id	sid	tid	token	lemma	pos
ejpam-3312	1	1	other	other	ADJ
ejpam-3312	1	2	kinds	kind	NOUN
ejpam-3312	1	3	of	of	ADP
ejpam-3312	1	4	soft	soft	ADJ
ejpam-3312	1	5	$	$	SYM
ejpam-3312	1	6	�	�	NOUN
ejpam-3312	1	7	eta	eta	CCONJ
ejpam-3312	1	8	$	$	SYM
ejpam-3312	1	9	mappings	mapping	NOUN
ejpam-3312	1	10	via	via	ADP
ejpam-3312	1	11	soft	soft	ADJ
ejpam-3312	1	12	topological	topological	ADJ
ejpam-3312	1	13	ordered	order	VERB
ejpam-3312	1	14	spaces	space	NOUN
ejpam-3312	1	15	european	european	PROPN
ejpam-3312	1	16	journal	journal	PROPN
ejpam-3312	1	17	of	of	ADP
ejpam-3312	1	18	pure	pure	ADJ
ejpam-3312	1	19	and	and	CCONJ
ejpam-3312	1	20	applied	apply	VERB
ejpam-3312	1	21	mathematics	mathematic	NOUN
ejpam-3312	1	22	vol	vol	NOUN
ejpam-3312	1	23	.	.	PROPN
ejpam-3312	1	24	12	12	NUM
ejpam-3312	1	25	,	,	PUNCT
ejpam-3312	1	26	no	no	INTJ
ejpam-3312	1	27	.	.	NOUN
ejpam-3312	1	28	1	1	NUM
ejpam-3312	1	29	,	,	PUNCT
ejpam-3312	1	30	2019	2019	NUM
ejpam-3312	1	31	,	,	PUNCT
ejpam-3312	1	32	176	176	NUM
ejpam-3312	1	33	-	-	SYM
ejpam-3312	1	34	193	193	NUM
ejpam-3312	1	35	issn	issn	PROPN
ejpam-3312	1	36	1307	1307	NUM
ejpam-3312	1	37	-	-	SYM
ejpam-3312	1	38	5543	5543	NUM
ejpam-3312	1	39	–	–	PUNCT
ejpam-3312	1	40	www.ejpam.com	www.ejpam.com	X
ejpam-3312	1	41	published	publish	VERB
ejpam-3312	1	42	by	by	ADP
ejpam-3312	1	43	new	new	PROPN
ejpam-3312	1	44	york	york	PROPN
ejpam-3312	1	45	business	business	PROPN
ejpam-3312	1	46	global	global	ADJ
ejpam-3312	1	47	other	other	ADJ
ejpam-3312	1	48	kinds	kind	NOUN
ejpam-3312	1	49	of	of	ADP
ejpam-3312	1	50	soft	soft	ADJ
ejpam-3312	1	51	β	β	NOUN
ejpam-3312	1	52	mappings	mapping	NOUN
ejpam-3312	1	53	via	via	ADP
ejpam-3312	1	54	soft	soft	ADJ
ejpam-3312	1	55	topological	topological	ADJ
ejpam-3312	1	56	ordered	order	VERB
ejpam-3312	1	57	spaces	space	NOUN
ejpam-3312	1	58	tareq	tareq	PROPN
ejpam-3312	1	59	m.	m.	PROPN
ejpam-3312	1	60	al	al	PROPN
ejpam-3312	1	61	-	-	PUNCT
ejpam-3312	1	62	shami1,2∗	shami1,2∗	PROPN
ejpam-3312	1	63	,	,	PUNCT
ejpam-3312	1	64	mohammed	mohammed	PROPN
ejpam-3312	1	65	e.	e.	PROPN
ejpam-3312	1	66	el	el	PROPN
ejpam-3312	1	67	-	-	PROPN
ejpam-3312	1	68	shafei1	shafei1	PROPN
ejpam-3312	1	69	,	,	PUNCT
ejpam-3312	1	70	baravan	baravan	ADJ
ejpam-3312	1	71	a.	a.	NOUN
ejpam-3312	1	72	asaad3,4	asaad3,4	PROPN
ejpam-3312	1	73	1	1	NUM
ejpam-3312	1	74	department	department	NOUN
ejpam-3312	1	75	of	of	ADP
ejpam-3312	1	76	mathematics	mathematic	NOUN
ejpam-3312	1	77	,	,	PUNCT
ejpam-3312	1	78	faculty	faculty	NOUN
ejpam-3312	1	79	of	of	ADP
ejpam-3312	1	80	science	science	NOUN
ejpam-3312	1	81	,	,	PUNCT
ejpam-3312	1	82	mansoura	mansoura	PROPN
ejpam-3312	1	83	university	university	NOUN
ejpam-3312	1	84	,	,	PUNCT
ejpam-3312	1	85	mansoura	mansoura	PROPN
ejpam-3312	1	86	,	,	PUNCT
ejpam-3312	1	87	egypt	egypt	PROPN
ejpam-3312	1	88	2	2	NUM
ejpam-3312	1	89	department	department	NOUN
ejpam-3312	1	90	of	of	ADP
ejpam-3312	1	91	mathematics	mathematic	NOUN
ejpam-3312	1	92	,	,	PUNCT
ejpam-3312	1	93	sana’a	sana’a	NOUN
ejpam-3312	1	94	university	university	NOUN
ejpam-3312	1	95	,	,	PUNCT
ejpam-3312	1	96	sana’a	sana’a	NOUN
ejpam-3312	1	97	,	,	PUNCT
ejpam-3312	1	98	yemen	yemen	PROPN
ejpam-3312	1	99	3	3	NUM
ejpam-3312	1	100	department	department	NOUN
ejpam-3312	1	101	of	of	ADP
ejpam-3312	1	102	computer	computer	NOUN
ejpam-3312	1	103	science	science	NOUN
ejpam-3312	1	104	,	,	PUNCT
ejpam-3312	1	105	college	college	NOUN
ejpam-3312	1	106	of	of	ADP
ejpam-3312	1	107	science	science	NOUN
ejpam-3312	1	108	,	,	PUNCT
ejpam-3312	1	109	cihan	cihan	VERB
ejpam-3312	1	110	university	university	NOUN
ejpam-3312	1	111	-	-	PUNCT
ejpam-3312	1	112	duhok	duhok	NOUN
ejpam-3312	1	113	,	,	PUNCT
ejpam-3312	1	114	kurdistan	kurdistan	ADJ
ejpam-3312	1	115	region	region	NOUN
ejpam-3312	1	116	,	,	PUNCT
ejpam-3312	1	117	iraq	iraq	PROPN
ejpam-3312	1	118	4	4	NUM
ejpam-3312	1	119	department	department	NOUN
ejpam-3312	1	120	of	of	ADP
ejpam-3312	1	121	mathematics	mathematic	NOUN
ejpam-3312	1	122	,	,	PUNCT
ejpam-3312	1	123	faculty	faculty	NOUN
ejpam-3312	1	124	of	of	ADP
ejpam-3312	1	125	science	science	NOUN
ejpam-3312	1	126	,	,	PUNCT
ejpam-3312	1	127	university	university	NOUN
ejpam-3312	1	128	of	of	ADP
ejpam-3312	1	129	zakho	zakho	PROPN
ejpam-3312	1	130	,	,	PUNCT
ejpam-3312	1	131	kurdistan	kurdistan	ADJ
ejpam-3312	1	132	region	region	NOUN
ejpam-3312	1	133	,	,	PUNCT
ejpam-3312	1	134	iraq	iraq	PROPN
ejpam-3312	1	135	abstract	abstract	NOUN
ejpam-3312	1	136	.	.	PUNCT
ejpam-3312	2	1	the	the	DET
ejpam-3312	2	2	authors	author	NOUN
ejpam-3312	2	3	of	of	ADP
ejpam-3312	2	4	[	[	X
ejpam-3312	2	5	13	13	NUM
ejpam-3312	2	6	]	]	PUNCT
ejpam-3312	2	7	formulated	formulate	VERB
ejpam-3312	2	8	a	a	DET
ejpam-3312	2	9	soft	soft	ADJ
ejpam-3312	2	10	topological	topological	ADJ
ejpam-3312	2	11	ordered	order	VERB
ejpam-3312	2	12	spaces	space	NOUN
ejpam-3312	2	13	concept	concept	NOUN
ejpam-3312	2	14	and	and	CCONJ
ejpam-3312	2	15	then	then	ADV
ejpam-3312	2	16	they	they	PRON
ejpam-3312	2	17	established	establish	VERB
ejpam-3312	2	18	and	and	CCONJ
ejpam-3312	2	19	studied	study	VERB
ejpam-3312	2	20	some	some	DET
ejpam-3312	2	21	ordered	order	VERB
ejpam-3312	2	22	mappings	mapping	NOUN
ejpam-3312	2	23	[	[	X
ejpam-3312	2	24	14	14	NUM
ejpam-3312	2	25	]	]	PUNCT
ejpam-3312	2	26	.	.	PUNCT
ejpam-3312	3	1	in	in	ADP
ejpam-3312	3	2	the	the	DET
ejpam-3312	3	3	present	present	ADJ
ejpam-3312	3	4	work	work	NOUN
ejpam-3312	3	5	,	,	PUNCT
ejpam-3312	3	6	we	we	PRON
ejpam-3312	3	7	define	define	VERB
ejpam-3312	3	8	new	new	ADJ
ejpam-3312	3	9	ordered	order	VERB
ejpam-3312	3	10	mappings	mapping	NOUN
ejpam-3312	3	11	via	via	ADP
ejpam-3312	3	12	soft	soft	ADJ
ejpam-3312	3	13	topological	topological	ADJ
ejpam-3312	3	14	ordered	order	VERB
ejpam-3312	3	15	spaces	space	NOUN
ejpam-3312	3	16	based	base	VERB
ejpam-3312	3	17	on	on	ADP
ejpam-3312	3	18	soft	soft	ADJ
ejpam-3312	3	19	β	β	NOUN
ejpam-3312	3	20	-	-	ADJ
ejpam-3312	3	21	open	open	ADJ
ejpam-3312	3	22	sets	set	NOUN
ejpam-3312	3	23	,	,	PUNCT
ejpam-3312	3	24	namely	namely	ADV
ejpam-3312	3	25	soft	soft	ADJ
ejpam-3312	3	26	xβ	xβ	NOUN
ejpam-3312	3	27	-	-	PUNCT
ejpam-3312	3	28	continuous	continuous	ADJ
ejpam-3312	3	29	,	,	PUNCT
ejpam-3312	3	30	soft	soft	ADJ
ejpam-3312	3	31	xβ	xβ	NOUN
ejpam-3312	3	32	-	-	ADJ
ejpam-3312	3	33	open	open	ADJ
ejpam-3312	3	34	,	,	PUNCT
ejpam-3312	3	35	soft	soft	ADJ
ejpam-3312	3	36	xβ	xβ	NOUN
ejpam-3312	3	37	-	-	PUNCT
ejpam-3312	3	38	closed	closed	ADJ
ejpam-3312	3	39	and	and	CCONJ
ejpam-3312	3	40	soft	soft	ADJ
ejpam-3312	3	41	xβ	xβ	NOUN
ejpam-3312	3	42	-	-	PUNCT
ejpam-3312	3	43	homeomorphism	homeomorphism	NOUN
ejpam-3312	3	44	mappings	mapping	NOUN
ejpam-3312	3	45	,	,	PUNCT
ejpam-3312	3	46	for	for	ADP
ejpam-3312	3	47	x	x	PROPN
ejpam-3312	3	48	∈	∈	PROPN
ejpam-3312	3	49	{	{	PUNCT
ejpam-3312	3	50	i	i	PROPN
ejpam-3312	3	51	,	,	PUNCT
ejpam-3312	3	52	d	d	PROPN
ejpam-3312	3	53	,	,	PUNCT
ejpam-3312	3	54	b	b	NOUN
ejpam-3312	3	55	}	}	PUNCT
ejpam-3312	3	56	.	.	PUNCT
ejpam-3312	4	1	we	we	PRON
ejpam-3312	4	2	give	give	VERB
ejpam-3312	4	3	various	various	ADJ
ejpam-3312	4	4	characterizations	characterization	NOUN
ejpam-3312	4	5	of	of	ADP
ejpam-3312	4	6	each	each	DET
ejpam-3312	4	7	one	one	NUM
ejpam-3312	4	8	of	of	ADP
ejpam-3312	4	9	the	the	DET
ejpam-3312	4	10	introduced	introduce	VERB
ejpam-3312	4	11	soft	soft	ADJ
ejpam-3312	4	12	mappings	mapping	NOUN
ejpam-3312	4	13	.	.	PUNCT
ejpam-3312	5	1	one	one	NUM
ejpam-3312	5	2	of	of	ADP
ejpam-3312	5	3	the	the	DET
ejpam-3312	5	4	most	most	ADV
ejpam-3312	5	5	important	important	ADJ
ejpam-3312	5	6	obtained	obtain	VERB
ejpam-3312	5	7	results	result	NOUN
ejpam-3312	5	8	is	be	AUX
ejpam-3312	5	9	that	that	SCONJ
ejpam-3312	5	10	an	an	DET
ejpam-3312	5	11	extended	extended	ADJ
ejpam-3312	5	12	soft	soft	ADJ
ejpam-3312	5	13	topologies	topology	NOUN
ejpam-3312	5	14	notion	notion	NOUN
ejpam-3312	5	15	guarantees	guarantee	VERB
ejpam-3312	5	16	the	the	DET
ejpam-3312	5	17	equivalent	equivalent	NOUN
ejpam-3312	5	18	between	between	ADP
ejpam-3312	5	19	the	the	DET
ejpam-3312	5	20	soft	soft	ADJ
ejpam-3312	5	21	mappings	mapping	NOUN
ejpam-3312	5	22	initiated	initiate	VERB
ejpam-3312	5	23	herein	herein	NOUN
ejpam-3312	5	24	and	and	CCONJ
ejpam-3312	5	25	their	their	PRON
ejpam-3312	5	26	counterparts	counterpart	NOUN
ejpam-3312	5	27	of	of	ADP
ejpam-3312	5	28	mappings	mapping	NOUN
ejpam-3312	5	29	on	on	ADP
ejpam-3312	5	30	topological	topological	ADJ
ejpam-3312	5	31	ordered	order	VERB
ejpam-3312	5	32	spaces	space	NOUN
ejpam-3312	5	33	.	.	PUNCT
ejpam-3312	6	1	we	we	PRON
ejpam-3312	6	2	provide	provide	VERB
ejpam-3312	6	3	several	several	ADJ
ejpam-3312	6	4	interesting	interesting	ADJ
ejpam-3312	6	5	examples	example	NOUN
ejpam-3312	6	6	to	to	PART
ejpam-3312	6	7	examine	examine	VERB
ejpam-3312	6	8	the	the	DET
ejpam-3312	6	9	relationships	relationship	NOUN
ejpam-3312	6	10	among	among	ADP
ejpam-3312	6	11	these	these	DET
ejpam-3312	6	12	soft	soft	ADJ
ejpam-3312	6	13	mappings	mapping	NOUN
ejpam-3312	6	14	.	.	PUNCT
ejpam-3312	7	1	2010	2010	NUM
ejpam-3312	7	2	mathematics	mathematic	NOUN
ejpam-3312	7	3	subject	subject	NOUN
ejpam-3312	7	4	classifications	classification	NOUN
ejpam-3312	7	5	:	:	PUNCT
ejpam-3312	7	6	54f05	54f05	NUM
ejpam-3312	7	7	,	,	PUNCT
ejpam-3312	7	8	54f15	54f15	NUM
ejpam-3312	7	9	key	key	ADJ
ejpam-3312	7	10	words	word	NOUN
ejpam-3312	7	11	and	and	CCONJ
ejpam-3312	7	12	phrases	phrase	NOUN
ejpam-3312	7	13	:	:	PUNCT
ejpam-3312	7	14	soft	soft	ADJ
ejpam-3312	7	15	i(d	i(d	NOUN
ejpam-3312	7	16	,	,	PUNCT
ejpam-3312	7	17	b)β	b)β	NOUN
ejpam-3312	7	18	-	-	ADJ
ejpam-3312	7	19	continuous	continuous	ADJ
ejpam-3312	7	20	mapping	mapping	NOUN
ejpam-3312	7	21	;	;	PUNCT
ejpam-3312	7	22	soft	soft	ADJ
ejpam-3312	7	23	i(d	i(d	NOUN
ejpam-3312	7	24	,	,	PUNCT
ejpam-3312	7	25	b)β	b)β	NOUN
ejpam-3312	7	26	-	-	PUNCT
ejpam-3312	7	27	open	open	ADJ
ejpam-3312	7	28	mapping	mapping	NOUN
ejpam-3312	7	29	;	;	PUNCT
ejpam-3312	7	30	soft	soft	ADJ
ejpam-3312	7	31	i(d	i(d	NOUN
ejpam-3312	7	32	,	,	PUNCT
ejpam-3312	7	33	b)β	b)β	NOUN
ejpam-3312	7	34	-	-	PUNCT
ejpam-3312	7	35	homeomorphism	homeomorphism	NOUN
ejpam-3312	7	36	mapping	mapping	NOUN
ejpam-3312	7	37	and	and	CCONJ
ejpam-3312	7	38	soft	soft	ADJ
ejpam-3312	7	39	ordered	order	VERB
ejpam-3312	7	40	separation	separation	NOUN
ejpam-3312	7	41	axioms	axiom	NOUN
ejpam-3312	7	42	.	.	PUNCT
ejpam-3312	8	1	1	1	X
ejpam-3312	8	2	.	.	X
ejpam-3312	8	3	introduction	introduction	NOUN
ejpam-3312	8	4	in	in	ADP
ejpam-3312	8	5	the	the	DET
ejpam-3312	8	6	year	year	NOUN
ejpam-3312	8	7	1965	1965	NUM
ejpam-3312	8	8	,	,	PUNCT
ejpam-3312	8	9	nachbin	nachbin	PROPN
ejpam-3312	8	10	[	[	X
ejpam-3312	8	11	37	37	NUM
ejpam-3312	8	12	]	]	PUNCT
ejpam-3312	8	13	started	start	VERB
ejpam-3312	8	14	studying	study	VERB
ejpam-3312	8	15	the	the	DET
ejpam-3312	8	16	topological	topological	ADJ
ejpam-3312	8	17	ordered	order	VERB
ejpam-3312	8	18	spaces	space	NOUN
ejpam-3312	8	19	concept	concept	NOUN
ejpam-3312	8	20	by	by	ADP
ejpam-3312	8	21	defining	define	VERB
ejpam-3312	8	22	two	two	NUM
ejpam-3312	8	23	independent	independent	ADJ
ejpam-3312	8	24	mathematical	mathematical	ADJ
ejpam-3312	8	25	structures	structure	NOUN
ejpam-3312	8	26	,	,	PUNCT
ejpam-3312	8	27	on	on	ADP
ejpam-3312	8	28	a	a	DET
ejpam-3312	8	29	non	non	ADJ
ejpam-3312	8	30	-	-	ADJ
ejpam-3312	8	31	empty	empty	ADJ
ejpam-3312	8	32	set	set	NOUN
ejpam-3312	8	33	x	x	NOUN
ejpam-3312	8	34	,	,	PUNCT
ejpam-3312	8	35	namely	namely	ADV
ejpam-3312	8	36	a	a	DET
ejpam-3312	8	37	topology	topology	NOUN
ejpam-3312	8	38	τ	τ	PROPN
ejpam-3312	8	39	and	and	CCONJ
ejpam-3312	8	40	a	a	DET
ejpam-3312	8	41	partial	partial	ADJ
ejpam-3312	8	42	order	order	NOUN
ejpam-3312	8	43	relation	relation	NOUN
ejpam-3312	8	44	�	�	PROPN
ejpam-3312	8	45	.	.	PUNCT
ejpam-3312	9	1	depending	depend	VERB
ejpam-3312	9	2	on	on	ADP
ejpam-3312	9	3	these	these	DET
ejpam-3312	9	4	two	two	NUM
ejpam-3312	9	5	structures	structure	NOUN
ejpam-3312	9	6	,	,	PUNCT
ejpam-3312	9	7	he	he	PRON
ejpam-3312	9	8	redefine	redefine	VERB
ejpam-3312	9	9	and	and	CCONJ
ejpam-3312	9	10	reinvestigate	reinvestigate	VERB
ejpam-3312	9	11	some	some	DET
ejpam-3312	9	12	topological	topological	ADJ
ejpam-3312	9	13	concepts	concept	NOUN
ejpam-3312	9	14	such	such	ADJ
ejpam-3312	9	15	as	as	ADP
ejpam-3312	9	16	normal	normal	ADJ
ejpam-3312	9	17	,	,	PUNCT
ejpam-3312	9	18	regular	regular	ADJ
ejpam-3312	9	19	and	and	CCONJ
ejpam-3312	9	20	and	and	CCONJ
ejpam-3312	9	21	completely	completely	ADV
ejpam-3312	9	22	regular	regular	ADJ
ejpam-3312	9	23	spaces	space	NOUN
ejpam-3312	9	24	to	to	PART
ejpam-3312	9	25	be	be	AUX
ejpam-3312	9	26	normally	normally	ADV
ejpam-3312	9	27	ordered	order	VERB
ejpam-3312	9	28	,	,	PUNCT
ejpam-3312	9	29	regularly	regularly	ADV
ejpam-3312	9	30	ordered	order	VERB
ejpam-3312	9	31	and	and	CCONJ
ejpam-3312	9	32	completely	completely	ADV
ejpam-3312	9	33	regular	regular	ADJ
ejpam-3312	9	34	ordered	order	VERB
ejpam-3312	9	35	spaces	space	NOUN
ejpam-3312	9	36	,	,	PUNCT
ejpam-3312	9	37	respectively	respectively	ADV
ejpam-3312	9	38	,	,	PUNCT
ejpam-3312	9	39	on	on	ADP
ejpam-3312	9	40	topological	topological	ADJ
ejpam-3312	9	41	ordered	order	VERB
ejpam-3312	9	42	spaces	space	NOUN
ejpam-3312	9	43	.	.	PUNCT
ejpam-3312	10	1	later	later	ADV
ejpam-3312	10	2	on	on	ADV
ejpam-3312	10	3	,	,	PUNCT
ejpam-3312	10	4	mccartan	mccartan	ADJ
ejpam-3312	11	1	[	[	X
ejpam-3312	11	2	32	32	NUM
ejpam-3312	11	3	]	]	PUNCT
ejpam-3312	11	4	presented	present	VERB
ejpam-3312	11	5	the	the	DET
ejpam-3312	11	6	notions	notion	NOUN
ejpam-3312	11	7	of	of	ADP
ejpam-3312	11	8	ti	ti	NOUN
ejpam-3312	11	9	-	-	ADJ
ejpam-3312	11	10	ordered	order	VERB
ejpam-3312	11	11	and	and	CCONJ
ejpam-3312	11	12	strong	strong	ADJ
ejpam-3312	11	13	ti	ti	ADJ
ejpam-3312	11	14	-	-	ADJ
ejpam-3312	11	15	ordered	order	VERB
ejpam-3312	11	16	spaces	space	NOUN
ejpam-3312	11	17	(	(	PUNCT
ejpam-3312	11	18	i	i	NOUN
ejpam-3312	11	19	=	=	NOUN
ejpam-3312	11	20	0	0	NUM
ejpam-3312	11	21	,	,	PUNCT
ejpam-3312	11	22	1	1	NUM
ejpam-3312	11	23	,	,	PUNCT
ejpam-3312	11	24	2	2	NUM
ejpam-3312	11	25	,	,	PUNCT
ejpam-3312	11	26	3	3	NUM
ejpam-3312	11	27	,	,	PUNCT
ejpam-3312	11	28	4	4	NUM
ejpam-3312	11	29	)	)	PUNCT
ejpam-3312	11	30	and	and	CCONJ
ejpam-3312	11	31	compared	compare	VERB
ejpam-3312	11	32	them	they	PRON
ejpam-3312	11	33	with	with	ADP
ejpam-3312	11	34	ti	ti	NOUN
ejpam-3312	11	35	-	-	NOUN
ejpam-3312	11	36	spaces	space	NOUN
ejpam-3312	11	37	.	.	PUNCT
ejpam-3312	12	1	also	also	ADV
ejpam-3312	12	2	,	,	PUNCT
ejpam-3312	12	3	he	he	PRON
ejpam-3312	12	4	completely	completely	ADV
ejpam-3312	12	5	descried	descry	VERB
ejpam-3312	12	6	ti	ti	NOUN
ejpam-3312	12	7	-	-	ADJ
ejpam-3312	12	8	ordered	order	VERB
ejpam-3312	12	9	and	and	CCONJ
ejpam-3312	12	10	supplied	supply	VERB
ejpam-3312	12	11	interesting	interesting	ADJ
ejpam-3312	12	12	examples	example	NOUN
ejpam-3312	12	13	∗corresponding	∗corresponde	VERB
ejpam-3312	12	14	author	author	NOUN
ejpam-3312	12	15	.	.	PUNCT
ejpam-3312	13	1	doi	doi	NOUN
ejpam-3312	13	2	:	:	PUNCT
ejpam-3312	13	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3312	https://doi.org/10.29020/nybg.ejpam.v12i1.3312	ADJ
ejpam-3312	13	4	email	email	NOUN
ejpam-3312	13	5	addresses	address	VERB
ejpam-3312	13	6	:	:	PUNCT
ejpam-3312	13	7	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-3312	13	8	(	(	PUNCT
ejpam-3312	13	9	t.	t.	PROPN
ejpam-3312	13	10	m.	m.	PROPN
ejpam-3312	13	11	al	al	PROPN
ejpam-3312	13	12	-	-	PUNCT
ejpam-3312	13	13	shami	shami	PROPN
ejpam-3312	13	14	)	)	PUNCT
ejpam-3312	13	15	,	,	PUNCT
ejpam-3312	13	16	meshafei@hotmail.com	meshafei@hotmail.com	X
ejpam-3312	13	17	(	(	PUNCT
ejpam-3312	13	18	m.	m.	PROPN
ejpam-3312	13	19	e.	e.	PROPN
ejpam-3312	13	20	el	el	PROPN
ejpam-3312	13	21	-	-	PROPN
ejpam-3312	13	22	shafei	shafei	PROPN
ejpam-3312	13	23	)	)	PUNCT
ejpam-3312	13	24	,	,	PUNCT
ejpam-3312	13	25	baravan.asaad@uoz.edu.krd	baravan.asaad@uoz.edu.krd	PROPN
ejpam-3312	13	26	(	(	PUNCT
ejpam-3312	13	27	b.	b.	PROPN
ejpam-3312	13	28	a.	a.	PROPN
ejpam-3312	13	29	asaad	asaad	PROPN
ejpam-3312	13	30	)	)	PUNCT
ejpam-3312	13	31	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3312	14	1	176	176	NUM
ejpam-3312	15	1	c	c	X
ejpam-3312	15	2	©	©	PROPN
ejpam-3312	15	3	2019	2019	NUM
ejpam-3312	15	4	ejpam	ejpam	NOUN
ejpam-3312	15	5	all	all	DET
ejpam-3312	15	6	rights	right	NOUN
ejpam-3312	15	7	reserved	reserve	VERB
ejpam-3312	15	8	.	.	PUNCT
ejpam-3312	16	1	t.	t.	PROPN
ejpam-3312	16	2	m.	m.	PROPN
ejpam-3312	16	3	al	al	PROPN
ejpam-3312	16	4	-	-	PUNCT
ejpam-3312	16	5	shami	shami	PROPN
ejpam-3312	16	6	,	,	PUNCT
ejpam-3312	16	7	m.	m.	PROPN
ejpam-3312	16	8	e.	e.	PROPN
ejpam-3312	16	9	el	el	PROPN
ejpam-3312	16	10	-	-	PROPN
ejpam-3312	16	11	shafei	shafei	PROPN
ejpam-3312	16	12	,	,	PUNCT
ejpam-3312	16	13	b.	b.	PROPN
ejpam-3312	16	14	a.	a.	PROPN
ejpam-3312	16	15	asaad	asaad	PROPN
ejpam-3312	16	16	/	/	SYM
ejpam-3312	16	17	eur	eur	PROPN
ejpam-3312	16	18	.	.	PUNCT
ejpam-3312	17	1	j.	j.	PROPN
ejpam-3312	17	2	pure	pure	PROPN
ejpam-3312	17	3	appl	appl	PROPN
ejpam-3312	17	4	.	.	PROPN
ejpam-3312	17	5	math	math	PROPN
ejpam-3312	17	6	,	,	PUNCT
ejpam-3312	17	7	12	12	NUM
ejpam-3312	17	8	(	(	PUNCT
ejpam-3312	17	9	1	1	NUM
ejpam-3312	17	10	)	)	PUNCT
ejpam-3312	17	11	(	(	PUNCT
ejpam-3312	17	12	2019	2019	NUM
ejpam-3312	17	13	)	)	PUNCT
ejpam-3312	17	14	,	,	PUNCT
ejpam-3312	17	15	176	176	NUM
ejpam-3312	17	16	-	-	SYM
ejpam-3312	17	17	193	193	NUM
ejpam-3312	17	18	177	177	NUM
ejpam-3312	17	19	to	to	PART
ejpam-3312	17	20	illustrate	illustrate	VERB
ejpam-3312	17	21	the	the	DET
ejpam-3312	17	22	concepts	concept	NOUN
ejpam-3312	17	23	introduced	introduce	VERB
ejpam-3312	17	24	and	and	CCONJ
ejpam-3312	17	25	findings	finding	NOUN
ejpam-3312	17	26	obtained	obtain	VERB
ejpam-3312	17	27	therein	therein	ADV
ejpam-3312	17	28	.	.	PUNCT
ejpam-3312	18	1	based	base	VERB
ejpam-3312	18	2	on	on	ADP
ejpam-3312	18	3	β	β	ADJ
ejpam-3312	18	4	-	-	ADJ
ejpam-3312	18	5	open	open	ADJ
ejpam-3312	18	6	sets	set	NOUN
ejpam-3312	18	7	[	[	X
ejpam-3312	18	8	2	2	NUM
ejpam-3312	18	9	]	]	PUNCT
ejpam-3312	18	10	,	,	PUNCT
ejpam-3312	18	11	leela	leela	PROPN
ejpam-3312	18	12	and	and	CCONJ
ejpam-3312	18	13	balasubramanian	balasubramanian	ADJ
ejpam-3312	18	14	[	[	X
ejpam-3312	18	15	28	28	NUM
ejpam-3312	18	16	]	]	PUNCT
ejpam-3312	18	17	in	in	ADP
ejpam-3312	18	18	2002	2002	NUM
ejpam-3312	18	19	,	,	PUNCT
ejpam-3312	18	20	probed	probe	VERB
ejpam-3312	18	21	new	new	ADJ
ejpam-3312	18	22	ordered	order	VERB
ejpam-3312	18	23	axioms	axiom	NOUN
ejpam-3312	18	24	;	;	PUNCT
ejpam-3312	18	25	and	and	CCONJ
ejpam-3312	18	26	rao	rao	NOUN
ejpam-3312	18	27	and	and	CCONJ
ejpam-3312	18	28	chudamani	chudamani	ADJ
ejpam-3312	19	1	[	[	X
ejpam-3312	19	2	42	42	NUM
ejpam-3312	19	3	]	]	PUNCT
ejpam-3312	19	4	in	in	ADP
ejpam-3312	19	5	2012	2012	NUM
ejpam-3312	19	6	,	,	PUNCT
ejpam-3312	19	7	defined	define	VERB
ejpam-3312	19	8	new	new	ADJ
ejpam-3312	19	9	kinds	kind	NOUN
ejpam-3312	19	10	of	of	ADP
ejpam-3312	19	11	continuous	continuous	ADJ
ejpam-3312	19	12	and	and	CCONJ
ejpam-3312	19	13	homeomorphism	homeomorphism	ADJ
ejpam-3312	19	14	mappings	mapping	NOUN
ejpam-3312	19	15	on	on	ADP
ejpam-3312	19	16	topological	topological	ADJ
ejpam-3312	19	17	ordered	order	VERB
ejpam-3312	19	18	spaces	space	NOUN
ejpam-3312	19	19	.	.	PUNCT
ejpam-3312	20	1	with	with	ADP
ejpam-3312	20	2	regard	regard	NOUN
ejpam-3312	20	3	to	to	ADP
ejpam-3312	20	4	the	the	DET
ejpam-3312	20	5	generalizations	generalization	NOUN
ejpam-3312	20	6	of	of	ADP
ejpam-3312	20	7	topological	topological	ADJ
ejpam-3312	20	8	ordered	order	VERB
ejpam-3312	20	9	spaces	space	NOUN
ejpam-3312	20	10	,	,	PUNCT
ejpam-3312	20	11	we	we	PRON
ejpam-3312	20	12	observe	observe	VERB
ejpam-3312	20	13	that	that	SCONJ
ejpam-3312	20	14	this	this	DET
ejpam-3312	20	15	topic	topic	NOUN
ejpam-3312	20	16	takes	take	VERB
ejpam-3312	20	17	two	two	NUM
ejpam-3312	20	18	directions	direction	NOUN
ejpam-3312	20	19	,	,	PUNCT
ejpam-3312	20	20	the	the	DET
ejpam-3312	20	21	first	first	ADJ
ejpam-3312	20	22	one	one	NOUN
ejpam-3312	20	23	is	be	AUX
ejpam-3312	20	24	formulated	formulate	VERB
ejpam-3312	20	25	by	by	ADP
ejpam-3312	20	26	generalizing	generalize	VERB
ejpam-3312	20	27	a	a	DET
ejpam-3312	20	28	partial	partial	ADJ
ejpam-3312	20	29	order	order	NOUN
ejpam-3312	20	30	relation	relation	NOUN
ejpam-3312	20	31	(	(	PUNCT
ejpam-3312	20	32	see	see	VERB
ejpam-3312	20	33	,	,	PUNCT
ejpam-3312	20	34	for	for	ADP
ejpam-3312	20	35	example	example	NOUN
ejpam-3312	20	36	,	,	PUNCT
ejpam-3312	21	1	[	[	X
ejpam-3312	21	2	25	25	NUM
ejpam-3312	21	3	]	]	PUNCT
ejpam-3312	21	4	,	,	PUNCT
ejpam-3312	21	5	[	[	X
ejpam-3312	21	6	33	33	NUM
ejpam-3312	21	7	]	]	PUNCT
ejpam-3312	21	8	,	,	PUNCT
ejpam-3312	21	9	[	[	X
ejpam-3312	21	10	34	34	NUM
ejpam-3312	21	11	]	]	PUNCT
ejpam-3312	21	12	,	,	PUNCT
ejpam-3312	21	13	[	[	X
ejpam-3312	21	14	40	40	NUM
ejpam-3312	21	15	]	]	PUNCT
ejpam-3312	21	16	)	)	PUNCT
ejpam-3312	21	17	and	and	CCONJ
ejpam-3312	21	18	the	the	DET
ejpam-3312	21	19	second	second	ADJ
ejpam-3312	21	20	one	one	NOUN
ejpam-3312	21	21	is	be	AUX
ejpam-3312	21	22	formulated	formulate	VERB
ejpam-3312	21	23	by	by	ADP
ejpam-3312	21	24	generalizing	generalize	VERB
ejpam-3312	21	25	a	a	DET
ejpam-3312	21	26	topology	topology	NOUN
ejpam-3312	21	27	(	(	PUNCT
ejpam-3312	21	28	see	see	VERB
ejpam-3312	21	29	,	,	PUNCT
ejpam-3312	21	30	for	for	ADP
ejpam-3312	21	31	example	example	NOUN
ejpam-3312	21	32	,	,	PUNCT
ejpam-3312	21	33	[	[	X
ejpam-3312	21	34	3	3	NUM
ejpam-3312	21	35	]	]	PUNCT
ejpam-3312	21	36	,	,	PUNCT
ejpam-3312	22	1	[	[	X
ejpam-3312	22	2	8	8	NUM
ejpam-3312	22	3	]	]	PUNCT
ejpam-3312	22	4	,	,	PUNCT
ejpam-3312	22	5	[	[	X
ejpam-3312	22	6	10	10	NUM
ejpam-3312	22	7	]	]	PUNCT
ejpam-3312	22	8	,	,	PUNCT
ejpam-3312	22	9	[	[	X
ejpam-3312	22	10	12	12	NUM
ejpam-3312	22	11	]	]	PUNCT
ejpam-3312	22	12	,	,	PUNCT
ejpam-3312	22	13	[	[	X
ejpam-3312	22	14	18	18	NUM
ejpam-3312	22	15	]	]	PUNCT
ejpam-3312	22	16	,	,	PUNCT
ejpam-3312	22	17	[	[	X
ejpam-3312	22	18	20	20	NUM
ejpam-3312	22	19	]	]	PUNCT
ejpam-3312	22	20	,	,	PUNCT
ejpam-3312	22	21	[	[	X
ejpam-3312	22	22	21	21	NUM
ejpam-3312	22	23	]	]	PUNCT
ejpam-3312	22	24	)	)	PUNCT
ejpam-3312	22	25	.	.	PUNCT
ejpam-3312	23	1	to	to	PART
ejpam-3312	23	2	handle	handle	VERB
ejpam-3312	23	3	problems	problem	NOUN
ejpam-3312	23	4	and	and	CCONJ
ejpam-3312	23	5	phenomena	phenomenon	NOUN
ejpam-3312	23	6	which	which	PRON
ejpam-3312	23	7	suffering	suffer	VERB
ejpam-3312	23	8	from	from	ADP
ejpam-3312	23	9	uncertainties	uncertainty	NOUN
ejpam-3312	23	10	and	and	CCONJ
ejpam-3312	23	11	incomplete	incomplete	ADJ
ejpam-3312	23	12	of	of	ADP
ejpam-3312	23	13	data	datum	NOUN
ejpam-3312	23	14	,	,	PUNCT
ejpam-3312	23	15	molotdsov	molotdsov	NOUN
ejpam-3312	24	1	[	[	X
ejpam-3312	24	2	36	36	NUM
ejpam-3312	24	3	]	]	PUNCT
ejpam-3312	24	4	in	in	ADP
ejpam-3312	24	5	1999	1999	NUM
ejpam-3312	24	6	,	,	PUNCT
ejpam-3312	24	7	proposed	propose	VERB
ejpam-3312	24	8	a	a	DET
ejpam-3312	24	9	new	new	ADJ
ejpam-3312	24	10	mathematical	mathematical	ADJ
ejpam-3312	24	11	tool	tool	NOUN
ejpam-3312	24	12	,	,	PUNCT
ejpam-3312	24	13	namely	namely	ADV
ejpam-3312	24	14	soft	soft	ADJ
ejpam-3312	24	15	sets	set	NOUN
ejpam-3312	24	16	.	.	PUNCT
ejpam-3312	25	1	he	he	PRON
ejpam-3312	25	2	pointed	point	VERB
ejpam-3312	25	3	out	out	ADP
ejpam-3312	25	4	that	that	SCONJ
ejpam-3312	25	5	the	the	DET
ejpam-3312	25	6	previous	previous	ADJ
ejpam-3312	25	7	theories	theory	NOUN
ejpam-3312	25	8	such	such	ADJ
ejpam-3312	25	9	as	as	ADP
ejpam-3312	25	10	probability	probability	NOUN
ejpam-3312	25	11	and	and	CCONJ
ejpam-3312	25	12	fuzzy	fuzzy	ADJ
ejpam-3312	25	13	set	set	NOUN
ejpam-3312	25	14	theory	theory	NOUN
ejpam-3312	25	15	have	have	VERB
ejpam-3312	25	16	difficulties	difficulty	NOUN
ejpam-3312	25	17	which	which	PRON
ejpam-3312	25	18	attributed	attribute	VERB
ejpam-3312	25	19	to	to	ADP
ejpam-3312	25	20	the	the	DET
ejpam-3312	25	21	inadequacies	inadequacy	NOUN
ejpam-3312	25	22	of	of	ADP
ejpam-3312	25	23	their	their	PRON
ejpam-3312	25	24	parameterizations	parameterization	NOUN
ejpam-3312	25	25	tools	tool	NOUN
ejpam-3312	25	26	and	and	CCONJ
ejpam-3312	25	27	show	show	VERB
ejpam-3312	25	28	that	that	SCONJ
ejpam-3312	25	29	soft	soft	ADJ
ejpam-3312	25	30	set	set	NOUN
ejpam-3312	25	31	theory	theory	NOUN
ejpam-3312	25	32	is	be	AUX
ejpam-3312	25	33	more	more	ADV
ejpam-3312	25	34	suitable	suitable	ADJ
ejpam-3312	25	35	for	for	ADP
ejpam-3312	25	36	dealing	deal	VERB
ejpam-3312	25	37	with	with	ADP
ejpam-3312	25	38	uncertainties	uncertainty	NOUN
ejpam-3312	25	39	with	with	ADP
ejpam-3312	25	40	adequate	adequate	ADJ
ejpam-3312	25	41	parameterizations	parameterization	NOUN
ejpam-3312	25	42	.	.	PUNCT
ejpam-3312	26	1	maji	maji	PROPN
ejpam-3312	26	2	et	et	PROPN
ejpam-3312	26	3	al	al	PROPN
ejpam-3312	26	4	.	.	PUNCT
ejpam-3312	27	1	[	[	X
ejpam-3312	27	2	31	31	NUM
ejpam-3312	27	3	]	]	PUNCT
ejpam-3312	27	4	introduced	introduce	VERB
ejpam-3312	27	5	some	some	DET
ejpam-3312	27	6	soft	soft	ADJ
ejpam-3312	27	7	operators	operator	NOUN
ejpam-3312	27	8	such	such	ADJ
ejpam-3312	27	9	as	as	ADP
ejpam-3312	27	10	soft	soft	ADJ
ejpam-3312	27	11	equality	equality	NOUN
ejpam-3312	27	12	relation	relation	NOUN
ejpam-3312	27	13	,	,	PUNCT
ejpam-3312	27	14	soft	soft	ADJ
ejpam-3312	27	15	union	union	NOUN
ejpam-3312	27	16	and	and	CCONJ
ejpam-3312	27	17	intersection	intersection	NOUN
ejpam-3312	27	18	between	between	ADP
ejpam-3312	27	19	two	two	NUM
ejpam-3312	27	20	soft	soft	ADJ
ejpam-3312	27	21	sets	set	NOUN
ejpam-3312	27	22	.	.	PUNCT
ejpam-3312	28	1	these	these	DET
ejpam-3312	28	2	soft	soft	ADJ
ejpam-3312	28	3	operators	operator	NOUN
ejpam-3312	28	4	were	be	AUX
ejpam-3312	28	5	generalized	generalize	VERB
ejpam-3312	28	6	and	and	CCONJ
ejpam-3312	28	7	studied	study	VERB
ejpam-3312	28	8	in	in	ADP
ejpam-3312	28	9	several	several	ADJ
ejpam-3312	28	10	directions	direction	NOUN
ejpam-3312	28	11	in	in	ADP
ejpam-3312	28	12	[	[	X
ejpam-3312	28	13	17	17	NUM
ejpam-3312	28	14	]	]	PUNCT
ejpam-3312	28	15	,	,	PUNCT
ejpam-3312	28	16	[	[	X
ejpam-3312	28	17	24	24	NUM
ejpam-3312	28	18	]	]	PUNCT
ejpam-3312	28	19	,	,	PUNCT
ejpam-3312	28	20	[	[	X
ejpam-3312	28	21	29	29	NUM
ejpam-3312	28	22	]	]	PUNCT
ejpam-3312	28	23	,	,	PUNCT
ejpam-3312	28	24	[	[	X
ejpam-3312	28	25	30	30	NUM
ejpam-3312	28	26	]	]	PUNCT
ejpam-3312	28	27	and	and	CCONJ
ejpam-3312	28	28	[	[	X
ejpam-3312	28	29	41	41	NUM
ejpam-3312	28	30	]	]	PUNCT
ejpam-3312	28	31	.	.	PUNCT
ejpam-3312	29	1	aktas	akta	NOUN
ejpam-3312	29	2	and	and	CCONJ
ejpam-3312	29	3	cağman	cağman	PROPN
ejpam-3312	30	1	[	[	X
ejpam-3312	30	2	6	6	NUM
ejpam-3312	30	3	]	]	PUNCT
ejpam-3312	30	4	were	be	AUX
ejpam-3312	30	5	the	the	DET
ejpam-3312	30	6	first	first	ADJ
ejpam-3312	30	7	who	who	PRON
ejpam-3312	30	8	studied	study	VERB
ejpam-3312	30	9	soft	soft	ADJ
ejpam-3312	30	10	algebraic	algebraic	ADJ
ejpam-3312	30	11	structure	structure	NOUN
ejpam-3312	30	12	.	.	PUNCT
ejpam-3312	31	1	they	they	PRON
ejpam-3312	31	2	introduced	introduce	VERB
ejpam-3312	31	3	the	the	DET
ejpam-3312	31	4	soft	soft	ADJ
ejpam-3312	31	5	group	group	NOUN
ejpam-3312	31	6	and	and	CCONJ
ejpam-3312	31	7	soft	soft	ADJ
ejpam-3312	31	8	subgroup	subgroup	NOUN
ejpam-3312	31	9	notions	notion	NOUN
ejpam-3312	31	10	and	and	CCONJ
ejpam-3312	31	11	concluded	conclude	VERB
ejpam-3312	31	12	their	their	PRON
ejpam-3312	31	13	basic	basic	ADJ
ejpam-3312	31	14	properties	property	NOUN
ejpam-3312	31	15	.	.	PUNCT
ejpam-3312	32	1	in	in	ADP
ejpam-3312	32	2	2010	2010	NUM
ejpam-3312	32	3	,	,	PUNCT
ejpam-3312	32	4	acar	acar	VERB
ejpam-3312	32	5	et	et	PROPN
ejpam-3312	32	6	al	al	PROPN
ejpam-3312	32	7	.	.	PUNCT
ejpam-3312	33	1	[	[	X
ejpam-3312	33	2	4	4	X
ejpam-3312	33	3	]	]	PUNCT
ejpam-3312	33	4	presented	present	VERB
ejpam-3312	33	5	a	a	DET
ejpam-3312	33	6	concept	concept	NOUN
ejpam-3312	33	7	of	of	ADP
ejpam-3312	33	8	soft	soft	ADJ
ejpam-3312	33	9	rings	ring	NOUN
ejpam-3312	33	10	and	and	CCONJ
ejpam-3312	33	11	investigated	investigate	VERB
ejpam-3312	33	12	its	its	PRON
ejpam-3312	33	13	main	main	ADJ
ejpam-3312	33	14	features	feature	NOUN
ejpam-3312	33	15	;	;	PUNCT
ejpam-3312	33	16	and	and	CCONJ
ejpam-3312	33	17	in	in	ADP
ejpam-3312	33	18	2013	2013	NUM
ejpam-3312	33	19	,	,	PUNCT
ejpam-3312	33	20	shah	shah	NOUN
ejpam-3312	33	21	and	and	CCONJ
ejpam-3312	33	22	shaheen	shaheen	PROPN
ejpam-3312	34	1	[	[	X
ejpam-3312	34	2	45	45	NUM
ejpam-3312	34	3	]	]	PUNCT
ejpam-3312	34	4	established	establish	VERB
ejpam-3312	34	5	the	the	DET
ejpam-3312	34	6	notions	notion	NOUN
ejpam-3312	34	7	of	of	ADP
ejpam-3312	34	8	a	a	DET
ejpam-3312	34	9	soft	soft	ADJ
ejpam-3312	34	10	topological	topological	ADJ
ejpam-3312	34	11	group	group	NOUN
ejpam-3312	34	12	and	and	CCONJ
ejpam-3312	34	13	a	a	DET
ejpam-3312	34	14	soft	soft	ADJ
ejpam-3312	34	15	topological	topological	ADJ
ejpam-3312	34	16	ring	ring	NOUN
ejpam-3312	34	17	over	over	ADP
ejpam-3312	34	18	a	a	DET
ejpam-3312	34	19	group	group	NOUN
ejpam-3312	34	20	and	and	CCONJ
ejpam-3312	34	21	a	a	DET
ejpam-3312	34	22	ring	ring	NOUN
ejpam-3312	34	23	,	,	PUNCT
ejpam-3312	34	24	respectively	respectively	ADV
ejpam-3312	34	25	.	.	PUNCT
ejpam-3312	35	1	hida	hida	PROPN
ejpam-3312	36	1	[	[	X
ejpam-3312	36	2	27	27	NUM
ejpam-3312	36	3	]	]	PUNCT
ejpam-3312	36	4	adopted	adopt	VERB
ejpam-3312	36	5	a	a	DET
ejpam-3312	36	6	differen	differen	NOUN
ejpam-3312	36	7	view	view	NOUN
ejpam-3312	36	8	to	to	PART
ejpam-3312	36	9	define	define	VERB
ejpam-3312	36	10	soft	soft	ADJ
ejpam-3312	36	11	topological	topological	ADJ
ejpam-3312	36	12	group	group	NOUN
ejpam-3312	36	13	which	which	PRON
ejpam-3312	36	14	help	help	VERB
ejpam-3312	36	15	to	to	PART
ejpam-3312	36	16	make	make	VERB
ejpam-3312	36	17	it	it	PRON
ejpam-3312	36	18	a	a	DET
ejpam-3312	36	19	natural	natural	ADJ
ejpam-3312	36	20	extension	extension	NOUN
ejpam-3312	36	21	of	of	ADP
ejpam-3312	36	22	the	the	DET
ejpam-3312	36	23	usual	usual	ADJ
ejpam-3312	36	24	topological	topological	ADJ
ejpam-3312	36	25	group	group	NOUN
ejpam-3312	36	26	notion	notion	NOUN
ejpam-3312	36	27	.	.	PUNCT
ejpam-3312	37	1	in	in	ADP
ejpam-3312	37	2	the	the	DET
ejpam-3312	37	3	year	year	NOUN
ejpam-3312	37	4	2011	2011	NUM
ejpam-3312	37	5	,	,	PUNCT
ejpam-3312	37	6	shabir	shabir	NOUN
ejpam-3312	37	7	and	and	CCONJ
ejpam-3312	37	8	naz	naz	PROPN
ejpam-3312	38	1	[	[	X
ejpam-3312	38	2	44	44	NUM
ejpam-3312	38	3	]	]	PUNCT
ejpam-3312	38	4	initiated	initiate	VERB
ejpam-3312	38	5	the	the	DET
ejpam-3312	38	6	concept	concept	NOUN
ejpam-3312	38	7	of	of	ADP
ejpam-3312	38	8	soft	soft	ADJ
ejpam-3312	38	9	topological	topological	ADJ
ejpam-3312	38	10	spaces	space	NOUN
ejpam-3312	38	11	and	and	CCONJ
ejpam-3312	38	12	gave	give	VERB
ejpam-3312	38	13	its	its	PRON
ejpam-3312	38	14	fundamental	fundamental	ADJ
ejpam-3312	38	15	notions	notion	NOUN
ejpam-3312	38	16	such	such	ADJ
ejpam-3312	38	17	as	as	ADP
ejpam-3312	38	18	soft	soft	ADJ
ejpam-3312	38	19	open	open	ADJ
ejpam-3312	38	20	and	and	CCONJ
ejpam-3312	38	21	soft	soft	ADJ
ejpam-3312	38	22	closed	closed	ADJ
ejpam-3312	38	23	sets	set	NOUN
ejpam-3312	38	24	,	,	PUNCT
ejpam-3312	38	25	soft	soft	ADJ
ejpam-3312	38	26	neighborhoods	neighborhood	NOUN
ejpam-3312	38	27	,	,	PUNCT
ejpam-3312	38	28	soft	soft	ADJ
ejpam-3312	38	29	interior	interior	ADJ
ejpam-3312	38	30	and	and	CCONJ
ejpam-3312	38	31	soft	soft	ADJ
ejpam-3312	38	32	closure	closure	NOUN
ejpam-3312	38	33	points	point	NOUN
ejpam-3312	38	34	.	.	PUNCT
ejpam-3312	39	1	they	they	PRON
ejpam-3312	39	2	also	also	ADV
ejpam-3312	39	3	probed	probe	VERB
ejpam-3312	39	4	soft	soft	ADJ
ejpam-3312	39	5	separation	separation	NOUN
ejpam-3312	39	6	axioms	axiom	NOUN
ejpam-3312	39	7	and	and	CCONJ
ejpam-3312	39	8	examined	examine	VERB
ejpam-3312	39	9	their	their	PRON
ejpam-3312	39	10	properties	property	NOUN
ejpam-3312	39	11	.	.	PUNCT
ejpam-3312	40	1	min	min	NOUN
ejpam-3312	41	1	[	[	X
ejpam-3312	41	2	35	35	NUM
ejpam-3312	41	3	]	]	PUNCT
ejpam-3312	41	4	gave	give	VERB
ejpam-3312	41	5	deeper	deep	ADJ
ejpam-3312	41	6	explanation	explanation	NOUN
ejpam-3312	41	7	for	for	ADP
ejpam-3312	41	8	soft	soft	ADJ
ejpam-3312	41	9	regular	regular	ADJ
ejpam-3312	41	10	spaces	space	NOUN
ejpam-3312	41	11	and	and	CCONJ
ejpam-3312	41	12	corrected	correct	VERB
ejpam-3312	41	13	some	some	DET
ejpam-3312	41	14	errors	error	NOUN
ejpam-3312	41	15	in	in	ADP
ejpam-3312	41	16	[	[	X
ejpam-3312	41	17	44	44	NUM
ejpam-3312	41	18	]	]	PUNCT
ejpam-3312	41	19	.	.	PUNCT
ejpam-3312	42	1	later	later	ADV
ejpam-3312	42	2	on	on	ADV
ejpam-3312	42	3	,	,	PUNCT
ejpam-3312	42	4	desire	desire	NOUN
ejpam-3312	42	5	of	of	ADP
ejpam-3312	42	6	obtaining	obtain	VERB
ejpam-3312	42	7	a	a	DET
ejpam-3312	42	8	deeper	deep	ADJ
ejpam-3312	42	9	understanding	understanding	NOUN
ejpam-3312	42	10	of	of	ADP
ejpam-3312	42	11	soft	soft	ADJ
ejpam-3312	42	12	topology	topology	NOUN
ejpam-3312	42	13	prompted	prompt	VERB
ejpam-3312	42	14	interested	interested	ADJ
ejpam-3312	42	15	researchers	researcher	NOUN
ejpam-3312	42	16	to	to	PART
ejpam-3312	42	17	carry	carry	VERB
ejpam-3312	42	18	out	out	ADP
ejpam-3312	42	19	many	many	ADJ
ejpam-3312	42	20	studies	study	NOUN
ejpam-3312	42	21	on	on	ADP
ejpam-3312	42	22	soft	soft	ADJ
ejpam-3312	42	23	topological	topological	ADJ
ejpam-3312	42	24	notions	notion	NOUN
ejpam-3312	42	25	and	and	CCONJ
ejpam-3312	42	26	their	their	PRON
ejpam-3312	42	27	features	feature	NOUN
ejpam-3312	42	28	.	.	PUNCT
ejpam-3312	43	1	in	in	ADP
ejpam-3312	43	2	2012	2012	NUM
ejpam-3312	43	3	,	,	PUNCT
ejpam-3312	43	4	rong	rong	PROPN
ejpam-3312	44	1	[	[	X
ejpam-3312	44	2	43	43	NUM
ejpam-3312	44	3	]	]	PUNCT
ejpam-3312	44	4	investigated	investigate	VERB
ejpam-3312	44	5	the	the	DET
ejpam-3312	44	6	countability	countability	NOUN
ejpam-3312	44	7	axioms	axiom	NOUN
ejpam-3312	44	8	of	of	ADP
ejpam-3312	44	9	soft	soft	ADJ
ejpam-3312	44	10	topological	topological	ADJ
ejpam-3312	44	11	spaces	space	NOUN
ejpam-3312	44	12	and	and	CCONJ
ejpam-3312	44	13	and	and	CCONJ
ejpam-3312	44	14	studied	study	VERB
ejpam-3312	44	15	the	the	DET
ejpam-3312	44	16	possibility	possibility	NOUN
ejpam-3312	44	17	of	of	ADP
ejpam-3312	44	18	carry	carry	VERB
ejpam-3312	44	19	over	over	ADP
ejpam-3312	44	20	the	the	DET
ejpam-3312	44	21	results	result	NOUN
ejpam-3312	44	22	of	of	ADP
ejpam-3312	44	23	countability	countability	NOUN
ejpam-3312	44	24	axioms	axiom	NOUN
ejpam-3312	44	25	via	via	ADP
ejpam-3312	44	26	general	general	ADJ
ejpam-3312	44	27	topology	topology	NOUN
ejpam-3312	44	28	to	to	ADP
ejpam-3312	44	29	the	the	DET
ejpam-3312	44	30	soft	soft	ADJ
ejpam-3312	44	31	topology	topology	NOUN
ejpam-3312	44	32	setting	setting	NOUN
ejpam-3312	44	33	.	.	PUNCT
ejpam-3312	45	1	aygünoǧlu	aygünoǧlu	NOUN
ejpam-3312	45	2	and	and	CCONJ
ejpam-3312	45	3	aygün	aygün	NOUN
ejpam-3312	45	4	[	[	X
ejpam-3312	45	5	16	16	NUM
ejpam-3312	45	6	]	]	PUNCT
ejpam-3312	45	7	introduced	introduce	VERB
ejpam-3312	45	8	and	and	CCONJ
ejpam-3312	45	9	studied	study	VERB
ejpam-3312	45	10	a	a	DET
ejpam-3312	45	11	soft	soft	ADJ
ejpam-3312	45	12	compactness	compactness	NOUN
ejpam-3312	45	13	concept	concept	NOUN
ejpam-3312	45	14	;	;	PUNCT
ejpam-3312	45	15	and	and	CCONJ
ejpam-3312	45	16	hida	hida	PROPN
ejpam-3312	46	1	[	[	X
ejpam-3312	46	2	26	26	NUM
ejpam-3312	46	3	]	]	PUNCT
ejpam-3312	46	4	gave	give	VERB
ejpam-3312	46	5	two	two	NUM
ejpam-3312	46	6	types	type	NOUN
ejpam-3312	46	7	of	of	ADP
ejpam-3312	46	8	soft	soft	ADJ
ejpam-3312	46	9	compactness	compactness	NOUN
ejpam-3312	46	10	and	and	CCONJ
ejpam-3312	46	11	pointed	point	VERB
ejpam-3312	46	12	out	out	ADP
ejpam-3312	46	13	the	the	DET
ejpam-3312	46	14	relationships	relationship	NOUN
ejpam-3312	46	15	between	between	ADP
ejpam-3312	46	16	them	they	PRON
ejpam-3312	46	17	.	.	PUNCT
ejpam-3312	47	1	the	the	DET
ejpam-3312	47	2	authors	author	NOUN
ejpam-3312	47	3	of	of	ADP
ejpam-3312	47	4	[	[	X
ejpam-3312	47	5	5	5	NUM
ejpam-3312	47	6	]	]	PUNCT
ejpam-3312	47	7	and	and	CCONJ
ejpam-3312	47	8	[	[	X
ejpam-3312	47	9	1	1	X
ejpam-3312	47	10	]	]	PUNCT
ejpam-3312	47	11	introduced	introduce	VERB
ejpam-3312	47	12	the	the	DET
ejpam-3312	47	13	notions	notion	NOUN
ejpam-3312	47	14	of	of	ADP
ejpam-3312	47	15	soft	soft	ADJ
ejpam-3312	47	16	β	β	ADJ
ejpam-3312	47	17	-	-	ADJ
ejpam-3312	47	18	open	open	ADJ
ejpam-3312	47	19	sets	set	NOUN
ejpam-3312	47	20	and	and	CCONJ
ejpam-3312	47	21	soft	soft	ADJ
ejpam-3312	47	22	β	β	NOUN
ejpam-3312	47	23	-	-	ADJ
ejpam-3312	47	24	separations	separation	NOUN
ejpam-3312	47	25	axioms	axiom	NOUN
ejpam-3312	47	26	,	,	PUNCT
ejpam-3312	47	27	respectively	respectively	ADV
ejpam-3312	47	28	.	.	PUNCT
ejpam-3312	48	1	they	they	PRON
ejpam-3312	48	2	examined	examine	VERB
ejpam-3312	48	3	which	which	PRON
ejpam-3312	48	4	results	result	NOUN
ejpam-3312	48	5	related	relate	VERB
ejpam-3312	48	6	to	to	ADP
ejpam-3312	48	7	β	β	ADJ
ejpam-3312	48	8	-	-	ADJ
ejpam-3312	48	9	open	open	ADJ
ejpam-3312	48	10	sets	set	NOUN
ejpam-3312	48	11	and	and	CCONJ
ejpam-3312	48	12	βti	βti	NOUN
ejpam-3312	48	13	-	-	NOUN
ejpam-3312	48	14	spaces	space	NOUN
ejpam-3312	48	15	from	from	ADP
ejpam-3312	48	16	the	the	DET
ejpam-3312	48	17	topological	topological	ADJ
ejpam-3312	48	18	spaces	space	NOUN
ejpam-3312	48	19	remain	remain	VERB
ejpam-3312	48	20	valid	valid	ADJ
ejpam-3312	48	21	in	in	ADP
ejpam-3312	48	22	the	the	DET
ejpam-3312	48	23	context	context	NOUN
ejpam-3312	48	24	of	of	ADP
ejpam-3312	48	25	soft	soft	ADJ
ejpam-3312	48	26	topological	topological	ADJ
ejpam-3312	48	27	spaces	space	NOUN
ejpam-3312	48	28	.	.	PUNCT
ejpam-3312	49	1	recently	recently	ADV
ejpam-3312	49	2	,	,	PUNCT
ejpam-3312	49	3	al	al	PROPN
ejpam-3312	49	4	-	-	PUNCT
ejpam-3312	49	5	shami	shami	PROPN
ejpam-3312	49	6	et	et	PROPN
ejpam-3312	49	7	al	al	PROPN
ejpam-3312	49	8	.	.	PUNCT
ejpam-3312	50	1	[	[	X
ejpam-3312	50	2	13	13	NUM
ejpam-3312	50	3	]	]	PUNCT
ejpam-3312	50	4	introduced	introduce	VERB
ejpam-3312	50	5	a	a	DET
ejpam-3312	50	6	concept	concept	NOUN
ejpam-3312	50	7	of	of	ADP
ejpam-3312	50	8	soft	soft	ADJ
ejpam-3312	50	9	topological	topological	ADJ
ejpam-3312	50	10	ordered	order	VERB
ejpam-3312	50	11	spaces	space	NOUN
ejpam-3312	50	12	and	and	CCONJ
ejpam-3312	50	13	established	establish	VERB
ejpam-3312	50	14	the	the	DET
ejpam-3312	50	15	notions	notion	NOUN
ejpam-3312	50	16	of	of	ADP
ejpam-3312	50	17	p	p	NOUN
ejpam-3312	50	18	-	-	PUNCT
ejpam-3312	50	19	soft	soft	ADJ
ejpam-3312	50	20	ti	ti	NOUN
ejpam-3312	50	21	-	-	ADJ
ejpam-3312	50	22	ordered	order	VERB
ejpam-3312	50	23	spaces	space	NOUN
ejpam-3312	50	24	(	(	PUNCT
ejpam-3312	50	25	i	i	NOUN
ejpam-3312	50	26	=	=	NOUN
ejpam-3312	50	27	0	0	NUM
ejpam-3312	50	28	,	,	PUNCT
ejpam-3312	50	29	1	1	NUM
ejpam-3312	50	30	,	,	PUNCT
ejpam-3312	50	31	2	2	NUM
ejpam-3312	50	32	,	,	PUNCT
ejpam-3312	50	33	3	3	NUM
ejpam-3312	50	34	,	,	PUNCT
ejpam-3312	50	35	4	4	NUM
ejpam-3312	50	36	)	)	PUNCT
ejpam-3312	50	37	depending	depend	VERB
ejpam-3312	50	38	on	on	ADP
ejpam-3312	50	39	totally	totally	ADV
ejpam-3312	50	40	non	non	ADJ
ejpam-3312	50	41	belong	belong	PROPN
ejpam-3312	50	42	relations	relation	NOUN
ejpam-3312	50	43	,	,	PUNCT
ejpam-3312	50	44	which	which	PRON
ejpam-3312	50	45	introduced	introduce	VERB
ejpam-3312	50	46	in	in	ADP
ejpam-3312	50	47	[	[	X
ejpam-3312	50	48	23	23	NUM
ejpam-3312	50	49	]	]	PUNCT
ejpam-3312	50	50	,	,	PUNCT
ejpam-3312	50	51	and	and	CCONJ
ejpam-3312	50	52	monotone	monotone	ADJ
ejpam-3312	50	53	soft	soft	ADJ
ejpam-3312	50	54	neighborhoods	neighborhood	NOUN
ejpam-3312	50	55	.	.	PUNCT
ejpam-3312	51	1	also	also	ADV
ejpam-3312	51	2	,	,	PUNCT
ejpam-3312	51	3	they	they	PRON
ejpam-3312	51	4	[	[	X
ejpam-3312	51	5	14	14	NUM
ejpam-3312	51	6	]	]	PUNCT
ejpam-3312	51	7	defined	define	VERB
ejpam-3312	51	8	newly	newly	ADV
ejpam-3312	51	9	ordered	order	VERB
ejpam-3312	51	10	mappings	mapping	NOUN
ejpam-3312	51	11	via	via	ADP
ejpam-3312	51	12	topological	topological	ADJ
ejpam-3312	51	13	ordered	order	VERB
ejpam-3312	51	14	spaces	space	NOUN
ejpam-3312	51	15	and	and	CCONJ
ejpam-3312	51	16	obtained	obtain	VERB
ejpam-3312	51	17	interesting	interesting	ADJ
ejpam-3312	51	18	results	result	NOUN
ejpam-3312	51	19	.	.	PUNCT
ejpam-3312	52	1	al	al	PROPN
ejpam-3312	52	2	-	-	PUNCT
ejpam-3312	52	3	shami	shami	PROPN
ejpam-3312	52	4	and	and	CCONJ
ejpam-3312	52	5	kočinac	kočinac	PROPN
ejpam-3312	53	1	[	[	X
ejpam-3312	53	2	15	15	NUM
ejpam-3312	53	3	]	]	PUNCT
ejpam-3312	53	4	verified	verify	VERB
ejpam-3312	53	5	the	the	DET
ejpam-3312	53	6	equivalence	equivalence	NOUN
ejpam-3312	53	7	between	between	ADP
ejpam-3312	53	8	the	the	DET
ejpam-3312	53	9	enriched	enrich	VERB
ejpam-3312	53	10	and	and	CCONJ
ejpam-3312	53	11	extended	extended	ADJ
ejpam-3312	53	12	soft	soft	ADJ
ejpam-3312	53	13	topologies	topology	NOUN
ejpam-3312	53	14	and	and	CCONJ
ejpam-3312	53	15	concluded	conclude	VERB
ejpam-3312	53	16	many	many	ADJ
ejpam-3312	53	17	findings	finding	NOUN
ejpam-3312	53	18	related	relate	VERB
ejpam-3312	53	19	to	to	ADP
ejpam-3312	53	20	soft	soft	ADJ
ejpam-3312	53	21	mappings	mapping	NOUN
ejpam-3312	53	22	and	and	CCONJ
ejpam-3312	53	23	soft	soft	ADJ
ejpam-3312	53	24	axioms	axiom	NOUN
ejpam-3312	53	25	.	.	PUNCT
ejpam-3312	54	1	t.	t.	PROPN
ejpam-3312	54	2	m.	m.	PROPN
ejpam-3312	54	3	al	al	PROPN
ejpam-3312	54	4	-	-	PUNCT
ejpam-3312	54	5	shami	shami	PROPN
ejpam-3312	54	6	,	,	PUNCT
ejpam-3312	54	7	m.	m.	PROPN
ejpam-3312	54	8	e.	e.	PROPN
ejpam-3312	54	9	el	el	PROPN
ejpam-3312	54	10	-	-	PROPN
ejpam-3312	54	11	shafei	shafei	PROPN
ejpam-3312	54	12	,	,	PUNCT
ejpam-3312	54	13	b.	b.	PROPN
ejpam-3312	54	14	a.	a.	PROPN
ejpam-3312	54	15	asaad	asaad	PROPN
ejpam-3312	54	16	/	/	SYM
ejpam-3312	54	17	eur	eur	PROPN
ejpam-3312	54	18	.	.	PUNCT
ejpam-3312	55	1	j.	j.	PROPN
ejpam-3312	55	2	pure	pure	PROPN
ejpam-3312	55	3	appl	appl	PROPN
ejpam-3312	55	4	.	.	PROPN
ejpam-3312	55	5	math	math	PROPN
ejpam-3312	55	6	,	,	PUNCT
ejpam-3312	55	7	12	12	NUM
ejpam-3312	55	8	(	(	PUNCT
ejpam-3312	55	9	1	1	NUM
ejpam-3312	55	10	)	)	PUNCT
ejpam-3312	55	11	(	(	PUNCT
ejpam-3312	55	12	2019	2019	NUM
ejpam-3312	55	13	)	)	PUNCT
ejpam-3312	55	14	,	,	PUNCT
ejpam-3312	55	15	176	176	NUM
ejpam-3312	55	16	-	-	SYM
ejpam-3312	55	17	193	193	NUM
ejpam-3312	55	18	178	178	NUM
ejpam-3312	55	19	we	we	PRON
ejpam-3312	55	20	aim	aim	VERB
ejpam-3312	55	21	in	in	ADP
ejpam-3312	55	22	this	this	DET
ejpam-3312	55	23	study	study	NOUN
ejpam-3312	55	24	to	to	PART
ejpam-3312	55	25	propose	propose	VERB
ejpam-3312	55	26	and	and	CCONJ
ejpam-3312	55	27	investigate	investigate	VERB
ejpam-3312	55	28	newly	newly	ADV
ejpam-3312	55	29	ordered	order	VERB
ejpam-3312	55	30	mappings	mapping	NOUN
ejpam-3312	55	31	on	on	ADP
ejpam-3312	55	32	soft	soft	ADJ
ejpam-3312	55	33	topological	topological	ADJ
ejpam-3312	55	34	ordered	order	VERB
ejpam-3312	55	35	spaces	space	NOUN
ejpam-3312	55	36	,	,	PUNCT
ejpam-3312	55	37	namely	namely	ADV
ejpam-3312	55	38	soft	soft	ADJ
ejpam-3312	55	39	xβ	xβ	NOUN
ejpam-3312	55	40	-	-	PUNCT
ejpam-3312	55	41	continuous	continuous	ADJ
ejpam-3312	55	42	,	,	PUNCT
ejpam-3312	55	43	soft	soft	ADJ
ejpam-3312	55	44	xβ	xβ	NOUN
ejpam-3312	55	45	-	-	ADJ
ejpam-3312	55	46	open	open	ADJ
ejpam-3312	55	47	,	,	PUNCT
ejpam-3312	55	48	soft	soft	ADJ
ejpam-3312	55	49	xβ	xβ	NOUN
ejpam-3312	55	50	-	-	PUNCT
ejpam-3312	55	51	closed	closed	ADJ
ejpam-3312	55	52	and	and	CCONJ
ejpam-3312	55	53	soft	soft	ADJ
ejpam-3312	55	54	xβ	xβ	NOUN
ejpam-3312	55	55	-	-	PUNCT
ejpam-3312	55	56	homeomorphism	homeomorphism	NOUN
ejpam-3312	55	57	mappings	mapping	NOUN
ejpam-3312	55	58	,	,	PUNCT
ejpam-3312	55	59	for	for	ADP
ejpam-3312	55	60	x	x	PROPN
ejpam-3312	55	61	∈	∈	PROPN
ejpam-3312	55	62	{	{	PUNCT
ejpam-3312	55	63	i	i	PROPN
ejpam-3312	55	64	,	,	PUNCT
ejpam-3312	55	65	d	d	PROPN
ejpam-3312	55	66	,	,	PUNCT
ejpam-3312	55	67	b	b	NOUN
ejpam-3312	55	68	}	}	PUNCT
ejpam-3312	55	69	.	.	PUNCT
ejpam-3312	56	1	the	the	DET
ejpam-3312	56	2	examples	example	NOUN
ejpam-3312	56	3	which	which	PRON
ejpam-3312	56	4	illustrate	illustrate	VERB
ejpam-3312	56	5	the	the	DET
ejpam-3312	56	6	relationships	relationship	NOUN
ejpam-3312	56	7	among	among	ADP
ejpam-3312	56	8	these	these	DET
ejpam-3312	56	9	soft	soft	ADJ
ejpam-3312	56	10	mappings	mapping	NOUN
ejpam-3312	56	11	are	be	AUX
ejpam-3312	56	12	given	give	VERB
ejpam-3312	56	13	and	and	CCONJ
ejpam-3312	56	14	the	the	DET
ejpam-3312	56	15	conditions	condition	NOUN
ejpam-3312	56	16	which	which	PRON
ejpam-3312	56	17	guarantee	guarantee	VERB
ejpam-3312	56	18	the	the	DET
ejpam-3312	56	19	equivalent	equivalent	NOUN
ejpam-3312	56	20	between	between	ADP
ejpam-3312	56	21	soft	soft	ADJ
ejpam-3312	56	22	xβ	xβ	NOUN
ejpam-3312	56	23	-	-	PUNCT
ejpam-3312	56	24	open	open	ADJ
ejpam-3312	56	25	and	and	CCONJ
ejpam-3312	56	26	soft	soft	ADJ
ejpam-3312	56	27	xβ	xβ	NOUN
ejpam-3312	56	28	-	-	PUNCT
ejpam-3312	56	29	closed	close	VERB
ejpam-3312	56	30	mappings	mapping	NOUN
ejpam-3312	56	31	are	be	AUX
ejpam-3312	56	32	discussed	discuss	VERB
ejpam-3312	56	33	,	,	PUNCT
ejpam-3312	56	34	for	for	ADP
ejpam-3312	56	35	x	x	PROPN
ejpam-3312	56	36	∈	∈	PROPN
ejpam-3312	56	37	{	{	PUNCT
ejpam-3312	56	38	i	i	PROPN
ejpam-3312	56	39	,	,	PUNCT
ejpam-3312	56	40	d	d	PROPN
ejpam-3312	56	41	,	,	PUNCT
ejpam-3312	56	42	b	b	NOUN
ejpam-3312	56	43	}	}	PUNCT
ejpam-3312	56	44	.	.	PUNCT
ejpam-3312	57	1	also	also	ADV
ejpam-3312	57	2	,	,	PUNCT
ejpam-3312	57	3	the	the	DET
ejpam-3312	57	4	various	various	ADJ
ejpam-3312	57	5	characterizations	characterization	NOUN
ejpam-3312	57	6	of	of	ADP
ejpam-3312	57	7	each	each	DET
ejpam-3312	57	8	one	one	NUM
ejpam-3312	57	9	of	of	ADP
ejpam-3312	57	10	the	the	DET
ejpam-3312	57	11	initiated	initiate	VERB
ejpam-3312	57	12	soft	soft	ADJ
ejpam-3312	57	13	mappings	mapping	NOUN
ejpam-3312	57	14	are	be	AUX
ejpam-3312	57	15	investigated	investigate	VERB
ejpam-3312	57	16	and	and	CCONJ
ejpam-3312	57	17	the	the	DET
ejpam-3312	57	18	interrelations	interrelation	NOUN
ejpam-3312	57	19	between	between	ADP
ejpam-3312	57	20	these	these	DET
ejpam-3312	57	21	soft	soft	ADJ
ejpam-3312	57	22	mappings	mapping	NOUN
ejpam-3312	57	23	and	and	CCONJ
ejpam-3312	57	24	their	their	PRON
ejpam-3312	57	25	counterparts	counterpart	NOUN
ejpam-3312	57	26	of	of	ADP
ejpam-3312	57	27	mappings	mapping	NOUN
ejpam-3312	57	28	in	in	ADP
ejpam-3312	57	29	topological	topological	ADJ
ejpam-3312	57	30	ordered	order	VERB
ejpam-3312	57	31	spaces	space	NOUN
ejpam-3312	57	32	are	be	AUX
ejpam-3312	57	33	studied	study	VERB
ejpam-3312	57	34	amply	amply	ADV
ejpam-3312	57	35	.	.	PUNCT
ejpam-3312	58	1	2	2	X
ejpam-3312	58	2	.	.	X
ejpam-3312	58	3	preliminaries	preliminary	NOUN
ejpam-3312	58	4	in	in	ADP
ejpam-3312	58	5	what	what	PRON
ejpam-3312	58	6	follows	follow	VERB
ejpam-3312	58	7	,	,	PUNCT
ejpam-3312	58	8	we	we	PRON
ejpam-3312	58	9	mention	mention	VERB
ejpam-3312	58	10	the	the	DET
ejpam-3312	58	11	definitions	definition	NOUN
ejpam-3312	58	12	and	and	CCONJ
ejpam-3312	58	13	results	result	NOUN
ejpam-3312	58	14	related	relate	VERB
ejpam-3312	58	15	to	to	ADP
ejpam-3312	58	16	soft	soft	ADJ
ejpam-3312	58	17	set	set	NOUN
ejpam-3312	58	18	,	,	PUNCT
ejpam-3312	58	19	soft	soft	ADJ
ejpam-3312	58	20	topological	topological	ADJ
ejpam-3312	58	21	spaces	space	NOUN
ejpam-3312	58	22	and	and	CCONJ
ejpam-3312	58	23	ordered	order	VERB
ejpam-3312	58	24	spaces	space	NOUN
ejpam-3312	58	25	that	that	PRON
ejpam-3312	58	26	will	will	AUX
ejpam-3312	58	27	be	be	AUX
ejpam-3312	58	28	needed	need	VERB
ejpam-3312	58	29	in	in	ADP
ejpam-3312	58	30	investigating	investigate	VERB
ejpam-3312	58	31	the	the	DET
ejpam-3312	58	32	concepts	concept	NOUN
ejpam-3312	58	33	introduced	introduce	VERB
ejpam-3312	58	34	and	and	CCONJ
ejpam-3312	58	35	results	result	NOUN
ejpam-3312	58	36	obtained	obtain	VERB
ejpam-3312	58	37	herein	herein	NOUN
ejpam-3312	58	38	.	.	PUNCT
ejpam-3312	59	1	definition	definition	NOUN
ejpam-3312	59	2	1	1	NUM
ejpam-3312	59	3	.	.	PUNCT
ejpam-3312	60	1	[	[	X
ejpam-3312	60	2	36	36	NUM
ejpam-3312	60	3	]	]	PUNCT
ejpam-3312	60	4	a	a	DET
ejpam-3312	60	5	notation	notation	NOUN
ejpam-3312	60	6	ge	ge	PROPN
ejpam-3312	60	7	is	be	AUX
ejpam-3312	60	8	said	say	VERB
ejpam-3312	60	9	to	to	PART
ejpam-3312	60	10	be	be	AUX
ejpam-3312	60	11	a	a	DET
ejpam-3312	60	12	soft	soft	ADJ
ejpam-3312	60	13	set	set	NOUN
ejpam-3312	60	14	over	over	ADP
ejpam-3312	60	15	x	x	PUNCT
ejpam-3312	60	16	if	if	SCONJ
ejpam-3312	60	17	g	g	PROPN
ejpam-3312	60	18	is	be	AUX
ejpam-3312	60	19	a	a	DET
ejpam-3312	60	20	mapping	mapping	NOUN
ejpam-3312	60	21	of	of	ADP
ejpam-3312	60	22	a	a	DET
ejpam-3312	60	23	set	set	NOUN
ejpam-3312	60	24	of	of	ADP
ejpam-3312	60	25	parameters	parameter	NOUN
ejpam-3312	60	26	e	e	VERB
ejpam-3312	60	27	into	into	ADP
ejpam-3312	60	28	2x	2x	NUM
ejpam-3312	60	29	and	and	CCONJ
ejpam-3312	60	30	it	it	PRON
ejpam-3312	60	31	is	be	AUX
ejpam-3312	60	32	written	write	VERB
ejpam-3312	60	33	as	as	ADP
ejpam-3312	60	34	a	a	DET
ejpam-3312	60	35	set	set	NOUN
ejpam-3312	60	36	of	of	ADP
ejpam-3312	60	37	ordered	order	VERB
ejpam-3312	60	38	pairs	pair	NOUN
ejpam-3312	60	39	ge	ge	PROPN
ejpam-3312	60	40	=	=	PUNCT
ejpam-3312	60	41	{	{	PUNCT
ejpam-3312	60	42	(	(	PUNCT
ejpam-3312	60	43	e	e	NOUN
ejpam-3312	60	44	,	,	PUNCT
ejpam-3312	60	45	g(e	g(e	PROPN
ejpam-3312	60	46	)	)	PUNCT
ejpam-3312	60	47	)	)	PUNCT
ejpam-3312	60	48	:	:	PUNCT
ejpam-3312	61	1	e	e	X
ejpam-3312	61	2	∈	∈	PROPN
ejpam-3312	61	3	e	e	X
ejpam-3312	61	4	and	and	CCONJ
ejpam-3312	61	5	g(e	g(e	PROPN
ejpam-3312	61	6	)	)	PUNCT
ejpam-3312	61	7	∈	∈	PROPN
ejpam-3312	61	8	2x	2x	NUM
ejpam-3312	61	9	}	}	PUNCT
ejpam-3312	61	10	.	.	PUNCT
ejpam-3312	62	1	for	for	ADP
ejpam-3312	62	2	x	x	SYM
ejpam-3312	62	3	∈	∈	PROPN
ejpam-3312	62	4	x	x	X
ejpam-3312	62	5	and	and	CCONJ
ejpam-3312	62	6	a	a	DET
ejpam-3312	62	7	soft	soft	ADJ
ejpam-3312	62	8	set	set	NOUN
ejpam-3312	62	9	ge	ge	PROPN
ejpam-3312	62	10	over	over	ADP
ejpam-3312	62	11	x	x	PROPN
ejpam-3312	62	12	,	,	PUNCT
ejpam-3312	62	13	we	we	PRON
ejpam-3312	62	14	say	say	VERB
ejpam-3312	62	15	that	that	SCONJ
ejpam-3312	62	16	x	x	PUNCT
ejpam-3312	62	17	∈	∈	PROPN
ejpam-3312	62	18	ge	ge	PROPN
ejpam-3312	62	19	if	if	SCONJ
ejpam-3312	62	20	x	x	PROPN
ejpam-3312	62	21	∈	∈	PROPN
ejpam-3312	62	22	g(e	g(e	PROPN
ejpam-3312	62	23	)	)	PUNCT
ejpam-3312	62	24	,	,	PUNCT
ejpam-3312	62	25	for	for	ADP
ejpam-3312	62	26	each	each	DET
ejpam-3312	62	27	e	e	NOUN
ejpam-3312	62	28	∈	∈	PROPN
ejpam-3312	62	29	e	e	X
ejpam-3312	62	30	and	and	CCONJ
ejpam-3312	62	31	x	x	PROPN
ejpam-3312	62	32	6∈	6∈	PROPN
ejpam-3312	62	33	ge	ge	PROPN
ejpam-3312	62	34	if	if	SCONJ
ejpam-3312	62	35	x	x	PROPN
ejpam-3312	62	36	6∈	6∈	PROPN
ejpam-3312	62	37	g(e	g(e	PROPN
ejpam-3312	62	38	)	)	PUNCT
ejpam-3312	62	39	,	,	PUNCT
ejpam-3312	62	40	for	for	ADP
ejpam-3312	62	41	some	some	DET
ejpam-3312	62	42	e	e	PROPN
ejpam-3312	62	43	∈	∈	PROPN
ejpam-3312	62	44	e.	e.	PROPN
ejpam-3312	62	45	definition	definition	NOUN
ejpam-3312	62	46	2	2	NUM
ejpam-3312	62	47	.	.	PUNCT
ejpam-3312	63	1	[	[	X
ejpam-3312	63	2	31	31	NUM
ejpam-3312	63	3	]	]	PUNCT
ejpam-3312	63	4	a	a	DET
ejpam-3312	63	5	soft	soft	ADJ
ejpam-3312	63	6	set	set	NOUN
ejpam-3312	63	7	ge	ge	PROPN
ejpam-3312	63	8	over	over	ADP
ejpam-3312	63	9	x	x	PROPN
ejpam-3312	63	10	is	be	AUX
ejpam-3312	63	11	called	call	VERB
ejpam-3312	63	12	a	a	DET
ejpam-3312	63	13	null	null	ADJ
ejpam-3312	63	14	soft	soft	ADJ
ejpam-3312	63	15	set	set	NOUN
ejpam-3312	63	16	,	,	PUNCT
ejpam-3312	63	17	denoting	denote	VERB
ejpam-3312	63	18	by	by	ADP
ejpam-3312	63	19	φ̃	φ̃	PROPN
ejpam-3312	63	20	,	,	PUNCT
ejpam-3312	63	21	if	if	SCONJ
ejpam-3312	63	22	g(e	g(e	PROPN
ejpam-3312	63	23	)	)	PUNCT
ejpam-3312	64	1	=	=	NOUN
ejpam-3312	64	2	∅	∅	NOUN
ejpam-3312	64	3	,	,	PUNCT
ejpam-3312	64	4	for	for	ADP
ejpam-3312	64	5	each	each	DET
ejpam-3312	64	6	e	e	PROPN
ejpam-3312	64	7	∈	∈	PROPN
ejpam-3312	64	8	e	e	NOUN
ejpam-3312	64	9	;	;	PUNCT
ejpam-3312	64	10	and	and	CCONJ
ejpam-3312	64	11	it	it	PRON
ejpam-3312	64	12	is	be	AUX
ejpam-3312	64	13	called	call	VERB
ejpam-3312	64	14	an	an	DET
ejpam-3312	64	15	absolute	absolute	ADJ
ejpam-3312	64	16	soft	soft	ADJ
ejpam-3312	64	17	set	set	NOUN
ejpam-3312	64	18	,	,	PUNCT
ejpam-3312	64	19	denoting	denote	VERB
ejpam-3312	64	20	by	by	ADP
ejpam-3312	64	21	x̃	x̃	PROPN
ejpam-3312	64	22	,	,	PUNCT
ejpam-3312	64	23	if	if	SCONJ
ejpam-3312	64	24	g(e	g(e	PROPN
ejpam-3312	64	25	)	)	PUNCT
ejpam-3312	65	1	=	=	SYM
ejpam-3312	65	2	x	x	X
ejpam-3312	65	3	,	,	PUNCT
ejpam-3312	65	4	for	for	ADP
ejpam-3312	65	5	each	each	DET
ejpam-3312	65	6	e	e	PROPN
ejpam-3312	65	7	∈	∈	PROPN
ejpam-3312	65	8	e.	e.	PROPN
ejpam-3312	65	9	definition	definition	NOUN
ejpam-3312	65	10	3	3	NUM
ejpam-3312	65	11	.	.	PUNCT
ejpam-3312	66	1	[	[	X
ejpam-3312	66	2	7	7	X
ejpam-3312	66	3	]	]	X
ejpam-3312	66	4	the	the	DET
ejpam-3312	66	5	relative	relative	ADJ
ejpam-3312	66	6	complement	complement	NOUN
ejpam-3312	66	7	of	of	ADP
ejpam-3312	66	8	a	a	DET
ejpam-3312	66	9	soft	soft	ADJ
ejpam-3312	66	10	set	set	NOUN
ejpam-3312	66	11	ge	ge	PROPN
ejpam-3312	66	12	is	be	AUX
ejpam-3312	66	13	denoted	denote	VERB
ejpam-3312	66	14	by	by	ADP
ejpam-3312	66	15	gce	gce	PROPN
ejpam-3312	66	16	,	,	PUNCT
ejpam-3312	66	17	where	where	SCONJ
ejpam-3312	66	18	gc	gc	PROPN
ejpam-3312	66	19	:	:	PUNCT
ejpam-3312	66	20	e	e	X
ejpam-3312	66	21	→	→	X
ejpam-3312	66	22	2x	2x	NUM
ejpam-3312	66	23	is	be	AUX
ejpam-3312	66	24	a	a	DET
ejpam-3312	66	25	mapping	mapping	NOUN
ejpam-3312	66	26	defined	define	VERB
ejpam-3312	66	27	by	by	ADP
ejpam-3312	66	28	gc(e	gc(e	NOUN
ejpam-3312	66	29	)	)	PUNCT
ejpam-3312	66	30	=	=	SYM
ejpam-3312	66	31	x	x	PUNCT
ejpam-3312	66	32	\g(e	\g(e	PROPN
ejpam-3312	66	33	)	)	PUNCT
ejpam-3312	66	34	,	,	PUNCT
ejpam-3312	66	35	for	for	ADP
ejpam-3312	66	36	each	each	DET
ejpam-3312	66	37	e	e	PROPN
ejpam-3312	66	38	∈	∈	PROPN
ejpam-3312	66	39	e.	e.	PROPN
ejpam-3312	66	40	in	in	ADP
ejpam-3312	66	41	this	this	DET
ejpam-3312	66	42	connection	connection	NOUN
ejpam-3312	66	43	,	,	PUNCT
ejpam-3312	66	44	it	it	PRON
ejpam-3312	66	45	is	be	AUX
ejpam-3312	66	46	worth	worth	ADJ
ejpam-3312	66	47	noting	note	VERB
ejpam-3312	66	48	that	that	SCONJ
ejpam-3312	66	49	x	x	SYM
ejpam-3312	66	50	6∈	6∈	PROPN
ejpam-3312	66	51	ge	ge	PROPN
ejpam-3312	66	52	does	do	AUX
ejpam-3312	66	53	not	not	PART
ejpam-3312	66	54	imply	imply	VERB
ejpam-3312	66	55	that	that	SCONJ
ejpam-3312	66	56	x	x	PROPN
ejpam-3312	66	57	∈	∈	PROPN
ejpam-3312	66	58	gce	gce	PROPN
ejpam-3312	66	59	.	.	PUNCT
ejpam-3312	67	1	definition	definition	NOUN
ejpam-3312	67	2	4	4	NUM
ejpam-3312	67	3	.	.	PUNCT
ejpam-3312	68	1	[	[	X
ejpam-3312	68	2	44	44	NUM
ejpam-3312	68	3	]	]	PUNCT
ejpam-3312	68	4	a	a	DET
ejpam-3312	68	5	soft	soft	ADJ
ejpam-3312	68	6	topology	topology	NOUN
ejpam-3312	68	7	on	on	ADP
ejpam-3312	68	8	a	a	DET
ejpam-3312	68	9	non	non	ADJ
ejpam-3312	68	10	-	-	ADJ
ejpam-3312	68	11	empty	empty	ADJ
ejpam-3312	68	12	set	set	NOUN
ejpam-3312	68	13	x	x	PUNCT
ejpam-3312	68	14	is	be	AUX
ejpam-3312	68	15	a	a	DET
ejpam-3312	68	16	collection	collection	NOUN
ejpam-3312	68	17	τ	τ	X
ejpam-3312	68	18	of	of	ADP
ejpam-3312	68	19	soft	soft	ADJ
ejpam-3312	68	20	sets	set	NOUN
ejpam-3312	68	21	over	over	ADP
ejpam-3312	68	22	x	x	PUNCT
ejpam-3312	68	23	under	under	ADP
ejpam-3312	68	24	a	a	DET
ejpam-3312	68	25	parameters	parameter	NOUN
ejpam-3312	68	26	set	set	VERB
ejpam-3312	68	27	e	e	NOUN
ejpam-3312	68	28	satisfying	satisfy	VERB
ejpam-3312	68	29	the	the	DET
ejpam-3312	68	30	following	follow	VERB
ejpam-3312	68	31	axioms	axiom	NOUN
ejpam-3312	68	32	:	:	PUNCT
ejpam-3312	68	33	(	(	PUNCT
ejpam-3312	68	34	i	i	NOUN
ejpam-3312	68	35	)	)	PUNCT
ejpam-3312	68	36	x̃	x̃	PROPN
ejpam-3312	68	37	and	and	CCONJ
ejpam-3312	68	38	∅̃	∅̃	NOUN
ejpam-3312	68	39	belong	belong	VERB
ejpam-3312	68	40	to	to	ADP
ejpam-3312	68	41	τ	τ	PROPN
ejpam-3312	68	42	.	.	PUNCT
ejpam-3312	69	1	(	(	PUNCT
ejpam-3312	69	2	ii	ii	NOUN
ejpam-3312	69	3	)	)	PUNCT
ejpam-3312	69	4	τ	τ	PROPN
ejpam-3312	69	5	is	be	AUX
ejpam-3312	69	6	closed	close	VERB
ejpam-3312	69	7	under	under	ADP
ejpam-3312	69	8	finite	finite	ADJ
ejpam-3312	69	9	soft	soft	ADJ
ejpam-3312	69	10	intersection	intersection	NOUN
ejpam-3312	69	11	.	.	PUNCT
ejpam-3312	70	1	(	(	PUNCT
ejpam-3312	70	2	iii	iii	X
ejpam-3312	70	3	)	)	PUNCT
ejpam-3312	70	4	τ	τ	PROPN
ejpam-3312	70	5	is	be	AUX
ejpam-3312	70	6	closed	close	VERB
ejpam-3312	70	7	under	under	ADP
ejpam-3312	70	8	arbitrary	arbitrary	ADJ
ejpam-3312	70	9	soft	soft	ADJ
ejpam-3312	70	10	union	union	NOUN
ejpam-3312	70	11	.	.	PUNCT
ejpam-3312	71	1	the	the	DET
ejpam-3312	71	2	triple	triple	ADJ
ejpam-3312	71	3	(	(	PUNCT
ejpam-3312	71	4	x	x	NOUN
ejpam-3312	71	5	,	,	PUNCT
ejpam-3312	71	6	τ	τ	PROPN
ejpam-3312	71	7	,	,	PUNCT
ejpam-3312	71	8	e	e	NOUN
ejpam-3312	71	9	)	)	PUNCT
ejpam-3312	71	10	is	be	AUX
ejpam-3312	71	11	called	call	VERB
ejpam-3312	71	12	a	a	DET
ejpam-3312	71	13	soft	soft	ADJ
ejpam-3312	71	14	topological	topological	ADJ
ejpam-3312	71	15	space	space	NOUN
ejpam-3312	71	16	.	.	PUNCT
ejpam-3312	72	1	every	every	DET
ejpam-3312	72	2	member	member	NOUN
ejpam-3312	72	3	of	of	ADP
ejpam-3312	72	4	τ	τ	PROPN
ejpam-3312	72	5	is	be	AUX
ejpam-3312	72	6	called	call	VERB
ejpam-3312	72	7	a	a	DET
ejpam-3312	72	8	soft	soft	ADJ
ejpam-3312	72	9	open	open	ADJ
ejpam-3312	72	10	set	set	NOUN
ejpam-3312	72	11	and	and	CCONJ
ejpam-3312	72	12	its	its	PRON
ejpam-3312	72	13	relative	relative	ADJ
ejpam-3312	72	14	complement	complement	NOUN
ejpam-3312	72	15	is	be	AUX
ejpam-3312	72	16	called	call	VERB
ejpam-3312	72	17	soft	soft	ADJ
ejpam-3312	72	18	closed	closed	ADJ
ejpam-3312	72	19	.	.	PUNCT
ejpam-3312	73	1	proposition	proposition	NOUN
ejpam-3312	73	2	1	1	NUM
ejpam-3312	73	3	.	.	PUNCT
ejpam-3312	74	1	[	[	X
ejpam-3312	74	2	44	44	NUM
ejpam-3312	74	3	]	]	PUNCT
ejpam-3312	74	4	let	let	VERB
ejpam-3312	74	5	(	(	PUNCT
ejpam-3312	74	6	x	x	NOUN
ejpam-3312	74	7	,	,	PUNCT
ejpam-3312	74	8	τ	τ	PROPN
ejpam-3312	74	9	,	,	PUNCT
ejpam-3312	74	10	e	e	NOUN
ejpam-3312	74	11	)	)	PUNCT
ejpam-3312	74	12	be	be	AUX
ejpam-3312	74	13	a	a	DET
ejpam-3312	74	14	soft	soft	ADJ
ejpam-3312	74	15	topological	topological	ADJ
ejpam-3312	74	16	space	space	NOUN
ejpam-3312	74	17	.	.	PUNCT
ejpam-3312	75	1	then	then	ADV
ejpam-3312	75	2	τe	τe	ADV
ejpam-3312	75	3	=	=	SYM
ejpam-3312	75	4	{	{	PUNCT
ejpam-3312	75	5	g(e	g(e	PROPN
ejpam-3312	75	6	)	)	PUNCT
ejpam-3312	75	7	:	:	PUNCT
ejpam-3312	75	8	ge	ge	PROPN
ejpam-3312	75	9	∈	∈	PROPN
ejpam-3312	75	10	τ	τ	PROPN
ejpam-3312	75	11	}	}	PUNCT
ejpam-3312	75	12	defines	define	VERB
ejpam-3312	75	13	a	a	DET
ejpam-3312	75	14	topology	topology	NOUN
ejpam-3312	75	15	on	on	ADP
ejpam-3312	75	16	x	x	NOUN
ejpam-3312	75	17	,	,	PUNCT
ejpam-3312	75	18	for	for	ADP
ejpam-3312	75	19	each	each	DET
ejpam-3312	75	20	e	e	PROPN
ejpam-3312	75	21	∈	∈	PROPN
ejpam-3312	75	22	e.	e.	PROPN
ejpam-3312	75	23	definition	definition	NOUN
ejpam-3312	75	24	5	5	NUM
ejpam-3312	75	25	.	.	PUNCT
ejpam-3312	76	1	[	[	X
ejpam-3312	76	2	38	38	NUM
ejpam-3312	76	3	]	]	PUNCT
ejpam-3312	76	4	consider	consider	VERB
ejpam-3312	76	5	(	(	PUNCT
ejpam-3312	76	6	x	x	NOUN
ejpam-3312	76	7	,	,	PUNCT
ejpam-3312	76	8	τ	τ	PROPN
ejpam-3312	76	9	,	,	PUNCT
ejpam-3312	76	10	e	e	NOUN
ejpam-3312	76	11	)	)	PUNCT
ejpam-3312	76	12	is	be	AUX
ejpam-3312	76	13	a	a	DET
ejpam-3312	76	14	soft	soft	ADJ
ejpam-3312	76	15	topological	topological	ADJ
ejpam-3312	76	16	space	space	NOUN
ejpam-3312	76	17	and	and	CCONJ
ejpam-3312	76	18	τe	τe	ADV
ejpam-3312	76	19	is	be	AUX
ejpam-3312	76	20	a	a	DET
ejpam-3312	76	21	topology	topology	NOUN
ejpam-3312	76	22	on	on	ADP
ejpam-3312	76	23	x	x	PUNCT
ejpam-3312	76	24	as	as	ADP
ejpam-3312	76	25	in	in	ADP
ejpam-3312	76	26	the	the	DET
ejpam-3312	76	27	above	above	ADJ
ejpam-3312	76	28	proposition	proposition	NOUN
ejpam-3312	76	29	.	.	PUNCT
ejpam-3312	77	1	then	then	ADV
ejpam-3312	77	2	τ	τ	X
ejpam-3312	77	3	?	?	PUNCT
ejpam-3312	77	4	=	=	PRON
ejpam-3312	77	5	{	{	PUNCT
ejpam-3312	77	6	ge	ge	PROPN
ejpam-3312	77	7	:	:	PUNCT
ejpam-3312	77	8	g(e	g(e	PROPN
ejpam-3312	77	9	)	)	PUNCT
ejpam-3312	77	10	∈	∈	PROPN
ejpam-3312	77	11	τe	τe	ADP
ejpam-3312	77	12	,	,	PUNCT
ejpam-3312	77	13	for	for	SCONJ
ejpam-3312	77	14	each	each	DET
ejpam-3312	77	15	e	e	PROPN
ejpam-3312	77	16	∈	∈	PROPN
ejpam-3312	77	17	e	e	PROPN
ejpam-3312	77	18	}	}	PUNCT
ejpam-3312	77	19	is	be	AUX
ejpam-3312	77	20	a	a	DET
ejpam-3312	77	21	soft	soft	ADJ
ejpam-3312	77	22	topology	topology	NOUN
ejpam-3312	77	23	on	on	ADP
ejpam-3312	77	24	x	x	SYM
ejpam-3312	77	25	finer	fine	ADJ
ejpam-3312	77	26	than	than	ADP
ejpam-3312	77	27	τ	τ	PROPN
ejpam-3312	77	28	.	.	PUNCT
ejpam-3312	78	1	in	in	ADP
ejpam-3312	78	2	[	[	X
ejpam-3312	78	3	15	15	NUM
ejpam-3312	78	4	]	]	PUNCT
ejpam-3312	78	5	,	,	PUNCT
ejpam-3312	78	6	the	the	DET
ejpam-3312	78	7	authors	author	NOUN
ejpam-3312	78	8	termed	term	VERB
ejpam-3312	78	9	τ	τ	X
ejpam-3312	78	10	?	?	PUNCT
ejpam-3312	79	1	an	an	DET
ejpam-3312	79	2	extended	extended	ADJ
ejpam-3312	79	3	soft	soft	ADJ
ejpam-3312	79	4	topology	topology	NOUN
ejpam-3312	79	5	.	.	PUNCT
ejpam-3312	80	1	t.	t.	PROPN
ejpam-3312	80	2	m.	m.	PROPN
ejpam-3312	80	3	al	al	PROPN
ejpam-3312	80	4	-	-	PUNCT
ejpam-3312	80	5	shami	shami	PROPN
ejpam-3312	80	6	,	,	PUNCT
ejpam-3312	80	7	m.	m.	PROPN
ejpam-3312	80	8	e.	e.	PROPN
ejpam-3312	80	9	el	el	PROPN
ejpam-3312	80	10	-	-	PROPN
ejpam-3312	80	11	shafei	shafei	PROPN
ejpam-3312	80	12	,	,	PUNCT
ejpam-3312	80	13	b.	b.	PROPN
ejpam-3312	80	14	a.	a.	PROPN
ejpam-3312	80	15	asaad	asaad	PROPN
ejpam-3312	80	16	/	/	SYM
ejpam-3312	80	17	eur	eur	PROPN
ejpam-3312	80	18	.	.	PUNCT
ejpam-3312	81	1	j.	j.	PROPN
ejpam-3312	81	2	pure	pure	PROPN
ejpam-3312	81	3	appl	appl	PROPN
ejpam-3312	81	4	.	.	PROPN
ejpam-3312	81	5	math	math	PROPN
ejpam-3312	81	6	,	,	PUNCT
ejpam-3312	81	7	12	12	NUM
ejpam-3312	81	8	(	(	PUNCT
ejpam-3312	81	9	1	1	NUM
ejpam-3312	81	10	)	)	PUNCT
ejpam-3312	81	11	(	(	PUNCT
ejpam-3312	81	12	2019	2019	NUM
ejpam-3312	81	13	)	)	PUNCT
ejpam-3312	81	14	,	,	PUNCT
ejpam-3312	81	15	176	176	NUM
ejpam-3312	81	16	-	-	SYM
ejpam-3312	81	17	193	193	NUM
ejpam-3312	81	18	179	179	NUM
ejpam-3312	81	19	definition	definition	NOUN
ejpam-3312	81	20	6	6	NUM
ejpam-3312	81	21	.	.	PUNCT
ejpam-3312	82	1	[	[	X
ejpam-3312	82	2	46	46	NUM
ejpam-3312	82	3	]	]	PUNCT
ejpam-3312	82	4	consider	consider	VERB
ejpam-3312	82	5	f	f	X
ejpam-3312	82	6	:	:	PUNCT
ejpam-3312	82	7	x	x	X
ejpam-3312	82	8	→	→	SYM
ejpam-3312	82	9	y	y	PROPN
ejpam-3312	82	10	and	and	CCONJ
ejpam-3312	82	11	φ	φ	NUM
ejpam-3312	82	12	:	:	PUNCT
ejpam-3312	82	13	a	a	DET
ejpam-3312	82	14	→	→	SYM
ejpam-3312	82	15	b	b	PROPN
ejpam-3312	82	16	are	be	AUX
ejpam-3312	82	17	two	two	NUM
ejpam-3312	82	18	mappings	mapping	NOUN
ejpam-3312	82	19	and	and	CCONJ
ejpam-3312	82	20	let	let	VERB
ejpam-3312	82	21	fφ	fφ	PRON
ejpam-3312	82	22	:	:	PUNCT
ejpam-3312	82	23	s(xa	s(xa	PROPN
ejpam-3312	82	24	)	)	PUNCT
ejpam-3312	82	25	→	→	SYM
ejpam-3312	83	1	s(yb	s(yb	NUM
ejpam-3312	83	2	)	)	PUNCT
ejpam-3312	83	3	be	be	AUX
ejpam-3312	83	4	a	a	DET
ejpam-3312	83	5	soft	soft	ADJ
ejpam-3312	83	6	mapping	mapping	NOUN
ejpam-3312	83	7	.	.	PUNCT
ejpam-3312	84	1	let	let	VERB
ejpam-3312	84	2	gk	gk	NOUN
ejpam-3312	84	3	and	and	CCONJ
ejpam-3312	84	4	hl	hl	NOUN
ejpam-3312	84	5	be	be	AUX
ejpam-3312	84	6	soft	soft	ADJ
ejpam-3312	84	7	subsets	subset	NOUN
ejpam-3312	84	8	of	of	ADP
ejpam-3312	84	9	s(xa	s(xa	NOUN
ejpam-3312	84	10	)	)	PUNCT
ejpam-3312	84	11	and	and	CCONJ
ejpam-3312	84	12	s(yb	s(yb	NUM
ejpam-3312	84	13	)	)	PUNCT
ejpam-3312	84	14	,	,	PUNCT
ejpam-3312	84	15	respectively	respectively	ADV
ejpam-3312	84	16	.	.	PUNCT
ejpam-3312	85	1	then	then	ADV
ejpam-3312	85	2	(	(	PUNCT
ejpam-3312	85	3	i	i	NOUN
ejpam-3312	85	4	)	)	PUNCT
ejpam-3312	85	5	fφ(gk	fφ(gk	NOUN
ejpam-3312	85	6	)	)	PUNCT
ejpam-3312	85	7	=	=	SYM
ejpam-3312	85	8	(	(	PUNCT
ejpam-3312	85	9	fφ(g))b	fφ(g))b	PROPN
ejpam-3312	85	10	is	be	AUX
ejpam-3312	85	11	a	a	DET
ejpam-3312	85	12	soft	soft	ADJ
ejpam-3312	85	13	subset	subset	NOUN
ejpam-3312	85	14	of	of	ADP
ejpam-3312	85	15	s(yb	s(yb	NOUN
ejpam-3312	85	16	)	)	PUNCT
ejpam-3312	85	17	such	such	ADJ
ejpam-3312	85	18	that	that	DET
ejpam-3312	85	19	fφ(g)(b	fφ(g)(b	NUM
ejpam-3312	85	20	)	)	PUNCT
ejpam-3312	86	1	=	=	PRON
ejpam-3312	86	2	{	{	PUNCT
ejpam-3312	86	3	⋃	⋃	NOUN
ejpam-3312	86	4	a∈φ−1(b	a∈φ−1(b	NOUN
ejpam-3312	86	5	)	)	PUNCT
ejpam-3312	86	6	⋂	⋂	PROPN
ejpam-3312	86	7	k	k	PROPN
ejpam-3312	86	8	f(g(a	f(g(a	PROPN
ejpam-3312	86	9	)	)	PUNCT
ejpam-3312	86	10	)	)	PUNCT
ejpam-3312	86	11	:	:	PUNCT
ejpam-3312	87	1	φ−1(b	φ−1(b	PROPN
ejpam-3312	87	2	)	)	PUNCT
ejpam-3312	88	1	⋂	⋂	PROPN
ejpam-3312	88	2	k	k	PROPN
ejpam-3312	88	3	6=	6=	PROPN
ejpam-3312	88	4	∅	∅	NOUN
ejpam-3312	88	5	∅	∅	NOUN
ejpam-3312	88	6	:	:	PUNCT
ejpam-3312	88	7	φ−1(b	φ−1(b	PROPN
ejpam-3312	88	8	)	)	PUNCT
ejpam-3312	88	9	⋂	⋂	PROPN
ejpam-3312	88	10	k	k	NOUN
ejpam-3312	88	11	=	=	NOUN
ejpam-3312	88	12	∅	∅	NOUN
ejpam-3312	88	13	for	for	ADP
ejpam-3312	88	14	each	each	DET
ejpam-3312	88	15	b	b	PROPN
ejpam-3312	88	16	∈	∈	PROPN
ejpam-3312	88	17	b.	b.	PROPN
ejpam-3312	88	18	(	(	PUNCT
ejpam-3312	88	19	ii	ii	NOUN
ejpam-3312	88	20	)	)	PUNCT
ejpam-3312	88	21	f−1φ	f−1φ	NOUN
ejpam-3312	88	22	(	(	PUNCT
ejpam-3312	88	23	hl	hl	NOUN
ejpam-3312	88	24	)	)	PUNCT
ejpam-3312	88	25	=	=	SYM
ejpam-3312	88	26	(	(	PUNCT
ejpam-3312	88	27	f−1φ	f−1φ	NOUN
ejpam-3312	88	28	(	(	PUNCT
ejpam-3312	88	29	h))a	h))a	NOUN
ejpam-3312	88	30	is	be	AUX
ejpam-3312	88	31	a	a	DET
ejpam-3312	88	32	soft	soft	ADJ
ejpam-3312	88	33	subset	subset	NOUN
ejpam-3312	88	34	of	of	ADP
ejpam-3312	88	35	s(xa	s(xa	NOUN
ejpam-3312	88	36	)	)	PUNCT
ejpam-3312	88	37	such	such	ADJ
ejpam-3312	88	38	that	that	SCONJ
ejpam-3312	88	39	f−1φ	f−1φ	NOUN
ejpam-3312	88	40	(	(	PUNCT
ejpam-3312	88	41	h)(a	h)(a	NOUN
ejpam-3312	88	42	)	)	PUNCT
ejpam-3312	88	43	=	=	PRON
ejpam-3312	88	44	{	{	PUNCT
ejpam-3312	88	45	f−1(h(φ(a	f−1(h(φ(a	ADJ
ejpam-3312	88	46	)	)	PUNCT
ejpam-3312	88	47	)	)	PUNCT
ejpam-3312	88	48	)	)	PUNCT
ejpam-3312	88	49	:	:	PUNCT
ejpam-3312	88	50	φ(a	φ(a	ADJ
ejpam-3312	88	51	)	)	PUNCT
ejpam-3312	88	52	∈	∈	PROPN
ejpam-3312	88	53	l	l	NOUN
ejpam-3312	88	54	∅	∅	NOUN
ejpam-3312	88	55	:	:	PUNCT
ejpam-3312	88	56	φ(a	φ(a	ADJ
ejpam-3312	88	57	)	)	PUNCT
ejpam-3312	88	58	6∈	6∈	NOUN
ejpam-3312	88	59	l	l	NOUN
ejpam-3312	88	60	for	for	ADP
ejpam-3312	88	61	each	each	DET
ejpam-3312	88	62	a	a	DET
ejpam-3312	88	63	∈	∈	PROPN
ejpam-3312	88	64	a.	a.	NOUN
ejpam-3312	88	65	remark	remark	NOUN
ejpam-3312	88	66	1	1	NUM
ejpam-3312	88	67	.	.	PUNCT
ejpam-3312	89	1	henceforth	henceforth	ADV
ejpam-3312	89	2	,	,	PUNCT
ejpam-3312	89	3	a	a	DET
ejpam-3312	89	4	soft	soft	ADJ
ejpam-3312	89	5	mapping	mapping	NOUN
ejpam-3312	89	6	fφ	fφ	NOUN
ejpam-3312	89	7	:	:	PUNCT
ejpam-3312	89	8	s(xa	s(xa	PROPN
ejpam-3312	89	9	)	)	PUNCT
ejpam-3312	89	10	→	→	SYM
ejpam-3312	89	11	s(yb	s(yb	NUM
ejpam-3312	89	12	)	)	PUNCT
ejpam-3312	89	13	implies	imply	VERB
ejpam-3312	89	14	that	that	SCONJ
ejpam-3312	89	15	a	a	DET
ejpam-3312	89	16	mapping	mapping	NOUN
ejpam-3312	89	17	f	f	NOUN
ejpam-3312	89	18	of	of	ADP
ejpam-3312	89	19	the	the	DET
ejpam-3312	89	20	universe	universe	NOUN
ejpam-3312	89	21	set	set	NOUN
ejpam-3312	89	22	x	x	PUNCT
ejpam-3312	89	23	into	into	ADP
ejpam-3312	89	24	the	the	DET
ejpam-3312	89	25	universe	universe	NOUN
ejpam-3312	89	26	set	set	VERB
ejpam-3312	89	27	y	y	PROPN
ejpam-3312	89	28	and	and	CCONJ
ejpam-3312	89	29	a	a	DET
ejpam-3312	89	30	mapping	mapping	NOUN
ejpam-3312	89	31	φ	φ	NOUN
ejpam-3312	89	32	of	of	ADP
ejpam-3312	89	33	the	the	DET
ejpam-3312	89	34	set	set	NOUN
ejpam-3312	89	35	of	of	ADP
ejpam-3312	89	36	parameters	parameter	NOUN
ejpam-3312	89	37	a	a	PRON
ejpam-3312	89	38	into	into	ADP
ejpam-3312	89	39	the	the	DET
ejpam-3312	89	40	set	set	NOUN
ejpam-3312	89	41	of	of	ADP
ejpam-3312	89	42	parameters	parameter	NOUN
ejpam-3312	89	43	b	b	PROPN
ejpam-3312	89	44	definition	definition	NOUN
ejpam-3312	89	45	7	7	NUM
ejpam-3312	89	46	.	.	PUNCT
ejpam-3312	90	1	[	[	X
ejpam-3312	90	2	46	46	NUM
ejpam-3312	90	3	]	]	PUNCT
ejpam-3312	90	4	a	a	DET
ejpam-3312	90	5	soft	soft	ADJ
ejpam-3312	90	6	mapping	mapping	NOUN
ejpam-3312	90	7	fφ	fφ	NOUN
ejpam-3312	90	8	:	:	PUNCT
ejpam-3312	90	9	s(xa	s(xa	PROPN
ejpam-3312	90	10	)	)	PUNCT
ejpam-3312	90	11	→	→	SYM
ejpam-3312	90	12	s(yb	s(yb	NUM
ejpam-3312	90	13	)	)	PUNCT
ejpam-3312	90	14	is	be	AUX
ejpam-3312	90	15	said	say	VERB
ejpam-3312	90	16	to	to	PART
ejpam-3312	90	17	be	be	AUX
ejpam-3312	90	18	injective	injective	ADJ
ejpam-3312	90	19	(	(	PUNCT
ejpam-3312	90	20	resp	resp	NOUN
ejpam-3312	90	21	.	.	PUNCT
ejpam-3312	91	1	surjective	surjective	PROPN
ejpam-3312	91	2	,	,	PUNCT
ejpam-3312	91	3	bijective	bijective	ADJ
ejpam-3312	91	4	)	)	PUNCT
ejpam-3312	91	5	if	if	SCONJ
ejpam-3312	91	6	f	f	PROPN
ejpam-3312	91	7	and	and	CCONJ
ejpam-3312	91	8	φ	φ	PROPN
ejpam-3312	91	9	are	be	AUX
ejpam-3312	91	10	injective	injective	ADJ
ejpam-3312	91	11	(	(	PUNCT
ejpam-3312	91	12	resp	resp	NOUN
ejpam-3312	91	13	.	.	PUNCT
ejpam-3312	92	1	surjective	surjective	ADJ
ejpam-3312	92	2	,	,	PUNCT
ejpam-3312	92	3	bijective	bijective	ADJ
ejpam-3312	92	4	)	)	PUNCT
ejpam-3312	92	5	.	.	PUNCT
ejpam-3312	93	1	proposition	proposition	NOUN
ejpam-3312	93	2	2	2	NUM
ejpam-3312	93	3	.	.	PUNCT
ejpam-3312	94	1	[	[	X
ejpam-3312	94	2	46	46	NUM
ejpam-3312	94	3	]	]	PUNCT
ejpam-3312	94	4	consider	consider	VERB
ejpam-3312	94	5	fφ	fφ	PRON
ejpam-3312	94	6	:	:	PUNCT
ejpam-3312	94	7	s(xa)→	s(xa)→	PROPN
ejpam-3312	94	8	s(yb	s(yb	PROPN
ejpam-3312	94	9	)	)	PUNCT
ejpam-3312	94	10	is	be	AUX
ejpam-3312	94	11	a	a	DET
ejpam-3312	94	12	soft	soft	ADJ
ejpam-3312	94	13	mapping	mapping	NOUN
ejpam-3312	94	14	and	and	CCONJ
ejpam-3312	94	15	let	let	VERB
ejpam-3312	94	16	ga	ga	PROPN
ejpam-3312	94	17	and	and	CCONJ
ejpam-3312	94	18	hb	hb	PROPN
ejpam-3312	94	19	be	be	AUX
ejpam-3312	94	20	two	two	NUM
ejpam-3312	94	21	soft	soft	ADJ
ejpam-3312	94	22	subsets	subset	NOUN
ejpam-3312	94	23	of	of	ADP
ejpam-3312	94	24	s(xa	s(xa	NOUN
ejpam-3312	94	25	)	)	PUNCT
ejpam-3312	94	26	and	and	CCONJ
ejpam-3312	94	27	s(yb	s(yb	NUM
ejpam-3312	94	28	)	)	PUNCT
ejpam-3312	94	29	,	,	PUNCT
ejpam-3312	94	30	respectively	respectively	ADV
ejpam-3312	94	31	.	.	PUNCT
ejpam-3312	95	1	then	then	ADV
ejpam-3312	95	2	we	we	PRON
ejpam-3312	95	3	have	have	VERB
ejpam-3312	95	4	the	the	DET
ejpam-3312	95	5	following	follow	VERB
ejpam-3312	95	6	results	result	NOUN
ejpam-3312	95	7	:	:	PUNCT
ejpam-3312	95	8	(	(	PUNCT
ejpam-3312	95	9	i	i	NOUN
ejpam-3312	95	10	)	)	PUNCT
ejpam-3312	95	11	ga⊆̃f−1φ	ga⊆̃f−1φ	PROPN
ejpam-3312	95	12	fφ(ga	fφ(ga	NOUN
ejpam-3312	95	13	)	)	PUNCT
ejpam-3312	95	14	and	and	CCONJ
ejpam-3312	95	15	the	the	DET
ejpam-3312	95	16	equality	equality	NOUN
ejpam-3312	95	17	relation	relation	NOUN
ejpam-3312	95	18	holds	hold	VERB
ejpam-3312	95	19	if	if	SCONJ
ejpam-3312	95	20	fφ	fφ	PROPN
ejpam-3312	95	21	is	be	AUX
ejpam-3312	95	22	injective	injective	ADJ
ejpam-3312	95	23	.	.	PUNCT
ejpam-3312	96	1	(	(	PUNCT
ejpam-3312	96	2	ii	ii	NOUN
ejpam-3312	96	3	)	)	PUNCT
ejpam-3312	96	4	fφf	fφf	PROPN
ejpam-3312	96	5	−1	−1	NOUN
ejpam-3312	96	6	φ	φ	PROPN
ejpam-3312	96	7	(	(	PUNCT
ejpam-3312	96	8	hb)⊆̃hb	hb)⊆̃hb	PROPN
ejpam-3312	96	9	and	and	CCONJ
ejpam-3312	96	10	the	the	DET
ejpam-3312	96	11	equality	equality	NOUN
ejpam-3312	96	12	relation	relation	NOUN
ejpam-3312	96	13	holds	hold	VERB
ejpam-3312	96	14	if	if	SCONJ
ejpam-3312	96	15	fφ	fφ	PROPN
ejpam-3312	96	16	is	be	AUX
ejpam-3312	96	17	surjective	surjective	ADJ
ejpam-3312	96	18	.	.	PUNCT
ejpam-3312	97	1	definition	definition	NOUN
ejpam-3312	97	2	8	8	NUM
ejpam-3312	97	3	.	.	PUNCT
ejpam-3312	98	1	[	[	X
ejpam-3312	98	2	5	5	NUM
ejpam-3312	98	3	]	]	PUNCT
ejpam-3312	98	4	a	a	DET
ejpam-3312	98	5	soft	soft	ADJ
ejpam-3312	98	6	subset	subset	NOUN
ejpam-3312	98	7	he	he	PRON
ejpam-3312	98	8	of	of	ADP
ejpam-3312	98	9	(	(	PUNCT
ejpam-3312	98	10	x	x	PROPN
ejpam-3312	98	11	,	,	PUNCT
ejpam-3312	98	12	τ	τ	PROPN
ejpam-3312	98	13	,	,	PUNCT
ejpam-3312	98	14	e	e	NOUN
ejpam-3312	98	15	)	)	PUNCT
ejpam-3312	98	16	is	be	AUX
ejpam-3312	98	17	said	say	VERB
ejpam-3312	98	18	to	to	PART
ejpam-3312	98	19	be	be	AUX
ejpam-3312	98	20	soft	soft	ADJ
ejpam-3312	98	21	β	β	NOUN
ejpam-3312	98	22	-	-	ADJ
ejpam-3312	98	23	open	open	ADJ
ejpam-3312	98	24	if	if	SCONJ
ejpam-3312	98	25	he⊆̃cl(int(cl(he	he⊆̃cl(int(cl(he	NUM
ejpam-3312	98	26	)	)	PUNCT
ejpam-3312	98	27	)	)	PUNCT
ejpam-3312	98	28	)	)	PUNCT
ejpam-3312	98	29	.	.	PUNCT
ejpam-3312	99	1	and	and	CCONJ
ejpam-3312	99	2	its	its	PRON
ejpam-3312	99	3	relative	relative	ADJ
ejpam-3312	99	4	complement	complement	NOUN
ejpam-3312	99	5	is	be	AUX
ejpam-3312	99	6	said	say	VERB
ejpam-3312	99	7	to	to	PART
ejpam-3312	99	8	be	be	AUX
ejpam-3312	99	9	soft	soft	ADJ
ejpam-3312	99	10	β	β	NOUN
ejpam-3312	99	11	-	-	VERB
ejpam-3312	99	12	closed	closed	ADJ
ejpam-3312	99	13	.	.	PUNCT
ejpam-3312	100	1	definition	definition	NOUN
ejpam-3312	100	2	9	9	NUM
ejpam-3312	100	3	.	.	PUNCT
ejpam-3312	101	1	(	(	PUNCT
ejpam-3312	101	2	[	[	X
ejpam-3312	101	3	5	5	NUM
ejpam-3312	101	4	]	]	PUNCT
ejpam-3312	101	5	,	,	PUNCT
ejpam-3312	101	6	[	[	X
ejpam-3312	101	7	44	44	NUM
ejpam-3312	101	8	]	]	PUNCT
ejpam-3312	101	9	)	)	PUNCT
ejpam-3312	101	10	for	for	ADP
ejpam-3312	101	11	a	a	DET
ejpam-3312	101	12	soft	soft	ADJ
ejpam-3312	101	13	subset	subset	NOUN
ejpam-3312	101	14	he	he	PRON
ejpam-3312	101	15	of	of	ADP
ejpam-3312	101	16	(	(	PUNCT
ejpam-3312	101	17	x	x	PROPN
ejpam-3312	101	18	,	,	PUNCT
ejpam-3312	101	19	τ	τ	PROPN
ejpam-3312	101	20	,	,	PUNCT
ejpam-3312	101	21	e	e	NOUN
ejpam-3312	101	22	)	)	PUNCT
ejpam-3312	101	23	,	,	PUNCT
ejpam-3312	101	24	we	we	PRON
ejpam-3312	101	25	define	define	VERB
ejpam-3312	101	26	the	the	DET
ejpam-3312	101	27	following	follow	VERB
ejpam-3312	101	28	four	four	NUM
ejpam-3312	101	29	operators	operator	NOUN
ejpam-3312	101	30	:	:	PUNCT
ejpam-3312	101	31	(	(	PUNCT
ejpam-3312	101	32	i	i	NOUN
ejpam-3312	101	33	)	)	PUNCT
ejpam-3312	101	34	int(he	int(he	NOUN
ejpam-3312	101	35	)	)	PUNCT
ejpam-3312	101	36	(	(	PUNCT
ejpam-3312	101	37	resp	resp	NOUN
ejpam-3312	101	38	.	.	PUNCT
ejpam-3312	102	1	intβ(he	intβ(he	PROPN
ejpam-3312	102	2	)	)	PUNCT
ejpam-3312	102	3	)	)	PUNCT
ejpam-3312	102	4	is	be	AUX
ejpam-3312	102	5	the	the	DET
ejpam-3312	102	6	largest	large	ADJ
ejpam-3312	102	7	soft	soft	ADJ
ejpam-3312	102	8	open	open	ADJ
ejpam-3312	102	9	(	(	PUNCT
ejpam-3312	102	10	resp	resp	NOUN
ejpam-3312	102	11	.	.	PUNCT
ejpam-3312	103	1	soft	soft	ADJ
ejpam-3312	103	2	β	β	NOUN
ejpam-3312	103	3	-	-	ADJ
ejpam-3312	103	4	open	open	ADJ
ejpam-3312	103	5	)	)	PUNCT
ejpam-3312	103	6	set	set	NOUN
ejpam-3312	103	7	contained	contain	VERB
ejpam-3312	103	8	in	in	ADP
ejpam-3312	103	9	he	he	PRON
ejpam-3312	103	10	.	.	PUNCT
ejpam-3312	104	1	(	(	PUNCT
ejpam-3312	104	2	ii	ii	NOUN
ejpam-3312	104	3	)	)	PUNCT
ejpam-3312	104	4	cl(he	cl(he	NOUN
ejpam-3312	104	5	)	)	PUNCT
ejpam-3312	104	6	(	(	PUNCT
ejpam-3312	104	7	resp	resp	NOUN
ejpam-3312	104	8	.	.	PUNCT
ejpam-3312	104	9	clβ(he	clβ(he	NUM
ejpam-3312	104	10	)	)	PUNCT
ejpam-3312	104	11	)	)	PUNCT
ejpam-3312	104	12	is	be	AUX
ejpam-3312	104	13	the	the	DET
ejpam-3312	104	14	smallest	small	ADJ
ejpam-3312	104	15	soft	soft	ADJ
ejpam-3312	104	16	closed	closed	ADJ
ejpam-3312	104	17	(	(	PUNCT
ejpam-3312	104	18	resp	resp	NOUN
ejpam-3312	104	19	.	.	PUNCT
ejpam-3312	105	1	soft	soft	ADJ
ejpam-3312	105	2	β	β	NOUN
ejpam-3312	105	3	-	-	VERB
ejpam-3312	105	4	closed	closed	ADJ
ejpam-3312	105	5	)	)	PUNCT
ejpam-3312	105	6	set	set	NOUN
ejpam-3312	105	7	containing	contain	VERB
ejpam-3312	105	8	he	he	PRON
ejpam-3312	105	9	.	.	PUNCT
ejpam-3312	106	1	definition	definition	NOUN
ejpam-3312	106	2	10	10	NUM
ejpam-3312	106	3	.	.	PUNCT
ejpam-3312	107	1	[	[	X
ejpam-3312	107	2	5	5	NUM
ejpam-3312	107	3	]	]	PUNCT
ejpam-3312	107	4	a	a	DET
ejpam-3312	107	5	soft	soft	ADJ
ejpam-3312	107	6	mapping	mapping	NOUN
ejpam-3312	107	7	fφ	fφ	NOUN
ejpam-3312	107	8	:	:	PUNCT
ejpam-3312	107	9	(	(	PUNCT
ejpam-3312	107	10	x	x	X
ejpam-3312	107	11	,	,	PUNCT
ejpam-3312	107	12	τ	τ	PROPN
ejpam-3312	107	13	,	,	PUNCT
ejpam-3312	107	14	a)→	a)→	NOUN
ejpam-3312	107	15	(	(	PUNCT
ejpam-3312	107	16	y	y	PROPN
ejpam-3312	107	17	,	,	PUNCT
ejpam-3312	107	18	θ	θ	PROPN
ejpam-3312	107	19	,	,	PUNCT
ejpam-3312	107	20	b	b	NOUN
ejpam-3312	107	21	)	)	PUNCT
ejpam-3312	107	22	is	be	AUX
ejpam-3312	107	23	said	say	VERB
ejpam-3312	107	24	to	to	PART
ejpam-3312	107	25	be	be	AUX
ejpam-3312	107	26	:	:	PUNCT
ejpam-3312	107	27	(	(	PUNCT
ejpam-3312	107	28	i	i	NOUN
ejpam-3312	107	29	)	)	PUNCT
ejpam-3312	107	30	soft	soft	ADJ
ejpam-3312	107	31	β	β	NOUN
ejpam-3312	107	32	-	-	ADJ
ejpam-3312	107	33	continuous	continuous	ADJ
ejpam-3312	107	34	if	if	SCONJ
ejpam-3312	107	35	the	the	DET
ejpam-3312	107	36	inverse	inverse	ADJ
ejpam-3312	107	37	image	image	NOUN
ejpam-3312	107	38	of	of	ADP
ejpam-3312	107	39	each	each	DET
ejpam-3312	107	40	soft	soft	ADJ
ejpam-3312	107	41	open	open	ADJ
ejpam-3312	107	42	subset	subset	NOUN
ejpam-3312	107	43	of	of	ADP
ejpam-3312	107	44	(	(	PUNCT
ejpam-3312	107	45	y	y	PROPN
ejpam-3312	107	46	,	,	PUNCT
ejpam-3312	107	47	θ	θ	PROPN
ejpam-3312	107	48	,	,	PUNCT
ejpam-3312	107	49	b	b	NOUN
ejpam-3312	107	50	)	)	PUNCT
ejpam-3312	107	51	is	be	AUX
ejpam-3312	107	52	a	a	DET
ejpam-3312	107	53	soft	soft	ADJ
ejpam-3312	107	54	β	β	NOUN
ejpam-3312	107	55	-	-	ADJ
ejpam-3312	107	56	open	open	ADJ
ejpam-3312	107	57	subset	subset	NOUN
ejpam-3312	107	58	of	of	ADP
ejpam-3312	107	59	(	(	PUNCT
ejpam-3312	107	60	x	x	PROPN
ejpam-3312	107	61	,	,	PUNCT
ejpam-3312	107	62	τ	τ	PROPN
ejpam-3312	107	63	,	,	PUNCT
ejpam-3312	107	64	a	a	PRON
ejpam-3312	107	65	)	)	PUNCT
ejpam-3312	107	66	.	.	PUNCT
ejpam-3312	108	1	t.	t.	PROPN
ejpam-3312	108	2	m.	m.	PROPN
ejpam-3312	108	3	al	al	PROPN
ejpam-3312	108	4	-	-	PUNCT
ejpam-3312	108	5	shami	shami	PROPN
ejpam-3312	108	6	,	,	PUNCT
ejpam-3312	108	7	m.	m.	PROPN
ejpam-3312	108	8	e.	e.	PROPN
ejpam-3312	108	9	el	el	PROPN
ejpam-3312	108	10	-	-	PROPN
ejpam-3312	108	11	shafei	shafei	PROPN
ejpam-3312	108	12	,	,	PUNCT
ejpam-3312	108	13	b.	b.	PROPN
ejpam-3312	108	14	a.	a.	PROPN
ejpam-3312	108	15	asaad	asaad	PROPN
ejpam-3312	108	16	/	/	SYM
ejpam-3312	108	17	eur	eur	PROPN
ejpam-3312	108	18	.	.	PUNCT
ejpam-3312	109	1	j.	j.	PROPN
ejpam-3312	109	2	pure	pure	PROPN
ejpam-3312	109	3	appl	appl	PROPN
ejpam-3312	109	4	.	.	PROPN
ejpam-3312	109	5	math	math	PROPN
ejpam-3312	109	6	,	,	PUNCT
ejpam-3312	109	7	12	12	NUM
ejpam-3312	109	8	(	(	PUNCT
ejpam-3312	109	9	1	1	NUM
ejpam-3312	109	10	)	)	PUNCT
ejpam-3312	109	11	(	(	PUNCT
ejpam-3312	109	12	2019	2019	NUM
ejpam-3312	109	13	)	)	PUNCT
ejpam-3312	109	14	,	,	PUNCT
ejpam-3312	109	15	176	176	NUM
ejpam-3312	109	16	-	-	SYM
ejpam-3312	109	17	193	193	NUM
ejpam-3312	109	18	180	180	NUM
ejpam-3312	109	19	(	(	PUNCT
ejpam-3312	109	20	ii	ii	NOUN
ejpam-3312	109	21	)	)	PUNCT
ejpam-3312	109	22	soft	soft	ADJ
ejpam-3312	109	23	β	β	X
ejpam-3312	109	24	-	-	ADJ
ejpam-3312	109	25	open	open	ADJ
ejpam-3312	109	26	(	(	PUNCT
ejpam-3312	109	27	resp	resp	NOUN
ejpam-3312	109	28	.	.	PUNCT
ejpam-3312	110	1	soft	soft	ADJ
ejpam-3312	110	2	β	β	NOUN
ejpam-3312	110	3	-	-	VERB
ejpam-3312	110	4	closed	closed	ADJ
ejpam-3312	110	5	)	)	PUNCT
ejpam-3312	110	6	if	if	SCONJ
ejpam-3312	110	7	the	the	DET
ejpam-3312	110	8	image	image	NOUN
ejpam-3312	110	9	of	of	ADP
ejpam-3312	110	10	each	each	DET
ejpam-3312	110	11	soft	soft	ADJ
ejpam-3312	110	12	open	open	ADJ
ejpam-3312	110	13	(	(	PUNCT
ejpam-3312	110	14	resp	resp	NOUN
ejpam-3312	110	15	.	.	PUNCT
ejpam-3312	111	1	soft	soft	ADJ
ejpam-3312	111	2	closed	closed	ADJ
ejpam-3312	111	3	)	)	PUNCT
ejpam-3312	111	4	subset	subset	NOUN
ejpam-3312	111	5	of	of	ADP
ejpam-3312	111	6	(	(	PUNCT
ejpam-3312	111	7	x	x	PROPN
ejpam-3312	111	8	,	,	PUNCT
ejpam-3312	111	9	τ	τ	PROPN
ejpam-3312	111	10	,	,	PUNCT
ejpam-3312	111	11	a	a	PRON
ejpam-3312	111	12	)	)	PUNCT
ejpam-3312	111	13	is	be	AUX
ejpam-3312	111	14	a	a	DET
ejpam-3312	111	15	soft	soft	ADJ
ejpam-3312	111	16	β	β	NOUN
ejpam-3312	111	17	-	-	ADJ
ejpam-3312	111	18	open	open	ADJ
ejpam-3312	111	19	(	(	PUNCT
ejpam-3312	111	20	resp	resp	NOUN
ejpam-3312	111	21	.	.	PUNCT
ejpam-3312	112	1	soft	soft	ADJ
ejpam-3312	112	2	β	β	NOUN
ejpam-3312	112	3	-	-	VERB
ejpam-3312	112	4	closed	closed	ADJ
ejpam-3312	112	5	)	)	PUNCT
ejpam-3312	112	6	subset	subset	NOUN
ejpam-3312	112	7	of	of	ADP
ejpam-3312	112	8	(	(	PUNCT
ejpam-3312	112	9	y	y	PROPN
ejpam-3312	112	10	,	,	PUNCT
ejpam-3312	112	11	θ	θ	PROPN
ejpam-3312	112	12	,	,	PUNCT
ejpam-3312	112	13	b	b	NOUN
ejpam-3312	112	14	)	)	PUNCT
ejpam-3312	112	15	.	.	PUNCT
ejpam-3312	113	1	(	(	PUNCT
ejpam-3312	113	2	iii	iii	X
ejpam-3312	113	3	)	)	PUNCT
ejpam-3312	113	4	soft	soft	ADJ
ejpam-3312	113	5	β	β	NOUN
ejpam-3312	113	6	-	-	PUNCT
ejpam-3312	113	7	homeomorphism	homeomorphism	NOUN
ejpam-3312	113	8	if	if	SCONJ
ejpam-3312	113	9	it	it	PRON
ejpam-3312	113	10	is	be	AUX
ejpam-3312	113	11	bijective	bijective	ADJ
ejpam-3312	113	12	,	,	PUNCT
ejpam-3312	113	13	soft	soft	ADJ
ejpam-3312	113	14	β	β	NOUN
ejpam-3312	113	15	-	-	ADJ
ejpam-3312	113	16	continuous	continuous	ADJ
ejpam-3312	113	17	and	and	CCONJ
ejpam-3312	113	18	soft	soft	ADJ
ejpam-3312	113	19	β	β	NOUN
ejpam-3312	113	20	-	-	ADJ
ejpam-3312	113	21	open	open	ADJ
ejpam-3312	113	22	.	.	PUNCT
ejpam-3312	114	1	definition	definition	NOUN
ejpam-3312	114	2	11	11	NUM
ejpam-3312	114	3	.	.	PUNCT
ejpam-3312	115	1	[	[	X
ejpam-3312	115	2	19	19	NUM
ejpam-3312	115	3	,	,	PUNCT
ejpam-3312	115	4	38	38	NUM
ejpam-3312	115	5	]	]	PUNCT
ejpam-3312	115	6	a	a	DET
ejpam-3312	115	7	soft	soft	ADJ
ejpam-3312	115	8	set	set	NOUN
ejpam-3312	115	9	pe	pe	INTJ
ejpam-3312	115	10	over	over	ADP
ejpam-3312	115	11	x	x	VERB
ejpam-3312	115	12	is	be	AUX
ejpam-3312	115	13	called	call	VERB
ejpam-3312	115	14	soft	soft	ADJ
ejpam-3312	115	15	point	point	NOUN
ejpam-3312	115	16	if	if	SCONJ
ejpam-3312	115	17	there	there	PRON
ejpam-3312	115	18	exists	exist	VERB
ejpam-3312	115	19	e	e	X
ejpam-3312	115	20	∈	∈	NOUN
ejpam-3312	115	21	e	e	X
ejpam-3312	115	22	and	and	CCONJ
ejpam-3312	115	23	there	there	PRON
ejpam-3312	115	24	exists	exist	VERB
ejpam-3312	115	25	x	x	X
ejpam-3312	115	26	∈	∈	PROPN
ejpam-3312	115	27	x	x	X
ejpam-3312	116	1	such	such	ADJ
ejpam-3312	116	2	that	that	SCONJ
ejpam-3312	116	3	p	p	X
ejpam-3312	116	4	(	(	PUNCT
ejpam-3312	116	5	e	e	NOUN
ejpam-3312	116	6	)	)	PUNCT
ejpam-3312	116	7	=	=	SYM
ejpam-3312	116	8	{	{	PUNCT
ejpam-3312	116	9	x	x	NOUN
ejpam-3312	116	10	}	}	PUNCT
ejpam-3312	116	11	and	and	CCONJ
ejpam-3312	116	12	p	p	X
ejpam-3312	116	13	(	(	PUNCT
ejpam-3312	116	14	a	a	NOUN
ejpam-3312	116	15	)	)	PUNCT
ejpam-3312	116	16	=	=	NOUN
ejpam-3312	116	17	∅	∅	NOUN
ejpam-3312	116	18	,	,	PUNCT
ejpam-3312	116	19	for	for	ADP
ejpam-3312	116	20	each	each	DET
ejpam-3312	116	21	a	a	DET
ejpam-3312	116	22	∈	∈	PROPN
ejpam-3312	116	23	e	e	X
ejpam-3312	116	24	\	\	X
ejpam-3312	116	25	{	{	PUNCT
ejpam-3312	116	26	e	e	NOUN
ejpam-3312	116	27	}	}	PUNCT
ejpam-3312	116	28	.	.	PUNCT
ejpam-3312	117	1	a	a	DET
ejpam-3312	117	2	soft	soft	ADJ
ejpam-3312	117	3	point	point	NOUN
ejpam-3312	117	4	will	will	AUX
ejpam-3312	117	5	be	be	AUX
ejpam-3312	117	6	shortly	shortly	ADV
ejpam-3312	117	7	denoted	denote	VERB
ejpam-3312	117	8	by	by	ADP
ejpam-3312	117	9	p	p	PROPN
ejpam-3312	117	10	xe	xe	PROPN
ejpam-3312	117	11	and	and	CCONJ
ejpam-3312	117	12	we	we	PRON
ejpam-3312	117	13	say	say	VERB
ejpam-3312	117	14	that	that	SCONJ
ejpam-3312	117	15	p	p	PROPN
ejpam-3312	117	16	xe	xe	PROPN
ejpam-3312	117	17	∈	∈	PROPN
ejpam-3312	117	18	ge	ge	PROPN
ejpam-3312	117	19	,	,	PUNCT
ejpam-3312	117	20	if	if	SCONJ
ejpam-3312	117	21	x	x	PROPN
ejpam-3312	117	22	∈	∈	PROPN
ejpam-3312	117	23	g(e	g(e	PROPN
ejpam-3312	117	24	)	)	PUNCT
ejpam-3312	117	25	.	.	PUNCT
ejpam-3312	118	1	definition	definition	NOUN
ejpam-3312	118	2	12	12	NUM
ejpam-3312	118	3	.	.	PUNCT
ejpam-3312	119	1	[	[	X
ejpam-3312	119	2	13	13	NUM
ejpam-3312	119	3	]	]	PUNCT
ejpam-3312	119	4	let	let	VERB
ejpam-3312	119	5	�	�	PROPN
ejpam-3312	119	6	be	be	AUX
ejpam-3312	119	7	a	a	DET
ejpam-3312	119	8	partial	partial	ADJ
ejpam-3312	119	9	order	order	NOUN
ejpam-3312	119	10	relation	relation	NOUN
ejpam-3312	119	11	on	on	ADP
ejpam-3312	119	12	a	a	DET
ejpam-3312	119	13	non	non	ADJ
ejpam-3312	119	14	-	-	ADJ
ejpam-3312	119	15	empty	empty	ADJ
ejpam-3312	119	16	set	set	NOUN
ejpam-3312	119	17	x	x	PUNCT
ejpam-3312	119	18	and	and	CCONJ
ejpam-3312	119	19	let	let	VERB
ejpam-3312	119	20	e	e	PRON
ejpam-3312	119	21	be	be	AUX
ejpam-3312	119	22	a	a	DET
ejpam-3312	119	23	set	set	NOUN
ejpam-3312	119	24	of	of	ADP
ejpam-3312	119	25	parameters	parameter	NOUN
ejpam-3312	119	26	.	.	PUNCT
ejpam-3312	120	1	a	a	PRON
ejpam-3312	120	2	triple	triple	ADJ
ejpam-3312	120	3	(	(	PUNCT
ejpam-3312	120	4	x	x	NOUN
ejpam-3312	120	5	,	,	PUNCT
ejpam-3312	120	6	e	e	NOUN
ejpam-3312	120	7	,	,	PUNCT
ejpam-3312	120	8	�	�	PROPN
ejpam-3312	120	9	)	)	PUNCT
ejpam-3312	120	10	is	be	AUX
ejpam-3312	120	11	said	say	VERB
ejpam-3312	120	12	to	to	PART
ejpam-3312	120	13	be	be	AUX
ejpam-3312	120	14	a	a	DET
ejpam-3312	120	15	partially	partially	ADV
ejpam-3312	120	16	ordered	order	VERB
ejpam-3312	120	17	soft	soft	ADJ
ejpam-3312	120	18	set	set	NOUN
ejpam-3312	120	19	.	.	PUNCT
ejpam-3312	121	1	definition	definition	NOUN
ejpam-3312	121	2	13	13	NUM
ejpam-3312	121	3	.	.	PUNCT
ejpam-3312	122	1	[	[	X
ejpam-3312	122	2	13	13	NUM
ejpam-3312	122	3	]	]	PUNCT
ejpam-3312	122	4	we	we	PRON
ejpam-3312	122	5	define	define	VERB
ejpam-3312	122	6	an	an	DET
ejpam-3312	122	7	increasing	increase	VERB
ejpam-3312	122	8	soft	soft	ADJ
ejpam-3312	122	9	operator	operator	NOUN
ejpam-3312	122	10	i	i	PRON
ejpam-3312	122	11	:	:	PUNCT
ejpam-3312	122	12	(	(	PUNCT
ejpam-3312	122	13	ss(xe),	ss(xe),	NOUN
ejpam-3312	122	14	�	�	PROPN
ejpam-3312	122	15	)→	)→	PROPN
ejpam-3312	122	16	(	(	PUNCT
ejpam-3312	122	17	ss(xe	ss(xe	PROPN
ejpam-3312	122	18	)	)	PUNCT
ejpam-3312	122	19	,	,	PUNCT
ejpam-3312	122	20	�	�	PROPN
ejpam-3312	122	21	)	)	PUNCT
ejpam-3312	122	22	and	and	CCONJ
ejpam-3312	122	23	a	a	DET
ejpam-3312	122	24	decreasing	decrease	VERB
ejpam-3312	122	25	soft	soft	ADJ
ejpam-3312	122	26	operator	operator	NOUN
ejpam-3312	122	27	d	d	NOUN
ejpam-3312	122	28	:	:	PUNCT
ejpam-3312	122	29	(	(	PUNCT
ejpam-3312	122	30	ss(xe),	ss(xe),	NOUN
ejpam-3312	122	31	�	�	PROPN
ejpam-3312	122	32	)→	)→	PROPN
ejpam-3312	122	33	(	(	PUNCT
ejpam-3312	122	34	ss(xe	ss(xe	NOUN
ejpam-3312	122	35	)	)	PUNCT
ejpam-3312	122	36	,	,	PUNCT
ejpam-3312	122	37	�	�	PROPN
ejpam-3312	122	38	)	)	PUNCT
ejpam-3312	122	39	as	as	SCONJ
ejpam-3312	122	40	follows	follow	VERB
ejpam-3312	122	41	,	,	PUNCT
ejpam-3312	122	42	for	for	ADP
ejpam-3312	122	43	each	each	DET
ejpam-3312	122	44	soft	soft	ADJ
ejpam-3312	122	45	subset	subset	NOUN
ejpam-3312	122	46	ge	ge	PROPN
ejpam-3312	122	47	of	of	ADP
ejpam-3312	122	48	ss(xe	ss(xe	PROPN
ejpam-3312	122	49	)	)	PUNCT
ejpam-3312	122	50	(	(	PUNCT
ejpam-3312	122	51	i	i	NOUN
ejpam-3312	122	52	)	)	PUNCT
ejpam-3312	122	53	i(ge	i(ge	PROPN
ejpam-3312	122	54	)	)	PUNCT
ejpam-3312	122	55	=	=	SYM
ejpam-3312	122	56	(	(	PUNCT
ejpam-3312	122	57	ig)e	ig)e	PROPN
ejpam-3312	122	58	,	,	PUNCT
ejpam-3312	122	59	where	where	SCONJ
ejpam-3312	122	60	ig	ig	PROPN
ejpam-3312	122	61	is	be	AUX
ejpam-3312	122	62	a	a	DET
ejpam-3312	122	63	mapping	mapping	NOUN
ejpam-3312	122	64	of	of	ADP
ejpam-3312	122	65	e	e	NOUN
ejpam-3312	122	66	into	into	ADP
ejpam-3312	122	67	x	x	PUNCT
ejpam-3312	122	68	given	give	VERB
ejpam-3312	122	69	by	by	ADP
ejpam-3312	122	70	ig(e	ig(e	PRON
ejpam-3312	122	71	)	)	PUNCT
ejpam-3312	122	72	=	=	SYM
ejpam-3312	122	73	i(g(e	i(g(e	PROPN
ejpam-3312	122	74	)	)	PUNCT
ejpam-3312	122	75	)	)	PUNCT
ejpam-3312	123	1	=	=	PRON
ejpam-3312	123	2	{	{	PUNCT
ejpam-3312	123	3	x	x	PUNCT
ejpam-3312	123	4	∈	∈	PROPN
ejpam-3312	123	5	x	x	X
ejpam-3312	123	6	:	:	PUNCT
ejpam-3312	123	7	y	y	PROPN
ejpam-3312	123	8	�	�	PROPN
ejpam-3312	123	9	x	x	PROPN
ejpam-3312	123	10	,	,	PUNCT
ejpam-3312	123	11	for	for	ADP
ejpam-3312	123	12	some	some	DET
ejpam-3312	123	13	y	y	PROPN
ejpam-3312	123	14	∈	∈	PROPN
ejpam-3312	123	15	g(e	g(e	PROPN
ejpam-3312	123	16	)	)	PUNCT
ejpam-3312	123	17	}	}	PUNCT
ejpam-3312	123	18	.	.	PUNCT
ejpam-3312	124	1	(	(	PUNCT
ejpam-3312	124	2	ii	ii	NOUN
ejpam-3312	124	3	)	)	PUNCT
ejpam-3312	124	4	d(ge	d(ge	PROPN
ejpam-3312	124	5	)	)	PUNCT
ejpam-3312	125	1	=	=	SYM
ejpam-3312	125	2	(	(	PUNCT
ejpam-3312	125	3	dg)e	dg)e	PROPN
ejpam-3312	125	4	,	,	PUNCT
ejpam-3312	125	5	where	where	SCONJ
ejpam-3312	125	6	dg	dg	PROPN
ejpam-3312	125	7	is	be	AUX
ejpam-3312	125	8	a	a	DET
ejpam-3312	125	9	mapping	mapping	NOUN
ejpam-3312	125	10	of	of	ADP
ejpam-3312	125	11	e	e	NOUN
ejpam-3312	125	12	into	into	ADP
ejpam-3312	125	13	x	x	PUNCT
ejpam-3312	125	14	given	give	VERB
ejpam-3312	125	15	by	by	ADP
ejpam-3312	125	16	dg(e	dg(e	PUNCT
ejpam-3312	125	17	)	)	PUNCT
ejpam-3312	126	1	=	=	SYM
ejpam-3312	126	2	d(g(e	d(g(e	ADJ
ejpam-3312	126	3	)	)	PUNCT
ejpam-3312	126	4	)	)	PUNCT
ejpam-3312	127	1	=	=	PRON
ejpam-3312	127	2	{	{	PUNCT
ejpam-3312	127	3	x	x	PUNCT
ejpam-3312	127	4	∈	∈	NOUN
ejpam-3312	127	5	x	x	X
ejpam-3312	127	6	:	:	PUNCT
ejpam-3312	127	7	x	x	PUNCT
ejpam-3312	127	8	�	�	PROPN
ejpam-3312	127	9	y	y	PROPN
ejpam-3312	127	10	,	,	PUNCT
ejpam-3312	127	11	for	for	ADP
ejpam-3312	127	12	some	some	DET
ejpam-3312	127	13	y	y	PROPN
ejpam-3312	127	14	∈	∈	PROPN
ejpam-3312	127	15	g(e	g(e	PROPN
ejpam-3312	127	16	)	)	PUNCT
ejpam-3312	127	17	}	}	PUNCT
ejpam-3312	127	18	.	.	PUNCT
ejpam-3312	128	1	definition	definition	NOUN
ejpam-3312	128	2	14	14	NUM
ejpam-3312	128	3	.	.	PUNCT
ejpam-3312	129	1	[	[	X
ejpam-3312	129	2	13	13	NUM
ejpam-3312	129	3	]	]	PUNCT
ejpam-3312	129	4	a	a	DET
ejpam-3312	129	5	soft	soft	ADJ
ejpam-3312	129	6	subset	subset	NOUN
ejpam-3312	129	7	ge	ge	PROPN
ejpam-3312	129	8	of	of	ADP
ejpam-3312	129	9	a	a	DET
ejpam-3312	129	10	partially	partially	ADV
ejpam-3312	129	11	ordered	order	VERB
ejpam-3312	129	12	soft	soft	ADJ
ejpam-3312	129	13	set	set	NOUN
ejpam-3312	129	14	(	(	PUNCT
ejpam-3312	129	15	x	x	X
ejpam-3312	129	16	,	,	PUNCT
ejpam-3312	129	17	e	e	NOUN
ejpam-3312	129	18	,	,	PUNCT
ejpam-3312	129	19	�	�	PROPN
ejpam-3312	129	20	)	)	PUNCT
ejpam-3312	129	21	is	be	AUX
ejpam-3312	129	22	said	say	VERB
ejpam-3312	129	23	to	to	PART
ejpam-3312	129	24	be	be	AUX
ejpam-3312	129	25	increasing	increase	VERB
ejpam-3312	129	26	(	(	PUNCT
ejpam-3312	129	27	resp	resp	NOUN
ejpam-3312	129	28	.	.	PUNCT
ejpam-3312	130	1	decreasing	decrease	VERB
ejpam-3312	130	2	)	)	PUNCT
ejpam-3312	130	3	if	if	SCONJ
ejpam-3312	130	4	ge	ge	PROPN
ejpam-3312	130	5	=	=	PROPN
ejpam-3312	130	6	i(ge)(resp	i(ge)(resp	PROPN
ejpam-3312	130	7	.	.	PUNCT
ejpam-3312	131	1	ge	ge	PROPN
ejpam-3312	131	2	=	=	PROPN
ejpam-3312	131	3	d(ge	d(ge	PROPN
ejpam-3312	131	4	)	)	PUNCT
ejpam-3312	131	5	)	)	PUNCT
ejpam-3312	131	6	.	.	PUNCT
ejpam-3312	132	1	theorem	theorem	NOUN
ejpam-3312	132	2	1	1	NUM
ejpam-3312	132	3	.	.	PUNCT
ejpam-3312	133	1	[	[	X
ejpam-3312	133	2	13	13	NUM
ejpam-3312	133	3	]	]	X
ejpam-3312	133	4	if	if	SCONJ
ejpam-3312	133	5	a	a	DET
ejpam-3312	133	6	soft	soft	ADJ
ejpam-3312	133	7	mapping	mapping	NOUN
ejpam-3312	133	8	fφ	fφ	NOUN
ejpam-3312	133	9	:	:	PUNCT
ejpam-3312	133	10	(	(	PUNCT
ejpam-3312	133	11	s(xa),	s(xa),	VERB
ejpam-3312	133	12	�	�	NOUN
ejpam-3312	133	13	1	1	NUM
ejpam-3312	133	14	)	)	PUNCT
ejpam-3312	133	15	→	→	SYM
ejpam-3312	133	16	(	(	PUNCT
ejpam-3312	133	17	s(yb),	s(yb),	X
ejpam-3312	133	18	�	�	X
ejpam-3312	133	19	2	2	NUM
ejpam-3312	133	20	)	)	PUNCT
ejpam-3312	133	21	is	be	AUX
ejpam-3312	133	22	increasing	increase	VERB
ejpam-3312	133	23	,	,	PUNCT
ejpam-3312	133	24	then	then	ADV
ejpam-3312	133	25	the	the	DET
ejpam-3312	133	26	inverse	inverse	ADJ
ejpam-3312	133	27	image	image	NOUN
ejpam-3312	133	28	of	of	ADP
ejpam-3312	133	29	each	each	DET
ejpam-3312	133	30	increasing	increase	VERB
ejpam-3312	133	31	(	(	PUNCT
ejpam-3312	133	32	resp	resp	NOUN
ejpam-3312	133	33	.	.	PUNCT
ejpam-3312	134	1	decreasing	decrease	VERB
ejpam-3312	134	2	)	)	PUNCT
ejpam-3312	134	3	soft	soft	ADJ
ejpam-3312	134	4	subset	subset	NOUN
ejpam-3312	134	5	of	of	ADP
ejpam-3312	134	6	ỹ	ỹ	PROPN
ejpam-3312	134	7	is	be	AUX
ejpam-3312	134	8	an	an	DET
ejpam-3312	134	9	increasing	increase	VERB
ejpam-3312	134	10	(	(	PUNCT
ejpam-3312	134	11	resp	resp	NOUN
ejpam-3312	134	12	.	.	PUNCT
ejpam-3312	135	1	a	a	DET
ejpam-3312	135	2	decreasing	decrease	VERB
ejpam-3312	135	3	)	)	PUNCT
ejpam-3312	135	4	soft	soft	ADJ
ejpam-3312	135	5	subset	subset	NOUN
ejpam-3312	135	6	of	of	ADP
ejpam-3312	135	7	x̃.	x̃.	ADJ
ejpam-3312	135	8	definition	definition	NOUN
ejpam-3312	135	9	15	15	NUM
ejpam-3312	135	10	.	.	PUNCT
ejpam-3312	136	1	[	[	X
ejpam-3312	136	2	13	13	NUM
ejpam-3312	136	3	]	]	PUNCT
ejpam-3312	136	4	a	a	DET
ejpam-3312	136	5	quadrable	quadrable	ADJ
ejpam-3312	136	6	system	system	NOUN
ejpam-3312	136	7	(	(	PUNCT
ejpam-3312	136	8	x	x	X
ejpam-3312	136	9	,	,	PUNCT
ejpam-3312	136	10	τ	τ	PROPN
ejpam-3312	136	11	,	,	PUNCT
ejpam-3312	136	12	e	e	NOUN
ejpam-3312	136	13	,	,	PUNCT
ejpam-3312	136	14	�	�	PROPN
ejpam-3312	136	15	)	)	PUNCT
ejpam-3312	136	16	is	be	AUX
ejpam-3312	136	17	said	say	VERB
ejpam-3312	136	18	to	to	PART
ejpam-3312	136	19	be	be	AUX
ejpam-3312	136	20	a	a	DET
ejpam-3312	136	21	soft	soft	ADJ
ejpam-3312	136	22	topological	topological	ADJ
ejpam-3312	136	23	ordered	order	VERB
ejpam-3312	136	24	space	space	NOUN
ejpam-3312	136	25	,	,	PUNCT
ejpam-3312	136	26	where	where	SCONJ
ejpam-3312	136	27	(	(	PUNCT
ejpam-3312	136	28	x	x	X
ejpam-3312	136	29	,	,	PUNCT
ejpam-3312	136	30	τ	τ	PROPN
ejpam-3312	136	31	,	,	PUNCT
ejpam-3312	136	32	e	e	NOUN
ejpam-3312	136	33	)	)	PUNCT
ejpam-3312	136	34	is	be	AUX
ejpam-3312	136	35	a	a	DET
ejpam-3312	136	36	soft	soft	ADJ
ejpam-3312	136	37	topological	topological	ADJ
ejpam-3312	136	38	space	space	NOUN
ejpam-3312	136	39	and	and	CCONJ
ejpam-3312	136	40	(	(	PUNCT
ejpam-3312	136	41	x	x	X
ejpam-3312	136	42	,	,	PUNCT
ejpam-3312	136	43	e	e	NOUN
ejpam-3312	136	44	,	,	PUNCT
ejpam-3312	136	45	�	�	PROPN
ejpam-3312	136	46	)	)	PUNCT
ejpam-3312	136	47	is	be	AUX
ejpam-3312	136	48	a	a	DET
ejpam-3312	136	49	partially	partially	ADV
ejpam-3312	136	50	ordered	order	VERB
ejpam-3312	136	51	soft	soft	ADJ
ejpam-3312	136	52	set	set	NOUN
ejpam-3312	136	53	.	.	PUNCT
ejpam-3312	137	1	henceforth	henceforth	ADV
ejpam-3312	137	2	,	,	PUNCT
ejpam-3312	137	3	the	the	DET
ejpam-3312	137	4	two	two	NUM
ejpam-3312	137	5	notations	notation	NOUN
ejpam-3312	137	6	(	(	PUNCT
ejpam-3312	137	7	x	x	X
ejpam-3312	137	8	,	,	PUNCT
ejpam-3312	137	9	τ	τ	PROPN
ejpam-3312	137	10	,	,	PUNCT
ejpam-3312	137	11	e,	e,	X
ejpam-3312	137	12	�	�	X
ejpam-3312	137	13	1	1	NUM
ejpam-3312	137	14	)	)	PUNCT
ejpam-3312	137	15	and	and	CCONJ
ejpam-3312	137	16	(	(	PUNCT
ejpam-3312	137	17	y	y	PROPN
ejpam-3312	137	18	,	,	PUNCT
ejpam-3312	137	19	θ	θ	PROPN
ejpam-3312	137	20	,	,	PUNCT
ejpam-3312	137	21	f,	f,	X
ejpam-3312	137	22	�	�	SYM
ejpam-3312	137	23	2	2	NUM
ejpam-3312	137	24	)	)	PUNCT
ejpam-3312	137	25	stand	stand	VERB
ejpam-3312	137	26	for	for	ADP
ejpam-3312	137	27	soft	soft	ADJ
ejpam-3312	137	28	topological	topological	ADJ
ejpam-3312	137	29	ordered	order	VERB
ejpam-3312	137	30	spaces	space	NOUN
ejpam-3312	137	31	.	.	PUNCT
ejpam-3312	138	1	definition	definition	NOUN
ejpam-3312	138	2	16	16	NUM
ejpam-3312	138	3	.	.	PUNCT
ejpam-3312	139	1	[	[	X
ejpam-3312	139	2	42	42	NUM
ejpam-3312	139	3	]	]	PUNCT
ejpam-3312	139	4	a	a	DET
ejpam-3312	139	5	mapping	mapping	NOUN
ejpam-3312	139	6	(	(	PUNCT
ejpam-3312	139	7	x	x	NOUN
ejpam-3312	139	8	,	,	PUNCT
ejpam-3312	139	9	τ,	τ,	NOUN
ejpam-3312	139	10	�	�	X
ejpam-3312	139	11	1)→	1)→	NUM
ejpam-3312	139	12	(	(	PUNCT
ejpam-3312	139	13	y	y	PROPN
ejpam-3312	139	14	,	,	PUNCT
ejpam-3312	139	15	θ,	θ,	NOUN
ejpam-3312	139	16	�	�	NOUN
ejpam-3312	139	17	2	2	NUM
ejpam-3312	139	18	)	)	PUNCT
ejpam-3312	139	19	is	be	AUX
ejpam-3312	139	20	said	say	VERB
ejpam-3312	139	21	to	to	PART
ejpam-3312	139	22	be	be	AUX
ejpam-3312	139	23	:	:	PUNCT
ejpam-3312	139	24	(	(	PUNCT
ejpam-3312	139	25	i	i	NOUN
ejpam-3312	139	26	)	)	PUNCT
ejpam-3312	139	27	i	i	PRON
ejpam-3312	139	28	(	(	PUNCT
ejpam-3312	139	29	resp	resp	NOUN
ejpam-3312	139	30	.	.	PUNCT
ejpam-3312	140	1	d	d	X
ejpam-3312	140	2	,	,	PUNCT
ejpam-3312	140	3	b	b	NOUN
ejpam-3312	140	4	)	)	PUNCT
ejpam-3312	140	5	β	β	NOUN
ejpam-3312	140	6	-	-	NOUN
ejpam-3312	140	7	continuous	continuous	ADJ
ejpam-3312	140	8	if	if	SCONJ
ejpam-3312	140	9	the	the	DET
ejpam-3312	140	10	inverse	inverse	ADJ
ejpam-3312	140	11	image	image	NOUN
ejpam-3312	140	12	of	of	ADP
ejpam-3312	140	13	each	each	DET
ejpam-3312	140	14	open	open	ADJ
ejpam-3312	140	15	set	set	NOUN
ejpam-3312	140	16	is	be	AUX
ejpam-3312	140	17	i	i	PRON
ejpam-3312	140	18	(	(	PUNCT
ejpam-3312	140	19	resp	resp	NOUN
ejpam-3312	140	20	.	.	PUNCT
ejpam-3312	141	1	d	d	X
ejpam-3312	141	2	,	,	PUNCT
ejpam-3312	141	3	b	b	NOUN
ejpam-3312	141	4	)	)	PUNCT
ejpam-3312	141	5	β	β	NOUN
ejpam-3312	141	6	-	-	NOUN
ejpam-3312	141	7	open	open	ADJ
ejpam-3312	141	8	.	.	PUNCT
ejpam-3312	142	1	(	(	PUNCT
ejpam-3312	142	2	ii	ii	X
ejpam-3312	142	3	)	)	PUNCT
ejpam-3312	142	4	i	i	PRON
ejpam-3312	142	5	(	(	PUNCT
ejpam-3312	142	6	resp	resp	NOUN
ejpam-3312	142	7	.	.	PUNCT
ejpam-3312	143	1	d	d	X
ejpam-3312	143	2	,	,	PUNCT
ejpam-3312	143	3	b	b	NOUN
ejpam-3312	143	4	)	)	PUNCT
ejpam-3312	143	5	β	β	X
ejpam-3312	143	6	-	-	VERB
ejpam-3312	143	7	open	open	ADJ
ejpam-3312	143	8	if	if	SCONJ
ejpam-3312	143	9	the	the	DET
ejpam-3312	143	10	image	image	NOUN
ejpam-3312	143	11	of	of	ADP
ejpam-3312	143	12	each	each	DET
ejpam-3312	143	13	open	open	ADJ
ejpam-3312	143	14	set	set	NOUN
ejpam-3312	143	15	is	be	AUX
ejpam-3312	143	16	i	i	PRON
ejpam-3312	143	17	(	(	PUNCT
ejpam-3312	143	18	resp	resp	NOUN
ejpam-3312	143	19	.	.	PUNCT
ejpam-3312	144	1	d	d	X
ejpam-3312	144	2	,	,	PUNCT
ejpam-3312	144	3	b	b	NOUN
ejpam-3312	144	4	)	)	PUNCT
ejpam-3312	144	5	β	β	NOUN
ejpam-3312	144	6	-	-	NOUN
ejpam-3312	144	7	open	open	ADJ
ejpam-3312	144	8	.	.	PUNCT
ejpam-3312	145	1	(	(	PUNCT
ejpam-3312	145	2	iii	iii	X
ejpam-3312	145	3	)	)	PUNCT
ejpam-3312	145	4	i	i	PRON
ejpam-3312	145	5	(	(	PUNCT
ejpam-3312	145	6	resp	resp	NOUN
ejpam-3312	145	7	.	.	PUNCT
ejpam-3312	146	1	d	d	X
ejpam-3312	146	2	,	,	PUNCT
ejpam-3312	146	3	b	b	NOUN
ejpam-3312	146	4	)	)	PUNCT
ejpam-3312	146	5	β	β	X
ejpam-3312	146	6	-	-	PUNCT
ejpam-3312	146	7	closed	closed	ADJ
ejpam-3312	146	8	if	if	SCONJ
ejpam-3312	146	9	the	the	DET
ejpam-3312	146	10	image	image	NOUN
ejpam-3312	146	11	of	of	ADP
ejpam-3312	146	12	each	each	DET
ejpam-3312	146	13	open	open	ADJ
ejpam-3312	146	14	set	set	NOUN
ejpam-3312	146	15	is	be	AUX
ejpam-3312	146	16	i	i	PRON
ejpam-3312	146	17	(	(	PUNCT
ejpam-3312	146	18	resp	resp	NOUN
ejpam-3312	146	19	.	.	PUNCT
ejpam-3312	147	1	d	d	X
ejpam-3312	147	2	,	,	PUNCT
ejpam-3312	147	3	b	b	NOUN
ejpam-3312	147	4	)	)	PUNCT
ejpam-3312	147	5	β	β	NOUN
ejpam-3312	147	6	-	-	VERB
ejpam-3312	147	7	closed	closed	ADJ
ejpam-3312	147	8	.	.	PUNCT
ejpam-3312	148	1	(	(	PUNCT
ejpam-3312	148	2	iv	iv	X
ejpam-3312	148	3	)	)	PUNCT
ejpam-3312	148	4	i	i	PRON
ejpam-3312	148	5	(	(	PUNCT
ejpam-3312	148	6	resp	resp	NOUN
ejpam-3312	148	7	.	.	PUNCT
ejpam-3312	149	1	d	d	X
ejpam-3312	149	2	,	,	PUNCT
ejpam-3312	149	3	b	b	NOUN
ejpam-3312	149	4	)	)	PUNCT
ejpam-3312	149	5	β	β	NOUN
ejpam-3312	149	6	-	-	PUNCT
ejpam-3312	149	7	homeomorphism	homeomorphism	X
ejpam-3312	149	8	if	if	SCONJ
ejpam-3312	149	9	it	it	PRON
ejpam-3312	149	10	is	be	AUX
ejpam-3312	149	11	bijective	bijective	ADJ
ejpam-3312	149	12	,	,	PUNCT
ejpam-3312	149	13	i	i	PRON
ejpam-3312	149	14	(	(	PUNCT
ejpam-3312	149	15	resp	resp	NOUN
ejpam-3312	149	16	.	.	PUNCT
ejpam-3312	150	1	d	d	X
ejpam-3312	150	2	,	,	PUNCT
ejpam-3312	150	3	b	b	NOUN
ejpam-3312	150	4	)	)	PUNCT
ejpam-3312	150	5	β	β	NOUN
ejpam-3312	150	6	-	-	ADJ
ejpam-3312	150	7	continuous	continuous	ADJ
ejpam-3312	150	8	and	and	CCONJ
ejpam-3312	150	9	i	i	PRON
ejpam-3312	150	10	(	(	PUNCT
ejpam-3312	150	11	resp	resp	NOUN
ejpam-3312	150	12	.	.	PUNCT
ejpam-3312	151	1	d	d	X
ejpam-3312	151	2	,	,	PUNCT
ejpam-3312	151	3	b	b	NOUN
ejpam-3312	151	4	)	)	PUNCT
ejpam-3312	151	5	β	β	NOUN
ejpam-3312	151	6	-	-	PUNCT
ejpam-3312	151	7	open	open	ADJ
ejpam-3312	151	8	.	.	PUNCT
ejpam-3312	152	1	definition	definition	NOUN
ejpam-3312	152	2	17	17	NUM
ejpam-3312	152	3	.	.	PUNCT
ejpam-3312	153	1	[	[	X
ejpam-3312	153	2	14	14	NUM
ejpam-3312	153	3	]	]	X
ejpam-3312	153	4	the	the	DET
ejpam-3312	153	5	composition	composition	NOUN
ejpam-3312	153	6	of	of	ADP
ejpam-3312	153	7	two	two	NUM
ejpam-3312	153	8	soft	soft	ADJ
ejpam-3312	153	9	mappings	mapping	NOUN
ejpam-3312	153	10	fφ	fφ	NOUN
ejpam-3312	153	11	:	:	PUNCT
ejpam-3312	153	12	(	(	PUNCT
ejpam-3312	153	13	x	x	X
ejpam-3312	153	14	,	,	PUNCT
ejpam-3312	153	15	τ	τ	PROPN
ejpam-3312	153	16	,	,	PUNCT
ejpam-3312	153	17	e,	e,	X
ejpam-3312	153	18	�	�	X
ejpam-3312	153	19	1)→	1)→	NUM
ejpam-3312	153	20	(	(	PUNCT
ejpam-3312	153	21	y	y	PROPN
ejpam-3312	153	22	,	,	PUNCT
ejpam-3312	153	23	θ	θ	PROPN
ejpam-3312	153	24	,	,	PUNCT
ejpam-3312	153	25	f,	f,	X
ejpam-3312	153	26	�	�	SYM
ejpam-3312	153	27	2	2	NUM
ejpam-3312	153	28	)	)	PUNCT
ejpam-3312	153	29	and	and	CCONJ
ejpam-3312	153	30	gλ	gλ	NOUN
ejpam-3312	153	31	:	:	PUNCT
ejpam-3312	153	32	(	(	PUNCT
ejpam-3312	153	33	y	y	PROPN
ejpam-3312	153	34	,	,	PUNCT
ejpam-3312	153	35	θ	θ	PROPN
ejpam-3312	153	36	,	,	PUNCT
ejpam-3312	153	37	f,	f,	X
ejpam-3312	153	38	�	�	PROPN
ejpam-3312	153	39	2	2	NUM
ejpam-3312	153	40	)	)	PUNCT
ejpam-3312	153	41	→	→	SYM
ejpam-3312	153	42	(	(	PUNCT
ejpam-3312	153	43	z	z	NOUN
ejpam-3312	153	44	,	,	PUNCT
ejpam-3312	153	45	υ	υ	NOUN
ejpam-3312	153	46	,	,	PUNCT
ejpam-3312	153	47	k,	k,	NOUN
ejpam-3312	153	48	�	�	X
ejpam-3312	153	49	3	3	NUM
ejpam-3312	153	50	)	)	PUNCT
ejpam-3312	153	51	is	be	AUX
ejpam-3312	153	52	a	a	DET
ejpam-3312	153	53	soft	soft	ADJ
ejpam-3312	153	54	mapping	mapping	NOUN
ejpam-3312	153	55	fφ	fφ	AUX
ejpam-3312	153	56	◦	◦	VERB
ejpam-3312	153	57	gλ	gλ	NOUN
ejpam-3312	153	58	:	:	PUNCT
ejpam-3312	153	59	(	(	PUNCT
ejpam-3312	153	60	x	x	X
ejpam-3312	153	61	,	,	PUNCT
ejpam-3312	153	62	τ	τ	PROPN
ejpam-3312	153	63	,	,	PUNCT
ejpam-3312	153	64	e,	e,	X
ejpam-3312	153	65	�	�	X
ejpam-3312	153	66	1	1	NUM
ejpam-3312	153	67	)	)	PUNCT
ejpam-3312	153	68	→	→	SYM
ejpam-3312	153	69	(	(	PUNCT
ejpam-3312	153	70	z	z	NOUN
ejpam-3312	153	71	,	,	PUNCT
ejpam-3312	153	72	υ	υ	NOUN
ejpam-3312	153	73	,	,	PUNCT
ejpam-3312	153	74	k,	k,	NOUN
ejpam-3312	153	75	�	�	X
ejpam-3312	153	76	3	3	NUM
ejpam-3312	153	77	)	)	PUNCT
ejpam-3312	153	78	and	and	CCONJ
ejpam-3312	153	79	is	be	AUX
ejpam-3312	153	80	given	give	VERB
ejpam-3312	153	81	by	by	ADP
ejpam-3312	153	82	(	(	PUNCT
ejpam-3312	153	83	fφ	fφ	NOUN
ejpam-3312	153	84	◦	◦	NOUN
ejpam-3312	153	85	gλ)(p	gλ)(p	X
ejpam-3312	153	86	xe	xe	PROPN
ejpam-3312	153	87	)	)	PUNCT
ejpam-3312	154	1	=	=	SYM
ejpam-3312	154	2	fφ(gλ(p	fφ(gλ(p	PROPN
ejpam-3312	154	3	xe	xe	PROPN
ejpam-3312	154	4	)	)	PUNCT
ejpam-3312	154	5	)	)	PUNCT
ejpam-3312	154	6	.	.	PUNCT
ejpam-3312	155	1	t.	t.	PROPN
ejpam-3312	155	2	m.	m.	PROPN
ejpam-3312	155	3	al	al	PROPN
ejpam-3312	155	4	-	-	PUNCT
ejpam-3312	155	5	shami	shami	PROPN
ejpam-3312	155	6	,	,	PUNCT
ejpam-3312	155	7	m.	m.	PROPN
ejpam-3312	155	8	e.	e.	PROPN
ejpam-3312	155	9	el	el	PROPN
ejpam-3312	155	10	-	-	PROPN
ejpam-3312	155	11	shafei	shafei	PROPN
ejpam-3312	155	12	,	,	PUNCT
ejpam-3312	155	13	b.	b.	PROPN
ejpam-3312	155	14	a.	a.	PROPN
ejpam-3312	155	15	asaad	asaad	PROPN
ejpam-3312	155	16	/	/	SYM
ejpam-3312	155	17	eur	eur	PROPN
ejpam-3312	155	18	.	.	PUNCT
ejpam-3312	156	1	j.	j.	PROPN
ejpam-3312	156	2	pure	pure	PROPN
ejpam-3312	156	3	appl	appl	PROPN
ejpam-3312	156	4	.	.	PROPN
ejpam-3312	156	5	math	math	PROPN
ejpam-3312	156	6	,	,	PUNCT
ejpam-3312	156	7	12	12	NUM
ejpam-3312	156	8	(	(	PUNCT
ejpam-3312	156	9	1	1	NUM
ejpam-3312	156	10	)	)	PUNCT
ejpam-3312	156	11	(	(	PUNCT
ejpam-3312	156	12	2019	2019	NUM
ejpam-3312	156	13	)	)	PUNCT
ejpam-3312	156	14	,	,	PUNCT
ejpam-3312	156	15	176	176	NUM
ejpam-3312	156	16	-	-	SYM
ejpam-3312	156	17	193	193	NUM
ejpam-3312	156	18	181	181	NUM
ejpam-3312	156	19	3	3	NUM
ejpam-3312	156	20	.	.	PUNCT
ejpam-3312	156	21	soft	soft	ADJ
ejpam-3312	156	22	i(d	i(d	NOUN
ejpam-3312	156	23	,	,	PUNCT
ejpam-3312	156	24	b)β	b)β	NOUN
ejpam-3312	156	25	-	-	PUNCT
ejpam-3312	156	26	continuity	continuity	NOUN
ejpam-3312	156	27	in	in	ADP
ejpam-3312	156	28	this	this	DET
ejpam-3312	156	29	section	section	NOUN
ejpam-3312	156	30	,	,	PUNCT
ejpam-3312	156	31	the	the	DET
ejpam-3312	156	32	notions	notion	NOUN
ejpam-3312	156	33	of	of	ADP
ejpam-3312	156	34	i(d	i(d	NOUN
ejpam-3312	156	35	,	,	PUNCT
ejpam-3312	156	36	b)β	b)β	NOUN
ejpam-3312	156	37	-	-	PUNCT
ejpam-3312	156	38	continuity	continuity	NOUN
ejpam-3312	156	39	at	at	ADP
ejpam-3312	156	40	soft	soft	ADJ
ejpam-3312	156	41	point	point	NOUN
ejpam-3312	156	42	,	,	PUNCT
ejpam-3312	156	43	ordinary	ordinary	ADJ
ejpam-3312	156	44	point	point	NOUN
ejpam-3312	156	45	and	and	CCONJ
ejpam-3312	156	46	on	on	ADP
ejpam-3312	156	47	the	the	DET
ejpam-3312	156	48	universe	universe	NOUN
ejpam-3312	156	49	set	set	NOUN
ejpam-3312	156	50	are	be	AUX
ejpam-3312	156	51	given	give	VERB
ejpam-3312	156	52	and	and	CCONJ
ejpam-3312	156	53	studied	study	VERB
ejpam-3312	156	54	.	.	PUNCT
ejpam-3312	157	1	each	each	DET
ejpam-3312	157	2	one	one	NUM
ejpam-3312	157	3	of	of	ADP
ejpam-3312	157	4	the	the	DET
ejpam-3312	157	5	introduced	introduce	VERB
ejpam-3312	157	6	soft	soft	ADJ
ejpam-3312	157	7	mappings	mapping	NOUN
ejpam-3312	157	8	are	be	AUX
ejpam-3312	157	9	characterized	characterize	VERB
ejpam-3312	157	10	and	and	CCONJ
ejpam-3312	157	11	some	some	DET
ejpam-3312	157	12	examples	example	NOUN
ejpam-3312	157	13	are	be	AUX
ejpam-3312	157	14	provided	provide	VERB
ejpam-3312	157	15	to	to	PART
ejpam-3312	157	16	show	show	VERB
ejpam-3312	157	17	the	the	DET
ejpam-3312	157	18	relationships	relationship	NOUN
ejpam-3312	157	19	among	among	ADP
ejpam-3312	157	20	them	they	PRON
ejpam-3312	157	21	.	.	PUNCT
ejpam-3312	158	1	definition	definition	NOUN
ejpam-3312	158	2	18	18	NUM
ejpam-3312	158	3	.	.	PUNCT
ejpam-3312	159	1	a	a	DET
ejpam-3312	159	2	soft	soft	ADJ
ejpam-3312	159	3	subset	subset	NOUN
ejpam-3312	159	4	he	he	PRON
ejpam-3312	159	5	of	of	ADP
ejpam-3312	159	6	(	(	PUNCT
ejpam-3312	159	7	x	x	PROPN
ejpam-3312	159	8	,	,	PUNCT
ejpam-3312	159	9	τ	τ	PROPN
ejpam-3312	159	10	,	,	PUNCT
ejpam-3312	159	11	e,	e,	X
ejpam-3312	159	12	�	�	X
ejpam-3312	159	13	1	1	NUM
ejpam-3312	159	14	)	)	PUNCT
ejpam-3312	159	15	is	be	AUX
ejpam-3312	159	16	said	say	VERB
ejpam-3312	159	17	to	to	PART
ejpam-3312	159	18	be	be	AUX
ejpam-3312	159	19	:	:	PUNCT
ejpam-3312	159	20	(	(	PUNCT
ejpam-3312	159	21	i	i	NOUN
ejpam-3312	159	22	)	)	PUNCT
ejpam-3312	159	23	soft	soft	ADJ
ejpam-3312	159	24	i	i	PRON
ejpam-3312	159	25	(	(	PUNCT
ejpam-3312	159	26	resp	resp	NOUN
ejpam-3312	159	27	.	.	PUNCT
ejpam-3312	160	1	soft	soft	ADJ
ejpam-3312	160	2	d	d	NOUN
ejpam-3312	160	3	,	,	PUNCT
ejpam-3312	160	4	soft	soft	ADJ
ejpam-3312	160	5	b	b	NOUN
ejpam-3312	160	6	)	)	PUNCT
ejpam-3312	160	7	β	β	X
ejpam-3312	160	8	-	-	VERB
ejpam-3312	160	9	open	open	ADJ
ejpam-3312	160	10	if	if	SCONJ
ejpam-3312	160	11	it	it	PRON
ejpam-3312	160	12	is	be	AUX
ejpam-3312	160	13	soft	soft	ADJ
ejpam-3312	161	1	β	β	NOUN
ejpam-3312	161	2	-	-	ADJ
ejpam-3312	161	3	open	open	ADJ
ejpam-3312	161	4	and	and	CCONJ
ejpam-3312	161	5	increasing	increase	VERB
ejpam-3312	161	6	(	(	PUNCT
ejpam-3312	161	7	resp	resp	NOUN
ejpam-3312	161	8	.	.	PUNCT
ejpam-3312	162	1	decreasing	decrease	VERB
ejpam-3312	162	2	,	,	PUNCT
ejpam-3312	162	3	balancing	balancing	NOUN
ejpam-3312	162	4	)	)	PUNCT
ejpam-3312	162	5	.	.	PUNCT
ejpam-3312	163	1	(	(	PUNCT
ejpam-3312	163	2	ii	ii	NOUN
ejpam-3312	163	3	)	)	PUNCT
ejpam-3312	163	4	soft	soft	ADJ
ejpam-3312	163	5	i	i	PRON
ejpam-3312	163	6	(	(	PUNCT
ejpam-3312	163	7	resp	resp	NOUN
ejpam-3312	163	8	.	.	PUNCT
ejpam-3312	164	1	soft	soft	ADJ
ejpam-3312	164	2	d	d	NOUN
ejpam-3312	164	3	,	,	PUNCT
ejpam-3312	164	4	soft	soft	ADJ
ejpam-3312	164	5	b	b	NOUN
ejpam-3312	164	6	)	)	PUNCT
ejpam-3312	164	7	β	β	X
ejpam-3312	164	8	-	-	PUNCT
ejpam-3312	164	9	closed	closed	ADJ
ejpam-3312	164	10	if	if	SCONJ
ejpam-3312	164	11	it	it	PRON
ejpam-3312	164	12	is	be	AUX
ejpam-3312	164	13	soft	soft	ADJ
ejpam-3312	164	14	β	β	NOUN
ejpam-3312	164	15	-	-	VERB
ejpam-3312	164	16	closed	closed	ADJ
ejpam-3312	164	17	and	and	CCONJ
ejpam-3312	164	18	increasing	increase	VERB
ejpam-3312	164	19	(	(	PUNCT
ejpam-3312	164	20	resp	resp	NOUN
ejpam-3312	164	21	.	.	PUNCT
ejpam-3312	165	1	decreasing	decrease	VERB
ejpam-3312	165	2	,	,	PUNCT
ejpam-3312	165	3	balancing	balancing	NOUN
ejpam-3312	165	4	)	)	PUNCT
ejpam-3312	165	5	.	.	PUNCT
ejpam-3312	166	1	definition	definition	NOUN
ejpam-3312	166	2	19	19	NUM
ejpam-3312	166	3	.	.	PUNCT
ejpam-3312	167	1	a	a	DET
ejpam-3312	167	2	soft	soft	ADJ
ejpam-3312	167	3	mapping	mapping	NOUN
ejpam-3312	167	4	fφ	fφ	NOUN
ejpam-3312	167	5	:	:	PUNCT
ejpam-3312	167	6	(	(	PUNCT
ejpam-3312	167	7	x	x	X
ejpam-3312	167	8	,	,	PUNCT
ejpam-3312	167	9	τ	τ	PROPN
ejpam-3312	167	10	,	,	PUNCT
ejpam-3312	167	11	e,	e,	X
ejpam-3312	167	12	�	�	X
ejpam-3312	167	13	1)→	1)→	NUM
ejpam-3312	167	14	(	(	PUNCT
ejpam-3312	167	15	y	y	PROPN
ejpam-3312	167	16	,	,	PUNCT
ejpam-3312	167	17	θ	θ	PROPN
ejpam-3312	167	18	,	,	PUNCT
ejpam-3312	167	19	f,	f,	X
ejpam-3312	167	20	�	�	NOUN
ejpam-3312	167	21	2	2	NUM
ejpam-3312	167	22	)	)	PUNCT
ejpam-3312	167	23	is	be	AUX
ejpam-3312	167	24	called	call	VERB
ejpam-3312	167	25	:	:	PUNCT
ejpam-3312	167	26	(	(	PUNCT
ejpam-3312	167	27	i	i	NOUN
ejpam-3312	167	28	)	)	PUNCT
ejpam-3312	167	29	soft	soft	ADJ
ejpam-3312	167	30	i	i	PRON
ejpam-3312	167	31	(	(	PUNCT
ejpam-3312	167	32	resp	resp	NOUN
ejpam-3312	167	33	.	.	PUNCT
ejpam-3312	168	1	soft	soft	ADJ
ejpam-3312	168	2	d	d	NOUN
ejpam-3312	168	3	,	,	PUNCT
ejpam-3312	168	4	soft	soft	ADJ
ejpam-3312	168	5	b	b	NOUN
ejpam-3312	168	6	)	)	PUNCT
ejpam-3312	168	7	β	β	NOUN
ejpam-3312	168	8	-	-	NOUN
ejpam-3312	168	9	continuous	continuous	ADJ
ejpam-3312	168	10	at	at	ADP
ejpam-3312	168	11	p	p	PROPN
ejpam-3312	168	12	xe	xe	PROPN
ejpam-3312	168	13	∈	∈	PROPN
ejpam-3312	168	14	x̃	x̃	PROPN
ejpam-3312	168	15	if	if	SCONJ
ejpam-3312	168	16	for	for	ADP
ejpam-3312	168	17	each	each	DET
ejpam-3312	168	18	soft	soft	ADJ
ejpam-3312	168	19	open	open	ADJ
ejpam-3312	168	20	set	set	VERB
ejpam-3312	168	21	hf	hf	NOUN
ejpam-3312	168	22	containing	contain	VERB
ejpam-3312	168	23	fφ(p	fφ(p	PROPN
ejpam-3312	168	24	xe	xe	PROPN
ejpam-3312	168	25	)	)	PUNCT
ejpam-3312	168	26	,	,	PUNCT
ejpam-3312	168	27	there	there	PRON
ejpam-3312	168	28	exists	exist	VERB
ejpam-3312	168	29	a	a	DET
ejpam-3312	168	30	soft	soft	ADJ
ejpam-3312	168	31	i	i	NOUN
ejpam-3312	168	32	(	(	PUNCT
ejpam-3312	168	33	resp	resp	NOUN
ejpam-3312	168	34	.	.	PUNCT
ejpam-3312	169	1	soft	soft	ADJ
ejpam-3312	169	2	d	d	NOUN
ejpam-3312	169	3	,	,	PUNCT
ejpam-3312	169	4	soft	soft	ADJ
ejpam-3312	169	5	b	b	NOUN
ejpam-3312	169	6	)	)	PUNCT
ejpam-3312	169	7	β	β	X
ejpam-3312	169	8	-	-	ADJ
ejpam-3312	169	9	open	open	ADJ
ejpam-3312	169	10	set	set	NOUN
ejpam-3312	169	11	ge	ge	PROPN
ejpam-3312	169	12	containing	contain	VERB
ejpam-3312	169	13	p	p	PROPN
ejpam-3312	169	14	xe	xe	PROPN
ejpam-3312	169	15	such	such	ADJ
ejpam-3312	169	16	that	that	DET
ejpam-3312	169	17	fφ(ge)⊆̃hf	fφ(ge)⊆̃hf	PROPN
ejpam-3312	169	18	.	.	PUNCT
ejpam-3312	170	1	(	(	PUNCT
ejpam-3312	170	2	ii	ii	NOUN
ejpam-3312	170	3	)	)	PUNCT
ejpam-3312	170	4	soft	soft	ADJ
ejpam-3312	170	5	i	i	PRON
ejpam-3312	170	6	(	(	PUNCT
ejpam-3312	170	7	resp	resp	NOUN
ejpam-3312	170	8	.	.	PUNCT
ejpam-3312	171	1	soft	soft	ADJ
ejpam-3312	171	2	d	d	NOUN
ejpam-3312	171	3	,	,	PUNCT
ejpam-3312	171	4	soft	soft	ADJ
ejpam-3312	171	5	b	b	NOUN
ejpam-3312	171	6	)	)	PUNCT
ejpam-3312	171	7	β	β	NOUN
ejpam-3312	171	8	-	-	NOUN
ejpam-3312	171	9	continuous	continuous	ADJ
ejpam-3312	171	10	at	at	ADP
ejpam-3312	171	11	x	x	X
ejpam-3312	171	12	∈	∈	PROPN
ejpam-3312	171	13	x	x	INTJ
ejpam-3312	171	14	if	if	SCONJ
ejpam-3312	171	15	it	it	PRON
ejpam-3312	171	16	is	be	AUX
ejpam-3312	171	17	soft	soft	ADJ
ejpam-3312	172	1	i	i	PRON
ejpam-3312	172	2	(	(	PUNCT
ejpam-3312	172	3	resp	resp	NOUN
ejpam-3312	172	4	.	.	PUNCT
ejpam-3312	173	1	soft	soft	ADJ
ejpam-3312	173	2	d	d	NOUN
ejpam-3312	173	3	,	,	PUNCT
ejpam-3312	173	4	soft	soft	ADJ
ejpam-3312	173	5	b	b	NOUN
ejpam-3312	173	6	)	)	PUNCT
ejpam-3312	173	7	β	β	NOUN
ejpam-3312	173	8	-	-	NOUN
ejpam-3312	173	9	continuous	continuous	ADJ
ejpam-3312	173	10	at	at	ADP
ejpam-3312	173	11	each	each	DET
ejpam-3312	173	12	p	p	PROPN
ejpam-3312	173	13	xe	xe	PROPN
ejpam-3312	173	14	.	.	PUNCT
ejpam-3312	174	1	(	(	PUNCT
ejpam-3312	174	2	iii	iii	NOUN
ejpam-3312	174	3	)	)	PUNCT
ejpam-3312	174	4	soft	soft	ADJ
ejpam-3312	174	5	i	i	PRON
ejpam-3312	174	6	(	(	PUNCT
ejpam-3312	174	7	resp	resp	NOUN
ejpam-3312	174	8	.	.	PUNCT
ejpam-3312	175	1	soft	soft	ADJ
ejpam-3312	175	2	d	d	NOUN
ejpam-3312	175	3	,	,	PUNCT
ejpam-3312	175	4	soft	soft	ADJ
ejpam-3312	175	5	b	b	NOUN
ejpam-3312	175	6	)	)	PUNCT
ejpam-3312	175	7	β	β	NOUN
ejpam-3312	175	8	-	-	NOUN
ejpam-3312	175	9	continuous	continuous	ADJ
ejpam-3312	175	10	if	if	SCONJ
ejpam-3312	175	11	it	it	PRON
ejpam-3312	175	12	is	be	AUX
ejpam-3312	175	13	soft	soft	ADJ
ejpam-3312	176	1	i	i	PRON
ejpam-3312	176	2	(	(	PUNCT
ejpam-3312	176	3	resp	resp	NOUN
ejpam-3312	176	4	.	.	PUNCT
ejpam-3312	177	1	soft	soft	ADJ
ejpam-3312	177	2	d	d	NOUN
ejpam-3312	177	3	,	,	PUNCT
ejpam-3312	177	4	soft	soft	ADJ
ejpam-3312	177	5	b	b	NOUN
ejpam-3312	177	6	)	)	PUNCT
ejpam-3312	177	7	β	β	NOUN
ejpam-3312	177	8	-	-	NOUN
ejpam-3312	177	9	continuous	continuous	ADJ
ejpam-3312	177	10	at	at	ADP
ejpam-3312	177	11	each	each	PRON
ejpam-3312	177	12	x	x	SYM
ejpam-3312	177	13	∈	∈	PROPN
ejpam-3312	177	14	x.	x.	NOUN
ejpam-3312	177	15	theorem	theorem	VERB
ejpam-3312	177	16	2	2	NUM
ejpam-3312	177	17	.	.	PUNCT
ejpam-3312	177	18	a	a	DET
ejpam-3312	177	19	soft	soft	ADJ
ejpam-3312	177	20	mapping	mapping	NOUN
ejpam-3312	177	21	fφ	fφ	NOUN
ejpam-3312	177	22	:	:	PUNCT
ejpam-3312	177	23	(	(	PUNCT
ejpam-3312	177	24	x	x	X
ejpam-3312	177	25	,	,	PUNCT
ejpam-3312	177	26	τ	τ	PROPN
ejpam-3312	177	27	,	,	PUNCT
ejpam-3312	177	28	e,	e,	X
ejpam-3312	177	29	�	�	X
ejpam-3312	177	30	1)→	1)→	NUM
ejpam-3312	177	31	(	(	PUNCT
ejpam-3312	177	32	y	y	PROPN
ejpam-3312	177	33	,	,	PUNCT
ejpam-3312	177	34	θ	θ	PROPN
ejpam-3312	177	35	,	,	PUNCT
ejpam-3312	177	36	f,	f,	X
ejpam-3312	177	37	�	�	NOUN
ejpam-3312	177	38	2	2	NUM
ejpam-3312	177	39	)	)	PUNCT
ejpam-3312	177	40	is	be	AUX
ejpam-3312	177	41	soft	soft	ADJ
ejpam-3312	177	42	i	i	PRON
ejpam-3312	177	43	(	(	PUNCT
ejpam-3312	177	44	resp	resp	NOUN
ejpam-3312	177	45	.	.	PUNCT
ejpam-3312	178	1	soft	soft	ADJ
ejpam-3312	178	2	d	d	NOUN
ejpam-3312	178	3	,	,	PUNCT
ejpam-3312	178	4	soft	soft	ADJ
ejpam-3312	178	5	b	b	NOUN
ejpam-3312	178	6	)	)	PUNCT
ejpam-3312	178	7	β	β	NOUN
ejpam-3312	178	8	-	-	ADJ
ejpam-3312	178	9	continuous	continuous	ADJ
ejpam-3312	178	10	if	if	SCONJ
ejpam-3312	178	11	and	and	CCONJ
ejpam-3312	178	12	only	only	ADV
ejpam-3312	178	13	if	if	SCONJ
ejpam-3312	178	14	the	the	DET
ejpam-3312	178	15	inverse	inverse	ADJ
ejpam-3312	178	16	image	image	NOUN
ejpam-3312	178	17	of	of	ADP
ejpam-3312	178	18	each	each	DET
ejpam-3312	178	19	soft	soft	ADJ
ejpam-3312	178	20	open	open	ADJ
ejpam-3312	178	21	subset	subset	NOUN
ejpam-3312	178	22	of	of	ADP
ejpam-3312	178	23	ỹ	ỹ	PROPN
ejpam-3312	178	24	is	be	AUX
ejpam-3312	178	25	a	a	DET
ejpam-3312	178	26	soft	soft	ADJ
ejpam-3312	178	27	i	i	NOUN
ejpam-3312	178	28	(	(	PUNCT
ejpam-3312	178	29	resp	resp	NOUN
ejpam-3312	178	30	.	.	PUNCT
ejpam-3312	179	1	soft	soft	ADJ
ejpam-3312	179	2	d	d	NOUN
ejpam-3312	179	3	,	,	PUNCT
ejpam-3312	179	4	soft	soft	ADJ
ejpam-3312	179	5	b	b	NOUN
ejpam-3312	179	6	)	)	PUNCT
ejpam-3312	179	7	β	β	X
ejpam-3312	179	8	-	-	ADJ
ejpam-3312	179	9	open	open	ADJ
ejpam-3312	179	10	subset	subset	NOUN
ejpam-3312	179	11	of	of	ADP
ejpam-3312	179	12	x̃.	x̃.	ADJ
ejpam-3312	179	13	proof	proof	NOUN
ejpam-3312	179	14	.	.	PUNCT
ejpam-3312	180	1	we	we	PRON
ejpam-3312	180	2	prove	prove	VERB
ejpam-3312	180	3	the	the	DET
ejpam-3312	180	4	theorem	theorem	NOUN
ejpam-3312	180	5	in	in	ADP
ejpam-3312	180	6	the	the	DET
ejpam-3312	180	7	case	case	NOUN
ejpam-3312	180	8	of	of	ADP
ejpam-3312	180	9	fφ	fφ	PROPN
ejpam-3312	180	10	is	be	AUX
ejpam-3312	180	11	soft	soft	ADJ
ejpam-3312	180	12	dβ	dβ	ADJ
ejpam-3312	180	13	-	-	PUNCT
ejpam-3312	180	14	continuous	continuous	ADJ
ejpam-3312	180	15	and	and	CCONJ
ejpam-3312	180	16	the	the	DET
ejpam-3312	180	17	other	other	ADJ
ejpam-3312	180	18	cases	case	NOUN
ejpam-3312	180	19	can	can	AUX
ejpam-3312	180	20	be	be	AUX
ejpam-3312	180	21	achieved	achieve	VERB
ejpam-3312	180	22	similarly	similarly	ADV
ejpam-3312	180	23	.	.	PUNCT
ejpam-3312	181	1	necessity	necessity	NOUN
ejpam-3312	181	2	:	:	PUNCT
ejpam-3312	181	3	let	let	VERB
ejpam-3312	181	4	gf	gf	PART
ejpam-3312	181	5	be	be	AUX
ejpam-3312	181	6	a	a	DET
ejpam-3312	181	7	soft	soft	ADJ
ejpam-3312	181	8	open	open	ADJ
ejpam-3312	181	9	subset	subset	NOUN
ejpam-3312	181	10	of	of	ADP
ejpam-3312	181	11	ỹ	ỹ	PROPN
ejpam-3312	181	12	,	,	PUNCT
ejpam-3312	181	13	then	then	ADV
ejpam-3312	181	14	we	we	PRON
ejpam-3312	181	15	have	have	VERB
ejpam-3312	181	16	the	the	DET
ejpam-3312	181	17	following	follow	VERB
ejpam-3312	181	18	two	two	NUM
ejpam-3312	181	19	cases	case	NOUN
ejpam-3312	181	20	:	:	PUNCT
ejpam-3312	181	21	(	(	PUNCT
ejpam-3312	181	22	i	i	NOUN
ejpam-3312	181	23	)	)	PUNCT
ejpam-3312	181	24	either	either	CCONJ
ejpam-3312	181	25	f−1φ	f−1φ	NOUN
ejpam-3312	181	26	(	(	PUNCT
ejpam-3312	181	27	gf	gf	NOUN
ejpam-3312	181	28	)	)	PUNCT
ejpam-3312	182	1	=	=	PUNCT
ejpam-3312	182	2	∅̃.	∅̃.	NOUN
ejpam-3312	182	3	(	(	PUNCT
ejpam-3312	182	4	ii	ii	NOUN
ejpam-3312	182	5	)	)	PUNCT
ejpam-3312	182	6	or	or	CCONJ
ejpam-3312	182	7	f−1(gf	f−1(gf	NOUN
ejpam-3312	182	8	)	)	PUNCT
ejpam-3312	182	9	6=	6=	NUM
ejpam-3312	182	10	∅̃.	∅̃.	NOUN
ejpam-3312	182	11	by	by	ADP
ejpam-3312	182	12	choosing	choose	VERB
ejpam-3312	182	13	p	p	PROPN
ejpam-3312	182	14	xe	xe	PROPN
ejpam-3312	182	15	∈	∈	PROPN
ejpam-3312	182	16	x	x	PUNCT
ejpam-3312	182	17	such	such	ADJ
ejpam-3312	182	18	that	that	SCONJ
ejpam-3312	182	19	p	p	PROPN
ejpam-3312	182	20	xe	xe	PROPN
ejpam-3312	182	21	∈	∈	PROPN
ejpam-3312	182	22	f−1φ	f−1φ	NOUN
ejpam-3312	182	23	(	(	PUNCT
ejpam-3312	182	24	gf	gf	PROPN
ejpam-3312	182	25	)	)	PUNCT
ejpam-3312	182	26	,	,	PUNCT
ejpam-3312	182	27	we	we	PRON
ejpam-3312	182	28	obtain	obtain	VERB
ejpam-3312	182	29	fφ(p	fφ(p	PUNCT
ejpam-3312	182	30	xe	xe	PROPN
ejpam-3312	182	31	)	)	PUNCT
ejpam-3312	182	32	∈	∈	PROPN
ejpam-3312	182	33	gf	gf	NOUN
ejpam-3312	182	34	.	.	PUNCT
ejpam-3312	183	1	so	so	ADV
ejpam-3312	183	2	there	there	PRON
ejpam-3312	183	3	exists	exist	VERB
ejpam-3312	183	4	a	a	DET
ejpam-3312	183	5	soft	soft	ADJ
ejpam-3312	183	6	dβ	dβ	ADJ
ejpam-3312	183	7	-	-	PUNCT
ejpam-3312	183	8	open	open	NOUN
ejpam-3312	183	9	set	set	NOUN
ejpam-3312	183	10	he	he	PRON
ejpam-3312	183	11	containing	contain	VERB
ejpam-3312	183	12	p	p	PROPN
ejpam-3312	183	13	xe	xe	PROPN
ejpam-3312	183	14	such	such	ADJ
ejpam-3312	183	15	that	that	DET
ejpam-3312	183	16	fφ(he)⊆̃gf	fφ(he)⊆̃gf	PROPN
ejpam-3312	183	17	.	.	PUNCT
ejpam-3312	184	1	since	since	SCONJ
ejpam-3312	184	2	p	p	PROPN
ejpam-3312	184	3	xe	xe	PROPN
ejpam-3312	184	4	is	be	AUX
ejpam-3312	184	5	chosen	choose	VERB
ejpam-3312	184	6	arbitrary	arbitrary	ADJ
ejpam-3312	184	7	,	,	PUNCT
ejpam-3312	184	8	then	then	ADV
ejpam-3312	184	9	f−1φ	f−1φ	NOUN
ejpam-3312	184	10	(	(	PUNCT
ejpam-3312	184	11	gf	gf	X
ejpam-3312	184	12	)	)	PUNCT
ejpam-3312	184	13	=	=	SYM
ejpam-3312	184	14	⋃̃	⋃̃	PROPN
ejpam-3312	184	15	pxe	pxe	NOUN
ejpam-3312	184	16	∈f	∈f	PROPN
ejpam-3312	184	17	−1	−1	NOUN
ejpam-3312	184	18	φ	φ	PROPN
ejpam-3312	184	19	(	(	PUNCT
ejpam-3312	184	20	gf	gf	PROPN
ejpam-3312	184	21	)	)	PUNCT
ejpam-3312	184	22	he	he	PRON
ejpam-3312	184	23	.	.	PUNCT
ejpam-3312	185	1	from	from	ADP
ejpam-3312	185	2	the	the	DET
ejpam-3312	185	3	two	two	NUM
ejpam-3312	185	4	cases	case	NOUN
ejpam-3312	185	5	above	above	ADV
ejpam-3312	185	6	,	,	PUNCT
ejpam-3312	185	7	we	we	PRON
ejpam-3312	185	8	conclude	conclude	VERB
ejpam-3312	185	9	that	that	SCONJ
ejpam-3312	185	10	f−1φ	f−1φ	NOUN
ejpam-3312	185	11	(	(	PUNCT
ejpam-3312	185	12	gf	gf	NOUN
ejpam-3312	185	13	)	)	PUNCT
ejpam-3312	185	14	is	be	AUX
ejpam-3312	185	15	a	a	DET
ejpam-3312	185	16	soft	soft	ADJ
ejpam-3312	185	17	dβ	dβ	ADJ
ejpam-3312	185	18	-	-	PUNCT
ejpam-3312	185	19	open	open	NOUN
ejpam-3312	185	20	subset	subset	NOUN
ejpam-3312	185	21	of	of	ADP
ejpam-3312	185	22	x̃.	x̃.	ADJ
ejpam-3312	185	23	sufficiency	sufficiency	NOUN
ejpam-3312	185	24	:	:	PUNCT
ejpam-3312	185	25	let	let	VERB
ejpam-3312	185	26	gf	gf	PART
ejpam-3312	185	27	be	be	AUX
ejpam-3312	185	28	a	a	DET
ejpam-3312	185	29	soft	soft	ADJ
ejpam-3312	185	30	open	open	ADJ
ejpam-3312	185	31	subset	subset	NOUN
ejpam-3312	185	32	of	of	ADP
ejpam-3312	185	33	ỹ	ỹ	PROPN
ejpam-3312	185	34	containing	contain	VERB
ejpam-3312	185	35	fφ(p	fφ(p	PROPN
ejpam-3312	185	36	xe	xe	PROPN
ejpam-3312	185	37	)	)	PUNCT
ejpam-3312	185	38	.	.	PUNCT
ejpam-3312	186	1	then	then	ADV
ejpam-3312	186	2	p	p	PROPN
ejpam-3312	186	3	xe	xe	PROPN
ejpam-3312	186	4	∈	∈	PROPN
ejpam-3312	186	5	f−1φ	f−1φ	NOUN
ejpam-3312	186	6	(	(	PUNCT
ejpam-3312	186	7	gf	gf	NOUN
ejpam-3312	186	8	)	)	PUNCT
ejpam-3312	186	9	.	.	PUNCT
ejpam-3312	187	1	by	by	ADP
ejpam-3312	187	2	hypothesis	hypothesis	NOUN
ejpam-3312	187	3	,	,	PUNCT
ejpam-3312	187	4	f−1φ	f−1φ	NOUN
ejpam-3312	187	5	(	(	PUNCT
ejpam-3312	187	6	gf	gf	NOUN
ejpam-3312	187	7	)	)	PUNCT
ejpam-3312	187	8	is	be	AUX
ejpam-3312	187	9	a	a	DET
ejpam-3312	187	10	soft	soft	ADJ
ejpam-3312	187	11	dβ	dβ	ADJ
ejpam-3312	187	12	-	-	PUNCT
ejpam-3312	187	13	open	open	NOUN
ejpam-3312	187	14	set	set	NOUN
ejpam-3312	187	15	.	.	PUNCT
ejpam-3312	188	1	since	since	SCONJ
ejpam-3312	188	2	fφ(f−1φ	fφ(f−1φ	NOUN
ejpam-3312	188	3	(	(	PUNCT
ejpam-3312	188	4	gf	gf	NOUN
ejpam-3312	188	5	)	)	PUNCT
ejpam-3312	188	6	)	)	PUNCT
ejpam-3312	189	1	⊆̃gf	⊆̃gf	NOUN
ejpam-3312	189	2	,	,	PUNCT
ejpam-3312	189	3	then	then	ADV
ejpam-3312	189	4	fφ	fφ	PROPN
ejpam-3312	189	5	is	be	AUX
ejpam-3312	189	6	a	a	DET
ejpam-3312	189	7	soft	soft	ADJ
ejpam-3312	189	8	dβ	dβ	ADJ
ejpam-3312	189	9	-	-	PUNCT
ejpam-3312	189	10	continuous	continuous	ADJ
ejpam-3312	189	11	mapping	mapping	NOUN
ejpam-3312	189	12	at	at	ADP
ejpam-3312	189	13	p	p	PROPN
ejpam-3312	189	14	xe	xe	PROPN
ejpam-3312	189	15	∈	∈	PROPN
ejpam-3312	189	16	x	x	X
ejpam-3312	189	17	and	and	CCONJ
ejpam-3312	189	18	since	since	SCONJ
ejpam-3312	189	19	p	p	PROPN
ejpam-3312	189	20	xe	xe	PROPN
ejpam-3312	189	21	is	be	AUX
ejpam-3312	189	22	chosen	choose	VERB
ejpam-3312	189	23	arbitrary	arbitrary	ADJ
ejpam-3312	189	24	,	,	PUNCT
ejpam-3312	189	25	then	then	ADV
ejpam-3312	189	26	fφ	fφ	PROPN
ejpam-3312	189	27	is	be	AUX
ejpam-3312	189	28	a	a	DET
ejpam-3312	189	29	soft	soft	ADJ
ejpam-3312	189	30	dβ	dβ	ADJ
ejpam-3312	189	31	-	-	PUNCT
ejpam-3312	189	32	continuous	continuous	ADJ
ejpam-3312	189	33	mapping	mapping	NOUN
ejpam-3312	189	34	.	.	PUNCT
ejpam-3312	190	1	t.	t.	PROPN
ejpam-3312	190	2	m.	m.	PROPN
ejpam-3312	190	3	al	al	PROPN
ejpam-3312	190	4	-	-	PUNCT
ejpam-3312	190	5	shami	shami	PROPN
ejpam-3312	190	6	,	,	PUNCT
ejpam-3312	190	7	m.	m.	PROPN
ejpam-3312	190	8	e.	e.	PROPN
ejpam-3312	190	9	el	el	PROPN
ejpam-3312	190	10	-	-	PROPN
ejpam-3312	190	11	shafei	shafei	PROPN
ejpam-3312	190	12	,	,	PUNCT
ejpam-3312	190	13	b.	b.	PROPN
ejpam-3312	190	14	a.	a.	PROPN
ejpam-3312	190	15	asaad	asaad	PROPN
ejpam-3312	190	16	/	/	SYM
ejpam-3312	190	17	eur	eur	PROPN
ejpam-3312	190	18	.	.	PUNCT
ejpam-3312	191	1	j.	j.	PROPN
ejpam-3312	191	2	pure	pure	PROPN
ejpam-3312	191	3	appl	appl	PROPN
ejpam-3312	191	4	.	.	PROPN
ejpam-3312	191	5	math	math	PROPN
ejpam-3312	191	6	,	,	PUNCT
ejpam-3312	191	7	12	12	NUM
ejpam-3312	191	8	(	(	PUNCT
ejpam-3312	191	9	1	1	NUM
ejpam-3312	191	10	)	)	PUNCT
ejpam-3312	191	11	(	(	PUNCT
ejpam-3312	191	12	2019	2019	NUM
ejpam-3312	191	13	)	)	PUNCT
ejpam-3312	191	14	,	,	PUNCT
ejpam-3312	191	15	176	176	NUM
ejpam-3312	191	16	-	-	SYM
ejpam-3312	191	17	193	193	NUM
ejpam-3312	191	18	182	182	NUM
ejpam-3312	191	19	remark	remark	NOUN
ejpam-3312	191	20	2	2	NUM
ejpam-3312	191	21	.	.	PUNCT
ejpam-3312	192	1	from	from	ADP
ejpam-3312	192	2	definition	definition	NOUN
ejpam-3312	192	3	(	(	PUNCT
ejpam-3312	192	4	19	19	NUM
ejpam-3312	192	5	)	)	PUNCT
ejpam-3312	192	6	,	,	PUNCT
ejpam-3312	192	7	we	we	PRON
ejpam-3312	192	8	can	can	AUX
ejpam-3312	192	9	note	note	VERB
ejpam-3312	192	10	the	the	DET
ejpam-3312	192	11	following	following	NOUN
ejpam-3312	192	12	:	:	PUNCT
ejpam-3312	192	13	(	(	PUNCT
ejpam-3312	192	14	i	i	NOUN
ejpam-3312	192	15	)	)	PUNCT
ejpam-3312	192	16	every	every	PRON
ejpam-3312	192	17	soft	soft	ADJ
ejpam-3312	192	18	i	i	PRON
ejpam-3312	192	19	(	(	PUNCT
ejpam-3312	192	20	d	d	PROPN
ejpam-3312	192	21	,	,	PUNCT
ejpam-3312	192	22	b	b	NOUN
ejpam-3312	192	23	)	)	PUNCT
ejpam-3312	192	24	β	β	ADJ
ejpam-3312	192	25	-	-	ADJ
ejpam-3312	192	26	continuous	continuous	ADJ
ejpam-3312	192	27	mapping	mapping	NOUN
ejpam-3312	192	28	is	be	AUX
ejpam-3312	192	29	always	always	ADV
ejpam-3312	192	30	soft	soft	ADJ
ejpam-3312	193	1	β	β	ADJ
ejpam-3312	193	2	-	-	ADJ
ejpam-3312	193	3	continuous	continuous	ADJ
ejpam-3312	193	4	.	.	PUNCT
ejpam-3312	194	1	(	(	PUNCT
ejpam-3312	194	2	ii	ii	NOUN
ejpam-3312	194	3	)	)	PUNCT
ejpam-3312	194	4	every	every	DET
ejpam-3312	194	5	soft	soft	ADJ
ejpam-3312	194	6	bβ	bβ	NOUN
ejpam-3312	194	7	-	-	PUNCT
ejpam-3312	194	8	continuous	continuous	ADJ
ejpam-3312	194	9	mapping	mapping	NOUN
ejpam-3312	194	10	is	be	AUX
ejpam-3312	194	11	soft	soft	ADJ
ejpam-3312	194	12	iβ	iβ	ADP
ejpam-3312	194	13	-	-	ADJ
ejpam-3312	194	14	continuous	continuous	ADJ
ejpam-3312	194	15	or	or	CCONJ
ejpam-3312	194	16	soft	soft	ADJ
ejpam-3312	194	17	dβ	dβ	ADJ
ejpam-3312	194	18	-	-	PUNCT
ejpam-3312	194	19	continuous	continuous	ADJ
ejpam-3312	194	20	.	.	PUNCT
ejpam-3312	195	1	the	the	DET
ejpam-3312	195	2	two	two	NUM
ejpam-3312	195	3	examples	example	NOUN
ejpam-3312	195	4	below	below	ADV
ejpam-3312	195	5	elucidates	elucidate	VERB
ejpam-3312	195	6	that	that	SCONJ
ejpam-3312	195	7	the	the	DET
ejpam-3312	195	8	converse	converse	NOUN
ejpam-3312	195	9	of	of	ADP
ejpam-3312	195	10	the	the	DET
ejpam-3312	195	11	two	two	NUM
ejpam-3312	195	12	results	result	NOUN
ejpam-3312	195	13	of	of	ADP
ejpam-3312	195	14	the	the	DET
ejpam-3312	195	15	remark	remark	NOUN
ejpam-3312	195	16	above	above	ADP
ejpam-3312	195	17	need	need	AUX
ejpam-3312	195	18	not	not	PART
ejpam-3312	195	19	be	be	AUX
ejpam-3312	195	20	true	true	ADJ
ejpam-3312	195	21	in	in	ADP
ejpam-3312	195	22	general	general	ADJ
ejpam-3312	195	23	.	.	PUNCT
ejpam-3312	195	24	example	example	NOUN
ejpam-3312	196	1	1	1	NUM
ejpam-3312	196	2	.	.	PUNCT
ejpam-3312	196	3	let	let	VERB
ejpam-3312	196	4	the	the	DET
ejpam-3312	196	5	two	two	NUM
ejpam-3312	196	6	parameters	parameter	NOUN
ejpam-3312	196	7	sets	set	VERB
ejpam-3312	196	8	a	a	PRON
ejpam-3312	196	9	=	=	SYM
ejpam-3312	196	10	{	{	PUNCT
ejpam-3312	196	11	12	12	NUM
ejpam-3312	196	12	,	,	PUNCT
ejpam-3312	196	13	1	1	NUM
ejpam-3312	196	14	4	4	NUM
ejpam-3312	196	15	}	}	PUNCT
ejpam-3312	196	16	,	,	PUNCT
ejpam-3312	196	17	b	b	X
ejpam-3312	196	18	=	=	SYM
ejpam-3312	196	19	{	{	PUNCT
ejpam-3312	196	20	13	13	NUM
ejpam-3312	196	21	,	,	PUNCT
ejpam-3312	196	22	1	1	NUM
ejpam-3312	196	23	5	5	NUM
ejpam-3312	196	24	}	}	PUNCT
ejpam-3312	196	25	and	and	CCONJ
ejpam-3312	196	26	the	the	DET
ejpam-3312	196	27	two	two	NUM
ejpam-3312	196	28	universe	universe	NOUN
ejpam-3312	196	29	sets	set	NOUN
ejpam-3312	196	30	x	x	PUNCT
ejpam-3312	196	31	=	=	PUNCT
ejpam-3312	196	32	{	{	PUNCT
ejpam-3312	196	33	m	m	PROPN
ejpam-3312	196	34	,	,	PUNCT
ejpam-3312	196	35	n	n	CCONJ
ejpam-3312	196	36	,	,	PUNCT
ejpam-3312	196	37	r	r	NOUN
ejpam-3312	196	38	,	,	PUNCT
ejpam-3312	196	39	s	s	PART
ejpam-3312	196	40	}	}	PUNCT
ejpam-3312	196	41	,	,	PUNCT
ejpam-3312	196	42	y	y	PROPN
ejpam-3312	196	43	=	=	PRON
ejpam-3312	196	44	{	{	PUNCT
ejpam-3312	196	45	u	u	NOUN
ejpam-3312	196	46	,	,	PUNCT
ejpam-3312	196	47	v	v	NOUN
ejpam-3312	196	48	,	,	PUNCT
ejpam-3312	196	49	w	w	NOUN
ejpam-3312	196	50	}	}	PUNCT
ejpam-3312	196	51	.	.	PUNCT
ejpam-3312	197	1	consider	consider	VERB
ejpam-3312	197	2	a	a	DET
ejpam-3312	197	3	mapping	mapping	NOUN
ejpam-3312	197	4	φ	φ	NOUN
ejpam-3312	197	5	:	:	PUNCT
ejpam-3312	197	6	a	a	DET
ejpam-3312	197	7	→	→	SYM
ejpam-3312	197	8	b	b	NOUN
ejpam-3312	197	9	is	be	AUX
ejpam-3312	197	10	defined	define	VERB
ejpam-3312	197	11	as	as	ADP
ejpam-3312	197	12	,	,	PUNCT
ejpam-3312	197	13	φ(12	φ(12	ADJ
ejpam-3312	197	14	)	)	PUNCT
ejpam-3312	197	15	=	=	SYM
ejpam-3312	197	16	1	1	NUM
ejpam-3312	197	17	3	3	NUM
ejpam-3312	197	18	and	and	CCONJ
ejpam-3312	197	19	φ(14	φ(14	NOUN
ejpam-3312	197	20	)	)	PUNCT
ejpam-3312	197	21	=	=	SYM
ejpam-3312	197	22	1	1	NUM
ejpam-3312	197	23	5	5	NUM
ejpam-3312	197	24	,	,	PUNCT
ejpam-3312	197	25	and	and	CCONJ
ejpam-3312	197	26	a	a	DET
ejpam-3312	197	27	mapping	mapping	NOUN
ejpam-3312	197	28	f	f	NOUN
ejpam-3312	197	29	:	:	PUNCT
ejpam-3312	197	30	x	x	X
ejpam-3312	197	31	→	→	SYM
ejpam-3312	197	32	y	y	PROPN
ejpam-3312	197	33	is	be	AUX
ejpam-3312	197	34	defined	define	VERB
ejpam-3312	197	35	as	as	ADP
ejpam-3312	197	36	,	,	PUNCT
ejpam-3312	197	37	f(m	f(m	PROPN
ejpam-3312	197	38	)	)	PUNCT
ejpam-3312	197	39	=	=	SYM
ejpam-3312	197	40	u	u	NOUN
ejpam-3312	197	41	,	,	PUNCT
ejpam-3312	197	42	f(n	f(n	PROPN
ejpam-3312	197	43	)	)	PUNCT
ejpam-3312	198	1	=	=	SYM
ejpam-3312	198	2	v	v	NOUN
ejpam-3312	198	3	and	and	CCONJ
ejpam-3312	198	4	f(r	f(r	NOUN
ejpam-3312	198	5	)	)	PUNCT
ejpam-3312	198	6	=	=	PUNCT
ejpam-3312	198	7	f(s	f(s	X
ejpam-3312	198	8	)	)	PUNCT
ejpam-3312	199	1	=	=	SYM
ejpam-3312	199	2	w.	w.	NOUN
ejpam-3312	199	3	we	we	PRON
ejpam-3312	199	4	define	define	VERB
ejpam-3312	199	5	a	a	DET
ejpam-3312	199	6	partial	partial	ADJ
ejpam-3312	199	7	order	order	NOUN
ejpam-3312	199	8	relation	relation	NOUN
ejpam-3312	199	9	on	on	ADP
ejpam-3312	199	10	x	x	PUNCT
ejpam-3312	199	11	as	as	ADP
ejpam-3312	199	12	�	�	NOUN
ejpam-3312	199	13	=	=	NOUN
ejpam-3312	199	14	4	4	NUM
ejpam-3312	199	15	⋃	⋃	NOUN
ejpam-3312	199	16	{	{	PUNCT
ejpam-3312	199	17	(	(	PUNCT
ejpam-3312	199	18	m	m	PROPN
ejpam-3312	199	19	,	,	PUNCT
ejpam-3312	199	20	n	n	CCONJ
ejpam-3312	199	21	)	)	PUNCT
ejpam-3312	199	22	,	,	PUNCT
ejpam-3312	199	23	(	(	PUNCT
ejpam-3312	199	24	n	n	X
ejpam-3312	199	25	,	,	PUNCT
ejpam-3312	199	26	r	r	NOUN
ejpam-3312	199	27	)	)	PUNCT
ejpam-3312	199	28	,	,	PUNCT
ejpam-3312	199	29	(	(	PUNCT
ejpam-3312	199	30	m	m	NOUN
ejpam-3312	199	31	,	,	PUNCT
ejpam-3312	199	32	r	r	NOUN
ejpam-3312	199	33	)	)	PUNCT
ejpam-3312	199	34	}	}	PUNCT
ejpam-3312	199	35	and	and	CCONJ
ejpam-3312	199	36	we	we	PRON
ejpam-3312	199	37	define	define	VERB
ejpam-3312	199	38	two	two	NUM
ejpam-3312	199	39	soft	soft	ADJ
ejpam-3312	199	40	topologies	topology	NOUN
ejpam-3312	199	41	τ	τ	X
ejpam-3312	199	42	and	and	CCONJ
ejpam-3312	199	43	θ	θ	PROPN
ejpam-3312	199	44	on	on	ADP
ejpam-3312	199	45	x	x	X
ejpam-3312	199	46	and	and	CCONJ
ejpam-3312	199	47	y	y	PROPN
ejpam-3312	199	48	,	,	PUNCT
ejpam-3312	199	49	respectively	respectively	ADV
ejpam-3312	199	50	,	,	PUNCT
ejpam-3312	199	51	as	as	ADP
ejpam-3312	199	52	τ	τ	X
ejpam-3312	199	53	=	=	SYM
ejpam-3312	199	54	{	{	PUNCT
ejpam-3312	199	55	∅̃	∅̃	NOUN
ejpam-3312	199	56	,	,	PUNCT
ejpam-3312	199	57	x̃	x̃	PROPN
ejpam-3312	199	58	,	,	PUNCT
ejpam-3312	199	59	fa	fa	PROPN
ejpam-3312	199	60	,	,	PUNCT
ejpam-3312	199	61	ga	ga	PROPN
ejpam-3312	199	62	}	}	PUNCT
ejpam-3312	199	63	and	and	CCONJ
ejpam-3312	199	64	θ	θ	PROPN
ejpam-3312	199	65	=	=	SYM
ejpam-3312	199	66	{	{	PUNCT
ejpam-3312	199	67	∅̃	∅̃	NOUN
ejpam-3312	199	68	,	,	PUNCT
ejpam-3312	199	69	ỹ	ỹ	PROPN
ejpam-3312	199	70	,	,	PUNCT
ejpam-3312	199	71	hb	hb	PROPN
ejpam-3312	199	72	}	}	PUNCT
ejpam-3312	199	73	,	,	PUNCT
ejpam-3312	199	74	where	where	SCONJ
ejpam-3312	199	75	fa	fa	PROPN
ejpam-3312	199	76	=	=	PUNCT
ejpam-3312	199	77	{	{	PUNCT
ejpam-3312	199	78	(	(	PUNCT
ejpam-3312	199	79	12	12	NUM
ejpam-3312	199	80	,	,	PUNCT
ejpam-3312	199	81	{	{	PUNCT
ejpam-3312	199	82	m	m	NOUN
ejpam-3312	199	83	,	,	PUNCT
ejpam-3312	199	84	n	n	CCONJ
ejpam-3312	199	85	,	,	PUNCT
ejpam-3312	199	86	s	s	NOUN
ejpam-3312	199	87	}	}	PUNCT
ejpam-3312	199	88	)	)	PUNCT
ejpam-3312	199	89	,	,	PUNCT
ejpam-3312	199	90	(	(	PUNCT
ejpam-3312	199	91	1	1	NUM
ejpam-3312	199	92	4	4	NUM
ejpam-3312	199	93	,	,	PUNCT
ejpam-3312	199	94	{	{	PUNCT
ejpam-3312	199	95	m	m	NOUN
ejpam-3312	199	96	,	,	PUNCT
ejpam-3312	199	97	r	r	NOUN
ejpam-3312	199	98	}	}	PUNCT
ejpam-3312	199	99	)	)	PUNCT
ejpam-3312	199	100	}	}	PUNCT
ejpam-3312	199	101	,	,	PUNCT
ejpam-3312	199	102	ga	ga	PROPN
ejpam-3312	199	103	=	=	PRON
ejpam-3312	199	104	{	{	PUNCT
ejpam-3312	199	105	(	(	PUNCT
ejpam-3312	199	106	12	12	NUM
ejpam-3312	199	107	,	,	PUNCT
ejpam-3312	199	108	∅	∅	NOUN
ejpam-3312	199	109	)	)	PUNCT
ejpam-3312	199	110	,	,	PUNCT
ejpam-3312	199	111	(	(	PUNCT
ejpam-3312	199	112	1	1	NUM
ejpam-3312	199	113	4	4	NUM
ejpam-3312	199	114	,	,	PUNCT
ejpam-3312	199	115	{	{	PUNCT
ejpam-3312	199	116	r	r	NOUN
ejpam-3312	199	117	}	}	PUNCT
ejpam-3312	199	118	)	)	PUNCT
ejpam-3312	199	119	}	}	PUNCT
ejpam-3312	199	120	and	and	CCONJ
ejpam-3312	199	121	hb	hb	X
ejpam-3312	199	122	=	=	SYM
ejpam-3312	199	123	{	{	PUNCT
ejpam-3312	199	124	(	(	PUNCT
ejpam-3312	199	125	13	13	NUM
ejpam-3312	199	126	,	,	PUNCT
ejpam-3312	199	127	{	{	PUNCT
ejpam-3312	199	128	u	u	NOUN
ejpam-3312	199	129	}	}	PUNCT
ejpam-3312	199	130	)	)	PUNCT
ejpam-3312	199	131	,	,	PUNCT
ejpam-3312	199	132	(	(	PUNCT
ejpam-3312	199	133	1	1	NUM
ejpam-3312	199	134	5	5	NUM
ejpam-3312	199	135	,	,	PUNCT
ejpam-3312	199	136	{	{	PUNCT
ejpam-3312	199	137	w	w	NOUN
ejpam-3312	199	138	}	}	PUNCT
ejpam-3312	199	139	)	)	PUNCT
ejpam-3312	199	140	}	}	PUNCT
ejpam-3312	199	141	.	.	PUNCT
ejpam-3312	200	1	since	since	SCONJ
ejpam-3312	200	2	f−1φ	f−1φ	NOUN
ejpam-3312	200	3	(	(	PUNCT
ejpam-3312	200	4	hb	hb	X
ejpam-3312	200	5	)	)	PUNCT
ejpam-3312	200	6	=	=	PRON
ejpam-3312	200	7	{	{	PUNCT
ejpam-3312	200	8	(	(	PUNCT
ejpam-3312	200	9	12	12	NUM
ejpam-3312	200	10	,	,	PUNCT
ejpam-3312	200	11	{	{	PUNCT
ejpam-3312	200	12	m	m	NOUN
ejpam-3312	200	13	}	}	PUNCT
ejpam-3312	200	14	)	)	PUNCT
ejpam-3312	200	15	,	,	PUNCT
ejpam-3312	200	16	(	(	PUNCT
ejpam-3312	200	17	1	1	NUM
ejpam-3312	200	18	4	4	NUM
ejpam-3312	200	19	,	,	PUNCT
ejpam-3312	200	20	{	{	PUNCT
ejpam-3312	200	21	r	r	NOUN
ejpam-3312	200	22	,	,	PUNCT
ejpam-3312	200	23	s	s	NOUN
ejpam-3312	200	24	}	}	PUNCT
ejpam-3312	200	25	)	)	PUNCT
ejpam-3312	200	26	}	}	PUNCT
ejpam-3312	200	27	is	be	AUX
ejpam-3312	200	28	a	a	DET
ejpam-3312	200	29	soft	soft	ADJ
ejpam-3312	200	30	β	β	NOUN
ejpam-3312	200	31	-	-	ADJ
ejpam-3312	200	32	open	open	ADJ
ejpam-3312	200	33	set	set	NOUN
ejpam-3312	200	34	,	,	PUNCT
ejpam-3312	200	35	then	then	ADV
ejpam-3312	200	36	fφ	fφ	VERB
ejpam-3312	200	37	:	:	PUNCT
ejpam-3312	200	38	s(xa	s(xa	PROPN
ejpam-3312	200	39	)	)	PUNCT
ejpam-3312	200	40	→	→	SYM
ejpam-3312	200	41	s(yb	s(yb	NUM
ejpam-3312	200	42	)	)	PUNCT
ejpam-3312	200	43	is	be	AUX
ejpam-3312	200	44	a	a	DET
ejpam-3312	200	45	soft	soft	ADJ
ejpam-3312	200	46	β	β	ADJ
ejpam-3312	200	47	-	-	ADJ
ejpam-3312	200	48	continuous	continuous	ADJ
ejpam-3312	200	49	mapping	mapping	NOUN
ejpam-3312	200	50	.	.	PUNCT
ejpam-3312	201	1	on	on	ADP
ejpam-3312	201	2	the	the	DET
ejpam-3312	201	3	other	other	ADJ
ejpam-3312	201	4	hand	hand	NOUN
ejpam-3312	201	5	,	,	PUNCT
ejpam-3312	201	6	f−1φ	f−1φ	NOUN
ejpam-3312	201	7	(	(	PUNCT
ejpam-3312	201	8	hb	hb	X
ejpam-3312	201	9	)	)	PUNCT
ejpam-3312	201	10	is	be	AUX
ejpam-3312	201	11	neither	neither	CCONJ
ejpam-3312	201	12	a	a	DET
ejpam-3312	201	13	soft	soft	ADJ
ejpam-3312	201	14	dβ	dβ	ADJ
ejpam-3312	201	15	-	-	PUNCT
ejpam-3312	201	16	open	open	NOUN
ejpam-3312	201	17	nor	nor	CCONJ
ejpam-3312	201	18	a	a	DET
ejpam-3312	201	19	soft	soft	ADJ
ejpam-3312	201	20	iβ	iβ	NOUN
ejpam-3312	201	21	-	-	ADJ
ejpam-3312	201	22	open	open	ADJ
ejpam-3312	201	23	set	set	NOUN
ejpam-3312	201	24	.	.	PUNCT
ejpam-3312	202	1	hence	hence	ADV
ejpam-3312	202	2	fφ	fφ	PROPN
ejpam-3312	202	3	is	be	AUX
ejpam-3312	202	4	not	not	PART
ejpam-3312	202	5	soft	soft	ADJ
ejpam-3312	202	6	i	i	PRON
ejpam-3312	202	7	(	(	PUNCT
ejpam-3312	202	8	soft	soft	ADJ
ejpam-3312	202	9	d	d	NOUN
ejpam-3312	202	10	,	,	PUNCT
ejpam-3312	202	11	soft	soft	ADJ
ejpam-3312	202	12	b	b	NOUN
ejpam-3312	202	13	)	)	PUNCT
ejpam-3312	202	14	β	β	NOUN
ejpam-3312	202	15	-	-	ADJ
ejpam-3312	202	16	continuous	continuous	ADJ
ejpam-3312	202	17	.	.	PUNCT
ejpam-3312	202	18	example	example	NOUN
ejpam-3312	203	1	2	2	NUM
ejpam-3312	203	2	.	.	X
ejpam-3312	203	3	in	in	ADP
ejpam-3312	203	4	example	example	NOUN
ejpam-3312	203	5	above	above	ADV
ejpam-3312	203	6	,	,	PUNCT
ejpam-3312	203	7	if	if	SCONJ
ejpam-3312	203	8	we	we	PRON
ejpam-3312	203	9	only	only	ADV
ejpam-3312	203	10	replace	replace	VERB
ejpam-3312	203	11	the	the	DET
ejpam-3312	203	12	partial	partial	ADJ
ejpam-3312	203	13	order	order	NOUN
ejpam-3312	203	14	relation	relation	NOUN
ejpam-3312	203	15	by	by	ADP
ejpam-3312	203	16	�	�	NOUN
ejpam-3312	203	17	=	=	PROPN
ejpam-3312	203	18	4	4	NUM
ejpam-3312	203	19	⋃	⋃	NOUN
ejpam-3312	203	20	{	{	PUNCT
ejpam-3312	203	21	(	(	PUNCT
ejpam-3312	203	22	m	m	PROPN
ejpam-3312	203	23	,	,	PUNCT
ejpam-3312	203	24	n)}(resp	n)}(resp	PROPN
ejpam-3312	203	25	.	.	PUNCT
ejpam-3312	203	26	�	�	PROPN
ejpam-3312	203	27	=	=	NOUN
ejpam-3312	203	28	4	4	NUM
ejpam-3312	203	29	⋃	⋃	NOUN
ejpam-3312	203	30	{	{	PUNCT
ejpam-3312	203	31	(	(	PUNCT
ejpam-3312	203	32	n	n	X
ejpam-3312	203	33	,	,	PUNCT
ejpam-3312	203	34	r	r	NOUN
ejpam-3312	203	35	)	)	PUNCT
ejpam-3312	203	36	}	}	PUNCT
ejpam-3312	203	37	)	)	PUNCT
ejpam-3312	203	38	,	,	PUNCT
ejpam-3312	203	39	then	then	ADV
ejpam-3312	203	40	the	the	DET
ejpam-3312	203	41	soft	soft	ADJ
ejpam-3312	203	42	mapping	mapping	NOUN
ejpam-3312	203	43	fφ	fφ	NOUN
ejpam-3312	203	44	is	be	AUX
ejpam-3312	203	45	soft	soft	ADJ
ejpam-3312	203	46	d	d	ADJ
ejpam-3312	203	47	-	-	ADJ
ejpam-3312	203	48	continuous	continuous	ADJ
ejpam-3312	203	49	(	(	PUNCT
ejpam-3312	203	50	resp	resp	NOUN
ejpam-3312	203	51	.	.	PUNCT
ejpam-3312	204	1	soft	soft	ADJ
ejpam-3312	204	2	i	i	NOUN
ejpam-3312	204	3	-	-	PUNCT
ejpam-3312	204	4	continuous	continuous	ADJ
ejpam-3312	204	5	)	)	PUNCT
ejpam-3312	204	6	,	,	PUNCT
ejpam-3312	204	7	but	but	CCONJ
ejpam-3312	204	8	is	be	AUX
ejpam-3312	204	9	not	not	PART
ejpam-3312	204	10	soft	soft	ADJ
ejpam-3312	204	11	b	b	NOUN
ejpam-3312	204	12	-	-	PUNCT
ejpam-3312	204	13	continuous	continuous	ADJ
ejpam-3312	204	14	.	.	PUNCT
ejpam-3312	205	1	definition	definition	NOUN
ejpam-3312	205	2	20	20	NUM
ejpam-3312	205	3	.	.	PUNCT
ejpam-3312	206	1	for	for	ADP
ejpam-3312	206	2	a	a	DET
ejpam-3312	206	3	soft	soft	ADJ
ejpam-3312	206	4	subset	subset	NOUN
ejpam-3312	206	5	he	he	PRON
ejpam-3312	206	6	of	of	ADP
ejpam-3312	206	7	(	(	PUNCT
ejpam-3312	206	8	x	x	PROPN
ejpam-3312	206	9	,	,	PUNCT
ejpam-3312	206	10	τ	τ	PROPN
ejpam-3312	206	11	,	,	PUNCT
ejpam-3312	206	12	e	e	NOUN
ejpam-3312	206	13	,	,	PUNCT
ejpam-3312	206	14	�	�	PROPN
ejpam-3312	206	15	)	)	PUNCT
ejpam-3312	206	16	,	,	PUNCT
ejpam-3312	206	17	we	we	PRON
ejpam-3312	206	18	define	define	VERB
ejpam-3312	206	19	the	the	DET
ejpam-3312	206	20	following	follow	VERB
ejpam-3312	206	21	six	six	NUM
ejpam-3312	206	22	operators	operator	NOUN
ejpam-3312	206	23	:	:	PUNCT
ejpam-3312	206	24	(	(	PUNCT
ejpam-3312	206	25	i	i	NOUN
ejpam-3312	206	26	)	)	PUNCT
ejpam-3312	206	27	h	h	PROPN
ejpam-3312	207	1	iβo	iβo	ADV
ejpam-3312	207	2	e	e	X
ejpam-3312	207	3	(	(	PUNCT
ejpam-3312	207	4	resp	resp	PROPN
ejpam-3312	207	5	.	.	PUNCT
ejpam-3312	208	1	hdβo	hdβo	PROPN
ejpam-3312	208	2	e	e	PROPN
ejpam-3312	208	3	,	,	PUNCT
ejpam-3312	208	4	hbβo	hbβo	ADJ
ejpam-3312	208	5	e	e	NOUN
ejpam-3312	208	6	)	)	PUNCT
ejpam-3312	208	7	is	be	AUX
ejpam-3312	208	8	the	the	DET
ejpam-3312	208	9	largest	large	ADJ
ejpam-3312	208	10	soft	soft	ADJ
ejpam-3312	208	11	i	i	PRON
ejpam-3312	208	12	(	(	PUNCT
ejpam-3312	208	13	resp	resp	NOUN
ejpam-3312	208	14	.	.	PUNCT
ejpam-3312	209	1	soft	soft	ADJ
ejpam-3312	209	2	d	d	NOUN
ejpam-3312	209	3	,	,	PUNCT
ejpam-3312	209	4	soft	soft	ADJ
ejpam-3312	209	5	b	b	NOUN
ejpam-3312	209	6	)	)	PUNCT
ejpam-3312	209	7	β	β	X
ejpam-3312	209	8	-	-	ADJ
ejpam-3312	209	9	open	open	ADJ
ejpam-3312	209	10	set	set	NOUN
ejpam-3312	209	11	contained	contain	VERB
ejpam-3312	209	12	in	in	ADP
ejpam-3312	209	13	he	he	PRON
ejpam-3312	209	14	.	.	PUNCT
ejpam-3312	210	1	(	(	PUNCT
ejpam-3312	210	2	ii	ii	NOUN
ejpam-3312	210	3	)	)	PUNCT
ejpam-3312	210	4	h	h	NOUN
ejpam-3312	210	5	iβcl	iβcl	NOUN
ejpam-3312	210	6	e	e	PROPN
ejpam-3312	210	7	(	(	PUNCT
ejpam-3312	210	8	resp	resp	NOUN
ejpam-3312	210	9	.	.	PUNCT
ejpam-3312	211	1	hdβcl	hdβcl	PROPN
ejpam-3312	211	2	e	e	PROPN
ejpam-3312	211	3	,	,	PUNCT
ejpam-3312	211	4	hbβcl	hbβcl	PROPN
ejpam-3312	211	5	e	e	X
ejpam-3312	211	6	)	)	PUNCT
ejpam-3312	211	7	is	be	AUX
ejpam-3312	211	8	the	the	DET
ejpam-3312	211	9	smallest	small	ADJ
ejpam-3312	211	10	soft	soft	ADJ
ejpam-3312	211	11	i	i	PRON
ejpam-3312	211	12	(	(	PUNCT
ejpam-3312	211	13	resp	resp	NOUN
ejpam-3312	211	14	.	.	PUNCT
ejpam-3312	212	1	soft	soft	ADJ
ejpam-3312	212	2	d	d	NOUN
ejpam-3312	212	3	,	,	PUNCT
ejpam-3312	212	4	soft	soft	ADJ
ejpam-3312	212	5	b	b	NOUN
ejpam-3312	212	6	)	)	PUNCT
ejpam-3312	212	7	β	β	X
ejpam-3312	212	8	-	-	VERB
ejpam-3312	212	9	closed	closed	ADJ
ejpam-3312	212	10	set	set	NOUN
ejpam-3312	212	11	containing	contain	VERB
ejpam-3312	212	12	he	he	PRON
ejpam-3312	212	13	.	.	PUNCT
ejpam-3312	213	1	lemma	lemma	PROPN
ejpam-3312	213	2	1	1	NUM
ejpam-3312	213	3	.	.	PUNCT
ejpam-3312	214	1	for	for	ADP
ejpam-3312	214	2	any	any	DET
ejpam-3312	214	3	soft	soft	ADJ
ejpam-3312	214	4	subset	subset	NOUN
ejpam-3312	214	5	he	he	PRON
ejpam-3312	214	6	of	of	ADP
ejpam-3312	214	7	(	(	PUNCT
ejpam-3312	214	8	x	x	PROPN
ejpam-3312	214	9	,	,	PUNCT
ejpam-3312	214	10	τ	τ	PROPN
ejpam-3312	214	11	,	,	PUNCT
ejpam-3312	214	12	e	e	NOUN
ejpam-3312	214	13	,	,	PUNCT
ejpam-3312	214	14	�	�	PROPN
ejpam-3312	214	15	)	)	PUNCT
ejpam-3312	214	16	,	,	PUNCT
ejpam-3312	214	17	the	the	DET
ejpam-3312	214	18	following	follow	VERB
ejpam-3312	214	19	statements	statement	NOUN
ejpam-3312	214	20	hold	hold	VERB
ejpam-3312	214	21	:	:	PUNCT
ejpam-3312	214	22	(	(	PUNCT
ejpam-3312	214	23	i	i	NOUN
ejpam-3312	214	24	)	)	PUNCT
ejpam-3312	214	25	(	(	PUNCT
ejpam-3312	214	26	hdβcl	hdβcl	NOUN
ejpam-3312	214	27	e	e	NOUN
ejpam-3312	214	28	)	)	PUNCT
ejpam-3312	214	29	c	c	NOUN
ejpam-3312	215	1	=	=	SYM
ejpam-3312	215	2	(	(	PUNCT
ejpam-3312	215	3	hc	hc	PROPN
ejpam-3312	215	4	e)iβo	e)iβo	NOUN
ejpam-3312	215	5	.	.	PUNCT
ejpam-3312	216	1	(	(	PUNCT
ejpam-3312	216	2	ii	ii	NOUN
ejpam-3312	216	3	)	)	PUNCT
ejpam-3312	216	4	(	(	PUNCT
ejpam-3312	216	5	h	h	NOUN
ejpam-3312	216	6	iβcl	iβcl	NOUN
ejpam-3312	216	7	e	e	NOUN
ejpam-3312	216	8	)	)	PUNCT
ejpam-3312	216	9	c	c	NOUN
ejpam-3312	216	10	=	=	SYM
ejpam-3312	216	11	(	(	PUNCT
ejpam-3312	216	12	hc	hc	PROPN
ejpam-3312	216	13	e)dβo	e)dβo	PROPN
ejpam-3312	216	14	.	.	PUNCT
ejpam-3312	217	1	(	(	PUNCT
ejpam-3312	217	2	iii	iii	X
ejpam-3312	217	3	)	)	PUNCT
ejpam-3312	217	4	(	(	PUNCT
ejpam-3312	217	5	hbβcl	hbβcl	PROPN
ejpam-3312	217	6	e	e	NOUN
ejpam-3312	217	7	)	)	PUNCT
ejpam-3312	217	8	c	c	NOUN
ejpam-3312	217	9	=	=	SYM
ejpam-3312	217	10	(	(	PUNCT
ejpam-3312	217	11	hc	hc	PROPN
ejpam-3312	217	12	e)bβo	e)bβo	PROPN
ejpam-3312	217	13	.	.	PUNCT
ejpam-3312	218	1	proof	proof	NOUN
ejpam-3312	218	2	.	.	PUNCT
ejpam-3312	219	1	(	(	PUNCT
ejpam-3312	219	2	i	i	NOUN
ejpam-3312	219	3	)	)	PUNCT
ejpam-3312	219	4	(	(	PUNCT
ejpam-3312	219	5	hdβcl	hdβcl	NOUN
ejpam-3312	219	6	e	e	NOUN
ejpam-3312	219	7	)	)	PUNCT
ejpam-3312	219	8	c	c	NOUN
ejpam-3312	219	9	=	=	PRON
ejpam-3312	219	10	{	{	PUNCT
ejpam-3312	219	11	⋃̃	⋃̃	PROPN
ejpam-3312	219	12	fe	fe	X
ejpam-3312	219	13	:	:	PUNCT
ejpam-3312	219	14	fe	fe	X
ejpam-3312	219	15	is	be	AUX
ejpam-3312	219	16	a	a	DET
ejpam-3312	219	17	soft	soft	ADJ
ejpam-3312	219	18	dβ	dβ	ADJ
ejpam-3312	219	19	-	-	PUNCT
ejpam-3312	219	20	closed	closed	ADJ
ejpam-3312	219	21	set	set	NOUN
ejpam-3312	219	22	containing	contain	VERB
ejpam-3312	219	23	he}c	he}c	PROPN
ejpam-3312	219	24	=	=	SYM
ejpam-3312	219	25	⋂̃	⋂̃	X
ejpam-3312	219	26	{	{	PUNCT
ejpam-3312	219	27	f	f	PROPN
ejpam-3312	219	28	ce	ce	PROPN
ejpam-3312	219	29	:	:	PUNCT
ejpam-3312	219	30	f	f	PROPN
ejpam-3312	219	31	ce	ce	PROPN
ejpam-3312	219	32	is	be	AUX
ejpam-3312	219	33	a	a	DET
ejpam-3312	219	34	soft	soft	ADJ
ejpam-3312	219	35	iβ	iβ	ADJ
ejpam-3312	219	36	-	-	ADJ
ejpam-3312	219	37	open	open	ADJ
ejpam-3312	219	38	set	set	NOUN
ejpam-3312	219	39	contained	contain	VERB
ejpam-3312	219	40	in	in	ADP
ejpam-3312	219	41	hc	hc	PROPN
ejpam-3312	219	42	e	e	NOUN
ejpam-3312	219	43	}	}	PUNCT
ejpam-3312	219	44	=	=	SYM
ejpam-3312	219	45	(	(	PUNCT
ejpam-3312	219	46	hc	hc	PROPN
ejpam-3312	219	47	e)iβo	e)iβo	NOUN
ejpam-3312	219	48	.	.	PUNCT
ejpam-3312	220	1	by	by	ADP
ejpam-3312	220	2	analogy	analogy	NOUN
ejpam-3312	220	3	with	with	ADP
ejpam-3312	220	4	(	(	PUNCT
ejpam-3312	220	5	i	i	NOUN
ejpam-3312	220	6	)	)	PUNCT
ejpam-3312	220	7	,	,	PUNCT
ejpam-3312	220	8	one	one	PRON
ejpam-3312	220	9	can	can	AUX
ejpam-3312	220	10	prove	prove	VERB
ejpam-3312	220	11	(	(	PUNCT
ejpam-3312	220	12	ii	ii	NOUN
ejpam-3312	220	13	)	)	PUNCT
ejpam-3312	220	14	and	and	CCONJ
ejpam-3312	220	15	(	(	PUNCT
ejpam-3312	220	16	iii	iii	NOUN
ejpam-3312	220	17	)	)	PUNCT
ejpam-3312	220	18	.	.	PUNCT
ejpam-3312	221	1	t.	t.	PROPN
ejpam-3312	221	2	m.	m.	PROPN
ejpam-3312	221	3	al	al	PROPN
ejpam-3312	221	4	-	-	PUNCT
ejpam-3312	221	5	shami	shami	PROPN
ejpam-3312	221	6	,	,	PUNCT
ejpam-3312	221	7	m.	m.	PROPN
ejpam-3312	221	8	e.	e.	PROPN
ejpam-3312	221	9	el	el	PROPN
ejpam-3312	221	10	-	-	PROPN
ejpam-3312	221	11	shafei	shafei	PROPN
ejpam-3312	221	12	,	,	PUNCT
ejpam-3312	221	13	b.	b.	PROPN
ejpam-3312	221	14	a.	a.	PROPN
ejpam-3312	221	15	asaad	asaad	PROPN
ejpam-3312	221	16	/	/	SYM
ejpam-3312	221	17	eur	eur	PROPN
ejpam-3312	221	18	.	.	PUNCT
ejpam-3312	222	1	j.	j.	PROPN
ejpam-3312	222	2	pure	pure	PROPN
ejpam-3312	222	3	appl	appl	PROPN
ejpam-3312	222	4	.	.	PROPN
ejpam-3312	222	5	math	math	PROPN
ejpam-3312	222	6	,	,	PUNCT
ejpam-3312	222	7	12	12	NUM
ejpam-3312	222	8	(	(	PUNCT
ejpam-3312	222	9	1	1	NUM
ejpam-3312	222	10	)	)	PUNCT
ejpam-3312	222	11	(	(	PUNCT
ejpam-3312	222	12	2019	2019	NUM
ejpam-3312	222	13	)	)	PUNCT
ejpam-3312	222	14	,	,	PUNCT
ejpam-3312	222	15	176	176	NUM
ejpam-3312	222	16	-	-	SYM
ejpam-3312	222	17	193	193	NUM
ejpam-3312	222	18	183	183	NUM
ejpam-3312	222	19	theorem	theorem	NOUN
ejpam-3312	222	20	3	3	NUM
ejpam-3312	222	21	.	.	PUNCT
ejpam-3312	223	1	the	the	DET
ejpam-3312	223	2	following	follow	VERB
ejpam-3312	223	3	five	five	NUM
ejpam-3312	223	4	properties	property	NOUN
ejpam-3312	223	5	of	of	ADP
ejpam-3312	223	6	a	a	DET
ejpam-3312	223	7	soft	soft	ADJ
ejpam-3312	223	8	mapping	mapping	NOUN
ejpam-3312	223	9	fφ	fφ	NOUN
ejpam-3312	223	10	:	:	PUNCT
ejpam-3312	223	11	(	(	PUNCT
ejpam-3312	223	12	x	x	X
ejpam-3312	223	13	,	,	PUNCT
ejpam-3312	223	14	τ	τ	X
ejpam-3312	223	15	,	,	PUNCT
ejpam-3312	223	16	e	e	X
ejpam-3312	223	17	�	�	PROPN
ejpam-3312	223	18	1)→	1)→	NUM
ejpam-3312	223	19	(	(	PUNCT
ejpam-3312	223	20	y	y	PROPN
ejpam-3312	223	21	,	,	PUNCT
ejpam-3312	223	22	θ	θ	PROPN
ejpam-3312	223	23	,	,	PUNCT
ejpam-3312	223	24	f,	f,	X
ejpam-3312	223	25	�	�	SYM
ejpam-3312	223	26	2	2	NUM
ejpam-3312	223	27	)	)	PUNCT
ejpam-3312	223	28	are	be	AUX
ejpam-3312	223	29	equivalent	equivalent	ADJ
ejpam-3312	223	30	:	:	PUNCT
ejpam-3312	223	31	(	(	PUNCT
ejpam-3312	223	32	i	i	NOUN
ejpam-3312	223	33	)	)	PUNCT
ejpam-3312	223	34	fφ	fφ	VERB
ejpam-3312	223	35	is	be	AUX
ejpam-3312	223	36	soft	soft	ADJ
ejpam-3312	223	37	iβ	iβ	ADP
ejpam-3312	223	38	-	-	ADJ
ejpam-3312	223	39	continuous	continuous	ADJ
ejpam-3312	223	40	;	;	PUNCT
ejpam-3312	223	41	(	(	PUNCT
ejpam-3312	223	42	ii	ii	NOUN
ejpam-3312	223	43	)	)	PUNCT
ejpam-3312	223	44	f−1φ	f−1φ	NOUN
ejpam-3312	223	45	(	(	PUNCT
ejpam-3312	223	46	lf	lf	NOUN
ejpam-3312	223	47	)	)	PUNCT
ejpam-3312	223	48	is	be	AUX
ejpam-3312	223	49	a	a	DET
ejpam-3312	223	50	soft	soft	ADJ
ejpam-3312	223	51	dβ	dβ	ADJ
ejpam-3312	223	52	-	-	PUNCT
ejpam-3312	223	53	closed	closed	ADJ
ejpam-3312	223	54	subset	subset	NOUN
ejpam-3312	223	55	of	of	ADP
ejpam-3312	223	56	x̃	x̃	PROPN
ejpam-3312	223	57	,	,	PUNCT
ejpam-3312	223	58	for	for	ADP
ejpam-3312	223	59	each	each	DET
ejpam-3312	223	60	soft	soft	ADJ
ejpam-3312	223	61	closed	closed	ADJ
ejpam-3312	223	62	subset	subset	NOUN
ejpam-3312	223	63	lf	lf	NOUN
ejpam-3312	223	64	of	of	ADP
ejpam-3312	223	65	ỹ	ỹ	PROPN
ejpam-3312	223	66	;	;	PUNCT
ejpam-3312	223	67	(	(	PUNCT
ejpam-3312	223	68	iii	iii	X
ejpam-3312	223	69	)	)	PUNCT
ejpam-3312	223	70	(	(	PUNCT
ejpam-3312	223	71	f−1φ	f−1φ	NOUN
ejpam-3312	223	72	(	(	PUNCT
ejpam-3312	223	73	mf	mf	X
ejpam-3312	223	74	)	)	PUNCT
ejpam-3312	223	75	)	)	PUNCT
ejpam-3312	224	1	dβcl⊆̃f−1φ	dβcl⊆̃f−1φ	PROPN
ejpam-3312	224	2	(	(	PUNCT
ejpam-3312	224	3	cl(mf	cl(mf	ADJ
ejpam-3312	224	4	)	)	PUNCT
ejpam-3312	224	5	)	)	PUNCT
ejpam-3312	224	6	,	,	PUNCT
ejpam-3312	224	7	for	for	ADP
ejpam-3312	224	8	every	every	DET
ejpam-3312	224	9	mf	mf	NOUN
ejpam-3312	224	10	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	224	11	;	;	PUNCT
ejpam-3312	224	12	(	(	PUNCT
ejpam-3312	224	13	iv	iv	X
ejpam-3312	224	14	)	)	PUNCT
ejpam-3312	224	15	fφ(ndβcl	fφ(ndβcl	NOUN
ejpam-3312	224	16	e	e	X
ejpam-3312	224	17	)	)	PUNCT
ejpam-3312	224	18	⊆̃cl(fφ(ne	⊆̃cl(fφ(ne	PROPN
ejpam-3312	224	19	)	)	PUNCT
ejpam-3312	224	20	)	)	PUNCT
ejpam-3312	224	21	,	,	PUNCT
ejpam-3312	224	22	for	for	ADP
ejpam-3312	224	23	every	every	DET
ejpam-3312	224	24	ne⊆̃x̃	ne⊆̃x̃	NOUN
ejpam-3312	224	25	;	;	PUNCT
ejpam-3312	224	26	(	(	PUNCT
ejpam-3312	224	27	v	v	NOUN
ejpam-3312	224	28	)	)	PUNCT
ejpam-3312	224	29	f−1φ	f−1φ	NOUN
ejpam-3312	224	30	(	(	PUNCT
ejpam-3312	224	31	int(mf	int(mf	ADJ
ejpam-3312	224	32	)	)	PUNCT
ejpam-3312	224	33	)	)	PUNCT
ejpam-3312	224	34	⊆̃(f−1φ	⊆̃(f−1φ	NOUN
ejpam-3312	224	35	(	(	PUNCT
ejpam-3312	224	36	mf	mf	X
ejpam-3312	224	37	)	)	PUNCT
ejpam-3312	224	38	)	)	PUNCT
ejpam-3312	224	39	iβo	iβo	NOUN
ejpam-3312	224	40	,	,	PUNCT
ejpam-3312	224	41	for	for	ADP
ejpam-3312	224	42	every	every	DET
ejpam-3312	224	43	mf	mf	NOUN
ejpam-3312	224	44	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	224	45	.	.	PUNCT
ejpam-3312	225	1	proof	proof	NOUN
ejpam-3312	225	2	.	.	PUNCT
ejpam-3312	226	1	(	(	PUNCT
ejpam-3312	226	2	i	i	NOUN
ejpam-3312	226	3	)	)	PUNCT
ejpam-3312	226	4	⇒	⇒	PROPN
ejpam-3312	226	5	(	(	PUNCT
ejpam-3312	226	6	ii	ii	NOUN
ejpam-3312	226	7	)	)	PUNCT
ejpam-3312	226	8	:	:	PUNCT
ejpam-3312	226	9	consider	consider	VERB
ejpam-3312	226	10	lf	lf	ADP
ejpam-3312	226	11	is	be	AUX
ejpam-3312	226	12	a	a	DET
ejpam-3312	226	13	soft	soft	ADJ
ejpam-3312	226	14	closed	closed	ADJ
ejpam-3312	226	15	subset	subset	NOUN
ejpam-3312	226	16	of	of	ADP
ejpam-3312	226	17	ỹ	ỹ	PROPN
ejpam-3312	226	18	.	.	PUNCT
ejpam-3312	227	1	by	by	ADP
ejpam-3312	227	2	hypothesis	hypothesis	NOUN
ejpam-3312	227	3	,	,	PUNCT
ejpam-3312	227	4	f−1φ	f−1φ	NOUN
ejpam-3312	227	5	(	(	PUNCT
ejpam-3312	227	6	lcf	lcf	PROPN
ejpam-3312	227	7	)	)	PUNCT
ejpam-3312	227	8	is	be	AUX
ejpam-3312	227	9	a	a	DET
ejpam-3312	227	10	soft	soft	ADJ
ejpam-3312	227	11	iβ	iβ	ADJ
ejpam-3312	227	12	-	-	ADJ
ejpam-3312	227	13	open	open	ADJ
ejpam-3312	227	14	subset	subset	NOUN
ejpam-3312	227	15	of	of	ADP
ejpam-3312	227	16	x̃	x̃	PROPN
ejpam-3312	227	17	and	and	CCONJ
ejpam-3312	227	18	by	by	ADP
ejpam-3312	227	19	the	the	DET
ejpam-3312	227	20	fact	fact	NOUN
ejpam-3312	227	21	that	that	SCONJ
ejpam-3312	227	22	f−1φ	f−1φ	NOUN
ejpam-3312	227	23	(	(	PUNCT
ejpam-3312	227	24	lcf	lcf	PROPN
ejpam-3312	227	25	)	)	PUNCT
ejpam-3312	227	26	=	=	PUNCT
ejpam-3312	227	27	(	(	PUNCT
ejpam-3312	227	28	f−1φ	f−1φ	NOUN
ejpam-3312	227	29	(	(	PUNCT
ejpam-3312	227	30	lf	lf	NOUN
ejpam-3312	227	31	)	)	PUNCT
ejpam-3312	227	32	)	)	PUNCT
ejpam-3312	228	1	c	c	X
ejpam-3312	228	2	,	,	PUNCT
ejpam-3312	228	3	we	we	PRON
ejpam-3312	228	4	obtain	obtain	VERB
ejpam-3312	228	5	f−1φ	f−1φ	NOUN
ejpam-3312	228	6	(	(	PUNCT
ejpam-3312	228	7	lf	lf	NOUN
ejpam-3312	228	8	)	)	PUNCT
ejpam-3312	228	9	is	be	AUX
ejpam-3312	228	10	soft	soft	ADJ
ejpam-3312	228	11	dβ	dβ	NOUN
ejpam-3312	228	12	-	-	PUNCT
ejpam-3312	228	13	closed	closed	ADJ
ejpam-3312	228	14	as	as	SCONJ
ejpam-3312	228	15	required	require	VERB
ejpam-3312	228	16	.	.	PUNCT
ejpam-3312	229	1	(	(	PUNCT
ejpam-3312	229	2	ii	ii	NOUN
ejpam-3312	229	3	)	)	PUNCT
ejpam-3312	229	4	⇒	⇒	NOUN
ejpam-3312	229	5	(	(	PUNCT
ejpam-3312	229	6	iii	iii	NOUN
ejpam-3312	229	7	)	)	PUNCT
ejpam-3312	229	8	:	:	PUNCT
ejpam-3312	229	9	it	it	PRON
ejpam-3312	229	10	follows	follow	VERB
ejpam-3312	229	11	from	from	ADP
ejpam-3312	229	12	(	(	PUNCT
ejpam-3312	229	13	ii	ii	NOUN
ejpam-3312	229	14	)	)	PUNCT
ejpam-3312	229	15	that	that	PRON
ejpam-3312	229	16	f−1φ	f−1φ	NOUN
ejpam-3312	229	17	(	(	PUNCT
ejpam-3312	229	18	cl(me	cl(me	PROPN
ejpam-3312	229	19	)	)	PUNCT
ejpam-3312	229	20	)	)	PUNCT
ejpam-3312	229	21	is	be	AUX
ejpam-3312	229	22	a	a	DET
ejpam-3312	229	23	soft	soft	ADJ
ejpam-3312	229	24	dβ	dβ	ADJ
ejpam-3312	229	25	-	-	PUNCT
ejpam-3312	229	26	closed	closed	ADJ
ejpam-3312	229	27	subset	subset	NOUN
ejpam-3312	229	28	of	of	ADP
ejpam-3312	229	29	x̃	x̃	PROPN
ejpam-3312	229	30	,	,	PUNCT
ejpam-3312	229	31	for	for	SCONJ
ejpam-3312	229	32	every	every	DET
ejpam-3312	229	33	mf	mf	NOUN
ejpam-3312	229	34	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	229	35	.	.	PUNCT
ejpam-3312	230	1	so	so	ADV
ejpam-3312	230	2	(	(	PUNCT
ejpam-3312	230	3	f−1φ	f−1φ	NOUN
ejpam-3312	230	4	(	(	PUNCT
ejpam-3312	230	5	mf	mf	X
ejpam-3312	230	6	)	)	PUNCT
ejpam-3312	230	7	)	)	PUNCT
ejpam-3312	231	1	dβcl⊆̃(f−1φ	dβcl⊆̃(f−1φ	PROPN
ejpam-3312	231	2	(	(	PUNCT
ejpam-3312	231	3	cl(mf	cl(mf	ADJ
ejpam-3312	231	4	)	)	PUNCT
ejpam-3312	231	5	)	)	PUNCT
ejpam-3312	231	6	dβcl	dβcl	NOUN
ejpam-3312	231	7	=	=	PUNCT
ejpam-3312	231	8	f−1φ	f−1φ	NOUN
ejpam-3312	231	9	(	(	PUNCT
ejpam-3312	231	10	cl(mf	cl(mf	ADJ
ejpam-3312	231	11	)	)	PUNCT
ejpam-3312	231	12	)	)	PUNCT
ejpam-3312	231	13	.	.	PUNCT
ejpam-3312	232	1	(	(	PUNCT
ejpam-3312	232	2	iii	iii	X
ejpam-3312	232	3	)	)	PUNCT
ejpam-3312	232	4	⇒	⇒	NOUN
ejpam-3312	232	5	(	(	PUNCT
ejpam-3312	232	6	iv	iv	NUM
ejpam-3312	232	7	)	)	PUNCT
ejpam-3312	232	8	:	:	PUNCT
ejpam-3312	232	9	from	from	ADP
ejpam-3312	232	10	the	the	DET
ejpam-3312	232	11	fact	fact	NOUN
ejpam-3312	232	12	that	that	SCONJ
ejpam-3312	232	13	ndβcl	ndβcl	NOUN
ejpam-3312	232	14	e	e	NOUN
ejpam-3312	232	15	⊆̃(f−1φ	⊆̃(f−1φ	NOUN
ejpam-3312	232	16	(	(	PUNCT
ejpam-3312	232	17	fφ(ne))dβcl	fφ(ne))dβcl	NOUN
ejpam-3312	232	18	and	and	CCONJ
ejpam-3312	232	19	from	from	ADP
ejpam-3312	232	20	(	(	PUNCT
ejpam-3312	232	21	iii	iii	NOUN
ejpam-3312	232	22	)	)	PUNCT
ejpam-3312	232	23	,	,	PUNCT
ejpam-3312	232	24	we	we	PRON
ejpam-3312	232	25	have	have	AUX
ejpam-3312	232	26	(	(	PUNCT
ejpam-3312	232	27	f−1φ	f−1φ	NOUN
ejpam-3312	232	28	(	(	PUNCT
ejpam-3312	232	29	fφ(ne))dβcl	fφ(ne))dβcl	NOUN
ejpam-3312	232	30	⊆̃f−1φ	⊆̃f−1φ	NOUN
ejpam-3312	232	31	(	(	PUNCT
ejpam-3312	232	32	cl(fφ(ne	cl(fφ(ne	NOUN
ejpam-3312	232	33	)	)	PUNCT
ejpam-3312	232	34	)	)	PUNCT
ejpam-3312	232	35	.	.	PUNCT
ejpam-3312	233	1	this	this	PRON
ejpam-3312	233	2	implies	imply	VERB
ejpam-3312	233	3	that	that	SCONJ
ejpam-3312	233	4	fφ(ndβcl	fφ(ndβcl	PROPN
ejpam-3312	233	5	e	e	NOUN
ejpam-3312	233	6	)	)	PUNCT
ejpam-3312	233	7	⊆̃cl(fφ(ne	⊆̃cl(fφ(ne	PROPN
ejpam-3312	233	8	)	)	PUNCT
ejpam-3312	233	9	)	)	PUNCT
ejpam-3312	233	10	.	.	PUNCT
ejpam-3312	234	1	(	(	PUNCT
ejpam-3312	234	2	iv	iv	X
ejpam-3312	234	3	)	)	PUNCT
ejpam-3312	234	4	⇒	⇒	NOUN
ejpam-3312	234	5	(	(	PUNCT
ejpam-3312	234	6	v	v	NOUN
ejpam-3312	234	7	)	)	PUNCT
ejpam-3312	234	8	:	:	PUNCT
ejpam-3312	234	9	for	for	ADP
ejpam-3312	234	10	any	any	DET
ejpam-3312	234	11	soft	soft	ADJ
ejpam-3312	234	12	subset	subset	NOUN
ejpam-3312	234	13	mf	mf	NOUN
ejpam-3312	234	14	of	of	ADP
ejpam-3312	234	15	ỹ	ỹ	PROPN
ejpam-3312	234	16	,	,	PUNCT
ejpam-3312	234	17	we	we	PRON
ejpam-3312	234	18	obtain	obtain	VERB
ejpam-3312	234	19	from	from	ADP
ejpam-3312	234	20	lemma	lemma	PROPN
ejpam-3312	234	21	(	(	PUNCT
ejpam-3312	234	22	1	1	NUM
ejpam-3312	234	23	)	)	PUNCT
ejpam-3312	235	1	that	that	PRON
ejpam-3312	235	2	fφ(x̃	fφ(x̃	PROPN
ejpam-3312	235	3	−	−	PROPN
ejpam-3312	236	1	(	(	PUNCT
ejpam-3312	236	2	f−1φ	f−1φ	NOUN
ejpam-3312	236	3	(	(	PUNCT
ejpam-3312	236	4	ne))iβo	ne))iβo	PROPN
ejpam-3312	236	5	)	)	PUNCT
ejpam-3312	236	6	=	=	SYM
ejpam-3312	236	7	fφ(((f−1φ	fφ(((f−1φ	NOUN
ejpam-3312	236	8	(	(	PUNCT
ejpam-3312	236	9	ne))c)dβcl	ne))c)dβcl	NOUN
ejpam-3312	236	10	)	)	PUNCT
ejpam-3312	236	11	.	.	PUNCT
ejpam-3312	237	1	it	it	PRON
ejpam-3312	237	2	follows	follow	VERB
ejpam-3312	237	3	from	from	ADP
ejpam-3312	237	4	(	(	PUNCT
ejpam-3312	237	5	iv	iv	X
ejpam-3312	237	6	)	)	PUNCT
ejpam-3312	237	7	,	,	PUNCT
ejpam-3312	237	8	that	that	SCONJ
ejpam-3312	237	9	fφ(((f−1φ	fφ(((f−1φ	NOUN
ejpam-3312	237	10	(	(	PUNCT
ejpam-3312	237	11	ne))c)dβcl	ne))c)dβcl	NOUN
ejpam-3312	237	12	)	)	PUNCT
ejpam-3312	237	13	⊆̃cl(fφ(f−1φ	⊆̃cl(fφ(f−1φ	NOUN
ejpam-3312	237	14	(	(	PUNCT
ejpam-3312	237	15	ne))c	ne))c	PROPN
ejpam-3312	237	16	)	)	PUNCT
ejpam-3312	238	1	=	=	SYM
ejpam-3312	238	2	cl(fφ(f−1φ	cl(fφ(f−1φ	NOUN
ejpam-3312	238	3	(	(	PUNCT
ejpam-3312	238	4	n	n	NOUN
ejpam-3312	238	5	c	c	NOUN
ejpam-3312	238	6	e)))⊆̃cl(ỹ	e)))⊆̃cl(ỹ	X
ejpam-3312	238	7	−	−	PROPN
ejpam-3312	238	8	ne	ne	PROPN
ejpam-3312	238	9	)	)	PUNCT
ejpam-3312	238	10	=	=	SYM
ejpam-3312	238	11	ỹ	ỹ	PROPN
ejpam-3312	238	12	−	−	NOUN
ejpam-3312	238	13	int(ne	int(ne	NOUN
ejpam-3312	238	14	)	)	PUNCT
ejpam-3312	238	15	.	.	PUNCT
ejpam-3312	239	1	therefore	therefore	ADV
ejpam-3312	239	2	(	(	PUNCT
ejpam-3312	239	3	x̃	x̃	PROPN
ejpam-3312	239	4	−	−	PROPN
ejpam-3312	239	5	(	(	PUNCT
ejpam-3312	239	6	f−1φ	f−1φ	NOUN
ejpam-3312	239	7	(	(	PUNCT
ejpam-3312	239	8	ne))iβo)⊆̃f−1φ	ne))iβo)⊆̃f−1φ	PROPN
ejpam-3312	239	9	(	(	PUNCT
ejpam-3312	239	10	ỹ−int(ne	ỹ−int(ne	PROPN
ejpam-3312	239	11	)	)	PUNCT
ejpam-3312	239	12	)	)	PUNCT
ejpam-3312	240	1	=	=	SYM
ejpam-3312	240	2	x̃−f−1φ	x̃−f−1φ	PROPN
ejpam-3312	240	3	(	(	PUNCT
ejpam-3312	240	4	int(ne	int(ne	NOUN
ejpam-3312	240	5	)	)	PUNCT
ejpam-3312	240	6	)	)	PUNCT
ejpam-3312	240	7	.	.	PUNCT
ejpam-3312	241	1	thus	thus	ADV
ejpam-3312	241	2	f−1φ	f−1φ	NOUN
ejpam-3312	241	3	(	(	PUNCT
ejpam-3312	241	4	int(ne))⊆̃(f−1φ	int(ne))⊆̃(f−1φ	NOUN
ejpam-3312	241	5	(	(	PUNCT
ejpam-3312	241	6	ne))iβo	ne))iβo	PROPN
ejpam-3312	241	7	.	.	PUNCT
ejpam-3312	241	8	(	(	PUNCT
ejpam-3312	241	9	v	v	NOUN
ejpam-3312	241	10	)	)	PUNCT
ejpam-3312	241	11	⇒	⇒	NOUN
ejpam-3312	241	12	(	(	PUNCT
ejpam-3312	241	13	i	i	NOUN
ejpam-3312	241	14	):	):	PUNCT
ejpam-3312	241	15	consider	consider	VERB
ejpam-3312	241	16	mf	mf	NOUN
ejpam-3312	241	17	is	be	AUX
ejpam-3312	241	18	a	a	DET
ejpam-3312	241	19	soft	soft	ADJ
ejpam-3312	241	20	open	open	ADJ
ejpam-3312	241	21	subset	subset	NOUN
ejpam-3312	241	22	of	of	ADP
ejpam-3312	241	23	ỹ	ỹ	PROPN
ejpam-3312	241	24	.	.	PUNCT
ejpam-3312	242	1	then	then	ADV
ejpam-3312	242	2	f−1φ	f−1φ	VERB
ejpam-3312	242	3	(	(	PUNCT
ejpam-3312	242	4	mf	mf	X
ejpam-3312	242	5	)	)	PUNCT
ejpam-3312	242	6	=	=	SYM
ejpam-3312	242	7	f−1φ	f−1φ	NOUN
ejpam-3312	242	8	(	(	PUNCT
ejpam-3312	242	9	int(mf	int(mf	ADJ
ejpam-3312	242	10	)	)	PUNCT
ejpam-3312	242	11	)	)	PUNCT
ejpam-3312	242	12	⊆̃	⊆̃	NOUN
ejpam-3312	242	13	(	(	PUNCT
ejpam-3312	242	14	f−1φ	f−1φ	NOUN
ejpam-3312	242	15	(	(	PUNCT
ejpam-3312	242	16	mf	mf	X
ejpam-3312	242	17	)	)	PUNCT
ejpam-3312	242	18	)	)	PUNCT
ejpam-3312	242	19	iβo	iβo	NOUN
ejpam-3312	242	20	.	.	PUNCT
ejpam-3312	243	1	so	so	ADV
ejpam-3312	243	2	(	(	PUNCT
ejpam-3312	243	3	f−1φ	f−1φ	NOUN
ejpam-3312	243	4	(	(	PUNCT
ejpam-3312	243	5	mf	mf	X
ejpam-3312	243	6	)	)	PUNCT
ejpam-3312	243	7	)	)	PUNCT
ejpam-3312	243	8	iβo	iβo	NOUN
ejpam-3312	243	9	=	=	SYM
ejpam-3312	243	10	f−1φ	f−1φ	NOUN
ejpam-3312	243	11	(	(	PUNCT
ejpam-3312	243	12	mf	mf	X
ejpam-3312	243	13	)	)	PUNCT
ejpam-3312	243	14	and	and	CCONJ
ejpam-3312	243	15	this	this	PRON
ejpam-3312	243	16	means	mean	VERB
ejpam-3312	243	17	that	that	SCONJ
ejpam-3312	243	18	f−1φ	f−1φ	NOUN
ejpam-3312	243	19	(	(	PUNCT
ejpam-3312	243	20	mf	mf	X
ejpam-3312	243	21	)	)	PUNCT
ejpam-3312	243	22	is	be	AUX
ejpam-3312	243	23	a	a	DET
ejpam-3312	243	24	soft	soft	ADJ
ejpam-3312	243	25	iβ	iβ	ADJ
ejpam-3312	243	26	-	-	ADJ
ejpam-3312	243	27	open	open	ADJ
ejpam-3312	243	28	subset	subset	NOUN
ejpam-3312	243	29	of	of	ADP
ejpam-3312	243	30	x̃.	x̃.	PROPN
ejpam-3312	243	31	hence	hence	ADV
ejpam-3312	243	32	the	the	DET
ejpam-3312	243	33	desired	desire	VERB
ejpam-3312	243	34	result	result	NOUN
ejpam-3312	243	35	is	be	AUX
ejpam-3312	243	36	proved	prove	VERB
ejpam-3312	243	37	.	.	PUNCT
ejpam-3312	244	1	theorem	theorem	ADJ
ejpam-3312	244	2	4	4	NUM
ejpam-3312	244	3	.	.	PUNCT
ejpam-3312	245	1	the	the	DET
ejpam-3312	245	2	following	follow	VERB
ejpam-3312	245	3	five	five	NUM
ejpam-3312	245	4	properties	property	NOUN
ejpam-3312	245	5	of	of	ADP
ejpam-3312	245	6	a	a	DET
ejpam-3312	245	7	soft	soft	ADJ
ejpam-3312	245	8	mapping	mapping	NOUN
ejpam-3312	245	9	fφ	fφ	NOUN
ejpam-3312	245	10	:	:	PUNCT
ejpam-3312	245	11	(	(	PUNCT
ejpam-3312	245	12	x	x	X
ejpam-3312	245	13	,	,	PUNCT
ejpam-3312	245	14	τ	τ	X
ejpam-3312	245	15	,	,	PUNCT
ejpam-3312	245	16	e	e	X
ejpam-3312	245	17	�	�	PROPN
ejpam-3312	245	18	1)→	1)→	NUM
ejpam-3312	245	19	(	(	PUNCT
ejpam-3312	245	20	y	y	PROPN
ejpam-3312	245	21	,	,	PUNCT
ejpam-3312	245	22	θ	θ	PROPN
ejpam-3312	245	23	,	,	PUNCT
ejpam-3312	245	24	f,	f,	X
ejpam-3312	245	25	�	�	SYM
ejpam-3312	245	26	2	2	NUM
ejpam-3312	245	27	)	)	PUNCT
ejpam-3312	245	28	are	be	AUX
ejpam-3312	245	29	equivalent	equivalent	ADJ
ejpam-3312	245	30	:	:	PUNCT
ejpam-3312	245	31	(	(	PUNCT
ejpam-3312	245	32	i	i	NOUN
ejpam-3312	245	33	)	)	PUNCT
ejpam-3312	245	34	fφ	fφ	VERB
ejpam-3312	245	35	is	be	AUX
ejpam-3312	245	36	soft	soft	ADJ
ejpam-3312	245	37	dβ	dβ	ADJ
ejpam-3312	245	38	-	-	PUNCT
ejpam-3312	245	39	continuous	continuous	ADJ
ejpam-3312	245	40	(	(	PUNCT
ejpam-3312	245	41	resp	resp	NOUN
ejpam-3312	245	42	.	.	PUNCT
ejpam-3312	246	1	soft	soft	ADJ
ejpam-3312	246	2	bβ	bβ	NOUN
ejpam-3312	246	3	-	-	PUNCT
ejpam-3312	246	4	continuous	continuous	ADJ
ejpam-3312	246	5	)	)	PUNCT
ejpam-3312	246	6	;	;	PUNCT
ejpam-3312	247	1	(	(	PUNCT
ejpam-3312	247	2	ii	ii	NOUN
ejpam-3312	247	3	)	)	PUNCT
ejpam-3312	247	4	f−1φ	f−1φ	NOUN
ejpam-3312	247	5	(	(	PUNCT
ejpam-3312	247	6	lf	lf	NOUN
ejpam-3312	247	7	)	)	PUNCT
ejpam-3312	247	8	is	be	AUX
ejpam-3312	247	9	a	a	DET
ejpam-3312	247	10	soft	soft	ADJ
ejpam-3312	247	11	iβ	iβ	ADJ
ejpam-3312	247	12	-	-	ADJ
ejpam-3312	247	13	closed	closed	ADJ
ejpam-3312	247	14	(	(	PUNCT
ejpam-3312	247	15	resp	resp	NOUN
ejpam-3312	247	16	.	.	PUNCT
ejpam-3312	247	17	soft	soft	ADJ
ejpam-3312	247	18	bβ	bβ	NOUN
ejpam-3312	247	19	-	-	PUNCT
ejpam-3312	247	20	closed	closed	ADJ
ejpam-3312	247	21	)	)	PUNCT
ejpam-3312	247	22	subset	subset	NOUN
ejpam-3312	247	23	of	of	ADP
ejpam-3312	247	24	x̃	x̃	PROPN
ejpam-3312	247	25	,	,	PUNCT
ejpam-3312	247	26	for	for	ADP
ejpam-3312	247	27	each	each	DET
ejpam-3312	247	28	soft	soft	ADJ
ejpam-3312	247	29	closed	closed	ADJ
ejpam-3312	247	30	subset	subset	NOUN
ejpam-3312	247	31	lf	lf	NOUN
ejpam-3312	247	32	of	of	ADP
ejpam-3312	247	33	ỹ	ỹ	PROPN
ejpam-3312	247	34	;	;	PUNCT
ejpam-3312	247	35	(	(	PUNCT
ejpam-3312	247	36	iii	iii	X
ejpam-3312	247	37	)	)	PUNCT
ejpam-3312	247	38	(	(	PUNCT
ejpam-3312	247	39	f−1φ	f−1φ	NOUN
ejpam-3312	247	40	(	(	PUNCT
ejpam-3312	247	41	mf	mf	X
ejpam-3312	247	42	)	)	PUNCT
ejpam-3312	247	43	)	)	PUNCT
ejpam-3312	248	1	iβcl⊆̃f−1φ	iβcl⊆̃f−1φ	PROPN
ejpam-3312	248	2	(	(	PUNCT
ejpam-3312	248	3	cl(mf	cl(mf	ADJ
ejpam-3312	248	4	)	)	PUNCT
ejpam-3312	248	5	)	)	PUNCT
ejpam-3312	248	6	(	(	PUNCT
ejpam-3312	248	7	resp	resp	NOUN
ejpam-3312	248	8	.	.	PUNCT
ejpam-3312	249	1	(	(	PUNCT
ejpam-3312	249	2	f−1φ	f−1φ	NOUN
ejpam-3312	249	3	(	(	PUNCT
ejpam-3312	249	4	mf	mf	X
ejpam-3312	249	5	)	)	PUNCT
ejpam-3312	249	6	)	)	PUNCT
ejpam-3312	250	1	bβcl⊆̃f−1φ	bβcl⊆̃f−1φ	PROPN
ejpam-3312	250	2	(	(	PUNCT
ejpam-3312	250	3	cl(mf	cl(mf	ADJ
ejpam-3312	250	4	)	)	PUNCT
ejpam-3312	250	5	)	)	PUNCT
ejpam-3312	250	6	,	,	PUNCT
ejpam-3312	250	7	for	for	ADP
ejpam-3312	250	8	every	every	DET
ejpam-3312	250	9	mf	mf	NOUN
ejpam-3312	250	10	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	250	11	;	;	PUNCT
ejpam-3312	250	12	(	(	PUNCT
ejpam-3312	250	13	iv	iv	X
ejpam-3312	250	14	)	)	PUNCT
ejpam-3312	250	15	fφ(n	fφ(n	X
ejpam-3312	250	16	iβcl	iβcl	NOUN
ejpam-3312	250	17	e	e	NOUN
ejpam-3312	250	18	)	)	PUNCT
ejpam-3312	250	19	⊆̃cl(fφ(ne	⊆̃cl(fφ(ne	PROPN
ejpam-3312	250	20	)	)	PUNCT
ejpam-3312	250	21	)	)	PUNCT
ejpam-3312	250	22	(	(	PUNCT
ejpam-3312	250	23	resp	resp	NOUN
ejpam-3312	250	24	.	.	PUNCT
ejpam-3312	251	1	fφ(n	fφ(n	PROPN
ejpam-3312	251	2	bβcl	bβcl	X
ejpam-3312	251	3	e	e	NOUN
ejpam-3312	251	4	)	)	PUNCT
ejpam-3312	251	5	⊆̃cl(fφ(ne	⊆̃cl(fφ(ne	PROPN
ejpam-3312	251	6	)	)	PUNCT
ejpam-3312	251	7	)	)	PUNCT
ejpam-3312	251	8	,	,	PUNCT
ejpam-3312	251	9	for	for	ADP
ejpam-3312	251	10	every	every	DET
ejpam-3312	251	11	ne⊆̃x̃	ne⊆̃x̃	NOUN
ejpam-3312	251	12	;	;	PUNCT
ejpam-3312	251	13	(	(	PUNCT
ejpam-3312	251	14	v	v	NOUN
ejpam-3312	251	15	)	)	PUNCT
ejpam-3312	251	16	f−1φ	f−1φ	NOUN
ejpam-3312	251	17	(	(	PUNCT
ejpam-3312	251	18	int(mf	int(mf	ADJ
ejpam-3312	251	19	)	)	PUNCT
ejpam-3312	251	20	)	)	PUNCT
ejpam-3312	251	21	⊆̃(f−1φ	⊆̃(f−1φ	NOUN
ejpam-3312	251	22	(	(	PUNCT
ejpam-3312	251	23	mf	mf	X
ejpam-3312	251	24	)	)	PUNCT
ejpam-3312	251	25	)	)	PUNCT
ejpam-3312	252	1	dβo	dβo	PROPN
ejpam-3312	252	2	(	(	PUNCT
ejpam-3312	252	3	resp	resp	NOUN
ejpam-3312	252	4	.	.	PUNCT
ejpam-3312	253	1	f−1φ	f−1φ	NOUN
ejpam-3312	253	2	(	(	PUNCT
ejpam-3312	253	3	int(mf	int(mf	ADJ
ejpam-3312	253	4	)	)	PUNCT
ejpam-3312	253	5	)	)	PUNCT
ejpam-3312	253	6	⊆̃(f−1φ	⊆̃(f−1φ	NOUN
ejpam-3312	253	7	(	(	PUNCT
ejpam-3312	253	8	mf	mf	X
ejpam-3312	253	9	)	)	PUNCT
ejpam-3312	253	10	)	)	PUNCT
ejpam-3312	253	11	bβo	bβo	NOUN
ejpam-3312	253	12	,	,	PUNCT
ejpam-3312	253	13	for	for	ADP
ejpam-3312	253	14	every	every	DET
ejpam-3312	253	15	mf	mf	NOUN
ejpam-3312	253	16	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	253	17	.	.	PUNCT
ejpam-3312	254	1	proof	proof	NOUN
ejpam-3312	254	2	.	.	PUNCT
ejpam-3312	255	1	the	the	DET
ejpam-3312	255	2	proof	proof	NOUN
ejpam-3312	255	3	is	be	AUX
ejpam-3312	255	4	similar	similar	ADJ
ejpam-3312	255	5	to	to	ADP
ejpam-3312	255	6	that	that	PRON
ejpam-3312	255	7	of	of	ADP
ejpam-3312	255	8	theorem	theorem	NOUN
ejpam-3312	255	9	(	(	PUNCT
ejpam-3312	255	10	3	3	NUM
ejpam-3312	255	11	)	)	PUNCT
ejpam-3312	255	12	.	.	PUNCT
ejpam-3312	256	1	t.	t.	PROPN
ejpam-3312	256	2	m.	m.	PROPN
ejpam-3312	256	3	al	al	PROPN
ejpam-3312	256	4	-	-	PUNCT
ejpam-3312	256	5	shami	shami	PROPN
ejpam-3312	256	6	,	,	PUNCT
ejpam-3312	256	7	m.	m.	PROPN
ejpam-3312	256	8	e.	e.	PROPN
ejpam-3312	256	9	el	el	PROPN
ejpam-3312	256	10	-	-	PROPN
ejpam-3312	256	11	shafei	shafei	PROPN
ejpam-3312	256	12	,	,	PUNCT
ejpam-3312	256	13	b.	b.	PROPN
ejpam-3312	256	14	a.	a.	PROPN
ejpam-3312	256	15	asaad	asaad	PROPN
ejpam-3312	256	16	/	/	SYM
ejpam-3312	256	17	eur	eur	PROPN
ejpam-3312	256	18	.	.	PUNCT
ejpam-3312	257	1	j.	j.	PROPN
ejpam-3312	257	2	pure	pure	PROPN
ejpam-3312	257	3	appl	appl	PROPN
ejpam-3312	257	4	.	.	PROPN
ejpam-3312	257	5	math	math	PROPN
ejpam-3312	257	6	,	,	PUNCT
ejpam-3312	257	7	12	12	NUM
ejpam-3312	257	8	(	(	PUNCT
ejpam-3312	257	9	1	1	NUM
ejpam-3312	257	10	)	)	PUNCT
ejpam-3312	257	11	(	(	PUNCT
ejpam-3312	257	12	2019	2019	NUM
ejpam-3312	257	13	)	)	PUNCT
ejpam-3312	257	14	,	,	PUNCT
ejpam-3312	257	15	176	176	NUM
ejpam-3312	257	16	-	-	SYM
ejpam-3312	257	17	193	193	NUM
ejpam-3312	257	18	184	184	NUM
ejpam-3312	257	19	theorem	theorem	NOUN
ejpam-3312	257	20	5	5	NUM
ejpam-3312	257	21	.	.	PUNCT
ejpam-3312	258	1	let	let	VERB
ejpam-3312	258	2	τ	τ	PROPN
ejpam-3312	258	3	?	?	PROPN
ejpam-3312	258	4	be	be	AUX
ejpam-3312	258	5	an	an	DET
ejpam-3312	258	6	extended	extended	ADJ
ejpam-3312	258	7	soft	soft	ADJ
ejpam-3312	258	8	topology	topology	NOUN
ejpam-3312	258	9	on	on	ADP
ejpam-3312	258	10	x.	x.	NOUN
ejpam-3312	258	11	then	then	ADV
ejpam-3312	258	12	a	a	DET
ejpam-3312	258	13	soft	soft	ADJ
ejpam-3312	258	14	mapping	mapping	NOUN
ejpam-3312	258	15	gφ	gφ	NOUN
ejpam-3312	258	16	:	:	PUNCT
ejpam-3312	258	17	(	(	PUNCT
ejpam-3312	258	18	x	x	X
ejpam-3312	258	19	,	,	PUNCT
ejpam-3312	258	20	τ	τ	PROPN
ejpam-3312	258	21	?	?	PROPN
ejpam-3312	258	22	,	,	PUNCT
ejpam-3312	258	23	e,	e,	X
ejpam-3312	258	24	�	�	X
ejpam-3312	258	25	1	1	NUM
ejpam-3312	258	26	)	)	PUNCT
ejpam-3312	258	27	→	→	SYM
ejpam-3312	258	28	(	(	PUNCT
ejpam-3312	258	29	y	y	PROPN
ejpam-3312	258	30	,	,	PUNCT
ejpam-3312	258	31	θ	θ	PROPN
ejpam-3312	258	32	,	,	PUNCT
ejpam-3312	258	33	f,	f,	X
ejpam-3312	258	34	�	�	NOUN
ejpam-3312	258	35	2	2	NUM
ejpam-3312	258	36	)	)	PUNCT
ejpam-3312	258	37	is	be	AUX
ejpam-3312	258	38	soft	soft	ADJ
ejpam-3312	259	1	i	i	PRON
ejpam-3312	259	2	(	(	PUNCT
ejpam-3312	259	3	resp	resp	NOUN
ejpam-3312	259	4	.	.	PUNCT
ejpam-3312	260	1	soft	soft	ADJ
ejpam-3312	260	2	d	d	NOUN
ejpam-3312	260	3	,	,	PUNCT
ejpam-3312	260	4	soft	soft	ADJ
ejpam-3312	260	5	b	b	NOUN
ejpam-3312	260	6	)	)	PUNCT
ejpam-3312	260	7	β	β	NOUN
ejpam-3312	260	8	-	-	ADJ
ejpam-3312	260	9	continuous	continuous	ADJ
ejpam-3312	260	10	if	if	SCONJ
ejpam-3312	260	11	and	and	CCONJ
ejpam-3312	260	12	only	only	ADV
ejpam-3312	260	13	if	if	SCONJ
ejpam-3312	260	14	a	a	DET
ejpam-3312	260	15	mapping	mapping	NOUN
ejpam-3312	260	16	g	g	NOUN
ejpam-3312	260	17	:	:	PUNCT
ejpam-3312	260	18	(	(	PUNCT
ejpam-3312	260	19	x	x	X
ejpam-3312	260	20	,	,	PUNCT
ejpam-3312	260	21	τ?e	τ?e	PROPN
ejpam-3312	260	22	,	,	PUNCT
ejpam-3312	260	23	�	�	PROPN
ejpam-3312	260	24	1)→	1)→	NUM
ejpam-3312	260	25	(	(	PUNCT
ejpam-3312	260	26	y	y	PROPN
ejpam-3312	260	27	,	,	PUNCT
ejpam-3312	260	28	θφ(e),	θφ(e),	ADJ
ejpam-3312	260	29	�	�	NOUN
ejpam-3312	260	30	2	2	NUM
ejpam-3312	260	31	)	)	PUNCT
ejpam-3312	260	32	is	be	AUX
ejpam-3312	260	33	i	i	PRON
ejpam-3312	260	34	(	(	PUNCT
ejpam-3312	260	35	resp	resp	NOUN
ejpam-3312	260	36	.	.	PUNCT
ejpam-3312	261	1	d	d	X
ejpam-3312	261	2	,	,	PUNCT
ejpam-3312	261	3	b	b	NOUN
ejpam-3312	261	4	)	)	PUNCT
ejpam-3312	261	5	β	β	NOUN
ejpam-3312	261	6	-	-	ADJ
ejpam-3312	261	7	continuous	continuous	ADJ
ejpam-3312	261	8	.	.	PUNCT
ejpam-3312	262	1	proof	proof	NOUN
ejpam-3312	262	2	.	.	PUNCT
ejpam-3312	263	1	necessity	necessity	NOUN
ejpam-3312	263	2	:	:	PUNCT
ejpam-3312	263	3	let	let	VERB
ejpam-3312	263	4	u	u	PRON
ejpam-3312	263	5	be	be	AUX
ejpam-3312	263	6	an	an	DET
ejpam-3312	263	7	open	open	ADJ
ejpam-3312	263	8	subset	subset	NOUN
ejpam-3312	263	9	of	of	ADP
ejpam-3312	263	10	(	(	PUNCT
ejpam-3312	263	11	y	y	PROPN
ejpam-3312	263	12	,	,	PUNCT
ejpam-3312	263	13	θφ(e),	θφ(e),	ADJ
ejpam-3312	263	14	�	�	NOUN
ejpam-3312	263	15	2	2	NUM
ejpam-3312	263	16	)	)	PUNCT
ejpam-3312	263	17	.	.	PUNCT
ejpam-3312	264	1	then	then	ADV
ejpam-3312	264	2	there	there	PRON
ejpam-3312	264	3	exists	exist	VERB
ejpam-3312	264	4	a	a	DET
ejpam-3312	264	5	soft	soft	ADJ
ejpam-3312	264	6	open	open	ADJ
ejpam-3312	264	7	subset	subset	NOUN
ejpam-3312	264	8	gf	gf	PROPN
ejpam-3312	264	9	of	of	ADP
ejpam-3312	264	10	(	(	PUNCT
ejpam-3312	264	11	y	y	PROPN
ejpam-3312	264	12	,	,	PUNCT
ejpam-3312	264	13	θ	θ	PROPN
ejpam-3312	264	14	,	,	PUNCT
ejpam-3312	264	15	f,	f,	X
ejpam-3312	264	16	�	�	NOUN
ejpam-3312	264	17	2	2	NUM
ejpam-3312	264	18	)	)	PUNCT
ejpam-3312	264	19	such	such	ADJ
ejpam-3312	264	20	that	that	SCONJ
ejpam-3312	264	21	g(φ(e	g(φ(e	NOUN
ejpam-3312	264	22	)	)	PUNCT
ejpam-3312	264	23	)	)	PUNCT
ejpam-3312	265	1	=	=	SYM
ejpam-3312	265	2	u	u	PROPN
ejpam-3312	265	3	.	.	PUNCT
ejpam-3312	266	1	since	since	SCONJ
ejpam-3312	266	2	gφ	gφ	PROPN
ejpam-3312	266	3	is	be	AUX
ejpam-3312	266	4	a	a	DET
ejpam-3312	266	5	soft	soft	ADJ
ejpam-3312	266	6	i	i	NOUN
ejpam-3312	266	7	(	(	PUNCT
ejpam-3312	266	8	resp	resp	NOUN
ejpam-3312	266	9	.	.	PUNCT
ejpam-3312	267	1	soft	soft	ADJ
ejpam-3312	267	2	d	d	NOUN
ejpam-3312	267	3	,	,	PUNCT
ejpam-3312	267	4	soft	soft	ADJ
ejpam-3312	267	5	b	b	NOUN
ejpam-3312	267	6	)	)	PUNCT
ejpam-3312	267	7	β	β	ADJ
ejpam-3312	267	8	-	-	ADJ
ejpam-3312	267	9	continuous	continuous	ADJ
ejpam-3312	267	10	mapping	mapping	NOUN
ejpam-3312	267	11	,	,	PUNCT
ejpam-3312	267	12	then	then	ADV
ejpam-3312	267	13	g−1φ	g−1φ	VERB
ejpam-3312	267	14	(	(	PUNCT
ejpam-3312	267	15	gf	gf	NOUN
ejpam-3312	267	16	)	)	PUNCT
ejpam-3312	267	17	is	be	AUX
ejpam-3312	267	18	a	a	DET
ejpam-3312	267	19	soft	soft	ADJ
ejpam-3312	267	20	i	i	NOUN
ejpam-3312	267	21	(	(	PUNCT
ejpam-3312	267	22	resp	resp	NOUN
ejpam-3312	267	23	.	.	PUNCT
ejpam-3312	268	1	soft	soft	ADJ
ejpam-3312	268	2	d	d	NOUN
ejpam-3312	268	3	,	,	PUNCT
ejpam-3312	268	4	soft	soft	ADJ
ejpam-3312	268	5	b	b	NOUN
ejpam-3312	268	6	)	)	PUNCT
ejpam-3312	268	7	β	β	X
ejpam-3312	268	8	-	-	ADJ
ejpam-3312	268	9	open	open	ADJ
ejpam-3312	268	10	set	set	NOUN
ejpam-3312	268	11	.	.	PUNCT
ejpam-3312	269	1	from	from	ADP
ejpam-3312	269	2	definition	definition	NOUN
ejpam-3312	269	3	(	(	PUNCT
ejpam-3312	269	4	6	6	NUM
ejpam-3312	269	5	)	)	PUNCT
ejpam-3312	269	6	,	,	PUNCT
ejpam-3312	269	7	it	it	PRON
ejpam-3312	269	8	follows	follow	VERB
ejpam-3312	269	9	that	that	SCONJ
ejpam-3312	269	10	a	a	DET
ejpam-3312	269	11	soft	soft	ADJ
ejpam-3312	269	12	subset	subset	NOUN
ejpam-3312	269	13	g−1φ	g−1φ	NOUN
ejpam-3312	269	14	(	(	PUNCT
ejpam-3312	269	15	gf	gf	NOUN
ejpam-3312	269	16	)	)	PUNCT
ejpam-3312	269	17	=	=	SYM
ejpam-3312	269	18	(	(	PUNCT
ejpam-3312	269	19	g−1φ	g−1φ	X
ejpam-3312	269	20	(	(	PUNCT
ejpam-3312	269	21	g))e	g))e	NOUN
ejpam-3312	269	22	of	of	ADP
ejpam-3312	269	23	(	(	PUNCT
ejpam-3312	269	24	x	x	PROPN
ejpam-3312	269	25	,	,	PUNCT
ejpam-3312	269	26	τ	τ	PROPN
ejpam-3312	269	27	,	,	PUNCT
ejpam-3312	269	28	e,	e,	X
ejpam-3312	269	29	�	�	X
ejpam-3312	269	30	1	1	NUM
ejpam-3312	269	31	)	)	PUNCT
ejpam-3312	269	32	is	be	AUX
ejpam-3312	269	33	given	give	VERB
ejpam-3312	269	34	by	by	ADP
ejpam-3312	269	35	g−1φ	g−1φ	NOUN
ejpam-3312	269	36	(	(	PUNCT
ejpam-3312	269	37	g)(e	g)(e	NOUN
ejpam-3312	269	38	)	)	PUNCT
ejpam-3312	269	39	=	=	SYM
ejpam-3312	269	40	g−1(g(φ(e	g−1(g(φ(e	NOUN
ejpam-3312	269	41	)	)	PUNCT
ejpam-3312	269	42	)	)	PUNCT
ejpam-3312	269	43	)	)	PUNCT
ejpam-3312	269	44	,	,	PUNCT
ejpam-3312	269	45	for	for	ADP
ejpam-3312	269	46	each	each	DET
ejpam-3312	269	47	e	e	PROPN
ejpam-3312	269	48	∈	∈	PROPN
ejpam-3312	269	49	e.	e.	PROPN
ejpam-3312	269	50	by	by	ADP
ejpam-3312	269	51	hypothesis	hypothesis	NOUN
ejpam-3312	269	52	,	,	PUNCT
ejpam-3312	269	53	τ	τ	PROPN
ejpam-3312	269	54	?	?	PROPN
ejpam-3312	269	55	is	be	AUX
ejpam-3312	269	56	an	an	DET
ejpam-3312	269	57	extended	extended	ADJ
ejpam-3312	269	58	soft	soft	ADJ
ejpam-3312	269	59	topology	topology	NOUN
ejpam-3312	269	60	on	on	ADP
ejpam-3312	269	61	x	x	SYM
ejpam-3312	269	62	,	,	PUNCT
ejpam-3312	269	63	we	we	PRON
ejpam-3312	269	64	obtain	obtain	VERB
ejpam-3312	269	65	a	a	DET
ejpam-3312	269	66	subset	subset	NOUN
ejpam-3312	269	67	g−1(g(φ(e	g−1(g(φ(e	NOUN
ejpam-3312	269	68	)	)	PUNCT
ejpam-3312	269	69	)	)	PUNCT
ejpam-3312	269	70	)	)	PUNCT
ejpam-3312	270	1	=	=	SYM
ejpam-3312	270	2	g−1(u	g−1(u	PROPN
ejpam-3312	270	3	)	)	PUNCT
ejpam-3312	270	4	of	of	ADP
ejpam-3312	270	5	(	(	PUNCT
ejpam-3312	270	6	x	x	NOUN
ejpam-3312	270	7	,	,	PUNCT
ejpam-3312	270	8	τe,	τe,	PROPN
ejpam-3312	270	9	�	�	PROPN
ejpam-3312	270	10	1	1	NUM
ejpam-3312	270	11	)	)	PUNCT
ejpam-3312	270	12	is	be	AUX
ejpam-3312	270	13	i	i	PRON
ejpam-3312	270	14	(	(	PUNCT
ejpam-3312	270	15	resp	resp	NOUN
ejpam-3312	270	16	.	.	PUNCT
ejpam-3312	271	1	d	d	X
ejpam-3312	271	2	,	,	PUNCT
ejpam-3312	271	3	b	b	NOUN
ejpam-3312	271	4	)	)	PUNCT
ejpam-3312	271	5	β	β	NOUN
ejpam-3312	271	6	-	-	VERB
ejpam-3312	271	7	open	open	ADJ
ejpam-3312	271	8	.	.	PUNCT
ejpam-3312	272	1	hence	hence	ADV
ejpam-3312	272	2	a	a	DET
ejpam-3312	272	3	mapping	mapping	NOUN
ejpam-3312	272	4	g	g	NOUN
ejpam-3312	272	5	is	be	AUX
ejpam-3312	272	6	i	i	PRON
ejpam-3312	272	7	(	(	PUNCT
ejpam-3312	272	8	resp	resp	NOUN
ejpam-3312	272	9	.	.	PUNCT
ejpam-3312	273	1	d	d	X
ejpam-3312	273	2	,	,	PUNCT
ejpam-3312	273	3	b	b	NOUN
ejpam-3312	273	4	)	)	PUNCT
ejpam-3312	273	5	β	β	NOUN
ejpam-3312	273	6	-	-	ADJ
ejpam-3312	273	7	continuous	continuous	ADJ
ejpam-3312	273	8	.	.	PUNCT
ejpam-3312	274	1	sufficiency	sufficiency	NOUN
ejpam-3312	274	2	:	:	PUNCT
ejpam-3312	274	3	let	let	VERB
ejpam-3312	274	4	gf	gf	PART
ejpam-3312	274	5	be	be	AUX
ejpam-3312	274	6	a	a	DET
ejpam-3312	274	7	soft	soft	ADJ
ejpam-3312	274	8	open	open	ADJ
ejpam-3312	274	9	subset	subset	NOUN
ejpam-3312	274	10	of	of	ADP
ejpam-3312	274	11	(	(	PUNCT
ejpam-3312	274	12	y	y	PROPN
ejpam-3312	274	13	,	,	PUNCT
ejpam-3312	274	14	θ	θ	PROPN
ejpam-3312	274	15	,	,	PUNCT
ejpam-3312	274	16	f,	f,	X
ejpam-3312	274	17	�	�	PROPN
ejpam-3312	274	18	2	2	NUM
ejpam-3312	274	19	)	)	PUNCT
ejpam-3312	274	20	.	.	PUNCT
ejpam-3312	275	1	then	then	ADV
ejpam-3312	275	2	from	from	ADP
ejpam-3312	275	3	definition	definition	NOUN
ejpam-3312	275	4	(	(	PUNCT
ejpam-3312	275	5	6	6	NUM
ejpam-3312	275	6	)	)	PUNCT
ejpam-3312	275	7	,	,	PUNCT
ejpam-3312	275	8	it	it	PRON
ejpam-3312	275	9	follows	follow	VERB
ejpam-3312	275	10	that	that	SCONJ
ejpam-3312	275	11	a	a	DET
ejpam-3312	275	12	soft	soft	ADJ
ejpam-3312	275	13	subset	subset	NOUN
ejpam-3312	275	14	g−1φ	g−1φ	NOUN
ejpam-3312	275	15	(	(	PUNCT
ejpam-3312	275	16	gf	gf	NOUN
ejpam-3312	275	17	)	)	PUNCT
ejpam-3312	275	18	=	=	SYM
ejpam-3312	275	19	(	(	PUNCT
ejpam-3312	275	20	g−1φ	g−1φ	X
ejpam-3312	275	21	(	(	PUNCT
ejpam-3312	275	22	g))e	g))e	NOUN
ejpam-3312	275	23	of	of	ADP
ejpam-3312	275	24	(	(	PUNCT
ejpam-3312	275	25	x	x	PROPN
ejpam-3312	275	26	,	,	PUNCT
ejpam-3312	275	27	τ	τ	PROPN
ejpam-3312	275	28	?	?	PROPN
ejpam-3312	275	29	,	,	PUNCT
ejpam-3312	275	30	e,	e,	X
ejpam-3312	275	31	�	�	X
ejpam-3312	275	32	1	1	NUM
ejpam-3312	275	33	)	)	PUNCT
ejpam-3312	275	34	is	be	AUX
ejpam-3312	275	35	given	give	VERB
ejpam-3312	275	36	by	by	ADP
ejpam-3312	275	37	g−1φ	g−1φ	NOUN
ejpam-3312	275	38	(	(	PUNCT
ejpam-3312	275	39	g)(e	g)(e	NOUN
ejpam-3312	275	40	)	)	PUNCT
ejpam-3312	275	41	=	=	SYM
ejpam-3312	275	42	g−1(g(φ(e	g−1(g(φ(e	NOUN
ejpam-3312	275	43	)	)	PUNCT
ejpam-3312	275	44	)	)	PUNCT
ejpam-3312	275	45	)	)	PUNCT
ejpam-3312	275	46	,	,	PUNCT
ejpam-3312	275	47	for	for	ADP
ejpam-3312	275	48	each	each	DET
ejpam-3312	275	49	e	e	PROPN
ejpam-3312	275	50	∈	∈	PROPN
ejpam-3312	275	51	e.	e.	PROPN
ejpam-3312	275	52	since	since	SCONJ
ejpam-3312	275	53	a	a	DET
ejpam-3312	275	54	mapping	mapping	NOUN
ejpam-3312	275	55	g	g	NOUN
ejpam-3312	275	56	is	be	AUX
ejpam-3312	275	57	i	i	PRON
ejpam-3312	275	58	(	(	PUNCT
ejpam-3312	275	59	resp	resp	NOUN
ejpam-3312	275	60	.	.	PUNCT
ejpam-3312	276	1	d	d	X
ejpam-3312	276	2	,	,	PUNCT
ejpam-3312	276	3	b	b	NOUN
ejpam-3312	276	4	)	)	PUNCT
ejpam-3312	276	5	β	β	NOUN
ejpam-3312	276	6	-	-	NOUN
ejpam-3312	276	7	continuous	continuous	ADJ
ejpam-3312	276	8	,	,	PUNCT
ejpam-3312	276	9	then	then	ADV
ejpam-3312	276	10	a	a	DET
ejpam-3312	276	11	subset	subset	NOUN
ejpam-3312	276	12	g−1(g(φ(e	g−1(g(φ(e	NOUN
ejpam-3312	276	13	)	)	PUNCT
ejpam-3312	276	14	)	)	PUNCT
ejpam-3312	276	15	)	)	PUNCT
ejpam-3312	277	1	of	of	ADP
ejpam-3312	277	2	(	(	PUNCT
ejpam-3312	277	3	x	x	X
ejpam-3312	277	4	,	,	PUNCT
ejpam-3312	277	5	τ?e	τ?e	PROPN
ejpam-3312	277	6	,	,	PUNCT
ejpam-3312	277	7	�	�	PROPN
ejpam-3312	277	8	1	1	NUM
ejpam-3312	277	9	)	)	PUNCT
ejpam-3312	277	10	is	be	AUX
ejpam-3312	277	11	i	i	PRON
ejpam-3312	277	12	(	(	PUNCT
ejpam-3312	277	13	resp	resp	NOUN
ejpam-3312	277	14	.	.	PUNCT
ejpam-3312	278	1	d	d	X
ejpam-3312	278	2	,	,	PUNCT
ejpam-3312	278	3	b	b	NOUN
ejpam-3312	278	4	)	)	PUNCT
ejpam-3312	278	5	β	β	NOUN
ejpam-3312	278	6	-	-	VERB
ejpam-3312	278	7	open	open	ADJ
ejpam-3312	278	8	.	.	PUNCT
ejpam-3312	279	1	by	by	ADP
ejpam-3312	279	2	hypothesis	hypothesis	NOUN
ejpam-3312	279	3	,	,	PUNCT
ejpam-3312	279	4	τ	τ	PROPN
ejpam-3312	279	5	?	?	PROPN
ejpam-3312	279	6	is	be	AUX
ejpam-3312	279	7	an	an	DET
ejpam-3312	279	8	extended	extended	ADJ
ejpam-3312	279	9	soft	soft	ADJ
ejpam-3312	279	10	topology	topology	NOUN
ejpam-3312	279	11	on	on	ADP
ejpam-3312	279	12	x	x	NOUN
ejpam-3312	279	13	,	,	PUNCT
ejpam-3312	279	14	we	we	PRON
ejpam-3312	279	15	obtain	obtain	VERB
ejpam-3312	279	16	g−1φ	g−1φ	NOUN
ejpam-3312	279	17	(	(	PUNCT
ejpam-3312	279	18	gf	gf	NOUN
ejpam-3312	279	19	)	)	PUNCT
ejpam-3312	279	20	is	be	AUX
ejpam-3312	279	21	a	a	DET
ejpam-3312	279	22	soft	soft	ADJ
ejpam-3312	279	23	i	i	NOUN
ejpam-3312	279	24	(	(	PUNCT
ejpam-3312	279	25	resp	resp	NOUN
ejpam-3312	279	26	.	.	PUNCT
ejpam-3312	280	1	soft	soft	ADJ
ejpam-3312	280	2	d	d	NOUN
ejpam-3312	280	3	,	,	PUNCT
ejpam-3312	280	4	soft	soft	ADJ
ejpam-3312	280	5	b	b	NOUN
ejpam-3312	280	6	)	)	PUNCT
ejpam-3312	280	7	βopen	βopen	ADJ
ejpam-3312	280	8	subset	subset	NOUN
ejpam-3312	280	9	of	of	ADP
ejpam-3312	280	10	(	(	PUNCT
ejpam-3312	280	11	x	x	PROPN
ejpam-3312	280	12	,	,	PUNCT
ejpam-3312	280	13	τ	τ	PROPN
ejpam-3312	280	14	?	?	PROPN
ejpam-3312	280	15	,	,	PUNCT
ejpam-3312	280	16	e,	e,	X
ejpam-3312	280	17	�	�	X
ejpam-3312	280	18	1	1	NUM
ejpam-3312	280	19	)	)	PUNCT
ejpam-3312	280	20	.	.	PUNCT
ejpam-3312	281	1	hence	hence	ADV
ejpam-3312	281	2	a	a	DET
ejpam-3312	281	3	soft	soft	ADJ
ejpam-3312	281	4	mapping	mapping	NOUN
ejpam-3312	281	5	gφ	gφ	NOUN
ejpam-3312	281	6	is	be	AUX
ejpam-3312	281	7	soft	soft	ADJ
ejpam-3312	281	8	i	i	PRON
ejpam-3312	281	9	(	(	PUNCT
ejpam-3312	281	10	resp	resp	NOUN
ejpam-3312	281	11	.	.	PUNCT
ejpam-3312	282	1	soft	soft	ADJ
ejpam-3312	282	2	d	d	NOUN
ejpam-3312	282	3	,	,	PUNCT
ejpam-3312	282	4	soft	soft	ADJ
ejpam-3312	282	5	b	b	NOUN
ejpam-3312	282	6	)	)	PUNCT
ejpam-3312	282	7	β	β	NOUN
ejpam-3312	282	8	-	-	ADJ
ejpam-3312	282	9	continuous	continuous	ADJ
ejpam-3312	282	10	.	.	PUNCT
ejpam-3312	282	11	proposition	proposition	NOUN
ejpam-3312	282	12	3	3	X
ejpam-3312	282	13	.	.	PUNCT
ejpam-3312	283	1	let	let	VERB
ejpam-3312	283	2	a	a	DET
ejpam-3312	283	3	surjective	surjective	ADJ
ejpam-3312	283	4	soft	soft	ADJ
ejpam-3312	283	5	mapping	mapping	NOUN
ejpam-3312	283	6	fφ	fφ	NOUN
ejpam-3312	283	7	:	:	PUNCT
ejpam-3312	283	8	(	(	PUNCT
ejpam-3312	283	9	x	x	X
ejpam-3312	283	10	,	,	PUNCT
ejpam-3312	283	11	τ	τ	X
ejpam-3312	283	12	,	,	PUNCT
ejpam-3312	283	13	e	e	X
ejpam-3312	283	14	�	�	PROPN
ejpam-3312	283	15	1	1	NUM
ejpam-3312	283	16	)	)	PUNCT
ejpam-3312	283	17	→	→	SYM
ejpam-3312	283	18	(	(	PUNCT
ejpam-3312	283	19	y	y	PROPN
ejpam-3312	283	20	,	,	PUNCT
ejpam-3312	283	21	θ	θ	PROPN
ejpam-3312	283	22	,	,	PUNCT
ejpam-3312	283	23	f,	f,	X
ejpam-3312	283	24	�	�	PROPN
ejpam-3312	283	25	2	2	NUM
ejpam-3312	283	26	)	)	PUNCT
ejpam-3312	283	27	be	be	AUX
ejpam-3312	283	28	soft	soft	ADJ
ejpam-3312	283	29	bβ	bβ	NOUN
ejpam-3312	283	30	-	-	PUNCT
ejpam-3312	283	31	continuous	continuous	ADJ
ejpam-3312	283	32	.	.	PUNCT
ejpam-3312	284	1	then	then	ADV
ejpam-3312	284	2	:	:	PUNCT
ejpam-3312	284	3	(	(	PUNCT
ejpam-3312	284	4	i	i	NOUN
ejpam-3312	284	5	)	)	PUNCT
ejpam-3312	284	6	if	if	SCONJ
ejpam-3312	284	7	�	�	NOUN
ejpam-3312	284	8	1	1	NUM
ejpam-3312	284	9	is	be	AUX
ejpam-3312	284	10	linearly	linearly	ADV
ejpam-3312	284	11	order	order	NOUN
ejpam-3312	284	12	,	,	PUNCT
ejpam-3312	284	13	then	then	ADV
ejpam-3312	284	14	θ	θ	PROPN
ejpam-3312	284	15	is	be	AUX
ejpam-3312	284	16	the	the	DET
ejpam-3312	284	17	soft	soft	ADJ
ejpam-3312	284	18	indiscrete	indiscrete	ADJ
ejpam-3312	284	19	topology	topology	NOUN
ejpam-3312	284	20	.	.	PUNCT
ejpam-3312	285	1	(	(	PUNCT
ejpam-3312	285	2	ii	ii	NOUN
ejpam-3312	285	3	)	)	PUNCT
ejpam-3312	285	4	if	if	SCONJ
ejpam-3312	285	5	θ	θ	PROPN
ejpam-3312	285	6	is	be	AUX
ejpam-3312	285	7	the	the	DET
ejpam-3312	285	8	soft	soft	ADJ
ejpam-3312	285	9	discrete	discrete	ADJ
ejpam-3312	285	10	topology	topology	NOUN
ejpam-3312	285	11	,	,	PUNCT
ejpam-3312	285	12	then	then	ADV
ejpam-3312	285	13	�	�	PROPN
ejpam-3312	285	14	1	1	NUM
ejpam-3312	285	15	is	be	AUX
ejpam-3312	285	16	an	an	DET
ejpam-3312	285	17	equality	equality	NOUN
ejpam-3312	285	18	relation	relation	NOUN
ejpam-3312	285	19	.	.	PUNCT
ejpam-3312	286	1	4	4	X
ejpam-3312	286	2	.	.	X
ejpam-3312	286	3	soft	soft	ADJ
ejpam-3312	286	4	i(d	i(d	NOUN
ejpam-3312	286	5	,	,	PUNCT
ejpam-3312	286	6	b)β	b)β	NOUN
ejpam-3312	286	7	-	-	NOUN
ejpam-3312	286	8	openness	openness	NOUN
ejpam-3312	286	9	and	and	CCONJ
ejpam-3312	286	10	soft	soft	ADJ
ejpam-3312	286	11	i(d	i(d	NOUN
ejpam-3312	286	12	,	,	PUNCT
ejpam-3312	286	13	b)β	b)β	NOUN
ejpam-3312	286	14	-	-	PUNCT
ejpam-3312	286	15	closedness	closedness	NOUN
ejpam-3312	286	16	in	in	ADP
ejpam-3312	286	17	this	this	DET
ejpam-3312	286	18	section	section	NOUN
ejpam-3312	286	19	,	,	PUNCT
ejpam-3312	286	20	the	the	DET
ejpam-3312	286	21	concepts	concept	NOUN
ejpam-3312	286	22	of	of	ADP
ejpam-3312	286	23	soft	soft	ADJ
ejpam-3312	286	24	i(d	i(d	NOUN
ejpam-3312	286	25	,	,	PUNCT
ejpam-3312	286	26	b)-open	b)-open	PUNCT
ejpam-3312	286	27	and	and	CCONJ
ejpam-3312	286	28	soft	soft	ADJ
ejpam-3312	286	29	i(d	i(d	NOUN
ejpam-3312	286	30	,	,	PUNCT
ejpam-3312	286	31	b)-closed	b)-close	VERB
ejpam-3312	286	32	mappings	mapping	NOUN
ejpam-3312	286	33	are	be	AUX
ejpam-3312	286	34	introduced	introduce	VERB
ejpam-3312	286	35	and	and	CCONJ
ejpam-3312	286	36	two	two	NUM
ejpam-3312	286	37	examples	example	NOUN
ejpam-3312	286	38	are	be	AUX
ejpam-3312	286	39	provided	provide	VERB
ejpam-3312	286	40	to	to	PART
ejpam-3312	286	41	elucidate	elucidate	VERB
ejpam-3312	286	42	the	the	DET
ejpam-3312	286	43	relationships	relationship	NOUN
ejpam-3312	286	44	among	among	ADP
ejpam-3312	286	45	them	they	PRON
ejpam-3312	286	46	.	.	PUNCT
ejpam-3312	287	1	then	then	ADV
ejpam-3312	287	2	the	the	DET
ejpam-3312	287	3	equivalent	equivalent	ADJ
ejpam-3312	287	4	conditions	condition	NOUN
ejpam-3312	287	5	for	for	ADP
ejpam-3312	287	6	each	each	DET
ejpam-3312	287	7	one	one	NUM
ejpam-3312	287	8	of	of	ADP
ejpam-3312	287	9	these	these	DET
ejpam-3312	287	10	soft	soft	ADJ
ejpam-3312	287	11	mappings	mapping	NOUN
ejpam-3312	287	12	are	be	AUX
ejpam-3312	287	13	discussed	discuss	VERB
ejpam-3312	287	14	and	and	CCONJ
ejpam-3312	287	15	some	some	DET
ejpam-3312	287	16	results	result	NOUN
ejpam-3312	287	17	related	relate	VERB
ejpam-3312	287	18	to	to	ADP
ejpam-3312	287	19	them	they	PRON
ejpam-3312	287	20	are	be	AUX
ejpam-3312	287	21	initiated	initiate	VERB
ejpam-3312	287	22	.	.	PUNCT
ejpam-3312	288	1	definition	definition	NOUN
ejpam-3312	288	2	21	21	NUM
ejpam-3312	288	3	.	.	PUNCT
ejpam-3312	289	1	a	a	DET
ejpam-3312	289	2	soft	soft	ADJ
ejpam-3312	289	3	mapping	mapping	NOUN
ejpam-3312	289	4	fφ	fφ	NOUN
ejpam-3312	289	5	:	:	PUNCT
ejpam-3312	289	6	(	(	PUNCT
ejpam-3312	289	7	x	x	X
ejpam-3312	289	8	,	,	PUNCT
ejpam-3312	289	9	τ	τ	PROPN
ejpam-3312	289	10	,	,	PUNCT
ejpam-3312	289	11	e,	e,	X
ejpam-3312	289	12	�	�	X
ejpam-3312	289	13	1)→	1)→	NUM
ejpam-3312	289	14	(	(	PUNCT
ejpam-3312	289	15	y	y	PROPN
ejpam-3312	289	16	,	,	PUNCT
ejpam-3312	289	17	τ	τ	PROPN
ejpam-3312	289	18	,	,	PUNCT
ejpam-3312	289	19	f,	f,	X
ejpam-3312	289	20	�	�	PROPN
ejpam-3312	289	21	2	2	NUM
ejpam-3312	289	22	)	)	PUNCT
ejpam-3312	289	23	is	be	AUX
ejpam-3312	289	24	called	call	VERB
ejpam-3312	289	25	:	:	PUNCT
ejpam-3312	289	26	(	(	PUNCT
ejpam-3312	289	27	i	i	NOUN
ejpam-3312	289	28	)	)	PUNCT
ejpam-3312	289	29	soft	soft	ADJ
ejpam-3312	289	30	i	i	PRON
ejpam-3312	289	31	(	(	PUNCT
ejpam-3312	289	32	resp	resp	NOUN
ejpam-3312	289	33	.	.	PUNCT
ejpam-3312	290	1	soft	soft	ADJ
ejpam-3312	290	2	d	d	NOUN
ejpam-3312	290	3	,	,	PUNCT
ejpam-3312	290	4	soft	soft	ADJ
ejpam-3312	290	5	b	b	NOUN
ejpam-3312	290	6	)	)	PUNCT
ejpam-3312	290	7	β	β	X
ejpam-3312	290	8	-	-	VERB
ejpam-3312	290	9	open	open	ADJ
ejpam-3312	290	10	if	if	SCONJ
ejpam-3312	290	11	the	the	DET
ejpam-3312	290	12	image	image	NOUN
ejpam-3312	290	13	of	of	ADP
ejpam-3312	290	14	every	every	DET
ejpam-3312	290	15	soft	soft	ADJ
ejpam-3312	290	16	open	open	ADJ
ejpam-3312	290	17	subset	subset	NOUN
ejpam-3312	290	18	of	of	ADP
ejpam-3312	290	19	x̃	x̃	PROPN
ejpam-3312	290	20	is	be	AUX
ejpam-3312	290	21	a	a	DET
ejpam-3312	290	22	soft	soft	ADJ
ejpam-3312	290	23	i	i	NOUN
ejpam-3312	290	24	(	(	PUNCT
ejpam-3312	290	25	resp	resp	NOUN
ejpam-3312	290	26	.	.	PUNCT
ejpam-3312	291	1	soft	soft	ADJ
ejpam-3312	291	2	d	d	NOUN
ejpam-3312	291	3	,	,	PUNCT
ejpam-3312	291	4	soft	soft	ADJ
ejpam-3312	291	5	b	b	NOUN
ejpam-3312	291	6	)	)	PUNCT
ejpam-3312	291	7	β	β	X
ejpam-3312	291	8	-	-	ADJ
ejpam-3312	291	9	open	open	ADJ
ejpam-3312	291	10	subset	subset	NOUN
ejpam-3312	291	11	of	of	ADP
ejpam-3312	291	12	ỹ	ỹ	PROPN
ejpam-3312	291	13	.	.	PUNCT
ejpam-3312	292	1	(	(	PUNCT
ejpam-3312	292	2	ii	ii	NOUN
ejpam-3312	292	3	)	)	PUNCT
ejpam-3312	292	4	soft	soft	ADJ
ejpam-3312	292	5	i	i	PRON
ejpam-3312	292	6	(	(	PUNCT
ejpam-3312	292	7	resp	resp	NOUN
ejpam-3312	292	8	.	.	PUNCT
ejpam-3312	293	1	soft	soft	ADJ
ejpam-3312	293	2	d	d	NOUN
ejpam-3312	293	3	,	,	PUNCT
ejpam-3312	293	4	soft	soft	ADJ
ejpam-3312	293	5	b	b	NOUN
ejpam-3312	293	6	)	)	PUNCT
ejpam-3312	293	7	β	β	X
ejpam-3312	293	8	-	-	PUNCT
ejpam-3312	293	9	closed	closed	ADJ
ejpam-3312	293	10	if	if	SCONJ
ejpam-3312	293	11	the	the	DET
ejpam-3312	293	12	image	image	NOUN
ejpam-3312	293	13	of	of	ADP
ejpam-3312	293	14	every	every	DET
ejpam-3312	293	15	soft	soft	ADJ
ejpam-3312	293	16	closed	closed	ADJ
ejpam-3312	293	17	subset	subset	NOUN
ejpam-3312	293	18	of	of	ADP
ejpam-3312	293	19	x̃	x̃	PROPN
ejpam-3312	293	20	is	be	AUX
ejpam-3312	293	21	a	a	DET
ejpam-3312	293	22	soft	soft	ADJ
ejpam-3312	293	23	i	i	NOUN
ejpam-3312	293	24	(	(	PUNCT
ejpam-3312	293	25	resp	resp	NOUN
ejpam-3312	293	26	.	.	PUNCT
ejpam-3312	294	1	soft	soft	ADJ
ejpam-3312	294	2	d	d	NOUN
ejpam-3312	294	3	,	,	PUNCT
ejpam-3312	294	4	soft	soft	ADJ
ejpam-3312	294	5	b	b	NOUN
ejpam-3312	294	6	)	)	PUNCT
ejpam-3312	294	7	β	β	X
ejpam-3312	294	8	-	-	ADJ
ejpam-3312	294	9	closed	closed	ADJ
ejpam-3312	294	10	subset	subset	NOUN
ejpam-3312	294	11	of	of	ADP
ejpam-3312	294	12	ỹ	ỹ	PROPN
ejpam-3312	294	13	.	.	PUNCT
ejpam-3312	295	1	remark	remark	VERB
ejpam-3312	295	2	3	3	NUM
ejpam-3312	295	3	.	.	PUNCT
ejpam-3312	296	1	from	from	ADP
ejpam-3312	296	2	definition	definition	NOUN
ejpam-3312	296	3	(	(	PUNCT
ejpam-3312	296	4	21	21	NUM
ejpam-3312	296	5	)	)	PUNCT
ejpam-3312	296	6	,	,	PUNCT
ejpam-3312	296	7	we	we	PRON
ejpam-3312	296	8	can	can	AUX
ejpam-3312	296	9	note	note	VERB
ejpam-3312	296	10	the	the	DET
ejpam-3312	296	11	following	following	NOUN
ejpam-3312	296	12	:	:	PUNCT
ejpam-3312	296	13	(	(	PUNCT
ejpam-3312	296	14	i	i	NOUN
ejpam-3312	296	15	)	)	PUNCT
ejpam-3312	296	16	every	every	PRON
ejpam-3312	296	17	soft	soft	ADJ
ejpam-3312	296	18	i	i	PRON
ejpam-3312	296	19	(	(	PUNCT
ejpam-3312	296	20	d	d	PROPN
ejpam-3312	296	21	,	,	PUNCT
ejpam-3312	296	22	b	b	NOUN
ejpam-3312	296	23	)	)	PUNCT
ejpam-3312	296	24	β	β	X
ejpam-3312	296	25	-	-	ADJ
ejpam-3312	296	26	open	open	ADJ
ejpam-3312	296	27	mapping	mapping	NOUN
ejpam-3312	296	28	is	be	AUX
ejpam-3312	296	29	soft	soft	ADJ
ejpam-3312	296	30	β	β	NOUN
ejpam-3312	296	31	-	-	ADJ
ejpam-3312	296	32	open	open	ADJ
ejpam-3312	296	33	.	.	PUNCT
ejpam-3312	297	1	(	(	PUNCT
ejpam-3312	297	2	ii	ii	NOUN
ejpam-3312	297	3	)	)	PUNCT
ejpam-3312	297	4	every	every	PRON
ejpam-3312	297	5	soft	soft	ADJ
ejpam-3312	297	6	i	i	PRON
ejpam-3312	297	7	(	(	PUNCT
ejpam-3312	297	8	d	d	PROPN
ejpam-3312	297	9	,	,	PUNCT
ejpam-3312	297	10	b	b	NOUN
ejpam-3312	297	11	)	)	PUNCT
ejpam-3312	297	12	β	β	X
ejpam-3312	297	13	-	-	PUNCT
ejpam-3312	297	14	closed	closed	ADJ
ejpam-3312	297	15	mapping	mapping	NOUN
ejpam-3312	297	16	is	be	AUX
ejpam-3312	297	17	soft	soft	ADJ
ejpam-3312	297	18	β	β	NOUN
ejpam-3312	297	19	-	-	VERB
ejpam-3312	297	20	closed	closed	ADJ
ejpam-3312	297	21	.	.	PUNCT
ejpam-3312	298	1	t.	t.	PROPN
ejpam-3312	298	2	m.	m.	PROPN
ejpam-3312	298	3	al	al	PROPN
ejpam-3312	298	4	-	-	PUNCT
ejpam-3312	298	5	shami	shami	PROPN
ejpam-3312	298	6	,	,	PUNCT
ejpam-3312	298	7	m.	m.	PROPN
ejpam-3312	298	8	e.	e.	PROPN
ejpam-3312	298	9	el	el	PROPN
ejpam-3312	298	10	-	-	PROPN
ejpam-3312	298	11	shafei	shafei	PROPN
ejpam-3312	298	12	,	,	PUNCT
ejpam-3312	298	13	b.	b.	PROPN
ejpam-3312	298	14	a.	a.	PROPN
ejpam-3312	298	15	asaad	asaad	PROPN
ejpam-3312	298	16	/	/	SYM
ejpam-3312	298	17	eur	eur	PROPN
ejpam-3312	298	18	.	.	PUNCT
ejpam-3312	299	1	j.	j.	PROPN
ejpam-3312	299	2	pure	pure	PROPN
ejpam-3312	299	3	appl	appl	PROPN
ejpam-3312	299	4	.	.	PROPN
ejpam-3312	299	5	math	math	PROPN
ejpam-3312	299	6	,	,	PUNCT
ejpam-3312	299	7	12	12	NUM
ejpam-3312	299	8	(	(	PUNCT
ejpam-3312	299	9	1	1	NUM
ejpam-3312	299	10	)	)	PUNCT
ejpam-3312	299	11	(	(	PUNCT
ejpam-3312	299	12	2019	2019	NUM
ejpam-3312	299	13	)	)	PUNCT
ejpam-3312	299	14	,	,	PUNCT
ejpam-3312	299	15	176	176	NUM
ejpam-3312	299	16	-	-	SYM
ejpam-3312	299	17	193	193	NUM
ejpam-3312	299	18	185	185	NUM
ejpam-3312	299	19	(	(	PUNCT
ejpam-3312	299	20	iii	iii	NOUN
ejpam-3312	299	21	)	)	PUNCT
ejpam-3312	299	22	every	every	DET
ejpam-3312	299	23	soft	soft	ADJ
ejpam-3312	299	24	bβ	bβ	NOUN
ejpam-3312	299	25	-	-	PUNCT
ejpam-3312	299	26	open	open	ADJ
ejpam-3312	299	27	(	(	PUNCT
ejpam-3312	299	28	resp	resp	NOUN
ejpam-3312	299	29	.	.	PUNCT
ejpam-3312	299	30	soft	soft	ADJ
ejpam-3312	299	31	bβ	bβ	NOUN
ejpam-3312	299	32	-	-	PUNCT
ejpam-3312	299	33	closed	closed	ADJ
ejpam-3312	299	34	)	)	PUNCT
ejpam-3312	299	35	mapping	mapping	NOUN
ejpam-3312	299	36	is	be	AUX
ejpam-3312	299	37	soft	soft	ADJ
ejpam-3312	299	38	iβ	iβ	ADJ
ejpam-3312	299	39	-	-	ADJ
ejpam-3312	299	40	open	open	ADJ
ejpam-3312	299	41	or	or	CCONJ
ejpam-3312	299	42	soft	soft	ADJ
ejpam-3312	299	43	dβ	dβ	ADJ
ejpam-3312	299	44	-	-	PUNCT
ejpam-3312	299	45	open	open	ADJ
ejpam-3312	299	46	(	(	PUNCT
ejpam-3312	299	47	resp	resp	NOUN
ejpam-3312	299	48	.	.	PUNCT
ejpam-3312	300	1	soft	soft	ADJ
ejpam-3312	300	2	iβ	iβ	ADJ
ejpam-3312	300	3	-	-	PUNCT
ejpam-3312	300	4	closed	closed	ADJ
ejpam-3312	300	5	or	or	CCONJ
ejpam-3312	300	6	soft	soft	ADJ
ejpam-3312	300	7	dβ	dβ	ADJ
ejpam-3312	300	8	-	-	PUNCT
ejpam-3312	300	9	closed	closed	ADJ
ejpam-3312	300	10	)	)	PUNCT
ejpam-3312	300	11	.	.	PUNCT
ejpam-3312	301	1	we	we	PRON
ejpam-3312	301	2	construct	construct	VERB
ejpam-3312	301	3	the	the	DET
ejpam-3312	301	4	following	follow	VERB
ejpam-3312	301	5	two	two	NUM
ejpam-3312	301	6	examples	example	NOUN
ejpam-3312	301	7	to	to	PART
ejpam-3312	301	8	show	show	VERB
ejpam-3312	301	9	that	that	SCONJ
ejpam-3312	301	10	the	the	DET
ejpam-3312	301	11	converse	converse	NOUN
ejpam-3312	301	12	of	of	ADP
ejpam-3312	301	13	the	the	DET
ejpam-3312	301	14	three	three	NUM
ejpam-3312	301	15	statements	statement	NOUN
ejpam-3312	301	16	of	of	ADP
ejpam-3312	301	17	remark	remark	NOUN
ejpam-3312	301	18	above	above	ADP
ejpam-3312	301	19	fails	fail	VERB
ejpam-3312	301	20	.	.	PUNCT
ejpam-3312	302	1	example	example	NOUN
ejpam-3312	303	1	3	3	X
ejpam-3312	303	2	.	.	PUNCT
ejpam-3312	303	3	let	let	VERB
ejpam-3312	303	4	the	the	DET
ejpam-3312	303	5	two	two	NUM
ejpam-3312	303	6	soft	soft	ADJ
ejpam-3312	303	7	topological	topological	ADJ
ejpam-3312	303	8	spaces	space	NOUN
ejpam-3312	303	9	(	(	PUNCT
ejpam-3312	303	10	x	x	X
ejpam-3312	303	11	,	,	PUNCT
ejpam-3312	303	12	τ	τ	PROPN
ejpam-3312	303	13	,	,	PUNCT
ejpam-3312	303	14	a	a	PRON
ejpam-3312	303	15	)	)	PUNCT
ejpam-3312	303	16	,	,	PUNCT
ejpam-3312	303	17	(	(	PUNCT
ejpam-3312	303	18	y	y	PROPN
ejpam-3312	303	19	,	,	PUNCT
ejpam-3312	303	20	θ	θ	PROPN
ejpam-3312	303	21	,	,	PUNCT
ejpam-3312	303	22	b	b	NOUN
ejpam-3312	303	23	)	)	PUNCT
ejpam-3312	303	24	and	and	CCONJ
ejpam-3312	303	25	the	the	DET
ejpam-3312	303	26	two	two	NUM
ejpam-3312	303	27	mappings	mapping	NOUN
ejpam-3312	303	28	f	f	NOUN
ejpam-3312	303	29	:	:	PUNCT
ejpam-3312	303	30	x	x	X
ejpam-3312	303	31	→	→	SYM
ejpam-3312	303	32	y	y	PROPN
ejpam-3312	303	33	,	,	PUNCT
ejpam-3312	303	34	φ	φ	PROPN
ejpam-3312	303	35	:	:	PUNCT
ejpam-3312	303	36	a→	a→	PUNCT
ejpam-3312	303	37	b	b	X
ejpam-3312	303	38	be	be	AUX
ejpam-3312	303	39	the	the	DET
ejpam-3312	303	40	same	same	ADJ
ejpam-3312	303	41	as	as	ADP
ejpam-3312	303	42	in	in	ADP
ejpam-3312	303	43	example	example	NOUN
ejpam-3312	303	44	(	(	PUNCT
ejpam-3312	303	45	1	1	NUM
ejpam-3312	303	46	)	)	PUNCT
ejpam-3312	303	47	.	.	PUNCT
ejpam-3312	304	1	consider	consider	VERB
ejpam-3312	304	2	a	a	DET
ejpam-3312	304	3	partial	partial	ADJ
ejpam-3312	304	4	order	order	NOUN
ejpam-3312	304	5	relation	relation	NOUN
ejpam-3312	304	6	on	on	ADP
ejpam-3312	304	7	y	y	PROPN
ejpam-3312	304	8	as	as	ADP
ejpam-3312	304	9	�	�	PROPN
ejpam-3312	304	10	=	=	NOUN
ejpam-3312	304	11	4	4	NUM
ejpam-3312	304	12	⋃	⋃	NOUN
ejpam-3312	304	13	{	{	PUNCT
ejpam-3312	304	14	(	(	PUNCT
ejpam-3312	304	15	u	u	NOUN
ejpam-3312	304	16	,	,	PUNCT
ejpam-3312	304	17	w	w	NOUN
ejpam-3312	304	18	)	)	PUNCT
ejpam-3312	304	19	,	,	PUNCT
ejpam-3312	304	20	(	(	PUNCT
ejpam-3312	304	21	w	w	NOUN
ejpam-3312	304	22	,	,	PUNCT
ejpam-3312	304	23	v	v	NOUN
ejpam-3312	304	24	)	)	PUNCT
ejpam-3312	304	25	,	,	PUNCT
ejpam-3312	304	26	(	(	PUNCT
ejpam-3312	304	27	u	u	NOUN
ejpam-3312	304	28	,	,	PUNCT
ejpam-3312	304	29	v	v	NOUN
ejpam-3312	304	30	)	)	PUNCT
ejpam-3312	304	31	}	}	PUNCT
ejpam-3312	304	32	.	.	PUNCT
ejpam-3312	305	1	then	then	ADV
ejpam-3312	305	2	one	one	PRON
ejpam-3312	305	3	can	can	AUX
ejpam-3312	305	4	easily	easily	ADV
ejpam-3312	305	5	noted	note	VERB
ejpam-3312	305	6	that	that	SCONJ
ejpam-3312	305	7	fφ	fφ	PRON
ejpam-3312	305	8	:	:	PUNCT
ejpam-3312	305	9	s(xa)→	s(xa)→	PROPN
ejpam-3312	305	10	s(yb	s(yb	PROPN
ejpam-3312	305	11	)	)	PUNCT
ejpam-3312	305	12	is	be	AUX
ejpam-3312	305	13	soft	soft	ADJ
ejpam-3312	305	14	β	β	NOUN
ejpam-3312	305	15	-	-	ADJ
ejpam-3312	305	16	open	open	ADJ
ejpam-3312	305	17	and	and	CCONJ
ejpam-3312	305	18	soft	soft	ADJ
ejpam-3312	305	19	β	β	NOUN
ejpam-3312	305	20	-	-	ADJ
ejpam-3312	305	21	closed	closed	ADJ
ejpam-3312	305	22	mapping	mapping	NOUN
ejpam-3312	305	23	.	.	PUNCT
ejpam-3312	306	1	because	because	SCONJ
ejpam-3312	306	2	fφ(ga	fφ(ga	PROPN
ejpam-3312	306	3	)	)	PUNCT
ejpam-3312	307	1	=	=	PRON
ejpam-3312	307	2	{	{	PUNCT
ejpam-3312	307	3	(	(	PUNCT
ejpam-3312	307	4	13	13	NUM
ejpam-3312	307	5	,	,	PUNCT
ejpam-3312	307	6	∅	∅	NOUN
ejpam-3312	307	7	)	)	PUNCT
ejpam-3312	307	8	,	,	PUNCT
ejpam-3312	307	9	(	(	PUNCT
ejpam-3312	307	10	1	1	NUM
ejpam-3312	307	11	5	5	NUM
ejpam-3312	307	12	,	,	PUNCT
ejpam-3312	307	13	{	{	PUNCT
ejpam-3312	307	14	w	w	NOUN
ejpam-3312	307	15	}	}	PUNCT
ejpam-3312	307	16	)	)	PUNCT
ejpam-3312	307	17	}	}	PUNCT
ejpam-3312	307	18	is	be	AUX
ejpam-3312	307	19	neither	neither	CCONJ
ejpam-3312	307	20	a	a	DET
ejpam-3312	307	21	soft	soft	ADJ
ejpam-3312	307	22	dβ	dβ	ADJ
ejpam-3312	307	23	-	-	PUNCT
ejpam-3312	307	24	open	open	NOUN
ejpam-3312	307	25	nor	nor	CCONJ
ejpam-3312	307	26	a	a	DET
ejpam-3312	307	27	soft	soft	ADJ
ejpam-3312	307	28	iβ	iβ	ADJ
ejpam-3312	307	29	-	-	ADJ
ejpam-3312	307	30	open	open	ADJ
ejpam-3312	307	31	set	set	NOUN
ejpam-3312	307	32	,	,	PUNCT
ejpam-3312	307	33	then	then	ADV
ejpam-3312	307	34	fφ	fφ	PROPN
ejpam-3312	307	35	is	be	AUX
ejpam-3312	307	36	not	not	PART
ejpam-3312	307	37	a	a	DET
ejpam-3312	307	38	soft	soft	ADJ
ejpam-3312	307	39	i	i	NOUN
ejpam-3312	307	40	(	(	PUNCT
ejpam-3312	307	41	soft	soft	ADJ
ejpam-3312	307	42	d	d	NOUN
ejpam-3312	307	43	,	,	PUNCT
ejpam-3312	307	44	soft	soft	ADJ
ejpam-3312	307	45	b	b	NOUN
ejpam-3312	307	46	)	)	PUNCT
ejpam-3312	307	47	β	β	X
ejpam-3312	307	48	-	-	ADJ
ejpam-3312	307	49	open	open	ADJ
ejpam-3312	307	50	mapping	mapping	NOUN
ejpam-3312	307	51	and	and	CCONJ
ejpam-3312	307	52	because	because	SCONJ
ejpam-3312	307	53	fφ(f	fφ(f	NOUN
ejpam-3312	307	54	ca	ca	NOUN
ejpam-3312	307	55	)	)	PUNCT
ejpam-3312	307	56	=	=	PRON
ejpam-3312	307	57	{	{	PUNCT
ejpam-3312	307	58	(	(	PUNCT
ejpam-3312	307	59	13	13	NUM
ejpam-3312	307	60	,	,	PUNCT
ejpam-3312	307	61	{	{	PUNCT
ejpam-3312	307	62	w	w	NOUN
ejpam-3312	307	63	}	}	PUNCT
ejpam-3312	307	64	)	)	PUNCT
ejpam-3312	307	65	,	,	PUNCT
ejpam-3312	307	66	(	(	PUNCT
ejpam-3312	307	67	1	1	NUM
ejpam-3312	307	68	5	5	NUM
ejpam-3312	307	69	,	,	PUNCT
ejpam-3312	307	70	{	{	PUNCT
ejpam-3312	307	71	v	v	NOUN
ejpam-3312	307	72	,	,	PUNCT
ejpam-3312	307	73	w	w	NOUN
ejpam-3312	307	74	}	}	PUNCT
ejpam-3312	307	75	)	)	PUNCT
ejpam-3312	307	76	}	}	PUNCT
ejpam-3312	307	77	is	be	AUX
ejpam-3312	307	78	neither	neither	CCONJ
ejpam-3312	307	79	a	a	DET
ejpam-3312	307	80	soft	soft	ADJ
ejpam-3312	307	81	dβ	dβ	NOUN
ejpam-3312	307	82	-	-	PUNCT
ejpam-3312	307	83	closed	closed	ADJ
ejpam-3312	307	84	nor	nor	CCONJ
ejpam-3312	307	85	a	a	DET
ejpam-3312	307	86	soft	soft	ADJ
ejpam-3312	307	87	iβ	iβ	ADJ
ejpam-3312	307	88	-	-	PUNCT
ejpam-3312	307	89	closed	closed	ADJ
ejpam-3312	307	90	set	set	NOUN
ejpam-3312	307	91	,	,	PUNCT
ejpam-3312	307	92	then	then	ADV
ejpam-3312	307	93	fφ	fφ	PROPN
ejpam-3312	307	94	is	be	AUX
ejpam-3312	307	95	not	not	PART
ejpam-3312	307	96	a	a	DET
ejpam-3312	307	97	soft	soft	ADJ
ejpam-3312	307	98	i	i	NOUN
ejpam-3312	307	99	(	(	PUNCT
ejpam-3312	307	100	soft	soft	ADJ
ejpam-3312	307	101	d	d	NOUN
ejpam-3312	307	102	,	,	PUNCT
ejpam-3312	307	103	soft	soft	ADJ
ejpam-3312	307	104	b	b	NOUN
ejpam-3312	307	105	)	)	PUNCT
ejpam-3312	307	106	β	β	X
ejpam-3312	307	107	-	-	PUNCT
ejpam-3312	307	108	closed	closed	ADJ
ejpam-3312	307	109	mapping	mapping	NOUN
ejpam-3312	307	110	.	.	PUNCT
ejpam-3312	308	1	example	example	NOUN
ejpam-3312	309	1	4	4	NUM
ejpam-3312	309	2	.	.	X
ejpam-3312	310	1	in	in	ADP
ejpam-3312	310	2	example	example	NOUN
ejpam-3312	310	3	above	above	ADV
ejpam-3312	310	4	,	,	PUNCT
ejpam-3312	310	5	if	if	SCONJ
ejpam-3312	310	6	we	we	PRON
ejpam-3312	310	7	only	only	ADV
ejpam-3312	310	8	replace	replace	VERB
ejpam-3312	310	9	the	the	DET
ejpam-3312	310	10	partial	partial	ADJ
ejpam-3312	310	11	order	order	NOUN
ejpam-3312	310	12	relation	relation	NOUN
ejpam-3312	310	13	by	by	ADP
ejpam-3312	310	14	�	�	NOUN
ejpam-3312	310	15	=	=	PROPN
ejpam-3312	310	16	4	4	NUM
ejpam-3312	310	17	⋃	⋃	NOUN
ejpam-3312	310	18	{	{	PUNCT
ejpam-3312	310	19	(	(	PUNCT
ejpam-3312	310	20	u	u	NOUN
ejpam-3312	310	21	,	,	PUNCT
ejpam-3312	310	22	w)}(resp	w)}(resp	PROPN
ejpam-3312	310	23	.	.	PUNCT
ejpam-3312	310	24	�	�	PROPN
ejpam-3312	310	25	=	=	NOUN
ejpam-3312	310	26	4	4	NUM
ejpam-3312	310	27	⋃	⋃	NOUN
ejpam-3312	310	28	{	{	PUNCT
ejpam-3312	310	29	(	(	PUNCT
ejpam-3312	310	30	w	w	PROPN
ejpam-3312	310	31	,	,	PUNCT
ejpam-3312	310	32	v	v	NOUN
ejpam-3312	310	33	)	)	PUNCT
ejpam-3312	310	34	}	}	PUNCT
ejpam-3312	310	35	)	)	PUNCT
ejpam-3312	310	36	,	,	PUNCT
ejpam-3312	310	37	then	then	ADV
ejpam-3312	310	38	the	the	DET
ejpam-3312	310	39	soft	soft	ADJ
ejpam-3312	310	40	mapping	mapping	NOUN
ejpam-3312	310	41	fφ	fφ	NOUN
ejpam-3312	310	42	is	be	AUX
ejpam-3312	310	43	soft	soft	ADJ
ejpam-3312	310	44	iβ	iβ	ADJ
ejpam-3312	310	45	-	-	ADJ
ejpam-3312	310	46	open	open	ADJ
ejpam-3312	310	47	and	and	CCONJ
ejpam-3312	310	48	soft	soft	ADJ
ejpam-3312	310	49	iβ	iβ	ADJ
ejpam-3312	310	50	-	-	ADJ
ejpam-3312	310	51	closed	closed	ADJ
ejpam-3312	310	52	(	(	PUNCT
ejpam-3312	310	53	resp	resp	NOUN
ejpam-3312	310	54	.	.	PUNCT
ejpam-3312	311	1	soft	soft	ADJ
ejpam-3312	311	2	dβ	dβ	ADJ
ejpam-3312	311	3	-	-	PUNCT
ejpam-3312	311	4	open	open	ADJ
ejpam-3312	311	5	and	and	CCONJ
ejpam-3312	311	6	soft	soft	ADJ
ejpam-3312	311	7	dβ	dβ	ADJ
ejpam-3312	311	8	-	-	PUNCT
ejpam-3312	311	9	closed	closed	ADJ
ejpam-3312	311	10	)	)	PUNCT
ejpam-3312	311	11	,	,	PUNCT
ejpam-3312	311	12	but	but	CCONJ
ejpam-3312	311	13	is	be	AUX
ejpam-3312	311	14	not	not	PART
ejpam-3312	311	15	soft	soft	ADJ
ejpam-3312	311	16	bβ	bβ	NOUN
ejpam-3312	311	17	-	-	PUNCT
ejpam-3312	311	18	open	open	ADJ
ejpam-3312	311	19	and	and	CCONJ
ejpam-3312	311	20	soft	soft	ADJ
ejpam-3312	311	21	bβclosed	bβclose	VERB
ejpam-3312	311	22	.	.	PUNCT
ejpam-3312	312	1	theorem	theorem	VERB
ejpam-3312	312	2	6	6	NUM
ejpam-3312	312	3	.	.	PUNCT
ejpam-3312	313	1	the	the	DET
ejpam-3312	313	2	following	follow	VERB
ejpam-3312	313	3	three	three	NUM
ejpam-3312	313	4	properties	property	NOUN
ejpam-3312	313	5	of	of	ADP
ejpam-3312	313	6	a	a	DET
ejpam-3312	313	7	soft	soft	ADJ
ejpam-3312	313	8	mapping	mapping	NOUN
ejpam-3312	313	9	fφ	fφ	NOUN
ejpam-3312	313	10	:	:	PUNCT
ejpam-3312	313	11	(	(	PUNCT
ejpam-3312	313	12	x	x	X
ejpam-3312	313	13	,	,	PUNCT
ejpam-3312	313	14	τ	τ	X
ejpam-3312	313	15	,	,	PUNCT
ejpam-3312	313	16	e	e	X
ejpam-3312	313	17	�	�	PROPN
ejpam-3312	313	18	1	1	NUM
ejpam-3312	313	19	)	)	PUNCT
ejpam-3312	313	20	→	→	SYM
ejpam-3312	313	21	(	(	PUNCT
ejpam-3312	313	22	y	y	PROPN
ejpam-3312	313	23	,	,	PUNCT
ejpam-3312	313	24	θ	θ	PROPN
ejpam-3312	313	25	,	,	PUNCT
ejpam-3312	313	26	f,	f,	X
ejpam-3312	313	27	�	�	NOUN
ejpam-3312	313	28	2	2	NUM
ejpam-3312	313	29	)	)	PUNCT
ejpam-3312	313	30	are	be	AUX
ejpam-3312	313	31	equivalent	equivalent	ADJ
ejpam-3312	313	32	:	:	PUNCT
ejpam-3312	313	33	(	(	PUNCT
ejpam-3312	313	34	i	i	NOUN
ejpam-3312	313	35	)	)	PUNCT
ejpam-3312	313	36	fφ	fφ	VERB
ejpam-3312	313	37	is	be	AUX
ejpam-3312	313	38	soft	soft	ADJ
ejpam-3312	313	39	iβ	iβ	ADJ
ejpam-3312	313	40	-	-	ADJ
ejpam-3312	313	41	open	open	ADJ
ejpam-3312	313	42	;	;	PUNCT
ejpam-3312	313	43	(	(	PUNCT
ejpam-3312	313	44	ii	ii	NOUN
ejpam-3312	313	45	)	)	PUNCT
ejpam-3312	313	46	int(f−1φ	int(f−1φ	PROPN
ejpam-3312	313	47	(	(	PUNCT
ejpam-3312	313	48	mf	mf	X
ejpam-3312	313	49	)	)	PUNCT
ejpam-3312	313	50	)	)	PUNCT
ejpam-3312	314	1	⊆̃f−1φ	⊆̃f−1φ	NOUN
ejpam-3312	314	2	(	(	PUNCT
ejpam-3312	314	3	m	m	VERB
ejpam-3312	314	4	iβo	iβo	NOUN
ejpam-3312	314	5	f	f	PROPN
ejpam-3312	314	6	)	)	PUNCT
ejpam-3312	314	7	,	,	PUNCT
ejpam-3312	314	8	for	for	ADP
ejpam-3312	314	9	every	every	DET
ejpam-3312	314	10	mf	mf	NOUN
ejpam-3312	314	11	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	314	12	;	;	PUNCT
ejpam-3312	314	13	(	(	PUNCT
ejpam-3312	314	14	iii	iii	NOUN
ejpam-3312	314	15	)	)	PUNCT
ejpam-3312	314	16	fφ(int(ne))⊆̃(fφ(ne))iβo	fφ(int(ne))⊆̃(fφ(ne))iβo	NOUN
ejpam-3312	314	17	,	,	PUNCT
ejpam-3312	314	18	for	for	ADP
ejpam-3312	314	19	every	every	DET
ejpam-3312	314	20	ne⊆̃x̃.	ne⊆̃x̃.	ADJ
ejpam-3312	314	21	proof	proof	NOUN
ejpam-3312	314	22	.	.	PUNCT
ejpam-3312	315	1	(	(	PUNCT
ejpam-3312	315	2	i)⇒	i)⇒	PROPN
ejpam-3312	315	3	(	(	PUNCT
ejpam-3312	315	4	ii	ii	NOUN
ejpam-3312	315	5	):	):	PUNCT
ejpam-3312	315	6	given	give	VERB
ejpam-3312	315	7	a	a	DET
ejpam-3312	315	8	soft	soft	ADJ
ejpam-3312	315	9	subsetmf	subsetmf	NOUN
ejpam-3312	315	10	of	of	ADP
ejpam-3312	315	11	ỹ	ỹ	PROPN
ejpam-3312	315	12	,	,	PUNCT
ejpam-3312	315	13	it	it	PRON
ejpam-3312	315	14	is	be	AUX
ejpam-3312	315	15	obvious	obvious	ADJ
ejpam-3312	315	16	that	that	SCONJ
ejpam-3312	315	17	int(f−1φ	int(f−1φ	NOUN
ejpam-3312	315	18	(	(	PUNCT
ejpam-3312	315	19	mf	mf	X
ejpam-3312	315	20	)	)	PUNCT
ejpam-3312	315	21	)	)	PUNCT
ejpam-3312	315	22	is	be	AUX
ejpam-3312	315	23	a	a	DET
ejpam-3312	315	24	soft	soft	ADJ
ejpam-3312	315	25	open	open	ADJ
ejpam-3312	315	26	subset	subset	NOUN
ejpam-3312	315	27	of	of	ADP
ejpam-3312	315	28	x̃.	x̃.	PROPN
ejpam-3312	315	29	then	then	ADV
ejpam-3312	315	30	,	,	PUNCT
ejpam-3312	315	31	by	by	ADP
ejpam-3312	315	32	hypothesis	hypothesis	NOUN
ejpam-3312	315	33	,	,	PUNCT
ejpam-3312	315	34	it	it	PRON
ejpam-3312	315	35	follows	follow	VERB
ejpam-3312	315	36	that	that	SCONJ
ejpam-3312	315	37	fφ(int(f−1φ	fφ(int(f−1φ	PROPN
ejpam-3312	315	38	(	(	PUNCT
ejpam-3312	315	39	mf	mf	X
ejpam-3312	315	40	)	)	PUNCT
ejpam-3312	315	41	)	)	PUNCT
ejpam-3312	315	42	)	)	PUNCT
ejpam-3312	315	43	is	be	AUX
ejpam-3312	315	44	a	a	DET
ejpam-3312	315	45	soft	soft	ADJ
ejpam-3312	315	46	iβ	iβ	ADJ
ejpam-3312	315	47	-	-	ADJ
ejpam-3312	315	48	open	open	ADJ
ejpam-3312	315	49	subset	subset	NOUN
ejpam-3312	315	50	of	of	ADP
ejpam-3312	315	51	ỹ	ỹ	PROPN
ejpam-3312	315	52	.	.	PUNCT
ejpam-3312	316	1	since	since	SCONJ
ejpam-3312	316	2	fφ(int(f−1φ	fφ(int(f−1φ	PROPN
ejpam-3312	316	3	(	(	PUNCT
ejpam-3312	316	4	mf	mf	X
ejpam-3312	316	5	)	)	PUNCT
ejpam-3312	316	6	)	)	PUNCT
ejpam-3312	316	7	)	)	PUNCT
ejpam-3312	316	8	⊆̃fφ(f−1φ	⊆̃fφ(f−1φ	X
ejpam-3312	316	9	(	(	PUNCT
ejpam-3312	316	10	mf	mf	X
ejpam-3312	316	11	)	)	PUNCT
ejpam-3312	316	12	)	)	PUNCT
ejpam-3312	316	13	⊆̃mf	⊆̃mf	PROPN
ejpam-3312	316	14	,	,	PUNCT
ejpam-3312	316	15	then	then	ADV
ejpam-3312	316	16	int(f−1φ	int(f−1φ	PROPN
ejpam-3312	316	17	(	(	PUNCT
ejpam-3312	316	18	mf	mf	X
ejpam-3312	316	19	)	)	PUNCT
ejpam-3312	316	20	)	)	PUNCT
ejpam-3312	316	21	⊆̃f−1φ	⊆̃f−1φ	NOUN
ejpam-3312	316	22	(	(	PUNCT
ejpam-3312	316	23	m	m	VERB
ejpam-3312	316	24	iβo	iβo	NOUN
ejpam-3312	316	25	f	f	PROPN
ejpam-3312	316	26	)	)	PUNCT
ejpam-3312	316	27	.	.	PUNCT
ejpam-3312	317	1	(	(	PUNCT
ejpam-3312	317	2	ii)⇒	ii)⇒	X
ejpam-3312	317	3	(	(	PUNCT
ejpam-3312	317	4	iii	iii	NOUN
ejpam-3312	317	5	):	):	PUNCT
ejpam-3312	317	6	given	give	VERB
ejpam-3312	317	7	a	a	DET
ejpam-3312	317	8	soft	soft	ADJ
ejpam-3312	317	9	subsetne	subsetne	NOUN
ejpam-3312	317	10	of	of	ADP
ejpam-3312	317	11	x̃	x̃	PROPN
ejpam-3312	317	12	,	,	PUNCT
ejpam-3312	317	13	from	from	ADP
ejpam-3312	317	14	(	(	PUNCT
ejpam-3312	317	15	ii	ii	NOUN
ejpam-3312	317	16	)	)	PUNCT
ejpam-3312	317	17	,	,	PUNCT
ejpam-3312	317	18	we	we	PRON
ejpam-3312	317	19	obtain	obtain	VERB
ejpam-3312	317	20	int(f−1φ	int(f−1φ	NOUN
ejpam-3312	317	21	(	(	PUNCT
ejpam-3312	317	22	fφ(ne)))⊆̃f−1φ	fφ(ne)))⊆̃f−1φ	PROPN
ejpam-3312	317	23	(	(	PUNCT
ejpam-3312	317	24	(	(	PUNCT
ejpam-3312	317	25	fφ(ne))iβo	fφ(ne))iβo	NOUN
ejpam-3312	317	26	)	)	PUNCT
ejpam-3312	317	27	.	.	PUNCT
ejpam-3312	318	1	since	since	SCONJ
ejpam-3312	318	2	int(ne)⊆̃f−1φ	int(ne)⊆̃f−1φ	NOUN
ejpam-3312	318	3	(	(	PUNCT
ejpam-3312	318	4	fφ(int(f−1φ	fφ(int(f−1φ	PROPN
ejpam-3312	318	5	(	(	PUNCT
ejpam-3312	318	6	fφ(ne)))))⊆̃f−1φ	fφ(ne)))))⊆̃f−1φ	NOUN
ejpam-3312	318	7	(	(	PUNCT
ejpam-3312	318	8	(	(	PUNCT
ejpam-3312	318	9	fφ(ne))iβo	fφ(ne))iβo	NOUN
ejpam-3312	318	10	)	)	PUNCT
ejpam-3312	318	11	,	,	PUNCT
ejpam-3312	318	12	then	then	ADV
ejpam-3312	318	13	fφ(int(ne))⊆̃(fφ(ne))iβo	fφ(int(ne))⊆̃(fφ(ne))iβo	VERB
ejpam-3312	318	14	as	as	SCONJ
ejpam-3312	318	15	required	require	VERB
ejpam-3312	318	16	.	.	PUNCT
ejpam-3312	319	1	(	(	PUNCT
ejpam-3312	319	2	iii)⇒	iii)⇒	PROPN
ejpam-3312	319	3	(	(	PUNCT
ejpam-3312	319	4	i	i	NOUN
ejpam-3312	319	5	):	):	PUNCT
ejpam-3312	319	6	let	let	VERB
ejpam-3312	319	7	ge	ge	PRON
ejpam-3312	319	8	be	be	AUX
ejpam-3312	319	9	a	a	DET
ejpam-3312	319	10	soft	soft	ADJ
ejpam-3312	319	11	open	open	ADJ
ejpam-3312	319	12	subset	subset	NOUN
ejpam-3312	319	13	of	of	ADP
ejpam-3312	319	14	x̃.	x̃.	ADJ
ejpam-3312	319	15	then	then	ADV
ejpam-3312	319	16	fφ(int(ge	fφ(int(ge	PROPN
ejpam-3312	319	17	)	)	PUNCT
ejpam-3312	319	18	)	)	PUNCT
ejpam-3312	320	1	=	=	PUNCT
ejpam-3312	320	2	fφ(ge)⊆̃(fφ(ge))iβo	fφ(ge)⊆̃(fφ(ge))iβo	NOUN
ejpam-3312	320	3	.	.	PROPN
ejpam-3312	321	1	hence	hence	ADV
ejpam-3312	321	2	fφ	fφ	PROPN
ejpam-3312	321	3	is	be	AUX
ejpam-3312	321	4	a	a	DET
ejpam-3312	321	5	soft	soft	ADJ
ejpam-3312	321	6	iβ	iβ	ADJ
ejpam-3312	321	7	-	-	ADJ
ejpam-3312	321	8	open	open	ADJ
ejpam-3312	321	9	mapping	mapping	NOUN
ejpam-3312	321	10	.	.	PUNCT
ejpam-3312	322	1	in	in	ADP
ejpam-3312	322	2	a	a	DET
ejpam-3312	322	3	similar	similar	ADJ
ejpam-3312	322	4	manner	manner	NOUN
ejpam-3312	322	5	,	,	PUNCT
ejpam-3312	322	6	one	one	PRON
ejpam-3312	322	7	can	can	AUX
ejpam-3312	322	8	prove	prove	VERB
ejpam-3312	322	9	the	the	DET
ejpam-3312	322	10	following	follow	VERB
ejpam-3312	322	11	theorem	theorem	VERB
ejpam-3312	322	12	.	.	PUNCT
ejpam-3312	322	13	theorem	theorem	PROPN
ejpam-3312	322	14	7	7	NUM
ejpam-3312	322	15	.	.	PUNCT
ejpam-3312	323	1	the	the	DET
ejpam-3312	323	2	following	follow	VERB
ejpam-3312	323	3	three	three	NUM
ejpam-3312	323	4	properties	property	NOUN
ejpam-3312	323	5	of	of	ADP
ejpam-3312	323	6	a	a	DET
ejpam-3312	323	7	soft	soft	ADJ
ejpam-3312	323	8	mapping	mapping	NOUN
ejpam-3312	323	9	fφ	fφ	NOUN
ejpam-3312	323	10	:	:	PUNCT
ejpam-3312	323	11	(	(	PUNCT
ejpam-3312	323	12	x	x	X
ejpam-3312	323	13	,	,	PUNCT
ejpam-3312	323	14	τ	τ	X
ejpam-3312	323	15	,	,	PUNCT
ejpam-3312	323	16	e	e	X
ejpam-3312	323	17	�	�	PROPN
ejpam-3312	323	18	1	1	NUM
ejpam-3312	323	19	)	)	PUNCT
ejpam-3312	323	20	→	→	SYM
ejpam-3312	323	21	(	(	PUNCT
ejpam-3312	323	22	y	y	PROPN
ejpam-3312	323	23	,	,	PUNCT
ejpam-3312	323	24	θ	θ	PROPN
ejpam-3312	323	25	,	,	PUNCT
ejpam-3312	323	26	f,	f,	X
ejpam-3312	323	27	�	�	NOUN
ejpam-3312	323	28	2	2	NUM
ejpam-3312	323	29	)	)	PUNCT
ejpam-3312	323	30	are	be	AUX
ejpam-3312	323	31	equivalent	equivalent	ADJ
ejpam-3312	323	32	:	:	PUNCT
ejpam-3312	323	33	(	(	PUNCT
ejpam-3312	323	34	i	i	NOUN
ejpam-3312	323	35	)	)	PUNCT
ejpam-3312	323	36	fφ	fφ	VERB
ejpam-3312	323	37	is	be	AUX
ejpam-3312	323	38	soft	soft	ADJ
ejpam-3312	323	39	dβ	dβ	ADJ
ejpam-3312	323	40	-	-	PUNCT
ejpam-3312	323	41	open	open	ADJ
ejpam-3312	323	42	(	(	PUNCT
ejpam-3312	323	43	resp	resp	NOUN
ejpam-3312	323	44	.	.	PUNCT
ejpam-3312	324	1	soft	soft	ADJ
ejpam-3312	324	2	bβ	bβ	NOUN
ejpam-3312	324	3	-	-	PUNCT
ejpam-3312	324	4	open	open	ADJ
ejpam-3312	324	5	)	)	PUNCT
ejpam-3312	325	1	;	;	PUNCT
ejpam-3312	325	2	(	(	PUNCT
ejpam-3312	325	3	ii	ii	X
ejpam-3312	325	4	)	)	PUNCT
ejpam-3312	325	5	int(f−1φ	int(f−1φ	PROPN
ejpam-3312	325	6	(	(	PUNCT
ejpam-3312	325	7	mf	mf	X
ejpam-3312	325	8	)	)	PUNCT
ejpam-3312	325	9	)	)	PUNCT
ejpam-3312	325	10	⊆̃f−1φ	⊆̃f−1φ	NOUN
ejpam-3312	325	11	(	(	PUNCT
ejpam-3312	325	12	mdβo	mdβo	NOUN
ejpam-3312	325	13	f	f	PROPN
ejpam-3312	325	14	)	)	PUNCT
ejpam-3312	325	15	(	(	PUNCT
ejpam-3312	325	16	resp	resp	NOUN
ejpam-3312	325	17	.	.	PUNCT
ejpam-3312	326	1	int(f−1φ	int(f−1φ	NOUN
ejpam-3312	326	2	(	(	PUNCT
ejpam-3312	326	3	mf	mf	X
ejpam-3312	326	4	)	)	PUNCT
ejpam-3312	326	5	)	)	PUNCT
ejpam-3312	326	6	⊆̃f−1φ	⊆̃f−1φ	NOUN
ejpam-3312	326	7	(	(	PUNCT
ejpam-3312	326	8	m	m	PROPN
ejpam-3312	326	9	bβo	bβo	PROPN
ejpam-3312	326	10	f	f	PROPN
ejpam-3312	326	11	)	)	PUNCT
ejpam-3312	326	12	)	)	PUNCT
ejpam-3312	326	13	,	,	PUNCT
ejpam-3312	326	14	for	for	ADP
ejpam-3312	326	15	every	every	DET
ejpam-3312	326	16	mf	mf	NOUN
ejpam-3312	326	17	⊆̃ỹ	⊆̃ỹ	VERB
ejpam-3312	326	18	;	;	PUNCT
ejpam-3312	326	19	(	(	PUNCT
ejpam-3312	326	20	iii	iii	X
ejpam-3312	326	21	)	)	PUNCT
ejpam-3312	326	22	fφ(int(ne))⊆̃(fφ(ne))dβo	fφ(int(ne))⊆̃(fφ(ne))dβo	PROPN
ejpam-3312	326	23	(	(	PUNCT
ejpam-3312	326	24	resp	resp	NOUN
ejpam-3312	326	25	.	.	PUNCT
ejpam-3312	327	1	fφ(int(ne))⊆̃(fφ(ne))bβo	fφ(int(ne))⊆̃(fφ(ne))bβo	NUM
ejpam-3312	327	2	)	)	PUNCT
ejpam-3312	327	3	,	,	PUNCT
ejpam-3312	327	4	for	for	ADP
ejpam-3312	327	5	every	every	DET
ejpam-3312	327	6	ne⊆̃x̃.	ne⊆̃x̃.	NUM
ejpam-3312	327	7	t.	t.	PROPN
ejpam-3312	327	8	m.	m.	NOUN
ejpam-3312	327	9	al	al	PROPN
ejpam-3312	327	10	-	-	PUNCT
ejpam-3312	327	11	shami	shami	PROPN
ejpam-3312	327	12	,	,	PUNCT
ejpam-3312	327	13	m.	m.	PROPN
ejpam-3312	327	14	e.	e.	PROPN
ejpam-3312	327	15	el	el	PROPN
ejpam-3312	327	16	-	-	PROPN
ejpam-3312	327	17	shafei	shafei	PROPN
ejpam-3312	327	18	,	,	PUNCT
ejpam-3312	327	19	b.	b.	PROPN
ejpam-3312	327	20	a.	a.	PROPN
ejpam-3312	327	21	asaad	asaad	PROPN
ejpam-3312	327	22	/	/	SYM
ejpam-3312	327	23	eur	eur	PROPN
ejpam-3312	327	24	.	.	PUNCT
ejpam-3312	328	1	j.	j.	PROPN
ejpam-3312	328	2	pure	pure	PROPN
ejpam-3312	328	3	appl	appl	PROPN
ejpam-3312	328	4	.	.	PROPN
ejpam-3312	328	5	math	math	PROPN
ejpam-3312	328	6	,	,	PUNCT
ejpam-3312	328	7	12	12	NUM
ejpam-3312	328	8	(	(	PUNCT
ejpam-3312	328	9	1	1	NUM
ejpam-3312	328	10	)	)	PUNCT
ejpam-3312	328	11	(	(	PUNCT
ejpam-3312	328	12	2019	2019	NUM
ejpam-3312	328	13	)	)	PUNCT
ejpam-3312	328	14	,	,	PUNCT
ejpam-3312	328	15	176	176	NUM
ejpam-3312	328	16	-	-	SYM
ejpam-3312	328	17	193	193	NUM
ejpam-3312	328	18	186	186	NUM
ejpam-3312	328	19	theorem	theorem	NOUN
ejpam-3312	328	20	8	8	NUM
ejpam-3312	328	21	.	.	PUNCT
ejpam-3312	329	1	the	the	DET
ejpam-3312	329	2	following	follow	VERB
ejpam-3312	329	3	three	three	NUM
ejpam-3312	329	4	statements	statement	NOUN
ejpam-3312	329	5	hold	hold	VERB
ejpam-3312	329	6	for	for	ADP
ejpam-3312	329	7	a	a	DET
ejpam-3312	329	8	soft	soft	ADJ
ejpam-3312	329	9	mapping	mapping	NOUN
ejpam-3312	329	10	fφ	fφ	NOUN
ejpam-3312	329	11	:	:	PUNCT
ejpam-3312	329	12	(	(	PUNCT
ejpam-3312	329	13	x	x	X
ejpam-3312	329	14	,	,	PUNCT
ejpam-3312	329	15	τ	τ	X
ejpam-3312	329	16	,	,	PUNCT
ejpam-3312	329	17	e	e	X
ejpam-3312	329	18	�	�	PROPN
ejpam-3312	329	19	1)→	1)→	NUM
ejpam-3312	329	20	(	(	PUNCT
ejpam-3312	329	21	y	y	PROPN
ejpam-3312	329	22	,	,	PUNCT
ejpam-3312	329	23	θ	θ	PROPN
ejpam-3312	329	24	,	,	PUNCT
ejpam-3312	329	25	f,	f,	X
ejpam-3312	329	26	�	�	X
ejpam-3312	329	27	2	2	NUM
ejpam-3312	329	28	):	):	PUNCT
ejpam-3312	329	29	(	(	PUNCT
ejpam-3312	329	30	i	i	NOUN
ejpam-3312	329	31	)	)	PUNCT
ejpam-3312	329	32	fφ	fφ	VERB
ejpam-3312	329	33	is	be	AUX
ejpam-3312	329	34	soft	soft	ADJ
ejpam-3312	329	35	iβ	iβ	ADJ
ejpam-3312	329	36	-	-	PUNCT
ejpam-3312	329	37	closed	closed	ADJ
ejpam-3312	329	38	if	if	SCONJ
ejpam-3312	329	39	and	and	CCONJ
ejpam-3312	329	40	only	only	ADV
ejpam-3312	329	41	if	if	SCONJ
ejpam-3312	329	42	(	(	PUNCT
ejpam-3312	329	43	fφ(ge))iβcl⊆̃fφ(cl(ge	fφ(ge))iβcl⊆̃fφ(cl(ge	INTJ
ejpam-3312	329	44	)	)	PUNCT
ejpam-3312	329	45	)	)	PUNCT
ejpam-3312	329	46	,	,	PUNCT
ejpam-3312	329	47	for	for	ADP
ejpam-3312	329	48	every	every	DET
ejpam-3312	329	49	ge⊆̃x̃.	ge⊆̃x̃.	NUM
ejpam-3312	329	50	(	(	PUNCT
ejpam-3312	329	51	ii	ii	NOUN
ejpam-3312	329	52	)	)	PUNCT
ejpam-3312	329	53	fφ	fφ	PROPN
ejpam-3312	329	54	is	be	AUX
ejpam-3312	329	55	soft	soft	ADJ
ejpam-3312	329	56	dβ	dβ	ADJ
ejpam-3312	329	57	-	-	PUNCT
ejpam-3312	329	58	closed	closed	ADJ
ejpam-3312	329	59	if	if	SCONJ
ejpam-3312	329	60	and	and	CCONJ
ejpam-3312	329	61	only	only	ADV
ejpam-3312	329	62	if	if	SCONJ
ejpam-3312	329	63	(	(	PUNCT
ejpam-3312	329	64	fφ(ge))dβcl⊆̃fφ(cl(ge	fφ(ge))dβcl⊆̃fφ(cl(ge	NOUN
ejpam-3312	329	65	)	)	PUNCT
ejpam-3312	329	66	)	)	PUNCT
ejpam-3312	329	67	,	,	PUNCT
ejpam-3312	329	68	for	for	ADP
ejpam-3312	329	69	every	every	DET
ejpam-3312	329	70	ge⊆̃x̃.	ge⊆̃x̃.	NUM
ejpam-3312	329	71	(	(	PUNCT
ejpam-3312	329	72	iii	iii	X
ejpam-3312	329	73	)	)	PUNCT
ejpam-3312	329	74	fφ	fφ	NOUN
ejpam-3312	329	75	is	be	AUX
ejpam-3312	329	76	soft	soft	ADJ
ejpam-3312	329	77	bβ	bβ	NOUN
ejpam-3312	329	78	-	-	PUNCT
ejpam-3312	329	79	closed	closed	ADJ
ejpam-3312	329	80	if	if	SCONJ
ejpam-3312	329	81	and	and	CCONJ
ejpam-3312	329	82	only	only	ADV
ejpam-3312	329	83	if	if	SCONJ
ejpam-3312	329	84	(	(	PUNCT
ejpam-3312	329	85	fφ(ge))bβcl⊆̃fφ(cl(ge	fφ(ge))bβcl⊆̃fφ(cl(ge	NOUN
ejpam-3312	329	86	)	)	PUNCT
ejpam-3312	329	87	)	)	PUNCT
ejpam-3312	329	88	,	,	PUNCT
ejpam-3312	329	89	for	for	ADP
ejpam-3312	329	90	every	every	DET
ejpam-3312	329	91	ge⊆̃x̃.	ge⊆̃x̃.	ADJ
ejpam-3312	329	92	proof	proof	NOUN
ejpam-3312	329	93	.	.	PUNCT
ejpam-3312	330	1	we	we	PRON
ejpam-3312	330	2	only	only	ADV
ejpam-3312	330	3	prove	prove	VERB
ejpam-3312	330	4	the	the	DET
ejpam-3312	330	5	first	first	ADJ
ejpam-3312	330	6	statement	statement	NOUN
ejpam-3312	330	7	and	and	CCONJ
ejpam-3312	330	8	the	the	DET
ejpam-3312	330	9	others	other	NOUN
ejpam-3312	330	10	follow	follow	VERB
ejpam-3312	330	11	similar	similar	ADJ
ejpam-3312	330	12	lines	line	NOUN
ejpam-3312	330	13	.	.	PUNCT
ejpam-3312	331	1	necessity	necessity	NOUN
ejpam-3312	331	2	:	:	PUNCT
ejpam-3312	331	3	since	since	SCONJ
ejpam-3312	331	4	fφ	fφ	PROPN
ejpam-3312	331	5	is	be	AUX
ejpam-3312	331	6	soft	soft	ADJ
ejpam-3312	331	7	iβ	iβ	ADJ
ejpam-3312	331	8	-	-	VERB
ejpam-3312	331	9	closed	closed	ADJ
ejpam-3312	331	10	,	,	PUNCT
ejpam-3312	331	11	then	then	ADV
ejpam-3312	331	12	fφ(cl(ge	fφ(cl(ge	NOUN
ejpam-3312	331	13	)	)	PUNCT
ejpam-3312	331	14	)	)	PUNCT
ejpam-3312	331	15	is	be	AUX
ejpam-3312	331	16	a	a	DET
ejpam-3312	331	17	soft	soft	ADJ
ejpam-3312	331	18	iβ	iβ	ADJ
ejpam-3312	331	19	-	-	ADJ
ejpam-3312	331	20	closed	closed	ADJ
ejpam-3312	331	21	subset	subset	NOUN
ejpam-3312	331	22	of	of	ADP
ejpam-3312	331	23	ỹ	ỹ	PROPN
ejpam-3312	331	24	and	and	CCONJ
ejpam-3312	331	25	since	since	SCONJ
ejpam-3312	331	26	fφ(ge)⊆̃fφ(cl(ge	fφ(ge)⊆̃fφ(cl(ge	NUM
ejpam-3312	331	27	)	)	PUNCT
ejpam-3312	331	28	)	)	PUNCT
ejpam-3312	331	29	,	,	PUNCT
ejpam-3312	331	30	then	then	ADV
ejpam-3312	331	31	(	(	PUNCT
ejpam-3312	331	32	fφ(ge))iβcl⊆̃fφ(cl(ge	fφ(ge))iβcl⊆̃fφ(cl(ge	INTJ
ejpam-3312	331	33	)	)	PUNCT
ejpam-3312	331	34	)	)	PUNCT
ejpam-3312	331	35	.	.	PUNCT
ejpam-3312	332	1	sufficiency	sufficiency	NOUN
ejpam-3312	332	2	:	:	PUNCT
ejpam-3312	333	1	considerhe	considerhe	NOUN
ejpam-3312	333	2	is	be	AUX
ejpam-3312	333	3	a	a	DET
ejpam-3312	333	4	soft	soft	ADJ
ejpam-3312	333	5	closed	closed	ADJ
ejpam-3312	333	6	subset	subset	NOUN
ejpam-3312	333	7	of	of	ADP
ejpam-3312	333	8	x̃.	x̃.	ADJ
ejpam-3312	333	9	then	then	ADV
ejpam-3312	333	10	fφ(he)⊆̃(fφ(he))iβcl⊆̃fφ(cl(he	fφ(he)⊆̃(fφ(he))iβcl⊆̃fφ(cl(he	PROPN
ejpam-3312	333	11	)	)	PUNCT
ejpam-3312	333	12	)	)	PUNCT
ejpam-3312	334	1	=	=	SYM
ejpam-3312	334	2	fφ(he	fφ(he	NOUN
ejpam-3312	334	3	)	)	PUNCT
ejpam-3312	334	4	.	.	PUNCT
ejpam-3312	335	1	therefore	therefore	ADV
ejpam-3312	335	2	fφ(he	fφ(he	ADJ
ejpam-3312	335	3	)	)	PUNCT
ejpam-3312	335	4	=	=	SYM
ejpam-3312	335	5	(	(	PUNCT
ejpam-3312	335	6	fφ(he))iβcl	fφ(he))iβcl	PROPN
ejpam-3312	335	7	.	.	PUNCT
ejpam-3312	336	1	this	this	PRON
ejpam-3312	336	2	means	mean	VERB
ejpam-3312	336	3	that	that	SCONJ
ejpam-3312	336	4	fφ(he	fφ(he	NOUN
ejpam-3312	336	5	)	)	PUNCT
ejpam-3312	336	6	is	be	AUX
ejpam-3312	336	7	a	a	DET
ejpam-3312	336	8	soft	soft	ADJ
ejpam-3312	336	9	iβ	iβ	ADJ
ejpam-3312	336	10	-	-	PUNCT
ejpam-3312	336	11	closed	closed	ADJ
ejpam-3312	336	12	set	set	NOUN
ejpam-3312	336	13	.	.	PUNCT
ejpam-3312	337	1	hence	hence	ADV
ejpam-3312	337	2	the	the	DET
ejpam-3312	337	3	proof	proof	NOUN
ejpam-3312	337	4	is	be	AUX
ejpam-3312	337	5	complete	complete	ADJ
ejpam-3312	337	6	.	.	PUNCT
ejpam-3312	338	1	theorem	theorem	NOUN
ejpam-3312	338	2	9	9	NUM
ejpam-3312	338	3	.	.	PUNCT
ejpam-3312	339	1	the	the	DET
ejpam-3312	339	2	following	follow	VERB
ejpam-3312	339	3	three	three	NUM
ejpam-3312	339	4	statements	statement	NOUN
ejpam-3312	339	5	hold	hold	VERB
ejpam-3312	339	6	for	for	ADP
ejpam-3312	339	7	a	a	DET
ejpam-3312	339	8	bijective	bijective	ADJ
ejpam-3312	339	9	soft	soft	ADJ
ejpam-3312	339	10	mapping	mapping	NOUN
ejpam-3312	339	11	fφ	fφ	NOUN
ejpam-3312	339	12	:	:	PUNCT
ejpam-3312	339	13	(	(	PUNCT
ejpam-3312	339	14	x	x	X
ejpam-3312	339	15	,	,	PUNCT
ejpam-3312	339	16	τ	τ	X
ejpam-3312	339	17	,	,	PUNCT
ejpam-3312	339	18	e	e	X
ejpam-3312	339	19	�	�	PROPN
ejpam-3312	339	20	1	1	NUM
ejpam-3312	339	21	)	)	PUNCT
ejpam-3312	339	22	→	→	SYM
ejpam-3312	339	23	(	(	PUNCT
ejpam-3312	339	24	y	y	PROPN
ejpam-3312	339	25	,	,	PUNCT
ejpam-3312	339	26	θ	θ	PROPN
ejpam-3312	339	27	,	,	PUNCT
ejpam-3312	339	28	f,	f,	X
ejpam-3312	339	29	�	�	X
ejpam-3312	339	30	2	2	NUM
ejpam-3312	339	31	):	):	PUNCT
ejpam-3312	339	32	(	(	PUNCT
ejpam-3312	339	33	i	i	NOUN
ejpam-3312	339	34	)	)	PUNCT
ejpam-3312	339	35	fφ	fφ	VERB
ejpam-3312	339	36	is	be	AUX
ejpam-3312	339	37	soft	soft	ADJ
ejpam-3312	339	38	i	i	PRON
ejpam-3312	339	39	(	(	PUNCT
ejpam-3312	339	40	resp	resp	NOUN
ejpam-3312	339	41	.	.	PUNCT
ejpam-3312	340	1	soft	soft	ADJ
ejpam-3312	340	2	d	d	NOUN
ejpam-3312	340	3	,	,	PUNCT
ejpam-3312	340	4	soft	soft	ADJ
ejpam-3312	340	5	b	b	NOUN
ejpam-3312	340	6	)	)	PUNCT
ejpam-3312	340	7	β	β	X
ejpam-3312	340	8	-	-	VERB
ejpam-3312	340	9	open	open	ADJ
ejpam-3312	340	10	if	if	SCONJ
ejpam-3312	340	11	and	and	CCONJ
ejpam-3312	340	12	only	only	ADV
ejpam-3312	340	13	if	if	SCONJ
ejpam-3312	340	14	fφ	fφ	PROPN
ejpam-3312	340	15	is	be	AUX
ejpam-3312	340	16	soft	soft	ADJ
ejpam-3312	340	17	d	d	NOUN
ejpam-3312	340	18	(	(	PUNCT
ejpam-3312	340	19	resp	resp	NOUN
ejpam-3312	340	20	.	.	PUNCT
ejpam-3312	341	1	soft	soft	ADJ
ejpam-3312	341	2	d	d	NOUN
ejpam-3312	341	3	,	,	PUNCT
ejpam-3312	341	4	soft	soft	ADJ
ejpam-3312	341	5	b	b	NOUN
ejpam-3312	341	6	)	)	PUNCT
ejpam-3312	341	7	β	β	NOUN
ejpam-3312	341	8	-	-	VERB
ejpam-3312	341	9	closed	closed	ADJ
ejpam-3312	341	10	.	.	PUNCT
ejpam-3312	342	1	(	(	PUNCT
ejpam-3312	342	2	ii	ii	NOUN
ejpam-3312	342	3	)	)	PUNCT
ejpam-3312	342	4	fφ	fφ	PROPN
ejpam-3312	342	5	is	be	AUX
ejpam-3312	342	6	soft	soft	ADJ
ejpam-3312	342	7	i	i	PRON
ejpam-3312	342	8	(	(	PUNCT
ejpam-3312	342	9	resp	resp	NOUN
ejpam-3312	342	10	.	.	PUNCT
ejpam-3312	343	1	soft	soft	ADJ
ejpam-3312	343	2	d	d	NOUN
ejpam-3312	343	3	,	,	PUNCT
ejpam-3312	343	4	soft	soft	ADJ
ejpam-3312	343	5	b	b	NOUN
ejpam-3312	343	6	)	)	PUNCT
ejpam-3312	343	7	β	β	X
ejpam-3312	343	8	-	-	VERB
ejpam-3312	343	9	open	open	ADJ
ejpam-3312	343	10	if	if	SCONJ
ejpam-3312	343	11	and	and	CCONJ
ejpam-3312	343	12	only	only	ADV
ejpam-3312	343	13	if	if	SCONJ
ejpam-3312	343	14	f−1φ	f−1φ	NOUN
ejpam-3312	343	15	is	be	AUX
ejpam-3312	343	16	soft	soft	ADJ
ejpam-3312	344	1	i	i	PRON
ejpam-3312	344	2	(	(	PUNCT
ejpam-3312	344	3	resp	resp	NOUN
ejpam-3312	344	4	.	.	PUNCT
ejpam-3312	345	1	soft	soft	ADJ
ejpam-3312	345	2	d	d	NOUN
ejpam-3312	345	3	,	,	PUNCT
ejpam-3312	345	4	soft	soft	ADJ
ejpam-3312	345	5	b	b	NOUN
ejpam-3312	345	6	)	)	PUNCT
ejpam-3312	345	7	β	β	NOUN
ejpam-3312	345	8	-	-	NOUN
ejpam-3312	345	9	continuous	continuous	ADJ
ejpam-3312	345	10	.	.	PUNCT
ejpam-3312	346	1	(	(	PUNCT
ejpam-3312	346	2	iii	iii	X
ejpam-3312	346	3	)	)	PUNCT
ejpam-3312	346	4	fφ	fφ	NOUN
ejpam-3312	346	5	is	be	AUX
ejpam-3312	346	6	soft	soft	ADJ
ejpam-3312	346	7	d	d	NOUN
ejpam-3312	346	8	(	(	PUNCT
ejpam-3312	346	9	resp	resp	NOUN
ejpam-3312	346	10	.	.	PUNCT
ejpam-3312	347	1	soft	soft	PROPN
ejpam-3312	347	2	i	i	NOUN
ejpam-3312	347	3	,	,	PUNCT
ejpam-3312	347	4	soft	soft	ADJ
ejpam-3312	347	5	b	b	NOUN
ejpam-3312	347	6	)	)	PUNCT
ejpam-3312	347	7	β	β	NOUN
ejpam-3312	347	8	-	-	PUNCT
ejpam-3312	347	9	closed	closed	ADJ
ejpam-3312	347	10	if	if	SCONJ
ejpam-3312	347	11	and	and	CCONJ
ejpam-3312	347	12	only	only	ADV
ejpam-3312	347	13	if	if	SCONJ
ejpam-3312	347	14	f−1φ	f−1φ	NOUN
ejpam-3312	347	15	is	be	AUX
ejpam-3312	347	16	soft	soft	ADJ
ejpam-3312	348	1	i	i	PRON
ejpam-3312	348	2	(	(	PUNCT
ejpam-3312	348	3	resp	resp	NOUN
ejpam-3312	348	4	.	.	PUNCT
ejpam-3312	349	1	soft	soft	ADJ
ejpam-3312	349	2	d	d	NOUN
ejpam-3312	349	3	,	,	PUNCT
ejpam-3312	349	4	soft	soft	ADJ
ejpam-3312	349	5	b	b	NOUN
ejpam-3312	349	6	)	)	PUNCT
ejpam-3312	349	7	β	β	NOUN
ejpam-3312	349	8	-	-	ADJ
ejpam-3312	349	9	continuous	continuous	ADJ
ejpam-3312	349	10	.	.	PUNCT
ejpam-3312	350	1	proof	proof	NOUN
ejpam-3312	350	2	.	.	PUNCT
ejpam-3312	351	1	for	for	ADP
ejpam-3312	351	2	the	the	DET
ejpam-3312	351	3	sake	sake	NOUN
ejpam-3312	351	4	of	of	ADP
ejpam-3312	351	5	brevity	brevity	NOUN
ejpam-3312	351	6	,	,	PUNCT
ejpam-3312	351	7	we	we	PRON
ejpam-3312	351	8	only	only	ADV
ejpam-3312	351	9	give	give	VERB
ejpam-3312	351	10	proofs	proof	NOUN
ejpam-3312	351	11	of	of	ADP
ejpam-3312	351	12	cases	case	NOUN
ejpam-3312	351	13	outside	outside	ADP
ejpam-3312	351	14	the	the	DET
ejpam-3312	351	15	parenthesis	parenthesis	NOUN
ejpam-3312	351	16	for	for	ADP
ejpam-3312	351	17	the	the	DET
ejpam-3312	351	18	three	three	NUM
ejpam-3312	351	19	statements	statement	NOUN
ejpam-3312	351	20	above	above	ADV
ejpam-3312	351	21	and	and	CCONJ
ejpam-3312	351	22	the	the	DET
ejpam-3312	351	23	cases	case	NOUN
ejpam-3312	351	24	between	between	ADP
ejpam-3312	351	25	parenthesis	parenthesis	NOUN
ejpam-3312	351	26	can	can	AUX
ejpam-3312	351	27	be	be	AUX
ejpam-3312	351	28	made	make	VERB
ejpam-3312	351	29	similarly	similarly	ADV
ejpam-3312	351	30	.	.	PUNCT
ejpam-3312	352	1	(	(	PUNCT
ejpam-3312	352	2	i	i	NOUN
ejpam-3312	352	3	)	)	PUNCT
ejpam-3312	352	4	to	to	PART
ejpam-3312	352	5	prove	prove	VERB
ejpam-3312	352	6	the	the	DET
ejpam-3312	352	7	necessary	necessary	ADJ
ejpam-3312	352	8	condition	condition	NOUN
ejpam-3312	352	9	,	,	PUNCT
ejpam-3312	352	10	let	let	VERB
ejpam-3312	352	11	he	he	PRON
ejpam-3312	352	12	be	be	AUX
ejpam-3312	352	13	a	a	DET
ejpam-3312	352	14	soft	soft	ADJ
ejpam-3312	352	15	closed	closed	ADJ
ejpam-3312	352	16	subset	subset	NOUN
ejpam-3312	352	17	of	of	ADP
ejpam-3312	352	18	x̃	x̃	PROPN
ejpam-3312	352	19	and	and	CCONJ
ejpam-3312	352	20	consider	consider	VERB
ejpam-3312	352	21	fφ	fφ	PRON
ejpam-3312	352	22	is	be	AUX
ejpam-3312	352	23	a	a	DET
ejpam-3312	352	24	soft	soft	ADJ
ejpam-3312	352	25	iβ	iβ	ADJ
ejpam-3312	352	26	-	-	ADJ
ejpam-3312	352	27	open	open	ADJ
ejpam-3312	352	28	mapping	mapping	NOUN
ejpam-3312	352	29	.	.	PUNCT
ejpam-3312	353	1	then	then	ADV
ejpam-3312	353	2	hc	hc	PROPN
ejpam-3312	353	3	e	e	PROPN
ejpam-3312	353	4	is	be	AUX
ejpam-3312	353	5	soft	soft	ADJ
ejpam-3312	353	6	open	open	ADJ
ejpam-3312	353	7	and	and	CCONJ
ejpam-3312	353	8	fφ(hc	fφ(hc	NOUN
ejpam-3312	353	9	e	e	X
ejpam-3312	353	10	)	)	PUNCT
ejpam-3312	353	11	is	be	AUX
ejpam-3312	353	12	soft	soft	ADJ
ejpam-3312	353	13	iβ	iβ	ADJ
ejpam-3312	353	14	-	-	ADJ
ejpam-3312	353	15	open	open	ADJ
ejpam-3312	353	16	.	.	PUNCT
ejpam-3312	354	1	it	it	PRON
ejpam-3312	354	2	follows	follow	VERB
ejpam-3312	354	3	from	from	ADP
ejpam-3312	354	4	the	the	DET
ejpam-3312	354	5	bijectiveness	bijectiveness	NOUN
ejpam-3312	354	6	of	of	ADP
ejpam-3312	354	7	fφ	fφ	PROPN
ejpam-3312	354	8	,	,	PUNCT
ejpam-3312	354	9	that	that	SCONJ
ejpam-3312	354	10	fφ(hc	fφ(hc	NOUN
ejpam-3312	354	11	e	e	X
ejpam-3312	354	12	)	)	PUNCT
ejpam-3312	354	13	=	=	NOUN
ejpam-3312	355	1	[	[	X
ejpam-3312	355	2	fφ(he)]c	fφ(he)]c	NOUN
ejpam-3312	355	3	.	.	PUNCT
ejpam-3312	356	1	this	this	PRON
ejpam-3312	356	2	automatically	automatically	ADV
ejpam-3312	356	3	implies	imply	VERB
ejpam-3312	356	4	that	that	SCONJ
ejpam-3312	356	5	fφ(he	fφ(he	NOUN
ejpam-3312	356	6	)	)	PUNCT
ejpam-3312	356	7	is	be	AUX
ejpam-3312	356	8	soft	soft	ADJ
ejpam-3312	356	9	dβ	dβ	ADV
ejpam-3312	356	10	-	-	PUNCT
ejpam-3312	356	11	closed	closed	ADJ
ejpam-3312	356	12	.	.	PUNCT
ejpam-3312	357	1	thus	thus	ADV
ejpam-3312	357	2	fφ	fφ	PROPN
ejpam-3312	357	3	is	be	AUX
ejpam-3312	357	4	a	a	DET
ejpam-3312	357	5	soft	soft	ADJ
ejpam-3312	357	6	dβ	dβ	ADJ
ejpam-3312	357	7	-	-	PUNCT
ejpam-3312	357	8	closed	close	VERB
ejpam-3312	357	9	mapping	mapping	NOUN
ejpam-3312	357	10	.	.	PUNCT
ejpam-3312	358	1	in	in	ADP
ejpam-3312	358	2	a	a	DET
ejpam-3312	358	3	similar	similar	ADJ
ejpam-3312	358	4	manner	manner	NOUN
ejpam-3312	358	5	,	,	PUNCT
ejpam-3312	358	6	we	we	PRON
ejpam-3312	358	7	can	can	AUX
ejpam-3312	358	8	prove	prove	VERB
ejpam-3312	358	9	the	the	DET
ejpam-3312	358	10	sufficiency	sufficiency	NOUN
ejpam-3312	358	11	condition	condition	NOUN
ejpam-3312	358	12	.	.	PUNCT
ejpam-3312	359	1	(	(	PUNCT
ejpam-3312	359	2	ii	ii	NOUN
ejpam-3312	359	3	)	)	PUNCT
ejpam-3312	359	4	necessity	necessity	NOUN
ejpam-3312	359	5	:	:	PUNCT
ejpam-3312	359	6	let	let	VERB
ejpam-3312	359	7	ge	ge	PROPN
ejpam-3312	359	8	be	be	AUX
ejpam-3312	359	9	a	a	DET
ejpam-3312	359	10	soft	soft	ADJ
ejpam-3312	359	11	open	open	ADJ
ejpam-3312	359	12	subset	subset	NOUN
ejpam-3312	359	13	of	of	ADP
ejpam-3312	359	14	x̃	x̃	PROPN
ejpam-3312	359	15	and	and	CCONJ
ejpam-3312	359	16	consider	consider	VERB
ejpam-3312	359	17	fφ	fφ	PRON
ejpam-3312	359	18	is	be	AUX
ejpam-3312	359	19	a	a	DET
ejpam-3312	359	20	soft	soft	ADJ
ejpam-3312	359	21	iβ	iβ	ADJ
ejpam-3312	359	22	-	-	ADJ
ejpam-3312	359	23	open	open	ADJ
ejpam-3312	359	24	mapping	mapping	NOUN
ejpam-3312	359	25	.	.	PUNCT
ejpam-3312	360	1	then	then	ADV
ejpam-3312	360	2	fφ(ge	fφ(ge	PROPN
ejpam-3312	360	3	)	)	PUNCT
ejpam-3312	360	4	is	be	AUX
ejpam-3312	360	5	soft	soft	ADJ
ejpam-3312	360	6	iβ	iβ	ADJ
ejpam-3312	360	7	-	-	ADJ
ejpam-3312	360	8	open	open	ADJ
ejpam-3312	360	9	.	.	PUNCT
ejpam-3312	361	1	it	it	PRON
ejpam-3312	361	2	follows	follow	VERB
ejpam-3312	361	3	from	from	ADP
ejpam-3312	361	4	the	the	DET
ejpam-3312	361	5	bijectiveness	bijectiveness	NOUN
ejpam-3312	361	6	of	of	ADP
ejpam-3312	361	7	fφ	fφ	PROPN
ejpam-3312	361	8	,	,	PUNCT
ejpam-3312	361	9	that	that	PRON
ejpam-3312	361	10	fφ(ge	fφ(ge	NOUN
ejpam-3312	361	11	)	)	PUNCT
ejpam-3312	362	1	=	=	PRON
ejpam-3312	362	2	(	(	PUNCT
ejpam-3312	362	3	f−1φ	f−1φ	NOUN
ejpam-3312	362	4	)	)	PUNCT
ejpam-3312	362	5	−1(ge	−1(ge	NOUN
ejpam-3312	362	6	)	)	PUNCT
ejpam-3312	362	7	.	.	PUNCT
ejpam-3312	363	1	this	this	PRON
ejpam-3312	363	2	automatically	automatically	ADV
ejpam-3312	363	3	implies	imply	VERB
ejpam-3312	363	4	that	that	SCONJ
ejpam-3312	363	5	(	(	PUNCT
ejpam-3312	363	6	f−1φ	f−1φ	NOUN
ejpam-3312	363	7	)	)	PUNCT
ejpam-3312	363	8	−1(ge	−1(ge	NOUN
ejpam-3312	363	9	)	)	PUNCT
ejpam-3312	363	10	is	be	AUX
ejpam-3312	363	11	soft	soft	ADJ
ejpam-3312	363	12	iβopen	iβopen	NOUN
ejpam-3312	363	13	.	.	PUNCT
ejpam-3312	364	1	thus	thus	ADV
ejpam-3312	364	2	f−1φ	f−1φ	NOUN
ejpam-3312	364	3	is	be	AUX
ejpam-3312	364	4	a	a	DET
ejpam-3312	364	5	soft	soft	ADJ
ejpam-3312	364	6	iβ	iβ	ADJ
ejpam-3312	364	7	-	-	ADJ
ejpam-3312	364	8	continuous	continuous	ADJ
ejpam-3312	364	9	mapping	mapping	NOUN
ejpam-3312	364	10	.	.	PUNCT
ejpam-3312	365	1	in	in	ADP
ejpam-3312	365	2	a	a	DET
ejpam-3312	365	3	similar	similar	ADJ
ejpam-3312	365	4	manner	manner	NOUN
ejpam-3312	365	5	,	,	PUNCT
ejpam-3312	365	6	we	we	PRON
ejpam-3312	365	7	can	can	AUX
ejpam-3312	365	8	prove	prove	VERB
ejpam-3312	365	9	the	the	DET
ejpam-3312	365	10	sufficiency	sufficiency	NOUN
ejpam-3312	365	11	condition	condition	NOUN
ejpam-3312	365	12	.	.	PUNCT
ejpam-3312	366	1	(	(	PUNCT
ejpam-3312	366	2	iii	iii	X
ejpam-3312	366	3	)	)	PUNCT
ejpam-3312	366	4	the	the	DET
ejpam-3312	366	5	proof	proof	NOUN
ejpam-3312	366	6	of	of	ADP
ejpam-3312	366	7	this	this	DET
ejpam-3312	366	8	statement	statement	NOUN
ejpam-3312	366	9	comes	come	VERB
ejpam-3312	366	10	immediately	immediately	ADV
ejpam-3312	366	11	from	from	ADP
ejpam-3312	366	12	(	(	PUNCT
ejpam-3312	366	13	i	i	NOUN
ejpam-3312	366	14	)	)	PUNCT
ejpam-3312	366	15	and	and	CCONJ
ejpam-3312	366	16	(	(	PUNCT
ejpam-3312	366	17	ii	ii	NOUN
ejpam-3312	366	18	)	)	PUNCT
ejpam-3312	366	19	above	above	ADV
ejpam-3312	366	20	.	.	PUNCT
ejpam-3312	367	1	t.	t.	PROPN
ejpam-3312	367	2	m.	m.	PROPN
ejpam-3312	367	3	al	al	PROPN
ejpam-3312	367	4	-	-	PUNCT
ejpam-3312	367	5	shami	shami	PROPN
ejpam-3312	367	6	,	,	PUNCT
ejpam-3312	367	7	m.	m.	PROPN
ejpam-3312	367	8	e.	e.	PROPN
ejpam-3312	367	9	el	el	PROPN
ejpam-3312	367	10	-	-	PROPN
ejpam-3312	367	11	shafei	shafei	PROPN
ejpam-3312	367	12	,	,	PUNCT
ejpam-3312	367	13	b.	b.	PROPN
ejpam-3312	367	14	a.	a.	PROPN
ejpam-3312	367	15	asaad	asaad	PROPN
ejpam-3312	367	16	/	/	SYM
ejpam-3312	367	17	eur	eur	PROPN
ejpam-3312	367	18	.	.	PUNCT
ejpam-3312	368	1	j.	j.	PROPN
ejpam-3312	368	2	pure	pure	PROPN
ejpam-3312	368	3	appl	appl	PROPN
ejpam-3312	368	4	.	.	PROPN
ejpam-3312	368	5	math	math	PROPN
ejpam-3312	368	6	,	,	PUNCT
ejpam-3312	368	7	12	12	NUM
ejpam-3312	368	8	(	(	PUNCT
ejpam-3312	368	9	1	1	NUM
ejpam-3312	368	10	)	)	PUNCT
ejpam-3312	368	11	(	(	PUNCT
ejpam-3312	368	12	2019	2019	NUM
ejpam-3312	368	13	)	)	PUNCT
ejpam-3312	368	14	,	,	PUNCT
ejpam-3312	368	15	176	176	NUM
ejpam-3312	368	16	-	-	SYM
ejpam-3312	368	17	193	193	NUM
ejpam-3312	368	18	187	187	NUM
ejpam-3312	368	19	theorem	theorem	NOUN
ejpam-3312	368	20	10	10	NUM
ejpam-3312	368	21	.	.	PUNCT
ejpam-3312	369	1	let	let	VERB
ejpam-3312	369	2	θ	θ	X
ejpam-3312	369	3	?	?	PROPN
ejpam-3312	369	4	be	be	AUX
ejpam-3312	369	5	an	an	DET
ejpam-3312	369	6	extended	extended	ADJ
ejpam-3312	369	7	soft	soft	ADJ
ejpam-3312	369	8	topology	topology	NOUN
ejpam-3312	369	9	on	on	ADP
ejpam-3312	369	10	y	y	PROPN
ejpam-3312	369	11	and	and	CCONJ
ejpam-3312	369	12	φ	φ	PROPN
ejpam-3312	369	13	is	be	AUX
ejpam-3312	369	14	an	an	DET
ejpam-3312	369	15	injective	injective	ADJ
ejpam-3312	369	16	mapping	mapping	NOUN
ejpam-3312	369	17	.	.	PUNCT
ejpam-3312	370	1	then	then	ADV
ejpam-3312	370	2	a	a	DET
ejpam-3312	370	3	soft	soft	ADJ
ejpam-3312	370	4	mapping	mapping	NOUN
ejpam-3312	370	5	gφ	gφ	NOUN
ejpam-3312	370	6	:	:	PUNCT
ejpam-3312	370	7	(	(	PUNCT
ejpam-3312	370	8	x	x	X
ejpam-3312	370	9	,	,	PUNCT
ejpam-3312	370	10	τ	τ	PROPN
ejpam-3312	370	11	,	,	PUNCT
ejpam-3312	370	12	e,	e,	X
ejpam-3312	370	13	�	�	X
ejpam-3312	370	14	1	1	NUM
ejpam-3312	370	15	)	)	PUNCT
ejpam-3312	370	16	→	→	SYM
ejpam-3312	370	17	(	(	PUNCT
ejpam-3312	370	18	y	y	PROPN
ejpam-3312	370	19	,	,	PUNCT
ejpam-3312	370	20	θ	θ	PROPN
ejpam-3312	370	21	?	?	NOUN
ejpam-3312	370	22	,	,	PUNCT
ejpam-3312	370	23	f,	f,	PROPN
ejpam-3312	370	24	�	�	NOUN
ejpam-3312	370	25	2	2	NUM
ejpam-3312	370	26	)	)	PUNCT
ejpam-3312	370	27	is	be	AUX
ejpam-3312	370	28	soft	soft	ADJ
ejpam-3312	370	29	i	i	PRON
ejpam-3312	370	30	(	(	PUNCT
ejpam-3312	370	31	resp	resp	NOUN
ejpam-3312	370	32	.	.	PUNCT
ejpam-3312	371	1	soft	soft	ADJ
ejpam-3312	371	2	d	d	NOUN
ejpam-3312	371	3	,	,	PUNCT
ejpam-3312	371	4	soft	soft	ADJ
ejpam-3312	371	5	b	b	NOUN
ejpam-3312	371	6	)	)	PUNCT
ejpam-3312	371	7	β	β	X
ejpam-3312	371	8	-	-	VERB
ejpam-3312	371	9	open	open	ADJ
ejpam-3312	371	10	if	if	SCONJ
ejpam-3312	371	11	and	and	CCONJ
ejpam-3312	371	12	only	only	ADV
ejpam-3312	371	13	if	if	SCONJ
ejpam-3312	371	14	a	a	DET
ejpam-3312	371	15	mapping	mapping	NOUN
ejpam-3312	371	16	g	g	NOUN
ejpam-3312	371	17	:	:	PUNCT
ejpam-3312	371	18	(	(	PUNCT
ejpam-3312	371	19	x	x	X
ejpam-3312	371	20	,	,	PUNCT
ejpam-3312	371	21	τe,	τe,	PROPN
ejpam-3312	371	22	�	�	PROPN
ejpam-3312	371	23	1)→	1)→	NUM
ejpam-3312	371	24	(	(	PUNCT
ejpam-3312	371	25	y	y	PROPN
ejpam-3312	371	26	,	,	PUNCT
ejpam-3312	371	27	θ?φ(e),	θ?φ(e),	NOUN
ejpam-3312	371	28	�	�	NOUN
ejpam-3312	371	29	2	2	NUM
ejpam-3312	371	30	)	)	PUNCT
ejpam-3312	371	31	is	be	AUX
ejpam-3312	371	32	i	i	PRON
ejpam-3312	371	33	(	(	PUNCT
ejpam-3312	371	34	resp	resp	NOUN
ejpam-3312	371	35	.	.	PUNCT
ejpam-3312	372	1	d	d	X
ejpam-3312	372	2	,	,	PUNCT
ejpam-3312	372	3	b	b	NOUN
ejpam-3312	372	4	)	)	PUNCT
ejpam-3312	372	5	β	β	NOUN
ejpam-3312	372	6	-	-	ADJ
ejpam-3312	372	7	open	open	ADJ
ejpam-3312	372	8	.	.	PUNCT
ejpam-3312	373	1	proof	proof	NOUN
ejpam-3312	373	2	.	.	PUNCT
ejpam-3312	374	1	to	to	PART
ejpam-3312	374	2	prove	prove	VERB
ejpam-3312	374	3	the	the	DET
ejpam-3312	374	4	necessary	necessary	ADJ
ejpam-3312	374	5	part	part	NOUN
ejpam-3312	374	6	,	,	PUNCT
ejpam-3312	374	7	let	let	VERB
ejpam-3312	374	8	u	u	PRON
ejpam-3312	374	9	be	be	AUX
ejpam-3312	374	10	an	an	DET
ejpam-3312	374	11	open	open	ADJ
ejpam-3312	374	12	subset	subset	NOUN
ejpam-3312	374	13	of	of	ADP
ejpam-3312	374	14	(	(	PUNCT
ejpam-3312	374	15	x	x	PROPN
ejpam-3312	374	16	,	,	PUNCT
ejpam-3312	374	17	τe,	τe,	PROPN
ejpam-3312	374	18	�	�	PROPN
ejpam-3312	374	19	1	1	NUM
ejpam-3312	374	20	)	)	PUNCT
ejpam-3312	374	21	and	and	CCONJ
ejpam-3312	374	22	φ(e	φ(e	NUM
ejpam-3312	374	23	)	)	PUNCT
ejpam-3312	375	1	=	=	SYM
ejpam-3312	375	2	f	f	X
ejpam-3312	375	3	.	.	PUNCT
ejpam-3312	376	1	then	then	ADV
ejpam-3312	376	2	there	there	PRON
ejpam-3312	376	3	exists	exist	VERB
ejpam-3312	376	4	a	a	DET
ejpam-3312	376	5	soft	soft	ADJ
ejpam-3312	376	6	open	open	ADJ
ejpam-3312	376	7	subset	subset	NOUN
ejpam-3312	376	8	ge	ge	PROPN
ejpam-3312	376	9	of	of	ADP
ejpam-3312	376	10	(	(	PUNCT
ejpam-3312	376	11	x	x	PROPN
ejpam-3312	376	12	,	,	PUNCT
ejpam-3312	376	13	τ	τ	PROPN
ejpam-3312	376	14	,	,	PUNCT
ejpam-3312	376	15	e,	e,	X
ejpam-3312	376	16	�	�	X
ejpam-3312	376	17	1	1	NUM
ejpam-3312	376	18	)	)	PUNCT
ejpam-3312	376	19	such	such	ADJ
ejpam-3312	376	20	that	that	DET
ejpam-3312	376	21	g(e	g(e	PROPN
ejpam-3312	376	22	)	)	PUNCT
ejpam-3312	377	1	=	=	SYM
ejpam-3312	377	2	u	u	PROPN
ejpam-3312	377	3	.	.	PUNCT
ejpam-3312	378	1	since	since	SCONJ
ejpam-3312	378	2	gφ	gφ	PROPN
ejpam-3312	378	3	is	be	AUX
ejpam-3312	378	4	a	a	DET
ejpam-3312	378	5	soft	soft	ADJ
ejpam-3312	378	6	i	i	NOUN
ejpam-3312	378	7	(	(	PUNCT
ejpam-3312	378	8	resp	resp	NOUN
ejpam-3312	378	9	.	.	PUNCT
ejpam-3312	379	1	soft	soft	ADJ
ejpam-3312	379	2	d	d	NOUN
ejpam-3312	379	3	,	,	PUNCT
ejpam-3312	379	4	soft	soft	ADJ
ejpam-3312	379	5	b	b	NOUN
ejpam-3312	379	6	)	)	PUNCT
ejpam-3312	379	7	β	β	ADJ
ejpam-3312	379	8	-	-	ADJ
ejpam-3312	379	9	open	open	ADJ
ejpam-3312	379	10	mapping	mapping	NOUN
ejpam-3312	379	11	,	,	PUNCT
ejpam-3312	379	12	then	then	ADV
ejpam-3312	379	13	gφ(ge	gφ(ge	VERB
ejpam-3312	379	14	)	)	PUNCT
ejpam-3312	379	15	is	be	AUX
ejpam-3312	379	16	a	a	DET
ejpam-3312	379	17	soft	soft	ADJ
ejpam-3312	379	18	i	i	NOUN
ejpam-3312	379	19	(	(	PUNCT
ejpam-3312	379	20	resp	resp	NOUN
ejpam-3312	379	21	.	.	PUNCT
ejpam-3312	380	1	soft	soft	ADJ
ejpam-3312	380	2	d	d	NOUN
ejpam-3312	380	3	,	,	PUNCT
ejpam-3312	380	4	soft	soft	ADJ
ejpam-3312	380	5	b	b	NOUN
ejpam-3312	380	6	)	)	PUNCT
ejpam-3312	380	7	β	β	X
ejpam-3312	380	8	-	-	ADJ
ejpam-3312	380	9	open	open	ADJ
ejpam-3312	380	10	set	set	NOUN
ejpam-3312	380	11	.	.	PUNCT
ejpam-3312	381	1	from	from	ADP
ejpam-3312	381	2	definition	definition	NOUN
ejpam-3312	381	3	(	(	PUNCT
ejpam-3312	381	4	6	6	NUM
ejpam-3312	381	5	)	)	PUNCT
ejpam-3312	381	6	,	,	PUNCT
ejpam-3312	381	7	it	it	PRON
ejpam-3312	381	8	follows	follow	VERB
ejpam-3312	381	9	that	that	SCONJ
ejpam-3312	381	10	a	a	DET
ejpam-3312	381	11	soft	soft	ADJ
ejpam-3312	381	12	subset	subset	NOUN
ejpam-3312	381	13	gφ(ge	gφ(ge	NOUN
ejpam-3312	381	14	)	)	PUNCT
ejpam-3312	382	1	=	=	PRON
ejpam-3312	383	1	(	(	PUNCT
ejpam-3312	383	2	gφ(g))f	gφ(g))f	X
ejpam-3312	383	3	of	of	ADP
ejpam-3312	383	4	(	(	PUNCT
ejpam-3312	383	5	y	y	PROPN
ejpam-3312	383	6	,	,	PUNCT
ejpam-3312	383	7	θ	θ	PROPN
ejpam-3312	383	8	,	,	PUNCT
ejpam-3312	383	9	f,	f,	X
ejpam-3312	383	10	�	�	NOUN
ejpam-3312	383	11	2	2	NUM
ejpam-3312	383	12	)	)	PUNCT
ejpam-3312	383	13	is	be	AUX
ejpam-3312	383	14	given	give	VERB
ejpam-3312	383	15	by	by	ADP
ejpam-3312	383	16	gφ(g)(f	gφ(g)(f	PROPN
ejpam-3312	383	17	)	)	PUNCT
ejpam-3312	384	1	=	=	SYM
ejpam-3312	384	2	⋃	⋃	NOUN
ejpam-3312	384	3	e∈φ−1(f	e∈φ−1(f	NOUN
ejpam-3312	384	4	)	)	PUNCT
ejpam-3312	384	5	g(g(e	g(g(e	ADV
ejpam-3312	384	6	)	)	PUNCT
ejpam-3312	384	7	)	)	PUNCT
ejpam-3312	384	8	,	,	PUNCT
ejpam-3312	384	9	for	for	ADP
ejpam-3312	384	10	each	each	DET
ejpam-3312	384	11	f	f	PROPN
ejpam-3312	384	12	∈	∈	PROPN
ejpam-3312	384	13	f	f	PROPN
ejpam-3312	384	14	.	.	PUNCT
ejpam-3312	385	1	by	by	ADP
ejpam-3312	385	2	hypothesis	hypothesis	NOUN
ejpam-3312	385	3	,	,	PUNCT
ejpam-3312	385	4	θ	θ	PROPN
ejpam-3312	385	5	?	?	PROPN
ejpam-3312	385	6	is	be	AUX
ejpam-3312	385	7	an	an	DET
ejpam-3312	385	8	extended	extended	ADJ
ejpam-3312	385	9	soft	soft	ADJ
ejpam-3312	385	10	topology	topology	NOUN
ejpam-3312	385	11	on	on	ADP
ejpam-3312	385	12	y	y	PROPN
ejpam-3312	385	13	,	,	PUNCT
ejpam-3312	385	14	a	a	DET
ejpam-3312	385	15	subset	subset	NOUN
ejpam-3312	385	16	⋃	⋃	NOUN
ejpam-3312	385	17	e∈φ−1(f	e∈φ−1(f	NOUN
ejpam-3312	385	18	)	)	PUNCT
ejpam-3312	385	19	g(g(e	g(g(e	ADV
ejpam-3312	385	20	)	)	PUNCT
ejpam-3312	385	21	)	)	PUNCT
ejpam-3312	386	1	=	=	SYM
ejpam-3312	386	2	g(u	g(u	PROPN
ejpam-3312	386	3	)	)	PUNCT
ejpam-3312	386	4	of	of	ADP
ejpam-3312	386	5	(	(	PUNCT
ejpam-3312	386	6	y	y	PROPN
ejpam-3312	386	7	,	,	PUNCT
ejpam-3312	386	8	θφ(e),	θφ(e),	ADJ
ejpam-3312	386	9	�	�	NOUN
ejpam-3312	386	10	2	2	NUM
ejpam-3312	386	11	)	)	PUNCT
ejpam-3312	386	12	is	be	AUX
ejpam-3312	386	13	i	i	PRON
ejpam-3312	386	14	(	(	PUNCT
ejpam-3312	386	15	resp	resp	NOUN
ejpam-3312	386	16	.	.	PUNCT
ejpam-3312	387	1	d	d	X
ejpam-3312	387	2	,	,	PUNCT
ejpam-3312	387	3	b	b	NOUN
ejpam-3312	387	4	)	)	PUNCT
ejpam-3312	387	5	β	β	NOUN
ejpam-3312	387	6	-	-	VERB
ejpam-3312	387	7	open	open	ADJ
ejpam-3312	387	8	.	.	PUNCT
ejpam-3312	388	1	hence	hence	ADV
ejpam-3312	388	2	a	a	DET
ejpam-3312	388	3	mapping	mapping	NOUN
ejpam-3312	388	4	g	g	NOUN
ejpam-3312	388	5	is	be	AUX
ejpam-3312	388	6	i	i	PRON
ejpam-3312	388	7	(	(	PUNCT
ejpam-3312	388	8	resp	resp	NOUN
ejpam-3312	388	9	.	.	PUNCT
ejpam-3312	389	1	d	d	X
ejpam-3312	389	2	,	,	PUNCT
ejpam-3312	389	3	b	b	NOUN
ejpam-3312	389	4	)	)	PUNCT
ejpam-3312	389	5	β	β	NOUN
ejpam-3312	389	6	-	-	VERB
ejpam-3312	389	7	open	open	ADJ
ejpam-3312	389	8	.	.	PUNCT
ejpam-3312	390	1	to	to	PART
ejpam-3312	390	2	prove	prove	VERB
ejpam-3312	390	3	the	the	DET
ejpam-3312	390	4	sufficient	sufficient	ADJ
ejpam-3312	390	5	part	part	NOUN
ejpam-3312	390	6	,	,	PUNCT
ejpam-3312	390	7	let	let	VERB
ejpam-3312	390	8	ge	ge	PRON
ejpam-3312	390	9	be	be	AUX
ejpam-3312	390	10	a	a	DET
ejpam-3312	390	11	soft	soft	ADJ
ejpam-3312	390	12	open	open	ADJ
ejpam-3312	390	13	subset	subset	NOUN
ejpam-3312	390	14	of	of	ADP
ejpam-3312	390	15	(	(	PUNCT
ejpam-3312	390	16	x	x	PROPN
ejpam-3312	390	17	,	,	PUNCT
ejpam-3312	390	18	τ	τ	PROPN
ejpam-3312	390	19	,	,	PUNCT
ejpam-3312	390	20	e,	e,	X
ejpam-3312	390	21	�	�	X
ejpam-3312	390	22	1	1	NUM
ejpam-3312	390	23	)	)	PUNCT
ejpam-3312	390	24	.	.	PUNCT
ejpam-3312	391	1	then	then	ADV
ejpam-3312	391	2	from	from	ADP
ejpam-3312	391	3	definition	definition	NOUN
ejpam-3312	391	4	(	(	PUNCT
ejpam-3312	391	5	6	6	NUM
ejpam-3312	391	6	)	)	PUNCT
ejpam-3312	391	7	,	,	PUNCT
ejpam-3312	391	8	it	it	PRON
ejpam-3312	391	9	follows	follow	VERB
ejpam-3312	391	10	that	that	SCONJ
ejpam-3312	391	11	a	a	DET
ejpam-3312	391	12	soft	soft	ADJ
ejpam-3312	391	13	subset	subset	NOUN
ejpam-3312	391	14	gφ(ge	gφ(ge	NOUN
ejpam-3312	391	15	)	)	PUNCT
ejpam-3312	391	16	=	=	PRON
ejpam-3312	391	17	(	(	PUNCT
ejpam-3312	391	18	gφ(g))f	gφ(g))f	X
ejpam-3312	391	19	of	of	ADP
ejpam-3312	391	20	(	(	PUNCT
ejpam-3312	391	21	y	y	PROPN
ejpam-3312	391	22	,	,	PUNCT
ejpam-3312	391	23	θ	θ	PROPN
ejpam-3312	391	24	?	?	NOUN
ejpam-3312	391	25	,	,	PUNCT
ejpam-3312	391	26	f,	f,	PROPN
ejpam-3312	391	27	�	�	NOUN
ejpam-3312	391	28	2	2	NUM
ejpam-3312	391	29	)	)	PUNCT
ejpam-3312	391	30	is	be	AUX
ejpam-3312	391	31	given	give	VERB
ejpam-3312	391	32	by	by	ADP
ejpam-3312	391	33	gφ(g)(f	gφ(g)(f	PROPN
ejpam-3312	391	34	)	)	PUNCT
ejpam-3312	392	1	=	=	SYM
ejpam-3312	392	2	⋃	⋃	NOUN
ejpam-3312	392	3	e∈φ−1(f	e∈φ−1(f	NOUN
ejpam-3312	392	4	)	)	PUNCT
ejpam-3312	392	5	g(g(e	g(g(e	ADV
ejpam-3312	392	6	)	)	PUNCT
ejpam-3312	392	7	)	)	PUNCT
ejpam-3312	392	8	,	,	PUNCT
ejpam-3312	392	9	for	for	ADP
ejpam-3312	392	10	each	each	DET
ejpam-3312	392	11	f	f	PROPN
ejpam-3312	392	12	∈	∈	PROPN
ejpam-3312	392	13	f	f	PROPN
ejpam-3312	392	14	.	.	PUNCT
ejpam-3312	393	1	since	since	SCONJ
ejpam-3312	393	2	a	a	DET
ejpam-3312	393	3	mapping	mapping	NOUN
ejpam-3312	393	4	g	g	NOUN
ejpam-3312	393	5	is	be	AUX
ejpam-3312	393	6	i	i	PRON
ejpam-3312	393	7	(	(	PUNCT
ejpam-3312	393	8	resp	resp	NOUN
ejpam-3312	393	9	.	.	PUNCT
ejpam-3312	394	1	d	d	X
ejpam-3312	394	2	,	,	PUNCT
ejpam-3312	394	3	b	b	NOUN
ejpam-3312	394	4	)	)	PUNCT
ejpam-3312	394	5	β	β	X
ejpam-3312	394	6	-	-	NOUN
ejpam-3312	394	7	open	open	ADJ
ejpam-3312	394	8	,	,	PUNCT
ejpam-3312	394	9	then	then	ADV
ejpam-3312	394	10	a	a	DET
ejpam-3312	394	11	subset	subset	NOUN
ejpam-3312	394	12	⋃	⋃	NOUN
ejpam-3312	394	13	e∈φ−1(f	e∈φ−1(f	NOUN
ejpam-3312	394	14	)	)	PUNCT
ejpam-3312	394	15	g(g(e	g(g(e	ADV
ejpam-3312	394	16	)	)	PUNCT
ejpam-3312	394	17	)	)	PUNCT
ejpam-3312	394	18	of	of	ADP
ejpam-3312	394	19	(	(	PUNCT
ejpam-3312	394	20	y	y	PROPN
ejpam-3312	394	21	,	,	PUNCT
ejpam-3312	394	22	θ?φ(e),	θ?φ(e),	NOUN
ejpam-3312	394	23	�	�	NOUN
ejpam-3312	394	24	2	2	NUM
ejpam-3312	394	25	)	)	PUNCT
ejpam-3312	394	26	is	be	AUX
ejpam-3312	394	27	i	i	PRON
ejpam-3312	394	28	(	(	PUNCT
ejpam-3312	394	29	resp	resp	NOUN
ejpam-3312	394	30	.	.	PUNCT
ejpam-3312	395	1	d	d	X
ejpam-3312	395	2	,	,	PUNCT
ejpam-3312	395	3	b	b	NOUN
ejpam-3312	395	4	)	)	PUNCT
ejpam-3312	395	5	β	β	NOUN
ejpam-3312	395	6	-	-	VERB
ejpam-3312	395	7	open	open	ADJ
ejpam-3312	395	8	.	.	PUNCT
ejpam-3312	396	1	by	by	ADP
ejpam-3312	396	2	hypothesis	hypothesis	NOUN
ejpam-3312	396	3	,	,	PUNCT
ejpam-3312	396	4	θ	θ	PROPN
ejpam-3312	396	5	?	?	PROPN
ejpam-3312	396	6	is	be	AUX
ejpam-3312	396	7	an	an	DET
ejpam-3312	396	8	extended	extended	ADJ
ejpam-3312	396	9	soft	soft	ADJ
ejpam-3312	396	10	topology	topology	NOUN
ejpam-3312	396	11	on	on	ADP
ejpam-3312	396	12	y	y	PROPN
ejpam-3312	396	13	,	,	PUNCT
ejpam-3312	396	14	gφ(ge	gφ(ge	PROPN
ejpam-3312	396	15	)	)	PUNCT
ejpam-3312	396	16	is	be	AUX
ejpam-3312	396	17	a	a	DET
ejpam-3312	396	18	soft	soft	ADJ
ejpam-3312	396	19	i	i	NOUN
ejpam-3312	396	20	(	(	PUNCT
ejpam-3312	396	21	resp	resp	NOUN
ejpam-3312	396	22	.	.	PUNCT
ejpam-3312	397	1	soft	soft	ADJ
ejpam-3312	397	2	d	d	NOUN
ejpam-3312	397	3	,	,	PUNCT
ejpam-3312	397	4	soft	soft	ADJ
ejpam-3312	397	5	b	b	NOUN
ejpam-3312	397	6	)	)	PUNCT
ejpam-3312	397	7	β	β	X
ejpam-3312	397	8	-	-	ADJ
ejpam-3312	397	9	open	open	ADJ
ejpam-3312	397	10	subset	subset	NOUN
ejpam-3312	397	11	of	of	ADP
ejpam-3312	397	12	(	(	PUNCT
ejpam-3312	397	13	y	y	PROPN
ejpam-3312	397	14	,	,	PUNCT
ejpam-3312	397	15	θ	θ	PROPN
ejpam-3312	397	16	?	?	NOUN
ejpam-3312	397	17	,	,	PUNCT
ejpam-3312	397	18	f,	f,	PROPN
ejpam-3312	397	19	�	�	PROPN
ejpam-3312	397	20	2	2	NUM
ejpam-3312	397	21	)	)	PUNCT
ejpam-3312	397	22	.	.	PUNCT
ejpam-3312	398	1	hence	hence	ADV
ejpam-3312	398	2	a	a	DET
ejpam-3312	398	3	soft	soft	ADJ
ejpam-3312	398	4	mapping	mapping	NOUN
ejpam-3312	398	5	gφ	gφ	NOUN
ejpam-3312	398	6	is	be	AUX
ejpam-3312	398	7	soft	soft	ADJ
ejpam-3312	398	8	i	i	PRON
ejpam-3312	398	9	(	(	PUNCT
ejpam-3312	398	10	resp	resp	NOUN
ejpam-3312	398	11	.	.	PUNCT
ejpam-3312	399	1	soft	soft	ADJ
ejpam-3312	399	2	d	d	NOUN
ejpam-3312	399	3	,	,	PUNCT
ejpam-3312	399	4	soft	soft	ADJ
ejpam-3312	399	5	b	b	NOUN
ejpam-3312	399	6	)	)	PUNCT
ejpam-3312	399	7	β	β	NOUN
ejpam-3312	399	8	-	-	NOUN
ejpam-3312	399	9	open	open	ADJ
ejpam-3312	399	10	.	.	PUNCT
ejpam-3312	400	1	the	the	DET
ejpam-3312	400	2	result	result	NOUN
ejpam-3312	400	3	above	above	ADV
ejpam-3312	400	4	is	be	AUX
ejpam-3312	400	5	restated	restate	VERB
ejpam-3312	400	6	in	in	ADP
ejpam-3312	400	7	the	the	DET
ejpam-3312	400	8	case	case	NOUN
ejpam-3312	400	9	of	of	ADP
ejpam-3312	400	10	a	a	DET
ejpam-3312	400	11	soft	soft	ADJ
ejpam-3312	400	12	i	i	NOUN
ejpam-3312	400	13	(	(	PUNCT
ejpam-3312	400	14	resp	resp	NOUN
ejpam-3312	400	15	.	.	PUNCT
ejpam-3312	401	1	soft	soft	ADJ
ejpam-3312	401	2	d	d	NOUN
ejpam-3312	401	3	,	,	PUNCT
ejpam-3312	401	4	soft	soft	ADJ
ejpam-3312	401	5	b	b	NOUN
ejpam-3312	401	6	)	)	PUNCT
ejpam-3312	401	7	β	β	X
ejpam-3312	401	8	-	-	PUNCT
ejpam-3312	401	9	closed	closed	ADJ
ejpam-3312	401	10	mapping	mapping	NOUN
ejpam-3312	401	11	and	and	CCONJ
ejpam-3312	401	12	one	one	PRON
ejpam-3312	401	13	can	can	AUX
ejpam-3312	401	14	prove	prove	VERB
ejpam-3312	401	15	them	they	PRON
ejpam-3312	401	16	similarly	similarly	ADV
ejpam-3312	401	17	.	.	PUNCT
ejpam-3312	402	1	so	so	ADV
ejpam-3312	402	2	the	the	DET
ejpam-3312	402	3	proof	proof	NOUN
ejpam-3312	402	4	will	will	AUX
ejpam-3312	402	5	be	be	AUX
ejpam-3312	402	6	omitted	omit	VERB
ejpam-3312	402	7	.	.	PUNCT
ejpam-3312	403	1	theorem	theorem	VERB
ejpam-3312	403	2	11	11	NUM
ejpam-3312	403	3	.	.	PUNCT
ejpam-3312	404	1	let	let	VERB
ejpam-3312	404	2	θ	θ	X
ejpam-3312	404	3	?	?	PROPN
ejpam-3312	404	4	be	be	AUX
ejpam-3312	404	5	an	an	DET
ejpam-3312	404	6	extended	extended	ADJ
ejpam-3312	404	7	soft	soft	ADJ
ejpam-3312	404	8	topology	topology	NOUN
ejpam-3312	404	9	on	on	ADP
ejpam-3312	404	10	y	y	PROPN
ejpam-3312	404	11	and	and	CCONJ
ejpam-3312	404	12	φ	φ	PROPN
ejpam-3312	404	13	is	be	AUX
ejpam-3312	404	14	an	an	DET
ejpam-3312	404	15	injective	injective	ADJ
ejpam-3312	404	16	mapping	mapping	NOUN
ejpam-3312	404	17	.	.	PUNCT
ejpam-3312	405	1	then	then	ADV
ejpam-3312	405	2	a	a	DET
ejpam-3312	405	3	soft	soft	ADJ
ejpam-3312	405	4	mapping	mapping	NOUN
ejpam-3312	405	5	gφ	gφ	NOUN
ejpam-3312	405	6	:	:	PUNCT
ejpam-3312	405	7	(	(	PUNCT
ejpam-3312	405	8	x	x	X
ejpam-3312	405	9	,	,	PUNCT
ejpam-3312	405	10	τ	τ	PROPN
ejpam-3312	405	11	,	,	PUNCT
ejpam-3312	405	12	e,	e,	X
ejpam-3312	405	13	�	�	X
ejpam-3312	405	14	1	1	NUM
ejpam-3312	405	15	)	)	PUNCT
ejpam-3312	405	16	→	→	SYM
ejpam-3312	405	17	(	(	PUNCT
ejpam-3312	405	18	y	y	PROPN
ejpam-3312	405	19	,	,	PUNCT
ejpam-3312	405	20	θ	θ	PROPN
ejpam-3312	405	21	?	?	NOUN
ejpam-3312	405	22	,	,	PUNCT
ejpam-3312	405	23	f,	f,	PROPN
ejpam-3312	405	24	�	�	NOUN
ejpam-3312	405	25	2	2	NUM
ejpam-3312	405	26	)	)	PUNCT
ejpam-3312	405	27	is	be	AUX
ejpam-3312	405	28	soft	soft	ADJ
ejpam-3312	405	29	i	i	PRON
ejpam-3312	405	30	(	(	PUNCT
ejpam-3312	405	31	resp	resp	NOUN
ejpam-3312	405	32	.	.	PUNCT
ejpam-3312	406	1	soft	soft	ADJ
ejpam-3312	406	2	d	d	NOUN
ejpam-3312	406	3	,	,	PUNCT
ejpam-3312	406	4	soft	soft	ADJ
ejpam-3312	406	5	b	b	NOUN
ejpam-3312	406	6	)	)	PUNCT
ejpam-3312	406	7	βclosed	βclose	VERB
ejpam-3312	406	8	if	if	SCONJ
ejpam-3312	406	9	and	and	CCONJ
ejpam-3312	406	10	only	only	ADV
ejpam-3312	406	11	if	if	SCONJ
ejpam-3312	406	12	a	a	DET
ejpam-3312	406	13	mapping	mapping	NOUN
ejpam-3312	406	14	g	g	NOUN
ejpam-3312	406	15	:	:	PUNCT
ejpam-3312	406	16	(	(	PUNCT
ejpam-3312	406	17	x	x	X
ejpam-3312	406	18	,	,	PUNCT
ejpam-3312	406	19	τe,	τe,	PROPN
ejpam-3312	406	20	�	�	PROPN
ejpam-3312	406	21	1)→	1)→	NUM
ejpam-3312	406	22	(	(	PUNCT
ejpam-3312	406	23	y	y	PROPN
ejpam-3312	406	24	,	,	PUNCT
ejpam-3312	406	25	θ?φ(e),	θ?φ(e),	NOUN
ejpam-3312	406	26	�	�	NOUN
ejpam-3312	406	27	2	2	NUM
ejpam-3312	406	28	)	)	PUNCT
ejpam-3312	406	29	is	be	AUX
ejpam-3312	406	30	i	i	PRON
ejpam-3312	406	31	(	(	PUNCT
ejpam-3312	406	32	resp	resp	NOUN
ejpam-3312	406	33	.	.	PUNCT
ejpam-3312	407	1	d	d	X
ejpam-3312	407	2	,	,	PUNCT
ejpam-3312	407	3	b	b	NOUN
ejpam-3312	407	4	)	)	PUNCT
ejpam-3312	407	5	β	β	NOUN
ejpam-3312	407	6	-	-	VERB
ejpam-3312	407	7	closed	closed	ADJ
ejpam-3312	407	8	.	.	PUNCT
ejpam-3312	408	1	proposition	proposition	NOUN
ejpam-3312	408	2	4	4	NUM
ejpam-3312	408	3	.	.	PUNCT
ejpam-3312	408	4	consider	consider	VERB
ejpam-3312	408	5	τ	τ	PROPN
ejpam-3312	408	6	is	be	AUX
ejpam-3312	408	7	not	not	PART
ejpam-3312	408	8	the	the	DET
ejpam-3312	408	9	indiscrete	indiscrete	ADJ
ejpam-3312	408	10	topology	topology	NOUN
ejpam-3312	408	11	on	on	ADP
ejpam-3312	408	12	x.	x.	NOUN
ejpam-3312	408	13	if	if	SCONJ
ejpam-3312	408	14	an	an	DET
ejpam-3312	408	15	injective	injective	ADJ
ejpam-3312	408	16	soft	soft	ADJ
ejpam-3312	408	17	mapping	mapping	NOUN
ejpam-3312	408	18	fφ	fφ	NOUN
ejpam-3312	408	19	:	:	PUNCT
ejpam-3312	408	20	(	(	PUNCT
ejpam-3312	408	21	x	x	X
ejpam-3312	408	22	,	,	PUNCT
ejpam-3312	408	23	τ	τ	X
ejpam-3312	408	24	,	,	PUNCT
ejpam-3312	408	25	e	e	X
ejpam-3312	408	26	�	�	PROPN
ejpam-3312	408	27	1	1	NUM
ejpam-3312	408	28	)	)	PUNCT
ejpam-3312	408	29	→	→	SYM
ejpam-3312	408	30	(	(	PUNCT
ejpam-3312	408	31	y	y	PROPN
ejpam-3312	408	32	,	,	PUNCT
ejpam-3312	408	33	θ	θ	PROPN
ejpam-3312	408	34	,	,	PUNCT
ejpam-3312	408	35	f,	f,	X
ejpam-3312	408	36	�	�	NOUN
ejpam-3312	408	37	2	2	NUM
ejpam-3312	408	38	)	)	PUNCT
ejpam-3312	408	39	is	be	AUX
ejpam-3312	408	40	soft	soft	ADJ
ejpam-3312	408	41	bβ	bβ	NOUN
ejpam-3312	408	42	-	-	PUNCT
ejpam-3312	408	43	open	open	ADJ
ejpam-3312	408	44	or	or	CCONJ
ejpam-3312	408	45	soft	soft	ADJ
ejpam-3312	408	46	bβ	bβ	NOUN
ejpam-3312	408	47	-	-	PUNCT
ejpam-3312	408	48	closed	closed	ADJ
ejpam-3312	408	49	,	,	PUNCT
ejpam-3312	408	50	then	then	ADV
ejpam-3312	408	51	�	�	PROPN
ejpam-3312	408	52	2	2	NUM
ejpam-3312	408	53	is	be	AUX
ejpam-3312	408	54	not	not	PART
ejpam-3312	408	55	linearly	linearly	ADV
ejpam-3312	408	56	ordered	order	VERB
ejpam-3312	408	57	.	.	PUNCT
ejpam-3312	409	1	proposition	proposition	NOUN
ejpam-3312	409	2	5	5	NUM
ejpam-3312	409	3	.	.	PUNCT
ejpam-3312	410	1	let	let	VERB
ejpam-3312	410	2	fφ	fφ	VERB
ejpam-3312	410	3	:	:	PUNCT
ejpam-3312	410	4	(	(	PUNCT
ejpam-3312	410	5	x	x	X
ejpam-3312	410	6	,	,	PUNCT
ejpam-3312	410	7	τ	τ	PROPN
ejpam-3312	410	8	,	,	PUNCT
ejpam-3312	410	9	e,	e,	X
ejpam-3312	410	10	�	�	X
ejpam-3312	410	11	1)→	1)→	NUM
ejpam-3312	410	12	(	(	PUNCT
ejpam-3312	410	13	y	y	PROPN
ejpam-3312	410	14	,	,	PUNCT
ejpam-3312	410	15	θ	θ	PROPN
ejpam-3312	410	16	,	,	PUNCT
ejpam-3312	410	17	f,	f,	X
ejpam-3312	410	18	�	�	NOUN
ejpam-3312	410	19	2	2	NUM
ejpam-3312	410	20	)	)	PUNCT
ejpam-3312	410	21	and	and	CCONJ
ejpam-3312	410	22	gλ	gλ	NOUN
ejpam-3312	410	23	:	:	PUNCT
ejpam-3312	410	24	(	(	PUNCT
ejpam-3312	410	25	y	y	PROPN
ejpam-3312	410	26	,	,	PUNCT
ejpam-3312	410	27	θ	θ	PROPN
ejpam-3312	410	28	,	,	PUNCT
ejpam-3312	410	29	f,	f,	X
ejpam-3312	410	30	�	�	SYM
ejpam-3312	410	31	2)→	2)→	NUM
ejpam-3312	410	32	(	(	PUNCT
ejpam-3312	410	33	z	z	NOUN
ejpam-3312	410	34	,	,	PUNCT
ejpam-3312	410	35	υ	υ	NOUN
ejpam-3312	410	36	,	,	PUNCT
ejpam-3312	410	37	k,	k,	NOUN
ejpam-3312	410	38	�	�	X
ejpam-3312	410	39	3	3	NUM
ejpam-3312	410	40	)	)	PUNCT
ejpam-3312	410	41	be	be	AUX
ejpam-3312	410	42	two	two	NUM
ejpam-3312	410	43	soft	soft	ADJ
ejpam-3312	410	44	mappings	mapping	NOUN
ejpam-3312	410	45	.	.	PUNCT
ejpam-3312	411	1	then	then	ADV
ejpam-3312	411	2	then	then	ADV
ejpam-3312	411	3	following	follow	VERB
ejpam-3312	411	4	properties	property	NOUN
ejpam-3312	411	5	hold	hold	VERB
ejpam-3312	411	6	,	,	PUNCT
ejpam-3312	411	7	for	for	ADP
ejpam-3312	411	8	x	x	PROPN
ejpam-3312	411	9	∈	∈	PROPN
ejpam-3312	411	10	{	{	PUNCT
ejpam-3312	411	11	i	i	PROPN
ejpam-3312	411	12	,	,	PUNCT
ejpam-3312	411	13	d	d	PROPN
ejpam-3312	411	14	,	,	PUNCT
ejpam-3312	411	15	b	b	NOUN
ejpam-3312	411	16	}	}	PUNCT
ejpam-3312	411	17	.	.	PUNCT
ejpam-3312	412	1	(	(	PUNCT
ejpam-3312	412	2	i	i	NOUN
ejpam-3312	412	3	)	)	PUNCT
ejpam-3312	412	4	if	if	SCONJ
ejpam-3312	412	5	fφ	fφ	PROPN
ejpam-3312	412	6	is	be	AUX
ejpam-3312	412	7	a	a	DET
ejpam-3312	412	8	soft	soft	ADJ
ejpam-3312	412	9	xβ	xβ	NOUN
ejpam-3312	412	10	-	-	PUNCT
ejpam-3312	412	11	continuous	continuous	ADJ
ejpam-3312	412	12	mapping	mapping	NOUN
ejpam-3312	412	13	and	and	CCONJ
ejpam-3312	412	14	gλ	gλ	NOUN
ejpam-3312	412	15	is	be	AUX
ejpam-3312	412	16	a	a	DET
ejpam-3312	412	17	soft	soft	ADJ
ejpam-3312	412	18	continuous	continuous	ADJ
ejpam-3312	412	19	mapping	mapping	NOUN
ejpam-3312	412	20	,	,	PUNCT
ejpam-3312	412	21	then	then	ADV
ejpam-3312	412	22	gλ	gλ	NOUN
ejpam-3312	412	23	◦	◦	NOUN
ejpam-3312	412	24	fφ	fφ	NOUN
ejpam-3312	412	25	is	be	AUX
ejpam-3312	412	26	a	a	DET
ejpam-3312	412	27	soft	soft	ADJ
ejpam-3312	412	28	x	x	ADJ
ejpam-3312	412	29	-	-	ADJ
ejpam-3312	412	30	continuous	continuous	ADJ
ejpam-3312	412	31	mapping	mapping	NOUN
ejpam-3312	412	32	.	.	PUNCT
ejpam-3312	413	1	(	(	PUNCT
ejpam-3312	413	2	ii	ii	NOUN
ejpam-3312	413	3	)	)	PUNCT
ejpam-3312	413	4	if	if	SCONJ
ejpam-3312	413	5	fφ	fφ	PROPN
ejpam-3312	413	6	is	be	AUX
ejpam-3312	413	7	a	a	DET
ejpam-3312	413	8	soft	soft	ADJ
ejpam-3312	413	9	open	open	ADJ
ejpam-3312	413	10	(	(	PUNCT
ejpam-3312	413	11	resp	resp	NOUN
ejpam-3312	413	12	.	.	PUNCT
ejpam-3312	414	1	soft	soft	ADJ
ejpam-3312	414	2	closed	closed	ADJ
ejpam-3312	414	3	)	)	PUNCT
ejpam-3312	414	4	mapping	mapping	NOUN
ejpam-3312	414	5	and	and	CCONJ
ejpam-3312	414	6	gλ	gλ	NOUN
ejpam-3312	414	7	is	be	AUX
ejpam-3312	414	8	a	a	DET
ejpam-3312	414	9	soft	soft	ADJ
ejpam-3312	414	10	xβ	xβ	NOUN
ejpam-3312	414	11	-	-	PUNCT
ejpam-3312	414	12	open	open	ADJ
ejpam-3312	414	13	(	(	PUNCT
ejpam-3312	414	14	resp	resp	NOUN
ejpam-3312	414	15	.	.	PUNCT
ejpam-3312	415	1	xβclosed	xβclose	VERB
ejpam-3312	415	2	)	)	PUNCT
ejpam-3312	416	1	mapping	mapping	NOUN
ejpam-3312	416	2	,	,	PUNCT
ejpam-3312	416	3	then	then	ADV
ejpam-3312	416	4	gλ	gλ	VERB
ejpam-3312	416	5	◦	◦	NOUN
ejpam-3312	416	6	fφ	fφ	NOUN
ejpam-3312	416	7	is	be	AUX
ejpam-3312	416	8	a	a	DET
ejpam-3312	416	9	soft	soft	ADJ
ejpam-3312	416	10	x	x	NOUN
ejpam-3312	416	11	-	-	ADJ
ejpam-3312	416	12	open	open	ADJ
ejpam-3312	416	13	(	(	PUNCT
ejpam-3312	416	14	resp	resp	NOUN
ejpam-3312	416	15	.	.	PUNCT
ejpam-3312	417	1	xβ	xβ	NOUN
ejpam-3312	417	2	-	-	PUNCT
ejpam-3312	417	3	closed	closed	ADJ
ejpam-3312	417	4	)	)	PUNCT
ejpam-3312	417	5	mapping	mapping	NOUN
ejpam-3312	417	6	.	.	PUNCT
ejpam-3312	418	1	(	(	PUNCT
ejpam-3312	418	2	iii	iii	X
ejpam-3312	418	3	)	)	PUNCT
ejpam-3312	418	4	if	if	SCONJ
ejpam-3312	418	5	gλ	gλ	NOUN
ejpam-3312	418	6	◦	◦	VERB
ejpam-3312	418	7	fφ	fφ	NOUN
ejpam-3312	418	8	is	be	AUX
ejpam-3312	418	9	a	a	DET
ejpam-3312	418	10	soft	soft	ADJ
ejpam-3312	418	11	x	x	ADJ
ejpam-3312	418	12	-	-	ADJ
ejpam-3312	418	13	open	open	ADJ
ejpam-3312	418	14	mapping	mapping	NOUN
ejpam-3312	418	15	and	and	CCONJ
ejpam-3312	418	16	fφ	fφ	PROPN
ejpam-3312	418	17	is	be	AUX
ejpam-3312	418	18	surjective	surjective	ADJ
ejpam-3312	418	19	soft	soft	ADJ
ejpam-3312	418	20	continuous	continuous	ADJ
ejpam-3312	418	21	,	,	PUNCT
ejpam-3312	418	22	then	then	ADV
ejpam-3312	418	23	gλ	gλ	NOUN
ejpam-3312	418	24	is	be	AUX
ejpam-3312	418	25	a	a	DET
ejpam-3312	418	26	soft	soft	ADJ
ejpam-3312	418	27	x	x	ADJ
ejpam-3312	418	28	-	-	ADJ
ejpam-3312	418	29	open	open	ADJ
ejpam-3312	418	30	mapping	mapping	NOUN
ejpam-3312	418	31	.	.	PUNCT
ejpam-3312	419	1	(	(	PUNCT
ejpam-3312	419	2	iv	iv	X
ejpam-3312	419	3	)	)	PUNCT
ejpam-3312	419	4	if	if	SCONJ
ejpam-3312	419	5	gλ	gλ	NOUN
ejpam-3312	419	6	◦	◦	VERB
ejpam-3312	419	7	fφ	fφ	NOUN
ejpam-3312	419	8	is	be	AUX
ejpam-3312	419	9	a	a	DET
ejpam-3312	419	10	soft	soft	ADJ
ejpam-3312	419	11	closed	closed	ADJ
ejpam-3312	419	12	mapping	mapping	NOUN
ejpam-3312	419	13	and	and	CCONJ
ejpam-3312	419	14	gλ	gλ	NOUN
ejpam-3312	419	15	is	be	AUX
ejpam-3312	419	16	an	an	DET
ejpam-3312	419	17	injective	injective	ADJ
ejpam-3312	419	18	soft	soft	ADJ
ejpam-3312	419	19	x	x	ADJ
ejpam-3312	419	20	-	-	ADJ
ejpam-3312	419	21	continuous	continuous	ADJ
ejpam-3312	419	22	mapping	mapping	NOUN
ejpam-3312	419	23	,	,	PUNCT
ejpam-3312	419	24	then	then	ADV
ejpam-3312	419	25	fφ	fφ	PROPN
ejpam-3312	419	26	is	be	AUX
ejpam-3312	419	27	a	a	DET
ejpam-3312	419	28	soft	soft	ADJ
ejpam-3312	419	29	y	y	NOUN
ejpam-3312	419	30	-	-	PUNCT
ejpam-3312	419	31	closed	close	VERB
ejpam-3312	419	32	mapping	mapping	NOUN
ejpam-3312	419	33	,	,	PUNCT
ejpam-3312	419	34	where	where	SCONJ
ejpam-3312	419	35	(	(	PUNCT
ejpam-3312	419	36	x	x	NOUN
ejpam-3312	419	37	,	,	PUNCT
ejpam-3312	419	38	y	y	NOUN
ejpam-3312	419	39	)	)	PUNCT
ejpam-3312	419	40	∈	∈	NOUN
ejpam-3312	419	41	{	{	PUNCT
ejpam-3312	419	42	(	(	PUNCT
ejpam-3312	419	43	i	i	NOUN
ejpam-3312	419	44	,	,	PUNCT
ejpam-3312	419	45	d	d	PROPN
ejpam-3312	419	46	)	)	PUNCT
ejpam-3312	419	47	,	,	PUNCT
ejpam-3312	419	48	(	(	PUNCT
ejpam-3312	419	49	d	d	X
ejpam-3312	419	50	,	,	PUNCT
ejpam-3312	419	51	i	i	NOUN
ejpam-3312	419	52	)	)	PUNCT
ejpam-3312	419	53	,	,	PUNCT
ejpam-3312	419	54	(	(	PUNCT
ejpam-3312	419	55	b	b	X
ejpam-3312	419	56	,	,	PUNCT
ejpam-3312	419	57	b	b	NOUN
ejpam-3312	419	58	)	)	PUNCT
ejpam-3312	419	59	}	}	PUNCT
ejpam-3312	419	60	.	.	PUNCT
ejpam-3312	420	1	t.	t.	PROPN
ejpam-3312	420	2	m.	m.	PROPN
ejpam-3312	420	3	al	al	PROPN
ejpam-3312	420	4	-	-	PUNCT
ejpam-3312	420	5	shami	shami	PROPN
ejpam-3312	420	6	,	,	PUNCT
ejpam-3312	420	7	m.	m.	PROPN
ejpam-3312	420	8	e.	e.	PROPN
ejpam-3312	420	9	el	el	PROPN
ejpam-3312	420	10	-	-	PROPN
ejpam-3312	420	11	shafei	shafei	PROPN
ejpam-3312	420	12	,	,	PUNCT
ejpam-3312	420	13	b.	b.	PROPN
ejpam-3312	420	14	a.	a.	PROPN
ejpam-3312	420	15	asaad	asaad	PROPN
ejpam-3312	420	16	/	/	SYM
ejpam-3312	420	17	eur	eur	PROPN
ejpam-3312	420	18	.	.	PUNCT
ejpam-3312	421	1	j.	j.	PROPN
ejpam-3312	421	2	pure	pure	PROPN
ejpam-3312	421	3	appl	appl	PROPN
ejpam-3312	421	4	.	.	PROPN
ejpam-3312	421	5	math	math	PROPN
ejpam-3312	421	6	,	,	PUNCT
ejpam-3312	421	7	12	12	NUM
ejpam-3312	421	8	(	(	PUNCT
ejpam-3312	421	9	1	1	NUM
ejpam-3312	421	10	)	)	PUNCT
ejpam-3312	421	11	(	(	PUNCT
ejpam-3312	421	12	2019	2019	NUM
ejpam-3312	421	13	)	)	PUNCT
ejpam-3312	421	14	,	,	PUNCT
ejpam-3312	421	15	176	176	NUM
ejpam-3312	421	16	-	-	SYM
ejpam-3312	421	17	193	193	NUM
ejpam-3312	421	18	188	188	NUM
ejpam-3312	421	19	5	5	NUM
ejpam-3312	421	20	.	.	PUNCT
ejpam-3312	421	21	soft	soft	ADJ
ejpam-3312	421	22	i(d	i(d	NOUN
ejpam-3312	421	23	,	,	PUNCT
ejpam-3312	421	24	b)β	b)β	NOUN
ejpam-3312	421	25	-	-	PUNCT
ejpam-3312	421	26	homeomorphism	homeomorphism	VERB
ejpam-3312	421	27	the	the	DET
ejpam-3312	421	28	concepts	concept	NOUN
ejpam-3312	421	29	of	of	ADP
ejpam-3312	421	30	soft	soft	ADJ
ejpam-3312	421	31	i(d	i(d	NOUN
ejpam-3312	421	32	,	,	PUNCT
ejpam-3312	421	33	b)-homeomorphism	b)-homeomorphism	NOUN
ejpam-3312	421	34	mappings	mapping	NOUN
ejpam-3312	421	35	are	be	AUX
ejpam-3312	421	36	established	establish	VERB
ejpam-3312	421	37	and	and	CCONJ
ejpam-3312	421	38	their	their	PRON
ejpam-3312	421	39	main	main	ADJ
ejpam-3312	421	40	properties	property	NOUN
ejpam-3312	421	41	are	be	AUX
ejpam-3312	421	42	discussed	discuss	VERB
ejpam-3312	421	43	.	.	PUNCT
ejpam-3312	422	1	illustrative	illustrative	ADJ
ejpam-3312	422	2	examples	example	NOUN
ejpam-3312	422	3	are	be	AUX
ejpam-3312	422	4	provided	provide	VERB
ejpam-3312	422	5	to	to	PART
ejpam-3312	422	6	show	show	VERB
ejpam-3312	422	7	the	the	DET
ejpam-3312	422	8	relationships	relationship	NOUN
ejpam-3312	422	9	among	among	ADP
ejpam-3312	422	10	them	they	PRON
ejpam-3312	422	11	.	.	PUNCT
ejpam-3312	423	1	definition	definition	NOUN
ejpam-3312	423	2	22	22	NUM
ejpam-3312	423	3	.	.	PUNCT
ejpam-3312	424	1	a	a	DET
ejpam-3312	424	2	bijective	bijective	ADJ
ejpam-3312	424	3	soft	soft	ADJ
ejpam-3312	424	4	mapping	mapping	NOUN
ejpam-3312	424	5	gφ	gφ	NOUN
ejpam-3312	424	6	:	:	PUNCT
ejpam-3312	424	7	(	(	PUNCT
ejpam-3312	424	8	x	x	X
ejpam-3312	424	9	,	,	PUNCT
ejpam-3312	424	10	τ	τ	PROPN
ejpam-3312	424	11	,	,	PUNCT
ejpam-3312	424	12	e,	e,	X
ejpam-3312	424	13	�	�	X
ejpam-3312	424	14	1	1	NUM
ejpam-3312	424	15	)	)	PUNCT
ejpam-3312	424	16	→	→	SYM
ejpam-3312	424	17	(	(	PUNCT
ejpam-3312	424	18	y	y	PROPN
ejpam-3312	424	19	,	,	PUNCT
ejpam-3312	424	20	θ	θ	PROPN
ejpam-3312	424	21	,	,	PUNCT
ejpam-3312	424	22	f,	f,	X
ejpam-3312	424	23	�	�	NOUN
ejpam-3312	424	24	2	2	NUM
ejpam-3312	424	25	)	)	PUNCT
ejpam-3312	424	26	is	be	AUX
ejpam-3312	424	27	called	call	VERB
ejpam-3312	424	28	soft	soft	ADJ
ejpam-3312	424	29	i	i	PRON
ejpam-3312	424	30	(	(	PUNCT
ejpam-3312	424	31	resp	resp	NOUN
ejpam-3312	424	32	.	.	PUNCT
ejpam-3312	425	1	soft	soft	ADJ
ejpam-3312	425	2	d	d	NOUN
ejpam-3312	425	3	,	,	PUNCT
ejpam-3312	425	4	soft	soft	ADJ
ejpam-3312	425	5	b	b	NOUN
ejpam-3312	425	6	)	)	PUNCT
ejpam-3312	425	7	β	β	NOUN
ejpam-3312	425	8	-	-	PUNCT
ejpam-3312	425	9	homeomorphism	homeomorphism	X
ejpam-3312	425	10	if	if	SCONJ
ejpam-3312	425	11	it	it	PRON
ejpam-3312	425	12	is	be	AUX
ejpam-3312	425	13	soft	soft	ADJ
ejpam-3312	425	14	iβ	iβ	ADP
ejpam-3312	425	15	-	-	ADJ
ejpam-3312	425	16	continuous	continuous	ADJ
ejpam-3312	425	17	and	and	CCONJ
ejpam-3312	425	18	soft	soft	ADJ
ejpam-3312	425	19	iβ	iβ	ADJ
ejpam-3312	425	20	-	-	ADJ
ejpam-3312	425	21	open	open	ADJ
ejpam-3312	425	22	(	(	PUNCT
ejpam-3312	425	23	resp	resp	NOUN
ejpam-3312	425	24	.	.	PUNCT
ejpam-3312	426	1	soft	soft	ADJ
ejpam-3312	426	2	dβ	dβ	ADJ
ejpam-3312	426	3	-	-	PUNCT
ejpam-3312	426	4	continuous	continuous	ADJ
ejpam-3312	426	5	and	and	CCONJ
ejpam-3312	426	6	soft	soft	ADJ
ejpam-3312	426	7	dβ	dβ	ADJ
ejpam-3312	426	8	-	-	PUNCT
ejpam-3312	426	9	open	open	ADJ
ejpam-3312	426	10	,	,	PUNCT
ejpam-3312	426	11	soft	soft	ADJ
ejpam-3312	426	12	bβ	bβ	NOUN
ejpam-3312	426	13	-	-	PUNCT
ejpam-3312	426	14	continuous	continuous	ADJ
ejpam-3312	426	15	and	and	CCONJ
ejpam-3312	426	16	soft	soft	ADJ
ejpam-3312	426	17	bβ	bβ	NOUN
ejpam-3312	426	18	-	-	PUNCT
ejpam-3312	426	19	open	open	ADJ
ejpam-3312	426	20	)	)	PUNCT
ejpam-3312	426	21	.	.	PUNCT
ejpam-3312	426	22	remark	remark	PROPN
ejpam-3312	426	23	4	4	NUM
ejpam-3312	426	24	.	.	PUNCT
ejpam-3312	427	1	from	from	ADP
ejpam-3312	427	2	definition	definition	NOUN
ejpam-3312	427	3	(	(	PUNCT
ejpam-3312	427	4	22	22	NUM
ejpam-3312	427	5	)	)	PUNCT
ejpam-3312	427	6	,	,	PUNCT
ejpam-3312	427	7	we	we	PRON
ejpam-3312	427	8	can	can	AUX
ejpam-3312	427	9	note	note	VERB
ejpam-3312	427	10	the	the	DET
ejpam-3312	427	11	following	following	NOUN
ejpam-3312	427	12	:	:	PUNCT
ejpam-3312	427	13	(	(	PUNCT
ejpam-3312	427	14	i	i	NOUN
ejpam-3312	427	15	)	)	PUNCT
ejpam-3312	427	16	every	every	PRON
ejpam-3312	427	17	soft	soft	ADJ
ejpam-3312	427	18	i	i	PRON
ejpam-3312	427	19	(	(	PUNCT
ejpam-3312	427	20	soft	soft	ADJ
ejpam-3312	427	21	d	d	NOUN
ejpam-3312	427	22	,	,	PUNCT
ejpam-3312	427	23	soft	soft	ADJ
ejpam-3312	427	24	b	b	NOUN
ejpam-3312	427	25	)	)	PUNCT
ejpam-3312	427	26	β	β	NOUN
ejpam-3312	427	27	-	-	PUNCT
ejpam-3312	427	28	homeomorphism	homeomorphism	ADJ
ejpam-3312	427	29	mapping	mapping	NOUN
ejpam-3312	427	30	is	be	AUX
ejpam-3312	427	31	soft	soft	ADJ
ejpam-3312	427	32	β	β	NOUN
ejpam-3312	427	33	-	-	NOUN
ejpam-3312	427	34	homeomorphism	homeomorphism	X
ejpam-3312	427	35	.	.	PUNCT
ejpam-3312	428	1	(	(	PUNCT
ejpam-3312	428	2	ii	ii	NOUN
ejpam-3312	428	3	)	)	PUNCT
ejpam-3312	428	4	every	every	DET
ejpam-3312	428	5	soft	soft	ADJ
ejpam-3312	428	6	bβ	bβ	NOUN
ejpam-3312	428	7	-	-	PUNCT
ejpam-3312	428	8	homeomorphism	homeomorphism	NOUN
ejpam-3312	428	9	mapping	mapping	NOUN
ejpam-3312	428	10	is	be	AUX
ejpam-3312	428	11	soft	soft	ADJ
ejpam-3312	428	12	iβ	iβ	NOUN
ejpam-3312	428	13	-	-	PUNCT
ejpam-3312	428	14	homeomorphism	homeomorphism	NOUN
ejpam-3312	428	15	or	or	CCONJ
ejpam-3312	428	16	soft	soft	ADJ
ejpam-3312	428	17	dβ	dβ	NOUN
ejpam-3312	428	18	-	-	PUNCT
ejpam-3312	428	19	homeomorphism	homeomorphism	NOUN
ejpam-3312	428	20	.	.	PUNCT
ejpam-3312	429	1	the	the	DET
ejpam-3312	429	2	two	two	NUM
ejpam-3312	429	3	items	item	NOUN
ejpam-3312	429	4	of	of	ADP
ejpam-3312	429	5	the	the	DET
ejpam-3312	429	6	remark	remark	NOUN
ejpam-3312	429	7	above	above	ADV
ejpam-3312	429	8	are	be	AUX
ejpam-3312	429	9	not	not	PART
ejpam-3312	429	10	conversely	conversely	ADV
ejpam-3312	429	11	as	as	SCONJ
ejpam-3312	429	12	the	the	DET
ejpam-3312	429	13	following	follow	VERB
ejpam-3312	429	14	examples	example	NOUN
ejpam-3312	429	15	show	show	NOUN
ejpam-3312	429	16	.	.	PUNCT
ejpam-3312	430	1	example	example	NOUN
ejpam-3312	431	1	5	5	NUM
ejpam-3312	431	2	.	.	PUNCT
ejpam-3312	431	3	let	let	VERB
ejpam-3312	431	4	x	x	PUNCT
ejpam-3312	431	5	=	=	PRON
ejpam-3312	431	6	{	{	PUNCT
ejpam-3312	431	7	u	u	NOUN
ejpam-3312	431	8	,	,	PUNCT
ejpam-3312	431	9	v	v	NOUN
ejpam-3312	431	10	,	,	PUNCT
ejpam-3312	431	11	w	w	PROPN
ejpam-3312	431	12	,	,	PUNCT
ejpam-3312	431	13	x	x	NOUN
ejpam-3312	431	14	,	,	PUNCT
ejpam-3312	431	15	y	y	PROPN
ejpam-3312	431	16	,	,	PUNCT
ejpam-3312	431	17	z	z	NOUN
ejpam-3312	431	18	}	}	PUNCT
ejpam-3312	431	19	be	be	AUX
ejpam-3312	431	20	an	an	DET
ejpam-3312	431	21	universe	universe	NOUN
ejpam-3312	431	22	set	set	NOUN
ejpam-3312	431	23	and	and	CCONJ
ejpam-3312	431	24	a	a	DET
ejpam-3312	431	25	=	=	X
ejpam-3312	431	26	{	{	PUNCT
ejpam-3312	431	27	a1	a1	PROPN
ejpam-3312	431	28	,	,	PUNCT
ejpam-3312	431	29	a2	a2	PROPN
ejpam-3312	431	30	}	}	PUNCT
ejpam-3312	431	31	be	be	VERB
ejpam-3312	431	32	a	a	DET
ejpam-3312	431	33	parameters	parameter	NOUN
ejpam-3312	431	34	set	set	VERB
ejpam-3312	431	35	.	.	PUNCT
ejpam-3312	432	1	consider	consider	VERB
ejpam-3312	432	2	φ	φ	PROPN
ejpam-3312	432	3	:	:	PUNCT
ejpam-3312	432	4	a→	a→	PUNCT
ejpam-3312	432	5	a	a	PRON
ejpam-3312	432	6	and	and	CCONJ
ejpam-3312	432	7	f	f	NOUN
ejpam-3312	432	8	:	:	PUNCT
ejpam-3312	432	9	x	x	X
ejpam-3312	432	10	→	→	PUNCT
ejpam-3312	432	11	x	x	SYM
ejpam-3312	432	12	are	be	AUX
ejpam-3312	432	13	both	both	PRON
ejpam-3312	432	14	identity	identity	NOUN
ejpam-3312	432	15	mappings	mapping	NOUN
ejpam-3312	432	16	.	.	PUNCT
ejpam-3312	433	1	we	we	PRON
ejpam-3312	433	2	define	define	VERB
ejpam-3312	433	3	two	two	NUM
ejpam-3312	433	4	partial	partial	ADJ
ejpam-3312	433	5	order	order	NOUN
ejpam-3312	433	6	relations	relation	NOUN
ejpam-3312	433	7	on	on	ADP
ejpam-3312	433	8	x	x	PUNCT
ejpam-3312	433	9	and	and	CCONJ
ejpam-3312	433	10	y	y	PROPN
ejpam-3312	433	11	,	,	PUNCT
ejpam-3312	433	12	respectively	respectively	ADV
ejpam-3312	433	13	,	,	PUNCT
ejpam-3312	433	14	as	as	ADP
ejpam-3312	433	15	�	�	X
ejpam-3312	433	16	1=	1=	X
ejpam-3312	433	17	4	4	NUM
ejpam-3312	433	18	⋃	⋃	NOUN
ejpam-3312	433	19	{	{	PUNCT
ejpam-3312	433	20	(	(	PUNCT
ejpam-3312	433	21	w	w	PROPN
ejpam-3312	433	22	,	,	PUNCT
ejpam-3312	433	23	v	v	NOUN
ejpam-3312	433	24	)	)	PUNCT
ejpam-3312	433	25	}	}	PUNCT
ejpam-3312	433	26	and	and	CCONJ
ejpam-3312	433	27	�	�	PRON
ejpam-3312	433	28	2=	2=	NUM
ejpam-3312	433	29	4	4	NUM
ejpam-3312	433	30	⋃	⋃	NOUN
ejpam-3312	433	31	{	{	PUNCT
ejpam-3312	433	32	(	(	PUNCT
ejpam-3312	433	33	z	z	NOUN
ejpam-3312	433	34	,	,	PUNCT
ejpam-3312	433	35	x	x	NOUN
ejpam-3312	433	36	)	)	PUNCT
ejpam-3312	433	37	}	}	PUNCT
ejpam-3312	433	38	and	and	CCONJ
ejpam-3312	433	39	we	we	PRON
ejpam-3312	433	40	define	define	VERB
ejpam-3312	433	41	two	two	NUM
ejpam-3312	433	42	soft	soft	ADJ
ejpam-3312	433	43	topologies	topology	NOUN
ejpam-3312	433	44	τ	τ	X
ejpam-3312	433	45	and	and	CCONJ
ejpam-3312	433	46	θ	θ	PROPN
ejpam-3312	433	47	on	on	ADP
ejpam-3312	433	48	x	x	X
ejpam-3312	433	49	and	and	CCONJ
ejpam-3312	433	50	y	y	PROPN
ejpam-3312	433	51	,	,	PUNCT
ejpam-3312	433	52	respectively	respectively	ADV
ejpam-3312	433	53	,	,	PUNCT
ejpam-3312	433	54	as	as	ADP
ejpam-3312	433	55	τ	τ	X
ejpam-3312	433	56	=	=	SYM
ejpam-3312	433	57	{	{	PUNCT
ejpam-3312	433	58	∅̃	∅̃	NOUN
ejpam-3312	433	59	,	,	PUNCT
ejpam-3312	433	60	x̃	x̃	PROPN
ejpam-3312	433	61	,	,	PUNCT
ejpam-3312	433	62	fa	fa	PROPN
ejpam-3312	433	63	,	,	PUNCT
ejpam-3312	433	64	ga	ga	PROPN
ejpam-3312	433	65	,	,	PUNCT
ejpam-3312	433	66	ha	ha	INTJ
ejpam-3312	433	67	}	}	PUNCT
ejpam-3312	433	68	and	and	CCONJ
ejpam-3312	433	69	θ	θ	PROPN
ejpam-3312	433	70	=	=	SYM
ejpam-3312	433	71	{	{	PUNCT
ejpam-3312	433	72	∅̃	∅̃	NOUN
ejpam-3312	433	73	,	,	PUNCT
ejpam-3312	433	74	ỹ	ỹ	PROPN
ejpam-3312	433	75	,	,	PUNCT
ejpam-3312	433	76	la	la	PROPN
ejpam-3312	433	77	}	}	PUNCT
ejpam-3312	433	78	,	,	PUNCT
ejpam-3312	433	79	where	where	SCONJ
ejpam-3312	433	80	fa	fa	PROPN
ejpam-3312	433	81	=	=	SYM
ejpam-3312	433	82	{	{	PUNCT
ejpam-3312	433	83	(	(	PUNCT
ejpam-3312	433	84	a1	a1	NOUN
ejpam-3312	433	85	,	,	PUNCT
ejpam-3312	433	86	x	x	NOUN
ejpam-3312	433	87	)	)	PUNCT
ejpam-3312	433	88	,	,	PUNCT
ejpam-3312	433	89	(	(	PUNCT
ejpam-3312	433	90	a2	a2	PROPN
ejpam-3312	433	91	,	,	PUNCT
ejpam-3312	433	92	{	{	PUNCT
ejpam-3312	433	93	w	w	PROPN
ejpam-3312	433	94	,	,	PUNCT
ejpam-3312	433	95	z	z	NOUN
ejpam-3312	433	96	}	}	PUNCT
ejpam-3312	433	97	)	)	PUNCT
ejpam-3312	433	98	}	}	PUNCT
ejpam-3312	433	99	,	,	PUNCT
ejpam-3312	433	100	ga	ga	PROPN
ejpam-3312	433	101	=	=	PRON
ejpam-3312	433	102	{	{	PUNCT
ejpam-3312	433	103	(	(	PUNCT
ejpam-3312	433	104	a1	a1	NOUN
ejpam-3312	433	105	,	,	PUNCT
ejpam-3312	433	106	{	{	PUNCT
ejpam-3312	433	107	u	u	NOUN
ejpam-3312	433	108	,	,	PUNCT
ejpam-3312	433	109	v	v	NOUN
ejpam-3312	433	110	}	}	PUNCT
ejpam-3312	433	111	)	)	PUNCT
ejpam-3312	433	112	,	,	PUNCT
ejpam-3312	433	113	(	(	PUNCT
ejpam-3312	433	114	a2	a2	PROPN
ejpam-3312	433	115	,	,	PUNCT
ejpam-3312	433	116	x	x	NOUN
ejpam-3312	433	117	)	)	PUNCT
ejpam-3312	433	118	}	}	PUNCT
ejpam-3312	433	119	,	,	PUNCT
ejpam-3312	433	120	ha	ha	INTJ
ejpam-3312	433	121	=	=	SYM
ejpam-3312	433	122	{	{	PUNCT
ejpam-3312	433	123	(	(	PUNCT
ejpam-3312	433	124	a1	a1	NOUN
ejpam-3312	433	125	,	,	PUNCT
ejpam-3312	433	126	{	{	PUNCT
ejpam-3312	433	127	u	u	NOUN
ejpam-3312	433	128	,	,	PUNCT
ejpam-3312	433	129	v	v	NOUN
ejpam-3312	433	130	}	}	PUNCT
ejpam-3312	433	131	)	)	PUNCT
ejpam-3312	433	132	,	,	PUNCT
ejpam-3312	433	133	(	(	PUNCT
ejpam-3312	433	134	a2	a2	PROPN
ejpam-3312	433	135	,	,	PUNCT
ejpam-3312	433	136	{	{	PUNCT
ejpam-3312	433	137	w	w	PROPN
ejpam-3312	433	138	,	,	PUNCT
ejpam-3312	433	139	z	z	NOUN
ejpam-3312	433	140	}	}	PUNCT
ejpam-3312	433	141	)	)	PUNCT
ejpam-3312	433	142	}	}	PUNCT
ejpam-3312	433	143	and	and	CCONJ
ejpam-3312	433	144	la	la	NOUN
ejpam-3312	433	145	=	=	SYM
ejpam-3312	433	146	{	{	PUNCT
ejpam-3312	433	147	(	(	PUNCT
ejpam-3312	433	148	a1	a1	NOUN
ejpam-3312	433	149	,	,	PUNCT
ejpam-3312	433	150	{	{	PUNCT
ejpam-3312	433	151	u	u	NOUN
ejpam-3312	433	152	,	,	PUNCT
ejpam-3312	433	153	z	z	NOUN
ejpam-3312	433	154	}	}	PUNCT
ejpam-3312	433	155	)	)	PUNCT
ejpam-3312	433	156	,	,	PUNCT
ejpam-3312	433	157	(	(	PUNCT
ejpam-3312	433	158	a2	a2	PROPN
ejpam-3312	433	159	,	,	PUNCT
ejpam-3312	433	160	{	{	PUNCT
ejpam-3312	433	161	v	v	NOUN
ejpam-3312	433	162	}	}	PUNCT
ejpam-3312	433	163	)	)	PUNCT
ejpam-3312	433	164	}	}	PUNCT
ejpam-3312	433	165	.	.	PUNCT
ejpam-3312	434	1	then	then	ADV
ejpam-3312	434	2	one	one	PRON
ejpam-3312	434	3	can	can	AUX
ejpam-3312	434	4	readily	readily	ADV
ejpam-3312	434	5	check	check	VERB
ejpam-3312	434	6	that	that	SCONJ
ejpam-3312	434	7	a	a	DET
ejpam-3312	434	8	soft	soft	ADJ
ejpam-3312	434	9	mapping	mapping	NOUN
ejpam-3312	434	10	fφ	fφ	NOUN
ejpam-3312	434	11	:	:	PUNCT
ejpam-3312	434	12	s(xa	s(xa	PROPN
ejpam-3312	434	13	)	)	PUNCT
ejpam-3312	434	14	→	→	SYM
ejpam-3312	434	15	s(yb	s(yb	NUM
ejpam-3312	434	16	)	)	PUNCT
ejpam-3312	434	17	is	be	AUX
ejpam-3312	434	18	soft	soft	ADJ
ejpam-3312	434	19	β	β	NOUN
ejpam-3312	434	20	-	-	NOUN
ejpam-3312	434	21	homeomorphism	homeomorphism	NOUN
ejpam-3312	434	22	.	.	PUNCT
ejpam-3312	435	1	on	on	ADP
ejpam-3312	435	2	the	the	DET
ejpam-3312	435	3	other	other	ADJ
ejpam-3312	435	4	hand	hand	NOUN
ejpam-3312	435	5	,	,	PUNCT
ejpam-3312	435	6	fφ(fa	fφ(fa	PROPN
ejpam-3312	435	7	)	)	PUNCT
ejpam-3312	436	1	=	=	SYM
ejpam-3312	436	2	fa	fa	PROPN
ejpam-3312	436	3	is	be	AUX
ejpam-3312	436	4	not	not	PART
ejpam-3312	436	5	a	a	DET
ejpam-3312	436	6	soft	soft	ADJ
ejpam-3312	436	7	iβ	iβ	ADJ
ejpam-3312	436	8	-	-	ADJ
ejpam-3312	436	9	open	open	ADJ
ejpam-3312	436	10	set	set	NOUN
ejpam-3312	436	11	and	and	CCONJ
ejpam-3312	436	12	f−1φ	f−1φ	NOUN
ejpam-3312	436	13	(	(	PUNCT
ejpam-3312	436	14	la	la	NOUN
ejpam-3312	436	15	)	)	PUNCT
ejpam-3312	436	16	=	=	PUNCT
ejpam-3312	437	1	la	la	X
ejpam-3312	437	2	is	be	AUX
ejpam-3312	437	3	not	not	PART
ejpam-3312	437	4	a	a	DET
ejpam-3312	437	5	soft	soft	ADJ
ejpam-3312	437	6	dβ	dβ	ADJ
ejpam-3312	437	7	-	-	PUNCT
ejpam-3312	437	8	open	open	NOUN
ejpam-3312	437	9	set	set	NOUN
ejpam-3312	437	10	.	.	PUNCT
ejpam-3312	438	1	hence	hence	ADV
ejpam-3312	438	2	fφ	fφ	PROPN
ejpam-3312	438	3	is	be	AUX
ejpam-3312	438	4	not	not	PART
ejpam-3312	438	5	soft	soft	ADJ
ejpam-3312	438	6	i	i	PRON
ejpam-3312	438	7	(	(	PUNCT
ejpam-3312	438	8	soft	soft	ADJ
ejpam-3312	438	9	d	d	NOUN
ejpam-3312	438	10	,	,	PUNCT
ejpam-3312	438	11	soft	soft	ADJ
ejpam-3312	438	12	b	b	NOUN
ejpam-3312	438	13	)	)	PUNCT
ejpam-3312	438	14	β	β	NOUN
ejpam-3312	438	15	-	-	PUNCT
ejpam-3312	438	16	homeomorphism	homeomorphism	PROPN
ejpam-3312	438	17	.	.	PUNCT
ejpam-3312	439	1	example	example	NOUN
ejpam-3312	439	2	6	6	NUM
ejpam-3312	439	3	.	.	PUNCT
ejpam-3312	440	1	in	in	ADP
ejpam-3312	440	2	example	example	NOUN
ejpam-3312	440	3	above	above	ADV
ejpam-3312	440	4	,	,	PUNCT
ejpam-3312	440	5	if	if	SCONJ
ejpam-3312	440	6	we	we	PRON
ejpam-3312	440	7	only	only	ADV
ejpam-3312	440	8	replace	replace	VERB
ejpam-3312	440	9	the	the	DET
ejpam-3312	440	10	partial	partial	ADJ
ejpam-3312	440	11	order	order	NOUN
ejpam-3312	440	12	relation	relation	NOUN
ejpam-3312	440	13	�	�	PROPN
ejpam-3312	440	14	1	1	NUM
ejpam-3312	440	15	by	by	ADP
ejpam-3312	440	16	�	�	NOUN
ejpam-3312	440	17	=	=	NOUN
ejpam-3312	440	18	4	4	NUM
ejpam-3312	440	19	⋃	⋃	NOUN
ejpam-3312	440	20	{	{	PUNCT
ejpam-3312	440	21	(	(	PUNCT
ejpam-3312	440	22	w	w	PROPN
ejpam-3312	440	23	,	,	PUNCT
ejpam-3312	440	24	x	x	NOUN
ejpam-3312	440	25	)	)	PUNCT
ejpam-3312	440	26	}	}	PUNCT
ejpam-3312	440	27	,	,	PUNCT
ejpam-3312	440	28	then	then	ADV
ejpam-3312	440	29	the	the	DET
ejpam-3312	440	30	soft	soft	ADJ
ejpam-3312	440	31	mapping	mapping	NOUN
ejpam-3312	440	32	fφ	fφ	NOUN
ejpam-3312	440	33	is	be	AUX
ejpam-3312	440	34	soft	soft	ADJ
ejpam-3312	440	35	d	d	NOUN
ejpam-3312	440	36	-	-	PUNCT
ejpam-3312	440	37	homeomorphism	homeomorphism	ADJ
ejpam-3312	440	38	,	,	PUNCT
ejpam-3312	440	39	but	but	CCONJ
ejpam-3312	440	40	is	be	AUX
ejpam-3312	440	41	not	not	PART
ejpam-3312	440	42	soft	soft	ADJ
ejpam-3312	440	43	bhomeomorphism	bhomeomorphism	NOUN
ejpam-3312	440	44	.	.	PUNCT
ejpam-3312	441	1	also	also	ADV
ejpam-3312	441	2	,	,	PUNCT
ejpam-3312	441	3	if	if	SCONJ
ejpam-3312	441	4	we	we	PRON
ejpam-3312	441	5	only	only	ADV
ejpam-3312	441	6	replace	replace	VERB
ejpam-3312	441	7	the	the	DET
ejpam-3312	441	8	partial	partial	ADJ
ejpam-3312	441	9	order	order	NOUN
ejpam-3312	441	10	relation	relation	NOUN
ejpam-3312	441	11	�	�	NOUN
ejpam-3312	441	12	2	2	NUM
ejpam-3312	441	13	by	by	ADP
ejpam-3312	441	14	�	�	NOUN
ejpam-3312	441	15	=	=	PROPN
ejpam-3312	441	16	4	4	NUM
ejpam-3312	441	17	⋃	⋃	NOUN
ejpam-3312	441	18	{	{	PUNCT
ejpam-3312	441	19	(	(	PUNCT
ejpam-3312	441	20	y	y	PROPN
ejpam-3312	441	21	,	,	PUNCT
ejpam-3312	441	22	z	z	NOUN
ejpam-3312	441	23	)	)	PUNCT
ejpam-3312	441	24	}	}	PUNCT
ejpam-3312	441	25	,	,	PUNCT
ejpam-3312	441	26	then	then	ADV
ejpam-3312	441	27	the	the	DET
ejpam-3312	441	28	soft	soft	ADJ
ejpam-3312	441	29	mapping	mapping	NOUN
ejpam-3312	441	30	fφ	fφ	NOUN
ejpam-3312	441	31	is	be	AUX
ejpam-3312	441	32	soft	soft	ADJ
ejpam-3312	441	33	i	i	NOUN
ejpam-3312	441	34	-	-	PUNCT
ejpam-3312	441	35	homeomorphism	homeomorphism	PROPN
ejpam-3312	441	36	,	,	PUNCT
ejpam-3312	441	37	but	but	CCONJ
ejpam-3312	441	38	is	be	AUX
ejpam-3312	441	39	not	not	PART
ejpam-3312	441	40	soft	soft	ADJ
ejpam-3312	441	41	b	b	NOUN
ejpam-3312	441	42	-	-	PUNCT
ejpam-3312	441	43	homeomorphism	homeomorphism	NOUN
ejpam-3312	441	44	.	.	PUNCT
ejpam-3312	442	1	theorem	theorem	NOUN
ejpam-3312	442	2	12	12	NUM
ejpam-3312	442	3	.	.	PUNCT
ejpam-3312	443	1	consider	consider	VERB
ejpam-3312	443	2	fφ	fφ	PRON
ejpam-3312	443	3	:	:	PUNCT
ejpam-3312	443	4	(	(	PUNCT
ejpam-3312	443	5	x	x	X
ejpam-3312	443	6	,	,	PUNCT
ejpam-3312	443	7	τ	τ	PROPN
ejpam-3312	443	8	,	,	PUNCT
ejpam-3312	443	9	e,	e,	X
ejpam-3312	443	10	�	�	X
ejpam-3312	443	11	1	1	NUM
ejpam-3312	443	12	)	)	PUNCT
ejpam-3312	443	13	→	→	SYM
ejpam-3312	443	14	(	(	PUNCT
ejpam-3312	443	15	y	y	PROPN
ejpam-3312	443	16	,	,	PUNCT
ejpam-3312	443	17	θ	θ	PROPN
ejpam-3312	443	18	,	,	PUNCT
ejpam-3312	443	19	f,	f,	X
ejpam-3312	443	20	�	�	NOUN
ejpam-3312	443	21	2	2	NUM
ejpam-3312	443	22	)	)	PUNCT
ejpam-3312	443	23	is	be	AUX
ejpam-3312	443	24	a	a	DET
ejpam-3312	443	25	bijective	bijective	ADJ
ejpam-3312	443	26	soft	soft	ADJ
ejpam-3312	443	27	mapping	mapping	NOUN
ejpam-3312	443	28	and	and	CCONJ
ejpam-3312	443	29	let	let	VERB
ejpam-3312	443	30	(	(	PUNCT
ejpam-3312	443	31	γ	γ	X
ejpam-3312	443	32	,	,	PUNCT
ejpam-3312	443	33	λ	λ	NOUN
ejpam-3312	443	34	)	)	PUNCT
ejpam-3312	443	35	∈	∈	PROPN
ejpam-3312	443	36	{	{	PUNCT
ejpam-3312	443	37	(	(	PUNCT
ejpam-3312	443	38	iβ	iβ	NOUN
ejpam-3312	443	39	,	,	PUNCT
ejpam-3312	443	40	dβcl	dβcl	NOUN
ejpam-3312	443	41	)	)	PUNCT
ejpam-3312	443	42	,	,	PUNCT
ejpam-3312	443	43	(	(	PUNCT
ejpam-3312	443	44	dβ	dβ	ADJ
ejpam-3312	443	45	,	,	PUNCT
ejpam-3312	443	46	iβcl	iβcl	NOUN
ejpam-3312	443	47	)	)	PUNCT
ejpam-3312	443	48	,	,	PUNCT
ejpam-3312	443	49	(	(	PUNCT
ejpam-3312	443	50	bβ	bβ	NOUN
ejpam-3312	443	51	,	,	PUNCT
ejpam-3312	443	52	bβcl	bβcl	ADJ
ejpam-3312	443	53	)	)	PUNCT
ejpam-3312	443	54	}	}	PUNCT
ejpam-3312	443	55	.	.	PUNCT
ejpam-3312	444	1	then	then	ADV
ejpam-3312	444	2	fφ	fφ	PROPN
ejpam-3312	444	3	is	be	AUX
ejpam-3312	444	4	soft	soft	ADJ
ejpam-3312	444	5	γ	γ	X
ejpam-3312	444	6	-	-	PUNCT
ejpam-3312	444	7	homeomorphism	homeomorphism	NOUN
ejpam-3312	444	8	if	if	SCONJ
ejpam-3312	444	9	and	and	CCONJ
ejpam-3312	444	10	only	only	ADV
ejpam-3312	444	11	if	if	SCONJ
ejpam-3312	444	12	(	(	PUNCT
ejpam-3312	444	13	fφ(ge))λ	fφ(ge))λ	NOUN
ejpam-3312	444	14	=	=	NOUN
ejpam-3312	444	15	fφ(cl(ge	fφ(cl(ge	NOUN
ejpam-3312	444	16	)	)	PUNCT
ejpam-3312	444	17	)	)	PUNCT
ejpam-3312	445	1	=	=	PUNCT
ejpam-3312	445	2	cl(fφ(ge	cl(fφ(ge	X
ejpam-3312	445	3	)	)	PUNCT
ejpam-3312	445	4	)	)	PUNCT
ejpam-3312	446	1	=	=	PUNCT
ejpam-3312	446	2	fφ(gλe	fφ(gλe	NOUN
ejpam-3312	446	3	)	)	PUNCT
ejpam-3312	446	4	,	,	PUNCT
ejpam-3312	446	5	for	for	ADP
ejpam-3312	446	6	every	every	DET
ejpam-3312	446	7	ge⊆̃x̃.	ge⊆̃x̃.	ADJ
ejpam-3312	446	8	proof	proof	NOUN
ejpam-3312	446	9	.	.	PUNCT
ejpam-3312	447	1	we	we	PRON
ejpam-3312	447	2	make	make	VERB
ejpam-3312	447	3	a	a	DET
ejpam-3312	447	4	proof	proof	NOUN
ejpam-3312	447	5	for	for	ADP
ejpam-3312	447	6	the	the	DET
ejpam-3312	447	7	theorem	theorem	NOUN
ejpam-3312	447	8	in	in	ADP
ejpam-3312	447	9	the	the	DET
ejpam-3312	447	10	case	case	NOUN
ejpam-3312	447	11	of	of	ADP
ejpam-3312	447	12	(	(	PUNCT
ejpam-3312	447	13	γ	γ	X
ejpam-3312	447	14	,	,	PUNCT
ejpam-3312	447	15	λ	λ	NOUN
ejpam-3312	447	16	)	)	PUNCT
ejpam-3312	447	17	=	=	SYM
ejpam-3312	447	18	(	(	PUNCT
ejpam-3312	447	19	iβ	iβ	NOUN
ejpam-3312	447	20	,	,	PUNCT
ejpam-3312	447	21	dβcl	dβcl	NOUN
ejpam-3312	447	22	)	)	PUNCT
ejpam-3312	447	23	and	and	CCONJ
ejpam-3312	447	24	the	the	DET
ejpam-3312	447	25	other	other	ADJ
ejpam-3312	447	26	follow	follow	VERB
ejpam-3312	447	27	similar	similar	ADJ
ejpam-3312	447	28	line	line	NOUN
ejpam-3312	447	29	.	.	PUNCT
ejpam-3312	448	1	necessity	necessity	NOUN
ejpam-3312	448	2	:	:	PUNCT
ejpam-3312	448	3	the	the	DET
ejpam-3312	448	4	property	property	NOUN
ejpam-3312	448	5	fφ	fφ	NOUN
ejpam-3312	448	6	is	be	AUX
ejpam-3312	448	7	a	a	DET
ejpam-3312	448	8	soft	soft	ADJ
ejpam-3312	448	9	iβ	iβ	NOUN
ejpam-3312	448	10	-	-	PUNCT
ejpam-3312	448	11	homeomorphism	homeomorphism	ADJ
ejpam-3312	448	12	mapping	mapping	NOUN
ejpam-3312	448	13	implies	imply	VERB
ejpam-3312	448	14	that	that	SCONJ
ejpam-3312	448	15	fφ(gdβcle	fφ(gdβcle	PROPN
ejpam-3312	448	16	)	)	PUNCT
ejpam-3312	448	17	⊆̃	⊆̃	NOUN
ejpam-3312	448	18	cl(fφ(ge	cl(fφ(ge	NOUN
ejpam-3312	448	19	)	)	PUNCT
ejpam-3312	448	20	)	)	PUNCT
ejpam-3312	448	21	and	and	CCONJ
ejpam-3312	448	22	(	(	PUNCT
ejpam-3312	448	23	fφ(ge))dβcl⊆̃fφ(cl(ge	fφ(ge))dβcl⊆̃fφ(cl(ge	PROPN
ejpam-3312	448	24	)	)	PUNCT
ejpam-3312	448	25	)	)	PUNCT
ejpam-3312	448	26	,	,	PUNCT
ejpam-3312	448	27	for	for	SCONJ
ejpam-3312	448	28	every	every	DET
ejpam-3312	448	29	ge⊆̃x̃.	ge⊆̃x̃.	NUM
ejpam-3312	448	30	so	so	ADV
ejpam-3312	448	31	fφ(cl(ge))⊆̃fφ(gdβcle	fφ(cl(ge))⊆̃fφ(gdβcle	X
ejpam-3312	448	32	)	)	PUNCT
ejpam-3312	448	33	⊆̃cl(fφ(ge))⊆̃(fφ(ge))dβcl	⊆̃cl(fφ(ge))⊆̃(fφ(ge))dβcl	NOUN
ejpam-3312	448	34	and	and	CCONJ
ejpam-3312	448	35	cl(fφ(ge))⊆̃(fφ(ge))dβcl⊆̃fφ(cl(ge))⊆̃fφ(gdβcle	cl(fφ(ge))⊆̃(fφ(ge))dβcl⊆̃fφ(cl(ge))⊆̃fφ(gdβcle	NOUN
ejpam-3312	448	36	)	)	PUNCT
ejpam-3312	448	37	.	.	PUNCT
ejpam-3312	449	1	by	by	ADP
ejpam-3312	449	2	the	the	DET
ejpam-3312	449	3	preceding	precede	VERB
ejpam-3312	449	4	two	two	NUM
ejpam-3312	449	5	inclusion	inclusion	NOUN
ejpam-3312	449	6	relations	relation	NOUN
ejpam-3312	449	7	,	,	PUNCT
ejpam-3312	449	8	we	we	PRON
ejpam-3312	449	9	obtain	obtain	VERB
ejpam-3312	449	10	the	the	DET
ejpam-3312	449	11	required	require	VERB
ejpam-3312	449	12	equality	equality	NOUN
ejpam-3312	449	13	relation	relation	NOUN
ejpam-3312	449	14	.	.	PUNCT
ejpam-3312	450	1	sufficiency	sufficiency	NOUN
ejpam-3312	450	2	:	:	PUNCT
ejpam-3312	450	3	the	the	DET
ejpam-3312	450	4	equality	equality	NOUN
ejpam-3312	450	5	relation	relation	NOUN
ejpam-3312	450	6	(	(	PUNCT
ejpam-3312	450	7	fφ(ge))dβcl	fφ(ge))dβcl	NOUN
ejpam-3312	450	8	=	=	SYM
ejpam-3312	450	9	fφ(cl(ge	fφ(cl(ge	NOUN
ejpam-3312	450	10	)	)	PUNCT
ejpam-3312	450	11	)	)	PUNCT
ejpam-3312	450	12	=	=	PUNCT
ejpam-3312	451	1	cl(fφ(ge	cl(fφ(ge	X
ejpam-3312	451	2	)	)	PUNCT
ejpam-3312	451	3	)	)	PUNCT
ejpam-3312	452	1	=	=	SYM
ejpam-3312	452	2	fφ(gdβcle	fφ(gdβcle	PROPN
ejpam-3312	452	3	)	)	PUNCT
ejpam-3312	452	4	implies	imply	VERB
ejpam-3312	452	5	that	that	SCONJ
ejpam-3312	452	6	fφ(gdβcle	fφ(gdβcle	PROPN
ejpam-3312	452	7	)	)	PUNCT
ejpam-3312	452	8	⊆̃cl(fφ(ge	⊆̃cl(fφ(ge	NOUN
ejpam-3312	452	9	)	)	PUNCT
ejpam-3312	452	10	)	)	PUNCT
ejpam-3312	453	1	and	and	CCONJ
ejpam-3312	453	2	(	(	PUNCT
ejpam-3312	453	3	fφ(ge))dβcl⊆̃fφ(cl(ge	fφ(ge))dβcl⊆̃fφ(cl(ge	PROPN
ejpam-3312	453	4	)	)	PUNCT
ejpam-3312	453	5	)	)	PUNCT
ejpam-3312	453	6	.	.	PUNCT
ejpam-3312	454	1	so	so	ADV
ejpam-3312	454	2	fφ	fφ	PROPN
ejpam-3312	454	3	is	be	AUX
ejpam-3312	454	4	soft	soft	ADJ
ejpam-3312	454	5	iβ	iβ	ADP
ejpam-3312	454	6	-	-	ADJ
ejpam-3312	454	7	continuous	continuous	ADJ
ejpam-3312	454	8	and	and	CCONJ
ejpam-3312	454	9	soft	soft	ADJ
ejpam-3312	454	10	dβ	dβ	ADJ
ejpam-3312	454	11	-	-	PUNCT
ejpam-3312	454	12	closed	close	VERB
ejpam-3312	454	13	mapping	mapping	NOUN
ejpam-3312	454	14	.	.	PUNCT
ejpam-3312	455	1	hence	hence	ADV
ejpam-3312	455	2	the	the	DET
ejpam-3312	455	3	desired	desire	VERB
ejpam-3312	455	4	result	result	NOUN
ejpam-3312	455	5	is	be	AUX
ejpam-3312	455	6	proved	prove	VERB
ejpam-3312	455	7	.	.	PUNCT
ejpam-3312	456	1	t.	t.	PROPN
ejpam-3312	456	2	m.	m.	PROPN
ejpam-3312	456	3	al	al	PROPN
ejpam-3312	456	4	-	-	PUNCT
ejpam-3312	456	5	shami	shami	PROPN
ejpam-3312	456	6	,	,	PUNCT
ejpam-3312	456	7	m.	m.	PROPN
ejpam-3312	456	8	e.	e.	PROPN
ejpam-3312	456	9	el	el	PROPN
ejpam-3312	456	10	-	-	PROPN
ejpam-3312	456	11	shafei	shafei	PROPN
ejpam-3312	456	12	,	,	PUNCT
ejpam-3312	456	13	b.	b.	PROPN
ejpam-3312	456	14	a.	a.	PROPN
ejpam-3312	456	15	asaad	asaad	PROPN
ejpam-3312	456	16	/	/	SYM
ejpam-3312	456	17	eur	eur	PROPN
ejpam-3312	456	18	.	.	PUNCT
ejpam-3312	457	1	j.	j.	PROPN
ejpam-3312	457	2	pure	pure	PROPN
ejpam-3312	457	3	appl	appl	PROPN
ejpam-3312	457	4	.	.	PROPN
ejpam-3312	457	5	math	math	PROPN
ejpam-3312	457	6	,	,	PUNCT
ejpam-3312	457	7	12	12	NUM
ejpam-3312	457	8	(	(	PUNCT
ejpam-3312	457	9	1	1	NUM
ejpam-3312	457	10	)	)	PUNCT
ejpam-3312	457	11	(	(	PUNCT
ejpam-3312	457	12	2019	2019	NUM
ejpam-3312	457	13	)	)	PUNCT
ejpam-3312	457	14	,	,	PUNCT
ejpam-3312	457	15	176	176	NUM
ejpam-3312	457	16	-	-	SYM
ejpam-3312	457	17	193	193	NUM
ejpam-3312	457	18	189	189	NUM
ejpam-3312	457	19	theorem	theorem	NOUN
ejpam-3312	457	20	13	13	NUM
ejpam-3312	457	21	.	.	PUNCT
ejpam-3312	458	1	if	if	SCONJ
ejpam-3312	458	2	a	a	DET
ejpam-3312	458	3	bijective	bijective	ADJ
ejpam-3312	458	4	soft	soft	ADJ
ejpam-3312	458	5	mapping	mapping	NOUN
ejpam-3312	458	6	fφ	fφ	NOUN
ejpam-3312	458	7	:	:	PUNCT
ejpam-3312	458	8	(	(	PUNCT
ejpam-3312	458	9	x	x	X
ejpam-3312	458	10	,	,	PUNCT
ejpam-3312	458	11	τ	τ	PROPN
ejpam-3312	458	12	,	,	PUNCT
ejpam-3312	458	13	e,	e,	X
ejpam-3312	458	14	�	�	X
ejpam-3312	458	15	1	1	NUM
ejpam-3312	458	16	)	)	PUNCT
ejpam-3312	458	17	→	→	SYM
ejpam-3312	458	18	(	(	PUNCT
ejpam-3312	458	19	y	y	PROPN
ejpam-3312	458	20	,	,	PUNCT
ejpam-3312	458	21	θ	θ	PROPN
ejpam-3312	458	22	,	,	PUNCT
ejpam-3312	458	23	f,	f,	X
ejpam-3312	458	24	�	�	NOUN
ejpam-3312	458	25	2	2	NUM
ejpam-3312	458	26	)	)	PUNCT
ejpam-3312	458	27	is	be	AUX
ejpam-3312	458	28	soft	soft	ADJ
ejpam-3312	458	29	iβcontinuous	iβcontinuous	ADJ
ejpam-3312	458	30	(	(	PUNCT
ejpam-3312	458	31	resp	resp	NOUN
ejpam-3312	458	32	.	.	PUNCT
ejpam-3312	459	1	soft	soft	ADJ
ejpam-3312	459	2	dβ	dβ	ADJ
ejpam-3312	459	3	-	-	PUNCT
ejpam-3312	459	4	continuous	continuous	ADJ
ejpam-3312	459	5	,	,	PUNCT
ejpam-3312	459	6	soft	soft	ADJ
ejpam-3312	459	7	bβ	bβ	NOUN
ejpam-3312	459	8	-	-	PUNCT
ejpam-3312	459	9	continuous	continuous	ADJ
ejpam-3312	459	10	)	)	PUNCT
ejpam-3312	460	1	,	,	PUNCT
ejpam-3312	460	2	then	then	ADV
ejpam-3312	460	3	the	the	DET
ejpam-3312	460	4	following	follow	VERB
ejpam-3312	460	5	three	three	NUM
ejpam-3312	460	6	statements	statement	NOUN
ejpam-3312	460	7	are	be	AUX
ejpam-3312	460	8	equivalent	equivalent	ADJ
ejpam-3312	460	9	:	:	PUNCT
ejpam-3312	460	10	(	(	PUNCT
ejpam-3312	460	11	i	i	NOUN
ejpam-3312	460	12	)	)	PUNCT
ejpam-3312	460	13	fφ	fφ	VERB
ejpam-3312	460	14	is	be	AUX
ejpam-3312	460	15	soft	soft	ADJ
ejpam-3312	460	16	iβ	iβ	NOUN
ejpam-3312	460	17	-	-	PUNCT
ejpam-3312	460	18	homeomorphism	homeomorphism	NOUN
ejpam-3312	460	19	(	(	PUNCT
ejpam-3312	460	20	resp	resp	NOUN
ejpam-3312	460	21	.	.	PUNCT
ejpam-3312	461	1	soft	soft	ADJ
ejpam-3312	461	2	dβ	dβ	ADJ
ejpam-3312	461	3	-	-	PUNCT
ejpam-3312	461	4	homeomorphism	homeomorphism	NOUN
ejpam-3312	461	5	,	,	PUNCT
ejpam-3312	461	6	soft	soft	ADJ
ejpam-3312	461	7	bβ	bβ	NOUN
ejpam-3312	461	8	-	-	PUNCT
ejpam-3312	461	9	homeomorphism	homeomorphism	NOUN
ejpam-3312	461	10	)	)	PUNCT
ejpam-3312	461	11	;	;	PUNCT
ejpam-3312	461	12	(	(	PUNCT
ejpam-3312	461	13	ii	ii	X
ejpam-3312	461	14	)	)	PUNCT
ejpam-3312	461	15	f−1φ	f−1φ	NOUN
ejpam-3312	461	16	is	be	AUX
ejpam-3312	461	17	soft	soft	ADJ
ejpam-3312	461	18	iβ	iβ	ADP
ejpam-3312	461	19	-	-	ADJ
ejpam-3312	461	20	continuous	continuous	ADJ
ejpam-3312	461	21	(	(	PUNCT
ejpam-3312	461	22	resp	resp	NOUN
ejpam-3312	461	23	.	.	PUNCT
ejpam-3312	462	1	soft	soft	ADJ
ejpam-3312	462	2	dβ	dβ	ADJ
ejpam-3312	462	3	-	-	PUNCT
ejpam-3312	462	4	continuous	continuous	ADJ
ejpam-3312	462	5	,	,	PUNCT
ejpam-3312	462	6	soft	soft	ADJ
ejpam-3312	462	7	bβ	bβ	NOUN
ejpam-3312	462	8	-	-	PUNCT
ejpam-3312	462	9	continuous	continuous	ADJ
ejpam-3312	462	10	)	)	PUNCT
ejpam-3312	463	1	;	;	PUNCT
ejpam-3312	463	2	(	(	PUNCT
ejpam-3312	463	3	iii	iii	X
ejpam-3312	463	4	)	)	PUNCT
ejpam-3312	463	5	fφ	fφ	NOUN
ejpam-3312	463	6	is	be	AUX
ejpam-3312	463	7	soft	soft	ADJ
ejpam-3312	463	8	dβ	dβ	ADJ
ejpam-3312	463	9	-	-	PUNCT
ejpam-3312	463	10	closed	closed	ADJ
ejpam-3312	463	11	(	(	PUNCT
ejpam-3312	463	12	resp	resp	NOUN
ejpam-3312	463	13	.	.	PUNCT
ejpam-3312	464	1	soft	soft	ADJ
ejpam-3312	464	2	iβ	iβ	ADJ
ejpam-3312	464	3	-	-	PUNCT
ejpam-3312	464	4	closed	closed	ADJ
ejpam-3312	464	5	,	,	PUNCT
ejpam-3312	464	6	soft	soft	ADJ
ejpam-3312	464	7	bβ	bβ	NOUN
ejpam-3312	464	8	-	-	PUNCT
ejpam-3312	464	9	closed	closed	ADJ
ejpam-3312	464	10	)	)	PUNCT
ejpam-3312	464	11	.	.	PUNCT
ejpam-3312	465	1	proof	proof	NOUN
ejpam-3312	465	2	.	.	PUNCT
ejpam-3312	466	1	(	(	PUNCT
ejpam-3312	466	2	i)⇒	i)⇒	PROPN
ejpam-3312	466	3	(	(	PUNCT
ejpam-3312	466	4	ii	ii	NOUN
ejpam-3312	466	5	)	)	PUNCT
ejpam-3312	466	6	since	since	SCONJ
ejpam-3312	466	7	fφ	fφ	PROPN
ejpam-3312	466	8	is	be	AUX
ejpam-3312	466	9	a	a	DET
ejpam-3312	466	10	soft	soft	ADJ
ejpam-3312	466	11	iβ	iβ	NOUN
ejpam-3312	466	12	-	-	PUNCT
ejpam-3312	466	13	homeomorphism	homeomorphism	NOUN
ejpam-3312	466	14	(	(	PUNCT
ejpam-3312	466	15	resp	resp	NOUN
ejpam-3312	466	16	.	.	PUNCT
ejpam-3312	467	1	soft	soft	ADJ
ejpam-3312	467	2	dβ	dβ	NOUN
ejpam-3312	467	3	-	-	PUNCT
ejpam-3312	467	4	homeomorphism	homeomorphism	NOUN
ejpam-3312	467	5	,	,	PUNCT
ejpam-3312	467	6	soft	soft	ADJ
ejpam-3312	467	7	bβ	bβ	NOUN
ejpam-3312	467	8	-	-	PUNCT
ejpam-3312	467	9	homeomorphism	homeomorphism	NOUN
ejpam-3312	467	10	)	)	PUNCT
ejpam-3312	467	11	mapping	mapping	NOUN
ejpam-3312	467	12	,	,	PUNCT
ejpam-3312	467	13	then	then	ADV
ejpam-3312	467	14	fφ	fφ	PROPN
ejpam-3312	467	15	is	be	AUX
ejpam-3312	467	16	soft	soft	ADJ
ejpam-3312	467	17	iβ	iβ	ADJ
ejpam-3312	467	18	-	-	ADJ
ejpam-3312	467	19	open	open	ADJ
ejpam-3312	467	20	(	(	PUNCT
ejpam-3312	467	21	resp	resp	NOUN
ejpam-3312	467	22	.	.	PUNCT
ejpam-3312	468	1	soft	soft	ADJ
ejpam-3312	468	2	dβ	dβ	ADJ
ejpam-3312	468	3	-	-	PUNCT
ejpam-3312	468	4	open	open	ADJ
ejpam-3312	468	5	,	,	PUNCT
ejpam-3312	468	6	soft	soft	ADJ
ejpam-3312	468	7	bβ	bβ	NOUN
ejpam-3312	468	8	-	-	PUNCT
ejpam-3312	468	9	open	open	ADJ
ejpam-3312	468	10	)	)	PUNCT
ejpam-3312	468	11	.	.	PUNCT
ejpam-3312	469	1	it	it	PRON
ejpam-3312	469	2	follows	follow	VERB
ejpam-3312	469	3	from	from	ADP
ejpam-3312	469	4	item	item	NOUN
ejpam-3312	469	5	(	(	PUNCT
ejpam-3312	469	6	ii	ii	NOUN
ejpam-3312	469	7	)	)	PUNCT
ejpam-3312	469	8	of	of	ADP
ejpam-3312	469	9	theorem	theorem	NOUN
ejpam-3312	469	10	(	(	PUNCT
ejpam-3312	469	11	9	9	NUM
ejpam-3312	469	12	)	)	PUNCT
ejpam-3312	469	13	,	,	PUNCT
ejpam-3312	469	14	that	that	SCONJ
ejpam-3312	469	15	f−1φ	f−1φ	NOUN
ejpam-3312	469	16	is	be	AUX
ejpam-3312	469	17	soft	soft	ADJ
ejpam-3312	469	18	iβ	iβ	ADP
ejpam-3312	469	19	-	-	ADJ
ejpam-3312	469	20	continuous	continuous	ADJ
ejpam-3312	469	21	(	(	PUNCT
ejpam-3312	469	22	resp	resp	NOUN
ejpam-3312	469	23	.	.	PUNCT
ejpam-3312	470	1	soft	soft	ADJ
ejpam-3312	470	2	dβ	dβ	ADJ
ejpam-3312	470	3	-	-	PUNCT
ejpam-3312	470	4	continuous	continuous	ADJ
ejpam-3312	470	5	,	,	PUNCT
ejpam-3312	470	6	soft	soft	ADJ
ejpam-3312	470	7	bβ	bβ	NOUN
ejpam-3312	470	8	-	-	PUNCT
ejpam-3312	470	9	continuous	continuous	ADJ
ejpam-3312	470	10	)	)	PUNCT
ejpam-3312	470	11	.	.	PUNCT
ejpam-3312	471	1	(	(	PUNCT
ejpam-3312	471	2	ii)⇒	ii)⇒	X
ejpam-3312	471	3	(	(	PUNCT
ejpam-3312	471	4	iii	iii	X
ejpam-3312	471	5	)	)	PUNCT
ejpam-3312	471	6	the	the	DET
ejpam-3312	471	7	proof	proof	NOUN
ejpam-3312	471	8	follows	follow	VERB
ejpam-3312	471	9	from	from	ADP
ejpam-3312	471	10	item	item	NOUN
ejpam-3312	471	11	(	(	PUNCT
ejpam-3312	471	12	iii	iii	NOUN
ejpam-3312	471	13	)	)	PUNCT
ejpam-3312	471	14	of	of	ADP
ejpam-3312	471	15	theorem	theorem	NOUN
ejpam-3312	471	16	(	(	PUNCT
ejpam-3312	471	17	9	9	NUM
ejpam-3312	471	18	)	)	PUNCT
ejpam-3312	471	19	.	.	PUNCT
ejpam-3312	472	1	(	(	PUNCT
ejpam-3312	472	2	iii	iii	X
ejpam-3312	472	3	)	)	PUNCT
ejpam-3312	472	4	⇒	⇒	NOUN
ejpam-3312	472	5	(	(	PUNCT
ejpam-3312	472	6	i	i	NOUN
ejpam-3312	472	7	)	)	PUNCT
ejpam-3312	472	8	it	it	PRON
ejpam-3312	472	9	sufficient	sufficient	ADJ
ejpam-3312	472	10	to	to	PART
ejpam-3312	472	11	prove	prove	VERB
ejpam-3312	472	12	that	that	SCONJ
ejpam-3312	472	13	fφ	fφ	PROPN
ejpam-3312	472	14	is	be	AUX
ejpam-3312	472	15	a	a	DET
ejpam-3312	472	16	soft	soft	ADJ
ejpam-3312	472	17	iβ	iβ	NOUN
ejpam-3312	472	18	-	-	ADJ
ejpam-3312	472	19	open	open	ADJ
ejpam-3312	472	20	(	(	PUNCT
ejpam-3312	472	21	resp	resp	NOUN
ejpam-3312	472	22	.	.	PUNCT
ejpam-3312	473	1	soft	soft	ADJ
ejpam-3312	473	2	dβ	dβ	ADJ
ejpam-3312	473	3	-	-	PUNCT
ejpam-3312	473	4	open	open	ADJ
ejpam-3312	473	5	,	,	PUNCT
ejpam-3312	473	6	soft	soft	ADJ
ejpam-3312	473	7	bβopen	bβopen	NOUN
ejpam-3312	473	8	)	)	PUNCT
ejpam-3312	473	9	mapping	mapping	NOUN
ejpam-3312	473	10	.	.	PUNCT
ejpam-3312	474	1	this	this	PRON
ejpam-3312	474	2	follows	follow	VERB
ejpam-3312	474	3	from	from	ADP
ejpam-3312	474	4	item	item	NOUN
ejpam-3312	474	5	(	(	PUNCT
ejpam-3312	474	6	i	i	NOUN
ejpam-3312	474	7	)	)	PUNCT
ejpam-3312	474	8	of	of	ADP
ejpam-3312	474	9	theorem	theorem	NOUN
ejpam-3312	474	10	(	(	PUNCT
ejpam-3312	474	11	9	9	NUM
ejpam-3312	474	12	)	)	PUNCT
ejpam-3312	474	13	.	.	PUNCT
ejpam-3312	475	1	theorem	theorem	ADJ
ejpam-3312	475	2	14	14	NUM
ejpam-3312	475	3	.	.	PUNCT
ejpam-3312	476	1	let	let	VERB
ejpam-3312	476	2	τ	τ	PROPN
ejpam-3312	476	3	?	?	PUNCT
ejpam-3312	476	4	and	and	CCONJ
ejpam-3312	476	5	θ	θ	X
ejpam-3312	476	6	?	?	PROPN
ejpam-3312	476	7	be	be	AUX
ejpam-3312	476	8	extended	extend	VERB
ejpam-3312	476	9	soft	soft	ADJ
ejpam-3312	476	10	topologies	topology	NOUN
ejpam-3312	476	11	on	on	ADP
ejpam-3312	476	12	x	x	PUNCT
ejpam-3312	476	13	and	and	CCONJ
ejpam-3312	476	14	y	y	PROPN
ejpam-3312	476	15	,	,	PUNCT
ejpam-3312	476	16	respectively	respectively	ADV
ejpam-3312	476	17	.	.	PUNCT
ejpam-3312	477	1	then	then	ADV
ejpam-3312	477	2	a	a	DET
ejpam-3312	477	3	soft	soft	ADJ
ejpam-3312	477	4	mapping	mapping	NOUN
ejpam-3312	477	5	gφ	gφ	NOUN
ejpam-3312	477	6	:	:	PUNCT
ejpam-3312	477	7	(	(	PUNCT
ejpam-3312	477	8	x	x	X
ejpam-3312	477	9	,	,	PUNCT
ejpam-3312	477	10	τ	τ	PROPN
ejpam-3312	477	11	?	?	PROPN
ejpam-3312	477	12	,	,	PUNCT
ejpam-3312	477	13	e,	e,	X
ejpam-3312	477	14	�	�	X
ejpam-3312	477	15	1	1	NUM
ejpam-3312	477	16	)	)	PUNCT
ejpam-3312	477	17	→	→	SYM
ejpam-3312	477	18	(	(	PUNCT
ejpam-3312	477	19	y	y	PROPN
ejpam-3312	477	20	,	,	PUNCT
ejpam-3312	477	21	θ	θ	PROPN
ejpam-3312	477	22	?	?	NOUN
ejpam-3312	477	23	,	,	PUNCT
ejpam-3312	477	24	f,	f,	PROPN
ejpam-3312	477	25	�	�	NOUN
ejpam-3312	477	26	2	2	NUM
ejpam-3312	477	27	)	)	PUNCT
ejpam-3312	477	28	is	be	AUX
ejpam-3312	477	29	soft	soft	ADJ
ejpam-3312	477	30	i	i	PRON
ejpam-3312	477	31	(	(	PUNCT
ejpam-3312	477	32	resp	resp	NOUN
ejpam-3312	477	33	.	.	PUNCT
ejpam-3312	478	1	soft	soft	ADJ
ejpam-3312	478	2	d	d	NOUN
ejpam-3312	478	3	,	,	PUNCT
ejpam-3312	478	4	soft	soft	ADJ
ejpam-3312	478	5	b	b	NOUN
ejpam-3312	478	6	)	)	PUNCT
ejpam-3312	478	7	βhomeomorphism	βhomeomorphism	NOUN
ejpam-3312	478	8	if	if	SCONJ
ejpam-3312	479	1	and	and	CCONJ
ejpam-3312	479	2	only	only	ADV
ejpam-3312	479	3	if	if	SCONJ
ejpam-3312	479	4	a	a	DET
ejpam-3312	479	5	mapping	mapping	NOUN
ejpam-3312	479	6	g	g	NOUN
ejpam-3312	479	7	:	:	PUNCT
ejpam-3312	479	8	(	(	PUNCT
ejpam-3312	479	9	x	x	X
ejpam-3312	479	10	,	,	PUNCT
ejpam-3312	479	11	τ?e	τ?e	PROPN
ejpam-3312	479	12	,	,	PUNCT
ejpam-3312	479	13	�	�	PROPN
ejpam-3312	479	14	1)→	1)→	NUM
ejpam-3312	479	15	(	(	PUNCT
ejpam-3312	479	16	y	y	PROPN
ejpam-3312	479	17	,	,	PUNCT
ejpam-3312	479	18	θ?φ(e),	θ?φ(e),	NOUN
ejpam-3312	479	19	�	�	NOUN
ejpam-3312	479	20	2	2	NUM
ejpam-3312	479	21	)	)	PUNCT
ejpam-3312	479	22	is	be	AUX
ejpam-3312	479	23	i	i	PRON
ejpam-3312	479	24	(	(	PUNCT
ejpam-3312	479	25	resp	resp	NOUN
ejpam-3312	479	26	.	.	PUNCT
ejpam-3312	480	1	d	d	X
ejpam-3312	480	2	,	,	PUNCT
ejpam-3312	480	3	b	b	NOUN
ejpam-3312	480	4	)	)	PUNCT
ejpam-3312	480	5	β	β	NOUN
ejpam-3312	480	6	-	-	PUNCT
ejpam-3312	480	7	homeomorphism	homeomorphism	NOUN
ejpam-3312	480	8	.	.	PUNCT
ejpam-3312	481	1	proof	proof	NOUN
ejpam-3312	481	2	.	.	PUNCT
ejpam-3312	482	1	the	the	DET
ejpam-3312	482	2	proof	proof	NOUN
ejpam-3312	482	3	is	be	AUX
ejpam-3312	482	4	obtained	obtain	VERB
ejpam-3312	482	5	immediately	immediately	ADV
ejpam-3312	482	6	from	from	ADP
ejpam-3312	482	7	theorem	theorem	ADJ
ejpam-3312	482	8	(	(	PUNCT
ejpam-3312	482	9	5	5	NUM
ejpam-3312	482	10	)	)	PUNCT
ejpam-3312	482	11	and	and	CCONJ
ejpam-3312	482	12	theorem	theorem	VERB
ejpam-3312	482	13	(	(	PUNCT
ejpam-3312	482	14	10	10	NUM
ejpam-3312	482	15	)	)	PUNCT
ejpam-3312	482	16	proposition	proposition	NOUN
ejpam-3312	482	17	6	6	NUM
ejpam-3312	482	18	.	.	PUNCT
ejpam-3312	483	1	let	let	VERB
ejpam-3312	483	2	a	a	DET
ejpam-3312	483	3	soft	soft	ADJ
ejpam-3312	483	4	mapping	mapping	NOUN
ejpam-3312	483	5	fφ	fφ	NOUN
ejpam-3312	483	6	:	:	PUNCT
ejpam-3312	483	7	(	(	PUNCT
ejpam-3312	483	8	x	x	X
ejpam-3312	483	9	,	,	PUNCT
ejpam-3312	483	10	τ	τ	X
ejpam-3312	483	11	,	,	PUNCT
ejpam-3312	483	12	e	e	X
ejpam-3312	483	13	�	�	PROPN
ejpam-3312	483	14	1)→	1)→	NUM
ejpam-3312	483	15	(	(	PUNCT
ejpam-3312	483	16	y	y	PROPN
ejpam-3312	483	17	,	,	PUNCT
ejpam-3312	483	18	θ	θ	PROPN
ejpam-3312	483	19	,	,	PUNCT
ejpam-3312	483	20	f,	f,	X
ejpam-3312	483	21	�	�	PROPN
ejpam-3312	483	22	2	2	NUM
ejpam-3312	483	23	)	)	PUNCT
ejpam-3312	483	24	be	be	AUX
ejpam-3312	483	25	soft	soft	ADJ
ejpam-3312	483	26	bβ	bβ	NOUN
ejpam-3312	483	27	-	-	PUNCT
ejpam-3312	483	28	homeomorphism	homeomorphism	NOUN
ejpam-3312	483	29	.	.	PUNCT
ejpam-3312	484	1	then	then	ADV
ejpam-3312	484	2	:	:	PUNCT
ejpam-3312	484	3	(	(	PUNCT
ejpam-3312	484	4	i	i	NOUN
ejpam-3312	484	5	)	)	PUNCT
ejpam-3312	484	6	if	if	SCONJ
ejpam-3312	484	7	�	�	NOUN
ejpam-3312	484	8	1	1	NUM
ejpam-3312	484	9	and	and	CCONJ
ejpam-3312	484	10	�	�	NOUN
ejpam-3312	484	11	2	2	NUM
ejpam-3312	484	12	are	be	AUX
ejpam-3312	484	13	linearly	linearly	ADV
ejpam-3312	484	14	order	order	NOUN
ejpam-3312	484	15	,	,	PUNCT
ejpam-3312	484	16	then	then	ADV
ejpam-3312	484	17	τ	τ	PROPN
ejpam-3312	484	18	and	and	CCONJ
ejpam-3312	484	19	θ	θ	PROPN
ejpam-3312	484	20	are	be	AUX
ejpam-3312	484	21	the	the	DET
ejpam-3312	484	22	soft	soft	ADJ
ejpam-3312	484	23	indiscrete	indiscrete	ADJ
ejpam-3312	484	24	topologies	topology	NOUN
ejpam-3312	484	25	.	.	PUNCT
ejpam-3312	485	1	(	(	PUNCT
ejpam-3312	485	2	ii	ii	NOUN
ejpam-3312	485	3	)	)	PUNCT
ejpam-3312	485	4	if	if	SCONJ
ejpam-3312	485	5	τ	τ	PROPN
ejpam-3312	485	6	and	and	CCONJ
ejpam-3312	485	7	θ	θ	PROPN
ejpam-3312	485	8	are	be	AUX
ejpam-3312	485	9	the	the	DET
ejpam-3312	485	10	soft	soft	ADJ
ejpam-3312	485	11	discrete	discrete	ADJ
ejpam-3312	485	12	topologies	topology	NOUN
ejpam-3312	485	13	,	,	PUNCT
ejpam-3312	485	14	then	then	ADV
ejpam-3312	485	15	�	�	PROPN
ejpam-3312	485	16	1	1	NUM
ejpam-3312	485	17	and	and	CCONJ
ejpam-3312	485	18	�	�	NOUN
ejpam-3312	485	19	2	2	NUM
ejpam-3312	485	20	are	be	AUX
ejpam-3312	485	21	equality	equality	NOUN
ejpam-3312	485	22	relations	relation	NOUN
ejpam-3312	485	23	.	.	PUNCT
ejpam-3312	486	1	conclusion	conclusion	NOUN
ejpam-3312	486	2	in	in	ADP
ejpam-3312	486	3	[	[	X
ejpam-3312	486	4	13	13	NUM
ejpam-3312	486	5	]	]	PUNCT
ejpam-3312	486	6	,	,	PUNCT
ejpam-3312	486	7	the	the	DET
ejpam-3312	486	8	authors	author	NOUN
ejpam-3312	486	9	have	have	AUX
ejpam-3312	486	10	initiated	initiate	VERB
ejpam-3312	486	11	the	the	DET
ejpam-3312	486	12	concept	concept	NOUN
ejpam-3312	486	13	of	of	ADP
ejpam-3312	486	14	soft	soft	ADJ
ejpam-3312	486	15	topological	topological	ADJ
ejpam-3312	486	16	ordered	order	VERB
ejpam-3312	486	17	spaces	space	NOUN
ejpam-3312	486	18	as	as	ADP
ejpam-3312	486	19	an	an	DET
ejpam-3312	486	20	extended	extended	ADJ
ejpam-3312	486	21	of	of	ADP
ejpam-3312	486	22	the	the	DET
ejpam-3312	486	23	soft	soft	ADJ
ejpam-3312	486	24	topological	topological	ADJ
ejpam-3312	486	25	spaces	space	NOUN
ejpam-3312	486	26	notion	notion	NOUN
ejpam-3312	486	27	and	and	CCONJ
ejpam-3312	486	28	have	have	AUX
ejpam-3312	486	29	defined	define	VERB
ejpam-3312	486	30	soft	soft	ADJ
ejpam-3312	486	31	ordered	order	VERB
ejpam-3312	486	32	separation	separation	NOUN
ejpam-3312	486	33	axioms	axiom	NOUN
ejpam-3312	486	34	.	.	PUNCT
ejpam-3312	487	1	then	then	ADV
ejpam-3312	487	2	they	they	PRON
ejpam-3312	487	3	[	[	X
ejpam-3312	487	4	14	14	NUM
ejpam-3312	487	5	]	]	PUNCT
ejpam-3312	487	6	have	have	AUX
ejpam-3312	487	7	introduced	introduce	VERB
ejpam-3312	487	8	several	several	ADJ
ejpam-3312	487	9	types	type	NOUN
ejpam-3312	487	10	of	of	ADP
ejpam-3312	487	11	ordered	order	VERB
ejpam-3312	487	12	mappings	mapping	NOUN
ejpam-3312	487	13	and	and	CCONJ
ejpam-3312	487	14	have	have	AUX
ejpam-3312	487	15	established	establish	VERB
ejpam-3312	487	16	main	main	ADJ
ejpam-3312	487	17	features	feature	NOUN
ejpam-3312	487	18	.	.	PUNCT
ejpam-3312	488	1	as	as	ADP
ejpam-3312	488	2	a	a	DET
ejpam-3312	488	3	contribution	contribution	NOUN
ejpam-3312	488	4	of	of	ADP
ejpam-3312	488	5	this	this	PRON
ejpam-3312	488	6	,	,	PUNCT
ejpam-3312	488	7	we	we	PRON
ejpam-3312	488	8	have	have	AUX
ejpam-3312	488	9	utilized	utilize	VERB
ejpam-3312	488	10	a	a	DET
ejpam-3312	488	11	soft	soft	ADJ
ejpam-3312	488	12	β	β	NOUN
ejpam-3312	488	13	-	-	ADJ
ejpam-3312	488	14	open	open	ADJ
ejpam-3312	488	15	set	set	NOUN
ejpam-3312	488	16	notion	notion	NOUN
ejpam-3312	488	17	to	to	PART
ejpam-3312	488	18	present	present	VERB
ejpam-3312	488	19	the	the	DET
ejpam-3312	488	20	concepts	concept	NOUN
ejpam-3312	488	21	of	of	ADP
ejpam-3312	488	22	soft	soft	ADJ
ejpam-3312	488	23	xβ	xβ	NOUN
ejpam-3312	488	24	-	-	PUNCT
ejpam-3312	488	25	continuous	continuous	ADJ
ejpam-3312	488	26	,	,	PUNCT
ejpam-3312	488	27	soft	soft	ADJ
ejpam-3312	488	28	xβ	xβ	NOUN
ejpam-3312	488	29	-	-	ADJ
ejpam-3312	488	30	open	open	ADJ
ejpam-3312	488	31	,	,	PUNCT
ejpam-3312	488	32	soft	soft	ADJ
ejpam-3312	488	33	xβ	xβ	NOUN
ejpam-3312	488	34	-	-	PUNCT
ejpam-3312	488	35	closed	closed	ADJ
ejpam-3312	488	36	and	and	CCONJ
ejpam-3312	488	37	soft	soft	ADJ
ejpam-3312	488	38	xβ	xβ	NOUN
ejpam-3312	488	39	-	-	PUNCT
ejpam-3312	488	40	homeomorphism	homeomorphism	NOUN
ejpam-3312	488	41	mappings	mapping	NOUN
ejpam-3312	488	42	,	,	PUNCT
ejpam-3312	488	43	for	for	ADP
ejpam-3312	488	44	x	x	PROPN
ejpam-3312	488	45	∈	∈	PROPN
ejpam-3312	488	46	{	{	PUNCT
ejpam-3312	488	47	i	i	PROPN
ejpam-3312	488	48	,	,	PUNCT
ejpam-3312	488	49	d	d	PROPN
ejpam-3312	488	50	,	,	PUNCT
ejpam-3312	488	51	b	b	NOUN
ejpam-3312	488	52	}	}	PUNCT
ejpam-3312	488	53	.	.	PUNCT
ejpam-3312	489	1	we	we	PRON
ejpam-3312	489	2	have	have	AUX
ejpam-3312	489	3	completely	completely	ADV
ejpam-3312	489	4	described	describe	VERB
ejpam-3312	489	5	these	these	DET
ejpam-3312	489	6	concepts	concept	NOUN
ejpam-3312	489	7	and	and	CCONJ
ejpam-3312	489	8	have	have	AUX
ejpam-3312	489	9	deduced	deduce	VERB
ejpam-3312	489	10	some	some	DET
ejpam-3312	489	11	results	result	NOUN
ejpam-3312	489	12	which	which	PRON
ejpam-3312	489	13	connect	connect	VERB
ejpam-3312	489	14	the	the	DET
ejpam-3312	489	15	initiated	initiate	VERB
ejpam-3312	489	16	soft	soft	ADJ
ejpam-3312	489	17	mappings	mapping	NOUN
ejpam-3312	489	18	with	with	ADP
ejpam-3312	489	19	those	those	DET
ejpam-3312	489	20	mappings	mapping	NOUN
ejpam-3312	489	21	via	via	ADP
ejpam-3312	489	22	topological	topological	ADJ
ejpam-3312	489	23	ordered	order	VERB
ejpam-3312	489	24	spaces	space	NOUN
ejpam-3312	489	25	.	.	PUNCT
ejpam-3312	490	1	it	it	PRON
ejpam-3312	490	2	can	can	AUX
ejpam-3312	490	3	be	be	AUX
ejpam-3312	490	4	seen	see	VERB
ejpam-3312	490	5	that	that	SCONJ
ejpam-3312	490	6	our	our	PRON
ejpam-3312	490	7	results	result	NOUN
ejpam-3312	490	8	are	be	AUX
ejpam-3312	490	9	certainly	certainly	ADV
ejpam-3312	490	10	more	more	ADV
ejpam-3312	490	11	general	general	ADJ
ejpam-3312	490	12	than	than	ADP
ejpam-3312	490	13	many	many	ADJ
ejpam-3312	490	14	results	result	NOUN
ejpam-3312	490	15	in	in	ADP
ejpam-3312	490	16	[	[	X
ejpam-3312	490	17	14	14	NUM
ejpam-3312	490	18	]	]	PUNCT
ejpam-3312	490	19	.	.	PUNCT
ejpam-3312	491	1	finally	finally	ADV
ejpam-3312	491	2	,	,	PUNCT
ejpam-3312	491	3	hopefully	hopefully	ADV
ejpam-3312	491	4	that	that	SCONJ
ejpam-3312	491	5	this	this	DET
ejpam-3312	491	6	study	study	NOUN
ejpam-3312	491	7	is	be	AUX
ejpam-3312	491	8	a	a	DET
ejpam-3312	491	9	good	good	ADJ
ejpam-3312	491	10	contribution	contribution	NOUN
ejpam-3312	491	11	for	for	ADP
ejpam-3312	491	12	the	the	DET
ejpam-3312	491	13	further	further	ADJ
ejpam-3312	491	14	researches	research	NOUN
ejpam-3312	491	15	on	on	ADP
ejpam-3312	491	16	soft	soft	ADJ
ejpam-3312	491	17	ordered	order	VERB
ejpam-3312	491	18	spaces	space	NOUN
ejpam-3312	491	19	.	.	PUNCT
ejpam-3312	492	1	references	reference	NOUN
ejpam-3312	492	2	190	190	NUM
ejpam-3312	492	3	acknowledgements	acknowledgement	NOUN
ejpam-3312	492	4	the	the	DET
ejpam-3312	492	5	authors	author	NOUN
ejpam-3312	492	6	thank	thank	VERB
ejpam-3312	492	7	the	the	DET
ejpam-3312	492	8	reviewers	reviewer	NOUN
ejpam-3312	492	9	for	for	ADP
ejpam-3312	492	10	their	their	PRON
ejpam-3312	492	11	valuable	valuable	ADJ
ejpam-3312	492	12	comments	comment	NOUN
ejpam-3312	492	13	.	.	PUNCT
ejpam-3312	493	1	references	reference	NOUN
ejpam-3312	493	2	[	[	X
ejpam-3312	493	3	1	1	NUM
ejpam-3312	493	4	]	]	PUNCT
ejpam-3312	493	5	a.	a.	NOUN
ejpam-3312	493	6	m.	m.	PROPN
ejpam-3312	493	7	abd	abd	PROPN
ejpam-3312	493	8	el	el	PROPN
ejpam-3312	493	9	-	-	PROPN
ejpam-3312	493	10	latif	latif	PROPN
ejpam-3312	493	11	and	and	CCONJ
ejpam-3312	493	12	r.	r.	PROPN
ejpam-3312	493	13	a.	a.	PROPN
ejpam-3312	493	14	hosny	hosny	PROPN
ejpam-3312	493	15	,	,	PUNCT
ejpam-3312	493	16	on	on	ADP
ejpam-3312	493	17	soft	soft	ADJ
ejpam-3312	493	18	separation	separation	NOUN
ejpam-3312	493	19	axioms	axiom	NOUN
ejpam-3312	493	20	via	via	ADP
ejpam-3312	493	21	β	β	X
ejpam-3312	493	22	-	-	ADJ
ejpam-3312	493	23	open	open	ADJ
ejpam-3312	493	24	soft	soft	ADJ
ejpam-3312	493	25	sets	set	NOUN
ejpam-3312	493	26	,	,	PUNCT
ejpam-3312	493	27	south	south	ADJ
ejpam-3312	493	28	asian	asian	ADJ
ejpam-3312	493	29	journal	journal	NOUN
ejpam-3312	493	30	of	of	ADP
ejpam-3312	493	31	mathematics	mathematic	NOUN
ejpam-3312	493	32	,	,	PUNCT
ejpam-3312	493	33	5	5	NUM
ejpam-3312	493	34	(	(	PUNCT
ejpam-3312	493	35	6	6	NUM
ejpam-3312	493	36	)	)	PUNCT
ejpam-3312	493	37	(	(	PUNCT
ejpam-3312	493	38	2015	2015	NUM
ejpam-3312	493	39	)	)	PUNCT
ejpam-3312	493	40	252	252	NUM
ejpam-3312	493	41	-	-	SYM
ejpam-3312	493	42	264	264	NUM
ejpam-3312	493	43	.	.	PUNCT
ejpam-3312	494	1	[	[	X
ejpam-3312	494	2	2	2	NUM
ejpam-3312	494	3	]	]	PUNCT
ejpam-3312	494	4	m.	m.	NOUN
ejpam-3312	494	5	e.	e.	PROPN
ejpam-3312	494	6	abd	abd	PROPN
ejpam-3312	495	1	el	el	PROPN
ejpam-3312	495	2	-	-	PROPN
ejpam-3312	495	3	monsef	monsef	PROPN
ejpam-3312	495	4	,	,	PUNCT
ejpam-3312	495	5	s.	s.	PROPN
ejpam-3312	495	6	n.	n.	PROPN
ejpam-3312	495	7	el	el	PROPN
ejpam-3312	495	8	-	-	PUNCT
ejpam-3312	495	9	deeb	deeb	PROPN
ejpam-3312	495	10	and	and	CCONJ
ejpam-3312	495	11	r.	r.	PROPN
ejpam-3312	495	12	a.	a.	PROPN
ejpam-3312	495	13	mahmoud	mahmoud	PROPN
ejpam-3312	495	14	,	,	PUNCT
ejpam-3312	495	15	β	β	ADJ
ejpam-3312	495	16	-	-	ADJ
ejpam-3312	495	17	open	open	ADJ
ejpam-3312	495	18	sets	set	NOUN
ejpam-3312	495	19	and	and	CCONJ
ejpam-3312	495	20	βcontinuous	βcontinuous	ADJ
ejpam-3312	495	21	mappings	mapping	NOUN
ejpam-3312	495	22	,	,	PUNCT
ejpam-3312	495	23	bulletin	bulletin	NOUN
ejpam-3312	495	24	of	of	ADP
ejpam-3312	495	25	the	the	DET
ejpam-3312	495	26	faculty	faculty	NOUN
ejpam-3312	495	27	of	of	ADP
ejpam-3312	495	28	science	science	PROPN
ejpam-3312	495	29	assiut	assiut	PROPN
ejpam-3312	495	30	university	university	PROPN
ejpam-3312	495	31	,	,	PUNCT
ejpam-3312	495	32	12	12	NUM
ejpam-3312	495	33	(	(	PUNCT
ejpam-3312	495	34	1983	1983	NUM
ejpam-3312	495	35	)	)	PUNCT
ejpam-3312	496	1	77	77	NUM
ejpam-3312	496	2	-	-	SYM
ejpam-3312	496	3	90	90	NUM
ejpam-3312	496	4	.	.	PUNCT
ejpam-3312	497	1	[	[	X
ejpam-3312	497	2	3	3	X
ejpam-3312	497	3	]	]	X
ejpam-3312	497	4	m.	m.	NOUN
ejpam-3312	497	5	abo	abo	NOUN
ejpam-3312	497	6	-	-	PUNCT
ejpam-3312	497	7	elhamayel	elhamayel	NOUN
ejpam-3312	497	8	and	and	CCONJ
ejpam-3312	497	9	t.	t.	PROPN
ejpam-3312	497	10	m.	m.	PROPN
ejpam-3312	497	11	al	al	PROPN
ejpam-3312	497	12	-	-	PUNCT
ejpam-3312	497	13	shami	shami	PROPN
ejpam-3312	497	14	,	,	PUNCT
ejpam-3312	497	15	supra	supra	PROPN
ejpam-3312	497	16	homeomorphism	homeomorphism	PROPN
ejpam-3312	497	17	in	in	ADP
ejpam-3312	497	18	supra	supra	PROPN
ejpam-3312	497	19	topological	topological	PROPN
ejpam-3312	497	20	ordered	order	VERB
ejpam-3312	497	21	spaces	space	NOUN
ejpam-3312	497	22	,	,	PUNCT
ejpam-3312	497	23	facta	facta	PROPN
ejpam-3312	497	24	universitatis	universitatis	PROPN
ejpam-3312	497	25	,	,	PUNCT
ejpam-3312	497	26	series	series	NOUN
ejpam-3312	497	27	:	:	PUNCT
ejpam-3312	497	28	mathematics	mathematic	NOUN
ejpam-3312	497	29	and	and	CCONJ
ejpam-3312	497	30	informatics	informatic	NOUN
ejpam-3312	497	31	,	,	PUNCT
ejpam-3312	497	32	31	31	NUM
ejpam-3312	497	33	(	(	PUNCT
ejpam-3312	497	34	5	5	NUM
ejpam-3312	497	35	)	)	PUNCT
ejpam-3312	497	36	(	(	PUNCT
ejpam-3312	497	37	2016	2016	NUM
ejpam-3312	497	38	)	)	PUNCT
ejpam-3312	497	39	1091	1091	NUM
ejpam-3312	497	40	-	-	SYM
ejpam-3312	497	41	1106	1106	NUM
ejpam-3312	497	42	.	.	PUNCT
ejpam-3312	498	1	[	[	X
ejpam-3312	498	2	4	4	X
ejpam-3312	498	3	]	]	X
ejpam-3312	498	4	u.	u.	NOUN
ejpam-3312	498	5	acar	acar	PROPN
ejpam-3312	498	6	,	,	PUNCT
ejpam-3312	498	7	f.	f.	PROPN
ejpam-3312	498	8	koyuncu	koyuncu	PROPN
ejpam-3312	498	9	and	and	CCONJ
ejpam-3312	498	10	b.	b.	PROPN
ejpam-3312	498	11	tanay	tanay	PROPN
ejpam-3312	498	12	,	,	PUNCT
ejpam-3312	498	13	soft	soft	ADJ
ejpam-3312	498	14	sets	set	NOUN
ejpam-3312	498	15	and	and	CCONJ
ejpam-3312	498	16	soft	soft	ADJ
ejpam-3312	498	17	rings	ring	NOUN
ejpam-3312	498	18	,	,	PUNCT
ejpam-3312	498	19	computers	computer	NOUN
ejpam-3312	498	20	and	and	CCONJ
ejpam-3312	498	21	mathematics	mathematic	NOUN
ejpam-3312	498	22	with	with	ADP
ejpam-3312	498	23	applications	application	NOUN
ejpam-3312	498	24	,	,	PUNCT
ejpam-3312	498	25	59	59	NUM
ejpam-3312	498	26	(	(	PUNCT
ejpam-3312	498	27	2010	2010	NUM
ejpam-3312	498	28	)	)	PUNCT
ejpam-3312	498	29	3458	3458	NUM
ejpam-3312	498	30	-	-	SYM
ejpam-3312	498	31	3463	3463	NUM
ejpam-3312	498	32	.	.	PUNCT
ejpam-3312	499	1	[	[	X
ejpam-3312	499	2	5	5	X
ejpam-3312	499	3	]	]	PUNCT
ejpam-3312	499	4	m.	m.	NOUN
ejpam-3312	499	5	akdag	akdag	PROPN
ejpam-3312	499	6	and	and	CCONJ
ejpam-3312	499	7	a.	a.	NOUN
ejpam-3312	499	8	ozkan	ozkan	PROPN
ejpam-3312	499	9	,	,	PUNCT
ejpam-3312	499	10	on	on	ADP
ejpam-3312	499	11	soft	soft	ADJ
ejpam-3312	499	12	β	β	NOUN
ejpam-3312	499	13	-	-	ADJ
ejpam-3312	499	14	open	open	ADJ
ejpam-3312	499	15	sets	set	NOUN
ejpam-3312	499	16	and	and	CCONJ
ejpam-3312	499	17	soft	soft	ADJ
ejpam-3312	499	18	β	β	ADJ
ejpam-3312	499	19	-	-	ADJ
ejpam-3312	499	20	continuous	continuous	ADJ
ejpam-3312	499	21	functions	function	NOUN
ejpam-3312	499	22	,	,	PUNCT
ejpam-3312	499	23	the	the	DET
ejpam-3312	499	24	scientific	scientific	ADJ
ejpam-3312	499	25	world	world	NOUN
ejpam-3312	499	26	journal	journal	NOUN
ejpam-3312	499	27	,	,	PUNCT
ejpam-3312	499	28	volume	volume	NOUN
ejpam-3312	499	29	2014	2014	NUM
ejpam-3312	499	30	,	,	PUNCT
ejpam-3312	499	31	article	article	NOUN
ejpam-3312	499	32	i	i	PROPN
ejpam-3312	499	33	d	d	PROPN
ejpam-3312	499	34	843456	843456	NUM
ejpam-3312	499	35	,	,	PUNCT
ejpam-3312	499	36	6	6	NUM
ejpam-3312	499	37	pages	page	NOUN
ejpam-3312	499	38	.	.	PUNCT
ejpam-3312	500	1	[	[	X
ejpam-3312	500	2	6	6	NUM
ejpam-3312	500	3	]	]	PUNCT
ejpam-3312	500	4	h.	h.	PROPN
ejpam-3312	500	5	aktas	aktas	PROPN
ejpam-3312	500	6	and	and	CCONJ
ejpam-3312	500	7	n.	n.	PROPN
ejpam-3312	500	8	cagman	cagman	PROPN
ejpam-3312	500	9	,	,	PUNCT
ejpam-3312	500	10	soft	soft	ADJ
ejpam-3312	500	11	sets	set	NOUN
ejpam-3312	500	12	and	and	CCONJ
ejpam-3312	500	13	soft	soft	ADJ
ejpam-3312	500	14	groups	group	NOUN
ejpam-3312	500	15	,	,	PUNCT
ejpam-3312	500	16	information	information	NOUN
ejpam-3312	500	17	sciences	science	NOUN
ejpam-3312	500	18	,	,	PUNCT
ejpam-3312	500	19	77	77	NUM
ejpam-3312	500	20	(	(	PUNCT
ejpam-3312	500	21	2007	2007	NUM
ejpam-3312	500	22	)	)	PUNCT
ejpam-3312	500	23	2726	2726	NUM
ejpam-3312	500	24	-	-	SYM
ejpam-3312	500	25	2735	2735	NUM
ejpam-3312	500	26	.	.	PUNCT
ejpam-3312	501	1	[	[	X
ejpam-3312	501	2	7	7	X
ejpam-3312	501	3	]	]	X
ejpam-3312	501	4	m.	m.	NOUN
ejpam-3312	501	5	i.	i.	PROPN
ejpam-3312	501	6	ali	ali	PROPN
ejpam-3312	501	7	,	,	PUNCT
ejpam-3312	501	8	f.	f.	PROPN
ejpam-3312	501	9	feng	feng	PROPN
ejpam-3312	501	10	,	,	PUNCT
ejpam-3312	501	11	x.	x.	PROPN
ejpam-3312	501	12	liu	liu	PROPN
ejpam-3312	501	13	,	,	PUNCT
ejpam-3312	501	14	w.	w.	PROPN
ejpam-3312	501	15	k.	k.	PROPN
ejpam-3312	501	16	min	min	PROPN
ejpam-3312	501	17	and	and	CCONJ
ejpam-3312	501	18	m.	m.	NOUN
ejpam-3312	501	19	shabir	shabir	PROPN
ejpam-3312	501	20	,	,	PUNCT
ejpam-3312	501	21	on	on	ADP
ejpam-3312	501	22	some	some	DET
ejpam-3312	501	23	new	new	ADJ
ejpam-3312	501	24	operations	operation	NOUN
ejpam-3312	501	25	in	in	ADP
ejpam-3312	501	26	soft	soft	ADJ
ejpam-3312	501	27	set	set	NOUN
ejpam-3312	501	28	theory	theory	NOUN
ejpam-3312	501	29	,	,	PUNCT
ejpam-3312	501	30	computers	computer	NOUN
ejpam-3312	501	31	and	and	CCONJ
ejpam-3312	501	32	mathematics	mathematic	NOUN
ejpam-3312	501	33	with	with	ADP
ejpam-3312	501	34	applications	application	NOUN
ejpam-3312	501	35	,	,	PUNCT
ejpam-3312	501	36	57	57	NUM
ejpam-3312	501	37	(	(	PUNCT
ejpam-3312	501	38	2009	2009	NUM
ejpam-3312	501	39	)	)	PUNCT
ejpam-3312	501	40	1547	1547	NUM
ejpam-3312	501	41	-	-	SYM
ejpam-3312	501	42	1553	1553	NUM
ejpam-3312	501	43	.	.	PUNCT
ejpam-3312	502	1	[	[	X
ejpam-3312	502	2	8	8	NUM
ejpam-3312	502	3	]	]	PUNCT
ejpam-3312	502	4	t.	t.	PROPN
ejpam-3312	502	5	m.	m.	PROPN
ejpam-3312	502	6	al	al	PROPN
ejpam-3312	502	7	-	-	PUNCT
ejpam-3312	502	8	shami	shami	PROPN
ejpam-3312	502	9	,	,	PUNCT
ejpam-3312	502	10	supra	supra	PROPN
ejpam-3312	502	11	β	β	NOUN
ejpam-3312	502	12	-	-	ADJ
ejpam-3312	502	13	bicontinuous	bicontinuous	ADJ
ejpam-3312	502	14	maps	map	NOUN
ejpam-3312	502	15	via	via	ADP
ejpam-3312	502	16	topological	topological	ADJ
ejpam-3312	502	17	ordered	order	VERB
ejpam-3312	502	18	spaces	space	NOUN
ejpam-3312	502	19	,	,	PUNCT
ejpam-3312	502	20	mathematical	mathematical	ADJ
ejpam-3312	502	21	sciences	science	NOUN
ejpam-3312	502	22	letters	letter	NOUN
ejpam-3312	502	23	,	,	PUNCT
ejpam-3312	502	24	6	6	NUM
ejpam-3312	502	25	(	(	PUNCT
ejpam-3312	502	26	3	3	NUM
ejpam-3312	502	27	)	)	PUNCT
ejpam-3312	502	28	(	(	PUNCT
ejpam-3312	502	29	2017	2017	NUM
ejpam-3312	502	30	)	)	PUNCT
ejpam-3312	502	31	239	239	NUM
ejpam-3312	502	32	-	-	SYM
ejpam-3312	502	33	247	247	NUM
ejpam-3312	502	34	.	.	PUNCT
ejpam-3312	503	1	[	[	X
ejpam-3312	503	2	9	9	NUM
ejpam-3312	503	3	]	]	PUNCT
ejpam-3312	503	4	t.	t.	PROPN
ejpam-3312	503	5	m.	m.	PROPN
ejpam-3312	503	6	al	al	PROPN
ejpam-3312	503	7	-	-	PUNCT
ejpam-3312	503	8	shami	shami	PROPN
ejpam-3312	503	9	,	,	PUNCT
ejpam-3312	503	10	corrigendum	corrigendum	ADJ
ejpam-3312	503	11	to	to	ADP
ejpam-3312	503	12	”	"	PUNCT
ejpam-3312	503	13	separation	separation	NOUN
ejpam-3312	503	14	axioms	axiom	NOUN
ejpam-3312	503	15	on	on	ADP
ejpam-3312	503	16	soft	soft	ADJ
ejpam-3312	503	17	topological	topological	ADJ
ejpam-3312	503	18	spaces	space	NOUN
ejpam-3312	503	19	,	,	PUNCT
ejpam-3312	503	20	ann	ann	PROPN
ejpam-3312	503	21	.	.	PROPN
ejpam-3312	503	22	fuzzy	fuzzy	ADJ
ejpam-3312	503	23	math	math	NOUN
ejpam-3312	503	24	.	.	PUNCT
ejpam-3312	504	1	inform	inform	NOUN
ejpam-3312	504	2	.	.	PUNCT
ejpam-3312	505	1	11	11	NUM
ejpam-3312	505	2	(	(	PUNCT
ejpam-3312	505	3	4	4	NUM
ejpam-3312	505	4	)	)	PUNCT
ejpam-3312	505	5	(	(	PUNCT
ejpam-3312	505	6	2016	2016	NUM
ejpam-3312	505	7	)	)	PUNCT
ejpam-3312	505	8	511	511	NUM
ejpam-3312	505	9	-	-	SYM
ejpam-3312	505	10	525	525	NUM
ejpam-3312	505	11	”	"	PUNCT
ejpam-3312	505	12	,	,	PUNCT
ejpam-3312	505	13	annals	annal	NOUN
ejpam-3312	505	14	of	of	ADP
ejpam-3312	505	15	fuzzy	fuzzy	ADJ
ejpam-3312	505	16	mathematics	mathematic	NOUN
ejpam-3312	505	17	and	and	CCONJ
ejpam-3312	505	18	informatics	informatic	NOUN
ejpam-3312	505	19	,	,	PUNCT
ejpam-3312	505	20	15	15	NUM
ejpam-3312	505	21	(	(	PUNCT
ejpam-3312	505	22	3	3	NUM
ejpam-3312	505	23	)	)	PUNCT
ejpam-3312	505	24	(	(	PUNCT
ejpam-3312	505	25	2018	2018	NUM
ejpam-3312	505	26	)	)	PUNCT
ejpam-3312	505	27	309	309	NUM
ejpam-3312	505	28	-	-	SYM
ejpam-3312	505	29	312	312	NUM
ejpam-3312	505	30	.	.	PUNCT
ejpam-3312	506	1	[	[	X
ejpam-3312	506	2	10	10	NUM
ejpam-3312	506	3	]	]	PUNCT
ejpam-3312	506	4	t.	t.	PROPN
ejpam-3312	506	5	m.	m.	PROPN
ejpam-3312	506	6	al	al	PROPN
ejpam-3312	506	7	-	-	PUNCT
ejpam-3312	506	8	shami	shami	PROPN
ejpam-3312	506	9	,	,	PUNCT
ejpam-3312	506	10	on	on	ADP
ejpam-3312	506	11	some	some	DET
ejpam-3312	506	12	maps	map	NOUN
ejpam-3312	506	13	in	in	ADP
ejpam-3312	506	14	supra	supra	PROPN
ejpam-3312	506	15	topological	topological	PROPN
ejpam-3312	506	16	ordered	order	VERB
ejpam-3312	506	17	spaces	space	NOUN
ejpam-3312	506	18	,	,	PUNCT
ejpam-3312	506	19	journal	journal	NOUN
ejpam-3312	506	20	of	of	ADP
ejpam-3312	506	21	new	new	ADJ
ejpam-3312	506	22	theory	theory	NOUN
ejpam-3312	506	23	,	,	PUNCT
ejpam-3312	506	24	20	20	NUM
ejpam-3312	506	25	(	(	PUNCT
ejpam-3312	506	26	2018	2018	NUM
ejpam-3312	506	27	)	)	PUNCT
ejpam-3312	506	28	76	76	NUM
ejpam-3312	506	29	-	-	SYM
ejpam-3312	506	30	92	92	NUM
ejpam-3312	506	31	.	.	PUNCT
ejpam-3312	507	1	[	[	X
ejpam-3312	507	2	11	11	NUM
ejpam-3312	507	3	]	]	PUNCT
ejpam-3312	507	4	t.	t.	PROPN
ejpam-3312	507	5	m.	m.	PROPN
ejpam-3312	507	6	al	al	PROPN
ejpam-3312	507	7	-	-	PUNCT
ejpam-3312	507	8	shami	shami	PROPN
ejpam-3312	507	9	,	,	PUNCT
ejpam-3312	507	10	soft	soft	ADJ
ejpam-3312	507	11	somewhere	somewhere	ADV
ejpam-3312	507	12	dense	dense	ADJ
ejpam-3312	507	13	sets	set	NOUN
ejpam-3312	507	14	on	on	ADP
ejpam-3312	507	15	soft	soft	ADJ
ejpam-3312	507	16	topological	topological	ADJ
ejpam-3312	507	17	spaces	space	NOUN
ejpam-3312	507	18	,	,	PUNCT
ejpam-3312	507	19	communications	communication	NOUN
ejpam-3312	507	20	of	of	ADP
ejpam-3312	507	21	the	the	DET
ejpam-3312	507	22	korean	korean	ADJ
ejpam-3312	507	23	mathematical	mathematical	ADJ
ejpam-3312	507	24	society	society	NOUN
ejpam-3312	507	25	,	,	PUNCT
ejpam-3312	507	26	(	(	PUNCT
ejpam-3312	507	27	2018	2018	NUM
ejpam-3312	507	28	)	)	PUNCT
ejpam-3312	507	29	accepted	accept	VERB
ejpam-3312	507	30	.	.	PUNCT
ejpam-3312	508	1	[	[	X
ejpam-3312	508	2	12	12	NUM
ejpam-3312	508	3	]	]	PUNCT
ejpam-3312	508	4	t.	t.	PROPN
ejpam-3312	508	5	m.	m.	PROPN
ejpam-3312	508	6	al	al	PROPN
ejpam-3312	508	7	-	-	PUNCT
ejpam-3312	508	8	shami	shami	PROPN
ejpam-3312	508	9	and	and	CCONJ
ejpam-3312	508	10	m.	m.	PROPN
ejpam-3312	508	11	k.	k.	PROPN
ejpam-3312	508	12	tahat	tahat	PROPN
ejpam-3312	508	13	,	,	PUNCT
ejpam-3312	508	14	i	i	PRON
ejpam-3312	508	15	(	(	PUNCT
ejpam-3312	508	16	d	d	PROPN
ejpam-3312	508	17	,	,	PUNCT
ejpam-3312	508	18	b)-supra	b)-supra	PUNCT
ejpam-3312	508	19	pre	pre	X
ejpam-3312	508	20	maps	map	NOUN
ejpam-3312	508	21	via	via	ADP
ejpam-3312	508	22	supra	supra	PROPN
ejpam-3312	508	23	topological	topological	PROPN
ejpam-3312	508	24	ordered	order	VERB
ejpam-3312	508	25	spaces	space	NOUN
ejpam-3312	508	26	,	,	PUNCT
ejpam-3312	508	27	journal	journal	NOUN
ejpam-3312	508	28	of	of	ADP
ejpam-3312	508	29	progressive	progressive	ADJ
ejpam-3312	508	30	research	research	NOUN
ejpam-3312	508	31	in	in	ADP
ejpam-3312	508	32	mathematics	mathematic	NOUN
ejpam-3312	508	33	,	,	PUNCT
ejpam-3312	508	34	12	12	NUM
ejpam-3312	508	35	(	(	PUNCT
ejpam-3312	508	36	3	3	NUM
ejpam-3312	508	37	)	)	PUNCT
ejpam-3312	508	38	(	(	PUNCT
ejpam-3312	508	39	2017	2017	NUM
ejpam-3312	508	40	)	)	PUNCT
ejpam-3312	508	41	19892001	19892001	NUM
ejpam-3312	508	42	.	.	PUNCT
ejpam-3312	509	1	references	reference	NOUN
ejpam-3312	509	2	191	191	NUM
ejpam-3312	510	1	[	[	X
ejpam-3312	510	2	13	13	NUM
ejpam-3312	510	3	]	]	PUNCT
ejpam-3312	510	4	t.	t.	PROPN
ejpam-3312	510	5	m.	m.	PROPN
ejpam-3312	510	6	al	al	PROPN
ejpam-3312	510	7	-	-	PUNCT
ejpam-3312	510	8	shami	shami	PROPN
ejpam-3312	510	9	,	,	PUNCT
ejpam-3312	510	10	m.	m.	PROPN
ejpam-3312	510	11	e.	e.	PROPN
ejpam-3312	510	12	el	el	PROPN
ejpam-3312	510	13	-	-	PROPN
ejpam-3312	510	14	shafei	shafei	PROPN
ejpam-3312	510	15	and	and	CCONJ
ejpam-3312	510	16	m.	m.	NOUN
ejpam-3312	510	17	abo	abo	NOUN
ejpam-3312	510	18	-	-	PUNCT
ejpam-3312	510	19	elhamayel	elhamayel	NOUN
ejpam-3312	510	20	,	,	PUNCT
ejpam-3312	510	21	on	on	ADP
ejpam-3312	510	22	soft	soft	ADJ
ejpam-3312	510	23	topological	topological	ADJ
ejpam-3312	510	24	ordered	order	VERB
ejpam-3312	510	25	spaces	space	NOUN
ejpam-3312	510	26	,	,	PUNCT
ejpam-3312	510	27	journal	journal	NOUN
ejpam-3312	510	28	of	of	ADP
ejpam-3312	510	29	king	king	PROPN
ejpam-3312	510	30	saud	saud	PROPN
ejpam-3312	510	31	university	university	PROPN
ejpam-3312	510	32	-	-	PUNCT
ejpam-3312	510	33	science	science	NOUN
ejpam-3312	510	34	,	,	PUNCT
ejpam-3312	510	35	(	(	PUNCT
ejpam-3312	510	36	2018	2018	NUM
ejpam-3312	510	37	)	)	PUNCT
ejpam-3312	510	38	https://doi.org/10.1016/j.jksus.2018.06.005	https://doi.org/10.1016/j.jksus.2018.06.005	NOUN
ejpam-3312	510	39	.	.	PUNCT
ejpam-3312	511	1	[	[	X
ejpam-3312	511	2	14	14	NUM
ejpam-3312	511	3	]	]	PUNCT
ejpam-3312	511	4	t.	t.	PROPN
ejpam-3312	511	5	m.	m.	PROPN
ejpam-3312	511	6	al	al	PROPN
ejpam-3312	511	7	-	-	PUNCT
ejpam-3312	511	8	shami	shami	PROPN
ejpam-3312	511	9	,	,	PUNCT
ejpam-3312	512	1	m.	m.	PROPN
ejpam-3312	512	2	e.	e.	PROPN
ejpam-3312	512	3	el	el	PROPN
ejpam-3312	512	4	-	-	PROPN
ejpam-3312	512	5	shafei	shafei	PROPN
ejpam-3312	512	6	and	and	CCONJ
ejpam-3312	512	7	m.	m.	NOUN
ejpam-3312	512	8	abo	abo	NOUN
ejpam-3312	512	9	-	-	PUNCT
ejpam-3312	512	10	elhamayel	elhamayel	NOUN
ejpam-3312	512	11	,	,	PUNCT
ejpam-3312	512	12	on	on	ADP
ejpam-3312	512	13	soft	soft	ADJ
ejpam-3312	512	14	ordered	order	VERB
ejpam-3312	512	15	maps	map	NOUN
ejpam-3312	512	16	,	,	PUNCT
ejpam-3312	512	17	submitted	submit	VERB
ejpam-3312	512	18	.	.	PUNCT
ejpam-3312	513	1	[	[	X
ejpam-3312	513	2	15	15	NUM
ejpam-3312	513	3	]	]	X
ejpam-3312	513	4	t.	t.	PROPN
ejpam-3312	513	5	m.	m.	PROPN
ejpam-3312	513	6	al	al	PROPN
ejpam-3312	513	7	-	-	PUNCT
ejpam-3312	513	8	shami	shami	PROPN
ejpam-3312	513	9	,	,	PUNCT
ejpam-3312	513	10	l.	l.	PROPN
ejpam-3312	513	11	d.	d.	PROPN
ejpam-3312	513	12	r.	r.	PROPN
ejpam-3312	513	13	kočinac	kočinac	PROPN
ejpam-3312	513	14	,	,	PUNCT
ejpam-3312	513	15	the	the	DET
ejpam-3312	513	16	equivalence	equivalence	NOUN
ejpam-3312	513	17	between	between	ADP
ejpam-3312	513	18	the	the	DET
ejpam-3312	513	19	enriched	enrich	VERB
ejpam-3312	513	20	and	and	CCONJ
ejpam-3312	513	21	extended	extended	ADJ
ejpam-3312	513	22	soft	soft	ADJ
ejpam-3312	513	23	topologies	topology	NOUN
ejpam-3312	513	24	,	,	PUNCT
ejpam-3312	513	25	submitted	submit	VERB
ejpam-3312	513	26	.	.	PUNCT
ejpam-3312	514	1	[	[	X
ejpam-3312	514	2	16	16	NUM
ejpam-3312	514	3	]	]	X
ejpam-3312	514	4	a.	a.	NOUN
ejpam-3312	514	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-3312	514	6	and	and	CCONJ
ejpam-3312	514	7	h.	h.	PROPN
ejpam-3312	514	8	aygün	aygün	PROPN
ejpam-3312	514	9	,	,	PUNCT
ejpam-3312	514	10	some	some	DET
ejpam-3312	514	11	notes	note	NOUN
ejpam-3312	514	12	on	on	ADP
ejpam-3312	514	13	soft	soft	ADJ
ejpam-3312	514	14	topological	topological	ADJ
ejpam-3312	514	15	spaces	space	NOUN
ejpam-3312	514	16	,	,	PUNCT
ejpam-3312	514	17	neural	neural	ADJ
ejpam-3312	514	18	computers	computer	NOUN
ejpam-3312	514	19	and	and	CCONJ
ejpam-3312	514	20	applications	application	NOUN
ejpam-3312	514	21	,	,	PUNCT
ejpam-3312	514	22	21	21	NUM
ejpam-3312	514	23	(	(	PUNCT
ejpam-3312	514	24	2012	2012	NUM
ejpam-3312	514	25	)	)	PUNCT
ejpam-3312	514	26	113	113	NUM
ejpam-3312	514	27	-	-	SYM
ejpam-3312	514	28	119	119	NUM
ejpam-3312	514	29	.	.	PUNCT
ejpam-3312	515	1	[	[	X
ejpam-3312	515	2	17	17	NUM
ejpam-3312	515	3	]	]	PUNCT
ejpam-3312	515	4	k.	k.	PROPN
ejpam-3312	516	1	v.	v.	PROPN
ejpam-3312	516	2	babitha	babitha	PROPN
ejpam-3312	516	3	and	and	CCONJ
ejpam-3312	516	4	j.j	j.j	PROPN
ejpam-3312	516	5	.	.	PROPN
ejpam-3312	516	6	sunil	sunil	PROPN
ejpam-3312	516	7	,	,	PUNCT
ejpam-3312	516	8	soft	soft	ADJ
ejpam-3312	516	9	set	set	NOUN
ejpam-3312	516	10	relations	relation	NOUN
ejpam-3312	516	11	and	and	CCONJ
ejpam-3312	516	12	functions	function	NOUN
ejpam-3312	516	13	,	,	PUNCT
ejpam-3312	516	14	computers	computer	NOUN
ejpam-3312	516	15	and	and	CCONJ
ejpam-3312	516	16	mathematics	mathematic	NOUN
ejpam-3312	516	17	with	with	ADP
ejpam-3312	516	18	applications	application	NOUN
ejpam-3312	516	19	,	,	PUNCT
ejpam-3312	516	20	60	60	NUM
ejpam-3312	516	21	(	(	PUNCT
ejpam-3312	516	22	2010	2010	NUM
ejpam-3312	516	23	)	)	PUNCT
ejpam-3312	516	24	1840	1840	NUM
ejpam-3312	516	25	-	-	SYM
ejpam-3312	516	26	1849	1849	NUM
ejpam-3312	516	27	.	.	PUNCT
ejpam-3312	517	1	[	[	X
ejpam-3312	517	2	18	18	NUM
ejpam-3312	517	3	]	]	PUNCT
ejpam-3312	517	4	p.	p.	PROPN
ejpam-3312	517	5	das	das	PROPN
ejpam-3312	517	6	,	,	PUNCT
ejpam-3312	517	7	separation	separation	NOUN
ejpam-3312	517	8	axioms	axiom	NOUN
ejpam-3312	517	9	in	in	ADP
ejpam-3312	517	10	ordered	order	VERB
ejpam-3312	517	11	spaces	space	NOUN
ejpam-3312	517	12	,	,	PUNCT
ejpam-3312	517	13	soochow	soochow	PROPN
ejpam-3312	517	14	journal	journal	NOUN
ejpam-3312	517	15	of	of	ADP
ejpam-3312	517	16	mathematics	mathematic	NOUN
ejpam-3312	517	17	,	,	PUNCT
ejpam-3312	517	18	30	30	NUM
ejpam-3312	517	19	(	(	PUNCT
ejpam-3312	517	20	4	4	NUM
ejpam-3312	517	21	)	)	PUNCT
ejpam-3312	517	22	(	(	PUNCT
ejpam-3312	517	23	2004	2004	NUM
ejpam-3312	517	24	)	)	PUNCT
ejpam-3312	517	25	447	447	NUM
ejpam-3312	517	26	-	-	SYM
ejpam-3312	517	27	454	454	NUM
ejpam-3312	517	28	.	.	PUNCT
ejpam-3312	518	1	[	[	X
ejpam-3312	518	2	19	19	NUM
ejpam-3312	518	3	]	]	X
ejpam-3312	518	4	s.	s.	PROPN
ejpam-3312	518	5	das	das	PROPN
ejpam-3312	518	6	and	and	CCONJ
ejpam-3312	518	7	s.	s.	PROPN
ejpam-3312	518	8	k.	k.	PROPN
ejpam-3312	518	9	samanta	samanta	PROPN
ejpam-3312	518	10	,	,	PUNCT
ejpam-3312	518	11	soft	soft	ADJ
ejpam-3312	518	12	metric	metric	ADJ
ejpam-3312	518	13	,	,	PUNCT
ejpam-3312	518	14	annals	annal	NOUN
ejpam-3312	518	15	of	of	ADP
ejpam-3312	518	16	fuzzy	fuzzy	ADJ
ejpam-3312	518	17	mathematics	mathematic	NOUN
ejpam-3312	518	18	and	and	CCONJ
ejpam-3312	518	19	informatics	informatic	NOUN
ejpam-3312	518	20	,	,	PUNCT
ejpam-3312	518	21	1	1	NUM
ejpam-3312	518	22	(	(	PUNCT
ejpam-3312	518	23	2013	2013	NUM
ejpam-3312	518	24	)	)	PUNCT
ejpam-3312	518	25	77	77	NUM
ejpam-3312	518	26	-	-	SYM
ejpam-3312	518	27	94	94	NUM
ejpam-3312	518	28	.	.	PUNCT
ejpam-3312	519	1	[	[	X
ejpam-3312	519	2	20	20	NUM
ejpam-3312	519	3	]	]	PUNCT
ejpam-3312	519	4	m.	m.	PROPN
ejpam-3312	519	5	e.	e.	PROPN
ejpam-3312	519	6	el	el	PROPN
ejpam-3312	519	7	-	-	PROPN
ejpam-3312	519	8	shafei	shafei	PROPN
ejpam-3312	519	9	,	,	PUNCT
ejpam-3312	519	10	m.	m.	NOUN
ejpam-3312	519	11	abo	abo	NOUN
ejpam-3312	519	12	-	-	PUNCT
ejpam-3312	519	13	elhamayel	elhamayel	NOUN
ejpam-3312	519	14	and	and	CCONJ
ejpam-3312	519	15	t.	t.	PROPN
ejpam-3312	519	16	m.	m.	PROPN
ejpam-3312	519	17	al	al	PROPN
ejpam-3312	519	18	-	-	PUNCT
ejpam-3312	519	19	shami	shami	PROPN
ejpam-3312	519	20	,	,	PUNCT
ejpam-3312	519	21	generating	generate	VERB
ejpam-3312	519	22	ordered	order	VERB
ejpam-3312	519	23	maps	map	NOUN
ejpam-3312	519	24	via	via	ADP
ejpam-3312	519	25	supra	supra	PROPN
ejpam-3312	519	26	topological	topological	PROPN
ejpam-3312	519	27	ordered	order	VERB
ejpam-3312	519	28	spaces	space	NOUN
ejpam-3312	519	29	,	,	PUNCT
ejpam-3312	519	30	international	international	ADJ
ejpam-3312	519	31	journal	journal	NOUN
ejpam-3312	519	32	of	of	ADP
ejpam-3312	519	33	modern	modern	ADJ
ejpam-3312	519	34	mathematical	mathematical	ADJ
ejpam-3312	519	35	sciences	science	NOUN
ejpam-3312	519	36	,	,	PUNCT
ejpam-3312	519	37	15	15	NUM
ejpam-3312	519	38	(	(	PUNCT
ejpam-3312	519	39	3	3	NUM
ejpam-3312	519	40	)	)	PUNCT
ejpam-3312	519	41	(	(	PUNCT
ejpam-3312	519	42	2017	2017	NUM
ejpam-3312	519	43	)	)	PUNCT
ejpam-3312	519	44	339	339	NUM
ejpam-3312	519	45	-	-	SYM
ejpam-3312	519	46	357	357	NUM
ejpam-3312	519	47	.	.	PUNCT
ejpam-3312	520	1	[	[	X
ejpam-3312	520	2	21	21	NUM
ejpam-3312	520	3	]	]	PUNCT
ejpam-3312	520	4	m.	m.	PROPN
ejpam-3312	520	5	e.	e.	PROPN
ejpam-3312	520	6	el	el	PROPN
ejpam-3312	520	7	-	-	PROPN
ejpam-3312	520	8	shafei	shafei	PROPN
ejpam-3312	520	9	,	,	PUNCT
ejpam-3312	520	10	m.	m.	NOUN
ejpam-3312	520	11	abo	abo	NOUN
ejpam-3312	520	12	-	-	PUNCT
ejpam-3312	520	13	elhamayel	elhamayel	NOUN
ejpam-3312	520	14	and	and	CCONJ
ejpam-3312	520	15	t.	t.	PROPN
ejpam-3312	520	16	m.	m.	PROPN
ejpam-3312	520	17	al	al	PROPN
ejpam-3312	520	18	-	-	PUNCT
ejpam-3312	520	19	shami	shami	PROPN
ejpam-3312	520	20	,	,	PUNCT
ejpam-3312	520	21	strong	strong	ADJ
ejpam-3312	520	22	separation	separation	NOUN
ejpam-3312	520	23	axioms	axiom	NOUN
ejpam-3312	520	24	in	in	ADP
ejpam-3312	520	25	supra	supra	PROPN
ejpam-3312	520	26	topological	topological	ADJ
ejpam-3312	520	27	ordered	order	VERB
ejpam-3312	520	28	spaces	space	NOUN
ejpam-3312	520	29	,	,	PUNCT
ejpam-3312	520	30	mathematical	mathematical	ADJ
ejpam-3312	520	31	sciences	science	NOUN
ejpam-3312	520	32	letters	letter	NOUN
ejpam-3312	520	33	,	,	PUNCT
ejpam-3312	520	34	6	6	NUM
ejpam-3312	520	35	(	(	PUNCT
ejpam-3312	520	36	3	3	NUM
ejpam-3312	520	37	)	)	PUNCT
ejpam-3312	520	38	(	(	PUNCT
ejpam-3312	520	39	2017	2017	NUM
ejpam-3312	520	40	)	)	PUNCT
ejpam-3312	520	41	271	271	NUM
ejpam-3312	520	42	-	-	SYM
ejpam-3312	520	43	277	277	NUM
ejpam-3312	520	44	.	.	PUNCT
ejpam-3312	521	1	[	[	X
ejpam-3312	521	2	22	22	NUM
ejpam-3312	521	3	]	]	PUNCT
ejpam-3312	521	4	m.	m.	PROPN
ejpam-3312	521	5	e.	e.	PROPN
ejpam-3312	521	6	el	el	PROPN
ejpam-3312	521	7	-	-	PROPN
ejpam-3312	521	8	shafei	shafei	PROPN
ejpam-3312	521	9	,	,	PUNCT
ejpam-3312	521	10	m.	m.	NOUN
ejpam-3312	521	11	abo	abo	NOUN
ejpam-3312	521	12	-	-	PUNCT
ejpam-3312	521	13	elhamayel	elhamayel	NOUN
ejpam-3312	521	14	and	and	CCONJ
ejpam-3312	521	15	t.	t.	PROPN
ejpam-3312	521	16	m.	m.	PROPN
ejpam-3312	521	17	al	al	PROPN
ejpam-3312	521	18	-	-	PUNCT
ejpam-3312	521	19	shami	shami	PROPN
ejpam-3312	521	20	,	,	PUNCT
ejpam-3312	521	21	supra	supra	PROPN
ejpam-3312	521	22	r	r	PROPN
ejpam-3312	521	23	-	-	PUNCT
ejpam-3312	521	24	homeomorphism	homeomorphism	PROPN
ejpam-3312	521	25	in	in	ADP
ejpam-3312	521	26	supra	supra	PROPN
ejpam-3312	521	27	topological	topological	PROPN
ejpam-3312	521	28	ordered	order	VERB
ejpam-3312	521	29	spaces	space	NOUN
ejpam-3312	521	30	,	,	PUNCT
ejpam-3312	521	31	international	international	ADJ
ejpam-3312	521	32	journal	journal	NOUN
ejpam-3312	521	33	of	of	ADP
ejpam-3312	521	34	algebra	algebra	PROPN
ejpam-3312	521	35	and	and	CCONJ
ejpam-3312	521	36	statistics	statistic	NOUN
ejpam-3312	521	37	,	,	PUNCT
ejpam-3312	521	38	6	6	NUM
ejpam-3312	521	39	(	(	PUNCT
ejpam-3312	521	40	1	1	NUM
ejpam-3312	521	41	-	-	SYM
ejpam-3312	521	42	2	2	NUM
ejpam-3312	521	43	)	)	PUNCT
ejpam-3312	521	44	(	(	PUNCT
ejpam-3312	521	45	2017	2017	NUM
ejpam-3312	521	46	)	)	PUNCT
ejpam-3312	521	47	158	158	NUM
ejpam-3312	521	48	-	-	SYM
ejpam-3312	521	49	167	167	NUM
ejpam-3312	521	50	.	.	PUNCT
ejpam-3312	522	1	[	[	X
ejpam-3312	522	2	23	23	NUM
ejpam-3312	522	3	]	]	PUNCT
ejpam-3312	522	4	m.	m.	PROPN
ejpam-3312	522	5	e.	e.	PROPN
ejpam-3312	522	6	el	el	PROPN
ejpam-3312	522	7	-	-	PROPN
ejpam-3312	522	8	shafei	shafei	PROPN
ejpam-3312	522	9	,	,	PUNCT
ejpam-3312	522	10	m.	m.	NOUN
ejpam-3312	522	11	abo	abo	NOUN
ejpam-3312	522	12	-	-	PUNCT
ejpam-3312	522	13	elhamayel	elhamayel	NOUN
ejpam-3312	522	14	and	and	CCONJ
ejpam-3312	522	15	t.	t.	PROPN
ejpam-3312	522	16	m.	m.	PROPN
ejpam-3312	522	17	al	al	PROPN
ejpam-3312	522	18	-	-	PUNCT
ejpam-3312	522	19	shami	shami	PROPN
ejpam-3312	522	20	,	,	PUNCT
ejpam-3312	522	21	partial	partial	ADJ
ejpam-3312	522	22	soft	soft	ADJ
ejpam-3312	522	23	separation	separation	NOUN
ejpam-3312	522	24	axioms	axiom	NOUN
ejpam-3312	522	25	and	and	CCONJ
ejpam-3312	522	26	soft	soft	ADJ
ejpam-3312	522	27	compac	compac	NOUN
ejpam-3312	522	28	spaces	space	NOUN
ejpam-3312	522	29	,	,	PUNCT
ejpam-3312	522	30	filomat	filomat	PROPN
ejpam-3312	522	31	32	32	NUM
ejpam-3312	522	32	(	(	PUNCT
ejpam-3312	522	33	2018	2018	NUM
ejpam-3312	522	34	)	)	PUNCT
ejpam-3312	522	35	accepted	accept	VERB
ejpam-3312	522	36	.	.	PUNCT
ejpam-3312	523	1	[	[	X
ejpam-3312	523	2	24	24	NUM
ejpam-3312	523	3	]	]	X
ejpam-3312	523	4	f.	f.	PROPN
ejpam-3312	523	5	feng	feng	PROPN
ejpam-3312	523	6	and	and	CCONJ
ejpam-3312	523	7	y.	y.	PROPN
ejpam-3312	523	8	m.	m.	PROPN
ejpam-3312	523	9	li	li	PROPN
ejpam-3312	523	10	,	,	PUNCT
ejpam-3312	523	11	soft	soft	ADJ
ejpam-3312	523	12	subsets	subset	NOUN
ejpam-3312	523	13	and	and	CCONJ
ejpam-3312	523	14	soft	soft	ADJ
ejpam-3312	523	15	product	product	NOUN
ejpam-3312	523	16	operations	operation	NOUN
ejpam-3312	523	17	,	,	PUNCT
ejpam-3312	523	18	information	information	NOUN
ejpam-3312	523	19	science	science	NOUN
ejpam-3312	523	20	,	,	PUNCT
ejpam-3312	523	21	232	232	NUM
ejpam-3312	523	22	(	(	PUNCT
ejpam-3312	523	23	2013	2013	NUM
ejpam-3312	523	24	)	)	PUNCT
ejpam-3312	523	25	1468	1468	NUM
ejpam-3312	523	26	-	-	SYM
ejpam-3312	523	27	1470	1470	NUM
ejpam-3312	523	28	.	.	PUNCT
ejpam-3312	524	1	[	[	X
ejpam-3312	524	2	25	25	NUM
ejpam-3312	524	3	]	]	PUNCT
ejpam-3312	524	4	m.	m.	NOUN
ejpam-3312	524	5	d.	d.	PROPN
ejpam-3312	524	6	green	green	PROPN
ejpam-3312	524	7	,	,	PUNCT
ejpam-3312	524	8	locally	locally	ADV
ejpam-3312	524	9	convex	convex	ADJ
ejpam-3312	524	10	topology	topology	NOUN
ejpam-3312	524	11	on	on	ADP
ejpam-3312	524	12	a	a	DET
ejpam-3312	524	13	preordered	preordere	VERB
ejpam-3312	524	14	space	space	NOUN
ejpam-3312	524	15	,	,	PUNCT
ejpam-3312	524	16	pascific	pascific	ADJ
ejpam-3312	524	17	journal	journal	NOUN
ejpam-3312	524	18	of	of	ADP
ejpam-3312	524	19	mathematics	mathematic	NOUN
ejpam-3312	524	20	,	,	PUNCT
ejpam-3312	524	21	26	26	NUM
ejpam-3312	524	22	(	(	PUNCT
ejpam-3312	524	23	1968	1968	NUM
ejpam-3312	524	24	)	)	PUNCT
ejpam-3312	524	25	487	487	NUM
ejpam-3312	524	26	-	-	SYM
ejpam-3312	524	27	491	491	NUM
ejpam-3312	524	28	.	.	PUNCT
ejpam-3312	525	1	[	[	X
ejpam-3312	525	2	26	26	NUM
ejpam-3312	525	3	]	]	PUNCT
ejpam-3312	525	4	t.	t.	PROPN
ejpam-3312	525	5	hida	hida	PROPN
ejpam-3312	525	6	,	,	PUNCT
ejpam-3312	525	7	a	a	DET
ejpam-3312	525	8	comprasion	comprasion	NOUN
ejpam-3312	525	9	of	of	ADP
ejpam-3312	525	10	two	two	NUM
ejpam-3312	525	11	formulations	formulation	NOUN
ejpam-3312	525	12	of	of	ADP
ejpam-3312	525	13	soft	soft	ADJ
ejpam-3312	525	14	compactness	compactness	NOUN
ejpam-3312	525	15	,	,	PUNCT
ejpam-3312	525	16	annals	annal	NOUN
ejpam-3312	525	17	of	of	ADP
ejpam-3312	525	18	fuzzy	fuzzy	ADJ
ejpam-3312	525	19	mathematics	mathematic	NOUN
ejpam-3312	525	20	and	and	CCONJ
ejpam-3312	525	21	informatics	informatic	NOUN
ejpam-3312	525	22	,	,	PUNCT
ejpam-3312	525	23	8(4	8(4	NUM
ejpam-3312	525	24	)	)	PUNCT
ejpam-3312	525	25	(	(	PUNCT
ejpam-3312	525	26	2014	2014	NUM
ejpam-3312	525	27	)	)	PUNCT
ejpam-3312	525	28	511	511	NUM
ejpam-3312	525	29	-	-	SYM
ejpam-3312	525	30	524	524	NUM
ejpam-3312	525	31	.	.	PUNCT
ejpam-3312	526	1	[	[	X
ejpam-3312	526	2	27	27	NUM
ejpam-3312	526	3	]	]	PUNCT
ejpam-3312	526	4	t.	t.	PROPN
ejpam-3312	526	5	hida	hida	PROPN
ejpam-3312	526	6	,	,	PUNCT
ejpam-3312	526	7	soft	soft	ADJ
ejpam-3312	526	8	topological	topological	ADJ
ejpam-3312	526	9	group	group	NOUN
ejpam-3312	526	10	,	,	PUNCT
ejpam-3312	526	11	annals	annal	NOUN
ejpam-3312	526	12	of	of	ADP
ejpam-3312	526	13	fuzzy	fuzzy	ADJ
ejpam-3312	526	14	mathematics	mathematic	NOUN
ejpam-3312	526	15	and	and	CCONJ
ejpam-3312	526	16	informatics	informatic	NOUN
ejpam-3312	526	17	,	,	PUNCT
ejpam-3312	526	18	8	8	NUM
ejpam-3312	526	19	(	(	PUNCT
ejpam-3312	526	20	6	6	NUM
ejpam-3312	526	21	)	)	PUNCT
ejpam-3312	526	22	(	(	PUNCT
ejpam-3312	526	23	2014	2014	NUM
ejpam-3312	526	24	)	)	PUNCT
ejpam-3312	526	25	1001	1001	NUM
ejpam-3312	526	26	-	-	SYM
ejpam-3312	526	27	1025	1025	NUM
ejpam-3312	526	28	.	.	PUNCT
ejpam-3312	527	1	references	reference	NOUN
ejpam-3312	527	2	192	192	NUM
ejpam-3312	527	3	[	[	X
ejpam-3312	527	4	28	28	NUM
ejpam-3312	527	5	]	]	X
ejpam-3312	527	6	d.	d.	PROPN
ejpam-3312	527	7	s.	s.	PROPN
ejpam-3312	527	8	leela	leela	PROPN
ejpam-3312	527	9	and	and	CCONJ
ejpam-3312	527	10	g.	g.	PROPN
ejpam-3312	527	11	balasubramanian	balasubramanian	PROPN
ejpam-3312	527	12	,	,	PUNCT
ejpam-3312	527	13	new	new	ADJ
ejpam-3312	527	14	separation	separation	NOUN
ejpam-3312	527	15	axioms	axiom	VERB
ejpam-3312	527	16	in	in	ADP
ejpam-3312	527	17	ordered	order	VERB
ejpam-3312	527	18	topological	topological	ADJ
ejpam-3312	527	19	spaces	space	NOUN
ejpam-3312	527	20	,	,	PUNCT
ejpam-3312	527	21	indian	indian	ADJ
ejpam-3312	527	22	journal	journal	NOUN
ejpam-3312	527	23	of	of	ADP
ejpam-3312	527	24	pure	pure	ADJ
ejpam-3312	527	25	and	and	CCONJ
ejpam-3312	527	26	applied	applied	ADJ
ejpam-3312	527	27	mathematics	mathematic	NOUN
ejpam-3312	527	28	,	,	PUNCT
ejpam-3312	527	29	33	33	NUM
ejpam-3312	527	30	(	(	PUNCT
ejpam-3312	527	31	2002	2002	NUM
ejpam-3312	527	32	)	)	PUNCT
ejpam-3312	527	33	1011	1011	NUM
ejpam-3312	527	34	-	-	SYM
ejpam-3312	527	35	1016	1016	NUM
ejpam-3312	527	36	.	.	PUNCT
ejpam-3312	528	1	[	[	X
ejpam-3312	528	2	29	29	NUM
ejpam-3312	528	3	]	]	X
ejpam-3312	528	4	f.	f.	PROPN
ejpam-3312	528	5	li	li	PROPN
ejpam-3312	528	6	,	,	PUNCT
ejpam-3312	528	7	notes	note	VERB
ejpam-3312	528	8	on	on	ADP
ejpam-3312	528	9	the	the	DET
ejpam-3312	528	10	soft	soft	ADJ
ejpam-3312	528	11	operations	operation	NOUN
ejpam-3312	528	12	,	,	PUNCT
ejpam-3312	528	13	arpn	arpn	VERB
ejpam-3312	528	14	journal	journal	NOUN
ejpam-3312	528	15	of	of	ADP
ejpam-3312	528	16	systems	system	NOUN
ejpam-3312	528	17	and	and	CCONJ
ejpam-3312	528	18	software	software	NOUN
ejpam-3312	528	19	,	,	PUNCT
ejpam-3312	528	20	1	1	NUM
ejpam-3312	528	21	(	(	PUNCT
ejpam-3312	528	22	6	6	NUM
ejpam-3312	528	23	)	)	PUNCT
ejpam-3312	528	24	(	(	PUNCT
ejpam-3312	528	25	2011	2011	NUM
ejpam-3312	528	26	)	)	PUNCT
ejpam-3312	528	27	205	205	NUM
ejpam-3312	528	28	-	-	SYM
ejpam-3312	528	29	208	208	NUM
ejpam-3312	528	30	.	.	PUNCT
ejpam-3312	529	1	[	[	X
ejpam-3312	529	2	30	30	NUM
ejpam-3312	529	3	]	]	PUNCT
ejpam-3312	529	4	x.	x.	NOUN
ejpam-3312	529	5	liu	liu	PROPN
ejpam-3312	529	6	and	and	CCONJ
ejpam-3312	529	7	f.	f.	PROPN
ejpam-3312	529	8	feng	feng	PROPN
ejpam-3312	529	9	,	,	PUNCT
ejpam-3312	529	10	y.	y.	PROPN
ejpam-3312	529	11	b.	b.	PROPN
ejpam-3312	529	12	jun	jun	PROPN
ejpam-3312	529	13	,	,	PUNCT
ejpam-3312	529	14	a	a	DET
ejpam-3312	529	15	note	note	NOUN
ejpam-3312	529	16	on	on	ADP
ejpam-3312	529	17	generalized	generalized	ADJ
ejpam-3312	529	18	soft	soft	ADJ
ejpam-3312	529	19	equal	equal	ADJ
ejpam-3312	529	20	relations	relation	NOUN
ejpam-3312	529	21	,	,	PUNCT
ejpam-3312	529	22	computers	computer	NOUN
ejpam-3312	529	23	and	and	CCONJ
ejpam-3312	529	24	mathematics	mathematic	NOUN
ejpam-3312	529	25	with	with	ADP
ejpam-3312	529	26	applications	application	NOUN
ejpam-3312	529	27	,	,	PUNCT
ejpam-3312	529	28	64	64	NUM
ejpam-3312	529	29	(	(	PUNCT
ejpam-3312	529	30	2012	2012	NUM
ejpam-3312	529	31	)	)	PUNCT
ejpam-3312	529	32	572	572	NUM
ejpam-3312	529	33	-	-	SYM
ejpam-3312	529	34	578	578	NUM
ejpam-3312	529	35	.	.	PUNCT
ejpam-3312	530	1	[	[	X
ejpam-3312	530	2	31	31	NUM
ejpam-3312	530	3	]	]	PUNCT
ejpam-3312	530	4	p.	p.	PROPN
ejpam-3312	530	5	k.	k.	PROPN
ejpam-3312	531	1	maji	maji	PROPN
ejpam-3312	531	2	,	,	PUNCT
ejpam-3312	531	3	r.	r.	PROPN
ejpam-3312	531	4	biswas	biswas	PROPN
ejpam-3312	531	5	and	and	CCONJ
ejpam-3312	531	6	r.	r.	PROPN
ejpam-3312	531	7	roy	roy	PROPN
ejpam-3312	531	8	,	,	PUNCT
ejpam-3312	531	9	soft	soft	ADJ
ejpam-3312	531	10	set	set	NOUN
ejpam-3312	531	11	theory	theory	NOUN
ejpam-3312	531	12	,	,	PUNCT
ejpam-3312	531	13	computers	computer	NOUN
ejpam-3312	531	14	and	and	CCONJ
ejpam-3312	531	15	mathematics	mathematic	NOUN
ejpam-3312	531	16	with	with	ADP
ejpam-3312	531	17	applications	application	NOUN
ejpam-3312	531	18	,	,	PUNCT
ejpam-3312	531	19	45	45	NUM
ejpam-3312	531	20	(	(	PUNCT
ejpam-3312	531	21	2003	2003	NUM
ejpam-3312	531	22	)	)	PUNCT
ejpam-3312	531	23	555	555	NUM
ejpam-3312	531	24	-	-	SYM
ejpam-3312	531	25	562	562	NUM
ejpam-3312	531	26	.	.	PUNCT
ejpam-3312	532	1	[	[	X
ejpam-3312	532	2	32	32	NUM
ejpam-3312	532	3	]	]	PUNCT
ejpam-3312	532	4	s.	s.	PROPN
ejpam-3312	532	5	d.	d.	PROPN
ejpam-3312	532	6	mccartan	mccartan	PROPN
ejpam-3312	532	7	,	,	PUNCT
ejpam-3312	532	8	separation	separation	NOUN
ejpam-3312	532	9	axioms	axiom	NOUN
ejpam-3312	532	10	for	for	ADP
ejpam-3312	532	11	topological	topological	ADJ
ejpam-3312	532	12	ordered	order	VERB
ejpam-3312	532	13	spaces	space	NOUN
ejpam-3312	532	14	,	,	PUNCT
ejpam-3312	532	15	mathematical	mathematical	ADJ
ejpam-3312	532	16	proceedings	proceeding	NOUN
ejpam-3312	532	17	of	of	ADP
ejpam-3312	532	18	the	the	DET
ejpam-3312	532	19	cambridge	cambridge	PROPN
ejpam-3312	532	20	philosophical	philosophical	ADJ
ejpam-3312	532	21	society	society	NOUN
ejpam-3312	532	22	,	,	PUNCT
ejpam-3312	532	23	64	64	NUM
ejpam-3312	532	24	(	(	PUNCT
ejpam-3312	532	25	1986	1986	NUM
ejpam-3312	532	26	)	)	PUNCT
ejpam-3312	532	27	965	965	NUM
ejpam-3312	532	28	-	-	SYM
ejpam-3312	532	29	973	973	NUM
ejpam-3312	532	30	.	.	PUNCT
ejpam-3312	533	1	[	[	X
ejpam-3312	533	2	33	33	NUM
ejpam-3312	533	3	]	]	PUNCT
ejpam-3312	533	4	s.	s.	PROPN
ejpam-3312	533	5	d.	d.	PROPN
ejpam-3312	533	6	mccartan	mccartan	PROPN
ejpam-3312	533	7	,	,	PUNCT
ejpam-3312	533	8	bicontinuous	bicontinuous	ADJ
ejpam-3312	533	9	preordered	preordere	VERB
ejpam-3312	533	10	topological	topological	ADJ
ejpam-3312	533	11	spaces	space	NOUN
ejpam-3312	533	12	,	,	PUNCT
ejpam-3312	533	13	pacific	pacific	PROPN
ejpam-3312	533	14	journal	journal	NOUN
ejpam-3312	533	15	of	of	ADP
ejpam-3312	533	16	mathematics	mathematic	NOUN
ejpam-3312	533	17	,	,	PUNCT
ejpam-3312	533	18	38	38	NUM
ejpam-3312	533	19	(	(	PUNCT
ejpam-3312	533	20	1971	1971	NUM
ejpam-3312	533	21	)	)	PUNCT
ejpam-3312	533	22	523	523	NUM
ejpam-3312	533	23	-	-	NUM
ejpam-3312	533	24	529	529	NUM
ejpam-3312	533	25	.	.	PUNCT
ejpam-3312	534	1	[	[	X
ejpam-3312	534	2	34	34	NUM
ejpam-3312	534	3	]	]	X
ejpam-3312	534	4	o.	o.	PROPN
ejpam-3312	534	5	mendez	mendez	PROPN
ejpam-3312	534	6	,	,	PUNCT
ejpam-3312	534	7	l.	l.	PROPN
ejpam-3312	534	8	h.	h.	PROPN
ejpam-3312	534	9	popescu	popescu	PROPN
ejpam-3312	534	10	and	and	CCONJ
ejpam-3312	534	11	e.	e.	PROPN
ejpam-3312	534	12	d.	d.	PROPN
ejpam-3312	534	13	schwab	schwab	PROPN
ejpam-3312	534	14	,	,	PUNCT
ejpam-3312	534	15	inner	inner	ADJ
ejpam-3312	534	16	separation	separation	NOUN
ejpam-3312	534	17	structures	structure	NOUN
ejpam-3312	534	18	for	for	ADP
ejpam-3312	534	19	topological	topological	ADJ
ejpam-3312	534	20	spaces	space	NOUN
ejpam-3312	534	21	,	,	PUNCT
ejpam-3312	534	22	blakan	blakan	PROPN
ejpam-3312	534	23	journal	journal	PROPN
ejpam-3312	534	24	of	of	ADP
ejpam-3312	534	25	geometry	geometry	NOUN
ejpam-3312	534	26	and	and	CCONJ
ejpam-3312	534	27	its	its	PRON
ejpam-3312	534	28	applications	application	NOUN
ejpam-3312	534	29	,	,	PUNCT
ejpam-3312	534	30	13	13	NUM
ejpam-3312	534	31	(	(	PUNCT
ejpam-3312	534	32	2008	2008	NUM
ejpam-3312	534	33	)	)	PUNCT
ejpam-3312	534	34	59	59	NUM
ejpam-3312	534	35	-	-	SYM
ejpam-3312	534	36	65	65	NUM
ejpam-3312	534	37	.	.	PUNCT
ejpam-3312	535	1	[	[	X
ejpam-3312	535	2	35	35	NUM
ejpam-3312	535	3	]	]	X
ejpam-3312	535	4	w.	w.	PROPN
ejpam-3312	535	5	k.	k.	PROPN
ejpam-3312	535	6	min	min	PROPN
ejpam-3312	535	7	,	,	PUNCT
ejpam-3312	535	8	a	a	DET
ejpam-3312	535	9	note	note	NOUN
ejpam-3312	535	10	on	on	ADP
ejpam-3312	535	11	soft	soft	ADJ
ejpam-3312	535	12	topological	topological	ADJ
ejpam-3312	535	13	spaces	space	NOUN
ejpam-3312	535	14	,	,	PUNCT
ejpam-3312	535	15	computers	computer	NOUN
ejpam-3312	535	16	and	and	CCONJ
ejpam-3312	535	17	mathematics	mathematic	NOUN
ejpam-3312	535	18	with	with	ADP
ejpam-3312	535	19	applications	application	NOUN
ejpam-3312	535	20	,	,	PUNCT
ejpam-3312	535	21	62	62	NUM
ejpam-3312	535	22	(	(	PUNCT
ejpam-3312	535	23	2011	2011	NUM
ejpam-3312	535	24	)	)	PUNCT
ejpam-3312	535	25	3524	3524	NUM
ejpam-3312	535	26	-	-	PUNCT
ejpam-3312	535	27	3528	3528	NUM
ejpam-3312	535	28	.	.	PUNCT
ejpam-3312	536	1	[	[	X
ejpam-3312	536	2	36	36	NUM
ejpam-3312	536	3	]	]	X
ejpam-3312	536	4	d.	d.	PROPN
ejpam-3312	536	5	molodtsov	molodtsov	PROPN
ejpam-3312	536	6	,	,	PUNCT
ejpam-3312	536	7	soft	soft	ADJ
ejpam-3312	536	8	set	set	NOUN
ejpam-3312	536	9	theory	theory	NOUN
ejpam-3312	536	10	-	-	PUNCT
ejpam-3312	536	11	first	first	ADJ
ejpam-3312	536	12	results	result	NOUN
ejpam-3312	536	13	,	,	PUNCT
ejpam-3312	536	14	computers	computer	NOUN
ejpam-3312	536	15	and	and	CCONJ
ejpam-3312	536	16	mathematics	mathematic	NOUN
ejpam-3312	536	17	with	with	ADP
ejpam-3312	536	18	applications	application	NOUN
ejpam-3312	536	19	,	,	PUNCT
ejpam-3312	536	20	37	37	NUM
ejpam-3312	536	21	(	(	PUNCT
ejpam-3312	536	22	1999	1999	NUM
ejpam-3312	536	23	)	)	PUNCT
ejpam-3312	536	24	19	19	NUM
ejpam-3312	536	25	-	-	SYM
ejpam-3312	536	26	31	31	NUM
ejpam-3312	536	27	.	.	PUNCT
ejpam-3312	537	1	[	[	X
ejpam-3312	537	2	37	37	NUM
ejpam-3312	537	3	]	]	X
ejpam-3312	537	4	l.	l.	PROPN
ejpam-3312	537	5	nachbin	nachbin	PROPN
ejpam-3312	537	6	,	,	PUNCT
ejpam-3312	537	7	topology	topology	NOUN
ejpam-3312	537	8	and	and	CCONJ
ejpam-3312	537	9	ordered	order	VERB
ejpam-3312	537	10	,	,	PUNCT
ejpam-3312	537	11	d.	d.	PROPN
ejpam-3312	537	12	van	van	PROPN
ejpam-3312	537	13	nostrand	nostrand	PROPN
ejpam-3312	537	14	inc	inc	PROPN
ejpam-3312	537	15	.	.	PROPN
ejpam-3312	537	16	princeton	princeton	PROPN
ejpam-3312	537	17	,	,	PUNCT
ejpam-3312	537	18	new	new	PROPN
ejpam-3312	537	19	jersey	jersey	PROPN
ejpam-3312	537	20	,	,	PUNCT
ejpam-3312	537	21	(	(	PUNCT
ejpam-3312	537	22	1965	1965	NUM
ejpam-3312	537	23	)	)	PUNCT
ejpam-3312	537	24	.	.	PUNCT
ejpam-3312	538	1	[	[	X
ejpam-3312	538	2	38	38	NUM
ejpam-3312	538	3	]	]	PUNCT
ejpam-3312	538	4	s.	s.	PROPN
ejpam-3312	538	5	nazmul	nazmul	PROPN
ejpam-3312	538	6	and	and	CCONJ
ejpam-3312	538	7	s.	s.	PROPN
ejpam-3312	538	8	k.	k.	PROPN
ejpam-3312	538	9	samanta	samanta	PROPN
ejpam-3312	538	10	,	,	PUNCT
ejpam-3312	538	11	neigbourhood	neigbourhood	PROPN
ejpam-3312	538	12	properties	property	NOUN
ejpam-3312	538	13	of	of	ADP
ejpam-3312	538	14	soft	soft	ADJ
ejpam-3312	538	15	topological	topological	ADJ
ejpam-3312	538	16	spaces	space	NOUN
ejpam-3312	538	17	,	,	PUNCT
ejpam-3312	538	18	annals	annal	NOUN
ejpam-3312	538	19	of	of	ADP
ejpam-3312	538	20	fuzzy	fuzzy	ADJ
ejpam-3312	538	21	mathematics	mathematic	NOUN
ejpam-3312	538	22	and	and	CCONJ
ejpam-3312	538	23	informatics	informatic	NOUN
ejpam-3312	538	24	,	,	PUNCT
ejpam-3312	538	25	1	1	NUM
ejpam-3312	538	26	(	(	PUNCT
ejpam-3312	538	27	2013	2013	NUM
ejpam-3312	538	28	)	)	PUNCT
ejpam-3312	538	29	1	1	NUM
ejpam-3312	538	30	-	-	SYM
ejpam-3312	538	31	15	15	NUM
ejpam-3312	538	32	.	.	PUNCT
ejpam-3312	539	1	[	[	X
ejpam-3312	539	2	39	39	NUM
ejpam-3312	539	3	]	]	PUNCT
ejpam-3312	539	4	d.	d.	PROPN
ejpam-3312	539	5	pei	pei	PROPN
ejpam-3312	539	6	and	and	CCONJ
ejpam-3312	539	7	d.	d.	PROPN
ejpam-3312	539	8	miao	miao	PROPN
ejpam-3312	539	9	,	,	PUNCT
ejpam-3312	539	10	from	from	ADP
ejpam-3312	539	11	soft	soft	ADJ
ejpam-3312	539	12	sets	set	NOUN
ejpam-3312	539	13	to	to	ADP
ejpam-3312	539	14	information	information	NOUN
ejpam-3312	539	15	system	system	NOUN
ejpam-3312	539	16	,	,	PUNCT
ejpam-3312	539	17	in	in	ADP
ejpam-3312	539	18	proceedings	proceeding	NOUN
ejpam-3312	539	19	of	of	ADP
ejpam-3312	539	20	the	the	DET
ejpam-3312	539	21	ieee	ieee	NOUN
ejpam-3312	539	22	international	international	PROPN
ejpam-3312	539	23	conference	conference	NOUN
ejpam-3312	539	24	on	on	ADP
ejpam-3312	539	25	granular	granular	ADJ
ejpam-3312	539	26	computing	computing	NOUN
ejpam-3312	539	27	,	,	PUNCT
ejpam-3312	539	28	2	2	NUM
ejpam-3312	539	29	(	(	PUNCT
ejpam-3312	539	30	2005	2005	NUM
ejpam-3312	539	31	)	)	PUNCT
ejpam-3312	539	32	617	617	NUM
ejpam-3312	539	33	-	-	SYM
ejpam-3312	539	34	621	621	NUM
ejpam-3312	539	35	.	.	PUNCT
ejpam-3312	540	1	[	[	X
ejpam-3312	540	2	40	40	NUM
ejpam-3312	540	3	]	]	PUNCT
ejpam-3312	540	4	l.	l.	PROPN
ejpam-3312	540	5	popescu	popescu	PROPN
ejpam-3312	540	6	,	,	PUNCT
ejpam-3312	540	7	r	r	NOUN
ejpam-3312	540	8	-	-	PUNCT
ejpam-3312	540	9	separated	separate	VERB
ejpam-3312	540	10	spaces	space	NOUN
ejpam-3312	540	11	,	,	PUNCT
ejpam-3312	540	12	blakan	blakan	PROPN
ejpam-3312	540	13	journal	journal	PROPN
ejpam-3312	540	14	of	of	ADP
ejpam-3312	540	15	geometry	geometry	NOUN
ejpam-3312	540	16	and	and	CCONJ
ejpam-3312	540	17	its	its	PRON
ejpam-3312	540	18	applications	application	NOUN
ejpam-3312	540	19	,	,	PUNCT
ejpam-3312	540	20	6	6	NUM
ejpam-3312	540	21	(	(	PUNCT
ejpam-3312	540	22	2001	2001	NUM
ejpam-3312	540	23	)	)	PUNCT
ejpam-3312	540	24	81	81	NUM
ejpam-3312	540	25	-	-	SYM
ejpam-3312	540	26	88	88	NUM
ejpam-3312	540	27	.	.	PUNCT
ejpam-3312	541	1	[	[	X
ejpam-3312	541	2	41	41	NUM
ejpam-3312	541	3	]	]	PUNCT
ejpam-3312	541	4	k.	k.	PROPN
ejpam-3312	541	5	qin	qin	PROPN
ejpam-3312	541	6	and	and	CCONJ
ejpam-3312	541	7	z.	z.	PROPN
ejpam-3312	541	8	hong	hong	PROPN
ejpam-3312	541	9	,	,	PUNCT
ejpam-3312	541	10	on	on	ADP
ejpam-3312	541	11	soft	soft	ADJ
ejpam-3312	541	12	equality	equality	NOUN
ejpam-3312	541	13	,	,	PUNCT
ejpam-3312	541	14	journal	journal	NOUN
ejpam-3312	541	15	of	of	ADP
ejpam-3312	541	16	computational	computational	ADJ
ejpam-3312	541	17	and	and	CCONJ
ejpam-3312	541	18	applied	applied	ADJ
ejpam-3312	541	19	mathematics	mathematic	NOUN
ejpam-3312	541	20	,	,	PUNCT
ejpam-3312	541	21	234	234	NUM
ejpam-3312	541	22	(	(	PUNCT
ejpam-3312	541	23	2010	2010	NUM
ejpam-3312	541	24	)	)	PUNCT
ejpam-3312	541	25	1347	1347	NUM
ejpam-3312	541	26	-	-	SYM
ejpam-3312	541	27	1355	1355	NUM
ejpam-3312	541	28	.	.	PUNCT
ejpam-3312	542	1	[	[	X
ejpam-3312	542	2	42	42	NUM
ejpam-3312	542	3	]	]	PUNCT
ejpam-3312	542	4	k.	k.	PROPN
ejpam-3312	542	5	k.	k.	PROPN
ejpam-3312	542	6	rao	rao	PROPN
ejpam-3312	542	7	and	and	CCONJ
ejpam-3312	542	8	r.	r.	PROPN
ejpam-3312	542	9	chudamani	chudamani	PROPN
ejpam-3312	542	10	,	,	PUNCT
ejpam-3312	542	11	β	β	X
ejpam-3312	542	12	-	-	PUNCT
ejpam-3312	542	13	homeomorphism	homeomorphism	PROPN
ejpam-3312	542	14	in	in	ADP
ejpam-3312	542	15	topological	topological	ADJ
ejpam-3312	542	16	ordered	order	VERB
ejpam-3312	542	17	spaces	space	NOUN
ejpam-3312	542	18	,	,	PUNCT
ejpam-3312	542	19	international	international	ADJ
ejpam-3312	542	20	journal	journal	NOUN
ejpam-3312	542	21	of	of	ADP
ejpam-3312	542	22	mathematical	mathematical	ADJ
ejpam-3312	542	23	and	and	CCONJ
ejpam-3312	542	24	engineering	engineering	NOUN
ejpam-3312	542	25	,	,	PUNCT
ejpam-3312	542	26	182	182	NUM
ejpam-3312	542	27	(	(	PUNCT
ejpam-3312	542	28	2012	2012	NUM
ejpam-3312	542	29	)	)	PUNCT
ejpam-3312	542	30	1734	1734	NUM
ejpam-3312	542	31	-	-	SYM
ejpam-3312	542	32	1755	1755	NUM
ejpam-3312	542	33	.	.	PUNCT
ejpam-3312	543	1	[	[	X
ejpam-3312	543	2	43	43	NUM
ejpam-3312	543	3	]	]	X
ejpam-3312	543	4	w.	w.	PROPN
ejpam-3312	543	5	rong	rong	PROPN
ejpam-3312	543	6	,	,	PUNCT
ejpam-3312	543	7	the	the	DET
ejpam-3312	543	8	countabilities	countabilitie	NOUN
ejpam-3312	543	9	of	of	ADP
ejpam-3312	543	10	soft	soft	ADJ
ejpam-3312	543	11	topological	topological	ADJ
ejpam-3312	543	12	spaces	space	NOUN
ejpam-3312	543	13	,	,	PUNCT
ejpam-3312	543	14	international	international	ADJ
ejpam-3312	543	15	journal	journal	NOUN
ejpam-3312	543	16	of	of	ADP
ejpam-3312	543	17	mathematical	mathematical	ADJ
ejpam-3312	543	18	,	,	PUNCT
ejpam-3312	543	19	computational	computational	ADJ
ejpam-3312	543	20	,	,	PUNCT
ejpam-3312	543	21	physical	physical	ADJ
ejpam-3312	543	22	,	,	PUNCT
ejpam-3312	543	23	electrical	electrical	ADJ
ejpam-3312	543	24	and	and	CCONJ
ejpam-3312	543	25	computer	computer	NOUN
ejpam-3312	543	26	engineering	engineering	NOUN
ejpam-3312	543	27	,	,	PUNCT
ejpam-3312	543	28	6	6	NUM
ejpam-3312	543	29	(	(	PUNCT
ejpam-3312	543	30	8)	8)	NUM
ejpam-3312	543	31	(	(	PUNCT
ejpam-3312	543	32	2012	2012	NUM
ejpam-3312	543	33	)	)	PUNCT
ejpam-3312	543	34	952	952	NUM
ejpam-3312	543	35	-	-	SYM
ejpam-3312	543	36	955	955	NUM
ejpam-3312	543	37	.	.	PUNCT
ejpam-3312	543	38	references	reference	NOUN
ejpam-3312	543	39	193	193	NUM
ejpam-3312	543	40	[	[	SYM
ejpam-3312	543	41	44	44	NUM
ejpam-3312	543	42	]	]	PUNCT
ejpam-3312	543	43	m.	m.	NOUN
ejpam-3312	543	44	shabir	shabir	PROPN
ejpam-3312	543	45	and	and	CCONJ
ejpam-3312	543	46	m.	m.	PROPN
ejpam-3312	543	47	naz	naz	PROPN
ejpam-3312	543	48	,	,	PUNCT
ejpam-3312	543	49	on	on	ADP
ejpam-3312	543	50	soft	soft	ADJ
ejpam-3312	543	51	topological	topological	ADJ
ejpam-3312	543	52	spaces	space	NOUN
ejpam-3312	543	53	,	,	PUNCT
ejpam-3312	543	54	computers	computer	NOUN
ejpam-3312	543	55	and	and	CCONJ
ejpam-3312	543	56	mathematics	mathematic	NOUN
ejpam-3312	543	57	with	with	ADP
ejpam-3312	543	58	applications	application	NOUN
ejpam-3312	543	59	,	,	PUNCT
ejpam-3312	543	60	61	61	NUM
ejpam-3312	543	61	(	(	PUNCT
ejpam-3312	543	62	2011	2011	NUM
ejpam-3312	543	63	)	)	PUNCT
ejpam-3312	543	64	1786	1786	NUM
ejpam-3312	543	65	-	-	SYM
ejpam-3312	543	66	1799	1799	NUM
ejpam-3312	543	67	.	.	PUNCT
ejpam-3312	544	1	[	[	X
ejpam-3312	544	2	45	45	NUM
ejpam-3312	544	3	]	]	PUNCT
ejpam-3312	544	4	t.	t.	NOUN
ejpam-3312	544	5	shah	shah	PROPN
ejpam-3312	544	6	and	and	CCONJ
ejpam-3312	544	7	s.	s.	PROPN
ejpam-3312	544	8	shaheen	shaheen	PROPN
ejpam-3312	544	9	,	,	PUNCT
ejpam-3312	544	10	soft	soft	ADJ
ejpam-3312	544	11	topological	topological	ADJ
ejpam-3312	544	12	groups	group	NOUN
ejpam-3312	544	13	and	and	CCONJ
ejpam-3312	544	14	rings	ring	NOUN
ejpam-3312	544	15	,	,	PUNCT
ejpam-3312	544	16	annals	annal	NOUN
ejpam-3312	544	17	of	of	ADP
ejpam-3312	544	18	fuzzy	fuzzy	ADJ
ejpam-3312	544	19	mathematics	mathematic	NOUN
ejpam-3312	544	20	and	and	CCONJ
ejpam-3312	544	21	informatics	informatic	NOUN
ejpam-3312	544	22	,	,	PUNCT
ejpam-3312	544	23	7	7	NUM
ejpam-3312	544	24	(	(	PUNCT
ejpam-3312	544	25	5	5	NUM
ejpam-3312	544	26	)	)	PUNCT
ejpam-3312	544	27	(	(	PUNCT
ejpam-3312	544	28	2014	2014	NUM
ejpam-3312	544	29	)	)	PUNCT
ejpam-3312	544	30	725	725	NUM
ejpam-3312	544	31	-	-	SYM
ejpam-3312	544	32	743	743	NUM
ejpam-3312	544	33	.	.	PUNCT
ejpam-3312	545	1	[	[	X
ejpam-3312	545	2	46	46	NUM
ejpam-3312	545	3	]	]	X
ejpam-3312	545	4	i.	i.	PROPN
ejpam-3312	545	5	zorlutuna	zorlutuna	PROPN
ejpam-3312	545	6	,	,	PUNCT
ejpam-3312	545	7	m.	m.	NOUN
ejpam-3312	545	8	akdag	akdag	PROPN
ejpam-3312	545	9	,	,	PUNCT
ejpam-3312	545	10	w.	w.	PROPN
ejpam-3312	545	11	k.	k.	PROPN
ejpam-3312	545	12	min	min	PROPN
ejpam-3312	545	13	and	and	CCONJ
ejpam-3312	545	14	s.	s.	PROPN
ejpam-3312	545	15	k.	k.	PROPN
ejpam-3312	545	16	samanta	samanta	PROPN
ejpam-3312	545	17	,	,	PUNCT
ejpam-3312	545	18	remarks	remark	VERB
ejpam-3312	545	19	on	on	ADP
ejpam-3312	545	20	soft	soft	ADJ
ejpam-3312	545	21	topological	topological	ADJ
ejpam-3312	545	22	spaces	space	NOUN
ejpam-3312	545	23	,	,	PUNCT
ejpam-3312	545	24	annals	annal	NOUN
ejpam-3312	545	25	of	of	ADP
ejpam-3312	545	26	fuzzy	fuzzy	ADJ
ejpam-3312	545	27	mathematics	mathematic	NOUN
ejpam-3312	545	28	and	and	CCONJ
ejpam-3312	545	29	informatics	informatic	NOUN
ejpam-3312	545	30	,	,	PUNCT
ejpam-3312	545	31	2	2	NUM
ejpam-3312	545	32	(	(	PUNCT
ejpam-3312	545	33	2012	2012	NUM
ejpam-3312	545	34	)	)	PUNCT
ejpam-3312	545	35	171	171	NUM
ejpam-3312	545	36	-	-	SYM
ejpam-3312	545	37	185	185	NUM
ejpam-3312	545	38	.	.	PUNCT