id	sid	tid	token	lemma	pos
american_scientific_journal-756	1	1	american	american	PROPN
american_scientific_journal-756	1	2	scientific	scientific	ADJ
american_scientific_journal-756	1	3	research	research	NOUN
american_scientific_journal-756	1	4	journal	journal	NOUN
american_scientific_journal-756	1	5	for	for	ADP
american_scientific_journal-756	1	6	engineering	engineering	NOUN
american_scientific_journal-756	1	7	,	,	PUNCT
american_scientific_journal-756	1	8	technology	technology	NOUN
american_scientific_journal-756	1	9	,	,	PUNCT
american_scientific_journal-756	1	10	and	and	CCONJ
american_scientific_journal-756	1	11	sciences	science	NOUN
american_scientific_journal-756	1	12	(	(	PUNCT
american_scientific_journal-756	1	13	asrjets	asrjet	NOUN
american_scientific_journal-756	1	14	)	)	PUNCT
american_scientific_journal-756	1	15	issn	issn	PROPN
american_scientific_journal-756	1	16	(	(	PUNCT
american_scientific_journal-756	1	17	print	print	NOUN
american_scientific_journal-756	1	18	)	)	PUNCT
american_scientific_journal-756	1	19	2313	2313	NUM
american_scientific_journal-756	1	20	-	-	SYM
american_scientific_journal-756	1	21	4410	4410	NUM
american_scientific_journal-756	1	22	,	,	PUNCT
american_scientific_journal-756	1	23	issn	issn	PROPN
american_scientific_journal-756	1	24	(	(	PUNCT
american_scientific_journal-756	1	25	online	online	ADJ
american_scientific_journal-756	1	26	)	)	PUNCT
american_scientific_journal-756	1	27	2313	2313	NUM
american_scientific_journal-756	1	28	-	-	SYM
american_scientific_journal-756	1	29	4402	4402	NUM
american_scientific_journal-756	1	30	©	©	PROPN
american_scientific_journal-756	1	31	global	global	ADJ
american_scientific_journal-756	1	32	society	society	NOUN
american_scientific_journal-756	1	33	of	of	ADP
american_scientific_journal-756	1	34	scientific	scientific	ADJ
american_scientific_journal-756	1	35	research	research	NOUN
american_scientific_journal-756	1	36	and	and	CCONJ
american_scientific_journal-756	1	37	researchers	researcher	NOUN
american_scientific_journal-756	1	38	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-756	1	39	upper	upper	ADJ
american_scientific_journal-756	1	40	and	and	CCONJ
american_scientific_journal-756	1	41	lower	low	ADJ
american_scientific_journal-756	1	42	𝜶-continuity	𝜶-continuity	NOUN
american_scientific_journal-756	1	43	of	of	ADP
american_scientific_journal-756	1	44	soft	soft	ADJ
american_scientific_journal-756	1	45	multifunctions	multifunction	NOUN
american_scientific_journal-756	1	46	akdağ	akdağ	NOUN
american_scientific_journal-756	1	47	metina	metina	NOUN
american_scientific_journal-756	1	48	,	,	PUNCT
american_scientific_journal-756	1	49	erol	erol	NOUN
american_scientific_journal-756	1	50	fethullahb	fethullahb	NOUN
american_scientific_journal-756	1	51	*	*	NOUN
american_scientific_journal-756	1	52	a	a	PRON
american_scientific_journal-756	1	53	,	,	PUNCT
american_scientific_journal-756	1	54	b	b	PROPN
american_scientific_journal-756	1	55	cumhuriyet	cumhuriyet	PROPN
american_scientific_journal-756	1	56	university	university	NOUN
american_scientific_journal-756	1	57	faculty	faculty	NOUN
american_scientific_journal-756	1	58	of	of	ADP
american_scientific_journal-756	1	59	science	science	PROPN
american_scientific_journal-756	1	60	department	department	PROPN
american_scientific_journal-756	1	61	of	of	ADP
american_scientific_journal-756	1	62	mathematics	mathematics	PROPN
american_scientific_journal-756	1	63	sivas	sivas	PROPN
american_scientific_journal-756	1	64	58140	58140	NUM
american_scientific_journal-756	1	65	turkey	turkey	NOUN
american_scientific_journal-756	1	66	aemail	aemail	NOUN
american_scientific_journal-756	1	67	:	:	PUNCT
american_scientific_journal-756	1	68	makdag@cumhuriyet.edu.tr	makdag@cumhuriyet.edu.tr	ADJ
american_scientific_journal-756	1	69	bemail	bemail	NOUN
american_scientific_journal-756	1	70	:	:	PUNCT
american_scientific_journal-756	1	71	feerol@cumhuriyet.edu.tr	feerol@cumhuriyet.edu.tr	PROPN
american_scientific_journal-756	1	72	abstract	abstract	NOUN
american_scientific_journal-756	1	73	in	in	ADP
american_scientific_journal-756	1	74	this	this	DET
american_scientific_journal-756	1	75	paper	paper	NOUN
american_scientific_journal-756	1	76	,	,	PUNCT
american_scientific_journal-756	1	77	we	we	PRON
american_scientific_journal-756	1	78	introduced	introduce	VERB
american_scientific_journal-756	1	79	the	the	DET
american_scientific_journal-756	1	80	upper	upper	ADJ
american_scientific_journal-756	1	81	and	and	CCONJ
american_scientific_journal-756	1	82	lower	low	ADJ
american_scientific_journal-756	1	83	α	α	ADJ
american_scientific_journal-756	1	84	-	-	ADJ
american_scientific_journal-756	1	85	continuous	continuous	ADJ
american_scientific_journal-756	1	86	soft	soft	ADJ
american_scientific_journal-756	1	87	multifunctions	multifunction	NOUN
american_scientific_journal-756	1	88	.	.	PUNCT
american_scientific_journal-756	2	1	also	also	ADV
american_scientific_journal-756	2	2	we	we	PRON
american_scientific_journal-756	2	3	obtain	obtain	VERB
american_scientific_journal-756	2	4	some	some	DET
american_scientific_journal-756	2	5	characterizations	characterization	NOUN
american_scientific_journal-756	2	6	and	and	CCONJ
american_scientific_journal-756	2	7	several	several	ADJ
american_scientific_journal-756	2	8	properties	property	NOUN
american_scientific_journal-756	2	9	concerning	concern	VERB
american_scientific_journal-756	2	10	upper	upper	ADJ
american_scientific_journal-756	2	11	and	and	CCONJ
american_scientific_journal-756	2	12	lower	low	ADJ
american_scientific_journal-756	2	13	α	α	ADJ
american_scientific_journal-756	2	14	-	-	ADJ
american_scientific_journal-756	2	15	continuous	continuous	ADJ
american_scientific_journal-756	2	16	soft	soft	ADJ
american_scientific_journal-756	2	17	multifunctions	multifunction	NOUN
american_scientific_journal-756	2	18	.	.	PUNCT
american_scientific_journal-756	3	1	keywords	keyword	NOUN
american_scientific_journal-756	3	2	:	:	PUNCT
american_scientific_journal-756	3	3	soft	soft	ADJ
american_scientific_journal-756	3	4	sets	set	NOUN
american_scientific_journal-756	3	5	;	;	PUNCT
american_scientific_journal-756	3	6	soft	soft	ADJ
american_scientific_journal-756	3	7	multifunction	multifunction	NOUN
american_scientific_journal-756	3	8	;	;	PUNCT
american_scientific_journal-756	3	9	soft	soft	ADJ
american_scientific_journal-756	3	10	continuity	continuity	NOUN
american_scientific_journal-756	3	11	;	;	PUNCT
american_scientific_journal-756	3	12	soft	soft	ADJ
american_scientific_journal-756	3	13	topological	topological	ADJ
american_scientific_journal-756	3	14	spaces	space	NOUN
american_scientific_journal-756	3	15	.	.	PUNCT
american_scientific_journal-756	4	1	1	1	X
american_scientific_journal-756	4	2	.	.	X
american_scientific_journal-756	4	3	introduction	introduction	NOUN
american_scientific_journal-756	4	4	there	there	PRON
american_scientific_journal-756	4	5	are	be	VERB
american_scientific_journal-756	4	6	various	various	ADJ
american_scientific_journal-756	4	7	types	type	NOUN
american_scientific_journal-756	4	8	of	of	ADP
american_scientific_journal-756	4	9	functions	function	NOUN
american_scientific_journal-756	4	10	which	which	PRON
american_scientific_journal-756	4	11	play	play	VERB
american_scientific_journal-756	4	12	an	an	DET
american_scientific_journal-756	4	13	important	important	ADJ
american_scientific_journal-756	4	14	role	role	NOUN
american_scientific_journal-756	4	15	in	in	ADP
american_scientific_journal-756	4	16	the	the	DET
american_scientific_journal-756	4	17	classical	classical	ADJ
american_scientific_journal-756	4	18	theory	theory	NOUN
american_scientific_journal-756	4	19	of	of	ADP
american_scientific_journal-756	4	20	set	set	VERB
american_scientific_journal-756	4	21	topology	topology	NOUN
american_scientific_journal-756	4	22	.	.	PUNCT
american_scientific_journal-756	5	1	one	one	NUM
american_scientific_journal-756	5	2	of	of	ADP
american_scientific_journal-756	5	3	them	they	PRON
american_scientific_journal-756	5	4	is	be	AUX
american_scientific_journal-756	5	5	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	5	6	functions	function	NOUN
american_scientific_journal-756	5	7	.	.	PUNCT
american_scientific_journal-756	6	1	o.	o.	PROPN
american_scientific_journal-756	6	2	njastad	njastad	PROPN
american_scientific_journal-756	7	1	[	[	X
american_scientific_journal-756	7	2	1	1	X
american_scientific_journal-756	7	3	]	]	PUNCT
american_scientific_journal-756	7	4	introduced	introduce	VERB
american_scientific_journal-756	7	5	a	a	DET
american_scientific_journal-756	7	6	weak	weak	ADJ
american_scientific_journal-756	7	7	form	form	NOUN
american_scientific_journal-756	7	8	of	of	ADP
american_scientific_journal-756	7	9	open	open	ADJ
american_scientific_journal-756	7	10	sets	set	NOUN
american_scientific_journal-756	7	11	called	call	VERB
american_scientific_journal-756	7	12	𝛼-sets	𝛼-set	NOUN
american_scientific_journal-756	7	13	.	.	PUNCT
american_scientific_journal-756	8	1	then	then	ADV
american_scientific_journal-756	8	2	,	,	PUNCT
american_scientific_journal-756	8	3	a.	a.	PROPN
american_scientific_journal-756	8	4	s.	s.	PROPN
american_scientific_journal-756	8	5	mashour	mashour	PROPN
american_scientific_journal-756	8	6	et	et	PROPN
american_scientific_journal-756	8	7	al	al	PROPN
american_scientific_journal-756	8	8	.	.	PUNCT
american_scientific_journal-756	9	1	[	[	X
american_scientific_journal-756	9	2	2	2	X
american_scientific_journal-756	9	3	]	]	PUNCT
american_scientific_journal-756	9	4	defined	define	VERB
american_scientific_journal-756	9	5	the	the	DET
american_scientific_journal-756	9	6	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	9	7	functions	function	NOUN
american_scientific_journal-756	9	8	and	and	CCONJ
american_scientific_journal-756	9	9	studied	study	VERB
american_scientific_journal-756	9	10	properties	property	NOUN
american_scientific_journal-756	9	11	of	of	ADP
american_scientific_journal-756	9	12	this	this	DET
american_scientific_journal-756	9	13	functions	function	NOUN
american_scientific_journal-756	9	14	.	.	PUNCT
american_scientific_journal-756	10	1	a	a	DET
american_scientific_journal-756	10	2	great	great	ADJ
american_scientific_journal-756	10	3	deal	deal	NOUN
american_scientific_journal-756	10	4	of	of	ADP
american_scientific_journal-756	10	5	works	work	NOUN
american_scientific_journal-756	10	6	on	on	ADP
american_scientific_journal-756	10	7	such	such	ADJ
american_scientific_journal-756	10	8	functions	function	NOUN
american_scientific_journal-756	10	9	has	have	AUX
american_scientific_journal-756	10	10	been	be	AUX
american_scientific_journal-756	10	11	extended	extend	VERB
american_scientific_journal-756	10	12	to	to	ADP
american_scientific_journal-756	10	13	the	the	DET
american_scientific_journal-756	10	14	setting	setting	NOUN
american_scientific_journal-756	10	15	of	of	ADP
american_scientific_journal-756	10	16	multifunctions	multifunction	NOUN
american_scientific_journal-756	10	17	.	.	PUNCT
american_scientific_journal-756	11	1	a	a	DET
american_scientific_journal-756	11	2	multifunction	multifunction	NOUN
american_scientific_journal-756	11	3	is	be	AUX
american_scientific_journal-756	11	4	a	a	DET
american_scientific_journal-756	11	5	set	set	NOUN
american_scientific_journal-756	11	6	-	-	PUNCT
american_scientific_journal-756	11	7	valued	value	VERB
american_scientific_journal-756	11	8	function	function	NOUN
american_scientific_journal-756	11	9	.	.	PUNCT
american_scientific_journal-756	12	1	the	the	DET
american_scientific_journal-756	12	2	theory	theory	NOUN
american_scientific_journal-756	12	3	of	of	ADP
american_scientific_journal-756	12	4	multifunction	multifunction	NOUN
american_scientific_journal-756	12	5	was	be	AUX
american_scientific_journal-756	12	6	first	first	ADV
american_scientific_journal-756	12	7	codified	codify	VERB
american_scientific_journal-756	12	8	by	by	ADP
american_scientific_journal-756	12	9	berge	berge	NOUN
american_scientific_journal-756	12	10	[	[	X
american_scientific_journal-756	12	11	3	3	NUM
american_scientific_journal-756	12	12	]	]	PUNCT
american_scientific_journal-756	12	13	.	.	PUNCT
american_scientific_journal-756	13	1	in	in	ADP
american_scientific_journal-756	13	2	the	the	DET
american_scientific_journal-756	13	3	last	last	ADJ
american_scientific_journal-756	13	4	three	three	NUM
american_scientific_journal-756	13	5	decades	decade	NOUN
american_scientific_journal-756	13	6	,	,	PUNCT
american_scientific_journal-756	13	7	the	the	DET
american_scientific_journal-756	13	8	theory	theory	NOUN
american_scientific_journal-756	13	9	of	of	ADP
american_scientific_journal-756	13	10	multifunction	multifunction	NOUN
american_scientific_journal-756	13	11	has	have	AUX
american_scientific_journal-756	13	12	advanced	advance	VERB
american_scientific_journal-756	13	13	in	in	ADP
american_scientific_journal-756	13	14	a	a	DET
american_scientific_journal-756	13	15	variety	variety	NOUN
american_scientific_journal-756	13	16	of	of	ADP
american_scientific_journal-756	13	17	ways	way	NOUN
american_scientific_journal-756	13	18	and	and	CCONJ
american_scientific_journal-756	13	19	applications	application	NOUN
american_scientific_journal-756	13	20	of	of	ADP
american_scientific_journal-756	13	21	this	this	DET
american_scientific_journal-756	13	22	theory	theory	NOUN
american_scientific_journal-756	13	23	,	,	PUNCT
american_scientific_journal-756	13	24	can	can	AUX
american_scientific_journal-756	13	25	be	be	AUX
american_scientific_journal-756	13	26	found	find	VERB
american_scientific_journal-756	13	27	for	for	ADP
american_scientific_journal-756	13	28	example	example	NOUN
american_scientific_journal-756	13	29	,	,	PUNCT
american_scientific_journal-756	13	30	in	in	ADP
american_scientific_journal-756	13	31	economic	economic	ADJ
american_scientific_journal-756	13	32	theory	theory	NOUN
american_scientific_journal-756	13	33	,	,	PUNCT
american_scientific_journal-756	13	34	noncooparative	noncooparative	ADJ
american_scientific_journal-756	13	35	games	game	NOUN
american_scientific_journal-756	13	36	,	,	PUNCT
american_scientific_journal-756	13	37	artificial	artificial	ADJ
american_scientific_journal-756	13	38	intelligence	intelligence	NOUN
american_scientific_journal-756	13	39	,	,	PUNCT
american_scientific_journal-756	13	40	medicine	medicine	NOUN
american_scientific_journal-756	13	41	,	,	PUNCT
american_scientific_journal-756	13	42	information	information	NOUN
american_scientific_journal-756	13	43	sciences	science	NOUN
american_scientific_journal-756	13	44	and	and	CCONJ
american_scientific_journal-756	13	45	decision	decision	NOUN
american_scientific_journal-756	13	46	theory	theory	NOUN
american_scientific_journal-756	13	47	.	.	PUNCT
american_scientific_journal-756	14	1	papageorgiou	papageorgiou	VERB
american_scientific_journal-756	15	1	[	[	X
american_scientific_journal-756	15	2	4	4	NUM
american_scientific_journal-756	15	3	]	]	PUNCT
american_scientific_journal-756	15	4	,	,	PUNCT
american_scientific_journal-756	15	5	allbrycht	allbrycht	NOUN
american_scientific_journal-756	15	6	and	and	CCONJ
american_scientific_journal-756	15	7	maltoba	maltoba	PROPN
american_scientific_journal-756	16	1	[	[	X
american_scientific_journal-756	16	2	5	5	NUM
american_scientific_journal-756	16	3	]	]	PUNCT
american_scientific_journal-756	16	4	,	,	PUNCT
american_scientific_journal-756	16	5	beg	beg	VERB
american_scientific_journal-756	16	6	[	[	X
american_scientific_journal-756	16	7	6	6	NUM
american_scientific_journal-756	16	8	]	]	PUNCT
american_scientific_journal-756	16	9	,	,	PUNCT
american_scientific_journal-756	16	10	heilpein	heilpein	ADJ
american_scientific_journal-756	17	1	[	[	X
american_scientific_journal-756	17	2	7	7	X
american_scientific_journal-756	17	3	]	]	PUNCT
american_scientific_journal-756	17	4	and	and	CCONJ
american_scientific_journal-756	17	5	butnairu	butnairu	NOUN
american_scientific_journal-756	18	1	[	[	X
american_scientific_journal-756	18	2	8	8	NUM
american_scientific_journal-756	18	3	]	]	PUNCT
american_scientific_journal-756	18	4	have	have	AUX
american_scientific_journal-756	18	5	started	start	VERB
american_scientific_journal-756	18	6	the	the	DET
american_scientific_journal-756	18	7	study	study	NOUN
american_scientific_journal-756	18	8	of	of	ADP
american_scientific_journal-756	18	9	fuzzy	fuzzy	ADJ
american_scientific_journal-756	18	10	multifunctions	multifunction	NOUN
american_scientific_journal-756	18	11	and	and	CCONJ
american_scientific_journal-756	18	12	obtained	obtain	VERB
american_scientific_journal-756	18	13	several	several	ADJ
american_scientific_journal-756	18	14	fixed	fix	VERB
american_scientific_journal-756	18	15	point	point	NOUN
american_scientific_journal-756	18	16	theorems	theorem	NOUN
american_scientific_journal-756	18	17	for	for	ADP
american_scientific_journal-756	18	18	fuzzy	fuzzy	ADJ
american_scientific_journal-756	18	19	mappings	mapping	NOUN
american_scientific_journal-756	18	20	.	.	PUNCT
american_scientific_journal-756	19	1	on	on	ADP
american_scientific_journal-756	19	2	the	the	DET
american_scientific_journal-756	19	3	other	other	ADJ
american_scientific_journal-756	19	4	hand	hand	NOUN
american_scientific_journal-756	19	5	,	,	PUNCT
american_scientific_journal-756	19	6	a	a	DET
american_scientific_journal-756	19	7	russian	russian	ADJ
american_scientific_journal-756	19	8	researcher	researcher	NOUN
american_scientific_journal-756	19	9	molodtsov	molodtsov	NOUN
american_scientific_journal-756	19	10	[	[	X
american_scientific_journal-756	19	11	9	9	NUM
american_scientific_journal-756	19	12	]	]	PUNCT
american_scientific_journal-756	19	13	introduced	introduce	VERB
american_scientific_journal-756	19	14	the	the	DET
american_scientific_journal-756	19	15	concept	concept	NOUN
american_scientific_journal-756	19	16	of	of	ADP
american_scientific_journal-756	19	17	soft	soft	ADJ
american_scientific_journal-756	19	18	sets	set	NOUN
american_scientific_journal-756	19	19	as	as	ADP
american_scientific_journal-756	19	20	a	a	DET
american_scientific_journal-756	19	21	general	general	ADJ
american_scientific_journal-756	19	22	mathematical	mathematical	ADJ
american_scientific_journal-756	19	23	tool	tool	NOUN
american_scientific_journal-756	19	24	for	for	ADP
american_scientific_journal-756	19	25	dealing	deal	VERB
american_scientific_journal-756	19	26	with	with	ADP
american_scientific_journal-756	19	27	uncertainty	uncertainty	NOUN
american_scientific_journal-756	19	28	and	and	CCONJ
american_scientific_journal-756	19	29	he	he	PRON
american_scientific_journal-756	19	30	successifully	successifully	ADV
american_scientific_journal-756	19	31	applied	apply	VERB
american_scientific_journal-756	19	32	the	the	DET
american_scientific_journal-756	19	33	soft	soft	ADJ
american_scientific_journal-756	19	34	set	set	NOUN
american_scientific_journal-756	19	35	theory	theory	NOUN
american_scientific_journal-756	19	36	into	into	ADP
american_scientific_journal-756	19	37	several	several	ADJ
american_scientific_journal-756	19	38	directions	direction	NOUN
american_scientific_journal-756	19	39	,	,	PUNCT
american_scientific_journal-756	19	40	such	such	ADJ
american_scientific_journal-756	19	41	as	as	ADP
american_scientific_journal-756	19	42	smoothness	smoothness	NOUN
american_scientific_journal-756	19	43	of	of	ADP
american_scientific_journal-756	19	44	functions	function	NOUN
american_scientific_journal-756	19	45	,	,	PUNCT
american_scientific_journal-756	19	46	theory	theory	NOUN
american_scientific_journal-756	19	47	of	of	ADP
american_scientific_journal-756	19	48	measurement	measurement	NOUN
american_scientific_journal-756	19	49	,	,	PUNCT
american_scientific_journal-756	19	50	game	game	NOUN
american_scientific_journal-756	19	51	theory	theory	NOUN
american_scientific_journal-756	19	52	,	,	PUNCT
american_scientific_journal-756	19	53	riemann	riemann	PROPN
american_scientific_journal-756	19	54	integration	integration	NOUN
american_scientific_journal-756	19	55	and	and	CCONJ
american_scientific_journal-756	19	56	so	so	ADV
american_scientific_journal-756	19	57	on	on	ADV
american_scientific_journal-756	19	58	.	.	PUNCT
american_scientific_journal-756	20	1	then	then	ADV
american_scientific_journal-756	20	2	,	,	PUNCT
american_scientific_journal-756	20	3	maji	maji	PROPN
american_scientific_journal-756	20	4	et	et	PROPN
american_scientific_journal-756	20	5	al	al	PROPN
american_scientific_journal-756	20	6	.	.	PUNCT
american_scientific_journal-756	21	1	[	[	X
american_scientific_journal-756	21	2	10	10	NUM
american_scientific_journal-756	21	3	]	]	PUNCT
american_scientific_journal-756	21	4	defined	define	VERB
american_scientific_journal-756	21	5	some	some	DET
american_scientific_journal-756	21	6	operations	operation	NOUN
american_scientific_journal-756	21	7	on	on	ADP
american_scientific_journal-756	21	8	soft	soft	ADJ
american_scientific_journal-756	21	9	sets	set	NOUN
american_scientific_journal-756	21	10	and	and	CCONJ
american_scientific_journal-756	21	11	some	some	DET
american_scientific_journal-756	21	12	basic	basic	ADJ
american_scientific_journal-756	21	13	properties	property	NOUN
american_scientific_journal-756	21	14	of	of	ADP
american_scientific_journal-756	21	15	these	these	DET
american_scientific_journal-756	21	16	operations	operation	NOUN
american_scientific_journal-756	21	17	are	be	AUX
american_scientific_journal-756	21	18	revealed	reveal	VERB
american_scientific_journal-756	21	19	in	in	ADP
american_scientific_journal-756	21	20	[	[	X
american_scientific_journal-756	21	21	11	11	NUM
american_scientific_journal-756	21	22	]	]	PUNCT
american_scientific_journal-756	21	23	.	.	PUNCT
american_scientific_journal-756	22	1	also	also	ADV
american_scientific_journal-756	22	2	,	,	PUNCT
american_scientific_journal-756	22	3	aktaş	aktaş	NOUN
american_scientific_journal-756	22	4	and	and	CCONJ
american_scientific_journal-756	22	5	çağman	çağman	NOUN
american_scientific_journal-756	22	6	[	[	X
american_scientific_journal-756	22	7	12	12	NUM
american_scientific_journal-756	22	8	]	]	PUNCT
american_scientific_journal-756	22	9	compared	compare	VERB
american_scientific_journal-756	22	10	soft	soft	ADJ
american_scientific_journal-756	22	11	sets	set	NOUN
american_scientific_journal-756	22	12	with	with	ADP
american_scientific_journal-756	22	13	fuzzy	fuzzy	ADJ
american_scientific_journal-756	22	14	sets	set	NOUN
american_scientific_journal-756	22	15	and	and	CCONJ
american_scientific_journal-756	22	16	rough	rough	ADJ
american_scientific_journal-756	22	17	sets	set	NOUN
american_scientific_journal-756	22	18	.	.	PUNCT
american_scientific_journal-756	23	1	applications	application	NOUN
american_scientific_journal-756	23	2	of	of	ADP
american_scientific_journal-756	23	3	soft	soft	ADJ
american_scientific_journal-756	23	4	set	set	NOUN
american_scientific_journal-756	23	5	theory	theory	NOUN
american_scientific_journal-756	23	6	in	in	ADP
american_scientific_journal-756	23	7	other	other	ADJ
american_scientific_journal-756	23	8	disciplines	discipline	NOUN
american_scientific_journal-756	23	9	and	and	CCONJ
american_scientific_journal-756	23	10	real	real	ADJ
american_scientific_journal-756	23	11	life	life	NOUN
american_scientific_journal-756	23	12	problems	problem	NOUN
american_scientific_journal-756	23	13	are	be	AUX
american_scientific_journal-756	23	14	now	now	ADV
american_scientific_journal-756	23	15	catching	catch	VERB
american_scientific_journal-756	23	16	momentum	momentum	NOUN
american_scientific_journal-756	23	17	.	.	PUNCT
american_scientific_journal-756	24	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-756	25	1	*	*	PUNCT
american_scientific_journal-756	25	2	corresponding	correspond	VERB
american_scientific_journal-756	25	3	author	author	NOUN
american_scientific_journal-756	25	4	.	.	PUNCT
american_scientific_journal-756	26	1	e	e	X
american_scientific_journal-756	26	2	-	-	NOUN
american_scientific_journal-756	26	3	mail	mail	NOUN
american_scientific_journal-756	26	4	address	address	NOUN
american_scientific_journal-756	26	5	:	:	PUNCT
american_scientific_journal-756	26	6	feerol@cumhuriyet.edu.tr	feerol@cumhuriyet.edu.tr	PROPN
american_scientific_journal-756	26	7	.	.	PUNCT
american_scientific_journal-756	27	1	96	96	NUM
american_scientific_journal-756	27	2	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-756	27	3	american	american	ADJ
american_scientific_journal-756	27	4	scientific	scientific	ADJ
american_scientific_journal-756	27	5	research	research	NOUN
american_scientific_journal-756	27	6	journal	journal	NOUN
american_scientific_journal-756	27	7	for	for	ADP
american_scientific_journal-756	27	8	engineering	engineering	NOUN
american_scientific_journal-756	27	9	,	,	PUNCT
american_scientific_journal-756	27	10	technology	technology	NOUN
american_scientific_journal-756	27	11	,	,	PUNCT
american_scientific_journal-756	27	12	and	and	CCONJ
american_scientific_journal-756	27	13	sciences	science	NOUN
american_scientific_journal-756	27	14	(	(	PUNCT
american_scientific_journal-756	27	15	asrjets	asrjet	NOUN
american_scientific_journal-756	27	16	)	)	PUNCT
american_scientific_journal-756	27	17	(	(	PUNCT
american_scientific_journal-756	27	18	2014	2014	NUM
american_scientific_journal-756	27	19	)	)	PUNCT
american_scientific_journal-756	27	20	volume	volume	NOUN
american_scientific_journal-756	27	21	8	8	NUM
american_scientific_journal-756	27	22	,	,	PUNCT
american_scientific_journal-756	27	23	no	no	DET
american_scientific_journal-756	27	24	1	1	NUM
american_scientific_journal-756	27	25	,	,	PUNCT
american_scientific_journal-756	27	26	pp	pp	ADV
american_scientific_journal-756	27	27	96	96	NUM
american_scientific_journal-756	27	28	-	-	SYM
american_scientific_journal-756	27	29	107	107	NUM
american_scientific_journal-756	27	30	the	the	DET
american_scientific_journal-756	27	31	topological	topological	ADJ
american_scientific_journal-756	27	32	structure	structure	NOUN
american_scientific_journal-756	27	33	of	of	ADP
american_scientific_journal-756	27	34	set	set	NOUN
american_scientific_journal-756	27	35	theories	theory	NOUN
american_scientific_journal-756	27	36	dealing	deal	VERB
american_scientific_journal-756	27	37	with	with	ADP
american_scientific_journal-756	27	38	uncertainties	uncertainty	NOUN
american_scientific_journal-756	27	39	were	be	AUX
american_scientific_journal-756	27	40	first	first	ADV
american_scientific_journal-756	27	41	studied	study	VERB
american_scientific_journal-756	27	42	by	by	ADP
american_scientific_journal-756	27	43	chang	chang	PROPN
american_scientific_journal-756	28	1	[	[	X
american_scientific_journal-756	28	2	13	13	NUM
american_scientific_journal-756	28	3	]	]	PUNCT
american_scientific_journal-756	28	4	.	.	PUNCT
american_scientific_journal-756	29	1	lashin	lashin	PROPN
american_scientific_journal-756	29	2	et	et	PROPN
american_scientific_journal-756	29	3	al	al	PROPN
american_scientific_journal-756	29	4	.	.	PUNCT
american_scientific_journal-756	30	1	[	[	X
american_scientific_journal-756	30	2	14	14	NUM
american_scientific_journal-756	30	3	]	]	X
american_scientific_journal-756	30	4	generalized	generalize	VERB
american_scientific_journal-756	30	5	rough	rough	ADJ
american_scientific_journal-756	30	6	set	set	NOUN
american_scientific_journal-756	30	7	theory	theory	NOUN
american_scientific_journal-756	30	8	in	in	ADP
american_scientific_journal-756	30	9	the	the	DET
american_scientific_journal-756	30	10	framework	framework	NOUN
american_scientific_journal-756	30	11	of	of	ADP
american_scientific_journal-756	30	12	topological	topological	ADJ
american_scientific_journal-756	30	13	spaces	space	NOUN
american_scientific_journal-756	30	14	.	.	PUNCT
american_scientific_journal-756	31	1	recently	recently	ADV
american_scientific_journal-756	31	2	,	,	PUNCT
american_scientific_journal-756	31	3	shabir	shabir	PROPN
american_scientific_journal-756	31	4	and	and	CCONJ
american_scientific_journal-756	31	5	naz	naz	PROPN
american_scientific_journal-756	31	6	[	[	X
american_scientific_journal-756	31	7	15	15	NUM
american_scientific_journal-756	31	8	]	]	PUNCT
american_scientific_journal-756	31	9	introduced	introduce	VERB
american_scientific_journal-756	31	10	the	the	DET
american_scientific_journal-756	31	11	notion	notion	NOUN
american_scientific_journal-756	31	12	of	of	ADP
american_scientific_journal-756	31	13	soft	soft	ADJ
american_scientific_journal-756	31	14	topological	topological	ADJ
american_scientific_journal-756	31	15	spaces	space	NOUN
american_scientific_journal-756	31	16	which	which	PRON
american_scientific_journal-756	31	17	are	be	AUX
american_scientific_journal-756	31	18	defined	define	VERB
american_scientific_journal-756	31	19	over	over	ADP
american_scientific_journal-756	31	20	an	an	DET
american_scientific_journal-756	31	21	initial	initial	ADJ
american_scientific_journal-756	31	22	universe	universe	NOUN
american_scientific_journal-756	31	23	with	with	ADP
american_scientific_journal-756	31	24	a	a	DET
american_scientific_journal-756	31	25	fixed	fix	VERB
american_scientific_journal-756	31	26	set	set	NOUN
american_scientific_journal-756	31	27	of	of	ADP
american_scientific_journal-756	31	28	parameters	parameter	NOUN
american_scientific_journal-756	31	29	.	.	PUNCT
american_scientific_journal-756	32	1	also	also	ADV
american_scientific_journal-756	32	2	they	they	PRON
american_scientific_journal-756	32	3	studied	study	VERB
american_scientific_journal-756	32	4	soft	soft	ADJ
american_scientific_journal-756	32	5	separation	separation	NOUN
american_scientific_journal-756	32	6	axioms	axiom	NOUN
american_scientific_journal-756	32	7	for	for	ADP
american_scientific_journal-756	32	8	soft	soft	ADJ
american_scientific_journal-756	32	9	topological	topological	ADJ
american_scientific_journal-756	32	10	spaces	space	NOUN
american_scientific_journal-756	32	11	.	.	PUNCT
american_scientific_journal-756	33	1	zorlutuna	zorlutuna	INTJ
american_scientific_journal-756	33	2	et	et	PROPN
american_scientific_journal-756	33	3	al	al	PROPN
american_scientific_journal-756	33	4	.	.	PUNCT
american_scientific_journal-756	34	1	[	[	X
american_scientific_journal-756	34	2	16	16	NUM
american_scientific_journal-756	34	3	]	]	PUNCT
american_scientific_journal-756	34	4	introduced	introduce	VERB
american_scientific_journal-756	34	5	the	the	DET
american_scientific_journal-756	34	6	concept	concept	NOUN
american_scientific_journal-756	34	7	of	of	ADP
american_scientific_journal-756	34	8	soft	soft	ADJ
american_scientific_journal-756	34	9	continuity	continuity	NOUN
american_scientific_journal-756	34	10	of	of	ADP
american_scientific_journal-756	34	11	functions	function	NOUN
american_scientific_journal-756	34	12	and	and	CCONJ
american_scientific_journal-756	34	13	studied	study	VERB
american_scientific_journal-756	34	14	some	some	PRON
american_scientific_journal-756	34	15	of	of	ADP
american_scientific_journal-756	34	16	its	its	PRON
american_scientific_journal-756	34	17	properties	property	NOUN
american_scientific_journal-756	34	18	.	.	PUNCT
american_scientific_journal-756	35	1	then	then	ADV
american_scientific_journal-756	35	2	aygunoglu	aygunoglu	PROPN
american_scientific_journal-756	35	3	and	and	CCONJ
american_scientific_journal-756	35	4	aygun	aygun	VERB
american_scientific_journal-756	36	1	[	[	X
american_scientific_journal-756	36	2	17	17	NUM
american_scientific_journal-756	36	3	]	]	PUNCT
american_scientific_journal-756	36	4	studied	study	VERB
american_scientific_journal-756	36	5	continuous	continuous	ADJ
american_scientific_journal-756	36	6	soft	soft	ADJ
american_scientific_journal-756	36	7	functions	function	NOUN
american_scientific_journal-756	36	8	.	.	PUNCT
american_scientific_journal-756	37	1	recently	recently	ADV
american_scientific_journal-756	37	2	,	,	PUNCT
american_scientific_journal-756	37	3	kharal	kharal	ADJ
american_scientific_journal-756	37	4	and	and	CCONJ
american_scientific_journal-756	37	5	ahmad	ahmad	PROPN
american_scientific_journal-756	37	6	[	[	X
american_scientific_journal-756	37	7	18	18	NUM
american_scientific_journal-756	37	8	]	]	PUNCT
american_scientific_journal-756	37	9	defined	define	VERB
american_scientific_journal-756	37	10	the	the	DET
american_scientific_journal-756	37	11	notion	notion	NOUN
american_scientific_journal-756	37	12	of	of	ADP
american_scientific_journal-756	37	13	a	a	DET
american_scientific_journal-756	37	14	mapping	mapping	NOUN
american_scientific_journal-756	37	15	on	on	ADP
american_scientific_journal-756	37	16	soft	soft	ADJ
american_scientific_journal-756	37	17	classes	class	NOUN
american_scientific_journal-756	37	18	and	and	CCONJ
american_scientific_journal-756	37	19	studied	study	VERB
american_scientific_journal-756	37	20	several	several	ADJ
american_scientific_journal-756	37	21	properties	property	NOUN
american_scientific_journal-756	37	22	of	of	ADP
american_scientific_journal-756	37	23	images	image	NOUN
american_scientific_journal-756	37	24	and	and	CCONJ
american_scientific_journal-756	37	25	inverse	inverse	NOUN
american_scientific_journal-756	37	26	images	image	NOUN
american_scientific_journal-756	37	27	of	of	ADP
american_scientific_journal-756	37	28	soft	soft	ADJ
american_scientific_journal-756	37	29	sets	set	NOUN
american_scientific_journal-756	37	30	.	.	PUNCT
american_scientific_journal-756	38	1	also	also	ADV
american_scientific_journal-756	38	2	they	they	PRON
american_scientific_journal-756	38	3	applied	apply	VERB
american_scientific_journal-756	38	4	these	these	DET
american_scientific_journal-756	38	5	concepts	concept	NOUN
american_scientific_journal-756	38	6	to	to	ADP
american_scientific_journal-756	38	7	the	the	DET
american_scientific_journal-756	38	8	problem	problem	NOUN
american_scientific_journal-756	38	9	of	of	ADP
american_scientific_journal-756	38	10	medical	medical	ADJ
american_scientific_journal-756	38	11	diagnosis	diagnosis	NOUN
american_scientific_journal-756	38	12	in	in	ADP
american_scientific_journal-756	38	13	medical	medical	ADJ
american_scientific_journal-756	38	14	expert	expert	NOUN
american_scientific_journal-756	38	15	systems	system	NOUN
american_scientific_journal-756	38	16	.	.	PUNCT
american_scientific_journal-756	39	1	then	then	ADV
american_scientific_journal-756	39	2	akdag	akdag	PROPN
american_scientific_journal-756	39	3	and	and	CCONJ
american_scientific_journal-756	39	4	özkan	özkan	VERB
american_scientific_journal-756	39	5	[	[	X
american_scientific_journal-756	39	6	19	19	NUM
american_scientific_journal-756	39	7	]	]	PUNCT
american_scientific_journal-756	39	8	introduced	introduce	VERB
american_scientific_journal-756	39	9	the	the	DET
american_scientific_journal-756	39	10	soft	soft	ADJ
american_scientific_journal-756	39	11	α	α	NOUN
american_scientific_journal-756	39	12	-	-	PUNCT
american_scientific_journal-756	39	13	sets	set	NOUN
american_scientific_journal-756	39	14	and	and	CCONJ
american_scientific_journal-756	39	15	soft	soft	ADJ
american_scientific_journal-756	39	16	α	α	PRON
american_scientific_journal-756	39	17	-	-	ADJ
american_scientific_journal-756	39	18	continuous	continuous	ADJ
american_scientific_journal-756	39	19	functions	function	NOUN
american_scientific_journal-756	39	20	.	.	PUNCT
american_scientific_journal-756	40	1	akdag	akdag	PROPN
american_scientific_journal-756	40	2	and	and	CCONJ
american_scientific_journal-756	40	3	erol	erol	NOUN
american_scientific_journal-756	40	4	[	[	X
american_scientific_journal-756	40	5	20	20	NUM
american_scientific_journal-756	40	6	]	]	PUNCT
american_scientific_journal-756	40	7	introduced	introduce	VERB
american_scientific_journal-756	40	8	the	the	DET
american_scientific_journal-756	40	9	soft	soft	ADJ
american_scientific_journal-756	40	10	multifunction	multifunction	NOUN
american_scientific_journal-756	40	11	and	and	CCONJ
american_scientific_journal-756	40	12	studied	study	VERB
american_scientific_journal-756	40	13	the	the	DET
american_scientific_journal-756	40	14	properties	property	NOUN
american_scientific_journal-756	40	15	of	of	ADP
american_scientific_journal-756	40	16	this	this	DET
american_scientific_journal-756	40	17	multifunction	multifunction	NOUN
american_scientific_journal-756	40	18	.	.	PUNCT
american_scientific_journal-756	41	1	also	also	ADV
american_scientific_journal-756	41	2	,	,	PUNCT
american_scientific_journal-756	41	3	they	they	PRON
american_scientific_journal-756	41	4	investigated	investigate	VERB
american_scientific_journal-756	41	5	the	the	DET
american_scientific_journal-756	41	6	relationship	relationship	NOUN
american_scientific_journal-756	41	7	between	between	ADP
american_scientific_journal-756	41	8	soft	soft	ADJ
american_scientific_journal-756	41	9	multifunction	multifunction	NOUN
american_scientific_journal-756	41	10	and	and	CCONJ
american_scientific_journal-756	41	11	information	information	NOUN
american_scientific_journal-756	41	12	systems	system	NOUN
american_scientific_journal-756	41	13	.	.	PUNCT
american_scientific_journal-756	42	1	we	we	PRON
american_scientific_journal-756	42	2	know	know	VERB
american_scientific_journal-756	42	3	that	that	SCONJ
american_scientific_journal-756	42	4	soft	soft	ADJ
american_scientific_journal-756	42	5	sets	set	NOUN
american_scientific_journal-756	42	6	are	be	AUX
american_scientific_journal-756	42	7	a	a	DET
american_scientific_journal-756	42	8	class	class	NOUN
american_scientific_journal-756	42	9	of	of	ADP
american_scientific_journal-756	42	10	special	special	ADJ
american_scientific_journal-756	42	11	information	information	NOUN
american_scientific_journal-756	42	12	systems	system	NOUN
american_scientific_journal-756	42	13	and	and	CCONJ
american_scientific_journal-756	42	14	both	both	DET
american_scientific_journal-756	42	15	researches	research	NOUN
american_scientific_journal-756	42	16	of	of	ADP
american_scientific_journal-756	42	17	soft	soft	ADJ
american_scientific_journal-756	42	18	sets	set	NOUN
american_scientific_journal-756	42	19	and	and	CCONJ
american_scientific_journal-756	42	20	information	information	NOUN
american_scientific_journal-756	42	21	systems	system	NOUN
american_scientific_journal-756	42	22	study	study	NOUN
american_scientific_journal-756	42	23	on	on	ADP
american_scientific_journal-756	42	24	the	the	DET
american_scientific_journal-756	42	25	same	same	ADJ
american_scientific_journal-756	42	26	formal	formal	ADJ
american_scientific_journal-756	42	27	structures	structure	NOUN
american_scientific_journal-756	42	28	.	.	PUNCT
american_scientific_journal-756	43	1	information	information	NOUN
american_scientific_journal-756	43	2	systems	system	NOUN
american_scientific_journal-756	43	3	have	have	AUX
american_scientific_journal-756	43	4	been	be	AUX
american_scientific_journal-756	43	5	studies	study	NOUN
american_scientific_journal-756	43	6	by	by	ADP
american_scientific_journal-756	43	7	many	many	ADJ
american_scientific_journal-756	43	8	researchers	researcher	NOUN
american_scientific_journal-756	43	9	from	from	ADP
american_scientific_journal-756	43	10	several	several	ADJ
american_scientific_journal-756	43	11	domains	domain	NOUN
american_scientific_journal-756	43	12	such	such	ADJ
american_scientific_journal-756	43	13	as	as	ADP
american_scientific_journal-756	43	14	knowledge	knowledge	NOUN
american_scientific_journal-756	43	15	engineering	engineering	NOUN
american_scientific_journal-756	43	16	[	[	X
american_scientific_journal-756	43	17	21	21	NUM
american_scientific_journal-756	43	18	,	,	PUNCT
american_scientific_journal-756	43	19	22	22	NUM
american_scientific_journal-756	43	20	]	]	PUNCT
american_scientific_journal-756	43	21	,	,	PUNCT
american_scientific_journal-756	43	22	rough	rough	ADJ
american_scientific_journal-756	43	23	set	set	NOUN
american_scientific_journal-756	43	24	theory	theory	NOUN
american_scientific_journal-756	43	25	[	[	X
american_scientific_journal-756	43	26	23	23	NUM
american_scientific_journal-756	43	27	]	]	PUNCT
american_scientific_journal-756	43	28	and	and	CCONJ
american_scientific_journal-756	43	29	granular	granular	ADJ
american_scientific_journal-756	43	30	computing	computing	NOUN
american_scientific_journal-756	43	31	[	[	X
american_scientific_journal-756	43	32	24	24	NUM
american_scientific_journal-756	43	33	,	,	PUNCT
american_scientific_journal-756	43	34	25	25	NUM
american_scientific_journal-756	43	35	]	]	PUNCT
american_scientific_journal-756	43	36	.	.	PUNCT
american_scientific_journal-756	44	1	pei	pei	PROPN
american_scientific_journal-756	44	2	and	and	CCONJ
american_scientific_journal-756	44	3	miao	miao	PROPN
american_scientific_journal-756	45	1	[	[	X
american_scientific_journal-756	45	2	26	26	NUM
american_scientific_journal-756	45	3	]	]	PUNCT
american_scientific_journal-756	45	4	showed	show	VERB
american_scientific_journal-756	45	5	the	the	DET
american_scientific_journal-756	45	6	operations	operation	NOUN
american_scientific_journal-756	45	7	of	of	ADP
american_scientific_journal-756	45	8	information	information	NOUN
american_scientific_journal-756	45	9	systems	system	NOUN
american_scientific_journal-756	45	10	are	be	AUX
american_scientific_journal-756	45	11	parallel	parallel	ADJ
american_scientific_journal-756	45	12	to	to	ADP
american_scientific_journal-756	45	13	those	those	PRON
american_scientific_journal-756	45	14	of	of	ADP
american_scientific_journal-756	45	15	soft	soft	ADJ
american_scientific_journal-756	45	16	sets	set	NOUN
american_scientific_journal-756	45	17	.	.	PUNCT
american_scientific_journal-756	46	1	they	they	PRON
american_scientific_journal-756	46	2	also	also	ADV
american_scientific_journal-756	46	3	investigated	investigate	VERB
american_scientific_journal-756	46	4	that	that	SCONJ
american_scientific_journal-756	46	5	there	there	PRON
american_scientific_journal-756	46	6	exist	exist	VERB
american_scientific_journal-756	46	7	some	some	DET
american_scientific_journal-756	46	8	compact	compact	ADJ
american_scientific_journal-756	46	9	connections	connection	NOUN
american_scientific_journal-756	46	10	between	between	ADP
american_scientific_journal-756	46	11	soft	soft	ADJ
american_scientific_journal-756	46	12	sets	set	NOUN
american_scientific_journal-756	46	13	and	and	CCONJ
american_scientific_journal-756	46	14	information	information	NOUN
american_scientific_journal-756	46	15	systems	system	NOUN
american_scientific_journal-756	46	16	.	.	PUNCT
american_scientific_journal-756	47	1	in	in	ADP
american_scientific_journal-756	47	2	this	this	DET
american_scientific_journal-756	47	3	paper	paper	NOUN
american_scientific_journal-756	47	4	our	our	PRON
american_scientific_journal-756	47	5	purpose	purpose	NOUN
american_scientific_journal-756	47	6	is	be	AUX
american_scientific_journal-756	47	7	to	to	PART
american_scientific_journal-756	47	8	introduce	introduce	VERB
american_scientific_journal-756	47	9	the	the	DET
american_scientific_journal-756	47	10	notion	notion	NOUN
american_scientific_journal-756	47	11	of	of	ADP
american_scientific_journal-756	47	12	soft	soft	ADJ
american_scientific_journal-756	47	13	upper	upper	ADJ
american_scientific_journal-756	47	14	(	(	PUNCT
american_scientific_journal-756	47	15	lower	low	ADJ
american_scientific_journal-756	47	16	)	)	PUNCT
american_scientific_journal-756	47	17	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	47	18	multifunction	multifunction	NOUN
american_scientific_journal-756	47	19	and	and	CCONJ
american_scientific_journal-756	47	20	to	to	PART
american_scientific_journal-756	47	21	obtain	obtain	VERB
american_scientific_journal-756	47	22	some	some	DET
american_scientific_journal-756	47	23	characterizations	characterization	NOUN
american_scientific_journal-756	47	24	and	and	CCONJ
american_scientific_journal-756	47	25	of	of	ADP
american_scientific_journal-756	47	26	basic	basic	ADJ
american_scientific_journal-756	47	27	properties	property	NOUN
american_scientific_journal-756	47	28	of	of	ADP
american_scientific_journal-756	47	29	this	this	DET
american_scientific_journal-756	47	30	multifunction	multifunction	NOUN
american_scientific_journal-756	47	31	.	.	PUNCT
american_scientific_journal-756	48	1	also	also	ADV
american_scientific_journal-756	48	2	we	we	PRON
american_scientific_journal-756	48	3	study	study	VERB
american_scientific_journal-756	48	4	relationship	relationship	NOUN
american_scientific_journal-756	48	5	between	between	ADP
american_scientific_journal-756	48	6	soft	soft	ADJ
american_scientific_journal-756	48	7	continuous	continuous	ADJ
american_scientific_journal-756	48	8	multifunction	multifunction	NOUN
american_scientific_journal-756	48	9	and	and	CCONJ
american_scientific_journal-756	48	10	soft	soft	ADJ
american_scientific_journal-756	48	11	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	48	12	multifunction	multifunction	NOUN
american_scientific_journal-756	48	13	.	.	PUNCT
american_scientific_journal-756	49	1	2	2	X
american_scientific_journal-756	49	2	.	.	X
american_scientific_journal-756	49	3	preliminaries	preliminary	NOUN
american_scientific_journal-756	49	4	molodtsov	molodtsov	NOUN
american_scientific_journal-756	50	1	[	[	X
american_scientific_journal-756	50	2	9	9	NUM
american_scientific_journal-756	50	3	]	]	SYM
american_scientific_journal-756	50	4	defined	define	VERB
american_scientific_journal-756	50	5	soft	soft	ADJ
american_scientific_journal-756	50	6	sets	set	NOUN
american_scientific_journal-756	50	7	in	in	ADP
american_scientific_journal-756	50	8	the	the	DET
american_scientific_journal-756	50	9	following	following	ADJ
american_scientific_journal-756	50	10	manner	manner	NOUN
american_scientific_journal-756	50	11	.	.	PUNCT
american_scientific_journal-756	51	1	let	let	VERB
american_scientific_journal-756	51	2	𝑈	𝑈	NOUN
american_scientific_journal-756	51	3	be	be	AUX
american_scientific_journal-756	51	4	an	an	DET
american_scientific_journal-756	51	5	initial	initial	ADJ
american_scientific_journal-756	51	6	universe	universe	NOUN
american_scientific_journal-756	51	7	set	set	VERB
american_scientific_journal-756	51	8	and	and	CCONJ
american_scientific_journal-756	51	9	𝐸	𝐸	PROPN
american_scientific_journal-756	51	10	be	be	VERB
american_scientific_journal-756	51	11	a	a	DET
american_scientific_journal-756	51	12	set	set	NOUN
american_scientific_journal-756	51	13	of	of	ADP
american_scientific_journal-756	51	14	parameters	parameter	NOUN
american_scientific_journal-756	51	15	.	.	PUNCT
american_scientific_journal-756	52	1	let	let	VERB
american_scientific_journal-756	52	2	𝑃(𝑈	𝑃(𝑈	NOUN
american_scientific_journal-756	52	3	)	)	PUNCT
american_scientific_journal-756	52	4	denote	denote	VERB
american_scientific_journal-756	52	5	the	the	DET
american_scientific_journal-756	52	6	power	power	NOUN
american_scientific_journal-756	52	7	set	set	NOUN
american_scientific_journal-756	52	8	of	of	ADP
american_scientific_journal-756	52	9	𝑈	𝑈	PROPN
american_scientific_journal-756	52	10	and	and	CCONJ
american_scientific_journal-756	52	11	let	let	VERB
american_scientific_journal-756	52	12	𝐵	𝐵	PRON
american_scientific_journal-756	52	13	⊆	⊆	NUM
american_scientific_journal-756	52	14	𝐸.	𝐸.	PROPN
american_scientific_journal-756	52	15	definition	definition	NOUN
american_scientific_journal-756	52	16	2.1	2.1	NUM
american_scientific_journal-756	52	17	.	.	PUNCT
american_scientific_journal-756	53	1	[	[	X
american_scientific_journal-756	53	2	9	9	NUM
american_scientific_journal-756	53	3	]	]	PUNCT
american_scientific_journal-756	53	4	a	a	DET
american_scientific_journal-756	53	5	pair	pair	NOUN
american_scientific_journal-756	53	6	(	(	PUNCT
american_scientific_journal-756	53	7	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	53	8	)	)	PUNCT
american_scientific_journal-756	53	9	is	be	AUX
american_scientific_journal-756	53	10	called	call	VERB
american_scientific_journal-756	53	11	a	a	DET
american_scientific_journal-756	53	12	soft	soft	ADJ
american_scientific_journal-756	53	13	set	set	NOUN
american_scientific_journal-756	53	14	over	over	ADP
american_scientific_journal-756	53	15	𝑈	𝑈	PROPN
american_scientific_journal-756	53	16	,	,	PUNCT
american_scientific_journal-756	53	17	where	where	SCONJ
american_scientific_journal-756	53	18	𝐺	𝐺	PROPN
american_scientific_journal-756	53	19	is	be	AUX
american_scientific_journal-756	53	20	a	a	DET
american_scientific_journal-756	53	21	mapping	mapping	NOUN
american_scientific_journal-756	53	22	given	give	VERB
american_scientific_journal-756	53	23	by	by	ADP
american_scientific_journal-756	53	24	𝐺:𝐵	𝐺:𝐵	NOUN
american_scientific_journal-756	53	25	→	→	SYM
american_scientific_journal-756	53	26	𝑃(𝑈	𝑃(𝑈	NOUN
american_scientific_journal-756	53	27	)	)	PUNCT
american_scientific_journal-756	53	28	.	.	PUNCT
american_scientific_journal-756	54	1	definition	definition	NOUN
american_scientific_journal-756	54	2	2.2	2.2	NUM
american_scientific_journal-756	54	3	.	.	PUNCT
american_scientific_journal-756	55	1	[	[	X
american_scientific_journal-756	55	2	26	26	NUM
american_scientific_journal-756	55	3	]	]	PUNCT
american_scientific_journal-756	55	4	for	for	ADP
american_scientific_journal-756	55	5	two	two	NUM
american_scientific_journal-756	55	6	soft	soft	ADJ
american_scientific_journal-756	55	7	sets	set	NOUN
american_scientific_journal-756	55	8	(	(	PUNCT
american_scientific_journal-756	55	9	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	55	10	)	)	PUNCT
american_scientific_journal-756	55	11	and	and	CCONJ
american_scientific_journal-756	55	12	(	(	PUNCT
american_scientific_journal-756	55	13	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	55	14	)	)	PUNCT
american_scientific_journal-756	55	15	over	over	ADP
american_scientific_journal-756	55	16	a	a	DET
american_scientific_journal-756	55	17	common	common	ADJ
american_scientific_journal-756	55	18	universe	universe	NOUN
american_scientific_journal-756	55	19	𝑈	𝑈	PROPN
american_scientific_journal-756	55	20	,	,	PUNCT
american_scientific_journal-756	55	21	(	(	PUNCT
american_scientific_journal-756	55	22	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	55	23	)	)	PUNCT
american_scientific_journal-756	55	24	is	be	AUX
american_scientific_journal-756	55	25	a	a	DET
american_scientific_journal-756	55	26	soft	soft	ADJ
american_scientific_journal-756	55	27	subset	subset	NOUN
american_scientific_journal-756	55	28	of	of	ADP
american_scientific_journal-756	55	29	(	(	PUNCT
american_scientific_journal-756	55	30	𝐻,𝐶	𝐻,𝐶	NOUN
american_scientific_journal-756	55	31	)	)	PUNCT
american_scientific_journal-756	55	32	,	,	PUNCT
american_scientific_journal-756	55	33	denoted	denote	VERB
american_scientific_journal-756	55	34	by	by	ADP
american_scientific_journal-756	55	35	(	(	PUNCT
american_scientific_journal-756	55	36	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	55	37	)	)	PUNCT
american_scientific_journal-756	55	38	⊆	⊆	NUM
american_scientific_journal-756	55	39	(	(	PUNCT
american_scientific_journal-756	55	40	𝐻,𝐶	𝐻,𝐶	NOUN
american_scientific_journal-756	55	41	)	)	PUNCT
american_scientific_journal-756	55	42	,	,	PUNCT
american_scientific_journal-756	55	43	if	if	SCONJ
american_scientific_journal-756	55	44	𝐵	𝐵	PROPN
american_scientific_journal-756	55	45	⊆	⊆	NUM
american_scientific_journal-756	55	46	𝐶	𝐶	PROPN
american_scientific_journal-756	55	47	and	and	CCONJ
american_scientific_journal-756	55	48	∀𝑥	∀𝑥	PROPN
american_scientific_journal-756	55	49	∈	∈	PROPN
american_scientific_journal-756	55	50	𝐵	𝐵	PROPN
american_scientific_journal-756	55	51	,	,	PUNCT
american_scientific_journal-756	55	52	𝐺(𝑥	𝐺(𝑥	NOUN
american_scientific_journal-756	55	53	)	)	PUNCT
american_scientific_journal-756	55	54	⊆	⊆	NUM
american_scientific_journal-756	55	55	𝐻(𝑥	𝐻(𝑥	NUM
american_scientific_journal-756	55	56	)	)	PUNCT
american_scientific_journal-756	55	57	.	.	PUNCT
american_scientific_journal-756	56	1	definition	definition	NOUN
american_scientific_journal-756	56	2	2.3	2.3	NUM
american_scientific_journal-756	56	3	.	.	PUNCT
american_scientific_journal-756	57	1	[	[	X
american_scientific_journal-756	57	2	10	10	NUM
american_scientific_journal-756	57	3	]	]	SYM
american_scientific_journal-756	57	4	two	two	NUM
american_scientific_journal-756	57	5	soft	soft	ADJ
american_scientific_journal-756	57	6	sets	set	NOUN
american_scientific_journal-756	57	7	(	(	PUNCT
american_scientific_journal-756	57	8	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	57	9	)	)	PUNCT
american_scientific_journal-756	57	10	and	and	CCONJ
american_scientific_journal-756	57	11	(	(	PUNCT
american_scientific_journal-756	57	12	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	57	13	)	)	PUNCT
american_scientific_journal-756	57	14	over	over	ADP
american_scientific_journal-756	57	15	a	a	DET
american_scientific_journal-756	57	16	common	common	ADJ
american_scientific_journal-756	57	17	universe	universe	NOUN
american_scientific_journal-756	57	18	𝑈	𝑈	PROPN
american_scientific_journal-756	57	19	are	be	AUX
american_scientific_journal-756	57	20	said	say	VERB
american_scientific_journal-756	57	21	to	to	PART
american_scientific_journal-756	57	22	be	be	AUX
american_scientific_journal-756	57	23	soft	soft	ADV
american_scientific_journal-756	57	24	equal	equal	ADJ
american_scientific_journal-756	57	25	if	if	SCONJ
american_scientific_journal-756	57	26	(	(	PUNCT
american_scientific_journal-756	57	27	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	57	28	)	)	PUNCT
american_scientific_journal-756	57	29	is	be	AUX
american_scientific_journal-756	57	30	a	a	DET
american_scientific_journal-756	57	31	soft	soft	ADJ
american_scientific_journal-756	57	32	subset	subset	NOUN
american_scientific_journal-756	57	33	of	of	ADP
american_scientific_journal-756	57	34	(	(	PUNCT
american_scientific_journal-756	57	35	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	57	36	)	)	PUNCT
american_scientific_journal-756	57	37	and	and	CCONJ
american_scientific_journal-756	57	38	(	(	PUNCT
american_scientific_journal-756	57	39	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	57	40	)	)	PUNCT
american_scientific_journal-756	57	41	is	be	AUX
american_scientific_journal-756	57	42	a	a	DET
american_scientific_journal-756	57	43	soft	soft	ADJ
american_scientific_journal-756	57	44	subset	subset	NOUN
american_scientific_journal-756	57	45	of	of	ADP
american_scientific_journal-756	57	46	(	(	PUNCT
american_scientific_journal-756	57	47	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	57	48	)	)	PUNCT
american_scientific_journal-756	57	49	.	.	PUNCT
american_scientific_journal-756	58	1	definition	definition	NOUN
american_scientific_journal-756	58	2	2.4	2.4	NUM
american_scientific_journal-756	58	3	.	.	PUNCT
american_scientific_journal-756	59	1	[	[	X
american_scientific_journal-756	59	2	27	27	NUM
american_scientific_journal-756	59	3	]	]	PUNCT
american_scientific_journal-756	59	4	the	the	DET
american_scientific_journal-756	59	5	complement	complement	NOUN
american_scientific_journal-756	59	6	of	of	ADP
american_scientific_journal-756	59	7	a	a	DET
american_scientific_journal-756	59	8	soft	soft	ADJ
american_scientific_journal-756	59	9	set	set	NOUN
american_scientific_journal-756	59	10	(	(	PUNCT
american_scientific_journal-756	59	11	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	59	12	)	)	PUNCT
american_scientific_journal-756	59	13	,	,	PUNCT
american_scientific_journal-756	59	14	denoted	denote	VERB
american_scientific_journal-756	59	15	by	by	ADP
american_scientific_journal-756	59	16	(	(	PUNCT
american_scientific_journal-756	59	17	𝐺,𝐵)𝑐	𝐺,𝐵)𝑐	ADJ
american_scientific_journal-756	59	18	,	,	PUNCT
american_scientific_journal-756	59	19	is	be	AUX
american_scientific_journal-756	59	20	defined	define	VERB
american_scientific_journal-756	59	21	by	by	ADP
american_scientific_journal-756	59	22	(	(	PUNCT
american_scientific_journal-756	59	23	𝐺,𝐵)𝑐	𝐺,𝐵)𝑐	NOUN
american_scientific_journal-756	59	24	=	=	SYM
american_scientific_journal-756	59	25	(	(	PUNCT
american_scientific_journal-756	59	26	𝐺𝑐	𝐺𝑐	PROPN
american_scientific_journal-756	59	27	,	,	PUNCT
american_scientific_journal-756	59	28	𝐵	𝐵	PROPN
american_scientific_journal-756	59	29	)	)	PUNCT
american_scientific_journal-756	59	30	.	.	PUNCT
american_scientific_journal-756	60	1	𝐺𝑐:𝐵	𝐺𝑐:𝐵	NOUN
american_scientific_journal-756	61	1	→	→	SYM
american_scientific_journal-756	61	2	𝑃(𝑈	𝑃(𝑈	NOUN
american_scientific_journal-756	61	3	)	)	PUNCT
american_scientific_journal-756	61	4	is	be	AUX
american_scientific_journal-756	61	5	a	a	DET
american_scientific_journal-756	61	6	mapping	mapping	NOUN
american_scientific_journal-756	61	7	given	give	VERB
american_scientific_journal-756	61	8	by	by	ADP
american_scientific_journal-756	61	9	𝐺𝑐(𝑥	𝐺𝑐(𝑥	ADJ
american_scientific_journal-756	61	10	)	)	PUNCT
american_scientific_journal-756	61	11	=	=	SYM
american_scientific_journal-756	61	12	𝑈	𝑈	NOUN
american_scientific_journal-756	61	13	−	−	NOUN
american_scientific_journal-756	61	14	𝐺(𝑥	𝐺(𝑥	NOUN
american_scientific_journal-756	61	15	)	)	PUNCT
american_scientific_journal-756	61	16	,	,	PUNCT
american_scientific_journal-756	61	17	∀𝑥	∀𝑥	PROPN
american_scientific_journal-756	61	18	∈	∈	PROPN
american_scientific_journal-756	61	19	𝐵.	𝐵.	PROPN
american_scientific_journal-756	61	20	𝐺𝑐	𝐺𝑐	PROPN
american_scientific_journal-756	61	21	is	be	AUX
american_scientific_journal-756	61	22	called	call	VERB
american_scientific_journal-756	61	23	the	the	DET
american_scientific_journal-756	61	24	soft	soft	ADJ
american_scientific_journal-756	61	25	complement	complement	NOUN
american_scientific_journal-756	61	26	function	function	NOUN
american_scientific_journal-756	61	27	of	of	ADP
american_scientific_journal-756	61	28	𝐺.	𝐺.	NOUN
american_scientific_journal-756	61	29	clearly	clearly	ADV
american_scientific_journal-756	61	30	,	,	PUNCT
american_scientific_journal-756	61	31	(	(	PUNCT
american_scientific_journal-756	61	32	𝐺𝑐)𝑐	𝐺𝑐)𝑐	NOUN
american_scientific_journal-756	61	33	is	be	AUX
american_scientific_journal-756	61	34	the	the	DET
american_scientific_journal-756	61	35	same	same	ADJ
american_scientific_journal-756	61	36	as	as	ADP
american_scientific_journal-756	61	37	𝐺	𝐺	PROPN
american_scientific_journal-756	61	38	and	and	CCONJ
american_scientific_journal-756	61	39	(	(	PUNCT
american_scientific_journal-756	61	40	(	(	PUNCT
american_scientific_journal-756	61	41	𝐺,𝐵)𝑐)𝑐	𝐺,𝐵)𝑐)𝑐	NOUN
american_scientific_journal-756	61	42	=	=	SYM
american_scientific_journal-756	61	43	(	(	PUNCT
american_scientific_journal-756	61	44	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	61	45	)	)	PUNCT
american_scientific_journal-756	61	46	.	.	PUNCT
american_scientific_journal-756	62	1	definition	definition	NOUN
american_scientific_journal-756	62	2	2.5	2.5	NUM
american_scientific_journal-756	62	3	.	.	PUNCT
american_scientific_journal-756	63	1	[	[	X
american_scientific_journal-756	63	2	10	10	NUM
american_scientific_journal-756	63	3	]	]	X
american_scientific_journal-756	63	4	a	a	DET
american_scientific_journal-756	63	5	soft	soft	ADJ
american_scientific_journal-756	63	6	set	set	NOUN
american_scientific_journal-756	63	7	(	(	PUNCT
american_scientific_journal-756	63	8	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	63	9	)	)	PUNCT
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american_scientific_journal-756	63	11	𝑈	𝑈	PROPN
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american_scientific_journal-756	63	13	said	say	VERB
american_scientific_journal-756	63	14	to	to	PART
american_scientific_journal-756	63	15	be	be	AUX
american_scientific_journal-756	63	16	a	a	DET
american_scientific_journal-756	63	17	null	null	ADJ
american_scientific_journal-756	63	18	soft	soft	ADJ
american_scientific_journal-756	63	19	set	set	NOUN
american_scientific_journal-756	63	20	,	,	PUNCT
american_scientific_journal-756	63	21	denoted	denote	VERB
american_scientific_journal-756	63	22	by	by	ADP
american_scientific_journal-756	63	23	𝛷	𝛷	PROPN
american_scientific_journal-756	63	24	,	,	PUNCT
american_scientific_journal-756	63	25	if	if	SCONJ
american_scientific_journal-756	63	26	∀𝑥	∀𝑥	PROPN
american_scientific_journal-756	63	27	∈	∈	PROPN
american_scientific_journal-756	63	28	𝐸	𝐸	PROPN
american_scientific_journal-756	63	29	,	,	PUNCT
american_scientific_journal-756	63	30	𝐺(𝑥	𝐺(𝑥	NOUN
american_scientific_journal-756	63	31	)	)	PUNCT
american_scientific_journal-756	63	32	=	=	PUNCT
american_scientific_journal-756	63	33	∅.	∅.	PRON
american_scientific_journal-756	63	34	definition	definition	NOUN
american_scientific_journal-756	63	35	2.6	2.6	NUM
american_scientific_journal-756	63	36	.	.	PUNCT
american_scientific_journal-756	64	1	[	[	X
american_scientific_journal-756	64	2	10	10	NUM
american_scientific_journal-756	64	3	]	]	X
american_scientific_journal-756	64	4	a	a	DET
american_scientific_journal-756	64	5	soft	soft	ADJ
american_scientific_journal-756	64	6	set	set	NOUN
american_scientific_journal-756	64	7	(	(	PUNCT
american_scientific_journal-756	64	8	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	64	9	)	)	PUNCT
american_scientific_journal-756	64	10	over	over	ADP
american_scientific_journal-756	64	11	𝑈	𝑈	PROPN
american_scientific_journal-756	64	12	is	be	AUX
american_scientific_journal-756	64	13	said	say	VERB
american_scientific_journal-756	64	14	to	to	PART
american_scientific_journal-756	64	15	be	be	AUX
american_scientific_journal-756	64	16	absolute	absolute	ADJ
american_scientific_journal-756	64	17	soft	soft	ADJ
american_scientific_journal-756	64	18	set	set	NOUN
american_scientific_journal-756	64	19	,	,	PUNCT
american_scientific_journal-756	64	20	denoted	denote	VERB
american_scientific_journal-756	64	21	by	by	ADP
american_scientific_journal-756	64	22	𝑈	𝑈	PROPN
american_scientific_journal-756	64	23	�	�	PROPN
american_scientific_journal-756	64	24	,	,	PUNCT
american_scientific_journal-756	64	25	if	if	SCONJ
american_scientific_journal-756	64	26	∀𝑥	∀𝑥	PROPN
american_scientific_journal-756	64	27	∈	∈	PROPN
american_scientific_journal-756	64	28	𝐸	𝐸	PROPN
american_scientific_journal-756	64	29	,	,	PUNCT
american_scientific_journal-756	64	30	𝐺(𝑥	𝐺(𝑥	NOUN
american_scientific_journal-756	64	31	)	)	PUNCT
american_scientific_journal-756	64	32	=	=	SYM
american_scientific_journal-756	64	33	𝑈.	𝑈.	PROPN
american_scientific_journal-756	64	34	97	97	NUM
american_scientific_journal-756	64	35	american	american	ADJ
american_scientific_journal-756	64	36	scientific	scientific	ADJ
american_scientific_journal-756	64	37	research	research	NOUN
american_scientific_journal-756	64	38	journal	journal	NOUN
american_scientific_journal-756	64	39	for	for	ADP
american_scientific_journal-756	64	40	engineering	engineering	NOUN
american_scientific_journal-756	64	41	,	,	PUNCT
american_scientific_journal-756	64	42	technology	technology	NOUN
american_scientific_journal-756	64	43	,	,	PUNCT
american_scientific_journal-756	64	44	and	and	CCONJ
american_scientific_journal-756	64	45	sciences	science	NOUN
american_scientific_journal-756	64	46	(	(	PUNCT
american_scientific_journal-756	64	47	asrjets	asrjet	NOUN
american_scientific_journal-756	64	48	)	)	PUNCT
american_scientific_journal-756	64	49	(	(	PUNCT
american_scientific_journal-756	64	50	2014	2014	NUM
american_scientific_journal-756	64	51	)	)	PUNCT
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american_scientific_journal-756	64	53	8	8	NUM
american_scientific_journal-756	64	54	,	,	PUNCT
american_scientific_journal-756	64	55	no	no	DET
american_scientific_journal-756	64	56	1	1	NUM
american_scientific_journal-756	64	57	,	,	PUNCT
american_scientific_journal-756	64	58	pp	pp	ADV
american_scientific_journal-756	64	59	96	96	NUM
american_scientific_journal-756	64	60	-	-	SYM
american_scientific_journal-756	64	61	107	107	NUM
american_scientific_journal-756	64	62	clearly	clearly	ADV
american_scientific_journal-756	64	63	,	,	PUNCT
american_scientific_journal-756	64	64	𝑈	𝑈	PROPN
american_scientific_journal-756	64	65	�	�	PROPN
american_scientific_journal-756	64	66	𝑐	𝑐	NOUN
american_scientific_journal-756	64	67	=	=	SYM
american_scientific_journal-756	64	68	𝛷	𝛷	PROPN
american_scientific_journal-756	64	69	and	and	CCONJ
american_scientific_journal-756	64	70	𝛷𝑐	𝛷𝑐	PROPN
american_scientific_journal-756	64	71	=	=	SYM
american_scientific_journal-756	64	72	𝑈	𝑈	PROPN
american_scientific_journal-756	64	73	�	�	PROPN
american_scientific_journal-756	64	74	.	.	PUNCT
american_scientific_journal-756	65	1	definition	definition	NOUN
american_scientific_journal-756	65	2	2.7	2.7	NUM
american_scientific_journal-756	65	3	.	.	PUNCT
american_scientific_journal-756	66	1	[	[	X
american_scientific_journal-756	66	2	10	10	NUM
american_scientific_journal-756	66	3	]	]	PUNCT
american_scientific_journal-756	66	4	the	the	DET
american_scientific_journal-756	66	5	union	union	NOUN
american_scientific_journal-756	66	6	of	of	ADP
american_scientific_journal-756	66	7	two	two	NUM
american_scientific_journal-756	66	8	soft	soft	ADJ
american_scientific_journal-756	66	9	sets	set	NOUN
american_scientific_journal-756	66	10	(	(	PUNCT
american_scientific_journal-756	66	11	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	66	12	)	)	PUNCT
american_scientific_journal-756	66	13	and	and	CCONJ
american_scientific_journal-756	66	14	(	(	PUNCT
american_scientific_journal-756	66	15	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	66	16	)	)	PUNCT
american_scientific_journal-756	66	17	over	over	ADP
american_scientific_journal-756	66	18	the	the	DET
american_scientific_journal-756	66	19	common	common	ADJ
american_scientific_journal-756	66	20	universe	universe	NOUN
american_scientific_journal-756	66	21	𝑈	𝑈	PROPN
american_scientific_journal-756	66	22	is	be	AUX
american_scientific_journal-756	66	23	the	the	DET
american_scientific_journal-756	66	24	soft	soft	ADJ
american_scientific_journal-756	66	25	set	set	NOUN
american_scientific_journal-756	66	26	(	(	PUNCT
american_scientific_journal-756	66	27	𝑇,𝐷	𝑇,𝐷	NOUN
american_scientific_journal-756	66	28	)	)	PUNCT
american_scientific_journal-756	66	29	,	,	PUNCT
american_scientific_journal-756	66	30	where	where	SCONJ
american_scientific_journal-756	66	31	𝐷	𝐷	NOUN
american_scientific_journal-756	66	32	=	=	NOUN
american_scientific_journal-756	66	33	𝐵	𝐵	PROPN
american_scientific_journal-756	66	34	∪	∪	PROPN
american_scientific_journal-756	66	35	𝐶	𝐶	PROPN
american_scientific_journal-756	66	36	and	and	CCONJ
american_scientific_journal-756	66	37	for	for	ADP
american_scientific_journal-756	66	38	all	all	PRON
american_scientific_journal-756	66	39	𝑥	𝑥	DET
american_scientific_journal-756	66	40	∈	∈	PROPN
american_scientific_journal-756	66	41	𝐷	𝐷	PROPN
american_scientific_journal-756	66	42	,	,	PUNCT
american_scientific_journal-756	66	43	𝑇(𝑥	𝑇(𝑥	NOUN
american_scientific_journal-756	66	44	)	)	PUNCT
american_scientific_journal-756	66	45	=	=	PROPN
american_scientific_journal-756	66	46	�	�	PROPN
american_scientific_journal-756	66	47	g(x	g(x	PROPN
american_scientific_journal-756	66	48	)	)	PUNCT
american_scientific_journal-756	66	49	,	,	PUNCT
american_scientific_journal-756	66	50	if	if	SCONJ
american_scientific_journal-756	66	51	x	x	SYM
american_scientific_journal-756	66	52	∈	∈	PROPN
american_scientific_journal-756	66	53	b\c	b\c	PROPN
american_scientific_journal-756	66	54	h(x	h(x	PROPN
american_scientific_journal-756	66	55	)	)	PUNCT
american_scientific_journal-756	66	56	,	,	PUNCT
american_scientific_journal-756	66	57	if	if	SCONJ
american_scientific_journal-756	66	58	x	x	SYM
american_scientific_journal-756	66	59	∈	∈	PROPN
american_scientific_journal-756	66	60	c\b	c\b	NOUN
american_scientific_journal-756	66	61	g(x	g(x	PROPN
american_scientific_journal-756	66	62	)	)	PUNCT
american_scientific_journal-756	66	63	∪	∪	ADP
american_scientific_journal-756	66	64	h(x	h(x	PROPN
american_scientific_journal-756	66	65	)	)	PUNCT
american_scientific_journal-756	66	66	,	,	PUNCT
american_scientific_journal-756	66	67	if	if	SCONJ
american_scientific_journal-756	66	68	x	x	SYM
american_scientific_journal-756	66	69	∈	∈	PROPN
american_scientific_journal-756	66	70	c	c	X
american_scientific_journal-756	66	71	∩	∩	PROPN
american_scientific_journal-756	66	72	b	b	PROPN
american_scientific_journal-756	66	73	this	this	DET
american_scientific_journal-756	66	74	relationship	relationship	NOUN
american_scientific_journal-756	66	75	is	be	AUX
american_scientific_journal-756	66	76	written	write	VERB
american_scientific_journal-756	66	77	as	as	ADP
american_scientific_journal-756	66	78	(	(	PUNCT
american_scientific_journal-756	66	79	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	66	80	)	)	PUNCT
american_scientific_journal-756	66	81	∪	∪	NOUN
american_scientific_journal-756	66	82	�	�	PROPN
american_scientific_journal-756	66	83	(	(	PUNCT
american_scientific_journal-756	66	84	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	66	85	)	)	PUNCT
american_scientific_journal-756	66	86	=	=	PUNCT
american_scientific_journal-756	66	87	(	(	PUNCT
american_scientific_journal-756	66	88	𝑇,𝐷	𝑇,𝐷	NOUN
american_scientific_journal-756	66	89	)	)	PUNCT
american_scientific_journal-756	66	90	.	.	PUNCT
american_scientific_journal-756	67	1	definition	definition	NOUN
american_scientific_journal-756	67	2	2.8	2.8	NUM
american_scientific_journal-756	67	3	.	.	PUNCT
american_scientific_journal-756	68	1	[	[	X
american_scientific_journal-756	68	2	26	26	NUM
american_scientific_journal-756	68	3	]	]	PUNCT
american_scientific_journal-756	68	4	the	the	DET
american_scientific_journal-756	68	5	intersection	intersection	NOUN
american_scientific_journal-756	68	6	of	of	ADP
american_scientific_journal-756	68	7	two	two	NUM
american_scientific_journal-756	68	8	soft	soft	ADJ
american_scientific_journal-756	68	9	sets	set	NOUN
american_scientific_journal-756	68	10	(	(	PUNCT
american_scientific_journal-756	68	11	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	68	12	)	)	PUNCT
american_scientific_journal-756	68	13	and	and	CCONJ
american_scientific_journal-756	68	14	(	(	PUNCT
american_scientific_journal-756	68	15	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	68	16	)	)	PUNCT
american_scientific_journal-756	68	17	over	over	ADP
american_scientific_journal-756	68	18	the	the	DET
american_scientific_journal-756	68	19	common	common	ADJ
american_scientific_journal-756	68	20	universe	universe	NOUN
american_scientific_journal-756	68	21	𝑈	𝑈	PROPN
american_scientific_journal-756	68	22	is	be	AUX
american_scientific_journal-756	68	23	the	the	DET
american_scientific_journal-756	68	24	soft	soft	ADJ
american_scientific_journal-756	68	25	set	set	NOUN
american_scientific_journal-756	68	26	(	(	PUNCT
american_scientific_journal-756	68	27	𝑇,𝐷	𝑇,𝐷	NOUN
american_scientific_journal-756	68	28	)	)	PUNCT
american_scientific_journal-756	68	29	,	,	PUNCT
american_scientific_journal-756	68	30	where	where	SCONJ
american_scientific_journal-756	68	31	𝐷	𝐷	NOUN
american_scientific_journal-756	68	32	=	=	SYM
american_scientific_journal-756	68	33	𝐵	𝐵	PROPN
american_scientific_journal-756	68	34	∩	∩	PROPN
american_scientific_journal-756	68	35	𝐶	𝐶	PROPN
american_scientific_journal-756	68	36	and	and	CCONJ
american_scientific_journal-756	68	37	for	for	ADP
american_scientific_journal-756	68	38	all	all	PRON
american_scientific_journal-756	68	39	𝑥	𝑥	DET
american_scientific_journal-756	68	40	∈	∈	PROPN
american_scientific_journal-756	68	41	𝐷	𝐷	NOUN
american_scientific_journal-756	68	42	,	,	PUNCT
american_scientific_journal-756	68	43	𝑇(𝑥	𝑇(𝑥	NOUN
american_scientific_journal-756	68	44	)	)	PUNCT
american_scientific_journal-756	68	45	=	=	SYM
american_scientific_journal-756	68	46	𝐻(𝑥	𝐻(𝑥	NOUN
american_scientific_journal-756	68	47	)	)	PUNCT
american_scientific_journal-756	68	48	∩	∩	NOUN
american_scientific_journal-756	68	49	𝐺(𝑥	𝐺(𝑥	NOUN
american_scientific_journal-756	68	50	)	)	PUNCT
american_scientific_journal-756	68	51	.	.	PUNCT
american_scientific_journal-756	69	1	this	this	DET
american_scientific_journal-756	69	2	relationship	relationship	NOUN
american_scientific_journal-756	69	3	is	be	AUX
american_scientific_journal-756	69	4	written	write	VERB
american_scientific_journal-756	69	5	as	as	ADP
american_scientific_journal-756	69	6	(	(	PUNCT
american_scientific_journal-756	69	7	𝐻,𝐶	𝐻,𝐶	X
american_scientific_journal-756	69	8	)	)	PUNCT
american_scientific_journal-756	69	9	∩	∩	ADJ
american_scientific_journal-756	69	10	�	�	PROPN
american_scientific_journal-756	69	11	(	(	PUNCT
american_scientific_journal-756	69	12	𝐺,𝐵	𝐺,𝐵	NOUN
american_scientific_journal-756	69	13	)	)	PUNCT
american_scientific_journal-756	69	14	=	=	PUNCT
american_scientific_journal-756	69	15	(	(	PUNCT
american_scientific_journal-756	69	16	𝑇,𝐷	𝑇,𝐷	NOUN
american_scientific_journal-756	69	17	)	)	PUNCT
american_scientific_journal-756	69	18	.	.	PUNCT
american_scientific_journal-756	70	1	proposition	proposition	NOUN
american_scientific_journal-756	70	2	2.9	2.9	NUM
american_scientific_journal-756	70	3	.	.	PUNCT
american_scientific_journal-756	71	1	[	[	X
american_scientific_journal-756	71	2	15	15	NUM
american_scientific_journal-756	71	3	]	]	X
american_scientific_journal-756	71	4	if	if	SCONJ
american_scientific_journal-756	71	5	(	(	PUNCT
american_scientific_journal-756	71	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	71	7	)	)	PUNCT
american_scientific_journal-756	71	8	and	and	CCONJ
american_scientific_journal-756	71	9	(	(	PUNCT
american_scientific_journal-756	71	10	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	71	11	)	)	PUNCT
american_scientific_journal-756	71	12	are	be	AUX
american_scientific_journal-756	71	13	two	two	NUM
american_scientific_journal-756	71	14	soft	soft	ADJ
american_scientific_journal-756	71	15	sets	set	NOUN
american_scientific_journal-756	71	16	over	over	ADP
american_scientific_journal-756	71	17	𝑈	𝑈	PROPN
american_scientific_journal-756	71	18	,	,	PUNCT
american_scientific_journal-756	71	19	then	then	ADV
american_scientific_journal-756	71	20	(	(	PUNCT
american_scientific_journal-756	71	21	1	1	X
american_scientific_journal-756	71	22	)	)	PUNCT
american_scientific_journal-756	71	23	(	(	PUNCT
american_scientific_journal-756	71	24	(	(	PUNCT
american_scientific_journal-756	71	25	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	71	26	)	)	PUNCT
american_scientific_journal-756	71	27	∪	∪	ADP
american_scientific_journal-756	71	28	�	�	PROPN
american_scientific_journal-756	71	29	(	(	PUNCT
american_scientific_journal-756	71	30	𝐻,𝐸))𝑐	𝐻,𝐸))𝑐	PROPN
american_scientific_journal-756	71	31	=	=	SYM
american_scientific_journal-756	71	32	(	(	PUNCT
american_scientific_journal-756	71	33	𝐺,𝐸)𝑐	𝐺,𝐸)𝑐	ADP
american_scientific_journal-756	71	34	∩	∩	ADJ
american_scientific_journal-756	71	35	�	�	PROPN
american_scientific_journal-756	71	36	(	(	PUNCT
american_scientific_journal-756	71	37	𝐻,𝐸)𝑐.	𝐻,𝐸)𝑐.	PROPN
american_scientific_journal-756	71	38	(	(	PUNCT
american_scientific_journal-756	71	39	2	2	NUM
american_scientific_journal-756	71	40	)	)	PUNCT
american_scientific_journal-756	71	41	(	(	PUNCT
american_scientific_journal-756	71	42	(	(	PUNCT
american_scientific_journal-756	71	43	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	71	44	)	)	PUNCT
american_scientific_journal-756	71	45	∩	∩	NOUN
american_scientific_journal-756	71	46	�	�	PROPN
american_scientific_journal-756	71	47	(	(	PUNCT
american_scientific_journal-756	71	48	𝐻,𝐸))𝑐	𝐻,𝐸))𝑐	PROPN
american_scientific_journal-756	71	49	=	=	SYM
american_scientific_journal-756	71	50	(	(	PUNCT
american_scientific_journal-756	71	51	𝐺,𝐸)𝑐	𝐺,𝐸)𝑐	ADV
american_scientific_journal-756	71	52	∪	∪	PROPN
american_scientific_journal-756	71	53	�	�	PROPN
american_scientific_journal-756	71	54	(	(	PUNCT
american_scientific_journal-756	71	55	𝐻,𝐸)𝑐.	𝐻,𝐸)𝑐.	PROPN
american_scientific_journal-756	71	56	definition	definition	NOUN
american_scientific_journal-756	71	57	2.10	2.10	NUM
american_scientific_journal-756	71	58	.	.	PUNCT
american_scientific_journal-756	72	1	[	[	X
american_scientific_journal-756	72	2	16	16	NUM
american_scientific_journal-756	72	3	]	]	PUNCT
american_scientific_journal-756	72	4	let	let	VERB
american_scientific_journal-756	72	5	𝐼	𝐼	PRON
american_scientific_journal-756	72	6	be	be	AUX
american_scientific_journal-756	72	7	arbitrary	arbitrary	ADJ
american_scientific_journal-756	72	8	index	index	NOUN
american_scientific_journal-756	72	9	set	set	VERB
american_scientific_journal-756	72	10	and	and	CCONJ
american_scientific_journal-756	72	11	{	{	PUNCT
american_scientific_journal-756	72	12	(	(	PUNCT
american_scientific_journal-756	72	13	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	72	14	,	,	PUNCT
american_scientific_journal-756	72	15	𝐸)}𝑖∈𝐼	𝐸)}𝑖∈𝐼	ADJ
american_scientific_journal-756	72	16	be	be	VERB
american_scientific_journal-756	72	17	soft	soft	ADJ
american_scientific_journal-756	72	18	sets	set	NOUN
american_scientific_journal-756	72	19	over	over	ADP
american_scientific_journal-756	72	20	𝑈.	𝑈.	PROPN
american_scientific_journal-756	72	21	(	(	PUNCT
american_scientific_journal-756	72	22	a	a	X
american_scientific_journal-756	72	23	)	)	PUNCT
american_scientific_journal-756	72	24	the	the	DET
american_scientific_journal-756	72	25	union	union	NOUN
american_scientific_journal-756	72	26	of	of	ADP
american_scientific_journal-756	72	27	these	these	DET
american_scientific_journal-756	72	28	soft	soft	ADJ
american_scientific_journal-756	72	29	sets	set	NOUN
american_scientific_journal-756	72	30	is	be	AUX
american_scientific_journal-756	72	31	the	the	DET
american_scientific_journal-756	72	32	soft	soft	ADJ
american_scientific_journal-756	72	33	set	set	NOUN
american_scientific_journal-756	72	34	(	(	PUNCT
american_scientific_journal-756	72	35	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	72	36	)	)	PUNCT
american_scientific_journal-756	72	37	,	,	PUNCT
american_scientific_journal-756	72	38	where	where	SCONJ
american_scientific_journal-756	72	39	𝐻(𝑥	𝐻(𝑥	VERB
american_scientific_journal-756	72	40	)	)	PUNCT
american_scientific_journal-756	73	1	=	=	NOUN
american_scientific_journal-756	73	2	∪𝑖∈𝐼	∪𝑖∈𝐼	ADJ
american_scientific_journal-756	73	3	𝐺𝑖(𝑥	𝐺𝑖(𝑥	ADJ
american_scientific_journal-756	73	4	)	)	PUNCT
american_scientific_journal-756	73	5	for	for	ADP
american_scientific_journal-756	73	6	each	each	DET
american_scientific_journal-756	73	7	𝑥	𝑥	PRON
american_scientific_journal-756	73	8	∈	∈	PROPN
american_scientific_journal-756	74	1	𝐸.	𝐸.	NOUN
american_scientific_journal-756	75	1	we	we	PRON
american_scientific_journal-756	75	2	write	write	VERB
american_scientific_journal-756	75	3	∪	∪	ADP
american_scientific_journal-756	75	4	�	�	PROPN
american_scientific_journal-756	75	5	(	(	PUNCT
american_scientific_journal-756	75	6	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	75	7	,	,	PUNCT
american_scientific_journal-756	75	8	𝐸	𝐸	PROPN
american_scientific_journal-756	75	9	)	)	PUNCT
american_scientific_journal-756	75	10	=	=	PUNCT
american_scientific_journal-756	75	11	(	(	PUNCT
american_scientific_journal-756	75	12	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	75	13	)	)	PUNCT
american_scientific_journal-756	75	14	.	.	PUNCT
american_scientific_journal-756	76	1	(	(	PUNCT
american_scientific_journal-756	76	2	b	b	X
american_scientific_journal-756	76	3	)	)	PUNCT
american_scientific_journal-756	76	4	the	the	DET
american_scientific_journal-756	76	5	intersection	intersection	NOUN
american_scientific_journal-756	76	6	of	of	ADP
american_scientific_journal-756	76	7	these	these	DET
american_scientific_journal-756	76	8	soft	soft	ADJ
american_scientific_journal-756	76	9	sets	set	NOUN
american_scientific_journal-756	76	10	is	be	AUX
american_scientific_journal-756	76	11	the	the	DET
american_scientific_journal-756	76	12	soft	soft	ADJ
american_scientific_journal-756	76	13	set	set	NOUN
american_scientific_journal-756	76	14	(	(	PUNCT
american_scientific_journal-756	76	15	𝑀,𝐸	𝑀,𝐸	PROPN
american_scientific_journal-756	76	16	)	)	PUNCT
american_scientific_journal-756	76	17	,	,	PUNCT
american_scientific_journal-756	76	18	where	where	SCONJ
american_scientific_journal-756	76	19	𝑀(𝑥	𝑀(𝑥	X
american_scientific_journal-756	76	20	)	)	PUNCT
american_scientific_journal-756	76	21	=	=	NOUN
american_scientific_journal-756	76	22	∩𝑖∈𝐼	∩𝑖∈𝐼	NOUN
american_scientific_journal-756	76	23	𝐺𝑖(𝑥	𝐺𝑖(𝑥	NOUN
american_scientific_journal-756	76	24	)	)	PUNCT
american_scientific_journal-756	76	25	for	for	ADP
american_scientific_journal-756	76	26	all	all	DET
american_scientific_journal-756	76	27	𝑥	𝑥	DET
american_scientific_journal-756	76	28	∈	∈	NOUN
american_scientific_journal-756	76	29	𝐸.	𝐸.	NOUN
american_scientific_journal-756	76	30	we	we	PRON
american_scientific_journal-756	76	31	write	write	VERB
american_scientific_journal-756	76	32	∩	∩	NOUN
american_scientific_journal-756	76	33	�	�	PROPN
american_scientific_journal-756	76	34	(	(	PUNCT
american_scientific_journal-756	76	35	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	76	36	,	,	PUNCT
american_scientific_journal-756	76	37	𝐸	𝐸	PROPN
american_scientific_journal-756	76	38	)	)	PUNCT
american_scientific_journal-756	76	39	=	=	PRON
american_scientific_journal-756	76	40	(	(	PUNCT
american_scientific_journal-756	76	41	𝑀,𝐸	𝑀,𝐸	PROPN
american_scientific_journal-756	76	42	)	)	PUNCT
american_scientific_journal-756	76	43	.	.	PUNCT
american_scientific_journal-756	77	1	proposition	proposition	NOUN
american_scientific_journal-756	77	2	2.11	2.11	NUM
american_scientific_journal-756	77	3	.	.	PUNCT
american_scientific_journal-756	78	1	[	[	X
american_scientific_journal-756	78	2	16	16	NUM
american_scientific_journal-756	78	3	]	]	PUNCT
american_scientific_journal-756	78	4	let	let	VERB
american_scientific_journal-756	78	5	𝐼	𝐼	PRON
american_scientific_journal-756	78	6	be	be	AUX
american_scientific_journal-756	78	7	arbitrary	arbitrary	ADJ
american_scientific_journal-756	78	8	index	index	NOUN
american_scientific_journal-756	78	9	set	set	VERB
american_scientific_journal-756	78	10	and	and	CCONJ
american_scientific_journal-756	78	11	{	{	PUNCT
american_scientific_journal-756	78	12	(	(	PUNCT
american_scientific_journal-756	78	13	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	78	14	,	,	PUNCT
american_scientific_journal-756	78	15	𝐸)}𝑖∈𝐼	𝐸)}𝑖∈𝐼	ADJ
american_scientific_journal-756	78	16	be	be	VERB
american_scientific_journal-756	78	17	soft	soft	ADJ
american_scientific_journal-756	78	18	sets	set	NOUN
american_scientific_journal-756	78	19	over	over	ADP
american_scientific_journal-756	78	20	𝑈	𝑈	PROPN
american_scientific_journal-756	78	21	,	,	PUNCT
american_scientific_journal-756	78	22	then	then	ADV
american_scientific_journal-756	78	23	(	(	PUNCT
american_scientific_journal-756	78	24	1	1	X
american_scientific_journal-756	78	25	)	)	PUNCT
american_scientific_journal-756	78	26	[	[	X
american_scientific_journal-756	78	27	∪	∪	X
american_scientific_journal-756	78	28	�	�	PROPN
american_scientific_journal-756	78	29	(	(	PUNCT
american_scientific_journal-756	78	30	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	78	31	,	,	PUNCT
american_scientific_journal-756	78	32	𝐸)]𝑐	𝐸)]𝑐	NOUN
american_scientific_journal-756	78	33	=	=	PROPN
american_scientific_journal-756	78	34	∩	∩	NOUN
american_scientific_journal-756	78	35	�	�	PROPN
american_scientific_journal-756	78	36	(	(	PUNCT
american_scientific_journal-756	78	37	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	78	38	,	,	PUNCT
american_scientific_journal-756	78	39	𝐸)𝑐	𝐸)𝑐	X
american_scientific_journal-756	78	40	(	(	PUNCT
american_scientific_journal-756	78	41	2	2	NUM
american_scientific_journal-756	78	42	)	)	PUNCT
american_scientific_journal-756	79	1	[	[	X
american_scientific_journal-756	79	2	∩	∩	NOUN
american_scientific_journal-756	79	3	�	�	PROPN
american_scientific_journal-756	79	4	(	(	PUNCT
american_scientific_journal-756	79	5	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	79	6	,	,	PUNCT
american_scientific_journal-756	79	7	𝐸)]𝑐	𝐸)]𝑐	NOUN
american_scientific_journal-756	79	8	=	=	SYM
american_scientific_journal-756	79	9	∪	∪	ADP
american_scientific_journal-756	79	10	�	�	PROPN
american_scientific_journal-756	79	11	(	(	PUNCT
american_scientific_journal-756	79	12	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	79	13	,	,	PUNCT
american_scientific_journal-756	79	14	𝐸)𝑐.	𝐸)𝑐.	ADJ
american_scientific_journal-756	79	15	definition	definition	NOUN
american_scientific_journal-756	79	16	2.12	2.12	NUM
american_scientific_journal-756	79	17	.	.	PUNCT
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american_scientific_journal-756	80	2	16	16	NUM
american_scientific_journal-756	80	3	]	]	PUNCT
american_scientific_journal-756	80	4	the	the	DET
american_scientific_journal-756	80	5	soft	soft	ADJ
american_scientific_journal-756	80	6	set	set	NOUN
american_scientific_journal-756	80	7	(	(	PUNCT
american_scientific_journal-756	80	8	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	80	9	)	)	PUNCT
american_scientific_journal-756	80	10	over	over	ADP
american_scientific_journal-756	80	11	𝑈	𝑈	PROPN
american_scientific_journal-756	80	12	is	be	AUX
american_scientific_journal-756	80	13	called	call	VERB
american_scientific_journal-756	80	14	a	a	DET
american_scientific_journal-756	80	15	soft	soft	ADJ
american_scientific_journal-756	80	16	point	point	NOUN
american_scientific_journal-756	80	17	in	in	ADP
american_scientific_journal-756	80	18	𝑈	𝑈	PROPN
american_scientific_journal-756	80	19	,	,	PUNCT
american_scientific_journal-756	80	20	denoted	denote	VERB
american_scientific_journal-756	80	21	by	by	ADP
american_scientific_journal-756	80	22	𝑒𝐺	𝑒𝐺	NOUN
american_scientific_journal-756	80	23	,	,	PUNCT
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american_scientific_journal-756	80	25	for	for	ADP
american_scientific_journal-756	80	26	the	the	DET
american_scientific_journal-756	80	27	element	element	NOUN
american_scientific_journal-756	80	28	𝑒	𝑒	PROPN
american_scientific_journal-756	80	29	∈	∈	PROPN
american_scientific_journal-756	80	30	𝐴	𝐴	PROPN
american_scientific_journal-756	80	31	,	,	PUNCT
american_scientific_journal-756	80	32	𝐺(𝑒	𝐺(𝑒	NUM
american_scientific_journal-756	80	33	)	)	PUNCT
american_scientific_journal-756	80	34	≠	≠	PROPN
american_scientific_journal-756	80	35	∅	∅	NOUN
american_scientific_journal-756	80	36	and	and	CCONJ
american_scientific_journal-756	80	37	𝐺(𝑒′	𝐺(𝑒′	NOUN
american_scientific_journal-756	80	38	)	)	PUNCT
american_scientific_journal-756	81	1	=	=	NOUN
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american_scientific_journal-756	81	4	all	all	DET
american_scientific_journal-756	81	5	𝑒′	𝑒′	NOUN
american_scientific_journal-756	81	6	∈	∈	PROPN
american_scientific_journal-756	81	7	𝐸	𝐸	PROPN
american_scientific_journal-756	81	8	−	−	PROPN
american_scientific_journal-756	81	9	{	{	PUNCT
american_scientific_journal-756	81	10	𝑒	𝑒	NOUN
american_scientific_journal-756	81	11	}	}	PUNCT
american_scientific_journal-756	81	12	.	.	PUNCT
american_scientific_journal-756	82	1	definition	definition	NOUN
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american_scientific_journal-756	82	3	.	.	PUNCT
american_scientific_journal-756	83	1	[	[	X
american_scientific_journal-756	83	2	16	16	NUM
american_scientific_journal-756	83	3	]	]	PUNCT
american_scientific_journal-756	83	4	the	the	DET
american_scientific_journal-756	83	5	soft	soft	ADJ
american_scientific_journal-756	83	6	point	point	NOUN
american_scientific_journal-756	83	7	𝑥𝐺	𝑥𝐺	NOUN
american_scientific_journal-756	83	8	is	be	AUX
american_scientific_journal-756	83	9	said	say	VERB
american_scientific_journal-756	83	10	to	to	PART
american_scientific_journal-756	83	11	be	be	AUX
american_scientific_journal-756	83	12	in	in	ADP
american_scientific_journal-756	83	13	the	the	DET
american_scientific_journal-756	83	14	soft	soft	ADJ
american_scientific_journal-756	83	15	set	set	NOUN
american_scientific_journal-756	83	16	(	(	PUNCT
american_scientific_journal-756	83	17	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	83	18	)	)	PUNCT
american_scientific_journal-756	83	19	,	,	PUNCT
american_scientific_journal-756	83	20	denoted	denote	VERB
american_scientific_journal-756	83	21	by	by	ADP
american_scientific_journal-756	83	22	𝑥𝐺	𝑥𝐺	PROPN
american_scientific_journal-756	83	23	∈	∈	PROPN
american_scientific_journal-756	83	24	�	�	PROPN
american_scientific_journal-756	83	25	(	(	PUNCT
american_scientific_journal-756	83	26	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	83	27	)	)	PUNCT
american_scientific_journal-756	83	28	,	,	PUNCT
american_scientific_journal-756	83	29	if	if	SCONJ
american_scientific_journal-756	83	30	for	for	ADP
american_scientific_journal-756	83	31	the	the	DET
american_scientific_journal-756	83	32	element	element	NOUN
american_scientific_journal-756	83	33	𝑥	𝑥	PROPN
american_scientific_journal-756	83	34	∈	∈	PROPN
american_scientific_journal-756	83	35	𝐸	𝐸	PROPN
american_scientific_journal-756	83	36	and	and	CCONJ
american_scientific_journal-756	83	37	𝐺(𝑥	𝐺(𝑥	NUM
american_scientific_journal-756	83	38	)	)	PUNCT
american_scientific_journal-756	83	39	⊆	⊆	NUM
american_scientific_journal-756	83	40	𝐻(𝑥	𝐻(𝑥	NUM
american_scientific_journal-756	83	41	)	)	PUNCT
american_scientific_journal-756	83	42	.	.	PUNCT
american_scientific_journal-756	84	1	proposition	proposition	NOUN
american_scientific_journal-756	84	2	2.14	2.14	NUM
american_scientific_journal-756	84	3	.	.	PUNCT
american_scientific_journal-756	85	1	[	[	X
american_scientific_journal-756	85	2	16	16	NUM
american_scientific_journal-756	85	3	]	]	PUNCT
american_scientific_journal-756	85	4	let	let	VERB
american_scientific_journal-756	85	5	𝑥𝐺	𝑥𝐺	NOUN
american_scientific_journal-756	85	6	∈	∈	PROPN
american_scientific_journal-756	85	7	�	�	PROPN
american_scientific_journal-756	85	8	𝑈	𝑈	PROPN
american_scientific_journal-756	85	9	�	�	PROPN
american_scientific_journal-756	85	10	and	and	CCONJ
american_scientific_journal-756	85	11	(	(	PUNCT
american_scientific_journal-756	85	12	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	85	13	)	)	PUNCT
american_scientific_journal-756	85	14	⊆	⊆	NUM
american_scientific_journal-756	85	15	𝑈	𝑈	PROPN
american_scientific_journal-756	85	16	�	�	PROPN
american_scientific_journal-756	85	17	.	.	PUNCT
american_scientific_journal-756	86	1	if	if	SCONJ
american_scientific_journal-756	86	2	𝑥𝐺	𝑥𝐺	NOUN
american_scientific_journal-756	86	3	∈	∈	PROPN
american_scientific_journal-756	86	4	�	�	PROPN
american_scientific_journal-756	86	5	(	(	PUNCT
american_scientific_journal-756	86	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	86	7	)	)	PUNCT
american_scientific_journal-756	86	8	,	,	PUNCT
american_scientific_journal-756	86	9	then	then	ADV
american_scientific_journal-756	86	10	𝑥𝐺	𝑥𝐺	PROPN
american_scientific_journal-756	86	11	∉	∉	PROPN
american_scientific_journal-756	86	12	�	�	PROPN
american_scientific_journal-756	86	13	(	(	PUNCT
american_scientific_journal-756	86	14	𝐺,𝐸)𝑐.	𝐺,𝐸)𝑐.	ADP
american_scientific_journal-756	86	15	98	98	NUM
american_scientific_journal-756	86	16	american	american	ADJ
american_scientific_journal-756	86	17	scientific	scientific	ADJ
american_scientific_journal-756	86	18	research	research	NOUN
american_scientific_journal-756	86	19	journal	journal	NOUN
american_scientific_journal-756	86	20	for	for	ADP
american_scientific_journal-756	86	21	engineering	engineering	NOUN
american_scientific_journal-756	86	22	,	,	PUNCT
american_scientific_journal-756	86	23	technology	technology	NOUN
american_scientific_journal-756	86	24	,	,	PUNCT
american_scientific_journal-756	86	25	and	and	CCONJ
american_scientific_journal-756	86	26	sciences	science	NOUN
american_scientific_journal-756	86	27	(	(	PUNCT
american_scientific_journal-756	86	28	asrjets	asrjet	NOUN
american_scientific_journal-756	86	29	)	)	PUNCT
american_scientific_journal-756	86	30	(	(	PUNCT
american_scientific_journal-756	86	31	2014	2014	NUM
american_scientific_journal-756	86	32	)	)	PUNCT
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american_scientific_journal-756	86	35	,	,	PUNCT
american_scientific_journal-756	86	36	no	no	DET
american_scientific_journal-756	86	37	1	1	NUM
american_scientific_journal-756	86	38	,	,	PUNCT
american_scientific_journal-756	86	39	pp	pp	ADV
american_scientific_journal-756	86	40	96	96	NUM
american_scientific_journal-756	86	41	-	-	SYM
american_scientific_journal-756	86	42	107	107	NUM
american_scientific_journal-756	86	43	definition	definition	NOUN
american_scientific_journal-756	86	44	2.15	2.15	NUM
american_scientific_journal-756	86	45	.	.	PUNCT
american_scientific_journal-756	87	1	[	[	X
american_scientific_journal-756	87	2	15	15	NUM
american_scientific_journal-756	87	3	]	]	PUNCT
american_scientific_journal-756	87	4	let	let	VERB
american_scientific_journal-756	87	5	𝜏	𝜏	PRON
american_scientific_journal-756	87	6	be	be	AUX
american_scientific_journal-756	87	7	the	the	DET
american_scientific_journal-756	87	8	collection	collection	NOUN
american_scientific_journal-756	87	9	of	of	ADP
american_scientific_journal-756	87	10	soft	soft	ADJ
american_scientific_journal-756	87	11	sets	set	NOUN
american_scientific_journal-756	87	12	over	over	ADP
american_scientific_journal-756	87	13	a	a	DET
american_scientific_journal-756	87	14	universe	universe	NOUN
american_scientific_journal-756	87	15	𝑈	𝑈	PROPN
american_scientific_journal-756	87	16	,	,	PUNCT
american_scientific_journal-756	87	17	then	then	ADV
american_scientific_journal-756	87	18	𝜏	𝜏	NOUN
american_scientific_journal-756	87	19	is	be	AUX
american_scientific_journal-756	87	20	called	call	VERB
american_scientific_journal-756	87	21	soft	soft	ADJ
american_scientific_journal-756	87	22	topology	topology	NOUN
american_scientific_journal-756	87	23	on	on	ADP
american_scientific_journal-756	87	24	𝑈	𝑈	PROPN
american_scientific_journal-756	87	25	if	if	SCONJ
american_scientific_journal-756	87	26	t1	t1	NOUN
american_scientific_journal-756	87	27	.	.	PUNCT
american_scientific_journal-756	88	1	𝑈	𝑈	NOUN
american_scientific_journal-756	88	2	and	and	CCONJ
american_scientific_journal-756	88	3	𝛷	𝛷	NOUN
american_scientific_journal-756	88	4	belong	belong	VERB
american_scientific_journal-756	88	5	to	to	ADP
american_scientific_journal-756	88	6	𝜏	𝜏	PROPN
american_scientific_journal-756	88	7	t2	t2	NOUN
american_scientific_journal-756	88	8	.	.	PUNCT
american_scientific_journal-756	89	1	the	the	DET
american_scientific_journal-756	89	2	union	union	NOUN
american_scientific_journal-756	89	3	of	of	ADP
american_scientific_journal-756	89	4	any	any	DET
american_scientific_journal-756	89	5	number	number	NOUN
american_scientific_journal-756	89	6	of	of	ADP
american_scientific_journal-756	89	7	soft	soft	ADJ
american_scientific_journal-756	89	8	sets	set	NOUN
american_scientific_journal-756	89	9	in	in	ADP
american_scientific_journal-756	89	10	𝜏	𝜏	PRON
american_scientific_journal-756	89	11	belongs	belong	VERB
american_scientific_journal-756	89	12	to	to	ADP
american_scientific_journal-756	89	13	𝜏	𝜏	PROPN
american_scientific_journal-756	89	14	t3	t3	NOUN
american_scientific_journal-756	89	15	.	.	PUNCT
american_scientific_journal-756	90	1	the	the	DET
american_scientific_journal-756	90	2	intersection	intersection	NOUN
american_scientific_journal-756	90	3	of	of	ADP
american_scientific_journal-756	90	4	any	any	DET
american_scientific_journal-756	90	5	two	two	NUM
american_scientific_journal-756	90	6	soft	soft	ADJ
american_scientific_journal-756	90	7	sets	set	NOUN
american_scientific_journal-756	90	8	in	in	ADP
american_scientific_journal-756	90	9	𝜏	𝜏	PRON
american_scientific_journal-756	90	10	belongs	belong	VERB
american_scientific_journal-756	90	11	to	to	PART
american_scientific_journal-756	90	12	𝜏.	𝜏.	VERB
american_scientific_journal-756	90	13	the	the	DET
american_scientific_journal-756	90	14	triplet	triplet	NOUN
american_scientific_journal-756	90	15	(	(	PUNCT
american_scientific_journal-756	90	16	𝑈	𝑈	PROPN
american_scientific_journal-756	90	17	,	,	PUNCT
american_scientific_journal-756	90	18	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	90	19	)	)	PUNCT
american_scientific_journal-756	90	20	is	be	AUX
american_scientific_journal-756	90	21	called	call	VERB
american_scientific_journal-756	90	22	soft	soft	ADJ
american_scientific_journal-756	90	23	topological	topological	ADJ
american_scientific_journal-756	90	24	space	space	NOUN
american_scientific_journal-756	90	25	over	over	ADP
american_scientific_journal-756	90	26	𝑈.	𝑈.	PRON
american_scientific_journal-756	90	27	the	the	DET
american_scientific_journal-756	90	28	members	member	NOUN
american_scientific_journal-756	90	29	of	of	ADP
american_scientific_journal-756	90	30	𝜏	𝜏	PRON
american_scientific_journal-756	90	31	are	be	AUX
american_scientific_journal-756	90	32	called	call	VERB
american_scientific_journal-756	90	33	soft	soft	ADJ
american_scientific_journal-756	90	34	open	open	ADJ
american_scientific_journal-756	90	35	sets	set	NOUN
american_scientific_journal-756	90	36	in	in	ADP
american_scientific_journal-756	90	37	𝑈	𝑈	NOUN
american_scientific_journal-756	90	38	and	and	CCONJ
american_scientific_journal-756	90	39	complements	complement	NOUN
american_scientific_journal-756	90	40	of	of	ADP
american_scientific_journal-756	90	41	their	their	PRON
american_scientific_journal-756	90	42	are	be	AUX
american_scientific_journal-756	90	43	called	call	VERB
american_scientific_journal-756	90	44	soft	soft	ADJ
american_scientific_journal-756	90	45	closed	closed	ADJ
american_scientific_journal-756	90	46	sets	set	NOUN
american_scientific_journal-756	90	47	in	in	ADP
american_scientific_journal-756	90	48	𝑈.	𝑈.	ADJ
american_scientific_journal-756	90	49	definition	definition	NOUN
american_scientific_journal-756	90	50	2.16	2.16	NUM
american_scientific_journal-756	90	51	.	.	PUNCT
american_scientific_journal-756	91	1	[	[	X
american_scientific_journal-756	91	2	16	16	NUM
american_scientific_journal-756	91	3	]	]	X
american_scientific_journal-756	91	4	a	a	DET
american_scientific_journal-756	91	5	soft	soft	ADJ
american_scientific_journal-756	91	6	set	set	NOUN
american_scientific_journal-756	91	7	(	(	PUNCT
american_scientific_journal-756	91	8	𝑇,𝐸	𝑇,𝐸	NOUN
american_scientific_journal-756	91	9	)	)	PUNCT
american_scientific_journal-756	91	10	in	in	ADP
american_scientific_journal-756	91	11	a	a	DET
american_scientific_journal-756	91	12	soft	soft	ADJ
american_scientific_journal-756	91	13	topological	topological	ADJ
american_scientific_journal-756	91	14	space	space	NOUN
american_scientific_journal-756	91	15	(	(	PUNCT
american_scientific_journal-756	91	16	𝑈	𝑈	PROPN
american_scientific_journal-756	91	17	,	,	PUNCT
american_scientific_journal-756	91	18	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	91	19	)	)	PUNCT
american_scientific_journal-756	91	20	is	be	AUX
american_scientific_journal-756	91	21	called	call	VERB
american_scientific_journal-756	91	22	a	a	DET
american_scientific_journal-756	91	23	soft	soft	ADJ
american_scientific_journal-756	91	24	neighborhood	neighborhood	NOUN
american_scientific_journal-756	91	25	of	of	ADP
american_scientific_journal-756	91	26	the	the	DET
american_scientific_journal-756	91	27	soft	soft	ADJ
american_scientific_journal-756	91	28	point	point	NOUN
american_scientific_journal-756	91	29	𝑥𝐺	𝑥𝐺	NOUN
american_scientific_journal-756	91	30	∈	∈	PROPN
american_scientific_journal-756	91	31	�	�	PROPN
american_scientific_journal-756	91	32	𝑈	𝑈	PROPN
american_scientific_journal-756	91	33	�	�	PROPN
american_scientific_journal-756	91	34	if	if	SCONJ
american_scientific_journal-756	91	35	there	there	PRON
american_scientific_journal-756	91	36	exists	exist	VERB
american_scientific_journal-756	91	37	a	a	DET
american_scientific_journal-756	91	38	soft	soft	ADJ
american_scientific_journal-756	91	39	open	open	ADJ
american_scientific_journal-756	91	40	set	set	NOUN
american_scientific_journal-756	91	41	(	(	PUNCT
american_scientific_journal-756	91	42	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	91	43	)	)	PUNCT
american_scientific_journal-756	91	44	such	such	ADJ
american_scientific_journal-756	91	45	that	that	SCONJ
american_scientific_journal-756	91	46	𝑥𝐺	𝑥𝐺	PROPN
american_scientific_journal-756	91	47	∈	∈	PROPN
american_scientific_journal-756	91	48	�	�	PROPN
american_scientific_journal-756	91	49	(	(	PUNCT
american_scientific_journal-756	91	50	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	91	51	)	)	PUNCT
american_scientific_journal-756	91	52	⊆	⊆	NOUN
american_scientific_journal-756	91	53	�	�	PROPN
american_scientific_journal-756	91	54	(	(	PUNCT
american_scientific_journal-756	91	55	𝑇,𝐸	𝑇,𝐸	NOUN
american_scientific_journal-756	91	56	)	)	PUNCT
american_scientific_journal-756	91	57	.	.	PUNCT
american_scientific_journal-756	92	1	the	the	DET
american_scientific_journal-756	92	2	neighborhood	neighborhood	NOUN
american_scientific_journal-756	92	3	system	system	NOUN
american_scientific_journal-756	92	4	of	of	ADP
american_scientific_journal-756	92	5	a	a	DET
american_scientific_journal-756	92	6	soft	soft	ADJ
american_scientific_journal-756	92	7	point	point	NOUN
american_scientific_journal-756	92	8	𝑥𝐺	𝑥𝐺	NOUN
american_scientific_journal-756	92	9	,	,	PUNCT
american_scientific_journal-756	92	10	denoted	denote	VERB
american_scientific_journal-756	92	11	by	by	ADP
american_scientific_journal-756	92	12	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	92	13	)	)	PUNCT
american_scientific_journal-756	92	14	,	,	PUNCT
american_scientific_journal-756	92	15	is	be	AUX
american_scientific_journal-756	92	16	the	the	DET
american_scientific_journal-756	92	17	family	family	NOUN
american_scientific_journal-756	92	18	of	of	ADP
american_scientific_journal-756	92	19	all	all	DET
american_scientific_journal-756	92	20	its	its	PRON
american_scientific_journal-756	92	21	neigborhoods	neigborhood	NOUN
american_scientific_journal-756	92	22	.	.	PUNCT
american_scientific_journal-756	93	1	definition	definition	NOUN
american_scientific_journal-756	93	2	2.17	2.17	NUM
american_scientific_journal-756	93	3	.	.	PUNCT
american_scientific_journal-756	94	1	[	[	X
american_scientific_journal-756	94	2	16	16	NUM
american_scientific_journal-756	94	3	]	]	X
american_scientific_journal-756	94	4	a	a	DET
american_scientific_journal-756	94	5	soft	soft	ADJ
american_scientific_journal-756	94	6	set	set	NOUN
american_scientific_journal-756	94	7	(	(	PUNCT
american_scientific_journal-756	94	8	𝑇,𝐸	𝑇,𝐸	NOUN
american_scientific_journal-756	94	9	)	)	PUNCT
american_scientific_journal-756	94	10	in	in	ADP
american_scientific_journal-756	94	11	a	a	DET
american_scientific_journal-756	94	12	soft	soft	ADJ
american_scientific_journal-756	94	13	topological	topological	ADJ
american_scientific_journal-756	94	14	space	space	NOUN
american_scientific_journal-756	94	15	(	(	PUNCT
american_scientific_journal-756	94	16	𝑈	𝑈	PROPN
american_scientific_journal-756	94	17	,	,	PUNCT
american_scientific_journal-756	94	18	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	94	19	)	)	PUNCT
american_scientific_journal-756	94	20	is	be	AUX
american_scientific_journal-756	94	21	called	call	VERB
american_scientific_journal-756	94	22	a	a	DET
american_scientific_journal-756	94	23	soft	soft	ADJ
american_scientific_journal-756	94	24	neighborhood	neighborhood	NOUN
american_scientific_journal-756	94	25	of	of	ADP
american_scientific_journal-756	94	26	the	the	DET
american_scientific_journal-756	94	27	soft	soft	ADJ
american_scientific_journal-756	94	28	set	set	NOUN
american_scientific_journal-756	94	29	(	(	PUNCT
american_scientific_journal-756	94	30	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	94	31	)	)	PUNCT
american_scientific_journal-756	94	32	if	if	SCONJ
american_scientific_journal-756	94	33	there	there	PRON
american_scientific_journal-756	94	34	exists	exist	VERB
american_scientific_journal-756	94	35	a	a	DET
american_scientific_journal-756	94	36	soft	soft	ADJ
american_scientific_journal-756	94	37	open	open	ADJ
american_scientific_journal-756	94	38	set	set	NOUN
american_scientific_journal-756	94	39	(	(	PUNCT
american_scientific_journal-756	94	40	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	94	41	)	)	PUNCT
american_scientific_journal-756	94	42	such	such	ADJ
american_scientific_journal-756	94	43	that	that	SCONJ
american_scientific_journal-756	94	44	(	(	PUNCT
american_scientific_journal-756	94	45	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	94	46	)	)	PUNCT
american_scientific_journal-756	94	47	⊆	⊆	NUM
american_scientific_journal-756	94	48	�	�	PROPN
american_scientific_journal-756	94	49	(	(	PUNCT
american_scientific_journal-756	94	50	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	94	51	)	)	PUNCT
american_scientific_journal-756	94	52	⊆	⊆	NOUN
american_scientific_journal-756	94	53	�	�	PROPN
american_scientific_journal-756	94	54	(	(	PUNCT
american_scientific_journal-756	94	55	𝑇,𝐸	𝑇,𝐸	NOUN
american_scientific_journal-756	94	56	)	)	PUNCT
american_scientific_journal-756	94	57	.	.	PUNCT
american_scientific_journal-756	95	1	theorem	theorem	VERB
american_scientific_journal-756	95	2	2.18	2.18	NUM
american_scientific_journal-756	95	3	.	.	PUNCT
american_scientific_journal-756	96	1	[	[	X
american_scientific_journal-756	96	2	16	16	NUM
american_scientific_journal-756	96	3	]	]	PUNCT
american_scientific_journal-756	96	4	the	the	DET
american_scientific_journal-756	96	5	neighborhood	neighborhood	NOUN
american_scientific_journal-756	96	6	system	system	NOUN
american_scientific_journal-756	96	7	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	96	8	)	)	PUNCT
american_scientific_journal-756	96	9	at	at	ADP
american_scientific_journal-756	96	10	𝑥𝐺	𝑥𝐺	NOUN
american_scientific_journal-756	96	11	in	in	ADP
american_scientific_journal-756	96	12	a	a	DET
american_scientific_journal-756	96	13	soft	soft	ADJ
american_scientific_journal-756	96	14	topological	topological	ADJ
american_scientific_journal-756	96	15	space	space	NOUN
american_scientific_journal-756	96	16	(	(	PUNCT
american_scientific_journal-756	96	17	𝑈	𝑈	PROPN
american_scientific_journal-756	96	18	,	,	PUNCT
american_scientific_journal-756	96	19	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	96	20	)	)	PUNCT
american_scientific_journal-756	96	21	has	have	VERB
american_scientific_journal-756	96	22	the	the	DET
american_scientific_journal-756	96	23	following	follow	VERB
american_scientific_journal-756	96	24	properties	property	NOUN
american_scientific_journal-756	96	25	:	:	PUNCT
american_scientific_journal-756	96	26	(	(	PUNCT
american_scientific_journal-756	96	27	a	a	X
american_scientific_journal-756	96	28	)	)	PUNCT
american_scientific_journal-756	96	29	if	if	SCONJ
american_scientific_journal-756	96	30	(	(	PUNCT
american_scientific_journal-756	96	31	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	96	32	)	)	PUNCT
american_scientific_journal-756	96	33	∈	∈	PROPN
american_scientific_journal-756	96	34	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	96	35	)	)	PUNCT
american_scientific_journal-756	96	36	,	,	PUNCT
american_scientific_journal-756	96	37	then	then	ADV
american_scientific_journal-756	96	38	𝑥𝐺	𝑥𝐺	PROPN
american_scientific_journal-756	96	39	∈	∈	PROPN
american_scientific_journal-756	96	40	�	�	PROPN
american_scientific_journal-756	96	41	(	(	PUNCT
american_scientific_journal-756	96	42	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	96	43	)	)	PUNCT
american_scientific_journal-756	96	44	,	,	PUNCT
american_scientific_journal-756	96	45	(	(	PUNCT
american_scientific_journal-756	96	46	b	b	X
american_scientific_journal-756	96	47	)	)	PUNCT
american_scientific_journal-756	96	48	if	if	SCONJ
american_scientific_journal-756	96	49	(	(	PUNCT
american_scientific_journal-756	96	50	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	96	51	)	)	PUNCT
american_scientific_journal-756	96	52	∈	∈	PROPN
american_scientific_journal-756	96	53	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	96	54	)	)	PUNCT
american_scientific_journal-756	96	55	and	and	CCONJ
american_scientific_journal-756	96	56	(	(	PUNCT
american_scientific_journal-756	96	57	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	96	58	)	)	PUNCT
american_scientific_journal-756	96	59	⊆	⊆	NOUN
american_scientific_journal-756	96	60	�	�	PROPN
american_scientific_journal-756	96	61	(	(	PUNCT
american_scientific_journal-756	96	62	𝑀,𝐸	𝑀,𝐸	PROPN
american_scientific_journal-756	96	63	)	)	PUNCT
american_scientific_journal-756	96	64	,	,	PUNCT
american_scientific_journal-756	96	65	then	then	ADV
american_scientific_journal-756	96	66	(	(	PUNCT
american_scientific_journal-756	96	67	𝑀,𝐸	𝑀,𝐸	VERB
american_scientific_journal-756	96	68	)	)	PUNCT
american_scientific_journal-756	96	69	∈	∈	PROPN
american_scientific_journal-756	96	70	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	96	71	)	)	PUNCT
american_scientific_journal-756	96	72	,	,	PUNCT
american_scientific_journal-756	96	73	(	(	PUNCT
american_scientific_journal-756	96	74	c	c	X
american_scientific_journal-756	96	75	)	)	PUNCT
american_scientific_journal-756	96	76	if	if	SCONJ
american_scientific_journal-756	96	77	(	(	PUNCT
american_scientific_journal-756	96	78	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	96	79	)	)	PUNCT
american_scientific_journal-756	96	80	,	,	PUNCT
american_scientific_journal-756	96	81	(	(	PUNCT
american_scientific_journal-756	96	82	𝑀,𝐸	𝑀,𝐸	VERB
american_scientific_journal-756	96	83	)	)	PUNCT
american_scientific_journal-756	96	84	∈	∈	PROPN
american_scientific_journal-756	96	85	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	96	86	)	)	PUNCT
american_scientific_journal-756	96	87	,	,	PUNCT
american_scientific_journal-756	96	88	then	then	ADV
american_scientific_journal-756	96	89	(	(	PUNCT
american_scientific_journal-756	96	90	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	96	91	)	)	PUNCT
american_scientific_journal-756	96	92	∩	∩	ADJ
american_scientific_journal-756	96	93	�	�	PROPN
american_scientific_journal-756	96	94	(	(	PUNCT
american_scientific_journal-756	96	95	𝑀,𝐸	𝑀,𝐸	VERB
american_scientific_journal-756	96	96	)	)	PUNCT
american_scientific_journal-756	96	97	∈	∈	PROPN
american_scientific_journal-756	96	98	𝑁𝜏(𝑥𝐺	𝑁𝜏(𝑥𝐺	NOUN
american_scientific_journal-756	96	99	)	)	PUNCT
american_scientific_journal-756	96	100	,	,	PUNCT
american_scientific_journal-756	96	101	definition	definition	NOUN
american_scientific_journal-756	96	102	2.19	2.19	NUM
american_scientific_journal-756	96	103	.	.	PUNCT
american_scientific_journal-756	97	1	let	let	AUX
american_scientific_journal-756	97	2	(	(	PUNCT
american_scientific_journal-756	97	3	𝑈	𝑈	NOUN
american_scientific_journal-756	97	4	,	,	PUNCT
american_scientific_journal-756	97	5	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	97	6	)	)	PUNCT
american_scientific_journal-756	97	7	be	be	VERB
american_scientific_journal-756	97	8	a	a	DET
american_scientific_journal-756	97	9	soft	soft	ADJ
american_scientific_journal-756	97	10	topological	topological	ADJ
american_scientific_journal-756	97	11	space	space	NOUN
american_scientific_journal-756	97	12	and	and	CCONJ
american_scientific_journal-756	97	13	let	let	AUX
american_scientific_journal-756	97	14	(	(	PUNCT
american_scientific_journal-756	97	15	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	97	16	)	)	PUNCT
american_scientific_journal-756	97	17	be	be	AUX
american_scientific_journal-756	97	18	a	a	DET
american_scientific_journal-756	97	19	soft	soft	ADJ
american_scientific_journal-756	97	20	set	set	NOUN
american_scientific_journal-756	97	21	over	over	ADP
american_scientific_journal-756	97	22	𝑈.	𝑈.	PROPN
american_scientific_journal-756	97	23	(	(	PUNCT
american_scientific_journal-756	97	24	a	a	NOUN
american_scientific_journal-756	97	25	)	)	PUNCT
american_scientific_journal-756	98	1	[	[	X
american_scientific_journal-756	98	2	15	15	NUM
american_scientific_journal-756	98	3	]	]	X
american_scientific_journal-756	98	4	the	the	DET
american_scientific_journal-756	98	5	soft	soft	ADJ
american_scientific_journal-756	98	6	closure	closure	NOUN
american_scientific_journal-756	98	7	of	of	ADP
american_scientific_journal-756	98	8	soft	soft	ADJ
american_scientific_journal-756	98	9	set	set	NOUN
american_scientific_journal-756	98	10	(	(	PUNCT
american_scientific_journal-756	98	11	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	98	12	)	)	PUNCT
american_scientific_journal-756	98	13	in	in	ADP
american_scientific_journal-756	98	14	(	(	PUNCT
american_scientific_journal-756	98	15	𝑈	𝑈	PROPN
american_scientific_journal-756	98	16	,	,	PUNCT
american_scientific_journal-756	98	17	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	98	18	)	)	PUNCT
american_scientific_journal-756	98	19	is	be	AUX
american_scientific_journal-756	98	20	the	the	DET
american_scientific_journal-756	98	21	soft	soft	ADJ
american_scientific_journal-756	98	22	set	set	NOUN
american_scientific_journal-756	98	23	𝑐𝑙(𝐺,𝐸	𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	98	24	)	)	PUNCT
american_scientific_journal-756	98	25	=	=	NOUN
american_scientific_journal-756	98	26	∩	∩	NOUN
american_scientific_journal-756	98	27	�	�	PROPN
american_scientific_journal-756	98	28	{	{	PUNCT
american_scientific_journal-756	98	29	(	(	PUNCT
american_scientific_journal-756	98	30	𝑆,𝐸	𝑆,𝐸	PROPN
american_scientific_journal-756	98	31	):	):	PUNCT
american_scientific_journal-756	98	32	(	(	PUNCT
american_scientific_journal-756	98	33	𝑆,𝐸	𝑆,𝐸	NOUN
american_scientific_journal-756	98	34	)	)	PUNCT
american_scientific_journal-756	98	35	𝑖𝑠	𝑖𝑠	NOUN
american_scientific_journal-756	98	36	𝑠𝑜𝑓𝑡	𝑠𝑜𝑓𝑡	NOUN
american_scientific_journal-756	98	37	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	VERB
american_scientific_journal-756	98	38	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
american_scientific_journal-756	98	39	(	(	PUNCT
american_scientific_journal-756	98	40	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	98	41	)	)	PUNCT
american_scientific_journal-756	99	1	⊆	⊆	NUM
american_scientific_journal-756	99	2	�	�	PROPN
american_scientific_journal-756	99	3	(	(	PUNCT
american_scientific_journal-756	99	4	𝑆,𝐸	𝑆,𝐸	NOUN
american_scientific_journal-756	99	5	)	)	PUNCT
american_scientific_journal-756	99	6	}	}	PUNCT
american_scientific_journal-756	99	7	.	.	PUNCT
american_scientific_journal-756	100	1	(	(	PUNCT
american_scientific_journal-756	100	2	b	b	X
american_scientific_journal-756	100	3	)	)	PUNCT
american_scientific_journal-756	101	1	[	[	X
american_scientific_journal-756	101	2	16	16	NUM
american_scientific_journal-756	101	3	]	]	PUNCT
american_scientific_journal-756	101	4	the	the	DET
american_scientific_journal-756	101	5	soft	soft	ADJ
american_scientific_journal-756	101	6	interior	interior	NOUN
american_scientific_journal-756	101	7	of	of	ADP
american_scientific_journal-756	101	8	soft	soft	ADJ
american_scientific_journal-756	101	9	set	set	NOUN
american_scientific_journal-756	101	10	(	(	PUNCT
american_scientific_journal-756	101	11	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	101	12	)	)	PUNCT
american_scientific_journal-756	101	13	in	in	ADP
american_scientific_journal-756	101	14	(	(	PUNCT
american_scientific_journal-756	101	15	𝑈	𝑈	PROPN
american_scientific_journal-756	101	16	,	,	PUNCT
american_scientific_journal-756	101	17	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	101	18	)	)	PUNCT
american_scientific_journal-756	101	19	is	be	AUX
american_scientific_journal-756	101	20	the	the	DET
american_scientific_journal-756	101	21	soft	soft	ADJ
american_scientific_journal-756	101	22	set	set	NOUN
american_scientific_journal-756	101	23	𝑖𝑛𝑡(𝐺,𝐸	𝑖𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	101	24	)	)	PUNCT
american_scientific_journal-756	101	25	=	=	SYM
american_scientific_journal-756	101	26	∪	∪	X
american_scientific_journal-756	101	27	�	�	PROPN
american_scientific_journal-756	101	28	{	{	PUNCT
american_scientific_journal-756	101	29	(	(	PUNCT
american_scientific_journal-756	101	30	𝑆,𝐸	𝑆,𝐸	PROPN
american_scientific_journal-756	101	31	):	):	PUNCT
american_scientific_journal-756	101	32	(	(	PUNCT
american_scientific_journal-756	101	33	𝑆,𝐸	𝑆,𝐸	NOUN
american_scientific_journal-756	101	34	)	)	PUNCT
american_scientific_journal-756	101	35	𝑖𝑠	𝑖𝑠	NOUN
american_scientific_journal-756	101	36	𝑠𝑜𝑓𝑡	𝑠𝑜𝑓𝑡	ADJ
american_scientific_journal-756	101	37	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
american_scientific_journal-756	101	38	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
american_scientific_journal-756	101	39	(	(	PUNCT
american_scientific_journal-756	101	40	𝑆,𝐸	𝑆,𝐸	PROPN
american_scientific_journal-756	101	41	)	)	PUNCT
american_scientific_journal-756	101	42	⊆	⊆	NUM
american_scientific_journal-756	101	43	�	�	PROPN
american_scientific_journal-756	101	44	(	(	PUNCT
american_scientific_journal-756	101	45	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	101	46	)	)	PUNCT
american_scientific_journal-756	101	47	}	}	PUNCT
american_scientific_journal-756	101	48	.	.	PUNCT
american_scientific_journal-756	102	1	𝑐𝑙(𝐺,𝐸	𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	102	2	)	)	PUNCT
american_scientific_journal-756	102	3	is	be	AUX
american_scientific_journal-756	102	4	soft	soft	ADJ
american_scientific_journal-756	102	5	closed	closed	ADJ
american_scientific_journal-756	102	6	and	and	CCONJ
american_scientific_journal-756	102	7	the	the	DET
american_scientific_journal-756	102	8	smallest	small	ADJ
american_scientific_journal-756	102	9	soft	soft	ADJ
american_scientific_journal-756	102	10	closed	closed	ADJ
american_scientific_journal-756	102	11	set	set	NOUN
american_scientific_journal-756	102	12	containing	contain	VERB
american_scientific_journal-756	102	13	(	(	PUNCT
american_scientific_journal-756	102	14	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	102	15	)	)	PUNCT
american_scientific_journal-756	102	16	,	,	PUNCT
american_scientific_journal-756	102	17	in	in	ADP
american_scientific_journal-756	102	18	the	the	DET
american_scientific_journal-756	102	19	sense	sense	NOUN
american_scientific_journal-756	102	20	that	that	SCONJ
american_scientific_journal-756	102	21	it	it	PRON
american_scientific_journal-756	102	22	is	be	AUX
american_scientific_journal-756	102	23	contained	contain	VERB
american_scientific_journal-756	102	24	in	in	ADP
american_scientific_journal-756	102	25	every	every	DET
american_scientific_journal-756	102	26	soft	soft	ADJ
american_scientific_journal-756	102	27	closed	closed	ADJ
american_scientific_journal-756	102	28	set	set	NOUN
american_scientific_journal-756	102	29	containing	contain	VERB
american_scientific_journal-756	102	30	(	(	PUNCT
american_scientific_journal-756	102	31	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	102	32	)	)	PUNCT
american_scientific_journal-756	102	33	.	.	PUNCT
american_scientific_journal-756	103	1	similarly	similarly	ADV
american_scientific_journal-756	103	2	,	,	PUNCT
american_scientific_journal-756	103	3	by	by	ADP
american_scientific_journal-756	103	4	property	property	NOUN
american_scientific_journal-756	103	5	t3	t3	NOUN
american_scientific_journal-756	103	6	for	for	ADP
american_scientific_journal-756	103	7	soft	soft	ADJ
american_scientific_journal-756	103	8	open	open	ADJ
american_scientific_journal-756	103	9	sets	set	NOUN
american_scientific_journal-756	103	10	,	,	PUNCT
american_scientific_journal-756	103	11	𝑖𝑛𝑡(𝐺,𝐸	𝑖𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	103	12	)	)	PUNCT
american_scientific_journal-756	103	13	is	be	AUX
american_scientific_journal-756	103	14	soft	soft	ADJ
american_scientific_journal-756	103	15	open	open	ADJ
american_scientific_journal-756	103	16	and	and	CCONJ
american_scientific_journal-756	103	17	the	the	DET
american_scientific_journal-756	103	18	largest	large	ADJ
american_scientific_journal-756	103	19	soft	soft	ADJ
american_scientific_journal-756	103	20	open	open	ADJ
american_scientific_journal-756	103	21	set	set	NOUN
american_scientific_journal-756	103	22	contained	contain	VERB
american_scientific_journal-756	103	23	in	in	ADP
american_scientific_journal-756	103	24	(	(	PUNCT
american_scientific_journal-756	103	25	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	103	26	)	)	PUNCT
american_scientific_journal-756	103	27	.	.	PUNCT
american_scientific_journal-756	104	1	corollary	corollary	ADJ
american_scientific_journal-756	104	2	2.20	2.20	NUM
american_scientific_journal-756	104	3	.	.	PUNCT
american_scientific_journal-756	105	1	let	let	AUX
american_scientific_journal-756	105	2	(	(	PUNCT
american_scientific_journal-756	105	3	𝑈	𝑈	NOUN
american_scientific_journal-756	105	4	,	,	PUNCT
american_scientific_journal-756	105	5	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	105	6	)	)	PUNCT
american_scientific_journal-756	105	7	be	be	VERB
american_scientific_journal-756	105	8	a	a	DET
american_scientific_journal-756	105	9	soft	soft	ADJ
american_scientific_journal-756	105	10	topological	topological	ADJ
american_scientific_journal-756	105	11	space	space	NOUN
american_scientific_journal-756	105	12	and	and	CCONJ
american_scientific_journal-756	105	13	let	let	AUX
american_scientific_journal-756	105	14	(	(	PUNCT
american_scientific_journal-756	105	15	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	105	16	)	)	PUNCT
american_scientific_journal-756	105	17	be	be	AUX
american_scientific_journal-756	105	18	a	a	DET
american_scientific_journal-756	105	19	soft	soft	ADJ
american_scientific_journal-756	105	20	set	set	NOUN
american_scientific_journal-756	105	21	over	over	ADP
american_scientific_journal-756	105	22	𝑈.	𝑈.	PROPN
american_scientific_journal-756	105	23	then	then	ADV
american_scientific_journal-756	105	24	(	(	PUNCT
american_scientific_journal-756	105	25	a	a	X
american_scientific_journal-756	105	26	)	)	PUNCT
american_scientific_journal-756	106	1	[	[	X
american_scientific_journal-756	106	2	15	15	NUM
american_scientific_journal-756	106	3	]	]	X
american_scientific_journal-756	106	4	(	(	PUNCT
american_scientific_journal-756	106	5	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	106	6	)	)	PUNCT
american_scientific_journal-756	106	7	is	be	AUX
american_scientific_journal-756	106	8	soft	soft	ADJ
american_scientific_journal-756	106	9	closed	closed	ADJ
american_scientific_journal-756	106	10	iff	iff	PROPN
american_scientific_journal-756	106	11	(	(	PUNCT
american_scientific_journal-756	106	12	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	106	13	)	)	PUNCT
american_scientific_journal-756	106	14	=	=	SYM
american_scientific_journal-756	106	15	𝑐𝑙(𝐺,𝐸	𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	106	16	)	)	PUNCT
american_scientific_journal-756	106	17	.	.	PUNCT
american_scientific_journal-756	107	1	99	99	NUM
american_scientific_journal-756	107	2	american	american	ADJ
american_scientific_journal-756	107	3	scientific	scientific	ADJ
american_scientific_journal-756	107	4	research	research	NOUN
american_scientific_journal-756	107	5	journal	journal	NOUN
american_scientific_journal-756	107	6	for	for	ADP
american_scientific_journal-756	107	7	engineering	engineering	NOUN
american_scientific_journal-756	107	8	,	,	PUNCT
american_scientific_journal-756	107	9	technology	technology	NOUN
american_scientific_journal-756	107	10	,	,	PUNCT
american_scientific_journal-756	107	11	and	and	CCONJ
american_scientific_journal-756	107	12	sciences	science	NOUN
american_scientific_journal-756	107	13	(	(	PUNCT
american_scientific_journal-756	107	14	asrjets	asrjet	NOUN
american_scientific_journal-756	107	15	)	)	PUNCT
american_scientific_journal-756	107	16	(	(	PUNCT
american_scientific_journal-756	107	17	2014	2014	NUM
american_scientific_journal-756	107	18	)	)	PUNCT
american_scientific_journal-756	107	19	volume	volume	NOUN
american_scientific_journal-756	107	20	8	8	NUM
american_scientific_journal-756	107	21	,	,	PUNCT
american_scientific_journal-756	107	22	no	no	DET
american_scientific_journal-756	107	23	1	1	NUM
american_scientific_journal-756	107	24	,	,	PUNCT
american_scientific_journal-756	107	25	pp	pp	ADV
american_scientific_journal-756	107	26	96	96	NUM
american_scientific_journal-756	107	27	-	-	SYM
american_scientific_journal-756	107	28	107	107	NUM
american_scientific_journal-756	107	29	(	(	PUNCT
american_scientific_journal-756	107	30	b	b	NOUN
american_scientific_journal-756	107	31	)	)	PUNCT
american_scientific_journal-756	108	1	[	[	X
american_scientific_journal-756	108	2	16	16	NUM
american_scientific_journal-756	108	3	]	]	PUNCT
american_scientific_journal-756	108	4	(	(	PUNCT
american_scientific_journal-756	108	5	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	108	6	)	)	PUNCT
american_scientific_journal-756	108	7	is	be	AUX
american_scientific_journal-756	108	8	soft	soft	ADJ
american_scientific_journal-756	108	9	open	open	ADJ
american_scientific_journal-756	108	10	iff	iff	PROPN
american_scientific_journal-756	108	11	(	(	PUNCT
american_scientific_journal-756	108	12	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	108	13	)	)	PUNCT
american_scientific_journal-756	108	14	=	=	SYM
american_scientific_journal-756	108	15	𝑖𝑛𝑡(𝐺,𝐸	𝑖𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	108	16	)	)	PUNCT
american_scientific_journal-756	108	17	.	.	PUNCT
american_scientific_journal-756	109	1	theorem	theorem	VERB
american_scientific_journal-756	109	2	2.21	2.21	NUM
american_scientific_journal-756	109	3	.	.	PUNCT
american_scientific_journal-756	110	1	[	[	X
american_scientific_journal-756	110	2	16	16	NUM
american_scientific_journal-756	110	3	]	]	X
american_scientific_journal-756	110	4	a	a	DET
american_scientific_journal-756	110	5	soft	soft	ADJ
american_scientific_journal-756	110	6	set	set	NOUN
american_scientific_journal-756	110	7	(	(	PUNCT
american_scientific_journal-756	110	8	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	110	9	)	)	PUNCT
american_scientific_journal-756	110	10	is	be	AUX
american_scientific_journal-756	110	11	soft	soft	ADJ
american_scientific_journal-756	110	12	open	open	ADJ
american_scientific_journal-756	110	13	if	if	SCONJ
american_scientific_journal-756	110	14	and	and	CCONJ
american_scientific_journal-756	110	15	only	only	ADV
american_scientific_journal-756	110	16	if	if	SCONJ
american_scientific_journal-756	110	17	for	for	ADP
american_scientific_journal-756	110	18	each	each	DET
american_scientific_journal-756	110	19	soft	soft	ADJ
american_scientific_journal-756	110	20	set	set	NOUN
american_scientific_journal-756	110	21	(	(	PUNCT
american_scientific_journal-756	110	22	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	110	23	)	)	PUNCT
american_scientific_journal-756	110	24	contained	contain	VERB
american_scientific_journal-756	110	25	in	in	ADP
american_scientific_journal-756	110	26	(	(	PUNCT
american_scientific_journal-756	110	27	g	g	NOUN
american_scientific_journal-756	110	28	,	,	PUNCT
american_scientific_journal-756	110	29	e	e	NOUN
american_scientific_journal-756	110	30	)	)	PUNCT
american_scientific_journal-756	110	31	,	,	PUNCT
american_scientific_journal-756	110	32	(	(	PUNCT
american_scientific_journal-756	110	33	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	110	34	)	)	PUNCT
american_scientific_journal-756	110	35	is	be	AUX
american_scientific_journal-756	110	36	a	a	DET
american_scientific_journal-756	110	37	soft	soft	ADJ
american_scientific_journal-756	110	38	neighborhood	neighborhood	NOUN
american_scientific_journal-756	110	39	of	of	ADP
american_scientific_journal-756	110	40	(	(	PUNCT
american_scientific_journal-756	110	41	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	110	42	)	)	PUNCT
american_scientific_journal-756	110	43	.	.	PUNCT
american_scientific_journal-756	111	1	proposition	proposition	NOUN
american_scientific_journal-756	111	2	2.22	2.22	NUM
american_scientific_journal-756	111	3	.	.	PUNCT
american_scientific_journal-756	112	1	let	let	AUX
american_scientific_journal-756	112	2	(	(	PUNCT
american_scientific_journal-756	112	3	𝑈	𝑈	NOUN
american_scientific_journal-756	112	4	,	,	PUNCT
american_scientific_journal-756	112	5	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	112	6	)	)	PUNCT
american_scientific_journal-756	112	7	be	be	VERB
american_scientific_journal-756	112	8	a	a	DET
american_scientific_journal-756	112	9	soft	soft	ADJ
american_scientific_journal-756	112	10	topological	topological	ADJ
american_scientific_journal-756	112	11	space	space	NOUN
american_scientific_journal-756	112	12	and	and	CCONJ
american_scientific_journal-756	112	13	let	let	VERB
american_scientific_journal-756	112	14	(	(	PUNCT
american_scientific_journal-756	112	15	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	112	16	)	)	PUNCT
american_scientific_journal-756	112	17	and	and	CCONJ
american_scientific_journal-756	112	18	(	(	PUNCT
american_scientific_journal-756	112	19	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	112	20	)	)	PUNCT
american_scientific_journal-756	112	21	be	be	AUX
american_scientific_journal-756	112	22	soft	soft	ADJ
american_scientific_journal-756	112	23	sets	set	NOUN
american_scientific_journal-756	112	24	over	over	ADP
american_scientific_journal-756	112	25	𝑈.	𝑈.	PROPN
american_scientific_journal-756	112	26	(	(	PUNCT
american_scientific_journal-756	112	27	a	a	NOUN
american_scientific_journal-756	112	28	)	)	PUNCT
american_scientific_journal-756	113	1	[	[	X
american_scientific_journal-756	113	2	15	15	NUM
american_scientific_journal-756	113	3	]	]	X
american_scientific_journal-756	113	4	if	if	SCONJ
american_scientific_journal-756	113	5	(	(	PUNCT
american_scientific_journal-756	113	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	113	7	)	)	PUNCT
american_scientific_journal-756	113	8	⊆	⊆	NUM
american_scientific_journal-756	113	9	�	�	PROPN
american_scientific_journal-756	113	10	(	(	PUNCT
american_scientific_journal-756	113	11	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	113	12	)	)	PUNCT
american_scientific_journal-756	113	13	,	,	PUNCT
american_scientific_journal-756	113	14	then	then	ADV
american_scientific_journal-756	113	15	𝑐𝑙(𝐺,𝐸	𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	113	16	)	)	PUNCT
american_scientific_journal-756	113	17	⊆	⊆	NUM
american_scientific_journal-756	113	18	�	�	PROPN
american_scientific_journal-756	113	19	𝑐𝑙(𝐻,𝐸	𝑐𝑙(𝐻,𝐸	NOUN
american_scientific_journal-756	113	20	)	)	PUNCT
american_scientific_journal-756	113	21	.	.	PUNCT
american_scientific_journal-756	114	1	(	(	PUNCT
american_scientific_journal-756	114	2	b	b	X
american_scientific_journal-756	114	3	)	)	PUNCT
american_scientific_journal-756	115	1	[	[	X
american_scientific_journal-756	115	2	16	16	NUM
american_scientific_journal-756	115	3	]	]	X
american_scientific_journal-756	115	4	if	if	SCONJ
american_scientific_journal-756	115	5	(	(	PUNCT
american_scientific_journal-756	115	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	115	7	)	)	PUNCT
american_scientific_journal-756	115	8	⊆	⊆	NUM
american_scientific_journal-756	115	9	�	�	PROPN
american_scientific_journal-756	115	10	(	(	PUNCT
american_scientific_journal-756	115	11	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	115	12	)	)	PUNCT
american_scientific_journal-756	115	13	,	,	PUNCT
american_scientific_journal-756	115	14	then	then	ADV
american_scientific_journal-756	115	15	𝑖𝑛𝑡(𝐺,𝐸	𝑖𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	115	16	)	)	PUNCT
american_scientific_journal-756	115	17	⊆	⊆	NUM
american_scientific_journal-756	115	18	�	�	PROPN
american_scientific_journal-756	115	19	𝑖𝑛𝑡(𝐻,𝐸	𝑖𝑛𝑡(𝐻,𝐸	NUM
american_scientific_journal-756	115	20	)	)	PUNCT
american_scientific_journal-756	115	21	.	.	PUNCT
american_scientific_journal-756	116	1	theorem	theorem	VERB
american_scientific_journal-756	116	2	2.23	2.23	NUM
american_scientific_journal-756	116	3	.	.	PUNCT
american_scientific_journal-756	117	1	[	[	X
american_scientific_journal-756	117	2	16	16	NUM
american_scientific_journal-756	117	3	]	]	X
american_scientific_journal-756	117	4	let	let	VERB
american_scientific_journal-756	117	5	(	(	PUNCT
american_scientific_journal-756	117	6	𝑈	𝑈	NOUN
american_scientific_journal-756	117	7	,	,	PUNCT
american_scientific_journal-756	117	8	𝜏,𝐸	𝜏,𝐸	NOUN
american_scientific_journal-756	117	9	)	)	PUNCT
american_scientific_journal-756	117	10	be	be	VERB
american_scientific_journal-756	117	11	a	a	DET
american_scientific_journal-756	117	12	soft	soft	ADJ
american_scientific_journal-756	117	13	topological	topological	ADJ
american_scientific_journal-756	117	14	space	space	NOUN
american_scientific_journal-756	117	15	and	and	CCONJ
american_scientific_journal-756	117	16	let	let	AUX
american_scientific_journal-756	117	17	(	(	PUNCT
american_scientific_journal-756	117	18	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	117	19	)	)	PUNCT
american_scientific_journal-756	117	20	be	be	AUX
american_scientific_journal-756	117	21	a	a	DET
american_scientific_journal-756	117	22	soft	soft	ADJ
american_scientific_journal-756	117	23	set	set	NOUN
american_scientific_journal-756	117	24	over	over	ADP
american_scientific_journal-756	117	25	𝑈.	𝑈.	PROPN
american_scientific_journal-756	117	26	(	(	PUNCT
american_scientific_journal-756	117	27	a	a	NOUN
american_scientific_journal-756	117	28	)	)	PUNCT
american_scientific_journal-756	117	29	(	(	PUNCT
american_scientific_journal-756	117	30	𝑐𝑙(𝐺,𝐸))𝑐	𝑐𝑙(𝐺,𝐸))𝑐	NOUN
american_scientific_journal-756	117	31	=	=	SYM
american_scientific_journal-756	117	32	𝑖𝑛𝑡((𝐺,𝐸)𝑐	𝑖𝑛𝑡((𝐺,𝐸)𝑐	NUM
american_scientific_journal-756	117	33	)	)	PUNCT
american_scientific_journal-756	117	34	.	.	PUNCT
american_scientific_journal-756	118	1	(	(	PUNCT
american_scientific_journal-756	118	2	b	b	X
american_scientific_journal-756	118	3	)	)	PUNCT
american_scientific_journal-756	118	4	(	(	PUNCT
american_scientific_journal-756	118	5	𝑖𝑛𝑡(𝐺,𝐸))𝑐	𝑖𝑛𝑡(𝐺,𝐸))𝑐	X
american_scientific_journal-756	118	6	=	=	SYM
american_scientific_journal-756	118	7	𝑐𝑙((𝐺,𝐸)𝑐	𝑐𝑙((𝐺,𝐸)𝑐	NUM
american_scientific_journal-756	118	8	)	)	PUNCT
american_scientific_journal-756	118	9	.	.	PUNCT
american_scientific_journal-756	119	1	3	3	X
american_scientific_journal-756	119	2	.	.	X
american_scientific_journal-756	119	3	𝜶-continuity	𝜶-continuity	NOUN
american_scientific_journal-756	119	4	of	of	ADP
american_scientific_journal-756	119	5	soft	soft	ADJ
american_scientific_journal-756	119	6	multifunction	multifunction	NOUN
american_scientific_journal-756	119	7	let	let	VERB
american_scientific_journal-756	119	8	𝒀	𝒀	PRON
american_scientific_journal-756	119	9	be	be	AUX
american_scientific_journal-756	119	10	an	an	DET
american_scientific_journal-756	119	11	initial	initial	ADJ
american_scientific_journal-756	119	12	universe	universe	NOUN
american_scientific_journal-756	119	13	set	set	VERB
american_scientific_journal-756	119	14	and	and	CCONJ
american_scientific_journal-756	119	15	𝑬	𝑬	PRON
american_scientific_journal-756	119	16	be	be	VERB
american_scientific_journal-756	119	17	the	the	DET
american_scientific_journal-756	119	18	non	non	ADJ
american_scientific_journal-756	119	19	-	-	ADJ
american_scientific_journal-756	119	20	empty	empty	ADJ
american_scientific_journal-756	119	21	set	set	NOUN
american_scientific_journal-756	119	22	of	of	ADP
american_scientific_journal-756	119	23	parameters	parameter	NOUN
american_scientific_journal-756	119	24	.	.	PUNCT
american_scientific_journal-756	120	1	definition	definition	NOUN
american_scientific_journal-756	120	2	3.1	3.1	NUM
american_scientific_journal-756	120	3	.	.	PUNCT
american_scientific_journal-756	121	1	[	[	X
american_scientific_journal-756	121	2	20	20	NUM
american_scientific_journal-756	121	3	]	]	PUNCT
american_scientific_journal-756	121	4	a	a	DET
american_scientific_journal-756	121	5	soft	soft	ADJ
american_scientific_journal-756	121	6	multifunction	multifunction	NOUN
american_scientific_journal-756	121	7	𝑭	𝑭	NOUN
american_scientific_journal-756	121	8	from	from	ADP
american_scientific_journal-756	121	9	an	an	DET
american_scientific_journal-756	121	10	ordinary	ordinary	ADJ
american_scientific_journal-756	121	11	topological	topological	ADJ
american_scientific_journal-756	121	12	space	space	NOUN
american_scientific_journal-756	121	13	(	(	PUNCT
american_scientific_journal-756	121	14	𝑿	𝑿	PROPN
american_scientific_journal-756	121	15	,	,	PUNCT
american_scientific_journal-756	121	16	𝝉	𝝉	NOUN
american_scientific_journal-756	121	17	)	)	PUNCT
american_scientific_journal-756	121	18	into	into	ADP
american_scientific_journal-756	121	19	a	a	DET
american_scientific_journal-756	121	20	soft	soft	ADJ
american_scientific_journal-756	121	21	topological	topological	ADJ
american_scientific_journal-756	121	22	space	space	NOUN
american_scientific_journal-756	121	23	(	(	PUNCT
american_scientific_journal-756	121	24	𝒀,𝝈,𝑬	𝒀,𝝈,𝑬	NOUN
american_scientific_journal-756	121	25	)	)	PUNCT
american_scientific_journal-756	121	26	assings	assing	NOUN
american_scientific_journal-756	121	27	to	to	ADP
american_scientific_journal-756	121	28	each	each	DET
american_scientific_journal-756	121	29	𝒙	𝒙	PROPN
american_scientific_journal-756	121	30	in	in	ADP
american_scientific_journal-756	121	31	𝑿	𝑿	PROPN
american_scientific_journal-756	121	32	a	a	DET
american_scientific_journal-756	121	33	soft	soft	ADJ
american_scientific_journal-756	121	34	set	set	NOUN
american_scientific_journal-756	121	35	𝑭(𝒙	𝑭(𝒙	NOUN
american_scientific_journal-756	121	36	)	)	PUNCT
american_scientific_journal-756	121	37	over	over	ADP
american_scientific_journal-756	121	38	𝒀.	𝒀.	NOUN
american_scientific_journal-756	121	39	a	a	DET
american_scientific_journal-756	121	40	soft	soft	ADJ
american_scientific_journal-756	121	41	multifunction	multifunction	NOUN
american_scientific_journal-756	121	42	will	will	AUX
american_scientific_journal-756	121	43	be	be	AUX
american_scientific_journal-756	121	44	denoted	denote	VERB
american_scientific_journal-756	121	45	by	by	ADP
american_scientific_journal-756	121	46	𝑭	𝑭	NOUN
american_scientific_journal-756	121	47	:	:	PUNCT
american_scientific_journal-756	121	48	(	(	PUNCT
american_scientific_journal-756	121	49	𝑿	𝑿	PROPN
american_scientific_journal-756	121	50	,	,	PUNCT
american_scientific_journal-756	121	51	𝝉	𝝉	NOUN
american_scientific_journal-756	121	52	)	)	PUNCT
american_scientific_journal-756	121	53	→	→	SYM
american_scientific_journal-756	121	54	(	(	PUNCT
american_scientific_journal-756	121	55	𝒀,𝝈,𝑬	𝒀,𝝈,𝑬	PROPN
american_scientific_journal-756	121	56	)	)	PUNCT
american_scientific_journal-756	121	57	.	.	PUNCT
american_scientific_journal-756	122	1	𝑭	𝑭	PROPN
american_scientific_journal-756	122	2	is	be	AUX
american_scientific_journal-756	122	3	said	say	VERB
american_scientific_journal-756	122	4	to	to	PART
american_scientific_journal-756	122	5	be	be	AUX
american_scientific_journal-756	122	6	onto	onto	ADP
american_scientific_journal-756	122	7	if	if	SCONJ
american_scientific_journal-756	122	8	for	for	ADP
american_scientific_journal-756	122	9	each	each	DET
american_scientific_journal-756	122	10	soft	soft	ADJ
american_scientific_journal-756	122	11	set	set	NOUN
american_scientific_journal-756	122	12	(	(	PUNCT
american_scientific_journal-756	122	13	𝑮,𝑬	𝑮,𝑬	ADV
american_scientific_journal-756	122	14	)	)	PUNCT
american_scientific_journal-756	122	15	over	over	ADP
american_scientific_journal-756	122	16	𝒀	𝒀	NOUN
american_scientific_journal-756	122	17	,	,	PUNCT
american_scientific_journal-756	122	18	there	there	PRON
american_scientific_journal-756	122	19	exists	exist	VERB
american_scientific_journal-756	122	20	a	a	DET
american_scientific_journal-756	122	21	point	point	NOUN
american_scientific_journal-756	122	22	𝒙	𝒙	PROPN
american_scientific_journal-756	122	23	∈	∈	NOUN
american_scientific_journal-756	122	24	𝑿	𝑿	NOUN
american_scientific_journal-756	122	25	such	such	ADJ
american_scientific_journal-756	122	26	that	that	SCONJ
american_scientific_journal-756	122	27	𝑭(𝒙	𝑭(𝒙	VERB
american_scientific_journal-756	122	28	)	)	PUNCT
american_scientific_journal-756	122	29	=	=	SYM
american_scientific_journal-756	122	30	(	(	PUNCT
american_scientific_journal-756	122	31	𝑮,𝑬	𝑮,𝑬	ADV
american_scientific_journal-756	122	32	)	)	PUNCT
american_scientific_journal-756	122	33	.	.	PUNCT
american_scientific_journal-756	123	1	definition	definition	NOUN
american_scientific_journal-756	123	2	3.2	3.2	NUM
american_scientific_journal-756	123	3	.	.	PUNCT
american_scientific_journal-756	124	1	[	[	X
american_scientific_journal-756	124	2	20	20	NUM
american_scientific_journal-756	124	3	]	]	PUNCT
american_scientific_journal-756	124	4	for	for	ADP
american_scientific_journal-756	124	5	a	a	DET
american_scientific_journal-756	124	6	soft	soft	ADJ
american_scientific_journal-756	124	7	multifunction	multifunction	NOUN
american_scientific_journal-756	124	8	𝑭	𝑭	NOUN
american_scientific_journal-756	124	9	:	:	PUNCT
american_scientific_journal-756	124	10	(	(	PUNCT
american_scientific_journal-756	124	11	𝑿	𝑿	PROPN
american_scientific_journal-756	124	12	,	,	PUNCT
american_scientific_journal-756	124	13	𝝉	𝝉	NOUN
american_scientific_journal-756	124	14	)	)	PUNCT
american_scientific_journal-756	124	15	→	→	SYM
american_scientific_journal-756	124	16	(	(	PUNCT
american_scientific_journal-756	124	17	𝒀,𝝈,𝑬	𝒀,𝝈,𝑬	PROPN
american_scientific_journal-756	124	18	)	)	PUNCT
american_scientific_journal-756	124	19	,	,	PUNCT
american_scientific_journal-756	124	20	the	the	DET
american_scientific_journal-756	124	21	upper	upper	ADJ
american_scientific_journal-756	124	22	inverse	inverse	NOUN
american_scientific_journal-756	124	23	𝑭⁺(𝑮,𝑬	𝑭⁺(𝑮,𝑬	PROPN
american_scientific_journal-756	124	24	)	)	PUNCT
american_scientific_journal-756	124	25	and	and	CCONJ
american_scientific_journal-756	124	26	the	the	DET
american_scientific_journal-756	124	27	lower	low	ADJ
american_scientific_journal-756	124	28	inverse	inverse	NOUN
american_scientific_journal-756	124	29	𝑭⁻(𝑮,𝑬	𝑭⁻(𝑮,𝑬	NUM
american_scientific_journal-756	124	30	)	)	PUNCT
american_scientific_journal-756	124	31	of	of	ADP
american_scientific_journal-756	124	32	a	a	DET
american_scientific_journal-756	124	33	soft	soft	ADJ
american_scientific_journal-756	124	34	set	set	NOUN
american_scientific_journal-756	124	35	(	(	PUNCT
american_scientific_journal-756	124	36	𝑮,𝑬	𝑮,𝑬	ADV
american_scientific_journal-756	124	37	)	)	PUNCT
american_scientific_journal-756	124	38	over	over	ADP
american_scientific_journal-756	124	39	𝒀	𝒀	NOUN
american_scientific_journal-756	124	40	are	be	AUX
american_scientific_journal-756	124	41	defined	define	VERB
american_scientific_journal-756	124	42	as	as	SCONJ
american_scientific_journal-756	124	43	follows	follow	VERB
american_scientific_journal-756	124	44	:	:	PUNCT
american_scientific_journal-756	124	45	𝑭⁺(𝑮,𝑬	𝑭⁺(𝑮,𝑬	PROPN
american_scientific_journal-756	124	46	)	)	PUNCT
american_scientific_journal-756	124	47	=	=	PUNCT
american_scientific_journal-756	125	1	{	{	PUNCT
american_scientific_journal-756	125	2	𝒙	𝒙	PROPN
american_scientific_journal-756	125	3	∈	∈	PROPN
american_scientific_journal-756	125	4	𝑿:𝑭(𝒙	𝑿:𝑭(𝒙	PROPN
american_scientific_journal-756	125	5	)	)	PUNCT
american_scientific_journal-756	125	6	⊆	⊆	PROPN
american_scientific_journal-756	125	7	�	�	PROPN
american_scientific_journal-756	125	8	(	(	PUNCT
american_scientific_journal-756	125	9	𝑮,𝑬	𝑮,𝑬	ADJ
american_scientific_journal-756	125	10	)	)	PUNCT
american_scientific_journal-756	125	11	}	}	PUNCT
american_scientific_journal-756	125	12	and	and	CCONJ
american_scientific_journal-756	125	13	𝑭⁻(𝑮,𝑬	𝑭⁻(𝑮,𝑬	NUM
american_scientific_journal-756	125	14	)	)	PUNCT
american_scientific_journal-756	126	1	=	=	PRON
american_scientific_journal-756	126	2	{	{	PUNCT
american_scientific_journal-756	126	3	𝒙	𝒙	PROPN
american_scientific_journal-756	126	4	∈	∈	PROPN
american_scientific_journal-756	126	5	𝑿:𝑭(𝒙	𝑿:𝑭(𝒙	PROPN
american_scientific_journal-756	126	6	)	)	PUNCT
american_scientific_journal-756	126	7	∩	∩	ADJ
american_scientific_journal-756	126	8	�	�	PROPN
american_scientific_journal-756	126	9	(	(	PUNCT
american_scientific_journal-756	126	10	𝑮,𝑬	𝑮,𝑬	ADV
american_scientific_journal-756	126	11	)	)	PUNCT
american_scientific_journal-756	126	12	≠	≠	PROPN
american_scientific_journal-756	126	13	𝜱	𝜱	PROPN
american_scientific_journal-756	126	14	}	}	PUNCT
american_scientific_journal-756	126	15	.	.	PUNCT
american_scientific_journal-756	127	1	moreover	moreover	ADV
american_scientific_journal-756	127	2	,	,	PUNCT
american_scientific_journal-756	127	3	for	for	ADP
american_scientific_journal-756	127	4	a	a	DET
american_scientific_journal-756	127	5	subset	subset	NOUN
american_scientific_journal-756	127	6	𝑴	𝑴	NOUN
american_scientific_journal-756	127	7	of	of	ADP
american_scientific_journal-756	127	8	𝑿	𝑿	PROPN
american_scientific_journal-756	127	9	,	,	PUNCT
american_scientific_journal-756	127	10	𝑭(𝑴	𝑭(𝑴	NOUN
american_scientific_journal-756	127	11	)	)	PUNCT
american_scientific_journal-756	127	12	=	=	SYM
american_scientific_journal-756	127	13	∪	∪	X
american_scientific_journal-756	127	14	�	�	PROPN
american_scientific_journal-756	127	15	{	{	PUNCT
american_scientific_journal-756	127	16	𝑭(𝒙):𝒙	𝑭(𝒙):𝒙	PROPN
american_scientific_journal-756	127	17	∈	∈	PROPN
american_scientific_journal-756	127	18	𝑿	𝑿	PROPN
american_scientific_journal-756	127	19	}	}	PUNCT
american_scientific_journal-756	127	20	.	.	PUNCT
american_scientific_journal-756	128	1	proposition	proposition	NOUN
american_scientific_journal-756	128	2	3.3	3.3	NUM
american_scientific_journal-756	128	3	.	.	PUNCT
american_scientific_journal-756	129	1	[	[	X
american_scientific_journal-756	129	2	20	20	NUM
american_scientific_journal-756	129	3	]	]	PUNCT
american_scientific_journal-756	129	4	let	let	VERB
american_scientific_journal-756	129	5	𝑴	𝑴	PRON
american_scientific_journal-756	129	6	be	be	AUX
american_scientific_journal-756	129	7	a	a	DET
american_scientific_journal-756	129	8	subset	subset	NOUN
american_scientific_journal-756	129	9	of	of	ADP
american_scientific_journal-756	129	10	𝑿.	𝑿.	PROPN
american_scientific_journal-756	129	11	then	then	ADV
american_scientific_journal-756	129	12	the	the	DET
american_scientific_journal-756	129	13	follows	follow	NOUN
american_scientific_journal-756	129	14	are	be	AUX
american_scientific_journal-756	129	15	true	true	ADJ
american_scientific_journal-756	129	16	for	for	ADP
american_scientific_journal-756	129	17	a	a	DET
american_scientific_journal-756	129	18	soft	soft	ADJ
american_scientific_journal-756	129	19	multifunction	multifunction	NOUN
american_scientific_journal-756	129	20	𝑭	𝑭	NOUN
american_scientific_journal-756	129	21	:	:	PUNCT
american_scientific_journal-756	129	22	(	(	PUNCT
american_scientific_journal-756	129	23	𝑿	𝑿	PROPN
american_scientific_journal-756	129	24	,	,	PUNCT
american_scientific_journal-756	129	25	𝝉	𝝉	NOUN
american_scientific_journal-756	129	26	)	)	PUNCT
american_scientific_journal-756	129	27	→	→	SYM
american_scientific_journal-756	129	28	(	(	PUNCT
american_scientific_journal-756	129	29	𝒀,𝝈,𝑬	𝒀,𝝈,𝑬	PROPN
american_scientific_journal-756	129	30	):	):	PUNCT
american_scientific_journal-756	129	31	(	(	PUNCT
american_scientific_journal-756	129	32	a	a	X
american_scientific_journal-756	129	33	)	)	PUNCT
american_scientific_journal-756	129	34	𝑀	𝑀	PROPN
american_scientific_journal-756	129	35	⊂	⊂	PROPN
american_scientific_journal-756	129	36	𝐹⁺(𝐹(𝑀	𝐹⁺(𝐹(𝑀	NUM
american_scientific_journal-756	129	37	)	)	PUNCT
american_scientific_journal-756	129	38	)	)	PUNCT
american_scientific_journal-756	129	39	.	.	PUNCT
american_scientific_journal-756	130	1	if	if	SCONJ
american_scientific_journal-756	130	2	𝐹	𝐹	PROPN
american_scientific_journal-756	130	3	is	be	AUX
american_scientific_journal-756	130	4	onto	onto	ADP
american_scientific_journal-756	130	5	𝑀	𝑀	PROPN
american_scientific_journal-756	130	6	=	=	SYM
american_scientific_journal-756	130	7	𝐹⁺(𝐹(𝑀	𝐹⁺(𝐹(𝑀	NUM
american_scientific_journal-756	130	8	)	)	PUNCT
american_scientific_journal-756	130	9	)	)	PUNCT
american_scientific_journal-756	130	10	.	.	PUNCT
american_scientific_journal-756	131	1	(	(	PUNCT
american_scientific_journal-756	131	2	b	b	X
american_scientific_journal-756	131	3	)	)	PUNCT
american_scientific_journal-756	131	4	𝑀	𝑀	PROPN
american_scientific_journal-756	131	5	⊂	⊂	PROPN
american_scientific_journal-756	131	6	𝐹⁻(𝐹(𝑀	𝐹⁻(𝐹(𝑀	PROPN
american_scientific_journal-756	131	7	)	)	PUNCT
american_scientific_journal-756	131	8	)	)	PUNCT
american_scientific_journal-756	131	9	.	.	PUNCT
american_scientific_journal-756	132	1	if	if	SCONJ
american_scientific_journal-756	132	2	𝐹	𝐹	PROPN
american_scientific_journal-756	132	3	is	be	AUX
american_scientific_journal-756	132	4	onto	onto	ADP
american_scientific_journal-756	132	5	𝑀	𝑀	PROPN
american_scientific_journal-756	132	6	=	=	PUNCT
american_scientific_journal-756	132	7	𝐹⁻(𝐹(𝑀	𝐹⁻(𝐹(𝑀	ADJ
american_scientific_journal-756	132	8	)	)	PUNCT
american_scientific_journal-756	132	9	)	)	PUNCT
american_scientific_journal-756	132	10	.	.	PUNCT
american_scientific_journal-756	133	1	proposition	proposition	NOUN
american_scientific_journal-756	133	2	3.4	3.4	NUM
american_scientific_journal-756	133	3	.	.	PUNCT
american_scientific_journal-756	134	1	[	[	X
american_scientific_journal-756	134	2	20	20	NUM
american_scientific_journal-756	134	3	]	]	X
american_scientific_journal-756	134	4	let	let	VERB
american_scientific_journal-756	134	5	(	(	PUNCT
american_scientific_journal-756	134	6	𝑮,𝑬	𝑮,𝑬	ADV
american_scientific_journal-756	134	7	)	)	PUNCT
american_scientific_journal-756	134	8	be	be	AUX
american_scientific_journal-756	134	9	a	a	DET
american_scientific_journal-756	134	10	soft	soft	ADJ
american_scientific_journal-756	134	11	set	set	NOUN
american_scientific_journal-756	134	12	over	over	ADP
american_scientific_journal-756	134	13	𝒀.	𝒀.	NOUN
american_scientific_journal-756	134	14	then	then	ADV
american_scientific_journal-756	134	15	the	the	DET
american_scientific_journal-756	134	16	followings	following	NOUN
american_scientific_journal-756	134	17	are	be	AUX
american_scientific_journal-756	134	18	true	true	ADJ
american_scientific_journal-756	134	19	for	for	ADP
american_scientific_journal-756	134	20	a	a	DET
american_scientific_journal-756	134	21	soft	soft	ADJ
american_scientific_journal-756	134	22	multifunction	multifunction	NOUN
american_scientific_journal-756	134	23	𝑭	𝑭	NOUN
american_scientific_journal-756	134	24	:	:	PUNCT
american_scientific_journal-756	134	25	(	(	PUNCT
american_scientific_journal-756	134	26	𝑿	𝑿	PROPN
american_scientific_journal-756	134	27	,	,	PUNCT
american_scientific_journal-756	134	28	𝝉	𝝉	NOUN
american_scientific_journal-756	134	29	)	)	PUNCT
american_scientific_journal-756	134	30	→	→	SYM
american_scientific_journal-756	134	31	(	(	PUNCT
american_scientific_journal-756	134	32	𝒀,𝝈,𝑬	𝒀,𝝈,𝑬	PROPN
american_scientific_journal-756	134	33	):	):	PUNCT
american_scientific_journal-756	134	34	(	(	PUNCT
american_scientific_journal-756	134	35	a	a	X
american_scientific_journal-756	134	36	)	)	PUNCT
american_scientific_journal-756	134	37	𝐹⁺((𝐺,𝐸)𝑐	𝐹⁺((𝐺,𝐸)𝑐	ADJ
american_scientific_journal-756	134	38	)	)	PUNCT
american_scientific_journal-756	134	39	=	=	SYM
american_scientific_journal-756	135	1	𝑋	𝑋	PROPN
american_scientific_journal-756	135	2	�	�	PROPN
american_scientific_journal-756	135	3	−	−	NUM
american_scientific_journal-756	135	4	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	135	5	)	)	PUNCT
american_scientific_journal-756	135	6	(	(	PUNCT
american_scientific_journal-756	135	7	b	b	X
american_scientific_journal-756	135	8	)	)	PUNCT
american_scientific_journal-756	135	9	𝑭⁻((𝑮,𝑬)𝒄	𝑭⁻((𝑮,𝑬)𝒄	NOUN
american_scientific_journal-756	135	10	)	)	PUNCT
american_scientific_journal-756	135	11	=	=	SYM
american_scientific_journal-756	135	12	𝑿	𝑿	PROPN
american_scientific_journal-756	135	13	�	�	PROPN
american_scientific_journal-756	135	14	−	−	PROPN
american_scientific_journal-756	135	15	𝑭⁺(𝑮,𝑬	𝑭⁺(𝑮,𝑬	PROPN
american_scientific_journal-756	135	16	)	)	PUNCT
american_scientific_journal-756	135	17	.	.	PUNCT
american_scientific_journal-756	136	1	100	100	NUM
american_scientific_journal-756	136	2	american	american	ADJ
american_scientific_journal-756	136	3	scientific	scientific	ADJ
american_scientific_journal-756	136	4	research	research	NOUN
american_scientific_journal-756	136	5	journal	journal	NOUN
american_scientific_journal-756	136	6	for	for	ADP
american_scientific_journal-756	136	7	engineering	engineering	NOUN
american_scientific_journal-756	136	8	,	,	PUNCT
american_scientific_journal-756	136	9	technology	technology	NOUN
american_scientific_journal-756	136	10	,	,	PUNCT
american_scientific_journal-756	136	11	and	and	CCONJ
american_scientific_journal-756	136	12	sciences	science	NOUN
american_scientific_journal-756	136	13	(	(	PUNCT
american_scientific_journal-756	136	14	asrjets	asrjet	NOUN
american_scientific_journal-756	136	15	)	)	PUNCT
american_scientific_journal-756	136	16	(	(	PUNCT
american_scientific_journal-756	136	17	2014	2014	NUM
american_scientific_journal-756	136	18	)	)	PUNCT
american_scientific_journal-756	136	19	volume	volume	NOUN
american_scientific_journal-756	136	20	8	8	NUM
american_scientific_journal-756	136	21	,	,	PUNCT
american_scientific_journal-756	136	22	no	no	DET
american_scientific_journal-756	136	23	1	1	NUM
american_scientific_journal-756	136	24	,	,	PUNCT
american_scientific_journal-756	136	25	pp	pp	ADV
american_scientific_journal-756	136	26	96	96	NUM
american_scientific_journal-756	136	27	-	-	SYM
american_scientific_journal-756	136	28	107	107	NUM
american_scientific_journal-756	136	29	proposition	proposition	NOUN
american_scientific_journal-756	136	30	3.5	3.5	NUM
american_scientific_journal-756	136	31	.	.	PUNCT
american_scientific_journal-756	137	1	[	[	X
american_scientific_journal-756	137	2	20	20	NUM
american_scientific_journal-756	137	3	]	]	X
american_scientific_journal-756	137	4	let	let	VERB
american_scientific_journal-756	137	5	(	(	PUNCT
american_scientific_journal-756	137	6	𝐺𝑖	𝐺𝑖	VERB
american_scientific_journal-756	137	7	,	,	PUNCT
american_scientific_journal-756	137	8	𝐸	𝐸	PROPN
american_scientific_journal-756	137	9	)	)	PUNCT
american_scientific_journal-756	137	10	be	be	AUX
american_scientific_journal-756	137	11	soft	soft	ADJ
american_scientific_journal-756	137	12	sets	set	NOUN
american_scientific_journal-756	137	13	over	over	ADP
american_scientific_journal-756	137	14	𝑌	𝑌	PROPN
american_scientific_journal-756	137	15	for	for	ADP
american_scientific_journal-756	137	16	each	each	DET
american_scientific_journal-756	137	17	𝑖	𝑖	SYM
american_scientific_journal-756	137	18	∈	∈	PROPN
american_scientific_journal-756	137	19	𝐼.	𝐼.	NOUN
american_scientific_journal-756	137	20	then	then	ADV
american_scientific_journal-756	137	21	the	the	DET
american_scientific_journal-756	137	22	follows	follow	NOUN
american_scientific_journal-756	137	23	are	be	AUX
american_scientific_journal-756	137	24	true	true	ADJ
american_scientific_journal-756	137	25	for	for	ADP
american_scientific_journal-756	137	26	a	a	DET
american_scientific_journal-756	137	27	soft	soft	ADJ
american_scientific_journal-756	137	28	multifunction	multifunction	NOUN
american_scientific_journal-756	137	29	𝐹	𝐹	PROPN
american_scientific_journal-756	137	30	:	:	PUNCT
american_scientific_journal-756	137	31	(	(	PUNCT
american_scientific_journal-756	137	32	𝑋	𝑋	PROPN
american_scientific_journal-756	137	33	,	,	PUNCT
american_scientific_journal-756	137	34	𝜏	𝜏	NOUN
american_scientific_journal-756	137	35	)	)	PUNCT
american_scientific_journal-756	137	36	→	→	SYM
american_scientific_journal-756	137	37	(	(	PUNCT
american_scientific_journal-756	137	38	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	137	39	)	)	PUNCT
american_scientific_journal-756	137	40	:	:	PUNCT
american_scientific_journal-756	137	41	(	(	PUNCT
american_scientific_journal-756	137	42	a	a	X
american_scientific_journal-756	137	43	)	)	PUNCT
american_scientific_journal-756	137	44	𝐹⁻(∪	𝐹⁻(∪	PROPN
american_scientific_journal-756	137	45	�	�	PROPN
american_scientific_journal-756	137	46	(	(	PUNCT
american_scientific_journal-756	137	47	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	137	48	,	,	PUNCT
american_scientific_journal-756	137	49	𝐸	𝐸	PROPN
american_scientific_journal-756	137	50	)	)	PUNCT
american_scientific_journal-756	137	51	)	)	PUNCT
american_scientific_journal-756	138	1	=	=	SYM
american_scientific_journal-756	138	2	∪	∪	X
american_scientific_journal-756	138	3	�	�	PROPN
american_scientific_journal-756	138	4	(	(	PUNCT
american_scientific_journal-756	138	5	𝐹⁻(𝐺𝑖	𝐹⁻(𝐺𝑖	NOUN
american_scientific_journal-756	138	6	,	,	PUNCT
american_scientific_journal-756	138	7	𝐸	𝐸	PROPN
american_scientific_journal-756	138	8	)	)	PUNCT
american_scientific_journal-756	138	9	)	)	PUNCT
american_scientific_journal-756	138	10	.	.	PUNCT
american_scientific_journal-756	139	1	(	(	PUNCT
american_scientific_journal-756	139	2	b	b	X
american_scientific_journal-756	139	3	)	)	PUNCT
american_scientific_journal-756	139	4	𝐹⁺(∩	𝐹⁺(∩	NOUN
american_scientific_journal-756	139	5	�	�	PROPN
american_scientific_journal-756	139	6	(	(	PUNCT
american_scientific_journal-756	139	7	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	139	8	,	,	PUNCT
american_scientific_journal-756	139	9	𝐸	𝐸	PROPN
american_scientific_journal-756	139	10	)	)	PUNCT
american_scientific_journal-756	139	11	)	)	PUNCT
american_scientific_journal-756	140	1	=	=	NOUN
american_scientific_journal-756	140	2	∩	∩	X
american_scientific_journal-756	140	3	�	�	PROPN
american_scientific_journal-756	140	4	(	(	PUNCT
american_scientific_journal-756	140	5	𝐹⁺(𝐺𝑖	𝐹⁺(𝐺𝑖	NUM
american_scientific_journal-756	140	6	,	,	PUNCT
american_scientific_journal-756	140	7	𝐸	𝐸	PROPN
american_scientific_journal-756	140	8	)	)	PUNCT
american_scientific_journal-756	140	9	)	)	PUNCT
american_scientific_journal-756	140	10	.	.	PUNCT
american_scientific_journal-756	141	1	definition	definition	NOUN
american_scientific_journal-756	141	2	3.6	3.6	NUM
american_scientific_journal-756	141	3	.	.	PUNCT
american_scientific_journal-756	142	1	let	let	VERB
american_scientific_journal-756	142	2	(	(	PUNCT
american_scientific_journal-756	142	3	𝑋	𝑋	NOUN
american_scientific_journal-756	142	4	,	,	PUNCT
american_scientific_journal-756	142	5	𝜏	𝜏	NOUN
american_scientific_journal-756	142	6	)	)	PUNCT
american_scientific_journal-756	142	7	be	be	VERB
american_scientific_journal-756	142	8	an	an	DET
american_scientific_journal-756	142	9	ordinary	ordinary	ADJ
american_scientific_journal-756	142	10	topological	topological	ADJ
american_scientific_journal-756	142	11	space	space	NOUN
american_scientific_journal-756	142	12	and	and	CCONJ
american_scientific_journal-756	142	13	(	(	PUNCT
american_scientific_journal-756	142	14	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	X
american_scientific_journal-756	142	15	)	)	PUNCT
american_scientific_journal-756	142	16	be	be	AUX
american_scientific_journal-756	142	17	a	a	DET
american_scientific_journal-756	142	18	soft	soft	ADJ
american_scientific_journal-756	142	19	topological	topological	ADJ
american_scientific_journal-756	142	20	space	space	NOUN
american_scientific_journal-756	142	21	.	.	PUNCT
american_scientific_journal-756	143	1	then	then	ADV
american_scientific_journal-756	143	2	the	the	DET
american_scientific_journal-756	143	3	soft	soft	ADJ
american_scientific_journal-756	143	4	multifunction	multifunction	NOUN
american_scientific_journal-756	143	5	𝐹	𝐹	PROPN
american_scientific_journal-756	143	6	:	:	PUNCT
american_scientific_journal-756	143	7	(	(	PUNCT
american_scientific_journal-756	143	8	𝑋	𝑋	PROPN
american_scientific_journal-756	143	9	,	,	PUNCT
american_scientific_journal-756	143	10	𝜏	𝜏	NOUN
american_scientific_journal-756	143	11	)	)	PUNCT
american_scientific_journal-756	143	12	→	→	X
american_scientific_journal-756	143	13	(	(	PUNCT
american_scientific_journal-756	143	14	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	143	15	)	)	PUNCT
american_scientific_journal-756	143	16	is	be	AUX
american_scientific_journal-756	143	17	said	say	VERB
american_scientific_journal-756	143	18	to	to	PART
american_scientific_journal-756	143	19	be	be	AUX
american_scientific_journal-756	143	20	;	;	PUNCT
american_scientific_journal-756	143	21	(	(	PUNCT
american_scientific_journal-756	143	22	a	a	X
american_scientific_journal-756	143	23	)	)	PUNCT
american_scientific_journal-756	143	24	soft	soft	ADJ
american_scientific_journal-756	143	25	upper	upper	ADJ
american_scientific_journal-756	143	26	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	143	27	at	at	ADP
american_scientific_journal-756	143	28	a	a	DET
american_scientific_journal-756	143	29	point	point	NOUN
american_scientific_journal-756	143	30	𝑥	𝑥	DET
american_scientific_journal-756	143	31	∈	∈	NOUN
american_scientific_journal-756	143	32	𝑋	𝑋	NOUN
american_scientific_journal-756	143	33	if	if	SCONJ
american_scientific_journal-756	143	34	for	for	ADP
american_scientific_journal-756	143	35	each	each	DET
american_scientific_journal-756	143	36	soft	soft	ADJ
american_scientific_journal-756	143	37	open	open	ADJ
american_scientific_journal-756	143	38	(	(	PUNCT
american_scientific_journal-756	143	39	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	143	40	)	)	PUNCT
american_scientific_journal-756	143	41	such	such	ADJ
american_scientific_journal-756	143	42	that	that	SCONJ
american_scientific_journal-756	143	43	𝐹(𝑥	𝐹(𝑥	X
american_scientific_journal-756	143	44	)	)	PUNCT
american_scientific_journal-756	143	45	⊆	⊆	NUM
american_scientific_journal-756	143	46	�	�	PROPN
american_scientific_journal-756	143	47	(	(	PUNCT
american_scientific_journal-756	143	48	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	143	49	)	)	PUNCT
american_scientific_journal-756	143	50	,	,	PUNCT
american_scientific_journal-756	143	51	there	there	PRON
american_scientific_journal-756	143	52	exists	exist	VERB
american_scientific_journal-756	143	53	an	an	DET
american_scientific_journal-756	143	54	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	143	55	neighborhood	neighborhood	NOUN
american_scientific_journal-756	143	56	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	143	57	)	)	PUNCT
american_scientific_journal-756	143	58	of	of	ADP
american_scientific_journal-756	143	59	𝑥	𝑥	PRON
american_scientific_journal-756	143	60	such	such	ADJ
american_scientific_journal-756	143	61	that	that	SCONJ
american_scientific_journal-756	143	62	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	143	63	)	)	PUNCT
american_scientific_journal-756	143	64	⊆	⊆	NUM
american_scientific_journal-756	143	65	�	�	PROPN
american_scientific_journal-756	143	66	(	(	PUNCT
american_scientific_journal-756	143	67	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	143	68	)	)	PUNCT
american_scientific_journal-756	143	69	for	for	ADP
american_scientific_journal-756	143	70	all	all	DET
american_scientific_journal-756	143	71	𝑧	𝑧	PRON
american_scientific_journal-756	143	72	∈	∈	PROPN
american_scientific_journal-756	143	73	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	143	74	)	)	PUNCT
american_scientific_journal-756	143	75	.	.	PUNCT
american_scientific_journal-756	144	1	(	(	PUNCT
american_scientific_journal-756	144	2	b	b	X
american_scientific_journal-756	144	3	)	)	PUNCT
american_scientific_journal-756	144	4	soft	soft	ADJ
american_scientific_journal-756	144	5	lower	low	ADJ
american_scientific_journal-756	144	6	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	144	7	at	at	ADP
american_scientific_journal-756	144	8	a	a	DET
american_scientific_journal-756	144	9	point	point	NOUN
american_scientific_journal-756	144	10	𝑥	𝑥	DET
american_scientific_journal-756	144	11	∈	∈	NOUN
american_scientific_journal-756	144	12	𝑋	𝑋	NOUN
american_scientific_journal-756	144	13	if	if	SCONJ
american_scientific_journal-756	144	14	for	for	ADP
american_scientific_journal-756	144	15	each	each	DET
american_scientific_journal-756	144	16	soft	soft	ADJ
american_scientific_journal-756	144	17	open	open	ADJ
american_scientific_journal-756	144	18	(	(	PUNCT
american_scientific_journal-756	144	19	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	144	20	)	)	PUNCT
american_scientific_journal-756	144	21	such	such	ADJ
american_scientific_journal-756	144	22	that	that	SCONJ
american_scientific_journal-756	144	23	𝐹(𝑥	𝐹(𝑥	X
american_scientific_journal-756	144	24	)	)	PUNCT
american_scientific_journal-756	144	25	∩	∩	ADJ
american_scientific_journal-756	144	26	�	�	PROPN
american_scientific_journal-756	144	27	(	(	PUNCT
american_scientific_journal-756	144	28	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	144	29	)	)	PUNCT
american_scientific_journal-756	144	30	≠	≠	PROPN
american_scientific_journal-756	144	31	𝛷	𝛷	PROPN
american_scientific_journal-756	144	32	,	,	PUNCT
american_scientific_journal-756	144	33	there	there	PRON
american_scientific_journal-756	144	34	exists	exist	VERB
american_scientific_journal-756	144	35	an	an	DET
american_scientific_journal-756	144	36	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	144	37	neighborhood	neighborhood	NOUN
american_scientific_journal-756	144	38	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	144	39	)	)	PUNCT
american_scientific_journal-756	144	40	of	of	ADP
american_scientific_journal-756	144	41	𝑥	𝑥	PRON
american_scientific_journal-756	144	42	such	such	ADJ
american_scientific_journal-756	144	43	that	that	PRON
american_scientific_journal-756	144	44	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	144	45	)	)	PUNCT
american_scientific_journal-756	144	46	∩	∩	ADJ
american_scientific_journal-756	144	47	�	�	PROPN
american_scientific_journal-756	144	48	(	(	PUNCT
american_scientific_journal-756	144	49	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	144	50	)	)	PUNCT
american_scientific_journal-756	144	51	≠	≠	PROPN
american_scientific_journal-756	144	52	𝛷	𝛷	NOUN
american_scientific_journal-756	144	53	for	for	ADP
american_scientific_journal-756	144	54	all	all	DET
american_scientific_journal-756	144	55	𝑧	𝑧	PRON
american_scientific_journal-756	144	56	∈	∈	PROPN
american_scientific_journal-756	144	57	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	144	58	)	)	PUNCT
american_scientific_journal-756	144	59	.	.	PUNCT
american_scientific_journal-756	145	1	(	(	PUNCT
american_scientific_journal-756	145	2	c	c	X
american_scientific_journal-756	145	3	)	)	PUNCT
american_scientific_journal-756	145	4	soft	soft	ADJ
american_scientific_journal-756	145	5	upper	upper	ADJ
american_scientific_journal-756	145	6	(	(	PUNCT
american_scientific_journal-756	145	7	lower	low	ADJ
american_scientific_journal-756	145	8	)	)	PUNCT
american_scientific_journal-756	145	9	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	145	10	if	if	SCONJ
american_scientific_journal-756	145	11	𝐹	𝐹	PROPN
american_scientific_journal-756	145	12	has	have	VERB
american_scientific_journal-756	145	13	this	this	DET
american_scientific_journal-756	145	14	property	property	NOUN
american_scientific_journal-756	145	15	at	at	ADP
american_scientific_journal-756	145	16	every	every	DET
american_scientific_journal-756	145	17	point	point	NOUN
american_scientific_journal-756	145	18	of	of	ADP
american_scientific_journal-756	145	19	𝑋.	𝑋.	PROPN
american_scientific_journal-756	145	20	proposition	proposition	NOUN
american_scientific_journal-756	145	21	3.7	3.7	NUM
american_scientific_journal-756	145	22	.	.	PUNCT
american_scientific_journal-756	146	1	a	a	DET
american_scientific_journal-756	146	2	soft	soft	ADJ
american_scientific_journal-756	146	3	multifunction	multifunction	NOUN
american_scientific_journal-756	146	4	𝐹	𝐹	PROPN
american_scientific_journal-756	146	5	:	:	PUNCT
american_scientific_journal-756	146	6	(	(	PUNCT
american_scientific_journal-756	146	7	𝑋	𝑋	PROPN
american_scientific_journal-756	146	8	,	,	PUNCT
american_scientific_journal-756	146	9	𝜏	𝜏	NOUN
american_scientific_journal-756	146	10	)	)	PUNCT
american_scientific_journal-756	146	11	→	→	X
american_scientific_journal-756	146	12	(	(	PUNCT
american_scientific_journal-756	146	13	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	146	14	)	)	PUNCT
american_scientific_journal-756	146	15	is	be	AUX
american_scientific_journal-756	146	16	soft	soft	ADJ
american_scientific_journal-756	146	17	upper	upper	ADJ
american_scientific_journal-756	146	18	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	146	19	if	if	SCONJ
american_scientific_journal-756	146	20	and	and	CCONJ
american_scientific_journal-756	146	21	only	only	ADV
american_scientific_journal-756	146	22	if	if	SCONJ
american_scientific_journal-756	146	23	for	for	ADP
american_scientific_journal-756	146	24	all	all	DET
american_scientific_journal-756	146	25	soft	soft	ADJ
american_scientific_journal-756	146	26	open	open	ADJ
american_scientific_journal-756	146	27	set	set	NOUN
american_scientific_journal-756	146	28	(	(	PUNCT
american_scientific_journal-756	146	29	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	146	30	)	)	PUNCT
american_scientific_journal-756	146	31	over	over	ADP
american_scientific_journal-756	146	32	𝑈	𝑈	PROPN
american_scientific_journal-756	146	33	,	,	PUNCT
american_scientific_journal-756	146	34	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	146	35	)	)	PUNCT
american_scientific_journal-756	146	36	is	be	AUX
american_scientific_journal-756	146	37	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	146	38	in	in	ADP
american_scientific_journal-756	146	39	𝑋.	𝑋.	PROPN
american_scientific_journal-756	146	40	proof	proof	NOUN
american_scientific_journal-756	146	41	.	.	PUNCT
american_scientific_journal-756	147	1	first	first	ADV
american_scientific_journal-756	147	2	suppose	suppose	VERB
american_scientific_journal-756	147	3	that	that	SCONJ
american_scientific_journal-756	147	4	𝐹	𝐹	PROPN
american_scientific_journal-756	147	5	is	be	AUX
american_scientific_journal-756	147	6	soft	soft	ADJ
american_scientific_journal-756	147	7	upper	upper	ADJ
american_scientific_journal-756	147	8	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	147	9	.	.	PUNCT
american_scientific_journal-756	148	1	let	let	VERB
american_scientific_journal-756	148	2	(	(	PUNCT
american_scientific_journal-756	148	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	148	4	)	)	PUNCT
american_scientific_journal-756	148	5	is	be	AUX
american_scientific_journal-756	148	6	be	be	AUX
american_scientific_journal-756	148	7	soft	soft	ADJ
american_scientific_journal-756	148	8	open	open	ADJ
american_scientific_journal-756	148	9	set	set	VERB
american_scientific_journal-756	148	10	over	over	ADP
american_scientific_journal-756	148	11	𝑌	𝑌	PROPN
american_scientific_journal-756	148	12	and	and	CCONJ
american_scientific_journal-756	148	13	𝑥	𝑥	DET
american_scientific_journal-756	148	14	∈	∈	NOUN
american_scientific_journal-756	148	15	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	148	16	)	)	PUNCT
american_scientific_journal-756	148	17	.	.	PUNCT
american_scientific_journal-756	149	1	then	then	ADV
american_scientific_journal-756	149	2	,	,	PUNCT
american_scientific_journal-756	149	3	from	from	ADP
american_scientific_journal-756	149	4	definition	definition	NOUN
american_scientific_journal-756	149	5	3.6	3.6	NUM
american_scientific_journal-756	149	6	we	we	PRON
american_scientific_journal-756	149	7	know	know	VERB
american_scientific_journal-756	149	8	that	that	SCONJ
american_scientific_journal-756	149	9	there	there	PRON
american_scientific_journal-756	149	10	exists	exist	VERB
american_scientific_journal-756	149	11	an	an	DET
american_scientific_journal-756	149	12	𝛼	𝛼	NOUN
american_scientific_journal-756	149	13	-open	-open	ADJ
american_scientific_journal-756	149	14	neighborhood	neighborhood	NOUN
american_scientific_journal-756	149	15	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	149	16	)	)	PUNCT
american_scientific_journal-756	149	17	of	of	ADP
american_scientific_journal-756	149	18	𝑥	𝑥	PRON
american_scientific_journal-756	149	19	such	such	ADJ
american_scientific_journal-756	149	20	that	that	PRON
american_scientific_journal-756	149	21	for	for	ADP
american_scientific_journal-756	149	22	all	all	DET
american_scientific_journal-756	149	23	𝑧	𝑧	PRON
american_scientific_journal-756	149	24	∈	∈	PROPN
american_scientific_journal-756	149	25	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	149	26	)	)	PUNCT
american_scientific_journal-756	149	27	,	,	PUNCT
american_scientific_journal-756	149	28	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	149	29	)	)	PUNCT
american_scientific_journal-756	149	30	⊆	⊆	NUM
american_scientific_journal-756	149	31	�	�	PROPN
american_scientific_journal-756	149	32	(	(	PUNCT
american_scientific_journal-756	149	33	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	149	34	)	)	PUNCT
american_scientific_journal-756	149	35	which	which	PRON
american_scientific_journal-756	149	36	means	mean	VERB
american_scientific_journal-756	149	37	that	that	SCONJ
american_scientific_journal-756	149	38	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	149	39	)	)	PUNCT
american_scientific_journal-756	149	40	is	be	AUX
american_scientific_journal-756	149	41	𝛼	𝛼	PRON
american_scientific_journal-756	149	42	-open	-open	NOUN
american_scientific_journal-756	149	43	as	as	SCONJ
american_scientific_journal-756	149	44	claimed	claim	VERB
american_scientific_journal-756	149	45	.	.	PUNCT
american_scientific_journal-756	150	1	the	the	DET
american_scientific_journal-756	150	2	other	other	ADJ
american_scientific_journal-756	150	3	direction	direction	NOUN
american_scientific_journal-756	150	4	is	be	AUX
american_scientific_journal-756	150	5	just	just	ADV
american_scientific_journal-756	150	6	the	the	DET
american_scientific_journal-756	150	7	definition	definition	NOUN
american_scientific_journal-756	150	8	of	of	ADP
american_scientific_journal-756	150	9	soft	soft	ADJ
american_scientific_journal-756	150	10	upper	upper	ADJ
american_scientific_journal-756	150	11	continuty	continuty	NOUN
american_scientific_journal-756	150	12	of	of	ADP
american_scientific_journal-756	150	13	𝐹.	𝐹.	PROPN
american_scientific_journal-756	150	14	proposition	proposition	NOUN
american_scientific_journal-756	150	15	3.8	3.8	NUM
american_scientific_journal-756	150	16	.	.	PUNCT
american_scientific_journal-756	151	1	𝐹	𝐹	PROPN
american_scientific_journal-756	151	2	:	:	PUNCT
american_scientific_journal-756	151	3	(	(	PUNCT
american_scientific_journal-756	151	4	𝑋	𝑋	PROPN
american_scientific_journal-756	151	5	,	,	PUNCT
american_scientific_journal-756	151	6	𝜏	𝜏	NOUN
american_scientific_journal-756	151	7	)	)	PUNCT
american_scientific_journal-756	151	8	→	→	X
american_scientific_journal-756	151	9	(	(	PUNCT
american_scientific_journal-756	151	10	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	151	11	)	)	PUNCT
american_scientific_journal-756	151	12	is	be	AUX
american_scientific_journal-756	151	13	soft	soft	ADJ
american_scientific_journal-756	151	14	lower	low	ADJ
american_scientific_journal-756	151	15	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	151	16	multifunction	multifunction	NOUN
american_scientific_journal-756	151	17	if	if	SCONJ
american_scientific_journal-756	151	18	and	and	CCONJ
american_scientific_journal-756	151	19	only	only	ADV
american_scientific_journal-756	151	20	if	if	SCONJ
american_scientific_journal-756	151	21	for	for	ADP
american_scientific_journal-756	151	22	every	every	DET
american_scientific_journal-756	151	23	soft	soft	ADJ
american_scientific_journal-756	151	24	set	set	NOUN
american_scientific_journal-756	151	25	(	(	PUNCT
american_scientific_journal-756	151	26	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	151	27	)	)	PUNCT
american_scientific_journal-756	151	28	over	over	ADP
american_scientific_journal-756	151	29	𝑌	𝑌	PROPN
american_scientific_journal-756	151	30	,	,	PUNCT
american_scientific_journal-756	151	31	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	PROPN
american_scientific_journal-756	151	32	)	)	PUNCT
american_scientific_journal-756	151	33	is	be	AUX
american_scientific_journal-756	151	34	open	open	ADJ
american_scientific_journal-756	151	35	set	set	VERB
american_scientific_journal-756	151	36	in	in	ADP
american_scientific_journal-756	151	37	𝑋.	𝑋.	PROPN
american_scientific_journal-756	151	38	proof	proof	NOUN
american_scientific_journal-756	151	39	.	.	PUNCT
american_scientific_journal-756	152	1	first	first	ADV
american_scientific_journal-756	152	2	assume	assume	VERB
american_scientific_journal-756	152	3	that	that	SCONJ
american_scientific_journal-756	152	4	𝐹	𝐹	PROPN
american_scientific_journal-756	152	5	is	be	AUX
american_scientific_journal-756	152	6	soft	soft	ADJ
american_scientific_journal-756	152	7	𝛼-lower	𝛼-lower	X
american_scientific_journal-756	152	8	continuous	continuous	ADJ
american_scientific_journal-756	152	9	.	.	PUNCT
american_scientific_journal-756	153	1	let	let	VERB
american_scientific_journal-756	153	2	(	(	PUNCT
american_scientific_journal-756	153	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	153	4	)	)	PUNCT
american_scientific_journal-756	153	5	soft	soft	ADJ
american_scientific_journal-756	153	6	open	open	ADJ
american_scientific_journal-756	153	7	set	set	VERB
american_scientific_journal-756	153	8	over	over	ADP
american_scientific_journal-756	153	9	𝑌	𝑌	PROPN
american_scientific_journal-756	153	10	and	and	CCONJ
american_scientific_journal-756	153	11	𝑥	𝑥	DET
american_scientific_journal-756	153	12	∈	∈	PROPN
american_scientific_journal-756	153	13	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	153	14	)	)	PUNCT
american_scientific_journal-756	153	15	.	.	PUNCT
american_scientific_journal-756	154	1	then	then	ADV
american_scientific_journal-756	154	2	there	there	PRON
american_scientific_journal-756	154	3	is	be	VERB
american_scientific_journal-756	154	4	an	an	DET
american_scientific_journal-756	154	5	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	154	6	neighborhood	neighborhood	NOUN
american_scientific_journal-756	154	7	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	154	8	)	)	PUNCT
american_scientific_journal-756	154	9	of	of	ADP
american_scientific_journal-756	154	10	𝑥	𝑥	PRON
american_scientific_journal-756	154	11	such	such	ADJ
american_scientific_journal-756	154	12	that	that	PRON
american_scientific_journal-756	154	13	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	154	14	)	)	PUNCT
american_scientific_journal-756	154	15	∩	∩	ADJ
american_scientific_journal-756	154	16	�	�	PROPN
american_scientific_journal-756	154	17	(	(	PUNCT
american_scientific_journal-756	154	18	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	154	19	)	)	PUNCT
american_scientific_journal-756	154	20	≠	≠	PROPN
american_scientific_journal-756	154	21	𝛷	𝛷	NOUN
american_scientific_journal-756	154	22	for	for	ADP
american_scientific_journal-756	154	23	all	all	DET
american_scientific_journal-756	154	24	𝑧	𝑧	PRON
american_scientific_journal-756	154	25	∈	∈	PROPN
american_scientific_journal-756	154	26	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	154	27	)	)	PUNCT
american_scientific_journal-756	154	28	.	.	PUNCT
american_scientific_journal-756	155	1	so	so	ADV
american_scientific_journal-756	155	2	𝑃(𝑥	𝑃(𝑥	PRON
american_scientific_journal-756	155	3	)	)	PUNCT
american_scientific_journal-756	155	4	⊆	⊆	NUM
american_scientific_journal-756	155	5	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	155	6	)	)	PUNCT
american_scientific_journal-756	155	7	which	which	PRON
american_scientific_journal-756	155	8	implies	imply	VERB
american_scientific_journal-756	155	9	that	that	SCONJ
american_scientific_journal-756	155	10	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	155	11	)	)	PUNCT
american_scientific_journal-756	155	12	is	be	AUX
american_scientific_journal-756	155	13	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	155	14	in	in	ADP
american_scientific_journal-756	155	15	𝑋.	𝑋.	PROPN
american_scientific_journal-756	155	16	now	now	ADV
american_scientific_journal-756	155	17	suppose	suppose	VERB
american_scientific_journal-756	155	18	that	that	SCONJ
american_scientific_journal-756	155	19	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	155	20	)	)	PUNCT
american_scientific_journal-756	155	21	is	be	AUX
american_scientific_journal-756	155	22	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	155	23	.	.	PUNCT
american_scientific_journal-756	156	1	let	let	VERB
american_scientific_journal-756	156	2	𝑥	𝑥	PRON
american_scientific_journal-756	156	3	∈	∈	PROPN
american_scientific_journal-756	156	4	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	156	5	)	)	PUNCT
american_scientific_journal-756	156	6	.	.	PUNCT
american_scientific_journal-756	157	1	then	then	ADV
american_scientific_journal-756	157	2	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	157	3	)	)	PUNCT
american_scientific_journal-756	157	4	is	be	AUX
american_scientific_journal-756	157	5	an	an	DET
american_scientific_journal-756	157	6	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	157	7	neighborhood	neighborhood	NOUN
american_scientific_journal-756	157	8	of	of	ADP
american_scientific_journal-756	157	9	𝑥	𝑥	PROPN
american_scientific_journal-756	157	10	and	and	CCONJ
american_scientific_journal-756	157	11	for	for	ADP
american_scientific_journal-756	157	12	all	all	DET
american_scientific_journal-756	157	13	𝑧	𝑧	DET
american_scientific_journal-756	157	14	∈	∈	PROPN
american_scientific_journal-756	157	15	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	157	16	)	)	PUNCT
american_scientific_journal-756	157	17	we	we	PRON
american_scientific_journal-756	157	18	have	have	VERB
american_scientific_journal-756	157	19	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	157	20	)	)	PUNCT
american_scientific_journal-756	157	21	∩	∩	ADJ
american_scientific_journal-756	157	22	�	�	PROPN
american_scientific_journal-756	157	23	(	(	PUNCT
american_scientific_journal-756	157	24	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	157	25	)	)	PUNCT
american_scientific_journal-756	157	26	≠	≠	PROPN
american_scientific_journal-756	157	27	𝛷.	𝛷.	PROPN
american_scientific_journal-756	158	1	so	so	ADV
american_scientific_journal-756	158	2	𝐹	𝐹	PROPN
american_scientific_journal-756	158	3	is	be	AUX
american_scientific_journal-756	158	4	soft	soft	ADJ
american_scientific_journal-756	158	5	lower	low	ADJ
american_scientific_journal-756	158	6	α	α	NOUN
american_scientific_journal-756	158	7	-	-	ADJ
american_scientific_journal-756	158	8	continuous	continuous	ADJ
american_scientific_journal-756	158	9	.	.	PUNCT
american_scientific_journal-756	159	1	definition	definition	NOUN
american_scientific_journal-756	159	2	3.9	3.9	NUM
american_scientific_journal-756	159	3	.	.	PUNCT
american_scientific_journal-756	160	1	[	[	X
american_scientific_journal-756	160	2	20	20	NUM
american_scientific_journal-756	160	3	]	]	PUNCT
american_scientific_journal-756	160	4	let	let	VERB
american_scientific_journal-756	160	5	(	(	PUNCT
american_scientific_journal-756	160	6	𝑋	𝑋	NOUN
american_scientific_journal-756	160	7	,	,	PUNCT
american_scientific_journal-756	160	8	𝜏	𝜏	NOUN
american_scientific_journal-756	160	9	)	)	PUNCT
american_scientific_journal-756	160	10	be	be	VERB
american_scientific_journal-756	160	11	an	an	DET
american_scientific_journal-756	160	12	ordinary	ordinary	ADJ
american_scientific_journal-756	160	13	topological	topological	ADJ
american_scientific_journal-756	160	14	space	space	NOUN
american_scientific_journal-756	160	15	and	and	CCONJ
american_scientific_journal-756	160	16	(	(	PUNCT
american_scientific_journal-756	160	17	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	X
american_scientific_journal-756	160	18	)	)	PUNCT
american_scientific_journal-756	160	19	be	be	VERB
american_scientific_journal-756	160	20	a	a	DET
american_scientific_journal-756	160	21	soft	soft	ADJ
american_scientific_journal-756	160	22	topological	topological	ADJ
american_scientific_journal-756	160	23	space	space	NOUN
american_scientific_journal-756	160	24	.	.	PUNCT
american_scientific_journal-756	161	1	then	then	ADV
american_scientific_journal-756	161	2	a	a	DET
american_scientific_journal-756	161	3	soft	soft	ADJ
american_scientific_journal-756	161	4	multifunction	multifunction	NOUN
american_scientific_journal-756	161	5	𝐹	𝐹	PROPN
american_scientific_journal-756	161	6	:	:	PUNCT
american_scientific_journal-756	161	7	(	(	PUNCT
american_scientific_journal-756	161	8	𝑋	𝑋	PROPN
american_scientific_journal-756	161	9	,	,	PUNCT
american_scientific_journal-756	161	10	𝜏	𝜏	NOUN
american_scientific_journal-756	161	11	)	)	PUNCT
american_scientific_journal-756	161	12	→	→	X
american_scientific_journal-756	161	13	(	(	PUNCT
american_scientific_journal-756	161	14	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	161	15	)	)	PUNCT
american_scientific_journal-756	161	16	is	be	AUX
american_scientific_journal-756	161	17	said	say	VERB
american_scientific_journal-756	161	18	to	to	PART
american_scientific_journal-756	161	19	be	be	AUX
american_scientific_journal-756	161	20	;	;	PUNCT
american_scientific_journal-756	161	21	(	(	PUNCT
american_scientific_journal-756	161	22	a	a	X
american_scientific_journal-756	161	23	)	)	PUNCT
american_scientific_journal-756	161	24	soft	soft	ADJ
american_scientific_journal-756	161	25	upper	upper	ADJ
american_scientific_journal-756	161	26	continuous	continuous	ADJ
american_scientific_journal-756	161	27	at	at	ADP
american_scientific_journal-756	161	28	a	a	DET
american_scientific_journal-756	161	29	point	point	NOUN
american_scientific_journal-756	161	30	𝑥	𝑥	DET
american_scientific_journal-756	161	31	∈	∈	NOUN
american_scientific_journal-756	161	32	𝑋	𝑋	NOUN
american_scientific_journal-756	161	33	if	if	SCONJ
american_scientific_journal-756	161	34	for	for	ADP
american_scientific_journal-756	161	35	each	each	DET
american_scientific_journal-756	161	36	soft	soft	ADJ
american_scientific_journal-756	161	37	open	open	ADJ
american_scientific_journal-756	161	38	(	(	PUNCT
american_scientific_journal-756	161	39	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	161	40	)	)	PUNCT
american_scientific_journal-756	161	41	such	such	ADJ
american_scientific_journal-756	161	42	that	that	SCONJ
american_scientific_journal-756	161	43	𝐹(𝑥	𝐹(𝑥	X
american_scientific_journal-756	161	44	)	)	PUNCT
american_scientific_journal-756	161	45	⊆	⊆	NUM
american_scientific_journal-756	161	46	�	�	PROPN
american_scientific_journal-756	161	47	(	(	PUNCT
american_scientific_journal-756	161	48	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	161	49	)	)	PUNCT
american_scientific_journal-756	161	50	,	,	PUNCT
american_scientific_journal-756	161	51	there	there	PRON
american_scientific_journal-756	161	52	exists	exist	VERB
american_scientific_journal-756	161	53	a	a	DET
american_scientific_journal-756	161	54	open	open	ADJ
american_scientific_journal-756	161	55	neighborhood	neighborhood	NOUN
american_scientific_journal-756	161	56	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	161	57	)	)	PUNCT
american_scientific_journal-756	161	58	of	of	ADP
american_scientific_journal-756	161	59	𝑥	𝑥	PRON
american_scientific_journal-756	161	60	such	such	ADJ
american_scientific_journal-756	161	61	that	that	SCONJ
american_scientific_journal-756	161	62	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	161	63	)	)	PUNCT
american_scientific_journal-756	161	64	⊆	⊆	NUM
american_scientific_journal-756	161	65	�	�	PROPN
american_scientific_journal-756	161	66	(	(	PUNCT
american_scientific_journal-756	161	67	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	161	68	)	)	PUNCT
american_scientific_journal-756	161	69	for	for	ADP
american_scientific_journal-756	161	70	all	all	DET
american_scientific_journal-756	161	71	𝑧	𝑧	PRON
american_scientific_journal-756	161	72	∈	∈	PROPN
american_scientific_journal-756	161	73	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	161	74	)	)	PUNCT
american_scientific_journal-756	161	75	.	.	PUNCT
american_scientific_journal-756	162	1	101	101	NUM
american_scientific_journal-756	162	2	american	american	PROPN
american_scientific_journal-756	162	3	scientific	scientific	ADJ
american_scientific_journal-756	162	4	research	research	NOUN
american_scientific_journal-756	162	5	journal	journal	NOUN
american_scientific_journal-756	162	6	for	for	ADP
american_scientific_journal-756	162	7	engineering	engineering	NOUN
american_scientific_journal-756	162	8	,	,	PUNCT
american_scientific_journal-756	162	9	technology	technology	NOUN
american_scientific_journal-756	162	10	,	,	PUNCT
american_scientific_journal-756	162	11	and	and	CCONJ
american_scientific_journal-756	162	12	sciences	science	NOUN
american_scientific_journal-756	162	13	(	(	PUNCT
american_scientific_journal-756	162	14	asrjets	asrjet	NOUN
american_scientific_journal-756	162	15	)	)	PUNCT
american_scientific_journal-756	162	16	(	(	PUNCT
american_scientific_journal-756	162	17	2014	2014	NUM
american_scientific_journal-756	162	18	)	)	PUNCT
american_scientific_journal-756	162	19	volume	volume	NOUN
american_scientific_journal-756	162	20	8	8	NUM
american_scientific_journal-756	162	21	,	,	PUNCT
american_scientific_journal-756	162	22	no	no	DET
american_scientific_journal-756	162	23	1	1	NUM
american_scientific_journal-756	162	24	,	,	PUNCT
american_scientific_journal-756	162	25	pp	pp	ADV
american_scientific_journal-756	162	26	96	96	NUM
american_scientific_journal-756	162	27	-	-	SYM
american_scientific_journal-756	162	28	107	107	NUM
american_scientific_journal-756	162	29	(	(	PUNCT
american_scientific_journal-756	162	30	b	b	NOUN
american_scientific_journal-756	162	31	)	)	PUNCT
american_scientific_journal-756	162	32	soft	soft	ADJ
american_scientific_journal-756	162	33	lower	lower	ADV
american_scientific_journal-756	162	34	continuous	continuous	ADJ
american_scientific_journal-756	162	35	at	at	ADP
american_scientific_journal-756	162	36	a	a	DET
american_scientific_journal-756	162	37	point	point	NOUN
american_scientific_journal-756	162	38	𝑥	𝑥	DET
american_scientific_journal-756	162	39	∈	∈	NOUN
american_scientific_journal-756	162	40	𝑋	𝑋	NOUN
american_scientific_journal-756	162	41	if	if	SCONJ
american_scientific_journal-756	162	42	for	for	ADP
american_scientific_journal-756	162	43	each	each	DET
american_scientific_journal-756	162	44	soft	soft	ADJ
american_scientific_journal-756	162	45	open	open	ADJ
american_scientific_journal-756	162	46	(	(	PUNCT
american_scientific_journal-756	162	47	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	162	48	)	)	PUNCT
american_scientific_journal-756	162	49	such	such	ADJ
american_scientific_journal-756	162	50	that	that	SCONJ
american_scientific_journal-756	162	51	𝐹(𝑥	𝐹(𝑥	X
american_scientific_journal-756	162	52	)	)	PUNCT
american_scientific_journal-756	162	53	∩	∩	ADJ
american_scientific_journal-756	162	54	�	�	PROPN
american_scientific_journal-756	162	55	(	(	PUNCT
american_scientific_journal-756	162	56	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	162	57	)	)	PUNCT
american_scientific_journal-756	162	58	≠	≠	PROPN
american_scientific_journal-756	162	59	𝛷	𝛷	PROPN
american_scientific_journal-756	162	60	,	,	PUNCT
american_scientific_journal-756	162	61	there	there	PRON
american_scientific_journal-756	162	62	exists	exist	VERB
american_scientific_journal-756	162	63	an	an	DET
american_scientific_journal-756	162	64	open	open	ADJ
american_scientific_journal-756	162	65	neighborhood	neighborhood	NOUN
american_scientific_journal-756	162	66	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	162	67	)	)	PUNCT
american_scientific_journal-756	162	68	of	of	ADP
american_scientific_journal-756	162	69	𝑥	𝑥	PRON
american_scientific_journal-756	162	70	such	such	ADJ
american_scientific_journal-756	162	71	that	that	PRON
american_scientific_journal-756	162	72	𝐹(𝑧	𝐹(𝑧	NUM
american_scientific_journal-756	162	73	)	)	PUNCT
american_scientific_journal-756	162	74	∩	∩	ADJ
american_scientific_journal-756	162	75	�	�	PROPN
american_scientific_journal-756	162	76	(	(	PUNCT
american_scientific_journal-756	162	77	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	162	78	)	)	PUNCT
american_scientific_journal-756	162	79	≠	≠	PROPN
american_scientific_journal-756	162	80	𝛷	𝛷	NOUN
american_scientific_journal-756	162	81	for	for	ADP
american_scientific_journal-756	162	82	all	all	DET
american_scientific_journal-756	162	83	𝑧	𝑧	PRON
american_scientific_journal-756	162	84	∈	∈	PROPN
american_scientific_journal-756	162	85	𝑃(𝑥	𝑃(𝑥	NOUN
american_scientific_journal-756	162	86	)	)	PUNCT
american_scientific_journal-756	162	87	.	.	PUNCT
american_scientific_journal-756	163	1	(	(	PUNCT
american_scientific_journal-756	163	2	c	c	X
american_scientific_journal-756	163	3	)	)	PUNCT
american_scientific_journal-756	163	4	soft	soft	ADJ
american_scientific_journal-756	163	5	upper	upper	ADJ
american_scientific_journal-756	163	6	(	(	PUNCT
american_scientific_journal-756	163	7	lower	low	ADJ
american_scientific_journal-756	163	8	)	)	PUNCT
american_scientific_journal-756	163	9	continuous	continuous	ADJ
american_scientific_journal-756	163	10	if	if	SCONJ
american_scientific_journal-756	163	11	𝐹	𝐹	PROPN
american_scientific_journal-756	163	12	has	have	VERB
american_scientific_journal-756	163	13	this	this	DET
american_scientific_journal-756	163	14	property	property	NOUN
american_scientific_journal-756	163	15	at	at	ADP
american_scientific_journal-756	163	16	every	every	DET
american_scientific_journal-756	163	17	point	point	NOUN
american_scientific_journal-756	163	18	of	of	ADP
american_scientific_journal-756	163	19	𝑋.	𝑋.	PROPN
american_scientific_journal-756	163	20	proposition	proposition	NOUN
american_scientific_journal-756	163	21	3.10	3.10	NUM
american_scientific_journal-756	163	22	.	.	PUNCT
american_scientific_journal-756	164	1	[	[	X
american_scientific_journal-756	164	2	20	20	NUM
american_scientific_journal-756	164	3	]	]	PUNCT
american_scientific_journal-756	164	4	for	for	ADP
american_scientific_journal-756	164	5	a	a	DET
american_scientific_journal-756	164	6	soft	soft	ADJ
american_scientific_journal-756	164	7	multifunction	multifunction	NOUN
american_scientific_journal-756	164	8	𝐹	𝐹	PROPN
american_scientific_journal-756	164	9	:	:	PUNCT
american_scientific_journal-756	164	10	(	(	PUNCT
american_scientific_journal-756	164	11	𝑋	𝑋	PROPN
american_scientific_journal-756	164	12	,	,	PUNCT
american_scientific_journal-756	164	13	𝜏	𝜏	NOUN
american_scientific_journal-756	164	14	)	)	PUNCT
american_scientific_journal-756	164	15	→	→	X
american_scientific_journal-756	164	16	(	(	PUNCT
american_scientific_journal-756	164	17	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	164	18	)	)	PUNCT
american_scientific_journal-756	164	19	the	the	DET
american_scientific_journal-756	164	20	followings	following	NOUN
american_scientific_journal-756	164	21	are	be	AUX
american_scientific_journal-756	164	22	true	true	ADJ
american_scientific_journal-756	164	23	(	(	PUNCT
american_scientific_journal-756	164	24	a	a	X
american_scientific_journal-756	164	25	)	)	PUNCT
american_scientific_journal-756	164	26	𝐹	𝐹	PROPN
american_scientific_journal-756	164	27	is	be	AUX
american_scientific_journal-756	164	28	soft	soft	ADJ
american_scientific_journal-756	164	29	upper	upper	ADJ
american_scientific_journal-756	164	30	continuous	continuous	ADJ
american_scientific_journal-756	164	31	for	for	ADP
american_scientific_journal-756	164	32	each	each	DET
american_scientific_journal-756	164	33	soft	soft	ADJ
american_scientific_journal-756	164	34	open	open	ADJ
american_scientific_journal-756	164	35	set	set	NOUN
american_scientific_journal-756	164	36	(	(	PUNCT
american_scientific_journal-756	164	37	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	164	38	)	)	PUNCT
american_scientific_journal-756	164	39	over	over	ADP
american_scientific_journal-756	164	40	𝑌	𝑌	PROPN
american_scientific_journal-756	164	41	,	,	PUNCT
american_scientific_journal-756	164	42	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	164	43	)	)	PUNCT
american_scientific_journal-756	164	44	is	be	AUX
american_scientific_journal-756	164	45	open	open	ADJ
american_scientific_journal-756	164	46	in	in	ADP
american_scientific_journal-756	164	47	𝑋.	𝑋.	PROPN
american_scientific_journal-756	164	48	(	(	PUNCT
american_scientific_journal-756	164	49	b	b	X
american_scientific_journal-756	164	50	)	)	PUNCT
american_scientific_journal-756	164	51	𝐹	𝐹	PROPN
american_scientific_journal-756	164	52	is	be	AUX
american_scientific_journal-756	164	53	soft	soft	ADJ
american_scientific_journal-756	164	54	lower	low	ADJ
american_scientific_journal-756	164	55	continuous	continuous	ADJ
american_scientific_journal-756	164	56	for	for	ADP
american_scientific_journal-756	164	57	each	each	DET
american_scientific_journal-756	164	58	soft	soft	ADJ
american_scientific_journal-756	164	59	open	open	ADJ
american_scientific_journal-756	164	60	set	set	NOUN
american_scientific_journal-756	164	61	(	(	PUNCT
american_scientific_journal-756	164	62	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	164	63	)	)	PUNCT
american_scientific_journal-756	164	64	over	over	ADP
american_scientific_journal-756	164	65	𝑌	𝑌	PROPN
american_scientific_journal-756	164	66	,	,	PUNCT
american_scientific_journal-756	164	67	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	PROPN
american_scientific_journal-756	164	68	)	)	PUNCT
american_scientific_journal-756	164	69	is	be	AUX
american_scientific_journal-756	164	70	open	open	ADJ
american_scientific_journal-756	164	71	in	in	ADP
american_scientific_journal-756	164	72	𝑋.	𝑋.	PROPN
american_scientific_journal-756	164	73	remark	remark	NOUN
american_scientific_journal-756	164	74	3.11	3.11	NUM
american_scientific_journal-756	164	75	.	.	PUNCT
american_scientific_journal-756	165	1	let	let	VERB
american_scientific_journal-756	165	2	𝐹	𝐹	PRON
american_scientific_journal-756	165	3	be	be	AUX
american_scientific_journal-756	165	4	soft	soft	ADJ
american_scientific_journal-756	165	5	upper	upper	ADJ
american_scientific_journal-756	165	6	(	(	PUNCT
american_scientific_journal-756	165	7	lower	low	ADJ
american_scientific_journal-756	165	8	)	)	PUNCT
american_scientific_journal-756	165	9	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	165	10	then	then	ADV
american_scientific_journal-756	165	11	𝐹	𝐹	PROPN
american_scientific_journal-756	165	12	is	be	AUX
american_scientific_journal-756	165	13	soft	soft	ADJ
american_scientific_journal-756	165	14	upper	upper	ADJ
american_scientific_journal-756	165	15	(	(	PUNCT
american_scientific_journal-756	165	16	lower	low	ADJ
american_scientific_journal-756	165	17	)	)	PUNCT
american_scientific_journal-756	165	18	continuous	continuous	ADJ
american_scientific_journal-756	165	19	,	,	PUNCT
american_scientific_journal-756	165	20	but	but	CCONJ
american_scientific_journal-756	165	21	this	this	DET
american_scientific_journal-756	165	22	inverse	inverse	NOUN
american_scientific_journal-756	165	23	is	be	AUX
american_scientific_journal-756	165	24	not	not	PART
american_scientific_journal-756	165	25	true	true	ADJ
american_scientific_journal-756	165	26	in	in	ADP
american_scientific_journal-756	165	27	general	general	ADJ
american_scientific_journal-756	165	28	by	by	ADP
american_scientific_journal-756	165	29	which	which	PRON
american_scientific_journal-756	165	30	following	follow	VERB
american_scientific_journal-756	165	31	example	example	NOUN
american_scientific_journal-756	165	32	.	.	PUNCT
american_scientific_journal-756	166	1	example	example	NOUN
american_scientific_journal-756	167	1	3.12	3.12	NUM
american_scientific_journal-756	167	2	.	.	PUNCT
american_scientific_journal-756	168	1	let	let	VERB
american_scientific_journal-756	168	2	𝜏	𝜏	VERB
american_scientific_journal-756	168	3	=	=	SYM
american_scientific_journal-756	168	4	{	{	PUNCT
american_scientific_journal-756	168	5	∅,𝑋	∅,𝑋	PROPN
american_scientific_journal-756	168	6	,	,	PUNCT
american_scientific_journal-756	168	7	{	{	PUNCT
american_scientific_journal-756	168	8	𝑎	𝑎	NOUN
american_scientific_journal-756	168	9	}	}	PUNCT
american_scientific_journal-756	168	10	,	,	PUNCT
american_scientific_journal-756	168	11	{	{	PUNCT
american_scientific_journal-756	168	12	𝑎	𝑎	X
american_scientific_journal-756	168	13	,	,	PUNCT
american_scientific_journal-756	168	14	𝑐	𝑐	NOUN
american_scientific_journal-756	168	15	}	}	PUNCT
american_scientific_journal-756	168	16	}	}	PUNCT
american_scientific_journal-756	168	17	be	be	AUX
american_scientific_journal-756	168	18	a	a	DET
american_scientific_journal-756	168	19	topology	topology	NOUN
american_scientific_journal-756	168	20	on	on	ADP
american_scientific_journal-756	168	21	𝑋	𝑋	PROPN
american_scientific_journal-756	168	22	=	=	PUNCT
american_scientific_journal-756	168	23	{	{	PUNCT
american_scientific_journal-756	168	24	𝑎	𝑎	PROPN
american_scientific_journal-756	168	25	,	,	PUNCT
american_scientific_journal-756	168	26	𝑏	𝑏	NOUN
american_scientific_journal-756	168	27	,	,	PUNCT
american_scientific_journal-756	168	28	𝑐	𝑐	NOUN
american_scientific_journal-756	168	29	}	}	PUNCT
american_scientific_journal-756	168	30	and	and	CCONJ
american_scientific_journal-756	168	31	let	let	VERB
american_scientific_journal-756	168	32	𝜎	𝜎	PRON
american_scientific_journal-756	168	33	=	=	SYM
american_scientific_journal-756	168	34	{	{	PUNCT
american_scientific_journal-756	168	35	𝛷,𝑌	𝛷,𝑌	NOUN
american_scientific_journal-756	168	36	�	�	PROPN
american_scientific_journal-756	168	37	,	,	PUNCT
american_scientific_journal-756	168	38	(	(	PUNCT
american_scientific_journal-756	168	39	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	168	40	)	)	PUNCT
american_scientific_journal-756	168	41	,	,	PUNCT
american_scientific_journal-756	168	42	(	(	PUNCT
american_scientific_journal-756	168	43	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	168	44	)	)	PUNCT
american_scientific_journal-756	168	45	}	}	PUNCT
american_scientific_journal-756	168	46	be	be	AUX
american_scientific_journal-756	168	47	a	a	DET
american_scientific_journal-756	168	48	soft	soft	ADJ
american_scientific_journal-756	168	49	topology	topology	NOUN
american_scientific_journal-756	168	50	over	over	ADP
american_scientific_journal-756	168	51	𝑌	𝑌	PROPN
american_scientific_journal-756	168	52	=	=	PUNCT
american_scientific_journal-756	168	53	{	{	PUNCT
american_scientific_journal-756	168	54	𝑦₁,𝑦₂,𝑦₃	𝑦₁,𝑦₂,𝑦₃	NOUN
american_scientific_journal-756	168	55	}	}	PUNCT
american_scientific_journal-756	168	56	where	where	SCONJ
american_scientific_journal-756	168	57	𝐸	𝐸	PROPN
american_scientific_journal-756	168	58	=	=	SYM
american_scientific_journal-756	168	59	{	{	PUNCT
american_scientific_journal-756	168	60	𝑒₁	𝑒₁	PROPN
american_scientific_journal-756	168	61	,	,	PUNCT
american_scientific_journal-756	168	62	𝑒₂	𝑒₂	NOUN
american_scientific_journal-756	168	63	,	,	PUNCT
american_scientific_journal-756	168	64	𝑒₃	𝑒₃	NOUN
american_scientific_journal-756	168	65	}	}	PUNCT
american_scientific_journal-756	168	66	,	,	PUNCT
american_scientific_journal-756	168	67	𝐺(𝑒₁	𝐺(𝑒₁	NOUN
american_scientific_journal-756	168	68	)	)	PUNCT
american_scientific_journal-756	168	69	=	=	PRON
american_scientific_journal-756	168	70	{	{	PUNCT
american_scientific_journal-756	168	71	𝑦₁	𝑦₁	PROPN
american_scientific_journal-756	168	72	}	}	PUNCT
american_scientific_journal-756	168	73	,	,	PUNCT
american_scientific_journal-756	168	74	𝐺(𝑒₂	𝐺(𝑒₂	PROPN
american_scientific_journal-756	168	75	)	)	PUNCT
american_scientific_journal-756	168	76	=	=	SYM
american_scientific_journal-756	168	77	{	{	PUNCT
american_scientific_journal-756	168	78	𝑦₃	𝑦₃	NOUN
american_scientific_journal-756	168	79	}	}	PUNCT
american_scientific_journal-756	168	80	and	and	CCONJ
american_scientific_journal-756	168	81	𝐺(𝑒₃	𝐺(𝑒₃	NOUN
american_scientific_journal-756	168	82	)	)	PUNCT
american_scientific_journal-756	168	83	=	=	NOUN
american_scientific_journal-756	168	84	∅	∅	NOUN
american_scientific_journal-756	168	85	,	,	PUNCT
american_scientific_journal-756	168	86	𝐻(𝑒₁	𝐻(𝑒₁	PROPN
american_scientific_journal-756	168	87	)	)	PUNCT
american_scientific_journal-756	168	88	=	=	SYM
american_scientific_journal-756	168	89	{	{	PUNCT
american_scientific_journal-756	168	90	𝑦₁,𝑦₂	𝑦₁,𝑦₂	PROPN
american_scientific_journal-756	168	91	}	}	PUNCT
american_scientific_journal-756	168	92	,	,	PUNCT
american_scientific_journal-756	168	93	𝐻(𝑒₂	𝐻(𝑒₂	PROPN
american_scientific_journal-756	168	94	)	)	PUNCT
american_scientific_journal-756	168	95	=	=	SYM
american_scientific_journal-756	168	96	{	{	PUNCT
american_scientific_journal-756	168	97	𝑦₃	𝑦₃	NOUN
american_scientific_journal-756	168	98	}	}	PUNCT
american_scientific_journal-756	168	99	and	and	CCONJ
american_scientific_journal-756	168	100	𝐻(𝑒₃	𝐻(𝑒₃	ADJ
american_scientific_journal-756	168	101	)	)	PUNCT
american_scientific_journal-756	168	102	=	=	SYM
american_scientific_journal-756	168	103	𝑌	𝑌	PROPN
american_scientific_journal-756	168	104	.	.	PUNCT
american_scientific_journal-756	169	1	then	then	ADV
american_scientific_journal-756	169	2	the	the	DET
american_scientific_journal-756	169	3	multifunction	multifunction	NOUN
american_scientific_journal-756	169	4	𝐹	𝐹	PROPN
american_scientific_journal-756	169	5	:	:	PUNCT
american_scientific_journal-756	169	6	(	(	PUNCT
american_scientific_journal-756	169	7	𝑋	𝑋	PROPN
american_scientific_journal-756	169	8	,	,	PUNCT
american_scientific_journal-756	169	9	𝜏	𝜏	NOUN
american_scientific_journal-756	169	10	)	)	PUNCT
american_scientific_journal-756	169	11	→	→	SYM
american_scientific_journal-756	169	12	(	(	PUNCT
american_scientific_journal-756	169	13	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	169	14	)	)	PUNCT
american_scientific_journal-756	169	15	given	give	VERB
american_scientific_journal-756	169	16	by	by	ADP
american_scientific_journal-756	169	17	𝐹(𝑎	𝐹(𝑎	NOUN
american_scientific_journal-756	169	18	)	)	PUNCT
american_scientific_journal-756	169	19	=	=	SYM
american_scientific_journal-756	169	20	(	(	PUNCT
american_scientific_journal-756	169	21	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	169	22	)	)	PUNCT
american_scientific_journal-756	169	23	,	,	PUNCT
american_scientific_journal-756	169	24	𝐹(𝑏	𝐹(𝑏	X
american_scientific_journal-756	169	25	)	)	PUNCT
american_scientific_journal-756	169	26	=	=	SYM
american_scientific_journal-756	169	27	(	(	PUNCT
american_scientific_journal-756	169	28	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	169	29	)	)	PUNCT
american_scientific_journal-756	169	30	and	and	CCONJ
american_scientific_journal-756	169	31	𝐹(𝑐	𝐹(𝑐	NUM
american_scientific_journal-756	169	32	)	)	PUNCT
american_scientific_journal-756	169	33	=	=	SYM
american_scientific_journal-756	169	34	𝑌	𝑌	PROPN
american_scientific_journal-756	169	35	is	be	AUX
american_scientific_journal-756	169	36	soft	soft	ADJ
american_scientific_journal-756	169	37	upper	upper	ADJ
american_scientific_journal-756	169	38	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	169	39	multifunction	multifunction	NOUN
american_scientific_journal-756	169	40	but	but	CCONJ
american_scientific_journal-756	169	41	is	be	AUX
american_scientific_journal-756	169	42	not	not	PART
american_scientific_journal-756	169	43	soft	soft	ADJ
american_scientific_journal-756	169	44	upper	upper	ADJ
american_scientific_journal-756	169	45	continuous	continuous	ADJ
american_scientific_journal-756	169	46	multifunction	multifunction	NOUN
american_scientific_journal-756	169	47	.	.	PUNCT
american_scientific_journal-756	170	1	because	because	SCONJ
american_scientific_journal-756	170	2	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	170	3	)	)	PUNCT
american_scientific_journal-756	170	4	=	=	SYM
american_scientific_journal-756	170	5	{	{	PUNCT
american_scientific_journal-756	170	6	𝑎	𝑎	NOUN
american_scientific_journal-756	170	7	}	}	PUNCT
american_scientific_journal-756	170	8	and	and	CCONJ
american_scientific_journal-756	170	9	𝐹⁺(𝐻,𝐸	𝐹⁺(𝐻,𝐸	NUM
american_scientific_journal-756	170	10	)	)	PUNCT
american_scientific_journal-756	170	11	=	=	NUM
american_scientific_journal-756	170	12	{	{	PUNCT
american_scientific_journal-756	170	13	𝑎	𝑎	NOUN
american_scientific_journal-756	170	14	,	,	PUNCT
american_scientific_journal-756	170	15	𝑏	𝑏	PRON
american_scientific_journal-756	170	16	}	}	PUNCT
american_scientific_journal-756	170	17	are	be	AUX
american_scientific_journal-756	170	18	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	170	19	sets	set	NOUN
american_scientific_journal-756	170	20	but	but	CCONJ
american_scientific_journal-756	170	21	{	{	PUNCT
american_scientific_journal-756	170	22	𝑎	𝑎	NOUN
american_scientific_journal-756	170	23	,	,	PUNCT
american_scientific_journal-756	170	24	𝑏	𝑏	NOUN
american_scientific_journal-756	170	25	}	}	PUNCT
american_scientific_journal-756	170	26	is	be	AUX
american_scientific_journal-756	170	27	not	not	PART
american_scientific_journal-756	170	28	open	open	ADJ
american_scientific_journal-756	170	29	sets	set	NOUN
american_scientific_journal-756	170	30	in	in	ADP
american_scientific_journal-756	170	31	𝑋.	𝑋.	PROPN
american_scientific_journal-756	170	32	theorem	theorem	VERB
american_scientific_journal-756	170	33	3.13	3.13	NUM
american_scientific_journal-756	170	34	.	.	PUNCT
american_scientific_journal-756	171	1	the	the	DET
american_scientific_journal-756	171	2	followings	following	NOUN
american_scientific_journal-756	171	3	are	be	AUX
american_scientific_journal-756	171	4	equivalent	equivalent	ADJ
american_scientific_journal-756	171	5	for	for	ADP
american_scientific_journal-756	171	6	a	a	DET
american_scientific_journal-756	171	7	soft	soft	ADJ
american_scientific_journal-756	171	8	multifunction	multifunction	NOUN
american_scientific_journal-756	171	9	𝐹	𝐹	PROPN
american_scientific_journal-756	171	10	:	:	PUNCT
american_scientific_journal-756	171	11	(	(	PUNCT
american_scientific_journal-756	171	12	𝑋	𝑋	PROPN
american_scientific_journal-756	171	13	,	,	PUNCT
american_scientific_journal-756	171	14	𝜏	𝜏	NOUN
american_scientific_journal-756	171	15	)	)	PUNCT
american_scientific_journal-756	171	16	→	→	X
american_scientific_journal-756	171	17	(	(	PUNCT
american_scientific_journal-756	171	18	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	X
american_scientific_journal-756	171	19	):	):	PUNCT
american_scientific_journal-756	171	20	(	(	PUNCT
american_scientific_journal-756	171	21	a	a	X
american_scientific_journal-756	171	22	)	)	PUNCT
american_scientific_journal-756	171	23	𝐹	𝐹	PROPN
american_scientific_journal-756	171	24	is	be	AUX
american_scientific_journal-756	171	25	soft	soft	ADJ
american_scientific_journal-756	171	26	upper	upper	ADJ
american_scientific_journal-756	171	27	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	171	28	.	.	PUNCT
american_scientific_journal-756	172	1	(	(	PUNCT
american_scientific_journal-756	172	2	b	b	X
american_scientific_journal-756	172	3	)	)	PUNCT
american_scientific_journal-756	172	4	for	for	ADP
american_scientific_journal-756	172	5	each	each	DET
american_scientific_journal-756	172	6	soft	soft	ADJ
american_scientific_journal-756	172	7	closed	closed	ADJ
american_scientific_journal-756	172	8	set	set	NOUN
american_scientific_journal-756	172	9	(	(	PUNCT
american_scientific_journal-756	172	10	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	172	11	)	)	PUNCT
american_scientific_journal-756	172	12	over	over	ADP
american_scientific_journal-756	172	13	𝑌	𝑌	PROPN
american_scientific_journal-756	172	14	,	,	PUNCT
american_scientific_journal-756	172	15	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	PROPN
american_scientific_journal-756	172	16	)	)	PUNCT
american_scientific_journal-756	172	17	is	be	AUX
american_scientific_journal-756	172	18	𝛼-closed	𝛼-close	VERB
american_scientific_journal-756	172	19	in	in	ADP
american_scientific_journal-756	172	20	𝑋.	𝑋.	PROPN
american_scientific_journal-756	172	21	(	(	PUNCT
american_scientific_journal-756	172	22	c	c	NOUN
american_scientific_journal-756	172	23	)	)	PUNCT
american_scientific_journal-756	172	24	for	for	ADP
american_scientific_journal-756	172	25	each	each	DET
american_scientific_journal-756	172	26	soft	soft	ADJ
american_scientific_journal-756	172	27	set	set	NOUN
american_scientific_journal-756	172	28	(	(	PUNCT
american_scientific_journal-756	172	29	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	172	30	)	)	PUNCT
american_scientific_journal-756	172	31	over	over	ADP
american_scientific_journal-756	172	32	𝑌	𝑌	PROPN
american_scientific_journal-756	172	33	,	,	PUNCT
american_scientific_journal-756	172	34	𝛼𝑐𝑙(𝐹⁻(𝐺,𝐸	𝛼𝑐𝑙(𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	172	35	)	)	PUNCT
american_scientific_journal-756	172	36	)	)	PUNCT
american_scientific_journal-756	172	37	⊆	⊆	NUM
american_scientific_journal-756	172	38	𝐹⁻(𝑐𝑙(𝐺,𝐸	𝐹⁻(𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	172	39	)	)	PUNCT
american_scientific_journal-756	172	40	)	)	PUNCT
american_scientific_journal-756	172	41	.	.	PUNCT
american_scientific_journal-756	173	1	(	(	PUNCT
american_scientific_journal-756	173	2	d	d	X
american_scientific_journal-756	173	3	)	)	PUNCT
american_scientific_journal-756	173	4	for	for	ADP
american_scientific_journal-756	173	5	each	each	DET
american_scientific_journal-756	173	6	soft	soft	ADJ
american_scientific_journal-756	173	7	set	set	NOUN
american_scientific_journal-756	173	8	(	(	PUNCT
american_scientific_journal-756	173	9	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	173	10	)	)	PUNCT
american_scientific_journal-756	173	11	over	over	ADP
american_scientific_journal-756	173	12	𝑌	𝑌	PROPN
american_scientific_journal-756	173	13	,	,	PUNCT
american_scientific_journal-756	173	14	𝐹⁺(𝐼𝑛𝑡(𝐺,𝐸	𝐹⁺(𝐼𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	173	15	)	)	PUNCT
american_scientific_journal-756	173	16	)	)	PUNCT
american_scientific_journal-756	173	17	⊆	⊆	NUM
american_scientific_journal-756	173	18	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	173	19	)	)	PUNCT
american_scientific_journal-756	173	20	)	)	PUNCT
american_scientific_journal-756	173	21	.	.	PUNCT
american_scientific_journal-756	174	1	proof	proof	NOUN
american_scientific_journal-756	174	2	.	.	PUNCT
american_scientific_journal-756	175	1	(	(	PUNCT
american_scientific_journal-756	175	2	a)⇒(b	a)⇒(b	NOUN
american_scientific_journal-756	175	3	)	)	PUNCT
american_scientific_journal-756	175	4	let	let	VERB
american_scientific_journal-756	175	5	(	(	PUNCT
american_scientific_journal-756	175	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	175	7	)	)	PUNCT
american_scientific_journal-756	175	8	be	be	VERB
american_scientific_journal-756	175	9	any	any	DET
american_scientific_journal-756	175	10	closed	closed	ADJ
american_scientific_journal-756	175	11	soft	soft	ADJ
american_scientific_journal-756	175	12	over	over	ADP
american_scientific_journal-756	175	13	𝑌.	𝑌.	PROPN
american_scientific_journal-756	175	14	then	then	ADV
american_scientific_journal-756	175	15	(	(	PUNCT
american_scientific_journal-756	175	16	𝐺,𝐸)𝑐	𝐺,𝐸)𝑐	ADV
american_scientific_journal-756	175	17	is	be	AUX
american_scientific_journal-756	175	18	soft	soft	ADJ
american_scientific_journal-756	175	19	open	open	ADJ
american_scientific_journal-756	175	20	and	and	CCONJ
american_scientific_journal-756	175	21	by	by	ADP
american_scientific_journal-756	175	22	proposition	proposition	NOUN
american_scientific_journal-756	175	23	1	1	NUM
american_scientific_journal-756	175	24	implies	imply	VERB
american_scientific_journal-756	175	25	𝐹⁺((𝐺,𝐸)𝑐	𝐹⁺((𝐺,𝐸)𝑐	ADJ
american_scientific_journal-756	175	26	)	)	PUNCT
american_scientific_journal-756	176	1	=	=	SYM
american_scientific_journal-756	176	2	𝑋	𝑋	PROPN
american_scientific_journal-756	176	3	−	−	PROPN
american_scientific_journal-756	176	4	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	176	5	)	)	PUNCT
american_scientific_journal-756	176	6	is	be	AUX
american_scientific_journal-756	176	7	𝛼-closed	𝛼-close	VERB
american_scientific_journal-756	176	8	set	set	VERB
american_scientific_journal-756	176	9	.	.	PUNCT
american_scientific_journal-756	177	1	so	so	ADV
american_scientific_journal-756	177	2	,	,	PUNCT
american_scientific_journal-756	177	3	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	PROPN
american_scientific_journal-756	177	4	)	)	PUNCT
american_scientific_journal-756	177	5	is	be	AUX
american_scientific_journal-756	177	6	𝛼-closed	𝛼-close	VERB
american_scientific_journal-756	177	7	in	in	ADP
american_scientific_journal-756	177	8	𝑋.	𝑋.	PROPN
american_scientific_journal-756	177	9	(	(	PUNCT
american_scientific_journal-756	177	10	b)⇒(c	b)⇒(c	NOUN
american_scientific_journal-756	177	11	)	)	PUNCT
american_scientific_journal-756	177	12	let	let	VERB
american_scientific_journal-756	177	13	(	(	PUNCT
american_scientific_journal-756	177	14	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	177	15	)	)	PUNCT
american_scientific_journal-756	177	16	be	be	AUX
american_scientific_journal-756	177	17	any	any	DET
american_scientific_journal-756	177	18	soft	soft	ADJ
american_scientific_journal-756	177	19	set	set	NOUN
american_scientific_journal-756	177	20	over	over	ADP
american_scientific_journal-756	177	21	𝑌.	𝑌.	PROPN
american_scientific_journal-756	177	22	then	then	ADV
american_scientific_journal-756	177	23	𝑐𝑙(𝐺,𝐸	𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	177	24	)	)	PUNCT
american_scientific_journal-756	177	25	is	be	AUX
american_scientific_journal-756	177	26	soft	soft	ADJ
american_scientific_journal-756	177	27	closed	closed	ADJ
american_scientific_journal-756	177	28	set	set	NOUN
american_scientific_journal-756	177	29	.	.	PUNCT
american_scientific_journal-756	178	1	by	by	ADP
american_scientific_journal-756	178	2	(	(	PUNCT
american_scientific_journal-756	178	3	b	b	NOUN
american_scientific_journal-756	178	4	)	)	PUNCT
american_scientific_journal-756	178	5	,	,	PUNCT
american_scientific_journal-756	178	6	𝐹⁻(𝑐𝑙(𝐺,𝐸	𝐹⁻(𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	178	7	)	)	PUNCT
american_scientific_journal-756	178	8	)	)	PUNCT
american_scientific_journal-756	178	9	is	be	AUX
american_scientific_journal-756	178	10	𝛼-closed	𝛼-close	VERB
american_scientific_journal-756	178	11	in	in	ADP
american_scientific_journal-756	178	12	𝑋.	𝑋.	PROPN
american_scientific_journal-756	178	13	hence	hence	ADV
american_scientific_journal-756	178	14	𝛼𝑐𝑙(𝐹⁻(𝐺,𝐸	𝛼𝑐𝑙(𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	178	15	)	)	PUNCT
american_scientific_journal-756	178	16	)	)	PUNCT
american_scientific_journal-756	179	1	⊆	⊆	NUM
american_scientific_journal-756	179	2	𝛼𝑐𝑙(𝐹⁻(𝑐𝑙(𝐺,𝐸	𝛼𝑐𝑙(𝐹⁻(𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	179	3	)	)	PUNCT
american_scientific_journal-756	179	4	)	)	PUNCT
american_scientific_journal-756	179	5	)	)	PUNCT
american_scientific_journal-756	180	1	=	=	SYM
american_scientific_journal-756	180	2	𝐹⁻(𝑐𝑙(𝐺,𝐸	𝐹⁻(𝑐𝑙(𝐺,𝐸	X
american_scientific_journal-756	180	3	)	)	PUNCT
american_scientific_journal-756	180	4	)	)	PUNCT
american_scientific_journal-756	180	5	.	.	PUNCT
american_scientific_journal-756	181	1	(	(	PUNCT
american_scientific_journal-756	181	2	c)⇒(d	c)⇒(d	NOUN
american_scientific_journal-756	181	3	)	)	PUNCT
american_scientific_journal-756	181	4	let	let	AUX
american_scientific_journal-756	181	5	(	(	PUNCT
american_scientific_journal-756	181	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	181	7	)	)	PUNCT
american_scientific_journal-756	181	8	be	be	VERB
american_scientific_journal-756	181	9	any	any	DET
american_scientific_journal-756	181	10	soft	soft	ADJ
american_scientific_journal-756	181	11	set	set	NOUN
american_scientific_journal-756	181	12	over	over	ADP
american_scientific_journal-756	181	13	𝑌	𝑌	PROPN
american_scientific_journal-756	181	14	.	.	PUNCT
american_scientific_journal-756	182	1	then	then	ADV
american_scientific_journal-756	182	2	𝐹⁺(𝐼𝑛𝑡(𝐺,𝐸	𝐹⁺(𝐼𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	182	3	)	)	PUNCT
american_scientific_journal-756	182	4	)	)	PUNCT
american_scientific_journal-756	183	1	=	=	PUNCT
american_scientific_journal-756	184	1	𝐹⁺(𝑋	𝐹⁺(𝑋	NUM
american_scientific_journal-756	184	2	−	−	PROPN
american_scientific_journal-756	184	3	(	(	PUNCT
american_scientific_journal-756	184	4	𝑋	𝑋	NOUN
american_scientific_journal-756	184	5	−	−	PROPN
american_scientific_journal-756	184	6	𝐼𝑛𝑡(𝐺,𝐸	𝐼𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	184	7	)	)	PUNCT
american_scientific_journal-756	184	8	)	)	PUNCT
american_scientific_journal-756	184	9	)	)	PUNCT
american_scientific_journal-756	185	1	=	=	PUNCT
american_scientific_journal-756	185	2	𝑋	𝑋	PROPN
american_scientific_journal-756	185	3	−	−	PROPN
american_scientific_journal-756	185	4	𝐹⁻(𝑋	𝐹⁻(𝑋	NOUN
american_scientific_journal-756	185	5	−	−	PROPN
american_scientific_journal-756	185	6	𝐼𝑛𝑡(𝐺,𝐸	𝐼𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	185	7	)	)	PUNCT
american_scientific_journal-756	185	8	)	)	PUNCT
american_scientific_journal-756	186	1	=	=	SYM
american_scientific_journal-756	186	2	𝑋	𝑋	PROPN
american_scientific_journal-756	186	3	−	−	PROPN
american_scientific_journal-756	186	4	𝐹⁻(𝑐𝑙(𝑋	𝐹⁻(𝑐𝑙(𝑋	NOUN
american_scientific_journal-756	187	1	−	−	PROPN
american_scientific_journal-756	187	2	(	(	PUNCT
american_scientific_journal-756	187	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	187	4	)	)	PUNCT
american_scientific_journal-756	187	5	)	)	PUNCT
american_scientific_journal-756	187	6	)	)	PUNCT
american_scientific_journal-756	187	7	.	.	PUNCT
american_scientific_journal-756	188	1	by	by	ADP
american_scientific_journal-756	188	2	(	(	PUNCT
american_scientific_journal-756	188	3	c	c	NOUN
american_scientific_journal-756	188	4	)	)	PUNCT
american_scientific_journal-756	188	5	,	,	PUNCT
american_scientific_journal-756	188	6	we	we	PRON
american_scientific_journal-756	188	7	have	have	VERB
american_scientific_journal-756	188	8	𝛼𝑐𝑙(𝐹⁻(𝑋	𝛼𝑐𝑙(𝐹⁻(𝑋	NUM
american_scientific_journal-756	188	9	−	−	PROPN
american_scientific_journal-756	188	10	(	(	PUNCT
american_scientific_journal-756	188	11	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	188	12	)	)	PUNCT
american_scientific_journal-756	188	13	)	)	PUNCT
american_scientific_journal-756	188	14	)	)	PUNCT
american_scientific_journal-756	188	15	)	)	PUNCT
american_scientific_journal-756	189	1	⊂	⊂	PROPN
american_scientific_journal-756	189	2	𝐹⁻(𝑐𝑙(𝑋	𝐹⁻(𝑐𝑙(𝑋	X
american_scientific_journal-756	190	1	−	−	PROPN
american_scientific_journal-756	190	2	(	(	PUNCT
american_scientific_journal-756	190	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	190	4	)	)	PUNCT
american_scientific_journal-756	190	5	)	)	PUNCT
american_scientific_journal-756	190	6	)	)	PUNCT
american_scientific_journal-756	191	1	then	then	ADV
american_scientific_journal-756	191	2	𝑋	𝑋	PROPN
american_scientific_journal-756	191	3	−	−	PROPN
american_scientific_journal-756	191	4	(	(	PUNCT
american_scientific_journal-756	191	5	𝐹⁻(𝑐𝑙(𝑋	𝐹⁻(𝑐𝑙(𝑋	NUM
american_scientific_journal-756	191	6	−	−	PROPN
american_scientific_journal-756	191	7	(	(	PUNCT
american_scientific_journal-756	191	8	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	191	9	)	)	PUNCT
american_scientific_journal-756	191	10	)	)	PUNCT
american_scientific_journal-756	191	11	)	)	PUNCT
american_scientific_journal-756	191	12	)	)	PUNCT
american_scientific_journal-756	192	1	⊂	⊂	PROPN
american_scientific_journal-756	193	1	𝑋	𝑋	NOUN
american_scientific_journal-756	193	2	−	−	PROPN
american_scientific_journal-756	193	3	𝛼𝑐𝑙(𝐹⁻(𝑋	𝛼𝑐𝑙(𝐹⁻(𝑋	NUM
american_scientific_journal-756	193	4	−	−	PROPN
american_scientific_journal-756	194	1	(	(	PUNCT
american_scientific_journal-756	194	2	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	194	3	)	)	PUNCT
american_scientific_journal-756	194	4	)	)	PUNCT
american_scientific_journal-756	194	5	)	)	PUNCT
american_scientific_journal-756	194	6	)	)	PUNCT
american_scientific_journal-756	194	7	.	.	PUNCT
american_scientific_journal-756	195	1	𝑋	𝑋	NOUN
american_scientific_journal-756	195	2	−	−	PROPN
american_scientific_journal-756	195	3	𝛼𝑐𝑙(𝐹⁻(𝑋	𝛼𝑐𝑙(𝐹⁻(𝑋	NUM
american_scientific_journal-756	195	4	−	−	PROPN
american_scientific_journal-756	196	1	(	(	PUNCT
american_scientific_journal-756	196	2	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	196	3	)	)	PUNCT
american_scientific_journal-756	196	4	)	)	PUNCT
american_scientific_journal-756	196	5	)	)	PUNCT
american_scientific_journal-756	196	6	)	)	PUNCT
american_scientific_journal-756	197	1	⊂	⊂	PROPN
american_scientific_journal-756	197	2	𝛼𝐼𝑛𝑡(𝑋	𝛼𝐼𝑛𝑡(𝑋	VERB
american_scientific_journal-756	197	3	−	−	PROPN
american_scientific_journal-756	197	4	𝐹⁻(𝑋	𝐹⁻(𝑋	PROPN
american_scientific_journal-756	197	5	−	−	PROPN
american_scientific_journal-756	197	6	(	(	PUNCT
american_scientific_journal-756	197	7	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	197	8	)	)	PUNCT
american_scientific_journal-756	197	9	)	)	PUNCT
american_scientific_journal-756	197	10	)	)	PUNCT
american_scientific_journal-756	197	11	)	)	PUNCT
american_scientific_journal-756	198	1	=	=	PRON
american_scientific_journal-756	198	2	𝛼𝐼𝑛𝑡(𝐹⁺(𝑋	𝛼𝐼𝑛𝑡(𝐹⁺(𝑋	VERB
american_scientific_journal-756	198	3	−	−	PROPN
american_scientific_journal-756	198	4	(	(	PUNCT
american_scientific_journal-756	198	5	𝑋	𝑋	PROPN
american_scientific_journal-756	198	6	−	−	PROPN
american_scientific_journal-756	198	7	(	(	PUNCT
american_scientific_journal-756	198	8	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	198	9	)	)	PUNCT
american_scientific_journal-756	198	10	)	)	PUNCT
american_scientific_journal-756	198	11	)	)	PUNCT
american_scientific_journal-756	198	12	)	)	PUNCT
american_scientific_journal-756	199	1	=	=	SYM
american_scientific_journal-756	199	2	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	199	3	)	)	PUNCT
american_scientific_journal-756	199	4	)	)	PUNCT
american_scientific_journal-756	199	5	.	.	PUNCT
american_scientific_journal-756	200	1	(	(	PUNCT
american_scientific_journal-756	200	2	d)⇒(a	d)⇒(a	NOUN
american_scientific_journal-756	200	3	)	)	PUNCT
american_scientific_journal-756	200	4	let	let	VERB
american_scientific_journal-756	200	5	(	(	PUNCT
american_scientific_journal-756	200	6	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	200	7	)	)	PUNCT
american_scientific_journal-756	200	8	be	be	VERB
american_scientific_journal-756	200	9	any	any	DET
american_scientific_journal-756	200	10	soft	soft	ADJ
american_scientific_journal-756	200	11	set	set	NOUN
american_scientific_journal-756	200	12	over	over	ADP
american_scientific_journal-756	200	13	𝑌	𝑌	PROPN
american_scientific_journal-756	200	14	.	.	PUNCT
american_scientific_journal-756	201	1	by	by	ADP
american_scientific_journal-756	201	2	(	(	PUNCT
american_scientific_journal-756	201	3	d	d	NOUN
american_scientific_journal-756	201	4	)	)	PUNCT
american_scientific_journal-756	201	5	,	,	PUNCT
american_scientific_journal-756	201	6	102	102	NUM
american_scientific_journal-756	201	7	american	american	ADJ
american_scientific_journal-756	201	8	scientific	scientific	ADJ
american_scientific_journal-756	201	9	research	research	NOUN
american_scientific_journal-756	201	10	journal	journal	NOUN
american_scientific_journal-756	201	11	for	for	ADP
american_scientific_journal-756	201	12	engineering	engineering	NOUN
american_scientific_journal-756	201	13	,	,	PUNCT
american_scientific_journal-756	201	14	technology	technology	NOUN
american_scientific_journal-756	201	15	,	,	PUNCT
american_scientific_journal-756	201	16	and	and	CCONJ
american_scientific_journal-756	201	17	sciences	science	NOUN
american_scientific_journal-756	201	18	(	(	PUNCT
american_scientific_journal-756	201	19	asrjets	asrjet	NOUN
american_scientific_journal-756	201	20	)	)	PUNCT
american_scientific_journal-756	201	21	(	(	PUNCT
american_scientific_journal-756	201	22	2014	2014	NUM
american_scientific_journal-756	201	23	)	)	PUNCT
american_scientific_journal-756	201	24	volume	volume	NOUN
american_scientific_journal-756	201	25	8	8	NUM
american_scientific_journal-756	201	26	,	,	PUNCT
american_scientific_journal-756	201	27	no	no	DET
american_scientific_journal-756	201	28	1	1	NUM
american_scientific_journal-756	201	29	,	,	PUNCT
american_scientific_journal-756	201	30	pp	pp	ADV
american_scientific_journal-756	201	31	96	96	NUM
american_scientific_journal-756	201	32	-	-	SYM
american_scientific_journal-756	201	33	107	107	NUM
american_scientific_journal-756	201	34	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	201	35	)	)	PUNCT
american_scientific_journal-756	201	36	)	)	PUNCT
american_scientific_journal-756	201	37	⊆	⊆	NUM
american_scientific_journal-756	201	38	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	201	39	)	)	PUNCT
american_scientific_journal-756	201	40	=	=	SYM
american_scientific_journal-756	201	41	𝐹⁺(𝐼𝑛𝑡(𝐺,𝐸	𝐹⁺(𝐼𝑛𝑡(𝐺,𝐸	X
american_scientific_journal-756	201	42	)	)	PUNCT
american_scientific_journal-756	201	43	)	)	PUNCT
american_scientific_journal-756	201	44	⊆	⊆	NUM
american_scientific_journal-756	201	45	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	𝛼𝐼𝑛𝑡(𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	201	46	)	)	PUNCT
american_scientific_journal-756	201	47	)	)	PUNCT
american_scientific_journal-756	201	48	.	.	PUNCT
american_scientific_journal-756	202	1	this	this	PRON
american_scientific_journal-756	202	2	shows	show	VERB
american_scientific_journal-756	202	3	that	that	SCONJ
american_scientific_journal-756	202	4	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	202	5	)	)	PUNCT
american_scientific_journal-756	202	6	is	be	AUX
american_scientific_journal-756	202	7	open	open	ADJ
american_scientific_journal-756	202	8	set	set	NOUN
american_scientific_journal-756	202	9	.	.	PUNCT
american_scientific_journal-756	203	1	then	then	ADV
american_scientific_journal-756	203	2	by	by	ADP
american_scientific_journal-756	203	3	proposition	proposition	NOUN
american_scientific_journal-756	203	4	3.7	3.7	NUM
american_scientific_journal-756	203	5	𝐹	𝐹	PROPN
american_scientific_journal-756	203	6	is	be	AUX
american_scientific_journal-756	203	7	soft	soft	ADJ
american_scientific_journal-756	203	8	upper	upper	ADJ
american_scientific_journal-756	203	9	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	203	10	.	.	PUNCT
american_scientific_journal-756	204	1	theorem	theorem	VERB
american_scientific_journal-756	204	2	3.14	3.14	NUM
american_scientific_journal-756	204	3	.	.	PUNCT
american_scientific_journal-756	205	1	the	the	DET
american_scientific_journal-756	205	2	following	follow	VERB
american_scientific_journal-756	205	3	are	be	AUX
american_scientific_journal-756	205	4	equivalent	equivalent	ADJ
american_scientific_journal-756	205	5	for	for	ADP
american_scientific_journal-756	205	6	a	a	DET
american_scientific_journal-756	205	7	soft	soft	ADJ
american_scientific_journal-756	205	8	multifunction	multifunction	NOUN
american_scientific_journal-756	205	9	𝐹	𝐹	PROPN
american_scientific_journal-756	205	10	:	:	PUNCT
american_scientific_journal-756	205	11	(	(	PUNCT
american_scientific_journal-756	205	12	𝑋	𝑋	PROPN
american_scientific_journal-756	205	13	,	,	PUNCT
american_scientific_journal-756	205	14	𝜏	𝜏	NOUN
american_scientific_journal-756	205	15	)	)	PUNCT
american_scientific_journal-756	205	16	→	→	X
american_scientific_journal-756	205	17	(	(	PUNCT
american_scientific_journal-756	205	18	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	X
american_scientific_journal-756	205	19	):	):	PUNCT
american_scientific_journal-756	205	20	(	(	PUNCT
american_scientific_journal-756	205	21	a	a	X
american_scientific_journal-756	205	22	)	)	PUNCT
american_scientific_journal-756	205	23	𝐹	𝐹	PROPN
american_scientific_journal-756	205	24	is	be	AUX
american_scientific_journal-756	205	25	soft	soft	ADJ
american_scientific_journal-756	205	26	lower	low	ADJ
american_scientific_journal-756	205	27	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	205	28	.	.	PUNCT
american_scientific_journal-756	206	1	(	(	PUNCT
american_scientific_journal-756	206	2	b	b	X
american_scientific_journal-756	206	3	)	)	PUNCT
american_scientific_journal-756	206	4	for	for	ADP
american_scientific_journal-756	206	5	each	each	DET
american_scientific_journal-756	206	6	soft	soft	ADJ
american_scientific_journal-756	206	7	closed	closed	ADJ
american_scientific_journal-756	206	8	set	set	NOUN
american_scientific_journal-756	206	9	(	(	PUNCT
american_scientific_journal-756	206	10	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	206	11	)	)	PUNCT
american_scientific_journal-756	206	12	over	over	ADP
american_scientific_journal-756	206	13	𝑌	𝑌	PROPN
american_scientific_journal-756	206	14	,	,	PUNCT
american_scientific_journal-756	206	15	𝐹⁺(𝐺,𝐸	𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	206	16	)	)	PUNCT
american_scientific_journal-756	206	17	is	be	AUX
american_scientific_journal-756	206	18	𝛼-closed	𝛼-close	VERB
american_scientific_journal-756	206	19	in	in	ADP
american_scientific_journal-756	206	20	𝑋.	𝑋.	PROPN
american_scientific_journal-756	206	21	(	(	PUNCT
american_scientific_journal-756	206	22	c	c	NOUN
american_scientific_journal-756	206	23	)	)	PUNCT
american_scientific_journal-756	206	24	for	for	ADP
american_scientific_journal-756	206	25	each	each	DET
american_scientific_journal-756	206	26	soft	soft	ADJ
american_scientific_journal-756	206	27	set	set	NOUN
american_scientific_journal-756	206	28	(	(	PUNCT
american_scientific_journal-756	206	29	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	206	30	)	)	PUNCT
american_scientific_journal-756	206	31	over	over	ADP
american_scientific_journal-756	206	32	𝑌	𝑌	PROPN
american_scientific_journal-756	206	33	,	,	PUNCT
american_scientific_journal-756	206	34	𝛼𝑐𝑙(𝐹⁺(𝐺,𝐸	𝛼𝑐𝑙(𝐹⁺(𝐺,𝐸	NOUN
american_scientific_journal-756	206	35	)	)	PUNCT
american_scientific_journal-756	206	36	)	)	PUNCT
american_scientific_journal-756	207	1	⊆	⊆	NUM
american_scientific_journal-756	207	2	𝐹⁺(𝑐𝑙(𝐺,𝐸	𝐹⁺(𝑐𝑙(𝐺,𝐸	NOUN
american_scientific_journal-756	207	3	)	)	PUNCT
american_scientific_journal-756	207	4	)	)	PUNCT
american_scientific_journal-756	207	5	.	.	PUNCT
american_scientific_journal-756	208	1	(	(	PUNCT
american_scientific_journal-756	208	2	d	d	X
american_scientific_journal-756	208	3	)	)	PUNCT
american_scientific_journal-756	208	4	for	for	ADP
american_scientific_journal-756	208	5	each	each	DET
american_scientific_journal-756	208	6	soft	soft	ADJ
american_scientific_journal-756	208	7	set	set	NOUN
american_scientific_journal-756	208	8	(	(	PUNCT
american_scientific_journal-756	208	9	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	208	10	)	)	PUNCT
american_scientific_journal-756	208	11	over	over	ADP
american_scientific_journal-756	208	12	𝑌	𝑌	PROPN
american_scientific_journal-756	208	13	,	,	PUNCT
american_scientific_journal-756	208	14	𝐹⁻(𝐼𝑛𝑡(𝐺,𝐸	𝐹⁻(𝐼𝑛𝑡(𝐺,𝐸	NOUN
american_scientific_journal-756	208	15	)	)	PUNCT
american_scientific_journal-756	208	16	)	)	PUNCT
american_scientific_journal-756	208	17	⊆	⊆	NUM
american_scientific_journal-756	208	18	𝛼𝑖𝑛𝑡(𝐹⁻(𝐺,𝐸	𝛼𝑖𝑛𝑡(𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	208	19	)	)	PUNCT
american_scientific_journal-756	208	20	)	)	PUNCT
american_scientific_journal-756	208	21	.	.	PUNCT
american_scientific_journal-756	209	1	proof	proof	NOUN
american_scientific_journal-756	209	2	.	.	PUNCT
american_scientific_journal-756	210	1	it	it	PRON
american_scientific_journal-756	210	2	is	be	AUX
american_scientific_journal-756	210	3	similar	similar	ADJ
american_scientific_journal-756	210	4	to	to	ADP
american_scientific_journal-756	210	5	that	that	PRON
american_scientific_journal-756	210	6	of	of	ADP
american_scientific_journal-756	210	7	theorem	theorem	NOUN
american_scientific_journal-756	210	8	3.13	3.13	NUM
american_scientific_journal-756	210	9	.	.	PUNCT
american_scientific_journal-756	211	1	definition	definition	NOUN
american_scientific_journal-756	211	2	3.15	3.15	NUM
american_scientific_journal-756	211	3	.	.	PUNCT
american_scientific_journal-756	212	1	[	[	X
american_scientific_journal-756	212	2	20	20	NUM
american_scientific_journal-756	212	3	]	]	PUNCT
american_scientific_journal-756	212	4	for	for	ADP
american_scientific_journal-756	212	5	a	a	DET
american_scientific_journal-756	212	6	soft	soft	ADJ
american_scientific_journal-756	212	7	multifunction	multifunction	NOUN
american_scientific_journal-756	212	8	𝐹	𝐹	PROPN
american_scientific_journal-756	212	9	:	:	PUNCT
american_scientific_journal-756	212	10	(	(	PUNCT
american_scientific_journal-756	212	11	𝑋	𝑋	PROPN
american_scientific_journal-756	212	12	,	,	PUNCT
american_scientific_journal-756	212	13	𝜏	𝜏	NOUN
american_scientific_journal-756	212	14	)	)	PUNCT
american_scientific_journal-756	212	15	→	→	SYM
american_scientific_journal-756	212	16	(	(	PUNCT
american_scientific_journal-756	212	17	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	212	18	)	)	PUNCT
american_scientific_journal-756	212	19	,	,	PUNCT
american_scientific_journal-756	212	20	the	the	DET
american_scientific_journal-756	212	21	graph	graph	NOUN
american_scientific_journal-756	212	22	multifunction	multifunction	NOUN
american_scientific_journal-756	212	23	𝐺𝐹:𝑋	𝐺𝐹:𝑋	NOUN
american_scientific_journal-756	212	24	→	→	SYM
american_scientific_journal-756	212	25	𝑋	𝑋	PROPN
american_scientific_journal-756	212	26	×	×	PROPN
american_scientific_journal-756	212	27	𝑌	𝑌	PROPN
american_scientific_journal-756	212	28	of	of	ADP
american_scientific_journal-756	212	29	𝐹	𝐹	PROPN
american_scientific_journal-756	212	30	is	be	AUX
american_scientific_journal-756	212	31	defined	define	VERB
american_scientific_journal-756	212	32	as	as	ADP
american_scientific_journal-756	212	33	𝐺𝐹(𝑥)=the	𝐺𝐹(𝑥)=the	PRON
american_scientific_journal-756	212	34	soft	soft	ADJ
american_scientific_journal-756	212	35	set	set	NOUN
american_scientific_journal-756	212	36	x₁	x₁	PROPN
american_scientific_journal-756	212	37	×	×	PROPN
american_scientific_journal-756	212	38	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	212	39	)	)	PUNCT
american_scientific_journal-756	212	40	,	,	PUNCT
american_scientific_journal-756	212	41	for	for	ADP
american_scientific_journal-756	212	42	every	every	DET
american_scientific_journal-756	212	43	𝑥	𝑥	PROPN
american_scientific_journal-756	212	44	∈	∈	PROPN
american_scientific_journal-756	212	45	𝑋.	𝑋.	PROPN
american_scientific_journal-756	212	46	over	over	ADP
american_scientific_journal-756	212	47	𝑋	𝑋	PROPN
american_scientific_journal-756	212	48	×	×	PROPN
american_scientific_journal-756	212	49	𝑌	𝑌	PROPN
american_scientific_journal-756	212	50	,	,	PUNCT
american_scientific_journal-756	212	51	where	where	SCONJ
american_scientific_journal-756	212	52	𝑥₁	𝑥₁	PROPN
american_scientific_journal-756	212	53	is	be	AUX
american_scientific_journal-756	212	54	the	the	DET
american_scientific_journal-756	212	55	soft	soft	ADJ
american_scientific_journal-756	212	56	set	set	NOUN
american_scientific_journal-756	212	57	over	over	ADP
american_scientific_journal-756	212	58	𝑋.	𝑋.	PROPN
american_scientific_journal-756	212	59	we	we	PRON
american_scientific_journal-756	212	60	shall	shall	AUX
american_scientific_journal-756	212	61	write	write	VERB
american_scientific_journal-756	212	62	{	{	PUNCT
american_scientific_journal-756	212	63	𝑥	𝑥	NOUN
american_scientific_journal-756	212	64	}	}	PUNCT
american_scientific_journal-756	212	65	×	×	NOUN
american_scientific_journal-756	212	66	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	212	67	)	)	PUNCT
american_scientific_journal-756	212	68	for	for	ADP
american_scientific_journal-756	212	69	𝑥₁	𝑥₁	ADJ
american_scientific_journal-756	212	70	×	×	PROPN
american_scientific_journal-756	212	71	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	212	72	)	)	PUNCT
american_scientific_journal-756	212	73	.	.	PUNCT
american_scientific_journal-756	213	1	lemma	lemma	PROPN
american_scientific_journal-756	213	2	3.16	3.16	NUM
american_scientific_journal-756	213	3	.	.	PUNCT
american_scientific_journal-756	214	1	[	[	X
american_scientific_journal-756	214	2	20	20	NUM
american_scientific_journal-756	214	3	]	]	PUNCT
american_scientific_journal-756	214	4	for	for	ADP
american_scientific_journal-756	214	5	a	a	DET
american_scientific_journal-756	214	6	soft	soft	ADJ
american_scientific_journal-756	214	7	multifunction	multifunction	NOUN
american_scientific_journal-756	214	8	𝐹	𝐹	PROPN
american_scientific_journal-756	214	9	:	:	PUNCT
american_scientific_journal-756	214	10	(	(	PUNCT
american_scientific_journal-756	214	11	𝑋	𝑋	PROPN
american_scientific_journal-756	214	12	,	,	PUNCT
american_scientific_journal-756	214	13	𝜏	𝜏	NOUN
american_scientific_journal-756	214	14	)	)	PUNCT
american_scientific_journal-756	214	15	→	→	SYM
american_scientific_journal-756	214	16	(	(	PUNCT
american_scientific_journal-756	214	17	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	214	18	)	)	PUNCT
american_scientific_journal-756	214	19	,	,	PUNCT
american_scientific_journal-756	214	20	the	the	DET
american_scientific_journal-756	214	21	followings	following	NOUN
american_scientific_journal-756	214	22	are	be	AUX
american_scientific_journal-756	214	23	hold	hold	ADJ
american_scientific_journal-756	214	24	:	:	PUNCT
american_scientific_journal-756	214	25	(	(	PUNCT
american_scientific_journal-756	214	26	a	a	X
american_scientific_journal-756	214	27	)	)	PUNCT
american_scientific_journal-756	214	28	𝐺𝐹+(𝑀	𝐺𝐹+(𝑀	PROPN
american_scientific_journal-756	214	29	×	×	NOUN
american_scientific_journal-756	214	30	(	(	PUNCT
american_scientific_journal-756	214	31	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	214	32	)	)	PUNCT
american_scientific_journal-756	214	33	)	)	PUNCT
american_scientific_journal-756	215	1	=	=	SYM
american_scientific_journal-756	215	2	𝑀	𝑀	PROPN
american_scientific_journal-756	215	3	∩	∩	NOUN
american_scientific_journal-756	215	4	𝐹⁺(𝐻,𝐸	𝐹⁺(𝐻,𝐸	NUM
american_scientific_journal-756	215	5	)	)	PUNCT
american_scientific_journal-756	215	6	(	(	PUNCT
american_scientific_journal-756	215	7	b	b	X
american_scientific_journal-756	215	8	)	)	PUNCT
american_scientific_journal-756	215	9	𝐺𝐹−(𝑀	𝐺𝐹−(𝑀	PROPN
american_scientific_journal-756	215	10	×	×	NOUN
american_scientific_journal-756	215	11	(	(	PUNCT
american_scientific_journal-756	215	12	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	215	13	)	)	PUNCT
american_scientific_journal-756	215	14	)	)	PUNCT
american_scientific_journal-756	216	1	=	=	SYM
american_scientific_journal-756	216	2	𝑀	𝑀	PROPN
american_scientific_journal-756	216	3	∩	∩	NOUN
american_scientific_journal-756	216	4	𝐹⁻(𝐻,𝐸	𝐹⁻(𝐻,𝐸	NUM
american_scientific_journal-756	216	5	)	)	PUNCT
american_scientific_journal-756	216	6	theorem	theorem	VERB
american_scientific_journal-756	216	7	3.17	3.17	NUM
american_scientific_journal-756	216	8	.	.	PUNCT
american_scientific_journal-756	217	1	let	let	VERB
american_scientific_journal-756	217	2	𝐹	𝐹	PRON
american_scientific_journal-756	217	3	:	:	PUNCT
american_scientific_journal-756	217	4	(	(	PUNCT
american_scientific_journal-756	217	5	𝑋	𝑋	PROPN
american_scientific_journal-756	217	6	,	,	PUNCT
american_scientific_journal-756	217	7	𝜏	𝜏	NOUN
american_scientific_journal-756	217	8	)	)	PUNCT
american_scientific_journal-756	217	9	→	→	X
american_scientific_journal-756	217	10	(	(	PUNCT
american_scientific_journal-756	217	11	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	217	12	)	)	PUNCT
american_scientific_journal-756	217	13	be	be	VERB
american_scientific_journal-756	217	14	a	a	DET
american_scientific_journal-756	217	15	soft	soft	ADJ
american_scientific_journal-756	217	16	multifunction	multifunction	NOUN
american_scientific_journal-756	217	17	.	.	PUNCT
american_scientific_journal-756	218	1	if	if	SCONJ
american_scientific_journal-756	218	2	the	the	DET
american_scientific_journal-756	218	3	soft	soft	ADJ
american_scientific_journal-756	218	4	graph	graph	NOUN
american_scientific_journal-756	218	5	function	function	NOUN
american_scientific_journal-756	218	6	of	of	ADP
american_scientific_journal-756	218	7	𝐹	𝐹	PROPN
american_scientific_journal-756	218	8	is	be	AUX
american_scientific_journal-756	218	9	soft	soft	ADV
american_scientific_journal-756	218	10	lower	low	ADJ
american_scientific_journal-756	218	11	(	(	PUNCT
american_scientific_journal-756	218	12	upper	upper	ADJ
american_scientific_journal-756	218	13	)	)	PUNCT
american_scientific_journal-756	218	14	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	218	15	,	,	PUNCT
american_scientific_journal-756	218	16	then	then	ADV
american_scientific_journal-756	218	17	𝐹	𝐹	PROPN
american_scientific_journal-756	218	18	is	be	AUX
american_scientific_journal-756	218	19	soft	soft	ADV
american_scientific_journal-756	218	20	lower	low	ADJ
american_scientific_journal-756	218	21	(	(	PUNCT
american_scientific_journal-756	218	22	upper	upper	ADJ
american_scientific_journal-756	218	23	)	)	PUNCT
american_scientific_journal-756	218	24	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	218	25	.	.	PUNCT
american_scientific_journal-756	219	1	proof	proof	NOUN
american_scientific_journal-756	219	2	.	.	PUNCT
american_scientific_journal-756	220	1	for	for	ADP
american_scientific_journal-756	220	2	a	a	DET
american_scientific_journal-756	220	3	subset	subset	ADJ
american_scientific_journal-756	220	4	𝑉	𝑉	PROPN
american_scientific_journal-756	220	5	of	of	ADP
american_scientific_journal-756	220	6	𝑋	𝑋	PROPN
american_scientific_journal-756	220	7	and	and	CCONJ
american_scientific_journal-756	220	8	(	(	PUNCT
american_scientific_journal-756	220	9	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	220	10	)	)	PUNCT
american_scientific_journal-756	220	11	a	a	DET
american_scientific_journal-756	220	12	soft	soft	ADJ
american_scientific_journal-756	220	13	set	set	NOUN
american_scientific_journal-756	220	14	over	over	ADP
american_scientific_journal-756	220	15	𝑈	𝑈	PROPN
american_scientific_journal-756	220	16	,	,	PUNCT
american_scientific_journal-756	220	17	we	we	PRON
american_scientific_journal-756	220	18	take	take	VERB
american_scientific_journal-756	220	19	(	(	PUNCT
american_scientific_journal-756	220	20	𝑉	𝑉	PROPN
american_scientific_journal-756	220	21	×	×	NOUN
american_scientific_journal-756	220	22	(	(	PUNCT
american_scientific_journal-756	220	23	𝐺,𝐸))(𝑧,𝑦	𝐺,𝐸))(𝑧,𝑦	NOUN
american_scientific_journal-756	220	24	)	)	PUNCT
american_scientific_journal-756	220	25	=	=	SYM
american_scientific_journal-756	220	26	�	�	PROPN
american_scientific_journal-756	220	27	∅	∅	NOUN
american_scientific_journal-756	220	28	,	,	PUNCT
american_scientific_journal-756	220	29	𝑖𝑓	𝑖𝑓	ADP
american_scientific_journal-756	220	30	𝑧	𝑧	DET
american_scientific_journal-756	220	31	∉	∉	PROPN
american_scientific_journal-756	220	32	𝑉	𝑉	PROPN
american_scientific_journal-756	220	33	𝐺(𝑦	𝐺(𝑦	PROPN
american_scientific_journal-756	220	34	)	)	PUNCT
american_scientific_journal-756	220	35	,	,	PUNCT
american_scientific_journal-756	220	36	𝑖𝑓	𝑖𝑓	ADP
american_scientific_journal-756	221	1	𝑧	𝑧	PRON
american_scientific_journal-756	221	2	∈	∈	PROPN
american_scientific_journal-756	221	3	𝑉	𝑉	PROPN
american_scientific_journal-756	221	4	let	let	VERB
american_scientific_journal-756	221	5	𝑥	𝑥	DET
american_scientific_journal-756	221	6	∈	∈	PROPN
american_scientific_journal-756	221	7	𝑋	𝑋	NOUN
american_scientific_journal-756	221	8	and	and	CCONJ
american_scientific_journal-756	221	9	let	let	AUX
american_scientific_journal-756	221	10	(	(	PUNCT
american_scientific_journal-756	221	11	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	221	12	)	)	PUNCT
american_scientific_journal-756	221	13	be	be	AUX
american_scientific_journal-756	221	14	soft	soft	ADJ
american_scientific_journal-756	221	15	open	open	ADJ
american_scientific_journal-756	221	16	set	set	NOUN
american_scientific_journal-756	221	17	such	such	ADJ
american_scientific_journal-756	221	18	that	that	SCONJ
american_scientific_journal-756	221	19	𝑥	𝑥	PROPN
american_scientific_journal-756	221	20	∈	∈	PROPN
american_scientific_journal-756	221	21	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	221	22	)	)	PUNCT
american_scientific_journal-756	221	23	.	.	PUNCT
american_scientific_journal-756	222	1	then	then	ADV
american_scientific_journal-756	222	2	we	we	PRON
american_scientific_journal-756	222	3	obtain	obtain	VERB
american_scientific_journal-756	222	4	that	that	SCONJ
american_scientific_journal-756	222	5	𝑥	𝑥	PROPN
american_scientific_journal-756	222	6	∈	∈	PROPN
american_scientific_journal-756	222	7	𝐺_{𝐹}⁻(𝑋	𝐺_{𝐹}⁻(𝑋	PRON
american_scientific_journal-756	222	8	×	×	NOUN
american_scientific_journal-756	222	9	(	(	PUNCT
american_scientific_journal-756	222	10	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	222	11	)	)	PUNCT
american_scientific_journal-756	222	12	)	)	PUNCT
american_scientific_journal-756	222	13	and	and	CCONJ
american_scientific_journal-756	222	14	𝑋	𝑋	PROPN
american_scientific_journal-756	222	15	×	×	NOUN
american_scientific_journal-756	222	16	(	(	PUNCT
american_scientific_journal-756	222	17	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	222	18	)	)	PUNCT
american_scientific_journal-756	222	19	is	be	AUX
american_scientific_journal-756	222	20	a	a	DET
american_scientific_journal-756	222	21	soft	soft	ADJ
american_scientific_journal-756	222	22	set	set	NOUN
american_scientific_journal-756	222	23	over	over	ADP
american_scientific_journal-756	222	24	𝑌	𝑌	PROPN
american_scientific_journal-756	222	25	.	.	PUNCT
american_scientific_journal-756	223	1	since	since	SCONJ
american_scientific_journal-756	223	2	the	the	DET
american_scientific_journal-756	223	3	soft	soft	ADJ
american_scientific_journal-756	223	4	graph	graph	NOUN
american_scientific_journal-756	223	5	multifuntion	multifuntion	NOUN
american_scientific_journal-756	223	6	𝐺_{𝐹	𝐺_{𝐹	NOUN
american_scientific_journal-756	223	7	}	}	PUNCT
american_scientific_journal-756	223	8	is	be	AUX
american_scientific_journal-756	223	9	soft	soft	ADJ
american_scientific_journal-756	223	10	lower	low	ADJ
american_scientific_journal-756	223	11	𝛼-continuons	𝛼-continuon	NOUN
american_scientific_journal-756	223	12	,	,	PUNCT
american_scientific_journal-756	223	13	it	it	PRON
american_scientific_journal-756	223	14	follows	follow	VERB
american_scientific_journal-756	223	15	that	that	SCONJ
american_scientific_journal-756	223	16	there	there	PRON
american_scientific_journal-756	223	17	exists	exist	VERB
american_scientific_journal-756	223	18	an	an	DET
american_scientific_journal-756	223	19	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	223	20	set	set	NOUN
american_scientific_journal-756	223	21	𝑃	𝑃	NOUN
american_scientific_journal-756	223	22	containing	contain	VERB
american_scientific_journal-756	223	23	𝑥	𝑥	PRON
american_scientific_journal-756	223	24	such	such	ADJ
american_scientific_journal-756	223	25	that	that	PRON
american_scientific_journal-756	223	26	𝑃	𝑃	VERB
american_scientific_journal-756	223	27	⊆	⊆	NUM
american_scientific_journal-756	223	28	𝐺_{𝐹}⁻(𝑋	𝐺_{𝐹}⁻(𝑋	NOUN
american_scientific_journal-756	223	29	×	×	NOUN
american_scientific_journal-756	223	30	(	(	PUNCT
american_scientific_journal-756	223	31	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	223	32	)	)	PUNCT
american_scientific_journal-756	223	33	.	.	PUNCT
american_scientific_journal-756	224	1	from	from	ADP
american_scientific_journal-756	224	2	here	here	ADV
american_scientific_journal-756	224	3	,	,	PUNCT
american_scientific_journal-756	224	4	we	we	PRON
american_scientific_journal-756	224	5	obtain	obtain	VERB
american_scientific_journal-756	224	6	that	that	PRON
american_scientific_journal-756	224	7	𝑃	𝑃	VERB
american_scientific_journal-756	224	8	⊆	⊆	NUM
american_scientific_journal-756	224	9	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	224	10	)	)	PUNCT
american_scientific_journal-756	224	11	.	.	PUNCT
american_scientific_journal-756	225	1	thus	thus	ADV
american_scientific_journal-756	225	2	𝐹	𝐹	PRON
american_scientific_journal-756	225	3	is	be	AUX
american_scientific_journal-756	225	4	soft	soft	ADJ
american_scientific_journal-756	225	5	lower	low	ADJ
american_scientific_journal-756	225	6	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	225	7	.	.	PUNCT
american_scientific_journal-756	226	1	the	the	DET
american_scientific_journal-756	226	2	proof	proof	NOUN
american_scientific_journal-756	226	3	of	of	ADP
american_scientific_journal-756	226	4	the	the	DET
american_scientific_journal-756	226	5	soft	soft	ADJ
american_scientific_journal-756	226	6	upper	upper	ADJ
american_scientific_journal-756	226	7	α	α	NOUN
american_scientific_journal-756	226	8	-	-	NOUN
american_scientific_journal-756	226	9	continuity	continuity	NOUN
american_scientific_journal-756	226	10	of	of	ADP
american_scientific_journal-756	226	11	𝐹	𝐹	PROPN
american_scientific_journal-756	226	12	is	be	AUX
american_scientific_journal-756	226	13	similar	similar	ADJ
american_scientific_journal-756	226	14	to	to	ADP
american_scientific_journal-756	226	15	the	the	DET
american_scientific_journal-756	226	16	above	above	ADJ
american_scientific_journal-756	226	17	.	.	PUNCT
american_scientific_journal-756	227	1	theorem	theorem	VERB
american_scientific_journal-756	227	2	3.18	3.18	NUM
american_scientific_journal-756	227	3	.	.	PUNCT
american_scientific_journal-756	228	1	let	let	VERB
american_scientific_journal-756	228	2	𝐹	𝐹	PRON
american_scientific_journal-756	228	3	:	:	PUNCT
american_scientific_journal-756	228	4	(	(	PUNCT
american_scientific_journal-756	228	5	𝑋	𝑋	PROPN
american_scientific_journal-756	228	6	,	,	PUNCT
american_scientific_journal-756	228	7	𝜏	𝜏	NOUN
american_scientific_journal-756	228	8	)	)	PUNCT
american_scientific_journal-756	228	9	→	→	X
american_scientific_journal-756	228	10	(	(	PUNCT
american_scientific_journal-756	228	11	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	228	12	)	)	PUNCT
american_scientific_journal-756	228	13	be	be	VERB
american_scientific_journal-756	228	14	a	a	DET
american_scientific_journal-756	228	15	soft	soft	ADJ
american_scientific_journal-756	228	16	multifunction	multifunction	NOUN
american_scientific_journal-756	228	17	and	and	CCONJ
american_scientific_journal-756	228	18	𝑀	𝑀	PROPN
american_scientific_journal-756	228	19	be	be	VERB
american_scientific_journal-756	228	20	an	an	DET
american_scientific_journal-756	228	21	𝛼	𝛼	X
american_scientific_journal-756	228	22	-open	-open	ADJ
american_scientific_journal-756	228	23	set	set	NOUN
american_scientific_journal-756	228	24	of	of	ADP
american_scientific_journal-756	228	25	𝑋	𝑋	PROPN
american_scientific_journal-756	228	26	.	.	PUNCT
american_scientific_journal-756	229	1	then	then	ADV
american_scientific_journal-756	229	2	the	the	DET
american_scientific_journal-756	229	3	restriction	restriction	NOUN
american_scientific_journal-756	229	4	𝐹|𝑀	𝐹|𝑀	PROPN
american_scientific_journal-756	229	5	is	be	AUX
american_scientific_journal-756	229	6	soft	soft	ADJ
american_scientific_journal-756	229	7	upper	upper	ADJ
american_scientific_journal-756	229	8	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	229	9	if	if	SCONJ
american_scientific_journal-756	229	10	𝐹	𝐹	PROPN
american_scientific_journal-756	229	11	is	be	AUX
american_scientific_journal-756	229	12	soft	soft	ADJ
american_scientific_journal-756	229	13	upper	upper	ADJ
american_scientific_journal-756	229	14	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	229	15	.	.	PUNCT
american_scientific_journal-756	230	1	proof	proof	NOUN
american_scientific_journal-756	230	2	.	.	PUNCT
american_scientific_journal-756	231	1	let	let	VERB
american_scientific_journal-756	231	2	(	(	PUNCT
american_scientific_journal-756	231	3	𝐻,𝐸	𝐻,𝐸	VERB
american_scientific_journal-756	231	4	)	)	PUNCT
american_scientific_journal-756	231	5	be	be	VERB
american_scientific_journal-756	231	6	any	any	DET
american_scientific_journal-756	231	7	soft	soft	ADJ
american_scientific_journal-756	231	8	open	open	ADJ
american_scientific_journal-756	231	9	set	set	VERB
american_scientific_journal-756	231	10	over	over	ADP
american_scientific_journal-756	231	11	𝑌	𝑌	PROPN
american_scientific_journal-756	231	12	such	such	ADJ
american_scientific_journal-756	231	13	that	that	DET
american_scientific_journal-756	231	14	𝐹|𝑀(𝑥	𝐹|𝑀(𝑥	NOUN
american_scientific_journal-756	231	15	)	)	PUNCT
american_scientific_journal-756	232	1	⊆	⊆	NUM
american_scientific_journal-756	232	2	(	(	PUNCT
american_scientific_journal-756	232	3	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	232	4	)	)	PUNCT
american_scientific_journal-756	232	5	.	.	PUNCT
american_scientific_journal-756	233	1	since	since	SCONJ
american_scientific_journal-756	233	2	𝐹	𝐹	PROPN
american_scientific_journal-756	233	3	is	be	AUX
american_scientific_journal-756	233	4	soft	soft	ADJ
american_scientific_journal-756	233	5	upper	upper	ADJ
american_scientific_journal-756	233	6	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	233	7	and	and	CCONJ
american_scientific_journal-756	233	8	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	233	9	)	)	PUNCT
american_scientific_journal-756	233	10	=	=	SYM
american_scientific_journal-756	233	11	𝐹|𝑀(𝑥	𝐹|𝑀(𝑥	PROPN
american_scientific_journal-756	233	12	)	)	PUNCT
american_scientific_journal-756	233	13	⊆	⊆	NUM
american_scientific_journal-756	233	14	(	(	PUNCT
american_scientific_journal-756	233	15	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	233	16	)	)	PUNCT
american_scientific_journal-756	233	17	,	,	PUNCT
american_scientific_journal-756	233	18	then	then	ADV
american_scientific_journal-756	233	19	there	there	PRON
american_scientific_journal-756	233	20	exists	exist	VERB
american_scientific_journal-756	233	21	𝛼-open	𝛼-open	PROPN
american_scientific_journal-756	233	22	set	set	VERB
american_scientific_journal-756	233	23	𝑈	𝑈	PROPN
american_scientific_journal-756	233	24	⊆	⊆	NUM
american_scientific_journal-756	233	25	𝑋	𝑋	NOUN
american_scientific_journal-756	233	26	containing	contain	VERB
american_scientific_journal-756	233	27	𝑥	𝑥	PRON
american_scientific_journal-756	233	28	such	such	ADJ
american_scientific_journal-756	233	29	that	that	SCONJ
american_scientific_journal-756	233	30	𝐹(𝑧	𝐹(𝑧	ADP
american_scientific_journal-756	233	31	)	)	PUNCT
american_scientific_journal-756	233	32	⊆	⊆	NUM
american_scientific_journal-756	233	33	(	(	PUNCT
american_scientific_journal-756	233	34	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	233	35	)	)	PUNCT
american_scientific_journal-756	233	36	for	for	SCONJ
american_scientific_journal-756	233	37	all	all	DET
american_scientific_journal-756	233	38	𝑧	𝑧	DET
american_scientific_journal-756	233	39	∈	∈	PROPN
american_scientific_journal-756	233	40	𝑈.	𝑈.	NOUN
american_scientific_journal-756	233	41	put	put	VERB
american_scientific_journal-756	233	42	𝑈₁	𝑈₁	NOUN
american_scientific_journal-756	233	43	=	=	SYM
american_scientific_journal-756	233	44	𝑈	𝑈	PROPN
american_scientific_journal-756	233	45	∩𝑀	∩𝑀	NOUN
american_scientific_journal-756	233	46	then	then	ADV
american_scientific_journal-756	233	47	we	we	PRON
american_scientific_journal-756	233	48	have	have	VERB
american_scientific_journal-756	233	49	𝑈₁	𝑈₁	PROPN
american_scientific_journal-756	233	50	is	be	AUX
american_scientific_journal-756	233	51	𝛼-open	𝛼-open	PROPN
american_scientific_journal-756	233	52	set	set	NOUN
american_scientific_journal-756	233	53	in	in	ADP
american_scientific_journal-756	233	54	𝑀	𝑀	PROPN
american_scientific_journal-756	233	55	containing	contain	VERB
american_scientific_journal-756	233	56	𝑥	𝑥	PROPN
american_scientific_journal-756	233	57	and	and	CCONJ
american_scientific_journal-756	233	58	𝐹(𝑈₁	𝐹(𝑈₁	NUM
american_scientific_journal-756	233	59	)	)	PUNCT
american_scientific_journal-756	233	60	=	=	SYM
american_scientific_journal-756	233	61	𝐹|𝑀(𝑈₁	𝐹|𝑀(𝑈₁	PROPN
american_scientific_journal-756	233	62	)	)	PUNCT
american_scientific_journal-756	233	63	⊆	⊆	NUM
american_scientific_journal-756	233	64	(	(	PUNCT
american_scientific_journal-756	233	65	𝐻,𝐸	𝐻,𝐸	NOUN
american_scientific_journal-756	233	66	)	)	PUNCT
american_scientific_journal-756	233	67	.	.	PUNCT
american_scientific_journal-756	234	1	this	this	DET
american_scientific_journal-756	234	2	103	103	NUM
american_scientific_journal-756	234	3	american	american	ADJ
american_scientific_journal-756	234	4	scientific	scientific	ADJ
american_scientific_journal-756	234	5	research	research	NOUN
american_scientific_journal-756	234	6	journal	journal	NOUN
american_scientific_journal-756	234	7	for	for	ADP
american_scientific_journal-756	234	8	engineering	engineering	NOUN
american_scientific_journal-756	234	9	,	,	PUNCT
american_scientific_journal-756	234	10	technology	technology	NOUN
american_scientific_journal-756	234	11	,	,	PUNCT
american_scientific_journal-756	234	12	and	and	CCONJ
american_scientific_journal-756	234	13	sciences	science	NOUN
american_scientific_journal-756	234	14	(	(	PUNCT
american_scientific_journal-756	234	15	asrjets	asrjet	NOUN
american_scientific_journal-756	234	16	)	)	PUNCT
american_scientific_journal-756	234	17	(	(	PUNCT
american_scientific_journal-756	234	18	2014	2014	NUM
american_scientific_journal-756	234	19	)	)	PUNCT
american_scientific_journal-756	234	20	volume	volume	NOUN
american_scientific_journal-756	234	21	8	8	NUM
american_scientific_journal-756	234	22	,	,	PUNCT
american_scientific_journal-756	234	23	no	no	DET
american_scientific_journal-756	234	24	1	1	NUM
american_scientific_journal-756	234	25	,	,	PUNCT
american_scientific_journal-756	234	26	pp	pp	ADV
american_scientific_journal-756	234	27	96	96	NUM
american_scientific_journal-756	234	28	-	-	SYM
american_scientific_journal-756	234	29	107	107	NUM
american_scientific_journal-756	234	30	shows	show	VERB
american_scientific_journal-756	234	31	that	that	SCONJ
american_scientific_journal-756	234	32	𝐹|𝑀	𝐹|𝑀	PROPN
american_scientific_journal-756	234	33	is	be	AUX
american_scientific_journal-756	234	34	soft	soft	ADJ
american_scientific_journal-756	234	35	upper	upper	ADJ
american_scientific_journal-756	234	36	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	234	37	.	.	PUNCT
american_scientific_journal-756	235	1	theorem	theorem	VERB
american_scientific_journal-756	235	2	3.19	3.19	NUM
american_scientific_journal-756	235	3	.	.	PUNCT
american_scientific_journal-756	236	1	let	let	VERB
american_scientific_journal-756	236	2	𝐹	𝐹	PRON
american_scientific_journal-756	236	3	:	:	PUNCT
american_scientific_journal-756	236	4	(	(	PUNCT
american_scientific_journal-756	236	5	𝑋	𝑋	PROPN
american_scientific_journal-756	236	6	,	,	PUNCT
american_scientific_journal-756	236	7	𝜏	𝜏	NOUN
american_scientific_journal-756	236	8	)	)	PUNCT
american_scientific_journal-756	236	9	→	→	X
american_scientific_journal-756	236	10	(	(	PUNCT
american_scientific_journal-756	236	11	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	236	12	)	)	PUNCT
american_scientific_journal-756	236	13	be	be	VERB
american_scientific_journal-756	236	14	a	a	DET
american_scientific_journal-756	236	15	soft	soft	ADJ
american_scientific_journal-756	236	16	multifunction	multifunction	NOUN
american_scientific_journal-756	236	17	and	and	CCONJ
american_scientific_journal-756	236	18	𝑀	𝑀	PROPN
american_scientific_journal-756	236	19	be	be	VERB
american_scientific_journal-756	236	20	an	an	DET
american_scientific_journal-756	236	21	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	236	22	set	set	NOUN
american_scientific_journal-756	236	23	of	of	ADP
american_scientific_journal-756	236	24	𝑋.	𝑋.	PROPN
american_scientific_journal-756	236	25	then	then	ADV
american_scientific_journal-756	236	26	𝐹	𝐹	PROPN
american_scientific_journal-756	236	27	is	be	AUX
american_scientific_journal-756	236	28	soft	soft	ADJ
american_scientific_journal-756	236	29	lower	low	ADJ
american_scientific_journal-756	236	30	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	236	31	if	if	SCONJ
american_scientific_journal-756	237	1	and	and	CCONJ
american_scientific_journal-756	237	2	only	only	ADV
american_scientific_journal-756	237	3	if	if	SCONJ
american_scientific_journal-756	237	4	the	the	DET
american_scientific_journal-756	237	5	restriction	restriction	NOUN
american_scientific_journal-756	237	6	𝐹|𝑀	𝐹|𝑀	PROPN
american_scientific_journal-756	237	7	is	be	AUX
american_scientific_journal-756	237	8	soft	soft	ADJ
american_scientific_journal-756	237	9	lower	low	ADJ
american_scientific_journal-756	237	10	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	237	11	.	.	PUNCT
american_scientific_journal-756	238	1	proof	proof	NOUN
american_scientific_journal-756	238	2	.	.	PUNCT
american_scientific_journal-756	239	1	let	let	VERB
american_scientific_journal-756	239	2	(	(	PUNCT
american_scientific_journal-756	239	3	𝐻,𝐸	𝐻,𝐸	VERB
american_scientific_journal-756	239	4	)	)	PUNCT
american_scientific_journal-756	239	5	be	be	VERB
american_scientific_journal-756	239	6	any	any	DET
american_scientific_journal-756	239	7	soft	soft	ADJ
american_scientific_journal-756	239	8	open	open	ADJ
american_scientific_journal-756	239	9	set	set	VERB
american_scientific_journal-756	239	10	over	over	ADP
american_scientific_journal-756	239	11	𝑌	𝑌	PROPN
american_scientific_journal-756	239	12	such	such	ADJ
american_scientific_journal-756	239	13	that	that	DET
american_scientific_journal-756	239	14	𝐹|𝑀(𝑥	𝐹|𝑀(𝑥	NOUN
american_scientific_journal-756	239	15	)	)	PUNCT
american_scientific_journal-756	240	1	∩	∩	NOUN
american_scientific_journal-756	240	2	(	(	PUNCT
american_scientific_journal-756	240	3	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	240	4	)	)	PUNCT
american_scientific_journal-756	240	5	≠	≠	PROPN
american_scientific_journal-756	240	6	𝛷	𝛷	NOUN
american_scientific_journal-756	240	7	.	.	PUNCT
american_scientific_journal-756	241	1	since	since	SCONJ
american_scientific_journal-756	241	2	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	241	3	)	)	PUNCT
american_scientific_journal-756	241	4	=	=	SYM
american_scientific_journal-756	241	5	𝐹|𝑀(𝑥	𝐹|𝑀(𝑥	PROPN
american_scientific_journal-756	241	6	)	)	PUNCT
american_scientific_journal-756	241	7	,	,	PUNCT
american_scientific_journal-756	241	8	then	then	ADV
american_scientific_journal-756	241	9	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	241	10	)	)	PUNCT
american_scientific_journal-756	241	11	∩	∩	NOUN
american_scientific_journal-756	241	12	(	(	PUNCT
american_scientific_journal-756	241	13	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	241	14	)	)	PUNCT
american_scientific_journal-756	241	15	≠	≠	PROPN
american_scientific_journal-756	241	16	𝛷.	𝛷.	PROPN
american_scientific_journal-756	241	17	also	also	ADV
american_scientific_journal-756	241	18	since	since	SCONJ
american_scientific_journal-756	241	19	𝐹	𝐹	PROPN
american_scientific_journal-756	241	20	is	be	AUX
american_scientific_journal-756	241	21	soft	soft	ADJ
american_scientific_journal-756	241	22	lower	low	ADJ
american_scientific_journal-756	241	23	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	241	24	there	there	PRON
american_scientific_journal-756	241	25	exists	exist	VERB
american_scientific_journal-756	241	26	𝛼-open	𝛼-open	PROPN
american_scientific_journal-756	241	27	set	set	VERB
american_scientific_journal-756	241	28	𝑈	𝑈	PROPN
american_scientific_journal-756	241	29	⊆	⊆	NUM
american_scientific_journal-756	241	30	𝑋	𝑋	NOUN
american_scientific_journal-756	241	31	containing	contain	VERB
american_scientific_journal-756	241	32	𝑥	𝑥	PRON
american_scientific_journal-756	241	33	such	such	ADJ
american_scientific_journal-756	241	34	that	that	PRON
american_scientific_journal-756	241	35	𝐹(𝑧	𝐹(𝑧	ADP
american_scientific_journal-756	241	36	)	)	PUNCT
american_scientific_journal-756	241	37	∩	∩	NOUN
american_scientific_journal-756	241	38	(	(	PUNCT
american_scientific_journal-756	241	39	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	241	40	)	)	PUNCT
american_scientific_journal-756	241	41	≠	≠	PROPN
american_scientific_journal-756	241	42	𝛷	𝛷	NOUN
american_scientific_journal-756	241	43	for	for	ADP
american_scientific_journal-756	241	44	all	all	DET
american_scientific_journal-756	241	45	𝑧	𝑧	DET
american_scientific_journal-756	241	46	∈	∈	PROPN
american_scientific_journal-756	241	47	𝑈.	𝑈.	NOUN
american_scientific_journal-756	241	48	put	put	VERB
american_scientific_journal-756	241	49	𝑈₁	𝑈₁	NOUN
american_scientific_journal-756	241	50	=	=	SYM
american_scientific_journal-756	241	51	𝑈	𝑈	PROPN
american_scientific_journal-756	241	52	∩	∩	NOUN
american_scientific_journal-756	241	53	𝑀	𝑀	PROPN
american_scientific_journal-756	241	54	then	then	ADV
american_scientific_journal-756	241	55	we	we	PRON
american_scientific_journal-756	241	56	have	have	VERB
american_scientific_journal-756	241	57	𝑈₁	𝑈₁	PROPN
american_scientific_journal-756	241	58	is	be	AUX
american_scientific_journal-756	241	59	𝛼-open	𝛼-open	PROPN
american_scientific_journal-756	241	60	set	set	NOUN
american_scientific_journal-756	241	61	in	in	ADP
american_scientific_journal-756	241	62	𝑀	𝑀	PROPN
american_scientific_journal-756	241	63	containing	contain	VERB
american_scientific_journal-756	241	64	𝑥	𝑥	PROPN
american_scientific_journal-756	241	65	and	and	CCONJ
american_scientific_journal-756	241	66	f(𝑈₁	f(𝑈₁	PROPN
american_scientific_journal-756	241	67	)	)	PUNCT
american_scientific_journal-756	241	68	∩	∩	NOUN
american_scientific_journal-756	241	69	(	(	PUNCT
american_scientific_journal-756	241	70	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	241	71	)	)	PUNCT
american_scientific_journal-756	241	72	≠	≠	PROPN
american_scientific_journal-756	241	73	𝛷.therefore	𝛷.therefore	ADJ
american_scientific_journal-756	241	74	𝐹|𝑀(𝑈₁	𝐹|𝑀(𝑈₁	PROPN
american_scientific_journal-756	241	75	)	)	PUNCT
american_scientific_journal-756	241	76	∩	∩	NOUN
american_scientific_journal-756	241	77	(	(	PUNCT
american_scientific_journal-756	241	78	𝐻,𝐸	𝐻,𝐸	ADJ
american_scientific_journal-756	241	79	)	)	PUNCT
american_scientific_journal-756	241	80	≠	≠	PROPN
american_scientific_journal-756	241	81	𝛷.	𝛷.	PROPN
american_scientific_journal-756	241	82	this	this	PRON
american_scientific_journal-756	241	83	shows	show	VERB
american_scientific_journal-756	241	84	that	that	SCONJ
american_scientific_journal-756	241	85	𝐹|𝑀	𝐹|𝑀	PROPN
american_scientific_journal-756	241	86	is	be	AUX
american_scientific_journal-756	241	87	soft	soft	ADJ
american_scientific_journal-756	241	88	lower	low	ADJ
american_scientific_journal-756	241	89	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	241	90	.	.	PUNCT
american_scientific_journal-756	242	1	corollary	corollary	ADJ
american_scientific_journal-756	242	2	3.20	3.20	NUM
american_scientific_journal-756	242	3	.	.	PUNCT
american_scientific_journal-756	243	1	let	let	VERB
american_scientific_journal-756	243	2	𝐹	𝐹	PRON
american_scientific_journal-756	243	3	:	:	PUNCT
american_scientific_journal-756	243	4	(	(	PUNCT
american_scientific_journal-756	243	5	𝑋	𝑋	PROPN
american_scientific_journal-756	243	6	,	,	PUNCT
american_scientific_journal-756	243	7	𝜏	𝜏	NOUN
american_scientific_journal-756	243	8	)	)	PUNCT
american_scientific_journal-756	243	9	→	→	X
american_scientific_journal-756	243	10	(	(	PUNCT
american_scientific_journal-756	243	11	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	243	12	)	)	PUNCT
american_scientific_journal-756	243	13	be	be	VERB
american_scientific_journal-756	243	14	a	a	DET
american_scientific_journal-756	243	15	soft	soft	ADJ
american_scientific_journal-756	243	16	multifunction	multifunction	NOUN
american_scientific_journal-756	243	17	and	and	CCONJ
american_scientific_journal-756	243	18	{	{	PUNCT
american_scientific_journal-756	243	19	𝐹|𝑀𝑖	𝐹|𝑀𝑖	NOUN
american_scientific_journal-756	243	20	:	:	PUNCT
american_scientific_journal-756	243	21	𝑖	𝑖	SYM
american_scientific_journal-756	243	22	∈	∈	PROPN
american_scientific_journal-756	243	23	𝐼	𝐼	PROPN
american_scientific_journal-756	243	24	}	}	PUNCT
american_scientific_journal-756	243	25	be	be	VERB
american_scientific_journal-756	243	26	an	an	DET
american_scientific_journal-756	243	27	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	243	28	cover	cover	NOUN
american_scientific_journal-756	243	29	set	set	NOUN
american_scientific_journal-756	243	30	of	of	ADP
american_scientific_journal-756	243	31	𝑋.	𝑋.	PROPN
american_scientific_journal-756	243	32	the	the	DET
american_scientific_journal-756	243	33	followings	following	NOUN
american_scientific_journal-756	243	34	are	be	AUX
american_scientific_journal-756	243	35	hold	hold	ADJ
american_scientific_journal-756	243	36	:	:	PUNCT
american_scientific_journal-756	243	37	(	(	PUNCT
american_scientific_journal-756	243	38	a	a	X
american_scientific_journal-756	243	39	)	)	PUNCT
american_scientific_journal-756	243	40	𝐹	𝐹	PROPN
american_scientific_journal-756	243	41	is	be	AUX
american_scientific_journal-756	243	42	soft	soft	ADJ
american_scientific_journal-756	243	43	lower	low	ADJ
american_scientific_journal-756	243	44	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	243	45	if	if	SCONJ
american_scientific_journal-756	244	1	and	and	CCONJ
american_scientific_journal-756	244	2	only	only	ADV
american_scientific_journal-756	244	3	if	if	SCONJ
american_scientific_journal-756	244	4	the	the	DET
american_scientific_journal-756	244	5	restriction	restriction	NOUN
american_scientific_journal-756	244	6	𝐹|𝑀𝑖	𝐹|𝑀𝑖	NOUN
american_scientific_journal-756	244	7	is	be	AUX
american_scientific_journal-756	244	8	soft	soft	ADJ
american_scientific_journal-756	244	9	lower	low	ADJ
american_scientific_journal-756	244	10	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	244	11	for	for	ADP
american_scientific_journal-756	244	12	every	every	DET
american_scientific_journal-756	244	13	𝑖	𝑖	PROPN
american_scientific_journal-756	244	14	∈	∈	PROPN
american_scientific_journal-756	244	15	𝐼.	𝐼.	PROPN
american_scientific_journal-756	244	16	(	(	PUNCT
american_scientific_journal-756	244	17	b	b	X
american_scientific_journal-756	244	18	)	)	PUNCT
american_scientific_journal-756	244	19	𝐹	𝐹	PROPN
american_scientific_journal-756	244	20	is	be	AUX
american_scientific_journal-756	244	21	soft	soft	ADJ
american_scientific_journal-756	244	22	upper	upper	ADJ
american_scientific_journal-756	244	23	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	244	24	if	if	SCONJ
american_scientific_journal-756	244	25	and	and	CCONJ
american_scientific_journal-756	244	26	only	only	ADV
american_scientific_journal-756	244	27	if	if	SCONJ
american_scientific_journal-756	244	28	the	the	DET
american_scientific_journal-756	244	29	restriction	restriction	NOUN
american_scientific_journal-756	244	30	𝐹|𝑀𝑖	𝐹|𝑀𝑖	NOUN
american_scientific_journal-756	244	31	is	be	AUX
american_scientific_journal-756	244	32	soft	soft	ADJ
american_scientific_journal-756	244	33	upper	upper	ADJ
american_scientific_journal-756	244	34	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	244	35	for	for	ADP
american_scientific_journal-756	244	36	every	every	DET
american_scientific_journal-756	244	37	𝑖	𝑖	PROPN
american_scientific_journal-756	244	38	∈	∈	PROPN
american_scientific_journal-756	244	39	𝐼.	𝐼.	NOUN
american_scientific_journal-756	244	40	proof	proof	NOUN
american_scientific_journal-756	244	41	.	.	PUNCT
american_scientific_journal-756	245	1	(	(	PUNCT
american_scientific_journal-756	245	2	a	a	X
american_scientific_journal-756	245	3	):	):	PUNCT
american_scientific_journal-756	245	4	let	let	VERB
american_scientific_journal-756	245	5	𝑥	𝑥	PRON
american_scientific_journal-756	245	6	∈	∈	PROPN
american_scientific_journal-756	245	7	𝑋	𝑋	NOUN
american_scientific_journal-756	245	8	and	and	CCONJ
american_scientific_journal-756	245	9	𝑥	𝑥	PRON
american_scientific_journal-756	245	10	∈	∈	PROPN
american_scientific_journal-756	245	11	𝑀𝑖	𝑀𝑖	PROPN
american_scientific_journal-756	245	12	for	for	ADP
american_scientific_journal-756	245	13	an	an	DET
american_scientific_journal-756	245	14	𝑖	𝑖	SYM
american_scientific_journal-756	245	15	∈	∈	PROPN
american_scientific_journal-756	245	16	𝐼.	𝐼.	NOUN
american_scientific_journal-756	245	17	let	let	VERB
american_scientific_journal-756	245	18	(	(	PUNCT
american_scientific_journal-756	245	19	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	245	20	)	)	PUNCT
american_scientific_journal-756	245	21	be	be	AUX
american_scientific_journal-756	245	22	a	a	DET
american_scientific_journal-756	245	23	soft	soft	ADJ
american_scientific_journal-756	245	24	closed	closed	ADJ
american_scientific_journal-756	245	25	set	set	VERB
american_scientific_journal-756	245	26	over	over	ADP
american_scientific_journal-756	245	27	𝑌	𝑌	PROPN
american_scientific_journal-756	245	28	with	with	ADP
american_scientific_journal-756	245	29	𝐹|𝑀𝑖(𝑥	𝐹|𝑀𝑖(𝑥	PROPN
american_scientific_journal-756	245	30	)	)	PUNCT
american_scientific_journal-756	245	31	∩	∩	NOUN
american_scientific_journal-756	245	32	(	(	PUNCT
american_scientific_journal-756	245	33	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	245	34	)	)	PUNCT
american_scientific_journal-756	245	35	≠	≠	PROPN
american_scientific_journal-756	245	36	𝛷.	𝛷.	PROPN
american_scientific_journal-756	245	37	since	since	SCONJ
american_scientific_journal-756	245	38	𝐹	𝐹	PROPN
american_scientific_journal-756	245	39	is	be	AUX
american_scientific_journal-756	245	40	soft	soft	ADJ
american_scientific_journal-756	245	41	lower	low	ADJ
american_scientific_journal-756	245	42	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	245	43	and	and	CCONJ
american_scientific_journal-756	245	44	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	245	45	)	)	PUNCT
american_scientific_journal-756	245	46	=	=	SYM
american_scientific_journal-756	245	47	𝐹|𝑀𝑖(𝑥	𝐹|𝑀𝑖(𝑥	PROPN
american_scientific_journal-756	245	48	)	)	PUNCT
american_scientific_journal-756	245	49	,	,	PUNCT
american_scientific_journal-756	245	50	there	there	PRON
american_scientific_journal-756	245	51	exists	exist	VERB
american_scientific_journal-756	245	52	an	an	DET
american_scientific_journal-756	245	53	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	245	54	set	set	NOUN
american_scientific_journal-756	245	55	𝑃	𝑃	NOUN
american_scientific_journal-756	245	56	containing	contain	VERB
american_scientific_journal-756	245	57	𝑥	𝑥	PRON
american_scientific_journal-756	245	58	such	such	ADJ
american_scientific_journal-756	245	59	that	that	PRON
american_scientific_journal-756	245	60	𝑃	𝑃	VERB
american_scientific_journal-756	245	61	⊆	⊆	NUM
american_scientific_journal-756	245	62	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	245	63	)	)	PUNCT
american_scientific_journal-756	245	64	.	.	PUNCT
american_scientific_journal-756	246	1	take	take	VERB
american_scientific_journal-756	246	2	𝑃₁	𝑃₁	NOUN
american_scientific_journal-756	246	3	=	=	PUNCT
american_scientific_journal-756	246	4	𝑃	𝑃	NOUN
american_scientific_journal-756	246	5	∩𝑀𝑖	∩𝑀𝑖	NOUN
american_scientific_journal-756	246	6	.	.	PUNCT
american_scientific_journal-756	247	1	then	then	ADV
american_scientific_journal-756	247	2	𝑃₁	𝑃₁	PROPN
american_scientific_journal-756	247	3	is	be	AUX
american_scientific_journal-756	247	4	an	an	DET
american_scientific_journal-756	247	5	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	247	6	set	set	NOUN
american_scientific_journal-756	247	7	in	in	ADP
american_scientific_journal-756	247	8	𝑀𝑖containing	𝑀𝑖containe	VERB
american_scientific_journal-756	247	9	𝑥.	𝑥.	ADV
american_scientific_journal-756	247	10	we	we	PRON
american_scientific_journal-756	247	11	have	have	VERB
american_scientific_journal-756	247	12	𝑃₁	𝑃₁	PROPN
american_scientific_journal-756	247	13	⊆	⊆	NUM
american_scientific_journal-756	247	14	�	�	SYM
american_scientific_journal-756	247	15	𝐹|𝑀𝑖	𝐹|𝑀𝑖	NOUN
american_scientific_journal-756	247	16	�	�	PROPN
american_scientific_journal-756	247	17	−(𝐺,𝐸	−(𝐺,𝐸	PROPN
american_scientific_journal-756	247	18	)	)	PUNCT
american_scientific_journal-756	247	19	.	.	PUNCT
american_scientific_journal-756	248	1	thus	thus	ADV
american_scientific_journal-756	248	2	𝐹|𝑀𝑖	𝐹|𝑀𝑖	NOUN
american_scientific_journal-756	248	3	is	be	AUX
american_scientific_journal-756	248	4	soft	soft	ADJ
american_scientific_journal-756	248	5	lower	low	ADJ
american_scientific_journal-756	248	6	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	248	7	.	.	PUNCT
american_scientific_journal-756	249	1	conversely	conversely	ADV
american_scientific_journal-756	249	2	,	,	PUNCT
american_scientific_journal-756	249	3	let	let	VERB
american_scientific_journal-756	249	4	𝑥	𝑥	PRON
american_scientific_journal-756	249	5	∈	∈	PROPN
american_scientific_journal-756	249	6	𝑋	𝑋	PROPN
american_scientific_journal-756	249	7	and	and	CCONJ
american_scientific_journal-756	249	8	(	(	PUNCT
american_scientific_journal-756	249	9	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	249	10	)	)	PUNCT
american_scientific_journal-756	249	11	be	be	VERB
american_scientific_journal-756	249	12	a	a	DET
american_scientific_journal-756	249	13	soft	soft	ADJ
american_scientific_journal-756	249	14	closed	closed	ADJ
american_scientific_journal-756	249	15	set	set	VERB
american_scientific_journal-756	249	16	over	over	ADP
american_scientific_journal-756	249	17	𝑌	𝑌	PROPN
american_scientific_journal-756	249	18	with	with	ADP
american_scientific_journal-756	249	19	𝐹(𝑥	𝐹(𝑥	NUM
american_scientific_journal-756	249	20	)	)	PUNCT
american_scientific_journal-756	249	21	⊆	⊆	NUM
american_scientific_journal-756	249	22	(	(	PUNCT
american_scientific_journal-756	249	23	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	249	24	)	)	PUNCT
american_scientific_journal-756	249	25	.	.	PUNCT
american_scientific_journal-756	250	1	since	since	SCONJ
american_scientific_journal-756	250	2	{	{	PUNCT
american_scientific_journal-756	250	3	𝑀𝑖	𝑀𝑖	NOUN
american_scientific_journal-756	250	4	:	:	PUNCT
american_scientific_journal-756	250	5	𝑖	𝑖	SYM
american_scientific_journal-756	250	6	∈	∈	PROPN
american_scientific_journal-756	250	7	𝐼	𝐼	PROPN
american_scientific_journal-756	250	8	}	}	PUNCT
american_scientific_journal-756	250	9	is	be	AUX
american_scientific_journal-756	250	10	an	an	DET
american_scientific_journal-756	250	11	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	250	12	cover	cover	NOUN
american_scientific_journal-756	250	13	set	set	NOUN
american_scientific_journal-756	250	14	of	of	ADP
american_scientific_journal-756	250	15	𝑋	𝑋	PROPN
american_scientific_journal-756	250	16	,	,	PUNCT
american_scientific_journal-756	250	17	then	then	ADV
american_scientific_journal-756	250	18	𝑥	𝑥	PROPN
american_scientific_journal-756	250	19	∈	∈	PROPN
american_scientific_journal-756	250	20	𝑀𝑖0for	𝑀𝑖0for	ADP
american_scientific_journal-756	250	21	an	an	DET
american_scientific_journal-756	250	22	𝑖0	𝑖0	PROPN
american_scientific_journal-756	250	23	∈	∈	PROPN
american_scientific_journal-756	250	24	𝐼.	𝐼.	NOUN
american_scientific_journal-756	250	25	we	we	PRON
american_scientific_journal-756	250	26	have	have	AUX
american_scientific_journal-756	250	27	�	�	VERB
american_scientific_journal-756	250	28	𝐹|𝑀𝑖0	𝐹|𝑀𝑖0	ADJ
american_scientific_journal-756	250	29	�	�	PROPN
american_scientific_journal-756	251	1	−	−	PROPN
american_scientific_journal-756	251	2	(	(	PUNCT
american_scientific_journal-756	251	3	𝑥	𝑥	NOUN
american_scientific_journal-756	251	4	)	)	PUNCT
american_scientific_journal-756	251	5	=	=	SYM
american_scientific_journal-756	251	6	𝐹(𝑥	𝐹(𝑥	X
american_scientific_journal-756	251	7	)	)	PUNCT
american_scientific_journal-756	251	8	and	and	CCONJ
american_scientific_journal-756	251	9	hence	hence	ADV
american_scientific_journal-756	251	10	𝑥	𝑥	DET
american_scientific_journal-756	251	11	∈	∈	PROPN
american_scientific_journal-756	251	12	�	�	PROPN
american_scientific_journal-756	251	13	𝐹|𝑀𝑖0	𝐹|𝑀𝑖0	ADJ
american_scientific_journal-756	251	14	�	�	PROPN
american_scientific_journal-756	252	1	−	−	PROPN
american_scientific_journal-756	252	2	(	(	PUNCT
american_scientific_journal-756	252	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	252	4	)	)	PUNCT
american_scientific_journal-756	252	5	.	.	PUNCT
american_scientific_journal-756	253	1	since	since	SCONJ
american_scientific_journal-756	253	2	�	�	PROPN
american_scientific_journal-756	253	3	𝐹|𝑀𝑖0	𝐹|𝑀𝑖0	PROPN
american_scientific_journal-756	253	4	�	�	PROPN
american_scientific_journal-756	253	5	−	−	PROPN
american_scientific_journal-756	253	6	is	be	AUX
american_scientific_journal-756	253	7	soft	soft	ADJ
american_scientific_journal-756	253	8	lower	low	ADJ
american_scientific_journal-756	253	9	𝛼	𝛼	NOUN
american_scientific_journal-756	253	10	-continuous	-continuous	ADJ
american_scientific_journal-756	253	11	,	,	PUNCT
american_scientific_journal-756	253	12	there	there	PRON
american_scientific_journal-756	253	13	exists	exist	VERB
american_scientific_journal-756	253	14	an	an	DET
american_scientific_journal-756	253	15	𝛼	𝛼	SYM
american_scientific_journal-756	253	16	-open	-open	NOUN
american_scientific_journal-756	253	17	set	set	VERB
american_scientific_journal-756	253	18	𝐵	𝐵	NOUN
american_scientific_journal-756	253	19	=	=	SYM
american_scientific_journal-756	253	20	𝐷	𝐷	PROPN
american_scientific_journal-756	253	21	∩𝑀𝑖0	∩𝑀𝑖0	ADJ
american_scientific_journal-756	253	22	in	in	ADP
american_scientific_journal-756	253	23	𝑀𝑖0	𝑀𝑖0	ADJ
american_scientific_journal-756	253	24	such	such	ADJ
american_scientific_journal-756	253	25	that	that	SCONJ
american_scientific_journal-756	253	26	𝑥	𝑥	PROPN
american_scientific_journal-756	253	27	∈	∈	PROPN
american_scientific_journal-756	253	28	𝐵	𝐵	NOUN
american_scientific_journal-756	253	29	and	and	CCONJ
american_scientific_journal-756	253	30	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	253	31	)	)	PUNCT
american_scientific_journal-756	253	32	∩𝑀𝑖0	∩𝑀𝑖0	NUM
american_scientific_journal-756	253	33	=	=	SYM
american_scientific_journal-756	253	34	�	�	PROPN
american_scientific_journal-756	253	35	𝐹|𝑀𝑖0	𝐹|𝑀𝑖0	ADJ
american_scientific_journal-756	253	36	�	�	PROPN
american_scientific_journal-756	254	1	−	−	PROPN
american_scientific_journal-756	254	2	(	(	PUNCT
american_scientific_journal-756	254	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	254	4	)	)	PUNCT
american_scientific_journal-756	254	5	⊃	⊃	PROPN
american_scientific_journal-756	254	6	𝐵	𝐵	PROPN
american_scientific_journal-756	254	7	=	=	SYM
american_scientific_journal-756	254	8	𝐷	𝐷	PROPN
american_scientific_journal-756	254	9	∩	∩	ADJ
american_scientific_journal-756	254	10	𝐷	𝐷	NOUN
american_scientific_journal-756	254	11	∩	∩	NOUN
american_scientific_journal-756	254	12	𝑀𝑖0	𝑀𝑖0	NOUN
american_scientific_journal-756	254	13	,	,	PUNCT
american_scientific_journal-756	254	14	where	where	SCONJ
american_scientific_journal-756	254	15	𝐷	𝐷	PROPN
american_scientific_journal-756	254	16	is	be	AUX
american_scientific_journal-756	254	17	an	an	DET
american_scientific_journal-756	254	18	𝛼	𝛼	X
american_scientific_journal-756	254	19	-open	-open	NOUN
american_scientific_journal-756	254	20	set	set	VERB
american_scientific_journal-756	254	21	in	in	ADP
american_scientific_journal-756	254	22	𝑋	𝑋	PROPN
american_scientific_journal-756	254	23	.	.	PUNCT
american_scientific_journal-756	255	1	we	we	PRON
american_scientific_journal-756	255	2	have	have	VERB
american_scientific_journal-756	255	3	𝑥	𝑥	DET
american_scientific_journal-756	255	4	∈	∈	PROPN
american_scientific_journal-756	255	5	𝐵	𝐵	NOUN
american_scientific_journal-756	255	6	=	=	SYM
american_scientific_journal-756	255	7	𝐷	𝐷	PROPN
american_scientific_journal-756	255	8	∩	∩	ADJ
american_scientific_journal-756	255	9	𝐷	𝐷	PROPN
american_scientific_journal-756	255	10	∩𝑀𝑖0	∩𝑀𝑖0	PROPN
american_scientific_journal-756	255	11	⊂	⊂	PROPN
american_scientific_journal-756	255	12	�	�	PROPN
american_scientific_journal-756	255	13	𝐹|𝑀𝑖0	𝐹|𝑀𝑖0	ADJ
american_scientific_journal-756	255	14	�	�	PROPN
american_scientific_journal-756	256	1	−	−	PROPN
american_scientific_journal-756	256	2	(	(	PUNCT
american_scientific_journal-756	256	3	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	256	4	)	)	PUNCT
american_scientific_journal-756	256	5	=	=	SYM
american_scientific_journal-756	256	6	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	256	7	)	)	PUNCT
american_scientific_journal-756	256	8	∩	∩	NOUN
american_scientific_journal-756	256	9	𝑀𝑖0	𝑀𝑖0	NOUN
american_scientific_journal-756	256	10	⊂	⊂	PROPN
american_scientific_journal-756	256	11	𝐹⁻(𝐺,𝐸	𝐹⁻(𝐺,𝐸	NOUN
american_scientific_journal-756	256	12	)	)	PUNCT
american_scientific_journal-756	256	13	.	.	PUNCT
american_scientific_journal-756	257	1	hence	hence	ADV
american_scientific_journal-756	257	2	𝐹	𝐹	PROPN
american_scientific_journal-756	257	3	is	be	AUX
american_scientific_journal-756	257	4	soft	soft	ADJ
american_scientific_journal-756	257	5	lower	low	ADJ
american_scientific_journal-756	257	6	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	257	7	.	.	PUNCT
american_scientific_journal-756	258	1	(	(	PUNCT
american_scientific_journal-756	258	2	b	b	X
american_scientific_journal-756	258	3	):	):	PUNCT
american_scientific_journal-756	258	4	it	it	PRON
american_scientific_journal-756	258	5	is	be	AUX
american_scientific_journal-756	258	6	similar	similar	ADJ
american_scientific_journal-756	258	7	to	to	ADP
american_scientific_journal-756	258	8	the	the	DET
american_scientific_journal-756	258	9	proof	proof	NOUN
american_scientific_journal-756	258	10	(	(	PUNCT
american_scientific_journal-756	258	11	a	a	X
american_scientific_journal-756	258	12	)	)	PUNCT
american_scientific_journal-756	258	13	.	.	PUNCT
american_scientific_journal-756	259	1	definition	definition	NOUN
american_scientific_journal-756	259	2	3.21	3.21	NUM
american_scientific_journal-756	259	3	.	.	PUNCT
american_scientific_journal-756	260	1	[	[	X
american_scientific_journal-756	260	2	20	20	NUM
american_scientific_journal-756	260	3	]	]	PUNCT
american_scientific_journal-756	260	4	let	let	VERB
american_scientific_journal-756	260	5	𝐹	𝐹	PRON
american_scientific_journal-756	260	6	:	:	PUNCT
american_scientific_journal-756	260	7	(	(	PUNCT
american_scientific_journal-756	260	8	𝑋	𝑋	PROPN
american_scientific_journal-756	260	9	,	,	PUNCT
american_scientific_journal-756	260	10	𝜏	𝜏	NOUN
american_scientific_journal-756	260	11	)	)	PUNCT
american_scientific_journal-756	260	12	→	→	SYM
american_scientific_journal-756	260	13	(	(	PUNCT
american_scientific_journal-756	260	14	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	260	15	)	)	PUNCT
american_scientific_journal-756	260	16	be	be	VERB
american_scientific_journal-756	260	17	a	a	DET
american_scientific_journal-756	260	18	multifunction	multifunction	NOUN
american_scientific_journal-756	260	19	and	and	CCONJ
american_scientific_journal-756	260	20	let	let	VERB
american_scientific_journal-756	260	21	𝐺	𝐺	NOUN
american_scientific_journal-756	260	22	:	:	PUNCT
american_scientific_journal-756	260	23	(	(	PUNCT
american_scientific_journal-756	260	24	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	260	25	)	)	PUNCT
american_scientific_journal-756	260	26	→	→	SYM
american_scientific_journal-756	260	27	(	(	PUNCT
american_scientific_journal-756	260	28	𝑍,𝜗,𝐸	𝑍,𝜗,𝐸	NOUN
american_scientific_journal-756	260	29	)	)	PUNCT
american_scientific_journal-756	260	30	be	be	AUX
american_scientific_journal-756	260	31	a	a	DET
american_scientific_journal-756	260	32	soft	soft	ADJ
american_scientific_journal-756	260	33	multifunction	multifunction	NOUN
american_scientific_journal-756	260	34	.	.	PUNCT
american_scientific_journal-756	261	1	then	then	ADV
american_scientific_journal-756	261	2	the	the	DET
american_scientific_journal-756	261	3	soft	soft	ADJ
american_scientific_journal-756	261	4	multifunction	multifunction	NOUN
american_scientific_journal-756	261	5	𝐺	𝐺	NOUN
american_scientific_journal-756	261	6	∘	∘	PROPN
american_scientific_journal-756	261	7	𝐹	𝐹	PROPN
american_scientific_journal-756	261	8	:	:	PUNCT
american_scientific_journal-756	261	9	(	(	PUNCT
american_scientific_journal-756	261	10	𝑋	𝑋	PROPN
american_scientific_journal-756	261	11	,	,	PUNCT
american_scientific_journal-756	261	12	𝜏	𝜏	NOUN
american_scientific_journal-756	261	13	)	)	PUNCT
american_scientific_journal-756	261	14	→	→	SYM
american_scientific_journal-756	261	15	(	(	PUNCT
american_scientific_journal-756	261	16	𝑍,𝜗,𝐸	𝑍,𝜗,𝐸	NOUN
american_scientific_journal-756	261	17	)	)	PUNCT
american_scientific_journal-756	261	18	is	be	AUX
american_scientific_journal-756	261	19	defined	define	VERB
american_scientific_journal-756	261	20	by	by	ADP
american_scientific_journal-756	261	21	(	(	PUNCT
american_scientific_journal-756	261	22	𝐺	𝐺	PROPN
american_scientific_journal-756	261	23	∘	∘	PROPN
american_scientific_journal-756	261	24	𝐹)(𝑥	𝐹)(𝑥	NOUN
american_scientific_journal-756	261	25	)	)	PUNCT
american_scientific_journal-756	261	26	=	=	SYM
american_scientific_journal-756	261	27	𝐺(𝐹(𝑥	𝐺(𝐹(𝑥	X
american_scientific_journal-756	261	28	)	)	PUNCT
american_scientific_journal-756	261	29	)	)	PUNCT
american_scientific_journal-756	261	30	.	.	PUNCT
american_scientific_journal-756	262	1	proposition	proposition	NOUN
american_scientific_journal-756	262	2	3.22	3.22	NUM
american_scientific_journal-756	262	3	.	.	PUNCT
american_scientific_journal-756	263	1	[	[	X
american_scientific_journal-756	263	2	20	20	NUM
american_scientific_journal-756	263	3	]	]	PUNCT
american_scientific_journal-756	263	4	let	let	VERB
american_scientific_journal-756	263	5	𝐹	𝐹	PRON
american_scientific_journal-756	263	6	:	:	PUNCT
american_scientific_journal-756	263	7	(	(	PUNCT
american_scientific_journal-756	263	8	𝑋	𝑋	PROPN
american_scientific_journal-756	263	9	,	,	PUNCT
american_scientific_journal-756	263	10	𝜏	𝜏	NOUN
american_scientific_journal-756	263	11	)	)	PUNCT
american_scientific_journal-756	263	12	→	→	SYM
american_scientific_journal-756	263	13	(	(	PUNCT
american_scientific_journal-756	263	14	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	263	15	)	)	PUNCT
american_scientific_journal-756	263	16	be	be	VERB
american_scientific_journal-756	263	17	a	a	DET
american_scientific_journal-756	263	18	multifunction	multifunction	NOUN
american_scientific_journal-756	263	19	and	and	CCONJ
american_scientific_journal-756	263	20	let	let	VERB
american_scientific_journal-756	263	21	𝐺	𝐺	NOUN
american_scientific_journal-756	263	22	:	:	PUNCT
american_scientific_journal-756	263	23	(	(	PUNCT
american_scientific_journal-756	263	24	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	263	25	)	)	PUNCT
american_scientific_journal-756	263	26	→	→	SYM
american_scientific_journal-756	263	27	(	(	PUNCT
american_scientific_journal-756	263	28	𝑍,𝜗,𝐸	𝑍,𝜗,𝐸	NOUN
american_scientific_journal-756	263	29	)	)	PUNCT
american_scientific_journal-756	263	30	be	be	AUX
american_scientific_journal-756	263	31	a	a	DET
american_scientific_journal-756	263	32	soft	soft	ADJ
american_scientific_journal-756	263	33	multifunction	multifunction	NOUN
american_scientific_journal-756	263	34	.	.	PUNCT
american_scientific_journal-756	264	1	then	then	ADV
american_scientific_journal-756	264	2	we	we	PRON
american_scientific_journal-756	264	3	have	have	VERB
american_scientific_journal-756	264	4	(	(	PUNCT
american_scientific_journal-756	264	5	a	a	X
american_scientific_journal-756	264	6	)	)	PUNCT
american_scientific_journal-756	264	7	(	(	PUNCT
american_scientific_journal-756	264	8	𝐺	𝐺	PROPN
american_scientific_journal-756	264	9	∘	∘	NOUN
american_scientific_journal-756	264	10	𝐹)⁺(𝐻,𝐸	𝐹)⁺(𝐻,𝐸	ADJ
american_scientific_journal-756	264	11	)	)	PUNCT
american_scientific_journal-756	264	12	=	=	SYM
american_scientific_journal-756	264	13	𝐹⁺(𝐺⁺(𝐻,𝐸	𝐹⁺(𝐺⁺(𝐻,𝐸	NUM
american_scientific_journal-756	264	14	)	)	PUNCT
american_scientific_journal-756	264	15	)	)	PUNCT
american_scientific_journal-756	265	1	(	(	PUNCT
american_scientific_journal-756	265	2	b	b	X
american_scientific_journal-756	265	3	)	)	PUNCT
american_scientific_journal-756	265	4	(	(	PUNCT
american_scientific_journal-756	265	5	𝐺	𝐺	PROPN
american_scientific_journal-756	265	6	∘	∘	X
american_scientific_journal-756	265	7	𝐹)⁻(𝐻,𝐸	𝐹)⁻(𝐻,𝐸	NOUN
american_scientific_journal-756	265	8	)	)	PUNCT
american_scientific_journal-756	265	9	=	=	SYM
american_scientific_journal-756	265	10	𝐹⁻(𝐺⁻(𝐻,𝐸	𝐹⁻(𝐺⁻(𝐻,𝐸	NUM
american_scientific_journal-756	265	11	)	)	PUNCT
american_scientific_journal-756	265	12	)	)	PUNCT
american_scientific_journal-756	265	13	definition	definition	NOUN
american_scientific_journal-756	265	14	3.23	3.23	NUM
american_scientific_journal-756	265	15	.	.	PUNCT
american_scientific_journal-756	266	1	[	[	X
american_scientific_journal-756	266	2	3	3	X
american_scientific_journal-756	266	3	]	]	X
american_scientific_journal-756	266	4	let	let	NOUN
american_scientific_journal-756	266	5	(	(	PUNCT
american_scientific_journal-756	266	6	𝑋	𝑋	NOUN
american_scientific_journal-756	266	7	,	,	PUNCT
american_scientific_journal-756	266	8	𝜏	𝜏	NOUN
american_scientific_journal-756	266	9	)	)	PUNCT
american_scientific_journal-756	266	10	and	and	CCONJ
american_scientific_journal-756	266	11	(	(	PUNCT
american_scientific_journal-756	266	12	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	266	13	)	)	PUNCT
american_scientific_journal-756	266	14	be	be	VERB
american_scientific_journal-756	266	15	two	two	NUM
american_scientific_journal-756	266	16	ordinary	ordinary	ADJ
american_scientific_journal-756	266	17	topological	topological	ADJ
american_scientific_journal-756	266	18	spaces	space	NOUN
american_scientific_journal-756	266	19	.	.	PUNCT
american_scientific_journal-756	267	1	then	then	ADV
american_scientific_journal-756	267	2	a	a	DET
american_scientific_journal-756	267	3	multifunction	multifunction	NOUN
american_scientific_journal-756	267	4	𝐹	𝐹	PROPN
american_scientific_journal-756	267	5	:	:	PUNCT
american_scientific_journal-756	267	6	(	(	PUNCT
american_scientific_journal-756	267	7	𝑋	𝑋	PROPN
american_scientific_journal-756	267	8	,	,	PUNCT
american_scientific_journal-756	267	9	𝜏	𝜏	NOUN
american_scientific_journal-756	267	10	)	)	PUNCT
american_scientific_journal-756	267	11	→	→	SYM
american_scientific_journal-756	267	12	104	104	NUM
american_scientific_journal-756	267	13	american	american	ADJ
american_scientific_journal-756	267	14	scientific	scientific	ADJ
american_scientific_journal-756	267	15	research	research	NOUN
american_scientific_journal-756	267	16	journal	journal	NOUN
american_scientific_journal-756	267	17	for	for	ADP
american_scientific_journal-756	267	18	engineering	engineering	NOUN
american_scientific_journal-756	267	19	,	,	PUNCT
american_scientific_journal-756	267	20	technology	technology	NOUN
american_scientific_journal-756	267	21	,	,	PUNCT
american_scientific_journal-756	267	22	and	and	CCONJ
american_scientific_journal-756	267	23	sciences	science	NOUN
american_scientific_journal-756	267	24	(	(	PUNCT
american_scientific_journal-756	267	25	asrjets	asrjet	NOUN
american_scientific_journal-756	267	26	)	)	PUNCT
american_scientific_journal-756	267	27	(	(	PUNCT
american_scientific_journal-756	267	28	2014	2014	NUM
american_scientific_journal-756	267	29	)	)	PUNCT
american_scientific_journal-756	267	30	volume	volume	NOUN
american_scientific_journal-756	267	31	8	8	NUM
american_scientific_journal-756	267	32	,	,	PUNCT
american_scientific_journal-756	267	33	no	no	DET
american_scientific_journal-756	267	34	1	1	NUM
american_scientific_journal-756	267	35	,	,	PUNCT
american_scientific_journal-756	267	36	pp	pp	ADV
american_scientific_journal-756	267	37	96	96	NUM
american_scientific_journal-756	267	38	-	-	SYM
american_scientific_journal-756	267	39	107	107	NUM
american_scientific_journal-756	267	40	(	(	PUNCT
american_scientific_journal-756	267	41	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	267	42	)	)	PUNCT
american_scientific_journal-756	267	43	is	be	AUX
american_scientific_journal-756	267	44	said	say	VERB
american_scientific_journal-756	267	45	to	to	PART
american_scientific_journal-756	267	46	be	be	AUX
american_scientific_journal-756	267	47	;	;	PUNCT
american_scientific_journal-756	267	48	(	(	PUNCT
american_scientific_journal-756	267	49	a	a	X
american_scientific_journal-756	267	50	)	)	PUNCT
american_scientific_journal-756	267	51	upper	upper	ADJ
american_scientific_journal-756	267	52	continuous	continuous	ADJ
american_scientific_journal-756	267	53	if	if	SCONJ
american_scientific_journal-756	267	54	for	for	ADP
american_scientific_journal-756	267	55	each	each	DET
american_scientific_journal-756	267	56	open	open	ADJ
american_scientific_journal-756	267	57	set	set	VERB
american_scientific_journal-756	267	58	𝑉	𝑉	PROPN
american_scientific_journal-756	267	59	in	in	ADP
american_scientific_journal-756	267	60	𝑌	𝑌	PROPN
american_scientific_journal-756	267	61	,	,	PUNCT
american_scientific_journal-756	267	62	𝐹⁺(𝑉	𝐹⁺(𝑉	PROPN
american_scientific_journal-756	267	63	)	)	PUNCT
american_scientific_journal-756	267	64	is	be	AUX
american_scientific_journal-756	267	65	an	an	DET
american_scientific_journal-756	267	66	open	open	ADJ
american_scientific_journal-756	267	67	set	set	NOUN
american_scientific_journal-756	267	68	in	in	ADP
american_scientific_journal-756	267	69	𝑋.	𝑋.	PROPN
american_scientific_journal-756	267	70	(	(	PUNCT
american_scientific_journal-756	267	71	b	b	NOUN
american_scientific_journal-756	267	72	)	)	PUNCT
american_scientific_journal-756	267	73	lower	low	ADJ
american_scientific_journal-756	267	74	continuous	continuous	ADJ
american_scientific_journal-756	267	75	if	if	SCONJ
american_scientific_journal-756	267	76	for	for	ADP
american_scientific_journal-756	267	77	each	each	DET
american_scientific_journal-756	267	78	open	open	ADJ
american_scientific_journal-756	267	79	set	set	VERB
american_scientific_journal-756	267	80	𝑉	𝑉	PROPN
american_scientific_journal-756	267	81	in	in	ADP
american_scientific_journal-756	267	82	𝑌	𝑌	PROPN
american_scientific_journal-756	267	83	,	,	PUNCT
american_scientific_journal-756	267	84	𝐹⁻(𝑉	𝐹⁻(𝑉	ADJ
american_scientific_journal-756	267	85	)	)	PUNCT
american_scientific_journal-756	267	86	is	be	AUX
american_scientific_journal-756	267	87	an	an	DET
american_scientific_journal-756	267	88	open	open	ADJ
american_scientific_journal-756	267	89	set	set	NOUN
american_scientific_journal-756	267	90	in	in	ADP
american_scientific_journal-756	267	91	𝑋.	𝑋.	PROPN
american_scientific_journal-756	267	92	theorem	theorem	VERB
american_scientific_journal-756	267	93	3.24	3.24	NUM
american_scientific_journal-756	267	94	.	.	PUNCT
american_scientific_journal-756	268	1	let	let	VERB
american_scientific_journal-756	268	2	𝐹	𝐹	PRON
american_scientific_journal-756	268	3	:	:	PUNCT
american_scientific_journal-756	268	4	(	(	PUNCT
american_scientific_journal-756	268	5	𝑋	𝑋	PROPN
american_scientific_journal-756	268	6	,	,	PUNCT
american_scientific_journal-756	268	7	𝜏	𝜏	NOUN
american_scientific_journal-756	268	8	)	)	PUNCT
american_scientific_journal-756	268	9	→	→	SYM
american_scientific_journal-756	268	10	(	(	PUNCT
american_scientific_journal-756	268	11	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	268	12	)	)	PUNCT
american_scientific_journal-756	268	13	be	be	VERB
american_scientific_journal-756	268	14	a	a	DET
american_scientific_journal-756	268	15	multifunction	multifunction	NOUN
american_scientific_journal-756	268	16	and	and	CCONJ
american_scientific_journal-756	268	17	let	let	VERB
american_scientific_journal-756	268	18	𝐺	𝐺	NOUN
american_scientific_journal-756	268	19	:	:	PUNCT
american_scientific_journal-756	268	20	(	(	PUNCT
american_scientific_journal-756	268	21	𝑌,𝜎	𝑌,𝜎	NUM
american_scientific_journal-756	268	22	)	)	PUNCT
american_scientific_journal-756	269	1	→	→	SYM
american_scientific_journal-756	269	2	(	(	PUNCT
american_scientific_journal-756	269	3	𝑍,𝜗,𝐸	𝑍,𝜗,𝐸	NOUN
american_scientific_journal-756	269	4	)	)	PUNCT
american_scientific_journal-756	269	5	be	be	AUX
american_scientific_journal-756	269	6	a	a	DET
american_scientific_journal-756	269	7	soft	soft	ADJ
american_scientific_journal-756	269	8	multifunction	multifunction	NOUN
american_scientific_journal-756	269	9	.	.	PUNCT
american_scientific_journal-756	270	1	if	if	SCONJ
american_scientific_journal-756	270	2	𝐹	𝐹	PROPN
american_scientific_journal-756	270	3	is	be	AUX
american_scientific_journal-756	270	4	upper	upper	ADJ
american_scientific_journal-756	270	5	(	(	PUNCT
american_scientific_journal-756	270	6	lower	low	ADJ
american_scientific_journal-756	270	7	)	)	PUNCT
american_scientific_journal-756	270	8	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	270	9	and	and	CCONJ
american_scientific_journal-756	270	10	𝐺	𝐺	PROPN
american_scientific_journal-756	270	11	is	be	AUX
american_scientific_journal-756	270	12	soft	soft	ADJ
american_scientific_journal-756	270	13	upper	upper	ADJ
american_scientific_journal-756	270	14	(	(	PUNCT
american_scientific_journal-756	270	15	lower	low	ADJ
american_scientific_journal-756	270	16	)	)	PUNCT
american_scientific_journal-756	270	17	continuous	continuous	ADJ
american_scientific_journal-756	270	18	then	then	ADV
american_scientific_journal-756	270	19	𝐺	𝐺	PROPN
american_scientific_journal-756	270	20	∘	∘	PROPN
american_scientific_journal-756	270	21	𝐹	𝐹	PROPN
american_scientific_journal-756	270	22	is	be	AUX
american_scientific_journal-756	270	23	soft	soft	ADJ
american_scientific_journal-756	270	24	upper	upper	ADJ
american_scientific_journal-756	270	25	(	(	PUNCT
american_scientific_journal-756	270	26	lower	low	ADJ
american_scientific_journal-756	270	27	)	)	PUNCT
american_scientific_journal-756	270	28	𝛼continuous	𝛼continuous	ADJ
american_scientific_journal-756	270	29	.	.	PUNCT
american_scientific_journal-756	271	1	proof	proof	NOUN
american_scientific_journal-756	271	2	.	.	PUNCT
american_scientific_journal-756	272	1	let	let	VERB
american_scientific_journal-756	272	2	(	(	PUNCT
american_scientific_journal-756	272	3	𝐻,𝐸	𝐻,𝐸	VERB
american_scientific_journal-756	272	4	)	)	PUNCT
american_scientific_journal-756	272	5	be	be	VERB
american_scientific_journal-756	272	6	any	any	DET
american_scientific_journal-756	272	7	soft	soft	ADJ
american_scientific_journal-756	272	8	open	open	ADJ
american_scientific_journal-756	272	9	set	set	VERB
american_scientific_journal-756	272	10	over	over	ADP
american_scientific_journal-756	272	11	𝑍.	𝑍.	PROPN
american_scientific_journal-756	272	12	since	since	SCONJ
american_scientific_journal-756	272	13	𝐺	𝐺	PROPN
american_scientific_journal-756	272	14	is	be	AUX
american_scientific_journal-756	272	15	soft	soft	ADJ
american_scientific_journal-756	272	16	upper	upper	ADJ
american_scientific_journal-756	272	17	continuous	continuous	ADJ
american_scientific_journal-756	272	18	then	then	ADV
american_scientific_journal-756	272	19	𝐺⁺(𝐻,𝐸	𝐺⁺(𝐻,𝐸	NUM
american_scientific_journal-756	272	20	)	)	PUNCT
american_scientific_journal-756	272	21	is	be	AUX
american_scientific_journal-756	272	22	open	open	ADJ
american_scientific_journal-756	272	23	in	in	ADP
american_scientific_journal-756	272	24	𝑌.	𝑌.	PROPN
american_scientific_journal-756	272	25	since	since	SCONJ
american_scientific_journal-756	272	26	𝐹	𝐹	PROPN
american_scientific_journal-756	272	27	is	be	AUX
american_scientific_journal-756	272	28	upper	upper	ADJ
american_scientific_journal-756	272	29	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	272	30	then	then	ADV
american_scientific_journal-756	272	31	𝐹⁺(𝐺⁺(𝐻,𝐸	𝐹⁺(𝐺⁺(𝐻,𝐸	NUM
american_scientific_journal-756	272	32	)	)	PUNCT
american_scientific_journal-756	272	33	)	)	PUNCT
american_scientific_journal-756	273	1	=	=	SYM
american_scientific_journal-756	273	2	(	(	PUNCT
american_scientific_journal-756	273	3	𝐺	𝐺	PROPN
american_scientific_journal-756	273	4	∘	∘	NOUN
american_scientific_journal-756	273	5	𝐹)⁺(𝐻,𝐸	𝐹)⁺(𝐻,𝐸	PROPN
american_scientific_journal-756	273	6	)	)	PUNCT
american_scientific_journal-756	273	7	is	be	AUX
american_scientific_journal-756	273	8	𝛼-open	𝛼-open	ADJ
american_scientific_journal-756	273	9	in	in	ADP
american_scientific_journal-756	273	10	𝑋.	𝑋.	PROPN
american_scientific_journal-756	273	11	therefore	therefore	ADV
american_scientific_journal-756	273	12	𝐺	𝐺	PROPN
american_scientific_journal-756	273	13	∘	∘	PROPN
american_scientific_journal-756	273	14	𝐹	𝐹	PROPN
american_scientific_journal-756	273	15	is	be	AUX
american_scientific_journal-756	273	16	soft	soft	ADJ
american_scientific_journal-756	273	17	upper	upper	ADJ
american_scientific_journal-756	273	18	𝛼continuous	𝛼continuous	ADJ
american_scientific_journal-756	273	19	.	.	PUNCT
american_scientific_journal-756	274	1	definition	definition	NOUN
american_scientific_journal-756	274	2	3.25	3.25	NUM
american_scientific_journal-756	274	3	.	.	PUNCT
american_scientific_journal-756	275	1	[	[	X
american_scientific_journal-756	275	2	16	16	NUM
american_scientific_journal-756	275	3	]	]	PUNCT
american_scientific_journal-756	275	4	a	a	DET
american_scientific_journal-756	275	5	family	family	NOUN
american_scientific_journal-756	275	6	𝛹	𝛹	NOUN
american_scientific_journal-756	275	7	of	of	ADP
american_scientific_journal-756	275	8	soft	soft	ADJ
american_scientific_journal-756	275	9	sets	set	NOUN
american_scientific_journal-756	275	10	is	be	AUX
american_scientific_journal-756	275	11	a	a	DET
american_scientific_journal-756	275	12	cover	cover	NOUN
american_scientific_journal-756	275	13	of	of	ADP
american_scientific_journal-756	275	14	a	a	DET
american_scientific_journal-756	275	15	soft	soft	ADJ
american_scientific_journal-756	275	16	set	set	NOUN
american_scientific_journal-756	275	17	(	(	PUNCT
american_scientific_journal-756	275	18	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	275	19	)	)	PUNCT
american_scientific_journal-756	275	20	if	if	SCONJ
american_scientific_journal-756	275	21	(	(	PUNCT
american_scientific_journal-756	275	22	𝐺,𝐸	𝐺,𝐸	NOUN
american_scientific_journal-756	275	23	)	)	PUNCT
american_scientific_journal-756	275	24	⊆	⊆	NUM
american_scientific_journal-756	275	25	�	�	PROPN
american_scientific_journal-756	275	26	∪	∪	NOUN
american_scientific_journal-756	275	27	�	�	PROPN
american_scientific_journal-756	275	28	{	{	PUNCT
american_scientific_journal-756	275	29	(	(	PUNCT
american_scientific_journal-756	275	30	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	275	31	,	,	PUNCT
american_scientific_journal-756	275	32	𝐸	𝐸	PROPN
american_scientific_journal-756	275	33	):	):	PUNCT
american_scientific_journal-756	275	34	(	(	PUNCT
american_scientific_journal-756	275	35	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	275	36	,	,	PUNCT
american_scientific_journal-756	275	37	𝐸	𝐸	PROPN
american_scientific_journal-756	275	38	)	)	PUNCT
american_scientific_journal-756	275	39	∈	∈	PROPN
american_scientific_journal-756	275	40	𝛹	𝛹	PROPN
american_scientific_journal-756	275	41	,	,	PUNCT
american_scientific_journal-756	275	42	𝑖	𝑖	SYM
american_scientific_journal-756	275	43	∈	∈	PROPN
american_scientific_journal-756	275	44	𝐼	𝐼	PROPN
american_scientific_journal-756	275	45	}	}	PUNCT
american_scientific_journal-756	275	46	.	.	PUNCT
american_scientific_journal-756	276	1	it	it	PRON
american_scientific_journal-756	276	2	is	be	AUX
american_scientific_journal-756	276	3	soft	soft	ADJ
american_scientific_journal-756	276	4	open	open	ADJ
american_scientific_journal-756	276	5	cover	cover	NOUN
american_scientific_journal-756	276	6	if	if	SCONJ
american_scientific_journal-756	276	7	each	each	DET
american_scientific_journal-756	276	8	member	member	NOUN
american_scientific_journal-756	276	9	of	of	ADP
american_scientific_journal-756	276	10	𝛹	𝛹	PROPN
american_scientific_journal-756	276	11	is	be	AUX
american_scientific_journal-756	276	12	a	a	DET
american_scientific_journal-756	276	13	soft	soft	ADJ
american_scientific_journal-756	276	14	open	open	ADJ
american_scientific_journal-756	276	15	set	set	NOUN
american_scientific_journal-756	276	16	.	.	PUNCT
american_scientific_journal-756	277	1	a	a	DET
american_scientific_journal-756	277	2	subcover	subcover	NOUN
american_scientific_journal-756	277	3	of	of	ADP
american_scientific_journal-756	277	4	𝛹	𝛹	PROPN
american_scientific_journal-756	277	5	is	be	AUX
american_scientific_journal-756	277	6	a	a	DET
american_scientific_journal-756	277	7	subfamily	subfamily	NOUN
american_scientific_journal-756	277	8	of	of	ADP
american_scientific_journal-756	277	9	𝛹	𝛹	PRON
american_scientific_journal-756	277	10	which	which	PRON
american_scientific_journal-756	277	11	is	be	AUX
american_scientific_journal-756	277	12	also	also	ADV
american_scientific_journal-756	277	13	cover	cover	NOUN
american_scientific_journal-756	277	14	.	.	PUNCT
american_scientific_journal-756	278	1	definition	definition	NOUN
american_scientific_journal-756	278	2	3.26	3.26	NUM
american_scientific_journal-756	278	3	.	.	PUNCT
american_scientific_journal-756	279	1	[	[	X
american_scientific_journal-756	279	2	16	16	NUM
american_scientific_journal-756	279	3	]	]	PUNCT
american_scientific_journal-756	279	4	a	a	DET
american_scientific_journal-756	279	5	soft	soft	ADJ
american_scientific_journal-756	279	6	topological	topological	ADJ
american_scientific_journal-756	279	7	space	space	NOUN
american_scientific_journal-756	279	8	(	(	PUNCT
american_scientific_journal-756	279	9	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	279	10	)	)	PUNCT
american_scientific_journal-756	279	11	is	be	AUX
american_scientific_journal-756	279	12	said	say	VERB
american_scientific_journal-756	279	13	to	to	PART
american_scientific_journal-756	279	14	be	be	AUX
american_scientific_journal-756	279	15	soft	soft	ADJ
american_scientific_journal-756	279	16	𝛼-compact	𝛼-compact	NOUN
american_scientific_journal-756	279	17	if	if	SCONJ
american_scientific_journal-756	279	18	each	each	DET
american_scientific_journal-756	279	19	soft	soft	ADJ
american_scientific_journal-756	279	20	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	279	21	cover	cover	NOUN
american_scientific_journal-756	279	22	of	of	ADP
american_scientific_journal-756	279	23	𝑌	𝑌	PROPN
american_scientific_journal-756	279	24	has	have	VERB
american_scientific_journal-756	279	25	a	a	DET
american_scientific_journal-756	279	26	finite	finite	ADJ
american_scientific_journal-756	279	27	soft	soft	ADJ
american_scientific_journal-756	279	28	subcover	subcover	PROPN
american_scientific_journal-756	279	29	.	.	PUNCT
american_scientific_journal-756	280	1	theorem	theorem	VERB
american_scientific_journal-756	280	2	3.27	3.27	NUM
american_scientific_journal-756	280	3	.	.	PUNCT
american_scientific_journal-756	281	1	let	let	VERB
american_scientific_journal-756	281	2	𝐹	𝐹	PRON
american_scientific_journal-756	281	3	:	:	PUNCT
american_scientific_journal-756	281	4	(	(	PUNCT
american_scientific_journal-756	281	5	𝑋	𝑋	PROPN
american_scientific_journal-756	281	6	,	,	PUNCT
american_scientific_journal-756	281	7	𝜏	𝜏	NOUN
american_scientific_journal-756	281	8	)	)	PUNCT
american_scientific_journal-756	281	9	→	→	X
american_scientific_journal-756	281	10	(	(	PUNCT
american_scientific_journal-756	281	11	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	281	12	)	)	PUNCT
american_scientific_journal-756	281	13	be	be	VERB
american_scientific_journal-756	281	14	an	an	DET
american_scientific_journal-756	281	15	soft	soft	ADJ
american_scientific_journal-756	281	16	upper	upper	ADJ
american_scientific_journal-756	281	17	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	281	18	surjective	surjective	ADJ
american_scientific_journal-756	281	19	multifunction	multifunction	NOUN
american_scientific_journal-756	281	20	and	and	CCONJ
american_scientific_journal-756	281	21	𝑋	𝑋	NOUN
american_scientific_journal-756	281	22	is	be	AUX
american_scientific_journal-756	281	23	𝛼compact	𝛼compact	ADJ
american_scientific_journal-756	281	24	then	then	ADV
american_scientific_journal-756	281	25	𝑌	𝑌	PROPN
american_scientific_journal-756	281	26	is	be	AUX
american_scientific_journal-756	281	27	soft	soft	ADJ
american_scientific_journal-756	281	28	compact	compact	ADJ
american_scientific_journal-756	281	29	.	.	PUNCT
american_scientific_journal-756	282	1	proof	proof	NOUN
american_scientific_journal-756	282	2	.	.	PUNCT
american_scientific_journal-756	283	1	let	let	VERB
american_scientific_journal-756	283	2	𝐹	𝐹	PRON
american_scientific_journal-756	283	3	:	:	PUNCT
american_scientific_journal-756	283	4	(	(	PUNCT
american_scientific_journal-756	283	5	𝑋	𝑋	PROPN
american_scientific_journal-756	283	6	,	,	PUNCT
american_scientific_journal-756	283	7	𝜏	𝜏	NOUN
american_scientific_journal-756	283	8	)	)	PUNCT
american_scientific_journal-756	283	9	→	→	X
american_scientific_journal-756	283	10	(	(	PUNCT
american_scientific_journal-756	283	11	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	283	12	)	)	PUNCT
american_scientific_journal-756	283	13	be	be	VERB
american_scientific_journal-756	283	14	an	an	PRON
american_scientific_journal-756	283	15	onto	onto	ADP
american_scientific_journal-756	283	16	soft	soft	ADJ
american_scientific_journal-756	283	17	multifunction	multifunction	NOUN
american_scientific_journal-756	283	18	and	and	CCONJ
american_scientific_journal-756	283	19	let	let	VERB
american_scientific_journal-756	283	20	𝛹	𝛹	PROPN
american_scientific_journal-756	283	21	=	=	PRON
american_scientific_journal-756	283	22	{	{	PUNCT
american_scientific_journal-756	283	23	(	(	PUNCT
american_scientific_journal-756	283	24	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	283	25	,	,	PUNCT
american_scientific_journal-756	283	26	𝐸	𝐸	PROPN
american_scientific_journal-756	283	27	):	):	PUNCT
american_scientific_journal-756	283	28	𝑖	𝑖	PROPN
american_scientific_journal-756	283	29	∈	∈	PROPN
american_scientific_journal-756	283	30	𝐼	𝐼	PROPN
american_scientific_journal-756	283	31	}	}	PUNCT
american_scientific_journal-756	283	32	be	be	AUX
american_scientific_journal-756	283	33	a	a	DET
american_scientific_journal-756	283	34	cover	cover	NOUN
american_scientific_journal-756	283	35	of	of	ADP
american_scientific_journal-756	283	36	𝑌	𝑌	PROPN
american_scientific_journal-756	283	37	by	by	ADP
american_scientific_journal-756	283	38	soft	soft	ADJ
american_scientific_journal-756	283	39	open	open	ADJ
american_scientific_journal-756	283	40	sets	set	NOUN
american_scientific_journal-756	283	41	.	.	PUNCT
american_scientific_journal-756	284	1	then	then	ADV
american_scientific_journal-756	284	2	since	since	SCONJ
american_scientific_journal-756	284	3	𝐹	𝐹	PROPN
american_scientific_journal-756	284	4	is	be	AUX
american_scientific_journal-756	284	5	soft	soft	ADJ
american_scientific_journal-756	284	6	upper	upper	ADJ
american_scientific_journal-756	284	7	𝛼-continuous	𝛼-continuous	NOUN
american_scientific_journal-756	284	8	,	,	PUNCT
american_scientific_journal-756	284	9	the	the	DET
american_scientific_journal-756	284	10	family	family	NOUN
american_scientific_journal-756	284	11	of	of	ADP
american_scientific_journal-756	284	12	all	all	DET
american_scientific_journal-756	284	13	open	open	ADJ
american_scientific_journal-756	284	14	sets	set	NOUN
american_scientific_journal-756	284	15	of	of	ADP
american_scientific_journal-756	284	16	the	the	DET
american_scientific_journal-756	284	17	form	form	NOUN
american_scientific_journal-756	284	18	𝐹⁺(𝐺𝑖	𝐹⁺(𝐺𝑖	PUNCT
american_scientific_journal-756	284	19	,	,	PUNCT
american_scientific_journal-756	284	20	𝐸	𝐸	PROPN
american_scientific_journal-756	284	21	)	)	PUNCT
american_scientific_journal-756	284	22	,	,	PUNCT
american_scientific_journal-756	284	23	for	for	ADP
american_scientific_journal-756	284	24	(	(	PUNCT
american_scientific_journal-756	284	25	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	284	26	,	,	PUNCT
american_scientific_journal-756	284	27	𝐸	𝐸	PROPN
american_scientific_journal-756	284	28	)	)	PUNCT
american_scientific_journal-756	284	29	∈	∈	PROPN
american_scientific_journal-756	284	30	𝛹	𝛹	PROPN
american_scientific_journal-756	284	31	is	be	AUX
american_scientific_journal-756	284	32	an	an	DET
american_scientific_journal-756	284	33	α	α	NOUN
american_scientific_journal-756	284	34	-	-	ADJ
american_scientific_journal-756	284	35	open	open	ADJ
american_scientific_journal-756	284	36	cover	cover	NOUN
american_scientific_journal-756	284	37	of	of	ADP
american_scientific_journal-756	284	38	𝑋	𝑋	PROPN
american_scientific_journal-756	284	39	which	which	PRON
american_scientific_journal-756	284	40	has	have	VERB
american_scientific_journal-756	284	41	a	a	DET
american_scientific_journal-756	284	42	finite	finite	ADJ
american_scientific_journal-756	284	43	subcover	subcover	PROPN
american_scientific_journal-756	284	44	.	.	PUNCT
american_scientific_journal-756	285	1	however	however	ADV
american_scientific_journal-756	285	2	since	since	SCONJ
american_scientific_journal-756	285	3	𝐹	𝐹	PROPN
american_scientific_journal-756	285	4	is	be	AUX
american_scientific_journal-756	285	5	surjective	surjective	ADJ
american_scientific_journal-756	285	6	,	,	PUNCT
american_scientific_journal-756	285	7	then	then	ADV
american_scientific_journal-756	285	8	it	it	PRON
american_scientific_journal-756	285	9	is	be	AUX
american_scientific_journal-756	285	10	easily	easily	ADV
american_scientific_journal-756	285	11	seen	see	VERB
american_scientific_journal-756	285	12	that	that	SCONJ
american_scientific_journal-756	285	13	𝐹(𝐹⁺(𝐺𝑖	𝐹(𝐹⁺(𝐺𝑖	NUM
american_scientific_journal-756	285	14	,	,	PUNCT
american_scientific_journal-756	285	15	𝐸	𝐸	PROPN
american_scientific_journal-756	285	16	)	)	PUNCT
american_scientific_journal-756	285	17	)	)	PUNCT
american_scientific_journal-756	286	1	=	=	PUNCT
american_scientific_journal-756	286	2	(	(	PUNCT
american_scientific_journal-756	286	3	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	286	4	,	,	PUNCT
american_scientific_journal-756	286	5	𝐸	𝐸	PROPN
american_scientific_journal-756	286	6	)	)	PUNCT
american_scientific_journal-756	286	7	for	for	ADP
american_scientific_journal-756	286	8	any	any	DET
american_scientific_journal-756	286	9	soft	soft	ADJ
american_scientific_journal-756	286	10	set	set	NOUN
american_scientific_journal-756	286	11	(	(	PUNCT
american_scientific_journal-756	286	12	𝐺𝑖	𝐺𝑖	PROPN
american_scientific_journal-756	286	13	,	,	PUNCT
american_scientific_journal-756	286	14	𝐸	𝐸	PROPN
american_scientific_journal-756	286	15	)	)	PUNCT
american_scientific_journal-756	286	16	over	over	ADP
american_scientific_journal-756	286	17	𝑌	𝑌	PROPN
american_scientific_journal-756	286	18	.	.	PUNCT
american_scientific_journal-756	287	1	there	there	PRON
american_scientific_journal-756	287	2	is	be	VERB
american_scientific_journal-756	287	3	the	the	DET
american_scientific_journal-756	287	4	family	family	NOUN
american_scientific_journal-756	287	5	of	of	ADP
american_scientific_journal-756	287	6	image	image	NOUN
american_scientific_journal-756	287	7	members	member	NOUN
american_scientific_journal-756	287	8	of	of	ADP
american_scientific_journal-756	287	9	subcover	subcover	PROPN
american_scientific_journal-756	287	10	is	be	AUX
american_scientific_journal-756	287	11	a	a	DET
american_scientific_journal-756	287	12	finite	finite	NOUN
american_scientific_journal-756	287	13	subfamily	subfamily	ADV
american_scientific_journal-756	287	14	of	of	ADP
american_scientific_journal-756	287	15	𝛹	𝛹	PRON
american_scientific_journal-756	287	16	which	which	PRON
american_scientific_journal-756	287	17	covers	cover	VERB
american_scientific_journal-756	287	18	𝑌.	𝑌.	PROPN
american_scientific_journal-756	287	19	consequently	consequently	ADV
american_scientific_journal-756	287	20	(	(	PUNCT
american_scientific_journal-756	287	21	𝑌,𝜎,𝐸	𝑌,𝜎,𝐸	NOUN
american_scientific_journal-756	287	22	)	)	PUNCT
american_scientific_journal-756	287	23	is	be	AUX
american_scientific_journal-756	287	24	soft	soft	ADJ
american_scientific_journal-756	287	25	compact	compact	ADJ
american_scientific_journal-756	287	26	.	.	PUNCT
american_scientific_journal-756	288	1	3	3	X
american_scientific_journal-756	288	2	.	.	X
american_scientific_journal-756	288	3	conclusion	conclusion	VERB
american_scientific_journal-756	288	4	our	our	PRON
american_scientific_journal-756	288	5	purpose	purpose	NOUN
american_scientific_journal-756	288	6	in	in	ADP
american_scientific_journal-756	288	7	this	this	DET
american_scientific_journal-756	288	8	paper	paper	NOUN
american_scientific_journal-756	288	9	is	be	AUX
american_scientific_journal-756	288	10	to	to	PART
american_scientific_journal-756	288	11	define	define	VERB
american_scientific_journal-756	288	12	upper	upper	ADJ
american_scientific_journal-756	288	13	and	and	CCONJ
american_scientific_journal-756	288	14	lower	low	ADJ
american_scientific_journal-756	288	15	soft	soft	ADJ
american_scientific_journal-756	288	16	𝜶-continuous	𝜶-continuous	ADJ
american_scientific_journal-756	288	17	multifunctions	multifunction	NOUN
american_scientific_journal-756	288	18	and	and	CCONJ
american_scientific_journal-756	288	19	study	study	VERB
american_scientific_journal-756	288	20	their	their	PRON
american_scientific_journal-756	288	21	various	various	ADJ
american_scientific_journal-756	288	22	properties	property	NOUN
american_scientific_journal-756	288	23	.	.	PUNCT
american_scientific_journal-756	289	1	moreover	moreover	ADV
american_scientific_journal-756	289	2	,	,	PUNCT
american_scientific_journal-756	289	3	we	we	PRON
american_scientific_journal-756	289	4	obtain	obtain	VERB
american_scientific_journal-756	289	5	some	some	DET
american_scientific_journal-756	289	6	characterizations	characterization	NOUN
american_scientific_journal-756	289	7	and	and	CCONJ
american_scientific_journal-756	289	8	several	several	ADJ
american_scientific_journal-756	289	9	properties	property	NOUN
american_scientific_journal-756	289	10	concerning	concern	VERB
american_scientific_journal-756	289	11	such	such	ADJ
american_scientific_journal-756	289	12	multifunctions	multifunction	NOUN
american_scientific_journal-756	289	13	.	.	PUNCT
american_scientific_journal-756	290	1	we	we	PRON
american_scientific_journal-756	290	2	expect	expect	VERB
american_scientific_journal-756	290	3	that	that	SCONJ
american_scientific_journal-756	290	4	results	result	NOUN
american_scientific_journal-756	290	5	in	in	ADP
american_scientific_journal-756	290	6	this	this	DET
american_scientific_journal-756	290	7	paper	paper	NOUN
american_scientific_journal-756	290	8	will	will	AUX
american_scientific_journal-756	290	9	be	be	AUX
american_scientific_journal-756	290	10	basis	basis	NOUN
american_scientific_journal-756	290	11	for	for	ADP
american_scientific_journal-756	290	12	further	further	ADJ
american_scientific_journal-756	290	13	applications	application	NOUN
american_scientific_journal-756	290	14	of	of	ADP
american_scientific_journal-756	290	15	soft	soft	ADJ
american_scientific_journal-756	290	16	mappings	mapping	NOUN
american_scientific_journal-756	290	17	in	in	ADP
american_scientific_journal-756	290	18	soft	soft	ADJ
american_scientific_journal-756	290	19	sets	set	NOUN
american_scientific_journal-756	290	20	theory	theory	NOUN
american_scientific_journal-756	290	21	and	and	CCONJ
american_scientific_journal-756	290	22	corresponding	correspond	VERB
american_scientific_journal-756	290	23	information	information	NOUN
american_scientific_journal-756	290	24	systems	system	NOUN
american_scientific_journal-756	290	25	.	.	PUNCT
american_scientific_journal-756	291	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-756	291	2	authors	author	NOUN
american_scientific_journal-756	291	3	are	be	AUX
american_scientific_journal-756	291	4	grateful	grateful	ADJ
american_scientific_journal-756	291	5	to	to	ADP
american_scientific_journal-756	291	6	the	the	DET
american_scientific_journal-756	291	7	reviewers	reviewer	NOUN
american_scientific_journal-756	291	8	and	and	CCONJ
american_scientific_journal-756	291	9	the	the	DET
american_scientific_journal-756	291	10	editor	editor	NOUN
american_scientific_journal-756	291	11	in	in	ADP
american_scientific_journal-756	291	12	chief	chief	NOUN
american_scientific_journal-756	291	13	for	for	ADP
american_scientific_journal-756	291	14	their	their	PRON
american_scientific_journal-756	291	15	helpful	helpful	ADJ
american_scientific_journal-756	291	16	comments	comment	NOUN
american_scientific_journal-756	291	17	and	and	CCONJ
american_scientific_journal-756	291	18	suggestions	suggestion	NOUN
american_scientific_journal-756	291	19	for	for	ADP
american_scientific_journal-756	291	20	improving	improve	VERB
american_scientific_journal-756	291	21	the	the	DET
american_scientific_journal-756	291	22	paper	paper	NOUN
american_scientific_journal-756	291	23	.	.	PUNCT
american_scientific_journal-756	292	1	105	105	NUM
american_scientific_journal-756	292	2	american	american	ADJ
american_scientific_journal-756	292	3	scientific	scientific	ADJ
american_scientific_journal-756	292	4	research	research	NOUN
american_scientific_journal-756	292	5	journal	journal	NOUN
american_scientific_journal-756	292	6	for	for	ADP
american_scientific_journal-756	292	7	engineering	engineering	NOUN
american_scientific_journal-756	292	8	,	,	PUNCT
american_scientific_journal-756	292	9	technology	technology	NOUN
american_scientific_journal-756	292	10	,	,	PUNCT
american_scientific_journal-756	292	11	and	and	CCONJ
american_scientific_journal-756	292	12	sciences	science	NOUN
american_scientific_journal-756	292	13	(	(	PUNCT
american_scientific_journal-756	292	14	asrjets	asrjet	NOUN
american_scientific_journal-756	292	15	)	)	PUNCT
american_scientific_journal-756	292	16	(	(	PUNCT
american_scientific_journal-756	292	17	2014	2014	NUM
american_scientific_journal-756	292	18	)	)	PUNCT
american_scientific_journal-756	292	19	volume	volume	NOUN
american_scientific_journal-756	292	20	8	8	NUM
american_scientific_journal-756	292	21	,	,	PUNCT
american_scientific_journal-756	292	22	no	no	DET
american_scientific_journal-756	292	23	1	1	NUM
american_scientific_journal-756	292	24	,	,	PUNCT
american_scientific_journal-756	292	25	pp	pp	ADV
american_scientific_journal-756	292	26	96	96	NUM
american_scientific_journal-756	292	27	-	-	SYM
american_scientific_journal-756	292	28	107	107	NUM
american_scientific_journal-756	292	29	references	reference	NOUN
american_scientific_journal-756	292	30	[	[	X
american_scientific_journal-756	292	31	1	1	NUM
american_scientific_journal-756	292	32	]	]	X
american_scientific_journal-756	292	33	o.	o.	PROPN
american_scientific_journal-756	292	34	njastad	njastad	PROPN
american_scientific_journal-756	292	35	,	,	PUNCT
american_scientific_journal-756	292	36	on	on	ADP
american_scientific_journal-756	292	37	some	some	DET
american_scientific_journal-756	292	38	classes	class	NOUN
american_scientific_journal-756	292	39	of	of	ADP
american_scientific_journal-756	292	40	nearly	nearly	ADV
american_scientific_journal-756	292	41	open	open	ADJ
american_scientific_journal-756	292	42	sets	set	NOUN
american_scientific_journal-756	292	43	,	,	PUNCT
american_scientific_journal-756	292	44	pacific	pacific	PROPN
american_scientific_journal-756	292	45	j.	j.	PROPN
american_scientific_journal-756	292	46	math	math	PROPN
american_scientific_journal-756	292	47	.	.	PUNCT
american_scientific_journal-756	292	48	,	,	PUNCT
american_scientific_journal-756	292	49	15	15	NUM
american_scientific_journal-756	292	50	(	(	PUNCT
american_scientific_journal-756	292	51	1965	1965	NUM
american_scientific_journal-756	292	52	)	)	PUNCT
american_scientific_journal-756	292	53	,	,	PUNCT
american_scientific_journal-756	292	54	961	961	NUM
american_scientific_journal-756	292	55	-	-	SYM
american_scientific_journal-756	292	56	970	970	NUM
american_scientific_journal-756	292	57	.	.	PUNCT
american_scientific_journal-756	293	1	[	[	X
american_scientific_journal-756	293	2	2	2	NUM
american_scientific_journal-756	293	3	]	]	X
american_scientific_journal-756	293	4	a.s.mashour	a.s.mashour	PROPN
american_scientific_journal-756	293	5	,	,	PUNCT
american_scientific_journal-756	293	6	i.a	i.a	PROPN
american_scientific_journal-756	293	7	.	.	PROPN
american_scientific_journal-756	293	8	hasanein	hasanein	PROPN
american_scientific_journal-756	293	9	,	,	PUNCT
american_scientific_journal-756	293	10	s.n	s.n	PROPN
american_scientific_journal-756	293	11	.	.	PROPN
american_scientific_journal-756	293	12	el	el	PROPN
american_scientific_journal-756	293	13	-	-	PUNCT
american_scientific_journal-756	293	14	deeb	deeb	PROPN
american_scientific_journal-756	293	15	,	,	PUNCT
american_scientific_journal-756	293	16	𝛼-continuous	𝛼-continuous	ADJ
american_scientific_journal-756	293	17	and	and	CCONJ
american_scientific_journal-756	293	18	𝛼-open	𝛼-open	NOUN
american_scientific_journal-756	293	19	mappings	mapping	NOUN
american_scientific_journal-756	293	20	,	,	PUNCT
american_scientific_journal-756	293	21	acta	acta	PROPN
american_scientific_journal-756	293	22	.	.	PUNCT
american_scientific_journal-756	294	1	math	math	PROPN
american_scientific_journal-756	294	2	.	.	PUNCT
american_scientific_journal-756	295	1	hung	hung	PROPN
american_scientific_journal-756	295	2	.	.	PROPN
american_scientific_journal-756	295	3	,	,	PUNCT
american_scientific_journal-756	295	4	41	41	NUM
american_scientific_journal-756	295	5	(	(	PUNCT
american_scientific_journal-756	295	6	1983	1983	NUM
american_scientific_journal-756	295	7	)	)	PUNCT
american_scientific_journal-756	295	8	,	,	PUNCT
american_scientific_journal-756	295	9	213	213	NUM
american_scientific_journal-756	295	10	-	-	SYM
american_scientific_journal-756	295	11	218	218	NUM
american_scientific_journal-756	295	12	.	.	PUNCT
american_scientific_journal-756	296	1	[	[	X
american_scientific_journal-756	296	2	3	3	X
american_scientific_journal-756	296	3	]	]	X
american_scientific_journal-756	296	4	c.	c.	PROPN
american_scientific_journal-756	296	5	berge	berge	PROPN
american_scientific_journal-756	296	6	,	,	PUNCT
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american_scientific_journal-756	296	9	,	,	PUNCT
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american_scientific_journal-756	296	14	,	,	PUNCT
american_scientific_journal-756	296	15	1963	1963	NUM
american_scientific_journal-756	296	16	.	.	PUNCT
american_scientific_journal-756	297	1	english	english	ADJ
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american_scientific_journal-756	297	4	e.	e.	PROPN
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american_scientific_journal-756	297	6	patterson	patterson	PROPN
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american_scientific_journal-756	297	10	,	,	PUNCT
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american_scientific_journal-756	297	13	,	,	PUNCT
american_scientific_journal-756	297	14	dunod	dunod	PROPN
american_scientific_journal-756	297	15	,	,	PUNCT
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american_scientific_journal-756	297	17	,	,	PUNCT
american_scientific_journal-756	297	18	1959	1959	NUM
american_scientific_journal-756	297	19	.	.	PUNCT
american_scientific_journal-756	298	1	[	[	X
american_scientific_journal-756	298	2	4	4	X
american_scientific_journal-756	298	3	]	]	X
american_scientific_journal-756	298	4	n.	n.	PROPN
american_scientific_journal-756	298	5	s.	s.	PROPN
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american_scientific_journal-756	298	7	,	,	PUNCT
american_scientific_journal-756	298	8	fuzzy	fuzzy	ADJ
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american_scientific_journal-756	298	10	.	.	PUNCT
american_scientific_journal-756	299	1	and	and	CCONJ
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american_scientific_journal-756	299	4	,	,	PUNCT
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american_scientific_journal-756	299	7	.	.	PUNCT
american_scientific_journal-756	300	1	anal	anal	PROPN
american_scientific_journal-756	300	2	.	.	PUNCT
american_scientific_journal-756	301	1	appl	appl	PROPN
american_scientific_journal-756	301	2	.	.	PROPN
american_scientific_journal-756	301	3	,	,	PUNCT
american_scientific_journal-756	301	4	109	109	NUM
american_scientific_journal-756	301	5	(	(	PUNCT
american_scientific_journal-756	301	6	1985	1985	NUM
american_scientific_journal-756	301	7	)	)	PUNCT
american_scientific_journal-756	301	8	397	397	NUM
american_scientific_journal-756	301	9	-	-	SYM
american_scientific_journal-756	301	10	425	425	NUM
american_scientific_journal-756	301	11	.	.	PUNCT
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american_scientific_journal-756	302	6	,	,	PUNCT
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american_scientific_journal-756	302	9	,	,	PUNCT
american_scientific_journal-756	302	10	on	on	ADP
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american_scientific_journal-756	302	19	,	,	PUNCT
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american_scientific_journal-756	302	21	(	(	PUNCT
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american_scientific_journal-756	302	23	)	)	PUNCT
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american_scientific_journal-756	302	25	-	-	SYM
american_scientific_journal-756	302	26	69	69	NUM
american_scientific_journal-756	302	27	.	.	PUNCT
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american_scientific_journal-756	303	11	multivalued	multivalue	VERB
american_scientific_journal-756	303	12	mappings	mapping	NOUN
american_scientific_journal-756	303	13	with	with	ADP
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american_scientific_journal-756	303	17	ordered	order	VERB
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american_scientific_journal-756	303	19	,	,	PUNCT
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american_scientific_journal-756	303	21	fuzzy	fuzzy	PROPN
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american_scientific_journal-756	303	23	.	.	PUNCT
american_scientific_journal-756	303	24	,	,	PUNCT
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american_scientific_journal-756	303	29	(	(	PUNCT
american_scientific_journal-756	303	30	1998	1998	NUM
american_scientific_journal-756	303	31	)	)	PUNCT
american_scientific_journal-756	303	32	127	127	NUM
american_scientific_journal-756	303	33	-	-	SYM
american_scientific_journal-756	303	34	131	131	NUM
american_scientific_journal-756	303	35	.	.	PUNCT
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american_scientific_journal-756	304	3	]	]	X
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american_scientific_journal-756	306	1	appl	appl	PROPN
american_scientific_journal-756	306	2	.	.	PROPN
american_scientific_journal-756	306	3	,	,	PUNCT
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american_scientific_journal-756	306	5	(	(	PUNCT
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american_scientific_journal-756	306	7	)	)	PUNCT
american_scientific_journal-756	306	8	566	566	NUM
american_scientific_journal-756	306	9	-	-	SYM
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american_scientific_journal-756	306	11	.	.	PUNCT
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american_scientific_journal-756	307	2	8	8	NUM
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american_scientific_journal-756	307	4	d.	d.	PROPN
american_scientific_journal-756	307	5	batnairu	batnairu	PROPN
american_scientific_journal-756	307	6	,	,	PUNCT
american_scientific_journal-756	307	7	fixed	fix	VERB
american_scientific_journal-756	307	8	points	point	NOUN
american_scientific_journal-756	307	9	for	for	ADP
american_scientific_journal-756	307	10	fuzzy	fuzzy	ADJ
american_scientific_journal-756	307	11	mappings	mapping	NOUN
american_scientific_journal-756	307	12	,	,	PUNCT
american_scientific_journal-756	307	13	fuzzy	fuzzy	ADJ
american_scientific_journal-756	307	14	sets	set	NOUN
american_scientific_journal-756	307	15	and	and	CCONJ
american_scientific_journal-756	307	16	systems	system	NOUN
american_scientific_journal-756	307	17	,	,	PUNCT
american_scientific_journal-756	307	18	7	7	NUM
american_scientific_journal-756	307	19	(	(	PUNCT
american_scientific_journal-756	307	20	1982	1982	NUM
american_scientific_journal-756	307	21	)	)	PUNCT
american_scientific_journal-756	307	22	191	191	NUM
american_scientific_journal-756	307	23	-	-	SYM
american_scientific_journal-756	307	24	207	207	NUM
american_scientific_journal-756	307	25	.	.	PUNCT
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american_scientific_journal-756	308	2	9	9	NUM
american_scientific_journal-756	308	3	]	]	X
american_scientific_journal-756	308	4	d.	d.	PROPN
american_scientific_journal-756	308	5	molodtsov	molodtsov	PROPN
american_scientific_journal-756	308	6	,	,	PUNCT
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american_scientific_journal-756	308	8	set	set	NOUN
american_scientific_journal-756	308	9	theory	theory	NOUN
american_scientific_journal-756	308	10	-	-	PUNCT
american_scientific_journal-756	308	11	first	first	ADJ
american_scientific_journal-756	308	12	results	result	NOUN
american_scientific_journal-756	308	13	,	,	PUNCT
american_scientific_journal-756	308	14	comput	comput	NOUN
american_scientific_journal-756	308	15	.	.	PUNCT
american_scientific_journal-756	308	16	math	math	NOUN
american_scientific_journal-756	308	17	.	.	PUNCT
american_scientific_journal-756	309	1	appl	appl	PROPN
american_scientific_journal-756	309	2	.	.	PUNCT
american_scientific_journal-756	310	1	37	37	NUM
american_scientific_journal-756	310	2	(	(	PUNCT
american_scientific_journal-756	310	3	4/5	4/5	NUM
american_scientific_journal-756	310	4	)	)	PUNCT
american_scientific_journal-756	310	5	(	(	PUNCT
american_scientific_journal-756	310	6	1999	1999	NUM
american_scientific_journal-756	310	7	)	)	PUNCT
american_scientific_journal-756	310	8	,	,	PUNCT
american_scientific_journal-756	310	9	19	19	NUM
american_scientific_journal-756	310	10	-	-	SYM
american_scientific_journal-756	310	11	31	31	NUM
american_scientific_journal-756	310	12	.	.	PUNCT
american_scientific_journal-756	311	1	[	[	X
american_scientific_journal-756	311	2	10	10	NUM
american_scientific_journal-756	311	3	]	]	PUNCT
american_scientific_journal-756	311	4	p.	p.	PROPN
american_scientific_journal-756	311	5	k.	k.	PROPN
american_scientific_journal-756	312	1	maji	maji	PROPN
american_scientific_journal-756	312	2	,	,	PUNCT
american_scientific_journal-756	312	3	r.	r.	PROPN
american_scientific_journal-756	312	4	biswas	biswas	PROPN
american_scientific_journal-756	312	5	,	,	PUNCT
american_scientific_journal-756	312	6	a.	a.	PROPN
american_scientific_journal-756	312	7	r.	r.	PROPN
american_scientific_journal-756	312	8	roy	roy	PROPN
american_scientific_journal-756	312	9	,	,	PUNCT
american_scientific_journal-756	312	10	soft	soft	ADJ
american_scientific_journal-756	312	11	set	set	NOUN
american_scientific_journal-756	312	12	theory	theory	NOUN
american_scientific_journal-756	312	13	,	,	PUNCT
american_scientific_journal-756	312	14	comput	comput	NOUN
american_scientific_journal-756	312	15	.	.	PUNCT
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american_scientific_journal-756	313	2	.	.	PUNCT
american_scientific_journal-756	314	1	appl	appl	PROPN
american_scientific_journal-756	314	2	.	.	PROPN
american_scientific_journal-756	315	1	45	45	NUM
american_scientific_journal-756	315	2	(	(	PUNCT
american_scientific_journal-756	315	3	2003	2003	NUM
american_scientific_journal-756	315	4	)	)	PUNCT
american_scientific_journal-756	315	5	,	,	PUNCT
american_scientific_journal-756	315	6	555	555	NUM
american_scientific_journal-756	315	7	-	-	SYM
american_scientific_journal-756	315	8	562	562	NUM
american_scientific_journal-756	315	9	.	.	PUNCT
american_scientific_journal-756	316	1	[	[	X
american_scientific_journal-756	316	2	11	11	NUM
american_scientific_journal-756	316	3	]	]	PUNCT
american_scientific_journal-756	316	4	p.	p.	PROPN
american_scientific_journal-756	316	5	k.	k.	PROPN
american_scientific_journal-756	317	1	maji	maji	PROPN
american_scientific_journal-756	317	2	,	,	PUNCT
american_scientific_journal-756	317	3	a.	a.	PROPN
american_scientific_journal-756	317	4	r.	r.	PROPN
american_scientific_journal-756	317	5	roy	roy	PROPN
american_scientific_journal-756	317	6	,	,	PUNCT
american_scientific_journal-756	317	7	r.	r.	PROPN
american_scientific_journal-756	317	8	biswas	biswas	PROPN
american_scientific_journal-756	317	9	,	,	PUNCT
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american_scientific_journal-756	317	12	of	of	ADP
american_scientific_journal-756	317	13	soft	soft	ADJ
american_scientific_journal-756	317	14	sets	set	NOUN
american_scientific_journal-756	317	15	in	in	ADP
american_scientific_journal-756	317	16	desicion	desicion	NOUN
american_scientific_journal-756	317	17	making	making	NOUN
american_scientific_journal-756	317	18	problem	problem	NOUN
american_scientific_journal-756	317	19	,	,	PUNCT
american_scientific_journal-756	317	20	comput	comput	NOUN
american_scientific_journal-756	317	21	.	.	PUNCT
american_scientific_journal-756	318	1	math	math	NOUN
american_scientific_journal-756	318	2	.	.	PUNCT
american_scientific_journal-756	319	1	appl	appl	PROPN
american_scientific_journal-756	319	2	.	.	PROPN
american_scientific_journal-756	320	1	44	44	NUM
american_scientific_journal-756	320	2	(	(	PUNCT
american_scientific_journal-756	320	3	2002	2002	NUM
american_scientific_journal-756	320	4	)	)	PUNCT
american_scientific_journal-756	320	5	,	,	PUNCT
american_scientific_journal-756	320	6	1077	1077	NUM
american_scientific_journal-756	320	7	-	-	SYM
american_scientific_journal-756	320	8	1083	1083	NUM
american_scientific_journal-756	320	9	.	.	PUNCT
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american_scientific_journal-756	321	2	12	12	NUM
american_scientific_journal-756	321	3	]	]	X
american_scientific_journal-756	321	4	h.	h.	PROPN
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american_scientific_journal-756	321	6	,	,	PUNCT
american_scientific_journal-756	321	7	n.	n.	PROPN
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american_scientific_journal-756	321	9	,	,	PUNCT
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american_scientific_journal-756	321	11	sets	set	NOUN
american_scientific_journal-756	321	12	and	and	CCONJ
american_scientific_journal-756	321	13	soft	soft	ADJ
american_scientific_journal-756	321	14	groups	group	NOUN
american_scientific_journal-756	321	15	,	,	PUNCT
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american_scientific_journal-756	321	17	.	.	PUNCT
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american_scientific_journal-756	322	2	.	.	PROPN
american_scientific_journal-756	322	3	,	,	PUNCT
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american_scientific_journal-756	322	5	)	)	PUNCT
american_scientific_journal-756	322	6	,	,	PUNCT
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american_scientific_journal-756	322	8	-	-	SYM
american_scientific_journal-756	322	9	2735	2735	NUM
american_scientific_journal-756	322	10	.	.	PUNCT
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american_scientific_journal-756	323	4	c.	c.	PROPN
american_scientific_journal-756	323	5	l.	l.	PROPN
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american_scientific_journal-756	323	7	,	,	PUNCT
american_scientific_journal-756	323	8	fuzzy	fuzzy	ADJ
american_scientific_journal-756	323	9	topological	topological	ADJ
american_scientific_journal-756	323	10	spaces	space	NOUN
american_scientific_journal-756	323	11	,	,	PUNCT
american_scientific_journal-756	323	12	journal	journal	NOUN
american_scientific_journal-756	323	13	of	of	ADP
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american_scientific_journal-756	323	15	.	.	PUNCT
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american_scientific_journal-756	324	3	and	and	CCONJ
american_scientific_journal-756	324	4	appl	appl	PROPN
american_scientific_journal-756	324	5	.	.	PROPN
american_scientific_journal-756	324	6	,	,	PUNCT
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american_scientific_journal-756	324	8	(	(	PUNCT
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american_scientific_journal-756	324	10	)	)	PUNCT
american_scientific_journal-756	324	11	,	,	PUNCT
american_scientific_journal-756	324	12	182	182	NUM
american_scientific_journal-756	324	13	-	-	SYM
american_scientific_journal-756	324	14	190	190	NUM
american_scientific_journal-756	324	15	.	.	PUNCT
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american_scientific_journal-756	325	2	14	14	NUM
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american_scientific_journal-756	325	4	e.	e.	PROPN
american_scientific_journal-756	325	5	f.	f.	PROPN
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american_scientific_journal-756	325	7	,	,	PUNCT
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american_scientific_journal-756	325	11	,	,	PUNCT
american_scientific_journal-756	325	12	a.	a.	NOUN
american_scientific_journal-756	325	13	a.	a.	NOUN
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american_scientific_journal-756	325	16	and	and	CCONJ
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american_scientific_journal-756	325	19	,	,	PUNCT
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american_scientific_journal-756	325	21	set	set	NOUN
american_scientific_journal-756	325	22	for	for	ADP
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american_scientific_journal-756	325	24	spaces	space	NOUN
american_scientific_journal-756	325	25	,	,	PUNCT
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american_scientific_journal-756	325	27	.	.	PUNCT
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american_scientific_journal-756	326	5	,	,	PUNCT
american_scientific_journal-756	326	6	40	40	NUM
american_scientific_journal-756	326	7	(	(	PUNCT
american_scientific_journal-756	326	8	2005	2005	NUM
american_scientific_journal-756	326	9	)	)	PUNCT
american_scientific_journal-756	326	10	,	,	PUNCT
american_scientific_journal-756	326	11	35	35	NUM
american_scientific_journal-756	326	12	-	-	SYM
american_scientific_journal-756	326	13	43	43	NUM
american_scientific_journal-756	326	14	.	.	PUNCT
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american_scientific_journal-756	327	7	m.	m.	PROPN
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american_scientific_journal-756	327	9	,	,	PUNCT
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american_scientific_journal-756	327	14	,	,	PUNCT
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american_scientific_journal-756	327	16	.	.	PUNCT
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american_scientific_journal-756	328	2	.	.	PUNCT
american_scientific_journal-756	329	1	appl	appl	PROPN
american_scientific_journal-756	329	2	.	.	PROPN
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american_scientific_journal-756	330	2	(	(	PUNCT
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american_scientific_journal-756	330	4	)	)	PUNCT
american_scientific_journal-756	330	5	,	,	PUNCT
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american_scientific_journal-756	330	7	-	-	SYM
american_scientific_journal-756	330	8	1799	1799	NUM
american_scientific_journal-756	330	9	.	.	PUNCT
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american_scientific_journal-756	331	2	16	16	NUM
american_scientific_journal-756	331	3	]	]	PUNCT
american_scientific_journal-756	331	4	i̇.	i̇.	PROPN
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american_scientific_journal-756	331	6	,	,	PUNCT
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american_scientific_journal-756	331	9	,	,	PUNCT
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american_scientific_journal-756	331	16	,	,	PUNCT
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american_scientific_journal-756	331	21	,	,	PUNCT
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american_scientific_journal-756	331	28	,	,	PUNCT
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american_scientific_journal-756	332	2	,	,	PUNCT
american_scientific_journal-756	332	3	no	no	INTJ
american_scientific_journal-756	332	4	:	:	SYM
american_scientific_journal-756	332	5	2	2	NUM
american_scientific_journal-756	332	6	,	,	PUNCT
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american_scientific_journal-756	332	8	-	-	SYM
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american_scientific_journal-756	332	10	(	(	PUNCT
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american_scientific_journal-756	332	13	.	.	PUNCT
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american_scientific_journal-756	333	21	,	,	PUNCT
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american_scientific_journal-756	333	23	:	:	PUNCT
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american_scientific_journal-756	333	25	/	/	SYM
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american_scientific_journal-756	333	27	-	-	PUNCT
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american_scientific_journal-756	333	29	-	-	PUNCT
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american_scientific_journal-756	333	31	-	-	PUNCT
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american_scientific_journal-756	335	4	.	.	PUNCT
american_scientific_journal-756	335	5	,	,	PUNCT
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american_scientific_journal-756	335	15	,	,	PUNCT
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american_scientific_journal-756	335	17	,	,	PUNCT
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american_scientific_journal-756	335	20	(	(	PUNCT
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