id	sid	tid	token	lemma	pos
ejpam-2055	1	1	compile	compile	NOUN
ejpam-2055	1	2	/	/	SYM
ejpam-2055	1	3	output.dvi	output.dvi	NOUN
ejpam-2055	1	4	european	european	ADJ
ejpam-2055	1	5	journal	journal	NOUN
ejpam-2055	1	6	of	of	ADP
ejpam-2055	1	7	pure	pure	ADJ
ejpam-2055	1	8	and	and	CCONJ
ejpam-2055	1	9	applied	apply	VERB
ejpam-2055	1	10	mathematics	mathematic	NOUN
ejpam-2055	1	11	vol	vol	NOUN
ejpam-2055	1	12	.	.	PROPN
ejpam-2055	1	13	8	8	NUM
ejpam-2055	1	14	,	,	PUNCT
ejpam-2055	1	15	no	no	INTJ
ejpam-2055	1	16	.	.	NOUN
ejpam-2055	1	17	2	2	NUM
ejpam-2055	1	18	,	,	PUNCT
ejpam-2055	1	19	2015	2015	NUM
ejpam-2055	1	20	,	,	PUNCT
ejpam-2055	1	21	185	185	NUM
ejpam-2055	1	22	-	-	SYM
ejpam-2055	1	23	200	200	NUM
ejpam-2055	1	24	issn	issn	PROPN
ejpam-2055	1	25	1307	1307	NUM
ejpam-2055	1	26	-	-	SYM
ejpam-2055	1	27	5543	5543	NUM
ejpam-2055	1	28	–	–	PUNCT
ejpam-2055	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2055	1	30	new	new	ADJ
ejpam-2055	1	31	type	type	NOUN
ejpam-2055	1	32	of	of	ADP
ejpam-2055	1	33	strongly	strongly	ADV
ejpam-2055	1	34	continuous	continuous	ADJ
ejpam-2055	1	35	functions	function	NOUN
ejpam-2055	1	36	in	in	ADP
ejpam-2055	1	37	topological	topological	ADJ
ejpam-2055	1	38	spaces	space	NOUN
ejpam-2055	1	39	via	via	ADP
ejpam-2055	1	40	δ−	δ−	PROPN
ejpam-2055	1	41	β	β	X
ejpam-2055	1	42	-	-	ADJ
ejpam-2055	1	43	open	open	ADJ
ejpam-2055	1	44	sets	set	NOUN
ejpam-2055	1	45	alaa	alaa	PROPN
ejpam-2055	1	46	mahmood	mahmood	PROPN
ejpam-2055	1	47	farhan1,2	farhan1,2	PROPN
ejpam-2055	1	48	,	,	PUNCT
ejpam-2055	1	49	xiao	xiao	NOUN
ejpam-2055	1	50	-	-	PUNCT
ejpam-2055	1	51	song	song	NOUN
ejpam-2055	1	52	yang1	yang1	NOUN
ejpam-2055	1	53	1	1	NUM
ejpam-2055	1	54	school	school	NOUN
ejpam-2055	1	55	of	of	ADP
ejpam-2055	1	56	mathematics	mathematic	NOUN
ejpam-2055	1	57	and	and	CCONJ
ejpam-2055	1	58	statistics	statistic	NOUN
ejpam-2055	1	59	,	,	PUNCT
ejpam-2055	1	60	huazhong	huazhong	PROPN
ejpam-2055	1	61	university	university	PROPN
ejpam-2055	1	62	of	of	ADP
ejpam-2055	1	63	science	science	NOUN
ejpam-2055	1	64	and	and	CCONJ
ejpam-2055	1	65	technology	technology	NOUN
ejpam-2055	1	66	,	,	PUNCT
ejpam-2055	1	67	hongshan	hongshan	PROPN
ejpam-2055	1	68	area	area	PROPN
ejpam-2055	1	69	,	,	PUNCT
ejpam-2055	1	70	wuhan	wuhan	PROPN
ejpam-2055	1	71	city	city	PROPN
ejpam-2055	1	72	,	,	PUNCT
ejpam-2055	1	73	hubei	hubei	PROPN
ejpam-2055	1	74	province	province	PROPN
ejpam-2055	1	75	,	,	PUNCT
ejpam-2055	1	76	china	china	PROPN
ejpam-2055	1	77	2	2	NUM
ejpam-2055	1	78	department	department	NOUN
ejpam-2055	1	79	of	of	ADP
ejpam-2055	1	80	mathematics	mathematic	NOUN
ejpam-2055	1	81	,	,	PUNCT
ejpam-2055	1	82	anbar	anbar	ADJ
ejpam-2055	1	83	university	university	PROPN
ejpam-2055	1	84	,	,	PUNCT
ejpam-2055	1	85	college	college	NOUN
ejpam-2055	1	86	of	of	ADP
ejpam-2055	1	87	education	education	NOUN
ejpam-2055	1	88	for	for	ADP
ejpam-2055	1	89	pure	pure	ADJ
ejpam-2055	1	90	sciences	science	NOUN
ejpam-2055	1	91	,	,	PUNCT
ejpam-2055	1	92	al	al	PROPN
ejpam-2055	1	93	-	-	PUNCT
ejpam-2055	1	94	ramadi	ramadi	PROPN
ejpam-2055	1	95	city	city	PROPN
ejpam-2055	1	96	,	,	PUNCT
ejpam-2055	1	97	iraq	iraq	PROPN
ejpam-2055	1	98	,	,	PUNCT
ejpam-2055	1	99	p.o.box	p.o.box	PROPN
ejpam-2055	1	100	:	:	PUNCT
ejpam-2055	1	101	(	(	PUNCT
ejpam-2055	1	102	55	55	NUM
ejpam-2055	1	103	ramadi	ramadi	NOUN
ejpam-2055	1	104	)	)	PUNCT
ejpam-2055	1	105	abstract	abstract	NOUN
ejpam-2055	1	106	.	.	PUNCT
ejpam-2055	2	1	in	in	ADP
ejpam-2055	2	2	this	this	DET
ejpam-2055	2	3	paper	paper	NOUN
ejpam-2055	2	4	we	we	PRON
ejpam-2055	2	5	introduce	introduce	VERB
ejpam-2055	2	6	and	and	CCONJ
ejpam-2055	2	7	investigate	investigate	VERB
ejpam-2055	2	8	a	a	DET
ejpam-2055	2	9	new	new	ADJ
ejpam-2055	2	10	class	class	NOUN
ejpam-2055	2	11	of	of	ADP
ejpam-2055	2	12	strong	strong	ADJ
ejpam-2055	2	13	continuous	continuous	ADJ
ejpam-2055	2	14	functions	function	NOUN
ejpam-2055	2	15	called	call	VERB
ejpam-2055	2	16	strongly	strongly	ADV
ejpam-2055	2	17	θ	θ	PROPN
ejpam-2055	2	18	−	−	PROPN
ejpam-2055	3	1	δ	δ	PROPN
ejpam-2055	3	2	−	−	PROPN
ejpam-2055	3	3	β	β	SYM
ejpam-2055	3	4	-continuous	-continuous	ADJ
ejpam-2055	3	5	functions	function	NOUN
ejpam-2055	3	6	by	by	ADP
ejpam-2055	3	7	using	use	VERB
ejpam-2055	3	8	two	two	NUM
ejpam-2055	3	9	new	new	ADJ
ejpam-2055	3	10	strong	strong	ADJ
ejpam-2055	3	11	forms	form	NOUN
ejpam-2055	3	12	of	of	ADP
ejpam-2055	3	13	δ	δ	PROPN
ejpam-2055	3	14	−	−	NOUN
ejpam-2055	3	15	β	β	X
ejpam-2055	3	16	-open	-open	NOUN
ejpam-2055	3	17	sets	set	NOUN
ejpam-2055	3	18	called	call	VERB
ejpam-2055	3	19	δ−	δ−	PROPN
ejpam-2055	3	20	β	β	SYM
ejpam-2055	3	21	-regular	-regular	ADJ
ejpam-2055	3	22	sets	set	NOUN
ejpam-2055	3	23	and	and	CCONJ
ejpam-2055	3	24	δ−	δ−	PROPN
ejpam-2055	3	25	βθ	βθ	ADP
ejpam-2055	3	26	-open	-open	ADJ
ejpam-2055	3	27	sets	set	NOUN
ejpam-2055	3	28	.	.	PUNCT
ejpam-2055	4	1	this	this	DET
ejpam-2055	4	2	class	class	NOUN
ejpam-2055	4	3	is	be	AUX
ejpam-2055	4	4	a	a	DET
ejpam-2055	4	5	generalization	generalization	NOUN
ejpam-2055	4	6	of	of	ADP
ejpam-2055	4	7	both	both	DET
ejpam-2055	4	8	strongly	strongly	ADV
ejpam-2055	4	9	θ	θ	NOUN
ejpam-2055	4	10	-e	-e	ADJ
ejpam-2055	4	11	-	-	PUNCT
ejpam-2055	4	12	continuous	continuous	ADJ
ejpam-2055	4	13	functions	function	NOUN
ejpam-2055	4	14	and	and	CCONJ
ejpam-2055	4	15	strongly	strongly	ADV
ejpam-2055	4	16	θ	θ	NOUN
ejpam-2055	4	17	−	−	NOUN
ejpam-2055	4	18	β	β	SYM
ejpam-2055	4	19	-continuous	-continuous	ADJ
ejpam-2055	4	20	functions	function	NOUN
ejpam-2055	4	21	.	.	PUNCT
ejpam-2055	5	1	several	several	ADJ
ejpam-2055	5	2	new	new	ADJ
ejpam-2055	5	3	characterizations	characterization	NOUN
ejpam-2055	5	4	and	and	CCONJ
ejpam-2055	5	5	fundamental	fundamental	ADJ
ejpam-2055	5	6	properties	property	NOUN
ejpam-2055	5	7	concerning	concern	VERB
ejpam-2055	5	8	strongly	strongly	ADV
ejpam-2055	5	9	θ	θ	PROPN
ejpam-2055	5	10	−δ−β	−δ−β	PROPN
ejpam-2055	5	11	-continuous	-continuous	ADJ
ejpam-2055	5	12	functions	function	NOUN
ejpam-2055	5	13	are	be	AUX
ejpam-2055	5	14	obtained	obtain	VERB
ejpam-2055	5	15	.	.	PUNCT
ejpam-2055	6	1	furthermore	furthermore	ADV
ejpam-2055	6	2	,	,	PUNCT
ejpam-2055	6	3	the	the	DET
ejpam-2055	6	4	relationships	relationship	NOUN
ejpam-2055	6	5	between	between	ADP
ejpam-2055	6	6	strongly	strongly	ADV
ejpam-2055	6	7	θ	θ	PROPN
ejpam-2055	6	8	−δ−β	−δ−β	PROPN
ejpam-2055	6	9	-continuous	-continuous	ADJ
ejpam-2055	6	10	functions	function	NOUN
ejpam-2055	6	11	and	and	CCONJ
ejpam-2055	6	12	other	other	ADJ
ejpam-2055	6	13	well	well	ADV
ejpam-2055	6	14	-	-	PUNCT
ejpam-2055	6	15	known	know	VERB
ejpam-2055	6	16	types	type	NOUN
ejpam-2055	6	17	of	of	ADP
ejpam-2055	6	18	strong	strong	ADJ
ejpam-2055	6	19	continuity	continuity	NOUN
ejpam-2055	6	20	are	be	AUX
ejpam-2055	6	21	also	also	ADV
ejpam-2055	6	22	discussed	discuss	VERB
ejpam-2055	6	23	.	.	PUNCT
ejpam-2055	7	1	2010	2010	NUM
ejpam-2055	7	2	mathematics	mathematic	NOUN
ejpam-2055	7	3	subject	subject	NOUN
ejpam-2055	7	4	classifications	classification	NOUN
ejpam-2055	7	5	:	:	PUNCT
ejpam-2055	7	6	54c05,54c08,54c10	54c05,54c08,54c10	NUM
ejpam-2055	7	7	key	key	ADJ
ejpam-2055	7	8	words	word	NOUN
ejpam-2055	7	9	and	and	CCONJ
ejpam-2055	7	10	phrases	phrase	NOUN
ejpam-2055	7	11	:	:	PUNCT
ejpam-2055	7	12	δ	δ	NOUN
ejpam-2055	7	13	−	−	NOUN
ejpam-2055	7	14	β	β	X
ejpam-2055	7	15	-open	-open	NOUN
ejpam-2055	7	16	sets	set	NOUN
ejpam-2055	7	17	,	,	PUNCT
ejpam-2055	8	1	δ	δ	PROPN
ejpam-2055	8	2	−	−	PROPN
ejpam-2055	8	3	βθ	βθ	CCONJ
ejpam-2055	8	4	-closed	-close	VERB
ejpam-2055	8	5	sets	set	NOUN
ejpam-2055	8	6	,	,	PUNCT
ejpam-2055	8	7	δ	δ	PROPN
ejpam-2055	8	8	−	−	PROPN
ejpam-2055	8	9	β	β	SYM
ejpam-2055	8	10	-regular	-regular	NOUN
ejpam-2055	8	11	sets	set	NOUN
ejpam-2055	8	12	,	,	PUNCT
ejpam-2055	8	13	strongly	strongly	ADV
ejpam-2055	8	14	θ	θ	PROPN
ejpam-2055	8	15	−	−	PROPN
ejpam-2055	8	16	δ	δ	PROPN
ejpam-2055	8	17	−	−	NOUN
ejpam-2055	8	18	β	β	NOUN
ejpam-2055	8	19	continuity	continuity	NOUN
ejpam-2055	8	20	1	1	NUM
ejpam-2055	8	21	.	.	PUNCT
ejpam-2055	8	22	introduction	introduction	NOUN
ejpam-2055	8	23	the	the	DET
ejpam-2055	8	24	notion	notion	NOUN
ejpam-2055	8	25	of	of	ADP
ejpam-2055	8	26	continuity	continuity	NOUN
ejpam-2055	8	27	is	be	AUX
ejpam-2055	8	28	an	an	DET
ejpam-2055	8	29	important	important	ADJ
ejpam-2055	8	30	concept	concept	NOUN
ejpam-2055	8	31	in	in	ADP
ejpam-2055	8	32	general	general	ADJ
ejpam-2055	8	33	topology	topology	NOUN
ejpam-2055	8	34	as	as	ADV
ejpam-2055	8	35	well	well	ADV
ejpam-2055	8	36	as	as	ADP
ejpam-2055	8	37	all	all	DET
ejpam-2055	8	38	branches	branch	NOUN
ejpam-2055	8	39	of	of	ADP
ejpam-2055	8	40	mathematics	mathematic	NOUN
ejpam-2055	8	41	and	and	CCONJ
ejpam-2055	8	42	quantum	quantum	NOUN
ejpam-2055	8	43	physics	physics	NOUN
ejpam-2055	8	44	of	of	ADP
ejpam-2055	8	45	course	course	NOUN
ejpam-2055	8	46	its	its	PRON
ejpam-2055	8	47	strong	strong	ADJ
ejpam-2055	8	48	forms	form	NOUN
ejpam-2055	8	49	are	be	AUX
ejpam-2055	8	50	important	important	ADJ
ejpam-2055	8	51	,	,	PUNCT
ejpam-2055	8	52	too	too	ADV
ejpam-2055	8	53	.	.	PUNCT
ejpam-2055	9	1	recently	recently	ADV
ejpam-2055	9	2	,	,	PUNCT
ejpam-2055	9	3	strong	strong	ADJ
ejpam-2055	9	4	continuity	continuity	NOUN
ejpam-2055	9	5	of	of	ADP
ejpam-2055	9	6	functions	function	NOUN
ejpam-2055	9	7	in	in	ADP
ejpam-2055	9	8	topological	topological	ADJ
ejpam-2055	9	9	spaces	space	NOUN
ejpam-2055	9	10	has	have	AUX
ejpam-2055	9	11	been	be	AUX
ejpam-2055	9	12	introduced	introduce	VERB
ejpam-2055	9	13	and	and	CCONJ
ejpam-2055	9	14	investigated	investigate	VERB
ejpam-2055	9	15	by	by	ADP
ejpam-2055	9	16	many	many	ADJ
ejpam-2055	9	17	mathematicians	mathematician	NOUN
ejpam-2055	9	18	and	and	CCONJ
ejpam-2055	9	19	quantum	quantum	NOUN
ejpam-2055	9	20	physicists	physicist	NOUN
ejpam-2055	9	21	.	.	PUNCT
ejpam-2055	10	1	furthermore	furthermore	ADV
ejpam-2055	10	2	,	,	PUNCT
ejpam-2055	10	3	generalized	generalize	VERB
ejpam-2055	10	4	open	open	ADJ
ejpam-2055	10	5	and	and	CCONJ
ejpam-2055	10	6	closed	closed	ADJ
ejpam-2055	10	7	sets	set	NOUN
ejpam-2055	10	8	are	be	AUX
ejpam-2055	10	9	,	,	PUNCT
ejpam-2055	10	10	as	as	ADV
ejpam-2055	10	11	well	well	ADV
ejpam-2055	10	12	-	-	PUNCT
ejpam-2055	10	13	known	know	VERB
ejpam-2055	10	14	,	,	PUNCT
ejpam-2055	10	15	the	the	DET
ejpam-2055	10	16	most	most	ADV
ejpam-2055	10	17	important	important	ADJ
ejpam-2055	10	18	notions	notion	NOUN
ejpam-2055	10	19	in	in	ADP
ejpam-2055	10	20	both	both	CCONJ
ejpam-2055	10	21	pure	pure	ADJ
ejpam-2055	10	22	and	and	CCONJ
ejpam-2055	10	23	applied	apply	VERB
ejpam-2055	10	24	mathematics.the	mathematics.the	DET
ejpam-2055	10	25	notion	notion	NOUN
ejpam-2055	10	26	of	of	ADP
ejpam-2055	10	27	continuity	continuity	NOUN
ejpam-2055	10	28	by	by	ADP
ejpam-2055	10	29	involving	involve	VERB
ejpam-2055	10	30	these	these	DET
ejpam-2055	10	31	notions	notion	NOUN
ejpam-2055	10	32	is	be	AUX
ejpam-2055	10	33	the	the	DET
ejpam-2055	10	34	subject	subject	NOUN
ejpam-2055	10	35	-	-	PUNCT
ejpam-2055	10	36	matter	matter	NOUN
ejpam-2055	10	37	of	of	ADP
ejpam-2055	10	38	topology	topology	NOUN
ejpam-2055	10	39	which	which	PRON
ejpam-2055	10	40	has	have	AUX
ejpam-2055	10	41	penetrated	penetrate	VERB
ejpam-2055	10	42	in	in	ADP
ejpam-2055	10	43	the	the	DET
ejpam-2055	10	44	whole	whole	ADJ
ejpam-2055	10	45	body	body	NOUN
ejpam-2055	10	46	of	of	ADP
ejpam-2055	10	47	science	science	NOUN
ejpam-2055	10	48	.	.	PUNCT
ejpam-2055	11	1	in	in	ADP
ejpam-2055	11	2	the	the	DET
ejpam-2055	11	3	course	course	NOUN
ejpam-2055	11	4	of	of	ADP
ejpam-2055	11	5	time	time	NOUN
ejpam-2055	11	6	,	,	PUNCT
ejpam-2055	11	7	mathematicians	mathematician	NOUN
ejpam-2055	11	8	realized	realize	VERB
ejpam-2055	11	9	that	that	SCONJ
ejpam-2055	11	10	it	it	PRON
ejpam-2055	11	11	is	be	AUX
ejpam-2055	11	12	very	very	ADV
ejpam-2055	11	13	useful	useful	ADJ
ejpam-2055	11	14	to	to	PART
ejpam-2055	11	15	generalize	generalize	VERB
ejpam-2055	11	16	the	the	DET
ejpam-2055	11	17	notions	notion	NOUN
ejpam-2055	11	18	of	of	ADP
ejpam-2055	11	19	open	open	ADJ
ejpam-2055	11	20	and	and	CCONJ
ejpam-2055	11	21	closed	closed	ADJ
ejpam-2055	11	22	sets	set	NOUN
ejpam-2055	11	23	and	and	CCONJ
ejpam-2055	11	24	accordingly	accordingly	ADV
ejpam-2055	11	25	the	the	DET
ejpam-2055	11	26	notion	notion	NOUN
ejpam-2055	11	27	of	of	ADP
ejpam-2055	11	28	continuity	continuity	NOUN
ejpam-2055	11	29	.	.	PUNCT
ejpam-2055	12	1	in	in	ADP
ejpam-2055	12	2	1980	1980	NUM
ejpam-2055	12	3	,	,	PUNCT
ejpam-2055	12	4	noiri	noiri	ADV
ejpam-2055	12	5	[	[	X
ejpam-2055	12	6	37	37	NUM
ejpam-2055	12	7	]	]	PUNCT
ejpam-2055	12	8	introduced	introduce	VERB
ejpam-2055	12	9	the	the	DET
ejpam-2055	12	10	notion	notion	NOUN
ejpam-2055	12	11	of	of	ADP
ejpam-2055	12	12	strong	strong	ADJ
ejpam-2055	12	13	θ	θ	PROPN
ejpam-2055	12	14	-continuity	-continuity	NOUN
ejpam-2055	12	15	which	which	PRON
ejpam-2055	12	16	is	be	AUX
ejpam-2055	12	17	stronger	strong	ADJ
ejpam-2055	12	18	than	than	ADP
ejpam-2055	12	19	δ	δ	NOUN
ejpam-2055	12	20	-	-	NOUN
ejpam-2055	12	21	continuity	continuity	NOUN
ejpam-2055	12	22	[	[	X
ejpam-2055	12	23	37	37	NUM
ejpam-2055	12	24	]	]	PUNCT
ejpam-2055	12	25	.	.	PUNCT
ejpam-2055	13	1	some	some	DET
ejpam-2055	13	2	properties	property	NOUN
ejpam-2055	13	3	of	of	ADP
ejpam-2055	13	4	strongly	strongly	ADV
ejpam-2055	13	5	θ	θ	NOUN
ejpam-2055	13	6	-continuous	-continuous	ADJ
ejpam-2055	13	7	functions	function	NOUN
ejpam-2055	13	8	are	be	AUX
ejpam-2055	13	9	studied	study	VERB
ejpam-2055	13	10	by	by	ADP
ejpam-2055	13	11	long	long	ADV
ejpam-2055	13	12	and	and	CCONJ
ejpam-2055	13	13	herrington	herrington	PROPN
ejpam-2055	14	1	[	[	X
ejpam-2055	14	2	32	32	NUM
ejpam-2055	14	3	]	]	PUNCT
ejpam-2055	14	4	.	.	PUNCT
ejpam-2055	15	1	recently	recently	ADV
ejpam-2055	15	2	,	,	PUNCT
ejpam-2055	15	3	five	five	NUM
ejpam-2055	15	4	generalizations	generalization	NOUN
ejpam-2055	15	5	of	of	ADP
ejpam-2055	15	6	strong	strong	ADJ
ejpam-2055	15	7	θ	θ	PROPN
ejpam-2055	15	8	-continuity	-continuity	PROPN
ejpam-2055	15	9	are	be	AUX
ejpam-2055	15	10	obtained	obtain	VERB
ejpam-2055	15	11	email	email	NOUN
ejpam-2055	15	12	addresses	address	NOUN
ejpam-2055	15	13	:	:	PUNCT
ejpam-2055	15	14	alaa_mf1970@yahoo.com	alaa_mf1970@yahoo.com	PROPN
ejpam-2055	15	15	(	(	PUNCT
ejpam-2055	15	16	a.	a.	NOUN
ejpam-2055	15	17	jumaili	jumaili	PROPN
ejpam-2055	15	18	)	)	PUNCT
ejpam-2055	15	19	,	,	PUNCT
ejpam-2055	15	20	yangxs@cqupt.edu.cn	yangxs@cqupt.edu.cn	PROPN
ejpam-2055	15	21	(	(	PUNCT
ejpam-2055	15	22	x.	x.	PROPN
ejpam-2055	15	23	yang	yang	PROPN
ejpam-2055	15	24	)	)	PUNCT
ejpam-2055	15	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2055	16	1	185	185	NUM
ejpam-2055	16	2	c	c	NOUN
ejpam-2055	16	3	©	©	PROPN
ejpam-2055	16	4	2015	2015	NUM
ejpam-2055	16	5	ejpam	ejpam	NOUN
ejpam-2055	16	6	all	all	DET
ejpam-2055	16	7	rights	right	NOUN
ejpam-2055	16	8	reserved	reserve	VERB
ejpam-2055	16	9	.	.	PUNCT
ejpam-2055	17	1	a.	a.	NOUN
ejpam-2055	17	2	m.	m.	PROPN
ejpam-2055	17	3	farhan	farhan	PROPN
ejpam-2055	17	4	and	and	CCONJ
ejpam-2055	17	5	x.	x.	PROPN
ejpam-2055	17	6	yang	yang	PROPN
ejpam-2055	17	7	/	/	SYM
ejpam-2055	17	8	eur	eur	PROPN
ejpam-2055	17	9	.	.	PUNCT
ejpam-2055	18	1	j.	j.	PROPN
ejpam-2055	18	2	pure	pure	PROPN
ejpam-2055	18	3	appl	appl	PROPN
ejpam-2055	18	4	.	.	PROPN
ejpam-2055	18	5	math	math	PROPN
ejpam-2055	18	6	,	,	PUNCT
ejpam-2055	18	7	8	8	NUM
ejpam-2055	18	8	(	(	PUNCT
ejpam-2055	18	9	2015	2015	NUM
ejpam-2055	18	10	)	)	PUNCT
ejpam-2055	18	11	,	,	PUNCT
ejpam-2055	18	12	185	185	NUM
ejpam-2055	18	13	-	-	SYM
ejpam-2055	18	14	200	200	NUM
ejpam-2055	18	15	186	186	NUM
ejpam-2055	18	16	by	by	ADP
ejpam-2055	18	17	jafari	jafari	PROPN
ejpam-2055	18	18	and	and	CCONJ
ejpam-2055	18	19	noiri	noiri	ADV
ejpam-2055	18	20	[	[	X
ejpam-2055	18	21	29	29	NUM
ejpam-2055	18	22	]	]	PUNCT
ejpam-2055	18	23	,	,	PUNCT
ejpam-2055	18	24	noiri	noiri	PROPN
ejpam-2055	19	1	[	[	X
ejpam-2055	19	2	38	38	NUM
ejpam-2055	19	3	]	]	PUNCT
ejpam-2055	19	4	,	,	PUNCT
ejpam-2055	19	5	noiri	noiri	PROPN
ejpam-2055	19	6	and	and	CCONJ
ejpam-2055	19	7	popa	popa	NOUN
ejpam-2055	20	1	[	[	X
ejpam-2055	20	2	39	39	NUM
ejpam-2055	20	3	]	]	PUNCT
ejpam-2055	20	4	,	,	PUNCT
ejpam-2055	20	5	park	park	NOUN
ejpam-2055	20	6	[	[	X
ejpam-2055	20	7	42	42	NUM
ejpam-2055	20	8	]	]	PUNCT
ejpam-2055	20	9	and	and	CCONJ
ejpam-2055	20	10	murad	murad	NOUN
ejpam-2055	20	11	äozkoc	äozkoc	VERB
ejpam-2055	20	12	and	and	CCONJ
ejpam-2055	20	13	gäulhan	gäulhan	ADV
ejpam-2055	20	14	aslim	aslim	NOUN
ejpam-2055	21	1	[	[	X
ejpam-2055	21	2	41	41	NUM
ejpam-2055	21	3	]	]	PUNCT
ejpam-2055	21	4	.	.	PUNCT
ejpam-2055	22	1	the	the	DET
ejpam-2055	22	2	purpose	purpose	NOUN
ejpam-2055	22	3	of	of	ADP
ejpam-2055	22	4	the	the	DET
ejpam-2055	22	5	present	present	ADJ
ejpam-2055	22	6	paper	paper	NOUN
ejpam-2055	22	7	is	be	AUX
ejpam-2055	22	8	to	to	PART
ejpam-2055	22	9	introduce	introduce	VERB
ejpam-2055	22	10	and	and	CCONJ
ejpam-2055	22	11	investigate	investigate	VERB
ejpam-2055	22	12	a	a	DET
ejpam-2055	22	13	new	new	ADJ
ejpam-2055	22	14	class	class	NOUN
ejpam-2055	22	15	of	of	ADP
ejpam-2055	22	16	strong	strong	ADJ
ejpam-2055	22	17	continuous	continuous	ADJ
ejpam-2055	22	18	functions	function	NOUN
ejpam-2055	22	19	called	call	VERB
ejpam-2055	22	20	strongly	strongly	ADV
ejpam-2055	22	21	θ	θ	PROPN
ejpam-2055	22	22	−	−	PROPN
ejpam-2055	23	1	δ	δ	PROPN
ejpam-2055	23	2	−	−	NOUN
ejpam-2055	23	3	β	β	SYM
ejpam-2055	23	4	-continuous	-continuous	ADJ
ejpam-2055	23	5	functions	function	NOUN
ejpam-2055	23	6	and	and	CCONJ
ejpam-2055	23	7	give	give	VERB
ejpam-2055	23	8	several	several	ADJ
ejpam-2055	23	9	characterizations	characterization	NOUN
ejpam-2055	23	10	and	and	CCONJ
ejpam-2055	23	11	fundamental	fundamental	ADJ
ejpam-2055	23	12	properties	property	NOUN
ejpam-2055	23	13	concerning	concern	VERB
ejpam-2055	23	14	strongly	strongly	ADV
ejpam-2055	23	15	θ−δ−β	θ−δ−β	PROPN
ejpam-2055	23	16	-continuous	-continuous	ADJ
ejpam-2055	23	17	functions	function	NOUN
ejpam-2055	23	18	by	by	ADP
ejpam-2055	23	19	using	use	VERB
ejpam-2055	23	20	δ	δ	PROPN
ejpam-2055	23	21	−	−	NOUN
ejpam-2055	23	22	β	β	NOUN
ejpam-2055	23	23	-open	-open	NOUN
ejpam-2055	23	24	sets	set	NOUN
ejpam-2055	23	25	due	due	ADJ
ejpam-2055	23	26	to	to	ADP
ejpam-2055	23	27	by	by	ADP
ejpam-2055	23	28	erdal	erdal	PROPN
ejpam-2055	23	29	ekici	ekici	PROPN
ejpam-2055	24	1	[	[	X
ejpam-2055	24	2	9	9	NUM
ejpam-2055	24	3	]	]	PUNCT
ejpam-2055	24	4	and	and	CCONJ
ejpam-2055	24	5	e.	e.	PROPN
ejpam-2055	24	6	hatir	hatir	PROPN
ejpam-2055	24	7	and	and	CCONJ
ejpam-2055	24	8	t.	t.	PROPN
ejpam-2055	24	9	noiri	noiri	PROPN
ejpam-2055	25	1	[	[	X
ejpam-2055	25	2	27	27	NUM
ejpam-2055	25	3	]	]	PUNCT
ejpam-2055	25	4	.	.	PUNCT
ejpam-2055	26	1	also	also	ADV
ejpam-2055	26	2	we	we	PRON
ejpam-2055	26	3	discussed	discuss	VERB
ejpam-2055	26	4	the	the	DET
ejpam-2055	26	5	relationships	relationship	NOUN
ejpam-2055	26	6	between	between	ADP
ejpam-2055	26	7	strongly	strongly	ADV
ejpam-2055	26	8	θ−δ−β	θ−δ−β	PROPN
ejpam-2055	26	9	-continuous	-continuous	ADJ
ejpam-2055	26	10	functions	function	NOUN
ejpam-2055	26	11	and	and	CCONJ
ejpam-2055	26	12	other	other	ADJ
ejpam-2055	26	13	well	well	ADV
ejpam-2055	26	14	-	-	PUNCT
ejpam-2055	26	15	known	know	VERB
ejpam-2055	26	16	types	type	NOUN
ejpam-2055	26	17	of	of	ADP
ejpam-2055	26	18	strong	strong	ADJ
ejpam-2055	26	19	continuity	continuity	NOUN
ejpam-2055	26	20	.	.	PUNCT
ejpam-2055	27	1	2	2	X
ejpam-2055	27	2	.	.	X
ejpam-2055	27	3	preliminaries	preliminary	NOUN
ejpam-2055	27	4	throughout	throughout	ADP
ejpam-2055	27	5	this	this	DET
ejpam-2055	27	6	paper	paper	NOUN
ejpam-2055	27	7	,	,	PUNCT
ejpam-2055	27	8	(	(	PUNCT
ejpam-2055	27	9	x	x	X
ejpam-2055	27	10	,	,	PUNCT
ejpam-2055	27	11	t	t	PROPN
ejpam-2055	27	12	)	)	PUNCT
ejpam-2055	27	13	and	and	CCONJ
ejpam-2055	27	14	(	(	PUNCT
ejpam-2055	27	15	y	y	PROPN
ejpam-2055	27	16	,	,	PUNCT
ejpam-2055	27	17	t	t	PROPN
ejpam-2055	27	18	∗	∗	NOUN
ejpam-2055	27	19	)	)	PUNCT
ejpam-2055	27	20	(	(	PUNCT
ejpam-2055	27	21	or	or	CCONJ
ejpam-2055	27	22	simply	simply	ADV
ejpam-2055	27	23	x	x	X
ejpam-2055	27	24	and	and	CCONJ
ejpam-2055	27	25	y	y	PROPN
ejpam-2055	27	26	)	)	PUNCT
ejpam-2055	28	1	mean	mean	VERB
ejpam-2055	28	2	topological	topological	ADJ
ejpam-2055	28	3	spaces	space	NOUN
ejpam-2055	28	4	on	on	ADP
ejpam-2055	28	5	which	which	PRON
ejpam-2055	28	6	no	no	DET
ejpam-2055	28	7	separation	separation	NOUN
ejpam-2055	28	8	axioms	axiom	NOUN
ejpam-2055	28	9	are	be	AUX
ejpam-2055	28	10	assumed	assume	VERB
ejpam-2055	28	11	unless	unless	SCONJ
ejpam-2055	28	12	explicitly	explicitly	ADV
ejpam-2055	28	13	stated	state	VERB
ejpam-2055	28	14	.	.	PUNCT
ejpam-2055	29	1	for	for	ADP
ejpam-2055	29	2	any	any	DET
ejpam-2055	29	3	subset	subset	NOUN
ejpam-2055	29	4	a	a	PRON
ejpam-2055	29	5	of	of	ADP
ejpam-2055	29	6	x	x	PRON
ejpam-2055	29	7	,	,	PUNCT
ejpam-2055	29	8	the	the	DET
ejpam-2055	29	9	closure	closure	NOUN
ejpam-2055	29	10	and	and	CCONJ
ejpam-2055	29	11	interior	interior	NOUN
ejpam-2055	29	12	of	of	ADP
ejpam-2055	29	13	a	a	PRON
ejpam-2055	29	14	are	be	AUX
ejpam-2055	29	15	denoted	denote	VERB
ejpam-2055	29	16	by	by	ADP
ejpam-2055	29	17	cl(a	cl(a	NOUN
ejpam-2055	29	18	)	)	PUNCT
ejpam-2055	29	19	and	and	CCONJ
ejpam-2055	29	20	int(a	int(a	PROPN
ejpam-2055	29	21	)	)	PUNCT
ejpam-2055	29	22	,	,	PUNCT
ejpam-2055	29	23	respectively	respectively	ADV
ejpam-2055	29	24	.	.	PUNCT
ejpam-2055	30	1	we	we	PRON
ejpam-2055	30	2	recall	recall	VERB
ejpam-2055	30	3	the	the	DET
ejpam-2055	30	4	following	follow	VERB
ejpam-2055	30	5	definitions	definition	NOUN
ejpam-2055	30	6	,	,	PUNCT
ejpam-2055	30	7	which	which	PRON
ejpam-2055	30	8	will	will	AUX
ejpam-2055	30	9	be	be	AUX
ejpam-2055	30	10	used	use	VERB
ejpam-2055	30	11	often	often	ADV
ejpam-2055	30	12	throughout	throughout	ADP
ejpam-2055	30	13	this	this	DET
ejpam-2055	30	14	paper	paper	NOUN
ejpam-2055	30	15	.	.	PUNCT
ejpam-2055	31	1	a	a	DET
ejpam-2055	31	2	subset	subset	NOUN
ejpam-2055	31	3	a	a	PRON
ejpam-2055	31	4	of	of	ADP
ejpam-2055	31	5	a	a	DET
ejpam-2055	31	6	space	space	NOUN
ejpam-2055	31	7	(	(	PUNCT
ejpam-2055	31	8	x	x	X
ejpam-2055	31	9	,	,	PUNCT
ejpam-2055	31	10	t	t	PROPN
ejpam-2055	31	11	)	)	PUNCT
ejpam-2055	31	12	is	be	AUX
ejpam-2055	31	13	called	call	VERB
ejpam-2055	31	14	δ	δ	NOUN
ejpam-2055	31	15	-	-	ADJ
ejpam-2055	31	16	open	open	ADJ
ejpam-2055	31	17	[	[	X
ejpam-2055	31	18	48	48	NUM
ejpam-2055	31	19	]	]	X
ejpam-2055	31	20	if	if	SCONJ
ejpam-2055	31	21	for	for	ADP
ejpam-2055	31	22	each	each	DET
ejpam-2055	31	23	x	x	SYM
ejpam-2055	31	24	∈	∈	PROPN
ejpam-2055	31	25	a	a	DET
ejpam-2055	31	26	there	there	PRON
ejpam-2055	31	27	exists	exist	VERB
ejpam-2055	31	28	a	a	DET
ejpam-2055	31	29	regular	regular	ADJ
ejpam-2055	31	30	open	open	NOUN
ejpam-2055	31	31	set	set	NOUN
ejpam-2055	31	32	v	v	ADP
ejpam-2055	31	33	such	such	ADJ
ejpam-2055	31	34	that	that	SCONJ
ejpam-2055	31	35	x	x	SYM
ejpam-2055	31	36	∈	∈	PROPN
ejpam-2055	31	37	v	v	ADP
ejpam-2055	31	38	⊂	⊂	PROPN
ejpam-2055	31	39	a.	a.	NOUN
ejpam-2055	31	40	the	the	DET
ejpam-2055	31	41	δ	δ	PROPN
ejpam-2055	31	42	-	-	NOUN
ejpam-2055	31	43	interior	interior	NOUN
ejpam-2055	31	44	of	of	ADP
ejpam-2055	31	45	a	a	PRON
ejpam-2055	31	46	is	be	AUX
ejpam-2055	31	47	the	the	DET
ejpam-2055	31	48	union	union	NOUN
ejpam-2055	31	49	of	of	ADP
ejpam-2055	31	50	all	all	DET
ejpam-2055	31	51	regular	regular	ADJ
ejpam-2055	31	52	open	open	ADJ
ejpam-2055	31	53	sets	set	NOUN
ejpam-2055	31	54	contained	contain	VERB
ejpam-2055	31	55	in	in	ADP
ejpam-2055	31	56	a	a	PRON
ejpam-2055	31	57	and	and	CCONJ
ejpam-2055	31	58	is	be	AUX
ejpam-2055	31	59	denoted	denote	VERB
ejpam-2055	31	60	by	by	ADP
ejpam-2055	31	61	intδ(a	intδ(a	NOUN
ejpam-2055	31	62	)	)	PUNCT
ejpam-2055	31	63	.	.	PUNCT
ejpam-2055	32	1	the	the	DET
ejpam-2055	32	2	subset	subset	NOUN
ejpam-2055	32	3	a	a	PRON
ejpam-2055	32	4	is	be	AUX
ejpam-2055	32	5	called	call	VERB
ejpam-2055	32	6	δ	δ	NOUN
ejpam-2055	32	7	-	-	ADJ
ejpam-2055	32	8	open	open	ADJ
ejpam-2055	33	1	[	[	X
ejpam-2055	33	2	48	48	NUM
ejpam-2055	33	3	]	]	PUNCT
ejpam-2055	33	4	if	if	SCONJ
ejpam-2055	33	5	a=	a=	VERB
ejpam-2055	33	6	intδ(a	intδ(a	NOUN
ejpam-2055	33	7	)	)	PUNCT
ejpam-2055	33	8	.	.	PUNCT
ejpam-2055	34	1	a	a	DET
ejpam-2055	34	2	point	point	NOUN
ejpam-2055	34	3	x	x	X
ejpam-2055	34	4	∈	∈	NOUN
ejpam-2055	34	5	x	x	PUNCT
ejpam-2055	34	6	is	be	AUX
ejpam-2055	34	7	called	call	VERB
ejpam-2055	34	8	a	a	DET
ejpam-2055	34	9	δ	δ	NOUN
ejpam-2055	34	10	-	-	PUNCT
ejpam-2055	34	11	cluster	cluster	NOUN
ejpam-2055	34	12	points	point	NOUN
ejpam-2055	34	13	of	of	ADP
ejpam-2055	34	14	a	a	PRON
ejpam-2055	34	15	[	[	X
ejpam-2055	34	16	48	48	NUM
ejpam-2055	34	17	]	]	PUNCT
ejpam-2055	34	18	if	if	SCONJ
ejpam-2055	34	19	a	a	DET
ejpam-2055	34	20	⋂	⋂	PROPN
ejpam-2055	34	21	int(cl(v	int(cl(v	NOUN
ejpam-2055	34	22	)	)	PUNCT
ejpam-2055	34	23	)	)	PUNCT
ejpam-2055	35	1	6=	6=	ADP
ejpam-2055	35	2	φ	φ	PROPN
ejpam-2055	35	3	for	for	ADP
ejpam-2055	35	4	each	each	DET
ejpam-2055	35	5	open	open	ADJ
ejpam-2055	35	6	set	set	VERB
ejpam-2055	35	7	v	v	NOUN
ejpam-2055	35	8	containing	contain	VERB
ejpam-2055	35	9	x.	x.	NOUN
ejpam-2055	35	10	the	the	DET
ejpam-2055	35	11	set	set	NOUN
ejpam-2055	35	12	of	of	ADP
ejpam-2055	35	13	all	all	DET
ejpam-2055	35	14	δ	δ	NOUN
ejpam-2055	35	15	-	-	PUNCT
ejpam-2055	35	16	cluster	cluster	NOUN
ejpam-2055	35	17	points	point	NOUN
ejpam-2055	35	18	of	of	ADP
ejpam-2055	35	19	a	a	PRON
ejpam-2055	35	20	is	be	AUX
ejpam-2055	35	21	called	call	VERB
ejpam-2055	35	22	the	the	DET
ejpam-2055	35	23	δ	δ	NOUN
ejpam-2055	35	24	-	-	NOUN
ejpam-2055	35	25	closure	closure	NOUN
ejpam-2055	35	26	of	of	ADP
ejpam-2055	35	27	a	a	PRON
ejpam-2055	35	28	and	and	CCONJ
ejpam-2055	35	29	is	be	AUX
ejpam-2055	35	30	denoted	denote	VERB
ejpam-2055	35	31	by	by	ADP
ejpam-2055	35	32	clδ(a).i	clδ(a).i	PROPN
ejpam-2055	35	33	f	f	PROPN
ejpam-2055	35	34	a=	a=	ADV
ejpam-2055	35	35	clδ(a	clδ(a	X
ejpam-2055	35	36	)	)	PUNCT
ejpam-2055	35	37	)	)	PUNCT
ejpam-2055	35	38	,	,	PUNCT
ejpam-2055	35	39	then	then	ADV
ejpam-2055	35	40	a	a	PRON
ejpam-2055	35	41	is	be	AUX
ejpam-2055	35	42	said	say	VERB
ejpam-2055	35	43	to	to	PART
ejpam-2055	35	44	be	be	AUX
ejpam-2055	35	45	δ	δ	NOUN
ejpam-2055	35	46	-	-	PUNCT
ejpam-2055	35	47	closed	closed	ADJ
ejpam-2055	35	48	[	[	X
ejpam-2055	35	49	48	48	NUM
ejpam-2055	35	50	]	]	PUNCT
ejpam-2055	35	51	.	.	PUNCT
ejpam-2055	36	1	the	the	DET
ejpam-2055	36	2	complement	complement	NOUN
ejpam-2055	36	3	of	of	ADP
ejpam-2055	36	4	δ	δ	PROPN
ejpam-2055	36	5	-	-	PUNCT
ejpam-2055	36	6	closed	close	VERB
ejpam-2055	36	7	set	set	NOUN
ejpam-2055	36	8	is	be	AUX
ejpam-2055	36	9	said	say	VERB
ejpam-2055	36	10	to	to	PART
ejpam-2055	36	11	be	be	AUX
ejpam-2055	36	12	δ	δ	NOUN
ejpam-2055	36	13	-	-	ADJ
ejpam-2055	36	14	open	open	ADJ
ejpam-2055	36	15	set	set	NOUN
ejpam-2055	36	16	.	.	PUNCT
ejpam-2055	37	1	a	a	DET
ejpam-2055	37	2	subset	subset	NOUN
ejpam-2055	37	3	a	a	PRON
ejpam-2055	37	4	of	of	ADP
ejpam-2055	37	5	a	a	DET
ejpam-2055	37	6	space	space	NOUN
ejpam-2055	37	7	x	x	PUNCT
ejpam-2055	37	8	is	be	AUX
ejpam-2055	37	9	called	call	VERB
ejpam-2055	37	10	δ−β	δ−β	PROPN
ejpam-2055	37	11	-open	-open	NOUN
ejpam-2055	37	12	[	[	X
ejpam-2055	37	13	27	27	NUM
ejpam-2055	37	14	]	]	PUNCT
ejpam-2055	37	15	or	or	CCONJ
ejpam-2055	37	16	e∗-open	e∗-open	VERB
ejpam-2055	37	17	[	[	X
ejpam-2055	37	18	9	9	NUM
ejpam-2055	37	19	]	]	PUNCT
ejpam-2055	37	20	,	,	PUNCT
ejpam-2055	37	21	if	if	SCONJ
ejpam-2055	37	22	a⊂	a⊂	NOUN
ejpam-2055	37	23	cl(int(δ−cl(a	cl(int(δ−cl(a	ADJ
ejpam-2055	37	24	)	)	PUNCT
ejpam-2055	37	25	)	)	PUNCT
ejpam-2055	37	26	)	)	PUNCT
ejpam-2055	37	27	,	,	PUNCT
ejpam-2055	37	28	the	the	DET
ejpam-2055	37	29	complement	complement	NOUN
ejpam-2055	37	30	of	of	ADP
ejpam-2055	37	31	a	a	DET
ejpam-2055	37	32	δ−β	δ−β	ADJ
ejpam-2055	37	33	-open	-open	ADJ
ejpam-2055	37	34	set	set	NOUN
ejpam-2055	37	35	is	be	AUX
ejpam-2055	37	36	called	call	VERB
ejpam-2055	37	37	δ−β	δ−β	PROPN
ejpam-2055	37	38	-closed	-close	VERB
ejpam-2055	37	39	.	.	PUNCT
ejpam-2055	38	1	the	the	DET
ejpam-2055	38	2	intersection	intersection	NOUN
ejpam-2055	38	3	of	of	ADP
ejpam-2055	38	4	all	all	DET
ejpam-2055	38	5	δ−β	δ−β	X
ejpam-2055	38	6	-closed	-close	VERB
ejpam-2055	38	7	sets	set	NOUN
ejpam-2055	38	8	containing	contain	VERB
ejpam-2055	38	9	a	a	PRON
ejpam-2055	38	10	is	be	AUX
ejpam-2055	38	11	called	call	VERB
ejpam-2055	38	12	the	the	DET
ejpam-2055	38	13	δ−β	δ−β	ADJ
ejpam-2055	38	14	-closure	-closure	NOUN
ejpam-2055	38	15	of	of	ADP
ejpam-2055	38	16	a	a	DET
ejpam-2055	38	17	[	[	X
ejpam-2055	38	18	27	27	NUM
ejpam-2055	38	19	]	]	PUNCT
ejpam-2055	38	20	and	and	CCONJ
ejpam-2055	38	21	is	be	AUX
ejpam-2055	38	22	denoted	denote	VERB
ejpam-2055	38	23	by	by	ADP
ejpam-2055	38	24	δ−β	δ−β	PROPN
ejpam-2055	38	25	-cl(a	-cl(a	NUM
ejpam-2055	38	26	)	)	PUNCT
ejpam-2055	38	27	.	.	PUNCT
ejpam-2055	39	1	the	the	DET
ejpam-2055	39	2	union	union	NOUN
ejpam-2055	39	3	of	of	ADP
ejpam-2055	39	4	all	all	DET
ejpam-2055	39	5	δ−β	δ−β	ADJ
ejpam-2055	39	6	-open	-open	ADJ
ejpam-2055	39	7	sets	set	NOUN
ejpam-2055	39	8	of	of	ADP
ejpam-2055	39	9	x	x	PUNCT
ejpam-2055	39	10	contained	contain	VERB
ejpam-2055	39	11	in	in	ADP
ejpam-2055	39	12	a	a	PRON
ejpam-2055	39	13	is	be	AUX
ejpam-2055	39	14	called	call	VERB
ejpam-2055	39	15	the	the	DET
ejpam-2055	39	16	δ−β	δ−β	ADJ
ejpam-2055	39	17	-interior	-interior	NOUN
ejpam-2055	39	18	[	[	X
ejpam-2055	39	19	27	27	NUM
ejpam-2055	39	20	]	]	PUNCT
ejpam-2055	39	21	of	of	ADP
ejpam-2055	39	22	a	a	PRON
ejpam-2055	39	23	and	and	CCONJ
ejpam-2055	39	24	is	be	AUX
ejpam-2055	39	25	denoted	denote	VERB
ejpam-2055	39	26	by	by	ADP
ejpam-2055	39	27	δ−β	δ−β	PROPN
ejpam-2055	39	28	-int(a	-int(a	PROPN
ejpam-2055	39	29	)	)	PUNCT
ejpam-2055	39	30	.	.	PUNCT
ejpam-2055	40	1	the	the	DET
ejpam-2055	40	2	family	family	NOUN
ejpam-2055	40	3	of	of	ADP
ejpam-2055	40	4	all	all	DET
ejpam-2055	40	5	δ−β	δ−β	PROPN
ejpam-2055	40	6	-open	-open	NOUN
ejpam-2055	40	7	(	(	PUNCT
ejpam-2055	40	8	resp	resp	NOUN
ejpam-2055	40	9	.	.	PUNCT
ejpam-2055	41	1	δ−β	δ−β	PROPN
ejpam-2055	41	2	-closed	-closed	ADJ
ejpam-2055	41	3	)	)	PUNCT
ejpam-2055	41	4	subsets	subset	NOUN
ejpam-2055	41	5	of	of	ADP
ejpam-2055	41	6	x	x	PUNCT
ejpam-2055	41	7	containing	contain	VERB
ejpam-2055	41	8	a	a	DET
ejpam-2055	41	9	point	point	NOUN
ejpam-2055	41	10	x	x	SYM
ejpam-2055	41	11	∈	∈	NOUN
ejpam-2055	41	12	x	x	PUNCT
ejpam-2055	41	13	is	be	AUX
ejpam-2055	41	14	denoted	denote	VERB
ejpam-2055	41	15	by	by	ADP
ejpam-2055	41	16	δ	δ	PROPN
ejpam-2055	41	17	−	−	PROPN
ejpam-2055	41	18	βς(x	βς(x	PUNCT
ejpam-2055	41	19	,	,	PUNCT
ejpam-2055	41	20	x	x	X
ejpam-2055	41	21	)	)	PUNCT
ejpam-2055	41	22	(	(	PUNCT
ejpam-2055	41	23	resp	resp	NOUN
ejpam-2055	41	24	.	.	PUNCT
ejpam-2055	42	1	δ	δ	PROPN
ejpam-2055	42	2	−	−	PROPN
ejpam-2055	42	3	βc(x	βc(x	NUM
ejpam-2055	42	4	,	,	PUNCT
ejpam-2055	42	5	x	x	NOUN
ejpam-2055	42	6	)	)	PUNCT
ejpam-2055	42	7	)	)	PUNCT
ejpam-2055	42	8	,	,	PUNCT
ejpam-2055	42	9	the	the	DET
ejpam-2055	42	10	family	family	NOUN
ejpam-2055	42	11	of	of	ADP
ejpam-2055	42	12	all	all	DET
ejpam-2055	42	13	δ	δ	NOUN
ejpam-2055	42	14	−	−	NOUN
ejpam-2055	42	15	β	β	X
ejpam-2055	42	16	-open	-open	NOUN
ejpam-2055	42	17	(	(	PUNCT
ejpam-2055	42	18	resp	resp	NOUN
ejpam-2055	42	19	.	.	PUNCT
ejpam-2055	43	1	δ	δ	X
ejpam-2055	43	2	−	−	PROPN
ejpam-2055	43	3	β	β	X
ejpam-2055	43	4	-closed	-closed	ADJ
ejpam-2055	43	5	)	)	PUNCT
ejpam-2055	43	6	sets	set	NOUN
ejpam-2055	43	7	in	in	ADP
ejpam-2055	43	8	x	x	SYM
ejpam-2055	43	9	are	be	AUX
ejpam-2055	43	10	denoted	denote	VERB
ejpam-2055	43	11	by	by	ADP
ejpam-2055	43	12	δ	δ	PROPN
ejpam-2055	43	13	−	−	PROPN
ejpam-2055	43	14	βς(x	βς(x	PUNCT
ejpam-2055	43	15	,	,	PUNCT
ejpam-2055	43	16	t	t	PROPN
ejpam-2055	43	17	)	)	PUNCT
ejpam-2055	43	18	(	(	PUNCT
ejpam-2055	43	19	resp	resp	NOUN
ejpam-2055	43	20	.	.	PUNCT
ejpam-2055	44	1	δ	δ	PROPN
ejpam-2055	44	2	−	−	PROPN
ejpam-2055	44	3	βc(x	βc(x	NUM
ejpam-2055	44	4	,	,	PUNCT
ejpam-2055	44	5	t	t	PROPN
ejpam-2055	44	6	)	)	PUNCT
ejpam-2055	44	7	)	)	PUNCT
ejpam-2055	44	8	.	.	PUNCT
ejpam-2055	45	1	a	a	DET
ejpam-2055	45	2	subset	subset	NOUN
ejpam-2055	45	3	a	a	PRON
ejpam-2055	45	4	is	be	AUX
ejpam-2055	45	5	said	say	VERB
ejpam-2055	45	6	to	to	PART
ejpam-2055	45	7	be	be	AUX
ejpam-2055	45	8	regular	regular	ADJ
ejpam-2055	45	9	open	open	ADJ
ejpam-2055	45	10	(	(	PUNCT
ejpam-2055	45	11	resp	resp	NOUN
ejpam-2055	45	12	.	.	PUNCT
ejpam-2055	46	1	regular	regular	ADJ
ejpam-2055	46	2	closed	closed	ADJ
ejpam-2055	46	3	)	)	PUNCT
ejpam-2055	46	4	if	if	SCONJ
ejpam-2055	46	5	a	a	PRON
ejpam-2055	46	6	=	=	SYM
ejpam-2055	46	7	int(cl(a	int(cl(a	PROPN
ejpam-2055	46	8	)	)	PUNCT
ejpam-2055	46	9	)	)	PUNCT
ejpam-2055	46	10	(	(	PUNCT
ejpam-2055	46	11	resp	resp	NOUN
ejpam-2055	46	12	.	.	PUNCT
ejpam-2055	47	1	a	a	DET
ejpam-2055	47	2	=	=	NOUN
ejpam-2055	47	3	cl(int(a	cl(int(a	NOUN
ejpam-2055	47	4	)	)	PUNCT
ejpam-2055	47	5	)	)	PUNCT
ejpam-2055	47	6	)	)	PUNCT
ejpam-2055	47	7	.	.	PUNCT
ejpam-2055	48	1	a	a	DET
ejpam-2055	48	2	subset	subset	NOUN
ejpam-2055	48	3	a	a	PRON
ejpam-2055	48	4	of	of	ADP
ejpam-2055	48	5	x	x	PRON
ejpam-2055	48	6	is	be	AUX
ejpam-2055	48	7	called	call	VERB
ejpam-2055	48	8	semiopen	semiopen	ADJ
ejpam-2055	49	1	[	[	X
ejpam-2055	49	2	31	31	NUM
ejpam-2055	49	3	]	]	PUNCT
ejpam-2055	49	4	(	(	PUNCT
ejpam-2055	49	5	resp	resp	NOUN
ejpam-2055	49	6	.	.	PUNCT
ejpam-2055	50	1	α	α	X
ejpam-2055	50	2	-	-	PUNCT
ejpam-2055	50	3	open	open	ADJ
ejpam-2055	50	4	[	[	X
ejpam-2055	50	5	36	36	NUM
ejpam-2055	50	6	]	]	PUNCT
ejpam-2055	50	7	,	,	PUNCT
ejpam-2055	50	8	preopen	preopen	ADJ
ejpam-2055	50	9	[	[	X
ejpam-2055	50	10	33	33	NUM
ejpam-2055	50	11	]	]	PUNCT
ejpam-2055	50	12	,	,	PUNCT
ejpam-2055	50	13	b	b	X
ejpam-2055	50	14	-	-	PUNCT
ejpam-2055	50	15	open	open	ADJ
ejpam-2055	50	16	[	[	X
ejpam-2055	50	17	2	2	NUM
ejpam-2055	50	18	]	]	PUNCT
ejpam-2055	50	19	,	,	PUNCT
ejpam-2055	50	20	semipreopen	semipreopen	VERB
ejpam-2055	51	1	[	[	X
ejpam-2055	51	2	1	1	NUM
ejpam-2055	51	3	]	]	PUNCT
ejpam-2055	51	4	(	(	PUNCT
ejpam-2055	51	5	or	or	CCONJ
ejpam-2055	51	6	β	β	X
ejpam-2055	51	7	-open	-open	NOUN
ejpam-2055	52	1	[	[	X
ejpam-2055	52	2	11	11	NUM
ejpam-2055	52	3	]	]	NUM
ejpam-2055	52	4	)	)	PUNCT
ejpam-2055	52	5	,	,	PUNCT
ejpam-2055	52	6	e	e	NOUN
ejpam-2055	52	7	-	-	NOUN
ejpam-2055	52	8	open	open	ADJ
ejpam-2055	52	9	[	[	X
ejpam-2055	52	10	8	8	NUM
ejpam-2055	52	11	]	]	SYM
ejpam-2055	52	12	)	)	PUNCT
ejpam-2055	52	13	if	if	SCONJ
ejpam-2055	52	14	a⊂	a⊂	DET
ejpam-2055	52	15	cl(int(a	cl(int(a	NOUN
ejpam-2055	52	16	)	)	PUNCT
ejpam-2055	52	17	)	)	PUNCT
ejpam-2055	52	18	(	(	PUNCT
ejpam-2055	52	19	resp	resp	NOUN
ejpam-2055	52	20	.	.	PUNCT
ejpam-2055	52	21	a⊂	a⊂	PUNCT
ejpam-2055	52	22	int(cl(int(a	int(cl(int(a	NOUN
ejpam-2055	52	23	)	)	PUNCT
ejpam-2055	52	24	)	)	PUNCT
ejpam-2055	52	25	)	)	PUNCT
ejpam-2055	52	26	,	,	PUNCT
ejpam-2055	52	27	a⊂	a⊂	VERB
ejpam-2055	52	28	int(cl(a	int(cl(a	PROPN
ejpam-2055	52	29	)	)	PUNCT
ejpam-2055	52	30	)	)	PUNCT
ejpam-2055	52	31	,	,	PUNCT
ejpam-2055	52	32	a⊂	a⊂	VERB
ejpam-2055	52	33	int(cl(a	int(cl(a	PROPN
ejpam-2055	52	34	)	)	PUNCT
ejpam-2055	52	35	)	)	PUNCT
ejpam-2055	53	1	⋃	⋃	NOUN
ejpam-2055	53	2	cl(int(a	cl(int(a	NOUN
ejpam-2055	53	3	)	)	PUNCT
ejpam-2055	53	4	)	)	PUNCT
ejpam-2055	53	5	,	,	PUNCT
ejpam-2055	53	6	a⊂	a⊂	NOUN
ejpam-2055	53	7	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-2055	53	8	)	)	PUNCT
ejpam-2055	53	9	)	)	PUNCT
ejpam-2055	53	10	)	)	PUNCT
ejpam-2055	53	11	,	,	PUNCT
ejpam-2055	53	12	a	a	DET
ejpam-2055	53	13	⊂	⊂	PROPN
ejpam-2055	53	14	cl(δ	cl(δ	NOUN
ejpam-2055	53	15	−	−	PROPN
ejpam-2055	53	16	int(a	int(a	NOUN
ejpam-2055	53	17	)	)	PUNCT
ejpam-2055	53	18	)	)	PUNCT
ejpam-2055	54	1	⋃	⋃	PUNCT
ejpam-2055	54	2	int(δ	int(δ	PROPN
ejpam-2055	54	3	−	−	PROPN
ejpam-2055	54	4	cl(a	cl(a	NUM
ejpam-2055	54	5	)	)	PUNCT
ejpam-2055	54	6	)	)	PUNCT
ejpam-2055	54	7	,	,	PUNCT
ejpam-2055	54	8	and	and	CCONJ
ejpam-2055	54	9	the	the	DET
ejpam-2055	54	10	complement	complement	NOUN
ejpam-2055	54	11	of	of	ADP
ejpam-2055	54	12	a	a	DET
ejpam-2055	54	13	semiopen	semiopen	ADJ
ejpam-2055	54	14	(	(	PUNCT
ejpam-2055	54	15	resp	resp	NOUN
ejpam-2055	54	16	.	.	PUNCT
ejpam-2055	55	1	α	α	X
ejpam-2055	55	2	-	-	ADJ
ejpam-2055	55	3	open	open	ADJ
ejpam-2055	55	4	,	,	PUNCT
ejpam-2055	55	5	preopen	preopen	ADJ
ejpam-2055	55	6	,	,	PUNCT
ejpam-2055	55	7	b	b	X
ejpam-2055	55	8	-	-	PUNCT
ejpam-2055	55	9	open	open	ADJ
ejpam-2055	55	10	,	,	PUNCT
ejpam-2055	55	11	semi	semi	ADJ
ejpam-2055	55	12	-	-	ADJ
ejpam-2055	55	13	preopen	preopen	ADJ
ejpam-2055	55	14	,	,	PUNCT
ejpam-2055	55	15	e	e	NOUN
ejpam-2055	55	16	-	-	ADJ
ejpam-2055	55	17	open	open	ADJ
ejpam-2055	55	18	)	)	PUNCT
ejpam-2055	55	19	set	set	NOUN
ejpam-2055	55	20	are	be	AUX
ejpam-2055	55	21	called	call	VERB
ejpam-2055	55	22	semiclosed	semiclose	VERB
ejpam-2055	55	23	(	(	PUNCT
ejpam-2055	55	24	resp	resp	NOUN
ejpam-2055	55	25	.	.	PUNCT
ejpam-2055	56	1	α	α	X
ejpam-2055	56	2	-	-	VERB
ejpam-2055	56	3	closed	closed	ADJ
ejpam-2055	56	4	,	,	PUNCT
ejpam-2055	56	5	preclosed	preclose	VERB
ejpam-2055	56	6	,	,	PUNCT
ejpam-2055	56	7	b	b	X
ejpam-2055	56	8	-	-	PUNCT
ejpam-2055	56	9	closed	closed	ADJ
ejpam-2055	56	10	,	,	PUNCT
ejpam-2055	56	11	semi	semi	ADV
ejpam-2055	56	12	-	-	ADJ
ejpam-2055	56	13	preclosed	preclosed	ADJ
ejpam-2055	56	14	,	,	PUNCT
ejpam-2055	56	15	e	e	NOUN
ejpam-2055	56	16	-	-	VERB
ejpam-2055	56	17	closed	closed	ADJ
ejpam-2055	56	18	)	)	PUNCT
ejpam-2055	56	19	.	.	PUNCT
ejpam-2055	56	20	remark	remark	PROPN
ejpam-2055	56	21	1	1	NUM
ejpam-2055	56	22	.	.	PUNCT
ejpam-2055	57	1	since	since	SCONJ
ejpam-2055	57	2	the	the	DET
ejpam-2055	57	3	notion	notion	NOUN
ejpam-2055	57	4	of	of	ADP
ejpam-2055	57	5	δ−	δ−	PROPN
ejpam-2055	57	6	β	β	X
ejpam-2055	57	7	-open	-open	NOUN
ejpam-2055	57	8	sets	set	NOUN
ejpam-2055	57	9	and	and	CCONJ
ejpam-2055	57	10	the	the	DET
ejpam-2055	57	11	notion	notion	NOUN
ejpam-2055	57	12	of	of	ADP
ejpam-2055	57	13	e∗-open	e∗-open	ADJ
ejpam-2055	57	14	sets	set	NOUN
ejpam-2055	57	15	are	be	AUX
ejpam-2055	57	16	same	same	ADJ
ejpam-2055	57	17	,	,	PUNCT
ejpam-2055	57	18	we	we	PRON
ejpam-2055	57	19	will	will	AUX
ejpam-2055	57	20	use	use	VERB
ejpam-2055	57	21	the	the	DET
ejpam-2055	57	22	term	term	NOUN
ejpam-2055	57	23	δ−	δ−	PROPN
ejpam-2055	57	24	β	β	X
ejpam-2055	57	25	-open	-open	PROPN
ejpam-2055	57	26	sets	set	NOUN
ejpam-2055	57	27	instead	instead	ADV
ejpam-2055	57	28	of	of	ADP
ejpam-2055	57	29	e∗-open	e∗-open	ADJ
ejpam-2055	57	30	sets	set	NOUN
ejpam-2055	57	31	.	.	PUNCT
ejpam-2055	58	1	remark	remark	NOUN
ejpam-2055	58	2	2	2	NUM
ejpam-2055	58	3	.	.	PUNCT
ejpam-2055	58	4	erdal	erdal	PROPN
ejpam-2055	58	5	ekici	ekici	PROPN
ejpam-2055	59	1	[	[	X
ejpam-2055	59	2	8	8	NUM
ejpam-2055	59	3	]	]	PUNCT
ejpam-2055	59	4	shows	show	VERB
ejpam-2055	59	5	that	that	SCONJ
ejpam-2055	59	6	the	the	DET
ejpam-2055	59	7	notions	notion	NOUN
ejpam-2055	59	8	of	of	ADP
ejpam-2055	59	9	e	e	NOUN
ejpam-2055	59	10	-	-	ADJ
ejpam-2055	59	11	open	open	ADJ
ejpam-2055	59	12	set	set	NOUN
ejpam-2055	59	13	and	and	CCONJ
ejpam-2055	59	14	b	b	NOUN
ejpam-2055	59	15	-	-	PUNCT
ejpam-2055	59	16	open	open	ADJ
ejpam-2055	59	17	set	set	NOUN
ejpam-2055	59	18	and	and	CCONJ
ejpam-2055	59	19	the	the	DET
ejpam-2055	59	20	notions	notion	NOUN
ejpam-2055	59	21	of	of	ADP
ejpam-2055	59	22	e	e	NOUN
ejpam-2055	59	23	-	-	ADJ
ejpam-2055	59	24	open	open	ADJ
ejpam-2055	59	25	set	set	NOUN
ejpam-2055	59	26	and	and	CCONJ
ejpam-2055	59	27	β	β	X
ejpam-2055	59	28	-open	-open	NOUN
ejpam-2055	59	29	set	set	VERB
ejpam-2055	59	30	and	and	CCONJ
ejpam-2055	59	31	the	the	DET
ejpam-2055	59	32	notions	notion	NOUN
ejpam-2055	59	33	of	of	ADP
ejpam-2055	59	34	e	e	NOUN
ejpam-2055	59	35	-	-	ADJ
ejpam-2055	59	36	open	open	ADJ
ejpam-2055	59	37	set	set	NOUN
ejpam-2055	59	38	and	and	CCONJ
ejpam-2055	59	39	semiopen	semiopen	VERB
ejpam-2055	59	40	set	set	NOUN
ejpam-2055	59	41	are	be	AUX
ejpam-2055	59	42	independent	independent	ADJ
ejpam-2055	59	43	,	,	PUNCT
ejpam-2055	59	44	see	see	VERB
ejpam-2055	59	45	example	example	NOUN
ejpam-2055	59	46	(	(	PUNCT
ejpam-2055	59	47	2.6	2.6	NUM
ejpam-2055	59	48	)	)	PUNCT
ejpam-2055	60	1	[	[	X
ejpam-2055	60	2	8	8	NUM
ejpam-2055	60	3	]	]	PUNCT
ejpam-2055	60	4	.	.	PUNCT
ejpam-2055	61	1	lemma	lemma	PROPN
ejpam-2055	61	2	1	1	NUM
ejpam-2055	61	3	(	(	PUNCT
ejpam-2055	61	4	[	[	X
ejpam-2055	61	5	9	9	NUM
ejpam-2055	61	6	,	,	PUNCT
ejpam-2055	61	7	28	28	NUM
ejpam-2055	61	8	]	]	PUNCT
ejpam-2055	61	9	)	)	PUNCT
ejpam-2055	61	10	.	.	PUNCT
ejpam-2055	62	1	the	the	DET
ejpam-2055	62	2	following	follow	VERB
ejpam-2055	62	3	hold	hold	NOUN
ejpam-2055	62	4	for	for	ADP
ejpam-2055	62	5	a	a	DET
ejpam-2055	62	6	subset	subset	NOUN
ejpam-2055	62	7	a	a	PRON
ejpam-2055	62	8	of	of	ADP
ejpam-2055	62	9	a	a	DET
ejpam-2055	62	10	space	space	NOUN
ejpam-2055	62	11	x	x	NOUN
ejpam-2055	62	12	:	:	PUNCT
ejpam-2055	62	13	a.	a.	NOUN
ejpam-2055	62	14	m.	m.	PROPN
ejpam-2055	62	15	farhan	farhan	PROPN
ejpam-2055	62	16	and	and	CCONJ
ejpam-2055	62	17	x.	x.	PROPN
ejpam-2055	62	18	yang	yang	PROPN
ejpam-2055	62	19	/	/	SYM
ejpam-2055	62	20	eur	eur	PROPN
ejpam-2055	62	21	.	.	PUNCT
ejpam-2055	63	1	j.	j.	PROPN
ejpam-2055	63	2	pure	pure	PROPN
ejpam-2055	63	3	appl	appl	PROPN
ejpam-2055	63	4	.	.	PROPN
ejpam-2055	63	5	math	math	PROPN
ejpam-2055	63	6	,	,	PUNCT
ejpam-2055	63	7	8	8	NUM
ejpam-2055	63	8	(	(	PUNCT
ejpam-2055	63	9	2015	2015	NUM
ejpam-2055	63	10	)	)	PUNCT
ejpam-2055	63	11	,	,	PUNCT
ejpam-2055	63	12	185	185	NUM
ejpam-2055	63	13	-	-	SYM
ejpam-2055	63	14	200	200	NUM
ejpam-2055	63	15	187	187	NUM
ejpam-2055	63	16	a	a	PRON
ejpam-2055	63	17	)	)	PUNCT
ejpam-2055	63	18	δ−	δ−	PROPN
ejpam-2055	63	19	β	β	X
ejpam-2055	63	20	-cl(a	-cl(a	NOUN
ejpam-2055	63	21	)	)	PUNCT
ejpam-2055	63	22	=	=	PUNCT
ejpam-2055	64	1	a	a	DET
ejpam-2055	64	2	⋃	⋃	PUNCT
ejpam-2055	64	3	int(cl(δ−	int(cl(δ−	NOUN
ejpam-2055	64	4	int(a	int(a	PROPN
ejpam-2055	64	5	)	)	PUNCT
ejpam-2055	64	6	)	)	PUNCT
ejpam-2055	64	7	)	)	PUNCT
ejpam-2055	64	8	;	;	PUNCT
ejpam-2055	64	9	b	b	X
ejpam-2055	64	10	)	)	PUNCT
ejpam-2055	64	11	δ−	δ−	PROPN
ejpam-2055	64	12	β	β	X
ejpam-2055	64	13	-int(a	-int(a	PROPN
ejpam-2055	64	14	)	)	PUNCT
ejpam-2055	64	15	=	=	PUNCT
ejpam-2055	65	1	a	a	DET
ejpam-2055	65	2	⋂	⋂	PROPN
ejpam-2055	65	3	cl(int(δ−	cl(int(δ−	NOUN
ejpam-2055	65	4	β	β	X
ejpam-2055	65	5	−	−	NOUN
ejpam-2055	65	6	cl(a	cl(a	NUM
ejpam-2055	65	7	)	)	PUNCT
ejpam-2055	65	8	)	)	PUNCT
ejpam-2055	65	9	)	)	PUNCT
ejpam-2055	65	10	;	;	PUNCT
ejpam-2055	65	11	c	c	X
ejpam-2055	65	12	)	)	PUNCT
ejpam-2055	65	13	a	a	PRON
ejpam-2055	65	14	is	be	AUX
ejpam-2055	65	15	δ−	δ−	PROPN
ejpam-2055	65	16	β	β	AUX
ejpam-2055	65	17	-closed	-close	VERB
ejpam-2055	65	18	if	if	SCONJ
ejpam-2055	65	19	and	and	CCONJ
ejpam-2055	65	20	only	only	ADV
ejpam-2055	65	21	if	if	SCONJ
ejpam-2055	65	22	a	a	DET
ejpam-2055	65	23	=	=	NOUN
ejpam-2055	65	24	δ−	δ−	PROPN
ejpam-2055	65	25	β	β	X
ejpam-2055	65	26	-cl(a	-cl(a	NUM
ejpam-2055	65	27	)	)	PUNCT
ejpam-2055	65	28	;	;	PUNCT
ejpam-2055	65	29	d	d	X
ejpam-2055	65	30	)	)	PUNCT
ejpam-2055	65	31	δ−	δ−	PROPN
ejpam-2055	65	32	β	β	X
ejpam-2055	65	33	-cl(a	-cl(a	NUM
ejpam-2055	65	34	)	)	PUNCT
ejpam-2055	65	35	is	be	AUX
ejpam-2055	65	36	δ−	δ−	PROPN
ejpam-2055	65	37	β	β	X
ejpam-2055	65	38	-closed	-close	VERB
ejpam-2055	65	39	;	;	PUNCT
ejpam-2055	65	40	e	e	X
ejpam-2055	65	41	)	)	PUNCT
ejpam-2055	65	42	x\	x\	NOUN
ejpam-2055	66	1	δ−	δ−	PROPN
ejpam-2055	66	2	β	β	X
ejpam-2055	66	3	-cl(a	-cl(a	NOUN
ejpam-2055	66	4	)	)	PUNCT
ejpam-2055	66	5	=	=	NOUN
ejpam-2055	66	6	δ−	δ−	PROPN
ejpam-2055	66	7	β	β	X
ejpam-2055	66	8	-int(x\a	-int(x\a	PROPN
ejpam-2055	66	9	)	)	PUNCT
ejpam-2055	66	10	;	;	PUNCT
ejpam-2055	66	11	f	f	X
ejpam-2055	66	12	)	)	PUNCT
ejpam-2055	66	13	x	x	SYM
ejpam-2055	66	14	∈	∈	PROPN
ejpam-2055	66	15	δ−	δ−	VERB
ejpam-2055	66	16	β	β	X
ejpam-2055	66	17	−	−	NOUN
ejpam-2055	66	18	cl(a	cl(a	PUNCT
ejpam-2055	66	19	)	)	PUNCT
ejpam-2055	66	20	if	if	SCONJ
ejpam-2055	66	21	a	a	DET
ejpam-2055	66	22	⋂	⋂	PROPN
ejpam-2055	66	23	u	u	NOUN
ejpam-2055	66	24	6=	6=	PROPN
ejpam-2055	66	25	φ	φ	PROPN
ejpam-2055	66	26	for	for	ADP
ejpam-2055	66	27	every	every	DET
ejpam-2055	66	28	δ−	δ−	PROPN
ejpam-2055	66	29	β	β	X
ejpam-2055	66	30	-open	-open	NOUN
ejpam-2055	66	31	set	set	VERB
ejpam-2055	66	32	u	u	NOUN
ejpam-2055	66	33	containing	contain	VERB
ejpam-2055	66	34	x.	x.	NOUN
ejpam-2055	66	35	remark	remark	NOUN
ejpam-2055	66	36	3	3	NUM
ejpam-2055	66	37	.	.	PUNCT
ejpam-2055	66	38	from	from	ADP
ejpam-2055	66	39	above	above	ADP
ejpam-2055	66	40	definitions	definition	NOUN
ejpam-2055	66	41	we	we	PRON
ejpam-2055	66	42	have	have	VERB
ejpam-2055	66	43	the	the	DET
ejpam-2055	66	44	following	follow	VERB
ejpam-2055	66	45	diagram	diagram	NOUN
ejpam-2055	66	46	in	in	ADP
ejpam-2055	66	47	which	which	PRON
ejpam-2055	66	48	the	the	DET
ejpam-2055	66	49	converses	converse	NOUN
ejpam-2055	66	50	of	of	ADP
ejpam-2055	66	51	implications	implication	NOUN
ejpam-2055	66	52	need	need	AUX
ejpam-2055	66	53	not	not	PART
ejpam-2055	66	54	be	be	AUX
ejpam-2055	66	55	true	true	ADJ
ejpam-2055	66	56	,	,	PUNCT
ejpam-2055	66	57	see	see	VERB
ejpam-2055	66	58	the	the	DET
ejpam-2055	66	59	examples	example	NOUN
ejpam-2055	66	60	in	in	ADP
ejpam-2055	66	61	[	[	X
ejpam-2055	66	62	8	8	NUM
ejpam-2055	66	63	,	,	PUNCT
ejpam-2055	66	64	9	9	NUM
ejpam-2055	66	65	,	,	PUNCT
ejpam-2055	66	66	28	28	NUM
ejpam-2055	66	67	]	]	PUNCT
ejpam-2055	66	68	.	.	PUNCT
ejpam-2055	67	1	figure	figure	NOUN
ejpam-2055	67	2	1	1	NUM
ejpam-2055	67	3	:	:	PUNCT
ejpam-2055	67	4	the	the	DET
ejpam-2055	67	5	relationships	relationship	NOUN
ejpam-2055	67	6	among	among	ADP
ejpam-2055	67	7	some	some	DET
ejpam-2055	67	8	well	well	ADV
ejpam-2055	67	9	-	-	PUNCT
ejpam-2055	67	10	known	know	VERB
ejpam-2055	67	11	generalized	generalize	VERB
ejpam-2055	67	12	open	open	ADJ
ejpam-2055	67	13	sets	set	NOUN
ejpam-2055	67	14	in	in	ADP
ejpam-2055	67	15	topological	topological	ADJ
ejpam-2055	67	16	spaces	space	NOUN
ejpam-2055	67	17	3	3	X
ejpam-2055	67	18	.	.	PUNCT
ejpam-2055	67	19	strong	strong	ADJ
ejpam-2055	67	20	forms	form	NOUN
ejpam-2055	67	21	of	of	ADP
ejpam-2055	67	22	δ−	δ−	PROPN
ejpam-2055	67	23	β	β	NOUN
ejpam-2055	67	24	-	-	ADJ
ejpam-2055	67	25	open	open	ADJ
ejpam-2055	67	26	sets	set	NOUN
ejpam-2055	67	27	in	in	ADP
ejpam-2055	67	28	this	this	DET
ejpam-2055	67	29	section	section	NOUN
ejpam-2055	67	30	we	we	PRON
ejpam-2055	67	31	introduce	introduce	VERB
ejpam-2055	67	32	two	two	NUM
ejpam-2055	67	33	new	new	ADJ
ejpam-2055	67	34	strong	strong	ADJ
ejpam-2055	67	35	forms	form	NOUN
ejpam-2055	67	36	of	of	ADP
ejpam-2055	67	37	δ−β	δ−β	ADJ
ejpam-2055	67	38	-open	-open	ADJ
ejpam-2055	67	39	sets	set	NOUN
ejpam-2055	67	40	,	,	PUNCT
ejpam-2055	67	41	called	call	VERB
ejpam-2055	67	42	δ−β	δ−β	ADJ
ejpam-2055	67	43	-regular	-regular	ADJ
ejpam-2055	67	44	sets	set	NOUN
ejpam-2055	67	45	and	and	CCONJ
ejpam-2055	67	46	δ	δ	NOUN
ejpam-2055	67	47	−	−	PROPN
ejpam-2055	67	48	βθ	βθ	INTJ
ejpam-2055	67	49	-open	-open	ADJ
ejpam-2055	67	50	sets	set	NOUN
ejpam-2055	67	51	.	.	PUNCT
ejpam-2055	68	1	by	by	ADP
ejpam-2055	68	2	using	use	VERB
ejpam-2055	68	3	these	these	DET
ejpam-2055	68	4	sets	set	NOUN
ejpam-2055	68	5	we	we	PRON
ejpam-2055	68	6	introduce	introduce	VERB
ejpam-2055	68	7	a	a	DET
ejpam-2055	68	8	several	several	ADJ
ejpam-2055	68	9	characterizations	characterization	NOUN
ejpam-2055	68	10	of	of	ADP
ejpam-2055	68	11	δ−	δ−	PROPN
ejpam-2055	68	12	β	β	X
ejpam-2055	68	13	-open	-open	NOUN
ejpam-2055	68	14	sets	set	NOUN
ejpam-2055	68	15	and	and	CCONJ
ejpam-2055	68	16	their	their	PRON
ejpam-2055	68	17	properties	property	NOUN
ejpam-2055	68	18	.	.	PUNCT
ejpam-2055	69	1	definition	definition	NOUN
ejpam-2055	69	2	1	1	NUM
ejpam-2055	69	3	.	.	PUNCT
ejpam-2055	70	1	a	a	DET
ejpam-2055	70	2	subset	subset	NOUN
ejpam-2055	70	3	a	a	PRON
ejpam-2055	70	4	of	of	ADP
ejpam-2055	70	5	a	a	DET
ejpam-2055	70	6	topological	topological	ADJ
ejpam-2055	70	7	space	space	NOUN
ejpam-2055	70	8	x	x	PUNCT
ejpam-2055	70	9	is	be	AUX
ejpam-2055	70	10	δ−	δ−	PROPN
ejpam-2055	70	11	β	β	SYM
ejpam-2055	70	12	-regular	-regular	ADJ
ejpam-2055	70	13	if	if	SCONJ
ejpam-2055	70	14	it	it	PRON
ejpam-2055	70	15	is	be	AUX
ejpam-2055	70	16	δ−	δ−	PROPN
ejpam-2055	70	17	β	β	PUNCT
ejpam-2055	70	18	-open	-open	ADJ
ejpam-2055	70	19	and	and	CCONJ
ejpam-2055	70	20	δ−	δ−	PROPN
ejpam-2055	70	21	β	β	PROPN
ejpam-2055	70	22	closed	close	VERB
ejpam-2055	70	23	.	.	PUNCT
ejpam-2055	71	1	the	the	DET
ejpam-2055	71	2	family	family	NOUN
ejpam-2055	71	3	of	of	ADP
ejpam-2055	71	4	all	all	PRON
ejpam-2055	71	5	δ−	δ−	PROPN
ejpam-2055	71	6	β	β	SYM
ejpam-2055	71	7	-regular	-regular	ADJ
ejpam-2055	71	8	subsets	subset	NOUN
ejpam-2055	71	9	of	of	ADP
ejpam-2055	71	10	x	x	PUNCT
ejpam-2055	71	11	containing	contain	VERB
ejpam-2055	71	12	a	a	DET
ejpam-2055	71	13	point	point	NOUN
ejpam-2055	71	14	x	x	SYM
ejpam-2055	71	15	∈	∈	NOUN
ejpam-2055	71	16	x	x	PUNCT
ejpam-2055	71	17	is	be	AUX
ejpam-2055	71	18	denoted	denote	VERB
ejpam-2055	71	19	by	by	ADP
ejpam-2055	71	20	δ−	δ−	PROPN
ejpam-2055	71	21	βr(x	βr(x	NUM
ejpam-2055	71	22	,	,	PUNCT
ejpam-2055	71	23	x	x	NOUN
ejpam-2055	71	24	)	)	PUNCT
ejpam-2055	71	25	,	,	PUNCT
ejpam-2055	71	26	the	the	DET
ejpam-2055	71	27	family	family	NOUN
ejpam-2055	71	28	of	of	ADP
ejpam-2055	71	29	all	all	DET
ejpam-2055	71	30	δ−	δ−	PROPN
ejpam-2055	71	31	β	β	SYM
ejpam-2055	71	32	-regular	-regular	ADJ
ejpam-2055	71	33	sets	set	NOUN
ejpam-2055	71	34	in	in	ADP
ejpam-2055	71	35	x	x	PUNCT
ejpam-2055	71	36	denoted	denote	VERB
ejpam-2055	71	37	by	by	ADP
ejpam-2055	71	38	δ−	δ−	PROPN
ejpam-2055	71	39	βr(x	βr(x	PROPN
ejpam-2055	71	40	,	,	PUNCT
ejpam-2055	71	41	t	t	PROPN
ejpam-2055	71	42	)	)	PUNCT
ejpam-2055	71	43	.	.	PUNCT
ejpam-2055	72	1	definition	definition	NOUN
ejpam-2055	72	2	2	2	NUM
ejpam-2055	72	3	.	.	PUNCT
ejpam-2055	72	4	a	a	DET
ejpam-2055	72	5	point	point	NOUN
ejpam-2055	72	6	x	x	PUNCT
ejpam-2055	72	7	of	of	ADP
ejpam-2055	72	8	x	x	PROPN
ejpam-2055	72	9	is	be	AUX
ejpam-2055	72	10	called	call	VERB
ejpam-2055	72	11	a	a	DET
ejpam-2055	72	12	δ	δ	NOUN
ejpam-2055	73	1	−	−	NOUN
ejpam-2055	74	1	βθ	βθ	ADP
ejpam-2055	75	1	-cluster	-cluster	NOUN
ejpam-2055	75	2	point	point	NOUN
ejpam-2055	75	3	of	of	ADP
ejpam-2055	75	4	a	a	DET
ejpam-2055	75	5	if	if	SCONJ
ejpam-2055	75	6	δ	δ	PROPN
ejpam-2055	75	7	−	−	NOUN
ejpam-2055	75	8	β	β	X
ejpam-2055	75	9	−	−	NOUN
ejpam-2055	75	10	cl(u	cl(u	PROPN
ejpam-2055	75	11	)	)	PUNCT
ejpam-2055	75	12	⋂	⋂	PROPN
ejpam-2055	75	13	a	a	PRON
ejpam-2055	75	14	6=	6=	ADP
ejpam-2055	75	15	φ	φ	NOUN
ejpam-2055	75	16	for	for	ADP
ejpam-2055	75	17	every	every	DET
ejpam-2055	75	18	u	u	PROPN
ejpam-2055	75	19	∈	∈	PROPN
ejpam-2055	75	20	δ	δ	PROPN
ejpam-2055	75	21	−	−	NOUN
ejpam-2055	75	22	βς(x	βς(x	PUNCT
ejpam-2055	75	23	,	,	PUNCT
ejpam-2055	75	24	x	x	X
ejpam-2055	75	25	)	)	PUNCT
ejpam-2055	75	26	.	.	PUNCT
ejpam-2055	76	1	the	the	DET
ejpam-2055	76	2	set	set	NOUN
ejpam-2055	76	3	of	of	ADP
ejpam-2055	76	4	all	all	DET
ejpam-2055	76	5	δ	δ	NOUN
ejpam-2055	76	6	−	−	NOUN
ejpam-2055	76	7	βθ	βθ	VERB
ejpam-2055	76	8	-cluster	-cluster	NOUN
ejpam-2055	76	9	points	point	NOUN
ejpam-2055	76	10	of	of	ADP
ejpam-2055	76	11	a	a	PRON
ejpam-2055	76	12	is	be	AUX
ejpam-2055	76	13	called	call	VERB
ejpam-2055	76	14	δ	δ	NOUN
ejpam-2055	76	15	−	−	NOUN
ejpam-2055	76	16	βθ	βθ	INTJ
ejpam-2055	76	17	-closure	-closure	NOUN
ejpam-2055	76	18	of	of	ADP
ejpam-2055	76	19	a	a	PRON
ejpam-2055	76	20	and	and	CCONJ
ejpam-2055	76	21	is	be	AUX
ejpam-2055	76	22	denoted	denote	VERB
ejpam-2055	76	23	by	by	ADP
ejpam-2055	76	24	δ−	δ−	PROPN
ejpam-2055	76	25	β	β	X
ejpam-2055	76	26	-clθ	-clθ	X
ejpam-2055	76	27	(	(	PUNCT
ejpam-2055	76	28	a	a	NOUN
ejpam-2055	76	29	)	)	PUNCT
ejpam-2055	76	30	.	.	PUNCT
ejpam-2055	77	1	a	a	DET
ejpam-2055	77	2	subset	subset	NOUN
ejpam-2055	77	3	a	a	PRON
ejpam-2055	77	4	is	be	AUX
ejpam-2055	77	5	said	say	VERB
ejpam-2055	77	6	to	to	PART
ejpam-2055	77	7	be	be	AUX
ejpam-2055	77	8	δ−	δ−	PROPN
ejpam-2055	77	9	βθ	βθ	AUX
ejpam-2055	77	10	-closed	-close	VERB
ejpam-2055	77	11	if	if	SCONJ
ejpam-2055	77	12	a	a	DET
ejpam-2055	77	13	=	=	NOUN
ejpam-2055	77	14	δ−	δ−	PROPN
ejpam-2055	77	15	β	β	X
ejpam-2055	77	16	-clθ	-clθ	X
ejpam-2055	77	17	(	(	PUNCT
ejpam-2055	77	18	a	a	NOUN
ejpam-2055	77	19	)	)	PUNCT
ejpam-2055	77	20	.	.	PUNCT
ejpam-2055	78	1	the	the	DET
ejpam-2055	78	2	complement	complement	NOUN
ejpam-2055	78	3	of	of	ADP
ejpam-2055	78	4	a	a	DET
ejpam-2055	78	5	δ−	δ−	PROPN
ejpam-2055	78	6	βθ	βθ	ADP
ejpam-2055	78	7	-closed	-closed	ADJ
ejpam-2055	78	8	set	set	NOUN
ejpam-2055	78	9	is	be	AUX
ejpam-2055	78	10	said	say	VERB
ejpam-2055	78	11	to	to	PART
ejpam-2055	78	12	be	be	AUX
ejpam-2055	78	13	δ−	δ−	PROPN
ejpam-2055	78	14	βθ	βθ	ADP
ejpam-2055	78	15	-open	-open	PROPN
ejpam-2055	78	16	.	.	PUNCT
ejpam-2055	79	1	remark	remark	PROPN
ejpam-2055	79	2	4	4	NUM
ejpam-2055	79	3	.	.	PUNCT
ejpam-2055	80	1	the	the	DET
ejpam-2055	80	2	union	union	NOUN
ejpam-2055	80	3	of	of	ADP
ejpam-2055	80	4	two	two	NUM
ejpam-2055	80	5	δ−βθ	δ−βθ	NOUN
ejpam-2055	80	6	-closed	-close	VERB
ejpam-2055	80	7	sets	set	NOUN
ejpam-2055	80	8	is	be	AUX
ejpam-2055	80	9	not	not	PART
ejpam-2055	80	10	necessarily	necessarily	ADV
ejpam-2055	80	11	δ−βθ	δ−βθ	AUX
ejpam-2055	80	12	-closed	-close	VERB
ejpam-2055	80	13	as	as	SCONJ
ejpam-2055	80	14	shown	show	VERB
ejpam-2055	80	15	by	by	ADP
ejpam-2055	80	16	the	the	DET
ejpam-2055	80	17	following	follow	VERB
ejpam-2055	80	18	example	example	NOUN
ejpam-2055	80	19	:	:	PUNCT
ejpam-2055	80	20	example	example	NOUN
ejpam-2055	80	21	1	1	X
ejpam-2055	80	22	.	.	PUNCT
ejpam-2055	81	1	let	let	VERB
ejpam-2055	81	2	x	x	PUNCT
ejpam-2055	81	3	=	=	PUNCT
ejpam-2055	81	4	{	{	PUNCT
ejpam-2055	81	5	1,2,3	1,2,3	NUM
ejpam-2055	81	6	}	}	PUNCT
ejpam-2055	81	7	,	,	PUNCT
ejpam-2055	81	8	define	define	VERB
ejpam-2055	81	9	a	a	DET
ejpam-2055	81	10	topology	topology	NOUN
ejpam-2055	81	11	t=	t=	NOUN
ejpam-2055	81	12	{	{	PUNCT
ejpam-2055	81	13	φ	φ	PROPN
ejpam-2055	81	14	,	,	PUNCT
ejpam-2055	81	15	x	x	INTJ
ejpam-2055	81	16	,	,	PUNCT
ejpam-2055	81	17	{	{	PUNCT
ejpam-2055	81	18	1	1	NUM
ejpam-2055	81	19	}	}	PUNCT
ejpam-2055	81	20	,	,	PUNCT
ejpam-2055	81	21	{	{	PUNCT
ejpam-2055	81	22	2	2	NUM
ejpam-2055	81	23	}	}	PUNCT
ejpam-2055	81	24	,	,	PUNCT
ejpam-2055	81	25	{	{	PUNCT
ejpam-2055	81	26	1,2	1,2	NUM
ejpam-2055	81	27	}	}	PUNCT
ejpam-2055	81	28	}	}	PUNCT
ejpam-2055	81	29	on	on	ADP
ejpam-2055	81	30	x.	x.	NOUN
ejpam-2055	81	31	the	the	DET
ejpam-2055	81	32	subsets	subset	NOUN
ejpam-2055	81	33	{	{	PUNCT
ejpam-2055	81	34	1	1	NUM
ejpam-2055	81	35	}	}	PUNCT
ejpam-2055	81	36	and	and	CCONJ
ejpam-2055	81	37	{	{	PUNCT
ejpam-2055	81	38	2	2	X
ejpam-2055	81	39	}	}	PUNCT
ejpam-2055	81	40	are	be	AUX
ejpam-2055	81	41	δ−	δ−	PROPN
ejpam-2055	81	42	βθ	βθ	AUX
ejpam-2055	81	43	-closed	-close	VERB
ejpam-2055	81	44	in	in	ADP
ejpam-2055	81	45	(	(	PUNCT
ejpam-2055	81	46	x	x	NOUN
ejpam-2055	81	47	,	,	PUNCT
ejpam-2055	81	48	t	t	PROPN
ejpam-2055	81	49	)	)	PUNCT
ejpam-2055	81	50	but	but	CCONJ
ejpam-2055	81	51	{	{	PUNCT
ejpam-2055	81	52	1,2	1,2	NUM
ejpam-2055	81	53	}	}	PUNCT
ejpam-2055	81	54	is	be	AUX
ejpam-2055	81	55	not	not	PART
ejpam-2055	81	56	δ−	δ−	ADJ
ejpam-2055	81	57	βθ	βθ	AUX
ejpam-2055	81	58	-closed	-closed	ADJ
ejpam-2055	81	59	.	.	PUNCT
ejpam-2055	82	1	a.	a.	NOUN
ejpam-2055	82	2	m.	m.	PROPN
ejpam-2055	82	3	farhan	farhan	PROPN
ejpam-2055	82	4	and	and	CCONJ
ejpam-2055	82	5	x.	x.	PROPN
ejpam-2055	82	6	yang	yang	PROPN
ejpam-2055	82	7	/	/	SYM
ejpam-2055	82	8	eur	eur	PROPN
ejpam-2055	82	9	.	.	PUNCT
ejpam-2055	83	1	j.	j.	PROPN
ejpam-2055	83	2	pure	pure	PROPN
ejpam-2055	83	3	appl	appl	PROPN
ejpam-2055	83	4	.	.	PROPN
ejpam-2055	83	5	math	math	PROPN
ejpam-2055	83	6	,	,	PUNCT
ejpam-2055	83	7	8	8	NUM
ejpam-2055	83	8	(	(	PUNCT
ejpam-2055	83	9	2015	2015	NUM
ejpam-2055	83	10	)	)	PUNCT
ejpam-2055	83	11	,	,	PUNCT
ejpam-2055	83	12	185	185	NUM
ejpam-2055	83	13	-	-	SYM
ejpam-2055	83	14	200	200	NUM
ejpam-2055	83	15	188	188	NUM
ejpam-2055	83	16	remark	remark	NOUN
ejpam-2055	83	17	5	5	NUM
ejpam-2055	83	18	.	.	PUNCT
ejpam-2055	84	1	it	it	PRON
ejpam-2055	84	2	can	can	AUX
ejpam-2055	84	3	be	be	AUX
ejpam-2055	84	4	easily	easily	ADV
ejpam-2055	84	5	shown	show	VERB
ejpam-2055	84	6	that	that	SCONJ
ejpam-2055	84	7	δ	δ	PROPN
ejpam-2055	84	8	−	−	NOUN
ejpam-2055	84	9	β	β	SYM
ejpam-2055	84	10	-regular	-regular	ADJ
ejpam-2055	84	11	⇒	⇒	NOUN
ejpam-2055	84	12	δ	δ	PROPN
ejpam-2055	84	13	−	−	NOUN
ejpam-2055	84	14	βθ	βθ	AUX
ejpam-2055	84	15	-open	-open	ADJ
ejpam-2055	84	16	⇒	⇒	NOUN
ejpam-2055	84	17	δ	δ	PROPN
ejpam-2055	84	18	−	−	NOUN
ejpam-2055	84	19	β	β	X
ejpam-2055	84	20	-open	-open	PROPN
ejpam-2055	84	21	.	.	PUNCT
ejpam-2055	85	1	but	but	CCONJ
ejpam-2055	85	2	the	the	DET
ejpam-2055	85	3	converses	converse	NOUN
ejpam-2055	85	4	are	be	AUX
ejpam-2055	85	5	not	not	PART
ejpam-2055	85	6	necessarily	necessarily	ADV
ejpam-2055	85	7	true	true	ADJ
ejpam-2055	85	8	as	as	SCONJ
ejpam-2055	85	9	shown	show	VERB
ejpam-2055	85	10	by	by	ADP
ejpam-2055	85	11	the	the	DET
ejpam-2055	85	12	following	follow	VERB
ejpam-2055	85	13	examples	example	NOUN
ejpam-2055	85	14	:	:	PUNCT
ejpam-2055	85	15	example	example	NOUN
ejpam-2055	86	1	2	2	X
ejpam-2055	86	2	.	.	PUNCT
ejpam-2055	87	1	let	let	VERB
ejpam-2055	87	2	x	x	PUNCT
ejpam-2055	87	3	=	=	PUNCT
ejpam-2055	87	4	{	{	PUNCT
ejpam-2055	87	5	1,2,3	1,2,3	NUM
ejpam-2055	87	6	}	}	PUNCT
ejpam-2055	87	7	,	,	PUNCT
ejpam-2055	87	8	define	define	VERB
ejpam-2055	87	9	a	a	DET
ejpam-2055	87	10	topology	topology	NOUN
ejpam-2055	87	11	t=	t=	NOUN
ejpam-2055	87	12	{	{	PUNCT
ejpam-2055	87	13	φ	φ	PROPN
ejpam-2055	87	14	,	,	PUNCT
ejpam-2055	87	15	x	x	INTJ
ejpam-2055	87	16	,	,	PUNCT
ejpam-2055	87	17	{	{	PUNCT
ejpam-2055	87	18	1	1	NUM
ejpam-2055	87	19	}	}	PUNCT
ejpam-2055	87	20	,	,	PUNCT
ejpam-2055	87	21	{	{	PUNCT
ejpam-2055	87	22	2	2	NUM
ejpam-2055	87	23	}	}	PUNCT
ejpam-2055	87	24	,	,	PUNCT
ejpam-2055	87	25	{	{	PUNCT
ejpam-2055	87	26	1,2	1,2	NUM
ejpam-2055	87	27	}	}	PUNCT
ejpam-2055	87	28	}	}	PUNCT
ejpam-2055	87	29	on	on	ADP
ejpam-2055	87	30	x.	x.	NOUN
ejpam-2055	87	31	the	the	DET
ejpam-2055	87	32	subsets	subset	NOUN
ejpam-2055	87	33	{	{	PUNCT
ejpam-2055	87	34	1,2	1,2	NUM
ejpam-2055	87	35	}	}	PUNCT
ejpam-2055	87	36	is	be	AUX
ejpam-2055	87	37	δ−	δ−	PROPN
ejpam-2055	87	38	βθ	βθ	AUX
ejpam-2055	87	39	-open	-open	VERB
ejpam-2055	87	40	in	in	ADP
ejpam-2055	87	41	x	x	X
ejpam-2055	87	42	but	but	CCONJ
ejpam-2055	87	43	not	not	PART
ejpam-2055	87	44	δ−	δ−	PROPN
ejpam-2055	87	45	β	β	X
ejpam-2055	87	46	-regular	-regular	PROPN
ejpam-2055	87	47	.	.	PUNCT
ejpam-2055	87	48	example	example	NOUN
ejpam-2055	88	1	3	3	X
ejpam-2055	88	2	.	.	PUNCT
ejpam-2055	88	3	let	let	VERB
ejpam-2055	88	4	x	x	PUNCT
ejpam-2055	88	5	=	=	PUNCT
ejpam-2055	88	6	{	{	PUNCT
ejpam-2055	88	7	1,2,3,4,5	1,2,3,4,5	NUM
ejpam-2055	88	8	}	}	PUNCT
ejpam-2055	88	9	,	,	PUNCT
ejpam-2055	88	10	define	define	VERB
ejpam-2055	88	11	a	a	DET
ejpam-2055	88	12	topology	topology	NOUN
ejpam-2055	88	13	t=	t=	NOUN
ejpam-2055	88	14	{	{	PUNCT
ejpam-2055	88	15	φ	φ	PROPN
ejpam-2055	88	16	,	,	PUNCT
ejpam-2055	88	17	x	x	INTJ
ejpam-2055	88	18	,	,	PUNCT
ejpam-2055	88	19	{	{	PUNCT
ejpam-2055	88	20	1	1	NUM
ejpam-2055	88	21	}	}	PUNCT
ejpam-2055	88	22	,	,	PUNCT
ejpam-2055	88	23	{	{	PUNCT
ejpam-2055	88	24	3	3	NUM
ejpam-2055	88	25	}	}	PUNCT
ejpam-2055	88	26	,	,	PUNCT
ejpam-2055	88	27	{	{	PUNCT
ejpam-2055	88	28	1,3	1,3	NUM
ejpam-2055	88	29	}	}	PUNCT
ejpam-2055	88	30	,	,	PUNCT
ejpam-2055	88	31	{	{	PUNCT
ejpam-2055	88	32	3,4	3,4	NUM
ejpam-2055	88	33	{	{	PUNCT
ejpam-2055	88	34	1,3,4	1,3,4	NUM
ejpam-2055	88	35	}	}	PUNCT
ejpam-2055	88	36	}	}	PUNCT
ejpam-2055	88	37	on	on	ADP
ejpam-2055	88	38	x.then	x.then	X
ejpam-2055	89	1	the	the	DET
ejpam-2055	89	2	subsets	subset	NOUN
ejpam-2055	89	3	{	{	PUNCT
ejpam-2055	89	4	1	1	NUM
ejpam-2055	89	5	}	}	PUNCT
ejpam-2055	89	6	is	be	AUX
ejpam-2055	89	7	δ−	δ−	PROPN
ejpam-2055	89	8	β	β	PART
ejpam-2055	89	9	-open	-open	VERB
ejpam-2055	89	10	in	in	ADP
ejpam-2055	89	11	x	x	X
ejpam-2055	89	12	but	but	CCONJ
ejpam-2055	89	13	not	not	PART
ejpam-2055	89	14	δ−	δ−	PROPN
ejpam-2055	89	15	βθ	βθ	ADP
ejpam-2055	89	16	-open	-open	VERB
ejpam-2055	89	17	.	.	PUNCT
ejpam-2055	90	1	the	the	DET
ejpam-2055	90	2	following	follow	VERB
ejpam-2055	90	3	interesting	interesting	ADJ
ejpam-2055	90	4	results	result	NOUN
ejpam-2055	90	5	will	will	AUX
ejpam-2055	90	6	play	play	VERB
ejpam-2055	90	7	an	an	DET
ejpam-2055	90	8	important	important	ADJ
ejpam-2055	90	9	role	role	NOUN
ejpam-2055	90	10	in	in	ADP
ejpam-2055	90	11	the	the	DET
ejpam-2055	90	12	sequel	sequel	NOUN
ejpam-2055	90	13	.	.	PUNCT
ejpam-2055	91	1	theorem	theorem	NOUN
ejpam-2055	91	2	1	1	NUM
ejpam-2055	91	3	.	.	PUNCT
ejpam-2055	92	1	the	the	DET
ejpam-2055	92	2	following	follow	VERB
ejpam-2055	92	3	properties	property	NOUN
ejpam-2055	92	4	hold	hold	VERB
ejpam-2055	92	5	for	for	ADP
ejpam-2055	92	6	a	a	DET
ejpam-2055	92	7	subset	subset	NOUN
ejpam-2055	92	8	a	a	PRON
ejpam-2055	92	9	of	of	ADP
ejpam-2055	92	10	a	a	DET
ejpam-2055	92	11	topological	topological	ADJ
ejpam-2055	92	12	space	space	NOUN
ejpam-2055	92	13	(	(	PUNCT
ejpam-2055	92	14	x	x	X
ejpam-2055	92	15	,	,	PUNCT
ejpam-2055	92	16	t	t	PROPN
ejpam-2055	92	17	):	):	PUNCT
ejpam-2055	92	18	a	a	X
ejpam-2055	92	19	)	)	PUNCT
ejpam-2055	92	20	a∈	a∈	PROPN
ejpam-2055	92	21	δ−	δ−	PROPN
ejpam-2055	92	22	βς(x	βς(x	PUNCT
ejpam-2055	92	23	,	,	PUNCT
ejpam-2055	92	24	t	t	PROPN
ejpam-2055	92	25	)	)	PUNCT
ejpam-2055	92	26	if	if	SCONJ
ejpam-2055	92	27	and	and	CCONJ
ejpam-2055	92	28	only	only	ADV
ejpam-2055	92	29	if	if	SCONJ
ejpam-2055	92	30	δ−	δ−	PROPN
ejpam-2055	92	31	β	β	X
ejpam-2055	92	32	-cl(a	-cl(a	X
ejpam-2055	92	33	)	)	PUNCT
ejpam-2055	92	34	∈	∈	PROPN
ejpam-2055	92	35	δ−	δ−	PROPN
ejpam-2055	92	36	βr(x	βr(x	NUM
ejpam-2055	92	37	,	,	PUNCT
ejpam-2055	92	38	t	t	PROPN
ejpam-2055	92	39	)	)	PUNCT
ejpam-2055	92	40	;	;	PUNCT
ejpam-2055	92	41	b	b	X
ejpam-2055	92	42	)	)	PUNCT
ejpam-2055	92	43	a∈	a∈	PROPN
ejpam-2055	92	44	δ−	δ−	PROPN
ejpam-2055	92	45	βc(x	βc(x	NUM
ejpam-2055	92	46	,	,	PUNCT
ejpam-2055	92	47	t	t	PROPN
ejpam-2055	92	48	)	)	PUNCT
ejpam-2055	93	1	if	if	SCONJ
ejpam-2055	93	2	and	and	CCONJ
ejpam-2055	93	3	only	only	ADV
ejpam-2055	93	4	if	if	SCONJ
ejpam-2055	93	5	δ−	δ−	PROPN
ejpam-2055	93	6	β	β	X
ejpam-2055	93	7	-int(a	-int(a	PROPN
ejpam-2055	93	8	)	)	PUNCT
ejpam-2055	93	9	∈	∈	PROPN
ejpam-2055	93	10	δ−	δ−	PROPN
ejpam-2055	93	11	βr(x	βr(x	NUM
ejpam-2055	93	12	,	,	PUNCT
ejpam-2055	93	13	t	t	PROPN
ejpam-2055	93	14	)	)	PUNCT
ejpam-2055	93	15	.	.	PUNCT
ejpam-2055	94	1	proof	proof	NOUN
ejpam-2055	94	2	.	.	PUNCT
ejpam-2055	95	1	a	a	PRON
ejpam-2055	95	2	)	)	PUNCT
ejpam-2055	95	3	.	.	PUNCT
ejpam-2055	96	1	(	(	PUNCT
ejpam-2055	96	2	necessity	necessity	NOUN
ejpam-2055	96	3	)	)	PUNCT
ejpam-2055	96	4	let	let	VERB
ejpam-2055	96	5	a	a	DET
ejpam-2055	96	6	∈	∈	PROPN
ejpam-2055	96	7	δ	δ	NOUN
ejpam-2055	96	8	−	−	NOUN
ejpam-2055	96	9	βς(x	βς(x	PUNCT
ejpam-2055	96	10	,	,	PUNCT
ejpam-2055	96	11	t	t	PROPN
ejpam-2055	96	12	)	)	PUNCT
ejpam-2055	96	13	,	,	PUNCT
ejpam-2055	96	14	then	then	ADV
ejpam-2055	96	15	we	we	PRON
ejpam-2055	96	16	have	have	VERB
ejpam-2055	96	17	a	a	DET
ejpam-2055	96	18	⊂	⊂	PROPN
ejpam-2055	96	19	cl(int(δ	cl(int(δ	NOUN
ejpam-2055	96	20	−	−	PROPN
ejpam-2055	96	21	cl(a	cl(a	NUM
ejpam-2055	96	22	)	)	PUNCT
ejpam-2055	96	23	)	)	PUNCT
ejpam-2055	96	24	)	)	PUNCT
ejpam-2055	97	1	and	and	CCONJ
ejpam-2055	97	2	hence	hence	ADV
ejpam-2055	97	3	δ−	δ−	PROPN
ejpam-2055	97	4	β	β	X
ejpam-2055	97	5	−	−	NOUN
ejpam-2055	97	6	cl(a	cl(a	PUNCT
ejpam-2055	97	7	)	)	PUNCT
ejpam-2055	98	1	⊂	⊂	PROPN
ejpam-2055	98	2	δ−	δ−	PROPN
ejpam-2055	98	3	β	β	X
ejpam-2055	98	4	−	−	PROPN
ejpam-2055	98	5	cl[cl(int(δ−	cl[cl(int(δ−	PROPN
ejpam-2055	98	6	cl(a	cl(a	NUM
ejpam-2055	98	7	)	)	PUNCT
ejpam-2055	98	8	)	)	PUNCT
ejpam-2055	98	9	)	)	PUNCT
ejpam-2055	98	10	]	]	PUNCT
ejpam-2055	99	1	=	=	SYM
ejpam-2055	99	2	cl(int(δ−	cl(int(δ−	NOUN
ejpam-2055	99	3	cl(a	cl(a	NUM
ejpam-2055	99	4	)	)	PUNCT
ejpam-2055	99	5	)	)	PUNCT
ejpam-2055	99	6	)	)	PUNCT
ejpam-2055	99	7	.	.	PUNCT
ejpam-2055	100	1	since	since	SCONJ
ejpam-2055	100	2	a⊂	a⊂	NOUN
ejpam-2055	100	3	δ−	δ−	PROPN
ejpam-2055	100	4	β	β	X
ejpam-2055	100	5	−	−	NOUN
ejpam-2055	100	6	cl(a	cl(a	NUM
ejpam-2055	100	7	)	)	PUNCT
ejpam-2055	100	8	,	,	PUNCT
ejpam-2055	100	9	we	we	PRON
ejpam-2055	100	10	have	have	VERB
ejpam-2055	100	11	δ−	δ−	PROPN
ejpam-2055	100	12	β	β	X
ejpam-2055	100	13	−	−	NOUN
ejpam-2055	100	14	cl(a	cl(a	PUNCT
ejpam-2055	100	15	)	)	PUNCT
ejpam-2055	100	16	⊂	⊂	PROPN
ejpam-2055	100	17	cl(int(δ−	cl(int(δ−	VERB
ejpam-2055	100	18	cl(δ−	cl(δ−	VERB
ejpam-2055	100	19	β	β	X
ejpam-2055	100	20	−	−	NOUN
ejpam-2055	100	21	cl(a	cl(a	NUM
ejpam-2055	100	22	)	)	PUNCT
ejpam-2055	100	23	)	)	PUNCT
ejpam-2055	100	24	)	)	PUNCT
ejpam-2055	100	25	)	)	PUNCT
ejpam-2055	100	26	.	.	PUNCT
ejpam-2055	101	1	this	this	PRON
ejpam-2055	101	2	shows	show	VERB
ejpam-2055	101	3	that	that	SCONJ
ejpam-2055	101	4	δ−β	δ−β	PROPN
ejpam-2055	101	5	-cl(a	-cl(a	NOUN
ejpam-2055	101	6	)	)	PUNCT
ejpam-2055	101	7	is	be	AUX
ejpam-2055	101	8	a	a	DET
ejpam-2055	101	9	δ−β	δ−β	ADJ
ejpam-2055	101	10	-open	-open	ADJ
ejpam-2055	101	11	set	set	NOUN
ejpam-2055	101	12	.	.	PUNCT
ejpam-2055	102	1	on	on	ADP
ejpam-2055	102	2	the	the	DET
ejpam-2055	102	3	other	other	ADJ
ejpam-2055	102	4	hand	hand	NOUN
ejpam-2055	102	5	,	,	PUNCT
ejpam-2055	102	6	δ−β	δ−β	PROPN
ejpam-2055	102	7	-cl(a	-cl(a	NUM
ejpam-2055	102	8	)	)	PUNCT
ejpam-2055	102	9	is	be	AUX
ejpam-2055	102	10	always	always	ADV
ejpam-2055	102	11	an	an	DET
ejpam-2055	102	12	δ−β	δ−β	ADJ
ejpam-2055	102	13	-closed	-close	VERB
ejpam-2055	102	14	set	set	NOUN
ejpam-2055	102	15	.	.	PUNCT
ejpam-2055	103	1	therefore	therefore	ADV
ejpam-2055	103	2	δ−	δ−	PROPN
ejpam-2055	103	3	β	β	X
ejpam-2055	103	4	−	−	NOUN
ejpam-2055	103	5	cl(a	cl(a	NUM
ejpam-2055	103	6	)	)	PUNCT
ejpam-2055	103	7	∈	∈	PROPN
ejpam-2055	103	8	δ−	δ−	PROPN
ejpam-2055	103	9	βr(x	βr(x	NUM
ejpam-2055	103	10	,	,	PUNCT
ejpam-2055	103	11	t	t	PROPN
ejpam-2055	103	12	)	)	PUNCT
ejpam-2055	103	13	.	.	PUNCT
ejpam-2055	104	1	(	(	PUNCT
ejpam-2055	104	2	sufficiency	sufficiency	NOUN
ejpam-2055	104	3	)	)	PUNCT
ejpam-2055	104	4	.	.	PUNCT
ejpam-2055	105	1	let	let	VERB
ejpam-2055	105	2	δ−	δ−	PROPN
ejpam-2055	105	3	β	β	X
ejpam-2055	105	4	−	−	NOUN
ejpam-2055	105	5	cl(a	cl(a	NUM
ejpam-2055	105	6	)	)	PUNCT
ejpam-2055	105	7	∈	∈	PROPN
ejpam-2055	105	8	δ−	δ−	PROPN
ejpam-2055	105	9	βr(x	βr(x	NUM
ejpam-2055	105	10	,	,	PUNCT
ejpam-2055	105	11	t	t	PROPN
ejpam-2055	105	12	)	)	PUNCT
ejpam-2055	105	13	.	.	PUNCT
ejpam-2055	106	1	then	then	ADV
ejpam-2055	106	2	we	we	PRON
ejpam-2055	106	3	have	have	VERB
ejpam-2055	106	4	a⊂	a⊂	NOUN
ejpam-2055	106	5	δ−	δ−	PROPN
ejpam-2055	106	6	β	β	X
ejpam-2055	106	7	−	−	NOUN
ejpam-2055	106	8	cl(a	cl(a	PUNCT
ejpam-2055	106	9	)	)	PUNCT
ejpam-2055	106	10	⊂	⊂	PROPN
ejpam-2055	106	11	cl(int(δ−	cl(int(δ−	VERB
ejpam-2055	106	12	cl(δ−	cl(δ−	VERB
ejpam-2055	106	13	β	β	X
ejpam-2055	106	14	−	−	NOUN
ejpam-2055	106	15	cl(a	cl(a	NUM
ejpam-2055	106	16	)	)	PUNCT
ejpam-2055	106	17	)	)	PUNCT
ejpam-2055	106	18	)	)	PUNCT
ejpam-2055	106	19	)	)	PUNCT
ejpam-2055	107	1	⊂	⊂	PROPN
ejpam-2055	107	2	cl(int(δ−	cl(int(δ−	VERB
ejpam-2055	107	3	cl(δ−	cl(δ−	PRON
ejpam-2055	107	4	cl(a	cl(a	NUM
ejpam-2055	107	5	)	)	PUNCT
ejpam-2055	107	6	)	)	PUNCT
ejpam-2055	107	7	)	)	PUNCT
ejpam-2055	107	8	)	)	PUNCT
ejpam-2055	108	1	=	=	NOUN
ejpam-2055	108	2	cl(int(δ−	cl(int(δ−	NOUN
ejpam-2055	108	3	cl(a	cl(a	NUM
ejpam-2055	108	4	)	)	PUNCT
ejpam-2055	108	5	)	)	PUNCT
ejpam-2055	108	6	)	)	PUNCT
ejpam-2055	108	7	.	.	PUNCT
ejpam-2055	109	1	hence	hence	ADV
ejpam-2055	109	2	we	we	PRON
ejpam-2055	109	3	have	have	VERB
ejpam-2055	109	4	a⊂	a⊂	NOUN
ejpam-2055	109	5	cl(int(δ−	cl(int(δ−	NOUN
ejpam-2055	109	6	cl(a	cl(a	NUM
ejpam-2055	109	7	)	)	PUNCT
ejpam-2055	109	8	)	)	PUNCT
ejpam-2055	109	9	)	)	PUNCT
ejpam-2055	109	10	,	,	PUNCT
ejpam-2055	109	11	there	there	ADV
ejpam-2055	109	12	for	for	ADP
ejpam-2055	109	13	a∈	a∈	PROPN
ejpam-2055	109	14	δ−	δ−	PROPN
ejpam-2055	109	15	βς(x	βς(x	PUNCT
ejpam-2055	109	16	,	,	PUNCT
ejpam-2055	109	17	t	t	PROPN
ejpam-2055	109	18	)	)	PUNCT
ejpam-2055	109	19	.	.	PUNCT
ejpam-2055	110	1	b	b	X
ejpam-2055	110	2	)	)	PUNCT
ejpam-2055	110	3	.	.	PUNCT
ejpam-2055	111	1	this	this	DET
ejpam-2055	111	2	proof	proof	NOUN
ejpam-2055	111	3	is	be	AUX
ejpam-2055	111	4	follows	follow	VERB
ejpam-2055	111	5	from	from	ADP
ejpam-2055	111	6	a	a	PRON
ejpam-2055	111	7	)	)	PUNCT
ejpam-2055	111	8	and	and	CCONJ
ejpam-2055	111	9	lemma	lemma	PROPN
ejpam-2055	111	10	(	(	PUNCT
ejpam-2055	111	11	1	1	NUM
ejpam-2055	111	12	)	)	PUNCT
ejpam-2055	111	13	.	.	PUNCT
ejpam-2055	112	1	theorem	theorem	NOUN
ejpam-2055	112	2	2	2	NUM
ejpam-2055	112	3	.	.	X
ejpam-2055	112	4	for	for	ADP
ejpam-2055	112	5	a	a	DET
ejpam-2055	112	6	subset	subset	NOUN
ejpam-2055	112	7	a	a	PRON
ejpam-2055	112	8	of	of	ADP
ejpam-2055	112	9	a	a	DET
ejpam-2055	112	10	topological	topological	ADJ
ejpam-2055	112	11	space	space	NOUN
ejpam-2055	112	12	x	x	NOUN
ejpam-2055	112	13	;	;	PUNCT
ejpam-2055	112	14	the	the	DET
ejpam-2055	112	15	following	following	NOUN
ejpam-2055	112	16	are	be	AUX
ejpam-2055	112	17	equivalent	equivalent	ADJ
ejpam-2055	112	18	:	:	PUNCT
ejpam-2055	112	19	a	a	X
ejpam-2055	112	20	)	)	PUNCT
ejpam-2055	112	21	a∈	a∈	PROPN
ejpam-2055	112	22	δ−	δ−	PROPN
ejpam-2055	112	23	βr(x	βr(x	NUM
ejpam-2055	112	24	,	,	PUNCT
ejpam-2055	112	25	t	t	PROPN
ejpam-2055	112	26	)	)	PUNCT
ejpam-2055	112	27	;	;	PUNCT
ejpam-2055	112	28	b	b	X
ejpam-2055	112	29	)	)	PUNCT
ejpam-2055	112	30	a	a	DET
ejpam-2055	112	31	=	=	PUNCT
ejpam-2055	112	32	δ−	δ−	PROPN
ejpam-2055	112	33	β	β	NOUN
ejpam-2055	112	34	−	−	PROPN
ejpam-2055	112	35	cl(δ−	cl(δ−	PRON
ejpam-2055	112	36	β	β	X
ejpam-2055	112	37	−	−	NOUN
ejpam-2055	112	38	int(a	int(a	NOUN
ejpam-2055	112	39	)	)	PUNCT
ejpam-2055	112	40	)	)	PUNCT
ejpam-2055	112	41	;	;	PUNCT
ejpam-2055	113	1	c	c	X
ejpam-2055	113	2	)	)	PUNCT
ejpam-2055	113	3	a=	a=	PROPN
ejpam-2055	113	4	δ−	δ−	X
ejpam-2055	113	5	β	β	X
ejpam-2055	113	6	−	−	PROPN
ejpam-2055	114	1	int(δ−	int(δ−	ADP
ejpam-2055	114	2	β	β	X
ejpam-2055	114	3	−	−	NOUN
ejpam-2055	114	4	cl(a	cl(a	NUM
ejpam-2055	114	5	)	)	PUNCT
ejpam-2055	114	6	)	)	PUNCT
ejpam-2055	114	7	.	.	PUNCT
ejpam-2055	115	1	proof	proof	NOUN
ejpam-2055	115	2	.	.	PUNCT
ejpam-2055	116	1	the	the	DET
ejpam-2055	116	2	proofs	proof	NOUN
ejpam-2055	116	3	of	of	ADP
ejpam-2055	116	4	the	the	DET
ejpam-2055	116	5	implications	implication	NOUN
ejpam-2055	116	6	(	(	PUNCT
ejpam-2055	116	7	a)⇒	a)⇒	PROPN
ejpam-2055	116	8	(	(	PUNCT
ejpam-2055	116	9	b	b	NOUN
ejpam-2055	116	10	)	)	PUNCT
ejpam-2055	116	11	and	and	CCONJ
ejpam-2055	116	12	(	(	PUNCT
ejpam-2055	116	13	a)⇒	a)⇒	PROPN
ejpam-2055	116	14	(	(	PUNCT
ejpam-2055	116	15	c	c	NOUN
ejpam-2055	116	16	)	)	PUNCT
ejpam-2055	116	17	are	be	AUX
ejpam-2055	116	18	obvious	obvious	ADJ
ejpam-2055	116	19	thus	thus	ADV
ejpam-2055	116	20	omitted	omit	VERB
ejpam-2055	116	21	.	.	PUNCT
ejpam-2055	117	1	(	(	PUNCT
ejpam-2055	117	2	b)⇒	b)⇒	PROPN
ejpam-2055	117	3	(	(	PUNCT
ejpam-2055	117	4	a	a	NOUN
ejpam-2055	117	5	)	)	PUNCT
ejpam-2055	117	6	since	since	SCONJ
ejpam-2055	117	7	δ−	δ−	PROPN
ejpam-2055	117	8	β	β	X
ejpam-2055	117	9	-cl(a	-cl(a	NUM
ejpam-2055	117	10	)	)	PUNCT
ejpam-2055	117	11	is	be	AUX
ejpam-2055	117	12	δ−	δ−	PROPN
ejpam-2055	117	13	β	β	X
ejpam-2055	117	14	-closed	-closed	PROPN
ejpam-2055	117	15	,	,	PUNCT
ejpam-2055	117	16	then	then	ADV
ejpam-2055	117	17	by	by	ADP
ejpam-2055	117	18	theorem	theorem	NOUN
ejpam-2055	117	19	(	(	PUNCT
ejpam-2055	117	20	1	1	X
ejpam-2055	117	21	)	)	PUNCT
ejpam-2055	117	22	we	we	PRON
ejpam-2055	117	23	have	have	VERB
ejpam-2055	117	24	δ−	δ−	PROPN
ejpam-2055	117	25	β	β	X
ejpam-2055	117	26	-int(δ−	-int(δ−	X
ejpam-2055	117	27	β	β	NOUN
ejpam-2055	117	28	−	−	NOUN
ejpam-2055	117	29	cl(a	cl(a	NUM
ejpam-2055	117	30	)	)	PUNCT
ejpam-2055	117	31	)	)	PUNCT
ejpam-2055	118	1	∈	∈	PROPN
ejpam-2055	118	2	δ−	δ−	PROPN
ejpam-2055	118	3	βr(x	βr(x	NUM
ejpam-2055	118	4	,	,	PUNCT
ejpam-2055	118	5	t	t	PROPN
ejpam-2055	118	6	)	)	PUNCT
ejpam-2055	118	7	and	and	CCONJ
ejpam-2055	118	8	a∈	a∈	PROPN
ejpam-2055	118	9	δ−	δ−	PROPN
ejpam-2055	118	10	βr(x	βr(x	NUM
ejpam-2055	118	11	,	,	PUNCT
ejpam-2055	118	12	t	t	PROPN
ejpam-2055	118	13	)	)	PUNCT
ejpam-2055	118	14	.	.	PUNCT
ejpam-2055	119	1	(	(	PUNCT
ejpam-2055	119	2	c)⇒	c)⇒	X
ejpam-2055	119	3	(	(	PUNCT
ejpam-2055	119	4	a	a	NOUN
ejpam-2055	119	5	)	)	PUNCT
ejpam-2055	119	6	since	since	SCONJ
ejpam-2055	119	7	δ−	δ−	PROPN
ejpam-2055	119	8	β	β	X
ejpam-2055	119	9	-int(a	-int(a	PROPN
ejpam-2055	119	10	)	)	PUNCT
ejpam-2055	119	11	is	be	AUX
ejpam-2055	119	12	δ−	δ−	PROPN
ejpam-2055	119	13	β	β	X
ejpam-2055	119	14	-open	-open	PROPN
ejpam-2055	119	15	,	,	PUNCT
ejpam-2055	119	16	then	then	ADV
ejpam-2055	119	17	by	by	ADP
ejpam-2055	119	18	theorem	theorem	NOUN
ejpam-2055	119	19	(	(	PUNCT
ejpam-2055	119	20	1	1	X
ejpam-2055	119	21	)	)	PUNCT
ejpam-2055	119	22	we	we	PRON
ejpam-2055	119	23	have	have	VERB
ejpam-2055	119	24	δ−	δ−	PROPN
ejpam-2055	119	25	β	β	X
ejpam-2055	119	26	−	−	PROPN
ejpam-2055	120	1	cl(δ−	cl(δ−	PRON
ejpam-2055	120	2	β	β	X
ejpam-2055	120	3	−	−	NOUN
ejpam-2055	120	4	int(a	int(a	NOUN
ejpam-2055	120	5	)	)	PUNCT
ejpam-2055	120	6	)	)	PUNCT
ejpam-2055	121	1	∈	∈	PROPN
ejpam-2055	121	2	δ−	δ−	PROPN
ejpam-2055	121	3	βr(x	βr(x	NUM
ejpam-2055	121	4	,	,	PUNCT
ejpam-2055	121	5	t	t	PROPN
ejpam-2055	121	6	)	)	PUNCT
ejpam-2055	121	7	and	and	CCONJ
ejpam-2055	121	8	a∈	a∈	PROPN
ejpam-2055	121	9	δ−	δ−	PROPN
ejpam-2055	121	10	βr(x	βr(x	NUM
ejpam-2055	121	11	,	,	PUNCT
ejpam-2055	121	12	t	t	PROPN
ejpam-2055	121	13	)	)	PUNCT
ejpam-2055	121	14	.	.	PUNCT
ejpam-2055	122	1	theorem	theorem	NOUN
ejpam-2055	122	2	3	3	NUM
ejpam-2055	122	3	.	.	X
ejpam-2055	122	4	for	for	ADP
ejpam-2055	122	5	each	each	DET
ejpam-2055	122	6	subset	subset	VERB
ejpam-2055	122	7	a	a	PRON
ejpam-2055	122	8	of	of	ADP
ejpam-2055	122	9	a	a	DET
ejpam-2055	122	10	topological	topological	ADJ
ejpam-2055	122	11	space	space	NOUN
ejpam-2055	122	12	(	(	PUNCT
ejpam-2055	122	13	x	x	X
ejpam-2055	122	14	,	,	PUNCT
ejpam-2055	122	15	t	t	PROPN
ejpam-2055	122	16	)	)	PUNCT
ejpam-2055	122	17	,	,	PUNCT
ejpam-2055	122	18	we	we	PRON
ejpam-2055	122	19	have	have	VERB
ejpam-2055	122	20	:	:	PUNCT
ejpam-2055	122	21	δ−	δ−	PROPN
ejpam-2055	122	22	β	β	X
ejpam-2055	122	23	−	−	PROPN
ejpam-2055	122	24	clθ	clθ	NOUN
ejpam-2055	122	25	(	(	PUNCT
ejpam-2055	122	26	a	a	X
ejpam-2055	122	27	)	)	PUNCT
ejpam-2055	123	1	=	=	SYM
ejpam-2055	123	2	⋂	⋂	PROPN
ejpam-2055	123	3	{	{	PUNCT
ejpam-2055	123	4	v	v	NOUN
ejpam-2055	123	5	:	:	PUNCT
ejpam-2055	123	6	a⊂	a⊂	X
ejpam-2055	123	7	v	v	NOUN
ejpam-2055	123	8	and	and	CCONJ
ejpam-2055	123	9	v	v	NOUN
ejpam-2055	123	10	is	be	AUX
ejpam-2055	123	11	δ−	δ−	PROPN
ejpam-2055	123	12	βθ	βθ	ADP
ejpam-2055	123	13	−	−	PROPN
ejpam-2055	123	14	closed	closed	ADJ
ejpam-2055	123	15	}	}	PUNCT
ejpam-2055	123	16	=	=	SYM
ejpam-2055	123	17	⋂	⋂	PROPN
ejpam-2055	123	18	{	{	PUNCT
ejpam-2055	123	19	v	v	NOUN
ejpam-2055	123	20	:	:	PUNCT
ejpam-2055	123	21	a⊂	a⊂	X
ejpam-2055	123	22	v	v	NOUN
ejpam-2055	123	23	and	and	CCONJ
ejpam-2055	123	24	v	v	NOUN
ejpam-2055	123	25	∈	∈	NOUN
ejpam-2055	123	26	δ−	δ−	PROPN
ejpam-2055	123	27	βr(x	βr(x	NUM
ejpam-2055	123	28	,	,	PUNCT
ejpam-2055	123	29	t	t	PROPN
ejpam-2055	123	30	)	)	PUNCT
ejpam-2055	123	31	}	}	PUNCT
ejpam-2055	123	32	.	.	PUNCT
ejpam-2055	124	1	a.	a.	NOUN
ejpam-2055	124	2	m.	m.	PROPN
ejpam-2055	124	3	farhan	farhan	PROPN
ejpam-2055	124	4	and	and	CCONJ
ejpam-2055	124	5	x.	x.	PROPN
ejpam-2055	124	6	yang	yang	PROPN
ejpam-2055	124	7	/	/	SYM
ejpam-2055	124	8	eur	eur	PROPN
ejpam-2055	124	9	.	.	PUNCT
ejpam-2055	125	1	j.	j.	PROPN
ejpam-2055	125	2	pure	pure	PROPN
ejpam-2055	125	3	appl	appl	PROPN
ejpam-2055	125	4	.	.	PROPN
ejpam-2055	125	5	math	math	PROPN
ejpam-2055	125	6	,	,	PUNCT
ejpam-2055	125	7	8	8	NUM
ejpam-2055	125	8	(	(	PUNCT
ejpam-2055	125	9	2015	2015	NUM
ejpam-2055	125	10	)	)	PUNCT
ejpam-2055	125	11	,	,	PUNCT
ejpam-2055	125	12	185	185	NUM
ejpam-2055	125	13	-	-	SYM
ejpam-2055	125	14	200	200	NUM
ejpam-2055	125	15	189	189	NUM
ejpam-2055	125	16	proof	proof	NOUN
ejpam-2055	125	17	.	.	PUNCT
ejpam-2055	126	1	we	we	PRON
ejpam-2055	126	2	prove	prove	VERB
ejpam-2055	126	3	only	only	ADV
ejpam-2055	126	4	the	the	DET
ejpam-2055	126	5	first	first	ADJ
ejpam-2055	126	6	equality	equality	NOUN
ejpam-2055	126	7	since	since	SCONJ
ejpam-2055	126	8	the	the	DET
ejpam-2055	126	9	other	other	ADJ
ejpam-2055	126	10	is	be	AUX
ejpam-2055	126	11	similarly	similarly	ADV
ejpam-2055	126	12	proved	prove	VERB
ejpam-2055	126	13	.	.	PUNCT
ejpam-2055	127	1	first	first	ADV
ejpam-2055	127	2	,	,	PUNCT
ejpam-2055	127	3	suppose	suppose	VERB
ejpam-2055	127	4	that	that	SCONJ
ejpam-2055	127	5	x	x	X
ejpam-2055	127	6	/∈	/∈	PUNCT
ejpam-2055	127	7	δ−	δ−	ADJ
ejpam-2055	127	8	β	β	X
ejpam-2055	127	9	−	−	PROPN
ejpam-2055	127	10	clθ	clθ	NOUN
ejpam-2055	127	11	(	(	PUNCT
ejpam-2055	127	12	a	a	NOUN
ejpam-2055	127	13	)	)	PUNCT
ejpam-2055	127	14	.	.	PUNCT
ejpam-2055	128	1	then	then	ADV
ejpam-2055	128	2	there	there	PRON
ejpam-2055	128	3	exists	exist	VERB
ejpam-2055	128	4	v	v	ADP
ejpam-2055	128	5	∈	∈	PROPN
ejpam-2055	128	6	δ−	δ−	PROPN
ejpam-2055	128	7	βς(x	βς(x	X
ejpam-2055	128	8	,	,	PUNCT
ejpam-2055	128	9	x	x	X
ejpam-2055	128	10	)	)	PUNCT
ejpam-2055	128	11	such	such	ADJ
ejpam-2055	128	12	that	that	SCONJ
ejpam-2055	128	13	δ−	δ−	PROPN
ejpam-2055	128	14	β	β	NOUN
ejpam-2055	128	15	−	−	NOUN
ejpam-2055	128	16	cl(v	cl(v	NOUN
ejpam-2055	128	17	)	)	PUNCT
ejpam-2055	128	18	⋂	⋂	PROPN
ejpam-2055	128	19	a=	a=	PROPN
ejpam-2055	128	20	φ	φ	PROPN
ejpam-2055	128	21	.	.	PUNCT
ejpam-2055	129	1	by	by	ADP
ejpam-2055	129	2	theorem	theorem	NOUN
ejpam-2055	129	3	1	1	NUM
ejpam-2055	129	4	,	,	PUNCT
ejpam-2055	129	5	x	x	PRON
ejpam-2055	129	6	\δ−	\δ−	NOUN
ejpam-2055	129	7	β	β	X
ejpam-2055	129	8	-cl(v	-cl(v	NOUN
ejpam-2055	129	9	)	)	PUNCT
ejpam-2055	129	10	is	be	AUX
ejpam-2055	129	11	δ−	δ−	PROPN
ejpam-2055	129	12	β	β	SYM
ejpam-2055	129	13	-regular	-regular	ADJ
ejpam-2055	129	14	and	and	CCONJ
ejpam-2055	129	15	hence	hence	ADV
ejpam-2055	129	16	x	x	X
ejpam-2055	129	17	\δ−β	\δ−β	PROPN
ejpam-2055	129	18	–	–	PUNCT
ejpam-2055	129	19	cl(v	cl(v	X
ejpam-2055	129	20	)	)	PUNCT
ejpam-2055	129	21	is	be	AUX
ejpam-2055	129	22	an	an	DET
ejpam-2055	129	23	δ−βθ	δ−βθ	NOUN
ejpam-2055	129	24	-closed	-close	VERB
ejpam-2055	129	25	set	set	NOUN
ejpam-2055	129	26	containing	contain	VERB
ejpam-2055	129	27	a	a	DET
ejpam-2055	129	28	and	and	CCONJ
ejpam-2055	129	29	x	x	SYM
ejpam-2055	129	30	/∈	/∈	PUNCT
ejpam-2055	129	31	x	x	PUNCT
ejpam-2055	129	32	\δ−β	\δ−β	PROPN
ejpam-2055	129	33	−cl(v	−cl(v	PROPN
ejpam-2055	129	34	)	)	PUNCT
ejpam-2055	129	35	.	.	PUNCT
ejpam-2055	130	1	therefore	therefore	ADV
ejpam-2055	130	2	,	,	PUNCT
ejpam-2055	130	3	we	we	PRON
ejpam-2055	130	4	have	have	VERB
ejpam-2055	130	5	x	x	PROPN
ejpam-2055	130	6	/∈	/∈	PROPN
ejpam-2055	130	7	⋂	⋂	PROPN
ejpam-2055	130	8	{	{	PUNCT
ejpam-2055	130	9	v	v	NOUN
ejpam-2055	130	10	:	:	PUNCT
ejpam-2055	130	11	a⊂	a⊂	X
ejpam-2055	130	12	v	v	NOUN
ejpam-2055	130	13	and	and	CCONJ
ejpam-2055	130	14	v	v	NOUN
ejpam-2055	130	15	is	be	AUX
ejpam-2055	130	16	δ−	δ−	PROPN
ejpam-2055	130	17	βθ	βθ	ADP
ejpam-2055	130	18	−	−	PROPN
ejpam-2055	130	19	closed	closed	ADJ
ejpam-2055	130	20	}	}	PUNCT
ejpam-2055	130	21	.	.	PUNCT
ejpam-2055	131	1	conversely	conversely	ADV
ejpam-2055	131	2	,	,	PUNCT
ejpam-2055	131	3	suppose	suppose	VERB
ejpam-2055	131	4	that	that	SCONJ
ejpam-2055	131	5	x	x	PROPN
ejpam-2055	131	6	/∈	/∈	PROPN
ejpam-2055	131	7	⋂	⋂	PROPN
ejpam-2055	131	8	{	{	PUNCT
ejpam-2055	131	9	v	v	NOUN
ejpam-2055	131	10	:	:	PUNCT
ejpam-2055	131	11	a⊂	a⊂	X
ejpam-2055	131	12	v	v	NOUN
ejpam-2055	131	13	and	and	CCONJ
ejpam-2055	131	14	v	v	NOUN
ejpam-2055	131	15	is	be	AUX
ejpam-2055	131	16	δ−	δ−	PROPN
ejpam-2055	131	17	βθ	βθ	ADP
ejpam-2055	131	18	−	−	PROPN
ejpam-2055	131	19	closed	closed	ADJ
ejpam-2055	131	20	}	}	PUNCT
ejpam-2055	131	21	.	.	PUNCT
ejpam-2055	132	1	there	there	PRON
ejpam-2055	132	2	exists	exist	VERB
ejpam-2055	132	3	an	an	DET
ejpam-2055	132	4	δ−	δ−	PROPN
ejpam-2055	132	5	βθ	βθ	ADP
ejpam-2055	132	6	closed	close	VERB
ejpam-2055	132	7	set	set	VERB
ejpam-2055	132	8	v	v	ADP
ejpam-2055	132	9	such	such	ADJ
ejpam-2055	132	10	that	that	SCONJ
ejpam-2055	132	11	a⊂	a⊂	VERB
ejpam-2055	132	12	v	v	NOUN
ejpam-2055	132	13	and	and	CCONJ
ejpam-2055	132	14	x	x	NOUN
ejpam-2055	132	15	/∈	/∈	NOUN
ejpam-2055	132	16	v	v	INTJ
ejpam-2055	132	17	.	.	PUNCT
ejpam-2055	133	1	there	there	PRON
ejpam-2055	133	2	exists	exist	VERB
ejpam-2055	133	3	u	u	PROPN
ejpam-2055	133	4	∈	∈	PROPN
ejpam-2055	133	5	δ−	δ−	PROPN
ejpam-2055	133	6	βς(x	βς(x	PUNCT
ejpam-2055	133	7	,	,	PUNCT
ejpam-2055	133	8	t	t	PROPN
ejpam-2055	133	9	)	)	PUNCT
ejpam-2055	133	10	such	such	ADJ
ejpam-2055	133	11	that	that	SCONJ
ejpam-2055	133	12	x	x	SYM
ejpam-2055	133	13	∈	∈	PROPN
ejpam-2055	133	14	u	u	NOUN
ejpam-2055	133	15	⊂	⊂	X
ejpam-2055	133	16	δ−	δ−	PROPN
ejpam-2055	133	17	β	β	X
ejpam-2055	133	18	−	−	NOUN
ejpam-2055	133	19	cl(u	cl(u	X
ejpam-2055	133	20	)	)	PUNCT
ejpam-2055	133	21	⊂	⊂	X
ejpam-2055	134	1	x	x	PUNCT
ejpam-2055	134	2	\	\	PROPN
ejpam-2055	134	3	v	v	NOUN
ejpam-2055	134	4	.	.	PUNCT
ejpam-2055	135	1	therefore	therefore	ADV
ejpam-2055	135	2	,	,	PUNCT
ejpam-2055	135	3	we	we	PRON
ejpam-2055	135	4	have	have	VERB
ejpam-2055	135	5	δ−	δ−	PROPN
ejpam-2055	135	6	β	β	X
ejpam-2055	135	7	−	−	NOUN
ejpam-2055	135	8	cl(u	cl(u	NOUN
ejpam-2055	135	9	)	)	PUNCT
ejpam-2055	135	10	⋂	⋂	PROPN
ejpam-2055	135	11	a⊂	a⊂	VERB
ejpam-2055	135	12	δ−	δ−	PROPN
ejpam-2055	135	13	β	β	X
ejpam-2055	135	14	−	−	NOUN
ejpam-2055	135	15	cl(u	cl(u	NOUN
ejpam-2055	135	16	)	)	PUNCT
ejpam-2055	135	17	⋂	⋂	PROPN
ejpam-2055	135	18	v	v	NOUN
ejpam-2055	135	19	=	=	SYM
ejpam-2055	135	20	φ	φ	PROPN
ejpam-2055	135	21	.	.	PUNCT
ejpam-2055	136	1	this	this	PRON
ejpam-2055	136	2	shows	show	VERB
ejpam-2055	136	3	that	that	SCONJ
ejpam-2055	136	4	x	x	X
ejpam-2055	136	5	/∈	/∈	PUNCT
ejpam-2055	136	6	δ−	δ−	ADJ
ejpam-2055	136	7	β	β	X
ejpam-2055	136	8	−	−	PROPN
ejpam-2055	136	9	clθ	clθ	NOUN
ejpam-2055	136	10	(	(	PUNCT
ejpam-2055	136	11	a	a	NOUN
ejpam-2055	136	12	)	)	PUNCT
ejpam-2055	136	13	.	.	PUNCT
ejpam-2055	137	1	theorem	theorem	ADJ
ejpam-2055	137	2	4	4	NUM
ejpam-2055	137	3	.	.	PUNCT
ejpam-2055	138	1	let	let	VERB
ejpam-2055	138	2	a	a	PRON
ejpam-2055	138	3	and	and	CCONJ
ejpam-2055	138	4	b	b	NOUN
ejpam-2055	138	5	be	be	AUX
ejpam-2055	138	6	any	any	DET
ejpam-2055	138	7	two	two	NUM
ejpam-2055	138	8	subsets	subset	NOUN
ejpam-2055	138	9	of	of	ADP
ejpam-2055	138	10	a	a	DET
ejpam-2055	138	11	topological	topological	ADJ
ejpam-2055	138	12	space	space	NOUN
ejpam-2055	138	13	(	(	PUNCT
ejpam-2055	138	14	x	x	X
ejpam-2055	138	15	,	,	PUNCT
ejpam-2055	138	16	t	t	PROPN
ejpam-2055	138	17	)	)	PUNCT
ejpam-2055	138	18	.	.	PUNCT
ejpam-2055	139	1	then	then	ADV
ejpam-2055	139	2	the	the	DET
ejpam-2055	139	3	following	follow	VERB
ejpam-2055	139	4	properties	property	NOUN
ejpam-2055	139	5	hold	hold	VERB
ejpam-2055	139	6	:	:	PUNCT
ejpam-2055	139	7	a	a	X
ejpam-2055	139	8	)	)	PUNCT
ejpam-2055	139	9	x	x	SYM
ejpam-2055	139	10	∈	∈	PROPN
ejpam-2055	139	11	δ−	δ−	VERB
ejpam-2055	139	12	β	β	X
ejpam-2055	139	13	−	−	PROPN
ejpam-2055	139	14	clθ	clθ	NOUN
ejpam-2055	139	15	(	(	PUNCT
ejpam-2055	139	16	a	a	X
ejpam-2055	139	17	)	)	PUNCT
ejpam-2055	139	18	if	if	SCONJ
ejpam-2055	140	1	and	and	CCONJ
ejpam-2055	140	2	only	only	ADV
ejpam-2055	140	3	if	if	SCONJ
ejpam-2055	140	4	u	u	PROPN
ejpam-2055	140	5	⋂	⋂	PROPN
ejpam-2055	140	6	a	a	PRON
ejpam-2055	140	7	6=	6=	NUM
ejpam-2055	140	8	φ	φ	PROPN
ejpam-2055	140	9	;	;	PUNCT
ejpam-2055	140	10	for	for	ADP
ejpam-2055	140	11	each	each	DET
ejpam-2055	140	12	u	u	PROPN
ejpam-2055	140	13	∈	∈	PROPN
ejpam-2055	140	14	δ−	δ−	PROPN
ejpam-2055	140	15	βr(x	βr(x	NUM
ejpam-2055	140	16	,	,	PUNCT
ejpam-2055	140	17	x	x	X
ejpam-2055	140	18	)	)	PUNCT
ejpam-2055	140	19	,	,	PUNCT
ejpam-2055	140	20	b	b	X
ejpam-2055	140	21	)	)	PUNCT
ejpam-2055	140	22	if	if	SCONJ
ejpam-2055	140	23	a⊂	a⊂	NOUN
ejpam-2055	140	24	b	b	NOUN
ejpam-2055	140	25	;	;	PUNCT
ejpam-2055	140	26	then	then	ADV
ejpam-2055	140	27	δ−	δ−	PROPN
ejpam-2055	140	28	β	β	NOUN
ejpam-2055	140	29	−	−	PROPN
ejpam-2055	140	30	clθ	clθ	NOUN
ejpam-2055	140	31	(	(	PUNCT
ejpam-2055	140	32	a	a	X
ejpam-2055	140	33	)	)	PUNCT
ejpam-2055	140	34	⊂	⊂	PROPN
ejpam-2055	140	35	δ−	δ−	VERB
ejpam-2055	140	36	β	β	X
ejpam-2055	140	37	−	−	NOUN
ejpam-2055	140	38	clθ	clθ	NOUN
ejpam-2055	140	39	(	(	PUNCT
ejpam-2055	140	40	b	b	NOUN
ejpam-2055	140	41	)	)	PUNCT
ejpam-2055	140	42	,	,	PUNCT
ejpam-2055	140	43	c	c	X
ejpam-2055	140	44	)	)	PUNCT
ejpam-2055	140	45	δ−	δ−	PROPN
ejpam-2055	140	46	β	β	NOUN
ejpam-2055	140	47	−	−	PROPN
ejpam-2055	140	48	clθ	clθ	NOUN
ejpam-2055	140	49	(	(	PUNCT
ejpam-2055	140	50	δ−	δ−	PROPN
ejpam-2055	140	51	β	β	X
ejpam-2055	140	52	−	−	PROPN
ejpam-2055	140	53	clθ	clθ	NOUN
ejpam-2055	140	54	(	(	PUNCT
ejpam-2055	140	55	a	a	NOUN
ejpam-2055	140	56	)	)	PUNCT
ejpam-2055	140	57	)	)	PUNCT
ejpam-2055	141	1	=	=	PUNCT
ejpam-2055	141	2	δ−	δ−	ADJ
ejpam-2055	141	3	β	β	X
ejpam-2055	141	4	−	−	NOUN
ejpam-2055	141	5	clθ	clθ	NOUN
ejpam-2055	141	6	(	(	PUNCT
ejpam-2055	141	7	a	a	NOUN
ejpam-2055	141	8	)	)	PUNCT
ejpam-2055	141	9	,	,	PUNCT
ejpam-2055	141	10	d	d	X
ejpam-2055	141	11	)	)	PUNCT
ejpam-2055	141	12	if	if	SCONJ
ejpam-2055	141	13	aλ	aλ	PROPN
ejpam-2055	141	14	is	be	AUX
ejpam-2055	141	15	δ−	δ−	PROPN
ejpam-2055	141	16	βθ	βθ	AUX
ejpam-2055	141	17	-closed	-close	VERB
ejpam-2055	141	18	in	in	ADP
ejpam-2055	141	19	x	x	PUNCT
ejpam-2055	141	20	for	for	SCONJ
ejpam-2055	141	21	each	each	DET
ejpam-2055	141	22	λ	λ	NOUN
ejpam-2055	141	23	∈∆	∈∆	ADV
ejpam-2055	141	24	;	;	PUNCT
ejpam-2055	141	25	then	then	ADV
ejpam-2055	141	26	⋂	⋂	PROPN
ejpam-2055	141	27	λ∈∆	λ∈∆	X
ejpam-2055	141	28	aλ	aλ	PROPN
ejpam-2055	141	29	is	be	AUX
ejpam-2055	141	30	δ−	δ−	PROPN
ejpam-2055	141	31	βθ	βθ	AUX
ejpam-2055	141	32	-closed	-close	VERB
ejpam-2055	141	33	in	in	ADP
ejpam-2055	141	34	x.	x.	NOUN
ejpam-2055	141	35	proof	proof	NOUN
ejpam-2055	141	36	.	.	PUNCT
ejpam-2055	142	1	the	the	DET
ejpam-2055	142	2	proofs	proof	NOUN
ejpam-2055	142	3	of	of	ADP
ejpam-2055	142	4	properties	property	NOUN
ejpam-2055	142	5	(	(	PUNCT
ejpam-2055	142	6	a	a	X
ejpam-2055	142	7	)	)	PUNCT
ejpam-2055	142	8	and	and	CCONJ
ejpam-2055	142	9	(	(	PUNCT
ejpam-2055	142	10	b	b	NOUN
ejpam-2055	142	11	)	)	PUNCT
ejpam-2055	142	12	are	be	AUX
ejpam-2055	142	13	obvious	obvious	ADJ
ejpam-2055	142	14	,	,	PUNCT
ejpam-2055	142	15	thus	thus	ADV
ejpam-2055	142	16	omitted	omit	VERB
ejpam-2055	142	17	.	.	PUNCT
ejpam-2055	143	1	(	(	PUNCT
ejpam-2055	143	2	c	c	X
ejpam-2055	143	3	)	)	PUNCT
ejpam-2055	143	4	generally	generally	ADV
ejpam-2055	143	5	we	we	PRON
ejpam-2055	143	6	have	have	VERB
ejpam-2055	143	7	δ−	δ−	PROPN
ejpam-2055	143	8	β	β	NOUN
ejpam-2055	143	9	−	−	PROPN
ejpam-2055	143	10	clθ	clθ	NOUN
ejpam-2055	143	11	(	(	PUNCT
ejpam-2055	143	12	δ−	δ−	PROPN
ejpam-2055	143	13	β	β	X
ejpam-2055	143	14	−	−	PROPN
ejpam-2055	143	15	clθ	clθ	NOUN
ejpam-2055	143	16	(	(	PUNCT
ejpam-2055	143	17	a	a	NOUN
ejpam-2055	143	18	)	)	PUNCT
ejpam-2055	143	19	)	)	PUNCT
ejpam-2055	144	1	⊃	⊃	PROPN
ejpam-2055	144	2	δ−	δ−	VERB
ejpam-2055	144	3	β	β	X
ejpam-2055	144	4	−	−	PROPN
ejpam-2055	144	5	clθ	clθ	NOUN
ejpam-2055	144	6	(	(	PUNCT
ejpam-2055	144	7	a	a	NOUN
ejpam-2055	144	8	)	)	PUNCT
ejpam-2055	144	9	.	.	PUNCT
ejpam-2055	145	1	suppose	suppose	VERB
ejpam-2055	145	2	that	that	SCONJ
ejpam-2055	145	3	x	x	PROPN
ejpam-2055	145	4	/∈	/∈	PUNCT
ejpam-2055	145	5	δ−	δ−	ADJ
ejpam-2055	145	6	β	β	X
ejpam-2055	145	7	−	−	PROPN
ejpam-2055	145	8	clθ	clθ	NOUN
ejpam-2055	145	9	(	(	PUNCT
ejpam-2055	145	10	a	a	NOUN
ejpam-2055	145	11	)	)	PUNCT
ejpam-2055	145	12	.	.	PUNCT
ejpam-2055	146	1	there	there	PRON
ejpam-2055	146	2	exists	exist	VERB
ejpam-2055	146	3	u	u	PROPN
ejpam-2055	146	4	∈	∈	PROPN
ejpam-2055	146	5	δ−	δ−	PROPN
ejpam-2055	146	6	βr(x	βr(x	NUM
ejpam-2055	146	7	,	,	PUNCT
ejpam-2055	146	8	x	x	X
ejpam-2055	146	9	)	)	PUNCT
ejpam-2055	146	10	such	such	ADJ
ejpam-2055	146	11	that	that	SCONJ
ejpam-2055	146	12	u	u	PROPN
ejpam-2055	146	13	⋂	⋂	PROPN
ejpam-2055	146	14	a=	a=	ADV
ejpam-2055	146	15	φ	φ	PROPN
ejpam-2055	146	16	.	.	PUNCT
ejpam-2055	147	1	since	since	SCONJ
ejpam-2055	147	2	u	u	NOUN
ejpam-2055	147	3	∈	∈	PROPN
ejpam-2055	147	4	δ−	δ−	PROPN
ejpam-2055	147	5	βr(x	βr(x	NUM
ejpam-2055	147	6	,	,	PUNCT
ejpam-2055	147	7	t	t	PROPN
ejpam-2055	147	8	)	)	PUNCT
ejpam-2055	147	9	;	;	PUNCT
ejpam-2055	147	10	we	we	PRON
ejpam-2055	147	11	have	have	VERB
ejpam-2055	147	12	δ	δ	NOUN
ejpam-2055	147	13	−	−	NOUN
ejpam-2055	147	14	β	β	NOUN
ejpam-2055	147	15	−	−	NOUN
ejpam-2055	147	16	clθ	clθ	NOUN
ejpam-2055	147	17	(	(	PUNCT
ejpam-2055	147	18	a	a	X
ejpam-2055	147	19	)	)	PUNCT
ejpam-2055	147	20	⋂	⋂	PROPN
ejpam-2055	147	21	u	u	NOUN
ejpam-2055	147	22	=	=	PROPN
ejpam-2055	147	23	φ	φ	PROPN
ejpam-2055	147	24	.	.	PUNCT
ejpam-2055	148	1	this	this	PRON
ejpam-2055	148	2	shows	show	VERB
ejpam-2055	148	3	that	that	SCONJ
ejpam-2055	148	4	x	x	X
ejpam-2055	148	5	/∈	/∈	PUNCT
ejpam-2055	149	1	δ	δ	PROPN
ejpam-2055	149	2	−	−	X
ejpam-2055	149	3	β	β	NOUN
ejpam-2055	149	4	−	−	NOUN
ejpam-2055	149	5	clθ	clθ	NOUN
ejpam-2055	149	6	(	(	PUNCT
ejpam-2055	149	7	δ	δ	NOUN
ejpam-2055	149	8	−	−	NOUN
ejpam-2055	149	9	β	β	NOUN
ejpam-2055	149	10	−	−	NOUN
ejpam-2055	149	11	clθ	clθ	NOUN
ejpam-2055	149	12	(	(	PUNCT
ejpam-2055	149	13	a	a	NOUN
ejpam-2055	149	14	)	)	PUNCT
ejpam-2055	149	15	)	)	PUNCT
ejpam-2055	149	16	.	.	PUNCT
ejpam-2055	150	1	therefore	therefore	ADV
ejpam-2055	150	2	,	,	PUNCT
ejpam-2055	150	3	we	we	PRON
ejpam-2055	150	4	obtain	obtain	VERB
ejpam-2055	150	5	δ−	δ−	PROPN
ejpam-2055	150	6	β	β	X
ejpam-2055	150	7	−	−	PROPN
ejpam-2055	150	8	clθ	clθ	NOUN
ejpam-2055	150	9	(	(	PUNCT
ejpam-2055	150	10	δ−	δ−	PROPN
ejpam-2055	150	11	β	β	X
ejpam-2055	150	12	−	−	PROPN
ejpam-2055	150	13	clθ	clθ	NOUN
ejpam-2055	150	14	(	(	PUNCT
ejpam-2055	150	15	a	a	NOUN
ejpam-2055	150	16	)	)	PUNCT
ejpam-2055	150	17	)	)	PUNCT
ejpam-2055	151	1	⊂	⊂	PROPN
ejpam-2055	151	2	δ−	δ−	VERB
ejpam-2055	151	3	β	β	X
ejpam-2055	151	4	−	−	NOUN
ejpam-2055	151	5	clθ	clθ	NOUN
ejpam-2055	151	6	(	(	PUNCT
ejpam-2055	151	7	a	a	NOUN
ejpam-2055	151	8	)	)	PUNCT
ejpam-2055	151	9	.	.	PUNCT
ejpam-2055	152	1	(	(	PUNCT
ejpam-2055	152	2	d	d	X
ejpam-2055	152	3	)	)	PUNCT
ejpam-2055	152	4	let	let	VERB
ejpam-2055	152	5	aλ	aλ	ADP
ejpam-2055	152	6	is	be	AUX
ejpam-2055	152	7	δ	δ	PROPN
ejpam-2055	152	8	−	−	PROPN
ejpam-2055	153	1	βθ	βθ	ADV
ejpam-2055	153	2	−	−	PROPN
ejpam-2055	153	3	closed	close	VERB
ejpam-2055	153	4	in	in	ADP
ejpam-2055	153	5	x	x	PUNCT
ejpam-2055	153	6	for	for	ADP
ejpam-2055	153	7	each	each	DET
ejpam-2055	153	8	λ	λ	PROPN
ejpam-2055	153	9	∈	∈	PROPN
ejpam-2055	153	10	∆.	∆.	NOUN
ejpam-2055	153	11	for	for	ADP
ejpam-2055	153	12	each	each	DET
ejpam-2055	153	13	λ	λ	PROPN
ejpam-2055	153	14	∈	∈	PROPN
ejpam-2055	153	15	∆.	∆.	X
ejpam-2055	153	16	aλ	aλ	PROPN
ejpam-2055	153	17	=	=	SYM
ejpam-2055	153	18	δ	δ	PROPN
ejpam-2055	153	19	−	−	NOUN
ejpam-2055	153	20	β	β	NOUN
ejpam-2055	153	21	−	−	NOUN
ejpam-2055	153	22	clθ	clθ	NOUN
ejpam-2055	153	23	(	(	PUNCT
ejpam-2055	153	24	aλ	aλ	PROPN
ejpam-2055	153	25	)	)	PUNCT
ejpam-2055	153	26	.	.	PUNCT
ejpam-2055	154	1	hence	hence	ADV
ejpam-2055	154	2	δ−	δ−	PROPN
ejpam-2055	154	3	β	β	NOUN
ejpam-2055	154	4	−	−	NOUN
ejpam-2055	154	5	clθ	clθ	NOUN
ejpam-2055	155	1	(	(	PUNCT
ejpam-2055	155	2	⋂	⋂	PROPN
ejpam-2055	155	3	λ∈∆	λ∈∆	X
ejpam-2055	155	4	aλ	aλ	PROPN
ejpam-2055	155	5	)	)	PUNCT
ejpam-2055	155	6	⊂	⊂	PROPN
ejpam-2055	155	7	⋂	⋂	PROPN
ejpam-2055	156	1	λ∈∆	λ∈∆	X
ejpam-2055	156	2	δ−	δ−	PROPN
ejpam-2055	156	3	β	β	NOUN
ejpam-2055	156	4	−	−	NOUN
ejpam-2055	156	5	clθ	clθ	NOUN
ejpam-2055	156	6	(	(	PUNCT
ejpam-2055	156	7	aλ	aλ	PROPN
ejpam-2055	156	8	)	)	PUNCT
ejpam-2055	156	9	=	=	SYM
ejpam-2055	157	1	⋂	⋂	PROPN
ejpam-2055	157	2	λ∈∆	λ∈∆	X
ejpam-2055	157	3	aλ	aλ	NUM
ejpam-2055	157	4	⊂	⊂	PROPN
ejpam-2055	157	5	δ−	δ−	PROPN
ejpam-2055	157	6	β	β	X
ejpam-2055	157	7	−	−	NOUN
ejpam-2055	157	8	clθ	clθ	NOUN
ejpam-2055	157	9	(	(	PUNCT
ejpam-2055	157	10	⋂	⋂	PROPN
ejpam-2055	157	11	λ∈∆	λ∈∆	X
ejpam-2055	157	12	aλ	aλ	PROPN
ejpam-2055	157	13	)	)	PUNCT
ejpam-2055	157	14	.	.	PUNCT
ejpam-2055	158	1	therefore	therefore	ADV
ejpam-2055	158	2	,	,	PUNCT
ejpam-2055	158	3	we	we	PRON
ejpam-2055	158	4	obtain	obtain	VERB
ejpam-2055	158	5	:	:	PUNCT
ejpam-2055	158	6	δ−	δ−	PROPN
ejpam-2055	158	7	β	β	X
ejpam-2055	158	8	−	−	NOUN
ejpam-2055	158	9	clθ	clθ	NOUN
ejpam-2055	158	10	(	(	PUNCT
ejpam-2055	158	11	⋂	⋂	PROPN
ejpam-2055	158	12	λ∈∆	λ∈∆	X
ejpam-2055	158	13	aλ	aλ	PROPN
ejpam-2055	158	14	)	)	PUNCT
ejpam-2055	158	15	=	=	SYM
ejpam-2055	159	1	⋂	⋂	PROPN
ejpam-2055	159	2	λ∈∆	λ∈∆	X
ejpam-2055	159	3	aλ	aλ	PROPN
ejpam-2055	159	4	.	.	PUNCT
ejpam-2055	160	1	this	this	PRON
ejpam-2055	160	2	shows	show	VERB
ejpam-2055	160	3	that⋂	that⋂	PRON
ejpam-2055	161	1	λ∈∆	λ∈∆	X
ejpam-2055	161	2	aλ	aλ	PROPN
ejpam-2055	161	3	is	be	AUX
ejpam-2055	161	4	δ−	δ−	PROPN
ejpam-2055	161	5	βθ	βθ	AUX
ejpam-2055	161	6	-closed	-close	VERB
ejpam-2055	161	7	in	in	ADP
ejpam-2055	161	8	x.	x.	NOUN
ejpam-2055	161	9	corollary	corollary	NOUN
ejpam-2055	162	1	1	1	X
ejpam-2055	162	2	.	.	PUNCT
ejpam-2055	163	1	let	let	VERB
ejpam-2055	163	2	a	a	PRON
ejpam-2055	163	3	and	and	CCONJ
ejpam-2055	163	4	aλ	aλ	INTJ
ejpam-2055	163	5	(	(	PUNCT
ejpam-2055	163	6	λ	λ	X
ejpam-2055	163	7	∈∆	∈∆	NOUN
ejpam-2055	163	8	)	)	PUNCT
ejpam-2055	163	9	be	be	VERB
ejpam-2055	163	10	any	any	DET
ejpam-2055	163	11	subsets	subset	NOUN
ejpam-2055	163	12	of	of	ADP
ejpam-2055	163	13	topological	topological	ADJ
ejpam-2055	163	14	space	space	NOUN
ejpam-2055	163	15	(	(	PUNCT
ejpam-2055	163	16	x	x	X
ejpam-2055	163	17	,	,	PUNCT
ejpam-2055	163	18	t	t	PROPN
ejpam-2055	163	19	)	)	PUNCT
ejpam-2055	163	20	.	.	PUNCT
ejpam-2055	164	1	then	then	ADV
ejpam-2055	164	2	the	the	DET
ejpam-2055	164	3	following	follow	VERB
ejpam-2055	164	4	properties	property	NOUN
ejpam-2055	164	5	hold	hold	VERB
ejpam-2055	164	6	:	:	PUNCT
ejpam-2055	164	7	a	a	X
ejpam-2055	164	8	)	)	PUNCT
ejpam-2055	164	9	a	a	PRON
ejpam-2055	164	10	is	be	AUX
ejpam-2055	164	11	δ−βθ	δ−βθ	NOUN
ejpam-2055	164	12	-open	-open	ADJ
ejpam-2055	164	13	in	in	ADP
ejpam-2055	164	14	x	x	SYM
ejpam-2055	164	15	if	if	SCONJ
ejpam-2055	165	1	and	and	CCONJ
ejpam-2055	165	2	only	only	ADV
ejpam-2055	165	3	if	if	SCONJ
ejpam-2055	165	4	for	for	ADP
ejpam-2055	165	5	each	each	DET
ejpam-2055	165	6	x	x	SYM
ejpam-2055	165	7	∈	∈	PROPN
ejpam-2055	165	8	a	a	DET
ejpam-2055	165	9	there	there	PRON
ejpam-2055	165	10	exists	exist	VERB
ejpam-2055	165	11	u	u	PROPN
ejpam-2055	165	12	∈	∈	PROPN
ejpam-2055	165	13	δ−βr(x	δ−βr(x	PROPN
ejpam-2055	165	14	,	,	PUNCT
ejpam-2055	165	15	x	x	X
ejpam-2055	165	16	)	)	PUNCT
ejpam-2055	165	17	such	such	ADJ
ejpam-2055	165	18	that	that	SCONJ
ejpam-2055	165	19	x	x	SYM
ejpam-2055	165	20	∈	∈	PROPN
ejpam-2055	165	21	u	u	X
ejpam-2055	165	22	⊂	⊂	PROPN
ejpam-2055	165	23	a	a	PRON
ejpam-2055	165	24	,	,	PUNCT
ejpam-2055	165	25	b	b	NOUN
ejpam-2055	165	26	)	)	PUNCT
ejpam-2055	165	27	δ−	δ−	PROPN
ejpam-2055	165	28	β	β	NOUN
ejpam-2055	165	29	−	−	PROPN
ejpam-2055	165	30	clθ	clθ	NOUN
ejpam-2055	165	31	(	(	PUNCT
ejpam-2055	165	32	a	a	NOUN
ejpam-2055	165	33	)	)	PUNCT
ejpam-2055	165	34	is	be	AUX
ejpam-2055	165	35	δ−	δ−	PROPN
ejpam-2055	165	36	βθ	βθ	ADP
ejpam-2055	165	37	-closed	-closed	ADJ
ejpam-2055	165	38	and	and	CCONJ
ejpam-2055	165	39	δ−	δ−	PROPN
ejpam-2055	165	40	β	β	SYM
ejpam-2055	165	41	−	−	PROPN
ejpam-2055	165	42	intθ	intθ	NOUN
ejpam-2055	165	43	(	(	PUNCT
ejpam-2055	165	44	a	a	X
ejpam-2055	165	45	)	)	PUNCT
ejpam-2055	165	46	is	be	AUX
ejpam-2055	165	47	δ−	δ−	PROPN
ejpam-2055	165	48	βθ	βθ	AUX
ejpam-2055	165	49	-open	-open	VERB
ejpam-2055	165	50	,	,	PUNCT
ejpam-2055	165	51	c	c	NOUN
ejpam-2055	165	52	)	)	PUNCT
ejpam-2055	165	53	if	if	SCONJ
ejpam-2055	165	54	aλ	aλ	PROPN
ejpam-2055	165	55	is	be	AUX
ejpam-2055	165	56	δ−	δ−	PROPN
ejpam-2055	165	57	βθ	βθ	AUX
ejpam-2055	165	58	-open	-open	VERB
ejpam-2055	165	59	in	in	ADP
ejpam-2055	165	60	x	x	PUNCT
ejpam-2055	165	61	for	for	SCONJ
ejpam-2055	165	62	each	each	DET
ejpam-2055	165	63	λ	λ	NOUN
ejpam-2055	165	64	∈∆	∈∆	NOUN
ejpam-2055	165	65	,	,	PUNCT
ejpam-2055	165	66	then	then	ADV
ejpam-2055	165	67	⋃	⋃	SCONJ
ejpam-2055	165	68	λ∈∆	λ∈∆	X
ejpam-2055	165	69	aλ	aλ	PROPN
ejpam-2055	165	70	is	be	AUX
ejpam-2055	165	71	δ−	δ−	PROPN
ejpam-2055	165	72	βθ	βθ	AUX
ejpam-2055	165	73	-open	-open	VERB
ejpam-2055	165	74	in	in	ADP
ejpam-2055	165	75	x.	x.	NOUN
ejpam-2055	165	76	theorem	theorem	VERB
ejpam-2055	165	77	5	5	NUM
ejpam-2055	165	78	.	.	X
ejpam-2055	165	79	for	for	ADP
ejpam-2055	165	80	a	a	DET
ejpam-2055	165	81	subset	subset	NOUN
ejpam-2055	165	82	a	a	PRON
ejpam-2055	165	83	of	of	ADP
ejpam-2055	165	84	a	a	DET
ejpam-2055	165	85	space	space	NOUN
ejpam-2055	165	86	x	x	NOUN
ejpam-2055	165	87	,	,	PUNCT
ejpam-2055	165	88	the	the	DET
ejpam-2055	165	89	following	follow	VERB
ejpam-2055	165	90	properties	property	NOUN
ejpam-2055	165	91	hold	hold	VERB
ejpam-2055	165	92	:	:	PUNCT
ejpam-2055	165	93	a	a	X
ejpam-2055	165	94	)	)	PUNCT
ejpam-2055	165	95	if	if	SCONJ
ejpam-2055	165	96	a∈	a∈	PROPN
ejpam-2055	165	97	δ−	δ−	PROPN
ejpam-2055	165	98	βς(x	βς(x	PUNCT
ejpam-2055	165	99	,	,	PUNCT
ejpam-2055	165	100	t	t	PROPN
ejpam-2055	165	101	)	)	PUNCT
ejpam-2055	165	102	,	,	PUNCT
ejpam-2055	165	103	then	then	ADV
ejpam-2055	165	104	δ−	δ−	PROPN
ejpam-2055	165	105	βcl(a	βcl(a	X
ejpam-2055	165	106	)	)	PUNCT
ejpam-2055	165	107	=	=	PUNCT
ejpam-2055	166	1	δ−	δ−	PROPN
ejpam-2055	166	2	β	β	X
ejpam-2055	166	3	−	−	NOUN
ejpam-2055	166	4	clθ	clθ	NOUN
ejpam-2055	166	5	(	(	PUNCT
ejpam-2055	166	6	a	a	NOUN
ejpam-2055	166	7	)	)	PUNCT
ejpam-2055	166	8	,	,	PUNCT
ejpam-2055	166	9	b	b	X
ejpam-2055	166	10	)	)	PUNCT
ejpam-2055	166	11	a∈	a∈	PROPN
ejpam-2055	166	12	δ−	δ−	PROPN
ejpam-2055	166	13	βr(x	βr(x	NUM
ejpam-2055	166	14	,	,	PUNCT
ejpam-2055	166	15	t	t	PROPN
ejpam-2055	166	16	)	)	PUNCT
ejpam-2055	166	17	if	if	SCONJ
ejpam-2055	166	18	and	and	CCONJ
ejpam-2055	166	19	only	only	ADV
ejpam-2055	166	20	if	if	SCONJ
ejpam-2055	166	21	a	a	PRON
ejpam-2055	166	22	is	be	AUX
ejpam-2055	166	23	δ−	δ−	PROPN
ejpam-2055	166	24	βθ	βθ	ADP
ejpam-2055	166	25	-open	-open	ADJ
ejpam-2055	166	26	and	and	CCONJ
ejpam-2055	166	27	δ−	δ−	PROPN
ejpam-2055	166	28	βθ	βθ	PROPN
ejpam-2055	166	29	-closed	-closed	ADJ
ejpam-2055	166	30	.	.	PUNCT
ejpam-2055	166	31	a.	a.	NOUN
ejpam-2055	166	32	m.	m.	PROPN
ejpam-2055	166	33	farhan	farhan	PROPN
ejpam-2055	166	34	and	and	CCONJ
ejpam-2055	166	35	x.	x.	PROPN
ejpam-2055	166	36	yang	yang	PROPN
ejpam-2055	166	37	/	/	SYM
ejpam-2055	166	38	eur	eur	PROPN
ejpam-2055	166	39	.	.	PUNCT
ejpam-2055	167	1	j.	j.	PROPN
ejpam-2055	167	2	pure	pure	PROPN
ejpam-2055	167	3	appl	appl	PROPN
ejpam-2055	167	4	.	.	PROPN
ejpam-2055	167	5	math	math	PROPN
ejpam-2055	167	6	,	,	PUNCT
ejpam-2055	167	7	8	8	NUM
ejpam-2055	167	8	(	(	PUNCT
ejpam-2055	167	9	2015	2015	NUM
ejpam-2055	167	10	)	)	PUNCT
ejpam-2055	167	11	,	,	PUNCT
ejpam-2055	167	12	185	185	NUM
ejpam-2055	167	13	-	-	SYM
ejpam-2055	167	14	200	200	NUM
ejpam-2055	167	15	190	190	NUM
ejpam-2055	167	16	proof	proof	NOUN
ejpam-2055	167	17	.	.	PUNCT
ejpam-2055	168	1	(	(	PUNCT
ejpam-2055	168	2	a	a	X
ejpam-2055	168	3	)	)	PUNCT
ejpam-2055	168	4	generally	generally	ADV
ejpam-2055	168	5	we	we	PRON
ejpam-2055	168	6	have	have	VERB
ejpam-2055	168	7	δ	δ	NOUN
ejpam-2055	168	8	−	−	NOUN
ejpam-2055	168	9	β	β	NOUN
ejpam-2055	168	10	−	−	NOUN
ejpam-2055	168	11	cl(b	cl(b	NOUN
ejpam-2055	168	12	)	)	PUNCT
ejpam-2055	169	1	⊂	⊂	PROPN
ejpam-2055	169	2	δ	δ	PROPN
ejpam-2055	169	3	−	−	NOUN
ejpam-2055	169	4	β	β	NOUN
ejpam-2055	169	5	−	−	NOUN
ejpam-2055	169	6	clθ	clθ	NOUN
ejpam-2055	169	7	(	(	PUNCT
ejpam-2055	169	8	b	b	NOUN
ejpam-2055	169	9	)	)	PUNCT
ejpam-2055	169	10	for	for	ADP
ejpam-2055	169	11	every	every	DET
ejpam-2055	169	12	subset	subset	NOUN
ejpam-2055	169	13	b	b	PROPN
ejpam-2055	169	14	of	of	ADP
ejpam-2055	169	15	x.	x.	NOUN
ejpam-2055	169	16	let	let	VERB
ejpam-2055	169	17	a	a	DET
ejpam-2055	169	18	∈	∈	PROPN
ejpam-2055	169	19	δ	δ	NOUN
ejpam-2055	169	20	−	−	NOUN
ejpam-2055	169	21	βς(x	βς(x	PUNCT
ejpam-2055	169	22	,	,	PUNCT
ejpam-2055	169	23	t	t	PROPN
ejpam-2055	169	24	)	)	PUNCT
ejpam-2055	169	25	.	.	PUNCT
ejpam-2055	170	1	suppose	suppose	VERB
ejpam-2055	170	2	that	that	SCONJ
ejpam-2055	170	3	x	x	X
ejpam-2055	170	4	/∈	/∈	PUNCT
ejpam-2055	171	1	δ	δ	PROPN
ejpam-2055	172	1	−	−	NOUN
ejpam-2055	172	2	β	β	NOUN
ejpam-2055	172	3	−	−	PROPN
ejpam-2055	172	4	cl(a).then	cl(a).then	PROPN
ejpam-2055	172	5	there	there	PRON
ejpam-2055	172	6	exists	exist	VERB
ejpam-2055	172	7	u	u	PROPN
ejpam-2055	172	8	∈	∈	PROPN
ejpam-2055	172	9	δ	δ	PROPN
ejpam-2055	172	10	−	−	NOUN
ejpam-2055	172	11	βς(x	βς(x	PUNCT
ejpam-2055	172	12	,	,	PUNCT
ejpam-2055	172	13	x	x	X
ejpam-2055	172	14	)	)	PUNCT
ejpam-2055	172	15	such	such	ADJ
ejpam-2055	172	16	that	that	SCONJ
ejpam-2055	172	17	u	u	PROPN
ejpam-2055	172	18	⋂	⋂	PROPN
ejpam-2055	172	19	a	a	DET
ejpam-2055	172	20	=	=	SYM
ejpam-2055	172	21	φ	φ	PROPN
ejpam-2055	172	22	.	.	PUNCT
ejpam-2055	173	1	since	since	SCONJ
ejpam-2055	173	2	a	a	DET
ejpam-2055	173	3	∈	∈	PROPN
ejpam-2055	173	4	δ	δ	NOUN
ejpam-2055	173	5	−	−	NOUN
ejpam-2055	173	6	βς(x	βς(x	PUNCT
ejpam-2055	173	7	,	,	PUNCT
ejpam-2055	173	8	t	t	PROPN
ejpam-2055	173	9	)	)	PUNCT
ejpam-2055	173	10	,	,	PUNCT
ejpam-2055	173	11	we	we	PRON
ejpam-2055	173	12	have	have	VERB
ejpam-2055	173	13	δ	δ	NOUN
ejpam-2055	173	14	−	−	NOUN
ejpam-2055	173	15	β	β	NOUN
ejpam-2055	173	16	−	−	NOUN
ejpam-2055	173	17	cl(u	cl(u	PROPN
ejpam-2055	173	18	)	)	PUNCT
ejpam-2055	173	19	⋂	⋂	PROPN
ejpam-2055	173	20	a	a	DET
ejpam-2055	173	21	=	=	SYM
ejpam-2055	173	22	φ	φ	PROPN
ejpam-2055	173	23	.	.	PUNCT
ejpam-2055	174	1	this	this	PRON
ejpam-2055	174	2	shows	show	VERB
ejpam-2055	174	3	that	that	SCONJ
ejpam-2055	174	4	x	x	X
ejpam-2055	174	5	/∈	/∈	PUNCT
ejpam-2055	175	1	δ	δ	PROPN
ejpam-2055	175	2	−	−	X
ejpam-2055	175	3	β	β	NOUN
ejpam-2055	175	4	−	−	NOUN
ejpam-2055	175	5	clθ	clθ	NOUN
ejpam-2055	175	6	(	(	PUNCT
ejpam-2055	175	7	a	a	NOUN
ejpam-2055	175	8	)	)	PUNCT
ejpam-2055	175	9	.	.	PUNCT
ejpam-2055	176	1	therefore	therefore	ADV
ejpam-2055	176	2	,	,	PUNCT
ejpam-2055	176	3	we	we	PRON
ejpam-2055	176	4	obtain	obtain	VERB
ejpam-2055	176	5	δ	δ	PROPN
ejpam-2055	176	6	−	−	NOUN
ejpam-2055	176	7	β	β	NOUN
ejpam-2055	176	8	−	−	NOUN
ejpam-2055	176	9	clθ	clθ	NOUN
ejpam-2055	176	10	(	(	PUNCT
ejpam-2055	176	11	a	a	X
ejpam-2055	176	12	)	)	PUNCT
ejpam-2055	176	13	⊂	⊂	PROPN
ejpam-2055	176	14	δ	δ	PROPN
ejpam-2055	176	15	−	−	NOUN
ejpam-2055	176	16	β	β	X
ejpam-2055	176	17	−	−	NOUN
ejpam-2055	176	18	cl(a	cl(a	NUM
ejpam-2055	176	19	)	)	PUNCT
ejpam-2055	176	20	.	.	PUNCT
ejpam-2055	177	1	hence	hence	ADV
ejpam-2055	177	2	δ−	δ−	PROPN
ejpam-2055	177	3	β	β	X
ejpam-2055	177	4	−	−	NOUN
ejpam-2055	177	5	cl(a	cl(a	PUNCT
ejpam-2055	177	6	)	)	PUNCT
ejpam-2055	177	7	=	=	PUNCT
ejpam-2055	177	8	δ−	δ−	PROPN
ejpam-2055	177	9	β	β	X
ejpam-2055	177	10	−	−	NOUN
ejpam-2055	177	11	clθ	clθ	NOUN
ejpam-2055	177	12	(	(	PUNCT
ejpam-2055	177	13	a	a	NOUN
ejpam-2055	177	14	)	)	PUNCT
ejpam-2055	177	15	.	.	PUNCT
ejpam-2055	178	1	(	(	PUNCT
ejpam-2055	178	2	b	b	X
ejpam-2055	178	3	)	)	PUNCT
ejpam-2055	178	4	leta∈	leta∈	NOUN
ejpam-2055	178	5	δ−βr(x	δ−βr(x	PROPN
ejpam-2055	178	6	,	,	PUNCT
ejpam-2055	178	7	t	t	PROPN
ejpam-2055	178	8	)	)	PUNCT
ejpam-2055	178	9	.	.	PUNCT
ejpam-2055	179	1	then	then	ADV
ejpam-2055	179	2	a∈	a∈	PROPN
ejpam-2055	179	3	δ−βς(x	δ−βς(x	PROPN
ejpam-2055	179	4	,	,	PUNCT
ejpam-2055	179	5	t	t	PROPN
ejpam-2055	179	6	)	)	PUNCT
ejpam-2055	179	7	and	and	CCONJ
ejpam-2055	179	8	by	by	ADP
ejpam-2055	179	9	(	(	PUNCT
ejpam-2055	179	10	a	a	X
ejpam-2055	179	11	)	)	PUNCT
ejpam-2055	179	12	,	,	PUNCT
ejpam-2055	179	13	a=	a=	ADJ
ejpam-2055	179	14	δ−β−cl(a	δ−β−cl(a	X
ejpam-2055	179	15	)	)	PUNCT
ejpam-2055	179	16	=	=	SYM
ejpam-2055	179	17	δ−β−clθ	δ−β−clθ	NOUN
ejpam-2055	179	18	(	(	PUNCT
ejpam-2055	179	19	a	a	NOUN
ejpam-2055	179	20	)	)	PUNCT
ejpam-2055	179	21	.	.	PUNCT
ejpam-2055	180	1	therefore	therefore	ADV
ejpam-2055	180	2	,	,	PUNCT
ejpam-2055	180	3	a	a	PRON
ejpam-2055	180	4	is	be	AUX
ejpam-2055	180	5	δ	δ	NOUN
ejpam-2055	180	6	−	−	NOUN
ejpam-2055	180	7	βθ	βθ	ADV
ejpam-2055	180	8	-closed	-closed	ADJ
ejpam-2055	180	9	.	.	PUNCT
ejpam-2055	181	1	since	since	SCONJ
ejpam-2055	181	2	x	x	X
ejpam-2055	181	3	\	\	PROPN
ejpam-2055	181	4	a	a	DET
ejpam-2055	181	5	∈	∈	PROPN
ejpam-2055	181	6	δ	δ	PROPN
ejpam-2055	181	7	−	−	NOUN
ejpam-2055	181	8	βr(x	βr(x	NUM
ejpam-2055	181	9	,	,	PUNCT
ejpam-2055	181	10	t	t	PROPN
ejpam-2055	181	11	)	)	PUNCT
ejpam-2055	181	12	,	,	PUNCT
ejpam-2055	181	13	by	by	ADP
ejpam-2055	181	14	the	the	DET
ejpam-2055	181	15	argument	argument	NOUN
ejpam-2055	181	16	above	above	ADV
ejpam-2055	181	17	.	.	PUNCT
ejpam-2055	182	1	we	we	PRON
ejpam-2055	182	2	have	have	VERB
ejpam-2055	182	3	x	x	NOUN
ejpam-2055	182	4	\	\	PROPN
ejpam-2055	182	5	a	a	PRON
ejpam-2055	182	6	is	be	AUX
ejpam-2055	182	7	δ−	δ−	PROPN
ejpam-2055	182	8	βθ	βθ	ADP
ejpam-2055	182	9	-closed	-closed	ADJ
ejpam-2055	182	10	and	and	CCONJ
ejpam-2055	182	11	hence	hence	ADV
ejpam-2055	182	12	a	a	PRON
ejpam-2055	182	13	is	be	AUX
ejpam-2055	182	14	δ−	δ−	PROPN
ejpam-2055	182	15	βθ	βθ	ADP
ejpam-2055	182	16	-open	-open	VERB
ejpam-2055	182	17	.	.	PUNCT
ejpam-2055	183	1	the	the	DET
ejpam-2055	183	2	converse	converse	NOUN
ejpam-2055	183	3	is	be	AUX
ejpam-2055	183	4	obvious	obvious	ADJ
ejpam-2055	183	5	4	4	NUM
ejpam-2055	183	6	.	.	PUNCT
ejpam-2055	183	7	characterizations	characterization	NOUN
ejpam-2055	183	8	of	of	ADP
ejpam-2055	183	9	strongly	strongly	ADV
ejpam-2055	183	10	δ−	δ−	ADJ
ejpam-2055	183	11	β	β	ADJ
ejpam-2055	183	12	-	-	ADJ
ejpam-2055	183	13	continuous	continuous	ADJ
ejpam-2055	183	14	functions	function	NOUN
ejpam-2055	183	15	in	in	ADP
ejpam-2055	183	16	this	this	DET
ejpam-2055	183	17	section	section	NOUN
ejpam-2055	183	18	,	,	PUNCT
ejpam-2055	183	19	we	we	PRON
ejpam-2055	183	20	introduce	introduce	VERB
ejpam-2055	183	21	some	some	DET
ejpam-2055	183	22	characterizations	characterization	NOUN
ejpam-2055	183	23	and	and	CCONJ
ejpam-2055	183	24	basic	basic	ADJ
ejpam-2055	183	25	properties	property	NOUN
ejpam-2055	183	26	concerning	concern	VERB
ejpam-2055	183	27	strongly	strongly	ADV
ejpam-2055	183	28	θ	θ	NOUN
ejpam-2055	183	29	−δ−	−δ−	ADJ
ejpam-2055	183	30	β	β	X
ejpam-2055	183	31	-continuous	-continuous	ADJ
ejpam-2055	183	32	functions	function	NOUN
ejpam-2055	183	33	.	.	PUNCT
ejpam-2055	184	1	definition	definition	NOUN
ejpam-2055	184	2	3	3	NUM
ejpam-2055	184	3	.	.	PUNCT
ejpam-2055	185	1	a	a	DET
ejpam-2055	185	2	function	function	NOUN
ejpam-2055	185	3	f	f	NOUN
ejpam-2055	185	4	:	:	PUNCT
ejpam-2055	185	5	(	(	PUNCT
ejpam-2055	185	6	x	x	X
ejpam-2055	185	7	,	,	PUNCT
ejpam-2055	185	8	t	t	NOUN
ejpam-2055	185	9	)	)	PUNCT
ejpam-2055	185	10	→	→	SYM
ejpam-2055	185	11	(	(	PUNCT
ejpam-2055	185	12	y	y	PROPN
ejpam-2055	185	13	,	,	PUNCT
ejpam-2055	185	14	t	t	PROPN
ejpam-2055	185	15	∗	∗	NOUN
ejpam-2055	185	16	)	)	PUNCT
ejpam-2055	185	17	is	be	AUX
ejpam-2055	185	18	said	say	VERB
ejpam-2055	185	19	to	to	PART
ejpam-2055	185	20	be	be	AUX
ejpam-2055	185	21	strongly	strongly	ADV
ejpam-2055	185	22	θ	θ	X
ejpam-2055	185	23	−δ−β	−δ−β	PROPN
ejpam-2055	185	24	-continuous	-continuous	ADJ
ejpam-2055	185	25	(	(	PUNCT
ejpam-2055	185	26	briefly	briefly	NOUN
ejpam-2055	185	27	,	,	PUNCT
ejpam-2055	185	28	st	st	PROPN
ejpam-2055	185	29	.	.	PROPN
ejpam-2055	185	30	θ	θ	PROPN
ejpam-2055	186	1	−	−	PROPN
ejpam-2055	187	1	δ	δ	PROPN
ejpam-2055	187	2	−	−	PROPN
ejpam-2055	187	3	β	β	PROPN
ejpam-2055	187	4	.c	.c	PROPN
ejpam-2055	187	5	.	.	PUNCT
ejpam-2055	187	6	)	)	PUNCT
ejpam-2055	188	1	if	if	SCONJ
ejpam-2055	188	2	for	for	ADP
ejpam-2055	188	3	each	each	DET
ejpam-2055	188	4	x	x	SYM
ejpam-2055	188	5	∈	∈	PROPN
ejpam-2055	188	6	x	x	X
ejpam-2055	188	7	and	and	CCONJ
ejpam-2055	188	8	each	each	DET
ejpam-2055	188	9	open	open	ADJ
ejpam-2055	188	10	set	set	VERB
ejpam-2055	188	11	v	v	NOUN
ejpam-2055	188	12	of	of	ADP
ejpam-2055	188	13	y	y	PROPN
ejpam-2055	188	14	containing	contain	VERB
ejpam-2055	188	15	f	f	PROPN
ejpam-2055	188	16	(	(	PUNCT
ejpam-2055	188	17	x	x	NOUN
ejpam-2055	188	18	)	)	PUNCT
ejpam-2055	188	19	,	,	PUNCT
ejpam-2055	188	20	there	there	PRON
ejpam-2055	188	21	exists	exist	VERB
ejpam-2055	188	22	an	an	DET
ejpam-2055	188	23	δ−	δ−	PROPN
ejpam-2055	188	24	β	β	X
ejpam-2055	188	25	-open	-open	NOUN
ejpam-2055	188	26	set	set	VERB
ejpam-2055	188	27	u	u	NOUN
ejpam-2055	188	28	of	of	ADP
ejpam-2055	188	29	x	x	SYM
ejpam-2055	188	30	containing	contain	VERB
ejpam-2055	188	31	x	x	NOUN
ejpam-2055	188	32	,	,	PUNCT
ejpam-2055	188	33	such	such	ADJ
ejpam-2055	188	34	that	that	SCONJ
ejpam-2055	188	35	f	f	PROPN
ejpam-2055	188	36	(	(	PUNCT
ejpam-2055	188	37	δ−	δ−	PROPN
ejpam-2055	188	38	β	β	X
ejpam-2055	188	39	−	−	NOUN
ejpam-2055	188	40	cl(u	cl(u	NOUN
ejpam-2055	188	41	)	)	PUNCT
ejpam-2055	188	42	)	)	PUNCT
ejpam-2055	189	1	⊂	⊂	PROPN
ejpam-2055	189	2	v	v	X
ejpam-2055	189	3	.	.	PUNCT
ejpam-2055	190	1	theorem	theorem	ADJ
ejpam-2055	190	2	6	6	NUM
ejpam-2055	190	3	.	.	PUNCT
ejpam-2055	190	4	for	for	ADP
ejpam-2055	190	5	a	a	DET
ejpam-2055	190	6	function	function	NOUN
ejpam-2055	190	7	f	f	NOUN
ejpam-2055	190	8	:	:	PUNCT
ejpam-2055	190	9	(	(	PUNCT
ejpam-2055	190	10	x	x	X
ejpam-2055	190	11	,	,	PUNCT
ejpam-2055	190	12	t	t	NOUN
ejpam-2055	190	13	)	)	PUNCT
ejpam-2055	190	14	→	→	SYM
ejpam-2055	190	15	(	(	PUNCT
ejpam-2055	190	16	y	y	PROPN
ejpam-2055	190	17	,	,	PUNCT
ejpam-2055	190	18	t	t	PROPN
ejpam-2055	190	19	∗	∗	NOUN
ejpam-2055	190	20	)	)	PUNCT
ejpam-2055	190	21	,	,	PUNCT
ejpam-2055	190	22	the	the	DET
ejpam-2055	190	23	following	follow	VERB
ejpam-2055	190	24	are	be	AUX
ejpam-2055	190	25	equivalent	equivalent	ADJ
ejpam-2055	190	26	:	:	PUNCT
ejpam-2055	190	27	a	a	X
ejpam-2055	190	28	)	)	PUNCT
ejpam-2055	190	29	f	f	NOUN
ejpam-2055	190	30	is	be	AUX
ejpam-2055	190	31	strongly	strongly	ADV
ejpam-2055	190	32	θ	θ	NOUN
ejpam-2055	190	33	−δ−	−δ−	ADJ
ejpam-2055	190	34	β	β	X
ejpam-2055	190	35	-continuous	-continuous	PROPN
ejpam-2055	190	36	,	,	PUNCT
ejpam-2055	190	37	b	b	NOUN
ejpam-2055	190	38	)	)	PUNCT
ejpam-2055	190	39	for	for	ADP
ejpam-2055	190	40	each	each	DET
ejpam-2055	190	41	x	x	SYM
ejpam-2055	190	42	∈	∈	PROPN
ejpam-2055	190	43	x	x	X
ejpam-2055	190	44	and	and	CCONJ
ejpam-2055	190	45	each	each	DET
ejpam-2055	190	46	open	open	ADJ
ejpam-2055	190	47	set	set	VERB
ejpam-2055	190	48	v	v	NOUN
ejpam-2055	190	49	of	of	ADP
ejpam-2055	190	50	y	y	PROPN
ejpam-2055	190	51	containing	contain	VERB
ejpam-2055	190	52	f	f	PROPN
ejpam-2055	190	53	(	(	PUNCT
ejpam-2055	190	54	x	x	NOUN
ejpam-2055	190	55	)	)	PUNCT
ejpam-2055	190	56	,	,	PUNCT
ejpam-2055	190	57	there	there	PRON
ejpam-2055	190	58	exists	exist	VERB
ejpam-2055	190	59	u	u	PROPN
ejpam-2055	190	60	∈	∈	PROPN
ejpam-2055	190	61	δ	δ	PROPN
ejpam-2055	190	62	−	−	NOUN
ejpam-2055	190	63	βr(x	βr(x	PUNCT
ejpam-2055	190	64	,	,	PUNCT
ejpam-2055	190	65	x	x	X
ejpam-2055	190	66	)	)	PUNCT
ejpam-2055	190	67	such	such	ADJ
ejpam-2055	190	68	that	that	SCONJ
ejpam-2055	190	69	f	f	PROPN
ejpam-2055	190	70	(	(	PUNCT
ejpam-2055	190	71	u	u	NOUN
ejpam-2055	190	72	)	)	PUNCT
ejpam-2055	190	73	⊂	⊂	PROPN
ejpam-2055	190	74	v	v	X
ejpam-2055	190	75	,	,	PUNCT
ejpam-2055	190	76	c	c	NOUN
ejpam-2055	190	77	)	)	PUNCT
ejpam-2055	190	78	f	f	PROPN
ejpam-2055	190	79	−1(v	−1(v	PROPN
ejpam-2055	190	80	)	)	PUNCT
ejpam-2055	190	81	is	be	AUX
ejpam-2055	190	82	δ−	δ−	PROPN
ejpam-2055	190	83	βθ	βθ	AUX
ejpam-2055	190	84	-open	-open	VERB
ejpam-2055	190	85	in	in	ADP
ejpam-2055	190	86	x	x	PUNCT
ejpam-2055	190	87	for	for	SCONJ
ejpam-2055	190	88	each	each	DET
ejpam-2055	190	89	open	open	ADJ
ejpam-2055	190	90	set	set	VERB
ejpam-2055	190	91	v	v	NOUN
ejpam-2055	190	92	of	of	ADP
ejpam-2055	190	93	y	y	PROPN
ejpam-2055	190	94	,	,	PUNCT
ejpam-2055	190	95	d	d	PROPN
ejpam-2055	190	96	)	)	PUNCT
ejpam-2055	190	97	f	f	PROPN
ejpam-2055	191	1	−1(f	−1(f	PROPN
ejpam-2055	191	2	)	)	PUNCT
ejpam-2055	191	3	is	be	AUX
ejpam-2055	191	4	δ−	δ−	PROPN
ejpam-2055	191	5	βθ	βθ	AUX
ejpam-2055	191	6	-closed	-close	VERB
ejpam-2055	191	7	in	in	ADP
ejpam-2055	191	8	x	x	PUNCT
ejpam-2055	191	9	for	for	ADP
ejpam-2055	191	10	each	each	DET
ejpam-2055	191	11	closed	close	VERB
ejpam-2055	191	12	set	set	VERB
ejpam-2055	191	13	f	f	PROPN
ejpam-2055	191	14	of	of	ADP
ejpam-2055	191	15	y	y	PROPN
ejpam-2055	191	16	,	,	PUNCT
ejpam-2055	191	17	e	e	NOUN
ejpam-2055	191	18	)	)	PUNCT
ejpam-2055	191	19	f	f	PROPN
ejpam-2055	191	20	(	(	PUNCT
ejpam-2055	191	21	δ−	δ−	PROPN
ejpam-2055	191	22	β	β	X
ejpam-2055	191	23	−	−	PROPN
ejpam-2055	191	24	clθ	clθ	NOUN
ejpam-2055	191	25	(	(	PUNCT
ejpam-2055	191	26	a	a	NOUN
ejpam-2055	191	27	)	)	PUNCT
ejpam-2055	191	28	)	)	PUNCT
ejpam-2055	192	1	⊂	⊂	PROPN
ejpam-2055	192	2	cl	cl	PROPN
ejpam-2055	192	3	(	(	PUNCT
ejpam-2055	192	4	f	f	PROPN
ejpam-2055	192	5	(	(	PUNCT
ejpam-2055	192	6	a	a	NOUN
ejpam-2055	192	7	)	)	PUNCT
ejpam-2055	192	8	)	)	PUNCT
ejpam-2055	192	9	for	for	ADP
ejpam-2055	192	10	each	each	PRON
ejpam-2055	192	11	subset	subset	VERB
ejpam-2055	192	12	a	a	PRON
ejpam-2055	192	13	of	of	ADP
ejpam-2055	192	14	x	x	PROPN
ejpam-2055	192	15	,	,	PUNCT
ejpam-2055	192	16	f	f	X
ejpam-2055	192	17	)	)	PUNCT
ejpam-2055	192	18	δ−	δ−	PROPN
ejpam-2055	192	19	β	β	NOUN
ejpam-2055	192	20	−	−	NOUN
ejpam-2055	192	21	clθ	clθ	NOUN
ejpam-2055	192	22	(	(	PUNCT
ejpam-2055	192	23	f	f	PROPN
ejpam-2055	192	24	−1(b	−1(b	NOUN
ejpam-2055	192	25	)	)	PUNCT
ejpam-2055	192	26	)	)	PUNCT
ejpam-2055	193	1	⊂	⊂	PROPN
ejpam-2055	193	2	f	f	X
ejpam-2055	193	3	−1(cl(b	−1(cl(b	PROPN
ejpam-2055	193	4	)	)	PUNCT
ejpam-2055	193	5	)	)	PUNCT
ejpam-2055	193	6	for	for	ADP
ejpam-2055	193	7	each	each	DET
ejpam-2055	193	8	subset	subset	NOUN
ejpam-2055	193	9	b	b	PROPN
ejpam-2055	193	10	of	of	ADP
ejpam-2055	193	11	y.	y.	PROPN
ejpam-2055	193	12	proof	proof	NOUN
ejpam-2055	193	13	.	.	PUNCT
ejpam-2055	194	1	(	(	PUNCT
ejpam-2055	194	2	a)⇒	a)⇒	PROPN
ejpam-2055	194	3	(	(	PUNCT
ejpam-2055	194	4	b	b	NOUN
ejpam-2055	194	5	)	)	PUNCT
ejpam-2055	194	6	.	.	PUNCT
ejpam-2055	195	1	it	it	PRON
ejpam-2055	195	2	follows	follow	VERB
ejpam-2055	195	3	directly	directly	ADV
ejpam-2055	195	4	from	from	ADP
ejpam-2055	195	5	theorem	theorem	ADJ
ejpam-2055	195	6	(	(	PUNCT
ejpam-2055	195	7	1	1	NUM
ejpam-2055	195	8	)	)	PUNCT
ejpam-2055	195	9	.	.	PUNCT
ejpam-2055	196	1	(	(	PUNCT
ejpam-2055	196	2	b	b	X
ejpam-2055	196	3	)	)	PUNCT
ejpam-2055	196	4	⇒	⇒	NOUN
ejpam-2055	196	5	(	(	PUNCT
ejpam-2055	196	6	c	c	NOUN
ejpam-2055	196	7	)	)	PUNCT
ejpam-2055	196	8	.	.	PUNCT
ejpam-2055	197	1	let	let	VERB
ejpam-2055	197	2	v	v	PART
ejpam-2055	197	3	be	be	AUX
ejpam-2055	197	4	any	any	DET
ejpam-2055	197	5	open	open	ADJ
ejpam-2055	197	6	set	set	NOUN
ejpam-2055	197	7	of	of	ADP
ejpam-2055	197	8	y	y	PROPN
ejpam-2055	197	9	and	and	CCONJ
ejpam-2055	197	10	x	x	SYM
ejpam-2055	197	11	∈	∈	PROPN
ejpam-2055	197	12	f	f	PROPN
ejpam-2055	197	13	−1(v	−1(v	NOUN
ejpam-2055	197	14	)	)	PUNCT
ejpam-2055	197	15	.	.	PUNCT
ejpam-2055	198	1	there	there	PRON
ejpam-2055	198	2	exists	exist	VERB
ejpam-2055	198	3	u	u	PROPN
ejpam-2055	198	4	∈	∈	PROPN
ejpam-2055	198	5	δ	δ	PROPN
ejpam-2055	198	6	−	−	NOUN
ejpam-2055	198	7	βr(x	βr(x	PUNCT
ejpam-2055	198	8	,	,	PUNCT
ejpam-2055	198	9	x	x	X
ejpam-2055	198	10	)	)	PUNCT
ejpam-2055	198	11	such	such	ADJ
ejpam-2055	198	12	that	that	SCONJ
ejpam-2055	198	13	f	f	PROPN
ejpam-2055	198	14	(	(	PUNCT
ejpam-2055	198	15	u	u	NOUN
ejpam-2055	198	16	)	)	PUNCT
ejpam-2055	198	17	⊂	⊂	PROPN
ejpam-2055	198	18	v	v	PROPN
ejpam-2055	198	19	.	.	PUNCT
ejpam-2055	199	1	therefore	therefore	ADV
ejpam-2055	199	2	,	,	PUNCT
ejpam-2055	199	3	we	we	PRON
ejpam-2055	199	4	have	have	VERB
ejpam-2055	199	5	x	x	X
ejpam-2055	199	6	∈	∈	PROPN
ejpam-2055	199	7	u	u	NOUN
ejpam-2055	199	8	⊂	⊂	PROPN
ejpam-2055	199	9	f	f	PROPN
ejpam-2055	199	10	−1(v	−1(v	PROPN
ejpam-2055	199	11	)	)	PUNCT
ejpam-2055	199	12	.	.	PUNCT
ejpam-2055	200	1	hence	hence	ADV
ejpam-2055	200	2	by	by	ADP
ejpam-2055	200	3	corollary	corollary	ADJ
ejpam-2055	200	4	(	(	PUNCT
ejpam-2055	200	5	1)(a	1)(a	NUM
ejpam-2055	200	6	)	)	PUNCT
ejpam-2055	200	7	,	,	PUNCT
ejpam-2055	200	8	f	f	PROPN
ejpam-2055	200	9	−1(v	−1(v	PROPN
ejpam-2055	200	10	)	)	PUNCT
ejpam-2055	200	11	is	be	AUX
ejpam-2055	200	12	δ−	δ−	PROPN
ejpam-2055	200	13	βθ	βθ	AUX
ejpam-2055	200	14	-open	-open	VERB
ejpam-2055	200	15	in	in	ADP
ejpam-2055	200	16	x.	x.	PROPN
ejpam-2055	200	17	(	(	PUNCT
ejpam-2055	200	18	c)⇒	c)⇒	X
ejpam-2055	200	19	(	(	PUNCT
ejpam-2055	200	20	d	d	NOUN
ejpam-2055	200	21	)	)	PUNCT
ejpam-2055	200	22	.	.	PUNCT
ejpam-2055	201	1	this	this	PRON
ejpam-2055	201	2	is	be	AUX
ejpam-2055	201	3	obvious	obvious	ADJ
ejpam-2055	201	4	thus	thus	ADV
ejpam-2055	201	5	omitted	omit	VERB
ejpam-2055	201	6	.	.	PUNCT
ejpam-2055	202	1	(	(	PUNCT
ejpam-2055	202	2	d)⇒	d)⇒	NOUN
ejpam-2055	202	3	(	(	PUNCT
ejpam-2055	202	4	e	e	NOUN
ejpam-2055	202	5	)	)	PUNCT
ejpam-2055	202	6	.	.	PUNCT
ejpam-2055	203	1	let	let	VERB
ejpam-2055	203	2	a	a	DET
ejpam-2055	203	3	be	be	AUX
ejpam-2055	203	4	any	any	DET
ejpam-2055	203	5	open	open	ADJ
ejpam-2055	203	6	set	set	NOUN
ejpam-2055	203	7	of	of	ADP
ejpam-2055	203	8	x.	x.	NOUN
ejpam-2055	203	9	since	since	SCONJ
ejpam-2055	203	10	cl	cl	NOUN
ejpam-2055	203	11	(	(	PUNCT
ejpam-2055	203	12	f	f	X
ejpam-2055	203	13	(	(	PUNCT
ejpam-2055	203	14	a	a	NOUN
ejpam-2055	203	15	)	)	PUNCT
ejpam-2055	203	16	)	)	PUNCT
ejpam-2055	203	17	is	be	AUX
ejpam-2055	203	18	closed	close	VERB
ejpam-2055	203	19	in	in	ADP
ejpam-2055	203	20	y	y	PROPN
ejpam-2055	203	21	,	,	PUNCT
ejpam-2055	203	22	by	by	ADP
ejpam-2055	203	23	(	(	PUNCT
ejpam-2055	203	24	d	d	X
ejpam-2055	203	25	)	)	PUNCT
ejpam-2055	203	26	f	f	PROPN
ejpam-2055	203	27	−1(cl	−1(cl	PROPN
ejpam-2055	203	28	(	(	PUNCT
ejpam-2055	203	29	f	f	PROPN
ejpam-2055	203	30	(	(	PUNCT
ejpam-2055	203	31	a	a	NOUN
ejpam-2055	203	32	)	)	PUNCT
ejpam-2055	203	33	)	)	PUNCT
ejpam-2055	203	34	)	)	PUNCT
ejpam-2055	203	35	is	be	AUX
ejpam-2055	203	36	δ−	δ−	PROPN
ejpam-2055	203	37	βθ	βθ	ADP
ejpam-2055	203	38	-closed	-close	VERB
ejpam-2055	203	39	and	and	CCONJ
ejpam-2055	203	40	we	we	PRON
ejpam-2055	203	41	have	have	VERB
ejpam-2055	203	42	,	,	PUNCT
ejpam-2055	203	43	δ−	δ−	PROPN
ejpam-2055	203	44	β	β	X
ejpam-2055	203	45	−	−	PROPN
ejpam-2055	203	46	clθ	clθ	NOUN
ejpam-2055	203	47	(	(	PUNCT
ejpam-2055	203	48	a	a	NOUN
ejpam-2055	203	49	)	)	PUNCT
ejpam-2055	203	50	)	)	PUNCT
ejpam-2055	204	1	⊂	⊂	PROPN
ejpam-2055	204	2	δ−	δ−	VERB
ejpam-2055	204	3	β	β	X
ejpam-2055	204	4	−	−	NOUN
ejpam-2055	204	5	clθ	clθ	NOUN
ejpam-2055	204	6	(	(	PUNCT
ejpam-2055	204	7	f	f	NOUN
ejpam-2055	204	8	−1	−1	PROPN
ejpam-2055	204	9	(	(	PUNCT
ejpam-2055	204	10	f	f	PROPN
ejpam-2055	204	11	(	(	PUNCT
ejpam-2055	204	12	a	a	NOUN
ejpam-2055	204	13	)	)	PUNCT
ejpam-2055	204	14	)	)	PUNCT
ejpam-2055	204	15	)	)	PUNCT
ejpam-2055	205	1	⊂	⊂	PRON
ejpam-2055	205	2	δ−	δ−	VERB
ejpam-2055	205	3	β	β	X
ejpam-2055	205	4	−	−	NOUN
ejpam-2055	205	5	clθ	clθ	NOUN
ejpam-2055	205	6	(	(	PUNCT
ejpam-2055	205	7	f	f	PROPN
ejpam-2055	205	8	−1(cl	−1(cl	PROPN
ejpam-2055	205	9	(	(	PUNCT
ejpam-2055	205	10	f	f	PROPN
ejpam-2055	205	11	(	(	PUNCT
ejpam-2055	205	12	a	a	NOUN
ejpam-2055	205	13	)	)	PUNCT
ejpam-2055	205	14	)	)	PUNCT
ejpam-2055	205	15	)	)	PUNCT
ejpam-2055	205	16	)	)	PUNCT
ejpam-2055	206	1	=	=	PUNCT
ejpam-2055	207	1	f	f	X
ejpam-2055	207	2	−1(cl	−1(cl	PROPN
ejpam-2055	207	3	(	(	PUNCT
ejpam-2055	207	4	f	f	PROPN
ejpam-2055	207	5	(	(	PUNCT
ejpam-2055	207	6	a	a	NOUN
ejpam-2055	207	7	)	)	PUNCT
ejpam-2055	207	8	)	)	PUNCT
ejpam-2055	207	9	)	)	PUNCT
ejpam-2055	207	10	.	.	PUNCT
ejpam-2055	208	1	there	there	ADV
ejpam-2055	208	2	for	for	ADP
ejpam-2055	208	3	,	,	PUNCT
ejpam-2055	208	4	we	we	PRON
ejpam-2055	208	5	obtain	obtain	VERB
ejpam-2055	208	6	f	f	X
ejpam-2055	208	7	(	(	PUNCT
ejpam-2055	208	8	δ−	δ−	PROPN
ejpam-2055	208	9	β	β	X
ejpam-2055	208	10	−	−	PROPN
ejpam-2055	208	11	clθ	clθ	NOUN
ejpam-2055	208	12	(	(	PUNCT
ejpam-2055	208	13	a	a	NOUN
ejpam-2055	208	14	)	)	PUNCT
ejpam-2055	208	15	)	)	PUNCT
ejpam-2055	209	1	⊂	⊂	PROPN
ejpam-2055	209	2	cl	cl	PROPN
ejpam-2055	209	3	(	(	PUNCT
ejpam-2055	209	4	f	f	PROPN
ejpam-2055	209	5	(	(	PUNCT
ejpam-2055	209	6	a	a	NOUN
ejpam-2055	209	7	)	)	PUNCT
ejpam-2055	209	8	)	)	PUNCT
ejpam-2055	209	9	.	.	PUNCT
ejpam-2055	210	1	(	(	PUNCT
ejpam-2055	210	2	e)⇒	e)⇒	NOUN
ejpam-2055	210	3	(	(	PUNCT
ejpam-2055	210	4	f	f	PROPN
ejpam-2055	210	5	)	)	PUNCT
ejpam-2055	210	6	.	.	PUNCT
ejpam-2055	211	1	let	let	VERB
ejpam-2055	211	2	b	b	X
ejpam-2055	211	3	be	be	AUX
ejpam-2055	211	4	any	any	DET
ejpam-2055	211	5	subset	subset	NOUN
ejpam-2055	211	6	of	of	ADP
ejpam-2055	211	7	y.	y.	PROPN
ejpam-2055	211	8	by	by	ADP
ejpam-2055	211	9	(	(	PUNCT
ejpam-2055	211	10	e	e	NOUN
ejpam-2055	211	11	)	)	PUNCT
ejpam-2055	211	12	,	,	PUNCT
ejpam-2055	211	13	we	we	PRON
ejpam-2055	211	14	obtain	obtain	VERB
ejpam-2055	211	15	f	f	PROPN
ejpam-2055	211	16	(	(	PUNCT
ejpam-2055	211	17	δ−β−clθ	δ−β−clθ	PROPN
ejpam-2055	211	18	(	(	PUNCT
ejpam-2055	211	19	f	f	PROPN
ejpam-2055	211	20	−1(b	−1(b	NOUN
ejpam-2055	211	21	)	)	PUNCT
ejpam-2055	211	22	)	)	PUNCT
ejpam-2055	211	23	)	)	PUNCT
ejpam-2055	212	1	⊂	⊂	PROPN
ejpam-2055	212	2	cl	cl	PROPN
ejpam-2055	212	3	(	(	PUNCT
ejpam-2055	212	4	f	f	PROPN
ejpam-2055	212	5	(	(	PUNCT
ejpam-2055	212	6	f	f	PROPN
ejpam-2055	212	7	−1(b	−1(b	NOUN
ejpam-2055	212	8	)	)	PUNCT
ejpam-2055	212	9	)	)	PUNCT
ejpam-2055	212	10	)	)	PUNCT
ejpam-2055	213	1	⊂	⊂	PROPN
ejpam-2055	213	2	cl(b	cl(b	NOUN
ejpam-2055	213	3	)	)	PUNCT
ejpam-2055	213	4	and	and	CCONJ
ejpam-2055	213	5	hence	hence	ADV
ejpam-2055	213	6	δ−β−clθ	δ−β−clθ	ADJ
ejpam-2055	213	7	(	(	PUNCT
ejpam-2055	213	8	f	f	PROPN
ejpam-2055	213	9	−1(b	−1(b	NOUN
ejpam-2055	213	10	)	)	PUNCT
ejpam-2055	213	11	)	)	PUNCT
ejpam-2055	214	1	⊂	⊂	PROPN
ejpam-2055	214	2	f	f	X
ejpam-2055	214	3	−1(cl(b	−1(cl(b	PROPN
ejpam-2055	214	4	)	)	PUNCT
ejpam-2055	214	5	)	)	PUNCT
ejpam-2055	214	6	.	.	PUNCT
ejpam-2055	215	1	(	(	PUNCT
ejpam-2055	215	2	f	f	X
ejpam-2055	215	3	)	)	PUNCT
ejpam-2055	215	4	⇒	⇒	PROPN
ejpam-2055	215	5	(	(	PUNCT
ejpam-2055	215	6	a	a	X
ejpam-2055	215	7	)	)	PUNCT
ejpam-2055	215	8	.	.	PUNCT
ejpam-2055	216	1	let	let	VERB
ejpam-2055	216	2	x	x	PUNCT
ejpam-2055	216	3	∈	∈	PROPN
ejpam-2055	216	4	x	x	X
ejpam-2055	216	5	and	and	CCONJ
ejpam-2055	216	6	v	v	X
ejpam-2055	216	7	be	be	AUX
ejpam-2055	216	8	any	any	DET
ejpam-2055	216	9	open	open	ADJ
ejpam-2055	216	10	set	set	NOUN
ejpam-2055	216	11	of	of	ADP
ejpam-2055	216	12	y	y	PROPN
ejpam-2055	216	13	containing	contain	VERB
ejpam-2055	216	14	f	f	PROPN
ejpam-2055	216	15	(	(	PUNCT
ejpam-2055	216	16	x	x	NOUN
ejpam-2055	216	17	)	)	PUNCT
ejpam-2055	216	18	.	.	PUNCT
ejpam-2055	217	1	since	since	SCONJ
ejpam-2055	217	2	y	y	PROPN
ejpam-2055	217	3	\v	\v	PROPN
ejpam-2055	217	4	is	be	AUX
ejpam-2055	217	5	closed	close	VERB
ejpam-2055	217	6	in	in	ADP
ejpam-2055	217	7	y	y	PROPN
ejpam-2055	217	8	,	,	PUNCT
ejpam-2055	217	9	we	we	PRON
ejpam-2055	217	10	a.	a.	NOUN
ejpam-2055	217	11	m.	m.	NOUN
ejpam-2055	217	12	farhan	farhan	PROPN
ejpam-2055	217	13	and	and	CCONJ
ejpam-2055	217	14	x.	x.	PROPN
ejpam-2055	217	15	yang	yang	PROPN
ejpam-2055	217	16	/	/	SYM
ejpam-2055	217	17	eur	eur	PROPN
ejpam-2055	217	18	.	.	PUNCT
ejpam-2055	218	1	j.	j.	PROPN
ejpam-2055	218	2	pure	pure	PROPN
ejpam-2055	218	3	appl	appl	PROPN
ejpam-2055	218	4	.	.	PROPN
ejpam-2055	218	5	math	math	PROPN
ejpam-2055	218	6	,	,	PUNCT
ejpam-2055	218	7	8	8	NUM
ejpam-2055	218	8	(	(	PUNCT
ejpam-2055	218	9	2015	2015	NUM
ejpam-2055	218	10	)	)	PUNCT
ejpam-2055	218	11	,	,	PUNCT
ejpam-2055	218	12	185	185	NUM
ejpam-2055	218	13	-	-	SYM
ejpam-2055	218	14	200	200	NUM
ejpam-2055	218	15	191	191	NUM
ejpam-2055	218	16	have	have	VERB
ejpam-2055	218	17	δ−β−clθ	δ−β−clθ	NOUN
ejpam-2055	218	18	(	(	PUNCT
ejpam-2055	218	19	f	f	PROPN
ejpam-2055	218	20	−1(y	−1(y	X
ejpam-2055	218	21	\v	\v	PROPN
ejpam-2055	218	22	)	)	PUNCT
ejpam-2055	218	23	)	)	PUNCT
ejpam-2055	219	1	⊂	⊂	PROPN
ejpam-2055	219	2	f	f	PROPN
ejpam-2055	219	3	−1(cl(y	−1(cl(y	PROPN
ejpam-2055	219	4	\v	\v	PUNCT
ejpam-2055	219	5	)	)	PUNCT
ejpam-2055	219	6	)	)	PUNCT
ejpam-2055	220	1	=	=	PUNCT
ejpam-2055	220	2	f	f	PROPN
ejpam-2055	220	3	−1(y	−1(y	ADV
ejpam-2055	220	4	\v	\v	PROPN
ejpam-2055	220	5	)	)	PUNCT
ejpam-2055	220	6	.	.	PUNCT
ejpam-2055	221	1	therefore	therefore	ADV
ejpam-2055	221	2	,	,	PUNCT
ejpam-2055	221	3	f	f	PROPN
ejpam-2055	221	4	−1(y	−1(y	X
ejpam-2055	221	5	\v	\v	PUNCT
ejpam-2055	221	6	)	)	PUNCT
ejpam-2055	221	7	is	be	AUX
ejpam-2055	221	8	δ−βθ	δ−βθ	NOUN
ejpam-2055	221	9	closed	close	VERB
ejpam-2055	221	10	in	in	ADP
ejpam-2055	221	11	x	x	X
ejpam-2055	221	12	and	and	CCONJ
ejpam-2055	221	13	f	f	PROPN
ejpam-2055	221	14	−1(v	−1(v	PROPN
ejpam-2055	221	15	)	)	PUNCT
ejpam-2055	221	16	is	be	AUX
ejpam-2055	221	17	an	an	DET
ejpam-2055	221	18	δ−βθ	δ−βθ	NOUN
ejpam-2055	221	19	-open	-open	ADJ
ejpam-2055	221	20	set	set	NOUN
ejpam-2055	221	21	containing	contain	VERB
ejpam-2055	221	22	x.	x.	NOUN
ejpam-2055	221	23	there	there	PRON
ejpam-2055	221	24	exists	exist	VERB
ejpam-2055	221	25	u	u	PROPN
ejpam-2055	221	26	∈	∈	PROPN
ejpam-2055	221	27	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	221	28	,	,	PUNCT
ejpam-2055	221	29	x	x	X
ejpam-2055	221	30	)	)	PUNCT
ejpam-2055	222	1	such	such	ADJ
ejpam-2055	222	2	that	that	SCONJ
ejpam-2055	222	3	δ	δ	PROPN
ejpam-2055	222	4	−	−	NOUN
ejpam-2055	222	5	β	β	X
ejpam-2055	222	6	−	−	NOUN
ejpam-2055	222	7	cl(u	cl(u	PROPN
ejpam-2055	222	8	)	)	PUNCT
ejpam-2055	222	9	⊂	⊂	PROPN
ejpam-2055	222	10	f	f	X
ejpam-2055	222	11	−1(v	−1(v	PROPN
ejpam-2055	222	12	)	)	PUNCT
ejpam-2055	222	13	and	and	CCONJ
ejpam-2055	222	14	hence	hence	ADV
ejpam-2055	222	15	f	f	PROPN
ejpam-2055	222	16	(	(	PUNCT
ejpam-2055	222	17	δ	δ	PROPN
ejpam-2055	223	1	−	−	NOUN
ejpam-2055	223	2	β	β	X
ejpam-2055	223	3	−	−	NOUN
ejpam-2055	223	4	cl(u	cl(u	PROPN
ejpam-2055	223	5	)	)	PUNCT
ejpam-2055	223	6	)	)	PUNCT
ejpam-2055	224	1	⊂	⊂	PROPN
ejpam-2055	224	2	v	v	X
ejpam-2055	224	3	.	.	PUNCT
ejpam-2055	225	1	this	this	PRON
ejpam-2055	225	2	shows	show	VERB
ejpam-2055	225	3	that	that	SCONJ
ejpam-2055	225	4	f	f	PROPN
ejpam-2055	225	5	is	be	AUX
ejpam-2055	225	6	strongly	strongly	ADV
ejpam-2055	225	7	θ	θ	NOUN
ejpam-2055	225	8	−δ−	−δ−	ADJ
ejpam-2055	225	9	β	β	X
ejpam-2055	225	10	-continuous	-continuous	PROPN
ejpam-2055	225	11	.	.	PUNCT
ejpam-2055	226	1	definition	definition	NOUN
ejpam-2055	226	2	4	4	NUM
ejpam-2055	226	3	(	(	PUNCT
ejpam-2055	226	4	[	[	X
ejpam-2055	226	5	9	9	NUM
ejpam-2055	226	6	,	,	PUNCT
ejpam-2055	226	7	27	27	NUM
ejpam-2055	226	8	]	]	PUNCT
ejpam-2055	226	9	)	)	PUNCT
ejpam-2055	226	10	.	.	PUNCT
ejpam-2055	227	1	a	a	DET
ejpam-2055	227	2	function	function	NOUN
ejpam-2055	227	3	f	f	NOUN
ejpam-2055	227	4	:	:	PUNCT
ejpam-2055	227	5	(	(	PUNCT
ejpam-2055	227	6	x	x	X
ejpam-2055	227	7	,	,	PUNCT
ejpam-2055	227	8	t	t	NOUN
ejpam-2055	227	9	)	)	PUNCT
ejpam-2055	227	10	→	→	SYM
ejpam-2055	227	11	(	(	PUNCT
ejpam-2055	227	12	y	y	PROPN
ejpam-2055	227	13	,	,	PUNCT
ejpam-2055	227	14	t	t	PROPN
ejpam-2055	227	15	∗	∗	NOUN
ejpam-2055	227	16	)	)	PUNCT
ejpam-2055	227	17	is	be	AUX
ejpam-2055	227	18	said	say	VERB
ejpam-2055	227	19	to	to	PART
ejpam-2055	227	20	be	be	AUX
ejpam-2055	227	21	δ−	δ−	PROPN
ejpam-2055	227	22	β	β	X
ejpam-2055	227	23	-continuous	-continuous	ADJ
ejpam-2055	227	24	if	if	SCONJ
ejpam-2055	227	25	f	f	PROPN
ejpam-2055	227	26	−1(a	−1(a	VERB
ejpam-2055	227	27	)	)	PUNCT
ejpam-2055	227	28	is	be	AUX
ejpam-2055	227	29	δ−	δ−	PROPN
ejpam-2055	227	30	β	β	PUNCT
ejpam-2055	227	31	-open	-open	VERB
ejpam-2055	227	32	in	in	ADP
ejpam-2055	227	33	x	x	PUNCT
ejpam-2055	227	34	for	for	ADP
ejpam-2055	227	35	every	every	DET
ejpam-2055	227	36	a∈	a∈	PROPN
ejpam-2055	227	37	t	t	PROPN
ejpam-2055	227	38	∗.	∗.	PROPN
ejpam-2055	227	39	theorem	theorem	PROPN
ejpam-2055	227	40	7	7	X
ejpam-2055	227	41	.	.	PUNCT
ejpam-2055	228	1	let	let	VERB
ejpam-2055	228	2	y	y	PRON
ejpam-2055	228	3	be	be	AUX
ejpam-2055	228	4	a	a	DET
ejpam-2055	228	5	regular	regular	ADJ
ejpam-2055	228	6	space	space	NOUN
ejpam-2055	228	7	.	.	PUNCT
ejpam-2055	229	1	then	then	ADV
ejpam-2055	229	2	f	f	X
ejpam-2055	229	3	:	:	PUNCT
ejpam-2055	229	4	(	(	PUNCT
ejpam-2055	229	5	x	x	X
ejpam-2055	229	6	,	,	PUNCT
ejpam-2055	229	7	t	t	NOUN
ejpam-2055	229	8	)	)	PUNCT
ejpam-2055	229	9	→	→	SYM
ejpam-2055	229	10	(	(	PUNCT
ejpam-2055	229	11	y	y	PROPN
ejpam-2055	229	12	,	,	PUNCT
ejpam-2055	229	13	t	t	PROPN
ejpam-2055	229	14	∗	∗	NOUN
ejpam-2055	229	15	)	)	PUNCT
ejpam-2055	229	16	is	be	AUX
ejpam-2055	229	17	strongly	strongly	ADV
ejpam-2055	229	18	θ	θ	X
ejpam-2055	229	19	−δ−β	−δ−β	PROPN
ejpam-2055	229	20	-continuous	-continuous	ADJ
ejpam-2055	229	21	if	if	SCONJ
ejpam-2055	229	22	and	and	CCONJ
ejpam-2055	229	23	only	only	ADV
ejpam-2055	229	24	if	if	SCONJ
ejpam-2055	229	25	f	f	PROPN
ejpam-2055	229	26	is	be	AUX
ejpam-2055	229	27	δ−	δ−	PROPN
ejpam-2055	229	28	β	β	X
ejpam-2055	229	29	-continuous	-continuous	ADJ
ejpam-2055	229	30	.	.	PUNCT
ejpam-2055	230	1	proof	proof	NOUN
ejpam-2055	230	2	.	.	PUNCT
ejpam-2055	231	1	let	let	VERB
ejpam-2055	231	2	x	x	PUNCT
ejpam-2055	231	3	∈	∈	PROPN
ejpam-2055	231	4	x	x	X
ejpam-2055	231	5	and	and	CCONJ
ejpam-2055	231	6	v	v	ADP
ejpam-2055	231	7	an	an	DET
ejpam-2055	231	8	open	open	ADJ
ejpam-2055	231	9	set	set	NOUN
ejpam-2055	231	10	of	of	ADP
ejpam-2055	231	11	y	y	PROPN
ejpam-2055	231	12	containing	contain	VERB
ejpam-2055	231	13	f	f	PROPN
ejpam-2055	231	14	(	(	PUNCT
ejpam-2055	231	15	x	x	NOUN
ejpam-2055	231	16	)	)	PUNCT
ejpam-2055	231	17	.	.	PUNCT
ejpam-2055	232	1	since	since	SCONJ
ejpam-2055	232	2	y	y	PROPN
ejpam-2055	232	3	is	be	AUX
ejpam-2055	232	4	regular	regular	ADJ
ejpam-2055	232	5	,	,	PUNCT
ejpam-2055	232	6	there	there	PRON
ejpam-2055	232	7	exists	exist	VERB
ejpam-2055	232	8	an	an	DET
ejpam-2055	232	9	open	open	ADJ
ejpam-2055	232	10	set	set	NOUN
ejpam-2055	232	11	h	h	NOUN
ejpam-2055	232	12	such	such	ADJ
ejpam-2055	232	13	that	that	SCONJ
ejpam-2055	232	14	f	f	PROPN
ejpam-2055	232	15	(	(	PUNCT
ejpam-2055	232	16	x	x	X
ejpam-2055	232	17	)	)	PUNCT
ejpam-2055	232	18	∈	∈	PROPN
ejpam-2055	232	19	h	h	NOUN
ejpam-2055	232	20	⊂	⊂	PROPN
ejpam-2055	232	21	cl(h	cl(h	X
ejpam-2055	232	22	)	)	PUNCT
ejpam-2055	233	1	⊂	⊂	PROPN
ejpam-2055	233	2	v	v	INTJ
ejpam-2055	233	3	.	.	PUNCT
ejpam-2055	234	1	if	if	SCONJ
ejpam-2055	234	2	f	f	PROPN
ejpam-2055	234	3	is	be	AUX
ejpam-2055	234	4	δ−	δ−	PROPN
ejpam-2055	234	5	β	β	X
ejpam-2055	234	6	-continuous	-continuous	PROPN
ejpam-2055	234	7	,	,	PUNCT
ejpam-2055	234	8	there	there	PRON
ejpam-2055	234	9	exists	exist	VERB
ejpam-2055	234	10	u	u	PROPN
ejpam-2055	234	11	∈	∈	PROPN
ejpam-2055	234	12	δ	δ	PROPN
ejpam-2055	234	13	−	−	NOUN
ejpam-2055	234	14	βς(x	βς(x	PUNCT
ejpam-2055	234	15	,	,	PUNCT
ejpam-2055	234	16	x	x	X
ejpam-2055	234	17	)	)	PUNCT
ejpam-2055	234	18	such	such	ADJ
ejpam-2055	234	19	that	that	SCONJ
ejpam-2055	234	20	f	f	PROPN
ejpam-2055	234	21	(	(	PUNCT
ejpam-2055	234	22	u	u	NOUN
ejpam-2055	234	23	)	)	PUNCT
ejpam-2055	234	24	⊂	⊂	PROPN
ejpam-2055	234	25	h.	h.	PROPN
ejpam-2055	235	1	we	we	PRON
ejpam-2055	235	2	shall	shall	AUX
ejpam-2055	235	3	show	show	VERB
ejpam-2055	235	4	that	that	SCONJ
ejpam-2055	235	5	f	f	PROPN
ejpam-2055	235	6	(	(	PUNCT
ejpam-2055	235	7	δ	δ	PROPN
ejpam-2055	235	8	−	−	NOUN
ejpam-2055	235	9	β	β	X
ejpam-2055	235	10	−	−	NOUN
ejpam-2055	235	11	cl(u	cl(u	PROPN
ejpam-2055	235	12	)	)	PUNCT
ejpam-2055	235	13	)	)	PUNCT
ejpam-2055	236	1	⊂	⊂	PROPN
ejpam-2055	236	2	cl(h	cl(h	PRON
ejpam-2055	236	3	)	)	PUNCT
ejpam-2055	236	4	.	.	PUNCT
ejpam-2055	237	1	suppose	suppose	VERB
ejpam-2055	237	2	that	that	SCONJ
ejpam-2055	237	3	y	y	PROPN
ejpam-2055	237	4	/∈	/∈	PUNCT
ejpam-2055	237	5	cl(h	cl(h	PROPN
ejpam-2055	237	6	)	)	PUNCT
ejpam-2055	237	7	.	.	PUNCT
ejpam-2055	238	1	there	there	PRON
ejpam-2055	238	2	exists	exist	VERB
ejpam-2055	238	3	an	an	DET
ejpam-2055	238	4	open	open	ADJ
ejpam-2055	238	5	set	set	NOUN
ejpam-2055	238	6	w	w	NOUN
ejpam-2055	238	7	containing	contain	VERB
ejpam-2055	238	8	y	y	PROPN
ejpam-2055	238	9	such	such	ADJ
ejpam-2055	238	10	that	that	SCONJ
ejpam-2055	239	1	w	w	PROPN
ejpam-2055	239	2	⋂	⋂	PROPN
ejpam-2055	239	3	h	h	NOUN
ejpam-2055	239	4	=	=	SYM
ejpam-2055	239	5	φ	φ	PROPN
ejpam-2055	239	6	.	.	PUNCT
ejpam-2055	240	1	since	since	SCONJ
ejpam-2055	240	2	f	f	PROPN
ejpam-2055	240	3	is	be	AUX
ejpam-2055	240	4	δ−	δ−	PROPN
ejpam-2055	240	5	β	β	X
ejpam-2055	240	6	-continuous	-continuous	PROPN
ejpam-2055	240	7	,	,	PUNCT
ejpam-2055	240	8	then	then	ADV
ejpam-2055	240	9	f	f	PROPN
ejpam-2055	240	10	−1(w	−1(w	ADV
ejpam-2055	240	11	)	)	PUNCT
ejpam-2055	240	12	∈	∈	PROPN
ejpam-2055	240	13	δ−	δ−	PROPN
ejpam-2055	240	14	βς(x	βς(x	PUNCT
ejpam-2055	240	15	,	,	PUNCT
ejpam-2055	240	16	t	t	PROPN
ejpam-2055	240	17	)	)	PUNCT
ejpam-2055	240	18	and	and	CCONJ
ejpam-2055	240	19	f	f	PROPN
ejpam-2055	240	20	−1(w	−1(w	ADV
ejpam-2055	240	21	)	)	PUNCT
ejpam-2055	240	22	⋂	⋂	PROPN
ejpam-2055	240	23	u	u	NOUN
ejpam-2055	240	24	=	=	PROPN
ejpam-2055	240	25	φ	φ	PROPN
ejpam-2055	240	26	.	.	PUNCT
ejpam-2055	241	1	and	and	CCONJ
ejpam-2055	241	2	hence	hence	ADV
ejpam-2055	241	3	f	f	PROPN
ejpam-2055	241	4	−1(w	−1(w	ADV
ejpam-2055	241	5	)	)	PUNCT
ejpam-2055	241	6	⋂	⋂	PROPN
ejpam-2055	241	7	δ−	δ−	PROPN
ejpam-2055	241	8	β	β	X
ejpam-2055	241	9	−	−	NOUN
ejpam-2055	241	10	cl(u	cl(u	NOUN
ejpam-2055	241	11	)	)	PUNCT
ejpam-2055	241	12	=	=	SYM
ejpam-2055	242	1	φ	φ	PROPN
ejpam-2055	242	2	.	.	PUNCT
ejpam-2055	243	1	therefore	therefore	ADV
ejpam-2055	243	2	,	,	PUNCT
ejpam-2055	243	3	we	we	PRON
ejpam-2055	243	4	obtain	obtain	VERB
ejpam-2055	243	5	w	w	ADP
ejpam-2055	243	6	⋂	⋂	PROPN
ejpam-2055	243	7	f	f	X
ejpam-2055	243	8	(	(	PUNCT
ejpam-2055	243	9	δ−	δ−	PROPN
ejpam-2055	243	10	β	β	X
ejpam-2055	243	11	−	−	NOUN
ejpam-2055	243	12	cl(u	cl(u	NOUN
ejpam-2055	243	13	)	)	PUNCT
ejpam-2055	243	14	)	)	PUNCT
ejpam-2055	244	1	=	=	PUNCT
ejpam-2055	244	2	φ	φ	PROPN
ejpam-2055	244	3	and	and	CCONJ
ejpam-2055	244	4	y	y	PROPN
ejpam-2055	244	5	/∈	/∈	PUNCT
ejpam-2055	245	1	f	f	PROPN
ejpam-2055	245	2	(	(	PUNCT
ejpam-2055	245	3	δ−	δ−	PROPN
ejpam-2055	245	4	β	β	X
ejpam-2055	245	5	−	−	NOUN
ejpam-2055	245	6	cl(u	cl(u	NOUN
ejpam-2055	245	7	)	)	PUNCT
ejpam-2055	245	8	)	)	PUNCT
ejpam-2055	245	9	.	.	PUNCT
ejpam-2055	246	1	consequently	consequently	ADV
ejpam-2055	246	2	,	,	PUNCT
ejpam-2055	246	3	we	we	PRON
ejpam-2055	246	4	have	have	VERB
ejpam-2055	246	5	f	f	PROPN
ejpam-2055	246	6	(	(	PUNCT
ejpam-2055	246	7	δ−	δ−	PROPN
ejpam-2055	246	8	β	β	X
ejpam-2055	246	9	−	−	NOUN
ejpam-2055	246	10	cl(u	cl(u	NOUN
ejpam-2055	246	11	)	)	PUNCT
ejpam-2055	246	12	)	)	PUNCT
ejpam-2055	247	1	⊂	⊂	PROPN
ejpam-2055	247	2	cl(h	cl(h	X
ejpam-2055	247	3	)	)	PUNCT
ejpam-2055	248	1	⊂	⊂	PROPN
ejpam-2055	248	2	v	v	NOUN
ejpam-2055	248	3	.	.	PUNCT
ejpam-2055	249	1	the	the	DET
ejpam-2055	249	2	converse	converse	NOUN
ejpam-2055	249	3	is	be	AUX
ejpam-2055	249	4	obvious	obvious	ADJ
ejpam-2055	249	5	.	.	PUNCT
ejpam-2055	250	1	definition	definition	NOUN
ejpam-2055	250	2	5	5	NUM
ejpam-2055	250	3	.	.	PUNCT
ejpam-2055	251	1	a	a	DET
ejpam-2055	251	2	space	space	NOUN
ejpam-2055	251	3	x	x	PUNCT
ejpam-2055	251	4	is	be	AUX
ejpam-2055	251	5	said	say	VERB
ejpam-2055	251	6	to	to	PART
ejpam-2055	251	7	be	be	AUX
ejpam-2055	251	8	δ	δ	NOUN
ejpam-2055	251	9	−	−	NOUN
ejpam-2055	251	10	β	β	NOUN
ejpam-2055	251	11	-regular	-regular	ADJ
ejpam-2055	251	12	if	if	SCONJ
ejpam-2055	251	13	for	for	SCONJ
ejpam-2055	251	14	each	each	DET
ejpam-2055	251	15	closed	close	VERB
ejpam-2055	251	16	set	set	VERB
ejpam-2055	251	17	f	f	PROPN
ejpam-2055	251	18	⊂	⊂	PROPN
ejpam-2055	251	19	x	x	X
ejpam-2055	251	20	and	and	CCONJ
ejpam-2055	251	21	each	each	DET
ejpam-2055	251	22	point	point	NOUN
ejpam-2055	251	23	x	x	X
ejpam-2055	251	24	∈	∈	NOUN
ejpam-2055	251	25	x	x	PUNCT
ejpam-2055	251	26	\	\	PROPN
ejpam-2055	252	1	f	f	X
ejpam-2055	252	2	,	,	PUNCT
ejpam-2055	252	3	there	there	PRON
ejpam-2055	252	4	exist	exist	VERB
ejpam-2055	252	5	disjoint	disjoint	NOUN
ejpam-2055	252	6	δ−	δ−	PROPN
ejpam-2055	252	7	β	β	X
ejpam-2055	252	8	-open	-open	PROPN
ejpam-2055	252	9	sets	set	VERB
ejpam-2055	252	10	u	u	NOUN
ejpam-2055	252	11	and	and	CCONJ
ejpam-2055	252	12	v	v	ADP
ejpam-2055	252	13	such	such	ADJ
ejpam-2055	252	14	that	that	SCONJ
ejpam-2055	252	15	x	x	SYM
ejpam-2055	252	16	∈	∈	PROPN
ejpam-2055	252	17	u	u	NOUN
ejpam-2055	252	18	and	and	CCONJ
ejpam-2055	252	19	f	f	PROPN
ejpam-2055	252	20	⊂	⊂	PROPN
ejpam-2055	252	21	v	v	PROPN
ejpam-2055	252	22	.	.	PUNCT
ejpam-2055	253	1	lemma	lemma	PROPN
ejpam-2055	253	2	2	2	NUM
ejpam-2055	253	3	.	.	X
ejpam-2055	253	4	for	for	ADP
ejpam-2055	253	5	a	a	DET
ejpam-2055	253	6	space	space	NOUN
ejpam-2055	253	7	x	x	PUNCT
ejpam-2055	253	8	the	the	DET
ejpam-2055	253	9	following	follow	VERB
ejpam-2055	253	10	are	be	AUX
ejpam-2055	253	11	equivalent	equivalent	ADJ
ejpam-2055	253	12	:	:	PUNCT
ejpam-2055	253	13	a	a	X
ejpam-2055	253	14	)	)	PUNCT
ejpam-2055	253	15	x	x	PUNCT
ejpam-2055	253	16	is	be	AUX
ejpam-2055	253	17	δ−	δ−	PROPN
ejpam-2055	253	18	β	β	SYM
ejpam-2055	253	19	-regular	-regular	PROPN
ejpam-2055	253	20	,	,	PUNCT
ejpam-2055	253	21	b	b	NOUN
ejpam-2055	253	22	)	)	PUNCT
ejpam-2055	253	23	for	for	ADP
ejpam-2055	253	24	each	each	DET
ejpam-2055	253	25	point	point	NOUN
ejpam-2055	253	26	x	x	X
ejpam-2055	253	27	∈	∈	NOUN
ejpam-2055	253	28	x	x	X
ejpam-2055	253	29	and	and	CCONJ
ejpam-2055	253	30	for	for	ADP
ejpam-2055	253	31	each	each	DET
ejpam-2055	253	32	open	open	ADJ
ejpam-2055	253	33	set	set	VERB
ejpam-2055	253	34	u	u	NOUN
ejpam-2055	253	35	of	of	ADP
ejpam-2055	253	36	x	x	PUNCT
ejpam-2055	253	37	containing	contain	VERB
ejpam-2055	253	38	x	x	PRON
ejpam-2055	253	39	,	,	PUNCT
ejpam-2055	253	40	there	there	PRON
ejpam-2055	253	41	exists	exist	VERB
ejpam-2055	253	42	v	v	PROPN
ejpam-2055	253	43	∈	∈	PROPN
ejpam-2055	253	44	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	253	45	,	,	PUNCT
ejpam-2055	253	46	t	t	PROPN
ejpam-2055	253	47	)	)	PUNCT
ejpam-2055	253	48	such	such	ADJ
ejpam-2055	253	49	that	that	SCONJ
ejpam-2055	253	50	x	x	SYM
ejpam-2055	253	51	∈	∈	PROPN
ejpam-2055	253	52	v	v	ADP
ejpam-2055	253	53	⊂	⊂	PROPN
ejpam-2055	253	54	δ−	δ−	PROPN
ejpam-2055	253	55	β	β	NOUN
ejpam-2055	253	56	−	−	NOUN
ejpam-2055	253	57	cl(v	cl(v	NOUN
ejpam-2055	253	58	)	)	PUNCT
ejpam-2055	254	1	⊂	⊂	PROPN
ejpam-2055	254	2	u	u	PROPN
ejpam-2055	254	3	,	,	PUNCT
ejpam-2055	254	4	c	c	NOUN
ejpam-2055	254	5	)	)	PUNCT
ejpam-2055	254	6	for	for	ADP
ejpam-2055	254	7	each	each	PRON
ejpam-2055	254	8	subset	subset	VERB
ejpam-2055	254	9	a	a	PRON
ejpam-2055	254	10	of	of	ADP
ejpam-2055	254	11	x	x	PUNCT
ejpam-2055	254	12	and	and	CCONJ
ejpam-2055	254	13	each	each	PRON
ejpam-2055	254	14	closed	close	VERB
ejpam-2055	254	15	set	set	VERB
ejpam-2055	254	16	f	f	PROPN
ejpam-2055	255	1	such	such	ADJ
ejpam-2055	255	2	that	that	SCONJ
ejpam-2055	255	3	a	a	DET
ejpam-2055	255	4	⋂	⋂	PROPN
ejpam-2055	255	5	f	f	X
ejpam-2055	255	6	=	=	SYM
ejpam-2055	255	7	φ	φ	PROPN
ejpam-2055	255	8	.	.	PUNCT
ejpam-2055	256	1	there	there	PRON
ejpam-2055	256	2	exist	exist	VERB
ejpam-2055	256	3	disjoint	disjoint	NOUN
ejpam-2055	256	4	u	u	NOUN
ejpam-2055	256	5	,	,	PUNCT
ejpam-2055	256	6	v	v	NOUN
ejpam-2055	256	7	∈	∈	PROPN
ejpam-2055	256	8	δ−	δ−	PROPN
ejpam-2055	256	9	βς(x	βς(x	X
ejpam-2055	256	10	,	,	PUNCT
ejpam-2055	256	11	t	t	PROPN
ejpam-2055	256	12	)	)	PUNCT
ejpam-2055	256	13	such	such	ADJ
ejpam-2055	256	14	that	that	SCONJ
ejpam-2055	256	15	a	a	DET
ejpam-2055	256	16	⋂	⋂	PROPN
ejpam-2055	256	17	u	u	PROPN
ejpam-2055	256	18	6=	6=	PROPN
ejpam-2055	256	19	φ	φ	PROPN
ejpam-2055	256	20	.	.	PUNCT
ejpam-2055	257	1	and	and	CCONJ
ejpam-2055	257	2	f	f	PROPN
ejpam-2055	257	3	⊂	⊂	PROPN
ejpam-2055	257	4	v	v	PROPN
ejpam-2055	257	5	,	,	PUNCT
ejpam-2055	257	6	d	d	NOUN
ejpam-2055	257	7	)	)	PUNCT
ejpam-2055	257	8	for	for	ADP
ejpam-2055	257	9	each	each	DET
ejpam-2055	257	10	closed	close	VERB
ejpam-2055	257	11	set	set	VERB
ejpam-2055	257	12	f	f	PROPN
ejpam-2055	257	13	of	of	ADP
ejpam-2055	257	14	x	x	PROPN
ejpam-2055	257	15	,	,	PUNCT
ejpam-2055	257	16	f	f	PROPN
ejpam-2055	257	17	=	=	SYM
ejpam-2055	257	18	⋂	⋂	PROPN
ejpam-2055	257	19	{	{	PUNCT
ejpam-2055	257	20	δ−	δ−	PROPN
ejpam-2055	257	21	β	β	NOUN
ejpam-2055	257	22	−	−	PROPN
ejpam-2055	257	23	cl(v	cl(v	NOUN
ejpam-2055	257	24	)	)	PUNCT
ejpam-2055	257	25	:	:	PUNCT
ejpam-2055	258	1	f	f	PROPN
ejpam-2055	258	2	⊂	⊂	PROPN
ejpam-2055	258	3	v	v	PROPN
ejpam-2055	258	4	,	,	PUNCT
ejpam-2055	258	5	v	v	NOUN
ejpam-2055	258	6	∈	∈	PROPN
ejpam-2055	258	7	δ−	δ−	PROPN
ejpam-2055	258	8	βς(x	βς(x	X
ejpam-2055	258	9	,	,	PUNCT
ejpam-2055	258	10	t	t	PROPN
ejpam-2055	258	11	)	)	PUNCT
ejpam-2055	258	12	}	}	PUNCT
ejpam-2055	258	13	.	.	PUNCT
ejpam-2055	259	1	theorem	theorem	VERB
ejpam-2055	259	2	8	8	NUM
ejpam-2055	259	3	.	.	PUNCT
ejpam-2055	260	1	a	a	DET
ejpam-2055	260	2	continuous	continuous	ADJ
ejpam-2055	260	3	function	function	NOUN
ejpam-2055	260	4	f	f	NOUN
ejpam-2055	260	5	:	:	PUNCT
ejpam-2055	260	6	(	(	PUNCT
ejpam-2055	260	7	x	x	X
ejpam-2055	260	8	,	,	PUNCT
ejpam-2055	260	9	t	t	NOUN
ejpam-2055	260	10	)	)	PUNCT
ejpam-2055	260	11	→	→	SYM
ejpam-2055	260	12	(	(	PUNCT
ejpam-2055	260	13	y	y	PROPN
ejpam-2055	260	14	,	,	PUNCT
ejpam-2055	260	15	t	t	PROPN
ejpam-2055	260	16	∗	∗	NOUN
ejpam-2055	260	17	)	)	PUNCT
ejpam-2055	260	18	is	be	AUX
ejpam-2055	260	19	strongly	strongly	ADV
ejpam-2055	260	20	θ	θ	NOUN
ejpam-2055	260	21	−δ−	−δ−	ADJ
ejpam-2055	261	1	β	β	AUX
ejpam-2055	261	2	-continuous	-continuous	ADJ
ejpam-2055	261	3	if	if	SCONJ
ejpam-2055	261	4	and	and	CCONJ
ejpam-2055	261	5	only	only	ADV
ejpam-2055	261	6	if	if	SCONJ
ejpam-2055	261	7	x	x	PRON
ejpam-2055	261	8	is	be	AUX
ejpam-2055	261	9	δ−	δ−	PROPN
ejpam-2055	261	10	β	β	SYM
ejpam-2055	261	11	-regular	-regular	ADJ
ejpam-2055	261	12	.	.	PUNCT
ejpam-2055	262	1	proof	proof	NOUN
ejpam-2055	262	2	.	.	PUNCT
ejpam-2055	263	1	(	(	PUNCT
ejpam-2055	263	2	necessity	necessity	NOUN
ejpam-2055	263	3	)	)	PUNCT
ejpam-2055	263	4	.	.	PUNCT
ejpam-2055	264	1	let	let	VERB
ejpam-2055	264	2	f	f	NOUN
ejpam-2055	264	3	:	:	PUNCT
ejpam-2055	264	4	x	x	X
ejpam-2055	264	5	→	→	PUNCT
ejpam-2055	264	6	x	x	PUNCT
ejpam-2055	264	7	be	be	AUX
ejpam-2055	264	8	the	the	DET
ejpam-2055	264	9	identity	identity	NOUN
ejpam-2055	264	10	function	function	NOUN
ejpam-2055	264	11	.	.	PUNCT
ejpam-2055	265	1	then	then	ADV
ejpam-2055	265	2	f	f	PROPN
ejpam-2055	265	3	is	be	AUX
ejpam-2055	265	4	continuous	continuous	ADJ
ejpam-2055	265	5	and	and	CCONJ
ejpam-2055	265	6	strongly	strongly	ADV
ejpam-2055	265	7	θ	θ	X
ejpam-2055	265	8	−δ−β	−δ−β	PROPN
ejpam-2055	265	9	-continuous	-continuous	ADJ
ejpam-2055	265	10	by	by	ADP
ejpam-2055	265	11	our	our	PRON
ejpam-2055	265	12	hypothesis	hypothesis	NOUN
ejpam-2055	265	13	.	.	PUNCT
ejpam-2055	266	1	for	for	ADP
ejpam-2055	266	2	any	any	DET
ejpam-2055	266	3	open	open	ADJ
ejpam-2055	266	4	set	set	NOUN
ejpam-2055	266	5	u	u	NOUN
ejpam-2055	266	6	of	of	ADP
ejpam-2055	266	7	x	x	PUNCT
ejpam-2055	266	8	and	and	CCONJ
ejpam-2055	266	9	any	any	DET
ejpam-2055	266	10	point	point	NOUN
ejpam-2055	266	11	x	x	SYM
ejpam-2055	266	12	∈	∈	NOUN
ejpam-2055	266	13	u	u	NOUN
ejpam-2055	266	14	,	,	PUNCT
ejpam-2055	266	15	we	we	PRON
ejpam-2055	266	16	have	have	VERB
ejpam-2055	266	17	f	f	PROPN
ejpam-2055	266	18	(	(	PUNCT
ejpam-2055	266	19	x	x	NOUN
ejpam-2055	266	20	)	)	PUNCT
ejpam-2055	266	21	=	=	PUNCT
ejpam-2055	266	22	x	x	SYM
ejpam-2055	266	23	∈	∈	PROPN
ejpam-2055	266	24	u	u	NOUN
ejpam-2055	266	25	and	and	CCONJ
ejpam-2055	266	26	there	there	PRON
ejpam-2055	266	27	exists	exist	VERB
ejpam-2055	266	28	v	v	ADP
ejpam-2055	266	29	∈	∈	PROPN
ejpam-2055	266	30	δ	δ	NOUN
ejpam-2055	266	31	−	−	NOUN
ejpam-2055	266	32	βς(x	βς(x	PUNCT
ejpam-2055	266	33	,	,	PUNCT
ejpam-2055	266	34	x	x	X
ejpam-2055	266	35	)	)	PUNCT
ejpam-2055	267	1	such	such	ADJ
ejpam-2055	267	2	that	that	SCONJ
ejpam-2055	267	3	f	f	PROPN
ejpam-2055	267	4	(	(	PUNCT
ejpam-2055	267	5	δ	δ	PROPN
ejpam-2055	267	6	−	−	NOUN
ejpam-2055	267	7	β	β	NOUN
ejpam-2055	267	8	−	−	NOUN
ejpam-2055	267	9	cl(v	cl(v	NOUN
ejpam-2055	267	10	)	)	PUNCT
ejpam-2055	267	11	)	)	PUNCT
ejpam-2055	268	1	⊂	⊂	PROPN
ejpam-2055	268	2	u	u	PROPN
ejpam-2055	268	3	.	.	PUNCT
ejpam-2055	269	1	therefore	therefore	ADV
ejpam-2055	269	2	,	,	PUNCT
ejpam-2055	269	3	we	we	PRON
ejpam-2055	269	4	have	have	VERB
ejpam-2055	269	5	x	x	X
ejpam-2055	269	6	∈	∈	PROPN
ejpam-2055	269	7	v	v	ADP
ejpam-2055	269	8	⊂	⊂	PROPN
ejpam-2055	269	9	δ−β−cl(v	δ−β−cl(v	NOUN
ejpam-2055	269	10	)	)	PUNCT
ejpam-2055	270	1	⊂	⊂	PROPN
ejpam-2055	270	2	u	u	PROPN
ejpam-2055	270	3	.	.	PUNCT
ejpam-2055	271	1	it	it	PRON
ejpam-2055	271	2	follows	follow	VERB
ejpam-2055	271	3	from	from	ADP
ejpam-2055	271	4	lemma	lemma	PROPN
ejpam-2055	271	5	2	2	NUM
ejpam-2055	271	6	that	that	PRON
ejpam-2055	271	7	x	x	PUNCT
ejpam-2055	271	8	is	be	AUX
ejpam-2055	271	9	δ−β	δ−β	ADJ
ejpam-2055	271	10	-regular	-regular	ADJ
ejpam-2055	271	11	.	.	PUNCT
ejpam-2055	272	1	(	(	PUNCT
ejpam-2055	272	2	sufficiency	sufficiency	NOUN
ejpam-2055	272	3	)	)	PUNCT
ejpam-2055	272	4	.	.	PUNCT
ejpam-2055	273	1	suppose	suppose	VERB
ejpam-2055	273	2	that	that	SCONJ
ejpam-2055	273	3	f	f	X
ejpam-2055	273	4	:	:	PUNCT
ejpam-2055	273	5	x	x	X
ejpam-2055	273	6	→	→	SYM
ejpam-2055	273	7	y	y	PROPN
ejpam-2055	273	8	is	be	AUX
ejpam-2055	273	9	continuous	continuous	ADJ
ejpam-2055	273	10	and	and	CCONJ
ejpam-2055	273	11	x	x	PRON
ejpam-2055	273	12	is	be	AUX
ejpam-2055	273	13	δ−β	δ−β	ADJ
ejpam-2055	273	14	-regular	-regular	ADJ
ejpam-2055	273	15	.	.	PUNCT
ejpam-2055	274	1	for	for	ADP
ejpam-2055	274	2	any	any	DET
ejpam-2055	274	3	x	x	SYM
ejpam-2055	274	4	∈	∈	PROPN
ejpam-2055	274	5	x	x	X
ejpam-2055	274	6	and	and	CCONJ
ejpam-2055	274	7	open	open	VERB
ejpam-2055	274	8	set	set	VERB
ejpam-2055	274	9	v	v	NOUN
ejpam-2055	274	10	containing	contain	VERB
ejpam-2055	274	11	f	f	X
ejpam-2055	274	12	(	(	PUNCT
ejpam-2055	274	13	x	x	NOUN
ejpam-2055	274	14	)	)	PUNCT
ejpam-2055	274	15	,	,	PUNCT
ejpam-2055	274	16	f	f	PROPN
ejpam-2055	274	17	−1(v	−1(v	PROPN
ejpam-2055	274	18	)	)	PUNCT
ejpam-2055	274	19	is	be	AUX
ejpam-2055	274	20	an	an	DET
ejpam-2055	274	21	open	open	ADJ
ejpam-2055	274	22	set	set	NOUN
ejpam-2055	274	23	containing	contain	VERB
ejpam-2055	274	24	x.	x.	NOUN
ejpam-2055	274	25	since	since	SCONJ
ejpam-2055	274	26	x	x	PRON
ejpam-2055	274	27	is	be	AUX
ejpam-2055	274	28	δ−β	δ−β	ADJ
ejpam-2055	274	29	-regular	-regular	ADJ
ejpam-2055	274	30	,	,	PUNCT
ejpam-2055	274	31	then	then	ADV
ejpam-2055	274	32	there	there	PRON
ejpam-2055	274	33	exists	exist	VERB
ejpam-2055	274	34	u	u	PROPN
ejpam-2055	274	35	∈	∈	PROPN
ejpam-2055	274	36	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	274	37	,	,	PUNCT
ejpam-2055	274	38	t	t	PROPN
ejpam-2055	274	39	)	)	PUNCT
ejpam-2055	274	40	such	such	ADJ
ejpam-2055	274	41	that	that	SCONJ
ejpam-2055	274	42	x	x	SYM
ejpam-2055	274	43	∈	∈	PROPN
ejpam-2055	274	44	u	u	NOUN
ejpam-2055	274	45	⊂	⊂	PROPN
ejpam-2055	274	46	δ−β	δ−β	PROPN
ejpam-2055	274	47	−cl(u	−cl(u	PROPN
ejpam-2055	274	48	)	)	PUNCT
ejpam-2055	274	49	⊂	⊂	PROPN
ejpam-2055	275	1	f	f	PROPN
ejpam-2055	275	2	−1(v	−1(v	PROPN
ejpam-2055	275	3	)	)	PUNCT
ejpam-2055	275	4	.	.	PUNCT
ejpam-2055	276	1	therefore	therefore	ADV
ejpam-2055	276	2	,	,	PUNCT
ejpam-2055	276	3	we	we	PRON
ejpam-2055	276	4	have	have	VERB
ejpam-2055	276	5	f	f	PROPN
ejpam-2055	276	6	(	(	PUNCT
ejpam-2055	276	7	δ−	δ−	PROPN
ejpam-2055	276	8	β	β	X
ejpam-2055	276	9	−	−	NOUN
ejpam-2055	276	10	cl(u	cl(u	NOUN
ejpam-2055	276	11	)	)	PUNCT
ejpam-2055	276	12	)	)	PUNCT
ejpam-2055	277	1	⊂	⊂	PROPN
ejpam-2055	277	2	v	v	X
ejpam-2055	277	3	.	.	PUNCT
ejpam-2055	278	1	this	this	PRON
ejpam-2055	278	2	shows	show	VERB
ejpam-2055	278	3	that	that	SCONJ
ejpam-2055	278	4	f	f	PROPN
ejpam-2055	278	5	is	be	AUX
ejpam-2055	278	6	strongly	strongly	ADV
ejpam-2055	278	7	θ	θ	NOUN
ejpam-2055	278	8	−δ−	−δ−	ADJ
ejpam-2055	278	9	β	β	AUX
ejpam-2055	278	10	-continuous	-continuous	PROPN
ejpam-2055	278	11	.	.	PUNCT
ejpam-2055	279	1	a.	a.	NOUN
ejpam-2055	279	2	m.	m.	PROPN
ejpam-2055	279	3	farhan	farhan	PROPN
ejpam-2055	279	4	and	and	CCONJ
ejpam-2055	279	5	x.	x.	PROPN
ejpam-2055	279	6	yang	yang	PROPN
ejpam-2055	279	7	/	/	SYM
ejpam-2055	279	8	eur	eur	PROPN
ejpam-2055	279	9	.	.	PUNCT
ejpam-2055	280	1	j.	j.	PROPN
ejpam-2055	280	2	pure	pure	PROPN
ejpam-2055	280	3	appl	appl	PROPN
ejpam-2055	280	4	.	.	PROPN
ejpam-2055	280	5	math	math	PROPN
ejpam-2055	280	6	,	,	PUNCT
ejpam-2055	280	7	8	8	NUM
ejpam-2055	280	8	(	(	PUNCT
ejpam-2055	280	9	2015	2015	NUM
ejpam-2055	280	10	)	)	PUNCT
ejpam-2055	280	11	,	,	PUNCT
ejpam-2055	280	12	185	185	NUM
ejpam-2055	280	13	-	-	SYM
ejpam-2055	280	14	200	200	NUM
ejpam-2055	280	15	192	192	NUM
ejpam-2055	280	16	theorem	theorem	NOUN
ejpam-2055	280	17	9	9	NUM
ejpam-2055	280	18	.	.	PUNCT
ejpam-2055	281	1	let	let	VERB
ejpam-2055	281	2	f	f	NOUN
ejpam-2055	281	3	:	:	PUNCT
ejpam-2055	281	4	x	x	X
ejpam-2055	281	5	→	→	SYM
ejpam-2055	281	6	y	y	X
ejpam-2055	281	7	be	be	AUX
ejpam-2055	281	8	a	a	DET
ejpam-2055	281	9	function	function	NOUN
ejpam-2055	281	10	and	and	CCONJ
ejpam-2055	281	11	g	g	NOUN
ejpam-2055	281	12	:	:	PUNCT
ejpam-2055	281	13	x	x	SYM
ejpam-2055	281	14	→	→	SYM
ejpam-2055	281	15	x	x	SYM
ejpam-2055	281	16	×	×	NOUN
ejpam-2055	281	17	y	y	NOUN
ejpam-2055	281	18	be	be	AUX
ejpam-2055	281	19	the	the	DET
ejpam-2055	281	20	graph	graph	NOUN
ejpam-2055	281	21	function	function	NOUN
ejpam-2055	281	22	of	of	ADP
ejpam-2055	281	23	f.	f.	PROPN
ejpam-2055	281	24	then	then	ADV
ejpam-2055	281	25	,	,	PUNCT
ejpam-2055	281	26	the	the	DET
ejpam-2055	281	27	following	follow	VERB
ejpam-2055	281	28	properties	property	NOUN
ejpam-2055	281	29	are	be	AUX
ejpam-2055	281	30	hold	hold	ADJ
ejpam-2055	281	31	:	:	PUNCT
ejpam-2055	281	32	a	a	X
ejpam-2055	281	33	)	)	PUNCT
ejpam-2055	281	34	if	if	SCONJ
ejpam-2055	281	35	g	g	PROPN
ejpam-2055	281	36	is	be	AUX
ejpam-2055	281	37	strongly	strongly	ADV
ejpam-2055	281	38	θ	θ	NOUN
ejpam-2055	281	39	−	−	PROPN
ejpam-2055	282	1	δ	δ	PROPN
ejpam-2055	282	2	−	−	NOUN
ejpam-2055	282	3	β	β	X
ejpam-2055	282	4	-continuous	-continuous	ADJ
ejpam-2055	282	5	,	,	PUNCT
ejpam-2055	282	6	then	then	ADV
ejpam-2055	282	7	f	f	PROPN
ejpam-2055	282	8	is	be	AUX
ejpam-2055	282	9	strongly	strongly	ADV
ejpam-2055	282	10	θ	θ	NOUN
ejpam-2055	282	11	−	−	PROPN
ejpam-2055	283	1	δ	δ	PROPN
ejpam-2055	283	2	−	−	NOUN
ejpam-2055	283	3	β	β	X
ejpam-2055	283	4	-continuous	-continuous	ADJ
ejpam-2055	283	5	.	.	PUNCT
ejpam-2055	284	1	and	and	CCONJ
ejpam-2055	284	2	x	x	X
ejpam-2055	284	3	is	be	AUX
ejpam-2055	284	4	δ−	δ−	PROPN
ejpam-2055	284	5	β	β	SYM
ejpam-2055	284	6	-regular	-regular	NOUN
ejpam-2055	284	7	.	.	PUNCT
ejpam-2055	285	1	b	b	X
ejpam-2055	285	2	)	)	PUNCT
ejpam-2055	285	3	if	if	SCONJ
ejpam-2055	285	4	f	f	PROPN
ejpam-2055	285	5	is	be	AUX
ejpam-2055	285	6	strongly	strongly	ADV
ejpam-2055	285	7	θ	θ	NOUN
ejpam-2055	285	8	−	−	PROPN
ejpam-2055	285	9	δ−	δ−	PROPN
ejpam-2055	285	10	β	β	X
ejpam-2055	285	11	-continuous	-continuous	ADJ
ejpam-2055	285	12	,	,	PUNCT
ejpam-2055	285	13	and	and	CCONJ
ejpam-2055	285	14	x	x	X
ejpam-2055	285	15	is	be	AUX
ejpam-2055	285	16	δ−	δ−	PROPN
ejpam-2055	285	17	β	β	SYM
ejpam-2055	285	18	-regular	-regular	ADJ
ejpam-2055	285	19	,	,	PUNCT
ejpam-2055	285	20	then	then	ADV
ejpam-2055	285	21	g	g	PROPN
ejpam-2055	285	22	is	be	AUX
ejpam-2055	285	23	strongly	strongly	ADV
ejpam-2055	285	24	θ	θ	NOUN
ejpam-2055	285	25	−	−	PROPN
ejpam-2055	286	1	δ−	δ−	PROPN
ejpam-2055	286	2	β	β	X
ejpam-2055	286	3	continuous	continuous	ADJ
ejpam-2055	286	4	.	.	PUNCT
ejpam-2055	287	1	proof	proof	NOUN
ejpam-2055	287	2	.	.	PUNCT
ejpam-2055	288	1	(	(	PUNCT
ejpam-2055	288	2	a	a	X
ejpam-2055	288	3	)	)	PUNCT
ejpam-2055	288	4	.	.	PUNCT
ejpam-2055	289	1	suppose	suppose	VERB
ejpam-2055	289	2	that	that	SCONJ
ejpam-2055	289	3	g	g	PROPN
ejpam-2055	289	4	is	be	AUX
ejpam-2055	289	5	strongly	strongly	ADV
ejpam-2055	289	6	θ	θ	NOUN
ejpam-2055	289	7	−	−	PROPN
ejpam-2055	289	8	δ	δ	PROPN
ejpam-2055	289	9	−	−	NOUN
ejpam-2055	289	10	β	β	X
ejpam-2055	289	11	-continuous	-continuous	ADJ
ejpam-2055	289	12	.	.	PUNCT
ejpam-2055	290	1	first	first	ADV
ejpam-2055	290	2	,	,	PUNCT
ejpam-2055	290	3	we	we	PRON
ejpam-2055	290	4	show	show	VERB
ejpam-2055	290	5	that	that	SCONJ
ejpam-2055	290	6	f	f	PROPN
ejpam-2055	290	7	is	be	AUX
ejpam-2055	290	8	strongly	strongly	ADV
ejpam-2055	290	9	θ	θ	NOUN
ejpam-2055	290	10	−	−	PROPN
ejpam-2055	290	11	δ	δ	PROPN
ejpam-2055	290	12	−	−	NOUN
ejpam-2055	290	13	β	β	X
ejpam-2055	290	14	-continuous	-continuous	ADJ
ejpam-2055	290	15	.	.	PUNCT
ejpam-2055	291	1	let	let	VERB
ejpam-2055	291	2	x	x	PUNCT
ejpam-2055	291	3	∈	∈	PROPN
ejpam-2055	291	4	x	x	X
ejpam-2055	291	5	and	and	CCONJ
ejpam-2055	291	6	v	v	ADP
ejpam-2055	291	7	an	an	DET
ejpam-2055	291	8	open	open	ADJ
ejpam-2055	291	9	set	set	NOUN
ejpam-2055	291	10	of	of	ADP
ejpam-2055	291	11	y	y	PROPN
ejpam-2055	291	12	containing	contain	VERB
ejpam-2055	291	13	f	f	PROPN
ejpam-2055	291	14	(	(	PUNCT
ejpam-2055	291	15	x	x	NOUN
ejpam-2055	291	16	)	)	PUNCT
ejpam-2055	291	17	.	.	PUNCT
ejpam-2055	292	1	then	then	ADV
ejpam-2055	292	2	x	x	X
ejpam-2055	292	3	×	×	NOUN
ejpam-2055	292	4	v	v	NOUN
ejpam-2055	292	5	is	be	AUX
ejpam-2055	292	6	an	an	DET
ejpam-2055	292	7	open	open	ADJ
ejpam-2055	292	8	set	set	NOUN
ejpam-2055	292	9	of	of	ADP
ejpam-2055	292	10	x	x	SYM
ejpam-2055	292	11	×	×	PROPN
ejpam-2055	292	12	y	y	NOUN
ejpam-2055	292	13	containing	contain	VERB
ejpam-2055	292	14	g(x	g(x	NOUN
ejpam-2055	292	15	)	)	PUNCT
ejpam-2055	292	16	.	.	PUNCT
ejpam-2055	293	1	since	since	SCONJ
ejpam-2055	293	2	g	g	PROPN
ejpam-2055	293	3	is	be	AUX
ejpam-2055	293	4	strongly	strongly	ADV
ejpam-2055	293	5	θ	θ	X
ejpam-2055	293	6	−δ−β	−δ−β	PROPN
ejpam-2055	293	7	-continuous	-continuous	ADJ
ejpam-2055	293	8	,	,	PUNCT
ejpam-2055	293	9	then	then	ADV
ejpam-2055	293	10	there	there	PRON
ejpam-2055	293	11	exists	exist	VERB
ejpam-2055	293	12	u	u	PROPN
ejpam-2055	293	13	∈	∈	PROPN
ejpam-2055	293	14	δ	δ	PROPN
ejpam-2055	293	15	−	−	NOUN
ejpam-2055	293	16	βς(x	βς(x	PUNCT
ejpam-2055	293	17	,	,	PUNCT
ejpam-2055	293	18	x	x	X
ejpam-2055	293	19	)	)	PUNCT
ejpam-2055	293	20	such	such	ADJ
ejpam-2055	293	21	that	that	SCONJ
ejpam-2055	293	22	g(δ	g(δ	PROPN
ejpam-2055	293	23	−	−	PROPN
ejpam-2055	293	24	β	β	NOUN
ejpam-2055	293	25	−	−	NOUN
ejpam-2055	293	26	cl(u	cl(u	PROPN
ejpam-2055	293	27	)	)	PUNCT
ejpam-2055	293	28	)	)	PUNCT
ejpam-2055	294	1	⊂	⊂	PUNCT
ejpam-2055	295	1	x	x	X
ejpam-2055	295	2	×	×	NOUN
ejpam-2055	295	3	v	v	NOUN
ejpam-2055	295	4	.	.	PUNCT
ejpam-2055	296	1	therefore	therefore	ADV
ejpam-2055	296	2	,	,	PUNCT
ejpam-2055	296	3	we	we	PRON
ejpam-2055	296	4	obtain	obtain	VERB
ejpam-2055	296	5	,	,	PUNCT
ejpam-2055	296	6	f	f	PROPN
ejpam-2055	296	7	(	(	PUNCT
ejpam-2055	296	8	δ−	δ−	PROPN
ejpam-2055	296	9	β	β	X
ejpam-2055	296	10	−	−	NOUN
ejpam-2055	296	11	cl(u	cl(u	NOUN
ejpam-2055	296	12	)	)	PUNCT
ejpam-2055	296	13	)	)	PUNCT
ejpam-2055	297	1	⊂	⊂	PROPN
ejpam-2055	297	2	v	v	INTJ
ejpam-2055	297	3	.	.	PUNCT
ejpam-2055	298	1	next	next	ADV
ejpam-2055	298	2	,	,	PUNCT
ejpam-2055	298	3	we	we	PRON
ejpam-2055	298	4	show	show	VERB
ejpam-2055	298	5	that	that	SCONJ
ejpam-2055	298	6	x	x	PRON
ejpam-2055	298	7	is	be	AUX
ejpam-2055	298	8	δ−	δ−	PROPN
ejpam-2055	298	9	β	β	SYM
ejpam-2055	298	10	-regular	-regular	PROPN
ejpam-2055	298	11	.	.	PUNCT
ejpam-2055	299	1	let	let	VERB
ejpam-2055	299	2	u	u	PRON
ejpam-2055	299	3	be	be	AUX
ejpam-2055	299	4	any	any	DET
ejpam-2055	299	5	open	open	ADJ
ejpam-2055	299	6	set	set	NOUN
ejpam-2055	299	7	of	of	ADP
ejpam-2055	299	8	x	x	PUNCT
ejpam-2055	299	9	and	and	CCONJ
ejpam-2055	299	10	x	x	SYM
ejpam-2055	299	11	∈	∈	PROPN
ejpam-2055	299	12	u	u	NOUN
ejpam-2055	299	13	.	.	PUNCT
ejpam-2055	300	1	since	since	SCONJ
ejpam-2055	300	2	g(x	g(x	NOUN
ejpam-2055	300	3	)	)	PUNCT
ejpam-2055	300	4	∈	∈	NOUN
ejpam-2055	300	5	u	u	NOUN
ejpam-2055	300	6	×y	×y	NOUN
ejpam-2055	300	7	and	and	CCONJ
ejpam-2055	300	8	u	u	PRON
ejpam-2055	300	9	×y	×y	PRON
ejpam-2055	300	10	is	be	AUX
ejpam-2055	300	11	an	an	DET
ejpam-2055	300	12	open	open	ADJ
ejpam-2055	300	13	in	in	ADP
ejpam-2055	300	14	x	x	PUNCT
ejpam-2055	300	15	×y	×y	PRON
ejpam-2055	300	16	,	,	PUNCT
ejpam-2055	300	17	then	then	ADV
ejpam-2055	300	18	there	there	PRON
ejpam-2055	300	19	exists	exist	VERB
ejpam-2055	300	20	w	w	PROPN
ejpam-2055	300	21	∈	∈	PROPN
ejpam-2055	300	22	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	300	23	,	,	PUNCT
ejpam-2055	300	24	x	x	X
ejpam-2055	300	25	)	)	PUNCT
ejpam-2055	300	26	such	such	ADJ
ejpam-2055	300	27	that	that	SCONJ
ejpam-2055	300	28	g(δ	g(δ	PROPN
ejpam-2055	300	29	−	−	PROPN
ejpam-2055	300	30	β	β	NOUN
ejpam-2055	300	31	−	−	PROPN
ejpam-2055	300	32	cl(w	cl(w	NOUN
ejpam-2055	300	33	)	)	PUNCT
ejpam-2055	300	34	)	)	PUNCT
ejpam-2055	301	1	⊂	⊂	PROPN
ejpam-2055	301	2	u	u	X
ejpam-2055	301	3	×	×	PROPN
ejpam-2055	301	4	y	y	PROPN
ejpam-2055	301	5	.	.	PUNCT
ejpam-2055	302	1	therefore	therefore	ADV
ejpam-2055	302	2	we	we	PRON
ejpam-2055	302	3	obtain	obtain	VERB
ejpam-2055	302	4	x	x	SYM
ejpam-2055	302	5	∈w	∈w	PROPN
ejpam-2055	302	6	⊂	⊂	PROPN
ejpam-2055	302	7	δ	δ	PROPN
ejpam-2055	302	8	−	−	NOUN
ejpam-2055	302	9	β	β	NOUN
ejpam-2055	302	10	−	−	PROPN
ejpam-2055	302	11	cl(w	cl(w	NOUN
ejpam-2055	302	12	)	)	PUNCT
ejpam-2055	303	1	⊂	⊂	PROPN
ejpam-2055	303	2	u	u	NOUN
ejpam-2055	303	3	and	and	CCONJ
ejpam-2055	303	4	hence	hence	ADV
ejpam-2055	303	5	x	x	PUNCT
ejpam-2055	303	6	is	be	AUX
ejpam-2055	303	7	δ−	δ−	PROPN
ejpam-2055	303	8	β	β	SYM
ejpam-2055	303	9	-regular	-regular	NOUN
ejpam-2055	303	10	.	.	PUNCT
ejpam-2055	304	1	(	(	PUNCT
ejpam-2055	304	2	b	b	NOUN
ejpam-2055	304	3	)	)	PUNCT
ejpam-2055	304	4	.	.	PUNCT
ejpam-2055	305	1	let	let	VERB
ejpam-2055	305	2	x	x	PUNCT
ejpam-2055	305	3	∈	∈	PROPN
ejpam-2055	305	4	x	x	X
ejpam-2055	305	5	and	and	CCONJ
ejpam-2055	305	6	h	h	DET
ejpam-2055	305	7	an	an	DET
ejpam-2055	305	8	open	open	ADJ
ejpam-2055	305	9	set	set	NOUN
ejpam-2055	305	10	of	of	ADP
ejpam-2055	305	11	x	x	SYM
ejpam-2055	305	12	×	×	PROPN
ejpam-2055	305	13	y	y	NOUN
ejpam-2055	305	14	containing	contain	VERB
ejpam-2055	305	15	g(x	g(x	NOUN
ejpam-2055	305	16	)	)	PUNCT
ejpam-2055	305	17	.	.	PUNCT
ejpam-2055	306	1	there	there	PRON
ejpam-2055	306	2	exists	exist	VERB
ejpam-2055	306	3	open	open	ADJ
ejpam-2055	306	4	sets	set	NOUN
ejpam-2055	306	5	u1	u1	VERB
ejpam-2055	306	6	⊂	⊂	PROPN
ejpam-2055	306	7	x	x	X
ejpam-2055	306	8	and	and	CCONJ
ejpam-2055	306	9	v	v	X
ejpam-2055	306	10	⊂	⊂	X
ejpam-2055	306	11	y	y	PROPN
ejpam-2055	306	12	such	such	ADJ
ejpam-2055	306	13	that	that	SCONJ
ejpam-2055	306	14	g(x	g(x	NOUN
ejpam-2055	306	15	)	)	PUNCT
ejpam-2055	307	1	=	=	SYM
ejpam-2055	307	2	(	(	PUNCT
ejpam-2055	307	3	x	x	INTJ
ejpam-2055	307	4	,	,	PUNCT
ejpam-2055	307	5	f	f	PROPN
ejpam-2055	307	6	(	(	PUNCT
ejpam-2055	307	7	x	x	NOUN
ejpam-2055	307	8	)	)	PUNCT
ejpam-2055	307	9	)	)	PUNCT
ejpam-2055	308	1	∈	∈	PROPN
ejpam-2055	308	2	u1×v	u1×v	PROPN
ejpam-2055	309	1	⊂	⊂	PROPN
ejpam-2055	309	2	h.	h.	PROPN
ejpam-2055	309	3	since	since	SCONJ
ejpam-2055	309	4	f	f	PROPN
ejpam-2055	309	5	is	be	AUX
ejpam-2055	309	6	strongly	strongly	ADV
ejpam-2055	309	7	θ	θ	X
ejpam-2055	309	8	−δ−β	−δ−β	PROPN
ejpam-2055	309	9	-continuous	-continuous	ADJ
ejpam-2055	309	10	,	,	PUNCT
ejpam-2055	309	11	there	there	PRON
ejpam-2055	309	12	exists	exist	VERB
ejpam-2055	309	13	u2	u2	PROPN
ejpam-2055	309	14	∈	∈	PROPN
ejpam-2055	309	15	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	309	16	,	,	PUNCT
ejpam-2055	309	17	x	x	X
ejpam-2055	309	18	)	)	PUNCT
ejpam-2055	309	19	such	such	ADJ
ejpam-2055	309	20	that	that	SCONJ
ejpam-2055	309	21	f	f	PROPN
ejpam-2055	309	22	(	(	PUNCT
ejpam-2055	309	23	δ−β	δ−β	PROPN
ejpam-2055	309	24	−	−	PROPN
ejpam-2055	309	25	cl(u2	cl(u2	NOUN
ejpam-2055	309	26	)	)	PUNCT
ejpam-2055	309	27	)	)	PUNCT
ejpam-2055	310	1	⊂	⊂	PROPN
ejpam-2055	310	2	v	v	X
ejpam-2055	310	3	.	.	PUNCT
ejpam-2055	311	1	since	since	SCONJ
ejpam-2055	311	2	x	x	PRON
ejpam-2055	311	3	is	be	AUX
ejpam-2055	311	4	δ−β	δ−β	ADJ
ejpam-2055	311	5	-regular	-regular	ADJ
ejpam-2055	311	6	and	and	CCONJ
ejpam-2055	311	7	u1	u1	VERB
ejpam-2055	311	8	⋂	⋂	PROPN
ejpam-2055	311	9	u2	u2	PROPN
ejpam-2055	311	10	∈	∈	PROPN
ejpam-2055	311	11	δ−	δ−	PROPN
ejpam-2055	311	12	βς(x	βς(x	X
ejpam-2055	311	13	,	,	PUNCT
ejpam-2055	311	14	x	x	X
ejpam-2055	311	15	)	)	PUNCT
ejpam-2055	311	16	,	,	PUNCT
ejpam-2055	311	17	so	so	CCONJ
ejpam-2055	311	18	there	there	PRON
ejpam-2055	311	19	exists	exist	VERB
ejpam-2055	311	20	u	u	PROPN
ejpam-2055	311	21	∈	∈	PROPN
ejpam-2055	311	22	δ−	δ−	PROPN
ejpam-2055	311	23	βς(x	βς(x	X
ejpam-2055	311	24	,	,	PUNCT
ejpam-2055	311	25	x	x	X
ejpam-2055	311	26	)	)	PUNCT
ejpam-2055	311	27	such	such	ADJ
ejpam-2055	311	28	that	that	SCONJ
ejpam-2055	311	29	x	x	SYM
ejpam-2055	311	30	∈	∈	PROPN
ejpam-2055	311	31	u	u	NOUN
ejpam-2055	311	32	⊂	⊂	X
ejpam-2055	311	33	δ−	δ−	PROPN
ejpam-2055	311	34	β	β	X
ejpam-2055	311	35	−	−	NOUN
ejpam-2055	311	36	cl(u	cl(u	PROPN
ejpam-2055	311	37	)	)	PUNCT
ejpam-2055	311	38	⊂	⊂	PRON
ejpam-2055	311	39	u1	u1	VERB
ejpam-2055	311	40	⋂	⋂	PROPN
ejpam-2055	311	41	u2	u2	PROPN
ejpam-2055	311	42	.	.	PUNCT
ejpam-2055	312	1	therefore	therefore	ADV
ejpam-2055	312	2	we	we	PRON
ejpam-2055	312	3	obtain	obtain	VERB
ejpam-2055	312	4	g(δ	g(δ	PROPN
ejpam-2055	312	5	−	−	PROPN
ejpam-2055	312	6	β	β	NOUN
ejpam-2055	312	7	−	−	NOUN
ejpam-2055	312	8	cl(u	cl(u	NOUN
ejpam-2055	312	9	)	)	PUNCT
ejpam-2055	312	10	)	)	PUNCT
ejpam-2055	313	1	⊂	⊂	PRON
ejpam-2055	313	2	u1	u1	VERB
ejpam-2055	313	3	×	×	PROPN
ejpam-2055	313	4	f	f	PROPN
ejpam-2055	313	5	(	(	PUNCT
ejpam-2055	313	6	δ	δ	PROPN
ejpam-2055	313	7	−	−	NOUN
ejpam-2055	313	8	β	β	NOUN
ejpam-2055	313	9	−	−	PROPN
ejpam-2055	313	10	cl(u2	cl(u2	PROPN
ejpam-2055	313	11	)	)	PUNCT
ejpam-2055	313	12	)	)	PUNCT
ejpam-2055	314	1	⊂	⊂	PRON
ejpam-2055	314	2	u1	u1	VERB
ejpam-2055	314	3	×	×	PROPN
ejpam-2055	314	4	v	v	ADP
ejpam-2055	314	5	⊂	⊂	PROPN
ejpam-2055	314	6	h.	h.	PROPN
ejpam-2055	315	1	this	this	PRON
ejpam-2055	315	2	show	show	VERB
ejpam-2055	315	3	that	that	SCONJ
ejpam-2055	315	4	g	g	PROPN
ejpam-2055	315	5	is	be	AUX
ejpam-2055	315	6	strongly	strongly	ADV
ejpam-2055	315	7	θ	θ	NOUN
ejpam-2055	315	8	−δ−	−δ−	ADJ
ejpam-2055	315	9	β	β	X
ejpam-2055	315	10	-continuous	-continuous	ADJ
ejpam-2055	315	11	.	.	PUNCT
ejpam-2055	316	1	5	5	NUM
ejpam-2055	316	2	.	.	X
ejpam-2055	316	3	comparisons	comparison	NOUN
ejpam-2055	316	4	and	and	CCONJ
ejpam-2055	316	5	examples	example	NOUN
ejpam-2055	316	6	in	in	ADP
ejpam-2055	316	7	this	this	DET
ejpam-2055	316	8	section	section	NOUN
ejpam-2055	316	9	,	,	PUNCT
ejpam-2055	316	10	we	we	PRON
ejpam-2055	316	11	investigate	investigate	VERB
ejpam-2055	316	12	the	the	DET
ejpam-2055	316	13	relationships	relationship	NOUN
ejpam-2055	316	14	between	between	ADP
ejpam-2055	316	15	strongly	strongly	ADV
ejpam-2055	316	16	θ	θ	PROPN
ejpam-2055	316	17	−	−	PROPN
ejpam-2055	317	1	δ	δ	PROPN
ejpam-2055	317	2	−	−	NOUN
ejpam-2055	317	3	β	β	X
ejpam-2055	317	4	-continuous	-continuous	ADJ
ejpam-2055	317	5	function	function	NOUN
ejpam-2055	317	6	and	and	CCONJ
ejpam-2055	317	7	other	other	ADJ
ejpam-2055	317	8	well	well	ADV
ejpam-2055	317	9	-	-	PUNCT
ejpam-2055	317	10	known	know	VERB
ejpam-2055	317	11	types	type	NOUN
ejpam-2055	317	12	of	of	ADP
ejpam-2055	317	13	strong	strong	ADJ
ejpam-2055	317	14	continuity	continuity	NOUN
ejpam-2055	317	15	.	.	PUNCT
ejpam-2055	318	1	definition	definition	NOUN
ejpam-2055	318	2	6	6	NUM
ejpam-2055	318	3	.	.	PUNCT
ejpam-2055	319	1	a	a	DET
ejpam-2055	319	2	function	function	NOUN
ejpam-2055	319	3	f	f	NOUN
ejpam-2055	319	4	:	:	PUNCT
ejpam-2055	319	5	(	(	PUNCT
ejpam-2055	319	6	x	x	X
ejpam-2055	319	7	,	,	PUNCT
ejpam-2055	319	8	t	t	NOUN
ejpam-2055	319	9	)	)	PUNCT
ejpam-2055	319	10	→	→	SYM
ejpam-2055	319	11	(	(	PUNCT
ejpam-2055	319	12	y	y	PROPN
ejpam-2055	319	13	,	,	PUNCT
ejpam-2055	319	14	t	t	PROPN
ejpam-2055	319	15	∗	∗	NOUN
ejpam-2055	319	16	)	)	PUNCT
ejpam-2055	319	17	is	be	AUX
ejpam-2055	319	18	said	say	VERB
ejpam-2055	319	19	to	to	PART
ejpam-2055	319	20	be	be	AUX
ejpam-2055	319	21	:	:	PUNCT
ejpam-2055	319	22	a	a	X
ejpam-2055	319	23	)	)	PUNCT
ejpam-2055	319	24	strongly	strongly	ADV
ejpam-2055	319	25	θ	θ	PROPN
ejpam-2055	319	26	-continuous	-continuous	ADJ
ejpam-2055	320	1	[	[	X
ejpam-2055	320	2	37	37	NUM
ejpam-2055	320	3	]	]	X
ejpam-2055	320	4	if	if	SCONJ
ejpam-2055	320	5	for	for	ADP
ejpam-2055	320	6	each	each	DET
ejpam-2055	320	7	x	x	SYM
ejpam-2055	320	8	∈	∈	PROPN
ejpam-2055	320	9	x	x	X
ejpam-2055	320	10	and	and	CCONJ
ejpam-2055	320	11	each	each	DET
ejpam-2055	320	12	open	open	ADJ
ejpam-2055	320	13	set	set	VERB
ejpam-2055	320	14	v	v	NOUN
ejpam-2055	320	15	of	of	ADP
ejpam-2055	320	16	y	y	PROPN
ejpam-2055	320	17	containing	contain	VERB
ejpam-2055	320	18	f	f	PROPN
ejpam-2055	320	19	(	(	PUNCT
ejpam-2055	320	20	x	x	NOUN
ejpam-2055	320	21	)	)	PUNCT
ejpam-2055	320	22	,	,	PUNCT
ejpam-2055	320	23	there	there	PRON
ejpam-2055	320	24	exists	exist	VERB
ejpam-2055	320	25	an	an	DET
ejpam-2055	320	26	open	open	ADJ
ejpam-2055	320	27	set	set	NOUN
ejpam-2055	320	28	u	u	NOUN
ejpam-2055	320	29	of	of	ADP
ejpam-2055	320	30	x	x	PUNCT
ejpam-2055	320	31	containing	contain	VERB
ejpam-2055	320	32	x	x	PUNCT
ejpam-2055	320	33	such	such	ADJ
ejpam-2055	320	34	that	that	SCONJ
ejpam-2055	320	35	f	f	PROPN
ejpam-2055	320	36	(	(	PUNCT
ejpam-2055	320	37	cl(u	cl(u	PROPN
ejpam-2055	320	38	)	)	PUNCT
ejpam-2055	320	39	)	)	PUNCT
ejpam-2055	321	1	⊂	⊂	PROPN
ejpam-2055	321	2	v	v	ADP
ejpam-2055	321	3	;	;	PUNCT
ejpam-2055	321	4	b	b	X
ejpam-2055	321	5	)	)	PUNCT
ejpam-2055	321	6	strongly	strongly	ADV
ejpam-2055	321	7	θ	θ	PROPN
ejpam-2055	321	8	-semicontinuous	-semicontinuous	ADJ
ejpam-2055	321	9	[	[	X
ejpam-2055	321	10	29	29	NUM
ejpam-2055	321	11	]	]	X
ejpam-2055	321	12	if	if	SCONJ
ejpam-2055	321	13	for	for	ADP
ejpam-2055	321	14	each	each	DET
ejpam-2055	321	15	x	x	SYM
ejpam-2055	321	16	∈	∈	PROPN
ejpam-2055	321	17	x	x	X
ejpam-2055	321	18	and	and	CCONJ
ejpam-2055	321	19	each	each	DET
ejpam-2055	321	20	open	open	ADJ
ejpam-2055	321	21	set	set	VERB
ejpam-2055	321	22	v	v	NOUN
ejpam-2055	321	23	of	of	ADP
ejpam-2055	321	24	y	y	PROPN
ejpam-2055	321	25	containing	contain	VERB
ejpam-2055	321	26	f	f	PROPN
ejpam-2055	321	27	(	(	PUNCT
ejpam-2055	321	28	x	x	NOUN
ejpam-2055	321	29	)	)	PUNCT
ejpam-2055	321	30	,	,	PUNCT
ejpam-2055	321	31	there	there	PRON
ejpam-2055	321	32	exists	exist	VERB
ejpam-2055	321	33	a	a	DET
ejpam-2055	321	34	semi	semi	ADJ
ejpam-2055	321	35	-	-	ADJ
ejpam-2055	321	36	open	open	ADJ
ejpam-2055	321	37	set	set	ADJ
ejpam-2055	321	38	u	u	NOUN
ejpam-2055	321	39	of	of	ADP
ejpam-2055	321	40	x	x	PUNCT
ejpam-2055	321	41	containing	contain	VERB
ejpam-2055	321	42	x	x	PUNCT
ejpam-2055	321	43	such	such	ADJ
ejpam-2055	321	44	that	that	SCONJ
ejpam-2055	321	45	f	f	PROPN
ejpam-2055	321	46	(	(	PUNCT
ejpam-2055	321	47	sc	sc	PROPN
ejpam-2055	321	48	l(u	l(u	PROPN
ejpam-2055	321	49	)	)	PUNCT
ejpam-2055	321	50	)	)	PUNCT
ejpam-2055	322	1	⊂	⊂	PROPN
ejpam-2055	322	2	v	v	ADP
ejpam-2055	322	3	;	;	PUNCT
ejpam-2055	322	4	c	c	X
ejpam-2055	322	5	)	)	PUNCT
ejpam-2055	322	6	strongly	strongly	ADV
ejpam-2055	322	7	θ	θ	PROPN
ejpam-2055	322	8	-precontinuous	-precontinuous	ADJ
ejpam-2055	322	9	[	[	X
ejpam-2055	322	10	38	38	NUM
ejpam-2055	322	11	]	]	PUNCT
ejpam-2055	322	12	if	if	SCONJ
ejpam-2055	322	13	for	for	SCONJ
ejpam-2055	322	14	each	each	DET
ejpam-2055	322	15	x	x	SYM
ejpam-2055	322	16	∈	∈	PROPN
ejpam-2055	322	17	x	x	X
ejpam-2055	322	18	and	and	CCONJ
ejpam-2055	322	19	each	each	DET
ejpam-2055	322	20	open	open	ADJ
ejpam-2055	322	21	set	set	VERB
ejpam-2055	322	22	v	v	NOUN
ejpam-2055	322	23	of	of	ADP
ejpam-2055	322	24	y	y	PROPN
ejpam-2055	322	25	containing	contain	VERB
ejpam-2055	322	26	f	f	PROPN
ejpam-2055	322	27	(	(	PUNCT
ejpam-2055	322	28	x	x	NOUN
ejpam-2055	322	29	)	)	PUNCT
ejpam-2055	322	30	,	,	PUNCT
ejpam-2055	322	31	there	there	PRON
ejpam-2055	322	32	exists	exist	VERB
ejpam-2055	322	33	a	a	DET
ejpam-2055	322	34	preopen	preopen	ADJ
ejpam-2055	322	35	set	set	NOUN
ejpam-2055	322	36	u	u	NOUN
ejpam-2055	322	37	of	of	ADP
ejpam-2055	322	38	x	x	PUNCT
ejpam-2055	322	39	containing	contain	VERB
ejpam-2055	322	40	x	x	PUNCT
ejpam-2055	322	41	such	such	ADJ
ejpam-2055	322	42	that	that	SCONJ
ejpam-2055	322	43	f	f	PROPN
ejpam-2055	322	44	(	(	PUNCT
ejpam-2055	322	45	pcl(u	pcl(u	PROPN
ejpam-2055	322	46	)	)	PUNCT
ejpam-2055	322	47	)	)	PUNCT
ejpam-2055	323	1	⊂	⊂	PROPN
ejpam-2055	323	2	v	v	ADP
ejpam-2055	323	3	;	;	PUNCT
ejpam-2055	323	4	d	d	X
ejpam-2055	323	5	)	)	PUNCT
ejpam-2055	323	6	strongly	strongly	ADV
ejpam-2055	323	7	θ−β	θ−β	NOUN
ejpam-2055	323	8	-continuous	-continuous	ADJ
ejpam-2055	323	9	[	[	X
ejpam-2055	323	10	39	39	NUM
ejpam-2055	323	11	]	]	PUNCT
ejpam-2055	323	12	if	if	SCONJ
ejpam-2055	323	13	for	for	ADP
ejpam-2055	323	14	each	each	DET
ejpam-2055	323	15	x	x	SYM
ejpam-2055	323	16	∈	∈	PROPN
ejpam-2055	323	17	x	x	X
ejpam-2055	323	18	and	and	CCONJ
ejpam-2055	323	19	each	each	DET
ejpam-2055	323	20	open	open	ADJ
ejpam-2055	323	21	set	set	VERB
ejpam-2055	323	22	v	v	NOUN
ejpam-2055	323	23	of	of	ADP
ejpam-2055	323	24	y	y	PROPN
ejpam-2055	323	25	containing	contain	VERB
ejpam-2055	323	26	f	f	PROPN
ejpam-2055	323	27	(	(	PUNCT
ejpam-2055	323	28	x	x	NOUN
ejpam-2055	323	29	)	)	PUNCT
ejpam-2055	323	30	,	,	PUNCT
ejpam-2055	323	31	there	there	PRON
ejpam-2055	323	32	exists	exist	VERB
ejpam-2055	323	33	a	a	DET
ejpam-2055	323	34	semi	semi	ADJ
ejpam-2055	323	35	-	-	ADJ
ejpam-2055	323	36	preopen	preopen	ADJ
ejpam-2055	323	37	set	set	NOUN
ejpam-2055	323	38	u	u	NOUN
ejpam-2055	323	39	of	of	ADP
ejpam-2055	323	40	x	x	PUNCT
ejpam-2055	323	41	containing	contain	VERB
ejpam-2055	323	42	x	x	PUNCT
ejpam-2055	323	43	such	such	ADJ
ejpam-2055	323	44	that	that	PRON
ejpam-2055	323	45	,	,	PUNCT
ejpam-2055	323	46	f	f	PROPN
ejpam-2055	323	47	(	(	PUNCT
ejpam-2055	323	48	βcl(u	βcl(u	PROPN
ejpam-2055	323	49	)	)	PUNCT
ejpam-2055	323	50	)	)	PUNCT
ejpam-2055	324	1	⊂	⊂	PROPN
ejpam-2055	324	2	v	v	ADP
ejpam-2055	324	3	;	;	PUNCT
ejpam-2055	324	4	e	e	X
ejpam-2055	324	5	)	)	PUNCT
ejpam-2055	324	6	strongly	strongly	ADV
ejpam-2055	324	7	θ	θ	NOUN
ejpam-2055	324	8	-b	-b	PUNCT
ejpam-2055	324	9	-	-	ADJ
ejpam-2055	324	10	continuous	continuous	ADJ
ejpam-2055	324	11	[	[	X
ejpam-2055	324	12	42	42	NUM
ejpam-2055	324	13	]	]	PUNCT
ejpam-2055	324	14	if	if	SCONJ
ejpam-2055	324	15	for	for	SCONJ
ejpam-2055	324	16	each	each	DET
ejpam-2055	324	17	x	x	SYM
ejpam-2055	324	18	∈	∈	PROPN
ejpam-2055	324	19	x	x	X
ejpam-2055	324	20	and	and	CCONJ
ejpam-2055	324	21	each	each	DET
ejpam-2055	324	22	open	open	ADJ
ejpam-2055	324	23	set	set	VERB
ejpam-2055	324	24	v	v	NOUN
ejpam-2055	324	25	of	of	ADP
ejpam-2055	324	26	y	y	PROPN
ejpam-2055	324	27	containing	contain	VERB
ejpam-2055	324	28	f	f	PROPN
ejpam-2055	324	29	(	(	PUNCT
ejpam-2055	324	30	x	x	NOUN
ejpam-2055	324	31	)	)	PUNCT
ejpam-2055	324	32	,	,	PUNCT
ejpam-2055	324	33	there	there	PRON
ejpam-2055	324	34	exists	exist	VERB
ejpam-2055	324	35	a	a	DET
ejpam-2055	324	36	b	b	NOUN
ejpam-2055	324	37	-	-	PUNCT
ejpam-2055	324	38	open	open	ADJ
ejpam-2055	324	39	set	set	NOUN
ejpam-2055	324	40	u	u	NOUN
ejpam-2055	324	41	of	of	ADP
ejpam-2055	324	42	x	x	PUNCT
ejpam-2055	324	43	containing	contain	VERB
ejpam-2055	324	44	x	x	PUNCT
ejpam-2055	324	45	such	such	ADJ
ejpam-2055	324	46	that	that	SCONJ
ejpam-2055	324	47	f	f	PROPN
ejpam-2055	324	48	(	(	PUNCT
ejpam-2055	324	49	bcl(u	bcl(u	PROPN
ejpam-2055	324	50	)	)	PUNCT
ejpam-2055	324	51	)	)	PUNCT
ejpam-2055	325	1	⊂	⊂	PROPN
ejpam-2055	325	2	v	v	ADP
ejpam-2055	325	3	;	;	PUNCT
ejpam-2055	325	4	a.	a.	NOUN
ejpam-2055	325	5	m.	m.	NOUN
ejpam-2055	325	6	farhan	farhan	PROPN
ejpam-2055	325	7	and	and	CCONJ
ejpam-2055	325	8	x.	x.	PROPN
ejpam-2055	325	9	yang	yang	PROPN
ejpam-2055	325	10	/	/	SYM
ejpam-2055	325	11	eur	eur	PROPN
ejpam-2055	325	12	.	.	PUNCT
ejpam-2055	326	1	j.	j.	PROPN
ejpam-2055	326	2	pure	pure	PROPN
ejpam-2055	326	3	appl	appl	PROPN
ejpam-2055	326	4	.	.	PROPN
ejpam-2055	326	5	math	math	PROPN
ejpam-2055	326	6	,	,	PUNCT
ejpam-2055	326	7	8	8	NUM
ejpam-2055	326	8	(	(	PUNCT
ejpam-2055	326	9	2015	2015	NUM
ejpam-2055	326	10	)	)	PUNCT
ejpam-2055	326	11	,	,	PUNCT
ejpam-2055	326	12	185	185	NUM
ejpam-2055	326	13	-	-	SYM
ejpam-2055	326	14	200	200	NUM
ejpam-2055	326	15	193	193	NUM
ejpam-2055	326	16	f	f	NOUN
ejpam-2055	326	17	)	)	PUNCT
ejpam-2055	326	18	strongly	strongly	ADV
ejpam-2055	326	19	b	b	X
ejpam-2055	326	20	-	-	ADJ
ejpam-2055	326	21	continuous	continuous	ADJ
ejpam-2055	326	22	[	[	X
ejpam-2055	326	23	10	10	NUM
ejpam-2055	326	24	]	]	X
ejpam-2055	326	25	if	if	SCONJ
ejpam-2055	326	26	for	for	ADP
ejpam-2055	326	27	each	each	DET
ejpam-2055	326	28	x	x	SYM
ejpam-2055	326	29	∈	∈	PROPN
ejpam-2055	326	30	x	x	X
ejpam-2055	326	31	and	and	CCONJ
ejpam-2055	326	32	each	each	DET
ejpam-2055	326	33	open	open	ADJ
ejpam-2055	326	34	set	set	VERB
ejpam-2055	326	35	v	v	NOUN
ejpam-2055	326	36	of	of	ADP
ejpam-2055	326	37	y	y	PROPN
ejpam-2055	326	38	containing	contain	VERB
ejpam-2055	326	39	f	f	PROPN
ejpam-2055	326	40	(	(	PUNCT
ejpam-2055	326	41	x	x	NOUN
ejpam-2055	326	42	)	)	PUNCT
ejpam-2055	327	1	,	,	PUNCT
ejpam-2055	327	2	there	there	PRON
ejpam-2055	327	3	exists	exist	VERB
ejpam-2055	327	4	u	u	PROPN
ejpam-2055	327	5	∈	∈	PROPN
ejpam-2055	327	6	bo(x	bo(x	NUM
ejpam-2055	327	7	,	,	PUNCT
ejpam-2055	327	8	x	x	X
ejpam-2055	327	9	)	)	PUNCT
ejpam-2055	327	10	such	such	ADJ
ejpam-2055	327	11	that	that	SCONJ
ejpam-2055	327	12	f	f	PROPN
ejpam-2055	327	13	(	(	PUNCT
ejpam-2055	327	14	u	u	NOUN
ejpam-2055	327	15	)	)	PUNCT
ejpam-2055	327	16	⊂	⊂	PROPN
ejpam-2055	327	17	v	v	ADP
ejpam-2055	327	18	;	;	PUNCT
ejpam-2055	327	19	g	g	NOUN
ejpam-2055	327	20	)	)	PUNCT
ejpam-2055	327	21	strongly	strongly	ADV
ejpam-2055	327	22	θ	θ	X
ejpam-2055	327	23	-e	-e	X
ejpam-2055	327	24	-	-	PUNCT
ejpam-2055	327	25	continuous	continuous	ADJ
ejpam-2055	327	26	[	[	X
ejpam-2055	327	27	41	41	NUM
ejpam-2055	327	28	]	]	X
ejpam-2055	327	29	if	if	SCONJ
ejpam-2055	327	30	for	for	ADP
ejpam-2055	327	31	each	each	DET
ejpam-2055	327	32	x	x	SYM
ejpam-2055	327	33	∈	∈	PROPN
ejpam-2055	327	34	x	x	X
ejpam-2055	327	35	and	and	CCONJ
ejpam-2055	327	36	each	each	DET
ejpam-2055	327	37	open	open	ADJ
ejpam-2055	327	38	set	set	VERB
ejpam-2055	327	39	v	v	NOUN
ejpam-2055	327	40	of	of	ADP
ejpam-2055	327	41	y	y	PROPN
ejpam-2055	327	42	containing	contain	VERB
ejpam-2055	327	43	f	f	PROPN
ejpam-2055	327	44	(	(	PUNCT
ejpam-2055	327	45	x	x	NOUN
ejpam-2055	327	46	)	)	PUNCT
ejpam-2055	327	47	,	,	PUNCT
ejpam-2055	327	48	there	there	PRON
ejpam-2055	327	49	exists	exist	VERB
ejpam-2055	327	50	an	an	DET
ejpam-2055	327	51	e	e	NOUN
ejpam-2055	327	52	-	-	ADJ
ejpam-2055	327	53	open	open	ADJ
ejpam-2055	327	54	set	set	ADJ
ejpam-2055	327	55	u	u	NOUN
ejpam-2055	327	56	of	of	ADP
ejpam-2055	327	57	x	x	PUNCT
ejpam-2055	327	58	containing	contain	VERB
ejpam-2055	327	59	x	x	PUNCT
ejpam-2055	327	60	such	such	ADJ
ejpam-2055	327	61	that	that	SCONJ
ejpam-2055	327	62	f	f	PROPN
ejpam-2055	327	63	(	(	PUNCT
ejpam-2055	327	64	e−	e−	X
ejpam-2055	327	65	cl(u	cl(u	PROPN
ejpam-2055	327	66	)	)	PUNCT
ejpam-2055	327	67	)	)	PUNCT
ejpam-2055	328	1	⊂	⊂	PROPN
ejpam-2055	328	2	v	v	X
ejpam-2055	328	3	.	.	PUNCT
ejpam-2055	329	1	remark	remark	PROPN
ejpam-2055	329	2	6	6	NUM
ejpam-2055	329	3	.	.	PUNCT
ejpam-2055	329	4	from	from	ADP
ejpam-2055	329	5	definitions	definition	NOUN
ejpam-2055	329	6	3	3	NUM
ejpam-2055	329	7	and	and	CCONJ
ejpam-2055	329	8	6	6	NUM
ejpam-2055	329	9	we	we	PRON
ejpam-2055	329	10	have	have	VERB
ejpam-2055	329	11	the	the	DET
ejpam-2055	329	12	following	follow	VERB
ejpam-2055	329	13	diagram	diagram	NOUN
ejpam-2055	329	14	.	.	PUNCT
ejpam-2055	330	1	however	however	ADV
ejpam-2055	330	2	the	the	DET
ejpam-2055	330	3	converses	converse	NOUN
ejpam-2055	330	4	are	be	AUX
ejpam-2055	330	5	not	not	PART
ejpam-2055	330	6	true	true	ADJ
ejpam-2055	330	7	in	in	ADP
ejpam-2055	330	8	general	general	ADJ
ejpam-2055	330	9	by	by	ADP
ejpam-2055	330	10	examples	example	NOUN
ejpam-2055	330	11	(	(	PUNCT
ejpam-2055	330	12	4.4,4.5,4.6,4.7,4.8	4.4,4.5,4.6,4.7,4.8	NUM
ejpam-2055	330	13	)	)	PUNCT
ejpam-2055	330	14	of	of	ADP
ejpam-2055	330	15	[	[	X
ejpam-2055	330	16	42	42	NUM
ejpam-2055	330	17	]	]	PUNCT
ejpam-2055	330	18	and	and	CCONJ
ejpam-2055	330	19	(	(	PUNCT
ejpam-2055	330	20	4.2,4.3,4.4,4.5	4.2,4.3,4.4,4.5	NUM
ejpam-2055	330	21	)	)	PUNCT
ejpam-2055	331	1	[	[	X
ejpam-2055	331	2	41	41	NUM
ejpam-2055	331	3	]	]	PUNCT
ejpam-2055	331	4	and	and	CCONJ
ejpam-2055	331	5	the	the	DET
ejpam-2055	331	6	following	follow	VERB
ejpam-2055	331	7	examples	example	NOUN
ejpam-2055	331	8	.	.	PUNCT
ejpam-2055	332	1	figure	figure	NOUN
ejpam-2055	332	2	2	2	NUM
ejpam-2055	332	3	:	:	PUNCT
ejpam-2055	332	4	the	the	DET
ejpam-2055	332	5	relationships	relationship	NOUN
ejpam-2055	332	6	between	between	ADP
ejpam-2055	332	7	strongly	strongly	ADV
ejpam-2055	332	8	îÿâĺšîťâĺšîš	îÿâĺšîťâĺšîš	ADJ
ejpam-2055	332	9	-	-	PUNCT
ejpam-2055	332	10	continuous	continuous	ADJ
ejpam-2055	332	11	functions	function	NOUN
ejpam-2055	332	12	and	and	CCONJ
ejpam-2055	332	13	other	other	ADJ
ejpam-2055	332	14	known	know	VERB
ejpam-2055	332	15	types	type	NOUN
ejpam-2055	332	16	of	of	ADP
ejpam-2055	332	17	strong	strong	ADJ
ejpam-2055	332	18	continuity	continuity	NOUN
ejpam-2055	332	19	example	example	NOUN
ejpam-2055	333	1	4	4	X
ejpam-2055	333	2	.	.	PUNCT
ejpam-2055	334	1	let	let	VERB
ejpam-2055	334	2	x	x	PUNCT
ejpam-2055	334	3	=	=	PUNCT
ejpam-2055	334	4	{	{	PUNCT
ejpam-2055	334	5	1,2,3,4,5	1,2,3,4,5	NUM
ejpam-2055	334	6	}	}	PUNCT
ejpam-2055	334	7	,	,	PUNCT
ejpam-2055	334	8	define	define	VERB
ejpam-2055	334	9	a	a	DET
ejpam-2055	334	10	topology	topology	NOUN
ejpam-2055	334	11	t	t	NOUN
ejpam-2055	334	12	=	=	SYM
ejpam-2055	334	13	{	{	PUNCT
ejpam-2055	334	14	φ	φ	PROPN
ejpam-2055	334	15	,	,	PUNCT
ejpam-2055	334	16	x	x	INTJ
ejpam-2055	334	17	,	,	PUNCT
ejpam-2055	334	18	{	{	PUNCT
ejpam-2055	334	19	1	1	NUM
ejpam-2055	334	20	}	}	PUNCT
ejpam-2055	334	21	,	,	PUNCT
ejpam-2055	334	22	{	{	PUNCT
ejpam-2055	334	23	3	3	NUM
ejpam-2055	334	24	}	}	PUNCT
ejpam-2055	334	25	,	,	PUNCT
ejpam-2055	334	26	{	{	PUNCT
ejpam-2055	334	27	1,3	1,3	NUM
ejpam-2055	334	28	}	}	PUNCT
ejpam-2055	334	29	,	,	PUNCT
ejpam-2055	334	30	{	{	PUNCT
ejpam-2055	334	31	3,4	3,4	NUM
ejpam-2055	334	32	}	}	PUNCT
ejpam-2055	334	33	,	,	PUNCT
ejpam-2055	334	34	{	{	PUNCT
ejpam-2055	334	35	1,3,4	1,3,4	NUM
ejpam-2055	334	36	}	}	PUNCT
ejpam-2055	334	37	}	}	PUNCT
ejpam-2055	334	38	on	on	ADP
ejpam-2055	334	39	x	x	PUNCT
ejpam-2055	334	40	and	and	CCONJ
ejpam-2055	334	41	a	a	DET
ejpam-2055	334	42	topology	topology	NOUN
ejpam-2055	334	43	t	t	NOUN
ejpam-2055	334	44	∗	∗	NOUN
ejpam-2055	334	45	=	=	SYM
ejpam-2055	334	46	{	{	PUNCT
ejpam-2055	334	47	φ	φ	PROPN
ejpam-2055	334	48	,	,	PUNCT
ejpam-2055	334	49	x	x	INTJ
ejpam-2055	334	50	,	,	PUNCT
ejpam-2055	334	51	{	{	PUNCT
ejpam-2055	334	52	4	4	NUM
ejpam-2055	334	53	}	}	PUNCT
ejpam-2055	334	54	}	}	PUNCT
ejpam-2055	334	55	on	on	ADP
ejpam-2055	334	56	y.	y.	PROPN
ejpam-2055	334	57	then	then	ADV
ejpam-2055	334	58	the	the	DET
ejpam-2055	334	59	identity	identity	NOUN
ejpam-2055	334	60	function	function	NOUN
ejpam-2055	334	61	f	f	NOUN
ejpam-2055	334	62	:	:	PUNCT
ejpam-2055	334	63	x	x	X
ejpam-2055	334	64	→	→	SYM
ejpam-2055	334	65	y	y	PROPN
ejpam-2055	334	66	is	be	AUX
ejpam-2055	334	67	strongly	strongly	ADV
ejpam-2055	334	68	θ	θ	NOUN
ejpam-2055	334	69	−δ−	−δ−	ADJ
ejpam-2055	335	1	β	β	X
ejpam-2055	335	2	-continuous	-continuous	ADJ
ejpam-2055	335	3	but	but	CCONJ
ejpam-2055	335	4	not	not	PART
ejpam-2055	335	5	strongly	strongly	ADV
ejpam-2055	335	6	θ	θ	NOUN
ejpam-2055	335	7	-b	-b	PUNCT
ejpam-2055	335	8	-	-	PUNCT
ejpam-2055	335	9	continuous	continuous	ADJ
ejpam-2055	335	10	.	.	PUNCT
ejpam-2055	335	11	example	example	NOUN
ejpam-2055	335	12	5	5	NUM
ejpam-2055	335	13	.	.	PUNCT
ejpam-2055	336	1	let	let	VERB
ejpam-2055	336	2	x	x	PUNCT
ejpam-2055	336	3	=	=	PUNCT
ejpam-2055	336	4	{	{	PUNCT
ejpam-2055	336	5	1,2,3,4,5	1,2,3,4,5	NUM
ejpam-2055	336	6	}	}	PUNCT
ejpam-2055	336	7	,	,	PUNCT
ejpam-2055	336	8	define	define	VERB
ejpam-2055	336	9	a	a	DET
ejpam-2055	336	10	topology	topology	NOUN
ejpam-2055	336	11	t	t	NOUN
ejpam-2055	336	12	=	=	SYM
ejpam-2055	336	13	{	{	PUNCT
ejpam-2055	336	14	φ	φ	PROPN
ejpam-2055	336	15	,	,	PUNCT
ejpam-2055	336	16	x	x	INTJ
ejpam-2055	336	17	,	,	PUNCT
ejpam-2055	336	18	{	{	PUNCT
ejpam-2055	336	19	1	1	NUM
ejpam-2055	336	20	}	}	PUNCT
ejpam-2055	336	21	,	,	PUNCT
ejpam-2055	336	22	{	{	PUNCT
ejpam-2055	336	23	3	3	NUM
ejpam-2055	336	24	}	}	PUNCT
ejpam-2055	336	25	,	,	PUNCT
ejpam-2055	336	26	{	{	PUNCT
ejpam-2055	336	27	1,3	1,3	NUM
ejpam-2055	336	28	}	}	PUNCT
ejpam-2055	336	29	,	,	PUNCT
ejpam-2055	336	30	{	{	PUNCT
ejpam-2055	336	31	3,4	3,4	NUM
ejpam-2055	336	32	}	}	PUNCT
ejpam-2055	336	33	,	,	PUNCT
ejpam-2055	336	34	{	{	PUNCT
ejpam-2055	336	35	1,3,4	1,3,4	NUM
ejpam-2055	336	36	}	}	PUNCT
ejpam-2055	336	37	}	}	PUNCT
ejpam-2055	336	38	on	on	ADP
ejpam-2055	336	39	x	x	PUNCT
ejpam-2055	336	40	and	and	CCONJ
ejpam-2055	336	41	a	a	DET
ejpam-2055	336	42	topology	topology	NOUN
ejpam-2055	336	43	t	t	NOUN
ejpam-2055	336	44	∗	∗	NOUN
ejpam-2055	336	45	=	=	SYM
ejpam-2055	336	46	{	{	PUNCT
ejpam-2055	336	47	φ	φ	PROPN
ejpam-2055	336	48	,	,	PUNCT
ejpam-2055	336	49	x	x	INTJ
ejpam-2055	336	50	,	,	PUNCT
ejpam-2055	336	51	{	{	PUNCT
ejpam-2055	336	52	2,3,4	2,3,4	NUM
ejpam-2055	336	53	}	}	PUNCT
ejpam-2055	336	54	}	}	PUNCT
ejpam-2055	336	55	on	on	ADP
ejpam-2055	336	56	y.then	y.then	ADP
ejpam-2055	336	57	the	the	DET
ejpam-2055	336	58	identity	identity	NOUN
ejpam-2055	336	59	function	function	NOUN
ejpam-2055	336	60	f	f	NOUN
ejpam-2055	336	61	:	:	PUNCT
ejpam-2055	336	62	x	x	X
ejpam-2055	336	63	→	→	SYM
ejpam-2055	336	64	y	y	PROPN
ejpam-2055	336	65	is	be	AUX
ejpam-2055	336	66	strongly	strongly	ADV
ejpam-2055	336	67	θ	θ	NOUN
ejpam-2055	336	68	−	−	NOUN
ejpam-2055	336	69	b	b	X
ejpam-2055	336	70	-	-	PUNCT
ejpam-2055	336	71	continuous	continuous	ADJ
ejpam-2055	336	72	but	but	CCONJ
ejpam-2055	336	73	not	not	PART
ejpam-2055	336	74	strongly	strongly	ADV
ejpam-2055	336	75	θ	θ	NOUN
ejpam-2055	336	76	-e	-e	NOUN
ejpam-2055	336	77	-	-	PUNCT
ejpam-2055	336	78	continuous	continuous	ADJ
ejpam-2055	336	79	.	.	PUNCT
ejpam-2055	336	80	example	example	NOUN
ejpam-2055	337	1	6	6	NUM
ejpam-2055	337	2	.	.	PUNCT
ejpam-2055	338	1	let	let	VERB
ejpam-2055	338	2	t	t	PROPN
ejpam-2055	338	3	be	be	AUX
ejpam-2055	338	4	the	the	DET
ejpam-2055	338	5	usual	usual	ADJ
ejpam-2055	338	6	topology	topology	NOUN
ejpam-2055	338	7	for	for	ADP
ejpam-2055	338	8	r	r	NOUN
ejpam-2055	338	9	and	and	CCONJ
ejpam-2055	338	10	t	t	NOUN
ejpam-2055	338	11	∗	∗	NOUN
ejpam-2055	338	12	=	=	SYM
ejpam-2055	338	13	{	{	PUNCT
ejpam-2055	338	14	[	[	X
ejpam-2055	338	15	0,1	0,1	NUM
ejpam-2055	338	16	]	]	PUNCT
ejpam-2055	338	17	⋃	⋃	NOUN
ejpam-2055	338	18	(	(	PUNCT
ejpam-2055	338	19	1,2	1,2	NUM
ejpam-2055	338	20	)	)	PUNCT
ejpam-2055	338	21	⋂	⋂	PROPN
ejpam-2055	338	22	q	q	NOUN
ejpam-2055	338	23	}	}	PUNCT
ejpam-2055	338	24	where	where	SCONJ
ejpam-2055	338	25	q	q	PROPN
ejpam-2055	338	26	denotes	denote	VERB
ejpam-2055	338	27	the	the	DET
ejpam-2055	338	28	set	set	NOUN
ejpam-2055	338	29	of	of	ADP
ejpam-2055	338	30	rational	rational	ADJ
ejpam-2055	338	31	numbers	number	NOUN
ejpam-2055	338	32	.	.	PUNCT
ejpam-2055	339	1	then	then	ADV
ejpam-2055	339	2	the	the	DET
ejpam-2055	339	3	identity	identity	NOUN
ejpam-2055	339	4	function	function	NOUN
ejpam-2055	339	5	f	f	NOUN
ejpam-2055	339	6	:	:	PUNCT
ejpam-2055	339	7	(	(	PUNCT
ejpam-2055	339	8	r	r	NOUN
ejpam-2055	339	9	,	,	PUNCT
ejpam-2055	339	10	t	t	NOUN
ejpam-2055	339	11	)	)	PUNCT
ejpam-2055	339	12	→	→	SYM
ejpam-2055	339	13	(	(	PUNCT
ejpam-2055	339	14	r	r	NOUN
ejpam-2055	339	15	,	,	PUNCT
ejpam-2055	339	16	t	t	PROPN
ejpam-2055	339	17	∗	∗	NOUN
ejpam-2055	339	18	)	)	PUNCT
ejpam-2055	339	19	is	be	AUX
ejpam-2055	339	20	strongly	strongly	ADV
ejpam-2055	339	21	θ	θ	X
ejpam-2055	339	22	−δ−β	−δ−β	PROPN
ejpam-2055	339	23	continuous	continuous	ADJ
ejpam-2055	339	24	but	but	CCONJ
ejpam-2055	339	25	neither	neither	PRON
ejpam-2055	339	26	strongly	strongly	ADV
ejpam-2055	339	27	θ	θ	ADP
ejpam-2055	339	28	-precontinuous	-precontinuous	ADJ
ejpam-2055	339	29	nor	nor	CCONJ
ejpam-2055	339	30	strongly	strongly	ADV
ejpam-2055	339	31	θ	θ	PROPN
ejpam-2055	339	32	-semicontinuous	-semicontinuous	PROPN
ejpam-2055	339	33	.	.	PUNCT
ejpam-2055	339	34	example	example	NOUN
ejpam-2055	340	1	7	7	NUM
ejpam-2055	340	2	.	.	PUNCT
ejpam-2055	341	1	let	let	VERB
ejpam-2055	341	2	x	x	PUNCT
ejpam-2055	341	3	=	=	PUNCT
ejpam-2055	341	4	{	{	PUNCT
ejpam-2055	341	5	1,2,3,4	1,2,3,4	NUM
ejpam-2055	341	6	}	}	PUNCT
ejpam-2055	341	7	,	,	PUNCT
ejpam-2055	341	8	define	define	VERB
ejpam-2055	341	9	t	t	NOUN
ejpam-2055	341	10	=	=	SYM
ejpam-2055	341	11	{	{	PUNCT
ejpam-2055	341	12	φ	φ	PROPN
ejpam-2055	341	13	,	,	PUNCT
ejpam-2055	341	14	x	x	INTJ
ejpam-2055	341	15	,	,	PUNCT
ejpam-2055	341	16	{	{	PUNCT
ejpam-2055	341	17	1	1	NUM
ejpam-2055	341	18	}	}	PUNCT
ejpam-2055	341	19	,	,	PUNCT
ejpam-2055	341	20	{	{	PUNCT
ejpam-2055	341	21	3	3	NUM
ejpam-2055	341	22	}	}	PUNCT
ejpam-2055	341	23	,	,	PUNCT
ejpam-2055	341	24	{	{	PUNCT
ejpam-2055	341	25	1,2	1,2	NUM
ejpam-2055	341	26	}	}	PUNCT
ejpam-2055	341	27	,	,	PUNCT
ejpam-2055	341	28	{	{	PUNCT
ejpam-2055	341	29	1,3	1,3	NUM
ejpam-2055	341	30	}	}	PUNCT
ejpam-2055	341	31	,	,	PUNCT
ejpam-2055	341	32	{	{	PUNCT
ejpam-2055	341	33	1,2,3	1,2,3	NUM
ejpam-2055	341	34	}	}	PUNCT
ejpam-2055	341	35	,	,	PUNCT
ejpam-2055	341	36	{	{	PUNCT
ejpam-2055	341	37	1,3,4	1,3,4	NUM
ejpam-2055	341	38	}	}	PUNCT
ejpam-2055	341	39	}	}	PUNCT
ejpam-2055	341	40	on	on	ADP
ejpam-2055	341	41	x	x	PUNCT
ejpam-2055	341	42	and	and	CCONJ
ejpam-2055	341	43	a	a	DET
ejpam-2055	341	44	topology	topology	NOUN
ejpam-2055	341	45	t	t	NOUN
ejpam-2055	341	46	∗	∗	NOUN
ejpam-2055	341	47	=	=	SYM
ejpam-2055	341	48	{	{	PUNCT
ejpam-2055	341	49	φ	φ	PROPN
ejpam-2055	341	50	,	,	PUNCT
ejpam-2055	341	51	x	x	INTJ
ejpam-2055	341	52	,	,	PUNCT
ejpam-2055	341	53	{	{	PUNCT
ejpam-2055	341	54	2,4	2,4	NUM
ejpam-2055	341	55	}	}	PUNCT
ejpam-2055	341	56	}	}	PUNCT
ejpam-2055	341	57	on	on	ADP
ejpam-2055	341	58	y.then	y.then	ADP
ejpam-2055	341	59	the	the	DET
ejpam-2055	341	60	identity	identity	NOUN
ejpam-2055	341	61	function	function	NOUN
ejpam-2055	341	62	f	f	NOUN
ejpam-2055	341	63	:	:	PUNCT
ejpam-2055	341	64	(	(	PUNCT
ejpam-2055	341	65	x	x	X
ejpam-2055	341	66	,	,	PUNCT
ejpam-2055	341	67	t	t	PROPN
ejpam-2055	341	68	)	)	PUNCT
ejpam-2055	341	69	→	→	SYM
ejpam-2055	341	70	(	(	PUNCT
ejpam-2055	341	71	x	x	X
ejpam-2055	341	72	,	,	PUNCT
ejpam-2055	341	73	t	t	PROPN
ejpam-2055	341	74	∗	∗	NOUN
ejpam-2055	341	75	)	)	PUNCT
ejpam-2055	341	76	is	be	AUX
ejpam-2055	341	77	strongly	strongly	ADV
ejpam-2055	341	78	θ	θ	X
ejpam-2055	341	79	−δ−β	−δ−β	PROPN
ejpam-2055	341	80	-continuous	-continuous	ADJ
ejpam-2055	341	81	but	but	CCONJ
ejpam-2055	341	82	neither	neither	PRON
ejpam-2055	341	83	strongly	strongly	ADV
ejpam-2055	341	84	θ	θ	NOUN
ejpam-2055	341	85	-e	-e	NOUN
ejpam-2055	341	86	-	-	PUNCT
ejpam-2055	341	87	continuous	continuous	ADJ
ejpam-2055	341	88	nor	nor	CCONJ
ejpam-2055	341	89	strongly	strongly	ADV
ejpam-2055	341	90	θ	θ	NOUN
ejpam-2055	341	91	−β	−β	PROPN
ejpam-2055	341	92	-continuous	-continuous	ADJ
ejpam-2055	341	93	.	.	PUNCT
ejpam-2055	342	1	recall	recall	VERB
ejpam-2055	342	2	that	that	SCONJ
ejpam-2055	342	3	a	a	DET
ejpam-2055	342	4	space	space	NOUN
ejpam-2055	342	5	x	x	PUNCT
ejpam-2055	342	6	is	be	AUX
ejpam-2055	342	7	said	say	VERB
ejpam-2055	342	8	to	to	PART
ejpam-2055	342	9	be	be	AUX
ejpam-2055	342	10	submaximal	submaximal	ADJ
ejpam-2055	342	11	[	[	X
ejpam-2055	342	12	45	45	NUM
ejpam-2055	342	13	]	]	PUNCT
ejpam-2055	342	14	if	if	SCONJ
ejpam-2055	342	15	each	each	DET
ejpam-2055	342	16	dense	dense	ADJ
ejpam-2055	342	17	subset	subset	NOUN
ejpam-2055	342	18	of	of	ADP
ejpam-2055	342	19	x	x	PUNCT
ejpam-2055	342	20	is	be	AUX
ejpam-2055	342	21	open	open	ADJ
ejpam-2055	342	22	in	in	ADP
ejpam-2055	342	23	x.	x.	NOUN
ejpam-2055	343	1	it	it	PRON
ejpam-2055	343	2	is	be	AUX
ejpam-2055	343	3	shown	show	VERB
ejpam-2055	343	4	in	in	ADP
ejpam-2055	343	5	[	[	X
ejpam-2055	343	6	45	45	NUM
ejpam-2055	343	7	]	]	PUNCT
ejpam-2055	343	8	that	that	SCONJ
ejpam-2055	343	9	a	a	DET
ejpam-2055	343	10	space	space	NOUN
ejpam-2055	343	11	x	x	PUNCT
ejpam-2055	343	12	is	be	AUX
ejpam-2055	343	13	submaximal	submaximal	ADJ
ejpam-2055	343	14	if	if	SCONJ
ejpam-2055	343	15	and	and	CCONJ
ejpam-2055	343	16	only	only	ADV
ejpam-2055	343	17	if	if	SCONJ
ejpam-2055	343	18	every	every	DET
ejpam-2055	343	19	preopen	preopen	ADJ
ejpam-2055	343	20	set	set	NOUN
ejpam-2055	343	21	of	of	ADP
ejpam-2055	343	22	x	x	PUNCT
ejpam-2055	343	23	is	be	AUX
ejpam-2055	343	24	open	open	ADJ
ejpam-2055	343	25	.	.	PUNCT
ejpam-2055	344	1	a	a	DET
ejpam-2055	344	2	space	space	NOUN
ejpam-2055	344	3	x	x	PUNCT
ejpam-2055	344	4	is	be	AUX
ejpam-2055	344	5	said	say	VERB
ejpam-2055	344	6	to	to	PART
ejpam-2055	344	7	be	be	AUX
ejpam-2055	344	8	extremally	extremally	ADV
ejpam-2055	344	9	disconnected	disconnect	VERB
ejpam-2055	345	1	[	[	X
ejpam-2055	345	2	3	3	X
ejpam-2055	345	3	]	]	PUNCT
ejpam-2055	345	4	if	if	SCONJ
ejpam-2055	345	5	the	the	DET
ejpam-2055	345	6	closure	closure	NOUN
ejpam-2055	345	7	of	of	ADP
ejpam-2055	345	8	each	each	DET
ejpam-2055	345	9	open	open	ADJ
ejpam-2055	345	10	set	set	NOUN
ejpam-2055	345	11	of	of	ADP
ejpam-2055	345	12	x	x	PUNCT
ejpam-2055	345	13	is	be	AUX
ejpam-2055	345	14	open	open	ADJ
ejpam-2055	345	15	.	.	PUNCT
ejpam-2055	346	1	note	note	VERB
ejpam-2055	346	2	that	that	SCONJ
ejpam-2055	346	3	an	an	DET
ejpam-2055	346	4	extremally	extremally	ADV
ejpam-2055	346	5	disconnected	disconnected	ADJ
ejpam-2055	346	6	space	space	NOUN
ejpam-2055	346	7	is	be	AUX
ejpam-2055	346	8	exactly	exactly	ADV
ejpam-2055	346	9	the	the	DET
ejpam-2055	346	10	space	space	NOUN
ejpam-2055	346	11	where	where	SCONJ
ejpam-2055	346	12	every	every	DET
ejpam-2055	346	13	semiopen	semiopen	NOUN
ejpam-2055	346	14	set	set	NOUN
ejpam-2055	346	15	is	be	AUX
ejpam-2055	346	16	α	α	NOUN
ejpam-2055	346	17	-	-	ADJ
ejpam-2055	346	18	open	open	ADJ
ejpam-2055	346	19	theorem	theorem	ADJ
ejpam-2055	346	20	10	10	NUM
ejpam-2055	346	21	.	.	PUNCT
ejpam-2055	347	1	let	let	VERB
ejpam-2055	347	2	x	x	PRON
ejpam-2055	347	3	be	be	AUX
ejpam-2055	347	4	a	a	DET
ejpam-2055	347	5	submaximal	submaximal	ADJ
ejpam-2055	347	6	extremally	extremally	ADV
ejpam-2055	347	7	disconnected	disconnected	ADJ
ejpam-2055	347	8	space	space	NOUN
ejpam-2055	347	9	.	.	PUNCT
ejpam-2055	348	1	then	then	ADV
ejpam-2055	348	2	the	the	DET
ejpam-2055	348	3	following	follow	VERB
ejpam-2055	348	4	properties	property	NOUN
ejpam-2055	348	5	are	be	AUX
ejpam-2055	348	6	equivalent	equivalent	ADJ
ejpam-2055	348	7	for	for	ADP
ejpam-2055	348	8	a	a	DET
ejpam-2055	348	9	function	function	NOUN
ejpam-2055	348	10	f	f	NOUN
ejpam-2055	348	11	:	:	PUNCT
ejpam-2055	348	12	x	x	X
ejpam-2055	348	13	→	→	SYM
ejpam-2055	348	14	y	y	PROPN
ejpam-2055	348	15	.	.	PUNCT
ejpam-2055	348	16	a.	a.	PROPN
ejpam-2055	348	17	m.	m.	PROPN
ejpam-2055	348	18	farhan	farhan	PROPN
ejpam-2055	348	19	and	and	CCONJ
ejpam-2055	348	20	x.	x.	PROPN
ejpam-2055	348	21	yang	yang	PROPN
ejpam-2055	348	22	/	/	SYM
ejpam-2055	348	23	eur	eur	PROPN
ejpam-2055	348	24	.	.	PUNCT
ejpam-2055	349	1	j.	j.	PROPN
ejpam-2055	349	2	pure	pure	PROPN
ejpam-2055	349	3	appl	appl	PROPN
ejpam-2055	349	4	.	.	PROPN
ejpam-2055	349	5	math	math	PROPN
ejpam-2055	349	6	,	,	PUNCT
ejpam-2055	349	7	8	8	NUM
ejpam-2055	349	8	(	(	PUNCT
ejpam-2055	349	9	2015	2015	NUM
ejpam-2055	349	10	)	)	PUNCT
ejpam-2055	349	11	,	,	PUNCT
ejpam-2055	349	12	185	185	NUM
ejpam-2055	349	13	-	-	SYM
ejpam-2055	349	14	200	200	NUM
ejpam-2055	349	15	194	194	NUM
ejpam-2055	349	16	a	a	NOUN
ejpam-2055	349	17	)	)	PUNCT
ejpam-2055	349	18	f	f	PROPN
ejpam-2055	349	19	is	be	AUX
ejpam-2055	349	20	strongly	strongly	ADV
ejpam-2055	349	21	θ	θ	NOUN
ejpam-2055	349	22	-continuous	-continuous	ADJ
ejpam-2055	349	23	;	;	PUNCT
ejpam-2055	349	24	b	b	X
ejpam-2055	349	25	)	)	PUNCT
ejpam-2055	349	26	f	f	PROPN
ejpam-2055	349	27	is	be	AUX
ejpam-2055	349	28	strongly	strongly	ADV
ejpam-2055	349	29	θ	θ	X
ejpam-2055	349	30	-semicontinuous	-semicontinuous	ADJ
ejpam-2055	349	31	;	;	PUNCT
ejpam-2055	349	32	c	c	X
ejpam-2055	349	33	)	)	PUNCT
ejpam-2055	349	34	f	f	PROPN
ejpam-2055	349	35	is	be	AUX
ejpam-2055	349	36	strongly	strongly	ADV
ejpam-2055	349	37	θ	θ	NOUN
ejpam-2055	349	38	-precontinuous	-precontinuous	ADJ
ejpam-2055	349	39	;	;	PUNCT
ejpam-2055	349	40	d	d	X
ejpam-2055	349	41	)	)	PUNCT
ejpam-2055	349	42	f	f	PROPN
ejpam-2055	349	43	is	be	AUX
ejpam-2055	349	44	strongly	strongly	ADV
ejpam-2055	349	45	θ	θ	NOUN
ejpam-2055	349	46	-b	-b	PUNCT
ejpam-2055	349	47	-	-	ADJ
ejpam-2055	349	48	continuous	continuous	ADJ
ejpam-2055	349	49	;	;	PUNCT
ejpam-2055	349	50	e	e	X
ejpam-2055	349	51	)	)	PUNCT
ejpam-2055	349	52	f	f	PROPN
ejpam-2055	349	53	is	be	AUX
ejpam-2055	349	54	strongly	strongly	ADV
ejpam-2055	349	55	θ	θ	NOUN
ejpam-2055	349	56	-e	-e	NOUN
ejpam-2055	349	57	-	-	PUNCT
ejpam-2055	349	58	continuous	continuous	ADJ
ejpam-2055	349	59	;	;	PUNCT
ejpam-2055	349	60	f	f	X
ejpam-2055	349	61	)	)	PUNCT
ejpam-2055	349	62	f	f	PROPN
ejpam-2055	349	63	is	be	AUX
ejpam-2055	349	64	strongly	strongly	ADV
ejpam-2055	349	65	θ	θ	NOUN
ejpam-2055	350	1	−	−	NOUN
ejpam-2055	350	2	β	β	X
ejpam-2055	350	3	-continuous	-continuous	ADJ
ejpam-2055	350	4	;	;	PUNCT
ejpam-2055	350	5	g	g	X
ejpam-2055	350	6	)	)	PUNCT
ejpam-2055	350	7	f	f	PROPN
ejpam-2055	350	8	is	be	AUX
ejpam-2055	350	9	strongly	strongly	ADV
ejpam-2055	350	10	θ	θ	NOUN
ejpam-2055	350	11	−δ−	−δ−	ADJ
ejpam-2055	350	12	β	β	AUX
ejpam-2055	350	13	-continuous	-continuous	ADJ
ejpam-2055	350	14	.	.	PUNCT
ejpam-2055	351	1	proof	proof	NOUN
ejpam-2055	351	2	.	.	PUNCT
ejpam-2055	352	1	it	it	PRON
ejpam-2055	352	2	follows	follow	VERB
ejpam-2055	352	3	from	from	ADP
ejpam-2055	352	4	the	the	DET
ejpam-2055	352	5	fact	fact	NOUN
ejpam-2055	352	6	that	that	SCONJ
ejpam-2055	352	7	if	if	SCONJ
ejpam-2055	352	8	x	x	PRON
ejpam-2055	352	9	is	be	AUX
ejpam-2055	352	10	submaximal	submaximal	ADJ
ejpam-2055	352	11	extremally	extremally	ADV
ejpam-2055	352	12	disconnected	disconnect	VERB
ejpam-2055	352	13	,	,	PUNCT
ejpam-2055	352	14	then	then	ADV
ejpam-2055	352	15	open	open	VERB
ejpam-2055	352	16	set	set	NOUN
ejpam-2055	352	17	,	,	PUNCT
ejpam-2055	352	18	preopen	preopen	ADJ
ejpam-2055	352	19	set	set	NOUN
ejpam-2055	352	20	,	,	PUNCT
ejpam-2055	352	21	semiopen	semiopen	ADJ
ejpam-2055	352	22	set	set	VERB
ejpam-2055	352	23	,	,	PUNCT
ejpam-2055	352	24	b	b	X
ejpam-2055	352	25	-	-	PUNCT
ejpam-2055	352	26	open	open	ADJ
ejpam-2055	352	27	set	set	NOUN
ejpam-2055	352	28	,	,	PUNCT
ejpam-2055	352	29	e	e	ADJ
ejpam-2055	352	30	-	-	ADJ
ejpam-2055	352	31	open	open	ADJ
ejpam-2055	352	32	set	set	NOUN
ejpam-2055	352	33	,	,	PUNCT
ejpam-2055	352	34	semipreopen	semipreopen	NOUN
ejpam-2055	352	35	set	set	VERB
ejpam-2055	352	36	and	and	CCONJ
ejpam-2055	352	37	θ	θ	PROPN
ejpam-2055	352	38	−β	−β	PROPN
ejpam-2055	352	39	-open	-open	PROPN
ejpam-2055	352	40	set	set	NOUN
ejpam-2055	352	41	are	be	AUX
ejpam-2055	352	42	equivalent	equivalent	ADJ
ejpam-2055	352	43	.	.	PUNCT
ejpam-2055	353	1	theorem	theorem	ADJ
ejpam-2055	353	2	11	11	NUM
ejpam-2055	353	3	.	.	PUNCT
ejpam-2055	354	1	let	let	VERB
ejpam-2055	354	2	f	f	NOUN
ejpam-2055	354	3	:	:	PUNCT
ejpam-2055	354	4	(	(	PUNCT
ejpam-2055	354	5	x	x	X
ejpam-2055	354	6	,	,	PUNCT
ejpam-2055	354	7	t	t	NOUN
ejpam-2055	354	8	)	)	PUNCT
ejpam-2055	354	9	→	→	SYM
ejpam-2055	354	10	(	(	PUNCT
ejpam-2055	354	11	y	y	PROPN
ejpam-2055	354	12	,	,	PUNCT
ejpam-2055	354	13	t	t	PROPN
ejpam-2055	354	14	∗	∗	NOUN
ejpam-2055	354	15	)	)	PUNCT
ejpam-2055	354	16	and	and	CCONJ
ejpam-2055	354	17	g	g	NOUN
ejpam-2055	354	18	:	:	PUNCT
ejpam-2055	354	19	(	(	PUNCT
ejpam-2055	354	20	y	y	PROPN
ejpam-2055	354	21	,	,	PUNCT
ejpam-2055	354	22	t	t	NOUN
ejpam-2055	354	23	∗)→	∗)→	NUM
ejpam-2055	354	24	(	(	PUNCT
ejpam-2055	354	25	z	z	NOUN
ejpam-2055	354	26	,	,	PUNCT
ejpam-2055	354	27	t	t	PROPN
ejpam-2055	354	28	∗∗	∗∗	PROPN
ejpam-2055	354	29	)	)	PUNCT
ejpam-2055	354	30	be	be	AUX
ejpam-2055	354	31	a	a	DET
ejpam-2055	354	32	functions	function	NOUN
ejpam-2055	354	33	.	.	PUNCT
ejpam-2055	355	1	if	if	SCONJ
ejpam-2055	355	2	f	f	PROPN
ejpam-2055	355	3	is	be	AUX
ejpam-2055	355	4	strongly	strongly	ADV
ejpam-2055	355	5	θ−δ−β	θ−δ−β	PROPN
ejpam-2055	355	6	-continuous	-continuous	ADJ
ejpam-2055	355	7	.	.	PUNCT
ejpam-2055	356	1	and	and	CCONJ
ejpam-2055	356	2	g	g	PROPN
ejpam-2055	356	3	is	be	AUX
ejpam-2055	356	4	continuous	continuous	ADJ
ejpam-2055	356	5	,	,	PUNCT
ejpam-2055	356	6	then	then	ADV
ejpam-2055	356	7	the	the	DET
ejpam-2055	356	8	composition	composition	NOUN
ejpam-2055	356	9	function	function	NOUN
ejpam-2055	356	10	go	go	VERB
ejpam-2055	356	11	f	f	NOUN
ejpam-2055	356	12	:	:	PUNCT
ejpam-2055	356	13	(	(	PUNCT
ejpam-2055	356	14	x	x	X
ejpam-2055	356	15	,	,	PUNCT
ejpam-2055	356	16	t	t	NOUN
ejpam-2055	356	17	)	)	PUNCT
ejpam-2055	356	18	→	→	SYM
ejpam-2055	356	19	(	(	PUNCT
ejpam-2055	356	20	z	z	NOUN
ejpam-2055	356	21	,	,	PUNCT
ejpam-2055	356	22	t	t	PROPN
ejpam-2055	356	23	∗∗	∗∗	PROPN
ejpam-2055	356	24	)	)	PUNCT
ejpam-2055	356	25	is	be	AUX
ejpam-2055	356	26	strongly	strongly	ADV
ejpam-2055	356	27	θ	θ	NOUN
ejpam-2055	356	28	−δ−	−δ−	ADJ
ejpam-2055	356	29	β	β	AUX
ejpam-2055	356	30	-continuous	-continuous	ADJ
ejpam-2055	356	31	.	.	PUNCT
ejpam-2055	357	1	proof	proof	NOUN
ejpam-2055	357	2	.	.	PUNCT
ejpam-2055	358	1	this	this	DET
ejpam-2055	358	2	proof	proof	NOUN
ejpam-2055	358	3	follows	follow	VERB
ejpam-2055	358	4	directly	directly	ADV
ejpam-2055	358	5	from	from	ADP
ejpam-2055	358	6	theorem	theorem	ADJ
ejpam-2055	358	7	6	6	NUM
ejpam-2055	358	8	.	.	NOUN
ejpam-2055	358	9	6	6	NUM
ejpam-2055	358	10	.	.	PUNCT
ejpam-2055	358	11	strongly	strongly	ADV
ejpam-2055	358	12	θ	θ	X
ejpam-2055	358	13	−δ−	−δ−	ADJ
ejpam-2055	358	14	β	β	X
ejpam-2055	358	15	-	-	ADJ
ejpam-2055	358	16	continuous	continuous	ADJ
ejpam-2055	358	17	functions	function	NOUN
ejpam-2055	358	18	and	and	CCONJ
ejpam-2055	358	19	separation	separation	NOUN
ejpam-2055	358	20	axioms	axiom	VERB
ejpam-2055	358	21	definition	definition	NOUN
ejpam-2055	358	22	7	7	NUM
ejpam-2055	358	23	(	(	PUNCT
ejpam-2055	358	24	[	[	X
ejpam-2055	358	25	7	7	NUM
ejpam-2055	358	26	,	,	PUNCT
ejpam-2055	358	27	28	28	NUM
ejpam-2055	358	28	]	]	PUNCT
ejpam-2055	358	29	)	)	PUNCT
ejpam-2055	358	30	.	.	PUNCT
ejpam-2055	359	1	a	a	DET
ejpam-2055	359	2	space	space	NOUN
ejpam-2055	359	3	x	x	PUNCT
ejpam-2055	359	4	is	be	AUX
ejpam-2055	359	5	said	say	VERB
ejpam-2055	359	6	to	to	PART
ejpam-2055	359	7	be	be	AUX
ejpam-2055	359	8	δ−β	δ−β	ADJ
ejpam-2055	359	9	−	−	NOUN
ejpam-2055	359	10	t2	t2	NOUN
ejpam-2055	359	11	if	if	SCONJ
ejpam-2055	359	12	for	for	ADP
ejpam-2055	359	13	each	each	DET
ejpam-2055	359	14	pair	pair	NOUN
ejpam-2055	359	15	of	of	ADP
ejpam-2055	359	16	distinct	distinct	ADJ
ejpam-2055	359	17	points	point	NOUN
ejpam-2055	359	18	x	x	PUNCT
ejpam-2055	359	19	and	and	CCONJ
ejpam-2055	359	20	y	y	PROPN
ejpam-2055	359	21	in	in	ADP
ejpam-2055	359	22	x	x	SYM
ejpam-2055	359	23	,	,	PUNCT
ejpam-2055	359	24	there	there	PRON
ejpam-2055	359	25	exist	exist	VERB
ejpam-2055	359	26	u	u	PROPN
ejpam-2055	359	27	∈	∈	NOUN
ejpam-2055	359	28	δ−	δ−	PROPN
ejpam-2055	359	29	βς(x	βς(x	X
ejpam-2055	359	30	,	,	PUNCT
ejpam-2055	359	31	x	x	X
ejpam-2055	359	32	)	)	PUNCT
ejpam-2055	359	33	and	and	CCONJ
ejpam-2055	360	1	v	v	ADP
ejpam-2055	360	2	∈	∈	PROPN
ejpam-2055	360	3	δ−	δ−	PROPN
ejpam-2055	360	4	βς(x	βς(x	X
ejpam-2055	360	5	,	,	PUNCT
ejpam-2055	360	6	y	y	PROPN
ejpam-2055	360	7	)	)	PUNCT
ejpam-2055	360	8	such	such	ADJ
ejpam-2055	360	9	that	that	SCONJ
ejpam-2055	360	10	u	u	PROPN
ejpam-2055	360	11	⋂	⋂	PROPN
ejpam-2055	360	12	v	v	NOUN
ejpam-2055	360	13	=	=	SYM
ejpam-2055	360	14	φ	φ	PROPN
ejpam-2055	360	15	.	.	PUNCT
ejpam-2055	361	1	lemma	lemma	PROPN
ejpam-2055	361	2	3	3	NUM
ejpam-2055	361	3	.	.	PUNCT
ejpam-2055	362	1	a	a	DET
ejpam-2055	362	2	space	space	NOUN
ejpam-2055	362	3	x	x	PUNCT
ejpam-2055	362	4	is	be	AUX
ejpam-2055	362	5	δ−β	δ−β	ADJ
ejpam-2055	362	6	−	−	NOUN
ejpam-2055	362	7	t2	t2	PROPN
ejpam-2055	362	8	if	if	SCONJ
ejpam-2055	362	9	and	and	CCONJ
ejpam-2055	362	10	only	only	ADV
ejpam-2055	362	11	if	if	SCONJ
ejpam-2055	362	12	for	for	ADP
ejpam-2055	362	13	each	each	DET
ejpam-2055	362	14	pair	pair	NOUN
ejpam-2055	362	15	of	of	ADP
ejpam-2055	362	16	distinct	distinct	ADJ
ejpam-2055	362	17	points	point	NOUN
ejpam-2055	362	18	x	x	PUNCT
ejpam-2055	362	19	and	and	CCONJ
ejpam-2055	362	20	y	y	PROPN
ejpam-2055	362	21	in	in	ADP
ejpam-2055	362	22	x	x	SYM
ejpam-2055	362	23	,	,	PUNCT
ejpam-2055	362	24	there	there	PRON
ejpam-2055	362	25	exist	exist	VERB
ejpam-2055	362	26	u	u	PROPN
ejpam-2055	362	27	∈	∈	NOUN
ejpam-2055	362	28	δ−	δ−	PROPN
ejpam-2055	362	29	βς(x	βς(x	X
ejpam-2055	362	30	,	,	PUNCT
ejpam-2055	362	31	x	x	X
ejpam-2055	362	32	)	)	PUNCT
ejpam-2055	362	33	and	and	CCONJ
ejpam-2055	362	34	v	v	ADP
ejpam-2055	362	35	∈	∈	PROPN
ejpam-2055	362	36	δ−	δ−	PROPN
ejpam-2055	362	37	βς(x	βς(x	X
ejpam-2055	362	38	,	,	PUNCT
ejpam-2055	362	39	y	y	PROPN
ejpam-2055	362	40	)	)	PUNCT
ejpam-2055	362	41	such	such	ADJ
ejpam-2055	363	1	that	that	SCONJ
ejpam-2055	363	2	δ−	δ−	PROPN
ejpam-2055	363	3	β	β	X
ejpam-2055	363	4	−	−	NOUN
ejpam-2055	363	5	cl(u	cl(u	NOUN
ejpam-2055	363	6	)	)	PUNCT
ejpam-2055	363	7	⋂	⋂	PROPN
ejpam-2055	363	8	δ−	δ−	PROPN
ejpam-2055	363	9	β	β	NOUN
ejpam-2055	363	10	−	−	NOUN
ejpam-2055	363	11	cl(v	cl(v	NOUN
ejpam-2055	363	12	)	)	PUNCT
ejpam-2055	363	13	=	=	SYM
ejpam-2055	363	14	φ	φ	X
ejpam-2055	363	15	.	.	PUNCT
ejpam-2055	363	16	theorem	theorem	PROPN
ejpam-2055	363	17	12	12	NUM
ejpam-2055	363	18	.	.	PUNCT
ejpam-2055	364	1	if	if	SCONJ
ejpam-2055	364	2	a	a	DET
ejpam-2055	364	3	function	function	NOUN
ejpam-2055	364	4	f	f	NOUN
ejpam-2055	364	5	:	:	PUNCT
ejpam-2055	364	6	(	(	PUNCT
ejpam-2055	364	7	x	x	X
ejpam-2055	364	8	,	,	PUNCT
ejpam-2055	364	9	t	t	NOUN
ejpam-2055	364	10	)	)	PUNCT
ejpam-2055	364	11	→	→	SYM
ejpam-2055	364	12	(	(	PUNCT
ejpam-2055	364	13	y	y	PROPN
ejpam-2055	364	14	,	,	PUNCT
ejpam-2055	364	15	t	t	PROPN
ejpam-2055	364	16	∗	∗	NOUN
ejpam-2055	364	17	)	)	PUNCT
ejpam-2055	364	18	is	be	AUX
ejpam-2055	364	19	(	(	PUNCT
ejpam-2055	364	20	st	st	PROPN
ejpam-2055	364	21	.	.	PROPN
ejpam-2055	364	22	θ	θ	PROPN
ejpam-2055	364	23	−	−	PROPN
ejpam-2055	364	24	δ−	δ−	PROPN
ejpam-2055	364	25	β	β	PROPN
ejpam-2055	364	26	.c	.c	PROPN
ejpam-2055	364	27	.	.	PUNCT
ejpam-2055	364	28	)	)	PUNCT
ejpam-2055	365	1	injection	injection	NOUN
ejpam-2055	365	2	and	and	CCONJ
ejpam-2055	365	3	y	y	PROPN
ejpam-2055	365	4	is	be	AUX
ejpam-2055	365	5	t0	t0	NOUN
ejpam-2055	365	6	,	,	PUNCT
ejpam-2055	365	7	then	then	ADV
ejpam-2055	365	8	x	x	PUNCT
ejpam-2055	365	9	is	be	AUX
ejpam-2055	365	10	δ−	δ−	PROPN
ejpam-2055	365	11	β	β	NOUN
ejpam-2055	365	12	−	−	PROPN
ejpam-2055	365	13	t2	t2	NOUN
ejpam-2055	365	14	.	.	PUNCT
ejpam-2055	366	1	proof	proof	NOUN
ejpam-2055	366	2	.	.	PUNCT
ejpam-2055	367	1	for	for	ADP
ejpam-2055	367	2	any	any	DET
ejpam-2055	367	3	distinct	distinct	ADJ
ejpam-2055	367	4	points	point	NOUN
ejpam-2055	367	5	x	x	PUNCT
ejpam-2055	367	6	and	and	CCONJ
ejpam-2055	367	7	y	y	PROPN
ejpam-2055	367	8	of	of	ADP
ejpam-2055	367	9	x	x	PRON
ejpam-2055	367	10	,	,	PUNCT
ejpam-2055	367	11	by	by	ADP
ejpam-2055	367	12	hypothesis	hypothesis	NOUN
ejpam-2055	367	13	f	f	PROPN
ejpam-2055	367	14	(	(	PUNCT
ejpam-2055	367	15	x	x	X
ejpam-2055	367	16	)	)	PUNCT
ejpam-2055	367	17	6=	6=	ADP
ejpam-2055	367	18	f	f	PROPN
ejpam-2055	367	19	(	(	PUNCT
ejpam-2055	367	20	y	y	NOUN
ejpam-2055	367	21	)	)	PUNCT
ejpam-2055	367	22	and	and	CCONJ
ejpam-2055	367	23	there	there	PRON
ejpam-2055	367	24	exists	exist	VERB
ejpam-2055	367	25	either	either	CCONJ
ejpam-2055	367	26	an	an	DET
ejpam-2055	367	27	open	open	ADJ
ejpam-2055	367	28	set	set	NOUN
ejpam-2055	367	29	v	v	NOUN
ejpam-2055	367	30	containing	contain	VERB
ejpam-2055	367	31	f	f	X
ejpam-2055	367	32	(	(	PUNCT
ejpam-2055	367	33	x	x	NOUN
ejpam-2055	367	34	)	)	PUNCT
ejpam-2055	367	35	not	not	PART
ejpam-2055	367	36	containing	contain	VERB
ejpam-2055	367	37	f	f	PROPN
ejpam-2055	367	38	(	(	PUNCT
ejpam-2055	367	39	y	y	NOUN
ejpam-2055	367	40	)	)	PUNCT
ejpam-2055	367	41	or	or	CCONJ
ejpam-2055	367	42	an	an	DET
ejpam-2055	367	43	open	open	ADJ
ejpam-2055	367	44	set	set	NOUN
ejpam-2055	367	45	h	h	NOUN
ejpam-2055	367	46	containing	contain	VERB
ejpam-2055	367	47	f	f	PROPN
ejpam-2055	367	48	(	(	PUNCT
ejpam-2055	367	49	y	y	NOUN
ejpam-2055	367	50	)	)	PUNCT
ejpam-2055	367	51	not	not	PART
ejpam-2055	367	52	containing	contain	VERB
ejpam-2055	367	53	f	f	X
ejpam-2055	367	54	(	(	PUNCT
ejpam-2055	367	55	x	x	NOUN
ejpam-2055	367	56	)	)	PUNCT
ejpam-2055	367	57	.	.	PUNCT
ejpam-2055	368	1	if	if	SCONJ
ejpam-2055	368	2	the	the	DET
ejpam-2055	368	3	first	first	ADJ
ejpam-2055	368	4	case	case	NOUN
ejpam-2055	368	5	holds	hold	VERB
ejpam-2055	368	6	,	,	PUNCT
ejpam-2055	368	7	then	then	ADV
ejpam-2055	368	8	there	there	PRON
ejpam-2055	368	9	exists	exist	VERB
ejpam-2055	368	10	u	u	PROPN
ejpam-2055	368	11	∈	∈	PROPN
ejpam-2055	368	12	δ	δ	PROPN
ejpam-2055	368	13	−	−	NOUN
ejpam-2055	368	14	βς(x	βς(x	PUNCT
ejpam-2055	368	15	,	,	PUNCT
ejpam-2055	368	16	x	x	X
ejpam-2055	368	17	)	)	PUNCT
ejpam-2055	369	1	such	such	ADJ
ejpam-2055	369	2	that	that	SCONJ
ejpam-2055	369	3	f	f	PROPN
ejpam-2055	369	4	(	(	PUNCT
ejpam-2055	369	5	δ−	δ−	PROPN
ejpam-2055	369	6	β	β	X
ejpam-2055	369	7	−	−	NOUN
ejpam-2055	369	8	cl(u	cl(u	NOUN
ejpam-2055	369	9	)	)	PUNCT
ejpam-2055	369	10	)	)	PUNCT
ejpam-2055	370	1	⊂	⊂	PROPN
ejpam-2055	370	2	v	v	X
ejpam-2055	370	3	.	.	PUNCT
ejpam-2055	371	1	thus	thus	ADV
ejpam-2055	371	2	,	,	PUNCT
ejpam-2055	371	3	we	we	PRON
ejpam-2055	371	4	obtain	obtain	VERB
ejpam-2055	371	5	f	f	PROPN
ejpam-2055	371	6	(	(	PUNCT
ejpam-2055	371	7	y	y	PROPN
ejpam-2055	371	8	)	)	PUNCT
ejpam-2055	371	9	/∈	/∈	PUNCT
ejpam-2055	372	1	f	f	NOUN
ejpam-2055	372	2	(	(	PUNCT
ejpam-2055	372	3	δ−	δ−	PROPN
ejpam-2055	372	4	β	β	X
ejpam-2055	372	5	−	−	NOUN
ejpam-2055	372	6	cl(u	cl(u	NOUN
ejpam-2055	372	7	)	)	PUNCT
ejpam-2055	372	8	)	)	PUNCT
ejpam-2055	372	9	and	and	CCONJ
ejpam-2055	372	10	hence	hence	ADV
ejpam-2055	372	11	x	x	PUNCT
ejpam-2055	372	12	\	\	PROPN
ejpam-2055	372	13	δ	δ	PROPN
ejpam-2055	373	1	−	−	PROPN
ejpam-2055	373	2	β	β	NOUN
ejpam-2055	373	3	−	−	NOUN
ejpam-2055	373	4	cl(u	cl(u	SYM
ejpam-2055	373	5	)	)	PUNCT
ejpam-2055	373	6	∈	∈	PROPN
ejpam-2055	373	7	δ	δ	PROPN
ejpam-2055	373	8	−	−	PROPN
ejpam-2055	373	9	βς(x	βς(x	PUNCT
ejpam-2055	373	10	,	,	PUNCT
ejpam-2055	373	11	y	y	PROPN
ejpam-2055	373	12	)	)	PUNCT
ejpam-2055	373	13	.	.	PUNCT
ejpam-2055	374	1	if	if	SCONJ
ejpam-2055	374	2	the	the	DET
ejpam-2055	374	3	second	second	ADJ
ejpam-2055	374	4	case	case	NOUN
ejpam-2055	374	5	holds	hold	VERB
ejpam-2055	374	6	,	,	PUNCT
ejpam-2055	374	7	then	then	ADV
ejpam-2055	374	8	we	we	PRON
ejpam-2055	374	9	obtain	obtain	VERB
ejpam-2055	374	10	a	a	DET
ejpam-2055	374	11	similar	similar	ADJ
ejpam-2055	374	12	result	result	NOUN
ejpam-2055	374	13	.	.	PUNCT
ejpam-2055	375	1	thus	thus	ADV
ejpam-2055	375	2	,	,	PUNCT
ejpam-2055	375	3	x	x	PRON
ejpam-2055	375	4	is	be	AUX
ejpam-2055	375	5	δ−	δ−	PROPN
ejpam-2055	375	6	β	β	NOUN
ejpam-2055	375	7	−	−	PROPN
ejpam-2055	375	8	t2	t2	PROPN
ejpam-2055	375	9	.	.	PUNCT
ejpam-2055	376	1	theorem	theorem	VERB
ejpam-2055	376	2	13	13	NUM
ejpam-2055	376	3	.	.	PUNCT
ejpam-2055	377	1	if	if	SCONJ
ejpam-2055	377	2	f	f	PROPN
ejpam-2055	377	3	:	:	PUNCT
ejpam-2055	377	4	(	(	PUNCT
ejpam-2055	377	5	x	x	X
ejpam-2055	377	6	,	,	PUNCT
ejpam-2055	377	7	t	t	NOUN
ejpam-2055	377	8	)	)	PUNCT
ejpam-2055	377	9	→	→	SYM
ejpam-2055	377	10	(	(	PUNCT
ejpam-2055	377	11	y	y	PROPN
ejpam-2055	377	12	,	,	PUNCT
ejpam-2055	377	13	t	t	PROPN
ejpam-2055	377	14	∗	∗	NOUN
ejpam-2055	377	15	)	)	PUNCT
ejpam-2055	377	16	(	(	PUNCT
ejpam-2055	377	17	st	st	PROPN
ejpam-2055	377	18	.	.	PROPN
ejpam-2055	377	19	θ	θ	PROPN
ejpam-2055	378	1	−	−	PROPN
ejpam-2055	378	2	δ	δ	PROPN
ejpam-2055	378	3	−	−	PROPN
ejpam-2055	378	4	β	β	NOUN
ejpam-2055	378	5	.c.)function	.c.)function	NOUN
ejpam-2055	378	6	and	and	CCONJ
ejpam-2055	378	7	y	y	PROPN
ejpam-2055	378	8	is	be	AUX
ejpam-2055	378	9	hausdorff	hausdorff	NOUN
ejpam-2055	378	10	,	,	PUNCT
ejpam-2055	378	11	then	then	ADV
ejpam-2055	378	12	the	the	DET
ejpam-2055	378	13	subset	subset	NOUN
ejpam-2055	378	14	a=	a=	VERB
ejpam-2055	378	15	{	{	PUNCT
ejpam-2055	378	16	(	(	PUNCT
ejpam-2055	378	17	x	x	INTJ
ejpam-2055	378	18	,	,	PUNCT
ejpam-2055	378	19	y	y	PROPN
ejpam-2055	378	20	)	)	PUNCT
ejpam-2055	378	21	:	:	PUNCT
ejpam-2055	379	1	f	f	X
ejpam-2055	379	2	(	(	PUNCT
ejpam-2055	379	3	x	x	X
ejpam-2055	379	4	)	)	PUNCT
ejpam-2055	379	5	=	=	SYM
ejpam-2055	379	6	f	f	PROPN
ejpam-2055	379	7	(	(	PUNCT
ejpam-2055	379	8	y	y	NOUN
ejpam-2055	379	9	)	)	PUNCT
ejpam-2055	379	10	}	}	PUNCT
ejpam-2055	379	11	is	be	AUX
ejpam-2055	379	12	δ−	δ−	PROPN
ejpam-2055	379	13	βθ	βθ	AUX
ejpam-2055	379	14	-closed	-close	VERB
ejpam-2055	379	15	in	in	ADP
ejpam-2055	379	16	x	x	PUNCT
ejpam-2055	379	17	×	×	PROPN
ejpam-2055	379	18	x	x	X
ejpam-2055	379	19	.	.	PUNCT
ejpam-2055	379	20	a.	a.	PROPN
ejpam-2055	379	21	m.	m.	PROPN
ejpam-2055	379	22	farhan	farhan	PROPN
ejpam-2055	379	23	and	and	CCONJ
ejpam-2055	379	24	x.	x.	PROPN
ejpam-2055	379	25	yang	yang	PROPN
ejpam-2055	379	26	/	/	SYM
ejpam-2055	379	27	eur	eur	PROPN
ejpam-2055	379	28	.	.	PUNCT
ejpam-2055	380	1	j.	j.	PROPN
ejpam-2055	380	2	pure	pure	PROPN
ejpam-2055	380	3	appl	appl	PROPN
ejpam-2055	380	4	.	.	PROPN
ejpam-2055	380	5	math	math	PROPN
ejpam-2055	380	6	,	,	PUNCT
ejpam-2055	380	7	8	8	NUM
ejpam-2055	380	8	(	(	PUNCT
ejpam-2055	380	9	2015	2015	NUM
ejpam-2055	380	10	)	)	PUNCT
ejpam-2055	380	11	,	,	PUNCT
ejpam-2055	380	12	185	185	NUM
ejpam-2055	380	13	-	-	SYM
ejpam-2055	380	14	200	200	NUM
ejpam-2055	380	15	195	195	NUM
ejpam-2055	380	16	proof	proof	NOUN
ejpam-2055	380	17	.	.	PUNCT
ejpam-2055	381	1	it	it	PRON
ejpam-2055	381	2	is	be	AUX
ejpam-2055	381	3	clear	clear	ADJ
ejpam-2055	382	1	that	that	SCONJ
ejpam-2055	382	2	f	f	PROPN
ejpam-2055	382	3	(	(	PUNCT
ejpam-2055	382	4	x	x	X
ejpam-2055	382	5	)	)	PUNCT
ejpam-2055	382	6	6=	6=	ADP
ejpam-2055	382	7	f	f	PROPN
ejpam-2055	382	8	(	(	PUNCT
ejpam-2055	382	9	y	y	NOUN
ejpam-2055	382	10	)	)	PUNCT
ejpam-2055	382	11	for	for	ADP
ejpam-2055	382	12	each	each	DET
ejpam-2055	382	13	(	(	PUNCT
ejpam-2055	382	14	x	x	PROPN
ejpam-2055	382	15	,	,	PUNCT
ejpam-2055	382	16	y	y	PROPN
ejpam-2055	382	17	)	)	PUNCT
ejpam-2055	382	18	/∈	/∈	PUNCT
ejpam-2055	383	1	a.	a.	NOUN
ejpam-2055	383	2	since	since	SCONJ
ejpam-2055	383	3	y	y	PROPN
ejpam-2055	383	4	is	be	AUX
ejpam-2055	383	5	hausdorff	hausdorff	NOUN
ejpam-2055	383	6	,	,	PUNCT
ejpam-2055	383	7	there	there	PRON
ejpam-2055	383	8	exist	exist	VERB
ejpam-2055	383	9	open	open	ADJ
ejpam-2055	383	10	sets	set	NOUN
ejpam-2055	383	11	v	v	NOUN
ejpam-2055	383	12	and	and	CCONJ
ejpam-2055	383	13	h	h	NOUN
ejpam-2055	383	14	of	of	ADP
ejpam-2055	383	15	y	y	PROPN
ejpam-2055	383	16	containing	contain	VERB
ejpam-2055	383	17	f	f	PROPN
ejpam-2055	383	18	(	(	PUNCT
ejpam-2055	383	19	x	x	NOUN
ejpam-2055	383	20	)	)	PUNCT
ejpam-2055	383	21	and	and	CCONJ
ejpam-2055	384	1	f	f	PROPN
ejpam-2055	384	2	(	(	PUNCT
ejpam-2055	384	3	y	y	NOUN
ejpam-2055	384	4	)	)	PUNCT
ejpam-2055	384	5	,	,	PUNCT
ejpam-2055	384	6	respectively	respectively	ADV
ejpam-2055	384	7	,	,	PUNCT
ejpam-2055	384	8	such	such	ADJ
ejpam-2055	384	9	that	that	SCONJ
ejpam-2055	384	10	v	v	ADP
ejpam-2055	384	11	⋂	⋂	NUM
ejpam-2055	384	12	h	h	NOUN
ejpam-2055	384	13	=	=	SYM
ejpam-2055	384	14	φ	φ	PROPN
ejpam-2055	384	15	.	.	PUNCT
ejpam-2055	385	1	since	since	SCONJ
ejpam-2055	385	2	f	f	PROPN
ejpam-2055	385	3	is	be	AUX
ejpam-2055	385	4	(	(	PUNCT
ejpam-2055	385	5	st	st	PROPN
ejpam-2055	385	6	.	.	PROPN
ejpam-2055	385	7	θ−δ−β	θ−δ−β	PROPN
ejpam-2055	385	8	.c	.c	PROPN
ejpam-2055	385	9	)	)	PUNCT
ejpam-2055	385	10	.	.	PUNCT
ejpam-2055	386	1	there	there	PRON
ejpam-2055	386	2	exist	exist	VERB
ejpam-2055	386	3	u	u	PROPN
ejpam-2055	386	4	∈	∈	PROPN
ejpam-2055	386	5	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	386	6	,	,	PUNCT
ejpam-2055	386	7	x	x	X
ejpam-2055	386	8	)	)	PUNCT
ejpam-2055	386	9	and	and	CCONJ
ejpam-2055	386	10	w	w	PROPN
ejpam-2055	386	11	∈	∈	PROPN
ejpam-2055	386	12	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	386	13	,	,	PUNCT
ejpam-2055	386	14	y	y	PROPN
ejpam-2055	386	15	)	)	PUNCT
ejpam-2055	386	16	such	such	ADJ
ejpam-2055	386	17	that	that	SCONJ
ejpam-2055	386	18	f	f	PROPN
ejpam-2055	386	19	(	(	PUNCT
ejpam-2055	386	20	δ−β−cl(u	δ−β−cl(u	NOUN
ejpam-2055	386	21	)	)	PUNCT
ejpam-2055	386	22	)	)	PUNCT
ejpam-2055	387	1	⊂	⊂	PROPN
ejpam-2055	387	2	v	v	PROPN
ejpam-2055	387	3	and	and	CCONJ
ejpam-2055	387	4	f	f	PROPN
ejpam-2055	387	5	(	(	PUNCT
ejpam-2055	387	6	δ	δ	PROPN
ejpam-2055	387	7	−	−	NOUN
ejpam-2055	387	8	β	β	NOUN
ejpam-2055	387	9	−	−	PROPN
ejpam-2055	387	10	cl(w	cl(w	NOUN
ejpam-2055	387	11	)	)	PUNCT
ejpam-2055	387	12	)	)	PUNCT
ejpam-2055	388	1	⊂	⊂	PROPN
ejpam-2055	388	2	h.	h.	PROPN
ejpam-2055	388	3	set	set	PROPN
ejpam-2055	389	1	d	d	PROPN
ejpam-2055	389	2	=	=	SYM
ejpam-2055	389	3	f	f	PROPN
ejpam-2055	389	4	(	(	PUNCT
ejpam-2055	389	5	δ	δ	PROPN
ejpam-2055	389	6	−	−	NOUN
ejpam-2055	389	7	β	β	NOUN
ejpam-2055	389	8	−	−	PROPN
ejpam-2055	389	9	cl(u))×	cl(u))×	INTJ
ejpam-2055	389	10	f	f	X
ejpam-2055	389	11	(	(	PUNCT
ejpam-2055	389	12	δ	δ	PROPN
ejpam-2055	389	13	−	−	NOUN
ejpam-2055	389	14	β	β	NOUN
ejpam-2055	389	15	−	−	NOUN
ejpam-2055	389	16	cl(w	cl(w	NOUN
ejpam-2055	389	17	)	)	PUNCT
ejpam-2055	389	18	)	)	PUNCT
ejpam-2055	389	19	.	.	PUNCT
ejpam-2055	390	1	it	it	PRON
ejpam-2055	390	2	follows	follow	VERB
ejpam-2055	390	3	that	that	SCONJ
ejpam-2055	390	4	(	(	PUNCT
ejpam-2055	390	5	x	x	X
ejpam-2055	390	6	,	,	PUNCT
ejpam-2055	390	7	y	y	PROPN
ejpam-2055	390	8	)	)	PUNCT
ejpam-2055	390	9	∈	∈	PROPN
ejpam-2055	390	10	d	d	X
ejpam-2055	390	11	∈	∈	PROPN
ejpam-2055	390	12	δ	δ	PROPN
ejpam-2055	391	1	−	−	NOUN
ejpam-2055	391	2	βr(x	βr(x	NUM
ejpam-2055	391	3	×	×	NOUN
ejpam-2055	391	4	x	x	PUNCT
ejpam-2055	391	5	)	)	PUNCT
ejpam-2055	392	1	and	and	CCONJ
ejpam-2055	392	2	d	d	X
ejpam-2055	392	3	⋂	⋂	PROPN
ejpam-2055	392	4	a	a	DET
ejpam-2055	392	5	=	=	SYM
ejpam-2055	392	6	φ	φ	PROPN
ejpam-2055	392	7	.	.	PUNCT
ejpam-2055	393	1	this	this	PRON
ejpam-2055	393	2	means	mean	VERB
ejpam-2055	393	3	δ	δ	PROPN
ejpam-2055	393	4	−	−	PROPN
ejpam-2055	393	5	β	β	NOUN
ejpam-2055	393	6	−	−	NOUN
ejpam-2055	393	7	clθ	clθ	NOUN
ejpam-2055	393	8	(	(	PUNCT
ejpam-2055	393	9	a	a	X
ejpam-2055	393	10	)	)	PUNCT
ejpam-2055	393	11	⊂	⊂	PROPN
ejpam-2055	393	12	a	a	PROPN
ejpam-2055	393	13	and	and	CCONJ
ejpam-2055	393	14	thus	thus	ADV
ejpam-2055	393	15	,	,	PUNCT
ejpam-2055	393	16	a	a	PRON
ejpam-2055	393	17	is	be	AUX
ejpam-2055	393	18	δ−	δ−	PROPN
ejpam-2055	393	19	βθ	βθ	AUX
ejpam-2055	393	20	-closed	-close	VERB
ejpam-2055	393	21	in	in	ADP
ejpam-2055	393	22	x	x	PUNCT
ejpam-2055	393	23	×	×	PROPN
ejpam-2055	393	24	x	x	X
ejpam-2055	393	25	.	.	PUNCT
ejpam-2055	394	1	recall	recall	VERB
ejpam-2055	394	2	that	that	PRON
ejpam-2055	394	3	for	for	ADP
ejpam-2055	394	4	a	a	DET
ejpam-2055	394	5	function	function	NOUN
ejpam-2055	394	6	f	f	NOUN
ejpam-2055	394	7	:	:	PUNCT
ejpam-2055	394	8	x	x	X
ejpam-2055	394	9	→	→	SYM
ejpam-2055	394	10	y	y	PROPN
ejpam-2055	394	11	,	,	PUNCT
ejpam-2055	394	12	the	the	DET
ejpam-2055	394	13	subset	subset	NOUN
ejpam-2055	394	14	{	{	PUNCT
ejpam-2055	394	15	(	(	PUNCT
ejpam-2055	394	16	x	x	INTJ
ejpam-2055	394	17	,	,	PUNCT
ejpam-2055	394	18	f	f	PROPN
ejpam-2055	394	19	(	(	PUNCT
ejpam-2055	394	20	x	x	NOUN
ejpam-2055	394	21	)	)	PUNCT
ejpam-2055	394	22	)	)	PUNCT
ejpam-2055	394	23	:	:	PUNCT
ejpam-2055	395	1	x	x	X
ejpam-2055	395	2	∈	∈	NOUN
ejpam-2055	395	3	x	x	PUNCT
ejpam-2055	395	4	}	}	PUNCT
ejpam-2055	395	5	of	of	ADP
ejpam-2055	395	6	x	x	SYM
ejpam-2055	395	7	×	×	PROPN
ejpam-2055	395	8	y	y	PROPN
ejpam-2055	395	9	is	be	AUX
ejpam-2055	395	10	called	call	VERB
ejpam-2055	395	11	the	the	DET
ejpam-2055	395	12	graph	graph	NOUN
ejpam-2055	395	13	of	of	ADP
ejpam-2055	395	14	f	f	PROPN
ejpam-2055	395	15	and	and	CCONJ
ejpam-2055	395	16	is	be	AUX
ejpam-2055	395	17	denoted	denote	VERB
ejpam-2055	395	18	by	by	ADP
ejpam-2055	395	19	g	g	PROPN
ejpam-2055	395	20	(	(	PUNCT
ejpam-2055	395	21	f	f	PROPN
ejpam-2055	395	22	)	)	PUNCT
ejpam-2055	395	23	.	.	PUNCT
ejpam-2055	396	1	definition	definition	NOUN
ejpam-2055	396	2	8	8	NUM
ejpam-2055	396	3	.	.	PUNCT
ejpam-2055	397	1	the	the	DET
ejpam-2055	397	2	graph	graph	NOUN
ejpam-2055	397	3	g	g	PROPN
ejpam-2055	397	4	(	(	PUNCT
ejpam-2055	397	5	f	f	PROPN
ejpam-2055	397	6	)	)	PUNCT
ejpam-2055	397	7	of	of	ADP
ejpam-2055	397	8	a	a	DET
ejpam-2055	397	9	function	function	NOUN
ejpam-2055	397	10	f	f	NOUN
ejpam-2055	397	11	:	:	PUNCT
ejpam-2055	397	12	x	x	X
ejpam-2055	397	13	→	→	SYM
ejpam-2055	397	14	y	y	PROPN
ejpam-2055	397	15	is	be	AUX
ejpam-2055	397	16	said	say	VERB
ejpam-2055	397	17	to	to	PART
ejpam-2055	397	18	be	be	AUX
ejpam-2055	397	19	strongly	strongly	ADV
ejpam-2055	397	20	δ	δ	NOUN
ejpam-2055	397	21	−	−	NOUN
ejpam-2055	397	22	β	β	AUX
ejpam-2055	397	23	-closed	-close	VERB
ejpam-2055	397	24	if	if	SCONJ
ejpam-2055	397	25	for	for	ADP
ejpam-2055	397	26	each	each	DET
ejpam-2055	397	27	(	(	PUNCT
ejpam-2055	397	28	x	x	PROPN
ejpam-2055	397	29	,	,	PUNCT
ejpam-2055	397	30	y	y	PROPN
ejpam-2055	397	31	)	)	PUNCT
ejpam-2055	397	32	∈	∈	PROPN
ejpam-2055	397	33	(	(	PUNCT
ejpam-2055	397	34	x	x	SYM
ejpam-2055	397	35	×	×	PROPN
ejpam-2055	397	36	y	y	PROPN
ejpam-2055	397	37	)	)	PUNCT
ejpam-2055	397	38	\	\	PROPN
ejpam-2055	398	1	g	g	PROPN
ejpam-2055	398	2	(	(	PUNCT
ejpam-2055	398	3	f	f	PROPN
ejpam-2055	398	4	)	)	PUNCT
ejpam-2055	398	5	;	;	PUNCT
ejpam-2055	398	6	there	there	PRON
ejpam-2055	398	7	exist	exist	VERB
ejpam-2055	398	8	u	u	PROPN
ejpam-2055	398	9	∈	∈	NOUN
ejpam-2055	398	10	δ−	δ−	PROPN
ejpam-2055	398	11	βς(x	βς(x	X
ejpam-2055	398	12	,	,	PUNCT
ejpam-2055	398	13	x	x	X
ejpam-2055	398	14	)	)	PUNCT
ejpam-2055	398	15	and	and	CCONJ
ejpam-2055	398	16	an	an	DET
ejpam-2055	398	17	open	open	ADJ
ejpam-2055	398	18	set	set	NOUN
ejpam-2055	398	19	v	v	NOUN
ejpam-2055	398	20	in	in	ADP
ejpam-2055	398	21	y	y	NOUN
ejpam-2055	398	22	containing	contain	VERB
ejpam-2055	398	23	y	y	PRON
ejpam-2055	398	24	such	such	ADJ
ejpam-2055	398	25	that	that	PRON
ejpam-2055	398	26	(	(	PUNCT
ejpam-2055	398	27	δ−	δ−	PROPN
ejpam-2055	398	28	β	β	X
ejpam-2055	398	29	−	−	ADP
ejpam-2055	398	30	cl(u)×	cl(u)×	PROPN
ejpam-2055	398	31	v	v	NOUN
ejpam-2055	398	32	)	)	PUNCT
ejpam-2055	398	33	⋂	⋂	PROPN
ejpam-2055	398	34	g	g	PROPN
ejpam-2055	398	35	(	(	PUNCT
ejpam-2055	398	36	f	f	PROPN
ejpam-2055	398	37	)	)	PUNCT
ejpam-2055	399	1	=	=	SYM
ejpam-2055	400	1	φ	φ	PROPN
ejpam-2055	400	2	.	.	PUNCT
ejpam-2055	401	1	lemma	lemma	PROPN
ejpam-2055	401	2	4	4	NUM
ejpam-2055	401	3	.	.	PUNCT
ejpam-2055	402	1	the	the	DET
ejpam-2055	402	2	graph	graph	NOUN
ejpam-2055	402	3	g	g	PROPN
ejpam-2055	402	4	(	(	PUNCT
ejpam-2055	402	5	f	f	PROPN
ejpam-2055	402	6	)	)	PUNCT
ejpam-2055	402	7	of	of	ADP
ejpam-2055	402	8	a	a	DET
ejpam-2055	402	9	function	function	NOUN
ejpam-2055	402	10	f	f	NOUN
ejpam-2055	402	11	:	:	PUNCT
ejpam-2055	402	12	x	x	X
ejpam-2055	402	13	→	→	SYM
ejpam-2055	402	14	y	y	PROPN
ejpam-2055	402	15	is	be	AUX
ejpam-2055	402	16	strongly	strongly	ADV
ejpam-2055	402	17	δ	δ	NOUN
ejpam-2055	402	18	−	−	NOUN
ejpam-2055	402	19	β	β	AUX
ejpam-2055	402	20	-closed	-close	VERB
ejpam-2055	402	21	if	if	SCONJ
ejpam-2055	402	22	and	and	CCONJ
ejpam-2055	402	23	only	only	ADV
ejpam-2055	402	24	if	if	SCONJ
ejpam-2055	402	25	for	for	ADP
ejpam-2055	402	26	each	each	DET
ejpam-2055	402	27	(	(	PUNCT
ejpam-2055	402	28	x	x	PROPN
ejpam-2055	402	29	,	,	PUNCT
ejpam-2055	402	30	y	y	PROPN
ejpam-2055	402	31	)	)	PUNCT
ejpam-2055	402	32	∈	∈	PROPN
ejpam-2055	402	33	(	(	PUNCT
ejpam-2055	402	34	x	x	SYM
ejpam-2055	402	35	×	×	PROPN
ejpam-2055	402	36	y	y	PROPN
ejpam-2055	402	37	)	)	PUNCT
ejpam-2055	402	38	\	\	PROPN
ejpam-2055	403	1	g	g	PROPN
ejpam-2055	403	2	(	(	PUNCT
ejpam-2055	403	3	f	f	PROPN
ejpam-2055	403	4	)	)	PUNCT
ejpam-2055	403	5	,	,	PUNCT
ejpam-2055	403	6	there	there	PRON
ejpam-2055	403	7	exist	exist	VERB
ejpam-2055	403	8	u	u	PROPN
ejpam-2055	403	9	∈	∈	NOUN
ejpam-2055	403	10	δ−	δ−	PROPN
ejpam-2055	403	11	βς(x	βς(x	X
ejpam-2055	403	12	,	,	PUNCT
ejpam-2055	403	13	x	x	X
ejpam-2055	403	14	)	)	PUNCT
ejpam-2055	403	15	and	and	CCONJ
ejpam-2055	403	16	an	an	DET
ejpam-2055	403	17	open	open	ADJ
ejpam-2055	403	18	set	set	NOUN
ejpam-2055	403	19	v	v	NOUN
ejpam-2055	403	20	in	in	ADP
ejpam-2055	403	21	y	y	NOUN
ejpam-2055	403	22	containing	contain	VERB
ejpam-2055	403	23	y	y	PRON
ejpam-2055	403	24	such	such	ADJ
ejpam-2055	403	25	that	that	SCONJ
ejpam-2055	403	26	f	f	PROPN
ejpam-2055	403	27	(	(	PUNCT
ejpam-2055	403	28	δ−	δ−	PROPN
ejpam-2055	403	29	β	β	X
ejpam-2055	403	30	−	−	NOUN
ejpam-2055	403	31	cl(u	cl(u	NOUN
ejpam-2055	403	32	)	)	PUNCT
ejpam-2055	403	33	)	)	PUNCT
ejpam-2055	404	1	⋂	⋂	PROPN
ejpam-2055	404	2	v	v	NOUN
ejpam-2055	404	3	=	=	SYM
ejpam-2055	404	4	φ	φ	PROPN
ejpam-2055	404	5	.	.	PUNCT
ejpam-2055	404	6	theorem	theorem	VERB
ejpam-2055	404	7	14	14	NUM
ejpam-2055	404	8	.	.	PUNCT
ejpam-2055	405	1	if	if	SCONJ
ejpam-2055	405	2	f	f	PROPN
ejpam-2055	405	3	:	:	PUNCT
ejpam-2055	405	4	x	x	X
ejpam-2055	405	5	→	→	SYM
ejpam-2055	405	6	y	y	PROPN
ejpam-2055	405	7	is	be	AUX
ejpam-2055	405	8	(	(	PUNCT
ejpam-2055	405	9	st	st	PROPN
ejpam-2055	405	10	.	.	PROPN
ejpam-2055	405	11	θ	θ	PROPN
ejpam-2055	405	12	−	−	PROPN
ejpam-2055	406	1	δ	δ	PROPN
ejpam-2055	406	2	−	−	PROPN
ejpam-2055	406	3	β	β	PROPN
ejpam-2055	406	4	.c	.c	PROPN
ejpam-2055	406	5	.	.	PUNCT
ejpam-2055	406	6	)	)	PUNCT
ejpam-2055	407	1	and	and	CCONJ
ejpam-2055	407	2	y	y	PROPN
ejpam-2055	407	3	is	be	AUX
ejpam-2055	407	4	hausdorff	hausdorff	NOUN
ejpam-2055	407	5	,	,	PUNCT
ejpam-2055	407	6	then	then	ADV
ejpam-2055	407	7	g(f	g(f	PROPN
ejpam-2055	407	8	)	)	PUNCT
ejpam-2055	407	9	is	be	AUX
ejpam-2055	407	10	strongly	strongly	ADV
ejpam-2055	407	11	δ−	δ−	PROPN
ejpam-2055	407	12	β	β	SYM
ejpam-2055	407	13	-closed	-close	VERB
ejpam-2055	407	14	in	in	ADP
ejpam-2055	407	15	x	x	PUNCT
ejpam-2055	407	16	×	×	PROPN
ejpam-2055	407	17	y	y	PROPN
ejpam-2055	407	18	.	.	PUNCT
ejpam-2055	408	1	proof	proof	NOUN
ejpam-2055	408	2	.	.	PUNCT
ejpam-2055	409	1	it	it	PRON
ejpam-2055	409	2	is	be	AUX
ejpam-2055	409	3	clear	clear	ADJ
ejpam-2055	409	4	that	that	SCONJ
ejpam-2055	409	5	f	f	PROPN
ejpam-2055	409	6	(	(	PUNCT
ejpam-2055	409	7	x	x	X
ejpam-2055	409	8	)	)	PUNCT
ejpam-2055	409	9	6=	6=	ADP
ejpam-2055	409	10	y	y	PROPN
ejpam-2055	409	11	for	for	ADP
ejpam-2055	409	12	each	each	DET
ejpam-2055	409	13	(	(	PUNCT
ejpam-2055	409	14	x	x	PROPN
ejpam-2055	409	15	,	,	PUNCT
ejpam-2055	409	16	y	y	PROPN
ejpam-2055	409	17	)	)	PUNCT
ejpam-2055	409	18	∈	∈	PROPN
ejpam-2055	409	19	(	(	PUNCT
ejpam-2055	409	20	x	x	NOUN
ejpam-2055	409	21	×y	×y	ADV
ejpam-2055	409	22	)	)	PUNCT
ejpam-2055	409	23	\g	\g	PROPN
ejpam-2055	409	24	(	(	PUNCT
ejpam-2055	409	25	f	f	PROPN
ejpam-2055	409	26	)	)	PUNCT
ejpam-2055	409	27	.	.	PUNCT
ejpam-2055	410	1	since	since	SCONJ
ejpam-2055	410	2	y	y	PROPN
ejpam-2055	410	3	is	be	AUX
ejpam-2055	410	4	hausdorff	hausdorff	NOUN
ejpam-2055	410	5	,	,	PUNCT
ejpam-2055	410	6	there	there	PRON
ejpam-2055	410	7	exist	exist	VERB
ejpam-2055	410	8	open	open	ADJ
ejpam-2055	410	9	sets	set	NOUN
ejpam-2055	410	10	v	v	NOUN
ejpam-2055	410	11	and	and	CCONJ
ejpam-2055	410	12	h	h	NOUN
ejpam-2055	410	13	in	in	ADP
ejpam-2055	410	14	y	y	PROPN
ejpam-2055	410	15	containing	contain	VERB
ejpam-2055	410	16	f	f	X
ejpam-2055	410	17	(	(	PUNCT
ejpam-2055	410	18	x	x	NOUN
ejpam-2055	410	19	)	)	PUNCT
ejpam-2055	410	20	and	and	CCONJ
ejpam-2055	410	21	y	y	PROPN
ejpam-2055	410	22	,	,	PUNCT
ejpam-2055	410	23	respectively	respectively	ADV
ejpam-2055	410	24	,	,	PUNCT
ejpam-2055	410	25	such	such	ADJ
ejpam-2055	410	26	that	that	SCONJ
ejpam-2055	410	27	v	v	ADP
ejpam-2055	410	28	⋂	⋂	NUM
ejpam-2055	410	29	h	h	NOUN
ejpam-2055	410	30	=	=	SYM
ejpam-2055	410	31	φ	φ	PROPN
ejpam-2055	410	32	.	.	PUNCT
ejpam-2055	411	1	since	since	SCONJ
ejpam-2055	411	2	f	f	PROPN
ejpam-2055	411	3	is	be	AUX
ejpam-2055	411	4	(	(	PUNCT
ejpam-2055	411	5	st	st	PROPN
ejpam-2055	411	6	.	.	PROPN
ejpam-2055	412	1	θ	θ	PROPN
ejpam-2055	412	2	−	−	PROPN
ejpam-2055	413	1	δ	δ	PROPN
ejpam-2055	413	2	−	−	PROPN
ejpam-2055	413	3	β	β	PROPN
ejpam-2055	413	4	.c	.c	PROPN
ejpam-2055	413	5	.	.	PUNCT
ejpam-2055	413	6	)	)	PUNCT
ejpam-2055	414	1	,	,	PUNCT
ejpam-2055	414	2	there	there	PRON
ejpam-2055	414	3	exist	exist	VERB
ejpam-2055	414	4	u	u	PROPN
ejpam-2055	414	5	∈	∈	PROPN
ejpam-2055	414	6	δ	δ	PROPN
ejpam-2055	414	7	−	−	NOUN
ejpam-2055	414	8	βς(x	βς(x	PUNCT
ejpam-2055	414	9	,	,	PUNCT
ejpam-2055	414	10	x	x	X
ejpam-2055	414	11	)	)	PUNCT
ejpam-2055	414	12	such	such	ADJ
ejpam-2055	414	13	that	that	SCONJ
ejpam-2055	414	14	f	f	PROPN
ejpam-2055	414	15	(	(	PUNCT
ejpam-2055	414	16	δ	δ	PROPN
ejpam-2055	414	17	−	−	NOUN
ejpam-2055	414	18	β	β	X
ejpam-2055	414	19	−	−	NOUN
ejpam-2055	414	20	cl(u	cl(u	PROPN
ejpam-2055	414	21	)	)	PUNCT
ejpam-2055	414	22	)	)	PUNCT
ejpam-2055	415	1	⊂	⊂	PROPN
ejpam-2055	415	2	v	v	X
ejpam-2055	415	3	.	.	PUNCT
ejpam-2055	416	1	thus	thus	ADV
ejpam-2055	416	2	,	,	PUNCT
ejpam-2055	416	3	f	f	PROPN
ejpam-2055	416	4	(	(	PUNCT
ejpam-2055	416	5	δ−β	δ−β	PROPN
ejpam-2055	416	6	−cl(u	−cl(u	PROPN
ejpam-2055	416	7	)	)	PUNCT
ejpam-2055	416	8	)	)	PUNCT
ejpam-2055	417	1	⋂	⋂	PROPN
ejpam-2055	417	2	h	h	NOUN
ejpam-2055	417	3	=	=	SYM
ejpam-2055	417	4	φ	φ	PROPN
ejpam-2055	417	5	and	and	CCONJ
ejpam-2055	417	6	then	then	ADV
ejpam-2055	417	7	by	by	ADP
ejpam-2055	417	8	lemma	lemma	PROPN
ejpam-2055	417	9	(	(	PUNCT
ejpam-2055	417	10	4),g	4),g	PROPN
ejpam-2055	417	11	(	(	PUNCT
ejpam-2055	417	12	f	f	PROPN
ejpam-2055	417	13	)	)	PUNCT
ejpam-2055	417	14	is	be	AUX
ejpam-2055	417	15	strongly	strongly	ADV
ejpam-2055	417	16	δ−β	δ−β	ADJ
ejpam-2055	417	17	-closed	-close	VERB
ejpam-2055	417	18	in	in	ADP
ejpam-2055	417	19	x	x	SYM
ejpam-2055	417	20	×y	×y	NOUN
ejpam-2055	417	21	.	.	PUNCT
ejpam-2055	418	1	7	7	X
ejpam-2055	418	2	.	.	X
ejpam-2055	418	3	covering	cover	VERB
ejpam-2055	418	4	properties	property	NOUN
ejpam-2055	418	5	definition	definition	NOUN
ejpam-2055	418	6	9	9	NUM
ejpam-2055	418	7	.	.	PUNCT
ejpam-2055	419	1	a	a	DET
ejpam-2055	419	2	space	space	NOUN
ejpam-2055	419	3	x	x	PUNCT
ejpam-2055	419	4	is	be	AUX
ejpam-2055	419	5	said	say	VERB
ejpam-2055	419	6	to	to	PART
ejpam-2055	419	7	be	be	AUX
ejpam-2055	419	8	:	:	PUNCT
ejpam-2055	419	9	a	a	X
ejpam-2055	419	10	)	)	PUNCT
ejpam-2055	419	11	δ	δ	NOUN
ejpam-2055	419	12	−	−	NOUN
ejpam-2055	419	13	β	β	NOUN
ejpam-2055	419	14	-closed	-close	VERB
ejpam-2055	419	15	if	if	SCONJ
ejpam-2055	419	16	every	every	DET
ejpam-2055	419	17	cover	cover	NOUN
ejpam-2055	419	18	of	of	ADP
ejpam-2055	419	19	x	x	PUNCT
ejpam-2055	419	20	by	by	ADP
ejpam-2055	419	21	δ	δ	PROPN
ejpam-2055	419	22	−	−	NOUN
ejpam-2055	419	23	β	β	NOUN
ejpam-2055	419	24	-open	-open	NOUN
ejpam-2055	419	25	sets	set	NOUN
ejpam-2055	419	26	has	have	VERB
ejpam-2055	419	27	a	a	DET
ejpam-2055	419	28	finite	finite	ADJ
ejpam-2055	419	29	subcover	subcover	NOUN
ejpam-2055	419	30	whose	whose	DET
ejpam-2055	419	31	preclosures	preclosure	NOUN
ejpam-2055	419	32	cover	cover	VERB
ejpam-2055	419	33	x	x	NOUN
ejpam-2055	419	34	,	,	PUNCT
ejpam-2055	419	35	b	b	NOUN
ejpam-2055	419	36	)	)	PUNCT
ejpam-2055	419	37	countably	countably	ADV
ejpam-2055	419	38	δ−β	δ−β	PROPN
ejpam-2055	419	39	-closed	-close	VERB
ejpam-2055	419	40	if	if	SCONJ
ejpam-2055	419	41	every	every	DET
ejpam-2055	419	42	countable	countable	ADJ
ejpam-2055	419	43	cover	cover	NOUN
ejpam-2055	419	44	of	of	ADP
ejpam-2055	419	45	x	x	PUNCT
ejpam-2055	419	46	by	by	ADP
ejpam-2055	419	47	δ−β	δ−β	ADJ
ejpam-2055	419	48	-open	-open	ADJ
ejpam-2055	419	49	sets	set	NOUN
ejpam-2055	419	50	has	have	VERB
ejpam-2055	419	51	a	a	DET
ejpam-2055	419	52	finite	finite	ADJ
ejpam-2055	419	53	subcover	subcover	NOUN
ejpam-2055	419	54	whose	whose	DET
ejpam-2055	419	55	preclosures	preclosure	NOUN
ejpam-2055	419	56	cover	cover	VERB
ejpam-2055	419	57	x.	x.	NOUN
ejpam-2055	419	58	a	a	DET
ejpam-2055	419	59	subset	subset	NOUN
ejpam-2055	419	60	k	k	NOUN
ejpam-2055	419	61	of	of	ADP
ejpam-2055	419	62	a	a	DET
ejpam-2055	419	63	space	space	NOUN
ejpam-2055	419	64	x	x	PUNCT
ejpam-2055	419	65	is	be	AUX
ejpam-2055	419	66	said	say	VERB
ejpam-2055	419	67	to	to	PART
ejpam-2055	419	68	be	be	AUX
ejpam-2055	419	69	δ−	δ−	PROPN
ejpam-2055	419	70	β	β	AUX
ejpam-2055	419	71	-closed	-close	VERB
ejpam-2055	419	72	relative	relative	ADJ
ejpam-2055	419	73	to	to	ADP
ejpam-2055	419	74	x	x	PRON
ejpam-2055	419	75	if	if	SCONJ
ejpam-2055	419	76	for	for	ADP
ejpam-2055	419	77	every	every	DET
ejpam-2055	419	78	cover	cover	NOUN
ejpam-2055	419	79	{	{	PUNCT
ejpam-2055	419	80	vλ	vλ	INTJ
ejpam-2055	419	81	:	:	PUNCT
ejpam-2055	419	82	λ	λ	NOUN
ejpam-2055	419	83	∈∆	∈∆	NOUN
ejpam-2055	419	84	}	}	PUNCT
ejpam-2055	419	85	of	of	ADP
ejpam-2055	419	86	k	k	X
ejpam-2055	419	87	by	by	ADP
ejpam-2055	419	88	δ−	δ−	PROPN
ejpam-2055	419	89	β	β	X
ejpam-2055	419	90	-open	-open	PROPN
ejpam-2055	419	91	sets	set	NOUN
ejpam-2055	419	92	of	of	ADP
ejpam-2055	419	93	x	x	NOUN
ejpam-2055	419	94	,	,	PUNCT
ejpam-2055	419	95	there	there	PRON
ejpam-2055	419	96	exists	exist	VERB
ejpam-2055	419	97	a	a	DET
ejpam-2055	419	98	finite	finite	NOUN
ejpam-2055	419	99	subset	subset	VERB
ejpam-2055	419	100	∆0	∆0	NUM
ejpam-2055	419	101	of	of	ADP
ejpam-2055	419	102	∆	∆	PROPN
ejpam-2055	419	103	such	such	ADJ
ejpam-2055	419	104	that	that	SCONJ
ejpam-2055	419	105	k	k	PROPN
ejpam-2055	419	106	⊂	⊂	X
ejpam-2055	419	107	⋃	⋃	ADV
ejpam-2055	419	108	{	{	PUNCT
ejpam-2055	419	109	δ−	δ−	PROPN
ejpam-2055	419	110	β	β	X
ejpam-2055	419	111	−	−	PROPN
ejpam-2055	419	112	cl(vλ	cl(vλ	NOUN
ejpam-2055	419	113	)	)	PUNCT
ejpam-2055	419	114	:	:	PUNCT
ejpam-2055	420	1	λ	λ	X
ejpam-2055	420	2	∈∆0	∈∆0	PROPN
ejpam-2055	420	3	}	}	PUNCT
ejpam-2055	420	4	.	.	PUNCT
ejpam-2055	421	1	theorem	theorem	NOUN
ejpam-2055	421	2	15	15	NUM
ejpam-2055	421	3	.	.	PUNCT
ejpam-2055	422	1	if	if	SCONJ
ejpam-2055	422	2	f	f	PROPN
ejpam-2055	422	3	:	:	PUNCT
ejpam-2055	422	4	x	x	X
ejpam-2055	422	5	→	→	SYM
ejpam-2055	422	6	y	y	PROPN
ejpam-2055	422	7	is	be	AUX
ejpam-2055	422	8	(	(	PUNCT
ejpam-2055	422	9	st	st	PROPN
ejpam-2055	422	10	.	.	PROPN
ejpam-2055	422	11	θ	θ	PROPN
ejpam-2055	422	12	−δ−β	−δ−β	PROPN
ejpam-2055	422	13	.c	.c	PROPN
ejpam-2055	422	14	.	.	PUNCT
ejpam-2055	422	15	)	)	PUNCT
ejpam-2055	423	1	and	and	CCONJ
ejpam-2055	423	2	k	k	PROPN
ejpam-2055	423	3	is	be	AUX
ejpam-2055	423	4	δ−β	δ−β	X
ejpam-2055	423	5	-closed	-closed	ADJ
ejpam-2055	423	6	relative	relative	ADJ
ejpam-2055	423	7	to	to	ADP
ejpam-2055	423	8	x	x	PRON
ejpam-2055	423	9	,	,	PUNCT
ejpam-2055	423	10	then	then	ADV
ejpam-2055	423	11	,	,	PUNCT
ejpam-2055	423	12	f(k	f(k	VERB
ejpam-2055	423	13	)	)	PUNCT
ejpam-2055	423	14	is	be	AUX
ejpam-2055	423	15	a	a	DET
ejpam-2055	423	16	compact	compact	ADJ
ejpam-2055	423	17	set	set	NOUN
ejpam-2055	423	18	of	of	ADP
ejpam-2055	423	19	y.	y.	PROPN
ejpam-2055	423	20	proof	proof	PROPN
ejpam-2055	423	21	.	.	PUNCT
ejpam-2055	424	1	suppose	suppose	VERB
ejpam-2055	424	2	that	that	SCONJ
ejpam-2055	424	3	f	f	X
ejpam-2055	424	4	:	:	PUNCT
ejpam-2055	424	5	x	x	X
ejpam-2055	424	6	→	→	SYM
ejpam-2055	424	7	y	y	PROPN
ejpam-2055	424	8	is	be	AUX
ejpam-2055	424	9	(	(	PUNCT
ejpam-2055	424	10	st	st	PROPN
ejpam-2055	424	11	.	.	PROPN
ejpam-2055	424	12	θ	θ	PROPN
ejpam-2055	424	13	−δ−	−δ−	VERB
ejpam-2055	424	14	β	β	X
ejpam-2055	424	15	.c	.c	PROPN
ejpam-2055	424	16	.	.	PUNCT
ejpam-2055	424	17	)	)	PUNCT
ejpam-2055	425	1	and	and	CCONJ
ejpam-2055	425	2	k	k	PROPN
ejpam-2055	425	3	is	be	AUX
ejpam-2055	425	4	δ−	δ−	PROPN
ejpam-2055	425	5	β	β	AUX
ejpam-2055	425	6	-closed	-close	VERB
ejpam-2055	425	7	relative	relative	ADJ
ejpam-2055	425	8	to	to	ADP
ejpam-2055	425	9	x	x	PRON
ejpam-2055	425	10	,	,	PUNCT
ejpam-2055	425	11	let	let	VERB
ejpam-2055	425	12	{	{	PUNCT
ejpam-2055	425	13	vλ	vλ	INTJ
ejpam-2055	425	14	:	:	PUNCT
ejpam-2055	425	15	λ	λ	NOUN
ejpam-2055	425	16	∈∆	∈∆	AUX
ejpam-2055	425	17	}	}	PUNCT
ejpam-2055	425	18	be	be	AUX
ejpam-2055	425	19	a	a	DET
ejpam-2055	425	20	cover	cover	NOUN
ejpam-2055	425	21	of	of	ADP
ejpam-2055	425	22	f	f	PROPN
ejpam-2055	425	23	(	(	PUNCT
ejpam-2055	425	24	k	k	NOUN
ejpam-2055	425	25	)	)	PUNCT
ejpam-2055	425	26	by	by	ADP
ejpam-2055	425	27	open	open	ADJ
ejpam-2055	425	28	sets	set	NOUN
ejpam-2055	425	29	of	of	ADP
ejpam-2055	425	30	y.	y.	NOUN
ejpam-2055	425	31	for	for	ADP
ejpam-2055	425	32	each	each	DET
ejpam-2055	425	33	point	point	NOUN
ejpam-2055	425	34	x	x	X
ejpam-2055	425	35	∈	∈	PROPN
ejpam-2055	425	36	k	k	NOUN
ejpam-2055	425	37	,	,	PUNCT
ejpam-2055	425	38	there	there	PRON
ejpam-2055	425	39	exists	exist	VERB
ejpam-2055	425	40	λ(x	λ(x	PROPN
ejpam-2055	425	41	)	)	PUNCT
ejpam-2055	425	42	∈∆	∈∆	NOUN
ejpam-2055	425	43	a.	a.	NOUN
ejpam-2055	425	44	m.	m.	NOUN
ejpam-2055	425	45	farhan	farhan	PROPN
ejpam-2055	425	46	and	and	CCONJ
ejpam-2055	425	47	x.	x.	PROPN
ejpam-2055	425	48	yang	yang	PROPN
ejpam-2055	425	49	/	/	SYM
ejpam-2055	425	50	eur	eur	PROPN
ejpam-2055	425	51	.	.	PUNCT
ejpam-2055	426	1	j.	j.	PROPN
ejpam-2055	426	2	pure	pure	PROPN
ejpam-2055	426	3	appl	appl	PROPN
ejpam-2055	426	4	.	.	PROPN
ejpam-2055	426	5	math	math	PROPN
ejpam-2055	426	6	,	,	PUNCT
ejpam-2055	426	7	8	8	NUM
ejpam-2055	426	8	(	(	PUNCT
ejpam-2055	426	9	2015	2015	NUM
ejpam-2055	426	10	)	)	PUNCT
ejpam-2055	426	11	,	,	PUNCT
ejpam-2055	426	12	185	185	NUM
ejpam-2055	426	13	-	-	SYM
ejpam-2055	426	14	200	200	NUM
ejpam-2055	426	15	196	196	NUM
ejpam-2055	426	16	such	such	ADJ
ejpam-2055	426	17	that	that	SCONJ
ejpam-2055	426	18	f	f	PROPN
ejpam-2055	426	19	(	(	PUNCT
ejpam-2055	426	20	x	x	X
ejpam-2055	426	21	)	)	PUNCT
ejpam-2055	426	22	∈	∈	PROPN
ejpam-2055	426	23	vλ(x	vλ(x	NOUN
ejpam-2055	426	24	)	)	PUNCT
ejpam-2055	426	25	.	.	PUNCT
ejpam-2055	427	1	since	since	SCONJ
ejpam-2055	427	2	f	f	PROPN
ejpam-2055	427	3	is	be	AUX
ejpam-2055	427	4	(	(	PUNCT
ejpam-2055	427	5	st	st	PROPN
ejpam-2055	427	6	.	.	PROPN
ejpam-2055	427	7	θ	θ	PROPN
ejpam-2055	427	8	−	−	PROPN
ejpam-2055	428	1	δ−	δ−	PROPN
ejpam-2055	428	2	β	β	PROPN
ejpam-2055	428	3	.c	.c	PROPN
ejpam-2055	428	4	.	.	PUNCT
ejpam-2055	428	5	)	)	PUNCT
ejpam-2055	429	1	,	,	PUNCT
ejpam-2055	429	2	there	there	PRON
ejpam-2055	429	3	exists	exist	VERB
ejpam-2055	429	4	ux	ux	PROPN
ejpam-2055	429	5	∈	∈	PROPN
ejpam-2055	429	6	δ−	δ−	PROPN
ejpam-2055	429	7	βς(x	βς(x	X
ejpam-2055	429	8	,	,	PUNCT
ejpam-2055	429	9	x	x	X
ejpam-2055	429	10	)	)	PUNCT
ejpam-2055	429	11	such	such	ADJ
ejpam-2055	429	12	that	that	SCONJ
ejpam-2055	429	13	f	f	PROPN
ejpam-2055	429	14	(	(	PUNCT
ejpam-2055	429	15	δ−β	δ−β	PROPN
ejpam-2055	429	16	−cl(ux	−cl(ux	NOUN
ejpam-2055	429	17	)	)	PUNCT
ejpam-2055	429	18	)	)	PUNCT
ejpam-2055	429	19	⊂	⊂	PROPN
ejpam-2055	429	20	vλ(x	vλ(x	NOUN
ejpam-2055	429	21	)	)	PUNCT
ejpam-2055	429	22	.	.	PUNCT
ejpam-2055	430	1	the	the	DET
ejpam-2055	430	2	family	family	NOUN
ejpam-2055	430	3	{	{	PUNCT
ejpam-2055	430	4	ux	ux	NOUN
ejpam-2055	430	5	:	:	PUNCT
ejpam-2055	430	6	x	x	SYM
ejpam-2055	430	7	∈	∈	PROPN
ejpam-2055	430	8	k	k	NOUN
ejpam-2055	430	9	}	}	PUNCT
ejpam-2055	430	10	is	be	AUX
ejpam-2055	430	11	a	a	DET
ejpam-2055	430	12	cover	cover	NOUN
ejpam-2055	430	13	of	of	ADP
ejpam-2055	430	14	k	k	X
ejpam-2055	430	15	by	by	ADP
ejpam-2055	430	16	δ−β	δ−β	PROPN
ejpam-2055	430	17	-open	-open	ADJ
ejpam-2055	430	18	sets	set	NOUN
ejpam-2055	430	19	of	of	ADP
ejpam-2055	430	20	x	x	PUNCT
ejpam-2055	430	21	and	and	CCONJ
ejpam-2055	430	22	hence	hence	ADV
ejpam-2055	430	23	there	there	PRON
ejpam-2055	430	24	exists	exist	VERB
ejpam-2055	430	25	a	a	DET
ejpam-2055	430	26	finite	finite	NOUN
ejpam-2055	430	27	subset	subset	VERB
ejpam-2055	430	28	k0	k0	PROPN
ejpam-2055	430	29	of	of	ADP
ejpam-2055	430	30	k	k	PROPN
ejpam-2055	430	31	such	such	ADJ
ejpam-2055	430	32	that	that	SCONJ
ejpam-2055	430	33	k	k	PROPN
ejpam-2055	430	34	⊂	⊂	X
ejpam-2055	430	35	⋃	⋃	PROPN
ejpam-2055	430	36	x∈ko	x∈ko	PROPN
ejpam-2055	430	37	δ−	δ−	PROPN
ejpam-2055	430	38	β	β	NOUN
ejpam-2055	430	39	−	−	NOUN
ejpam-2055	430	40	cl(ux	cl(ux	NOUN
ejpam-2055	430	41	)	)	PUNCT
ejpam-2055	430	42	.	.	PUNCT
ejpam-2055	431	1	therefore	therefore	ADV
ejpam-2055	431	2	,	,	PUNCT
ejpam-2055	431	3	we	we	PRON
ejpam-2055	431	4	obtain	obtain	VERB
ejpam-2055	431	5	f	f	PROPN
ejpam-2055	431	6	(	(	PUNCT
ejpam-2055	431	7	k	k	X
ejpam-2055	431	8	)	)	PUNCT
ejpam-2055	431	9	⊂	⊂	PROPN
ejpam-2055	431	10	⋃	⋃	PUNCT
ejpam-2055	431	11	x∈ko	x∈ko	PROPN
ejpam-2055	431	12	vα(x	vα(x	NOUN
ejpam-2055	431	13	)	)	PUNCT
ejpam-2055	431	14	.	.	PUNCT
ejpam-2055	432	1	this	this	PRON
ejpam-2055	432	2	shows	show	VERB
ejpam-2055	432	3	that	that	SCONJ
ejpam-2055	432	4	f	f	PROPN
ejpam-2055	432	5	(	(	PUNCT
ejpam-2055	432	6	k	k	NOUN
ejpam-2055	432	7	)	)	PUNCT
ejpam-2055	432	8	is	be	AUX
ejpam-2055	432	9	compact	compact	ADJ
ejpam-2055	432	10	.	.	PUNCT
ejpam-2055	433	1	corollary	corollary	ADJ
ejpam-2055	433	2	2	2	NUM
ejpam-2055	433	3	.	.	PUNCT
ejpam-2055	434	1	let	let	VERB
ejpam-2055	434	2	f	f	NOUN
ejpam-2055	434	3	:	:	PUNCT
ejpam-2055	434	4	x	x	X
ejpam-2055	434	5	→	→	SYM
ejpam-2055	434	6	y	y	PROPN
ejpam-2055	434	7	is	be	AUX
ejpam-2055	434	8	(	(	PUNCT
ejpam-2055	434	9	st	st	PROPN
ejpam-2055	434	10	.	.	PROPN
ejpam-2055	434	11	θ	θ	PROPN
ejpam-2055	434	12	−δ−	−δ−	VERB
ejpam-2055	434	13	β	β	PROPN
ejpam-2055	434	14	.c	.c	PROPN
ejpam-2055	434	15	.	.	PUNCT
ejpam-2055	434	16	)	)	PUNCT
ejpam-2055	435	1	surjection	surjection	PROPN
ejpam-2055	435	2	.	.	PUNCT
ejpam-2055	436	1	then	then	ADV
ejpam-2055	436	2	the	the	DET
ejpam-2055	436	3	following	follow	VERB
ejpam-2055	436	4	properties	property	NOUN
ejpam-2055	436	5	hold	hold	VERB
ejpam-2055	436	6	:	:	PUNCT
ejpam-2055	436	7	a	a	X
ejpam-2055	436	8	)	)	PUNCT
ejpam-2055	436	9	if	if	SCONJ
ejpam-2055	436	10	x	x	PRON
ejpam-2055	436	11	is	be	AUX
ejpam-2055	436	12	δ−	δ−	PROPN
ejpam-2055	436	13	β	β	X
ejpam-2055	436	14	-closed	-closed	PROPN
ejpam-2055	436	15	,	,	PUNCT
ejpam-2055	436	16	then	then	ADV
ejpam-2055	436	17	y	y	PROPN
ejpam-2055	436	18	is	be	AUX
ejpam-2055	436	19	compact	compact	ADJ
ejpam-2055	436	20	,	,	PUNCT
ejpam-2055	436	21	b	b	X
ejpam-2055	436	22	)	)	PUNCT
ejpam-2055	436	23	if	if	SCONJ
ejpam-2055	436	24	x	x	PRON
ejpam-2055	436	25	is	be	AUX
ejpam-2055	436	26	countably	countably	ADV
ejpam-2055	436	27	δ−	δ−	PROPN
ejpam-2055	436	28	β	β	X
ejpam-2055	436	29	-closed	-closed	PROPN
ejpam-2055	436	30	,	,	PUNCT
ejpam-2055	436	31	then	then	ADV
ejpam-2055	436	32	y	y	PROPN
ejpam-2055	436	33	is	be	AUX
ejpam-2055	436	34	countably	countably	ADV
ejpam-2055	436	35	compact	compact	ADJ
ejpam-2055	436	36	.	.	PUNCT
ejpam-2055	437	1	theorem	theorem	VERB
ejpam-2055	437	2	16	16	NUM
ejpam-2055	437	3	.	.	PUNCT
ejpam-2055	438	1	if	if	SCONJ
ejpam-2055	438	2	a	a	DET
ejpam-2055	438	3	function	function	NOUN
ejpam-2055	438	4	f	f	NOUN
ejpam-2055	438	5	:	:	PUNCT
ejpam-2055	438	6	x	x	X
ejpam-2055	438	7	→	→	SYM
ejpam-2055	438	8	y	y	PROPN
ejpam-2055	438	9	has	have	VERB
ejpam-2055	438	10	a	a	DET
ejpam-2055	438	11	strongly	strongly	ADV
ejpam-2055	438	12	δ−β	δ−β	ADJ
ejpam-2055	438	13	-closed	-close	VERB
ejpam-2055	438	14	graph	graph	NOUN
ejpam-2055	438	15	,	,	PUNCT
ejpam-2055	438	16	then	then	ADV
ejpam-2055	438	17	f(k	f(k	VERB
ejpam-2055	438	18	)	)	PUNCT
ejpam-2055	438	19	is	be	AUX
ejpam-2055	438	20	closed	close	VERB
ejpam-2055	438	21	in	in	ADP
ejpam-2055	438	22	y	y	PROPN
ejpam-2055	438	23	for	for	ADP
ejpam-2055	438	24	each	each	DET
ejpam-2055	438	25	subset	subset	NOUN
ejpam-2055	439	1	k	k	X
ejpam-2055	440	1	which	which	PRON
ejpam-2055	440	2	is	be	AUX
ejpam-2055	440	3	δ−	δ−	PROPN
ejpam-2055	440	4	β	β	AUX
ejpam-2055	440	5	-closed	-close	VERB
ejpam-2055	440	6	relative	relative	ADJ
ejpam-2055	440	7	to	to	ADP
ejpam-2055	440	8	x.	x.	NOUN
ejpam-2055	440	9	proof	proof	NOUN
ejpam-2055	440	10	.	.	PUNCT
ejpam-2055	441	1	let	let	VERB
ejpam-2055	441	2	k	k	PRON
ejpam-2055	441	3	be	be	AUX
ejpam-2055	441	4	δ	δ	PROPN
ejpam-2055	441	5	−	−	NOUN
ejpam-2055	441	6	β	β	X
ejpam-2055	441	7	-closed	-close	VERB
ejpam-2055	441	8	relative	relative	ADJ
ejpam-2055	441	9	to	to	ADP
ejpam-2055	441	10	x	x	PUNCT
ejpam-2055	441	11	and	and	CCONJ
ejpam-2055	442	1	y	y	PROPN
ejpam-2055	442	2	∈	∈	PROPN
ejpam-2055	442	3	y	y	PROPN
ejpam-2055	442	4	\	\	PROPN
ejpam-2055	442	5	f	f	PROPN
ejpam-2055	442	6	(	(	PUNCT
ejpam-2055	442	7	k	k	NOUN
ejpam-2055	442	8	)	)	PUNCT
ejpam-2055	442	9	.	.	PUNCT
ejpam-2055	443	1	then	then	ADV
ejpam-2055	443	2	for	for	ADP
ejpam-2055	443	3	each	each	DET
ejpam-2055	443	4	x	x	SYM
ejpam-2055	443	5	∈	∈	PROPN
ejpam-2055	444	1	k	k	NOUN
ejpam-2055	444	2	we	we	PRON
ejpam-2055	444	3	have	have	VERB
ejpam-2055	444	4	(	(	PUNCT
ejpam-2055	444	5	x	x	NOUN
ejpam-2055	444	6	,	,	PUNCT
ejpam-2055	444	7	y	y	PROPN
ejpam-2055	444	8	)	)	PUNCT
ejpam-2055	444	9	/∈	/∈	PUNCT
ejpam-2055	445	1	g	g	NOUN
ejpam-2055	445	2	(	(	PUNCT
ejpam-2055	445	3	f	f	PROPN
ejpam-2055	445	4	)	)	PUNCT
ejpam-2055	445	5	and	and	CCONJ
ejpam-2055	445	6	by	by	ADP
ejpam-2055	445	7	lemma	lemma	PROPN
ejpam-2055	445	8	4	4	NUM
ejpam-2055	445	9	there	there	ADV
ejpam-2055	445	10	exist	exist	VERB
ejpam-2055	445	11	ux	ux	PROPN
ejpam-2055	445	12	∈	∈	PROPN
ejpam-2055	445	13	δ	δ	PROPN
ejpam-2055	445	14	−	−	PROPN
ejpam-2055	445	15	βς(x	βς(x	PUNCT
ejpam-2055	445	16	,	,	PUNCT
ejpam-2055	445	17	x	x	X
ejpam-2055	445	18	)	)	PUNCT
ejpam-2055	445	19	and	and	CCONJ
ejpam-2055	445	20	an	an	DET
ejpam-2055	445	21	open	open	ADJ
ejpam-2055	445	22	set	set	NOUN
ejpam-2055	445	23	vx	vx	PROPN
ejpam-2055	445	24	of	of	ADP
ejpam-2055	445	25	y	y	PROPN
ejpam-2055	445	26	containing	contain	VERB
ejpam-2055	445	27	y	y	PRON
ejpam-2055	446	1	such	such	ADJ
ejpam-2055	446	2	that	that	SCONJ
ejpam-2055	446	3	f	f	PROPN
ejpam-2055	446	4	(	(	PUNCT
ejpam-2055	446	5	δ	δ	PROPN
ejpam-2055	446	6	−	−	NOUN
ejpam-2055	446	7	β	β	X
ejpam-2055	446	8	−	−	NOUN
ejpam-2055	446	9	cl(ux	cl(ux	NOUN
ejpam-2055	446	10	)	)	PUNCT
ejpam-2055	446	11	)	)	PUNCT
ejpam-2055	447	1	⋂	⋂	PROPN
ejpam-2055	447	2	vx	vx	PROPN
ejpam-2055	447	3	=	=	SYM
ejpam-2055	447	4	φ	φ	PROPN
ejpam-2055	447	5	.	.	PUNCT
ejpam-2055	448	1	the	the	DET
ejpam-2055	448	2	family	family	NOUN
ejpam-2055	448	3	{	{	PUNCT
ejpam-2055	448	4	ux	ux	NOUN
ejpam-2055	448	5	:	:	PUNCT
ejpam-2055	448	6	x	x	SYM
ejpam-2055	448	7	∈	∈	PROPN
ejpam-2055	448	8	k	k	NOUN
ejpam-2055	448	9	}	}	PUNCT
ejpam-2055	448	10	is	be	AUX
ejpam-2055	448	11	a	a	DET
ejpam-2055	448	12	cover	cover	NOUN
ejpam-2055	448	13	of	of	ADP
ejpam-2055	448	14	k	k	X
ejpam-2055	448	15	by	by	ADP
ejpam-2055	448	16	δ−	δ−	PROPN
ejpam-2055	448	17	β	β	X
ejpam-2055	448	18	-open	-open	PROPN
ejpam-2055	448	19	sets	set	NOUN
ejpam-2055	448	20	of	of	ADP
ejpam-2055	448	21	x.	x.	NOUN
ejpam-2055	448	22	since	since	SCONJ
ejpam-2055	448	23	k	k	PROPN
ejpam-2055	448	24	is	be	AUX
ejpam-2055	448	25	δ−	δ−	PROPN
ejpam-2055	448	26	β	β	AUX
ejpam-2055	448	27	-closed	-close	VERB
ejpam-2055	448	28	relative	relative	ADJ
ejpam-2055	448	29	to	to	ADP
ejpam-2055	448	30	x	x	PRON
ejpam-2055	448	31	,	,	PUNCT
ejpam-2055	448	32	there	there	PRON
ejpam-2055	448	33	exists	exist	VERB
ejpam-2055	448	34	a	a	DET
ejpam-2055	448	35	finite	finite	NOUN
ejpam-2055	448	36	subset	subset	VERB
ejpam-2055	448	37	k0	k0	PROPN
ejpam-2055	448	38	of	of	ADP
ejpam-2055	448	39	k	k	PROPN
ejpam-2055	448	40	such	such	ADJ
ejpam-2055	448	41	that	that	SCONJ
ejpam-2055	448	42	k	k	PROPN
ejpam-2055	448	43	⊂	⊂	X
ejpam-2055	448	44	⋃	⋃	ADV
ejpam-2055	448	45	{	{	PUNCT
ejpam-2055	448	46	δ−	δ−	PROPN
ejpam-2055	448	47	β	β	X
ejpam-2055	448	48	−	−	NOUN
ejpam-2055	448	49	cl(ux	cl(ux	NOUN
ejpam-2055	448	50	)	)	PUNCT
ejpam-2055	448	51	:	:	PUNCT
ejpam-2055	449	1	x	x	X
ejpam-2055	449	2	∈	∈	PROPN
ejpam-2055	449	3	k0	k0	PROPN
ejpam-2055	449	4	}	}	PUNCT
ejpam-2055	449	5	.	.	PUNCT
ejpam-2055	450	1	put	put	VERB
ejpam-2055	450	2	v	v	NUM
ejpam-2055	450	3	=	=	SYM
ejpam-2055	450	4	⋂	⋂	PROPN
ejpam-2055	450	5	{	{	PUNCT
ejpam-2055	450	6	vx	vx	X
ejpam-2055	450	7	:	:	PUNCT
ejpam-2055	450	8	x	x	PROPN
ejpam-2055	450	9	∈	∈	PROPN
ejpam-2055	450	10	k0	k0	PROPN
ejpam-2055	450	11	}	}	PUNCT
ejpam-2055	450	12	.	.	PUNCT
ejpam-2055	451	1	then	then	ADV
ejpam-2055	451	2	v	v	NOUN
ejpam-2055	451	3	is	be	AUX
ejpam-2055	451	4	an	an	DET
ejpam-2055	451	5	open	open	ADJ
ejpam-2055	451	6	set	set	NOUN
ejpam-2055	451	7	containing	contain	VERB
ejpam-2055	451	8	y	y	PROPN
ejpam-2055	451	9	and	and	CCONJ
ejpam-2055	451	10	f	f	PROPN
ejpam-2055	451	11	(	(	PUNCT
ejpam-2055	451	12	k	k	X
ejpam-2055	451	13	)	)	PUNCT
ejpam-2055	451	14	⋂	⋂	PROPN
ejpam-2055	451	15	v	v	ADP
ejpam-2055	451	16	⊂	⊂	PROPN
ejpam-2055	451	17	[	[	PUNCT
ejpam-2055	451	18	⋃	⋃	PROPN
ejpam-2055	451	19	x∈ko	x∈ko	PROPN
ejpam-2055	451	20	f	f	X
ejpam-2055	451	21	(	(	PUNCT
ejpam-2055	451	22	δ−	δ−	PROPN
ejpam-2055	451	23	β	β	X
ejpam-2055	451	24	−	−	NOUN
ejpam-2055	451	25	cl(ux	cl(ux	NOUN
ejpam-2055	451	26	)	)	PUNCT
ejpam-2055	451	27	)	)	PUNCT
ejpam-2055	451	28	]	]	PUNCT
ejpam-2055	452	1	⋂	⋂	PROPN
ejpam-2055	452	2	v	v	ADP
ejpam-2055	452	3	⊂	⊂	PROPN
ejpam-2055	452	4	⋃	⋃	PROPN
ejpam-2055	452	5	x∈ko	x∈ko	PROPN
ejpam-2055	452	6	[	[	PUNCT
ejpam-2055	452	7	f	f	X
ejpam-2055	452	8	(	(	PUNCT
ejpam-2055	452	9	δ−	δ−	PROPN
ejpam-2055	452	10	β	β	X
ejpam-2055	452	11	−	−	NOUN
ejpam-2055	452	12	cl(ux	cl(ux	NOUN
ejpam-2055	452	13	)	)	PUNCT
ejpam-2055	452	14	)	)	PUNCT
ejpam-2055	453	1	⋂	⋂	PROPN
ejpam-2055	453	2	vx	vx	X
ejpam-2055	453	3	]	]	X
ejpam-2055	453	4	=	=	SYM
ejpam-2055	453	5	φ	φ	PROPN
ejpam-2055	453	6	.	.	PUNCT
ejpam-2055	454	1	therefore	therefore	ADV
ejpam-2055	454	2	,	,	PUNCT
ejpam-2055	454	3	we	we	PRON
ejpam-2055	454	4	have	have	VERB
ejpam-2055	454	5	y	y	PROPN
ejpam-2055	454	6	/∈	/∈	PUNCT
ejpam-2055	454	7	cl	cl	NOUN
ejpam-2055	454	8	(	(	PUNCT
ejpam-2055	454	9	f	f	PROPN
ejpam-2055	454	10	(	(	PUNCT
ejpam-2055	454	11	k	k	NOUN
ejpam-2055	454	12	)	)	PUNCT
ejpam-2055	454	13	)	)	PUNCT
ejpam-2055	454	14	and	and	CCONJ
ejpam-2055	454	15	hence	hence	ADV
ejpam-2055	454	16	f	f	PROPN
ejpam-2055	454	17	(	(	PUNCT
ejpam-2055	454	18	k	k	NOUN
ejpam-2055	454	19	)	)	PUNCT
ejpam-2055	454	20	is	be	AUX
ejpam-2055	454	21	closed	close	VERB
ejpam-2055	454	22	in	in	ADP
ejpam-2055	454	23	y.	y.	PROPN
ejpam-2055	454	24	theorem	theorem	VERB
ejpam-2055	454	25	17	17	NUM
ejpam-2055	454	26	.	.	PUNCT
ejpam-2055	455	1	let	let	VERB
ejpam-2055	455	2	x	x	PRON
ejpam-2055	455	3	be	be	AUX
ejpam-2055	455	4	a	a	DET
ejpam-2055	455	5	submaximal	submaximal	ADJ
ejpam-2055	455	6	extremally	extremally	ADV
ejpam-2055	455	7	disconnected	disconnected	ADJ
ejpam-2055	455	8	space	space	NOUN
ejpam-2055	455	9	.	.	PUNCT
ejpam-2055	456	1	if	if	SCONJ
ejpam-2055	456	2	a	a	DET
ejpam-2055	456	3	function	function	NOUN
ejpam-2055	456	4	f	f	NOUN
ejpam-2055	456	5	:	:	PUNCT
ejpam-2055	456	6	x	x	X
ejpam-2055	456	7	→	→	SYM
ejpam-2055	456	8	y	y	PROPN
ejpam-2055	456	9	has	have	VERB
ejpam-2055	456	10	a	a	DET
ejpam-2055	456	11	strongly	strongly	ADV
ejpam-2055	456	12	δ−	δ−	PROPN
ejpam-2055	456	13	β	β	X
ejpam-2055	456	14	-closed	-close	VERB
ejpam-2055	456	15	graph	graph	NOUN
ejpam-2055	456	16	,	,	PUNCT
ejpam-2055	456	17	then	then	ADV
ejpam-2055	456	18	f	f	PROPN
ejpam-2055	456	19	−1(k	−1(k	NOUN
ejpam-2055	456	20	)	)	PUNCT
ejpam-2055	456	21	is	be	AUX
ejpam-2055	456	22	θ	θ	PROPN
ejpam-2055	456	23	-closed	-close	VERB
ejpam-2055	456	24	in	in	ADP
ejpam-2055	456	25	x	x	PUNCT
ejpam-2055	456	26	for	for	SCONJ
ejpam-2055	456	27	each	each	DET
ejpam-2055	456	28	compact	compact	ADJ
ejpam-2055	456	29	set	set	VERB
ejpam-2055	456	30	k	k	PROPN
ejpam-2055	456	31	of	of	ADP
ejpam-2055	456	32	y.	y.	PROPN
ejpam-2055	456	33	proof	proof	PROPN
ejpam-2055	456	34	.	.	PUNCT
ejpam-2055	457	1	let	let	VERB
ejpam-2055	457	2	k	k	PRON
ejpam-2055	457	3	be	be	AUX
ejpam-2055	457	4	a	a	DET
ejpam-2055	457	5	compact	compact	ADJ
ejpam-2055	457	6	set	set	NOUN
ejpam-2055	457	7	of	of	ADP
ejpam-2055	457	8	y	y	PROPN
ejpam-2055	457	9	and	and	CCONJ
ejpam-2055	457	10	x	x	PROPN
ejpam-2055	457	11	/∈	/∈	PROPN
ejpam-2055	457	12	f	f	PROPN
ejpam-2055	457	13	−1(k	−1(k	NOUN
ejpam-2055	457	14	)	)	PUNCT
ejpam-2055	457	15	.	.	PUNCT
ejpam-2055	458	1	then	then	ADV
ejpam-2055	458	2	for	for	ADP
ejpam-2055	458	3	each	each	DET
ejpam-2055	458	4	y	y	PROPN
ejpam-2055	458	5	∈	∈	PROPN
ejpam-2055	459	1	k	k	NOUN
ejpam-2055	459	2	we	we	PRON
ejpam-2055	459	3	have	have	VERB
ejpam-2055	459	4	(	(	PUNCT
ejpam-2055	459	5	x	x	NOUN
ejpam-2055	459	6	,	,	PUNCT
ejpam-2055	459	7	y	y	PROPN
ejpam-2055	459	8	)	)	PUNCT
ejpam-2055	459	9	/∈	/∈	PUNCT
ejpam-2055	460	1	g	g	NOUN
ejpam-2055	460	2	(	(	PUNCT
ejpam-2055	460	3	f	f	PROPN
ejpam-2055	460	4	)	)	PUNCT
ejpam-2055	460	5	and	and	CCONJ
ejpam-2055	460	6	by	by	ADP
ejpam-2055	460	7	lemma	lemma	PROPN
ejpam-2055	460	8	4	4	NUM
ejpam-2055	460	9	there	there	ADV
ejpam-2055	460	10	exist	exist	VERB
ejpam-2055	460	11	uy	uy	PROPN
ejpam-2055	460	12	∈	∈	PROPN
ejpam-2055	460	13	δ−βς(x	δ−βς(x	NOUN
ejpam-2055	460	14	,	,	PUNCT
ejpam-2055	460	15	x	x	X
ejpam-2055	460	16	)	)	PUNCT
ejpam-2055	460	17	and	and	CCONJ
ejpam-2055	460	18	an	an	DET
ejpam-2055	460	19	open	open	ADJ
ejpam-2055	460	20	set	set	NOUN
ejpam-2055	460	21	vy	vy	NOUN
ejpam-2055	460	22	of	of	ADP
ejpam-2055	460	23	y	y	PROPN
ejpam-2055	460	24	containing	contain	VERB
ejpam-2055	460	25	y	y	PRON
ejpam-2055	460	26	such	such	ADJ
ejpam-2055	460	27	that	that	SCONJ
ejpam-2055	460	28	f	f	PROPN
ejpam-2055	460	29	(	(	PUNCT
ejpam-2055	460	30	δ	δ	PROPN
ejpam-2055	460	31	−	−	NOUN
ejpam-2055	460	32	β	β	X
ejpam-2055	460	33	−	−	PROPN
ejpam-2055	460	34	cl(uy	cl(uy	NOUN
ejpam-2055	460	35	)	)	PUNCT
ejpam-2055	460	36	)	)	PUNCT
ejpam-2055	461	1	⋂	⋂	PROPN
ejpam-2055	461	2	vy	vy	NOUN
ejpam-2055	461	3	=	=	PROPN
ejpam-2055	461	4	φ	φ	PROPN
ejpam-2055	461	5	.	.	PUNCT
ejpam-2055	462	1	the	the	DET
ejpam-2055	462	2	family	family	NOUN
ejpam-2055	462	3	{	{	PUNCT
ejpam-2055	462	4	vy	vy	X
ejpam-2055	462	5	:	:	PUNCT
ejpam-2055	462	6	y	y	PROPN
ejpam-2055	462	7	∈	∈	PROPN
ejpam-2055	462	8	k	k	AUX
ejpam-2055	462	9	}	}	PUNCT
ejpam-2055	462	10	is	be	AUX
ejpam-2055	462	11	an	an	DET
ejpam-2055	462	12	open	open	ADJ
ejpam-2055	462	13	cover	cover	NOUN
ejpam-2055	462	14	of	of	ADP
ejpam-2055	462	15	k	k	PROPN
ejpam-2055	462	16	and	and	CCONJ
ejpam-2055	462	17	there	there	PRON
ejpam-2055	462	18	exists	exist	VERB
ejpam-2055	462	19	a	a	DET
ejpam-2055	462	20	finite	finite	NOUN
ejpam-2055	462	21	subset	subset	VERB
ejpam-2055	462	22	k0	k0	PROPN
ejpam-2055	462	23	of	of	ADP
ejpam-2055	462	24	k	k	PROPN
ejpam-2055	462	25	such	such	ADJ
ejpam-2055	462	26	that	that	SCONJ
ejpam-2055	462	27	k	k	PROPN
ejpam-2055	462	28	⊂	⊂	X
ejpam-2055	462	29	⋃	⋃	PROPN
ejpam-2055	462	30	y∈ko	y∈ko	ADJ
ejpam-2055	462	31	vy	vy	NOUN
ejpam-2055	462	32	.	.	PUNCT
ejpam-2055	463	1	since	since	SCONJ
ejpam-2055	463	2	x	x	PRON
ejpam-2055	463	3	is	be	AUX
ejpam-2055	463	4	submaximal	submaximal	ADJ
ejpam-2055	463	5	extremally	extremally	ADV
ejpam-2055	463	6	disconnected	disconnect	VERB
ejpam-2055	463	7	,	,	PUNCT
ejpam-2055	463	8	therefor	therefor	ADP
ejpam-2055	463	9	each	each	DET
ejpam-2055	463	10	uy	uy	NOUN
ejpam-2055	463	11	is	be	AUX
ejpam-2055	463	12	open	open	ADJ
ejpam-2055	463	13	in	in	ADP
ejpam-2055	463	14	x	x	X
ejpam-2055	463	15	and	and	CCONJ
ejpam-2055	463	16	δ−β	δ−β	PROPN
ejpam-2055	463	17	−cl(uy	−cl(uy	NOUN
ejpam-2055	463	18	)	)	PUNCT
ejpam-2055	464	1	=	=	SYM
ejpam-2055	464	2	cl(uy	cl(uy	NOUN
ejpam-2055	464	3	)	)	PUNCT
ejpam-2055	464	4	.	.	PUNCT
ejpam-2055	465	1	set	set	VERB
ejpam-2055	465	2	u	u	NOUN
ejpam-2055	465	3	=	=	PUNCT
ejpam-2055	465	4	⋂	⋂	PROPN
ejpam-2055	465	5	y∈ko	y∈ko	ADJ
ejpam-2055	465	6	uy	uy	NOUN
ejpam-2055	465	7	,	,	PUNCT
ejpam-2055	465	8	then	then	ADV
ejpam-2055	465	9	u	u	NOUN
ejpam-2055	465	10	is	be	AUX
ejpam-2055	465	11	an	an	DET
ejpam-2055	465	12	open	open	ADJ
ejpam-2055	465	13	set	set	NOUN
ejpam-2055	465	14	containing	contain	VERB
ejpam-2055	465	15	x	x	PROPN
ejpam-2055	465	16	and	and	CCONJ
ejpam-2055	465	17	f	f	PROPN
ejpam-2055	465	18	(	(	PUNCT
ejpam-2055	465	19	cl(u	cl(u	PROPN
ejpam-2055	465	20	)	)	PUNCT
ejpam-2055	465	21	)	)	PUNCT
ejpam-2055	466	1	⋂	⋂	PROPN
ejpam-2055	466	2	k	k	PROPN
ejpam-2055	466	3	⊂	⊂	PROPN
ejpam-2055	466	4	⋃	⋃	PROPN
ejpam-2055	466	5	x∈ko	x∈ko	PROPN
ejpam-2055	466	6	[	[	PUNCT
ejpam-2055	466	7	f	f	X
ejpam-2055	466	8	(	(	PUNCT
ejpam-2055	466	9	cl(u	cl(u	PROPN
ejpam-2055	466	10	)	)	PUNCT
ejpam-2055	466	11	)	)	PUNCT
ejpam-2055	467	1	⋂	⋂	PROPN
ejpam-2055	467	2	vy	vy	X
ejpam-2055	467	3	]	]	X
ejpam-2055	467	4	⊂	⊂	PROPN
ejpam-2055	467	5	⋃	⋃	PROPN
ejpam-2055	467	6	x∈ko	x∈ko	PROPN
ejpam-2055	467	7	[	[	PUNCT
ejpam-2055	467	8	f	f	X
ejpam-2055	467	9	(	(	PUNCT
ejpam-2055	467	10	δ−	δ−	PROPN
ejpam-2055	467	11	β	β	X
ejpam-2055	467	12	−	−	PROPN
ejpam-2055	467	13	cl(uy	cl(uy	NOUN
ejpam-2055	467	14	)	)	PUNCT
ejpam-2055	467	15	)	)	PUNCT
ejpam-2055	468	1	⋂	⋂	PROPN
ejpam-2055	468	2	vy	vy	X
ejpam-2055	468	3	]	]	X
ejpam-2055	468	4	=	=	SYM
ejpam-2055	468	5	φ	φ	PROPN
ejpam-2055	468	6	.	.	PUNCT
ejpam-2055	469	1	so	so	ADV
ejpam-2055	469	2	,	,	PUNCT
ejpam-2055	469	3	we	we	PRON
ejpam-2055	469	4	have	have	VERB
ejpam-2055	469	5	cl(u	cl(u	NOUN
ejpam-2055	469	6	)	)	PUNCT
ejpam-2055	469	7	⋂	⋂	PROPN
ejpam-2055	469	8	f	f	PROPN
ejpam-2055	469	9	−1(k	−1(k	NOUN
ejpam-2055	469	10	)	)	PUNCT
ejpam-2055	469	11	=	=	SYM
ejpam-2055	469	12	φ	φ	PROPN
ejpam-2055	469	13	and	and	CCONJ
ejpam-2055	469	14	hence	hence	ADV
ejpam-2055	469	15	x	x	NOUN
ejpam-2055	469	16	/∈	/∈	PUNCT
ejpam-2055	469	17	clθ	clθ	NOUN
ejpam-2055	469	18	(	(	PUNCT
ejpam-2055	469	19	f	f	NOUN
ejpam-2055	469	20	−1(k	−1(k	NOUN
ejpam-2055	469	21	)	)	PUNCT
ejpam-2055	469	22	)	)	PUNCT
ejpam-2055	469	23	.	.	PUNCT
ejpam-2055	470	1	this	this	PRON
ejpam-2055	470	2	shows	show	VERB
ejpam-2055	470	3	that	that	SCONJ
ejpam-2055	470	4	f	f	PROPN
ejpam-2055	470	5	−1(k	−1(k	NOUN
ejpam-2055	470	6	)	)	PUNCT
ejpam-2055	470	7	is	be	AUX
ejpam-2055	470	8	θ	θ	PROPN
ejpam-2055	470	9	-closed	-close	VERB
ejpam-2055	470	10	in	in	ADP
ejpam-2055	470	11	x.	x.	NOUN
ejpam-2055	470	12	corollary	corollary	NOUN
ejpam-2055	471	1	3	3	X
ejpam-2055	471	2	.	.	PUNCT
ejpam-2055	472	1	let	let	VERB
ejpam-2055	472	2	x	x	PRON
ejpam-2055	472	3	be	be	AUX
ejpam-2055	472	4	a	a	DET
ejpam-2055	472	5	submaximal	submaximal	ADJ
ejpam-2055	472	6	extremally	extremally	ADV
ejpam-2055	472	7	disconnected	disconnected	ADJ
ejpam-2055	472	8	space	space	NOUN
ejpam-2055	472	9	and	and	CCONJ
ejpam-2055	472	10	y	y	PROPN
ejpam-2055	472	11	be	be	AUX
ejpam-2055	472	12	a	a	DET
ejpam-2055	472	13	compact	compact	ADJ
ejpam-2055	472	14	hausdorff	hausdorff	NOUN
ejpam-2055	472	15	space	space	NOUN
ejpam-2055	472	16	.	.	PUNCT
ejpam-2055	473	1	for	for	ADP
ejpam-2055	473	2	a	a	DET
ejpam-2055	473	3	function	function	NOUN
ejpam-2055	473	4	f	f	NOUN
ejpam-2055	473	5	:	:	PUNCT
ejpam-2055	473	6	x	x	X
ejpam-2055	473	7	→	→	SYM
ejpam-2055	473	8	y	y	PROPN
ejpam-2055	473	9	,	,	PUNCT
ejpam-2055	473	10	the	the	DET
ejpam-2055	473	11	following	follow	VERB
ejpam-2055	473	12	properties	property	NOUN
ejpam-2055	473	13	are	be	AUX
ejpam-2055	473	14	equivalent	equivalent	ADJ
ejpam-2055	473	15	:	:	PUNCT
ejpam-2055	473	16	a	a	X
ejpam-2055	473	17	)	)	PUNCT
ejpam-2055	473	18	f	f	NOUN
ejpam-2055	473	19	is	be	AUX
ejpam-2055	473	20	(	(	PUNCT
ejpam-2055	473	21	st	st	PROPN
ejpam-2055	473	22	.	.	PROPN
ejpam-2055	474	1	θ	θ	PROPN
ejpam-2055	474	2	−δ−	−δ−	VERB
ejpam-2055	474	3	β	β	X
ejpam-2055	474	4	.c	.c	PROPN
ejpam-2055	474	5	.	.	PUNCT
ejpam-2055	474	6	)	)	PUNCT
ejpam-2055	474	7	;	;	PUNCT
ejpam-2055	474	8	b	b	X
ejpam-2055	474	9	)	)	PUNCT
ejpam-2055	474	10	g	g	PROPN
ejpam-2055	474	11	(	(	PUNCT
ejpam-2055	474	12	f	f	PROPN
ejpam-2055	474	13	)	)	PUNCT
ejpam-2055	474	14	is	be	AUX
ejpam-2055	474	15	strongly	strongly	ADV
ejpam-2055	474	16	δ−	δ−	PROPN
ejpam-2055	474	17	β	β	SYM
ejpam-2055	474	18	-closed	-close	VERB
ejpam-2055	474	19	in	in	ADP
ejpam-2055	474	20	x	x	SYM
ejpam-2055	474	21	×	×	PROPN
ejpam-2055	474	22	y	y	PROPN
ejpam-2055	474	23	;	;	PUNCT
ejpam-2055	474	24	c	c	X
ejpam-2055	474	25	)	)	PUNCT
ejpam-2055	474	26	f	f	PROPN
ejpam-2055	474	27	is	be	AUX
ejpam-2055	474	28	strongly	strongly	ADV
ejpam-2055	474	29	θ	θ	NOUN
ejpam-2055	474	30	-continuous	-continuous	ADJ
ejpam-2055	474	31	;	;	PUNCT
ejpam-2055	474	32	d	d	X
ejpam-2055	474	33	)	)	PUNCT
ejpam-2055	474	34	f	f	PROPN
ejpam-2055	474	35	is	be	AUX
ejpam-2055	474	36	continuous	continuous	ADJ
ejpam-2055	474	37	;	;	PUNCT
ejpam-2055	474	38	references	reference	NOUN
ejpam-2055	474	39	197	197	NUM
ejpam-2055	474	40	e	e	NOUN
ejpam-2055	474	41	)	)	PUNCT
ejpam-2055	474	42	f	f	PROPN
ejpam-2055	474	43	is	be	AUX
ejpam-2055	474	44	δ−	δ−	PROPN
ejpam-2055	474	45	β	β	X
ejpam-2055	474	46	-continuous	-continuous	ADJ
ejpam-2055	474	47	.	.	PUNCT
ejpam-2055	475	1	proof	proof	NOUN
ejpam-2055	475	2	.	.	PUNCT
ejpam-2055	476	1	(	(	PUNCT
ejpam-2055	476	2	a)⇒	a)⇒	PROPN
ejpam-2055	476	3	(	(	PUNCT
ejpam-2055	476	4	b	b	NOUN
ejpam-2055	476	5	)	)	PUNCT
ejpam-2055	476	6	.	.	PUNCT
ejpam-2055	477	1	it	it	PRON
ejpam-2055	477	2	follows	follow	VERB
ejpam-2055	477	3	directly	directly	ADV
ejpam-2055	477	4	from	from	ADP
ejpam-2055	477	5	theorem	theorem	ADJ
ejpam-2055	477	6	14	14	NUM
ejpam-2055	477	7	.	.	PUNCT
ejpam-2055	478	1	(	(	PUNCT
ejpam-2055	478	2	b)⇒	b)⇒	NOUN
ejpam-2055	478	3	(	(	PUNCT
ejpam-2055	478	4	c	c	NOUN
ejpam-2055	478	5	)	)	PUNCT
ejpam-2055	478	6	.	.	PUNCT
ejpam-2055	479	1	it	it	PRON
ejpam-2055	479	2	follows	follow	VERB
ejpam-2055	479	3	directly	directly	ADV
ejpam-2055	479	4	from	from	ADP
ejpam-2055	479	5	theorem	theorem	ADJ
ejpam-2055	479	6	17	17	NUM
ejpam-2055	479	7	.	.	PUNCT
ejpam-2055	480	1	(	(	PUNCT
ejpam-2055	480	2	c)⇒	c)⇒	X
ejpam-2055	480	3	(	(	PUNCT
ejpam-2055	480	4	d)⇒	d)⇒	PROPN
ejpam-2055	480	5	(	(	PUNCT
ejpam-2055	480	6	e	e	NOUN
ejpam-2055	480	7	)	)	PUNCT
ejpam-2055	480	8	.	.	PUNCT
ejpam-2055	481	1	these	these	PRON
ejpam-2055	481	2	are	be	AUX
ejpam-2055	481	3	clear	clear	ADJ
ejpam-2055	481	4	.	.	PUNCT
ejpam-2055	482	1	(	(	PUNCT
ejpam-2055	482	2	e)⇒	e)⇒	NOUN
ejpam-2055	482	3	(	(	PUNCT
ejpam-2055	482	4	a	a	NOUN
ejpam-2055	482	5	)	)	PUNCT
ejpam-2055	482	6	.	.	PUNCT
ejpam-2055	483	1	since	since	SCONJ
ejpam-2055	483	2	y	y	PROPN
ejpam-2055	483	3	is	be	AUX
ejpam-2055	483	4	regular	regular	ADJ
ejpam-2055	483	5	,	,	PUNCT
ejpam-2055	483	6	it	it	PRON
ejpam-2055	483	7	follows	follow	VERB
ejpam-2055	483	8	from	from	ADP
ejpam-2055	483	9	theorem	theorem	ADJ
ejpam-2055	483	10	7	7	NUM
ejpam-2055	483	11	.	.	NOUN
ejpam-2055	483	12	8	8	NUM
ejpam-2055	483	13	.	.	PUNCT
ejpam-2055	483	14	conclusion	conclusion	NOUN
ejpam-2055	483	15	topology	topology	NOUN
ejpam-2055	483	16	as	as	SCONJ
ejpam-2055	483	17	a	a	DET
ejpam-2055	483	18	field	field	NOUN
ejpam-2055	483	19	of	of	ADP
ejpam-2055	483	20	mathematics	mathematic	NOUN
ejpam-2055	483	21	is	be	AUX
ejpam-2055	483	22	concerned	concern	VERB
ejpam-2055	483	23	with	with	ADP
ejpam-2055	483	24	all	all	DET
ejpam-2055	483	25	questions	question	NOUN
ejpam-2055	483	26	directly	directly	ADV
ejpam-2055	483	27	or	or	CCONJ
ejpam-2055	483	28	indirectly	indirectly	ADV
ejpam-2055	483	29	related	relate	VERB
ejpam-2055	483	30	to	to	ADP
ejpam-2055	483	31	continuity	continuity	NOUN
ejpam-2055	483	32	.	.	PUNCT
ejpam-2055	484	1	therefore	therefore	ADV
ejpam-2055	484	2	,	,	PUNCT
ejpam-2055	484	3	generalization	generalization	NOUN
ejpam-2055	484	4	of	of	ADP
ejpam-2055	484	5	continuity	continuity	NOUN
ejpam-2055	484	6	is	be	AUX
ejpam-2055	484	7	one	one	NUM
ejpam-2055	484	8	of	of	ADP
ejpam-2055	484	9	the	the	DET
ejpam-2055	484	10	most	most	ADV
ejpam-2055	484	11	important	important	ADJ
ejpam-2055	484	12	subjects	subject	NOUN
ejpam-2055	484	13	in	in	ADP
ejpam-2055	484	14	topology	topology	NOUN
ejpam-2055	484	15	.	.	PUNCT
ejpam-2055	485	1	one	one	NUM
ejpam-2055	485	2	of	of	ADP
ejpam-2055	485	3	the	the	DET
ejpam-2055	485	4	most	most	ADV
ejpam-2055	485	5	important	important	ADJ
ejpam-2055	485	6	subjects	subject	NOUN
ejpam-2055	485	7	in	in	ADP
ejpam-2055	485	8	studying	study	VERB
ejpam-2055	485	9	topology	topology	NOUN
ejpam-2055	485	10	and	and	CCONJ
ejpam-2055	485	11	physics	physics	NOUN
ejpam-2055	485	12	is	be	AUX
ejpam-2055	485	13	continuity	continuity	NOUN
ejpam-2055	485	14	,	,	PUNCT
ejpam-2055	485	15	has	have	AUX
ejpam-2055	485	16	been	be	AUX
ejpam-2055	485	17	researched	research	VERB
ejpam-2055	485	18	and	and	CCONJ
ejpam-2055	485	19	investigated	investigate	VERB
ejpam-2055	485	20	by	by	ADP
ejpam-2055	485	21	many	many	ADJ
ejpam-2055	485	22	mathematicians	mathematician	NOUN
ejpam-2055	485	23	and	and	CCONJ
ejpam-2055	485	24	quantum	quantum	NOUN
ejpam-2055	485	25	physicists	physicist	NOUN
ejpam-2055	485	26	.	.	PUNCT
ejpam-2055	486	1	[	[	X
ejpam-2055	486	2	4–6	4–6	X
ejpam-2055	486	3	,	,	PUNCT
ejpam-2055	486	4	17	17	NUM
ejpam-2055	486	5	,	,	PUNCT
ejpam-2055	486	6	22	22	NUM
ejpam-2055	486	7	,	,	PUNCT
ejpam-2055	486	8	40	40	NUM
ejpam-2055	486	9	,	,	PUNCT
ejpam-2055	486	10	43	43	NUM
ejpam-2055	486	11	,	,	PUNCT
ejpam-2055	486	12	44	44	NUM
ejpam-2055	486	13	]	]	PUNCT
ejpam-2055	486	14	from	from	ADP
ejpam-2055	486	15	the	the	DET
ejpam-2055	486	16	different	different	ADJ
ejpam-2055	486	17	points	point	NOUN
ejpam-2055	486	18	of	of	ADP
ejpam-2055	486	19	views	view	NOUN
ejpam-2055	486	20	.	.	PUNCT
ejpam-2055	487	1	relation	relation	NOUN
ejpam-2055	487	2	of	of	ADP
ejpam-2055	487	3	topology	topology	NOUN
ejpam-2055	487	4	and	and	CCONJ
ejpam-2055	487	5	physics	physics	NOUN
ejpam-2055	487	6	have	have	AUX
ejpam-2055	487	7	been	be	AUX
ejpam-2055	487	8	appeared	appear	VERB
ejpam-2055	487	9	in	in	ADP
ejpam-2055	487	10	[	[	X
ejpam-2055	487	11	17	17	NUM
ejpam-2055	487	12	,	,	PUNCT
ejpam-2055	487	13	18	18	NUM
ejpam-2055	487	14	,	,	PUNCT
ejpam-2055	487	15	26	26	NUM
ejpam-2055	487	16	,	,	PUNCT
ejpam-2055	487	17	47	47	NUM
ejpam-2055	487	18	]	]	PUNCT
ejpam-2055	487	19	,	,	PUNCT
ejpam-2055	487	20	el	el	PROPN
ejpam-2055	487	21	-	-	NOUN
ejpam-2055	487	22	naschie	naschie	NOUN
ejpam-2055	487	23	in	in	ADP
ejpam-2055	487	24	[	[	X
ejpam-2055	487	25	13	13	NUM
ejpam-2055	487	26	,	,	PUNCT
ejpam-2055	487	27	17	17	NUM
ejpam-2055	487	28	,	,	PUNCT
ejpam-2055	487	29	26	26	NUM
ejpam-2055	487	30	]	]	PUNCT
ejpam-2055	487	31	have	have	AUX
ejpam-2055	487	32	indicate	indicate	VERB
ejpam-2055	487	33	that	that	SCONJ
ejpam-2055	487	34	topology	topology	NOUN
ejpam-2055	487	35	plays	play	VERB
ejpam-2055	487	36	a	a	DET
ejpam-2055	487	37	significant	significant	ADJ
ejpam-2055	487	38	role	role	NOUN
ejpam-2055	487	39	in	in	ADP
ejpam-2055	487	40	quantum	quantum	ADJ
ejpam-2055	487	41	physics	physics	NOUN
ejpam-2055	487	42	,	,	PUNCT
ejpam-2055	487	43	high	high	ADJ
ejpam-2055	487	44	energy	energy	NOUN
ejpam-2055	487	45	physics	physics	NOUN
ejpam-2055	487	46	and	and	CCONJ
ejpam-2055	487	47	superstring	superstring	NOUN
ejpam-2055	487	48	theory	theory	NOUN
ejpam-2055	487	49	.	.	PUNCT
ejpam-2055	488	1	one	one	PRON
ejpam-2055	488	2	can	can	AUX
ejpam-2055	488	3	observe	observe	VERB
ejpam-2055	488	4	the	the	DET
ejpam-2055	488	5	influence	influence	NOUN
ejpam-2055	488	6	made	make	VERB
ejpam-2055	488	7	in	in	ADP
ejpam-2055	488	8	the	the	DET
ejpam-2055	488	9	realms	realm	NOUN
ejpam-2055	488	10	of	of	ADP
ejpam-2055	488	11	applied	apply	VERB
ejpam-2055	488	12	research	research	NOUN
ejpam-2055	488	13	by	by	ADP
ejpam-2055	488	14	general	general	ADJ
ejpam-2055	488	15	topological	topological	ADJ
ejpam-2055	488	16	spaces	space	NOUN
ejpam-2055	488	17	,	,	PUNCT
ejpam-2055	488	18	properties	property	NOUN
ejpam-2055	488	19	and	and	CCONJ
ejpam-2055	488	20	structures	structure	NOUN
ejpam-2055	488	21	.	.	PUNCT
ejpam-2055	489	1	in	in	ADP
ejpam-2055	489	2	digital	digital	ADJ
ejpam-2055	489	3	topology	topology	NOUN
ejpam-2055	489	4	,	,	PUNCT
ejpam-2055	489	5	information	information	NOUN
ejpam-2055	489	6	systems	system	NOUN
ejpam-2055	489	7	,	,	PUNCT
ejpam-2055	489	8	particle	particle	NOUN
ejpam-2055	489	9	physic	physic	NOUN
ejpam-2055	489	10	[	[	X
ejpam-2055	489	11	30	30	NUM
ejpam-2055	489	12	]	]	PUNCT
ejpam-2055	489	13	,	,	PUNCT
ejpam-2055	489	14	computational	computational	ADJ
ejpam-2055	489	15	topology	topology	NOUN
ejpam-2055	489	16	for	for	ADP
ejpam-2055	489	17	geometric	geometric	ADJ
ejpam-2055	489	18	design	design	NOUN
ejpam-2055	489	19	and	and	CCONJ
ejpam-2055	489	20	molecular	molecular	ADJ
ejpam-2055	489	21	design	design	NOUN
ejpam-2055	489	22	[	[	X
ejpam-2055	489	23	35	35	NUM
ejpam-2055	489	24	]	]	PUNCT
ejpam-2055	489	25	,	,	PUNCT
ejpam-2055	489	26	furthermore	furthermore	ADV
ejpam-2055	489	27	,	,	PUNCT
ejpam-2055	489	28	rosen	rosen	PROPN
ejpam-2055	489	29	and	and	CCONJ
ejpam-2055	489	30	peters	peters	PROPN
ejpam-2055	489	31	[	[	X
ejpam-2055	489	32	46	46	NUM
ejpam-2055	489	33	]	]	PUNCT
ejpam-2055	489	34	have	have	AUX
ejpam-2055	489	35	used	use	VERB
ejpam-2055	489	36	topology	topology	NOUN
ejpam-2055	489	37	in	in	ADP
ejpam-2055	489	38	computer	computer	NOUN
ejpam-2055	489	39	-	-	PUNCT
ejpam-2055	489	40	aided	aid	VERB
ejpam-2055	489	41	geometric	geometric	ADJ
ejpam-2055	489	42	design	design	NOUN
ejpam-2055	489	43	and	and	CCONJ
ejpam-2055	489	44	engineering	engineering	NOUN
ejpam-2055	489	45	design	design	NOUN
ejpam-2055	489	46	.	.	PUNCT
ejpam-2055	490	1	also	also	ADV
ejpam-2055	490	2	since	since	SCONJ
ejpam-2055	490	3	el	el	PROPN
ejpam-2055	490	4	-	-	PUNCT
ejpam-2055	490	5	naschie	naschie	PROPN
ejpam-2055	490	6	has	have	AUX
ejpam-2055	490	7	shown	show	VERB
ejpam-2055	490	8	that	that	SCONJ
ejpam-2055	490	9	the	the	DET
ejpam-2055	490	10	notion	notion	NOUN
ejpam-2055	490	11	of	of	ADP
ejpam-2055	490	12	fuzzy	fuzzy	ADJ
ejpam-2055	490	13	topology	topology	NOUN
ejpam-2055	490	14	have	have	VERB
ejpam-2055	490	15	very	very	ADV
ejpam-2055	490	16	important	important	ADJ
ejpam-2055	490	17	applications	application	NOUN
ejpam-2055	490	18	in	in	ADP
ejpam-2055	490	19	quantum	quantum	ADJ
ejpam-2055	490	20	particle	particle	NOUN
ejpam-2055	490	21	physics	physics	NOUN
ejpam-2055	490	22	especially	especially	ADV
ejpam-2055	490	23	in	in	ADP
ejpam-2055	490	24	related	relate	VERB
ejpam-2055	490	25	to	to	ADP
ejpam-2055	490	26	both	both	DET
ejpam-2055	490	27	string	string	NOUN
ejpam-2055	490	28	theory	theory	NOUN
ejpam-2055	490	29	and	and	CCONJ
ejpam-2055	490	30	ǫ∞	ǫ∞	NOUN
ejpam-2055	490	31	theory	theory	NOUN
ejpam-2055	490	32	.	.	PUNCT
ejpam-2055	491	1	thus	thus	ADV
ejpam-2055	491	2	we	we	PRON
ejpam-2055	491	3	study	study	VERB
ejpam-2055	491	4	a	a	DET
ejpam-2055	491	5	new	new	ADJ
ejpam-2055	491	6	class	class	NOUN
ejpam-2055	491	7	of	of	ADP
ejpam-2055	491	8	strong	strong	ADJ
ejpam-2055	491	9	continuity	continuity	NOUN
ejpam-2055	491	10	which	which	PRON
ejpam-2055	491	11	may	may	AUX
ejpam-2055	491	12	have	have	VERB
ejpam-2055	491	13	very	very	ADV
ejpam-2055	491	14	important	important	ADJ
ejpam-2055	491	15	applications	application	NOUN
ejpam-2055	491	16	in	in	ADP
ejpam-2055	491	17	quantum	quantum	ADJ
ejpam-2055	491	18	particle	particle	NOUN
ejpam-2055	491	19	physics	physics	NOUN
ejpam-2055	491	20	,	,	PUNCT
ejpam-2055	491	21	theoretical	theoretical	ADJ
ejpam-2055	491	22	physics	physics	NOUN
ejpam-2055	491	23	,	,	PUNCT
ejpam-2055	491	24	particularly	particularly	ADV
ejpam-2055	491	25	in	in	ADP
ejpam-2055	491	26	connections	connection	NOUN
ejpam-2055	491	27	with	with	ADP
ejpam-2055	491	28	string	string	NOUN
ejpam-2055	491	29	theory	theory	NOUN
ejpam-2055	491	30	and	and	CCONJ
ejpam-2055	491	31	ǫ∞	ǫ∞	DET
ejpam-2055	491	32	theory	theory	NOUN
ejpam-2055	491	33	[	[	X
ejpam-2055	491	34	12	12	NUM
ejpam-2055	491	35	,	,	PUNCT
ejpam-2055	491	36	14–16	14–16	NUM
ejpam-2055	491	37	,	,	PUNCT
ejpam-2055	491	38	19–21	19–21	NUM
ejpam-2055	491	39	,	,	PUNCT
ejpam-2055	491	40	23–25	23–25	NUM
ejpam-2055	491	41	,	,	PUNCT
ejpam-2055	491	42	34	34	NUM
ejpam-2055	491	43	,	,	PUNCT
ejpam-2055	491	44	47	47	NUM
ejpam-2055	491	45	]	]	PUNCT
ejpam-2055	491	46	.	.	PUNCT
ejpam-2055	492	1	also	also	ADV
ejpam-2055	492	2	the	the	DET
ejpam-2055	492	3	fuzzy	fuzzy	ADJ
ejpam-2055	492	4	topological	topological	ADJ
ejpam-2055	492	5	version	version	NOUN
ejpam-2055	492	6	of	of	ADP
ejpam-2055	492	7	the	the	DET
ejpam-2055	492	8	concepts	concept	NOUN
ejpam-2055	492	9	and	and	CCONJ
ejpam-2055	492	10	results	result	NOUN
ejpam-2055	492	11	introduced	introduce	VERB
ejpam-2055	492	12	in	in	ADP
ejpam-2055	492	13	this	this	DET
ejpam-2055	492	14	paper	paper	NOUN
ejpam-2055	492	15	are	be	AUX
ejpam-2055	492	16	very	very	ADV
ejpam-2055	492	17	important	important	ADJ
ejpam-2055	492	18	.	.	PUNCT
ejpam-2055	493	1	acknowledgements	acknowledgement	NOUN
ejpam-2055	493	2	i	i	PRON
ejpam-2055	493	3	would	would	AUX
ejpam-2055	493	4	like	like	VERB
ejpam-2055	493	5	to	to	PART
ejpam-2055	493	6	express	express	VERB
ejpam-2055	493	7	my	my	PRON
ejpam-2055	493	8	sincere	sincere	ADJ
ejpam-2055	493	9	gratitude	gratitude	NOUN
ejpam-2055	493	10	to	to	ADP
ejpam-2055	493	11	the	the	DET
ejpam-2055	493	12	referees	referee	NOUN
ejpam-2055	493	13	for	for	ADP
ejpam-2055	493	14	their	their	PRON
ejpam-2055	493	15	valuable	valuable	ADJ
ejpam-2055	493	16	suggestions	suggestion	NOUN
ejpam-2055	493	17	and	and	CCONJ
ejpam-2055	493	18	comments	comment	NOUN
ejpam-2055	493	19	which	which	PRON
ejpam-2055	493	20	improved	improve	VERB
ejpam-2055	493	21	the	the	DET
ejpam-2055	493	22	paper	paper	NOUN
ejpam-2055	494	1	and	and	CCONJ
ejpam-2055	494	2	i	i	PRON
ejpam-2055	494	3	am	be	AUX
ejpam-2055	494	4	thankful	thankful	ADJ
ejpam-2055	494	5	to	to	ADP
ejpam-2055	494	6	professor	professor	NOUN
ejpam-2055	494	7	.	.	PUNCT
ejpam-2055	495	1	dr	dr	PROPN
ejpam-2055	495	2	.	.	PROPN
ejpam-2055	495	3	e.	e.	PROPN
ejpam-2055	495	4	ekici	ekici	PROPN
ejpam-2055	495	5	(	(	PUNCT
ejpam-2055	495	6	turkey	turkey	PROPN
ejpam-2055	495	7	)	)	PUNCT
ejpam-2055	495	8	for	for	ADP
ejpam-2055	495	9	sending	send	VERB
ejpam-2055	495	10	many	many	ADJ
ejpam-2055	495	11	of	of	ADP
ejpam-2055	495	12	his	his	PRON
ejpam-2055	495	13	papers	paper	NOUN
ejpam-2055	495	14	as	as	ADV
ejpam-2055	495	15	soon	soon	ADV
ejpam-2055	495	16	as	as	SCONJ
ejpam-2055	495	17	i	i	PRON
ejpam-2055	495	18	had	have	AUX
ejpam-2055	495	19	requested	request	VERB
ejpam-2055	495	20	and	and	CCONJ
ejpam-2055	495	21	dr	dr	PROPN
ejpam-2055	495	22	.	.	PROPN
ejpam-2055	495	23	mohammed	mohammed	PROPN
ejpam-2055	495	24	lutf	lutf	PROPN
ejpam-2055	495	25	(	(	PUNCT
ejpam-2055	495	26	yemen	yemen	PROPN
ejpam-2055	495	27	)	)	PUNCT
ejpam-2055	495	28	for	for	ADP
ejpam-2055	495	29	help	help	NOUN
ejpam-2055	495	30	.	.	PUNCT
ejpam-2055	496	1	references	reference	NOUN
ejpam-2055	496	2	[	[	X
ejpam-2055	496	3	1	1	X
ejpam-2055	496	4	]	]	PUNCT
ejpam-2055	496	5	d.	d.	PROPN
ejpam-2055	496	6	andrijevic	andrijevic	PROPN
ejpam-2055	496	7	.	.	PUNCT
ejpam-2055	497	1	semipreopen	semipreopen	ADJ
ejpam-2055	497	2	sets	set	NOUN
ejpam-2055	497	3	.	.	PUNCT
ejpam-2055	498	1	matematicki	matematicki	NOUN
ejpam-2055	498	2	vesnik	vesnik	NOUN
ejpam-2055	498	3	,	,	PUNCT
ejpam-2055	498	4	38(1):24–32	38(1):24–32	NUM
ejpam-2055	498	5	,	,	PUNCT
ejpam-2055	498	6	1986	1986	NUM
ejpam-2055	498	7	.	.	PUNCT
ejpam-2055	499	1	[	[	X
ejpam-2055	499	2	2	2	X
ejpam-2055	499	3	]	]	PUNCT
ejpam-2055	499	4	d.	d.	PROPN
ejpam-2055	499	5	andrijevic	andrijevic	VERB
ejpam-2055	499	6	.	.	PUNCT
ejpam-2055	500	1	on	on	ADP
ejpam-2055	500	2	b	b	X
ejpam-2055	500	3	-	-	PUNCT
ejpam-2055	500	4	open	open	ADJ
ejpam-2055	500	5	sets	set	NOUN
ejpam-2055	500	6	.	.	PUNCT
ejpam-2055	501	1	matematicki	matematicki	NOUN
ejpam-2055	501	2	vesnik	vesnik	PROPN
ejpam-2055	501	3	,	,	PUNCT
ejpam-2055	501	4	48:59–64	48:59–64	PROPN
ejpam-2055	501	5	,	,	PUNCT
ejpam-2055	501	6	1996	1996	NUM
ejpam-2055	501	7	.	.	PUNCT
ejpam-2055	502	1	[	[	X
ejpam-2055	502	2	3	3	X
ejpam-2055	502	3	]	]	X
ejpam-2055	502	4	n.	n.	NOUN
ejpam-2055	502	5	bourbaki	bourbaki	PROPN
ejpam-2055	502	6	.	.	PUNCT
ejpam-2055	503	1	elements	element	NOUN
ejpam-2055	503	2	of	of	ADP
ejpam-2055	503	3	mathematics	mathematic	NOUN
ejpam-2055	503	4	:	:	PUNCT
ejpam-2055	503	5	general	general	ADJ
ejpam-2055	503	6	topology	topology	NOUN
ejpam-2055	503	7	.	.	PUNCT
ejpam-2055	504	1	hermann	hermann	PROPN
ejpam-2055	504	2	,	,	PUNCT
ejpam-2055	504	3	1966	1966	NUM
ejpam-2055	504	4	.	.	PUNCT
ejpam-2055	505	1	[	[	X
ejpam-2055	505	2	4	4	NUM
ejpam-2055	505	3	]	]	PUNCT
ejpam-2055	505	4	m.	m.	NOUN
ejpam-2055	505	5	caldas	caldas	PROPN
ejpam-2055	505	6	,	,	PUNCT
ejpam-2055	505	7	s.	s.	PROPN
ejpam-2055	505	8	jafari	jafari	PROPN
ejpam-2055	505	9	,	,	PUNCT
ejpam-2055	505	10	t.	t.	PROPN
ejpam-2055	505	11	noiri	noiri	PROPN
ejpam-2055	505	12	,	,	PUNCT
ejpam-2055	505	13	and	and	CCONJ
ejpam-2055	505	14	r.	r.	PROPN
ejpam-2055	505	15	k.	k.	PROPN
ejpam-2055	505	16	saraf	saraf	PROPN
ejpam-2055	505	17	.	.	PUNCT
ejpam-2055	506	1	weak	weak	ADJ
ejpam-2055	506	2	and	and	CCONJ
ejpam-2055	506	3	strong	strong	ADJ
ejpam-2055	506	4	forms	form	NOUN
ejpam-2055	506	5	of	of	ADP
ejpam-2055	506	6	α	α	NOUN
ejpam-2055	506	7	-	-	PUNCT
ejpam-2055	506	8	irresolute	irresolute	ADJ
ejpam-2055	506	9	maps	map	NOUN
ejpam-2055	506	10	.	.	PUNCT
ejpam-2055	507	1	chaos	chaos	NOUN
ejpam-2055	507	2	,	,	PUNCT
ejpam-2055	507	3	solitons	soliton	NOUN
ejpam-2055	507	4	and	and	CCONJ
ejpam-2055	507	5	fractals	fractal	NOUN
ejpam-2055	507	6	,	,	PUNCT
ejpam-2055	507	7	24(1):223–228	24(1):223–228	PROPN
ejpam-2055	507	8	,	,	PUNCT
ejpam-2055	507	9	2005	2005	NUM
ejpam-2055	507	10	.	.	PUNCT
ejpam-2055	508	1	[	[	X
ejpam-2055	508	2	5	5	NUM
ejpam-2055	508	3	]	]	PUNCT
ejpam-2055	508	4	m.	m.	NOUN
ejpam-2055	508	5	caldas	caldas	PROPN
ejpam-2055	508	6	,	,	PUNCT
ejpam-2055	508	7	s.	s.	PROPN
ejpam-2055	508	8	jafari	jafari	PROPN
ejpam-2055	508	9	,	,	PUNCT
ejpam-2055	508	10	t.	t.	PROPN
ejpam-2055	508	11	noiri	noiri	PROPN
ejpam-2055	508	12	,	,	PUNCT
ejpam-2055	508	13	and	and	CCONJ
ejpam-2055	508	14	m.	m.	NOUN
ejpam-2055	508	15	simões	simões	PROPN
ejpam-2055	508	16	.	.	PUNCT
ejpam-2055	509	1	a	a	DET
ejpam-2055	509	2	new	new	ADJ
ejpam-2055	509	3	generalization	generalization	NOUN
ejpam-2055	509	4	of	of	ADP
ejpam-2055	509	5	contra	contra	PROPN
ejpam-2055	509	6	-	-	NOUN
ejpam-2055	509	7	continuity	continuity	NOUN
ejpam-2055	509	8	via	via	ADP
ejpam-2055	509	9	levine	levine	PROPN
ejpam-2055	509	10	’s	’s	PART
ejpam-2055	509	11	g	g	NOUN
ejpam-2055	509	12	-	-	PUNCT
ejpam-2055	509	13	closed	close	VERB
ejpam-2055	509	14	sets	set	NOUN
ejpam-2055	509	15	.	.	PUNCT
ejpam-2055	510	1	chaos	chaos	NOUN
ejpam-2055	510	2	,	,	PUNCT
ejpam-2055	510	3	solitons	soliton	NOUN
ejpam-2055	510	4	and	and	CCONJ
ejpam-2055	510	5	fractals	fractal	NOUN
ejpam-2055	510	6	,	,	PUNCT
ejpam-2055	510	7	32(4):1597–1603	32(4):1597–1603	NUM
ejpam-2055	510	8	,	,	PUNCT
ejpam-2055	510	9	2007	2007	NUM
ejpam-2055	510	10	.	.	PUNCT
ejpam-2055	511	1	references	reference	NOUN
ejpam-2055	511	2	198	198	NUM
ejpam-2055	511	3	[	[	X
ejpam-2055	511	4	6	6	NUM
ejpam-2055	511	5	]	]	PUNCT
ejpam-2055	511	6	e.	e.	PROPN
ejpam-2055	511	7	ekici	ekici	PROPN
ejpam-2055	511	8	.	.	PUNCT
ejpam-2055	512	1	on	on	ADP
ejpam-2055	512	2	almost	almost	ADV
ejpam-2055	512	3	πgp	πgp	VERB
ejpam-2055	512	4	-	-	PUNCT
ejpam-2055	512	5	continuous	continuous	ADJ
ejpam-2055	512	6	functions	function	NOUN
ejpam-2055	512	7	.	.	PUNCT
ejpam-2055	513	1	chaos	chaos	NOUN
ejpam-2055	513	2	,	,	PUNCT
ejpam-2055	513	3	solitons	soliton	NOUN
ejpam-2055	513	4	and	and	CCONJ
ejpam-2055	513	5	fractals	fractal	NOUN
ejpam-2055	513	6	,	,	PUNCT
ejpam-2055	513	7	32(5):1935	32(5):1935	NUM
ejpam-2055	513	8	–	–	PUNCT
ejpam-2055	513	9	1944	1944	NUM
ejpam-2055	513	10	,	,	PUNCT
ejpam-2055	513	11	2007	2007	NUM
ejpam-2055	513	12	.	.	PUNCT
ejpam-2055	514	1	[	[	X
ejpam-2055	514	2	7	7	X
ejpam-2055	514	3	]	]	X
ejpam-2055	514	4	e.	e.	PROPN
ejpam-2055	514	5	ekici	ekici	PROPN
ejpam-2055	514	6	.	.	PUNCT
ejpam-2055	515	1	new	new	ADJ
ejpam-2055	515	2	forms	form	NOUN
ejpam-2055	515	3	of	of	ADP
ejpam-2055	515	4	contra	contra	NOUN
ejpam-2055	515	5	-	-	NOUN
ejpam-2055	515	6	continuity	continuity	NOUN
ejpam-2055	515	7	.	.	PUNCT
ejpam-2055	516	1	carpathian	carpathian	ADJ
ejpam-2055	516	2	journal	journal	PROPN
ejpam-2055	516	3	of	of	ADP
ejpam-2055	516	4	mathematics	mathematic	NOUN
ejpam-2055	516	5	,	,	PUNCT
ejpam-2055	516	6	24(1):37	24(1):37	NUM
ejpam-2055	516	7	–	–	PUNCT
ejpam-2055	516	8	45	45	NUM
ejpam-2055	516	9	,	,	PUNCT
ejpam-2055	516	10	2008	2008	NUM
ejpam-2055	516	11	.	.	PUNCT
ejpam-2055	517	1	[	[	X
ejpam-2055	517	2	8	8	NUM
ejpam-2055	517	3	]	]	X
ejpam-2055	517	4	e.	e.	PROPN
ejpam-2055	517	5	ekici	ekici	PROPN
ejpam-2055	517	6	.	.	PUNCT
ejpam-2055	518	1	on	on	ADP
ejpam-2055	518	2	e	e	VERB
ejpam-2055	518	3	-	-	ADJ
ejpam-2055	518	4	open	open	ADJ
ejpam-2055	518	5	sets	set	NOUN
ejpam-2055	518	6	,	,	PUNCT
ejpam-2055	518	7	dp*-sets	dp*-set	NOUN
ejpam-2055	518	8	and	and	CCONJ
ejpam-2055	518	9	dpe*-sets	dpe*-set	NOUN
ejpam-2055	518	10	and	and	CCONJ
ejpam-2055	518	11	decompositions	decomposition	NOUN
ejpam-2055	518	12	of	of	ADP
ejpam-2055	518	13	continuity	continuity	NOUN
ejpam-2055	518	14	.	.	PUNCT
ejpam-2055	519	1	arabian	arabian	ADJ
ejpam-2055	519	2	journal	journal	PROPN
ejpam-2055	519	3	for	for	ADP
ejpam-2055	519	4	science	science	NOUN
ejpam-2055	519	5	and	and	CCONJ
ejpam-2055	519	6	engineering	engineering	NOUN
ejpam-2055	519	7	,	,	PUNCT
ejpam-2055	519	8	33(24):269–282	33(24):269–282	PROPN
ejpam-2055	519	9	,	,	PUNCT
ejpam-2055	519	10	2008	2008	NUM
ejpam-2055	519	11	.	.	PUNCT
ejpam-2055	520	1	[	[	X
ejpam-2055	520	2	9	9	X
ejpam-2055	520	3	]	]	PUNCT
ejpam-2055	520	4	e.	e.	PROPN
ejpam-2055	520	5	ekici	ekici	PROPN
ejpam-2055	520	6	.	.	PUNCT
ejpam-2055	521	1	on	on	ADP
ejpam-2055	521	2	e*-open	e*-open	PROPN
ejpam-2055	521	3	sets	set	NOUN
ejpam-2055	521	4	and	and	CCONJ
ejpam-2055	521	5	(	(	PUNCT
ejpam-2055	521	6	d	d	NOUN
ejpam-2055	521	7	,	,	PUNCT
ejpam-2055	521	8	s)*-sets	s)*-sets	PROPN
ejpam-2055	521	9	.	.	PUNCT
ejpam-2055	522	1	mathematica	mathematica	PROPN
ejpam-2055	522	2	moravica	moravica	PROPN
ejpam-2055	522	3	,	,	PUNCT
ejpam-2055	522	4	13(1):29–36	13(1):29–36	NUM
ejpam-2055	522	5	,	,	PUNCT
ejpam-2055	522	6	2009	2009	NUM
ejpam-2055	522	7	.	.	PUNCT
ejpam-2055	523	1	[	[	X
ejpam-2055	523	2	10	10	NUM
ejpam-2055	523	3	]	]	PUNCT
ejpam-2055	523	4	a.	a.	NOUN
ejpam-2055	523	5	a.	a.	PROPN
ejpam-2055	523	6	el	el	PROPN
ejpam-2055	523	7	-	-	PUNCT
ejpam-2055	523	8	atik	atik	PROPN
ejpam-2055	523	9	.	.	PUNCT
ejpam-2055	524	1	a	a	DET
ejpam-2055	524	2	study	study	NOUN
ejpam-2055	524	3	of	of	ADP
ejpam-2055	524	4	some	some	DET
ejpam-2055	524	5	types	type	NOUN
ejpam-2055	524	6	of	of	ADP
ejpam-2055	524	7	mappings	mapping	NOUN
ejpam-2055	524	8	on	on	ADP
ejpam-2055	524	9	topological	topological	ADJ
ejpam-2055	524	10	spaces	space	NOUN
ejpam-2055	524	11	.	.	PUNCT
ejpam-2055	525	1	phd	phd	NOUN
ejpam-2055	525	2	thesis	thesis	NOUN
ejpam-2055	525	3	,	,	PUNCT
ejpam-2055	525	4	masters	master	NOUN
ejpam-2055	525	5	thesis	thesis	NOUN
ejpam-2055	525	6	,	,	PUNCT
ejpam-2055	525	7	faculty	faculty	NOUN
ejpam-2055	525	8	of	of	ADP
ejpam-2055	525	9	science	science	PROPN
ejpam-2055	525	10	,	,	PUNCT
ejpam-2055	525	11	tanta	tanta	PROPN
ejpam-2055	525	12	university	university	PROPN
ejpam-2055	525	13	,	,	PUNCT
ejpam-2055	525	14	tanta	tanta	PROPN
ejpam-2055	525	15	,	,	PUNCT
ejpam-2055	525	16	egypt	egypt	PROPN
ejpam-2055	525	17	,	,	PUNCT
ejpam-2055	525	18	1997	1997	NUM
ejpam-2055	525	19	.	.	PUNCT
ejpam-2055	526	1	[	[	X
ejpam-2055	526	2	11	11	NUM
ejpam-2055	526	3	]	]	PUNCT
ejpam-2055	526	4	m.	m.	PROPN
ejpam-2055	526	5	e.	e.	PROPN
ejpam-2055	526	6	a.	a.	PROPN
ejpam-2055	526	7	el	el	PROPN
ejpam-2055	526	8	-	-	PROPN
ejpam-2055	526	9	monsef	monsef	ADJ
ejpam-2055	526	10	,	,	PUNCT
ejpam-2055	526	11	s.	s.	PROPN
ejpam-2055	526	12	n.	n.	PROPN
ejpam-2055	526	13	el	el	PROPN
ejpam-2055	526	14	-	-	PROPN
ejpam-2055	526	15	deeb	deeb	PROPN
ejpam-2055	526	16	,	,	PUNCT
ejpam-2055	526	17	and	and	CCONJ
ejpam-2055	526	18	r.	r.	PROPN
ejpam-2055	526	19	a.	a.	PROPN
ejpam-2055	526	20	mahmoud	mahmoud	PROPN
ejpam-2055	526	21	.	.	PUNCT
ejpam-2055	527	1	β	β	PROPN
ejpam-2055	527	2	-open	-open	PROPN
ejpam-2055	527	3	sets	set	NOUN
ejpam-2055	527	4	and	and	CCONJ
ejpam-2055	527	5	β	β	X
ejpam-2055	527	6	-continuous	-continuous	ADJ
ejpam-2055	527	7	mapping	mapping	NOUN
ejpam-2055	527	8	.	.	PUNCT
ejpam-2055	528	1	bulletin	bulletin	NOUN
ejpam-2055	528	2	of	of	ADP
ejpam-2055	528	3	the	the	DET
ejpam-2055	528	4	faculty	faculty	NOUN
ejpam-2055	528	5	of	of	ADP
ejpam-2055	528	6	science	science	PROPN
ejpam-2055	528	7	assiut	assiut	PROPN
ejpam-2055	528	8	university	university	PROPN
ejpam-2055	528	9	,	,	PUNCT
ejpam-2055	528	10	12(1):77–90	12(1):77–90	NUM
ejpam-2055	528	11	,	,	PUNCT
ejpam-2055	528	12	1983	1983	NUM
ejpam-2055	528	13	.	.	PUNCT
ejpam-2055	529	1	[	[	X
ejpam-2055	529	2	12	12	NUM
ejpam-2055	529	3	]	]	PUNCT
ejpam-2055	529	4	m.	m.	NOUN
ejpam-2055	529	5	s.	s.	PROPN
ejpam-2055	529	6	el	el	PROPN
ejpam-2055	529	7	-	-	PROPN
ejpam-2055	529	8	naschie	naschie	PROPN
ejpam-2055	529	9	.	.	PUNCT
ejpam-2055	530	1	fredholm	fredholm	NOUN
ejpam-2055	530	2	operators	operator	NOUN
ejpam-2055	530	3	and	and	CCONJ
ejpam-2055	530	4	the	the	DET
ejpam-2055	530	5	wave	wave	NOUN
ejpam-2055	530	6	-	-	PUNCT
ejpam-2055	530	7	particle	particle	NOUN
ejpam-2055	530	8	duality	duality	NOUN
ejpam-2055	530	9	in	in	ADP
ejpam-2055	530	10	cantorian	cantorian	ADJ
ejpam-2055	530	11	space	space	NOUN
ejpam-2055	530	12	.	.	PUNCT
ejpam-2055	531	1	chaos	chaos	NOUN
ejpam-2055	531	2	,	,	PUNCT
ejpam-2055	531	3	solitons	soliton	NOUN
ejpam-2055	531	4	and	and	CCONJ
ejpam-2055	531	5	fractals	fractal	NOUN
ejpam-2055	531	6	,	,	PUNCT
ejpam-2055	531	7	9(6):975–978	9(6):975–978	NUM
ejpam-2055	531	8	,	,	PUNCT
ejpam-2055	531	9	1998	1998	NUM
ejpam-2055	531	10	.	.	PUNCT
ejpam-2055	532	1	[	[	X
ejpam-2055	532	2	13	13	NUM
ejpam-2055	532	3	]	]	PUNCT
ejpam-2055	532	4	m.	m.	NOUN
ejpam-2055	532	5	s.	s.	PROPN
ejpam-2055	532	6	el	el	PROPN
ejpam-2055	532	7	-	-	PROPN
ejpam-2055	532	8	naschie	naschie	PROPN
ejpam-2055	532	9	.	.	PUNCT
ejpam-2055	533	1	on	on	ADP
ejpam-2055	533	2	the	the	DET
ejpam-2055	533	3	uncertainty	uncertainty	NOUN
ejpam-2055	533	4	of	of	ADP
ejpam-2055	533	5	cantorian	cantorian	ADJ
ejpam-2055	533	6	geometry	geometry	NOUN
ejpam-2055	533	7	and	and	CCONJ
ejpam-2055	533	8	the	the	DET
ejpam-2055	533	9	two	two	NUM
ejpam-2055	533	10	-	-	PUNCT
ejpam-2055	533	11	slit	slit	NOUN
ejpam-2055	533	12	experiment	experiment	NOUN
ejpam-2055	533	13	.	.	PUNCT
ejpam-2055	534	1	chaos	chaos	NOUN
ejpam-2055	534	2	,	,	PUNCT
ejpam-2055	534	3	solitons	soliton	NOUN
ejpam-2055	534	4	and	and	CCONJ
ejpam-2055	534	5	fractals	fractal	NOUN
ejpam-2055	534	6	,	,	PUNCT
ejpam-2055	534	7	9(3):517–529	9(3):517–529	NUM
ejpam-2055	534	8	,	,	PUNCT
ejpam-2055	534	9	1998	1998	NUM
ejpam-2055	534	10	.	.	PUNCT
ejpam-2055	535	1	[	[	X
ejpam-2055	535	2	14	14	NUM
ejpam-2055	535	3	]	]	PUNCT
ejpam-2055	535	4	m.	m.	NOUN
ejpam-2055	535	5	s.	s.	PROPN
ejpam-2055	535	6	el	el	PROPN
ejpam-2055	535	7	-	-	PROPN
ejpam-2055	535	8	naschie	naschie	PROPN
ejpam-2055	535	9	.	.	PUNCT
ejpam-2055	536	1	superstrings	superstring	NOUN
ejpam-2055	536	2	,	,	PUNCT
ejpam-2055	536	3	knots	knot	NOUN
ejpam-2055	536	4	,	,	PUNCT
ejpam-2055	536	5	and	and	CCONJ
ejpam-2055	536	6	noncommutative	noncommutative	ADJ
ejpam-2055	536	7	geometry	geometry	NOUN
ejpam-2055	536	8	in	in	ADP
ejpam-2055	536	9	space	space	NOUN
ejpam-2055	536	10	.	.	PUNCT
ejpam-2055	537	1	international	international	ADJ
ejpam-2055	537	2	journal	journal	PROPN
ejpam-2055	537	3	of	of	ADP
ejpam-2055	537	4	theoretical	theoretical	ADJ
ejpam-2055	537	5	physics	physics	NOUN
ejpam-2055	537	6	,	,	PUNCT
ejpam-2055	537	7	37(12):2935–2951	37(12):2935–2951	NUM
ejpam-2055	537	8	,	,	PUNCT
ejpam-2055	537	9	1998	1998	NUM
ejpam-2055	537	10	.	.	PUNCT
ejpam-2055	538	1	[	[	X
ejpam-2055	538	2	15	15	NUM
ejpam-2055	538	3	]	]	PUNCT
ejpam-2055	538	4	m.	m.	NOUN
ejpam-2055	538	5	s.	s.	PROPN
ejpam-2055	538	6	el	el	PROPN
ejpam-2055	538	7	-	-	PROPN
ejpam-2055	538	8	naschie	naschie	PROPN
ejpam-2055	538	9	.	.	PUNCT
ejpam-2055	539	1	on	on	ADP
ejpam-2055	539	2	a	a	DET
ejpam-2055	539	3	class	class	NOUN
ejpam-2055	539	4	of	of	ADP
ejpam-2055	539	5	general	general	ADJ
ejpam-2055	539	6	theories	theory	NOUN
ejpam-2055	539	7	for	for	ADP
ejpam-2055	539	8	high	high	ADJ
ejpam-2055	539	9	energy	energy	NOUN
ejpam-2055	539	10	particle	particle	NOUN
ejpam-2055	539	11	physics	physics	PROPN
ejpam-2055	539	12	.	.	PUNCT
ejpam-2055	539	13	chaos	chaos	NOUN
ejpam-2055	539	14	,	,	PUNCT
ejpam-2055	539	15	solitons	soliton	NOUN
ejpam-2055	539	16	and	and	CCONJ
ejpam-2055	539	17	fractals	fractal	NOUN
ejpam-2055	539	18	,	,	PUNCT
ejpam-2055	539	19	14(4):649–668	14(4):649–668	NOUN
ejpam-2055	539	20	,	,	PUNCT
ejpam-2055	539	21	2002	2002	NUM
ejpam-2055	539	22	.	.	PUNCT
ejpam-2055	540	1	[	[	X
ejpam-2055	540	2	16	16	NUM
ejpam-2055	540	3	]	]	PUNCT
ejpam-2055	540	4	m.	m.	NOUN
ejpam-2055	540	5	s.	s.	PROPN
ejpam-2055	540	6	el	el	PROPN
ejpam-2055	540	7	-	-	PROPN
ejpam-2055	540	8	naschie	naschie	PROPN
ejpam-2055	540	9	.	.	PUNCT
ejpam-2055	541	1	complex	complex	ADJ
ejpam-2055	541	2	vacuum	vacuum	NOUN
ejpam-2055	541	3	fluctuation	fluctuation	NOUN
ejpam-2055	541	4	as	as	ADP
ejpam-2055	541	5	a	a	DET
ejpam-2055	541	6	chaotic	chaotic	ADJ
ejpam-2055	541	7	limit	limit	NOUN
ejpam-2055	541	8	set	set	NOUN
ejpam-2055	541	9	of	of	ADP
ejpam-2055	541	10	any	any	DET
ejpam-2055	541	11	kleinian	kleinian	ADJ
ejpam-2055	541	12	group	group	NOUN
ejpam-2055	541	13	transformation	transformation	NOUN
ejpam-2055	541	14	and	and	CCONJ
ejpam-2055	541	15	the	the	DET
ejpam-2055	541	16	mass	mass	NOUN
ejpam-2055	541	17	spectrum	spectrum	NOUN
ejpam-2055	541	18	of	of	ADP
ejpam-2055	541	19	high	high	ADJ
ejpam-2055	541	20	energy	energy	NOUN
ejpam-2055	541	21	particle	particle	NOUN
ejpam-2055	541	22	physics	physics	NOUN
ejpam-2055	541	23	via	via	ADP
ejpam-2055	541	24	spontaneous	spontaneous	ADJ
ejpam-2055	541	25	self	self	NOUN
ejpam-2055	541	26	-	-	PUNCT
ejpam-2055	541	27	organization	organization	NOUN
ejpam-2055	541	28	.	.	PUNCT
ejpam-2055	542	1	chaos	chaos	NOUN
ejpam-2055	542	2	,	,	PUNCT
ejpam-2055	542	3	solitons	soliton	NOUN
ejpam-2055	542	4	and	and	CCONJ
ejpam-2055	542	5	fractals	fractal	NOUN
ejpam-2055	542	6	,	,	PUNCT
ejpam-2055	542	7	17(4):631–638	17(4):631–638	NOUN
ejpam-2055	542	8	,	,	PUNCT
ejpam-2055	542	9	2003	2003	NUM
ejpam-2055	542	10	.	.	PUNCT
ejpam-2055	543	1	[	[	X
ejpam-2055	543	2	17	17	NUM
ejpam-2055	543	3	]	]	PUNCT
ejpam-2055	543	4	m.	m.	NOUN
ejpam-2055	543	5	s.	s.	PROPN
ejpam-2055	543	6	el	el	PROPN
ejpam-2055	543	7	-	-	PROPN
ejpam-2055	543	8	naschie	naschie	PROPN
ejpam-2055	543	9	.	.	PUNCT
ejpam-2055	543	10	quantum	quantum	ADJ
ejpam-2055	543	11	gravity	gravity	NOUN
ejpam-2055	543	12	,	,	PUNCT
ejpam-2055	543	13	clifford	clifford	PROPN
ejpam-2055	543	14	algebras	algebras	PROPN
ejpam-2055	543	15	,	,	PUNCT
ejpam-2055	543	16	fuzzy	fuzzy	ADJ
ejpam-2055	543	17	set	set	NOUN
ejpam-2055	543	18	theory	theory	NOUN
ejpam-2055	543	19	and	and	CCONJ
ejpam-2055	543	20	the	the	DET
ejpam-2055	543	21	fundamental	fundamental	ADJ
ejpam-2055	543	22	constants	constant	NOUN
ejpam-2055	543	23	of	of	ADP
ejpam-2055	543	24	nature	nature	NOUN
ejpam-2055	543	25	.	.	PUNCT
ejpam-2055	544	1	chaos	chaos	NOUN
ejpam-2055	544	2	,	,	PUNCT
ejpam-2055	544	3	solitons	soliton	NOUN
ejpam-2055	544	4	and	and	CCONJ
ejpam-2055	544	5	fractals	fractal	NOUN
ejpam-2055	544	6	,	,	PUNCT
ejpam-2055	544	7	20(3):437–450	20(3):437–450	NUM
ejpam-2055	544	8	,	,	PUNCT
ejpam-2055	544	9	2004	2004	NUM
ejpam-2055	544	10	.	.	PUNCT
ejpam-2055	545	1	[	[	X
ejpam-2055	545	2	18	18	NUM
ejpam-2055	545	3	]	]	PUNCT
ejpam-2055	545	4	m.	m.	NOUN
ejpam-2055	545	5	s.	s.	PROPN
ejpam-2055	545	6	el	el	PROPN
ejpam-2055	545	7	-	-	PROPN
ejpam-2055	545	8	naschie	naschie	PROPN
ejpam-2055	545	9	.	.	PUNCT
ejpam-2055	546	1	the	the	DET
ejpam-2055	546	2	symplictic	symplictic	PROPN
ejpam-2055	546	3	vacuum	vacuum	NOUN
ejpam-2055	546	4	,	,	PUNCT
ejpam-2055	546	5	exotic	exotic	ADJ
ejpam-2055	546	6	quasi	quasi	NOUN
ejpam-2055	546	7	particles	particle	NOUN
ejpam-2055	546	8	and	and	CCONJ
ejpam-2055	546	9	gravitational	gravitational	ADJ
ejpam-2055	546	10	instanton	instanton	PROPN
ejpam-2055	546	11	.	.	PUNCT
ejpam-2055	547	1	chaos	chaos	NOUN
ejpam-2055	547	2	,	,	PUNCT
ejpam-2055	547	3	solitons	soliton	NOUN
ejpam-2055	547	4	and	and	CCONJ
ejpam-2055	547	5	fractals	fractal	NOUN
ejpam-2055	547	6	,	,	PUNCT
ejpam-2055	547	7	22(1):1–11	22(1):1–11	NUM
ejpam-2055	547	8	,	,	PUNCT
ejpam-2055	547	9	2004	2004	NUM
ejpam-2055	547	10	.	.	PUNCT
ejpam-2055	548	1	[	[	X
ejpam-2055	548	2	19	19	NUM
ejpam-2055	548	3	]	]	PUNCT
ejpam-2055	548	4	m.	m.	NOUN
ejpam-2055	548	5	s.	s.	PROPN
ejpam-2055	548	6	el	el	PROPN
ejpam-2055	548	7	-	-	PROPN
ejpam-2055	548	8	naschie	naschie	PROPN
ejpam-2055	548	9	.	.	PUNCT
ejpam-2055	549	1	a	a	DET
ejpam-2055	549	2	few	few	ADJ
ejpam-2055	549	3	hints	hint	NOUN
ejpam-2055	549	4	and	and	CCONJ
ejpam-2055	549	5	some	some	DET
ejpam-2055	549	6	theorems	theorem	NOUN
ejpam-2055	549	7	about	about	ADP
ejpam-2055	549	8	witten	witten	PROPN
ejpam-2055	549	9	’s	’s	PART
ejpam-2055	549	10	m	m	PROPN
ejpam-2055	549	11	-	-	NOUN
ejpam-2055	549	12	theory	theory	NOUN
ejpam-2055	549	13	and	and	CCONJ
ejpam-2055	549	14	t	t	NOUN
ejpam-2055	549	15	-	-	PUNCT
ejpam-2055	549	16	duality	duality	NOUN
ejpam-2055	549	17	.	.	PUNCT
ejpam-2055	550	1	chaos	chaos	NOUN
ejpam-2055	550	2	,	,	PUNCT
ejpam-2055	550	3	solitons	soliton	NOUN
ejpam-2055	550	4	and	and	CCONJ
ejpam-2055	550	5	fractals	fractal	NOUN
ejpam-2055	550	6	,	,	PUNCT
ejpam-2055	550	7	25(3):545–548	25(3):545–548	NUM
ejpam-2055	550	8	,	,	PUNCT
ejpam-2055	550	9	2005	2005	NUM
ejpam-2055	550	10	.	.	PUNCT
ejpam-2055	551	1	[	[	X
ejpam-2055	551	2	20	20	NUM
ejpam-2055	551	3	]	]	PUNCT
ejpam-2055	551	4	m.	m.	NOUN
ejpam-2055	551	5	s.	s.	PROPN
ejpam-2055	551	6	el	el	PROPN
ejpam-2055	551	7	-	-	PROPN
ejpam-2055	551	8	naschie	naschie	PROPN
ejpam-2055	551	9	.	.	PUNCT
ejpam-2055	552	1	on	on	ADP
ejpam-2055	552	2	a	a	DET
ejpam-2055	552	3	fuzzy	fuzzy	ADJ
ejpam-2055	552	4	kähler	kähler	NOUN
ejpam-2055	552	5	-	-	PUNCT
ejpam-2055	552	6	like	like	NOUN
ejpam-2055	552	7	manifold	manifold	NOUN
ejpam-2055	552	8	which	which	PRON
ejpam-2055	552	9	is	be	AUX
ejpam-2055	552	10	consistent	consistent	ADJ
ejpam-2055	552	11	with	with	ADP
ejpam-2055	552	12	the	the	DET
ejpam-2055	552	13	two	two	NUM
ejpam-2055	552	14	slit	slit	ADJ
ejpam-2055	552	15	experiment	experiment	NOUN
ejpam-2055	552	16	.	.	PUNCT
ejpam-2055	553	1	international	international	ADJ
ejpam-2055	553	2	journal	journal	PROPN
ejpam-2055	553	3	of	of	ADP
ejpam-2055	553	4	nonlinear	nonlinear	PROPN
ejpam-2055	553	5	sciences	sciences	PROPN
ejpam-2055	553	6	and	and	CCONJ
ejpam-2055	553	7	numerical	numerical	PROPN
ejpam-2055	553	8	simulation	simulation	PROPN
ejpam-2055	553	9	,	,	PUNCT
ejpam-2055	553	10	6(2):95–98	6(2):95–98	NUM
ejpam-2055	553	11	,	,	PUNCT
ejpam-2055	553	12	2005	2005	NUM
ejpam-2055	553	13	.	.	PUNCT
ejpam-2055	554	1	[	[	X
ejpam-2055	554	2	21	21	NUM
ejpam-2055	554	3	]	]	PUNCT
ejpam-2055	554	4	m.	m.	NOUN
ejpam-2055	554	5	s.	s.	PROPN
ejpam-2055	554	6	el	el	PROPN
ejpam-2055	554	7	-	-	PROPN
ejpam-2055	554	8	naschie	naschie	PROPN
ejpam-2055	554	9	.	.	PUNCT
ejpam-2055	555	1	elementary	elementary	ADJ
ejpam-2055	555	2	prerequisites	prerequisite	NOUN
ejpam-2055	555	3	for	for	ADP
ejpam-2055	555	4	e	e	NOUN
ejpam-2055	555	5	-	-	ADJ
ejpam-2055	555	6	infinity:(recommended	infinity:(recommended	ADJ
ejpam-2055	555	7	background	background	NOUN
ejpam-2055	555	8	readings	reading	NOUN
ejpam-2055	555	9	in	in	ADP
ejpam-2055	555	10	nonlinear	nonlinear	ADJ
ejpam-2055	555	11	dynamics	dynamic	NOUN
ejpam-2055	555	12	,	,	PUNCT
ejpam-2055	555	13	geometry	geometry	NOUN
ejpam-2055	555	14	and	and	CCONJ
ejpam-2055	555	15	topology	topology	NOUN
ejpam-2055	555	16	)	)	PUNCT
ejpam-2055	555	17	.	.	PUNCT
ejpam-2055	556	1	chaos	chaos	NOUN
ejpam-2055	556	2	,	,	PUNCT
ejpam-2055	556	3	solitons	soliton	NOUN
ejpam-2055	556	4	and	and	CCONJ
ejpam-2055	556	5	fractals	fractal	NOUN
ejpam-2055	556	6	,	,	PUNCT
ejpam-2055	556	7	30(3):579–605	30(3):579–605	NUM
ejpam-2055	556	8	,	,	PUNCT
ejpam-2055	556	9	2006	2006	NUM
ejpam-2055	556	10	.	.	PUNCT
ejpam-2055	557	1	references	reference	NOUN
ejpam-2055	557	2	199	199	NUM
ejpam-2055	557	3	[	[	X
ejpam-2055	557	4	22	22	NUM
ejpam-2055	557	5	]	]	PUNCT
ejpam-2055	557	6	m.	m.	NOUN
ejpam-2055	557	7	s.	s.	PROPN
ejpam-2055	557	8	el	el	PROPN
ejpam-2055	557	9	-	-	PROPN
ejpam-2055	557	10	naschie	naschie	PROPN
ejpam-2055	557	11	.	.	PUNCT
ejpam-2055	558	1	topics	topic	NOUN
ejpam-2055	558	2	in	in	ADP
ejpam-2055	558	3	the	the	DET
ejpam-2055	558	4	mathematical	mathematical	ADJ
ejpam-2055	558	5	physics	physics	NOUN
ejpam-2055	558	6	of	of	ADP
ejpam-2055	558	7	e	e	NOUN
ejpam-2055	558	8	-	-	NOUN
ejpam-2055	558	9	infinity	infinity	NOUN
ejpam-2055	558	10	theory	theory	NOUN
ejpam-2055	558	11	.	.	PUNCT
ejpam-2055	559	1	chaos	chaos	NOUN
ejpam-2055	559	2	,	,	PUNCT
ejpam-2055	559	3	solitons	soliton	NOUN
ejpam-2055	559	4	and	and	CCONJ
ejpam-2055	559	5	fractals	fractal	NOUN
ejpam-2055	559	6	,	,	PUNCT
ejpam-2055	559	7	30(3):656–663	30(3):656–663	NUM
ejpam-2055	559	8	,	,	PUNCT
ejpam-2055	559	9	2006	2006	NUM
ejpam-2055	559	10	.	.	PUNCT
ejpam-2055	560	1	[	[	X
ejpam-2055	560	2	23	23	NUM
ejpam-2055	560	3	]	]	PUNCT
ejpam-2055	560	4	m.	m.	NOUN
ejpam-2055	560	5	s.	s.	PROPN
ejpam-2055	560	6	el	el	PROPN
ejpam-2055	560	7	-	-	PROPN
ejpam-2055	560	8	naschie	naschie	PROPN
ejpam-2055	560	9	.	.	PUNCT
ejpam-2055	561	1	on	on	ADP
ejpam-2055	561	2	the	the	DET
ejpam-2055	561	3	topological	topological	ADJ
ejpam-2055	561	4	ground	ground	NOUN
ejpam-2055	561	5	state	state	NOUN
ejpam-2055	561	6	of	of	ADP
ejpam-2055	561	7	e	e	NOUN
ejpam-2055	561	8	-	-	NOUN
ejpam-2055	561	9	infinity	infinity	ADJ
ejpam-2055	561	10	spacetime	spacetime	NOUN
ejpam-2055	561	11	and	and	CCONJ
ejpam-2055	561	12	the	the	DET
ejpam-2055	561	13	super	super	ADJ
ejpam-2055	561	14	string	string	NOUN
ejpam-2055	561	15	connection	connection	NOUN
ejpam-2055	561	16	.	.	PUNCT
ejpam-2055	562	1	chaos	chaos	NOUN
ejpam-2055	562	2	,	,	PUNCT
ejpam-2055	562	3	solitons	soliton	NOUN
ejpam-2055	562	4	and	and	CCONJ
ejpam-2055	562	5	fractals	fractal	NOUN
ejpam-2055	562	6	,	,	PUNCT
ejpam-2055	562	7	32(2):468–470	32(2):468–470	NUM
ejpam-2055	562	8	,	,	PUNCT
ejpam-2055	562	9	2007	2007	NUM
ejpam-2055	562	10	.	.	PUNCT
ejpam-2055	563	1	[	[	X
ejpam-2055	563	2	24	24	NUM
ejpam-2055	563	3	]	]	PUNCT
ejpam-2055	563	4	m.	m.	NOUN
ejpam-2055	563	5	s.	s.	PROPN
ejpam-2055	563	6	el	el	PROPN
ejpam-2055	563	7	-	-	PROPN
ejpam-2055	563	8	naschie	naschie	PROPN
ejpam-2055	563	9	.	.	PUNCT
ejpam-2055	563	10	probability	probability	NOUN
ejpam-2055	563	11	set	set	VERB
ejpam-2055	563	12	particles	particle	NOUN
ejpam-2055	563	13	.	.	PUNCT
ejpam-2055	564	1	international	international	ADJ
ejpam-2055	564	2	journal	journal	PROPN
ejpam-2055	564	3	of	of	ADP
ejpam-2055	564	4	nonlinear	nonlinear	PROPN
ejpam-2055	564	5	sciences	sciences	PROPN
ejpam-2055	564	6	and	and	CCONJ
ejpam-2055	564	7	numerical	numerical	PROPN
ejpam-2055	564	8	simulation	simulation	PROPN
ejpam-2055	564	9	,	,	PUNCT
ejpam-2055	564	10	8(1):117–120	8(1):117–120	NUM
ejpam-2055	564	11	,	,	PUNCT
ejpam-2055	564	12	2007	2007	NUM
ejpam-2055	564	13	.	.	PUNCT
ejpam-2055	565	1	[	[	X
ejpam-2055	565	2	25	25	NUM
ejpam-2055	565	3	]	]	PUNCT
ejpam-2055	565	4	m.	m.	NOUN
ejpam-2055	565	5	s.	s.	PROPN
ejpam-2055	565	6	el	el	PROPN
ejpam-2055	565	7	-	-	PROPN
ejpam-2055	565	8	naschie	naschie	PROPN
ejpam-2055	565	9	.	.	PUNCT
ejpam-2055	566	1	su(5	su(5	NOUN
ejpam-2055	566	2	)	)	PUNCT
ejpam-2055	566	3	grand	grand	ADJ
ejpam-2055	566	4	unification	unification	NOUN
ejpam-2055	566	5	in	in	ADP
ejpam-2055	566	6	a	a	DET
ejpam-2055	566	7	transfinite	transfinite	ADJ
ejpam-2055	566	8	form	form	NOUN
ejpam-2055	566	9	.	.	PUNCT
ejpam-2055	567	1	chaos	chaos	NOUN
ejpam-2055	567	2	,	,	PUNCT
ejpam-2055	567	3	solitons	soliton	NOUN
ejpam-2055	567	4	and	and	CCONJ
ejpam-2055	567	5	fractals	fractal	NOUN
ejpam-2055	567	6	,	,	PUNCT
ejpam-2055	567	7	32(2):370–374	32(2):370–374	NUM
ejpam-2055	567	8	,	,	PUNCT
ejpam-2055	567	9	2007	2007	NUM
ejpam-2055	567	10	.	.	PUNCT
ejpam-2055	568	1	[	[	X
ejpam-2055	568	2	26	26	NUM
ejpam-2055	568	3	]	]	PUNCT
ejpam-2055	568	4	m.	m.	NOUN
ejpam-2055	568	5	s.	s.	PROPN
ejpam-2055	568	6	el	el	PROPN
ejpam-2055	568	7	-	-	PROPN
ejpam-2055	568	8	naschie	naschie	PROPN
ejpam-2055	568	9	,	,	PUNCT
ejpam-2055	568	10	o.	o.	PROPN
ejpam-2055	568	11	e.	e.	PROPN
ejpam-2055	568	12	rossler	rossler	PROPN
ejpam-2055	568	13	,	,	PUNCT
ejpam-2055	568	14	and	and	CCONJ
ejpam-2055	568	15	g.	g.	PROPN
ejpam-2055	568	16	oed	oed	PROPN
ejpam-2055	568	17	.	.	PUNCT
ejpam-2055	569	1	information	information	NOUN
ejpam-2055	569	2	and	and	CCONJ
ejpam-2055	569	3	diffusion	diffusion	NOUN
ejpam-2055	569	4	in	in	ADP
ejpam-2055	569	5	quantum	quantum	ADJ
ejpam-2055	569	6	physics	physic	NOUN
ejpam-2055	569	7	.	.	PUNCT
ejpam-2055	569	8	chaos	chaos	NOUN
ejpam-2055	569	9	,	,	PUNCT
ejpam-2055	569	10	solitons	soliton	NOUN
ejpam-2055	569	11	and	and	CCONJ
ejpam-2055	569	12	fractals	fractal	NOUN
ejpam-2055	569	13	,	,	PUNCT
ejpam-2055	569	14	7(5):special	7(5):special	NUM
ejpam-2055	569	15	issue	issue	NOUN
ejpam-2055	569	16	,	,	PUNCT
ejpam-2055	569	17	1996	1996	NUM
ejpam-2055	569	18	.	.	PUNCT
ejpam-2055	570	1	[	[	X
ejpam-2055	570	2	27	27	NUM
ejpam-2055	570	3	]	]	X
ejpam-2055	570	4	e.	e.	PROPN
ejpam-2055	570	5	hatir	hatir	PROPN
ejpam-2055	570	6	and	and	CCONJ
ejpam-2055	570	7	t.	t.	PROPN
ejpam-2055	570	8	noiri	noiri	PROPN
ejpam-2055	570	9	.	.	PUNCT
ejpam-2055	571	1	decompositions	decomposition	NOUN
ejpam-2055	571	2	of	of	ADP
ejpam-2055	571	3	continuity	continuity	NOUN
ejpam-2055	571	4	and	and	CCONJ
ejpam-2055	571	5	complete	complete	ADJ
ejpam-2055	571	6	continuity	continuity	NOUN
ejpam-2055	571	7	.	.	PUNCT
ejpam-2055	572	1	acta	acta	PROPN
ejpam-2055	572	2	mathematica	mathematica	PROPN
ejpam-2055	572	3	hungarica	hungarica	PROPN
ejpam-2055	572	4	,	,	PUNCT
ejpam-2055	572	5	113(4):281–287	113(4):281–287	NUM
ejpam-2055	572	6	,	,	PUNCT
ejpam-2055	572	7	2006	2006	NUM
ejpam-2055	572	8	.	.	PUNCT
ejpam-2055	573	1	[	[	X
ejpam-2055	573	2	28	28	NUM
ejpam-2055	573	3	]	]	X
ejpam-2055	573	4	e.	e.	PROPN
ejpam-2055	573	5	hatir	hatir	PROPN
ejpam-2055	573	6	and	and	CCONJ
ejpam-2055	573	7	t.	t.	PROPN
ejpam-2055	573	8	noiri	noiri	PROPN
ejpam-2055	573	9	.	.	PUNCT
ejpam-2055	574	1	on	on	ADP
ejpam-2055	574	2	δ	δ	PROPN
ejpam-2055	574	3	−	−	PROPN
ejpam-2055	574	4	β	β	SYM
ejpam-2055	574	5	-continuous	-continuous	ADJ
ejpam-2055	574	6	functions	function	NOUN
ejpam-2055	574	7	.	.	PUNCT
ejpam-2055	575	1	chaos	chaos	NOUN
ejpam-2055	575	2	,	,	PUNCT
ejpam-2055	575	3	solitons	soliton	NOUN
ejpam-2055	575	4	and	and	CCONJ
ejpam-2055	575	5	fractals	fractal	NOUN
ejpam-2055	575	6	,	,	PUNCT
ejpam-2055	575	7	42(1):205–211	42(1):205–211	NOUN
ejpam-2055	575	8	,	,	PUNCT
ejpam-2055	575	9	2009	2009	NUM
ejpam-2055	575	10	.	.	PUNCT
ejpam-2055	576	1	[	[	X
ejpam-2055	576	2	29	29	NUM
ejpam-2055	576	3	]	]	X
ejpam-2055	576	4	s.	s.	PROPN
ejpam-2055	576	5	jafari	jafari	PROPN
ejpam-2055	576	6	and	and	CCONJ
ejpam-2055	576	7	t.	t.	PROPN
ejpam-2055	576	8	noiri	noiri	PROPN
ejpam-2055	576	9	.	.	PUNCT
ejpam-2055	577	1	on	on	ADP
ejpam-2055	577	2	strongly	strongly	ADV
ejpam-2055	577	3	θ	θ	NOUN
ejpam-2055	577	4	-semi	-semi	NOUN
ejpam-2055	577	5	-	-	PUNCT
ejpam-2055	577	6	continuous	continuous	ADJ
ejpam-2055	577	7	functions	function	NOUN
ejpam-2055	577	8	.	.	PUNCT
ejpam-2055	578	1	indian	indian	ADJ
ejpam-2055	578	2	journal	journal	PROPN
ejpam-2055	578	3	of	of	ADP
ejpam-2055	578	4	pure	pure	ADJ
ejpam-2055	578	5	and	and	CCONJ
ejpam-2055	578	6	applied	applied	ADJ
ejpam-2055	578	7	mathematics	mathematic	NOUN
ejpam-2055	578	8	,	,	PUNCT
ejpam-2055	578	9	29(1):1195–1201	29(1):1195–1201	NUM
ejpam-2055	578	10	,	,	PUNCT
ejpam-2055	578	11	1998	1998	NUM
ejpam-2055	578	12	.	.	PUNCT
ejpam-2055	579	1	[	[	X
ejpam-2055	579	2	30	30	NUM
ejpam-2055	579	3	]	]	X
ejpam-2055	579	4	g.	g.	PROPN
ejpam-2055	579	5	landi	landi	PROPN
ejpam-2055	579	6	.	.	PUNCT
ejpam-2055	580	1	an	an	DET
ejpam-2055	580	2	introduction	introduction	NOUN
ejpam-2055	580	3	to	to	ADP
ejpam-2055	580	4	noncommutative	noncommutative	ADJ
ejpam-2055	580	5	spaces	space	NOUN
ejpam-2055	580	6	and	and	CCONJ
ejpam-2055	580	7	their	their	PRON
ejpam-2055	580	8	geometry	geometry	NOUN
ejpam-2055	580	9	.	.	PUNCT
ejpam-2055	581	1	lecture	lecture	NOUN
ejpam-2055	581	2	notes	note	NOUN
ejpam-2055	581	3	in	in	ADP
ejpam-2055	581	4	physics	physics	PROPN
ejpam-2055	581	5	,	,	PUNCT
ejpam-2055	581	6	new	new	PROPN
ejpam-2055	581	7	york	york	PROPN
ejpam-2055	581	8	,	,	PUNCT
ejpam-2055	581	9	springer	springer	NOUN
ejpam-2055	581	10	,	,	PUNCT
ejpam-2055	581	11	1997	1997	NUM
ejpam-2055	581	12	.	.	PUNCT
ejpam-2055	582	1	[	[	X
ejpam-2055	582	2	31	31	NUM
ejpam-2055	582	3	]	]	X
ejpam-2055	582	4	n.	n.	PROPN
ejpam-2055	582	5	levine	levine	PROPN
ejpam-2055	582	6	.	.	PUNCT
ejpam-2055	583	1	semi	semi	ADJ
ejpam-2055	583	2	-	-	ADJ
ejpam-2055	583	3	open	open	ADJ
ejpam-2055	583	4	sets	set	NOUN
ejpam-2055	583	5	and	and	CCONJ
ejpam-2055	583	6	semi	semi	ADJ
ejpam-2055	583	7	-	-	NOUN
ejpam-2055	583	8	continuity	continuity	NOUN
ejpam-2055	583	9	in	in	ADP
ejpam-2055	583	10	topological	topological	ADJ
ejpam-2055	583	11	spaces	space	NOUN
ejpam-2055	583	12	.	.	PUNCT
ejpam-2055	584	1	american	american	PROPN
ejpam-2055	584	2	mathematical	mathematical	PROPN
ejpam-2055	584	3	monthly	monthly	ADV
ejpam-2055	584	4	,	,	PUNCT
ejpam-2055	584	5	70(1):36–41	70(1):36–41	NUM
ejpam-2055	584	6	,	,	PUNCT
ejpam-2055	584	7	1963	1963	NUM
ejpam-2055	584	8	.	.	PUNCT
ejpam-2055	585	1	[	[	X
ejpam-2055	585	2	32	32	NUM
ejpam-2055	585	3	]	]	PUNCT
ejpam-2055	586	1	p.	p.	PROPN
ejpam-2055	586	2	e.	e.	PROPN
ejpam-2055	587	1	long	long	PROPN
ejpam-2055	587	2	and	and	CCONJ
ejpam-2055	587	3	l.	l.	PROPN
ejpam-2055	587	4	l.	l.	PROPN
ejpam-2055	587	5	herrington	herrington	PROPN
ejpam-2055	587	6	.	.	PUNCT
ejpam-2055	588	1	strongly	strongly	ADV
ejpam-2055	588	2	θ	θ	PROPN
ejpam-2055	588	3	-continuous	-continuous	ADJ
ejpam-2055	588	4	functions	function	NOUN
ejpam-2055	588	5	.	.	PUNCT
ejpam-2055	589	1	journal	journal	NOUN
ejpam-2055	589	2	of	of	ADP
ejpam-2055	589	3	the	the	DET
ejpam-2055	589	4	korean	korean	PROPN
ejpam-2055	589	5	mathematical	mathematical	ADJ
ejpam-2055	589	6	society	society	NOUN
ejpam-2055	589	7	,	,	PUNCT
ejpam-2055	589	8	18(1):21–28	18(1):21–28	NUM
ejpam-2055	589	9	,	,	PUNCT
ejpam-2055	589	10	1981/82	1981/82	NUM
ejpam-2055	589	11	.	.	PUNCT
ejpam-2055	590	1	[	[	X
ejpam-2055	590	2	33	33	NUM
ejpam-2055	590	3	]	]	PUNCT
ejpam-2055	590	4	a.	a.	NOUN
ejpam-2055	590	5	s.	s.	PROPN
ejpam-2055	590	6	mashhour	mashhour	PROPN
ejpam-2055	590	7	,	,	PUNCT
ejpam-2055	590	8	m.	m.	PROPN
ejpam-2055	590	9	e.	e.	PROPN
ejpam-2055	590	10	abd	abd	PROPN
ejpam-2055	590	11	-	-	PROPN
ejpam-2055	590	12	elmonsef	elmonsef	PROPN
ejpam-2055	590	13	,	,	PUNCT
ejpam-2055	590	14	and	and	CCONJ
ejpam-2055	590	15	s.	s.	PROPN
ejpam-2055	590	16	n.	n.	PROPN
ejpam-2055	590	17	el	el	PROPN
ejpam-2055	590	18	-	-	PROPN
ejpam-2055	590	19	deeb	deeb	PROPN
ejpam-2055	590	20	.	.	PUNCT
ejpam-2055	591	1	on	on	ADP
ejpam-2055	591	2	pre	pre	ADJ
ejpam-2055	591	3	-	-	ADJ
ejpam-2055	591	4	continuous	continuous	ADJ
ejpam-2055	591	5	and	and	CCONJ
ejpam-2055	591	6	weak	weak	ADJ
ejpam-2055	591	7	pre	pre	ADJ
ejpam-2055	591	8	continuous	continuous	ADJ
ejpam-2055	591	9	mappings	mapping	NOUN
ejpam-2055	591	10	.	.	PUNCT
ejpam-2055	592	1	proceedings	proceeding	NOUN
ejpam-2055	592	2	of	of	ADP
ejpam-2055	592	3	the	the	DET
ejpam-2055	592	4	mathematical	mathematical	ADJ
ejpam-2055	592	5	and	and	CCONJ
ejpam-2055	592	6	physical	physical	ADJ
ejpam-2055	592	7	society	society	NOUN
ejpam-2055	592	8	of	of	ADP
ejpam-2055	592	9	egypt	egypt	PROPN
ejpam-2055	592	10	,	,	PUNCT
ejpam-2055	592	11	53:47–53	53:47–53	NUM
ejpam-2055	592	12	,	,	PUNCT
ejpam-2055	592	13	1982	1982	NUM
ejpam-2055	592	14	.	.	PUNCT
ejpam-2055	593	1	[	[	X
ejpam-2055	593	2	34	34	NUM
ejpam-2055	593	3	]	]	X
ejpam-2055	593	4	r.	r.	PROPN
ejpam-2055	593	5	d.	d.	PROPN
ejpam-2055	593	6	mauldin	mauldin	PROPN
ejpam-2055	593	7	and	and	CCONJ
ejpam-2055	593	8	s.	s.	PROPN
ejpam-2055	593	9	c.	c.	PROPN
ejpam-2055	593	10	williams	williams	PROPN
ejpam-2055	593	11	.	.	PUNCT
ejpam-2055	594	1	random	random	ADJ
ejpam-2055	594	2	recursive	recursive	ADJ
ejpam-2055	594	3	constructions	construction	NOUN
ejpam-2055	594	4	:	:	PUNCT
ejpam-2055	594	5	asymptotic	asymptotic	ADJ
ejpam-2055	594	6	geometric	geometric	ADJ
ejpam-2055	594	7	and	and	CCONJ
ejpam-2055	594	8	topological	topological	ADJ
ejpam-2055	594	9	properties	property	NOUN
ejpam-2055	594	10	.	.	PUNCT
ejpam-2055	595	1	transactions	transaction	NOUN
ejpam-2055	595	2	of	of	ADP
ejpam-2055	595	3	the	the	DET
ejpam-2055	595	4	american	american	PROPN
ejpam-2055	595	5	mathematical	mathematical	PROPN
ejpam-2055	595	6	society	society	NOUN
ejpam-2055	595	7	,	,	PUNCT
ejpam-2055	595	8	295(1):325–346	295(1):325–346	NUM
ejpam-2055	595	9	,	,	PUNCT
ejpam-2055	595	10	1986	1986	NUM
ejpam-2055	595	11	.	.	PUNCT
ejpam-2055	596	1	[	[	X
ejpam-2055	596	2	35	35	NUM
ejpam-2055	596	3	]	]	X
ejpam-2055	596	4	e.	e.	PROPN
ejpam-2055	596	5	l.	l.	PROPN
ejpam-2055	596	6	f.	f.	PROPN
ejpam-2055	596	7	moore	moore	PROPN
ejpam-2055	596	8	and	and	CCONJ
ejpam-2055	596	9	t.	t.	PROPN
ejpam-2055	596	10	j.	j.	PROPN
ejpam-2055	596	11	peters	peters	PROPN
ejpam-2055	596	12	.	.	PUNCT
ejpam-2055	597	1	computational	computational	ADJ
ejpam-2055	597	2	topology	topology	NOUN
ejpam-2055	597	3	for	for	ADP
ejpam-2055	597	4	geometric	geometric	ADJ
ejpam-2055	597	5	design	design	NOUN
ejpam-2055	597	6	and	and	CCONJ
ejpam-2055	597	7	molecular	molecular	ADJ
ejpam-2055	597	8	design	design	NOUN
ejpam-2055	597	9	.	.	PUNCT
ejpam-2055	598	1	mathematics	mathematic	NOUN
ejpam-2055	598	2	for	for	ADP
ejpam-2055	598	3	industry	industry	NOUN
ejpam-2055	598	4	:	:	PUNCT
ejpam-2055	598	5	challenges	challenge	NOUN
ejpam-2055	598	6	and	and	CCONJ
ejpam-2055	598	7	frontiers	frontier	NOUN
ejpam-2055	598	8	.	.	PUNCT
ejpam-2055	599	1	siam	siam	PROPN
ejpam-2055	599	2	,	,	PUNCT
ejpam-2055	599	3	pages	page	NOUN
ejpam-2055	599	4	125–137	125–137	NUM
ejpam-2055	599	5	,	,	PUNCT
ejpam-2055	599	6	2005	2005	NUM
ejpam-2055	599	7	.	.	PUNCT
ejpam-2055	600	1	[	[	X
ejpam-2055	600	2	36	36	NUM
ejpam-2055	600	3	]	]	X
ejpam-2055	600	4	o.	o.	PROPN
ejpam-2055	600	5	njastad	njastad	PROPN
ejpam-2055	600	6	.	.	PUNCT
ejpam-2055	601	1	on	on	ADP
ejpam-2055	601	2	some	some	DET
ejpam-2055	601	3	classes	class	NOUN
ejpam-2055	601	4	of	of	ADP
ejpam-2055	601	5	nearly	nearly	ADV
ejpam-2055	601	6	open	open	ADJ
ejpam-2055	601	7	sets	set	NOUN
ejpam-2055	601	8	.	.	PUNCT
ejpam-2055	602	1	pacific	pacific	PROPN
ejpam-2055	602	2	journal	journal	PROPN
ejpam-2055	602	3	of	of	ADP
ejpam-2055	602	4	mathematics	mathematic	NOUN
ejpam-2055	602	5	,	,	PUNCT
ejpam-2055	602	6	15(3):961–970	15(3):961–970	PROPN
ejpam-2055	602	7	,	,	PUNCT
ejpam-2055	602	8	1965	1965	NUM
ejpam-2055	602	9	.	.	PUNCT
ejpam-2055	603	1	references	reference	NOUN
ejpam-2055	603	2	200	200	NUM
ejpam-2055	603	3	[	[	X
ejpam-2055	603	4	37	37	NUM
ejpam-2055	603	5	]	]	PUNCT
ejpam-2055	603	6	t.	t.	PROPN
ejpam-2055	603	7	noiri	noiri	PROPN
ejpam-2055	603	8	.	.	PUNCT
ejpam-2055	604	1	on	on	ADP
ejpam-2055	604	2	δ	δ	PROPN
ejpam-2055	604	3	-	-	ADJ
ejpam-2055	604	4	continuous	continuous	ADJ
ejpam-2055	604	5	functions	function	NOUN
ejpam-2055	604	6	.	.	PUNCT
ejpam-2055	605	1	journal	journal	NOUN
ejpam-2055	605	2	of	of	ADP
ejpam-2055	605	3	the	the	DET
ejpam-2055	605	4	korean	korean	PROPN
ejpam-2055	605	5	mathematical	mathematical	ADJ
ejpam-2055	605	6	society	society	NOUN
ejpam-2055	605	7	,	,	PUNCT
ejpam-2055	605	8	16(2):161–166	16(2):161–166	NUM
ejpam-2055	605	9	,	,	PUNCT
ejpam-2055	605	10	1979/80	1979/80	NUM
ejpam-2055	605	11	.	.	PUNCT
ejpam-2055	606	1	[	[	X
ejpam-2055	606	2	38	38	NUM
ejpam-2055	606	3	]	]	PUNCT
ejpam-2055	606	4	t.	t.	PROPN
ejpam-2055	606	5	noiri	noiri	PROPN
ejpam-2055	606	6	.	.	PUNCT
ejpam-2055	607	1	strongly	strongly	ADV
ejpam-2055	607	2	θ	θ	NOUN
ejpam-2055	607	3	-precontinuous	-precontinuous	ADJ
ejpam-2055	607	4	functions	function	NOUN
ejpam-2055	607	5	.	.	PUNCT
ejpam-2055	608	1	acta	acta	PROPN
ejpam-2055	608	2	mathematica	mathematica	PROPN
ejpam-2055	608	3	hungarica	hungarica	PROPN
ejpam-2055	608	4	,	,	PUNCT
ejpam-2055	608	5	90(4):307	90(4):307	NUM
ejpam-2055	608	6	–	–	PUNCT
ejpam-2055	608	7	316	316	NUM
ejpam-2055	608	8	,	,	PUNCT
ejpam-2055	608	9	2001	2001	NUM
ejpam-2055	608	10	.	.	PUNCT
ejpam-2055	609	1	[	[	X
ejpam-2055	609	2	39	39	NUM
ejpam-2055	609	3	]	]	PUNCT
ejpam-2055	609	4	t.	t.	PROPN
ejpam-2055	609	5	noiri	noiri	PROPN
ejpam-2055	609	6	and	and	CCONJ
ejpam-2055	609	7	v.	v.	ADP
ejpam-2055	609	8	popa	popa	NOUN
ejpam-2055	609	9	.	.	PUNCT
ejpam-2055	610	1	strongly	strongly	ADV
ejpam-2055	610	2	θ	θ	PROPN
ejpam-2055	610	3	-β	-β	SYM
ejpam-2055	610	4	-continuous	-continuous	ADJ
ejpam-2055	610	5	functions	function	NOUN
ejpam-2055	610	6	.	.	PUNCT
ejpam-2055	611	1	journal	journal	NOUN
ejpam-2055	611	2	of	of	ADP
ejpam-2055	611	3	pure	pure	ADJ
ejpam-2055	611	4	mathematics	mathematic	NOUN
ejpam-2055	611	5	,	,	PUNCT
ejpam-2055	611	6	19:31–39	19:31–39	NUM
ejpam-2055	611	7	,	,	PUNCT
ejpam-2055	611	8	2002	2002	NUM
ejpam-2055	611	9	.	.	PUNCT
ejpam-2055	612	1	[	[	X
ejpam-2055	612	2	40	40	NUM
ejpam-2055	612	3	]	]	PUNCT
ejpam-2055	612	4	t.	t.	PROPN
ejpam-2055	612	5	noiri	noiri	PROPN
ejpam-2055	612	6	and	and	CCONJ
ejpam-2055	612	7	v.	v.	ADP
ejpam-2055	612	8	popa	popa	NOUN
ejpam-2055	612	9	.	.	PUNCT
ejpam-2055	613	1	faintly	faintly	ADV
ejpam-2055	613	2	m	m	ADJ
ejpam-2055	613	3	-	-	ADJ
ejpam-2055	613	4	continuous	continuous	ADJ
ejpam-2055	613	5	functions	function	NOUN
ejpam-2055	613	6	.	.	PUNCT
ejpam-2055	614	1	chaos	chaos	NOUN
ejpam-2055	614	2	,	,	PUNCT
ejpam-2055	614	3	solitons	soliton	NOUN
ejpam-2055	614	4	and	and	CCONJ
ejpam-2055	614	5	fractals	fractal	NOUN
ejpam-2055	614	6	,	,	PUNCT
ejpam-2055	614	7	19(5):1147–1159	19(5):1147–1159	NUM
ejpam-2055	614	8	,	,	PUNCT
ejpam-2055	614	9	2004	2004	NUM
ejpam-2055	614	10	.	.	PUNCT
ejpam-2055	615	1	[	[	X
ejpam-2055	615	2	41	41	NUM
ejpam-2055	615	3	]	]	PUNCT
ejpam-2055	615	4	m.	m.	NOUN
ejpam-2055	615	5	özkoç	özkoç	NOUN
ejpam-2055	615	6	and	and	CCONJ
ejpam-2055	615	7	g.	g.	PROPN
ejpam-2055	615	8	aslim	aslim	PROPN
ejpam-2055	615	9	.	.	PUNCT
ejpam-2055	616	1	on	on	ADP
ejpam-2055	616	2	strongly	strongly	ADV
ejpam-2055	616	3	θ	θ	NOUN
ejpam-2055	616	4	-e	-e	ADJ
ejpam-2055	616	5	-	-	PUNCT
ejpam-2055	616	6	continuous	continuous	ADJ
ejpam-2055	616	7	functions	function	NOUN
ejpam-2055	616	8	.	.	PUNCT
ejpam-2055	617	1	bulletin	bulletin	NOUN
ejpam-2055	617	2	of	of	ADP
ejpam-2055	617	3	the	the	DET
ejpam-2055	617	4	korean	korean	PROPN
ejpam-2055	617	5	mathematical	mathematical	ADJ
ejpam-2055	617	6	society	society	NOUN
ejpam-2055	617	7	,	,	PUNCT
ejpam-2055	617	8	47(5):1025–1036	47(5):1025–1036	NOUN
ejpam-2055	617	9	,	,	PUNCT
ejpam-2055	617	10	2010	2010	NUM
ejpam-2055	617	11	.	.	PUNCT
ejpam-2055	618	1	[	[	X
ejpam-2055	618	2	42	42	NUM
ejpam-2055	618	3	]	]	PUNCT
ejpam-2055	618	4	j.	j.	PROPN
ejpam-2055	618	5	h.	h.	PROPN
ejpam-2055	618	6	park	park	PROPN
ejpam-2055	618	7	.	.	PUNCT
ejpam-2055	619	1	strongly	strongly	ADV
ejpam-2055	619	2	θ	θ	NOUN
ejpam-2055	619	3	-b	-b	ADJ
ejpam-2055	619	4	-	-	ADJ
ejpam-2055	619	5	continuous	continuous	ADJ
ejpam-2055	619	6	functions	function	NOUN
ejpam-2055	619	7	.	.	PUNCT
ejpam-2055	620	1	acta	acta	PROPN
ejpam-2055	620	2	mathematica	mathematica	PROPN
ejpam-2055	620	3	hungarica	hungarica	PROPN
ejpam-2055	620	4	,	,	PUNCT
ejpam-2055	620	5	110(4):347	110(4):347	NUM
ejpam-2055	620	6	–	–	PUNCT
ejpam-2055	620	7	359	359	NUM
ejpam-2055	620	8	,	,	PUNCT
ejpam-2055	620	9	2006	2006	NUM
ejpam-2055	620	10	.	.	PUNCT
ejpam-2055	621	1	[	[	X
ejpam-2055	621	2	43	43	NUM
ejpam-2055	621	3	]	]	X
ejpam-2055	621	4	j.	j.	PROPN
ejpam-2055	621	5	h.	h.	PROPN
ejpam-2055	621	6	park	park	PROPN
ejpam-2055	621	7	,	,	PUNCT
ejpam-2055	621	8	s.	s.	PROPN
ejpam-2055	621	9	w.	w.	PROPN
ejpam-2055	621	10	bae	bae	PROPN
ejpam-2055	621	11	,	,	PUNCT
ejpam-2055	621	12	and	and	CCONJ
ejpam-2055	621	13	y.	y.	PROPN
ejpam-2055	621	14	b.	b.	PROPN
ejpam-2055	621	15	park	park	PROPN
ejpam-2055	621	16	.	.	PUNCT
ejpam-2055	622	1	almost	almost	ADV
ejpam-2055	622	2	strongly	strongly	ADV
ejpam-2055	622	3	θ	θ	NOUN
ejpam-2055	622	4	-precontinuous	-precontinuous	ADJ
ejpam-2055	622	5	functions	function	NOUN
ejpam-2055	622	6	.	.	PUNCT
ejpam-2055	623	1	chaos	chaos	NOUN
ejpam-2055	623	2	,	,	PUNCT
ejpam-2055	623	3	solitons	soliton	NOUN
ejpam-2055	623	4	and	and	CCONJ
ejpam-2055	623	5	fractals	fractal	NOUN
ejpam-2055	623	6	,	,	PUNCT
ejpam-2055	623	7	28(1):32–41	28(1):32–41	NUM
ejpam-2055	623	8	,	,	PUNCT
ejpam-2055	623	9	2006	2006	NUM
ejpam-2055	623	10	.	.	PUNCT
ejpam-2055	624	1	[	[	X
ejpam-2055	624	2	44	44	NUM
ejpam-2055	624	3	]	]	PUNCT
ejpam-2055	624	4	j.	j.	PROPN
ejpam-2055	624	5	h.	h.	PROPN
ejpam-2055	624	6	park	park	PROPN
ejpam-2055	624	7	and	and	CCONJ
ejpam-2055	624	8	j.	j.	PROPN
ejpam-2055	624	9	k.	k.	PROPN
ejpam-2055	624	10	park	park	PROPN
ejpam-2055	624	11	.	.	PUNCT
ejpam-2055	625	1	on	on	ADP
ejpam-2055	625	2	πgp	πgp	ADJ
ejpam-2055	625	3	-	-	PUNCT
ejpam-2055	625	4	continuous	continuous	ADJ
ejpam-2055	625	5	functions	function	NOUN
ejpam-2055	625	6	in	in	ADP
ejpam-2055	625	7	topological	topological	ADJ
ejpam-2055	625	8	spaces	space	NOUN
ejpam-2055	625	9	.	.	PUNCT
ejpam-2055	626	1	chaos	chaos	NOUN
ejpam-2055	626	2	,	,	PUNCT
ejpam-2055	626	3	solitons	soliton	NOUN
ejpam-2055	626	4	and	and	CCONJ
ejpam-2055	626	5	fractals	fractal	NOUN
ejpam-2055	626	6	,	,	PUNCT
ejpam-2055	626	7	20(3):467–477	20(3):467–477	NOUN
ejpam-2055	626	8	,	,	PUNCT
ejpam-2055	626	9	2004	2004	NUM
ejpam-2055	626	10	.	.	PUNCT
ejpam-2055	627	1	[	[	X
ejpam-2055	627	2	45	45	NUM
ejpam-2055	627	3	]	]	PUNCT
ejpam-2055	627	4	i.	i.	PROPN
ejpam-2055	627	5	l.	l.	PROPN
ejpam-2055	627	6	reilly	reilly	PROPN
ejpam-2055	627	7	and	and	CCONJ
ejpam-2055	627	8	m.	m.	PROPN
ejpam-2055	627	9	k.	k.	PROPN
ejpam-2055	627	10	vamanamurthy	vamanamurthy	PROPN
ejpam-2055	627	11	.	.	PUNCT
ejpam-2055	628	1	on	on	ADP
ejpam-2055	628	2	some	some	DET
ejpam-2055	628	3	questions	question	NOUN
ejpam-2055	628	4	concerning	concern	VERB
ejpam-2055	628	5	preopen	preopen	ADJ
ejpam-2055	628	6	sets	set	NOUN
ejpam-2055	628	7	.	.	PUNCT
ejpam-2055	629	1	kyungpook	kyungpook	PROPN
ejpam-2055	629	2	mathematical	mathematical	PROPN
ejpam-2055	629	3	journal	journal	PROPN
ejpam-2055	629	4	,	,	PUNCT
ejpam-2055	629	5	30(1):87–93	30(1):87–93	NUM
ejpam-2055	629	6	,	,	PUNCT
ejpam-2055	629	7	1990	1990	NUM
ejpam-2055	629	8	.	.	PUNCT
ejpam-2055	630	1	[	[	X
ejpam-2055	630	2	46	46	NUM
ejpam-2055	630	3	]	]	X
ejpam-2055	630	4	d.	d.	PROPN
ejpam-2055	630	5	w.	w.	PROPN
ejpam-2055	630	6	rosen	rosen	PROPN
ejpam-2055	630	7	and	and	CCONJ
ejpam-2055	630	8	t.	t.	PROPN
ejpam-2055	630	9	j.	j.	PROPN
ejpam-2055	630	10	peters	peters	PROPN
ejpam-2055	630	11	.	.	PUNCT
ejpam-2055	631	1	the	the	DET
ejpam-2055	631	2	role	role	NOUN
ejpam-2055	631	3	of	of	ADP
ejpam-2055	631	4	topology	topology	NOUN
ejpam-2055	631	5	in	in	ADP
ejpam-2055	631	6	engineering	engineering	NOUN
ejpam-2055	631	7	design	design	NOUN
ejpam-2055	631	8	research	research	NOUN
ejpam-2055	631	9	.	.	PUNCT
ejpam-2055	632	1	research	research	NOUN
ejpam-2055	632	2	in	in	ADP
ejpam-2055	632	3	engineering	engineering	NOUN
ejpam-2055	632	4	design	design	NOUN
ejpam-2055	632	5	,	,	PUNCT
ejpam-2055	632	6	8(2):81–98	8(2):81–98	NUM
ejpam-2055	632	7	,	,	PUNCT
ejpam-2055	632	8	1996	1996	NUM
ejpam-2055	632	9	.	.	PUNCT
ejpam-2055	633	1	[	[	X
ejpam-2055	633	2	47	47	NUM
ejpam-2055	633	3	]	]	PUNCT
ejpam-2055	633	4	k.	k.	PROPN
ejpam-2055	633	5	svozil	svozil	PROPN
ejpam-2055	633	6	.	.	PUNCT
ejpam-2055	634	1	quantum	quantum	ADJ
ejpam-2055	634	2	field	field	NOUN
ejpam-2055	634	3	theory	theory	NOUN
ejpam-2055	634	4	on	on	ADP
ejpam-2055	634	5	fractal	fractal	ADJ
ejpam-2055	634	6	space	space	NOUN
ejpam-2055	634	7	-	-	PUNCT
ejpam-2055	634	8	time	time	NOUN
ejpam-2055	634	9	:	:	PUNCT
ejpam-2055	634	10	a	a	DET
ejpam-2055	634	11	new	new	ADJ
ejpam-2055	634	12	regularisation	regularisation	NOUN
ejpam-2055	634	13	method	method	NOUN
ejpam-2055	634	14	.	.	PUNCT
ejpam-2055	635	1	journal	journal	PROPN
ejpam-2055	635	2	of	of	ADP
ejpam-2055	635	3	physics	physics	PROPN
ejpam-2055	635	4	a	a	PRON
ejpam-2055	635	5	:	:	PUNCT
ejpam-2055	635	6	mathematical	mathematical	ADJ
ejpam-2055	635	7	and	and	CCONJ
ejpam-2055	635	8	general	general	ADJ
ejpam-2055	635	9	,	,	PUNCT
ejpam-2055	635	10	20(12):3861–3875	20(12):3861–3875	NUM
ejpam-2055	635	11	,	,	PUNCT
ejpam-2055	635	12	1987	1987	NUM
ejpam-2055	635	13	.	.	PUNCT
ejpam-2055	636	1	[	[	X
ejpam-2055	636	2	48	48	NUM
ejpam-2055	636	3	]	]	X
ejpam-2055	636	4	n.	n.	NOUN
ejpam-2055	636	5	v.	v.	ADP
ejpam-2055	636	6	velicko	velicko	NOUN
ejpam-2055	636	7	.	.	PUNCT
ejpam-2055	637	1	h	h	NOUN
ejpam-2055	637	2	-	-	PUNCT
ejpam-2055	637	3	closed	close	VERB
ejpam-2055	637	4	topological	topological	ADJ
ejpam-2055	637	5	spaces	space	NOUN
ejpam-2055	637	6	.	.	PUNCT
ejpam-2055	638	1	american	american	PROPN
ejpam-2055	638	2	mathematical	mathematical	ADJ
ejpam-2055	638	3	society	society	NOUN
ejpam-2055	638	4	translations	translation	NOUN
ejpam-2055	638	5	,	,	PUNCT
ejpam-2055	638	6	78:103–118	78:103–118	PROPN
ejpam-2055	638	7	,	,	PUNCT
ejpam-2055	638	8	1968	1968	NUM
ejpam-2055	638	9	.	.	PUNCT