id	sid	tid	token	lemma	pos
ejpam-137	1	1	european	european	PROPN
ejpam-137	1	2	journal	journal	PROPN
ejpam-137	1	3	of	of	ADP
ejpam-137	1	4	pure	pure	ADJ
ejpam-137	1	5	and	and	CCONJ
ejpam-137	1	6	applied	apply	VERB
ejpam-137	1	7	mathematics	mathematic	NOUN
ejpam-137	1	8	vol	vol	NOUN
ejpam-137	1	9	.	.	PROPN
ejpam-137	2	1	1	1	NUM
ejpam-137	2	2	,	,	PUNCT
ejpam-137	2	3	no	no	INTJ
ejpam-137	2	4	.	.	NOUN
ejpam-137	2	5	4	4	NUM
ejpam-137	2	6	,	,	PUNCT
ejpam-137	2	7	2008	2008	NUM
ejpam-137	2	8	,	,	PUNCT
ejpam-137	2	9	(	(	PUNCT
ejpam-137	2	10	22	22	NUM
ejpam-137	2	11	-	-	SYM
ejpam-137	2	12	29	29	NUM
ejpam-137	2	13	)	)	PUNCT
ejpam-137	2	14	issn	issn	PROPN
ejpam-137	2	15	1307	1307	NUM
ejpam-137	2	16	-	-	SYM
ejpam-137	2	17	5543	5543	NUM
ejpam-137	2	18	–	–	PUNCT
ejpam-137	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-137	2	20	on	on	ADP
ejpam-137	2	21	some	some	DET
ejpam-137	2	22	mappings	mapping	NOUN
ejpam-137	2	23	in	in	ADP
ejpam-137	2	24	topological	topological	ADJ
ejpam-137	2	25	spaces	space	NOUN
ejpam-137	2	26	bashir	bashir	PROPN
ejpam-137	2	27	ahmad1	ahmad1	PROPN
ejpam-137	2	28	,	,	PUNCT
ejpam-137	2	29	sabir	sabir	PROPN
ejpam-137	2	30	hussain2,∗	hussain2,∗	PROPN
ejpam-137	2	31	,	,	PUNCT
ejpam-137	2	32	takashi	takashi	PROPN
ejpam-137	2	33	noiri3	noiri3	PROPN
ejpam-137	2	34	1	1	NUM
ejpam-137	2	35	centre	centre	NOUN
ejpam-137	2	36	for	for	ADP
ejpam-137	2	37	advanced	advanced	ADJ
ejpam-137	2	38	studies	study	NOUN
ejpam-137	2	39	in	in	ADP
ejpam-137	2	40	pure	pure	ADJ
ejpam-137	2	41	and	and	CCONJ
ejpam-137	2	42	applied	applied	ADJ
ejpam-137	2	43	mathematics	mathematic	NOUN
ejpam-137	2	44	,	,	PUNCT
ejpam-137	2	45	bahauddin	bahauddin	PROPN
ejpam-137	2	46	zakariya	zakariya	PROPN
ejpam-137	2	47	university	university	PROPN
ejpam-137	2	48	,	,	PUNCT
ejpam-137	2	49	multan	multan	PROPN
ejpam-137	2	50	,	,	PUNCT
ejpam-137	2	51	pakistan	pakistan	PROPN
ejpam-137	2	52	.	.	PUNCT
ejpam-137	3	1	present	present	ADJ
ejpam-137	3	2	address	address	NOUN
ejpam-137	3	3	:	:	PUNCT
ejpam-137	3	4	department	department	NOUN
ejpam-137	3	5	of	of	ADP
ejpam-137	3	6	mathematics	mathematics	PROPN
ejpam-137	3	7	,	,	PUNCT
ejpam-137	3	8	king	king	NOUN
ejpam-137	3	9	abdul	abdul	PROPN
ejpam-137	3	10	aziz	aziz	PROPN
ejpam-137	3	11	university	university	PROPN
ejpam-137	3	12	p.	p.	PROPN
ejpam-137	3	13	o.	o.	PROPN
ejpam-137	3	14	box	box	PROPN
ejpam-137	3	15	80203	80203	NUM
ejpam-137	3	16	,	,	PUNCT
ejpam-137	3	17	jeddah	jeddah	PROPN
ejpam-137	3	18	21589	21589	NUM
ejpam-137	3	19	,	,	PUNCT
ejpam-137	3	20	saudi	saudi	PROPN
ejpam-137	3	21	arabia	arabia	PROPN
ejpam-137	3	22	.	.	PUNCT
ejpam-137	4	1	2	2	NUM
ejpam-137	4	2	department	department	NOUN
ejpam-137	4	3	of	of	ADP
ejpam-137	4	4	mathematics	mathematics	PROPN
ejpam-137	4	5	,	,	PUNCT
ejpam-137	4	6	islamia	islamia	PROPN
ejpam-137	4	7	university	university	PROPN
ejpam-137	4	8	bahawalpur	bahawalpur	NOUN
ejpam-137	4	9	,	,	PUNCT
ejpam-137	4	10	pakistan	pakistan	PROPN
ejpam-137	4	11	.	.	PUNCT
ejpam-137	5	1	3	3	NUM
ejpam-137	5	2	2949	2949	NUM
ejpam-137	5	3	-	-	SYM
ejpam-137	5	4	1	1	NUM
ejpam-137	5	5	shiokita	shiokita	NOUN
ejpam-137	5	6	-	-	PUNCT
ejpam-137	5	7	cho	cho	ADJ
ejpam-137	5	8	,	,	PUNCT
ejpam-137	5	9	hinagu	hinagu	ADJ
ejpam-137	5	10	,	,	PUNCT
ejpam-137	5	11	yatsushiro	yatsushiro	PROPN
ejpam-137	5	12	-	-	PUNCT
ejpam-137	5	13	shi	shi	PROPN
ejpam-137	5	14	,	,	PUNCT
ejpam-137	5	15	kumamoto	kumamoto	PROPN
ejpam-137	5	16	-	-	PUNCT
ejpam-137	5	17	ken	ken	PROPN
ejpam-137	5	18	,	,	PUNCT
ejpam-137	5	19	869	869	NUM
ejpam-137	5	20	-	-	SYM
ejpam-137	5	21	5142	5142	NUM
ejpam-137	5	22	,	,	PUNCT
ejpam-137	5	23	japan	japan	PROPN
ejpam-137	5	24	.	.	PUNCT
ejpam-137	6	1	abstract	abstract	PROPN
ejpam-137	6	2	.	.	PUNCT
ejpam-137	7	1	in	in	ADP
ejpam-137	7	2	this	this	DET
ejpam-137	7	3	paper	paper	NOUN
ejpam-137	7	4	,	,	PUNCT
ejpam-137	7	5	we	we	PRON
ejpam-137	7	6	continue	continue	VERB
ejpam-137	7	7	studying	study	VERB
ejpam-137	7	8	the	the	DET
ejpam-137	7	9	properties	property	NOUN
ejpam-137	7	10	of	of	ADP
ejpam-137	7	11	γ	γ	NOUN
ejpam-137	7	12	-	-	PUNCT
ejpam-137	7	13	semi	semi	ADV
ejpam-137	7	14	-	-	ADJ
ejpam-137	7	15	continuous	continuous	ADJ
ejpam-137	7	16	and	and	CCONJ
ejpam-137	7	17	γ	γ	DET
ejpam-137	7	18	-semi	-semi	NOUN
ejpam-137	7	19	-	-	PUNCT
ejpam-137	7	20	open	open	ADJ
ejpam-137	7	21	functions	function	NOUN
ejpam-137	7	22	introduced	introduce	VERB
ejpam-137	7	23	in	in	ADP
ejpam-137	7	24	[	[	X
ejpam-137	7	25	5	5	NUM
ejpam-137	7	26	]	]	PUNCT
ejpam-137	7	27	,	,	PUNCT
ejpam-137	7	28	[	[	X
ejpam-137	7	29	10	10	NUM
ejpam-137	7	30	]	]	PUNCT
ejpam-137	7	31	.	.	PUNCT
ejpam-137	8	1	we	we	PRON
ejpam-137	8	2	also	also	ADV
ejpam-137	8	3	introduce	introduce	VERB
ejpam-137	8	4	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	8	5	functions	function	NOUN
ejpam-137	8	6	and	and	CCONJ
ejpam-137	8	7	γ	γ	X
ejpam-137	8	8	-pre	-pre	X
ejpam-137	8	9	-	-	PUNCT
ejpam-137	8	10	semi	semi	ADV
ejpam-137	8	11	-	-	ADJ
ejpam-137	8	12	open	open	ADJ
ejpam-137	8	13	(	(	PUNCT
ejpam-137	8	14	closed	closed	ADJ
ejpam-137	8	15	)	)	PUNCT
ejpam-137	8	16	functions	function	NOUN
ejpam-137	8	17	and	and	CCONJ
ejpam-137	8	18	discuss	discuss	VERB
ejpam-137	8	19	their	their	PRON
ejpam-137	8	20	properties	property	NOUN
ejpam-137	8	21	.	.	PUNCT
ejpam-137	9	1	ams	am	NOUN
ejpam-137	9	2	subject	subject	ADJ
ejpam-137	9	3	classifications	classification	NOUN
ejpam-137	9	4	:	:	PUNCT
ejpam-137	9	5	54a05	54a05	NUM
ejpam-137	9	6	,	,	PUNCT
ejpam-137	9	7	54a10	54a10	NUM
ejpam-137	9	8	,	,	PUNCT
ejpam-137	9	9	54d10	54d10	NUM
ejpam-137	9	10	.	.	PUNCT
ejpam-137	10	1	key	key	ADJ
ejpam-137	10	2	words	word	NOUN
ejpam-137	10	3	:	:	PUNCT
ejpam-137	10	4	γ	γ	X
ejpam-137	10	5	-	-	ADJ
ejpam-137	10	6	closed	closed	ADJ
ejpam-137	10	7	(	(	PUNCT
ejpam-137	10	8	open	open	ADJ
ejpam-137	10	9	)	)	PUNCT
ejpam-137	10	10	,	,	PUNCT
ejpam-137	10	11	γ	γ	NOUN
ejpam-137	10	12	-	-	NOUN
ejpam-137	10	13	closure	closure	NOUN
ejpam-137	10	14	,	,	PUNCT
ejpam-137	10	15	γ∗-semi	γ∗-semi	NOUN
ejpam-137	10	16	-	-	ADJ
ejpam-137	10	17	closed	closed	ADJ
ejpam-137	10	18	(	(	PUNCT
ejpam-137	10	19	open	open	ADJ
ejpam-137	10	20	)	)	PUNCT
ejpam-137	10	21	,	,	PUNCT
ejpam-137	10	22	γ∗-semi	γ∗-semi	NOUN
ejpam-137	10	23	-	-	NOUN
ejpam-137	10	24	closure	closure	NOUN
ejpam-137	10	25	,	,	PUNCT
ejpam-137	10	26	γ	γ	NOUN
ejpam-137	10	27	-	-	ADJ
ejpam-137	10	28	regular	regular	ADJ
ejpam-137	10	29	,	,	PUNCT
ejpam-137	10	30	γ∗-semiinterior	γ∗-semiinterior	PROPN
ejpam-137	10	31	,	,	PUNCT
ejpam-137	10	32	γ	γ	NOUN
ejpam-137	10	33	-	-	PUNCT
ejpam-137	10	34	semi	semi	ADJ
ejpam-137	10	35	-	-	ADJ
ejpam-137	10	36	continuous	continuous	ADJ
ejpam-137	10	37	functions	function	NOUN
ejpam-137	10	38	,	,	PUNCT
ejpam-137	10	39	γ	γ	X
ejpam-137	10	40	-	-	PUNCT
ejpam-137	10	41	semi	semi	ADV
ejpam-137	10	42	-	-	ADJ
ejpam-137	10	43	open	open	ADJ
ejpam-137	10	44	(	(	PUNCT
ejpam-137	10	45	closed	closed	ADJ
ejpam-137	10	46	)	)	PUNCT
ejpam-137	10	47	functions	function	NOUN
ejpam-137	10	48	,	,	PUNCT
ejpam-137	10	49	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	10	50	functions	function	NOUN
ejpam-137	10	51	,	,	PUNCT
ejpam-137	10	52	γ	γ	PROPN
ejpam-137	10	53	-	-	PUNCT
ejpam-137	10	54	presemi	presemi	ADV
ejpam-137	10	55	-	-	PUNCT
ejpam-137	10	56	open(closed	open(close	VERB
ejpam-137	10	57	)	)	PUNCT
ejpam-137	10	58	functions	function	NOUN
ejpam-137	10	59	.	.	PUNCT
ejpam-137	11	1	1	1	X
ejpam-137	11	2	.	.	X
ejpam-137	11	3	introduction	introduction	NOUN
ejpam-137	11	4	a.	a.	NOUN
ejpam-137	11	5	csaszar	csaszar	VERB
ejpam-137	11	6	[	[	X
ejpam-137	11	7	7,8	7,8	NUM
ejpam-137	11	8	]	]	PUNCT
ejpam-137	11	9	defined	define	VERB
ejpam-137	11	10	generalized	generalized	ADJ
ejpam-137	11	11	open	open	ADJ
ejpam-137	11	12	sets	set	NOUN
ejpam-137	11	13	in	in	ADP
ejpam-137	11	14	generalized	generalized	ADJ
ejpam-137	11	15	topological	topological	ADJ
ejpam-137	11	16	spaces	space	NOUN
ejpam-137	11	17	.	.	PUNCT
ejpam-137	12	1	in	in	ADP
ejpam-137	12	2	1975	1975	NUM
ejpam-137	12	3	,	,	PUNCT
ejpam-137	12	4	maheshwari	maheshwari	NOUN
ejpam-137	12	5	and	and	CCONJ
ejpam-137	12	6	prasad	prasad	PROPN
ejpam-137	13	1	[	[	X
ejpam-137	13	2	13	13	NUM
ejpam-137	13	3	]	]	PUNCT
ejpam-137	13	4	introduced	introduce	VERB
ejpam-137	13	5	concepts	concept	NOUN
ejpam-137	13	6	of	of	ADP
ejpam-137	13	7	semit1	semit1	PROPN
ejpam-137	13	8	-	-	PUNCT
ejpam-137	13	9	spaces	space	NOUN
ejpam-137	13	10	and	and	CCONJ
ejpam-137	13	11	semi	semi	ADJ
ejpam-137	13	12	-	-	ADJ
ejpam-137	13	13	r0	r0	NOUN
ejpam-137	13	14	-	-	PUNCT
ejpam-137	13	15	spaces	space	NOUN
ejpam-137	13	16	.	.	PUNCT
ejpam-137	14	1	in	in	ADP
ejpam-137	14	2	1979	1979	NUM
ejpam-137	14	3	,	,	PUNCT
ejpam-137	14	4	s.	s.	PROPN
ejpam-137	14	5	kasahara	kasahara	PROPN
ejpam-137	15	1	[	[	X
ejpam-137	15	2	11	11	NUM
ejpam-137	15	3	]	]	PUNCT
ejpam-137	15	4	defined	define	VERB
ejpam-137	15	5	an	an	DET
ejpam-137	15	6	operation	operation	NOUN
ejpam-137	15	7	α	α	NOUN
ejpam-137	15	8	on	on	ADP
ejpam-137	15	9	topological	topological	ADJ
ejpam-137	15	10	spaces	space	NOUN
ejpam-137	15	11	.	.	PUNCT
ejpam-137	16	1	in	in	ADP
ejpam-137	16	2	1992	1992	NUM
ejpam-137	16	3	(	(	PUNCT
ejpam-137	16	4	1993	1993	NUM
ejpam-137	16	5	)	)	PUNCT
ejpam-137	16	6	,	,	PUNCT
ejpam-137	16	7	b.	b.	PROPN
ejpam-137	16	8	ahmad	ahmad	PROPN
ejpam-137	16	9	and	and	CCONJ
ejpam-137	16	10	f.u	f.u	PROPN
ejpam-137	16	11	.	.	PROPN
ejpam-137	16	12	rehman	rehman	NOUN
ejpam-137	17	1	[	[	X
ejpam-137	17	2	1	1	NUM
ejpam-137	17	3	]	]	PUNCT
ejpam-137	17	4	,	,	PUNCT
ejpam-137	17	5	[	[	X
ejpam-137	17	6	15	15	NUM
ejpam-137	17	7	]	]	PUNCT
ejpam-137	17	8	introduced	introduce	VERB
ejpam-137	17	9	the	the	DET
ejpam-137	17	10	notions	notion	NOUN
ejpam-137	17	11	of	of	ADP
ejpam-137	17	12	γ	γ	NOUN
ejpam-137	17	13	-	-	NOUN
ejpam-137	17	14	interior	interior	ADJ
ejpam-137	17	15	,	,	PUNCT
ejpam-137	17	16	γ	γ	NOUN
ejpam-137	17	17	-	-	ADJ
ejpam-137	17	18	boundary	boundary	ADJ
ejpam-137	17	19	and	and	CCONJ
ejpam-137	17	20	γexterior	γexterior	ADJ
ejpam-137	17	21	points	point	VERB
ejpam-137	17	22	in	in	ADP
ejpam-137	17	23	topological	topological	ADJ
ejpam-137	17	24	spaces	space	NOUN
ejpam-137	17	25	.	.	PUNCT
ejpam-137	18	1	they	they	PRON
ejpam-137	18	2	also	also	ADV
ejpam-137	18	3	studied	study	VERB
ejpam-137	18	4	properties	property	NOUN
ejpam-137	18	5	and	and	CCONJ
ejpam-137	18	6	characterizations	characterization	NOUN
ejpam-137	18	7	of	of	ADP
ejpam-137	18	8	(	(	PUNCT
ejpam-137	18	9	γ	γ	X
ejpam-137	18	10	,	,	PUNCT
ejpam-137	18	11	β)-continuous	β)-continuous	ADJ
ejpam-137	18	12	mappings	mapping	NOUN
ejpam-137	18	13	introduced	introduce	VERB
ejpam-137	18	14	by	by	ADP
ejpam-137	18	15	h.	h.	PROPN
ejpam-137	18	16	ogata	ogata	PROPN
ejpam-137	19	1	[	[	X
ejpam-137	19	2	14	14	NUM
ejpam-137	19	3	]	]	PUNCT
ejpam-137	19	4	.	.	PUNCT
ejpam-137	20	1	in	in	ADP
ejpam-137	20	2	1999	1999	NUM
ejpam-137	20	3	(	(	PUNCT
ejpam-137	20	4	resp	resp	NOUN
ejpam-137	20	5	.	.	PUNCT
ejpam-137	20	6	2005	2005	NUM
ejpam-137	20	7	)	)	PUNCT
ejpam-137	20	8	,	,	PUNCT
ejpam-137	20	9	b.	b.	PROPN
ejpam-137	20	10	ahmad	ahmad	PROPN
ejpam-137	20	11	and	and	CCONJ
ejpam-137	20	12	s.	s.	PROPN
ejpam-137	20	13	hussain	hussain	PROPN
ejpam-137	20	14	introduced	introduce	VERB
ejpam-137	20	15	the	the	DET
ejpam-137	20	16	concept	concept	NOUN
ejpam-137	20	17	of	of	ADP
ejpam-137	20	18	γ∗-regular	γ∗-regular	ADJ
ejpam-137	20	19	spaces	space	NOUN
ejpam-137	20	20	(	(	PUNCT
ejpam-137	20	21	resp	resp	NOUN
ejpam-137	20	22	.	.	PUNCT
ejpam-137	21	1	γ0	γ0	NOUN
ejpam-137	21	2	-	-	PUNCT
ejpam-137	21	3	compact	compact	ADJ
ejpam-137	21	4	,	,	PUNCT
ejpam-137	21	5	γ	γ	NOUN
ejpam-137	21	6	-	-	ADJ
ejpam-137	21	7	normal	normal	ADJ
ejpam-137	21	8	spaces	space	NOUN
ejpam-137	21	9	)	)	PUNCT
ejpam-137	22	1	and	and	CCONJ
ejpam-137	22	2	explored	explore	VERB
ejpam-137	22	3	their	their	PRON
ejpam-137	22	4	many	many	ADJ
ejpam-137	22	5	interesting	interesting	ADJ
ejpam-137	22	6	properties	property	NOUN
ejpam-137	22	7	.	.	PUNCT
ejpam-137	23	1	they	they	PRON
ejpam-137	23	2	initiated	initiate	VERB
ejpam-137	23	3	and	and	CCONJ
ejpam-137	23	4	discussed	discuss	VERB
ejpam-137	23	5	the	the	DET
ejpam-137	23	6	concepts	concept	NOUN
ejpam-137	23	7	of	of	ADP
ejpam-137	23	8	γ∗-semi	γ∗-semi	NOUN
ejpam-137	23	9	-	-	ADJ
ejpam-137	23	10	open	open	ADJ
ejpam-137	23	11	sets	set	NOUN
ejpam-137	23	12	which	which	PRON
ejpam-137	23	13	generalizes	generalize	VERB
ejpam-137	23	14	γ	γ	ADJ
ejpam-137	23	15	-	-	ADJ
ejpam-137	23	16	open	open	ADJ
ejpam-137	23	17	sets	set	NOUN
ejpam-137	23	18	introduced	introduce	VERB
ejpam-137	23	19	and	and	CCONJ
ejpam-137	23	20	discussed	discuss	VERB
ejpam-137	23	21	by	by	ADP
ejpam-137	23	22	h.	h.	PROPN
ejpam-137	23	23	ogata	ogata	PROPN
ejpam-137	24	1	[	[	X
ejpam-137	24	2	14	14	NUM
ejpam-137	24	3	]	]	PUNCT
ejpam-137	24	4	,	,	PUNCT
ejpam-137	24	5	γ∗-semi	γ∗-semi	NOUN
ejpam-137	24	6	-	-	PUNCT
ejpam-137	24	7	closed	closed	ADJ
ejpam-137	24	8	sets	set	NOUN
ejpam-137	24	9	,	,	PUNCT
ejpam-137	24	10	γ∗-semi	γ∗-semi	NOUN
ejpam-137	24	11	-	-	NOUN
ejpam-137	24	12	closure	closure	NOUN
ejpam-137	24	13	,	,	PUNCT
ejpam-137	24	14	γ∗-semi	γ∗-semi	NOUN
ejpam-137	24	15	-	-	ADJ
ejpam-137	24	16	interior	interior	ADJ
ejpam-137	24	17	point	point	NOUN
ejpam-137	24	18	in	in	ADP
ejpam-137	24	19	topological	topological	ADJ
ejpam-137	24	20	spaces	space	NOUN
ejpam-137	24	21	[	[	X
ejpam-137	24	22	5	5	NUM
ejpam-137	24	23	]	]	PUNCT
ejpam-137	24	24	,	,	PUNCT
ejpam-137	24	25	[	[	X
ejpam-137	24	26	9	9	NUM
ejpam-137	24	27	]	]	PUNCT
ejpam-137	24	28	.	.	PUNCT
ejpam-137	25	1	in	in	ADP
ejpam-137	25	2	2006	2006	NUM
ejpam-137	25	3	,	,	PUNCT
ejpam-137	25	4	they	they	PRON
ejpam-137	25	5	introduced	introduce	VERB
ejpam-137	25	6	λγs	λγs	NUM
ejpam-137	25	7	-set	-set	ADJ
ejpam-137	25	8	and	and	CCONJ
ejpam-137	25	9	λsγ	λsγ	NOUN
ejpam-137	25	10	-	-	PUNCT
ejpam-137	25	11	set	set	VERB
ejpam-137	25	12	by	by	ADP
ejpam-137	25	13	using	use	VERB
ejpam-137	25	14	γ∗-semi	γ∗-semi	NOUN
ejpam-137	25	15	-	-	ADJ
ejpam-137	25	16	open	open	ADJ
ejpam-137	25	17	sets	set	NOUN
ejpam-137	25	18	.	.	PUNCT
ejpam-137	26	1	moreover	moreover	ADV
ejpam-137	26	2	,	,	PUNCT
ejpam-137	26	3	they	they	PRON
ejpam-137	26	4	introduced	introduce	VERB
ejpam-137	26	5	the	the	DET
ejpam-137	26	6	γ	γ	NOUN
ejpam-137	26	7	-	-	PUNCT
ejpam-137	26	8	semi	semi	ADJ
ejpam-137	26	9	-	-	ADJ
ejpam-137	26	10	continuous	continuous	ADJ
ejpam-137	26	11	functions	function	NOUN
ejpam-137	26	12	and	and	CCONJ
ejpam-137	26	13	γ	γ	NOUN
ejpam-137	26	14	-	-	PUNCT
ejpam-137	26	15	semi	semi	ADV
ejpam-137	26	16	-	-	ADJ
ejpam-137	26	17	open	open	ADJ
ejpam-137	26	18	(	(	PUNCT
ejpam-137	26	19	closed	closed	ADJ
ejpam-137	26	20	)	)	PUNCT
ejpam-137	26	21	functions	function	NOUN
ejpam-137	26	22	in	in	ADP
ejpam-137	26	23	topological	topological	ADJ
ejpam-137	26	24	spaces	space	NOUN
ejpam-137	26	25	and	and	CCONJ
ejpam-137	26	26	established	establish	VERB
ejpam-137	26	27	several	several	ADJ
ejpam-137	26	28	interesting	interesting	ADJ
ejpam-137	26	29	properties	property	NOUN
ejpam-137	26	30	.	.	PUNCT
ejpam-137	27	1	in	in	ADP
ejpam-137	27	2	this	this	DET
ejpam-137	27	3	paper	paper	NOUN
ejpam-137	27	4	,	,	PUNCT
ejpam-137	27	5	we	we	PRON
ejpam-137	27	6	continue	continue	VERB
ejpam-137	27	7	studying	study	VERB
ejpam-137	27	8	the	the	DET
ejpam-137	27	9	properties	property	NOUN
ejpam-137	27	10	of	of	ADP
ejpam-137	27	11	γ	γ	NOUN
ejpam-137	27	12	-	-	PUNCT
ejpam-137	27	13	semi	semi	ADV
ejpam-137	27	14	-	-	ADJ
ejpam-137	27	15	continuous	continuous	ADJ
ejpam-137	27	16	and	and	CCONJ
ejpam-137	27	17	γ	γ	NOUN
ejpam-137	27	18	-	-	PUNCT
ejpam-137	27	19	semi	semi	ADJ
ejpam-137	27	20	-	-	ADJ
ejpam-137	27	21	open	open	ADJ
ejpam-137	27	22	functions	function	NOUN
ejpam-137	27	23	introduced	introduce	VERB
ejpam-137	27	24	by	by	ADP
ejpam-137	27	25	b.	b.	PROPN
ejpam-137	27	26	ahmad	ahmad	PROPN
ejpam-137	27	27	and	and	CCONJ
ejpam-137	27	28	s.	s.	PROPN
ejpam-137	27	29	hussain	hussain	PROPN
ejpam-137	28	1	[	[	X
ejpam-137	28	2	5	5	NUM
ejpam-137	28	3	]	]	PUNCT
ejpam-137	28	4	,	,	PUNCT
ejpam-137	28	5	[	[	X
ejpam-137	28	6	10	10	NUM
ejpam-137	28	7	]	]	PUNCT
ejpam-137	28	8	.	.	PUNCT
ejpam-137	29	1	we	we	PRON
ejpam-137	29	2	also	also	ADV
ejpam-137	29	3	introduce	introduce	VERB
ejpam-137	29	4	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	29	5	∗corresponding	∗corresponding	NOUN
ejpam-137	29	6	author	author	NOUN
ejpam-137	29	7	.	.	PUNCT
ejpam-137	30	1	email	email	NOUN
ejpam-137	30	2	addresses	address	NOUN
ejpam-137	30	3	:	:	PUNCT
ejpam-137	30	4	drbashir9@gmail.com	drbashir9@gmail.com	X
ejpam-137	30	5	(	(	PUNCT
ejpam-137	30	6	b.	b.	PROPN
ejpam-137	30	7	ahmad	ahmad	PROPN
ejpam-137	30	8	)	)	PUNCT
ejpam-137	30	9	sabiriub@yahoo.com	sabiriub@yahoo.com	PROPN
ejpam-137	31	1	(	(	PUNCT
ejpam-137	31	2	s.	s.	PROPN
ejpam-137	31	3	hussain	hussain	PROPN
ejpam-137	31	4	)	)	PUNCT
ejpam-137	31	5	,	,	PUNCT
ejpam-137	31	6	jt.noiri@nifty.com	jt.noiri@nifty.com	NOUN
ejpam-137	31	7	(	(	PUNCT
ejpam-137	31	8	t.	t.	PROPN
ejpam-137	31	9	noiri	noiri	PROPN
ejpam-137	31	10	)	)	PUNCT
ejpam-137	31	11	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-137	32	1	22	22	NUM
ejpam-137	32	2	c	c	X
ejpam-137	32	3	©	©	NOUN
ejpam-137	32	4	2008	2008	NUM
ejpam-137	32	5	ejpam	ejpam	VERB
ejpam-137	32	6	all	all	DET
ejpam-137	32	7	rights	right	NOUN
ejpam-137	32	8	reserved	reserve	VERB
ejpam-137	32	9	.	.	PUNCT
ejpam-137	33	1	b.	b.	PROPN
ejpam-137	33	2	ahmad	ahmad	PROPN
ejpam-137	33	3	,	,	PUNCT
ejpam-137	33	4	s.	s.	PROPN
ejpam-137	33	5	hussain	hussain	PROPN
ejpam-137	33	6	,	,	PUNCT
ejpam-137	33	7	and	and	CCONJ
ejpam-137	33	8	t.	t.	PROPN
ejpam-137	33	9	noiri	noiri	PROPN
ejpam-137	33	10	/	/	SYM
ejpam-137	33	11	eur	eur	PROPN
ejpam-137	33	12	.	.	PUNCT
ejpam-137	34	1	j.	j.	PROPN
ejpam-137	34	2	pure	pure	PROPN
ejpam-137	34	3	appl	appl	PROPN
ejpam-137	34	4	.	.	PROPN
ejpam-137	34	5	math	math	PROPN
ejpam-137	34	6	,	,	PUNCT
ejpam-137	34	7	1	1	NUM
ejpam-137	34	8	(	(	PUNCT
ejpam-137	34	9	2008	2008	NUM
ejpam-137	34	10	)	)	PUNCT
ejpam-137	34	11	,	,	PUNCT
ejpam-137	34	12	(	(	PUNCT
ejpam-137	34	13	22	22	NUM
ejpam-137	34	14	-	-	SYM
ejpam-137	34	15	29	29	NUM
ejpam-137	34	16	)	)	PUNCT
ejpam-137	34	17	23	23	NUM
ejpam-137	34	18	functions	function	NOUN
ejpam-137	34	19	and	and	CCONJ
ejpam-137	34	20	γ	γ	NOUN
ejpam-137	34	21	-	-	PUNCT
ejpam-137	34	22	pre	pre	ADJ
ejpam-137	34	23	-	-	ADJ
ejpam-137	34	24	semi	semi	ADJ
ejpam-137	34	25	-	-	ADJ
ejpam-137	34	26	open	open	ADJ
ejpam-137	34	27	(	(	PUNCT
ejpam-137	34	28	closed	closed	ADJ
ejpam-137	34	29	)	)	PUNCT
ejpam-137	34	30	functions	function	NOUN
ejpam-137	34	31	and	and	CCONJ
ejpam-137	34	32	discuss	discuss	VERB
ejpam-137	34	33	their	their	PRON
ejpam-137	34	34	properties	property	NOUN
ejpam-137	34	35	.	.	PUNCT
ejpam-137	35	1	hereafter	hereafter	ADV
ejpam-137	35	2	,	,	PUNCT
ejpam-137	35	3	we	we	PRON
ejpam-137	35	4	shall	shall	AUX
ejpam-137	35	5	write	write	VERB
ejpam-137	35	6	spaces	space	NOUN
ejpam-137	35	7	in	in	ADP
ejpam-137	35	8	place	place	NOUN
ejpam-137	35	9	of	of	ADP
ejpam-137	35	10	topological	topological	ADJ
ejpam-137	35	11	spaces	space	NOUN
ejpam-137	35	12	in	in	ADP
ejpam-137	35	13	the	the	DET
ejpam-137	35	14	sequel	sequel	NOUN
ejpam-137	35	15	.	.	PUNCT
ejpam-137	36	1	2	2	X
ejpam-137	36	2	.	.	X
ejpam-137	36	3	preliminaries	preliminary	NOUN
ejpam-137	36	4	we	we	PRON
ejpam-137	36	5	recall	recall	VERB
ejpam-137	36	6	some	some	DET
ejpam-137	36	7	definitions	definition	NOUN
ejpam-137	36	8	and	and	CCONJ
ejpam-137	36	9	results	result	NOUN
ejpam-137	36	10	used	use	VERB
ejpam-137	36	11	in	in	ADP
ejpam-137	36	12	this	this	DET
ejpam-137	36	13	paper	paper	NOUN
ejpam-137	36	14	to	to	PART
ejpam-137	36	15	make	make	VERB
ejpam-137	36	16	it	it	PRON
ejpam-137	36	17	self	self	NOUN
ejpam-137	36	18	-	-	PUNCT
ejpam-137	36	19	contained	contain	VERB
ejpam-137	36	20	.	.	PUNCT
ejpam-137	37	1	definition	definition	NOUN
ejpam-137	37	2	[	[	X
ejpam-137	37	3	11	11	NUM
ejpam-137	37	4	]	]	PUNCT
ejpam-137	37	5	.	.	PUNCT
ejpam-137	38	1	let	let	VERB
ejpam-137	38	2	(	(	PUNCT
ejpam-137	38	3	x	x	X
ejpam-137	38	4	,	,	PUNCT
ejpam-137	38	5	τ	τ	X
ejpam-137	38	6	)	)	PUNCT
ejpam-137	38	7	be	be	AUX
ejpam-137	38	8	a	a	DET
ejpam-137	38	9	space	space	NOUN
ejpam-137	38	10	.	.	PUNCT
ejpam-137	39	1	an	an	DET
ejpam-137	39	2	operation	operation	NOUN
ejpam-137	39	3	γ	γ	X
ejpam-137	39	4	:	:	PUNCT
ejpam-137	39	5	τ→	τ→	PUNCT
ejpam-137	39	6	p(x	p(x	PROPN
ejpam-137	39	7	)	)	PUNCT
ejpam-137	39	8	is	be	AUX
ejpam-137	39	9	a	a	DET
ejpam-137	39	10	function	function	NOUN
ejpam-137	39	11	from	from	ADP
ejpam-137	39	12	τ	τ	PROPN
ejpam-137	39	13	to	to	ADP
ejpam-137	39	14	the	the	DET
ejpam-137	39	15	power	power	NOUN
ejpam-137	39	16	set	set	NOUN
ejpam-137	39	17	of	of	ADP
ejpam-137	39	18	x	x	PUNCT
ejpam-137	39	19	such	such	ADJ
ejpam-137	39	20	that	that	PRON
ejpam-137	39	21	v	v	ADP
ejpam-137	39	22	⊆	⊆	NUM
ejpam-137	39	23	v	v	ADP
ejpam-137	39	24	γ	γ	X
ejpam-137	39	25	,	,	PUNCT
ejpam-137	39	26	for	for	ADP
ejpam-137	39	27	each	each	DET
ejpam-137	39	28	v	v	NOUN
ejpam-137	39	29	∈	∈	PROPN
ejpam-137	39	30	τ	τ	NOUN
ejpam-137	39	31	,	,	PUNCT
ejpam-137	39	32	where	where	SCONJ
ejpam-137	39	33	v	v	NOUN
ejpam-137	39	34	γ	γ	PROPN
ejpam-137	39	35	denotes	denote	VERB
ejpam-137	39	36	the	the	DET
ejpam-137	39	37	value	value	NOUN
ejpam-137	39	38	of	of	ADP
ejpam-137	39	39	γ	γ	NOUN
ejpam-137	39	40	at	at	ADP
ejpam-137	39	41	v.	v.	ADP
ejpam-137	39	42	the	the	DET
ejpam-137	39	43	operations	operation	NOUN
ejpam-137	39	44	defined	define	VERB
ejpam-137	39	45	by	by	ADP
ejpam-137	39	46	γ(g	γ(g	PROPN
ejpam-137	39	47	)	)	PUNCT
ejpam-137	39	48	=	=	SYM
ejpam-137	39	49	g	g	PROPN
ejpam-137	39	50	,	,	PUNCT
ejpam-137	39	51	γ(g	γ(g	PROPN
ejpam-137	39	52	)	)	PUNCT
ejpam-137	39	53	=	=	SYM
ejpam-137	39	54	cl(g	cl(g	X
ejpam-137	39	55	)	)	PUNCT
ejpam-137	39	56	and	and	CCONJ
ejpam-137	39	57	γ(g	γ(g	PROPN
ejpam-137	39	58	)	)	PUNCT
ejpam-137	40	1	=	=	SYM
ejpam-137	40	2	intcl(g	intcl(g	NOUN
ejpam-137	40	3	)	)	PUNCT
ejpam-137	40	4	are	be	AUX
ejpam-137	40	5	examples	example	NOUN
ejpam-137	40	6	of	of	ADP
ejpam-137	40	7	operation	operation	NOUN
ejpam-137	40	8	γ	γ	PROPN
ejpam-137	40	9	.	.	PROPN
ejpam-137	40	10	definition	definition	NOUN
ejpam-137	40	11	[	[	X
ejpam-137	40	12	14	14	NUM
ejpam-137	40	13	]	]	PUNCT
ejpam-137	40	14	.	.	PUNCT
ejpam-137	41	1	let	let	VERB
ejpam-137	41	2	a⊆	a⊆	VERB
ejpam-137	41	3	x.	x.	NOUN
ejpam-137	41	4	a	a	DET
ejpam-137	41	5	point	point	NOUN
ejpam-137	41	6	x∈	x∈	NOUN
ejpam-137	42	1	a	a	PRON
ejpam-137	42	2	is	be	AUX
ejpam-137	42	3	said	say	VERB
ejpam-137	42	4	to	to	PART
ejpam-137	42	5	be	be	AUX
ejpam-137	42	6	γ	γ	ADJ
ejpam-137	42	7	-	-	ADJ
ejpam-137	42	8	interior	interior	ADJ
ejpam-137	42	9	point	point	NOUN
ejpam-137	42	10	of	of	ADP
ejpam-137	42	11	a	a	DET
ejpam-137	42	12	iff	iff	NOUN
ejpam-137	42	13	there	there	PRON
ejpam-137	42	14	exists	exist	VERB
ejpam-137	42	15	an	an	DET
ejpam-137	42	16	open	open	ADJ
ejpam-137	42	17	nbd	nbd	PROPN
ejpam-137	42	18	n	n	PROPN
ejpam-137	42	19	of	of	ADP
ejpam-137	42	20	x	x	PUNCT
ejpam-137	42	21	such	such	ADJ
ejpam-137	42	22	that	that	DET
ejpam-137	42	23	nγ	nγ	NOUN
ejpam-137	42	24	⊆	⊆	NUM
ejpam-137	42	25	a	a	PRON
ejpam-137	43	1	and	and	CCONJ
ejpam-137	43	2	we	we	PRON
ejpam-137	43	3	denote	denote	VERB
ejpam-137	43	4	the	the	DET
ejpam-137	43	5	set	set	NOUN
ejpam-137	43	6	of	of	ADP
ejpam-137	43	7	all	all	DET
ejpam-137	43	8	such	such	ADJ
ejpam-137	43	9	points	point	NOUN
ejpam-137	43	10	by	by	ADP
ejpam-137	43	11	intγ(a	intγ(a	NOUN
ejpam-137	43	12	)	)	PUNCT
ejpam-137	43	13	.	.	PUNCT
ejpam-137	44	1	thus	thus	ADV
ejpam-137	44	2	intγ	intγ	ADJ
ejpam-137	44	3	(	(	PUNCT
ejpam-137	44	4	a	a	X
ejpam-137	44	5	)	)	PUNCT
ejpam-137	44	6	=	=	SYM
ejpam-137	44	7	{	{	PUNCT
ejpam-137	44	8	x	x	PUNCT
ejpam-137	44	9	∈	∈	PROPN
ejpam-137	44	10	a	a	DET
ejpam-137	44	11	:	:	PUNCT
ejpam-137	44	12	x	x	SYM
ejpam-137	44	13	∈	∈	PROPN
ejpam-137	44	14	n	n	PRON
ejpam-137	44	15	∈	∈	NOUN
ejpam-137	44	16	τ	τ	X
ejpam-137	44	17	and	and	CCONJ
ejpam-137	44	18	nγ	nγ	VERB
ejpam-137	44	19	⊆	⊆	NUM
ejpam-137	44	20	a	a	DET
ejpam-137	44	21	}	}	PUNCT
ejpam-137	44	22	⊆	⊆	NUM
ejpam-137	44	23	a.	a.	NOUN
ejpam-137	44	24	note	note	NOUN
ejpam-137	44	25	that	that	SCONJ
ejpam-137	44	26	a	a	PRON
ejpam-137	44	27	is	be	AUX
ejpam-137	44	28	γ	γ	X
ejpam-137	44	29	-	-	ADJ
ejpam-137	44	30	open	open	ADJ
ejpam-137	44	31	[	[	X
ejpam-137	44	32	14	14	NUM
ejpam-137	44	33	]	]	X
ejpam-137	44	34	iff	iff	VERB
ejpam-137	44	35	a	a	DET
ejpam-137	44	36	=	=	NOUN
ejpam-137	44	37	intγ(a	intγ(a	NOUN
ejpam-137	44	38	)	)	PUNCT
ejpam-137	44	39	.	.	PUNCT
ejpam-137	45	1	a	a	DET
ejpam-137	45	2	set	set	NOUN
ejpam-137	45	3	a	a	PRON
ejpam-137	45	4	is	be	AUX
ejpam-137	45	5	called	call	VERB
ejpam-137	45	6	γclosed	γclose	VERB
ejpam-137	45	7	[	[	X
ejpam-137	45	8	14	14	NUM
ejpam-137	45	9	]	]	X
ejpam-137	45	10	iff	iff	PROPN
ejpam-137	45	11	x	x	PUNCT
ejpam-137	45	12	-	-	PUNCT
ejpam-137	45	13	a	a	PRON
ejpam-137	45	14	is	be	AUX
ejpam-137	45	15	γ	γ	X
ejpam-137	45	16	-	-	ADJ
ejpam-137	45	17	open	open	ADJ
ejpam-137	45	18	.	.	PUNCT
ejpam-137	46	1	definition	definition	NOUN
ejpam-137	46	2	[	[	X
ejpam-137	46	3	14	14	NUM
ejpam-137	46	4	]	]	PUNCT
ejpam-137	46	5	.	.	PUNCT
ejpam-137	47	1	a	a	DET
ejpam-137	47	2	point	point	NOUN
ejpam-137	47	3	x∈	x∈	NOUN
ejpam-137	47	4	x	x	VERB
ejpam-137	47	5	is	be	AUX
ejpam-137	47	6	called	call	VERB
ejpam-137	47	7	a	a	DET
ejpam-137	47	8	γ	γ	NOUN
ejpam-137	47	9	-	-	PUNCT
ejpam-137	47	10	closure	closure	NOUN
ejpam-137	47	11	point	point	NOUN
ejpam-137	47	12	of	of	ADP
ejpam-137	47	13	a⊆	a⊆	PROPN
ejpam-137	47	14	x	x	X
ejpam-137	47	15	,	,	PUNCT
ejpam-137	47	16	if	if	SCONJ
ejpam-137	47	17	uγ	uγ	ADP
ejpam-137	47	18	∩	∩	NOUN
ejpam-137	47	19	a	a	DET
ejpam-137	47	20	6=	6=	NUM
ejpam-137	47	21	φ	φ	NUM
ejpam-137	47	22	,	,	PUNCT
ejpam-137	47	23	for	for	ADP
ejpam-137	47	24	each	each	DET
ejpam-137	47	25	open	open	ADJ
ejpam-137	47	26	nbd	nbd	PROPN
ejpam-137	47	27	u	u	PROPN
ejpam-137	47	28	of	of	ADP
ejpam-137	47	29	x.	x.	NOUN
ejpam-137	47	30	the	the	DET
ejpam-137	47	31	set	set	NOUN
ejpam-137	47	32	of	of	ADP
ejpam-137	47	33	all	all	DET
ejpam-137	47	34	γ	γ	NOUN
ejpam-137	47	35	-	-	PUNCT
ejpam-137	47	36	closure	closure	NOUN
ejpam-137	47	37	points	point	NOUN
ejpam-137	47	38	of	of	ADP
ejpam-137	47	39	a	a	PRON
ejpam-137	47	40	is	be	AUX
ejpam-137	47	41	called	call	VERB
ejpam-137	47	42	γ	γ	NOUN
ejpam-137	47	43	-	-	NOUN
ejpam-137	47	44	closure	closure	NOUN
ejpam-137	47	45	of	of	ADP
ejpam-137	47	46	a	a	PRON
ejpam-137	47	47	and	and	CCONJ
ejpam-137	47	48	is	be	AUX
ejpam-137	47	49	denoted	denote	VERB
ejpam-137	47	50	by	by	ADP
ejpam-137	47	51	clγ(a	clγ(a	PROPN
ejpam-137	47	52	)	)	PUNCT
ejpam-137	47	53	.	.	PUNCT
ejpam-137	48	1	a	a	DET
ejpam-137	48	2	subset	subset	NOUN
ejpam-137	48	3	a	a	PRON
ejpam-137	48	4	of	of	ADP
ejpam-137	48	5	x	x	PRON
ejpam-137	48	6	is	be	AUX
ejpam-137	48	7	called	call	VERB
ejpam-137	48	8	γ	γ	NOUN
ejpam-137	48	9	-	-	VERB
ejpam-137	48	10	closed	closed	ADJ
ejpam-137	48	11	,	,	PUNCT
ejpam-137	48	12	if	if	SCONJ
ejpam-137	48	13	clγ(a	clγ(a	PROPN
ejpam-137	48	14	)	)	PUNCT
ejpam-137	48	15	⊆a	⊆a	NOUN
ejpam-137	48	16	.	.	PUNCT
ejpam-137	49	1	note	note	VERB
ejpam-137	49	2	that	that	SCONJ
ejpam-137	49	3	clγ(a	clγ(a	PROPN
ejpam-137	49	4	)	)	PUNCT
ejpam-137	49	5	is	be	AUX
ejpam-137	49	6	contained	contain	VERB
ejpam-137	49	7	in	in	ADP
ejpam-137	49	8	every	every	DET
ejpam-137	49	9	γ	γ	PROPN
ejpam-137	49	10	-	-	ADJ
ejpam-137	49	11	closed	closed	ADJ
ejpam-137	49	12	superset	superset	NOUN
ejpam-137	49	13	of	of	ADP
ejpam-137	49	14	a.	a.	NOUN
ejpam-137	49	15	definition	definition	NOUN
ejpam-137	50	1	[	[	X
ejpam-137	50	2	14	14	NUM
ejpam-137	50	3	]	]	PUNCT
ejpam-137	50	4	.	.	PUNCT
ejpam-137	51	1	an	an	DET
ejpam-137	51	2	operation	operation	NOUN
ejpam-137	51	3	γ	γ	NOUN
ejpam-137	51	4	on	on	ADP
ejpam-137	51	5	τ	τ	PROPN
ejpam-137	51	6	is	be	AUX
ejpam-137	51	7	said	say	VERB
ejpam-137	51	8	be	be	AUX
ejpam-137	51	9	regular	regular	ADJ
ejpam-137	51	10	,	,	PUNCT
ejpam-137	51	11	if	if	SCONJ
ejpam-137	51	12	for	for	ADP
ejpam-137	51	13	any	any	DET
ejpam-137	51	14	open	open	ADJ
ejpam-137	51	15	nbds	nbds	NOUN
ejpam-137	51	16	u	u	NOUN
ejpam-137	51	17	,	,	PUNCT
ejpam-137	51	18	v	v	NOUN
ejpam-137	51	19	of	of	ADP
ejpam-137	51	20	x	x	PUNCT
ejpam-137	51	21	∈	∈	PROPN
ejpam-137	51	22	x	x	NOUN
ejpam-137	51	23	,	,	PUNCT
ejpam-137	51	24	there	there	PRON
ejpam-137	51	25	exists	exist	VERB
ejpam-137	51	26	an	an	DET
ejpam-137	51	27	open	open	ADJ
ejpam-137	51	28	nbd	nbd	PROPN
ejpam-137	51	29	w	w	PROPN
ejpam-137	51	30	of	of	ADP
ejpam-137	51	31	x	x	SYM
ejpam-137	52	1	such	such	ADJ
ejpam-137	52	2	that	that	SCONJ
ejpam-137	52	3	uγ	uγ	ADJ
ejpam-137	52	4	∩	∩	NOUN
ejpam-137	52	5	v	v	ADP
ejpam-137	52	6	γ	γ	NOUN
ejpam-137	52	7	⊇w	⊇w	ADP
ejpam-137	52	8	γ	γ	PROPN
ejpam-137	52	9	.	.	PUNCT
ejpam-137	52	10	definition	definition	NOUN
ejpam-137	52	11	[	[	X
ejpam-137	52	12	14	14	NUM
ejpam-137	52	13	]	]	PUNCT
ejpam-137	52	14	.	.	PUNCT
ejpam-137	53	1	an	an	DET
ejpam-137	53	2	operation	operation	NOUN
ejpam-137	53	3	γ	γ	NOUN
ejpam-137	53	4	on	on	ADP
ejpam-137	53	5	τ	τ	PROPN
ejpam-137	53	6	is	be	AUX
ejpam-137	53	7	said	say	VERB
ejpam-137	53	8	to	to	PART
ejpam-137	53	9	be	be	AUX
ejpam-137	53	10	open	open	ADJ
ejpam-137	53	11	,	,	PUNCT
ejpam-137	53	12	if	if	SCONJ
ejpam-137	53	13	for	for	ADP
ejpam-137	53	14	every	every	DET
ejpam-137	53	15	nbd	nbd	PROPN
ejpam-137	53	16	u	u	PROPN
ejpam-137	53	17	of	of	ADP
ejpam-137	53	18	each	each	DET
ejpam-137	53	19	x	x	SYM
ejpam-137	53	20	∈	∈	PROPN
ejpam-137	53	21	x	x	X
ejpam-137	53	22	,	,	PUNCT
ejpam-137	53	23	there	there	PRON
ejpam-137	53	24	exists	exist	VERB
ejpam-137	53	25	γ	γ	ADJ
ejpam-137	53	26	-	-	ADJ
ejpam-137	53	27	open	open	ADJ
ejpam-137	53	28	set	set	NOUN
ejpam-137	53	29	b	b	NOUN
ejpam-137	53	30	such	such	ADJ
ejpam-137	53	31	that	that	SCONJ
ejpam-137	53	32	x	x	SYM
ejpam-137	53	33	∈	∈	PROPN
ejpam-137	53	34	b	b	PROPN
ejpam-137	53	35	and	and	CCONJ
ejpam-137	53	36	uγ	uγ	PROPN
ejpam-137	53	37	⊇	⊇	PROPN
ejpam-137	53	38	b.	b.	PROPN
ejpam-137	54	1	we	we	PRON
ejpam-137	54	2	defined	define	VERB
ejpam-137	54	3	[	[	PUNCT
ejpam-137	54	4	9	9	NUM
ejpam-137	54	5	]	]	SYM
ejpam-137	54	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	54	7	-	-	ADJ
ejpam-137	54	8	open	open	ADJ
ejpam-137	54	9	sets	set	NOUN
ejpam-137	54	10	using	use	VERB
ejpam-137	54	11	γ	γ	ADJ
ejpam-137	54	12	-	-	ADJ
ejpam-137	54	13	open	open	ADJ
ejpam-137	54	14	sets	set	NOUN
ejpam-137	54	15	in	in	ADP
ejpam-137	54	16	the	the	DET
ejpam-137	54	17	sense	sense	NOUN
ejpam-137	54	18	of	of	ADP
ejpam-137	54	19	h.	h.	PROPN
ejpam-137	54	20	ogata	ogata	PROPN
ejpam-137	55	1	[	[	X
ejpam-137	55	2	14	14	NUM
ejpam-137	55	3	]	]	PUNCT
ejpam-137	55	4	as	as	ADP
ejpam-137	55	5	:	:	PUNCT
ejpam-137	55	6	definition	definition	NOUN
ejpam-137	55	7	[	[	X
ejpam-137	55	8	9	9	NUM
ejpam-137	55	9	]	]	PUNCT
ejpam-137	55	10	.	.	PUNCT
ejpam-137	56	1	a	a	DET
ejpam-137	56	2	subset	subset	NOUN
ejpam-137	56	3	a	a	PRON
ejpam-137	56	4	of	of	ADP
ejpam-137	56	5	a	a	DET
ejpam-137	56	6	space	space	NOUN
ejpam-137	56	7	(	(	PUNCT
ejpam-137	56	8	x	x	X
ejpam-137	56	9	,	,	PUNCT
ejpam-137	56	10	τ	τ	PROPN
ejpam-137	56	11	)	)	PUNCT
ejpam-137	56	12	is	be	AUX
ejpam-137	56	13	said	say	VERB
ejpam-137	56	14	to	to	PART
ejpam-137	56	15	be	be	AUX
ejpam-137	56	16	a	a	DET
ejpam-137	56	17	γ∗-semi	γ∗-semi	NOUN
ejpam-137	56	18	-	-	ADJ
ejpam-137	56	19	open	open	ADJ
ejpam-137	56	20	set	set	NOUN
ejpam-137	56	21	,	,	PUNCT
ejpam-137	56	22	if	if	SCONJ
ejpam-137	56	23	there	there	PRON
ejpam-137	56	24	exists	exist	VERB
ejpam-137	56	25	a	a	DET
ejpam-137	56	26	γ	γ	X
ejpam-137	56	27	-open	-open	NOUN
ejpam-137	56	28	set	set	NOUN
ejpam-137	56	29	o	o	NOUN
ejpam-137	56	30	such	such	ADJ
ejpam-137	56	31	that	that	SCONJ
ejpam-137	56	32	o	o	NOUN
ejpam-137	56	33	⊆	⊆	NUM
ejpam-137	56	34	a⊆	a⊆	NUM
ejpam-137	56	35	clγ(o	clγ(o	NOUN
ejpam-137	56	36	)	)	PUNCT
ejpam-137	56	37	.	.	PUNCT
ejpam-137	57	1	the	the	DET
ejpam-137	57	2	set	set	NOUN
ejpam-137	57	3	of	of	ADP
ejpam-137	57	4	all	all	DET
ejpam-137	57	5	γ∗-semi	γ∗-semi	NOUN
ejpam-137	57	6	-	-	ADJ
ejpam-137	57	7	open	open	ADJ
ejpam-137	57	8	sets	set	NOUN
ejpam-137	57	9	is	be	AUX
ejpam-137	57	10	denoted	denote	VERB
ejpam-137	57	11	by	by	ADP
ejpam-137	57	12	soγ∗(x	soγ∗(x	NOUN
ejpam-137	57	13	)	)	PUNCT
ejpam-137	57	14	.	.	PUNCT
ejpam-137	58	1	definition	definition	NOUN
ejpam-137	58	2	[	[	X
ejpam-137	58	3	5	5	NUM
ejpam-137	58	4	]	]	PUNCT
ejpam-137	58	5	.	.	PUNCT
ejpam-137	59	1	a	a	DET
ejpam-137	59	2	function	function	NOUN
ejpam-137	59	3	f	f	NOUN
ejpam-137	59	4	:	:	PUNCT
ejpam-137	59	5	(	(	PUNCT
ejpam-137	59	6	x	x	X
ejpam-137	59	7	,	,	PUNCT
ejpam-137	59	8	τ)→	τ)→	PROPN
ejpam-137	59	9	(	(	PUNCT
ejpam-137	59	10	y	y	PROPN
ejpam-137	59	11	,	,	PUNCT
ejpam-137	59	12	τ	τ	X
ejpam-137	59	13	)	)	PUNCT
ejpam-137	59	14	is	be	AUX
ejpam-137	59	15	said	say	VERB
ejpam-137	59	16	to	to	PART
ejpam-137	59	17	be	be	AUX
ejpam-137	59	18	γ	γ	X
ejpam-137	59	19	-	-	PUNCT
ejpam-137	59	20	semi	semi	ADV
ejpam-137	59	21	-	-	ADJ
ejpam-137	59	22	continuous	continuous	ADJ
ejpam-137	59	23	if	if	SCONJ
ejpam-137	59	24	for	for	ADP
ejpam-137	59	25	any	any	DET
ejpam-137	59	26	γ	γ	NOUN
ejpam-137	59	27	-	-	ADJ
ejpam-137	59	28	open	open	ADJ
ejpam-137	59	29	set	set	ADJ
ejpam-137	59	30	b	b	PROPN
ejpam-137	59	31	of	of	ADP
ejpam-137	59	32	y	y	PROPN
ejpam-137	59	33	,	,	PUNCT
ejpam-137	59	34	f	f	PROPN
ejpam-137	59	35	−1(b	−1(b	NOUN
ejpam-137	59	36	)	)	PUNCT
ejpam-137	59	37	is	be	AUX
ejpam-137	59	38	γ∗-semi	γ∗-semi	NOUN
ejpam-137	59	39	-	-	ADJ
ejpam-137	59	40	open	open	ADJ
ejpam-137	59	41	in	in	ADP
ejpam-137	59	42	x.	x.	NOUN
ejpam-137	59	43	definition	definition	NOUN
ejpam-137	60	1	[	[	X
ejpam-137	60	2	5	5	NUM
ejpam-137	60	3	]	]	PUNCT
ejpam-137	60	4	.	.	PUNCT
ejpam-137	61	1	a	a	DET
ejpam-137	61	2	function	function	NOUN
ejpam-137	61	3	f	f	NOUN
ejpam-137	61	4	:	:	PUNCT
ejpam-137	61	5	x	x	X
ejpam-137	61	6	→	→	SYM
ejpam-137	61	7	y	y	PROPN
ejpam-137	61	8	is	be	AUX
ejpam-137	61	9	said	say	VERB
ejpam-137	61	10	to	to	PART
ejpam-137	61	11	be	be	AUX
ejpam-137	61	12	γ	γ	X
ejpam-137	61	13	-	-	PUNCT
ejpam-137	61	14	semi	semi	ADV
ejpam-137	61	15	-	-	ADJ
ejpam-137	61	16	open	open	ADJ
ejpam-137	61	17	(	(	PUNCT
ejpam-137	61	18	closed	closed	ADJ
ejpam-137	61	19	)	)	PUNCT
ejpam-137	61	20	if	if	SCONJ
ejpam-137	61	21	for	for	ADP
ejpam-137	61	22	each	each	DET
ejpam-137	61	23	γ	γ	X
ejpam-137	61	24	-	-	ADJ
ejpam-137	61	25	open	open	ADJ
ejpam-137	61	26	(	(	PUNCT
ejpam-137	61	27	closed	closed	ADJ
ejpam-137	61	28	)	)	PUNCT
ejpam-137	61	29	set	set	VERB
ejpam-137	61	30	u	u	NOUN
ejpam-137	61	31	in	in	ADP
ejpam-137	61	32	x	x	PROPN
ejpam-137	61	33	,	,	PUNCT
ejpam-137	61	34	f	f	PROPN
ejpam-137	61	35	(	(	PUNCT
ejpam-137	61	36	u	u	NOUN
ejpam-137	61	37	)	)	PUNCT
ejpam-137	61	38	is	be	AUX
ejpam-137	61	39	γ∗-semi	γ∗-semi	NOUN
ejpam-137	61	40	-	-	ADJ
ejpam-137	61	41	open	open	ADJ
ejpam-137	61	42	(	(	PUNCT
ejpam-137	61	43	closed	closed	ADJ
ejpam-137	61	44	)	)	PUNCT
ejpam-137	61	45	in	in	ADP
ejpam-137	61	46	y.	y.	PROPN
ejpam-137	61	47	definition	definition	NOUN
ejpam-137	62	1	[	[	X
ejpam-137	62	2	5	5	NUM
ejpam-137	62	3	]	]	PUNCT
ejpam-137	62	4	.	.	PUNCT
ejpam-137	63	1	a	a	DET
ejpam-137	63	2	set	set	NOUN
ejpam-137	63	3	a	a	PRON
ejpam-137	63	4	in	in	ADP
ejpam-137	63	5	a	a	DET
ejpam-137	63	6	space	space	NOUN
ejpam-137	63	7	x	x	PUNCT
ejpam-137	63	8	is	be	AUX
ejpam-137	63	9	said	say	VERB
ejpam-137	63	10	to	to	PART
ejpam-137	63	11	be	be	AUX
ejpam-137	63	12	γ∗-semi	γ∗-semi	NOUN
ejpam-137	63	13	-	-	ADJ
ejpam-137	63	14	closed	closed	ADJ
ejpam-137	63	15	if	if	SCONJ
ejpam-137	63	16	there	there	PRON
ejpam-137	63	17	exists	exist	VERB
ejpam-137	63	18	a	a	DET
ejpam-137	63	19	γ	γ	X
ejpam-137	63	20	-	-	ADJ
ejpam-137	63	21	closed	closed	ADJ
ejpam-137	63	22	set	set	NOUN
ejpam-137	63	23	f	f	PROPN
ejpam-137	63	24	such	such	ADJ
ejpam-137	63	25	that	that	SCONJ
ejpam-137	63	26	intγ(f)⊆	intγ(f)⊆	ADP
ejpam-137	63	27	a⊆	a⊆	PROPN
ejpam-137	63	28	f	f	X
ejpam-137	63	29	.	.	PUNCT
ejpam-137	64	1	proposition	proposition	NOUN
ejpam-137	65	1	[	[	X
ejpam-137	65	2	5	5	NUM
ejpam-137	65	3	]	]	PUNCT
ejpam-137	65	4	.	.	PUNCT
ejpam-137	66	1	a	a	DET
ejpam-137	66	2	subset	subset	NOUN
ejpam-137	66	3	a	a	PRON
ejpam-137	66	4	of	of	ADP
ejpam-137	66	5	a	a	DET
ejpam-137	66	6	space	space	NOUN
ejpam-137	66	7	x	x	X
ejpam-137	66	8	is	be	AUX
ejpam-137	66	9	γ∗-semi	γ∗-semi	NOUN
ejpam-137	66	10	-	-	ADJ
ejpam-137	66	11	closed	closed	ADJ
ejpam-137	66	12	if	if	SCONJ
ejpam-137	66	13	x	x	ADP
ejpam-137	66	14	−	−	NOUN
ejpam-137	66	15	a	a	PRON
ejpam-137	66	16	is	be	AUX
ejpam-137	66	17	γ∗-semi	γ∗-semi	NOUN
ejpam-137	66	18	-	-	NOUN
ejpam-137	66	19	open	open	ADJ
ejpam-137	66	20	.	.	PUNCT
ejpam-137	67	1	definition	definition	NOUN
ejpam-137	67	2	[	[	X
ejpam-137	67	3	10	10	NUM
ejpam-137	67	4	]	]	PUNCT
ejpam-137	67	5	.	.	PUNCT
ejpam-137	68	1	a	a	DET
ejpam-137	68	2	subset	subset	NOUN
ejpam-137	68	3	a	a	PRON
ejpam-137	68	4	of	of	ADP
ejpam-137	68	5	a	a	DET
ejpam-137	68	6	space	space	NOUN
ejpam-137	68	7	x	x	PUNCT
ejpam-137	68	8	is	be	AUX
ejpam-137	68	9	said	say	VERB
ejpam-137	68	10	to	to	PART
ejpam-137	68	11	be	be	AUX
ejpam-137	68	12	γ	γ	X
ejpam-137	68	13	-	-	PUNCT
ejpam-137	68	14	semi	semi	NOUN
ejpam-137	68	15	-	-	NOUN
ejpam-137	68	16	nbd	nbd	NOUN
ejpam-137	68	17	of	of	ADP
ejpam-137	68	18	a	a	DET
ejpam-137	68	19	point	point	NOUN
ejpam-137	68	20	x	x	X
ejpam-137	68	21	∈	∈	NOUN
ejpam-137	68	22	x	x	INTJ
ejpam-137	68	23	if	if	SCONJ
ejpam-137	68	24	there	there	PRON
ejpam-137	68	25	exists	exist	VERB
ejpam-137	68	26	a	a	DET
ejpam-137	68	27	γ∗-semi	γ∗-semi	NOUN
ejpam-137	68	28	-	-	ADJ
ejpam-137	68	29	open	open	ADJ
ejpam-137	68	30	set	set	NOUN
ejpam-137	68	31	u	u	PRON
ejpam-137	68	32	such	such	ADJ
ejpam-137	68	33	that	that	SCONJ
ejpam-137	68	34	x	x	SYM
ejpam-137	68	35	∈	∈	NOUN
ejpam-137	68	36	u	u	NOUN
ejpam-137	69	1	⊆	⊆	NUM
ejpam-137	69	2	a.	a.	NOUN
ejpam-137	69	3	3	3	NUM
ejpam-137	69	4	.	.	PUNCT
ejpam-137	70	1	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	70	2	functions	function	NOUN
ejpam-137	70	3	definition	definition	NOUN
ejpam-137	70	4	3.1	3.1	NUM
ejpam-137	70	5	.	.	PUNCT
ejpam-137	71	1	let	let	VERB
ejpam-137	71	2	x	x	PRON
ejpam-137	71	3	and	and	CCONJ
ejpam-137	71	4	y	y	PROPN
ejpam-137	71	5	be	be	AUX
ejpam-137	71	6	spaces	space	NOUN
ejpam-137	71	7	.	.	PUNCT
ejpam-137	72	1	a	a	DET
ejpam-137	72	2	function	function	NOUN
ejpam-137	72	3	f	f	NOUN
ejpam-137	72	4	:	:	PUNCT
ejpam-137	72	5	x	x	X
ejpam-137	72	6	→	→	SYM
ejpam-137	72	7	y	y	PROPN
ejpam-137	72	8	is	be	AUX
ejpam-137	72	9	said	say	VERB
ejpam-137	72	10	to	to	PART
ejpam-137	72	11	be	be	AUX
ejpam-137	72	12	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	72	13	if	if	SCONJ
ejpam-137	73	1	and	and	CCONJ
ejpam-137	73	2	only	only	ADV
ejpam-137	73	3	if	if	SCONJ
ejpam-137	73	4	for	for	ADP
ejpam-137	73	5	any	any	DET
ejpam-137	73	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	73	7	-	-	ADJ
ejpam-137	73	8	open	open	ADJ
ejpam-137	73	9	subset	subset	NOUN
ejpam-137	73	10	s	s	PROPN
ejpam-137	73	11	of	of	ADP
ejpam-137	73	12	y	y	PROPN
ejpam-137	73	13	,	,	PUNCT
ejpam-137	73	14	f	f	PROPN
ejpam-137	73	15	−1(s	−1(	NOUN
ejpam-137	73	16	)	)	PUNCT
ejpam-137	73	17	is	be	AUX
ejpam-137	73	18	γ∗-semi	γ∗-semi	NOUN
ejpam-137	73	19	-	-	ADJ
ejpam-137	73	20	open	open	ADJ
ejpam-137	73	21	in	in	ADP
ejpam-137	73	22	x.	x.	PROPN
ejpam-137	73	23	b.	b.	PROPN
ejpam-137	73	24	ahmad	ahmad	PROPN
ejpam-137	73	25	,	,	PUNCT
ejpam-137	73	26	s.	s.	PROPN
ejpam-137	73	27	hussain	hussain	PROPN
ejpam-137	73	28	,	,	PUNCT
ejpam-137	73	29	and	and	CCONJ
ejpam-137	73	30	t.	t.	PROPN
ejpam-137	73	31	noiri	noiri	PROPN
ejpam-137	73	32	/	/	SYM
ejpam-137	73	33	eur	eur	PROPN
ejpam-137	73	34	.	.	PUNCT
ejpam-137	74	1	j.	j.	PROPN
ejpam-137	74	2	pure	pure	PROPN
ejpam-137	74	3	appl	appl	PROPN
ejpam-137	74	4	.	.	PROPN
ejpam-137	74	5	math	math	PROPN
ejpam-137	74	6	,	,	PUNCT
ejpam-137	74	7	1	1	NUM
ejpam-137	74	8	(	(	PUNCT
ejpam-137	74	9	2008	2008	NUM
ejpam-137	74	10	)	)	PUNCT
ejpam-137	74	11	,	,	PUNCT
ejpam-137	74	12	(	(	PUNCT
ejpam-137	74	13	22	22	NUM
ejpam-137	74	14	-	-	SYM
ejpam-137	74	15	29	29	NUM
ejpam-137	74	16	)	)	PUNCT
ejpam-137	74	17	24	24	NUM
ejpam-137	74	18	definition	definition	NOUN
ejpam-137	74	19	3.2[5	3.2[5	NUM
ejpam-137	74	20	]	]	PUNCT
ejpam-137	74	21	.	.	PUNCT
ejpam-137	75	1	an	an	DET
ejpam-137	75	2	operation	operation	NOUN
ejpam-137	75	3	γ	γ	NOUN
ejpam-137	75	4	is	be	AUX
ejpam-137	75	5	said	say	VERB
ejpam-137	75	6	to	to	PART
ejpam-137	75	7	be	be	AUX
ejpam-137	75	8	semi	semi	ADJ
ejpam-137	75	9	-	-	ADJ
ejpam-137	75	10	regular	regular	ADJ
ejpam-137	75	11	,	,	PUNCT
ejpam-137	75	12	if	if	SCONJ
ejpam-137	75	13	for	for	ADP
ejpam-137	75	14	any	any	DET
ejpam-137	75	15	semi	semi	ADJ
ejpam-137	75	16	-	-	ADJ
ejpam-137	75	17	open	open	ADJ
ejpam-137	75	18	sets	set	NOUN
ejpam-137	75	19	u	u	NOUN
ejpam-137	75	20	and	and	CCONJ
ejpam-137	75	21	v	v	NOUN
ejpam-137	75	22	containing	contain	VERB
ejpam-137	75	23	x	x	PUNCT
ejpam-137	75	24	∈	∈	PROPN
ejpam-137	75	25	x	x	NOUN
ejpam-137	75	26	,	,	PUNCT
ejpam-137	75	27	there	there	PRON
ejpam-137	75	28	exists	exist	VERB
ejpam-137	75	29	a	a	DET
ejpam-137	75	30	semi	semi	ADJ
ejpam-137	75	31	-	-	ADJ
ejpam-137	75	32	open	open	ADJ
ejpam-137	75	33	set	set	NOUN
ejpam-137	75	34	w	w	NOUN
ejpam-137	75	35	containing	contain	VERB
ejpam-137	75	36	x	x	PUNCT
ejpam-137	75	37	such	such	ADJ
ejpam-137	75	38	that	that	SCONJ
ejpam-137	75	39	uγ	uγ	ADJ
ejpam-137	75	40	∩	∩	NOUN
ejpam-137	75	41	v	v	ADP
ejpam-137	75	42	γ	γ	NOUN
ejpam-137	75	43	⊇w	⊇w	ADP
ejpam-137	75	44	γ	γ	PROPN
ejpam-137	75	45	.	.	PUNCT
ejpam-137	75	46	theorem	theorem	VERB
ejpam-137	75	47	3.3	3.3	NUM
ejpam-137	75	48	.	.	PUNCT
ejpam-137	76	1	a	a	DET
ejpam-137	76	2	function	function	NOUN
ejpam-137	76	3	f	f	NOUN
ejpam-137	76	4	:	:	PUNCT
ejpam-137	76	5	x	x	X
ejpam-137	76	6	→	→	SYM
ejpam-137	76	7	y	y	PROPN
ejpam-137	76	8	is	be	AUX
ejpam-137	76	9	γ∗-irresolute	γ∗-irresolute	ADJ
ejpam-137	76	10	if	if	SCONJ
ejpam-137	77	1	and	and	CCONJ
ejpam-137	77	2	only	only	ADV
ejpam-137	77	3	if	if	SCONJ
ejpam-137	77	4	for	for	ADP
ejpam-137	77	5	each	each	DET
ejpam-137	77	6	x	x	PUNCT
ejpam-137	77	7	in	in	ADP
ejpam-137	77	8	x	x	PRON
ejpam-137	77	9	,	,	PUNCT
ejpam-137	77	10	the	the	DET
ejpam-137	77	11	inverse	inverse	NOUN
ejpam-137	77	12	of	of	ADP
ejpam-137	77	13	every	every	DET
ejpam-137	77	14	γ	γ	PROPN
ejpam-137	77	15	-	-	PUNCT
ejpam-137	77	16	semi	semi	NOUN
ejpam-137	77	17	-	-	NOUN
ejpam-137	77	18	nbd	nbd	PROPN
ejpam-137	77	19	of	of	ADP
ejpam-137	77	20	f	f	PROPN
ejpam-137	77	21	(	(	PUNCT
ejpam-137	77	22	x	x	X
ejpam-137	77	23	)	)	PUNCT
ejpam-137	77	24	is	be	AUX
ejpam-137	77	25	a	a	DET
ejpam-137	77	26	γ	γ	NOUN
ejpam-137	77	27	-	-	PUNCT
ejpam-137	77	28	semi	semi	NOUN
ejpam-137	77	29	-	-	NOUN
ejpam-137	77	30	nbd	nbd	NOUN
ejpam-137	77	31	of	of	ADP
ejpam-137	77	32	x	x	PRON
ejpam-137	77	33	,	,	PUNCT
ejpam-137	77	34	where	where	SCONJ
ejpam-137	77	35	γ	γ	PROPN
ejpam-137	77	36	is	be	AUX
ejpam-137	77	37	a	a	DET
ejpam-137	77	38	semi	semi	ADJ
ejpam-137	77	39	regular	regular	ADJ
ejpam-137	77	40	operation	operation	NOUN
ejpam-137	77	41	.	.	PUNCT
ejpam-137	78	1	proof	proof	NOUN
ejpam-137	78	2	.	.	PUNCT
ejpam-137	79	1	let	let	VERB
ejpam-137	79	2	x	x	PUNCT
ejpam-137	79	3	∈	∈	PROPN
ejpam-137	79	4	x	x	X
ejpam-137	79	5	and	and	CCONJ
ejpam-137	79	6	a	a	DET
ejpam-137	79	7	a	a	DET
ejpam-137	79	8	γ	γ	X
ejpam-137	79	9	-	-	PUNCT
ejpam-137	79	10	semi	semi	NOUN
ejpam-137	79	11	-	-	NOUN
ejpam-137	79	12	nbd	nbd	PROPN
ejpam-137	79	13	of	of	ADP
ejpam-137	79	14	f	f	PROPN
ejpam-137	79	15	(	(	PUNCT
ejpam-137	79	16	x	x	NOUN
ejpam-137	79	17	)	)	PUNCT
ejpam-137	79	18	.	.	PUNCT
ejpam-137	80	1	by	by	ADP
ejpam-137	80	2	definition	definition	NOUN
ejpam-137	80	3	of	of	ADP
ejpam-137	80	4	γ	γ	X
ejpam-137	80	5	-	-	PUNCT
ejpam-137	80	6	semi	semi	NOUN
ejpam-137	80	7	-	-	NOUN
ejpam-137	80	8	nbd	nbd	PROPN
ejpam-137	80	9	,	,	PUNCT
ejpam-137	80	10	there	there	PRON
ejpam-137	80	11	exists	exist	VERB
ejpam-137	80	12	v	v	ADP
ejpam-137	80	13	∈	∈	PROPN
ejpam-137	80	14	soγ∗(y	soγ∗(y	PROPN
ejpam-137	80	15	)	)	PUNCT
ejpam-137	80	16	such	such	ADJ
ejpam-137	80	17	that	that	SCONJ
ejpam-137	80	18	f	f	PROPN
ejpam-137	80	19	(	(	PUNCT
ejpam-137	80	20	x	x	X
ejpam-137	80	21	)	)	PUNCT
ejpam-137	80	22	∈	∈	NOUN
ejpam-137	80	23	v	v	ADP
ejpam-137	80	24	⊆	⊆	NUM
ejpam-137	80	25	a.	a.	NOUN
ejpam-137	80	26	this	this	PRON
ejpam-137	80	27	implies	imply	VERB
ejpam-137	80	28	that	that	SCONJ
ejpam-137	81	1	x	x	SYM
ejpam-137	81	2	∈	∈	PROPN
ejpam-137	81	3	f	f	X
ejpam-137	81	4	−1(v	−1(v	NOUN
ejpam-137	81	5	)	)	PUNCT
ejpam-137	81	6	⊆	⊆	NUM
ejpam-137	81	7	f	f	X
ejpam-137	81	8	−1(a	−1(a	ADP
ejpam-137	81	9	)	)	PUNCT
ejpam-137	81	10	.	.	PUNCT
ejpam-137	82	1	since	since	SCONJ
ejpam-137	82	2	f	f	PROPN
ejpam-137	82	3	is	be	AUX
ejpam-137	82	4	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	82	5	,	,	PUNCT
ejpam-137	82	6	so	so	SCONJ
ejpam-137	82	7	f	f	PROPN
ejpam-137	82	8	−1(v	−1(v	PROPN
ejpam-137	82	9	)	)	PUNCT
ejpam-137	82	10	∈	∈	PROPN
ejpam-137	82	11	soγ∗(x	soγ∗(x	NOUN
ejpam-137	82	12	)	)	PUNCT
ejpam-137	82	13	.	.	PUNCT
ejpam-137	83	1	hence	hence	ADV
ejpam-137	83	2	f	f	PROPN
ejpam-137	83	3	−1(a	−1(a	CCONJ
ejpam-137	83	4	)	)	PUNCT
ejpam-137	83	5	is	be	AUX
ejpam-137	83	6	a	a	DET
ejpam-137	83	7	γ	γ	NOUN
ejpam-137	83	8	-	-	PUNCT
ejpam-137	83	9	semi	semi	NOUN
ejpam-137	83	10	-	-	NOUN
ejpam-137	83	11	nbd	nbd	NOUN
ejpam-137	83	12	of	of	ADP
ejpam-137	83	13	x.	x.	PROPN
ejpam-137	83	14	this	this	PRON
ejpam-137	83	15	proves	prove	VERB
ejpam-137	83	16	the	the	DET
ejpam-137	83	17	necessity	necessity	NOUN
ejpam-137	83	18	.	.	PUNCT
ejpam-137	84	1	conversely	conversely	ADV
ejpam-137	84	2	,	,	PUNCT
ejpam-137	84	3	let	let	VERB
ejpam-137	84	4	a∈	a∈	PROPN
ejpam-137	84	5	soγ∗(y	soγ∗(y	PROPN
ejpam-137	84	6	)	)	PUNCT
ejpam-137	84	7	.	.	PUNCT
ejpam-137	85	1	put	put	VERB
ejpam-137	85	2	b	b	NOUN
ejpam-137	85	3	=	=	X
ejpam-137	85	4	f	f	PROPN
ejpam-137	85	5	−1(a	−1(a	ADP
ejpam-137	85	6	)	)	PUNCT
ejpam-137	85	7	.	.	PUNCT
ejpam-137	86	1	let	let	VERB
ejpam-137	86	2	x	x	SYM
ejpam-137	86	3	∈	∈	PROPN
ejpam-137	86	4	b	b	PROPN
ejpam-137	86	5	,	,	PUNCT
ejpam-137	86	6	then	then	ADV
ejpam-137	86	7	f	f	PROPN
ejpam-137	86	8	(	(	PUNCT
ejpam-137	86	9	x	x	X
ejpam-137	86	10	)	)	PUNCT
ejpam-137	86	11	∈	∈	PROPN
ejpam-137	86	12	a	a	PRON
ejpam-137	86	13	.	.	PUNCT
ejpam-137	87	1	clearly	clearly	ADV
ejpam-137	87	2	,	,	PUNCT
ejpam-137	87	3	a	a	DET
ejpam-137	87	4	(	(	PUNCT
ejpam-137	87	5	being	be	AUX
ejpam-137	87	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	87	7	-	-	NOUN
ejpam-137	87	8	open	open	ADJ
ejpam-137	87	9	)	)	PUNCT
ejpam-137	87	10	is	be	AUX
ejpam-137	87	11	a	a	DET
ejpam-137	87	12	γ	γ	NOUN
ejpam-137	87	13	-	-	PUNCT
ejpam-137	87	14	semi	semi	NOUN
ejpam-137	87	15	-	-	NOUN
ejpam-137	87	16	nbd	nbd	PROPN
ejpam-137	87	17	of	of	ADP
ejpam-137	87	18	f	f	PROPN
ejpam-137	87	19	(	(	PUNCT
ejpam-137	87	20	x	x	NOUN
ejpam-137	87	21	)	)	PUNCT
ejpam-137	87	22	.	.	PUNCT
ejpam-137	88	1	so	so	ADV
ejpam-137	88	2	by	by	ADP
ejpam-137	88	3	hypothesis	hypothesis	NOUN
ejpam-137	88	4	,	,	PUNCT
ejpam-137	88	5	b	b	X
ejpam-137	88	6	=	=	SYM
ejpam-137	88	7	f	f	PROPN
ejpam-137	88	8	−1(a	−1(a	CCONJ
ejpam-137	88	9	)	)	PUNCT
ejpam-137	88	10	is	be	AUX
ejpam-137	88	11	a	a	DET
ejpam-137	88	12	γ	γ	NOUN
ejpam-137	88	13	-	-	PUNCT
ejpam-137	88	14	seminbd	seminbd	NOUN
ejpam-137	88	15	of	of	ADP
ejpam-137	88	16	x.	x.	NOUN
ejpam-137	88	17	hence	hence	ADV
ejpam-137	88	18	by	by	ADP
ejpam-137	88	19	definition	definition	NOUN
ejpam-137	88	20	,	,	PUNCT
ejpam-137	88	21	there	there	PRON
ejpam-137	88	22	exists	exist	VERB
ejpam-137	88	23	bx	bx	PROPN
ejpam-137	88	24	∈	∈	PROPN
ejpam-137	88	25	soγ∗(x	soγ∗(x	NOUN
ejpam-137	88	26	)	)	PUNCT
ejpam-137	88	27	such	such	ADJ
ejpam-137	88	28	that	that	SCONJ
ejpam-137	88	29	x	x	SYM
ejpam-137	88	30	∈	∈	NOUN
ejpam-137	88	31	bx	bx	VERB
ejpam-137	88	32	⊆	⊆	NUM
ejpam-137	88	33	b	b	NOUN
ejpam-137	88	34	.	.	PUNCT
ejpam-137	89	1	thus	thus	ADV
ejpam-137	89	2	b	b	X
ejpam-137	89	3	=	=	PUNCT
ejpam-137	89	4	⋃	⋃	PROPN
ejpam-137	89	5	x∈b	x∈b	NOUN
ejpam-137	89	6	bx	bx	PROPN
ejpam-137	89	7	.	.	PUNCT
ejpam-137	90	1	since	since	SCONJ
ejpam-137	90	2	γ	γ	PROPN
ejpam-137	90	3	is	be	AUX
ejpam-137	90	4	semi	semi	ADV
ejpam-137	90	5	regular	regular	ADJ
ejpam-137	90	6	,	,	PUNCT
ejpam-137	90	7	therefore	therefore	ADV
ejpam-137	90	8	it	it	PRON
ejpam-137	90	9	follows	follow	VERB
ejpam-137	90	10	that	that	SCONJ
ejpam-137	90	11	b	b	PROPN
ejpam-137	90	12	is	be	AUX
ejpam-137	90	13	γ∗-semi	γ∗-semi	NOUN
ejpam-137	90	14	-	-	NOUN
ejpam-137	90	15	open	open	ADJ
ejpam-137	90	16	in	in	ADP
ejpam-137	90	17	x	x	PUNCT
ejpam-137	91	1	[	[	X
ejpam-137	91	2	5	5	NUM
ejpam-137	91	3	]	]	PUNCT
ejpam-137	91	4	.	.	PUNCT
ejpam-137	92	1	therefore	therefore	ADV
ejpam-137	92	2	f	f	PROPN
ejpam-137	92	3	is	be	AUX
ejpam-137	92	4	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	92	5	.	.	NOUN
ejpam-137	92	6	remark	remark	PROPN
ejpam-137	92	7	3.4	3.4	NUM
ejpam-137	92	8	.	.	PUNCT
ejpam-137	93	1	γ	γ	ADJ
ejpam-137	93	2	-	-	PUNCT
ejpam-137	93	3	semi	semi	NOUN
ejpam-137	93	4	-	-	NOUN
ejpam-137	93	5	nbd	nbd	NOUN
ejpam-137	93	6	of	of	ADP
ejpam-137	93	7	x	x	PRON
ejpam-137	93	8	may	may	AUX
ejpam-137	93	9	be	be	AUX
ejpam-137	93	10	replaced	replace	VERB
ejpam-137	93	11	by	by	ADP
ejpam-137	93	12	γ∗-semi	γ∗-semi	NOUN
ejpam-137	93	13	-	-	ADJ
ejpam-137	93	14	open	open	ADJ
ejpam-137	93	15	nbd	nbd	PROPN
ejpam-137	93	16	of	of	ADP
ejpam-137	93	17	x	x	PROPN
ejpam-137	93	18	in	in	ADP
ejpam-137	93	19	theorem	theorem	ADJ
ejpam-137	93	20	3.3	3.3	NUM
ejpam-137	93	21	.	.	PUNCT
ejpam-137	94	1	theorem	theorem	VERB
ejpam-137	94	2	3.5	3.5	NUM
ejpam-137	94	3	.	.	PUNCT
ejpam-137	95	1	a	a	DET
ejpam-137	95	2	function	function	NOUN
ejpam-137	95	3	f	f	NOUN
ejpam-137	95	4	:	:	PUNCT
ejpam-137	95	5	x	x	X
ejpam-137	95	6	→	→	SYM
ejpam-137	95	7	y	y	PROPN
ejpam-137	95	8	is	be	AUX
ejpam-137	95	9	γ∗-irresolute	γ∗-irresolute	ADJ
ejpam-137	95	10	if	if	SCONJ
ejpam-137	96	1	and	and	CCONJ
ejpam-137	96	2	only	only	ADV
ejpam-137	96	3	if	if	SCONJ
ejpam-137	96	4	for	for	ADP
ejpam-137	96	5	each	each	DET
ejpam-137	96	6	x	x	PUNCT
ejpam-137	96	7	in	in	ADP
ejpam-137	96	8	x	x	X
ejpam-137	96	9	and	and	CCONJ
ejpam-137	96	10	each	each	DET
ejpam-137	96	11	γ	γ	NOUN
ejpam-137	96	12	-	-	PUNCT
ejpam-137	96	13	semi	semi	NOUN
ejpam-137	96	14	-	-	NOUN
ejpam-137	96	15	nbd	nbd	NOUN
ejpam-137	96	16	a	a	PRON
ejpam-137	96	17	of	of	ADP
ejpam-137	96	18	f	f	PROPN
ejpam-137	96	19	(	(	PUNCT
ejpam-137	96	20	x	x	X
ejpam-137	96	21	)	)	PUNCT
ejpam-137	96	22	,	,	PUNCT
ejpam-137	96	23	there	there	PRON
ejpam-137	96	24	is	be	VERB
ejpam-137	96	25	a	a	DET
ejpam-137	96	26	γ	γ	NOUN
ejpam-137	96	27	-	-	PUNCT
ejpam-137	96	28	semi	semi	ADJ
ejpam-137	96	29	-	-	PROPN
ejpam-137	96	30	nbd	nbd	PROPN
ejpam-137	96	31	b	b	PROPN
ejpam-137	96	32	of	of	ADP
ejpam-137	96	33	x	x	SYM
ejpam-137	96	34	such	such	ADJ
ejpam-137	96	35	that	that	SCONJ
ejpam-137	96	36	f	f	PROPN
ejpam-137	96	37	(	(	PUNCT
ejpam-137	96	38	b	b	NOUN
ejpam-137	96	39	)	)	PUNCT
ejpam-137	96	40	⊆	⊆	NUM
ejpam-137	96	41	a	a	PRON
ejpam-137	96	42	,	,	PUNCT
ejpam-137	96	43	where	where	SCONJ
ejpam-137	96	44	γ	γ	PROPN
ejpam-137	96	45	is	be	AUX
ejpam-137	96	46	a	a	DET
ejpam-137	96	47	semi	semi	ADJ
ejpam-137	96	48	regular	regular	ADJ
ejpam-137	96	49	operation	operation	NOUN
ejpam-137	96	50	.	.	PUNCT
ejpam-137	97	1	proof	proof	NOUN
ejpam-137	97	2	.	.	PUNCT
ejpam-137	98	1	let	let	VERB
ejpam-137	98	2	x	x	PUNCT
ejpam-137	98	3	∈	∈	PROPN
ejpam-137	98	4	x	x	X
ejpam-137	98	5	and	and	CCONJ
ejpam-137	98	6	a	a	DET
ejpam-137	98	7	a	a	DET
ejpam-137	98	8	γ	γ	X
ejpam-137	98	9	-	-	PUNCT
ejpam-137	98	10	semi	semi	NOUN
ejpam-137	98	11	-	-	NOUN
ejpam-137	98	12	nbd	nbd	PROPN
ejpam-137	98	13	of	of	ADP
ejpam-137	98	14	f	f	PROPN
ejpam-137	98	15	(	(	PUNCT
ejpam-137	98	16	x	x	NOUN
ejpam-137	98	17	)	)	PUNCT
ejpam-137	98	18	.	.	PUNCT
ejpam-137	99	1	then	then	ADV
ejpam-137	99	2	there	there	PRON
ejpam-137	99	3	exists	exist	VERB
ejpam-137	99	4	of	of	ADP
ejpam-137	99	5	(	(	PUNCT
ejpam-137	99	6	x	x	X
ejpam-137	99	7	)	)	PUNCT
ejpam-137	99	8	∈	∈	PROPN
ejpam-137	99	9	soγ∗(y	soγ∗(y	PROPN
ejpam-137	99	10	)	)	PUNCT
ejpam-137	99	11	such	such	ADJ
ejpam-137	99	12	that	that	SCONJ
ejpam-137	99	13	f	f	PROPN
ejpam-137	99	14	(	(	PUNCT
ejpam-137	99	15	x	x	X
ejpam-137	99	16	)	)	PUNCT
ejpam-137	99	17	∈	∈	NOUN
ejpam-137	99	18	of	of	ADP
ejpam-137	99	19	(	(	PUNCT
ejpam-137	99	20	x	x	X
ejpam-137	99	21	)	)	PUNCT
ejpam-137	99	22	⊆	⊆	NUM
ejpam-137	99	23	a	a	PRON
ejpam-137	99	24	.	.	PUNCT
ejpam-137	100	1	it	it	PRON
ejpam-137	100	2	follows	follow	VERB
ejpam-137	100	3	that	that	SCONJ
ejpam-137	100	4	x	x	PUNCT
ejpam-137	100	5	∈	∈	NOUN
ejpam-137	100	6	f	f	PROPN
ejpam-137	100	7	−1(of	−1(of	NOUN
ejpam-137	100	8	(	(	PUNCT
ejpam-137	100	9	x))⊆	x))⊆	NOUN
ejpam-137	100	10	f	f	PROPN
ejpam-137	100	11	−1(a	−1(a	ADP
ejpam-137	100	12	)	)	PUNCT
ejpam-137	100	13	.	.	PUNCT
ejpam-137	101	1	by	by	ADP
ejpam-137	101	2	hypothesis	hypothesis	NOUN
ejpam-137	101	3	,	,	PUNCT
ejpam-137	101	4	f	f	PROPN
ejpam-137	101	5	−1(of	−1(of	NOUN
ejpam-137	101	6	(	(	PUNCT
ejpam-137	101	7	x	x	NOUN
ejpam-137	101	8	)	)	PUNCT
ejpam-137	101	9	)	)	PUNCT
ejpam-137	101	10	∈	∈	PROPN
ejpam-137	101	11	soγ∗(x	soγ∗(x	NOUN
ejpam-137	101	12	)	)	PUNCT
ejpam-137	101	13	.	.	PUNCT
ejpam-137	102	1	let	let	VERB
ejpam-137	102	2	b	b	NOUN
ejpam-137	102	3	=	=	SYM
ejpam-137	102	4	f	f	PROPN
ejpam-137	102	5	−1(a	−1(a	ADP
ejpam-137	102	6	)	)	PUNCT
ejpam-137	102	7	.	.	PUNCT
ejpam-137	103	1	then	then	ADV
ejpam-137	103	2	it	it	PRON
ejpam-137	103	3	follows	follow	VERB
ejpam-137	103	4	that	that	SCONJ
ejpam-137	103	5	b	b	PROPN
ejpam-137	103	6	is	be	AUX
ejpam-137	103	7	γ	γ	X
ejpam-137	103	8	-	-	PUNCT
ejpam-137	103	9	semi	semi	NOUN
ejpam-137	103	10	-	-	NOUN
ejpam-137	103	11	nbd	nbd	NOUN
ejpam-137	103	12	of	of	ADP
ejpam-137	103	13	x	x	PROPN
ejpam-137	103	14	and	and	CCONJ
ejpam-137	103	15	f	f	PROPN
ejpam-137	103	16	(	(	PUNCT
ejpam-137	103	17	b	b	NOUN
ejpam-137	103	18	)	)	PUNCT
ejpam-137	103	19	=	=	PUNCT
ejpam-137	104	1	f	f	PROPN
ejpam-137	104	2	f	f	PROPN
ejpam-137	104	3	−1(a)⊆	−1(a)⊆	NOUN
ejpam-137	104	4	a	a	PRON
ejpam-137	104	5	.	.	PUNCT
ejpam-137	105	1	this	this	PRON
ejpam-137	105	2	proves	prove	VERB
ejpam-137	105	3	the	the	DET
ejpam-137	105	4	necessity	necessity	NOUN
ejpam-137	105	5	.	.	PUNCT
ejpam-137	106	1	conversely	conversely	ADV
ejpam-137	106	2	,	,	PUNCT
ejpam-137	106	3	let	let	VERB
ejpam-137	106	4	u	u	PRON
ejpam-137	106	5	∈	∈	PROPN
ejpam-137	106	6	soγ∗(y	soγ∗(y	PROPN
ejpam-137	106	7	)	)	PUNCT
ejpam-137	106	8	.	.	PUNCT
ejpam-137	107	1	take	take	VERB
ejpam-137	107	2	o	o	NOUN
ejpam-137	107	3	=	=	PUNCT
ejpam-137	107	4	f	f	PROPN
ejpam-137	107	5	−1(u	−1(u	NOUN
ejpam-137	107	6	)	)	PUNCT
ejpam-137	107	7	.	.	PUNCT
ejpam-137	108	1	let	let	VERB
ejpam-137	108	2	x	x	PUNCT
ejpam-137	108	3	∈	∈	PROPN
ejpam-137	108	4	o	o	NOUN
ejpam-137	108	5	,	,	PUNCT
ejpam-137	108	6	then	then	ADV
ejpam-137	108	7	f	f	X
ejpam-137	108	8	(	(	PUNCT
ejpam-137	108	9	x	x	X
ejpam-137	108	10	)	)	PUNCT
ejpam-137	108	11	∈	∈	PROPN
ejpam-137	108	12	u	u	NOUN
ejpam-137	108	13	.	.	PUNCT
ejpam-137	109	1	thus	thus	ADV
ejpam-137	109	2	u	u	NOUN
ejpam-137	109	3	is	be	AUX
ejpam-137	109	4	a	a	DET
ejpam-137	109	5	γ	γ	NOUN
ejpam-137	109	6	-	-	PUNCT
ejpam-137	109	7	semi	semi	NOUN
ejpam-137	109	8	-	-	NOUN
ejpam-137	109	9	nbd	nbd	PROPN
ejpam-137	109	10	of	of	ADP
ejpam-137	109	11	f	f	PROPN
ejpam-137	109	12	(	(	PUNCT
ejpam-137	109	13	x	x	NOUN
ejpam-137	109	14	)	)	PUNCT
ejpam-137	109	15	.	.	PUNCT
ejpam-137	110	1	so	so	ADV
ejpam-137	110	2	by	by	ADP
ejpam-137	110	3	hypothesis	hypothesis	NOUN
ejpam-137	110	4	,	,	PUNCT
ejpam-137	110	5	there	there	PRON
ejpam-137	110	6	exists	exist	VERB
ejpam-137	110	7	a	a	DET
ejpam-137	110	8	γ	γ	X
ejpam-137	110	9	-	-	PUNCT
ejpam-137	110	10	semi	semi	NOUN
ejpam-137	110	11	-	-	NOUN
ejpam-137	110	12	nbd	nbd	ADJ
ejpam-137	110	13	vx	vx	PROPN
ejpam-137	110	14	of	of	ADP
ejpam-137	110	15	x	x	SYM
ejpam-137	110	16	such	such	ADJ
ejpam-137	110	17	that	that	SCONJ
ejpam-137	110	18	f	f	PROPN
ejpam-137	110	19	(	(	PUNCT
ejpam-137	110	20	vx	vx	PROPN
ejpam-137	110	21	)	)	PUNCT
ejpam-137	110	22	⊆	⊆	NUM
ejpam-137	110	23	u	u	NOUN
ejpam-137	110	24	.	.	PUNCT
ejpam-137	111	1	thus	thus	ADV
ejpam-137	111	2	it	it	PRON
ejpam-137	111	3	follows	follow	VERB
ejpam-137	111	4	that	that	SCONJ
ejpam-137	111	5	x	x	PUNCT
ejpam-137	111	6	∈	∈	NOUN
ejpam-137	111	7	vx	vx	ADP
ejpam-137	111	8	⊆	⊆	NUM
ejpam-137	111	9	f	f	PROPN
ejpam-137	111	10	−1	−1	NOUN
ejpam-137	111	11	f	f	PROPN
ejpam-137	111	12	(	(	PUNCT
ejpam-137	111	13	vx	vx	PROPN
ejpam-137	111	14	)	)	PUNCT
ejpam-137	111	15	⊆	⊆	NUM
ejpam-137	111	16	f	f	NOUN
ejpam-137	111	17	−1(u	−1(u	X
ejpam-137	111	18	)	)	PUNCT
ejpam-137	112	1	=	=	SYM
ejpam-137	112	2	o	o	NOUN
ejpam-137	112	3	.	.	PUNCT
ejpam-137	113	1	so	so	ADV
ejpam-137	113	2	vx	vx	PROPN
ejpam-137	113	3	is	be	AUX
ejpam-137	113	4	a	a	DET
ejpam-137	113	5	γ	γ	NOUN
ejpam-137	113	6	-	-	PUNCT
ejpam-137	113	7	semi	semi	NOUN
ejpam-137	113	8	-	-	NOUN
ejpam-137	113	9	nbd	nbd	NOUN
ejpam-137	113	10	of	of	ADP
ejpam-137	113	11	x	x	PRON
ejpam-137	113	12	,	,	PUNCT
ejpam-137	113	13	which	which	PRON
ejpam-137	113	14	implies	imply	VERB
ejpam-137	113	15	there	there	PRON
ejpam-137	113	16	exists	exist	VERB
ejpam-137	113	17	an	an	DET
ejpam-137	113	18	ox	ox	ADJ
ejpam-137	113	19	∈	∈	PROPN
ejpam-137	113	20	soγ∗(x	soγ∗(x	NOUN
ejpam-137	113	21	)	)	PUNCT
ejpam-137	113	22	such	such	ADJ
ejpam-137	113	23	that	that	SCONJ
ejpam-137	113	24	x	x	SYM
ejpam-137	113	25	∈	∈	PROPN
ejpam-137	113	26	ox	ox	NOUN
ejpam-137	113	27	⊆	⊆	NUM
ejpam-137	113	28	o.	o.	NOUN
ejpam-137	114	1	thus	thus	ADV
ejpam-137	114	2	o	o	X
ejpam-137	114	3	=	=	PUNCT
ejpam-137	114	4	⋃	⋃	NOUN
ejpam-137	114	5	x∈o	x∈o	NOUN
ejpam-137	114	6	ox	ox	NOUN
ejpam-137	114	7	.	.	PUNCT
ejpam-137	115	1	since	since	SCONJ
ejpam-137	115	2	γ	γ	PROPN
ejpam-137	115	3	is	be	AUX
ejpam-137	115	4	semi	semi	ADV
ejpam-137	115	5	regular	regular	ADJ
ejpam-137	115	6	,	,	PUNCT
ejpam-137	115	7	then	then	ADV
ejpam-137	115	8	it	it	PRON
ejpam-137	115	9	follows	follow	VERB
ejpam-137	115	10	that	that	SCONJ
ejpam-137	115	11	o	o	PROPN
ejpam-137	115	12	is	be	AUX
ejpam-137	115	13	γ∗-semi	γ∗-semi	NOUN
ejpam-137	115	14	-	-	ADJ
ejpam-137	115	15	open	open	ADJ
ejpam-137	115	16	in	in	ADP
ejpam-137	115	17	x.	x.	NOUN
ejpam-137	115	18	thus	thus	ADV
ejpam-137	115	19	f	f	PROPN
ejpam-137	115	20	is	be	AUX
ejpam-137	115	21	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	115	22	.	.	PUNCT
ejpam-137	115	23	definition	definition	NOUN
ejpam-137	115	24	3.6[10	3.6[10	NUM
ejpam-137	115	25	]	]	PUNCT
ejpam-137	115	26	.	.	PUNCT
ejpam-137	116	1	let	let	VERB
ejpam-137	116	2	x	x	PRON
ejpam-137	116	3	be	be	AUX
ejpam-137	116	4	a	a	DET
ejpam-137	116	5	space	space	NOUN
ejpam-137	116	6	.	.	PUNCT
ejpam-137	117	1	a⊆	a⊆	NOUN
ejpam-137	117	2	x	x	PUNCT
ejpam-137	118	1	and	and	CCONJ
ejpam-137	118	2	p	p	NOUN
ejpam-137	118	3	∈	∈	PROPN
ejpam-137	118	4	x	x	X
ejpam-137	118	5	.	.	PUNCT
ejpam-137	119	1	then	then	ADV
ejpam-137	119	2	p	p	NOUN
ejpam-137	119	3	is	be	AUX
ejpam-137	119	4	called	call	VERB
ejpam-137	119	5	a	a	DET
ejpam-137	119	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	119	7	-	-	PUNCT
ejpam-137	119	8	limit	limit	NOUN
ejpam-137	119	9	point	point	NOUN
ejpam-137	119	10	of	of	ADP
ejpam-137	119	11	a	a	DET
ejpam-137	119	12	if	if	SCONJ
ejpam-137	119	13	u	u	PROPN
ejpam-137	119	14	∩	∩	X
ejpam-137	119	15	(	(	PUNCT
ejpam-137	119	16	a−{p	a−{p	PROPN
ejpam-137	119	17	}	}	PUNCT
ejpam-137	119	18	)	)	PUNCT
ejpam-137	120	1	6=	6=	ADP
ejpam-137	120	2	φ	φ	PROPN
ejpam-137	120	3	,	,	PUNCT
ejpam-137	120	4	for	for	ADP
ejpam-137	120	5	any	any	DET
ejpam-137	120	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	120	7	-	-	ADJ
ejpam-137	120	8	open	open	ADJ
ejpam-137	120	9	set	set	NOUN
ejpam-137	120	10	u	u	NOUN
ejpam-137	120	11	containing	contain	VERB
ejpam-137	120	12	p.	p.	NOUN
ejpam-137	120	13	the	the	DET
ejpam-137	120	14	set	set	NOUN
ejpam-137	120	15	of	of	ADP
ejpam-137	120	16	all	all	DET
ejpam-137	120	17	γ∗-semi	γ∗-semi	NOUN
ejpam-137	120	18	-	-	NOUN
ejpam-137	120	19	limit	limit	NOUN
ejpam-137	120	20	points	point	NOUN
ejpam-137	120	21	of	of	ADP
ejpam-137	120	22	a	a	PRON
ejpam-137	120	23	is	be	AUX
ejpam-137	120	24	called	call	VERB
ejpam-137	120	25	a	a	DET
ejpam-137	120	26	γ∗-semi	γ∗-semi	NOUN
ejpam-137	120	27	-	-	PUNCT
ejpam-137	120	28	derived	derive	VERB
ejpam-137	120	29	set	set	NOUN
ejpam-137	120	30	of	of	ADP
ejpam-137	120	31	a	a	PRON
ejpam-137	120	32	and	and	CCONJ
ejpam-137	120	33	is	be	AUX
ejpam-137	120	34	denoted	denote	VERB
ejpam-137	120	35	by	by	ADP
ejpam-137	120	36	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	120	37	)	)	PUNCT
ejpam-137	120	38	.	.	PUNCT
ejpam-137	121	1	clearly	clearly	ADV
ejpam-137	121	2	if	if	SCONJ
ejpam-137	121	3	a⊆	a⊆	PROPN
ejpam-137	121	4	b	b	NOUN
ejpam-137	121	5	then	then	ADV
ejpam-137	121	6	sdγ∗(a)⊆	sdγ∗(a)⊆	NOUN
ejpam-137	121	7	sdγ∗(b	sdγ∗(b	PROPN
ejpam-137	121	8	)	)	PUNCT
ejpam-137	121	9	.....	.....	PUNCT
ejpam-137	122	1	(	(	PUNCT
ejpam-137	122	2	*	*	PUNCT
ejpam-137	122	3	)	)	PUNCT
ejpam-137	122	4	denote	denote	NOUN
ejpam-137	122	5	γ(x	γ(x	PROPN
ejpam-137	122	6	)	)	PUNCT
ejpam-137	122	7	,	,	PUNCT
ejpam-137	122	8	the	the	DET
ejpam-137	122	9	set	set	NOUN
ejpam-137	122	10	of	of	ADP
ejpam-137	122	11	all	all	DET
ejpam-137	122	12	monotone	monotone	ADJ
ejpam-137	122	13	operators	operator	NOUN
ejpam-137	122	14	on	on	ADP
ejpam-137	122	15	x.	x.	NOUN
ejpam-137	122	16	then	then	ADV
ejpam-137	122	17	we	we	PRON
ejpam-137	122	18	have	have	VERB
ejpam-137	122	19	:	:	PUNCT
ejpam-137	122	20	definition	definition	NOUN
ejpam-137	122	21	3.7[9	3.7[9	NUM
ejpam-137	122	22	]	]	PUNCT
ejpam-137	122	23	.	.	PUNCT
ejpam-137	123	1	let	let	VERB
ejpam-137	123	2	a	a	DET
ejpam-137	123	3	be	be	AUX
ejpam-137	123	4	a	a	DET
ejpam-137	123	5	subset	subset	NOUN
ejpam-137	123	6	of	of	ADP
ejpam-137	123	7	space	space	NOUN
ejpam-137	123	8	x	x	X
ejpam-137	123	9	and	and	CCONJ
ejpam-137	123	10	γ	γ	PROPN
ejpam-137	123	11	∈	∈	PROPN
ejpam-137	123	12	γ(x	γ(x	PROPN
ejpam-137	123	13	)	)	PUNCT
ejpam-137	123	14	.	.	PUNCT
ejpam-137	124	1	the	the	DET
ejpam-137	124	2	intersection	intersection	NOUN
ejpam-137	124	3	of	of	ADP
ejpam-137	124	4	all	all	DET
ejpam-137	124	5	γ∗-semiclosed	γ∗-semiclose	VERB
ejpam-137	124	6	sets	set	NOUN
ejpam-137	124	7	containing	contain	VERB
ejpam-137	124	8	a	a	PRON
ejpam-137	124	9	is	be	AUX
ejpam-137	124	10	called	call	VERB
ejpam-137	124	11	γ∗-semi	γ∗-semi	NOUN
ejpam-137	124	12	-	-	NOUN
ejpam-137	124	13	closure	closure	NOUN
ejpam-137	124	14	of	of	ADP
ejpam-137	124	15	a	a	PRON
ejpam-137	124	16	and	and	CCONJ
ejpam-137	124	17	is	be	AUX
ejpam-137	124	18	denoted	denote	VERB
ejpam-137	124	19	by	by	ADP
ejpam-137	124	20	sclγ∗(a	sclγ∗(a	PROPN
ejpam-137	124	21	)	)	PUNCT
ejpam-137	124	22	.	.	PUNCT
ejpam-137	125	1	remark	remark	VERB
ejpam-137	125	2	3.8	3.8	NUM
ejpam-137	125	3	.	.	PUNCT
ejpam-137	126	1	from	from	ADP
ejpam-137	126	2	the	the	DET
ejpam-137	126	3	definition	definition	NOUN
ejpam-137	126	4	3.6	3.6	NUM
ejpam-137	126	5	,	,	PUNCT
ejpam-137	126	6	it	it	PRON
ejpam-137	126	7	follows	follow	VERB
ejpam-137	126	8	that	that	SCONJ
ejpam-137	126	9	p	p	NOUN
ejpam-137	126	10	is	be	AUX
ejpam-137	126	11	a	a	DET
ejpam-137	126	12	γ∗-semi	γ∗-semi	NOUN
ejpam-137	126	13	-	-	PUNCT
ejpam-137	126	14	limit	limit	NOUN
ejpam-137	126	15	point	point	NOUN
ejpam-137	126	16	of	of	ADP
ejpam-137	126	17	a	a	DET
ejpam-137	126	18	if	if	NOUN
ejpam-137	126	19	and	and	CCONJ
ejpam-137	126	20	only	only	ADV
ejpam-137	126	21	if	if	SCONJ
ejpam-137	126	22	p	p	PROPN
ejpam-137	126	23	∈	∈	PROPN
ejpam-137	126	24	sclγ∗(a−	sclγ∗(a−	X
ejpam-137	126	25	{	{	PUNCT
ejpam-137	126	26	p	p	NOUN
ejpam-137	126	27	}	}	PUNCT
ejpam-137	126	28	)	)	PUNCT
ejpam-137	126	29	.	.	PUNCT
ejpam-137	127	1	theorem	theorem	VERB
ejpam-137	127	2	3.9[10	3.9[10	NUM
ejpam-137	127	3	]	]	PUNCT
ejpam-137	127	4	.	.	PUNCT
ejpam-137	128	1	for	for	ADP
ejpam-137	128	2	any	any	DET
ejpam-137	128	3	a	a	NOUN
ejpam-137	128	4	,	,	PUNCT
ejpam-137	128	5	b	b	NOUN
ejpam-137	128	6	⊆	⊆	NUM
ejpam-137	128	7	x	x	SYM
ejpam-137	128	8	,	,	PUNCT
ejpam-137	128	9	the	the	DET
ejpam-137	128	10	γ∗-semi	γ∗-semi	NOUN
ejpam-137	128	11	-	-	PUNCT
ejpam-137	128	12	derived	derive	VERB
ejpam-137	128	13	sets	set	NOUN
ejpam-137	128	14	have	have	VERB
ejpam-137	128	15	the	the	DET
ejpam-137	128	16	following	follow	VERB
ejpam-137	128	17	properties	property	NOUN
ejpam-137	128	18	:	:	PUNCT
ejpam-137	128	19	(	(	PUNCT
ejpam-137	128	20	1	1	X
ejpam-137	128	21	)	)	PUNCT
ejpam-137	128	22	sclγ∗(a	sclγ∗(a	PROPN
ejpam-137	128	23	)	)	PUNCT
ejpam-137	128	24	=	=	SYM
ejpam-137	128	25	a∪	a∪	X
ejpam-137	128	26	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	128	27	)	)	PUNCT
ejpam-137	128	28	.	.	PUNCT
ejpam-137	129	1	(	(	PUNCT
ejpam-137	129	2	2	2	X
ejpam-137	129	3	)	)	PUNCT
ejpam-137	129	4	⋃	⋃	PUNCT
ejpam-137	129	5	i	i	PRON
ejpam-137	129	6	sdγ∗(ai	sdγ∗(ai	NOUN
ejpam-137	129	7	)	)	PUNCT
ejpam-137	129	8	=	=	SYM
ejpam-137	129	9	sdγ∗	sdγ∗	NOUN
ejpam-137	129	10	(	(	PUNCT
ejpam-137	129	11	⋃	⋃	PROPN
ejpam-137	129	12	i	i	PRON
ejpam-137	129	13	ai	ai	VERB
ejpam-137	129	14	)	)	PUNCT
ejpam-137	129	15	.	.	PUNCT
ejpam-137	130	1	(	(	PUNCT
ejpam-137	130	2	3	3	X
ejpam-137	130	3	)	)	PUNCT
ejpam-137	130	4	sdγ∗(sdγ∗(a))⊆	sdγ∗(sdγ∗(a))⊆	NOUN
ejpam-137	130	5	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	130	6	)	)	PUNCT
ejpam-137	130	7	.	.	PUNCT
ejpam-137	131	1	(	(	PUNCT
ejpam-137	131	2	4	4	X
ejpam-137	131	3	)	)	PUNCT
ejpam-137	131	4	sclγ∗(sdγ∗(a	sclγ∗(sdγ∗(a	NOUN
ejpam-137	131	5	)	)	PUNCT
ejpam-137	131	6	)	)	PUNCT
ejpam-137	132	1	=	=	PUNCT
ejpam-137	132	2	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	132	3	)	)	PUNCT
ejpam-137	132	4	.	.	PUNCT
ejpam-137	133	1	in	in	ADP
ejpam-137	133	2	terms	term	NOUN
ejpam-137	133	3	of	of	ADP
ejpam-137	133	4	γ∗-semi	γ∗-semi	NOUN
ejpam-137	133	5	-	-	ADJ
ejpam-137	133	6	derived	derive	VERB
ejpam-137	133	7	sets	set	NOUN
ejpam-137	133	8	,	,	PUNCT
ejpam-137	133	9	we	we	PRON
ejpam-137	133	10	use	use	VERB
ejpam-137	133	11	theorem	theorem	ADJ
ejpam-137	133	12	3.9	3.9	NUM
ejpam-137	133	13	and	and	CCONJ
ejpam-137	133	14	characterize	characterize	VERB
ejpam-137	133	15	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	133	16	funcb	funcb	NOUN
ejpam-137	133	17	.	.	PUNCT
ejpam-137	134	1	ahmad	ahmad	PROPN
ejpam-137	134	2	,	,	PUNCT
ejpam-137	134	3	s.	s.	PROPN
ejpam-137	134	4	hussain	hussain	PROPN
ejpam-137	134	5	,	,	PUNCT
ejpam-137	134	6	and	and	CCONJ
ejpam-137	134	7	t.	t.	PROPN
ejpam-137	134	8	noiri	noiri	PROPN
ejpam-137	134	9	/	/	SYM
ejpam-137	134	10	eur	eur	PROPN
ejpam-137	134	11	.	.	PUNCT
ejpam-137	135	1	j.	j.	PROPN
ejpam-137	135	2	pure	pure	PROPN
ejpam-137	135	3	appl	appl	PROPN
ejpam-137	135	4	.	.	PROPN
ejpam-137	135	5	math	math	PROPN
ejpam-137	135	6	,	,	PUNCT
ejpam-137	135	7	1	1	NUM
ejpam-137	135	8	(	(	PUNCT
ejpam-137	135	9	2008	2008	NUM
ejpam-137	135	10	)	)	PUNCT
ejpam-137	135	11	,	,	PUNCT
ejpam-137	135	12	(	(	PUNCT
ejpam-137	135	13	22	22	NUM
ejpam-137	135	14	-	-	SYM
ejpam-137	135	15	29	29	NUM
ejpam-137	135	16	)	)	PUNCT
ejpam-137	135	17	25	25	NUM
ejpam-137	135	18	tions	tion	NOUN
ejpam-137	135	19	as	as	ADP
ejpam-137	135	20	:	:	PUNCT
ejpam-137	135	21	theorem	theorem	NOUN
ejpam-137	135	22	3.10	3.10	NUM
ejpam-137	135	23	.	.	PUNCT
ejpam-137	136	1	a	a	DET
ejpam-137	136	2	function	function	NOUN
ejpam-137	136	3	f	f	NOUN
ejpam-137	136	4	:	:	PUNCT
ejpam-137	136	5	x	x	X
ejpam-137	136	6	→	→	SYM
ejpam-137	136	7	y	y	PROPN
ejpam-137	136	8	is	be	AUX
ejpam-137	136	9	γ∗-irresolute	γ∗-irresolute	ADJ
ejpam-137	136	10	if	if	SCONJ
ejpam-137	137	1	and	and	CCONJ
ejpam-137	137	2	only	only	ADV
ejpam-137	137	3	if	if	SCONJ
ejpam-137	137	4	f	f	PROPN
ejpam-137	137	5	(	(	PUNCT
ejpam-137	137	6	sdγ∗(a))⊆	sdγ∗(a))⊆	PROPN
ejpam-137	137	7	sclγ∗	sclγ∗	VERB
ejpam-137	137	8	(	(	PUNCT
ejpam-137	137	9	f	f	PROPN
ejpam-137	137	10	(	(	PUNCT
ejpam-137	137	11	a	a	NOUN
ejpam-137	137	12	)	)	PUNCT
ejpam-137	137	13	)	)	PUNCT
ejpam-137	137	14	,	,	PUNCT
ejpam-137	137	15	for	for	ADP
ejpam-137	137	16	all	all	DET
ejpam-137	137	17	a⊆	a⊆	NOUN
ejpam-137	137	18	x	x	X
ejpam-137	137	19	.	.	PUNCT
ejpam-137	138	1	proof	proof	NOUN
ejpam-137	138	2	.	.	PUNCT
ejpam-137	139	1	let	let	VERB
ejpam-137	139	2	f	f	NOUN
ejpam-137	139	3	:	:	PUNCT
ejpam-137	139	4	x	x	X
ejpam-137	139	5	→	→	SYM
ejpam-137	139	6	y	y	PROPN
ejpam-137	139	7	be	be	AUX
ejpam-137	139	8	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	139	9	.	.	PUNCT
ejpam-137	140	1	let	let	VERB
ejpam-137	140	2	a⊆	a⊆	VERB
ejpam-137	140	3	x	x	PRON
ejpam-137	140	4	,	,	PUNCT
ejpam-137	140	5	and	and	CCONJ
ejpam-137	140	6	x	x	PUNCT
ejpam-137	140	7	∈	∈	PROPN
ejpam-137	140	8	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	140	9	)	)	PUNCT
ejpam-137	140	10	.	.	PUNCT
ejpam-137	141	1	assume	assume	VERB
ejpam-137	141	2	that	that	SCONJ
ejpam-137	141	3	f	f	PROPN
ejpam-137	141	4	(	(	PUNCT
ejpam-137	141	5	x	x	X
ejpam-137	141	6	)	)	PUNCT
ejpam-137	141	7	/∈	/∈	PUNCT
ejpam-137	142	1	f	f	X
ejpam-137	142	2	(	(	PUNCT
ejpam-137	142	3	a	a	NOUN
ejpam-137	142	4	)	)	PUNCT
ejpam-137	143	1	and	and	CCONJ
ejpam-137	143	2	let	let	VERB
ejpam-137	143	3	v	v	PART
ejpam-137	143	4	denote	denote	VERB
ejpam-137	143	5	a	a	DET
ejpam-137	143	6	γ	γ	X
ejpam-137	143	7	-	-	PUNCT
ejpam-137	143	8	semi	semi	NOUN
ejpam-137	143	9	-	-	NOUN
ejpam-137	143	10	nbd	nbd	PROPN
ejpam-137	143	11	of	of	ADP
ejpam-137	143	12	f	f	PROPN
ejpam-137	143	13	(	(	PUNCT
ejpam-137	143	14	x	x	NOUN
ejpam-137	143	15	)	)	PUNCT
ejpam-137	143	16	.	.	PUNCT
ejpam-137	144	1	since	since	SCONJ
ejpam-137	144	2	f	f	PROPN
ejpam-137	144	3	is	be	AUX
ejpam-137	144	4	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	144	5	,	,	PUNCT
ejpam-137	144	6	so	so	ADV
ejpam-137	144	7	by	by	ADP
ejpam-137	144	8	theorem	theorem	NOUN
ejpam-137	144	9	3.5	3.5	NUM
ejpam-137	144	10	,	,	PUNCT
ejpam-137	144	11	there	there	PRON
ejpam-137	144	12	exists	exist	VERB
ejpam-137	144	13	a	a	DET
ejpam-137	144	14	γ	γ	X
ejpam-137	144	15	-	-	PUNCT
ejpam-137	144	16	semi	semi	ADJ
ejpam-137	144	17	-	-	ADJ
ejpam-137	144	18	nbd	nbd	ADJ
ejpam-137	144	19	u	u	NOUN
ejpam-137	144	20	of	of	ADP
ejpam-137	144	21	x	x	SYM
ejpam-137	144	22	such	such	ADJ
ejpam-137	144	23	that	that	SCONJ
ejpam-137	144	24	f	f	PROPN
ejpam-137	144	25	(	(	PUNCT
ejpam-137	144	26	u	u	NOUN
ejpam-137	144	27	)	)	PUNCT
ejpam-137	144	28	⊆	⊆	NUM
ejpam-137	144	29	v	v	NOUN
ejpam-137	144	30	.	.	PUNCT
ejpam-137	145	1	from	from	ADP
ejpam-137	145	2	x	x	PROPN
ejpam-137	145	3	∈	∈	PROPN
ejpam-137	145	4	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	145	5	)	)	PUNCT
ejpam-137	145	6	,	,	PUNCT
ejpam-137	145	7	it	it	PRON
ejpam-137	145	8	follows	follow	VERB
ejpam-137	145	9	that	that	SCONJ
ejpam-137	145	10	u	u	PROPN
ejpam-137	145	11	∩	∩	NOUN
ejpam-137	145	12	a	a	DET
ejpam-137	145	13	6=	6=	NUM
ejpam-137	145	14	φ	φ	PROPN
ejpam-137	145	15	;	;	PUNCT
ejpam-137	145	16	there	there	PRON
ejpam-137	145	17	exists	exist	VERB
ejpam-137	145	18	,	,	PUNCT
ejpam-137	145	19	therefore	therefore	ADV
ejpam-137	145	20	,	,	PUNCT
ejpam-137	145	21	at	at	ADP
ejpam-137	145	22	least	least	ADV
ejpam-137	145	23	one	one	NUM
ejpam-137	145	24	element	element	NOUN
ejpam-137	145	25	a	a	DET
ejpam-137	145	26	∈	∈	PROPN
ejpam-137	145	27	u	u	NOUN
ejpam-137	145	28	∩	∩	NOUN
ejpam-137	145	29	a	a	DET
ejpam-137	145	30	such	such	ADJ
ejpam-137	146	1	that	that	SCONJ
ejpam-137	146	2	f	f	PROPN
ejpam-137	146	3	(	(	PUNCT
ejpam-137	146	4	a	a	X
ejpam-137	146	5	)	)	PUNCT
ejpam-137	146	6	∈	∈	PROPN
ejpam-137	146	7	f	f	X
ejpam-137	146	8	(	(	PUNCT
ejpam-137	146	9	a	a	NOUN
ejpam-137	146	10	)	)	PUNCT
ejpam-137	146	11	and	and	CCONJ
ejpam-137	146	12	f	f	X
ejpam-137	146	13	(	(	PUNCT
ejpam-137	146	14	a	a	X
ejpam-137	146	15	)	)	PUNCT
ejpam-137	146	16	∈	∈	PROPN
ejpam-137	146	17	v	v	NOUN
ejpam-137	146	18	.	.	PUNCT
ejpam-137	147	1	since	since	SCONJ
ejpam-137	147	2	f	f	PROPN
ejpam-137	147	3	(	(	PUNCT
ejpam-137	147	4	x	x	X
ejpam-137	147	5	)	)	PUNCT
ejpam-137	147	6	/∈	/∈	PUNCT
ejpam-137	148	1	f	f	X
ejpam-137	148	2	(	(	PUNCT
ejpam-137	148	3	a	a	X
ejpam-137	148	4	)	)	PUNCT
ejpam-137	148	5	,	,	PUNCT
ejpam-137	148	6	we	we	PRON
ejpam-137	148	7	have	have	VERB
ejpam-137	148	8	f	f	X
ejpam-137	148	9	(	(	PUNCT
ejpam-137	148	10	a	a	NOUN
ejpam-137	148	11	)	)	PUNCT
ejpam-137	148	12	6=	6=	ADP
ejpam-137	149	1	f	f	PROPN
ejpam-137	149	2	(	(	PUNCT
ejpam-137	149	3	x	x	NOUN
ejpam-137	149	4	)	)	PUNCT
ejpam-137	149	5	.	.	PUNCT
ejpam-137	150	1	thus	thus	ADV
ejpam-137	150	2	every	every	DET
ejpam-137	150	3	γ	γ	PROPN
ejpam-137	150	4	-	-	PUNCT
ejpam-137	150	5	semi	semi	NOUN
ejpam-137	150	6	-	-	NOUN
ejpam-137	150	7	nbd	nbd	PROPN
ejpam-137	150	8	of	of	ADP
ejpam-137	150	9	f	f	PROPN
ejpam-137	150	10	(	(	PUNCT
ejpam-137	150	11	x	x	X
ejpam-137	150	12	)	)	PUNCT
ejpam-137	150	13	contains	contain	VERB
ejpam-137	150	14	an	an	DET
ejpam-137	150	15	element	element	NOUN
ejpam-137	150	16	f	f	NOUN
ejpam-137	150	17	(	(	PUNCT
ejpam-137	150	18	a	a	NOUN
ejpam-137	150	19	)	)	PUNCT
ejpam-137	150	20	of	of	ADP
ejpam-137	150	21	f	f	PROPN
ejpam-137	150	22	(	(	PUNCT
ejpam-137	150	23	a	a	X
ejpam-137	150	24	)	)	PUNCT
ejpam-137	150	25	different	different	ADJ
ejpam-137	150	26	from	from	ADP
ejpam-137	150	27	f	f	PROPN
ejpam-137	150	28	(	(	PUNCT
ejpam-137	150	29	x	x	NOUN
ejpam-137	150	30	)	)	PUNCT
ejpam-137	150	31	.	.	PUNCT
ejpam-137	151	1	consequently	consequently	ADV
ejpam-137	151	2	,	,	PUNCT
ejpam-137	151	3	f	f	PROPN
ejpam-137	151	4	(	(	PUNCT
ejpam-137	151	5	x	x	X
ejpam-137	151	6	)	)	PUNCT
ejpam-137	151	7	∈	∈	PROPN
ejpam-137	151	8	sdγ∗	sdγ∗	NOUN
ejpam-137	151	9	(	(	PUNCT
ejpam-137	151	10	f	f	PROPN
ejpam-137	151	11	(	(	PUNCT
ejpam-137	151	12	a)).this	a)).this	PRON
ejpam-137	151	13	proves	prove	VERB
ejpam-137	151	14	the	the	DET
ejpam-137	151	15	necessity	necessity	NOUN
ejpam-137	151	16	.	.	PUNCT
ejpam-137	152	1	conversely	conversely	ADV
ejpam-137	152	2	,	,	PUNCT
ejpam-137	152	3	suppose	suppose	VERB
ejpam-137	152	4	that	that	SCONJ
ejpam-137	152	5	f	f	PROPN
ejpam-137	152	6	is	be	AUX
ejpam-137	152	7	not	not	PART
ejpam-137	152	8	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	152	9	.	.	NOUN
ejpam-137	152	10	then	then	ADV
ejpam-137	152	11	by	by	ADP
ejpam-137	152	12	theorem	theorem	NOUN
ejpam-137	152	13	3.5	3.5	NUM
ejpam-137	152	14	,	,	PUNCT
ejpam-137	152	15	there	there	PRON
ejpam-137	152	16	exists	exist	VERB
ejpam-137	152	17	x	x	X
ejpam-137	152	18	∈	∈	PROPN
ejpam-137	152	19	x	x	X
ejpam-137	152	20	and	and	CCONJ
ejpam-137	152	21	a	a	DET
ejpam-137	152	22	γ	γ	NOUN
ejpam-137	152	23	-	-	PUNCT
ejpam-137	152	24	semi	semi	NOUN
ejpam-137	152	25	-	-	NOUN
ejpam-137	152	26	nbd	nbd	ADJ
ejpam-137	152	27	v	v	NOUN
ejpam-137	152	28	of	of	ADP
ejpam-137	152	29	f	f	PROPN
ejpam-137	152	30	(	(	PUNCT
ejpam-137	152	31	x	x	X
ejpam-137	152	32	)	)	PUNCT
ejpam-137	152	33	such	such	ADJ
ejpam-137	152	34	that	that	SCONJ
ejpam-137	152	35	every	every	DET
ejpam-137	152	36	γ	γ	PROPN
ejpam-137	152	37	-	-	PUNCT
ejpam-137	152	38	semi	semi	ADJ
ejpam-137	152	39	-	-	ADJ
ejpam-137	152	40	nbd	nbd	ADJ
ejpam-137	152	41	u	u	PROPN
ejpam-137	152	42	of	of	ADP
ejpam-137	152	43	x	x	PUNCT
ejpam-137	152	44	contains	contain	VERB
ejpam-137	152	45	at	at	ADV
ejpam-137	152	46	least	least	ADV
ejpam-137	152	47	one	one	NUM
ejpam-137	152	48	element	element	NOUN
ejpam-137	152	49	a	a	DET
ejpam-137	152	50	∈	∈	PROPN
ejpam-137	152	51	u	u	NOUN
ejpam-137	152	52	for	for	ADP
ejpam-137	152	53	which	which	PRON
ejpam-137	152	54	f	f	X
ejpam-137	152	55	(	(	PUNCT
ejpam-137	152	56	a	a	PROPN
ejpam-137	152	57	)	)	PUNCT
ejpam-137	152	58	/∈	/∈	PUNCT
ejpam-137	152	59	v	v	X
ejpam-137	152	60	.	.	PUNCT
ejpam-137	153	1	put	put	VERB
ejpam-137	153	2	a=	a=	ADV
ejpam-137	153	3	{	{	PUNCT
ejpam-137	153	4	a	a	DET
ejpam-137	153	5	∈	∈	PROPN
ejpam-137	153	6	x	x	X
ejpam-137	153	7	:	:	PUNCT
ejpam-137	153	8	f	f	X
ejpam-137	153	9	(	(	PUNCT
ejpam-137	153	10	a	a	PROPN
ejpam-137	153	11	)	)	PUNCT
ejpam-137	153	12	/∈	/∈	PUNCT
ejpam-137	154	1	v	v	NOUN
ejpam-137	154	2	}	}	PUNCT
ejpam-137	154	3	.	.	PUNCT
ejpam-137	155	1	since	since	SCONJ
ejpam-137	155	2	f	f	PROPN
ejpam-137	155	3	(	(	PUNCT
ejpam-137	155	4	x	x	X
ejpam-137	155	5	)	)	PUNCT
ejpam-137	155	6	∈	∈	NOUN
ejpam-137	155	7	v	v	NOUN
ejpam-137	155	8	,	,	PUNCT
ejpam-137	155	9	therefore	therefore	ADV
ejpam-137	155	10	x	x	X
ejpam-137	155	11	/∈	/∈	PUNCT
ejpam-137	155	12	a	a	PRON
ejpam-137	155	13	and	and	CCONJ
ejpam-137	155	14	hence	hence	ADV
ejpam-137	155	15	f	f	PROPN
ejpam-137	155	16	(	(	PUNCT
ejpam-137	155	17	x	x	X
ejpam-137	155	18	)	)	PUNCT
ejpam-137	155	19	/∈	/∈	PUNCT
ejpam-137	156	1	f	f	X
ejpam-137	156	2	(	(	PUNCT
ejpam-137	156	3	a	a	NOUN
ejpam-137	156	4	)	)	PUNCT
ejpam-137	156	5	.	.	PUNCT
ejpam-137	157	1	since	since	SCONJ
ejpam-137	157	2	f	f	PROPN
ejpam-137	157	3	(	(	PUNCT
ejpam-137	157	4	a)∩(v	a)∩(v	ADV
ejpam-137	157	5	−	−	PROPN
ejpam-137	157	6	f	f	PROPN
ejpam-137	157	7	(	(	PUNCT
ejpam-137	157	8	x	x	NOUN
ejpam-137	157	9	)	)	PUNCT
ejpam-137	157	10	)	)	PUNCT
ejpam-137	158	1	=	=	SYM
ejpam-137	158	2	φ	φ	PROPN
ejpam-137	158	3	,	,	PUNCT
ejpam-137	158	4	therefore	therefore	ADV
ejpam-137	158	5	f	f	X
ejpam-137	158	6	(	(	PUNCT
ejpam-137	158	7	x	x	NOUN
ejpam-137	158	8	)	)	PUNCT
ejpam-137	158	9	/∈	/∈	PUNCT
ejpam-137	159	1	sdγ∗	sdγ∗	PROPN
ejpam-137	159	2	(	(	PUNCT
ejpam-137	159	3	f	f	PROPN
ejpam-137	159	4	(	(	PUNCT
ejpam-137	159	5	a	a	NOUN
ejpam-137	159	6	)	)	PUNCT
ejpam-137	159	7	)	)	PUNCT
ejpam-137	159	8	.	.	PUNCT
ejpam-137	160	1	it	it	PRON
ejpam-137	160	2	follows	follow	VERB
ejpam-137	160	3	that	that	SCONJ
ejpam-137	161	1	f	f	PROPN
ejpam-137	161	2	(	(	PUNCT
ejpam-137	161	3	x	x	X
ejpam-137	161	4	)	)	PUNCT
ejpam-137	161	5	∈	∈	PROPN
ejpam-137	161	6	f	f	X
ejpam-137	161	7	(	(	PUNCT
ejpam-137	161	8	sdγ∗(a))−	sdγ∗(a))−	PROPN
ejpam-137	161	9	(	(	PUNCT
ejpam-137	161	10	f	f	PROPN
ejpam-137	161	11	(	(	PUNCT
ejpam-137	161	12	a)∪	a)∪	ADV
ejpam-137	161	13	sdγ∗	sdγ∗	PROPN
ejpam-137	161	14	(	(	PUNCT
ejpam-137	161	15	f	f	PROPN
ejpam-137	161	16	(	(	PUNCT
ejpam-137	161	17	a	a	NOUN
ejpam-137	161	18	)	)	PUNCT
ejpam-137	161	19	)	)	PUNCT
ejpam-137	161	20	)	)	PUNCT
ejpam-137	161	21	6=	6=	ADP
ejpam-137	162	1	φ	φ	PROPN
ejpam-137	162	2	,	,	PUNCT
ejpam-137	162	3	which	which	PRON
ejpam-137	162	4	is	be	AUX
ejpam-137	162	5	a	a	DET
ejpam-137	162	6	contradiction	contradiction	NOUN
ejpam-137	162	7	to	to	ADP
ejpam-137	162	8	the	the	DET
ejpam-137	162	9	given	give	VERB
ejpam-137	162	10	condition	condition	NOUN
ejpam-137	162	11	.	.	PUNCT
ejpam-137	163	1	this	this	PRON
ejpam-137	163	2	proves	prove	VERB
ejpam-137	163	3	sufficiency	sufficiency	NOUN
ejpam-137	163	4	.	.	PUNCT
ejpam-137	164	1	theorem	theorem	PROPN
ejpam-137	164	2	3.11	3.11	NUM
ejpam-137	164	3	.	.	PUNCT
ejpam-137	165	1	let	let	VERB
ejpam-137	165	2	f	f	NOUN
ejpam-137	165	3	:	:	PUNCT
ejpam-137	165	4	x	x	X
ejpam-137	165	5	→	→	SYM
ejpam-137	165	6	y	y	PROPN
ejpam-137	165	7	be	be	AUX
ejpam-137	165	8	one	one	NUM
ejpam-137	165	9	-	-	PUNCT
ejpam-137	165	10	to	to	ADP
ejpam-137	165	11	-	-	PUNCT
ejpam-137	165	12	one	one	NUM
ejpam-137	165	13	function	function	NOUN
ejpam-137	165	14	.	.	PUNCT
ejpam-137	166	1	then	then	ADV
ejpam-137	166	2	f	f	PROPN
ejpam-137	166	3	is	be	AUX
ejpam-137	166	4	γ∗-irresolute	γ∗-irresolute	ADJ
ejpam-137	166	5	if	if	SCONJ
ejpam-137	167	1	and	and	CCONJ
ejpam-137	167	2	only	only	ADV
ejpam-137	167	3	if	if	SCONJ
ejpam-137	167	4	f	f	PROPN
ejpam-137	167	5	(	(	PUNCT
ejpam-137	167	6	sdγ∗(a))⊆	sdγ∗(a))⊆	PROPN
ejpam-137	167	7	sdγ∗	sdγ∗	NOUN
ejpam-137	167	8	(	(	PUNCT
ejpam-137	167	9	f	f	PROPN
ejpam-137	167	10	(	(	PUNCT
ejpam-137	167	11	a	a	NOUN
ejpam-137	167	12	)	)	PUNCT
ejpam-137	167	13	)	)	PUNCT
ejpam-137	167	14	,	,	PUNCT
ejpam-137	167	15	for	for	ADP
ejpam-137	167	16	all	all	DET
ejpam-137	167	17	a⊆	a⊆	NOUN
ejpam-137	167	18	x	x	X
ejpam-137	167	19	.	.	PUNCT
ejpam-137	168	1	proof	proof	NOUN
ejpam-137	168	2	.	.	PUNCT
ejpam-137	169	1	let	let	VERB
ejpam-137	169	2	a⊆	a⊆	VERB
ejpam-137	169	3	x	x	PRON
ejpam-137	169	4	,	,	PUNCT
ejpam-137	169	5	x	x	SYM
ejpam-137	169	6	∈	∈	PROPN
ejpam-137	169	7	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	169	8	)	)	PUNCT
ejpam-137	169	9	and	and	CCONJ
ejpam-137	169	10	v	v	AUX
ejpam-137	169	11	be	be	AUX
ejpam-137	169	12	a	a	DET
ejpam-137	169	13	γ	γ	NOUN
ejpam-137	169	14	-	-	PUNCT
ejpam-137	169	15	semi	semi	NOUN
ejpam-137	169	16	-	-	NOUN
ejpam-137	169	17	nbd	nbd	PROPN
ejpam-137	169	18	of	of	ADP
ejpam-137	169	19	f	f	PROPN
ejpam-137	169	20	(	(	PUNCT
ejpam-137	169	21	x	x	NOUN
ejpam-137	169	22	)	)	PUNCT
ejpam-137	169	23	.	.	PUNCT
ejpam-137	170	1	since	since	SCONJ
ejpam-137	170	2	f	f	PROPN
ejpam-137	170	3	is	be	AUX
ejpam-137	170	4	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	170	5	,	,	PUNCT
ejpam-137	170	6	so	so	ADV
ejpam-137	170	7	by	by	ADP
ejpam-137	170	8	theorem	theorem	NOUN
ejpam-137	170	9	3.5	3.5	NUM
ejpam-137	170	10	,	,	PUNCT
ejpam-137	170	11	there	there	PRON
ejpam-137	170	12	exists	exist	VERB
ejpam-137	170	13	a	a	DET
ejpam-137	170	14	γ	γ	X
ejpam-137	170	15	-	-	PUNCT
ejpam-137	170	16	semi	semi	ADJ
ejpam-137	170	17	-	-	ADJ
ejpam-137	170	18	nbd	nbd	ADJ
ejpam-137	170	19	u	u	NOUN
ejpam-137	170	20	of	of	ADP
ejpam-137	170	21	x	x	SYM
ejpam-137	170	22	such	such	ADJ
ejpam-137	170	23	that	that	SCONJ
ejpam-137	170	24	f	f	PROPN
ejpam-137	170	25	(	(	PUNCT
ejpam-137	170	26	u)⊆	u)⊆	PROPN
ejpam-137	170	27	v	v	NOUN
ejpam-137	170	28	.	.	PUNCT
ejpam-137	171	1	but	but	CCONJ
ejpam-137	171	2	x	x	X
ejpam-137	171	3	∈	∈	PROPN
ejpam-137	171	4	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	171	5	)	)	PUNCT
ejpam-137	171	6	gives	give	VERB
ejpam-137	171	7	there	there	ADV
ejpam-137	171	8	exists	exist	VERB
ejpam-137	171	9	an	an	DET
ejpam-137	171	10	element	element	NOUN
ejpam-137	171	11	a	a	DET
ejpam-137	171	12	∈	∈	PROPN
ejpam-137	171	13	u	u	NOUN
ejpam-137	171	14	∩	∩	NOUN
ejpam-137	171	15	a	a	DET
ejpam-137	171	16	such	such	ADJ
ejpam-137	171	17	that	that	SCONJ
ejpam-137	171	18	a	a	DET
ejpam-137	171	19	6=	6=	NOUN
ejpam-137	171	20	x	x	X
ejpam-137	171	21	.	.	PUNCT
ejpam-137	172	1	clearly	clearly	ADV
ejpam-137	172	2	f	f	X
ejpam-137	172	3	(	(	PUNCT
ejpam-137	172	4	a	a	X
ejpam-137	172	5	)	)	PUNCT
ejpam-137	172	6	∈	∈	PROPN
ejpam-137	172	7	f	f	X
ejpam-137	172	8	(	(	PUNCT
ejpam-137	172	9	a	a	NOUN
ejpam-137	172	10	)	)	PUNCT
ejpam-137	172	11	and	and	CCONJ
ejpam-137	172	12	since	since	SCONJ
ejpam-137	172	13	f	f	PROPN
ejpam-137	172	14	is	be	AUX
ejpam-137	172	15	one	one	NUM
ejpam-137	172	16	to	to	ADP
ejpam-137	172	17	one	one	NUM
ejpam-137	172	18	,	,	PUNCT
ejpam-137	172	19	f	f	PROPN
ejpam-137	172	20	(	(	PUNCT
ejpam-137	172	21	a	a	NOUN
ejpam-137	172	22	)	)	PUNCT
ejpam-137	172	23	6=	6=	ADP
ejpam-137	173	1	f	f	PROPN
ejpam-137	173	2	(	(	PUNCT
ejpam-137	173	3	x	x	NOUN
ejpam-137	173	4	)	)	PUNCT
ejpam-137	173	5	.	.	PUNCT
ejpam-137	174	1	thus	thus	ADV
ejpam-137	174	2	every	every	DET
ejpam-137	174	3	γ	γ	PROPN
ejpam-137	174	4	-	-	PUNCT
ejpam-137	174	5	semi	semi	NOUN
ejpam-137	174	6	-	-	NOUN
ejpam-137	174	7	nbd	nbd	ADJ
ejpam-137	174	8	v	v	NOUN
ejpam-137	174	9	of	of	ADP
ejpam-137	174	10	f	f	PROPN
ejpam-137	174	11	(	(	PUNCT
ejpam-137	174	12	x	x	X
ejpam-137	174	13	)	)	PUNCT
ejpam-137	174	14	contains	contain	VERB
ejpam-137	174	15	an	an	DET
ejpam-137	174	16	element	element	NOUN
ejpam-137	174	17	f	f	NOUN
ejpam-137	174	18	(	(	PUNCT
ejpam-137	174	19	a	a	NOUN
ejpam-137	174	20	)	)	PUNCT
ejpam-137	174	21	of	of	ADP
ejpam-137	174	22	f	f	PROPN
ejpam-137	174	23	(	(	PUNCT
ejpam-137	174	24	a	a	X
ejpam-137	174	25	)	)	PUNCT
ejpam-137	174	26	different	different	ADJ
ejpam-137	174	27	from	from	ADP
ejpam-137	174	28	f	f	PROPN
ejpam-137	174	29	(	(	PUNCT
ejpam-137	174	30	x	x	NOUN
ejpam-137	174	31	)	)	PUNCT
ejpam-137	174	32	.	.	PUNCT
ejpam-137	175	1	consequently	consequently	ADV
ejpam-137	175	2	f	f	X
ejpam-137	175	3	(	(	PUNCT
ejpam-137	175	4	x	x	X
ejpam-137	175	5	)	)	PUNCT
ejpam-137	175	6	∈	∈	PROPN
ejpam-137	175	7	sdγ∗	sdγ∗	NOUN
ejpam-137	175	8	(	(	PUNCT
ejpam-137	175	9	f	f	PROPN
ejpam-137	175	10	(	(	PUNCT
ejpam-137	175	11	a	a	NOUN
ejpam-137	175	12	)	)	PUNCT
ejpam-137	175	13	)	)	PUNCT
ejpam-137	175	14	.	.	PUNCT
ejpam-137	176	1	therefore	therefore	ADV
ejpam-137	176	2	we	we	PRON
ejpam-137	176	3	have	have	VERB
ejpam-137	176	4	f	f	PROPN
ejpam-137	176	5	(	(	PUNCT
ejpam-137	176	6	sdγ∗(a	sdγ∗(a	NOUN
ejpam-137	176	7	)	)	PUNCT
ejpam-137	176	8	)	)	PUNCT
ejpam-137	177	1	⊆	⊆	NUM
ejpam-137	177	2	sdγ∗	sdγ∗	NOUN
ejpam-137	177	3	(	(	PUNCT
ejpam-137	177	4	f	f	X
ejpam-137	177	5	(	(	PUNCT
ejpam-137	177	6	a	a	NOUN
ejpam-137	177	7	)	)	PUNCT
ejpam-137	177	8	)	)	PUNCT
ejpam-137	177	9	.	.	PUNCT
ejpam-137	178	1	this	this	PRON
ejpam-137	178	2	proves	prove	VERB
ejpam-137	178	3	the	the	DET
ejpam-137	178	4	necessity	necessity	NOUN
ejpam-137	178	5	.	.	PUNCT
ejpam-137	179	1	sufficiency	sufficiency	PROPN
ejpam-137	179	2	follows	follow	VERB
ejpam-137	179	3	from	from	ADP
ejpam-137	179	4	theorem	theorem	ADJ
ejpam-137	179	5	3.10	3.10	NUM
ejpam-137	179	6	.	.	PUNCT
ejpam-137	180	1	this	this	PRON
ejpam-137	180	2	completes	complete	VERB
ejpam-137	180	3	the	the	DET
ejpam-137	180	4	proof	proof	NOUN
ejpam-137	180	5	.	.	PUNCT
ejpam-137	181	1	h.	h.	PROPN
ejpam-137	181	2	ogata	ogata	PROPN
ejpam-137	182	1	[	[	X
ejpam-137	182	2	14	14	NUM
ejpam-137	182	3	]	]	PUNCT
ejpam-137	182	4	defined	define	VERB
ejpam-137	182	5	the	the	DET
ejpam-137	182	6	notion	notion	NOUN
ejpam-137	182	7	of	of	ADP
ejpam-137	182	8	γ	γ	PROPN
ejpam-137	182	9	-	-	ADJ
ejpam-137	182	10	t2	t2	ADJ
ejpam-137	182	11	spaces	space	NOUN
ejpam-137	182	12	in	in	ADP
ejpam-137	182	13	topological	topological	ADJ
ejpam-137	182	14	spaces	space	NOUN
ejpam-137	182	15	,	,	PUNCT
ejpam-137	182	16	we	we	PRON
ejpam-137	182	17	generalize	generalize	VERB
ejpam-137	182	18	this	this	DET
ejpam-137	182	19	notion	notion	NOUN
ejpam-137	182	20	and	and	CCONJ
ejpam-137	182	21	define	define	VERB
ejpam-137	182	22	:	:	PUNCT
ejpam-137	182	23	definition	definition	NOUN
ejpam-137	182	24	3.12	3.12	NUM
ejpam-137	182	25	.	.	PUNCT
ejpam-137	183	1	a	a	DET
ejpam-137	183	2	space	space	NOUN
ejpam-137	183	3	x	x	PUNCT
ejpam-137	183	4	is	be	AUX
ejpam-137	183	5	said	say	VERB
ejpam-137	183	6	to	to	PART
ejpam-137	183	7	be	be	AUX
ejpam-137	183	8	γ	γ	X
ejpam-137	183	9	-	-	PUNCT
ejpam-137	183	10	semi	semi	NOUN
ejpam-137	183	11	-	-	NOUN
ejpam-137	183	12	t2	t2	ADJ
ejpam-137	183	13	,	,	PUNCT
ejpam-137	183	14	if	if	SCONJ
ejpam-137	183	15	for	for	ADP
ejpam-137	183	16	each	each	DET
ejpam-137	183	17	two	two	NUM
ejpam-137	183	18	distinct	distinct	ADJ
ejpam-137	183	19	points	point	NOUN
ejpam-137	183	20	x	x	X
ejpam-137	183	21	,	,	PUNCT
ejpam-137	183	22	y	y	PROPN
ejpam-137	183	23	∈	∈	PROPN
ejpam-137	183	24	x	x	PUNCT
ejpam-137	183	25	there	there	PRON
ejpam-137	183	26	exist	exist	VERB
ejpam-137	183	27	u	u	NOUN
ejpam-137	183	28	,	,	PUNCT
ejpam-137	183	29	v	v	NOUN
ejpam-137	183	30	∈	∈	PROPN
ejpam-137	183	31	soγ∗(x	soγ∗(x	NOUN
ejpam-137	183	32	)	)	PUNCT
ejpam-137	183	33	such	such	ADJ
ejpam-137	183	34	that	that	SCONJ
ejpam-137	183	35	x	x	SYM
ejpam-137	183	36	∈	∈	PROPN
ejpam-137	183	37	u	u	NOUN
ejpam-137	183	38	,	,	PUNCT
ejpam-137	183	39	y	y	PROPN
ejpam-137	183	40	∈	∈	PROPN
ejpam-137	183	41	v	v	NOUN
ejpam-137	183	42	and	and	CCONJ
ejpam-137	183	43	u	u	NOUN
ejpam-137	183	44	∩	∩	NOUN
ejpam-137	183	45	v	v	NOUN
ejpam-137	183	46	=	=	SYM
ejpam-137	183	47	φ	φ	PROPN
ejpam-137	183	48	.	.	PUNCT
ejpam-137	184	1	theorem	theorem	VERB
ejpam-137	184	2	3.13	3.13	NUM
ejpam-137	184	3	.	.	PUNCT
ejpam-137	185	1	if	if	SCONJ
ejpam-137	185	2	f	f	PROPN
ejpam-137	185	3	:	:	PUNCT
ejpam-137	185	4	x	x	X
ejpam-137	185	5	→	→	SYM
ejpam-137	185	6	y	y	PROPN
ejpam-137	185	7	is	be	AUX
ejpam-137	185	8	a	a	DET
ejpam-137	185	9	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	185	10	injection	injection	NOUN
ejpam-137	185	11	and	and	CCONJ
ejpam-137	185	12	y	y	PROPN
ejpam-137	185	13	is	be	AUX
ejpam-137	185	14	γ	γ	NOUN
ejpam-137	185	15	-	-	PUNCT
ejpam-137	185	16	semi	semi	NOUN
ejpam-137	185	17	-	-	NOUN
ejpam-137	185	18	t2	t2	NOUN
ejpam-137	185	19	,	,	PUNCT
ejpam-137	185	20	then	then	ADV
ejpam-137	185	21	x	x	PUNCT
ejpam-137	185	22	is	be	AUX
ejpam-137	185	23	γ	γ	X
ejpam-137	185	24	-	-	PUNCT
ejpam-137	185	25	semi	semi	NOUN
ejpam-137	185	26	-	-	NOUN
ejpam-137	185	27	t2	t2	NOUN
ejpam-137	185	28	.	.	PUNCT
ejpam-137	186	1	proof	proof	NOUN
ejpam-137	186	2	.	.	PUNCT
ejpam-137	187	1	let	let	VERB
ejpam-137	187	2	x1	x1	PROPN
ejpam-137	187	3	and	and	CCONJ
ejpam-137	187	4	x2	x2	PROPN
ejpam-137	187	5	be	be	VERB
ejpam-137	187	6	two	two	NUM
ejpam-137	187	7	distinct	distinct	ADJ
ejpam-137	187	8	points	point	NOUN
ejpam-137	187	9	of	of	ADP
ejpam-137	187	10	x.	x.	NOUN
ejpam-137	187	11	since	since	SCONJ
ejpam-137	187	12	f	f	PROPN
ejpam-137	187	13	is	be	AUX
ejpam-137	187	14	injective	injective	ADJ
ejpam-137	187	15	,	,	PUNCT
ejpam-137	187	16	therefore	therefore	ADV
ejpam-137	187	17	f	f	X
ejpam-137	187	18	(	(	PUNCT
ejpam-137	187	19	x1	x1	PROPN
ejpam-137	187	20	)	)	PUNCT
ejpam-137	187	21	6=	6=	ADP
ejpam-137	188	1	f	f	PROPN
ejpam-137	188	2	(	(	PUNCT
ejpam-137	188	3	x2	x2	PROPN
ejpam-137	188	4	)	)	PUNCT
ejpam-137	188	5	.	.	PUNCT
ejpam-137	189	1	since	since	SCONJ
ejpam-137	189	2	y	y	PROPN
ejpam-137	189	3	is	be	AUX
ejpam-137	189	4	γ	γ	NOUN
ejpam-137	189	5	-	-	PUNCT
ejpam-137	189	6	semi	semi	NOUN
ejpam-137	189	7	-	-	NOUN
ejpam-137	189	8	t2	t2	NOUN
ejpam-137	189	9	,	,	PUNCT
ejpam-137	189	10	there	there	PRON
ejpam-137	189	11	exist	exist	VERB
ejpam-137	189	12	v1	v1	NOUN
ejpam-137	189	13	,	,	PUNCT
ejpam-137	189	14	v2	v2	PROPN
ejpam-137	189	15	∈	∈	PROPN
ejpam-137	189	16	soγ∗(y	soγ∗(y	PROPN
ejpam-137	189	17	)	)	PUNCT
ejpam-137	189	18	such	such	ADJ
ejpam-137	189	19	that	that	SCONJ
ejpam-137	189	20	f	f	PROPN
ejpam-137	189	21	(	(	PUNCT
ejpam-137	189	22	x1	x1	PROPN
ejpam-137	189	23	)	)	PUNCT
ejpam-137	189	24	∈	∈	PROPN
ejpam-137	189	25	v1	v1	NOUN
ejpam-137	189	26	,	,	PUNCT
ejpam-137	189	27	f	f	PROPN
ejpam-137	189	28	(	(	PUNCT
ejpam-137	189	29	x2	x2	ADJ
ejpam-137	189	30	)	)	PUNCT
ejpam-137	189	31	∈	∈	PROPN
ejpam-137	189	32	v2	v2	NOUN
ejpam-137	189	33	and	and	CCONJ
ejpam-137	189	34	v1	v1	NOUN
ejpam-137	189	35	∩	∩	ADJ
ejpam-137	189	36	v2	v2	NOUN
ejpam-137	189	37	=	=	SYM
ejpam-137	189	38	φ	φ	PROPN
ejpam-137	189	39	.	.	PUNCT
ejpam-137	190	1	then	then	ADV
ejpam-137	190	2	x1	x1	PROPN
ejpam-137	190	3	∈	∈	PROPN
ejpam-137	190	4	f	f	X
ejpam-137	190	5	−1(v1	−1(v1	X
ejpam-137	190	6	)	)	PUNCT
ejpam-137	190	7	,	,	PUNCT
ejpam-137	190	8	x2	x2	PROPN
ejpam-137	190	9	∈	∈	PROPN
ejpam-137	190	10	f	f	PROPN
ejpam-137	190	11	−1(v2	−1(v2	NOUN
ejpam-137	190	12	)	)	PUNCT
ejpam-137	190	13	and	and	CCONJ
ejpam-137	190	14	f	f	PROPN
ejpam-137	190	15	−1(v1	−1(v1	X
ejpam-137	190	16	)	)	PUNCT
ejpam-137	190	17	∩	∩	PROPN
ejpam-137	190	18	f	f	PROPN
ejpam-137	190	19	−1(v2	−1(v2	PROPN
ejpam-137	190	20	)	)	PUNCT
ejpam-137	190	21	=	=	SYM
ejpam-137	191	1	φ	φ	PROPN
ejpam-137	191	2	.	.	PUNCT
ejpam-137	192	1	since	since	SCONJ
ejpam-137	192	2	f	f	PROPN
ejpam-137	192	3	is	be	AUX
ejpam-137	192	4	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	192	5	,	,	PUNCT
ejpam-137	192	6	so	so	SCONJ
ejpam-137	192	7	f	f	PROPN
ejpam-137	192	8	−1(v1	−1(v1	X
ejpam-137	192	9	)	)	PUNCT
ejpam-137	192	10	,	,	PUNCT
ejpam-137	192	11	f	f	PROPN
ejpam-137	192	12	−1(v2	−1(v2	NOUN
ejpam-137	192	13	)	)	PUNCT
ejpam-137	192	14	∈	∈	PROPN
ejpam-137	192	15	soγ∗(x	soγ∗(x	NOUN
ejpam-137	192	16	)	)	PUNCT
ejpam-137	192	17	.	.	PUNCT
ejpam-137	193	1	this	this	PRON
ejpam-137	193	2	proves	prove	VERB
ejpam-137	193	3	that	that	SCONJ
ejpam-137	193	4	x	x	PRON
ejpam-137	193	5	is	be	AUX
ejpam-137	193	6	γ	γ	X
ejpam-137	193	7	-	-	PUNCT
ejpam-137	193	8	semi	semi	NOUN
ejpam-137	193	9	-	-	NOUN
ejpam-137	193	10	t2	t2	NOUN
ejpam-137	193	11	.	.	PUNCT
ejpam-137	194	1	4	4	X
ejpam-137	194	2	.	.	X
ejpam-137	194	3	γ	γ	X
ejpam-137	194	4	-	-	PUNCT
ejpam-137	194	5	pre	pre	ADJ
ejpam-137	194	6	-	-	ADJ
ejpam-137	194	7	semi	semi	ADJ
ejpam-137	194	8	-	-	ADJ
ejpam-137	194	9	open	open	ADJ
ejpam-137	194	10	functions	function	NOUN
ejpam-137	194	11	definition	definition	NOUN
ejpam-137	194	12	4.1	4.1	NUM
ejpam-137	194	13	.	.	PUNCT
ejpam-137	195	1	let	let	VERB
ejpam-137	195	2	x	x	PRON
ejpam-137	195	3	and	and	CCONJ
ejpam-137	195	4	y	y	PROPN
ejpam-137	195	5	be	be	AUX
ejpam-137	195	6	spaces	space	NOUN
ejpam-137	195	7	.	.	PUNCT
ejpam-137	196	1	then	then	ADV
ejpam-137	196	2	a	a	DET
ejpam-137	196	3	function	function	NOUN
ejpam-137	196	4	f	f	NOUN
ejpam-137	196	5	:	:	PUNCT
ejpam-137	196	6	x	x	X
ejpam-137	196	7	→	→	SYM
ejpam-137	196	8	y	y	PROPN
ejpam-137	196	9	is	be	AUX
ejpam-137	196	10	said	say	VERB
ejpam-137	196	11	to	to	PART
ejpam-137	196	12	be	be	AUX
ejpam-137	196	13	γ	γ	X
ejpam-137	196	14	-	-	PUNCT
ejpam-137	196	15	pre	pre	ADJ
ejpam-137	196	16	-	-	ADJ
ejpam-137	196	17	semiopen	semiopen	ADJ
ejpam-137	196	18	if	if	SCONJ
ejpam-137	196	19	and	and	CCONJ
ejpam-137	196	20	only	only	ADV
ejpam-137	196	21	if	if	SCONJ
ejpam-137	196	22	for	for	SCONJ
ejpam-137	196	23	each	each	DET
ejpam-137	196	24	a∈	a∈	PROPN
ejpam-137	196	25	soγ∗(x	soγ∗(x	NOUN
ejpam-137	196	26	)	)	PUNCT
ejpam-137	196	27	,	,	PUNCT
ejpam-137	196	28	f	f	PROPN
ejpam-137	196	29	(	(	PUNCT
ejpam-137	196	30	a	a	PRON
ejpam-137	196	31	)	)	PUNCT
ejpam-137	196	32	∈	∈	PROPN
ejpam-137	196	33	soγ∗(y	soγ∗(y	PROPN
ejpam-137	196	34	)	)	PUNCT
ejpam-137	196	35	.	.	PUNCT
ejpam-137	197	1	b.	b.	PROPN
ejpam-137	197	2	ahmad	ahmad	PROPN
ejpam-137	197	3	,	,	PUNCT
ejpam-137	197	4	s.	s.	PROPN
ejpam-137	197	5	hussain	hussain	PROPN
ejpam-137	197	6	,	,	PUNCT
ejpam-137	197	7	and	and	CCONJ
ejpam-137	197	8	t.	t.	PROPN
ejpam-137	197	9	noiri	noiri	PROPN
ejpam-137	197	10	/	/	SYM
ejpam-137	197	11	eur	eur	PROPN
ejpam-137	197	12	.	.	PUNCT
ejpam-137	198	1	j.	j.	PROPN
ejpam-137	198	2	pure	pure	PROPN
ejpam-137	198	3	appl	appl	PROPN
ejpam-137	198	4	.	.	PROPN
ejpam-137	198	5	math	math	PROPN
ejpam-137	198	6	,	,	PUNCT
ejpam-137	198	7	1	1	NUM
ejpam-137	198	8	(	(	PUNCT
ejpam-137	198	9	2008	2008	NUM
ejpam-137	198	10	)	)	PUNCT
ejpam-137	198	11	,	,	PUNCT
ejpam-137	198	12	(	(	PUNCT
ejpam-137	198	13	22	22	NUM
ejpam-137	198	14	-	-	SYM
ejpam-137	198	15	29	29	NUM
ejpam-137	198	16	)	)	PUNCT
ejpam-137	198	17	26	26	NUM
ejpam-137	198	18	remark	remark	NOUN
ejpam-137	198	19	4.2	4.2	NUM
ejpam-137	198	20	.	.	PUNCT
ejpam-137	199	1	the	the	DET
ejpam-137	199	2	class	class	NOUN
ejpam-137	199	3	of	of	ADP
ejpam-137	199	4	γ	γ	X
ejpam-137	199	5	-	-	PUNCT
ejpam-137	199	6	pre	pre	ADJ
ejpam-137	199	7	-	-	ADJ
ejpam-137	199	8	semi	semi	ADJ
ejpam-137	199	9	-	-	ADJ
ejpam-137	199	10	open	open	ADJ
ejpam-137	199	11	functions	function	NOUN
ejpam-137	199	12	is	be	AUX
ejpam-137	199	13	a	a	DET
ejpam-137	199	14	subclass	subclass	NOUN
ejpam-137	199	15	of	of	ADP
ejpam-137	199	16	class	class	NOUN
ejpam-137	199	17	of	of	ADP
ejpam-137	199	18	γ	γ	X
ejpam-137	199	19	-	-	PUNCT
ejpam-137	199	20	semi	semi	ADJ
ejpam-137	199	21	-	-	ADJ
ejpam-137	199	22	open	open	ADJ
ejpam-137	199	23	functions	function	NOUN
ejpam-137	199	24	defined	define	VERB
ejpam-137	199	25	in	in	ADP
ejpam-137	199	26	[	[	X
ejpam-137	199	27	5	5	NUM
ejpam-137	199	28	]	]	PUNCT
ejpam-137	199	29	.	.	PUNCT
ejpam-137	200	1	note	note	VERB
ejpam-137	200	2	that	that	SCONJ
ejpam-137	200	3	if	if	SCONJ
ejpam-137	200	4	f	f	X
ejpam-137	200	5	:	:	PUNCT
ejpam-137	200	6	x	x	X
ejpam-137	200	7	→	→	SYM
ejpam-137	200	8	y	y	PROPN
ejpam-137	200	9	and	and	CCONJ
ejpam-137	200	10	g	g	PROPN
ejpam-137	200	11	:	:	PUNCT
ejpam-137	200	12	y	y	PROPN
ejpam-137	200	13	→	→	SYM
ejpam-137	200	14	z	z	X
ejpam-137	200	15	be	be	AUX
ejpam-137	200	16	any	any	DET
ejpam-137	200	17	two	two	NUM
ejpam-137	200	18	γ	γ	NOUN
ejpam-137	200	19	-	-	PUNCT
ejpam-137	200	20	pre	pre	ADJ
ejpam-137	200	21	-	-	ADJ
ejpam-137	200	22	semi	semi	ADJ
ejpam-137	200	23	-	-	ADJ
ejpam-137	200	24	open	open	ADJ
ejpam-137	200	25	functions	function	NOUN
ejpam-137	200	26	,	,	PUNCT
ejpam-137	200	27	then	then	ADV
ejpam-137	200	28	the	the	DET
ejpam-137	200	29	composition	composition	NOUN
ejpam-137	200	30	go	go	VERB
ejpam-137	200	31	f	f	NOUN
ejpam-137	200	32	:	:	PUNCT
ejpam-137	200	33	x	x	X
ejpam-137	200	34	→	→	SYM
ejpam-137	200	35	z	z	NOUN
ejpam-137	200	36	is	be	AUX
ejpam-137	200	37	a	a	DET
ejpam-137	200	38	γ	γ	X
ejpam-137	200	39	-	-	PUNCT
ejpam-137	200	40	pre	pre	ADJ
ejpam-137	200	41	-	-	ADJ
ejpam-137	200	42	semi	semi	ADJ
ejpam-137	200	43	-	-	ADJ
ejpam-137	200	44	open	open	ADJ
ejpam-137	200	45	function	function	NOUN
ejpam-137	200	46	.	.	PUNCT
ejpam-137	201	1	the	the	DET
ejpam-137	201	2	following	follow	VERB
ejpam-137	201	3	theorem	theorem	NOUN
ejpam-137	201	4	is	be	AUX
ejpam-137	201	5	easy	easy	ADJ
ejpam-137	201	6	to	to	PART
ejpam-137	201	7	prove	prove	VERB
ejpam-137	201	8	:	:	PUNCT
ejpam-137	201	9	theorem	theorem	VERB
ejpam-137	201	10	4.3	4.3	NUM
ejpam-137	201	11	.	.	PUNCT
ejpam-137	202	1	a	a	DET
ejpam-137	202	2	function	function	NOUN
ejpam-137	202	3	f	f	NOUN
ejpam-137	202	4	:	:	PUNCT
ejpam-137	202	5	x	x	X
ejpam-137	202	6	→	→	SYM
ejpam-137	202	7	y	y	PROPN
ejpam-137	202	8	is	be	AUX
ejpam-137	202	9	γ	γ	PROPN
ejpam-137	202	10	-	-	PUNCT
ejpam-137	202	11	pre	pre	ADJ
ejpam-137	202	12	-	-	ADJ
ejpam-137	202	13	semi	semi	ADJ
ejpam-137	202	14	-	-	ADJ
ejpam-137	202	15	open	open	ADJ
ejpam-137	202	16	if	if	SCONJ
ejpam-137	202	17	and	and	CCONJ
ejpam-137	202	18	only	only	ADV
ejpam-137	202	19	if	if	SCONJ
ejpam-137	202	20	for	for	ADP
ejpam-137	202	21	each	each	DET
ejpam-137	202	22	x	x	SYM
ejpam-137	202	23	∈	∈	PROPN
ejpam-137	202	24	x	x	X
ejpam-137	202	25	and	and	CCONJ
ejpam-137	202	26	for	for	SCONJ
ejpam-137	202	27	every	every	DET
ejpam-137	202	28	a∈	a∈	PROPN
ejpam-137	202	29	soγ∗(x	soγ∗(x	VERB
ejpam-137	202	30	)	)	PUNCT
ejpam-137	202	31	such	such	ADJ
ejpam-137	202	32	that	that	SCONJ
ejpam-137	202	33	x	x	SYM
ejpam-137	202	34	∈	∈	PROPN
ejpam-137	202	35	a	a	PRON
ejpam-137	202	36	,	,	PUNCT
ejpam-137	202	37	there	there	PRON
ejpam-137	202	38	exists	exist	VERB
ejpam-137	202	39	b	b	PROPN
ejpam-137	202	40	∈	∈	PROPN
ejpam-137	202	41	soγ∗(y	soγ∗(y	PROPN
ejpam-137	202	42	)	)	PUNCT
ejpam-137	203	1	such	such	ADJ
ejpam-137	203	2	that	that	SCONJ
ejpam-137	203	3	f	f	PROPN
ejpam-137	203	4	(	(	PUNCT
ejpam-137	203	5	x	x	X
ejpam-137	203	6	)	)	PUNCT
ejpam-137	203	7	∈	∈	PROPN
ejpam-137	203	8	b	b	PROPN
ejpam-137	203	9	and	and	CCONJ
ejpam-137	203	10	b	b	PROPN
ejpam-137	203	11	⊆	⊆	NUM
ejpam-137	203	12	f	f	X
ejpam-137	203	13	(	(	PUNCT
ejpam-137	203	14	a	a	NOUN
ejpam-137	203	15	)	)	PUNCT
ejpam-137	203	16	.	.	PUNCT
ejpam-137	204	1	theorem	theorem	VERB
ejpam-137	204	2	4.4	4.4	NUM
ejpam-137	204	3	.	.	PUNCT
ejpam-137	205	1	a	a	DET
ejpam-137	205	2	function	function	NOUN
ejpam-137	205	3	f	f	NOUN
ejpam-137	205	4	:	:	PUNCT
ejpam-137	205	5	x	x	X
ejpam-137	205	6	→	→	SYM
ejpam-137	205	7	y	y	PROPN
ejpam-137	205	8	is	be	AUX
ejpam-137	205	9	γ	γ	PROPN
ejpam-137	205	10	-	-	PUNCT
ejpam-137	205	11	pre	pre	ADJ
ejpam-137	205	12	-	-	ADJ
ejpam-137	205	13	semi	semi	ADJ
ejpam-137	205	14	-	-	ADJ
ejpam-137	205	15	open	open	ADJ
ejpam-137	205	16	if	if	SCONJ
ejpam-137	205	17	and	and	CCONJ
ejpam-137	205	18	only	only	ADV
ejpam-137	205	19	if	if	SCONJ
ejpam-137	205	20	for	for	ADP
ejpam-137	205	21	each	each	DET
ejpam-137	205	22	x	x	SYM
ejpam-137	205	23	∈	∈	PROPN
ejpam-137	205	24	x	x	X
ejpam-137	205	25	and	and	CCONJ
ejpam-137	205	26	for	for	ADP
ejpam-137	205	27	every	every	DET
ejpam-137	205	28	γ	γ	PROPN
ejpam-137	205	29	-	-	PUNCT
ejpam-137	205	30	semi	semi	ADJ
ejpam-137	205	31	-	-	ADJ
ejpam-137	205	32	nbd	nbd	ADJ
ejpam-137	205	33	u	u	NOUN
ejpam-137	205	34	of	of	ADP
ejpam-137	205	35	x	x	PUNCT
ejpam-137	205	36	in	in	ADP
ejpam-137	205	37	x	x	NOUN
ejpam-137	205	38	,	,	PUNCT
ejpam-137	205	39	there	there	PRON
ejpam-137	205	40	exists	exist	VERB
ejpam-137	205	41	a	a	DET
ejpam-137	205	42	γ	γ	X
ejpam-137	205	43	-	-	PUNCT
ejpam-137	205	44	semi	semi	NOUN
ejpam-137	205	45	-	-	NOUN
ejpam-137	205	46	nbd	nbd	ADJ
ejpam-137	205	47	v	v	NOUN
ejpam-137	205	48	of	of	ADP
ejpam-137	205	49	f	f	PROPN
ejpam-137	205	50	(	(	PUNCT
ejpam-137	205	51	x	x	X
ejpam-137	205	52	)	)	PUNCT
ejpam-137	205	53	in	in	ADP
ejpam-137	205	54	y	y	PRON
ejpam-137	206	1	such	such	ADJ
ejpam-137	206	2	that	that	PRON
ejpam-137	206	3	v	v	ADP
ejpam-137	206	4	⊆	⊆	NUM
ejpam-137	206	5	f	f	PROPN
ejpam-137	206	6	(	(	PUNCT
ejpam-137	206	7	u	u	NOUN
ejpam-137	206	8	)	)	PUNCT
ejpam-137	206	9	.	.	PUNCT
ejpam-137	207	1	proof	proof	NOUN
ejpam-137	207	2	.	.	PUNCT
ejpam-137	208	1	let	let	VERB
ejpam-137	208	2	u	u	PRON
ejpam-137	208	3	be	be	AUX
ejpam-137	208	4	a	a	DET
ejpam-137	208	5	γ	γ	NOUN
ejpam-137	208	6	-	-	PUNCT
ejpam-137	208	7	semi	semi	NOUN
ejpam-137	208	8	-	-	NOUN
ejpam-137	208	9	nbd	nbd	NOUN
ejpam-137	208	10	of	of	ADP
ejpam-137	208	11	x	x	SYM
ejpam-137	208	12	∈	∈	PROPN
ejpam-137	208	13	x	x	X
ejpam-137	208	14	.	.	PUNCT
ejpam-137	209	1	then	then	ADV
ejpam-137	209	2	by	by	ADP
ejpam-137	209	3	definition	definition	NOUN
ejpam-137	209	4	there	there	PRON
ejpam-137	209	5	exists	exist	VERB
ejpam-137	209	6	w	w	PROPN
ejpam-137	209	7	∈	∈	PROPN
ejpam-137	209	8	soγ∗(x	soγ∗(x	NOUN
ejpam-137	209	9	)	)	PUNCT
ejpam-137	209	10	such	such	ADJ
ejpam-137	209	11	that	that	SCONJ
ejpam-137	209	12	x	x	SYM
ejpam-137	209	13	∈w	∈w	VERB
ejpam-137	209	14	⊆	⊆	NUM
ejpam-137	209	15	u	u	NOUN
ejpam-137	209	16	.	.	PUNCT
ejpam-137	210	1	then	then	ADV
ejpam-137	210	2	f	f	X
ejpam-137	210	3	(	(	PUNCT
ejpam-137	210	4	x	x	X
ejpam-137	210	5	)	)	PUNCT
ejpam-137	210	6	∈	∈	PROPN
ejpam-137	210	7	f	f	X
ejpam-137	210	8	(	(	PUNCT
ejpam-137	210	9	w	w	PROPN
ejpam-137	210	10	)	)	PUNCT
ejpam-137	210	11	⊆	⊆	NUM
ejpam-137	210	12	f	f	X
ejpam-137	210	13	(	(	PUNCT
ejpam-137	210	14	u	u	NOUN
ejpam-137	210	15	)	)	PUNCT
ejpam-137	210	16	.	.	PUNCT
ejpam-137	211	1	since	since	SCONJ
ejpam-137	211	2	f	f	PROPN
ejpam-137	211	3	is	be	AUX
ejpam-137	211	4	γ	γ	PROPN
ejpam-137	211	5	-	-	PUNCT
ejpam-137	211	6	pre	pre	ADJ
ejpam-137	211	7	-	-	ADJ
ejpam-137	211	8	semi	semi	ADJ
ejpam-137	211	9	-	-	ADJ
ejpam-137	211	10	open	open	ADJ
ejpam-137	211	11	,	,	PUNCT
ejpam-137	211	12	therefore	therefore	ADV
ejpam-137	211	13	f	f	PROPN
ejpam-137	211	14	(	(	PUNCT
ejpam-137	211	15	w	w	PROPN
ejpam-137	211	16	)	)	PUNCT
ejpam-137	211	17	∈	∈	PROPN
ejpam-137	211	18	soγ∗(y	soγ∗(y	PROPN
ejpam-137	211	19	)	)	PUNCT
ejpam-137	211	20	.	.	PUNCT
ejpam-137	212	1	hence	hence	ADV
ejpam-137	212	2	v	v	NOUN
ejpam-137	212	3	=	=	SYM
ejpam-137	212	4	f	f	X
ejpam-137	212	5	(	(	PUNCT
ejpam-137	212	6	w	w	NOUN
ejpam-137	212	7	)	)	PUNCT
ejpam-137	212	8	is	be	AUX
ejpam-137	212	9	a	a	DET
ejpam-137	212	10	γ	γ	NOUN
ejpam-137	212	11	-	-	PUNCT
ejpam-137	212	12	semi	semi	NOUN
ejpam-137	212	13	-	-	NOUN
ejpam-137	212	14	nbd	nbd	PROPN
ejpam-137	212	15	of	of	ADP
ejpam-137	212	16	f	f	PROPN
ejpam-137	212	17	(	(	PUNCT
ejpam-137	212	18	x	x	NOUN
ejpam-137	212	19	)	)	PUNCT
ejpam-137	212	20	and	and	CCONJ
ejpam-137	212	21	v	v	ADP
ejpam-137	212	22	⊆	⊆	NUM
ejpam-137	212	23	f	f	PROPN
ejpam-137	212	24	(	(	PUNCT
ejpam-137	212	25	u	u	NOUN
ejpam-137	212	26	)	)	PUNCT
ejpam-137	212	27	.	.	PUNCT
ejpam-137	213	1	conversely	conversely	ADV
ejpam-137	213	2	,	,	PUNCT
ejpam-137	213	3	let	let	VERB
ejpam-137	213	4	u	u	PRON
ejpam-137	213	5	∈	∈	PROPN
ejpam-137	213	6	soγ∗(x	soγ∗(x	NOUN
ejpam-137	213	7	)	)	PUNCT
ejpam-137	213	8	and	and	CCONJ
ejpam-137	213	9	x	x	PUNCT
ejpam-137	213	10	∈	∈	PROPN
ejpam-137	213	11	u	u	NOUN
ejpam-137	213	12	.	.	PUNCT
ejpam-137	214	1	then	then	ADV
ejpam-137	214	2	u	u	PROPN
ejpam-137	214	3	is	be	AUX
ejpam-137	214	4	a	a	DET
ejpam-137	214	5	γ	γ	NOUN
ejpam-137	214	6	-	-	PUNCT
ejpam-137	214	7	semi	semi	NOUN
ejpam-137	214	8	-	-	NOUN
ejpam-137	214	9	nbd	nbd	NOUN
ejpam-137	214	10	of	of	ADP
ejpam-137	214	11	x.	x.	PROPN
ejpam-137	214	12	so	so	ADV
ejpam-137	214	13	by	by	ADP
ejpam-137	214	14	hypothesis	hypothesis	NOUN
ejpam-137	214	15	,	,	PUNCT
ejpam-137	214	16	there	there	PRON
ejpam-137	214	17	exists	exist	VERB
ejpam-137	214	18	a	a	DET
ejpam-137	214	19	γ	γ	X
ejpam-137	214	20	-	-	PUNCT
ejpam-137	214	21	semi	semi	NOUN
ejpam-137	214	22	-	-	NOUN
ejpam-137	214	23	nbd	nbd	ADJ
ejpam-137	214	24	v	v	NOUN
ejpam-137	214	25	of	of	ADP
ejpam-137	214	26	f	f	PROPN
ejpam-137	214	27	(	(	PUNCT
ejpam-137	214	28	x	x	X
ejpam-137	214	29	)	)	PUNCT
ejpam-137	214	30	such	such	ADJ
ejpam-137	214	31	that	that	SCONJ
ejpam-137	214	32	f	f	PROPN
ejpam-137	214	33	(	(	PUNCT
ejpam-137	214	34	x	x	X
ejpam-137	214	35	)	)	PUNCT
ejpam-137	214	36	∈	∈	NOUN
ejpam-137	214	37	v	v	ADP
ejpam-137	214	38	⊆	⊆	NUM
ejpam-137	214	39	f	f	PROPN
ejpam-137	214	40	(	(	PUNCT
ejpam-137	214	41	u	u	NOUN
ejpam-137	214	42	)	)	PUNCT
ejpam-137	214	43	.	.	PUNCT
ejpam-137	215	1	that	that	PRON
ejpam-137	215	2	is	be	AUX
ejpam-137	215	3	,	,	PUNCT
ejpam-137	215	4	f	f	PROPN
ejpam-137	215	5	(	(	PUNCT
ejpam-137	215	6	u	u	NOUN
ejpam-137	215	7	)	)	PUNCT
ejpam-137	215	8	is	be	AUX
ejpam-137	215	9	a	a	DET
ejpam-137	215	10	γ	γ	NOUN
ejpam-137	215	11	-	-	PUNCT
ejpam-137	215	12	semi	semi	NOUN
ejpam-137	215	13	-	-	NOUN
ejpam-137	215	14	nbd	nbd	PROPN
ejpam-137	215	15	of	of	ADP
ejpam-137	215	16	f	f	PROPN
ejpam-137	215	17	(	(	PUNCT
ejpam-137	215	18	x	x	NOUN
ejpam-137	215	19	)	)	PUNCT
ejpam-137	215	20	.	.	PUNCT
ejpam-137	216	1	thus	thus	ADV
ejpam-137	216	2	f	f	X
ejpam-137	216	3	(	(	PUNCT
ejpam-137	216	4	u	u	NOUN
ejpam-137	216	5	)	)	PUNCT
ejpam-137	216	6	is	be	AUX
ejpam-137	216	7	a	a	DET
ejpam-137	216	8	γ	γ	NOUN
ejpam-137	216	9	-	-	PUNCT
ejpam-137	216	10	semi	semi	NOUN
ejpam-137	216	11	-	-	NOUN
ejpam-137	216	12	nbd	nbd	PROPN
ejpam-137	216	13	of	of	ADP
ejpam-137	216	14	each	each	PRON
ejpam-137	216	15	of	of	ADP
ejpam-137	216	16	its	its	PRON
ejpam-137	216	17	points	point	NOUN
ejpam-137	216	18	.	.	PUNCT
ejpam-137	217	1	thus	thus	ADV
ejpam-137	217	2	f	f	X
ejpam-137	217	3	(	(	PUNCT
ejpam-137	217	4	u	u	NOUN
ejpam-137	217	5	)	)	PUNCT
ejpam-137	217	6	is	be	AUX
ejpam-137	217	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	217	8	-	-	NOUN
ejpam-137	217	9	open	open	ADJ
ejpam-137	217	10	.	.	PUNCT
ejpam-137	218	1	hence	hence	ADV
ejpam-137	218	2	f	f	PROPN
ejpam-137	218	3	is	be	AUX
ejpam-137	218	4	γ	γ	PROPN
ejpam-137	218	5	-	-	PUNCT
ejpam-137	218	6	pre	pre	ADJ
ejpam-137	218	7	-	-	ADJ
ejpam-137	218	8	semi	semi	ADJ
ejpam-137	218	9	-	-	ADJ
ejpam-137	218	10	open	open	ADJ
ejpam-137	218	11	.	.	PUNCT
ejpam-137	219	1	this	this	PRON
ejpam-137	219	2	completes	complete	VERB
ejpam-137	219	3	the	the	DET
ejpam-137	219	4	proof	proof	NOUN
ejpam-137	219	5	.	.	PUNCT
ejpam-137	220	1	definition	definition	NOUN
ejpam-137	220	2	4.5[9	4.5[9	NUM
ejpam-137	220	3	]	]	PUNCT
ejpam-137	220	4	.	.	PUNCT
ejpam-137	221	1	let	let	VERB
ejpam-137	221	2	a	a	DET
ejpam-137	221	3	be	be	AUX
ejpam-137	221	4	a	a	DET
ejpam-137	221	5	subset	subset	NOUN
ejpam-137	221	6	of	of	ADP
ejpam-137	221	7	a	a	DET
ejpam-137	221	8	space	space	NOUN
ejpam-137	221	9	x	x	NOUN
ejpam-137	221	10	and	and	CCONJ
ejpam-137	221	11	γ	γ	PROPN
ejpam-137	221	12	∈	∈	PROPN
ejpam-137	221	13	γ(x	γ(x	PROPN
ejpam-137	221	14	)	)	PUNCT
ejpam-137	221	15	.	.	PUNCT
ejpam-137	222	1	the	the	DET
ejpam-137	222	2	union	union	NOUN
ejpam-137	222	3	of	of	ADP
ejpam-137	222	4	all	all	DET
ejpam-137	222	5	γ∗-semi	γ∗-semi	NOUN
ejpam-137	222	6	-	-	ADJ
ejpam-137	222	7	open	open	ADJ
ejpam-137	222	8	sets	set	NOUN
ejpam-137	222	9	of	of	ADP
ejpam-137	222	10	x	x	PUNCT
ejpam-137	222	11	contained	contain	VERB
ejpam-137	222	12	in	in	ADP
ejpam-137	222	13	a	a	PRON
ejpam-137	222	14	is	be	AUX
ejpam-137	222	15	called	call	VERB
ejpam-137	222	16	γ∗-semi	γ∗-semi	NOUN
ejpam-137	222	17	-	-	NOUN
ejpam-137	222	18	interior	interior	NOUN
ejpam-137	222	19	of	of	ADP
ejpam-137	222	20	a	a	PRON
ejpam-137	222	21	and	and	CCONJ
ejpam-137	222	22	is	be	AUX
ejpam-137	222	23	denoted	denote	VERB
ejpam-137	222	24	by	by	ADP
ejpam-137	222	25	sintγ∗(a	sintγ∗(a	PROPN
ejpam-137	222	26	)	)	PUNCT
ejpam-137	222	27	.	.	PUNCT
ejpam-137	223	1	theorem	theorem	VERB
ejpam-137	223	2	4.6	4.6	NUM
ejpam-137	223	3	.	.	PUNCT
ejpam-137	224	1	a	a	DET
ejpam-137	224	2	function	function	NOUN
ejpam-137	224	3	f	f	NOUN
ejpam-137	224	4	:	:	PUNCT
ejpam-137	224	5	x	x	X
ejpam-137	224	6	→	→	SYM
ejpam-137	224	7	y	y	PROPN
ejpam-137	224	8	is	be	AUX
ejpam-137	224	9	γ	γ	PROPN
ejpam-137	224	10	-	-	PUNCT
ejpam-137	224	11	pre	pre	ADJ
ejpam-137	224	12	-	-	ADJ
ejpam-137	224	13	semi	semi	ADJ
ejpam-137	224	14	-	-	ADJ
ejpam-137	224	15	open	open	ADJ
ejpam-137	224	16	if	if	SCONJ
ejpam-137	224	17	and	and	CCONJ
ejpam-137	224	18	only	only	ADV
ejpam-137	224	19	if	if	SCONJ
ejpam-137	224	20	f	f	PROPN
ejpam-137	224	21	(	(	PUNCT
ejpam-137	224	22	sintγ∗(a))⊆	sintγ∗(a))⊆	NOUN
ejpam-137	224	23	sintγ∗	sintγ∗	PROPN
ejpam-137	224	24	(	(	PUNCT
ejpam-137	224	25	f	f	PROPN
ejpam-137	224	26	(	(	PUNCT
ejpam-137	224	27	a	a	NOUN
ejpam-137	224	28	)	)	PUNCT
ejpam-137	224	29	)	)	PUNCT
ejpam-137	224	30	,	,	PUNCT
ejpam-137	224	31	for	for	ADP
ejpam-137	224	32	all	all	DET
ejpam-137	224	33	a⊆	a⊆	NOUN
ejpam-137	224	34	x	x	X
ejpam-137	224	35	.	.	PUNCT
ejpam-137	225	1	proof	proof	NOUN
ejpam-137	225	2	.	.	PUNCT
ejpam-137	226	1	let	let	VERB
ejpam-137	226	2	x	x	PUNCT
ejpam-137	226	3	∈	∈	PROPN
ejpam-137	226	4	sintγ∗(a	sintγ∗(a	PROPN
ejpam-137	226	5	)	)	PUNCT
ejpam-137	226	6	.	.	PUNCT
ejpam-137	227	1	then	then	ADV
ejpam-137	227	2	there	there	PRON
ejpam-137	227	3	exists	exist	VERB
ejpam-137	227	4	u	u	PROPN
ejpam-137	227	5	∈	∈	PROPN
ejpam-137	227	6	soγ∗(x	soγ∗(x	NOUN
ejpam-137	227	7	)	)	PUNCT
ejpam-137	227	8	such	such	ADJ
ejpam-137	227	9	that	that	SCONJ
ejpam-137	227	10	x	x	SYM
ejpam-137	227	11	∈	∈	NOUN
ejpam-137	227	12	u	u	NOUN
ejpam-137	227	13	⊆	⊆	NUM
ejpam-137	227	14	a.	a.	NOUN
ejpam-137	228	1	so	so	ADV
ejpam-137	228	2	f	f	X
ejpam-137	228	3	(	(	PUNCT
ejpam-137	228	4	x	x	X
ejpam-137	228	5	)	)	PUNCT
ejpam-137	228	6	∈	∈	PROPN
ejpam-137	228	7	f	f	X
ejpam-137	228	8	(	(	PUNCT
ejpam-137	228	9	u	u	NOUN
ejpam-137	228	10	)	)	PUNCT
ejpam-137	228	11	⊆	⊆	NUM
ejpam-137	228	12	f	f	X
ejpam-137	228	13	(	(	PUNCT
ejpam-137	228	14	a	a	NOUN
ejpam-137	228	15	)	)	PUNCT
ejpam-137	228	16	.	.	PUNCT
ejpam-137	229	1	since	since	SCONJ
ejpam-137	229	2	f	f	PROPN
ejpam-137	229	3	is	be	AUX
ejpam-137	229	4	γ	γ	PROPN
ejpam-137	229	5	-	-	PUNCT
ejpam-137	229	6	pre	pre	ADJ
ejpam-137	229	7	-	-	ADJ
ejpam-137	229	8	semi	semi	ADJ
ejpam-137	229	9	-	-	ADJ
ejpam-137	229	10	open	open	ADJ
ejpam-137	229	11	,	,	PUNCT
ejpam-137	229	12	therefore	therefore	ADV
ejpam-137	229	13	f	f	X
ejpam-137	229	14	(	(	PUNCT
ejpam-137	229	15	u	u	NOUN
ejpam-137	229	16	)	)	PUNCT
ejpam-137	229	17	is	be	AUX
ejpam-137	229	18	γ∗-semi	γ∗-semi	NOUN
ejpam-137	229	19	-	-	NOUN
ejpam-137	229	20	open	open	ADJ
ejpam-137	229	21	in	in	ADP
ejpam-137	229	22	y.	y.	PROPN
ejpam-137	229	23	hence	hence	ADV
ejpam-137	229	24	f	f	PROPN
ejpam-137	229	25	(	(	PUNCT
ejpam-137	229	26	x	x	X
ejpam-137	229	27	)	)	PUNCT
ejpam-137	229	28	∈	∈	PROPN
ejpam-137	229	29	sintγ∗	sintγ∗	PROPN
ejpam-137	229	30	(	(	PUNCT
ejpam-137	229	31	f	f	PROPN
ejpam-137	229	32	(	(	PUNCT
ejpam-137	229	33	a	a	NOUN
ejpam-137	229	34	)	)	PUNCT
ejpam-137	229	35	)	)	PUNCT
ejpam-137	229	36	.	.	PUNCT
ejpam-137	230	1	thus	thus	ADV
ejpam-137	230	2	f	f	X
ejpam-137	230	3	(	(	PUNCT
ejpam-137	230	4	sintγ∗(a))⊆	sintγ∗(a))⊆	NOUN
ejpam-137	230	5	sintγ∗	sintγ∗	PROPN
ejpam-137	230	6	(	(	PUNCT
ejpam-137	230	7	f	f	PROPN
ejpam-137	230	8	(	(	PUNCT
ejpam-137	230	9	a	a	NOUN
ejpam-137	230	10	)	)	PUNCT
ejpam-137	230	11	)	)	PUNCT
ejpam-137	230	12	.	.	PUNCT
ejpam-137	231	1	this	this	PRON
ejpam-137	231	2	proves	prove	VERB
ejpam-137	231	3	necessity	necessity	NOUN
ejpam-137	231	4	.	.	PUNCT
ejpam-137	232	1	conversely	conversely	ADV
ejpam-137	232	2	let	let	VERB
ejpam-137	232	3	u	u	PRON
ejpam-137	232	4	∈	∈	PROPN
ejpam-137	232	5	soγ∗(x	soγ∗(x	NOUN
ejpam-137	232	6	)	)	PUNCT
ejpam-137	232	7	.	.	PUNCT
ejpam-137	233	1	then	then	ADV
ejpam-137	233	2	by	by	ADP
ejpam-137	233	3	hypothesis	hypothesis	NOUN
ejpam-137	233	4	,	,	PUNCT
ejpam-137	233	5	f	f	PROPN
ejpam-137	233	6	(	(	PUNCT
ejpam-137	233	7	u	u	NOUN
ejpam-137	233	8	)	)	PUNCT
ejpam-137	233	9	=	=	SYM
ejpam-137	233	10	f	f	PROPN
ejpam-137	233	11	(	(	PUNCT
ejpam-137	233	12	sintγ∗(u	sintγ∗(u	PROPN
ejpam-137	233	13	)	)	PUNCT
ejpam-137	233	14	)	)	PUNCT
ejpam-137	234	1	⊆	⊆	NUM
ejpam-137	234	2	sintγ∗	sintγ∗	PROPN
ejpam-137	234	3	(	(	PUNCT
ejpam-137	234	4	f	f	PROPN
ejpam-137	234	5	(	(	PUNCT
ejpam-137	234	6	u	u	NOUN
ejpam-137	234	7	)	)	PUNCT
ejpam-137	234	8	)	)	PUNCT
ejpam-137	235	1	⊆	⊆	NUM
ejpam-137	235	2	f	f	X
ejpam-137	235	3	(	(	PUNCT
ejpam-137	235	4	u	u	NOUN
ejpam-137	235	5	)	)	PUNCT
ejpam-137	235	6	or	or	CCONJ
ejpam-137	235	7	f	f	PROPN
ejpam-137	235	8	(	(	PUNCT
ejpam-137	235	9	u	u	NOUN
ejpam-137	235	10	)	)	PUNCT
ejpam-137	235	11	⊆	⊆	NUM
ejpam-137	235	12	sintγ∗	sintγ∗	PROPN
ejpam-137	235	13	(	(	PUNCT
ejpam-137	235	14	f	f	PROPN
ejpam-137	235	15	(	(	PUNCT
ejpam-137	235	16	u	u	NOUN
ejpam-137	235	17	)	)	PUNCT
ejpam-137	235	18	)	)	PUNCT
ejpam-137	236	1	⊆	⊆	NUM
ejpam-137	236	2	f	f	X
ejpam-137	236	3	(	(	PUNCT
ejpam-137	236	4	u	u	NOUN
ejpam-137	236	5	)	)	PUNCT
ejpam-137	236	6	.	.	PUNCT
ejpam-137	237	1	this	this	PRON
ejpam-137	237	2	implies	imply	VERB
ejpam-137	237	3	f	f	PROPN
ejpam-137	237	4	(	(	PUNCT
ejpam-137	237	5	u	u	NOUN
ejpam-137	237	6	)	)	PUNCT
ejpam-137	237	7	is	be	AUX
ejpam-137	237	8	γ∗-semi	γ∗-semi	NOUN
ejpam-137	237	9	-	-	NOUN
ejpam-137	237	10	open	open	ADJ
ejpam-137	237	11	in	in	ADP
ejpam-137	237	12	y.	y.	PROPN
ejpam-137	238	1	so	so	PROPN
ejpam-137	238	2	f	f	PROPN
ejpam-137	238	3	is	be	AUX
ejpam-137	238	4	γ	γ	PROPN
ejpam-137	238	5	-	-	PUNCT
ejpam-137	238	6	presemi	presemi	ADV
ejpam-137	238	7	-	-	PUNCT
ejpam-137	238	8	open	open	ADJ
ejpam-137	238	9	.	.	PUNCT
ejpam-137	239	1	we	we	PRON
ejpam-137	239	2	use	use	VERB
ejpam-137	239	3	theorem	theorem	ADJ
ejpam-137	239	4	4.6	4.6	NUM
ejpam-137	239	5	and	and	CCONJ
ejpam-137	239	6	prove	prove	VERB
ejpam-137	239	7	:	:	PUNCT
ejpam-137	239	8	theorem	theorem	VERB
ejpam-137	239	9	4.7	4.7	NUM
ejpam-137	239	10	.	.	PUNCT
ejpam-137	240	1	a	a	DET
ejpam-137	240	2	function	function	NOUN
ejpam-137	240	3	f	f	NOUN
ejpam-137	240	4	:	:	PUNCT
ejpam-137	240	5	x	x	X
ejpam-137	240	6	→	→	SYM
ejpam-137	240	7	y	y	PROPN
ejpam-137	240	8	is	be	AUX
ejpam-137	240	9	γ	γ	PROPN
ejpam-137	240	10	-	-	PUNCT
ejpam-137	240	11	pre	pre	ADJ
ejpam-137	240	12	-	-	ADJ
ejpam-137	240	13	semi	semi	ADJ
ejpam-137	240	14	-	-	ADJ
ejpam-137	240	15	open	open	ADJ
ejpam-137	240	16	if	if	SCONJ
ejpam-137	240	17	and	and	CCONJ
ejpam-137	240	18	only	only	ADV
ejpam-137	240	19	if	if	SCONJ
ejpam-137	240	20	sintγ∗	sintγ∗	PROPN
ejpam-137	240	21	(	(	PUNCT
ejpam-137	240	22	f	f	PROPN
ejpam-137	240	23	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	240	24	f	f	PROPN
ejpam-137	240	25	−1(sintγ∗(a	−1(sintγ∗(a	PROPN
ejpam-137	240	26	)	)	PUNCT
ejpam-137	240	27	)	)	PUNCT
ejpam-137	240	28	,	,	PUNCT
ejpam-137	240	29	for	for	ADP
ejpam-137	240	30	all	all	DET
ejpam-137	240	31	a⊆	a⊆	NOUN
ejpam-137	240	32	x	x	X
ejpam-137	240	33	.	.	PUNCT
ejpam-137	241	1	proof	proof	NOUN
ejpam-137	241	2	.	.	PUNCT
ejpam-137	242	1	let	let	VERB
ejpam-137	242	2	a	a	DET
ejpam-137	242	3	be	be	AUX
ejpam-137	242	4	any	any	DET
ejpam-137	242	5	subset	subset	NOUN
ejpam-137	242	6	of	of	ADP
ejpam-137	242	7	y.	y.	PROPN
ejpam-137	242	8	clearly	clearly	ADV
ejpam-137	242	9	,	,	PUNCT
ejpam-137	242	10	sintγ∗	sintγ∗	PROPN
ejpam-137	242	11	(	(	PUNCT
ejpam-137	242	12	f	f	PROPN
ejpam-137	242	13	−1(a	−1(a	ADP
ejpam-137	242	14	)	)	PUNCT
ejpam-137	242	15	)	)	PUNCT
ejpam-137	242	16	is	be	AUX
ejpam-137	242	17	γ∗-semi	γ∗-semi	NOUN
ejpam-137	242	18	-	-	NOUN
ejpam-137	242	19	open	open	ADJ
ejpam-137	242	20	in	in	ADP
ejpam-137	242	21	y.	y.	PROPN
ejpam-137	242	22	also	also	PROPN
ejpam-137	243	1	f	f	PROPN
ejpam-137	243	2	(	(	PUNCT
ejpam-137	243	3	sintγ∗	sintγ∗	PROPN
ejpam-137	243	4	(	(	PUNCT
ejpam-137	243	5	f	f	PROPN
ejpam-137	243	6	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	243	7	f	f	PROPN
ejpam-137	244	1	(	(	PUNCT
ejpam-137	244	2	f	f	PROPN
ejpam-137	244	3	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	244	4	a	a	PRON
ejpam-137	244	5	.	.	PUNCT
ejpam-137	245	1	since	since	SCONJ
ejpam-137	245	2	f	f	PROPN
ejpam-137	245	3	is	be	AUX
ejpam-137	245	4	γ	γ	PROPN
ejpam-137	245	5	-	-	PUNCT
ejpam-137	245	6	pre	pre	ADJ
ejpam-137	245	7	-	-	ADJ
ejpam-137	245	8	semi	semi	ADJ
ejpam-137	245	9	-	-	ADJ
ejpam-137	245	10	open	open	ADJ
ejpam-137	245	11	,	,	PUNCT
ejpam-137	245	12	by	by	ADP
ejpam-137	245	13	theorem	theorem	NOUN
ejpam-137	245	14	4.6	4.6	NUM
ejpam-137	245	15	we	we	PRON
ejpam-137	245	16	have	have	VERB
ejpam-137	245	17	f	f	PROPN
ejpam-137	245	18	(	(	PUNCT
ejpam-137	245	19	sintγ∗	sintγ∗	PROPN
ejpam-137	245	20	(	(	PUNCT
ejpam-137	245	21	f	f	PROPN
ejpam-137	245	22	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	245	23	sintγ∗(a	sintγ∗(a	PROPN
ejpam-137	245	24	)	)	PUNCT
ejpam-137	245	25	.	.	PUNCT
ejpam-137	246	1	therefore	therefore	ADV
ejpam-137	246	2	,	,	PUNCT
ejpam-137	246	3	sintγ∗	sintγ∗	PROPN
ejpam-137	246	4	(	(	PUNCT
ejpam-137	246	5	f	f	PROPN
ejpam-137	246	6	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	246	7	f	f	PROPN
ejpam-137	246	8	(	(	PUNCT
ejpam-137	246	9	f	f	PROPN
ejpam-137	246	10	−1(sintγ∗	−1(sintγ∗	PROPN
ejpam-137	246	11	(	(	PUNCT
ejpam-137	246	12	f	f	PROPN
ejpam-137	246	13	−1(a))))⊆	−1(a))))⊆	NOUN
ejpam-137	246	14	f	f	PROPN
ejpam-137	246	15	−1(sintγ∗(a	−1(sintγ∗(a	PROPN
ejpam-137	246	16	)	)	PUNCT
ejpam-137	246	17	)	)	PUNCT
ejpam-137	246	18	or	or	CCONJ
ejpam-137	246	19	sintγ∗	sintγ∗	PROPN
ejpam-137	246	20	(	(	PUNCT
ejpam-137	246	21	f	f	PROPN
ejpam-137	246	22	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	246	23	f	f	PROPN
ejpam-137	246	24	−1(sintγ∗(a	−1(sintγ∗(a	PROPN
ejpam-137	246	25	)	)	PUNCT
ejpam-137	246	26	)	)	PUNCT
ejpam-137	246	27	.	.	PUNCT
ejpam-137	247	1	this	this	PRON
ejpam-137	247	2	proves	prove	VERB
ejpam-137	247	3	necessity	necessity	NOUN
ejpam-137	247	4	.	.	PUNCT
ejpam-137	248	1	conversely	conversely	ADV
ejpam-137	248	2	,	,	PUNCT
ejpam-137	248	3	let	let	VERB
ejpam-137	248	4	b	b	NOUN
ejpam-137	248	5	⊆	⊆	NUM
ejpam-137	248	6	x	x	X
ejpam-137	248	7	.	.	PUNCT
ejpam-137	249	1	by	by	ADP
ejpam-137	249	2	hypothesis	hypothesis	NOUN
ejpam-137	249	3	,	,	PUNCT
ejpam-137	249	4	we	we	PRON
ejpam-137	249	5	obtain	obtain	VERB
ejpam-137	249	6	sintγ∗(b)⊆	sintγ∗(b)⊆	PROPN
ejpam-137	249	7	sintγ∗	sintγ∗	PROPN
ejpam-137	249	8	(	(	PUNCT
ejpam-137	249	9	f	f	PROPN
ejpam-137	249	10	−1	−1	NOUN
ejpam-137	249	11	f	f	PROPN
ejpam-137	249	12	(	(	PUNCT
ejpam-137	249	13	b))⊆	b))⊆	X
ejpam-137	249	14	f	f	X
ejpam-137	249	15	−1(sintγ∗	−1(sintγ∗	PROPN
ejpam-137	249	16	f	f	PROPN
ejpam-137	249	17	(	(	PUNCT
ejpam-137	249	18	b	b	NOUN
ejpam-137	249	19	)	)	PUNCT
ejpam-137	249	20	)	)	PUNCT
ejpam-137	249	21	.	.	PUNCT
ejpam-137	250	1	this	this	PRON
ejpam-137	250	2	implies	imply	VERB
ejpam-137	250	3	that	that	SCONJ
ejpam-137	250	4	f	f	PROPN
ejpam-137	250	5	(	(	PUNCT
ejpam-137	250	6	sintγ∗(b))⊆	sintγ∗(b))⊆	PROPN
ejpam-137	250	7	f	f	PROPN
ejpam-137	250	8	(	(	PUNCT
ejpam-137	250	9	sintγ∗	sintγ∗	PROPN
ejpam-137	250	10	(	(	PUNCT
ejpam-137	250	11	f	f	PROPN
ejpam-137	250	12	−1	−1	NOUN
ejpam-137	250	13	f	f	PROPN
ejpam-137	250	14	(	(	PUNCT
ejpam-137	250	15	b)))⊆	b)))⊆	NOUN
ejpam-137	250	16	f	f	PROPN
ejpam-137	250	17	(	(	PUNCT
ejpam-137	250	18	f	f	X
ejpam-137	250	19	−1(sintγ∗	−1(sintγ∗	PROPN
ejpam-137	250	20	f	f	PROPN
ejpam-137	250	21	(	(	PUNCT
ejpam-137	250	22	b	b	NOUN
ejpam-137	250	23	)	)	PUNCT
ejpam-137	250	24	)	)	PUNCT
ejpam-137	250	25	)	)	PUNCT
ejpam-137	251	1	⊆	⊆	NUM
ejpam-137	251	2	sintγ∗	sintγ∗	PROPN
ejpam-137	251	3	(	(	PUNCT
ejpam-137	251	4	f	f	PROPN
ejpam-137	251	5	(	(	PUNCT
ejpam-137	251	6	b	b	NOUN
ejpam-137	251	7	)	)	PUNCT
ejpam-137	251	8	)	)	PUNCT
ejpam-137	251	9	.	.	PUNCT
ejpam-137	252	1	consequently	consequently	ADV
ejpam-137	252	2	,	,	PUNCT
ejpam-137	252	3	f	f	PROPN
ejpam-137	252	4	(	(	PUNCT
ejpam-137	252	5	sintγ∗(b	sintγ∗(b	PROPN
ejpam-137	252	6	)	)	PUNCT
ejpam-137	252	7	)	)	PUNCT
ejpam-137	252	8	⊆	⊆	NUM
ejpam-137	252	9	sintγ∗	sintγ∗	PROPN
ejpam-137	252	10	(	(	PUNCT
ejpam-137	252	11	f	f	PROPN
ejpam-137	252	12	(	(	PUNCT
ejpam-137	252	13	b	b	NOUN
ejpam-137	252	14	)	)	PUNCT
ejpam-137	252	15	)	)	PUNCT
ejpam-137	252	16	,	,	PUNCT
ejpam-137	252	17	for	for	ADP
ejpam-137	252	18	all	all	DET
ejpam-137	252	19	b	b	NOUN
ejpam-137	252	20	⊆	⊆	NUM
ejpam-137	252	21	x	x	X
ejpam-137	252	22	.	.	PUNCT
ejpam-137	253	1	by	by	ADP
ejpam-137	253	2	theorem	theorem	NOUN
ejpam-137	253	3	4.6	4.6	NUM
ejpam-137	253	4	,	,	PUNCT
ejpam-137	253	5	f	f	PROPN
ejpam-137	253	6	is	be	AUX
ejpam-137	253	7	γ	γ	PROPN
ejpam-137	253	8	-	-	PUNCT
ejpam-137	253	9	pre	pre	ADJ
ejpam-137	253	10	-	-	ADJ
ejpam-137	253	11	semi	semi	ADJ
ejpam-137	253	12	-	-	ADJ
ejpam-137	253	13	open	open	ADJ
ejpam-137	253	14	.	.	PUNCT
ejpam-137	254	1	b.	b.	PROPN
ejpam-137	254	2	ahmad	ahmad	PROPN
ejpam-137	254	3	,	,	PUNCT
ejpam-137	254	4	s.	s.	PROPN
ejpam-137	254	5	hussain	hussain	PROPN
ejpam-137	254	6	,	,	PUNCT
ejpam-137	254	7	and	and	CCONJ
ejpam-137	254	8	t.	t.	PROPN
ejpam-137	254	9	noiri	noiri	PROPN
ejpam-137	254	10	/	/	SYM
ejpam-137	254	11	eur	eur	PROPN
ejpam-137	254	12	.	.	PUNCT
ejpam-137	255	1	j.	j.	PROPN
ejpam-137	255	2	pure	pure	PROPN
ejpam-137	255	3	appl	appl	PROPN
ejpam-137	255	4	.	.	PROPN
ejpam-137	255	5	math	math	PROPN
ejpam-137	255	6	,	,	PUNCT
ejpam-137	255	7	1	1	NUM
ejpam-137	255	8	(	(	PUNCT
ejpam-137	255	9	2008	2008	NUM
ejpam-137	255	10	)	)	PUNCT
ejpam-137	255	11	,	,	PUNCT
ejpam-137	255	12	(	(	PUNCT
ejpam-137	255	13	22	22	NUM
ejpam-137	255	14	-	-	SYM
ejpam-137	255	15	29	29	NUM
ejpam-137	255	16	)	)	PUNCT
ejpam-137	255	17	27	27	NUM
ejpam-137	255	18	we	we	PRON
ejpam-137	255	19	use	use	VERB
ejpam-137	255	20	theorem	theorem	ADJ
ejpam-137	255	21	4.7	4.7	NUM
ejpam-137	255	22	and	and	CCONJ
ejpam-137	255	23	prove	prove	VERB
ejpam-137	255	24	:	:	PUNCT
ejpam-137	255	25	theorem	theorem	NOUN
ejpam-137	255	26	4.8	4.8	NUM
ejpam-137	255	27	.	.	PUNCT
ejpam-137	256	1	a	a	DET
ejpam-137	256	2	function	function	NOUN
ejpam-137	256	3	f	f	NOUN
ejpam-137	256	4	:	:	PUNCT
ejpam-137	256	5	x	x	X
ejpam-137	256	6	→	→	SYM
ejpam-137	256	7	y	y	PROPN
ejpam-137	256	8	is	be	AUX
ejpam-137	256	9	γ	γ	PROPN
ejpam-137	256	10	-	-	PUNCT
ejpam-137	256	11	pre	pre	ADJ
ejpam-137	256	12	-	-	ADJ
ejpam-137	256	13	semi	semi	ADJ
ejpam-137	256	14	-	-	ADJ
ejpam-137	256	15	open	open	ADJ
ejpam-137	256	16	if	if	SCONJ
ejpam-137	256	17	and	and	CCONJ
ejpam-137	256	18	only	only	ADV
ejpam-137	256	19	if	if	SCONJ
ejpam-137	256	20	f	f	PROPN
ejpam-137	256	21	−1(sclγ∗(a))⊆	−1(sclγ∗(a))⊆	PUNCT
ejpam-137	256	22	sclγ∗	sclγ∗	PROPN
ejpam-137	256	23	(	(	PUNCT
ejpam-137	256	24	f	f	NOUN
ejpam-137	256	25	−1(a	−1(a	ADP
ejpam-137	256	26	)	)	PUNCT
ejpam-137	256	27	)	)	PUNCT
ejpam-137	256	28	,	,	PUNCT
ejpam-137	256	29	for	for	ADP
ejpam-137	256	30	all	all	DET
ejpam-137	256	31	a⊆	a⊆	NOUN
ejpam-137	256	32	x	x	X
ejpam-137	256	33	.	.	PUNCT
ejpam-137	257	1	proof	proof	NOUN
ejpam-137	257	2	.	.	PUNCT
ejpam-137	258	1	let	let	AUX
ejpam-137	258	2	a⊆	a⊆	VERB
ejpam-137	258	3	y	y	PRON
ejpam-137	258	4	.	.	PUNCT
ejpam-137	259	1	by	by	ADP
ejpam-137	259	2	theorem	theorem	NOUN
ejpam-137	259	3	4.7	4.7	NUM
ejpam-137	259	4	,	,	PUNCT
ejpam-137	259	5	sintγ∗	sintγ∗	PROPN
ejpam-137	259	6	(	(	PUNCT
ejpam-137	259	7	f	f	PROPN
ejpam-137	259	8	−1(y	−1(y	X
ejpam-137	259	9	−	−	PROPN
ejpam-137	259	10	a	a	NOUN
ejpam-137	259	11	)	)	PUNCT
ejpam-137	259	12	)	)	PUNCT
ejpam-137	260	1	⊆	⊆	NUM
ejpam-137	260	2	f	f	PROPN
ejpam-137	260	3	−1(sintγ∗(y	−1(sintγ∗(y	PROPN
ejpam-137	260	4	−	−	PROPN
ejpam-137	260	5	a	a	NOUN
ejpam-137	260	6	)	)	PUNCT
ejpam-137	260	7	)	)	PUNCT
ejpam-137	260	8	.	.	PUNCT
ejpam-137	261	1	this	this	PRON
ejpam-137	261	2	implies	imply	VERB
ejpam-137	261	3	that	that	SCONJ
ejpam-137	261	4	sintγ∗(x	sintγ∗(x	PROPN
ejpam-137	261	5	−	−	PROPN
ejpam-137	261	6	f	f	NOUN
ejpam-137	261	7	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	261	8	f	f	PROPN
ejpam-137	261	9	−1(sintγ∗(y	−1(sintγ∗(y	PROPN
ejpam-137	261	10	−	−	PROPN
ejpam-137	261	11	a	a	NOUN
ejpam-137	261	12	)	)	PUNCT
ejpam-137	261	13	)	)	PUNCT
ejpam-137	261	14	.	.	PUNCT
ejpam-137	262	1	as	as	ADP
ejpam-137	262	2	sintγ∗(a	sintγ∗(a	PROPN
ejpam-137	262	3	)	)	PUNCT
ejpam-137	262	4	=	=	SYM
ejpam-137	262	5	x	x	PUNCT
ejpam-137	262	6	−	−	PROPN
ejpam-137	262	7	sclγ∗(x	sclγ∗(x	PROPN
ejpam-137	262	8	−	−	PROPN
ejpam-137	262	9	a	a	NOUN
ejpam-137	262	10	)	)	PUNCT
ejpam-137	263	1	[	[	X
ejpam-137	263	2	5	5	NUM
ejpam-137	263	3	]	]	PUNCT
ejpam-137	263	4	,	,	PUNCT
ejpam-137	263	5	therefore	therefore	ADV
ejpam-137	263	6	x	x	X
ejpam-137	263	7	−	−	PROPN
ejpam-137	263	8	sclγ∗	sclγ∗	PROPN
ejpam-137	263	9	(	(	PUNCT
ejpam-137	263	10	f	f	NOUN
ejpam-137	263	11	−1(a	−1(a	ADP
ejpam-137	263	12	)	)	PUNCT
ejpam-137	263	13	)	)	PUNCT
ejpam-137	264	1	⊆	⊆	NUM
ejpam-137	264	2	f	f	X
ejpam-137	264	3	−1(y	−1(y	PRON
ejpam-137	264	4	−	−	PROPN
ejpam-137	264	5	sclγ∗(a	sclγ∗(a	PROPN
ejpam-137	264	6	)	)	PUNCT
ejpam-137	264	7	)	)	PUNCT
ejpam-137	264	8	.	.	PUNCT
ejpam-137	265	1	or	or	CCONJ
ejpam-137	265	2	x	x	X
ejpam-137	265	3	−	−	NOUN
ejpam-137	265	4	sclγ∗	sclγ∗	PROPN
ejpam-137	265	5	(	(	PUNCT
ejpam-137	265	6	f	f	NOUN
ejpam-137	265	7	−1(a	−1(a	ADP
ejpam-137	265	8	)	)	PUNCT
ejpam-137	265	9	)	)	PUNCT
ejpam-137	266	1	⊆	⊆	NUM
ejpam-137	266	2	x	x	SYM
ejpam-137	266	3	−	−	PROPN
ejpam-137	266	4	f	f	PROPN
ejpam-137	266	5	−1(sclγ∗(a	−1(sclγ∗(a	PROPN
ejpam-137	266	6	)	)	PUNCT
ejpam-137	266	7	)	)	PUNCT
ejpam-137	266	8	.	.	PUNCT
ejpam-137	267	1	hence	hence	ADV
ejpam-137	267	2	f	f	PROPN
ejpam-137	267	3	−1(sclγ∗(a))⊆	−1(sclγ∗(a))⊆	X
ejpam-137	267	4	sclγ∗	sclγ∗	PROPN
ejpam-137	267	5	(	(	PUNCT
ejpam-137	267	6	f	f	NOUN
ejpam-137	267	7	−1(a	−1(a	ADP
ejpam-137	267	8	)	)	PUNCT
ejpam-137	267	9	)	)	PUNCT
ejpam-137	267	10	.	.	PUNCT
ejpam-137	268	1	this	this	PRON
ejpam-137	268	2	proves	prove	VERB
ejpam-137	268	3	necessity	necessity	NOUN
ejpam-137	268	4	.	.	PUNCT
ejpam-137	269	1	conversely	conversely	ADV
ejpam-137	269	2	,	,	PUNCT
ejpam-137	269	3	let	let	VERB
ejpam-137	269	4	a	a	DET
ejpam-137	269	5	⊆	⊆	NUM
ejpam-137	269	6	y	y	NOUN
ejpam-137	269	7	.	.	PUNCT
ejpam-137	270	1	by	by	ADP
ejpam-137	270	2	hypothesis	hypothesis	NOUN
ejpam-137	270	3	,	,	PUNCT
ejpam-137	270	4	f	f	PROPN
ejpam-137	270	5	−1(sclγ∗(y	−1(sclγ∗(y	PROPN
ejpam-137	270	6	−	−	PROPN
ejpam-137	270	7	a	a	NOUN
ejpam-137	270	8	)	)	PUNCT
ejpam-137	270	9	)	)	PUNCT
ejpam-137	271	1	⊆	⊆	NUM
ejpam-137	271	2	sclγ∗	sclγ∗	NOUN
ejpam-137	271	3	(	(	PUNCT
ejpam-137	271	4	f	f	PROPN
ejpam-137	271	5	−1(y	−1(y	X
ejpam-137	271	6	−	−	PROPN
ejpam-137	271	7	a	a	NOUN
ejpam-137	271	8	)	)	PUNCT
ejpam-137	271	9	)	)	PUNCT
ejpam-137	271	10	.	.	PUNCT
ejpam-137	272	1	this	this	PRON
ejpam-137	272	2	implies	imply	VERB
ejpam-137	272	3	x	x	PUNCT
ejpam-137	272	4	−	−	NOUN
ejpam-137	272	5	sclγ∗	sclγ∗	ADJ
ejpam-137	272	6	(	(	PUNCT
ejpam-137	272	7	f	f	PROPN
ejpam-137	272	8	−1(y	−1(y	X
ejpam-137	272	9	−	−	PROPN
ejpam-137	272	10	a	a	NOUN
ejpam-137	272	11	)	)	PUNCT
ejpam-137	272	12	)	)	PUNCT
ejpam-137	273	1	⊆	⊆	NUM
ejpam-137	273	2	x	x	SYM
ejpam-137	273	3	−	−	PROPN
ejpam-137	273	4	f	f	PROPN
ejpam-137	273	5	−1(sclγ∗(y	−1(sclγ∗(y	PROPN
ejpam-137	273	6	−	−	PROPN
ejpam-137	273	7	a	a	NOUN
ejpam-137	273	8	)	)	PUNCT
ejpam-137	273	9	)	)	PUNCT
ejpam-137	273	10	.	.	PUNCT
ejpam-137	274	1	hence	hence	ADV
ejpam-137	274	2	x	x	PUNCT
ejpam-137	274	3	−	−	PROPN
ejpam-137	274	4	sclγ∗(x	sclγ∗(x	PROPN
ejpam-137	274	5	−	−	PROPN
ejpam-137	274	6	f	f	PROPN
ejpam-137	274	7	−1(a	−1(a	ADP
ejpam-137	274	8	)	)	PUNCT
ejpam-137	274	9	)	)	PUNCT
ejpam-137	275	1	⊆	⊆	NUM
ejpam-137	275	2	f	f	PROPN
ejpam-137	275	3	−1(y	−1(y	PROPN
ejpam-137	275	4	−(sclγ∗(y	−(sclγ∗(y	PROPN
ejpam-137	275	5	−a	−a	NOUN
ejpam-137	275	6	)	)	PUNCT
ejpam-137	275	7	)	)	PUNCT
ejpam-137	275	8	)	)	PUNCT
ejpam-137	275	9	.	.	PUNCT
ejpam-137	276	1	this	this	PRON
ejpam-137	276	2	gives	give	VERB
ejpam-137	276	3	sintγ∗	sintγ∗	PROPN
ejpam-137	276	4	(	(	PUNCT
ejpam-137	276	5	f	f	PROPN
ejpam-137	276	6	−1(a))⊆	−1(a))⊆	PROPN
ejpam-137	276	7	f	f	PROPN
ejpam-137	276	8	−1(sintγ∗(a	−1(sintγ∗(a	PROPN
ejpam-137	276	9	)	)	PUNCT
ejpam-137	276	10	)	)	PUNCT
ejpam-137	276	11	.	.	PUNCT
ejpam-137	277	1	now	now	ADV
ejpam-137	277	2	from	from	ADP
ejpam-137	277	3	theorem	theorem	ADJ
ejpam-137	277	4	4.7	4.7	NUM
ejpam-137	277	5	,	,	PUNCT
ejpam-137	277	6	it	it	PRON
ejpam-137	277	7	follows	follow	VERB
ejpam-137	277	8	that	that	SCONJ
ejpam-137	277	9	f	f	PROPN
ejpam-137	277	10	is	be	AUX
ejpam-137	277	11	γ	γ	PROPN
ejpam-137	277	12	-	-	PUNCT
ejpam-137	277	13	pre	pre	ADJ
ejpam-137	277	14	-	-	ADJ
ejpam-137	277	15	semi	semi	ADJ
ejpam-137	277	16	-	-	ADJ
ejpam-137	277	17	open	open	ADJ
ejpam-137	277	18	.	.	PUNCT
ejpam-137	278	1	this	this	PRON
ejpam-137	278	2	completes	complete	VERB
ejpam-137	278	3	the	the	DET
ejpam-137	278	4	proof	proof	NOUN
ejpam-137	278	5	.	.	PUNCT
ejpam-137	279	1	definition	definition	NOUN
ejpam-137	279	2	4.9[14	4.9[14	PROPN
ejpam-137	279	3	]	]	X
ejpam-137	279	4	.	.	PUNCT
ejpam-137	280	1	a	a	DET
ejpam-137	280	2	function	function	NOUN
ejpam-137	280	3	f	f	NOUN
ejpam-137	280	4	:	:	PUNCT
ejpam-137	280	5	(	(	PUNCT
ejpam-137	280	6	x	x	X
ejpam-137	280	7	,	,	PUNCT
ejpam-137	280	8	τ)→	τ)→	PROPN
ejpam-137	280	9	(	(	PUNCT
ejpam-137	280	10	y	y	PROPN
ejpam-137	280	11	,	,	PUNCT
ejpam-137	280	12	τ	τ	X
ejpam-137	280	13	)	)	PUNCT
ejpam-137	280	14	is	be	AUX
ejpam-137	280	15	said	say	VERB
ejpam-137	280	16	to	to	PART
ejpam-137	280	17	be	be	AUX
ejpam-137	280	18	(	(	PUNCT
ejpam-137	280	19	γ	γ	X
ejpam-137	280	20	,	,	PUNCT
ejpam-137	280	21	β	β	NOUN
ejpam-137	280	22	)	)	PUNCT
ejpam-137	280	23	-continuous	-continuous	ADJ
ejpam-137	280	24	,	,	PUNCT
ejpam-137	280	25	if	if	SCONJ
ejpam-137	280	26	for	for	SCONJ
ejpam-137	280	27	each	each	DET
ejpam-137	280	28	x	x	SYM
ejpam-137	280	29	∈	∈	PROPN
ejpam-137	280	30	x	x	X
ejpam-137	280	31	and	and	CCONJ
ejpam-137	280	32	each	each	DET
ejpam-137	280	33	open	open	ADJ
ejpam-137	280	34	set	set	VERB
ejpam-137	280	35	v	v	NOUN
ejpam-137	280	36	containing	contain	VERB
ejpam-137	280	37	f	f	X
ejpam-137	280	38	(	(	PUNCT
ejpam-137	280	39	x	x	X
ejpam-137	280	40	)	)	PUNCT
ejpam-137	280	41	,	,	PUNCT
ejpam-137	280	42	there	there	PRON
ejpam-137	280	43	exists	exist	VERB
ejpam-137	280	44	an	an	DET
ejpam-137	280	45	open	open	ADJ
ejpam-137	280	46	set	set	NOUN
ejpam-137	280	47	u	u	PRON
ejpam-137	280	48	such	such	ADJ
ejpam-137	280	49	that	that	SCONJ
ejpam-137	280	50	x	x	SYM
ejpam-137	280	51	∈	∈	PROPN
ejpam-137	280	52	u	u	NOUN
ejpam-137	280	53	and	and	CCONJ
ejpam-137	280	54	f	f	PROPN
ejpam-137	280	55	(	(	PUNCT
ejpam-137	280	56	uγ)⊆	uγ)⊆	PROPN
ejpam-137	280	57	vβ	vβ	NOUN
ejpam-137	280	58	,	,	PUNCT
ejpam-137	280	59	where	where	SCONJ
ejpam-137	280	60	γ	γ	PROPN
ejpam-137	280	61	and	and	CCONJ
ejpam-137	280	62	β	β	X
ejpam-137	280	63	are	be	AUX
ejpam-137	280	64	operations	operation	NOUN
ejpam-137	280	65	on	on	ADP
ejpam-137	280	66	τ	τ	PROPN
ejpam-137	280	67	and	and	CCONJ
ejpam-137	280	68	δ	δ	PROPN
ejpam-137	280	69	respectively	respectively	ADV
ejpam-137	280	70	.	.	PUNCT
ejpam-137	281	1	definition	definition	NOUN
ejpam-137	281	2	4.10[14	4.10[14	NUM
ejpam-137	281	3	]	]	X
ejpam-137	281	4	.	.	PUNCT
ejpam-137	282	1	a	a	DET
ejpam-137	282	2	function	function	NOUN
ejpam-137	282	3	f	f	NOUN
ejpam-137	282	4	:	:	PUNCT
ejpam-137	282	5	(	(	PUNCT
ejpam-137	282	6	x	x	X
ejpam-137	282	7	,	,	PUNCT
ejpam-137	282	8	τ)→	τ)→	PROPN
ejpam-137	282	9	(	(	PUNCT
ejpam-137	282	10	y	y	PROPN
ejpam-137	282	11	,	,	PUNCT
ejpam-137	282	12	τ	τ	X
ejpam-137	282	13	)	)	PUNCT
ejpam-137	282	14	is	be	AUX
ejpam-137	282	15	said	say	VERB
ejpam-137	282	16	to	to	PART
ejpam-137	282	17	be	be	AUX
ejpam-137	282	18	(	(	PUNCT
ejpam-137	282	19	γ	γ	X
ejpam-137	282	20	,	,	PUNCT
ejpam-137	282	21	β)-open	β)-open	PUNCT
ejpam-137	282	22	(	(	PUNCT
ejpam-137	282	23	closed	closed	ADJ
ejpam-137	282	24	)	)	PUNCT
ejpam-137	282	25	,	,	PUNCT
ejpam-137	282	26	if	if	SCONJ
ejpam-137	282	27	for	for	ADP
ejpam-137	282	28	any	any	DET
ejpam-137	282	29	γ	γ	NOUN
ejpam-137	282	30	-	-	ADJ
ejpam-137	282	31	open	open	ADJ
ejpam-137	282	32	(	(	PUNCT
ejpam-137	282	33	closed	closed	ADJ
ejpam-137	282	34	)	)	PUNCT
ejpam-137	282	35	set	set	VERB
ejpam-137	282	36	a	a	PRON
ejpam-137	282	37	of	of	ADP
ejpam-137	282	38	x	x	PRON
ejpam-137	282	39	,	,	PUNCT
ejpam-137	282	40	f	f	PROPN
ejpam-137	282	41	(	(	PUNCT
ejpam-137	282	42	a	a	NOUN
ejpam-137	282	43	)	)	PUNCT
ejpam-137	282	44	is	be	AUX
ejpam-137	282	45	β	β	X
ejpam-137	282	46	-	-	PUNCT
ejpam-137	282	47	open(closed	open(close	VERB
ejpam-137	282	48	)	)	PUNCT
ejpam-137	282	49	in	in	ADP
ejpam-137	282	50	y.	y.	NOUN
ejpam-137	282	51	in	in	ADP
ejpam-137	282	52	[	[	X
ejpam-137	282	53	10	10	NUM
ejpam-137	282	54	]	]	PUNCT
ejpam-137	282	55	,	,	PUNCT
ejpam-137	282	56	we	we	PRON
ejpam-137	282	57	proved	prove	VERB
ejpam-137	282	58	the	the	DET
ejpam-137	282	59	following	follow	VERB
ejpam-137	282	60	theorem	theorem	NOUN
ejpam-137	282	61	:	:	PUNCT
ejpam-137	282	62	theorem	theorem	NOUN
ejpam-137	282	63	4.11[10	4.11[10	NUM
ejpam-137	282	64	]	]	PUNCT
ejpam-137	282	65	.	.	PUNCT
ejpam-137	283	1	if	if	SCONJ
ejpam-137	283	2	f	f	PROPN
ejpam-137	283	3	:	:	PUNCT
ejpam-137	283	4	x	x	X
ejpam-137	283	5	→	→	SYM
ejpam-137	283	6	y	y	PROPN
ejpam-137	283	7	is	be	AUX
ejpam-137	283	8	a	a	DET
ejpam-137	283	9	(	(	PUNCT
ejpam-137	283	10	γ	γ	X
ejpam-137	283	11	,	,	PUNCT
ejpam-137	283	12	β)-open	β)-open	PUNCT
ejpam-137	283	13	and	and	CCONJ
ejpam-137	283	14	(	(	PUNCT
ejpam-137	283	15	γ	γ	PROPN
ejpam-137	283	16	,	,	PUNCT
ejpam-137	283	17	β)-continuous	β)-continuous	ADJ
ejpam-137	283	18	function	function	NOUN
ejpam-137	283	19	,	,	PUNCT
ejpam-137	283	20	then	then	ADV
ejpam-137	283	21	f	f	PROPN
ejpam-137	283	22	−1(b	−1(b	NOUN
ejpam-137	283	23	)	)	PUNCT
ejpam-137	283	24	∈	∈	PROPN
ejpam-137	283	25	soγ∗(x	soγ∗(x	NOUN
ejpam-137	283	26	)	)	PUNCT
ejpam-137	283	27	,	,	PUNCT
ejpam-137	283	28	for	for	ADP
ejpam-137	283	29	every	every	DET
ejpam-137	283	30	b	b	PROPN
ejpam-137	283	31	∈	∈	PROPN
ejpam-137	283	32	soβ∗(y	soβ∗(y	NOUN
ejpam-137	283	33	)	)	PUNCT
ejpam-137	283	34	,	,	PUNCT
ejpam-137	283	35	where	where	SCONJ
ejpam-137	283	36	β	β	PROPN
ejpam-137	283	37	is	be	AUX
ejpam-137	283	38	an	an	DET
ejpam-137	283	39	open	open	ADJ
ejpam-137	283	40	operation	operation	NOUN
ejpam-137	283	41	.	.	PUNCT
ejpam-137	284	1	we	we	PRON
ejpam-137	284	2	use	use	VERB
ejpam-137	284	3	this	this	DET
ejpam-137	284	4	theorem	theorem	NOUN
ejpam-137	284	5	and	and	CCONJ
ejpam-137	284	6	prove	prove	VERB
ejpam-137	284	7	:	:	PUNCT
ejpam-137	284	8	theorem	theorem	VERB
ejpam-137	284	9	4.12	4.12	NUM
ejpam-137	284	10	.	.	PUNCT
ejpam-137	285	1	let	let	VERB
ejpam-137	285	2	x	x	PRON
ejpam-137	285	3	,	,	PUNCT
ejpam-137	285	4	y	y	PROPN
ejpam-137	285	5	and	and	CCONJ
ejpam-137	285	6	z	z	NOUN
ejpam-137	285	7	be	be	VERB
ejpam-137	285	8	three	three	NUM
ejpam-137	285	9	spaces	space	NOUN
ejpam-137	285	10	,	,	PUNCT
ejpam-137	285	11	and	and	CCONJ
ejpam-137	285	12	let	let	VERB
ejpam-137	285	13	f	f	PRON
ejpam-137	285	14	:	:	PUNCT
ejpam-137	285	15	x	x	X
ejpam-137	285	16	→	→	SYM
ejpam-137	285	17	y	y	PROPN
ejpam-137	285	18	and	and	CCONJ
ejpam-137	285	19	g	g	PROPN
ejpam-137	285	20	:	:	PUNCT
ejpam-137	285	21	y	y	PROPN
ejpam-137	285	22	→	→	SYM
ejpam-137	285	23	z	z	X
ejpam-137	285	24	be	be	AUX
ejpam-137	285	25	two	two	NUM
ejpam-137	285	26	functions	function	NOUN
ejpam-137	285	27	such	such	ADJ
ejpam-137	285	28	that	that	PRON
ejpam-137	285	29	go	go	VERB
ejpam-137	285	30	f	f	NOUN
ejpam-137	285	31	:	:	PUNCT
ejpam-137	285	32	x	x	X
ejpam-137	285	33	→	→	SYM
ejpam-137	285	34	z	z	X
ejpam-137	285	35	a	a	DET
ejpam-137	285	36	γ	γ	X
ejpam-137	285	37	-	-	PUNCT
ejpam-137	285	38	pre	pre	ADJ
ejpam-137	285	39	-	-	ADJ
ejpam-137	285	40	semi	semi	ADJ
ejpam-137	285	41	-	-	ADJ
ejpam-137	285	42	open	open	ADJ
ejpam-137	285	43	function	function	NOUN
ejpam-137	285	44	.	.	PUNCT
ejpam-137	286	1	then	then	ADV
ejpam-137	286	2	(	(	PUNCT
ejpam-137	286	3	1	1	X
ejpam-137	286	4	)	)	PUNCT
ejpam-137	286	5	if	if	SCONJ
ejpam-137	286	6	f	f	PROPN
ejpam-137	286	7	is	be	AUX
ejpam-137	286	8	a	a	DET
ejpam-137	286	9	(	(	PUNCT
ejpam-137	286	10	γ	γ	X
ejpam-137	286	11	,	,	PUNCT
ejpam-137	286	12	β)-open	β)-open	PUNCT
ejpam-137	286	13	and	and	CCONJ
ejpam-137	286	14	(	(	PUNCT
ejpam-137	286	15	γ	γ	PROPN
ejpam-137	286	16	,	,	PUNCT
ejpam-137	286	17	β)-continuous	β)-continuous	ADJ
ejpam-137	286	18	surjection	surjection	NOUN
ejpam-137	286	19	,	,	PUNCT
ejpam-137	286	20	then	then	ADV
ejpam-137	286	21	g	g	PROPN
ejpam-137	286	22	is	be	AUX
ejpam-137	286	23	β	β	NOUN
ejpam-137	286	24	-pre	-pre	NOUN
ejpam-137	286	25	-	-	PUNCT
ejpam-137	286	26	semi	semi	ADV
ejpam-137	286	27	-	-	ADJ
ejpam-137	286	28	open	open	ADJ
ejpam-137	286	29	.	.	PUNCT
ejpam-137	287	1	(	(	PUNCT
ejpam-137	287	2	2	2	X
ejpam-137	287	3	)	)	PUNCT
ejpam-137	287	4	if	if	SCONJ
ejpam-137	287	5	g	g	PROPN
ejpam-137	287	6	is	be	AUX
ejpam-137	287	7	a	a	DET
ejpam-137	287	8	(	(	PUNCT
ejpam-137	287	9	β	β	X
ejpam-137	287	10	,	,	PUNCT
ejpam-137	287	11	δ)-open	δ)-open	PUNCT
ejpam-137	287	12	and	and	CCONJ
ejpam-137	287	13	(	(	PUNCT
ejpam-137	287	14	β	β	X
ejpam-137	287	15	,	,	PUNCT
ejpam-137	287	16	δ)-continuous	δ)-continuous	ADJ
ejpam-137	287	17	injection	injection	NOUN
ejpam-137	287	18	,	,	PUNCT
ejpam-137	287	19	then	then	ADV
ejpam-137	287	20	f	f	PROPN
ejpam-137	287	21	is	be	AUX
ejpam-137	287	22	γ	γ	PROPN
ejpam-137	287	23	-	-	PUNCT
ejpam-137	287	24	pre	pre	ADJ
ejpam-137	287	25	-	-	ADJ
ejpam-137	287	26	semi	semi	ADJ
ejpam-137	287	27	-	-	ADJ
ejpam-137	287	28	open	open	ADJ
ejpam-137	287	29	.	.	PUNCT
ejpam-137	288	1	proof.(1	proof.(1	X
ejpam-137	288	2	)	)	PUNCT
ejpam-137	288	3	.	.	PUNCT
ejpam-137	289	1	let	let	VERB
ejpam-137	289	2	v	v	PART
ejpam-137	289	3	be	be	AUX
ejpam-137	289	4	an	an	DET
ejpam-137	289	5	arbitrary	arbitrary	ADJ
ejpam-137	289	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	289	7	-	-	ADJ
ejpam-137	289	8	open	open	ADJ
ejpam-137	289	9	set	set	NOUN
ejpam-137	289	10	in	in	ADP
ejpam-137	289	11	y.	y.	NOUN
ejpam-137	289	12	since	since	SCONJ
ejpam-137	289	13	f	f	PROPN
ejpam-137	289	14	is	be	AUX
ejpam-137	289	15	a	a	DET
ejpam-137	289	16	(	(	PUNCT
ejpam-137	289	17	γ	γ	X
ejpam-137	289	18	,	,	PUNCT
ejpam-137	289	19	β)-open	β)-open	PUNCT
ejpam-137	289	20	and	and	CCONJ
ejpam-137	289	21	(	(	PUNCT
ejpam-137	289	22	γ	γ	X
ejpam-137	289	23	,	,	PUNCT
ejpam-137	289	24	β)continuous	β)continuous	NUM
ejpam-137	289	25	,	,	PUNCT
ejpam-137	289	26	then	then	ADV
ejpam-137	289	27	by	by	ADP
ejpam-137	289	28	theorem	theorem	NOUN
ejpam-137	289	29	4.11	4.11	NUM
ejpam-137	289	30	,	,	PUNCT
ejpam-137	289	31	f	f	PROPN
ejpam-137	289	32	−1(v	−1(v	PROPN
ejpam-137	289	33	)	)	PUNCT
ejpam-137	289	34	is	be	AUX
ejpam-137	289	35	a	a	DET
ejpam-137	289	36	γ∗-semi	γ∗-semi	NOUN
ejpam-137	289	37	-	-	ADJ
ejpam-137	289	38	open	open	ADJ
ejpam-137	289	39	set	set	NOUN
ejpam-137	289	40	in	in	ADP
ejpam-137	289	41	x.	x.	NOUN
ejpam-137	289	42	also	also	ADV
ejpam-137	289	43	go	go	VERB
ejpam-137	289	44	f	f	PROPN
ejpam-137	289	45	is	be	AUX
ejpam-137	289	46	γ	γ	PROPN
ejpam-137	289	47	-	-	PUNCT
ejpam-137	289	48	pre	pre	ADJ
ejpam-137	289	49	-	-	ADJ
ejpam-137	289	50	semiopen	semiopen	ADJ
ejpam-137	289	51	and	and	CCONJ
ejpam-137	289	52	f	f	PROPN
ejpam-137	289	53	is	be	AUX
ejpam-137	289	54	surjection	surjection	NOUN
ejpam-137	289	55	,	,	PUNCT
ejpam-137	289	56	we	we	PRON
ejpam-137	289	57	have	have	VERB
ejpam-137	289	58	g(v	g(v	PROPN
ejpam-137	289	59	)	)	PUNCT
ejpam-137	290	1	=	=	PUNCT
ejpam-137	290	2	(	(	PUNCT
ejpam-137	290	3	go	go	VERB
ejpam-137	290	4	f	f	NOUN
ejpam-137	290	5	)	)	PUNCT
ejpam-137	290	6	(	(	PUNCT
ejpam-137	290	7	f	f	PROPN
ejpam-137	290	8	−1(v	−1(v	PROPN
ejpam-137	290	9	)	)	PUNCT
ejpam-137	290	10	)	)	PUNCT
ejpam-137	290	11	is	be	AUX
ejpam-137	290	12	a	a	DET
ejpam-137	290	13	β∗-semi	β∗-semi	ADV
ejpam-137	290	14	-	-	PUNCT
ejpam-137	290	15	open	open	ADJ
ejpam-137	290	16	set	set	NOUN
ejpam-137	290	17	in	in	ADP
ejpam-137	290	18	z.	z.	PROPN
ejpam-137	290	19	this	this	PRON
ejpam-137	290	20	proves	prove	VERB
ejpam-137	290	21	that	that	SCONJ
ejpam-137	290	22	g	g	PROPN
ejpam-137	290	23	is	be	AUX
ejpam-137	290	24	β	β	NOUN
ejpam-137	290	25	-	-	ADJ
ejpam-137	290	26	pre	pre	ADJ
ejpam-137	290	27	-	-	ADJ
ejpam-137	290	28	semi	semi	ADJ
ejpam-137	290	29	-	-	ADJ
ejpam-137	290	30	open	open	ADJ
ejpam-137	290	31	.	.	PUNCT
ejpam-137	291	1	(	(	PUNCT
ejpam-137	291	2	2	2	NUM
ejpam-137	291	3	)	)	PUNCT
ejpam-137	291	4	.	.	PUNCT
ejpam-137	292	1	since	since	SCONJ
ejpam-137	292	2	g	g	PROPN
ejpam-137	292	3	is	be	AUX
ejpam-137	292	4	injective	injective	ADJ
ejpam-137	292	5	so	so	ADV
ejpam-137	292	6	for	for	SCONJ
ejpam-137	292	7	every	every	DET
ejpam-137	292	8	subset	subset	NOUN
ejpam-137	292	9	a	a	PRON
ejpam-137	292	10	of	of	ADP
ejpam-137	292	11	x	x	PRON
ejpam-137	292	12	,	,	PUNCT
ejpam-137	292	13	f	f	PROPN
ejpam-137	292	14	(	(	PUNCT
ejpam-137	292	15	a	a	NOUN
ejpam-137	292	16	)	)	PUNCT
ejpam-137	292	17	=	=	SYM
ejpam-137	292	18	g−1(g	g−1(g	PROPN
ejpam-137	292	19	(	(	PUNCT
ejpam-137	292	20	f	f	PROPN
ejpam-137	292	21	(	(	PUNCT
ejpam-137	292	22	a	a	NOUN
ejpam-137	292	23	)	)	PUNCT
ejpam-137	292	24	)	)	PUNCT
ejpam-137	292	25	)	)	PUNCT
ejpam-137	292	26	.	.	PUNCT
ejpam-137	293	1	let	let	VERB
ejpam-137	293	2	u	u	PRON
ejpam-137	293	3	be	be	AUX
ejpam-137	293	4	an	an	DET
ejpam-137	293	5	arbitrary	arbitrary	ADJ
ejpam-137	293	6	γ∗-semi	γ∗-semi	NOUN
ejpam-137	293	7	-	-	ADJ
ejpam-137	293	8	open	open	ADJ
ejpam-137	293	9	set	set	NOUN
ejpam-137	293	10	in	in	ADP
ejpam-137	293	11	x.	x.	NOUN
ejpam-137	293	12	then	then	ADV
ejpam-137	293	13	(	(	PUNCT
ejpam-137	293	14	go	go	VERB
ejpam-137	293	15	f	f	NOUN
ejpam-137	293	16	)	)	PUNCT
ejpam-137	293	17	(	(	PUNCT
ejpam-137	293	18	u	u	NOUN
ejpam-137	293	19	)	)	PUNCT
ejpam-137	293	20	is	be	AUX
ejpam-137	293	21	γ∗-semi	γ∗-semi	NOUN
ejpam-137	293	22	-	-	NOUN
ejpam-137	293	23	open	open	ADJ
ejpam-137	293	24	.	.	PUNCT
ejpam-137	294	1	since	since	SCONJ
ejpam-137	294	2	g	g	PROPN
ejpam-137	294	3	is	be	AUX
ejpam-137	294	4	a	a	DET
ejpam-137	294	5	(	(	PUNCT
ejpam-137	294	6	β	β	X
ejpam-137	294	7	,	,	PUNCT
ejpam-137	294	8	δ)-open	δ)-open	PUNCT
ejpam-137	294	9	and	and	CCONJ
ejpam-137	294	10	(	(	PUNCT
ejpam-137	294	11	β	β	X
ejpam-137	294	12	,	,	PUNCT
ejpam-137	294	13	δ)semi	δ)semi	ADV
ejpam-137	294	14	-	-	ADJ
ejpam-137	294	15	continuous	continuous	ADJ
ejpam-137	294	16	,	,	PUNCT
ejpam-137	294	17	therefore	therefore	ADV
ejpam-137	294	18	by	by	ADP
ejpam-137	294	19	above	above	ADP
ejpam-137	294	20	theorem	theorem	NOUN
ejpam-137	294	21	4.11	4.11	NUM
ejpam-137	294	22	,	,	PUNCT
ejpam-137	294	23	f	f	PROPN
ejpam-137	294	24	(	(	PUNCT
ejpam-137	294	25	u	u	NOUN
ejpam-137	294	26	)	)	PUNCT
ejpam-137	294	27	is	be	AUX
ejpam-137	294	28	γ∗-semi	γ∗-semi	NOUN
ejpam-137	294	29	-	-	NOUN
ejpam-137	294	30	open	open	ADJ
ejpam-137	294	31	in	in	ADP
ejpam-137	294	32	y.	y.	PROPN
ejpam-137	294	33	this	this	PRON
ejpam-137	294	34	shows	show	VERB
ejpam-137	294	35	that	that	SCONJ
ejpam-137	294	36	f	f	PROPN
ejpam-137	294	37	is	be	AUX
ejpam-137	294	38	γ	γ	PROPN
ejpam-137	294	39	-	-	PUNCT
ejpam-137	294	40	pre	pre	ADJ
ejpam-137	294	41	-	-	ADJ
ejpam-137	294	42	semi	semi	ADJ
ejpam-137	294	43	-	-	ADJ
ejpam-137	294	44	open	open	ADJ
ejpam-137	294	45	.	.	PUNCT
ejpam-137	295	1	theorem	theorem	VERB
ejpam-137	295	2	4.13	4.13	NUM
ejpam-137	295	3	.	.	PUNCT
ejpam-137	296	1	let	let	VERB
ejpam-137	296	2	f	f	NOUN
ejpam-137	296	3	:	:	PUNCT
ejpam-137	296	4	x	x	X
ejpam-137	296	5	→	→	SYM
ejpam-137	296	6	y	y	PROPN
ejpam-137	296	7	and	and	CCONJ
ejpam-137	296	8	g	g	PROPN
ejpam-137	296	9	:	:	PUNCT
ejpam-137	296	10	y	y	PROPN
ejpam-137	296	11	→	→	SYM
ejpam-137	296	12	z	z	X
ejpam-137	296	13	be	be	AUX
ejpam-137	296	14	two	two	NUM
ejpam-137	296	15	functions	function	NOUN
ejpam-137	296	16	such	such	ADJ
ejpam-137	296	17	that	that	PRON
ejpam-137	296	18	go	go	VERB
ejpam-137	296	19	f	f	NOUN
ejpam-137	296	20	:	:	PUNCT
ejpam-137	296	21	x	x	X
ejpam-137	296	22	→	→	SYM
ejpam-137	296	23	z	z	NOUN
ejpam-137	296	24	is	be	AUX
ejpam-137	296	25	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	296	26	.	.	PUNCT
ejpam-137	297	1	then	then	ADV
ejpam-137	297	2	(	(	PUNCT
ejpam-137	297	3	1	1	X
ejpam-137	297	4	)	)	PUNCT
ejpam-137	297	5	if	if	SCONJ
ejpam-137	297	6	g	g	PROPN
ejpam-137	297	7	is	be	AUX
ejpam-137	297	8	a	a	DET
ejpam-137	297	9	β	β	NOUN
ejpam-137	297	10	-	-	ADJ
ejpam-137	297	11	pre	pre	ADJ
ejpam-137	297	12	-	-	ADJ
ejpam-137	297	13	semi	semi	ADJ
ejpam-137	297	14	-	-	ADJ
ejpam-137	297	15	open	open	ADJ
ejpam-137	297	16	injection	injection	NOUN
ejpam-137	297	17	,	,	PUNCT
ejpam-137	297	18	then	then	ADV
ejpam-137	297	19	f	f	PROPN
ejpam-137	297	20	is	be	AUX
ejpam-137	297	21	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	297	22	.	.	PUNCT
ejpam-137	298	1	(	(	PUNCT
ejpam-137	298	2	2	2	X
ejpam-137	298	3	)	)	PUNCT
ejpam-137	298	4	if	if	SCONJ
ejpam-137	298	5	f	f	PROPN
ejpam-137	298	6	is	be	AUX
ejpam-137	298	7	a	a	DET
ejpam-137	298	8	γ	γ	X
ejpam-137	298	9	-	-	PUNCT
ejpam-137	298	10	pre	pre	ADJ
ejpam-137	298	11	-	-	ADJ
ejpam-137	298	12	semi	semi	ADJ
ejpam-137	298	13	-	-	ADJ
ejpam-137	298	14	open	open	ADJ
ejpam-137	298	15	surjection	surjection	NOUN
ejpam-137	298	16	,	,	PUNCT
ejpam-137	298	17	then	then	ADV
ejpam-137	298	18	g	g	PROPN
ejpam-137	298	19	is	be	AUX
ejpam-137	298	20	β∗-irresolute	β∗-irresolute	NOUN
ejpam-137	298	21	.	.	PUNCT
ejpam-137	298	22	proof.(1	proof.(1	NUM
ejpam-137	298	23	)	)	PUNCT
ejpam-137	298	24	.	.	PUNCT
ejpam-137	299	1	let	let	VERB
ejpam-137	299	2	u	u	PRON
ejpam-137	299	3	∈	∈	PROPN
ejpam-137	299	4	soβ∗(y	soβ∗(y	PROPN
ejpam-137	299	5	)	)	PUNCT
ejpam-137	299	6	.	.	PUNCT
ejpam-137	300	1	since	since	SCONJ
ejpam-137	300	2	g	g	PROPN
ejpam-137	300	3	is	be	AUX
ejpam-137	300	4	β	β	X
ejpam-137	300	5	-	-	ADJ
ejpam-137	300	6	pre	pre	ADJ
ejpam-137	300	7	-	-	ADJ
ejpam-137	300	8	semi	semi	ADJ
ejpam-137	300	9	-	-	ADJ
ejpam-137	300	10	open	open	ADJ
ejpam-137	300	11	,	,	PUNCT
ejpam-137	300	12	then	then	ADV
ejpam-137	300	13	g(u	g(u	PROPN
ejpam-137	300	14	)	)	PUNCT
ejpam-137	300	15	∈	∈	PROPN
ejpam-137	300	16	soδ∗(z	soδ∗(z	NOUN
ejpam-137	300	17	)	)	PUNCT
ejpam-137	300	18	.	.	PUNCT
ejpam-137	301	1	also	also	ADV
ejpam-137	301	2	go	go	VERB
ejpam-137	301	3	f	f	PROPN
ejpam-137	301	4	is	be	AUX
ejpam-137	301	5	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	301	6	,	,	PUNCT
ejpam-137	301	7	and	and	CCONJ
ejpam-137	301	8	therefore	therefore	ADV
ejpam-137	301	9	;	;	PUNCT
ejpam-137	301	10	(	(	PUNCT
ejpam-137	301	11	go	go	VERB
ejpam-137	301	12	f	f	NOUN
ejpam-137	301	13	)	)	PUNCT
ejpam-137	301	14	−1(g(u	−1(g(u	PROPN
ejpam-137	301	15	)	)	PUNCT
ejpam-137	301	16	)	)	PUNCT
ejpam-137	302	1	∈	∈	PROPN
ejpam-137	302	2	soγ∗(x	soγ∗(x	NOUN
ejpam-137	302	3	)	)	PUNCT
ejpam-137	302	4	.	.	PUNCT
ejpam-137	303	1	since	since	SCONJ
ejpam-137	303	2	g	g	PROPN
ejpam-137	303	3	is	be	AUX
ejpam-137	303	4	injective	injective	ADJ
ejpam-137	303	5	(	(	PUNCT
ejpam-137	303	6	go	go	VERB
ejpam-137	303	7	f	f	NOUN
ejpam-137	303	8	)	)	PUNCT
ejpam-137	303	9	−1(g(u	−1(g(u	PROPN
ejpam-137	303	10	)	)	PUNCT
ejpam-137	303	11	)	)	PUNCT
ejpam-137	304	1	=	=	PRON
ejpam-137	304	2	(	(	PUNCT
ejpam-137	304	3	f	f	PROPN
ejpam-137	304	4	−1og−1)g(u	−1og−1)g(u	X
ejpam-137	304	5	)	)	PUNCT
ejpam-137	304	6	=	=	SYM
ejpam-137	305	1	f	f	PROPN
ejpam-137	305	2	−1(g−1	−1(g−1	PROPN
ejpam-137	305	3	g(u	g(u	PROPN
ejpam-137	305	4	)	)	PUNCT
ejpam-137	305	5	)	)	PUNCT
ejpam-137	306	1	=	=	SYM
ejpam-137	306	2	f	f	NOUN
ejpam-137	306	3	−1(u	−1(u	NOUN
ejpam-137	306	4	)	)	PUNCT
ejpam-137	306	5	.	.	PUNCT
ejpam-137	307	1	consequently	consequently	ADV
ejpam-137	307	2	,	,	PUNCT
ejpam-137	307	3	f	f	PROPN
ejpam-137	307	4	−1(u	−1(u	X
ejpam-137	307	5	)	)	PUNCT
ejpam-137	307	6	is	be	AUX
ejpam-137	307	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	307	8	-	-	NOUN
ejpam-137	307	9	open	open	ADJ
ejpam-137	307	10	in	in	ADP
ejpam-137	307	11	x.	x.	PROPN
ejpam-137	307	12	this	this	PRON
ejpam-137	307	13	b.	b.	PROPN
ejpam-137	307	14	ahmad	ahmad	PROPN
ejpam-137	307	15	,	,	PUNCT
ejpam-137	307	16	s.	s.	PROPN
ejpam-137	307	17	hussain	hussain	PROPN
ejpam-137	307	18	,	,	PUNCT
ejpam-137	307	19	and	and	CCONJ
ejpam-137	307	20	t.	t.	PROPN
ejpam-137	307	21	noiri	noiri	PROPN
ejpam-137	307	22	/	/	SYM
ejpam-137	307	23	eur	eur	PROPN
ejpam-137	307	24	.	.	PUNCT
ejpam-137	308	1	j.	j.	PROPN
ejpam-137	308	2	pure	pure	PROPN
ejpam-137	308	3	appl	appl	PROPN
ejpam-137	308	4	.	.	PROPN
ejpam-137	308	5	math	math	PROPN
ejpam-137	308	6	,	,	PUNCT
ejpam-137	308	7	1	1	NUM
ejpam-137	308	8	(	(	PUNCT
ejpam-137	308	9	2008	2008	NUM
ejpam-137	308	10	)	)	PUNCT
ejpam-137	308	11	,	,	PUNCT
ejpam-137	308	12	(	(	PUNCT
ejpam-137	308	13	22	22	NUM
ejpam-137	308	14	-	-	SYM
ejpam-137	308	15	29	29	NUM
ejpam-137	308	16	)	)	PUNCT
ejpam-137	308	17	28	28	NUM
ejpam-137	308	18	proves	prove	VERB
ejpam-137	308	19	that	that	SCONJ
ejpam-137	308	20	f	f	PROPN
ejpam-137	308	21	is	be	AUX
ejpam-137	308	22	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	308	23	.	.	PUNCT
ejpam-137	309	1	this	this	PRON
ejpam-137	309	2	proves	prove	VERB
ejpam-137	309	3	(	(	PUNCT
ejpam-137	309	4	1	1	NUM
ejpam-137	309	5	)	)	PUNCT
ejpam-137	309	6	.	.	PUNCT
ejpam-137	310	1	(	(	PUNCT
ejpam-137	310	2	2	2	NUM
ejpam-137	310	3	)	)	PUNCT
ejpam-137	310	4	.	.	PUNCT
ejpam-137	311	1	let	let	VERB
ejpam-137	311	2	v	v	NUM
ejpam-137	311	3	∈	∈	PROPN
ejpam-137	311	4	soδ∗(z	soδ∗(z	NOUN
ejpam-137	311	5	)	)	PUNCT
ejpam-137	311	6	.	.	PUNCT
ejpam-137	312	1	since	since	SCONJ
ejpam-137	312	2	go	go	VERB
ejpam-137	312	3	f	f	PROPN
ejpam-137	312	4	is	be	AUX
ejpam-137	312	5	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	312	6	,	,	PUNCT
ejpam-137	312	7	then	then	ADV
ejpam-137	312	8	(	(	PUNCT
ejpam-137	312	9	go	go	VERB
ejpam-137	312	10	f	f	NOUN
ejpam-137	312	11	)	)	PUNCT
ejpam-137	312	12	−1(v	−1(v	PROPN
ejpam-137	312	13	)	)	PUNCT
ejpam-137	313	1	∈	∈	PROPN
ejpam-137	313	2	soγ∗(x	soγ∗(x	NOUN
ejpam-137	313	3	)	)	PUNCT
ejpam-137	313	4	.	.	PUNCT
ejpam-137	314	1	also	also	ADV
ejpam-137	314	2	f	f	PROPN
ejpam-137	314	3	is	be	AUX
ejpam-137	314	4	γ	γ	PROPN
ejpam-137	314	5	-	-	PUNCT
ejpam-137	314	6	pre	pre	ADJ
ejpam-137	314	7	-	-	ADJ
ejpam-137	314	8	semi	semi	ADJ
ejpam-137	314	9	-	-	ADJ
ejpam-137	314	10	open	open	ADJ
ejpam-137	314	11	,	,	PUNCT
ejpam-137	314	12	so	so	CCONJ
ejpam-137	314	13	f	f	PROPN
ejpam-137	314	14	(	(	PUNCT
ejpam-137	314	15	go	go	VERB
ejpam-137	314	16	f	f	NOUN
ejpam-137	314	17	)	)	PUNCT
ejpam-137	314	18	−1(v	−1(v	PROPN
ejpam-137	314	19	)	)	PUNCT
ejpam-137	314	20	is	be	AUX
ejpam-137	314	21	β∗-semi	β∗-semi	NOUN
ejpam-137	314	22	-	-	NOUN
ejpam-137	314	23	open	open	ADJ
ejpam-137	314	24	in	in	ADP
ejpam-137	314	25	y.	y.	PROPN
ejpam-137	314	26	since	since	SCONJ
ejpam-137	314	27	f	f	PROPN
ejpam-137	314	28	is	be	AUX
ejpam-137	314	29	surjective	surjective	ADJ
ejpam-137	314	30	,	,	PUNCT
ejpam-137	314	31	we	we	PRON
ejpam-137	314	32	obtain	obtain	VERB
ejpam-137	314	33	f	f	PROPN
ejpam-137	314	34	o(go	o(go	ADJ
ejpam-137	314	35	f	f	PROPN
ejpam-137	314	36	)	)	PUNCT
ejpam-137	314	37	−1(v	−1(v	PROPN
ejpam-137	314	38	)	)	PUNCT
ejpam-137	315	1	=	=	PUNCT
ejpam-137	316	1	f	f	X
ejpam-137	316	2	o	o	X
ejpam-137	316	3	(	(	PUNCT
ejpam-137	316	4	f	f	X
ejpam-137	316	5	−1og−1)(v	−1og−1)(v	X
ejpam-137	316	6	)	)	PUNCT
ejpam-137	316	7	=	=	PUNCT
ejpam-137	317	1	(	(	PUNCT
ejpam-137	317	2	f	f	X
ejpam-137	317	3	o	o	X
ejpam-137	317	4	f	f	X
ejpam-137	317	5	−1)og−1(v	−1)og−1(v	NOUN
ejpam-137	317	6	)	)	PUNCT
ejpam-137	318	1	=	=	PUNCT
ejpam-137	318	2	g−1(v	g−1(v	NOUN
ejpam-137	318	3	)	)	PUNCT
ejpam-137	318	4	.	.	PUNCT
ejpam-137	319	1	it	it	PRON
ejpam-137	319	2	follows	follow	VERB
ejpam-137	319	3	that	that	DET
ejpam-137	319	4	g−1(v	g−1(v	NOUN
ejpam-137	319	5	)	)	PUNCT
ejpam-137	320	1	∈	∈	PROPN
ejpam-137	320	2	soγ∗(y	soγ∗(y	PROPN
ejpam-137	320	3	)	)	PUNCT
ejpam-137	320	4	.	.	PUNCT
ejpam-137	321	1	this	this	PRON
ejpam-137	321	2	proves	prove	VERB
ejpam-137	321	3	that	that	SCONJ
ejpam-137	321	4	g	g	PROPN
ejpam-137	321	5	is	be	AUX
ejpam-137	321	6	a	a	DET
ejpam-137	321	7	β∗-irresolute	β∗-irresolute	NOUN
ejpam-137	321	8	function	function	NOUN
ejpam-137	321	9	.	.	PUNCT
ejpam-137	322	1	5	5	X
ejpam-137	322	2	.	.	X
ejpam-137	322	3	γ	γ	X
ejpam-137	322	4	-	-	PUNCT
ejpam-137	322	5	pre	pre	ADJ
ejpam-137	322	6	-	-	ADJ
ejpam-137	322	7	semi	semi	ADJ
ejpam-137	322	8	-	-	ADJ
ejpam-137	322	9	closed	closed	ADJ
ejpam-137	322	10	functions	function	NOUN
ejpam-137	322	11	definition	definition	NOUN
ejpam-137	322	12	5.1	5.1	NUM
ejpam-137	322	13	.	.	PUNCT
ejpam-137	323	1	a	a	DET
ejpam-137	323	2	function	function	NOUN
ejpam-137	323	3	f	f	NOUN
ejpam-137	323	4	:	:	PUNCT
ejpam-137	323	5	x	x	X
ejpam-137	323	6	→	→	SYM
ejpam-137	323	7	y	y	PROPN
ejpam-137	323	8	is	be	AUX
ejpam-137	323	9	γ	γ	PROPN
ejpam-137	323	10	-	-	PUNCT
ejpam-137	323	11	pre	pre	ADJ
ejpam-137	323	12	-	-	ADJ
ejpam-137	323	13	semi	semi	ADJ
ejpam-137	323	14	-	-	ADJ
ejpam-137	323	15	closed	closed	ADJ
ejpam-137	323	16	if	if	SCONJ
ejpam-137	323	17	and	and	CCONJ
ejpam-137	323	18	only	only	ADV
ejpam-137	323	19	if	if	SCONJ
ejpam-137	323	20	the	the	DET
ejpam-137	323	21	image	image	NOUN
ejpam-137	323	22	set	set	VERB
ejpam-137	323	23	f	f	PROPN
ejpam-137	323	24	(	(	PUNCT
ejpam-137	323	25	a	a	NOUN
ejpam-137	323	26	)	)	PUNCT
ejpam-137	323	27	is	be	AUX
ejpam-137	323	28	γ∗-semi	γ∗-semi	NOUN
ejpam-137	323	29	-	-	ADJ
ejpam-137	323	30	closed	closed	ADJ
ejpam-137	323	31	,	,	PUNCT
ejpam-137	323	32	for	for	SCONJ
ejpam-137	323	33	each	each	DET
ejpam-137	323	34	γ∗-semi	γ∗-semi	NOUN
ejpam-137	323	35	-	-	ADJ
ejpam-137	323	36	closed	closed	ADJ
ejpam-137	323	37	subset	subset	NOUN
ejpam-137	323	38	a	a	PRON
ejpam-137	323	39	of	of	ADP
ejpam-137	323	40	x.	x.	NOUN
ejpam-137	323	41	it	it	PRON
ejpam-137	323	42	is	be	AUX
ejpam-137	323	43	obvious	obvious	ADJ
ejpam-137	323	44	that	that	SCONJ
ejpam-137	323	45	the	the	DET
ejpam-137	323	46	composition	composition	NOUN
ejpam-137	323	47	of	of	ADP
ejpam-137	323	48	two	two	NUM
ejpam-137	323	49	γ	γ	NOUN
ejpam-137	323	50	-	-	PUNCT
ejpam-137	323	51	pre	pre	ADJ
ejpam-137	323	52	-	-	ADJ
ejpam-137	323	53	semi	semi	ADJ
ejpam-137	323	54	-	-	ADJ
ejpam-137	323	55	closed	closed	ADJ
ejpam-137	323	56	mappings	mapping	NOUN
ejpam-137	323	57	is	be	AUX
ejpam-137	323	58	a	a	DET
ejpam-137	323	59	γ	γ	X
ejpam-137	323	60	-	-	PUNCT
ejpam-137	323	61	pre	pre	ADJ
ejpam-137	323	62	-	-	ADJ
ejpam-137	323	63	semi	semi	ADJ
ejpam-137	323	64	-	-	ADJ
ejpam-137	323	65	closed	closed	ADJ
ejpam-137	323	66	mapping	mapping	NOUN
ejpam-137	323	67	.	.	PUNCT
ejpam-137	324	1	theorem	theorem	VERB
ejpam-137	324	2	5.2	5.2	NUM
ejpam-137	324	3	.	.	PUNCT
ejpam-137	325	1	a	a	DET
ejpam-137	325	2	function	function	NOUN
ejpam-137	325	3	f	f	NOUN
ejpam-137	325	4	:	:	PUNCT
ejpam-137	325	5	x	x	X
ejpam-137	325	6	→	→	SYM
ejpam-137	325	7	y	y	PROPN
ejpam-137	325	8	is	be	AUX
ejpam-137	325	9	γ	γ	PROPN
ejpam-137	325	10	-	-	PUNCT
ejpam-137	325	11	pre	pre	ADJ
ejpam-137	325	12	-	-	ADJ
ejpam-137	325	13	semi	semi	ADJ
ejpam-137	325	14	-	-	ADJ
ejpam-137	325	15	closed	closed	ADJ
ejpam-137	325	16	if	if	SCONJ
ejpam-137	325	17	and	and	CCONJ
ejpam-137	325	18	only	only	ADV
ejpam-137	325	19	if	if	SCONJ
ejpam-137	325	20	sclγ∗	sclγ∗	PROPN
ejpam-137	325	21	f	f	PROPN
ejpam-137	325	22	(	(	PUNCT
ejpam-137	325	23	b)⊆	b)⊆	PROPN
ejpam-137	325	24	f	f	PROPN
ejpam-137	325	25	(	(	PUNCT
ejpam-137	325	26	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	325	27	)	)	PUNCT
ejpam-137	325	28	)	)	PUNCT
ejpam-137	325	29	,	,	PUNCT
ejpam-137	325	30	for	for	ADP
ejpam-137	325	31	every	every	DET
ejpam-137	325	32	subset	subset	NOUN
ejpam-137	325	33	b	b	PROPN
ejpam-137	325	34	of	of	ADP
ejpam-137	325	35	x.	x.	NOUN
ejpam-137	325	36	proof	proof	NOUN
ejpam-137	325	37	.	.	PUNCT
ejpam-137	326	1	suppose	suppose	VERB
ejpam-137	326	2	f	f	PROPN
ejpam-137	326	3	is	be	AUX
ejpam-137	326	4	γ	γ	PROPN
ejpam-137	326	5	-	-	PUNCT
ejpam-137	326	6	pre	pre	ADJ
ejpam-137	326	7	-	-	ADJ
ejpam-137	326	8	semi	semi	ADJ
ejpam-137	326	9	-	-	ADJ
ejpam-137	326	10	closed	closed	ADJ
ejpam-137	326	11	and	and	CCONJ
ejpam-137	326	12	let	let	VERB
ejpam-137	326	13	b	b	NOUN
ejpam-137	326	14	⊆	⊆	NUM
ejpam-137	326	15	x	x	X
ejpam-137	326	16	.	.	PUNCT
ejpam-137	327	1	since	since	SCONJ
ejpam-137	327	2	f	f	PROPN
ejpam-137	327	3	is	be	AUX
ejpam-137	327	4	γ	γ	PROPN
ejpam-137	327	5	-	-	PUNCT
ejpam-137	327	6	pre	pre	ADJ
ejpam-137	327	7	-	-	ADJ
ejpam-137	327	8	semi	semi	ADJ
ejpam-137	327	9	-	-	ADJ
ejpam-137	327	10	closed	closed	ADJ
ejpam-137	327	11	,	,	PUNCT
ejpam-137	327	12	therefore	therefore	ADV
ejpam-137	327	13	f	f	X
ejpam-137	327	14	(	(	PUNCT
ejpam-137	327	15	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	327	16	)	)	PUNCT
ejpam-137	327	17	)	)	PUNCT
ejpam-137	327	18	is	be	AUX
ejpam-137	327	19	γ∗-semi	γ∗-semi	NOUN
ejpam-137	327	20	-	-	PUNCT
ejpam-137	327	21	closed	closed	ADJ
ejpam-137	327	22	in	in	ADP
ejpam-137	327	23	y.	y.	PROPN
ejpam-137	327	24	since	since	SCONJ
ejpam-137	327	25	f	f	PROPN
ejpam-137	327	26	(	(	PUNCT
ejpam-137	327	27	b)⊆	b)⊆	PROPN
ejpam-137	327	28	f	f	PROPN
ejpam-137	327	29	(	(	PUNCT
ejpam-137	327	30	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	327	31	)	)	PUNCT
ejpam-137	327	32	)	)	PUNCT
ejpam-137	327	33	,	,	PUNCT
ejpam-137	327	34	we	we	PRON
ejpam-137	327	35	obtain	obtain	VERB
ejpam-137	327	36	sclγ∗	sclγ∗	ADJ
ejpam-137	327	37	(	(	PUNCT
ejpam-137	327	38	f	f	PROPN
ejpam-137	327	39	(	(	PUNCT
ejpam-137	327	40	b))⊆	b))⊆	X
ejpam-137	327	41	f	f	X
ejpam-137	327	42	(	(	PUNCT
ejpam-137	327	43	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	327	44	)	)	PUNCT
ejpam-137	327	45	)	)	PUNCT
ejpam-137	327	46	.	.	PUNCT
ejpam-137	328	1	this	this	PRON
ejpam-137	328	2	proves	prove	VERB
ejpam-137	328	3	necessity	necessity	NOUN
ejpam-137	328	4	.	.	PUNCT
ejpam-137	329	1	conversely	conversely	ADV
ejpam-137	329	2	,	,	PUNCT
ejpam-137	329	3	suppose	suppose	VERB
ejpam-137	329	4	a	a	PRON
ejpam-137	329	5	is	be	AUX
ejpam-137	329	6	a	a	DET
ejpam-137	329	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	329	8	-	-	PUNCT
ejpam-137	329	9	closed	closed	ADJ
ejpam-137	329	10	set	set	NOUN
ejpam-137	329	11	in	in	ADP
ejpam-137	329	12	x.	x.	NOUN
ejpam-137	329	13	by	by	ADP
ejpam-137	329	14	hypothesis	hypothesis	NOUN
ejpam-137	329	15	,	,	PUNCT
ejpam-137	329	16	we	we	PRON
ejpam-137	329	17	obtain	obtain	VERB
ejpam-137	329	18	f	f	X
ejpam-137	329	19	(	(	PUNCT
ejpam-137	329	20	a	a	NOUN
ejpam-137	329	21	)	)	PUNCT
ejpam-137	329	22	⊆	⊆	NUM
ejpam-137	329	23	sclγ∗	sclγ∗	ADJ
ejpam-137	329	24	(	(	PUNCT
ejpam-137	329	25	f	f	X
ejpam-137	329	26	(	(	PUNCT
ejpam-137	329	27	a	a	NOUN
ejpam-137	329	28	)	)	PUNCT
ejpam-137	329	29	)	)	PUNCT
ejpam-137	330	1	⊆	⊆	NUM
ejpam-137	330	2	f	f	X
ejpam-137	330	3	(	(	PUNCT
ejpam-137	330	4	sclγ∗(a	sclγ∗(a	PROPN
ejpam-137	330	5	)	)	PUNCT
ejpam-137	330	6	)	)	PUNCT
ejpam-137	331	1	=	=	SYM
ejpam-137	331	2	f	f	X
ejpam-137	331	3	(	(	PUNCT
ejpam-137	331	4	a	a	NOUN
ejpam-137	331	5	)	)	PUNCT
ejpam-137	331	6	.	.	PUNCT
ejpam-137	332	1	hence	hence	ADV
ejpam-137	332	2	f	f	PROPN
ejpam-137	332	3	(	(	PUNCT
ejpam-137	332	4	a	a	X
ejpam-137	332	5	)	)	PUNCT
ejpam-137	332	6	=	=	SYM
ejpam-137	332	7	sclγ∗	sclγ∗	PROPN
ejpam-137	332	8	(	(	PUNCT
ejpam-137	332	9	f	f	PROPN
ejpam-137	332	10	(	(	PUNCT
ejpam-137	332	11	a	a	NOUN
ejpam-137	332	12	)	)	PUNCT
ejpam-137	332	13	)	)	PUNCT
ejpam-137	332	14	.	.	PUNCT
ejpam-137	333	1	thus	thus	ADV
ejpam-137	333	2	f	f	X
ejpam-137	333	3	(	(	PUNCT
ejpam-137	333	4	a	a	NOUN
ejpam-137	333	5	)	)	PUNCT
ejpam-137	333	6	is	be	AUX
ejpam-137	333	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	333	8	-	-	PUNCT
ejpam-137	333	9	closed	closed	ADJ
ejpam-137	333	10	set	set	NOUN
ejpam-137	333	11	in	in	ADP
ejpam-137	333	12	y.	y.	NOUN
ejpam-137	333	13	this	this	PRON
ejpam-137	333	14	proves	prove	VERB
ejpam-137	333	15	that	that	SCONJ
ejpam-137	333	16	f	f	PROPN
ejpam-137	333	17	is	be	AUX
ejpam-137	333	18	γ	γ	PROPN
ejpam-137	333	19	-	-	PUNCT
ejpam-137	333	20	pre	pre	ADJ
ejpam-137	333	21	-	-	ADJ
ejpam-137	333	22	semi	semi	ADJ
ejpam-137	333	23	-	-	ADJ
ejpam-137	333	24	closed	closed	ADJ
ejpam-137	333	25	.	.	PUNCT
ejpam-137	334	1	theorem	theorem	VERB
ejpam-137	334	2	5.3	5.3	NUM
ejpam-137	334	3	.	.	PUNCT
ejpam-137	335	1	a	a	DET
ejpam-137	335	2	function	function	NOUN
ejpam-137	335	3	f	f	NOUN
ejpam-137	335	4	:	:	PUNCT
ejpam-137	335	5	x	x	X
ejpam-137	335	6	→	→	SYM
ejpam-137	335	7	y	y	PROPN
ejpam-137	335	8	is	be	AUX
ejpam-137	335	9	γ	γ	PROPN
ejpam-137	335	10	-	-	PUNCT
ejpam-137	335	11	pre	pre	ADJ
ejpam-137	335	12	-	-	ADJ
ejpam-137	335	13	semi	semi	ADJ
ejpam-137	335	14	-	-	ADJ
ejpam-137	335	15	closed	closed	ADJ
ejpam-137	335	16	if	if	SCONJ
ejpam-137	335	17	and	and	CCONJ
ejpam-137	335	18	only	only	ADV
ejpam-137	335	19	if	if	SCONJ
ejpam-137	335	20	intγ(clγ	intγ(clγ	VERB
ejpam-137	335	21	(	(	PUNCT
ejpam-137	335	22	f	f	PROPN
ejpam-137	335	23	(	(	PUNCT
ejpam-137	335	24	b)))⊆	b)))⊆	NOUN
ejpam-137	335	25	f	f	PROPN
ejpam-137	335	26	(	(	PUNCT
ejpam-137	335	27	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	335	28	)	)	PUNCT
ejpam-137	335	29	)	)	PUNCT
ejpam-137	335	30	,	,	PUNCT
ejpam-137	335	31	for	for	ADP
ejpam-137	335	32	every	every	DET
ejpam-137	335	33	subset	subset	NOUN
ejpam-137	335	34	b	b	PROPN
ejpam-137	335	35	of	of	ADP
ejpam-137	335	36	x.	x.	NOUN
ejpam-137	335	37	proof	proof	NOUN
ejpam-137	335	38	.	.	PUNCT
ejpam-137	336	1	suppose	suppose	VERB
ejpam-137	336	2	f	f	PROPN
ejpam-137	336	3	is	be	AUX
ejpam-137	336	4	γ	γ	PROPN
ejpam-137	336	5	-	-	PUNCT
ejpam-137	336	6	pre	pre	ADJ
ejpam-137	336	7	-	-	ADJ
ejpam-137	336	8	semi	semi	ADJ
ejpam-137	336	9	-	-	ADJ
ejpam-137	336	10	closed	closed	ADJ
ejpam-137	336	11	and	and	CCONJ
ejpam-137	336	12	b	b	NOUN
ejpam-137	336	13	is	be	AUX
ejpam-137	336	14	any	any	DET
ejpam-137	336	15	subset	subset	NOUN
ejpam-137	336	16	of	of	ADP
ejpam-137	336	17	x.	x.	NOUN
ejpam-137	337	1	then	then	ADV
ejpam-137	337	2	f	f	PROPN
ejpam-137	337	3	(	(	PUNCT
ejpam-137	337	4	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	337	5	)	)	PUNCT
ejpam-137	337	6	)	)	PUNCT
ejpam-137	337	7	is	be	AUX
ejpam-137	337	8	γ∗semi	γ∗semi	NOUN
ejpam-137	337	9	-	-	PUNCT
ejpam-137	337	10	closed	closed	ADJ
ejpam-137	337	11	in	in	ADP
ejpam-137	337	12	y.	y.	PROPN
ejpam-137	337	13	this	this	PRON
ejpam-137	337	14	implies	imply	VERB
ejpam-137	337	15	that	that	SCONJ
ejpam-137	337	16	there	there	PRON
ejpam-137	337	17	exists	exist	VERB
ejpam-137	337	18	a	a	DET
ejpam-137	337	19	γ	γ	X
ejpam-137	337	20	-	-	ADJ
ejpam-137	337	21	closed	closed	ADJ
ejpam-137	337	22	subset	subset	NOUN
ejpam-137	337	23	a	a	PRON
ejpam-137	337	24	of	of	ADP
ejpam-137	337	25	y	y	PRON
ejpam-137	337	26	such	such	ADJ
ejpam-137	337	27	that	that	DET
ejpam-137	337	28	intγ(a	intγ(a	NOUN
ejpam-137	337	29	)	)	PUNCT
ejpam-137	337	30	⊆	⊆	NUM
ejpam-137	337	31	f	f	X
ejpam-137	337	32	(	(	PUNCT
ejpam-137	337	33	sclγ∗(b))⊆	sclγ∗(b))⊆	PROPN
ejpam-137	337	34	a	a	PRON
ejpam-137	337	35	.	.	PUNCT
ejpam-137	338	1	this	this	PRON
ejpam-137	338	2	gives	give	VERB
ejpam-137	338	3	that	that	PRON
ejpam-137	338	4	intγclγ	intγclγ	ADJ
ejpam-137	338	5	(	(	PUNCT
ejpam-137	338	6	f	f	X
ejpam-137	338	7	(	(	PUNCT
ejpam-137	338	8	sclγ∗(b)))⊆	sclγ∗(b)))⊆	NOUN
ejpam-137	338	9	intγ(a)⊆	intγ(a)⊆	PROPN
ejpam-137	338	10	f	f	X
ejpam-137	338	11	(	(	PUNCT
ejpam-137	338	12	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	338	13	)	)	PUNCT
ejpam-137	338	14	)	)	PUNCT
ejpam-137	338	15	.	.	PUNCT
ejpam-137	339	1	then	then	ADV
ejpam-137	339	2	intγ(clγ	intγ(clγ	PROPN
ejpam-137	339	3	(	(	PUNCT
ejpam-137	339	4	f	f	PROPN
ejpam-137	339	5	(	(	PUNCT
ejpam-137	339	6	b))⊆	b))⊆	X
ejpam-137	339	7	intγ(clγ	intγ(clγ	NOUN
ejpam-137	339	8	(	(	PUNCT
ejpam-137	339	9	f	f	PROPN
ejpam-137	339	10	(	(	PUNCT
ejpam-137	339	11	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	339	12	)	)	PUNCT
ejpam-137	339	13	)	)	PUNCT
ejpam-137	339	14	)	)	PUNCT
ejpam-137	339	15	)	)	PUNCT
ejpam-137	339	16	gives	give	VERB
ejpam-137	339	17	intγ(clγ	intγ(clγ	VERB
ejpam-137	339	18	(	(	PUNCT
ejpam-137	339	19	f	f	PROPN
ejpam-137	339	20	(	(	PUNCT
ejpam-137	339	21	b)))⊆	b)))⊆	NOUN
ejpam-137	339	22	f	f	PROPN
ejpam-137	339	23	(	(	PUNCT
ejpam-137	339	24	sclγ∗(b	sclγ∗(b	PROPN
ejpam-137	339	25	)	)	PUNCT
ejpam-137	339	26	)	)	PUNCT
ejpam-137	339	27	.	.	PUNCT
ejpam-137	340	1	this	this	PRON
ejpam-137	340	2	proves	prove	VERB
ejpam-137	340	3	necessity	necessity	NOUN
ejpam-137	340	4	.	.	PUNCT
ejpam-137	341	1	conversely	conversely	ADV
ejpam-137	341	2	,	,	PUNCT
ejpam-137	341	3	suppose	suppose	VERB
ejpam-137	341	4	a	a	PRON
ejpam-137	341	5	is	be	AUX
ejpam-137	341	6	a	a	DET
ejpam-137	341	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	341	8	-	-	PUNCT
ejpam-137	341	9	closed	closed	ADJ
ejpam-137	341	10	set	set	NOUN
ejpam-137	341	11	in	in	ADP
ejpam-137	341	12	x.	x.	NOUN
ejpam-137	341	13	then	then	ADV
ejpam-137	341	14	by	by	ADP
ejpam-137	341	15	hypothesis	hypothesis	NOUN
ejpam-137	341	16	,	,	PUNCT
ejpam-137	341	17	intγ(clγ	intγ(clγ	PROPN
ejpam-137	341	18	(	(	PUNCT
ejpam-137	341	19	f	f	PROPN
ejpam-137	341	20	(	(	PUNCT
ejpam-137	341	21	a	a	NOUN
ejpam-137	341	22	)	)	PUNCT
ejpam-137	341	23	)	)	PUNCT
ejpam-137	342	1	⊆	⊆	NUM
ejpam-137	342	2	f	f	X
ejpam-137	342	3	(	(	PUNCT
ejpam-137	342	4	sclγ∗(a	sclγ∗(a	PROPN
ejpam-137	342	5	)	)	PUNCT
ejpam-137	342	6	)	)	PUNCT
ejpam-137	343	1	=	=	SYM
ejpam-137	343	2	f	f	X
ejpam-137	343	3	(	(	PUNCT
ejpam-137	343	4	a	a	NOUN
ejpam-137	343	5	)	)	PUNCT
ejpam-137	343	6	.	.	PUNCT
ejpam-137	344	1	put	put	VERB
ejpam-137	344	2	b	b	NOUN
ejpam-137	345	1	=	=	X
ejpam-137	345	2	clγ	clγ	PROPN
ejpam-137	345	3	(	(	PUNCT
ejpam-137	345	4	f	f	X
ejpam-137	345	5	(	(	PUNCT
ejpam-137	345	6	a	a	NOUN
ejpam-137	345	7	)	)	PUNCT
ejpam-137	345	8	)	)	PUNCT
ejpam-137	345	9	.	.	PUNCT
ejpam-137	346	1	clearly	clearly	ADV
ejpam-137	346	2	,	,	PUNCT
ejpam-137	346	3	b	b	PROPN
ejpam-137	346	4	is	be	AUX
ejpam-137	346	5	γ	γ	NOUN
ejpam-137	346	6	-	-	ADJ
ejpam-137	346	7	closed	closed	ADJ
ejpam-137	346	8	in	in	ADP
ejpam-137	346	9	y.	y.	PROPN
ejpam-137	346	10	this	this	PRON
ejpam-137	346	11	implies	imply	VERB
ejpam-137	346	12	that	that	SCONJ
ejpam-137	346	13	intγ(b)⊆	intγ(b)⊆	NOUN
ejpam-137	346	14	f	f	X
ejpam-137	346	15	(	(	PUNCT
ejpam-137	346	16	a)⊆	a)⊆	X
ejpam-137	346	17	b.	b.	PROPN
ejpam-137	347	1	hence	hence	ADV
ejpam-137	347	2	f	f	PROPN
ejpam-137	347	3	(	(	PUNCT
ejpam-137	347	4	a	a	NOUN
ejpam-137	347	5	)	)	PUNCT
ejpam-137	347	6	is	be	AUX
ejpam-137	347	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	347	8	-	-	PUNCT
ejpam-137	347	9	closed	closed	ADJ
ejpam-137	347	10	in	in	ADP
ejpam-137	347	11	y.	y.	PROPN
ejpam-137	347	12	this	this	PRON
ejpam-137	347	13	implies	imply	VERB
ejpam-137	347	14	f	f	PROPN
ejpam-137	347	15	is	be	AUX
ejpam-137	347	16	γ	γ	PROPN
ejpam-137	347	17	-	-	PUNCT
ejpam-137	347	18	pre	pre	ADJ
ejpam-137	347	19	-	-	ADJ
ejpam-137	347	20	semi	semi	ADJ
ejpam-137	347	21	-	-	ADJ
ejpam-137	347	22	closed	closed	ADJ
ejpam-137	347	23	.	.	PUNCT
ejpam-137	348	1	theorem	theorem	VERB
ejpam-137	348	2	5.4	5.4	NUM
ejpam-137	348	3	.	.	PUNCT
ejpam-137	349	1	a	a	DET
ejpam-137	349	2	bijective	bijective	ADJ
ejpam-137	349	3	function	function	NOUN
ejpam-137	349	4	f	f	NOUN
ejpam-137	349	5	:	:	PUNCT
ejpam-137	349	6	x	x	X
ejpam-137	349	7	→	→	SYM
ejpam-137	349	8	y	y	PROPN
ejpam-137	349	9	is	be	AUX
ejpam-137	349	10	a	a	DET
ejpam-137	349	11	γ	γ	X
ejpam-137	349	12	-	-	PUNCT
ejpam-137	349	13	pre	pre	ADJ
ejpam-137	349	14	-	-	ADJ
ejpam-137	349	15	semi	semi	ADJ
ejpam-137	349	16	-	-	ADJ
ejpam-137	349	17	closed	closed	ADJ
ejpam-137	349	18	if	if	SCONJ
ejpam-137	349	19	and	and	CCONJ
ejpam-137	349	20	only	only	ADV
ejpam-137	349	21	if	if	SCONJ
ejpam-137	349	22	for	for	SCONJ
ejpam-137	349	23	each	each	PRON
ejpam-137	349	24	subset	subset	VERB
ejpam-137	349	25	a	a	PRON
ejpam-137	349	26	of	of	ADP
ejpam-137	349	27	y	y	PROPN
ejpam-137	349	28	and	and	CCONJ
ejpam-137	349	29	each	each	DET
ejpam-137	349	30	γ∗-semi	γ∗-semi	NOUN
ejpam-137	349	31	-	-	ADJ
ejpam-137	349	32	open	open	ADJ
ejpam-137	349	33	set	set	NOUN
ejpam-137	349	34	b	b	NOUN
ejpam-137	349	35	in	in	ADP
ejpam-137	349	36	x	x	PUNCT
ejpam-137	349	37	containing	contain	VERB
ejpam-137	349	38	f	f	PROPN
ejpam-137	349	39	−1(a	−1(a	ADP
ejpam-137	349	40	)	)	PUNCT
ejpam-137	349	41	,	,	PUNCT
ejpam-137	349	42	there	there	PRON
ejpam-137	349	43	exists	exist	VERB
ejpam-137	349	44	a	a	DET
ejpam-137	349	45	γ∗-semi	γ∗-semi	NOUN
ejpam-137	349	46	-	-	ADJ
ejpam-137	349	47	open	open	ADJ
ejpam-137	349	48	set	set	NOUN
ejpam-137	349	49	c	c	NOUN
ejpam-137	349	50	in	in	ADP
ejpam-137	349	51	y	y	NOUN
ejpam-137	349	52	containing	contain	VERB
ejpam-137	349	53	a	a	DET
ejpam-137	349	54	such	such	ADJ
ejpam-137	349	55	that	that	SCONJ
ejpam-137	349	56	f	f	PROPN
ejpam-137	349	57	−1(c)⊆	−1(c)⊆	PROPN
ejpam-137	349	58	b	b	PROPN
ejpam-137	349	59	,	,	PUNCT
ejpam-137	349	60	where	where	SCONJ
ejpam-137	349	61	γ	γ	PROPN
ejpam-137	349	62	is	be	AUX
ejpam-137	349	63	a	a	DET
ejpam-137	349	64	semi	semi	ADJ
ejpam-137	349	65	regular	regular	ADJ
ejpam-137	349	66	operation	operation	NOUN
ejpam-137	349	67	.	.	PUNCT
ejpam-137	350	1	proof	proof	NOUN
ejpam-137	350	2	.	.	PUNCT
ejpam-137	351	1	let	let	VERB
ejpam-137	351	2	c	c	NOUN
ejpam-137	351	3	=	=	SYM
ejpam-137	352	1	y	y	PROPN
ejpam-137	352	2	−	−	PROPN
ejpam-137	352	3	f	f	PROPN
ejpam-137	352	4	(	(	PUNCT
ejpam-137	352	5	x	x	PROPN
ejpam-137	352	6	−	−	PROPN
ejpam-137	352	7	b	b	NOUN
ejpam-137	352	8	)	)	PUNCT
ejpam-137	352	9	.	.	PUNCT
ejpam-137	353	1	then	then	ADV
ejpam-137	353	2	c	c	PROPN
ejpam-137	353	3	c	c	PROPN
ejpam-137	353	4	=	=	SYM
ejpam-137	353	5	f	f	PROPN
ejpam-137	353	6	(	(	PUNCT
ejpam-137	353	7	bc	bc	PROPN
ejpam-137	353	8	)	)	PUNCT
ejpam-137	353	9	.	.	PUNCT
ejpam-137	354	1	since	since	SCONJ
ejpam-137	354	2	f	f	PROPN
ejpam-137	354	3	is	be	AUX
ejpam-137	354	4	γ	γ	PROPN
ejpam-137	354	5	-	-	PUNCT
ejpam-137	354	6	pre	pre	ADJ
ejpam-137	354	7	-	-	ADJ
ejpam-137	354	8	semi	semi	ADJ
ejpam-137	354	9	-	-	ADJ
ejpam-137	354	10	closed	closed	ADJ
ejpam-137	354	11	,	,	PUNCT
ejpam-137	354	12	so	so	SCONJ
ejpam-137	354	13	c	c	PROPN
ejpam-137	354	14	is	be	AUX
ejpam-137	354	15	γ∗-semi	γ∗-semi	NOUN
ejpam-137	354	16	-	-	NOUN
ejpam-137	354	17	open	open	ADJ
ejpam-137	354	18	.	.	PUNCT
ejpam-137	355	1	since	since	SCONJ
ejpam-137	355	2	f	f	PROPN
ejpam-137	355	3	−1(a	−1(a	ADP
ejpam-137	355	4	)	)	PUNCT
ejpam-137	355	5	⊆	⊆	NUM
ejpam-137	355	6	b	b	NOUN
ejpam-137	355	7	,	,	PUNCT
ejpam-137	355	8	we	we	PRON
ejpam-137	355	9	have	have	VERB
ejpam-137	355	10	c	c	NOUN
ejpam-137	355	11	c	c	NOUN
ejpam-137	355	12	=	=	SYM
ejpam-137	355	13	f	f	PROPN
ejpam-137	355	14	(	(	PUNCT
ejpam-137	355	15	bc	bc	PROPN
ejpam-137	355	16	)	)	PUNCT
ejpam-137	355	17	⊆	⊆	NUM
ejpam-137	355	18	f	f	NOUN
ejpam-137	355	19	(	(	PUNCT
ejpam-137	355	20	f	f	PROPN
ejpam-137	355	21	−1(ac	−1(ac	PROPN
ejpam-137	355	22	)	)	PUNCT
ejpam-137	355	23	)	)	PUNCT
ejpam-137	356	1	⊆	⊆	NUM
ejpam-137	356	2	ac	ac	PROPN
ejpam-137	356	3	.	.	PUNCT
ejpam-137	357	1	hence	hence	ADV
ejpam-137	357	2	,	,	PUNCT
ejpam-137	357	3	a	a	DET
ejpam-137	357	4	⊆	⊆	NUM
ejpam-137	357	5	c	c	NOUN
ejpam-137	357	6	,	,	PUNCT
ejpam-137	357	7	and	and	CCONJ
ejpam-137	357	8	thus	thus	ADV
ejpam-137	357	9	c	c	PROPN
ejpam-137	357	10	is	be	AUX
ejpam-137	357	11	a	a	DET
ejpam-137	357	12	γ	γ	NOUN
ejpam-137	357	13	-	-	PUNCT
ejpam-137	357	14	semi	semi	ADJ
ejpam-137	357	15	-	-	ADJ
ejpam-137	357	16	open	open	ADJ
ejpam-137	357	17	nbd	nbd	PROPN
ejpam-137	357	18	of	of	ADP
ejpam-137	357	19	a.	a.	PROPN
ejpam-137	357	20	further	far	ADV
ejpam-137	357	21	bc	bc	PROPN
ejpam-137	357	22	⊆	⊆	NUM
ejpam-137	357	23	f	f	PROPN
ejpam-137	357	24	−1	−1	PROPN
ejpam-137	357	25	(	(	PUNCT
ejpam-137	357	26	f	f	PROPN
ejpam-137	357	27	(	(	PUNCT
ejpam-137	357	28	bc	bc	PROPN
ejpam-137	357	29	)	)	PUNCT
ejpam-137	357	30	)	)	PUNCT
ejpam-137	358	1	=	=	PUNCT
ejpam-137	359	1	f	f	X
ejpam-137	359	2	−1(c	−1(c	NUM
ejpam-137	359	3	c	c	X
ejpam-137	359	4	)	)	PUNCT
ejpam-137	359	5	=	=	NOUN
ejpam-137	360	1	(	(	PUNCT
ejpam-137	360	2	f	f	PROPN
ejpam-137	360	3	−1(c))c	−1(c))c	PROPN
ejpam-137	360	4	.	.	PUNCT
ejpam-137	361	1	this	this	PRON
ejpam-137	361	2	proves	prove	VERB
ejpam-137	361	3	that	that	SCONJ
ejpam-137	361	4	f	f	PROPN
ejpam-137	361	5	−1(c)⊆	−1(c)⊆	PROPN
ejpam-137	361	6	b	b	PROPN
ejpam-137	361	7	.	.	PUNCT
ejpam-137	362	1	conversely	conversely	ADV
ejpam-137	362	2	,	,	PUNCT
ejpam-137	362	3	suppose	suppose	VERB
ejpam-137	362	4	f	f	PROPN
ejpam-137	362	5	is	be	AUX
ejpam-137	362	6	a	a	DET
ejpam-137	362	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	362	8	-	-	PUNCT
ejpam-137	362	9	closed	closed	ADJ
ejpam-137	362	10	set	set	NOUN
ejpam-137	362	11	in	in	ADP
ejpam-137	362	12	x.	x.	NOUN
ejpam-137	362	13	let	let	VERB
ejpam-137	362	14	y	y	PROPN
ejpam-137	362	15	∈	∈	PROPN
ejpam-137	363	1	y	y	PROPN
ejpam-137	363	2	−	−	PROPN
ejpam-137	364	1	f	f	PROPN
ejpam-137	364	2	(	(	PUNCT
ejpam-137	364	3	f	f	PROPN
ejpam-137	364	4	)	)	PUNCT
ejpam-137	364	5	.	.	PUNCT
ejpam-137	365	1	then	then	ADV
ejpam-137	365	2	f	f	PROPN
ejpam-137	365	3	−1(y	−1(y	PROPN
ejpam-137	365	4	)	)	PUNCT
ejpam-137	366	1	⊆	⊆	NUM
ejpam-137	366	2	x	x	SYM
ejpam-137	366	3	−	−	PROPN
ejpam-137	366	4	f	f	NOUN
ejpam-137	366	5	−1	−1	NOUN
ejpam-137	366	6	(	(	PUNCT
ejpam-137	366	7	f	f	PROPN
ejpam-137	366	8	(	(	PUNCT
ejpam-137	366	9	f	f	NOUN
ejpam-137	366	10	)	)	PUNCT
ejpam-137	366	11	)	)	PUNCT
ejpam-137	367	1	⊆	⊆	NUM
ejpam-137	367	2	x	x	SYM
ejpam-137	367	3	−	−	PROPN
ejpam-137	367	4	f	f	PROPN
ejpam-137	367	5	and	and	CCONJ
ejpam-137	367	6	x	x	SYM
ejpam-137	367	7	−	−	PROPN
ejpam-137	367	8	f	f	PROPN
ejpam-137	367	9	is	be	AUX
ejpam-137	367	10	γ∗-semi	γ∗-semi	NOUN
ejpam-137	367	11	-	-	ADJ
ejpam-137	367	12	open	open	ADJ
ejpam-137	367	13	in	in	ADP
ejpam-137	367	14	x.	x.	NOUN
ejpam-137	367	15	hence	hence	ADV
ejpam-137	367	16	by	by	ADP
ejpam-137	367	17	hypothesis	hypothesis	NOUN
ejpam-137	367	18	,	,	PUNCT
ejpam-137	367	19	there	there	PRON
ejpam-137	367	20	exists	exist	VERB
ejpam-137	367	21	a	a	DET
ejpam-137	367	22	γ∗-semi	γ∗-semi	NOUN
ejpam-137	367	23	-	-	ADJ
ejpam-137	367	24	open	open	ADJ
ejpam-137	367	25	set	set	NOUN
ejpam-137	367	26	c	c	NOUN
ejpam-137	367	27	containing	contain	VERB
ejpam-137	367	28	y	y	PRON
ejpam-137	367	29	such	such	ADJ
ejpam-137	367	30	that	that	SCONJ
ejpam-137	367	31	f	f	PROPN
ejpam-137	367	32	−1(c	−1(c	ADV
ejpam-137	367	33	)	)	PUNCT
ejpam-137	368	1	⊆	⊆	NUM
ejpam-137	368	2	x	x	SYM
ejpam-137	368	3	−	−	PROPN
ejpam-137	368	4	f	f	NOUN
ejpam-137	368	5	.	.	PUNCT
ejpam-137	369	1	since	since	SCONJ
ejpam-137	369	2	f	f	PROPN
ejpam-137	369	3	is	be	AUX
ejpam-137	369	4	one	one	NUM
ejpam-137	369	5	-	-	PUNCT
ejpam-137	369	6	one	one	NUM
ejpam-137	369	7	,	,	PUNCT
ejpam-137	369	8	we	we	PRON
ejpam-137	369	9	have	have	VERB
ejpam-137	369	10	references	reference	NOUN
ejpam-137	369	11	29	29	NUM
ejpam-137	369	12	y	y	PROPN
ejpam-137	369	13	∈	∈	PROPN
ejpam-137	369	14	c	c	PROPN
ejpam-137	369	15	⊆	⊆	NUM
ejpam-137	369	16	y	y	PROPN
ejpam-137	369	17	−	−	PROPN
ejpam-137	370	1	f	f	PROPN
ejpam-137	370	2	(	(	PUNCT
ejpam-137	370	3	f	f	NOUN
ejpam-137	370	4	)	)	PUNCT
ejpam-137	370	5	.	.	PUNCT
ejpam-137	371	1	thus	thus	ADV
ejpam-137	371	2	y	y	PROPN
ejpam-137	371	3	−	−	PROPN
ejpam-137	371	4	f	f	PROPN
ejpam-137	371	5	(	(	PUNCT
ejpam-137	371	6	f	f	X
ejpam-137	371	7	)	)	PUNCT
ejpam-137	372	1	=	=	PUNCT
ejpam-137	372	2	⋃	⋃	ADP
ejpam-137	372	3	y∈y−	y∈y−	PROPN
ejpam-137	372	4	f	f	X
ejpam-137	372	5	(	(	PUNCT
ejpam-137	372	6	f	f	X
ejpam-137	372	7	)	)	PUNCT
ejpam-137	372	8	c	c	NOUN
ejpam-137	372	9	.	.	PUNCT
ejpam-137	373	1	hence	hence	ADV
ejpam-137	373	2	y	y	PROPN
ejpam-137	374	1	−	−	PROPN
ejpam-137	374	2	f	f	PROPN
ejpam-137	374	3	(	(	PUNCT
ejpam-137	374	4	f	f	X
ejpam-137	374	5	)	)	PUNCT
ejpam-137	374	6	is	be	AUX
ejpam-137	374	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	374	8	-	-	ADJ
ejpam-137	374	9	open	open	ADJ
ejpam-137	374	10	set	set	NOUN
ejpam-137	374	11	[	[	X
ejpam-137	374	12	5	5	NUM
ejpam-137	374	13	]	]	PUNCT
ejpam-137	374	14	.	.	PUNCT
ejpam-137	375	1	this	this	PRON
ejpam-137	375	2	proves	prove	VERB
ejpam-137	375	3	that	that	SCONJ
ejpam-137	375	4	f	f	PROPN
ejpam-137	375	5	is	be	AUX
ejpam-137	375	6	γ	γ	PROPN
ejpam-137	375	7	-	-	PUNCT
ejpam-137	375	8	pre	pre	ADJ
ejpam-137	375	9	-	-	ADJ
ejpam-137	375	10	semi	semi	ADJ
ejpam-137	375	11	-	-	ADJ
ejpam-137	375	12	closed	closed	ADJ
ejpam-137	375	13	.	.	PUNCT
ejpam-137	376	1	we	we	PRON
ejpam-137	376	2	use	use	VERB
ejpam-137	376	3	theorem	theorem	NOUN
ejpam-137	376	4	4.8	4.8	NUM
ejpam-137	376	5	and	and	CCONJ
ejpam-137	376	6	give	give	VERB
ejpam-137	376	7	the	the	DET
ejpam-137	376	8	following	follow	VERB
ejpam-137	376	9	characterizations	characterization	NOUN
ejpam-137	376	10	:	:	PUNCT
ejpam-137	376	11	theorem	theorem	VERB
ejpam-137	376	12	5.5	5.5	NUM
ejpam-137	376	13	.	.	PUNCT
ejpam-137	377	1	let	let	VERB
ejpam-137	377	2	f	f	NOUN
ejpam-137	377	3	:	:	PUNCT
ejpam-137	377	4	x	x	X
ejpam-137	377	5	→	→	SYM
ejpam-137	377	6	y	y	X
ejpam-137	377	7	be	be	AUX
ejpam-137	377	8	a	a	DET
ejpam-137	377	9	bijective	bijective	ADJ
ejpam-137	377	10	function	function	NOUN
ejpam-137	377	11	.	.	PUNCT
ejpam-137	378	1	then	then	ADV
ejpam-137	378	2	the	the	DET
ejpam-137	378	3	following	follow	VERB
ejpam-137	378	4	are	be	AUX
ejpam-137	378	5	equivalent	equivalent	ADJ
ejpam-137	378	6	:	:	PUNCT
ejpam-137	378	7	(	(	PUNCT
ejpam-137	378	8	1	1	X
ejpam-137	378	9	)	)	PUNCT
ejpam-137	378	10	f	f	PROPN
ejpam-137	378	11	is	be	AUX
ejpam-137	378	12	γ	γ	PROPN
ejpam-137	378	13	-	-	PUNCT
ejpam-137	378	14	pre	pre	ADJ
ejpam-137	378	15	-	-	ADJ
ejpam-137	378	16	semi	semi	ADJ
ejpam-137	378	17	-	-	ADJ
ejpam-137	378	18	closed	closed	ADJ
ejpam-137	378	19	.	.	PUNCT
ejpam-137	379	1	(	(	PUNCT
ejpam-137	379	2	2	2	X
ejpam-137	379	3	)	)	PUNCT
ejpam-137	379	4	f	f	PROPN
ejpam-137	379	5	is	be	AUX
ejpam-137	379	6	γ	γ	PROPN
ejpam-137	379	7	-	-	PUNCT
ejpam-137	379	8	pre	pre	ADJ
ejpam-137	379	9	-	-	ADJ
ejpam-137	379	10	semi	semi	ADJ
ejpam-137	379	11	-	-	ADJ
ejpam-137	379	12	open	open	ADJ
ejpam-137	379	13	.	.	PUNCT
ejpam-137	380	1	(	(	PUNCT
ejpam-137	380	2	3	3	X
ejpam-137	380	3	)	)	PUNCT
ejpam-137	380	4	f	f	NOUN
ejpam-137	380	5	−1	−1	NOUN
ejpam-137	380	6	is	be	AUX
ejpam-137	380	7	γ∗-irresolute	γ∗-irresolute	NOUN
ejpam-137	380	8	.	.	PUNCT
ejpam-137	380	9	proof	proof	NOUN
ejpam-137	380	10	.	.	PUNCT
ejpam-137	381	1	(	(	PUNCT
ejpam-137	381	2	1)⇒	1)⇒	NUM
ejpam-137	381	3	(	(	PUNCT
ejpam-137	381	4	2	2	NUM
ejpam-137	381	5	)	)	PUNCT
ejpam-137	381	6	it	it	PRON
ejpam-137	381	7	is	be	AUX
ejpam-137	381	8	straightforward	straightforward	ADJ
ejpam-137	381	9	.	.	PUNCT
ejpam-137	382	1	(	(	PUNCT
ejpam-137	382	2	2	2	X
ejpam-137	382	3	)	)	PUNCT
ejpam-137	382	4	⇒	⇒	NOUN
ejpam-137	382	5	(	(	PUNCT
ejpam-137	382	6	3	3	NUM
ejpam-137	382	7	)	)	PUNCT
ejpam-137	382	8	.	.	PUNCT
ejpam-137	383	1	let	let	VERB
ejpam-137	383	2	a	a	DET
ejpam-137	383	3	⊆	⊆	NUM
ejpam-137	383	4	x	x	SYM
ejpam-137	383	5	.	.	PUNCT
ejpam-137	384	1	since	since	SCONJ
ejpam-137	384	2	f	f	PROPN
ejpam-137	384	3	is	be	AUX
ejpam-137	384	4	γ	γ	PROPN
ejpam-137	384	5	-	-	PUNCT
ejpam-137	384	6	pre	pre	ADJ
ejpam-137	384	7	-	-	ADJ
ejpam-137	384	8	semi	semi	ADJ
ejpam-137	384	9	-	-	ADJ
ejpam-137	384	10	open	open	ADJ
ejpam-137	384	11	,	,	PUNCT
ejpam-137	384	12	by	by	ADP
ejpam-137	384	13	theorem	theorem	NOUN
ejpam-137	384	14	4.9	4.9	NUM
ejpam-137	384	15	,	,	PUNCT
ejpam-137	384	16	f	f	PROPN
ejpam-137	384	17	−1(sclγ∗	−1(sclγ∗	X
ejpam-137	384	18	(	(	PUNCT
ejpam-137	384	19	f	f	PROPN
ejpam-137	384	20	(	(	PUNCT
ejpam-137	384	21	a	a	NOUN
ejpam-137	384	22	)	)	PUNCT
ejpam-137	384	23	)	)	PUNCT
ejpam-137	384	24	)	)	PUNCT
ejpam-137	385	1	⊆	⊆	X
ejpam-137	385	2	sclγ∗	sclγ∗	NOUN
ejpam-137	385	3	(	(	PUNCT
ejpam-137	385	4	f	f	NOUN
ejpam-137	385	5	−1	−1	NOUN
ejpam-137	385	6	f	f	PROPN
ejpam-137	385	7	(	(	PUNCT
ejpam-137	385	8	a	a	NOUN
ejpam-137	385	9	)	)	PUNCT
ejpam-137	385	10	)	)	PUNCT
ejpam-137	385	11	implies	imply	VERB
ejpam-137	385	12	sclγ∗	sclγ∗	PROPN
ejpam-137	385	13	(	(	PUNCT
ejpam-137	385	14	f	f	PROPN
ejpam-137	385	15	(	(	PUNCT
ejpam-137	385	16	a))⊆	a))⊆	PROPN
ejpam-137	385	17	f	f	PROPN
ejpam-137	385	18	(	(	PUNCT
ejpam-137	385	19	sclγ∗(a	sclγ∗(a	PROPN
ejpam-137	385	20	)	)	PUNCT
ejpam-137	385	21	)	)	PUNCT
ejpam-137	385	22	.	.	PUNCT
ejpam-137	386	1	thus	thus	ADV
ejpam-137	386	2	sclγ∗	sclγ∗	VERB
ejpam-137	386	3	(	(	PUNCT
ejpam-137	386	4	f	f	NOUN
ejpam-137	386	5	−1)−1(a	−1)−1(a	PROPN
ejpam-137	386	6	)	)	PUNCT
ejpam-137	386	7	is	be	AUX
ejpam-137	386	8	contained	contain	VERB
ejpam-137	386	9	in	in	ADP
ejpam-137	386	10	(	(	PUNCT
ejpam-137	386	11	f	f	PROPN
ejpam-137	386	12	−1)−1(sclγ∗(a	−1)−1(sclγ∗(a	PROPN
ejpam-137	386	13	)	)	PUNCT
ejpam-137	386	14	)	)	PUNCT
ejpam-137	386	15	,	,	PUNCT
ejpam-137	386	16	for	for	ADP
ejpam-137	386	17	every	every	DET
ejpam-137	386	18	subset	subset	NOUN
ejpam-137	386	19	a	a	PRON
ejpam-137	386	20	of	of	ADP
ejpam-137	386	21	x.	x.	NOUN
ejpam-137	386	22	then	then	ADV
ejpam-137	386	23	again	again	ADV
ejpam-137	386	24	by	by	ADP
ejpam-137	386	25	theorem	theorem	NOUN
ejpam-137	386	26	4.8	4.8	NUM
ejpam-137	386	27	,	,	PUNCT
ejpam-137	386	28	it	it	PRON
ejpam-137	386	29	follows	follow	VERB
ejpam-137	386	30	that	that	SCONJ
ejpam-137	386	31	f	f	PROPN
ejpam-137	386	32	−1	−1	NOUN
ejpam-137	386	33	is	be	AUX
ejpam-137	386	34	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	386	35	.	.	PUNCT
ejpam-137	387	1	(	(	PUNCT
ejpam-137	387	2	3)⇒	3)⇒	NUM
ejpam-137	387	3	(	(	PUNCT
ejpam-137	387	4	1	1	NUM
ejpam-137	387	5	)	)	PUNCT
ejpam-137	387	6	.	.	PUNCT
ejpam-137	388	1	let	let	VERB
ejpam-137	388	2	a	a	PRON
ejpam-137	388	3	be	be	AUX
ejpam-137	388	4	a	a	DET
ejpam-137	388	5	γ∗-semi	γ∗-semi	NOUN
ejpam-137	388	6	-	-	PUNCT
ejpam-137	388	7	closed	closed	ADJ
ejpam-137	388	8	set	set	NOUN
ejpam-137	388	9	in	in	ADP
ejpam-137	388	10	x.	x.	NOUN
ejpam-137	388	11	then	then	ADV
ejpam-137	388	12	x	x	PUNCT
ejpam-137	388	13	−	−	NOUN
ejpam-137	388	14	a	a	PRON
ejpam-137	388	15	is	be	AUX
ejpam-137	388	16	γ∗-semi	γ∗-semi	NOUN
ejpam-137	388	17	-	-	NOUN
ejpam-137	388	18	open	open	ADJ
ejpam-137	388	19	in	in	ADP
ejpam-137	388	20	x.	x.	NOUN
ejpam-137	388	21	since	since	SCONJ
ejpam-137	388	22	f	f	PROPN
ejpam-137	388	23	−1	−1	NOUN
ejpam-137	388	24	is	be	AUX
ejpam-137	388	25	γ∗-irresolute	γ∗-irresolute	PROPN
ejpam-137	388	26	,	,	PUNCT
ejpam-137	388	27	(	(	PUNCT
ejpam-137	388	28	f	f	PROPN
ejpam-137	388	29	−1)−1(x	−1)−1(x	PROPN
ejpam-137	388	30	−a	−a	NOUN
ejpam-137	388	31	)	)	PUNCT
ejpam-137	388	32	is	be	AUX
ejpam-137	388	33	γ∗-semi	γ∗-semi	NOUN
ejpam-137	388	34	-	-	NOUN
ejpam-137	388	35	open	open	ADJ
ejpam-137	388	36	in	in	ADP
ejpam-137	388	37	y.	y.	PROPN
ejpam-137	388	38	but	but	CCONJ
ejpam-137	388	39	(	(	PUNCT
ejpam-137	388	40	f	f	X
ejpam-137	388	41	−1)−1(x	−1)−1(x	NOUN
ejpam-137	388	42	−a	−a	NOUN
ejpam-137	388	43	)	)	PUNCT
ejpam-137	389	1	=	=	SYM
ejpam-137	389	2	f	f	X
ejpam-137	389	3	(	(	PUNCT
ejpam-137	389	4	x	x	NOUN
ejpam-137	389	5	−a	−a	ADV
ejpam-137	389	6	)	)	PUNCT
ejpam-137	389	7	=	=	PUNCT
ejpam-137	390	1	y	y	PROPN
ejpam-137	390	2	−	−	PROPN
ejpam-137	390	3	f	f	PROPN
ejpam-137	390	4	(	(	PUNCT
ejpam-137	390	5	a	a	NOUN
ejpam-137	390	6	)	)	PUNCT
ejpam-137	390	7	.	.	PUNCT
ejpam-137	391	1	thus	thus	ADV
ejpam-137	391	2	f	f	X
ejpam-137	391	3	(	(	PUNCT
ejpam-137	391	4	a	a	NOUN
ejpam-137	391	5	)	)	PUNCT
ejpam-137	391	6	is	be	AUX
ejpam-137	391	7	γ∗-semi	γ∗-semi	NOUN
ejpam-137	391	8	-	-	PUNCT
ejpam-137	391	9	closed	closed	ADJ
ejpam-137	391	10	in	in	ADP
ejpam-137	391	11	y.	y.	NOUN
ejpam-137	391	12	this	this	PRON
ejpam-137	391	13	proves	prove	VERB
ejpam-137	391	14	that	that	SCONJ
ejpam-137	391	15	f	f	PROPN
ejpam-137	391	16	is	be	AUX
ejpam-137	391	17	γ	γ	PROPN
ejpam-137	391	18	-	-	PUNCT
ejpam-137	391	19	pre	pre	ADJ
ejpam-137	391	20	-	-	ADJ
ejpam-137	391	21	semi	semi	ADJ
ejpam-137	391	22	-	-	ADJ
ejpam-137	391	23	closed	closed	ADJ
ejpam-137	391	24	.	.	PUNCT
ejpam-137	392	1	this	this	PRON
ejpam-137	392	2	completes	complete	VERB
ejpam-137	392	3	the	the	DET
ejpam-137	392	4	proof	proof	NOUN
ejpam-137	392	5	.	.	PUNCT
ejpam-137	393	1	references	reference	NOUN
ejpam-137	393	2	[	[	X
ejpam-137	393	3	1	1	NUM
ejpam-137	393	4	]	]	PUNCT
ejpam-137	393	5	b.	b.	PROPN
ejpam-137	393	6	ahmad	ahmad	PROPN
ejpam-137	393	7	and	and	CCONJ
ejpam-137	393	8	f.	f.	PROPN
ejpam-137	393	9	u.	u.	PROPN
ejpam-137	393	10	rehman	rehman	PROPN
ejpam-137	393	11	:	:	PUNCT
ejpam-137	393	12	operations	operation	NOUN
ejpam-137	393	13	on	on	ADP
ejpam-137	393	14	topological	topological	PROPN
ejpam-137	393	15	spaces	space	NOUN
ejpam-137	393	16	ii	ii	PROPN
ejpam-137	393	17	,	,	PUNCT
ejpam-137	393	18	math	math	NOUN
ejpam-137	393	19	.	.	PUNCT
ejpam-137	394	1	today	today	NOUN
ejpam-137	394	2	,	,	PUNCT
ejpam-137	394	3	11(1993	11(1993	NUM
ejpam-137	394	4	)	)	PUNCT
ejpam-137	394	5	,	,	PUNCT
ejpam-137	394	6	13	13	NUM
ejpam-137	394	7	-	-	SYM
ejpam-137	394	8	20	20	NUM
ejpam-137	394	9	.	.	PUNCT
ejpam-137	395	1	[	[	X
ejpam-137	395	2	2	2	NUM
ejpam-137	395	3	]	]	X
ejpam-137	395	4	b.	b.	PROPN
ejpam-137	395	5	ahmad	ahmad	PROPN
ejpam-137	395	6	and	and	CCONJ
ejpam-137	395	7	s.	s.	PROPN
ejpam-137	395	8	hussain	hussain	PROPN
ejpam-137	395	9	:	:	PUNCT
ejpam-137	395	10	properties	property	NOUN
ejpam-137	395	11	of	of	ADP
ejpam-137	395	12	γ	γ	NOUN
ejpam-137	395	13	-	-	NOUN
ejpam-137	395	14	operations	operation	NOUN
ejpam-137	395	15	on	on	ADP
ejpam-137	395	16	topological	topological	ADJ
ejpam-137	395	17	spaces	space	NOUN
ejpam-137	395	18	,	,	PUNCT
ejpam-137	395	19	aligarh	aligarh	PROPN
ejpam-137	395	20	bull	bull	PROPN
ejpam-137	395	21	.	.	PUNCT
ejpam-137	396	1	math	math	NOUN
ejpam-137	396	2	.	.	PUNCT
ejpam-137	397	1	22(1	22(1	NUM
ejpam-137	397	2	)	)	PUNCT
ejpam-137	398	1	(	(	PUNCT
ejpam-137	398	2	2003	2003	NUM
ejpam-137	398	3	)	)	PUNCT
ejpam-137	398	4	,	,	PUNCT
ejpam-137	398	5	45	45	NUM
ejpam-137	398	6	-	-	SYM
ejpam-137	398	7	51	51	NUM
ejpam-137	398	8	.	.	PUNCT
ejpam-137	399	1	[	[	X
ejpam-137	399	2	3	3	X
ejpam-137	399	3	]	]	X
ejpam-137	399	4	b.	b.	PROPN
ejpam-137	399	5	ahmad	ahmad	PROPN
ejpam-137	399	6	and	and	CCONJ
ejpam-137	399	7	s.	s.	PROPN
ejpam-137	399	8	hussain	hussain	PROPN
ejpam-137	399	9	:	:	PUNCT
ejpam-137	399	10	γ	γ	NOUN
ejpam-137	399	11	-	-	NOUN
ejpam-137	399	12	convergence	convergence	NOUN
ejpam-137	399	13	in	in	ADP
ejpam-137	399	14	topological	topological	ADJ
ejpam-137	399	15	spaces	space	NOUN
ejpam-137	399	16	,	,	PUNCT
ejpam-137	399	17	southeast	southeast	ADJ
ejpam-137	399	18	asian	asian	ADJ
ejpam-137	399	19	bull	bull	NOUN
ejpam-137	399	20	.	.	PUNCT
ejpam-137	400	1	math	math	NOUN
ejpam-137	400	2	.	.	PUNCT
ejpam-137	400	3	,	,	PUNCT
ejpam-137	400	4	29(5)(2005	29(5)(2005	NUM
ejpam-137	400	5	)	)	PUNCT
ejpam-137	400	6	,	,	PUNCT
ejpam-137	400	7	835	835	NUM
ejpam-137	400	8	-	-	SYM
ejpam-137	400	9	842	842	NUM
ejpam-137	400	10	.	.	PUNCT
ejpam-137	401	1	[	[	X
ejpam-137	401	2	4	4	X
ejpam-137	401	3	]	]	X
ejpam-137	401	4	b.	b.	PROPN
ejpam-137	401	5	ahmad	ahmad	PROPN
ejpam-137	401	6	and	and	CCONJ
ejpam-137	401	7	s.	s.	PROPN
ejpam-137	401	8	hussain	hussain	PROPN
ejpam-137	401	9	:	:	PUNCT
ejpam-137	401	10	γ∗regular	γ∗regular	ADJ
ejpam-137	401	11	and	and	CCONJ
ejpam-137	401	12	γ	γ	NOUN
ejpam-137	401	13	-	-	ADJ
ejpam-137	401	14	normal	normal	ADJ
ejpam-137	401	15	spaces	space	NOUN
ejpam-137	401	16	,	,	PUNCT
ejpam-137	401	17	math	math	NOUN
ejpam-137	401	18	.	.	PUNCT
ejpam-137	402	1	today	today	NOUN
ejpam-137	402	2	,	,	PUNCT
ejpam-137	402	3	22(1)(2006	22(1)(2006	NUM
ejpam-137	402	4	)	)	PUNCT
ejpam-137	402	5	,	,	PUNCT
ejpam-137	402	6	37	37	NUM
ejpam-137	402	7	-	-	SYM
ejpam-137	402	8	44	44	NUM
ejpam-137	402	9	.	.	PUNCT
ejpam-137	403	1	[	[	X
ejpam-137	403	2	5	5	X
ejpam-137	403	3	]	]	PUNCT
ejpam-137	403	4	b.	b.	PROPN
ejpam-137	403	5	ahmad	ahmad	PROPN
ejpam-137	403	6	and	and	CCONJ
ejpam-137	403	7	s.	s.	PROPN
ejpam-137	403	8	hussain	hussain	PROPN
ejpam-137	403	9	:	:	PUNCT
ejpam-137	403	10	γ∗-semi	γ∗-semi	NOUN
ejpam-137	403	11	-	-	ADJ
ejpam-137	403	12	open	open	ADJ
ejpam-137	403	13	sets	set	NOUN
ejpam-137	403	14	in	in	ADP
ejpam-137	403	15	topological	topological	ADJ
ejpam-137	403	16	spaces	space	NOUN
ejpam-137	403	17	-	-	PUNCT
ejpam-137	403	18	ii	ii	NOUN
ejpam-137	403	19	,	,	PUNCT
ejpam-137	403	20	(	(	PUNCT
ejpam-137	403	21	submitted	submit	VERB
ejpam-137	403	22	)	)	PUNCT
ejpam-137	403	23	.	.	PUNCT
ejpam-137	404	1	[	[	X
ejpam-137	404	2	6	6	NUM
ejpam-137	404	3	]	]	PUNCT
ejpam-137	404	4	m.	m.	NOUN
ejpam-137	404	5	caldas	caldas	PROPN
ejpam-137	404	6	and	and	CCONJ
ejpam-137	404	7	j.	j.	PROPN
ejpam-137	404	8	dontchev	dontchev	PROPN
ejpam-137	404	9	:	:	PUNCT
ejpam-137	404	10	g.	g.	PROPN
ejpam-137	404	11	λs	λs	NOUN
ejpam-137	404	12	-	-	PUNCT
ejpam-137	404	13	sets	set	NOUN
ejpam-137	404	14	and	and	CCONJ
ejpam-137	404	15	g.	g.	PROPN
ejpam-137	404	16	vs	vs	NOUN
ejpam-137	404	17	-	-	PUNCT
ejpam-137	404	18	sets	set	NOUN
ejpam-137	404	19	,	,	PUNCT
ejpam-137	404	20	mem	mem	PROPN
ejpam-137	404	21	.	.	PUNCT
ejpam-137	405	1	fac	fac	PROPN
ejpam-137	405	2	.	.	PUNCT
ejpam-137	406	1	sci	sci	PROPN
ejpam-137	406	2	.	.	PROPN
ejpam-137	406	3	kochi	kochi	PROPN
ejpam-137	406	4	univ	univ	PROPN
ejpam-137	406	5	.	.	PROPN
ejpam-137	406	6	,	,	PUNCT
ejpam-137	406	7	21(2000	21(2000	NUM
ejpam-137	406	8	)	)	PUNCT
ejpam-137	406	9	,	,	PUNCT
ejpam-137	406	10	21	21	NUM
ejpam-137	406	11	-	-	SYM
ejpam-137	406	12	30	30	NUM
ejpam-137	406	13	.	.	PUNCT
ejpam-137	407	1	[	[	X
ejpam-137	407	2	7	7	X
ejpam-137	407	3	]	]	PUNCT
ejpam-137	407	4	a.	a.	NOUN
ejpam-137	407	5	csaszar	csaszar	PROPN
ejpam-137	407	6	:	:	PUNCT
ejpam-137	407	7	generalized	generalize	VERB
ejpam-137	407	8	open	open	ADJ
ejpam-137	407	9	sets	set	NOUN
ejpam-137	407	10	,	,	PUNCT
ejpam-137	407	11	acta	acta	PROPN
ejpam-137	407	12	math	math	PROPN
ejpam-137	407	13	.	.	PUNCT
ejpam-137	408	1	hungar	hungar	PROPN
ejpam-137	408	2	.	.	PUNCT
ejpam-137	408	3	,	,	PUNCT
ejpam-137	408	4	75(1997	75(1997	NUM
ejpam-137	408	5	)	)	PUNCT
ejpam-137	408	6	,	,	PUNCT
ejpam-137	408	7	65	65	NUM
ejpam-137	408	8	-	-	SYM
ejpam-137	408	9	87	87	NUM
ejpam-137	408	10	.	.	PUNCT
ejpam-137	409	1	[	[	X
ejpam-137	409	2	8	8	NUM
ejpam-137	409	3	]	]	PUNCT
ejpam-137	409	4	a.	a.	NOUN
ejpam-137	409	5	csaszar	csaszar	PROPN
ejpam-137	409	6	:	:	PUNCT
ejpam-137	409	7	generalized	generalized	ADJ
ejpam-137	409	8	topology	topology	NOUN
ejpam-137	409	9	,	,	PUNCT
ejpam-137	409	10	generalized	generalized	ADJ
ejpam-137	409	11	continuity	continuity	NOUN
ejpam-137	409	12	,	,	PUNCT
ejpam-137	409	13	acta	acta	PROPN
ejpam-137	409	14	math	math	PROPN
ejpam-137	409	15	.	.	PUNCT
ejpam-137	410	1	hungar	hungar	PROPN
ejpam-137	410	2	.	.	PUNCT
ejpam-137	410	3	,	,	PUNCT
ejpam-137	410	4	96(2002	96(2002	NUM
ejpam-137	410	5	)	)	PUNCT
ejpam-137	410	6	,	,	PUNCT
ejpam-137	410	7	351	351	NUM
ejpam-137	410	8	-	-	SYM
ejpam-137	410	9	357	357	NUM
ejpam-137	410	10	.	.	PUNCT
ejpam-137	411	1	[	[	X
ejpam-137	411	2	9	9	NUM
ejpam-137	411	3	]	]	PUNCT
ejpam-137	411	4	s.	s.	PROPN
ejpam-137	411	5	hussain	hussain	PROPN
ejpam-137	411	6	,	,	PUNCT
ejpam-137	411	7	b.	b.	PROPN
ejpam-137	411	8	ahmad	ahmad	PROPN
ejpam-137	411	9	and	and	CCONJ
ejpam-137	411	10	t.	t.	PROPN
ejpam-137	411	11	noiri	noiri	PROPN
ejpam-137	411	12	:	:	PUNCT
ejpam-137	411	13	γ∗-semi	γ∗-semi	X
ejpam-137	411	14	-	-	ADJ
ejpam-137	411	15	open	open	ADJ
ejpam-137	411	16	sets	set	NOUN
ejpam-137	411	17	in	in	ADP
ejpam-137	411	18	topological	topological	ADJ
ejpam-137	411	19	spaces	space	NOUN
ejpam-137	411	20	,	,	PUNCT
ejpam-137	411	21	(	(	PUNCT
ejpam-137	411	22	submitted	submit	VERB
ejpam-137	411	23	)	)	PUNCT
ejpam-137	411	24	.	.	PUNCT
ejpam-137	412	1	[	[	X
ejpam-137	412	2	10	10	NUM
ejpam-137	412	3	]	]	PUNCT
ejpam-137	412	4	s.	s.	PROPN
ejpam-137	412	5	hussain	hussain	PROPN
ejpam-137	412	6	,	,	PUNCT
ejpam-137	412	7	b.	b.	PROPN
ejpam-137	412	8	ahmad	ahmad	PROPN
ejpam-137	412	9	and	and	CCONJ
ejpam-137	412	10	t.noiri	t.noiri	ADV
ejpam-137	412	11	:	:	PUNCT
ejpam-137	412	12	on	on	ADP
ejpam-137	412	13	γ	γ	X
ejpam-137	412	14	-	-	PUNCT
ejpam-137	412	15	semi	semi	ADJ
ejpam-137	412	16	continuous	continuous	ADJ
ejpam-137	412	17	functions	function	NOUN
ejpam-137	412	18	,	,	PUNCT
ejpam-137	412	19	(	(	PUNCT
ejpam-137	412	20	submitted	submit	VERB
ejpam-137	412	21	)	)	PUNCT
ejpam-137	412	22	.	.	PUNCT
ejpam-137	413	1	[	[	X
ejpam-137	413	2	11	11	NUM
ejpam-137	413	3	]	]	PUNCT
ejpam-137	413	4	s.	s.	PROPN
ejpam-137	413	5	kasahara	kasahara	PROPN
ejpam-137	413	6	:	:	PUNCT
ejpam-137	413	7	operation	operation	NOUN
ejpam-137	413	8	-	-	PUNCT
ejpam-137	413	9	compact	compact	ADJ
ejpam-137	413	10	spaces	space	NOUN
ejpam-137	413	11	,	,	PUNCT
ejpam-137	413	12	math	math	NOUN
ejpam-137	413	13	.	.	PUNCT
ejpam-137	414	1	japon	japon	PROPN
ejpam-137	414	2	.	.	PROPN
ejpam-137	414	3	,	,	PUNCT
ejpam-137	414	4	24(1979	24(1979	NUM
ejpam-137	414	5	)	)	PUNCT
ejpam-137	414	6	,	,	PUNCT
ejpam-137	414	7	97	97	NUM
ejpam-137	414	8	-	-	SYM
ejpam-137	414	9	105	105	NUM
ejpam-137	414	10	.	.	PUNCT
ejpam-137	415	1	[	[	X
ejpam-137	415	2	12	12	NUM
ejpam-137	415	3	]	]	X
ejpam-137	415	4	n.	n.	PROPN
ejpam-137	415	5	levine	levine	PROPN
ejpam-137	415	6	:	:	PUNCT
ejpam-137	415	7	semi	semi	ADJ
ejpam-137	415	8	-	-	ADJ
ejpam-137	415	9	open	open	ADJ
ejpam-137	415	10	sets	set	NOUN
ejpam-137	415	11	and	and	CCONJ
ejpam-137	415	12	semi	semi	ADJ
ejpam-137	415	13	continuity	continuity	NOUN
ejpam-137	415	14	in	in	ADP
ejpam-137	415	15	topological	topological	ADJ
ejpam-137	415	16	spaces	space	NOUN
ejpam-137	415	17	,	,	PUNCT
ejpam-137	415	18	amer	amer	PROPN
ejpam-137	415	19	.	.	PROPN
ejpam-137	415	20	math	math	PROPN
ejpam-137	415	21	.	.	PUNCT
ejpam-137	416	1	monthly	monthly	ADJ
ejpam-137	416	2	,	,	PUNCT
ejpam-137	416	3	70(1963	70(1963	NUM
ejpam-137	416	4	)	)	PUNCT
ejpam-137	416	5	,	,	PUNCT
ejpam-137	416	6	36	36	NUM
ejpam-137	416	7	-	-	SYM
ejpam-137	416	8	41	41	NUM
ejpam-137	416	9	.	.	PUNCT
ejpam-137	417	1	[	[	X
ejpam-137	417	2	13	13	NUM
ejpam-137	417	3	]	]	PUNCT
ejpam-137	417	4	s.	s.	PROPN
ejpam-137	417	5	n.	n.	PROPN
ejpam-137	417	6	maheshwari	maheshwari	PROPN
ejpam-137	417	7	and	and	CCONJ
ejpam-137	417	8	r.	r.	PROPN
ejpam-137	417	9	prasad	prasad	PROPN
ejpam-137	417	10	:	:	PUNCT
ejpam-137	417	11	on	on	ADP
ejpam-137	417	12	r0	r0	NOUN
ejpam-137	417	13	-	-	PUNCT
ejpam-137	417	14	spaces	space	NOUN
ejpam-137	417	15	,	,	PUNCT
ejpam-137	417	16	portugal	portugal	PROPN
ejpam-137	417	17	math	math	NOUN
ejpam-137	417	18	.	.	PUNCT
ejpam-137	417	19	,	,	PUNCT
ejpam-137	417	20	34(1975	34(1975	NUM
ejpam-137	417	21	)	)	PUNCT
ejpam-137	417	22	,	,	PUNCT
ejpam-137	417	23	213	213	NUM
ejpam-137	417	24	-	-	SYM
ejpam-137	417	25	217	217	NUM
ejpam-137	417	26	.	.	PUNCT
ejpam-137	418	1	[	[	X
ejpam-137	418	2	14	14	NUM
ejpam-137	418	3	]	]	X
ejpam-137	418	4	h.	h.	PROPN
ejpam-137	418	5	ogata	ogata	PROPN
ejpam-137	418	6	:	:	PUNCT
ejpam-137	418	7	operations	operation	NOUN
ejpam-137	418	8	on	on	ADP
ejpam-137	418	9	topological	topological	ADJ
ejpam-137	418	10	spaces	space	NOUN
ejpam-137	418	11	and	and	CCONJ
ejpam-137	418	12	associated	associate	VERB
ejpam-137	418	13	topogy	topogy	NOUN
ejpam-137	418	14	,	,	PUNCT
ejpam-137	418	15	math	math	NOUN
ejpam-137	418	16	.	.	PUNCT
ejpam-137	419	1	japon	japon	PROPN
ejpam-137	419	2	.	.	PROPN
ejpam-137	419	3	,	,	PUNCT
ejpam-137	419	4	36(1)(1991	36(1)(1991	NUM
ejpam-137	419	5	)	)	PUNCT
ejpam-137	419	6	,	,	PUNCT
ejpam-137	419	7	175	175	NUM
ejpam-137	419	8	-	-	SYM
ejpam-137	419	9	18	18	NUM
ejpam-137	420	1	[	[	X
ejpam-137	420	2	15	15	NUM
ejpam-137	420	3	]	]	X
ejpam-137	420	4	f.u	f.u	PROPN
ejpam-137	420	5	.	.	PROPN
ejpam-137	420	6	rehman	rehman	PROPN
ejpam-137	420	7	and	and	CCONJ
ejpam-137	420	8	b.	b.	PROPN
ejpam-137	420	9	ahmad	ahmad	PROPN
ejpam-137	420	10	:	:	PUNCT
ejpam-137	420	11	operations	operation	NOUN
ejpam-137	420	12	on	on	ADP
ejpam-137	420	13	topological	topological	ADJ
ejpam-137	420	14	spaces	space	NOUN
ejpam-137	420	15	i	i	PRON
ejpam-137	420	16	,	,	PUNCT
ejpam-137	420	17	math	math	NOUN
ejpam-137	420	18	.	.	PUNCT
ejpam-137	421	1	today	today	NOUN
ejpam-137	421	2	,	,	PUNCT
ejpam-137	421	3	10(1992	10(1992	NUM
ejpam-137	421	4	)	)	PUNCT
ejpam-137	421	5	,	,	PUNCT
ejpam-137	421	6	29	29	NUM
ejpam-137	421	7	-	-	SYM
ejpam-137	421	8	36	36	NUM
ejpam-137	421	9	.	.	PUNCT