id	sid	tid	token	lemma	pos
american_scientific_journal-2059	1	1	42	42	NUM
american_scientific_journal-2059	1	2	american	american	ADJ
american_scientific_journal-2059	1	3	scientific	scientific	ADJ
american_scientific_journal-2059	1	4	research	research	NOUN
american_scientific_journal-2059	1	5	journal	journal	NOUN
american_scientific_journal-2059	1	6	for	for	ADP
american_scientific_journal-2059	1	7	engineering	engineering	NOUN
american_scientific_journal-2059	1	8	,	,	PUNCT
american_scientific_journal-2059	1	9	technology	technology	NOUN
american_scientific_journal-2059	1	10	,	,	PUNCT
american_scientific_journal-2059	1	11	and	and	CCONJ
american_scientific_journal-2059	1	12	sciences	science	NOUN
american_scientific_journal-2059	1	13	(	(	PUNCT
american_scientific_journal-2059	1	14	asrjets	asrjet	NOUN
american_scientific_journal-2059	1	15	)	)	PUNCT
american_scientific_journal-2059	1	16	issn	issn	PROPN
american_scientific_journal-2059	1	17	(	(	PUNCT
american_scientific_journal-2059	1	18	print	print	NOUN
american_scientific_journal-2059	1	19	)	)	PUNCT
american_scientific_journal-2059	1	20	2313	2313	NUM
american_scientific_journal-2059	1	21	-	-	SYM
american_scientific_journal-2059	1	22	4410	4410	NUM
american_scientific_journal-2059	1	23	,	,	PUNCT
american_scientific_journal-2059	1	24	issn	issn	PROPN
american_scientific_journal-2059	1	25	(	(	PUNCT
american_scientific_journal-2059	1	26	online	online	ADJ
american_scientific_journal-2059	1	27	)	)	PUNCT
american_scientific_journal-2059	1	28	2313	2313	NUM
american_scientific_journal-2059	1	29	-	-	SYM
american_scientific_journal-2059	1	30	4402	4402	NUM
american_scientific_journal-2059	1	31	©	©	PROPN
american_scientific_journal-2059	1	32	global	global	ADJ
american_scientific_journal-2059	1	33	society	society	NOUN
american_scientific_journal-2059	1	34	of	of	ADP
american_scientific_journal-2059	1	35	scientific	scientific	ADJ
american_scientific_journal-2059	1	36	research	research	NOUN
american_scientific_journal-2059	1	37	and	and	CCONJ
american_scientific_journal-2059	1	38	researchers	researcher	NOUN
american_scientific_journal-2059	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-2059	1	40	soft	soft	ADJ
american_scientific_journal-2059	1	41	pre	pre	ADJ
american_scientific_journal-2059	1	42	-	-	ADJ
american_scientific_journal-2059	1	43	open	open	ADJ
american_scientific_journal-2059	1	44	sets	set	NOUN
american_scientific_journal-2059	1	45	in	in	ADP
american_scientific_journal-2059	1	46	soft	soft	ADJ
american_scientific_journal-2059	1	47	bitopological	bitopological	ADJ
american_scientific_journal-2059	1	48	spaces	space	NOUN
american_scientific_journal-2059	1	49	ameer	ameer	PROPN
american_scientific_journal-2059	1	50	mohammed	mohammed	PROPN
american_scientific_journal-2059	1	51	hussein	hussein	PROPN
american_scientific_journal-2059	1	52	hasan	hasan	PROPN
american_scientific_journal-2059	1	53	*	*	PROPN
american_scientific_journal-2059	1	54	department	department	PROPN
american_scientific_journal-2059	1	55	of	of	ADP
american_scientific_journal-2059	1	56	mathematics	mathematics	PROPN
american_scientific_journal-2059	1	57	faculty	faculty	NOUN
american_scientific_journal-2059	1	58	of	of	ADP
american_scientific_journal-2059	1	59	mathematics	mathematic	NOUN
american_scientific_journal-2059	1	60	and	and	CCONJ
american_scientific_journal-2059	1	61	computer	computer	NOUN
american_scientific_journal-2059	1	62	science	science	PROPN
american_scientific_journal-2059	1	63	university	university	PROPN
american_scientific_journal-2059	1	64	of	of	ADP
american_scientific_journal-2059	1	65	kufa	kufa	PROPN
american_scientific_journal-2059	1	66	,	,	PUNCT
american_scientific_journal-2059	1	67	najaf	najaf	PROPN
american_scientific_journal-2059	1	68	,	,	PUNCT
american_scientific_journal-2059	1	69	iraq	iraq	PROPN
american_scientific_journal-2059	1	70	email	email	NOUN
american_scientific_journal-2059	1	71	:	:	PUNCT
american_scientific_journal-2059	1	72	ameerm.hasan@uokufa.edu.iq	ameerm.hasan@uokufa.edu.iq	ADJ
american_scientific_journal-2059	1	73	abstract	abstract	ADV
american_scientific_journal-2059	1	74	in	in	ADP
american_scientific_journal-2059	1	75	this	this	DET
american_scientific_journal-2059	1	76	work	work	NOUN
american_scientific_journal-2059	1	77	,	,	PUNCT
american_scientific_journal-2059	1	78	i	i	PRON
american_scientific_journal-2059	1	79	introduce	introduce	VERB
american_scientific_journal-2059	1	80	the	the	DET
american_scientific_journal-2059	1	81	concept	concept	NOUN
american_scientific_journal-2059	1	82	of	of	ADP
american_scientific_journal-2059	1	83	soft	soft	ADJ
american_scientific_journal-2059	1	84	bitopological	bitopological	ADJ
american_scientific_journal-2059	1	85	space	space	NOUN
american_scientific_journal-2059	1	86	on	on	ADP
american_scientific_journal-2059	1	87	a	a	DET
american_scientific_journal-2059	1	88	soft	soft	ADJ
american_scientific_journal-2059	1	89	set	set	NOUN
american_scientific_journal-2059	1	90	and	and	CCONJ
american_scientific_journal-2059	1	91	some	some	DET
american_scientific_journal-2059	1	92	definitions	definition	NOUN
american_scientific_journal-2059	1	93	on	on	ADP
american_scientific_journal-2059	1	94	soft	soft	ADJ
american_scientific_journal-2059	1	95	preopen	preopen	NOUN
american_scientific_journal-2059	1	96	set	set	VERB
american_scientific_journal-2059	1	97	on	on	ADP
american_scientific_journal-2059	1	98	soft	soft	ADJ
american_scientific_journal-2059	1	99	bitopological	bitopological	ADJ
american_scientific_journal-2059	1	100	space	space	NOUN
american_scientific_journal-2059	1	101	.	.	PUNCT
american_scientific_journal-2059	2	1	also	also	ADV
american_scientific_journal-2059	2	2	introduce	introduce	VERB
american_scientific_journal-2059	2	3	soft	soft	ADJ
american_scientific_journal-2059	2	4	pre	pre	NOUN
american_scientific_journal-2059	2	5	separation	separation	NOUN
american_scientific_journal-2059	2	6	axioms	axiom	NOUN
american_scientific_journal-2059	2	7	,	,	PUNCT
american_scientific_journal-2059	2	8	spret	spret	NUM
american_scientific_journal-2059	2	9	,	,	PUNCT
american_scientific_journal-2059	2	10	spre1	spre1	PROPN
american_scientific_journal-2059	2	11	t	t	PROPN
american_scientific_journal-2059	2	12	and	and	CCONJ
american_scientific_journal-2059	2	13	spre2	spre2	PROPN
american_scientific_journal-2059	2	14	t	t	NOUN
american_scientific_journal-2059	2	15	,	,	PUNCT
american_scientific_journal-2059	2	16	with	with	ADP
american_scientific_journal-2059	2	17	study	study	VERB
american_scientific_journal-2059	2	18	some	some	DET
american_scientific_journal-2059	2	19	properties	property	NOUN
american_scientific_journal-2059	2	20	in	in	ADP
american_scientific_journal-2059	2	21	soft	soft	ADJ
american_scientific_journal-2059	2	22	bitopological	bitopological	ADJ
american_scientific_journal-2059	2	23	space	space	NOUN
american_scientific_journal-2059	2	24	.	.	PUNCT
american_scientific_journal-2059	3	1	keywords	keyword	NOUN
american_scientific_journal-2059	3	2	:	:	PUNCT
american_scientific_journal-2059	3	3	soft	soft	ADJ
american_scientific_journal-2059	3	4	set	set	NOUN
american_scientific_journal-2059	3	5	;	;	PUNCT
american_scientific_journal-2059	3	6	soft	soft	ADJ
american_scientific_journal-2059	3	7	pre	pre	ADJ
american_scientific_journal-2059	3	8	-	-	ADJ
american_scientific_journal-2059	3	9	open	open	ADJ
american_scientific_journal-2059	3	10	;	;	PUNCT
american_scientific_journal-2059	3	11	soft	soft	ADJ
american_scientific_journal-2059	3	12	topology	topology	NOUN
american_scientific_journal-2059	3	13	;	;	PUNCT
american_scientific_journal-2059	3	14	soft	soft	ADJ
american_scientific_journal-2059	3	15	bitopological	bitopological	ADJ
american_scientific_journal-2059	3	16	spaces	space	NOUN
american_scientific_journal-2059	3	17	.	.	PUNCT
american_scientific_journal-2059	4	1	1	1	X
american_scientific_journal-2059	4	2	.	.	X
american_scientific_journal-2059	4	3	introduction	introduction	NOUN
american_scientific_journal-2059	4	4	many	many	ADJ
american_scientific_journal-2059	4	5	classical	classical	ADJ
american_scientific_journal-2059	4	6	methods	method	NOUN
american_scientific_journal-2059	4	7	have	have	AUX
american_scientific_journal-2059	4	8	been	be	AUX
american_scientific_journal-2059	4	9	used	use	VERB
american_scientific_journal-2059	4	10	to	to	PART
american_scientific_journal-2059	4	11	solve	solve	VERB
american_scientific_journal-2059	4	12	some	some	DET
american_scientific_journal-2059	4	13	complicated	complicated	ADJ
american_scientific_journal-2059	4	14	problems	problem	NOUN
american_scientific_journal-2059	4	15	in	in	ADP
american_scientific_journal-2059	4	16	engineering	engineer	VERB
american_scientific_journal-2059	4	17	economics	economic	NOUN
american_scientific_journal-2059	4	18	and	and	CCONJ
american_scientific_journal-2059	4	19	environment	environment	NOUN
american_scientific_journal-2059	4	20	.	.	PUNCT
american_scientific_journal-2059	5	1	for	for	ADP
american_scientific_journal-2059	5	2	instance	instance	NOUN
american_scientific_journal-2059	5	3	,	,	PUNCT
american_scientific_journal-2059	5	4	the	the	DET
american_scientific_journal-2059	5	5	interval	interval	NOUN
american_scientific_journal-2059	5	6	mathematics	mathematic	NOUN
american_scientific_journal-2059	5	7	,	,	PUNCT
american_scientific_journal-2059	5	8	theory	theory	NOUN
american_scientific_journal-2059	5	9	of	of	ADP
american_scientific_journal-2059	5	10	fuzzy	fuzzy	ADJ
american_scientific_journal-2059	5	11	,	,	PUNCT
american_scientific_journal-2059	5	12	theory	theory	NOUN
american_scientific_journal-2059	5	13	of	of	ADP
american_scientific_journal-2059	5	14	probability	probability	NOUN
american_scientific_journal-2059	5	15	,	,	PUNCT
american_scientific_journal-2059	5	16	and	and	CCONJ
american_scientific_journal-2059	5	17	sets	set	NOUN
american_scientific_journal-2059	5	18	which	which	PRON
american_scientific_journal-2059	5	19	can	can	AUX
american_scientific_journal-2059	5	20	consider	consider	VERB
american_scientific_journal-2059	5	21	as	as	ADP
american_scientific_journal-2059	5	22	mathematical	mathematical	ADJ
american_scientific_journal-2059	5	23	tools	tool	NOUN
american_scientific_journal-2059	5	24	for	for	ADP
american_scientific_journal-2059	5	25	dealing	deal	VERB
american_scientific_journal-2059	5	26	with	with	ADP
american_scientific_journal-2059	5	27	uncertainties	uncertainty	NOUN
american_scientific_journal-2059	5	28	since	since	SCONJ
american_scientific_journal-2059	5	29	all	all	DET
american_scientific_journal-2059	5	30	these	these	DET
american_scientific_journal-2059	5	31	theories	theory	NOUN
american_scientific_journal-2059	5	32	have	have	VERB
american_scientific_journal-2059	5	33	their	their	PRON
american_scientific_journal-2059	5	34	own	own	ADJ
american_scientific_journal-2059	5	35	problems	problem	NOUN
american_scientific_journal-2059	5	36	and	and	CCONJ
american_scientific_journal-2059	5	37	difficulties	difficulty	NOUN
american_scientific_journal-2059	5	38	.	.	PUNCT
american_scientific_journal-2059	6	1	in	in	ADP
american_scientific_journal-2059	6	2	[	[	X
american_scientific_journal-2059	6	3	2	2	NUM
american_scientific_journal-2059	6	4	]	]	PUNCT
american_scientific_journal-2059	6	5	,	,	PUNCT
american_scientific_journal-2059	6	6	the	the	DET
american_scientific_journal-2059	6	7	author	author	NOUN
american_scientific_journal-2059	6	8	in	in	ADP
american_scientific_journal-2059	6	9	1999	1999	NUM
american_scientific_journal-2059	6	10	introduced	introduce	VERB
american_scientific_journal-2059	6	11	the	the	DET
american_scientific_journal-2059	6	12	notion	notion	NOUN
american_scientific_journal-2059	6	13	of	of	ADP
american_scientific_journal-2059	6	14	soft	soft	ADJ
american_scientific_journal-2059	6	15	set	set	NOUN
american_scientific_journal-2059	6	16	,	,	PUNCT
american_scientific_journal-2059	6	17	which	which	PRON
american_scientific_journal-2059	6	18	is	be	AUX
american_scientific_journal-2059	6	19	free	free	ADJ
american_scientific_journal-2059	6	20	of	of	ADP
american_scientific_journal-2059	6	21	difficulties	difficulty	NOUN
american_scientific_journal-2059	6	22	in	in	ADP
american_scientific_journal-2059	6	23	solving	solve	VERB
american_scientific_journal-2059	6	24	aforementioned	aforementione	VERB
american_scientific_journal-2059	6	25	problems	problem	NOUN
american_scientific_journal-2059	6	26	,	,	PUNCT
american_scientific_journal-2059	6	27	and	and	CCONJ
american_scientific_journal-2059	6	28	it	it	PRON
american_scientific_journal-2059	6	29	has	have	AUX
american_scientific_journal-2059	6	30	been	be	AUX
american_scientific_journal-2059	6	31	applied	apply	VERB
american_scientific_journal-2059	6	32	over	over	ADP
american_scientific_journal-2059	6	33	many	many	ADJ
american_scientific_journal-2059	6	34	different	different	ADJ
american_scientific_journal-2059	6	35	fields	field	NOUN
american_scientific_journal-2059	6	36	.	.	PUNCT
american_scientific_journal-2059	7	1	in	in	ADP
american_scientific_journal-2059	7	2	2011	2011	NUM
american_scientific_journal-2059	7	3	,	,	PUNCT
american_scientific_journal-2059	7	4	naim	naim	PROPN
american_scientific_journal-2059	7	5	cagman	cagman	PROPN
american_scientific_journal-2059	7	6	and	and	CCONJ
american_scientific_journal-2059	7	7	his	his	PRON
american_scientific_journal-2059	7	8	colleagues	colleague	NOUN
american_scientific_journal-2059	7	9	introduced	introduce	VERB
american_scientific_journal-2059	7	10	a	a	DET
american_scientific_journal-2059	7	11	new	new	ADJ
american_scientific_journal-2059	7	12	concept	concept	NOUN
american_scientific_journal-2059	7	13	of	of	ADP
american_scientific_journal-2059	7	14	soft	soft	ADJ
american_scientific_journal-2059	7	15	set	set	NOUN
american_scientific_journal-2059	7	16	called	call	VERB
american_scientific_journal-2059	7	17	soft	soft	ADJ
american_scientific_journal-2059	7	18	topology	topology	NOUN
american_scientific_journal-2059	7	19	define	define	NOUN
american_scientific_journal-2059	7	20	by	by	ADP
american_scientific_journal-2059	7	21	using	use	VERB
american_scientific_journal-2059	7	22	the	the	DET
american_scientific_journal-2059	7	23	soft	soft	ADJ
american_scientific_journal-2059	7	24	power	power	NOUN
american_scientific_journal-2059	7	25	set	set	NOUN
american_scientific_journal-2059	7	26	of	of	ADP
american_scientific_journal-2059	7	27	soft	soft	ADJ
american_scientific_journal-2059	7	28	set	set	NOUN
american_scientific_journal-2059	7	29	,	,	PUNCT
american_scientific_journal-2059	7	30	and	and	CCONJ
american_scientific_journal-2059	7	31	this	this	DET
american_scientific_journal-2059	7	32	first	first	ADJ
american_scientific_journal-2059	7	33	idea	idea	NOUN
american_scientific_journal-2059	7	34	to	to	ADP
american_scientific_journal-2059	7	35	soft	soft	ADJ
american_scientific_journal-2059	7	36	mathematical	mathematical	ADJ
american_scientific_journal-2059	7	37	concepts	concept	NOUN
american_scientific_journal-2059	7	38	and	and	CCONJ
american_scientific_journal-2059	7	39	structures	structure	NOUN
american_scientific_journal-2059	7	40	that	that	PRON
american_scientific_journal-2059	7	41	are	be	AUX
american_scientific_journal-2059	7	42	based	base	VERB
american_scientific_journal-2059	7	43	on	on	ADP
american_scientific_journal-2059	7	44	the	the	DET
american_scientific_journal-2059	7	45	operations	operation	NOUN
american_scientific_journal-2059	7	46	of	of	ADP
american_scientific_journal-2059	7	47	theoretic	theoretic	ADJ
american_scientific_journal-2059	7	48	soft	soft	ADJ
american_scientific_journal-2059	7	49	set	set	NOUN
american_scientific_journal-2059	7	50	[	[	X
american_scientific_journal-2059	7	51	6	6	NUM
american_scientific_journal-2059	7	52	]	]	PUNCT
american_scientific_journal-2059	7	53	.	.	PUNCT
american_scientific_journal-2059	8	1	in	in	ADP
american_scientific_journal-2059	8	2	2011[7	2011[7	NUM
american_scientific_journal-2059	8	3	]	]	PUNCT
american_scientific_journal-2059	8	4	,	,	PUNCT
american_scientific_journal-2059	8	5	the	the	DET
american_scientific_journal-2059	8	6	authors	author	NOUN
american_scientific_journal-2059	8	7	defined	define	VERB
american_scientific_journal-2059	8	8	the	the	DET
american_scientific_journal-2059	8	9	concept	concept	NOUN
american_scientific_journal-2059	8	10	of"soft	of"soft	ADJ
american_scientific_journal-2059	8	11	topology	topology	NOUN
american_scientific_journal-2059	8	12	on	on	ADP
american_scientific_journal-2059	8	13	the	the	DET
american_scientific_journal-2059	8	14	collection	collection	NOUN
american_scientific_journal-2059	8	15	of	of	ADP
american_scientific_journal-2059	8	16	soft	soft	ADJ
american_scientific_journal-2059	8	17	sets	set	NOUN
american_scientific_journal-2059	8	18	over"with	over"with	ADP
american_scientific_journal-2059	8	19	some	some	DET
american_scientific_journal-2059	8	20	basic	basic	ADJ
american_scientific_journal-2059	8	21	notations	notation	NOUN
american_scientific_journal-2059	8	22	of	of	ADP
american_scientific_journal-2059	8	23	soft	soft	ADJ
american_scientific_journal-2059	8	24	topological	topological	ADJ
american_scientific_journal-2059	8	25	spaces	space	NOUN
american_scientific_journal-2059	8	26	.	.	PUNCT
american_scientific_journal-2059	9	1	in	in	ADP
american_scientific_journal-2059	9	2	[	[	X
american_scientific_journal-2059	9	3	6	6	NUM
american_scientific_journal-2059	9	4	]	]	PUNCT
american_scientific_journal-2059	9	5	,	,	PUNCT
american_scientific_journal-2059	9	6	the	the	DET
american_scientific_journal-2059	9	7	notion	notion	NOUN
american_scientific_journal-2059	9	8	of	of	ADP
american_scientific_journal-2059	9	9	soft	soft	ADJ
american_scientific_journal-2059	9	10	topology	topology	NOUN
american_scientific_journal-2059	9	11	was	be	AUX
american_scientific_journal-2059	9	12	more	more	ADV
american_scientific_journal-2059	9	13	general	general	ADJ
american_scientific_journal-2059	9	14	than	than	ADP
american_scientific_journal-2059	9	15	that	that	PRON
american_scientific_journal-2059	9	16	in	in	ADP
american_scientific_journal-2059	9	17	[	[	X
american_scientific_journal-2059	9	18	7	7	NUM
american_scientific_journal-2059	9	19	]	]	PUNCT
american_scientific_journal-2059	9	20	.	.	PUNCT
american_scientific_journal-2059	10	1	therefore	therefore	ADV
american_scientific_journal-2059	10	2	,	,	PUNCT
american_scientific_journal-2059	10	3	algebraists	algebraist	NOUN
american_scientific_journal-2059	10	4	continue	continue	VERB
american_scientific_journal-2059	10	5	investigating	investigate	VERB
american_scientific_journal-2059	10	6	the	the	DET
american_scientific_journal-2059	10	7	work	work	NOUN
american_scientific_journal-2059	10	8	of	of	ADP
american_scientific_journal-2059	10	9	cagman	cagman	NOUN
american_scientific_journal-2059	10	10	[	[	X
american_scientific_journal-2059	10	11	6]"and	6]"and	VERB
american_scientific_journal-2059	10	12	follow	follow	VERB
american_scientific_journal-2059	10	13	their	their	PRON
american_scientific_journal-2059	10	14	notations	notation	NOUN
american_scientific_journal-2059	10	15	and	and	CCONJ
american_scientific_journal-2059	10	16	mathematical	mathematical	ADJ
american_scientific_journal-2059	10	17	formalism	formalism	NOUN
american_scientific_journal-2059	10	18	.	.	PUNCT
american_scientific_journal-2059	11	1	in	in	ADP
american_scientific_journal-2059	11	2	2013	2013	NUM
american_scientific_journal-2059	11	3	j.	j.	PROPN
american_scientific_journal-2059	11	4	subhashini	subhashini	PROPN
american_scientific_journal-2059	11	5	and	and	CCONJ
american_scientific_journal-2059	11	6	c.	c.	PROPN
american_scientific_journal-2059	11	7	sekar	sekar	PROPN
american_scientific_journal-2059	11	8	defined	define	VERB
american_scientific_journal-2059	11	9	soft	soft	ADJ
american_scientific_journal-2059	11	10	pre	pre	ADJ
american_scientific_journal-2059	11	11	-	-	ADJ
american_scientific_journal-2059	11	12	open	open	ADJ
american_scientific_journal-2059	11	13	sets	set	NOUN
american_scientific_journal-2059	11	14	[	[	X
american_scientific_journal-2059	11	15	4]"by	4]"by	PROPN
american_scientific_journal-2059	11	16	following	follow	VERB
american_scientific_journal-2059	11	17	cagman	cagman	NOUN
american_scientific_journal-2059	11	18	’s	’s	PART
american_scientific_journal-2059	11	19	theory	theory	NOUN
american_scientific_journal-2059	11	20	of	of	ADP
american_scientific_journal-2059	11	21	soft	soft	ADJ
american_scientific_journal-2059	11	22	topology	topology	NOUN
american_scientific_journal-2059	11	23	.	.	PUNCT
american_scientific_journal-2059	12	1	therefore	therefore	ADV
american_scientific_journal-2059	12	2	,	,	PUNCT
american_scientific_journal-2059	12	3	this	this	DET
american_scientific_journal-2059	12	4	paper	paper	NOUN
american_scientific_journal-2059	12	5	has	have	AUX
american_scientific_journal-2059	12	6	introduced	introduce	VERB
american_scientific_journal-2059	12	7	soft	soft	ADJ
american_scientific_journal-2059	12	8	bitopological	bitopological	ADJ
american_scientific_journal-2059	12	9	space	space	NOUN
american_scientific_journal-2059	12	10	relying	rely	VERB
american_scientific_journal-2059	12	11	on	on	ADP
american_scientific_journal-2059	12	12	[	[	X
american_scientific_journal-2059	12	13	6	6	NUM
american_scientific_journal-2059	12	14	]	]	PUNCT
american_scientific_journal-2059	12	15	and	and	CCONJ
american_scientific_journal-2059	12	16	defined	define	VERB
american_scientific_journal-2059	12	17	the	the	DET
american_scientific_journal-2059	12	18	soft	soft	ADJ
american_scientific_journal-2059	12	19	pre	pre	ADJ
american_scientific_journal-2059	12	20	-	-	ADJ
american_scientific_journal-2059	12	21	open	open	ADJ
american_scientific_journal-2059	12	22	set	set	NOUN
american_scientific_journal-2059	12	23	of	of	ADP
american_scientific_journal-2059	12	24	soft	soft	ADJ
american_scientific_journal-2059	12	25	bitopological	bitopological	ADJ
american_scientific_journal-2059	12	26	space	space	NOUN
american_scientific_journal-2059	12	27	.	.	PUNCT
american_scientific_journal-2059	13	1	also	also	ADV
american_scientific_journal-2059	13	2	,	,	PUNCT
american_scientific_journal-2059	13	3	i	i	PRON
american_scientific_journal-2059	13	4	have	have	AUX
american_scientific_journal-2059	13	5	discussed	discuss	VERB
american_scientific_journal-2059	13	6	soft	soft	ADJ
american_scientific_journal-2059	13	7	pre	pre	NOUN
american_scientific_journal-2059	13	8	separation	separation	NOUN
american_scientific_journal-2059	13	9	axioms	axiom	NOUN
american_scientific_journal-2059	13	10	,	,	PUNCT
american_scientific_journal-2059	13	11	spret	spret	NUM
american_scientific_journal-2059	13	12	,	,	PUNCT
american_scientific_journal-2059	13	13	spre1	spre1	PROPN
american_scientific_journal-2059	13	14	t	t	PROPN
american_scientific_journal-2059	13	15	and	and	CCONJ
american_scientific_journal-2059	13	16	spre2	spre2	PROPN
american_scientific_journal-2059	13	17	t	t	NOUN
american_scientific_journal-2059	13	18	.	.	PUNCT
american_scientific_journal-2059	14	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-2059	15	1	*	*	PUNCT
american_scientific_journal-2059	15	2	corresponding	correspond	VERB
american_scientific_journal-2059	15	3	author	author	NOUN
american_scientific_journal-2059	15	4	.	.	PUNCT
american_scientific_journal-2059	16	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-2059	16	2	american	american	PROPN
american_scientific_journal-2059	16	3	scientific	scientific	PROPN
american_scientific_journal-2059	16	4	research	research	NOUN
american_scientific_journal-2059	16	5	journal	journal	NOUN
american_scientific_journal-2059	16	6	for	for	ADP
american_scientific_journal-2059	16	7	engineering	engineering	NOUN
american_scientific_journal-2059	16	8	,	,	PUNCT
american_scientific_journal-2059	16	9	technology	technology	NOUN
american_scientific_journal-2059	16	10	,	,	PUNCT
american_scientific_journal-2059	16	11	and	and	CCONJ
american_scientific_journal-2059	16	12	sciences	science	NOUN
american_scientific_journal-2059	16	13	(	(	PUNCT
american_scientific_journal-2059	16	14	asrjets	asrjet	NOUN
american_scientific_journal-2059	16	15	)	)	PUNCT
american_scientific_journal-2059	16	16	(	(	PUNCT
american_scientific_journal-2059	16	17	2016	2016	NUM
american_scientific_journal-2059	16	18	)	)	PUNCT
american_scientific_journal-2059	16	19	volume	volume	NOUN
american_scientific_journal-2059	16	20	26	26	NUM
american_scientific_journal-2059	16	21	,	,	PUNCT
american_scientific_journal-2059	16	22	no	no	DET
american_scientific_journal-2059	16	23	4	4	NUM
american_scientific_journal-2059	16	24	,	,	PUNCT
american_scientific_journal-2059	16	25	pp	pp	ADV
american_scientific_journal-2059	16	26	42	42	NUM
american_scientific_journal-2059	16	27	-	-	SYM
american_scientific_journal-2059	16	28	53	53	NUM
american_scientific_journal-2059	16	29	43	43	NUM
american_scientific_journal-2059	16	30	2	2	NUM
american_scientific_journal-2059	16	31	.	.	PUNCT
american_scientific_journal-2059	16	32	preliminaries	preliminary	NOUN
american_scientific_journal-2059	16	33	through	through	ADP
american_scientific_journal-2059	16	34	this	this	DET
american_scientific_journal-2059	16	35	section	section	NOUN
american_scientific_journal-2059	16	36	,	,	PUNCT
american_scientific_journal-2059	16	37	i	i	PRON
american_scientific_journal-2059	16	38	give	give	VERB
american_scientific_journal-2059	16	39	and	and	CCONJ
american_scientific_journal-2059	16	40	introduction	introduction	NOUN
american_scientific_journal-2059	16	41	some	some	DET
american_scientific_journal-2059	16	42	important	important	ADJ
american_scientific_journal-2059	16	43	definitions	definition	NOUN
american_scientific_journal-2059	16	44	and	and	CCONJ
american_scientific_journal-2059	16	45	facts	fact	NOUN
american_scientific_journal-2059	16	46	about	about	ADP
american_scientific_journal-2059	16	47	soft	soft	ADJ
american_scientific_journal-2059	16	48	topology	topology	NOUN
american_scientific_journal-2059	16	49	and	and	CCONJ
american_scientific_journal-2059	16	50	recall	recall	VERB
american_scientific_journal-2059	16	51	primary	primary	ADJ
american_scientific_journal-2059	16	52	definition	definition	NOUN
american_scientific_journal-2059	16	53	soft	soft	ADJ
american_scientific_journal-2059	16	54	set	set	NOUN
american_scientific_journal-2059	16	55	that	that	PRON
american_scientific_journal-2059	16	56	need	need	VERB
american_scientific_journal-2059	16	57	in	in	ADP
american_scientific_journal-2059	16	58	this	this	DET
american_scientific_journal-2059	16	59	work	work	NOUN
american_scientific_journal-2059	16	60	.	.	PUNCT
american_scientific_journal-2059	17	1	2.1	2.1	NUM
american_scientific_journal-2059	17	2	.	.	PUNCT
american_scientific_journal-2059	17	3	definition	definition	NOUN
american_scientific_journal-2059	17	4	[	[	X
american_scientific_journal-2059	17	5	2	2	X
american_scientific_journal-2059	17	6	]	]	PUNCT
american_scientific_journal-2059	17	7	the	the	DET
american_scientific_journal-2059	17	8	set	set	NOUN
american_scientific_journal-2059	17	9	of	of	ADP
american_scientific_journal-2059	17	10	ordered	order	VERB
american_scientific_journal-2059	17	11	pairs	pair	NOUN
american_scientific_journal-2059	17	12	represents	represent	VERB
american_scientific_journal-2059	17	13	a	a	DET
american_scientific_journal-2059	17	14	soft	soft	ADJ
american_scientific_journal-2059	17	15	set	set	NOUN
american_scientific_journal-2059	17	16	af	af	NOUN
american_scientific_journal-2059	17	17	on	on	ADP
american_scientific_journal-2059	17	18	the	the	DET
american_scientific_journal-2059	17	19	universe	universe	ADJ
american_scientific_journal-2059	17	20	u	u	NOUN
american_scientific_journal-2059	17	21	,	,	PUNCT
american_scientific_journal-2059	17	22	where	where	SCONJ
american_scientific_journal-2059	17	23	is	be	AUX
american_scientific_journal-2059	17	24	mapping	mapping	NOUN
american_scientific_journal-2059	17	25	and	and	CCONJ
american_scientific_journal-2059	17	26	af	af	PROPN
american_scientific_journal-2059	17	27	is	be	AUX
american_scientific_journal-2059	17	28	called	call	VERB
american_scientific_journal-2059	17	29	an	an	DET
american_scientific_journal-2059	17	30	approximate	approximate	ADJ
american_scientific_journal-2059	17	31	function	function	NOUN
american_scientific_journal-2059	17	32	of	of	ADP
american_scientific_journal-2059	17	33	the	the	DET
american_scientific_journal-2059	17	34	soft	soft	ADJ
american_scientific_journal-2059	17	35	set	set	NOUN
american_scientific_journal-2059	17	36	af	af	PROPN
american_scientific_journal-2059	17	37	.	.	PUNCT
american_scientific_journal-2059	18	1	however	however	ADV
american_scientific_journal-2059	18	2	,	,	PUNCT
american_scientific_journal-2059	18	3	the	the	DET
american_scientific_journal-2059	18	4	set	set	NOUN
american_scientific_journal-2059	18	5	of	of	ADP
american_scientific_journal-2059	18	6	all	all	DET
american_scientific_journal-2059	18	7	soft	soft	ADJ
american_scientific_journal-2059	18	8	sets	set	NOUN
american_scientific_journal-2059	18	9	over	over	ADP
american_scientific_journal-2059	18	10	u	u	NOUN
american_scientific_journal-2059	18	11	is	be	AUX
american_scientific_journal-2059	18	12	denoted	denote	VERB
american_scientific_journal-2059	18	13	by	by	ADP
american_scientific_journal-2059	18	14	)	)	PUNCT
american_scientific_journal-2059	18	15	(	(	PUNCT
american_scientific_journal-2059	18	16	uss	uss	PROPN
american_scientific_journal-2059	18	17	.	.	PUNCT
american_scientific_journal-2059	19	1	2.2	2.2	NUM
american_scientific_journal-2059	19	2	.	.	PUNCT
american_scientific_journal-2059	20	1	definition	definition	NOUN
american_scientific_journal-2059	20	2	[	[	X
american_scientific_journal-2059	20	3	5	5	NUM
american_scientific_journal-2059	20	4	]	]	PUNCT
american_scientific_journal-2059	20	5	let	let	NOUN
american_scientific_journal-2059	20	6	)	)	PUNCT
american_scientific_journal-2059	20	7	(	(	PUNCT
american_scientific_journal-2059	20	8	usf	usf	PROPN
american_scientific_journal-2059	20	9	sa	sa	PROPN
american_scientific_journal-2059	20	10	∈	∈	PROPN
american_scientific_journal-2059	20	11	.	.	PUNCT
american_scientific_journal-2059	21	1	if	if	SCONJ
american_scientific_journal-2059	21	2	for	for	ADP
american_scientific_journal-2059	21	3	all	all	DET
american_scientific_journal-2059	21	4	ax∈	ax∈	NOUN
american_scientific_journal-2059	21	5	,	,	PUNCT
american_scientific_journal-2059	21	6	then	then	ADV
american_scientific_journal-2059	21	7	af	af	PROPN
american_scientific_journal-2059	21	8	is	be	AUX
american_scientific_journal-2059	21	9	called	call	VERB
american_scientific_journal-2059	21	10	an	an	DET
american_scientific_journal-2059	21	11	empty	empty	ADJ
american_scientific_journal-2059	21	12	set	set	NOUN
american_scientific_journal-2059	21	13	and	and	CCONJ
american_scientific_journal-2059	21	14	denoted	denote	VERB
american_scientific_journal-2059	21	15	by	by	ADP
american_scientific_journal-2059	21	16	φf	φf	PRON
american_scientific_journal-2059	21	17	.	.	PUNCT
american_scientific_journal-2059	22	1	moreover	moreover	ADV
american_scientific_journal-2059	22	2	,	,	PUNCT
american_scientific_journal-2059	22	3	if	if	SCONJ
american_scientific_journal-2059	22	4	uf	uf	PROPN
american_scientific_journal-2059	22	5	a	a	X
american_scientific_journal-2059	22	6	=	=	PUNCT
american_scientific_journal-2059	22	7	for	for	ADP
american_scientific_journal-2059	22	8	all	all	DET
american_scientific_journal-2059	22	9	ax∈	ax∈	NOUN
american_scientific_journal-2059	22	10	,	,	PUNCT
american_scientific_journal-2059	22	11	then	then	ADV
american_scientific_journal-2059	22	12	af	af	PROPN
american_scientific_journal-2059	22	13	is	be	AUX
american_scientific_journal-2059	22	14	called	call	VERB
american_scientific_journal-2059	22	15	an	an	DET
american_scientific_journal-2059	22	16	a	a	PRON
american_scientific_journal-2059	22	17	-universal	-universal	ADJ
american_scientific_journal-2059	22	18	soft	soft	ADJ
american_scientific_journal-2059	22	19	set	set	NOUN
american_scientific_journal-2059	22	20	and	and	CCONJ
american_scientific_journal-2059	22	21	denoted	denote	VERB
american_scientific_journal-2059	22	22	by	by	ADP
american_scientific_journal-2059	22	23	af	af	PROPN
american_scientific_journal-2059	22	24	ˆ	ˆ	PROPN
american_scientific_journal-2059	22	25	.	.	PUNCT
american_scientific_journal-2059	23	1	but	but	CCONJ
american_scientific_journal-2059	23	2	,	,	PUNCT
american_scientific_journal-2059	23	3	if	if	SCONJ
american_scientific_journal-2059	23	4	ea	ea	NOUN
american_scientific_journal-2059	23	5	=	=	SYM
american_scientific_journal-2059	23	6	,	,	PUNCT
american_scientific_journal-2059	23	7	then	then	ADV
american_scientific_journal-2059	23	8	a	a	DET
american_scientific_journal-2059	23	9	-universal	-universal	ADJ
american_scientific_journal-2059	23	10	soft	soft	ADJ
american_scientific_journal-2059	23	11	set	set	NOUN
american_scientific_journal-2059	23	12	is	be	AUX
american_scientific_journal-2059	23	13	called	call	VERB
american_scientific_journal-2059	23	14	universal	universal	ADJ
american_scientific_journal-2059	23	15	soft	soft	ADJ
american_scientific_journal-2059	23	16	set	set	NOUN
american_scientific_journal-2059	23	17	and	and	CCONJ
american_scientific_journal-2059	23	18	denoted	denote	VERB
american_scientific_journal-2059	23	19	by	by	ADP
american_scientific_journal-2059	23	20	ef~	ef~	PROPN
american_scientific_journal-2059	23	21	.	.	PUNCT
american_scientific_journal-2059	24	1	2.3	2.3	NUM
american_scientific_journal-2059	24	2	.	.	PUNCT
american_scientific_journal-2059	24	3	definition	definition	NOUN
american_scientific_journal-2059	24	4	[	[	X
american_scientific_journal-2059	24	5	5	5	NUM
american_scientific_journal-2059	24	6	]	]	PUNCT
american_scientific_journal-2059	24	7	let	let	NOUN
american_scientific_journal-2059	24	8	)	)	PUNCT
american_scientific_journal-2059	24	9	(	(	PUNCT
american_scientific_journal-2059	24	10	,	,	PUNCT
american_scientific_journal-2059	24	11	usff	usff	PROPN
american_scientific_journal-2059	24	12	sba	sba	PROPN
american_scientific_journal-2059	24	13	∈	∈	PROPN
american_scientific_journal-2059	24	14	.	.	PUNCT
american_scientific_journal-2059	25	1	if	if	SCONJ
american_scientific_journal-2059	25	2	)	)	PUNCT
american_scientific_journal-2059	25	3	(	(	PUNCT
american_scientific_journal-2059	25	4	)	)	PUNCT
american_scientific_journal-2059	25	5	(	(	PUNCT
american_scientific_journal-2059	25	6	xfxf	xfxf	PROPN
american_scientific_journal-2059	25	7	ba	ba	PROPN
american_scientific_journal-2059	25	8	⊆	⊆	NUM
american_scientific_journal-2059	25	9	for	for	ADP
american_scientific_journal-2059	25	10	all	all	PRON
american_scientific_journal-2059	25	11	x	x	NOUN
american_scientific_journal-2059	25	12	,	,	PUNCT
american_scientific_journal-2059	25	13	then	then	ADV
american_scientific_journal-2059	25	14	,	,	PUNCT
american_scientific_journal-2059	25	15	af	af	PROPN
american_scientific_journal-2059	25	16	is	be	AUX
american_scientific_journal-2059	25	17	a	a	DET
american_scientific_journal-2059	25	18	soft	soft	ADJ
american_scientific_journal-2059	25	19	subset	subset	NOUN
american_scientific_journal-2059	25	20	of	of	ADP
american_scientific_journal-2059	25	21	bf	bf	NOUN
american_scientific_journal-2059	25	22	and	and	CCONJ
american_scientific_journal-2059	25	23	denoted	denote	VERB
american_scientific_journal-2059	25	24	by	by	ADP
american_scientific_journal-2059	25	25	.	.	PUNCT
american_scientific_journal-2059	26	1	2.4	2.4	NUM
american_scientific_journal-2059	26	2	.	.	PUNCT
american_scientific_journal-2059	27	1	definition	definition	NOUN
american_scientific_journal-2059	27	2	[	[	X
american_scientific_journal-2059	27	3	5	5	NUM
american_scientific_journal-2059	27	4	]	]	PUNCT
american_scientific_journal-2059	27	5	let	let	NOUN
american_scientific_journal-2059	27	6	)	)	PUNCT
american_scientific_journal-2059	27	7	(	(	PUNCT
american_scientific_journal-2059	27	8	,	,	PUNCT
american_scientific_journal-2059	27	9	usff	usff	PROPN
american_scientific_journal-2059	27	10	sba	sba	PROPN
american_scientific_journal-2059	27	11	∈	∈	PROPN
american_scientific_journal-2059	27	12	.	.	PUNCT
american_scientific_journal-2059	28	1	then	then	ADV
american_scientific_journal-2059	28	2	,	,	PUNCT
american_scientific_journal-2059	28	3	the	the	DET
american_scientific_journal-2059	28	4	soft	soft	ADJ
american_scientific_journal-2059	28	5	union	union	NOUN
american_scientific_journal-2059	28	6	is	be	AUX
american_scientific_journal-2059	28	7	denoted	denote	VERB
american_scientific_journal-2059	28	8	by	by	ADP
american_scientific_journal-2059	28	9	ba	ba	PROPN
american_scientific_journal-2059	28	10	ff	ff	PROPN
american_scientific_journal-2059	28	11	∪~	∪~	PROPN
american_scientific_journal-2059	28	12	,	,	PUNCT
american_scientific_journal-2059	28	13	however	however	ADV
american_scientific_journal-2059	28	14	,	,	PUNCT
american_scientific_journal-2059	28	15	the	the	DET
american_scientific_journal-2059	28	16	soft	soft	ADJ
american_scientific_journal-2059	28	17	intersection	intersection	NOUN
american_scientific_journal-2059	28	18	is	be	AUX
american_scientific_journal-2059	28	19	denoted	denote	VERB
american_scientific_journal-2059	28	20	by	by	ADP
american_scientific_journal-2059	28	21	ba	ba	PROPN
american_scientific_journal-2059	28	22	ff	ff	PROPN
american_scientific_journal-2059	28	23	∩~	∩~	PROPN
american_scientific_journal-2059	28	24	also	also	ADV
american_scientific_journal-2059	28	25	,	,	PUNCT
american_scientific_journal-2059	28	26	the	the	DET
american_scientific_journal-2059	28	27	soft	soft	ADJ
american_scientific_journal-2059	28	28	difference	difference	NOUN
american_scientific_journal-2059	28	29	of	of	ADP
american_scientific_journal-2059	28	30	af	af	PROPN
american_scientific_journal-2059	28	31	and	and	CCONJ
american_scientific_journal-2059	28	32	bf	bf	NOUN
american_scientific_journal-2059	28	33	is	be	AUX
american_scientific_journal-2059	28	34	denoted	denote	VERB
american_scientific_journal-2059	28	35	by	by	ADP
american_scientific_journal-2059	28	36	ba	ba	PROPN
american_scientific_journal-2059	28	37	ff	ff	PROPN
american_scientific_journal-2059	28	38	∆~	∆~	PROPN
american_scientific_journal-2059	28	39	,	,	PUNCT
american_scientific_journal-2059	28	40	are	be	AUX
american_scientific_journal-2059	28	41	defined	define	VERB
american_scientific_journal-2059	28	42	by	by	ADP
american_scientific_journal-2059	28	43	the	the	DET
american_scientific_journal-2059	28	44	approximate	approximate	ADJ
american_scientific_journal-2059	28	45	functions	function	NOUN
american_scientific_journal-2059	28	46	,	,	PUNCT
american_scientific_journal-2059	28	47	,	,	PUNCT
american_scientific_journal-2059	28	48	,	,	PUNCT
american_scientific_journal-2059	28	49	respectively	respectively	ADV
american_scientific_journal-2059	28	50	,	,	PUNCT
american_scientific_journal-2059	28	51	on	on	ADP
american_scientific_journal-2059	28	52	the	the	DET
american_scientific_journal-2059	28	53	onther	onther	ADJ
american_scientific_journal-2059	28	54	hand	hand	NOUN
american_scientific_journal-2059	28	55	,	,	PUNCT
american_scientific_journal-2059	29	1	the	the	DET
american_scientific_journal-2059	29	2	soft	soft	ADJ
american_scientific_journal-2059	29	3	complement	complement	NOUN
american_scientific_journal-2059	29	4	c	c	NOUN
american_scientific_journal-2059	29	5	af	af	VERB
american_scientific_journal-2059	29	6	~	~	PUNCT
american_scientific_journal-2059	29	7	of	of	ADP
american_scientific_journal-2059	29	8	af	af	PROPN
american_scientific_journal-2059	29	9	is	be	AUX
american_scientific_journal-2059	29	10	defined	define	VERB
american_scientific_journal-2059	29	11	by	by	ADP
american_scientific_journal-2059	29	12	the	the	DET
american_scientific_journal-2059	29	13	approximate	approximate	ADJ
american_scientific_journal-2059	29	14	function	function	NOUN
american_scientific_journal-2059	29	15	)	)	PUNCT
american_scientific_journal-2059	29	16	(	(	PUNCT
american_scientific_journal-2059	29	17	=)	=)	PROPN
american_scientific_journal-2059	29	18	(	(	PUNCT
american_scientific_journal-2059	29	19	xfxf	xfxf	PROPN
american_scientific_journal-2059	29	20	c	c	PROPN
american_scientific_journal-2059	29	21	aca	aca	PROPN
american_scientific_journal-2059	29	22	,	,	PUNCT
american_scientific_journal-2059	29	23	where	where	SCONJ
american_scientific_journal-2059	29	24	)	)	PUNCT
american_scientific_journal-2059	29	25	(	(	PUNCT
american_scientific_journal-2059	29	26	xf	xf	PROPN
american_scientific_journal-2059	29	27	c	c	PROPN
american_scientific_journal-2059	29	28	a	a	PRON
american_scientific_journal-2059	29	29	is	be	AUX
american_scientific_journal-2059	29	30	the	the	DET
american_scientific_journal-2059	29	31	complement	complement	NOUN
american_scientific_journal-2059	29	32	of	of	ADP
american_scientific_journal-2059	29	33	the	the	DET
american_scientific_journal-2059	29	34	set	set	NOUN
american_scientific_journal-2059	29	35	)	)	PUNCT
american_scientific_journal-2059	29	36	(	(	PUNCT
american_scientific_journal-2059	29	37	xf	xf	PROPN
american_scientific_journal-2059	29	38	a	a	PROPN
american_scientific_journal-2059	29	39	;	;	PUNCT
american_scientific_journal-2059	29	40	that	that	PRON
american_scientific_journal-2059	29	41	is	is	ADV
american_scientific_journal-2059	29	42	,	,	PUNCT
american_scientific_journal-2059	29	43	)	)	PUNCT
american_scientific_journal-2059	29	44	(	(	PUNCT
american_scientific_journal-2059	29	45	=)	=)	X
american_scientific_journal-2059	29	46	(	(	PUNCT
american_scientific_journal-2059	29	47	xfuxf	xfuxf	VERB
american_scientific_journal-2059	29	48	a	a	DET
american_scientific_journal-2059	29	49	c	c	NOUN
american_scientific_journal-2059	29	50	a	a	DET
american_scientific_journal-2059	29	51	−	−	NOUN
american_scientific_journal-2059	29	52	for	for	ADP
american_scientific_journal-2059	29	53	all	all	DET
american_scientific_journal-2059	29	54	ax∈	ax∈	NOUN
american_scientific_journal-2059	29	55	.	.	PUNCT
american_scientific_journal-2059	30	1	it	it	PRON
american_scientific_journal-2059	30	2	is	be	AUX
american_scientific_journal-2059	30	3	easy	easy	ADJ
american_scientific_journal-2059	30	4	to	to	PART
american_scientific_journal-2059	30	5	see	see	VERB
american_scientific_journal-2059	30	6	that	that	SCONJ
american_scientific_journal-2059	30	7	a	a	DET
american_scientific_journal-2059	30	8	cc	cc	X
american_scientific_journal-2059	30	9	a	a	DET
american_scientific_journal-2059	30	10	ff	ff	NOUN
american_scientific_journal-2059	30	11	=)	=)	PROPN
american_scientific_journal-2059	30	12	(	(	PUNCT
american_scientific_journal-2059	30	13	~~	~~	NUM
american_scientific_journal-2059	30	14	and	and	CCONJ
american_scientific_journal-2059	30	15	e	e	X
american_scientific_journal-2059	30	16	c	c	PROPN
american_scientific_journal-2059	30	17	ff	ff	X
american_scientific_journal-2059	30	18	~	~	PUNCT
american_scientific_journal-2059	30	19	~	~	PUNCT
american_scientific_journal-2059	30	20	=	=	SYM
american_scientific_journal-2059	30	21	φ	φ	X
american_scientific_journal-2059	30	22	.	.	PUNCT
american_scientific_journal-2059	31	1	2.5	2.5	NUM
american_scientific_journal-2059	31	2	.	.	PUNCT
american_scientific_journal-2059	32	1	proposition	proposition	NOUN
american_scientific_journal-2059	32	2	[	[	X
american_scientific_journal-2059	32	3	5	5	NUM
american_scientific_journal-2059	32	4	]	]	PUNCT
american_scientific_journal-2059	32	5	let	let	NOUN
american_scientific_journal-2059	32	6	)	)	PUNCT
american_scientific_journal-2059	32	7	(	(	PUNCT
american_scientific_journal-2059	32	8	,	,	PUNCT
american_scientific_journal-2059	32	9	,	,	PUNCT
american_scientific_journal-2059	32	10	usfff	usfff	ADJ
american_scientific_journal-2059	32	11	scba	scba	NOUN
american_scientific_journal-2059	32	12	∈	∈	PROPN
american_scientific_journal-2059	32	13	.	.	PUNCT
american_scientific_journal-2059	33	1	then	then	ADV
american_scientific_journal-2059	33	2	,	,	PUNCT
american_scientific_journal-2059	33	3	1	1	X
american_scientific_journal-2059	33	4	.	.	PUNCT
american_scientific_journal-2059	34	1	american	american	PROPN
american_scientific_journal-2059	34	2	scientific	scientific	ADJ
american_scientific_journal-2059	34	3	research	research	PROPN
american_scientific_journal-2059	34	4	journal	journal	NOUN
american_scientific_journal-2059	34	5	for	for	ADP
american_scientific_journal-2059	34	6	engineering	engineering	NOUN
american_scientific_journal-2059	34	7	,	,	PUNCT
american_scientific_journal-2059	34	8	technology	technology	NOUN
american_scientific_journal-2059	34	9	,	,	PUNCT
american_scientific_journal-2059	34	10	and	and	CCONJ
american_scientific_journal-2059	34	11	sciences	science	NOUN
american_scientific_journal-2059	34	12	(	(	PUNCT
american_scientific_journal-2059	34	13	asrjets	asrjet	NOUN
american_scientific_journal-2059	34	14	)	)	PUNCT
american_scientific_journal-2059	34	15	(	(	PUNCT
american_scientific_journal-2059	34	16	2016	2016	NUM
american_scientific_journal-2059	34	17	)	)	PUNCT
american_scientific_journal-2059	34	18	volume	volume	NOUN
american_scientific_journal-2059	34	19	26	26	NUM
american_scientific_journal-2059	34	20	,	,	PUNCT
american_scientific_journal-2059	34	21	no	no	DET
american_scientific_journal-2059	34	22	4	4	NUM
american_scientific_journal-2059	34	23	,	,	PUNCT
american_scientific_journal-2059	34	24	pp	pp	ADV
american_scientific_journal-2059	34	25	42	42	NUM
american_scientific_journal-2059	34	26	-	-	SYM
american_scientific_journal-2059	34	27	53	53	NUM
american_scientific_journal-2059	34	28	44	44	NUM
american_scientific_journal-2059	34	29	2	2	NUM
american_scientific_journal-2059	34	30	.	.	PUNCT
american_scientific_journal-2059	34	31	3	3	NUM
american_scientific_journal-2059	34	32	.	.	X
american_scientific_journal-2059	35	1	4	4	NUM
american_scientific_journal-2059	35	2	.	.	NOUN
american_scientific_journal-2059	35	3	5	5	NUM
american_scientific_journal-2059	35	4	.	.	NOUN
american_scientific_journal-2059	35	5	6	6	NUM
american_scientific_journal-2059	35	6	.	.	X
american_scientific_journal-2059	35	7	7	7	X
american_scientific_journal-2059	35	8	.	.	X
american_scientific_journal-2059	35	9	8)~(~)~(=)~(~&)~(~)~(=)~(~	8)~(~)~(=)~(~&)~(~)~(=)~(~	NUM
american_scientific_journal-2059	35	10	cabacbacabacba	cabacbacabacba	ADJ
american_scientific_journal-2059	35	11	ffffffffffffff	ffffffffffffff	ADJ
american_scientific_journal-2059	35	12	∩∪∩∪∩∪∩∪∩∪	∩∪∩∪∩∪∩∪∩∪	NOUN
american_scientific_journal-2059	35	13	.	.	PUNCT
american_scientific_journal-2059	36	1	2.6	2.6	NUM
american_scientific_journal-2059	36	2	.	.	PUNCT
american_scientific_journal-2059	36	3	definition	definition	NOUN
american_scientific_journal-2059	36	4	[	[	X
american_scientific_journal-2059	36	5	6	6	NUM
american_scientific_journal-2059	36	6	]	]	PUNCT
american_scientific_journal-2059	36	7	let	let	NOUN
american_scientific_journal-2059	36	8	)	)	PUNCT
american_scientific_journal-2059	36	9	(	(	PUNCT
american_scientific_journal-2059	36	10	usf	usf	PROPN
american_scientific_journal-2059	36	11	sa	sa	PROPN
american_scientific_journal-2059	36	12	∈	∈	PROPN
american_scientific_journal-2059	36	13	."the	."the	DET
american_scientific_journal-2059	36	14	soft	soft	ADJ
american_scientific_journal-2059	36	15	power	power	NOUN
american_scientific_journal-2059	36	16	set	set	NOUN
american_scientific_journal-2059	36	17	of	of	ADP
american_scientific_journal-2059	36	18	af	af	PROPN
american_scientific_journal-2059	36	19	is	be	AUX
american_scientific_journal-2059	36	20	defined	define	VERB
american_scientific_journal-2059	36	21	by	by	ADP
american_scientific_journal-2059	36	22	"	"	PUNCT
american_scientific_journal-2059	36	23	.	.	PUNCT
american_scientific_journal-2059	37	1	and	and	CCONJ
american_scientific_journal-2059	37	2	its	its	PRON
american_scientific_journal-2059	37	3	cardinality	cardinality	NOUN
american_scientific_journal-2059	37	4	is	be	AUX
american_scientific_journal-2059	37	5	defined	define	VERB
american_scientific_journal-2059	37	6	by	by	ADP
american_scientific_journal-2059	37	7	,	,	PUNCT
american_scientific_journal-2059	37	8	where	where	SCONJ
american_scientific_journal-2059	37	9	|)(|	|)(|	ADP
american_scientific_journal-2059	37	10	xf	xf	PROPN
american_scientific_journal-2059	37	11	a	a	PROPN
american_scientific_journal-2059	37	12	is	be	AUX
american_scientific_journal-2059	37	13	the	the	DET
american_scientific_journal-2059	37	14	cardinality	cardinality	NOUN
american_scientific_journal-2059	37	15	of	of	ADP
american_scientific_journal-2059	37	16	)	)	PUNCT
american_scientific_journal-2059	37	17	(	(	PUNCT
american_scientific_journal-2059	37	18	xf	xf	PROPN
american_scientific_journal-2059	37	19	a	a	PROPN
american_scientific_journal-2059	37	20	.	.	PROPN
american_scientific_journal-2059	38	1	2.7	2.7	NUM
american_scientific_journal-2059	38	2	.	.	PUNCT
american_scientific_journal-2059	39	1	definition	definition	NOUN
american_scientific_journal-2059	39	2	[	[	X
american_scientific_journal-2059	39	3	6	6	NUM
american_scientific_journal-2059	39	4	]	]	PUNCT
american_scientific_journal-2059	39	5	let	let	NOUN
american_scientific_journal-2059	39	6	)	)	PUNCT
american_scientific_journal-2059	39	7	(	(	PUNCT
american_scientific_journal-2059	39	8	usf	usf	PROPN
american_scientific_journal-2059	39	9	sa	sa	PROPN
american_scientific_journal-2059	39	10	∈	∈	PROPN
american_scientific_journal-2059	39	11	.	.	PUNCT
american_scientific_journal-2059	40	1	a	a	DET
american_scientific_journal-2059	40	2	soft	soft	ADJ
american_scientific_journal-2059	40	3	topology	topology	NOUN
american_scientific_journal-2059	40	4	on	on	ADP
american_scientific_journal-2059	40	5	af	af	PROPN
american_scientific_journal-2059	40	6	,	,	PUNCT
american_scientific_journal-2059	40	7	denoted	denote	VERB
american_scientific_journal-2059	40	8	by	by	ADP
american_scientific_journal-2059	40	9	τ~	τ~	PROPN
american_scientific_journal-2059	40	10	,	,	PUNCT
american_scientific_journal-2059	40	11	is	be	AUX
american_scientific_journal-2059	40	12	a	a	DET
american_scientific_journal-2059	40	13	collection	collection	NOUN
american_scientific_journal-2059	40	14	of	of	ADP
american_scientific_journal-2059	40	15	soft	soft	ADJ
american_scientific_journal-2059	40	16	subsets	subset	NOUN
american_scientific_journal-2059	40	17	of	of	ADP
american_scientific_journal-2059	40	18	af	af	VERB
american_scientific_journal-2059	40	19	having	have	VERB
american_scientific_journal-2059	40	20	the	the	DET
american_scientific_journal-2059	40	21	following	follow	VERB
american_scientific_journal-2059	40	22	properties	property	NOUN
american_scientific_journal-2059	40	23	:	:	PUNCT
american_scientific_journal-2059	40	24	•	•	NUM
american_scientific_journal-2059	40	25	τφ	τφ	ADP
american_scientific_journal-2059	40	26	~	~	NOUN
american_scientific_journal-2059	40	27	,	,	PUNCT
american_scientific_journal-2059	40	28	∈aff	∈aff	NUM
american_scientific_journal-2059	40	29	.	.	PUNCT
american_scientific_journal-2059	41	1	•	•	INTJ
american_scientific_journal-2059	41	2	.	.	PUNCT
american_scientific_journal-2059	42	1	•	•	NOUN
american_scientific_journal-2059	42	2	.	.	PUNCT
american_scientific_journal-2059	43	1	2.8	2.8	NUM
american_scientific_journal-2059	43	2	.	.	PUNCT
american_scientific_journal-2059	43	3	definition	definition	NOUN
american_scientific_journal-2059	43	4	[	[	X
american_scientific_journal-2059	43	5	6	6	NUM
american_scientific_journal-2059	43	6	]	]	PUNCT
american_scientific_journal-2059	43	7	let	let	NOUN
american_scientific_journal-2059	43	8	)	)	PUNCT
american_scientific_journal-2059	43	9	~	~	PUNCT
american_scientific_journal-2059	43	10	,	,	PUNCT
american_scientific_journal-2059	43	11	(	(	PUNCT
american_scientific_journal-2059	43	12	τaf	τaf	ADV
american_scientific_journal-2059	43	13	be	be	AUX
american_scientific_journal-2059	43	14	a	a	DET
american_scientific_journal-2059	43	15	soft	soft	ADJ
american_scientific_journal-2059	43	16	space	space	NOUN
american_scientific_journal-2059	43	17	on	on	ADP
american_scientific_journal-2059	43	18	af	af	PROPN
american_scientific_journal-2059	43	19	.	.	PUNCT
american_scientific_journal-2059	44	1	every	every	DET
american_scientific_journal-2059	44	2	element	element	NOUN
american_scientific_journal-2059	44	3	of	of	ADP
american_scientific_journal-2059	44	4	τ~	τ~	PROPN
american_scientific_journal-2059	44	5	is	be	AUX
american_scientific_journal-2059	44	6	called	call	VERB
american_scientific_journal-2059	44	7	a	a	DET
american_scientific_journal-2059	44	8	soft	soft	ADJ
american_scientific_journal-2059	44	9	open	open	ADJ
american_scientific_journal-2059	44	10	sets	set	NOUN
american_scientific_journal-2059	44	11	.	.	PUNCT
american_scientific_journal-2059	45	1	2.9	2.9	NUM
american_scientific_journal-2059	45	2	.	.	PUNCT
american_scientific_journal-2059	45	3	definition	definition	NOUN
american_scientific_journal-2059	45	4	[	[	X
american_scientific_journal-2059	45	5	6	6	NUM
american_scientific_journal-2059	45	6	]	]	PUNCT
american_scientific_journal-2059	45	7	let	let	NOUN
american_scientific_journal-2059	45	8	)	)	PUNCT
american_scientific_journal-2059	45	9	~	~	PUNCT
american_scientific_journal-2059	45	10	,	,	PUNCT
american_scientific_journal-2059	45	11	(	(	PUNCT
american_scientific_journal-2059	45	12	τaf	τaf	ADV
american_scientific_journal-2059	45	13	be	be	AUX
american_scientific_journal-2059	45	14	a	a	DET
american_scientific_journal-2059	45	15	soft	soft	ADJ
american_scientific_journal-2059	45	16	space	space	NOUN
american_scientific_journal-2059	45	17	on	on	ADP
american_scientific_journal-2059	45	18	af	af	PROPN
american_scientific_journal-2059	45	19	and	and	CCONJ
american_scientific_journal-2059	45	20	ab	ab	PROPN
american_scientific_journal-2059	45	21	ff	ff	PROPN
american_scientific_journal-2059	45	22	⊆~	⊆~	PROPN
american_scientific_journal-2059	45	23	.	.	PUNCT
american_scientific_journal-2059	46	1	then	then	ADV
american_scientific_journal-2059	46	2	,	,	PUNCT
american_scientific_journal-2059	46	3	the	the	DET
american_scientific_journal-2059	46	4	collection	collection	NOUN
american_scientific_journal-2059	46	5	american	american	PROPN
american_scientific_journal-2059	46	6	scientific	scientific	PROPN
american_scientific_journal-2059	46	7	research	research	PROPN
american_scientific_journal-2059	46	8	journal	journal	NOUN
american_scientific_journal-2059	46	9	for	for	ADP
american_scientific_journal-2059	46	10	engineering	engineering	NOUN
american_scientific_journal-2059	46	11	,	,	PUNCT
american_scientific_journal-2059	46	12	technology	technology	NOUN
american_scientific_journal-2059	46	13	,	,	PUNCT
american_scientific_journal-2059	46	14	and	and	CCONJ
american_scientific_journal-2059	46	15	sciences	science	NOUN
american_scientific_journal-2059	46	16	(	(	PUNCT
american_scientific_journal-2059	46	17	asrjets	asrjet	NOUN
american_scientific_journal-2059	46	18	)	)	PUNCT
american_scientific_journal-2059	46	19	(	(	PUNCT
american_scientific_journal-2059	46	20	2016	2016	NUM
american_scientific_journal-2059	46	21	)	)	PUNCT
american_scientific_journal-2059	46	22	volume	volume	NOUN
american_scientific_journal-2059	46	23	26	26	NUM
american_scientific_journal-2059	46	24	,	,	PUNCT
american_scientific_journal-2059	46	25	no	no	DET
american_scientific_journal-2059	46	26	4	4	NUM
american_scientific_journal-2059	46	27	,	,	PUNCT
american_scientific_journal-2059	46	28	pp	pp	ADV
american_scientific_journal-2059	46	29	42	42	NUM
american_scientific_journal-2059	46	30	-	-	SYM
american_scientific_journal-2059	46	31	53	53	NUM
american_scientific_journal-2059	46	32	45	45	NUM
american_scientific_journal-2059	46	33	}	}	PUNCT
american_scientific_journal-2059	46	34	,	,	PUNCT
american_scientific_journal-2059	46	35	~:~{=~	~:~{=~	NOUN
american_scientific_journal-2059	46	36	niifff	niifff	ADJ
american_scientific_journal-2059	46	37	iabiabf	iabiabf	NOUN
american_scientific_journal-2059	46	38	⊆∈∈∩	⊆∈∈∩	PRON
american_scientific_journal-2059	46	39	ττ	ττ	PROPN
american_scientific_journal-2059	46	40	is	be	AUX
american_scientific_journal-2059	46	41	called	call	VERB
american_scientific_journal-2059	46	42	a	a	DET
american_scientific_journal-2059	46	43	soft	soft	ADJ
american_scientific_journal-2059	46	44	subspace	subspace	NOUN
american_scientific_journal-2059	46	45	topology	topology	NOUN
american_scientific_journal-2059	46	46	on	on	ADP
american_scientific_journal-2059	46	47	bf	bf	NOUN
american_scientific_journal-2059	46	48	.	.	PUNCT
american_scientific_journal-2059	47	1	hence	hence	ADV
american_scientific_journal-2059	47	2	,	,	PUNCT
american_scientific_journal-2059	47	3	)	)	PUNCT
american_scientific_journal-2059	47	4	~	~	PUNCT
american_scientific_journal-2059	47	5	,	,	PUNCT
american_scientific_journal-2059	47	6	(	(	PUNCT
american_scientific_journal-2059	47	7	bfbf	bfbf	ADJ
american_scientific_journal-2059	47	8	τ	τ	PROPN
american_scientific_journal-2059	47	9	is	be	AUX
american_scientific_journal-2059	47	10	called	call	VERB
american_scientific_journal-2059	47	11	a	a	DET
american_scientific_journal-2059	47	12	soft	soft	ADJ
american_scientific_journal-2059	47	13	topological	topological	ADJ
american_scientific_journal-2059	47	14	subspace	subspace	NOUN
american_scientific_journal-2059	47	15	of	of	ADP
american_scientific_journal-2059	47	16	)	)	PUNCT
american_scientific_journal-2059	47	17	~	~	PUNCT
american_scientific_journal-2059	47	18	,	,	PUNCT
american_scientific_journal-2059	47	19	(	(	PUNCT
american_scientific_journal-2059	47	20	τaf	τaf	INTJ
american_scientific_journal-2059	47	21	.	.	PUNCT
american_scientific_journal-2059	48	1	2.10	2.10	NUM
american_scientific_journal-2059	48	2	.	.	PUNCT
american_scientific_journal-2059	48	3	definition	definition	NOUN
american_scientific_journal-2059	48	4	[	[	X
american_scientific_journal-2059	48	5	6	6	NUM
american_scientific_journal-2059	48	6	]	]	PUNCT
american_scientific_journal-2059	48	7	let	let	NOUN
american_scientific_journal-2059	48	8	)	)	PUNCT
american_scientific_journal-2059	48	9	~	~	PUNCT
american_scientific_journal-2059	48	10	,	,	PUNCT
american_scientific_journal-2059	48	11	(	(	PUNCT
american_scientific_journal-2059	48	12	τaf	τaf	ADV
american_scientific_journal-2059	48	13	be	be	AUX
american_scientific_journal-2059	48	14	a	a	DET
american_scientific_journal-2059	48	15	soft	soft	ADJ
american_scientific_journal-2059	48	16	space	space	NOUN
american_scientific_journal-2059	48	17	on	on	ADP
american_scientific_journal-2059	48	18	af	af	PROPN
american_scientific_journal-2059	48	19	and	and	CCONJ
american_scientific_journal-2059	48	20	ab	ab	PROPN
american_scientific_journal-2059	48	21	ff	ff	PROPN
american_scientific_journal-2059	48	22	⊆~	⊆~	PROPN
american_scientific_journal-2059	48	23	.	.	PUNCT
american_scientific_journal-2059	49	1	the	the	DET
american_scientific_journal-2059	49	2	soft	soft	ADJ
american_scientific_journal-2059	49	3	interior	interior	NOUN
american_scientific_journal-2059	49	4	of	of	ADP
american_scientific_journal-2059	49	5	bf	bf	NOUN
american_scientific_journal-2059	49	6	,	,	PUNCT
american_scientific_journal-2059	49	7	denoted	denote	VERB
american_scientific_journal-2059	49	8			PROPN
american_scientific_journal-2059	49	9	bf	bf	NOUN
american_scientific_journal-2059	49	10	,	,	PUNCT
american_scientific_journal-2059	49	11	is	be	AUX
american_scientific_journal-2059	49	12	defined	define	VERB
american_scientific_journal-2059	49	13	as	as	ADP
american_scientific_journal-2059	49	14	the	the	DET
american_scientific_journal-2059	49	15	union	union	NOUN
american_scientific_journal-2059	49	16	of	of	ADP
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american_scientific_journal-2059	49	18	soft	soft	ADJ
american_scientific_journal-2059	49	19	open	open	ADJ
american_scientific_journal-2059	49	20	subsets	subset	NOUN
american_scientific_journal-2059	49	21	of	of	ADP
american_scientific_journal-2059	49	22	bf	bf	NOUN
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american_scientific_journal-2059	50	1	note	note	VERB
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american_scientific_journal-2059	50	3			PROPN
american_scientific_journal-2059	50	4	bf	bf	NOUN
american_scientific_journal-2059	50	5	is	be	AUX
american_scientific_journal-2059	50	6	the	the	DET
american_scientific_journal-2059	50	7	biggest	big	ADJ
american_scientific_journal-2059	50	8	soft	soft	ADJ
american_scientific_journal-2059	50	9	open	open	ADJ
american_scientific_journal-2059	50	10	set	set	NOUN
american_scientific_journal-2059	50	11	that	that	PRON
american_scientific_journal-2059	50	12	is	be	AUX
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american_scientific_journal-2059	50	14	by	by	ADP
american_scientific_journal-2059	50	15	bf	bf	NOUN
american_scientific_journal-2059	50	16	.	.	PUNCT
american_scientific_journal-2059	51	1	2.11	2.11	NUM
american_scientific_journal-2059	51	2	.	.	PUNCT
american_scientific_journal-2059	51	3	theorem	theorem	VERB
american_scientific_journal-2059	51	4	[	[	PUNCT
american_scientific_journal-2059	51	5	6	6	NUM
american_scientific_journal-2059	51	6	]	]	PUNCT
american_scientific_journal-2059	51	7	let	let	NOUN
american_scientific_journal-2059	51	8	)	)	PUNCT
american_scientific_journal-2059	51	9	~	~	PUNCT
american_scientific_journal-2059	51	10	,	,	PUNCT
american_scientific_journal-2059	51	11	(	(	PUNCT
american_scientific_journal-2059	51	12	τaf	τaf	ADV
american_scientific_journal-2059	51	13	be	be	AUX
american_scientific_journal-2059	51	14	a	a	DET
american_scientific_journal-2059	51	15	soft	soft	ADJ
american_scientific_journal-2059	51	16	space	space	NOUN
american_scientific_journal-2059	51	17	on	on	ADP
american_scientific_journal-2059	51	18	af	af	PROPN
american_scientific_journal-2059	51	19	and	and	CCONJ
american_scientific_journal-2059	51	20	acb	acb	VERB
american_scientific_journal-2059	51	21	fff	fff	PROPN
american_scientific_journal-2059	51	22	⊆~	⊆~	PROPN
american_scientific_journal-2059	51	23	,	,	PUNCT
american_scientific_journal-2059	51	24	.	.	PUNCT
american_scientific_journal-2059	52	1	then	then	ADV
american_scientific_journal-2059	52	2	,	,	PUNCT
american_scientific_journal-2059	52	3	1	1	PROPN
american_scientific_journal-2059	52	4	bb	bb	INTJ
american_scientific_journal-2059	52	5	ff	ff	INTJ
american_scientific_journal-2059	52	6	=)	=)	PROPN
american_scientific_journal-2059	52	7	(	(	PUNCT
american_scientific_journal-2059	52	8	2cb	2cb	ADJ
american_scientific_journal-2059	52	9	ff	ff	NOUN
american_scientific_journal-2059	52	10	⊆~	⊆~	PROPN
american_scientific_journal-2059	52	11	.	.	PUNCT
american_scientific_journal-2059	53	1	then	then	ADV
american_scientific_journal-2059	53	2	,	,	PUNCT
american_scientific_journal-2059	53	3			PUNCT
american_scientific_journal-2059	53	4	cb	cb	PROPN
american_scientific_journal-2059	53	5	ff	ff	PROPN
american_scientific_journal-2059	53	6	⊆~	⊆~	PROPN
american_scientific_journal-2059	53	7	3	3	NUM
american_scientific_journal-2059	53	8	)	)	PUNCT
american_scientific_journal-2059	53	9	~(=~	~(=~	PROPN
american_scientific_journal-2059	53	10	cbcb	cbcb	ADJ
american_scientific_journal-2059	53	11	ffff	ffff	PROPN
american_scientific_journal-2059	53	12	∩∩	∩∩	PROPN
american_scientific_journal-2059	53	13	4	4	PROPN
american_scientific_journal-2059	53	14	)	)	PUNCT
american_scientific_journal-2059	53	15	~(~~	~(~~	PUNCT
american_scientific_journal-2059	53	16	cbcb	cbcb	ADJ
american_scientific_journal-2059	53	17	ffff	ffff	PROPN
american_scientific_journal-2059	53	18	∪⊆∪	∪⊆∪	PROPN
american_scientific_journal-2059	53	19	2.12	2.12	NUM
american_scientific_journal-2059	53	20	.	.	PUNCT
american_scientific_journal-2059	54	1	definition	definition	NOUN
american_scientific_journal-2059	54	2	[	[	X
american_scientific_journal-2059	54	3	6	6	NUM
american_scientific_journal-2059	54	4	]	]	PUNCT
american_scientific_journal-2059	54	5	let	let	NOUN
american_scientific_journal-2059	54	6	)	)	PUNCT
american_scientific_journal-2059	54	7	~	~	PUNCT
american_scientific_journal-2059	54	8	,	,	PUNCT
american_scientific_journal-2059	54	9	(	(	PUNCT
american_scientific_journal-2059	54	10	τaf	τaf	ADV
american_scientific_journal-2059	54	11	be	be	AUX
american_scientific_journal-2059	54	12	a	a	DET
american_scientific_journal-2059	54	13	soft	soft	ADJ
american_scientific_journal-2059	54	14	space	space	NOUN
american_scientific_journal-2059	54	15	on	on	ADP
american_scientific_journal-2059	54	16	af	af	PROPN
american_scientific_journal-2059	54	17	and	and	CCONJ
american_scientific_journal-2059	54	18	ab	ab	PROPN
american_scientific_journal-2059	54	19	ff	ff	PROPN
american_scientific_journal-2059	54	20	⊆~	⊆~	PROPN
american_scientific_journal-2059	54	21	.	.	PUNCT
american_scientific_journal-2059	55	1	then	then	ADV
american_scientific_journal-2059	55	2	,	,	PUNCT
american_scientific_journal-2059	55	3	the	the	DET
american_scientific_journal-2059	55	4	soft	soft	ADJ
american_scientific_journal-2059	55	5	closure	closure	NOUN
american_scientific_journal-2059	55	6	of	of	ADP
american_scientific_journal-2059	55	7	bf	bf	NOUN
american_scientific_journal-2059	55	8	,	,	PUNCT
american_scientific_journal-2059	55	9	denoted	denote	VERB
american_scientific_journal-2059	55	10	bf	bf	NOUN
american_scientific_journal-2059	55	11	is	be	AUX
american_scientific_journal-2059	55	12	defined	define	VERB
american_scientific_journal-2059	55	13	as	as	ADP
american_scientific_journal-2059	55	14	the	the	DET
american_scientific_journal-2059	55	15	soft	soft	ADJ
american_scientific_journal-2059	55	16	intersection	intersection	NOUN
american_scientific_journal-2059	55	17	of	of	ADP
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american_scientific_journal-2059	55	19	soft	soft	ADJ
american_scientific_journal-2059	55	20	closed	closed	ADJ
american_scientific_journal-2059	55	21	superset	superset	NOUN
american_scientific_journal-2059	55	22	of	of	ADP
american_scientific_journal-2059	55	23	bf	bf	NOUN
american_scientific_journal-2059	55	24	.	.	PUNCT
american_scientific_journal-2059	56	1	note	note	VERB
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american_scientific_journal-2059	56	3	bf	bf	NOUN
american_scientific_journal-2059	56	4	is	be	AUX
american_scientific_journal-2059	56	5	the	the	DET
american_scientific_journal-2059	56	6	smallest	small	ADJ
american_scientific_journal-2059	56	7	soft	soft	ADJ
american_scientific_journal-2059	56	8	closed	closed	ADJ
american_scientific_journal-2059	56	9	set	set	NOUN
american_scientific_journal-2059	56	10	that	that	SCONJ
american_scientific_journal-2059	56	11	containing	contain	VERB
american_scientific_journal-2059	56	12	bf	bf	NOUN
american_scientific_journal-2059	56	13	.	.	PUNCT
american_scientific_journal-2059	57	1	2.13	2.13	NUM
american_scientific_journal-2059	57	2	.	.	PUNCT
american_scientific_journal-2059	57	3	theorem	theorem	VERB
american_scientific_journal-2059	57	4	[	[	PUNCT
american_scientific_journal-2059	57	5	6	6	NUM
american_scientific_journal-2059	57	6	]	]	PUNCT
american_scientific_journal-2059	57	7	let	let	NOUN
american_scientific_journal-2059	57	8	)	)	PUNCT
american_scientific_journal-2059	57	9	~	~	PUNCT
american_scientific_journal-2059	57	10	,	,	PUNCT
american_scientific_journal-2059	57	11	(	(	PUNCT
american_scientific_journal-2059	57	12	τaf	τaf	ADV
american_scientific_journal-2059	57	13	be	be	AUX
american_scientific_journal-2059	57	14	a	a	DET
american_scientific_journal-2059	57	15	soft	soft	ADJ
american_scientific_journal-2059	57	16	space	space	NOUN
american_scientific_journal-2059	57	17	on	on	ADP
american_scientific_journal-2059	57	18	af	af	PROPN
american_scientific_journal-2059	57	19	and	and	CCONJ
american_scientific_journal-2059	57	20	acb	acb	VERB
american_scientific_journal-2059	57	21	fff	fff	PROPN
american_scientific_journal-2059	57	22	⊆~	⊆~	PROPN
american_scientific_journal-2059	57	23	,	,	PUNCT
american_scientific_journal-2059	57	24	.	.	PUNCT
american_scientific_journal-2059	58	1	then	then	ADV
american_scientific_journal-2059	58	2	,	,	PUNCT
american_scientific_journal-2059	58	3	1bb	1bb	PROPN
american_scientific_journal-2059	58	4	ff	ff	NOUN
american_scientific_journal-2059	58	5	=)	=)	PROPN
american_scientific_journal-2059	58	6	(	(	PUNCT
american_scientific_journal-2059	58	7	.	.	PUNCT
american_scientific_journal-2059	58	8	2)(=	2)(=	NUM
american_scientific_journal-2059	58	9	)	)	PUNCT
american_scientific_journal-2059	58	10	(	(	PUNCT
american_scientific_journal-2059	58	11	~~	~~	NUM
american_scientific_journal-2059	58	12	c	c	PROPN
american_scientific_journal-2059	58	13	b	b	PROPN
american_scientific_journal-2059	58	14	c	c	NOUN
american_scientific_journal-2059	58	15	b	b	PROPN
american_scientific_journal-2059	58	16	ff	ff	NOUN
american_scientific_journal-2059	58	17	.	.	PUNCT
american_scientific_journal-2059	59	1	3cb	3cb	ADJ
american_scientific_journal-2059	60	1	ff	ff	NOUN
american_scientific_journal-2059	60	2	⊆~	⊆~	PUNCT
american_scientific_journal-2059	60	3	.	.	PUNCT
american_scientific_journal-2059	61	1	then	then	ADV
american_scientific_journal-2059	61	2	,	,	PUNCT
american_scientific_journal-2059	61	3	.	.	PUNCT
american_scientific_journal-2059	62	1	american	american	PROPN
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american_scientific_journal-2059	62	3	research	research	PROPN
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american_scientific_journal-2059	62	7	,	,	PUNCT
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american_scientific_journal-2059	62	9	,	,	PUNCT
american_scientific_journal-2059	62	10	and	and	CCONJ
american_scientific_journal-2059	62	11	sciences	science	NOUN
american_scientific_journal-2059	62	12	(	(	PUNCT
american_scientific_journal-2059	62	13	asrjets	asrjet	NOUN
american_scientific_journal-2059	62	14	)	)	PUNCT
american_scientific_journal-2059	62	15	(	(	PUNCT
american_scientific_journal-2059	62	16	2016	2016	NUM
american_scientific_journal-2059	62	17	)	)	PUNCT
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american_scientific_journal-2059	62	20	,	,	PUNCT
american_scientific_journal-2059	62	21	no	no	DET
american_scientific_journal-2059	62	22	4	4	NUM
american_scientific_journal-2059	62	23	,	,	PUNCT
american_scientific_journal-2059	62	24	pp	pp	ADV
american_scientific_journal-2059	62	25	42	42	NUM
american_scientific_journal-2059	62	26	-	-	SYM
american_scientific_journal-2059	62	27	53	53	NUM
american_scientific_journal-2059	62	28	46	46	NUM
american_scientific_journal-2059	62	29	4	4	NUM
american_scientific_journal-2059	62	30	.	.	PUNCT
american_scientific_journal-2059	62	31	5	5	NUM
american_scientific_journal-2059	62	32	.	.	X
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american_scientific_journal-2059	62	34	.	.	PUNCT
american_scientific_journal-2059	63	1	theorem	theorem	VERB
american_scientific_journal-2059	63	2	[	[	PUNCT
american_scientific_journal-2059	63	3	6	6	NUM
american_scientific_journal-2059	63	4	]	]	PUNCT
american_scientific_journal-2059	63	5	let	let	NOUN
american_scientific_journal-2059	63	6	)	)	PUNCT
american_scientific_journal-2059	64	1	~	~	PUNCT
american_scientific_journal-2059	64	2	,	,	PUNCT
american_scientific_journal-2059	64	3	(	(	PUNCT
american_scientific_journal-2059	64	4	τaf	τaf	ADV
american_scientific_journal-2059	64	5	be	be	AUX
american_scientific_journal-2059	64	6	a	a	DET
american_scientific_journal-2059	64	7	soft	soft	ADJ
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american_scientific_journal-2059	64	9	on	on	ADP
american_scientific_journal-2059	64	10	af	af	PROPN
american_scientific_journal-2059	64	11	and	and	CCONJ
american_scientific_journal-2059	64	12	ab	ab	PROPN
american_scientific_journal-2059	64	13	ff	ff	PROPN
american_scientific_journal-2059	64	14	⊆~	⊆~	PUNCT
american_scientific_journal-2059	64	15	then	then	ADV
american_scientific_journal-2059	64	16	bbb	bbb	PROPN
american_scientific_journal-2059	64	17	fff	fff	PROPN
american_scientific_journal-2059	64	18	⊆⊆	⊆⊆	PROPN
american_scientific_journal-2059	64	19	~~	~~	PROPN
american_scientific_journal-2059	64	20	.	.	PUNCT
american_scientific_journal-2059	65	1	2.15	2.15	NUM
american_scientific_journal-2059	65	2	.	.	PUNCT
american_scientific_journal-2059	65	3	definition	definition	NOUN
american_scientific_journal-2059	65	4	let	let	VERB
american_scientific_journal-2059	65	5	)	)	PUNCT
american_scientific_journal-2059	66	1	~	~	PUNCT
american_scientific_journal-2059	66	2	,	,	PUNCT
american_scientific_journal-2059	66	3	(	(	PUNCT
american_scientific_journal-2059	66	4	1τaf	1τaf	NUM
american_scientific_journal-2059	66	5	and	and	CCONJ
american_scientific_journal-2059	66	6	)	)	PUNCT
american_scientific_journal-2059	66	7	~	~	PUNCT
american_scientific_journal-2059	66	8	,	,	PUNCT
american_scientific_journal-2059	66	9	(	(	PUNCT
american_scientific_journal-2059	66	10	2τaf	2τaf	NUM
american_scientific_journal-2059	66	11	be	be	AUX
american_scientific_journal-2059	66	12	the	the	DET
american_scientific_journal-2059	66	13	two	two	NUM
american_scientific_journal-2059	66	14	different	different	ADJ
american_scientific_journal-2059	66	15	soft	soft	ADJ
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american_scientific_journal-2059	66	17	on	on	ADP
american_scientific_journal-2059	66	18	af	af	PROPN
american_scientific_journal-2059	66	19	.	.	PUNCT
american_scientific_journal-2059	67	1	then	then	ADV
american_scientific_journal-2059	67	2	)	)	PUNCT
american_scientific_journal-2059	67	3	~,~	~,~	NUM
american_scientific_journal-2059	67	4	,	,	PUNCT
american_scientific_journal-2059	67	5	(	(	PUNCT
american_scientific_journal-2059	67	6	21	21	NUM
american_scientific_journal-2059	67	7	ττaf	ττaf	NOUN
american_scientific_journal-2059	67	8	is	be	AUX
american_scientific_journal-2059	67	9	called	call	VERB
american_scientific_journal-2059	67	10	a	a	DET
american_scientific_journal-2059	67	11	soft	soft	ADJ
american_scientific_journal-2059	67	12	bitopological	bitopological	ADJ
american_scientific_journal-2059	67	13	space	space	NOUN
american_scientific_journal-2059	67	14	.	.	PUNCT
american_scientific_journal-2059	68	1	2.16	2.16	NUM
american_scientific_journal-2059	68	2	.	.	PUNCT
american_scientific_journal-2059	68	3	example	example	NOUN
american_scientific_journal-2059	68	4	let	let	VERB
american_scientific_journal-2059	68	5	}	}	PUNCT
american_scientific_journal-2059	68	6	,	,	PUNCT
american_scientific_journal-2059	68	7	,	,	PUNCT
american_scientific_journal-2059	68	8	,	,	PUNCT
american_scientific_journal-2059	68	9	{	{	PUNCT
american_scientific_journal-2059	68	10	=	=	NOUN
american_scientific_journal-2059	68	11	4321	4321	NUM
american_scientific_journal-2059	68	12	uuuuu	uuuuu	NOUN
american_scientific_journal-2059	68	13	,	,	PUNCT
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american_scientific_journal-2059	68	15	,	,	PUNCT
american_scientific_journal-2059	68	16	,	,	PUNCT
american_scientific_journal-2059	68	17	{	{	PUNCT
american_scientific_journal-2059	68	18	=	=	NOUN
american_scientific_journal-2059	68	19	321	321	NUM
american_scientific_journal-2059	68	20	wwwe	wwwe	NOUN
american_scientific_journal-2059	68	21	,	,	PUNCT
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american_scientific_journal-2059	68	23	,	,	PUNCT
american_scientific_journal-2059	68	24	{	{	PUNCT
american_scientific_journal-2059	68	25	=	=	NOUN
american_scientific_journal-2059	68	26	21	21	NUM
american_scientific_journal-2059	68	27	wwa	wwa	AUX
american_scientific_journal-2059	68	28	such	such	ADJ
american_scientific_journal-2059	68	29	that	that	SCONJ
american_scientific_journal-2059	68	30	ea⊆~	ea⊆~	NUM
american_scientific_journal-2059	68	31	and	and	CCONJ
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american_scientific_journal-2059	68	34	)	)	PUNCT
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american_scientific_journal-2059	68	36	{	{	PUNCT
american_scientific_journal-2059	68	37	,	,	PUNCT
american_scientific_journal-2059	68	38	{	{	PUNCT
american_scientific_journal-2059	68	39	(=	(=	PROPN
american_scientific_journal-2059	68	40	111	111	NUM
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american_scientific_journal-2059	68	42	}	}	PUNCT
american_scientific_journal-2059	68	43	)	)	PUNCT
american_scientific_journal-2059	68	44	}	}	PUNCT
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american_scientific_journal-2059	68	46	,	,	PUNCT
american_scientific_journal-2059	68	47	{	{	PUNCT
american_scientific_journal-2059	68	48	(=	(=	NOUN
american_scientific_journal-2059	68	49	212	212	NUM
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american_scientific_journal-2059	68	51	}	}	PUNCT
american_scientific_journal-2059	68	52	)	)	PUNCT
american_scientific_journal-2059	68	53	}	}	PUNCT
american_scientific_journal-2059	68	54	{	{	PUNCT
american_scientific_journal-2059	68	55	,	,	PUNCT
american_scientific_journal-2059	68	56	{	{	PUNCT
american_scientific_journal-2059	68	57	(=	(=	NOUN
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american_scientific_journal-2059	68	59	uwfa	uwfa	ADJ
american_scientific_journal-2059	68	60	}	}	PUNCT
american_scientific_journal-2059	68	61	)	)	PUNCT
american_scientific_journal-2059	68	62	}	}	PUNCT
american_scientific_journal-2059	68	63	{	{	PUNCT
american_scientific_journal-2059	68	64	,	,	PUNCT
american_scientific_journal-2059	68	65	{	{	PUNCT
american_scientific_journal-2059	68	66	(=	(=	NOUN
american_scientific_journal-2059	68	67	425	425	NUM
american_scientific_journal-2059	68	68	uwfa	uwfa	PROPN
american_scientific_journal-2059	68	69	}	}	PUNCT
american_scientific_journal-2059	68	70	)	)	PUNCT
american_scientific_journal-2059	68	71	}	}	PUNCT
american_scientific_journal-2059	68	72	,	,	PUNCT
american_scientific_journal-2059	68	73	{	{	PUNCT
american_scientific_journal-2059	68	74	,	,	PUNCT
american_scientific_journal-2059	68	75	{	{	PUNCT
american_scientific_journal-2059	68	76	(=	(=	PROPN
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american_scientific_journal-2059	68	79	}	}	PUNCT
american_scientific_journal-2059	68	80	)	)	PUNCT
american_scientific_journal-2059	68	81	}	}	PUNCT
american_scientific_journal-2059	68	82	{	{	PUNCT
american_scientific_journal-2059	68	83	,	,	PUNCT
american_scientific_journal-2059	68	84	(	(	PUNCT
american_scientific_journal-2059	68	85	}	}	PUNCT
american_scientific_journal-2059	68	86	)	)	PUNCT
american_scientific_journal-2059	68	87	,	,	PUNCT
american_scientific_journal-2059	68	88	{	{	PUNCT
american_scientific_journal-2059	68	89	,	,	PUNCT
american_scientific_journal-2059	68	90	{	{	PUNCT
american_scientific_journal-2059	68	91	(=	(=	PROPN
american_scientific_journal-2059	68	92	32117	32117	NUM
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american_scientific_journal-2059	68	94	}	}	PUNCT
american_scientific_journal-2059	68	95	)	)	PUNCT
american_scientific_journal-2059	68	96	}	}	PUNCT
american_scientific_journal-2059	68	97	{	{	PUNCT
american_scientific_journal-2059	68	98	,	,	PUNCT
american_scientific_journal-2059	68	99	(	(	PUNCT
american_scientific_journal-2059	68	100	}	}	PUNCT
american_scientific_journal-2059	68	101	)	)	PUNCT
american_scientific_journal-2059	68	102	,	,	PUNCT
american_scientific_journal-2059	68	103	{	{	PUNCT
american_scientific_journal-2059	68	104	,	,	PUNCT
american_scientific_journal-2059	68	105	{	{	PUNCT
american_scientific_journal-2059	68	106	(=	(=	NOUN
american_scientific_journal-2059	68	107	42118	42118	NUM
american_scientific_journal-2059	68	108	uwuwfa	uwuwfa	NOUN
american_scientific_journal-2059	68	109	}	}	PUNCT
american_scientific_journal-2059	68	110	)	)	PUNCT
american_scientific_journal-2059	68	111	}	}	PUNCT
american_scientific_journal-2059	68	112	{	{	PUNCT
american_scientific_journal-2059	68	113	,	,	PUNCT
american_scientific_journal-2059	68	114	(	(	PUNCT
american_scientific_journal-2059	68	115	(	(	PUNCT
american_scientific_journal-2059	68	116	}	}	PUNCT
american_scientific_journal-2059	68	117	)	)	PUNCT
american_scientific_journal-2059	68	118	,	,	PUNCT
american_scientific_journal-2059	68	119	{	{	PUNCT
american_scientific_journal-2059	68	120	,	,	PUNCT
american_scientific_journal-2059	68	121	{	{	PUNCT
american_scientific_journal-2059	68	122	(=	(=	NOUN
american_scientific_journal-2059	68	123	322110	322110	NUM
american_scientific_journal-2059	68	124	uwuwfa	uwuwfa	ADJ
american_scientific_journal-2059	68	125	american	american	PROPN
american_scientific_journal-2059	68	126	scientific	scientific	PROPN
american_scientific_journal-2059	68	127	research	research	PROPN
american_scientific_journal-2059	68	128	journal	journal	NOUN
american_scientific_journal-2059	68	129	for	for	ADP
american_scientific_journal-2059	68	130	engineering	engineering	NOUN
american_scientific_journal-2059	68	131	,	,	PUNCT
american_scientific_journal-2059	68	132	technology	technology	NOUN
american_scientific_journal-2059	68	133	,	,	PUNCT
american_scientific_journal-2059	68	134	and	and	CCONJ
american_scientific_journal-2059	68	135	sciences	science	NOUN
american_scientific_journal-2059	68	136	(	(	PUNCT
american_scientific_journal-2059	68	137	asrjets	asrjet	NOUN
american_scientific_journal-2059	68	138	)	)	PUNCT
american_scientific_journal-2059	68	139	(	(	PUNCT
american_scientific_journal-2059	68	140	2016	2016	NUM
american_scientific_journal-2059	68	141	)	)	PUNCT
american_scientific_journal-2059	68	142	volume	volume	NOUN
american_scientific_journal-2059	68	143	26	26	NUM
american_scientific_journal-2059	68	144	,	,	PUNCT
american_scientific_journal-2059	68	145	no	no	DET
american_scientific_journal-2059	68	146	4	4	NUM
american_scientific_journal-2059	68	147	,	,	PUNCT
american_scientific_journal-2059	68	148	pp	pp	ADV
american_scientific_journal-2059	68	149	42	42	NUM
american_scientific_journal-2059	68	150	-	-	SYM
american_scientific_journal-2059	68	151	53	53	NUM
american_scientific_journal-2059	68	152	47	47	NUM
american_scientific_journal-2059	68	153	}	}	PUNCT
american_scientific_journal-2059	68	154	)	)	PUNCT
american_scientific_journal-2059	68	155	}	}	PUNCT
american_scientific_journal-2059	68	156	{	{	PUNCT
american_scientific_journal-2059	68	157	,	,	PUNCT
american_scientific_journal-2059	68	158	(	(	PUNCT
american_scientific_journal-2059	68	159	}	}	PUNCT
american_scientific_journal-2059	68	160	)	)	PUNCT
american_scientific_journal-2059	68	161	,	,	PUNCT
american_scientific_journal-2059	68	162	{	{	PUNCT
american_scientific_journal-2059	68	163	,	,	PUNCT
american_scientific_journal-2059	68	164	{	{	PUNCT
american_scientific_journal-2059	68	165	(=	(=	PROPN
american_scientific_journal-2059	68	166	422111	422111	NUM
american_scientific_journal-2059	68	167	uwuwfa	uwuwfa	NOUN
american_scientific_journal-2059	68	168	}	}	PUNCT
american_scientific_journal-2059	68	169	)	)	PUNCT
american_scientific_journal-2059	68	170	}	}	PUNCT
american_scientific_journal-2059	68	171	,	,	PUNCT
american_scientific_journal-2059	68	172	{	{	PUNCT
american_scientific_journal-2059	68	173	,	,	PUNCT
american_scientific_journal-2059	68	174	(	(	PUNCT
american_scientific_journal-2059	68	175	}	}	PUNCT
american_scientific_journal-2059	68	176	)	)	PUNCT
american_scientific_journal-2059	68	177	,	,	PUNCT
american_scientific_journal-2059	68	178	{	{	PUNCT
american_scientific_journal-2059	68	179	,	,	PUNCT
american_scientific_journal-2059	68	180	{	{	PUNCT
american_scientific_journal-2059	68	181	(=	(=	NOUN
american_scientific_journal-2059	68	182	4322112	4322112	NUM
american_scientific_journal-2059	68	183	uuwuwfa	uuwuwfa	NOUN
american_scientific_journal-2059	68	184	}	}	PUNCT
american_scientific_journal-2059	68	185	)	)	PUNCT
american_scientific_journal-2059	68	186	}	}	PUNCT
american_scientific_journal-2059	68	187	{	{	PUNCT
american_scientific_journal-2059	68	188	,	,	PUNCT
american_scientific_journal-2059	68	189	(	(	PUNCT
american_scientific_journal-2059	68	190	}	}	PUNCT
american_scientific_journal-2059	68	191	)	)	PUNCT
american_scientific_journal-2059	68	192	,	,	PUNCT
american_scientific_journal-2059	68	193	,	,	PUNCT
american_scientific_journal-2059	68	194	{	{	PUNCT
american_scientific_journal-2059	68	195	,	,	PUNCT
american_scientific_journal-2059	68	196	{	{	PUNCT
american_scientific_journal-2059	68	197	(=	(=	NOUN
american_scientific_journal-2059	68	198	4221114	4221114	NUM
american_scientific_journal-2059	68	199	uwuuwfa	uwuuwfa	ADJ
american_scientific_journal-2059	68	200	aa	aa	NOUN
american_scientific_journal-2059	68	201	ff	ff	NOUN
american_scientific_journal-2059	68	202	=	=	NOUN
american_scientific_journal-2059	68	203	15	15	NUM
american_scientific_journal-2059	68	204	φffa	φffa	NOUN
american_scientific_journal-2059	68	205	=	=	NOUN
american_scientific_journal-2059	68	206	16	16	NUM
american_scientific_journal-2059	68	207	then	then	ADV
american_scientific_journal-2059	68	208	}	}	PUNCT
american_scientific_journal-2059	68	209	,	,	PUNCT
american_scientific_journal-2059	68	210	{	{	PUNCT
american_scientific_journal-2059	68	211	=	=	SYM
american_scientific_journal-2059	68	212	~	~	SYM
american_scientific_journal-2059	68	213	1	1	NUM
american_scientific_journal-2059	68	214	affφτ	affφτ	NOUN
american_scientific_journal-2059	68	215	and	and	CCONJ
american_scientific_journal-2059	68	216	}	}	PUNCT
american_scientific_journal-2059	68	217	,	,	PUNCT
american_scientific_journal-2059	68	218	,	,	PUNCT
american_scientific_journal-2059	68	219	,	,	PUNCT
american_scientific_journal-2059	68	220	{	{	PUNCT
american_scientific_journal-2059	68	221	=	=	SYM
american_scientific_journal-2059	68	222	~	~	SYM
american_scientific_journal-2059	68	223	1122	1122	NUM
american_scientific_journal-2059	68	224	aaa	aaa	NOUN
american_scientific_journal-2059	68	225	ffffφτ	ffffφτ	NOUN
american_scientific_journal-2059	68	226	are	be	AUX
american_scientific_journal-2059	68	227	a	a	DET
american_scientific_journal-2059	68	228	soft	soft	ADJ
american_scientific_journal-2059	68	229	topology	topology	NOUN
american_scientific_journal-2059	68	230	of	of	ADP
american_scientific_journal-2059	68	231	af	af	PROPN
american_scientific_journal-2059	68	232	then	then	ADV
american_scientific_journal-2059	68	233	)	)	PUNCT
american_scientific_journal-2059	68	234	~,~	~,~	NUM
american_scientific_journal-2059	68	235	,	,	PUNCT
american_scientific_journal-2059	68	236	(	(	PUNCT
american_scientific_journal-2059	68	237	21	21	NUM
american_scientific_journal-2059	68	238	ττaf	ττaf	NOUN
american_scientific_journal-2059	68	239	,	,	PUNCT
american_scientific_journal-2059	68	240	is	be	AUX
american_scientific_journal-2059	68	241	a	a	DET
american_scientific_journal-2059	68	242	soft	soft	ADJ
american_scientific_journal-2059	68	243	bitopological	bitopological	ADJ
american_scientific_journal-2059	68	244	space	space	NOUN
american_scientific_journal-2059	68	245	.	.	PUNCT
american_scientific_journal-2059	69	1	2.17	2.17	NUM
american_scientific_journal-2059	69	2	.	.	PUNCT
american_scientific_journal-2059	70	1	definition	definition	NOUN
american_scientific_journal-2059	70	2	let	let	VERB
american_scientific_journal-2059	70	3	)	)	PUNCT
american_scientific_journal-2059	70	4	~,~	~,~	X
american_scientific_journal-2059	70	5	,	,	PUNCT
american_scientific_journal-2059	70	6	(	(	PUNCT
american_scientific_journal-2059	70	7	21	21	NUM
american_scientific_journal-2059	70	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	70	9	be	be	AUX
american_scientific_journal-2059	70	10	a	a	DET
american_scientific_journal-2059	70	11	soft	soft	ADJ
american_scientific_journal-2059	70	12	bitopological	bitopological	ADJ
american_scientific_journal-2059	70	13	space	space	NOUN
american_scientific_journal-2059	70	14	over	over	ADP
american_scientific_journal-2059	70	15	af	af	PROPN
american_scientific_journal-2059	70	16	and	and	CCONJ
american_scientific_journal-2059	70	17	ab	ab	PROPN
american_scientific_journal-2059	70	18	ff	ff	PROPN
american_scientific_journal-2059	70	19	⊆~	⊆~	PROPN
american_scientific_journal-2059	70	20	.	.	PUNCT
american_scientific_journal-2059	71	1	then	then	ADV
american_scientific_journal-2059	71	2	}	}	PUNCT
american_scientific_journal-2059	71	3	,	,	PUNCT
american_scientific_journal-2059	71	4	~:~{=~	~:~{=~	ADJ
american_scientific_journal-2059	71	5	11	11	NUM
american_scientific_journal-2059	71	6	niiffff	niiffff	NOUN
american_scientific_journal-2059	71	7	iabiab	iabiab	NOUN
american_scientific_journal-2059	71	8	⊆∈∈∩	⊆∈∈∩	NOUN
american_scientific_journal-2059	71	9	ττ	ττ	NOUN
american_scientific_journal-2059	71	10	and	and	CCONJ
american_scientific_journal-2059	71	11	}	}	PUNCT
american_scientific_journal-2059	71	12	,	,	PUNCT
american_scientific_journal-2059	71	13	~:~{=~	~:~{=~	NOUN
american_scientific_journal-2059	71	14	22	22	NUM
american_scientific_journal-2059	71	15	niiffff	niiffff	NOUN
american_scientific_journal-2059	71	16	iabiab	iabiab	NOUN
american_scientific_journal-2059	71	17	⊆∈∈∩	⊆∈∈∩	PROPN
american_scientific_journal-2059	71	18	ττ	ττ	PROPN
american_scientific_journal-2059	71	19	are	be	AUX
american_scientific_journal-2059	71	20	said	say	VERB
american_scientific_journal-2059	71	21	to	to	PART
american_scientific_journal-2059	71	22	be	be	AUX
american_scientific_journal-2059	71	23	the	the	DET
american_scientific_journal-2059	71	24	relative	relative	ADJ
american_scientific_journal-2059	71	25	topologies	topology	NOUN
american_scientific_journal-2059	71	26	on	on	ADP
american_scientific_journal-2059	71	27	bf	bf	NOUN
american_scientific_journal-2059	71	28	.	.	PUNCT
american_scientific_journal-2059	72	1	then	then	ADV
american_scientific_journal-2059	72	2	)	)	PUNCT
american_scientific_journal-2059	72	3	~,~	~,~	NUM
american_scientific_journal-2059	72	4	,	,	PUNCT
american_scientific_journal-2059	72	5	(	(	PUNCT
american_scientific_journal-2059	72	6	21	21	NUM
american_scientific_journal-2059	72	7	bbb	bbb	PROPN
american_scientific_journal-2059	72	8	fff	fff	PROPN
american_scientific_journal-2059	72	9	ττ	ττ	PROPN
american_scientific_journal-2059	72	10	is	be	AUX
american_scientific_journal-2059	72	11	called	call	VERB
american_scientific_journal-2059	72	12	a	a	DET
american_scientific_journal-2059	72	13	relative	relative	ADJ
american_scientific_journal-2059	72	14	soft	soft	ADJ
american_scientific_journal-2059	72	15	bitopological	bitopological	ADJ
american_scientific_journal-2059	72	16	space	space	NOUN
american_scientific_journal-2059	72	17	of	of	ADP
american_scientific_journal-2059	72	18	)	)	PUNCT
american_scientific_journal-2059	72	19	~,~	~,~	NUM
american_scientific_journal-2059	72	20	,	,	PUNCT
american_scientific_journal-2059	72	21	(	(	PUNCT
american_scientific_journal-2059	72	22	21	21	NUM
american_scientific_journal-2059	72	23	ττaf	ττaf	NOUN
american_scientific_journal-2059	72	24	2.18	2.18	NUM
american_scientific_journal-2059	72	25	.	.	PUNCT
american_scientific_journal-2059	72	26	theorem	theorem	VERB
american_scientific_journal-2059	72	27	if	if	SCONJ
american_scientific_journal-2059	72	28	)	)	PUNCT
american_scientific_journal-2059	72	29	~,~	~,~	NUM
american_scientific_journal-2059	72	30	,	,	PUNCT
american_scientific_journal-2059	72	31	(	(	PUNCT
american_scientific_journal-2059	72	32	21	21	NUM
american_scientific_journal-2059	72	33	ττaf	ττaf	NOUN
american_scientific_journal-2059	72	34	is	be	AUX
american_scientific_journal-2059	72	35	a	a	DET
american_scientific_journal-2059	72	36	soft	soft	ADJ
american_scientific_journal-2059	72	37	bitopological	bitopological	ADJ
american_scientific_journal-2059	72	38	space	space	NOUN
american_scientific_journal-2059	72	39	then	then	ADV
american_scientific_journal-2059	72	40	21	21	NUM
american_scientific_journal-2059	72	41	~~~	~~~	PUNCT
american_scientific_journal-2059	72	42	ττ	ττ	NOUN
american_scientific_journal-2059	72	43	∩	∩	NOUN
american_scientific_journal-2059	72	44	is	be	AUX
american_scientific_journal-2059	72	45	a	a	DET
american_scientific_journal-2059	72	46	soft	soft	ADJ
american_scientific_journal-2059	72	47	topological	topological	ADJ
american_scientific_journal-2059	72	48	space	space	NOUN
american_scientific_journal-2059	72	49	over	over	ADP
american_scientific_journal-2059	72	50	af	af	PROPN
american_scientific_journal-2059	72	51	.	.	PUNCT
american_scientific_journal-2059	73	1	proof	proof	NOUN
american_scientific_journal-2059	73	2	:	:	PUNCT
american_scientific_journal-2059	73	3	•	•	NUM
american_scientific_journal-2059	73	4	21	21	NUM
american_scientific_journal-2059	73	5	~~~	~~~	PUNCT
american_scientific_journal-2059	73	6	,	,	PUNCT
american_scientific_journal-2059	73	7	ττφ	ττφ	NOUN
american_scientific_journal-2059	73	8	∩∈aff	∩∈aff	NUM
american_scientific_journal-2059	73	9	.	.	PUNCT
american_scientific_journal-2059	74	1	•	•	NUM
american_scientific_journal-2059	74	2	let	let	VERB
american_scientific_journal-2059	74	3	}	}	PUNCT
american_scientific_journal-2059	74	4	,	,	PUNCT
american_scientific_journal-2059	74	5	{	{	PUNCT
american_scientific_journal-2059	74	6	iif	iif	PROPN
american_scientific_journal-2059	74	7	ia	ia	PROPN
american_scientific_journal-2059	74	8	∈	∈	PROPN
american_scientific_journal-2059	74	9	be	be	AUX
american_scientific_journal-2059	74	10	a	a	DET
american_scientific_journal-2059	74	11	family	family	NOUN
american_scientific_journal-2059	74	12	of	of	ADP
american_scientific_journal-2059	74	13	soft	soft	ADJ
american_scientific_journal-2059	74	14	sets	set	NOUN
american_scientific_journal-2059	74	15	in	in	ADP
american_scientific_journal-2059	74	16	121	121	NUM
american_scientific_journal-2059	74	17	~~~~	~~~~	PUNCT
american_scientific_journal-2059	75	1	τττ	τττ	NOUN
american_scientific_journal-2059	75	2	∈⇒∩	∈⇒∩	NOUN
american_scientific_journal-2059	75	3	iaf	iaf	NOUN
american_scientific_journal-2059	75	4	and	and	CCONJ
american_scientific_journal-2059	75	5	2	2	NUM
american_scientific_journal-2059	75	6	~τ∈	~τ∈	VERB
american_scientific_journal-2059	75	7	iaf	iaf	NOUN
american_scientific_journal-2059	75	8	for	for	ADP
american_scientific_journal-2059	75	9	all	all	DET
american_scientific_journal-2059	75	10	ii∈	ii∈	ADJ
american_scientific_journal-2059	75	11	.	.	PUNCT
american_scientific_journal-2059	76	1	therefore	therefore	ADV
american_scientific_journal-2059	76	2	1	1	NUM
american_scientific_journal-2059	76	3	~τ∈	~τ∈	VERB
american_scientific_journal-2059	76	4	∈	∈	PROPN
american_scientific_journal-2059	76	5	iaii	iaii	ADV
american_scientific_journal-2059	76	6	f	f	NOUN
american_scientific_journal-2059	76	7	and	and	CCONJ
american_scientific_journal-2059	76	8	2	2	NUM
american_scientific_journal-2059	76	9	~τ∈	~τ∈	VERB
american_scientific_journal-2059	76	10	∈	∈	PROPN
american_scientific_journal-2059	76	11	iaii	iaii	ADV
american_scientific_journal-2059	76	12	f	f	NOUN
american_scientific_journal-2059	76	13	.	.	PUNCT
american_scientific_journal-2059	77	1	thus	thus	ADV
american_scientific_journal-2059	77	2	21	21	NUM
american_scientific_journal-2059	77	3	~~~	~~~	PUNCT
american_scientific_journal-2059	77	4	ττ	ττ	NOUN
american_scientific_journal-2059	77	5	∩∈	∩∈	NUM
american_scientific_journal-2059	77	6	∈	∈	PROPN
american_scientific_journal-2059	77	7	iaii	iaii	NOUN
american_scientific_journal-2059	77	8	f	f	PROPN
american_scientific_journal-2059	77	9	.	.	PUNCT
american_scientific_journal-2059	78	1	•	•	NUM
american_scientific_journal-2059	78	2	let	let	VERB
american_scientific_journal-2059	78	3	.	.	PUNCT
american_scientific_journal-2059	79	1	then	then	ADV
american_scientific_journal-2059	79	2	1	1	NUM
american_scientific_journal-2059	79	3	~τ∈	~τ∈	X
american_scientific_journal-2059	79	4	iaf	iaf	NOUN
american_scientific_journal-2059	79	5	and	and	CCONJ
american_scientific_journal-2059	79	6	.	.	PUNCT
american_scientific_journal-2059	80	1	since	since	SCONJ
american_scientific_journal-2059	80	2	11=	11=	NUM
american_scientific_journal-2059	80	3	~τ∈	~τ∈	PROPN
american_scientific_journal-2059	80	4	′	′	NUM
american_scientific_journal-2059	80	5	ia	ia	PROPN
american_scientific_journal-2059	80	6	n	n	PROPN
american_scientific_journal-2059	80	7	i	i	NOUN
american_scientific_journal-2059	80	8	f1	f1	NOUN
american_scientific_journal-2059	80	9	and	and	CCONJ
american_scientific_journal-2059	80	10	21=	21=	NUM
american_scientific_journal-2059	80	11	~τ∈	~τ∈	X
american_scientific_journal-2059	80	12	′	′	NUM
american_scientific_journal-2059	80	13	ia	ia	PROPN
american_scientific_journal-2059	81	1	n	n	PROPN
american_scientific_journal-2059	81	2	i	i	PROPN
american_scientific_journal-2059	81	3	f1	f1	PROPN
american_scientific_journal-2059	81	4	.	.	PUNCT
american_scientific_journal-2059	82	1	therefore	therefore	ADV
american_scientific_journal-2059	82	2	nnnif	nnnif	VERB
american_scientific_journal-2059	82	3	ia	ia	PROPN
american_scientific_journal-2059	82	4	n	n	ADV
american_scientific_journal-2059	82	5	i	i	PRON
american_scientific_journal-2059	82	6	∈′′≤≤∩∈	∈′′≤≤∩∈	VERB
american_scientific_journal-2059	82	7	′	′	VERB
american_scientific_journal-2059	82	8	,	,	PUNCT
american_scientific_journal-2059	82	9	,	,	PUNCT
american_scientific_journal-2059	82	10	1~~~	1~~~	NUM
american_scientific_journal-2059	82	11	211=	211=	NUM
american_scientific_journal-2059	82	12	ττ1	ττ1	NOUN
american_scientific_journal-2059	82	13	.	.	PUNCT
american_scientific_journal-2059	83	1	american	american	PROPN
american_scientific_journal-2059	83	2	scientific	scientific	ADJ
american_scientific_journal-2059	83	3	research	research	PROPN
american_scientific_journal-2059	83	4	journal	journal	NOUN
american_scientific_journal-2059	83	5	for	for	ADP
american_scientific_journal-2059	83	6	engineering	engineering	NOUN
american_scientific_journal-2059	83	7	,	,	PUNCT
american_scientific_journal-2059	83	8	technology	technology	NOUN
american_scientific_journal-2059	83	9	,	,	PUNCT
american_scientific_journal-2059	83	10	and	and	CCONJ
american_scientific_journal-2059	83	11	sciences	science	NOUN
american_scientific_journal-2059	83	12	(	(	PUNCT
american_scientific_journal-2059	83	13	asrjets	asrjet	NOUN
american_scientific_journal-2059	83	14	)	)	PUNCT
american_scientific_journal-2059	83	15	(	(	PUNCT
american_scientific_journal-2059	83	16	2016	2016	NUM
american_scientific_journal-2059	83	17	)	)	PUNCT
american_scientific_journal-2059	83	18	volume	volume	NOUN
american_scientific_journal-2059	83	19	26	26	NUM
american_scientific_journal-2059	83	20	,	,	PUNCT
american_scientific_journal-2059	83	21	no	no	DET
american_scientific_journal-2059	83	22	4	4	NUM
american_scientific_journal-2059	83	23	,	,	PUNCT
american_scientific_journal-2059	83	24	pp	pp	ADV
american_scientific_journal-2059	83	25	42	42	NUM
american_scientific_journal-2059	83	26	-	-	SYM
american_scientific_journal-2059	83	27	53	53	NUM
american_scientific_journal-2059	83	28	48	48	NUM
american_scientific_journal-2059	83	29	2.19	2.19	NUM
american_scientific_journal-2059	83	30	.	.	PUNCT
american_scientific_journal-2059	84	1	remark	remark	VERB
american_scientific_journal-2059	84	2	if	if	SCONJ
american_scientific_journal-2059	84	3	)	)	PUNCT
american_scientific_journal-2059	84	4	~,~	~,~	NUM
american_scientific_journal-2059	84	5	,	,	PUNCT
american_scientific_journal-2059	84	6	(	(	PUNCT
american_scientific_journal-2059	84	7	21	21	NUM
american_scientific_journal-2059	84	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	84	9	is	be	AUX
american_scientific_journal-2059	84	10	a	a	DET
american_scientific_journal-2059	84	11	soft	soft	ADJ
american_scientific_journal-2059	84	12	bitopological	bitopological	ADJ
american_scientific_journal-2059	84	13	space	space	NOUN
american_scientific_journal-2059	84	14	then	then	ADV
american_scientific_journal-2059	84	15	21	21	NUM
american_scientific_journal-2059	84	16	~~~	~~~	PUNCT
american_scientific_journal-2059	84	17	ττ	ττ	NOUN
american_scientific_journal-2059	84	18	∪	∪	NOUN
american_scientific_journal-2059	84	19	is	be	AUX
american_scientific_journal-2059	84	20	not	not	PART
american_scientific_journal-2059	84	21	a	a	DET
american_scientific_journal-2059	84	22	soft	soft	ADJ
american_scientific_journal-2059	84	23	topological	topological	ADJ
american_scientific_journal-2059	84	24	space	space	NOUN
american_scientific_journal-2059	84	25	over	over	ADP
american_scientific_journal-2059	84	26	af	af	PROPN
american_scientific_journal-2059	84	27	.	.	PUNCT
american_scientific_journal-2059	85	1	2.20	2.20	NUM
american_scientific_journal-2059	85	2	.	.	PUNCT
american_scientific_journal-2059	85	3	example	example	NOUN
american_scientific_journal-2059	85	4	let	let	VERB
american_scientific_journal-2059	85	5	us	we	PRON
american_scientific_journal-2059	85	6	consider	consider	VERB
american_scientific_journal-2059	85	7	2.16	2.16	NUM
american_scientific_journal-2059	85	8	and	and	CCONJ
american_scientific_journal-2059	85	9	let	let	VERB
american_scientific_journal-2059	85	10	}	}	PUNCT
american_scientific_journal-2059	85	11	,	,	PUNCT
american_scientific_journal-2059	85	12	,	,	PUNCT
american_scientific_journal-2059	85	13	{	{	PUNCT
american_scientific_journal-2059	85	14	=	=	SYM
american_scientific_journal-2059	85	15	~	~	SYM
american_scientific_journal-2059	85	16	11	11	NUM
american_scientific_journal-2059	85	17	aa	aa	PROPN
american_scientific_journal-2059	85	18	fffφτ	fffφτ	NOUN
american_scientific_journal-2059	85	19	and	and	CCONJ
american_scientific_journal-2059	85	20	}	}	PUNCT
american_scientific_journal-2059	85	21	,	,	PUNCT
american_scientific_journal-2059	85	22	,	,	PUNCT
american_scientific_journal-2059	85	23	{	{	PUNCT
american_scientific_journal-2059	85	24	=	=	SYM
american_scientific_journal-2059	85	25	~	~	SYM
american_scientific_journal-2059	85	26	22	22	NUM
american_scientific_journal-2059	85	27	aa	aa	PROPN
american_scientific_journal-2059	85	28	fffφτ	fffφτ	NOUN
american_scientific_journal-2059	85	29	are	be	AUX
american_scientific_journal-2059	85	30	soft	soft	ADJ
american_scientific_journal-2059	85	31	topology	topology	NOUN
american_scientific_journal-2059	85	32	of	of	ADP
american_scientific_journal-2059	85	33	af	af	PROPN
american_scientific_journal-2059	85	34	then	then	ADV
american_scientific_journal-2059	85	35	)	)	PUNCT
american_scientific_journal-2059	85	36	~,~	~,~	NUM
american_scientific_journal-2059	85	37	,	,	PUNCT
american_scientific_journal-2059	85	38	(	(	PUNCT
american_scientific_journal-2059	85	39	21	21	NUM
american_scientific_journal-2059	85	40	ττaf	ττaf	NOUN
american_scientific_journal-2059	85	41	is	be	AUX
american_scientific_journal-2059	85	42	soft	soft	ADJ
american_scientific_journal-2059	85	43	bitopological	bitopological	ADJ
american_scientific_journal-2059	85	44	space	space	NOUN
american_scientific_journal-2059	85	45	.	.	PUNCT
american_scientific_journal-2059	86	1	now	now	ADV
american_scientific_journal-2059	86	2	}	}	PUNCT
american_scientific_journal-2059	86	3	,	,	PUNCT
american_scientific_journal-2059	86	4	,	,	PUNCT
american_scientific_journal-2059	86	5	,	,	PUNCT
american_scientific_journal-2059	86	6	{	{	PUNCT
american_scientific_journal-2059	86	7	=	=	NOUN
american_scientific_journal-2059	86	8	~~~	~~~	SYM
american_scientific_journal-2059	86	9	2121	2121	NUM
american_scientific_journal-2059	86	10	aaa	aaa	NOUN
american_scientific_journal-2059	86	11	ffffφττ	ffffφττ	VERB
american_scientific_journal-2059	86	12	∪	∪	ADV
american_scientific_journal-2059	86	13	.	.	PUNCT
american_scientific_journal-2059	87	1	if	if	SCONJ
american_scientific_journal-2059	87	2	take	take	VERB
american_scientific_journal-2059	87	3	21	21	NUM
american_scientific_journal-2059	87	4	,	,	PUNCT
american_scientific_journal-2059	87	5	aa	aa	NOUN
american_scientific_journal-2059	87	6	ff	ff	NOUN
american_scientific_journal-2059	87	7	,	,	PUNCT
american_scientific_journal-2059	87	8	21211121	21211121	NUM
american_scientific_journal-2059	88	1	~~~})}{,(}),{,{(=~	~~~})}{,(}),{,{(=~	PRON
american_scientific_journal-2059	88	2	ττ	ττ	NOUN
american_scientific_journal-2059	88	3	∪∉∪	∪∉∪	PROPN
american_scientific_journal-2059	89	1	uxuxff	uxuxff	ADJ
american_scientific_journal-2059	89	2	aa	aa	NOUN
american_scientific_journal-2059	89	3	.	.	PUNCT
american_scientific_journal-2059	90	1	thus	thus	ADV
american_scientific_journal-2059	90	2	21	21	NUM
american_scientific_journal-2059	90	3	~~~	~~~	PUNCT
american_scientific_journal-2059	90	4	ττ	ττ	NOUN
american_scientific_journal-2059	90	5	∪	∪	NOUN
american_scientific_journal-2059	90	6	is	be	AUX
american_scientific_journal-2059	90	7	not	not	PART
american_scientific_journal-2059	90	8	soft	soft	ADJ
american_scientific_journal-2059	90	9	topology	topology	NOUN
american_scientific_journal-2059	90	10	on	on	ADP
american_scientific_journal-2059	90	11	af	af	PROPN
american_scientific_journal-2059	90	12	.	.	PUNCT
american_scientific_journal-2059	91	1	3	3	X
american_scientific_journal-2059	91	2	.	.	X
american_scientific_journal-2059	92	1	some	some	DET
american_scientific_journal-2059	92	2	definition	definition	NOUN
american_scientific_journal-2059	92	3	of	of	ADP
american_scientific_journal-2059	92	4	soft	soft	ADJ
american_scientific_journal-2059	92	5	pre	pre	ADJ
american_scientific_journal-2059	92	6	-	-	ADJ
american_scientific_journal-2059	92	7	open	open	ADJ
american_scientific_journal-2059	92	8	set	set	NOUN
american_scientific_journal-2059	92	9	in	in	ADP
american_scientific_journal-2059	92	10	soft	soft	ADJ
american_scientific_journal-2059	92	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	92	12	space	space	NOUN
american_scientific_journal-2059	92	13	in	in	ADP
american_scientific_journal-2059	92	14	this	this	DET
american_scientific_journal-2059	92	15	section	section	NOUN
american_scientific_journal-2059	92	16	introduce	introduce	VERB
american_scientific_journal-2059	92	17	some	some	DET
american_scientific_journal-2059	92	18	definitions	definition	NOUN
american_scientific_journal-2059	92	19	of	of	ADP
american_scientific_journal-2059	92	20	soft	soft	ADJ
american_scientific_journal-2059	92	21	pre	pre	ADJ
american_scientific_journal-2059	92	22	-	-	ADJ
american_scientific_journal-2059	92	23	open	open	ADJ
american_scientific_journal-2059	92	24	set	set	NOUN
american_scientific_journal-2059	92	25	,	,	PUNCT
american_scientific_journal-2059	92	26	soft	soft	ADJ
american_scientific_journal-2059	92	27	pre	pre	ADJ
american_scientific_journal-2059	92	28	-	-	ADJ
american_scientific_journal-2059	92	29	closed	closed	ADJ
american_scientific_journal-2059	92	30	,	,	PUNCT
american_scientific_journal-2059	92	31	soft	soft	ADJ
american_scientific_journal-2059	92	32	pre	pre	ADJ
american_scientific_journal-2059	92	33	-	-	ADJ
american_scientific_journal-2059	92	34	neighborhood	neighborhood	ADJ
american_scientific_journal-2059	92	35	,	,	PUNCT
american_scientific_journal-2059	92	36	soft	soft	ADJ
american_scientific_journal-2059	92	37	preclosure	preclosure	ADJ
american_scientific_journal-2059	92	38	and	and	CCONJ
american_scientific_journal-2059	92	39	soft	soft	ADJ
american_scientific_journal-2059	92	40	pre	pre	ADJ
american_scientific_journal-2059	92	41	-	-	ADJ
american_scientific_journal-2059	92	42	interior	interior	ADJ
american_scientific_journal-2059	92	43	on	on	ADP
american_scientific_journal-2059	92	44	soft	soft	ADJ
american_scientific_journal-2059	92	45	bitopological	bitopological	ADJ
american_scientific_journal-2059	92	46	space	space	NOUN
american_scientific_journal-2059	92	47	.	.	PUNCT
american_scientific_journal-2059	93	1	3.1	3.1	NUM
american_scientific_journal-2059	93	2	.	.	PUNCT
american_scientific_journal-2059	93	3	definition	definition	NOUN
american_scientific_journal-2059	93	4	let	let	VERB
american_scientific_journal-2059	93	5	)	)	PUNCT
american_scientific_journal-2059	93	6	~,~	~,~	X
american_scientific_journal-2059	93	7	,	,	PUNCT
american_scientific_journal-2059	93	8	(	(	PUNCT
american_scientific_journal-2059	93	9	21	21	NUM
american_scientific_journal-2059	93	10	ττaf	ττaf	NOUN
american_scientific_journal-2059	93	11	be	be	AUX
american_scientific_journal-2059	93	12	soft	soft	ADJ
american_scientific_journal-2059	93	13	bitopological	bitopological	ADJ
american_scientific_journal-2059	93	14	space	space	NOUN
american_scientific_journal-2059	93	15	and	and	CCONJ
american_scientific_journal-2059	93	16	let	let	VERB
american_scientific_journal-2059	93	17	ab	ab	PROPN
american_scientific_journal-2059	93	18	ff	ff	PROPN
american_scientific_journal-2059	93	19	⊆~	⊆~	PROPN
american_scientific_journal-2059	93	20	,	,	PUNCT
american_scientific_journal-2059	93	21	bf	bf	NOUN
american_scientific_journal-2059	93	22	is	be	AUX
american_scientific_journal-2059	93	23	called	call	VERB
american_scientific_journal-2059	93	24	soft	soft	ADJ
american_scientific_journal-2059	93	25	pre	pre	ADJ
american_scientific_journal-2059	93	26	-	-	ADJ
american_scientific_journal-2059	93	27	open	open	ADJ
american_scientific_journal-2059	93	28	set	set	VERB
american_scientific_journal-2059	93	29	with	with	ADP
american_scientific_journal-2059	93	30	respect	respect	NOUN
american_scientific_journal-2059	93	31	to	to	ADP
american_scientific_journal-2059	93	32	the	the	DET
american_scientific_journal-2059	93	33	two	two	NUM
american_scientific_journal-2059	93	34	soft	soft	ADJ
american_scientific_journal-2059	93	35	topological	topological	ADJ
american_scientific_journal-2059	93	36	spaces	space	NOUN
american_scientific_journal-2059	93	37	1	1	NUM
american_scientific_journal-2059	93	38	~τ	~τ	PUNCT
american_scientific_journal-2059	93	39	and	and	CCONJ
american_scientific_journal-2059	93	40	2	2	NUM
american_scientific_journal-2059	93	41	~τ	~τ	PUNCT
american_scientific_journal-2059	93	42	if	if	SCONJ
american_scientific_journal-2059	93	43	)(~	)(~	ADV
american_scientific_journal-2059	93	44	bb	bb	INTJ
american_scientific_journal-2059	93	45	ff	ff	NOUN
american_scientific_journal-2059	93	46	⊆	⊆	NUM
american_scientific_journal-2059	93	47	.	.	PUNCT
american_scientific_journal-2059	94	1	3.2	3.2	NUM
american_scientific_journal-2059	94	2	.	.	PUNCT
american_scientific_journal-2059	95	1	notes	note	VERB
american_scientific_journal-2059	95	2	1the	1the	PROPN
american_scientific_journal-2059	95	3	set	set	NOUN
american_scientific_journal-2059	95	4	of	of	ADP
american_scientific_journal-2059	95	5	all	all	DET
american_scientific_journal-2059	95	6	soft	soft	ADJ
american_scientific_journal-2059	95	7	pre	pre	ADJ
american_scientific_journal-2059	95	8	-	-	ADJ
american_scientific_journal-2059	95	9	open	open	ADJ
american_scientific_journal-2059	95	10	set	set	VERB
american_scientific_journal-2059	95	11	with	with	ADP
american_scientific_journal-2059	95	12	respect	respect	NOUN
american_scientific_journal-2059	95	13	to	to	ADP
american_scientific_journal-2059	95	14	the	the	DET
american_scientific_journal-2059	95	15	two	two	NUM
american_scientific_journal-2059	95	16	soft	soft	ADJ
american_scientific_journal-2059	95	17	topologies	topology	NOUN
american_scientific_journal-2059	95	18	is	be	AUX
american_scientific_journal-2059	95	19	denoted	denote	VERB
american_scientific_journal-2059	95	20	by	by	ADP
american_scientific_journal-2059	95	21	pre	pre	PROPN
american_scientific_journal-2059	95	22	(	(	PUNCT
american_scientific_journal-2059	95	23	af	af	PROPN
american_scientific_journal-2059	95	24	)	)	PUNCT
american_scientific_journal-2059	95	25	.	.	PUNCT
american_scientific_journal-2059	96	1	2the	2the	DET
american_scientific_journal-2059	96	2	relative	relative	ADJ
american_scientific_journal-2059	96	3	soft	soft	ADJ
american_scientific_journal-2059	96	4	bitopological	bitopological	ADJ
american_scientific_journal-2059	96	5	space	space	NOUN
american_scientific_journal-2059	96	6	for	for	ADP
american_scientific_journal-2059	96	7	bf	bf	NOUN
american_scientific_journal-2059	96	8	with	with	ADP
american_scientific_journal-2059	96	9	respect	respect	NOUN
american_scientific_journal-2059	96	10	to	to	ADP
american_scientific_journal-2059	96	11	soft	soft	ADJ
american_scientific_journal-2059	96	12	pre	pre	ADJ
american_scientific_journal-2059	96	13	-	-	ADJ
american_scientific_journal-2059	96	14	open	open	ADJ
american_scientific_journal-2059	96	15	sets	set	NOUN
american_scientific_journal-2059	96	16	is	be	AUX
american_scientific_journal-2059	96	17	the	the	DET
american_scientific_journal-2059	96	18	collection	collection	NOUN
american_scientific_journal-2059	96	19	pre	pre	ADJ
american_scientific_journal-2059	96	20	bfaf	bfaf	NOUN
american_scientific_journal-2059	96	21	)	)	PUNCT
american_scientific_journal-2059	96	22	(	(	PUNCT
american_scientific_journal-2059	96	23	given	give	VERB
american_scientific_journal-2059	96	24	by	by	ADP
american_scientific_journal-2059	96	25	pre	pre	ADJ
american_scientific_journal-2059	96	26	)	)	PUNCT
american_scientific_journal-2059	96	27	}	}	PUNCT
american_scientific_journal-2059	96	28	(:	(:	VERB
american_scientific_journal-2059	96	29	~{=	~{=	NUM
american_scientific_journal-2059	96	30	)	)	PUNCT
american_scientific_journal-2059	96	31	(	(	PUNCT
american_scientific_journal-2059	96	32	acbcbfa	acbcbfa	PROPN
american_scientific_journal-2059	96	33	fpreffff	fpreffff	PROPN
american_scientific_journal-2059	96	34	∈∩	∈∩	PROPN
american_scientific_journal-2059	96	35	3any	3any	NUM
american_scientific_journal-2059	96	36	2	2	NUM
american_scientific_journal-2059	96	37	~τ	~τ	PUNCT
american_scientific_journal-2059	96	38	-open	-open	ADJ
american_scientific_journal-2059	96	39	soft	soft	ADJ
american_scientific_journal-2059	96	40	set	set	NOUN
american_scientific_journal-2059	96	41	is	be	AUX
american_scientific_journal-2059	96	42	not	not	PART
american_scientific_journal-2059	96	43	necessarily	necessarily	ADV
american_scientific_journal-2059	96	44	to	to	PART
american_scientific_journal-2059	96	45	be	be	AUX
american_scientific_journal-2059	96	46	soft	soft	ADJ
american_scientific_journal-2059	96	47	pre	pre	ADJ
american_scientific_journal-2059	96	48	-	-	ADJ
american_scientific_journal-2059	96	49	open	open	ADJ
american_scientific_journal-2059	96	50	set	set	NOUN
american_scientific_journal-2059	96	51	.	.	PUNCT
american_scientific_journal-2059	97	1	4any	4any	NUM
american_scientific_journal-2059	97	2	soft	soft	ADJ
american_scientific_journal-2059	97	3	pre	pre	ADJ
american_scientific_journal-2059	97	4	-	-	ADJ
american_scientific_journal-2059	97	5	open	open	ADJ
american_scientific_journal-2059	97	6	set	set	NOUN
american_scientific_journal-2059	97	7	is	be	AUX
american_scientific_journal-2059	97	8	not	not	PART
american_scientific_journal-2059	97	9	necessarily	necessarily	ADV
american_scientific_journal-2059	97	10	to	to	PART
american_scientific_journal-2059	97	11	be	be	AUX
american_scientific_journal-2059	97	12	of	of	ADP
american_scientific_journal-2059	97	13	1	1	NUM
american_scientific_journal-2059	97	14	~τ	~τ	PUNCT
american_scientific_journal-2059	97	15	-open	-open	NOUN
american_scientific_journal-2059	97	16	(	(	PUNCT
american_scientific_journal-2059	97	17	2	2	NUM
american_scientific_journal-2059	97	18	~τ	~τ	PUNCT
american_scientific_journal-2059	97	19	-open	-open	ADJ
american_scientific_journal-2059	97	20	)	)	PUNCT
american_scientific_journal-2059	97	21	soft	soft	ADJ
american_scientific_journal-2059	97	22	set	set	NOUN
american_scientific_journal-2059	97	23	.	.	PUNCT
american_scientific_journal-2059	98	1	3.3	3.3	NUM
american_scientific_journal-2059	98	2	.	.	PUNCT
american_scientific_journal-2059	98	3	example	example	NOUN
american_scientific_journal-2059	98	4	let	let	VERB
american_scientific_journal-2059	98	5	us	we	PRON
american_scientific_journal-2059	98	6	consider	consider	VERB
american_scientific_journal-2059	98	7	example	example	NOUN
american_scientific_journal-2059	98	8	2.20	2.20	NUM
american_scientific_journal-2059	98	9	,	,	PUNCT
american_scientific_journal-2059	98	10	)	)	PUNCT
american_scientific_journal-2059	98	11	~,~	~,~	NUM
american_scientific_journal-2059	98	12	,	,	PUNCT
american_scientific_journal-2059	98	13	(	(	PUNCT
american_scientific_journal-2059	98	14	21	21	NUM
american_scientific_journal-2059	98	15	ττaf	ττaf	NOUN
american_scientific_journal-2059	98	16	is	be	AUX
american_scientific_journal-2059	98	17	soft	soft	ADJ
american_scientific_journal-2059	98	18	bitopological	bitopological	ADJ
american_scientific_journal-2059	98	19	space	space	NOUN
american_scientific_journal-2059	98	20	.	.	PUNCT
american_scientific_journal-2059	99	1	take	take	VERB
american_scientific_journal-2059	99	2	aa	aa	NOUN
american_scientific_journal-2059	99	3	ff	ff	NOUN
american_scientific_journal-2059	99	4	⊆~	⊆~	ADP
american_scientific_journal-2059	99	5	1	1	NUM
american_scientific_journal-2059	99	6	then	then	ADV
american_scientific_journal-2059	99	7	111	111	NUM
american_scientific_journal-2059	99	8	)	)	PUNCT
american_scientific_journal-2059	99	9	(	(	PUNCT
american_scientific_journal-2059	99	10	~	~	PUNCT
american_scientific_journal-2059	99	11	aaa	aaa	NOUN
american_scientific_journal-2059	99	12	fff	fff	PROPN
american_scientific_journal-2059	99	13	⇒⊆	⇒⊆	PROPN
american_scientific_journal-2059	99	14			PROPN
american_scientific_journal-2059	99	15	is	be	AUX
american_scientific_journal-2059	99	16	soft	soft	ADJ
american_scientific_journal-2059	99	17	per	per	ADP
american_scientific_journal-2059	99	18	-	-	PUNCT
american_scientific_journal-2059	99	19	open	open	NOUN
american_scientific_journal-2059	99	20	set	set	NOUN
american_scientific_journal-2059	99	21	with	with	ADP
american_scientific_journal-2059	99	22	respect	respect	NOUN
american_scientific_journal-2059	99	23	to	to	ADP
american_scientific_journal-2059	99	24	the	the	DET
american_scientific_journal-2059	99	25	two	two	NUM
american_scientific_journal-2059	99	26	soft	soft	ADJ
american_scientific_journal-2059	99	27	topological	topological	ADJ
american_scientific_journal-2059	99	28	spaces	space	NOUN
american_scientific_journal-2059	99	29	1	1	NUM
american_scientific_journal-2059	99	30	~τ	~τ	PUNCT
american_scientific_journal-2059	99	31	and	and	CCONJ
american_scientific_journal-2059	99	32	2	2	NUM
american_scientific_journal-2059	99	33	~τ	~τ	PUNCT
american_scientific_journal-2059	99	34	.	.	PUNCT
american_scientific_journal-2059	100	1	3.4	3.4	NUM
american_scientific_journal-2059	100	2	.	.	PUNCT
american_scientific_journal-2059	100	3	remarks	remark	VERB
american_scientific_journal-2059	100	4	1the	1the	ADJ
american_scientific_journal-2059	100	5	intersection	intersection	NOUN
american_scientific_journal-2059	100	6	of	of	ADP
american_scientific_journal-2059	100	7	any	any	DET
american_scientific_journal-2059	100	8	soft	soft	ADJ
american_scientific_journal-2059	100	9	pre	pre	ADJ
american_scientific_journal-2059	100	10	-	-	ADJ
american_scientific_journal-2059	100	11	open	open	ADJ
american_scientific_journal-2059	100	12	sets	set	NOUN
american_scientific_journal-2059	100	13	is	be	AUX
american_scientific_journal-2059	100	14	not	not	PART
american_scientific_journal-2059	100	15	necessary	necessary	ADJ
american_scientific_journal-2059	100	16	a	a	DET
american_scientific_journal-2059	100	17	soft	soft	ADJ
american_scientific_journal-2059	100	18	pre	pre	ADJ
american_scientific_journal-2059	100	19	-	-	ADJ
american_scientific_journal-2059	100	20	open	open	ADJ
american_scientific_journal-2059	100	21	set	set	VERB
american_scientific_journal-2059	100	22	american	american	ADJ
american_scientific_journal-2059	100	23	scientific	scientific	ADJ
american_scientific_journal-2059	100	24	research	research	NOUN
american_scientific_journal-2059	100	25	journal	journal	NOUN
american_scientific_journal-2059	100	26	for	for	ADP
american_scientific_journal-2059	100	27	engineering	engineering	NOUN
american_scientific_journal-2059	100	28	,	,	PUNCT
american_scientific_journal-2059	100	29	technology	technology	NOUN
american_scientific_journal-2059	100	30	,	,	PUNCT
american_scientific_journal-2059	100	31	and	and	CCONJ
american_scientific_journal-2059	100	32	sciences	science	NOUN
american_scientific_journal-2059	100	33	(	(	PUNCT
american_scientific_journal-2059	100	34	asrjets	asrjet	NOUN
american_scientific_journal-2059	100	35	)	)	PUNCT
american_scientific_journal-2059	100	36	(	(	PUNCT
american_scientific_journal-2059	100	37	2016	2016	NUM
american_scientific_journal-2059	100	38	)	)	PUNCT
american_scientific_journal-2059	100	39	volume	volume	NOUN
american_scientific_journal-2059	100	40	26	26	NUM
american_scientific_journal-2059	100	41	,	,	PUNCT
american_scientific_journal-2059	100	42	no	no	DET
american_scientific_journal-2059	100	43	4	4	NUM
american_scientific_journal-2059	100	44	,	,	PUNCT
american_scientific_journal-2059	100	45	pp	pp	ADV
american_scientific_journal-2059	100	46	42	42	NUM
american_scientific_journal-2059	100	47	-	-	SYM
american_scientific_journal-2059	100	48	53	53	NUM
american_scientific_journal-2059	100	49	49	49	NUM
american_scientific_journal-2059	100	50	2the	2the	PROPN
american_scientific_journal-2059	100	51	union	union	NOUN
american_scientific_journal-2059	100	52	of	of	ADP
american_scientific_journal-2059	100	53	any	any	DET
american_scientific_journal-2059	100	54	soft	soft	ADJ
american_scientific_journal-2059	100	55	pre	pre	ADJ
american_scientific_journal-2059	100	56	-	-	ADJ
american_scientific_journal-2059	100	57	open	open	ADJ
american_scientific_journal-2059	100	58	sets	set	NOUN
american_scientific_journal-2059	100	59	is	be	AUX
american_scientific_journal-2059	100	60	soft	soft	ADJ
american_scientific_journal-2059	100	61	pre	pre	ADJ
american_scientific_journal-2059	100	62	-	-	ADJ
american_scientific_journal-2059	100	63	open	open	ADJ
american_scientific_journal-2059	100	64	set	set	VERB
american_scientific_journal-2059	100	65	with	with	ADP
american_scientific_journal-2059	100	66	respect	respect	NOUN
american_scientific_journal-2059	100	67	to	to	ADP
american_scientific_journal-2059	100	68	soft	soft	ADJ
american_scientific_journal-2059	100	69	bitopological	bitopological	ADJ
american_scientific_journal-2059	100	70	space	space	NOUN
american_scientific_journal-2059	100	71	.	.	PUNCT
american_scientific_journal-2059	101	1	the	the	DET
american_scientific_journal-2059	101	2	example	example	NOUN
american_scientific_journal-2059	101	3	to	to	ADP
american_scientific_journal-2059	101	4	part	part	NOUN
american_scientific_journal-2059	101	5	(	(	PUNCT
american_scientific_journal-2059	101	6	1	1	NUM
american_scientific_journal-2059	101	7	)	)	PUNCT
american_scientific_journal-2059	101	8	is	be	AUX
american_scientific_journal-2059	101	9	simply	simply	ADV
american_scientific_journal-2059	101	10	.	.	PUNCT
american_scientific_journal-2059	102	1	the	the	DET
american_scientific_journal-2059	102	2	following	follow	VERB
american_scientific_journal-2059	102	3	proof	proof	NOUN
american_scientific_journal-2059	102	4	explain	explain	VERB
american_scientific_journal-2059	102	5	the	the	DET
american_scientific_journal-2059	102	6	part	part	NOUN
american_scientific_journal-2059	102	7	(	(	PUNCT
american_scientific_journal-2059	102	8	2	2	NUM
american_scientific_journal-2059	102	9	)	)	PUNCT
american_scientific_journal-2059	102	10	of	of	ADP
american_scientific_journal-2059	102	11	the	the	DET
american_scientific_journal-2059	102	12	remark	remark	NOUN
american_scientific_journal-2059	102	13	3.4	3.4	NUM
american_scientific_journal-2059	102	14	.	.	PUNCT
american_scientific_journal-2059	103	1	let	let	VERB
american_scientific_journal-2059	103	2	bf	bf	NOUN
american_scientific_journal-2059	103	3	and	and	CCONJ
american_scientific_journal-2059	103	4	cf	cf	AUX
american_scientific_journal-2059	103	5	be	be	AUX
american_scientific_journal-2059	103	6	a	a	DET
american_scientific_journal-2059	103	7	two	two	NUM
american_scientific_journal-2059	103	8	soft	soft	ADJ
american_scientific_journal-2059	103	9	pre	pre	ADJ
american_scientific_journal-2059	103	10	-	-	ADJ
american_scientific_journal-2059	103	11	open	open	ADJ
american_scientific_journal-2059	103	12	sets	set	NOUN
american_scientific_journal-2059	103	13	with	with	ADP
american_scientific_journal-2059	103	14	respect	respect	NOUN
american_scientific_journal-2059	103	15	to	to	ADP
american_scientific_journal-2059	103	16	soft	soft	ADJ
american_scientific_journal-2059	103	17	bitopological	bitopological	ADJ
american_scientific_journal-2059	103	18	space	space	NOUN
american_scientific_journal-2059	103	19	)	)	PUNCT
american_scientific_journal-2059	103	20	~,~	~,~	NUM
american_scientific_journal-2059	103	21	,	,	PUNCT
american_scientific_journal-2059	103	22	(	(	PUNCT
american_scientific_journal-2059	103	23	21	21	NUM
american_scientific_journal-2059	103	24	ττaf	ττaf	NOUN
american_scientific_journal-2059	103	25	.	.	PUNCT
american_scientific_journal-2059	104	1	i.e.	i.e.	X
american_scientific_journal-2059	104	2	)(~	)(~	X
american_scientific_journal-2059	104	3	bb	bb	INTJ
american_scientific_journal-2059	104	4	ff	ff	NOUN
american_scientific_journal-2059	104	5	⊆	⊆	NUM
american_scientific_journal-2059	104	6	and	and	CCONJ
american_scientific_journal-2059	104	7	)(~	)(~	NOUN
american_scientific_journal-2059	104	8	cc	cc	AUX
american_scientific_journal-2059	104	9	ff	ff	VERB
american_scientific_journal-2059	104	10	⊆	⊆	NUM
american_scientific_journal-2059	104	11	with	with	ADP
american_scientific_journal-2059	104	12	respect	respect	NOUN
american_scientific_journal-2059	104	13	to	to	ADP
american_scientific_journal-2059	104	14	the	the	DET
american_scientific_journal-2059	104	15	two	two	NUM
american_scientific_journal-2059	104	16	soft	soft	ADJ
american_scientific_journal-2059	104	17	topological	topological	ADJ
american_scientific_journal-2059	104	18	spaces	space	NOUN
american_scientific_journal-2059	104	19	1	1	NUM
american_scientific_journal-2059	104	20	~τ	~τ	PUNCT
american_scientific_journal-2059	104	21	and	and	CCONJ
american_scientific_journal-2059	104	22			NUM
american_scientific_journal-2059	104	23	)	)	PUNCT
american_scientific_journal-2059	104	24	~(~)(~)(~~~	~(~)(~)(~~~	PROPN
american_scientific_journal-2059	104	25	2	2	NUM
american_scientific_journal-2059	104	26	cbcbcb	cbcbcb	PROPN
american_scientific_journal-2059	104	27	ffffff	ffffff	PROPN
american_scientific_journal-2059	104	28	∪⊆∪⊆∪⇒τ	∪⊆∪⊆∪⇒τ	PROPN
american_scientific_journal-2059	104	29	.	.	PUNCT
american_scientific_journal-2059	105	1	since	since	SCONJ
american_scientific_journal-2059	105	2	then	then	ADV
american_scientific_journal-2059	105	3	)~(~~	)~(~~	VERB
american_scientific_journal-2059	105	4	cbcb	cbcb	ADJ
american_scientific_journal-2059	105	5	ffff	ffff	NOUN
american_scientific_journal-2059	105	6	∪⊆∪	∪⊆∪	PROPN
american_scientific_journal-2059	105	7	with	with	ADP
american_scientific_journal-2059	105	8	respect	respect	NOUN
american_scientific_journal-2059	105	9	to	to	ADP
american_scientific_journal-2059	105	10	the	the	DET
american_scientific_journal-2059	105	11	two	two	NUM
american_scientific_journal-2059	105	12	soft	soft	ADJ
american_scientific_journal-2059	105	13	topological	topological	ADJ
american_scientific_journal-2059	105	14	spaces	space	NOUN
american_scientific_journal-2059	105	15	1	1	NUM
american_scientific_journal-2059	105	16	~τ	~τ	PUNCT
american_scientific_journal-2059	105	17	and	and	CCONJ
american_scientific_journal-2059	105	18	2	2	NUM
american_scientific_journal-2059	105	19	~τ	~τ	PUNCT
american_scientific_journal-2059	105	20	.	.	PUNCT
american_scientific_journal-2059	106	1	3.5	3.5	NUM
american_scientific_journal-2059	106	2	.	.	PUNCT
american_scientific_journal-2059	107	1	definition	definition	NOUN
american_scientific_journal-2059	107	2	let	let	VERB
american_scientific_journal-2059	107	3	)	)	PUNCT
american_scientific_journal-2059	107	4	~,~	~,~	X
american_scientific_journal-2059	107	5	,	,	PUNCT
american_scientific_journal-2059	107	6	(	(	PUNCT
american_scientific_journal-2059	107	7	21	21	NUM
american_scientific_journal-2059	107	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	107	9	is	be	AUX
american_scientific_journal-2059	107	10	soft	soft	ADJ
american_scientific_journal-2059	107	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	107	12	space	space	NOUN
american_scientific_journal-2059	107	13	and	and	CCONJ
american_scientific_journal-2059	107	14	let	let	VERB
american_scientific_journal-2059	107	15	ab	ab	PROPN
american_scientific_journal-2059	107	16	ff	ff	PROPN
american_scientific_journal-2059	107	17	⊆~	⊆~	PROPN
american_scientific_journal-2059	107	18	,	,	PUNCT
american_scientific_journal-2059	107	19	bf	bf	NOUN
american_scientific_journal-2059	107	20	is	be	AUX
american_scientific_journal-2059	107	21	called	call	VERB
american_scientific_journal-2059	107	22	soft	soft	ADJ
american_scientific_journal-2059	107	23	pre	pre	ADJ
american_scientific_journal-2059	107	24	-	-	ADJ
american_scientific_journal-2059	107	25	closed	closed	ADJ
american_scientific_journal-2059	107	26	set	set	NOUN
american_scientific_journal-2059	107	27	of	of	ADP
american_scientific_journal-2059	107	28	af	af	PROPN
american_scientific_journal-2059	107	29	if	if	SCONJ
american_scientific_journal-2059	108	1	and	and	CCONJ
american_scientific_journal-2059	108	2	only	only	ADV
american_scientific_journal-2059	108	3	if	if	SCONJ
american_scientific_journal-2059	108	4	c	c	NOUN
american_scientific_journal-2059	108	5	bf	bf	NOUN
american_scientific_journal-2059	108	6	~	~	PUNCT
american_scientific_journal-2059	108	7	is	be	AUX
american_scientific_journal-2059	108	8	soft	soft	ADJ
american_scientific_journal-2059	108	9	pre	pre	ADJ
american_scientific_journal-2059	108	10	-	-	ADJ
american_scientific_journal-2059	108	11	open	open	ADJ
american_scientific_journal-2059	108	12	set	set	NOUN
american_scientific_journal-2059	108	13	of	of	ADP
american_scientific_journal-2059	108	14	af	af	PROPN
american_scientific_journal-2059	108	15	.	.	PUNCT
american_scientific_journal-2059	109	1	3.6	3.6	NUM
american_scientific_journal-2059	109	2	.	.	PUNCT
american_scientific_journal-2059	110	1	definition	definition	NOUN
american_scientific_journal-2059	110	2	let	let	VERB
american_scientific_journal-2059	110	3	)	)	PUNCT
american_scientific_journal-2059	110	4	~,~	~,~	X
american_scientific_journal-2059	110	5	,	,	PUNCT
american_scientific_journal-2059	110	6	(	(	PUNCT
american_scientific_journal-2059	110	7	21	21	NUM
american_scientific_journal-2059	110	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	110	9	is	be	AUX
american_scientific_journal-2059	110	10	soft	soft	ADJ
american_scientific_journal-2059	110	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	110	12	space	space	NOUN
american_scientific_journal-2059	110	13	and	and	CCONJ
american_scientific_journal-2059	110	14	af∈α	af∈α	PROPN
american_scientific_journal-2059	110	15	,	,	PUNCT
american_scientific_journal-2059	110	16	ab	ab	PROPN
american_scientific_journal-2059	110	17	ff	ff	PROPN
american_scientific_journal-2059	110	18	⊆~	⊆~	PROPN
american_scientific_journal-2059	110	19	is	be	AUX
american_scientific_journal-2059	110	20	said	say	VERB
american_scientific_journal-2059	110	21	to	to	PART
american_scientific_journal-2059	110	22	be	be	AUX
american_scientific_journal-2059	110	23	soft	soft	ADJ
american_scientific_journal-2059	110	24	pre	pre	ADJ
american_scientific_journal-2059	110	25	-	-	ADJ
american_scientific_journal-2059	110	26	neighborhood	neighborhood	NOUN
american_scientific_journal-2059	110	27	of	of	ADP
american_scientific_journal-2059	110	28	a	a	DET
american_scientific_journal-2059	110	29	point	point	NOUN
american_scientific_journal-2059	110	30	α	α	NOUN
american_scientific_journal-2059	110	31	if	if	SCONJ
american_scientific_journal-2059	110	32	there	there	PRON
american_scientific_journal-2059	110	33	is	be	VERB
american_scientific_journal-2059	110	34	a	a	DET
american_scientific_journal-2059	110	35	soft	soft	ADJ
american_scientific_journal-2059	110	36	pre	pre	ADJ
american_scientific_journal-2059	110	37	-	-	ADJ
american_scientific_journal-2059	110	38	open	open	ADJ
american_scientific_journal-2059	110	39	set	set	ADJ
american_scientific_journal-2059	110	40	cf	cf	NOUN
american_scientific_journal-2059	110	41	such	such	ADJ
american_scientific_journal-2059	110	42	that	that	SCONJ
american_scientific_journal-2059	110	43	bc	bc	PROPN
american_scientific_journal-2059	110	44	ff	ff	NOUN
american_scientific_journal-2059	110	45	⊆∈	⊆∈	NUM
american_scientific_journal-2059	110	46	~α	~α	PUNCT
american_scientific_journal-2059	110	47	.	.	PUNCT
american_scientific_journal-2059	111	1	the	the	DET
american_scientific_journal-2059	111	2	set	set	NOUN
american_scientific_journal-2059	111	3	of	of	ADP
american_scientific_journal-2059	111	4	all	all	DET
american_scientific_journal-2059	111	5	soft	soft	ADJ
american_scientific_journal-2059	111	6	pre	pre	NOUN
american_scientific_journal-2059	111	7	-	-	NOUN
american_scientific_journal-2059	111	8	neighborhoods	neighborhood	NOUN
american_scientific_journal-2059	111	9	of	of	ADP
american_scientific_journal-2059	111	10	a	a	DET
american_scientific_journal-2059	111	11	point	point	NOUN
american_scientific_journal-2059	111	12	α	α	NOUN
american_scientific_journal-2059	111	13	is	be	AUX
american_scientific_journal-2059	111	14	denoted	denote	VERB
american_scientific_journal-2059	111	15	by	by	ADP
american_scientific_journal-2059	111	16	spre)(~	spre)(~	ADP
american_scientific_journal-2059	111	17	αυ	αυ	NOUN
american_scientific_journal-2059	111	18	.	.	PUNCT
american_scientific_journal-2059	112	1	3.7	3.7	NUM
american_scientific_journal-2059	112	2	.	.	PUNCT
american_scientific_journal-2059	113	1	definition	definition	NOUN
american_scientific_journal-2059	113	2	let	let	VERB
american_scientific_journal-2059	113	3	)	)	PUNCT
american_scientific_journal-2059	113	4	~,~	~,~	X
american_scientific_journal-2059	113	5	,	,	PUNCT
american_scientific_journal-2059	113	6	(	(	PUNCT
american_scientific_journal-2059	113	7	21	21	NUM
american_scientific_journal-2059	113	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	113	9	is	be	AUX
american_scientific_journal-2059	113	10	soft	soft	ADJ
american_scientific_journal-2059	113	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	113	12	space	space	NOUN
american_scientific_journal-2059	113	13	,	,	PUNCT
american_scientific_journal-2059	113	14	and	and	CCONJ
american_scientific_journal-2059	113	15	ab	ab	PROPN
american_scientific_journal-2059	113	16	ff	ff	PROPN
american_scientific_journal-2059	113	17	⊆~	⊆~	PROPN
american_scientific_journal-2059	113	18	.	.	PUNCT
american_scientific_journal-2059	114	1	a	a	DET
american_scientific_journal-2059	114	2	point	point	NOUN
american_scientific_journal-2059	114	3	af∈α	af∈α	PROPN
american_scientific_journal-2059	114	4	is	be	AUX
american_scientific_journal-2059	114	5	said	say	VERB
american_scientific_journal-2059	114	6	to	to	PART
american_scientific_journal-2059	114	7	be	be	AUX
american_scientific_journal-2059	114	8	soft	soft	ADJ
american_scientific_journal-2059	114	9	pre	pre	ADJ
american_scientific_journal-2059	114	10	-	-	ADJ
american_scientific_journal-2059	114	11	interior	interior	ADJ
american_scientific_journal-2059	114	12	point	point	NOUN
american_scientific_journal-2059	114	13	of	of	ADP
american_scientific_journal-2059	114	14	bf	bf	NOUN
american_scientific_journal-2059	114	15	with	with	ADP
american_scientific_journal-2059	114	16	respect	respect	NOUN
american_scientific_journal-2059	114	17	to	to	ADP
american_scientific_journal-2059	114	18	the	the	DET
american_scientific_journal-2059	114	19	two	two	NUM
american_scientific_journal-2059	114	20	soft	soft	ADJ
american_scientific_journal-2059	114	21	topological	topological	ADJ
american_scientific_journal-2059	114	22	spaces	space	NOUN
american_scientific_journal-2059	114	23	1	1	NUM
american_scientific_journal-2059	114	24	~τ	~τ	PUNCT
american_scientific_journal-2059	114	25	and	and	CCONJ
american_scientific_journal-2059	114	26	2	2	NUM
american_scientific_journal-2059	114	27	~τ	~τ	PUNCT
american_scientific_journal-2059	114	28	if	if	SCONJ
american_scientific_journal-2059	114	29	there	there	PRON
american_scientific_journal-2059	114	30	is	be	VERB
american_scientific_journal-2059	114	31	a	a	DET
american_scientific_journal-2059	114	32	soft	soft	ADJ
american_scientific_journal-2059	114	33	pre	pre	ADJ
american_scientific_journal-2059	114	34	-	-	ADJ
american_scientific_journal-2059	114	35	open	open	ADJ
american_scientific_journal-2059	114	36	cf	cf	NOUN
american_scientific_journal-2059	114	37	such	such	ADJ
american_scientific_journal-2059	114	38	that	that	SCONJ
american_scientific_journal-2059	114	39	bc	bc	PROPN
american_scientific_journal-2059	114	40	ff	ff	NOUN
american_scientific_journal-2059	114	41	⊆∈	⊆∈	NUM
american_scientific_journal-2059	114	42	~α	~α	PUNCT
american_scientific_journal-2059	114	43	.	.	PUNCT
american_scientific_journal-2059	115	1	the	the	DET
american_scientific_journal-2059	115	2	set	set	NOUN
american_scientific_journal-2059	115	3	of	of	ADP
american_scientific_journal-2059	115	4	all	all	DET
american_scientific_journal-2059	115	5	soft	soft	ADJ
american_scientific_journal-2059	115	6	pre	pre	ADJ
american_scientific_journal-2059	115	7	-	-	ADJ
american_scientific_journal-2059	115	8	interior	interior	ADJ
american_scientific_journal-2059	115	9	points	point	NOUN
american_scientific_journal-2059	115	10	of	of	ADP
american_scientific_journal-2059	115	11	bf	bf	NOUN
american_scientific_journal-2059	115	12	with	with	ADP
american_scientific_journal-2059	115	13	respect	respect	NOUN
american_scientific_journal-2059	115	14	to	to	ADP
american_scientific_journal-2059	115	15	the	the	DET
american_scientific_journal-2059	115	16	two	two	NUM
american_scientific_journal-2059	115	17	soft	soft	ADJ
american_scientific_journal-2059	115	18	topological	topological	ADJ
american_scientific_journal-2059	115	19	spaces	space	NOUN
american_scientific_journal-2059	115	20	1	1	NUM
american_scientific_journal-2059	115	21	~τ	~τ	PUNCT
american_scientific_journal-2059	115	22	and	and	CCONJ
american_scientific_journal-2059	115	23	2	2	NUM
american_scientific_journal-2059	115	24	~τ	~τ	NUM
american_scientific_journal-2059	115	25	denoted	denote	VERB
american_scientific_journal-2059	115	26	by	by	ADP
american_scientific_journal-2059	115	27	spre	spre	ADJ
american_scientific_journal-2059	115	28	-	-	ADJ
american_scientific_journal-2059	115	29	int	int	ADJ
american_scientific_journal-2059	115	30	(	(	PUNCT
american_scientific_journal-2059	115	31	bf	bf	NOUN
american_scientific_journal-2059	115	32	)	)	PUNCT
american_scientific_journal-2059	115	33	.	.	PUNCT
american_scientific_journal-2059	116	1	3.8	3.8	NUM
american_scientific_journal-2059	116	2	.	.	PUNCT
american_scientific_journal-2059	117	1	definition	definition	NOUN
american_scientific_journal-2059	117	2	let	let	VERB
american_scientific_journal-2059	117	3	)	)	PUNCT
american_scientific_journal-2059	117	4	~,~	~,~	X
american_scientific_journal-2059	117	5	,	,	PUNCT
american_scientific_journal-2059	117	6	(	(	PUNCT
american_scientific_journal-2059	117	7	21	21	NUM
american_scientific_journal-2059	117	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	117	9	is	be	AUX
american_scientific_journal-2059	117	10	soft	soft	ADJ
american_scientific_journal-2059	117	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	117	12	space	space	NOUN
american_scientific_journal-2059	117	13	.	.	PUNCT
american_scientific_journal-2059	118	1	a	a	DET
american_scientific_journal-2059	118	2	point	point	NOUN
american_scientific_journal-2059	118	3	α	α	NOUN
american_scientific_journal-2059	118	4	is	be	AUX
american_scientific_journal-2059	118	5	called	call	VERB
american_scientific_journal-2059	118	6	soft	soft	ADJ
american_scientific_journal-2059	118	7	pre	pre	ADJ
american_scientific_journal-2059	118	8	-	-	ADJ
american_scientific_journal-2059	118	9	limit	limit	ADJ
american_scientific_journal-2059	118	10	point	point	NOUN
american_scientific_journal-2059	118	11	of	of	ADP
american_scientific_journal-2059	118	12	soft	soft	ADJ
american_scientific_journal-2059	118	13	subset	subset	NOUN
american_scientific_journal-2059	118	14	bf	bf	NOUN
american_scientific_journal-2059	118	15	of	of	ADP
american_scientific_journal-2059	118	16	af	af	PROPN
american_scientific_journal-2059	118	17	with	with	ADP
american_scientific_journal-2059	118	18	respect	respect	NOUN
american_scientific_journal-2059	118	19	to	to	ADP
american_scientific_journal-2059	118	20	the	the	DET
american_scientific_journal-2059	118	21	two	two	NUM
american_scientific_journal-2059	118	22	soft	soft	ADJ
american_scientific_journal-2059	118	23	topological	topological	ADJ
american_scientific_journal-2059	118	24	spaces	space	NOUN
american_scientific_journal-2059	118	25	1	1	NUM
american_scientific_journal-2059	118	26	~τ	~τ	PUNCT
american_scientific_journal-2059	118	27	and	and	CCONJ
american_scientific_journal-2059	118	28	2	2	NUM
american_scientific_journal-2059	118	29	~τ	~τ	PUNCT
american_scientific_journal-2059	118	30	if	if	SCONJ
american_scientific_journal-2059	118	31	and	and	CCONJ
american_scientific_journal-2059	118	32	only	only	ADV
american_scientific_journal-2059	118	33	if	if	SCONJ
american_scientific_journal-2059	118	34	for	for	ADP
american_scientific_journal-2059	118	35	each	each	DET
american_scientific_journal-2059	118	36	a	a	DET
american_scientific_journal-2059	118	37	soft	soft	ADJ
american_scientific_journal-2059	118	38	pre	pre	ADJ
american_scientific_journal-2059	118	39	-	-	ADJ
american_scientific_journal-2059	118	40	open	open	ADJ
american_scientific_journal-2059	118	41	set	set	VERB
american_scientific_journal-2059	118	42	cf	cf	NOUN
american_scientific_journal-2059	118	43	containing	contain	VERB
american_scientific_journal-2059	118	44	another	another	DET
american_scientific_journal-2059	118	45	point	point	NOUN
american_scientific_journal-2059	118	46	different	different	ADJ
american_scientific_journal-2059	118	47	from	from	ADP
american_scientific_journal-2059	118	48	α	α	NOUN
american_scientific_journal-2059	118	49	in	in	ADP
american_scientific_journal-2059	118	50	bf	bf	NOUN
american_scientific_journal-2059	118	51	,	,	PUNCT
american_scientific_journal-2059	118	52	that	that	ADV
american_scientific_journal-2059	118	53	is	be	AUX
american_scientific_journal-2059	118	54	φα	φα	ADP
american_scientific_journal-2059	118	55	≠∩	≠∩	PROPN
american_scientific_journal-2059	118	56	bc	bc	PROPN
american_scientific_journal-2059	118	57	ff	ff	PROPN
american_scientific_journal-2059	118	58	~})/	~})/	PROPN
american_scientific_journal-2059	118	59	{	{	PUNCT
american_scientific_journal-2059	118	60	(	(	PUNCT
american_scientific_journal-2059	118	61	.	.	PUNCT
american_scientific_journal-2059	119	1	the	the	DET
american_scientific_journal-2059	119	2	set	set	NOUN
american_scientific_journal-2059	119	3	of	of	ADP
american_scientific_journal-2059	119	4	all	all	DET
american_scientific_journal-2059	119	5	soft	soft	ADJ
american_scientific_journal-2059	119	6	pre	pre	ADJ
american_scientific_journal-2059	119	7	-	-	ADJ
american_scientific_journal-2059	119	8	limit	limit	ADJ
american_scientific_journal-2059	119	9	points	point	NOUN
american_scientific_journal-2059	119	10	of	of	ADP
american_scientific_journal-2059	119	11	bf	bf	NOUN
american_scientific_journal-2059	119	12	be	be	AUX
american_scientific_journal-2059	119	13	denoted	denote	VERB
american_scientific_journal-2059	119	14	by	by	ADP
american_scientific_journal-2059	119	15	spre	spre	PROPN
american_scientific_journal-2059	119	16	-	-	PUNCT
american_scientific_journal-2059	119	17	lm	lm	INTJ
american_scientific_journal-2059	119	18	(	(	PUNCT
american_scientific_journal-2059	119	19	bf	bf	NOUN
american_scientific_journal-2059	119	20	)	)	PUNCT
american_scientific_journal-2059	119	21	.	.	PUNCT
american_scientific_journal-2059	120	1	3.9	3.9	NUM
american_scientific_journal-2059	120	2	.	.	PUNCT
american_scientific_journal-2059	121	1	definition	definition	NOUN
american_scientific_journal-2059	121	2	american	american	PROPN
american_scientific_journal-2059	121	3	scientific	scientific	PROPN
american_scientific_journal-2059	121	4	research	research	PROPN
american_scientific_journal-2059	121	5	journal	journal	NOUN
american_scientific_journal-2059	121	6	for	for	ADP
american_scientific_journal-2059	121	7	engineering	engineering	NOUN
american_scientific_journal-2059	121	8	,	,	PUNCT
american_scientific_journal-2059	121	9	technology	technology	NOUN
american_scientific_journal-2059	121	10	,	,	PUNCT
american_scientific_journal-2059	121	11	and	and	CCONJ
american_scientific_journal-2059	121	12	sciences	science	NOUN
american_scientific_journal-2059	121	13	(	(	PUNCT
american_scientific_journal-2059	121	14	asrjets	asrjet	NOUN
american_scientific_journal-2059	121	15	)	)	PUNCT
american_scientific_journal-2059	121	16	(	(	PUNCT
american_scientific_journal-2059	121	17	2016	2016	NUM
american_scientific_journal-2059	121	18	)	)	PUNCT
american_scientific_journal-2059	121	19	volume	volume	NOUN
american_scientific_journal-2059	121	20	26	26	NUM
american_scientific_journal-2059	121	21	,	,	PUNCT
american_scientific_journal-2059	121	22	no	no	DET
american_scientific_journal-2059	121	23	4	4	NUM
american_scientific_journal-2059	121	24	,	,	PUNCT
american_scientific_journal-2059	121	25	pp	pp	ADV
american_scientific_journal-2059	121	26	42	42	NUM
american_scientific_journal-2059	121	27	-	-	SYM
american_scientific_journal-2059	121	28	53	53	NUM
american_scientific_journal-2059	121	29	50	50	NUM
american_scientific_journal-2059	121	30	let	let	NOUN
american_scientific_journal-2059	121	31	)	)	PUNCT
american_scientific_journal-2059	121	32	~,~	~,~	NUM
american_scientific_journal-2059	121	33	,	,	PUNCT
american_scientific_journal-2059	121	34	(	(	PUNCT
american_scientific_journal-2059	121	35	21	21	NUM
american_scientific_journal-2059	121	36	ττaf	ττaf	NOUN
american_scientific_journal-2059	121	37	is	be	AUX
american_scientific_journal-2059	121	38	soft	soft	ADJ
american_scientific_journal-2059	121	39	bitopological	bitopological	ADJ
american_scientific_journal-2059	121	40	space	space	NOUN
american_scientific_journal-2059	121	41	,	,	PUNCT
american_scientific_journal-2059	121	42	and	and	CCONJ
american_scientific_journal-2059	121	43	ab	ab	PROPN
american_scientific_journal-2059	121	44	ff	ff	PROPN
american_scientific_journal-2059	121	45	⊆~	⊆~	PROPN
american_scientific_journal-2059	121	46	,	,	PUNCT
american_scientific_journal-2059	121	47	the	the	DET
american_scientific_journal-2059	121	48	intersection	intersection	NOUN
american_scientific_journal-2059	121	49	of	of	ADP
american_scientific_journal-2059	121	50	all	all	DET
american_scientific_journal-2059	121	51	soft	soft	ADJ
american_scientific_journal-2059	121	52	pre	pre	ADJ
american_scientific_journal-2059	121	53	-	-	ADJ
american_scientific_journal-2059	121	54	closed	closed	ADJ
american_scientific_journal-2059	121	55	sets	set	NOUN
american_scientific_journal-2059	121	56	containing	contain	VERB
american_scientific_journal-2059	121	57	bf	bf	NOUN
american_scientific_journal-2059	121	58	is	be	AUX
american_scientific_journal-2059	121	59	called	call	VERB
american_scientific_journal-2059	121	60	soft	soft	ADJ
american_scientific_journal-2059	121	61	pre	pre	NOUN
american_scientific_journal-2059	121	62	-	-	NOUN
american_scientific_journal-2059	121	63	closure	closure	NOUN
american_scientific_journal-2059	121	64	of	of	ADP
american_scientific_journal-2059	121	65	bf	bf	NOUN
american_scientific_journal-2059	121	66	,	,	PUNCT
american_scientific_journal-2059	121	67	and	and	CCONJ
american_scientific_journal-2059	121	68	is	be	AUX
american_scientific_journal-2059	121	69	denoted	denote	VERB
american_scientific_journal-2059	121	70	by	by	ADP
american_scientific_journal-2059	121	71	spre	spre	ADJ
american_scientific_journal-2059	121	72	-	-	PUNCT
american_scientific_journal-2059	121	73	cl	cl	ADJ
american_scientific_journal-2059	121	74	(	(	PUNCT
american_scientific_journal-2059	121	75	bf	bf	NOUN
american_scientific_journal-2059	121	76	)	)	PUNCT
american_scientific_journal-2059	121	77	.	.	PUNCT
american_scientific_journal-2059	122	1	in	in	ADP
american_scientific_journal-2059	122	2	the	the	DET
american_scientific_journal-2059	122	3	year	year	NOUN
american_scientific_journal-2059	122	4	2014	2014	NUM
american_scientific_journal-2059	122	5	j.	j.	PROPN
american_scientific_journal-2059	122	6	subhashinin	subhashinin	PROPN
american_scientific_journal-2059	122	7	and	and	CCONJ
american_scientific_journal-2059	122	8	dr	dr	PROPN
american_scientific_journal-2059	122	9	.	.	PROPN
american_scientific_journal-2059	122	10	c.sekar	c.sekar	PROPN
american_scientific_journal-2059	123	1	[	[	X
american_scientific_journal-2059	123	2	3	3	NUM
american_scientific_journal-2059	123	3	]	]	PUNCT
american_scientific_journal-2059	123	4	by	by	ADP
american_scientific_journal-2059	123	5	depending	depend	VERB
american_scientific_journal-2059	123	6	on	on	ADP
american_scientific_journal-2059	123	7	the	the	PRON
american_scientific_journal-2059	123	8	[	[	X
american_scientific_journal-2059	123	9	6	6	NUM
american_scientific_journal-2059	123	10	]	]	PUNCT
american_scientific_journal-2059	123	11	and	and	CCONJ
american_scientific_journal-2059	123	12	[	[	X
american_scientific_journal-2059	123	13	4	4	X
american_scientific_journal-2059	123	14	]	]	PUNCT
american_scientific_journal-2059	123	15	introduces	introduce	VERB
american_scientific_journal-2059	123	16	soft	soft	ADJ
american_scientific_journal-2059	123	17	pre	pre	NOUN
american_scientific_journal-2059	123	18	separation	separation	NOUN
american_scientific_journal-2059	123	19	axioms	axiom	NOUN
american_scientific_journal-2059	123	20	,	,	PUNCT
american_scientific_journal-2059	123	21	soft	soft	ADJ
american_scientific_journal-2059	123	22	p	p	NOUN
american_scientific_journal-2059	123	23	t	t	NOUN
american_scientific_journal-2059	123	24	-space	-space	NOUN
american_scientific_journal-2059	123	25	and	and	CCONJ
american_scientific_journal-2059	123	26	some	some	PRON
american_scientific_journal-2059	123	27	of	of	ADP
american_scientific_journal-2059	123	28	its	its	PRON
american_scientific_journal-2059	123	29	properties	property	NOUN
american_scientific_journal-2059	123	30	in	in	ADP
american_scientific_journal-2059	123	31	the	the	DET
american_scientific_journal-2059	123	32	soft	soft	ADJ
american_scientific_journal-2059	123	33	topological	topological	ADJ
american_scientific_journal-2059	123	34	spaces	space	NOUN
american_scientific_journal-2059	123	35	.	.	PUNCT
american_scientific_journal-2059	124	1	now	now	ADV
american_scientific_journal-2059	124	2	begin	begin	VERB
american_scientific_journal-2059	124	3	to	to	ADP
american_scientific_journal-2059	124	4	important	important	ADJ
american_scientific_journal-2059	124	5	section	section	NOUN
american_scientific_journal-2059	124	6	to	to	PART
american_scientific_journal-2059	124	7	discuss	discuss	VERB
american_scientific_journal-2059	124	8	soft	soft	ADJ
american_scientific_journal-2059	124	9	pre	pre	NOUN
american_scientific_journal-2059	124	10	separation	separation	NOUN
american_scientific_journal-2059	124	11	axioms	axiom	NOUN
american_scientific_journal-2059	124	12	and	and	CCONJ
american_scientific_journal-2059	124	13	some	some	DET
american_scientific_journal-2059	124	14	result	result	NOUN
american_scientific_journal-2059	124	15	.	.	PUNCT
american_scientific_journal-2059	125	1	4	4	X
american_scientific_journal-2059	125	2	.	.	X
american_scientific_journal-2059	125	3	the	the	DET
american_scientific_journal-2059	125	4	separation	separation	NOUN
american_scientific_journal-2059	125	5	axioms	axiom	VERB
american_scientific_journal-2059	125	6	in	in	ADP
american_scientific_journal-2059	125	7	soft	soft	ADJ
american_scientific_journal-2059	125	8	bitopological	bitopological	ADJ
american_scientific_journal-2059	125	9	space	space	NOUN
american_scientific_journal-2059	125	10	in	in	ADP
american_scientific_journal-2059	125	11	section	section	NOUN
american_scientific_journal-2059	125	12	four	four	NUM
american_scientific_journal-2059	125	13	,	,	PUNCT
american_scientific_journal-2059	125	14	i	i	PRON
american_scientific_journal-2059	125	15	introduce	introduce	VERB
american_scientific_journal-2059	125	16	some	some	DET
american_scientific_journal-2059	125	17	soft	soft	ADJ
american_scientific_journal-2059	125	18	pre	pre	NOUN
american_scientific_journal-2059	125	19	separation	separation	NOUN
american_scientific_journal-2059	125	20	axioms	axiom	NOUN
american_scientific_journal-2059	125	21	,	,	PUNCT
american_scientific_journal-2059	125	22	spret	spret	NUM
american_scientific_journal-2059	125	23	,	,	PUNCT
american_scientific_journal-2059	125	24	spre1	spre1	PROPN
american_scientific_journal-2059	125	25	t	t	PROPN
american_scientific_journal-2059	125	26	and	and	CCONJ
american_scientific_journal-2059	125	27	spre2	spre2	PROPN
american_scientific_journal-2059	125	28	t	t	NOUN
american_scientific_journal-2059	125	29	and	and	CCONJ
american_scientific_journal-2059	125	30	illustrate	illustrate	VERB
american_scientific_journal-2059	125	31	transmission	transmission	NOUN
american_scientific_journal-2059	125	32	this	this	DET
american_scientific_journal-2059	125	33	properties	property	NOUN
american_scientific_journal-2059	125	34	to	to	ADP
american_scientific_journal-2059	125	35	the	the	DET
american_scientific_journal-2059	125	36	relative	relative	ADJ
american_scientific_journal-2059	125	37	soft	soft	ADJ
american_scientific_journal-2059	125	38	bitopological	bitopological	ADJ
american_scientific_journal-2059	125	39	space	space	NOUN
american_scientific_journal-2059	125	40	with	with	ADP
american_scientific_journal-2059	125	41	some	some	DET
american_scientific_journal-2059	125	42	result	result	NOUN
american_scientific_journal-2059	125	43	of	of	ADP
american_scientific_journal-2059	125	44	soft	soft	ADJ
american_scientific_journal-2059	125	45	pre	pre	NOUN
american_scientific_journal-2059	125	46	separation	separation	NOUN
american_scientific_journal-2059	125	47	axioms	axiom	NOUN
american_scientific_journal-2059	125	48	.	.	PUNCT
american_scientific_journal-2059	126	1	4.1	4.1	NUM
american_scientific_journal-2059	126	2	.	.	PUNCT
american_scientific_journal-2059	126	3	definition	definition	NOUN
american_scientific_journal-2059	126	4	let	let	VERB
american_scientific_journal-2059	126	5	)	)	PUNCT
american_scientific_journal-2059	126	6	~,~	~,~	X
american_scientific_journal-2059	126	7	,	,	PUNCT
american_scientific_journal-2059	126	8	(	(	PUNCT
american_scientific_journal-2059	126	9	21	21	NUM
american_scientific_journal-2059	126	10	ττaf	ττaf	NOUN
american_scientific_journal-2059	126	11	is	be	AUX
american_scientific_journal-2059	126	12	soft	soft	ADJ
american_scientific_journal-2059	126	13	bitopological	bitopological	ADJ
american_scientific_journal-2059	126	14	space	space	NOUN
american_scientific_journal-2059	126	15	,	,	PUNCT
american_scientific_journal-2059	126	16	then	then	ADV
american_scientific_journal-2059	126	17	)	)	PUNCT
american_scientific_journal-2059	126	18	~,~	~,~	NUM
american_scientific_journal-2059	126	19	,	,	PUNCT
american_scientific_journal-2059	126	20	(	(	PUNCT
american_scientific_journal-2059	126	21	21	21	NUM
american_scientific_journal-2059	126	22	ττaf	ττaf	NOUN
american_scientific_journal-2059	126	23	is	be	AUX
american_scientific_journal-2059	126	24	called	call	VERB
american_scientific_journal-2059	126	25	spret	spret	NUM
american_scientific_journal-2059	126	26	space	space	NOUN
american_scientific_journal-2059	126	27	if	if	SCONJ
american_scientific_journal-2059	126	28	and	and	CCONJ
american_scientific_journal-2059	126	29	only	only	ADV
american_scientific_journal-2059	126	30	if	if	SCONJ
american_scientific_journal-2059	126	31	for	for	ADP
american_scientific_journal-2059	126	32	all	all	DET
american_scientific_journal-2059	126	33	pair	pair	NOUN
american_scientific_journal-2059	126	34	of	of	ADP
american_scientific_journal-2059	126	35	soft	soft	ADJ
american_scientific_journal-2059	126	36	point	point	NOUN
american_scientific_journal-2059	126	37	af∈21,αα	af∈21,αα	NOUN
american_scientific_journal-2059	126	38	such	such	ADJ
american_scientific_journal-2059	126	39	that	that	DET
american_scientific_journal-2059	126	40	21	21	NUM
american_scientific_journal-2059	126	41	αα	αα	ADP
american_scientific_journal-2059	126	42	≠	≠	PROPN
american_scientific_journal-2059	126	43	,	,	PUNCT
american_scientific_journal-2059	126	44	there	there	PRON
american_scientific_journal-2059	126	45	exists	exist	VERB
american_scientific_journal-2059	126	46	soft	soft	ADJ
american_scientific_journal-2059	126	47	pre	pre	ADJ
american_scientific_journal-2059	126	48	-	-	ADJ
american_scientific_journal-2059	126	49	open	open	ADJ
american_scientific_journal-2059	126	50	set	set	VERB
american_scientific_journal-2059	126	51	bf	bf	NOUN
american_scientific_journal-2059	126	52	containing	contain	VERB
american_scientific_journal-2059	126	53	1α	1α	NOUN
american_scientific_journal-2059	126	54	but	but	CCONJ
american_scientific_journal-2059	126	55	not	not	PART
american_scientific_journal-2059	126	56	2α	2α	NOUN
american_scientific_journal-2059	126	57	or	or	CCONJ
american_scientific_journal-2059	126	58	soft	soft	ADJ
american_scientific_journal-2059	126	59	pre	pre	ADJ
american_scientific_journal-2059	126	60	-	-	ADJ
american_scientific_journal-2059	126	61	open	open	ADJ
american_scientific_journal-2059	126	62	set	set	VERB
american_scientific_journal-2059	126	63	cf	cf	NOUN
american_scientific_journal-2059	126	64	containing	contain	VERB
american_scientific_journal-2059	126	65	2α	2α	NOUN
american_scientific_journal-2059	126	66	but	but	CCONJ
american_scientific_journal-2059	126	67	not	not	PART
american_scientific_journal-2059	126	68	1α	1α	NUM
american_scientific_journal-2059	126	69	.	.	PUNCT
american_scientific_journal-2059	127	1	4.2	4.2	NUM
american_scientific_journal-2059	127	2	.	.	PUNCT
american_scientific_journal-2059	127	3	theorem	theorem	VERB
american_scientific_journal-2059	127	4	a	a	DET
american_scientific_journal-2059	127	5	soft	soft	ADJ
american_scientific_journal-2059	127	6	bitopological	bitopological	ADJ
american_scientific_journal-2059	127	7	space	space	NOUN
american_scientific_journal-2059	127	8	)	)	PUNCT
american_scientific_journal-2059	127	9	~,~	~,~	NUM
american_scientific_journal-2059	127	10	,	,	PUNCT
american_scientific_journal-2059	127	11	(	(	PUNCT
american_scientific_journal-2059	127	12	21	21	NUM
american_scientific_journal-2059	127	13	ττaf	ττaf	NOUN
american_scientific_journal-2059	127	14	is	be	AUX
american_scientific_journal-2059	127	15	spret	spret	NUM
american_scientific_journal-2059	127	16	space	space	NOUN
american_scientific_journal-2059	127	17	if	if	SCONJ
american_scientific_journal-2059	128	1	and	and	CCONJ
american_scientific_journal-2059	128	2	only	only	ADV
american_scientific_journal-2059	128	3	if	if	SCONJ
american_scientific_journal-2059	128	4	for	for	ADP
american_scientific_journal-2059	128	5	each	each	DET
american_scientific_journal-2059	128	6	distinct	distinct	ADJ
american_scientific_journal-2059	128	7	soft	soft	ADJ
american_scientific_journal-2059	128	8	points	point	NOUN
american_scientific_journal-2059	128	9	21,αα	21,αα	NUM
american_scientific_journal-2059	128	10	in	in	ADP
american_scientific_journal-2059	128	11	af	af	PROPN
american_scientific_journal-2059	128	12	,	,	PUNCT
american_scientific_journal-2059	128	13	spre	spre	ADJ
american_scientific_journal-2059	128	14	-	-	NOUN
american_scientific_journal-2059	128	15	cl	cl	NOUN
american_scientific_journal-2059	128	16	(	(	PUNCT
american_scientific_journal-2059	128	17	}	}	PUNCT
american_scientific_journal-2059	128	18	{	{	PUNCT
american_scientific_journal-2059	128	19	1α	1α	NUM
american_scientific_journal-2059	128	20	)	)	PUNCT
american_scientific_journal-2059	128	21	≠	≠	PROPN
american_scientific_journal-2059	128	22	spre	spre	ADJ
american_scientific_journal-2059	128	23	-	-	NOUN
american_scientific_journal-2059	128	24	cl	cl	NOUN
american_scientific_journal-2059	128	25	(	(	PUNCT
american_scientific_journal-2059	128	26	}	}	PUNCT
american_scientific_journal-2059	128	27	{	{	PUNCT
american_scientific_journal-2059	128	28	2α	2α	NOUN
american_scientific_journal-2059	128	29	)	)	PUNCT
american_scientific_journal-2059	128	30	.	.	PUNCT
american_scientific_journal-2059	129	1	proof	proof	NOUN
american_scientific_journal-2059	129	2	:	:	PUNCT
american_scientific_journal-2059	129	3	let	let	VERB
american_scientific_journal-2059	129	4	af∈21,αα	af∈21,αα	NOUN
american_scientific_journal-2059	129	5	such	such	ADJ
american_scientific_journal-2059	129	6	that	that	DET
american_scientific_journal-2059	129	7	21	21	NUM
american_scientific_journal-2059	129	8	αα	αα	ADP
american_scientific_journal-2059	129	9	≠	≠	PROPN
american_scientific_journal-2059	129	10	and	and	CCONJ
american_scientific_journal-2059	129	11	spre	spre	ADJ
american_scientific_journal-2059	129	12	-	-	NOUN
american_scientific_journal-2059	129	13	cl	cl	NOUN
american_scientific_journal-2059	129	14	(	(	PUNCT
american_scientific_journal-2059	129	15	}	}	PUNCT
american_scientific_journal-2059	129	16	{	{	PUNCT
american_scientific_journal-2059	129	17	1α	1α	NUM
american_scientific_journal-2059	129	18	)	)	PUNCT
american_scientific_journal-2059	129	19	≠	≠	PROPN
american_scientific_journal-2059	129	20	spre	spre	ADJ
american_scientific_journal-2059	129	21	-	-	NOUN
american_scientific_journal-2059	129	22	cl	cl	NOUN
american_scientific_journal-2059	129	23	(	(	PUNCT
american_scientific_journal-2059	129	24	}	}	PUNCT
american_scientific_journal-2059	129	25	{	{	PUNCT
american_scientific_journal-2059	129	26	2α	2α	NOUN
american_scientific_journal-2059	129	27	)	)	PUNCT
american_scientific_journal-2059	129	28	.	.	PUNCT
american_scientific_journal-2059	130	1	then	then	ADV
american_scientific_journal-2059	130	2	there	there	PRON
american_scientific_journal-2059	130	3	exists	exist	VERB
american_scientific_journal-2059	130	4	at	at	ADP
american_scientific_journal-2059	130	5	least	least	ADV
american_scientific_journal-2059	130	6	one	one	NUM
american_scientific_journal-2059	130	7	soft	soft	ADJ
american_scientific_journal-2059	130	8	point	point	NOUN
american_scientific_journal-2059	130	9	3α	3α	NOUN
american_scientific_journal-2059	130	10	in	in	ADP
american_scientific_journal-2059	130	11	af	af	PROPN
american_scientific_journal-2059	130	12	such	such	ADJ
american_scientific_journal-2059	130	13	that	that	PRON
american_scientific_journal-2059	130	14	,	,	PUNCT
american_scientific_journal-2059	130	15	∈3α	∈3α	PROPN
american_scientific_journal-2059	130	16	spre	spre	PROPN
american_scientific_journal-2059	130	17	-	-	NOUN
american_scientific_journal-2059	130	18	cl	cl	NOUN
american_scientific_journal-2059	130	19	(	(	PUNCT
american_scientific_journal-2059	130	20	}	}	PUNCT
american_scientific_journal-2059	130	21	{	{	PUNCT
american_scientific_journal-2059	130	22	1α	1α	NOUN
american_scientific_journal-2059	130	23	)	)	PUNCT
american_scientific_journal-2059	130	24	but	but	CCONJ
american_scientific_journal-2059	130	25	∉3α	∉3α	PUNCT
american_scientific_journal-2059	130	26	spre	spre	ADJ
american_scientific_journal-2059	130	27	-	-	NOUN
american_scientific_journal-2059	130	28	cl	cl	NOUN
american_scientific_journal-2059	130	29	(	(	PUNCT
american_scientific_journal-2059	130	30	}	}	PUNCT
american_scientific_journal-2059	130	31	{	{	PUNCT
american_scientific_journal-2059	130	32	2α	2α	NOUN
american_scientific_journal-2059	130	33	)	)	PUNCT
american_scientific_journal-2059	130	34	.	.	PUNCT
american_scientific_journal-2059	131	1	suppose	suppose	VERB
american_scientific_journal-2059	131	2	∈3α	∈3α	PROPN
american_scientific_journal-2059	131	3	spre	spre	PROPN
american_scientific_journal-2059	131	4	-	-	NOUN
american_scientific_journal-2059	131	5	cl	cl	NOUN
american_scientific_journal-2059	131	6	(	(	PUNCT
american_scientific_journal-2059	131	7	}	}	PUNCT
american_scientific_journal-2059	131	8	{	{	PUNCT
american_scientific_journal-2059	131	9	1α	1α	NUM
american_scientific_journal-2059	131	10	)	)	PUNCT
american_scientific_journal-2059	131	11	,	,	PUNCT
american_scientific_journal-2059	131	12	to	to	PART
american_scientific_journal-2059	131	13	show	show	VERB
american_scientific_journal-2059	131	14	that	that	SCONJ
american_scientific_journal-2059	131	15	∉1α	∉1α	NUM
american_scientific_journal-2059	131	16	spre	spre	ADJ
american_scientific_journal-2059	131	17	-	-	NOUN
american_scientific_journal-2059	131	18	cl	cl	NOUN
american_scientific_journal-2059	131	19	(	(	PUNCT
american_scientific_journal-2059	131	20	}	}	PUNCT
american_scientific_journal-2059	131	21	{	{	PUNCT
american_scientific_journal-2059	131	22	2α	2α	NOUN
american_scientific_journal-2059	131	23	)	)	PUNCT
american_scientific_journal-2059	131	24	.	.	PUNCT
american_scientific_journal-2059	132	1	if	if	SCONJ
american_scientific_journal-2059	132	2	∈1α	∈1α	PROPN
american_scientific_journal-2059	132	3	spre	spre	PROPN
american_scientific_journal-2059	132	4	-	-	NOUN
american_scientific_journal-2059	132	5	cl	cl	NOUN
american_scientific_journal-2059	132	6	(	(	PUNCT
american_scientific_journal-2059	132	7	}	}	PUNCT
american_scientific_journal-2059	132	8	{	{	PUNCT
american_scientific_journal-2059	132	9	2α	2α	NOUN
american_scientific_journal-2059	132	10	)	)	PUNCT
american_scientific_journal-2059	132	11	,	,	PUNCT
american_scientific_journal-2059	132	12	then	then	ADV
american_scientific_journal-2059	132	13	⊂~	⊂~	PROPN
american_scientific_journal-2059	132	14	}	}	PUNCT
american_scientific_journal-2059	132	15	{	{	PUNCT
american_scientific_journal-2059	132	16	1α	1α	NUM
american_scientific_journal-2059	132	17	sprecl	sprecl	PROPN
american_scientific_journal-2059	132	18	(	(	PUNCT
american_scientific_journal-2059	132	19	}	}	PUNCT
american_scientific_journal-2059	132	20	{	{	PUNCT
american_scientific_journal-2059	132	21	2α	2α	NOUN
american_scientific_journal-2059	132	22	)	)	PUNCT
american_scientific_journal-2059	132	23	.	.	PUNCT
american_scientific_journal-2059	133	1	so	so	ADV
american_scientific_journal-2059	133	2	spre	spre	ADJ
american_scientific_journal-2059	133	3	-	-	NOUN
american_scientific_journal-2059	133	4	cl	cl	NOUN
american_scientific_journal-2059	133	5	(	(	PUNCT
american_scientific_journal-2059	133	6	}	}	PUNCT
american_scientific_journal-2059	133	7	{	{	PUNCT
american_scientific_journal-2059	133	8	1α	1α	NUM
american_scientific_journal-2059	133	9	)	)	PUNCT
american_scientific_journal-2059	134	1	⊂~	⊂~	PROPN
american_scientific_journal-2059	134	2	spre	spre	ADJ
american_scientific_journal-2059	134	3	-	-	PUNCT
american_scientific_journal-2059	134	4	cl(spre	cl(spre	NOUN
american_scientific_journal-2059	134	5	-	-	NOUN
american_scientific_journal-2059	134	6	cl	cl	NOUN
american_scientific_journal-2059	134	7	(	(	PUNCT
american_scientific_journal-2059	134	8	}	}	PUNCT
american_scientific_journal-2059	134	9	{	{	PUNCT
american_scientific_journal-2059	134	10	2α	2α	NOUN
american_scientific_journal-2059	134	11	)	)	PUNCT
american_scientific_journal-2059	134	12	)	)	PUNCT
american_scientific_journal-2059	135	1	=	=	SYM
american_scientific_journal-2059	135	2	spre	spre	ADJ
american_scientific_journal-2059	135	3	-	-	NOUN
american_scientific_journal-2059	135	4	cl	cl	NOUN
american_scientific_journal-2059	135	5	(	(	PUNCT
american_scientific_journal-2059	135	6	}	}	PUNCT
american_scientific_journal-2059	135	7	{	{	PUNCT
american_scientific_journal-2059	135	8	2α	2α	NOUN
american_scientific_journal-2059	135	9	)	)	PUNCT
american_scientific_journal-2059	135	10	,	,	PUNCT
american_scientific_journal-2059	135	11	hence	hence	ADV
american_scientific_journal-2059	135	12	∈3α	∈3α	PROPN
american_scientific_journal-2059	135	13	spre	spre	PROPN
american_scientific_journal-2059	135	14	-	-	NOUN
american_scientific_journal-2059	135	15	cl	cl	NOUN
american_scientific_journal-2059	135	16	(	(	PUNCT
american_scientific_journal-2059	135	17	}	}	PUNCT
american_scientific_journal-2059	135	18	{	{	PUNCT
american_scientific_journal-2059	135	19	1α	1α	NUM
american_scientific_journal-2059	135	20	)	)	PUNCT
american_scientific_journal-2059	135	21	,	,	PUNCT
american_scientific_journal-2059	135	22	then	then	ADV
american_scientific_journal-2059	135	23	∈3α	∈3α	PROPN
american_scientific_journal-2059	135	24	spre	spre	PROPN
american_scientific_journal-2059	135	25	-	-	NOUN
american_scientific_journal-2059	135	26	cl	cl	NOUN
american_scientific_journal-2059	135	27	(	(	PUNCT
american_scientific_journal-2059	135	28	}	}	PUNCT
american_scientific_journal-2059	135	29	{	{	PUNCT
american_scientific_journal-2059	135	30	2α	2α	NOUN
american_scientific_journal-2059	135	31	)	)	PUNCT
american_scientific_journal-2059	135	32	which	which	PRON
american_scientific_journal-2059	135	33	is	be	AUX
american_scientific_journal-2059	135	34	contradiction	contradiction	NOUN
american_scientific_journal-2059	135	35	.	.	PUNCT
american_scientific_journal-2059	136	1	hence	hence	ADV
american_scientific_journal-2059	136	2	∉1α	∉1α	PUNCT
american_scientific_journal-2059	136	3	spre	spre	ADJ
american_scientific_journal-2059	136	4	-	-	NOUN
american_scientific_journal-2059	136	5	cl	cl	NOUN
american_scientific_journal-2059	136	6	(	(	PUNCT
american_scientific_journal-2059	136	7	}	}	PUNCT
american_scientific_journal-2059	136	8	{	{	PUNCT
american_scientific_journal-2059	136	9	2α	2α	NOUN
american_scientific_journal-2059	136	10	)	)	PUNCT
american_scientific_journal-2059	136	11	,	,	PUNCT
american_scientific_journal-2059	136	12	consequently	consequently	ADV
american_scientific_journal-2059	136	13	af∈1α	af∈1α	PROPN
american_scientific_journal-2059	136	14	-spre	-spre	NOUN
american_scientific_journal-2059	136	15	-	-	PUNCT
american_scientific_journal-2059	136	16	cl	cl	NOUN
american_scientific_journal-2059	136	17	(	(	PUNCT
american_scientific_journal-2059	136	18	}	}	PUNCT
american_scientific_journal-2059	136	19	{	{	PUNCT
american_scientific_journal-2059	136	20	2α	2α	NOUN
american_scientific_journal-2059	136	21	)	)	PUNCT
american_scientific_journal-2059	136	22	but	but	CCONJ
american_scientific_journal-2059	136	23	spre	spre	NOUN
american_scientific_journal-2059	136	24	-	-	NOUN
american_scientific_journal-2059	136	25	cl	cl	NOUN
american_scientific_journal-2059	136	26	(	(	PUNCT
american_scientific_journal-2059	136	27	}	}	PUNCT
american_scientific_journal-2059	136	28	{	{	PUNCT
american_scientific_journal-2059	136	29	2α	2α	NOUN
american_scientific_journal-2059	136	30	)	)	PUNCT
american_scientific_journal-2059	136	31	is	be	AUX
american_scientific_journal-2059	136	32	soft	soft	ADJ
american_scientific_journal-2059	136	33	pre	pre	ADJ
american_scientific_journal-2059	136	34	-	-	ADJ
american_scientific_journal-2059	136	35	closed	closed	ADJ
american_scientific_journal-2059	136	36	,	,	PUNCT
american_scientific_journal-2059	136	37	so	so	ADV
american_scientific_journal-2059	136	38	af	af	VERB
american_scientific_journal-2059	136	39	-spre	-spre	NOUN
american_scientific_journal-2059	136	40	-	-	PUNCT
american_scientific_journal-2059	136	41	cl	cl	NOUN
american_scientific_journal-2059	136	42	(	(	PUNCT
american_scientific_journal-2059	136	43	}	}	PUNCT
american_scientific_journal-2059	136	44	{	{	PUNCT
american_scientific_journal-2059	136	45	2α	2α	NOUN
american_scientific_journal-2059	136	46	)	)	PUNCT
american_scientific_journal-2059	136	47	is	be	AUX
american_scientific_journal-2059	136	48	soft	soft	ADJ
american_scientific_journal-2059	136	49	pre	pre	ADJ
american_scientific_journal-2059	136	50	-	-	ADJ
american_scientific_journal-2059	136	51	open	open	ADJ
american_scientific_journal-2059	136	52	which	which	PRON
american_scientific_journal-2059	136	53	contains	contain	VERB
american_scientific_journal-2059	136	54	1α	1α	NUM
american_scientific_journal-2059	136	55	but	but	CCONJ
american_scientific_journal-2059	136	56	not	not	PART
american_scientific_journal-2059	136	57	2α	2α	NOUN
american_scientific_journal-2059	136	58	.	.	PUNCT
american_scientific_journal-2059	137	1	it	it	PRON
american_scientific_journal-2059	137	2	follows	follow	VERB
american_scientific_journal-2059	137	3	that	that	PRON
american_scientific_journal-2059	137	4	)	)	PUNCT
american_scientific_journal-2059	137	5	~,~	~,~	NUM
american_scientific_journal-2059	137	6	,	,	PUNCT
american_scientific_journal-2059	137	7	(	(	PUNCT
american_scientific_journal-2059	137	8	21	21	NUM
american_scientific_journal-2059	137	9	ττaf	ττaf	NOUN
american_scientific_journal-2059	137	10	is	be	AUX
american_scientific_journal-2059	137	11	spret	spret	NUM
american_scientific_journal-2059	137	12	space	space	NOUN
american_scientific_journal-2059	137	13	.	.	PUNCT
american_scientific_journal-2059	138	1	conversely	conversely	ADV
american_scientific_journal-2059	138	2	,	,	PUNCT
american_scientific_journal-2059	138	3	since	since	SCONJ
american_scientific_journal-2059	138	4	)	)	PUNCT
american_scientific_journal-2059	138	5	~,~	~,~	NUM
american_scientific_journal-2059	138	6	,	,	PUNCT
american_scientific_journal-2059	138	7	(	(	PUNCT
american_scientific_journal-2059	138	8	21	21	NUM
american_scientific_journal-2059	138	9	ττaf	ττaf	NOUN
american_scientific_journal-2059	138	10	is	be	AUX
american_scientific_journal-2059	138	11	spret	spret	NUM
american_scientific_journal-2059	138	12	space	space	NOUN
american_scientific_journal-2059	138	13	,	,	PUNCT
american_scientific_journal-2059	138	14	then	then	ADV
american_scientific_journal-2059	138	15	for	for	ADP
american_scientific_journal-2059	138	16	each	each	DET
american_scientific_journal-2059	138	17	tow	tow	VERB
american_scientific_journal-2059	138	18	distinct	distinct	ADJ
american_scientific_journal-2059	138	19	soft	soft	ADJ
american_scientific_journal-2059	138	20	points	point	NOUN
american_scientific_journal-2059	138	21	af∈21,αα	af∈21,αα	NOUN
american_scientific_journal-2059	138	22	there	there	PRON
american_scientific_journal-2059	138	23	american	american	ADJ
american_scientific_journal-2059	138	24	scientific	scientific	ADJ
american_scientific_journal-2059	138	25	research	research	NOUN
american_scientific_journal-2059	138	26	journal	journal	NOUN
american_scientific_journal-2059	138	27	for	for	ADP
american_scientific_journal-2059	138	28	engineering	engineering	NOUN
american_scientific_journal-2059	138	29	,	,	PUNCT
american_scientific_journal-2059	138	30	technology	technology	NOUN
american_scientific_journal-2059	138	31	,	,	PUNCT
american_scientific_journal-2059	138	32	and	and	CCONJ
american_scientific_journal-2059	138	33	sciences	science	NOUN
american_scientific_journal-2059	138	34	(	(	PUNCT
american_scientific_journal-2059	138	35	asrjets	asrjet	NOUN
american_scientific_journal-2059	138	36	)	)	PUNCT
american_scientific_journal-2059	138	37	(	(	PUNCT
american_scientific_journal-2059	138	38	2016	2016	NUM
american_scientific_journal-2059	138	39	)	)	PUNCT
american_scientific_journal-2059	138	40	volume	volume	NOUN
american_scientific_journal-2059	138	41	26	26	NUM
american_scientific_journal-2059	138	42	,	,	PUNCT
american_scientific_journal-2059	138	43	no	no	DET
american_scientific_journal-2059	138	44	4	4	NUM
american_scientific_journal-2059	138	45	,	,	PUNCT
american_scientific_journal-2059	138	46	pp	pp	ADV
american_scientific_journal-2059	138	47	42	42	NUM
american_scientific_journal-2059	138	48	-	-	SYM
american_scientific_journal-2059	138	49	53	53	NUM
american_scientific_journal-2059	138	50	51	51	NUM
american_scientific_journal-2059	138	51	exists	exist	VERB
american_scientific_journal-2059	138	52	soft	soft	ADJ
american_scientific_journal-2059	138	53	pre	pre	ADJ
american_scientific_journal-2059	138	54	-	-	ADJ
american_scientific_journal-2059	138	55	open	open	ADJ
american_scientific_journal-2059	138	56	set	set	VERB
american_scientific_journal-2059	138	57	bf	bf	NOUN
american_scientific_journal-2059	139	1	such	such	ADJ
american_scientific_journal-2059	139	2	that	that	SCONJ
american_scientific_journal-2059	139	3	bf∈1α	bf∈1α	ADV
american_scientific_journal-2059	139	4	,	,	PUNCT
american_scientific_journal-2059	139	5	bf∉2α	bf∉2α	INTJ
american_scientific_journal-2059	139	6	.	.	PUNCT
american_scientific_journal-2059	140	1	ba	ba	PROPN
american_scientific_journal-2059	141	1	ff	ff	NOUN
american_scientific_journal-2059	141	2	−	−	PROPN
american_scientific_journal-2059	141	3	is	be	AUX
american_scientific_journal-2059	141	4	soft	soft	ADJ
american_scientific_journal-2059	141	5	closed	closed	ADJ
american_scientific_journal-2059	141	6	set	set	NOUN
american_scientific_journal-2059	141	7	which	which	PRON
american_scientific_journal-2059	141	8	does	do	AUX
american_scientific_journal-2059	141	9	not	not	PART
american_scientific_journal-2059	141	10	contain	contain	VERB
american_scientific_journal-2059	141	11	1α	1α	NOUN
american_scientific_journal-2059	141	12	but	but	CCONJ
american_scientific_journal-2059	141	13	contains	contain	VERB
american_scientific_journal-2059	141	14	2α	2α	NOUN
american_scientific_journal-2059	141	15	,	,	PUNCT
american_scientific_journal-2059	141	16	by	by	ADP
american_scientific_journal-2059	141	17	definition	definition	NOUN
american_scientific_journal-2059	141	18	(	(	PUNCT
american_scientific_journal-2059	141	19	3.9	3.9	NUM
american_scientific_journal-2059	141	20	)	)	PUNCT
american_scientific_journal-2059	141	21	spre	spre	NOUN
american_scientific_journal-2059	141	22	-	-	NOUN
american_scientific_journal-2059	141	23	cl	cl	NOUN
american_scientific_journal-2059	141	24	(	(	PUNCT
american_scientific_journal-2059	141	25	}	}	PUNCT
american_scientific_journal-2059	141	26	{	{	PUNCT
american_scientific_journal-2059	141	27	2α	2α	NOUN
american_scientific_journal-2059	141	28	)	)	PUNCT
american_scientific_journal-2059	141	29	is	be	AUX
american_scientific_journal-2059	141	30	the"soft	the"soft	NOUN
american_scientific_journal-2059	141	31	intersection	intersection	NOUN
american_scientific_journal-2059	141	32	of	of	ADP
american_scientific_journal-2059	141	33	all	all	DET
american_scientific_journal-2059	141	34	soft	soft	ADJ
american_scientific_journal-2059	141	35	pre	pre	ADJ
american_scientific_journal-2059	141	36	-	-	ADJ
american_scientific_journal-2059	141	37	closed"which	closed"which	ADJ
american_scientific_journal-2059	141	38	contain	contain	VERB
american_scientific_journal-2059	141	39	}	}	PUNCT
american_scientific_journal-2059	141	40	{	{	PUNCT
american_scientific_journal-2059	141	41	2α	2α	NOUN
american_scientific_journal-2059	141	42	.	.	PUNCT
american_scientific_journal-2059	142	1	thus	thus	ADV
american_scientific_journal-2059	142	2	,	,	PUNCT
american_scientific_journal-2059	142	3	spre	spre	NOUN
american_scientific_journal-2059	142	4	-	-	NOUN
american_scientific_journal-2059	142	5	cl	cl	NOUN
american_scientific_journal-2059	142	6	(	(	PUNCT
american_scientific_journal-2059	142	7	}	}	PUNCT
american_scientific_journal-2059	142	8	{	{	PUNCT
american_scientific_journal-2059	142	9	2α	2α	NOUN
american_scientific_journal-2059	142	10	)	)	PUNCT
american_scientific_journal-2059	142	11	ba	ba	PROPN
american_scientific_journal-2059	143	1	ff	ff	VERB
american_scientific_journal-2059	143	2	−⊂~	−⊂~	NOUN
american_scientific_journal-2059	143	3	then	then	ADV
american_scientific_journal-2059	143	4	ba	ba	PROPN
american_scientific_journal-2059	144	1	ff	ff	INTJ
american_scientific_journal-2059	144	2	−∉1α	−∉1α	NOUN
american_scientific_journal-2059	144	3	.this	.this	PRON
american_scientific_journal-2059	144	4	implies	imply	VERB
american_scientific_journal-2059	144	5	that	that	SCONJ
american_scientific_journal-2059	144	6	∉1α	∉1α	NUM
american_scientific_journal-2059	144	7	spre	spre	ADJ
american_scientific_journal-2059	144	8	-	-	NOUN
american_scientific_journal-2059	144	9	cl	cl	NOUN
american_scientific_journal-2059	144	10	(	(	PUNCT
american_scientific_journal-2059	144	11	}	}	PUNCT
american_scientific_journal-2059	144	12	{	{	PUNCT
american_scientific_journal-2059	144	13	2α	2α	NOUN
american_scientific_journal-2059	144	14	)	)	PUNCT
american_scientific_journal-2059	144	15	.	.	PUNCT
american_scientific_journal-2059	145	1	so	so	ADV
american_scientific_journal-2059	145	2	we	we	PRON
american_scientific_journal-2059	145	3	have	have	VERB
american_scientific_journal-2059	145	4	∈1α	∈1α	ADJ
american_scientific_journal-2059	145	5	spre	spre	ADJ
american_scientific_journal-2059	145	6	-	-	NOUN
american_scientific_journal-2059	145	7	cl	cl	NOUN
american_scientific_journal-2059	145	8	(	(	PUNCT
american_scientific_journal-2059	145	9	}	}	PUNCT
american_scientific_journal-2059	145	10	{	{	PUNCT
american_scientific_journal-2059	145	11	1α	1α	NUM
american_scientific_journal-2059	145	12	)	)	PUNCT
american_scientific_journal-2059	145	13	,	,	PUNCT
american_scientific_journal-2059	145	14	∉1α	∉1α	PUNCT
american_scientific_journal-2059	145	15	spre	spre	NOUN
american_scientific_journal-2059	145	16	-	-	NOUN
american_scientific_journal-2059	145	17	cl	cl	NOUN
american_scientific_journal-2059	145	18	(	(	PUNCT
american_scientific_journal-2059	145	19	}	}	PUNCT
american_scientific_journal-2059	145	20	{	{	PUNCT
american_scientific_journal-2059	145	21	2α	2α	NOUN
american_scientific_journal-2059	145	22	)	)	PUNCT
american_scientific_journal-2059	145	23	.	.	PUNCT
american_scientific_journal-2059	146	1	therefore	therefore	ADV
american_scientific_journal-2059	146	2	spre	spre	ADJ
american_scientific_journal-2059	146	3	-	-	NOUN
american_scientific_journal-2059	146	4	cl	cl	NOUN
american_scientific_journal-2059	146	5	(	(	PUNCT
american_scientific_journal-2059	146	6	}	}	PUNCT
american_scientific_journal-2059	146	7	{	{	PUNCT
american_scientific_journal-2059	146	8	1α	1α	NUM
american_scientific_journal-2059	146	9	)	)	PUNCT
american_scientific_journal-2059	146	10	≠	≠	PROPN
american_scientific_journal-2059	146	11	spre	spre	ADJ
american_scientific_journal-2059	146	12	-	-	NOUN
american_scientific_journal-2059	146	13	cl	cl	NOUN
american_scientific_journal-2059	146	14	(	(	PUNCT
american_scientific_journal-2059	146	15	}	}	PUNCT
american_scientific_journal-2059	146	16	{	{	PUNCT
american_scientific_journal-2059	146	17	2α	2α	NOUN
american_scientific_journal-2059	146	18	)	)	PUNCT
american_scientific_journal-2059	146	19	4.3	4.3	NUM
american_scientific_journal-2059	146	20	.	.	PUNCT
american_scientific_journal-2059	147	1	theorem	theorem	VERB
american_scientific_journal-2059	147	2	every	every	DET
american_scientific_journal-2059	147	3	soft	soft	ADJ
american_scientific_journal-2059	147	4	subspace	subspace	NOUN
american_scientific_journal-2059	147	5	of	of	ADP
american_scientific_journal-2059	147	6	spret	spret	NUM
american_scientific_journal-2059	147	7	space	space	NOUN
american_scientific_journal-2059	147	8	is	be	AUX
american_scientific_journal-2059	147	9	spret	spret	NUM
american_scientific_journal-2059	147	10	space	space	NOUN
american_scientific_journal-2059	147	11	.	.	PUNCT
american_scientific_journal-2059	148	1	proof	proof	NOUN
american_scientific_journal-2059	148	2	:	:	PUNCT
american_scientific_journal-2059	148	3	let	let	VERB
american_scientific_journal-2059	148	4	)	)	PUNCT
american_scientific_journal-2059	148	5	~,~	~,~	X
american_scientific_journal-2059	148	6	,	,	PUNCT
american_scientific_journal-2059	148	7	(	(	PUNCT
american_scientific_journal-2059	148	8	21	21	NUM
american_scientific_journal-2059	148	9	bbb	bbb	NOUN
american_scientific_journal-2059	148	10	fff	fff	PROPN
american_scientific_journal-2059	148	11	ττ	ττ	PROPN
american_scientific_journal-2059	148	12	be	be	AUX
american_scientific_journal-2059	148	13	a	a	DET
american_scientific_journal-2059	148	14	soft	soft	ADJ
american_scientific_journal-2059	148	15	sub	sub	NOUN
american_scientific_journal-2059	148	16	space	space	NOUN
american_scientific_journal-2059	148	17	of	of	ADP
american_scientific_journal-2059	148	18	spret	spret	NUM
american_scientific_journal-2059	148	19	space	space	NOUN
american_scientific_journal-2059	148	20	)	)	PUNCT
american_scientific_journal-2059	148	21	~,~	~,~	NUM
american_scientific_journal-2059	148	22	,	,	PUNCT
american_scientific_journal-2059	148	23	(	(	PUNCT
american_scientific_journal-2059	148	24	21	21	NUM
american_scientific_journal-2059	148	25	ττaf	ττaf	NOUN
american_scientific_journal-2059	148	26	.	.	PUNCT
american_scientific_journal-2059	149	1	to	to	PART
american_scientific_journal-2059	149	2	prove	prove	VERB
american_scientific_journal-2059	149	3	that	that	SCONJ
american_scientific_journal-2059	149	4	the	the	DET
american_scientific_journal-2059	149	5	soft	soft	ADJ
american_scientific_journal-2059	149	6	sub	sub	NOUN
american_scientific_journal-2059	149	7	space	space	NOUN
american_scientific_journal-2059	149	8	is	be	AUX
american_scientific_journal-2059	149	9	spret	spret	NUM
american_scientific_journal-2059	149	10	space	space	NOUN
american_scientific_journal-2059	149	11	,	,	PUNCT
american_scientific_journal-2059	149	12	let	let	VERB
american_scientific_journal-2059	149	13	bf∈21,ββ	bf∈21,ββ	NOUN
american_scientific_journal-2059	149	14	such	such	ADJ
american_scientific_journal-2059	149	15	that	that	SCONJ
american_scientific_journal-2059	149	16	21	21	NUM
american_scientific_journal-2059	149	17	ββ	ββ	NOUN
american_scientific_journal-2059	149	18	≠	≠	PROPN
american_scientific_journal-2059	149	19	.	.	PUNCT
american_scientific_journal-2059	150	1	since	since	SCONJ
american_scientific_journal-2059	150	2	ab	ab	PROPN
american_scientific_journal-2059	150	3	ff	ff	PROPN
american_scientific_journal-2059	150	4	⊆~	⊆~	PUNCT
american_scientific_journal-2059	150	5	then	then	ADV
american_scientific_journal-2059	150	6	af∈≠	af∈≠	PROPN
american_scientific_journal-2059	150	7	21	21	NUM
american_scientific_journal-2059	150	8	ββ	ββ	NOUN
american_scientific_journal-2059	150	9	and	and	CCONJ
american_scientific_journal-2059	150	10	)	)	PUNCT
american_scientific_journal-2059	150	11	~,~	~,~	NUM
american_scientific_journal-2059	150	12	,	,	PUNCT
american_scientific_journal-2059	150	13	(	(	PUNCT
american_scientific_journal-2059	150	14	21	21	NUM
american_scientific_journal-2059	150	15	ττaf	ττaf	NOUN
american_scientific_journal-2059	150	16	is	be	AUX
american_scientific_journal-2059	150	17	spret	spret	NUM
american_scientific_journal-2059	150	18	space	space	NOUN
american_scientific_journal-2059	150	19	,	,	PUNCT
american_scientific_journal-2059	150	20	then	then	ADV
american_scientific_journal-2059	150	21	there	there	PRON
american_scientific_journal-2059	150	22	is	be	VERB
american_scientific_journal-2059	150	23	a	a	DET
american_scientific_journal-2059	150	24	soft	soft	ADJ
american_scientific_journal-2059	150	25	pre	pre	ADJ
american_scientific_journal-2059	150	26	-	-	ADJ
american_scientific_journal-2059	150	27	open	open	ADJ
american_scientific_journal-2059	150	28	set	set	VERB
american_scientific_journal-2059	150	29	cf	cf	NOUN
american_scientific_journal-2059	150	30	in	in	ADP
american_scientific_journal-2059	150	31	af	af	PROPN
american_scientific_journal-2059	150	32	,	,	PUNCT
american_scientific_journal-2059	150	33	such	such	ADJ
american_scientific_journal-2059	150	34	that	that	SCONJ
american_scientific_journal-2059	150	35	cc	cc	PROPN
american_scientific_journal-2059	150	36	ff	ff	INTJ
american_scientific_journal-2059	150	37	∉∈	∉∈	PROPN
american_scientific_journal-2059	150	38	21	21	NUM
american_scientific_journal-2059	150	39	,	,	PUNCT
american_scientific_journal-2059	150	40	ββ	ββ	INTJ
american_scientific_journal-2059	150	41	.	.	PUNCT
american_scientific_journal-2059	151	1	so	so	ADV
american_scientific_journal-2059	151	2	bc	bc	PROPN
american_scientific_journal-2059	151	3	ff	ff	PROPN
american_scientific_journal-2059	151	4	∩~	∩~	PROPN
american_scientific_journal-2059	151	5	is	be	AUX
american_scientific_journal-2059	151	6	soft	soft	ADJ
american_scientific_journal-2059	151	7	pre	pre	ADJ
american_scientific_journal-2059	151	8	-	-	ADJ
american_scientific_journal-2059	151	9	open	open	ADJ
american_scientific_journal-2059	151	10	set	set	NOUN
american_scientific_journal-2059	151	11	in	in	ADP
american_scientific_journal-2059	151	12	bf	bf	NOUN
american_scientific_journal-2059	151	13	and	and	CCONJ
american_scientific_journal-2059	151	14	bc	bc	PROPN
american_scientific_journal-2059	151	15	ff	ff	NUM
american_scientific_journal-2059	151	16	∩∈	∩∈	NUM
american_scientific_journal-2059	151	17	~	~	SYM
american_scientific_journal-2059	151	18	1β	1β	NUM
american_scientific_journal-2059	151	19	and	and	CCONJ
american_scientific_journal-2059	151	20	bc	bc	PROPN
american_scientific_journal-2059	151	21	ff	ff	PROPN
american_scientific_journal-2059	151	22	∩∉	∩∉	PUNCT
american_scientific_journal-2059	151	23	~	~	PUNCT
american_scientific_journal-2059	151	24	2β	2β	NOUN
american_scientific_journal-2059	151	25	.	.	PUNCT
american_scientific_journal-2059	152	1	hence	hence	ADV
american_scientific_journal-2059	152	2	)	)	PUNCT
american_scientific_journal-2059	152	3	~,~	~,~	NUM
american_scientific_journal-2059	152	4	,	,	PUNCT
american_scientific_journal-2059	152	5	(	(	PUNCT
american_scientific_journal-2059	152	6	21	21	NUM
american_scientific_journal-2059	152	7	bbb	bbb	PROPN
american_scientific_journal-2059	152	8	fff	fff	PROPN
american_scientific_journal-2059	152	9	ττ	ττ	PROPN
american_scientific_journal-2059	152	10	is	be	AUX
american_scientific_journal-2059	152	11	spret	spret	NUM
american_scientific_journal-2059	152	12	space	space	NOUN
american_scientific_journal-2059	152	13	.	.	PUNCT
american_scientific_journal-2059	153	1	4.4	4.4	NUM
american_scientific_journal-2059	153	2	.	.	PUNCT
american_scientific_journal-2059	154	1	definition	definition	NOUN
american_scientific_journal-2059	154	2	let	let	VERB
american_scientific_journal-2059	154	3	)	)	PUNCT
american_scientific_journal-2059	154	4	~,~	~,~	X
american_scientific_journal-2059	154	5	,	,	PUNCT
american_scientific_journal-2059	154	6	(	(	PUNCT
american_scientific_journal-2059	154	7	21	21	NUM
american_scientific_journal-2059	154	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	154	9	is	be	AUX
american_scientific_journal-2059	154	10	soft	soft	ADJ
american_scientific_journal-2059	154	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	154	12	space	space	NOUN
american_scientific_journal-2059	154	13	,	,	PUNCT
american_scientific_journal-2059	154	14	then	then	ADV
american_scientific_journal-2059	154	15	)	)	PUNCT
american_scientific_journal-2059	154	16	~,~	~,~	NUM
american_scientific_journal-2059	154	17	,	,	PUNCT
american_scientific_journal-2059	154	18	(	(	PUNCT
american_scientific_journal-2059	154	19	21	21	NUM
american_scientific_journal-2059	154	20	ττaf	ττaf	NOUN
american_scientific_journal-2059	154	21	is	be	AUX
american_scientific_journal-2059	154	22	called	call	VERB
american_scientific_journal-2059	154	23	spre1	spre1	PROPN
american_scientific_journal-2059	154	24	t	t	PROPN
american_scientific_journal-2059	154	25	space	space	NOUN
american_scientific_journal-2059	154	26	if	if	SCONJ
american_scientific_journal-2059	154	27	and	and	CCONJ
american_scientific_journal-2059	154	28	only	only	ADV
american_scientific_journal-2059	154	29	if	if	SCONJ
american_scientific_journal-2059	154	30	for	for	ADP
american_scientific_journal-2059	154	31	all	all	DET
american_scientific_journal-2059	154	32	pair	pair	NOUN
american_scientific_journal-2059	154	33	of	of	ADP
american_scientific_journal-2059	154	34	soft	soft	ADJ
american_scientific_journal-2059	154	35	point	point	NOUN
american_scientific_journal-2059	154	36	af∈21,αα	af∈21,αα	NOUN
american_scientific_journal-2059	154	37	,	,	PUNCT
american_scientific_journal-2059	154	38	there	there	PRON
american_scientific_journal-2059	154	39	are	be	VERB
american_scientific_journal-2059	154	40	two	two	NUM
american_scientific_journal-2059	154	41	soft	soft	ADJ
american_scientific_journal-2059	154	42	pre	pre	ADJ
american_scientific_journal-2059	154	43	-	-	ADJ
american_scientific_journal-2059	154	44	open	open	ADJ
american_scientific_journal-2059	154	45	sets	set	NOUN
american_scientific_journal-2059	154	46	cb	cb	PROPN
american_scientific_journal-2059	154	47	ff	ff	PROPN
american_scientific_journal-2059	154	48	,	,	PUNCT
american_scientific_journal-2059	154	49	such	such	ADJ
american_scientific_journal-2059	154	50	that	that	DET
american_scientific_journal-2059	154	51	bf	bf	NOUN
american_scientific_journal-2059	154	52	contains	contain	VERB
american_scientific_journal-2059	154	53	1α	1α	NUM
american_scientific_journal-2059	154	54	but	but	CCONJ
american_scientific_journal-2059	154	55	not	not	PART
american_scientific_journal-2059	154	56	2α	2α	NOUN
american_scientific_journal-2059	154	57	and	and	CCONJ
american_scientific_journal-2059	154	58	cf	cf	NOUN
american_scientific_journal-2059	154	59	contains	contain	VERB
american_scientific_journal-2059	154	60	2α	2α	NOUN
american_scientific_journal-2059	154	61	but	but	CCONJ
american_scientific_journal-2059	154	62	not	not	PART
american_scientific_journal-2059	154	63	1α	1α	NUM
american_scientific_journal-2059	154	64	.	.	PUNCT
american_scientific_journal-2059	155	1	4.5	4.5	NUM
american_scientific_journal-2059	155	2	.	.	PUNCT
american_scientific_journal-2059	155	3	theorem	theorem	VERB
american_scientific_journal-2059	155	4	every	every	DET
american_scientific_journal-2059	155	5	soft	soft	ADJ
american_scientific_journal-2059	155	6	subspace	subspace	NOUN
american_scientific_journal-2059	155	7	of	of	ADP
american_scientific_journal-2059	155	8	spre1	spre1	PROPN
american_scientific_journal-2059	155	9	t	t	PROPN
american_scientific_journal-2059	155	10	space	space	NOUN
american_scientific_journal-2059	155	11	is	be	AUX
american_scientific_journal-2059	155	12	spre1	spre1	PROPN
american_scientific_journal-2059	155	13	t	t	NOUN
american_scientific_journal-2059	155	14	space	space	NOUN
american_scientific_journal-2059	155	15	.	.	PUNCT
american_scientific_journal-2059	156	1	proof	proof	NOUN
american_scientific_journal-2059	156	2	:	:	PUNCT
american_scientific_journal-2059	156	3	let	let	VERB
american_scientific_journal-2059	156	4	)	)	PUNCT
american_scientific_journal-2059	156	5	~,~	~,~	X
american_scientific_journal-2059	156	6	,	,	PUNCT
american_scientific_journal-2059	156	7	(	(	PUNCT
american_scientific_journal-2059	156	8	21	21	NUM
american_scientific_journal-2059	156	9	bbb	bbb	NOUN
american_scientific_journal-2059	156	10	fff	fff	PROPN
american_scientific_journal-2059	156	11	ττ	ττ	PROPN
american_scientific_journal-2059	156	12	be	be	AUX
american_scientific_journal-2059	156	13	a	a	DET
american_scientific_journal-2059	156	14	soft	soft	ADJ
american_scientific_journal-2059	156	15	sub	sub	NOUN
american_scientific_journal-2059	156	16	space	space	NOUN
american_scientific_journal-2059	156	17	of	of	ADP
american_scientific_journal-2059	156	18	spre1	spre1	PROPN
american_scientific_journal-2059	156	19	t	t	PROPN
american_scientific_journal-2059	156	20	space	space	NOUN
american_scientific_journal-2059	156	21	)	)	PUNCT
american_scientific_journal-2059	156	22	~,~	~,~	NUM
american_scientific_journal-2059	156	23	,	,	PUNCT
american_scientific_journal-2059	156	24	(	(	PUNCT
american_scientific_journal-2059	156	25	21	21	NUM
american_scientific_journal-2059	156	26	ττaf	ττaf	NOUN
american_scientific_journal-2059	156	27	.	.	PUNCT
american_scientific_journal-2059	157	1	to	to	PART
american_scientific_journal-2059	157	2	prove	prove	VERB
american_scientific_journal-2059	157	3	that	that	SCONJ
american_scientific_journal-2059	157	4	the	the	DET
american_scientific_journal-2059	157	5	soft	soft	ADJ
american_scientific_journal-2059	157	6	sub	sub	NOUN
american_scientific_journal-2059	157	7	space	space	NOUN
american_scientific_journal-2059	157	8	is	be	AUX
american_scientific_journal-2059	157	9	spre1	spre1	PROPN
american_scientific_journal-2059	157	10	t	t	PROPN
american_scientific_journal-2059	157	11	space	space	NOUN
american_scientific_journal-2059	157	12	,	,	PUNCT
american_scientific_journal-2059	157	13	let	let	VERB
american_scientific_journal-2059	157	14	bf∈21,ββ	bf∈21,ββ	NOUN
american_scientific_journal-2059	157	15	such	such	ADJ
american_scientific_journal-2059	157	16	that	that	SCONJ
american_scientific_journal-2059	157	17	21	21	NUM
american_scientific_journal-2059	157	18	ββ	ββ	NOUN
american_scientific_journal-2059	157	19	≠	≠	PROPN
american_scientific_journal-2059	157	20	.	.	PUNCT
american_scientific_journal-2059	158	1	since	since	SCONJ
american_scientific_journal-2059	158	2	ab	ab	PROPN
american_scientific_journal-2059	158	3	ff	ff	PROPN
american_scientific_journal-2059	158	4	⊆~	⊆~	PUNCT
american_scientific_journal-2059	158	5	then	then	ADV
american_scientific_journal-2059	158	6	af∈≠	af∈≠	PROPN
american_scientific_journal-2059	158	7	21	21	NUM
american_scientific_journal-2059	158	8	ββ	ββ	NOUN
american_scientific_journal-2059	158	9	and	and	CCONJ
american_scientific_journal-2059	158	10	)	)	PUNCT
american_scientific_journal-2059	158	11	~,~	~,~	NUM
american_scientific_journal-2059	158	12	,	,	PUNCT
american_scientific_journal-2059	158	13	(	(	PUNCT
american_scientific_journal-2059	158	14	21	21	NUM
american_scientific_journal-2059	158	15	ττaf	ττaf	NOUN
american_scientific_journal-2059	158	16	is	be	AUX
american_scientific_journal-2059	158	17	spret	spret	NUM
american_scientific_journal-2059	158	18	space	space	NOUN
american_scientific_journal-2059	158	19	,	,	PUNCT
american_scientific_journal-2059	158	20	then	then	ADV
american_scientific_journal-2059	158	21	there	there	PRON
american_scientific_journal-2059	158	22	exists	exist	VERB
american_scientific_journal-2059	158	23	two	two	NUM
american_scientific_journal-2059	158	24	soft	soft	ADJ
american_scientific_journal-2059	158	25	pre	pre	ADJ
american_scientific_journal-2059	158	26	-	-	ADJ
american_scientific_journal-2059	158	27	open	open	ADJ
american_scientific_journal-2059	158	28	set	set	VERB
american_scientific_journal-2059	158	29	cf	cf	NOUN
american_scientific_journal-2059	158	30	,	,	PUNCT
american_scientific_journal-2059	158	31	df	df	PROPN
american_scientific_journal-2059	158	32	in	in	ADP
american_scientific_journal-2059	158	33	af	af	PROPN
american_scientific_journal-2059	158	34	,	,	PUNCT
american_scientific_journal-2059	158	35	such	such	ADJ
american_scientific_journal-2059	158	36	that	that	SCONJ
american_scientific_journal-2059	158	37	cf∈1β	cf∈1β	PROPN
american_scientific_journal-2059	158	38	but	but	CCONJ
american_scientific_journal-2059	158	39	cf∉2β	cf∉2β	PROPN
american_scientific_journal-2059	158	40	and	and	CCONJ
american_scientific_journal-2059	158	41	df∈2β	df∈2β	PROPN
american_scientific_journal-2059	158	42	but	but	CCONJ
american_scientific_journal-2059	158	43	df∉1β	df∉1β	PROPN
american_scientific_journal-2059	158	44	.	.	PUNCT
american_scientific_journal-2059	159	1	then	then	ADV
american_scientific_journal-2059	159	2	we	we	PRON
american_scientific_journal-2059	159	3	obtain	obtain	VERB
american_scientific_journal-2059	159	4	two	two	NUM
american_scientific_journal-2059	159	5	soft	soft	ADJ
american_scientific_journal-2059	159	6	set	set	VERB
american_scientific_journal-2059	159	7	bddbcc	bddbcc	PROPN
american_scientific_journal-2059	159	8	ffffff	ffffff	PROPN
american_scientific_journal-2059	159	9	∩∩	∩∩	PROPN
american_scientific_journal-2059	160	1	~=,~=	~=,~=	NOUN
american_scientific_journal-2059	160	2	11	11	NUM
american_scientific_journal-2059	160	3	are	be	AUX
american_scientific_journal-2059	160	4	soft	soft	ADJ
american_scientific_journal-2059	160	5	pre	pre	ADJ
american_scientific_journal-2059	160	6	-	-	ADJ
american_scientific_journal-2059	160	7	open	open	ADJ
american_scientific_journal-2059	160	8	sets	set	NOUN
american_scientific_journal-2059	160	9	in	in	ADP
american_scientific_journal-2059	160	10	bf	bf	NOUN
american_scientific_journal-2059	160	11	,	,	PUNCT
american_scientific_journal-2059	160	12	we	we	PRON
american_scientific_journal-2059	160	13	have	have	VERB
american_scientific_journal-2059	160	14	11	11	NUM
american_scientific_journal-2059	160	15	cf∈β	cf∈β	NOUN
american_scientific_journal-2059	160	16	but	but	CCONJ
american_scientific_journal-2059	160	17	1212	1212	NUM
american_scientific_journal-2059	160	18	;	;	PUNCT
american_scientific_journal-2059	160	19	dc	dc	PROPN
american_scientific_journal-2059	160	20	ff	ff	PROPN
american_scientific_journal-2059	160	21	∈∉	∈∉	PROPN
american_scientific_journal-2059	160	22	ββ	ββ	PROPN
american_scientific_journal-2059	160	23	,	,	PUNCT
american_scientific_journal-2059	160	24	but	but	CCONJ
american_scientific_journal-2059	160	25	11	11	NUM
american_scientific_journal-2059	160	26	df∈β	df∈β	NOUN
american_scientific_journal-2059	160	27	.	.	PUNCT
american_scientific_journal-2059	161	1	hence	hence	ADV
american_scientific_journal-2059	161	2	)	)	PUNCT
american_scientific_journal-2059	161	3	~,~	~,~	NUM
american_scientific_journal-2059	161	4	,	,	PUNCT
american_scientific_journal-2059	161	5	(	(	PUNCT
american_scientific_journal-2059	161	6	21	21	NUM
american_scientific_journal-2059	161	7	bbb	bbb	PROPN
american_scientific_journal-2059	161	8	fff	fff	PROPN
american_scientific_journal-2059	161	9	ττ	ττ	PROPN
american_scientific_journal-2059	161	10	is	be	AUX
american_scientific_journal-2059	161	11	spre1	spre1	PROPN
american_scientific_journal-2059	161	12	t	t	PROPN
american_scientific_journal-2059	161	13	space	space	NOUN
american_scientific_journal-2059	161	14	.	.	PUNCT
american_scientific_journal-2059	162	1	american	american	ADJ
american_scientific_journal-2059	162	2	scientific	scientific	ADJ
american_scientific_journal-2059	162	3	research	research	PROPN
american_scientific_journal-2059	162	4	journal	journal	NOUN
american_scientific_journal-2059	162	5	for	for	ADP
american_scientific_journal-2059	162	6	engineering	engineering	NOUN
american_scientific_journal-2059	162	7	,	,	PUNCT
american_scientific_journal-2059	162	8	technology	technology	NOUN
american_scientific_journal-2059	162	9	,	,	PUNCT
american_scientific_journal-2059	162	10	and	and	CCONJ
american_scientific_journal-2059	162	11	sciences	science	NOUN
american_scientific_journal-2059	162	12	(	(	PUNCT
american_scientific_journal-2059	162	13	asrjets	asrjet	NOUN
american_scientific_journal-2059	162	14	)	)	PUNCT
american_scientific_journal-2059	162	15	(	(	PUNCT
american_scientific_journal-2059	162	16	2016	2016	NUM
american_scientific_journal-2059	162	17	)	)	PUNCT
american_scientific_journal-2059	162	18	volume	volume	NOUN
american_scientific_journal-2059	162	19	26	26	NUM
american_scientific_journal-2059	162	20	,	,	PUNCT
american_scientific_journal-2059	162	21	no	no	DET
american_scientific_journal-2059	162	22	4	4	NUM
american_scientific_journal-2059	162	23	,	,	PUNCT
american_scientific_journal-2059	162	24	pp	pp	ADV
american_scientific_journal-2059	162	25	42	42	NUM
american_scientific_journal-2059	162	26	-	-	SYM
american_scientific_journal-2059	162	27	53	53	NUM
american_scientific_journal-2059	162	28	52	52	NUM
american_scientific_journal-2059	162	29	4.6	4.6	NUM
american_scientific_journal-2059	162	30	.	.	PUNCT
american_scientific_journal-2059	163	1	theorem	theorem	VERB
american_scientific_journal-2059	163	2	if	if	SCONJ
american_scientific_journal-2059	163	3	every	every	DET
american_scientific_journal-2059	163	4	singleton	singleton	NOUN
american_scientific_journal-2059	163	5	soft	soft	ADJ
american_scientific_journal-2059	163	6	subset	subset	NOUN
american_scientific_journal-2059	163	7	of	of	ADP
american_scientific_journal-2059	163	8	soft	soft	ADJ
american_scientific_journal-2059	163	9	bitopological	bitopological	ADJ
american_scientific_journal-2059	163	10	space	space	NOUN
american_scientific_journal-2059	163	11	)	)	PUNCT
american_scientific_journal-2059	163	12	~,~	~,~	NUM
american_scientific_journal-2059	163	13	,	,	PUNCT
american_scientific_journal-2059	163	14	(	(	PUNCT
american_scientific_journal-2059	163	15	21	21	NUM
american_scientific_journal-2059	163	16	ττaf	ττaf	NOUN
american_scientific_journal-2059	163	17	is	be	AUX
american_scientific_journal-2059	163	18	soft	soft	ADJ
american_scientific_journal-2059	163	19	pre	pre	ADJ
american_scientific_journal-2059	163	20	-	-	ADJ
american_scientific_journal-2059	163	21	closed	closed	ADJ
american_scientific_journal-2059	163	22	,	,	PUNCT
american_scientific_journal-2059	163	23	then	then	ADV
american_scientific_journal-2059	163	24	)	)	PUNCT
american_scientific_journal-2059	163	25	~,~	~,~	NUM
american_scientific_journal-2059	163	26	,	,	PUNCT
american_scientific_journal-2059	163	27	(	(	PUNCT
american_scientific_journal-2059	163	28	21	21	NUM
american_scientific_journal-2059	163	29	ττaf	ττaf	NOUN
american_scientific_journal-2059	163	30	is	be	AUX
american_scientific_journal-2059	163	31	spre1	spre1	PROPN
american_scientific_journal-2059	163	32	t	t	NOUN
american_scientific_journal-2059	163	33	space	space	NOUN
american_scientific_journal-2059	163	34	.	.	PUNCT
american_scientific_journal-2059	164	1	proof	proof	NOUN
american_scientific_journal-2059	164	2	:	:	PUNCT
american_scientific_journal-2059	164	3	-this	-this	PROPN
american_scientific_journal-2059	164	4	is	be	AUX
american_scientific_journal-2059	164	5	clearly	clearly	ADV
american_scientific_journal-2059	164	6	seen	see	VERB
american_scientific_journal-2059	164	7	.	.	PUNCT
american_scientific_journal-2059	165	1	4.7	4.7	X
american_scientific_journal-2059	165	2	.	.	PUNCT
american_scientific_journal-2059	165	3	theorem	theorem	VERB
american_scientific_journal-2059	165	4	a	a	DET
american_scientific_journal-2059	165	5	soft	soft	ADJ
american_scientific_journal-2059	165	6	bitopological	bitopological	ADJ
american_scientific_journal-2059	165	7	space	space	NOUN
american_scientific_journal-2059	165	8	)	)	PUNCT
american_scientific_journal-2059	165	9	~,~	~,~	NUM
american_scientific_journal-2059	165	10	,	,	PUNCT
american_scientific_journal-2059	165	11	(	(	PUNCT
american_scientific_journal-2059	165	12	21	21	NUM
american_scientific_journal-2059	165	13	ττaf	ττaf	NOUN
american_scientific_journal-2059	165	14	is	be	AUX
american_scientific_journal-2059	165	15	a	a	DET
american_scientific_journal-2059	165	16	spre1	spre1	PROPN
american_scientific_journal-2059	165	17	t	t	NOUN
american_scientific_journal-2059	165	18	space	space	NOUN
american_scientific_journal-2059	166	1	if	if	SCONJ
american_scientific_journal-2059	166	2	and	and	CCONJ
american_scientific_journal-2059	166	3	only	only	ADV
american_scientific_journal-2059	166	4	if	if	SCONJ
american_scientific_journal-2059	166	5	spre	spre	NOUN
american_scientific_journal-2059	166	6	-	-	NOUN
american_scientific_journal-2059	166	7	cl	cl	NOUN
american_scientific_journal-2059	166	8	φα	φα	NOUN
american_scientific_journal-2059	166	9	=	=	NOUN
american_scientific_journal-2059	166	10	}	}	PUNCT
american_scientific_journal-2059	166	11	)	)	PUNCT
american_scientific_journal-2059	166	12	(	(	PUNCT
american_scientific_journal-2059	166	13	{	{	PUNCT
american_scientific_journal-2059	166	14	,	,	PUNCT
american_scientific_journal-2059	166	15	for	for	ADP
american_scientific_journal-2059	166	16	each	each	DET
american_scientific_journal-2059	166	17	af∈α	af∈α	PROPN
american_scientific_journal-2059	166	18	.	.	PUNCT
american_scientific_journal-2059	167	1	proof	proof	NOUN
american_scientific_journal-2059	167	2	:	:	PUNCT
american_scientific_journal-2059	167	3	-this	-this	PRON
american_scientific_journal-2059	167	4	is	be	AUX
american_scientific_journal-2059	167	5	clearly	clearly	ADV
american_scientific_journal-2059	167	6	by	by	ADP
american_scientific_journal-2059	167	7	using	use	VERB
american_scientific_journal-2059	167	8	prove	prove	ADJ
american_scientific_journal-2059	167	9	contradiction	contradiction	NOUN
american_scientific_journal-2059	167	10	.	.	PUNCT
american_scientific_journal-2059	168	1	4.8	4.8	NUM
american_scientific_journal-2059	168	2	.	.	PUNCT
american_scientific_journal-2059	169	1	definition	definition	NOUN
american_scientific_journal-2059	169	2	let	let	VERB
american_scientific_journal-2059	169	3	)	)	PUNCT
american_scientific_journal-2059	169	4	~,~	~,~	X
american_scientific_journal-2059	169	5	,	,	PUNCT
american_scientific_journal-2059	169	6	(	(	PUNCT
american_scientific_journal-2059	169	7	21	21	NUM
american_scientific_journal-2059	169	8	ττaf	ττaf	NOUN
american_scientific_journal-2059	169	9	is	be	AUX
american_scientific_journal-2059	169	10	soft	soft	ADJ
american_scientific_journal-2059	169	11	bitopological	bitopological	ADJ
american_scientific_journal-2059	169	12	space	space	NOUN
american_scientific_journal-2059	169	13	,	,	PUNCT
american_scientific_journal-2059	169	14	then	then	ADV
american_scientific_journal-2059	169	15	)	)	PUNCT
american_scientific_journal-2059	169	16	~,~	~,~	NUM
american_scientific_journal-2059	169	17	,	,	PUNCT
american_scientific_journal-2059	169	18	(	(	PUNCT
american_scientific_journal-2059	169	19	21	21	NUM
american_scientific_journal-2059	169	20	ττaf	ττaf	NOUN
american_scientific_journal-2059	169	21	is	be	AUX
american_scientific_journal-2059	169	22	called	call	VERB
american_scientific_journal-2059	169	23	spre2	spre2	PROPN
american_scientific_journal-2059	169	24	t	t	NOUN
american_scientific_journal-2059	169	25	space	space	NOUN
american_scientific_journal-2059	169	26	(	(	PUNCT
american_scientific_journal-2059	169	27	spre	spre	ADJ
american_scientific_journal-2059	169	28	-	-	ADJ
american_scientific_journal-2059	169	29	hausdorf	hausdorf	ADJ
american_scientific_journal-2059	169	30	)	)	PUNCT
american_scientific_journal-2059	170	1	if	if	SCONJ
american_scientific_journal-2059	170	2	and	and	CCONJ
american_scientific_journal-2059	170	3	only	only	ADV
american_scientific_journal-2059	170	4	if	if	SCONJ
american_scientific_journal-2059	170	5	for	for	ADP
american_scientific_journal-2059	170	6	each	each	DET
american_scientific_journal-2059	170	7	pair	pair	NOUN
american_scientific_journal-2059	170	8	of	of	ADP
american_scientific_journal-2059	170	9	distinct	distinct	ADJ
american_scientific_journal-2059	170	10	soft	soft	ADJ
american_scientific_journal-2059	170	11	point	point	NOUN
american_scientific_journal-2059	170	12	af∈21,αα	af∈21,αα	NOUN
american_scientific_journal-2059	170	13	,	,	PUNCT
american_scientific_journal-2059	170	14	there	there	PRON
american_scientific_journal-2059	170	15	exists	exist	VERB
american_scientific_journal-2059	170	16	two	two	NUM
american_scientific_journal-2059	170	17	soft	soft	ADJ
american_scientific_journal-2059	170	18	pre	pre	ADJ
american_scientific_journal-2059	170	19	-	-	ADJ
american_scientific_journal-2059	170	20	open	open	ADJ
american_scientific_journal-2059	170	21	sets	set	NOUN
american_scientific_journal-2059	170	22	cb	cb	PROPN
american_scientific_journal-2059	170	23	ff	ff	PROPN
american_scientific_journal-2059	170	24	,	,	PUNCT
american_scientific_journal-2059	170	25	in	in	ADP
american_scientific_journal-2059	170	26	af	af	PROPN
american_scientific_journal-2059	170	27	such	such	ADJ
american_scientific_journal-2059	170	28	that	that	SCONJ
american_scientific_journal-2059	170	29	cb	cb	PROPN
american_scientific_journal-2059	170	30	ff	ff	PROPN
american_scientific_journal-2059	170	31	∈∈	∈∈	NOUN
american_scientific_journal-2059	170	32	21	21	NUM
american_scientific_journal-2059	170	33	,	,	PUNCT
american_scientific_journal-2059	170	34	αα	αα	ADP
american_scientific_journal-2059	170	35	and	and	CCONJ
american_scientific_journal-2059	170	36	φ=~	φ=~	NOUN
american_scientific_journal-2059	170	37	cb	cb	PROPN
american_scientific_journal-2059	170	38	ff	ff	PROPN
american_scientific_journal-2059	170	39	∩	∩	PROPN
american_scientific_journal-2059	170	40	.	.	PUNCT
american_scientific_journal-2059	171	1	4.9	4.9	NUM
american_scientific_journal-2059	171	2	.	.	PUNCT
american_scientific_journal-2059	171	3	theorem	theorem	VERB
american_scientific_journal-2059	171	4	each	each	DET
american_scientific_journal-2059	171	5	soft	soft	ADJ
american_scientific_journal-2059	171	6	subspace	subspace	NOUN
american_scientific_journal-2059	171	7	of	of	ADP
american_scientific_journal-2059	171	8	spre2	spre2	PROPN
american_scientific_journal-2059	171	9	t	t	NOUN
american_scientific_journal-2059	171	10	space	space	NOUN
american_scientific_journal-2059	171	11	is	be	AUX
american_scientific_journal-2059	171	12	spre2	spre2	PROPN
american_scientific_journal-2059	171	13	t	t	NOUN
american_scientific_journal-2059	171	14	space	space	NOUN
american_scientific_journal-2059	171	15	.	.	PUNCT
american_scientific_journal-2059	172	1	proof	proof	NOUN
american_scientific_journal-2059	172	2	:	:	PUNCT
american_scientific_journal-2059	172	3	let	let	VERB
american_scientific_journal-2059	172	4	)	)	PUNCT
american_scientific_journal-2059	172	5	~,~	~,~	X
american_scientific_journal-2059	172	6	,	,	PUNCT
american_scientific_journal-2059	172	7	(	(	PUNCT
american_scientific_journal-2059	172	8	21	21	NUM
american_scientific_journal-2059	172	9	bbb	bbb	NOUN
american_scientific_journal-2059	172	10	fff	fff	PROPN
american_scientific_journal-2059	172	11	ττ	ττ	PROPN
american_scientific_journal-2059	172	12	be	be	AUX
american_scientific_journal-2059	172	13	a	a	DET
american_scientific_journal-2059	172	14	soft	soft	ADJ
american_scientific_journal-2059	172	15	sub	sub	NOUN
american_scientific_journal-2059	172	16	space	space	NOUN
american_scientific_journal-2059	172	17	of	of	ADP
american_scientific_journal-2059	172	18	spre2	spre2	PROPN
american_scientific_journal-2059	172	19	t	t	NOUN
american_scientific_journal-2059	172	20	space	space	NOUN
american_scientific_journal-2059	172	21	)	)	PUNCT
american_scientific_journal-2059	172	22	~,~	~,~	NUM
american_scientific_journal-2059	172	23	,	,	PUNCT
american_scientific_journal-2059	172	24	(	(	PUNCT
american_scientific_journal-2059	172	25	21	21	NUM
american_scientific_journal-2059	172	26	ττaf	ττaf	ADJ
american_scientific_journal-2059	172	27	and	and	CCONJ
american_scientific_journal-2059	172	28	let	let	VERB
american_scientific_journal-2059	172	29	φ≠bf	φ≠bf	PRON
american_scientific_journal-2059	172	30	be	be	AUX
american_scientific_journal-2059	172	31	a	a	DET
american_scientific_journal-2059	172	32	soft	soft	ADJ
american_scientific_journal-2059	172	33	subset	subset	NOUN
american_scientific_journal-2059	172	34	of	of	ADP
american_scientific_journal-2059	172	35	af	af	PROPN
american_scientific_journal-2059	172	36	,	,	PUNCT
american_scientific_journal-2059	172	37	and	and	CCONJ
american_scientific_journal-2059	172	38	bf∈≠	bf∈≠	PROPN
american_scientific_journal-2059	172	39	21	21	NUM
american_scientific_journal-2059	172	40	αα	αα	VERB
american_scientific_journal-2059	172	41	then	then	ADV
american_scientific_journal-2059	172	42	af∈21,αα	af∈21,αα	NOUN
american_scientific_journal-2059	172	43	,	,	PUNCT
american_scientific_journal-2059	172	44	since	since	SCONJ
american_scientific_journal-2059	172	45	)	)	PUNCT
american_scientific_journal-2059	172	46	~,~	~,~	NUM
american_scientific_journal-2059	172	47	,	,	PUNCT
american_scientific_journal-2059	172	48	(	(	PUNCT
american_scientific_journal-2059	172	49	21	21	NUM
american_scientific_journal-2059	172	50	ττaf	ττaf	NOUN
american_scientific_journal-2059	172	51	is	be	AUX
american_scientific_journal-2059	172	52	spre2	spre2	PROPN
american_scientific_journal-2059	172	53	t	t	NOUN
american_scientific_journal-2059	172	54	space	space	NOUN
american_scientific_journal-2059	172	55	,	,	PUNCT
american_scientific_journal-2059	172	56	there	there	PRON
american_scientific_journal-2059	172	57	exists	exist	VERB
american_scientific_journal-2059	172	58	two	two	NUM
american_scientific_journal-2059	172	59	soft	soft	ADJ
american_scientific_journal-2059	172	60	preopen	preopen	ADJ
american_scientific_journal-2059	172	61	sets	set	NOUN
american_scientific_journal-2059	172	62	cd	cd	PROPN
american_scientific_journal-2059	172	63	ff	ff	INTJ
american_scientific_journal-2059	172	64	,	,	PUNCT
american_scientific_journal-2059	172	65	in	in	ADP
american_scientific_journal-2059	172	66	af	af	PROPN
american_scientific_journal-2059	172	67	such	such	ADJ
american_scientific_journal-2059	172	68	that	that	DET
american_scientific_journal-2059	172	69	cd	cd	PROPN
american_scientific_journal-2059	172	70	ff	ff	NOUN
american_scientific_journal-2059	172	71	∈∈	∈∈	ADV
american_scientific_journal-2059	172	72	21	21	NUM
american_scientific_journal-2059	172	73	,	,	PUNCT
american_scientific_journal-2059	172	74	αα	αα	ADP
american_scientific_journal-2059	172	75	and	and	CCONJ
american_scientific_journal-2059	172	76	φ=~	φ=~	ADJ
american_scientific_journal-2059	172	77	cd	cd	NOUN
american_scientific_journal-2059	172	78	ff	ff	PROPN
american_scientific_journal-2059	172	79	∩	∩	NOUN
american_scientific_journal-2059	172	80	.	.	PUNCT
american_scientific_journal-2059	173	1	so	so	ADV
american_scientific_journal-2059	173	2	bcbd	bcbd	PROPN
american_scientific_journal-2059	173	3	ffff	ffff	PROPN
american_scientific_journal-2059	173	4	∩∩	∩∩	PROPN
american_scientific_journal-2059	173	5	~,~	~,~	NOUN
american_scientific_journal-2059	173	6	are	be	AUX
american_scientific_journal-2059	173	7	soft	soft	ADJ
american_scientific_journal-2059	173	8	pre	pre	ADJ
american_scientific_journal-2059	173	9	-	-	ADJ
american_scientific_journal-2059	173	10	open	open	ADJ
american_scientific_journal-2059	173	11	sets	set	NOUN
american_scientific_journal-2059	173	12	in	in	ADP
american_scientific_journal-2059	173	13	bf	bf	NOUN
american_scientific_journal-2059	173	14	and	and	CCONJ
american_scientific_journal-2059	173	15	bcbd	bcbd	PROPN
american_scientific_journal-2059	173	16	ffff	ffff	PROPN
american_scientific_journal-2059	173	17	∩∈∩∈	∩∈∩∈	PROPN
american_scientific_journal-2059	174	1	~,~	~,~	NUM
american_scientific_journal-2059	174	2	21	21	NUM
american_scientific_journal-2059	174	3	αα	αα	NOUN
american_scientific_journal-2059	174	4	;	;	PUNCT
american_scientific_journal-2059	174	5	and	and	CCONJ
american_scientific_journal-2059	174	6	φ=~)~(=)~(~)~	φ=~)~(=)~(~)~	NUM
american_scientific_journal-2059	174	7	(	(	PUNCT
american_scientific_journal-2059	174	8	bcdbcbd	bcdbcbd	X
american_scientific_journal-2059	174	9	fffffff	fffffff	PROPN
american_scientific_journal-2059	174	10	∩∩∩∩∩	∩∩∩∩∩	PROPN
american_scientific_journal-2059	174	11	.	.	PUNCT
american_scientific_journal-2059	175	1	hence	hence	ADV
american_scientific_journal-2059	175	2	)	)	PUNCT
american_scientific_journal-2059	175	3	~,~	~,~	NUM
american_scientific_journal-2059	175	4	,	,	PUNCT
american_scientific_journal-2059	175	5	(	(	PUNCT
american_scientific_journal-2059	175	6	21	21	NUM
american_scientific_journal-2059	175	7	bbb	bbb	PROPN
american_scientific_journal-2059	175	8	fff	fff	PROPN
american_scientific_journal-2059	175	9	ττ	ττ	PROPN
american_scientific_journal-2059	175	10	is	be	AUX
american_scientific_journal-2059	175	11	a	a	DET
american_scientific_journal-2059	175	12	spre2	spre2	PROPN
american_scientific_journal-2059	175	13	t	t	NOUN
american_scientific_journal-2059	175	14	space	space	NOUN
american_scientific_journal-2059	175	15	.	.	PUNCT
american_scientific_journal-2059	176	1	4.10	4.10	NUM
american_scientific_journal-2059	176	2	.	.	PUNCT
american_scientific_journal-2059	176	3	theorem	theorem	VERB
american_scientific_journal-2059	176	4	each	each	DET
american_scientific_journal-2059	176	5	singleton	singleton	PROPN
american_scientific_journal-2059	176	6	soft	soft	ADJ
american_scientific_journal-2059	176	7	subset	subset	NOUN
american_scientific_journal-2059	176	8	of	of	ADP
american_scientific_journal-2059	176	9	spre2	spre2	PROPN
american_scientific_journal-2059	176	10	t	t	NOUN
american_scientific_journal-2059	176	11	space	space	NOUN
american_scientific_journal-2059	176	12	is	be	AUX
american_scientific_journal-2059	176	13	a	a	DET
american_scientific_journal-2059	176	14	soft	soft	ADJ
american_scientific_journal-2059	176	15	pre	pre	ADJ
american_scientific_journal-2059	176	16	-	-	ADJ
american_scientific_journal-2059	176	17	closed	closed	ADJ
american_scientific_journal-2059	176	18	.	.	PUNCT
american_scientific_journal-2059	177	1	proof	proof	NOUN
american_scientific_journal-2059	177	2	:	:	PUNCT
american_scientific_journal-2059	177	3	-this	-this	PROPN
american_scientific_journal-2059	177	4	is	be	AUX
american_scientific_journal-2059	177	5	clearly	clearly	ADV
american_scientific_journal-2059	177	6	seen	see	VERB
american_scientific_journal-2059	177	7	.	.	PUNCT
american_scientific_journal-2059	178	1	american	american	ADJ
american_scientific_journal-2059	178	2	scientific	scientific	ADJ
american_scientific_journal-2059	178	3	research	research	PROPN
american_scientific_journal-2059	178	4	journal	journal	NOUN
american_scientific_journal-2059	178	5	for	for	ADP
american_scientific_journal-2059	178	6	engineering	engineering	NOUN
american_scientific_journal-2059	178	7	,	,	PUNCT
american_scientific_journal-2059	178	8	technology	technology	NOUN
american_scientific_journal-2059	178	9	,	,	PUNCT
american_scientific_journal-2059	178	10	and	and	CCONJ
american_scientific_journal-2059	178	11	sciences	science	NOUN
american_scientific_journal-2059	178	12	(	(	PUNCT
american_scientific_journal-2059	178	13	asrjets	asrjet	NOUN
american_scientific_journal-2059	178	14	)	)	PUNCT
american_scientific_journal-2059	178	15	(	(	PUNCT
american_scientific_journal-2059	178	16	2016	2016	NUM
american_scientific_journal-2059	178	17	)	)	PUNCT
american_scientific_journal-2059	178	18	volume	volume	NOUN
american_scientific_journal-2059	178	19	26	26	NUM
american_scientific_journal-2059	178	20	,	,	PUNCT
american_scientific_journal-2059	178	21	no	no	DET
american_scientific_journal-2059	178	22	4	4	NUM
american_scientific_journal-2059	178	23	,	,	PUNCT
american_scientific_journal-2059	178	24	pp	pp	ADV
american_scientific_journal-2059	178	25	42	42	NUM
american_scientific_journal-2059	178	26	-	-	SYM
american_scientific_journal-2059	178	27	53	53	NUM
american_scientific_journal-2059	178	28	53	53	NUM
american_scientific_journal-2059	178	29	5	5	NUM
american_scientific_journal-2059	178	30	.	.	PUNCT
american_scientific_journal-2059	178	31	conclusion	conclusion	NOUN
american_scientific_journal-2059	178	32	in	in	ADP
american_scientific_journal-2059	178	33	the	the	DET
american_scientific_journal-2059	178	34	conclusion	conclusion	NOUN
american_scientific_journal-2059	178	35	of	of	ADP
american_scientific_journal-2059	178	36	a	a	DET
american_scientific_journal-2059	178	37	work	work	NOUN
american_scientific_journal-2059	178	38	paper	paper	NOUN
american_scientific_journal-2059	178	39	,	,	PUNCT
american_scientific_journal-2059	178	40	many	many	ADJ
american_scientific_journal-2059	178	41	of	of	ADP
american_scientific_journal-2059	178	42	the	the	DET
american_scientific_journal-2059	178	43	basic	basic	ADJ
american_scientific_journal-2059	178	44	concepts	concept	NOUN
american_scientific_journal-2059	178	45	on	on	ADP
american_scientific_journal-2059	178	46	soft	soft	ADJ
american_scientific_journal-2059	178	47	bitopological	bitopological	ADJ
american_scientific_journal-2059	178	48	space	space	NOUN
american_scientific_journal-2059	178	49	,	,	PUNCT
american_scientific_journal-2059	178	50	introduced	introduce	VERB
american_scientific_journal-2059	178	51	soft	soft	ADJ
american_scientific_journal-2059	178	52	bitopology	bitopology	NOUN
american_scientific_journal-2059	178	53	.	.	PUNCT
american_scientific_journal-2059	179	1	furthermore	furthermore	ADV
american_scientific_journal-2059	179	2	,	,	PUNCT
american_scientific_journal-2059	179	3	introduced	introduce	VERB
american_scientific_journal-2059	179	4	relative	relative	ADJ
american_scientific_journal-2059	179	5	soft	soft	ADJ
american_scientific_journal-2059	179	6	bitopological	bitopological	ADJ
american_scientific_journal-2059	179	7	space	space	NOUN
american_scientific_journal-2059	179	8	,	,	PUNCT
american_scientific_journal-2059	179	9	soft	soft	ADJ
american_scientific_journal-2059	179	10	pre	pre	ADJ
american_scientific_journal-2059	179	11	-	-	ADJ
american_scientific_journal-2059	179	12	open	open	ADJ
american_scientific_journal-2059	179	13	set	set	NOUN
american_scientific_journal-2059	179	14	and	and	CCONJ
american_scientific_journal-2059	179	15	some	some	DET
american_scientific_journal-2059	179	16	definitions	definition	NOUN
american_scientific_journal-2059	179	17	on	on	ADP
american_scientific_journal-2059	179	18	bitopology	bitopology	NOUN
american_scientific_journal-2059	179	19	by"soft	by"soft	ADV
american_scientific_journal-2059	179	20	pre	pre	ADJ
american_scientific_journal-2059	179	21	-	-	ADJ
american_scientific_journal-2059	179	22	open	open	ADJ
american_scientific_journal-2059	179	23	set	set	NOUN
american_scientific_journal-2059	179	24	as	as	ADP
american_scientific_journal-2059	179	25	(	(	PUNCT
american_scientific_journal-2059	179	26	soft	soft	ADJ
american_scientific_journal-2059	179	27	pre	pre	ADJ
american_scientific_journal-2059	179	28	-	-	ADJ
american_scientific_journal-2059	179	29	closed	closed	ADJ
american_scientific_journal-2059	179	30	,	,	PUNCT
american_scientific_journal-2059	179	31	soft	soft	ADJ
american_scientific_journal-2059	179	32	pre	pre	ADJ
american_scientific_journal-2059	179	33	-	-	ADJ
american_scientific_journal-2059	179	34	neighborhood	neighborhood	ADJ
american_scientific_journal-2059	179	35	,	,	PUNCT
american_scientific_journal-2059	179	36	soft	soft	ADJ
american_scientific_journal-2059	179	37	pre	pre	ADJ
american_scientific_journal-2059	179	38	-	-	ADJ
american_scientific_journal-2059	179	39	interior	interior	ADJ
american_scientific_journal-2059	179	40	,	,	PUNCT
american_scientific_journal-2059	179	41	soft	soft	ADJ
american_scientific_journal-2059	179	42	pre	pre	ADJ
american_scientific_journal-2059	179	43	-	-	ADJ
american_scientific_journal-2059	179	44	limit	limit	ADJ
american_scientific_journal-2059	179	45	point	point	NOUN
american_scientific_journal-2059	179	46	and	and	CCONJ
american_scientific_journal-2059	179	47	soft	soft	ADJ
american_scientific_journal-2059	179	48	pre	pre	ADJ
american_scientific_journal-2059	179	49	-	-	ADJ
american_scientific_journal-2059	179	50	closure	closure	ADJ
american_scientific_journal-2059	179	51	)	)	PUNCT
american_scientific_journal-2059	179	52	these"definitions	these"definition	NOUN
american_scientific_journal-2059	179	53	using	use	VERB
american_scientific_journal-2059	179	54	in	in	ADP
american_scientific_journal-2059	179	55	other	other	ADJ
american_scientific_journal-2059	179	56	sections	section	NOUN
american_scientific_journal-2059	179	57	from	from	ADP
american_scientific_journal-2059	179	58	the	the	DET
american_scientific_journal-2059	179	59	work	work	NOUN
american_scientific_journal-2059	179	60	and	and	CCONJ
american_scientific_journal-2059	179	61	introduce	introduce	VERB
american_scientific_journal-2059	179	62	some	some	DET
american_scientific_journal-2059	179	63	soft	soft	ADJ
american_scientific_journal-2059	179	64	pre	pre	NOUN
american_scientific_journal-2059	179	65	separation	separation	NOUN
american_scientific_journal-2059	179	66	axioms	axiom	NOUN
american_scientific_journal-2059	179	67	and	and	CCONJ
american_scientific_journal-2059	179	68	studied	study	VERB
american_scientific_journal-2059	179	69	properties	property	NOUN
american_scientific_journal-2059	179	70	on	on	ADP
american_scientific_journal-2059	179	71	soft	soft	ADJ
american_scientific_journal-2059	179	72	bitopological	bitopological	ADJ
american_scientific_journal-2059	179	73	space	space	NOUN
american_scientific_journal-2059	179	74	with	with	ADP
american_scientific_journal-2059	179	75	some	some	DET
american_scientific_journal-2059	179	76	important	important	ADJ
american_scientific_journal-2059	179	77	results	result	NOUN
american_scientific_journal-2059	179	78	,	,	PUNCT
american_scientific_journal-2059	179	79	one	one	PRON
american_scientific_journal-2059	179	80	could	could	AUX
american_scientific_journal-2059	179	81	study	study	VERB
american_scientific_journal-2059	179	82	the	the	DET
american_scientific_journal-2059	179	83	soft	soft	ADJ
american_scientific_journal-2059	179	84	ideal	ideal	ADJ
american_scientific_journal-2059	179	85	bitopology	bitopology	NOUN
american_scientific_journal-2059	179	86	and	and	CCONJ
american_scientific_journal-2059	179	87	get	get	VERB
american_scientific_journal-2059	179	88	some	some	DET
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american_scientific_journal-2059	179	92	.	.	PUNCT
american_scientific_journal-2059	180	1	references	reference	NOUN
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american_scientific_journal-2059	180	3	1	1	NUM
american_scientific_journal-2059	180	4	]	]	PUNCT
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american_scientific_journal-2059	180	8	,	,	PUNCT
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american_scientific_journal-2059	180	18	,	,	PUNCT
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american_scientific_journal-2059	180	20	107	107	NUM
american_scientific_journal-2059	180	21	,	,	PUNCT
american_scientific_journal-2059	180	22	no	no	INTJ
american_scientific_journal-2059	180	23	.	.	NOUN
american_scientific_journal-2059	180	24	7	7	NUM
american_scientific_journal-2059	180	25	,	,	PUNCT
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american_scientific_journal-2059	180	27	2014	2014	NUM
american_scientific_journal-2059	180	28	.	.	PUNCT
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american_scientific_journal-2059	181	3	]	]	X
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american_scientific_journal-2059	181	5	.	.	PROPN
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american_scientific_journal-2059	181	7	,	,	PUNCT
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american_scientific_journal-2059	181	11	-	-	PUNCT
american_scientific_journal-2059	181	12	first	first	ADJ
american_scientific_journal-2059	181	13	results	result	NOUN
american_scientific_journal-2059	181	14	,	,	PUNCT
american_scientific_journal-2059	181	15	computers	computer	NOUN
american_scientific_journal-2059	181	16	and	and	CCONJ
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american_scientific_journal-2059	181	20	37	37	NUM
american_scientific_journal-2059	181	21	(	(	PUNCT
american_scientific_journal-2059	181	22	1999	1999	NUM
american_scientific_journal-2059	181	23	)	)	PUNCT
american_scientific_journal-2059	181	24	19	19	NUM
american_scientific_journal-2059	181	25	-	-	SYM
american_scientific_journal-2059	181	26	31	31	NUM
american_scientific_journal-2059	181	27	.	.	PUNCT
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american_scientific_journal-2059	182	7	,	,	PUNCT
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american_scientific_journal-2059	182	10	t1	t1	NOUN
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american_scientific_journal-2059	182	12	in	in	ADP
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american_scientific_journal-2059	182	17	,	,	PUNCT
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american_scientific_journal-2059	182	25	,	,	PUNCT
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american_scientific_journal-2059	182	27	4	4	NUM
american_scientific_journal-2059	182	28	,	,	PUNCT
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american_scientific_journal-2059	182	31	(	(	PUNCT
american_scientific_journal-2059	182	32	2014	2014	NUM
american_scientific_journal-2059	182	33	)	)	PUNCT
american_scientific_journal-2059	182	34	,	,	PUNCT
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american_scientific_journal-2059	182	36	.	.	PUNCT
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american_scientific_journal-2059	183	2	-	-	SYM
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american_scientific_journal-2059	183	4	.	.	PUNCT
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american_scientific_journal-2059	184	17	-	-	PUNCT
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american_scientific_journal-2059	184	40	-	-	SYM
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american_scientific_journal-2059	184	42	.	.	PUNCT
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american_scientific_journal-2059	185	30	-	-	SYM
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american_scientific_journal-2059	185	57	-	-	SYM
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american_scientific_journal-2059	185	59	.	.	PUNCT
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american_scientific_journal-2059	186	27	-	-	SYM
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