id	sid	tid	token	lemma	pos
bibechana-4043	1	1	microsoft	microsoft	PROPN
bibechana-4043	1	2	word	word	PROPN
bibechana-4043	1	3	g.	g.	PROPN
bibechana-4043	1	4	palei	palei	VERB
bibechana-4043	1	5	_	_	NOUN
bibechana-4043	1	6	39	39	NUM
bibechana-4043	1	7	-	-	PUNCT
bibechana-4043	1	8	43_.doc	43_.doc	NUM
bibechana-4043	1	9	g.k	g.k	PROPN
bibechana-4043	1	10	.	.	PROPN
bibechana-4043	1	11	palei	palei	PROPN
bibechana-4043	1	12	and	and	CCONJ
bibechana-4043	1	13	n.p	n.p	PROPN
bibechana-4043	1	14	.	.	PROPN
bibechana-4043	1	15	sah	sah	PROPN
bibechana-4043	1	16	/	/	SYM
bibechana-4043	1	17	bibechana	bibechana	PROPN
bibechana-4043	1	18	7	7	NUM
bibechana-4043	1	19	(	(	PUNCT
bibechana-4043	1	20	2011	2011	NUM
bibechana-4043	1	21	)	)	PUNCT
bibechana-4043	1	22	39	39	NUM
bibechana-4043	1	23	-	-	SYM
bibechana-4043	1	24	43	43	NUM
bibechana-4043	1	25	:	:	PUNCT
bibechana-4043	1	26	bmhss	bmhss	NOUN
bibechana-4043	1	27	39	39	NUM
bibechana-4043	1	28	bibechana	bibechana	NOUN
bibechana-4043	1	29	a	a	DET
bibechana-4043	1	30	multidisciplinary	multidisciplinary	ADJ
bibechana-4043	1	31	journal	journal	NOUN
bibechana-4043	1	32	of	of	ADP
bibechana-4043	1	33	science	science	NOUN
bibechana-4043	1	34	,	,	PUNCT
bibechana-4043	1	35	technology	technology	NOUN
bibechana-4043	1	36	and	and	CCONJ
bibechana-4043	1	37	mathematics	mathematic	NOUN
bibechana-4043	1	38	issn	issn	VERB
bibechana-4043	1	39	2091	2091	NUM
bibechana-4043	1	40	-	-	SYM
bibechana-4043	1	41	0762	0762	NUM
bibechana-4043	1	42	(	(	PUNCT
bibechana-4043	1	43	online	online	ADJ
bibechana-4043	1	44	)	)	PUNCT
bibechana-4043	1	45	journal	journal	NOUN
bibechana-4043	1	46	homepage	homepage	NOUN
bibechana-4043	1	47	:	:	PUNCT
bibechana-4043	1	48	http://nepjol.info/index.php/bibichana	http://nepjol.info/index.php/bibichana	X
bibechana-4043	1	49	some	some	DET
bibechana-4043	1	50	results	result	VERB
bibechana-4043	1	51	on	on	ADP
bibechana-4043	1	52	asymptotically	asymptotically	ADV
bibechana-4043	1	53	normable	normable	ADJ
bibechana-4043	1	54	frechet	frechet	PROPN
bibechana-4043	1	55	spaces	space	VERB
bibechana-4043	1	56	g.k	g.k	PROPN
bibechana-4043	1	57	.	.	PROPN
bibechana-4043	1	58	paleia	paleia	PROPN
bibechana-4043	1	59	,	,	PUNCT
bibechana-4043	1	60	n.p	n.p	PROPN
bibechana-4043	1	61	.	.	PROPN
bibechana-4043	1	62	sahb	sahb	PROPN
bibechana-4043	1	63	∗∗∗∗	∗∗∗∗	PROPN
bibechana-4043	1	64	a	a	DET
bibechana-4043	1	65	department	department	NOUN
bibechana-4043	1	66	of	of	ADP
bibechana-4043	1	67	mathematics	mathematics	PROPN
bibechana-4043	1	68	,	,	PUNCT
bibechana-4043	1	69	b.n	b.n	PROPN
bibechana-4043	1	70	.	.	PROPN
bibechana-4043	1	71	college	college	PROPN
bibechana-4043	1	72	,	,	PUNCT
bibechana-4043	1	73	patna	patna	PROPN
bibechana-4043	1	74	university	university	PROPN
bibechana-4043	1	75	,	,	PUNCT
bibechana-4043	1	76	patna	patna	PROPN
bibechana-4043	1	77	,	,	PUNCT
bibechana-4043	1	78	india	india	PROPN
bibechana-4043	1	79	b	b	PROPN
bibechana-4043	1	80	department	department	PROPN
bibechana-4043	1	81	of	of	ADP
bibechana-4043	1	82	mathematics	mathematics	PROPN
bibechana-4043	1	83	,	,	PUNCT
bibechana-4043	1	84	m.m.a.m	m.m.a.m	PROPN
bibechana-4043	1	85	.	.	PUNCT
bibechana-4043	1	86	campus	campus	PROPN
bibechana-4043	1	87	(	(	PUNCT
bibechana-4043	1	88	tribhuvan	tribhuvan	PROPN
bibechana-4043	1	89	university	university	PROPN
bibechana-4043	1	90	)	)	PUNCT
bibechana-4043	1	91	,	,	PUNCT
bibechana-4043	1	92	biratnagar	biratnagar	NOUN
bibechana-4043	1	93	,	,	PUNCT
bibechana-4043	1	94	nepal	nepal	ADJ
bibechana-4043	1	95	article	article	NOUN
bibechana-4043	1	96	history	history	NOUN
bibechana-4043	1	97	:	:	PUNCT
bibechana-4043	1	98	received	receive	VERB
bibechana-4043	1	99	8	8	NUM
bibechana-4043	1	100	october	october	PROPN
bibechana-4043	1	101	2010	2010	NUM
bibechana-4043	1	102	;	;	PUNCT
bibechana-4043	1	103	revised	revise	VERB
bibechana-4043	1	104	18	18	NUM
bibechana-4043	1	105	november	november	PROPN
bibechana-4043	1	106	2010	2010	NUM
bibechana-4043	1	107	;	;	PUNCT
bibechana-4043	1	108	accepted	accept	VERB
bibechana-4043	1	109	20	20	NUM
bibechana-4043	1	110	november	november	PROPN
bibechana-4043	1	111	2010	2010	NUM
bibechana-4043	1	112	abstract	abstract	NOUN
bibechana-4043	1	113	.	.	PUNCT
bibechana-4043	2	1	in	in	ADP
bibechana-4043	2	2	this	this	DET
bibechana-4043	2	3	paper	paper	NOUN
bibechana-4043	2	4	,	,	PUNCT
bibechana-4043	2	5	it	it	PRON
bibechana-4043	2	6	is	be	AUX
bibechana-4043	2	7	shown	show	VERB
bibechana-4043	2	8	that	that	SCONJ
bibechana-4043	2	9	the	the	DET
bibechana-4043	2	10	asymptotically	asymptotically	ADV
bibechana-4043	2	11	normable	normable	ADJ
bibechana-4043	2	12	spaces	space	NOUN
bibechana-4043	2	13	are	be	AUX
bibechana-4043	2	14	the	the	DET
bibechana-4043	2	15	smallest	small	ADJ
bibechana-4043	2	16	class	class	NOUN
bibechana-4043	2	17	of	of	ADP
bibechana-4043	2	18	frechet	frechet	PROPN
bibechana-4043	2	19	spaces	space	NOUN
bibechana-4043	2	20	which	which	PRON
bibechana-4043	2	21	contains	contain	VERB
bibechana-4043	2	22	the	the	DET
bibechana-4043	2	23	nuclear	nuclear	ADJ
bibechana-4043	2	24	kothe	kothe	NOUN
bibechana-4043	2	25	spaces	space	NOUN
bibechana-4043	2	26	with	with	ADP
bibechana-4043	2	27	continuous	continuous	ADJ
bibechana-4043	2	28	norm	norm	NOUN
bibechana-4043	2	29	,	,	PUNCT
bibechana-4043	2	30	the	the	DET
bibechana-4043	2	31	banach	banach	NOUN
bibechana-4043	2	32	spaces	space	NOUN
bibechana-4043	2	33	and	and	CCONJ
bibechana-4043	2	34	is	be	AUX
bibechana-4043	2	35	closed	close	VERB
bibechana-4043	2	36	under	under	ADP
bibechana-4043	2	37	ε	ε	PROPN
bibechana-4043	2	38	-	-	PUNCT
bibechana-4043	2	39	tensor	tensor	NOUN
bibechana-4043	2	40	products	product	NOUN
bibechana-4043	2	41	and	and	CCONJ
bibechana-4043	2	42	sub	sub	NOUN
bibechana-4043	2	43	-	-	NOUN
bibechana-4043	2	44	spaces	space	NOUN
bibechana-4043	2	45	.	.	PUNCT
bibechana-4043	3	1	again	again	ADV
bibechana-4043	3	2	our	our	PRON
bibechana-4043	3	3	main	main	ADJ
bibechana-4043	3	4	aim	aim	NOUN
bibechana-4043	3	5	will	will	AUX
bibechana-4043	3	6	be	be	AUX
bibechana-4043	3	7	to	to	PART
bibechana-4043	3	8	construct	construct	VERB
bibechana-4043	3	9	an	an	DET
bibechana-4043	3	10	example	example	NOUN
bibechana-4043	3	11	of	of	ADP
bibechana-4043	3	12	a	a	DET
bibechana-4043	3	13	kothe	kothe	ADJ
bibechana-4043	3	14	space	space	NOUN
bibechana-4043	3	15	which	which	PRON
bibechana-4043	3	16	is	be	AUX
bibechana-4043	3	17	montel	montel	PROPN
bibechana-4043	3	18	,	,	PUNCT
bibechana-4043	3	19	admits	admit	VERB
bibechana-4043	3	20	a	a	DET
bibechana-4043	3	21	continuous	continuous	ADJ
bibechana-4043	3	22	norm	norm	NOUN
bibechana-4043	3	23	,	,	PUNCT
bibechana-4043	3	24	but	but	CCONJ
bibechana-4043	3	25	still	still	ADV
bibechana-4043	3	26	is	be	AUX
bibechana-4043	3	27	not	not	PART
bibechana-4043	3	28	asymptotically	asymptotically	ADV
bibechana-4043	3	29	normable	normable	ADJ
bibechana-4043	3	30	.	.	PUNCT
bibechana-4043	4	1	keywords	keyword	NOUN
bibechana-4043	4	2	:	:	PUNCT
bibechana-4043	4	3	asymptotically	asymptotically	ADV
bibechana-4043	4	4	normable	normable	ADJ
bibechana-4043	4	5	;	;	PUNCT
bibechana-4043	4	6	frechet	frechet	NOUN
bibechana-4043	4	7	space	space	NOUN
bibechana-4043	4	8	;	;	PUNCT
bibechana-4043	4	9	kothe	kothe	ADJ
bibechana-4043	4	10	space	space	NOUN
bibechana-4043	4	11	introduction	introduction	NOUN
bibechana-4043	4	12	let	let	VERB
bibechana-4043	4	13	e	e	PRON
bibechana-4043	4	14	be	be	AUX
bibechana-4043	4	15	a	a	DET
bibechana-4043	4	16	frechet	frechet	ADJ
bibechana-4043	4	17	space	space	NOUN
bibechana-4043	4	18	,	,	PUNCT
bibechana-4043	4	19	||	||	NOUN
bibechana-4043	4	20	||1	||1	NOUN
bibechana-4043	4	21	≤	≤	NOUN
bibechana-4043	4	22	||	||	NOUN
bibechana-4043	4	23	||2	||2	NOUN
bibechana-4043	4	24	≤	≤	PROPN
bibechana-4043	4	25	......	......	PUNCT
bibechana-4043	5	1	a	a	DET
bibechana-4043	5	2	fundamental	fundamental	ADJ
bibechana-4043	5	3	system	system	NOUN
bibechana-4043	5	4	of	of	ADP
bibechana-4043	5	5	seminorms	seminorm	NOUN
bibechana-4043	5	6	on	on	ADP
bibechana-4043	5	7	e	e	PROPN
bibechana-4043	5	8	and	and	CCONJ
bibechana-4043	5	9	uk	uk	PROPN
bibechana-4043	5	10	=	=	PRON
bibechana-4043	5	11	{	{	PUNCT
bibechana-4043	5	12	x	x	PUNCT
bibechana-4043	5	13	∈	∈	NOUN
bibechana-4043	5	14	e	e	NOUN
bibechana-4043	5	15	:	:	PUNCT
bibechana-4043	5	16	||x||k	||x||k	NOUN
bibechana-4043	5	17	≤	≤	NUM
bibechana-4043	5	18	1	1	NUM
bibechana-4043	5	19	}	}	PUNCT
bibechana-4043	5	20	for	for	ADP
bibechana-4043	5	21	every	every	DET
bibechana-4043	5	22	k.	k.	PROPN
bibechana-4043	5	23	e	e	PROPN
bibechana-4043	5	24	is	be	AUX
bibechana-4043	5	25	called	call	VERB
bibechana-4043	5	26	asymptotically	asymptotically	ADV
bibechana-4043	5	27	normable	normable	ADJ
bibechana-4043	5	28	,	,	PUNCT
bibechana-4043	5	29	if	if	SCONJ
bibechana-4043	5	30	there	there	PRON
bibechana-4043	5	31	is	be	VERB
bibechana-4043	5	32	a	a	DET
bibechana-4043	5	33	ko	ko	NOUN
bibechana-4043	5	34	such	such	ADJ
bibechana-4043	5	35	that	that	PRON
bibechana-4043	5	36	for	for	ADP
bibechana-4043	5	37	every	every	DET
bibechana-4043	5	38	k	k	PROPN
bibechana-4043	5	39	≥	≥	NOUN
bibechana-4043	5	40	ko	ko	NOUN
bibechana-4043	5	41	there	there	PRON
bibechana-4043	5	42	is	be	VERB
bibechana-4043	5	43	a	a	DET
bibechana-4043	5	44	p	p	NOUN
bibechana-4043	5	45	so	so	SCONJ
bibechana-4043	5	46	that	that	SCONJ
bibechana-4043	5	47	the	the	DET
bibechana-4043	5	48	seminorms	seminorm	NOUN
bibechana-4043	6	1	||	||	PROPN
bibechana-4043	7	1	||	||	CCONJ
bibechana-4043	8	1	ok	ok	INTJ
bibechana-4043	9	1	and	and	CCONJ
bibechana-4043	9	2	||	||	NOUN
bibechana-4043	9	3	||	||	PUNCT
bibechana-4043	10	1	k	k	NOUN
bibechana-4043	10	2	define	define	VERB
bibechana-4043	10	3	equivalent	equivalent	ADJ
bibechana-4043	10	4	topologies	topology	NOUN
bibechana-4043	10	5	on	on	ADP
bibechana-4043	10	6	up	up	ADP
bibechana-4043	10	7	.	.	PUNCT
bibechana-4043	11	1	it	it	PRON
bibechana-4043	11	2	is	be	AUX
bibechana-4043	11	3	easy	easy	ADJ
bibechana-4043	11	4	to	to	PART
bibechana-4043	11	5	see	see	VERB
bibechana-4043	11	6	that	that	SCONJ
bibechana-4043	11	7	in	in	ADP
bibechana-4043	11	8	this	this	DET
bibechana-4043	11	9	case	case	NOUN
bibechana-4043	11	10	||	||	NOUN
bibechana-4043	12	1	||	||	CCONJ
bibechana-4043	13	1	ok	ok	INTJ
bibechana-4043	13	2	is	be	AUX
bibechana-4043	13	3	in	in	ADP
bibechana-4043	13	4	fact	fact	NOUN
bibechana-4043	13	5	a	a	DET
bibechana-4043	13	6	norm	norm	NOUN
bibechana-4043	13	7	.	.	PUNCT
bibechana-4043	14	1	this	this	DET
bibechana-4043	14	2	class	class	NOUN
bibechana-4043	14	3	of	of	ADP
bibechana-4043	14	4	spaces	space	NOUN
bibechana-4043	14	5	appears	appear	VERB
bibechana-4043	14	6	in	in	ADP
bibechana-4043	14	7	investigations	investigation	NOUN
bibechana-4043	14	8	about	about	ADP
bibechana-4043	14	9	the	the	DET
bibechana-4043	14	10	structure	structure	NOUN
bibechana-4043	14	11	of	of	ADP
bibechana-4043	14	12	frechet	frechet	PROPN
bibechana-4043	14	13	spaces	space	NOUN
bibechana-4043	14	14	and	and	CCONJ
bibechana-4043	14	15	about	about	ADP
bibechana-4043	14	16	the	the	DET
bibechana-4043	14	17	behaviour	behaviour	NOUN
bibechana-4043	14	18	of	of	ADP
bibechana-4043	14	19	their	their	PRON
bibechana-4043	14	20	operators	operator	NOUN
bibechana-4043	14	21	as	as	ADP
bibechana-4043	14	22	a	a	DET
bibechana-4043	14	23	natural	natural	ADJ
bibechana-4043	14	24	counterpart	counterpart	NOUN
bibechana-4043	14	25	of	of	ADP
bibechana-4043	14	26	the	the	DET
bibechana-4043	14	27	class	class	NOUN
bibechana-4043	14	28	of	of	ADP
bibechana-4043	14	29	quasi	quasi	ADJ
bibechana-4043	14	30	-	-	ADJ
bibechana-4043	14	31	normable	normable	ADJ
bibechana-4043	14	32	spaces	space	NOUN
bibechana-4043	14	33	introduced	introduce	VERB
bibechana-4043	14	34	by	by	ADP
bibechana-4043	14	35	grothendieck	grothendieck	NOUN
bibechana-4043	14	36	[	[	X
bibechana-4043	14	37	1	1	NUM
bibechana-4043	14	38	]	]	PUNCT
bibechana-4043	14	39	.	.	PUNCT
bibechana-4043	15	1	while	while	SCONJ
bibechana-4043	15	2	the	the	DET
bibechana-4043	15	3	quasi	quasi	ADJ
bibechana-4043	15	4	-	-	ADJ
bibechana-4043	15	5	normable	normable	ADJ
bibechana-4043	15	6	frechet	frechet	NOUN
bibechana-4043	15	7	spaces	space	NOUN
bibechana-4043	15	8	e	e	X
bibechana-4043	15	9	are	be	AUX
bibechana-4043	15	10	those	those	PRON
bibechana-4043	15	11	which	which	PRON
bibechana-4043	15	12	admit	admit	VERB
bibechana-4043	15	13	an	an	DET
bibechana-4043	15	14	ω	ω	ADJ
bibechana-4043	15	15	-	-	PUNCT
bibechana-4043	15	16	type	type	NOUN
bibechana-4043	15	17	condition	condition	NOUN
bibechana-4043	15	18	[	[	X
bibechana-4043	15	19	2	2	NUM
bibechana-4043	15	20	]	]	PUNCT
bibechana-4043	15	21	and	and	CCONJ
bibechana-4043	15	22	for	for	ADP
bibechana-4043	15	23	which	which	PRON
bibechana-4043	15	24	there	there	PRON
bibechana-4043	15	25	exists	exist	VERB
bibechana-4043	15	26	a	a	DET
bibechana-4043	15	27	nontrivial	nontrivial	ADJ
bibechana-4043	15	28	frechet	frechet	NOUN
bibechana-4043	15	29	space	space	NOUN
bibechana-4043	15	30	f	f	PROPN
bibechana-4043	15	31	with	with	ADP
bibechana-4043	15	32	ext	ext	PROPN
bibechana-4043	15	33	1	1	NUM
bibechana-4043	15	34	(	(	PUNCT
bibechana-4043	15	35	f	f	NUM
bibechana-4043	15	36	,	,	PUNCT
bibechana-4043	15	37	e	e	NOUN
bibechana-4043	15	38	)	)	PUNCT
bibechana-4043	15	39	=	=	SYM
bibechana-4043	15	40	0	0	PUNCT
bibechana-4043	16	1	[	[	X
bibechana-4043	16	2	2	2	NUM
bibechana-4043	16	3	]	]	PUNCT
bibechana-4043	16	4	,	,	PUNCT
bibechana-4043	16	5	the	the	DET
bibechana-4043	16	6	asymptotically	asymptotically	ADV
bibechana-4043	16	7	normable	normable	ADJ
bibechana-4043	16	8	frechet	frechet	NOUN
bibechana-4043	16	9	spaces	space	NOUN
bibechana-4043	16	10	e	e	X
bibechana-4043	16	11	are	be	AUX
bibechana-4043	16	12	those	those	PRON
bibechana-4043	16	13	which	which	PRON
bibechana-4043	16	14	admit	admit	VERB
bibechana-4043	16	15	a	a	DET
bibechana-4043	16	16	dntype	dntype	ADJ
bibechana-4043	16	17	condition	condition	NOUN
bibechana-4043	16	18	[	[	X
bibechana-4043	16	19	3	3	X
bibechana-4043	16	20	]	]	PUNCT
bibechana-4043	16	21	and	and	CCONJ
bibechana-4043	16	22	for	for	ADP
bibechana-4043	16	23	which	which	PRON
bibechana-4043	16	24	thee	thee	NOUN
bibechana-4043	16	25	exists	exist	VERB
bibechana-4043	16	26	a	a	DET
bibechana-4043	16	27	nontrivial	nontrivial	ADJ
bibechana-4043	16	28	frechet	frechet	NOUN
bibechana-4043	16	29	space	space	NOUN
bibechana-4043	16	30	f	f	PROPN
bibechana-4043	16	31	with	with	ADP
bibechana-4043	16	32	ext	ext	PROPN
bibechana-4043	16	33	1	1	NUM
bibechana-4043	16	34	(	(	PUNCT
bibechana-4043	16	35	e	e	NOUN
bibechana-4043	16	36	,	,	PUNCT
bibechana-4043	16	37	f	f	X
bibechana-4043	16	38	)	)	PUNCT
bibechana-4043	16	39	=	=	SYM
bibechana-4043	16	40	0	0	X
bibechana-4043	16	41	.	.	PUNCT
bibechana-4043	16	42	nontrivial	nontrivial	NOUN
bibechana-4043	16	43	here	here	ADV
bibechana-4043	16	44	could	could	AUX
bibechana-4043	16	45	mean	mean	VERB
bibechana-4043	16	46	:	:	PUNCT
bibechana-4043	16	47	an	an	DET
bibechana-4043	16	48	infinite	infinite	ADJ
bibechana-4043	16	49	dimensional	dimensional	ADJ
bibechana-4043	16	50	nuclear	nuclear	ADJ
bibechana-4043	16	51	kothe	kothe	NOUN
bibechana-4043	16	52	space	space	NOUN
bibechana-4043	16	53	.	.	PUNCT
bibechana-4043	17	1	in	in	ADP
bibechana-4043	17	2	[	[	X
bibechana-4043	17	3	2	2	X
bibechana-4043	17	4	]	]	PUNCT
bibechana-4043	17	5	it	it	PRON
bibechana-4043	17	6	is	be	AUX
bibechana-4043	17	7	shown	show	VERB
bibechana-4043	17	8	that	that	SCONJ
bibechana-4043	17	9	the	the	DET
bibechana-4043	17	10	quasi	quasi	ADJ
bibechana-4043	17	11	-	-	ADJ
bibechana-4043	17	12	normable	normable	ADJ
bibechana-4043	17	13	spaces	space	NOUN
bibechana-4043	17	14	are	be	AUX
bibechana-4043	17	15	the	the	DET
bibechana-4043	17	16	quotient	quotient	NOUN
bibechana-4043	17	17	spaces	space	NOUN
bibechana-4043	17	18	of	of	ADP
bibechana-4043	17	19	standard	standard	ADJ
bibechana-4043	17	20	spaces	space	NOUN
bibechana-4043	17	21	of	of	ADP
bibechana-4043	17	22	the	the	DET
bibechana-4043	17	23	form	form	NOUN
bibechana-4043	17	24	:	:	PUNCT
bibechana-4043	18	1	for	for	ADP
bibechana-4043	18	2	allλ	allλ	NOUN
bibechana-4043	18	3			PROPN
bibechana-4043	18	4			NOUN
bibechana-4043	18	5	=	=	SYM
bibechana-4043	18	6	∈	∈	PROPN
bibechana-4043	18	7	=	=	PUNCT
bibechana-4043	19	1	<	<	X
bibechana-4043	19	2	+	+	X
bibechana-4043	19	3	∞	∞	VERB
bibechana-4043	19	4			PROPN
bibechana-4043	19	5			ADJ
bibechana-4043	19	6			NOUN
bibechana-4043	19	7	∑	∑	PROPN
bibechana-4043	19	8	j	j	PROPN
bibechana-4043	19	9	k	k	PROPN
bibechana-4043	19	10	n	n	PROPN
bibechana-4043	19	11	j	j	PROPN
bibechana-4043	19	12	j	j	PROPN
bibechana-4043	20	1	k	k	PROPN
bibechana-4043	20	2	j	j	PROPN
bibechana-4043	20	3	k	k	PROPN
bibechana-4043	20	4	j	j	PROPN
bibechana-4043	20	5	,	,	PUNCT
bibechana-4043	20	6	k(a	k(a	PROPN
bibechana-4043	20	7	,	,	PUNCT
bibechana-4043	20	8	e	e	NOUN
bibechana-4043	20	9	)	)	PUNCT
bibechana-4043	20	10	x	x	SYM
bibechana-4043	20	11	=(	=(	NOUN
bibechana-4043	20	12	x	x	SYM
bibechana-4043	20	13	)	)	PUNCT
bibechana-4043	21	1	e	e	X
bibechana-4043	21	2	||	||	NOUN
bibechana-4043	22	1	x	x	SYM
bibechana-4043	22	2	||	||	NOUN
bibechana-4043	22	3	||	||	NOUN
bibechana-4043	23	1	x	x	X
bibechana-4043	23	2	||	||	ADP
bibechana-4043	23	3	a	a	PRON
bibechana-4043	23	4	where	where	SCONJ
bibechana-4043	23	5	e	e	NOUN
bibechana-4043	23	6	is	be	AUX
bibechana-4043	23	7	a	a	DET
bibechana-4043	23	8	banach	banach	NOUN
bibechana-4043	23	9	space	space	NOUN
bibechana-4043	23	10	and	and	CCONJ
bibechana-4043	23	11	a	a	DET
bibechana-4043	23	12	=	=	X
bibechana-4043	23	13	(	(	PUNCT
bibechana-4043	23	14	aj	aj	PROPN
bibechana-4043	23	15	,	,	PUNCT
bibechana-4043	23	16	k	k	NOUN
bibechana-4043	23	17	)	)	PUNCT
bibechana-4043	23	18	a	a	DET
bibechana-4043	23	19	matrix	matrix	NOUN
bibechana-4043	23	20	with	with	ADP
bibechana-4043	23	21	o	o	NOUN
bibechana-4043	23	22	<	<	X
bibechana-4043	23	23	aj	aj	PROPN
bibechana-4043	23	24	,	,	PUNCT
bibechana-4043	23	25	k	k	PROPN
bibechana-4043	23	26	≤	≤	PROPN
bibechana-4043	23	27	aj	aj	PROPN
bibechana-4043	23	28	,	,	PUNCT
bibechana-4043	23	29	k+1	k+1	X
bibechana-4043	23	30	for	for	ADP
bibechana-4043	23	31	all	all	DET
bibechana-4043	23	32	k	k	PROPN
bibechana-4043	23	33	and	and	CCONJ
bibechana-4043	23	34	∗	∗	NOUN
bibechana-4043	23	35	corresponding	correspond	VERB
bibechana-4043	23	36	author	author	NOUN
bibechana-4043	23	37	:	:	PUNCT
bibechana-4043	23	38	nagendra	nagendra	PROPN
bibechana-4043	23	39	pd	pd	PROPN
bibechana-4043	23	40	.	.	PROPN
bibechana-4043	23	41	sah	sah	PROPN
bibechana-4043	23	42	,	,	PUNCT
bibechana-4043	23	43	department	department	NOUN
bibechana-4043	23	44	of	of	ADP
bibechana-4043	23	45	mathematics	mathematics	PROPN
bibechana-4043	23	46	,	,	PUNCT
bibechana-4043	23	47	m.m.a.m	m.m.a.m	PROPN
bibechana-4043	23	48	.	.	PUNCT
bibechana-4043	24	1	campus(tribhuvan	campus(tribhuvan	ADJ
bibechana-4043	24	2	university	university	NOUN
bibechana-4043	24	3	)	)	PUNCT
bibechana-4043	24	4	,	,	PUNCT
bibechana-4043	24	5	biratnagar	biratnagar	NOUN
bibechana-4043	24	6	,	,	PUNCT
bibechana-4043	24	7	nepal	nepal	PROPN
bibechana-4043	24	8	g.k	g.k	PROPN
bibechana-4043	24	9	.	.	PROPN
bibechana-4043	24	10	palei	palei	PROPN
bibechana-4043	24	11	and	and	CCONJ
bibechana-4043	24	12	n.p	n.p	PROPN
bibechana-4043	24	13	.	.	PROPN
bibechana-4043	24	14	sah	sah	PROPN
bibechana-4043	24	15	/	/	SYM
bibechana-4043	24	16	bibechana	bibechana	PROPN
bibechana-4043	24	17	7	7	NUM
bibechana-4043	24	18	(	(	PUNCT
bibechana-4043	24	19	2011	2011	NUM
bibechana-4043	24	20	)	)	PUNCT
bibechana-4043	24	21	39	39	NUM
bibechana-4043	24	22	-	-	SYM
bibechana-4043	24	23	43	43	NUM
bibechana-4043	24	24	:	:	PUNCT
bibechana-4043	24	25	bmhss	bmhss	NOUN
bibechana-4043	24	26	40	40	NUM
bibechana-4043	24	27	∞∑	∞∑	PROPN
bibechana-4043	24	28	j	j	PROPN
bibechana-4043	24	29	,	,	PUNCT
bibechana-4043	24	30	k	k	PROPN
bibechana-4043	24	31	j	j	PROPN
bibechana-4043	24	32	j	j	PROPN
bibechana-4043	24	33	,	,	PUNCT
bibechana-4043	24	34	k+1	k+1	X
bibechana-4043	24	35	a	a	DET
bibechana-4043	24	36	<	<	X
bibechana-4043	24	37	+	+	NOUN
bibechana-4043	24	38	a	a	PRON
bibechana-4043	24	39	we	we	PRON
bibechana-4043	24	40	can	can	AUX
bibechana-4043	24	41	show	show	VERB
bibechana-4043	24	42	that	that	SCONJ
bibechana-4043	24	43	the	the	DET
bibechana-4043	24	44	asymptotically	asymptotically	ADV
bibechana-4043	24	45	normable	normable	ADJ
bibechana-4043	24	46	spaces	space	NOUN
bibechana-4043	24	47	are	be	AUX
bibechana-4043	24	48	the	the	DET
bibechana-4043	24	49	subspaces	subspace	NOUN
bibechana-4043	24	50	of	of	ADP
bibechana-4043	24	51	these	these	DET
bibechana-4043	24	52	standard	standard	ADJ
bibechana-4043	24	53	spaces	space	NOUN
bibechana-4043	24	54	.	.	PUNCT
bibechana-4043	25	1	they	they	PRON
bibechana-4043	25	2	are	be	AUX
bibechana-4043	25	3	the	the	DET
bibechana-4043	25	4	smallest	small	ADJ
bibechana-4043	25	5	class	class	NOUN
bibechana-4043	25	6	of	of	ADP
bibechana-4043	25	7	frechet	frechet	PROPN
bibechana-4043	25	8	spaces	space	NOUN
bibechana-4043	25	9	which	which	PRON
bibechana-4043	25	10	contains	contain	VERB
bibechana-4043	25	11	the	the	DET
bibechana-4043	25	12	nuclear	nuclear	ADJ
bibechana-4043	25	13	kothe	kothe	NOUN
bibechana-4043	25	14	spaces	space	NOUN
bibechana-4043	25	15	with	with	ADP
bibechana-4043	25	16	continuous	continuous	ADJ
bibechana-4043	25	17	norm	norm	NOUN
bibechana-4043	25	18	,	,	PUNCT
bibechana-4043	25	19	the	the	DET
bibechana-4043	25	20	banach	banach	NOUN
bibechana-4043	25	21	spaces	space	NOUN
bibechana-4043	25	22	and	and	CCONJ
bibechana-4043	25	23	is	be	AUX
bibechana-4043	25	24	closed	close	VERB
bibechana-4043	25	25	under	under	ADP
bibechana-4043	25	26	ε	ε	PROPN
bibechana-4043	25	27	-	-	PUNCT
bibechana-4043	25	28	tensor	tensor	NOUN
bibechana-4043	25	29	products	product	NOUN
bibechana-4043	25	30	and	and	CCONJ
bibechana-4043	25	31	subspaces	subspace	NOUN
bibechana-4043	25	32	.	.	PUNCT
bibechana-4043	26	1	a.	a.	NOUN
bibechana-4043	26	2	we	we	PRON
bibechana-4043	26	3	use	use	VERB
bibechana-4043	26	4	the	the	DET
bibechana-4043	26	5	standard	standard	ADJ
bibechana-4043	26	6	terminology	terminology	NOUN
bibechana-4043	26	7	of	of	ADP
bibechana-4043	26	8	the	the	DET
bibechana-4043	26	9	theory	theory	NOUN
bibechana-4043	26	10	of	of	ADP
bibechana-4043	26	11	locally	locally	ADV
bibechana-4043	26	12	convex	convex	ADJ
bibechana-4043	26	13	spaces	space	NOUN
bibechana-4043	26	14	as	as	ADP
bibechana-4043	26	15	in	in	ADP
bibechana-4043	26	16	[	[	X
bibechana-4043	26	17	4	4	NUM
bibechana-4043	26	18	]	]	PUNCT
bibechana-4043	26	19	.	.	PUNCT
bibechana-4043	27	1	for	for	ADP
bibechana-4043	27	2	the	the	DET
bibechana-4043	27	3	theory	theory	NOUN
bibechana-4043	27	4	of	of	ADP
bibechana-4043	27	5	ext	ext	PROPN
bibechana-4043	27	6	&	&	CCONJ
bibechana-4043	27	7	the	the	DET
bibechana-4043	27	8	splitting	splitting	NOUN
bibechana-4043	27	9	conditions	condition	NOUN
bibechana-4043	27	10	we	we	PRON
bibechana-4043	27	11	refer	refer	VERB
bibechana-4043	27	12	to	to	ADP
bibechana-4043	27	13	[	[	X
bibechana-4043	27	14	3	3	NUM
bibechana-4043	27	15	]	]	PUNCT
bibechana-4043	27	16	&	&	CCONJ
bibechana-4043	27	17	[	[	X
bibechana-4043	27	18	5	5	NUM
bibechana-4043	27	19	]	]	PUNCT
bibechana-4043	27	20	.	.	PUNCT
bibechana-4043	28	1	by	by	ADP
bibechana-4043	28	2	(	(	PUNCT
bibechana-4043	28	3	||	||	PROPN
bibechana-4043	28	4	||k	||k	PROPN
bibechana-4043	28	5	)	)	PUNCT
bibechana-4043	28	6	we	we	PRON
bibechana-4043	28	7	always	always	ADV
bibechana-4043	28	8	denote	denote	VERB
bibechana-4043	28	9	an	an	DET
bibechana-4043	28	10	increasing	increase	VERB
bibechana-4043	28	11	sequence	sequence	NOUN
bibechana-4043	28	12	of	of	ADP
bibechana-4043	28	13	seminorms	seminorm	NOUN
bibechana-4043	28	14	defining	define	VERB
bibechana-4043	28	15	the	the	DET
bibechana-4043	28	16	topology	topology	NOUN
bibechana-4043	28	17	of	of	ADP
bibechana-4043	28	18	a	a	DET
bibechana-4043	28	19	frechet	frechet	NOUN
bibechana-4043	28	20	space	space	NOUN
bibechana-4043	28	21	e	e	NOUN
bibechana-4043	28	22	and	and	CCONJ
bibechana-4043	28	23	uk	uk	PROPN
bibechana-4043	28	24	=	=	SYM
bibechana-4043	28	25	{	{	PUNCT
bibechana-4043	28	26	x	x	PUNCT
bibechana-4043	28	27	∈	∈	PROPN
bibechana-4043	28	28	e	e	NOUN
bibechana-4043	28	29	:	:	PUNCT
bibechana-4043	28	30	||x||k	||x||k	NOUN
bibechana-4043	28	31	≤	≤	NUM
bibechana-4043	28	32	1	1	NUM
bibechana-4043	28	33	}	}	PUNCT
bibechana-4043	28	34	.	.	PUNCT
bibechana-4043	29	1	in	in	ADP
bibechana-4043	29	2	this	this	DET
bibechana-4043	29	3	section	section	NOUN
bibechana-4043	29	4	we	we	PRON
bibechana-4043	29	5	collect	collect	VERB
bibechana-4043	29	6	some	some	DET
bibechana-4043	29	7	simple	simple	ADJ
bibechana-4043	29	8	results	result	NOUN
bibechana-4043	29	9	in	in	ADP
bibechana-4043	29	10	order	order	NOUN
bibechana-4043	29	11	to	to	PART
bibechana-4043	29	12	see	see	VERB
bibechana-4043	29	13	the	the	DET
bibechana-4043	29	14	concept	concept	NOUN
bibechana-4043	29	15	of	of	ADP
bibechana-4043	29	16	asymptotic	asymptotic	ADJ
bibechana-4043	29	17	normability	normability	NOUN
bibechana-4043	29	18	in	in	ADP
bibechana-4043	29	19	a	a	DET
bibechana-4043	29	20	proper	proper	ADJ
bibechana-4043	29	21	perspective	perspective	NOUN
bibechana-4043	29	22	.	.	PUNCT
bibechana-4043	30	1	let	let	VERB
bibechana-4043	30	2	ϕ	ϕ	NOUN
bibechana-4043	30	3	:	:	PUNCT
bibechana-4043	30	4	(	(	PUNCT
bibechana-4043	30	5	0	0	NUM
bibechana-4043	30	6	,	,	PUNCT
bibechana-4043	30	7	∞	∞	PROPN
bibechana-4043	30	8	)	)	PUNCT
bibechana-4043	30	9	→	→	SYM
bibechana-4043	30	10	(	(	PUNCT
bibechana-4043	30	11	0	0	NUM
bibechana-4043	30	12	,	,	PUNCT
bibechana-4043	30	13	∞	∞	PROPN
bibechana-4043	30	14	,	,	PUNCT
bibechana-4043	30	15	be	be	AUX
bibechana-4043	30	16	a	a	DET
bibechana-4043	30	17	strictly	strictly	ADV
bibechana-4043	30	18	increasing	increase	VERB
bibechana-4043	30	19	function	function	NOUN
bibechana-4043	30	20	.	.	PUNCT
bibechana-4043	31	1	we	we	PRON
bibechana-4043	31	2	say	say	VERB
bibechana-4043	31	3	e	e	NOUN
bibechana-4043	31	4	satisfies	satisfie	NOUN
bibechana-4043	31	5	(	(	PUNCT
bibechana-4043	31	6	dnϕ	dnϕ	PROPN
bibechana-4043	31	7	)	)	PUNCT
bibechana-4043	31	8	if	if	SCONJ
bibechana-4043	31	9	we	we	PRON
bibechana-4043	31	10	have	have	VERB
bibechana-4043	31	11	a	a	DET
bibechana-4043	31	12	ko	ko	NOUN
bibechana-4043	31	13	with	with	ADP
bibechana-4043	31	14	the	the	DET
bibechana-4043	31	15	property	property	NOUN
bibechana-4043	31	16	that	that	PRON
bibechana-4043	31	17	for	for	ADP
bibechana-4043	31	18	every	every	DET
bibechana-4043	31	19	k	k	NOUN
bibechana-4043	31	20	there	there	PRON
bibechana-4043	31	21	is	be	VERB
bibechana-4043	31	22	a	a	DET
bibechana-4043	31	23	p	p	NOUN
bibechana-4043	31	24	and	and	CCONJ
bibechana-4043	31	25	c	c	NOUN
bibechana-4043	31	26	>	>	PUNCT
bibechana-4043	31	27	0	0	PUNCT
bibechana-4043	32	1	so	so	SCONJ
bibechana-4043	32	2	that	that	SCONJ
bibechana-4043	32	3	the	the	DET
bibechana-4043	32	4	inequality	inequality	NOUN
bibechana-4043	32	5	||x||k	||x||k	PROPN
bibechana-4043	32	6	≤	≤	NUM
bibechana-4043	32	7	cϕ(γ	cϕ(γ	NOUN
bibechana-4043	32	8	)	)	PUNCT
bibechana-4043	32	9	ko	ko	PROPN
bibechana-4043	32	10	||	||	PROPN
bibechana-4043	33	1	x	x	PUNCT
bibechana-4043	33	2	||	||	NOUN
bibechana-4043	34	1	+	+	CCONJ
bibechana-4043	34	2	1	1	NUM
bibechana-4043	34	3	γ	γ	PRON
bibechana-4043	34	4	||x||p	||x||p	PROPN
bibechana-4043	34	5	holds	hold	VERB
bibechana-4043	34	6	for	for	ADP
bibechana-4043	34	7	every	every	DET
bibechana-4043	34	8	x	x	SYM
bibechana-4043	34	9	∈	∈	PROPN
bibechana-4043	34	10	e	e	NOUN
bibechana-4043	34	11	and	and	CCONJ
bibechana-4043	34	12	γ	γ	X
bibechana-4043	34	13	>	>	X
bibechana-4043	34	14	0	0	PUNCT
bibechana-4043	35	1	[	[	X
bibechana-4043	35	2	3	3	NUM
bibechana-4043	35	3	]	]	PUNCT
bibechana-4043	35	4	.	.	PUNCT
bibechana-4043	36	1	in	in	ADP
bibechana-4043	36	2	the	the	DET
bibechana-4043	36	3	case	case	NOUN
bibechana-4043	36	4	ϕ(γ	ϕ(γ	X
bibechana-4043	36	5	)	)	PUNCT
bibechana-4043	36	6	=	=	SYM
bibechana-4043	37	1	γ	γ	X
bibechana-4043	37	2	this	this	DET
bibechana-4043	37	3	condition	condition	NOUN
bibechana-4043	37	4	,	,	PUNCT
bibechana-4043	37	5	denoted	denote	VERB
bibechana-4043	37	6	by	by	ADP
bibechana-4043	37	7	(	(	PUNCT
bibechana-4043	37	8	dn	dn	PROPN
bibechana-4043	37	9	)	)	PUNCT
bibechana-4043	37	10	,	,	PUNCT
bibechana-4043	37	11	was	be	AUX
bibechana-4043	37	12	introduced	introduce	VERB
bibechana-4043	37	13	by	by	ADP
bibechana-4043	37	14	d.	d.	PROPN
bibechana-4043	37	15	vog	vog	PROPN
bibechana-4043	37	16	t	t	PROPN
bibechana-4043	37	17	in	in	ADP
bibechana-4043	37	18	[	[	X
bibechana-4043	37	19	3	3	NUM
bibechana-4043	37	20	]	]	PUNCT
bibechana-4043	37	21	to	to	PART
bibechana-4043	37	22	characterize	characterize	VERB
bibechana-4043	37	23	initially	initially	ADV
bibechana-4043	37	24	the	the	DET
bibechana-4043	37	25	subspaces	subspace	NOUN
bibechana-4043	37	26	of	of	ADP
bibechana-4043	37	27	the	the	DET
bibechana-4043	37	28	space	space	NOUN
bibechana-4043	37	29	(	(	PUNCT
bibechana-4043	37	30	s	s	NOUN
bibechana-4043	37	31	)	)	PUNCT
bibechana-4043	37	32	of	of	ADP
bibechana-4043	37	33	rapidly	rapidly	ADV
bibechana-4043	37	34	decreasing	decrease	VERB
bibechana-4043	37	35	sequences	sequence	NOUN
bibechana-4043	37	36	.	.	PUNCT
bibechana-4043	38	1	subsequently	subsequently	ADV
bibechana-4043	38	2	it	it	PRON
bibechana-4043	38	3	was	be	AUX
bibechana-4043	38	4	proved	prove	VERB
bibechana-4043	38	5	by	by	ADP
bibechana-4043	38	6	him	he	PRON
bibechana-4043	38	7	in	in	ADP
bibechana-4043	38	8	[	[	X
bibechana-4043	38	9	5	5	NUM
bibechana-4043	38	10	]	]	PUNCT
bibechana-4043	38	11	that	that	SCONJ
bibechana-4043	38	12	every	every	DET
bibechana-4043	38	13	space	space	NOUN
bibechana-4043	38	14	of	of	ADP
bibechana-4043	38	15	type	type	NOUN
bibechana-4043	38	16	(	(	PUNCT
bibechana-4043	38	17	dn	dn	NOUN
bibechana-4043	38	18	)	)	PUNCT
bibechana-4043	38	19	is	be	AUX
bibechana-4043	38	20	isomorphic	isomorphic	ADJ
bibechana-4043	38	21	to	to	ADP
bibechana-4043	38	22	a	a	DET
bibechana-4043	38	23	subspace	subspace	NOUN
bibechana-4043	38	24	of	of	ADP
bibechana-4043	38	25	l∞(i)⊗π	l∞(i)⊗π	PROPN
bibechana-4043	38	26	(	(	PUNCT
bibechana-4043	38	27	s	s	NOUN
bibechana-4043	38	28	)	)	PUNCT
bibechana-4043	38	29	for	for	ADP
bibechana-4043	38	30	some	some	DET
bibechana-4043	38	31	index	index	NOUN
bibechana-4043	38	32	set	set	VERB
bibechana-4043	38	33	i.	i.	NOUN
bibechana-4043	38	34	consider	consider	VERB
bibechana-4043	38	35	also	also	ADV
bibechana-4043	38	36	the	the	DET
bibechana-4043	38	37	following	follow	VERB
bibechana-4043	38	38	condition	condition	NOUN
bibechana-4043	38	39	:	:	PUNCT
bibechana-4043	38	40	there	there	PRON
bibechana-4043	38	41	is	be	VERB
bibechana-4043	38	42	a	a	DET
bibechana-4043	38	43	ko	ko	NOUN
bibechana-4043	38	44	such	such	ADJ
bibechana-4043	38	45	that	that	PRON
bibechana-4043	38	46	for	for	ADP
bibechana-4043	38	47	every	every	DET
bibechana-4043	38	48	k	k	PROPN
bibechana-4043	38	49	≥	≥	PUNCT
bibechana-4043	38	50	ko	ko	PROPN
bibechana-4043	38	51	we	we	PRON
bibechana-4043	38	52	have	have	VERB
bibechana-4043	38	53	p	p	X
bibechana-4043	38	54	≥	≥	NOUN
bibechana-4043	38	55	ko	ko	VERB
bibechana-4043	38	56	with	with	ADP
bibechana-4043	38	57	the	the	DET
bibechana-4043	38	58	following	follow	VERB
bibechana-4043	38	59	property	property	NOUN
bibechana-4043	38	60	:	:	PUNCT
bibechana-4043	38	61	every	every	DET
bibechana-4043	38	62	sequence	sequence	NOUN
bibechana-4043	38	63	in	in	ADP
bibechana-4043	38	64	e	e	NOUN
bibechana-4043	38	65	which	which	PRON
bibechana-4043	38	66	is	be	AUX
bibechana-4043	38	67	cauchy	cauchy	ADJ
bibechana-4043	38	68	with	with	ADP
bibechana-4043	38	69	respect	respect	NOUN
bibechana-4043	38	70	to	to	ADP
bibechana-4043	38	71	||	||	NOUN
bibechana-4043	38	72	||p	||p	PROPN
bibechana-4043	38	73	and	and	CCONJ
bibechana-4043	38	74	converges	converge	VERB
bibechana-4043	38	75	to	to	ADP
bibechana-4043	38	76	0	0	NUM
bibechana-4043	38	77	with	with	ADP
bibechana-4043	38	78	respect	respect	NOUN
bibechana-4043	38	79	to	to	ADP
bibechana-4043	38	80	||	||	PROPN
bibechana-4043	38	81	||	||	PUNCT
bibechana-4043	39	1	ok	ok	INTJ
bibechana-4043	39	2	even	even	ADV
bibechana-4043	39	3	converges	converge	VERB
bibechana-4043	39	4	to	to	ADP
bibechana-4043	39	5	0	0	NUM
bibechana-4043	39	6	with	with	ADP
bibechana-4043	39	7	respect	respect	NOUN
bibechana-4043	39	8	to	to	ADP
bibechana-4043	39	9	||	||	NOUN
bibechana-4043	39	10	||k	||k	PROPN
bibechana-4043	39	11	.	.	PUNCT
bibechana-4043	40	1	proposition	proposition	NOUN
bibechana-4043	40	2	1.1	1.1	NUM
bibechana-4043	40	3	every	every	DET
bibechana-4043	40	4	asymptotically	asymptotically	ADV
bibechana-4043	40	5	normable	normable	ADJ
bibechana-4043	40	6	frechet	frechet	NOUN
bibechana-4043	40	7	space	space	NOUN
bibechana-4043	40	8	is	be	AUX
bibechana-4043	40	9	countably	countably	ADV
bibechana-4043	40	10	normable	normable	ADJ
bibechana-4043	40	11	.	.	PUNCT
bibechana-4043	41	1	we	we	PRON
bibechana-4043	41	2	can	can	AUX
bibechana-4043	41	3	obtain	obtain	VERB
bibechana-4043	41	4	the	the	DET
bibechana-4043	41	5	proof	proof	NOUN
bibechana-4043	41	6	from	from	ADP
bibechana-4043	41	7	[	[	X
bibechana-4043	41	8	1	1	NUM
bibechana-4043	41	9	]	]	PUNCT
bibechana-4043	41	10	,	,	PUNCT
bibechana-4043	41	11	page	page	NOUN
bibechana-4043	41	12	176	176	NUM
bibechana-4043	41	13	.	.	PUNCT
bibechana-4043	42	1	proposition	proposition	NOUN
bibechana-4043	42	2	1.2	1.2	NUM
bibechana-4043	42	3	the	the	DET
bibechana-4043	42	4	following	following	NOUN
bibechana-4043	42	5	are	be	AUX
bibechana-4043	42	6	equivalent	equivalent	ADJ
bibechana-4043	42	7	for	for	ADP
bibechana-4043	42	8	a	a	DET
bibechana-4043	42	9	frechet	frechet	NOUN
bibechana-4043	42	10	space	space	NOUN
bibechana-4043	42	11	e	e	NOUN
bibechana-4043	42	12	:	:	PUNCT
bibechana-4043	42	13	(	(	PUNCT
bibechana-4043	42	14	1	1	X
bibechana-4043	42	15	)	)	PUNCT
bibechana-4043	42	16	e	e	NOUN
bibechana-4043	42	17	is	be	AUX
bibechana-4043	42	18	asymptotically	asymptotically	ADV
bibechana-4043	42	19	normable	normable	ADJ
bibechana-4043	42	20	.	.	PUNCT
bibechana-4043	43	1	(	(	PUNCT
bibechana-4043	43	2	2	2	X
bibechana-4043	43	3	)	)	PUNCT
bibechana-4043	43	4	there	there	PRON
bibechana-4043	43	5	is	be	VERB
bibechana-4043	43	6	ko	ko	PROPN
bibechana-4043	43	7	such	such	ADJ
bibechana-4043	43	8	that	that	PRON
bibechana-4043	43	9	for	for	ADP
bibechana-4043	43	10	every	every	DET
bibechana-4043	43	11	k	k	NOUN
bibechana-4043	43	12	there	there	PRON
bibechana-4043	43	13	is	be	VERB
bibechana-4043	43	14	a	a	DET
bibechana-4043	43	15	p	p	NOUN
bibechana-4043	43	16	such	such	ADJ
bibechana-4043	43	17	that	that	PRON
bibechana-4043	43	18	for	for	ADP
bibechana-4043	43	19	every	every	DET
bibechana-4043	43	20	ε	ε	PROPN
bibechana-4043	43	21	>	>	X
bibechana-4043	43	22	0	0	NUM
bibechana-4043	44	1	we	we	PRON
bibechana-4043	44	2	can	can	AUX
bibechana-4043	44	3	choose	choose	VERB
bibechana-4043	44	4	m	m	PROPN
bibechana-4043	44	5	>	>	X
bibechana-4043	44	6	0	0	PUNCT
bibechana-4043	44	7	with	with	ADP
bibechana-4043	44	8	||	||	PROPN
bibechana-4043	44	9	||k	||k	PROPN
bibechana-4043	44	10	≤	≤	PUNCT
bibechana-4043	44	11	m	m	VERB
bibechana-4043	44	12	||	||	NOUN
bibechana-4043	45	1	||	||	PROPN
bibechana-4043	46	1	ok	ok	INTJ
bibechana-4043	46	2	+	+	CCONJ
bibechana-4043	46	3	ε||	ε||	ADP
bibechana-4043	46	4	||p	||p	NOUN
bibechana-4043	46	5	.	.	PUNCT
bibechana-4043	47	1	(	(	PUNCT
bibechana-4043	47	2	3	3	X
bibechana-4043	47	3	)	)	PUNCT
bibechana-4043	47	4	e	e	NOUN
bibechana-4043	47	5	has	have	VERB
bibechana-4043	47	6	property	property	NOUN
bibechana-4043	47	7	(	(	PUNCT
bibechana-4043	47	8	dnϕ	dnϕ	PROPN
bibechana-4043	47	9	)	)	PUNCT
bibechana-4043	47	10	for	for	ADP
bibechana-4043	47	11	some	some	DET
bibechana-4043	47	12	ϕ.	ϕ.	ADJ
bibechana-4043	47	13	proposition	proposition	NOUN
bibechana-4043	47	14	1.3	1.3	NUM
bibechana-4043	47	15	a	a	DET
bibechana-4043	47	16	frechet	frechet	NOUN
bibechana-4043	47	17	-	-	PUNCT
bibechana-4043	47	18	schwartz	schwartz	PROPN
bibechana-4043	47	19	space	space	NOUN
bibechana-4043	47	20	is	be	AUX
bibechana-4043	47	21	asymptotically	asymptotically	ADV
bibechana-4043	47	22	normable	normable	ADJ
bibechana-4043	47	23	if	if	SCONJ
bibechana-4043	47	24	and	and	CCONJ
bibechana-4043	47	25	only	only	ADV
bibechana-4043	47	26	if	if	SCONJ
bibechana-4043	47	27	it	it	PRON
bibechana-4043	47	28	is	be	AUX
bibechana-4043	47	29	countably	countably	ADV
bibechana-4043	47	30	normable	normable	ADJ
bibechana-4043	47	31	.	.	PUNCT
bibechana-4043	48	1	the	the	DET
bibechana-4043	48	2	question	question	NOUN
bibechana-4043	48	3	whether	whether	SCONJ
bibechana-4043	48	4	these	these	DET
bibechana-4043	48	5	classes	class	NOUN
bibechana-4043	48	6	coincide	coincide	VERB
bibechana-4043	48	7	in	in	ADP
bibechana-4043	48	8	general	general	ADJ
bibechana-4043	48	9	we	we	PRON
bibechana-4043	48	10	shall	shall	AUX
bibechana-4043	48	11	answer	answer	VERB
bibechana-4043	48	12	in	in	ADP
bibechana-4043	48	13	the	the	DET
bibechana-4043	48	14	negative	negative	ADJ
bibechana-4043	48	15	in	in	ADP
bibechana-4043	48	16	the	the	DET
bibechana-4043	48	17	next	next	ADJ
bibechana-4043	48	18	section	section	NOUN
bibechana-4043	48	19	.	.	PUNCT
bibechana-4043	49	1	before	before	SCONJ
bibechana-4043	49	2	we	we	PRON
bibechana-4043	49	3	do	do	VERB
bibechana-4043	49	4	this	this	PRON
bibechana-4043	49	5	let	let	VERB
bibechana-4043	49	6	us	we	PRON
bibechana-4043	49	7	recall	recall	VERB
bibechana-4043	49	8	that	that	SCONJ
bibechana-4043	49	9	a	a	DET
bibechana-4043	49	10	frechet	frechet	NOUN
bibechana-4043	49	11	space	space	NOUN
bibechana-4043	49	12	e	e	NOUN
bibechana-4043	49	13	is	be	AUX
bibechana-4043	49	14	called	call	VERB
bibechana-4043	49	15	locally	locally	ADV
bibechana-4043	49	16	normable	normable	ADJ
bibechana-4043	49	17	[	[	X
bibechana-4043	49	18	6	6	NUM
bibechana-4043	49	19	]	]	PUNCT
bibechana-4043	49	20	if	if	SCONJ
bibechana-4043	49	21	there	there	PRON
bibechana-4043	49	22	is	be	VERB
bibechana-4043	49	23	a	a	DET
bibechana-4043	49	24	ko	ko	NOUN
bibechana-4043	49	25	such	such	ADJ
bibechana-4043	49	26	that	that	SCONJ
bibechana-4043	49	27	on	on	ADP
bibechana-4043	49	28	every	every	DET
bibechana-4043	49	29	bounded	bound	VERB
bibechana-4043	49	30	set	set	NOUN
bibechana-4043	49	31	b	b	PROPN
bibechana-4043	49	32	the	the	DET
bibechana-4043	49	33	topologies	topology	NOUN
bibechana-4043	49	34	induced	induce	VERB
bibechana-4043	49	35	by	by	ADP
bibechana-4043	49	36	e	e	NOUN
bibechana-4043	49	37	and	and	CCONJ
bibechana-4043	49	38	by	by	ADP
bibechana-4043	49	39	||	||	PROPN
bibechana-4043	49	40	||	||	CCONJ
bibechana-4043	49	41	ok	ok	ADJ
bibechana-4043	49	42	coincide	coincide	NOUN
bibechana-4043	49	43	.	.	PUNCT
bibechana-4043	50	1	obviously	obviously	ADV
bibechana-4043	50	2	every	every	DET
bibechana-4043	50	3	asymptotically	asymptotically	ADV
bibechana-4043	50	4	normable	normable	ADJ
bibechana-4043	50	5	space	space	NOUN
bibechana-4043	50	6	is	be	AUX
bibechana-4043	50	7	locally	locally	ADV
bibechana-4043	50	8	normable	normable	ADJ
bibechana-4043	50	9	.	.	PUNCT
bibechana-4043	51	1	on	on	ADP
bibechana-4043	51	2	the	the	DET
bibechana-4043	51	3	other	other	ADJ
bibechana-4043	51	4	hand	hand	NOUN
bibechana-4043	51	5	every	every	DET
bibechana-4043	51	6	frechet	frechet	PROPN
bibechana-4043	51	7	-	-	PUNCT
bibechana-4043	51	8	montel	montel	PROPN
bibechana-4043	51	9	space	space	NOUN
bibechana-4043	51	10	admitting	admit	VERB
bibechana-4043	51	11	a	a	DET
bibechana-4043	51	12	continuous	continuous	ADJ
bibechana-4043	51	13	norm	norm	NOUN
bibechana-4043	51	14	is	be	AUX
bibechana-4043	51	15	locally	locally	ADV
bibechana-4043	51	16	normable	normable	ADJ
bibechana-4043	51	17	.	.	PUNCT
bibechana-4043	52	1	hence	hence	ADV
bibechana-4043	52	2	,	,	PUNCT
bibechana-4043	52	3	in	in	ADP
bibechana-4043	52	4	view	view	NOUN
bibechana-4043	52	5	of	of	ADP
bibechana-4043	52	6	proposition	proposition	NOUN
bibechana-4043	52	7	1.3	1.3	NUM
bibechana-4043	52	8	,	,	PUNCT
bibechana-4043	52	9	every	every	DET
bibechana-4043	52	10	frechet	frechet	NOUN
bibechana-4043	52	11	-	-	PUNCT
bibechana-4043	52	12	schwartz	schwartz	PROPN
bibechana-4043	52	13	space	space	NOUN
bibechana-4043	52	14	admitting	admit	VERB
bibechana-4043	52	15	a	a	DET
bibechana-4043	52	16	continuous	continuous	ADJ
bibechana-4043	52	17	norm	norm	NOUN
bibechana-4043	52	18	but	but	CCONJ
bibechana-4043	52	19	not	not	PART
bibechana-4043	52	20	countably	countably	ADV
bibechana-4043	52	21	normable	normable	ADJ
bibechana-4043	52	22	[	[	X
bibechana-4043	52	23	7	7	NUM
bibechana-4043	52	24	]	]	PUNCT
bibechana-4043	52	25	,	,	PUNCT
bibechana-4043	52	26	gives	give	VERB
bibechana-4043	52	27	an	an	DET
bibechana-4043	52	28	example	example	NOUN
bibechana-4043	52	29	of	of	ADP
bibechana-4043	52	30	a	a	DET
bibechana-4043	52	31	locally	locally	ADV
bibechana-4043	52	32	normable	normable	ADJ
bibechana-4043	52	33	space	space	NOUN
bibechana-4043	52	34	which	which	PRON
bibechana-4043	52	35	is	be	AUX
bibechana-4043	52	36	not	not	PART
bibechana-4043	52	37	asymptotically	asymptotically	ADV
bibechana-4043	52	38	normable	normable	ADJ
bibechana-4043	52	39	(	(	PUNCT
bibechana-4043	52	40	see	see	VERB
bibechana-4043	52	41	also	also	ADV
bibechana-4043	52	42	section	section	NOUN
bibechana-4043	52	43	2	2	NUM
bibechana-4043	52	44	)	)	PUNCT
bibechana-4043	52	45	.	.	PUNCT
bibechana-4043	53	1	b.	b.	PROPN
bibechana-4043	54	1	in	in	ADP
bibechana-4043	54	2	this	this	DET
bibechana-4043	54	3	section	section	NOUN
bibechana-4043	54	4	we	we	PRON
bibechana-4043	54	5	shall	shall	AUX
bibechana-4043	54	6	consider	consider	VERB
bibechana-4043	54	7	kothe	kothe	NOUN
bibechana-4043	54	8	sequence	sequence	NOUN
bibechana-4043	54	9	spaces	space	NOUN
bibechana-4043	54	10	.	.	PUNCT
bibechana-4043	55	1	our	our	PRON
bibechana-4043	55	2	main	main	ADJ
bibechana-4043	55	3	aim	aim	NOUN
bibechana-4043	55	4	will	will	AUX
bibechana-4043	55	5	be	be	AUX
bibechana-4043	55	6	to	to	PART
bibechana-4043	55	7	construct	construct	VERB
bibechana-4043	55	8	an	an	DET
bibechana-4043	55	9	example	example	NOUN
bibechana-4043	55	10	of	of	ADP
bibechana-4043	55	11	a	a	DET
bibechana-4043	55	12	kothe	kothe	ADJ
bibechana-4043	55	13	space	space	NOUN
bibechana-4043	55	14	λ	λ	NOUN
bibechana-4043	55	15	(	(	PUNCT
bibechana-4043	55	16	b	b	NOUN
bibechana-4043	55	17	)	)	PUNCT
bibechana-4043	55	18	which	which	PRON
bibechana-4043	55	19	is	be	AUX
bibechana-4043	55	20	montel	montel	PROPN
bibechana-4043	55	21	,	,	PUNCT
bibechana-4043	55	22	admits	admit	VERB
bibechana-4043	55	23	a	a	DET
bibechana-4043	55	24	continuous	continuous	ADJ
bibechana-4043	55	25	norm	norm	NOUN
bibechana-4043	55	26	,	,	PUNCT
bibechana-4043	55	27	but	but	CCONJ
bibechana-4043	55	28	still	still	ADV
bibechana-4043	55	29	is	be	AUX
bibechana-4043	55	30	not	not	PART
bibechana-4043	55	31	asymptotically	asymptotically	ADV
bibechana-4043	55	32	normable	normable	ADJ
bibechana-4043	55	33	.	.	PUNCT
bibechana-4043	56	1	in	in	ADP
bibechana-4043	56	2	particular	particular	ADJ
bibechana-4043	56	3	,	,	PUNCT
bibechana-4043	56	4	λ	λ	PROPN
bibechana-4043	56	5	(	(	PUNCT
bibechana-4043	56	6	b	b	NOUN
bibechana-4043	56	7	)	)	PUNCT
bibechana-4043	56	8	will	will	AUX
bibechana-4043	56	9	be	be	AUX
bibechana-4043	56	10	an	an	DET
bibechana-4043	56	11	example	example	NOUN
bibechana-4043	56	12	of	of	ADP
bibechana-4043	56	13	a	a	DET
bibechana-4043	56	14	locally	locally	ADV
bibechana-4043	56	15	normable	normable	ADJ
bibechana-4043	56	16	kothe	kothe	NOUN
bibechana-4043	56	17	space	space	NOUN
bibechana-4043	56	18	which	which	PRON
bibechana-4043	56	19	is	be	AUX
bibechana-4043	56	20	not	not	PART
bibechana-4043	56	21	asymptotically	asymptotically	ADV
bibechana-4043	56	22	normable	normable	ADJ
bibechana-4043	56	23	.	.	PUNCT
bibechana-4043	57	1	by	by	ADP
bibechana-4043	57	2	proposition	proposition	NOUN
bibechana-4043	57	3	1.3	1.3	NUM
bibechana-4043	57	4	,	,	PUNCT
bibechana-4043	57	5	λ	λ	PROPN
bibechana-4043	57	6	(	(	PUNCT
bibechana-4043	57	7	b	b	NOUN
bibechana-4043	57	8	)	)	PUNCT
bibechana-4043	57	9	can	can	AUX
bibechana-4043	57	10	not	not	PART
bibechana-4043	57	11	be	be	AUX
bibechana-4043	57	12	a	a	DET
bibechana-4043	57	13	schwartz	schwartz	NOUN
bibechana-4043	57	14	space	space	NOUN
bibechana-4043	57	15	.	.	PUNCT
bibechana-4043	58	1	in	in	ADP
bibechana-4043	58	2	this	this	DET
bibechana-4043	58	3	context	context	NOUN
bibechana-4043	58	4	we	we	PRON
bibechana-4043	58	5	should	should	AUX
bibechana-4043	58	6	like	like	VERB
bibechana-4043	58	7	to	to	PART
bibechana-4043	58	8	mention	mention	VERB
bibechana-4043	58	9	that	that	SCONJ
bibechana-4043	58	10	the	the	DET
bibechana-4043	58	11	well	well	ADV
bibechana-4043	58	12	-	-	PUNCT
bibechana-4043	58	13	known	know	VERB
bibechana-4043	58	14	example	example	NOUN
bibechana-4043	58	15	constructed	construct	VERB
bibechana-4043	58	16	by	by	ADP
bibechana-4043	58	17	kothe	kothe	NOUN
bibechana-4043	58	18	in	in	ADP
bibechana-4043	58	19	[	[	X
bibechana-4043	58	20	4	4	NUM
bibechana-4043	58	21	]	]	PUNCT
bibechana-4043	58	22	of	of	ADP
bibechana-4043	58	23	a	a	DET
bibechana-4043	58	24	montel	montel	PROPN
bibechana-4043	58	25	space	space	NOUN
bibechana-4043	58	26	which	which	PRON
bibechana-4043	58	27	is	be	AUX
bibechana-4043	58	28	not	not	PART
bibechana-4043	58	29	∧	∧	PROPN
bibechana-4043	58	30	g.k	g.k	PROPN
bibechana-4043	58	31	.	.	PROPN
bibechana-4043	58	32	palei	palei	PROPN
bibechana-4043	58	33	and	and	CCONJ
bibechana-4043	58	34	n.p	n.p	PROPN
bibechana-4043	58	35	.	.	PROPN
bibechana-4043	58	36	sah	sah	PROPN
bibechana-4043	58	37	/	/	SYM
bibechana-4043	58	38	bibechana	bibechana	PROPN
bibechana-4043	58	39	7	7	NUM
bibechana-4043	58	40	(	(	PUNCT
bibechana-4043	58	41	2011	2011	NUM
bibechana-4043	58	42	)	)	PUNCT
bibechana-4043	58	43	39	39	NUM
bibechana-4043	58	44	-	-	SYM
bibechana-4043	58	45	43	43	NUM
bibechana-4043	58	46	:	:	PUNCT
bibechana-4043	58	47	bmhss	bmhss	PROPN
bibechana-4043	58	48	41	41	NUM
bibechana-4043	58	49	a	a	DET
bibechana-4043	58	50	schwartz	schwartz	NOUN
bibechana-4043	58	51	space	space	NOUN
bibechana-4043	58	52	,	,	PUNCT
bibechana-4043	58	53	is	be	AUX
bibechana-4043	58	54	asymptotically	asymptotically	ADV
bibechana-4043	58	55	normable	normable	ADJ
bibechana-4043	58	56	by	by	ADP
bibechana-4043	58	57	the	the	DET
bibechana-4043	58	58	following	follow	VERB
bibechana-4043	58	59	proposition	proposition	NOUN
bibechana-4043	58	60	which	which	PRON
bibechana-4043	58	61	is	be	AUX
bibechana-4043	58	62	an	an	DET
bibechana-4043	58	63	immediate	immediate	ADJ
bibechana-4043	58	64	consequence	consequence	NOUN
bibechana-4043	58	65	of	of	ADP
bibechana-4043	58	66	proposition	proposition	NOUN
bibechana-4043	58	67	1.2	1.2	NUM
bibechana-4043	58	68	and	and	CCONJ
bibechana-4043	58	69	gives	give	VERB
bibechana-4043	58	70	a	a	DET
bibechana-4043	58	71	characterization	characterization	NOUN
bibechana-4043	58	72	of	of	ADP
bibechana-4043	58	73	asymptotically	asymptotically	ADV
bibechana-4043	58	74	normable	normable	ADJ
bibechana-4043	58	75	kothe	kothe	NOUN
bibechana-4043	58	76	spaces	space	NOUN
bibechana-4043	58	77	in	in	ADP
bibechana-4043	58	78	terms	term	NOUN
bibechana-4043	58	79	of	of	ADP
bibechana-4043	58	80	the	the	DET
bibechana-4043	58	81	defining	define	VERB
bibechana-4043	58	82	matrix	matrix	NOUN
bibechana-4043	58	83	.	.	PUNCT
bibechana-4043	59	1	proposition	proposition	NOUN
bibechana-4043	59	2	2.1	2.1	NUM
bibechana-4043	59	3	a	a	DET
bibechana-4043	59	4	kothe	kothe	ADJ
bibechana-4043	59	5	space	space	NOUN
bibechana-4043	59	6	λ	λ	NOUN
bibechana-4043	59	7	(	(	PUNCT
bibechana-4043	59	8	a	a	NOUN
bibechana-4043	59	9	)	)	PUNCT
bibechana-4043	59	10	is	be	AUX
bibechana-4043	59	11	asymptotically	asymptotically	ADV
bibechana-4043	59	12	normable	normable	ADJ
bibechana-4043	59	13	if	if	SCONJ
bibechana-4043	60	1	and	and	CCONJ
bibechana-4043	60	2	only	only	ADV
bibechana-4043	60	3	if	if	SCONJ
bibechana-4043	60	4	there	there	PRON
bibechana-4043	60	5	is	be	VERB
bibechana-4043	60	6	ko	ko	PROPN
bibechana-4043	60	7	such	such	ADJ
bibechana-4043	60	8	that	that	PRON
bibechana-4043	60	9	for	for	ADP
bibechana-4043	60	10	every	every	DET
bibechana-4043	60	11	k	k	NOUN
bibechana-4043	60	12	we	we	PRON
bibechana-4043	60	13	have	have	VERB
bibechana-4043	60	14	p	p	NOUN
bibechana-4043	61	1	so	so	SCONJ
bibechana-4043	61	2	that	that	SCONJ
bibechana-4043	61	3	for	for	ADP
bibechana-4043	61	4	every	every	DET
bibechana-4043	61	5	ε	ε	PROPN
bibechana-4043	61	6	>	>	X
bibechana-4043	61	7	0	0	PUNCT
bibechana-4043	62	1	there	there	PRON
bibechana-4043	62	2	is	be	VERB
bibechana-4043	62	3	an	an	DET
bibechana-4043	62	4	m	m	NOUN
bibechana-4043	62	5	>	>	X
bibechana-4043	62	6	0	0	NUM
bibechana-4043	62	7	with	with	ADP
bibechana-4043	62	8	≤	≤	NUM
bibechana-4043	62	9	ε	ε	PROPN
bibechana-4043	62	10	∈	∈	PROPN
bibechana-4043	62	11	oj	oj	PROPN
bibechana-4043	62	12	,	,	PUNCT
bibechana-4043	62	13	k	k	PROPN
bibechana-4043	62	14	j	j	PROPN
bibechana-4043	62	15	,	,	PUNCT
bibechana-4043	62	16	k	k	PROPN
bibechana-4043	62	17	j	j	PROPN
bibechana-4043	62	18	,	,	PUNCT
bibechana-4043	62	19	p	p	X
bibechana-4043	62	20	'	'	PUNCT
bibechana-4043	62	21	a	a	DET
bibechana-4043	62	22	ma	ma	PROPN
bibechana-4043	62	23	+	+	CCONJ
bibechana-4043	62	24	a	a	DET
bibechana-4043	62	25	j	j	PROPN
bibechana-4043	62	26	n	n	PRON
bibechana-4043	62	27	example	example	NOUN
bibechana-4043	62	28	2.2	2.2	NUM
bibechana-4043	62	29	we	we	PRON
bibechana-4043	62	30	define	define	VERB
bibechana-4043	62	31	(	(	PUNCT
bibechana-4043	62	32	i	i	PRON
bibechana-4043	62	33	j	j	PROPN
bibechana-4043	62	34	v	v	NOUN
bibechana-4043	62	35	)	)	PUNCT
bibechana-4043	62	36	k	k	PROPN
bibechana-4043	62	37	for	for	ADP
bibechana-4043	62	38	k	k	PROPN
bibechana-4043	62	39	≤	≤	PROPN
bibechana-4043	62	40	v	v	ADP
bibechana-4043	62	41	bi	bi	PROPN
bibechana-4043	62	42	j	j	PROPN
bibechana-4043	62	43	,	,	PUNCT
bibechana-4043	62	44	v	v	ADP
bibechana-4043	62	45	;	;	PUNCT
bibechana-4043	62	46	k	k	X
bibechana-4043	63	1	=	=	PUNCT
bibechana-4043	63	2	i	i	PRON
bibechana-4043	63	3	v	v	X
bibechana-4043	63	4	(	(	PUNCT
bibechana-4043	63	5	j	j	PROPN
bibechana-4043	63	6	v	v	NOUN
bibechana-4043	63	7	)	)	PUNCT
bibechana-4043	63	8	k	k	PROPN
bibechana-4043	63	9	for	for	ADP
bibechana-4043	63	10	v	v	ADP
bibechana-4043	63	11	<	<	X
bibechana-4043	63	12	k	k	PROPN
bibechana-4043	63	13	≤	≤	PROPN
bibechana-4043	63	14	j	j	PROPN
bibechana-4043	64	1	+	+	CCONJ
bibechana-4043	64	2	v	v	ADJ
bibechana-4043	64	3	ik	ik	PROPN
bibechana-4043	64	4	-	-	PROPN
bibechana-4043	64	5	j	j	PROPN
bibechana-4043	64	6	(	(	PUNCT
bibechana-4043	64	7	j	j	PROPN
bibechana-4043	64	8	v	v	PROPN
bibechana-4043	64	9	)	)	PUNCT
bibechana-4043	64	10	k	k	PROPN
bibechana-4043	64	11	for	for	ADP
bibechana-4043	64	12	j	j	PROPN
bibechana-4043	65	1	+	+	PROPN
bibechana-4043	65	2	v	v	ADP
bibechana-4043	65	3	<	<	X
bibechana-4043	65	4	k	k	X
bibechana-4043	65	5	then	then	ADV
bibechana-4043	65	6	the	the	DET
bibechana-4043	65	7	kothe	kothe	ADJ
bibechana-4043	65	8	space	space	NOUN
bibechana-4043	65	9	λ	λ	PROPN
bibechana-4043	65	10	(	(	PUNCT
bibechana-4043	65	11	b	b	NOUN
bibechana-4043	65	12	)	)	PUNCT
bibechana-4043	65	13	is	be	AUX
bibechana-4043	65	14	montel	montel	PROPN
bibechana-4043	65	15	,	,	PUNCT
bibechana-4043	65	16	admits	admit	VERB
bibechana-4043	65	17	a	a	DET
bibechana-4043	65	18	continuous	continuous	ADJ
bibechana-4043	65	19	norm	norm	NOUN
bibechana-4043	65	20	but	but	CCONJ
bibechana-4043	65	21	is	be	AUX
bibechana-4043	65	22	not	not	PART
bibechana-4043	65	23	asymptotically	asymptotically	ADV
bibechana-4043	65	24	normable	normable	ADJ
bibechana-4043	65	25	.	.	PUNCT
bibechana-4043	66	1	proof	proof	NOUN
bibechana-4043	66	2	.	.	PUNCT
bibechana-4043	66	3	:	:	PUNCT
bibechana-4043	66	4	suppose	suppose	VERB
bibechana-4043	66	5	for	for	SCONJ
bibechana-4043	66	6	some	some	PRON
bibechana-4043	66	7	k	k	PROPN
bibechana-4043	66	8	there	there	PRON
bibechana-4043	66	9	is	be	VERB
bibechana-4043	66	10	a	a	DET
bibechana-4043	66	11	p	p	NOUN
bibechana-4043	66	12	such	such	ADJ
bibechana-4043	66	13	that	that	PRON
bibechana-4043	66	14	for	for	ADP
bibechana-4043	66	15	every	every	DET
bibechana-4043	66	16	ε	ε	PROPN
bibechana-4043	66	17	>	>	X
bibechana-4043	66	18	0	0	PUNCT
bibechana-4043	67	1	there	there	PRON
bibechana-4043	67	2	is	be	VERB
bibechana-4043	67	3	m	m	PROPN
bibechana-4043	67	4	>	>	X
bibechana-4043	67	5	0	0	PUNCT
bibechana-4043	68	1	with	with	ADP
bibechana-4043	68	2	bi	bi	PROPN
bibechana-4043	68	3	j	j	PROPN
bibechana-4043	68	4	,	,	PUNCT
bibechana-4043	68	5	v	v	PROPN
bibechana-4043	68	6	;	;	PUNCT
bibechana-4043	68	7	k+1	k+1	X
bibechana-4043	68	8	≤	≤	NUM
bibechana-4043	68	9	m	m	VERB
bibechana-4043	68	10	bi	bi	PROPN
bibechana-4043	68	11	j	j	PROPN
bibechana-4043	68	12	,	,	PUNCT
bibechana-4043	68	13	v	v	PROPN
bibechana-4043	68	14	;	;	PUNCT
bibechana-4043	68	15	k	k	PROPN
bibechana-4043	68	16	+	+	PROPN
bibechana-4043	68	17	ε	ε	PROPN
bibechana-4043	68	18	bi	bi	PROPN
bibechana-4043	68	19	j	j	PROPN
bibechana-4043	68	20	,	,	PUNCT
bibechana-4043	68	21	v	v	ADP
bibechana-4043	68	22	;	;	PUNCT
bibechana-4043	68	23	p	p	NOUN
bibechana-4043	68	24	for	for	ADP
bibechana-4043	68	25	all	all	PRON
bibechana-4043	68	26	(	(	PUNCT
bibechana-4043	68	27	i	i	PROPN
bibechana-4043	68	28	,	,	PUNCT
bibechana-4043	68	29	j	j	PROPN
bibechana-4043	68	30	,	,	PUNCT
bibechana-4043	68	31	k	k	PROPN
bibechana-4043	68	32	)	)	PUNCT
bibechana-4043	68	33	∈	∈	PROPN
bibechana-4043	68	34	n	n	PRON
bibechana-4043	68	35	3	3	NUM
bibechana-4043	68	36	.	.	PUNCT
bibechana-4043	69	1	we	we	PRON
bibechana-4043	69	2	may	may	AUX
bibechana-4043	69	3	assume	assume	VERB
bibechana-4043	69	4	p	p	PRON
bibechana-4043	69	5	>	>	X
bibechana-4043	69	6	k	k	PROPN
bibechana-4043	70	1	+	+	PROPN
bibechana-4043	70	2	1	1	NUM
bibechana-4043	70	3	,	,	PUNCT
bibechana-4043	70	4	set	set	VERB
bibechana-4043	70	5	v	v	NOUN
bibechana-4043	70	6	=	=	SYM
bibechana-4043	70	7	k	k	PROPN
bibechana-4043	71	1	+	+	PROPN
bibechana-4043	71	2	1	1	NUM
bibechana-4043	71	3	,	,	PUNCT
bibechana-4043	71	4	j	j	PROPN
bibechana-4043	71	5	=	=	PUNCT
bibechana-4043	71	6	p	p	PROPN
bibechana-4043	71	7	–	–	PUNCT
bibechana-4043	71	8	v	v	NOUN
bibechana-4043	71	9	and	and	CCONJ
bibechana-4043	71	10	obtain	obtain	VERB
bibechana-4043	71	11	(	(	PUNCT
bibechana-4043	71	12	i	i	PRON
bibechana-4043	71	13	j	j	PROPN
bibechana-4043	71	14	v	v	NOUN
bibechana-4043	71	15	)	)	PUNCT
bibechana-4043	72	1	k+1	k+1	PROPN
bibechana-4043	72	2	≤	≤	NUM
bibechana-4043	72	3	m	m	VERB
bibechana-4043	72	4	(	(	PUNCT
bibechana-4043	72	5	i	i	PRON
bibechana-4043	72	6	j	j	PROPN
bibechana-4043	72	7	v	v	NOUN
bibechana-4043	72	8	)	)	PUNCT
bibechana-4043	72	9	k	k	PROPN
bibechana-4043	73	1	+	+	CCONJ
bibechana-4043	73	2	ε	ε	PROPN
bibechana-4043	74	1	i	i	PRON
bibechana-4043	74	2	k+1	k+1	X
bibechana-4043	74	3	(	(	PUNCT
bibechana-4043	74	4	j	j	PROPN
bibechana-4043	74	5	v	v	NOUN
bibechana-4043	74	6	)	)	PUNCT
bibechana-4043	74	7	p	p	NOUN
bibechana-4043	74	8	for	for	ADP
bibechana-4043	74	9	ε	ε	PROPN
bibechana-4043	74	10	<	<	X
bibechana-4043	74	11	(	(	PUNCT
bibechana-4043	74	12	j	j	PROPN
bibechana-4043	74	13	v	v	NOUN
bibechana-4043	74	14	)	)	PUNCT
bibechana-4043	74	15	k+1	k+1	NOUN
bibechana-4043	74	16	-	-	PUNCT
bibechana-4043	74	17	p	p	NOUN
bibechana-4043	74	18	,	,	PUNCT
bibechana-4043	74	19	we	we	PRON
bibechana-4043	74	20	let	let	VERB
bibechana-4043	74	21	i	i	PRON
bibechana-4043	74	22	tend	tend	VERB
bibechana-4043	74	23	to	to	PART
bibechana-4043	74	24	infinity	infinity	VERB
bibechana-4043	74	25	and	and	CCONJ
bibechana-4043	74	26	get	get	VERB
bibechana-4043	74	27	a	a	DET
bibechana-4043	74	28	contradiction	contradiction	NOUN
bibechana-4043	74	29	.	.	PUNCT
bibechana-4043	75	1	hence	hence	ADV
bibechana-4043	75	2	the	the	DET
bibechana-4043	75	3	kothe	kothe	ADJ
bibechana-4043	75	4	space	space	NOUN
bibechana-4043	75	5	λ	λ	PROPN
bibechana-4043	75	6	(	(	PUNCT
bibechana-4043	75	7	b	b	NOUN
bibechana-4043	75	8	)	)	PUNCT
bibechana-4043	75	9	is	be	AUX
bibechana-4043	75	10	not	not	PART
bibechana-4043	75	11	asymptotically	asymptotically	ADV
bibechana-4043	75	12	normable	normable	ADJ
bibechana-4043	75	13	by	by	ADP
bibechana-4043	75	14	proposition	proposition	NOUN
bibechana-4043	75	15	1.2	1.2	NUM
bibechana-4043	75	16	.	.	PUNCT
bibechana-4043	76	1	suppose	suppose	VERB
bibechana-4043	76	2	we	we	PRON
bibechana-4043	76	3	fix	fix	VERB
bibechana-4043	76	4	ko	ko	PROPN
bibechana-4043	76	5	and	and	CCONJ
bibechana-4043	76	6	let	let	VERB
bibechana-4043	76	7	i	i	PRON
bibechana-4043	76	8	⊂	⊂	PROPN
bibechana-4043	76	9	n	n	ADV
bibechana-4043	76	10	3	3	NUM
bibechana-4043	76	11	be	be	AUX
bibechana-4043	76	12	an	an	DET
bibechana-4043	76	13	index	index	NOUN
bibechana-4043	76	14	set	set	VERB
bibechana-4043	76	15	such	such	ADJ
bibechana-4043	76	16	that	that	PRON
bibechana-4043	76	17	for	for	ADP
bibechana-4043	76	18	all	all	PRON
bibechana-4043	77	1	k	k	PROPN
bibechana-4043	78	1	we	we	PRON
bibechana-4043	78	2	have	have	VERB
bibechana-4043	78	3	bi	bi	PROPN
bibechana-4043	78	4	j	j	PROPN
bibechana-4043	78	5	v	v	PROPN
bibechana-4043	78	6	;	;	PUNCT
bibechana-4043	78	7	k	k	PROPN
bibechana-4043	78	8	≤	≤	PROPN
bibechana-4043	78	9	ρ(k)bi	ρ(k)bi	PRON
bibechana-4043	78	10	j	j	PROPN
bibechana-4043	78	11	,	,	PUNCT
bibechana-4043	78	12	v	v	PROPN
bibechana-4043	78	13	;	;	PUNCT
bibechana-4043	78	14	k	k	X
bibechana-4043	78	15	for	for	ADP
bibechana-4043	78	16	some	some	DET
bibechana-4043	78	17	ρ(k	ρ(k	NOUN
bibechana-4043	78	18	)	)	PUNCT
bibechana-4043	78	19	>	>	X
bibechana-4043	78	20	0	0	PUNCT
bibechana-4043	79	1	and	and	CCONJ
bibechana-4043	79	2	(	(	PUNCT
bibechana-4043	79	3	i	i	PROPN
bibechana-4043	79	4	,	,	PUNCT
bibechana-4043	79	5	j	j	PROPN
bibechana-4043	79	6	,	,	PUNCT
bibechana-4043	79	7	v	v	NOUN
bibechana-4043	79	8	)	)	PUNCT
bibechana-4043	79	9	∈	∈	PROPN
bibechana-4043	79	10	i.	i.	NOUN
bibechana-4043	79	11	if	if	SCONJ
bibechana-4043	79	12	we	we	PRON
bibechana-4043	79	13	show	show	VERB
bibechana-4043	79	14	that	that	SCONJ
bibechana-4043	79	15	i	i	PRON
bibechana-4043	79	16	must	must	AUX
bibechana-4043	79	17	be	be	AUX
bibechana-4043	79	18	finite	finite	ADJ
bibechana-4043	79	19	,	,	PUNCT
bibechana-4043	79	20	then	then	ADV
bibechana-4043	79	21	we	we	PRON
bibechana-4043	79	22	have	have	VERB
bibechana-4043	79	23	that	that	DET
bibechana-4043	79	24	λ	λ	PROPN
bibechana-4043	79	25	(	(	PUNCT
bibechana-4043	79	26	b	b	NOUN
bibechana-4043	79	27	)	)	PUNCT
bibechana-4043	79	28	is	be	AUX
bibechana-4043	79	29	a	a	DET
bibechana-4043	79	30	montel	montel	PROPN
bibechana-4043	79	31	space	space	NOUN
bibechana-4043	79	32	[	[	X
bibechana-4043	79	33	4	4	NUM
bibechana-4043	79	34	]	]	PUNCT
bibechana-4043	79	35	.	.	PUNCT
bibechana-4043	80	1	since	since	SCONJ
bibechana-4043	80	2	the	the	DET
bibechana-4043	80	3	exponent	exponent	NOUN
bibechana-4043	80	4	of	of	ADP
bibechana-4043	80	5	i	i	PRON
bibechana-4043	80	6	is	be	AUX
bibechana-4043	80	7	increasing	increase	VERB
bibechana-4043	80	8	with	with	ADP
bibechana-4043	80	9	k	k	PROPN
bibechana-4043	80	10	,	,	PUNCT
bibechana-4043	80	11	we	we	PRON
bibechana-4043	80	12	have	have	VERB
bibechana-4043	80	13	j	j	PROPN
bibechana-4043	80	14	v	v	ADJ
bibechana-4043	80	15	≤	≤	NUM
bibechana-4043	80	16	ρ(ko+1	ρ(ko+1	NOUN
bibechana-4043	80	17	)	)	PUNCT
bibechana-4043	80	18	for	for	ADP
bibechana-4043	80	19	all	all	PRON
bibechana-4043	80	20	(	(	PUNCT
bibechana-4043	80	21	i	i	PROPN
bibechana-4043	80	22	,	,	PUNCT
bibechana-4043	80	23	j	j	PROPN
bibechana-4043	80	24	,	,	PUNCT
bibechana-4043	80	25	v	v	NOUN
bibechana-4043	80	26	)	)	PUNCT
bibechana-4043	80	27	∈	∈	PROPN
bibechana-4043	80	28	i.	i.	NOUN
bibechana-4043	80	29	for	for	ADP
bibechana-4043	80	30	any	any	DET
bibechana-4043	80	31	given	give	VERB
bibechana-4043	80	32	jo	jo	NOUN
bibechana-4043	80	33	,	,	PUNCT
bibechana-4043	80	34	vo	vo	X
bibechana-4043	80	35	let	let	VERB
bibechana-4043	80	36	k	k	PROPN
bibechana-4043	80	37	>	>	X
bibechana-4043	80	38	jo	jo	PROPN
bibechana-4043	81	1	+	+	CCONJ
bibechana-4043	81	2	vo	vo	PROPN
bibechana-4043	82	1	+	+	CCONJ
bibechana-4043	82	2	ko	ko	PROPN
bibechana-4043	82	3	.	.	PUNCT
bibechana-4043	83	1	if	if	SCONJ
bibechana-4043	83	2	(	(	PUNCT
bibechana-4043	83	3	i	i	PROPN
bibechana-4043	83	4	,	,	PUNCT
bibechana-4043	83	5	jo	jo	PROPN
bibechana-4043	83	6	,	,	PUNCT
bibechana-4043	83	7	vo	vo	NOUN
bibechana-4043	83	8	)	)	PUNCT
bibechana-4043	83	9	∈	∈	PROPN
bibechana-4043	83	10	i	i	PRON
bibechana-4043	83	11	,	,	PUNCT
bibechana-4043	83	12	we	we	PRON
bibechana-4043	83	13	get	get	VERB
bibechana-4043	83	14	(	(	PUNCT
bibechana-4043	83	15	≤	≤	NUM
bibechana-4043	83	16	ρokj	ρokj	NOUN
bibechana-4043	84	1	i	i	PRON
bibechana-4043	84	2	k	k	PROPN
bibechana-4043	84	3	okk	okk	INTJ
bibechana-4043	84	4	m	m	VERB
bibechana-4043	85	1	o	o	NOUN
bibechana-4043	86	1	o	o	X
bibechana-4043	87	1	o	o	X
bibechana-4043	87	2	o	o	X
bibechana-4043	87	3	(	(	PUNCT
bibechana-4043	87	4	j	j	PROPN
bibechana-4043	87	5	v	v	NOUN
bibechana-4043	87	6	)	)	PUNCT
bibechana-4043	87	7	)	)	PUNCT
bibechana-4043	88	1	i	i	PRON
bibechana-4043	88	2	(	(	PUNCT
bibechana-4043	88	3	j	j	PROPN
bibechana-4043	88	4	v	v	NOUN
bibechana-4043	88	5	)	)	PUNCT
bibechana-4043	88	6	where	where	SCONJ
bibechana-4043	88	7	m	m	NOUN
bibechana-4043	88	8	is	be	AUX
bibechana-4043	88	9	some	some	DET
bibechana-4043	88	10	integer	integer	NOUN
bibechana-4043	88	11	which	which	PRON
bibechana-4043	88	12	is	be	AUX
bibechana-4043	88	13	strictly	strictly	ADV
bibechana-4043	88	14	less	less	ADJ
bibechana-4043	88	15	than	than	ADP
bibechana-4043	88	16	k	k	PROPN
bibechana-4043	88	17	–	–	PUNCT
bibechana-4043	88	18	jo	jo	NOUN
bibechana-4043	88	19	in	in	ADP
bibechana-4043	88	20	all	all	DET
bibechana-4043	88	21	cases	case	NOUN
bibechana-4043	88	22	.	.	PUNCT
bibechana-4043	89	1	hence	hence	ADV
bibechana-4043	89	2	{	{	PUNCT
bibechana-4043	89	3	i	i	NOUN
bibechana-4043	89	4	:	:	PUNCT
bibechana-4043	89	5	(	(	PUNCT
bibechana-4043	89	6	i	i	PROPN
bibechana-4043	89	7	,	,	PUNCT
bibechana-4043	89	8	jo	jo	PROPN
bibechana-4043	89	9	,	,	PUNCT
bibechana-4043	89	10	vo	vo	NOUN
bibechana-4043	89	11	)	)	PUNCT
bibechana-4043	89	12	∈	∈	PROPN
bibechana-4043	90	1	i	i	PRON
bibechana-4043	90	2	}	}	PUNCT
bibechana-4043	90	3	is	be	AUX
bibechana-4043	90	4	finite	finite	ADJ
bibechana-4043	91	1	and	and	CCONJ
bibechana-4043	91	2	so	so	ADV
bibechana-4043	91	3	i	i	PRON
bibechana-4043	91	4	must	must	AUX
bibechana-4043	91	5	also	also	ADV
bibechana-4043	91	6	be	be	AUX
bibechana-4043	91	7	finite	finite	ADJ
bibechana-4043	91	8	.	.	PUNCT
bibechana-4043	92	1	c.	c.	NOUN
bibechana-4043	92	2	this	this	DET
bibechana-4043	92	3	section	section	NOUN
bibechana-4043	92	4	is	be	AUX
bibechana-4043	92	5	devoted	devote	VERB
bibechana-4043	92	6	to	to	ADP
bibechana-4043	92	7	the	the	DET
bibechana-4043	92	8	proof	proof	NOUN
bibechana-4043	92	9	of	of	ADP
bibechana-4043	92	10	our	our	PRON
bibechana-4043	92	11	main	main	ADJ
bibechana-4043	92	12	theorem	theorem	NOUN
bibechana-4043	92	13	3.3	3.3	NUM
bibechana-4043	92	14	.	.	PUNCT
bibechana-4043	93	1	for	for	ADP
bibechana-4043	93	2	this	this	PRON
bibechana-4043	93	3	,	,	PUNCT
bibechana-4043	93	4	we	we	PRON
bibechana-4043	93	5	state	state	VERB
bibechana-4043	93	6	the	the	DET
bibechana-4043	93	7	following	follow	VERB
bibechana-4043	93	8	lemma	lemma	PROPN
bibechana-4043	93	9	without	without	ADP
bibechana-4043	93	10	proof	proof	NOUN
bibechana-4043	93	11	:	:	PUNCT
bibechana-4043	93	12	lemma	lemma	PROPN
bibechana-4043	93	13	3.1	3.1	NUM
bibechana-4043	93	14	let	let	VERB
bibechana-4043	93	15	a	a	DET
bibechana-4043	93	16	=	=	X
bibechana-4043	93	17	(	(	PUNCT
bibechana-4043	93	18	ai	ai	PROPN
bibechana-4043	93	19	,	,	PUNCT
bibechana-4043	93	20	k	k	NOUN
bibechana-4043	93	21	;	;	PUNCT
bibechana-4043	93	22	m	m	VERB
bibechana-4043	93	23	)	)	PUNCT
bibechana-4043	93	24	be	be	AUX
bibechana-4043	93	25	a	a	DET
bibechana-4043	93	26	doubly	doubly	ADV
bibechana-4043	93	27	indexed	index	VERB
bibechana-4043	93	28	matrix	matrix	NOUN
bibechana-4043	93	29	and	and	CCONJ
bibechana-4043	93	30	ak	ak	PROPN
bibechana-4043	93	31	=	=	PUNCT
bibechana-4043	93	32	(	(	PUNCT
bibechana-4043	93	33	ai	ai	PROPN
bibechana-4043	93	34	,	,	PUNCT
bibechana-4043	93	35	k	k	NOUN
bibechana-4043	93	36	;	;	PUNCT
bibechana-4043	93	37	m	m	VERB
bibechana-4043	93	38	+	+	NUM
bibechana-4043	93	39	ai+1	ai+1	NUM
bibechana-4043	93	40	,	,	PUNCT
bibechana-4043	93	41	k	k	NOUN
bibechana-4043	93	42	;	;	PUNCT
bibechana-4043	93	43	m	m	NOUN
bibechana-4043	93	44	)	)	PUNCT
bibechana-4043	93	45	.	.	PUNCT
bibechana-4043	94	1	we	we	PRON
bibechana-4043	94	2	assume	assume	VERB
bibechana-4043	94	3	that	that	SCONJ
bibechana-4043	94	4	with	with	ADP
bibechana-4043	94	5	suitable	suitable	ADJ
bibechana-4043	94	6	sequences	sequence	NOUN
bibechana-4043	94	7	i(m	i(m	NOUN
bibechana-4043	94	8	)	)	PUNCT
bibechana-4043	94	9	and	and	CCONJ
bibechana-4043	94	10	s(m	s(m	PROPN
bibechana-4043	94	11	)	)	PUNCT
bibechana-4043	94	12	≥	≥	NOUN
bibechana-4043	94	13	m	m	VERB
bibechana-4043	94	14	we	we	PRON
bibechana-4043	94	15	have	have	VERB
bibechana-4043	94	16	the	the	DET
bibechana-4043	94	17	following	following	NOUN
bibechana-4043	94	18	:	:	PUNCT
bibechana-4043	94	19	(	(	PUNCT
bibechana-4043	94	20	1	1	X
bibechana-4043	94	21	)	)	PUNCT
bibechana-4043	94	22	ai	ai	VERB
bibechana-4043	94	23	,	,	PUNCT
bibechana-4043	94	24	k;k	k;k	ADJ
bibechana-4043	95	1	=	=	NOUN
bibechana-4043	95	2	1	1	NUM
bibechana-4043	95	3	for	for	ADP
bibechana-4043	95	4	all	all	DET
bibechana-4043	95	5	i	i	PROPN
bibechana-4043	95	6	,	,	PUNCT
bibechana-4043	95	7	k.	k.	PROPN
bibechana-4043	96	1	(	(	PUNCT
bibechana-4043	96	2	2	2	X
bibechana-4043	96	3	)	)	PUNCT
bibechana-4043	96	4	ai	ai	VERB
bibechana-4043	96	5	,	,	PUNCT
bibechana-4043	96	6	k	k	NOUN
bibechana-4043	96	7	;	;	PUNCT
bibechana-4043	96	8	m	m	VERB
bibechana-4043	96	9	≥	≥	NOUN
bibechana-4043	96	10	ai+1	ai+1	NUM
bibechana-4043	96	11	,	,	PUNCT
bibechana-4043	96	12	k;m	k;m	PROPN
bibechana-4043	96	13	for	for	ADP
bibechana-4043	96	14	all	all	DET
bibechana-4043	96	15	i	i	PROPN
bibechana-4043	96	16	,	,	PUNCT
bibechana-4043	96	17	m	m	VERB
bibechana-4043	96	18	≤	≤	PROPN
bibechana-4043	97	1	k.	k.	PROPN
bibechana-4043	97	2	ai	ai	PROPN
bibechana-4043	97	3	,	,	PUNCT
bibechana-4043	97	4	k	k	NOUN
bibechana-4043	97	5	;	;	PUNCT
bibechana-4043	97	6	m	m	VERB
bibechana-4043	97	7	≤	≤	NUM
bibechana-4043	97	8	ai+1	ai+1	NUM
bibechana-4043	97	9	,	,	PUNCT
bibechana-4043	97	10	k;m	k;m	PROPN
bibechana-4043	97	11	for	for	ADP
bibechana-4043	97	12	all	all	PRON
bibechana-4043	97	13	i	i	PRON
bibechana-4043	97	14	≥	≥	VERB
bibechana-4043	97	15	i	i	NOUN
bibechana-4043	97	16	(	(	PUNCT
bibechana-4043	97	17	m	m	PROPN
bibechana-4043	97	18	)	)	PUNCT
bibechana-4043	97	19	,	,	PUNCT
bibechana-4043	97	20	m	m	VERB
bibechana-4043	97	21	>	>	X
bibechana-4043	97	22	k.	k.	PROPN
bibechana-4043	97	23	(	(	PUNCT
bibechana-4043	97	24	3	3	X
bibechana-4043	97	25	)	)	PUNCT
bibechana-4043	97	26	ai	ai	VERB
bibechana-4043	97	27	,	,	PUNCT
bibechana-4043	97	28	k	k	NOUN
bibechana-4043	97	29	;	;	PUNCT
bibechana-4043	97	30	m	m	VERB
bibechana-4043	97	31	=	=	NOUN
bibechana-4043	97	32	0	0	NUM
bibechana-4043	97	33	for	for	ADP
bibechana-4043	97	34	all	all	DET
bibechana-4043	97	35	m	m	PROPN
bibechana-4043	97	36	<	<	X
bibechana-4043	97	37	k.	k.	X
bibechana-4043	98	1	(	(	PUNCT
bibechana-4043	98	2	4	4	X
bibechana-4043	98	3	)	)	PUNCT
bibechana-4043	98	4	∞∑	∞∑	PROPN
bibechana-4043	98	5	i	i	PRON
bibechana-4043	98	6	,	,	PUNCT
bibechana-4043	98	7	k;m	k;m	PROPN
bibechana-4043	99	1	i	i	PRON
bibechana-4043	99	2	i	i	PROPN
bibechana-4043	99	3	,	,	PUNCT
bibechana-4043	99	4	k	k	PROPN
bibechana-4043	99	5	;	;	PUNCT
bibechana-4043	99	6	s(m	s(m	PROPN
bibechana-4043	99	7	)	)	PUNCT
bibechana-4043	100	1	a	a	DET
bibechana-4043	100	2	<	<	X
bibechana-4043	100	3	+	+	NOUN
bibechana-4043	100	4	a	a	DET
bibechana-4043	100	5	then	then	ADV
bibechana-4043	100	6	there	there	PRON
bibechana-4043	100	7	exists	exist	VERB
bibechana-4043	100	8	an	an	DET
bibechana-4043	100	9	exact	exact	ADJ
bibechana-4043	100	10	sequence	sequence	NOUN
bibechana-4043	100	11	0	0	NUM
bibechana-4043	100	12	→	→	SYM
bibechana-4043	100	13	λ	λ	PROPN
bibechana-4043	100	14	(	(	PUNCT
bibechana-4043	100	15	ak	ak	PROPN
bibechana-4043	100	16	)	)	PUNCT
bibechana-4043	100	17	→	→	SYM
bibechana-4043	100	18	λ	λ	X
bibechana-4043	100	19	(	(	PUNCT
bibechana-4043	100	20	a	a	NOUN
bibechana-4043	100	21	)	)	PUNCT
bibechana-4043	100	22	→	→	SYM
bibechana-4043	100	23	ω	ω	PROPN
bibechana-4043	100	24	→	→	SYM
bibechana-4043	100	25	0	0	NUM
bibechana-4043	100	26	.	.	PUNCT
bibechana-4043	101	1	we	we	PRON
bibechana-4043	101	2	will	will	AUX
bibechana-4043	101	3	now	now	ADV
bibechana-4043	101	4	show	show	VERB
bibechana-4043	101	5	that	that	SCONJ
bibechana-4043	101	6	for	for	ADP
bibechana-4043	101	7	a	a	DET
bibechana-4043	101	8	given	give	VERB
bibechana-4043	101	9	kothe	kothe	ADJ
bibechana-4043	101	10	-	-	PUNCT
bibechana-4043	101	11	schwartz	schwartz	NOUN
bibechana-4043	101	12	space	space	NOUN
bibechana-4043	101	13	λ	λ	PROPN
bibechana-4043	101	14	(	(	PUNCT
bibechana-4043	101	15	b	b	NOUN
bibechana-4043	101	16	)	)	PUNCT
bibechana-4043	101	17	there	there	PRON
bibechana-4043	101	18	is	be	VERB
bibechana-4043	101	19	another	another	DET
bibechana-4043	101	20	such	such	ADJ
bibechana-4043	101	21	space	space	NOUN
bibechana-4043	101	22	λ	λ	NOUN
bibechana-4043	101	23	(	(	PUNCT
bibechana-4043	101	24	a	a	NOUN
bibechana-4043	101	25	)	)	PUNCT
bibechana-4043	101	26	and	and	CCONJ
bibechana-4043	101	27	a	a	DET
bibechana-4043	101	28	surjection	surjection	NOUN
bibechana-4043	101	29	of	of	ADP
bibechana-4043	101	30	λ	λ	PROPN
bibechana-4043	101	31	(	(	PUNCT
bibechana-4043	101	32	a	a	NOUN
bibechana-4043	101	33	)	)	PUNCT
bibechana-4043	101	34	onto	onto	ADP
bibechana-4043	101	35	ω	ω	NUM
bibechana-4043	101	36	whose	whose	DET
bibechana-4043	101	37	kernel	kernel	NOUN
bibechana-4043	101	38	is	be	AUX
bibechana-4043	101	39	isomorphic	isomorphic	ADJ
bibechana-4043	101	40	to	to	ADP
bibechana-4043	101	41	λ	λ	PROPN
bibechana-4043	101	42	(	(	PUNCT
bibechana-4043	101	43	b	b	NOUN
bibechana-4043	101	44	)	)	PUNCT
bibechana-4043	101	45	.	.	PUNCT
bibechana-4043	102	1	proposition	proposition	NOUN
bibechana-4043	102	2	3.2	3.2	NUM
bibechana-4043	102	3	for	for	ADP
bibechana-4043	102	4	every	every	DET
bibechana-4043	102	5	kothe	kothe	ADJ
bibechana-4043	102	6	-	-	PUNCT
bibechana-4043	102	7	schwartz	schwartz	NOUN
bibechana-4043	102	8	space	space	NOUN
bibechana-4043	102	9	λ	λ	PROPN
bibechana-4043	102	10	(	(	PUNCT
bibechana-4043	102	11	b	b	NOUN
bibechana-4043	102	12	)	)	PUNCT
bibechana-4043	102	13	with	with	ADP
bibechana-4043	102	14	a	a	DET
bibechana-4043	102	15	continuous	continuous	ADJ
bibechana-4043	102	16	norm	norm	NOUN
bibechana-4043	102	17	,	,	PUNCT
bibechana-4043	102	18	there	there	PRON
bibechana-4043	102	19	exists	exist	VERB
bibechana-4043	102	20	a	a	DET
bibechana-4043	102	21	kothe	kothe	ADJ
bibechana-4043	102	22	-	-	PUNCT
bibechana-4043	102	23	schwartz	schwartz	NOUN
bibechana-4043	102	24	space	space	NOUN
bibechana-4043	102	25	λ	λ	PROPN
bibechana-4043	102	26	(	(	PUNCT
bibechana-4043	102	27	a	a	NOUN
bibechana-4043	102	28	)	)	PUNCT
bibechana-4043	102	29	with	with	ADP
bibechana-4043	102	30	a	a	DET
bibechana-4043	102	31	continuous	continuous	ADJ
bibechana-4043	102	32	norm	norm	NOUN
bibechana-4043	102	33	and	and	CCONJ
bibechana-4043	102	34	an	an	DET
bibechana-4043	102	35	exact	exact	ADJ
bibechana-4043	102	36	sequence	sequence	NOUN
bibechana-4043	102	37	0	0	NUM
bibechana-4043	102	38	→	→	SYM
bibechana-4043	102	39	λ	λ	X
bibechana-4043	102	40	(	(	PUNCT
bibechana-4043	102	41	b	b	NOUN
bibechana-4043	102	42	)	)	PUNCT
bibechana-4043	102	43	→	→	SYM
bibechana-4043	102	44	λ	λ	X
bibechana-4043	102	45	(	(	PUNCT
bibechana-4043	102	46	a	a	NOUN
bibechana-4043	102	47	)	)	PUNCT
bibechana-4043	102	48	→	→	SYM
bibechana-4043	102	49	ω	ω	PROPN
bibechana-4043	102	50	→	→	SYM
bibechana-4043	102	51	0	0	NUM
bibechana-4043	102	52	.	.	PUNCT
bibechana-4043	103	1	further	far	ADV
bibechana-4043	103	2	,	,	PUNCT
bibechana-4043	103	3	if	if	SCONJ
bibechana-4043	103	4	λ	λ	X
bibechana-4043	103	5	(	(	PUNCT
bibechana-4043	103	6	b	b	NOUN
bibechana-4043	103	7	)	)	PUNCT
bibechana-4043	103	8	is	be	AUX
bibechana-4043	103	9	nuclear	nuclear	ADJ
bibechana-4043	103	10	,	,	PUNCT
bibechana-4043	103	11	then	then	ADV
bibechana-4043	103	12	λ	λ	X
bibechana-4043	103	13	(	(	PUNCT
bibechana-4043	103	14	a	a	PRON
bibechana-4043	103	15	)	)	PUNCT
bibechana-4043	103	16	is	be	AUX
bibechana-4043	103	17	also	also	ADV
bibechana-4043	103	18	nuclear	nuclear	ADJ
bibechana-4043	103	19	.	.	PUNCT
bibechana-4043	104	1	o	o	X
bibechana-4043	105	1	lim	lim	NOUN
bibechana-4043	105	2	i	i	PRON
bibechana-4043	105	3	sup	sup	VERB
bibechana-4043	105	4	k	k	PROPN
bibechana-4043	105	5	g.k	g.k	PROPN
bibechana-4043	105	6	.	.	PROPN
bibechana-4043	105	7	palei	palei	PROPN
bibechana-4043	105	8	and	and	CCONJ
bibechana-4043	105	9	n.p	n.p	PROPN
bibechana-4043	105	10	.	.	PROPN
bibechana-4043	105	11	sah	sah	PROPN
bibechana-4043	105	12	/	/	SYM
bibechana-4043	105	13	bibechana	bibechana	PROPN
bibechana-4043	105	14	7	7	NUM
bibechana-4043	105	15	(	(	PUNCT
bibechana-4043	105	16	2011	2011	NUM
bibechana-4043	105	17	)	)	PUNCT
bibechana-4043	105	18	39	39	NUM
bibechana-4043	105	19	-	-	SYM
bibechana-4043	105	20	43	43	NUM
bibechana-4043	105	21	:	:	PUNCT
bibechana-4043	105	22	bmhss	bmhss	NOUN
bibechana-4043	105	23	42	42	NUM
bibechana-4043	105	24	proof	proof	NOUN
bibechana-4043	105	25	:	:	PUNCT
bibechana-4043	105	26	we	we	PRON
bibechana-4043	105	27	assume	assume	VERB
bibechana-4043	105	28	without	without	SCONJ
bibechana-4043	105	29	loss	loss	NOUN
bibechana-4043	105	30	of	of	ADP
bibechana-4043	105	31	generally	generally	ADV
bibechana-4043	105	32	bj	bj	VERB
bibechana-4043	105	33	;	;	PUNCT
bibechana-4043	105	34	1	1	NUM
bibechana-4043	105	35	>	>	SYM
bibechana-4043	105	36	0	0	PUNCT
bibechana-4043	106	1	for	for	ADP
bibechana-4043	106	2	all	all	DET
bibechana-4043	106	3	j	j	PROPN
bibechana-4043	106	4	and	and	CCONJ
bibechana-4043	106	5	j;m	j;m	PROPN
bibechana-4043	106	6	j;m+	j;m+	PROPN
bibechana-4043	106	7	b	b	PROPN
bibechana-4043	106	8	=	=	SYM
bibechana-4043	106	9	b	b	SYM
bibechana-4043	106	10	1	1	NUM
bibechana-4043	106	11	0	0	NUM
bibechana-4043	106	12	for	for	ADP
bibechana-4043	106	13	all	all	DET
bibechana-4043	106	14	m.	m.	NOUN
bibechana-4043	106	15	we	we	PRON
bibechana-4043	106	16	determine	determine	VERB
bibechana-4043	106	17	inductively	inductively	ADV
bibechana-4043	106	18	disjoint	disjoint	NOUN
bibechana-4043	106	19	,	,	PUNCT
bibechana-4043	106	20	infinite	infinite	ADJ
bibechana-4043	106	21	sets	set	NOUN
bibechana-4043	106	22	of	of	ADP
bibechana-4043	106	23	integers	integer	NOUN
bibechana-4043	106	24	mk	mk	NOUN
bibechana-4043	106	25	=	=	PUNCT
bibechana-4043	106	26	{	{	PUNCT
bibechana-4043	106	27	n(i	n(i	PROPN
bibechana-4043	106	28	,	,	PUNCT
bibechana-4043	106	29	k	k	NOUN
bibechana-4043	106	30	)	)	PUNCT
bibechana-4043	106	31	:	:	PUNCT
bibechana-4043	106	32	i	i	NOUN
bibechana-4043	106	33	=	=	NOUN
bibechana-4043	106	34	1	1	NUM
bibechana-4043	106	35	,	,	PUNCT
bibechana-4043	106	36	2	2	NUM
bibechana-4043	106	37	,	,	PUNCT
bibechana-4043	106	38	...	...	PUNCT
bibechana-4043	106	39	}	}	PUNCT
bibechana-4043	106	40	with	with	ADP
bibechana-4043	106	41	∪mk	∪mk	PROPN
bibechana-4043	106	42	=	=	PROPN
bibechana-4043	106	43	n	n	PROPN
bibechana-4043	106	44	such	such	ADJ
bibechana-4043	106	45	that	that	SCONJ
bibechana-4043	106	46	the	the	DET
bibechana-4043	106	47	following	follow	VERB
bibechana-4043	106	48	are	be	AUX
bibechana-4043	106	49	true	true	ADJ
bibechana-4043	106	50	:	:	PUNCT
bibechana-4043	106	51	(	(	PUNCT
bibechana-4043	106	52	5	5	X
bibechana-4043	106	53	)	)	PUNCT
bibechana-4043	106	54	≥	≥	NOUN
bibechana-4043	106	55	n(i	n(i	PROPN
bibechana-4043	106	56	,	,	PUNCT
bibechana-4043	106	57	k	k	NOUN
bibechana-4043	106	58	)	)	PUNCT
bibechana-4043	106	59	;	;	PUNCT
bibechana-4043	107	1	m	m	VERB
bibechana-4043	107	2	n(i+1	n(i+1	NOUN
bibechana-4043	107	3	,	,	PUNCT
bibechana-4043	107	4	k	k	PROPN
bibechana-4043	107	5	)	)	PUNCT
bibechana-4043	107	6	;	;	PUNCT
bibechana-4043	107	7	m	m	VERB
bibechana-4043	107	8	n(i	n(i	PROPN
bibechana-4043	107	9	,	,	PUNCT
bibechana-4043	107	10	k	k	NOUN
bibechana-4043	107	11	)	)	PUNCT
bibechana-4043	107	12	;	;	PUNCT
bibechana-4043	107	13	k	k	PROPN
bibechana-4043	107	14	n(i+1	n(i+1	PROPN
bibechana-4043	107	15	,	,	PUNCT
bibechana-4043	107	16	k	k	PROPN
bibechana-4043	107	17	)	)	PUNCT
bibechana-4043	107	18	;	;	PUNCT
bibechana-4043	107	19	k	k	PROPN
bibechana-4043	107	20	b	b	PROPN
bibechana-4043	107	21	b	b	PROPN
bibechana-4043	107	22	b	b	PROPN
bibechana-4043	107	23	b	b	PROPN
bibechana-4043	107	24	for	for	ADP
bibechana-4043	107	25	m	m	PRON
bibechana-4043	107	26	<	<	X
bibechana-4043	107	27	k	k	X
bibechana-4043	107	28	(	(	PUNCT
bibechana-4043	107	29	6	6	NUM
bibechana-4043	107	30	)	)	PUNCT
bibechana-4043	107	31	≤	≤	NOUN
bibechana-4043	107	32	n(i	n(i	PROPN
bibechana-4043	107	33	,	,	PUNCT
bibechana-4043	107	34	k	k	NOUN
bibechana-4043	107	35	)	)	PUNCT
bibechana-4043	107	36	;	;	PUNCT
bibechana-4043	107	37	m	m	VERB
bibechana-4043	107	38	n(i+1	n(i+1	NOUN
bibechana-4043	107	39	,	,	PUNCT
bibechana-4043	107	40	k	k	PROPN
bibechana-4043	107	41	)	)	PUNCT
bibechana-4043	107	42	;	;	PUNCT
bibechana-4043	107	43	m	m	VERB
bibechana-4043	107	44	n(i	n(i	PROPN
bibechana-4043	107	45	,	,	PUNCT
bibechana-4043	107	46	k	k	NOUN
bibechana-4043	107	47	)	)	PUNCT
bibechana-4043	107	48	;	;	PUNCT
bibechana-4043	107	49	k	k	PROPN
bibechana-4043	107	50	n(i+1	n(i+1	PROPN
bibechana-4043	107	51	,	,	PUNCT
bibechana-4043	107	52	k	k	PROPN
bibechana-4043	107	53	)	)	PUNCT
bibechana-4043	107	54	;	;	PUNCT
bibechana-4043	107	55	k	k	PROPN
bibechana-4043	107	56	b	b	PROPN
bibechana-4043	107	57	b	b	PROPN
bibechana-4043	107	58	b	b	PROPN
bibechana-4043	107	59	b	b	PROPN
bibechana-4043	107	60	for	for	ADP
bibechana-4043	107	61	m	m	PROPN
bibechana-4043	107	62	>	>	X
bibechana-4043	107	63	k	k	PROPN
bibechana-4043	107	64	,	,	PUNCT
bibechana-4043	107	65	i	i	PRON
bibechana-4043	107	66	≥	≥	VERB
bibechana-4043	107	67	m	m	VERB
bibechana-4043	107	68	(	(	PUNCT
bibechana-4043	107	69	7	7	NUM
bibechana-4043	107	70	)	)	PUNCT
bibechana-4043	107	71	2−≤	2−≤	NUM
bibechana-4043	107	72	in(i	in(i	ADJ
bibechana-4043	107	73	,	,	PUNCT
bibechana-4043	107	74	k	k	NOUN
bibechana-4043	107	75	)	)	PUNCT
bibechana-4043	107	76	;	;	PUNCT
bibechana-4043	107	77	m	m	VERB
bibechana-4043	107	78	n(i	n(i	PROPN
bibechana-4043	107	79	,	,	PUNCT
bibechana-4043	107	80	k	k	NOUN
bibechana-4043	107	81	)	)	PUNCT
bibechana-4043	107	82	;	;	PUNCT
bibechana-4043	107	83	m+1	m+1	PROPN
bibechana-4043	107	84	b	b	X
bibechana-4043	107	85	b	b	PROPN
bibechana-4043	107	86	for	for	ADP
bibechana-4043	107	87	m	m	PROPN
bibechana-4043	107	88	≤	≤	NOUN
bibechana-4043	107	89	i.	i.	NOUN
bibechana-4043	107	90	for	for	ADP
bibechana-4043	107	91	a	a	DET
bibechana-4043	107	92	fixed	fixed	ADJ
bibechana-4043	107	93	k	k	NOUN
bibechana-4043	107	94	,	,	PUNCT
bibechana-4043	107	95	the	the	DET
bibechana-4043	107	96	sequence	sequence	NOUN
bibechana-4043	107	97	(	(	PUNCT
bibechana-4043	107	98	n(i	n(i	PROPN
bibechana-4043	107	99	,	,	PUNCT
bibechana-4043	107	100	k))i=1,2	k))i=1,2	PROPN
bibechana-4043	107	101	,	,	PUNCT
bibechana-4043	107	102	......	......	PUNCT
bibechana-4043	107	103	can	can	AUX
bibechana-4043	107	104	be	be	AUX
bibechana-4043	107	105	chosen	choose	VERB
bibechana-4043	107	106	inductively	inductively	ADV
bibechana-4043	107	107	,	,	PUNCT
bibechana-4043	107	108	starting	start	VERB
bibechana-4043	107	109	with	with	ADP
bibechana-4043	107	110	n(1	n(1	PROPN
bibechana-4043	107	111	,	,	PUNCT
bibechana-4043	107	112	k	k	NOUN
bibechana-4043	107	113	)	)	PUNCT
bibechana-4043	107	114	=	=	SYM
bibechana-4043	108	1	min	min	NOUN
bibechana-4043	108	2	n	n	PRON
bibechana-4043	108	3	\	\	NOUN
bibechana-4043	108	4			PROPN
bibechana-4043	108	5			NOUN
bibechana-4043	108	6			PRON
bibechana-4043	108	7			PROPN
bibechana-4043	108	8			ADJ
bibechana-4043	108	9			NOUN
bibechana-4043	108	10	u	u	PROPN
bibechana-4043	108	11	k-1	k-1	PROPN
bibechana-4043	108	12	l	l	PROPN
bibechana-4043	109	1	l=1	l=1	NOUN
bibechana-4043	109	2	m	m	VERB
bibechana-4043	109	3	and	and	CCONJ
bibechana-4043	109	4	such	such	ADJ
bibechana-4043	109	5	that	that	SCONJ
bibechana-4043	109	6	n	n	CCONJ
bibechana-4043	109	7	\	\	NOUN
bibechana-4043	109	8			PROPN
bibechana-4043	109	9			NOUN
bibechana-4043	109	10			PRON
bibechana-4043	109	11			PROPN
bibechana-4043	109	12			ADJ
bibechana-4043	109	13			NOUN
bibechana-4043	109	14	u	u	NOUN
bibechana-4043	109	15	k	k	PROPN
bibechana-4043	109	16	l	l	PROPN
bibechana-4043	110	1	l=1	l=1	NOUN
bibechana-4043	110	2	m	m	VERB
bibechana-4043	110	3	remains	remain	VERB
bibechana-4043	110	4	infinite	infinite	ADJ
bibechana-4043	110	5	.	.	PUNCT
bibechana-4043	111	1	we	we	PRON
bibechana-4043	111	2	now	now	ADV
bibechana-4043	111	3	set	set	VERB
bibechana-4043	111	4	n(i	n(i	PROPN
bibechana-4043	111	5	,	,	PUNCT
bibechana-4043	111	6	k	k	NOUN
bibechana-4043	111	7	)	)	PUNCT
bibechana-4043	111	8	;	;	PUNCT
bibechana-4043	111	9	m	m	VERB
bibechana-4043	111	10	n(i	n(i	PROPN
bibechana-4043	111	11	,	,	PUNCT
bibechana-4043	111	12	k	k	NOUN
bibechana-4043	111	13	)	)	PUNCT
bibechana-4043	111	14	;	;	PUNCT
bibechana-4043	111	15	k	k	PROPN
bibechana-4043	111	16	b	b	PROPN
bibechana-4043	111	17	b	b	PROPN
bibechana-4043	111	18	for	for	ADP
bibechana-4043	111	19	m	m	PRON
bibechana-4043	111	20	<	<	X
bibechana-4043	111	21	k	k	X
bibechana-4043	111	22	ai	ai	PROPN
bibechana-4043	111	23	,	,	PUNCT
bibechana-4043	111	24	k	k	NOUN
bibechana-4043	111	25	;	;	PUNCT
bibechana-4043	111	26	m	m	PROPN
bibechana-4043	111	27	=	=	SYM
bibechana-4043	111	28	n(i-1,k	n(i-1,k	PROPN
bibechana-4043	111	29	)	)	PUNCT
bibechana-4043	111	30	;	;	PUNCT
bibechana-4043	111	31	m	m	PROPN
bibechana-4043	111	32	n(i-1,k	n(i-1,k	PROPN
bibechana-4043	111	33	)	)	PUNCT
bibechana-4043	111	34	;	;	PUNCT
bibechana-4043	111	35	k	k	PROPN
bibechana-4043	111	36	b	b	PROPN
bibechana-4043	111	37	b	b	PROPN
bibechana-4043	111	38	for	for	ADP
bibechana-4043	111	39	m	m	PROPN
bibechana-4043	111	40	>	>	X
bibechana-4043	112	1	k	k	PROPN
bibechana-4043	112	2	,	,	PUNCT
bibechana-4043	112	3	i	i	PRON
bibechana-4043	112	4	≥	≥	VERB
bibechana-4043	112	5	2	2	NUM
bibechana-4043	112	6	1	1	NUM
bibechana-4043	112	7	elsewhere	elsewhere	ADV
bibechana-4043	112	8	since	since	SCONJ
bibechana-4043	112	9	ai	ai	VERB
bibechana-4043	112	10	,	,	PUNCT
bibechana-4043	112	11	k	k	NOUN
bibechana-4043	112	12	;	;	PUNCT
bibechana-4043	112	13	k	k	PROPN
bibechana-4043	112	14	=	=	SYM
bibechana-4043	112	15	ai+1	ai+1	PROPN
bibechana-4043	112	16	,	,	PUNCT
bibechana-4043	112	17	k	k	X
bibechana-4043	112	18	;	;	PUNCT
bibechana-4043	112	19	k	k	X
bibechana-4043	112	20	=	=	SYM
bibechana-4043	112	21	1	1	NUM
bibechana-4043	112	22	,	,	PUNCT
bibechana-4043	112	23	we	we	PRON
bibechana-4043	112	24	note	note	VERB
bibechana-4043	112	25	that	that	SCONJ
bibechana-4043	112	26	(	(	PUNCT
bibechana-4043	112	27	ai	ai	AUX
bibechana-4043	112	28	,	,	PUNCT
bibechana-4043	112	29	k	k	NOUN
bibechana-4043	112	30	;	;	PUNCT
bibechana-4043	112	31	m	m	VERB
bibechana-4043	112	32	)	)	PUNCT
bibechana-4043	112	33	is	be	AUX
bibechana-4043	112	34	increasing	increase	VERB
bibechana-4043	112	35	in	in	ADP
bibechana-4043	112	36	m.	m.	NOUN
bibechana-4043	112	37	then	then	ADV
bibechana-4043	112	38	(	(	PUNCT
bibechana-4043	112	39	1	1	NUM
bibechana-4043	112	40	)	)	PUNCT
bibechana-4043	112	41	.....	.....	PUNCT
bibechana-4043	113	1	(	(	PUNCT
bibechana-4043	113	2	4	4	X
bibechana-4043	113	3	)	)	PUNCT
bibechana-4043	113	4	of	of	ADP
bibechana-4043	113	5	3.1	3.1	NUM
bibechana-4043	113	6	lemma	lemma	PROPN
bibechana-4043	113	7	are	be	AUX
bibechana-4043	113	8	satisfied	satisfied	ADJ
bibechana-4043	113	9	and	and	CCONJ
bibechana-4043	113	10	hence	hence	ADV
bibechana-4043	113	11	we	we	PRON
bibechana-4043	113	12	have	have	VERB
bibechana-4043	113	13	an	an	DET
bibechana-4043	113	14	exact	exact	ADJ
bibechana-4043	113	15	sequence	sequence	NOUN
bibechana-4043	113	16	0	0	NUM
bibechana-4043	114	1	→	→	SYM
bibechana-4043	114	2	λ	λ	PROPN
bibechana-4043	114	3	(	(	PUNCT
bibechana-4043	114	4	ak	ak	PROPN
bibechana-4043	114	5	)	)	PUNCT
bibechana-4043	114	6	→	→	SYM
bibechana-4043	114	7	λ	λ	X
bibechana-4043	114	8	(	(	PUNCT
bibechana-4043	114	9	a	a	NOUN
bibechana-4043	114	10	)	)	PUNCT
bibechana-4043	114	11	→	→	SYM
bibechana-4043	114	12	ω	ω	PROPN
bibechana-4043	114	13	→	→	SYM
bibechana-4043	114	14	0	0	NUM
bibechana-4043	114	15	.	.	PUNCT
bibechana-4043	115	1	one	one	PRON
bibechana-4043	115	2	can	can	AUX
bibechana-4043	115	3	check	check	VERB
bibechana-4043	115	4	easily	easily	ADV
bibechana-4043	115	5	that	that	SCONJ
bibechana-4043	115	6	λ	λ	X
bibechana-4043	115	7	(	(	PUNCT
bibechana-4043	115	8	a	a	PRON
bibechana-4043	115	9	)	)	PUNCT
bibechana-4043	115	10	is	be	AUX
bibechana-4043	115	11	a	a	DET
bibechana-4043	115	12	schwartz	schwartz	NOUN
bibechana-4043	115	13	space	space	NOUN
bibechana-4043	115	14	or	or	CCONJ
bibechana-4043	115	15	if	if	SCONJ
bibechana-4043	115	16	λ	λ	X
bibechana-4043	115	17	(	(	PUNCT
bibechana-4043	115	18	b	b	NOUN
bibechana-4043	115	19	)	)	PUNCT
bibechana-4043	115	20	is	be	AUX
bibechana-4043	115	21	nuclear	nuclear	ADJ
bibechana-4043	115	22	,	,	PUNCT
bibechana-4043	115	23	then	then	ADV
bibechana-4043	115	24	λ	λ	X
bibechana-4043	115	25	(	(	PUNCT
bibechana-4043	115	26	a	a	PRON
bibechana-4043	115	27	)	)	PUNCT
bibechana-4043	115	28	is	be	AUX
bibechana-4043	115	29	also	also	ADV
bibechana-4043	115	30	nuclear	nuclear	ADJ
bibechana-4043	115	31	.	.	PUNCT
bibechana-4043	116	1	for	for	ADP
bibechana-4043	116	2	m	m	PROPN
bibechana-4043	116	3	<	<	X
bibechana-4043	116	4	k	k	PROPN
bibechana-4043	116	5	and	and	CCONJ
bibechana-4043	116	6	m	m	PROPN
bibechana-4043	116	7	≥	≥	NOUN
bibechana-4043	116	8	k	k	NOUN
bibechana-4043	116	9	using	use	VERB
bibechana-4043	116	10	(	(	PUNCT
bibechana-4043	116	11	5	5	NUM
bibechana-4043	116	12	)	)	PUNCT
bibechana-4043	116	13	and	and	CCONJ
bibechana-4043	116	14	(	(	PUNCT
bibechana-4043	116	15	6	6	NUM
bibechana-4043	116	16	)	)	PUNCT
bibechana-4043	116	17	are	be	AUX
bibechana-4043	116	18	estimate	estimate	NOUN
bibechana-4043	116	19	in	in	ADP
bibechana-4043	116	20	different	different	ADJ
bibechana-4043	116	21	ways	way	NOUN
bibechana-4043	116	22	and	and	CCONJ
bibechana-4043	116	23	obtain	obtain	VERB
bibechana-4043	116	24	2≤	2≤	NUM
bibechana-4043	116	25	≤	≤	ADJ
bibechana-4043	116	26	n(i	n(i	PROPN
bibechana-4043	116	27	,	,	PUNCT
bibechana-4043	116	28	k	k	NOUN
bibechana-4043	116	29	)	)	PUNCT
bibechana-4043	116	30	;	;	PUNCT
bibechana-4043	117	1	m	m	VERB
bibechana-4043	117	2	n(i	n(i	PROPN
bibechana-4043	117	3	,	,	PUNCT
bibechana-4043	117	4	k	k	NOUN
bibechana-4043	117	5	)	)	PUNCT
bibechana-4043	117	6	;	;	PUNCT
bibechana-4043	117	7	m	m	VERB
bibechana-4043	117	8	i	i	PROPN
bibechana-4043	117	9	,	,	PUNCT
bibechana-4043	117	10	k;m	k;m	PROPN
bibechana-4043	117	11	i+1,k;m	i+1,k;m	PROPN
bibechana-4043	117	12	n(i	n(i	PROPN
bibechana-4043	117	13	,	,	PUNCT
bibechana-4043	117	14	k	k	NOUN
bibechana-4043	117	15	)	)	PUNCT
bibechana-4043	117	16	;	;	PUNCT
bibechana-4043	117	17	k	k	PROPN
bibechana-4043	117	18	n(i	n(i	PROPN
bibechana-4043	117	19	,	,	PUNCT
bibechana-4043	117	20	k	k	NOUN
bibechana-4043	117	21	)	)	PUNCT
bibechana-4043	117	22	;	;	PUNCT
bibechana-4043	118	1	k	k	PROPN
bibechana-4043	118	2	b	b	PROPN
bibechana-4043	118	3	b	b	PROPN
bibechana-4043	118	4	a	a	DET
bibechana-4043	118	5	+	+	NOUN
bibechana-4043	118	6	a	a	DET
bibechana-4043	118	7	b	b	PROPN
bibechana-4043	118	8	b	b	NOUN
bibechana-4043	118	9	for	for	ADP
bibechana-4043	118	10	i	i	PRON
bibechana-4043	118	11	>	>	X
bibechana-4043	118	12	m.	m.	NOUN
bibechana-4043	118	13	therefore	therefore	ADV
bibechana-4043	118	14	λ	λ	PROPN
bibechana-4043	118	15	(	(	PUNCT
bibechana-4043	118	16	ak	ak	PROPN
bibechana-4043	118	17	)	)	PUNCT
bibechana-4043	118	18	is	be	AUX
bibechana-4043	118	19	isomorphic	isomorphic	ADJ
bibechana-4043	118	20	to	to	ADP
bibechana-4043	118	21	λ	λ	PROPN
bibechana-4043	118	22	(	(	PUNCT
bibechana-4043	118	23	b	b	NOUN
bibechana-4043	118	24	)	)	PUNCT
bibechana-4043	118	25	by	by	ADP
bibechana-4043	118	26	diagonal	diagonal	ADJ
bibechana-4043	118	27	transformation	transformation	NOUN
bibechana-4043	118	28	.	.	PUNCT
bibechana-4043	119	1	theorem	theorem	VERB
bibechana-4043	119	2	3.3	3.3	NUM
bibechana-4043	119	3	a	a	DET
bibechana-4043	119	4	frechet	frechet	NOUN
bibechana-4043	119	5	space	space	NOUN
bibechana-4043	119	6	e	e	NOUN
bibechana-4043	119	7	is	be	AUX
bibechana-4043	119	8	asymptotically	asymptotically	ADV
bibechana-4043	119	9	normable	normable	ADJ
bibechana-4043	119	10	if	if	SCONJ
bibechana-4043	119	11	and	and	CCONJ
bibechana-4043	119	12	ony	ony	ADJ
bibechana-4043	119	13	if	if	SCONJ
bibechana-4043	119	14	there	there	PRON
bibechana-4043	119	15	is	be	VERB
bibechana-4043	119	16	an	an	DET
bibechana-4043	119	17	index	index	NOUN
bibechana-4043	119	18	set	set	VERB
bibechana-4043	119	19	i	i	PRON
bibechana-4043	119	20	and	and	CCONJ
bibechana-4043	119	21	a	a	DET
bibechana-4043	119	22	nuclear	nuclear	ADJ
bibechana-4043	119	23	kothe	kothe	NOUN
bibechana-4043	119	24	space	space	NOUN
bibechana-4043	119	25	λ	λ	PROPN
bibechana-4043	119	26	(	(	PUNCT
bibechana-4043	119	27	a	a	NOUN
bibechana-4043	119	28	)	)	PUNCT
bibechana-4043	119	29	with	with	ADP
bibechana-4043	119	30	a	a	DET
bibechana-4043	119	31	continuous	continuous	ADJ
bibechana-4043	119	32	norm	norm	NOUN
bibechana-4043	119	33	such	such	ADJ
bibechana-4043	119	34	that	that	SCONJ
bibechana-4043	119	35	e	e	NOUN
bibechana-4043	119	36	is	be	AUX
bibechana-4043	119	37	isomorphic	isomorphic	ADJ
bibechana-4043	119	38	to	to	ADP
bibechana-4043	119	39	a	a	DET
bibechana-4043	119	40	subspace	subspace	NOUN
bibechana-4043	119	41	of	of	ADP
bibechana-4043	119	42	l∞(i)⊗π	l∞(i)⊗π	PROPN
bibechana-4043	119	43	λ(a	λ(a	NOUN
bibechana-4043	119	44	)	)	PUNCT
bibechana-4043	119	45	.	.	PUNCT
bibechana-4043	120	1	proof	proof	NOUN
bibechana-4043	120	2	:	:	PUNCT
bibechana-4043	120	3	we	we	PRON
bibechana-4043	120	4	have	have	VERB
bibechana-4043	120	5	a	a	DET
bibechana-4043	120	6	nuclear	nuclear	ADJ
bibechana-4043	120	7	kothe	kothe	NOUN
bibechana-4043	120	8	space	space	NOUN
bibechana-4043	120	9	λ	λ	X
bibechana-4043	120	10	(	(	PUNCT
bibechana-4043	120	11	b	b	NOUN
bibechana-4043	120	12	)	)	PUNCT
bibechana-4043	120	13	with	with	ADP
bibechana-4043	120	14	a	a	DET
bibechana-4043	120	15	continuous	continuous	ADJ
bibechana-4043	120	16	norm	norm	NOUN
bibechana-4043	121	1	such	such	ADJ
bibechana-4043	121	2	that	that	SCONJ
bibechana-4043	121	3	(	(	PUNCT
bibechana-4043	121	4	e	e	NOUN
bibechana-4043	121	5	,	,	PUNCT
bibechana-4043	121	6	λ	λ	PROPN
bibechana-4043	121	7	(	(	PUNCT
bibechana-4043	121	8	b	b	NOUN
bibechana-4043	121	9	)	)	PUNCT
bibechana-4043	121	10	)	)	PUNCT
bibechana-4043	121	11	∈	∈	PROPN
bibechana-4043	121	12	(	(	PUNCT
bibechana-4043	121	13	)	)	PUNCT
bibechana-4043	121	14	*	*	PUNCT
bibechana-4043	121	15	1	1	NUM
bibechana-4043	121	16	s	s	NOUN
bibechana-4043	121	17	by	by	ADP
bibechana-4043	121	18	lemma	lemma	PROPN
bibechana-4043	121	19	5.4	5.4	NUM
bibechana-4043	121	20	in	in	ADP
bibechana-4043	121	21	[	[	X
bibechana-4043	121	22	3	3	NUM
bibechana-4043	121	23	]	]	PUNCT
bibechana-4043	121	24	.	.	PUNCT
bibechana-4043	122	1	by	by	ADP
bibechana-4043	122	2	the	the	DET
bibechana-4043	122	3	previous	previous	ADJ
bibechana-4043	122	4	result	result	NOUN
bibechana-4043	122	5	we	we	PRON
bibechana-4043	122	6	construct	construct	VERB
bibechana-4043	122	7	an	an	DET
bibechana-4043	122	8	exact	exact	ADJ
bibechana-4043	122	9	sequence	sequence	NOUN
bibechana-4043	122	10	.	.	PUNCT
bibechana-4043	122	11	0	0	PUNCT
bibechana-4043	123	1	→	→	SYM
bibechana-4043	123	2	λ	λ	X
bibechana-4043	123	3	(	(	PUNCT
bibechana-4043	123	4	b	b	NOUN
bibechana-4043	123	5	)	)	PUNCT
bibechana-4043	123	6	→	→	SYM
bibechana-4043	123	7	λ	λ	X
bibechana-4043	123	8	(	(	PUNCT
bibechana-4043	123	9	a	a	NOUN
bibechana-4043	123	10	)	)	PUNCT
bibechana-4043	123	11	→	→	SYM
bibechana-4043	123	12	ω	ω	PROPN
bibechana-4043	123	13	→	→	SYM
bibechana-4043	123	14	0	0	NUM
bibechana-4043	123	15	.	.	PUNCT
bibechana-4043	124	1	if	if	SCONJ
bibechana-4043	124	2	e	e	PROPN
bibechana-4043	124	3	is	be	AUX
bibechana-4043	124	4	a	a	DET
bibechana-4043	124	5	banach	banach	NOUN
bibechana-4043	124	6	space	space	NOUN
bibechana-4043	124	7	,	,	PUNCT
bibechana-4043	124	8	our	our	PRON
bibechana-4043	124	9	theorem	theorem	NOUN
bibechana-4043	124	10	is	be	AUX
bibechana-4043	124	11	trivial	trivial	ADJ
bibechana-4043	124	12	.	.	PUNCT
bibechana-4043	125	1	if	if	SCONJ
bibechana-4043	125	2	e	e	PROPN
bibechana-4043	125	3	is	be	AUX
bibechana-4043	125	4	a	a	DET
bibechana-4043	125	5	proper	proper	ADJ
bibechana-4043	125	6	frechet	frechet	NOUN
bibechana-4043	125	7	space	space	NOUN
bibechana-4043	125	8	,	,	PUNCT
bibechana-4043	125	9	then	then	ADV
bibechana-4043	125	10	(	(	PUNCT
bibechana-4043	125	11	e	e	X
bibechana-4043	125	12	,	,	PUNCT
bibechana-4043	125	13	λ	λ	PROPN
bibechana-4043	125	14	(	(	PUNCT
bibechana-4043	125	15	b	b	NOUN
bibechana-4043	125	16	)	)	PUNCT
bibechana-4043	125	17	)	)	PUNCT
bibechana-4043	125	18	∈	∈	PROPN
bibechana-4043	125	19	(	(	PUNCT
bibechana-4043	125	20	)	)	PUNCT
bibechana-4043	125	21	o	o	NOUN
bibechana-4043	126	1	*	*	PUNCT
bibechana-4043	126	2	1	1	NUM
bibechana-4043	126	3	s	s	NOUN
bibechana-4043	126	4	by	by	ADP
bibechana-4043	126	5	lemma	lemma	PROPN
bibechana-4043	126	6	3.3	3.3	NUM
bibechana-4043	126	7	in	in	ADP
bibechana-4043	126	8	[	[	X
bibechana-4043	126	9	5	5	NUM
bibechana-4043	126	10	]	]	PUNCT
bibechana-4043	126	11	.	.	PUNCT
bibechana-4043	127	1	now	now	ADV
bibechana-4043	127	2	we	we	PRON
bibechana-4043	127	3	choose	choose	VERB
bibechana-4043	127	4	a	a	DET
bibechana-4043	127	5	set	set	NOUN
bibechana-4043	127	6	i	i	PRON
bibechana-4043	127	7	such	such	ADJ
bibechana-4043	127	8	that	that	SCONJ
bibechana-4043	127	9	each	each	DET
bibechana-4043	127	10	banach	banach	NOUN
bibechana-4043	127	11	space	space	NOUN
bibechana-4043	127	12	ek	ek	NOUN
bibechana-4043	127	13	is	be	AUX
bibechana-4043	127	14	isomorphic	isomorphic	ADJ
bibechana-4043	127	15	to	to	ADP
bibechana-4043	127	16	a	a	DET
bibechana-4043	127	17	subspace	subspace	NOUN
bibechana-4043	127	18	of	of	ADP
bibechana-4043	127	19	l∞(i	l∞(i	NOUN
bibechana-4043	127	20	)	)	PUNCT
bibechana-4043	127	21	,	,	PUNCT
bibechana-4043	127	22	where	where	SCONJ
bibechana-4043	127	23	ek	ek	PROPN
bibechana-4043	127	24	is	be	AUX
bibechana-4043	127	25	the	the	DET
bibechana-4043	127	26	completion	completion	NOUN
bibechana-4043	127	27	of	of	ADP
bibechana-4043	127	28	(	(	PUNCT
bibechana-4043	127	29	e	e	NOUN
bibechana-4043	127	30	,	,	PUNCT
bibechana-4043	127	31	||	||	ADJ
bibechana-4043	128	1	||k	||k	PROPN
bibechana-4043	128	2	)	)	PUNCT
bibechana-4043	128	3	.	.	PUNCT
bibechana-4043	129	1	we	we	PRON
bibechana-4043	129	2	identify	identify	VERB
bibechana-4043	129	3	the	the	DET
bibechana-4043	129	4	tensor	tensor	NOUN
bibechana-4043	129	5	product	product	NOUN
bibechana-4043	129	6	l∞(i)⊗π	l∞(i)⊗π	NOUN
bibechana-4043	129	7	λ(b	λ(b	PROPN
bibechana-4043	129	8	)	)	PUNCT
bibechana-4043	129	9	with	with	ADP
bibechana-4043	129	10	the	the	DET
bibechana-4043	129	11	space	space	NOUN
bibechana-4043	129	12	of	of	ADP
bibechana-4043	129	13	all	all	PRON
bibechana-4043	129	14	y	y	PROPN
bibechana-4043	129	15	=	=	SYM
bibechana-4043	129	16	(	(	PUNCT
bibechana-4043	129	17	yj	yj	PROPN
bibechana-4043	129	18	)	)	PUNCT
bibechana-4043	129	19	,	,	PUNCT
bibechana-4043	129	20	such	such	DET
bibechana-4043	129	21	each	each	DET
bibechana-4043	129	22	vj	vj	PROPN
bibechana-4043	129	23	∈	∈	PROPN
bibechana-4043	129	24	l∞(i	l∞(i	PROPN
bibechana-4043	129	25	)	)	PUNCT
bibechana-4043	129	26	and	and	CCONJ
bibechana-4043	129	27	for	for	ADP
bibechana-4043	129	28	every	every	DET
bibechana-4043	129	29	k	k	PROPN
bibechana-4043	129	30	∈	∈	PROPN
bibechana-4043	129	31	n	n	CCONJ
bibechana-4043	129	32	we	we	PRON
bibechana-4043	129	33	have	have	VERB
bibechana-4043	129	34	||y||k	||y||k	NOUN
bibechana-4043	129	35	=	=	NOUN
bibechana-4043	129	36	sup	sup	NOUN
bibechana-4043	129	37	||yj||∞bj;k	||yj||∞bj;k	NOUN
bibechana-4043	129	38	<	<	X
bibechana-4043	130	1	+	+	X
bibechana-4043	130	2	∞	∞	NUM
bibechana-4043	130	3	where	where	SCONJ
bibechana-4043	130	4	||	||	PROPN
bibechana-4043	130	5	||∞	||∞	PROPN
bibechana-4043	130	6	denotes	denote	VERB
bibechana-4043	130	7	the	the	DET
bibechana-4043	130	8	norm	norm	NOUN
bibechana-4043	130	9	of	of	ADP
bibechana-4043	130	10	l∞(i	l∞(i	NOUN
bibechana-4043	130	11	)	)	PUNCT
bibechana-4043	130	12	.	.	PUNCT
bibechana-4043	131	1	an	an	DET
bibechana-4043	131	2	obvious	obvious	ADJ
bibechana-4043	131	3	modification	modification	NOUN
bibechana-4043	131	4	of	of	ADP
bibechana-4043	131	5	proposition	proposition	NOUN
bibechana-4043	131	6	3.5	3.5	NUM
bibechana-4043	131	7	in	in	ADP
bibechana-4043	131	8	[	[	X
bibechana-4043	131	9	5	5	NUM
bibechana-4043	131	10	]	]	X
bibechana-4043	131	11	yields	yield	NOUN
bibechana-4043	131	12	(	(	PUNCT
bibechana-4043	131	13	e	e	NOUN
bibechana-4043	131	14	,	,	PUNCT
bibechana-4043	131	15	l∞(i)⊗π	l∞(i)⊗π	PROPN
bibechana-4043	131	16	λ(b	λ(b	PROPN
bibechana-4043	131	17	)	)	PUNCT
bibechana-4043	131	18	∈	∈	PROPN
bibechana-4043	131	19	(	(	PUNCT
bibechana-4043	131	20	s1	s1	NOUN
bibechana-4043	131	21	)	)	PUNCT
bibechana-4043	131	22	.	.	PUNCT
bibechana-4043	132	1	taking	take	VERB
bibechana-4043	132	2	tensor	tensor	NOUN
bibechana-4043	132	3	product	product	NOUN
bibechana-4043	132	4	with	with	ADP
bibechana-4043	132	5	l∞(i	l∞(i	NOUN
bibechana-4043	132	6	)	)	PUNCT
bibechana-4043	132	7	we	we	PRON
bibechana-4043	132	8	get	get	VERB
bibechana-4043	132	9	an	an	DET
bibechana-4043	132	10	exact	exact	ADJ
bibechana-4043	132	11	sequence	sequence	NOUN
bibechana-4043	132	12	lim	lim	PROPN
bibechana-4043	132	13	j	j	PROPN
bibechana-4043	133	1	∧	∧	PROPN
bibechana-4043	133	2	∧	∧	PROPN
bibechana-4043	133	3	j	j	PROPN
bibechana-4043	133	4	g.k	g.k	PROPN
bibechana-4043	133	5	.	.	PROPN
bibechana-4043	133	6	palei	palei	PROPN
bibechana-4043	133	7	and	and	CCONJ
bibechana-4043	133	8	n.p	n.p	PROPN
bibechana-4043	133	9	.	.	PROPN
bibechana-4043	133	10	sah	sah	PROPN
bibechana-4043	133	11	/	/	SYM
bibechana-4043	133	12	bibechana	bibechana	PROPN
bibechana-4043	133	13	7	7	NUM
bibechana-4043	133	14	(	(	PUNCT
bibechana-4043	133	15	2011	2011	NUM
bibechana-4043	133	16	)	)	PUNCT
bibechana-4043	133	17	39	39	NUM
bibechana-4043	133	18	-	-	SYM
bibechana-4043	133	19	43	43	NUM
bibechana-4043	133	20	:	:	PUNCT
bibechana-4043	133	21	bmhss	bmhss	NOUN
bibechana-4043	133	22	43	43	NUM
bibechana-4043	133	23	0	0	NUM
bibechana-4043	133	24	→	→	SYM
bibechana-4043	133	25	l∞(i)⊗π	l∞(i)⊗π	NOUN
bibechana-4043	133	26	λ(b	λ(b	PROPN
bibechana-4043	133	27	)	)	PUNCT
bibechana-4043	133	28	→	→	SYM
bibechana-4043	133	29	l∞(i)⊗π	l∞(i)⊗π	NOUN
bibechana-4043	133	30	λ(a	λ(a	PROPN
bibechana-4043	133	31	)	)	PUNCT
bibechana-4043	133	32	→	→	SYM
bibechana-4043	133	33	l∞(i	l∞(i	NOUN
bibechana-4043	133	34	)	)	PUNCT
bibechana-4043	133	35	n	n	PROPN
bibechana-4043	133	36	→	→	SYM
bibechana-4043	133	37	0	0	NUM
bibechana-4043	133	38	since	since	SCONJ
bibechana-4043	133	39	ext	ext	NOUN
bibechana-4043	133	40	(	(	PUNCT
bibechana-4043	133	41	e	e	NOUN
bibechana-4043	133	42	,	,	PUNCT
bibechana-4043	133	43	l∞(i)⊗π	l∞(i)⊗π	PROPN
bibechana-4043	133	44	λ(b	λ(b	PROPN
bibechana-4043	133	45	)	)	PUNCT
bibechana-4043	133	46	)	)	PUNCT
bibechana-4043	134	1	=	=	SYM
bibechana-4043	134	2	0	0	NUM
bibechana-4043	134	3	,	,	PUNCT
bibechana-4043	134	4	the	the	DET
bibechana-4043	134	5	natural	natural	ADJ
bibechana-4043	134	6	imbedding	imbedding	ADJ
bibechana-4043	134	7	t	t	PROPN
bibechana-4043	134	8	of	of	ADP
bibechana-4043	134	9	e	e	PROPN
bibechana-4043	134	10	into	into	ADP
bibechana-4043	134	11	l∞(i	l∞(i	NOUN
bibechana-4043	134	12	)	)	PUNCT
bibechana-4043	134	13	n	n	VERB
bibechana-4043	134	14	can	can	AUX
bibechana-4043	134	15	be	be	AUX
bibechana-4043	134	16	lifted	lift	VERB
bibechana-4043	134	17	to	to	ADP
bibechana-4043	134	18	a	a	DET
bibechana-4043	134	19	continuous	continuous	ADJ
bibechana-4043	134	20	linear	linear	NOUN
bibechana-4043	134	21	operator	operator	NOUN
bibechana-4043	134	22	t	t	NOUN
bibechana-4043	134	23	:	:	PUNCT
bibechana-4043	134	24	e	e	X
bibechana-4043	134	25	→	→	SYM
bibechana-4043	134	26	l∞(i)⊗π	l∞(i)⊗π	PROPN
bibechana-4043	134	27	λ(a	λ(a	PROPN
bibechana-4043	134	28	)	)	PUNCT
bibechana-4043	134	29	.	.	PUNCT
bibechana-4043	135	1	it	it	PRON
bibechana-4043	135	2	is	be	AUX
bibechana-4043	135	3	easily	easily	ADV
bibechana-4043	135	4	checked	check	VERB
bibechana-4043	135	5	that	that	SCONJ
bibechana-4043	135	6	t	t	PROPN
bibechana-4043	135	7	is	be	AUX
bibechana-4043	135	8	one	one	NUM
bibechana-4043	135	9	-	-	PUNCT
bibechana-4043	135	10	to	to	ADP
bibechana-4043	135	11	-	-	PUNCT
bibechana-4043	135	12	one	one	NUM
bibechana-4043	135	13	and	and	CCONJ
bibechana-4043	135	14	has	have	VERB
bibechana-4043	135	15	a	a	DET
bibechana-4043	135	16	closed	closed	ADJ
bibechana-4043	135	17	range	range	NOUN
bibechana-4043	135	18	.	.	PUNCT
bibechana-4043	136	1	we	we	PRON
bibechana-4043	136	2	would	would	AUX
bibechana-4043	136	3	like	like	VERB
bibechana-4043	136	4	to	to	PART
bibechana-4043	136	5	point	point	VERB
bibechana-4043	136	6	out	out	ADP
bibechana-4043	136	7	that	that	SCONJ
bibechana-4043	136	8	the	the	DET
bibechana-4043	136	9	kothe	kothe	ADJ
bibechana-4043	136	10	space	space	NOUN
bibechana-4043	136	11	λ(a	λ(a	NOUN
bibechana-4043	136	12	)	)	PUNCT
bibechana-4043	136	13	we	we	PRON
bibechana-4043	136	14	have	have	AUX
bibechana-4043	136	15	constructed	construct	VERB
bibechana-4043	136	16	actually	actually	ADV
bibechana-4043	136	17	depends	depend	VERB
bibechana-4043	136	18	only	only	ADV
bibechana-4043	136	19	on	on	ADP
bibechana-4043	136	20	ϕ.	ϕ.	PROPN
bibechana-4043	136	21	this	this	PRON
bibechana-4043	136	22	is	be	AUX
bibechana-4043	136	23	so	so	ADV
bibechana-4043	136	24	,	,	PUNCT
bibechana-4043	136	25	because	because	SCONJ
bibechana-4043	136	26	for	for	ADP
bibechana-4043	136	27	each	each	DET
bibechana-4043	136	28	strictly	strictly	ADV
bibechana-4043	136	29	increasing	increase	VERB
bibechana-4043	136	30	function	function	NOUN
bibechana-4043	136	31	ϕ	ϕ	NOUN
bibechana-4043	136	32	:	:	PUNCT
bibechana-4043	136	33	(	(	PUNCT
bibechana-4043	136	34	0	0	NUM
bibechana-4043	136	35	,	,	PUNCT
bibechana-4043	136	36	∞	∞	PROPN
bibechana-4043	136	37	)	)	PUNCT
bibechana-4043	136	38	→	→	SYM
bibechana-4043	136	39	(	(	PUNCT
bibechana-4043	136	40	0	0	NUM
bibechana-4043	136	41	,	,	PUNCT
bibechana-4043	136	42	∞	∞	PROPN
bibechana-4043	136	43	)	)	PUNCT
bibechana-4043	136	44	,	,	PUNCT
bibechana-4043	136	45	an	an	DET
bibechana-4043	136	46	examination	examination	NOUN
bibechana-4043	136	47	of	of	ADP
bibechana-4043	136	48	the	the	DET
bibechana-4043	136	49	proof	proof	NOUN
bibechana-4043	136	50	of	of	ADP
bibechana-4043	136	51	lemma	lemma	PROPN
bibechana-4043	136	52	5.4	5.4	NUM
bibechana-4043	136	53	in	in	ADP
bibechana-4043	136	54	[	[	X
bibechana-4043	136	55	3	3	NUM
bibechana-4043	136	56	]	]	PUNCT
bibechana-4043	136	57	reveals	reveal	VERB
bibechana-4043	136	58	that	that	SCONJ
bibechana-4043	136	59	there	there	PRON
bibechana-4043	136	60	is	be	VERB
bibechana-4043	136	61	a	a	DET
bibechana-4043	136	62	nuclear	nuclear	ADJ
bibechana-4043	136	63	kothe	kothe	NOUN
bibechana-4043	136	64	space	space	NOUN
bibechana-4043	136	65	λ(b	λ(b	PROPN
bibechana-4043	136	66	)	)	PUNCT
bibechana-4043	136	67	such	such	ADJ
bibechana-4043	136	68	that	that	SCONJ
bibechana-4043	136	69	(	(	PUNCT
bibechana-4043	136	70	e	e	NOUN
bibechana-4043	136	71	,	,	PUNCT
bibechana-4043	136	72	λ(b	λ(b	PROPN
bibechana-4043	136	73	)	)	PUNCT
bibechana-4043	136	74	)	)	PUNCT
bibechana-4043	136	75	∈	∈	PROPN
bibechana-4043	136	76	(	(	PUNCT
bibechana-4043	136	77	)	)	PUNCT
bibechana-4043	136	78	*	*	PUNCT
bibechana-4043	136	79	1	1	NUM
bibechana-4043	136	80	s	s	NOUN
bibechana-4043	136	81	for	for	ADP
bibechana-4043	136	82	any	any	DET
bibechana-4043	136	83	frechet	frechet	NOUN
bibechana-4043	136	84	space	space	NOUN
bibechana-4043	136	85	e	e	NOUN
bibechana-4043	136	86	which	which	PRON
bibechana-4043	136	87	satisfies	satisfy	VERB
bibechana-4043	136	88	(	(	PUNCT
bibechana-4043	136	89	dnϕ	dnϕ	PROPN
bibechana-4043	136	90	)	)	PUNCT
bibechana-4043	136	91	.	.	PUNCT
bibechana-4043	137	1	finally	finally	ADV
bibechana-4043	137	2	,	,	PUNCT
bibechana-4043	137	3	we	we	PRON
bibechana-4043	137	4	would	would	AUX
bibechana-4043	137	5	like	like	VERB
bibechana-4043	137	6	to	to	PART
bibechana-4043	137	7	note	note	VERB
bibechana-4043	137	8	that	that	SCONJ
bibechana-4043	137	9	l.	l.	PROPN
bibechana-4043	137	10	holmstrom	holmstrom	PROPN
bibechana-4043	138	1	[	[	X
bibechana-4043	138	2	8	8	NUM
bibechana-4043	138	3	]	]	PUNCT
bibechana-4043	138	4	proved	prove	VERB
bibechana-4043	138	5	that	that	SCONJ
bibechana-4043	138	6	every	every	DET
bibechana-4043	138	7	nuclear	nuclear	ADJ
bibechana-4043	138	8	asymptotically	asymptotically	ADV
bibechana-4043	138	9	normable	normable	ADJ
bibechana-4043	138	10	frechet	frechet	NOUN
bibechana-4043	138	11	space	space	NOUN
bibechana-4043	138	12	is	be	AUX
bibechana-4043	138	13	isomorphic	isomorphic	ADJ
bibechana-4043	138	14	to	to	ADP
bibechana-4043	138	15	a	a	DET
bibechana-4043	138	16	subspace	subspace	NOUN
bibechana-4043	138	17	of	of	ADP
bibechana-4043	138	18	some	some	DET
bibechana-4043	138	19	nuclear	nuclear	ADJ
bibechana-4043	138	20	kothe	kothe	NOUN
bibechana-4043	138	21	space	space	NOUN
bibechana-4043	138	22	which	which	PRON
bibechana-4043	138	23	admits	admit	VERB
bibechana-4043	138	24	a	a	DET
bibechana-4043	138	25	continuous	continuous	ADJ
bibechana-4043	138	26	norm	norm	NOUN
bibechana-4043	138	27	.	.	PUNCT
bibechana-4043	139	1	d.	d.	PROPN
bibechana-4043	139	2	finally	finally	ADV
bibechana-4043	139	3	we	we	PRON
bibechana-4043	139	4	use	use	VERB
bibechana-4043	139	5	the	the	DET
bibechana-4043	139	6	results	result	NOUN
bibechana-4043	139	7	of	of	ADP
bibechana-4043	139	8	section	section	NOUN
bibechana-4043	139	9	3	3	NUM
bibechana-4043	139	10	for	for	ADP
bibechana-4043	139	11	another	another	DET
bibechana-4043	139	12	description	description	NOUN
bibechana-4043	139	13	of	of	ADP
bibechana-4043	139	14	the	the	DET
bibechana-4043	139	15	class	class	NOUN
bibechana-4043	139	16	of	of	ADP
bibechana-4043	139	17	asymptotically	asymptotically	ADV
bibechana-4043	139	18	normable	normable	ADJ
bibechana-4043	139	19	frechet	frechet	NOUN
bibechana-4043	139	20	spaces	space	NOUN
bibechana-4043	139	21	and	and	CCONJ
bibechana-4043	139	22	for	for	ADP
bibechana-4043	139	23	a	a	DET
bibechana-4043	139	24	comparison	comparison	NOUN
bibechana-4043	139	25	with	with	ADP
bibechana-4043	139	26	the	the	DET
bibechana-4043	139	27	class	class	NOUN
bibechana-4043	139	28	quasi	quasi	ADJ
bibechana-4043	139	29	-	-	ADJ
bibechana-4043	139	30	normable	normable	ADJ
bibechana-4043	139	31	frechet	frechet	NOUN
bibechana-4043	139	32	spaces	space	VERB
bibechana-4043	139	33	.	.	PUNCT
bibechana-4043	140	1	the	the	DET
bibechana-4043	140	2	first	first	ADJ
bibechana-4043	140	3	lemma	lemma	PROPN
bibechana-4043	140	4	is	be	AUX
bibechana-4043	140	5	obvious	obvious	ADJ
bibechana-4043	140	6	.	.	PUNCT
bibechana-4043	141	1	lemma	lemma	PROPN
bibechana-4043	141	2	4.1	4.1	NUM
bibechana-4043	141	3	if	if	SCONJ
bibechana-4043	141	4	e	e	NOUN
bibechana-4043	141	5	is	be	AUX
bibechana-4043	141	6	asymptotically	asymptotically	ADV
bibechana-4043	141	7	normable	normable	ADJ
bibechana-4043	141	8	and	and	CCONJ
bibechana-4043	141	9	h	h	NOUN
bibechana-4043	141	10	⊂	⊂	PROPN
bibechana-4043	141	11	e	e	NOUN
bibechana-4043	141	12	a	a	DET
bibechana-4043	141	13	subspace	subspace	NOUN
bibechana-4043	141	14	then	then	ADV
bibechana-4043	141	15	h	h	PROPN
bibechana-4043	141	16	is	be	AUX
bibechana-4043	141	17	asymptotically	asymptotically	ADV
bibechana-4043	141	18	normable	normable	ADJ
bibechana-4043	141	19	.	.	PUNCT
bibechana-4043	142	1	lemma	lemma	PROPN
bibechana-4043	142	2	4.2	4.2	NUM
bibechana-4043	142	3	if	if	SCONJ
bibechana-4043	142	4	e	e	PROPN
bibechana-4043	142	5	and	and	CCONJ
bibechana-4043	142	6	f	f	PROPN
bibechana-4043	142	7	are	be	AUX
bibechana-4043	142	8	asymptotically	asymptotically	ADV
bibechana-4043	142	9	normable	normable	ADJ
bibechana-4043	143	1	then	then	ADV
bibechana-4043	143	2	so	so	ADV
bibechana-4043	143	3	is	be	AUX
bibechana-4043	143	4	1	1	NUM
bibechana-4043	143	5	b	b	NOUN
bibechana-4043	143	6	b	b	PROPN
bibechana-4043	143	7	l	l	NOUN
bibechana-4043	143	8	(	(	PUNCT
bibechana-4043	143	9	e	e	NOUN
bibechana-4043	143	10	,	,	PUNCT
bibechana-4043	143	11	f	f	PROPN
bibechana-4043	143	12	)	)	PUNCT
bibechana-4043	143	13	.	.	PUNCT
bibechana-4043	144	1	proof	proof	NOUN
bibechana-4043	144	2	:	:	PUNCT
bibechana-4043	144	3	the	the	DET
bibechana-4043	144	4	proof	proof	NOUN
bibechana-4043	144	5	is	be	AUX
bibechana-4043	144	6	straightforward	straightforward	ADJ
bibechana-4043	144	7	if	if	SCONJ
bibechana-4043	144	8	one	one	NUM
bibechana-4043	144	9	notices	notice	VERB
bibechana-4043	144	10	that	that	SCONJ
bibechana-4043	144	11	e	e	NOUN
bibechana-4043	144	12	being	be	AUX
bibechana-4043	144	13	asymptotically	asymptotically	ADV
bibechana-4043	144	14	normable	normable	ADJ
bibechana-4043	144	15	is	be	AUX
bibechana-4043	144	16	equivalent	equivalent	ADJ
bibechana-4043	144	17	to	to	ADP
bibechana-4043	144	18	:	:	PUNCT
bibechana-4043	144	19	there	there	PRON
bibechana-4043	144	20	is	be	VERB
bibechana-4043	144	21	ko	ko	PROPN
bibechana-4043	144	22	such	such	ADJ
bibechana-4043	144	23	that	that	PRON
bibechana-4043	144	24	for	for	ADP
bibechana-4043	144	25	every	every	DET
bibechana-4043	144	26	k	k	NOUN
bibechana-4043	144	27	there	there	PRON
bibechana-4043	144	28	is	be	VERB
bibechana-4043	144	29	a	a	DET
bibechana-4043	144	30	p	p	NOUN
bibechana-4043	144	31	so	so	SCONJ
bibechana-4043	144	32	that	that	SCONJ
bibechana-4043	144	33	for	for	ADP
bibechana-4043	144	34	every	every	DET
bibechana-4043	144	35	ε	ε	PROPN
bibechana-4043	144	36	>	>	X
bibechana-4043	144	37	0	0	NUM
bibechana-4043	144	38	we	we	PRON
bibechana-4043	144	39	can	can	AUX
bibechana-4043	144	40	choose	choose	VERB
bibechana-4043	144	41	m	m	PROPN
bibechana-4043	144	42	>	>	X
bibechana-4043	144	43	0	0	PUNCT
bibechana-4043	145	1	with	with	ADP
bibechana-4043	145	2	⊂	⊂	PROPN
bibechana-4043	145	3	ε	ε	PROPN
bibechana-4043	146	1	o	o	NOUN
bibechana-4043	147	1	o	o	X
bibechana-4043	148	1	o	o	X
bibechana-4043	148	2	o	o	X
bibechana-4043	148	3	k	k	X
bibechana-4043	148	4	k	k	PROPN
bibechana-4043	148	5	pu	pu	PROPN
bibechana-4043	148	6	mu	mu	PROPN
bibechana-4043	148	7	+	+	CCONJ
bibechana-4043	148	8	u	u	NOUN
bibechana-4043	148	9	from	from	ADP
bibechana-4043	148	10	these	these	DET
bibechana-4043	148	11	lemmas	lemma	NOUN
bibechana-4043	148	12	and	and	CCONJ
bibechana-4043	148	13	theorem	theorem	VERB
bibechana-4043	148	14	3.3	3.3	NUM
bibechana-4043	148	15	,	,	PUNCT
bibechana-4043	148	16	we	we	PRON
bibechana-4043	148	17	can	can	AUX
bibechana-4043	148	18	obtain	obtain	VERB
bibechana-4043	148	19	:	:	PUNCT
bibechana-4043	148	20	theorem	theorem	VERB
bibechana-4043	148	21	4.3	4.3	NUM
bibechana-4043	148	22	the	the	DET
bibechana-4043	148	23	class	class	NOUN
bibechana-4043	148	24	of	of	ADP
bibechana-4043	148	25	asymptotically	asymptotically	ADV
bibechana-4043	148	26	normable	normable	ADJ
bibechana-4043	148	27	frechet	frechet	NOUN
bibechana-4043	148	28	spaces	space	NOUN
bibechana-4043	148	29	is	be	AUX
bibechana-4043	148	30	the	the	DET
bibechana-4043	148	31	smallest	small	ADJ
bibechana-4043	148	32	class	class	NOUN
bibechana-4043	148	33	of	of	ADP
bibechana-4043	148	34	frechet	frechet	PROPN
bibechana-4043	148	35	spaces	space	NOUN
bibechana-4043	148	36	containing	contain	VERB
bibechana-4043	148	37	the	the	DET
bibechana-4043	148	38	nuclear	nuclear	ADJ
bibechana-4043	148	39	kothe	kothe	NOUN
bibechana-4043	148	40	spaces	space	NOUN
bibechana-4043	148	41	with	with	ADP
bibechana-4043	148	42	continuous	continuous	ADJ
bibechana-4043	148	43	norm	norm	NOUN
bibechana-4043	148	44	the	the	DET
bibechana-4043	148	45	banach	banach	NOUN
bibechana-4043	148	46	spaces	space	NOUN
bibechana-4043	148	47	and	and	CCONJ
bibechana-4043	148	48	is	be	AUX
bibechana-4043	148	49	closed	close	VERB
bibechana-4043	148	50	under	under	ADP
bibechana-4043	148	51	ε	ε	PROPN
bibechana-4043	148	52	-	-	PUNCT
bibechana-4043	148	53	tensor	tensor	NOUN
bibechana-4043	148	54	products	product	NOUN
bibechana-4043	148	55	and	and	CCONJ
bibechana-4043	148	56	subspaces	subspace	NOUN
bibechana-4043	148	57	.	.	PUNCT
bibechana-4043	149	1	for	for	ADP
bibechana-4043	149	2	comparison	comparison	NOUN
bibechana-4043	149	3	we	we	PRON
bibechana-4043	149	4	recall	recall	VERB
bibechana-4043	149	5	that	that	SCONJ
bibechana-4043	149	6	the	the	DET
bibechana-4043	149	7	class	class	NOUN
bibechana-4043	149	8	of	of	ADP
bibechana-4043	149	9	quasi	quasi	ADJ
bibechana-4043	149	10	-	-	ADJ
bibechana-4043	149	11	normable	normable	ADJ
bibechana-4043	149	12	frechet	frechet	NOUN
bibechana-4043	149	13	spaces	space	NOUN
bibechana-4043	149	14	is	be	AUX
bibechana-4043	149	15	the	the	DET
bibechana-4043	149	16	smallest	small	ADJ
bibechana-4043	149	17	class	class	NOUN
bibechana-4043	149	18	of	of	ADP
bibechana-4043	149	19	frechet	frechet	PROPN
bibechana-4043	149	20	spaces	space	NOUN
bibechana-4043	149	21	containing	contain	VERB
bibechana-4043	149	22	the	the	DET
bibechana-4043	149	23	nuclear	nuclear	ADJ
bibechana-4043	149	24	kothe	kothe	NOUN
bibechana-4043	149	25	spaces	space	NOUN
bibechana-4043	149	26	(	(	PUNCT
bibechana-4043	149	27	or	or	CCONJ
bibechana-4043	149	28	nuclear	nuclear	ADJ
bibechana-4043	149	29	kothe	kothe	NOUN
bibechana-4043	149	30	spaces	space	NOUN
bibechana-4043	149	31	with	with	ADP
bibechana-4043	149	32	continuous	continuous	ADJ
bibechana-4043	149	33	norms	norm	NOUN
bibechana-4043	149	34	,	,	PUNCT
bibechana-4043	149	35	or	or	CCONJ
bibechana-4043	149	36	schwartz	schwartz	PROPN
bibechana-4043	149	37	spaces	space	VERB
bibechana-4043	149	38	,	,	PUNCT
bibechana-4043	149	39	or	or	CCONJ
bibechana-4043	149	40	countably	countably	ADV
bibechana-4043	149	41	normable	normable	ADJ
bibechana-4043	149	42	schwartz	schwartz	NOUN
bibechana-4043	149	43	spaces	space	NOUN
bibechana-4043	149	44	)	)	PUNCT
bibechana-4043	149	45	and	and	CCONJ
bibechana-4043	149	46	the	the	DET
bibechana-4043	149	47	banach	banach	NOUN
bibechana-4043	149	48	spaces	space	NOUN
bibechana-4043	149	49	and	and	CCONJ
bibechana-4043	149	50	is	be	AUX
bibechana-4043	149	51	closed	close	VERB
bibechana-4043	149	52	under	under	ADP
bibechana-4043	149	53	π	π	PROPN
bibechana-4043	149	54	-	-	PUNCT
bibechana-4043	149	55	tensor	tensor	NOUN
bibechana-4043	149	56	products	product	NOUN
bibechana-4043	149	57	and	and	CCONJ
bibechana-4043	149	58	quotient	quotient	NOUN
bibechana-4043	149	59	spaces	space	NOUN
bibechana-4043	149	60	.	.	PUNCT
bibechana-4043	150	1	references	reference	NOUN
bibechana-4043	150	2	[	[	X
bibechana-4043	150	3	1	1	NUM
bibechana-4043	150	4	]	]	PUNCT
bibechana-4043	150	5	a.	a.	NOUN
bibechana-4043	150	6	grothendieck	grothendieck	PROPN
bibechana-4043	150	7	,	,	PUNCT
bibechana-4043	150	8	topological	topological	ADJ
bibechana-4043	150	9	vector	vector	NOUN
bibechana-4043	150	10	spaces	space	NOUN
bibechana-4043	150	11	,	,	PUNCT
bibechana-4043	150	12	new	new	PROPN
bibechana-4043	150	13	york	york	PROPN
bibechana-4043	150	14	–	–	PUNCT
bibechana-4043	150	15	london	london	PROPN
bibechana-4043	150	16	-	-	PUNCT
bibechana-4043	150	17	paris	paris	PROPN
bibechana-4043	150	18	,	,	PUNCT
bibechana-4043	150	19	(	(	PUNCT
bibechana-4043	150	20	1973	1973	NUM
bibechana-4043	150	21	)	)	PUNCT
bibechana-4043	150	22	.	.	PUNCT
bibechana-4043	151	1	[	[	X
bibechana-4043	151	2	2	2	NUM
bibechana-4043	151	3	]	]	X
bibechana-4043	151	4	r.	r.	PROPN
bibechana-4043	151	5	meise	meise	PROPN
bibechana-4043	151	6	,	,	PUNCT
bibechana-4043	151	7	d.	d.	PROPN
bibechana-4043	151	8	vogt	vogt	PROPN
bibechana-4043	151	9	,	,	PUNCT
bibechana-4043	151	10	math	math	NOUN
bibechana-4043	151	11	.	.	PUNCT
bibechana-4043	152	1	nachr	nachr	PROPN
bibechana-4043	152	2	.	.	PROPN
bibechana-4043	152	3	,	,	PUNCT
bibechana-4043	152	4	122	122	NUM
bibechana-4043	152	5	(	(	PUNCT
bibechana-4043	152	6	1985	1985	NUM
bibechana-4043	152	7	)	)	PUNCT
bibechana-4043	152	8	141	141	NUM
bibechana-4043	152	9	.	.	PUNCT
bibechana-4043	153	1	[	[	X
bibechana-4043	153	2	3	3	X
bibechana-4043	153	3	]	]	X
bibechana-4043	153	4	d.	d.	PROPN
bibechana-4043	153	5	vogt	vogt	PROPN
bibechana-4043	153	6	,	,	PUNCT
bibechana-4043	153	7	some	some	DET
bibechana-4043	153	8	results	result	NOUN
bibechana-4043	153	9	on	on	ADP
bibechana-4043	153	10	continuous	continuous	ADJ
bibechana-4043	153	11	linear	linear	NOUN
bibechana-4043	153	12	maps	map	NOUN
bibechana-4043	153	13	between	between	ADP
bibechana-4043	153	14	frechet	frechet	PROPN
bibechana-4043	153	15	spaces	space	NOUN
bibechana-4043	153	16	,	,	PUNCT
bibechana-4043	153	17	in	in	ADP
bibechana-4043	153	18	bierstedt	bierstedt	PROPN
bibechana-4043	153	19	k.d	k.d	PROPN
bibechana-4043	153	20	.	.	PROPN
bibechana-4043	153	21	,	,	PUNCT
bibechana-4043	153	22	fuchssteiner	fuchssteiner	PROPN
bibechana-4043	153	23	b.	b.	PROPN
bibechana-4043	153	24	(	(	PUNCT
bibechana-4043	153	25	eds	eds	PROPN
bibechana-4043	153	26	.	.	PUNCT
bibechana-4043	153	27	)	)	PUNCT
bibechana-4043	153	28	,	,	PUNCT
bibechana-4043	153	29	<	<	X
bibechana-4043	153	30	<	<	X
bibechana-4043	153	31	functional	functional	ADJ
bibechana-4043	153	32	analysis	analysis	NOUN
bibechana-4043	153	33	:	:	PUNCT
bibechana-4043	153	34	surveys	survey	NOUN
bibechana-4043	153	35	and	and	CCONJ
bibechana-4043	153	36	recent	recent	ADJ
bibechana-4043	153	37	results	result	NOUN
bibechana-4043	153	38	ii	ii	PROPN
bibechana-4043	153	39	>	>	X
bibechana-4043	153	40	>	>	PROPN
bibechana-4043	153	41	,	,	PUNCT
bibechana-4043	153	42	north	north	NOUN
bibechana-4043	153	43	-	-	PUNCT
bibechana-4043	153	44	holland	holland	PROPN
bibechana-4043	153	45	math	math	NOUN
bibechana-4043	153	46	.	.	PUNCT
bibechana-4043	154	1	studies	study	NOUN
bibechana-4043	154	2	,	,	PUNCT
bibechana-4043	154	3	90	90	NUM
bibechana-4043	154	4	(	(	PUNCT
bibechana-4043	154	5	1984	1984	NUM
bibechana-4043	154	6	)	)	PUNCT
bibechana-4043	154	7	,	,	PUNCT
bibechana-4043	154	8	pp	pp	ADJ
bibechana-4043	154	9	.	.	PUNCT
bibechana-4043	155	1	349	349	NUM
bibechana-4043	155	2	-	-	SYM
bibechana-4043	155	3	381	381	NUM
bibechana-4043	155	4	.	.	PUNCT
bibechana-4043	156	1	[	[	X
bibechana-4043	156	2	4	4	X
bibechana-4043	156	3	]	]	X
bibechana-4043	156	4	g.	g.	NOUN
bibechana-4043	156	5	kothe	kothe	PROPN
bibechana-4043	156	6	,	,	PUNCT
bibechana-4043	156	7	topological	topological	ADJ
bibechana-4043	156	8	vector	vector	NOUN
bibechana-4043	156	9	spaces	space	NOUN
bibechana-4043	156	10	,	,	PUNCT
bibechana-4043	156	11	i	i	PRON
bibechana-4043	156	12	,	,	PUNCT
bibechana-4043	156	13	ii	ii	PROPN
bibechana-4043	156	14	,	,	PUNCT
bibechana-4043	156	15	new	new	PROPN
bibechana-4043	156	16	york	york	PROPN
bibechana-4043	156	17	-	-	PUNCT
bibechana-4043	156	18	heildelber	heildelber	NOUN
bibechana-4043	156	19	-	-	PUNCT
bibechana-4043	156	20	berlin	berlin	NOUN
bibechana-4043	156	21	,	,	PUNCT
bibechana-4043	156	22	3	3	NUM
bibechana-4043	156	23	(	(	PUNCT
bibechana-4043	156	24	1969	1969	NUM
bibechana-4043	156	25	,	,	PUNCT
bibechana-4043	156	26	1979	1979	NUM
bibechana-4043	156	27	)	)	PUNCT
bibechana-4043	156	28	.	.	PUNCT
bibechana-4043	157	1	[	[	X
bibechana-4043	157	2	5	5	X
bibechana-4043	157	3	]	]	PUNCT
bibechana-4043	157	4	d.	d.	PROPN
bibechana-4043	157	5	vogt	vogt	PROPN
bibechana-4043	157	6	,	,	PUNCT
bibechana-4043	157	7	studia	studia	PROPN
bibechana-4043	157	8	math	math	PROPN
bibechana-4043	157	9	.	.	PUNCT
bibechana-4043	157	10	,	,	PUNCT
bibechana-4043	157	11	85	85	NUM
bibechana-4043	157	12	(	(	PUNCT
bibechana-4043	157	13	1987	1987	NUM
bibechana-4043	157	14	)	)	PUNCT
bibechana-4043	157	15	163	163	NUM
bibechana-4043	157	16	.	.	PUNCT
bibechana-4043	158	1	[	[	X
bibechana-4043	158	2	6	6	NUM
bibechana-4043	158	3	]	]	PUNCT
bibechana-4043	158	4	t.	t.	PROPN
bibechana-4043	158	5	terzioglu	terzioglu	NOUN
bibechana-4043	158	6	,	,	PUNCT
bibechana-4043	158	7	d.	d.	PROPN
bibechana-4043	158	8	vogt	vogt	PROPN
bibechana-4043	158	9	,	,	PUNCT
bibechana-4043	158	10	math	math	NOUN
bibechana-4043	158	11	.	.	PROPN
bibechana-4043	158	12	,	,	PUNCT
bibechana-4043	158	13	54	54	NUM
bibechana-4043	158	14	(	(	PUNCT
bibechana-4043	158	15	1990)180	1990)180	NOUN
bibechana-4043	158	16	.	.	PUNCT
bibechana-4043	159	1	[	[	X
bibechana-4043	159	2	7	7	X
bibechana-4043	159	3	]	]	X
bibechana-4043	159	4	e.	e.	PROPN
bibechana-4043	159	5	dubinsky	dubinsky	PROPN
bibechana-4043	159	6	,	,	PUNCT
bibechana-4043	159	7	studia	studia	PROPN
bibechana-4043	159	8	math	math	NOUN
bibechana-4043	159	9	.	.	PUNCT
bibechana-4043	159	10	,	,	PUNCT
bibechana-4043	159	11	71	71	NUM
bibechana-4043	159	12	(	(	PUNCT
bibechana-4043	159	13	1981	1981	NUM
bibechana-4043	159	14	)	)	PUNCT
bibechana-4043	159	15	85	85	NUM
bibechana-4043	159	16	.	.	PUNCT
bibechana-4043	160	1	[	[	X
bibechana-4043	160	2	8	8	NUM
bibechana-4043	160	3	]	]	X
bibechana-4043	160	4	l.	l.	PROPN
bibechana-4043	160	5	holmstrom	holmstrom	PROPN
bibechana-4043	160	6	,	,	PUNCT
bibechana-4043	160	7	proc	proc	PROPN
bibechana-4043	160	8	.	.	PUNCT
bibechana-4043	161	1	amer	amer	PROPN
bibechana-4043	161	2	.	.	PUNCT
bibechana-4043	161	3	math	math	PROPN
bibechana-4043	161	4	.	.	PUNCT
bibechana-4043	162	1	soc	soc	PROPN
bibechana-4043	162	2	.	.	PUNCT
bibechana-4043	162	3	,	,	PUNCT
bibechana-4043	162	4	89	89	NUM
bibechana-4043	162	5	(	(	PUNCT
bibechana-4043	162	6	1983)453	1983)453	NUM
bibechana-4043	162	7	.	.	PUNCT
bibechana-4043	162	8	further	further	ADJ
bibechana-4043	162	9	reading	read	VERB
bibechana-4043	162	10	[	[	X
bibechana-4043	162	11	1	1	X
bibechana-4043	162	12	]	]	PUNCT
bibechana-4043	162	13	e.	e.	PROPN
bibechana-4043	162	14	dubinsky	dubinsky	PROPN
bibechana-4043	162	15	,	,	PUNCT
bibechana-4043	162	16	the	the	DET
bibechana-4043	162	17	structure	structure	NOUN
bibechana-4043	162	18	of	of	ADP
bibechana-4043	162	19	nuclear	nuclear	ADJ
bibechana-4043	162	20	frechet	frechet	NOUN
bibechana-4043	162	21	spaces	space	NOUN
bibechana-4043	162	22	,	,	PUNCT
bibechana-4043	162	23	lecture	lecture	NOUN
bibechana-4043	162	24	notes	note	NOUN
bibechana-4043	162	25	in	in	ADP
bibechana-4043	162	26	math	math	NOUN
bibechana-4043	162	27	.	.	PUNCT
bibechana-4043	163	1	,	,	PUNCT
bibechana-4043	163	2	720	720	NUM
bibechana-4043	163	3	(	(	PUNCT
bibechana-4043	163	4	1979	1979	NUM
bibechana-4043	163	5	)	)	PUNCT
bibechana-4043	163	6	,	,	PUNCT
bibechana-4043	163	7	berlin	berlin	PROPN
bibechana-4043	163	8	-	-	PUNCT
bibechana-4043	163	9	heildel	heildel	PROPN
bibechana-4043	163	10	-	-	PUNCT
bibechana-4043	163	11	berg	berg	PROPN
bibechana-4043	163	12	-	-	PUNCT
bibechana-4043	163	13	new	new	PROPN
bibechana-4043	163	14	york	york	PROPN
bibechana-4043	163	15	.	.	PUNCT
bibechana-4043	164	1	[	[	X
bibechana-4043	164	2	3	3	X
bibechana-4043	164	3	]	]	X
bibechana-4043	164	4	e.	e.	PROPN
bibechana-4043	164	5	dubinsky	dubinsky	PROPN
bibechana-4043	164	6	,	,	PUNCT
bibechana-4043	164	7	d.	d.	PROPN
bibechana-4043	164	8	vogt	vogt	PROPN
bibechana-4043	164	9	,	,	PUNCT
bibechana-4043	164	10	frechet	frechet	PROPN
bibechana-4043	164	11	spaces	space	VERB
bibechana-4043	164	12	with	with	ADP
bibechana-4043	164	13	quotients	quotient	NOUN
bibechana-4043	164	14	failing	fail	VERB
bibechana-4043	164	15	the	the	DET
bibechana-4043	164	16	bounded	bounded	ADJ
bibechana-4043	164	17	approximation	approximation	NOUN
bibechana-4043	164	18	property	property	NOUN
bibechana-4043	164	19	,	,	PUNCT
bibechana-4043	164	20	studia	studia	PROPN
bibechana-4043	164	21	math	math	NOUN
bibechana-4043	164	22	.	.	PUNCT
bibechana-4043	165	1	,	,	PUNCT
bibechana-4043	165	2	81	81	NUM
bibechana-4043	165	3	(	(	PUNCT
bibechana-4043	165	4	1985	1985	NUM
bibechana-4043	165	5	)	)	PUNCT
bibechana-4043	165	6	,	,	PUNCT
bibechana-4043	165	7	pp.71	pp.71	NOUN
bibechana-4043	165	8	-	-	PUNCT
bibechana-4043	165	9	77	77	NUM
bibechana-4043	165	10	.	.	PUNCT
bibechana-4043	166	1	[	[	X
bibechana-4043	166	2	11	11	NUM
bibechana-4043	166	3	]	]	X
bibechana-4043	166	4	g.l	g.l	PROPN
bibechana-4043	166	5	.	.	PROPN
bibechana-4043	166	6	,	,	PUNCT
bibechana-4043	166	7	litvinov	litvinov	PROPN
bibechana-4043	166	8	,	,	PUNCT
bibechana-4043	166	9	nuclear	nuclear	ADJ
bibechana-4043	166	10	space	space	NOUN
bibechana-4043	166	11	,	,	PUNCT
bibechana-4043	166	12	springer	springer	NOUN
bibechana-4043	166	13	verlag	verlag	PROPN
bibechana-4043	166	14	,	,	PUNCT
bibechana-4043	166	15	new	new	PROPN
bibechana-4043	166	16	york	york	PROPN
bibechana-4043	166	17	,	,	PUNCT
bibechana-4043	166	18	(	(	PUNCT
bibechana-4043	166	19	2001	2001	NUM
bibechana-4043	166	20	)	)	PUNCT
bibechana-4043	166	21	.	.	PUNCT
bibechana-4043	167	1	∧	∧	NOUN
bibechana-4043	167	2	∧	∧	PROPN
bibechana-4043	167	3	∧	∧	PROPN
bibechana-4043	167	4	∧	∧	PROPN