	6	some	some	DET
ejpam-6541	31	7	results	result	NOUN
ejpam-6541	31	8	and	and	CCONJ
ejpam-6541	31	9	presented	present	VERB
ejpam-6541	31	10	the	the	DET
ejpam-6541	31	11	idea	idea	NOUN
ejpam-6541	31	12	of	of	ADP
ejpam-6541	31	13	intuitionistic	intuitionistic	ADJ
ejpam-6541	31	14	fuzzy	fuzzy	ADJ
ejpam-6541	31	15	n	n	CCONJ
ejpam-6541	31	16	-	-	PUNCT
ejpam-6541	31	17	normed	norme	VERB
ejpam-6541	31	18	linear	linear	ADJ
ejpam-6541	31	19	space	space	NOUN
ejpam-6541	31	20	.	.	PUNCT
ejpam-6541	32	1	bag	bag	NOUN
ejpam-6541	32	2	et	et	PROPN
ejpam-6541	32	3	al	al	PROPN
ejpam-6541	32	4	.	.	PROPN
ejpam-6541	32	5	,	,	PUNCT
ejpam-6541	33	1	[	[	X
ejpam-6541	33	2	10	10	NUM
ejpam-6541	33	3	]	]	PUNCT
ejpam-6541	33	4	,	,	PUNCT
ejpam-6541	33	5	introduced	introduce	VERB
ejpam-6541	33	6	the	the	DET
ejpam-6541	33	7	concept	concept	NOUN
ejpam-6541	33	8	of	of	ADP
ejpam-6541	33	9	a	a	DET
ejpam-6541	33	10	fuzzy	fuzzy	ADJ
ejpam-6541	33	11	normed	norme	VERB
ejpam-6541	33	12	linear	linear	ADJ
ejpam-6541	33	13	space	space	NOUN
ejpam-6541	33	14	,	,	PUNCT
ejpam-6541	33	15	which	which	DET
ejpam-6541	33	16	t.k	t.k	PROPN
ejpam-6541	33	17	.	.	PROPN
ejpam-6541	33	18	samanta	samanta	PROPN
ejpam-6541	33	19	et	et	PROPN
ejpam-6541	33	20	al	al	PROPN
ejpam-6541	33	21	.	.	PUNCT
ejpam-6541	34	1	[	[	X
ejpam-6541	34	2	14	14	NUM
ejpam-6541	34	3	]	]	PUNCT
ejpam-6541	34	4	examined	examine	VERB
ejpam-6541	34	5	.	.	PUNCT
ejpam-6541	35	1	they	they	PRON
ejpam-6541	35	2	stated	state	VERB
ejpam-6541	35	3	an	an	DET
ejpam-6541	35	4	intuitionistic	intuitionistic	ADJ
ejpam-6541	35	5	fuzzy	fuzzy	ADJ
ejpam-6541	35	6	normed	norme	VERB
ejpam-6541	35	7	linear	linear	ADJ
ejpam-6541	35	8	space	space	NOUN
ejpam-6541	35	9	through	through	ADP
ejpam-6541	35	10	a	a	DET
ejpam-6541	35	11	general	general	ADJ
ejpam-6541	35	12	context	context	NOUN
ejpam-6541	35	13	(	(	PUNCT
ejpam-6541	35	14	using	use	VERB
ejpam-6541	35	15	the	the	DET
ejpam-6541	35	16	t	t	NOUN
ejpam-6541	35	17	-	-	PUNCT
ejpam-6541	35	18	norm	norm	NOUN
ejpam-6541	35	19	∗	∗	NOUN
ejpam-6541	35	20	along	along	ADV
ejpam-6541	35	21	with	with	ADP
ejpam-6541	35	22	the	the	DET
ejpam-6541	35	23	t	t	PROPN
ejpam-6541	35	24	-	-	PUNCT
ejpam-6541	35	25	co	co	NOUN
ejpam-6541	35	26	-	-	ADJ
ejpam-6541	35	27	norm	norm	ADJ
ejpam-6541	35	28	⋄	⋄	NOUN
ejpam-6541	35	29	correspondingly	correspondingly	ADV
ejpam-6541	35	30	)	)	PUNCT
ejpam-6541	35	31	.	.	PUNCT
ejpam-6541	36	1	in	in	ADP
ejpam-6541	36	2	finite	finite	ADJ
ejpam-6541	36	3	dimensional	dimensional	ADJ
ejpam-6541	36	4	intuitionistic	intuitionistic	ADJ
ejpam-6541	36	5	fuzzy	fuzzy	ADJ
ejpam-6541	36	6	normed	norme	VERB
ejpam-6541	36	7	linear	linear	ADJ
ejpam-6541	36	8	space	space	NOUN
ejpam-6541	36	9	,	,	PUNCT
ejpam-6541	36	10	they	they	PRON
ejpam-6541	36	11	mostly	mostly	ADV
ejpam-6541	36	12	examined	examine	VERB
ejpam-6541	36	13	various	various	ADJ
ejpam-6541	36	14	outcomes	outcome	NOUN
ejpam-6541	36	15	.	.	PUNCT
ejpam-6541	37	1	however	however	ADV
ejpam-6541	37	2	,	,	PUNCT
ejpam-6541	37	3	their	their	PRON
ejpam-6541	37	4	findings	finding	NOUN
ejpam-6541	37	5	rely	rely	VERB
ejpam-6541	37	6	on	on	ADP
ejpam-6541	37	7	the	the	DET
ejpam-6541	37	8	intuitionistic	intuitionistic	ADJ
ejpam-6541	37	9	fuzzy	fuzzy	ADJ
ejpam-6541	37	10	norm	norm	NOUN
ejpam-6541	37	11	’s	’s	PART
ejpam-6541	37	12	decomposition	decomposition	NOUN
ejpam-6541	37	13	theorem	theorem	NOUN
ejpam-6541	37	14	as	as	ADP
ejpam-6541	37	15	part	part	NOUN
ejpam-6541	37	16	of	of	ADP
ejpam-6541	37	17	a	a	DET
ejpam-6541	37	18	family	family	NOUN
ejpam-6541	37	19	of	of	ADP
ejpam-6541	37	20	crisp	crisp	ADJ
ejpam-6541	37	21	norm	norm	NOUN
ejpam-6541	37	22	pairings	pairing	NOUN
ejpam-6541	37	23	,	,	PUNCT
ejpam-6541	37	24	because	because	SCONJ
ejpam-6541	37	25	they	they	PRON
ejpam-6541	37	26	have	have	AUX
ejpam-6541	37	27	added	add	VERB
ejpam-6541	37	28	requirements	requirement	NOUN
ejpam-6541	37	29	on	on	ADP
ejpam-6541	37	30	the	the	DET
ejpam-6541	37	31	t	t	NOUN
ejpam-6541	37	32	-	-	PUNCT
ejpam-6541	37	33	norm	norm	NOUN
ejpam-6541	37	34	and	and	CCONJ
ejpam-6541	37	35	t	t	NOUN
ejpam-6541	37	36	-	-	PUNCT
ejpam-6541	37	37	conorm	conorm	NOUN
ejpam-6541	37	38	as	as	ADP
ejpam-6541	37	39	a1	a1	NOUN
ejpam-6541	37	40	∗	∗	NOUN
ejpam-6541	37	41	a1	a1	NOUN
ejpam-6541	37	42	=	=	NOUN
ejpam-6541	37	43	a1	a1	NOUN
ejpam-6541	37	44	and	and	CCONJ
ejpam-6541	37	45	a1	a1	NOUN
ejpam-6541	37	46	⋄	⋄	NOUN
ejpam-6541	37	47	a1	a1	NOUN
ejpam-6541	37	48	=	=	PUNCT
ejpam-6541	37	49	a1	a1	NOUN
ejpam-6541	37	50	,	,	PUNCT
ejpam-6541	37	51	∀a1	∀a1	VERB
ejpam-6541	37	52	∈	∈	PROPN
ejpam-6541	37	53	0	0	NUM
ejpam-6541	37	54	,	,	PUNCT
ejpam-6541	37	55	1	1	NUM
ejpam-6541	37	56	,	,	PUNCT
ejpam-6541	37	57	leading	lead	VERB
ejpam-6541	37	58	to	to	ADP
ejpam-6541	37	59	∗	∗	NOUN
ejpam-6541	37	60	=	=	SYM
ejpam-6541	37	61	min	min	NOUN
ejpam-6541	37	62	and	and	CCONJ
ejpam-6541	37	63	⋄	⋄	PROPN
ejpam-6541	37	64	=	=	SYM
ejpam-6541	37	65	max	max	PROPN
ejpam-6541	37	66	.	.	PUNCT
ejpam-6541	38	1	the	the	DET
ejpam-6541	38	2	abstraction	abstraction	NOUN
ejpam-6541	38	3	of	of	ADP
ejpam-6541	38	4	the	the	DET
ejpam-6541	38	5	t	t	NOUN
ejpam-6541	38	6	-	-	PUNCT
ejpam-6541	38	7	norm	norm	NOUN
ejpam-6541	38	8	and	and	CCONJ
ejpam-6541	38	9	t	t	PROPN
ejpam-6541	38	10	-	-	PUNCT
ejpam-6541	38	11	conorm	conorm	NOUN
ejpam-6541	38	12	is	be	AUX
ejpam-6541	38	13	thus	thus	ADV
ejpam-6541	38	14	practically	practically	ADV
ejpam-6541	38	15	lost	lose	VERB
ejpam-6541	38	16	.	.	PUNCT
ejpam-6541	39	1	however	however	ADV
ejpam-6541	39	2	,	,	PUNCT
ejpam-6541	39	3	certain	certain	ADJ
ejpam-6541	39	4	of	of	ADP
ejpam-6541	39	5	the	the	DET
ejpam-6541	39	6	requirements	requirement	NOUN
ejpam-6541	39	7	involving	involve	VERB
ejpam-6541	39	8	the	the	DET
ejpam-6541	39	9	functions	function	NOUN
ejpam-6541	39	10	n(x1	n(x1	NOUN
ejpam-6541	39	11	,	,	PUNCT
ejpam-6541	39	12	t1	t1	NOUN
ejpam-6541	39	13	)	)	PUNCT
ejpam-6541	39	14	and	and	CCONJ
ejpam-6541	39	15	m(x1	m(x1	PROPN
ejpam-6541	39	16	,	,	PUNCT
ejpam-6541	39	17	t1	t1	NOUN
ejpam-6541	39	18	)	)	PUNCT
ejpam-6541	39	19	in	in	ADP
ejpam-6541	39	20	the	the	DET
ejpam-6541	39	21	definition	definition	NOUN
ejpam-6541	39	22	taken	take	VERB
ejpam-6541	39	23	into	into	ADP
ejpam-6541	39	24	consideration	consideration	NOUN
ejpam-6541	39	25	,	,	PUNCT
ejpam-6541	39	26	the	the	DET
ejpam-6541	39	27	relation	relation	NOUN
ejpam-6541	39	28	n(x1	n(x1	NOUN
ejpam-6541	39	29	,	,	PUNCT
ejpam-6541	39	30	t1	t1	PROPN
ejpam-6541	39	31	)	)	PUNCT
ejpam-6541	40	1	+	+	X
ejpam-6541	40	2	m(x1	m(x1	X
ejpam-6541	40	3	,	,	PUNCT
ejpam-6541	40	4	t1	t1	NOUN
ejpam-6541	40	5	)	)	PUNCT
ejpam-6541	40	6	≤	≤	NUM
ejpam-6541	41	1	1	1	NUM
ejpam-6541	41	2	.	.	PUNCT
ejpam-6541	42	1	the	the	DET
ejpam-6541	42	2	following	following	NOUN
ejpam-6541	42	3	describes	describe	VERB
ejpam-6541	42	4	how	how	SCONJ
ejpam-6541	42	5	the	the	DET
ejpam-6541	42	6	paper	paper	NOUN
ejpam-6541	42	7	is	be	AUX
ejpam-6541	42	8	structured	structure	VERB
ejpam-6541	42	9	:	:	PUNCT
ejpam-6541	42	10	section	section	NOUN
ejpam-6541	42	11	2	2	NUM
ejpam-6541	42	12	describes	describe	VERB
ejpam-6541	42	13	,	,	PUNCT
ejpam-6541	42	14	some	some	PRON
ejpam-6541	42	15	preliminary	preliminary	ADJ
ejpam-6541	42	16	the	the	DET
ejpam-6541	42	17	outcomes	outcome	NOUN
ejpam-6541	42	18	were	be	AUX
ejpam-6541	42	19	presented	present	VERB
ejpam-6541	42	20	,	,	PUNCT
ejpam-6541	42	21	notion	notion	NOUN
ejpam-6541	42	22	of	of	ADP
ejpam-6541	42	23	hesitant	hesitant	ADJ
ejpam-6541	42	24	fuzzy	fuzzy	ADJ
ejpam-6541	42	25	and	and	CCONJ
ejpam-6541	42	26	intuitionistic	intuitionistic	ADJ
ejpam-6541	42	27	hesitant	hesitant	ADJ
ejpam-6541	42	28	fuzzy	fuzzy	ADJ
ejpam-6541	42	29	normed	normed	ADJ
ejpam-6541	42	30	linear	linear	PROPN
ejpam-6541	42	31	spaces	space	NOUN
ejpam-6541	42	32	.	.	PUNCT
ejpam-6541	43	1	section	section	NOUN
ejpam-6541	43	2	3	3	NUM
ejpam-6541	43	3	and	and	CCONJ
ejpam-6541	43	4	section	section	NOUN
ejpam-6541	43	5	4	4	NUM
ejpam-6541	43	6	demonstrates	demonstrate	VERB
ejpam-6541	43	7	some	some	DET
ejpam-6541	43	8	fundamental	fundamental	ADJ
ejpam-6541	43	9	findings	finding	NOUN
ejpam-6541	43	10	about	about	ADP
ejpam-6541	43	11	completeness	completeness	NOUN
ejpam-6541	43	12	and	and	CCONJ
ejpam-6541	43	13	compactness	compactness	NOUN
ejpam-6541	43	14	are	be	AUX
ejpam-6541	43	15	demonstrated	demonstrate	VERB
ejpam-6541	43	16	in	in	ADP
ejpam-6541	43	17	finite	finite	ADJ
ejpam-6541	43	18	dimension	dimension	NOUN
ejpam-6541	43	19	hesitant	hesitant	ADJ
ejpam-6541	43	20	fuzzy	fuzzy	ADJ
ejpam-6541	43	21	normed	norme	VERB
ejpam-6541	43	22	linear	linear	ADJ
ejpam-6541	43	23	space	space	NOUN
ejpam-6541	43	24	along	along	ADP
ejpam-6541	43	25	with	with	ADP
ejpam-6541	43	26	intuitionistic	intuitionistic	ADJ
ejpam-6541	43	27	hesitant	hesitant	ADJ
ejpam-6541	43	28	fuzzy	fuzzy	ADJ
ejpam-6541	43	29	normed	norme	VERB
ejpam-6541	43	30	linear	linear	ADJ
ejpam-6541	43	31	space	space	NOUN
ejpam-6541	43	32	.	.	PUNCT
ejpam-6541	44	1	2	2	X
ejpam-6541	44	2	.	.	X
ejpam-6541	44	3	preliminaries	preliminary	NOUN
ejpam-6541	44	4	this	this	DET
ejpam-6541	44	5	section	section	NOUN
ejpam-6541	44	6	provides	provide	VERB
ejpam-6541	44	7	pre	pre	ADJ
ejpam-6541	44	8	-	-	ADJ
ejpam-6541	44	9	existing	existing	ADJ
ejpam-6541	44	10	definitions	definition	NOUN
ejpam-6541	44	11	of	of	ADP
ejpam-6541	44	12	fuzzy	fuzzy	ADJ
ejpam-6541	44	13	sets	set	NOUN
ejpam-6541	44	14	,	,	PUNCT
ejpam-6541	44	15	including	include	VERB
ejpam-6541	44	16	some	some	DET
ejpam-6541	44	17	fundamental	fundamental	ADJ
ejpam-6541	44	18	notions	notion	NOUN
ejpam-6541	44	19	.	.	PUNCT
ejpam-6541	45	1	definition	definition	NOUN
ejpam-6541	45	2	1	1	NUM
ejpam-6541	45	3	.	.	PUNCT
ejpam-6541	46	1	[	[	X
ejpam-6541	46	2	15	15	NUM
ejpam-6541	46	3	]	]	X
ejpam-6541	46	4	∗	∗	NOUN
ejpam-6541	46	5	:	:	PUNCT
ejpam-6541	47	1	[	[	X
ejpam-6541	47	2	0	0	NUM
ejpam-6541	47	3	,	,	PUNCT
ejpam-6541	47	4	1	1	NUM
ejpam-6541	47	5	]	]	SYM
ejpam-6541	47	6	×	×	NOUN
ejpam-6541	47	7	[	[	X
ejpam-6541	47	8	0	0	NUM
ejpam-6541	47	9	,	,	PUNCT
ejpam-6541	47	10	1	1	NUM
ejpam-6541	47	11	]	]	PUNCT
ejpam-6541	47	12	→	→	PUNCT
ejpam-6541	47	13	[	[	X
ejpam-6541	47	14	0	0	NUM
ejpam-6541	47	15	,	,	PUNCT
ejpam-6541	47	16	1	1	NUM
ejpam-6541	47	17	]	]	PUNCT
ejpam-6541	47	18	in	in	ADP
ejpam-6541	47	19	binary	binary	ADJ
ejpam-6541	47	20	exists	exist	VERB
ejpam-6541	47	21	t−norm	t−norm	ADP
ejpam-6541	47	22	in	in	ADP
ejpam-6541	47	23	case	case	NOUN
ejpam-6541	47	24	it	it	PRON
ejpam-6541	47	25	meets	meet	VERB
ejpam-6541	47	26	these	these	DET
ejpam-6541	47	27	requirements	requirement	NOUN
ejpam-6541	47	28	listed	list	VERB
ejpam-6541	47	29	below	below	ADP
ejpam-6541	47	30	:	:	PUNCT
ejpam-6541	48	1	k.	k.	PROPN
ejpam-6541	48	2	kavitha	kavitha	PROPN
ejpam-6541	48	3	,	,	PUNCT
ejpam-6541	48	4	p.	p.	PROPN
ejpam-6541	48	5	muralikrishna	muralikrishna	PROPN
ejpam-6541	48	6	/	/	SYM
ejpam-6541	48	7	eur	eur	PROPN
ejpam-6541	48	8	.	.	PUNCT
ejpam-6541	49	1	j.	j.	PROPN
ejpam-6541	49	2	pure	pure	PROPN
ejpam-6541	49	3	appl	appl	PROPN
ejpam-6541	49	4	.	.	PROPN
ejpam-6541	49	5	math	math	PROPN
ejpam-6541	49	6	,	,	PUNCT
ejpam-6541	49	7	18	18	NUM
ejpam-6541	49	8	(	(	PUNCT
ejpam-6541	49	9	4	4	NUM
ejpam-6541	49	10	)	)	PUNCT
ejpam-6541	49	11	(	(	PUNCT
ejpam-6541	49	12	2025	2025	NUM
ejpam-6541	49	13	)	)	PUNCT
ejpam-6541	49	14	,	,	PUNCT
ejpam-6541	49	15	6541	6541	NUM
ejpam-6541	49	16	3	3	NUM
ejpam-6541	49	17	of	of	ADP
ejpam-6541	49	18	14	14	NUM
ejpam-6541	50	1	[	[	X
ejpam-6541	50	2	a	a	X
ejpam-6541	50	3	]	]	X
ejpam-6541	50	4	∗	∗	NOUN
ejpam-6541	50	5	is	be	AUX
ejpam-6541	50	6	associative	associative	ADJ
ejpam-6541	50	7	and	and	CCONJ
ejpam-6541	50	8	commutative	commutative	ADJ
ejpam-6541	50	9	.	.	PUNCT
ejpam-6541	51	1	[	[	X
ejpam-6541	51	2	b	b	X
ejpam-6541	51	3	]	]	X
ejpam-6541	51	4	a11	a11	PROPN
ejpam-6541	51	5	∗	∗	PROPN
ejpam-6541	51	6	1	1	NUM
ejpam-6541	51	7	=	=	SYM
ejpam-6541	51	8	a11	a11	PROPN
ejpam-6541	51	9	,	,	PUNCT
ejpam-6541	51	10	∀	∀	NOUN
ejpam-6541	51	11	a11	a11	PROPN
ejpam-6541	51	12	∈	∈	PROPN
ejpam-6541	52	1	[	[	X
ejpam-6541	52	2	0	0	NUM
ejpam-6541	52	3	,	,	PUNCT
ejpam-6541	52	4	1	1	NUM
ejpam-6541	52	5	]	]	PUNCT
ejpam-6541	52	6	.	.	PUNCT
ejpam-6541	53	1	[	[	X
ejpam-6541	53	2	c	c	X
ejpam-6541	53	3	]	]	X
ejpam-6541	53	4	a11∗b11	a11∗b11	PROPN
ejpam-6541	53	5	≤	≤	PUNCT
ejpam-6541	53	6	c11∗d11	c11∗d11	PROPN
ejpam-6541	53	7	whenever	whenever	SCONJ
ejpam-6541	53	8	a11	a11	PROPN
ejpam-6541	53	9	≤	≤	PROPN
ejpam-6541	53	10	c11	c11	NOUN
ejpam-6541	53	11	and	and	CCONJ
ejpam-6541	53	12	b11	b11	PROPN
ejpam-6541	53	13	≤	≤	PROPN
ejpam-6541	53	14	d11	d11	PROPN
ejpam-6541	53	15	for	for	ADP
ejpam-6541	53	16	each	each	DET
ejpam-6541	53	17	a11	a11	PROPN
ejpam-6541	53	18	,	,	PUNCT
ejpam-6541	53	19	b11	b11	PROPN
ejpam-6541	53	20	,	,	PUNCT
ejpam-6541	53	21	c11	c11	NOUN
ejpam-6541	53	22	,	,	PUNCT
ejpam-6541	53	23	d11	d11	PROPN
ejpam-6541	53	24	∈	∈	PROPN
ejpam-6541	54	1	[	[	X
ejpam-6541	54	2	0	0	NUM
ejpam-6541	54	3	,	,	PUNCT
ejpam-6541	54	4	1	1	NUM
ejpam-6541	54	5	]	]	PUNCT
ejpam-6541	54	6	.	.	PUNCT
ejpam-6541	55	1	it	it	PRON
ejpam-6541	55	2	can	can	AUX
ejpam-6541	55	3	be	be	AUX
ejpam-6541	55	4	described	describe	VERB
ejpam-6541	55	5	as	as	ADP
ejpam-6541	55	6	the	the	DET
ejpam-6541	55	7	continuous	continuous	ADJ
ejpam-6541	55	8	t−norm	t−norm	NOUN
ejpam-6541	55	9	if	if	SCONJ
ejpam-6541	55	10	∗	∗	NOUN
ejpam-6541	55	11	is	be	AUX
ejpam-6541	55	12	continuous	continuous	ADJ
ejpam-6541	55	13	.	.	PUNCT
ejpam-6541	56	1	definition	definition	NOUN
ejpam-6541	56	2	2	2	NUM
ejpam-6541	56	3	.	.	PUNCT
ejpam-6541	57	1	[	[	X
ejpam-6541	57	2	15	15	NUM
ejpam-6541	57	3	]	]	X
ejpam-6541	57	4	an	an	DET
ejpam-6541	57	5	operation	operation	NOUN
ejpam-6541	57	6	that	that	PRON
ejpam-6541	57	7	is	be	AUX
ejpam-6541	57	8	binary	binary	ADJ
ejpam-6541	57	9	⋄	⋄	PROPN
ejpam-6541	57	10	:	:	PUNCT
ejpam-6541	58	1	[	[	X
ejpam-6541	58	2	0	0	NUM
ejpam-6541	58	3	,	,	PUNCT
ejpam-6541	58	4	1]×	1]×	NUM
ejpam-6541	59	1	[	[	X
ejpam-6541	59	2	0	0	NUM
ejpam-6541	59	3	,	,	PUNCT
ejpam-6541	59	4	1	1	NUM
ejpam-6541	59	5	]	]	PUNCT
ejpam-6541	59	6	→	→	PUNCT
ejpam-6541	59	7	[	[	X
ejpam-6541	59	8	0	0	NUM
ejpam-6541	59	9	,	,	PUNCT
ejpam-6541	59	10	1	1	NUM
ejpam-6541	59	11	]	]	PUNCT
ejpam-6541	59	12	is	be	AUX
ejpam-6541	59	13	a	a	DET
ejpam-6541	59	14	t−co	t−co	ADJ
ejpam-6541	59	15	-	-	PUNCT
ejpam-6541	59	16	norm	norm	NOUN
ejpam-6541	59	17	when	when	SCONJ
ejpam-6541	59	18	it	it	PRON
ejpam-6541	59	19	meets	meet	VERB
ejpam-6541	59	20	the	the	DET
ejpam-6541	59	21	requirements	requirement	NOUN
ejpam-6541	59	22	listed	list	VERB
ejpam-6541	59	23	below	below	ADV
ejpam-6541	59	24	:	:	PUNCT
ejpam-6541	60	1	[	[	X
ejpam-6541	60	2	a	a	X
ejpam-6541	60	3	]	]	X
ejpam-6541	60	4	⋄	⋄	NOUN
ejpam-6541	60	5	is	be	AUX
ejpam-6541	60	6	associative	associative	ADJ
ejpam-6541	60	7	and	and	CCONJ
ejpam-6541	60	8	commutative	commutative	ADJ
ejpam-6541	60	9	.	.	PUNCT
ejpam-6541	61	1	[	[	X
ejpam-6541	61	2	b	b	X
ejpam-6541	61	3	]	]	X
ejpam-6541	61	4	a11	a11	PROPN
ejpam-6541	61	5	⋄	⋄	PROPN
ejpam-6541	61	6	1	1	NUM
ejpam-6541	61	7	=	=	SYM
ejpam-6541	61	8	a11	a11	PROPN
ejpam-6541	61	9	,	,	PUNCT
ejpam-6541	61	10	∀	∀	NOUN
ejpam-6541	61	11	a11	a11	PROPN
ejpam-6541	61	12	∈	∈	PROPN
ejpam-6541	62	1	[	[	X
ejpam-6541	62	2	0	0	NUM
ejpam-6541	62	3	,	,	PUNCT
ejpam-6541	62	4	1	1	NUM
ejpam-6541	62	5	]	]	PUNCT
ejpam-6541	62	6	.	.	PUNCT
ejpam-6541	63	1	[	[	X
ejpam-6541	63	2	c	c	X
ejpam-6541	63	3	]	]	X
ejpam-6541	63	4	a11⋄b11	a11⋄b11	PROPN
ejpam-6541	63	5	≤	≤	PROPN
ejpam-6541	63	6	c11⋄d11	c11⋄d11	PROPN
ejpam-6541	63	7	whenever	whenever	SCONJ
ejpam-6541	63	8	a11	a11	PROPN
ejpam-6541	63	9	≤	≤	PROPN
ejpam-6541	63	10	c11	c11	NOUN
ejpam-6541	63	11	and	and	CCONJ
ejpam-6541	63	12	b11	b11	PROPN
ejpam-6541	63	13	≤	≤	PROPN
ejpam-6541	63	14	d11	d11	PROPN
ejpam-6541	63	15	for	for	ADP
ejpam-6541	63	16	each	each	DET
ejpam-6541	63	17	a11	a11	PROPN
ejpam-6541	63	18	,	,	PUNCT
ejpam-6541	63	19	b11	b11	PROPN
ejpam-6541	63	20	,	,	PUNCT
ejpam-6541	63	21	c11	c11	NOUN
ejpam-6541	63	22	,	,	PUNCT
ejpam-6541	63	23	d11	d11	PROPN
ejpam-6541	63	24	∈	∈	PROPN
ejpam-6541	64	1	[	[	X
ejpam-6541	64	2	0	0	NUM
ejpam-6541	64	3	,	,	PUNCT
ejpam-6541	64	4	1	1	NUM
ejpam-6541	64	5	]	]	PUNCT
ejpam-6541	64	6	.	.	PUNCT
ejpam-6541	65	1	when	when	SCONJ
ejpam-6541	65	2	⋄	⋄	PROPN
ejpam-6541	65	3	is	be	AUX
ejpam-6541	65	4	continuous	continuous	ADJ
ejpam-6541	65	5	,	,	PUNCT
ejpam-6541	65	6	it	it	PRON
ejpam-6541	65	7	has	have	VERB
ejpam-6541	65	8	to	to	PART
ejpam-6541	65	9	be	be	AUX
ejpam-6541	65	10	referred	refer	VERB
ejpam-6541	65	11	as	as	ADP
ejpam-6541	65	12	continuous	continuous	ADJ
ejpam-6541	65	13	t−co	t−co	ADJ
ejpam-6541	65	14	-	-	PUNCT
ejpam-6541	65	15	norm	norm	NOUN
ejpam-6541	65	16	.	.	PUNCT
ejpam-6541	66	1	definition	definition	NOUN
ejpam-6541	66	2	3	3	NUM
ejpam-6541	66	3	.	.	PUNCT
ejpam-6541	67	1	[	[	X
ejpam-6541	67	2	16	16	NUM
ejpam-6541	67	3	]	]	PUNCT
ejpam-6541	67	4	consider	consider	VERB
ejpam-6541	67	5	the	the	DET
ejpam-6541	67	6	nonempty	nonempty	ADJ
ejpam-6541	67	7	set	set	VERB
ejpam-6541	67	8	v	v	ADP
ejpam-6541	67	9	combined	combine	VERB
ejpam-6541	67	10	with	with	ADP
ejpam-6541	67	11	algebraic	algebraic	ADJ
ejpam-6541	67	12	operations	operation	NOUN
ejpam-6541	67	13	+	+	ADP
ejpam-6541	67	14	,	,	PUNCT
ejpam-6541	67	15	�	�	PROPN
ejpam-6541	67	16	fulfil	fulfil	PROPN
ejpam-6541	67	17	,	,	PUNCT
ejpam-6541	67	18	(	(	PUNCT
ejpam-6541	67	19	v,+	v,+	NUM
ejpam-6541	67	20	)	)	PUNCT
ejpam-6541	67	21	is	be	AUX
ejpam-6541	67	22	a	a	DET
ejpam-6541	67	23	group	group	NOUN
ejpam-6541	67	24	and	and	CCONJ
ejpam-6541	67	25	regarding	regard	VERB
ejpam-6541	67	26	scalar	scalar	ADJ
ejpam-6541	67	27	multiplication	multiplication	NOUN
ejpam-6541	67	28	,	,	PUNCT
ejpam-6541	67	29	(	(	PUNCT
ejpam-6541	67	30	i	i	NOUN
ejpam-6541	67	31	)	)	PUNCT
ejpam-6541	67	32	k1(a1	k1(a1	PROPN
ejpam-6541	67	33	+	+	CCONJ
ejpam-6541	67	34	b1	b1	NOUN
ejpam-6541	67	35	)	)	PUNCT
ejpam-6541	67	36	=	=	PUNCT
ejpam-6541	68	1	k1a1	k1a1	X
ejpam-6541	68	2	+	+	CCONJ
ejpam-6541	68	3	k1b1	k1b1	PROPN
ejpam-6541	68	4	(	(	PUNCT
ejpam-6541	68	5	ii	ii	NOUN
ejpam-6541	68	6	)	)	PUNCT
ejpam-6541	68	7	(	(	PUNCT
ejpam-6541	68	8	k1	k1	NOUN
ejpam-6541	68	9	+	+	CCONJ
ejpam-6541	68	10	l1)a1	l1)a1	NOUN
ejpam-6541	68	11	=	=	SYM
ejpam-6541	68	12	k1a1	k1a1	X
ejpam-6541	68	13	+1	+1	X
ejpam-6541	68	14	k1b	k1b	PROPN
ejpam-6541	68	15	(	(	PUNCT
ejpam-6541	68	16	iii	iii	NOUN
ejpam-6541	68	17	)	)	PUNCT
ejpam-6541	68	18	k1(la1	k1(la1	X
ejpam-6541	68	19	)	)	PUNCT
ejpam-6541	68	20	=	=	SYM
ejpam-6541	68	21	(	(	PUNCT
ejpam-6541	68	22	k1l1)a1	k1l1)a1	X
ejpam-6541	68	23	(	(	PUNCT
ejpam-6541	68	24	iv	iv	X
ejpam-6541	68	25	)	)	PUNCT
ejpam-6541	68	26	1.a1	1.a1	NUM
ejpam-6541	68	27	=	=	SYM
ejpam-6541	68	28	a1	a1	PROPN
ejpam-6541	68	29	,	,	PUNCT
ejpam-6541	68	30	∀a1	∀a1	NOUN
ejpam-6541	68	31	,	,	PUNCT
ejpam-6541	68	32	b1	b1	PROPN
ejpam-6541	68	33	,	,	PUNCT
ejpam-6541	68	34	c1	c1	PROPN
ejpam-6541	68	35	∈	∈	PROPN
ejpam-6541	68	36	v	v	PROPN
ejpam-6541	68	37	and	and	CCONJ
ejpam-6541	68	38	k1	k1	PROPN
ejpam-6541	68	39	,	,	PUNCT
ejpam-6541	68	40	l1	l1	PROPN
ejpam-6541	68	41	∈	∈	PROPN
ejpam-6541	68	42	r∗	r∗	VERB
ejpam-6541	68	43	the	the	DET
ejpam-6541	68	44	triple	triple	ADJ
ejpam-6541	68	45	(	(	PUNCT
ejpam-6541	68	46	v,+	v,+	NUM
ejpam-6541	68	47	,	,	PUNCT
ejpam-6541	68	48	�	�	PROPN
ejpam-6541	68	49	)	)	PUNCT
ejpam-6541	68	50	is	be	AUX
ejpam-6541	68	51	referred	refer	VERB
ejpam-6541	68	52	to	to	ADP
ejpam-6541	68	53	as	as	ADP
ejpam-6541	68	54	vector	vector	NOUN
ejpam-6541	68	55	space	space	NOUN
ejpam-6541	68	56	.	.	PUNCT
ejpam-6541	69	1	definition	definition	NOUN
ejpam-6541	69	2	4	4	NUM
ejpam-6541	69	3	.	.	PUNCT
ejpam-6541	70	1	[	[	X
ejpam-6541	70	2	17	17	NUM
ejpam-6541	70	3	]	]	PUNCT
ejpam-6541	70	4	the	the	DET
ejpam-6541	70	5	fuzzy	fuzzy	ADJ
ejpam-6541	70	6	set	set	VERB
ejpam-6541	70	7	n	n	NOUN
ejpam-6541	70	8	in	in	ADV
ejpam-6541	70	9	x×	x×	PUNCT
ejpam-6541	71	1	[	[	X
ejpam-6541	71	2	0,∞	0,∞	NOUN
ejpam-6541	71	3	)	)	PUNCT
ejpam-6541	71	4	over	over	ADP
ejpam-6541	71	5	a	a	DET
ejpam-6541	71	6	linear	linear	ADJ
ejpam-6541	71	7	space	space	NOUN
ejpam-6541	71	8	x	x	PRON
ejpam-6541	71	9	constitutes	constitute	VERB
ejpam-6541	71	10	a	a	DET
ejpam-6541	71	11	fuzzy	fuzzy	ADJ
ejpam-6541	71	12	norm	norm	NOUN
ejpam-6541	71	13	over	over	ADP
ejpam-6541	71	14	x	x	X
ejpam-6541	71	15	when	when	SCONJ
ejpam-6541	71	16	it	it	PRON
ejpam-6541	71	17	meets	meet	VERB
ejpam-6541	71	18	this	this	DET
ejpam-6541	71	19	criteria	criterion	NOUN
ejpam-6541	71	20	,	,	PUNCT
ejpam-6541	71	21	(	(	PUNCT
ejpam-6541	71	22	i	i	NOUN
ejpam-6541	71	23	)	)	PUNCT
ejpam-6541	71	24	(	(	PUNCT
ejpam-6541	71	25	fn1	fn1	NOUN
ejpam-6541	71	26	)	)	PUNCT
ejpam-6541	71	27	n(x1	n(x1	NOUN
ejpam-6541	71	28	,	,	PUNCT
ejpam-6541	71	29	0	0	NUM
ejpam-6541	71	30	)	)	PUNCT
ejpam-6541	71	31	=	=	SYM
ejpam-6541	71	32	0	0	NUM
ejpam-6541	71	33	,	,	PUNCT
ejpam-6541	71	34	∀x1	∀x1	ADP
ejpam-6541	71	35	∈	∈	NOUN
ejpam-6541	71	36	x	x	SYM
ejpam-6541	71	37	(	(	PUNCT
ejpam-6541	71	38	ii	ii	NOUN
ejpam-6541	71	39	)	)	PUNCT
ejpam-6541	71	40	(	(	PUNCT
ejpam-6541	71	41	fn2	fn2	NOUN
ejpam-6541	71	42	)	)	PUNCT
ejpam-6541	71	43	n(x1	n(x1	NOUN
ejpam-6541	71	44	,	,	PUNCT
ejpam-6541	71	45	t	t	PROPN
ejpam-6541	71	46	)	)	PUNCT
ejpam-6541	71	47	=	=	SYM
ejpam-6541	71	48	1	1	NUM
ejpam-6541	71	49	,	,	PUNCT
ejpam-6541	71	50	∀t	∀t	PROPN
ejpam-6541	71	51	>	>	X
ejpam-6541	71	52	0	0	PUNCT
ejpam-6541	72	1	iff	iff	PROPN
ejpam-6541	72	2	x1	x1	PROPN
ejpam-6541	72	3	=	=	PROPN
ejpam-6541	72	4	0	0	PROPN
ejpam-6541	72	5	.	.	PUNCT
ejpam-6541	73	1	(	(	PUNCT
ejpam-6541	73	2	iii	iii	NOUN
ejpam-6541	73	3	)	)	PUNCT
ejpam-6541	73	4	(	(	PUNCT
ejpam-6541	73	5	fn3)n(λx1	fn3)n(λx1	PROPN
ejpam-6541	73	6	,	,	PUNCT
ejpam-6541	73	7	t	t	NOUN
ejpam-6541	73	8	)	)	PUNCT
ejpam-6541	73	9	=	=	SYM
ejpam-6541	74	1	n	n	CCONJ
ejpam-6541	74	2	(	(	PUNCT
ejpam-6541	74	3	x1	x1	PROPN
ejpam-6541	74	4	,	,	PUNCT
ejpam-6541	74	5	t	t	PROPN
ejpam-6541	74	6	|λ|	|λ|	PROPN
ejpam-6541	74	7	)	)	PUNCT
ejpam-6541	74	8	,	,	PUNCT
ejpam-6541	74	9	∀	∀	PUNCT
ejpam-6541	74	10	x1	x1	PROPN
ejpam-6541	74	11	∈	∈	PROPN
ejpam-6541	74	12	x,∀	x,∀	PUNCT
ejpam-6541	75	1	t	t	PROPN
ejpam-6541	75	2	>	>	X
ejpam-6541	75	3	0	0	NUM
ejpam-6541	75	4	,	,	PUNCT
ejpam-6541	75	5	∀	∀	PUNCT
ejpam-6541	75	6	λ	λ	X
ejpam-6541	75	7	∈	∈	PROPN
ejpam-6541	75	8	k∗	k∗	NOUN
ejpam-6541	75	9	,	,	PUNCT
ejpam-6541	75	10	(	(	PUNCT
ejpam-6541	75	11	k∗	k∗	PROPN
ejpam-6541	75	12	is	be	AUX
ejpam-6541	75	13	non	non	ADJ
ejpam-6541	75	14	negative	negative	ADJ
ejpam-6541	75	15	real	real	ADJ
ejpam-6541	75	16	numbers	number	NOUN
ejpam-6541	75	17	)	)	PUNCT
ejpam-6541	75	18	(	(	PUNCT
ejpam-6541	75	19	iv	iv	X
ejpam-6541	75	20	)	)	PUNCT
ejpam-6541	75	21	(	(	PUNCT
ejpam-6541	75	22	fn4)n(x1	fn4)n(x1	PROPN
ejpam-6541	75	23	+	+	NUM
ejpam-6541	75	24	y1	y1	NOUN
ejpam-6541	75	25	,	,	PUNCT
ejpam-6541	75	26	t+	t+	NOUN
ejpam-6541	75	27	s	s	NOUN
ejpam-6541	75	28	)	)	PUNCT
ejpam-6541	75	29	≥	≥	NOUN
ejpam-6541	75	30	n(x1	n(x1	NOUN
ejpam-6541	75	31	,	,	PUNCT
ejpam-6541	75	32	t	t	PROPN
ejpam-6541	75	33	)	)	PUNCT
ejpam-6541	75	34	∗n(y1	∗n(y1	PROPN
ejpam-6541	75	35	,	,	PUNCT
ejpam-6541	75	36	s	s	PART
ejpam-6541	75	37	)	)	PUNCT
ejpam-6541	75	38	,	,	PUNCT
ejpam-6541	75	39	∀	∀	X
ejpam-6541	75	40	x1	x1	ADJ
ejpam-6541	75	41	,	,	PUNCT
ejpam-6541	75	42	y1	y1	PROPN
ejpam-6541	75	43	∈	∈	PROPN
ejpam-6541	75	44	x,∀	x,∀	PROPN
ejpam-6541	76	1	t	t	PROPN
ejpam-6541	76	2	,	,	PUNCT
ejpam-6541	76	3	s	s	PART
ejpam-6541	76	4	>	>	X
ejpam-6541	76	5	0	0	NUM
ejpam-6541	76	6	.	.	PUNCT
ejpam-6541	77	1	(	(	PUNCT
ejpam-6541	77	2	v	v	NOUN
ejpam-6541	77	3	)	)	PUNCT
ejpam-6541	77	4	(	(	PUNCT
ejpam-6541	77	5	fn5	fn5	NOUN
ejpam-6541	77	6	)	)	PUNCT
ejpam-6541	77	7	∀x1	∀x1	ADP
ejpam-6541	77	8	∈	∈	PROPN
ejpam-6541	77	9	x	x	SYM
ejpam-6541	77	10	,	,	PUNCT
ejpam-6541	77	11	n(x1	n(x1	ADJ
ejpam-6541	77	12	,	,	PUNCT
ejpam-6541	77	13	•	•	NUM
ejpam-6541	77	14	)	)	PUNCT
ejpam-6541	77	15	is	be	AUX
ejpam-6541	77	16	left	leave	VERB
ejpam-6541	77	17	continuous	continuous	ADJ
ejpam-6541	77	18	along	along	ADP
ejpam-6541	77	19	with	with	ADP
ejpam-6541	77	20	limt→∞n(x1	limt→∞n(x1	PROPN
ejpam-6541	77	21	,	,	PUNCT
ejpam-6541	77	22	t	t	PROPN
ejpam-6541	77	23	)	)	PUNCT
ejpam-6541	77	24	=	=	SYM
ejpam-6541	78	1	1	1	X
ejpam-6541	78	2	.	.	X
ejpam-6541	78	3	thus,(x	thus,(x	PROPN
ejpam-6541	78	4	,	,	PUNCT
ejpam-6541	78	5	n	n	CCONJ
ejpam-6541	78	6	,	,	PUNCT
ejpam-6541	78	7	∗	∗	NOUN
ejpam-6541	78	8	)	)	PUNCT
ejpam-6541	78	9	known	know	VERB
ejpam-6541	78	10	as	as	ADP
ejpam-6541	78	11	fuzzy	fuzzy	ADJ
ejpam-6541	78	12	normed	norme	VERB
ejpam-6541	78	13	linear	linear	ADJ
ejpam-6541	78	14	space	space	NOUN
ejpam-6541	78	15	.	.	PUNCT
ejpam-6541	79	1	definition	definition	NOUN
ejpam-6541	79	2	5	5	NUM
ejpam-6541	79	3	.	.	PUNCT
ejpam-6541	80	1	[	[	X
ejpam-6541	80	2	16	16	NUM
ejpam-6541	80	3	]	]	X
ejpam-6541	80	4	hesitant	hesitant	ADJ
ejpam-6541	80	5	fuzzy	fuzzy	ADJ
ejpam-6541	80	6	normed	norme	VERB
ejpam-6541	80	7	linear	linear	ADJ
ejpam-6541	80	8	space	space	NOUN
ejpam-6541	80	9	:	:	PUNCT
ejpam-6541	80	10	given	give	VERB
ejpam-6541	80	11	a	a	DET
ejpam-6541	80	12	vector	vector	NOUN
ejpam-6541	80	13	space	space	NOUN
ejpam-6541	80	14	v	v	NOUN
ejpam-6541	80	15	through	through	ADP
ejpam-6541	80	16	this	this	DET
ejpam-6541	80	17	field	field	NOUN
ejpam-6541	80	18	f	f	X
ejpam-6541	80	19	,	,	PUNCT
ejpam-6541	80	20	∗	∗	NOUN
ejpam-6541	80	21	consists	consist	VERB
ejpam-6541	80	22	of	of	ADP
ejpam-6541	80	23	t	t	NOUN
ejpam-6541	80	24	-	-	PUNCT
ejpam-6541	80	25	norm	norm	NOUN
ejpam-6541	80	26	,	,	PUNCT
ejpam-6541	80	27	together	together	ADV
ejpam-6541	80	28	with	with	ADP
ejpam-6541	80	29	h	h	NOUN
ejpam-6541	80	30	:	:	PUNCT
ejpam-6541	80	31	v	v	NUM
ejpam-6541	80	32	×	×	NOUN
ejpam-6541	81	1	[	[	X
ejpam-6541	81	2	0,∞	0,∞	NOUN
ejpam-6541	81	3	)	)	PUNCT
ejpam-6541	81	4	→	→	PUNCT
ejpam-6541	82	1	p	p	X
ejpam-6541	82	2	[	[	X
ejpam-6541	82	3	0	0	NUM
ejpam-6541	82	4	,	,	PUNCT
ejpam-6541	82	5	1	1	NUM
ejpam-6541	82	6	]	]	PUNCT
ejpam-6541	82	7	exists	exist	VERB
ejpam-6541	82	8	as	as	ADP
ejpam-6541	82	9	a	a	DET
ejpam-6541	82	10	hesitant	hesitant	ADJ
ejpam-6541	82	11	fuzzy	fuzzy	ADJ
ejpam-6541	82	12	set	set	VERB
ejpam-6541	82	13	with	with	ADP
ejpam-6541	82	14	the	the	DET
ejpam-6541	82	15	subsequent	subsequent	ADJ
ejpam-6541	82	16	characteristics	characteristic	NOUN
ejpam-6541	82	17	,	,	PUNCT
ejpam-6541	82	18	t1	t1	NOUN
ejpam-6541	82	19	,	,	PUNCT
ejpam-6541	82	20	t2	t2	NOUN
ejpam-6541	82	21	>	>	X
ejpam-6541	82	22	0	0	NUM
ejpam-6541	82	23	and	and	CCONJ
ejpam-6541	82	24	∀	∀	NUM
ejpam-6541	82	25	x	x	NOUN
ejpam-6541	82	26	,	,	PUNCT
ejpam-6541	82	27	y	y	PROPN
ejpam-6541	82	28	∈	∈	PROPN
ejpam-6541	82	29	v	v	PROPN
ejpam-6541	82	30	(	(	PUNCT
ejpam-6541	82	31	i	i	NOUN
ejpam-6541	82	32	)	)	PUNCT
ejpam-6541	82	33	h(x	h(x	PROPN
ejpam-6541	82	34	,	,	PUNCT
ejpam-6541	82	35	0	0	NUM
ejpam-6541	82	36	)	)	PUNCT
ejpam-6541	82	37	=	=	PUNCT
ejpam-6541	83	1	∅∗	∅∗	PROPN
ejpam-6541	83	2	(	(	PUNCT
ejpam-6541	83	3	empty	empty	ADJ
ejpam-6541	83	4	set	set	NOUN
ejpam-6541	83	5	)	)	PUNCT
ejpam-6541	83	6	,	,	PUNCT
ejpam-6541	83	7	∀	∀	PUNCT
ejpam-6541	83	8	x	x	SYM
ejpam-6541	83	9	∈	∈	PROPN
ejpam-6541	83	10	v.	v.	PROPN
ejpam-6541	83	11	(	(	PUNCT
ejpam-6541	83	12	ii	ii	PROPN
ejpam-6541	83	13	)	)	PUNCT
ejpam-6541	83	14	h(x	h(x	PROPN
ejpam-6541	83	15	,	,	PUNCT
ejpam-6541	83	16	t	t	PROPN
ejpam-6541	83	17	)	)	PUNCT
ejpam-6541	83	18	=	=	PUNCT
ejpam-6541	84	1	u∗	u∗	INTJ
ejpam-6541	84	2	(	(	PUNCT
ejpam-6541	84	3	full	full	ADJ
ejpam-6541	84	4	set	set	NOUN
ejpam-6541	84	5	)	)	PUNCT
ejpam-6541	84	6	,	,	PUNCT
ejpam-6541	84	7	∀t	∀t	PROPN
ejpam-6541	84	8	>	>	X
ejpam-6541	84	9	0	0	NUM
ejpam-6541	85	1	iff	iff	NOUN
ejpam-6541	85	2	x	x	PROPN
ejpam-6541	85	3	=	=	NOUN
ejpam-6541	85	4	0	0	PROPN
ejpam-6541	85	5	.	.	PUNCT
ejpam-6541	85	6	k.	k.	PROPN
ejpam-6541	85	7	kavitha	kavitha	PROPN
ejpam-6541	85	8	,	,	PUNCT
ejpam-6541	85	9	p.	p.	PROPN
ejpam-6541	85	10	muralikrishna	muralikrishna	PROPN
ejpam-6541	85	11	/	/	SYM
ejpam-6541	85	12	eur	eur	PROPN
ejpam-6541	85	13	.	.	PUNCT
ejpam-6541	86	1	j.	j.	PROPN
ejpam-6541	86	2	pure	pure	PROPN
ejpam-6541	86	3	appl	appl	PROPN
ejpam-6541	86	4	.	.	PROPN
ejpam-6541	86	5	math	math	PROPN
ejpam-6541	86	6	,	,	PUNCT
ejpam-6541	86	7	18	18	NUM
ejpam-6541	86	8	(	(	PUNCT
ejpam-6541	86	9	4	4	NUM
ejpam-6541	86	10	)	)	PUNCT
ejpam-6541	86	11	(	(	PUNCT
ejpam-6541	86	12	2025	2025	NUM
ejpam-6541	86	13	)	)	PUNCT
ejpam-6541	86	14	,	,	PUNCT
ejpam-6541	86	15	6541	6541	NUM
ejpam-6541	86	16	4	4	NUM
ejpam-6541	86	17	of	of	ADP
ejpam-6541	86	18	14	14	NUM
ejpam-6541	86	19	(	(	PUNCT
ejpam-6541	86	20	iii	iii	NOUN
ejpam-6541	86	21	)	)	PUNCT
ejpam-6541	86	22	h(µx	h(µx	PROPN
ejpam-6541	86	23	,	,	PUNCT
ejpam-6541	86	24	t	t	PROPN
ejpam-6541	86	25	)	)	PUNCT
ejpam-6541	86	26	=	=	SYM
ejpam-6541	87	1	h(x	h(x	PROPN
ejpam-6541	87	2	,	,	PUNCT
ejpam-6541	87	3	t	t	PROPN
ejpam-6541	87	4	|µ|	|µ|	PROPN
ejpam-6541	87	5	)	)	PUNCT
ejpam-6541	87	6	,	,	PUNCT
ejpam-6541	87	7	∀x	∀x	VERB
ejpam-6541	87	8	∈	∈	PROPN
ejpam-6541	87	9	v,∀t	v,∀t	ADJ
ejpam-6541	87	10	≥	≥	NOUN
ejpam-6541	87	11	0	0	NUM
ejpam-6541	87	12	,	,	PUNCT
ejpam-6541	87	13	∀µ	∀µ	PROPN
ejpam-6541	87	14	∈	∈	PROPN
ejpam-6541	87	15	r∗.	r∗.	NOUN
ejpam-6541	87	16	(	(	PUNCT
ejpam-6541	87	17	iv	iv	X
ejpam-6541	87	18	)	)	PUNCT
ejpam-6541	87	19	h(x	h(x	PROPN
ejpam-6541	87	20	+	+	CCONJ
ejpam-6541	87	21	y	y	PROPN
ejpam-6541	87	22	,	,	PUNCT
ejpam-6541	87	23	t1	t1	NOUN
ejpam-6541	87	24	+	+	CCONJ
ejpam-6541	87	25	t2	t2	NOUN
ejpam-6541	87	26	)	)	PUNCT
ejpam-6541	87	27	⊇	⊇	PROPN
ejpam-6541	87	28	h(x	h(x	PROPN
ejpam-6541	87	29	,	,	PUNCT
ejpam-6541	87	30	t1	t1	NOUN
ejpam-6541	87	31	)	)	PUNCT
ejpam-6541	87	32	∩h(y	∩h(y	NOUN
ejpam-6541	87	33	,	,	PUNCT
ejpam-6541	87	34	t2	t2	NOUN
ejpam-6541	87	35	)	)	PUNCT
ejpam-6541	87	36	,	,	PUNCT
ejpam-6541	87	37	∀x	∀x	X
ejpam-6541	87	38	,	,	PUNCT
ejpam-6541	87	39	y	y	PROPN
ejpam-6541	87	40	∈	∈	PROPN
ejpam-6541	87	41	v	v	NOUN
ejpam-6541	87	42	,	,	PUNCT
ejpam-6541	87	43	∀	∀	X
ejpam-6541	87	44	t1	t1	NOUN
ejpam-6541	87	45	,	,	PUNCT
ejpam-6541	87	46	t2	t2	NOUN
ejpam-6541	87	47	≥	≥	NOUN
ejpam-6541	87	48	0	0	NUM
ejpam-6541	87	49	.	.	PUNCT
ejpam-6541	88	1	(	(	PUNCT
ejpam-6541	88	2	v	v	NOUN
ejpam-6541	88	3	)	)	PUNCT
ejpam-6541	88	4	limt→∞h(x	limt→∞h(x	PROPN
ejpam-6541	88	5	,	,	PUNCT
ejpam-6541	88	6	t	t	PROPN
ejpam-6541	88	7	)	)	PUNCT
ejpam-6541	88	8	=	=	PUNCT
ejpam-6541	89	1	u∗.	u∗.	PROPN
ejpam-6541	89	2	definition	definition	NOUN
ejpam-6541	89	3	6	6	NUM
ejpam-6541	89	4	.	.	PUNCT
ejpam-6541	90	1	[	[	X
ejpam-6541	90	2	16	16	NUM
ejpam-6541	90	3	]	]	X
ejpam-6541	90	4	a	a	DET
ejpam-6541	90	5	sequence	sequence	NOUN
ejpam-6541	90	6	vn	vn	NOUN
ejpam-6541	90	7	with	with	ADP
ejpam-6541	90	8	a	a	DET
ejpam-6541	90	9	hesitant	hesitant	ADJ
ejpam-6541	90	10	fuzzy	fuzzy	ADJ
ejpam-6541	90	11	normed	norme	VERB
ejpam-6541	90	12	linear	linear	ADJ
ejpam-6541	90	13	space	space	NOUN
ejpam-6541	90	14	(	(	PUNCT
ejpam-6541	90	15	v	v	NOUN
ejpam-6541	90	16	,	,	PUNCT
ejpam-6541	90	17	h	h	NOUN
ejpam-6541	90	18	)	)	PUNCT
ejpam-6541	90	19	,	,	PUNCT
ejpam-6541	90	20	known	know	VERB
ejpam-6541	90	21	as	as	ADP
ejpam-6541	90	22	converges	converge	NOUN
ejpam-6541	90	23	towards	towards	ADP
ejpam-6541	90	24	v	v	NUM
ejpam-6541	90	25	∈	∈	PROPN
ejpam-6541	90	26	v	v	NOUN
ejpam-6541	90	27	suppose	suppose	VERB
ejpam-6541	90	28	every	every	DET
ejpam-6541	90	29	s∗	s∗	PROPN
ejpam-6541	90	30	̸=	̸=	PROPN
ejpam-6541	90	31	∅∗	∅∗	PROPN
ejpam-6541	90	32	and	and	CCONJ
ejpam-6541	90	33	t	t	PROPN
ejpam-6541	90	34	>	>	X
ejpam-6541	90	35	0,we	0,we	PRON
ejpam-6541	90	36	could	could	AUX
ejpam-6541	90	37	locate	locate	VERB
ejpam-6541	90	38	n	n	ADP
ejpam-6541	90	39	using	use	VERB
ejpam-6541	90	40	h(vn	h(vn	PROPN
ejpam-6541	90	41	−	−	PROPN
ejpam-6541	90	42	v	v	PROPN
ejpam-6541	90	43	,	,	PUNCT
ejpam-6541	90	44	t	t	PROPN
ejpam-6541	90	45	)	)	PUNCT
ejpam-6541	91	1	⊃	⊃	PROPN
ejpam-6541	91	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	91	3	∀	∀	X
ejpam-6541	91	4	n	n	PRON
ejpam-6541	91	5	≥	≥	NOUN
ejpam-6541	91	6	n.	n.	NOUN
ejpam-6541	91	7	(	(	PUNCT
ejpam-6541	91	8	or	or	CCONJ
ejpam-6541	91	9	)	)	PUNCT
ejpam-6541	91	10	limn→∞h(vn	limn→∞h(vn	NOUN
ejpam-6541	92	1	−	−	PROPN
ejpam-6541	92	2	v	v	NOUN
ejpam-6541	92	3	,	,	PUNCT
ejpam-6541	92	4	t	t	PROPN
ejpam-6541	92	5	)	)	PUNCT
ejpam-6541	92	6	=	=	PUNCT
ejpam-6541	93	1	u∗.	u∗.	PROPN
ejpam-6541	93	2	definition	definition	NOUN
ejpam-6541	93	3	7	7	NUM
ejpam-6541	93	4	.	.	PUNCT
ejpam-6541	94	1	[	[	X
ejpam-6541	94	2	16	16	NUM
ejpam-6541	94	3	]	]	X
ejpam-6541	94	4	a	a	DET
ejpam-6541	94	5	sequence	sequence	NOUN
ejpam-6541	94	6	vn	vn	NOUN
ejpam-6541	94	7	in	in	ADP
ejpam-6541	94	8	a	a	DET
ejpam-6541	94	9	hesitant	hesitant	ADJ
ejpam-6541	94	10	fuzzy	fuzzy	ADJ
ejpam-6541	94	11	normed	normed	ADJ
ejpam-6541	94	12	space	space	NOUN
ejpam-6541	94	13	(	(	PUNCT
ejpam-6541	94	14	v	v	NOUN
ejpam-6541	94	15	,	,	PUNCT
ejpam-6541	94	16	h	h	NOUN
ejpam-6541	94	17	,	,	PUNCT
ejpam-6541	94	18	∗	∗	NOUN
ejpam-6541	94	19	)	)	PUNCT
ejpam-6541	94	20	is	be	AUX
ejpam-6541	94	21	said	say	VERB
ejpam-6541	94	22	to	to	PART
ejpam-6541	94	23	be	be	AUX
ejpam-6541	94	24	a	a	DET
ejpam-6541	94	25	cauchy	cauchy	ADJ
ejpam-6541	94	26	sequence	sequence	NOUN
ejpam-6541	94	27	if	if	SCONJ
ejpam-6541	94	28	for	for	ADP
ejpam-6541	94	29	all	all	DET
ejpam-6541	94	30	∅∗	∅∗	VERB
ejpam-6541	94	31	⊂	⊂	PROPN
ejpam-6541	94	32	s∗	s∗	PROPN
ejpam-6541	94	33	⊂	⊂	PROPN
ejpam-6541	94	34	u∗	u∗	PROPN
ejpam-6541	94	35	,	,	PUNCT
ejpam-6541	94	36	t	t	X
ejpam-6541	94	37	>	>	X
ejpam-6541	94	38	0	0	PUNCT
ejpam-6541	95	1	there	there	PRON
ejpam-6541	95	2	is	be	VERB
ejpam-6541	95	3	number	number	NOUN
ejpam-6541	95	4	n	n	NOUN
ejpam-6541	95	5	with	with	ADP
ejpam-6541	95	6	h(vm	h(vm	PROPN
ejpam-6541	95	7	−	−	PROPN
ejpam-6541	95	8	vn	vn	PROPN
ejpam-6541	95	9	,	,	PUNCT
ejpam-6541	95	10	t	t	PROPN
ejpam-6541	95	11	)	)	PUNCT
ejpam-6541	95	12	⊃	⊃	PROPN
ejpam-6541	95	13	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	95	14	for	for	ADP
ejpam-6541	95	15	all	all	DET
ejpam-6541	95	16	m	m	PROPN
ejpam-6541	95	17	,	,	PUNCT
ejpam-6541	95	18	n	n	PRON
ejpam-6541	95	19	≥	≥	NOUN
ejpam-6541	95	20	n.	n.	NOUN
ejpam-6541	95	21	(	(	PUNCT
ejpam-6541	95	22	or	or	CCONJ
ejpam-6541	95	23	)	)	PUNCT
ejpam-6541	95	24	limn→∞h(vn	limn→∞h(vn	NOUN
ejpam-6541	96	1	−	−	PROPN
ejpam-6541	96	2	v	v	NOUN
ejpam-6541	96	3	,	,	PUNCT
ejpam-6541	96	4	t	t	PROPN
ejpam-6541	96	5	)	)	PUNCT
ejpam-6541	96	6	=	=	SYM
ejpam-6541	96	7	u∗.	u∗.	PROPN
ejpam-6541	96	8	3	3	NUM
ejpam-6541	96	9	.	.	PUNCT
ejpam-6541	97	1	finite	finite	PROPN
ejpam-6541	97	2	dimensional	dimensional	ADJ
ejpam-6541	97	3	hesitant	hesitant	ADJ
ejpam-6541	97	4	fuzzy	fuzzy	ADJ
ejpam-6541	97	5	normed	norme	VERB
ejpam-6541	97	6	linear	linear	PROPN
ejpam-6541	97	7	space	space	NOUN
ejpam-6541	97	8	finite	finite	ADJ
ejpam-6541	97	9	dimensional	dimensional	ADJ
ejpam-6541	97	10	hesitant	hesitant	ADJ
ejpam-6541	97	11	fuzzy	fuzzy	ADJ
ejpam-6541	97	12	normed	normed	PROPN
ejpam-6541	97	13	linear	linear	PROPN
ejpam-6541	97	14	spaces	space	NOUN
ejpam-6541	97	15	are	be	AUX
ejpam-6541	97	16	defined	define	VERB
ejpam-6541	97	17	,	,	PUNCT
ejpam-6541	97	18	their	their	PRON
ejpam-6541	97	19	completeness	completeness	NOUN
ejpam-6541	97	20	,	,	PUNCT
ejpam-6541	97	21	and	and	CCONJ
ejpam-6541	97	22	their	their	PRON
ejpam-6541	97	23	compactness	compactness	NOUN
ejpam-6541	97	24	are	be	AUX
ejpam-6541	97	25	examined	examine	VERB
ejpam-6541	97	26	in	in	ADP
ejpam-6541	97	27	this	this	DET
ejpam-6541	97	28	section	section	NOUN
ejpam-6541	97	29	.	.	PUNCT
ejpam-6541	98	1	definition	definition	NOUN
ejpam-6541	98	2	8	8	NUM
ejpam-6541	98	3	.	.	PUNCT
ejpam-6541	99	1	let	let	VERB
ejpam-6541	99	2	(	(	PUNCT
ejpam-6541	99	3	v	v	NOUN
ejpam-6541	99	4	,	,	PUNCT
ejpam-6541	99	5	h	h	NOUN
ejpam-6541	99	6	,	,	PUNCT
ejpam-6541	99	7	∗	∗	NOUN
ejpam-6541	99	8	)	)	PUNCT
ejpam-6541	99	9	be	be	VERB
ejpam-6541	99	10	a	a	DET
ejpam-6541	99	11	hesitant	hesitant	ADJ
ejpam-6541	99	12	fuzzy	fuzzy	ADJ
ejpam-6541	99	13	normed	norme	VERB
ejpam-6541	99	14	linear	linear	ADJ
ejpam-6541	99	15	space	space	NOUN
ejpam-6541	99	16	.	.	PUNCT
ejpam-6541	100	1	if	if	SCONJ
ejpam-6541	100	2	dimension	dimension	NOUN
ejpam-6541	100	3	of	of	ADP
ejpam-6541	100	4	a	a	DET
ejpam-6541	100	5	vector	vector	NOUN
ejpam-6541	100	6	space	space	NOUN
ejpam-6541	100	7	v	v	NOUN
ejpam-6541	100	8	is	be	AUX
ejpam-6541	100	9	finite	finite	NOUN
ejpam-6541	100	10	then	then	ADV
ejpam-6541	100	11	it	it	PRON
ejpam-6541	100	12	is	be	AUX
ejpam-6541	100	13	called	call	VERB
ejpam-6541	100	14	finite	finite	ADJ
ejpam-6541	100	15	dimensional	dimensional	ADJ
ejpam-6541	100	16	hesitant	hesitant	ADJ
ejpam-6541	100	17	fuzzy	fuzzy	ADJ
ejpam-6541	100	18	normed	norme	VERB
ejpam-6541	100	19	linear	linear	ADJ
ejpam-6541	100	20	space	space	NOUN
ejpam-6541	100	21	.	.	PUNCT
ejpam-6541	101	1	definition	definition	NOUN
ejpam-6541	101	2	9	9	NUM
ejpam-6541	101	3	.	.	PUNCT
ejpam-6541	102	1	given	give	VERB
ejpam-6541	102	2	a	a	DET
ejpam-6541	102	3	hesitant	hesitant	ADJ
ejpam-6541	102	4	fuzzy	fuzzy	ADJ
ejpam-6541	102	5	normed	normed	ADJ
ejpam-6541	102	6	space	space	NOUN
ejpam-6541	102	7	(	(	PUNCT
ejpam-6541	102	8	v	v	NOUN
ejpam-6541	102	9	,	,	PUNCT
ejpam-6541	102	10	h	h	NOUN
ejpam-6541	102	11	,	,	PUNCT
ejpam-6541	102	12	∗	∗	NOUN
ejpam-6541	102	13	)	)	PUNCT
ejpam-6541	102	14	as	as	ADV
ejpam-6541	102	15	well	well	ADV
ejpam-6541	102	16	as	as	ADP
ejpam-6541	102	17	a	a	DET
ejpam-6541	102	18	subset	subset	NOUN
ejpam-6541	102	19	w	w	NOUN
ejpam-6541	102	20	of	of	ADP
ejpam-6541	102	21	v	v	NOUN
ejpam-6541	102	22	,	,	PUNCT
ejpam-6541	102	23	w	w	NOUN
ejpam-6541	102	24	signifies	signify	VERB
ejpam-6541	102	25	the	the	DET
ejpam-6541	102	26	closure	closure	NOUN
ejpam-6541	102	27	of	of	ADP
ejpam-6541	102	28	w	w	NOUN
ejpam-6541	102	29	,	,	PUNCT
ejpam-6541	102	30	which	which	PRON
ejpam-6541	102	31	corresponds	correspond	VERB
ejpam-6541	102	32	to	to	ADP
ejpam-6541	102	33	⋂	⋂	PROPN
ejpam-6541	102	34	{	{	PUNCT
ejpam-6541	102	35	w	w	PROPN
ejpam-6541	102	36	⊆	⊆	NUM
ejpam-6541	102	37	b	b	NOUN
ejpam-6541	102	38	:	:	PUNCT
ejpam-6541	102	39	b	b	NOUN
ejpam-6541	102	40	is	be	AUX
ejpam-6541	102	41	closed	close	VERB
ejpam-6541	102	42	in	in	ADP
ejpam-6541	102	43	v	v	NOUN
ejpam-6541	102	44	}	}	PUNCT
ejpam-6541	102	45	.	.	PUNCT
ejpam-6541	103	1	lemma	lemma	PROPN
ejpam-6541	103	2	1	1	X
ejpam-6541	103	3	.	.	X
ejpam-6541	104	1	consider	consider	VERB
ejpam-6541	104	2	(	(	PUNCT
ejpam-6541	104	3	v	v	NOUN
ejpam-6541	104	4	,	,	PUNCT
ejpam-6541	104	5	h	h	NOUN
ejpam-6541	104	6	,	,	PUNCT
ejpam-6541	104	7	∗	∗	NOUN
ejpam-6541	104	8	)	)	PUNCT
ejpam-6541	104	9	to	to	PART
ejpam-6541	104	10	become	become	VERB
ejpam-6541	104	11	hesitant	hesitant	ADJ
ejpam-6541	104	12	fuzzy	fuzzy	ADJ
ejpam-6541	104	13	normed	normed	ADJ
ejpam-6541	104	14	space	space	NOUN
ejpam-6541	104	15	,	,	PUNCT
ejpam-6541	104	16	along	along	ADP
ejpam-6541	104	17	with	with	ADP
ejpam-6541	104	18	w	w	NOUN
ejpam-6541	104	19	exists	exist	NOUN
ejpam-6541	104	20	as	as	ADP
ejpam-6541	104	21	a	a	DET
ejpam-6541	104	22	subset	subset	NOUN
ejpam-6541	104	23	of	of	ADP
ejpam-6541	104	24	v.	v.	ADP
ejpam-6541	104	25	a	a	DET
ejpam-6541	104	26	sequence	sequence	NOUN
ejpam-6541	104	27	{	{	PUNCT
ejpam-6541	104	28	wn	wn	NOUN
ejpam-6541	104	29	}	}	PUNCT
ejpam-6541	104	30	within	within	ADP
ejpam-6541	104	31	w	w	ADP
ejpam-6541	104	32	converges	converge	NOUN
ejpam-6541	104	33	towards	towards	ADP
ejpam-6541	104	34	y	y	PRON
ejpam-6541	104	35	,	,	PUNCT
ejpam-6541	104	36	if	if	SCONJ
ejpam-6541	104	37	and	and	CCONJ
ejpam-6541	104	38	only	only	ADV
ejpam-6541	104	39	if	if	SCONJ
ejpam-6541	104	40	y	y	PROPN
ejpam-6541	104	41	∈	∈	PROPN
ejpam-6541	104	42	w.	w.	PROPN
ejpam-6541	104	43	definition	definition	NOUN
ejpam-6541	104	44	10	10	NUM
ejpam-6541	104	45	.	.	PUNCT
ejpam-6541	105	1	the	the	DET
ejpam-6541	105	2	completeness	completeness	NOUN
ejpam-6541	105	3	of	of	ADP
ejpam-6541	105	4	a	a	DET
ejpam-6541	105	5	hesitant	hesitant	ADJ
ejpam-6541	105	6	fuzzy	fuzzy	ADJ
ejpam-6541	105	7	normed	normed	ADJ
ejpam-6541	105	8	space	space	NOUN
ejpam-6541	105	9	(	(	PUNCT
ejpam-6541	105	10	v	v	NOUN
ejpam-6541	105	11	,	,	PUNCT
ejpam-6541	105	12	h	h	NOUN
ejpam-6541	105	13	,	,	PUNCT
ejpam-6541	105	14	∗	∗	NOUN
ejpam-6541	105	15	)	)	PUNCT
ejpam-6541	105	16	is	be	AUX
ejpam-6541	105	17	defined	define	VERB
ejpam-6541	105	18	as	as	ADP
ejpam-6541	105	19	the	the	DET
ejpam-6541	105	20	convergence	convergence	NOUN
ejpam-6541	105	21	of	of	ADP
ejpam-6541	105	22	all	all	DET
ejpam-6541	105	23	cauchy	cauchy	ADJ
ejpam-6541	105	24	sequences	sequence	NOUN
ejpam-6541	105	25	in	in	ADP
ejpam-6541	105	26	v	v	NOUN
ejpam-6541	105	27	toward	toward	ADP
ejpam-6541	105	28	point	point	NOUN
ejpam-6541	105	29	in	in	ADP
ejpam-6541	105	30	v.	v.	ADP
ejpam-6541	105	31	definition	definition	NOUN
ejpam-6541	105	32	11	11	NUM
ejpam-6541	105	33	.	.	PUNCT
ejpam-6541	106	1	the	the	DET
ejpam-6541	106	2	hesitant	hesitant	ADJ
ejpam-6541	106	3	fuzzy	fuzzy	ADJ
ejpam-6541	106	4	normed	normed	ADJ
ejpam-6541	106	5	space	space	NOUN
ejpam-6541	106	6	(	(	PUNCT
ejpam-6541	106	7	v	v	NOUN
ejpam-6541	106	8	,	,	PUNCT
ejpam-6541	106	9	h	h	NOUN
ejpam-6541	106	10	,	,	PUNCT
ejpam-6541	106	11	∗	∗	NOUN
ejpam-6541	106	12	)	)	PUNCT
ejpam-6541	106	13	is	be	AUX
ejpam-6541	106	14	considered	consider	VERB
ejpam-6541	106	15	complete	complete	ADJ
ejpam-6541	106	16	if	if	SCONJ
ejpam-6541	106	17	all	all	PRON
ejpam-6541	106	18	of	of	ADP
ejpam-6541	106	19	the	the	DET
ejpam-6541	106	20	cauchy	cauchy	ADJ
ejpam-6541	106	21	sequences	sequence	NOUN
ejpam-6541	106	22	in	in	ADP
ejpam-6541	106	23	v	v	NUM
ejpam-6541	106	24	converge	converge	NOUN
ejpam-6541	106	25	toward	toward	ADP
ejpam-6541	106	26	point	point	NOUN
ejpam-6541	106	27	in	in	ADP
ejpam-6541	106	28	v	v	NUM
ejpam-6541	106	29	.	.	PUNCT
ejpam-6541	107	1	definition	definition	NOUN
ejpam-6541	107	2	12	12	NUM
ejpam-6541	107	3	.	.	PUNCT
ejpam-6541	108	1	the	the	DET
ejpam-6541	108	2	sequence	sequence	NOUN
ejpam-6541	108	3	{	{	PUNCT
ejpam-6541	108	4	an}∞n=1	an}∞n=1	X
ejpam-6541	108	5	in	in	ADP
ejpam-6541	108	6	r	r	NOUN
ejpam-6541	108	7	is	be	AUX
ejpam-6541	108	8	said	say	VERB
ejpam-6541	108	9	to	to	PART
ejpam-6541	108	10	be	be	AUX
ejpam-6541	108	11	hesitant	hesitant	ADJ
ejpam-6541	108	12	fuzzy	fuzzy	ADJ
ejpam-6541	108	13	bounded	bound	VERB
ejpam-6541	108	14	if	if	SCONJ
ejpam-6541	108	15	there	there	PRON
ejpam-6541	108	16	exists	exist	VERB
ejpam-6541	108	17	s∗	s∗	PROPN
ejpam-6541	108	18	∈	∈	PROPN
ejpam-6541	108	19	p	p	X
ejpam-6541	109	1	[	[	X
ejpam-6541	109	2	0	0	NUM
ejpam-6541	109	3	,	,	PUNCT
ejpam-6541	109	4	1	1	NUM
ejpam-6541	109	5	]	]	PUNCT
ejpam-6541	110	1	such	such	ADJ
ejpam-6541	110	2	that	that	SCONJ
ejpam-6541	110	3	hr(an	hr(an	PROPN
ejpam-6541	110	4	,	,	PUNCT
ejpam-6541	110	5	t	t	PROPN
ejpam-6541	110	6	)	)	PUNCT
ejpam-6541	110	7	⊃	⊃	PROPN
ejpam-6541	110	8	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	110	9	,	,	PUNCT
ejpam-6541	110	10	∀t	∀t	PROPN
ejpam-6541	110	11	>	>	X
ejpam-6541	110	12	0	0	X
ejpam-6541	110	13	.	.	PUNCT
ejpam-6541	110	14	theorem	theorem	NOUN
ejpam-6541	110	15	1	1	NUM
ejpam-6541	110	16	.	.	PUNCT
ejpam-6541	111	1	let	let	VERB
ejpam-6541	111	2	(	(	PUNCT
ejpam-6541	111	3	v	v	NOUN
ejpam-6541	111	4	,	,	PUNCT
ejpam-6541	111	5	hv	hv	PROPN
ejpam-6541	111	6	,	,	PUNCT
ejpam-6541	111	7	∗	∗	PROPN
ejpam-6541	111	8	)	)	PUNCT
ejpam-6541	111	9	,	,	PUNCT
ejpam-6541	111	10	(	(	PUNCT
ejpam-6541	111	11	r	r	NOUN
ejpam-6541	111	12	,	,	PUNCT
ejpam-6541	111	13	hr	hr	NOUN
ejpam-6541	111	14	,	,	PUNCT
ejpam-6541	111	15	∗	∗	NOUN
ejpam-6541	111	16	)	)	PUNCT
ejpam-6541	111	17	be	be	VERB
ejpam-6541	111	18	two	two	NUM
ejpam-6541	111	19	hesitant	hesitant	ADJ
ejpam-6541	111	20	fuzzy	fuzzy	ADJ
ejpam-6541	111	21	normed	norme	VERB
ejpam-6541	111	22	linear	linear	PROPN
ejpam-6541	111	23	spaces	space	NOUN
ejpam-6541	111	24	along	along	ADP
ejpam-6541	111	25	with	with	ADP
ejpam-6541	111	26	{	{	PUNCT
ejpam-6541	111	27	v1	v1	NOUN
ejpam-6541	111	28	,	,	PUNCT
ejpam-6541	111	29	v2	v2	PROPN
ejpam-6541	111	30	.	.	PUNCT
ejpam-6541	111	31	.	.	PUNCT
ejpam-6541	111	32	.	.	PUNCT
ejpam-6541	112	1	vn	vn	AUX
ejpam-6541	112	2	}	}	PUNCT
ejpam-6541	112	3	be	be	AUX
ejpam-6541	112	4	linearly	linearly	ADV
ejpam-6541	112	5	independent	independent	ADJ
ejpam-6541	112	6	set	set	NOUN
ejpam-6541	112	7	in	in	ADP
ejpam-6541	112	8	(	(	PUNCT
ejpam-6541	112	9	v	v	NOUN
ejpam-6541	112	10	,	,	PUNCT
ejpam-6541	112	11	hv	hv	PROPN
ejpam-6541	112	12	,	,	PUNCT
ejpam-6541	112	13	∗).then	∗).then	ADV
ejpam-6541	112	14	there	there	PRON
ejpam-6541	112	15	is	be	VERB
ejpam-6541	112	16	∅∗	∅∗	PROPN
ejpam-6541	112	17	⊂	⊂	PROPN
ejpam-6541	112	18	s∗	s∗	PROPN
ejpam-6541	112	19	3	3	NUM
ejpam-6541	112	20	⊂	⊂	NOUN
ejpam-6541	112	21	u∗	u∗	ADJ
ejpam-6541	112	22	such	such	ADJ
ejpam-6541	112	23	that	that	DET
ejpam-6541	112	24	hv	hv	PROPN
ejpam-6541	112	25	[	[	PUNCT
ejpam-6541	112	26	β1v1	β1v1	X
ejpam-6541	112	27	+	+	X
ejpam-6541	112	28	·	·	PUNCT
ejpam-6541	112	29	·	·	PUNCT
ejpam-6541	112	30	·	·	PUNCT
ejpam-6541	113	1	+	+	CCONJ
ejpam-6541	113	2	βnvn	βnvn	ADV
ejpam-6541	113	3	,	,	PUNCT
ejpam-6541	113	4	t	t	X
ejpam-6541	113	5	]	]	PUNCT
ejpam-6541	113	6	⊆	⊆	NUM
ejpam-6541	113	7	s∗	s∗	PROPN
ejpam-6541	113	8	3	3	NUM
ejpam-6541	113	9	∗	∗	NOUN
ejpam-6541	113	10	hr(βj	hr(βj	PROPN
ejpam-6541	113	11	,	,	PUNCT
ejpam-6541	113	12	t	t	PROPN
ejpam-6541	113	13	)	)	PUNCT
ejpam-6541	113	14	for	for	ADP
ejpam-6541	113	15	some	some	PRON
ejpam-6541	113	16	1	1	NUM
ejpam-6541	113	17	≤	≤	NUM
ejpam-6541	113	18	j	j	PROPN
ejpam-6541	113	19	≤	≤	PROPN
ejpam-6541	113	20	n.	n.	NOUN
ejpam-6541	113	21	proof	proof	NOUN
ejpam-6541	113	22	.	.	PUNCT
ejpam-6541	114	1	if	if	SCONJ
ejpam-6541	114	2	this	this	PRON
ejpam-6541	114	3	is	be	AUX
ejpam-6541	114	4	n’t	not	PART
ejpam-6541	114	5	the	the	DET
ejpam-6541	114	6	case	case	NOUN
ejpam-6541	114	7	,	,	PUNCT
ejpam-6541	114	8	we	we	PRON
ejpam-6541	114	9	may	may	AUX
ejpam-6541	114	10	discover	discover	VERB
ejpam-6541	114	11	a	a	DET
ejpam-6541	114	12	sequence	sequence	NOUN
ejpam-6541	114	13	{	{	PUNCT
ejpam-6541	114	14	vm	vm	NOUN
ejpam-6541	114	15	}	}	PUNCT
ejpam-6541	114	16	in	in	ADP
ejpam-6541	114	17	v	v	NUM
ejpam-6541	114	18	where	where	SCONJ
ejpam-6541	114	19	vm	vm	NOUN
ejpam-6541	114	20	=	=	NOUN
ejpam-6541	114	21	β1mv1	β1mv1	PROPN
ejpam-6541	114	22	+	+	PROPN
ejpam-6541	114	23	,	,	PUNCT
ejpam-6541	114	24	.	.	PUNCT
ejpam-6541	114	25	.	.	PUNCT
ejpam-6541	114	26	.	.	PUNCT
ejpam-6541	115	1	,	,	PUNCT
ejpam-6541	115	2	+	+	NOUN
ejpam-6541	115	3	β1nvn	β1nvn	ADJ
ejpam-6541	115	4	so	so	SCONJ
ejpam-6541	115	5	that	that	DET
ejpam-6541	115	6	limn→∞hv	limn→∞hv	PROPN
ejpam-6541	115	7	(	(	PUNCT
ejpam-6541	115	8	vm	vm	PROPN
ejpam-6541	115	9	,	,	PUNCT
ejpam-6541	115	10	t	t	PROPN
ejpam-6541	115	11	)	)	PUNCT
ejpam-6541	115	12	=	=	PUNCT
ejpam-6541	115	13	u∗.	u∗.	PROPN
ejpam-6541	115	14	for	for	ADP
ejpam-6541	115	15	every	every	DET
ejpam-6541	115	16	fixed	fixed	ADJ
ejpam-6541	115	17	j	j	PROPN
ejpam-6541	115	18	,	,	PUNCT
ejpam-6541	115	19	we	we	PRON
ejpam-6541	115	20	now	now	ADV
ejpam-6541	115	21	have	have	VERB
ejpam-6541	115	22	a	a	DET
ejpam-6541	115	23	sequence	sequence	NOUN
ejpam-6541	115	24	βjm	βjm	NOUN
ejpam-6541	115	25	=	=	PUNCT
ejpam-6541	115	26	{	{	PUNCT
ejpam-6541	115	27	βj1	βj1	NOUN
ejpam-6541	115	28	.	.	PUNCT
ejpam-6541	115	29	.	.	PUNCT
ejpam-6541	116	1	.	.	PUNCT
ejpam-6541	117	1	,	,	PUNCT
ejpam-6541	117	2	βjm	βjm	INTJ
ejpam-6541	117	3	,	,	PUNCT
ejpam-6541	117	4	.	.	PUNCT
ejpam-6541	117	5	.	.	PUNCT
ejpam-6541	118	1	.	.	PUNCT
ejpam-6541	118	2	,	,	PUNCT
ejpam-6541	118	3	)	)	PUNCT
ejpam-6541	118	4	represents	represent	VERB
ejpam-6541	118	5	hesitant	hesitant	ADJ
ejpam-6541	118	6	fuzzy	fuzzy	PROPN
ejpam-6541	118	7	bounded	bound	VERB
ejpam-6541	118	8	,	,	PUNCT
ejpam-6541	118	9	because	because	SCONJ
ejpam-6541	118	10	if	if	SCONJ
ejpam-6541	118	11	the	the	DET
ejpam-6541	118	12	sequence	sequence	NOUN
ejpam-6541	118	13	{	{	PUNCT
ejpam-6541	118	14	an}∞n=1	an}∞n=1	X
ejpam-6541	118	15	in	in	ADP
ejpam-6541	118	16	r	r	NOUN
ejpam-6541	118	17	is	be	AUX
ejpam-6541	118	18	hesitant	hesitant	ADJ
ejpam-6541	118	19	fuzzy	fuzzy	ADJ
ejpam-6541	118	20	approaches	approach	VERB
ejpam-6541	118	21	the	the	DET
ejpam-6541	118	22	limit	limit	NOUN
ejpam-6541	119	1	′a′	′a′	INTJ
ejpam-6541	119	2	then	then	ADV
ejpam-6541	119	3	it	it	PRON
ejpam-6541	119	4	is	be	AUX
ejpam-6541	119	5	hesitant	hesitant	ADJ
ejpam-6541	120	1	fuzzy	fuzzy	ADJ
ejpam-6541	120	2	bounded	bound	VERB
ejpam-6541	120	3	.	.	PUNCT
ejpam-6541	121	1	considering	consider	VERB
ejpam-6541	121	2	∅∗	∅∗	PROPN
ejpam-6541	121	3	⊆	⊆	NUM
ejpam-6541	121	4	hr(βjm	hr(βjm	NOUN
ejpam-6541	121	5	,	,	PUNCT
ejpam-6541	121	6	t	t	PROPN
ejpam-6541	121	7	)	)	PUNCT
ejpam-6541	121	8	⊆	⊆	NUM
ejpam-6541	121	9	u∗	u∗	ADJ
ejpam-6541	121	10	,	,	PUNCT
ejpam-6541	121	11	so	so	CCONJ
ejpam-6541	121	12	{	{	PUNCT
ejpam-6541	121	13	βjm	βjm	NOUN
ejpam-6541	121	14	}	}	PUNCT
ejpam-6541	121	15	k.	k.	PROPN
ejpam-6541	121	16	kavitha	kavitha	PROPN
ejpam-6541	121	17	,	,	PUNCT
ejpam-6541	121	18	p.	p.	PROPN
ejpam-6541	121	19	muralikrishna	muralikrishna	PROPN
ejpam-6541	121	20	/	/	SYM
ejpam-6541	121	21	eur	eur	PROPN
ejpam-6541	121	22	.	.	PUNCT
ejpam-6541	122	1	j.	j.	PROPN
ejpam-6541	122	2	pure	pure	PROPN
ejpam-6541	122	3	appl	appl	PROPN
ejpam-6541	122	4	.	.	PROPN
ejpam-6541	122	5	math	math	PROPN
ejpam-6541	122	6	,	,	PUNCT
ejpam-6541	122	7	18	18	NUM
ejpam-6541	122	8	(	(	PUNCT
ejpam-6541	122	9	4	4	NUM
ejpam-6541	122	10	)	)	PUNCT
ejpam-6541	122	11	(	(	PUNCT
ejpam-6541	122	12	2025	2025	NUM
ejpam-6541	122	13	)	)	PUNCT
ejpam-6541	122	14	,	,	PUNCT
ejpam-6541	122	15	6541	6541	NUM
ejpam-6541	122	16	5	5	NUM
ejpam-6541	122	17	of	of	ADP
ejpam-6541	122	18	14	14	NUM
ejpam-6541	122	19	has	have	VERB
ejpam-6541	122	20	a	a	DET
ejpam-6541	122	21	convergent	convergent	NOUN
ejpam-6541	122	22	subsequence	subsequence	NOUN
ejpam-6541	122	23	.	.	PUNCT
ejpam-6541	123	1	for	for	ADP
ejpam-6541	123	2	every	every	DET
ejpam-6541	123	3	1	1	NUM
ejpam-6541	123	4	≤	≤	NUM
ejpam-6541	123	5	j	j	PROPN
ejpam-6541	123	6	≤	≤	PROPN
ejpam-6541	123	7	n.	n.	NOUN
ejpam-6541	123	8	,	,	PUNCT
ejpam-6541	123	9	let	let	VERB
ejpam-6541	123	10	βj	βj	PRON
ejpam-6541	123	11	represent	represent	VERB
ejpam-6541	123	12	the	the	DET
ejpam-6541	123	13	limit	limit	NOUN
ejpam-6541	123	14	of	of	ADP
ejpam-6541	123	15	the	the	DET
ejpam-6541	123	16	subsequence	subsequence	NOUN
ejpam-6541	123	17	{	{	PUNCT
ejpam-6541	123	18	βjm	βjm	NOUN
ejpam-6541	123	19	}	}	PUNCT
ejpam-6541	123	20	.	.	PUNCT
ejpam-6541	124	1	an	an	DET
ejpam-6541	124	2	analogous	analogous	ADJ
ejpam-6541	124	3	subsequence	subsequence	NOUN
ejpam-6541	124	4	of	of	ADP
ejpam-6541	124	5	scalars	scalar	NOUN
ejpam-6541	124	6	βjm	βjm	NOUN
ejpam-6541	124	7	converges	converge	NOUN
ejpam-6541	124	8	for	for	ADP
ejpam-6541	124	9	βj	βj	PRON
ejpam-6541	124	10	for	for	ADP
ejpam-6541	124	11	every	every	DET
ejpam-6541	124	12	1	1	NUM
ejpam-6541	124	13	≤	≤	NUM
ejpam-6541	124	14	j	j	PROPN
ejpam-6541	124	15	≤	≤	PROPN
ejpam-6541	124	16	n.	n.	NOUN
ejpam-6541	124	17	,	,	PUNCT
ejpam-6541	124	18	where	where	SCONJ
ejpam-6541	124	19	{	{	PUNCT
ejpam-6541	124	20	vjm	vjm	NOUN
ejpam-6541	124	21	}	}	PUNCT
ejpam-6541	124	22	represents	represent	VERB
ejpam-6541	124	23	the	the	DET
ejpam-6541	124	24	corresponding	corresponding	ADJ
ejpam-6541	124	25	subsequence	subsequence	NOUN
ejpam-6541	124	26	of	of	ADP
ejpam-6541	124	27	{	{	PUNCT
ejpam-6541	124	28	vm	vm	NOUN
ejpam-6541	124	29	}	}	PUNCT
ejpam-6541	124	30	.	.	PUNCT
ejpam-6541	125	1	now	now	ADV
ejpam-6541	125	2	,	,	PUNCT
ejpam-6541	125	3	put	put	VERB
ejpam-6541	125	4	v	v	NOUN
ejpam-6541	125	5	=	=	PUNCT
ejpam-6541	125	6	∑∞	∑∞	NOUN
ejpam-6541	126	1	j=1	j=1	NOUN
ejpam-6541	127	1	βjvj	βjvj	PROPN
ejpam-6541	127	2	then	then	ADV
ejpam-6541	127	3	{	{	PUNCT
ejpam-6541	127	4	vm	vm	NOUN
ejpam-6541	127	5	}	}	PUNCT
ejpam-6541	127	6	has	have	VERB
ejpam-6541	127	7	a	a	DET
ejpam-6541	127	8	subsequence	subsequence	NOUN
ejpam-6541	127	9	{	{	PUNCT
ejpam-6541	127	10	vjm	vjm	PROPN
ejpam-6541	127	11	}	}	PUNCT
ejpam-6541	127	12	converges	converge	NOUN
ejpam-6541	127	13	to	to	ADP
ejpam-6541	127	14	v	v	NOUN
ejpam-6541	127	15	,	,	PUNCT
ejpam-6541	127	16	since	since	SCONJ
ejpam-6541	127	17	{	{	PUNCT
ejpam-6541	127	18	v1	v1	NOUN
ejpam-6541	127	19	,	,	PUNCT
ejpam-6541	127	20	v2	v2	NOUN
ejpam-6541	127	21	,	,	PUNCT
ejpam-6541	127	22	.	.	PUNCT
ejpam-6541	127	23	.	.	PUNCT
ejpam-6541	128	1	.	.	PUNCT
ejpam-6541	129	1	,	,	PUNCT
ejpam-6541	129	2	vn	vn	AUX
ejpam-6541	129	3	}	}	PUNCT
ejpam-6541	129	4	is	be	AUX
ejpam-6541	129	5	linearly	linearly	ADV
ejpam-6541	129	6	independen	independen	ADJ
ejpam-6541	129	7	set	set	VERB
ejpam-6541	129	8	so	so	ADV
ejpam-6541	129	9	v	v	ADP
ejpam-6541	129	10	̸=	̸=	PROPN
ejpam-6541	129	11	0	0	NUM
ejpam-6541	129	12	.	.	PUNCT
ejpam-6541	130	1	now	now	ADV
ejpam-6541	130	2	{	{	PUNCT
ejpam-6541	130	3	vjm	vjm	PROPN
ejpam-6541	130	4	}	}	PUNCT
ejpam-6541	130	5	→	→	SYM
ejpam-6541	130	6	v	v	X
ejpam-6541	130	7	=	=	NOUN
ejpam-6541	130	8	⇒	⇒	VERB
ejpam-6541	130	9	the	the	DET
ejpam-6541	130	10	fuzzy	fuzzy	ADJ
ejpam-6541	130	11	continuity	continuity	NOUN
ejpam-6541	130	12	of	of	ADP
ejpam-6541	130	13	the	the	DET
ejpam-6541	130	14	hesitant	hesitant	ADJ
ejpam-6541	130	15	fuzzy	fuzzy	ADJ
ejpam-6541	130	16	norm	norm	NOUN
ejpam-6541	130	17	is	be	AUX
ejpam-6541	130	18	hv(vjm	hv(vjm	PROPN
ejpam-6541	130	19	,	,	PUNCT
ejpam-6541	130	20	v	v	NOUN
ejpam-6541	130	21	)	)	PUNCT
ejpam-6541	130	22	.	.	PUNCT
ejpam-6541	131	1	but	but	CCONJ
ejpam-6541	131	2	,	,	PUNCT
ejpam-6541	131	3	h(vm	h(vm	PROPN
ejpam-6541	131	4	,	,	PUNCT
ejpam-6541	131	5	1	1	NUM
ejpam-6541	131	6	)	)	PUNCT
ejpam-6541	131	7	→	→	PUNCT
ejpam-6541	131	8	u∗	u∗	VERB
ejpam-6541	131	9	by	by	ADP
ejpam-6541	131	10	our	our	PRON
ejpam-6541	131	11	assumption	assumption	NOUN
ejpam-6541	131	12	and	and	CCONJ
ejpam-6541	131	13	{	{	PUNCT
ejpam-6541	131	14	vjm	vjm	PROPN
ejpam-6541	131	15	}	}	PUNCT
ejpam-6541	131	16	is	be	AUX
ejpam-6541	131	17	a	a	DET
ejpam-6541	131	18	subsequence	subsequence	NOUN
ejpam-6541	131	19	of	of	ADP
ejpam-6541	131	20	{	{	PUNCT
ejpam-6541	131	21	vm	vm	NOUN
ejpam-6541	131	22	}	}	PUNCT
ejpam-6541	131	23	.	.	PUNCT
ejpam-6541	132	1	thus	thus	ADV
ejpam-6541	132	2	hv(vjm	hv(vjm	PROPN
ejpam-6541	132	3	,	,	PUNCT
ejpam-6541	132	4	v	v	NOUN
ejpam-6541	132	5	)	)	PUNCT
ejpam-6541	132	6	→	→	SYM
ejpam-6541	132	7	u∗.	u∗.	PROPN
ejpam-6541	132	8	hence	hence	ADV
ejpam-6541	132	9	h(v	h(v	PROPN
ejpam-6541	132	10	,	,	PUNCT
ejpam-6541	132	11	t	t	PROPN
ejpam-6541	132	12	)	)	PUNCT
ejpam-6541	132	13	=	=	SYM
ejpam-6541	132	14	u∗.	u∗.	PROPN
ejpam-6541	132	15	so	so	ADV
ejpam-6541	132	16	,	,	PUNCT
ejpam-6541	132	17	v	v	NOUN
ejpam-6541	132	18	=	=	SYM
ejpam-6541	132	19	0	0	PROPN
ejpam-6541	132	20	.	.	PUNCT
ejpam-6541	133	1	this	this	PRON
ejpam-6541	133	2	contradicts	contradict	VERB
ejpam-6541	133	3	v	v	ADP
ejpam-6541	133	4	̸=	̸=	PROPN
ejpam-6541	133	5	0	0	NUM
ejpam-6541	133	6	.	.	PUNCT
ejpam-6541	134	1	theorem	theorem	NOUN
ejpam-6541	134	2	2	2	NUM
ejpam-6541	134	3	.	.	X
ejpam-6541	135	1	consider	consider	VERB
ejpam-6541	135	2	a	a	DET
ejpam-6541	135	3	hesitant	hesitant	ADJ
ejpam-6541	135	4	fuzzy	fuzzy	ADJ
ejpam-6541	135	5	normed	normed	ADJ
ejpam-6541	135	6	space	space	NOUN
ejpam-6541	135	7	(	(	PUNCT
ejpam-6541	135	8	v	v	NOUN
ejpam-6541	135	9	,	,	PUNCT
ejpam-6541	135	10	hv	hv	PROPN
ejpam-6541	135	11	,	,	PUNCT
ejpam-6541	135	12	∗	∗	PROPN
ejpam-6541	135	13	)	)	PUNCT
ejpam-6541	135	14	.	.	PUNCT
ejpam-6541	136	1	w	w	PROPN
ejpam-6541	136	2	is	be	AUX
ejpam-6541	136	3	complete	complete	ADJ
ejpam-6541	136	4	if	if	SCONJ
ejpam-6541	136	5	it	it	PRON
ejpam-6541	136	6	is	be	AUX
ejpam-6541	136	7	a	a	DET
ejpam-6541	136	8	finite	finite	ADJ
ejpam-6541	136	9	-	-	ADJ
ejpam-6541	136	10	dimensional	dimensional	ADJ
ejpam-6541	136	11	subspace	subspace	NOUN
ejpam-6541	136	12	of	of	ADP
ejpam-6541	136	13	v	v	NOUN
ejpam-6541	136	14	.	.	PUNCT
ejpam-6541	137	1	proof	proof	NOUN
ejpam-6541	137	2	.	.	PUNCT
ejpam-6541	138	1	assume	assume	VERB
ejpam-6541	138	2	that	that	SCONJ
ejpam-6541	138	3	the	the	DET
ejpam-6541	138	4	sequence	sequence	NOUN
ejpam-6541	138	5	{	{	PUNCT
ejpam-6541	138	6	vm	vm	NOUN
ejpam-6541	138	7	}	}	PUNCT
ejpam-6541	138	8	is	be	AUX
ejpam-6541	138	9	cauchy	cauchy	NOUN
ejpam-6541	138	10	in	in	ADP
ejpam-6541	138	11	w.	w.	PROPN
ejpam-6541	138	12	assume	assume	VERB
ejpam-6541	138	13	dim	dim	ADJ
ejpam-6541	138	14	w	w	NOUN
ejpam-6541	138	15	=	=	PUNCT
ejpam-6541	138	16	n	n	PROPN
ejpam-6541	138	17	and	and	CCONJ
ejpam-6541	138	18	b	b	X
ejpam-6541	138	19	=	=	SYM
ejpam-6541	138	20	{	{	PUNCT
ejpam-6541	138	21	w1	w1	NOUN
ejpam-6541	138	22	,	,	PUNCT
ejpam-6541	138	23	w2	w2	NOUN
ejpam-6541	138	24	,	,	PUNCT
ejpam-6541	138	25	.	.	PUNCT
ejpam-6541	138	26	.	.	PUNCT
ejpam-6541	139	1	.	.	PUNCT
ejpam-6541	140	1	,	,	PUNCT
ejpam-6541	140	2	wn	wn	PROPN
ejpam-6541	140	3	}	}	PUNCT
ejpam-6541	140	4	become	become	VERB
ejpam-6541	140	5	any	any	DET
ejpam-6541	140	6	basis	basis	NOUN
ejpam-6541	140	7	to	to	ADP
ejpam-6541	140	8	w.	w.	NOUN
ejpam-6541	140	9	after	after	ADP
ejpam-6541	140	10	that	that	PRON
ejpam-6541	140	11	,	,	PUNCT
ejpam-6541	140	12	every	every	DET
ejpam-6541	140	13	vm	vm	PROPN
ejpam-6541	140	14	is	be	AUX
ejpam-6541	140	15	represented	represent	VERB
ejpam-6541	140	16	in	in	ADP
ejpam-6541	140	17	a	a	DET
ejpam-6541	140	18	distinctive	distinctive	ADJ
ejpam-6541	140	19	way	way	NOUN
ejpam-6541	140	20	as	as	ADP
ejpam-6541	140	21	vm	vm	NOUN
ejpam-6541	140	22	=	=	NOUN
ejpam-6541	140	23	γ1mw1	γ1mw1	PROPN
ejpam-6541	140	24	+	+	PROPN
ejpam-6541	140	25	,	,	PUNCT
ejpam-6541	140	26	.	.	PUNCT
ejpam-6541	140	27	.	.	PUNCT
ejpam-6541	140	28	.	.	PUNCT
ejpam-6541	141	1	,	,	PUNCT
ejpam-6541	142	1	+	+	NOUN
ejpam-6541	142	2	γnmwn	γnmwn	NOUN
ejpam-6541	142	3	.	.	PUNCT
ejpam-6541	143	1	given	give	VERB
ejpam-6541	143	2	that	that	SCONJ
ejpam-6541	143	3	the	the	DET
ejpam-6541	143	4	sequence	sequence	NOUN
ejpam-6541	143	5	{	{	PUNCT
ejpam-6541	143	6	vm	vm	NOUN
ejpam-6541	143	7	}	}	PUNCT
ejpam-6541	143	8	is	be	AUX
ejpam-6541	143	9	cauchy	cauchy	NOUN
ejpam-6541	143	10	,	,	PUNCT
ejpam-6541	143	11	for	for	ADP
ejpam-6541	143	12	any	any	DET
ejpam-6541	143	13	m	m	NOUN
ejpam-6541	143	14	,	,	PUNCT
ejpam-6541	143	15	n	n	PRON
ejpam-6541	143	16	≥	≥	NOUN
ejpam-6541	143	17	n.	n.	NOUN
ejpam-6541	143	18	now	now	ADV
ejpam-6541	143	19	by	by	ADP
ejpam-6541	143	20	theorem	theorem	NOUN
ejpam-6541	143	21	1	1	NUM
ejpam-6541	143	22	,	,	PUNCT
ejpam-6541	143	23	we	we	PRON
ejpam-6541	143	24	possess	possess	VERB
ejpam-6541	143	25	some	some	PRON
ejpam-6541	143	26	∅∗	∅∗	VERB
ejpam-6541	144	1	⊂	⊂	PROPN
ejpam-6541	144	2	s∗	s∗	VERB
ejpam-6541	144	3	3	3	NUM
ejpam-6541	144	4	⊂	⊂	NOUN
ejpam-6541	144	5	u∗	u∗	VERB
ejpam-6541	144	6	such	such	ADJ
ejpam-6541	144	7	that	that	DET
ejpam-6541	144	8	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	144	9	3	3	NUM
ejpam-6541	144	10	⊂	⊂	PROPN
ejpam-6541	144	11	hv(vm	hv(vm	VERB
ejpam-6541	144	12	−	−	PROPN
ejpam-6541	145	1	vn	vn	PROPN
ejpam-6541	145	2	,	,	PUNCT
ejpam-6541	145	3	t	t	PROPN
ejpam-6541	145	4	)	)	PUNCT
ejpam-6541	145	5	=	=	SYM
ejpam-6541	145	6	hv	hv	PROPN
ejpam-6541	145	7	(	(	PUNCT
ejpam-6541	145	8	∑n	∑n	PROPN
ejpam-6541	145	9	j=1(γjm	j=1(γjm	PROPN
ejpam-6541	146	1	−	−	PROPN
ejpam-6541	146	2	γjn)wj	γjn)wj	INTJ
ejpam-6541	146	3	,	,	PUNCT
ejpam-6541	146	4	t	t	X
ejpam-6541	146	5	]	]	PUNCT
ejpam-6541	146	6	)	)	PUNCT
ejpam-6541	147	1	⊆	⊆	NUM
ejpam-6541	147	2	s∗	s∗	PROPN
ejpam-6541	147	3	3	3	NUM
ejpam-6541	147	4	∩	∩	ADJ
ejpam-6541	147	5	hr(γjm	hr(γjm	NOUN
ejpam-6541	147	6	−	−	PROPN
ejpam-6541	147	7	γjn	γjn	NOUN
ejpam-6541	147	8	,	,	PUNCT
ejpam-6541	147	9	t	t	NOUN
ejpam-6541	147	10	)	)	PUNCT
ejpam-6541	147	11	=	=	NOUN
ejpam-6541	147	12	⇒	⇒	NOUN
ejpam-6541	147	13	hr(γjm	hr(γjm	NOUN
ejpam-6541	147	14	−	−	PROPN
ejpam-6541	147	15	γjn	γjn	NOUN
ejpam-6541	147	16	,	,	PUNCT
ejpam-6541	147	17	t	t	PROPN
ejpam-6541	147	18	)	)	PUNCT
ejpam-6541	147	19	⊃	⊃	NOUN
ejpam-6541	148	1	[	[	X
ejpam-6541	148	2	u∗	u∗	NOUN
ejpam-6541	148	3	∩	∩	NOUN
ejpam-6541	148	4	s∗	s∗	VERB
ejpam-6541	148	5	5	5	NUM
ejpam-6541	148	6	]	]	PUNCT
ejpam-6541	148	7	\s∗	\s∗	ADP
ejpam-6541	148	8	3	3	NUM
ejpam-6541	148	9	.	.	PUNCT
ejpam-6541	149	1	the	the	DET
ejpam-6541	149	2	following	following	NOUN
ejpam-6541	149	3	demonstrates	demonstrate	VERB
ejpam-6541	149	4	that	that	SCONJ
ejpam-6541	149	5	(	(	PUNCT
ejpam-6541	149	6	γjm	γjm	ADJ
ejpam-6541	149	7	)	)	PUNCT
ejpam-6541	149	8	=	=	SYM
ejpam-6541	149	9	(	(	PUNCT
ejpam-6541	149	10	γj1	γj1	ADJ
ejpam-6541	149	11	,	,	PUNCT
ejpam-6541	149	12	γj2	γj2	NOUN
ejpam-6541	149	13	,	,	PUNCT
ejpam-6541	149	14	.	.	PUNCT
ejpam-6541	149	15	.	.	PUNCT
ejpam-6541	150	1	.	.	PUNCT
ejpam-6541	151	1	,	,	PUNCT
ejpam-6541	151	2	)	)	PUNCT
ejpam-6541	151	3	is	be	AUX
ejpam-6541	151	4	a	a	DET
ejpam-6541	151	5	cauchy	cauchy	ADJ
ejpam-6541	151	6	sequence	sequence	NOUN
ejpam-6541	151	7	in	in	ADP
ejpam-6541	151	8	r	r	NOUN
ejpam-6541	151	9	or	or	CCONJ
ejpam-6541	151	10	c	c	NOUN
ejpam-6541	151	11	,	,	PUNCT
ejpam-6541	151	12	thus	thus	ADV
ejpam-6541	151	13	γjm	γjm	ADJ
ejpam-6541	151	14	→	→	SYM
ejpam-6541	151	15	γj	γj	NOUN
ejpam-6541	151	16	for	for	ADP
ejpam-6541	151	17	each	each	DET
ejpam-6541	151	18	1	1	NUM
ejpam-6541	151	19	≤	≤	NUM
ejpam-6541	151	20	j	j	PROPN
ejpam-6541	151	21	≤	≤	PROPN
ejpam-6541	151	22	n.	n.	PROPN
ejpam-6541	151	23	let	let	VERB
ejpam-6541	151	24	a	a	DET
ejpam-6541	151	25	=	=	SYM
ejpam-6541	151	26	∑	∑	PROPN
ejpam-6541	151	27	j=1	j=1	PROPN
ejpam-6541	151	28	γjwj	γjwj	ADV
ejpam-6541	151	29	,	,	PUNCT
ejpam-6541	151	30	clearly	clearly	ADV
ejpam-6541	151	31	a	a	DET
ejpam-6541	151	32	∈	∈	PROPN
ejpam-6541	151	33	w.	w.	NOUN
ejpam-6541	151	34	also	also	ADV
ejpam-6541	151	35	now	now	ADV
ejpam-6541	151	36	for	for	ADP
ejpam-6541	151	37	all	all	DET
ejpam-6541	151	38	m	m	PROPN
ejpam-6541	151	39	>	>	X
ejpam-6541	151	40	n	n	CCONJ
ejpam-6541	151	41	,	,	PUNCT
ejpam-6541	151	42	hv(vm	hv(vm	VERB
ejpam-6541	151	43	−	−	PROPN
ejpam-6541	151	44	v	v	PROPN
ejpam-6541	151	45	,	,	PUNCT
ejpam-6541	151	46	t	t	PROPN
ejpam-6541	151	47	)	)	PUNCT
ejpam-6541	152	1	=	=	SYM
ejpam-6541	152	2	hv	hv	PROPN
ejpam-6541	152	3	(	(	PUNCT
ejpam-6541	152	4	∑n	∑n	PROPN
ejpam-6541	152	5	j=1(γjm	j=1(γjm	PROPN
ejpam-6541	152	6	−	−	PROPN
ejpam-6541	153	1	γjn)wj	γjn)wj	INTJ
ejpam-6541	153	2	,	,	PUNCT
ejpam-6541	153	3	t	t	PROPN
ejpam-6541	153	4	)	)	PUNCT
ejpam-6541	153	5	⊇	⊇	PROPN
ejpam-6541	153	6	hv	hv	PROPN
ejpam-6541	153	7	(	(	PUNCT
ejpam-6541	153	8	w1	w1	PROPN
ejpam-6541	153	9	,	,	PUNCT
ejpam-6541	153	10	t	t	PROPN
ejpam-6541	153	11	n|γ1m−γ1|	n|γ1m−γ1|	PROPN
ejpam-6541	153	12	)	)	PUNCT
ejpam-6541	153	13	∩	∩	PROPN
ejpam-6541	153	14	hv	hv	PROPN
ejpam-6541	153	15	(	(	PUNCT
ejpam-6541	153	16	w1	w1	PROPN
ejpam-6541	153	17	,	,	PUNCT
ejpam-6541	153	18	t	t	PROPN
ejpam-6541	153	19	n|γ2m−γ2|	n|γ2m−γ2|	PROPN
ejpam-6541	153	20	)	)	PUNCT
ejpam-6541	153	21	∩	∩	NOUN
ejpam-6541	153	22	,	,	PUNCT
ejpam-6541	153	23	.	.	PUNCT
ejpam-6541	153	24	.	.	PUNCT
ejpam-6541	153	25	.	.	PUNCT
ejpam-6541	154	1	,	,	PUNCT
ejpam-6541	154	2	∩	∩	PROPN
ejpam-6541	154	3	hv	hv	PROPN
ejpam-6541	154	4	(	(	PUNCT
ejpam-6541	154	5	w1	w1	PROPN
ejpam-6541	154	6	,	,	PUNCT
ejpam-6541	154	7	t	t	PROPN
ejpam-6541	154	8	n|γnm−γn|	n|γnm−γn|	PUNCT
ejpam-6541	154	9	)	)	PUNCT
ejpam-6541	154	10	hv(vm	hv(vm	VERB
ejpam-6541	154	11	−	−	PROPN
ejpam-6541	154	12	v	v	PROPN
ejpam-6541	154	13	,	,	PUNCT
ejpam-6541	154	14	t	t	PROPN
ejpam-6541	154	15	)	)	PUNCT
ejpam-6541	154	16	⊇	⊇	NOUN
ejpam-6541	154	17	(	(	PUNCT
ejpam-6541	154	18	u∗\s∗31	u∗\s∗31	ADJ
ejpam-6541	154	19	)	)	PUNCT
ejpam-6541	154	20	∩	∩	NOUN
ejpam-6541	154	21	(	(	PUNCT
ejpam-6541	154	22	u∗\s∗32	u∗\s∗32	NOUN
ejpam-6541	154	23	)	)	PUNCT
ejpam-6541	154	24	∩	∩	NOUN
ejpam-6541	154	25	,	,	PUNCT
ejpam-6541	154	26	.	.	PUNCT
ejpam-6541	154	27	.	.	PUNCT
ejpam-6541	154	28	.	.	PUNCT
ejpam-6541	155	1	,	,	PUNCT
ejpam-6541	155	2	(	(	PUNCT
ejpam-6541	155	3	u∗\s∗3n	u∗\s∗3n	PROPN
ejpam-6541	155	4	)	)	PUNCT
ejpam-6541	155	5	.	.	PUNCT
ejpam-6541	156	1	where	where	SCONJ
ejpam-6541	156	2	hv	hv	PROPN
ejpam-6541	156	3	(	(	PUNCT
ejpam-6541	156	4	wj	wj	PROPN
ejpam-6541	156	5	,	,	PUNCT
ejpam-6541	156	6	t	t	PROPN
ejpam-6541	156	7	n|γjm−γj	n|γjm−γj	NOUN
ejpam-6541	156	8	|	|	ADV
ejpam-6541	156	9	)	)	PUNCT
ejpam-6541	157	1	=	=	SYM
ejpam-6541	157	2	(	(	PUNCT
ejpam-6541	157	3	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	157	4	3j)for	3j)for	VERB
ejpam-6541	157	5	some	some	PRON
ejpam-6541	157	6	∅∗	∅∗	ADP
ejpam-6541	157	7	⊂	⊂	PROPN
ejpam-6541	157	8	(	(	PUNCT
ejpam-6541	157	9	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	157	10	3j	3j	NUM
ejpam-6541	157	11	)	)	PUNCT
ejpam-6541	158	1	⊂	⊂	PROPN
ejpam-6541	158	2	u∗	u∗	PROPN
ejpam-6541	158	3	,	,	PUNCT
ejpam-6541	158	4	j	j	PROPN
ejpam-6541	158	5	=	=	SYM
ejpam-6541	158	6	1	1	NUM
ejpam-6541	158	7	,	,	PUNCT
ejpam-6541	158	8	2	2	NUM
ejpam-6541	158	9	,	,	PUNCT
ejpam-6541	158	10	.	.	PUNCT
ejpam-6541	158	11	.	.	PUNCT
ejpam-6541	158	12	.	.	PUNCT
ejpam-6541	159	1	,	,	PUNCT
ejpam-6541	159	2	n.	n.	PROPN
ejpam-6541	159	3	let	let	VERB
ejpam-6541	159	4	(	(	PUNCT
ejpam-6541	159	5	u∗\s∗31	u∗\s∗31	ADJ
ejpam-6541	159	6	)	)	PUNCT
ejpam-6541	159	7	∩	∩	NOUN
ejpam-6541	159	8	(	(	PUNCT
ejpam-6541	159	9	u∗\s∗32)∩	u∗\s∗32)∩	ADJ
ejpam-6541	159	10	,	,	PUNCT
ejpam-6541	159	11	.	.	PUNCT
ejpam-6541	159	12	.	.	PUNCT
ejpam-6541	159	13	.	.	PUNCT
ejpam-6541	160	1	,	,	PUNCT
ejpam-6541	160	2	∩	∩	NOUN
ejpam-6541	160	3	(	(	PUNCT
ejpam-6541	160	4	u∗\s∗3n	u∗\s∗3n	PROPN
ejpam-6541	160	5	)	)	PUNCT
ejpam-6541	160	6	⊃	⊃	PROPN
ejpam-6541	160	7	(	(	PUNCT
ejpam-6541	160	8	u∗\s∗4	u∗\s∗4	NOUN
ejpam-6541	160	9	)	)	PUNCT
ejpam-6541	160	10	.	.	PUNCT
ejpam-6541	161	1	so	so	ADV
ejpam-6541	161	2	,	,	PUNCT
ejpam-6541	161	3	hv(vm	hv(vm	PROPN
ejpam-6541	161	4	−	−	PROPN
ejpam-6541	161	5	v	v	PROPN
ejpam-6541	161	6	,	,	PUNCT
ejpam-6541	161	7	t	t	PROPN
ejpam-6541	161	8	)	)	PUNCT
ejpam-6541	161	9	⊃	⊃	PROPN
ejpam-6541	161	10	(	(	PUNCT
ejpam-6541	161	11	u∗\s∗4	u∗\s∗4	PROPN
ejpam-6541	161	12	)	)	PUNCT
ejpam-6541	161	13	where	where	SCONJ
ejpam-6541	161	14	s∗4	s∗4	ADJ
ejpam-6541	161	15	∈	∈	PROPN
ejpam-6541	161	16	p[0	p[0	NOUN
ejpam-6541	161	17	,	,	PUNCT
ejpam-6541	161	18	1],∀m	1],∀m	NUM
ejpam-6541	161	19	>	>	X
ejpam-6541	161	20	n.	n.	NOUN
ejpam-6541	161	21	hence	hence	ADV
ejpam-6541	161	22	vm	vm	PROPN
ejpam-6541	161	23	→	→	PUNCT
ejpam-6541	161	24	v.	v.	CCONJ
ejpam-6541	161	25	theorem	theorem	ADJ
ejpam-6541	161	26	3	3	X
ejpam-6541	161	27	.	.	NOUN
ejpam-6541	161	28	fuzzy	fuzzy	ADJ
ejpam-6541	161	29	normed	normed	ADJ
ejpam-6541	161	30	space	space	NOUN
ejpam-6541	161	31	(	(	PUNCT
ejpam-6541	161	32	v	v	NOUN
ejpam-6541	161	33	,	,	PUNCT
ejpam-6541	161	34	h	h	NOUN
ejpam-6541	161	35	,	,	PUNCT
ejpam-6541	161	36	∗	∗	NOUN
ejpam-6541	161	37	)	)	PUNCT
ejpam-6541	161	38	is	be	AUX
ejpam-6541	161	39	compact	compact	ADJ
ejpam-6541	161	40	if	if	SCONJ
ejpam-6541	162	1	and	and	CCONJ
ejpam-6541	162	2	only	only	ADV
ejpam-6541	162	3	if	if	SCONJ
ejpam-6541	162	4	each	each	PRON
ejpam-6541	162	5	{	{	PUNCT
ejpam-6541	162	6	vn	vn	NOUN
ejpam-6541	162	7	}	}	PUNCT
ejpam-6541	162	8	at	at	ADP
ejpam-6541	162	9	v	v	NOUN
ejpam-6541	162	10	includes	include	VERB
ejpam-6541	162	11	{	{	PUNCT
ejpam-6541	162	12	vnk	vnk	NOUN
ejpam-6541	162	13	}	}	PUNCT
ejpam-6541	162	14	using	use	VERB
ejpam-6541	162	15	{	{	PUNCT
ejpam-6541	162	16	vnk	vnk	NOUN
ejpam-6541	162	17	}	}	PUNCT
ejpam-6541	162	18	→	→	PUNCT
ejpam-6541	162	19	v.	v.	ADP
ejpam-6541	162	20	4	4	NUM
ejpam-6541	162	21	.	.	PUNCT
ejpam-6541	163	1	finite	finite	VERB
ejpam-6541	163	2	dimensional	dimensional	ADJ
ejpam-6541	163	3	intuitionistic	intuitionistic	ADJ
ejpam-6541	163	4	hesitant	hesitant	ADJ
ejpam-6541	163	5	fuzzy	fuzzy	ADJ
ejpam-6541	163	6	normed	normed	PROPN
ejpam-6541	163	7	linear	linear	PROPN
ejpam-6541	163	8	spaces	space	VERB
ejpam-6541	163	9	the	the	DET
ejpam-6541	163	10	completeness	completeness	NOUN
ejpam-6541	163	11	along	along	ADP
ejpam-6541	163	12	with	with	ADP
ejpam-6541	163	13	compactness	compactness	NOUN
ejpam-6541	163	14	features	feature	NOUN
ejpam-6541	163	15	regarding	regard	VERB
ejpam-6541	163	16	intuitionistic	intuitionistic	ADJ
ejpam-6541	163	17	hesitant	hesitant	ADJ
ejpam-6541	163	18	fuzzy	fuzzy	ADJ
ejpam-6541	163	19	normed	normed	PROPN
ejpam-6541	163	20	linear	linear	PROPN
ejpam-6541	163	21	spaces	space	NOUN
ejpam-6541	163	22	with	with	ADP
ejpam-6541	163	23	finite	finite	ADJ
ejpam-6541	163	24	dimensions	dimension	NOUN
ejpam-6541	163	25	are	be	AUX
ejpam-6541	163	26	examined	examine	VERB
ejpam-6541	163	27	in	in	ADP
ejpam-6541	163	28	this	this	DET
ejpam-6541	163	29	section	section	NOUN
ejpam-6541	163	30	.	.	PUNCT
ejpam-6541	164	1	definition	definition	NOUN
ejpam-6541	164	2	13	13	NUM
ejpam-6541	164	3	.	.	PUNCT
ejpam-6541	165	1	intuitionistic	intuitionistic	ADJ
ejpam-6541	165	2	fuzzy	fuzzy	ADJ
ejpam-6541	165	3	norm	norm	NOUN
ejpam-6541	165	4	:	:	PUNCT
ejpam-6541	165	5	[	[	X
ejpam-6541	165	6	18	18	NUM
ejpam-6541	165	7	]	]	SYM
ejpam-6541	165	8	v	v	NOUN
ejpam-6541	165	9	is	be	AUX
ejpam-6541	165	10	a	a	DET
ejpam-6541	165	11	linear	linear	ADJ
ejpam-6541	165	12	space	space	NOUN
ejpam-6541	165	13	throughout	throughout	ADP
ejpam-6541	165	14	the	the	DET
ejpam-6541	165	15	field	field	NOUN
ejpam-6541	165	16	f.	f.	PROPN
ejpam-6541	165	17	suppose	suppose	VERB
ejpam-6541	165	18	∗	∗	NOUN
ejpam-6541	165	19	constitute	constitute	VERB
ejpam-6541	165	20	a	a	DET
ejpam-6541	165	21	continuous	continuous	ADJ
ejpam-6541	165	22	t	t	NOUN
ejpam-6541	165	23	-	-	PUNCT
ejpam-6541	165	24	norm	norm	NOUN
ejpam-6541	165	25	as	as	ADV
ejpam-6541	165	26	well	well	ADV
ejpam-6541	165	27	as	as	ADP
ejpam-6541	165	28	⋄	⋄	PROPN
ejpam-6541	165	29	represent	represent	VERB
ejpam-6541	165	30	a	a	DET
ejpam-6541	165	31	continuous	continuous	ADJ
ejpam-6541	165	32	t	t	NOUN
ejpam-6541	165	33	-	-	PUNCT
ejpam-6541	165	34	co	co	NOUN
ejpam-6541	165	35	-	-	NOUN
ejpam-6541	165	36	norm	norm	NOUN
ejpam-6541	165	37	over	over	ADP
ejpam-6541	165	38	v	v	NOUN
ejpam-6541	165	39	,	,	PUNCT
ejpam-6541	165	40	an	an	DET
ejpam-6541	165	41	intuitionistic	intuitionistic	ADJ
ejpam-6541	165	42	fuzzy	fuzzy	ADJ
ejpam-6541	165	43	norm	norm	NOUN
ejpam-6541	165	44	is	be	AUX
ejpam-6541	165	45	an	an	DET
ejpam-6541	165	46	object	object	NOUN
ejpam-6541	165	47	regarding	regard	VERB
ejpam-6541	165	48	the	the	DET
ejpam-6541	165	49	following	follow	VERB
ejpam-6541	165	50	form	form	NOUN
ejpam-6541	165	51	{	{	PUNCT
ejpam-6541	165	52	(	(	PUNCT
ejpam-6541	165	53	(	(	PUNCT
ejpam-6541	165	54	x11	x11	NOUN
ejpam-6541	165	55	,	,	PUNCT
ejpam-6541	165	56	t11	t11	NOUN
ejpam-6541	165	57	)	)	PUNCT
ejpam-6541	165	58	,	,	PUNCT
ejpam-6541	165	59	ni(x11	ni(x11	PROPN
ejpam-6541	165	60	,	,	PUNCT
ejpam-6541	165	61	t11),mi(x11	t11),mi(x11	PRON
ejpam-6541	165	62	,	,	PUNCT
ejpam-6541	165	63	t11	t11	NOUN
ejpam-6541	165	64	)	)	PUNCT
ejpam-6541	165	65	)	)	PUNCT
ejpam-6541	165	66	:	:	PUNCT
ejpam-6541	165	67	(	(	PUNCT
ejpam-6541	165	68	x11	x11	NOUN
ejpam-6541	165	69	,	,	PUNCT
ejpam-6541	165	70	t11	t11	NOUN
ejpam-6541	165	71	)	)	PUNCT
ejpam-6541	165	72	∈	∈	PROPN
ejpam-6541	165	73	v×r+},wherein	v×r+},wherein	PUNCT
ejpam-6541	165	74	ni	ni	PROPN
ejpam-6541	165	75	,	,	PUNCT
ejpam-6541	165	76	mi	mi	PROPN
ejpam-6541	165	77	have	have	AUX
ejpam-6541	165	78	been	be	AUX
ejpam-6541	165	79	fuzzy	fuzzy	ADJ
ejpam-6541	165	80	k.	k.	PROPN
ejpam-6541	165	81	kavitha	kavitha	PROPN
ejpam-6541	165	82	,	,	PUNCT
ejpam-6541	165	83	p.	p.	PROPN
ejpam-6541	165	84	muralikrishna	muralikrishna	PROPN
ejpam-6541	165	85	/	/	SYM
ejpam-6541	165	86	eur	eur	PROPN
ejpam-6541	165	87	.	.	PUNCT
ejpam-6541	166	1	j.	j.	PROPN
ejpam-6541	166	2	pure	pure	PROPN
ejpam-6541	166	3	appl	appl	PROPN
ejpam-6541	166	4	.	.	PROPN
ejpam-6541	166	5	math	math	PROPN
ejpam-6541	166	6	,	,	PUNCT
ejpam-6541	166	7	18	18	NUM
ejpam-6541	166	8	(	(	PUNCT
ejpam-6541	166	9	4	4	NUM
ejpam-6541	166	10	)	)	PUNCT
ejpam-6541	166	11	(	(	PUNCT
ejpam-6541	166	12	2025	2025	NUM
ejpam-6541	166	13	)	)	PUNCT
ejpam-6541	166	14	,	,	PUNCT
ejpam-6541	166	15	6541	6541	NUM
ejpam-6541	166	16	6	6	NUM
ejpam-6541	166	17	of	of	ADP
ejpam-6541	166	18	14	14	NUM
ejpam-6541	166	19	sets	set	NOUN
ejpam-6541	166	20	overv	overv	X
ejpam-6541	166	21	×r+,nindicates	×r+,nindicate	VERB
ejpam-6541	166	22	the	the	DET
ejpam-6541	166	23	degree	degree	NOUN
ejpam-6541	166	24	of	of	ADP
ejpam-6541	166	25	membership	membership	NOUN
ejpam-6541	166	26	along	along	ADP
ejpam-6541	166	27	with	with	ADP
ejpam-6541	166	28	mindicates	mindicate	NOUN
ejpam-6541	166	29	the	the	DET
ejpam-6541	166	30	degree	degree	NOUN
ejpam-6541	166	31	of	of	ADP
ejpam-6541	166	32	non	non	ADJ
ejpam-6541	166	33	-	-	NOUN
ejpam-6541	166	34	membership	membership	ADJ
ejpam-6541	166	35	(	(	PUNCT
ejpam-6541	166	36	x11	x11	NOUN
ejpam-6541	166	37	,	,	PUNCT
ejpam-6541	166	38	t11	t11	NOUN
ejpam-6541	166	39	)	)	PUNCT
ejpam-6541	166	40	∈	∈	PROPN
ejpam-6541	166	41	v	v	ADP
ejpam-6541	166	42	×	×	NOUN
ejpam-6541	166	43	r+	r+	PUNCT
ejpam-6541	166	44	staisfying	staisfying	NOUN
ejpam-6541	166	45	conditions	condition	NOUN
ejpam-6541	166	46	listed	list	VERB
ejpam-6541	166	47	below	below	ADV
ejpam-6541	166	48	,	,	PUNCT
ejpam-6541	166	49	(	(	PUNCT
ejpam-6541	166	50	i	i	NOUN
ejpam-6541	166	51	)	)	PUNCT
ejpam-6541	166	52	ni(x11	ni(x11	PROPN
ejpam-6541	166	53	,	,	PUNCT
ejpam-6541	166	54	t11	t11	NOUN
ejpam-6541	166	55	)	)	PUNCT
ejpam-6541	167	1	+	+	NOUN
ejpam-6541	167	2	mi(x11	mi(x11	NOUN
ejpam-6541	167	3	,	,	PUNCT
ejpam-6541	167	4	t11	t11	NOUN
ejpam-6541	167	5	)	)	PUNCT
ejpam-6541	167	6	≤	≤	NOUN
ejpam-6541	167	7	1	1	NUM
ejpam-6541	167	8	,	,	PUNCT
ejpam-6541	167	9	∀(x11	∀(x11	PROPN
ejpam-6541	167	10	,	,	PUNCT
ejpam-6541	167	11	t11	t11	NOUN
ejpam-6541	167	12	)	)	PUNCT
ejpam-6541	167	13	∈	∈	PROPN
ejpam-6541	167	14	v	v	ADP
ejpam-6541	167	15	×	×	NOUN
ejpam-6541	167	16	r+	r+	X
ejpam-6541	167	17	.	.	PUNCT
ejpam-6541	168	1	(	(	PUNCT
ejpam-6541	168	2	ii	ii	X
ejpam-6541	168	3	)	)	PUNCT
ejpam-6541	168	4	ni(x11	ni(x11	PROPN
ejpam-6541	168	5	,	,	PUNCT
ejpam-6541	168	6	t11	t11	NOUN
ejpam-6541	168	7	)	)	PUNCT
ejpam-6541	168	8	>	>	X
ejpam-6541	168	9	0	0	X
ejpam-6541	168	10	.	.	PUNCT
ejpam-6541	169	1	(	(	PUNCT
ejpam-6541	169	2	iii	iii	X
ejpam-6541	169	3	)	)	PUNCT
ejpam-6541	169	4	ni(x11	ni(x11	PROPN
ejpam-6541	169	5	,	,	PUNCT
ejpam-6541	169	6	t11	t11	NOUN
ejpam-6541	169	7	)	)	PUNCT
ejpam-6541	169	8	=	=	SYM
ejpam-6541	169	9	1	1	NUM
ejpam-6541	169	10	iff	iff	PROPN
ejpam-6541	169	11	x11	x11	PROPN
ejpam-6541	169	12	=	=	NOUN
ejpam-6541	169	13	0	0	PROPN
ejpam-6541	169	14	.	.	PUNCT
ejpam-6541	169	15	(	(	PUNCT
ejpam-6541	169	16	iv	iv	X
ejpam-6541	169	17	)	)	PUNCT
ejpam-6541	169	18	ni(cx11	ni(cx11	PROPN
ejpam-6541	169	19	,	,	PUNCT
ejpam-6541	169	20	t11	t11	NOUN
ejpam-6541	169	21	)	)	PUNCT
ejpam-6541	169	22	=	=	SYM
ejpam-6541	169	23	ni(x11	ni(x11	PROPN
ejpam-6541	169	24	,	,	PUNCT
ejpam-6541	169	25	t11	t11	PROPN
ejpam-6541	169	26	|c|	|c|	PROPN
ejpam-6541	169	27	)	)	PUNCT
ejpam-6541	169	28	,	,	PUNCT
ejpam-6541	169	29	c	c	PROPN
ejpam-6541	169	30	̸=	̸=	PROPN
ejpam-6541	169	31	0	0	NUM
ejpam-6541	169	32	,	,	PUNCT
ejpam-6541	169	33	c	c	PROPN
ejpam-6541	169	34	∈	∈	PROPN
ejpam-6541	169	35	f	f	X
ejpam-6541	169	36	(	(	PUNCT
ejpam-6541	169	37	v	v	NOUN
ejpam-6541	169	38	)	)	PUNCT
ejpam-6541	169	39	ni(x11	ni(x11	PROPN
ejpam-6541	169	40	,	,	PUNCT
ejpam-6541	169	41	s11	s11	PROPN
ejpam-6541	169	42	)	)	PUNCT
ejpam-6541	169	43	∗ni(y11	∗ni(y11	NOUN
ejpam-6541	169	44	,	,	PUNCT
ejpam-6541	169	45	t11	t11	NOUN
ejpam-6541	169	46	)	)	PUNCT
ejpam-6541	169	47	≤	≤	NOUN
ejpam-6541	169	48	ni(x11	ni(x11	ADP
ejpam-6541	169	49	+	+	CCONJ
ejpam-6541	169	50	y11	y11	NOUN
ejpam-6541	169	51	,	,	PUNCT
ejpam-6541	169	52	s11	s11	PROPN
ejpam-6541	169	53	+	+	CCONJ
ejpam-6541	169	54	t11	t11	NOUN
ejpam-6541	169	55	)	)	PUNCT
ejpam-6541	169	56	.	.	PUNCT
ejpam-6541	170	1	(	(	PUNCT
ejpam-6541	170	2	vi	vi	X
ejpam-6541	170	3	)	)	PUNCT
ejpam-6541	170	4	ni(x11	ni(x11	PROPN
ejpam-6541	170	5	,	,	PUNCT
ejpam-6541	170	6	�	�	PROPN
ejpam-6541	170	7	)	)	PUNCT
ejpam-6541	170	8	is	be	AUX
ejpam-6541	170	9	non	non	ADJ
ejpam-6541	170	10	-	-	ADJ
ejpam-6541	170	11	decreasing	decrease	VERB
ejpam-6541	170	12	function	function	NOUN
ejpam-6541	170	13	of	of	ADP
ejpam-6541	170	14	r+	r+	NOUN
ejpam-6541	170	15	and	and	CCONJ
ejpam-6541	170	16	limt11→∞ni(x11	limt11→∞ni(x11	PROPN
ejpam-6541	170	17	,	,	PUNCT
ejpam-6541	170	18	t11	t11	NOUN
ejpam-6541	170	19	)	)	PUNCT
ejpam-6541	170	20	=	=	SYM
ejpam-6541	171	1	1	1	X
ejpam-6541	171	2	.	.	PUNCT
ejpam-6541	171	3	(	(	PUNCT
ejpam-6541	171	4	vii	vii	PROPN
ejpam-6541	171	5	)	)	PUNCT
ejpam-6541	171	6	mi(x11	mi(x11	PROPN
ejpam-6541	171	7	,	,	PUNCT
ejpam-6541	171	8	t11	t11	NOUN
ejpam-6541	171	9	)	)	PUNCT
ejpam-6541	171	10	>	>	X
ejpam-6541	171	11	0	0	X
ejpam-6541	171	12	.	.	PUNCT
ejpam-6541	172	1	(	(	PUNCT
ejpam-6541	172	2	viii	viii	NOUN
ejpam-6541	172	3	)	)	PUNCT
ejpam-6541	172	4	mi(x11	mi(x11	NOUN
ejpam-6541	172	5	,	,	PUNCT
ejpam-6541	172	6	t11	t11	NOUN
ejpam-6541	172	7	)	)	PUNCT
ejpam-6541	172	8	=	=	SYM
ejpam-6541	172	9	0	0	NUM
ejpam-6541	173	1	iff	iff	PROPN
ejpam-6541	173	2	x11	x11	PROPN
ejpam-6541	173	3	=	=	NOUN
ejpam-6541	173	4	0	0	PROPN
ejpam-6541	173	5	.	.	PUNCT
ejpam-6541	174	1	(	(	PUNCT
ejpam-6541	174	2	ix	ix	NOUN
ejpam-6541	174	3	)	)	PUNCT
ejpam-6541	174	4	mi(cx11	mi(cx11	NOUN
ejpam-6541	174	5	,	,	PUNCT
ejpam-6541	174	6	t11	t11	NOUN
ejpam-6541	174	7	)	)	PUNCT
ejpam-6541	174	8	=	=	SYM
ejpam-6541	174	9	mi(x11	mi(x11	NOUN
ejpam-6541	174	10	,	,	PUNCT
ejpam-6541	174	11	t11	t11	PROPN
ejpam-6541	174	12	|c|	|c|	PROPN
ejpam-6541	174	13	)	)	PUNCT
ejpam-6541	174	14	,	,	PUNCT
ejpam-6541	174	15	c	c	PROPN
ejpam-6541	174	16	̸=	̸=	PROPN
ejpam-6541	174	17	0	0	NUM
ejpam-6541	174	18	,	,	PUNCT
ejpam-6541	174	19	c	c	PROPN
ejpam-6541	174	20	∈	∈	PROPN
ejpam-6541	174	21	f	f	X
ejpam-6541	174	22	(	(	PUNCT
ejpam-6541	174	23	x	x	NOUN
ejpam-6541	174	24	)	)	PUNCT
ejpam-6541	174	25	mi(x11	mi(x11	NOUN
ejpam-6541	174	26	,	,	PUNCT
ejpam-6541	174	27	s11	s11	PROPN
ejpam-6541	174	28	)	)	PUNCT
ejpam-6541	174	29	⋄mi(y11	⋄mi(y11	PROPN
ejpam-6541	174	30	,	,	PUNCT
ejpam-6541	174	31	t11	t11	NOUN
ejpam-6541	174	32	)	)	PUNCT
ejpam-6541	174	33	≥	≥	NOUN
ejpam-6541	174	34	mi(x11	mi(x11	NOUN
ejpam-6541	174	35	+	+	NOUN
ejpam-6541	174	36	y11	y11	NOUN
ejpam-6541	174	37	,	,	PUNCT
ejpam-6541	174	38	s11	s11	PROPN
ejpam-6541	174	39	+	+	CCONJ
ejpam-6541	174	40	t11	t11	NOUN
ejpam-6541	174	41	)	)	PUNCT
ejpam-6541	174	42	.	.	PUNCT
ejpam-6541	175	1	(	(	PUNCT
ejpam-6541	175	2	xi	xi	X
ejpam-6541	175	3	)	)	PUNCT
ejpam-6541	175	4	mi(x11	mi(x11	PROPN
ejpam-6541	175	5	,	,	PUNCT
ejpam-6541	175	6	�	�	PROPN
ejpam-6541	175	7	)	)	PUNCT
ejpam-6541	175	8	is	be	AUX
ejpam-6541	175	9	non	non	ADJ
ejpam-6541	175	10	-	-	ADJ
ejpam-6541	175	11	increasing	increasing	ADJ
ejpam-6541	175	12	function	function	NOUN
ejpam-6541	175	13	of	of	ADP
ejpam-6541	175	14	r+	r+	NOUN
ejpam-6541	175	15	as	as	ADV
ejpam-6541	175	16	well	well	ADV
ejpam-6541	175	17	as	as	ADP
ejpam-6541	175	18	limt11→∞mi(x11	limt11→∞mi(x11	PROPN
ejpam-6541	175	19	,	,	PUNCT
ejpam-6541	175	20	t11	t11	NOUN
ejpam-6541	175	21	)	)	PUNCT
ejpam-6541	175	22	=	=	NOUN
ejpam-6541	176	1	0	0	X
ejpam-6541	176	2	.	.	PUNCT
ejpam-6541	177	1	according	accord	VERB
ejpam-6541	177	2	to	to	ADP
ejpam-6541	177	3	this	this	DET
ejpam-6541	177	4	definition	definition	NOUN
ejpam-6541	177	5	,	,	PUNCT
ejpam-6541	177	6	the	the	DET
ejpam-6541	177	7	5−tuple	5−tuple	NUM
ejpam-6541	177	8	(	(	PUNCT
ejpam-6541	177	9	v	v	NOUN
ejpam-6541	177	10	,	,	PUNCT
ejpam-6541	177	11	mi	mi	PROPN
ejpam-6541	177	12	,	,	PUNCT
ejpam-6541	177	13	ni	ni	PROPN
ejpam-6541	177	14	,	,	PUNCT
ejpam-6541	177	15	∗	∗	NOUN
ejpam-6541	177	16	,	,	PUNCT
ejpam-6541	177	17	⋄	⋄	PROPN
ejpam-6541	177	18	)	)	PUNCT
ejpam-6541	177	19	constitutes	constitute	VERB
ejpam-6541	177	20	an	an	DET
ejpam-6541	177	21	intuitionistic	intuitionistic	ADJ
ejpam-6541	177	22	fuzzy	fuzzy	ADJ
ejpam-6541	177	23	normed	norme	VERB
ejpam-6541	177	24	linear	linear	ADJ
ejpam-6541	177	25	space	space	NOUN
ejpam-6541	177	26	,	,	PUNCT
ejpam-6541	177	27	whereas	whereas	SCONJ
ejpam-6541	177	28	(	(	PUNCT
ejpam-6541	177	29	mi	mi	PROPN
ejpam-6541	177	30	,	,	PUNCT
ejpam-6541	177	31	ni	ni	NOUN
ejpam-6541	177	32	)	)	PUNCT
ejpam-6541	177	33	represents	represent	VERB
ejpam-6541	177	34	an	an	DET
ejpam-6541	177	35	intuitionistic	intuitionistic	ADJ
ejpam-6541	177	36	fuzzy	fuzzy	ADJ
ejpam-6541	177	37	norm	norm	NOUN
ejpam-6541	177	38	.	.	PUNCT
ejpam-6541	178	1	definition	definition	NOUN
ejpam-6541	178	2	14	14	NUM
ejpam-6541	178	3	.	.	PUNCT
ejpam-6541	179	1	intuitionistic	intuitionistic	ADJ
ejpam-6541	179	2	hesitant	hesitant	ADJ
ejpam-6541	179	3	fuzzy	fuzzy	ADJ
ejpam-6541	179	4	set	set	NOUN
ejpam-6541	179	5	:	:	PUNCT
ejpam-6541	180	1	[	[	X
ejpam-6541	180	2	19	19	NUM
ejpam-6541	180	3	]	]	PUNCT
ejpam-6541	180	4	when	when	SCONJ
ejpam-6541	180	5	applied	apply	VERB
ejpam-6541	180	6	to	to	ADP
ejpam-6541	180	7	x	x	PRON
ejpam-6541	180	8	,	,	PUNCT
ejpam-6541	180	9	the	the	DET
ejpam-6541	180	10	functions	function	NOUN
ejpam-6541	180	11	h	h	NOUN
ejpam-6541	180	12	and	and	CCONJ
ejpam-6541	180	13	h	h	NOUN
ejpam-6541	180	14	′	′	NUM
ejpam-6541	180	15	yield	yield	NOUN
ejpam-6541	180	16	subsets	subset	NOUN
ejpam-6541	180	17	regarding	regard	VERB
ejpam-6541	180	18	[	[	X
ejpam-6541	180	19	0	0	NUM
ejpam-6541	180	20	,	,	PUNCT
ejpam-6541	180	21	1	1	NUM
ejpam-6541	180	22	]	]	PUNCT
ejpam-6541	180	23	,	,	PUNCT
ejpam-6541	180	24	which	which	PRON
ejpam-6541	180	25	might	might	AUX
ejpam-6541	180	26	be	be	AUX
ejpam-6541	180	27	expressed	express	VERB
ejpam-6541	180	28	mathematically	mathematically	ADV
ejpam-6541	180	29	e	e	NOUN
ejpam-6541	180	30	=	=	SYM
ejpam-6541	180	31	{	{	PUNCT
ejpam-6541	180	32	(	(	PUNCT
ejpam-6541	180	33	x	x	NOUN
ejpam-6541	180	34	,	,	PUNCT
ejpam-6541	180	35	h(x	h(x	PROPN
ejpam-6541	180	36	)	)	PUNCT
ejpam-6541	180	37	,	,	PUNCT
ejpam-6541	181	1	h	h	NOUN
ejpam-6541	181	2	′	′	NUM
ejpam-6541	182	1	(	(	PUNCT
ejpam-6541	182	2	x))/x	x))/x	NOUN
ejpam-6541	182	3	∈	∈	PROPN
ejpam-6541	182	4	x	x	NOUN
ejpam-6541	182	5	}	}	PUNCT
ejpam-6541	182	6	.	.	PUNCT
ejpam-6541	183	1	this	this	PRON
ejpam-6541	183	2	consists	consist	VERB
ejpam-6541	183	3	of	of	ADP
ejpam-6541	183	4	intuitioistic	intuitioistic	ADJ
ejpam-6541	183	5	hesitant	hesitant	ADJ
ejpam-6541	183	6	fuzzy	fuzzy	ADJ
ejpam-6541	183	7	set	set	VERB
ejpam-6541	183	8	on	on	ADP
ejpam-6541	183	9	x	x	PUNCT
ejpam-6541	183	10	,	,	PUNCT
ejpam-6541	183	11	wherein	wherein	SCONJ
ejpam-6541	183	12	sets	set	NOUN
ejpam-6541	183	13	of	of	ADP
ejpam-6541	183	14	some	some	DET
ejpam-6541	183	15	values	value	NOUN
ejpam-6541	183	16	in	in	ADP
ejpam-6541	183	17	[	[	X
ejpam-6541	183	18	0	0	NUM
ejpam-6541	183	19	,	,	PUNCT
ejpam-6541	183	20	1	1	NUM
ejpam-6541	183	21	]	]	PUNCT
ejpam-6541	183	22	are	be	AUX
ejpam-6541	183	23	represented	represent	VERB
ejpam-6541	183	24	by	by	ADP
ejpam-6541	183	25	h(x	h(x	PROPN
ejpam-6541	183	26	)	)	PUNCT
ejpam-6541	183	27	,	,	PUNCT
ejpam-6541	184	1	h	h	NOUN
ejpam-6541	184	2	′	′	NUM
ejpam-6541	185	1	(	(	PUNCT
ejpam-6541	185	2	x	x	X
ejpam-6541	185	3	)	)	PUNCT
ejpam-6541	185	4	,	,	PUNCT
ejpam-6541	185	5	the	the	DET
ejpam-6541	185	6	elements	element	NOUN
ejpam-6541	185	7	x	x	PUNCT
ejpam-6541	185	8	∈	∈	NOUN
ejpam-6541	185	9	x	x	NOUN
ejpam-6541	185	10	that	that	PRON
ejpam-6541	185	11	represent	represent	VERB
ejpam-6541	185	12	the	the	DET
ejpam-6541	185	13	membership	membership	NOUN
ejpam-6541	185	14	along	along	ADP
ejpam-6541	185	15	with	with	ADP
ejpam-6541	185	16	non	non	ADJ
ejpam-6541	185	17	-	-	ADJ
ejpam-6541	185	18	membership	membership	ADJ
ejpam-6541	185	19	degrees	degree	NOUN
ejpam-6541	185	20	of	of	ADP
ejpam-6541	185	21	the	the	DET
ejpam-6541	185	22	set	set	NOUN
ejpam-6541	185	23	e	e	NOUN
ejpam-6541	185	24	,	,	PUNCT
ejpam-6541	185	25	suppose	suppose	VERB
ejpam-6541	185	26	that	that	SCONJ
ejpam-6541	185	27	max(h(x))+min(h	max(h(x))+min(h	INTJ
ejpam-6541	185	28	′	′	NUM
ejpam-6541	185	29	(	(	PUNCT
ejpam-6541	185	30	x	x	NOUN
ejpam-6541	185	31	)	)	PUNCT
ejpam-6541	185	32	)	)	PUNCT
ejpam-6541	186	1	≤	≤	NUM
ejpam-6541	187	1	1along	1along	NUM
ejpam-6541	187	2	with	with	ADP
ejpam-6541	187	3	min(h(x))+max(h	min(h(x))+max(h	PROPN
ejpam-6541	187	4	′	′	NUM
ejpam-6541	187	5	(	(	PUNCT
ejpam-6541	187	6	x	x	NOUN
ejpam-6541	187	7	)	)	PUNCT
ejpam-6541	187	8	)	)	PUNCT
ejpam-6541	188	1	≤	≤	NUM
ejpam-6541	188	2	1	1	NUM
ejpam-6541	188	3	,	,	PUNCT
ejpam-6541	188	4	because	because	SCONJ
ejpam-6541	188	5	(	(	PUNCT
ejpam-6541	188	6	h(x	h(x	PROPN
ejpam-6541	188	7	)	)	PUNCT
ejpam-6541	188	8	,	,	PUNCT
ejpam-6541	188	9	h	h	NOUN
ejpam-6541	188	10	′	′	NUM
ejpam-6541	188	11	(	(	PUNCT
ejpam-6541	188	12	x	x	NOUN
ejpam-6541	188	13	)	)	PUNCT
ejpam-6541	188	14	)	)	PUNCT
ejpam-6541	188	15	is	be	AUX
ejpam-6541	188	16	an	an	DET
ejpam-6541	188	17	intuitionistic	intuitionistic	ADJ
ejpam-6541	188	18	hesitant	hesitant	ADJ
ejpam-6541	188	19	fuzzy	fuzzy	ADJ
ejpam-6541	188	20	element	element	NOUN
ejpam-6541	188	21	.	.	PUNCT
ejpam-6541	189	1	definition	definition	NOUN
ejpam-6541	189	2	15	15	NUM
ejpam-6541	189	3	.	.	PUNCT
ejpam-6541	190	1	intuitionistic	intuitionistic	ADJ
ejpam-6541	190	2	hesitant	hesitant	ADJ
ejpam-6541	190	3	fuzzy	fuzzy	ADJ
ejpam-6541	190	4	norm	norm	NOUN
ejpam-6541	190	5	:	:	PUNCT
ejpam-6541	191	1	[	[	X
ejpam-6541	191	2	19	19	NUM
ejpam-6541	191	3	]	]	PUNCT
ejpam-6541	191	4	over	over	ADP
ejpam-6541	191	5	the	the	DET
ejpam-6541	191	6	field	field	NOUN
ejpam-6541	191	7	f	f	X
ejpam-6541	191	8	,	,	PUNCT
ejpam-6541	191	9	v	v	PROPN
ejpam-6541	191	10	represents	represent	VERB
ejpam-6541	191	11	a	a	DET
ejpam-6541	191	12	linear	linear	ADJ
ejpam-6541	191	13	space	space	NOUN
ejpam-6541	191	14	.	.	PUNCT
ejpam-6541	192	1	let	let	VERB
ejpam-6541	192	2	∗	∗	NOUN
ejpam-6541	192	3	represent	represent	VERB
ejpam-6541	192	4	a	a	DET
ejpam-6541	192	5	continuous	continuous	ADJ
ejpam-6541	192	6	t	t	NOUN
ejpam-6541	192	7	-	-	PUNCT
ejpam-6541	192	8	norm	norm	NOUN
ejpam-6541	192	9	,	,	PUNCT
ejpam-6541	192	10	as	as	ADV
ejpam-6541	192	11	well	well	ADV
ejpam-6541	192	12	as	as	ADP
ejpam-6541	192	13	⋄	⋄	PROPN
ejpam-6541	192	14	represent	represent	VERB
ejpam-6541	192	15	a	a	DET
ejpam-6541	192	16	continuous	continuous	ADJ
ejpam-6541	192	17	t	t	NOUN
ejpam-6541	192	18	-	-	PUNCT
ejpam-6541	192	19	co	co	NOUN
ejpam-6541	192	20	-	-	NOUN
ejpam-6541	192	21	norm	norm	NOUN
ejpam-6541	192	22	and	and	CCONJ
ejpam-6541	192	23	an	an	DET
ejpam-6541	192	24	item	item	NOUN
ejpam-6541	192	25	of	of	ADP
ejpam-6541	192	26	the	the	DET
ejpam-6541	192	27	following	follow	VERB
ejpam-6541	192	28	type	type	NOUN
ejpam-6541	192	29	is	be	AUX
ejpam-6541	192	30	an	an	DET
ejpam-6541	192	31	intuitionistic	intuitionistic	ADJ
ejpam-6541	192	32	hesitant	hesitant	ADJ
ejpam-6541	192	33	fuzzy	fuzzy	ADJ
ejpam-6541	192	34	norm	norm	NOUN
ejpam-6541	192	35	on	on	ADP
ejpam-6541	192	36	v	v	ADP
ejpam-6541	192	37	{	{	PUNCT
ejpam-6541	192	38	hihf	hihf	NOUN
ejpam-6541	192	39	=	=	SYM
ejpam-6541	192	40	(	(	PUNCT
ejpam-6541	192	41	(	(	PUNCT
ejpam-6541	192	42	x11	x11	NOUN
ejpam-6541	192	43	,	,	PUNCT
ejpam-6541	192	44	t11),ni(x11	t11),ni(x11	PRON
ejpam-6541	192	45	,	,	PUNCT
ejpam-6541	192	46	t11),mi(x11	t11),mi(x11	PRON
ejpam-6541	192	47	,	,	PUNCT
ejpam-6541	192	48	t11	t11	NOUN
ejpam-6541	192	49	)	)	PUNCT
ejpam-6541	192	50	)	)	PUNCT
ejpam-6541	192	51	:	:	PUNCT
ejpam-6541	192	52	(	(	PUNCT
ejpam-6541	192	53	x11	x11	NOUN
ejpam-6541	192	54	,	,	PUNCT
ejpam-6541	192	55	t11	t11	NOUN
ejpam-6541	192	56	)	)	PUNCT
ejpam-6541	192	57	∈	∈	PROPN
ejpam-6541	192	58	v×r+},wherein	v×r+},wherein	PUNCT
ejpam-6541	192	59	ni	ni	PROPN
ejpam-6541	192	60	,	,	PUNCT
ejpam-6541	192	61	mi	mi	PROPN
ejpam-6541	192	62	are	be	AUX
ejpam-6541	192	63	fuzzy	fuzzy	ADJ
ejpam-6541	192	64	sets	set	NOUN
ejpam-6541	192	65	overv	overv	X
ejpam-6541	192	66	×	×	PROPN
ejpam-6541	192	67	r+,ni	r+,ni	PROPN
ejpam-6541	192	68	indicates	indicate	VERB
ejpam-6541	192	69	the	the	DET
ejpam-6541	192	70	degree	degree	NOUN
ejpam-6541	192	71	of	of	ADP
ejpam-6541	192	72	membership	membership	NOUN
ejpam-6541	192	73	along	along	ADP
ejpam-6541	192	74	with	with	ADP
ejpam-6541	192	75	mi	mi	PROPN
ejpam-6541	192	76	denote	denote	VERB
ejpam-6541	192	77	the	the	DET
ejpam-6541	192	78	degree	degree	NOUN
ejpam-6541	192	79	of	of	ADP
ejpam-6541	192	80	non	non	ADJ
ejpam-6541	192	81	-	-	NOUN
ejpam-6541	192	82	membership	membership	ADJ
ejpam-6541	192	83	(	(	PUNCT
ejpam-6541	192	84	x11	x11	NOUN
ejpam-6541	192	85	,	,	PUNCT
ejpam-6541	192	86	t11	t11	NOUN
ejpam-6541	192	87	)	)	PUNCT
ejpam-6541	192	88	∈	∈	PROPN
ejpam-6541	192	89	v	v	ADP
ejpam-6541	192	90	×	×	NOUN
ejpam-6541	192	91	r+	r+	PUNCT
ejpam-6541	192	92	meeting	meet	VERB
ejpam-6541	192	93	the	the	DET
ejpam-6541	192	94	requirements	requirement	NOUN
ejpam-6541	192	95	listed	list	VERB
ejpam-6541	192	96	here	here	ADV
ejpam-6541	192	97	,	,	PUNCT
ejpam-6541	192	98	(	(	PUNCT
ejpam-6541	192	99	i	i	NOUN
ejpam-6541	192	100	)	)	PUNCT
ejpam-6541	192	101	ni(x11	ni(x11	PROPN
ejpam-6541	192	102	,	,	PUNCT
ejpam-6541	192	103	t11	t11	NOUN
ejpam-6541	192	104	)	)	PUNCT
ejpam-6541	192	105	∪mi(x11	∪mi(x11	NOUN
ejpam-6541	192	106	,	,	PUNCT
ejpam-6541	192	107	t11	t11	NOUN
ejpam-6541	192	108	)	)	PUNCT
ejpam-6541	193	1	⊆	⊆	NUM
ejpam-6541	193	2	u∗	u∗	NOUN
ejpam-6541	193	3	,	,	PUNCT
ejpam-6541	193	4	∀(x11	∀(x11	PROPN
ejpam-6541	193	5	,	,	PUNCT
ejpam-6541	193	6	t11	t11	NOUN
ejpam-6541	193	7	)	)	PUNCT
ejpam-6541	193	8	∈	∈	PROPN
ejpam-6541	193	9	v	v	ADP
ejpam-6541	193	10	×	×	NOUN
ejpam-6541	193	11	r+	r+	X
ejpam-6541	193	12	.	.	PUNCT
ejpam-6541	194	1	(	(	PUNCT
ejpam-6541	194	2	ii	ii	X
ejpam-6541	194	3	)	)	PUNCT
ejpam-6541	194	4	ni(x11	ni(x11	PROPN
ejpam-6541	194	5	,	,	PUNCT
ejpam-6541	194	6	t11	t11	NOUN
ejpam-6541	194	7	)	)	PUNCT
ejpam-6541	194	8	̸=	̸=	PROPN
ejpam-6541	194	9	∅∗.	∅∗.	NUM
ejpam-6541	194	10	(	(	PUNCT
ejpam-6541	194	11	iii	iii	X
ejpam-6541	194	12	)	)	PUNCT
ejpam-6541	194	13	ni(x11	ni(x11	PROPN
ejpam-6541	194	14	,	,	PUNCT
ejpam-6541	194	15	t11	t11	NOUN
ejpam-6541	194	16	)	)	PUNCT
ejpam-6541	194	17	=	=	PUNCT
ejpam-6541	195	1	u∗	u∗	PROPN
ejpam-6541	195	2	iff	iff	PROPN
ejpam-6541	195	3	x11	x11	PROPN
ejpam-6541	195	4	=	=	SYM
ejpam-6541	195	5	0	0	PROPN
ejpam-6541	195	6	.	.	PUNCT
ejpam-6541	196	1	k.	k.	PROPN
ejpam-6541	196	2	kavitha	kavitha	PROPN
ejpam-6541	196	3	,	,	PUNCT
ejpam-6541	196	4	p.	p.	PROPN
ejpam-6541	196	5	muralikrishna	muralikrishna	PROPN
ejpam-6541	196	6	/	/	SYM
ejpam-6541	196	7	eur	eur	PROPN
ejpam-6541	196	8	.	.	PUNCT
ejpam-6541	197	1	j.	j.	PROPN
ejpam-6541	197	2	pure	pure	PROPN
ejpam-6541	197	3	appl	appl	PROPN
ejpam-6541	197	4	.	.	PROPN
ejpam-6541	197	5	math	math	PROPN
ejpam-6541	197	6	,	,	PUNCT
ejpam-6541	197	7	18	18	NUM
ejpam-6541	197	8	(	(	PUNCT
ejpam-6541	197	9	4	4	NUM
ejpam-6541	197	10	)	)	PUNCT
ejpam-6541	197	11	(	(	PUNCT
ejpam-6541	197	12	2025	2025	NUM
ejpam-6541	197	13	)	)	PUNCT
ejpam-6541	197	14	,	,	PUNCT
ejpam-6541	197	15	6541	6541	NUM
ejpam-6541	197	16	7	7	NUM
ejpam-6541	197	17	of	of	ADP
ejpam-6541	197	18	14	14	NUM
ejpam-6541	197	19	(	(	PUNCT
ejpam-6541	197	20	iv	iv	X
ejpam-6541	197	21	)	)	PUNCT
ejpam-6541	197	22	ni(cx11	ni(cx11	PROPN
ejpam-6541	197	23	,	,	PUNCT
ejpam-6541	197	24	t11	t11	NOUN
ejpam-6541	197	25	)	)	PUNCT
ejpam-6541	197	26	=	=	SYM
ejpam-6541	197	27	ni	ni	PROPN
ejpam-6541	197	28	(	(	PUNCT
ejpam-6541	197	29	x11	x11	PROPN
ejpam-6541	197	30	,	,	PUNCT
ejpam-6541	197	31	t11	t11	PROPN
ejpam-6541	197	32	|c|	|c|	PROPN
ejpam-6541	197	33	)	)	PUNCT
ejpam-6541	197	34	,	,	PUNCT
ejpam-6541	198	1	c	c	PROPN
ejpam-6541	198	2	̸=	̸=	PROPN
ejpam-6541	198	3	0	0	NUM
ejpam-6541	198	4	,	,	PUNCT
ejpam-6541	198	5	c	c	PROPN
ejpam-6541	198	6	∈	∈	PROPN
ejpam-6541	198	7	f	f	X
ejpam-6541	198	8	(	(	PUNCT
ejpam-6541	198	9	v	v	NOUN
ejpam-6541	198	10	)	)	PUNCT
ejpam-6541	198	11	ni(x11	ni(x11	PROPN
ejpam-6541	198	12	,	,	PUNCT
ejpam-6541	198	13	s11	s11	PROPN
ejpam-6541	198	14	)	)	PUNCT
ejpam-6541	198	15	∗	∗	PROPN
ejpam-6541	198	16	ni(y11	ni(y11	PROPN
ejpam-6541	198	17	,	,	PUNCT
ejpam-6541	198	18	t11	t11	NOUN
ejpam-6541	198	19	)	)	PUNCT
ejpam-6541	198	20	⊆	⊆	NUM
ejpam-6541	198	21	ni(x11	ni(x11	NOUN
ejpam-6541	198	22	+	+	CCONJ
ejpam-6541	198	23	y11	y11	NOUN
ejpam-6541	198	24	,	,	PUNCT
ejpam-6541	198	25	s11	s11	PROPN
ejpam-6541	198	26	+	+	CCONJ
ejpam-6541	198	27	t11	t11	NOUN
ejpam-6541	198	28	)	)	PUNCT
ejpam-6541	198	29	.	.	PUNCT
ejpam-6541	199	1	(	(	PUNCT
ejpam-6541	199	2	vi	vi	X
ejpam-6541	199	3	)	)	PUNCT
ejpam-6541	199	4	ni(x11	ni(x11	PROPN
ejpam-6541	199	5	,	,	PUNCT
ejpam-6541	199	6	�	�	PROPN
ejpam-6541	199	7	)	)	PUNCT
ejpam-6541	199	8	is	be	AUX
ejpam-6541	199	9	non	non	ADJ
ejpam-6541	199	10	-	-	ADJ
ejpam-6541	199	11	decreasing	decrease	VERB
ejpam-6541	199	12	function	function	NOUN
ejpam-6541	199	13	of	of	ADP
ejpam-6541	199	14	r+	r+	NOUN
ejpam-6541	199	15	and	and	CCONJ
ejpam-6541	199	16	limt11→∞ni(x11	limt11→∞ni(x11	PROPN
ejpam-6541	199	17	,	,	PUNCT
ejpam-6541	199	18	t11	t11	NOUN
ejpam-6541	200	1	)	)	PUNCT
ejpam-6541	200	2	=	=	SYM
ejpam-6541	200	3	u∗.	u∗.	PROPN
ejpam-6541	200	4	(	(	PUNCT
ejpam-6541	200	5	vii	vii	PROPN
ejpam-6541	200	6	)	)	PUNCT
ejpam-6541	200	7	mi(x11	mi(x11	PROPN
ejpam-6541	200	8	,	,	PUNCT
ejpam-6541	200	9	t11	t11	NOUN
ejpam-6541	200	10	)	)	PUNCT
ejpam-6541	200	11	̸=	̸=	PROPN
ejpam-6541	200	12	∅∗.	∅∗.	NUM
ejpam-6541	200	13	(	(	PUNCT
ejpam-6541	200	14	viii	viii	NOUN
ejpam-6541	200	15	)	)	PUNCT
ejpam-6541	200	16	mi(x11	mi(x11	NOUN
ejpam-6541	200	17	,	,	PUNCT
ejpam-6541	200	18	t11	t11	NOUN
ejpam-6541	200	19	)	)	PUNCT
ejpam-6541	200	20	=	=	PUNCT
ejpam-6541	200	21	∅∗	∅∗	PROPN
ejpam-6541	200	22	iff	iff	VERB
ejpam-6541	200	23	x11	x11	PROPN
ejpam-6541	200	24	=	=	NOUN
ejpam-6541	200	25	0	0	PROPN
ejpam-6541	200	26	.	.	PUNCT
ejpam-6541	201	1	(	(	PUNCT
ejpam-6541	201	2	ix	ix	NOUN
ejpam-6541	201	3	)	)	PUNCT
ejpam-6541	201	4	mi(cx11	mi(cx11	NOUN
ejpam-6541	201	5	,	,	PUNCT
ejpam-6541	201	6	t11	t11	NOUN
ejpam-6541	201	7	)	)	PUNCT
ejpam-6541	201	8	=	=	SYM
ejpam-6541	201	9	mi	mi	PROPN
ejpam-6541	201	10	(	(	PUNCT
ejpam-6541	201	11	x11	x11	PROPN
ejpam-6541	201	12	,	,	PUNCT
ejpam-6541	201	13	t11	t11	PROPN
ejpam-6541	201	14	|c|	|c|	PROPN
ejpam-6541	201	15	)	)	PUNCT
ejpam-6541	201	16	,	,	PUNCT
ejpam-6541	202	1	c	c	PROPN
ejpam-6541	202	2	̸=	̸=	PROPN
ejpam-6541	202	3	0	0	NUM
ejpam-6541	202	4	,	,	PUNCT
ejpam-6541	202	5	c	c	PROPN
ejpam-6541	202	6	∈	∈	PROPN
ejpam-6541	202	7	f	f	X
ejpam-6541	202	8	(	(	PUNCT
ejpam-6541	202	9	x	x	NOUN
ejpam-6541	202	10	)	)	PUNCT
ejpam-6541	202	11	mi(x11	mi(x11	NOUN
ejpam-6541	202	12	,	,	PUNCT
ejpam-6541	202	13	s11	s11	PROPN
ejpam-6541	202	14	)	)	PUNCT
ejpam-6541	202	15	⋄mi(y11	⋄mi(y11	PROPN
ejpam-6541	202	16	,	,	PUNCT
ejpam-6541	202	17	t11	t11	NOUN
ejpam-6541	202	18	)	)	PUNCT
ejpam-6541	202	19	⊇	⊇	NOUN
ejpam-6541	202	20	mi(x11	mi(x11	NOUN
ejpam-6541	202	21	+	+	CCONJ
ejpam-6541	202	22	y11	y11	NOUN
ejpam-6541	202	23	,	,	PUNCT
ejpam-6541	202	24	s11	s11	PROPN
ejpam-6541	202	25	+	+	CCONJ
ejpam-6541	202	26	t11	t11	NOUN
ejpam-6541	202	27	)	)	PUNCT
ejpam-6541	202	28	.	.	PUNCT
ejpam-6541	203	1	(	(	PUNCT
ejpam-6541	203	2	xi	xi	X
ejpam-6541	203	3	)	)	PUNCT
ejpam-6541	203	4	mi(x11	mi(x11	PROPN
ejpam-6541	203	5	,	,	PUNCT
ejpam-6541	203	6	�	�	PROPN
ejpam-6541	203	7	)	)	PUNCT
ejpam-6541	203	8	is	be	AUX
ejpam-6541	203	9	non	non	ADJ
ejpam-6541	203	10	-	-	ADJ
ejpam-6541	203	11	increasing	increasing	ADJ
ejpam-6541	203	12	function	function	NOUN
ejpam-6541	203	13	of	of	ADP
ejpam-6541	203	14	r+	r+	NOUN
ejpam-6541	203	15	as	as	ADV
ejpam-6541	203	16	well	well	ADV
ejpam-6541	203	17	as	as	ADP
ejpam-6541	203	18	limt11→∞mi(x11	limt11→∞mi(x11	PROPN
ejpam-6541	203	19	,	,	PUNCT
ejpam-6541	203	20	t11	t11	NOUN
ejpam-6541	203	21	)	)	PUNCT
ejpam-6541	203	22	=	=	SYM
ejpam-6541	203	23	∅∗.	∅∗.	NUM
ejpam-6541	203	24	definition	definition	NOUN
ejpam-6541	203	25	16	16	NUM
ejpam-6541	203	26	.	.	PUNCT
ejpam-6541	204	1	intuitionistic	intuitionistic	ADJ
ejpam-6541	204	2	hesitant	hesitant	ADJ
ejpam-6541	204	3	fuzzy	fuzzy	ADJ
ejpam-6541	204	4	normed	norme	VERB
ejpam-6541	204	5	linear	linear	ADJ
ejpam-6541	204	6	space	space	NOUN
ejpam-6541	204	7	:	:	PUNCT
ejpam-6541	205	1	[	[	X
ejpam-6541	205	2	19	19	NUM
ejpam-6541	205	3	]	]	PUNCT
ejpam-6541	205	4	assuming	assume	VERB
ejpam-6541	205	5	that	that	DET
ejpam-6541	205	6	hihf	hihf	NOUN
ejpam-6541	205	7	represents	represent	VERB
ejpam-6541	205	8	an	an	DET
ejpam-6541	205	9	intuitionistic	intuitionistic	ADJ
ejpam-6541	205	10	hesitant	hesitant	ADJ
ejpam-6541	205	11	fuzzy	fuzzy	ADJ
ejpam-6541	205	12	norm	norm	NOUN
ejpam-6541	205	13	over	over	ADP
ejpam-6541	205	14	v	v	NOUN
ejpam-6541	205	15	on	on	ADP
ejpam-6541	205	16	f	f	NOUN
ejpam-6541	205	17	,	,	PUNCT
ejpam-6541	205	18	afterwards	afterwards	ADV
ejpam-6541	205	19	(	(	PUNCT
ejpam-6541	205	20	v	v	NOUN
ejpam-6541	205	21	,	,	PUNCT
ejpam-6541	205	22	hihf	hihf	PROPN
ejpam-6541	205	23	)	)	PUNCT
ejpam-6541	205	24	is	be	AUX
ejpam-6541	205	25	an	an	DET
ejpam-6541	205	26	intuitionistic	intuitionistic	ADJ
ejpam-6541	205	27	hesitant	hesitant	ADJ
ejpam-6541	205	28	fuzzy	fuzzy	ADJ
ejpam-6541	205	29	normed	norme	VERB
ejpam-6541	205	30	linear	linear	ADJ
ejpam-6541	205	31	space	space	NOUN
ejpam-6541	205	32	or	or	CCONJ
ejpam-6541	205	33	ihfnls	ihfnls	NOUN
ejpam-6541	205	34	.	.	PUNCT
ejpam-6541	206	1	example	example	NOUN
ejpam-6541	206	2	:	:	PUNCT
ejpam-6541	207	1	[	[	X
ejpam-6541	207	2	19	19	NUM
ejpam-6541	207	3	]	]	PUNCT
ejpam-6541	207	4	consider	consider	VERB
ejpam-6541	207	5	the	the	DET
ejpam-6541	207	6	normed	normed	ADJ
ejpam-6541	207	7	linear	linear	ADJ
ejpam-6541	207	8	space	space	NOUN
ejpam-6541	207	9	(	(	PUNCT
ejpam-6541	207	10	v	v	NOUN
ejpam-6541	207	11	=	=	SYM
ejpam-6541	207	12	r	r	NOUN
ejpam-6541	207	13	,	,	PUNCT
ejpam-6541	207	14	∥	∥	X
ejpam-6541	207	15	�	�	NOUN
ejpam-6541	207	16	∥	∥	NUM
ejpam-6541	207	17	)	)	PUNCT
ejpam-6541	207	18	,	,	PUNCT
ejpam-6541	207	19	wherein	wherein	SCONJ
ejpam-6541	207	20	∥	∥	PROPN
ejpam-6541	207	21	x	x	SYM
ejpam-6541	207	22	∥=	∥=	NOUN
ejpam-6541	207	23	|x|	|x|	PROPN
ejpam-6541	207	24	,	,	PUNCT
ejpam-6541	207	25	∀x	∀x	X
ejpam-6541	207	26	∈	∈	PROPN
ejpam-6541	207	27	r.	r.	NOUN
ejpam-6541	207	28	describe	describe	VERB
ejpam-6541	207	29	for	for	ADP
ejpam-6541	207	30	all	all	DET
ejpam-6541	207	31	s∗1	s∗1	NOUN
ejpam-6541	207	32	,	,	PUNCT
ejpam-6541	207	33	s	s	NOUN
ejpam-6541	207	34	∗	∗	NOUN
ejpam-6541	207	35	2	2	NUM
ejpam-6541	207	36	∈	∈	PROPN
ejpam-6541	207	37	p[0	p[0	NOUN
ejpam-6541	207	38	,	,	PUNCT
ejpam-6541	207	39	1],s∗1	1],s∗1	NUM
ejpam-6541	207	40	∗	∗	NOUN
ejpam-6541	207	41	s∗2	s∗2	NOUN
ejpam-6541	207	42	=	=	SYM
ejpam-6541	207	43	s∗1	s∗1	ADJ
ejpam-6541	207	44	∩	∩	ADJ
ejpam-6541	207	45	s∗2	s∗2	NOUN
ejpam-6541	207	46	and	and	CCONJ
ejpam-6541	207	47	s∗1	s∗1	ADJ
ejpam-6541	207	48	⋄	⋄	PROPN
ejpam-6541	207	49	s∗2	s∗2	NOUN
ejpam-6541	207	50	=	=	SYM
ejpam-6541	207	51	s∗1	s∗1	NOUN
ejpam-6541	207	52	∪	∪	PROPN
ejpam-6541	207	53	s∗2	s∗2	PROPN
ejpam-6541	207	54	.	.	PUNCT
ejpam-6541	208	1	also	also	ADV
ejpam-6541	208	2	define	define	VERB
ejpam-6541	208	3	ni(x1	ni(x1	ADJ
ejpam-6541	208	4	,	,	PUNCT
ejpam-6541	208	5	t1	t1	NOUN
ejpam-6541	208	6	)	)	PUNCT
ejpam-6541	209	1	=	=	PUNCT
ejpam-6541	210	1			PROPN
ejpam-6541	210	2	∅∗	∅∗	VERB
ejpam-6541	210	3	if	if	SCONJ
ejpam-6541	210	4	t1	t1	NOUN
ejpam-6541	210	5	=	=	SYM
ejpam-6541	210	6	0	0	NUM
ejpam-6541	210	7	and	and	CCONJ
ejpam-6541	210	8	∀	∀	NUM
ejpam-6541	211	1	x1	x1	PRON
ejpam-6541	211	2	>	>	X
ejpam-6541	211	3	0	0	NUM
ejpam-6541	211	4	∈	∈	PROPN
ejpam-6541	211	5	v	v	NOUN
ejpam-6541	211	6	,	,	PUNCT
ejpam-6541	211	7	u∗	u∗	ADV
ejpam-6541	211	8	if	if	SCONJ
ejpam-6541	211	9	x1	x1	PROPN
ejpam-6541	211	10	=	=	SYM
ejpam-6541	211	11	0	0	NUM
ejpam-6541	211	12	and	and	CCONJ
ejpam-6541	211	13	∀	∀	NUM
ejpam-6541	211	14	t1	t1	NOUN
ejpam-6541	211	15	>	>	X
ejpam-6541	211	16	0	0	PROPN
ejpam-6541	211	17	,	,	PUNCT
ejpam-6541	211	18	s∗	s∗	PROPN
ejpam-6541	211	19	otherwise	otherwise	ADV
ejpam-6541	211	20	s∗	s∗	PROPN
ejpam-6541	211	21	∈	∈	PROPN
ejpam-6541	211	22	p[0	p[0	PROPN
ejpam-6541	211	23	,	,	PUNCT
ejpam-6541	211	24	1	1	NUM
ejpam-6541	211	25	]	]	PUNCT
ejpam-6541	211	26	,	,	PUNCT
ejpam-6541	211	27	where	where	SCONJ
ejpam-6541	211	28	s∗	s∗	PROPN
ejpam-6541	211	29	is	be	AUX
ejpam-6541	211	30	an	an	DET
ejpam-6541	211	31	arbitrary	arbitrary	ADJ
ejpam-6541	211	32	subset	subset	NOUN
ejpam-6541	211	33	of	of	ADP
ejpam-6541	211	34	p[0	p[0	NOUN
ejpam-6541	211	35	,	,	PUNCT
ejpam-6541	211	36	1	1	NUM
ejpam-6541	211	37	]	]	PUNCT
ejpam-6541	211	38	.	.	PUNCT
ejpam-6541	212	1	and	and	CCONJ
ejpam-6541	212	2	mi(x1	mi(x1	NOUN
ejpam-6541	212	3	,	,	PUNCT
ejpam-6541	212	4	t1	t1	NOUN
ejpam-6541	212	5	)	)	PUNCT
ejpam-6541	213	1	=	=	PUNCT
ejpam-6541	214	1			PRON
ejpam-6541	214	2	u∗	u∗	VERB
ejpam-6541	214	3	if	if	SCONJ
ejpam-6541	214	4	t1	t1	NOUN
ejpam-6541	214	5	=	=	SYM
ejpam-6541	214	6	0	0	NUM
ejpam-6541	214	7	and	and	CCONJ
ejpam-6541	214	8	∀	∀	NUM
ejpam-6541	215	1	x1	x1	PRON
ejpam-6541	215	2	>	>	X
ejpam-6541	215	3	0	0	NUM
ejpam-6541	215	4	∈	∈	PROPN
ejpam-6541	215	5	v	v	NOUN
ejpam-6541	215	6	,	,	PUNCT
ejpam-6541	215	7	∅∗	∅∗	ADP
ejpam-6541	215	8	if	if	SCONJ
ejpam-6541	215	9	x1	x1	PROPN
ejpam-6541	215	10	=	=	SYM
ejpam-6541	215	11	0	0	NUM
ejpam-6541	215	12	and	and	CCONJ
ejpam-6541	215	13	∀	∀	NUM
ejpam-6541	215	14	t1	t1	NOUN
ejpam-6541	215	15	>	>	X
ejpam-6541	215	16	0	0	PROPN
ejpam-6541	215	17	,	,	PUNCT
ejpam-6541	215	18	s∗	s∗	PROPN
ejpam-6541	215	19	otherwise	otherwise	ADV
ejpam-6541	215	20	s∗	s∗	PROPN
ejpam-6541	215	21	∈	∈	PROPN
ejpam-6541	215	22	p[0	p[0	PROPN
ejpam-6541	215	23	,	,	PUNCT
ejpam-6541	215	24	1	1	NUM
ejpam-6541	215	25	]	]	PUNCT
ejpam-6541	215	26	,	,	PUNCT
ejpam-6541	215	27	where	where	SCONJ
ejpam-6541	215	28	s∗	s∗	PROPN
ejpam-6541	215	29	is	be	AUX
ejpam-6541	215	30	an	an	DET
ejpam-6541	215	31	arbitrary	arbitrary	ADJ
ejpam-6541	215	32	subset	subset	NOUN
ejpam-6541	215	33	of	of	ADP
ejpam-6541	215	34	p[0	p[0	NOUN
ejpam-6541	215	35	,	,	PUNCT
ejpam-6541	215	36	1	1	NUM
ejpam-6541	215	37	]	]	PUNCT
ejpam-6541	215	38	.	.	PUNCT
ejpam-6541	216	1	definition	definition	NOUN
ejpam-6541	216	2	17	17	NUM
ejpam-6541	216	3	.	.	PUNCT
ejpam-6541	217	1	let	let	AUX
ejpam-6541	217	2	(	(	PUNCT
ejpam-6541	217	3	v	v	NOUN
ejpam-6541	217	4	,	,	PUNCT
ejpam-6541	217	5	hihf	hihf	PROPN
ejpam-6541	217	6	)	)	PUNCT
ejpam-6541	217	7	be	be	AUX
ejpam-6541	217	8	an	an	DET
ejpam-6541	217	9	intuitionistic	intuitionistic	ADJ
ejpam-6541	217	10	hesitant	hesitant	ADJ
ejpam-6541	217	11	fuzzy	fuzzy	ADJ
ejpam-6541	217	12	normed	norme	VERB
ejpam-6541	217	13	linear	linear	ADJ
ejpam-6541	217	14	space	space	NOUN
ejpam-6541	217	15	.	.	PUNCT
ejpam-6541	218	1	if	if	SCONJ
ejpam-6541	218	2	dimension	dimension	NOUN
ejpam-6541	218	3	of	of	ADP
ejpam-6541	218	4	a	a	DET
ejpam-6541	218	5	vector	vector	NOUN
ejpam-6541	218	6	space	space	NOUN
ejpam-6541	218	7	v	v	NOUN
ejpam-6541	218	8	is	be	AUX
ejpam-6541	218	9	finite	finite	NOUN
ejpam-6541	218	10	then	then	ADV
ejpam-6541	218	11	it	it	PRON
ejpam-6541	218	12	is	be	AUX
ejpam-6541	218	13	called	call	VERB
ejpam-6541	218	14	finite	finite	ADJ
ejpam-6541	218	15	dimensional	dimensional	ADJ
ejpam-6541	218	16	intuitionistic	intuitionistic	ADJ
ejpam-6541	218	17	hesitant	hesitant	ADJ
ejpam-6541	218	18	fuzzy	fuzzy	ADJ
ejpam-6541	218	19	normed	norme	VERB
ejpam-6541	218	20	linear	linear	ADJ
ejpam-6541	218	21	space	space	NOUN
ejpam-6541	218	22	.	.	PUNCT
ejpam-6541	219	1	definition	definition	NOUN
ejpam-6541	219	2	18	18	NUM
ejpam-6541	219	3	.	.	PUNCT
ejpam-6541	220	1	[	[	X
ejpam-6541	220	2	19	19	NUM
ejpam-6541	220	3	]	]	X
ejpam-6541	220	4	if	if	SCONJ
ejpam-6541	220	5	given	give	VERB
ejpam-6541	220	6	s∗	s∗	PROPN
ejpam-6541	220	7	1	1	NUM
ejpam-6541	220	8	̸=	̸=	PROPN
ejpam-6541	220	9	∅∗	∅∗	PROPN
ejpam-6541	220	10	,	,	PUNCT
ejpam-6541	220	11	t	t	PROPN
ejpam-6541	220	12	>	>	X
ejpam-6541	220	13	0	0	NUM
ejpam-6541	220	14	,	,	PUNCT
ejpam-6541	220	15	∅∗	∅∗	PROPN
ejpam-6541	221	1	⊂	⊂	PROPN
ejpam-6541	221	2	s∗	s∗	VERB
ejpam-6541	221	3	1	1	NUM
ejpam-6541	221	4	⊂	⊂	PROPN
ejpam-6541	221	5	u∗,∃	u∗,∃	PROPN
ejpam-6541	221	6	n0	n0	X
ejpam-6541	221	7	∈	∈	PROPN
ejpam-6541	222	1	n	n	PRON
ejpam-6541	222	2	so	so	ADV
ejpam-6541	222	3	that	that	SCONJ
ejpam-6541	222	4	,	,	PUNCT
ejpam-6541	222	5	nihf	nihf	PROPN
ejpam-6541	222	6	(	(	PUNCT
ejpam-6541	222	7	xn	xn	PROPN
ejpam-6541	223	1	−	−	PROPN
ejpam-6541	223	2	x1	x1	PROPN
ejpam-6541	223	3	,	,	PUNCT
ejpam-6541	223	4	t1	t1	PROPN
ejpam-6541	223	5	)	)	PUNCT
ejpam-6541	223	6	⊃	⊃	PROPN
ejpam-6541	223	7	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	223	8	1	1	NUM
ejpam-6541	223	9	and	and	CCONJ
ejpam-6541	223	10	mihf	mihf	PROPN
ejpam-6541	223	11	(	(	PUNCT
ejpam-6541	223	12	xn	xn	PROPN
ejpam-6541	223	13	−	−	PROPN
ejpam-6541	223	14	x1	x1	PROPN
ejpam-6541	223	15	,	,	PUNCT
ejpam-6541	223	16	t1	t1	PROPN
ejpam-6541	223	17	)	)	PUNCT
ejpam-6541	224	1	⊂	⊂	PRON
ejpam-6541	224	2	s∗	s∗	VERB
ejpam-6541	224	3	1	1	NUM
ejpam-6541	224	4	,	,	PUNCT
ejpam-6541	224	5	∀	∀	X
ejpam-6541	224	6	n	n	PRON
ejpam-6541	224	7	≥	≥	NOUN
ejpam-6541	224	8	n0	n0	NUM
ejpam-6541	224	9	.	.	PUNCT
ejpam-6541	224	10	theorem	theorem	VERB
ejpam-6541	224	11	4	4	NUM
ejpam-6541	224	12	.	.	PUNCT
ejpam-6541	225	1	[	[	X
ejpam-6541	225	2	19	19	NUM
ejpam-6541	225	3	]	]	PUNCT
ejpam-6541	225	4	in	in	ADP
ejpam-6541	225	5	an	an	DET
ejpam-6541	225	6	ihfnls	ihfnls	NOUN
ejpam-6541	225	7	(	(	PUNCT
ejpam-6541	225	8	v	v	NOUN
ejpam-6541	225	9	,	,	PUNCT
ejpam-6541	225	10	hihf	hihf	PROPN
ejpam-6541	225	11	)	)	PUNCT
ejpam-6541	225	12	,	,	PUNCT
ejpam-6541	225	13	a	a	DET
ejpam-6541	225	14	sequence	sequence	NOUN
ejpam-6541	225	15	{	{	PUNCT
ejpam-6541	225	16	xn}n	xn}n	PROPN
ejpam-6541	225	17	converges	converge	VERB
ejpam-6541	225	18	to	to	ADP
ejpam-6541	225	19	x1	x1	PROPN
ejpam-6541	225	20	∈	∈	PROPN
ejpam-6541	225	21	v	v	NOUN
ejpam-6541	225	22	if	if	SCONJ
ejpam-6541	225	23	and	and	CCONJ
ejpam-6541	225	24	only	only	ADV
ejpam-6541	225	25	if	if	SCONJ
ejpam-6541	225	26	limn→∞	limn→∞	PROPN
ejpam-6541	225	27	nihf	nihf	PROPN
ejpam-6541	225	28	(	(	PUNCT
ejpam-6541	225	29	xn	xn	PROPN
ejpam-6541	225	30	−	−	PROPN
ejpam-6541	225	31	x1	x1	PROPN
ejpam-6541	225	32	,	,	PUNCT
ejpam-6541	225	33	t1	t1	PROPN
ejpam-6541	225	34	)	)	PUNCT
ejpam-6541	225	35	=	=	PUNCT
ejpam-6541	226	1	u∗	u∗	ADJ
ejpam-6541	226	2	along	along	ADV
ejpam-6541	226	3	with	with	ADP
ejpam-6541	226	4	limn→∞	limn→∞	PROPN
ejpam-6541	226	5	mihf	mihf	PROPN
ejpam-6541	226	6	(	(	PUNCT
ejpam-6541	226	7	xn	xn	PROPN
ejpam-6541	226	8	−	−	PROPN
ejpam-6541	226	9	x1	x1	PROPN
ejpam-6541	226	10	,	,	PUNCT
ejpam-6541	226	11	t1	t1	NOUN
ejpam-6541	226	12	)	)	PUNCT
ejpam-6541	226	13	=	=	SYM
ejpam-6541	226	14	∅∗.	∅∗.	NUM
ejpam-6541	226	15	theorem	theorem	AUX
ejpam-6541	226	16	5	5	NUM
ejpam-6541	226	17	.	.	PUNCT
ejpam-6541	227	1	[	[	X
ejpam-6541	227	2	19	19	NUM
ejpam-6541	227	3	]	]	PUNCT
ejpam-6541	227	4	in	in	ADP
ejpam-6541	227	5	an	an	DET
ejpam-6541	227	6	ihfnls	ihfnls	NOUN
ejpam-6541	227	7	(	(	PUNCT
ejpam-6541	227	8	v	v	NOUN
ejpam-6541	227	9	,	,	PUNCT
ejpam-6541	227	10	hihf	hihf	PROPN
ejpam-6541	227	11	)	)	PUNCT
ejpam-6541	227	12	,	,	PUNCT
ejpam-6541	227	13	a	a	DET
ejpam-6541	227	14	sequence	sequence	NOUN
ejpam-6541	227	15	{	{	PUNCT
ejpam-6541	227	16	xn}n	xn}n	PROPN
ejpam-6541	227	17	has	have	AUX
ejpam-6541	227	18	a	a	DET
ejpam-6541	227	19	unique	unique	ADJ
ejpam-6541	227	20	limit	limit	NOUN
ejpam-6541	227	21	if	if	SCONJ
ejpam-6541	227	22	it	it	PRON
ejpam-6541	227	23	is	be	AUX
ejpam-6541	227	24	convergent	convergent	ADJ
ejpam-6541	227	25	.	.	PUNCT
ejpam-6541	228	1	k.	k.	PROPN
ejpam-6541	228	2	kavitha	kavitha	PROPN
ejpam-6541	228	3	,	,	PUNCT
ejpam-6541	228	4	p.	p.	PROPN
ejpam-6541	228	5	muralikrishna	muralikrishna	PROPN
ejpam-6541	228	6	/	/	SYM
ejpam-6541	228	7	eur	eur	PROPN
ejpam-6541	228	8	.	.	PUNCT
ejpam-6541	229	1	j.	j.	PROPN
ejpam-6541	229	2	pure	pure	PROPN
ejpam-6541	229	3	appl	appl	PROPN
ejpam-6541	229	4	.	.	PROPN
ejpam-6541	229	5	math	math	PROPN
ejpam-6541	229	6	,	,	PUNCT
ejpam-6541	229	7	18	18	NUM
ejpam-6541	229	8	(	(	PUNCT
ejpam-6541	229	9	4	4	NUM
ejpam-6541	229	10	)	)	PUNCT
ejpam-6541	229	11	(	(	PUNCT
ejpam-6541	229	12	2025	2025	NUM
ejpam-6541	229	13	)	)	PUNCT
ejpam-6541	229	14	,	,	PUNCT
ejpam-6541	229	15	6541	6541	NUM
ejpam-6541	229	16	8	8	NUM
ejpam-6541	229	17	of	of	ADP
ejpam-6541	229	18	14	14	NUM
ejpam-6541	229	19	lemma	lemma	PROPN
ejpam-6541	229	20	2	2	NUM
ejpam-6541	229	21	.	.	PUNCT
ejpam-6541	229	22	consider	consider	VERB
ejpam-6541	229	23	an	an	DET
ejpam-6541	229	24	intuitionistic	intuitionistic	ADJ
ejpam-6541	229	25	hesitant	hesitant	ADJ
ejpam-6541	229	26	fuzzy	fuzzy	ADJ
ejpam-6541	229	27	normed	norme	VERB
ejpam-6541	229	28	linear	linear	ADJ
ejpam-6541	229	29	space	space	NOUN
ejpam-6541	229	30	(	(	PUNCT
ejpam-6541	229	31	v	v	NOUN
ejpam-6541	229	32	,	,	PUNCT
ejpam-6541	229	33	hihf	hihf	PROPN
ejpam-6541	229	34	)	)	PUNCT
ejpam-6541	229	35	,	,	PUNCT
ejpam-6541	229	36	where	where	SCONJ
ejpam-6541	229	37	{	{	PUNCT
ejpam-6541	229	38	x1	x1	ADJ
ejpam-6541	229	39	,	,	PUNCT
ejpam-6541	229	40	x2	x2	PROPN
ejpam-6541	229	41	,	,	PUNCT
ejpam-6541	229	42	.	.	PUNCT
ejpam-6541	229	43	.	.	PUNCT
ejpam-6541	230	1	.	.	PUNCT
ejpam-6541	231	1	,	,	PUNCT
ejpam-6541	231	2	xn	xn	X
ejpam-6541	231	3	}	}	PUNCT
ejpam-6541	231	4	is	be	AUX
ejpam-6541	231	5	a	a	DET
ejpam-6541	231	6	set	set	NOUN
ejpam-6541	231	7	of	of	ADP
ejpam-6541	231	8	vectors	vector	NOUN
ejpam-6541	231	9	in	in	ADP
ejpam-6541	231	10	v	v	NOUN
ejpam-6541	231	11	,	,	PUNCT
ejpam-6541	231	12	that	that	PRON
ejpam-6541	231	13	are	be	AUX
ejpam-6541	231	14	linearly	linearly	ADV
ejpam-6541	231	15	independent	independent	ADJ
ejpam-6541	231	16	along	along	ADP
ejpam-6541	231	17	with	with	ADP
ejpam-6541	231	18	the	the	DET
ejpam-6541	231	19	underlying	underlying	ADJ
ejpam-6541	231	20	t	t	NOUN
ejpam-6541	231	21	-	-	PUNCT
ejpam-6541	231	22	norm	norm	NOUN
ejpam-6541	231	23	∗	∗	NOUN
ejpam-6541	231	24	along	along	ADP
ejpam-6541	231	25	with	with	ADP
ejpam-6541	231	26	t	t	PROPN
ejpam-6541	231	27	-	-	PUNCT
ejpam-6541	231	28	co	co	NOUN
ejpam-6541	231	29	–	–	PUNCT
ejpam-6541	231	30	norm	norm	ADJ
ejpam-6541	231	31	⋄	⋄	PROPN
ejpam-6541	231	32	are	be	AUX
ejpam-6541	231	33	continuous	continuous	ADJ
ejpam-6541	231	34	at	at	ADP
ejpam-6541	231	35	(	(	PUNCT
ejpam-6541	231	36	0	0	NUM
ejpam-6541	231	37	,	,	PUNCT
ejpam-6541	231	38	0	0	NUM
ejpam-6541	231	39	)	)	PUNCT
ejpam-6541	231	40	and	and	CCONJ
ejpam-6541	231	41	(	(	PUNCT
ejpam-6541	231	42	1	1	NUM
ejpam-6541	231	43	,	,	PUNCT
ejpam-6541	231	44	1	1	NUM
ejpam-6541	231	45	)	)	PUNCT
ejpam-6541	231	46	respectively	respectively	ADV
ejpam-6541	231	47	.	.	PUNCT
ejpam-6541	232	1	then	then	ADV
ejpam-6541	232	2	there	there	PRON
ejpam-6541	232	3	exists	exist	VERB
ejpam-6541	232	4	h1	h1	PROPN
ejpam-6541	232	5	,	,	PUNCT
ejpam-6541	232	6	h2	h2	PROPN
ejpam-6541	232	7	>	>	X
ejpam-6541	232	8	0	0	PUNCT
ejpam-6541	233	1	and	and	CCONJ
ejpam-6541	233	2	there	there	PRON
ejpam-6541	233	3	exists	exist	VERB
ejpam-6541	233	4	s∗	s∗	PROPN
ejpam-6541	233	5	1	1	NUM
ejpam-6541	233	6	,	,	PUNCT
ejpam-6541	233	7	s	s	NOUN
ejpam-6541	233	8	∗	∗	NOUN
ejpam-6541	233	9	2	2	NUM
ejpam-6541	233	10	∈	∈	NOUN
ejpam-6541	233	11	p[0	p[0	NOUN
ejpam-6541	233	12	,	,	PUNCT
ejpam-6541	233	13	1	1	NUM
ejpam-6541	233	14	]	]	PUNCT
ejpam-6541	234	1	so	so	SCONJ
ejpam-6541	234	2	that	that	SCONJ
ejpam-6541	234	3	for	for	ADP
ejpam-6541	234	4	any	any	DET
ejpam-6541	234	5	collection	collection	NOUN
ejpam-6541	234	6	of	of	ADP
ejpam-6541	234	7	scalars	scalar	NOUN
ejpam-6541	234	8	,	,	PUNCT
ejpam-6541	234	9	{	{	PUNCT
ejpam-6541	234	10	δ1	δ1	NOUN
ejpam-6541	234	11	,	,	PUNCT
ejpam-6541	234	12	δ2	δ2	PROPN
ejpam-6541	234	13	,	,	PUNCT
ejpam-6541	234	14	.	.	PUNCT
ejpam-6541	234	15	.	.	PUNCT
ejpam-6541	234	16	.	.	PUNCT
ejpam-6541	234	17	,	,	PUNCT
ejpam-6541	234	18	δn	δn	NOUN
ejpam-6541	234	19	}	}	PUNCT
ejpam-6541	234	20	,	,	PUNCT
ejpam-6541	234	21	nihf	nihf	PROPN
ejpam-6541	234	22	{	{	PUNCT
ejpam-6541	234	23	δ1x1	δ1x1	ADP
ejpam-6541	234	24	+	+	X
ejpam-6541	234	25	δ2x2	δ2x2	NOUN
ejpam-6541	234	26	+	+	X
ejpam-6541	234	27	.	.	PUNCT
ejpam-6541	234	28	.	.	PUNCT
ejpam-6541	234	29	.	.	PUNCT
ejpam-6541	235	1	,	,	PUNCT
ejpam-6541	235	2	+	+	NOUN
ejpam-6541	235	3	δnxn	δnxn	NOUN
ejpam-6541	235	4	,	,	PUNCT
ejpam-6541	235	5	h1	h1	NOUN
ejpam-6541	235	6	n∑	n∑	NOUN
ejpam-6541	235	7	k=1	k=1	PUNCT
ejpam-6541	236	1	|δk|	|δk|	X
ejpam-6541	236	2	}	}	PUNCT
ejpam-6541	237	1	⊂	⊂	PROPN
ejpam-6541	238	1	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	238	2	1	1	NUM
ejpam-6541	238	3	(	(	PUNCT
ejpam-6541	238	4	1	1	NUM
ejpam-6541	238	5	)	)	PUNCT
ejpam-6541	238	6	mihf	mihf	NOUN
ejpam-6541	238	7	{	{	PUNCT
ejpam-6541	238	8	δ1x1	δ1x1	ADP
ejpam-6541	238	9	+	+	X
ejpam-6541	238	10	δ2x2	δ2x2	NOUN
ejpam-6541	238	11	+	+	X
ejpam-6541	238	12	.	.	PUNCT
ejpam-6541	238	13	.	.	PUNCT
ejpam-6541	238	14	.	.	PUNCT
ejpam-6541	239	1	,	,	PUNCT
ejpam-6541	239	2	+	+	NOUN
ejpam-6541	239	3	δnxn	δnxn	NOUN
ejpam-6541	239	4	,	,	PUNCT
ejpam-6541	239	5	h2	h2	PROPN
ejpam-6541	239	6	n∑	n∑	NOUN
ejpam-6541	239	7	k=1	k=1	PUNCT
ejpam-6541	240	1	|δk|	|δk|	PROPN
ejpam-6541	240	2	}	}	PUNCT
ejpam-6541	240	3	⊃	⊃	NOUN
ejpam-6541	240	4	s∗	s∗	PROPN
ejpam-6541	240	5	2	2	NUM
ejpam-6541	240	6	(	(	PUNCT
ejpam-6541	240	7	2	2	NUM
ejpam-6541	240	8	)	)	PUNCT
ejpam-6541	240	9	proof	proof	NOUN
ejpam-6541	240	10	.	.	PUNCT
ejpam-6541	241	1	let	let	VERB
ejpam-6541	241	2	t	t	NOUN
ejpam-6541	241	3	=	=	SYM
ejpam-6541	241	4	|δ1|	|δ1|	ADJ
ejpam-6541	241	5	+	+	CCONJ
ejpam-6541	241	6	|δ2|	|δ2|	NOUN
ejpam-6541	241	7	+	+	X
ejpam-6541	241	8	·	·	PUNCT
ejpam-6541	241	9	·	·	PUNCT
ejpam-6541	241	10	·	·	PUNCT
ejpam-6541	242	1	+	+	PUNCT
ejpam-6541	242	2	|δn|	|δn|	PROPN
ejpam-6541	242	3	.	.	PUNCT
ejpam-6541	243	1	if	if	SCONJ
ejpam-6541	243	2	t	t	NOUN
ejpam-6541	243	3	=	=	SYM
ejpam-6541	243	4	0	0	NUM
ejpam-6541	243	5	,	,	PUNCT
ejpam-6541	243	6	then	then	ADV
ejpam-6541	243	7	δk	δk	ADP
ejpam-6541	243	8	=	=	SYM
ejpam-6541	243	9	0	0	NUM
ejpam-6541	243	10	,	,	PUNCT
ejpam-6541	243	11	∀k	∀k	NOUN
ejpam-6541	243	12	=	=	SYM
ejpam-6541	243	13	1	1	NUM
ejpam-6541	243	14	,	,	PUNCT
ejpam-6541	243	15	2	2	NUM
ejpam-6541	243	16	,	,	PUNCT
ejpam-6541	243	17	.	.	PUNCT
ejpam-6541	243	18	.	.	PUNCT
ejpam-6541	243	19	.	.	PUNCT
ejpam-6541	244	1	n	n	CCONJ
ejpam-6541	244	2	and	and	CCONJ
ejpam-6541	244	3	the	the	DET
ejpam-6541	244	4	relation	relation	NOUN
ejpam-6541	244	5	,	,	PUNCT
ejpam-6541	244	6	nihf{δ1x1	nihf{δ1x1	VERB
ejpam-6541	244	7	+	+	PUNCT
ejpam-6541	244	8	δ2x2	δ2x2	X
ejpam-6541	244	9	+	+	X
ejpam-6541	244	10	.	.	PUNCT
ejpam-6541	244	11	.	.	PUNCT
ejpam-6541	244	12	.	.	PUNCT
ejpam-6541	245	1	,	,	PUNCT
ejpam-6541	245	2	+	+	NOUN
ejpam-6541	245	3	δnxn	δnxn	NOUN
ejpam-6541	245	4	,	,	PUNCT
ejpam-6541	245	5	h1	h1	VERB
ejpam-6541	245	6	∑n	∑n	PROPN
ejpam-6541	245	7	k=1	k=1	PUNCT
ejpam-6541	245	8	|δk|	|δk|	PROPN
ejpam-6541	245	9	}	}	PUNCT
ejpam-6541	245	10	⊂	⊂	PROPN
ejpam-6541	245	11	u∗\s∗1	u∗\s∗1	PROPN
ejpam-6541	245	12	is	be	AUX
ejpam-6541	245	13	true	true	ADJ
ejpam-6541	245	14	for	for	ADP
ejpam-6541	245	15	any	any	DET
ejpam-6541	245	16	h	h	NOUN
ejpam-6541	245	17	>	>	X
ejpam-6541	245	18	0,and	0,and	NUM
ejpam-6541	245	19	s∗	s∗	PROPN
ejpam-6541	245	20	∈	∈	PROPN
ejpam-6541	245	21	p[0	p[0	PROPN
ejpam-6541	245	22	,	,	PUNCT
ejpam-6541	245	23	1	1	NUM
ejpam-6541	245	24	]	]	PUNCT
ejpam-6541	245	25	.	.	PUNCT
ejpam-6541	246	1	then	then	ADV
ejpam-6541	246	2	,	,	PUNCT
ejpam-6541	246	3	we	we	PRON
ejpam-6541	246	4	assume	assume	VERB
ejpam-6541	246	5	that	that	SCONJ
ejpam-6541	246	6	t	t	PROPN
ejpam-6541	246	7	>	>	X
ejpam-6541	246	8	0	0	PROPN
ejpam-6541	246	9	.	.	PUNCT
ejpam-6541	247	1	then	then	ADV
ejpam-6541	247	2	(	(	PUNCT
ejpam-6541	247	3	1	1	X
ejpam-6541	247	4	)	)	PUNCT
ejpam-6541	247	5	is	be	AUX
ejpam-6541	247	6	equivalent	equivalent	ADJ
ejpam-6541	247	7	to	to	PART
ejpam-6541	247	8	nihf	nihf	VERB
ejpam-6541	247	9	{	{	PUNCT
ejpam-6541	247	10	ω1x1	ω1x1	X
ejpam-6541	247	11	+	+	X
ejpam-6541	247	12	ω2x2	ω2x2	X
ejpam-6541	247	13	+	+	CCONJ
ejpam-6541	247	14	.	.	PUNCT
ejpam-6541	247	15	.	.	PUNCT
ejpam-6541	247	16	.	.	PUNCT
ejpam-6541	248	1	,	,	PUNCT
ejpam-6541	248	2	+	+	PUNCT
ejpam-6541	248	3	ωnxn	ωnxn	ADJ
ejpam-6541	248	4	,	,	PUNCT
ejpam-6541	248	5	h1	h1	PROPN
ejpam-6541	248	6	}	}	PUNCT
ejpam-6541	248	7	⊂	⊂	X
ejpam-6541	248	8	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	248	9	1	1	NUM
ejpam-6541	248	10	(	(	PUNCT
ejpam-6541	248	11	3	3	NUM
ejpam-6541	248	12	)	)	PUNCT
ejpam-6541	248	13	for	for	ADP
ejpam-6541	248	14	any	any	DET
ejpam-6541	248	15	scalars	scalar	NOUN
ejpam-6541	248	16	ω′s	ω′s	PROPN
ejpam-6541	248	17	with	with	ADP
ejpam-6541	248	18	∑n	∑n	PROPN
ejpam-6541	249	1	k=1	k=1	PROPN
ejpam-6541	249	2	|ωk|	|ωk|	PROPN
ejpam-6541	249	3	=	=	SYM
ejpam-6541	249	4	1	1	NUM
ejpam-6541	249	5	and	and	CCONJ
ejpam-6541	249	6	for	for	ADP
ejpam-6541	249	7	some	some	DET
ejpam-6541	249	8	h1	h1	NOUN
ejpam-6541	249	9	>	>	X
ejpam-6541	249	10	0	0	PUNCT
ejpam-6541	249	11	and	and	CCONJ
ejpam-6541	249	12	s∗	s∗	PROPN
ejpam-6541	249	13	∈	∈	PROPN
ejpam-6541	249	14	p[0	p[0	NOUN
ejpam-6541	249	15	,	,	PUNCT
ejpam-6541	249	16	1	1	NUM
ejpam-6541	249	17	]	]	PUNCT
ejpam-6541	249	18	.	.	PUNCT
ejpam-6541	250	1	assume	assume	VERB
ejpam-6541	250	2	(	(	PUNCT
ejpam-6541	250	3	3	3	X
ejpam-6541	250	4	)	)	PUNCT
ejpam-6541	250	5	is	be	AUX
ejpam-6541	250	6	not	not	PART
ejpam-6541	250	7	true	true	ADJ
ejpam-6541	250	8	,	,	PUNCT
ejpam-6541	250	9	if	if	SCONJ
ejpam-6541	250	10	at	at	ADV
ejpam-6541	250	11	all	all	ADV
ejpam-6541	250	12	possible	possible	ADJ
ejpam-6541	250	13	.	.	PUNCT
ejpam-6541	251	1	consequently	consequently	ADV
ejpam-6541	251	2	,	,	PUNCT
ejpam-6541	251	3	for	for	ADP
ejpam-6541	251	4	each	each	DET
ejpam-6541	251	5	h	h	NOUN
ejpam-6541	251	6	>	>	X
ejpam-6541	251	7	0	0	PUNCT
ejpam-6541	251	8	and	and	CCONJ
ejpam-6541	251	9	s∗	s∗	PROPN
ejpam-6541	251	10	1	1	NUM
ejpam-6541	251	11	∈	∈	PROPN
ejpam-6541	251	12	p[0	p[0	NOUN
ejpam-6541	251	13	,	,	PUNCT
ejpam-6541	251	14	1	1	NUM
ejpam-6541	251	15	]	]	PUNCT
ejpam-6541	251	16	,	,	PUNCT
ejpam-6541	251	17	there	there	PRON
ejpam-6541	251	18	will	will	AUX
ejpam-6541	251	19	be	be	AUX
ejpam-6541	251	20	a	a	DET
ejpam-6541	251	21	collection	collection	NOUN
ejpam-6541	251	22	regarding	regard	VERB
ejpam-6541	251	23	scalars	scalars	PROPN
ejpam-6541	251	24	{	{	PUNCT
ejpam-6541	251	25	ω1	ω1	PROPN
ejpam-6541	251	26	,	,	PUNCT
ejpam-6541	251	27	ω2	ω2	ADJ
ejpam-6541	251	28	,	,	PUNCT
ejpam-6541	251	29	.	.	PUNCT
ejpam-6541	251	30	.	.	PUNCT
ejpam-6541	251	31	.	.	PUNCT
ejpam-6541	252	1	ωn	ωn	AUX
ejpam-6541	252	2	}	}	PUNCT
ejpam-6541	252	3	using	use	VERB
ejpam-6541	252	4	∑n	∑n	PROPN
ejpam-6541	252	5	k=1	k=1	PROPN
ejpam-6541	252	6	|ωk|	|ωk|	PROPN
ejpam-6541	252	7	=	=	NOUN
ejpam-6541	252	8	1	1	NUM
ejpam-6541	252	9	for	for	ADP
ejpam-6541	252	10	which	which	PRON
ejpam-6541	252	11	,	,	PUNCT
ejpam-6541	252	12	nihf	nihf	PROPN
ejpam-6541	252	13	{	{	PUNCT
ejpam-6541	252	14	ω1x1	ω1x1	X
ejpam-6541	252	15	+	+	X
ejpam-6541	252	16	ω2x2	ω2x2	X
ejpam-6541	252	17	+	+	CCONJ
ejpam-6541	252	18	.	.	PUNCT
ejpam-6541	252	19	.	.	PUNCT
ejpam-6541	252	20	.	.	PUNCT
ejpam-6541	253	1	,	,	PUNCT
ejpam-6541	253	2	+	+	NOUN
ejpam-6541	253	3	ωnxn	ωnxn	ADJ
ejpam-6541	253	4	,	,	PUNCT
ejpam-6541	253	5	h	h	NOUN
ejpam-6541	253	6	}	}	PUNCT
ejpam-6541	253	7	⊇	⊇	NOUN
ejpam-6541	253	8	u∗\s∗.	u∗\s∗.	ADJ
ejpam-6541	253	9	then	then	ADV
ejpam-6541	253	10	for	for	ADP
ejpam-6541	253	11	h	h	NOUN
ejpam-6541	253	12	=	=	SYM
ejpam-6541	253	13	{	{	PUNCT
ejpam-6541	253	14	1	1	NUM
ejpam-6541	253	15	m},m	m},m	NOUN
ejpam-6541	253	16	=	=	SYM
ejpam-6541	253	17	1	1	NUM
ejpam-6541	253	18	,	,	PUNCT
ejpam-6541	253	19	2	2	NUM
ejpam-6541	253	20	,	,	PUNCT
ejpam-6541	253	21	.	.	PUNCT
ejpam-6541	253	22	.	.	PUNCT
ejpam-6541	254	1	.	.	PUNCT
ejpam-6541	255	1	,	,	PUNCT
ejpam-6541	255	2	there	there	PRON
ejpam-6541	255	3	will	will	AUX
ejpam-6541	255	4	be	be	AUX
ejpam-6541	255	5	a	a	DET
ejpam-6541	255	6	collection	collection	NOUN
ejpam-6541	255	7	regarding	regard	VERB
ejpam-6541	255	8	scalars	scalar	NOUN
ejpam-6541	255	9	{	{	PUNCT
ejpam-6541	255	10	ωm	ωm	NUM
ejpam-6541	255	11	1	1	NUM
ejpam-6541	255	12	,	,	PUNCT
ejpam-6541	255	13	ωm	ωm	NUM
ejpam-6541	255	14	2	2	NUM
ejpam-6541	255	15	,	,	PUNCT
ejpam-6541	255	16	.	.	PUNCT
ejpam-6541	255	17	.	.	PUNCT
ejpam-6541	256	1	.	.	PUNCT
ejpam-6541	257	1	,	,	PUNCT
ejpam-6541	257	2	ωm	ωm	PUNCT
ejpam-6541	257	3	n	n	CCONJ
ejpam-6541	257	4	}	}	PUNCT
ejpam-6541	257	5	with	with	ADP
ejpam-6541	257	6	∑n	∑n	PROPN
ejpam-6541	258	1	k=1	k=1	X
ejpam-6541	258	2	|ωm	|ωm	NUM
ejpam-6541	259	1	k	k	NOUN
ejpam-6541	260	1	|	|	NOUN
ejpam-6541	260	2	=	=	SYM
ejpam-6541	260	3	1	1	NUM
ejpam-6541	260	4	so	so	SCONJ
ejpam-6541	260	5	that	that	SCONJ
ejpam-6541	260	6	nihf(ym	nihf(ym	NOUN
ejpam-6541	260	7	,	,	PUNCT
ejpam-6541	260	8	1	1	NUM
ejpam-6541	260	9	m	m	NOUN
ejpam-6541	260	10	)	)	PUNCT
ejpam-6541	260	11	⊃	⊃	PROPN
ejpam-6541	260	12	u∗\	u∗\	NOUN
ejpam-6541	260	13	{	{	PUNCT
ejpam-6541	260	14	1	1	NUM
ejpam-6541	260	15	m	m	NOUN
ejpam-6541	260	16	}	}	PUNCT
ejpam-6541	260	17	where	where	SCONJ
ejpam-6541	260	18	ym	ym	PROPN
ejpam-6541	260	19	=	=	SYM
ejpam-6541	260	20	ωm	ωm	PUNCT
ejpam-6541	261	1	1	1	NUM
ejpam-6541	261	2	x1	x1	PROPN
ejpam-6541	261	3	+	+	CCONJ
ejpam-6541	261	4	ωm	ωm	ADJ
ejpam-6541	261	5	2	2	NUM
ejpam-6541	261	6	x2	x2	PROPN
ejpam-6541	261	7	+	+	PROPN
ejpam-6541	261	8	,	,	PUNCT
ejpam-6541	261	9	.	.	PUNCT
ejpam-6541	261	10	.	.	PUNCT
ejpam-6541	261	11	.	.	PUNCT
ejpam-6541	262	1	,	,	PUNCT
ejpam-6541	262	2	ωm	ωm	PROPN
ejpam-6541	262	3	n	n	ADV
ejpam-6541	262	4	xn	xn	PROPN
ejpam-6541	262	5	.	.	PUNCT
ejpam-6541	263	1	since	since	SCONJ
ejpam-6541	263	2	,	,	PUNCT
ejpam-6541	263	3	∑n	∑n	PROPN
ejpam-6541	263	4	k=1	k=1	X
ejpam-6541	263	5	|ωm	|ωm	NUM
ejpam-6541	264	1	k	k	NOUN
ejpam-6541	265	1	|	|	NOUN
ejpam-6541	265	2	=	=	NOUN
ejpam-6541	265	3	1	1	NUM
ejpam-6541	265	4	,	,	PUNCT
ejpam-6541	265	5	we	we	PRON
ejpam-6541	265	6	have	have	VERB
ejpam-6541	265	7	0	0	NUM
ejpam-6541	265	8	≤	≤	NUM
ejpam-6541	265	9	|ωm	|ωm	ADP
ejpam-6541	266	1	k	k	NOUN
ejpam-6541	267	1	|	|	ADV
ejpam-6541	267	2	≤	≤	NUM
ejpam-6541	267	3	1	1	NUM
ejpam-6541	267	4	for	for	ADP
ejpam-6541	267	5	k	k	PROPN
ejpam-6541	267	6	=	=	SYM
ejpam-6541	267	7	1	1	NUM
ejpam-6541	267	8	,	,	PUNCT
ejpam-6541	267	9	2	2	NUM
ejpam-6541	267	10	,	,	PUNCT
ejpam-6541	267	11	.	.	PUNCT
ejpam-6541	267	12	.	.	PUNCT
ejpam-6541	267	13	.	.	PUNCT
ejpam-6541	268	1	n.	n.	PROPN
ejpam-6541	268	2	consequently	consequently	ADV
ejpam-6541	268	3	,	,	PUNCT
ejpam-6541	268	4	ωm	ωm	NUM
ejpam-6541	268	5	1	1	NUM
ejpam-6541	268	6	has	have	VERB
ejpam-6541	268	7	a	a	DET
ejpam-6541	268	8	convergent	convergent	NOUN
ejpam-6541	268	9	subsequence	subsequence	NOUN
ejpam-6541	268	10	since	since	SCONJ
ejpam-6541	268	11	the	the	DET
ejpam-6541	268	12	sequence	sequence	NOUN
ejpam-6541	268	13	{	{	PUNCT
ejpam-6541	268	14	ωm	ωm	X
ejpam-6541	268	15	k	k	X
ejpam-6541	268	16	}	}	PUNCT
ejpam-6541	268	17	is	be	AUX
ejpam-6541	268	18	confined	confine	VERB
ejpam-6541	268	19	for	for	ADP
ejpam-6541	268	20	each	each	DET
ejpam-6541	268	21	fixed	fix	VERB
ejpam-6541	268	22	k.	k.	PROPN
ejpam-6541	268	23	let	let	VERB
ejpam-6541	268	24	ω1	ω1	PROPN
ejpam-6541	268	25	represent	represent	VERB
ejpam-6541	268	26	the	the	DET
ejpam-6541	268	27	subsequence	subsequence	NOUN
ejpam-6541	268	28	’s	’s	PART
ejpam-6541	268	29	limit	limit	NOUN
ejpam-6541	268	30	,	,	PUNCT
ejpam-6541	268	31	as	as	ADV
ejpam-6541	268	32	well	well	ADV
ejpam-6541	268	33	as	as	ADP
ejpam-6541	268	34	allow	allow	VERB
ejpam-6541	268	35	{	{	PUNCT
ejpam-6541	268	36	y1	y1	NOUN
ejpam-6541	268	37	m	m	VERB
ejpam-6541	268	38	}	}	PUNCT
ejpam-6541	268	39	represent	represent	VERB
ejpam-6541	268	40	the	the	DET
ejpam-6541	268	41	equivalent	equivalent	ADJ
ejpam-6541	268	42	subsequence	subsequence	NOUN
ejpam-6541	268	43	regarding	regard	VERB
ejpam-6541	268	44	{	{	PUNCT
ejpam-6541	268	45	ym	ym	NOUN
ejpam-6541	268	46	}	}	PUNCT
ejpam-6541	268	47	.	.	PUNCT
ejpam-6541	269	1	the	the	DET
ejpam-6541	269	2	equivalent	equivalent	ADJ
ejpam-6541	269	3	subsequence	subsequence	NOUN
ejpam-6541	269	4	of	of	ADP
ejpam-6541	269	5	scalars	scalars	PROPN
ejpam-6541	269	6	{	{	PUNCT
ejpam-6541	269	7	ωm	ωm	NUM
ejpam-6541	269	8	2	2	NUM
ejpam-6541	269	9	}	}	PUNCT
ejpam-6541	269	10	converges	converge	VERB
ejpam-6541	269	11	to	to	ADP
ejpam-6541	269	12	ω2	ω2	NUM
ejpam-6541	269	13	.	.	PUNCT
ejpam-6541	270	1	for	for	ADP
ejpam-6541	270	2	the	the	DET
ejpam-6541	270	3	subsequence	subsequence	NOUN
ejpam-6541	270	4	{	{	PUNCT
ejpam-6541	270	5	y1	y1	NOUN
ejpam-6541	270	6	m	m	PROPN
ejpam-6541	270	7	}	}	PUNCT
ejpam-6541	270	8	,	,	PUNCT
ejpam-6541	270	9	according	accord	VERB
ejpam-6541	270	10	to	to	ADP
ejpam-6541	270	11	the	the	DET
ejpam-6541	270	12	same	same	ADJ
ejpam-6541	270	13	argument	argument	NOUN
ejpam-6541	270	14	.	.	PUNCT
ejpam-6541	271	1	following	follow	VERB
ejpam-6541	271	2	this	this	DET
ejpam-6541	271	3	procedure	procedure	NOUN
ejpam-6541	271	4	,	,	PUNCT
ejpam-6541	271	5	we	we	PRON
ejpam-6541	271	6	get	get	VERB
ejpam-6541	271	7	a	a	DET
ejpam-6541	271	8	subsequence	subsequence	NOUN
ejpam-6541	271	9	after	after	ADP
ejpam-6541	271	10	n	n	ADP
ejpam-6541	271	11	steps	step	NOUN
ejpam-6541	271	12	,	,	PUNCT
ejpam-6541	271	13	{	{	PUNCT
ejpam-6541	271	14	ynm	ynm	NOUN
ejpam-6541	271	15	}	}	PUNCT
ejpam-6541	271	16	whereas	whereas	SCONJ
ejpam-6541	271	17	y1	y1	NOUN
ejpam-6541	271	18	m	m	NOUN
ejpam-6541	271	19	=	=	ADJ
ejpam-6541	271	20	∑n	∑n	PROPN
ejpam-6541	271	21	k=1	k=1	PROPN
ejpam-6541	271	22	η	η	PROPN
ejpam-6541	271	23	m	m	PROPN
ejpam-6541	271	24	k	k	PROPN
ejpam-6541	271	25	xk	xk	PROPN
ejpam-6541	271	26	with	with	ADP
ejpam-6541	271	27	∑n	∑n	PROPN
ejpam-6541	271	28	k=1	k=1	PROPN
ejpam-6541	271	29	|ηmk	|ηmk	PROPN
ejpam-6541	271	30	|	|	NOUN
ejpam-6541	271	31	=	=	NOUN
ejpam-6541	271	32	1	1	NUM
ejpam-6541	271	33	,	,	PUNCT
ejpam-6541	271	34	and	and	CCONJ
ejpam-6541	271	35	ηmk	ηmk	NOUN
ejpam-6541	271	36	→	→	SYM
ejpam-6541	271	37	ωk	ωk	ADP
ejpam-6541	271	38	as	as	SCONJ
ejpam-6541	271	39	m	m	PROPN
ejpam-6541	271	40	→	→	SYM
ejpam-6541	271	41	∞.	∞.	PROPN
ejpam-6541	271	42	let	let	VERB
ejpam-6541	271	43	y	y	PROPN
ejpam-6541	271	44	=	=	PUNCT
ejpam-6541	271	45	η1x1	η1x1	PROPN
ejpam-6541	271	46	+	+	X
ejpam-6541	271	47	·	·	PUNCT
ejpam-6541	271	48	·	·	PUNCT
ejpam-6541	271	49	·	·	PUNCT
ejpam-6541	272	1	+	+	CCONJ
ejpam-6541	272	2	ηkxk	ηkxk	VERB
ejpam-6541	272	3	now	now	ADV
ejpam-6541	272	4	we	we	PRON
ejpam-6541	272	5	show	show	VERB
ejpam-6541	272	6	that	that	SCONJ
ejpam-6541	272	7	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	272	8	(	(	PUNCT
ejpam-6541	272	9	yn	yn	PROPN
ejpam-6541	272	10	,	,	PUNCT
ejpam-6541	272	11	m	m	VERB
ejpam-6541	272	12	−	−	PROPN
ejpam-6541	272	13	y	y	PROPN
ejpam-6541	272	14	,	,	PUNCT
ejpam-6541	272	15	t	t	PROPN
ejpam-6541	272	16	)	)	PUNCT
ejpam-6541	272	17	=	=	VERB
ejpam-6541	272	18	u∗	u∗	PROPN
ejpam-6541	272	19	,	,	PUNCT
ejpam-6541	272	20	∀	∀	X
ejpam-6541	272	21	t	t	NOUN
ejpam-6541	272	22	>	>	X
ejpam-6541	272	23	0	0	X
ejpam-6541	272	24	.	.	PUNCT
ejpam-6541	273	1	we	we	PRON
ejpam-6541	273	2	possess	possess	VERB
ejpam-6541	273	3	nihf	nihf	PROPN
ejpam-6541	273	4	(	(	PUNCT
ejpam-6541	273	5	yn	yn	PROPN
ejpam-6541	273	6	,	,	PUNCT
ejpam-6541	273	7	m	m	VERB
ejpam-6541	273	8	−	−	PROPN
ejpam-6541	273	9	y	y	PROPN
ejpam-6541	273	10	,	,	PUNCT
ejpam-6541	273	11	t	t	PROPN
ejpam-6541	273	12	)	)	PUNCT
ejpam-6541	273	13	=	=	SYM
ejpam-6541	273	14	nihf	nihf	PROPN
ejpam-6541	273	15	(	(	PUNCT
ejpam-6541	273	16	∑n	∑n	PROPN
ejpam-6541	273	17	k=1(η	k=1(η	PROPN
ejpam-6541	273	18	m	m	PROPN
ejpam-6541	273	19	k	k	NOUN
ejpam-6541	273	20	−	−	PROPN
ejpam-6541	273	21	ωk)xk	ωk)xk	PROPN
ejpam-6541	273	22	,	,	PUNCT
ejpam-6541	273	23	t	t	PROPN
ejpam-6541	273	24	)	)	PUNCT
ejpam-6541	273	25	⊇	⊇	PROPN
ejpam-6541	273	26	nihf	nihf	PROPN
ejpam-6541	273	27	(	(	PUNCT
ejpam-6541	273	28	x1	x1	PROPN
ejpam-6541	273	29	,	,	PUNCT
ejpam-6541	273	30	t	t	PROPN
ejpam-6541	273	31	n|ηm1	n|ηm1	PROPN
ejpam-6541	273	32	−ω1|	−ω1|	PROPN
ejpam-6541	273	33	)	)	PUNCT
ejpam-6541	273	34	∗	∗	NOUN
ejpam-6541	273	35	·	·	PUNCT
ejpam-6541	273	36	·	·	PUNCT
ejpam-6541	273	37	·	·	PUNCT
ejpam-6541	273	38	∗	∗	X
ejpam-6541	273	39	nihf	nihf	PROPN
ejpam-6541	273	40	(	(	PUNCT
ejpam-6541	273	41	x1	x1	PROPN
ejpam-6541	273	42	,	,	PUNCT
ejpam-6541	273	43	t	t	PROPN
ejpam-6541	273	44	n|ηmn	n|ηmn	PROPN
ejpam-6541	273	45	−ωn|	−ωn|	PROPN
ejpam-6541	273	46	)	)	PUNCT
ejpam-6541	273	47	so	so	ADV
ejpam-6541	273	48	,	,	PUNCT
ejpam-6541	273	49	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	273	50	(	(	PUNCT
ejpam-6541	273	51	yn	yn	PROPN
ejpam-6541	273	52	,	,	PUNCT
ejpam-6541	273	53	m−y	m−y	PROPN
ejpam-6541	273	54	,	,	PUNCT
ejpam-6541	273	55	t	t	PROPN
ejpam-6541	273	56	)	)	PUNCT
ejpam-6541	273	57	⊇	⊇	PROPN
ejpam-6541	273	58	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	273	59	(	(	PUNCT
ejpam-6541	273	60	x1	x1	PROPN
ejpam-6541	273	61	,	,	PUNCT
ejpam-6541	273	62	t	t	PROPN
ejpam-6541	273	63	n|ηm1	n|ηm1	PROPN
ejpam-6541	273	64	−ω1|)∗	−ω1|)∗	PROPN
ejpam-6541	273	65	·	·	PUNCT
ejpam-6541	273	66	·	·	PUNCT
ejpam-6541	273	67	·	·	PUNCT
ejpam-6541	273	68	∗limm→∞nihf	∗limm→∞nihf	X
ejpam-6541	273	69	(	(	PUNCT
ejpam-6541	273	70	x1	x1	PROPN
ejpam-6541	273	71	,	,	PUNCT
ejpam-6541	273	72	t	t	PROPN
ejpam-6541	273	73	n|ηmn	n|ηmn	PROPN
ejpam-6541	273	74	−ωn|	−ωn|	PROPN
ejpam-6541	273	75	)	)	PUNCT
ejpam-6541	273	76	=	=	VERB
ejpam-6541	273	77	⇒	⇒	NOUN
ejpam-6541	273	78	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	273	79	(	(	PUNCT
ejpam-6541	273	80	yn	yn	PROPN
ejpam-6541	273	81	,	,	PUNCT
ejpam-6541	273	82	m−y	m−y	PROPN
ejpam-6541	273	83	,	,	PUNCT
ejpam-6541	273	84	t	t	PROPN
ejpam-6541	273	85	)	)	PUNCT
ejpam-6541	273	86	⊇	⊇	PROPN
ejpam-6541	273	87	u∗	u∗	PROPN
ejpam-6541	273	88	∗	∗	NOUN
ejpam-6541	273	89	·	·	PUNCT
ejpam-6541	273	90	·	·	PUNCT
ejpam-6541	273	91	·	·	PUNCT
ejpam-6541	273	92	∗u∗	∗u∗	PROPN
ejpam-6541	273	93	(	(	PUNCT
ejpam-6541	273	94	through	through	ADP
ejpam-6541	273	95	the	the	DET
ejpam-6541	273	96	t	t	NOUN
ejpam-6541	273	97	-	-	PUNCT
ejpam-6541	273	98	norm	norm	NOUN
ejpam-6541	273	99	∗	∗	NOUN
ejpam-6541	273	100	’s	’s	PART
ejpam-6541	273	101	continuity	continuity	NOUN
ejpam-6541	273	102	at	at	ADP
ejpam-6541	273	103	(	(	PUNCT
ejpam-6541	273	104	1,1	1,1	NUM
ejpam-6541	273	105	)	)	PUNCT
ejpam-6541	273	106	)	)	PUNCT
ejpam-6541	274	1	lim	lim	PROPN
ejpam-6541	274	2	m→∞	m→∞	NUM
ejpam-6541	274	3	nihf	nihf	PROPN
ejpam-6541	274	4	(	(	PUNCT
ejpam-6541	274	5	yn	yn	PROPN
ejpam-6541	274	6	,	,	PUNCT
ejpam-6541	274	7	m	m	VERB
ejpam-6541	274	8	−	−	PROPN
ejpam-6541	274	9	y	y	PROPN
ejpam-6541	274	10	,	,	PUNCT
ejpam-6541	274	11	t	t	PROPN
ejpam-6541	274	12	)	)	PUNCT
ejpam-6541	274	13	=	=	VERB
ejpam-6541	275	1	u∗	u∗	PROPN
ejpam-6541	275	2	,	,	PUNCT
ejpam-6541	275	3	∀t	∀t	PROPN
ejpam-6541	275	4	>	>	X
ejpam-6541	275	5	0	0	NUM
ejpam-6541	275	6	.	.	PUNCT
ejpam-6541	276	1	(	(	PUNCT
ejpam-6541	276	2	4	4	X
ejpam-6541	276	3	)	)	PUNCT
ejpam-6541	276	4	select	select	NOUN
ejpam-6541	276	5	m	m	VERB
ejpam-6541	276	6	so	so	SCONJ
ejpam-6541	276	7	that	that	SCONJ
ejpam-6541	276	8	1	1	NUM
ejpam-6541	276	9	m	m	NOUN
ejpam-6541	276	10	<	<	X
ejpam-6541	276	11	l.	l.	NOUN
ejpam-6541	276	12	for	for	ADP
ejpam-6541	276	13	l	l	PROPN
ejpam-6541	276	14	>	>	X
ejpam-6541	276	15	0	0	X
ejpam-6541	276	16	.	.	PUNCT
ejpam-6541	277	1	we	we	PRON
ejpam-6541	277	2	have	have	VERB
ejpam-6541	277	3	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	277	4	(	(	PUNCT
ejpam-6541	277	5	yn	yn	PROPN
ejpam-6541	277	6	,	,	PUNCT
ejpam-6541	277	7	m	m	PROPN
ejpam-6541	277	8	,	,	PUNCT
ejpam-6541	277	9	l	l	NOUN
ejpam-6541	277	10	)	)	PUNCT
ejpam-6541	278	1	=	=	SYM
ejpam-6541	278	2	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	278	3	(	(	PUNCT
ejpam-6541	278	4	yn	yn	PROPN
ejpam-6541	278	5	,	,	PUNCT
ejpam-6541	278	6	m+0	m+0	PROPN
ejpam-6541	278	7	,	,	PUNCT
ejpam-6541	278	8	1	1	NUM
ejpam-6541	278	9	m	m	NOUN
ejpam-6541	278	10	+	+	NOUN
ejpam-6541	278	11	l−	l−	NOUN
ejpam-6541	278	12	1	1	NUM
ejpam-6541	278	13	m	m	NOUN
ejpam-6541	278	14	)	)	PUNCT
ejpam-6541	278	15	⊇	⊇	PROPN
ejpam-6541	278	16	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	278	17	(	(	PUNCT
ejpam-6541	278	18	yn	yn	PROPN
ejpam-6541	278	19	,	,	PUNCT
ejpam-6541	278	20	m	m	PROPN
ejpam-6541	278	21	,	,	PUNCT
ejpam-6541	278	22	1	1	NUM
ejpam-6541	278	23	m)∗	m)∗	PROPN
ejpam-6541	278	24	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	278	25	(	(	PUNCT
ejpam-6541	278	26	0	0	NUM
ejpam-6541	278	27	,	,	PUNCT
ejpam-6541	278	28	l	l	NOUN
ejpam-6541	278	29	−	−	PROPN
ejpam-6541	278	30	1	1	NUM
ejpam-6541	278	31	m	m	NOUN
ejpam-6541	278	32	)	)	PUNCT
ejpam-6541	278	33	⊇	⊇	NOUN
ejpam-6541	278	34	(	(	PUNCT
ejpam-6541	278	35	u∗\	u∗\	ADJ
ejpam-6541	278	36	1	1	NUM
ejpam-6541	278	37	m	m	NOUN
ejpam-6541	278	38	)	)	PUNCT
ejpam-6541	278	39	∗	∗	NOUN
ejpam-6541	278	40	u∗	u∗	NOUN
ejpam-6541	278	41	=	=	SYM
ejpam-6541	278	42	u∗\	u∗\	NOUN
ejpam-6541	278	43	1	1	NUM
ejpam-6541	278	44	m	m	NOUN
ejpam-6541	278	45	=	=	NOUN
ejpam-6541	278	46	⇒	⇒	X
ejpam-6541	278	47	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	278	48	(	(	PUNCT
ejpam-6541	278	49	yn	yn	PROPN
ejpam-6541	278	50	,	,	PUNCT
ejpam-6541	278	51	m	m	PROPN
ejpam-6541	278	52	,	,	PUNCT
ejpam-6541	278	53	l	l	NOUN
ejpam-6541	278	54	)	)	PUNCT
ejpam-6541	278	55	⊇	⊇	NOUN
ejpam-6541	278	56	u∗	u∗	NOUN
ejpam-6541	278	57	=	=	SYM
ejpam-6541	278	58	⇒	⇒	PROPN
ejpam-6541	278	59	lim	lim	PROPN
ejpam-6541	278	60	m→∞	m→∞	NUM
ejpam-6541	278	61	nihf	nihf	PROPN
ejpam-6541	278	62	(	(	PUNCT
ejpam-6541	278	63	yn	yn	PROPN
ejpam-6541	278	64	,	,	PUNCT
ejpam-6541	278	65	m	m	PROPN
ejpam-6541	278	66	,	,	PUNCT
ejpam-6541	278	67	l	l	NOUN
ejpam-6541	278	68	)	)	PUNCT
ejpam-6541	278	69	=	=	PUNCT
ejpam-6541	279	1	u∗	u∗	INTJ
ejpam-6541	279	2	(	(	PUNCT
ejpam-6541	279	3	5	5	NUM
ejpam-6541	279	4	)	)	PUNCT
ejpam-6541	279	5	k.	k.	PROPN
ejpam-6541	279	6	kavitha	kavitha	PROPN
ejpam-6541	279	7	,	,	PUNCT
ejpam-6541	279	8	p.	p.	PROPN
ejpam-6541	279	9	muralikrishna	muralikrishna	PROPN
ejpam-6541	279	10	/	/	SYM
ejpam-6541	279	11	eur	eur	PROPN
ejpam-6541	279	12	.	.	PUNCT
ejpam-6541	280	1	j.	j.	PROPN
ejpam-6541	280	2	pure	pure	PROPN
ejpam-6541	280	3	appl	appl	PROPN
ejpam-6541	280	4	.	.	PROPN
ejpam-6541	280	5	math	math	PROPN
ejpam-6541	280	6	,	,	PUNCT
ejpam-6541	280	7	18	18	NUM
ejpam-6541	280	8	(	(	PUNCT
ejpam-6541	280	9	4	4	NUM
ejpam-6541	280	10	)	)	PUNCT
ejpam-6541	280	11	(	(	PUNCT
ejpam-6541	280	12	2025	2025	NUM
ejpam-6541	280	13	)	)	PUNCT
ejpam-6541	280	14	,	,	PUNCT
ejpam-6541	280	15	6541	6541	NUM
ejpam-6541	280	16	9	9	NUM
ejpam-6541	280	17	of	of	ADP
ejpam-6541	280	18	14	14	NUM
ejpam-6541	280	19	now	now	ADV
ejpam-6541	280	20	,	,	PUNCT
ejpam-6541	280	21	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	280	22	(	(	PUNCT
ejpam-6541	280	23	y	y	PROPN
ejpam-6541	280	24	,	,	PUNCT
ejpam-6541	280	25	2l	2l	NUM
ejpam-6541	280	26	)	)	PUNCT
ejpam-6541	280	27	=	=	SYM
ejpam-6541	281	1	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	281	2	(	(	PUNCT
ejpam-6541	281	3	y	y	PROPN
ejpam-6541	281	4	−	−	PROPN
ejpam-6541	281	5	yn	yn	PROPN
ejpam-6541	281	6	,	,	PUNCT
ejpam-6541	281	7	m	m	VERB
ejpam-6541	281	8	+	+	PROPN
ejpam-6541	281	9	yn	yn	PROPN
ejpam-6541	281	10	,	,	PUNCT
ejpam-6541	281	11	m	m	PROPN
ejpam-6541	281	12	,	,	PUNCT
ejpam-6541	281	13	l	l	PROPN
ejpam-6541	281	14	+	+	NUM
ejpam-6541	281	15	l	l	NOUN
ejpam-6541	281	16	)	)	PUNCT
ejpam-6541	281	17	⊇	⊇	PROPN
ejpam-6541	281	18	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	281	19	(	(	PUNCT
ejpam-6541	281	20	y	y	PROPN
ejpam-6541	281	21	−	−	PROPN
ejpam-6541	281	22	yn	yn	PROPN
ejpam-6541	281	23	,	,	PUNCT
ejpam-6541	281	24	m	m	PROPN
ejpam-6541	281	25	,	,	PUNCT
ejpam-6541	281	26	l	l	NOUN
ejpam-6541	281	27	)	)	PUNCT
ejpam-6541	281	28	∗	∗	NOUN
ejpam-6541	281	29	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	281	30	(	(	PUNCT
ejpam-6541	281	31	yn	yn	PROPN
ejpam-6541	281	32	,	,	PUNCT
ejpam-6541	281	33	m	m	PROPN
ejpam-6541	281	34	,	,	PUNCT
ejpam-6541	281	35	l	l	NOUN
ejpam-6541	281	36	)	)	PUNCT
ejpam-6541	282	1	=	=	NOUN
ejpam-6541	282	2	⇒	⇒	NOUN
ejpam-6541	282	3	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	282	4	(	(	PUNCT
ejpam-6541	282	5	y	y	PROPN
ejpam-6541	282	6	,	,	PUNCT
ejpam-6541	282	7	2l	2l	NUM
ejpam-6541	282	8	)	)	PUNCT
ejpam-6541	282	9	⊇	⊇	PROPN
ejpam-6541	282	10	u∗	u∗	PROPN
ejpam-6541	282	11	∗	∗	X
ejpam-6541	282	12	u∗	u∗	NOUN
ejpam-6541	282	13	(	(	PUNCT
ejpam-6541	282	14	through	through	ADP
ejpam-6541	282	15	the	the	DET
ejpam-6541	282	16	t	t	NOUN
ejpam-6541	282	17	-	-	PUNCT
ejpam-6541	282	18	norm	norm	NOUN
ejpam-6541	282	19	∗	∗	NOUN
ejpam-6541	282	20	’s	’s	PART
ejpam-6541	282	21	continuity	continuity	NOUN
ejpam-6541	282	22	at	at	ADP
ejpam-6541	282	23	(	(	PUNCT
ejpam-6541	282	24	1,1	1,1	NUM
ejpam-6541	282	25	)	)	PUNCT
ejpam-6541	282	26	)	)	PUNCT
ejpam-6541	283	1	=	=	SYM
ejpam-6541	283	2	⇒	⇒	NOUN
ejpam-6541	283	3	limm→∞nihf	limm→∞nihf	PROPN
ejpam-6541	283	4	(	(	PUNCT
ejpam-6541	283	5	y	y	PROPN
ejpam-6541	283	6	,	,	PUNCT
ejpam-6541	283	7	2l	2l	NUM
ejpam-6541	283	8	)	)	PUNCT
ejpam-6541	283	9	=	=	PUNCT
ejpam-6541	284	1	u∗	u∗	ADJ
ejpam-6541	284	2	∗u∗	∗u∗	NUM
ejpam-6541	285	1	=	=	SYM
ejpam-6541	285	2	u∗.	u∗.	PROPN
ejpam-6541	285	3	(	(	PUNCT
ejpam-6541	285	4	by	by	ADP
ejpam-6541	285	5	(	(	PUNCT
ejpam-6541	285	6	4	4	NUM
ejpam-6541	285	7	)	)	PUNCT
ejpam-6541	285	8	and	and	CCONJ
ejpam-6541	285	9	(	(	PUNCT
ejpam-6541	285	10	5	5	NUM
ejpam-6541	285	11	)	)	PUNCT
ejpam-6541	285	12	)	)	PUNCT
ejpam-6541	286	1	this	this	PRON
ejpam-6541	286	2	is	be	AUX
ejpam-6541	286	3	because	because	SCONJ
ejpam-6541	286	4	l	l	NOUN
ejpam-6541	286	5	>	>	X
ejpam-6541	286	6	0	0	PUNCT
ejpam-6541	286	7	becomes	become	VERB
ejpam-6541	286	8	random	random	ADJ
ejpam-6541	286	9	.	.	PUNCT
ejpam-6541	287	1	in	in	ADP
ejpam-6541	287	2	addition	addition	NOUN
ejpam-6541	287	3	,	,	PUNCT
ejpam-6541	287	4	given	give	VERB
ejpam-6541	287	5	that	that	SCONJ
ejpam-6541	287	6	∑n	∑n	PROPN
ejpam-6541	287	7	k=1	k=1	X
ejpam-6541	287	8	|ωm	|ωm	NUM
ejpam-6541	288	1	k	k	NOUN
ejpam-6541	289	1	|	|	ADV
ejpam-6541	289	2	=	=	SYM
ejpam-6541	289	3	1,the	1,the	PRON
ejpam-6541	289	4	linear	linear	ADJ
ejpam-6541	289	5	independence	independence	NOUN
ejpam-6541	289	6	of	of	ADP
ejpam-6541	289	7	the	the	DET
ejpam-6541	289	8	vectors	vector	NOUN
ejpam-6541	289	9	{	{	PUNCT
ejpam-6541	289	10	x1	x1	PROPN
ejpam-6541	289	11	,	,	PUNCT
ejpam-6541	289	12	x2	x2	PROPN
ejpam-6541	289	13	,	,	PUNCT
ejpam-6541	289	14	.	.	PUNCT
ejpam-6541	289	15	.	.	PUNCT
ejpam-6541	289	16	.	.	PUNCT
ejpam-6541	290	1	xn	xn	X
ejpam-6541	290	2	}	}	PUNCT
ejpam-6541	290	3	is	be	AUX
ejpam-6541	290	4	established	establish	VERB
ejpam-6541	290	5	.	.	PUNCT
ejpam-6541	291	1	consequently	consequently	ADV
ejpam-6541	291	2	,	,	PUNCT
ejpam-6541	291	3	y	y	PROPN
ejpam-6541	291	4	=	=	PUNCT
ejpam-6541	291	5	ω1x1	ω1x1	X
ejpam-6541	291	6	+	+	X
ejpam-6541	291	7	ω2x2	ω2x2	X
ejpam-6541	291	8	+	+	CCONJ
ejpam-6541	291	9	.	.	PUNCT
ejpam-6541	291	10	.	.	PUNCT
ejpam-6541	291	11	.	.	PUNCT
ejpam-6541	292	1	,	,	PUNCT
ejpam-6541	292	2	+	+	NOUN
ejpam-6541	292	3	ωnxn	ωnxn	ADJ
ejpam-6541	292	4	̸=	̸=	PROPN
ejpam-6541	292	5	0.the	0.the	DET
ejpam-6541	292	6	result	result	NOUN
ejpam-6541	292	7	is	be	AUX
ejpam-6541	292	8	a	a	DET
ejpam-6541	292	9	contradiction	contradiction	NOUN
ejpam-6541	292	10	.	.	PUNCT
ejpam-6541	293	1	we	we	PRON
ejpam-6541	293	2	now	now	ADV
ejpam-6541	293	3	demonstrate	demonstrate	VERB
ejpam-6541	293	4	the	the	DET
ejpam-6541	293	5	relationship	relationship	NOUN
ejpam-6541	293	6	.	.	PUNCT
ejpam-6541	294	1	mihf	mihf	PROPN
ejpam-6541	294	2	{	{	PUNCT
ejpam-6541	294	3	δ1x1	δ1x1	ADP
ejpam-6541	294	4	+	+	X
ejpam-6541	294	5	δ2x2	δ2x2	NOUN
ejpam-6541	294	6	+	+	X
ejpam-6541	294	7	.	.	PUNCT
ejpam-6541	294	8	.	.	PUNCT
ejpam-6541	294	9	.	.	PUNCT
ejpam-6541	295	1	,	,	PUNCT
ejpam-6541	296	1	+	+	NOUN
ejpam-6541	296	2	δnxn	δnxn	NOUN
ejpam-6541	296	3	,	,	PUNCT
ejpam-6541	296	4	h2	h2	NOUN
ejpam-6541	296	5	∑n	∑n	PROPN
ejpam-6541	296	6	k=1	k=1	PROPN
ejpam-6541	296	7	|δk|	|δk|	PROPN
ejpam-6541	296	8	}	}	PUNCT
ejpam-6541	296	9	⊃	⊃	NOUN
ejpam-6541	296	10	s∗	s∗	PROPN
ejpam-6541	296	11	2	2	NUM
ejpam-6541	296	12	.	.	PUNCT
ejpam-6541	297	1	if	if	SCONJ
ejpam-6541	297	2	t	t	PROPN
ejpam-6541	297	3	=	=	SYM
ejpam-6541	297	4	0	0	NUM
ejpam-6541	297	5	,	,	PUNCT
ejpam-6541	297	6	then	then	ADV
ejpam-6541	297	7	δk	δk	ADP
ejpam-6541	297	8	=	=	NOUN
ejpam-6541	297	9	0,∀k	0,∀k	PUNCT
ejpam-6541	297	10	=	=	SYM
ejpam-6541	297	11	1	1	NUM
ejpam-6541	297	12	,	,	PUNCT
ejpam-6541	297	13	2	2	NUM
ejpam-6541	297	14	,	,	PUNCT
ejpam-6541	297	15	.	.	PUNCT
ejpam-6541	297	16	.	.	PUNCT
ejpam-6541	297	17	.	.	PUNCT
ejpam-6541	298	1	n	n	CCONJ
ejpam-6541	298	2	and	and	CCONJ
ejpam-6541	298	3	the	the	DET
ejpam-6541	298	4	relation	relation	NOUN
ejpam-6541	298	5	,	,	PUNCT
ejpam-6541	298	6	mihf	mihf	X
ejpam-6541	298	7	{	{	PUNCT
ejpam-6541	298	8	δ1x1	δ1x1	NOUN
ejpam-6541	298	9	+	+	X
ejpam-6541	298	10	δ2x2	δ2x2	NOUN
ejpam-6541	298	11	+	+	X
ejpam-6541	298	12	.	.	PUNCT
ejpam-6541	298	13	.	.	PUNCT
ejpam-6541	298	14	.	.	PUNCT
ejpam-6541	299	1	,	,	PUNCT
ejpam-6541	299	2	+	+	NOUN
ejpam-6541	299	3	δnxn	δnxn	NOUN
ejpam-6541	299	4	,	,	PUNCT
ejpam-6541	299	5	h2	h2	NOUN
ejpam-6541	299	6	∑n	∑n	PROPN
ejpam-6541	299	7	k=1	k=1	PROPN
ejpam-6541	299	8	|δk|	|δk|	PROPN
ejpam-6541	299	9	}	}	PUNCT
ejpam-6541	299	10	⊃	⊃	NOUN
ejpam-6541	299	11	s∗	s∗	PROPN
ejpam-6541	299	12	2	2	NUM
ejpam-6541	299	13	remains	remain	VERB
ejpam-6541	299	14	true	true	ADJ
ejpam-6541	299	15	for	for	ADP
ejpam-6541	299	16	every	every	DET
ejpam-6541	299	17	h	h	NOUN
ejpam-6541	299	18	>	>	X
ejpam-6541	299	19	0	0	NUM
ejpam-6541	299	20	,	,	PUNCT
ejpam-6541	299	21	and	and	CCONJ
ejpam-6541	299	22	s∗	s∗	PROPN
ejpam-6541	299	23	∈	∈	PROPN
ejpam-6541	299	24	p[0	p[0	PROPN
ejpam-6541	299	25	,	,	PUNCT
ejpam-6541	299	26	1	1	NUM
ejpam-6541	299	27	]	]	PUNCT
ejpam-6541	299	28	.	.	PUNCT
ejpam-6541	300	1	then	then	ADV
ejpam-6541	300	2	,	,	PUNCT
ejpam-6541	300	3	assuming	assume	VERB
ejpam-6541	300	4	that	that	SCONJ
ejpam-6541	300	5	t	t	PROPN
ejpam-6541	300	6	>	>	X
ejpam-6541	300	7	0	0	NUM
ejpam-6541	300	8	,	,	PUNCT
ejpam-6541	300	9	(	(	PUNCT
ejpam-6541	300	10	2	2	X
ejpam-6541	300	11	)	)	PUNCT
ejpam-6541	300	12	is	be	AUX
ejpam-6541	300	13	equal	equal	ADJ
ejpam-6541	300	14	to	to	PART
ejpam-6541	300	15	mihf	mihf	VERB
ejpam-6541	300	16	{	{	PUNCT
ejpam-6541	300	17	ω1x1	ω1x1	X
ejpam-6541	300	18	+	+	X
ejpam-6541	300	19	ω2x2	ω2x2	X
ejpam-6541	300	20	+	+	CCONJ
ejpam-6541	300	21	.	.	PUNCT
ejpam-6541	300	22	.	.	PUNCT
ejpam-6541	300	23	.	.	PUNCT
ejpam-6541	301	1	,	,	PUNCT
ejpam-6541	301	2	+	+	NOUN
ejpam-6541	301	3	ωnxn	ωnxn	ADJ
ejpam-6541	301	4	,	,	PUNCT
ejpam-6541	301	5	h2	h2	PROPN
ejpam-6541	301	6	}	}	PUNCT
ejpam-6541	301	7	⊃	⊃	NOUN
ejpam-6541	301	8	s∗	s∗	PROPN
ejpam-6541	301	9	2	2	NUM
ejpam-6541	301	10	(	(	PUNCT
ejpam-6541	301	11	6	6	NUM
ejpam-6541	301	12	)	)	PUNCT
ejpam-6541	301	13	for	for	ADP
ejpam-6541	301	14	any	any	DET
ejpam-6541	301	15	scalars	scalar	NOUN
ejpam-6541	301	16	ω′s	ω′s	PROPN
ejpam-6541	301	17	with	with	ADP
ejpam-6541	301	18	∑n	∑n	PROPN
ejpam-6541	301	19	k=1	k=1	PROPN
ejpam-6541	301	20	|ωk|	|ωk|	PROPN
ejpam-6541	301	21	=	=	SYM
ejpam-6541	301	22	1	1	X
ejpam-6541	301	23	.	.	PUNCT
ejpam-6541	301	24	and	and	CCONJ
ejpam-6541	301	25	for	for	ADP
ejpam-6541	301	26	some	some	DET
ejpam-6541	301	27	h2	h2	NOUN
ejpam-6541	301	28	>	>	X
ejpam-6541	301	29	0	0	PUNCT
ejpam-6541	301	30	and	and	CCONJ
ejpam-6541	301	31	s∗	s∗	PROPN
ejpam-6541	301	32	2	2	NUM
ejpam-6541	301	33	∈	∈	PROPN
ejpam-6541	301	34	p[0	p[0	NOUN
ejpam-6541	301	35	,	,	PUNCT
ejpam-6541	301	36	1	1	NUM
ejpam-6541	301	37	]	]	PUNCT
ejpam-6541	301	38	.	.	PUNCT
ejpam-6541	302	1	if	if	SCONJ
ejpam-6541	302	2	at	at	ADV
ejpam-6541	302	3	all	all	ADV
ejpam-6541	302	4	feasible	feasible	ADJ
ejpam-6541	302	5	,	,	PUNCT
ejpam-6541	302	6	assume	assume	VERB
ejpam-6541	302	7	that	that	SCONJ
ejpam-6541	302	8	(	(	PUNCT
ejpam-6541	302	9	6	6	NUM
ejpam-6541	302	10	)	)	PUNCT
ejpam-6541	302	11	is	be	AUX
ejpam-6541	302	12	not	not	PART
ejpam-6541	302	13	true	true	ADJ
ejpam-6541	302	14	.	.	PUNCT
ejpam-6541	303	1	consequently	consequently	ADV
ejpam-6541	303	2	,	,	PUNCT
ejpam-6541	303	3	for	for	ADP
ejpam-6541	303	4	every	every	DET
ejpam-6541	303	5	h	h	NOUN
ejpam-6541	303	6	>	>	X
ejpam-6541	303	7	0	0	PUNCT
ejpam-6541	303	8	and	and	CCONJ
ejpam-6541	303	9	s∗	s∗	PROPN
ejpam-6541	303	10	∈	∈	PROPN
ejpam-6541	303	11	p[0	p[0	NOUN
ejpam-6541	303	12	,	,	PUNCT
ejpam-6541	303	13	1	1	NUM
ejpam-6541	303	14	]	]	PUNCT
ejpam-6541	303	15	,	,	PUNCT
ejpam-6541	303	16	there	there	PRON
ejpam-6541	303	17	is	be	VERB
ejpam-6541	303	18	such	such	DET
ejpam-6541	303	19	a	a	DET
ejpam-6541	303	20	collection	collection	NOUN
ejpam-6541	303	21	regarding	regard	VERB
ejpam-6541	303	22	scalars	scalars	PROPN
ejpam-6541	303	23	{	{	PUNCT
ejpam-6541	303	24	ω1	ω1	PROPN
ejpam-6541	303	25	,	,	PUNCT
ejpam-6541	303	26	ω2	ω2	ADJ
ejpam-6541	303	27	,	,	PUNCT
ejpam-6541	303	28	.	.	PUNCT
ejpam-6541	303	29	.	.	PUNCT
ejpam-6541	303	30	.	.	PUNCT
ejpam-6541	304	1	ωn}along	ωn}along	ADJ
ejpam-6541	304	2	side	side	NOUN
ejpam-6541	304	3	∑n	∑n	PROPN
ejpam-6541	304	4	k=1	k=1	X
ejpam-6541	304	5	|ωk|	|ωk|	PROPN
ejpam-6541	304	6	=	=	NOUN
ejpam-6541	304	7	1	1	NUM
ejpam-6541	304	8	that	that	PRON
ejpam-6541	304	9	,	,	PUNCT
ejpam-6541	304	10	mihf	mihf	X
ejpam-6541	304	11	{	{	PUNCT
ejpam-6541	304	12	ω1x1+ω2x2	ω1x1+ω2x2	X
ejpam-6541	304	13	+	+	NUM
ejpam-6541	304	14	.	.	PUNCT
ejpam-6541	304	15	.	.	PUNCT
ejpam-6541	304	16	.	.	PUNCT
ejpam-6541	305	1	,	,	PUNCT
ejpam-6541	305	2	+	+	NOUN
ejpam-6541	305	3	ωnxn	ωnxn	ADJ
ejpam-6541	305	4	,	,	PUNCT
ejpam-6541	305	5	h	h	NOUN
ejpam-6541	305	6	}	}	PUNCT
ejpam-6541	305	7	⊆	⊆	NUM
ejpam-6541	305	8	s∗.	s∗.	ADJ
ejpam-6541	305	9	then	then	ADV
ejpam-6541	305	10	for	for	ADP
ejpam-6541	305	11	h	h	NOUN
ejpam-6541	305	12	=	=	SYM
ejpam-6541	305	13	{	{	PUNCT
ejpam-6541	305	14	1	1	NUM
ejpam-6541	305	15	m},m	m},m	NOUN
ejpam-6541	305	16	=	=	SYM
ejpam-6541	305	17	1	1	NUM
ejpam-6541	305	18	,	,	PUNCT
ejpam-6541	305	19	2	2	NUM
ejpam-6541	305	20	,	,	PUNCT
ejpam-6541	305	21	.	.	PUNCT
ejpam-6541	305	22	.	.	PUNCT
ejpam-6541	306	1	.	.	PUNCT
ejpam-6541	307	1	,	,	PUNCT
ejpam-6541	307	2	a	a	DET
ejpam-6541	307	3	collection	collection	NOUN
ejpam-6541	307	4	of	of	ADP
ejpam-6541	307	5	scalars	scalar	NOUN
ejpam-6541	307	6	{	{	PUNCT
ejpam-6541	307	7	ηm1	ηm1	NOUN
ejpam-6541	307	8	,	,	PUNCT
ejpam-6541	307	9	ηm2	ηm2	PROPN
ejpam-6541	307	10	,	,	PUNCT
ejpam-6541	307	11	.	.	PUNCT
ejpam-6541	307	12	.	.	PUNCT
ejpam-6541	308	1	.	.	PUNCT
ejpam-6541	309	1	,	,	PUNCT
ejpam-6541	309	2	ηmn	ηmn	NOUN
ejpam-6541	309	3	}	}	PUNCT
ejpam-6541	309	4	exists	exist	VERB
ejpam-6541	309	5	.	.	PUNCT
ejpam-6541	310	1	with	with	ADP
ejpam-6541	310	2	∑n	∑n	PROPN
ejpam-6541	310	3	k=1	k=1	PROPN
ejpam-6541	310	4	|ηmk	|ηmk	PROPN
ejpam-6541	311	1	|	|	NOUN
ejpam-6541	311	2	=	=	SYM
ejpam-6541	311	3	1	1	NUM
ejpam-6541	311	4	so	so	SCONJ
ejpam-6541	311	5	that	that	DET
ejpam-6541	311	6	mihf	mihf	PROPN
ejpam-6541	311	7	(	(	PUNCT
ejpam-6541	311	8	zm	zm	PROPN
ejpam-6541	311	9	,	,	PUNCT
ejpam-6541	311	10	1	1	NUM
ejpam-6541	311	11	m	m	NOUN
ejpam-6541	311	12	)	)	PUNCT
ejpam-6541	312	1	⊆	⊆	NUM
ejpam-6541	312	2	{	{	PUNCT
ejpam-6541	312	3	1	1	NUM
ejpam-6541	312	4	m	m	NOUN
ejpam-6541	312	5	}	}	PUNCT
ejpam-6541	312	6	where	where	SCONJ
ejpam-6541	312	7	zm	zm	PROPN
ejpam-6541	312	8	=	=	PUNCT
ejpam-6541	312	9	ηm1	ηm1	NOUN
ejpam-6541	312	10	x1	x1	PROPN
ejpam-6541	313	1	+	+	PROPN
ejpam-6541	313	2	,	,	PUNCT
ejpam-6541	313	3	ηm2	ηm2	PROPN
ejpam-6541	313	4	x2	x2	PROPN
ejpam-6541	313	5	+	+	PROPN
ejpam-6541	313	6	,	,	PUNCT
ejpam-6541	313	7	.	.	PUNCT
ejpam-6541	313	8	.	.	PUNCT
ejpam-6541	314	1	.	.	PUNCT
ejpam-6541	315	1	,	,	PUNCT
ejpam-6541	315	2	ηnx	ηnx	NOUN
ejpam-6541	315	3	m	m	PROPN
ejpam-6541	315	4	n	n	NOUN
ejpam-6541	315	5	.	.	PUNCT
ejpam-6541	316	1	since	since	ADV
ejpam-6541	316	2	,	,	PUNCT
ejpam-6541	316	3	∑n	∑n	PROPN
ejpam-6541	316	4	k=1	k=1	PROPN
ejpam-6541	316	5	|ηmk	|ηmk	PROPN
ejpam-6541	316	6	|	|	NOUN
ejpam-6541	316	7	=	=	SYM
ejpam-6541	316	8	1	1	NUM
ejpam-6541	316	9	,	,	PUNCT
ejpam-6541	316	10	we	we	PRON
ejpam-6541	316	11	have	have	VERB
ejpam-6541	316	12	0	0	NUM
ejpam-6541	316	13	≤	≤	NOUN
ejpam-6541	316	14	|ηmk	|ηmk	PROPN
ejpam-6541	316	15	|	|	ADV
ejpam-6541	316	16	≤	≤	NOUN
ejpam-6541	316	17	1	1	NUM
ejpam-6541	316	18	regarding	regard	VERB
ejpam-6541	316	19	k	k	PROPN
ejpam-6541	316	20	=	=	SYM
ejpam-6541	316	21	1	1	NUM
ejpam-6541	316	22	,	,	PUNCT
ejpam-6541	316	23	2	2	NUM
ejpam-6541	316	24	,	,	PUNCT
ejpam-6541	316	25	.	.	PUNCT
ejpam-6541	316	26	.	.	PUNCT
ejpam-6541	316	27	.	.	PUNCT
ejpam-6541	317	1	n.	n.	PROPN
ejpam-6541	317	2	afterwards	afterwards	ADV
ejpam-6541	317	3	,	,	PUNCT
ejpam-6541	317	4	using	use	VERB
ejpam-6541	317	5	the	the	DET
ejpam-6541	317	6	similar	similar	ADJ
ejpam-6541	317	7	justification	justification	NOUN
ejpam-6541	317	8	as	as	ADP
ejpam-6541	317	9	before	before	ADV
ejpam-6541	317	10	,	,	PUNCT
ejpam-6541	317	11	we	we	PRON
ejpam-6541	317	12	obtain	obtain	VERB
ejpam-6541	317	13	a	a	DET
ejpam-6541	317	14	subsequence	subsequence	NOUN
ejpam-6541	317	15	{	{	PUNCT
ejpam-6541	317	16	znm	znm	NOUN
ejpam-6541	317	17	}	}	PUNCT
ejpam-6541	317	18	where	where	SCONJ
ejpam-6541	317	19	znm	znm	NOUN
ejpam-6541	317	20	=	=	SYM
ejpam-6541	317	21	∑n	∑n	NOUN
ejpam-6541	318	1	k=1	k=1	PUNCT
ejpam-6541	319	1	ξ	ξ	PROPN
ejpam-6541	319	2	m	m	VERB
ejpam-6541	319	3	k	k	PROPN
ejpam-6541	319	4	xk	xk	PROPN
ejpam-6541	319	5	with	with	ADP
ejpam-6541	319	6	∑n	∑n	PROPN
ejpam-6541	319	7	k=1	k=1	PROPN
ejpam-6541	319	8	|ξmk	|ξmk	NOUN
ejpam-6541	319	9	|	|	NOUN
ejpam-6541	319	10	=	=	NOUN
ejpam-6541	319	11	1	1	NUM
ejpam-6541	319	12	,	,	PUNCT
ejpam-6541	319	13	and	and	CCONJ
ejpam-6541	319	14	ξmk	ξmk	NOUN
ejpam-6541	319	15	→	→	SYM
ejpam-6541	319	16	ξk	ξk	ADP
ejpam-6541	319	17	as	as	ADP
ejpam-6541	319	18	m	m	PROPN
ejpam-6541	319	19	→	→	SYM
ejpam-6541	319	20	∞.	∞.	PROPN
ejpam-6541	319	21	thus	thus	ADV
ejpam-6541	319	22	∑n	∑n	PROPN
ejpam-6541	319	23	k=1	k=1	ADJ
ejpam-6541	319	24	|ξk|	|ξk|	NOUN
ejpam-6541	319	25	=	=	SYM
ejpam-6541	319	26	1	1	X
ejpam-6541	319	27	.	.	PUNCT
ejpam-6541	319	28	let	let	VERB
ejpam-6541	319	29	z	z	NOUN
ejpam-6541	319	30	=	=	SYM
ejpam-6541	319	31	ξ1x1	ξ1x1	NUM
ejpam-6541	319	32	+	+	X
ejpam-6541	319	33	·	·	PUNCT
ejpam-6541	319	34	·	·	PUNCT
ejpam-6541	319	35	·	·	PUNCT
ejpam-6541	320	1	+	+	CCONJ
ejpam-6541	320	2	ξkxk.then	ξkxk.then	ADV
ejpam-6541	320	3	we	we	PRON
ejpam-6541	320	4	have	have	VERB
ejpam-6541	320	5	lim	lim	PROPN
ejpam-6541	320	6	m→∞	m→∞	NUM
ejpam-6541	320	7	mihf	mihf	NOUN
ejpam-6541	320	8	(	(	PUNCT
ejpam-6541	320	9	zn	zn	PROPN
ejpam-6541	320	10	,	,	PUNCT
ejpam-6541	320	11	m	m	VERB
ejpam-6541	320	12	−	−	PROPN
ejpam-6541	320	13	z	z	PROPN
ejpam-6541	320	14	,	,	PUNCT
ejpam-6541	320	15	t	t	PROPN
ejpam-6541	320	16	)	)	PUNCT
ejpam-6541	321	1	=	=	PUNCT
ejpam-6541	321	2	∅∗	∅∗	PROPN
ejpam-6541	321	3	,	,	PUNCT
ejpam-6541	321	4	∀t	∀t	PROPN
ejpam-6541	321	5	>	>	X
ejpam-6541	321	6	0	0	NUM
ejpam-6541	321	7	.	.	PUNCT
ejpam-6541	322	1	(	(	PUNCT
ejpam-6541	322	2	7	7	X
ejpam-6541	322	3	)	)	PUNCT
ejpam-6541	322	4	in	in	ADP
ejpam-6541	322	5	this	this	DET
ejpam-6541	322	6	case	case	NOUN
ejpam-6541	322	7	,	,	PUNCT
ejpam-6541	322	8	l	l	NOUN
ejpam-6541	322	9	>	>	X
ejpam-6541	322	10	0	0	NUM
ejpam-6541	322	11	,	,	PUNCT
ejpam-6541	322	12	select	select	ADJ
ejpam-6541	322	13	m	m	VERB
ejpam-6541	322	14	so	so	SCONJ
ejpam-6541	322	15	that	that	SCONJ
ejpam-6541	322	16	1	1	NUM
ejpam-6541	322	17	m	m	VERB
ejpam-6541	322	18	<	<	X
ejpam-6541	322	19	l.	l.	X
ejpam-6541	322	20	we	we	PRON
ejpam-6541	322	21	now	now	ADV
ejpam-6541	322	22	possess	possess	VERB
ejpam-6541	322	23	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	322	24	(	(	PUNCT
ejpam-6541	322	25	zn	zn	PROPN
ejpam-6541	322	26	,	,	PUNCT
ejpam-6541	322	27	m	m	PROPN
ejpam-6541	322	28	,	,	PUNCT
ejpam-6541	322	29	l	l	NOUN
ejpam-6541	322	30	)	)	PUNCT
ejpam-6541	323	1	=	=	SYM
ejpam-6541	323	2	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	323	3	(	(	PUNCT
ejpam-6541	323	4	zn	zn	PROPN
ejpam-6541	323	5	,	,	PUNCT
ejpam-6541	323	6	m	m	VERB
ejpam-6541	323	7	+	+	ADJ
ejpam-6541	323	8	0	0	NUM
ejpam-6541	323	9	,	,	PUNCT
ejpam-6541	323	10	1	1	NUM
ejpam-6541	323	11	m	m	NOUN
ejpam-6541	323	12	+	+	ADJ
ejpam-6541	323	13	l	l	NOUN
ejpam-6541	323	14	−	−	NUM
ejpam-6541	323	15	1	1	NUM
ejpam-6541	323	16	m	m	NOUN
ejpam-6541	323	17	)	)	PUNCT
ejpam-6541	323	18	⊆	⊆	NUM
ejpam-6541	323	19	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	323	20	(	(	PUNCT
ejpam-6541	323	21	zn	zn	PROPN
ejpam-6541	323	22	,	,	PUNCT
ejpam-6541	323	23	m	m	PROPN
ejpam-6541	323	24	,	,	PUNCT
ejpam-6541	323	25	1	1	NUM
ejpam-6541	323	26	m	m	NOUN
ejpam-6541	323	27	)	)	PUNCT
ejpam-6541	323	28	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	323	29	(	(	PUNCT
ejpam-6541	323	30	0	0	NUM
ejpam-6541	323	31	,	,	PUNCT
ejpam-6541	323	32	l	l	NOUN
ejpam-6541	323	33	−	−	PROPN
ejpam-6541	323	34	1	1	NUM
ejpam-6541	323	35	m	m	NOUN
ejpam-6541	323	36	)	)	PUNCT
ejpam-6541	323	37	⊆	⊆	NUM
ejpam-6541	323	38	∅∗	∅∗	PROPN
ejpam-6541	323	39	⋄	⋄	PROPN
ejpam-6541	323	40	∅∗	∅∗	PROPN
ejpam-6541	323	41	=	=	SYM
ejpam-6541	323	42	∅∗	∅∗	VERB
ejpam-6541	324	1	=	=	NOUN
ejpam-6541	324	2	⇒	⇒	PROPN
ejpam-6541	324	3	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	324	4	(	(	PUNCT
ejpam-6541	324	5	zn	zn	PROPN
ejpam-6541	324	6	,	,	PUNCT
ejpam-6541	324	7	m	m	PROPN
ejpam-6541	324	8	,	,	PUNCT
ejpam-6541	324	9	l	l	NOUN
ejpam-6541	324	10	)	)	PUNCT
ejpam-6541	324	11	⊆	⊆	NUM
ejpam-6541	325	1	∅∗	∅∗	VERB
ejpam-6541	325	2	=	=	NOUN
ejpam-6541	325	3	⇒	⇒	PROPN
ejpam-6541	325	4	lim	lim	PROPN
ejpam-6541	325	5	m→∞	m→∞	NUM
ejpam-6541	325	6	mihf	mihf	PROPN
ejpam-6541	325	7	(	(	PUNCT
ejpam-6541	325	8	zn	zn	PROPN
ejpam-6541	325	9	,	,	PUNCT
ejpam-6541	325	10	m	m	PROPN
ejpam-6541	325	11	,	,	PUNCT
ejpam-6541	325	12	l	l	NOUN
ejpam-6541	325	13	)	)	PUNCT
ejpam-6541	325	14	=	=	SYM
ejpam-6541	325	15	∅∗	∅∗	PROPN
ejpam-6541	325	16	(	(	PUNCT
ejpam-6541	325	17	8)	8)	NUM
ejpam-6541	325	18	now	now	ADV
ejpam-6541	325	19	,	,	PUNCT
ejpam-6541	325	20	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	325	21	(	(	PUNCT
ejpam-6541	325	22	z	z	PROPN
ejpam-6541	325	23	,	,	PUNCT
ejpam-6541	325	24	2l	2l	NUM
ejpam-6541	325	25	)	)	PUNCT
ejpam-6541	325	26	=	=	SYM
ejpam-6541	325	27	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	325	28	(	(	PUNCT
ejpam-6541	325	29	z	z	NOUN
ejpam-6541	325	30	−	−	PROPN
ejpam-6541	325	31	zn	zn	PROPN
ejpam-6541	325	32	,	,	PUNCT
ejpam-6541	325	33	m	m	PROPN
ejpam-6541	325	34	+	+	ADJ
ejpam-6541	325	35	zn	zn	NUM
ejpam-6541	325	36	,	,	PUNCT
ejpam-6541	325	37	m	m	PROPN
ejpam-6541	325	38	,	,	PUNCT
ejpam-6541	325	39	l	l	PROPN
ejpam-6541	325	40	+	+	NUM
ejpam-6541	325	41	l	l	NOUN
ejpam-6541	325	42	)	)	PUNCT
ejpam-6541	325	43	⊆	⊆	NUM
ejpam-6541	325	44	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	325	45	(	(	PUNCT
ejpam-6541	325	46	z	z	NOUN
ejpam-6541	325	47	−	−	PROPN
ejpam-6541	325	48	zn	zn	PROPN
ejpam-6541	325	49	,	,	PUNCT
ejpam-6541	325	50	m	m	PROPN
ejpam-6541	325	51	,	,	PUNCT
ejpam-6541	325	52	l	l	NOUN
ejpam-6541	325	53	)	)	PUNCT
ejpam-6541	325	54	⋄	⋄	PROPN
ejpam-6541	325	55	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	325	56	(	(	PUNCT
ejpam-6541	325	57	zn	zn	PROPN
ejpam-6541	325	58	,	,	PUNCT
ejpam-6541	325	59	m	m	PROPN
ejpam-6541	325	60	,	,	PUNCT
ejpam-6541	325	61	l	l	NOUN
ejpam-6541	325	62	)	)	PUNCT
ejpam-6541	326	1	=	=	NOUN
ejpam-6541	326	2	⇒	⇒	NOUN
ejpam-6541	326	3	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	326	4	(	(	PUNCT
ejpam-6541	326	5	z	z	PROPN
ejpam-6541	326	6	,	,	PUNCT
ejpam-6541	326	7	2l	2l	NUM
ejpam-6541	326	8	)	)	PUNCT
ejpam-6541	326	9	⊆	⊆	NUM
ejpam-6541	326	10	∅∗	∅∗	PROPN
ejpam-6541	326	11	⋄	⋄	PROPN
ejpam-6541	327	1	∅∗	∅∗	PROPN
ejpam-6541	327	2	(	(	PUNCT
ejpam-6541	327	3	according	accord	VERB
ejpam-6541	327	4	to	to	ADP
ejpam-6541	327	5	tco	tco	PROPN
ejpam-6541	327	6	–	–	PUNCT
ejpam-6541	327	7	norm	norm	NOUN
ejpam-6541	327	8	⋄	⋄	PROPN
ejpam-6541	327	9	’s	’s	PART
ejpam-6541	327	10	continuity	continuity	NOUN
ejpam-6541	327	11	at	at	ADP
ejpam-6541	327	12	(	(	PUNCT
ejpam-6541	327	13	0,0	0,0	NOUN
ejpam-6541	327	14	)	)	PUNCT
ejpam-6541	327	15	)	)	PUNCT
ejpam-6541	328	1	=	=	VERB
ejpam-6541	328	2	⇒	⇒	NOUN
ejpam-6541	328	3	limm→∞mihf	limm→∞mihf	PROPN
ejpam-6541	328	4	(	(	PUNCT
ejpam-6541	328	5	z	z	PROPN
ejpam-6541	328	6	,	,	PUNCT
ejpam-6541	328	7	2l	2l	NUM
ejpam-6541	328	8	)	)	PUNCT
ejpam-6541	328	9	=	=	SYM
ejpam-6541	328	10	∅∗	∅∗	PROPN
ejpam-6541	328	11	⋄	⋄	PROPN
ejpam-6541	328	12	∅∗	∅∗	PROPN
ejpam-6541	328	13	=	=	PRON
ejpam-6541	328	14	∅∗.	∅∗.	NUM
ejpam-6541	328	15	(	(	PUNCT
ejpam-6541	328	16	by	by	ADP
ejpam-6541	328	17	(	(	PUNCT
ejpam-6541	328	18	7	7	NUM
ejpam-6541	328	19	)	)	PUNCT
ejpam-6541	328	20	and	and	CCONJ
ejpam-6541	328	21	(	(	PUNCT
ejpam-6541	328	22	8)	8)	NUM
ejpam-6541	328	23	)	)	PUNCT
ejpam-6541	328	24	assuming	assume	VERB
ejpam-6541	328	25	that	that	SCONJ
ejpam-6541	328	26	l	l	NOUN
ejpam-6541	328	27	>	>	X
ejpam-6541	328	28	0	0	PUNCT
ejpam-6541	328	29	is	be	AUX
ejpam-6541	328	30	random	random	ADJ
ejpam-6541	328	31	.	.	PUNCT
ejpam-6541	329	1	therefore	therefore	ADV
ejpam-6541	329	2	,	,	PUNCT
ejpam-6541	329	3	z	z	NOUN
ejpam-6541	329	4	=	=	SYM
ejpam-6541	329	5	0	0	X
ejpam-6541	329	6	.	.	PUNCT
ejpam-6541	330	1	once	once	ADV
ejpam-6541	330	2	again	again	ADV
ejpam-6541	330	3	because	because	SCONJ
ejpam-6541	330	4	∑n	∑n	PROPN
ejpam-6541	330	5	k=1	k=1	PROPN
ejpam-6541	330	6	|ξmk	|ξmk	NOUN
ejpam-6541	331	1	|	|	ADV
ejpam-6541	331	2	=	=	NOUN
ejpam-6541	331	3	1	1	NUM
ejpam-6541	331	4	along	along	ADP
ejpam-6541	331	5	with	with	ADP
ejpam-6541	331	6	{	{	PUNCT
ejpam-6541	331	7	x1	x1	PROPN
ejpam-6541	331	8	,	,	PUNCT
ejpam-6541	331	9	x2	x2	PROPN
ejpam-6541	331	10	,	,	PUNCT
ejpam-6541	331	11	.	.	PUNCT
ejpam-6541	331	12	.	.	PUNCT
ejpam-6541	331	13	.	.	PUNCT
ejpam-6541	332	1	xn	xn	X
ejpam-6541	332	2	}	}	PUNCT
ejpam-6541	332	3	is	be	AUX
ejpam-6541	332	4	a	a	DET
ejpam-6541	332	5	collection	collection	NOUN
ejpam-6541	332	6	of	of	ADP
ejpam-6541	332	7	vectors	vector	NOUN
ejpam-6541	332	8	that	that	PRON
ejpam-6541	332	9	are	be	AUX
ejpam-6541	332	10	linearly	linearly	ADV
ejpam-6541	332	11	independent	independent	ADJ
ejpam-6541	332	12	.	.	PUNCT
ejpam-6541	333	1	so	so	ADV
ejpam-6541	333	2	z	z	NOUN
ejpam-6541	333	3	=	=	SYM
ejpam-6541	333	4	ξ1x1	ξ1x1	NUM
ejpam-6541	333	5	+	+	SYM
ejpam-6541	333	6	ξ2x2	ξ2x2	X
ejpam-6541	333	7	+	+	X
ejpam-6541	333	8	.	.	PUNCT
ejpam-6541	333	9	.	.	PUNCT
ejpam-6541	333	10	.	.	PUNCT
ejpam-6541	334	1	,	,	PUNCT
ejpam-6541	334	2	+	+	NOUN
ejpam-6541	334	3	ξnxn	ξnxn	NOUN
ejpam-6541	334	4	̸=	̸=	PROPN
ejpam-6541	334	5	0.consequently	0.consequently	NUM
ejpam-6541	334	6	,	,	PUNCT
ejpam-6541	334	7	this	this	PRON
ejpam-6541	334	8	leads	lead	VERB
ejpam-6541	334	9	to	to	ADP
ejpam-6541	334	10	a	a	DET
ejpam-6541	334	11	contradiction	contradiction	NOUN
ejpam-6541	334	12	,	,	PUNCT
ejpam-6541	334	13	this	this	PRON
ejpam-6541	334	14	brings	bring	VERB
ejpam-6541	334	15	the	the	DET
ejpam-6541	334	16	lemma	lemma	PROPN
ejpam-6541	334	17	to	to	ADP
ejpam-6541	334	18	an	an	DET
ejpam-6541	334	19	end	end	NOUN
ejpam-6541	334	20	.	.	PUNCT
ejpam-6541	335	1	k.	k.	PROPN
ejpam-6541	335	2	kavitha	kavitha	PROPN
ejpam-6541	335	3	,	,	PUNCT
ejpam-6541	335	4	p.	p.	PROPN
ejpam-6541	335	5	muralikrishna	muralikrishna	PROPN
ejpam-6541	335	6	/	/	SYM
ejpam-6541	335	7	eur	eur	PROPN
ejpam-6541	335	8	.	.	PUNCT
ejpam-6541	336	1	j.	j.	PROPN
ejpam-6541	336	2	pure	pure	PROPN
ejpam-6541	336	3	appl	appl	PROPN
ejpam-6541	336	4	.	.	PROPN
ejpam-6541	336	5	math	math	PROPN
ejpam-6541	336	6	,	,	PUNCT
ejpam-6541	336	7	18	18	NUM
ejpam-6541	336	8	(	(	PUNCT
ejpam-6541	336	9	4	4	NUM
ejpam-6541	336	10	)	)	PUNCT
ejpam-6541	336	11	(	(	PUNCT
ejpam-6541	336	12	2025	2025	NUM
ejpam-6541	336	13	)	)	PUNCT
ejpam-6541	336	14	,	,	PUNCT
ejpam-6541	336	15	6541	6541	NUM
ejpam-6541	336	16	10	10	NUM
ejpam-6541	336	17	of	of	ADP
ejpam-6541	336	18	14	14	NUM
ejpam-6541	336	19	theorem	theorem	NOUN
ejpam-6541	336	20	6	6	NUM
ejpam-6541	336	21	.	.	PUNCT
ejpam-6541	337	1	all	all	DET
ejpam-6541	337	2	finite	finite	ADJ
ejpam-6541	337	3	-	-	ADJ
ejpam-6541	337	4	dimensional	dimensional	ADJ
ejpam-6541	337	5	ihfnnls	ihfnnls	NOUN
ejpam-6541	337	6	(	(	PUNCT
ejpam-6541	337	7	v	v	NOUN
ejpam-6541	337	8	,	,	PUNCT
ejpam-6541	337	9	hihf	hihf	PROPN
ejpam-6541	337	10	)	)	PUNCT
ejpam-6541	337	11	are	be	AUX
ejpam-6541	337	12	complete	complete	ADJ
ejpam-6541	337	13	if	if	SCONJ
ejpam-6541	337	14	the	the	DET
ejpam-6541	337	15	underlying	underlying	ADJ
ejpam-6541	337	16	t	t	NOUN
ejpam-6541	337	17	-	-	PUNCT
ejpam-6541	337	18	norm	norm	NOUN
ejpam-6541	337	19	∗	∗	NOUN
ejpam-6541	337	20	at	at	ADP
ejpam-6541	337	21	(	(	PUNCT
ejpam-6541	337	22	1	1	NUM
ejpam-6541	337	23	,	,	PUNCT
ejpam-6541	337	24	1	1	NUM
ejpam-6541	337	25	)	)	PUNCT
ejpam-6541	337	26	together	together	ADV
ejpam-6541	337	27	with	with	ADP
ejpam-6541	337	28	t	t	PROPN
ejpam-6541	337	29	-	-	PUNCT
ejpam-6541	337	30	co	co	NOUN
ejpam-6541	337	31	-	-	NOUN
ejpam-6541	337	32	norm	norm	ADJ
ejpam-6541	337	33	⋄	⋄	PROPN
ejpam-6541	337	34	at	at	ADP
ejpam-6541	337	35	(	(	PUNCT
ejpam-6541	337	36	0	0	NUM
ejpam-6541	337	37	,	,	PUNCT
ejpam-6541	337	38	0	0	NUM
ejpam-6541	337	39	)	)	PUNCT
ejpam-6541	337	40	are	be	AUX
ejpam-6541	337	41	continuous	continuous	ADJ
ejpam-6541	337	42	.	.	PUNCT
ejpam-6541	338	1	proof	proof	NOUN
ejpam-6541	338	2	.	.	PUNCT
ejpam-6541	339	1	assume	assume	VERB
ejpam-6541	339	2	that	that	SCONJ
ejpam-6541	339	3	dimv	dimv	NOUN
ejpam-6541	339	4	=	=	PROPN
ejpam-6541	339	5	k	k	PROPN
ejpam-6541	339	6	and	and	CCONJ
ejpam-6541	339	7	that	that	SCONJ
ejpam-6541	339	8	(	(	PUNCT
ejpam-6541	339	9	v	v	NOUN
ejpam-6541	339	10	,	,	PUNCT
ejpam-6541	339	11	hihf	hihf	PROPN
ejpam-6541	339	12	)	)	PUNCT
ejpam-6541	339	13	is	be	AUX
ejpam-6541	339	14	an	an	DET
ejpam-6541	339	15	intuitionistic	intuitionistic	ADJ
ejpam-6541	339	16	hesitant	hesitant	ADJ
ejpam-6541	339	17	fuzzy	fuzzy	ADJ
ejpam-6541	339	18	normed	norme	VERB
ejpam-6541	339	19	linear	linear	ADJ
ejpam-6541	339	20	space	space	NOUN
ejpam-6541	339	21	.	.	PUNCT
ejpam-6541	340	1	consider	consider	VERB
ejpam-6541	340	2	{	{	PUNCT
ejpam-6541	340	3	xn	xn	NOUN
ejpam-6541	340	4	}	}	PUNCT
ejpam-6541	340	5	to	to	PART
ejpam-6541	340	6	become	become	VERB
ejpam-6541	340	7	a	a	DET
ejpam-6541	340	8	cauchy	cauchy	ADJ
ejpam-6541	340	9	sequence	sequence	NOUN
ejpam-6541	340	10	in	in	ADP
ejpam-6541	340	11	v	v	NOUN
ejpam-6541	340	12	and	and	CCONJ
ejpam-6541	340	13	{	{	PUNCT
ejpam-6541	340	14	e1	e1	PROPN
ejpam-6541	340	15	,	,	PUNCT
ejpam-6541	340	16	e2	e2	PROPN
ejpam-6541	340	17	,	,	PUNCT
ejpam-6541	340	18	.	.	PUNCT
ejpam-6541	340	19	.	.	PUNCT
ejpam-6541	340	20	.	.	PUNCT
ejpam-6541	341	1	,	,	PUNCT
ejpam-6541	341	2	ek	ek	AUX
ejpam-6541	341	3	}	}	PUNCT
ejpam-6541	341	4	providing	provide	VERB
ejpam-6541	341	5	a	a	DET
ejpam-6541	341	6	basis	basis	NOUN
ejpam-6541	341	7	of	of	ADP
ejpam-6541	341	8	v.	v.	INTJ
ejpam-6541	341	9	let	let	VERB
ejpam-6541	341	10	xn	xn	PROPN
ejpam-6541	342	1	=	=	SYM
ejpam-6541	342	2	ωn	ωn	SYM
ejpam-6541	342	3	1	1	NUM
ejpam-6541	342	4	e1	e1	NOUN
ejpam-6541	342	5	+	+	CCONJ
ejpam-6541	342	6	ωn	ωn	SYM
ejpam-6541	342	7	2	2	NUM
ejpam-6541	342	8	e2	e2	NOUN
ejpam-6541	342	9	+	+	PROPN
ejpam-6541	342	10	,	,	PUNCT
ejpam-6541	342	11	.	.	PUNCT
ejpam-6541	342	12	.	.	PUNCT
ejpam-6541	342	13	.	.	PUNCT
ejpam-6541	343	1	,	,	PUNCT
ejpam-6541	343	2	ωn	ωn	PROPN
ejpam-6541	343	3	k	k	PROPN
ejpam-6541	343	4	ek	ek	PROPN
ejpam-6541	343	5	.	.	PROPN
ejpam-6541	344	1	where	where	SCONJ
ejpam-6541	344	2	ωn	ωn	ADV
ejpam-6541	344	3	1	1	NUM
ejpam-6541	344	4	,	,	PUNCT
ejpam-6541	344	5	ω	ω	PROPN
ejpam-6541	344	6	n	n	PRON
ejpam-6541	344	7	2	2	NUM
ejpam-6541	344	8	,	,	PUNCT
ejpam-6541	344	9	.	.	PUNCT
ejpam-6541	344	10	.	.	PUNCT
ejpam-6541	344	11	.	.	PUNCT
ejpam-6541	345	1	,	,	PUNCT
ejpam-6541	345	2	ω	ω	PROPN
ejpam-6541	345	3	n	n	CCONJ
ejpam-6541	345	4	k	k	NOUN
ejpam-6541	345	5	are	be	AUX
ejpam-6541	345	6	appropriate	appropriate	ADJ
ejpam-6541	345	7	scalars	scalar	NOUN
ejpam-6541	345	8	.	.	PUNCT
ejpam-6541	346	1	thus	thus	ADV
ejpam-6541	346	2	,	,	PUNCT
ejpam-6541	346	3	lim	lim	PROPN
ejpam-6541	346	4	m	m	PROPN
ejpam-6541	346	5	,	,	PUNCT
ejpam-6541	346	6	n→∞	n→∞	X
ejpam-6541	346	7	nihf	nihf	PROPN
ejpam-6541	346	8	(	(	PUNCT
ejpam-6541	346	9	xm	xm	PROPN
ejpam-6541	346	10	−	−	PROPN
ejpam-6541	346	11	xn	xn	PROPN
ejpam-6541	346	12	,	,	PUNCT
ejpam-6541	346	13	t	t	PROPN
ejpam-6541	346	14	)	)	PUNCT
ejpam-6541	346	15	=	=	VERB
ejpam-6541	346	16	u∗	u∗	PROPN
ejpam-6541	346	17	,	,	PUNCT
ejpam-6541	346	18	∀	∀	X
ejpam-6541	346	19	t	t	NOUN
ejpam-6541	346	20	>	>	X
ejpam-6541	346	21	0	0	PUNCT
ejpam-6541	347	1	(	(	PUNCT
ejpam-6541	347	2	9	9	NUM
ejpam-6541	347	3	)	)	PUNCT
ejpam-6541	347	4	along	along	ADP
ejpam-6541	347	5	with	with	ADP
ejpam-6541	347	6	lim	lim	PROPN
ejpam-6541	347	7	m	m	PROPN
ejpam-6541	347	8	,	,	PUNCT
ejpam-6541	347	9	n→∞	n→∞	X
ejpam-6541	347	10	nihf	nihf	PROPN
ejpam-6541	347	11	(	(	PUNCT
ejpam-6541	347	12	xm	xm	PROPN
ejpam-6541	347	13	−	−	PROPN
ejpam-6541	348	1	xn	xn	PROPN
ejpam-6541	348	2	,	,	PUNCT
ejpam-6541	348	3	t	t	PROPN
ejpam-6541	348	4	)	)	PUNCT
ejpam-6541	348	5	=	=	PUNCT
ejpam-6541	349	1	∅∗	∅∗	PROPN
ejpam-6541	349	2	,	,	PUNCT
ejpam-6541	349	3	∀	∀	X
ejpam-6541	349	4	t	t	NOUN
ejpam-6541	349	5	>	>	X
ejpam-6541	349	6	0	0	PUNCT
ejpam-6541	349	7	(	(	PUNCT
ejpam-6541	349	8	10	10	NUM
ejpam-6541	349	9	)	)	PUNCT
ejpam-6541	349	10	it	it	PRON
ejpam-6541	349	11	is	be	AUX
ejpam-6541	349	12	evident	evident	ADJ
ejpam-6541	349	13	out	out	ADP
ejpam-6541	349	14	of	of	ADP
ejpam-6541	349	15	lemma	lemma	PROPN
ejpam-6541	349	16	(	(	PUNCT
ejpam-6541	349	17	2	2	NUM
ejpam-6541	349	18	)	)	PUNCT
ejpam-6541	349	19	that	that	SCONJ
ejpam-6541	349	20	,	,	PUNCT
ejpam-6541	349	21	there	there	PRON
ejpam-6541	349	22	exists	exist	VERB
ejpam-6541	349	23	h1	h1	PROPN
ejpam-6541	349	24	,	,	PUNCT
ejpam-6541	349	25	h2	h2	PROPN
ejpam-6541	349	26	>	>	X
ejpam-6541	349	27	0	0	PUNCT
ejpam-6541	349	28	and	and	CCONJ
ejpam-6541	349	29	s∗	s∗	PROPN
ejpam-6541	349	30	1	1	NUM
ejpam-6541	349	31	,	,	PUNCT
ejpam-6541	349	32	s	s	NOUN
ejpam-6541	349	33	∗	∗	NOUN
ejpam-6541	349	34	2	2	NUM
ejpam-6541	349	35	∈	∈	NOUN
ejpam-6541	349	36	p[0	p[0	NOUN
ejpam-6541	349	37	,	,	PUNCT
ejpam-6541	349	38	1	1	NUM
ejpam-6541	349	39	]	]	PUNCT
ejpam-6541	349	40	such	such	ADJ
ejpam-6541	349	41	that	that	DET
ejpam-6541	349	42	nihf	nihf	NOUN
ejpam-6541	349	43	(	(	PUNCT
ejpam-6541	349	44	k∑	k∑	PROPN
ejpam-6541	349	45	i=1	i=1	PROPN
ejpam-6541	349	46	(	(	PUNCT
ejpam-6541	349	47	ωm	ωm	PROPN
ejpam-6541	349	48	i	i	NOUN
ejpam-6541	349	49	−	−	PROPN
ejpam-6541	349	50	ωn	ωn	VERB
ejpam-6541	349	51	i	i	PROPN
ejpam-6541	349	52	)	)	PUNCT
ejpam-6541	349	53	ei	ei	PROPN
ejpam-6541	349	54	,	,	PUNCT
ejpam-6541	349	55	h1	h1	PROPN
ejpam-6541	349	56	k∑	k∑	VERB
ejpam-6541	349	57	i=1	i=1	PROPN
ejpam-6541	350	1	(	(	PUNCT
ejpam-6541	350	2	|ωm	|ωm	INTJ
ejpam-6541	350	3	i	i	PRON
ejpam-6541	350	4	−	−	PROPN
ejpam-6541	350	5	ωn	ωn	INTJ
ejpam-6541	350	6	i	i	PROPN
ejpam-6541	350	7	|	|	NOUN
ejpam-6541	350	8	)	)	PUNCT
ejpam-6541	350	9	)	)	PUNCT
ejpam-6541	351	1	⊂	⊂	PROPN
ejpam-6541	351	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	351	3	1	1	NUM
ejpam-6541	351	4	(	(	PUNCT
ejpam-6541	351	5	11	11	NUM
ejpam-6541	351	6	)	)	PUNCT
ejpam-6541	351	7	mihf	mihf	PROPN
ejpam-6541	351	8	(	(	PUNCT
ejpam-6541	351	9	k∑	k∑	NOUN
ejpam-6541	351	10	i=1	i=1	PROPN
ejpam-6541	351	11	(	(	PUNCT
ejpam-6541	351	12	ωm	ωm	PROPN
ejpam-6541	351	13	i	i	NOUN
ejpam-6541	351	14	−	−	PROPN
ejpam-6541	351	15	ωn	ωn	VERB
ejpam-6541	351	16	i	i	PROPN
ejpam-6541	351	17	)	)	PUNCT
ejpam-6541	351	18	ei	ei	PROPN
ejpam-6541	351	19	,	,	PUNCT
ejpam-6541	351	20	h2	h2	PROPN
ejpam-6541	351	21	k∑	k∑	PROPN
ejpam-6541	351	22	i=1	i=1	PROPN
ejpam-6541	352	1	(	(	PUNCT
ejpam-6541	352	2	|ωm	|ωm	INTJ
ejpam-6541	352	3	i	i	PRON
ejpam-6541	352	4	−	−	PROPN
ejpam-6541	352	5	ωn	ωn	INTJ
ejpam-6541	352	6	i	i	PRON
ejpam-6541	352	7	|	|	NOUN
ejpam-6541	352	8	)	)	PUNCT
ejpam-6541	352	9	)	)	PUNCT
ejpam-6541	353	1	⊃	⊃	NOUN
ejpam-6541	353	2	s∗	s∗	PROPN
ejpam-6541	353	3	2	2	NUM
ejpam-6541	353	4	(	(	PUNCT
ejpam-6541	353	5	12	12	NUM
ejpam-6541	353	6	)	)	PUNCT
ejpam-6541	353	7	again	again	ADV
ejpam-6541	353	8	for	for	ADP
ejpam-6541	353	9	u∗	u∗	PROPN
ejpam-6541	353	10	⊃	⊃	PROPN
ejpam-6541	353	11	s∗	s∗	PROPN
ejpam-6541	353	12	1	1	NUM
ejpam-6541	353	13	⊃	⊃	PROPN
ejpam-6541	353	14	∅∗	∅∗	VERB
ejpam-6541	353	15	out	out	ADP
ejpam-6541	353	16	of	of	ADP
ejpam-6541	353	17	(	(	PUNCT
ejpam-6541	353	18	9	9	NUM
ejpam-6541	353	19	)	)	PUNCT
ejpam-6541	353	20	,	,	PUNCT
ejpam-6541	353	21	consequently	consequently	ADV
ejpam-6541	353	22	,	,	PUNCT
ejpam-6541	353	23	a	a	DET
ejpam-6541	353	24	positive	positive	ADJ
ejpam-6541	353	25	integer	integer	NOUN
ejpam-6541	353	26	n0	n0	PROPN
ejpam-6541	353	27	exists	exist	VERB
ejpam-6541	353	28	with	with	ADP
ejpam-6541	353	29	regard	regard	NOUN
ejpam-6541	353	30	to	to	ADP
ejpam-6541	353	31	nihf	nihf	PROPN
ejpam-6541	353	32	(	(	PUNCT
ejpam-6541	353	33	k∑	k∑	PROPN
ejpam-6541	353	34	i=1	i=1	PROPN
ejpam-6541	353	35	(	(	PUNCT
ejpam-6541	353	36	ωm	ωm	PROPN
ejpam-6541	353	37	i	i	NOUN
ejpam-6541	353	38	−	−	PROPN
ejpam-6541	353	39	ωn	ωn	VERB
ejpam-6541	353	40	i	i	PROPN
ejpam-6541	353	41	)	)	PUNCT
ejpam-6541	353	42	ei	ei	PROPN
ejpam-6541	353	43	,	,	PUNCT
ejpam-6541	353	44	t	t	PROPN
ejpam-6541	353	45	)	)	PUNCT
ejpam-6541	354	1	⊃	⊃	PROPN
ejpam-6541	354	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	354	3	1	1	NUM
ejpam-6541	354	4	,	,	PUNCT
ejpam-6541	354	5	∀	∀	X
ejpam-6541	354	6	m	m	NOUN
ejpam-6541	354	7	,	,	PUNCT
ejpam-6541	354	8	n	n	PRON
ejpam-6541	354	9	≥	≥	NOUN
ejpam-6541	354	10	n0	n0	NUM
ejpam-6541	354	11	.	.	PUNCT
ejpam-6541	355	1	(	(	PUNCT
ejpam-6541	355	2	13	13	NUM
ejpam-6541	355	3	)	)	PUNCT
ejpam-6541	355	4	and	and	CCONJ
ejpam-6541	355	5	for	for	ADP
ejpam-6541	355	6	u∗	u∗	PROPN
ejpam-6541	355	7	⊃	⊃	PROPN
ejpam-6541	355	8	s∗	s∗	PROPN
ejpam-6541	355	9	2	2	NUM
ejpam-6541	355	10	⊃	⊃	PROPN
ejpam-6541	355	11	∅∗	∅∗	VERB
ejpam-6541	355	12	out	out	ADP
ejpam-6541	355	13	of	of	ADP
ejpam-6541	355	14	(	(	PUNCT
ejpam-6541	355	15	10	10	NUM
ejpam-6541	355	16	)	)	PUNCT
ejpam-6541	355	17	,	,	PUNCT
ejpam-6541	355	18	consequently	consequently	ADV
ejpam-6541	355	19	,	,	PUNCT
ejpam-6541	355	20	a	a	DET
ejpam-6541	355	21	positive	positive	ADJ
ejpam-6541	355	22	integer	integer	NOUN
ejpam-6541	355	23	exists	exist	VERB
ejpam-6541	355	24	.	.	PUNCT
ejpam-6541	356	1	m0	m0	PROPN
ejpam-6541	356	2	such	such	ADJ
ejpam-6541	356	3	that	that	DET
ejpam-6541	356	4	mihf	mihf	PROPN
ejpam-6541	356	5	(	(	PUNCT
ejpam-6541	356	6	k∑	k∑	NOUN
ejpam-6541	356	7	i=1	i=1	PROPN
ejpam-6541	356	8	(	(	PUNCT
ejpam-6541	356	9	ωm	ωm	PROPN
ejpam-6541	356	10	i	i	NOUN
ejpam-6541	356	11	−	−	PROPN
ejpam-6541	356	12	ωn	ωn	VERB
ejpam-6541	356	13	i	i	PROPN
ejpam-6541	356	14	)	)	PUNCT
ejpam-6541	356	15	ei	ei	PROPN
ejpam-6541	356	16	,	,	PUNCT
ejpam-6541	356	17	t	t	PROPN
ejpam-6541	356	18	)	)	PUNCT
ejpam-6541	357	1	⊂	⊂	PROPN
ejpam-6541	357	2	s∗	s∗	VERB
ejpam-6541	357	3	2	2	NUM
ejpam-6541	357	4	,	,	PUNCT
ejpam-6541	357	5	∀	∀	X
ejpam-6541	357	6	m	m	NOUN
ejpam-6541	357	7	,	,	PUNCT
ejpam-6541	357	8	n	n	PRON
ejpam-6541	357	9	≥	≥	NOUN
ejpam-6541	357	10	m0	m0	NOUN
ejpam-6541	357	11	.	.	PUNCT
ejpam-6541	358	1	(	(	PUNCT
ejpam-6541	358	2	14	14	NUM
ejpam-6541	358	3	)	)	PUNCT
ejpam-6541	358	4	now	now	ADV
ejpam-6541	358	5	from	from	ADP
ejpam-6541	358	6	(	(	PUNCT
ejpam-6541	358	7	11	11	NUM
ejpam-6541	358	8	)	)	PUNCT
ejpam-6541	358	9	and	and	CCONJ
ejpam-6541	358	10	(	(	PUNCT
ejpam-6541	358	11	13	13	X
ejpam-6541	358	12	)	)	PUNCT
ejpam-6541	358	13	we	we	PRON
ejpam-6541	358	14	have	have	VERB
ejpam-6541	358	15	,	,	PUNCT
ejpam-6541	358	16	nihf	nihf	PROPN
ejpam-6541	358	17	(	(	PUNCT
ejpam-6541	358	18	∑k	∑k	PROPN
ejpam-6541	358	19	i=1(ω	i=1(ω	PROPN
ejpam-6541	358	20	m	m	VERB
ejpam-6541	358	21	i	i	PRON
ejpam-6541	358	22	−	−	PROPN
ejpam-6541	358	23	ωn	ωn	VERB
ejpam-6541	358	24	i	i	PROPN
ejpam-6541	358	25	)	)	PUNCT
ejpam-6541	358	26	ei	ei	PROPN
ejpam-6541	358	27	,	,	PUNCT
ejpam-6541	358	28	t	t	PROPN
ejpam-6541	358	29	)	)	PUNCT
ejpam-6541	359	1	⊃	⊃	PROPN
ejpam-6541	359	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	359	3	1	1	NUM
ejpam-6541	359	4	⊃	⊃	PROPN
ejpam-6541	359	5	nihf	nihf	X
ejpam-6541	359	6	(	(	PUNCT
ejpam-6541	359	7	∑k	∑k	PROPN
ejpam-6541	359	8	i=1(ω	i=1(ω	PROPN
ejpam-6541	359	9	m	m	VERB
ejpam-6541	359	10	i	i	PRON
ejpam-6541	359	11	−	−	PROPN
ejpam-6541	359	12	ωn	ωn	VERB
ejpam-6541	359	13	i	i	PROPN
ejpam-6541	359	14	)	)	PUNCT
ejpam-6541	359	15	ei	ei	PROPN
ejpam-6541	359	16	,	,	PUNCT
ejpam-6541	359	17	h1	h1	PROPN
ejpam-6541	359	18	∑k	∑k	PROPN
ejpam-6541	359	19	i=1(|ωm	i=1(|ωm	PROPN
ejpam-6541	360	1	i	i	PRON
ejpam-6541	361	1	−	−	PROPN
ejpam-6541	362	1	ωn	ωn	VERB
ejpam-6541	362	2	i	i	PROPN
ejpam-6541	362	3	|	|	NOUN
ejpam-6541	362	4	)	)	PUNCT
ejpam-6541	362	5	)	)	PUNCT
ejpam-6541	362	6	∀	∀	PUNCT
ejpam-6541	363	1	m	m	PROPN
ejpam-6541	363	2	,	,	PUNCT
ejpam-6541	363	3	n	n	PRON
ejpam-6541	363	4	≥	≥	NOUN
ejpam-6541	363	5	n0	n0	NUM
ejpam-6541	363	6	.	.	PUNCT
ejpam-6541	364	1	=	=	PRON
ejpam-6541	364	2	⇒	⇒	NOUN
ejpam-6541	364	3	h1	h1	PROPN
ejpam-6541	364	4	∑k	∑k	PROPN
ejpam-6541	364	5	i=1(|ωm	i=1(|ωm	PROPN
ejpam-6541	364	6	i	i	PRON
ejpam-6541	364	7	−	−	PROPN
ejpam-6541	365	1	ωn	ωn	VERB
ejpam-6541	366	1	i	i	PROPN
ejpam-6541	367	1	|	|	NOUN
ejpam-6541	367	2	)	)	PUNCT
ejpam-6541	368	1	<	<	X
ejpam-6541	368	2	t,∀	t,∀	PUNCT
ejpam-6541	368	3	m	m	PROPN
ejpam-6541	368	4	,	,	PUNCT
ejpam-6541	368	5	n	n	PRON
ejpam-6541	368	6	≥	≥	NOUN
ejpam-6541	368	7	n0	n0	NUM
ejpam-6541	368	8	(	(	PUNCT
ejpam-6541	368	9	given	give	VERB
ejpam-6541	368	10	that	that	DET
ejpam-6541	368	11	ni(x	ni(x	NUM
ejpam-6541	368	12	,	,	PUNCT
ejpam-6541	368	13	�	�	PROPN
ejpam-6541	368	14	)	)	PUNCT
ejpam-6541	368	15	is	be	AUX
ejpam-6541	368	16	non	non	ADJ
ejpam-6541	368	17	decreasing	decrease	VERB
ejpam-6541	368	18	in	in	ADP
ejpam-6541	368	19	t	t	NOUN
ejpam-6541	368	20	)	)	PUNCT
ejpam-6541	369	1	=	=	NOUN
ejpam-6541	369	2	⇒	⇒	NOUN
ejpam-6541	369	3	∑k	∑k	PROPN
ejpam-6541	369	4	i=1(|ωm	i=1(|ωm	PROPN
ejpam-6541	370	1	i	i	PRON
ejpam-6541	370	2	−	−	PROPN
ejpam-6541	371	1	ωn	ωn	VERB
ejpam-6541	371	2	i	i	PROPN
ejpam-6541	371	3	|	|	NOUN
ejpam-6541	371	4	)	)	PUNCT
ejpam-6541	371	5	<	<	X
ejpam-6541	371	6	t	t	X
ejpam-6541	371	7	h1	h1	NOUN
ejpam-6541	371	8	,	,	PUNCT
ejpam-6541	371	9	∀	∀	X
ejpam-6541	371	10	m	m	NOUN
ejpam-6541	371	11	,	,	PUNCT
ejpam-6541	371	12	n	n	PRON
ejpam-6541	371	13	≥	≥	NOUN
ejpam-6541	371	14	n0	n0	NUM
ejpam-6541	371	15	=	=	NOUN
ejpam-6541	371	16	⇒	⇒	PROPN
ejpam-6541	371	17	|ωm	|ωm	VERB
ejpam-6541	372	1	i	i	PRON
ejpam-6541	372	2	−	−	PROPN
ejpam-6541	373	1	ωn	ωn	INTJ
ejpam-6541	373	2	i	i	PRON
ejpam-6541	374	1	|	|	ADV
ejpam-6541	374	2	<	<	X
ejpam-6541	374	3	t	t	X
ejpam-6541	374	4	h1	h1	NOUN
ejpam-6541	374	5	,	,	PUNCT
ejpam-6541	374	6	∀	∀	X
ejpam-6541	374	7	m	m	NOUN
ejpam-6541	374	8	,	,	PUNCT
ejpam-6541	374	9	n	n	PRON
ejpam-6541	374	10	≥	≥	NOUN
ejpam-6541	374	11	n0	n0	NUM
ejpam-6541	374	12	alon	alon	PROPN
ejpam-6541	374	13	with	with	ADP
ejpam-6541	374	14	i	i	PROPN
ejpam-6541	374	15	=	=	SYM
ejpam-6541	374	16	1	1	NUM
ejpam-6541	374	17	,	,	PUNCT
ejpam-6541	374	18	2	2	NUM
ejpam-6541	374	19	,	,	PUNCT
ejpam-6541	374	20	.	.	PUNCT
ejpam-6541	374	21	.	.	PUNCT
ejpam-6541	374	22	.	.	PUNCT
ejpam-6541	375	1	k.	k.	PROPN
ejpam-6541	376	1	given	give	VERB
ejpam-6541	376	2	that	that	PRON
ejpam-6541	376	3	t	t	PROPN
ejpam-6541	376	4	>	>	X
ejpam-6541	376	5	0	0	PUNCT
ejpam-6541	376	6	is	be	AUX
ejpam-6541	376	7	random	random	ADJ
ejpam-6541	376	8	,	,	PUNCT
ejpam-6541	376	9	based	base	VERB
ejpam-6541	376	10	on	on	ADP
ejpam-6541	376	11	previously	previously	ADV
ejpam-6541	376	12	mentioned	mention	VERB
ejpam-6541	376	13	,	,	PUNCT
ejpam-6541	376	14	we	we	PRON
ejpam-6541	376	15	possess	possess	VERB
ejpam-6541	376	16	limm	limm	NOUN
ejpam-6541	376	17	,	,	PUNCT
ejpam-6541	376	18	n→∞	n→∞	NUM
ejpam-6541	377	1	|ωm	|ωm	ADP
ejpam-6541	377	2	i	i	PRON
ejpam-6541	377	3	−	−	PROPN
ejpam-6541	378	1	ωn	ωn	INTJ
ejpam-6541	378	2	i	i	PRON
ejpam-6541	378	3	|	|	ADV
ejpam-6541	378	4	=	=	SYM
ejpam-6541	378	5	0	0	NUM
ejpam-6541	379	1	for	for	ADP
ejpam-6541	379	2	i	i	PRON
ejpam-6541	379	3	=	=	SYM
ejpam-6541	379	4	1	1	NUM
ejpam-6541	379	5	,	,	PUNCT
ejpam-6541	379	6	2	2	NUM
ejpam-6541	379	7	.	.	PUNCT
ejpam-6541	379	8	.	.	PUNCT
ejpam-6541	379	9	.	.	PUNCT
ejpam-6541	380	1	,	,	PUNCT
ejpam-6541	380	2	k.	k.	X
ejpam-6541	381	1	=	=	AUX
ejpam-6541	381	2	⇒	⇒	PROPN
ejpam-6541	381	3	{	{	PUNCT
ejpam-6541	381	4	ωn	ωn	VERB
ejpam-6541	381	5	i	i	PROPN
ejpam-6541	381	6	}	}	PUNCT
ejpam-6541	381	7	this	this	PRON
ejpam-6541	381	8	constitutes	constitute	VERB
ejpam-6541	381	9	a	a	DET
ejpam-6541	381	10	cauchy	cauchy	ADJ
ejpam-6541	381	11	sequence	sequence	NOUN
ejpam-6541	381	12	of	of	ADP
ejpam-6541	381	13	scalars	scalar	NOUN
ejpam-6541	381	14	for	for	ADP
ejpam-6541	381	15	every	every	DET
ejpam-6541	381	16	i	i	NOUN
ejpam-6541	381	17	=	=	NOUN
ejpam-6541	381	18	1	1	NUM
ejpam-6541	381	19	,	,	PUNCT
ejpam-6541	381	20	2	2	NUM
ejpam-6541	381	21	.	.	PUNCT
ejpam-6541	381	22	.	.	PUNCT
ejpam-6541	382	1	.	.	PUNCT
ejpam-6541	383	1	,	,	PUNCT
ejpam-6541	383	2	k	k	X
ejpam-6541	383	3	..	..	PUNCT
ejpam-6541	383	4	thus	thus	ADV
ejpam-6541	383	5	,	,	PUNCT
ejpam-6541	383	6	every	every	DET
ejpam-6541	383	7	sequence	sequence	NOUN
ejpam-6541	383	8	{	{	PUNCT
ejpam-6541	383	9	ωn	ωn	PROPN
ejpam-6541	383	10	i	i	PROPN
ejpam-6541	383	11	}	}	PUNCT
ejpam-6541	383	12	converges	converge	VERB
ejpam-6541	383	13	.	.	PUNCT
ejpam-6541	384	1	let	let	VERB
ejpam-6541	384	2	limn→∞	limn→∞	PROPN
ejpam-6541	384	3	ωn	ωn	ADP
ejpam-6541	384	4	i	i	NOUN
ejpam-6541	384	5	=	=	PUNCT
ejpam-6541	384	6	ωi	ωi	PROPN
ejpam-6541	384	7	regarding	regard	VERB
ejpam-6541	384	8	i	i	PRON
ejpam-6541	384	9	=	=	SYM
ejpam-6541	384	10	1	1	NUM
ejpam-6541	384	11	,	,	PUNCT
ejpam-6541	384	12	2	2	NUM
ejpam-6541	384	13	.	.	PUNCT
ejpam-6541	384	14	.	.	PUNCT
ejpam-6541	385	1	.	.	PUNCT
ejpam-6541	386	1	,	,	PUNCT
ejpam-6541	386	2	k.	k.	PROPN
ejpam-6541	386	3	along	along	ADP
ejpam-6541	386	4	with	with	ADP
ejpam-6541	386	5	x	x	X
ejpam-6541	386	6	=	=	SYM
ejpam-6541	386	7	∑k	∑k	PROPN
ejpam-6541	386	8	i=1	i=1	PROPN
ejpam-6541	386	9	ωiei	ωiei	PROPN
ejpam-6541	386	10	.	.	PUNCT
ejpam-6541	387	1	obviously	obviously	ADV
ejpam-6541	387	2	,	,	PUNCT
ejpam-6541	387	3	x	x	PUNCT
ejpam-6541	387	4	∈	∈	PROPN
ejpam-6541	387	5	v.	v.	ADP
ejpam-6541	387	6	afterwards	afterwards	ADV
ejpam-6541	387	7	∀	∀	X
ejpam-6541	387	8	t	t	X
ejpam-6541	387	9	>	>	X
ejpam-6541	387	10	0	0	NUM
ejpam-6541	387	11	,	,	PUNCT
ejpam-6541	387	12	nihf	nihf	PROPN
ejpam-6541	387	13	(	(	PUNCT
ejpam-6541	387	14	xn−x	xn−x	PROPN
ejpam-6541	387	15	,	,	PUNCT
ejpam-6541	387	16	t	t	PROPN
ejpam-6541	387	17	)	)	PUNCT
ejpam-6541	387	18	=	=	SYM
ejpam-6541	387	19	nihf	nihf	PROPN
ejpam-6541	387	20	(	(	PUNCT
ejpam-6541	387	21	∑k	∑k	PROPN
ejpam-6541	387	22	i=1	i=1	PROPN
ejpam-6541	387	23	ω	ω	PROPN
ejpam-6541	388	1	n	n	INTJ
ejpam-6541	388	2	i	i	PRON
ejpam-6541	388	3	ei	ei	VERB
ejpam-6541	389	1	−	−	PROPN
ejpam-6541	389	2	∑k	∑k	PROPN
ejpam-6541	389	3	i=1	i=1	PROPN
ejpam-6541	389	4	ωiei	ωiei	PROPN
ejpam-6541	389	5	,	,	PUNCT
ejpam-6541	389	6	t	t	NOUN
ejpam-6541	389	7	)	)	PUNCT
ejpam-6541	389	8	=	=	SYM
ejpam-6541	389	9	nihf	nihf	PROPN
ejpam-6541	389	10	(	(	PUNCT
ejpam-6541	389	11	∑k	∑k	PROPN
ejpam-6541	389	12	i=1(ω	i=1(ω	PROPN
ejpam-6541	389	13	n	n	NOUN
ejpam-6541	389	14	i	i	PRON
ejpam-6541	389	15	−	−	PROPN
ejpam-6541	389	16	ωi)ei	ωi)ei	NUM
ejpam-6541	389	17	,	,	PUNCT
ejpam-6541	389	18	t	t	NOUN
ejpam-6541	389	19	)	)	PUNCT
ejpam-6541	389	20	that	that	PRON
ejpam-6541	389	21	is	be	AUX
ejpam-6541	389	22	nihf	nihf	NOUN
ejpam-6541	389	23	(	(	PUNCT
ejpam-6541	389	24	xn	xn	PROPN
ejpam-6541	389	25	−	−	PROPN
ejpam-6541	389	26	x	x	SYM
ejpam-6541	389	27	,	,	PUNCT
ejpam-6541	389	28	t	t	PROPN
ejpam-6541	389	29	)	)	PUNCT
ejpam-6541	389	30	⊇	⊇	PROPN
ejpam-6541	389	31	nihf	nihf	PROPN
ejpam-6541	389	32	(	(	PUNCT
ejpam-6541	389	33	e1	e1	PROPN
ejpam-6541	389	34	,	,	PUNCT
ejpam-6541	389	35	t	t	PROPN
ejpam-6541	389	36	k|ωn	k|ωn	NOUN
ejpam-6541	389	37	1	1	NUM
ejpam-6541	389	38	−	−	NOUN
ejpam-6541	389	39	ω1|	ω1|	NOUN
ejpam-6541	389	40	)	)	PUNCT
ejpam-6541	389	41	∗	∗	NOUN
ejpam-6541	389	42	·	·	PUNCT
ejpam-6541	389	43	·	·	PUNCT
ejpam-6541	389	44	·	·	PUNCT
ejpam-6541	390	1	∗	∗	X
ejpam-6541	390	2	nihf	nihf	PROPN
ejpam-6541	390	3	(	(	PUNCT
ejpam-6541	390	4	ek	ek	PROPN
ejpam-6541	390	5	,	,	PUNCT
ejpam-6541	390	6	t	t	PROPN
ejpam-6541	390	7	k|ωn	k|ωn	PROPN
ejpam-6541	391	1	k	k	PROPN
ejpam-6541	391	2	−	−	PROPN
ejpam-6541	391	3	ωk|	ωk|	PROPN
ejpam-6541	391	4	)	)	PUNCT
ejpam-6541	391	5	(	(	PUNCT
ejpam-6541	391	6	15	15	NUM
ejpam-6541	391	7	)	)	PUNCT
ejpam-6541	391	8	k.	k.	PROPN
ejpam-6541	391	9	kavitha	kavitha	PROPN
ejpam-6541	391	10	,	,	PUNCT
ejpam-6541	391	11	p.	p.	PROPN
ejpam-6541	391	12	muralikrishna	muralikrishna	PROPN
ejpam-6541	391	13	/	/	SYM
ejpam-6541	391	14	eur	eur	PROPN
ejpam-6541	391	15	.	.	PUNCT
ejpam-6541	392	1	j.	j.	PROPN
ejpam-6541	392	2	pure	pure	PROPN
ejpam-6541	392	3	appl	appl	PROPN
ejpam-6541	392	4	.	.	PROPN
ejpam-6541	392	5	math	math	PROPN
ejpam-6541	392	6	,	,	PUNCT
ejpam-6541	392	7	18	18	NUM
ejpam-6541	392	8	(	(	PUNCT
ejpam-6541	392	9	4	4	NUM
ejpam-6541	392	10	)	)	PUNCT
ejpam-6541	392	11	(	(	PUNCT
ejpam-6541	392	12	2025	2025	NUM
ejpam-6541	392	13	)	)	PUNCT
ejpam-6541	392	14	,	,	PUNCT
ejpam-6541	392	15	6541	6541	NUM
ejpam-6541	392	16	11	11	NUM
ejpam-6541	392	17	of	of	ADP
ejpam-6541	392	18	14	14	NUM
ejpam-6541	392	19	when	when	SCONJ
ejpam-6541	392	20	n	n	X
ejpam-6541	392	21	→	→	SYM
ejpam-6541	392	22	∞	∞	PROPN
ejpam-6541	392	23	,	,	PUNCT
ejpam-6541	392	24	then	then	ADV
ejpam-6541	392	25	t	t	PROPN
ejpam-6541	392	26	k|ωn	k|ωn	NOUN
ejpam-6541	393	1	i	i	PRON
ejpam-6541	393	2	−ωi|	−ωi|	PROPN
ejpam-6541	394	1	→	→	SYM
ejpam-6541	395	1	∞	∞	PROPN
ejpam-6541	396	1	(	(	PUNCT
ejpam-6541	397	1	since	since	SCONJ
ejpam-6541	397	2	ωn	ωn	PROPN
ejpam-6541	397	3	i	i	PROPN
ejpam-6541	397	4	→	→	SYM
ejpam-6541	397	5	ωi	ωi	PROPN
ejpam-6541	397	6	)	)	PUNCT
ejpam-6541	397	7	for	for	ADP
ejpam-6541	397	8	i	i	PROPN
ejpam-6541	397	9	=	=	SYM
ejpam-6541	397	10	1	1	NUM
ejpam-6541	397	11	,	,	PUNCT
ejpam-6541	397	12	2	2	NUM
ejpam-6541	397	13	.	.	PUNCT
ejpam-6541	397	14	.	.	PUNCT
ejpam-6541	397	15	.	.	PUNCT
ejpam-6541	398	1	,	,	PUNCT
ejpam-6541	398	2	k.	k.	PROPN
ejpam-6541	398	3	and	and	CCONJ
ejpam-6541	398	4	t	t	PROPN
ejpam-6541	398	5	>	>	X
ejpam-6541	398	6	0	0	X
ejpam-6541	398	7	.	.	PUNCT
ejpam-6541	399	1	utilizing	utilize	VERB
ejpam-6541	399	2	the	the	DET
ejpam-6541	399	3	t	t	NOUN
ejpam-6541	399	4	-	-	PUNCT
ejpam-6541	399	5	norm	norm	NOUN
ejpam-6541	399	6	∗	∗	NOUN
ejpam-6541	399	7	continuity	continuity	NOUN
ejpam-6541	399	8	at	at	ADP
ejpam-6541	399	9	(	(	PUNCT
ejpam-6541	399	10	1,1	1,1	NUM
ejpam-6541	399	11	)	)	PUNCT
ejpam-6541	399	12	,	,	PUNCT
ejpam-6541	399	13	we	we	PRON
ejpam-6541	399	14	derive	derive	VERB
ejpam-6541	399	15	from	from	ADP
ejpam-6541	399	16	(	(	PUNCT
ejpam-6541	399	17	15	15	NUM
ejpam-6541	399	18	)	)	PUNCT
ejpam-6541	399	19	limn→∞nihf	limn→∞nihf	PROPN
ejpam-6541	399	20	(	(	PUNCT
ejpam-6541	399	21	xn	xn	PROPN
ejpam-6541	400	1	−	−	PROPN
ejpam-6541	400	2	x	x	SYM
ejpam-6541	400	3	,	,	PUNCT
ejpam-6541	400	4	t	t	PROPN
ejpam-6541	400	5	)	)	PUNCT
ejpam-6541	400	6	⊇	⊇	PROPN
ejpam-6541	400	7	u∗	u∗	NOUN
ejpam-6541	400	8	∗	∗	NOUN
ejpam-6541	400	9	·	·	PUNCT
ejpam-6541	400	10	·	·	PUNCT
ejpam-6541	400	11	·	·	PUNCT
ejpam-6541	400	12	∗	∗	NOUN
ejpam-6541	400	13	u∗	u∗	PROPN
ejpam-6541	400	14	,	,	PUNCT
ejpam-6541	400	15	∀	∀	X
ejpam-6541	400	16	t	t	X
ejpam-6541	400	17	>	>	X
ejpam-6541	400	18	0	0	NUM
ejpam-6541	400	19	.	.	PUNCT
ejpam-6541	401	1	=	=	NOUN
ejpam-6541	401	2	⇒	⇒	PROPN
ejpam-6541	401	3	lim	lim	PROPN
ejpam-6541	401	4	n→∞	n→∞	PRON
ejpam-6541	401	5	nihf	nihf	PROPN
ejpam-6541	401	6	(	(	PUNCT
ejpam-6541	401	7	xn	xn	PROPN
ejpam-6541	401	8	−	−	PROPN
ejpam-6541	401	9	x	x	SYM
ejpam-6541	401	10	,	,	PUNCT
ejpam-6541	401	11	t	t	PROPN
ejpam-6541	401	12	)	)	PUNCT
ejpam-6541	401	13	=	=	VERB
ejpam-6541	401	14	u∗	u∗	PROPN
ejpam-6541	401	15	,	,	PUNCT
ejpam-6541	401	16	∀	∀	X
ejpam-6541	401	17	t	t	NOUN
ejpam-6541	401	18	>	>	X
ejpam-6541	401	19	0	0	NUM
ejpam-6541	401	20	.	.	PUNCT
ejpam-6541	402	1	(	(	PUNCT
ejpam-6541	402	2	16	16	NUM
ejpam-6541	402	3	)	)	PUNCT
ejpam-6541	402	4	now	now	ADV
ejpam-6541	402	5	from	from	ADP
ejpam-6541	402	6	(	(	PUNCT
ejpam-6541	402	7	12	12	NUM
ejpam-6541	402	8	)	)	PUNCT
ejpam-6541	402	9	and	and	CCONJ
ejpam-6541	402	10	(	(	PUNCT
ejpam-6541	402	11	14	14	NUM
ejpam-6541	402	12	)	)	PUNCT
ejpam-6541	402	13	we	we	PRON
ejpam-6541	402	14	have	have	VERB
ejpam-6541	402	15	,	,	PUNCT
ejpam-6541	402	16	mihf	mihf	PROPN
ejpam-6541	402	17	(	(	PUNCT
ejpam-6541	402	18	∑k	∑k	PROPN
ejpam-6541	402	19	i=1(ω	i=1(ω	PROPN
ejpam-6541	402	20	m	m	VERB
ejpam-6541	402	21	i	i	PRON
ejpam-6541	402	22	−	−	PROPN
ejpam-6541	402	23	ωn	ωn	VERB
ejpam-6541	402	24	i	i	PROPN
ejpam-6541	402	25	)	)	PUNCT
ejpam-6541	402	26	ei	ei	PROPN
ejpam-6541	402	27	,	,	PUNCT
ejpam-6541	402	28	t	t	PROPN
ejpam-6541	402	29	)	)	PUNCT
ejpam-6541	403	1	⊂	⊂	PRON
ejpam-6541	403	2	s∗	s∗	VERB
ejpam-6541	403	3	2	2	NUM
ejpam-6541	403	4	⊂	⊂	NOUN
ejpam-6541	403	5	mihf	mihf	PROPN
ejpam-6541	403	6	(	(	PUNCT
ejpam-6541	403	7	∑k	∑k	PROPN
ejpam-6541	403	8	i=1(ω	i=1(ω	PROPN
ejpam-6541	403	9	m	m	VERB
ejpam-6541	403	10	i	i	PRON
ejpam-6541	403	11	−	−	PROPN
ejpam-6541	403	12	ωn	ωn	VERB
ejpam-6541	403	13	i	i	PROPN
ejpam-6541	403	14	)	)	PUNCT
ejpam-6541	403	15	ei	ei	PROPN
ejpam-6541	403	16	,	,	PUNCT
ejpam-6541	403	17	h2	h2	PROPN
ejpam-6541	403	18	∑k	∑k	PROPN
ejpam-6541	403	19	i=1(|ωm	i=1(|ωm	PROPN
ejpam-6541	404	1	i	i	PRON
ejpam-6541	404	2	−	−	PROPN
ejpam-6541	405	1	ωn	ωn	VERB
ejpam-6541	405	2	i	i	PROPN
ejpam-6541	405	3	|	|	NOUN
ejpam-6541	405	4	)	)	PUNCT
ejpam-6541	405	5	)	)	PUNCT
ejpam-6541	405	6	∀	∀	PUNCT
ejpam-6541	406	1	m	m	PROPN
ejpam-6541	406	2	,	,	PUNCT
ejpam-6541	406	3	n	n	PRON
ejpam-6541	406	4	≥	≥	NOUN
ejpam-6541	406	5	n0	n0	NUM
ejpam-6541	406	6	.	.	PUNCT
ejpam-6541	407	1	=	=	AUX
ejpam-6541	408	1	⇒	⇒	NOUN
ejpam-6541	408	2	h2	h2	NOUN
ejpam-6541	408	3	∑k	∑k	PROPN
ejpam-6541	408	4	i=1(|ωm	i=1(|ωm	PROPN
ejpam-6541	408	5	i	i	PRON
ejpam-6541	408	6	−	−	PROPN
ejpam-6541	408	7	ωn	ωn	VERB
ejpam-6541	408	8	i	i	PROPN
ejpam-6541	408	9	|	|	NOUN
ejpam-6541	408	10	)	)	PUNCT
ejpam-6541	408	11	<	<	X
ejpam-6541	408	12	t	t	PROPN
ejpam-6541	408	13	,	,	PUNCT
ejpam-6541	408	14	∀	∀	X
ejpam-6541	408	15	m	m	NOUN
ejpam-6541	408	16	,	,	PUNCT
ejpam-6541	408	17	n	n	PRON
ejpam-6541	408	18	≥	≥	NOUN
ejpam-6541	408	19	n0	n0	NUM
ejpam-6541	408	20	(	(	PUNCT
ejpam-6541	408	21	because	because	SCONJ
ejpam-6541	408	22	mi(x	mi(x	NOUN
ejpam-6541	408	23	,	,	PUNCT
ejpam-6541	408	24	�	�	PROPN
ejpam-6541	408	25	)	)	PUNCT
ejpam-6541	408	26	has	have	AUX
ejpam-6541	408	27	non	non	ADJ
ejpam-6541	408	28	increasing	increase	VERB
ejpam-6541	408	29	in	in	ADP
ejpam-6541	408	30	t	t	PROPN
ejpam-6541	408	31	)	)	PUNCT
ejpam-6541	409	1	=	=	NOUN
ejpam-6541	409	2	⇒	⇒	NOUN
ejpam-6541	409	3	∑k	∑k	PROPN
ejpam-6541	409	4	i=1(|ωm	i=1(|ωm	PROPN
ejpam-6541	410	1	i	i	PRON
ejpam-6541	410	2	−	−	PROPN
ejpam-6541	411	1	ωn	ωn	VERB
ejpam-6541	411	2	i	i	PROPN
ejpam-6541	411	3	|	|	NOUN
ejpam-6541	411	4	)	)	PUNCT
ejpam-6541	411	5	<	<	X
ejpam-6541	411	6	t	t	PROPN
ejpam-6541	411	7	h2	h2	PROPN
ejpam-6541	411	8	,	,	PUNCT
ejpam-6541	411	9	∀	∀	X
ejpam-6541	411	10	m	m	PROPN
ejpam-6541	411	11	,	,	PUNCT
ejpam-6541	411	12	n	n	PRON
ejpam-6541	411	13	≥	≥	NOUN
ejpam-6541	411	14	m0	m0	NOUN
ejpam-6541	411	15	=	=	NOUN
ejpam-6541	411	16	⇒	⇒	NOUN
ejpam-6541	411	17	|ωm	|ωm	VERB
ejpam-6541	412	1	i	i	PRON
ejpam-6541	412	2	−	−	PROPN
ejpam-6541	413	1	ωn	ωn	INTJ
ejpam-6541	413	2	i	i	PRON
ejpam-6541	414	1	|	|	ADV
ejpam-6541	414	2	<	<	X
ejpam-6541	414	3	t	t	PROPN
ejpam-6541	414	4	h2	h2	NOUN
ejpam-6541	414	5	,	,	PUNCT
ejpam-6541	414	6	∀	∀	X
ejpam-6541	414	7	m	m	NOUN
ejpam-6541	414	8	,	,	PUNCT
ejpam-6541	414	9	n	n	PRON
ejpam-6541	414	10	≥	≥	NOUN
ejpam-6541	414	11	m0	m0	NOUN
ejpam-6541	414	12	in	in	ADP
ejpam-6541	414	13	addition	addition	NOUN
ejpam-6541	414	14	i	i	NOUN
ejpam-6541	414	15	=	=	NOUN
ejpam-6541	414	16	1	1	NUM
ejpam-6541	414	17	,	,	PUNCT
ejpam-6541	414	18	2	2	NUM
ejpam-6541	414	19	,	,	PUNCT
ejpam-6541	414	20	.	.	PUNCT
ejpam-6541	414	21	.	.	PUNCT
ejpam-6541	414	22	.	.	PUNCT
ejpam-6541	415	1	k.	k.	PROPN
ejpam-6541	416	1	given	give	VERB
ejpam-6541	416	2	that	that	PRON
ejpam-6541	416	3	t	t	PROPN
ejpam-6541	416	4	>	>	X
ejpam-6541	416	5	0	0	PUNCT
ejpam-6541	416	6	is	be	AUX
ejpam-6541	416	7	random	random	ADJ
ejpam-6541	416	8	,	,	PUNCT
ejpam-6541	416	9	we	we	PRON
ejpam-6541	416	10	can	can	AUX
ejpam-6541	416	11	derive	derive	VERB
ejpam-6541	416	12	limm	limm	NOUN
ejpam-6541	416	13	,	,	PUNCT
ejpam-6541	416	14	n→∞	n→∞	NUM
ejpam-6541	417	1	|ωm	|ωm	ADP
ejpam-6541	417	2	i	i	PRON
ejpam-6541	417	3	−	−	PROPN
ejpam-6541	418	1	ωn	ωn	INTJ
ejpam-6541	418	2	i	i	PRON
ejpam-6541	418	3	|	|	ADV
ejpam-6541	418	4	=	=	SYM
ejpam-6541	418	5	0	0	NUM
ejpam-6541	419	1	over	over	ADP
ejpam-6541	419	2	i	i	PROPN
ejpam-6541	419	3	=	=	NOUN
ejpam-6541	419	4	1	1	NUM
ejpam-6541	419	5	,	,	PUNCT
ejpam-6541	419	6	2	2	NUM
ejpam-6541	419	7	.	.	PUNCT
ejpam-6541	419	8	.	.	PUNCT
ejpam-6541	419	9	.	.	PUNCT
ejpam-6541	420	1	,	,	PUNCT
ejpam-6541	420	2	k.	k.	PROPN
ejpam-6541	420	3	for	for	ADP
ejpam-6541	420	4	every	every	DET
ejpam-6541	420	5	i	i	NOUN
ejpam-6541	420	6	=	=	NOUN
ejpam-6541	420	7	1	1	NUM
ejpam-6541	420	8	,	,	PUNCT
ejpam-6541	420	9	2	2	NUM
ejpam-6541	420	10	.	.	PUNCT
ejpam-6541	420	11	.	.	PUNCT
ejpam-6541	420	12	.	.	PUNCT
ejpam-6541	421	1	,	,	PUNCT
ejpam-6541	421	2	k.	k.	PROPN
ejpam-6541	421	3	is	be	AUX
ejpam-6541	421	4	a	a	DET
ejpam-6541	421	5	cauchy	cauchy	ADJ
ejpam-6541	421	6	sequence	sequence	NOUN
ejpam-6541	421	7	of	of	ADP
ejpam-6541	421	8	scalars	scalar	NOUN
ejpam-6541	421	9	.	.	PUNCT
ejpam-6541	422	1	thus	thus	ADV
ejpam-6541	422	2	,	,	PUNCT
ejpam-6541	422	3	every	every	DET
ejpam-6541	422	4	sequence	sequence	NOUN
ejpam-6541	422	5	{	{	PUNCT
ejpam-6541	422	6	ωn	ωn	PROPN
ejpam-6541	422	7	i	i	PROPN
ejpam-6541	422	8	}	}	PUNCT
ejpam-6541	422	9	converges	converge	VERB
ejpam-6541	422	10	.	.	PUNCT
ejpam-6541	423	1	let	let	VERB
ejpam-6541	423	2	limn→∞	limn→∞	PROPN
ejpam-6541	423	3	ωn	ωn	ADP
ejpam-6541	423	4	i	i	NOUN
ejpam-6541	423	5	=	=	PUNCT
ejpam-6541	423	6	ωi	ωi	PROPN
ejpam-6541	423	7	for	for	ADP
ejpam-6541	423	8	i	i	PRON
ejpam-6541	423	9	=	=	NOUN
ejpam-6541	423	10	1	1	NUM
ejpam-6541	423	11	,	,	PUNCT
ejpam-6541	423	12	2	2	NUM
ejpam-6541	423	13	.	.	PUNCT
ejpam-6541	423	14	.	.	PUNCT
ejpam-6541	424	1	.	.	PUNCT
ejpam-6541	425	1	,	,	PUNCT
ejpam-6541	425	2	k.	k.	PROPN
ejpam-6541	425	3	together	together	ADV
ejpam-6541	425	4	with	with	ADP
ejpam-6541	425	5	x	x	PROPN
ejpam-6541	426	1	=	=	PUNCT
ejpam-6541	426	2	∑k	∑k	PROPN
ejpam-6541	426	3	i=1	i=1	PROPN
ejpam-6541	426	4	ωiei	ωiei	PROPN
ejpam-6541	426	5	.	.	PUNCT
ejpam-6541	427	1	evidently	evidently	ADV
ejpam-6541	427	2	x	x	SYM
ejpam-6541	427	3	∈	∈	PROPN
ejpam-6541	427	4	v.	v.	CCONJ
ejpam-6541	427	5	afterwards	afterwards	ADV
ejpam-6541	427	6	∀	∀	X
ejpam-6541	427	7	t	t	X
ejpam-6541	427	8	>	>	X
ejpam-6541	427	9	0	0	PROPN
ejpam-6541	427	10	,	,	PUNCT
ejpam-6541	427	11	mihf	mihf	PROPN
ejpam-6541	427	12	(	(	PUNCT
ejpam-6541	427	13	xn	xn	PROPN
ejpam-6541	427	14	−	−	PROPN
ejpam-6541	427	15	x	x	SYM
ejpam-6541	427	16	,	,	PUNCT
ejpam-6541	427	17	t	t	PROPN
ejpam-6541	427	18	)	)	PUNCT
ejpam-6541	427	19	=	=	SYM
ejpam-6541	427	20	mihf	mihf	PROPN
ejpam-6541	427	21	(	(	PUNCT
ejpam-6541	427	22	∑k	∑k	PROPN
ejpam-6541	427	23	i=1	i=1	PROPN
ejpam-6541	428	1	ω	ω	PROPN
ejpam-6541	429	1	n	n	INTJ
ejpam-6541	429	2	i	i	PRON
ejpam-6541	429	3	ei	ei	VERB
ejpam-6541	430	1	−	−	PROPN
ejpam-6541	430	2	∑k	∑k	PROPN
ejpam-6541	430	3	i=1	i=1	PROPN
ejpam-6541	430	4	ωiei	ωiei	PROPN
ejpam-6541	430	5	,	,	PUNCT
ejpam-6541	430	6	t	t	PROPN
ejpam-6541	430	7	)	)	PUNCT
ejpam-6541	431	1	=	=	SYM
ejpam-6541	431	2	mihf	mihf	PROPN
ejpam-6541	431	3	(	(	PUNCT
ejpam-6541	431	4	∑k	∑k	PROPN
ejpam-6541	431	5	i=1(ω	i=1(ω	PROPN
ejpam-6541	431	6	n	n	NOUN
ejpam-6541	431	7	i	i	PRON
ejpam-6541	431	8	−	−	PROPN
ejpam-6541	431	9	ωi)ei	ωi)ei	NUM
ejpam-6541	431	10	,	,	PUNCT
ejpam-6541	431	11	t	t	NOUN
ejpam-6541	431	12	)	)	PUNCT
ejpam-6541	431	13	that	that	PRON
ejpam-6541	431	14	is	be	AUX
ejpam-6541	431	15	mihf	mihf	NOUN
ejpam-6541	431	16	(	(	PUNCT
ejpam-6541	431	17	xn	xn	PROPN
ejpam-6541	431	18	−	−	PROPN
ejpam-6541	431	19	x	x	SYM
ejpam-6541	431	20	,	,	PUNCT
ejpam-6541	431	21	t	t	PROPN
ejpam-6541	431	22	)	)	PUNCT
ejpam-6541	431	23	⊇	⊇	PROPN
ejpam-6541	431	24	mihf	mihf	PROPN
ejpam-6541	431	25	(	(	PUNCT
ejpam-6541	431	26	e1	e1	PROPN
ejpam-6541	431	27	,	,	PUNCT
ejpam-6541	431	28	t	t	PROPN
ejpam-6541	431	29	k|ωn	k|ωn	NOUN
ejpam-6541	431	30	1	1	NUM
ejpam-6541	431	31	−	−	NOUN
ejpam-6541	431	32	ω1|	ω1|	NOUN
ejpam-6541	431	33	)	)	PUNCT
ejpam-6541	431	34	⋄	⋄	NOUN
ejpam-6541	431	35	·	·	PUNCT
ejpam-6541	431	36	·	·	PUNCT
ejpam-6541	431	37	·	·	PUNCT
ejpam-6541	431	38	⋄mihf	⋄mihf	PROPN
ejpam-6541	432	1	(	(	PUNCT
ejpam-6541	432	2	ek	ek	PROPN
ejpam-6541	432	3	,	,	PUNCT
ejpam-6541	432	4	t	t	PROPN
ejpam-6541	432	5	k|ωn	k|ωn	PROPN
ejpam-6541	433	1	k	k	PROPN
ejpam-6541	433	2	−	−	PROPN
ejpam-6541	433	3	ωk|	ωk|	PROPN
ejpam-6541	433	4	)	)	PUNCT
ejpam-6541	433	5	(	(	PUNCT
ejpam-6541	433	6	17	17	NUM
ejpam-6541	433	7	)	)	PUNCT
ejpam-6541	433	8	when	when	SCONJ
ejpam-6541	433	9	n	n	X
ejpam-6541	433	10	→	→	SYM
ejpam-6541	433	11	∞	∞	PROPN
ejpam-6541	433	12	,	,	PUNCT
ejpam-6541	433	13	then	then	ADV
ejpam-6541	433	14	t	t	PROPN
ejpam-6541	433	15	k|ωn	k|ωn	NOUN
ejpam-6541	434	1	i	i	PRON
ejpam-6541	434	2	−ωi|	−ωi|	PROPN
ejpam-6541	435	1	→	→	SYM
ejpam-6541	436	1	∞	∞	PROPN
ejpam-6541	437	1	(	(	PUNCT
ejpam-6541	438	1	since	since	SCONJ
ejpam-6541	438	2	ωn	ωn	PROPN
ejpam-6541	438	3	i	i	PROPN
ejpam-6541	438	4	→	→	SYM
ejpam-6541	438	5	ωi	ωi	PROPN
ejpam-6541	438	6	)	)	PUNCT
ejpam-6541	438	7	for	for	ADP
ejpam-6541	438	8	i	i	PROPN
ejpam-6541	438	9	=	=	SYM
ejpam-6541	438	10	1	1	NUM
ejpam-6541	438	11	,	,	PUNCT
ejpam-6541	438	12	2	2	NUM
ejpam-6541	438	13	.	.	PUNCT
ejpam-6541	438	14	.	.	PUNCT
ejpam-6541	438	15	.	.	PUNCT
ejpam-6541	439	1	,	,	PUNCT
ejpam-6541	439	2	k.	k.	PROPN
ejpam-6541	439	3	and	and	CCONJ
ejpam-6541	439	4	t	t	PROPN
ejpam-6541	439	5	>	>	X
ejpam-6541	439	6	0	0	X
ejpam-6541	439	7	.	.	PUNCT
ejpam-6541	440	1	applying	apply	VERB
ejpam-6541	440	2	the	the	DET
ejpam-6541	440	3	t	t	PROPN
ejpam-6541	440	4	-	-	PUNCT
ejpam-6541	440	5	co	co	NOUN
ejpam-6541	440	6	-	-	NOUN
ejpam-6541	440	7	norm	norm	NOUN
ejpam-6541	440	8	’s	’s	PART
ejpam-6541	440	9	continuity	continuity	NOUN
ejpam-6541	440	10	⋄	⋄	PROPN
ejpam-6541	440	11	at	at	ADP
ejpam-6541	440	12	(	(	PUNCT
ejpam-6541	440	13	0,0	0,0	NOUN
ejpam-6541	440	14	)	)	PUNCT
ejpam-6541	440	15	,	,	PUNCT
ejpam-6541	440	16	we	we	PRON
ejpam-6541	440	17	obtain	obtain	VERB
ejpam-6541	440	18	from	from	ADP
ejpam-6541	440	19	(	(	PUNCT
ejpam-6541	440	20	17	17	NUM
ejpam-6541	440	21	)	)	PUNCT
ejpam-6541	440	22	.	.	PUNCT
ejpam-6541	441	1	limn→∞mihf	limn→∞mihf	NOUN
ejpam-6541	441	2	(	(	PUNCT
ejpam-6541	441	3	xn	xn	PROPN
ejpam-6541	441	4	−	−	PROPN
ejpam-6541	441	5	x	x	SYM
ejpam-6541	441	6	,	,	PUNCT
ejpam-6541	441	7	t	t	PROPN
ejpam-6541	441	8	)	)	PUNCT
ejpam-6541	441	9	⊇	⊇	PROPN
ejpam-6541	441	10	∅∗	∅∗	PROPN
ejpam-6541	441	11	⋄	⋄	PROPN
ejpam-6541	441	12	·	·	PUNCT
ejpam-6541	441	13	·	·	PUNCT
ejpam-6541	441	14	·	·	PUNCT
ejpam-6541	442	1	⋄	⋄	PROPN
ejpam-6541	442	2	∅∗	∅∗	PROPN
ejpam-6541	442	3	,	,	PUNCT
ejpam-6541	442	4	∀	∀	X
ejpam-6541	442	5	t	t	NOUN
ejpam-6541	442	6	>	>	X
ejpam-6541	442	7	0	0	NUM
ejpam-6541	442	8	.	.	PUNCT
ejpam-6541	443	1	=	=	NOUN
ejpam-6541	443	2	⇒	⇒	PROPN
ejpam-6541	443	3	lim	lim	PROPN
ejpam-6541	443	4	n→∞	n→∞	PRON
ejpam-6541	443	5	mihf	mihf	PROPN
ejpam-6541	443	6	(	(	PUNCT
ejpam-6541	443	7	xn	xn	PROPN
ejpam-6541	443	8	−	−	PROPN
ejpam-6541	443	9	x	x	SYM
ejpam-6541	443	10	,	,	PUNCT
ejpam-6541	443	11	t	t	PROPN
ejpam-6541	443	12	)	)	PUNCT
ejpam-6541	443	13	=	=	PUNCT
ejpam-6541	443	14	∅∗	∅∗	PROPN
ejpam-6541	443	15	,	,	PUNCT
ejpam-6541	443	16	∀	∀	X
ejpam-6541	443	17	t	t	NOUN
ejpam-6541	443	18	>	>	X
ejpam-6541	443	19	0	0	NUM
ejpam-6541	443	20	.	.	PUNCT
ejpam-6541	444	1	(	(	PUNCT
ejpam-6541	444	2	18	18	NUM
ejpam-6541	444	3	)	)	PUNCT
ejpam-6541	444	4	we	we	PRON
ejpam-6541	444	5	obtain	obtain	VERB
ejpam-6541	444	6	xn	xn	PUNCT
ejpam-6541	445	1	→	→	SYM
ejpam-6541	445	2	x	x	X
ejpam-6541	445	3	as	as	ADP
ejpam-6541	445	4	n	n	NOUN
ejpam-6541	445	5	→	→	SYM
ejpam-6541	445	6	∞.	∞.	PROPN
ejpam-6541	445	7	by	by	ADP
ejpam-6541	445	8	(	(	PUNCT
ejpam-6541	445	9	16	16	NUM
ejpam-6541	445	10	)	)	PUNCT
ejpam-6541	445	11	and	and	CCONJ
ejpam-6541	445	12	(	(	PUNCT
ejpam-6541	445	13	18	18	NUM
ejpam-6541	445	14	)	)	PUNCT
ejpam-6541	445	15	.	.	PUNCT
ejpam-6541	446	1	consequently	consequently	ADV
ejpam-6541	446	2	(	(	PUNCT
ejpam-6541	446	3	v	v	NOUN
ejpam-6541	446	4	,	,	PUNCT
ejpam-6541	446	5	hihf	hihf	PROPN
ejpam-6541	446	6	)	)	PUNCT
ejpam-6541	446	7	is	be	AUX
ejpam-6541	446	8	complete	complete	ADJ
ejpam-6541	446	9	.	.	PUNCT
ejpam-6541	447	1	definition	definition	NOUN
ejpam-6541	447	2	19	19	NUM
ejpam-6541	447	3	.	.	PUNCT
ejpam-6541	447	4	consider	consider	VERB
ejpam-6541	447	5	the	the	DET
ejpam-6541	447	6	ihfnls	ihfnls	NOUN
ejpam-6541	447	7	(	(	PUNCT
ejpam-6541	447	8	v	v	NOUN
ejpam-6541	447	9	,	,	PUNCT
ejpam-6541	447	10	hihf	hihf	NOUN
ejpam-6541	447	11	)	)	PUNCT
ejpam-6541	447	12	and	and	CCONJ
ejpam-6541	448	1	x	x	X
ejpam-6541	448	2	⊂	⊂	PROPN
ejpam-6541	448	3	v.	v.	CCONJ
ejpam-6541	448	4	for	for	ADP
ejpam-6541	448	5	every	every	DET
ejpam-6541	448	6	s∗	s∗	PROPN
ejpam-6541	448	7	,	,	PUNCT
ejpam-6541	448	8	x	x	PRON
ejpam-6541	448	9	is	be	AUX
ejpam-6541	448	10	considered	consider	VERB
ejpam-6541	448	11	to	to	PART
ejpam-6541	448	12	be	be	AUX
ejpam-6541	448	13	bounded	bound	VERB
ejpam-6541	448	14	,	,	PUNCT
ejpam-6541	448	15	∅∗	∅∗	PROPN
ejpam-6541	448	16	⊂	⊂	PROPN
ejpam-6541	448	17	s∗	s∗	PROPN
ejpam-6541	448	18	⊂	⊂	PROPN
ejpam-6541	448	19	u∗	u∗	PROPN
ejpam-6541	448	20	,	,	PUNCT
ejpam-6541	448	21	∃t1	∃t1	PROPN
ejpam-6541	448	22	,	,	PUNCT
ejpam-6541	448	23	t2	t2	NOUN
ejpam-6541	448	24	>	>	X
ejpam-6541	448	25	0	0	NUM
ejpam-6541	449	1	such	such	ADJ
ejpam-6541	449	2	that	that	DET
ejpam-6541	449	3	nihf	nihf	NOUN
ejpam-6541	449	4	(	(	PUNCT
ejpam-6541	449	5	x	x	NOUN
ejpam-6541	449	6	,	,	PUNCT
ejpam-6541	449	7	t1	t1	NUM
ejpam-6541	449	8	)	)	PUNCT
ejpam-6541	450	1	⊃	⊃	PROPN
ejpam-6541	450	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	450	3	and	and	CCONJ
ejpam-6541	450	4	mihf	mihf	PROPN
ejpam-6541	450	5	(	(	PUNCT
ejpam-6541	450	6	x	x	NOUN
ejpam-6541	450	7	,	,	PUNCT
ejpam-6541	450	8	t2	t2	PROPN
ejpam-6541	450	9	)	)	PUNCT
ejpam-6541	450	10	⊂	⊂	PROPN
ejpam-6541	450	11	s∗	s∗	PROPN
ejpam-6541	450	12	,	,	PUNCT
ejpam-6541	450	13	∀x	∀x	X
ejpam-6541	450	14	∈	∈	PROPN
ejpam-6541	450	15	x.	x.	NOUN
ejpam-6541	450	16	theorem	theorem	VERB
ejpam-6541	450	17	7	7	NUM
ejpam-6541	450	18	.	.	PUNCT
ejpam-6541	450	19	a	a	DET
ejpam-6541	450	20	subset	subset	NOUN
ejpam-6541	450	21	x	x	X
ejpam-6541	450	22	is	be	AUX
ejpam-6541	450	23	compact	compact	ADJ
ejpam-6541	450	24	if	if	SCONJ
ejpam-6541	450	25	and	and	CCONJ
ejpam-6541	450	26	only	only	ADV
ejpam-6541	450	27	if	if	SCONJ
ejpam-6541	450	28	it	it	PRON
ejpam-6541	450	29	is	be	AUX
ejpam-6541	450	30	closed	close	VERB
ejpam-6541	450	31	and	and	CCONJ
ejpam-6541	450	32	bounded	bound	VERB
ejpam-6541	450	33	in	in	ADP
ejpam-6541	450	34	the	the	DET
ejpam-6541	450	35	finite	finite	ADJ
ejpam-6541	450	36	dimensional	dimensional	ADJ
ejpam-6541	450	37	ihfnls	ihfnls	NOUN
ejpam-6541	450	38	(	(	PUNCT
ejpam-6541	450	39	v	v	NOUN
ejpam-6541	450	40	,	,	PUNCT
ejpam-6541	450	41	hihf	hihf	PROPN
ejpam-6541	450	42	)	)	PUNCT
ejpam-6541	450	43	,	,	PUNCT
ejpam-6541	450	44	where	where	SCONJ
ejpam-6541	450	45	both	both	PRON
ejpam-6541	450	46	the	the	DET
ejpam-6541	450	47	t	t	PROPN
ejpam-6541	450	48	-	-	PUNCT
ejpam-6541	450	49	co	co	NOUN
ejpam-6541	450	50	-	-	NOUN
ejpam-6541	450	51	norm	norm	ADJ
ejpam-6541	450	52	⋄	⋄	NOUN
ejpam-6541	450	53	along	along	ADP
ejpam-6541	450	54	with	with	ADP
ejpam-6541	450	55	the	the	DET
ejpam-6541	450	56	underlying	underlying	ADJ
ejpam-6541	450	57	t	t	NOUN
ejpam-6541	450	58	-	-	PUNCT
ejpam-6541	450	59	norm	norm	NOUN
ejpam-6541	450	60	∗	∗	NOUN
ejpam-6541	450	61	are	be	AUX
ejpam-6541	450	62	continuous	continuous	ADJ
ejpam-6541	450	63	at	at	ADP
ejpam-6541	450	64	(	(	PUNCT
ejpam-6541	450	65	0,0	0,0	NOUN
ejpam-6541	450	66	)	)	PUNCT
ejpam-6541	450	67	together	together	ADV
ejpam-6541	450	68	with	with	ADP
ejpam-6541	450	69	(	(	PUNCT
ejpam-6541	450	70	1,1	1,1	NUM
ejpam-6541	450	71	)	)	PUNCT
ejpam-6541	450	72	respectively	respectively	ADV
ejpam-6541	450	73	.	.	PUNCT
ejpam-6541	451	1	proof	proof	NOUN
ejpam-6541	451	2	.	.	PUNCT
ejpam-6541	452	1	we	we	PRON
ejpam-6541	452	2	start	start	VERB
ejpam-6541	452	3	by	by	ADP
ejpam-6541	452	4	assuming	assume	VERB
ejpam-6541	452	5	that	that	SCONJ
ejpam-6541	452	6	x	x	PRON
ejpam-6541	452	7	is	be	AUX
ejpam-6541	452	8	compact	compact	ADJ
ejpam-6541	452	9	.	.	PUNCT
ejpam-6541	453	1	we	we	PRON
ejpam-6541	453	2	need	need	VERB
ejpam-6541	453	3	for	for	PART
ejpam-6541	453	4	prove	prove	VERB
ejpam-6541	453	5	it	it	PRON
ejpam-6541	453	6	x	x	PUNCT
ejpam-6541	453	7	is	be	AUX
ejpam-6541	453	8	bounded	bound	VERB
ejpam-6541	453	9	alongwith	alongwith	NOUN
ejpam-6541	453	10	closed	close	VERB
ejpam-6541	453	11	.	.	PUNCT
ejpam-6541	454	1	take	take	VERB
ejpam-6541	454	2	x	x	SYM
ejpam-6541	454	3	∈	∈	NOUN
ejpam-6541	454	4	x.	x.	NOUN
ejpam-6541	454	5	then	then	ADV
ejpam-6541	454	6	limn→∞	limn→∞	PROPN
ejpam-6541	454	7	xn	xn	PUNCT
ejpam-6541	455	1	=	=	PUNCT
ejpam-6541	455	2	x.	x.	NOUN
ejpam-6541	455	3	indicates	indicate	VERB
ejpam-6541	455	4	that	that	SCONJ
ejpam-6541	455	5	there	there	PRON
ejpam-6541	455	6	is	be	VERB
ejpam-6541	455	7	a	a	DET
ejpam-6541	455	8	sequence	sequence	NOUN
ejpam-6541	455	9	{	{	PUNCT
ejpam-6541	455	10	xn	xn	NOUN
ejpam-6541	455	11	}	}	PUNCT
ejpam-6541	455	12	in	in	ADP
ejpam-6541	455	13	x.	x.	NOUN
ejpam-6541	455	14	there	there	PRON
ejpam-6541	455	15	is	be	VERB
ejpam-6541	455	16	a	a	DET
ejpam-6541	455	17	subsequence	subsequence	NOUN
ejpam-6541	455	18	{	{	PUNCT
ejpam-6541	455	19	xnk	xnk	PROPN
ejpam-6541	455	20	}	}	PUNCT
ejpam-6541	455	21	of	of	ADP
ejpam-6541	455	22	{	{	PUNCT
ejpam-6541	455	23	xn	xn	INTJ
ejpam-6541	455	24	}	}	PUNCT
ejpam-6541	455	25	that	that	PRON
ejpam-6541	455	26	converges	converge	VERB
ejpam-6541	455	27	to	to	ADP
ejpam-6541	455	28	a	a	DET
ejpam-6541	455	29	point	point	NOUN
ejpam-6541	455	30	in	in	ADP
ejpam-6541	455	31	x	x	PUNCT
ejpam-6541	455	32	because	because	SCONJ
ejpam-6541	455	33	x	x	PRON
ejpam-6541	455	34	is	be	AUX
ejpam-6541	455	35	compact	compact	ADJ
ejpam-6541	455	36	.	.	PUNCT
ejpam-6541	456	1	afterwards	afterwards	ADV
ejpam-6541	456	2	,	,	PUNCT
ejpam-6541	456	3	{	{	PUNCT
ejpam-6541	456	4	xn	xn	X
ejpam-6541	456	5	}	}	PUNCT
ejpam-6541	456	6	→	→	SYM
ejpam-6541	456	7	x	x	X
ejpam-6541	456	8	,	,	PUNCT
ejpam-6541	456	9	and	and	CCONJ
ejpam-6541	456	10	since	since	SCONJ
ejpam-6541	456	11	x	x	PROPN
ejpam-6541	456	12	∈	∈	PROPN
ejpam-6541	456	13	x	x	X
ejpam-6541	456	14	,	,	PUNCT
ejpam-6541	456	15	x	x	X
ejpam-6541	456	16	is	be	AUX
ejpam-6541	456	17	closed	closed	ADJ
ejpam-6541	456	18	.	.	PUNCT
ejpam-6541	457	1	if	if	SCONJ
ejpam-6541	457	2	at	at	ADV
ejpam-6541	457	3	all	all	ADV
ejpam-6541	457	4	possible	possible	ADJ
ejpam-6541	457	5	,	,	PUNCT
ejpam-6541	457	6	assume	assume	VERB
ejpam-6541	457	7	that	that	SCONJ
ejpam-6541	457	8	x	x	PRON
ejpam-6541	457	9	is	be	AUX
ejpam-6541	457	10	unbounded	unbounded	ADJ
ejpam-6541	457	11	.	.	PUNCT
ejpam-6541	458	1	then	then	ADV
ejpam-6541	458	2	there	there	PRON
ejpam-6541	458	3	exists	exist	VERB
ejpam-6541	458	4	a	a	DET
ejpam-6541	458	5	s∗	s∗	NOUN
ejpam-6541	458	6	0	0	NUM
ejpam-6541	458	7	with	with	ADP
ejpam-6541	458	8	∅∗	∅∗	PROPN
ejpam-6541	458	9	⊂	⊂	PROPN
ejpam-6541	458	10	s∗	s∗	PROPN
ejpam-6541	458	11	0	0	NUM
ejpam-6541	459	1	⊂	⊂	PROPN
ejpam-6541	459	2	u∗	u∗	ADJ
ejpam-6541	459	3	so	so	SCONJ
ejpam-6541	459	4	that	that	SCONJ
ejpam-6541	459	5	for	for	ADP
ejpam-6541	459	6	any	any	DET
ejpam-6541	459	7	positive	positive	ADJ
ejpam-6541	459	8	number	number	NOUN
ejpam-6541	459	9	n	n	CCONJ
ejpam-6541	459	10	,	,	PUNCT
ejpam-6541	459	11	there	there	PRON
ejpam-6541	459	12	exists	exist	VERB
ejpam-6541	459	13	x0	x0	PROPN
ejpam-6541	459	14	∈	∈	PROPN
ejpam-6541	459	15	x	x	PUNCT
ejpam-6541	459	16	in	in	ADP
ejpam-6541	459	17	a	a	DET
ejpam-6541	459	18	manner	manner	NOUN
ejpam-6541	459	19	that	that	SCONJ
ejpam-6541	459	20	,	,	PUNCT
ejpam-6541	459	21	nihf	nihf	PROPN
ejpam-6541	459	22	(	(	PUNCT
ejpam-6541	459	23	xn	xn	PROPN
ejpam-6541	459	24	,	,	PUNCT
ejpam-6541	459	25	n	n	CCONJ
ejpam-6541	459	26	)	)	PUNCT
ejpam-6541	459	27	⊆	⊆	NUM
ejpam-6541	459	28	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	459	29	0	0	NUM
ejpam-6541	460	1	or	or	CCONJ
ejpam-6541	460	2	k.	k.	PROPN
ejpam-6541	460	3	kavitha	kavitha	PROPN
ejpam-6541	460	4	,	,	PUNCT
ejpam-6541	460	5	p.	p.	PROPN
ejpam-6541	460	6	muralikrishna	muralikrishna	PROPN
ejpam-6541	460	7	/	/	SYM
ejpam-6541	460	8	eur	eur	PROPN
ejpam-6541	460	9	.	.	PUNCT
ejpam-6541	461	1	j.	j.	PROPN
ejpam-6541	461	2	pure	pure	PROPN
ejpam-6541	461	3	appl	appl	PROPN
ejpam-6541	461	4	.	.	PROPN
ejpam-6541	461	5	math	math	PROPN
ejpam-6541	461	6	,	,	PUNCT
ejpam-6541	461	7	18	18	NUM
ejpam-6541	461	8	(	(	PUNCT
ejpam-6541	461	9	4	4	NUM
ejpam-6541	461	10	)	)	PUNCT
ejpam-6541	461	11	(	(	PUNCT
ejpam-6541	461	12	2025	2025	NUM
ejpam-6541	461	13	)	)	PUNCT
ejpam-6541	461	14	,	,	PUNCT
ejpam-6541	461	15	6541	6541	NUM
ejpam-6541	461	16	12	12	NUM
ejpam-6541	461	17	of	of	ADP
ejpam-6541	461	18	14	14	NUM
ejpam-6541	461	19	mihf	mihf	NOUN
ejpam-6541	461	20	(	(	PUNCT
ejpam-6541	461	21	xn	xn	PROPN
ejpam-6541	461	22	,	,	PUNCT
ejpam-6541	461	23	n	n	CCONJ
ejpam-6541	461	24	)	)	PUNCT
ejpam-6541	461	25	⊇	⊇	PROPN
ejpam-6541	461	26	s∗	s∗	PROPN
ejpam-6541	461	27	0	0	NUM
ejpam-6541	461	28	.	.	PUNCT
ejpam-6541	462	1	so	so	ADV
ejpam-6541	462	2	there	there	PRON
ejpam-6541	462	3	exists	exist	VERB
ejpam-6541	462	4	a	a	DET
ejpam-6541	462	5	subsequence	subsequence	NOUN
ejpam-6541	462	6	of	of	ADP
ejpam-6541	462	7	{	{	PUNCT
ejpam-6541	462	8	xn	xn	NOUN
ejpam-6541	462	9	}	}	PUNCT
ejpam-6541	462	10	whereby	whereby	SCONJ
ejpam-6541	462	11	minimum	minimum	NOUN
ejpam-6541	462	12	of	of	ADP
ejpam-6541	462	13	one	one	NUM
ejpam-6541	462	14	of	of	ADP
ejpam-6541	462	15	the	the	DET
ejpam-6541	462	16	relationships	relationship	NOUN
ejpam-6541	462	17	have	have	AUX
ejpam-6541	462	18	nihf	nihf	NOUN
ejpam-6541	462	19	(	(	PUNCT
ejpam-6541	462	20	xnk	xnk	PROPN
ejpam-6541	462	21	,	,	PUNCT
ejpam-6541	462	22	nk	nk	PROPN
ejpam-6541	462	23	)	)	PUNCT
ejpam-6541	462	24	⊆	⊆	NUM
ejpam-6541	462	25	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	462	26	0	0	NUM
ejpam-6541	462	27	,	,	PUNCT
ejpam-6541	462	28	∀	∀	NOUN
ejpam-6541	462	29	n	n	PRON
ejpam-6541	462	30	∈	∈	PROPN
ejpam-6541	462	31	n.	n.	NOUN
ejpam-6541	462	32	(	(	PUNCT
ejpam-6541	462	33	19	19	NUM
ejpam-6541	462	34	)	)	PUNCT
ejpam-6541	462	35	mihf	mihf	PROPN
ejpam-6541	462	36	(	(	PUNCT
ejpam-6541	462	37	xnk	xnk	PROPN
ejpam-6541	462	38	,	,	PUNCT
ejpam-6541	462	39	nk	nk	PROPN
ejpam-6541	462	40	)	)	PUNCT
ejpam-6541	462	41	⊇	⊇	PROPN
ejpam-6541	462	42	s∗	s∗	PROPN
ejpam-6541	462	43	0	0	NUM
ejpam-6541	462	44	,	,	PUNCT
ejpam-6541	462	45	∀	∀	NOUN
ejpam-6541	462	46	n	n	PRON
ejpam-6541	462	47	∈	∈	PROPN
ejpam-6541	462	48	n.	n.	NOUN
ejpam-6541	462	49	(	(	PUNCT
ejpam-6541	462	50	20	20	NUM
ejpam-6541	462	51	)	)	PUNCT
ejpam-6541	462	52	possesses	possesse	NOUN
ejpam-6541	462	53	.	.	PUNCT
ejpam-6541	463	1	initially	initially	ADV
ejpam-6541	463	2	,	,	PUNCT
ejpam-6541	463	3	we	we	PRON
ejpam-6541	463	4	consider	consider	VERB
ejpam-6541	463	5	that	that	PRON
ejpam-6541	463	6	nihf	nihf	NOUN
ejpam-6541	463	7	(	(	PUNCT
ejpam-6541	463	8	xnk	xnk	PROPN
ejpam-6541	463	9	,	,	PUNCT
ejpam-6541	463	10	nk	nk	PROPN
ejpam-6541	463	11	)	)	PUNCT
ejpam-6541	463	12	⊆	⊆	NUM
ejpam-6541	463	13	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	463	14	0	0	NUM
ejpam-6541	463	15	,	,	PUNCT
ejpam-6541	463	16	∀n	∀n	NUM
ejpam-6541	463	17	∈	∈	PROPN
ejpam-6541	463	18	n	n	PRON
ejpam-6541	463	19	holds	hold	VERB
ejpam-6541	463	20	.	.	PUNCT
ejpam-6541	464	1	now	now	ADV
ejpam-6541	464	2	for	for	ADP
ejpam-6541	464	3	t	t	PROPN
ejpam-6541	464	4	>	>	X
ejpam-6541	464	5	0	0	NUM
ejpam-6541	464	6	,	,	PUNCT
ejpam-6541	464	7	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	464	8	0	0	NUM
ejpam-6541	464	9	⊇	⊇	PROPN
ejpam-6541	464	10	nihf	nihf	PROPN
ejpam-6541	464	11	(	(	PUNCT
ejpam-6541	464	12	xnk	xnk	PROPN
ejpam-6541	464	13	,	,	PUNCT
ejpam-6541	464	14	nk	nk	PROPN
ejpam-6541	464	15	)	)	PUNCT
ejpam-6541	464	16	=	=	SYM
ejpam-6541	464	17	nihf	nihf	PROPN
ejpam-6541	464	18	(	(	PUNCT
ejpam-6541	464	19	xnk	xnk	PROPN
ejpam-6541	464	20	−	−	PROPN
ejpam-6541	464	21	x+	x+	PUNCT
ejpam-6541	464	22	x	x	X
ejpam-6541	464	23	,	,	PUNCT
ejpam-6541	464	24	nk	nk	PROPN
ejpam-6541	464	25	−	−	PROPN
ejpam-6541	464	26	t	t	PROPN
ejpam-6541	464	27	+	+	CCONJ
ejpam-6541	464	28	t	t	PROPN
ejpam-6541	464	29	)	)	PUNCT
ejpam-6541	464	30	where	where	SCONJ
ejpam-6541	464	31	t	t	PROPN
ejpam-6541	464	32	>	>	X
ejpam-6541	464	33	0	0	NUM
ejpam-6541	464	34	.	.	PUNCT
ejpam-6541	465	1	=	=	VERB
ejpam-6541	465	2	⇒	⇒	VERB
ejpam-6541	465	3	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	465	4	0	0	NUM
ejpam-6541	465	5	⊇	⊇	PROPN
ejpam-6541	465	6	nihf	nihf	PROPN
ejpam-6541	465	7	(	(	PUNCT
ejpam-6541	465	8	xnk	xnk	PROPN
ejpam-6541	465	9	,	,	PUNCT
ejpam-6541	465	10	nk	nk	PROPN
ejpam-6541	465	11	)	)	PUNCT
ejpam-6541	465	12	=	=	SYM
ejpam-6541	465	13	nihf	nihf	PROPN
ejpam-6541	465	14	(	(	PUNCT
ejpam-6541	465	15	xnk	xnk	PROPN
ejpam-6541	465	16	−	−	PROPN
ejpam-6541	465	17	x	x	SYM
ejpam-6541	465	18	,	,	PUNCT
ejpam-6541	465	19	t	t	PROPN
ejpam-6541	465	20	)	)	PUNCT
ejpam-6541	465	21	∗	∗	PROPN
ejpam-6541	465	22	nihf	nihf	PROPN
ejpam-6541	465	23	(	(	PUNCT
ejpam-6541	465	24	x	x	NOUN
ejpam-6541	465	25	,	,	PUNCT
ejpam-6541	465	26	nk	nk	PROPN
ejpam-6541	465	27	−	−	PROPN
ejpam-6541	465	28	t	t	PROPN
ejpam-6541	465	29	)	)	PUNCT
ejpam-6541	466	1	=	=	VERB
ejpam-6541	466	2	⇒	⇒	VERB
ejpam-6541	466	3	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	466	4	0	0	NUM
ejpam-6541	466	5	⊇	⊇	PROPN
ejpam-6541	466	6	limk→∞nihf	limk→∞nihf	X
ejpam-6541	466	7	(	(	PUNCT
ejpam-6541	466	8	xnk	xnk	PROPN
ejpam-6541	466	9	−	−	PROPN
ejpam-6541	466	10	x	x	SYM
ejpam-6541	466	11	,	,	PUNCT
ejpam-6541	466	12	t	t	PROPN
ejpam-6541	466	13	)	)	PUNCT
ejpam-6541	466	14	∗	∗	NOUN
ejpam-6541	466	15	limk→∞nihf	limk→∞nihf	X
ejpam-6541	466	16	(	(	PUNCT
ejpam-6541	466	17	x	x	X
ejpam-6541	466	18	,	,	PUNCT
ejpam-6541	466	19	nk	nk	PROPN
ejpam-6541	466	20	−	−	PROPN
ejpam-6541	466	21	t	t	PROPN
ejpam-6541	466	22	)	)	PUNCT
ejpam-6541	467	1	=	=	VERB
ejpam-6541	467	2	⇒	⇒	VERB
ejpam-6541	467	3	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	467	4	0	0	NUM
ejpam-6541	467	5	⊇	⊇	PROPN
ejpam-6541	467	6	u∗∗u∗	u∗∗u∗	PROPN
ejpam-6541	467	7	=	=	SYM
ejpam-6541	467	8	u∗.	u∗.	PROPN
ejpam-6541	467	9	(	(	PUNCT
ejpam-6541	467	10	applying	apply	VERB
ejpam-6541	467	11	the	the	DET
ejpam-6541	467	12	t	t	NOUN
ejpam-6541	467	13	-	-	PUNCT
ejpam-6541	467	14	norm	norm	NOUN
ejpam-6541	467	15	’s	’s	PART
ejpam-6541	467	16	continuity	continuity	NOUN
ejpam-6541	467	17	at	at	ADP
ejpam-6541	467	18	(	(	PUNCT
ejpam-6541	467	19	1,1	1,1	NUM
ejpam-6541	467	20	)	)	PUNCT
ejpam-6541	467	21	)	)	PUNCT
ejpam-6541	468	1	=	=	SYM
ejpam-6541	468	2	⇒	⇒	VERB
ejpam-6541	468	3	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	468	4	0	0	NUM
ejpam-6541	468	5	⊇	⊇	PROPN
ejpam-6541	468	6	u∗	u∗	PROPN
ejpam-6541	468	7	which	which	PRON
ejpam-6541	468	8	is	be	AUX
ejpam-6541	468	9	a	a	DET
ejpam-6541	468	10	contradiction	contradiction	NOUN
ejpam-6541	468	11	.	.	PUNCT
ejpam-6541	469	1	in	in	ADP
ejpam-6541	469	2	case	case	NOUN
ejpam-6541	469	3	mihf	mihf	PROPN
ejpam-6541	469	4	(	(	PUNCT
ejpam-6541	469	5	xnk	xnk	PROPN
ejpam-6541	469	6	,	,	PUNCT
ejpam-6541	469	7	nk	nk	PROPN
ejpam-6541	469	8	)	)	PUNCT
ejpam-6541	469	9	⊇	⊇	PROPN
ejpam-6541	469	10	s∗	s∗	PROPN
ejpam-6541	469	11	0	0	NUM
ejpam-6541	469	12	,	,	PUNCT
ejpam-6541	469	13	∀n	∀n	NUM
ejpam-6541	469	14	∈	∈	NOUN
ejpam-6541	469	15	n	n	PRON
ejpam-6541	469	16	possess	possess	VERB
ejpam-6541	469	17	,	,	PUNCT
ejpam-6541	469	18	examining	examine	VERB
ejpam-6541	469	19	the	the	DET
ejpam-6541	469	20	function	function	NOUN
ejpam-6541	469	21	mihf	mihf	NOUN
ejpam-6541	469	22	(	(	PUNCT
ejpam-6541	469	23	x	x	X
ejpam-6541	469	24	,	,	PUNCT
ejpam-6541	469	25	t	t	PROPN
ejpam-6541	469	26	)	)	PUNCT
ejpam-6541	469	27	and	and	CCONJ
ejpam-6541	469	28	continuing	continue	VERB
ejpam-6541	469	29	as	as	ADV
ejpam-6541	469	30	previously	previously	ADV
ejpam-6541	469	31	mentioned	mention	VERB
ejpam-6541	469	32	,	,	PUNCT
ejpam-6541	469	33	we	we	PRON
ejpam-6541	469	34	get	get	VERB
ejpam-6541	469	35	a	a	DET
ejpam-6541	469	36	contradiction	contradiction	NOUN
ejpam-6541	469	37	,	,	PUNCT
ejpam-6541	469	38	hence	hence	ADV
ejpam-6541	469	39	x	x	VERB
ejpam-6541	469	40	is	be	AUX
ejpam-6541	469	41	bounded	bound	VERB
ejpam-6541	469	42	.	.	PUNCT
ejpam-6541	470	1	conversly	conversly	ADV
ejpam-6541	470	2	,	,	PUNCT
ejpam-6541	470	3	assuming	assume	VERB
ejpam-6541	470	4	that	that	SCONJ
ejpam-6541	470	5	x	x	PRON
ejpam-6541	470	6	is	be	AUX
ejpam-6541	470	7	bounded	bound	VERB
ejpam-6541	470	8	and	and	CCONJ
ejpam-6541	470	9	closed	closed	ADJ
ejpam-6541	470	10	,	,	PUNCT
ejpam-6541	470	11	we	we	PRON
ejpam-6541	470	12	must	must	AUX
ejpam-6541	470	13	demonstrate	demonstrate	VERB
ejpam-6541	470	14	that	that	SCONJ
ejpam-6541	470	15	x	x	PRON
ejpam-6541	470	16	is	be	AUX
ejpam-6541	470	17	compact	compact	ADJ
ejpam-6541	470	18	.	.	PUNCT
ejpam-6541	471	1	consider	consider	VERB
ejpam-6541	471	2	dimv	dimv	NOUN
ejpam-6541	471	3	=	=	PUNCT
ejpam-6541	471	4	n	n	CCONJ
ejpam-6541	471	5	along	along	ADV
ejpam-6541	471	6	with	with	ADP
ejpam-6541	471	7	{	{	PUNCT
ejpam-6541	471	8	e1	e1	PROPN
ejpam-6541	471	9	,	,	PUNCT
ejpam-6541	471	10	e2	e2	PROPN
ejpam-6541	471	11	,	,	PUNCT
ejpam-6541	471	12	.	.	PUNCT
ejpam-6541	471	13	.	.	PUNCT
ejpam-6541	471	14	.	.	PUNCT
ejpam-6541	472	1	en	en	ADP
ejpam-6541	472	2	}	}	PUNCT
ejpam-6541	472	3	as	as	ADP
ejpam-6541	472	4	a	a	DET
ejpam-6541	472	5	basis	basis	NOUN
ejpam-6541	472	6	of	of	ADP
ejpam-6541	472	7	v	v	NOUN
ejpam-6541	472	8	respectively	respectively	ADV
ejpam-6541	472	9	.	.	PUNCT
ejpam-6541	473	1	select	select	ADJ
ejpam-6541	473	2	{	{	PUNCT
ejpam-6541	473	3	xk	xk	NOUN
ejpam-6541	473	4	}	}	PUNCT
ejpam-6541	473	5	as	as	ADP
ejpam-6541	473	6	a	a	DET
ejpam-6541	473	7	sequence	sequence	NOUN
ejpam-6541	473	8	inxwhile	inxwhile	NOUN
ejpam-6541	473	9	assume	assume	VERB
ejpam-6541	473	10	xk	xk	PROPN
ejpam-6541	473	11	=	=	PROPN
ejpam-6541	473	12	ω	ω	PROPN
ejpam-6541	473	13	(	(	PUNCT
ejpam-6541	473	14	k	k	NOUN
ejpam-6541	473	15	)	)	PUNCT
ejpam-6541	473	16	1	1	NUM
ejpam-6541	473	17	e1	e1	PROPN
ejpam-6541	473	18	+	+	PROPN
ejpam-6541	473	19	·	·	PUNCT
ejpam-6541	473	20	·	·	PUNCT
ejpam-6541	473	21	·	·	PUNCT
ejpam-6541	474	1	+	+	NOUN
ejpam-6541	474	2	ω	ω	PROPN
ejpam-6541	474	3	(	(	PUNCT
ejpam-6541	474	4	k	k	NOUN
ejpam-6541	474	5	)	)	PUNCT
ejpam-6541	474	6	n	n	X
ejpam-6541	474	7	en	en	ADV
ejpam-6541	474	8	here	here	ADV
ejpam-6541	474	9	ω	ω	X
ejpam-6541	474	10	(	(	PUNCT
ejpam-6541	474	11	k	k	NOUN
ejpam-6541	474	12	)	)	PUNCT
ejpam-6541	474	13	1	1	NUM
ejpam-6541	474	14	,	,	PUNCT
ejpam-6541	474	15	.	.	PUNCT
ejpam-6541	474	16	.	.	PUNCT
ejpam-6541	474	17	.	.	PUNCT
ejpam-6541	475	1	ω	ω	INTJ
ejpam-6541	475	2	(	(	PUNCT
ejpam-6541	475	3	k	k	NOUN
ejpam-6541	475	4	)	)	PUNCT
ejpam-6541	475	5	n	n	PRON
ejpam-6541	475	6	are	be	AUX
ejpam-6541	475	7	scalars	scalar	NOUN
ejpam-6541	475	8	.	.	PUNCT
ejpam-6541	476	1	now	now	ADV
ejpam-6541	476	2	,	,	PUNCT
ejpam-6541	476	3	according	accord	VERB
ejpam-6541	476	4	to	to	ADP
ejpam-6541	476	5	lemma	lemma	PROPN
ejpam-6541	476	6	(	(	PUNCT
ejpam-6541	476	7	1	1	NUM
ejpam-6541	476	8	)	)	PUNCT
ejpam-6541	476	9	,	,	PUNCT
ejpam-6541	476	10	there	there	PRON
ejpam-6541	476	11	is	be	VERB
ejpam-6541	476	12	h1	h1	NOUN
ejpam-6541	476	13	,	,	PUNCT
ejpam-6541	476	14	h2	h2	PROPN
ejpam-6541	476	15	>	>	X
ejpam-6541	476	16	0	0	PUNCT
ejpam-6541	477	1	and	and	CCONJ
ejpam-6541	477	2	there	there	PRON
ejpam-6541	477	3	exists	exist	VERB
ejpam-6541	477	4	s∗	s∗	PROPN
ejpam-6541	477	5	1	1	NUM
ejpam-6541	477	6	,	,	PUNCT
ejpam-6541	477	7	s	s	NOUN
ejpam-6541	477	8	∗	∗	NOUN
ejpam-6541	477	9	2	2	NUM
ejpam-6541	477	10	∈	∈	NOUN
ejpam-6541	477	11	p[0	p[0	NOUN
ejpam-6541	477	12	,	,	PUNCT
ejpam-6541	477	13	1	1	NUM
ejpam-6541	477	14	]	]	PUNCT
ejpam-6541	477	15	such	such	ADJ
ejpam-6541	477	16	that	that	DET
ejpam-6541	477	17	nihf	nihf	NOUN
ejpam-6541	477	18	(	(	PUNCT
ejpam-6541	477	19	n∑	n∑	NOUN
ejpam-6541	477	20	i=1	i=1	PROPN
ejpam-6541	477	21	ω	ω	PROPN
ejpam-6541	477	22	(	(	PUNCT
ejpam-6541	477	23	k	k	NOUN
ejpam-6541	477	24	)	)	PUNCT
ejpam-6541	477	25	i	i	PRON
ejpam-6541	477	26	ei	ei	VERB
ejpam-6541	477	27	,	,	PUNCT
ejpam-6541	477	28	h1	h1	PROPN
ejpam-6541	477	29	n∑	n∑	PROPN
ejpam-6541	477	30	i=1	i=1	PROPN
ejpam-6541	478	1	|ω(k	|ω(k	PROPN
ejpam-6541	478	2	)	)	PUNCT
ejpam-6541	479	1	i	i	PRON
ejpam-6541	479	2	|	|	ADV
ejpam-6541	479	3	)	)	PUNCT
ejpam-6541	480	1	⊂	⊂	PROPN
ejpam-6541	480	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	480	3	1	1	NUM
ejpam-6541	480	4	(	(	PUNCT
ejpam-6541	480	5	21	21	NUM
ejpam-6541	480	6	)	)	PUNCT
ejpam-6541	480	7	and	and	CCONJ
ejpam-6541	480	8	mihf	mihf	PROPN
ejpam-6541	480	9	(	(	PUNCT
ejpam-6541	480	10	n∑	n∑	NOUN
ejpam-6541	480	11	i=1	i=1	PROPN
ejpam-6541	480	12	ω	ω	PROPN
ejpam-6541	480	13	(	(	PUNCT
ejpam-6541	480	14	k	k	NOUN
ejpam-6541	480	15	)	)	PUNCT
ejpam-6541	480	16	i	i	PRON
ejpam-6541	480	17	ei	ei	PROPN
ejpam-6541	480	18	,	,	PUNCT
ejpam-6541	480	19	h2	h2	PROPN
ejpam-6541	480	20	n∑	n∑	PROPN
ejpam-6541	480	21	i=1	i=1	PROPN
ejpam-6541	481	1	|ω(k	|ω(k	PROPN
ejpam-6541	481	2	)	)	PUNCT
ejpam-6541	482	1	i	i	PRON
ejpam-6541	482	2	|	|	ADV
ejpam-6541	482	3	)	)	PUNCT
ejpam-6541	483	1	⊃	⊃	NOUN
ejpam-6541	483	2	s∗	s∗	PROPN
ejpam-6541	483	3	2	2	NUM
ejpam-6541	483	4	(	(	PUNCT
ejpam-6541	483	5	22	22	NUM
ejpam-6541	483	6	)	)	PUNCT
ejpam-6541	483	7	again	again	ADV
ejpam-6541	483	8	since	since	SCONJ
ejpam-6541	483	9	x	x	PROPN
ejpam-6541	483	10	is	be	AUX
ejpam-6541	483	11	bounded	bound	VERB
ejpam-6541	483	12	,	,	PUNCT
ejpam-6541	483	13	for	for	ADP
ejpam-6541	483	14	s∗	s∗	PROPN
ejpam-6541	483	15	1	1	NUM
ejpam-6541	483	16	∈	∈	PROPN
ejpam-6541	483	17	p[0	p[0	NOUN
ejpam-6541	483	18	,	,	PUNCT
ejpam-6541	483	19	1],∃	1],∃	NUM
ejpam-6541	483	20	t1	t1	NOUN
ejpam-6541	483	21	>	>	X
ejpam-6541	483	22	0	0	PROPN
ejpam-6541	483	23	,	,	PUNCT
ejpam-6541	483	24	so	so	SCONJ
ejpam-6541	483	25	that	that	PRON
ejpam-6541	483	26	nihf	nihf	NOUN
ejpam-6541	483	27	(	(	PUNCT
ejpam-6541	483	28	x	x	NOUN
ejpam-6541	483	29	,	,	PUNCT
ejpam-6541	483	30	t1	t1	NUM
ejpam-6541	483	31	)	)	PUNCT
ejpam-6541	484	1	⊃	⊃	PROPN
ejpam-6541	484	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	484	3	1	1	NUM
ejpam-6541	484	4	and	and	CCONJ
ejpam-6541	484	5	there	there	PRON
ejpam-6541	484	6	exists	exist	VERB
ejpam-6541	484	7	t2	t2	PROPN
ejpam-6541	484	8	>	>	X
ejpam-6541	484	9	0	0	NUM
ejpam-6541	484	10	,	,	PUNCT
ejpam-6541	484	11	so	so	SCONJ
ejpam-6541	484	12	that	that	SCONJ
ejpam-6541	484	13	mihf	mihf	PROPN
ejpam-6541	484	14	(	(	PUNCT
ejpam-6541	484	15	x	x	NOUN
ejpam-6541	484	16	,	,	PUNCT
ejpam-6541	484	17	t2	t2	PROPN
ejpam-6541	484	18	)	)	PUNCT
ejpam-6541	484	19	⊂	⊂	PROPN
ejpam-6541	484	20	s∗	s∗	VERB
ejpam-6541	484	21	1	1	NUM
ejpam-6541	484	22	,	,	PUNCT
ejpam-6541	484	23	∀	∀	X
ejpam-6541	485	1	x	x	SYM
ejpam-6541	485	2	∈	∈	NOUN
ejpam-6541	485	3	x.	x.	NOUN
ejpam-6541	486	1	so	so	ADV
ejpam-6541	486	2	,	,	PUNCT
ejpam-6541	486	3	nihf	nihf	PROPN
ejpam-6541	486	4	(	(	PUNCT
ejpam-6541	486	5	n∑	n∑	NOUN
ejpam-6541	486	6	i=1	i=1	PROPN
ejpam-6541	486	7	ω	ω	PROPN
ejpam-6541	486	8	(	(	PUNCT
ejpam-6541	486	9	k	k	NOUN
ejpam-6541	486	10	)	)	PUNCT
ejpam-6541	486	11	i	i	PRON
ejpam-6541	486	12	ei	ei	PROPN
ejpam-6541	486	13	,	,	PUNCT
ejpam-6541	486	14	t1	t1	PROPN
ejpam-6541	486	15	)	)	PUNCT
ejpam-6541	487	1	⊃	⊃	PROPN
ejpam-6541	487	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	487	3	1	1	NUM
ejpam-6541	487	4	(	(	PUNCT
ejpam-6541	487	5	23	23	NUM
ejpam-6541	487	6	)	)	PUNCT
ejpam-6541	487	7	and	and	CCONJ
ejpam-6541	487	8	mihf	mihf	PROPN
ejpam-6541	487	9	(	(	PUNCT
ejpam-6541	487	10	n∑	n∑	NOUN
ejpam-6541	487	11	i=1	i=1	PROPN
ejpam-6541	487	12	ω	ω	PROPN
ejpam-6541	487	13	(	(	PUNCT
ejpam-6541	487	14	k	k	NOUN
ejpam-6541	487	15	)	)	PUNCT
ejpam-6541	487	16	i	i	PRON
ejpam-6541	487	17	ei	ei	PROPN
ejpam-6541	487	18	,	,	PUNCT
ejpam-6541	487	19	t1	t1	PROPN
ejpam-6541	487	20	)	)	PUNCT
ejpam-6541	488	1	⊂	⊂	PRON
ejpam-6541	488	2	s∗	s∗	VERB
ejpam-6541	488	3	2	2	NUM
ejpam-6541	488	4	(	(	PUNCT
ejpam-6541	488	5	24	24	NUM
ejpam-6541	488	6	)	)	PUNCT
ejpam-6541	488	7	from	from	ADP
ejpam-6541	488	8	(	(	PUNCT
ejpam-6541	488	9	21	21	NUM
ejpam-6541	488	10	)	)	PUNCT
ejpam-6541	488	11	and	and	CCONJ
ejpam-6541	488	12	(	(	PUNCT
ejpam-6541	488	13	23	23	NUM
ejpam-6541	488	14	)	)	PUNCT
ejpam-6541	488	15	we	we	PRON
ejpam-6541	488	16	get	get	VERB
ejpam-6541	488	17	,	,	PUNCT
ejpam-6541	488	18	nihf	nihf	PROPN
ejpam-6541	488	19	(	(	PUNCT
ejpam-6541	488	20	∑n	∑n	PROPN
ejpam-6541	488	21	i=1	i=1	PROPN
ejpam-6541	488	22	ω	ω	PROPN
ejpam-6541	488	23	(	(	PUNCT
ejpam-6541	488	24	k	k	NOUN
ejpam-6541	488	25	)	)	PUNCT
ejpam-6541	489	1	i	i	PRON
ejpam-6541	489	2	ei	ei	AUX
ejpam-6541	489	3	,	,	PUNCT
ejpam-6541	489	4	h1	h1	VERB
ejpam-6541	489	5	∑n	∑n	PROPN
ejpam-6541	489	6	i=1	i=1	PROPN
ejpam-6541	489	7	|ω	|ω	X
ejpam-6541	489	8	(	(	PUNCT
ejpam-6541	489	9	k	k	X
ejpam-6541	489	10	)	)	PUNCT
ejpam-6541	489	11	i	i	PRON
ejpam-6541	489	12	|	|	ADV
ejpam-6541	489	13	)	)	PUNCT
ejpam-6541	490	1	⊂	⊂	PROPN
ejpam-6541	490	2	u∗\s∗	u∗\s∗	ADJ
ejpam-6541	490	3	1	1	NUM
ejpam-6541	490	4	⊂	⊂	ADJ
ejpam-6541	490	5	nihf	nihf	PROPN
ejpam-6541	490	6	(	(	PUNCT
ejpam-6541	490	7	∑n	∑n	PROPN
ejpam-6541	490	8	i=1	i=1	PROPN
ejpam-6541	490	9	ω	ω	PROPN
ejpam-6541	490	10	(	(	PUNCT
ejpam-6541	490	11	k	k	NOUN
ejpam-6541	490	12	)	)	PUNCT
ejpam-6541	490	13	i	i	PRON
ejpam-6541	490	14	ei	ei	PROPN
ejpam-6541	490	15	,	,	PUNCT
ejpam-6541	490	16	t1	t1	NOUN
ejpam-6541	490	17	)	)	PUNCT
ejpam-6541	491	1	=	=	VERB
ejpam-6541	491	2	⇒	⇒	NOUN
ejpam-6541	491	3	nihf	nihf	NOUN
ejpam-6541	491	4	(	(	PUNCT
ejpam-6541	491	5	∑n	∑n	PROPN
ejpam-6541	491	6	i=1	i=1	PROPN
ejpam-6541	491	7	ω	ω	PROPN
ejpam-6541	491	8	(	(	PUNCT
ejpam-6541	491	9	k	k	NOUN
ejpam-6541	491	10	)	)	PUNCT
ejpam-6541	491	11	i	i	PRON
ejpam-6541	491	12	ei	ei	VERB
ejpam-6541	491	13	,	,	PUNCT
ejpam-6541	491	14	h1	h1	VERB
ejpam-6541	491	15	∑n	∑n	PROPN
ejpam-6541	491	16	i=1	i=1	PROPN
ejpam-6541	491	17	|ω	|ω	X
ejpam-6541	491	18	(	(	PUNCT
ejpam-6541	491	19	k	k	X
ejpam-6541	491	20	)	)	PUNCT
ejpam-6541	491	21	i	i	PRON
ejpam-6541	491	22	|	|	ADV
ejpam-6541	491	23	)	)	PUNCT
ejpam-6541	492	1	⊂	⊂	PRON
ejpam-6541	492	2	nihf	nihf	PROPN
ejpam-6541	492	3	(	(	PUNCT
ejpam-6541	492	4	∑n	∑n	PROPN
ejpam-6541	492	5	i=1	i=1	PROPN
ejpam-6541	492	6	ω	ω	PROPN
ejpam-6541	492	7	(	(	PUNCT
ejpam-6541	492	8	k	k	NOUN
ejpam-6541	492	9	)	)	PUNCT
ejpam-6541	492	10	i	i	PRON
ejpam-6541	492	11	ei	ei	PROPN
ejpam-6541	492	12	,	,	PUNCT
ejpam-6541	492	13	t1	t1	NOUN
ejpam-6541	492	14	)	)	PUNCT
ejpam-6541	493	1	=	=	PRON
ejpam-6541	493	2	⇒	⇒	NOUN
ejpam-6541	493	3	h1	h1	VERB
ejpam-6541	493	4	∑n	∑n	PROPN
ejpam-6541	493	5	i=1	i=1	PROPN
ejpam-6541	493	6	|ω	|ω	X
ejpam-6541	493	7	(	(	PUNCT
ejpam-6541	493	8	k	k	X
ejpam-6541	493	9	)	)	PUNCT
ejpam-6541	493	10	i	i	PRON
ejpam-6541	493	11	|	|	ADV
ejpam-6541	493	12	<	<	X
ejpam-6541	493	13	t1	t1	NOUN
ejpam-6541	493	14	(	(	PUNCT
ejpam-6541	493	15	given	give	VERB
ejpam-6541	493	16	that	that	PRON
ejpam-6541	493	17	nihf	nihf	NOUN
ejpam-6541	493	18	(	(	PUNCT
ejpam-6541	493	19	x	x	NOUN
ejpam-6541	493	20	,	,	PUNCT
ejpam-6541	493	21	�	�	PROPN
ejpam-6541	493	22	)	)	PUNCT
ejpam-6541	493	23	is	be	AUX
ejpam-6541	493	24	nondecreasing	nondecrease	VERB
ejpam-6541	493	25	)	)	PUNCT
ejpam-6541	494	1	=	=	AUX
ejpam-6541	494	2	⇒	⇒	X
ejpam-6541	494	3	|ω(k	|ω(k	PROPN
ejpam-6541	494	4	)	)	PUNCT
ejpam-6541	495	1	i	i	PRON
ejpam-6541	495	2	|	|	ADV
ejpam-6541	495	3	≤	≤	NUM
ejpam-6541	495	4	t1	t1	NOUN
ejpam-6541	495	5	h1	h1	NOUN
ejpam-6541	495	6	where	where	SCONJ
ejpam-6541	495	7	i	i	PRON
ejpam-6541	495	8	=	=	NOUN
ejpam-6541	495	9	1	1	NUM
ejpam-6541	495	10	,	,	PUNCT
ejpam-6541	495	11	2	2	NUM
ejpam-6541	495	12	.	.	PUNCT
ejpam-6541	495	13	.	.	PUNCT
ejpam-6541	495	14	.	.	PUNCT
ejpam-6541	496	1	n.	n.	NOUN
ejpam-6541	496	2	and	and	CCONJ
ejpam-6541	496	3	k	k	NOUN
ejpam-6541	496	4	=	=	SYM
ejpam-6541	496	5	1	1	NUM
ejpam-6541	496	6	,	,	PUNCT
ejpam-6541	496	7	2	2	NUM
ejpam-6541	496	8	.	.	PUNCT
ejpam-6541	496	9	.	.	PUNCT
ejpam-6541	496	10	.	.	PUNCT
ejpam-6541	497	1	thus	thus	ADV
ejpam-6541	497	2	,	,	PUNCT
ejpam-6541	497	3	for	for	ADP
ejpam-6541	497	4	every	every	DET
ejpam-6541	497	5	{	{	PUNCT
ejpam-6541	497	6	ω(k	ω(k	PROPN
ejpam-6541	497	7	)	)	PUNCT
ejpam-6541	497	8	i	i	PRON
ejpam-6541	497	9	}	}	PUNCT
ejpam-6541	497	10	it	it	PRON
ejpam-6541	497	11	is	be	AUX
ejpam-6541	497	12	bounded	bound	VERB
ejpam-6541	497	13	(	(	PUNCT
ejpam-6541	497	14	i	i	NOUN
ejpam-6541	497	15	=	=	NOUN
ejpam-6541	497	16	1	1	NUM
ejpam-6541	497	17	,	,	PUNCT
ejpam-6541	497	18	2	2	NUM
ejpam-6541	497	19	,	,	PUNCT
ejpam-6541	497	20	.	.	PUNCT
ejpam-6541	497	21	.	.	PUNCT
ejpam-6541	497	22	.	.	PUNCT
ejpam-6541	498	1	n	n	CCONJ
ejpam-6541	498	2	)	)	PUNCT
ejpam-6541	498	3	.	.	PUNCT
ejpam-6541	499	1	as	as	ADP
ejpam-6541	499	2	a	a	DET
ejpam-6541	499	3	result	result	NOUN
ejpam-6541	499	4	of	of	ADP
ejpam-6541	499	5	repeatedly	repeatedly	ADV
ejpam-6541	499	6	applying	apply	VERB
ejpam-6541	499	7	the	the	DET
ejpam-6541	499	8	bolzano	bolzano	NOUN
ejpam-6541	499	9	-weierstrass	-weierstrass	NOUN
ejpam-6541	499	10	theorem	theorem	NOUN
ejpam-6541	499	11	,	,	PUNCT
ejpam-6541	499	12	every	every	DET
ejpam-6541	499	13	sequence	sequence	NOUN
ejpam-6541	499	14	in	in	ADP
ejpam-6541	499	15	{	{	PUNCT
ejpam-6541	499	16	ω(k	ω(k	PROPN
ejpam-6541	499	17	)	)	PUNCT
ejpam-6541	499	18	i	i	PRON
ejpam-6541	499	19	}	}	PUNCT
ejpam-6541	499	20	possesses	possess	VERB
ejpam-6541	499	21	a	a	DET
ejpam-6541	499	22	subsequence	subsequence	NOUN
ejpam-6541	499	23	that	that	PRON
ejpam-6541	499	24	converges	converge	VERB
ejpam-6541	499	25	{	{	PUNCT
ejpam-6541	499	26	ω(kl	ω(kl	PROPN
ejpam-6541	499	27	)	)	PUNCT
ejpam-6541	499	28	i	i	PRON
ejpam-6541	499	29	}	}	PUNCT
ejpam-6541	499	30	,	,	PUNCT
ejpam-6541	499	31	∀	∀	PUNCT
ejpam-6541	500	1	i	i	NOUN
ejpam-6541	500	2	=	=	NOUN
ejpam-6541	500	3	1	1	NUM
ejpam-6541	500	4	,	,	PUNCT
ejpam-6541	500	5	2	2	NUM
ejpam-6541	500	6	,	,	PUNCT
ejpam-6541	500	7	.	.	PUNCT
ejpam-6541	500	8	.	.	PUNCT
ejpam-6541	500	9	.	.	PUNCT
ejpam-6541	501	1	n.	n.	PROPN
ejpam-6541	501	2	assume	assume	PROPN
ejpam-6541	501	3	k.	k.	PROPN
ejpam-6541	501	4	kavitha	kavitha	PROPN
ejpam-6541	501	5	,	,	PUNCT
ejpam-6541	501	6	p.	p.	PROPN
ejpam-6541	501	7	muralikrishna	muralikrishna	PROPN
ejpam-6541	501	8	/	/	SYM
ejpam-6541	501	9	eur	eur	PROPN
ejpam-6541	501	10	.	.	PUNCT
ejpam-6541	502	1	j.	j.	PROPN
ejpam-6541	502	2	pure	pure	PROPN
ejpam-6541	502	3	appl	appl	PROPN
ejpam-6541	502	4	.	.	PROPN
ejpam-6541	502	5	math	math	PROPN
ejpam-6541	502	6	,	,	PUNCT
ejpam-6541	502	7	18	18	NUM
ejpam-6541	502	8	(	(	PUNCT
ejpam-6541	502	9	4	4	NUM
ejpam-6541	502	10	)	)	PUNCT
ejpam-6541	502	11	(	(	PUNCT
ejpam-6541	502	12	2025	2025	NUM
ejpam-6541	502	13	)	)	PUNCT
ejpam-6541	502	14	,	,	PUNCT
ejpam-6541	502	15	6541	6541	NUM
ejpam-6541	502	16	13	13	NUM
ejpam-6541	502	17	of	of	ADP
ejpam-6541	502	18	14	14	NUM
ejpam-6541	502	19	that	that	PRON
ejpam-6541	502	20	xkl	xkl	NOUN
ejpam-6541	502	21	=	=	SYM
ejpam-6541	502	22	ω	ω	PROPN
ejpam-6541	502	23	(	(	PUNCT
ejpam-6541	502	24	kl	kl	PROPN
ejpam-6541	502	25	)	)	PUNCT
ejpam-6541	502	26	i	i	PRON
ejpam-6541	502	27	e1	e1	VERB
ejpam-6541	502	28	+	+	X
ejpam-6541	502	29	·	·	PUNCT
ejpam-6541	502	30	·	·	PUNCT
ejpam-6541	502	31	·	·	PUNCT
ejpam-6541	503	1	+	+	NUM
ejpam-6541	503	2	ω	ω	NUM
ejpam-6541	503	3	(	(	PUNCT
ejpam-6541	503	4	kl	kl	PROPN
ejpam-6541	503	5	)	)	PUNCT
ejpam-6541	503	6	i	i	PRON
ejpam-6541	503	7	en	en	ADV
ejpam-6541	503	8	and	and	CCONJ
ejpam-6541	503	9	that	that	SCONJ
ejpam-6541	503	10	{	{	PUNCT
ejpam-6541	503	11	ω(kl	ω(kl	PROPN
ejpam-6541	503	12	)	)	PUNCT
ejpam-6541	503	13	1	1	NUM
ejpam-6541	503	14	}	}	PUNCT
ejpam-6541	503	15	,	,	PUNCT
ejpam-6541	503	16	{	{	PUNCT
ejpam-6541	503	17	ω(kl	ω(kl	PROPN
ejpam-6541	503	18	)	)	PUNCT
ejpam-6541	503	19	2	2	NUM
ejpam-6541	503	20	}	}	PUNCT
ejpam-6541	503	21	,	,	PUNCT
ejpam-6541	503	22	.	.	PUNCT
ejpam-6541	503	23	.	.	PUNCT
ejpam-6541	503	24	.	.	PUNCT
ejpam-6541	504	1	{	{	PUNCT
ejpam-6541	504	2	ω(kl	ω(kl	PROPN
ejpam-6541	504	3	)	)	PUNCT
ejpam-6541	504	4	n	n	CCONJ
ejpam-6541	504	5	}	}	PUNCT
ejpam-6541	504	6	are	be	AUX
ejpam-6541	504	7	all	all	PRON
ejpam-6541	504	8	convergent	convergent	NOUN
ejpam-6541	504	9	.	.	PUNCT
ejpam-6541	505	1	consider	consider	VERB
ejpam-6541	505	2	ωi	ωi	NOUN
ejpam-6541	505	3	=	=	PUNCT
ejpam-6541	505	4	liml→∞	liml→∞	PROPN
ejpam-6541	505	5	ω	ω	PROPN
ejpam-6541	505	6	(	(	PUNCT
ejpam-6541	505	7	kl	kl	PROPN
ejpam-6541	505	8	)	)	PUNCT
ejpam-6541	506	1	i	i	PRON
ejpam-6541	506	2	,	,	PUNCT
ejpam-6541	506	3	i	i	PRON
ejpam-6541	506	4	=	=	NOUN
ejpam-6541	506	5	1	1	NUM
ejpam-6541	506	6	,	,	PUNCT
ejpam-6541	506	7	2	2	NUM
ejpam-6541	506	8	.	.	PUNCT
ejpam-6541	506	9	.	.	PUNCT
ejpam-6541	506	10	.	.	PUNCT
ejpam-6541	507	1	n.	n.	NOUN
ejpam-6541	507	2	and	and	CCONJ
ejpam-6541	507	3	x	x	X
ejpam-6541	508	1	=	=	PUNCT
ejpam-6541	508	2	ω1e1	ω1e1	PROPN
ejpam-6541	508	3	+	+	X
ejpam-6541	508	4	ω2e21	ω2e21	X
ejpam-6541	508	5	+	+	X
ejpam-6541	508	6	·	·	PUNCT
ejpam-6541	508	7	·	·	PUNCT
ejpam-6541	508	8	·	·	PUNCT
ejpam-6541	509	1	+	+	CCONJ
ejpam-6541	509	2	ωnen	ωnen	ADJ
ejpam-6541	509	3	.	.	PUNCT
ejpam-6541	510	1	currently	currently	ADV
ejpam-6541	510	2	,	,	PUNCT
ejpam-6541	510	3	for	for	ADP
ejpam-6541	510	4	t	t	PROPN
ejpam-6541	510	5	>	>	X
ejpam-6541	510	6	0	0	PROPN
ejpam-6541	510	7	,	,	PUNCT
ejpam-6541	510	8	we	we	PRON
ejpam-6541	510	9	possess	possess	VERB
ejpam-6541	510	10	nihf	nihf	NOUN
ejpam-6541	510	11	(	(	PUNCT
ejpam-6541	510	12	xkll	xkll	VERB
ejpam-6541	510	13	−	−	PROPN
ejpam-6541	510	14	x	x	SYM
ejpam-6541	510	15	,	,	PUNCT
ejpam-6541	510	16	t	t	PROPN
ejpam-6541	510	17	)	)	PUNCT
ejpam-6541	510	18	=	=	SYM
ejpam-6541	510	19	nihf	nihf	PROPN
ejpam-6541	510	20	(	(	PUNCT
ejpam-6541	510	21	∑n	∑n	PROPN
ejpam-6541	510	22	i=1(ω	i=1(ω	NUM
ejpam-6541	510	23	(	(	PUNCT
ejpam-6541	510	24	kl	kl	NOUN
ejpam-6541	510	25	)	)	PUNCT
ejpam-6541	510	26	i	i	PRON
ejpam-6541	510	27	−	−	PROPN
ejpam-6541	510	28	ωi)ei	ωi)ei	NUM
ejpam-6541	510	29	,	,	PUNCT
ejpam-6541	510	30	t	t	PROPN
ejpam-6541	510	31	)	)	PUNCT
ejpam-6541	510	32	)	)	PUNCT
ejpam-6541	511	1	⊇	⊇	PROPN
ejpam-6541	511	2	nihf	nihf	PROPN
ejpam-6541	511	3	(	(	PUNCT
ejpam-6541	511	4	e1	e1	PROPN
ejpam-6541	511	5	,	,	PUNCT
ejpam-6541	511	6	t	t	PROPN
ejpam-6541	511	7	|ω(kl	|ω(kl	PROPN
ejpam-6541	511	8	)	)	PUNCT
ejpam-6541	511	9	1	1	NUM
ejpam-6541	511	10	−ω1|	−ω1|	NOUN
ejpam-6541	511	11	)	)	PUNCT
ejpam-6541	511	12	∗	∗	NOUN
ejpam-6541	511	13	·	·	PUNCT
ejpam-6541	511	14	·	·	PUNCT
ejpam-6541	511	15	·	·	PUNCT
ejpam-6541	511	16	∗	∗	X
ejpam-6541	511	17	nihf	nihf	PROPN
ejpam-6541	511	18	(	(	PUNCT
ejpam-6541	511	19	en	en	X
ejpam-6541	511	20	,	,	PUNCT
ejpam-6541	511	21	t	t	PROPN
ejpam-6541	511	22	|ω(kl	|ω(kl	PROPN
ejpam-6541	511	23	)	)	PUNCT
ejpam-6541	511	24	n	n	PROPN
ejpam-6541	511	25	−ωn|	−ωn|	NOUN
ejpam-6541	511	26	)	)	PUNCT
ejpam-6541	512	1	=	=	SYM
ejpam-6541	512	2	⇒	⇒	NOUN
ejpam-6541	512	3	liml→∞nihf	liml→∞nihf	PROPN
ejpam-6541	512	4	(	(	PUNCT
ejpam-6541	512	5	xkl	xkl	PROPN
ejpam-6541	512	6	−	−	PROPN
ejpam-6541	512	7	x	x	SYM
ejpam-6541	512	8	,	,	PUNCT
ejpam-6541	512	9	t	t	PROPN
ejpam-6541	512	10	)	)	PUNCT
ejpam-6541	512	11	⊇	⊇	PROPN
ejpam-6541	512	12	u∗	u∗	NOUN
ejpam-6541	512	13	∗	∗	NOUN
ejpam-6541	512	14	·	·	PUNCT
ejpam-6541	512	15	·	·	PUNCT
ejpam-6541	512	16	·	·	PUNCT
ejpam-6541	512	17	∗	∗	NOUN
ejpam-6541	512	18	u∗.(ω	u∗.(ω	NUM
ejpam-6541	512	19	(	(	PUNCT
ejpam-6541	512	20	kl	kl	NOUN
ejpam-6541	512	21	)	)	PUNCT
ejpam-6541	512	22	n	n	PROPN
ejpam-6541	512	23	→	→	SYM
ejpam-6541	512	24	ωi	ωi	PROPN
ejpam-6541	512	25	as	as	ADP
ejpam-6541	512	26	l	l	PROPN
ejpam-6541	512	27	→	→	PUNCT
ejpam-6541	512	28	∞)(with	∞)(with	ADP
ejpam-6541	512	29	the	the	DET
ejpam-6541	512	30	use	use	NOUN
ejpam-6541	512	31	of	of	ADP
ejpam-6541	512	32	contuity	contuity	NOUN
ejpam-6541	512	33	of	of	ADP
ejpam-6541	512	34	tnorm	tnorm	NOUN
ejpam-6541	512	35	∗	∗	NOUN
ejpam-6541	512	36	at	at	ADP
ejpam-6541	512	37	(	(	PUNCT
ejpam-6541	512	38	1	1	NUM
ejpam-6541	512	39	,	,	PUNCT
ejpam-6541	512	40	1	1	NUM
ejpam-6541	512	41	)	)	PUNCT
ejpam-6541	512	42	)	)	PUNCT
ejpam-6541	512	43	.	.	PUNCT
ejpam-6541	513	1	=	=	PRON
ejpam-6541	513	2	⇒	⇒	NOUN
ejpam-6541	513	3	lim	lim	PROPN
ejpam-6541	513	4	l→∞	l→∞	NUM
ejpam-6541	513	5	nihf	nihf	PROPN
ejpam-6541	513	6	(	(	PUNCT
ejpam-6541	513	7	xkl	xkl	PROPN
ejpam-6541	513	8	−	−	PROPN
ejpam-6541	513	9	x	x	SYM
ejpam-6541	513	10	,	,	PUNCT
ejpam-6541	513	11	t	t	PROPN
ejpam-6541	513	12	)	)	PUNCT
ejpam-6541	513	13	=	=	PUNCT
ejpam-6541	514	1	u∗	u∗	INTJ
ejpam-6541	514	2	(	(	PUNCT
ejpam-6541	514	3	25	25	NUM
ejpam-6541	514	4	)	)	PUNCT
ejpam-6541	514	5	currently	currently	ADV
ejpam-6541	514	6	,	,	PUNCT
ejpam-6541	514	7	for	for	ADP
ejpam-6541	514	8	t	t	PROPN
ejpam-6541	514	9	>	>	X
ejpam-6541	514	10	0	0	PROPN
ejpam-6541	514	11	,	,	PUNCT
ejpam-6541	514	12	we	we	PRON
ejpam-6541	514	13	possess	possess	VERB
ejpam-6541	514	14	mihf	mihf	NOUN
ejpam-6541	514	15	(	(	PUNCT
ejpam-6541	514	16	xkll	xkll	VERB
ejpam-6541	514	17	−	−	PROPN
ejpam-6541	514	18	x	x	SYM
ejpam-6541	514	19	,	,	PUNCT
ejpam-6541	514	20	t	t	PROPN
ejpam-6541	514	21	)	)	PUNCT
ejpam-6541	514	22	=	=	SYM
ejpam-6541	515	1	mihf	mihf	NOUN
ejpam-6541	515	2	(	(	PUNCT
ejpam-6541	515	3	∑n	∑n	PROPN
ejpam-6541	515	4	i=1(ω	i=1(ω	NUM
ejpam-6541	515	5	(	(	PUNCT
ejpam-6541	515	6	kl	kl	NOUN
ejpam-6541	515	7	)	)	PUNCT
ejpam-6541	515	8	i	i	PRON
ejpam-6541	515	9	−	−	PROPN
ejpam-6541	515	10	ωi)ei	ωi)ei	NUM
ejpam-6541	515	11	,	,	PUNCT
ejpam-6541	515	12	t	t	PROPN
ejpam-6541	515	13	)	)	PUNCT
ejpam-6541	515	14	)	)	PUNCT
ejpam-6541	516	1	⊆	⊆	NUM
ejpam-6541	516	2	mihf	mihf	NOUN
ejpam-6541	516	3	(	(	PUNCT
ejpam-6541	516	4	e1	e1	PROPN
ejpam-6541	516	5	,	,	PUNCT
ejpam-6541	516	6	t	t	PROPN
ejpam-6541	516	7	|ω(kl	|ω(kl	PROPN
ejpam-6541	516	8	)	)	PUNCT
ejpam-6541	516	9	1	1	NUM
ejpam-6541	516	10	−ω1|	−ω1|	NOUN
ejpam-6541	516	11	)	)	PUNCT
ejpam-6541	516	12	⋄	⋄	NOUN
ejpam-6541	516	13	·	·	PUNCT
ejpam-6541	516	14	·	·	PUNCT
ejpam-6541	516	15	·	·	PUNCT
ejpam-6541	516	16	⋄mihf	⋄mihf	PROPN
ejpam-6541	516	17	(	(	PUNCT
ejpam-6541	516	18	en	en	X
ejpam-6541	516	19	,	,	PUNCT
ejpam-6541	516	20	t	t	PROPN
ejpam-6541	516	21	|ω(kl	|ω(kl	PROPN
ejpam-6541	516	22	)	)	PUNCT
ejpam-6541	516	23	n	n	PROPN
ejpam-6541	516	24	−ωn|	−ωn|	NOUN
ejpam-6541	516	25	)	)	PUNCT
ejpam-6541	517	1	=	=	NOUN
ejpam-6541	517	2	⇒	⇒	NOUN
ejpam-6541	517	3	liml→∞mihf	liml→∞mihf	PROPN
ejpam-6541	517	4	(	(	PUNCT
ejpam-6541	517	5	xkl	xkl	PROPN
ejpam-6541	517	6	−	−	PROPN
ejpam-6541	517	7	x	x	SYM
ejpam-6541	517	8	,	,	PUNCT
ejpam-6541	517	9	t	t	PROPN
ejpam-6541	517	10	)	)	PUNCT
ejpam-6541	517	11	⊇	⊇	PROPN
ejpam-6541	517	12	∅∗	∅∗	PROPN
ejpam-6541	517	13	⋄	⋄	PROPN
ejpam-6541	517	14	·	·	PUNCT
ejpam-6541	517	15	·	·	PUNCT
ejpam-6541	517	16	·	·	PUNCT
ejpam-6541	517	17	⋄	⋄	NOUN
ejpam-6541	517	18	∅∗.(ω(kl	∅∗.(ω(kl	NOUN
ejpam-6541	517	19	)	)	PUNCT
ejpam-6541	517	20	n	n	CCONJ
ejpam-6541	517	21	→	→	SYM
ejpam-6541	517	22	ωiasl	ωiasl	NOUN
ejpam-6541	517	23	→	→	PUNCT
ejpam-6541	517	24	∞)(using	∞)(use	VERB
ejpam-6541	517	25	the	the	DET
ejpam-6541	517	26	contuity	contuity	NOUN
ejpam-6541	517	27	of	of	ADP
ejpam-6541	517	28	t	t	PROPN
ejpam-6541	517	29	-	-	PUNCT
ejpam-6541	517	30	conorm	conorm	NOUN
ejpam-6541	517	31	⋄	⋄	PROPN
ejpam-6541	517	32	at	at	ADP
ejpam-6541	517	33	(	(	PUNCT
ejpam-6541	517	34	0,0	0,0	NOUN
ejpam-6541	517	35	)	)	PUNCT
ejpam-6541	517	36	)	)	PUNCT
ejpam-6541	517	37	.	.	PUNCT
ejpam-6541	518	1	=	=	PRON
ejpam-6541	518	2	⇒	⇒	NOUN
ejpam-6541	518	3	lim	lim	PROPN
ejpam-6541	518	4	l→∞	l→∞	NUM
ejpam-6541	518	5	nihf	nihf	PROPN
ejpam-6541	518	6	(	(	PUNCT
ejpam-6541	518	7	xkl	xkl	PROPN
ejpam-6541	518	8	−	−	PROPN
ejpam-6541	518	9	x	x	SYM
ejpam-6541	518	10	,	,	PUNCT
ejpam-6541	518	11	t	t	PROPN
ejpam-6541	518	12	)	)	PUNCT
ejpam-6541	518	13	=	=	PUNCT
ejpam-6541	519	1	∅∗	∅∗	PROPN
ejpam-6541	519	2	(	(	PUNCT
ejpam-6541	519	3	26	26	NUM
ejpam-6541	519	4	)	)	PUNCT
ejpam-6541	519	5	according	accord	VERB
ejpam-6541	519	6	to	to	ADP
ejpam-6541	519	7	(	(	PUNCT
ejpam-6541	519	8	25	25	NUM
ejpam-6541	519	9	)	)	PUNCT
ejpam-6541	519	10	and	and	CCONJ
ejpam-6541	519	11	(	(	PUNCT
ejpam-6541	519	12	26	26	NUM
ejpam-6541	519	13	)	)	PUNCT
ejpam-6541	519	14	,	,	PUNCT
ejpam-6541	519	15	x(kl	x(kl	PROPN
ejpam-6541	519	16	)	)	PUNCT
ejpam-6541	519	17	→	→	SYM
ejpam-6541	519	18	x.	x.	NOUN
ejpam-6541	519	19	given	give	VERB
ejpam-6541	519	20	that	that	SCONJ
ejpam-6541	519	21	x	x	PRON
ejpam-6541	519	22	is	be	AUX
ejpam-6541	519	23	closed	closed	ADJ
ejpam-6541	519	24	,	,	PUNCT
ejpam-6541	519	25	x	x	SYM
ejpam-6541	519	26	∈	∈	NOUN
ejpam-6541	519	27	x	x	PRON
ejpam-6541	519	28	implies	imply	VERB
ejpam-6541	519	29	that	that	SCONJ
ejpam-6541	519	30	x	x	PRON
ejpam-6541	519	31	is	be	AUX
ejpam-6541	519	32	compact	compact	ADJ
ejpam-6541	519	33	.	.	PUNCT
ejpam-6541	520	1	thus	thus	ADV
ejpam-6541	520	2	,	,	PUNCT
ejpam-6541	520	3	the	the	DET
ejpam-6541	520	4	proof	proof	NOUN
ejpam-6541	520	5	is	be	AUX
ejpam-6541	520	6	completed	complete	VERB
ejpam-6541	520	7	.	.	PUNCT
ejpam-6541	521	1	5	5	X
ejpam-6541	521	2	.	.	X
ejpam-6541	521	3	conclusion	conclusion	NOUN
ejpam-6541	521	4	we	we	PRON
ejpam-6541	521	5	extended	extend	VERB
ejpam-6541	521	6	the	the	DET
ejpam-6541	521	7	foundational	foundational	ADJ
ejpam-6541	521	8	work	work	NOUN
ejpam-6541	521	9	on	on	ADP
ejpam-6541	521	10	fuzzy	fuzzy	ADJ
ejpam-6541	521	11	normed	norme	VERB
ejpam-6541	521	12	linear	linear	ADJ
ejpam-6541	521	13	space	space	NOUN
ejpam-6541	521	14	,	,	PUNCT
ejpam-6541	521	15	initially	initially	ADV
ejpam-6541	521	16	proposed	propose	VERB
ejpam-6541	521	17	by	by	ADP
ejpam-6541	521	18	samanta	samanta	PROPN
ejpam-6541	521	19	et	et	PROPN
ejpam-6541	521	20	al	al	PROPN
ejpam-6541	521	21	.	.	PROPN
ejpam-6541	521	22	,	,	PUNCT
ejpam-6541	521	23	to	to	ADP
ejpam-6541	521	24	the	the	DET
ejpam-6541	521	25	domain	domain	NOUN
ejpam-6541	521	26	of	of	ADP
ejpam-6541	521	27	hesitant	hesitant	ADJ
ejpam-6541	521	28	fuzzy	fuzzy	ADJ
ejpam-6541	521	29	normed	norme	VERB
ejpam-6541	521	30	linear	linear	ADJ
ejpam-6541	521	31	space	space	NOUN
ejpam-6541	521	32	and	and	CCONJ
ejpam-6541	521	33	also	also	ADV
ejpam-6541	521	34	examine	examine	VERB
ejpam-6541	521	35	the	the	DET
ejpam-6541	521	36	properties	property	NOUN
ejpam-6541	521	37	of	of	ADP
ejpam-6541	521	38	completeness	completeness	NOUN
ejpam-6541	521	39	and	and	CCONJ
ejpam-6541	521	40	compactness	compactness	NOUN
ejpam-6541	521	41	on	on	ADP
ejpam-6541	521	42	hesitant	hesitant	ADJ
ejpam-6541	521	43	fuzzy	fuzzy	ADJ
ejpam-6541	521	44	normed	norme	VERB
ejpam-6541	521	45	linear	linear	ADJ
ejpam-6541	521	46	space	space	NOUN
ejpam-6541	521	47	,	,	PUNCT
ejpam-6541	521	48	also	also	ADV
ejpam-6541	521	49	address	address	VERB
ejpam-6541	521	50	the	the	DET
ejpam-6541	521	51	same	same	ADJ
ejpam-6541	521	52	properties	property	NOUN
ejpam-6541	521	53	on	on	ADP
ejpam-6541	521	54	intuitionistic	intuitionistic	ADJ
ejpam-6541	521	55	hesitant	hesitant	ADJ
ejpam-6541	521	56	fuzzy	fuzzy	ADJ
ejpam-6541	521	57	normed	norme	VERB
ejpam-6541	521	58	linear	linear	ADJ
ejpam-6541	521	59	space	space	NOUN
ejpam-6541	521	60	in	in	ADP
ejpam-6541	521	61	finite	finite	ADJ
ejpam-6541	521	62	dimension	dimension	NOUN
ejpam-6541	521	63	using	use	VERB
ejpam-6541	521	64	definitions	definition	NOUN
ejpam-6541	521	65	,	,	PUNCT
ejpam-6541	521	66	lemmas	lemmas	ADJ
ejpam-6541	521	67	,	,	PUNCT
ejpam-6541	521	68	and	and	CCONJ
ejpam-6541	521	69	theorems	theorem	NOUN
ejpam-6541	521	70	.	.	PUNCT
ejpam-6541	522	1	we	we	PRON
ejpam-6541	522	2	also	also	ADV
ejpam-6541	522	3	investigate	investigate	VERB
ejpam-6541	522	4	the	the	DET
ejpam-6541	522	5	continuity	continuity	NOUN
ejpam-6541	522	6	of	of	ADP
ejpam-6541	522	7	underlying	underlie	VERB
ejpam-6541	522	8	t	t	NOUN
ejpam-6541	522	9	-	-	PUNCT
ejpam-6541	522	10	norms	norm	NOUN
ejpam-6541	522	11	and	and	CCONJ
ejpam-6541	522	12	co	co	NOUN
ejpam-6541	522	13	-	-	ADJ
ejpam-6541	522	14	t	t	NOUN
ejpam-6541	522	15	-	-	PUNCT
ejpam-6541	522	16	norm	norm	NOUN
ejpam-6541	522	17	on	on	ADP
ejpam-6541	522	18	finite	finite	ADJ
ejpam-6541	522	19	-	-	ADJ
ejpam-6541	522	20	dimensional	dimensional	ADJ
ejpam-6541	522	21	intuitionistic	intuitionistic	ADJ
ejpam-6541	522	22	hesitant	hesitant	ADJ
ejpam-6541	522	23	fuzzy	fuzzy	ADJ
ejpam-6541	522	24	normed	norme	VERB
ejpam-6541	522	25	linear	linear	ADJ
ejpam-6541	522	26	space	space	NOUN
ejpam-6541	522	27	.	.	PUNCT
ejpam-6541	523	1	in	in	ADP
ejpam-6541	523	2	this	this	DET
ejpam-6541	523	3	context	context	NOUN
ejpam-6541	523	4	,	,	PUNCT
ejpam-6541	523	5	there	there	PRON
ejpam-6541	523	6	is	be	VERB
ejpam-6541	523	7	room	room	NOUN
ejpam-6541	523	8	for	for	ADP
ejpam-6541	523	9	more	more	ADJ
ejpam-6541	523	10	work	work	NOUN
ejpam-6541	523	11	(	(	PUNCT
ejpam-6541	523	12	if	if	SCONJ
ejpam-6541	523	13	possible	possible	ADJ
ejpam-6541	523	14	in	in	ADP
ejpam-6541	523	15	practical	practical	ADJ
ejpam-6541	523	16	scenario	scenario	NOUN
ejpam-6541	523	17	)	)	PUNCT
ejpam-6541	523	18	.	.	PUNCT
ejpam-6541	524	1	acknowledgements	acknowledgement	NOUN
ejpam-6541	524	2	the	the	DET
ejpam-6541	524	3	authors	author	NOUN
ejpam-6541	524	4	are	be	AUX
ejpam-6541	524	5	grateful	grateful	ADJ
ejpam-6541	524	6	to	to	ADP
ejpam-6541	524	7	dr	dr	PROPN
ejpam-6541	524	8	.	.	PROPN
ejpam-6541	524	9	m.	m.	PROPN
ejpam-6541	524	10	padmini	padmini	PROPN
ejpam-6541	524	11	,	,	PUNCT
ejpam-6541	524	12	head	head	NOUN
ejpam-6541	524	13	,	,	PUNCT
ejpam-6541	524	14	department	department	NOUN
ejpam-6541	524	15	of	of	ADP
ejpam-6541	524	16	mathematics	mathematic	NOUN
ejpam-6541	524	17	,	,	PUNCT
ejpam-6541	524	18	who	who	PRON
ejpam-6541	524	19	motivated	motivate	VERB
ejpam-6541	524	20	with	with	ADP
ejpam-6541	524	21	the	the	DET
ejpam-6541	524	22	right	right	ADJ
ejpam-6541	524	23	guidance	guidance	NOUN
ejpam-6541	524	24	and	and	CCONJ
ejpam-6541	524	25	support	support	NOUN
ejpam-6541	524	26	.	.	PUNCT
ejpam-6541	525	1	references	reference	NOUN
ejpam-6541	525	2	[	[	X
ejpam-6541	525	3	1	1	NUM
ejpam-6541	525	4	]	]	PUNCT
ejpam-6541	525	5	l.	l.	PROPN
ejpam-6541	525	6	zadeh	zadeh	PROPN
ejpam-6541	525	7	.	.	PUNCT
ejpam-6541	526	1	fuzzy	fuzzy	ADJ
ejpam-6541	526	2	sets	set	NOUN
ejpam-6541	526	3	.	.	PUNCT
ejpam-6541	527	1	information	information	NOUN
ejpam-6541	527	2	and	and	CCONJ
ejpam-6541	527	3	control	control	NOUN
ejpam-6541	527	4	,	,	PUNCT
ejpam-6541	527	5	8(3):338–353	8(3):338–353	NUM
ejpam-6541	527	6	,	,	PUNCT
ejpam-6541	527	7	1965	1965	NUM
ejpam-6541	527	8	.	.	PUNCT
ejpam-6541	528	1	k.	k.	PROPN
ejpam-6541	528	2	kavitha	kavitha	PROPN
ejpam-6541	528	3	,	,	PUNCT
ejpam-6541	528	4	p.	p.	PROPN
ejpam-6541	528	5	muralikrishna	muralikrishna	PROPN
ejpam-6541	528	6	/	/	SYM
ejpam-6541	528	7	eur	eur	PROPN
ejpam-6541	528	8	.	.	PUNCT
ejpam-6541	529	1	j.	j.	PROPN
ejpam-6541	529	2	pure	pure	PROPN
ejpam-6541	529	3	appl	appl	PROPN
ejpam-6541	529	4	.	.	PROPN
ejpam-6541	529	5	math	math	PROPN
ejpam-6541	529	6	,	,	PUNCT
ejpam-6541	529	7	18	18	NUM
ejpam-6541	529	8	(	(	PUNCT
ejpam-6541	529	9	4	4	NUM
ejpam-6541	529	10	)	)	PUNCT
ejpam-6541	529	11	(	(	PUNCT
ejpam-6541	529	12	2025	2025	NUM
ejpam-6541	529	13	)	)	PUNCT
ejpam-6541	529	14	,	,	PUNCT
ejpam-6541	529	15	6541	6541	NUM
ejpam-6541	529	16	14	14	NUM
ejpam-6541	529	17	of	of	ADP
ejpam-6541	529	18	14	14	NUM
ejpam-6541	529	19	[	[	X
ejpam-6541	529	20	2	2	X
ejpam-6541	529	21	]	]	PUNCT
ejpam-6541	529	22	t.	t.	NOUN
ejpam-6541	529	23	bag	bag	NOUN
ejpam-6541	529	24	and	and	CCONJ
ejpam-6541	529	25	s.	s.	PROPN
ejpam-6541	529	26	k.	k.	PROPN
ejpam-6541	529	27	samanta	samanta	PROPN
ejpam-6541	529	28	.	.	PUNCT
ejpam-6541	530	1	fuzzy	fuzzy	PROPN
ejpam-6541	530	2	bounded	bound	VERB
ejpam-6541	530	3	linear	linear	PROPN
ejpam-6541	530	4	operators	operator	NOUN
ejpam-6541	530	5	.	.	PUNCT
ejpam-6541	531	1	fuzzy	fuzzy	ADJ
ejpam-6541	531	2	sets	set	NOUN
ejpam-6541	531	3	and	and	CCONJ
ejpam-6541	531	4	systems	system	NOUN
ejpam-6541	531	5	,	,	PUNCT
ejpam-6541	531	6	151:513–547	151:513–547	NUM
ejpam-6541	531	7	,	,	PUNCT
ejpam-6541	531	8	2005	2005	NUM
ejpam-6541	531	9	.	.	PUNCT
ejpam-6541	532	1	[	[	X
ejpam-6541	532	2	3	3	X
ejpam-6541	532	3	]	]	PUNCT
ejpam-6541	532	4	s.	s.	PROPN
ejpam-6541	532	5	c.	c.	PROPN
ejpam-6541	532	6	cheng	cheng	PROPN
ejpam-6541	532	7	and	and	CCONJ
ejpam-6541	532	8	j.	j.	PROPN
ejpam-6541	532	9	n.	n.	PROPN
ejpam-6541	532	10	mordeson	mordeson	PROPN
ejpam-6541	532	11	.	.	PUNCT
ejpam-6541	533	1	fuzzy	fuzzy	ADJ
ejpam-6541	533	2	linear	linear	PROPN
ejpam-6541	533	3	operators	operator	NOUN
ejpam-6541	533	4	and	and	CCONJ
ejpam-6541	533	5	fuzzy	fuzzy	ADJ
ejpam-6541	533	6	normed	normed	ADJ
ejpam-6541	533	7	linear	linear	PROPN
ejpam-6541	533	8	spaces	space	NOUN
ejpam-6541	533	9	.	.	PUNCT
ejpam-6541	534	1	bulletin	bulletin	NOUN
ejpam-6541	534	2	of	of	ADP
ejpam-6541	534	3	the	the	DET
ejpam-6541	534	4	korean	korean	PROPN
ejpam-6541	534	5	mathematical	mathematical	ADJ
ejpam-6541	534	6	society	society	NOUN
ejpam-6541	534	7	,	,	PUNCT
ejpam-6541	534	8	86:429–436	86:429–436	NUM
ejpam-6541	534	9	,	,	PUNCT
ejpam-6541	534	10	2007	2007	NUM
ejpam-6541	534	11	.	.	PUNCT
ejpam-6541	535	1	[	[	X
ejpam-6541	535	2	4	4	X
ejpam-6541	535	3	]	]	PUNCT
ejpam-6541	535	4	t.	t.	NOUN
ejpam-6541	535	5	bag	bag	NOUN
ejpam-6541	535	6	and	and	CCONJ
ejpam-6541	535	7	s.	s.	PROPN
ejpam-6541	535	8	k.	k.	PROPN
ejpam-6541	535	9	samanta	samanta	PROPN
ejpam-6541	535	10	.	.	PUNCT
ejpam-6541	536	1	fixed	fix	VERB
ejpam-6541	536	2	point	point	NOUN
ejpam-6541	536	3	theorems	theorem	NOUN
ejpam-6541	536	4	on	on	ADP
ejpam-6541	536	5	fuzzy	fuzzy	ADJ
ejpam-6541	536	6	normed	norme	VERB
ejpam-6541	536	7	linear	linear	PROPN
ejpam-6541	536	8	spaces	space	NOUN
ejpam-6541	536	9	.	.	PUNCT
ejpam-6541	537	1	information	information	NOUN
ejpam-6541	537	2	sciences	science	NOUN
ejpam-6541	537	3	,	,	PUNCT
ejpam-6541	537	4	176:2910–2931	176:2910–2931	NOUN
ejpam-6541	537	5	,	,	PUNCT
ejpam-6541	537	6	2006	2006	NUM
ejpam-6541	537	7	.	.	PUNCT
ejpam-6541	538	1	[	[	X
ejpam-6541	538	2	5	5	NUM
ejpam-6541	538	3	]	]	PUNCT
ejpam-6541	538	4	c.	c.	NOUN
ejpam-6541	538	5	felbin	felbin	NOUN
ejpam-6541	538	6	.	.	PUNCT
ejpam-6541	539	1	finite	finite	ADJ
ejpam-6541	539	2	dimensional	dimensional	ADJ
ejpam-6541	539	3	fuzzy	fuzzy	ADJ
ejpam-6541	539	4	normed	norme	VERB
ejpam-6541	539	5	linear	linear	PROPN
ejpam-6541	539	6	spaces	space	NOUN
ejpam-6541	539	7	.	.	PUNCT
ejpam-6541	540	1	fuzzy	fuzzy	ADJ
ejpam-6541	540	2	sets	set	NOUN
ejpam-6541	540	3	and	and	CCONJ
ejpam-6541	540	4	systems	system	NOUN
ejpam-6541	540	5	,	,	PUNCT
ejpam-6541	540	6	48:239–248	48:239–248	PROPN
ejpam-6541	540	7	,	,	PUNCT
ejpam-6541	540	8	1992	1992	NUM
ejpam-6541	540	9	.	.	PUNCT
ejpam-6541	541	1	[	[	X
ejpam-6541	541	2	6	6	NUM
ejpam-6541	541	3	]	]	X
ejpam-6541	541	4	o.	o.	PROPN
ejpam-6541	541	5	kaleva	kaleva	PROPN
ejpam-6541	541	6	and	and	CCONJ
ejpam-6541	541	7	s.	s.	PROPN
ejpam-6541	541	8	seikkala	seikkala	PROPN
ejpam-6541	541	9	.	.	PUNCT
ejpam-6541	542	1	on	on	ADP
ejpam-6541	542	2	fuzzy	fuzzy	ADJ
ejpam-6541	542	3	metric	metric	ADJ
ejpam-6541	542	4	spaces	space	NOUN
ejpam-6541	542	5	.	.	PUNCT
ejpam-6541	543	1	fuzzy	fuzzy	ADJ
ejpam-6541	543	2	sets	set	NOUN
ejpam-6541	543	3	and	and	CCONJ
ejpam-6541	543	4	systems	system	NOUN
ejpam-6541	543	5	,	,	PUNCT
ejpam-6541	543	6	12:215	12:215	NUM
ejpam-6541	543	7	–	–	PUNCT
ejpam-6541	543	8	229	229	NUM
ejpam-6541	543	9	,	,	PUNCT
ejpam-6541	543	10	1984	1984	NUM
ejpam-6541	543	11	.	.	PUNCT
ejpam-6541	544	1	[	[	X
ejpam-6541	544	2	7	7	NUM
ejpam-6541	544	3	]	]	PUNCT
ejpam-6541	544	4	a.	a.	NOUN
ejpam-6541	544	5	k.	k.	PROPN
ejpam-6541	544	6	katsaras	katsaras	PROPN
ejpam-6541	544	7	.	.	PUNCT
ejpam-6541	545	1	fuzzy	fuzzy	ADJ
ejpam-6541	545	2	topological	topological	ADJ
ejpam-6541	545	3	vector	vector	NOUN
ejpam-6541	545	4	spaces	space	NOUN
ejpam-6541	545	5	.	.	PUNCT
ejpam-6541	546	1	fuzzy	fuzzy	ADJ
ejpam-6541	546	2	sets	set	NOUN
ejpam-6541	546	3	and	and	CCONJ
ejpam-6541	546	4	systems	system	NOUN
ejpam-6541	546	5	,	,	PUNCT
ejpam-6541	546	6	12:143–154	12:143–154	PROPN
ejpam-6541	546	7	,	,	PUNCT
ejpam-6541	546	8	1984	1984	NUM
ejpam-6541	546	9	.	.	PUNCT
ejpam-6541	547	1	[	[	X
ejpam-6541	547	2	8	8	NUM
ejpam-6541	547	3	]	]	PUNCT
ejpam-6541	547	4	k.	k.	PROPN
ejpam-6541	547	5	atanassov	atanassov	PROPN
ejpam-6541	547	6	.	.	PUNCT
ejpam-6541	548	1	intuitionistic	intuitionistic	ADJ
ejpam-6541	548	2	fuzzy	fuzzy	ADJ
ejpam-6541	548	3	sets	set	NOUN
ejpam-6541	548	4	.	.	PUNCT
ejpam-6541	549	1	fuzzy	fuzzy	ADJ
ejpam-6541	549	2	sets	set	NOUN
ejpam-6541	549	3	and	and	CCONJ
ejpam-6541	549	4	systems	system	NOUN
ejpam-6541	549	5	,	,	PUNCT
ejpam-6541	549	6	20:87–96	20:87–96	NUM
ejpam-6541	549	7	,	,	PUNCT
ejpam-6541	549	8	1986	1986	NUM
ejpam-6541	549	9	.	.	PUNCT
ejpam-6541	550	1	[	[	X
ejpam-6541	550	2	9	9	NUM
ejpam-6541	550	3	]	]	PUNCT
ejpam-6541	550	4	j.	j.	PROPN
ejpam-6541	550	5	h.	h.	PROPN
ejpam-6541	550	6	park	park	PROPN
ejpam-6541	550	7	.	.	PUNCT
ejpam-6541	551	1	intuitionistic	intuitionistic	ADJ
ejpam-6541	551	2	fuzzy	fuzzy	ADJ
ejpam-6541	551	3	metric	metric	ADJ
ejpam-6541	551	4	spaces	space	NOUN
ejpam-6541	551	5	.	.	PUNCT
ejpam-6541	552	1	chaos	chaos	NOUN
ejpam-6541	552	2	,	,	PUNCT
ejpam-6541	552	3	solitons	soliton	NOUN
ejpam-6541	552	4	&	&	CCONJ
ejpam-6541	552	5	fractals	fractal	NOUN
ejpam-6541	552	6	,	,	PUNCT
ejpam-6541	552	7	22:1039	22:1039	NUM
ejpam-6541	552	8	–	–	PUNCT
ejpam-6541	552	9	1046	1046	NUM
ejpam-6541	552	10	,	,	PUNCT
ejpam-6541	552	11	2004	2004	NUM
ejpam-6541	552	12	.	.	PUNCT
ejpam-6541	553	1	[	[	X
ejpam-6541	553	2	10	10	NUM
ejpam-6541	553	3	]	]	PUNCT
ejpam-6541	553	4	tapas	tapas	NOUN
ejpam-6541	553	5	kumar	kumar	PROPN
ejpam-6541	553	6	mondal	mondal	PROPN
ejpam-6541	553	7	and	and	CCONJ
ejpam-6541	553	8	s.	s.	PROPN
ejpam-6541	553	9	k.	k.	PROPN
ejpam-6541	553	10	samanta	samanta	PROPN
ejpam-6541	553	11	.	.	PUNCT
ejpam-6541	554	1	topology	topology	NOUN
ejpam-6541	554	2	of	of	ADP
ejpam-6541	554	3	interval	interval	NOUN
ejpam-6541	554	4	-	-	PUNCT
ejpam-6541	554	5	valued	value	VERB
ejpam-6541	554	6	intuitionistic	intuitionistic	ADJ
ejpam-6541	554	7	fuzzy	fuzzy	ADJ
ejpam-6541	554	8	sets	set	NOUN
ejpam-6541	554	9	.	.	PUNCT
ejpam-6541	555	1	fuzzy	fuzzy	ADJ
ejpam-6541	555	2	sets	set	NOUN
ejpam-6541	555	3	and	and	CCONJ
ejpam-6541	555	4	systems	system	NOUN
ejpam-6541	555	5	,	,	PUNCT
ejpam-6541	555	6	119:483–494	119:483–494	NUM
ejpam-6541	555	7	,	,	PUNCT
ejpam-6541	555	8	2001	2001	NUM
ejpam-6541	555	9	.	.	PUNCT
ejpam-6541	556	1	[	[	X
ejpam-6541	556	2	11	11	NUM
ejpam-6541	556	3	]	]	PUNCT
ejpam-6541	556	4	tapas	tapas	NOUN
ejpam-6541	556	5	kumar	kumar	PROPN
ejpam-6541	556	6	mondal	mondal	PROPN
ejpam-6541	556	7	and	and	CCONJ
ejpam-6541	556	8	s.	s.	PROPN
ejpam-6541	556	9	k.	k.	PROPN
ejpam-6541	556	10	samanta	samanta	PROPN
ejpam-6541	556	11	.	.	PUNCT
ejpam-6541	557	1	on	on	ADP
ejpam-6541	557	2	intuitionistic	intuitionistic	ADJ
ejpam-6541	557	3	gradation	gradation	NOUN
ejpam-6541	557	4	of	of	ADP
ejpam-6541	557	5	openness	openness	NOUN
ejpam-6541	557	6	.	.	PUNCT
ejpam-6541	558	1	fuzzy	fuzzy	ADJ
ejpam-6541	558	2	sets	set	NOUN
ejpam-6541	558	3	and	and	CCONJ
ejpam-6541	558	4	systems	system	NOUN
ejpam-6541	558	5	,	,	PUNCT
ejpam-6541	558	6	131:323–336	131:323–336	NUM
ejpam-6541	558	7	,	,	PUNCT
ejpam-6541	558	8	2002	2002	NUM
ejpam-6541	558	9	.	.	PUNCT
ejpam-6541	559	1	[	[	X
ejpam-6541	559	2	12	12	NUM
ejpam-6541	559	3	]	]	X
ejpam-6541	559	4	n.	n.	PROPN
ejpam-6541	559	5	thillaigovindan	thillaigovindan	PROPN
ejpam-6541	559	6	,	,	PUNCT
ejpam-6541	559	7	s.	s.	PROPN
ejpam-6541	559	8	anita	anita	PROPN
ejpam-6541	559	9	shanthi	shanthi	PROPN
ejpam-6541	559	10	,	,	PUNCT
ejpam-6541	559	11	and	and	CCONJ
ejpam-6541	559	12	y.	y.	PROPN
ejpam-6541	559	13	b.	b.	PROPN
ejpam-6541	559	14	jun	jun	PROPN
ejpam-6541	559	15	.	.	PROPN
ejpam-6541	560	1	on	on	ADP
ejpam-6541	560	2	lacunary	lacunary	ADJ
ejpam-6541	560	3	statistical	statistical	ADJ
ejpam-6541	560	4	convergence	convergence	NOUN
ejpam-6541	560	5	in	in	ADP
ejpam-6541	560	6	intuitionistic	intuitionistic	ADJ
ejpam-6541	560	7	n	n	CCONJ
ejpam-6541	560	8	-	-	PUNCT
ejpam-6541	560	9	normed	norme	VERB
ejpam-6541	560	10	linear	linear	ADJ
ejpam-6541	560	11	spaces	space	NOUN
ejpam-6541	560	12	.	.	PUNCT
ejpam-6541	561	1	annals	annal	NOUN
ejpam-6541	561	2	of	of	ADP
ejpam-6541	561	3	fuzzy	fuzzy	ADJ
ejpam-6541	561	4	mathematics	mathematic	NOUN
ejpam-6541	561	5	and	and	CCONJ
ejpam-6541	561	6	informatics	informatic	NOUN
ejpam-6541	561	7	,	,	PUNCT
ejpam-6541	561	8	1(2):119–131	1(2):119–131	NUM
ejpam-6541	561	9	,	,	PUNCT
ejpam-6541	561	10	2011	2011	NUM
ejpam-6541	561	11	.	.	PUNCT
ejpam-6541	562	1	[	[	X
ejpam-6541	562	2	13	13	NUM
ejpam-6541	562	3	]	]	PUNCT
ejpam-6541	562	4	s.	s.	PROPN
ejpam-6541	562	5	vijayabalaji	vijayabalaji	PROPN
ejpam-6541	562	6	,	,	PUNCT
ejpam-6541	562	7	n.	n.	PROPN
ejpam-6541	562	8	thillaigovindan	thillaigovindan	PROPN
ejpam-6541	562	9	,	,	PUNCT
ejpam-6541	562	10	and	and	CCONJ
ejpam-6541	562	11	y.	y.	PROPN
ejpam-6541	562	12	bae	bae	PROPN
ejpam-6541	562	13	jun	jun	PROPN
ejpam-6541	562	14	.	.	PROPN
ejpam-6541	562	15	intuitionistic	intuitionistic	ADJ
ejpam-6541	562	16	fuzzy	fuzzy	ADJ
ejpam-6541	562	17	n	n	CCONJ
ejpam-6541	562	18	-	-	PUNCT
ejpam-6541	562	19	normed	norme	VERB
ejpam-6541	562	20	linear	linear	ADJ
ejpam-6541	562	21	space	space	NOUN
ejpam-6541	562	22	.	.	PUNCT
ejpam-6541	563	1	bulletin	bulletin	NOUN
ejpam-6541	563	2	of	of	ADP
ejpam-6541	563	3	the	the	DET
ejpam-6541	563	4	korean	korean	PROPN
ejpam-6541	563	5	mathematical	mathematical	ADJ
ejpam-6541	563	6	society	society	NOUN
ejpam-6541	563	7	,	,	PUNCT
ejpam-6541	563	8	44(2):291–308	44(2):291–308	PROPN
ejpam-6541	563	9	,	,	PUNCT
ejpam-6541	563	10	2007	2007	NUM
ejpam-6541	563	11	.	.	PUNCT
ejpam-6541	564	1	[	[	X
ejpam-6541	564	2	14	14	NUM
ejpam-6541	564	3	]	]	PUNCT
ejpam-6541	564	4	t.	t.	PROPN
ejpam-6541	564	5	k.	k.	PROPN
ejpam-6541	564	6	samanta	samanta	PROPN
ejpam-6541	564	7	and	and	CCONJ
ejpam-6541	564	8	iqbal	iqbal	PROPN
ejpam-6541	564	9	h.	h.	PROPN
ejpam-6541	564	10	jebril	jebril	PROPN
ejpam-6541	564	11	.	.	PUNCT
ejpam-6541	565	1	finite	finite	VERB
ejpam-6541	565	2	dimensional	dimensional	ADJ
ejpam-6541	565	3	intuitionistic	intuitionistic	ADJ
ejpam-6541	565	4	fuzzy	fuzzy	ADJ
ejpam-6541	565	5	normed	norme	VERB
ejpam-6541	565	6	linear	linear	ADJ
ejpam-6541	565	7	space	space	NOUN
ejpam-6541	565	8	.	.	PUNCT
ejpam-6541	566	1	international	international	ADJ
ejpam-6541	566	2	journal	journal	NOUN
ejpam-6541	566	3	of	of	ADP
ejpam-6541	566	4	open	open	ADJ
ejpam-6541	566	5	problems	problem	NOUN
ejpam-6541	566	6	in	in	ADP
ejpam-6541	566	7	computer	computer	NOUN
ejpam-6541	566	8	science	science	NOUN
ejpam-6541	566	9	and	and	CCONJ
ejpam-6541	566	10	mathematics	mathematic	NOUN
ejpam-6541	566	11	,	,	PUNCT
ejpam-6541	566	12	2(4	2(4	NUM
ejpam-6541	566	13	)	)	PUNCT
ejpam-6541	566	14	,	,	PUNCT
ejpam-6541	566	15	2009	2009	NUM
ejpam-6541	566	16	.	.	PUNCT
ejpam-6541	567	1	[	[	X
ejpam-6541	567	2	15	15	NUM
ejpam-6541	567	3	]	]	X
ejpam-6541	567	4	george	george	PROPN
ejpam-6541	567	5	j.	j.	PROPN
ejpam-6541	567	6	klir	klir	PROPN
ejpam-6541	567	7	and	and	CCONJ
ejpam-6541	567	8	bo	bo	PROPN
ejpam-6541	567	9	yuan	yuan	PROPN
ejpam-6541	567	10	.	.	PUNCT
ejpam-6541	568	1	fuzzy	fuzzy	ADJ
ejpam-6541	568	2	sets	set	NOUN
ejpam-6541	568	3	and	and	CCONJ
ejpam-6541	568	4	fuzzy	fuzzy	ADJ
ejpam-6541	568	5	logic	logic	NOUN
ejpam-6541	568	6	.	.	PUNCT
ejpam-6541	569	1	prentice	prentice	NOUN
ejpam-6541	569	2	-	-	PUNCT
ejpam-6541	569	3	hall	hall	NOUN
ejpam-6541	569	4	of	of	ADP
ejpam-6541	569	5	india	india	PROPN
ejpam-6541	569	6	private	private	PROPN
ejpam-6541	569	7	limited	limited	ADJ
ejpam-6541	569	8	,	,	PUNCT
ejpam-6541	569	9	new	new	ADJ
ejpam-6541	569	10	delhi	delhi	PROPN
ejpam-6541	569	11	,	,	PUNCT
ejpam-6541	569	12	1997	1997	NUM
ejpam-6541	569	13	.	.	PUNCT
ejpam-6541	570	1	[	[	X
ejpam-6541	570	2	16	16	NUM
ejpam-6541	570	3	]	]	X
ejpam-6541	570	4	prakasam	prakasam	NOUN
ejpam-6541	570	5	muralikrishna	muralikrishna	NOUN
ejpam-6541	570	6	and	and	CCONJ
ejpam-6541	570	7	krishnamoorthy	krishnamoorthy	PROPN
ejpam-6541	570	8	kavitha	kavitha	PROPN
ejpam-6541	570	9	.	.	PUNCT
ejpam-6541	571	1	an	an	DET
ejpam-6541	571	2	exploration	exploration	NOUN
ejpam-6541	571	3	of	of	ADP
ejpam-6541	571	4	hesitant	hesitant	ADJ
ejpam-6541	571	5	fuzzy	fuzzy	ADJ
ejpam-6541	571	6	normed	norme	VERB
ejpam-6541	571	7	linear	linear	ADJ
ejpam-6541	571	8	space	space	NOUN
ejpam-6541	571	9	.	.	PUNCT
ejpam-6541	572	1	international	international	ADJ
ejpam-6541	572	2	journal	journal	PROPN
ejpam-6541	572	3	of	of	ADP
ejpam-6541	572	4	neutrosophic	neutrosophic	ADJ
ejpam-6541	572	5	science	science	NOUN
ejpam-6541	572	6	,	,	PUNCT
ejpam-6541	572	7	25(3):373	25(3):373	NUM
ejpam-6541	572	8	–	–	PUNCT
ejpam-6541	572	9	384	384	NUM
ejpam-6541	572	10	,	,	PUNCT
ejpam-6541	572	11	2025	2025	NUM
ejpam-6541	572	12	.	.	PUNCT
ejpam-6541	573	1	[	[	X
ejpam-6541	573	2	17	17	NUM
ejpam-6541	573	3	]	]	PUNCT
ejpam-6541	573	4	t.	t.	NOUN
ejpam-6541	573	5	bag	bag	NOUN
ejpam-6541	573	6	and	and	CCONJ
ejpam-6541	573	7	s.	s.	PROPN
ejpam-6541	573	8	k.	k.	PROPN
ejpam-6541	573	9	samanta	samanta	PROPN
ejpam-6541	573	10	.	.	PUNCT
ejpam-6541	574	1	finite	finite	PROPN
ejpam-6541	574	2	dimensional	dimensional	ADJ
ejpam-6541	574	3	fuzzy	fuzzy	ADJ
ejpam-6541	574	4	normed	norme	VERB
ejpam-6541	574	5	linear	linear	PROPN
ejpam-6541	574	6	spaces	space	NOUN
ejpam-6541	574	7	.	.	PUNCT
ejpam-6541	575	1	the	the	DET
ejpam-6541	575	2	journal	journal	NOUN
ejpam-6541	575	3	of	of	ADP
ejpam-6541	575	4	fuzzy	fuzzy	ADJ
ejpam-6541	575	5	mathematics	mathematic	NOUN
ejpam-6541	575	6	,	,	PUNCT
ejpam-6541	575	7	11(3):687–705	11(3):687–705	NUM
ejpam-6541	575	8	,	,	PUNCT
ejpam-6541	575	9	2003	2003	NUM
ejpam-6541	575	10	.	.	PUNCT
ejpam-6541	576	1	[	[	X
ejpam-6541	576	2	18	18	NUM
ejpam-6541	576	3	]	]	X
ejpam-6541	576	4	r.	r.	PROPN
ejpam-6541	576	5	saadati	saadati	PROPN
ejpam-6541	576	6	and	and	CCONJ
ejpam-6541	576	7	j.	j.	PROPN
ejpam-6541	576	8	h.	h.	PROPN
ejpam-6541	576	9	park	park	PROPN
ejpam-6541	576	10	.	.	PUNCT
ejpam-6541	577	1	on	on	ADP
ejpam-6541	577	2	the	the	DET
ejpam-6541	577	3	intuitionistic	intuitionistic	ADJ
ejpam-6541	577	4	fuzzy	fuzzy	ADJ
ejpam-6541	577	5	topological	topological	ADJ
ejpam-6541	577	6	spaces	space	NOUN
ejpam-6541	577	7	.	.	PUNCT
ejpam-6541	578	1	chaos	chaos	NOUN
ejpam-6541	578	2	,	,	PUNCT
ejpam-6541	578	3	solitons	soliton	NOUN
ejpam-6541	578	4	&	&	CCONJ
ejpam-6541	578	5	fractals	fractal	NOUN
ejpam-6541	578	6	,	,	PUNCT
ejpam-6541	578	7	27:331–344	27:331–344	NUM
ejpam-6541	578	8	,	,	PUNCT
ejpam-6541	578	9	2006	2006	NUM
ejpam-6541	578	10	.	.	PUNCT
ejpam-6541	579	1	[	[	X
ejpam-6541	579	2	19	19	NUM
ejpam-6541	579	3	]	]	X
ejpam-6541	579	4	krishnamoorthy	krishnamoorthy	PROPN
ejpam-6541	579	5	kavitha	kavitha	PROPN
ejpam-6541	579	6	and	and	CCONJ
ejpam-6541	579	7	prakasam	prakasam	PROPN
ejpam-6541	579	8	muralikrishna	muralikrishna	NOUN
ejpam-6541	579	9	.	.	PUNCT
ejpam-6541	580	1	finite	finite	VERB
ejpam-6541	580	2	dimensional	dimensional	ADJ
ejpam-6541	580	3	intuitionistic	intuitionistic	ADJ
ejpam-6541	580	4	hesitant	hesitant	ADJ
ejpam-6541	580	5	fuzzy	fuzzy	ADJ
ejpam-6541	580	6	normed	norme	VERB
ejpam-6541	580	7	linear	linear	ADJ
ejpam-6541	580	8	space	space	NOUN
ejpam-6541	580	9	.	.	PUNCT
ejpam-6541	581	1	submitted	submit	VERB
ejpam-6541	581	2	to	to	ADP
ejpam-6541	581	3	the	the	DET
ejpam-6541	581	4	first	first	ADJ
ejpam-6541	581	5	international	international	ADJ
ejpam-6541	581	6	society	society	NOUN
ejpam-6541	581	7	of	of	ADP
ejpam-6541	581	8	fuzzy	fuzzy	ADJ
ejpam-6541	581	9	sets	set	NOUN
ejpam-6541	581	10	extensions	extension	NOUN
ejpam-6541	581	11	and	and	CCONJ
ejpam-6541	581	12	applications	application	NOUN
ejpam-6541	581	13	conference	conference	NOUN
ejpam-6541	581	14	,	,	PUNCT
ejpam-6541	581	15	2025	2025	NUM
ejpam-6541	581	16	.	.	PUNCT