id	sid	tid	token	lemma	pos
bibechana-10397	1	1	161	161	NUM
bibechana-10397	1	2	-	-	SYM
bibechana-10397	1	3	164	164	NUM
bibechana-10397	1	4	s.n	s.n	PROPN
bibechana-10397	1	5	.	.	PROPN
bibechana-10397	1	6	sah	sah	PROPN
bibechana-10397	1	7	r	r	NOUN
bibechana-10397	1	8	c	c	NOUN
bibechana-10397	1	9	o	o	NOUN
bibechana-10397	1	10	s	s	PROPN
bibechana-10397	1	11	t	t	PROPN
bibechana-10397	1	12	n	n	PROPN
bibechana-10397	1	13	s.	s.	PROPN
bibechana-10397	1	14	n.	n.	PROPN
bibechana-10397	1	15	sah	sah	PROPN
bibechana-10397	1	16	/	/	SYM
bibechana-10397	1	17	bibechana	bibechana	PROPN
bibechana-10397	1	18	11(1	11(1	NUM
bibechana-10397	1	19	)	)	PUNCT
bibechana-10397	1	20	(	(	PUNCT
bibechana-10397	1	21	2014	2014	NUM
bibechana-10397	1	22	)	)	PUNCT
bibechana-10397	1	23	161	161	NUM
bibechana-10397	1	24	-	-	SYM
bibechana-10397	1	25	164	164	NUM
bibechana-10397	1	26	:	:	PUNCT
bibechana-10397	1	27	(	(	PUNCT
bibechana-10397	1	28	online	online	ADJ
bibechana-10397	1	29	publication	publication	NOUN
bibechana-10397	1	30	:	:	PUNCT
bibechana-10397	1	31	march	march	PROPN
bibechana-10397	1	32	,	,	PUNCT
bibechana-10397	1	33	2014	2014	NUM
bibechana-10397	1	34	)	)	PUNCT
bibechana-10397	1	35	p.161	p.161	VERB
bibechana-10397	1	36	bibechana	bibechana	NOUN
bibechana-10397	1	37	a	a	DET
bibechana-10397	1	38	multidisciplinary	multidisciplinary	ADJ
bibechana-10397	1	39	journal	journal	NOUN
bibechana-10397	1	40	of	of	ADP
bibechana-10397	1	41	science	science	NOUN
bibechana-10397	1	42	,	,	PUNCT
bibechana-10397	1	43	technology	technology	NOUN
bibechana-10397	1	44	and	and	CCONJ
bibechana-10397	1	45	mathematics	mathematic	NOUN
bibechana-10397	1	46	issn	issn	VERB
bibechana-10397	1	47	2091	2091	NUM
bibechana-10397	1	48	-	-	SYM
bibechana-10397	1	49	0762	0762	NUM
bibechana-10397	1	50	(	(	PUNCT
bibechana-10397	1	51	online	online	ADJ
bibechana-10397	1	52	)	)	PUNCT
bibechana-10397	1	53	journal	journal	NOUN
bibechana-10397	1	54	homepage	homepage	NOUN
bibechana-10397	1	55	:	:	PUNCT
bibechana-10397	2	1	http://nepjol.info/index.php/bibechana	http://nepjol.info/index.php/bibechana	PROPN
bibechana-10397	2	2	characterization	characterization	NOUN
bibechana-10397	2	3	of	of	ADP
bibechana-10397	2	4	frechet	frechet	PROPN
bibechana-10397	2	5	spaces	space	NOUN
bibechana-10397	2	6	with	with	ADP
bibechana-10397	2	7	nuclear	nuclear	ADJ
bibechana-10397	2	8	kothe	kothe	NOUN
bibechana-10397	2	9	quotients	quotient	VERB
bibechana-10397	2	10	satya	satya	PROPN
bibechana-10397	2	11	narayan	narayan	PROPN
bibechana-10397	2	12	sah	sah	PROPN
bibechana-10397	2	13	department	department	PROPN
bibechana-10397	2	14	of	of	ADP
bibechana-10397	2	15	mathematics	mathematics	PROPN
bibechana-10397	2	16	m.m.a.m	m.m.a.m	PROPN
bibechana-10397	2	17	.	.	PUNCT
bibechana-10397	2	18	campus	campus	PROPN
bibechana-10397	2	19	,	,	PUNCT
bibechana-10397	2	20	t.u	t.u	PROPN
bibechana-10397	2	21	.	.	PROPN
bibechana-10397	2	22	,	,	PUNCT
bibechana-10397	2	23	biratnagar	biratnagar	NOUN
bibechana-10397	2	24	,	,	PUNCT
bibechana-10397	2	25	nepal	nepal	ADJ
bibechana-10397	2	26	e	e	NOUN
bibechana-10397	2	27	-	-	NOUN
bibechana-10397	2	28	mail	mail	NOUN
bibechana-10397	2	29	:	:	PUNCT
bibechana-10397	2	30	satyanarayansah33@yahoo.com	satyanarayansah33@yahoo.com	X
bibechana-10397	2	31	accepted	accept	VERB
bibechana-10397	2	32	for	for	ADP
bibechana-10397	2	33	publication	publication	NOUN
bibechana-10397	2	34	:	:	PUNCT
bibechana-10397	2	35	february	february	PROPN
bibechana-10397	2	36	02	02	NUM
bibechana-10397	2	37	,	,	PUNCT
bibechana-10397	2	38	2014	2014	NUM
bibechana-10397	2	39	abstract	abstract	NOUN
bibechana-10397	2	40	in	in	ADP
bibechana-10397	2	41	this	this	DET
bibechana-10397	2	42	paper	paper	NOUN
bibechana-10397	2	43	our	our	PRON
bibechana-10397	2	44	result	result	NOUN
bibechana-10397	2	45	based	base	VERB
bibechana-10397	2	46	on	on	ADP
bibechana-10397	2	47	the	the	DET
bibechana-10397	2	48	characterization	characterization	NOUN
bibechana-10397	2	49	of	of	ADP
bibechana-10397	2	50	frechet	frechet	PROPN
bibechana-10397	2	51	spaces	space	NOUN
bibechana-10397	2	52	with	with	ADP
bibechana-10397	2	53	nuclear	nuclear	ADJ
bibechana-10397	2	54	kothe	kothe	NOUN
bibechana-10397	2	55	quotients	quotient	NOUN
bibechana-10397	2	56	is	be	AUX
bibechana-10397	2	57	in	in	ADP
bibechana-10397	2	58	terms	term	NOUN
bibechana-10397	2	59	of	of	ADP
bibechana-10397	2	60	the	the	DET
bibechana-10397	2	61	following	follow	VERB
bibechana-10397	2	62	condition	condition	NOUN
bibechana-10397	2	63	which	which	PRON
bibechana-10397	2	64	labeled	label	VERB
bibechana-10397	2	65	as	as	ADP
bibechana-10397	2	66	⍟	⍟	PROPN
bibechana-10397	2	67	.	.	PUNCT
bibechana-10397	3	1	we	we	PRON
bibechana-10397	3	2	show	show	VERB
bibechana-10397	3	3	that	that	SCONJ
bibechana-10397	3	4	a	a	DET
bibechana-10397	3	5	frechet	frechet	NOUN
bibechana-10397	3	6	spaces	space	NOUN
bibechana-10397	3	7	e	e	NOUN
bibechana-10397	3	8	satisfies	satisfy	VERB
bibechana-10397	3	9	condition	condition	NOUN
bibechana-10397	3	10	⍟	⍟	NOUN
bibechana-10397	3	11	if	if	SCONJ
bibechana-10397	3	12	and	and	CCONJ
bibechana-10397	3	13	only	only	ADV
bibechana-10397	3	14	if	if	SCONJ
bibechana-10397	3	15	it	it	PRON
bibechana-10397	3	16	has	have	VERB
bibechana-10397	3	17	a	a	DET
bibechana-10397	3	18	quotient	quotient	NOUN
bibechana-10397	3	19	which	which	PRON
bibechana-10397	3	20	admits	admit	VERB
bibechana-10397	3	21	continuous	continuous	ADJ
bibechana-10397	3	22	norm	norm	NOUN
bibechana-10397	3	23	and	and	CCONJ
bibechana-10397	3	24	satisfies	satisfy	VERB
bibechana-10397	3	25	condition	condition	NOUN
bibechana-10397	3	26	⍟	⍟	PROPN
bibechana-10397	3	27	.	.	PUNCT
bibechana-10397	4	1	for	for	ADP
bibechana-10397	4	2	the	the	DET
bibechana-10397	4	3	condition	condition	NOUN
bibechana-10397	4	4	⍟	⍟	NOUN
bibechana-10397	4	5	,	,	PUNCT
bibechana-10397	4	6	there	there	PRON
bibechana-10397	4	7	exists	exist	VERB
bibechana-10397	4	8	ℓ	ℓ	NOUN
bibechana-10397	4	9	such	such	ADJ
bibechana-10397	4	10	that	that	PRON
bibechana-10397	4	11	for	for	ADP
bibechana-10397	4	12	every	every	DET
bibechana-10397	4	13	k	k	NOUN
bibechana-10397	4	14	there	there	PRON
bibechana-10397	4	15	exists	exist	VERB
bibechana-10397	4	16	j	j	NOUN
bibechana-10397	4	17	such	such	ADJ
bibechana-10397	4	18	that	that	SCONJ
bibechana-10397	4	19	the	the	DET
bibechana-10397	4	20	‖.	‖.	PROPN
bibechana-10397	4	21	‖	‖	PROPN
bibechana-10397	4	22	�	�	PROPN
bibechana-10397	4	23	closure	closure	NOUN
bibechana-10397	4	24	of	of	ADP
bibechana-10397	4	25	eℓ	eℓ	NOUN
bibechana-10397	4	26	′	′	NOUN
bibechana-10397	4	27	is	be	AUX
bibechana-10397	4	28	not	not	PART
bibechana-10397	4	29	closed	close	VERB
bibechana-10397	4	30	in	in	ADP
bibechana-10397	4	31	e	e	PROPN
bibechana-10397	4	32	�	�	PROPN
bibechana-10397	4	33	′.	′.	NOUN
bibechana-10397	4	34	©	©	PROPN
bibechana-10397	4	35	2014	2014	NUM
bibechana-10397	4	36	rcost	rcost	NOUN
bibechana-10397	4	37	:	:	PUNCT
bibechana-10397	4	38	all	all	DET
bibechana-10397	4	39	rights	right	NOUN
bibechana-10397	4	40	reserved	reserve	VERB
bibechana-10397	4	41	.	.	PUNCT
bibechana-10397	5	1	keywords	keyword	NOUN
bibechana-10397	5	2	:	:	PUNCT
bibechana-10397	5	3	frechet	frechet	PROPN
bibechana-10397	5	4	spaces	space	NOUN
bibechana-10397	5	5	;	;	PUNCT
bibechana-10397	5	6	kothe	kothe	NOUN
bibechana-10397	5	7	spaces	space	NOUN
bibechana-10397	5	8	;	;	PUNCT
bibechana-10397	5	9	quotient	quotient	NOUN
bibechana-10397	5	10	.	.	PUNCT
bibechana-10397	6	1	1	1	X
bibechana-10397	6	2	.	.	X
bibechana-10397	7	1	introduction	introduction	NOUN
bibechana-10397	7	2	frechet	frechet	PROPN
bibechana-10397	7	3	spaces	space	NOUN
bibechana-10397	7	4	have	have	AUX
bibechana-10397	7	5	played	play	VERB
bibechana-10397	7	6	an	an	DET
bibechana-10397	7	7	important	important	ADJ
bibechana-10397	7	8	role	role	NOUN
bibechana-10397	7	9	in	in	ADP
bibechana-10397	7	10	functional	functional	ADJ
bibechana-10397	7	11	analysis	analysis	NOUN
bibechana-10397	7	12	from	from	ADP
bibechana-10397	7	13	its	its	PRON
bibechana-10397	7	14	very	very	ADJ
bibechana-10397	7	15	beginning	beginning	NOUN
bibechana-10397	7	16	.	.	PUNCT
bibechana-10397	8	1	many	many	ADJ
bibechana-10397	8	2	linear	linear	ADJ
bibechana-10397	8	3	spaces	space	NOUN
bibechana-10397	8	4	of	of	ADP
bibechana-10397	8	5	holomorfic	holomorfic	NOUN
bibechana-10397	8	6	,	,	PUNCT
bibechana-10397	8	7	differentiable	differentiable	ADJ
bibechana-10397	8	8	or	or	CCONJ
bibechana-10397	8	9	continuous	continuous	ADJ
bibechana-10397	8	10	functions	function	NOUN
bibechana-10397	8	11	which	which	PRON
bibechana-10397	8	12	arise	arise	VERB
bibechana-10397	8	13	in	in	ADP
bibechana-10397	8	14	connection	connection	NOUN
bibechana-10397	8	15	with	with	ADP
bibechana-10397	8	16	various	various	ADJ
bibechana-10397	8	17	problems	problem	NOUN
bibechana-10397	8	18	in	in	ADP
bibechana-10397	8	19	analysis	analysis	NOUN
bibechana-10397	8	20	and	and	CCONJ
bibechana-10397	8	21	its	its	PRON
bibechana-10397	8	22	applications	application	NOUN
bibechana-10397	8	23	are	be	AUX
bibechana-10397	8	24	defined	define	VERB
bibechana-10397	8	25	by	by	ADP
bibechana-10397	8	26	(	(	PUNCT
bibechana-10397	8	27	at	at	ADP
bibechana-10397	8	28	most	most	ADV
bibechana-10397	8	29	)	)	PUNCT
bibechana-10397	8	30	countably	countably	ADV
bibechana-10397	8	31	many	many	ADJ
bibechana-10397	8	32	conditions	condition	NOUN
bibechana-10397	8	33	,	,	PUNCT
bibechana-10397	8	34	whence	whence	SCONJ
bibechana-10397	8	35	they	they	PRON
bibechana-10397	8	36	carry	carry	VERB
bibechana-10397	8	37	a	a	DET
bibechana-10397	8	38	natural	natural	ADJ
bibechana-10397	8	39	frechet	frechet	NOUN
bibechana-10397	8	40	topology	topology	NOUN
bibechana-10397	8	41	(	(	PUNCT
bibechana-10397	8	42	if	if	SCONJ
bibechana-10397	8	43	they	they	PRON
bibechana-10397	8	44	are	be	AUX
bibechana-10397	8	45	,	,	PUNCT
bibechana-10397	8	46	in	in	ADP
bibechana-10397	8	47	addition	addition	NOUN
bibechana-10397	8	48	,	,	PUNCT
bibechana-10397	8	49	complete	complete	ADJ
bibechana-10397	8	50	)	)	PUNCT
bibechana-10397	8	51	.	.	PUNCT
bibechana-10397	9	1	c.	c.	PROPN
bibechana-10397	9	2	bessaga	bessaga	PROPN
bibechana-10397	9	3	and	and	CCONJ
bibechana-10397	9	4	a.	a.	NOUN
bibechana-10397	9	5	pelczynski	pelczynski	NOUN
bibechana-10397	9	6	showed	show	VERB
bibechana-10397	9	7	that	that	SCONJ
bibechana-10397	9	8	a	a	DET
bibechana-10397	9	9	frechet	frechet	NOUN
bibechana-10397	9	10	space	space	NOUN
bibechana-10397	9	11	fails	fail	VERB
bibechana-10397	9	12	to	to	PART
bibechana-10397	9	13	admit	admit	VERB
bibechana-10397	9	14	a	a	DET
bibechana-10397	9	15	continuous	continuous	ADJ
bibechana-10397	9	16	norm	norm	NOUN
bibechana-10397	9	17	if	if	SCONJ
bibechana-10397	9	18	it	it	PRON
bibechana-10397	9	19	has	have	VERB
bibechana-10397	9	20	a	a	DET
bibechana-10397	9	21	subspace	subspace	NOUN
bibechana-10397	9	22	isomorphic	isomorphic	ADJ
bibechana-10397	9	23	to	to	ADP
bibechana-10397	9	24	ω	ω	PROPN
bibechana-10397	9	25	in	in	ADP
bibechana-10397	9	26	1957	1957	NUM
bibechana-10397	9	27	[	[	X
bibechana-10397	9	28	1	1	NUM
bibechana-10397	9	29	]	]	PUNCT
bibechana-10397	9	30	.	.	PUNCT
bibechana-10397	10	1	if	if	SCONJ
bibechana-10397	10	2	a	a	DET
bibechana-10397	10	3	frechet	frechet	PROPN
bibechana-10397	10	4	space	space	NOUN
bibechana-10397	10	5	admits	admit	VERB
bibechana-10397	10	6	a	a	DET
bibechana-10397	10	7	continuous	continuous	ADJ
bibechana-10397	10	8	norm	norm	NOUN
bibechana-10397	10	9	then	then	ADV
bibechana-10397	10	10	so	so	ADV
bibechana-10397	10	11	does	do	VERB
bibechana-10397	10	12	every	every	DET
bibechana-10397	10	13	subspace	subspace	NOUN
bibechana-10397	10	14	,	,	PUNCT
bibechana-10397	10	15	which	which	PRON
bibechana-10397	10	16	simplifies	simplify	VERB
bibechana-10397	10	17	the	the	DET
bibechana-10397	10	18	problem	problem	NOUN
bibechana-10397	10	19	a	a	DET
bibechana-10397	10	20	little	little	ADJ
bibechana-10397	10	21	.	.	PUNCT
bibechana-10397	11	1	again	again	ADV
bibechana-10397	11	2	,	,	PUNCT
bibechana-10397	11	3	in	in	ADP
bibechana-10397	11	4	1959	1959	NUM
bibechana-10397	11	5	,	,	PUNCT
bibechana-10397	11	6	bessaga	bessaga	NOUN
bibechana-10397	11	7	,	,	PUNCT
bibechana-10397	11	8	pelczynski	pelczynski	NOUN
bibechana-10397	11	9	and	and	CCONJ
bibechana-10397	11	10	s.	s.	PROPN
bibechana-10397	11	11	rolewicz	rolewicz	PROPN
bibechana-10397	11	12	showed	show	VERB
bibechana-10397	11	13	that	that	SCONJ
bibechana-10397	11	14	a	a	DET
bibechana-10397	11	15	frechet	frechet	NOUN
bibechana-10397	11	16	space	space	NOUN
bibechana-10397	11	17	which	which	PRON
bibechana-10397	11	18	admits	admit	VERB
bibechana-10397	11	19	continuous	continuous	ADJ
bibechana-10397	11	20	norm	norm	NOUN
bibechana-10397	11	21	has	have	VERB
bibechana-10397	11	22	a	a	DET
bibechana-10397	11	23	nuclear	nuclear	ADJ
bibechana-10397	11	24	kothe	kothe	NOUN
bibechana-10397	11	25	subspace	subspace	PROPN
bibechana-10397	11	26	iff	iff	PROPN
bibechana-10397	11	27	it	it	PRON
bibechana-10397	11	28	is	be	AUX
bibechana-10397	11	29	not	not	PART
bibechana-10397	11	30	banach	banach	ADV
bibechana-10397	11	31	[	[	X
bibechana-10397	11	32	2	2	NUM
bibechana-10397	11	33	]	]	PUNCT
bibechana-10397	11	34	.	.	PUNCT
bibechana-10397	12	1	thus	thus	ADV
bibechana-10397	12	2	it	it	PRON
bibechana-10397	12	3	follows	follow	VERB
bibechana-10397	12	4	that	that	SCONJ
bibechana-10397	12	5	,	,	PUNCT
bibechana-10397	12	6	in	in	ADP
bibechana-10397	12	7	general	general	ADJ
bibechana-10397	12	8	,	,	PUNCT
bibechana-10397	12	9	a	a	DET
bibechana-10397	12	10	frechet	frechet	NOUN
bibechana-10397	12	11	space	space	NOUN
bibechana-10397	12	12	has	have	VERB
bibechana-10397	12	13	a	a	DET
bibechana-10397	12	14	nuclear	nuclear	ADJ
bibechana-10397	12	15	kothe	kothe	NOUN
bibechana-10397	12	16	subspace	subspace	PROPN
bibechana-10397	12	17	iff	iff	PROPN
bibechana-10397	12	18	it	it	PRON
bibechana-10397	12	19	has	have	VERB
bibechana-10397	12	20	a	a	DET
bibechana-10397	12	21	non	non	ADJ
bibechana-10397	12	22	-	-	ADJ
bibechana-10397	12	23	banach	banach	ADJ
bibechana-10397	12	24	subspace	subspace	NOUN
bibechana-10397	12	25	which	which	PRON
bibechana-10397	12	26	admits	admit	VERB
bibechana-10397	12	27	continuous	continuous	ADJ
bibechana-10397	12	28	norm	norm	NOUN
bibechana-10397	12	29	.	.	PUNCT
bibechana-10397	13	1	if	if	SCONJ
bibechana-10397	13	2	we	we	PRON
bibechana-10397	13	3	consider	consider	VERB
bibechana-10397	13	4	only	only	ADV
bibechana-10397	13	5	nuclear	nuclear	ADJ
bibechana-10397	13	6	frechet	frechet	NOUN
bibechana-10397	13	7	spaces	space	VERB
bibechana-10397	13	8	,	,	PUNCT
bibechana-10397	13	9	then	then	ADV
bibechana-10397	13	10	we	we	PRON
bibechana-10397	13	11	are	be	AUX
bibechana-10397	13	12	looking	look	VERB
bibechana-10397	13	13	for	for	ADP
bibechana-10397	13	14	kothe	kothe	ADJ
bibechana-10397	13	15	quotients	quotient	NOUN
bibechana-10397	13	16	and	and	CCONJ
bibechana-10397	13	17	here	here	ADV
bibechana-10397	13	18	the	the	DET
bibechana-10397	13	19	problem	problem	NOUN
bibechana-10397	13	20	has	have	VERB
bibechana-10397	13	21	a	a	DET
bibechana-10397	13	22	positive	positive	ADJ
bibechana-10397	13	23	solution	solution	NOUN
bibechana-10397	13	24	:	:	PUNCT
bibechana-10397	13	25	every	every	DET
bibechana-10397	13	26	nuclear	nuclear	ADJ
bibechana-10397	13	27	frechet	frechet	NOUN
bibechana-10397	13	28	space	space	NOUN
bibechana-10397	13	29	not	not	PART
bibechana-10397	13	30	isomorphic	isomorphic	ADJ
bibechana-10397	13	31	to	to	ADP
bibechana-10397	13	32	ω	ω	PROPN
bibechana-10397	13	33	has	have	VERB
bibechana-10397	13	34	a	a	DET
bibechana-10397	13	35	kothe	kothe	ADJ
bibechana-10397	13	36	quotient	quotient	NOUN
bibechana-10397	13	37	.	.	PUNCT
bibechana-10397	14	1	the	the	DET
bibechana-10397	14	2	proof	proof	NOUN
bibechana-10397	14	3	is	be	AUX
bibechana-10397	14	4	given	give	VERB
bibechana-10397	14	5	in	in	ADP
bibechana-10397	14	6	[	[	X
bibechana-10397	14	7	3	3	NUM
bibechana-10397	14	8	]	]	PUNCT
bibechana-10397	14	9	.	.	PUNCT
bibechana-10397	15	1	in	in	ADP
bibechana-10397	15	2	the	the	DET
bibechana-10397	15	3	present	present	ADJ
bibechana-10397	15	4	paper	paper	NOUN
bibechana-10397	15	5	we	we	PRON
bibechana-10397	15	6	find	find	VERB
bibechana-10397	15	7	some	some	DET
bibechana-10397	15	8	characterization	characterization	NOUN
bibechana-10397	15	9	of	of	ADP
bibechana-10397	15	10	the	the	DET
bibechana-10397	15	11	frechet	frechet	NOUN
bibechana-10397	15	12	spaces	space	VERB
bibechana-10397	15	13	with	with	ADP
bibechana-10397	15	14	nuclear	nuclear	ADJ
bibechana-10397	15	15	kothe	kothe	NOUN
bibechana-10397	15	16	quotients	quotient	VERB
bibechana-10397	15	17	.	.	PUNCT
bibechana-10397	16	1	in	in	ADP
bibechana-10397	16	2	view	view	NOUN
bibechana-10397	16	3	of	of	ADP
bibechana-10397	16	4	the	the	DET
bibechana-10397	16	5	open	open	ADJ
bibechana-10397	16	6	mapping	mapping	NOUN
bibechana-10397	16	7	theorem	theorem	VERB
bibechana-10397	16	8	the	the	DET
bibechana-10397	16	9	condition	condition	NOUN
bibechana-10397	16	10	⍟	⍟	PROPN
bibechana-10397	16	11	has	have	VERB
bibechana-10397	16	12	the	the	DET
bibechana-10397	16	13	following	follow	VERB
bibechana-10397	16	14	equivalent	equivalent	ADJ
bibechana-10397	16	15	formulation	formulation	NOUN
bibechana-10397	16	16	:	:	PUNCT
bibechana-10397	16	17	∃	∃	PROPN
bibechana-10397	16	18	∋∋	∋∋	X
bibechana-10397	16	19	∃	∃	PROPN
bibechana-10397	16	20	∋	∋	NOUN
bibechana-10397	17	1	l	l	PROPN
bibechana-10397	17	2	k	k	PROPN
bibechana-10397	17	3	j	j	PROPN
bibechana-10397	17	4	sup	sup	INTJ
bibechana-10397	17	5	{	{	PUNCT
bibechana-10397	17	6	ǁ.ǁ'k	ǁ.ǁ'k	PROPN
bibechana-10397	17	7	:	:	PUNCT
bibechana-10397	17	8	uϵel	uϵel	ADJ
bibechana-10397	17	9	'	'	PUNCT
bibechana-10397	17	10	,	,	PUNCT
bibechana-10397	17	11	ǁ.ǁ'j≤1	ǁ.ǁ'j≤1	ADJ
bibechana-10397	17	12	}	}	PUNCT
bibechana-10397	17	13	=	=	SYM
bibechana-10397	17	14	∞	∞	NUM
bibechana-10397	17	15	in	in	ADP
bibechana-10397	17	16	this	this	DET
bibechana-10397	17	17	form	form	NOUN
bibechana-10397	17	18	our	our	PRON
bibechana-10397	17	19	condition	condition	NOUN
bibechana-10397	17	20	is	be	AUX
bibechana-10397	17	21	very	very	ADV
bibechana-10397	17	22	close	close	ADJ
bibechana-10397	17	23	to	to	ADP
bibechana-10397	17	24	being	be	AUX
bibechana-10397	17	25	a	a	DET
bibechana-10397	17	26	dual	dual	ADJ
bibechana-10397	17	27	to	to	ADP
bibechana-10397	17	28	the	the	DET
bibechana-10397	17	29	following	follow	VERB
bibechana-10397	17	30	condition	condition	NOUN
bibechana-10397	17	31	used	use	VERB
bibechana-10397	17	32	by	by	ADP
bibechana-10397	17	33	bessaga	bessaga	ADJ
bibechana-10397	17	34	,	,	PUNCT
bibechana-10397	17	35	pelczynski	pelczynski	ADJ
bibechana-10397	17	36	and	and	CCONJ
bibechana-10397	17	37	rolewicz	rolewicz	ADJ
bibechana-10397	18	1	[	[	X
bibechana-10397	18	2	4	4	NUM
bibechana-10397	18	3	]	]	PUNCT
bibechana-10397	18	4	in	in	ADP
bibechana-10397	18	5	thier	thier	PRON
bibechana-10397	18	6	determination	determination	NOUN
bibechana-10397	18	7	of	of	ADP
bibechana-10397	18	8	those	those	DET
bibechana-10397	18	9	frechet	frechet	PROPN
bibechana-10397	18	10	spaces	space	NOUN
bibechana-10397	18	11	which	which	PRON
bibechana-10397	18	12	have	have	VERB
bibechana-10397	18	13	nuclear	nuclear	ADJ
bibechana-10397	18	14	kothe	kothe	NOUN
bibechana-10397	18	15	subspaces	subspace	NOUN
bibechana-10397	18	16	:	:	PUNCT
bibechana-10397	18	17	∋	∋	X
bibechana-10397	18	18	k	k	PROPN
bibechana-10397	18	19	∃	∃	PROPN
bibechana-10397	18	20	∋	∋	PROPN
bibechana-10397	18	21	j	j	PROPN
bibechana-10397	18	22	sup	sup	PROPN
bibechana-10397	18	23	{	{	PUNCT
bibechana-10397	18	24	||x||j	||x||j	PROPN
bibechana-10397	18	25	:	:	PUNCT
bibechana-10397	18	26	x	x	PUNCT
bibechana-10397	18	27	ϵ	ϵ	X
bibechana-10397	18	28	y	y	PROPN
bibechana-10397	18	29	,	,	PUNCT
bibechana-10397	18	30	||x||k	||x||k	PROPN
bibechana-10397	18	31	≤	≤	NUM
bibechana-10397	18	32	1	1	NUM
bibechana-10397	18	33	}	}	PUNCT
bibechana-10397	18	34	=	=	SYM
bibechana-10397	18	35	∞	∞	PROPN
bibechana-10397	18	36	for	for	ADP
bibechana-10397	18	37	every	every	DET
bibechana-10397	18	38	subspace	subspace	NOUN
bibechana-10397	18	39	y	y	PROPN
bibechana-10397	18	40	of	of	ADP
bibechana-10397	18	41	e	e	PROPN
bibechana-10397	18	42	with	with	ADP
bibechana-10397	18	43	finite	finite	PROPN
bibechana-10397	18	44	co	co	NOUN
bibechana-10397	18	45	-	-	NOUN
bibechana-10397	18	46	dimension	dimension	NOUN
bibechana-10397	18	47	.	.	PUNCT
bibechana-10397	19	1	s.	s.	PROPN
bibechana-10397	19	2	n.	n.	PROPN
bibechana-10397	19	3	sah	sah	PROPN
bibechana-10397	19	4	/	/	SYM
bibechana-10397	19	5	bibechana	bibechana	PROPN
bibechana-10397	19	6	11(1	11(1	NUM
bibechana-10397	19	7	)	)	PUNCT
bibechana-10397	19	8	(	(	PUNCT
bibechana-10397	19	9	2014	2014	NUM
bibechana-10397	19	10	)	)	PUNCT
bibechana-10397	19	11	161	161	NUM
bibechana-10397	19	12	-	-	SYM
bibechana-10397	19	13	164	164	NUM
bibechana-10397	19	14	:	:	PUNCT
bibechana-10397	19	15	(	(	PUNCT
bibechana-10397	19	16	online	online	ADJ
bibechana-10397	19	17	publication	publication	NOUN
bibechana-10397	19	18	:	:	PUNCT
bibechana-10397	19	19	march	march	PROPN
bibechana-10397	19	20	,	,	PUNCT
bibechana-10397	19	21	2014	2014	NUM
bibechana-10397	19	22	)	)	PUNCT
bibechana-10397	20	1	p.162	p.162	ADP
bibechana-10397	20	2	it	it	PRON
bibechana-10397	20	3	is	be	AUX
bibechana-10397	20	4	easy	easy	ADJ
bibechana-10397	20	5	to	to	PART
bibechana-10397	20	6	check	check	VERB
bibechana-10397	20	7	that	that	SCONJ
bibechana-10397	20	8	this	this	DET
bibechana-10397	20	9	condition	condition	NOUN
bibechana-10397	20	10	⍟	⍟	NOUN
bibechana-10397	20	11	is	be	AUX
bibechana-10397	20	12	independent	independent	ADJ
bibechana-10397	20	13	of	of	ADP
bibechana-10397	20	14	the	the	DET
bibechana-10397	20	15	choice	choice	NOUN
bibechana-10397	20	16	of	of	ADP
bibechana-10397	20	17	(	(	PUNCT
bibechana-10397	20	18	ǁ·ǁk	ǁ·ǁk	NOUN
bibechana-10397	20	19	)	)	PUNCT
bibechana-10397	20	20	.	.	PUNCT
bibechana-10397	21	1	for	for	ADP
bibechana-10397	21	2	definitions	definition	NOUN
bibechana-10397	21	3	and	and	CCONJ
bibechana-10397	21	4	notations	notation	NOUN
bibechana-10397	21	5	we	we	PRON
bibechana-10397	21	6	refer	refer	VERB
bibechana-10397	21	7	to	to	ADP
bibechana-10397	21	8	the	the	DET
bibechana-10397	21	9	book	book	NOUN
bibechana-10397	21	10	of	of	ADP
bibechana-10397	21	11	g.	g.	PROPN
bibechana-10397	21	12	kothe	kothe	PROPN
bibechana-10397	22	1	[	[	X
bibechana-10397	22	2	5	5	NUM
bibechana-10397	22	3	]	]	PUNCT
bibechana-10397	22	4	.	.	PUNCT
bibechana-10397	23	1	some	some	PRON
bibechana-10397	23	2	of	of	ADP
bibechana-10397	23	3	them	they	PRON
bibechana-10397	23	4	which	which	PRON
bibechana-10397	23	5	are	be	AUX
bibechana-10397	23	6	used	use	VERB
bibechana-10397	23	7	in	in	ADP
bibechana-10397	23	8	this	this	DET
bibechana-10397	23	9	paper	paper	NOUN
bibechana-10397	23	10	are	be	AUX
bibechana-10397	23	11	following	follow	VERB
bibechana-10397	23	12	:	:	PUNCT
bibechana-10397	23	13	2	2	X
bibechana-10397	23	14	.	.	NOUN
bibechana-10397	23	15	notations	notation	NOUN
bibechana-10397	23	16	e	e	NOUN
bibechana-10397	23	17	'	'	PUNCT
bibechana-10397	23	18	–	–	PUNCT
bibechana-10397	23	19	the	the	DET
bibechana-10397	23	20	dual	dual	ADJ
bibechana-10397	23	21	of	of	ADP
bibechana-10397	23	22	e	e	NOUN
bibechana-10397	23	23	will	will	AUX
bibechana-10397	23	24	be	be	AUX
bibechana-10397	23	25	considered	consider	VERB
bibechana-10397	23	26	to	to	PART
bibechana-10397	23	27	have	have	VERB
bibechana-10397	23	28	the	the	DET
bibechana-10397	23	29	strong	strong	ADJ
bibechana-10397	23	30	topology	topology	NOUN
bibechana-10397	23	31	from	from	ADP
bibechana-10397	23	32	e	e	PROPN
bibechana-10397	23	33	e	e	PROPN
bibechana-10397	23	34	*	*	PUNCT
bibechana-10397	23	35	–	–	PUNCT
bibechana-10397	23	36	the	the	DET
bibechana-10397	23	37	completion	completion	NOUN
bibechana-10397	23	38	of	of	ADP
bibechana-10397	23	39	e	e	NOUN
bibechana-10397	23	40	e	e	NOUN
bibechana-10397	23	41	''	''	PUNCT
bibechana-10397	23	42	–	–	PUNCT
bibechana-10397	23	43	the	the	DET
bibechana-10397	23	44	dual	dual	ADJ
bibechana-10397	23	45	of	of	ADP
bibechana-10397	23	46	e	e	NOUN
bibechana-10397	23	47	'	'	PART
bibechana-10397	23	48	a0	a0	NOUN
bibechana-10397	23	49	–	–	PUNCT
bibechana-10397	23	50	the	the	DET
bibechana-10397	23	51	polar	polar	NOUN
bibechana-10397	23	52	in	in	ADP
bibechana-10397	23	53	e	e	NOUN
bibechana-10397	23	54	or	or	CCONJ
bibechana-10397	23	55	e	e	NOUN
bibechana-10397	23	56	'	'	PUNCT
bibechana-10397	23	57	where	where	SCONJ
bibechana-10397	23	58	a⊆	a⊆	VERB
bibechana-10397	23	59	⊆	⊆	NUM
bibechana-10397	23	60	e	e	NOUN
bibechana-10397	23	61	or	or	CCONJ
bibechana-10397	23	62	a	a	DET
bibechana-10397	23	63	e	e	NOUN
bibechana-10397	23	64	'	'	PUNCT
bibechana-10397	23	65	||	||	NUM
bibechana-10397	23	66	·	·	SYM
bibechana-10397	23	67	||k	||k	PROPN
bibechana-10397	23	68	–	–	PUNCT
bibechana-10397	23	69	the	the	DET
bibechana-10397	23	70	semi	semi	NOUN
bibechana-10397	23	71	-	-	NOUN
bibechana-10397	23	72	norm	norm	NOUN
bibechana-10397	23	73	on	on	ADP
bibechana-10397	23	74	e	e	NOUN
bibechana-10397	23	75	,	,	PUNCT
bibechana-10397	23	76	where	where	SCONJ
bibechana-10397	23	77	k	k	PROPN
bibechana-10397	23	78	=	=	SYM
bibechana-10397	23	79	1,2,3	1,2,3	NUM
bibechana-10397	23	80	,	,	PUNCT
bibechana-10397	23	81	……	……	NOUN
bibechana-10397	23	82	..	..	PUNCT
bibechana-10397	24	1	||	||	NUM
bibechana-10397	24	2	·	·	PUNCT
bibechana-10397	24	3	||	||	NUM
bibechana-10397	24	4	'	'	PUNCT
bibechana-10397	24	5	k	k	X
bibechana-10397	24	6	–	–	PUNCT
bibechana-10397	24	7	the	the	DET
bibechana-10397	24	8	dual	dual	ADJ
bibechana-10397	24	9	norm	norm	NOUN
bibechana-10397	24	10	on	on	ADP
bibechana-10397	24	11	e	e	NOUN
bibechana-10397	24	12	'	'	PUNCT
bibechana-10397	24	13	(	(	PUNCT
bibechana-10397	24	14	||	||	NOUN
bibechana-10397	24	15	·	·	SYM
bibechana-10397	24	16	||k	||k	PROPN
bibechana-10397	24	17	)	)	PUNCT
bibechana-10397	24	18	–	–	PUNCT
bibechana-10397	24	19	the	the	DET
bibechana-10397	24	20	fundamental	fundamental	ADJ
bibechana-10397	24	21	sequence	sequence	NOUN
bibechana-10397	24	22	of	of	ADP
bibechana-10397	24	23	semi	semi	NOUN
bibechana-10397	24	24	-	-	NOUN
bibechana-10397	24	25	norms	norms	ADJ
bibechana-10397	24	26	e'k	e'k	NOUN
bibechana-10397	24	27	–	–	PUNCT
bibechana-10397	24	28	the	the	DET
bibechana-10397	24	29	banach	banach	NOUN
bibechana-10397	24	30	space	space	NOUN
bibechana-10397	24	31	determined	determine	VERB
bibechana-10397	24	32	by	by	ADP
bibechana-10397	24	33	the	the	DET
bibechana-10397	24	34	unit	unit	NOUN
bibechana-10397	24	35	ball	ball	NOUN
bibechana-10397	24	36	of	of	ADP
bibechana-10397	24	37	the	the	DET
bibechana-10397	24	38	dual	dual	ADJ
bibechana-10397	24	39	norm	norm	NOUN
bibechana-10397	24	40	||	||	PROPN
bibechana-10397	24	41	·	·	PUNCT
bibechana-10397	24	42	||	||	NUM
bibechana-10397	24	43	'	'	PUNCT
bibechana-10397	24	44	k	k	NOUN
bibechana-10397	24	45	on	on	ADP
bibechana-10397	24	46	e	e	PROPN
bibechana-10397	24	47	'	'	PROPN
bibechana-10397	24	48	,	,	PUNCT
bibechana-10397	24	49	where	where	SCONJ
bibechana-10397	24	50	k	k	PROPN
bibechana-10397	24	51	ϵ	ϵ	X
bibechana-10397	24	52	n	n	PROPN
bibechana-10397	24	53	3	3	NUM
bibechana-10397	24	54	.	.	PUNCT
bibechana-10397	25	1	definitions	definition	NOUN
bibechana-10397	25	2	definition	definition	NOUN
bibechana-10397	25	3	3.1	3.1	NUM
bibechana-10397	25	4	.	.	PUNCT
bibechana-10397	26	1	a	a	DET
bibechana-10397	26	2	frechet	frechet	PROPN
bibechana-10397	26	3	space	space	NOUN
bibechana-10397	26	4	is	be	AUX
bibechana-10397	26	5	a	a	DET
bibechana-10397	26	6	metrizable	metrizable	ADJ
bibechana-10397	26	7	,	,	PUNCT
bibechana-10397	26	8	complete	complete	ADJ
bibechana-10397	26	9	cocally	cocally	ADV
bibechana-10397	26	10	convex	convex	VERB
bibechana-10397	26	11	vector	vector	NOUN
bibechana-10397	26	12	space	space	NOUN
bibechana-10397	26	13	[	[	X
bibechana-10397	26	14	6	6	NUM
bibechana-10397	26	15	]	]	PUNCT
bibechana-10397	26	16	.	.	PUNCT
bibechana-10397	27	1	#	#	NOUN
bibechana-10397	27	2	its	its	PRON
bibechana-10397	27	3	topology	topology	NOUN
bibechana-10397	27	4	is	be	AUX
bibechana-10397	27	5	defined	define	VERB
bibechana-10397	27	6	by	by	ADP
bibechana-10397	27	7	an	an	DET
bibechana-10397	27	8	increasing	increase	VERB
bibechana-10397	27	9	sequence	sequence	NOUN
bibechana-10397	27	10	of	of	ADP
bibechana-10397	27	11	semi	semi	ADJ
bibechana-10397	27	12	norms	norm	NOUN
bibechana-10397	27	13	(	(	PUNCT
bibechana-10397	27	14	ǁ·ǁ)k	ǁ·ǁ)k	VERB
bibechana-10397	27	15	called	call	VERB
bibechana-10397	27	16	a	a	DET
bibechana-10397	27	17	fundamental	fundamental	ADJ
bibechana-10397	27	18	sequence	sequence	NOUN
bibechana-10397	27	19	of	of	ADP
bibechana-10397	27	20	semi	semi	NOUN
bibechana-10397	27	21	-	-	NOUN
bibechana-10397	27	22	norms	norm	NOUN
bibechana-10397	27	23	.	.	PUNCT
bibechana-10397	28	1	if	if	SCONJ
bibechana-10397	28	2	one	one	NUM
bibechana-10397	28	3	of	of	ADP
bibechana-10397	28	4	these	these	DET
bibechana-10397	28	5	semi	semi	NOUN
bibechana-10397	28	6	-	-	NOUN
bibechana-10397	28	7	norms	norm	NOUN
bibechana-10397	28	8	is	be	AUX
bibechana-10397	28	9	a	a	DET
bibechana-10397	28	10	norm	norm	NOUN
bibechana-10397	28	11	we	we	PRON
bibechana-10397	28	12	say	say	VERB
bibechana-10397	28	13	that	that	SCONJ
bibechana-10397	28	14	the	the	DET
bibechana-10397	28	15	space	space	NOUN
bibechana-10397	28	16	admits	admit	VERB
bibechana-10397	28	17	continuous	continuous	ADJ
bibechana-10397	28	18	norm	norm	NOUN
bibechana-10397	28	19	.	.	PUNCT
bibechana-10397	29	1	#	#	NOUN
bibechana-10397	29	2	a	a	DET
bibechana-10397	29	3	metrizable	metrizable	ADJ
bibechana-10397	29	4	topological	topological	ADJ
bibechana-10397	29	5	vector	vector	NOUN
bibechana-10397	29	6	space	space	NOUN
bibechana-10397	29	7	(	(	PUNCT
bibechana-10397	29	8	tvs	tvs	PROPN
bibechana-10397	29	9	)	)	PUNCT
bibechana-10397	29	10	is	be	AUX
bibechana-10397	29	11	complete	complete	ADJ
bibechana-10397	29	12	if	if	SCONJ
bibechana-10397	29	13	every	every	DET
bibechana-10397	29	14	cauchy	cauchy	ADJ
bibechana-10397	29	15	sequence	sequence	NOUN
bibechana-10397	29	16	is	be	AUX
bibechana-10397	29	17	convergent	convergent	ADJ
bibechana-10397	29	18	[	[	X
bibechana-10397	29	19	5,7	5,7	NUM
bibechana-10397	29	20	]	]	PUNCT
bibechana-10397	29	21	.	.	PUNCT
bibechana-10397	30	1	definition	definition	NOUN
bibechana-10397	30	2	3.2	3.2	NUM
bibechana-10397	30	3	.	.	PUNCT
bibechana-10397	31	1	nuclear	nuclear	ADJ
bibechana-10397	31	2	kothe	kothe	NOUN
bibechana-10397	31	3	spaces	space	NOUN
bibechana-10397	31	4	are	be	AUX
bibechana-10397	31	5	those	those	DET
bibechana-10397	31	6	frechet	frechet	PROPN
bibechana-10397	31	7	spaces	space	NOUN
bibechana-10397	31	8	which	which	PRON
bibechana-10397	31	9	have	have	VERB
bibechana-10397	31	10	quotients	quotient	NOUN
bibechana-10397	31	11	that	that	PRON
bibechana-10397	31	12	are	be	AUX
bibechana-10397	31	13	nuclear	nuclear	ADJ
bibechana-10397	31	14	,	,	PUNCT
bibechana-10397	31	15	admit	admit	VERB
bibechana-10397	31	16	continuous	continuous	ADJ
bibechana-10397	31	17	norm	norm	NOUN
bibechana-10397	31	18	and	and	CCONJ
bibechana-10397	31	19	have	have	VERB
bibechana-10397	31	20	a	a	DET
bibechana-10397	31	21	basis	basis	NOUN
bibechana-10397	31	22	.	.	PUNCT
bibechana-10397	32	1	definition	definition	NOUN
bibechana-10397	32	2	3.3	3.3	NUM
bibechana-10397	32	3	.	.	PUNCT
bibechana-10397	33	1	let	let	VERB
bibechana-10397	33	2	a	a	DET
bibechana-10397	33	3	linear	linear	ADJ
bibechana-10397	33	4	subspace	subspace	NOUN
bibechana-10397	33	5	m	m	VERB
bibechana-10397	33	6	of	of	ADP
bibechana-10397	33	7	a	a	DET
bibechana-10397	33	8	linear	linear	ADJ
bibechana-10397	33	9	space	space	NOUN
bibechana-10397	33	10	e	e	NOUN
bibechana-10397	33	11	,	,	PUNCT
bibechana-10397	33	12	consider	consider	VERB
bibechana-10397	33	13	the	the	DET
bibechana-10397	33	14	sets	set	NOUN
bibechana-10397	33	15	x	x	SYM
bibechana-10397	33	16	(	(	PUNCT
bibechana-10397	33	17	m	m	NOUN
bibechana-10397	33	18	)	)	PUNCT
bibechana-10397	33	19	=	=	SYM
bibechana-10397	34	1	x	x	PUNCT
bibechana-10397	35	1	+	+	NUM
bibechana-10397	35	2	m	m	VERB
bibechana-10397	35	3	=	=	SYM
bibechana-10397	35	4	{	{	PUNCT
bibechana-10397	35	5	x	x	PROPN
bibechana-10397	36	1	+	+	NUM
bibechana-10397	36	2	y	y	NOUN
bibechana-10397	36	3	:	:	PUNCT
bibechana-10397	36	4	y	y	PROPN
bibechana-10397	36	5	ϵ	ϵ	X
bibechana-10397	36	6	m	m	VERB
bibechana-10397	36	7	}	}	PUNCT
bibechana-10397	36	8	for	for	ADP
bibechana-10397	36	9	each	each	DET
bibechana-10397	36	10	element	element	NOUN
bibechana-10397	36	11	x	x	X
bibechana-10397	37	1	ϵ	ϵ	X
bibechana-10397	37	2	e.	e.	PROPN
bibechana-10397	38	1	the	the	DET
bibechana-10397	38	2	collection	collection	NOUN
bibechana-10397	38	3	of	of	ADP
bibechana-10397	38	4	these	these	DET
bibechana-10397	38	5	so	so	ADV
bibechana-10397	38	6	called	call	VERB
bibechana-10397	38	7	equivalence	equivalence	NOUN
bibechana-10397	38	8	classes	class	NOUN
bibechana-10397	38	9	becomes	become	VERB
bibechana-10397	38	10	a	a	DET
bibechana-10397	38	11	linear	linear	ADJ
bibechana-10397	38	12	space	space	NOUN
bibechana-10397	38	13	e	e	NOUN
bibechana-10397	38	14	/	/	SYM
bibechana-10397	38	15	m	m	PROPN
bibechana-10397	38	16	,	,	PUNCT
bibechana-10397	38	17	the	the	DET
bibechana-10397	38	18	quotient	quotient	NOUN
bibechana-10397	38	19	space	space	NOUN
bibechana-10397	38	20	of	of	ADP
bibechana-10397	38	21	e	e	PROPN
bibechana-10397	38	22	by	by	ADP
bibechana-10397	38	23	m	m	PROPN
bibechana-10397	38	24	if	if	SCONJ
bibechana-10397	38	25	x(m	x(m	PROPN
bibechana-10397	38	26	)	)	PUNCT
bibechana-10397	39	1	+	+	PUNCT
bibechana-10397	39	2	y(m	y(m	X
bibechana-10397	39	3	)	)	PUNCT
bibechana-10397	40	1	=	=	SYM
bibechana-10397	40	2	x	x	PUNCT
bibechana-10397	41	1	+	+	PUNCT
bibechana-10397	41	2	y	y	PROPN
bibechana-10397	42	1	+	+	NOUN
bibechana-10397	42	2	m	m	VERB
bibechana-10397	42	3	=	=	X
bibechana-10397	42	4	{	{	PUNCT
bibechana-10397	42	5	x	x	PROPN
bibechana-10397	43	1	+	+	NUM
bibechana-10397	43	2	y	y	PROPN
bibechana-10397	44	1	+	+	NOUN
bibechana-10397	44	2	z	z	NOUN
bibechana-10397	44	3	:	:	PUNCT
bibechana-10397	45	1	z	z	NOUN
bibechana-10397	45	2	ϵ	ϵ	X
bibechana-10397	45	3	m	m	VERB
bibechana-10397	45	4	}	}	PUNCT
bibechana-10397	45	5	and	and	CCONJ
bibechana-10397	45	6	αx(m	αx(m	NUM
bibechana-10397	45	7	)	)	PUNCT
bibechana-10397	46	1	=	=	PUNCT
bibechana-10397	46	2	αx	αx	NOUN
bibechana-10397	47	1	+	+	NOUN
bibechana-10397	47	2	m	m	VERB
bibechana-10397	47	3	=	=	PUNCT
bibechana-10397	47	4	{	{	PUNCT
bibechana-10397	47	5	αx	αx	PROPN
bibechana-10397	48	1	+	+	CCONJ
bibechana-10397	48	2	z	z	NOUN
bibechana-10397	48	3	:	:	PUNCT
bibechana-10397	49	1	z	z	NOUN
bibechana-10397	49	2	ϵ	ϵ	X
bibechana-10397	49	3	m	m	VERB
bibechana-10397	49	4	}	}	PUNCT
bibechana-10397	50	1	[	[	X
bibechana-10397	50	2	8,9	8,9	NUM
bibechana-10397	50	3	]	]	PUNCT
bibechana-10397	50	4	.	.	PUNCT
bibechana-10397	51	1	4	4	X
bibechana-10397	51	2	.	.	X
bibechana-10397	51	3	theorems	theorem	NOUN
bibechana-10397	51	4	theorem	theorem	VERB
bibechana-10397	51	5	4.1	4.1	NUM
bibechana-10397	51	6	.	.	PUNCT
bibechana-10397	52	1	(	(	PUNCT
bibechana-10397	52	2	open	open	ADJ
bibechana-10397	52	3	mapping	mapping	NOUN
bibechana-10397	52	4	theorem	theorem	NOUN
bibechana-10397	52	5	)	)	PUNCT
bibechana-10397	52	6	if	if	SCONJ
bibechana-10397	52	7	e	e	PROPN
bibechana-10397	52	8	and	and	CCONJ
bibechana-10397	52	9	f	f	PROPN
bibechana-10397	52	10	are	be	AUX
bibechana-10397	52	11	frechet	frechet	PROPN
bibechana-10397	52	12	spaces	space	NOUN
bibechana-10397	52	13	,	,	PUNCT
bibechana-10397	52	14	a	a	DET
bibechana-10397	52	15	:	:	PUNCT
bibechana-10397	52	16	e→f	e→f	NUM
bibechana-10397	52	17	linear	linear	ADJ
bibechana-10397	52	18	,	,	PUNCT
bibechana-10397	52	19	continuous	continuous	ADJ
bibechana-10397	52	20	and	and	CCONJ
bibechana-10397	52	21	surjective	surjective	ADJ
bibechana-10397	52	22	,	,	PUNCT
bibechana-10397	52	23	then	then	ADV
bibechana-10397	52	24	a	a	PRON
bibechana-10397	52	25	is	be	AUX
bibechana-10397	52	26	open	open	ADJ
bibechana-10397	52	27	[	[	X
bibechana-10397	52	28	6	6	NUM
bibechana-10397	52	29	]	]	PUNCT
bibechana-10397	52	30	.	.	PUNCT
bibechana-10397	53	1	theorem	theorem	VERB
bibechana-10397	53	2	4.2	4.2	NUM
bibechana-10397	53	3	.	.	PUNCT
bibechana-10397	54	1	(	(	PUNCT
bibechana-10397	54	2	bipolar	bipolar	ADJ
bibechana-10397	54	3	theorem	theorem	NOUN
bibechana-10397	54	4	)	)	PUNCT
bibechana-10397	54	5	if	if	SCONJ
bibechana-10397	54	6	e	e	PRON
bibechana-10397	54	7	is	be	AUX
bibechana-10397	54	8	a	a	DET
bibechana-10397	54	9	locally	locally	ADV
bibechana-10397	54	10	convex	convex	NOUN
bibechana-10397	54	11	and	and	CCONJ
bibechana-10397	54	12	m	m	NOUN
bibechana-10397	54	13	⊂	⊂	NOUN
bibechana-10397	54	14	e	e	NOUN
bibechana-10397	54	15	absolutely	absolutely	ADV
bibechana-10397	54	16	convex	convex	VERB
bibechana-10397	54	17	then	then	ADV
bibechana-10397	54	18	m00	m00	VERB
bibechana-10397	55	1	=	=	PROPN
bibechana-10397	55	2	m[6	m[6	PROPN
bibechana-10397	55	3	]	]	PUNCT
bibechana-10397	55	4	.	.	PUNCT
bibechana-10397	55	5	theorem	theorem	VERB
bibechana-10397	55	6	4.3	4.3	NUM
bibechana-10397	55	7	.	.	PUNCT
bibechana-10397	56	1	if	if	SCONJ
bibechana-10397	56	2	e	e	PROPN
bibechana-10397	56	3	is	be	AUX
bibechana-10397	56	4	a	a	DET
bibechana-10397	56	5	frechet	frechet	ADJ
bibechana-10397	56	6	space	space	NOUN
bibechana-10397	56	7	and	and	CCONJ
bibechana-10397	56	8	m	m	PROPN
bibechana-10397	56	9	⊂	⊂	PROPN
bibechana-10397	56	10	e	e	X
bibechana-10397	56	11	a	a	DET
bibechana-10397	56	12	closed	closed	ADJ
bibechana-10397	56	13	subspace	subspace	NOUN
bibechana-10397	56	14	then	then	ADV
bibechana-10397	56	15	m	m	VERB
bibechana-10397	56	16	and	and	CCONJ
bibechana-10397	56	17	e	e	X
bibechana-10397	56	18	/	/	SYM
bibechana-10397	56	19	m	m	VERB
bibechana-10397	56	20	are	be	AUX
bibechana-10397	56	21	frechet	frechet	PROPN
bibechana-10397	56	22	spaces	space	NOUN
bibechana-10397	56	23	.	.	PUNCT
bibechana-10397	57	1	corollary	corollary	ADJ
bibechana-10397	57	2	4.4	4.4	NUM
bibechana-10397	57	3	.	.	PUNCT
bibechana-10397	58	1	if	if	SCONJ
bibechana-10397	58	2	e	e	PROPN
bibechana-10397	58	3	is	be	AUX
bibechana-10397	58	4	a	a	DET
bibechana-10397	58	5	frechet	frechet	ADJ
bibechana-10397	58	6	space	space	NOUN
bibechana-10397	58	7	then	then	ADV
bibechana-10397	58	8	e	e	X
bibechana-10397	58	9	'	'	PUNCT
bibechana-10397	58	10	is	be	AUX
bibechana-10397	58	11	a	a	DET
bibechana-10397	58	12	complete	complete	ADJ
bibechana-10397	58	13	locally	locally	ADV
bibechana-10397	58	14	convex	convex	ADJ
bibechana-10397	58	15	space	space	NOUN
bibechana-10397	58	16	which	which	PRON
bibechana-10397	58	17	has	have	VERB
bibechana-10397	58	18	a	a	DET
bibechana-10397	58	19	countable	countable	ADJ
bibechana-10397	58	20	fundamental	fundamental	ADJ
bibechana-10397	58	21	system	system	NOUN
bibechana-10397	58	22	of	of	ADP
bibechana-10397	58	23	bounded	bounded	ADJ
bibechana-10397	58	24	sets	set	NOUN
bibechana-10397	58	25	.	.	PUNCT
bibechana-10397	59	1	s.	s.	PROPN
bibechana-10397	59	2	n.	n.	PROPN
bibechana-10397	59	3	sah	sah	PROPN
bibechana-10397	59	4	/	/	SYM
bibechana-10397	59	5	bibechana	bibechana	PROPN
bibechana-10397	59	6	11(1	11(1	NUM
bibechana-10397	59	7	)	)	PUNCT
bibechana-10397	59	8	(	(	PUNCT
bibechana-10397	59	9	2014	2014	NUM
bibechana-10397	59	10	)	)	PUNCT
bibechana-10397	59	11	1	1	NUM
bibechana-10397	59	12	corollary	corollary	NOUN
bibechana-10397	59	13	4.5	4.5	NUM
bibechana-10397	59	14	.	.	PUNCT
bibechana-10397	60	1	if	if	SCONJ
bibechana-10397	60	2	e	e	PROPN
bibechana-10397	60	3	is	be	AUX
bibechana-10397	60	4	isomorphic	isomorphic	ADJ
bibechana-10397	60	5	to	to	ADP
bibechana-10397	60	6	a	a	DET
bibechana-10397	60	7	countable	countable	ADJ
bibechana-10397	60	8	product	product	NOUN
bibechana-10397	60	9	of	of	ADP
bibechana-10397	60	10	banach	banach	NOUN
bibechana-10397	60	11	spaces	space	NOUN
bibechana-10397	60	12	then	then	ADV
bibechana-10397	60	13	e	e	PROPN
bibechana-10397	60	14	does	do	AUX
bibechana-10397	60	15	not	not	PART
bibechana-10397	60	16	have	have	VERB
bibechana-10397	60	17	a	a	DET
bibechana-10397	60	18	nuclear	nuclear	ADJ
bibechana-10397	60	19	kothe	kothe	NOUN
bibechana-10397	60	20	quotient	quotient	NOUN
bibechana-10397	60	21	.	.	PUNCT
bibechana-10397	61	1	corollary	corollary	ADJ
bibechana-10397	61	2	4.6	4.6	NUM
bibechana-10397	61	3	.	.	PUNCT
bibechana-10397	62	1	every	every	DET
bibechana-10397	62	2	frechet	frechet	NOUN
bibechana-10397	62	3	montel	montel	PROPN
bibechana-10397	62	4	space	space	NOUN
bibechana-10397	62	5	not	not	PART
bibechana-10397	62	6	isomorphic	isomorphic	ADJ
bibechana-10397	62	7	to	to	ADP
bibechana-10397	62	8	proof	proof	NOUN
bibechana-10397	62	9	:	:	PUNCT
bibechana-10397	62	10	if	if	SCONJ
bibechana-10397	62	11	e	e	NOUN
bibechana-10397	62	12	is	be	AUX
bibechana-10397	62	13	a	a	DET
bibechana-10397	62	14	frechet	frechet	NOUN
bibechana-10397	62	15	montel	montel	PROPN
bibechana-10397	62	16	space	space	NOUN
bibechana-10397	62	17	then	then	ADV
bibechana-10397	62	18	e	e	PROPN
bibechana-10397	62	19	is	be	AUX
bibechana-10397	62	20	separable	separable	ADJ
bibechana-10397	62	21	and	and	CCONJ
bibechana-10397	62	22	reflexive	reflexive	ADJ
bibechana-10397	62	23	.	.	PUNCT
bibechana-10397	63	1	we	we	PRON
bibechana-10397	63	2	will	will	AUX
bibechana-10397	63	3	prove	prove	VERB
bibechana-10397	63	4	that	that	SCONJ
bibechana-10397	63	5	e	e	NOUN
bibechana-10397	63	6	is	be	AUX
bibechana-10397	63	7	not	not	PART
bibechana-10397	63	8	a	a	DET
bibechana-10397	63	9	quojection	quojection	NOUN
bibechana-10397	63	10	.	.	PUNCT
bibechana-10397	64	1	let	let	VERB
bibechana-10397	64	2	e	e	PRON
bibechana-10397	64	3	be	be	AUX
bibechana-10397	64	4	the	the	DET
bibechana-10397	64	5	projective	projective	ADJ
bibechana-10397	64	6	limit	limit	NOUN
bibechana-10397	64	7	of	of	ADP
bibechana-10397	64	8	the	the	DET
bibechana-10397	64	9	surjections	surjection	NOUN
bibechana-10397	64	10	a	a	PRON
bibechana-10397	64	11	of	of	ADP
bibechana-10397	64	12	ek+1	ek+1	NOUN
bibechana-10397	64	13	on	on	ADP
bibechana-10397	64	14	to	to	ADP
bibechana-10397	64	15	the	the	DET
bibechana-10397	64	16	unit	unit	NOUN
bibechana-10397	64	17	ball	ball	NOUN
bibechana-10397	64	18	of	of	ADP
bibechana-10397	64	19	ek	ek	PROPN
bibechana-10397	64	20	.	.	PUNCT
bibechana-10397	65	1	also	also	ADV
bibechana-10397	65	2	,	,	PUNCT
bibechana-10397	65	3	since	since	SCONJ
bibechana-10397	65	4	e	e	NOUN
bibechana-10397	65	5	is	be	AUX
bibechana-10397	65	6	not	not	PART
bibechana-10397	65	7	isomorphic	isomorphic	ADJ
bibechana-10397	65	8	to	to	ADP
bibechana-10397	65	9	dimensional	dimensional	ADJ
bibechana-10397	65	10	.	.	PUNCT
bibechana-10397	66	1	then	then	ADV
bibechana-10397	66	2	,	,	PUNCT
bibechana-10397	66	3	viewing	view	VERB
bibechana-10397	66	4	e	e	NOUN
bibechana-10397	66	5	as	as	ADP
bibechana-10397	66	6	the	the	DET
bibechana-10397	66	7	projective	projective	ADJ
bibechana-10397	66	8	limit	limit	NOUN
bibechana-10397	66	9	,	,	PUNCT
bibechana-10397	66	10	it	it	PRON
bibechana-10397	66	11	is	be	AUX
bibechana-10397	66	12	easy	easy	ADJ
bibechana-10397	66	13	to	to	PART
bibechana-10397	66	14	see	see	VERB
bibechana-10397	66	15	that	that	SCONJ
bibechana-10397	66	16	{	{	PUNCT
bibechana-10397	66	17	(	(	PUNCT
bibechana-10397	66	18	x	x	SYM
bibechana-10397	66	19	ek∋k	ek∋k	PRON
bibechana-10397	66	20	}	}	PUNCT
bibechana-10397	66	21	is	be	AUX
bibechana-10397	66	22	closed	closed	ADJ
bibechana-10397	66	23	,	,	PUNCT
bibechana-10397	66	24	bounded	bound	VERB
bibechana-10397	66	25	subset	subset	PROPN
bibechana-10397	66	26	of	of	ADP
bibechana-10397	66	27	e.	e.	PROPN
bibechana-10397	66	28	but	but	CCONJ
bibechana-10397	66	29	the	the	DET
bibechana-10397	66	30	projection	projection	NOUN
bibechana-10397	66	31	of	of	ADP
bibechana-10397	66	32	this	this	DET
bibechana-10397	66	33	set	set	NOUN
bibechana-10397	66	34	in	in	ADP
bibechana-10397	66	35	e	e	PROPN
bibechana-10397	66	36	compact	compact	ADJ
bibechana-10397	66	37	[	[	X
bibechana-10397	66	38	10,11	10,11	NOUN
bibechana-10397	66	39	]	]	PUNCT
bibechana-10397	66	40	.	.	PUNCT
bibechana-10397	67	1	hence	hence	ADV
bibechana-10397	67	2	the	the	DET
bibechana-10397	67	3	set	set	NOUN
bibechana-10397	67	4	is	be	AUX
bibechana-10397	67	5	not	not	PART
bibechana-10397	67	6	compact	compact	ADJ
bibechana-10397	67	7	in	in	ADP
bibechana-10397	67	8	e	e	NOUN
bibechana-10397	67	9	which	which	PRON
bibechana-10397	67	10	is	be	AUX
bibechana-10397	67	11	a	a	DET
bibechana-10397	67	12	contradiction	contradiction	NOUN
bibechana-10397	67	13	.	.	PUNCT
bibechana-10397	68	1	we	we	PRON
bibechana-10397	68	2	are	be	AUX
bibechana-10397	68	3	now	now	ADV
bibechana-10397	68	4	ready	ready	ADJ
bibechana-10397	68	5	for	for	ADP
bibechana-10397	68	6	the	the	DET
bibechana-10397	68	7	main	main	ADJ
bibechana-10397	68	8	result	result	NOUN
bibechana-10397	68	9	of	of	ADP
bibechana-10397	68	10	this	this	DET
bibechana-10397	68	11	paper	paper	NOUN
bibechana-10397	68	12	.	.	PUNCT
bibechana-10397	69	1	proposition	proposition	NOUN
bibechana-10397	69	2	4.6	4.6	NUM
bibechana-10397	69	3	.	.	PUNCT
bibechana-10397	70	1	a	a	DET
bibechana-10397	70	2	frechet	frechet	NOUN
bibechana-10397	70	3	space	space	NOUN
bibechana-10397	70	4	e	e	NOUN
bibechana-10397	70	5	satisfies	satisfy	VERB
bibechana-10397	70	6	condition	condition	NOUN
bibechana-10397	70	7	condition	condition	NOUN
bibechana-10397	70	8	⍟	⍟	PROPN
bibechana-10397	70	9	.	.	PUNCT
bibechana-10397	71	1	proof	proof	NOUN
bibechana-10397	71	2	:	:	PUNCT
bibechana-10397	71	3	suppose	suppose	VERB
bibechana-10397	71	4	that	that	SCONJ
bibechana-10397	71	5	the	the	DET
bibechana-10397	71	6	frechet	frechet	NOUN
bibechana-10397	71	7	space	space	NOUN
bibechana-10397	71	8	e	e	NOUN
bibechana-10397	71	9	satisfies	satisfy	VERB
bibechana-10397	71	10	condition	condition	NOUN
bibechana-10397	71	11	let	let	VERB
bibechana-10397	71	12	m	m	VERB
bibechana-10397	71	13	=	=	SYM
bibechana-10397	71	14	(	(	PUNCT
bibechana-10397	71	15	)	)	PUNCT
bibechana-10397	71	16	°	°	NOUN
bibechana-10397	71	17	°	°	NOUN
bibechana-10397	71	18	which	which	PRON
bibechana-10397	71	19	,	,	PUNCT
bibechana-10397	71	20	by	by	ADP
bibechana-10397	71	21	the	the	DET
bibechana-10397	71	22	bipolar	bipolar	ADJ
bibechana-10397	71	23	theorem	theorem	NOUN
bibechana-10397	71	24	,	,	PUNCT
bibechana-10397	71	25	is	be	AUX
bibechana-10397	71	26	the	the	DET
bibechana-10397	71	27	closure	closure	NOUN
bibechana-10397	71	28	of	of	ADP
bibechana-10397	71	29	in	in	ADP
bibechana-10397	71	30	prove	prove	VERB
bibechana-10397	71	31	that	that	SCONJ
bibechana-10397	71	32	e	e	NOUN
bibechana-10397	71	33	/	/	SYM
bibechana-10397	71	34	m	m	NOUN
bibechana-10397	71	35	°	°	NOUN
bibechana-10397	71	36	is	be	AUX
bibechana-10397	71	37	the	the	DET
bibechana-10397	71	38	desired	desire	VERB
bibechana-10397	71	39	quotient	quotient	NOUN
bibechana-10397	71	40	.	.	PUNCT
bibechana-10397	72	1	at	at	ADP
bibechana-10397	72	2	first	first	ADV
bibechana-10397	72	3	,	,	PUNCT
bibechana-10397	72	4	we	we	PRON
bibechana-10397	72	5	check	check	VERB
bibechana-10397	72	6	that	that	SCONJ
bibechana-10397	72	7	e	e	NOUN
bibechana-10397	72	8	/	/	SYM
bibechana-10397	72	9	m	m	NOUN
bibechana-10397	72	10	°	°	PROPN
bibechana-10397	72	11	admits	admit	VERB
bibechana-10397	72	12	continuous	continuous	ADJ
bibechana-10397	72	13	norm	norm	NOUN
bibechana-10397	72	14	.	.	PUNCT
bibechana-10397	73	1	for	for	ADP
bibechana-10397	73	2	this	this	PRON
bibechana-10397	73	3	,	,	PUNCT
bibechana-10397	73	4	let	let	VERB
bibechana-10397	73	5	x	x	PRON
bibechana-10397	73	6	e	e	VERB
bibechana-10397	73	7	/	/	SYM
bibechana-10397	73	8	m	m	NOUN
bibechana-10397	73	9	°	°	PROPN
bibechana-10397	73	10	induced	induce	VERB
bibechana-10397	73	11	by	by	ADP
bibechana-10397	73	12	ǁ·ǁl	ǁ·ǁl	PROPN
bibechana-10397	73	13	,	,	PUNCT
bibechana-10397	73	14	annihilates	annihilate	VERB
bibechana-10397	73	15	x	x	PUNCT
bibechana-10397	73	16	+	+	PUNCT
bibechana-10397	73	17	m	m	NOUN
bibechana-10397	73	18	°	°	NOUN
bibechana-10397	73	19	.	.	PUNCT
bibechana-10397	74	1	this	this	PRON
bibechana-10397	74	2	means	mean	VERB
bibechana-10397	74	3	that	that	SCONJ
bibechana-10397	74	4	∃	∃	PROPN
bibechana-10397	74	5	⊂(yn	⊂(yn	ADJ
bibechana-10397	74	6	)	)	PUNCT
bibechana-10397	74	7	m	m	PROPN
bibechana-10397	74	8	°	°	NOUN
bibechana-10397	74	9	϶	϶	PUNCT
bibechana-10397	74	10	limn	limn	NOUN
bibechana-10397	74	11	ǁx	ǁx	INTJ
bibechana-10397	74	12	let	let	VERB
bibechana-10397	74	13	u	u	PRON
bibechana-10397	74	14	ϵ	ϵ	X
bibechana-10397	74	15	m.	m.	NOUN
bibechana-10397	74	16	then	then	ADV
bibechana-10397	74	17	,	,	PUNCT
bibechana-10397	74	18	∃	∃	PROPN
bibechana-10397	74	19	�	�	PROPN
bibechana-10397	74	20	ϵ	ϵ	PROPN
bibechana-10397	74	21	϶	϶	PUNCT
bibechana-10397	74	22	|u(x)-v(x)|	|u(x)-v(x)|	PRON
bibechana-10397	75	1	so	so	ADV
bibechana-10397	75	2	we	we	PRON
bibechana-10397	75	3	have	have	VERB
bibechana-10397	75	4	|u(x)|	|u(x)|	NOUN
bibechana-10397	75	5	≤	≤	VERB
bibechana-10397	76	1	|v(x)|	|v(x)|	PROPN
bibechana-10397	76	2	+	+	PROPN
bibechana-10397	76	3	|u(x	|u(x	PROPN
bibechana-10397	76	4	)	)	PUNCT
bibechana-10397	76	5	v(x)|	v(x)|	NOUN
bibechana-10397	76	6	since	since	SCONJ
bibechana-10397	76	7	v	v	NUM
bibechana-10397	76	8	ϵ	ϵ	X
bibechana-10397	76	9	e'l	e'l	PRON
bibechana-10397	76	10	it	it	PRON
bibechana-10397	76	11	follows	follow	VERB
bibechana-10397	76	12	that	that	SCONJ
bibechana-10397	76	13	lim	lim	PROPN
bibechana-10397	76	14	v(x	v(x	PROPN
bibechana-10397	76	15	+	+	CCONJ
bibechana-10397	76	16	yk	yk	NOUN
bibechana-10397	76	17	)	)	PUNCT
bibechana-10397	76	18	=	=	SYM
bibechana-10397	77	1	o	o	NOUN
bibechana-10397	77	2	,	,	PUNCT
bibechana-10397	77	3	so	so	ADV
bibechana-10397	77	4	|u(x	|u(x	PROPN
bibechana-10397	77	5	)	)	PUNCT
bibechana-10397	77	6	by	by	ADP
bibechana-10397	77	7	ǁ·ǁl	ǁ·ǁl	PROPN
bibechana-10397	77	8	,	,	PUNCT
bibechana-10397	77	9	is	be	AUX
bibechana-10397	77	10	a	a	DET
bibechana-10397	77	11	norm	norm	NOUN
bibechana-10397	77	12	.	.	PUNCT
bibechana-10397	78	1	next	next	ADV
bibechana-10397	78	2	,	,	PUNCT
bibechana-10397	78	3	we	we	PRON
bibechana-10397	78	4	verify	verify	VERB
bibechana-10397	78	5	condition	condition	NOUN
bibechana-10397	78	6	⍟	⍟	PROPN
bibechana-10397	78	7	for	for	ADP
bibechana-10397	78	8	e	e	PROPN
bibechana-10397	78	9	/	/	SYM
bibechana-10397	78	10	m	m	NOUN
bibechana-10397	78	11	°	°	NOUN
bibechana-10397	78	12	.	.	PUNCT
bibechana-10397	79	1	we	we	PRON
bibechana-10397	79	2	fix	fix	VERB
bibechana-10397	79	3	k	k	NOUN
bibechana-10397	79	4	and	and	CCONJ
bibechana-10397	79	5	let	let	VERB
bibechana-10397	79	6	u	u	PRON
bibechana-10397	79	7	condition	condition	NOUN
bibechana-10397	79	8	⍟	⍟	PROPN
bibechana-10397	79	9	,	,	PUNCT
bibechana-10397	79	10	we	we	PRON
bibechana-10397	79	11	have	have	VERB
bibechana-10397	79	12	a	a	DET
bibechana-10397	79	13	sequence	sequence	NOUN
bibechana-10397	79	14	(	(	PUNCT
bibechana-10397	79	15	u	u	NOUN
bibechana-10397	79	16	~	~	PUNCT
bibechana-10397	79	17	u	u	NOUN
bibechana-10397	79	18	�	�	PROPN
bibechana-10397	79	19	so	so	SCONJ
bibechana-10397	79	20	a	a	DET
bibechana-10397	79	21	fortiori	fortiori	PROPN
bibechana-10397	79	22	un	un	PROPN
bibechana-10397	79	23	∉	∉	PROPN
bibechana-10397	79	24	(	(	PUNCT
bibechana-10397	79	25	uk	uk	PROPN
bibechana-10397	79	26	+	+	PROPN
bibechana-10397	79	27	m	m	NOUN
bibechana-10397	79	28	°	°	NOUN
bibechana-10397	79	29	)	)	PUNCT
bibechana-10397	79	30	°	°	PROPN
bibechana-10397	79	31	.	.	PUNCT
bibechana-10397	80	1	moreover	moreover	ADV
bibechana-10397	80	2	,	,	PUNCT
bibechana-10397	80	3	if	if	SCONJ
bibechana-10397	80	4	x	x	ADP
bibechana-10397	80	5	|nun(x+	|nun(x+	PROPN
bibechana-10397	80	6	y	y	NOUN
bibechana-10397	80	7	)	)	PUNCT
bibechana-10397	80	8	|	|	NOUN
bibechana-10397	80	9	=	=	SYM
bibechana-10397	80	10	|nun	|nun	NOUN
bibechana-10397	80	11	(	(	PUNCT
bibechana-10397	80	12	x)|	x)|	PROPN
bibechana-10397	80	13	hence	hence	ADV
bibechana-10397	80	14	un	un	PROPN
bibechana-10397	80	15	ϵ	ϵ	PROPN
bibechana-10397	80	16	�	�	PROPN
bibechana-10397	80	17	�	�	PROPN
bibechana-10397	80	18	(	(	PUNCT
bibechana-10397	80	19	uk+1	uk+1	X
bibechana-10397	80	20	+	+	NUM
bibechana-10397	80	21	m	m	NOUN
bibechana-10397	80	22	°	°	NOUN
bibechana-10397	80	23	)	)	PUNCT
bibechana-10397	80	24	°	°	PROPN
bibechana-10397	80	25	.	.	PUNCT
bibechana-10397	81	1	thus	thus	ADV
bibechana-10397	81	2	we	we	PRON
bibechana-10397	81	3	have	have	AUX
bibechana-10397	81	4	prove	prove	VERB
bibechana-10397	81	5	m	m	PROPN
bibechana-10397	81	6	and	and	CCONJ
bibechana-10397	81	7	the	the	DET
bibechana-10397	81	8	unit	unit	NOUN
bibechana-10397	81	9	ball	ball	NOUN
bibechana-10397	81	10	of	of	ADP
bibechana-10397	81	11	the	the	DET
bibechana-10397	81	12	dual	dual	ADJ
bibechana-10397	81	13	norm	norm	NOUN
bibechana-10397	81	14	of	of	ADP
bibechana-10397	81	15	the	the	DET
bibechana-10397	81	16	norm	norm	NOUN
bibechana-10397	81	17	in	in	ADP
bibechana-10397	81	18	e	e	PROPN
bibechana-10397	81	19	/	/	SYM
bibechana-10397	81	20	m	m	NOUN
bibechana-10397	81	21	°	°	PROPN
bibechana-10397	81	22	induced	induce	VERB
bibechana-10397	81	23	by	by	ADP
bibechana-10397	81	24	||	||	PROPN
bibechana-10397	81	25	·	·	PUNCT
bibechana-10397	81	26	||k	||k	PROPN
bibechana-10397	81	27	is	be	AUX
bibechana-10397	81	28	(	(	PUNCT
bibechana-10397	81	29	uk	uk	PROPN
bibechana-10397	81	30	+	+	PROPN
bibechana-10397	81	31	m	m	NOUN
bibechana-10397	81	32	°	°	NOUN
bibechana-10397	81	33	)	)	PUNCT
bibechana-10397	81	34	°	°	PROPN
bibechana-10397	81	35	.	.	PUNCT
bibechana-10397	82	1	this	this	PRON
bibechana-10397	82	2	proves	prove	VERB
bibechana-10397	82	3	that	that	SCONJ
bibechana-10397	82	4	e	e	NOUN
bibechana-10397	82	5	/	/	SYM
bibechana-10397	82	6	m	m	NOUN
bibechana-10397	82	7	°	°	NOUN
bibechana-10397	82	8	satisfies	satisfie	NOUN
bibechana-10397	82	9	condition	condition	NOUN
bibechana-10397	82	10	⍟	⍟	PROPN
bibechana-10397	82	11	.	.	PUNCT
bibechana-10397	83	1	now	now	ADV
bibechana-10397	83	2	,	,	PUNCT
bibechana-10397	83	3	conversely	conversely	ADV
bibechana-10397	83	4	assume	assume	VERB
bibechana-10397	83	5	that	that	SCONJ
bibechana-10397	83	6	e	e	NOUN
bibechana-10397	83	7	/	/	SYM
bibechana-10397	83	8	f	f	X
bibechana-10397	83	9	be	be	AUX
bibechana-10397	83	10	a	a	DET
bibechana-10397	83	11	quotient	quotient	NOUN
bibechana-10397	83	12	of	of	ADP
bibechana-10397	83	13	e.	e.	PROPN
bibechana-10397	83	14	e	e	PROPN
bibechana-10397	83	15	then	then	ADV
bibechana-10397	83	16	by	by	ADP
bibechana-10397	83	17	general	general	ADJ
bibechana-10397	83	18	duality	duality	NOUN
bibechana-10397	83	19	,	,	PUNCT
bibechana-10397	83	20	(	(	PUNCT
bibechana-10397	83	21	e	e	NOUN
bibechana-10397	83	22	/	/	SYM
bibechana-10397	83	23	f	f	NOUN
bibechana-10397	83	24	)	)	PUNCT
bibechana-10397	83	25	'	'	PUNCT
bibechana-10397	83	26	can	can	AUX
bibechana-10397	83	27	be	be	AUX
bibechana-10397	83	28	represented	represent	VERB
bibechana-10397	83	29	as	as	ADP
bibechana-10397	83	30	a	a	DET
bibechana-10397	83	31	vector	vector	NOUN
bibechana-10397	83	32	subspace	subspace	NOUN
bibechana-10397	83	33	of	of	ADP
bibechana-10397	83	34	e	e	NOUN
bibechana-10397	83	35	'	'	PUNCT
bibechana-10397	83	36	and	and	CCONJ
bibechana-10397	83	37	a	a	DET
bibechana-10397	83	38	fundamental	fundamental	ADJ
bibechana-10397	83	39	/	/	SYM
bibechana-10397	83	40	bibechana	bibechana	NOUN
bibechana-10397	83	41	11(1	11(1	NUM
bibechana-10397	83	42	)	)	PUNCT
bibechana-10397	83	43	(	(	PUNCT
bibechana-10397	83	44	2014	2014	NUM
bibechana-10397	83	45	)	)	PUNCT
bibechana-10397	83	46	161	161	NUM
bibechana-10397	83	47	-	-	SYM
bibechana-10397	83	48	164	164	NUM
bibechana-10397	83	49	:	:	PUNCT
bibechana-10397	83	50	(	(	PUNCT
bibechana-10397	83	51	online	online	ADJ
bibechana-10397	83	52	publication	publication	NOUN
bibechana-10397	83	53	:	:	PUNCT
bibechana-10397	83	54	march	march	PROPN
bibechana-10397	83	55	,	,	PUNCT
bibechana-10397	83	56	2014	2014	NUM
bibechana-10397	83	57	)	)	PUNCT
bibechana-10397	83	58	p.163	p.163	NOUN
bibechana-10397	83	59	if	if	SCONJ
bibechana-10397	83	60	e	e	NOUN
bibechana-10397	83	61	is	be	AUX
bibechana-10397	83	62	isomorphic	isomorphic	ADJ
bibechana-10397	83	63	to	to	ADP
bibechana-10397	83	64	a	a	DET
bibechana-10397	83	65	countable	countable	ADJ
bibechana-10397	83	66	product	product	NOUN
bibechana-10397	83	67	of	of	ADP
bibechana-10397	83	68	banach	banach	NOUN
bibechana-10397	83	69	spaces	space	NOUN
bibechana-10397	83	70	then	then	ADV
bibechana-10397	83	71	e	e	PROPN
bibechana-10397	83	72	does	do	AUX
bibechana-10397	83	73	not	not	PART
bibechana-10397	83	74	have	have	VERB
bibechana-10397	83	75	a	a	DET
bibechana-10397	83	76	nuclear	nuclear	ADJ
bibechana-10397	83	77	kothe	kothe	NOUN
bibechana-10397	83	78	space	space	NOUN
bibechana-10397	83	79	not	not	PART
bibechana-10397	83	80	isomorphic	isomorphic	ADJ
bibechana-10397	83	81	to	to	ADP
bibechana-10397	83	82	ω	ω	PROPN
bibechana-10397	83	83	has	have	VERB
bibechana-10397	83	84	a	a	DET
bibechana-10397	83	85	nuclear	nuclear	ADJ
bibechana-10397	83	86	kothe	kothe	NOUN
bibechana-10397	83	87	quotient	quotient	NOUN
bibechana-10397	83	88	.	.	PUNCT
bibechana-10397	84	1	if	if	SCONJ
bibechana-10397	84	2	e	e	PROPN
bibechana-10397	84	3	is	be	AUX
bibechana-10397	84	4	a	a	DET
bibechana-10397	84	5	frechet	frechet	NOUN
bibechana-10397	84	6	montel	montel	PROPN
bibechana-10397	84	7	space	space	NOUN
bibechana-10397	84	8	then	then	ADV
bibechana-10397	84	9	e	e	PROPN
bibechana-10397	84	10	is	be	AUX
bibechana-10397	84	11	separable	separable	ADJ
bibechana-10397	84	12	and	and	CCONJ
bibechana-10397	84	13	reflexive	reflexive	ADJ
bibechana-10397	84	14	.	.	PUNCT
bibechana-10397	85	1	we	we	PRON
bibechana-10397	85	2	will	will	AUX
bibechana-10397	85	3	prove	prove	VERB
bibechana-10397	85	4	that	that	SCONJ
bibechana-10397	85	5	e	e	NOUN
bibechana-10397	85	6	is	be	AUX
bibechana-10397	85	7	not	not	PART
bibechana-10397	85	8	a	a	DET
bibechana-10397	85	9	quojection	quojection	NOUN
bibechana-10397	85	10	.	.	PUNCT
bibechana-10397	86	1	let	let	VERB
bibechana-10397	86	2	e	e	PRON
bibechana-10397	86	3	be	be	AUX
bibechana-10397	86	4	the	the	DET
bibechana-10397	86	5	projective	projective	ADJ
bibechana-10397	86	6	limit	limit	NOUN
bibechana-10397	86	7	of	of	ADP
bibechana-10397	86	8	the	the	DET
bibechana-10397	86	9	surjections	surjection	NOUN
bibechana-10397	86	10	ak	ak	PROPN
bibechana-10397	86	11	:	:	PUNCT
bibechana-10397	86	12	ek+1→ek	ek+1→ek	PROPN
bibechana-10397	86	13	.	.	PUNCT
bibechana-10397	87	1	we	we	PRON
bibechana-10397	87	2	may	may	AUX
bibechana-10397	87	3	assume	assume	VERB
bibechana-10397	87	4	that	that	SCONJ
bibechana-10397	87	5	ak	ak	PROPN
bibechana-10397	87	6	.	.	PUNCT
bibechana-10397	88	1	also	also	ADV
bibechana-10397	88	2	,	,	PUNCT
bibechana-10397	88	3	since	since	SCONJ
bibechana-10397	88	4	e	e	NOUN
bibechana-10397	88	5	is	be	AUX
bibechana-10397	88	6	not	not	PART
bibechana-10397	88	7	isomorphic	isomorphic	ADJ
bibechana-10397	88	8	to	to	ADP
bibechana-10397	88	9	ω	ω	NUM
bibechana-10397	88	10	we	we	PRON
bibechana-10397	88	11	may	may	AUX
bibechana-10397	88	12	assume	assume	VERB
bibechana-10397	88	13	that	that	SCONJ
bibechana-10397	88	14	e	e	PROPN
bibechana-10397	88	15	dimensional	dimensional	ADJ
bibechana-10397	88	16	.	.	PUNCT
bibechana-10397	89	1	then	then	ADV
bibechana-10397	89	2	,	,	PUNCT
bibechana-10397	89	3	viewing	view	VERB
bibechana-10397	89	4	e	e	NOUN
bibechana-10397	89	5	as	as	ADP
bibechana-10397	89	6	the	the	DET
bibechana-10397	89	7	projective	projective	ADJ
bibechana-10397	89	8	limit	limit	NOUN
bibechana-10397	89	9	,	,	PUNCT
bibechana-10397	89	10	it	it	PRON
bibechana-10397	89	11	is	be	AUX
bibechana-10397	89	12	easy	easy	ADJ
bibechana-10397	89	13	to	to	PART
bibechana-10397	89	14	see	see	VERB
bibechana-10397	89	15	that	that	SCONJ
bibechana-10397	89	16	{	{	PUNCT
bibechana-10397	89	17	(	(	PUNCT
bibechana-10397	89	18	xk)ϵe	xk)ϵe	NOUN
bibechana-10397	89	19	:	:	PUNCT
bibechana-10397	89	20	xk	xk	PROPN
bibechana-10397	89	21	is	be	AUX
bibechana-10397	89	22	in	in	ADP
bibechana-10397	89	23	the	the	DET
bibechana-10397	89	24	unit	unit	NOUN
bibechana-10397	89	25	ball	ball	NOUN
bibechana-10397	89	26	of	of	ADP
bibechana-10397	89	27	ed	ed	PROPN
bibechana-10397	89	28	,	,	PUNCT
bibechana-10397	89	29	bounded	bounded	ADJ
bibechana-10397	89	30	subset	subset	PROPN
bibechana-10397	89	31	of	of	ADP
bibechana-10397	89	32	e.	e.	PROPN
bibechana-10397	89	33	but	but	CCONJ
bibechana-10397	89	34	the	the	DET
bibechana-10397	89	35	projection	projection	NOUN
bibechana-10397	89	36	of	of	ADP
bibechana-10397	89	37	this	this	DET
bibechana-10397	89	38	set	set	NOUN
bibechana-10397	89	39	in	in	ADP
bibechana-10397	89	40	el	el	PROPN
bibechana-10397	89	41	is	be	AUX
bibechana-10397	89	42	the	the	DET
bibechana-10397	89	43	unit	unit	NOUN
bibechana-10397	89	44	ball	ball	NOUN
bibechana-10397	89	45	so	so	SCONJ
bibechana-10397	89	46	it	it	PRON
bibechana-10397	89	47	is	be	AUX
bibechana-10397	89	48	not	not	PART
bibechana-10397	89	49	compact	compact	ADJ
bibechana-10397	89	50	[	[	X
bibechana-10397	89	51	10,11	10,11	NOUN
bibechana-10397	89	52	]	]	PUNCT
bibechana-10397	89	53	.	.	PUNCT
bibechana-10397	90	1	hence	hence	ADV
bibechana-10397	90	2	the	the	DET
bibechana-10397	90	3	set	set	NOUN
bibechana-10397	90	4	is	be	AUX
bibechana-10397	90	5	not	not	PART
bibechana-10397	90	6	compact	compact	ADJ
bibechana-10397	90	7	in	in	ADP
bibechana-10397	90	8	e	e	NOUN
bibechana-10397	90	9	which	which	PRON
bibechana-10397	90	10	is	be	AUX
bibechana-10397	90	11	a	a	DET
bibechana-10397	90	12	contradiction	contradiction	NOUN
bibechana-10397	90	13	.	.	PUNCT
bibechana-10397	91	1	we	we	PRON
bibechana-10397	91	2	are	be	AUX
bibechana-10397	91	3	now	now	ADV
bibechana-10397	91	4	ready	ready	ADJ
bibechana-10397	91	5	for	for	ADP
bibechana-10397	91	6	the	the	DET
bibechana-10397	91	7	main	main	ADJ
bibechana-10397	91	8	result	result	NOUN
bibechana-10397	91	9	of	of	ADP
bibechana-10397	91	10	this	this	DET
bibechana-10397	91	11	paper	paper	NOUN
bibechana-10397	91	12	.	.	PUNCT
bibechana-10397	92	1	ace	ace	NOUN
bibechana-10397	92	2	e	e	PROPN
bibechana-10397	92	3	satisfies	satisfy	VERB
bibechana-10397	92	4	condition	condition	NOUN
bibechana-10397	92	5	⍟	⍟	PROPN
bibechana-10397	92	6	iff	iff	NOUN
bibechana-10397	92	7	it	it	PRON
bibechana-10397	92	8	has	have	VERB
bibechana-10397	92	9	a	a	DET
bibechana-10397	92	10	quotient	quotient	NOUN
bibechana-10397	92	11	which	which	PRON
bibechana-10397	92	12	admits	admit	VERB
bibechana-10397	92	13	continuous	continuous	ADJ
bibechana-10397	92	14	norm	norm	NOUN
bibechana-10397	92	15	and	and	CCONJ
bibechana-10397	92	16	satisfies	satisfie	NOUN
bibechana-10397	92	17	suppose	suppose	VERB
bibechana-10397	92	18	that	that	SCONJ
bibechana-10397	92	19	the	the	DET
bibechana-10397	92	20	frechet	frechet	NOUN
bibechana-10397	92	21	space	space	NOUN
bibechana-10397	92	22	e	e	NOUN
bibechana-10397	92	23	satisfies	satisfy	VERB
bibechana-10397	92	24	condition	condition	NOUN
bibechana-10397	92	25	.	.	PUNCT
bibechana-10397	93	1	we	we	PRON
bibechana-10397	93	2	may	may	AUX
bibechana-10397	93	3	take	take	VERB
bibechana-10397	93	4	ℓ=1	ℓ=1	PUNCT
bibechana-10397	93	5	and	and	CCONJ
bibechana-10397	93	6	j	j	PROPN
bibechana-10397	93	7	=	=	SYM
bibechana-10397	93	8	k	k	PROPN
bibechana-10397	94	1	+	+	PROPN
bibechana-10397	94	2	1fo	1fo	ADJ
bibechana-10397	94	3	�	�	PROPN
bibechana-10397	94	4	°	°	NUM
bibechana-10397	94	5	which	which	PRON
bibechana-10397	94	6	,	,	PUNCT
bibechana-10397	94	7	by	by	ADP
bibechana-10397	94	8	the	the	DET
bibechana-10397	94	9	bipolar	bipolar	ADJ
bibechana-10397	94	10	theorem	theorem	NOUN
bibechana-10397	94	11	,	,	PUNCT
bibechana-10397	94	12	is	be	AUX
bibechana-10397	94	13	the	the	DET
bibechana-10397	94	14	closure	closure	NOUN
bibechana-10397	94	15	of	of	ADP
bibechana-10397	94	16	in	in	ADP
bibechana-10397	94	17	the	the	DET
bibechana-10397	94	18	weak	weak	ADJ
bibechana-10397	94	19	topology	topology	NOUN
bibechana-10397	94	20	from	from	ADP
bibechana-10397	94	21	e.	e.	PROPN
bibechana-10397	94	22	now	now	ADV
bibechana-10397	94	23	we	we	PRON
bibechana-10397	94	24	prove	prove	VERB
bibechana-10397	94	25	that	that	SCONJ
bibechana-10397	94	26	e	e	NOUN
bibechana-10397	94	27	/	/	SYM
bibechana-10397	94	28	m	m	NOUN
bibechana-10397	94	29	°	°	NOUN
bibechana-10397	94	30	is	be	AUX
bibechana-10397	94	31	the	the	DET
bibechana-10397	94	32	desired	desire	VERB
bibechana-10397	94	33	quotient	quotient	NOUN
bibechana-10397	94	34	.	.	PUNCT
bibechana-10397	95	1	at	at	ADP
bibechana-10397	95	2	first	first	ADV
bibechana-10397	95	3	,	,	PUNCT
bibechana-10397	95	4	we	we	PRON
bibechana-10397	95	5	check	check	VERB
bibechana-10397	95	6	that	that	SCONJ
bibechana-10397	95	7	e	e	NOUN
bibechana-10397	95	8	/	/	SYM
bibechana-10397	95	9	m	m	NOUN
bibechana-10397	95	10	°	°	PROPN
bibechana-10397	95	11	admits	admit	VERB
bibechana-10397	95	12	continuous	continuous	ADJ
bibechana-10397	95	13	norm	norm	NOUN
bibechana-10397	95	14	.	.	PUNCT
bibechana-10397	96	1	for	for	ADP
bibechana-10397	96	2	this	this	PRON
bibechana-10397	96	3	,	,	PUNCT
bibechana-10397	96	4	let	let	VERB
bibechana-10397	96	5	x	x	PUNCT
bibechana-10397	96	6	ϵ	ϵ	X
bibechana-10397	96	7	e	e	NOUN
bibechana-10397	96	8	and	and	CCONJ
bibechana-10397	96	9	assume	assume	VERB
bibechana-10397	96	10	that	that	SCONJ
bibechana-10397	96	11	the	the	DET
bibechana-10397	96	12	seminorm	seminorm	NOUN
bibechana-10397	96	13	in	in	ADP
bibechana-10397	96	14	l	l	NOUN
bibechana-10397	96	15	,	,	PUNCT
bibechana-10397	96	16	annihilates	annihilate	VERB
bibechana-10397	96	17	x	x	PUNCT
bibechana-10397	96	18	+	+	NUM
bibechana-10397	96	19	m	m	NOUN
bibechana-10397	96	20	°	°	NOUN
bibechana-10397	96	21	.	.	PUNCT
bibechana-10397	97	1	this	this	PRON
bibechana-10397	97	2	means	mean	VERB
bibechana-10397	97	3	that	that	SCONJ
bibechana-10397	97	4	϶	϶	PUNCT
bibechana-10397	97	5	limn	limn	ADV
bibechana-10397	97	6	ǁx	ǁx	INTJ
bibechana-10397	97	7	–	–	PUNCT
bibechana-10397	97	8	yn	yn	PROPN
bibechana-10397	97	9	ǁl	ǁl	NOUN
bibechana-10397	97	10	=	=	NOUN
bibechana-10397	97	11	0	0	PROPN
bibechana-10397	97	12	.	.	PUNCT
bibechana-10397	97	13	v(x)|	v(x)|	NOUN
bibechana-10397	97	14	≤	≤	ADJ
bibechana-10397	97	15	1	1	NUM
bibechana-10397	97	16	.	.	PUNCT
bibechana-10397	97	17	v(x)|	v(x)|	NOUN
bibechana-10397	97	18	≤	≤	PUNCT
bibechana-10397	98	1	|v(x	|v(x	PROPN
bibechana-10397	98	2	+	+	PROPN
bibechana-10397	98	3	yn	yn	PROPN
bibechana-10397	98	4	)	)	PUNCT
bibechana-10397	98	5	|+	|+	NOUN
bibechana-10397	98	6	1	1	NUM
bibechana-10397	98	7	.	.	PUNCT
bibechana-10397	99	1	it	it	PRON
bibechana-10397	99	2	follows	follow	VERB
bibechana-10397	99	3	that	that	SCONJ
bibechana-10397	99	4	lim	lim	PROPN
bibechana-10397	99	5	v(x	v(x	PROPN
bibechana-10397	99	6	+	+	CCONJ
bibechana-10397	99	7	yk	yk	NOUN
bibechana-10397	99	8	)	)	PUNCT
bibechana-10397	99	9	=	=	SYM
bibechana-10397	100	1	o	o	NOUN
bibechana-10397	100	2	,	,	PUNCT
bibechana-10397	100	3	so	so	ADV
bibechana-10397	100	4	|u(x)|	|u(x)|	PROPN
bibechana-10397	100	5	≤	≤	NOUN
bibechana-10397	100	6	1	1	X
bibechana-10397	100	7	.	.	PUNCT
bibechana-10397	101	1	this	this	PRON
bibechana-10397	101	2	shows	show	VERB
bibechana-10397	101	3	x	x	PUNCT
bibechana-10397	101	4	ϵ	ϵ	X
bibechana-10397	101	5	m	m	NOUN
bibechana-10397	101	6	°	°	NOUN
bibechana-10397	101	7	,	,	PUNCT
bibechana-10397	101	8	so	so	ADV
bibechana-10397	101	9	the	the	DET
bibechana-10397	101	10	semi	semi	ADJ
bibechana-10397	101	11	for	for	ADP
bibechana-10397	101	12	e	e	NOUN
bibechana-10397	101	13	/	/	SYM
bibechana-10397	101	14	m	m	NOUN
bibechana-10397	101	15	°	°	NOUN
bibechana-10397	101	16	.	.	PUNCT
bibechana-10397	102	1	we	we	PRON
bibechana-10397	102	2	fix	fix	VERB
bibechana-10397	102	3	k	k	NOUN
bibechana-10397	102	4	and	and	CCONJ
bibechana-10397	102	5	let	let	VERB
bibechana-10397	102	6	uk	uk	PROPN
bibechana-10397	102	7	be	be	AUX
bibechana-10397	102	8	the	the	DET
bibechana-10397	102	9	unit	unit	NOUN
bibechana-10397	102	10	ball	ball	NOUN
bibechana-10397	102	11	of	of	ADP
bibechana-10397	102	12	ǁ·ǁk	ǁ·ǁk	PROPN
bibechana-10397	102	13	in	in	ADP
bibechana-10397	102	14	e.	e.	PROPN
bibechana-10397	102	15	since	since	SCONJ
bibechana-10397	102	16	e	e	PROPN
bibechana-10397	102	17	satisfies	satisfie	NOUN
bibechana-10397	102	18	we	we	PRON
bibechana-10397	102	19	have	have	VERB
bibechana-10397	102	20	a	a	DET
bibechana-10397	102	21	sequence	sequence	NOUN
bibechana-10397	102	22	(	(	PUNCT
bibechana-10397	102	23	un	un	PROPN
bibechana-10397	102	24	)	)	PUNCT
bibechana-10397	102	25	⊂	⊂	PROPN
bibechana-10397	102	26	e'l	e'l	PROPN
bibechana-10397	102	27	with	with	ADP
bibechana-10397	102	28	ǁunǁ'k	ǁunǁ'k	PROPN
bibechana-10397	102	29	>	>	SYM
bibechana-10397	102	30	1	1	NUM
bibechana-10397	102	31	and	and	CCONJ
bibechana-10397	102	32	ǁunǁ'k+1	ǁunǁ'k+1	VERB
bibechana-10397	102	33	≤	≤	NUM
bibechana-10397	102	34	�	�	PROPN
bibechana-10397	102	35	�	�	PROPN
bibechana-10397	102	36	.	.	PUNCT
bibechana-10397	103	1	this	this	PRON
bibechana-10397	103	2	implies	imply	VERB
bibechana-10397	103	3	that	that	SCONJ
bibechana-10397	103	4	,	,	PUNCT
bibechana-10397	103	5	u	u	PROPN
bibechana-10397	103	6	+	+	X
bibechana-10397	103	7	m	m	NOUN
bibechana-10397	103	8	°	°	NOUN
bibechana-10397	103	9	)	)	PUNCT
bibechana-10397	103	10	°	°	PROPN
bibechana-10397	103	11	.	.	PUNCT
bibechana-10397	104	1	moreover	moreover	ADV
bibechana-10397	104	2	,	,	PUNCT
bibechana-10397	104	3	if	if	SCONJ
bibechana-10397	104	4	x	x	PROPN
bibechana-10397	104	5	ϵ	ϵ	VERB
bibechana-10397	104	6	uk+1,y	uk+1,y	NOUN
bibechana-10397	104	7	ϵ	ϵ	PROPN
bibechana-10397	104	8	m	m	NOUN
bibechana-10397	104	9	°	°	NOUN
bibechana-10397	104	10	,	,	PUNCT
bibechana-10397	104	11	then	then	ADV
bibechana-10397	104	12	as	as	ADP
bibechana-10397	104	13	un	un	PROPN
bibechana-10397	104	14	ϵ	ϵ	PROPN
bibechana-10397	104	15	m	m	PROPN
bibechana-10397	104	16	,	,	PUNCT
bibechana-10397	104	17	we	we	PRON
bibechana-10397	104	18	have	have	VERB
bibechana-10397	104	19	|nun(x+	|nun(x+	PROPN
bibechana-10397	104	20	y	y	NOUN
bibechana-10397	104	21	)	)	PUNCT
bibechana-10397	105	1	|	|	NOUN
bibechana-10397	106	1	=	=	SYM
bibechana-10397	106	2	|nun	|nun	NOUN
bibechana-10397	106	3	(	(	PUNCT
bibechana-10397	106	4	x)|	x)|	PROPN
bibechana-10397	106	5	≤	≤	NUM
bibechana-10397	106	6	1	1	NUM
bibechana-10397	106	7	.	.	PUNCT
bibechana-10397	107	1	(	(	PUNCT
bibechana-10397	107	2	uk+1	uk+1	X
bibechana-10397	107	3	+	+	NUM
bibechana-10397	107	4	m	m	NOUN
bibechana-10397	107	5	°	°	NOUN
bibechana-10397	107	6	)	)	PUNCT
bibechana-10397	107	7	°	°	PROPN
bibechana-10397	107	8	.	.	PUNCT
bibechana-10397	108	1	thus	thus	ADV
bibechana-10397	108	2	we	we	PRON
bibechana-10397	108	3	have	have	AUX
bibechana-10397	108	4	proved	prove	VERB
bibechana-10397	108	5	that	that	SCONJ
bibechana-10397	108	6	un	un	PROPN
bibechana-10397	108	7	ϵ	ϵ	PROPN
bibechana-10397	108	8	�	�	PROPN
bibechana-10397	108	9	�	�	PROPN
bibechana-10397	108	10	(	(	PUNCT
bibechana-10397	108	11	uk+1	uk+1	PROPN
bibechana-10397	108	12	+	+	NUM
bibechana-10397	108	13	m	m	NOUN
bibechana-10397	108	14	°	°	NOUN
bibechana-10397	108	15	)	)	PUNCT
bibechana-10397	108	16	°	°	PROPN
bibechana-10397	108	17	~	~	SYM
bibechana-10397	108	18	(	(	PUNCT
bibechana-10397	108	19	uk+m	uk+m	NOUN
bibechana-10397	108	20	°	°	NUM
bibechana-10397	108	21	)	)	PUNCT
bibechana-10397	108	22	°	°	PROPN
bibechana-10397	108	23	.	.	PUNCT
bibechana-10397	109	1	but	but	CCONJ
bibechana-10397	109	2	,	,	PUNCT
bibechana-10397	109	3	(	(	PUNCT
bibechana-10397	109	4	e	e	X
bibechana-10397	109	5	/	/	SYM
bibechana-10397	109	6	m	m	NOUN
bibechana-10397	109	7	°	°	NOUN
bibechana-10397	109	8	)	)	PUNCT
bibechana-10397	109	9	'	'	PUNCT
bibechana-10397	110	1	=	=	VERB
bibechana-10397	110	2	m	m	PROPN
bibechana-10397	110	3	and	and	CCONJ
bibechana-10397	110	4	the	the	DET
bibechana-10397	110	5	unit	unit	NOUN
bibechana-10397	110	6	ball	ball	NOUN
bibechana-10397	110	7	of	of	ADP
bibechana-10397	110	8	the	the	DET
bibechana-10397	110	9	dual	dual	ADJ
bibechana-10397	110	10	norm	norm	NOUN
bibechana-10397	110	11	of	of	ADP
bibechana-10397	110	12	the	the	DET
bibechana-10397	110	13	norm	norm	NOUN
bibechana-10397	110	14	in	in	ADP
bibechana-10397	110	15	e	e	PROPN
bibechana-10397	110	16	/	/	SYM
bibechana-10397	110	17	m	m	NOUN
bibechana-10397	110	18	°	°	PROPN
bibechana-10397	110	19	induced	induce	VERB
bibechana-10397	110	20	by	by	ADP
bibechana-10397	110	21	||	||	PROPN
bibechana-10397	110	22	·	·	PUNCT
bibechana-10397	110	23	||k	||k	PROPN
bibechana-10397	110	24	is	be	AUX
bibechana-10397	110	25	(	(	PUNCT
bibechana-10397	110	26	uk	uk	PROPN
bibechana-10397	110	27	+	+	PROPN
bibechana-10397	110	28	m	m	NOUN
bibechana-10397	110	29	°	°	NOUN
bibechana-10397	110	30	)	)	PUNCT
bibechana-10397	110	31	°	°	PROPN
bibechana-10397	110	32	.	.	PUNCT
bibechana-10397	111	1	this	this	PRON
bibechana-10397	111	2	proves	prove	VERB
bibechana-10397	111	3	that	that	SCONJ
bibechana-10397	111	4	now	now	ADV
bibechana-10397	111	5	,	,	PUNCT
bibechana-10397	111	6	conversely	conversely	ADV
bibechana-10397	111	7	assume	assume	VERB
bibechana-10397	111	8	that	that	SCONJ
bibechana-10397	111	9	e	e	NOUN
bibechana-10397	111	10	/	/	SYM
bibechana-10397	111	11	f	f	X
bibechana-10397	111	12	be	be	AUX
bibechana-10397	111	13	a	a	DET
bibechana-10397	111	14	quotient	quotient	NOUN
bibechana-10397	111	15	of	of	ADP
bibechana-10397	111	16	e.	e.	PROPN
bibechana-10397	111	17	if	if	SCONJ
bibechana-10397	111	18	(	(	PUNCT
bibechana-10397	111	19	uk	uk	PROPN
bibechana-10397	111	20	)	)	PUNCT
bibechana-10397	111	21	is	be	AUX
bibechana-10397	111	22	a	a	DET
bibechana-10397	111	23	fundamental	fundamental	ADJ
bibechana-10397	111	24	sequence	sequence	NOUN
bibechana-10397	111	25	of	of	ADP
bibechana-10397	111	26	nbds	nbds	NOUN
bibechana-10397	111	27	.	.	PUNCT
bibechana-10397	112	1	of	of	ADP
bibechana-10397	112	2	0	0	NUM
bibechana-10397	113	1	for	for	ADP
bibechana-10397	113	2	e	e	PROPN
bibechana-10397	113	3	then	then	ADV
bibechana-10397	113	4	by	by	ADP
bibechana-10397	113	5	general	general	ADJ
bibechana-10397	113	6	duality	duality	NOUN
bibechana-10397	113	7	,	,	PUNCT
bibechana-10397	113	8	(	(	PUNCT
bibechana-10397	113	9	e	e	NOUN
bibechana-10397	113	10	/	/	SYM
bibechana-10397	113	11	f	f	NOUN
bibechana-10397	113	12	)	)	PUNCT
bibechana-10397	113	13	'	'	PUNCT
bibechana-10397	113	14	can	can	AUX
bibechana-10397	113	15	be	be	AUX
bibechana-10397	113	16	represented	represent	VERB
bibechana-10397	113	17	as	as	ADP
bibechana-10397	113	18	a	a	DET
bibechana-10397	113	19	vector	vector	NOUN
bibechana-10397	113	20	subspace	subspace	NOUN
bibechana-10397	113	21	of	of	ADP
bibechana-10397	113	22	e	e	NOUN
bibechana-10397	113	23	'	'	PUNCT
bibechana-10397	113	24	and	and	CCONJ
bibechana-10397	113	25	a	a	DET
bibechana-10397	113	26	fundamental	fundamental	ADJ
bibechana-10397	113	27	publication	publication	NOUN
bibechana-10397	113	28	:	:	PUNCT
bibechana-10397	113	29	march	march	PROPN
bibechana-10397	113	30	,	,	PUNCT
bibechana-10397	113	31	2014	2014	NUM
bibechana-10397	113	32	)	)	PUNCT
bibechana-10397	113	33	p.163	p.163	NOUN
bibechana-10397	113	34	if	if	SCONJ
bibechana-10397	113	35	e	e	NOUN
bibechana-10397	113	36	is	be	AUX
bibechana-10397	113	37	isomorphic	isomorphic	ADJ
bibechana-10397	113	38	to	to	ADP
bibechana-10397	113	39	a	a	DET
bibechana-10397	113	40	countable	countable	ADJ
bibechana-10397	113	41	product	product	NOUN
bibechana-10397	113	42	of	of	ADP
bibechana-10397	113	43	banach	banach	NOUN
bibechana-10397	113	44	spaces	space	NOUN
bibechana-10397	113	45	then	then	ADV
bibechana-10397	113	46	e	e	PROPN
bibechana-10397	113	47	does	do	AUX
bibechana-10397	113	48	not	not	PART
bibechana-10397	113	49	have	have	VERB
bibechana-10397	113	50	a	a	DET
bibechana-10397	113	51	nuclear	nuclear	ADJ
bibechana-10397	113	52	kothe	kothe	NOUN
bibechana-10397	113	53	if	if	SCONJ
bibechana-10397	113	54	e	e	NOUN
bibechana-10397	113	55	is	be	AUX
bibechana-10397	113	56	a	a	DET
bibechana-10397	113	57	frechet	frechet	NOUN
bibechana-10397	113	58	montel	montel	PROPN
bibechana-10397	113	59	space	space	NOUN
bibechana-10397	114	1	then	then	ADV
bibechana-10397	114	2	e	e	PROPN
bibechana-10397	114	3	is	be	AUX
bibechana-10397	114	4	separable	separable	ADJ
bibechana-10397	114	5	and	and	CCONJ
bibechana-10397	114	6	reflexive	reflexive	ADJ
bibechana-10397	114	7	.	.	PUNCT
bibechana-10397	115	1	we	we	PRON
bibechana-10397	115	2	will	will	AUX
bibechana-10397	115	3	prove	prove	VERB
bibechana-10397	115	4	that	that	SCONJ
bibechana-10397	115	5	e	e	NOUN
bibechana-10397	115	6	is	be	AUX
bibechana-10397	115	7	not	not	PART
bibechana-10397	115	8	a	a	DET
bibechana-10397	115	9	quojection	quojection	NOUN
bibechana-10397	115	10	.	.	PUNCT
bibechana-10397	116	1	maps	map	VERB
bibechana-10397	116	2	the	the	DET
bibechana-10397	116	3	unit	unit	NOUN
bibechana-10397	116	4	ball	ball	NOUN
bibechana-10397	116	5	we	we	PRON
bibechana-10397	116	6	may	may	AUX
bibechana-10397	116	7	assume	assume	VERB
bibechana-10397	116	8	that	that	SCONJ
bibechana-10397	116	9	el	el	PROPN
bibechana-10397	116	10	is	be	AUX
bibechana-10397	116	11	infinite	infinite	ADJ
bibechana-10397	116	12	is	be	AUX
bibechana-10397	116	13	in	in	ADP
bibechana-10397	116	14	the	the	DET
bibechana-10397	116	15	unit	unit	NOUN
bibechana-10397	116	16	ball	ball	NOUN
bibechana-10397	116	17	of	of	ADP
bibechana-10397	116	18	is	be	AUX
bibechana-10397	116	19	the	the	DET
bibechana-10397	116	20	unit	unit	NOUN
bibechana-10397	116	21	ball	ball	NOUN
bibechana-10397	116	22	so	so	SCONJ
bibechana-10397	116	23	it	it	PRON
bibechana-10397	116	24	is	be	AUX
bibechana-10397	116	25	not	not	PART
bibechana-10397	116	26	iff	iff	VERB
bibechana-10397	116	27	it	it	PRON
bibechana-10397	116	28	has	have	VERB
bibechana-10397	116	29	a	a	DET
bibechana-10397	116	30	quotient	quotient	NOUN
bibechana-10397	116	31	which	which	PRON
bibechana-10397	116	32	admits	admit	VERB
bibechana-10397	116	33	continuous	continuous	ADJ
bibechana-10397	116	34	norm	norm	NOUN
bibechana-10397	116	35	and	and	CCONJ
bibechana-10397	116	36	satisfies	satisfy	VERB
bibechana-10397	116	37	1for	1for	NUM
bibechana-10397	116	38	this	this	DET
bibechana-10397	116	39	condition	condition	NOUN
bibechana-10397	116	40	.	.	PUNCT
bibechana-10397	117	1	�	�	PROPN
bibechana-10397	117	2	the	the	DET
bibechana-10397	117	3	weak	weak	ADJ
bibechana-10397	117	4	topology	topology	NOUN
bibechana-10397	117	5	from	from	ADP
bibechana-10397	117	6	e.	e.	PROPN
bibechana-10397	118	1	now	now	ADV
bibechana-10397	118	2	we	we	PRON
bibechana-10397	118	3	e	e	VERB
bibechana-10397	118	4	and	and	CCONJ
bibechana-10397	118	5	assume	assume	VERB
bibechana-10397	118	6	that	that	SCONJ
bibechana-10397	118	7	the	the	DET
bibechana-10397	118	8	seminorm	seminorm	NOUN
bibechana-10397	118	9	in	in	ADP
bibechana-10397	118	10	m	m	NOUN
bibechana-10397	118	11	°	°	NOUN
bibechana-10397	118	12	,	,	PUNCT
bibechana-10397	118	13	so	so	SCONJ
bibechana-10397	118	14	the	the	DET
bibechana-10397	118	15	semi	semi	ADJ
bibechana-10397	118	16	-	-	ADJ
bibechana-10397	118	17	norm	norm	ADJ
bibechana-10397	118	18	induced	induce	VERB
bibechana-10397	118	19	in	in	ADP
bibechana-10397	118	20	e.	e.	PROPN
bibechana-10397	118	21	since	since	SCONJ
bibechana-10397	118	22	e	e	PROPN
bibechana-10397	118	23	satisfies	satisfie	NOUN
bibechana-10397	118	24	.	.	PUNCT
bibechana-10397	119	1	this	this	PRON
bibechana-10397	119	2	implies	imply	VERB
bibechana-10397	119	3	that	that	SCONJ
bibechana-10397	119	4	,	,	PUNCT
bibechana-10397	119	5	un	un	PROPN
bibechana-10397	119	6	ϵ	ϵ	PROPN
bibechana-10397	119	7	�	�	PROPN
bibechana-10397	119	8	�	�	PROPN
bibechana-10397	119	9	u	u	PROPN
bibechana-10397	119	10	�	�	PROPN
bibechana-10397	119	11	�	�	PROPN
bibechana-10397	119	12	�	�	PROPN
bibechana-10397	119	13	m	m	PROPN
bibechana-10397	119	14	,	,	PUNCT
bibechana-10397	119	15	we	we	PRON
bibechana-10397	119	16	have	have	AUX
bibechana-10397	119	17	(	(	PUNCT
bibechana-10397	119	18	uk+1	uk+1	PROPN
bibechana-10397	119	19	+	+	NUM
bibechana-10397	119	20	m	m	NOUN
bibechana-10397	119	21	°	°	NOUN
bibechana-10397	119	22	)	)	PUNCT
bibechana-10397	119	23	°	°	PROPN
bibechana-10397	119	24	~	~	SYM
bibechana-10397	119	25	(	(	PUNCT
bibechana-10397	119	26	uk+m	uk+m	NOUN
bibechana-10397	119	27	°	°	NUM
bibechana-10397	119	28	)	)	PUNCT
bibechana-10397	119	29	°	°	PROPN
bibechana-10397	119	30	.	.	PUNCT
bibechana-10397	120	1	but	but	CCONJ
bibechana-10397	120	2	,	,	PUNCT
bibechana-10397	120	3	(	(	PUNCT
bibechana-10397	120	4	e	e	X
bibechana-10397	120	5	/	/	SYM
bibechana-10397	120	6	m	m	NOUN
bibechana-10397	120	7	°	°	NOUN
bibechana-10397	120	8	)	)	PUNCT
bibechana-10397	120	9	'	'	PUNCT
bibechana-10397	121	1	=	=	VERB
bibechana-10397	121	2	m	m	PROPN
bibechana-10397	121	3	and	and	CCONJ
bibechana-10397	121	4	the	the	DET
bibechana-10397	121	5	unit	unit	NOUN
bibechana-10397	121	6	ball	ball	NOUN
bibechana-10397	121	7	of	of	ADP
bibechana-10397	121	8	the	the	DET
bibechana-10397	121	9	dual	dual	ADJ
bibechana-10397	121	10	norm	norm	NOUN
bibechana-10397	121	11	of	of	ADP
bibechana-10397	121	12	the	the	DET
bibechana-10397	121	13	norm	norm	NOUN
bibechana-10397	121	14	in	in	ADP
bibechana-10397	121	15	e	e	PROPN
bibechana-10397	121	16	/	/	SYM
bibechana-10397	121	17	m	m	NOUN
bibechana-10397	121	18	°	°	PROPN
bibechana-10397	121	19	induced	induce	VERB
bibechana-10397	121	20	by	by	ADP
bibechana-10397	121	21	||	||	PROPN
bibechana-10397	121	22	·	·	PUNCT
bibechana-10397	121	23	||k	||k	PROPN
bibechana-10397	121	24	is	be	AUX
bibechana-10397	121	25	(	(	PUNCT
bibechana-10397	121	26	uk	uk	PROPN
bibechana-10397	121	27	+	+	PROPN
bibechana-10397	121	28	m	m	NOUN
bibechana-10397	121	29	°	°	NOUN
bibechana-10397	121	30	)	)	PUNCT
bibechana-10397	121	31	°	°	PROPN
bibechana-10397	121	32	.	.	PUNCT
bibechana-10397	122	1	this	this	PRON
bibechana-10397	122	2	proves	prove	VERB
bibechana-10397	122	3	that	that	SCONJ
bibechana-10397	122	4	if	if	SCONJ
bibechana-10397	122	5	(	(	PUNCT
bibechana-10397	122	6	uk	uk	NOUN
bibechana-10397	122	7	)	)	PUNCT
bibechana-10397	122	8	is	be	AUX
bibechana-10397	122	9	a	a	DET
bibechana-10397	122	10	fundamental	fundamental	ADJ
bibechana-10397	122	11	sequence	sequence	NOUN
bibechana-10397	122	12	of	of	ADP
bibechana-10397	122	13	nbds	nbds	NOUN
bibechana-10397	122	14	.	.	PUNCT
bibechana-10397	123	1	of	of	ADP
bibechana-10397	123	2	0	0	NUM
bibechana-10397	124	1	for	for	ADP
bibechana-10397	124	2	e	e	PROPN
bibechana-10397	124	3	then	then	ADV
bibechana-10397	124	4	by	by	ADP
bibechana-10397	124	5	general	general	ADJ
bibechana-10397	124	6	duality	duality	NOUN
bibechana-10397	124	7	,	,	PUNCT
bibechana-10397	124	8	(	(	PUNCT
bibechana-10397	124	9	e	e	NOUN
bibechana-10397	124	10	/	/	SYM
bibechana-10397	124	11	f	f	NOUN
bibechana-10397	124	12	)	)	PUNCT
bibechana-10397	124	13	'	'	PUNCT
bibechana-10397	124	14	can	can	AUX
bibechana-10397	124	15	be	be	AUX
bibechana-10397	124	16	represented	represent	VERB
bibechana-10397	124	17	as	as	ADP
bibechana-10397	124	18	a	a	DET
bibechana-10397	124	19	vector	vector	NOUN
bibechana-10397	124	20	subspace	subspace	NOUN
bibechana-10397	124	21	of	of	ADP
bibechana-10397	124	22	e	e	NOUN
bibechana-10397	124	23	'	'	PUNCT
bibechana-10397	124	24	and	and	CCONJ
bibechana-10397	124	25	a	a	DET
bibechana-10397	124	26	fundamental	fundamental	ADJ
bibechana-10397	124	27	s.	s.	PROPN
bibechana-10397	124	28	n.	n.	PROPN
bibechana-10397	124	29	sah	sah	PROPN
bibechana-10397	124	30	/	/	SYM
bibechana-10397	124	31	bibechana	bibechana	PROPN
bibechana-10397	124	32	11(1	11(1	NUM
bibechana-10397	124	33	)	)	PUNCT
bibechana-10397	124	34	(	(	PUNCT
bibechana-10397	124	35	2014	2014	NUM
bibechana-10397	124	36	)	)	PUNCT
bibechana-10397	124	37	1	1	NUM
bibechana-10397	124	38	sequence	sequence	NOUN
bibechana-10397	124	39	of	of	ADP
bibechana-10397	124	40	equicontinuous	equicontinuous	ADJ
bibechana-10397	124	41	sets	set	NOUN
bibechana-10397	124	42	for	for	ADP
bibechana-10397	124	43	(	(	PUNCT
bibechana-10397	124	44	e	e	NOUN
bibechana-10397	124	45	/	/	SYM
bibechana-10397	124	46	f	f	NOUN
bibechana-10397	124	47	)	)	PUNCT
bibechana-10397	124	48	'	'	PUNCT
bibechana-10397	124	49	is	be	AUX
bibechana-10397	124	50	given	give	VERB
bibechana-10397	124	51	by	by	ADP
bibechana-10397	124	52	(	(	PUNCT
bibechana-10397	124	53	with	with	ADP
bibechana-10397	124	54	l	l	NOUN
bibechana-10397	124	55	=	=	SYM
bibechana-10397	124	56	1	1	NUM
bibechana-10397	124	57	and	and	CCONJ
bibechana-10397	124	58	j	j	PROPN
bibechana-10397	124	59	=	=	SYM
bibechana-10397	124	60	k+1	k+1	PROPN
bibechana-10397	124	61	)	)	PUNCT
bibechana-10397	124	62	then	then	ADV
bibechana-10397	124	63	∃	∃	PROPN
bibechana-10397	124	64	(	(	PUNCT
bibechana-10397	124	65	un	un	PROPN
bibechana-10397	124	66	)	)	PUNCT
bibechana-10397	124	67	u	u	NOUN
bibechana-10397	124	68	�	�	PROPN
bibechana-10397	124	69	�	�	PROPN
bibechana-10397	124	70	�	�	PROPN
bibechana-10397	124	71	�	�	PROPN
bibechana-10397	124	72	∽∩	∽∩	PROPN
bibechana-10397	124	73	f	f	PROPN
bibechana-10397	124	74	°	°	NUM
bibechana-10397	124	75	)	)	PUNCT
bibechana-10397	124	76	(	(	PUNCT
bibechana-10397	124	77	u	u	NOUN
bibechana-10397	124	78	�	�	PROPN
bibechana-10397	124	79	�	�	PROPN
bibechana-10397	124	80	∩f	∩f	NOUN
bibechana-10397	124	81	°	°	NUM
bibechana-10397	124	82	)	)	PUNCT
bibechana-10397	124	83	.	.	PUNCT
bibechana-10397	125	1	it	it	PRON
bibechana-10397	125	2	follows	follow	VERB
bibechana-10397	125	3	that	that	SCONJ
bibechana-10397	125	4	un	un	PROPN
bibechana-10397	125	5	>	>	X
bibechana-10397	126	1	1	1	X
bibechana-10397	126	2	.	.	PUNCT
bibechana-10397	126	3	therefore	therefore	ADV
bibechana-10397	126	4	,	,	PUNCT
bibechana-10397	126	5	e	e	NOUN
bibechana-10397	126	6	satisfies	satisfy	VERB
bibechana-10397	126	7	condition	condition	NOUN
bibechana-10397	126	8	7	7	NUM
bibechana-10397	126	9	.	.	PUNCT
bibechana-10397	126	10	conclusion	conclusion	NOUN
bibechana-10397	126	11	a	a	DET
bibechana-10397	126	12	frechet	frechet	NOUN
bibechana-10397	126	13	space	space	NOUN
bibechana-10397	126	14	which	which	PRON
bibechana-10397	126	15	admits	admit	VERB
bibechana-10397	126	16	continuous	continuous	ADJ
bibechana-10397	126	17	norm	norm	NOUN
bibechana-10397	126	18	has	have	VERB
bibechana-10397	126	19	a	a	DET
bibechana-10397	126	20	nuclear	nuclear	ADJ
bibechana-10397	126	21	kothe	kothe	NOUN
bibechana-10397	126	22	subspace	subspace	NOUN
bibechana-10397	126	23	if	if	SCONJ
bibechana-10397	126	24	and	and	CCONJ
bibechana-10397	126	25	only	only	ADV
bibechana-10397	126	26	if	if	SCONJ
bibechana-10397	126	27	it	it	PRON
bibechana-10397	126	28	is	be	AUX
bibechana-10397	126	29	not	not	PART
bibechana-10397	126	30	banach	banach	ADJ
bibechana-10397	126	31	.	.	PUNCT
bibechana-10397	127	1	thus	thus	ADV
bibechana-10397	127	2	it	it	PRON
bibechana-10397	127	3	follows	follow	VERB
bibechana-10397	127	4	that	that	SCONJ
bibechana-10397	127	5	,	,	PUNCT
bibechana-10397	127	6	in	in	ADP
bibechana-10397	127	7	general	general	ADJ
bibechana-10397	127	8	,	,	PUNCT
bibechana-10397	127	9	a	a	DET
bibechana-10397	127	10	frechet	frechet	NOUN
bibechana-10397	127	11	space	space	NOUN
bibechana-10397	127	12	has	have	VERB
bibechana-10397	127	13	a	a	DET
bibechana-10397	127	14	nuclear	nuclear	ADJ
bibechana-10397	127	15	kothe	kothe	NOUN
bibechana-10397	127	16	subspace	subspace	PROPN
bibechana-10397	127	17	iff	iff	PROPN
bibechana-10397	127	18	it	it	PRON
bibechana-10397	127	19	has	have	VERB
bibechana-10397	127	20	a	a	DET
bibechana-10397	127	21	non	non	ADJ
bibechana-10397	127	22	banach	banach	NOUN
bibechana-10397	127	23	subspace	subspace	NOUN
bibechana-10397	127	24	which	which	PRON
bibechana-10397	127	25	admits	admit	VERB
bibechana-10397	127	26	continuous	continuous	ADJ
bibechana-10397	127	27	norm	norm	NOUN
bibechana-10397	127	28	.	.	PUNCT
bibechana-10397	128	1	references	reference	NOUN
bibechana-10397	128	2	[	[	X
bibechana-10397	128	3	1	1	NUM
bibechana-10397	128	4	]	]	PUNCT
bibechana-10397	128	5	c.	c.	PROPN
bibechana-10397	128	6	bessaga	bessaga	PROPN
bibechana-10397	128	7	,	,	PUNCT
bibechana-10397	128	8	a.	a.	NOUN
bibechana-10397	128	9	pelczynski	pelczynski	NOUN
bibechana-10397	128	10	,	,	PUNCT
bibechana-10397	128	11	bull	bull	NOUN
bibechana-10397	128	12	.	.	PUNCT
bibechana-10397	129	1	acad	acad	PROPN
bibechana-10397	129	2	.	.	PUNCT
bibechana-10397	130	1	polon	polon	NOUN
bibechana-10397	130	2	.	.	PUNCT
bibechana-10397	131	1	sei	sei	ADJ
bibechana-10397	131	2	.	.	PUNCT
bibechana-10397	132	1	cl	cl	NOUN
bibechana-10397	132	2	.	.	PUNCT
bibechana-10397	133	1	ill	ill	ADJ
bibechana-10397	133	2	[	[	X
bibechana-10397	133	3	2	2	NUM
bibechana-10397	133	4	]	]	PUNCT
bibechana-10397	133	5	c.	c.	PROPN
bibechana-10397	133	6	bessaga	bessaga	PROPN
bibechana-10397	133	7	,	,	PUNCT
bibechana-10397	133	8	a.	a.	NOUN
bibechana-10397	133	9	pelczynski	pelczynski	NOUN
bibechana-10397	133	10	,	,	PUNCT
bibechana-10397	133	11	s.	s.	PROPN
bibechana-10397	133	12	rolewicz	rolewicz	PROPN
bibechana-10397	133	13	,	,	PUNCT
bibechana-10397	133	14	bull	bull	NOUN
bibechana-10397	133	15	.	.	PUNCT
bibechana-10397	134	1	acad	acad	PROPN
bibechana-10397	134	2	.	.	PUNCT
bibechana-10397	135	1	polon	polon	NOUN
bibechana-10397	135	2	.	.	PUNCT
bibechana-10397	136	1	sei	sei	ADJ
bibechana-10397	136	2	.	.	PUNCT
bibechana-10397	137	1	[	[	X
bibechana-10397	137	2	3	3	NUM
bibechana-10397	137	3	]	]	X
bibechana-10397	137	4	g.l	g.l	PROPN
bibechana-10397	137	5	.	.	PROPN
bibechana-10397	137	6	litvinov	litvinov	PROPN
bibechana-10397	137	7	,	,	PUNCT
bibechana-10397	137	8	nuclear	nuclear	ADJ
bibechana-10397	137	9	space	space	NOUN
bibechana-10397	137	10	,	,	PUNCT
bibechana-10397	137	11	springer	springer	NOUN
bibechana-10397	137	12	[	[	X
bibechana-10397	137	13	4	4	NUM
bibechana-10397	137	14	]	]	X
bibechana-10397	137	15	c.	c.	NOUN
bibechana-10397	137	16	bessaga	bessaga	NOUN
bibechana-10397	137	17	and	and	CCONJ
bibechana-10397	137	18	ed	ed	PROPN
bibechana-10397	137	19	dubinsky	dubinsky	PROPN
bibechana-10397	137	20	,	,	PUNCT
bibechana-10397	137	21	arch	arch	ADJ
bibechana-10397	137	22	math	math	NOUN
bibechana-10397	137	23	.	.	PUNCT
bibechana-10397	138	1	[	[	X
bibechana-10397	138	2	5	5	X
bibechana-10397	138	3	]	]	PUNCT
bibechana-10397	138	4	g.	g.	NOUN
bibechana-10397	138	5	kothe	kothe	PROPN
bibechana-10397	138	6	,	,	PUNCT
bibechana-10397	138	7	topological	topological	ADJ
bibechana-10397	138	8	vector	vector	NOUN
bibechana-10397	138	9	space	space	NOUN
bibechana-10397	138	10	i	i	PRON
bibechana-10397	138	11	,	,	PUNCT
bibechana-10397	138	12	spiringer	spiringer	NOUN
bibechana-10397	139	1	[	[	X
bibechana-10397	139	2	6	6	NUM
bibechana-10397	139	3	]	]	X
bibechana-10397	139	4	d.	d.	PROPN
bibechana-10397	139	5	vogat	vogat	PROPN
bibechana-10397	139	6	,	,	PUNCT
bibechana-10397	139	7	lectures	lecture	NOUN
bibechana-10397	139	8	on	on	ADP
bibechana-10397	139	9	frechet	frechet	PROPN
bibechana-10397	139	10	spaces	space	NOUN
bibechana-10397	139	11	,	,	PUNCT
bibechana-10397	139	12	bergische	bergische	PROPN
bibechana-10397	139	13	universitat	universitat	PROPN
bibechana-10397	139	14	wuppertal	wuppertal	NOUN
bibechana-10397	139	15	,	,	PUNCT
bibechana-10397	139	16	sommer	sommer	NOUN
bibechana-10397	139	17	semester	semester	NOUN
bibechana-10397	140	1	[	[	X
bibechana-10397	140	2	7	7	NUM
bibechana-10397	140	3	]	]	X
bibechana-10397	140	4	a.e.taylor	a.e.taylor	NOUN
bibechana-10397	140	5	,	,	PUNCT
bibechana-10397	140	6	introduction	introduction	NOUN
bibechana-10397	140	7	to	to	ADP
bibechana-10397	140	8	functional	functional	ADJ
bibechana-10397	140	9	analysis	analysis	NOUN
bibechana-10397	140	10	,	,	PUNCT
bibechana-10397	140	11	john	john	PROPN
bibechana-10397	140	12	willey	willey	PROPN
bibechana-10397	140	13	and	and	CCONJ
bibechana-10397	140	14	sons	son	NOUN
bibechana-10397	140	15	,	,	PUNCT
bibechana-10397	140	16	inc	inc	PROPN
bibechana-10397	140	17	.	.	PROPN
bibechana-10397	140	18	,	,	PUNCT
bibechana-10397	140	19	london,1961	london,1961	ADJ
bibechana-10397	140	20	.	.	PUNCT
bibechana-10397	141	1	[	[	X
bibechana-10397	141	2	8	8	NUM
bibechana-10397	141	3	]	]	PUNCT
bibechana-10397	141	4	a.	a.	NOUN
bibechana-10397	141	5	pietsch	pietsch	PROPN
bibechana-10397	141	6	,	,	PUNCT
bibechana-10397	141	7	nuclear	nuclear	ADJ
bibechana-10397	141	8	locally	locally	ADV
bibechana-10397	141	9	convex	convex	ADJ
bibechana-10397	141	10	space	space	NOUN
bibechana-10397	141	11	,	,	PUNCT
bibechana-10397	141	12	springer	springer	NOUN
bibechana-10397	141	13	[	[	X
bibechana-10397	141	14	9	9	NUM
bibechana-10397	141	15	]	]	X
bibechana-10397	141	16	a.p	a.p	PROPN
bibechana-10397	141	17	.	.	PROPN
bibechana-10397	141	18	robertson	robertson	PROPN
bibechana-10397	141	19	,	,	PUNCT
bibechana-10397	141	20	w.	w.	PROPN
bibechana-10397	141	21	robertson	robertson	PROPN
bibechana-10397	141	22	,	,	PUNCT
bibechana-10397	141	23	topological	topological	ADJ
bibechana-10397	141	24	vector	vector	NOUN
bibechana-10397	141	25	spaces	space	NOUN
bibechana-10397	141	26	,	,	PUNCT
bibechana-10397	141	27	cambridge	cambridge	PROPN
bibechana-10397	141	28	university	university	PROPN
bibechana-10397	141	29	press	press	NOUN
bibechana-10397	141	30	,	,	PUNCT
bibechana-10397	141	31	1964	1964	NUM
bibechana-10397	141	32	.	.	PUNCT
bibechana-10397	142	1	[	[	X
bibechana-10397	142	2	10	10	NUM
bibechana-10397	142	3	]	]	X
bibechana-10397	142	4	ed	ed	PROPN
bibechana-10397	142	5	dubinsky	dubinsky	PROPN
bibechana-10397	142	6	,	,	PUNCT
bibechana-10397	142	7	springer	springer	NOUN
bibechana-10397	142	8	-	-	PUNCT
bibechana-10397	142	9	verlag	verlag	PROPN
bibechana-10397	142	10	,	,	PUNCT
bibechana-10397	142	11	berlin	berlin	PROPN
bibechana-10397	142	12	and	and	CCONJ
bibechana-10397	142	13	new	new	PROPN
bibechana-10397	142	14	york	york	PROPN
bibechana-10397	143	1	[	[	X
bibechana-10397	143	2	11	11	NUM
bibechana-10397	143	3	]	]	X
bibechana-10397	143	4	v.b	v.b	PROPN
bibechana-10397	143	5	.	.	PROPN
bibechana-10397	143	6	moscatelli	moscatelli	PROPN
bibechana-10397	143	7	,	,	PUNCT
bibechana-10397	143	8	bull	bull	PROPN
bibechana-10397	143	9	.	.	PUNCT
bibechana-10397	144	1	london	london	PROPN
bibechana-10397	144	2	math	math	PROPN
bibechana-10397	144	3	.	.	PUNCT
bibechana-10397	145	1	soc	soc	PROPN
bibechana-10397	145	2	.	.	PUNCT
bibechana-10397	146	1	[	[	X
bibechana-10397	146	2	12	12	NUM
bibechana-10397	146	3	]	]	X
bibechana-10397	146	4	l.	l.	PROPN
bibechana-10397	146	5	holmstrom	holmstrom	PROPN
bibechana-10397	146	6	,	,	PUNCT
bibechana-10397	146	7	journal	journal	NOUN
bibechana-10397	146	8	of	of	ADP
bibechana-10397	146	9	functional	functional	ADJ
bibechana-10397	146	10	analysis	analysis	NOUN
bibechana-10397	146	11	[	[	X
bibechana-10397	146	12	13	13	NUM
bibechana-10397	146	13	]	]	SYM
bibechana-10397	146	14	ed	ed	NOUN
bibechana-10397	146	15	.	.	PUNCT
bibechana-10397	146	16	dubinsky	dubinsky	PROPN
bibechana-10397	146	17	,	,	PUNCT
bibechana-10397	146	18	w.	w.	PROPN
bibechana-10397	146	19	robinson	robinson	PROPN
bibechana-10397	146	20	,	,	PUNCT
bibechana-10397	146	21	studia	studia	PROPN
bibechana-10397	146	22	math	math	NOUN
bibechana-10397	147	1	[	[	X
bibechana-10397	147	2	14	14	NUM
bibechana-10397	147	3	]	]	X
bibechana-10397	147	4	w.	w.	PROPN
bibechana-10397	147	5	sliwa	sliwa	PROPN
bibechana-10397	147	6	,	,	PUNCT
bibechana-10397	147	7	trans	trans	PROPN
bibechana-10397	147	8	.	.	PROPN
bibechana-10397	147	9	amer	amer	PROPN
bibechana-10397	147	10	.	.	PUNCT
bibechana-10397	147	11	math	math	PROPN
bibechana-10397	147	12	.	.	PUNCT
bibechana-10397	148	1	soc	soc	PROPN
bibechana-10397	148	2	.	.	PUNCT
bibechana-10397	149	1	[	[	X
bibechana-10397	149	2	15	15	NUM
bibechana-10397	149	3	]	]	X
bibechana-10397	149	4	w.	w.	PROPN
bibechana-10397	149	5	sliwa	sliwa	PROPN
bibechana-10397	149	6	,	,	PUNCT
bibechana-10397	149	7	bull	bull	NOUN
bibechana-10397	149	8	.	.	PUNCT
bibechana-10397	150	1	belg	belg	PROPN
bibechana-10397	150	2	.	.	PUNCT
bibechana-10397	151	1	math	math	NOUN
bibechana-10397	151	2	.	.	PUNCT
bibechana-10397	152	1	soc	soc	PROPN
bibechana-10397	152	2	.	.	PUNCT
bibechana-10397	153	1	simon	simon	PROPN
bibechana-10397	153	2	stevin	stevin	PROPN
bibechana-10397	153	3	/	/	SYM
bibechana-10397	153	4	bibechana	bibechana	PROPN
bibechana-10397	153	5	11(1	11(1	NUM
bibechana-10397	153	6	)	)	PUNCT
bibechana-10397	153	7	(	(	PUNCT
bibechana-10397	153	8	2014	2014	NUM
bibechana-10397	153	9	)	)	PUNCT
bibechana-10397	153	10	161	161	NUM
bibechana-10397	153	11	-	-	SYM
bibechana-10397	153	12	164	164	NUM
bibechana-10397	153	13	:	:	PUNCT
bibechana-10397	153	14	(	(	PUNCT
bibechana-10397	153	15	online	online	ADJ
bibechana-10397	153	16	publication	publication	NOUN
bibechana-10397	153	17	:	:	PUNCT
bibechana-10397	153	18	march	march	PROPN
bibechana-10397	153	19	,	,	PUNCT
bibechana-10397	153	20	2014	2014	NUM
bibechana-10397	153	21	)	)	PUNCT
bibechana-10397	153	22	p.164	p.164	NOUN
bibechana-10397	153	23	equicontinuous	equicontinuous	ADJ
bibechana-10397	153	24	sets	set	NOUN
bibechana-10397	153	25	for	for	ADP
bibechana-10397	153	26	(	(	PUNCT
bibechana-10397	153	27	e	e	NOUN
bibechana-10397	153	28	/	/	SYM
bibechana-10397	153	29	f	f	NOUN
bibechana-10397	153	30	)	)	PUNCT
bibechana-10397	153	31	'	'	PUNCT
bibechana-10397	153	32	is	be	AUX
bibechana-10397	153	33	given	give	VERB
bibechana-10397	153	34	by	by	ADP
bibechana-10397	153	35	(	(	PUNCT
bibechana-10397	153	36	u	u	PROPN
bibechana-10397	153	37	�	�	PROPN
bibechana-10397	153	38	�	�	PROPN
bibechana-10397	153	39	∩+-f	∩+-f	PROPN
bibechana-10397	153	40	°	°	NOUN
bibechana-10397	153	41	)	)	PUNCT
bibechana-10397	153	42	k.	k.	NOUN
bibechana-10397	154	1	so	so	ADV
bibechana-10397	154	2	if	if	SCONJ
bibechana-10397	154	3	e	e	PROPN
bibechana-10397	154	4	/	/	SYM
bibechana-10397	154	5	f	f	PROPN
bibechana-10397	154	6	satisfies	satisfie	NOUN
bibechana-10397	154	7	condition	condition	NOUN
bibechana-10397	154	8	)	)	PUNCT
bibechana-10397	155	1	⊂	⊂	PROPN
bibechana-10397	156	1	f	f	PROPN
bibechana-10397	156	2	°	°	PRON
bibechana-10397	156	3	and	and	CCONJ
bibechana-10397	156	4	a	a	DET
bibechana-10397	156	5	sequence	sequence	NOUN
bibechana-10397	156	6	of	of	ADP
bibechana-10397	156	7	constants	constant	NOUN
bibechana-10397	156	8	(	(	PUNCT
bibechana-10397	156	9	cn	cn	PROPN
bibechana-10397	156	10	)	)	PUNCT
bibechana-10397	156	11	with	with	ADP
bibechana-10397	156	12	un	un	PROPN
bibechana-10397	156	13	ϵ	ϵ	PROPN
bibechana-10397	156	14	(	(	PUNCT
bibechana-10397	156	15	c	c	NOUN
bibechana-10397	156	16	f	f	PROPN
bibechana-10397	156	17	°	°	NUM
bibechana-10397	156	18	)	)	PUNCT
bibechana-10397	156	19	.	.	PUNCT
bibechana-10397	157	1	it	it	PRON
bibechana-10397	157	2	follows	follow	VERB
bibechana-10397	157	3	that	that	SCONJ
bibechana-10397	157	4	unϵ	unϵ	PROPN
bibechana-10397	157	5	e'l	e'l	PROPN
bibechana-10397	157	6	,	,	PUNCT
bibechana-10397	157	7	||un||'k+1	||un||'k+1	NOUN
bibechana-10397	157	8	≤	≤	NOUN
bibechana-10397	157	9	but	but	CCONJ
bibechana-10397	157	10	since	since	SCONJ
bibechana-10397	157	11	un	un	PROPN
bibechana-10397	157	12	ϵ	ϵ	PROPN
bibechana-10397	157	13	f	f	PROPN
bibechana-10397	157	14	°	°	PROPN
bibechana-10397	157	15	then	then	ADV
bibechana-10397	157	16	un	un	PROPN
bibechana-10397	157	17	>	>	X
bibechana-10397	157	18	1	1	X
bibechana-10397	157	19	.	.	PUNCT
bibechana-10397	158	1	therefore	therefore	ADV
bibechana-10397	158	2	,	,	PUNCT
bibechana-10397	158	3	e	e	NOUN
bibechana-10397	158	4	satisfies	satisfy	VERB
bibechana-10397	158	5	condition	condition	NOUN
bibechana-10397	158	6	⍟	⍟	PROPN
bibechana-10397	158	7	.	.	PUNCT
bibechana-10397	159	1	a	a	DET
bibechana-10397	159	2	frechet	frechet	PROPN
bibechana-10397	159	3	space	space	NOUN
bibechana-10397	159	4	which	which	PRON
bibechana-10397	159	5	admits	admit	VERB
bibechana-10397	159	6	continuous	continuous	ADJ
bibechana-10397	159	7	norm	norm	NOUN
bibechana-10397	159	8	has	have	VERB
bibechana-10397	159	9	a	a	DET
bibechana-10397	159	10	nuclear	nuclear	ADJ
bibechana-10397	159	11	kothe	kothe	NOUN
bibechana-10397	159	12	subspace	subspace	NOUN
bibechana-10397	159	13	if	if	SCONJ
bibechana-10397	160	1	and	and	CCONJ
bibechana-10397	160	2	only	only	ADV
bibechana-10397	160	3	if	if	SCONJ
bibechana-10397	160	4	it	it	PRON
bibechana-10397	160	5	is	be	AUX
bibechana-10397	160	6	not	not	PART
bibechana-10397	160	7	.	.	PUNCT
bibechana-10397	161	1	thus	thus	ADV
bibechana-10397	161	2	it	it	PRON
bibechana-10397	161	3	follows	follow	VERB
bibechana-10397	161	4	that	that	SCONJ
bibechana-10397	161	5	,	,	PUNCT
bibechana-10397	161	6	in	in	ADP
bibechana-10397	161	7	general	general	ADJ
bibechana-10397	161	8	,	,	PUNCT
bibechana-10397	161	9	a	a	DET
bibechana-10397	161	10	frechet	frechet	NOUN
bibechana-10397	161	11	space	space	NOUN
bibechana-10397	161	12	has	have	VERB
bibechana-10397	161	13	a	a	DET
bibechana-10397	161	14	nuclear	nuclear	ADJ
bibechana-10397	161	15	kothe	kothe	NOUN
bibechana-10397	161	16	subspace	subspace	PROPN
bibechana-10397	161	17	iff	iff	PROPN
bibechana-10397	161	18	it	it	PRON
bibechana-10397	161	19	has	have	VERB
bibechana-10397	161	20	a	a	DET
bibechana-10397	161	21	non	non	ADJ
bibechana-10397	161	22	banach	banach	NOUN
bibechana-10397	161	23	subspace	subspace	NOUN
bibechana-10397	161	24	which	which	PRON
bibechana-10397	161	25	admits	admit	VERB
bibechana-10397	161	26	continuous	continuous	ADJ
bibechana-10397	161	27	norm	norm	NOUN
bibechana-10397	161	28	.	.	PUNCT
bibechana-10397	162	1	[	[	X
bibechana-10397	162	2	1	1	X
bibechana-10397	162	3	]	]	X
bibechana-10397	162	4	c.	c.	PROPN
bibechana-10397	162	5	bessaga	bessaga	PROPN
bibechana-10397	162	6	,	,	PUNCT
bibechana-10397	162	7	a.	a.	NOUN
bibechana-10397	162	8	pelczynski	pelczynski	NOUN
bibechana-10397	162	9	,	,	PUNCT
bibechana-10397	162	10	bull	bull	NOUN
bibechana-10397	162	11	.	.	PUNCT
bibechana-10397	163	1	acad	acad	PROPN
bibechana-10397	163	2	.	.	PUNCT
bibechana-10397	164	1	polon	polon	NOUN
bibechana-10397	164	2	.	.	PUNCT
bibechana-10397	165	1	sei	sei	ADJ
bibechana-10397	165	2	.	.	PUNCT
bibechana-10397	165	3	cl	cl	NOUN
bibechana-10397	165	4	.	.	PUNCT
bibechana-10397	166	1	ill	ill	ADJ
bibechana-10397	166	2	,	,	PUNCT
bibechana-10397	166	3	4	4	NUM
bibechana-10397	166	4	(	(	PUNCT
bibechana-10397	166	5	1957	1957	NUM
bibechana-10397	166	6	)	)	PUNCT
bibechana-10397	166	7	375	375	NUM
bibechana-10397	166	8	.	.	PUNCT
bibechana-10397	167	1	elczynski	elczynski	ADJ
bibechana-10397	167	2	,	,	PUNCT
bibechana-10397	167	3	s.	s.	PROPN
bibechana-10397	167	4	rolewicz	rolewicz	PROPN
bibechana-10397	167	5	,	,	PUNCT
bibechana-10397	167	6	bull	bull	NOUN
bibechana-10397	167	7	.	.	PUNCT
bibechana-10397	168	1	acad	acad	PROPN
bibechana-10397	168	2	.	.	PUNCT
bibechana-10397	169	1	polon	polon	NOUN
bibechana-10397	169	2	.	.	PUNCT
bibechana-10397	170	1	sei	sei	PROPN
bibechana-10397	170	2	.	.	PROPN
bibechana-10397	170	3	,	,	PUNCT
bibechana-10397	170	4	9	9	NUM
bibechana-10397	170	5	(	(	PUNCT
bibechana-10397	170	6	1961	1961	NUM
bibechana-10397	170	7	)	)	PUNCT
bibechana-10397	170	8	677	677	NUM
bibechana-10397	170	9	.	.	PUNCT
bibechana-10397	171	1	[	[	X
bibechana-10397	171	2	3	3	NUM
bibechana-10397	171	3	]	]	X
bibechana-10397	171	4	g.l	g.l	PROPN
bibechana-10397	171	5	.	.	PROPN
bibechana-10397	171	6	litvinov	litvinov	PROPN
bibechana-10397	171	7	,	,	PUNCT
bibechana-10397	171	8	nuclear	nuclear	ADJ
bibechana-10397	171	9	space	space	NOUN
bibechana-10397	171	10	,	,	PUNCT
bibechana-10397	171	11	springer	springer	NOUN
bibechana-10397	171	12	-	-	PUNCT
bibechana-10397	171	13	verlag	verlag	PROPN
bibechana-10397	171	14	,	,	PUNCT
bibechana-10397	171	15	2001	2001	NUM
bibechana-10397	171	16	.	.	PUNCT
bibechana-10397	172	1	[	[	X
bibechana-10397	172	2	4	4	NUM
bibechana-10397	172	3	]	]	X
bibechana-10397	172	4	c.	c.	NOUN
bibechana-10397	172	5	bessaga	bessaga	NOUN
bibechana-10397	172	6	and	and	CCONJ
bibechana-10397	172	7	ed	ed	PROPN
bibechana-10397	172	8	dubinsky	dubinsky	PROPN
bibechana-10397	172	9	,	,	PUNCT
bibechana-10397	172	10	arch	arch	ADJ
bibechana-10397	172	11	math	math	NOUN
bibechana-10397	172	12	.	.	PUNCT
bibechana-10397	173	1	,	,	PUNCT
bibechana-10397	173	2	31	31	NUM
bibechana-10397	173	3	(	(	PUNCT
bibechana-10397	173	4	1978	1978	NUM
bibechana-10397	173	5	)	)	PUNCT
bibechana-10397	173	6	597	597	NUM
bibechana-10397	173	7	.	.	PUNCT
bibechana-10397	174	1	[	[	X
bibechana-10397	174	2	5	5	X
bibechana-10397	174	3	]	]	PUNCT
bibechana-10397	174	4	g.	g.	NOUN
bibechana-10397	174	5	kothe	kothe	PROPN
bibechana-10397	174	6	,	,	PUNCT
bibechana-10397	174	7	topological	topological	ADJ
bibechana-10397	174	8	vector	vector	NOUN
bibechana-10397	174	9	space	space	NOUN
bibechana-10397	174	10	i	i	PRON
bibechana-10397	174	11	,	,	PUNCT
bibechana-10397	174	12	spiringer	spiringer	NOUN
bibechana-10397	174	13	-	-	PUNCT
bibechana-10397	174	14	verlag	verlag	PROPN
bibechana-10397	174	15	,	,	PUNCT
bibechana-10397	174	16	1969	1969	NUM
bibechana-10397	174	17	.	.	PUNCT
bibechana-10397	175	1	at	at	ADP
bibechana-10397	175	2	,	,	PUNCT
bibechana-10397	175	3	lectures	lecture	NOUN
bibechana-10397	175	4	on	on	ADP
bibechana-10397	175	5	frechet	frechet	PROPN
bibechana-10397	175	6	spaces	space	NOUN
bibechana-10397	175	7	,	,	PUNCT
bibechana-10397	175	8	bergische	bergische	PROPN
bibechana-10397	175	9	universitat	universitat	PROPN
bibechana-10397	175	10	wuppertal	wuppertal	NOUN
bibechana-10397	175	11	,	,	PUNCT
bibechana-10397	175	12	sommer	sommer	NOUN
bibechana-10397	175	13	semester	semester	NOUN
bibechana-10397	175	14	[	[	X
bibechana-10397	175	15	7	7	NUM
bibechana-10397	175	16	]	]	X
bibechana-10397	175	17	a.e.taylor	a.e.taylor	NOUN
bibechana-10397	175	18	,	,	PUNCT
bibechana-10397	175	19	introduction	introduction	NOUN
bibechana-10397	175	20	to	to	ADP
bibechana-10397	175	21	functional	functional	ADJ
bibechana-10397	175	22	analysis	analysis	NOUN
bibechana-10397	175	23	,	,	PUNCT
bibechana-10397	175	24	john	john	PROPN
bibechana-10397	175	25	willey	willey	PROPN
bibechana-10397	175	26	and	and	CCONJ
bibechana-10397	175	27	sons	son	NOUN
bibechana-10397	175	28	,	,	PUNCT
bibechana-10397	175	29	inc	inc	PROPN
bibechana-10397	175	30	.	.	PROPN
bibechana-10397	175	31	,	,	PUNCT
bibechana-10397	175	32	london,1961	london,1961	ADJ
bibechana-10397	175	33	.	.	PUNCT
bibechana-10397	176	1	[	[	X
bibechana-10397	176	2	8	8	NUM
bibechana-10397	176	3	]	]	PUNCT
bibechana-10397	176	4	a.	a.	NOUN
bibechana-10397	176	5	pietsch	pietsch	PROPN
bibechana-10397	176	6	,	,	PUNCT
bibechana-10397	176	7	nuclear	nuclear	ADJ
bibechana-10397	176	8	locally	locally	ADV
bibechana-10397	176	9	convex	convex	ADJ
bibechana-10397	176	10	space	space	NOUN
bibechana-10397	176	11	,	,	PUNCT
bibechana-10397	176	12	springer	springer	NOUN
bibechana-10397	176	13	-	-	PUNCT
bibechana-10397	176	14	verlag	verlag	PROPN
bibechana-10397	176	15	berlin	berlin	PROPN
bibechana-10397	176	16	heidelberg	heidelberg	PROPN
bibechana-10397	176	17	,	,	PUNCT
bibechana-10397	176	18	new	new	PROPN
bibechana-10397	176	19	york,1972	york,1972	PROPN
bibechana-10397	176	20	.	.	PUNCT
bibechana-10397	177	1	[	[	X
bibechana-10397	177	2	9	9	NUM
bibechana-10397	177	3	]	]	X
bibechana-10397	177	4	a.p	a.p	PROPN
bibechana-10397	177	5	.	.	PROPN
bibechana-10397	177	6	robertson	robertson	PROPN
bibechana-10397	177	7	,	,	PUNCT
bibechana-10397	177	8	w.	w.	PROPN
bibechana-10397	177	9	robertson	robertson	PROPN
bibechana-10397	177	10	,	,	PUNCT
bibechana-10397	177	11	topological	topological	ADJ
bibechana-10397	177	12	vector	vector	NOUN
bibechana-10397	177	13	spaces	space	NOUN
bibechana-10397	177	14	,	,	PUNCT
bibechana-10397	177	15	cambridge	cambridge	PROPN
bibechana-10397	177	16	university	university	PROPN
bibechana-10397	177	17	press	press	NOUN
bibechana-10397	177	18	,	,	PUNCT
bibechana-10397	177	19	1964	1964	NUM
bibechana-10397	177	20	.	.	PUNCT
bibechana-10397	178	1	verlag	verlag	PROPN
bibechana-10397	178	2	,	,	PUNCT
bibechana-10397	178	3	berlin	berlin	PROPN
bibechana-10397	178	4	and	and	CCONJ
bibechana-10397	178	5	new	new	PROPN
bibechana-10397	178	6	york	york	PROPN
bibechana-10397	178	7	,	,	PUNCT
bibechana-10397	178	8	720	720	NUM
bibechana-10397	178	9	(	(	PUNCT
bibechana-10397	178	10	1979	1979	NUM
bibechana-10397	178	11	)	)	PUNCT
bibechana-10397	178	12	123	123	NUM
bibechana-10397	178	13	.	.	PUNCT
bibechana-10397	179	1	[	[	X
bibechana-10397	179	2	11	11	NUM
bibechana-10397	179	3	]	]	X
bibechana-10397	179	4	v.b	v.b	PROPN
bibechana-10397	179	5	.	.	PROPN
bibechana-10397	179	6	moscatelli	moscatelli	PROPN
bibechana-10397	179	7	,	,	PUNCT
bibechana-10397	179	8	bull	bull	PROPN
bibechana-10397	179	9	.	.	PUNCT
bibechana-10397	180	1	london	london	PROPN
bibechana-10397	180	2	math	math	PROPN
bibechana-10397	180	3	.	.	PUNCT
bibechana-10397	181	1	soc	soc	PROPN
bibechana-10397	181	2	.	.	PROPN
bibechana-10397	181	3	,	,	PUNCT
bibechana-10397	181	4	12	12	NUM
bibechana-10397	181	5	(	(	PUNCT
bibechana-10397	181	6	1980	1980	NUM
bibechana-10397	181	7	)	)	PUNCT
bibechana-10397	181	8	63	63	NUM
bibechana-10397	181	9	.	.	PUNCT
bibechana-10397	182	1	[	[	X
bibechana-10397	182	2	12	12	NUM
bibechana-10397	182	3	]	]	X
bibechana-10397	182	4	l.	l.	PROPN
bibechana-10397	182	5	holmstrom	holmstrom	PROPN
bibechana-10397	182	6	,	,	PUNCT
bibechana-10397	182	7	journal	journal	NOUN
bibechana-10397	182	8	of	of	ADP
bibechana-10397	182	9	functional	functional	ADJ
bibechana-10397	182	10	analysis	analysis	NOUN
bibechana-10397	182	11	,	,	PUNCT
bibechana-10397	182	12	348	348	NUM
bibechana-10397	182	13	(	(	PUNCT
bibechana-10397	182	14	1982	1982	NUM
bibechana-10397	182	15	)	)	PUNCT
bibechana-10397	182	16	12	12	NUM
bibechana-10397	182	17	.	.	PUNCT
bibechana-10397	182	18	dubinsky	dubinsky	PROPN
bibechana-10397	182	19	,	,	PUNCT
bibechana-10397	182	20	w.	w.	PROPN
bibechana-10397	182	21	robinson	robinson	PROPN
bibechana-10397	182	22	,	,	PUNCT
bibechana-10397	182	23	studia	studia	PROPN
bibechana-10397	182	24	math	math	NOUN
bibechana-10397	182	25	,	,	PUNCT
bibechana-10397	182	26	63	63	NUM
bibechana-10397	182	27	(	(	PUNCT
bibechana-10397	182	28	1978	1978	NUM
bibechana-10397	182	29	)	)	PUNCT
bibechana-10397	182	30	267	267	NUM
bibechana-10397	182	31	.	.	PUNCT
bibechana-10397	183	1	trans	trans	PROPN
bibechana-10397	183	2	.	.	PUNCT
bibechana-10397	184	1	amer	amer	PROPN
bibechana-10397	184	2	.	.	PUNCT
bibechana-10397	184	3	math	math	PROPN
bibechana-10397	184	4	.	.	PUNCT
bibechana-10397	185	1	soc	soc	PROPN
bibechana-10397	185	2	.	.	PUNCT
bibechana-10397	185	3	,	,	PUNCT
bibechana-10397	185	4	362	362	NUM
bibechana-10397	185	5	(	(	PUNCT
bibechana-10397	185	6	2010	2010	NUM
bibechana-10397	185	7	)	)	PUNCT
bibechana-10397	185	8	3273	3273	NUM
bibechana-10397	185	9	.	.	PUNCT
bibechana-10397	186	1	[	[	X
bibechana-10397	186	2	15	15	NUM
bibechana-10397	186	3	]	]	X
bibechana-10397	186	4	w.	w.	PROPN
bibechana-10397	186	5	sliwa	sliwa	PROPN
bibechana-10397	186	6	,	,	PUNCT
bibechana-10397	186	7	bull	bull	NOUN
bibechana-10397	186	8	.	.	PUNCT
bibechana-10397	187	1	belg	belg	PROPN
bibechana-10397	187	2	.	.	PUNCT
bibechana-10397	188	1	math	math	NOUN
bibechana-10397	188	2	.	.	PUNCT
bibechana-10397	189	1	soc	soc	PROPN
bibechana-10397	189	2	.	.	PUNCT
bibechana-10397	190	1	simon	simon	PROPN
bibechana-10397	190	2	stevin	stevin	PROPN
bibechana-10397	190	3	,	,	PUNCT
bibechana-10397	190	4	14	14	NUM
bibechana-10397	190	5	(	(	PUNCT
bibechana-10397	190	6	2007	2007	NUM
bibechana-10397	190	7	)	)	PUNCT
bibechana-10397	190	8	1017	1017	NUM
bibechana-10397	190	9	.	.	PUNCT
bibechana-10397	191	1	publication	publication	NOUN
bibechana-10397	191	2	:	:	PUNCT
bibechana-10397	191	3	march	march	PROPN
bibechana-10397	191	4	,	,	PUNCT
bibechana-10397	191	5	2014	2014	NUM
bibechana-10397	191	6	)	)	PUNCT
bibechana-10397	191	7	p.164	p.164	NOUN
bibechana-10397	191	8	f	f	SYM
bibechana-10397	191	9	°	°	NUM
bibechana-10397	191	10	)	)	PUNCT
bibechana-10397	191	11	k.	k.	NOUN
bibechana-10397	192	1	so	so	ADV
bibechana-10397	192	2	if	if	SCONJ
bibechana-10397	192	3	e	e	PROPN
bibechana-10397	192	4	/	/	SYM
bibechana-10397	192	5	f	f	PROPN
bibechana-10397	192	6	satisfies	satisfy	VERB
bibechana-10397	192	7	condition	condition	PROPN
bibechana-10397	192	8	⍟	⍟	PROPN
bibechana-10397	192	9	(	(	PUNCT
bibechana-10397	192	10	say	say	VERB
bibechana-10397	192	11	ϵ	ϵ	X
bibechana-10397	192	12	(	(	PUNCT
bibechana-10397	192	13	cnu	cnu	PROPN
bibechana-10397	192	14	�	�	PROPN
bibechana-10397	192	15	�	�	PROPN
bibechana-10397	192	16	∩	∩	PROPN
bibechana-10397	192	17	f	f	PROPN
bibechana-10397	192	18	°	°	PRON
bibechana-10397	192	19	)	)	PUNCT
bibechana-10397	192	20	∩	∩	NOUN
bibechana-10397	192	21	(	(	PUNCT
bibechana-10397	192	22	∉	∉	PROPN
bibechana-10397	192	23	u	u	PROPN
bibechana-10397	192	24	�	�	PROPN
bibechana-10397	192	25	�	�	PROPN
bibechana-10397	192	26	;	;	PUNCT
bibechana-10397	192	27	so	so	ADV
bibechana-10397	192	28	||	||	PROPN
bibechana-10397	192	29	un	un	PROPN
bibechana-10397	192	30	||'k	||'k	PROPN
bibechana-10397	192	31	a	a	DET
bibechana-10397	192	32	frechet	frechet	PROPN
bibechana-10397	192	33	space	space	NOUN
bibechana-10397	192	34	which	which	PRON
bibechana-10397	192	35	admits	admit	VERB
bibechana-10397	192	36	continuous	continuous	ADJ
bibechana-10397	192	37	norm	norm	NOUN
bibechana-10397	192	38	has	have	VERB
bibechana-10397	192	39	a	a	DET
bibechana-10397	192	40	nuclear	nuclear	ADJ
bibechana-10397	192	41	kothe	kothe	NOUN
bibechana-10397	192	42	subspace	subspace	NOUN
bibechana-10397	193	1	if	if	SCONJ
bibechana-10397	194	1	and	and	CCONJ
bibechana-10397	194	2	only	only	ADV
bibechana-10397	194	3	if	if	SCONJ
bibechana-10397	194	4	it	it	PRON
bibechana-10397	194	5	is	be	AUX
bibechana-10397	194	6	not	not	PART
bibechana-10397	194	7	.	.	PUNCT
bibechana-10397	195	1	thus	thus	ADV
bibechana-10397	195	2	it	it	PRON
bibechana-10397	195	3	follows	follow	VERB
bibechana-10397	195	4	that	that	SCONJ
bibechana-10397	195	5	,	,	PUNCT
bibechana-10397	195	6	in	in	ADP
bibechana-10397	195	7	general	general	ADJ
bibechana-10397	195	8	,	,	PUNCT
bibechana-10397	195	9	a	a	DET
bibechana-10397	195	10	frechet	frechet	NOUN
bibechana-10397	195	11	space	space	NOUN
bibechana-10397	195	12	has	have	VERB
bibechana-10397	195	13	a	a	DET
bibechana-10397	195	14	nuclear	nuclear	ADJ
bibechana-10397	195	15	kothe	kothe	NOUN
bibechana-10397	195	16	subspace	subspace	PROPN
bibechana-10397	195	17	iff	iff	PROPN
bibechana-10397	195	18	it	it	PRON
bibechana-10397	195	19	has	have	VERB
bibechana-10397	195	20	a	a	DET
bibechana-10397	195	21	nonat	nonat	NOUN
bibechana-10397	195	22	,	,	PUNCT
bibechana-10397	195	23	lectures	lecture	NOUN
bibechana-10397	195	24	on	on	ADP
bibechana-10397	195	25	frechet	frechet	PROPN
bibechana-10397	195	26	spaces	space	NOUN
bibechana-10397	195	27	,	,	PUNCT
bibechana-10397	195	28	bergische	bergische	PROPN
bibechana-10397	195	29	universitat	universitat	PROPN
bibechana-10397	195	30	wuppertal	wuppertal	NOUN
bibechana-10397	195	31	,	,	PUNCT
bibechana-10397	195	32	sommer	sommer	NOUN
bibechana-10397	195	33	semester	semester	NOUN
bibechana-10397	195	34	,	,	PUNCT
bibechana-10397	195	35	2000	2000	NUM
bibechana-10397	195	36	.	.	PUNCT
bibechana-10397	196	1	[	[	X
bibechana-10397	196	2	7	7	NUM
bibechana-10397	196	3	]	]	X
bibechana-10397	196	4	a.e.taylor	a.e.taylor	NOUN
bibechana-10397	196	5	,	,	PUNCT
bibechana-10397	196	6	introduction	introduction	NOUN
bibechana-10397	196	7	to	to	ADP
bibechana-10397	196	8	functional	functional	ADJ
bibechana-10397	196	9	analysis	analysis	NOUN
bibechana-10397	196	10	,	,	PUNCT
bibechana-10397	196	11	john	john	PROPN
bibechana-10397	196	12	willey	willey	PROPN
bibechana-10397	196	13	and	and	CCONJ
bibechana-10397	196	14	sons	son	NOUN
bibechana-10397	196	15	,	,	PUNCT
bibechana-10397	196	16	inc	inc	PROPN
bibechana-10397	196	17	.	.	PROPN
bibechana-10397	196	18	,	,	PUNCT
bibechana-10397	196	19	london,1961	london,1961	PROPN
bibechana-10397	196	20	.	.	PUNCT
bibechana-10397	197	1	berlin	berlin	PROPN
bibechana-10397	197	2	heidelberg	heidelberg	PROPN
bibechana-10397	197	3	,	,	PUNCT
bibechana-10397	197	4	new	new	PROPN
bibechana-10397	197	5	york,1972	york,1972	PROPN
bibechana-10397	197	6	.	.	PUNCT
bibechana-10397	198	1	[	[	X
bibechana-10397	198	2	9	9	NUM
bibechana-10397	198	3	]	]	X
bibechana-10397	198	4	a.p	a.p	PROPN
bibechana-10397	198	5	.	.	PROPN
bibechana-10397	198	6	robertson	robertson	PROPN
bibechana-10397	198	7	,	,	PUNCT
bibechana-10397	198	8	w.	w.	PROPN
bibechana-10397	198	9	robertson	robertson	PROPN
bibechana-10397	198	10	,	,	PUNCT
bibechana-10397	198	11	topological	topological	ADJ
bibechana-10397	198	12	vector	vector	NOUN
bibechana-10397	198	13	spaces	space	NOUN
bibechana-10397	198	14	,	,	PUNCT
bibechana-10397	198	15	cambridge	cambridge	PROPN
bibechana-10397	198	16	university	university	PROPN
bibechana-10397	198	17	press	press	NOUN
bibechana-10397	198	18	,	,	PUNCT
bibechana-10397	198	19	1964	1964	NUM
bibechana-10397	198	20	.	.	PUNCT