id	sid	tid	token	lemma	pos
american_scientific_journal-2676	1	1	225	225	NUM
american_scientific_journal-2676	1	2	american	american	ADJ
american_scientific_journal-2676	1	3	scientific	scientific	ADJ
american_scientific_journal-2676	1	4	research	research	NOUN
american_scientific_journal-2676	1	5	journal	journal	NOUN
american_scientific_journal-2676	1	6	for	for	ADP
american_scientific_journal-2676	1	7	engineering	engineering	NOUN
american_scientific_journal-2676	1	8	,	,	PUNCT
american_scientific_journal-2676	1	9	technology	technology	NOUN
american_scientific_journal-2676	1	10	,	,	PUNCT
american_scientific_journal-2676	1	11	and	and	CCONJ
american_scientific_journal-2676	1	12	sciences	science	NOUN
american_scientific_journal-2676	1	13	(	(	PUNCT
american_scientific_journal-2676	1	14	asrjets	asrjet	NOUN
american_scientific_journal-2676	1	15	)	)	PUNCT
american_scientific_journal-2676	1	16	issn	issn	PROPN
american_scientific_journal-2676	1	17	(	(	PUNCT
american_scientific_journal-2676	1	18	print	print	NOUN
american_scientific_journal-2676	1	19	)	)	PUNCT
american_scientific_journal-2676	1	20	2313	2313	NUM
american_scientific_journal-2676	1	21	-	-	SYM
american_scientific_journal-2676	1	22	4410	4410	NUM
american_scientific_journal-2676	1	23	,	,	PUNCT
american_scientific_journal-2676	1	24	issn	issn	PROPN
american_scientific_journal-2676	1	25	(	(	PUNCT
american_scientific_journal-2676	1	26	online	online	ADJ
american_scientific_journal-2676	1	27	)	)	PUNCT
american_scientific_journal-2676	1	28	2313	2313	NUM
american_scientific_journal-2676	1	29	-	-	SYM
american_scientific_journal-2676	1	30	4402	4402	NUM
american_scientific_journal-2676	1	31	©	©	PROPN
american_scientific_journal-2676	1	32	global	global	ADJ
american_scientific_journal-2676	1	33	society	society	NOUN
american_scientific_journal-2676	1	34	of	of	ADP
american_scientific_journal-2676	1	35	scientific	scientific	ADJ
american_scientific_journal-2676	1	36	research	research	NOUN
american_scientific_journal-2676	1	37	and	and	CCONJ
american_scientific_journal-2676	1	38	researchers	researcher	NOUN
american_scientific_journal-2676	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-2676	1	40	on	on	ADP
american_scientific_journal-2676	1	41	pairwise	pairwise	NOUN
american_scientific_journal-2676	1	42	𝝀𝝀-open	𝝀𝝀-open	ADJ
american_scientific_journal-2676	1	43	soft	soft	ADJ
american_scientific_journal-2676	1	44	sets	set	NOUN
american_scientific_journal-2676	1	45	and	and	CCONJ
american_scientific_journal-2676	1	46	pairwise	pairwise	NOUN
american_scientific_journal-2676	1	47	locally	locally	ADV
american_scientific_journal-2676	1	48	closed	close	VERB
american_scientific_journal-2676	1	49	soft	soft	ADJ
american_scientific_journal-2676	1	50	sets	set	NOUN
american_scientific_journal-2676	1	51	kandila	kandila	NOUN
american_scientific_journal-2676	1	52	,	,	PUNCT
american_scientific_journal-2676	1	53	o.	o.	PROPN
american_scientific_journal-2676	1	54	a.	a.	PROPN
american_scientific_journal-2676	1	55	e.	e.	PROPN
american_scientific_journal-2676	1	56	tantawyb	tantawyb	PROPN
american_scientific_journal-2676	1	57	,	,	PUNCT
american_scientific_journal-2676	2	1	s.	s.	PROPN
american_scientific_journal-2676	2	2	a.	a.	PROPN
american_scientific_journal-2676	2	3	el	el	PROPN
american_scientific_journal-2676	2	4	-	-	PUNCT
american_scientific_journal-2676	2	5	sheikhc	sheikhc	PROPN
american_scientific_journal-2676	2	6	,	,	PUNCT
american_scientific_journal-2676	2	7	shawqi	shawqi	ADJ
american_scientific_journal-2676	2	8	.	.	PUNCT
american_scientific_journal-2676	3	1	a.	a.	NOUN
american_scientific_journal-2676	3	2	hazzad	hazzad	PROPN
american_scientific_journal-2676	3	3	*	*	PROPN
american_scientific_journal-2676	3	4	adepartment	adepartment	NOUN
american_scientific_journal-2676	3	5	of	of	ADP
american_scientific_journal-2676	3	6	mathematics	mathematic	NOUN
american_scientific_journal-2676	3	7	,	,	PUNCT
american_scientific_journal-2676	3	8	faculty	faculty	NOUN
american_scientific_journal-2676	3	9	of	of	ADP
american_scientific_journal-2676	3	10	science	science	NOUN
american_scientific_journal-2676	3	11	,	,	PUNCT
american_scientific_journal-2676	3	12	helwan	helwan	PROPN
american_scientific_journal-2676	3	13	university	university	PROPN
american_scientific_journal-2676	3	14	,	,	PUNCT
american_scientific_journal-2676	3	15	helwan	helwan	PROPN
american_scientific_journal-2676	3	16	,	,	PUNCT
american_scientific_journal-2676	3	17	egypt	egypt	PROPN
american_scientific_journal-2676	3	18	bdepartment	bdepartment	NOUN
american_scientific_journal-2676	3	19	of	of	ADP
american_scientific_journal-2676	3	20	mathematics	mathematic	NOUN
american_scientific_journal-2676	3	21	,	,	PUNCT
american_scientific_journal-2676	3	22	faculty	faculty	NOUN
american_scientific_journal-2676	3	23	of	of	ADP
american_scientific_journal-2676	3	24	science	science	NOUN
american_scientific_journal-2676	3	25	,	,	PUNCT
american_scientific_journal-2676	3	26	zagazig	zagazig	PROPN
american_scientific_journal-2676	3	27	university	university	PROPN
american_scientific_journal-2676	3	28	,	,	PUNCT
american_scientific_journal-2676	3	29	zagazig	zagazig	PROPN
american_scientific_journal-2676	3	30	,	,	PUNCT
american_scientific_journal-2676	3	31	egypt	egypt	PROPN
american_scientific_journal-2676	3	32	cdepartment	cdepartment	PROPN
american_scientific_journal-2676	3	33	of	of	ADP
american_scientific_journal-2676	3	34	mathematics	mathematic	NOUN
american_scientific_journal-2676	3	35	,	,	PUNCT
american_scientific_journal-2676	3	36	faculty	faculty	NOUN
american_scientific_journal-2676	3	37	of	of	ADP
american_scientific_journal-2676	3	38	education	education	NOUN
american_scientific_journal-2676	3	39	,	,	PUNCT
american_scientific_journal-2676	3	40	ain	ain	PROPN
american_scientific_journal-2676	3	41	shams	shams	PROPN
american_scientific_journal-2676	3	42	university	university	PROPN
american_scientific_journal-2676	3	43	,	,	PUNCT
american_scientific_journal-2676	3	44	cairo	cairo	PROPN
american_scientific_journal-2676	3	45	,	,	PUNCT
american_scientific_journal-2676	3	46	egypt	egypt	PROPN
american_scientific_journal-2676	3	47	ddepartment	ddepartment	NOUN
american_scientific_journal-2676	3	48	of	of	ADP
american_scientific_journal-2676	3	49	mathematics	mathematic	NOUN
american_scientific_journal-2676	3	50	,	,	PUNCT
american_scientific_journal-2676	3	51	faculty	faculty	NOUN
american_scientific_journal-2676	3	52	of	of	ADP
american_scientific_journal-2676	3	53	education	education	NOUN
american_scientific_journal-2676	3	54	,	,	PUNCT
american_scientific_journal-2676	3	55	taiz	taiz	PROPN
american_scientific_journal-2676	3	56	university	university	NOUN
american_scientific_journal-2676	3	57	,	,	PUNCT
american_scientific_journal-2676	3	58	taiz	taiz	PROPN
american_scientific_journal-2676	3	59	,	,	PUNCT
american_scientific_journal-2676	3	60	yemen	yemen	PROPN
american_scientific_journal-2676	3	61	aemail	aemail	NOUN
american_scientific_journal-2676	3	62	:	:	PUNCT
american_scientific_journal-2676	3	63	dr.ali_kandil@yahoo.com	dr.ali_kandil@yahoo.com	X
american_scientific_journal-2676	3	64	bemail	bemail	NOUN
american_scientific_journal-2676	3	65	:	:	PUNCT
american_scientific_journal-2676	3	66	drosamat@yahoo.com	drosamat@yahoo.com	X
american_scientific_journal-2676	3	67	cemail	cemail	NOUN
american_scientific_journal-2676	3	68	:	:	PUNCT
american_scientific_journal-2676	3	69	sobhyelsheikh@yahoo.com	sobhyelsheikh@yahoo.com	X
american_scientific_journal-2676	4	1	demail	demail	NOUN
american_scientific_journal-2676	4	2	:	:	PUNCT
american_scientific_journal-2676	4	3	shawqialalimi@yahoo.com	shawqialalimi@yahoo.com	PROPN
american_scientific_journal-2676	4	4	abstract	abstract	ADJ
american_scientific_journal-2676	4	5	kandil	kandil	PROPN
american_scientific_journal-2676	4	6	and	and	CCONJ
american_scientific_journal-2676	4	7	his	his	PRON
american_scientific_journal-2676	4	8	colleagues	colleague	NOUN
american_scientific_journal-2676	5	1	[	[	X
american_scientific_journal-2676	5	2	10	10	NUM
american_scientific_journal-2676	5	3	]	]	PUNCT
american_scientific_journal-2676	5	4	,	,	PUNCT
american_scientific_journal-2676	5	5	introduced	introduce	VERB
american_scientific_journal-2676	5	6	the	the	DET
american_scientific_journal-2676	5	7	notion	notion	NOUN
american_scientific_journal-2676	5	8	of	of	ADP
american_scientific_journal-2676	5	9	λp	λp	PUNCT
american_scientific_journal-2676	5	10	-closed	-close	VERB
american_scientific_journal-2676	5	11	soft	soft	ADJ
american_scientific_journal-2676	5	12	set	set	NOUN
american_scientific_journal-2676	5	13	by	by	ADP
american_scientific_journal-2676	5	14	involving	involve	VERB
american_scientific_journal-2676	5	15	λp	λp	PRON
american_scientific_journal-2676	5	16	-soft	-soft	NOUN
american_scientific_journal-2676	5	17	set	set	VERB
american_scientific_journal-2676	5	18	and	and	CCONJ
american_scientific_journal-2676	5	19	p	p	NOUN
american_scientific_journal-2676	5	20	closed	close	VERB
american_scientific_journal-2676	5	21	soft	soft	ADJ
american_scientific_journal-2676	5	22	set	set	NOUN
american_scientific_journal-2676	5	23	.	.	PUNCT
american_scientific_journal-2676	6	1	in	in	ADP
american_scientific_journal-2676	6	2	this	this	DET
american_scientific_journal-2676	6	3	paper	paper	NOUN
american_scientific_journal-2676	6	4	,	,	PUNCT
american_scientific_journal-2676	6	5	we	we	PRON
american_scientific_journal-2676	6	6	give	give	VERB
american_scientific_journal-2676	6	7	some	some	DET
american_scientific_journal-2676	6	8	additional	additional	ADJ
american_scientific_journal-2676	6	9	properties	property	NOUN
american_scientific_journal-2676	6	10	of	of	ADP
american_scientific_journal-2676	6	11	λp	λp	PRON
american_scientific_journal-2676	6	12	-closed	-close	VERB
american_scientific_journal-2676	6	13	soft	soft	ADJ
american_scientific_journal-2676	6	14	sets	set	NOUN
american_scientific_journal-2676	6	15	.	.	PUNCT
american_scientific_journal-2676	7	1	we	we	PRON
american_scientific_journal-2676	7	2	also	also	ADV
american_scientific_journal-2676	7	3	introduce	introduce	VERB
american_scientific_journal-2676	7	4	and	and	CCONJ
american_scientific_journal-2676	7	5	study	study	VERB
american_scientific_journal-2676	7	6	a	a	DET
american_scientific_journal-2676	7	7	related	relate	VERB
american_scientific_journal-2676	7	8	new	new	ADJ
american_scientific_journal-2676	7	9	class	class	NOUN
american_scientific_journal-2676	7	10	of	of	ADP
american_scientific_journal-2676	7	11	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	7	12	4	4	NUM
american_scientific_journal-2676	7	13	�	�	PROPN
american_scientific_journal-2676	7	14	∗	∗	NOUN
american_scientific_journal-2676	7	15	-spaces	-space	NOUN
american_scientific_journal-2676	7	16	which	which	PRON
american_scientific_journal-2676	7	17	lies	lie	VERB
american_scientific_journal-2676	7	18	between	between	ADP
american_scientific_journal-2676	7	19	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	NOUN
american_scientific_journal-2676	7	20	and	and	CCONJ
american_scientific_journal-2676	7	21	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	7	22	2	2	NUM
american_scientific_journal-2676	7	23	�	�	PROPN
american_scientific_journal-2676	7	24	∗	∗	NOUN
american_scientific_journal-2676	7	25	.	.	PUNCT
american_scientific_journal-2676	8	1	moreover	moreover	ADV
american_scientific_journal-2676	8	2	,	,	PUNCT
american_scientific_journal-2676	8	3	we	we	PRON
american_scientific_journal-2676	8	4	show	show	VERB
american_scientific_journal-2676	8	5	that	that	SCONJ
american_scientific_journal-2676	8	6	there	there	PRON
american_scientific_journal-2676	8	7	exists	exist	VERB
american_scientific_journal-2676	8	8	a	a	DET
american_scientific_journal-2676	8	9	very	very	ADV
american_scientific_journal-2676	8	10	important	important	ADJ
american_scientific_journal-2676	8	11	relation	relation	NOUN
american_scientific_journal-2676	8	12	between	between	ADP
american_scientific_journal-2676	8	13	the	the	DET
american_scientific_journal-2676	8	14	notion	notion	NOUN
american_scientific_journal-2676	8	15	of	of	ADP
american_scientific_journal-2676	8	16	λp	λp	PUNCT
american_scientific_journal-2676	8	17	-closed	-close	VERB
american_scientific_journal-2676	8	18	soft	soft	ADJ
american_scientific_journal-2676	8	19	sets	set	NOUN
american_scientific_journal-2676	8	20	and	and	CCONJ
american_scientific_journal-2676	8	21	the	the	DET
american_scientific_journal-2676	8	22	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	8	23	4	4	NUM
american_scientific_journal-2676	8	24	�	�	PROPN
american_scientific_journal-2676	8	25	∗	∗	NOUN
american_scientific_journal-2676	8	26	property	property	NOUN
american_scientific_journal-2676	8	27	,	,	PUNCT
american_scientific_journal-2676	8	28	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-2676	8	29	=	=	SYM
american_scientific_journal-2676	9	1	0	0	NUM
american_scientific_journal-2676	9	2	,	,	PUNCT
american_scientific_journal-2676	9	3	1	1	NUM
american_scientific_journal-2676	9	4	4	4	NUM
american_scientific_journal-2676	9	5	�	�	NOUN
american_scientific_journal-2676	9	6	,	,	PUNCT
american_scientific_journal-2676	9	7	1	1	NUM
american_scientific_journal-2676	9	8	2	2	NUM
american_scientific_journal-2676	9	9	�	�	PROPN
american_scientific_journal-2676	9	10	.	.	PUNCT
american_scientific_journal-2676	10	1	in	in	ADP
american_scientific_journal-2676	10	2	addition	addition	NOUN
american_scientific_journal-2676	10	3	,	,	PUNCT
american_scientific_journal-2676	10	4	we	we	PRON
american_scientific_journal-2676	10	5	offer	offer	VERB
american_scientific_journal-2676	10	6	the	the	DET
american_scientific_journal-2676	10	7	notion	notion	NOUN
american_scientific_journal-2676	10	8	of	of	ADP
american_scientific_journal-2676	10	9	p	p	NOUN
american_scientific_journal-2676	10	10	-locally	-locally	ADV
american_scientific_journal-2676	10	11	closed	close	VERB
american_scientific_journal-2676	10	12	soft	soft	ADJ
american_scientific_journal-2676	10	13	sets	set	NOUN
american_scientific_journal-2676	10	14	and	and	CCONJ
american_scientific_journal-2676	10	15	we	we	PRON
american_scientific_journal-2676	10	16	investigate	investigate	VERB
american_scientific_journal-2676	10	17	a	a	DET
american_scientific_journal-2676	10	18	related	relate	VERB
american_scientific_journal-2676	10	19	new	new	ADJ
american_scientific_journal-2676	10	20	pairwise	pairwise	NOUN
american_scientific_journal-2676	10	21	soft	soft	ADJ
american_scientific_journal-2676	10	22	separation	separation	NOUN
american_scientific_journal-2676	10	23	axiom	axiom	NOUN
american_scientific_journal-2676	10	24	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	10	25	which	which	PRON
american_scientific_journal-2676	10	26	is	be	AUX
american_scientific_journal-2676	10	27	independent	independent	ADJ
american_scientific_journal-2676	10	28	from	from	ADP
american_scientific_journal-2676	10	29	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	10	30	4	4	NUM
american_scientific_journal-2676	10	31	�	�	PROPN
american_scientific_journal-2676	10	32	∗	∗	NOUN
american_scientific_journal-2676	10	33	.	.	PUNCT
american_scientific_journal-2676	11	1	the	the	DET
american_scientific_journal-2676	11	2	relationships	relationship	NOUN
american_scientific_journal-2676	11	3	between	between	ADP
american_scientific_journal-2676	11	4	the	the	DET
american_scientific_journal-2676	11	5	λp	λp	ADV
american_scientific_journal-2676	11	6	-closed	-close	VERB
american_scientific_journal-2676	11	7	soft	soft	ADJ
american_scientific_journal-2676	11	8	sets	set	NOUN
american_scientific_journal-2676	11	9	and	and	CCONJ
american_scientific_journal-2676	11	10	the	the	DET
american_scientific_journal-2676	11	11	p	p	NOUN
american_scientific_journal-2676	11	12	-locally	-locally	ADV
american_scientific_journal-2676	11	13	closed	closed	ADJ
american_scientific_journal-2676	11	14	soft	soft	ADJ
american_scientific_journal-2676	11	15	sets	set	NOUN
american_scientific_journal-2676	11	16	are	be	AUX
american_scientific_journal-2676	11	17	obtained	obtain	VERB
american_scientific_journal-2676	11	18	.	.	PUNCT
american_scientific_journal-2676	12	1	furthermore	furthermore	ADV
american_scientific_journal-2676	12	2	,	,	PUNCT
american_scientific_journal-2676	12	3	we	we	PRON
american_scientific_journal-2676	12	4	introduce	introduce	VERB
american_scientific_journal-2676	12	5	the	the	DET
american_scientific_journal-2676	12	6	notion	notion	NOUN
american_scientific_journal-2676	12	7	of	of	ADP
american_scientific_journal-2676	12	8	λp	λp	PUNCT
american_scientific_journal-2676	12	9	-open	-open	ADJ
american_scientific_journal-2676	12	10	soft	soft	ADJ
american_scientific_journal-2676	12	11	sets	set	NOUN
american_scientific_journal-2676	12	12	and	and	CCONJ
american_scientific_journal-2676	12	13	we	we	PRON
american_scientific_journal-2676	12	14	construct	construct	VERB
american_scientific_journal-2676	12	15	supra	supra	PROPN
american_scientific_journal-2676	12	16	soft	soft	ADJ
american_scientific_journal-2676	12	17	topology	topology	NOUN
american_scientific_journal-2676	12	18	associated	associate	VERB
american_scientific_journal-2676	12	19	with	with	ADP
american_scientific_journal-2676	12	20	the	the	DET
american_scientific_journal-2676	12	21	class	class	NOUN
american_scientific_journal-2676	12	22	of	of	ADP
american_scientific_journal-2676	12	23	λp	λp	X
american_scientific_journal-2676	12	24	-open	-open	ADJ
american_scientific_journal-2676	12	25	soft	soft	ADJ
american_scientific_journal-2676	12	26	sets	set	NOUN
american_scientific_journal-2676	12	27	and	and	CCONJ
american_scientific_journal-2676	12	28	we	we	PRON
american_scientific_journal-2676	12	29	present	present	VERB
american_scientific_journal-2676	12	30	pairwise	pairwise	NOUN
american_scientific_journal-2676	12	31	soft	soft	ADJ
american_scientific_journal-2676	12	32	separation	separation	NOUN
american_scientific_journal-2676	12	33	axioms	axiom	NOUN
american_scientific_journal-2676	12	34	related	relate	VERB
american_scientific_journal-2676	12	35	to	to	ADP
american_scientific_journal-2676	12	36	such	such	ADJ
american_scientific_journal-2676	12	37	soft	soft	ADJ
american_scientific_journal-2676	12	38	sets	set	NOUN
american_scientific_journal-2676	12	39	,	,	PUNCT
american_scientific_journal-2676	12	40	namely	namely	ADV
american_scientific_journal-2676	12	41	*	*	PUNCT
american_scientific_journal-2676	12	42	λpst	λpst	NOUN
american_scientific_journal-2676	12	43	.	.	PUNCT
american_scientific_journal-2676	13	1	we	we	PRON
american_scientific_journal-2676	13	2	provide	provide	VERB
american_scientific_journal-2676	13	3	some	some	DET
american_scientific_journal-2676	13	4	illustrative	illustrative	ADJ
american_scientific_journal-2676	13	5	examples	example	NOUN
american_scientific_journal-2676	13	6	to	to	PART
american_scientific_journal-2676	13	7	support	support	VERB
american_scientific_journal-2676	13	8	the	the	DET
american_scientific_journal-2676	13	9	results	result	NOUN
american_scientific_journal-2676	13	10	.	.	PUNCT
american_scientific_journal-2676	14	1	keywords	keyword	NOUN
american_scientific_journal-2676	14	2	:	:	PUNCT
american_scientific_journal-2676	14	3	soft	soft	ADJ
american_scientific_journal-2676	14	4	set	set	NOUN
american_scientific_journal-2676	14	5	;	;	PUNCT
american_scientific_journal-2676	14	6	soft	soft	ADJ
american_scientific_journal-2676	14	7	topology	topology	NOUN
american_scientific_journal-2676	14	8	;	;	PUNCT
american_scientific_journal-2676	14	9	soft	soft	ADJ
american_scientific_journal-2676	14	10	bitopology	bitopology	NOUN
american_scientific_journal-2676	14	11	;	;	PUNCT
american_scientific_journal-2676	14	12	soft	soft	ADJ
american_scientific_journal-2676	14	13	bitopological	bitopological	ADJ
american_scientific_journal-2676	14	14	spaces	space	NOUN
american_scientific_journal-2676	14	15	;	;	PUNCT
american_scientific_journal-2676	14	16	pairwise	pairwise	NOUN
american_scientific_journal-2676	14	17	soft	soft	ADJ
american_scientific_journal-2676	14	18	separation	separation	NOUN
american_scientific_journal-2676	14	19	axioms	axiom	NOUN
american_scientific_journal-2676	14	20	;	;	PUNCT
american_scientific_journal-2676	14	21	λp	λp	PRON
american_scientific_journal-2676	14	22	closed	close	VERB
american_scientific_journal-2676	14	23	soft	soft	ADJ
american_scientific_journal-2676	14	24	sets	set	NOUN
american_scientific_journal-2676	14	25	;	;	PUNCT
american_scientific_journal-2676	14	26	pairwise	pairwise	NOUN
american_scientific_journal-2676	14	27	λp	λp	X
american_scientific_journal-2676	14	28	-open	-open	ADJ
american_scientific_journal-2676	14	29	soft	soft	ADJ
american_scientific_journal-2676	14	30	sets	set	NOUN
american_scientific_journal-2676	14	31	;	;	PUNCT
american_scientific_journal-2676	14	32	and	and	CCONJ
american_scientific_journal-2676	14	33	p	p	DET
american_scientific_journal-2676	14	34	locally	locally	ADV
american_scientific_journal-2676	14	35	closed	close	VERB
american_scientific_journal-2676	14	36	soft	soft	ADJ
american_scientific_journal-2676	14	37	sets	set	NOUN
american_scientific_journal-2676	14	38	.	.	PUNCT
american_scientific_journal-2676	15	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-2676	16	1	*	*	PUNCT
american_scientific_journal-2676	16	2	corresponding	correspond	VERB
american_scientific_journal-2676	16	3	author	author	NOUN
american_scientific_journal-2676	16	4	.	.	PUNCT
american_scientific_journal-2676	17	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-2676	17	2	american	american	PROPN
american_scientific_journal-2676	17	3	scientific	scientific	PROPN
american_scientific_journal-2676	17	4	research	research	NOUN
american_scientific_journal-2676	17	5	journal	journal	NOUN
american_scientific_journal-2676	17	6	for	for	ADP
american_scientific_journal-2676	17	7	engineering	engineering	NOUN
american_scientific_journal-2676	17	8	,	,	PUNCT
american_scientific_journal-2676	17	9	technology	technology	NOUN
american_scientific_journal-2676	17	10	,	,	PUNCT
american_scientific_journal-2676	17	11	and	and	CCONJ
american_scientific_journal-2676	17	12	sciences	science	NOUN
american_scientific_journal-2676	17	13	(	(	PUNCT
american_scientific_journal-2676	17	14	asrjets	asrjet	NOUN
american_scientific_journal-2676	17	15	)	)	PUNCT
american_scientific_journal-2676	17	16	(	(	PUNCT
american_scientific_journal-2676	17	17	2017	2017	NUM
american_scientific_journal-2676	17	18	)	)	PUNCT
american_scientific_journal-2676	17	19	volume	volume	NOUN
american_scientific_journal-2676	17	20	28	28	NUM
american_scientific_journal-2676	17	21	,	,	PUNCT
american_scientific_journal-2676	17	22	no	no	DET
american_scientific_journal-2676	17	23	1	1	NUM
american_scientific_journal-2676	17	24	,	,	PUNCT
american_scientific_journal-2676	17	25	pp	pp	ADV
american_scientific_journal-2676	17	26	225	225	NUM
american_scientific_journal-2676	17	27	-	-	SYM
american_scientific_journal-2676	17	28	247	247	NUM
american_scientific_journal-2676	17	29	226	226	NUM
american_scientific_journal-2676	17	30	1	1	NUM
american_scientific_journal-2676	17	31	.	.	PUNCT
american_scientific_journal-2676	17	32	introduction	introduction	NOUN
american_scientific_journal-2676	17	33	in	in	ADP
american_scientific_journal-2676	17	34	1999	1999	NUM
american_scientific_journal-2676	17	35	,	,	PUNCT
american_scientific_journal-2676	17	36	molodtsov	molodtsov	NOUN
american_scientific_journal-2676	18	1	[	[	X
american_scientific_journal-2676	18	2	14	14	NUM
american_scientific_journal-2676	18	3	]	]	PUNCT
american_scientific_journal-2676	18	4	introduced	introduce	VERB
american_scientific_journal-2676	18	5	the	the	DET
american_scientific_journal-2676	18	6	concept	concept	NOUN
american_scientific_journal-2676	18	7	of	of	ADP
american_scientific_journal-2676	18	8	soft	soft	ADJ
american_scientific_journal-2676	18	9	set	set	NOUN
american_scientific_journal-2676	18	10	as	as	ADP
american_scientific_journal-2676	18	11	a	a	DET
american_scientific_journal-2676	18	12	mathematical	mathematical	ADJ
american_scientific_journal-2676	18	13	modeling	modeling	NOUN
american_scientific_journal-2676	18	14	for	for	ADP
american_scientific_journal-2676	18	15	dealing	deal	VERB
american_scientific_journal-2676	18	16	with	with	ADP
american_scientific_journal-2676	18	17	uncertainties	uncertainty	NOUN
american_scientific_journal-2676	18	18	inherent	inherent	ADJ
american_scientific_journal-2676	18	19	in	in	ADP
american_scientific_journal-2676	18	20	many	many	ADJ
american_scientific_journal-2676	18	21	of	of	ADP
american_scientific_journal-2676	18	22	real	real	ADJ
american_scientific_journal-2676	18	23	world	world	NOUN
american_scientific_journal-2676	18	24	problems	problem	NOUN
american_scientific_journal-2676	18	25	.	.	PUNCT
american_scientific_journal-2676	19	1	shabir	shabir	PROPN
american_scientific_journal-2676	19	2	and	and	CCONJ
american_scientific_journal-2676	19	3	naz	naz	PROPN
american_scientific_journal-2676	19	4	[	[	X
american_scientific_journal-2676	19	5	20	20	NUM
american_scientific_journal-2676	19	6	]	]	PUNCT
american_scientific_journal-2676	19	7	introduced	introduce	VERB
american_scientific_journal-2676	19	8	the	the	DET
american_scientific_journal-2676	19	9	concept	concept	NOUN
american_scientific_journal-2676	19	10	of	of	ADP
american_scientific_journal-2676	19	11	soft	soft	ADJ
american_scientific_journal-2676	19	12	topological	topological	ADJ
american_scientific_journal-2676	19	13	spaces	space	NOUN
american_scientific_journal-2676	19	14	and	and	CCONJ
american_scientific_journal-2676	19	15	investigate	investigate	VERB
american_scientific_journal-2676	19	16	some	some	DET
american_scientific_journal-2676	19	17	fundamental	fundamental	ADJ
american_scientific_journal-2676	19	18	properties	property	NOUN
american_scientific_journal-2676	19	19	of	of	ADP
american_scientific_journal-2676	19	20	such	such	ADJ
american_scientific_journal-2676	19	21	spaces	space	NOUN
american_scientific_journal-2676	19	22	.	.	PUNCT
american_scientific_journal-2676	20	1	many	many	ADJ
american_scientific_journal-2676	20	2	researches	research	NOUN
american_scientific_journal-2676	20	3	(	(	PUNCT
american_scientific_journal-2676	20	4	see	see	VERB
american_scientific_journal-2676	20	5	,	,	PUNCT
american_scientific_journal-2676	20	6	for	for	ADP
american_scientific_journal-2676	20	7	example	example	NOUN
american_scientific_journal-2676	20	8	,	,	PUNCT
american_scientific_journal-2676	20	9	[	[	X
american_scientific_journal-2676	20	10	1,3,4,5,6,7,8,15,16,18	1,3,4,5,6,7,8,15,16,18	NUM
american_scientific_journal-2676	20	11	]	]	PUNCT
american_scientific_journal-2676	20	12	)	)	PUNCT
american_scientific_journal-2676	20	13	introduced	introduce	VERB
american_scientific_journal-2676	20	14	and	and	CCONJ
american_scientific_journal-2676	20	15	discuss	discuss	VERB
american_scientific_journal-2676	20	16	new	new	ADJ
american_scientific_journal-2676	20	17	notions	notion	NOUN
american_scientific_journal-2676	20	18	of	of	ADP
american_scientific_journal-2676	20	19	soft	soft	ADJ
american_scientific_journal-2676	20	20	topological	topological	ADJ
american_scientific_journal-2676	20	21	spaces	space	NOUN
american_scientific_journal-2676	20	22	.	.	PUNCT
american_scientific_journal-2676	21	1	ittanagi	ittanagi	VERB
american_scientific_journal-2676	21	2	[	[	X
american_scientific_journal-2676	21	3	2	2	X
american_scientific_journal-2676	21	4	]	]	PUNCT
american_scientific_journal-2676	21	5	introduced	introduce	VERB
american_scientific_journal-2676	21	6	the	the	DET
american_scientific_journal-2676	21	7	notion	notion	NOUN
american_scientific_journal-2676	21	8	of	of	ADP
american_scientific_journal-2676	21	9	soft	soft	ADJ
american_scientific_journal-2676	21	10	bitopological	bitopological	ADJ
american_scientific_journal-2676	21	11	space	space	NOUN
american_scientific_journal-2676	21	12	.	.	PUNCT
american_scientific_journal-2676	22	1	he	he	PRON
american_scientific_journal-2676	22	2	also	also	ADV
american_scientific_journal-2676	22	3	offer	offer	VERB
american_scientific_journal-2676	22	4	some	some	DET
american_scientific_journal-2676	22	5	types	type	NOUN
american_scientific_journal-2676	22	6	of	of	ADP
american_scientific_journal-2676	22	7	soft	soft	ADJ
american_scientific_journal-2676	22	8	separation	separation	NOUN
american_scientific_journal-2676	22	9	axioms	axiom	NOUN
american_scientific_journal-2676	22	10	in	in	ADP
american_scientific_journal-2676	22	11	soft	soft	ADJ
american_scientific_journal-2676	22	12	bitopological	bitopological	ADJ
american_scientific_journal-2676	22	13	space	space	NOUN
american_scientific_journal-2676	22	14	.	.	PUNCT
american_scientific_journal-2676	23	1	kandil	kandil	NOUN
american_scientific_journal-2676	23	2	and	and	CCONJ
american_scientific_journal-2676	23	3	his	his	PRON
american_scientific_journal-2676	23	4	colleagues	colleague	NOUN
american_scientific_journal-2676	24	1	[	[	X
american_scientific_journal-2676	24	2	10	10	NUM
american_scientific_journal-2676	24	3	]	]	PUNCT
american_scientific_journal-2676	24	4	introduced	introduce	VERB
american_scientific_journal-2676	24	5	the	the	DET
american_scientific_journal-2676	24	6	notions	notion	NOUN
american_scientific_journal-2676	24	7	of	of	ADP
american_scientific_journal-2676	24	8	λp	λp	PRON
american_scientific_journal-2676	24	9	-soft	-soft	ADJ
american_scientific_journal-2676	24	10	sets	set	NOUN
american_scientific_journal-2676	24	11	and	and	CCONJ
american_scientific_journal-2676	24	12	λp	λp	ADP
american_scientific_journal-2676	24	13	-closed	-close	VERB
american_scientific_journal-2676	24	14	soft	soft	ADJ
american_scientific_journal-2676	24	15	sets	set	NOUN
american_scientific_journal-2676	24	16	in	in	ADP
american_scientific_journal-2676	24	17	soft	soft	ADJ
american_scientific_journal-2676	24	18	bitopological	bitopological	ADJ
american_scientific_journal-2676	24	19	spaces	space	NOUN
american_scientific_journal-2676	24	20	.	.	PUNCT
american_scientific_journal-2676	25	1	they	they	PRON
american_scientific_journal-2676	25	2	the	the	DET
american_scientific_journal-2676	25	3	family	family	NOUN
american_scientific_journal-2676	25	4	of	of	ADP
american_scientific_journal-2676	25	5	all	all	DET
american_scientific_journal-2676	25	6	λp	λp	PRON
american_scientific_journal-2676	25	7	-soft	-soft	ADJ
american_scientific_journal-2676	25	8	sets	set	NOUN
american_scientific_journal-2676	25	9	defines	define	VERB
american_scientific_journal-2676	25	10	an	an	DET
american_scientific_journal-2676	25	11	alexandroff	alexandroff	NOUN
american_scientific_journal-2676	25	12	soft	soft	ADJ
american_scientific_journal-2676	25	13	topology	topology	NOUN
american_scientific_journal-2676	25	14	.	.	PUNCT
american_scientific_journal-2676	26	1	kandil	kandil	PROPN
american_scientific_journal-2676	26	2	and	and	CCONJ
american_scientific_journal-2676	26	3	his	his	PRON
american_scientific_journal-2676	26	4	colleagues	colleague	NOUN
american_scientific_journal-2676	27	1	[	[	X
american_scientific_journal-2676	27	2	9	9	NUM
american_scientific_journal-2676	27	3	]	]	PUNCT
american_scientific_journal-2676	27	4	introduced	introduce	VERB
american_scientific_journal-2676	27	5	the	the	DET
american_scientific_journal-2676	27	6	concept	concept	NOUN
american_scientific_journal-2676	27	7	of	of	ADP
american_scientific_journal-2676	27	8	gp	gp	NOUN
american_scientific_journal-2676	27	9	-closed	-close	VERB
american_scientific_journal-2676	27	10	soft	soft	ADJ
american_scientific_journal-2676	27	11	sets	set	NOUN
american_scientific_journal-2676	27	12	and	and	CCONJ
american_scientific_journal-2676	27	13	defined	define	VERB
american_scientific_journal-2676	27	14	the	the	DET
american_scientific_journal-2676	27	15	associated	associated	ADJ
american_scientific_journal-2676	27	16	pairwise	pairwise	NOUN
american_scientific_journal-2676	27	17	soft	soft	ADJ
american_scientific_journal-2676	27	18	separation	separation	NOUN
american_scientific_journal-2676	27	19	axioms	axiom	NOUN
american_scientific_journal-2676	27	20	,	,	PUNCT
american_scientific_journal-2676	27	21	namely	namely	ADV
american_scientific_journal-2676	27	22	,	,	PUNCT
american_scientific_journal-2676	27	23	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	27	24	2	2	NUM
american_scientific_journal-2676	27	25	�	�	PROPN
american_scientific_journal-2676	27	26	∗	∗	NOUN
american_scientific_journal-2676	27	27	and	and	CCONJ
american_scientific_journal-2676	27	28	𝑃𝑃𝑃𝑃𝑅𝑅0∗	𝑃𝑃𝑃𝑃𝑅𝑅0∗	NOUN
american_scientific_journal-2676	27	29	.	.	PUNCT
american_scientific_journal-2676	28	1	recently	recently	ADV
american_scientific_journal-2676	28	2	,	,	PUNCT
american_scientific_journal-2676	28	3	kandil	kandil	PROPN
american_scientific_journal-2676	28	4	and	and	CCONJ
american_scientific_journal-2676	28	5	his	his	PRON
american_scientific_journal-2676	28	6	colleagues	colleague	NOUN
american_scientific_journal-2676	29	1	[	[	X
american_scientific_journal-2676	29	2	11	11	NUM
american_scientific_journal-2676	29	3	]	]	PUNCT
american_scientific_journal-2676	29	4	introduced	introduce	VERB
american_scientific_journal-2676	29	5	some	some	DET
american_scientific_journal-2676	29	6	types	type	NOUN
american_scientific_journal-2676	29	7	of	of	ADP
american_scientific_journal-2676	29	8	pairwise	pairwise	NOUN
american_scientific_journal-2676	29	9	soft	soft	ADJ
american_scientific_journal-2676	29	10	separation	separation	NOUN
american_scientific_journal-2676	29	11	axioms	axiom	NOUN
american_scientific_journal-2676	29	12	,	,	PUNCT
american_scientific_journal-2676	29	13	namely	namely	ADV
american_scientific_journal-2676	29	14	,	,	PUNCT
american_scientific_journal-2676	29	15	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	PROPN
american_scientific_journal-2676	29	16	,	,	PUNCT
american_scientific_journal-2676	29	17	𝑃𝑃𝑃𝑃𝑇𝑇1∗	𝑃𝑃𝑃𝑃𝑇𝑇1∗	NOUN
american_scientific_journal-2676	29	18	,	,	PUNCT
american_scientific_journal-2676	29	19	𝑃𝑃𝑃𝑃𝑇𝑇2∗	𝑃𝑃𝑃𝑃𝑇𝑇2∗	NOUN
american_scientific_journal-2676	29	20	and	and	CCONJ
american_scientific_journal-2676	29	21	𝑃𝑃𝑃𝑃𝑅𝑅1∗	𝑃𝑃𝑃𝑃𝑅𝑅1∗	NOUN
american_scientific_journal-2676	29	22	.	.	PUNCT
american_scientific_journal-2676	30	1	they	they	PRON
american_scientific_journal-2676	30	2	studied	study	VERB
american_scientific_journal-2676	30	3	the	the	DET
american_scientific_journal-2676	30	4	characterization	characterization	NOUN
american_scientific_journal-2676	30	5	and	and	CCONJ
american_scientific_journal-2676	30	6	implications	implication	NOUN
american_scientific_journal-2676	30	7	among	among	ADP
american_scientific_journal-2676	30	8	these	these	DET
american_scientific_journal-2676	30	9	types	type	NOUN
american_scientific_journal-2676	30	10	of	of	ADP
american_scientific_journal-2676	30	11	separation	separation	NOUN
american_scientific_journal-2676	30	12	axioms	axiom	VERB
american_scientific_journal-2676	30	13	.	.	PUNCT
american_scientific_journal-2676	31	1	the	the	DET
american_scientific_journal-2676	31	2	motivation	motivation	NOUN
american_scientific_journal-2676	31	3	of	of	ADP
american_scientific_journal-2676	31	4	the	the	DET
american_scientific_journal-2676	31	5	present	present	ADJ
american_scientific_journal-2676	31	6	paper	paper	NOUN
american_scientific_journal-2676	31	7	is	be	AUX
american_scientific_journal-2676	31	8	to	to	PART
american_scientific_journal-2676	31	9	introduce	introduce	VERB
american_scientific_journal-2676	31	10	new	new	ADJ
american_scientific_journal-2676	31	11	classes	class	NOUN
american_scientific_journal-2676	31	12	of	of	ADP
american_scientific_journal-2676	31	13	soft	soft	ADJ
american_scientific_journal-2676	31	14	sets	set	NOUN
american_scientific_journal-2676	31	15	called	call	VERB
american_scientific_journal-2676	31	16	p	p	NOUN
american_scientific_journal-2676	31	17	-locally	-locally	ADV
american_scientific_journal-2676	31	18	closed	close	VERB
american_scientific_journal-2676	31	19	soft	soft	ADJ
american_scientific_journal-2676	31	20	sets	set	NOUN
american_scientific_journal-2676	31	21	and	and	CCONJ
american_scientific_journal-2676	31	22	λp	λp	ADP
american_scientific_journal-2676	31	23	-open	-open	ADJ
american_scientific_journal-2676	31	24	soft	soft	ADJ
american_scientific_journal-2676	31	25	sets	set	NOUN
american_scientific_journal-2676	31	26	in	in	ADP
american_scientific_journal-2676	31	27	soft	soft	ADJ
american_scientific_journal-2676	31	28	bitopological	bitopological	ADJ
american_scientific_journal-2676	31	29	spaces	space	NOUN
american_scientific_journal-2676	31	30	.	.	PUNCT
american_scientific_journal-2676	32	1	it	it	PRON
american_scientific_journal-2676	32	2	turn	turn	VERB
american_scientific_journal-2676	32	3	out	out	ADP
american_scientific_journal-2676	32	4	that	that	SCONJ
american_scientific_journal-2676	32	5	λp	λp	ADP
american_scientific_journal-2676	32	6	-closed	-close	VERB
american_scientific_journal-2676	32	7	soft	soft	ADJ
american_scientific_journal-2676	32	8	sets	set	NOUN
american_scientific_journal-2676	32	9	,	,	PUNCT
american_scientific_journal-2676	32	10	λp	λp	X
american_scientific_journal-2676	32	11	-open	-open	VERB
american_scientific_journal-2676	32	12	soft	soft	ADJ
american_scientific_journal-2676	32	13	sets	set	NOUN
american_scientific_journal-2676	32	14	and	and	CCONJ
american_scientific_journal-2676	32	15	p	p	NOUN
american_scientific_journal-2676	32	16	-locally	-locally	ADV
american_scientific_journal-2676	32	17	closed	close	VERB
american_scientific_journal-2676	32	18	soft	soft	ADJ
american_scientific_journal-2676	32	19	sets	set	NOUN
american_scientific_journal-2676	32	20	are	be	AUX
american_scientific_journal-2676	32	21	weaker	weak	ADJ
american_scientific_journal-2676	32	22	forms	form	NOUN
american_scientific_journal-2676	32	23	of	of	ADP
american_scientific_journal-2676	32	24	p	p	NOUN
american_scientific_journal-2676	32	25	-open	-open	ADJ
american_scientific_journal-2676	32	26	and	and	CCONJ
american_scientific_journal-2676	32	27	p	p	NOUN
american_scientific_journal-2676	32	28	-closed	-close	VERB
american_scientific_journal-2676	32	29	soft	soft	ADJ
american_scientific_journal-2676	32	30	sets	set	NOUN
american_scientific_journal-2676	32	31	.	.	PUNCT
american_scientific_journal-2676	33	1	we	we	PRON
american_scientific_journal-2676	33	2	also	also	ADV
american_scientific_journal-2676	33	3	conclude	conclude	VERB
american_scientific_journal-2676	33	4	several	several	ADJ
american_scientific_journal-2676	33	5	important	important	ADJ
american_scientific_journal-2676	33	6	properties	property	NOUN
american_scientific_journal-2676	33	7	of	of	ADP
american_scientific_journal-2676	33	8	such	such	ADJ
american_scientific_journal-2676	33	9	soft	soft	ADJ
american_scientific_journal-2676	33	10	sets	set	NOUN
american_scientific_journal-2676	33	11	.	.	PUNCT
american_scientific_journal-2676	34	1	moreover	moreover	ADV
american_scientific_journal-2676	34	2	,	,	PUNCT
american_scientific_journal-2676	34	3	we	we	PRON
american_scientific_journal-2676	34	4	introduce	introduce	VERB
american_scientific_journal-2676	34	5	and	and	CCONJ
american_scientific_journal-2676	34	6	study	study	VERB
american_scientific_journal-2676	34	7	a	a	DET
american_scientific_journal-2676	34	8	related	relate	VERB
american_scientific_journal-2676	34	9	pairwise	pairwise	NOUN
american_scientific_journal-2676	34	10	soft	soft	ADJ
american_scientific_journal-2676	34	11	separation	separation	NOUN
american_scientific_journal-2676	34	12	axioms	axiom	NOUN
american_scientific_journal-2676	34	13	,	,	PUNCT
american_scientific_journal-2676	34	14	namely	namely	ADV
american_scientific_journal-2676	34	15	,	,	PUNCT
american_scientific_journal-2676	34	16	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	34	17	4	4	NUM
american_scientific_journal-2676	34	18	�	�	PROPN
american_scientific_journal-2676	34	19	∗	∗	NOUN
american_scientific_journal-2676	34	20	,	,	PUNCT
american_scientific_journal-2676	34	21	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	34	22	and	and	CCONJ
american_scientific_journal-2676	34	23	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	NOUN
american_scientific_journal-2676	34	24	.	.	PUNCT
american_scientific_journal-2676	35	1	we	we	PRON
american_scientific_journal-2676	35	2	studied	study	VERB
american_scientific_journal-2676	35	3	the	the	DET
american_scientific_journal-2676	35	4	relationships	relationship	NOUN
american_scientific_journal-2676	35	5	between	between	ADP
american_scientific_journal-2676	35	6	these	these	DET
american_scientific_journal-2676	35	7	types	type	NOUN
american_scientific_journal-2676	35	8	of	of	ADP
american_scientific_journal-2676	35	9	separation	separation	NOUN
american_scientific_journal-2676	35	10	axioms	axiom	NOUN
american_scientific_journal-2676	35	11	and	and	CCONJ
american_scientific_journal-2676	35	12	the	the	DET
american_scientific_journal-2676	35	13	other	other	ADJ
american_scientific_journal-2676	35	14	in	in	ADP
american_scientific_journal-2676	35	15	[	[	X
american_scientific_journal-2676	35	16	9,11	9,11	NUM
american_scientific_journal-2676	35	17	]	]	X
american_scientific_journal-2676	35	18	.	.	PUNCT
american_scientific_journal-2676	36	1	2	2	X
american_scientific_journal-2676	36	2	.	.	X
american_scientific_journal-2676	36	3	preliminaries	preliminary	NOUN
american_scientific_journal-2676	36	4	in	in	ADP
american_scientific_journal-2676	36	5	this	this	DET
american_scientific_journal-2676	36	6	section	section	NOUN
american_scientific_journal-2676	36	7	,	,	PUNCT
american_scientific_journal-2676	36	8	we	we	PRON
american_scientific_journal-2676	36	9	briefly	briefly	ADV
american_scientific_journal-2676	36	10	review	review	VERB
american_scientific_journal-2676	36	11	some	some	DET
american_scientific_journal-2676	36	12	concepts	concept	NOUN
american_scientific_journal-2676	36	13	and	and	CCONJ
american_scientific_journal-2676	36	14	some	some	DET
american_scientific_journal-2676	36	15	related	related	ADJ
american_scientific_journal-2676	36	16	results	result	NOUN
american_scientific_journal-2676	36	17	of	of	ADP
american_scientific_journal-2676	36	18	soft	soft	ADJ
american_scientific_journal-2676	36	19	set	set	NOUN
american_scientific_journal-2676	36	20	,	,	PUNCT
american_scientific_journal-2676	36	21	soft	soft	ADJ
american_scientific_journal-2676	36	22	topological	topological	ADJ
american_scientific_journal-2676	36	23	space	space	NOUN
american_scientific_journal-2676	36	24	and	and	CCONJ
american_scientific_journal-2676	36	25	soft	soft	ADJ
american_scientific_journal-2676	36	26	bitopological	bitopological	ADJ
american_scientific_journal-2676	36	27	space	space	NOUN
american_scientific_journal-2676	36	28	which	which	PRON
american_scientific_journal-2676	36	29	are	be	AUX
american_scientific_journal-2676	36	30	needed	need	VERB
american_scientific_journal-2676	36	31	to	to	PART
american_scientific_journal-2676	36	32	used	use	VERB
american_scientific_journal-2676	36	33	in	in	ADP
american_scientific_journal-2676	36	34	current	current	ADJ
american_scientific_journal-2676	36	35	paper	paper	NOUN
american_scientific_journal-2676	36	36	.	.	PUNCT
american_scientific_journal-2676	37	1	for	for	ADP
american_scientific_journal-2676	37	2	more	more	ADJ
american_scientific_journal-2676	37	3	details	detail	NOUN
american_scientific_journal-2676	37	4	about	about	ADP
american_scientific_journal-2676	37	5	these	these	DET
american_scientific_journal-2676	37	6	concepts	concept	NOUN
american_scientific_journal-2676	37	7	you	you	PRON
american_scientific_journal-2676	37	8	can	can	AUX
american_scientific_journal-2676	37	9	see	see	VERB
american_scientific_journal-2676	37	10	[	[	X
american_scientific_journal-2676	37	11	2,4,5,6,7,8,9,10,11,14,15,16,19,20,21,22	2,4,5,6,7,8,9,10,11,14,15,16,19,20,21,22	NUM
american_scientific_journal-2676	37	12	]	]	PUNCT
american_scientific_journal-2676	37	13	.	.	PUNCT
american_scientific_journal-2676	38	1	let	let	VERB
american_scientific_journal-2676	38	2	x	x	PRON
american_scientific_journal-2676	38	3	be	be	AUX
american_scientific_journal-2676	38	4	an	an	DET
american_scientific_journal-2676	38	5	initial	initial	ADJ
american_scientific_journal-2676	38	6	universe	universe	NOUN
american_scientific_journal-2676	38	7	,	,	PUNCT
american_scientific_journal-2676	38	8	e	e	PRON
american_scientific_journal-2676	38	9	be	be	AUX
american_scientific_journal-2676	38	10	a	a	DET
american_scientific_journal-2676	38	11	set	set	NOUN
american_scientific_journal-2676	38	12	of	of	ADP
american_scientific_journal-2676	38	13	parameters	parameter	NOUN
american_scientific_journal-2676	38	14	and	and	CCONJ
american_scientific_journal-2676	38	15	)	)	PUNCT
american_scientific_journal-2676	38	16	(	(	PUNCT
american_scientific_journal-2676	38	17	xp	xp	INTJ
american_scientific_journal-2676	38	18	be	be	AUX
american_scientific_journal-2676	38	19	the	the	DET
american_scientific_journal-2676	38	20	power	power	NOUN
american_scientific_journal-2676	38	21	set	set	NOUN
american_scientific_journal-2676	38	22	of	of	ADP
american_scientific_journal-2676	38	23	x	x	PROPN
american_scientific_journal-2676	38	24	.	.	PUNCT
american_scientific_journal-2676	39	1	definition	definition	NOUN
american_scientific_journal-2676	39	2	2.1	2.1	NUM
american_scientific_journal-2676	40	1	[	[	X
american_scientific_journal-2676	40	2	16	16	NUM
american_scientific_journal-2676	40	3	]	]	PUNCT
american_scientific_journal-2676	40	4	a	a	DET
american_scientific_journal-2676	40	5	pair	pair	NOUN
american_scientific_journal-2676	40	6	)	)	PUNCT
american_scientific_journal-2676	40	7	,	,	PUNCT
american_scientific_journal-2676	40	8	(	(	PUNCT
american_scientific_journal-2676	40	9	ef	ef	PROPN
american_scientific_journal-2676	40	10	is	be	AUX
american_scientific_journal-2676	40	11	called	call	VERB
american_scientific_journal-2676	40	12	a	a	DET
american_scientific_journal-2676	40	13	soft	soft	ADJ
american_scientific_journal-2676	40	14	set	set	NOUN
american_scientific_journal-2676	40	15	over	over	ADP
american_scientific_journal-2676	40	16	x	x	PUNCT
american_scientific_journal-2676	40	17	,	,	PUNCT
american_scientific_journal-2676	40	18	where	where	SCONJ
american_scientific_journal-2676	40	19	f	f	PROPN
american_scientific_journal-2676	40	20	is	be	AUX
american_scientific_journal-2676	40	21	a	a	DET
american_scientific_journal-2676	40	22	mapping	mapping	NOUN
american_scientific_journal-2676	40	23	given	give	VERB
american_scientific_journal-2676	40	24	by	by	ADP
american_scientific_journal-2676	40	25	)	)	PUNCT
american_scientific_journal-2676	40	26	(:	(:	NOUN
american_scientific_journal-2676	40	27	xpef	xpef	NOUN
american_scientific_journal-2676	40	28	→	→	PUNCT
american_scientific_journal-2676	40	29	.	.	PUNCT
american_scientific_journal-2676	41	1	a	a	DET
american_scientific_journal-2676	41	2	soft	soft	ADJ
american_scientific_journal-2676	41	3	set	set	NOUN
american_scientific_journal-2676	41	4	can	can	AUX
american_scientific_journal-2676	41	5	also	also	ADV
american_scientific_journal-2676	41	6	be	be	AUX
american_scientific_journal-2676	41	7	defined	define	VERB
american_scientific_journal-2676	41	8	by	by	ADP
american_scientific_journal-2676	41	9	the	the	DET
american_scientific_journal-2676	41	10	set	set	NOUN
american_scientific_journal-2676	41	11	of	of	ADP
american_scientific_journal-2676	41	12	ordered	order	VERB
american_scientific_journal-2676	41	13	pairs	pair	NOUN
american_scientific_journal-2676	41	14	)	)	PUNCT
american_scientific_journal-2676	41	15	}	}	PUNCT
american_scientific_journal-2676	41	16	(:	(:	VERB
american_scientific_journal-2676	41	17	,	,	PUNCT
american_scientific_journal-2676	41	18	:))	:))	PROPN
american_scientific_journal-2676	41	19	(	(	PUNCT
american_scientific_journal-2676	41	20	,	,	PUNCT
american_scientific_journal-2676	41	21	{	{	PUNCT
american_scientific_journal-2676	41	22	(=	(=	NOUN
american_scientific_journal-2676	41	23	)	)	PUNCT
american_scientific_journal-2676	41	24	,	,	PUNCT
american_scientific_journal-2676	41	25	(	(	PUNCT
american_scientific_journal-2676	41	26	xpefeeefeef	xpefeeefeef	PROPN
american_scientific_journal-2676	41	27	→∈	→∈	NOUN
american_scientific_journal-2676	41	28	.	.	PUNCT
american_scientific_journal-2676	42	1	from	from	ADP
american_scientific_journal-2676	42	2	now	now	ADV
american_scientific_journal-2676	42	3	on	on	ADV
american_scientific_journal-2676	42	4	,	,	PUNCT
american_scientific_journal-2676	42	5	exss	exss	NOUN
american_scientific_journal-2676	42	6	)	)	PUNCT
american_scientific_journal-2676	42	7	(	(	PUNCT
american_scientific_journal-2676	42	8	denotes	denote	VERB
american_scientific_journal-2676	42	9	the	the	DET
american_scientific_journal-2676	42	10	family	family	NOUN
american_scientific_journal-2676	42	11	of	of	ADP
american_scientific_journal-2676	42	12	all	all	DET
american_scientific_journal-2676	42	13	soft	soft	ADJ
american_scientific_journal-2676	42	14	sets	set	NOUN
american_scientific_journal-2676	42	15	over	over	ADP
american_scientific_journal-2676	42	16	x	x	PUNCT
american_scientific_journal-2676	42	17	with	with	ADP
american_scientific_journal-2676	42	18	a	a	DET
american_scientific_journal-2676	42	19	fixed	fix	VERB
american_scientific_journal-2676	42	20	set	set	NOUN
american_scientific_journal-2676	42	21	of	of	ADP
american_scientific_journal-2676	42	22	parameters	parameter	NOUN
american_scientific_journal-2676	42	23	e	e	X
american_scientific_journal-2676	42	24	.	.	PUNCT
american_scientific_journal-2676	43	1	for	for	ADP
american_scientific_journal-2676	43	2	two	two	NUM
american_scientific_journal-2676	43	3	soft	soft	ADJ
american_scientific_journal-2676	43	4	sets	set	NOUN
american_scientific_journal-2676	43	5	exssegef	exssegef	NOUN
american_scientific_journal-2676	43	6	)	)	PUNCT
american_scientific_journal-2676	43	7	(	(	PUNCT
american_scientific_journal-2676	43	8	)	)	PUNCT
american_scientific_journal-2676	43	9	,	,	PUNCT
american_scientific_journal-2676	43	10	(	(	PUNCT
american_scientific_journal-2676	43	11	)	)	PUNCT
american_scientific_journal-2676	43	12	,	,	PUNCT
american_scientific_journal-2676	43	13	,	,	PUNCT
american_scientific_journal-2676	43	14	(	(	PUNCT
american_scientific_journal-2676	43	15	∈	∈	PROPN
american_scientific_journal-2676	43	16	,	,	PUNCT
american_scientific_journal-2676	43	17	)	)	PUNCT
american_scientific_journal-2676	43	18	,	,	PUNCT
american_scientific_journal-2676	43	19	(	(	PUNCT
american_scientific_journal-2676	43	20	ef	ef	PROPN
american_scientific_journal-2676	43	21	is	be	AUX
american_scientific_journal-2676	43	22	called	call	VERB
american_scientific_journal-2676	43	23	a	a	DET
american_scientific_journal-2676	43	24	soft	soft	ADJ
american_scientific_journal-2676	43	25	subset	subset	NOUN
american_scientific_journal-2676	43	26	of	of	ADP
american_scientific_journal-2676	43	27	)	)	PUNCT
american_scientific_journal-2676	43	28	,	,	PUNCT
american_scientific_journal-2676	43	29	(	(	PUNCT
american_scientific_journal-2676	43	30	eg	eg	NOUN
american_scientific_journal-2676	43	31	,	,	PUNCT
american_scientific_journal-2676	43	32	denoted	denote	VERB
american_scientific_journal-2676	43	33	by	by	ADP
american_scientific_journal-2676	43	34	)	)	PUNCT
american_scientific_journal-2676	43	35	,	,	PUNCT
american_scientific_journal-2676	43	36	(	(	PUNCT
american_scientific_journal-2676	43	37	~	~	NOUN
american_scientific_journal-2676	43	38	)	)	PUNCT
american_scientific_journal-2676	43	39	,	,	PUNCT
american_scientific_journal-2676	43	40	(	(	PUNCT
american_scientific_journal-2676	43	41	egef	egef	VERB
american_scientific_journal-2676	43	42	⊆	⊆	NUM
american_scientific_journal-2676	43	43	,	,	PUNCT
american_scientific_journal-2676	43	44	if	if	SCONJ
american_scientific_journal-2676	43	45	)	)	PUNCT
american_scientific_journal-2676	43	46	(	(	PUNCT
american_scientific_journal-2676	43	47	)	)	PUNCT
american_scientific_journal-2676	43	48	(	(	PUNCT
american_scientific_journal-2676	43	49	egef	egef	VERB
american_scientific_journal-2676	43	50	⊆	⊆	NUM
american_scientific_journal-2676	43	51	,	,	PUNCT
american_scientific_journal-2676	43	52	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	43	53	.	.	PUNCT
american_scientific_journal-2676	44	1	in	in	ADP
american_scientific_journal-2676	44	2	this	this	DET
american_scientific_journal-2676	44	3	case	case	NOUN
american_scientific_journal-2676	44	4	,	,	PUNCT
american_scientific_journal-2676	44	5	)	)	PUNCT
american_scientific_journal-2676	44	6	,	,	PUNCT
american_scientific_journal-2676	44	7	(	(	PUNCT
american_scientific_journal-2676	44	8	eg	eg	NOUN
american_scientific_journal-2676	44	9	is	be	AUX
american_scientific_journal-2676	44	10	called	call	VERB
american_scientific_journal-2676	44	11	a	a	DET
american_scientific_journal-2676	44	12	soft	soft	ADJ
american_scientific_journal-2676	44	13	superset	superset	NOUN
american_scientific_journal-2676	44	14	of	of	ADP
american_scientific_journal-2676	44	15	)	)	PUNCT
american_scientific_journal-2676	44	16	,	,	PUNCT
american_scientific_journal-2676	44	17	(	(	PUNCT
american_scientific_journal-2676	44	18	ef	ef	X
american_scientific_journal-2676	44	19	.	.	PUNCT
american_scientific_journal-2676	45	1	in	in	ADP
american_scientific_journal-2676	45	2	american	american	ADJ
american_scientific_journal-2676	45	3	scientific	scientific	ADJ
american_scientific_journal-2676	45	4	research	research	NOUN
american_scientific_journal-2676	45	5	journal	journal	NOUN
american_scientific_journal-2676	45	6	for	for	ADP
american_scientific_journal-2676	45	7	engineering	engineering	NOUN
american_scientific_journal-2676	45	8	,	,	PUNCT
american_scientific_journal-2676	45	9	technology	technology	NOUN
american_scientific_journal-2676	45	10	,	,	PUNCT
american_scientific_journal-2676	45	11	and	and	CCONJ
american_scientific_journal-2676	45	12	sciences	science	NOUN
american_scientific_journal-2676	45	13	(	(	PUNCT
american_scientific_journal-2676	45	14	asrjets	asrjet	NOUN
american_scientific_journal-2676	45	15	)	)	PUNCT
american_scientific_journal-2676	45	16	(	(	PUNCT
american_scientific_journal-2676	45	17	2017	2017	NUM
american_scientific_journal-2676	45	18	)	)	PUNCT
american_scientific_journal-2676	45	19	volume	volume	NOUN
american_scientific_journal-2676	45	20	28	28	NUM
american_scientific_journal-2676	45	21	,	,	PUNCT
american_scientific_journal-2676	45	22	no	no	DET
american_scientific_journal-2676	45	23	1	1	NUM
american_scientific_journal-2676	45	24	,	,	PUNCT
american_scientific_journal-2676	45	25	pp	pp	ADV
american_scientific_journal-2676	45	26	225	225	NUM
american_scientific_journal-2676	45	27	-	-	SYM
american_scientific_journal-2676	45	28	247	247	NUM
american_scientific_journal-2676	45	29	227	227	NUM
american_scientific_journal-2676	45	30	addition	addition	NOUN
american_scientific_journal-2676	45	31	,	,	PUNCT
american_scientific_journal-2676	45	32	the	the	DET
american_scientific_journal-2676	45	33	union	union	NOUN
american_scientific_journal-2676	45	34	of	of	ADP
american_scientific_journal-2676	45	35	soft	soft	ADJ
american_scientific_journal-2676	45	36	sets	set	NOUN
american_scientific_journal-2676	45	37	)	)	PUNCT
american_scientific_journal-2676	45	38	,	,	PUNCT
american_scientific_journal-2676	45	39	(	(	PUNCT
american_scientific_journal-2676	45	40	ef	ef	PROPN
american_scientific_journal-2676	45	41	and	and	CCONJ
american_scientific_journal-2676	45	42	)	)	PUNCT
american_scientific_journal-2676	45	43	,	,	PUNCT
american_scientific_journal-2676	45	44	(	(	PUNCT
american_scientific_journal-2676	45	45	eg	eg	NOUN
american_scientific_journal-2676	45	46	,	,	PUNCT
american_scientific_journal-2676	45	47	denoted	denote	VERB
american_scientific_journal-2676	45	48	by	by	ADP
american_scientific_journal-2676	45	49	)	)	PUNCT
american_scientific_journal-2676	45	50	,	,	PUNCT
american_scientific_journal-2676	45	51	(	(	PUNCT
american_scientific_journal-2676	45	52	~	~	NOUN
american_scientific_journal-2676	45	53	)	)	PUNCT
american_scientific_journal-2676	45	54	,	,	PUNCT
american_scientific_journal-2676	45	55	(	(	PUNCT
american_scientific_journal-2676	45	56	egef	egef	VERB
american_scientific_journal-2676	45	57	∪	∪	ADJ
american_scientific_journal-2676	45	58	,	,	PUNCT
american_scientific_journal-2676	45	59	is	be	AUX
american_scientific_journal-2676	45	60	the	the	DET
american_scientific_journal-2676	45	61	soft	soft	ADJ
american_scientific_journal-2676	45	62	set	set	NOUN
american_scientific_journal-2676	45	63	)	)	PUNCT
american_scientific_journal-2676	45	64	,	,	PUNCT
american_scientific_journal-2676	45	65	(	(	PUNCT
american_scientific_journal-2676	45	66	eh	eh	INTJ
american_scientific_journal-2676	45	67	which	which	PRON
american_scientific_journal-2676	45	68	defined	define	VERB
american_scientific_journal-2676	45	69	as	as	ADP
american_scientific_journal-2676	45	70	)	)	PUNCT
american_scientific_journal-2676	45	71	(	(	PUNCT
american_scientific_journal-2676	45	72	)	)	PUNCT
american_scientific_journal-2676	45	73	(=	(=	X
american_scientific_journal-2676	45	74	)	)	PUNCT
american_scientific_journal-2676	45	75	(	(	PUNCT
american_scientific_journal-2676	45	76	egefeh	egefeh	X
american_scientific_journal-2676	45	77	∪	∪	NOUN
american_scientific_journal-2676	45	78	,	,	PUNCT
american_scientific_journal-2676	45	79	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	45	80	.	.	PUNCT
american_scientific_journal-2676	46	1	moreover	moreover	ADV
american_scientific_journal-2676	46	2	,	,	PUNCT
american_scientific_journal-2676	46	3	the	the	DET
american_scientific_journal-2676	46	4	intersection	intersection	NOUN
american_scientific_journal-2676	46	5	of	of	ADP
american_scientific_journal-2676	46	6	soft	soft	ADJ
american_scientific_journal-2676	46	7	sets	set	NOUN
american_scientific_journal-2676	46	8	)	)	PUNCT
american_scientific_journal-2676	46	9	,	,	PUNCT
american_scientific_journal-2676	46	10	(	(	PUNCT
american_scientific_journal-2676	46	11	ef	ef	PROPN
american_scientific_journal-2676	46	12	and	and	CCONJ
american_scientific_journal-2676	46	13	)	)	PUNCT
american_scientific_journal-2676	46	14	,	,	PUNCT
american_scientific_journal-2676	46	15	(	(	PUNCT
american_scientific_journal-2676	46	16	eg	eg	NOUN
american_scientific_journal-2676	46	17	,	,	PUNCT
american_scientific_journal-2676	46	18	denoted	denote	VERB
american_scientific_journal-2676	46	19	by	by	ADP
american_scientific_journal-2676	46	20	)	)	PUNCT
american_scientific_journal-2676	46	21	,	,	PUNCT
american_scientific_journal-2676	46	22	(	(	PUNCT
american_scientific_journal-2676	46	23	~	~	NOUN
american_scientific_journal-2676	46	24	)	)	PUNCT
american_scientific_journal-2676	46	25	,	,	PUNCT
american_scientific_journal-2676	46	26	(	(	PUNCT
american_scientific_journal-2676	46	27	egef	egef	NOUN
american_scientific_journal-2676	46	28	∩	∩	NOUN
american_scientific_journal-2676	46	29	,	,	PUNCT
american_scientific_journal-2676	46	30	is	be	AUX
american_scientific_journal-2676	46	31	the	the	DET
american_scientific_journal-2676	46	32	soft	soft	ADJ
american_scientific_journal-2676	46	33	set	set	NOUN
american_scientific_journal-2676	46	34	)	)	PUNCT
american_scientific_journal-2676	46	35	,	,	PUNCT
american_scientific_journal-2676	46	36	(	(	PUNCT
american_scientific_journal-2676	46	37	em	em	PRON
american_scientific_journal-2676	46	38	which	which	PRON
american_scientific_journal-2676	46	39	defined	define	VERB
american_scientific_journal-2676	46	40	as	as	ADP
american_scientific_journal-2676	46	41	,	,	PUNCT
american_scientific_journal-2676	46	42	)	)	PUNCT
american_scientific_journal-2676	46	43	(	(	PUNCT
american_scientific_journal-2676	46	44	)	)	PUNCT
american_scientific_journal-2676	46	45	(=	(=	X
american_scientific_journal-2676	46	46	)	)	PUNCT
american_scientific_journal-2676	46	47	(	(	PUNCT
american_scientific_journal-2676	46	48	egefem	egefem	X
american_scientific_journal-2676	46	49	∩	∩	NOUN
american_scientific_journal-2676	46	50	,	,	PUNCT
american_scientific_journal-2676	46	51	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	46	52	.	.	PUNCT
american_scientific_journal-2676	47	1	the	the	DET
american_scientific_journal-2676	47	2	complement	complement	NOUN
american_scientific_journal-2676	47	3	of	of	ADP
american_scientific_journal-2676	47	4	a	a	DET
american_scientific_journal-2676	47	5	soft	soft	ADJ
american_scientific_journal-2676	47	6	set	set	NOUN
american_scientific_journal-2676	47	7	)	)	PUNCT
american_scientific_journal-2676	47	8	,	,	PUNCT
american_scientific_journal-2676	47	9	(	(	PUNCT
american_scientific_journal-2676	47	10	ef	ef	PROPN
american_scientific_journal-2676	47	11	,	,	PUNCT
american_scientific_journal-2676	47	12	denoted	denote	VERB
american_scientific_journal-2676	47	13	by	by	ADP
american_scientific_journal-2676	47	14	cef	cef	PROPN
american_scientific_journal-2676	47	15	)	)	PUNCT
american_scientific_journal-2676	47	16	,	,	PUNCT
american_scientific_journal-2676	47	17	(	(	PUNCT
american_scientific_journal-2676	47	18	,	,	PUNCT
american_scientific_journal-2676	47	19	is	be	AUX
american_scientific_journal-2676	47	20	defined	define	VERB
american_scientific_journal-2676	47	21	as	as	ADP
american_scientific_journal-2676	47	22	,	,	PUNCT
american_scientific_journal-2676	47	23	)	)	PUNCT
american_scientific_journal-2676	47	24	,	,	PUNCT
american_scientific_journal-2676	47	25	(	(	PUNCT
american_scientific_journal-2676	47	26	=)	=)	INTJ
american_scientific_journal-2676	47	27	,	,	PUNCT
american_scientific_journal-2676	47	28	(	(	PUNCT
american_scientific_journal-2676	47	29	efef	efef	PROPN
american_scientific_journal-2676	47	30	cc	cc	PROPN
american_scientific_journal-2676	47	31	,	,	PUNCT
american_scientific_journal-2676	47	32	where	where	SCONJ
american_scientific_journal-2676	47	33	)	)	PUNCT
american_scientific_journal-2676	47	34	(:	(:	VERB
american_scientific_journal-2676	47	35	xpef	xpef	NOUN
american_scientific_journal-2676	48	1	c	c	PROPN
american_scientific_journal-2676	48	2	→	→	X
american_scientific_journal-2676	48	3	is	be	AUX
american_scientific_journal-2676	48	4	a	a	DET
american_scientific_journal-2676	48	5	mapping	mapping	NOUN
american_scientific_journal-2676	48	6	given	give	VERB
american_scientific_journal-2676	48	7	by	by	ADP
american_scientific_journal-2676	48	8	)	)	PUNCT
american_scientific_journal-2676	48	9	(	(	PUNCT
american_scientific_journal-2676	48	10	\=	\=	PROPN
american_scientific_journal-2676	48	11	)	)	PUNCT
american_scientific_journal-2676	48	12	(	(	PUNCT
american_scientific_journal-2676	48	13	efxef	efxef	PROPN
american_scientific_journal-2676	48	14	c	c	NOUN
american_scientific_journal-2676	48	15	,	,	PUNCT
american_scientific_journal-2676	48	16	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	48	17	.	.	PUNCT
american_scientific_journal-2676	49	1	the	the	DET
american_scientific_journal-2676	49	2	difference	difference	NOUN
american_scientific_journal-2676	49	3	of	of	ADP
american_scientific_journal-2676	49	4	soft	soft	ADJ
american_scientific_journal-2676	49	5	sets	set	NOUN
american_scientific_journal-2676	49	6	)	)	PUNCT
american_scientific_journal-2676	49	7	,	,	PUNCT
american_scientific_journal-2676	49	8	(	(	PUNCT
american_scientific_journal-2676	49	9	ef	ef	PROPN
american_scientific_journal-2676	49	10	and	and	CCONJ
american_scientific_journal-2676	49	11	)	)	PUNCT
american_scientific_journal-2676	49	12	,	,	PUNCT
american_scientific_journal-2676	49	13	(	(	PUNCT
american_scientific_journal-2676	49	14	eg	eg	NOUN
american_scientific_journal-2676	49	15	,	,	PUNCT
american_scientific_journal-2676	49	16	denoted	denote	VERB
american_scientific_journal-2676	49	17	by	by	ADP
american_scientific_journal-2676	49	18	)	)	PUNCT
american_scientific_journal-2676	49	19	,	,	PUNCT
american_scientific_journal-2676	49	20	(	(	PUNCT
american_scientific_journal-2676	49	21	\	\	PROPN
american_scientific_journal-2676	49	22	)	)	PUNCT
american_scientific_journal-2676	49	23	,	,	PUNCT
american_scientific_journal-2676	49	24	(	(	PUNCT
american_scientific_journal-2676	49	25	egef	egef	VERB
american_scientific_journal-2676	49	26	,	,	PUNCT
american_scientific_journal-2676	49	27	is	be	AUX
american_scientific_journal-2676	49	28	the	the	DET
american_scientific_journal-2676	49	29	soft	soft	ADJ
american_scientific_journal-2676	49	30	set	set	NOUN
american_scientific_journal-2676	49	31	)	)	PUNCT
american_scientific_journal-2676	49	32	,	,	PUNCT
american_scientific_journal-2676	49	33	(	(	PUNCT
american_scientific_journal-2676	49	34	eh	eh	INTJ
american_scientific_journal-2676	49	35	,	,	PUNCT
american_scientific_journal-2676	49	36	which	which	PRON
american_scientific_journal-2676	49	37	defined	define	VERB
american_scientific_journal-2676	49	38	as	as	ADP
american_scientific_journal-2676	49	39	,	,	PUNCT
american_scientific_journal-2676	49	40	)	)	PUNCT
american_scientific_journal-2676	49	41	(	(	PUNCT
american_scientific_journal-2676	49	42	\)(=	\)(=	NOUN
american_scientific_journal-2676	49	43	)	)	PUNCT
american_scientific_journal-2676	49	44	(	(	PUNCT
american_scientific_journal-2676	49	45	egefeh	egefeh	X
american_scientific_journal-2676	49	46	,	,	PUNCT
american_scientific_journal-2676	49	47	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	49	48	.	.	PUNCT
american_scientific_journal-2676	50	1	clearly	clearly	ADV
american_scientific_journal-2676	50	2	,	,	PUNCT
american_scientific_journal-2676	50	3	cegefegef	cegefegef	NOUN
american_scientific_journal-2676	50	4	)	)	PUNCT
american_scientific_journal-2676	50	5	,	,	PUNCT
american_scientific_journal-2676	50	6	(	(	PUNCT
american_scientific_journal-2676	50	7	~),(=),(\	~),(=),(\	PROPN
american_scientific_journal-2676	50	8	)	)	PUNCT
american_scientific_journal-2676	50	9	,	,	PUNCT
american_scientific_journal-2676	50	10	(	(	PUNCT
american_scientific_journal-2676	50	11	∩	∩	PROPN
american_scientific_journal-2676	50	12	.	.	PUNCT
american_scientific_journal-2676	51	1	a	a	DET
american_scientific_journal-2676	51	2	soft	soft	ADJ
american_scientific_journal-2676	51	3	set	set	NOUN
american_scientific_journal-2676	51	4	)	)	PUNCT
american_scientific_journal-2676	51	5	,	,	PUNCT
american_scientific_journal-2676	51	6	(	(	PUNCT
american_scientific_journal-2676	51	7	ef	ef	PROPN
american_scientific_journal-2676	51	8	is	be	AUX
american_scientific_journal-2676	51	9	called	call	VERB
american_scientific_journal-2676	51	10	a	a	DET
american_scientific_journal-2676	51	11	null	null	ADJ
american_scientific_journal-2676	51	12	soft	soft	ADJ
american_scientific_journal-2676	51	13	set	set	NOUN
american_scientific_journal-2676	51	14	,	,	PUNCT
american_scientific_journal-2676	51	15	denoted	denote	VERB
american_scientific_journal-2676	51	16	by	by	ADP
american_scientific_journal-2676	51	17	)	)	PUNCT
american_scientific_journal-2676	51	18	,	,	PUNCT
american_scientific_journal-2676	51	19	~	~	PROPN
american_scientific_journal-2676	51	20	(	(	PUNCT
american_scientific_journal-2676	51	21	eφ	eφ	INTJ
american_scientific_journal-2676	51	22	,	,	PUNCT
american_scientific_journal-2676	51	23	if	if	SCONJ
american_scientific_journal-2676	51	24	φ=)(ef	φ=)(ef	NOUN
american_scientific_journal-2676	51	25	,	,	PUNCT
american_scientific_journal-2676	51	26	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	51	27	.	.	PUNCT
american_scientific_journal-2676	52	1	moreover	moreover	ADV
american_scientific_journal-2676	52	2	,	,	PUNCT
american_scientific_journal-2676	52	3	a	a	DET
american_scientific_journal-2676	52	4	soft	soft	ADJ
american_scientific_journal-2676	52	5	set	set	NOUN
american_scientific_journal-2676	52	6	)	)	PUNCT
american_scientific_journal-2676	52	7	,	,	PUNCT
american_scientific_journal-2676	52	8	(	(	PUNCT
american_scientific_journal-2676	52	9	ef	ef	PROPN
american_scientific_journal-2676	52	10	is	be	AUX
american_scientific_journal-2676	52	11	called	call	VERB
american_scientific_journal-2676	52	12	an	an	DET
american_scientific_journal-2676	52	13	absolute	absolute	ADJ
american_scientific_journal-2676	52	14	soft	soft	ADJ
american_scientific_journal-2676	52	15	set	set	NOUN
american_scientific_journal-2676	52	16	,	,	PUNCT
american_scientific_journal-2676	52	17	denoted	denote	VERB
american_scientific_journal-2676	52	18	by	by	ADP
american_scientific_journal-2676	52	19	)	)	PUNCT
american_scientific_journal-2676	52	20	,	,	PUNCT
american_scientific_journal-2676	52	21	~	~	PUNCT
american_scientific_journal-2676	52	22	(	(	PUNCT
american_scientific_journal-2676	52	23	ex	ex	X
american_scientific_journal-2676	52	24	,	,	PUNCT
american_scientific_journal-2676	52	25	if	if	SCONJ
american_scientific_journal-2676	52	26	xef	xef	PROPN
american_scientific_journal-2676	52	27	=)	=)	PROPN
american_scientific_journal-2676	52	28	(	(	PUNCT
american_scientific_journal-2676	52	29	,	,	PUNCT
american_scientific_journal-2676	52	30	ee∈∀	ee∈∀	PROPN
american_scientific_journal-2676	52	31	.	.	PUNCT
american_scientific_journal-2676	53	1	clearly	clearly	ADV
american_scientific_journal-2676	53	2	,	,	PUNCT
american_scientific_journal-2676	53	3	we	we	PRON
american_scientific_journal-2676	53	4	have	have	VERB
american_scientific_journal-2676	53	5	)	)	PUNCT
american_scientific_journal-2676	53	6	,	,	PUNCT
american_scientific_journal-2676	53	7	~(=),~	~(=),~	PROPN
american_scientific_journal-2676	53	8	(	(	PUNCT
american_scientific_journal-2676	53	9	exe	exe	NOUN
american_scientific_journal-2676	53	10	cφ	cφ	NOUN
american_scientific_journal-2676	53	11	and	and	CCONJ
american_scientific_journal-2676	53	12	)	)	PUNCT
american_scientific_journal-2676	53	13	,	,	PUNCT
american_scientific_journal-2676	53	14	~(=),~	~(=),~	PROPN
american_scientific_journal-2676	53	15	(	(	PUNCT
american_scientific_journal-2676	53	16	eex	eex	PROPN
american_scientific_journal-2676	53	17	c	c	PROPN
american_scientific_journal-2676	53	18	φ	φ	PROPN
american_scientific_journal-2676	53	19	.	.	PUNCT
american_scientific_journal-2676	54	1	moreover	moreover	ADV
american_scientific_journal-2676	54	2	,	,	PUNCT
american_scientific_journal-2676	54	3	a	a	DET
american_scientific_journal-2676	54	4	soft	soft	ADJ
american_scientific_journal-2676	54	5	set	set	NOUN
american_scientific_journal-2676	54	6	)	)	PUNCT
american_scientific_journal-2676	54	7	,	,	PUNCT
american_scientific_journal-2676	54	8	(	(	PUNCT
american_scientific_journal-2676	54	9	eg	eg	NOUN
american_scientific_journal-2676	54	10	is	be	AUX
american_scientific_journal-2676	54	11	said	say	VERB
american_scientific_journal-2676	54	12	to	to	PART
american_scientific_journal-2676	54	13	be	be	AUX
american_scientific_journal-2676	54	14	a	a	DET
american_scientific_journal-2676	54	15	finite	finite	ADJ
american_scientific_journal-2676	54	16	soft	soft	ADJ
american_scientific_journal-2676	54	17	set	set	NOUN
american_scientific_journal-2676	54	18	if	if	SCONJ
american_scientific_journal-2676	54	19	)	)	PUNCT
american_scientific_journal-2676	54	20	(	(	PUNCT
american_scientific_journal-2676	54	21	eg	eg	NOUN
american_scientific_journal-2676	54	22	is	be	AUX
american_scientific_journal-2676	54	23	a	a	DET
american_scientific_journal-2676	54	24	finite	finite	NOUN
american_scientific_journal-2676	54	25	set	set	VERB
american_scientific_journal-2676	54	26	for	for	ADP
american_scientific_journal-2676	54	27	all	all	DET
american_scientific_journal-2676	54	28	ee∈	ee∈	PROPN
american_scientific_journal-2676	54	29	.	.	PUNCT
american_scientific_journal-2676	55	1	otherwise	otherwise	ADV
american_scientific_journal-2676	55	2	,	,	PUNCT
american_scientific_journal-2676	55	3	it	it	PRON
american_scientific_journal-2676	55	4	is	be	AUX
american_scientific_journal-2676	55	5	called	call	VERB
american_scientific_journal-2676	55	6	an	an	DET
american_scientific_journal-2676	55	7	infinite	infinite	ADJ
american_scientific_journal-2676	55	8	soft	soft	ADJ
american_scientific_journal-2676	55	9	set	set	NOUN
american_scientific_journal-2676	55	10	.	.	PUNCT
american_scientific_journal-2676	56	1	definition	definition	NOUN
american_scientific_journal-2676	56	2	2.2	2.2	NUM
american_scientific_journal-2676	56	3	(	(	PUNCT
american_scientific_journal-2676	56	4	[	[	NOUN
american_scientific_journal-2676	56	5	15,17,21	15,17,21	NUM
american_scientific_journal-2676	56	6	]	]	SYM
american_scientific_journal-2676	56	7	)	)	PUNCT
american_scientific_journal-2676	56	8	a	a	DET
american_scientific_journal-2676	56	9	soft	soft	ADJ
american_scientific_journal-2676	56	10	set	set	NOUN
american_scientific_journal-2676	56	11	)	)	PUNCT
american_scientific_journal-2676	56	12	,	,	PUNCT
american_scientific_journal-2676	56	13	(	(	PUNCT
american_scientific_journal-2676	56	14	ef	ef	VERB
american_scientific_journal-2676	56	15	over	over	ADP
american_scientific_journal-2676	56	16	x	x	VERB
american_scientific_journal-2676	56	17	is	be	AUX
american_scientific_journal-2676	56	18	said	say	VERB
american_scientific_journal-2676	56	19	to	to	PART
american_scientific_journal-2676	56	20	be	be	AUX
american_scientific_journal-2676	56	21	a	a	DET
american_scientific_journal-2676	56	22	soft	soft	ADJ
american_scientific_journal-2676	56	23	point	point	NOUN
american_scientific_journal-2676	56	24	in	in	ADP
american_scientific_journal-2676	56	25	)	)	PUNCT
american_scientific_journal-2676	56	26	,	,	PUNCT
american_scientific_journal-2676	57	1	~	~	PUNCT
american_scientific_journal-2676	57	2	(	(	PUNCT
american_scientific_journal-2676	57	3	ex	ex	PUNCT
american_scientific_journal-2676	57	4	if	if	SCONJ
american_scientific_journal-2676	57	5	there	there	PRON
american_scientific_journal-2676	57	6	exist	exist	VERB
american_scientific_journal-2676	57	7	xx∈	xx∈	PROPN
american_scientific_journal-2676	57	8	and	and	CCONJ
american_scientific_journal-2676	57	9	ee∈	ee∈	PROPN
american_scientific_journal-2676	57	10	such	such	ADJ
american_scientific_journal-2676	57	11	that	that	SCONJ
american_scientific_journal-2676	57	12	}	}	PUNCT
american_scientific_journal-2676	57	13	{	{	PUNCT
american_scientific_journal-2676	57	14	=)	=)	PROPN
american_scientific_journal-2676	57	15	(	(	PUNCT
american_scientific_journal-2676	57	16	xef	xef	PROPN
american_scientific_journal-2676	57	17	and	and	CCONJ
american_scientific_journal-2676	57	18	φ=)(ef	φ=)(ef	PROPN
american_scientific_journal-2676	57	19	′	′	VERB
american_scientific_journal-2676	57	20	for	for	ADP
american_scientific_journal-2676	57	21	each	each	DET
american_scientific_journal-2676	57	22	}	}	PUNCT
american_scientific_journal-2676	57	23	{	{	PUNCT
american_scientific_journal-2676	57	24	\	\	PROPN
american_scientific_journal-2676	57	25	eee	eee	PROPN
american_scientific_journal-2676	57	26	∈′	∈′	PROPN
american_scientific_journal-2676	57	27	.	.	PUNCT
american_scientific_journal-2676	58	1	this	this	DET
american_scientific_journal-2676	58	2	soft	soft	ADJ
american_scientific_journal-2676	58	3	point	point	NOUN
american_scientific_journal-2676	58	4	is	be	AUX
american_scientific_journal-2676	58	5	denoted	denote	VERB
american_scientific_journal-2676	58	6	by	by	ADP
american_scientific_journal-2676	58	7	)	)	PUNCT
american_scientific_journal-2676	58	8	,	,	PUNCT
american_scientific_journal-2676	58	9	(	(	PUNCT
american_scientific_journal-2676	58	10	exe	exe	NOUN
american_scientific_journal-2676	58	11	or	or	CCONJ
american_scientific_journal-2676	58	12	ex	ex	ADJ
american_scientific_journal-2676	58	13	,	,	PUNCT
american_scientific_journal-2676	58	14	i.e.	i.e.	X
american_scientific_journal-2676	58	15	,	,	PUNCT
american_scientific_journal-2676	58	16	)	)	PUNCT
american_scientific_journal-2676	58	17	(:	(:	PROPN
american_scientific_journal-2676	58	18	xpexe	xpexe	PROPN
american_scientific_journal-2676	58	19	→	→	PUNCT
american_scientific_journal-2676	58	20	is	be	AUX
american_scientific_journal-2676	58	21	a	a	DET
american_scientific_journal-2676	58	22	mapping	mapping	NOUN
american_scientific_journal-2676	58	23	defined	define	VERB
american_scientific_journal-2676	58	24	as	as	ADP
american_scientific_journal-2676	58	25			ADJ
american_scientific_journal-2676	58	26			ADP
american_scientific_journal-2676	58	27			ADJ
american_scientific_journal-2676	58	28	≠	≠	ADJ
american_scientific_journal-2676	58	29	aeif	aeif	NOUN
american_scientific_journal-2676	58	30	aeifx	aeifx	NOUN
american_scientific_journal-2676	58	31	axe	axe	NOUN
american_scientific_journal-2676	58	32	φ	φ	PROPN
american_scientific_journal-2676	58	33	,	,	PUNCT
american_scientific_journal-2676	58	34	=	=	NOUN
american_scientific_journal-2676	58	35	}	}	PUNCT
american_scientific_journal-2676	58	36	{	{	PUNCT
american_scientific_journal-2676	58	37	=)	=)	X
american_scientific_journal-2676	58	38	(	(	PUNCT
american_scientific_journal-2676	58	39	for	for	ADP
american_scientific_journal-2676	58	40	all	all	DET
american_scientific_journal-2676	58	41	ea∈	ea∈	NOUN
american_scientific_journal-2676	58	42	.	.	PUNCT
american_scientific_journal-2676	59	1	a	a	DET
american_scientific_journal-2676	59	2	soft	soft	ADJ
american_scientific_journal-2676	59	3	point	point	NOUN
american_scientific_journal-2676	59	4	)	)	PUNCT
american_scientific_journal-2676	59	5	,	,	PUNCT
american_scientific_journal-2676	59	6	(	(	PUNCT
american_scientific_journal-2676	59	7	exe	exe	NOUN
american_scientific_journal-2676	59	8	is	be	AUX
american_scientific_journal-2676	59	9	said	say	VERB
american_scientific_journal-2676	59	10	to	to	PART
american_scientific_journal-2676	59	11	be	be	AUX
american_scientific_journal-2676	59	12	belonging	belong	VERB
american_scientific_journal-2676	59	13	to	to	ADP
american_scientific_journal-2676	59	14	the	the	DET
american_scientific_journal-2676	59	15	soft	soft	ADJ
american_scientific_journal-2676	59	16	set	set	NOUN
american_scientific_journal-2676	59	17	)	)	PUNCT
american_scientific_journal-2676	59	18	,	,	PUNCT
american_scientific_journal-2676	59	19	(	(	PUNCT
american_scientific_journal-2676	59	20	eg	eg	NOUN
american_scientific_journal-2676	59	21	,	,	PUNCT
american_scientific_journal-2676	59	22	denoted	denote	VERB
american_scientific_journal-2676	59	23	by	by	ADP
american_scientific_journal-2676	59	24	)	)	PUNCT
american_scientific_journal-2676	59	25	,	,	PUNCT
american_scientific_journal-2676	59	26	(	(	PUNCT
american_scientific_journal-2676	59	27	~	~	PUNCT
american_scientific_journal-2676	59	28	egxe	egxe	NOUN
american_scientific_journal-2676	59	29	∈	∈	NOUN
american_scientific_journal-2676	59	30	,	,	PUNCT
american_scientific_journal-2676	59	31	if	if	SCONJ
american_scientific_journal-2676	59	32	)	)	PUNCT
american_scientific_journal-2676	59	33	(	(	PUNCT
american_scientific_journal-2676	59	34	)	)	PUNCT
american_scientific_journal-2676	59	35	(	(	PUNCT
american_scientific_journal-2676	59	36	egexe	egexe	ADV
american_scientific_journal-2676	59	37	⊆	⊆	NUM
american_scientific_journal-2676	59	38	,	,	PUNCT
american_scientific_journal-2676	59	39	i.e.	i.e.	X
american_scientific_journal-2676	59	40	,	,	PUNCT
american_scientific_journal-2676	59	41	)	)	PUNCT
american_scientific_journal-2676	59	42	(	(	PUNCT
american_scientific_journal-2676	59	43	}	}	PUNCT
american_scientific_journal-2676	59	44	{	{	PUNCT
american_scientific_journal-2676	59	45	egx	egx	PROPN
american_scientific_journal-2676	59	46	⊆	⊆	NUM
american_scientific_journal-2676	59	47	.	.	PUNCT
american_scientific_journal-2676	60	1	clearly	clearly	ADV
american_scientific_journal-2676	60	2	,	,	PUNCT
american_scientific_journal-2676	60	3	)	)	PUNCT
american_scientific_journal-2676	60	4	,	,	PUNCT
american_scientific_journal-2676	60	5	(	(	PUNCT
american_scientific_journal-2676	60	6	~	~	PUNCT
american_scientific_journal-2676	60	7	egxe	egxe	NOUN
american_scientific_journal-2676	60	8	∈	∈	PROPN
american_scientific_journal-2676	60	9	if	if	SCONJ
american_scientific_journal-2676	60	10	and	and	CCONJ
american_scientific_journal-2676	60	11	only	only	ADV
american_scientific_journal-2676	60	12	if	if	SCONJ
american_scientific_journal-2676	60	13	)	)	PUNCT
american_scientific_journal-2676	60	14	,	,	PUNCT
american_scientific_journal-2676	60	15	(	(	PUNCT
american_scientific_journal-2676	60	16	~	~	NOUN
american_scientific_journal-2676	60	17	)	)	PUNCT
american_scientific_journal-2676	60	18	,	,	PUNCT
american_scientific_journal-2676	60	19	(	(	PUNCT
american_scientific_journal-2676	60	20	egexe	egexe	ADV
american_scientific_journal-2676	60	21	⊆	⊆	NUM
american_scientific_journal-2676	60	22	.	.	PUNCT
american_scientific_journal-2676	61	1	in	in	ADP
american_scientific_journal-2676	61	2	addition	addition	NOUN
american_scientific_journal-2676	61	3	,	,	PUNCT
american_scientific_journal-2676	61	4	two	two	NUM
american_scientific_journal-2676	61	5	soft	soft	ADJ
american_scientific_journal-2676	61	6	points	point	NOUN
american_scientific_journal-2676	61	7	1e	1e	NOUN
american_scientific_journal-2676	61	8	x	x	X
american_scientific_journal-2676	61	9	,	,	PUNCT
american_scientific_journal-2676	61	10	2ey	2ey	NOUN
american_scientific_journal-2676	61	11	over	over	ADP
american_scientific_journal-2676	61	12	x	x	VERB
american_scientific_journal-2676	61	13	are	be	AUX
american_scientific_journal-2676	61	14	said	say	VERB
american_scientific_journal-2676	61	15	to	to	PART
american_scientific_journal-2676	61	16	be	be	AUX
american_scientific_journal-2676	61	17	equal	equal	ADJ
american_scientific_journal-2676	61	18	if	if	SCONJ
american_scientific_journal-2676	61	19	yx	yx	NOUN
american_scientific_journal-2676	61	20	=	=	PUNCT
american_scientific_journal-2676	61	21	and	and	CCONJ
american_scientific_journal-2676	61	22	21	21	NUM
american_scientific_journal-2676	61	23	=	=	SYM
american_scientific_journal-2676	61	24	ee	ee	X
american_scientific_journal-2676	61	25	.	.	PUNCT
american_scientific_journal-2676	62	1	thus	thus	ADV
american_scientific_journal-2676	62	2	,	,	PUNCT
american_scientific_journal-2676	62	3	21	21	NUM
american_scientific_journal-2676	62	4	ee	ee	NOUN
american_scientific_journal-2676	62	5	yx	yx	PROPN
american_scientific_journal-2676	62	6	≠	≠	PROPN
american_scientific_journal-2676	62	7	iff	iff	PROPN
american_scientific_journal-2676	62	8	yx	yx	PROPN
american_scientific_journal-2676	62	9	≠	≠	PROPN
american_scientific_journal-2676	62	10	or	or	CCONJ
american_scientific_journal-2676	62	11	21	21	NUM
american_scientific_journal-2676	62	12	ee	ee	ADP
american_scientific_journal-2676	62	13	≠	≠	PROPN
american_scientific_journal-2676	62	14	.	.	PUNCT
american_scientific_journal-2676	63	1	the	the	DET
american_scientific_journal-2676	63	2	family	family	NOUN
american_scientific_journal-2676	63	3	of	of	ADP
american_scientific_journal-2676	63	4	all	all	DET
american_scientific_journal-2676	63	5	soft	soft	ADJ
american_scientific_journal-2676	63	6	points	point	NOUN
american_scientific_journal-2676	63	7	in	in	ADP
american_scientific_journal-2676	63	8	)	)	PUNCT
american_scientific_journal-2676	63	9	,	,	PUNCT
american_scientific_journal-2676	63	10	~	~	PUNCT
american_scientific_journal-2676	63	11	(	(	PUNCT
american_scientific_journal-2676	63	12	ex	ex	X
american_scientific_journal-2676	63	13	is	be	AUX
american_scientific_journal-2676	63	14	denoted	denote	VERB
american_scientific_journal-2676	63	15	by	by	ADP
american_scientific_journal-2676	63	16	ex	ex	X
american_scientific_journal-2676	63	17	)	)	PUNCT
american_scientific_journal-2676	63	18	(	(	PUNCT
american_scientific_journal-2676	63	19	ξ	ξ	PROPN
american_scientific_journal-2676	63	20	.	.	PUNCT
american_scientific_journal-2676	64	1	proposition	proposition	NOUN
american_scientific_journal-2676	64	2	2.1	2.1	NUM
american_scientific_journal-2676	64	3	[	[	X
american_scientific_journal-2676	64	4	21	21	NUM
american_scientific_journal-2676	64	5	]	]	PUNCT
american_scientific_journal-2676	64	6	the	the	DET
american_scientific_journal-2676	64	7	union	union	NOUN
american_scientific_journal-2676	64	8	of	of	ADP
american_scientific_journal-2676	64	9	any	any	DET
american_scientific_journal-2676	64	10	collection	collection	NOUN
american_scientific_journal-2676	64	11	of	of	ADP
american_scientific_journal-2676	64	12	soft	soft	ADJ
american_scientific_journal-2676	64	13	points	point	NOUN
american_scientific_journal-2676	64	14	can	can	AUX
american_scientific_journal-2676	64	15	be	be	AUX
american_scientific_journal-2676	64	16	considered	consider	VERB
american_scientific_journal-2676	64	17	as	as	ADP
american_scientific_journal-2676	64	18	a	a	DET
american_scientific_journal-2676	64	19	soft	soft	ADJ
american_scientific_journal-2676	64	20	set	set	NOUN
american_scientific_journal-2676	64	21	and	and	CCONJ
american_scientific_journal-2676	64	22	every	every	DET
american_scientific_journal-2676	64	23	soft	soft	ADJ
american_scientific_journal-2676	64	24	set	set	NOUN
american_scientific_journal-2676	64	25	can	can	AUX
american_scientific_journal-2676	64	26	be	be	AUX
american_scientific_journal-2676	64	27	expressed	express	VERB
american_scientific_journal-2676	64	28	as	as	ADP
american_scientific_journal-2676	64	29	a	a	DET
american_scientific_journal-2676	64	30	union	union	NOUN
american_scientific_journal-2676	64	31	of	of	ADP
american_scientific_journal-2676	64	32	all	all	DET
american_scientific_journal-2676	64	33	soft	soft	ADJ
american_scientific_journal-2676	64	34	points	point	NOUN
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american_scientific_journal-2676	64	36	to	to	ADP
american_scientific_journal-2676	64	37	it	it	PRON
american_scientific_journal-2676	64	38	,	,	PUNCT
american_scientific_journal-2676	64	39	i.e.	i.e.	X
american_scientific_journal-2676	64	40	,	,	PUNCT
american_scientific_journal-2676	64	41	)	)	PUNCT
american_scientific_journal-2676	64	42	}	}	PUNCT
american_scientific_journal-2676	64	43	,	,	PUNCT
american_scientific_journal-2676	64	44	(	(	PUNCT
american_scientific_journal-2676	64	45	~:),{(=	~:),{(=	ADJ
american_scientific_journal-2676	64	46	)	)	PUNCT
american_scientific_journal-2676	64	47	,	,	PUNCT
american_scientific_journal-2676	64	48	(	(	PUNCT
american_scientific_journal-2676	64	49	egxexeg	egxexeg	NOUN
american_scientific_journal-2676	64	50	ee	ee	X
american_scientific_journal-2676	64	51	∈	∈	ADJ
american_scientific_journal-2676	64	52	.	.	PUNCT
american_scientific_journal-2676	65	1	proposition	proposition	NOUN
american_scientific_journal-2676	65	2	2.2	2.2	NUM
american_scientific_journal-2676	65	3	[	[	X
american_scientific_journal-2676	65	4	21	21	NUM
american_scientific_journal-2676	65	5	]	]	PUNCT
american_scientific_journal-2676	65	6	let	let	NOUN
american_scientific_journal-2676	65	7	)	)	PUNCT
american_scientific_journal-2676	65	8	,	,	PUNCT
american_scientific_journal-2676	65	9	(	(	PUNCT
american_scientific_journal-2676	65	10	eg	eg	NOUN
american_scientific_journal-2676	65	11	,	,	PUNCT
american_scientific_journal-2676	65	12	)	)	PUNCT
american_scientific_journal-2676	65	13	,	,	PUNCT
american_scientific_journal-2676	65	14	(	(	PUNCT
american_scientific_journal-2676	65	15	eh	eh	INTJ
american_scientific_journal-2676	65	16	be	be	AUX
american_scientific_journal-2676	65	17	two	two	NUM
american_scientific_journal-2676	65	18	soft	soft	ADJ
american_scientific_journal-2676	65	19	sets	set	NOUN
american_scientific_journal-2676	65	20	over	over	ADP
american_scientific_journal-2676	65	21	x	x	X
american_scientific_journal-2676	65	22	.	.	PUNCT
american_scientific_journal-2676	66	1	then	then	ADV
american_scientific_journal-2676	66	2	,	,	PUNCT
american_scientific_journal-2676	66	3	1	1	X
american_scientific_journal-2676	66	4	)	)	PUNCT
american_scientific_journal-2676	66	5	c	c	NOUN
american_scientific_journal-2676	66	6	ee	ee	X
american_scientific_journal-2676	66	7	egxegx	egxegx	PROPN
american_scientific_journal-2676	66	8	)	)	PUNCT
american_scientific_journal-2676	66	9	,	,	PUNCT
american_scientific_journal-2676	66	10	(	(	PUNCT
american_scientific_journal-2676	66	11	~),(~	~),(~	NUM
american_scientific_journal-2676	66	12	∈/⇔∈	∈/⇔∈	NOUN
american_scientific_journal-2676	66	13	.	.	PUNCT
american_scientific_journal-2676	67	1	2	2	NUM
american_scientific_journal-2676	67	2	)	)	PUNCT
american_scientific_journal-2676	67	3	)	)	PUNCT
american_scientific_journal-2676	67	4	,	,	PUNCT
american_scientific_journal-2676	67	5	(	(	PUNCT
american_scientific_journal-2676	67	6	~),(~),(~	~),(~),(~	X
american_scientific_journal-2676	67	7	egxehegx	egxehegx	NOUN
american_scientific_journal-2676	67	8	ee	ee	ADP
american_scientific_journal-2676	67	9	∈⇔∪∈	∈⇔∪∈	NUM
american_scientific_journal-2676	67	10	or	or	CCONJ
american_scientific_journal-2676	67	11	)	)	PUNCT
american_scientific_journal-2676	67	12	,	,	PUNCT
american_scientific_journal-2676	67	13	(	(	PUNCT
american_scientific_journal-2676	67	14	~	~	PUNCT
american_scientific_journal-2676	67	15	ehxe	ehxe	ADJ
american_scientific_journal-2676	67	16	∈	∈	NOUN
american_scientific_journal-2676	67	17	.	.	PUNCT
american_scientific_journal-2676	68	1	3	3	X
american_scientific_journal-2676	68	2	)	)	PUNCT
american_scientific_journal-2676	68	3	)	)	PUNCT
american_scientific_journal-2676	68	4	,	,	PUNCT
american_scientific_journal-2676	68	5	(	(	PUNCT
american_scientific_journal-2676	68	6	~),(~),(~	~),(~),(~	NUM
american_scientific_journal-2676	68	7	egxehegx	egxehegx	NOUN
american_scientific_journal-2676	68	8	ee	ee	X
american_scientific_journal-2676	68	9	∈⇔∩∈	∈⇔∩∈	PROPN
american_scientific_journal-2676	68	10	and	and	CCONJ
american_scientific_journal-2676	68	11	american	american	ADJ
american_scientific_journal-2676	68	12	scientific	scientific	ADJ
american_scientific_journal-2676	68	13	research	research	NOUN
american_scientific_journal-2676	68	14	journal	journal	NOUN
american_scientific_journal-2676	68	15	for	for	ADP
american_scientific_journal-2676	68	16	engineering	engineering	NOUN
american_scientific_journal-2676	68	17	,	,	PUNCT
american_scientific_journal-2676	68	18	technology	technology	NOUN
american_scientific_journal-2676	68	19	,	,	PUNCT
american_scientific_journal-2676	68	20	and	and	CCONJ
american_scientific_journal-2676	68	21	sciences	science	NOUN
american_scientific_journal-2676	68	22	(	(	PUNCT
american_scientific_journal-2676	68	23	asrjets	asrjet	NOUN
american_scientific_journal-2676	68	24	)	)	PUNCT
american_scientific_journal-2676	68	25	(	(	PUNCT
american_scientific_journal-2676	68	26	2017	2017	NUM
american_scientific_journal-2676	68	27	)	)	PUNCT
american_scientific_journal-2676	68	28	volume	volume	NOUN
american_scientific_journal-2676	68	29	28	28	NUM
american_scientific_journal-2676	68	30	,	,	PUNCT
american_scientific_journal-2676	68	31	no	no	DET
american_scientific_journal-2676	68	32	1	1	NUM
american_scientific_journal-2676	68	33	,	,	PUNCT
american_scientific_journal-2676	68	34	pp	pp	ADV
american_scientific_journal-2676	68	35	225	225	NUM
american_scientific_journal-2676	68	36	-	-	SYM
american_scientific_journal-2676	68	37	247	247	NUM
american_scientific_journal-2676	68	38	228	228	NUM
american_scientific_journal-2676	68	39	)	)	PUNCT
american_scientific_journal-2676	68	40	,	,	PUNCT
american_scientific_journal-2676	68	41	(	(	PUNCT
american_scientific_journal-2676	68	42	~	~	PUNCT
american_scientific_journal-2676	68	43	ehxe	ehxe	ADJ
american_scientific_journal-2676	68	44	∈	∈	NOUN
american_scientific_journal-2676	68	45	.	.	PUNCT
american_scientific_journal-2676	69	1	4	4	NUM
american_scientific_journal-2676	69	2	)	)	PUNCT
american_scientific_journal-2676	69	3	)	)	PUNCT
american_scientific_journal-2676	70	1	]	]	PUNCT
american_scientific_journal-2676	70	2	,	,	PUNCT
american_scientific_journal-2676	70	3	(	(	PUNCT
american_scientific_journal-2676	70	4	~),(~[),(~	~),(~[),(~	ADV
american_scientific_journal-2676	70	5	)	)	PUNCT
american_scientific_journal-2676	70	6	,	,	PUNCT
american_scientific_journal-2676	70	7	(	(	PUNCT
american_scientific_journal-2676	70	8	ehxegxeheg	ehxegxeheg	NOUN
american_scientific_journal-2676	70	9	ee	ee	VERB
american_scientific_journal-2676	70	10	∈⇒∈⇔⊆	∈⇒∈⇔⊆	PROPN
american_scientific_journal-2676	70	11	.	.	PUNCT
american_scientific_journal-2676	71	1	for	for	ADP
american_scientific_journal-2676	71	2	more	more	ADJ
american_scientific_journal-2676	71	3	details	detail	NOUN
american_scientific_journal-2676	71	4	for	for	ADP
american_scientific_journal-2676	71	5	soft	soft	ADJ
american_scientific_journal-2676	71	6	point	point	NOUN
american_scientific_journal-2676	71	7	you	you	PRON
american_scientific_journal-2676	71	8	can	can	AUX
american_scientific_journal-2676	71	9	see	see	VERB
american_scientific_journal-2676	71	10	in	in	ADP
american_scientific_journal-2676	71	11	[	[	X
american_scientific_journal-2676	71	12	15,21,17	15,21,17	NOUN
american_scientific_journal-2676	71	13	]	]	PUNCT
american_scientific_journal-2676	71	14	.	.	PUNCT
american_scientific_journal-2676	72	1	definition	definition	NOUN
american_scientific_journal-2676	72	2	2.3	2.3	NUM
american_scientific_journal-2676	72	3	[	[	SYM
american_scientific_journal-2676	72	4	20	20	NUM
american_scientific_journal-2676	72	5	]	]	PUNCT
american_scientific_journal-2676	72	6	let	let	VERB
american_scientific_journal-2676	72	7	η	η	X
american_scientific_journal-2676	72	8	be	be	AUX
american_scientific_journal-2676	72	9	a	a	DET
american_scientific_journal-2676	72	10	collection	collection	NOUN
american_scientific_journal-2676	72	11	of	of	ADP
american_scientific_journal-2676	72	12	soft	soft	ADJ
american_scientific_journal-2676	72	13	sets	set	NOUN
american_scientific_journal-2676	72	14	over	over	ADP
american_scientific_journal-2676	72	15	a	a	DET
american_scientific_journal-2676	72	16	universe	universe	NOUN
american_scientific_journal-2676	72	17	x	x	PUNCT
american_scientific_journal-2676	72	18	with	with	ADP
american_scientific_journal-2676	72	19	a	a	DET
american_scientific_journal-2676	72	20	fixed	fix	VERB
american_scientific_journal-2676	72	21	set	set	NOUN
american_scientific_journal-2676	72	22	of	of	ADP
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american_scientific_journal-2676	72	24	e	e	NOUN
american_scientific_journal-2676	72	25	,	,	PUNCT
american_scientific_journal-2676	72	26	i.e.	i.e.	X
american_scientific_journal-2676	72	27	,	,	PUNCT
american_scientific_journal-2676	72	28	exss	exss	NOUN
american_scientific_journal-2676	72	29	)	)	PUNCT
american_scientific_journal-2676	72	30	(	(	PUNCT
american_scientific_journal-2676	72	31	⊆η	⊆η	NOUN
american_scientific_journal-2676	72	32	.	.	PUNCT
american_scientific_journal-2676	73	1	the	the	DET
american_scientific_journal-2676	73	2	collection	collection	PROPN
american_scientific_journal-2676	73	3	η	η	PROPN
american_scientific_journal-2676	73	4	is	be	AUX
american_scientific_journal-2676	73	5	called	call	VERB
american_scientific_journal-2676	73	6	a	a	DET
american_scientific_journal-2676	73	7	soft	soft	ADJ
american_scientific_journal-2676	73	8	topology	topology	NOUN
american_scientific_journal-2676	73	9	on	on	ADP
american_scientific_journal-2676	73	10	x	x	PUNCT
american_scientific_journal-2676	73	11	if	if	SCONJ
american_scientific_journal-2676	73	12	it	it	PRON
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american_scientific_journal-2676	73	14	the	the	DET
american_scientific_journal-2676	73	15	following	follow	VERB
american_scientific_journal-2676	73	16	axioms	axiom	NOUN
american_scientific_journal-2676	73	17	:	:	PUNCT
american_scientific_journal-2676	73	18	1	1	X
american_scientific_journal-2676	73	19	)	)	PUNCT
american_scientific_journal-2676	73	20	ηφ	ηφ	ADP
american_scientific_journal-2676	73	21	∈),~(),,~	∈),~(),,~	PROPN
american_scientific_journal-2676	73	22	(	(	PUNCT
american_scientific_journal-2676	73	23	eex	eex	NOUN
american_scientific_journal-2676	73	24	,	,	PUNCT
american_scientific_journal-2676	73	25	2	2	X
american_scientific_journal-2676	73	26	)	)	PUNCT
american_scientific_journal-2676	73	27	the	the	DET
american_scientific_journal-2676	73	28	union	union	NOUN
american_scientific_journal-2676	73	29	of	of	ADP
american_scientific_journal-2676	73	30	any	any	DET
american_scientific_journal-2676	73	31	number	number	NOUN
american_scientific_journal-2676	73	32	of	of	ADP
american_scientific_journal-2676	73	33	soft	soft	ADJ
american_scientific_journal-2676	73	34	sets	set	NOUN
american_scientific_journal-2676	73	35	in	in	ADP
american_scientific_journal-2676	73	36	η	η	PROPN
american_scientific_journal-2676	73	37	belongs	belong	VERB
american_scientific_journal-2676	73	38	to	to	ADP
american_scientific_journal-2676	73	39	η	η	PROPN
american_scientific_journal-2676	73	40	,	,	PUNCT
american_scientific_journal-2676	73	41	3	3	NUM
american_scientific_journal-2676	73	42	)	)	PUNCT
american_scientific_journal-2676	73	43	the	the	DET
american_scientific_journal-2676	73	44	intersection	intersection	NOUN
american_scientific_journal-2676	73	45	of	of	ADP
american_scientific_journal-2676	73	46	any	any	DET
american_scientific_journal-2676	73	47	two	two	NUM
american_scientific_journal-2676	73	48	soft	soft	ADJ
american_scientific_journal-2676	73	49	sets	set	NOUN
american_scientific_journal-2676	73	50	in	in	ADP
american_scientific_journal-2676	73	51	η	η	PROPN
american_scientific_journal-2676	73	52	belongs	belong	VERB
american_scientific_journal-2676	73	53	to	to	ADP
american_scientific_journal-2676	73	54	η	η	PROPN
american_scientific_journal-2676	73	55	.	.	PUNCT
american_scientific_journal-2676	74	1	the	the	DET
american_scientific_journal-2676	74	2	triple	triple	ADJ
american_scientific_journal-2676	74	3	)	)	PUNCT
american_scientific_journal-2676	74	4	,	,	PUNCT
american_scientific_journal-2676	74	5	,	,	PUNCT
american_scientific_journal-2676	74	6	(	(	PUNCT
american_scientific_journal-2676	74	7	ex	ex	X
american_scientific_journal-2676	74	8	η	η	PROPN
american_scientific_journal-2676	74	9	is	be	AUX
american_scientific_journal-2676	74	10	called	call	VERB
american_scientific_journal-2676	74	11	a	a	DET
american_scientific_journal-2676	74	12	soft	soft	ADJ
american_scientific_journal-2676	74	13	topological	topological	ADJ
american_scientific_journal-2676	74	14	space	space	NOUN
american_scientific_journal-2676	74	15	.	.	PUNCT
american_scientific_journal-2676	75	1	any	any	DET
american_scientific_journal-2676	75	2	member	member	NOUN
american_scientific_journal-2676	75	3	of	of	ADP
american_scientific_journal-2676	75	4	η	η	PROPN
american_scientific_journal-2676	75	5	is	be	AUX
american_scientific_journal-2676	75	6	said	say	VERB
american_scientific_journal-2676	75	7	to	to	PART
american_scientific_journal-2676	75	8	be	be	AUX
american_scientific_journal-2676	75	9	an	an	DET
american_scientific_journal-2676	75	10	open	open	ADJ
american_scientific_journal-2676	75	11	soft	soft	ADJ
american_scientific_journal-2676	75	12	set	set	NOUN
american_scientific_journal-2676	75	13	in	in	ADP
american_scientific_journal-2676	75	14	)	)	PUNCT
american_scientific_journal-2676	75	15	,	,	PUNCT
american_scientific_journal-2676	75	16	,	,	PUNCT
american_scientific_journal-2676	75	17	(	(	PUNCT
american_scientific_journal-2676	75	18	ex	ex	X
american_scientific_journal-2676	75	19	η	η	PROPN
american_scientific_journal-2676	75	20	.	.	PUNCT
american_scientific_journal-2676	76	1	a	a	DET
american_scientific_journal-2676	76	2	soft	soft	ADJ
american_scientific_journal-2676	76	3	set	set	NOUN
american_scientific_journal-2676	76	4	)	)	PUNCT
american_scientific_journal-2676	76	5	,	,	PUNCT
american_scientific_journal-2676	76	6	(	(	PUNCT
american_scientific_journal-2676	76	7	ef	ef	VERB
american_scientific_journal-2676	76	8	over	over	ADP
american_scientific_journal-2676	76	9	x	x	VERB
american_scientific_journal-2676	76	10	is	be	AUX
american_scientific_journal-2676	76	11	said	say	VERB
american_scientific_journal-2676	76	12	to	to	PART
american_scientific_journal-2676	76	13	be	be	AUX
american_scientific_journal-2676	76	14	a	a	DET
american_scientific_journal-2676	76	15	closed	closed	ADJ
american_scientific_journal-2676	76	16	soft	soft	ADJ
american_scientific_journal-2676	76	17	set	set	NOUN
american_scientific_journal-2676	76	18	in	in	ADP
american_scientific_journal-2676	76	19	)	)	PUNCT
american_scientific_journal-2676	76	20	,	,	PUNCT
american_scientific_journal-2676	76	21	,	,	PUNCT
american_scientific_journal-2676	76	22	(	(	PUNCT
american_scientific_journal-2676	76	23	ex	ex	X
american_scientific_journal-2676	76	24	η	η	PROPN
american_scientific_journal-2676	76	25	,	,	PUNCT
american_scientific_journal-2676	76	26	if	if	SCONJ
american_scientific_journal-2676	76	27	its	its	PRON
american_scientific_journal-2676	76	28	complement	complement	NOUN
american_scientific_journal-2676	76	29	cef	cef	PROPN
american_scientific_journal-2676	76	30	)	)	PUNCT
american_scientific_journal-2676	76	31	,	,	PUNCT
american_scientific_journal-2676	76	32	(	(	PUNCT
american_scientific_journal-2676	76	33	is	be	AUX
american_scientific_journal-2676	76	34	an	an	DET
american_scientific_journal-2676	76	35	open	open	ADJ
american_scientific_journal-2676	76	36	soft	soft	ADJ
american_scientific_journal-2676	76	37	set	set	NOUN
american_scientific_journal-2676	76	38	in	in	ADP
american_scientific_journal-2676	76	39	)	)	PUNCT
american_scientific_journal-2676	76	40	,	,	PUNCT
american_scientific_journal-2676	76	41	,	,	PUNCT
american_scientific_journal-2676	76	42	(	(	PUNCT
american_scientific_journal-2676	76	43	ex	ex	X
american_scientific_journal-2676	76	44	η	η	PROPN
american_scientific_journal-2676	76	45	.	.	PUNCT
american_scientific_journal-2676	77	1	we	we	PRON
american_scientific_journal-2676	77	2	denote	denote	VERB
american_scientific_journal-2676	77	3	the	the	DET
american_scientific_journal-2676	77	4	family	family	NOUN
american_scientific_journal-2676	77	5	of	of	ADP
american_scientific_journal-2676	77	6	all	all	DET
american_scientific_journal-2676	77	7	closed	closed	ADJ
american_scientific_journal-2676	77	8	soft	soft	ADJ
american_scientific_journal-2676	77	9	sets	set	NOUN
american_scientific_journal-2676	77	10	by	by	ADP
american_scientific_journal-2676	77	11	cη	cη	PROPN
american_scientific_journal-2676	77	12	.	.	PUNCT
american_scientific_journal-2676	78	1	definition	definition	NOUN
american_scientific_journal-2676	78	2	2.4	2.4	NUM
american_scientific_journal-2676	78	3	[	[	SYM
american_scientific_journal-2676	78	4	20	20	NUM
american_scientific_journal-2676	78	5	]	]	PUNCT
american_scientific_journal-2676	78	6	let	let	NOUN
american_scientific_journal-2676	78	7	)	)	PUNCT
american_scientific_journal-2676	78	8	,	,	PUNCT
american_scientific_journal-2676	78	9	,	,	PUNCT
american_scientific_journal-2676	78	10	(	(	PUNCT
american_scientific_journal-2676	78	11	ex	ex	X
american_scientific_journal-2676	78	12	η	η	PROPN
american_scientific_journal-2676	78	13	be	be	AUX
american_scientific_journal-2676	78	14	a	a	DET
american_scientific_journal-2676	78	15	soft	soft	ADJ
american_scientific_journal-2676	78	16	topological	topological	ADJ
american_scientific_journal-2676	78	17	space	space	NOUN
american_scientific_journal-2676	78	18	and	and	CCONJ
american_scientific_journal-2676	78	19	exssef	exssef	NOUN
american_scientific_journal-2676	78	20	)	)	PUNCT
american_scientific_journal-2676	78	21	(	(	PUNCT
american_scientific_journal-2676	78	22	)	)	PUNCT
american_scientific_journal-2676	78	23	,	,	PUNCT
american_scientific_journal-2676	78	24	(	(	PUNCT
american_scientific_journal-2676	78	25	∈	∈	PROPN
american_scientific_journal-2676	78	26	.	.	PUNCT
american_scientific_journal-2676	79	1	the	the	DET
american_scientific_journal-2676	79	2	soft	soft	ADJ
american_scientific_journal-2676	79	3	closure	closure	NOUN
american_scientific_journal-2676	79	4	of	of	ADP
american_scientific_journal-2676	79	5	)	)	PUNCT
american_scientific_journal-2676	79	6	,	,	PUNCT
american_scientific_journal-2676	79	7	(	(	PUNCT
american_scientific_journal-2676	79	8	ef	ef	PROPN
american_scientific_journal-2676	79	9	,	,	PUNCT
american_scientific_journal-2676	79	10	denoted	denote	VERB
american_scientific_journal-2676	79	11	by	by	ADP
american_scientific_journal-2676	79	12	)	)	PUNCT
american_scientific_journal-2676	79	13	,	,	PUNCT
american_scientific_journal-2676	79	14	(	(	PUNCT
american_scientific_journal-2676	79	15	efsclη	efsclη	NOUN
american_scientific_journal-2676	79	16	,	,	PUNCT
american_scientific_journal-2676	79	17	is	be	AUX
american_scientific_journal-2676	79	18	the	the	DET
american_scientific_journal-2676	79	19	intersection	intersection	NOUN
american_scientific_journal-2676	79	20	of	of	ADP
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american_scientific_journal-2676	79	22	closed	closed	ADJ
american_scientific_journal-2676	79	23	soft	soft	ADJ
american_scientific_journal-2676	79	24	super	super	ADJ
american_scientific_journal-2676	79	25	sets	set	NOUN
american_scientific_journal-2676	79	26	of	of	ADP
american_scientific_journal-2676	79	27	)	)	PUNCT
american_scientific_journal-2676	79	28	,	,	PUNCT
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american_scientific_journal-2676	79	30	ef	ef	PROPN
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american_scientific_journal-2676	79	33	,	,	PUNCT
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american_scientific_journal-2676	79	36	)	)	PUNCT
american_scientific_journal-2676	79	37	,	,	PUNCT
american_scientific_journal-2676	79	38	(	(	PUNCT
american_scientific_journal-2676	79	39	~),(:)(),{(=	~),(:)(),{(=	NUM
american_scientific_journal-2676	79	40	)	)	PUNCT
american_scientific_journal-2676	79	41	,	,	PUNCT
american_scientific_journal-2676	79	42	(	(	PUNCT
american_scientific_journal-2676	79	43	ehefxscehefscl	ehefxscehefscl	NOUN
american_scientific_journal-2676	79	44	⊆∈	⊆∈	NUM
american_scientific_journal-2676	79	45	ηη	ηη	ADP
american_scientific_journal-2676	79	46			PROPN
american_scientific_journal-2676	79	47	.	.	PUNCT
american_scientific_journal-2676	80	1	clearly	clearly	ADV
american_scientific_journal-2676	80	2	)	)	PUNCT
american_scientific_journal-2676	80	3	,	,	PUNCT
american_scientific_journal-2676	80	4	(	(	PUNCT
american_scientific_journal-2676	80	5	efsclη	efsclη	PROPN
american_scientific_journal-2676	80	6	is	be	AUX
american_scientific_journal-2676	80	7	the	the	DET
american_scientific_journal-2676	80	8	smallest	small	ADJ
american_scientific_journal-2676	80	9	closed	closed	ADJ
american_scientific_journal-2676	80	10	soft	soft	ADJ
american_scientific_journal-2676	80	11	set	set	NOUN
american_scientific_journal-2676	80	12	over	over	ADP
american_scientific_journal-2676	80	13	x	x	ADP
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american_scientific_journal-2676	80	16	)	)	PUNCT
american_scientific_journal-2676	80	17	,	,	PUNCT
american_scientific_journal-2676	80	18	(	(	PUNCT
american_scientific_journal-2676	80	19	ef	ef	X
american_scientific_journal-2676	80	20	.	.	PUNCT
american_scientific_journal-2676	81	1	definition	definition	NOUN
american_scientific_journal-2676	81	2	2.5	2.5	NUM
american_scientific_journal-2676	82	1	[	[	SYM
american_scientific_journal-2676	82	2	13	13	NUM
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american_scientific_journal-2676	82	4	a	a	DET
american_scientific_journal-2676	82	5	soft	soft	ADJ
american_scientific_journal-2676	82	6	set	set	NOUN
american_scientific_journal-2676	82	7	)	)	PUNCT
american_scientific_journal-2676	82	8	,	,	PUNCT
american_scientific_journal-2676	82	9	(	(	PUNCT
american_scientific_journal-2676	82	10	eg	eg	NOUN
american_scientific_journal-2676	82	11	in	in	ADP
american_scientific_journal-2676	82	12	a	a	DET
american_scientific_journal-2676	82	13	soft	soft	ADJ
american_scientific_journal-2676	82	14	topological	topological	ADJ
american_scientific_journal-2676	82	15	space	space	NOUN
american_scientific_journal-2676	82	16	)	)	PUNCT
american_scientific_journal-2676	82	17	,	,	PUNCT
american_scientific_journal-2676	82	18	,	,	PUNCT
american_scientific_journal-2676	82	19	(	(	PUNCT
american_scientific_journal-2676	82	20	ex	ex	X
american_scientific_journal-2676	82	21	η	η	PROPN
american_scientific_journal-2676	82	22	is	be	AUX
american_scientific_journal-2676	82	23	called	call	VERB
american_scientific_journal-2676	82	24	a	a	DET
american_scientific_journal-2676	82	25	generalized	generalize	VERB
american_scientific_journal-2676	82	26	closed	closed	ADJ
american_scientific_journal-2676	82	27	soft	soft	ADJ
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american_scientific_journal-2676	83	1	[	[	X
american_scientific_journal-2676	83	2	briefly	briefly	ADV
american_scientific_journal-2676	83	3	,	,	PUNCT
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american_scientific_journal-2676	83	5	-closed	-close	VERB
american_scientific_journal-2676	83	6	soft	soft	ADJ
american_scientific_journal-2676	83	7	set	set	NOUN
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american_scientific_journal-2676	83	9	if	if	SCONJ
american_scientific_journal-2676	83	10	)	)	PUNCT
american_scientific_journal-2676	83	11	,	,	PUNCT
american_scientific_journal-2676	83	12	(	(	PUNCT
american_scientific_journal-2676	83	13	~	~	NOUN
american_scientific_journal-2676	83	14	)	)	PUNCT
american_scientific_journal-2676	83	15	,	,	PUNCT
american_scientific_journal-2676	83	16	(	(	PUNCT
american_scientific_journal-2676	83	17	ehegscl	ehegscl	NOUN
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american_scientific_journal-2676	83	20	)	)	PUNCT
american_scientific_journal-2676	83	21	,	,	PUNCT
american_scientific_journal-2676	83	22	(	(	PUNCT
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american_scientific_journal-2676	83	24	)	)	PUNCT
american_scientific_journal-2676	83	25	,	,	PUNCT
american_scientific_journal-2676	83	26	(	(	PUNCT
american_scientific_journal-2676	83	27	eheg	eheg	VERB
american_scientific_journal-2676	83	28	⊆	⊆	NUM
american_scientific_journal-2676	83	29	and	and	CCONJ
american_scientific_journal-2676	83	30	η∈	η∈	NOUN
american_scientific_journal-2676	83	31	)	)	PUNCT
american_scientific_journal-2676	83	32	,	,	PUNCT
american_scientific_journal-2676	83	33	(	(	PUNCT
american_scientific_journal-2676	83	34	eh	eh	INTJ
american_scientific_journal-2676	83	35	.	.	PUNCT
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american_scientific_journal-2676	84	2	2.6	2.6	NUM
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american_scientific_journal-2676	85	2	16	16	NUM
american_scientific_journal-2676	85	3	]	]	PUNCT
american_scientific_journal-2676	85	4	a	a	DET
american_scientific_journal-2676	85	5	soft	soft	ADJ
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american_scientific_journal-2676	85	8	)	)	PUNCT
american_scientific_journal-2676	85	9	,	,	PUNCT
american_scientific_journal-2676	85	10	,	,	PUNCT
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american_scientific_journal-2676	85	12	ex	ex	X
american_scientific_journal-2676	85	13	η	η	PROPN
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american_scientific_journal-2676	85	15	said	say	VERB
american_scientific_journal-2676	85	16	to	to	PART
american_scientific_journal-2676	85	17	be	be	AUX
american_scientific_journal-2676	85	18	a	a	DET
american_scientific_journal-2676	85	19	soft	soft	ADJ
american_scientific_journal-2676	85	20	0	0	NUM
american_scientific_journal-2676	85	21	t	t	NOUN
american_scientific_journal-2676	85	22	[	[	X
american_scientific_journal-2676	85	23	briefly	briefly	NOUN
american_scientific_journal-2676	85	24	,	,	PUNCT
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american_scientific_journal-2676	85	27	if	if	SCONJ
american_scientific_journal-2676	85	28	for	for	ADP
american_scientific_journal-2676	85	29	each	each	DET
american_scientific_journal-2676	85	30	exyx	exyx	ADJ
american_scientific_journal-2676	85	31	)	)	PUNCT
american_scientific_journal-2676	85	32	(	(	PUNCT
american_scientific_journal-2676	85	33	,	,	PUNCT
american_scientific_journal-2676	85	34	ξβα	ξβα	VERB
american_scientific_journal-2676	85	35	∈	∈	NOUN
american_scientific_journal-2676	85	36	with	with	ADP
american_scientific_journal-2676	85	37	βα	βα	PROPN
american_scientific_journal-2676	85	38	yx	yx	ADP
american_scientific_journal-2676	85	39	≠	≠	PROPN
american_scientific_journal-2676	85	40	,	,	PUNCT
american_scientific_journal-2676	85	41	there	there	PRON
american_scientific_journal-2676	85	42	exists	exist	VERB
american_scientific_journal-2676	85	43	η∈	η∈	NOUN
american_scientific_journal-2676	85	44	)	)	PUNCT
american_scientific_journal-2676	85	45	,	,	PUNCT
american_scientific_journal-2676	85	46	(	(	PUNCT
american_scientific_journal-2676	85	47	eg	eg	ADP
american_scientific_journal-2676	85	48	such	such	ADJ
american_scientific_journal-2676	85	49	that	that	PRON
american_scientific_journal-2676	85	50	)	)	PUNCT
american_scientific_journal-2676	85	51	,	,	PUNCT
american_scientific_journal-2676	85	52	(	(	PUNCT
american_scientific_journal-2676	85	53	~	~	PUNCT
american_scientific_journal-2676	85	54	egx	egx	X
american_scientific_journal-2676	85	55	∈α	∈α	PROPN
american_scientific_journal-2676	85	56	,	,	PUNCT
american_scientific_journal-2676	85	57	)	)	PUNCT
american_scientific_journal-2676	85	58	,	,	PUNCT
american_scientific_journal-2676	85	59	(	(	PUNCT
american_scientific_journal-2676	85	60	~	~	PUNCT
american_scientific_journal-2676	85	61	egy	egy	PROPN
american_scientific_journal-2676	85	62	∈/β	∈/β	PROPN
american_scientific_journal-2676	85	63	or	or	CCONJ
american_scientific_journal-2676	85	64	)	)	PUNCT
american_scientific_journal-2676	85	65	,	,	PUNCT
american_scientific_journal-2676	85	66	(	(	PUNCT
american_scientific_journal-2676	85	67	~	~	PUNCT
american_scientific_journal-2676	85	68	egy	egy	X
american_scientific_journal-2676	85	69	∈β	∈β	PROPN
american_scientific_journal-2676	85	70	,	,	PUNCT
american_scientific_journal-2676	85	71	)	)	PUNCT
american_scientific_journal-2676	85	72	,	,	PUNCT
american_scientific_journal-2676	85	73	(	(	PUNCT
american_scientific_journal-2676	85	74	~	~	PUNCT
american_scientific_journal-2676	85	75	egx	egx	VERB
american_scientific_journal-2676	85	76	∈/α	∈/α	PROPN
american_scientific_journal-2676	85	77	.	.	PUNCT
american_scientific_journal-2676	86	1	definition	definition	NOUN
american_scientific_journal-2676	86	2	2.7	2.7	NUM
american_scientific_journal-2676	86	3	[	[	X
american_scientific_journal-2676	86	4	13	13	NUM
american_scientific_journal-2676	86	5	]	]	PUNCT
american_scientific_journal-2676	86	6	a	a	DET
american_scientific_journal-2676	86	7	soft	soft	ADJ
american_scientific_journal-2676	86	8	topological	topological	ADJ
american_scientific_journal-2676	86	9	space	space	NOUN
american_scientific_journal-2676	86	10	)	)	PUNCT
american_scientific_journal-2676	87	1	,	,	PUNCT
american_scientific_journal-2676	87	2	,	,	PUNCT
american_scientific_journal-2676	87	3	(	(	PUNCT
american_scientific_journal-2676	87	4	ex	ex	X
american_scientific_journal-2676	87	5	η	η	PROPN
american_scientific_journal-2676	87	6	is	be	AUX
american_scientific_journal-2676	87	7	called	call	VERB
american_scientific_journal-2676	87	8	a	a	DET
american_scientific_journal-2676	87	9	soft	soft	ADJ
american_scientific_journal-2676	87	10	𝑇𝑇1	𝑇𝑇1	NOUN
american_scientific_journal-2676	87	11	2	2	NUM
american_scientific_journal-2676	87	12	�	�	NOUN
american_scientific_journal-2676	87	13	[	[	X
american_scientific_journal-2676	87	14	briefly,𝑃𝑃	briefly,𝑃𝑃	NOUN
american_scientific_journal-2676	87	15	𝑇𝑇1	𝑇𝑇1	NOUN
american_scientific_journal-2676	87	16	2	2	NUM
american_scientific_journal-2676	87	17	�	�	NOUN
american_scientific_journal-2676	87	18	]	]	PUNCT
american_scientific_journal-2676	87	19	if	if	SCONJ
american_scientific_journal-2676	87	20	every	every	DET
american_scientific_journal-2676	87	21	g	g	NOUN
american_scientific_journal-2676	87	22	-closed	-close	VERB
american_scientific_journal-2676	87	23	soft	soft	ADJ
american_scientific_journal-2676	87	24	set	set	NOUN
american_scientific_journal-2676	87	25	is	be	AUX
american_scientific_journal-2676	87	26	a	a	DET
american_scientific_journal-2676	87	27	closed	closed	ADJ
american_scientific_journal-2676	87	28	soft	soft	ADJ
american_scientific_journal-2676	87	29	set	set	NOUN
american_scientific_journal-2676	87	30	.	.	PUNCT
american_scientific_journal-2676	88	1	theorem	theorem	VERB
american_scientific_journal-2676	88	2	2.1	2.1	NUM
american_scientific_journal-2676	89	1	[	[	SYM
american_scientific_journal-2676	89	2	9	9	NUM
american_scientific_journal-2676	89	3	]	]	PUNCT
american_scientific_journal-2676	89	4	a	a	DET
american_scientific_journal-2676	89	5	soft	soft	ADJ
american_scientific_journal-2676	89	6	topological	topological	ADJ
american_scientific_journal-2676	89	7	space	space	NOUN
american_scientific_journal-2676	89	8	)	)	PUNCT
american_scientific_journal-2676	89	9	,	,	PUNCT
american_scientific_journal-2676	89	10	,	,	PUNCT
american_scientific_journal-2676	89	11	(	(	PUNCT
american_scientific_journal-2676	89	12	ex	ex	X
american_scientific_journal-2676	89	13	η	η	PROPN
american_scientific_journal-2676	89	14	is	be	AUX
american_scientific_journal-2676	89	15	a	a	DET
american_scientific_journal-2676	89	16	soft	soft	ADJ
american_scientific_journal-2676	89	17	𝑇𝑇1	𝑇𝑇1	NOUN
american_scientific_journal-2676	89	18	2	2	NUM
american_scientific_journal-2676	89	19	�	�	PROPN
american_scientific_journal-2676	89	20	if	if	SCONJ
american_scientific_journal-2676	89	21	and	and	CCONJ
american_scientific_journal-2676	89	22	only	only	ADV
american_scientific_journal-2676	89	23	if	if	SCONJ
american_scientific_journal-2676	89	24	every	every	DET
american_scientific_journal-2676	89	25	soft	soft	ADJ
american_scientific_journal-2676	89	26	point	point	NOUN
american_scientific_journal-2676	89	27	either	either	CCONJ
american_scientific_journal-2676	89	28	open	open	ADJ
american_scientific_journal-2676	89	29	american	american	ADJ
american_scientific_journal-2676	89	30	scientific	scientific	ADJ
american_scientific_journal-2676	89	31	research	research	NOUN
american_scientific_journal-2676	89	32	journal	journal	NOUN
american_scientific_journal-2676	89	33	for	for	ADP
american_scientific_journal-2676	89	34	engineering	engineering	NOUN
american_scientific_journal-2676	89	35	,	,	PUNCT
american_scientific_journal-2676	89	36	technology	technology	NOUN
american_scientific_journal-2676	89	37	,	,	PUNCT
american_scientific_journal-2676	89	38	and	and	CCONJ
american_scientific_journal-2676	89	39	sciences	science	NOUN
american_scientific_journal-2676	89	40	(	(	PUNCT
american_scientific_journal-2676	89	41	asrjets	asrjet	NOUN
american_scientific_journal-2676	89	42	)	)	PUNCT
american_scientific_journal-2676	89	43	(	(	PUNCT
american_scientific_journal-2676	89	44	2017	2017	NUM
american_scientific_journal-2676	89	45	)	)	PUNCT
american_scientific_journal-2676	89	46	volume	volume	NOUN
american_scientific_journal-2676	89	47	28	28	NUM
american_scientific_journal-2676	89	48	,	,	PUNCT
american_scientific_journal-2676	89	49	no	no	DET
american_scientific_journal-2676	89	50	1	1	NUM
american_scientific_journal-2676	89	51	,	,	PUNCT
american_scientific_journal-2676	89	52	pp	pp	ADV
american_scientific_journal-2676	89	53	225	225	NUM
american_scientific_journal-2676	89	54	-	-	SYM
american_scientific_journal-2676	89	55	247	247	NUM
american_scientific_journal-2676	89	56	229	229	NUM
american_scientific_journal-2676	89	57	soft	soft	ADJ
american_scientific_journal-2676	89	58	set	set	NOUN
american_scientific_journal-2676	89	59	or	or	CCONJ
american_scientific_journal-2676	89	60	closed	close	VERB
american_scientific_journal-2676	89	61	soft	soft	ADJ
american_scientific_journal-2676	89	62	set	set	NOUN
american_scientific_journal-2676	89	63	.	.	PUNCT
american_scientific_journal-2676	90	1	definition	definition	NOUN
american_scientific_journal-2676	90	2	2.8	2.8	NUM
american_scientific_journal-2676	91	1	[	[	X
american_scientific_journal-2676	91	2	4	4	NUM
american_scientific_journal-2676	91	3	]	]	PUNCT
american_scientific_journal-2676	91	4	let	let	VERB
american_scientific_journal-2676	91	5	µ	µ	X
american_scientific_journal-2676	91	6	be	be	AUX
american_scientific_journal-2676	91	7	a	a	DET
american_scientific_journal-2676	91	8	collection	collection	NOUN
american_scientific_journal-2676	91	9	of	of	ADP
american_scientific_journal-2676	91	10	soft	soft	ADJ
american_scientific_journal-2676	91	11	sets	set	NOUN
american_scientific_journal-2676	91	12	over	over	ADP
american_scientific_journal-2676	91	13	x	x	PUNCT
american_scientific_journal-2676	92	1	[	[	X
american_scientific_journal-2676	92	2	i.e.	i.e.	X
american_scientific_journal-2676	92	3	,	,	PUNCT
american_scientific_journal-2676	92	4	exss	exss	NOUN
american_scientific_journal-2676	92	5	)	)	PUNCT
american_scientific_journal-2676	92	6	(	(	PUNCT
american_scientific_journal-2676	92	7	⊆µ	⊆µ	VERB
american_scientific_journal-2676	92	8	]	]	PUNCT
american_scientific_journal-2676	92	9	.	.	PUNCT
american_scientific_journal-2676	93	1	the	the	DET
american_scientific_journal-2676	93	2	collection	collection	NOUN
american_scientific_journal-2676	93	3	µ	µ	NOUN
american_scientific_journal-2676	93	4	is	be	AUX
american_scientific_journal-2676	93	5	called	call	VERB
american_scientific_journal-2676	93	6	a	a	DET
american_scientific_journal-2676	93	7	supra	supra	ADJ
american_scientific_journal-2676	93	8	soft	soft	ADJ
american_scientific_journal-2676	93	9	topology	topology	NOUN
american_scientific_journal-2676	93	10	on	on	ADP
american_scientific_journal-2676	93	11	x	x	PUNCT
american_scientific_journal-2676	93	12	if	if	SCONJ
american_scientific_journal-2676	93	13	it	it	PRON
american_scientific_journal-2676	93	14	satisfies	satisfy	VERB
american_scientific_journal-2676	93	15	the	the	DET
american_scientific_journal-2676	93	16	following	follow	VERB
american_scientific_journal-2676	93	17	axioms	axiom	NOUN
american_scientific_journal-2676	93	18	:	:	PUNCT
american_scientific_journal-2676	93	19	1	1	NUM
american_scientific_journal-2676	93	20	)	)	PUNCT
american_scientific_journal-2676	93	21	)	)	PUNCT
american_scientific_journal-2676	93	22	,	,	PUNCT
american_scientific_journal-2676	94	1	~	~	PUNCT
american_scientific_journal-2676	94	2	(	(	PUNCT
american_scientific_journal-2676	94	3	ex	ex	X
american_scientific_journal-2676	94	4	,	,	PUNCT
american_scientific_journal-2676	94	5	µφ	µφ	PROPN
american_scientific_journal-2676	94	6	∈),~	∈),~	NOUN
american_scientific_journal-2676	94	7	(	(	PUNCT
american_scientific_journal-2676	94	8	e	e	NOUN
american_scientific_journal-2676	94	9	,	,	PUNCT
american_scientific_journal-2676	94	10	2	2	X
american_scientific_journal-2676	94	11	)	)	PUNCT
american_scientific_journal-2676	94	12	the	the	DET
american_scientific_journal-2676	94	13	union	union	NOUN
american_scientific_journal-2676	94	14	of	of	ADP
american_scientific_journal-2676	94	15	any	any	DET
american_scientific_journal-2676	94	16	number	number	NOUN
american_scientific_journal-2676	94	17	of	of	ADP
american_scientific_journal-2676	94	18	soft	soft	ADJ
american_scientific_journal-2676	94	19	sets	set	NOUN
american_scientific_journal-2676	94	20	in	in	ADP
american_scientific_journal-2676	94	21	µ	µ	PRON
american_scientific_journal-2676	94	22	belongs	belong	VERB
american_scientific_journal-2676	94	23	to	to	ADP
american_scientific_journal-2676	94	24	µ	µ	PROPN
american_scientific_journal-2676	94	25	.	.	PUNCT
american_scientific_journal-2676	95	1	definition	definition	NOUN
american_scientific_journal-2676	95	2	2.9	2.9	NUM
american_scientific_journal-2676	96	1	[	[	X
american_scientific_journal-2676	96	2	2	2	NUM
american_scientific_journal-2676	96	3	]	]	PUNCT
american_scientific_journal-2676	96	4	a	a	DET
american_scientific_journal-2676	96	5	quadrable	quadrable	ADJ
american_scientific_journal-2676	96	6	system	system	NOUN
american_scientific_journal-2676	96	7	)	)	PUNCT
american_scientific_journal-2676	96	8	,	,	PUNCT
american_scientific_journal-2676	96	9	,	,	PUNCT
american_scientific_journal-2676	96	10	,	,	PUNCT
american_scientific_journal-2676	96	11	(	(	PUNCT
american_scientific_journal-2676	96	12	21	21	NUM
american_scientific_journal-2676	96	13	ex	ex	NOUN
american_scientific_journal-2676	96	14	ηη	ηη	PROPN
american_scientific_journal-2676	96	15	is	be	AUX
american_scientific_journal-2676	96	16	called	call	VERB
american_scientific_journal-2676	96	17	a	a	DET
american_scientific_journal-2676	96	18	soft	soft	ADJ
american_scientific_journal-2676	96	19	bitopological	bitopological	ADJ
american_scientific_journal-2676	96	20	space	space	NOUN
american_scientific_journal-2676	97	1	[	[	X
american_scientific_journal-2676	97	2	briefly	briefly	ADV
american_scientific_journal-2676	97	3	,	,	PUNCT
american_scientific_journal-2676	97	4	sbts	sbts	ADJ
american_scientific_journal-2676	97	5	]	]	PUNCT
american_scientific_journal-2676	97	6	,	,	PUNCT
american_scientific_journal-2676	97	7	where	where	SCONJ
american_scientific_journal-2676	97	8	1η	1η	NOUN
american_scientific_journal-2676	97	9	,	,	PUNCT
american_scientific_journal-2676	97	10	2η	2η	PROPN
american_scientific_journal-2676	97	11	are	be	AUX
american_scientific_journal-2676	97	12	arbitrary	arbitrary	ADJ
american_scientific_journal-2676	97	13	soft	soft	ADJ
american_scientific_journal-2676	97	14	topologies	topology	NOUN
american_scientific_journal-2676	97	15	on	on	ADP
american_scientific_journal-2676	97	16	x	x	PUNCT
american_scientific_journal-2676	97	17	with	with	ADP
american_scientific_journal-2676	97	18	a	a	DET
american_scientific_journal-2676	97	19	fixed	fix	VERB
american_scientific_journal-2676	97	20	set	set	NOUN
american_scientific_journal-2676	97	21	of	of	ADP
american_scientific_journal-2676	97	22	parameters	parameter	NOUN
american_scientific_journal-2676	97	23	e	e	NOUN
american_scientific_journal-2676	97	24	.	.	PUNCT
american_scientific_journal-2676	98	1	definition	definition	NOUN
american_scientific_journal-2676	98	2	2.10	2.10	NUM
american_scientific_journal-2676	98	3	[	[	SYM
american_scientific_journal-2676	98	4	10	10	NUM
american_scientific_journal-2676	98	5	]	]	PUNCT
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american_scientific_journal-2676	98	7	)	)	PUNCT
american_scientific_journal-2676	98	8	,	,	PUNCT
american_scientific_journal-2676	98	9	,	,	PUNCT
american_scientific_journal-2676	98	10	,	,	PUNCT
american_scientific_journal-2676	98	11	(	(	PUNCT
american_scientific_journal-2676	98	12	21	21	NUM
american_scientific_journal-2676	98	13	ex	ex	X
american_scientific_journal-2676	98	14	ηη	ηη	PROPN
american_scientific_journal-2676	98	15	be	be	AUX
american_scientific_journal-2676	98	16	a	a	DET
american_scientific_journal-2676	98	17	sbts	sbts	ADJ
american_scientific_journal-2676	98	18	.	.	PUNCT
american_scientific_journal-2676	99	1	a	a	DET
american_scientific_journal-2676	99	2	soft	soft	ADJ
american_scientific_journal-2676	99	3	set	set	NOUN
american_scientific_journal-2676	99	4	)	)	PUNCT
american_scientific_journal-2676	99	5	,	,	PUNCT
american_scientific_journal-2676	99	6	(	(	PUNCT
american_scientific_journal-2676	99	7	eg	eg	NOUN
american_scientific_journal-2676	99	8	over	over	ADP
american_scientific_journal-2676	99	9	x	x	VERB
american_scientific_journal-2676	99	10	is	be	AUX
american_scientific_journal-2676	99	11	said	say	VERB
american_scientific_journal-2676	99	12	to	to	PART
american_scientific_journal-2676	99	13	be	be	AUX
american_scientific_journal-2676	99	14	a	a	DET
american_scientific_journal-2676	99	15	pairwise	pairwise	NOUN
american_scientific_journal-2676	99	16	open	open	ADJ
american_scientific_journal-2676	99	17	soft	soft	ADJ
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american_scientific_journal-2676	99	19	in	in	ADP
american_scientific_journal-2676	99	20	)	)	PUNCT
american_scientific_journal-2676	99	21	,	,	PUNCT
american_scientific_journal-2676	99	22	,	,	PUNCT
american_scientific_journal-2676	99	23	,	,	PUNCT
american_scientific_journal-2676	99	24	(	(	PUNCT
american_scientific_journal-2676	99	25	21	21	NUM
american_scientific_journal-2676	99	26	ex	ex	NOUN
american_scientific_journal-2676	99	27	ηη	ηη	NOUN
american_scientific_journal-2676	100	1	[	[	X
american_scientific_journal-2676	100	2	briefly	briefly	ADV
american_scientific_journal-2676	100	3	,	,	PUNCT
american_scientific_journal-2676	100	4	p	p	NOUN
american_scientific_journal-2676	100	5	-open	-open	ADJ
american_scientific_journal-2676	100	6	soft	soft	ADJ
american_scientific_journal-2676	100	7	set	set	NOUN
american_scientific_journal-2676	100	8	]	]	PUNCT
american_scientific_journal-2676	100	9	if	if	SCONJ
american_scientific_journal-2676	100	10	there	there	PRON
american_scientific_journal-2676	100	11	exist	exist	VERB
american_scientific_journal-2676	100	12	an	an	DET
american_scientific_journal-2676	100	13	open	open	ADJ
american_scientific_journal-2676	100	14	soft	soft	ADJ
american_scientific_journal-2676	100	15	set	set	NOUN
american_scientific_journal-2676	100	16	)	)	PUNCT
american_scientific_journal-2676	100	17	,	,	PUNCT
american_scientific_journal-2676	100	18	(	(	PUNCT
american_scientific_journal-2676	100	19	1	1	NUM
american_scientific_journal-2676	100	20	eg	eg	NOUN
american_scientific_journal-2676	100	21	in	in	ADP
american_scientific_journal-2676	100	22	1η	1η	NOUN
american_scientific_journal-2676	100	23	and	and	CCONJ
american_scientific_journal-2676	100	24	an	an	DET
american_scientific_journal-2676	100	25	open	open	ADJ
american_scientific_journal-2676	100	26	soft	soft	ADJ
american_scientific_journal-2676	100	27	set	set	NOUN
american_scientific_journal-2676	100	28	)	)	PUNCT
american_scientific_journal-2676	100	29	,	,	PUNCT
american_scientific_journal-2676	100	30	(	(	PUNCT
american_scientific_journal-2676	100	31	2	2	NUM
american_scientific_journal-2676	100	32	eg	eg	NOUN
american_scientific_journal-2676	100	33	in	in	ADP
american_scientific_journal-2676	100	34	2η	2η	PRON
american_scientific_journal-2676	100	35	such	such	ADJ
american_scientific_journal-2676	100	36	that	that	PRON
american_scientific_journal-2676	100	37	)	)	PUNCT
american_scientific_journal-2676	100	38	,	,	PUNCT
american_scientific_journal-2676	100	39	(	(	PUNCT
american_scientific_journal-2676	100	40	~),(=	~),(=	NUM
american_scientific_journal-2676	100	41	)	)	PUNCT
american_scientific_journal-2676	100	42	,	,	PUNCT
american_scientific_journal-2676	100	43	(	(	PUNCT
american_scientific_journal-2676	100	44	21	21	NUM
american_scientific_journal-2676	100	45	egegeg	egegeg	NOUN
american_scientific_journal-2676	100	46	∪	∪	NOUN
american_scientific_journal-2676	100	47	.	.	PUNCT
american_scientific_journal-2676	101	1	a	a	DET
american_scientific_journal-2676	101	2	soft	soft	ADJ
american_scientific_journal-2676	101	3	set	set	NOUN
american_scientific_journal-2676	101	4	)	)	PUNCT
american_scientific_journal-2676	101	5	,	,	PUNCT
american_scientific_journal-2676	101	6	(	(	PUNCT
american_scientific_journal-2676	101	7	eg	eg	NOUN
american_scientific_journal-2676	101	8	over	over	ADP
american_scientific_journal-2676	101	9	x	x	VERB
american_scientific_journal-2676	101	10	is	be	AUX
american_scientific_journal-2676	101	11	said	say	VERB
american_scientific_journal-2676	101	12	to	to	PART
american_scientific_journal-2676	101	13	be	be	AUX
american_scientific_journal-2676	101	14	a	a	DET
american_scientific_journal-2676	101	15	pairwise	pairwise	NOUN
american_scientific_journal-2676	101	16	closed	close	VERB
american_scientific_journal-2676	101	17	soft	soft	ADJ
american_scientific_journal-2676	101	18	set	set	NOUN
american_scientific_journal-2676	101	19	in	in	ADP
american_scientific_journal-2676	101	20	)	)	PUNCT
american_scientific_journal-2676	101	21	,	,	PUNCT
american_scientific_journal-2676	101	22	,	,	PUNCT
american_scientific_journal-2676	101	23	,	,	PUNCT
american_scientific_journal-2676	101	24	(	(	PUNCT
american_scientific_journal-2676	101	25	21	21	NUM
american_scientific_journal-2676	101	26	ex	ex	NOUN
american_scientific_journal-2676	101	27	ηη	ηη	NOUN
american_scientific_journal-2676	102	1	[	[	X
american_scientific_journal-2676	102	2	briefly	briefly	ADV
american_scientific_journal-2676	102	3	,	,	PUNCT
american_scientific_journal-2676	102	4	p	p	X
american_scientific_journal-2676	102	5	-closed	-close	VERB
american_scientific_journal-2676	102	6	soft	soft	ADJ
american_scientific_journal-2676	102	7	set	set	NOUN
american_scientific_journal-2676	102	8	]	]	PUNCT
american_scientific_journal-2676	102	9	if	if	SCONJ
american_scientific_journal-2676	102	10	its	its	PRON
american_scientific_journal-2676	102	11	complement	complement	NOUN
american_scientific_journal-2676	102	12	is	be	AUX
american_scientific_journal-2676	102	13	a	a	DET
american_scientific_journal-2676	102	14	p	p	NOUN
american_scientific_journal-2676	102	15	-open	-open	ADJ
american_scientific_journal-2676	102	16	soft	soft	ADJ
american_scientific_journal-2676	102	17	set	set	NOUN
american_scientific_journal-2676	102	18	in	in	ADP
american_scientific_journal-2676	102	19	)	)	PUNCT
american_scientific_journal-2676	102	20	,	,	PUNCT
american_scientific_journal-2676	102	21	,	,	PUNCT
american_scientific_journal-2676	102	22	,	,	PUNCT
american_scientific_journal-2676	102	23	(	(	PUNCT
american_scientific_journal-2676	102	24	21	21	NUM
american_scientific_journal-2676	102	25	ex	ex	NOUN
american_scientific_journal-2676	102	26	ηη	ηη	NOUN
american_scientific_journal-2676	102	27	.	.	PUNCT
american_scientific_journal-2676	103	1	clearly	clearly	ADV
american_scientific_journal-2676	103	2	,	,	PUNCT
american_scientific_journal-2676	103	3	a	a	DET
american_scientific_journal-2676	103	4	soft	soft	ADJ
american_scientific_journal-2676	103	5	set	set	NOUN
american_scientific_journal-2676	103	6	)	)	PUNCT
american_scientific_journal-2676	103	7	,	,	PUNCT
american_scientific_journal-2676	103	8	(	(	PUNCT
american_scientific_journal-2676	103	9	ef	ef	VERB
american_scientific_journal-2676	103	10	over	over	ADP
american_scientific_journal-2676	103	11	x	x	PRON
american_scientific_journal-2676	103	12	is	be	AUX
american_scientific_journal-2676	103	13	a	a	DET
american_scientific_journal-2676	103	14	p	p	NOUN
american_scientific_journal-2676	103	15	-closed	-close	VERB
american_scientific_journal-2676	103	16	soft	soft	ADJ
american_scientific_journal-2676	103	17	set	set	NOUN
american_scientific_journal-2676	103	18	in	in	ADP
american_scientific_journal-2676	103	19	)	)	PUNCT
american_scientific_journal-2676	103	20	,	,	PUNCT
american_scientific_journal-2676	103	21	,	,	PUNCT
american_scientific_journal-2676	103	22	,	,	PUNCT
american_scientific_journal-2676	103	23	(	(	PUNCT
american_scientific_journal-2676	103	24	21	21	NUM
american_scientific_journal-2676	103	25	ex	ex	NOUN
american_scientific_journal-2676	103	26	ηη	ηη	ADV
american_scientific_journal-2676	103	27	if	if	SCONJ
american_scientific_journal-2676	103	28	there	there	PRON
american_scientific_journal-2676	103	29	exist	exist	VERB
american_scientific_journal-2676	103	30	an	an	DET
american_scientific_journal-2676	103	31	1η	1η	NUM
american_scientific_journal-2676	103	32	-closed	-close	VERB
american_scientific_journal-2676	103	33	soft	soft	ADJ
american_scientific_journal-2676	103	34	set	set	NOUN
american_scientific_journal-2676	103	35	)	)	PUNCT
american_scientific_journal-2676	103	36	,	,	PUNCT
american_scientific_journal-2676	103	37	(	(	PUNCT
american_scientific_journal-2676	103	38	1	1	NUM
american_scientific_journal-2676	103	39	ef	ef	NOUN
american_scientific_journal-2676	103	40	and	and	CCONJ
american_scientific_journal-2676	103	41	an	an	DET
american_scientific_journal-2676	103	42	2η	2η	PROPN
american_scientific_journal-2676	103	43	-closed	-close	VERB
american_scientific_journal-2676	103	44	soft	soft	ADJ
american_scientific_journal-2676	103	45	set	set	NOUN
american_scientific_journal-2676	103	46	)	)	PUNCT
american_scientific_journal-2676	103	47	,	,	PUNCT
american_scientific_journal-2676	103	48	(	(	PUNCT
american_scientific_journal-2676	103	49	2	2	NUM
american_scientific_journal-2676	103	50	ef	ef	NOUN
american_scientific_journal-2676	103	51	such	such	ADJ
american_scientific_journal-2676	103	52	that	that	PRON
american_scientific_journal-2676	103	53	)	)	PUNCT
american_scientific_journal-2676	103	54	,	,	PUNCT
american_scientific_journal-2676	103	55	(	(	PUNCT
american_scientific_journal-2676	103	56	~),(=	~),(=	NUM
american_scientific_journal-2676	103	57	)	)	PUNCT
american_scientific_journal-2676	103	58	,	,	PUNCT
american_scientific_journal-2676	103	59	(	(	PUNCT
american_scientific_journal-2676	103	60	21	21	NUM
american_scientific_journal-2676	103	61	efefef	efefef	PROPN
american_scientific_journal-2676	103	62	∩	∩	NOUN
american_scientific_journal-2676	103	63	.	.	PUNCT
american_scientific_journal-2676	104	1	the	the	DET
american_scientific_journal-2676	104	2	family	family	NOUN
american_scientific_journal-2676	104	3	of	of	ADP
american_scientific_journal-2676	104	4	all	all	DET
american_scientific_journal-2676	104	5	p	p	NOUN
american_scientific_journal-2676	104	6	-open	-open	NOUN
american_scientific_journal-2676	104	7	(	(	PUNCT
american_scientific_journal-2676	104	8	p	p	NOUN
american_scientific_journal-2676	104	9	-closed	-closed	ADJ
american_scientific_journal-2676	104	10	)	)	PUNCT
american_scientific_journal-2676	104	11	soft	soft	ADJ
american_scientific_journal-2676	104	12	sets	set	NOUN
american_scientific_journal-2676	104	13	in	in	ADP
american_scientific_journal-2676	104	14	a	a	DET
american_scientific_journal-2676	104	15	sbts	sbts	ADJ
american_scientific_journal-2676	104	16	)	)	PUNCT
american_scientific_journal-2676	104	17	,	,	PUNCT
american_scientific_journal-2676	104	18	,	,	PUNCT
american_scientific_journal-2676	104	19	,	,	PUNCT
american_scientific_journal-2676	104	20	(	(	PUNCT
american_scientific_journal-2676	104	21	21	21	NUM
american_scientific_journal-2676	104	22	ex	ex	NOUN
american_scientific_journal-2676	104	23	ηη	ηη	PROPN
american_scientific_journal-2676	104	24	is	be	AUX
american_scientific_journal-2676	104	25	denoted	denote	VERB
american_scientific_journal-2676	104	26	by	by	ADP
american_scientific_journal-2676	104	27	12η	12η	NOUN
american_scientific_journal-2676	104	28	(	(	PUNCT
american_scientific_journal-2676	104	29	c	c	NOUN
american_scientific_journal-2676	104	30	12η	12η	X
american_scientific_journal-2676	104	31	)	)	PUNCT
american_scientific_journal-2676	104	32	,	,	PUNCT
american_scientific_journal-2676	104	33	respectively	respectively	ADV
american_scientific_journal-2676	104	34	.	.	PUNCT
american_scientific_journal-2676	105	1	theorem	theorem	VERB
american_scientific_journal-2676	105	2	2.2	2.2	NUM
american_scientific_journal-2676	105	3	[	[	SYM
american_scientific_journal-2676	105	4	10	10	NUM
american_scientific_journal-2676	105	5	]	]	PUNCT
american_scientific_journal-2676	105	6	let	let	NOUN
american_scientific_journal-2676	105	7	)	)	PUNCT
american_scientific_journal-2676	105	8	,	,	PUNCT
american_scientific_journal-2676	105	9	,	,	PUNCT
american_scientific_journal-2676	105	10	,	,	PUNCT
american_scientific_journal-2676	105	11	(	(	PUNCT
american_scientific_journal-2676	105	12	21	21	NUM
american_scientific_journal-2676	105	13	ex	ex	X
american_scientific_journal-2676	105	14	ηη	ηη	PROPN
american_scientific_journal-2676	105	15	be	be	AUX
american_scientific_journal-2676	105	16	a	a	DET
american_scientific_journal-2676	105	17	sbts	sbts	ADJ
american_scientific_journal-2676	105	18	.	.	PUNCT
american_scientific_journal-2676	106	1	the	the	DET
american_scientific_journal-2676	106	2	family	family	NOUN
american_scientific_journal-2676	106	3	of	of	ADP
american_scientific_journal-2676	106	4	all	all	DET
american_scientific_journal-2676	106	5	p	p	PRON
american_scientific_journal-2676	106	6	-open	-open	ADJ
american_scientific_journal-2676	106	7	soft	soft	ADJ
american_scientific_journal-2676	106	8	sets	set	NOUN
american_scientific_journal-2676	106	9	12η	12η	NOUN
american_scientific_journal-2676	106	10	is	be	AUX
american_scientific_journal-2676	106	11	a	a	DET
american_scientific_journal-2676	106	12	supra	supra	ADJ
american_scientific_journal-2676	106	13	soft	soft	ADJ
american_scientific_journal-2676	106	14	topology	topology	NOUN
american_scientific_journal-2676	106	15	on	on	ADP
american_scientific_journal-2676	106	16	x	x	SYM
american_scientific_journal-2676	106	17	,	,	PUNCT
american_scientific_journal-2676	106	18	where	where	SCONJ
american_scientific_journal-2676	106	19	1,2}=,),(:),(~),(=),{(=	1,2}=,),(:),(~),(=),{(=	NUM
american_scientific_journal-2676	106	20	2112	2112	NUM
american_scientific_journal-2676	106	21	iegegegeg	iegegegeg	PROPN
american_scientific_journal-2676	106	22	ii	ii	PROPN
american_scientific_journal-2676	106	23	ηη	ηη	ADV
american_scientific_journal-2676	106	24	∈∪	∈∪	VERB
american_scientific_journal-2676	106	25	.	.	PUNCT
american_scientific_journal-2676	107	1	the	the	DET
american_scientific_journal-2676	107	2	triple	triple	ADJ
american_scientific_journal-2676	107	3	)	)	PUNCT
american_scientific_journal-2676	107	4	,	,	PUNCT
american_scientific_journal-2676	107	5	,	,	PUNCT
american_scientific_journal-2676	107	6	(	(	PUNCT
american_scientific_journal-2676	107	7	12	12	NUM
american_scientific_journal-2676	107	8	ex	ex	NOUN
american_scientific_journal-2676	107	9	η	η	PROPN
american_scientific_journal-2676	107	10	is	be	AUX
american_scientific_journal-2676	107	11	the	the	DET
american_scientific_journal-2676	107	12	supra	supra	PROPN
american_scientific_journal-2676	107	13	soft	soft	ADJ
american_scientific_journal-2676	107	14	topological	topological	ADJ
american_scientific_journal-2676	107	15	space	space	NOUN
american_scientific_journal-2676	107	16	associated	associate	VERB
american_scientific_journal-2676	107	17	to	to	ADP
american_scientific_journal-2676	107	18	the	the	DET
american_scientific_journal-2676	107	19	soft	soft	ADJ
american_scientific_journal-2676	107	20	bitopological	bitopological	ADJ
american_scientific_journal-2676	107	21	space	space	NOUN
american_scientific_journal-2676	107	22	)	)	PUNCT
american_scientific_journal-2676	107	23	,	,	PUNCT
american_scientific_journal-2676	107	24	,	,	PUNCT
american_scientific_journal-2676	107	25	,	,	PUNCT
american_scientific_journal-2676	107	26	(	(	PUNCT
american_scientific_journal-2676	107	27	21	21	NUM
american_scientific_journal-2676	107	28	ex	ex	NOUN
american_scientific_journal-2676	107	29	ηη	ηη	PROPN
american_scientific_journal-2676	107	30	.	.	PUNCT
american_scientific_journal-2676	108	1	definition	definition	NOUN
american_scientific_journal-2676	108	2	2.11	2.11	NUM
american_scientific_journal-2676	108	3	[	[	X
american_scientific_journal-2676	108	4	10	10	NUM
american_scientific_journal-2676	108	5	]	]	PUNCT
american_scientific_journal-2676	108	6	let	let	NOUN
american_scientific_journal-2676	108	7	)	)	PUNCT
american_scientific_journal-2676	108	8	,	,	PUNCT
american_scientific_journal-2676	108	9	,	,	PUNCT
american_scientific_journal-2676	108	10	,	,	PUNCT
american_scientific_journal-2676	108	11	(	(	PUNCT
american_scientific_journal-2676	108	12	21	21	NUM
american_scientific_journal-2676	108	13	ex	ex	X
american_scientific_journal-2676	108	14	ηη	ηη	PROPN
american_scientific_journal-2676	108	15	be	be	AUX
american_scientific_journal-2676	108	16	a	a	DET
american_scientific_journal-2676	108	17	sbts	sbts	ADJ
american_scientific_journal-2676	108	18	and	and	CCONJ
american_scientific_journal-2676	108	19	let	let	VERB
american_scientific_journal-2676	108	20	exsseg	exsseg	ADJ
american_scientific_journal-2676	108	21	)	)	PUNCT
american_scientific_journal-2676	108	22	(	(	PUNCT
american_scientific_journal-2676	108	23	)	)	PUNCT
american_scientific_journal-2676	108	24	,	,	PUNCT
american_scientific_journal-2676	108	25	(	(	PUNCT
american_scientific_journal-2676	108	26	∈	∈	PROPN
american_scientific_journal-2676	108	27	.	.	PUNCT
american_scientific_journal-2676	109	1	the	the	DET
american_scientific_journal-2676	109	2	pairwise	pairwise	NOUN
american_scientific_journal-2676	109	3	soft	soft	ADJ
american_scientific_journal-2676	109	4	closure	closure	NOUN
american_scientific_journal-2676	109	5	of	of	ADP
american_scientific_journal-2676	109	6	)	)	PUNCT
american_scientific_journal-2676	109	7	,	,	PUNCT
american_scientific_journal-2676	109	8	(	(	PUNCT
american_scientific_journal-2676	109	9	eg	eg	NOUN
american_scientific_journal-2676	109	10	,	,	PUNCT
american_scientific_journal-2676	109	11	denoted	denote	VERB
american_scientific_journal-2676	109	12	by	by	ADP
american_scientific_journal-2676	109	13	)	)	PUNCT
american_scientific_journal-2676	109	14	,	,	PUNCT
american_scientific_journal-2676	109	15	(	(	PUNCT
american_scientific_journal-2676	109	16	12	12	NUM
american_scientific_journal-2676	109	17	egscl	egscl	ADV
american_scientific_journal-2676	109	18	,	,	PUNCT
american_scientific_journal-2676	109	19	is	be	AUX
american_scientific_journal-2676	109	20	defined	define	VERB
american_scientific_journal-2676	109	21	by	by	ADP
american_scientific_journal-2676	109	22	)	)	PUNCT
american_scientific_journal-2676	109	23	}	}	PUNCT
american_scientific_journal-2676	109	24	,	,	PUNCT
american_scientific_journal-2676	109	25	(	(	PUNCT
american_scientific_journal-2676	109	26	~),(:),{(=	~),(:),{(=	ADP
american_scientific_journal-2676	109	27	)	)	PUNCT
american_scientific_journal-2676	109	28	,	,	PUNCT
american_scientific_journal-2676	109	29	(	(	PUNCT
american_scientific_journal-2676	109	30	1212	1212	NUM
american_scientific_journal-2676	109	31	efegefegscl	efegefegscl	PROPN
american_scientific_journal-2676	109	32	c	c	PROPN
american_scientific_journal-2676	109	33	⊆∈η	⊆∈η	PROPN
american_scientific_journal-2676	109	34	.	.	PUNCT
american_scientific_journal-2676	110	1	clearly	clearly	ADV
american_scientific_journal-2676	110	2	,	,	PUNCT
american_scientific_journal-2676	110	3	)	)	PUNCT
american_scientific_journal-2676	110	4	,	,	PUNCT
american_scientific_journal-2676	110	5	(	(	PUNCT
american_scientific_journal-2676	110	6	12	12	NUM
american_scientific_journal-2676	110	7	egscl	egscl	NOUN
american_scientific_journal-2676	110	8	is	be	AUX
american_scientific_journal-2676	110	9	the	the	DET
american_scientific_journal-2676	110	10	smallest	small	ADJ
american_scientific_journal-2676	110	11	p	p	NOUN
american_scientific_journal-2676	110	12	-closed	-close	VERB
american_scientific_journal-2676	110	13	soft	soft	ADJ
american_scientific_journal-2676	110	14	set	set	NOUN
american_scientific_journal-2676	110	15	contains	contain	VERB
american_scientific_journal-2676	110	16	)	)	PUNCT
american_scientific_journal-2676	110	17	,	,	PUNCT
american_scientific_journal-2676	110	18	(	(	PUNCT
american_scientific_journal-2676	110	19	eg	eg	NOUN
american_scientific_journal-2676	110	20	.for	.for	ADP
american_scientific_journal-2676	110	21	more	more	ADJ
american_scientific_journal-2676	110	22	details	detail	NOUN
american_scientific_journal-2676	110	23	about	about	ADP
american_scientific_journal-2676	110	24	the	the	DET
american_scientific_journal-2676	110	25	properties	property	NOUN
american_scientific_journal-2676	110	26	of	of	ADP
american_scientific_journal-2676	110	27	pairwise	pairwise	NOUN
american_scientific_journal-2676	110	28	soft	soft	ADJ
american_scientific_journal-2676	110	29	closure	closure	NOUN
american_scientific_journal-2676	110	30	operator	operator	NOUN
american_scientific_journal-2676	110	31	see	see	VERB
american_scientific_journal-2676	110	32	in	in	ADP
american_scientific_journal-2676	110	33	[	[	X
american_scientific_journal-2676	110	34	10	10	NUM
american_scientific_journal-2676	110	35	]	]	PUNCT
american_scientific_journal-2676	110	36	.	.	PUNCT
american_scientific_journal-2676	111	1	american	american	PROPN
american_scientific_journal-2676	111	2	scientific	scientific	ADJ
american_scientific_journal-2676	111	3	research	research	PROPN
american_scientific_journal-2676	111	4	journal	journal	NOUN
american_scientific_journal-2676	111	5	for	for	ADP
american_scientific_journal-2676	111	6	engineering	engineering	NOUN
american_scientific_journal-2676	111	7	,	,	PUNCT
american_scientific_journal-2676	111	8	technology	technology	NOUN
american_scientific_journal-2676	111	9	,	,	PUNCT
american_scientific_journal-2676	111	10	and	and	CCONJ
american_scientific_journal-2676	111	11	sciences	science	NOUN
american_scientific_journal-2676	111	12	(	(	PUNCT
american_scientific_journal-2676	111	13	asrjets	asrjet	NOUN
american_scientific_journal-2676	111	14	)	)	PUNCT
american_scientific_journal-2676	111	15	(	(	PUNCT
american_scientific_journal-2676	111	16	2017	2017	NUM
american_scientific_journal-2676	111	17	)	)	PUNCT
american_scientific_journal-2676	111	18	volume	volume	NOUN
american_scientific_journal-2676	111	19	28	28	NUM
american_scientific_journal-2676	111	20	,	,	PUNCT
american_scientific_journal-2676	111	21	no	no	DET
american_scientific_journal-2676	111	22	1	1	NUM
american_scientific_journal-2676	111	23	,	,	PUNCT
american_scientific_journal-2676	111	24	pp	pp	ADV
american_scientific_journal-2676	111	25	225	225	NUM
american_scientific_journal-2676	111	26	-	-	SYM
american_scientific_journal-2676	111	27	247	247	NUM
american_scientific_journal-2676	111	28	230	230	NUM
american_scientific_journal-2676	111	29	definition	definition	NOUN
american_scientific_journal-2676	111	30	2.12	2.12	NUM
american_scientific_journal-2676	111	31	[	[	X
american_scientific_journal-2676	111	32	10	10	NUM
american_scientific_journal-2676	111	33	]	]	PUNCT
american_scientific_journal-2676	111	34	let	let	NOUN
american_scientific_journal-2676	111	35	)	)	PUNCT
american_scientific_journal-2676	111	36	,	,	PUNCT
american_scientific_journal-2676	111	37	,	,	PUNCT
american_scientific_journal-2676	111	38	,	,	PUNCT
american_scientific_journal-2676	111	39	(	(	PUNCT
american_scientific_journal-2676	111	40	21	21	NUM
american_scientific_journal-2676	111	41	ex	ex	X
american_scientific_journal-2676	111	42	ηη	ηη	PROPN
american_scientific_journal-2676	111	43	be	be	AUX
american_scientific_journal-2676	111	44	a	a	DET
american_scientific_journal-2676	111	45	sbts	sbts	ADJ
american_scientific_journal-2676	111	46	and	and	CCONJ
american_scientific_journal-2676	111	47	let	let	VERB
american_scientific_journal-2676	111	48	exsseg	exsseg	ADJ
american_scientific_journal-2676	111	49	)	)	PUNCT
american_scientific_journal-2676	111	50	(	(	PUNCT
american_scientific_journal-2676	111	51	)	)	PUNCT
american_scientific_journal-2676	111	52	,	,	PUNCT
american_scientific_journal-2676	111	53	(	(	PUNCT
american_scientific_journal-2676	111	54	∈	∈	PROPN
american_scientific_journal-2676	111	55	.	.	PUNCT
american_scientific_journal-2676	112	1	the	the	DET
american_scientific_journal-2676	112	2	pairwise	pairwise	NOUN
american_scientific_journal-2676	112	3	soft	soft	ADJ
american_scientific_journal-2676	112	4	interior	interior	NOUN
american_scientific_journal-2676	112	5	of	of	ADP
american_scientific_journal-2676	112	6	)	)	PUNCT
american_scientific_journal-2676	112	7	,	,	PUNCT
american_scientific_journal-2676	112	8	(	(	PUNCT
american_scientific_journal-2676	112	9	eg	eg	NOUN
american_scientific_journal-2676	112	10	,	,	PUNCT
american_scientific_journal-2676	112	11	denoted	denote	VERB
american_scientific_journal-2676	112	12	by	by	ADP
american_scientific_journal-2676	112	13	)	)	PUNCT
american_scientific_journal-2676	112	14	,	,	PUNCT
american_scientific_journal-2676	112	15	(	(	PUNCT
american_scientific_journal-2676	112	16	12	12	NUM
american_scientific_journal-2676	112	17	egsint	egsint	NOUN
american_scientific_journal-2676	112	18	,	,	PUNCT
american_scientific_journal-2676	112	19	is	be	AUX
american_scientific_journal-2676	112	20	defined	define	VERB
american_scientific_journal-2676	112	21	by	by	ADP
american_scientific_journal-2676	112	22	)	)	PUNCT
american_scientific_journal-2676	112	23	}	}	PUNCT
american_scientific_journal-2676	112	24	,	,	PUNCT
american_scientific_journal-2676	112	25	(	(	PUNCT
american_scientific_journal-2676	112	26	~),(:),{(=	~),(:),{(=	ADP
american_scientific_journal-2676	112	27	)	)	PUNCT
american_scientific_journal-2676	112	28	,	,	PUNCT
american_scientific_journal-2676	112	29	(	(	PUNCT
american_scientific_journal-2676	112	30	1212	1212	NUM
american_scientific_journal-2676	112	31	egehehegsint	egehehegsint	NOUN
american_scientific_journal-2676	112	32	⊆∈η	⊆∈η	NOUN
american_scientific_journal-2676	112	33	.	.	PUNCT
american_scientific_journal-2676	113	1	clearly	clearly	ADV
american_scientific_journal-2676	113	2	,	,	PUNCT
american_scientific_journal-2676	113	3	)	)	PUNCT
american_scientific_journal-2676	113	4	,	,	PUNCT
american_scientific_journal-2676	113	5	(	(	PUNCT
american_scientific_journal-2676	113	6	12	12	NUM
american_scientific_journal-2676	113	7	egsint	egsint	NOUN
american_scientific_journal-2676	113	8	is	be	AUX
american_scientific_journal-2676	113	9	the	the	DET
american_scientific_journal-2676	113	10	largest	large	ADJ
american_scientific_journal-2676	113	11	p	p	NOUN
american_scientific_journal-2676	113	12	-open	-open	ADJ
american_scientific_journal-2676	113	13	soft	soft	ADJ
american_scientific_journal-2676	113	14	set	set	NOUN
american_scientific_journal-2676	113	15	contained	contain	VERB
american_scientific_journal-2676	113	16	in	in	ADP
american_scientific_journal-2676	113	17	)	)	PUNCT
american_scientific_journal-2676	113	18	,	,	PUNCT
american_scientific_journal-2676	113	19	(	(	PUNCT
american_scientific_journal-2676	113	20	eg	eg	NOUN
american_scientific_journal-2676	113	21	.	.	PUNCT
american_scientific_journal-2676	114	1	for	for	ADP
american_scientific_journal-2676	114	2	more	more	ADJ
american_scientific_journal-2676	114	3	details	detail	NOUN
american_scientific_journal-2676	114	4	about	about	ADP
american_scientific_journal-2676	114	5	the	the	DET
american_scientific_journal-2676	114	6	properties	property	NOUN
american_scientific_journal-2676	114	7	of	of	ADP
american_scientific_journal-2676	114	8	pairwise	pairwise	NOUN
american_scientific_journal-2676	114	9	soft	soft	ADJ
american_scientific_journal-2676	114	10	interior	interior	ADJ
american_scientific_journal-2676	114	11	operator	operator	NOUN
american_scientific_journal-2676	114	12	you	you	PRON
american_scientific_journal-2676	114	13	can	can	AUX
american_scientific_journal-2676	114	14	see	see	VERB
american_scientific_journal-2676	114	15	see	see	VERB
american_scientific_journal-2676	114	16	[	[	X
american_scientific_journal-2676	114	17	10	10	NUM
american_scientific_journal-2676	114	18	]	]	PUNCT
american_scientific_journal-2676	114	19	.	.	PUNCT
american_scientific_journal-2676	115	1	definition	definition	NOUN
american_scientific_journal-2676	115	2	2.13	2.13	NUM
american_scientific_journal-2676	115	3	[	[	X
american_scientific_journal-2676	115	4	10	10	NUM
american_scientific_journal-2676	115	5	]	]	PUNCT
american_scientific_journal-2676	115	6	let	let	NOUN
american_scientific_journal-2676	115	7	)	)	PUNCT
american_scientific_journal-2676	115	8	,	,	PUNCT
american_scientific_journal-2676	115	9	,	,	PUNCT
american_scientific_journal-2676	115	10	,	,	PUNCT
american_scientific_journal-2676	115	11	(	(	PUNCT
american_scientific_journal-2676	115	12	21	21	NUM
american_scientific_journal-2676	115	13	ex	ex	X
american_scientific_journal-2676	115	14	ηη	ηη	PROPN
american_scientific_journal-2676	115	15	be	be	AUX
american_scientific_journal-2676	115	16	a	a	DET
american_scientific_journal-2676	115	17	sbts	sbts	ADJ
american_scientific_journal-2676	115	18	and	and	CCONJ
american_scientific_journal-2676	115	19	let	let	VERB
american_scientific_journal-2676	115	20	exsseg	exsseg	ADJ
american_scientific_journal-2676	115	21	)	)	PUNCT
american_scientific_journal-2676	115	22	(	(	PUNCT
american_scientific_journal-2676	115	23	)	)	PUNCT
american_scientific_journal-2676	115	24	,	,	PUNCT
american_scientific_journal-2676	115	25	(	(	PUNCT
american_scientific_journal-2676	115	26	∈	∈	PROPN
american_scientific_journal-2676	115	27	.	.	PUNCT
american_scientific_journal-2676	116	1	the	the	DET
american_scientific_journal-2676	116	2	pairwise	pairwise	NOUN
american_scientific_journal-2676	116	3	soft	soft	ADJ
american_scientific_journal-2676	116	4	kernel	kernel	NOUN
american_scientific_journal-2676	116	5	of	of	ADP
american_scientific_journal-2676	116	6	)	)	PUNCT
american_scientific_journal-2676	116	7	,	,	PUNCT
american_scientific_journal-2676	116	8	(	(	PUNCT
american_scientific_journal-2676	116	9	eg	eg	NOUN
american_scientific_journal-2676	117	1	[	[	X
american_scientific_journal-2676	117	2	briefly	briefly	ADV
american_scientific_journal-2676	117	3	,	,	PUNCT
american_scientific_journal-2676	117	4	)	)	PUNCT
american_scientific_journal-2676	117	5	,	,	PUNCT
american_scientific_journal-2676	117	6	(	(	PUNCT
american_scientific_journal-2676	117	7	12	12	NUM
american_scientific_journal-2676	117	8	egsker	egsker	NOUN
american_scientific_journal-2676	117	9	]	]	X
american_scientific_journal-2676	117	10	,	,	PUNCT
american_scientific_journal-2676	117	11	is	be	AUX
american_scientific_journal-2676	117	12	the	the	DET
american_scientific_journal-2676	117	13	intersection	intersection	NOUN
american_scientific_journal-2676	117	14	of	of	ADP
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american_scientific_journal-2676	117	16	p	p	ADJ
american_scientific_journal-2676	117	17	-open	-open	ADJ
american_scientific_journal-2676	117	18	soft	soft	ADJ
american_scientific_journal-2676	117	19	supersets	superset	NOUN
american_scientific_journal-2676	117	20	of	of	ADP
american_scientific_journal-2676	117	21	)	)	PUNCT
american_scientific_journal-2676	117	22	,	,	PUNCT
american_scientific_journal-2676	117	23	(	(	PUNCT
american_scientific_journal-2676	117	24	eg	eg	NOUN
american_scientific_journal-2676	117	25	,	,	PUNCT
american_scientific_journal-2676	117	26	i.e.	i.e.	X
american_scientific_journal-2676	117	27	,	,	PUNCT
american_scientific_journal-2676	117	28	)	)	PUNCT
american_scientific_journal-2676	117	29	}	}	PUNCT
american_scientific_journal-2676	117	30	,	,	PUNCT
american_scientific_journal-2676	117	31	(	(	PUNCT
american_scientific_journal-2676	117	32	~),(:),{(=	~),(:),{(=	ADP
american_scientific_journal-2676	117	33	)	)	PUNCT
american_scientific_journal-2676	117	34	,	,	PUNCT
american_scientific_journal-2676	117	35	(	(	PUNCT
american_scientific_journal-2676	117	36	1212	1212	NUM
american_scientific_journal-2676	117	37	ehegehegsker	ehegehegsker	NOUN
american_scientific_journal-2676	117	38	⊆∈η	⊆∈η	PROPN
american_scientific_journal-2676	117	39	.	.	PUNCT
american_scientific_journal-2676	118	1	definition	definition	NOUN
american_scientific_journal-2676	118	2	2.14	2.14	NUM
american_scientific_journal-2676	118	3	[	[	X
american_scientific_journal-2676	118	4	10	10	NUM
american_scientific_journal-2676	118	5	]	]	X
american_scientific_journal-2676	118	6	a	a	DET
american_scientific_journal-2676	118	7	soft	soft	ADJ
american_scientific_journal-2676	118	8	set	set	NOUN
american_scientific_journal-2676	118	9	)	)	PUNCT
american_scientific_journal-2676	118	10	,	,	PUNCT
american_scientific_journal-2676	118	11	(	(	PUNCT
american_scientific_journal-2676	118	12	eg	eg	NOUN
american_scientific_journal-2676	118	13	is	be	AUX
american_scientific_journal-2676	118	14	said	say	VERB
american_scientific_journal-2676	118	15	to	to	PART
american_scientific_journal-2676	118	16	be	be	AUX
american_scientific_journal-2676	118	17	a	a	DET
american_scientific_journal-2676	118	18	pairwise	pairwise	NOUN
american_scientific_journal-2676	118	19	λ	λ	NOUN
american_scientific_journal-2676	118	20	soft	soft	ADJ
american_scientific_journal-2676	118	21	set	set	NOUN
american_scientific_journal-2676	118	22	in	in	ADP
american_scientific_journal-2676	118	23	a	a	DET
american_scientific_journal-2676	118	24	soft	soft	ADJ
american_scientific_journal-2676	118	25	bitopological	bitopological	ADJ
american_scientific_journal-2676	118	26	space	space	NOUN
american_scientific_journal-2676	118	27	)	)	PUNCT
american_scientific_journal-2676	118	28	,	,	PUNCT
american_scientific_journal-2676	118	29	,	,	PUNCT
american_scientific_journal-2676	118	30	,	,	PUNCT
american_scientific_journal-2676	118	31	(	(	PUNCT
american_scientific_journal-2676	118	32	21	21	NUM
american_scientific_journal-2676	118	33	ex	ex	NOUN
american_scientific_journal-2676	118	34	ηη	ηη	NOUN
american_scientific_journal-2676	119	1	[	[	X
american_scientific_journal-2676	119	2	briefly	briefly	ADV
american_scientific_journal-2676	119	3	,	,	PUNCT
american_scientific_journal-2676	119	4	λp	λp	X
american_scientific_journal-2676	119	5	-soft	-soft	NOUN
american_scientific_journal-2676	119	6	set	set	NOUN
american_scientific_journal-2676	119	7	]	]	PUNCT
american_scientific_journal-2676	119	8	if	if	SCONJ
american_scientific_journal-2676	119	9	)	)	PUNCT
american_scientific_journal-2676	119	10	,	,	PUNCT
american_scientific_journal-2676	119	11	(=	(=	ADV
american_scientific_journal-2676	119	12	)	)	PUNCT
american_scientific_journal-2676	119	13	,	,	PUNCT
american_scientific_journal-2676	119	14	(	(	PUNCT
american_scientific_journal-2676	119	15	12	12	NUM
american_scientific_journal-2676	119	16	egegsker	egegsker	NOUN
american_scientific_journal-2676	119	17	.	.	PUNCT
american_scientific_journal-2676	120	1	theorem	theorem	VERB
american_scientific_journal-2676	120	2	2.3	2.3	NUM
american_scientific_journal-2676	121	1	[	[	SYM
american_scientific_journal-2676	121	2	10	10	NUM
american_scientific_journal-2676	121	3	]	]	PUNCT
american_scientific_journal-2676	121	4	every	every	DET
american_scientific_journal-2676	121	5	p	p	NOUN
american_scientific_journal-2676	121	6	-open	-open	ADJ
american_scientific_journal-2676	121	7	soft	soft	ADJ
american_scientific_journal-2676	121	8	set	set	NOUN
american_scientific_journal-2676	121	9	is	be	AUX
american_scientific_journal-2676	121	10	a	a	DET
american_scientific_journal-2676	121	11	λp	λp	ADP
american_scientific_journal-2676	121	12	-soft	-soft	ADJ
american_scientific_journal-2676	121	13	set	set	NOUN
american_scientific_journal-2676	121	14	.	.	PUNCT
american_scientific_journal-2676	122	1	theorem	theorem	VERB
american_scientific_journal-2676	122	2	2.4	2.4	NUM
american_scientific_journal-2676	122	3	[	[	SYM
american_scientific_journal-2676	122	4	10	10	NUM
american_scientific_journal-2676	122	5	]	]	PUNCT
american_scientific_journal-2676	122	6	let	let	NOUN
american_scientific_journal-2676	122	7	)	)	PUNCT
american_scientific_journal-2676	122	8	,	,	PUNCT
american_scientific_journal-2676	122	9	,	,	PUNCT
american_scientific_journal-2676	122	10	,	,	PUNCT
american_scientific_journal-2676	122	11	(	(	PUNCT
american_scientific_journal-2676	122	12	21	21	NUM
american_scientific_journal-2676	122	13	ex	ex	X
american_scientific_journal-2676	122	14	ηη	ηη	PROPN
american_scientific_journal-2676	122	15	be	be	AUX
american_scientific_journal-2676	122	16	a	a	DET
american_scientific_journal-2676	122	17	sbts	sbts	ADJ
american_scientific_journal-2676	122	18	.	.	PUNCT
american_scientific_journal-2676	123	1	then	then	ADV
american_scientific_journal-2676	123	2	,	,	PUNCT
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american_scientific_journal-2676	123	7	λp	λp	PRON
american_scientific_journal-2676	123	8	-soft	-soft	ADJ
american_scientific_journal-2676	123	9	sets	set	NOUN
american_scientific_journal-2676	123	10	is	be	AUX
american_scientific_journal-2676	123	11	an	an	DET
american_scientific_journal-2676	123	12	alexandroff	alexandroff	ADJ
american_scientific_journal-2676	123	13	soft	soft	ADJ
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american_scientific_journal-2676	123	16	x	x	X
american_scientific_journal-2676	123	17	.	.	PUNCT
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american_scientific_journal-2676	124	5	denoted	denote	VERB
american_scientific_journal-2676	124	6	by	by	ADP
american_scientific_journal-2676	124	7	λpη	λpη	PROPN
american_scientific_journal-2676	124	8	.	.	PUNCT
american_scientific_journal-2676	125	1	the	the	DET
american_scientific_journal-2676	125	2	triple	triple	ADJ
american_scientific_journal-2676	125	3	)	)	PUNCT
american_scientific_journal-2676	125	4	,	,	PUNCT
american_scientific_journal-2676	125	5	,	,	PUNCT
american_scientific_journal-2676	125	6	(	(	PUNCT
american_scientific_journal-2676	125	7	ex	ex	X
american_scientific_journal-2676	125	8	pλη	pλη	VERB
american_scientific_journal-2676	125	9	is	be	AUX
american_scientific_journal-2676	125	10	the	the	DET
american_scientific_journal-2676	125	11	soft	soft	ADJ
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american_scientific_journal-2676	125	13	space	space	NOUN
american_scientific_journal-2676	125	14	associated	associate	VERB
american_scientific_journal-2676	125	15	to	to	ADP
american_scientific_journal-2676	125	16	the	the	DET
american_scientific_journal-2676	125	17	soft	soft	ADJ
american_scientific_journal-2676	125	18	bitopological	bitopological	ADJ
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american_scientific_journal-2676	125	20	)	)	PUNCT
american_scientific_journal-2676	125	21	,	,	PUNCT
american_scientific_journal-2676	125	22	,	,	PUNCT
american_scientific_journal-2676	125	23	,	,	PUNCT
american_scientific_journal-2676	125	24	(	(	PUNCT
american_scientific_journal-2676	125	25	21	21	NUM
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american_scientific_journal-2676	125	27	ηη	ηη	NOUN
american_scientific_journal-2676	125	28	,	,	PUNCT
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american_scientific_journal-2676	125	32	family	family	NOUN
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american_scientific_journal-2676	125	35	λp	λp	PRON
american_scientific_journal-2676	125	36	-soft	-soft	ADJ
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american_scientific_journal-2676	125	38	.	.	PUNCT
american_scientific_journal-2676	126	1	theorem	theorem	VERB
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american_scientific_journal-2676	126	3	[	[	SYM
american_scientific_journal-2676	126	4	10	10	NUM
american_scientific_journal-2676	126	5	]	]	PUNCT
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american_scientific_journal-2676	126	7	)	)	PUNCT
american_scientific_journal-2676	126	8	,	,	PUNCT
american_scientific_journal-2676	126	9	,	,	PUNCT
american_scientific_journal-2676	126	10	,	,	PUNCT
american_scientific_journal-2676	126	11	(	(	PUNCT
american_scientific_journal-2676	126	12	21	21	NUM
american_scientific_journal-2676	126	13	ex	ex	X
american_scientific_journal-2676	126	14	ηη	ηη	PROPN
american_scientific_journal-2676	126	15	be	be	AUX
american_scientific_journal-2676	126	16	a	a	DET
american_scientific_journal-2676	126	17	sbts	sbts	ADJ
american_scientific_journal-2676	126	18	.	.	PUNCT
american_scientific_journal-2676	127	1	then	then	ADV
american_scientific_journal-2676	127	2	,	,	PUNCT
american_scientific_journal-2676	127	3	ep	ep	PROPN
american_scientific_journal-2676	127	4	xss	xss	PROPN
american_scientific_journal-2676	127	5	)	)	PUNCT
american_scientific_journal-2676	127	6	(	(	PUNCT
american_scientific_journal-2676	127	7	1221	1221	NUM
american_scientific_journal-2676	127	8	⊆⊆⊆∪	⊆⊆⊆∪	ADJ
american_scientific_journal-2676	127	9	ληηηη	ληηηη	ADJ
american_scientific_journal-2676	127	10	.	.	PUNCT
american_scientific_journal-2676	128	1	definition	definition	NOUN
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american_scientific_journal-2676	128	3	[	[	X
american_scientific_journal-2676	128	4	10	10	NUM
american_scientific_journal-2676	128	5	]	]	X
american_scientific_journal-2676	128	6	a	a	DET
american_scientific_journal-2676	128	7	soft	soft	ADJ
american_scientific_journal-2676	128	8	set	set	NOUN
american_scientific_journal-2676	128	9	)	)	PUNCT
american_scientific_journal-2676	128	10	,	,	PUNCT
american_scientific_journal-2676	128	11	(	(	PUNCT
american_scientific_journal-2676	128	12	eg	eg	NOUN
american_scientific_journal-2676	128	13	is	be	AUX
american_scientific_journal-2676	128	14	said	say	VERB
american_scientific_journal-2676	128	15	to	to	PART
american_scientific_journal-2676	128	16	be	be	AUX
american_scientific_journal-2676	128	17	a	a	DET
american_scientific_journal-2676	128	18	pairwise	pairwise	NOUN
american_scientific_journal-2676	128	19	λ	λ	SYM
american_scientific_journal-2676	128	20	-closed	-close	VERB
american_scientific_journal-2676	128	21	soft	soft	ADJ
american_scientific_journal-2676	128	22	set	set	NOUN
american_scientific_journal-2676	128	23	in	in	ADP
american_scientific_journal-2676	128	24	a	a	DET
american_scientific_journal-2676	128	25	sbts	sbts	ADJ
american_scientific_journal-2676	128	26	)	)	PUNCT
american_scientific_journal-2676	128	27	,	,	PUNCT
american_scientific_journal-2676	128	28	,	,	PUNCT
american_scientific_journal-2676	128	29	,	,	PUNCT
american_scientific_journal-2676	128	30	(	(	PUNCT
american_scientific_journal-2676	128	31	21	21	NUM
american_scientific_journal-2676	128	32	ex	ex	NOUN
american_scientific_journal-2676	128	33	ηη	ηη	NOUN
american_scientific_journal-2676	129	1	[	[	X
american_scientific_journal-2676	129	2	briefly	briefly	ADV
american_scientific_journal-2676	129	3	,	,	PUNCT
american_scientific_journal-2676	129	4	λp	λp	X
american_scientific_journal-2676	129	5	-closed	-close	VERB
american_scientific_journal-2676	129	6	soft	soft	ADJ
american_scientific_journal-2676	129	7	set	set	NOUN
american_scientific_journal-2676	129	8	]	]	PUNCT
american_scientific_journal-2676	129	9	if	if	SCONJ
american_scientific_journal-2676	129	10	)	)	PUNCT
american_scientific_journal-2676	129	11	,	,	PUNCT
american_scientific_journal-2676	129	12	(	(	PUNCT
american_scientific_journal-2676	129	13	~),(=	~),(=	NUM
american_scientific_journal-2676	129	14	)	)	PUNCT
american_scientific_journal-2676	129	15	,	,	PUNCT
american_scientific_journal-2676	129	16	(	(	PUNCT
american_scientific_journal-2676	129	17	ehefeg	ehefeg	PROPN
american_scientific_journal-2676	129	18	∩	∩	NOUN
american_scientific_journal-2676	129	19	,	,	PUNCT
american_scientific_journal-2676	129	20	where	where	SCONJ
american_scientific_journal-2676	129	21	)	)	PUNCT
american_scientific_journal-2676	129	22	,	,	PUNCT
american_scientific_journal-2676	129	23	(	(	PUNCT
american_scientific_journal-2676	129	24	ef	ef	PROPN
american_scientific_journal-2676	129	25	is	be	AUX
american_scientific_journal-2676	129	26	a	a	DET
american_scientific_journal-2676	129	27	p	p	NOUN
american_scientific_journal-2676	129	28	-closed	-close	VERB
american_scientific_journal-2676	129	29	soft	soft	ADJ
american_scientific_journal-2676	129	30	set	set	NOUN
american_scientific_journal-2676	129	31	and	and	CCONJ
american_scientific_journal-2676	129	32	)	)	PUNCT
american_scientific_journal-2676	129	33	,	,	PUNCT
american_scientific_journal-2676	129	34	(	(	PUNCT
american_scientific_journal-2676	129	35	eh	eh	INTJ
american_scientific_journal-2676	129	36	is	be	AUX
american_scientific_journal-2676	129	37	a	a	DET
american_scientific_journal-2676	129	38	λp	λp	ADP
american_scientific_journal-2676	129	39	-soft	-soft	ADJ
american_scientific_journal-2676	129	40	set	set	NOUN
american_scientific_journal-2676	129	41	.	.	PUNCT
american_scientific_journal-2676	130	1	the	the	DET
american_scientific_journal-2676	130	2	family	family	NOUN
american_scientific_journal-2676	130	3	of	of	ADP
american_scientific_journal-2676	130	4	all	all	DET
american_scientific_journal-2676	130	5	λp	λp	ADP
american_scientific_journal-2676	130	6	-closed	-close	VERB
american_scientific_journal-2676	130	7	soft	soft	ADJ
american_scientific_journal-2676	130	8	sets	set	NOUN
american_scientific_journal-2676	130	9	we	we	PRON
american_scientific_journal-2676	130	10	denoted	denote	VERB
american_scientific_journal-2676	130	11	by	by	ADP
american_scientific_journal-2676	130	12	excsp	excsp	NOUN
american_scientific_journal-2676	130	13	)	)	PUNCT
american_scientific_journal-2676	130	14	,	,	PUNCT
american_scientific_journal-2676	130	15	,	,	PUNCT
american_scientific_journal-2676	130	16	(	(	PUNCT
american_scientific_journal-2676	130	17	21	21	NUM
american_scientific_journal-2676	130	18	ηηλ	ηηλ	NOUN
american_scientific_journal-2676	130	19	.	.	PUNCT
american_scientific_journal-2676	131	1	theorem	theorem	VERB
american_scientific_journal-2676	131	2	2.6	2.6	NUM
american_scientific_journal-2676	131	3	[	[	SYM
american_scientific_journal-2676	131	4	10	10	NUM
american_scientific_journal-2676	131	5	]	]	PUNCT
american_scientific_journal-2676	131	6	let	let	NOUN
american_scientific_journal-2676	131	7	)	)	PUNCT
american_scientific_journal-2676	131	8	,	,	PUNCT
american_scientific_journal-2676	131	9	,	,	PUNCT
american_scientific_journal-2676	131	10	,	,	PUNCT
american_scientific_journal-2676	131	11	(	(	PUNCT
american_scientific_journal-2676	131	12	21	21	NUM
american_scientific_journal-2676	131	13	ex	ex	X
american_scientific_journal-2676	131	14	ηη	ηη	PROPN
american_scientific_journal-2676	131	15	be	be	AUX
american_scientific_journal-2676	131	16	a	a	DET
american_scientific_journal-2676	131	17	sbts	sbts	ADJ
american_scientific_journal-2676	131	18	.	.	PUNCT
american_scientific_journal-2676	132	1	then	then	ADV
american_scientific_journal-2676	132	2	,	,	PUNCT
american_scientific_journal-2676	132	3	1	1	X
american_scientific_journal-2676	132	4	)	)	PUNCT
american_scientific_journal-2676	132	5	every	every	DET
american_scientific_journal-2676	132	6	p	p	NOUN
american_scientific_journal-2676	132	7	-closed	-close	VERB
american_scientific_journal-2676	132	8	soft	soft	ADJ
american_scientific_journal-2676	132	9	set	set	NOUN
american_scientific_journal-2676	132	10	is	be	AUX
american_scientific_journal-2676	132	11	a	a	DET
american_scientific_journal-2676	132	12	λp	λp	ADV
american_scientific_journal-2676	132	13	-closed	-close	VERB
american_scientific_journal-2676	132	14	soft	soft	ADJ
american_scientific_journal-2676	132	15	set	set	NOUN
american_scientific_journal-2676	132	16	.	.	PUNCT
american_scientific_journal-2676	133	1	2	2	X
american_scientific_journal-2676	133	2	)	)	PUNCT
american_scientific_journal-2676	133	3	every	every	DET
american_scientific_journal-2676	133	4	λp	λp	PRON
american_scientific_journal-2676	133	5	-soft	-soft	ADJ
american_scientific_journal-2676	133	6	set	set	NOUN
american_scientific_journal-2676	133	7	is	be	AUX
american_scientific_journal-2676	133	8	a	a	DET
american_scientific_journal-2676	133	9	λp	λp	ADV
american_scientific_journal-2676	133	10	-closed	-close	VERB
american_scientific_journal-2676	133	11	soft	soft	ADJ
american_scientific_journal-2676	133	12	set	set	NOUN
american_scientific_journal-2676	133	13	.	.	PUNCT
american_scientific_journal-2676	134	1	definition	definition	NOUN
american_scientific_journal-2676	134	2	2.16	2.16	NUM
american_scientific_journal-2676	135	1	[	[	X
american_scientific_journal-2676	135	2	12	12	NUM
american_scientific_journal-2676	135	3	]	]	X
american_scientific_journal-2676	135	4	let	let	NOUN
american_scientific_journal-2676	135	5	)	)	PUNCT
american_scientific_journal-2676	135	6	,	,	PUNCT
american_scientific_journal-2676	135	7	,	,	PUNCT
american_scientific_journal-2676	135	8	,	,	PUNCT
american_scientific_journal-2676	135	9	(	(	PUNCT
american_scientific_journal-2676	135	10	21	21	NUM
american_scientific_journal-2676	135	11	ex	ex	X
american_scientific_journal-2676	135	12	ηη	ηη	PROPN
american_scientific_journal-2676	135	13	be	be	AUX
american_scientific_journal-2676	135	14	a	a	DET
american_scientific_journal-2676	135	15	sbts	sbts	ADJ
american_scientific_journal-2676	135	16	and	and	CCONJ
american_scientific_journal-2676	135	17	let	let	VERB
american_scientific_journal-2676	135	18	exsseg	exsseg	ADJ
american_scientific_journal-2676	135	19	)	)	PUNCT
american_scientific_journal-2676	135	20	(	(	PUNCT
american_scientific_journal-2676	135	21	)	)	PUNCT
american_scientific_journal-2676	135	22	,	,	PUNCT
american_scientific_journal-2676	135	23	(	(	PUNCT
american_scientific_journal-2676	135	24	∈	∈	PROPN
american_scientific_journal-2676	135	25	.	.	PUNCT
american_scientific_journal-2676	136	1	the	the	DET
american_scientific_journal-2676	136	2	pairwise	pairwise	NOUN
american_scientific_journal-2676	136	3	soft	soft	ADJ
american_scientific_journal-2676	136	4	sub	sub	NOUN
american_scientific_journal-2676	136	5	kernel	kernel	NOUN
american_scientific_journal-2676	136	6	of	of	ADP
american_scientific_journal-2676	136	7	american	american	PROPN
american_scientific_journal-2676	136	8	scientific	scientific	ADJ
american_scientific_journal-2676	136	9	research	research	NOUN
american_scientific_journal-2676	136	10	journal	journal	NOUN
american_scientific_journal-2676	136	11	for	for	ADP
american_scientific_journal-2676	136	12	engineering	engineering	NOUN
american_scientific_journal-2676	136	13	,	,	PUNCT
american_scientific_journal-2676	136	14	technology	technology	NOUN
american_scientific_journal-2676	136	15	,	,	PUNCT
american_scientific_journal-2676	136	16	and	and	CCONJ
american_scientific_journal-2676	136	17	sciences	science	NOUN
american_scientific_journal-2676	136	18	(	(	PUNCT
american_scientific_journal-2676	136	19	asrjets	asrjet	NOUN
american_scientific_journal-2676	136	20	)	)	PUNCT
american_scientific_journal-2676	136	21	(	(	PUNCT
american_scientific_journal-2676	136	22	2017	2017	NUM
american_scientific_journal-2676	136	23	)	)	PUNCT
american_scientific_journal-2676	136	24	volume	volume	NOUN
american_scientific_journal-2676	136	25	28	28	NUM
american_scientific_journal-2676	136	26	,	,	PUNCT
american_scientific_journal-2676	136	27	no	no	DET
american_scientific_journal-2676	136	28	1	1	NUM
american_scientific_journal-2676	136	29	,	,	PUNCT
american_scientific_journal-2676	136	30	pp	pp	ADV
american_scientific_journal-2676	136	31	225	225	NUM
american_scientific_journal-2676	136	32	-	-	SYM
american_scientific_journal-2676	136	33	247	247	NUM
american_scientific_journal-2676	136	34	231	231	NUM
american_scientific_journal-2676	136	35	)	)	PUNCT
american_scientific_journal-2676	136	36	,	,	PUNCT
american_scientific_journal-2676	136	37	(	(	PUNCT
american_scientific_journal-2676	136	38	eg	eg	NOUN
american_scientific_journal-2676	136	39	[	[	X
american_scientific_journal-2676	136	40	briefly	briefly	ADV
american_scientific_journal-2676	136	41	,	,	PUNCT
american_scientific_journal-2676	136	42	)	)	PUNCT
american_scientific_journal-2676	136	43	,	,	PUNCT
american_scientific_journal-2676	136	44	(	(	PUNCT
american_scientific_journal-2676	136	45	*	*	PUNCT
american_scientific_journal-2676	136	46	12	12	NUM
american_scientific_journal-2676	136	47	egsker	egsker	NOUN
american_scientific_journal-2676	136	48	]	]	PUNCT
american_scientific_journal-2676	136	49	is	be	AUX
american_scientific_journal-2676	136	50	defined	define	VERB
american_scientific_journal-2676	136	51	by	by	ADP
american_scientific_journal-2676	136	52	)	)	PUNCT
american_scientific_journal-2676	136	53	}	}	PUNCT
american_scientific_journal-2676	136	54	,	,	PUNCT
american_scientific_journal-2676	136	55	(	(	PUNCT
american_scientific_journal-2676	136	56	~),(:),{(=	~),(:),{(=	ADP
american_scientific_journal-2676	136	57	)	)	PUNCT
american_scientific_journal-2676	136	58	,	,	PUNCT
american_scientific_journal-2676	136	59	(	(	PUNCT
american_scientific_journal-2676	136	60	12	12	NUM
american_scientific_journal-2676	136	61	*	*	SYM
american_scientific_journal-2676	136	62	12	12	NUM
american_scientific_journal-2676	136	63	egefefegsker	egefefegsker	NOUN
american_scientific_journal-2676	136	64	c	c	NOUN
american_scientific_journal-2676	136	65	⊆∈η	⊆∈η	X
american_scientific_journal-2676	136	66	.	.	PUNCT
american_scientific_journal-2676	137	1	for	for	ADP
american_scientific_journal-2676	137	2	more	more	ADJ
american_scientific_journal-2676	137	3	details	detail	NOUN
american_scientific_journal-2676	137	4	you	you	PRON
american_scientific_journal-2676	137	5	can	can	AUX
american_scientific_journal-2676	137	6	see	see	VERB
american_scientific_journal-2676	137	7	in	in	ADP
american_scientific_journal-2676	137	8	[	[	X
american_scientific_journal-2676	137	9	12	12	NUM
american_scientific_journal-2676	137	10	]	]	PUNCT
american_scientific_journal-2676	137	11	.	.	PUNCT
american_scientific_journal-2676	138	1	definition	definition	NOUN
american_scientific_journal-2676	138	2	2.17	2.17	NUM
american_scientific_journal-2676	139	1	[	[	X
american_scientific_journal-2676	139	2	12	12	NUM
american_scientific_journal-2676	139	3	]	]	PUNCT
american_scientific_journal-2676	139	4	a	a	DET
american_scientific_journal-2676	139	5	soft	soft	ADJ
american_scientific_journal-2676	139	6	set	set	NOUN
american_scientific_journal-2676	139	7	)	)	PUNCT
american_scientific_journal-2676	139	8	,	,	PUNCT
american_scientific_journal-2676	139	9	(	(	PUNCT
american_scientific_journal-2676	139	10	eg	eg	NOUN
american_scientific_journal-2676	139	11	is	be	AUX
american_scientific_journal-2676	139	12	said	say	VERB
american_scientific_journal-2676	139	13	to	to	PART
american_scientific_journal-2676	139	14	be	be	AUX
american_scientific_journal-2676	139	15	a	a	DET
american_scientific_journal-2676	139	16	pairwise	pairwise	NOUN
american_scientific_journal-2676	139	17	∨	∨	NUM
american_scientific_journal-2676	139	18	-soft	-soft	NOUN
american_scientific_journal-2676	139	19	set	set	NOUN
american_scientific_journal-2676	140	1	[	[	X
american_scientific_journal-2676	140	2	briefly	briefly	NOUN
american_scientific_journal-2676	140	3	,	,	PUNCT
american_scientific_journal-2676	140	4	∨p	∨p	NOUN
american_scientific_journal-2676	140	5	-soft	-soft	NOUN
american_scientific_journal-2676	140	6	set	set	NOUN
american_scientific_journal-2676	140	7	]	]	PUNCT
american_scientific_journal-2676	140	8	in	in	ADP
american_scientific_journal-2676	140	9	a	a	DET
american_scientific_journal-2676	140	10	sbts	sbts	ADJ
american_scientific_journal-2676	140	11	)	)	PUNCT
american_scientific_journal-2676	140	12	,	,	PUNCT
american_scientific_journal-2676	140	13	,	,	PUNCT
american_scientific_journal-2676	140	14	,	,	PUNCT
american_scientific_journal-2676	140	15	(	(	PUNCT
american_scientific_journal-2676	140	16	21	21	NUM
american_scientific_journal-2676	140	17	ex	ex	NOUN
american_scientific_journal-2676	140	18	ηη	ηη	NOUN
american_scientific_journal-2676	140	19	if	if	SCONJ
american_scientific_journal-2676	140	20	)	)	PUNCT
american_scientific_journal-2676	140	21	,	,	PUNCT
american_scientific_journal-2676	140	22	(	(	PUNCT
american_scientific_journal-2676	140	23	=)	=)	INTJ
american_scientific_journal-2676	140	24	,	,	PUNCT
american_scientific_journal-2676	140	25	(	(	PUNCT
american_scientific_journal-2676	140	26	*	*	PUNCT
american_scientific_journal-2676	140	27	12	12	NUM
american_scientific_journal-2676	140	28	egegsker	egegsker	NOUN
american_scientific_journal-2676	140	29	.	.	PUNCT
american_scientific_journal-2676	141	1	we	we	PRON
american_scientific_journal-2676	141	2	denote	denote	VERB
american_scientific_journal-2676	141	3	the	the	DET
american_scientific_journal-2676	141	4	family	family	NOUN
american_scientific_journal-2676	141	5	of	of	ADP
american_scientific_journal-2676	141	6	all	all	DET
american_scientific_journal-2676	141	7	∨p	∨p	NOUN
american_scientific_journal-2676	141	8	-soft	-soft	NOUN
american_scientific_journal-2676	141	9	sets	set	NOUN
american_scientific_journal-2676	141	10	by	by	ADP
american_scientific_journal-2676	141	11	exsp	exsp	NOUN
american_scientific_journal-2676	141	12	)	)	PUNCT
american_scientific_journal-2676	141	13	,	,	PUNCT
american_scientific_journal-2676	141	14	,	,	PUNCT
american_scientific_journal-2676	141	15	(	(	PUNCT
american_scientific_journal-2676	141	16	21	21	NUM
american_scientific_journal-2676	141	17	ηη∨	ηη∨	NOUN
american_scientific_journal-2676	141	18	.clearly	.clearly	ADV
american_scientific_journal-2676	141	19	,	,	PUNCT
american_scientific_journal-2676	141	20	)	)	PUNCT
american_scientific_journal-2676	141	21	,	,	PUNCT
american_scientific_journal-2676	141	22	(	(	PUNCT
american_scientific_journal-2676	141	23	eg	eg	NOUN
american_scientific_journal-2676	141	24	is	be	AUX
american_scientific_journal-2676	141	25	a	a	DET
american_scientific_journal-2676	141	26	λp	λp	PRON
american_scientific_journal-2676	141	27	-soft	-soft	NOUN
american_scientific_journal-2676	141	28	set	set	VERB
american_scientific_journal-2676	141	29	if	if	SCONJ
american_scientific_journal-2676	141	30	and	and	CCONJ
american_scientific_journal-2676	141	31	only	only	ADV
american_scientific_journal-2676	141	32	if	if	SCONJ
american_scientific_journal-2676	141	33	ceg	ceg	NOUN
american_scientific_journal-2676	141	34	)	)	PUNCT
american_scientific_journal-2676	141	35	,	,	PUNCT
american_scientific_journal-2676	141	36	(	(	PUNCT
american_scientific_journal-2676	141	37	is	be	AUX
american_scientific_journal-2676	141	38	a	a	DET
american_scientific_journal-2676	141	39	∨p	∨p	NOUN
american_scientific_journal-2676	141	40	-soft	-soft	NOUN
american_scientific_journal-2676	141	41	set	set	NOUN
american_scientific_journal-2676	141	42	.	.	PUNCT
american_scientific_journal-2676	142	1	corollary	corollary	ADJ
american_scientific_journal-2676	142	2	2.1	2.1	NUM
american_scientific_journal-2676	142	3	[	[	X
american_scientific_journal-2676	142	4	12	12	NUM
american_scientific_journal-2676	142	5	]	]	PUNCT
american_scientific_journal-2676	142	6	let	let	NOUN
american_scientific_journal-2676	142	7	)	)	PUNCT
american_scientific_journal-2676	142	8	,	,	PUNCT
american_scientific_journal-2676	142	9	,	,	PUNCT
american_scientific_journal-2676	142	10	,	,	PUNCT
american_scientific_journal-2676	142	11	(	(	PUNCT
american_scientific_journal-2676	142	12	21	21	NUM
american_scientific_journal-2676	142	13	ex	ex	X
american_scientific_journal-2676	142	14	ηη	ηη	PROPN
american_scientific_journal-2676	142	15	be	be	AUX
american_scientific_journal-2676	142	16	a	a	DET
american_scientific_journal-2676	142	17	sbts	sbts	ADJ
american_scientific_journal-2676	142	18	.	.	PUNCT
american_scientific_journal-2676	143	1	the	the	DET
american_scientific_journal-2676	143	2	family	family	NOUN
american_scientific_journal-2676	143	3	of	of	ADP
american_scientific_journal-2676	143	4	all	all	DET
american_scientific_journal-2676	143	5	∨p	∨p	NOUN
american_scientific_journal-2676	143	6	-soft	-soft	NOUN
american_scientific_journal-2676	143	7	sets	set	NOUN
american_scientific_journal-2676	143	8	is	be	AUX
american_scientific_journal-2676	143	9	an	an	DET
american_scientific_journal-2676	143	10	alexandroff	alexandroff	ADJ
american_scientific_journal-2676	143	11	soft	soft	ADJ
american_scientific_journal-2676	143	12	topology	topology	NOUN
american_scientific_journal-2676	143	13	on	on	ADP
american_scientific_journal-2676	143	14	x	x	X
american_scientific_journal-2676	143	15	.	.	PUNCT
american_scientific_journal-2676	144	1	this	this	DET
american_scientific_journal-2676	144	2	soft	soft	ADJ
american_scientific_journal-2676	144	3	topology	topology	NOUN
american_scientific_journal-2676	144	4	we	we	PRON
american_scientific_journal-2676	144	5	denoted	denote	VERB
american_scientific_journal-2676	144	6	by	by	ADP
american_scientific_journal-2676	144	7	∨pη	∨pη	PROPN
american_scientific_journal-2676	144	8	.	.	PUNCT
american_scientific_journal-2676	144	9	theorem	theorem	VERB
american_scientific_journal-2676	144	10	2.7	2.7	NUM
american_scientific_journal-2676	144	11	[	[	X
american_scientific_journal-2676	144	12	12	12	NUM
american_scientific_journal-2676	144	13	]	]	PUNCT
american_scientific_journal-2676	144	14	for	for	ADP
american_scientific_journal-2676	144	15	any	any	DET
american_scientific_journal-2676	144	16	sbts	sbts	ADJ
american_scientific_journal-2676	144	17	)	)	PUNCT
american_scientific_journal-2676	144	18	,	,	PUNCT
american_scientific_journal-2676	144	19	,	,	PUNCT
american_scientific_journal-2676	144	20	,	,	PUNCT
american_scientific_journal-2676	144	21	(	(	PUNCT
american_scientific_journal-2676	144	22	21	21	NUM
american_scientific_journal-2676	144	23	ex	ex	NOUN
american_scientific_journal-2676	144	24	ηη	ηη	NOUN
american_scientific_journal-2676	144	25	,	,	PUNCT
american_scientific_journal-2676	144	26	we	we	PRON
american_scientific_journal-2676	144	27	have	have	VERB
american_scientific_journal-2676	144	28	c	c	NOUN
american_scientific_journal-2676	144	29	pp	pp	NOUN
american_scientific_journal-2676	144	30	∨λ	∨λ	VERB
american_scientific_journal-2676	144	31	ηη	ηη	ADV
american_scientific_journal-2676	144	32	=	=	PUNCT
american_scientific_journal-2676	144	33	.	.	PUNCT
american_scientific_journal-2676	145	1	definition	definition	NOUN
american_scientific_journal-2676	145	2	2.18	2.18	NUM
american_scientific_journal-2676	145	3	[	[	X
american_scientific_journal-2676	145	4	11	11	NUM
american_scientific_journal-2676	145	5	]	]	PUNCT
american_scientific_journal-2676	145	6	a	a	DET
american_scientific_journal-2676	145	7	soft	soft	ADJ
american_scientific_journal-2676	145	8	bitopological	bitopological	ADJ
american_scientific_journal-2676	145	9	space	space	NOUN
american_scientific_journal-2676	145	10	)	)	PUNCT
american_scientific_journal-2676	145	11	,	,	PUNCT
american_scientific_journal-2676	145	12	,	,	PUNCT
american_scientific_journal-2676	145	13	,	,	PUNCT
american_scientific_journal-2676	145	14	(	(	PUNCT
american_scientific_journal-2676	145	15	21	21	NUM
american_scientific_journal-2676	145	16	ex	ex	X
american_scientific_journal-2676	145	17	ηη	ηη	PROPN
american_scientific_journal-2676	145	18	is	be	AUX
american_scientific_journal-2676	145	19	said	say	VERB
american_scientific_journal-2676	145	20	to	to	PART
american_scientific_journal-2676	145	21	be	be	AUX
american_scientific_journal-2676	145	22	a	a	DET
american_scientific_journal-2676	145	23	pairwise	pairwise	NOUN
american_scientific_journal-2676	145	24	soft	soft	ADJ
american_scientific_journal-2676	145	25	𝑻𝑻𝟎𝟎∗	𝑻𝑻𝟎𝟎∗	NOUN
american_scientific_journal-2676	146	1	[	[	X
american_scientific_journal-2676	146	2	briefly	briefly	ADV
american_scientific_journal-2676	146	3	,	,	PUNCT
american_scientific_journal-2676	146	4	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	NOUN
american_scientific_journal-2676	146	5	]	]	X
american_scientific_journal-2676	146	6	if	if	SCONJ
american_scientific_journal-2676	146	7	for	for	ADP
american_scientific_journal-2676	146	8	each	each	DET
american_scientific_journal-2676	146	9	exyx	exyx	ADJ
american_scientific_journal-2676	146	10	)	)	PUNCT
american_scientific_journal-2676	146	11	(	(	PUNCT
american_scientific_journal-2676	146	12	,	,	PUNCT
american_scientific_journal-2676	146	13	ξβα	ξβα	VERB
american_scientific_journal-2676	146	14	∈	∈	NOUN
american_scientific_journal-2676	146	15	with	with	ADP
american_scientific_journal-2676	146	16	βα	βα	PROPN
american_scientific_journal-2676	146	17	yx	yx	ADP
american_scientific_journal-2676	146	18	≠	≠	PROPN
american_scientific_journal-2676	146	19	,	,	PUNCT
american_scientific_journal-2676	146	20	there	there	PRON
american_scientific_journal-2676	146	21	exists	exist	VERB
american_scientific_journal-2676	146	22	12	12	NUM
american_scientific_journal-2676	146	23	)	)	PUNCT
american_scientific_journal-2676	146	24	,	,	PUNCT
american_scientific_journal-2676	146	25	(	(	PUNCT
american_scientific_journal-2676	146	26	η∈eg	η∈eg	VERB
american_scientific_journal-2676	146	27	such	such	ADJ
american_scientific_journal-2676	146	28	that	that	PRON
american_scientific_journal-2676	146	29	)	)	PUNCT
american_scientific_journal-2676	146	30	,	,	PUNCT
american_scientific_journal-2676	146	31	(	(	PUNCT
american_scientific_journal-2676	146	32	~	~	PUNCT
american_scientific_journal-2676	146	33	egx	egx	X
american_scientific_journal-2676	146	34	∈α	∈α	PROPN
american_scientific_journal-2676	146	35	,	,	PUNCT
american_scientific_journal-2676	146	36	)	)	PUNCT
american_scientific_journal-2676	146	37	,	,	PUNCT
american_scientific_journal-2676	146	38	(	(	PUNCT
american_scientific_journal-2676	146	39	~	~	PUNCT
american_scientific_journal-2676	146	40	egy	egy	PROPN
american_scientific_journal-2676	146	41	∈/β	∈/β	PROPN
american_scientific_journal-2676	146	42	or	or	CCONJ
american_scientific_journal-2676	146	43	)	)	PUNCT
american_scientific_journal-2676	146	44	,	,	PUNCT
american_scientific_journal-2676	146	45	(	(	PUNCT
american_scientific_journal-2676	146	46	~	~	PUNCT
american_scientific_journal-2676	146	47	egy	egy	X
american_scientific_journal-2676	146	48	∈β	∈β	PROPN
american_scientific_journal-2676	146	49	,	,	PUNCT
american_scientific_journal-2676	146	50	)	)	PUNCT
american_scientific_journal-2676	146	51	,	,	PUNCT
american_scientific_journal-2676	146	52	(	(	PUNCT
american_scientific_journal-2676	146	53	~	~	PUNCT
american_scientific_journal-2676	146	54	egx	egx	VERB
american_scientific_journal-2676	146	55	∈/α	∈/α	PROPN
american_scientific_journal-2676	146	56	.	.	PUNCT
american_scientific_journal-2676	147	1	theorem	theorem	VERB
american_scientific_journal-2676	147	2	2.8	2.8	NUM
american_scientific_journal-2676	147	3	[	[	SYM
american_scientific_journal-2676	147	4	11	11	NUM
american_scientific_journal-2676	147	5	]	]	PUNCT
american_scientific_journal-2676	147	6	let	let	NOUN
american_scientific_journal-2676	147	7	)	)	PUNCT
american_scientific_journal-2676	147	8	,	,	PUNCT
american_scientific_journal-2676	147	9	,	,	PUNCT
american_scientific_journal-2676	147	10	,	,	PUNCT
american_scientific_journal-2676	147	11	(	(	PUNCT
american_scientific_journal-2676	147	12	21	21	NUM
american_scientific_journal-2676	147	13	ex	ex	X
american_scientific_journal-2676	147	14	ηη	ηη	PROPN
american_scientific_journal-2676	147	15	be	be	AUX
american_scientific_journal-2676	147	16	a	a	DET
american_scientific_journal-2676	147	17	sbts	sbts	ADJ
american_scientific_journal-2676	147	18	.	.	PUNCT
american_scientific_journal-2676	148	1	then	then	ADV
american_scientific_journal-2676	148	2	)	)	PUNCT
american_scientific_journal-2676	148	3	,	,	PUNCT
american_scientific_journal-2676	148	4	,	,	PUNCT
american_scientific_journal-2676	148	5	,	,	PUNCT
american_scientific_journal-2676	148	6	(	(	PUNCT
american_scientific_journal-2676	148	7	21	21	NUM
american_scientific_journal-2676	148	8	ex	ex	X
american_scientific_journal-2676	148	9	ηη	ηη	PROPN
american_scientific_journal-2676	148	10	is	be	AUX
american_scientific_journal-2676	148	11	a	a	DET
american_scientific_journal-2676	148	12	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	NOUN
american_scientific_journal-2676	148	13	if	if	SCONJ
american_scientific_journal-2676	149	1	and	and	CCONJ
american_scientific_journal-2676	149	2	only	only	ADV
american_scientific_journal-2676	149	3	if	if	SCONJ
american_scientific_journal-2676	149	4	every	every	DET
american_scientific_journal-2676	149	5	soft	soft	ADJ
american_scientific_journal-2676	149	6	point	point	NOUN
american_scientific_journal-2676	149	7	ee	ee	ADP
american_scientific_journal-2676	149	8	xx	xx	NUM
american_scientific_journal-2676	149	9	)	)	PUNCT
american_scientific_journal-2676	150	1	(	(	PUNCT
american_scientific_journal-2676	150	2	ξ∈	ξ∈	NOUN
american_scientific_journal-2676	150	3	is	be	AUX
american_scientific_journal-2676	150	4	a	a	DET
american_scientific_journal-2676	150	5	λp	λp	ADV
american_scientific_journal-2676	150	6	-closed	-close	VERB
american_scientific_journal-2676	150	7	soft	soft	ADJ
american_scientific_journal-2676	150	8	set	set	NOUN
american_scientific_journal-2676	150	9	.	.	PUNCT
american_scientific_journal-2676	151	1	lemma	lemma	PROPN
american_scientific_journal-2676	151	2	2.1	2.1	NUM
american_scientific_journal-2676	152	1	[	[	SYM
american_scientific_journal-2676	152	2	11	11	NUM
american_scientific_journal-2676	152	3	]	]	PUNCT
american_scientific_journal-2676	152	4	let	let	NOUN
american_scientific_journal-2676	152	5	)	)	PUNCT
american_scientific_journal-2676	152	6	,	,	PUNCT
american_scientific_journal-2676	152	7	,	,	PUNCT
american_scientific_journal-2676	152	8	,	,	PUNCT
american_scientific_journal-2676	152	9	(	(	PUNCT
american_scientific_journal-2676	152	10	21	21	NUM
american_scientific_journal-2676	152	11	ex	ex	X
american_scientific_journal-2676	152	12	ηη	ηη	PROPN
american_scientific_journal-2676	152	13	be	be	AUX
american_scientific_journal-2676	152	14	a	a	DET
american_scientific_journal-2676	152	15	sbts	sbts	ADJ
american_scientific_journal-2676	152	16	.	.	PUNCT
american_scientific_journal-2676	153	1	then	then	ADV
american_scientific_journal-2676	153	2	)	)	PUNCT
american_scientific_journal-2676	153	3	,	,	PUNCT
american_scientific_journal-2676	153	4	,	,	PUNCT
american_scientific_journal-2676	153	5	,	,	PUNCT
american_scientific_journal-2676	153	6	(	(	PUNCT
american_scientific_journal-2676	153	7	21	21	NUM
american_scientific_journal-2676	153	8	ex	ex	X
american_scientific_journal-2676	153	9	ηη	ηη	PROPN
american_scientific_journal-2676	153	10	is	be	AUX
american_scientific_journal-2676	153	11	a	a	DET
american_scientific_journal-2676	153	12	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	𝑷𝑷𝑷𝑷𝑻𝑻𝟎𝟎∗	NOUN
american_scientific_journal-2676	153	13	if	if	SCONJ
american_scientific_journal-2676	154	1	and	and	CCONJ
american_scientific_journal-2676	154	2	only	only	ADV
american_scientific_journal-2676	154	3	if	if	SCONJ
american_scientific_journal-2676	154	4	for	for	ADP
american_scientific_journal-2676	154	5	all	all	DET
american_scientific_journal-2676	154	6	exyx	exyx	ADJ
american_scientific_journal-2676	154	7	)	)	PUNCT
american_scientific_journal-2676	154	8	(	(	PUNCT
american_scientific_journal-2676	154	9	,	,	PUNCT
american_scientific_journal-2676	154	10	ξβα	ξβα	NOUN
american_scientific_journal-2676	154	11	∈	∈	PROPN
american_scientific_journal-2676	154	12	,	,	PUNCT
american_scientific_journal-2676	154	13	βα	βα	X
american_scientific_journal-2676	154	14	yx	yx	ADP
american_scientific_journal-2676	154	15	≠	≠	PROPN
american_scientific_journal-2676	154	16	there	there	PRON
american_scientific_journal-2676	154	17	exists	exist	VERB
american_scientific_journal-2676	154	18	ceg	ceg	NOUN
american_scientific_journal-2676	154	19	1212	1212	NUM
american_scientific_journal-2676	154	20	)	)	PUNCT
american_scientific_journal-2676	154	21	,	,	PUNCT
american_scientific_journal-2676	154	22	(	(	PUNCT
american_scientific_journal-2676	154	23	ηη	ηη	PRON
american_scientific_journal-2676	154	24	∪∈	∪∈	VERB
american_scientific_journal-2676	154	25	such	such	ADJ
american_scientific_journal-2676	154	26	that	that	PRON
american_scientific_journal-2676	154	27	)	)	PUNCT
american_scientific_journal-2676	154	28	,	,	PUNCT
american_scientific_journal-2676	154	29	(	(	PUNCT
american_scientific_journal-2676	154	30	~	~	PUNCT
american_scientific_journal-2676	154	31	egx	egx	X
american_scientific_journal-2676	154	32	∈α	∈α	PROPN
american_scientific_journal-2676	154	33	and	and	CCONJ
american_scientific_journal-2676	154	34	)	)	PUNCT
american_scientific_journal-2676	154	35	,	,	PUNCT
american_scientific_journal-2676	154	36	(	(	PUNCT
american_scientific_journal-2676	154	37	~	~	PUNCT
american_scientific_journal-2676	154	38	egy	egy	PROPN
american_scientific_journal-2676	154	39	∈/β	∈/β	PROPN
american_scientific_journal-2676	154	40	.	.	PUNCT
american_scientific_journal-2676	155	1	definition	definition	NOUN
american_scientific_journal-2676	155	2	2.19	2.19	NUM
american_scientific_journal-2676	155	3	[	[	X
american_scientific_journal-2676	155	4	9	9	NUM
american_scientific_journal-2676	155	5	]	]	PUNCT
american_scientific_journal-2676	155	6	let	let	NOUN
american_scientific_journal-2676	155	7	)	)	PUNCT
american_scientific_journal-2676	155	8	,	,	PUNCT
american_scientific_journal-2676	155	9	,	,	PUNCT
american_scientific_journal-2676	155	10	,	,	PUNCT
american_scientific_journal-2676	155	11	(	(	PUNCT
american_scientific_journal-2676	155	12	21	21	NUM
american_scientific_journal-2676	155	13	ex	ex	X
american_scientific_journal-2676	155	14	ηη	ηη	PROPN
american_scientific_journal-2676	155	15	be	be	AUX
american_scientific_journal-2676	155	16	a	a	DET
american_scientific_journal-2676	155	17	sbts	sbts	ADJ
american_scientific_journal-2676	155	18	and	and	CCONJ
american_scientific_journal-2676	155	19	let	let	VERB
american_scientific_journal-2676	155	20	exsseg	exsseg	ADJ
american_scientific_journal-2676	155	21	)	)	PUNCT
american_scientific_journal-2676	155	22	(	(	PUNCT
american_scientific_journal-2676	155	23	)	)	PUNCT
american_scientific_journal-2676	155	24	,	,	PUNCT
american_scientific_journal-2676	155	25	(	(	PUNCT
american_scientific_journal-2676	155	26	∈	∈	PROPN
american_scientific_journal-2676	155	27	.	.	PUNCT
american_scientific_journal-2676	156	1	a	a	DET
american_scientific_journal-2676	156	2	soft	soft	ADJ
american_scientific_journal-2676	156	3	set	set	NOUN
american_scientific_journal-2676	156	4	)	)	PUNCT
american_scientific_journal-2676	156	5	,	,	PUNCT
american_scientific_journal-2676	156	6	(	(	PUNCT
american_scientific_journal-2676	156	7	eg	eg	NOUN
american_scientific_journal-2676	156	8	is	be	AUX
american_scientific_journal-2676	156	9	said	say	VERB
american_scientific_journal-2676	156	10	to	to	PART
american_scientific_journal-2676	156	11	be	be	AUX
american_scientific_journal-2676	156	12	a	a	DET
american_scientific_journal-2676	156	13	generalized	generalized	ADJ
american_scientific_journal-2676	156	14	pairwise	pairwise	NOUN
american_scientific_journal-2676	156	15	closed	close	VERB
american_scientific_journal-2676	156	16	soft	soft	ADJ
american_scientific_journal-2676	156	17	set	set	NOUN
american_scientific_journal-2676	157	1	[	[	X
american_scientific_journal-2676	157	2	briefly	briefly	ADV
american_scientific_journal-2676	157	3	,	,	PUNCT
american_scientific_journal-2676	157	4	gp	gp	NOUN
american_scientific_journal-2676	157	5	-closed	-close	VERB
american_scientific_journal-2676	157	6	soft	soft	ADJ
american_scientific_journal-2676	157	7	set	set	NOUN
american_scientific_journal-2676	157	8	]	]	PUNCT
american_scientific_journal-2676	157	9	if	if	SCONJ
american_scientific_journal-2676	157	10	)	)	PUNCT
american_scientific_journal-2676	157	11	,	,	PUNCT
american_scientific_journal-2676	157	12	(	(	PUNCT
american_scientific_journal-2676	157	13	~),(12	~),(12	ADP
american_scientific_journal-2676	157	14	ehegscl	ehegscl	NOUN
american_scientific_journal-2676	157	15	⊆	⊆	NUM
american_scientific_journal-2676	157	16	whenever	whenever	SCONJ
american_scientific_journal-2676	157	17	)	)	PUNCT
american_scientific_journal-2676	157	18	,	,	PUNCT
american_scientific_journal-2676	157	19	(	(	PUNCT
american_scientific_journal-2676	157	20	~	~	NOUN
american_scientific_journal-2676	157	21	)	)	PUNCT
american_scientific_journal-2676	157	22	,	,	PUNCT
american_scientific_journal-2676	157	23	(	(	PUNCT
american_scientific_journal-2676	157	24	eheg	eheg	VERB
american_scientific_journal-2676	157	25	⊆	⊆	NUM
american_scientific_journal-2676	157	26	and	and	CCONJ
american_scientific_journal-2676	157	27	)	)	PUNCT
american_scientific_journal-2676	157	28	,	,	PUNCT
american_scientific_journal-2676	157	29	(	(	PUNCT
american_scientific_journal-2676	157	30	eh	eh	INTJ
american_scientific_journal-2676	157	31	is	be	AUX
american_scientific_journal-2676	157	32	a	a	DET
american_scientific_journal-2676	157	33	p	p	NOUN
american_scientific_journal-2676	157	34	-open	-open	ADJ
american_scientific_journal-2676	157	35	soft	soft	ADJ
american_scientific_journal-2676	157	36	set	set	NOUN
american_scientific_journal-2676	157	37	.	.	PUNCT
american_scientific_journal-2676	158	1	definition	definition	NOUN
american_scientific_journal-2676	158	2	2.20	2.20	NUM
american_scientific_journal-2676	159	1	[	[	X
american_scientific_journal-2676	159	2	9	9	NUM
american_scientific_journal-2676	159	3	]	]	PUNCT
american_scientific_journal-2676	159	4	a	a	DET
american_scientific_journal-2676	159	5	soft	soft	ADJ
american_scientific_journal-2676	159	6	bitopological	bitopological	ADJ
american_scientific_journal-2676	159	7	space	space	NOUN
american_scientific_journal-2676	159	8	)	)	PUNCT
american_scientific_journal-2676	159	9	,	,	PUNCT
american_scientific_journal-2676	159	10	,	,	PUNCT
american_scientific_journal-2676	159	11	,	,	PUNCT
american_scientific_journal-2676	159	12	(	(	PUNCT
american_scientific_journal-2676	159	13	21	21	NUM
american_scientific_journal-2676	159	14	ex	ex	NOUN
american_scientific_journal-2676	159	15	ηη	ηη	PROPN
american_scientific_journal-2676	159	16	is	be	AUX
american_scientific_journal-2676	159	17	called	call	VERB
american_scientific_journal-2676	159	18	a	a	DET
american_scientific_journal-2676	159	19	pairwise	pairwise	NOUN
american_scientific_journal-2676	159	20	soft	soft	ADJ
american_scientific_journal-2676	159	21	𝑇𝑇1	𝑇𝑇1	PROPN
american_scientific_journal-2676	159	22	2	2	NUM
american_scientific_journal-2676	159	23	�	�	PROPN
american_scientific_journal-2676	159	24	∗	∗	NOUN
american_scientific_journal-2676	160	1	[	[	X
american_scientific_journal-2676	160	2	briefly	briefly	NOUN
american_scientific_journal-2676	160	3	,	,	PUNCT
american_scientific_journal-2676	160	4	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	160	5	2	2	NUM
american_scientific_journal-2676	160	6	�	�	PROPN
american_scientific_journal-2676	160	7	∗	∗	NOUN
american_scientific_journal-2676	160	8	]	]	PUNCT
american_scientific_journal-2676	160	9	if	if	SCONJ
american_scientific_journal-2676	160	10	every	every	DET
american_scientific_journal-2676	160	11	gp	gp	NOUN
american_scientific_journal-2676	160	12	-closed	-close	VERB
american_scientific_journal-2676	160	13	soft	soft	ADJ
american_scientific_journal-2676	160	14	set	set	NOUN
american_scientific_journal-2676	160	15	is	be	AUX
american_scientific_journal-2676	160	16	a	a	DET
american_scientific_journal-2676	160	17	p	p	NOUN
american_scientific_journal-2676	160	18	-closed	-close	VERB
american_scientific_journal-2676	160	19	soft	soft	ADJ
american_scientific_journal-2676	160	20	set	set	NOUN
american_scientific_journal-2676	160	21	.	.	PUNCT
american_scientific_journal-2676	161	1	american	american	PROPN
american_scientific_journal-2676	161	2	scientific	scientific	ADJ
american_scientific_journal-2676	161	3	research	research	PROPN
american_scientific_journal-2676	161	4	journal	journal	NOUN
american_scientific_journal-2676	161	5	for	for	ADP
american_scientific_journal-2676	161	6	engineering	engineering	NOUN
american_scientific_journal-2676	161	7	,	,	PUNCT
american_scientific_journal-2676	161	8	technology	technology	NOUN
american_scientific_journal-2676	161	9	,	,	PUNCT
american_scientific_journal-2676	161	10	and	and	CCONJ
american_scientific_journal-2676	161	11	sciences	science	NOUN
american_scientific_journal-2676	161	12	(	(	PUNCT
american_scientific_journal-2676	161	13	asrjets	asrjet	NOUN
american_scientific_journal-2676	161	14	)	)	PUNCT
american_scientific_journal-2676	161	15	(	(	PUNCT
american_scientific_journal-2676	161	16	2017	2017	NUM
american_scientific_journal-2676	161	17	)	)	PUNCT
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american_scientific_journal-2676	161	20	,	,	PUNCT
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american_scientific_journal-2676	161	22	1	1	NUM
american_scientific_journal-2676	161	23	,	,	PUNCT
american_scientific_journal-2676	161	24	pp	pp	ADV
american_scientific_journal-2676	161	25	225	225	NUM
american_scientific_journal-2676	161	26	-	-	SYM
american_scientific_journal-2676	161	27	247	247	NUM
american_scientific_journal-2676	161	28	232	232	NUM
american_scientific_journal-2676	161	29	theorem	theorem	VERB
american_scientific_journal-2676	161	30	2.9	2.9	NUM
american_scientific_journal-2676	162	1	[	[	SYM
american_scientific_journal-2676	162	2	9	9	NUM
american_scientific_journal-2676	162	3	]	]	X
american_scientific_journal-2676	162	4	let	let	NOUN
american_scientific_journal-2676	162	5	)	)	PUNCT
american_scientific_journal-2676	162	6	,	,	PUNCT
american_scientific_journal-2676	162	7	,	,	PUNCT
american_scientific_journal-2676	162	8	,	,	PUNCT
american_scientific_journal-2676	162	9	(	(	PUNCT
american_scientific_journal-2676	162	10	21	21	NUM
american_scientific_journal-2676	162	11	ex	ex	X
american_scientific_journal-2676	162	12	ηη	ηη	PROPN
american_scientific_journal-2676	162	13	be	be	AUX
american_scientific_journal-2676	162	14	a	a	DET
american_scientific_journal-2676	162	15	soft	soft	ADJ
american_scientific_journal-2676	162	16	bitopological	bitopological	ADJ
american_scientific_journal-2676	162	17	space	space	NOUN
american_scientific_journal-2676	162	18	.	.	PUNCT
american_scientific_journal-2676	163	1	then	then	ADV
american_scientific_journal-2676	163	2	,	,	PUNCT
american_scientific_journal-2676	163	3	)	)	PUNCT
american_scientific_journal-2676	163	4	,	,	PUNCT
american_scientific_journal-2676	163	5	,	,	PUNCT
american_scientific_journal-2676	163	6	,	,	PUNCT
american_scientific_journal-2676	163	7	(	(	PUNCT
american_scientific_journal-2676	163	8	21	21	NUM
american_scientific_journal-2676	163	9	ex	ex	X
american_scientific_journal-2676	163	10	ηη	ηη	PROPN
american_scientific_journal-2676	163	11	is	be	AUX
american_scientific_journal-2676	163	12	a	a	DET
american_scientific_journal-2676	163	13	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	163	14	2	2	NUM
american_scientific_journal-2676	163	15	�	�	PROPN
american_scientific_journal-2676	163	16	∗	∗	NOUN
american_scientific_journal-2676	163	17	if	if	SCONJ
american_scientific_journal-2676	163	18	and	and	CCONJ
american_scientific_journal-2676	163	19	only	only	ADV
american_scientific_journal-2676	163	20	if	if	SCONJ
american_scientific_journal-2676	163	21	every	every	DET
american_scientific_journal-2676	163	22	soft	soft	ADJ
american_scientific_journal-2676	163	23	point	point	NOUN
american_scientific_journal-2676	163	24	either	either	CCONJ
american_scientific_journal-2676	163	25	p	p	X
american_scientific_journal-2676	163	26	-open	-open	ADJ
american_scientific_journal-2676	163	27	soft	soft	ADJ
american_scientific_journal-2676	163	28	set	set	NOUN
american_scientific_journal-2676	163	29	or	or	CCONJ
american_scientific_journal-2676	163	30	p	p	NOUN
american_scientific_journal-2676	163	31	-closed	-close	VERB
american_scientific_journal-2676	163	32	soft	soft	ADJ
american_scientific_journal-2676	163	33	set	set	NOUN
american_scientific_journal-2676	163	34	.	.	PUNCT
american_scientific_journal-2676	164	1	theorem	theorem	VERB
american_scientific_journal-2676	164	2	2.10	2.10	NUM
american_scientific_journal-2676	164	3	[	[	NOUN
american_scientific_journal-2676	164	4	9	9	NUM
american_scientific_journal-2676	164	5	]	]	PUNCT
american_scientific_journal-2676	164	6	in	in	ADP
american_scientific_journal-2676	164	7	any	any	DET
american_scientific_journal-2676	164	8	sbts	sbts	ADJ
american_scientific_journal-2676	164	9	)	)	PUNCT
american_scientific_journal-2676	164	10	,	,	PUNCT
american_scientific_journal-2676	164	11	,	,	PUNCT
american_scientific_journal-2676	164	12	,	,	PUNCT
american_scientific_journal-2676	164	13	(	(	PUNCT
american_scientific_journal-2676	164	14	21	21	NUM
american_scientific_journal-2676	164	15	ex	ex	NOUN
american_scientific_journal-2676	164	16	ηη	ηη	NOUN
american_scientific_journal-2676	164	17	,	,	PUNCT
american_scientific_journal-2676	164	18	every	every	DET
american_scientific_journal-2676	164	19	soft	soft	ADJ
american_scientific_journal-2676	164	20	point	point	NOUN
american_scientific_journal-2676	164	21	either	either	CCONJ
american_scientific_journal-2676	164	22	p	p	X
american_scientific_journal-2676	164	23	-closed	-close	VERB
american_scientific_journal-2676	164	24	soft	soft	ADJ
american_scientific_journal-2676	164	25	set	set	NOUN
american_scientific_journal-2676	164	26	or	or	CCONJ
american_scientific_journal-2676	164	27	its	its	PRON
american_scientific_journal-2676	164	28	complement	complement	NOUN
american_scientific_journal-2676	164	29	is	be	AUX
american_scientific_journal-2676	164	30	a	a	DET
american_scientific_journal-2676	164	31	gp	gp	NOUN
american_scientific_journal-2676	164	32	-closed	-close	VERB
american_scientific_journal-2676	164	33	soft	soft	ADJ
american_scientific_journal-2676	164	34	set	set	NOUN
american_scientific_journal-2676	164	35	.	.	PUNCT
american_scientific_journal-2676	165	1	3	3	X
american_scientific_journal-2676	165	2	.	.	X
american_scientific_journal-2676	165	3	more	more	ADJ
american_scientific_journal-2676	165	4	on	on	ADP
american_scientific_journal-2676	165	5	𝒑𝒑𝝀𝝀	𝒑𝒑𝝀𝝀	ADJ
american_scientific_journal-2676	165	6	−closed	−close	VERB
american_scientific_journal-2676	165	7	soft	soft	ADJ
american_scientific_journal-2676	165	8	sets	set	NOUN
american_scientific_journal-2676	165	9	in	in	ADP
american_scientific_journal-2676	165	10	this	this	DET
american_scientific_journal-2676	165	11	section	section	NOUN
american_scientific_journal-2676	165	12	,	,	PUNCT
american_scientific_journal-2676	165	13	we	we	PRON
american_scientific_journal-2676	165	14	give	give	VERB
american_scientific_journal-2676	165	15	some	some	DET
american_scientific_journal-2676	165	16	additional	additional	ADJ
american_scientific_journal-2676	165	17	properties	property	NOUN
american_scientific_journal-2676	165	18	of	of	ADP
american_scientific_journal-2676	165	19	λp	λp	PRON
american_scientific_journal-2676	165	20	-closed	-close	VERB
american_scientific_journal-2676	165	21	soft	soft	ADJ
american_scientific_journal-2676	165	22	sets	set	NOUN
american_scientific_journal-2676	165	23	and	and	CCONJ
american_scientific_journal-2676	165	24	introduce	introduce	VERB
american_scientific_journal-2676	165	25	and	and	CCONJ
american_scientific_journal-2676	165	26	study	study	VERB
american_scientific_journal-2676	165	27	a	a	DET
american_scientific_journal-2676	165	28	related	relate	VERB
american_scientific_journal-2676	165	29	new	new	ADJ
american_scientific_journal-2676	165	30	pairwise	pairwise	NOUN
american_scientific_journal-2676	165	31	soft	soft	ADJ
american_scientific_journal-2676	165	32	separation	separation	NOUN
american_scientific_journal-2676	165	33	axiom	axiom	NOUN
american_scientific_journal-2676	165	34	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	165	35	4	4	NUM
american_scientific_journal-2676	165	36	�	�	PROPN
american_scientific_journal-2676	165	37	∗	∗	NOUN
american_scientific_journal-2676	165	38	.	.	PUNCT
american_scientific_journal-2676	166	1	theorem	theorem	VERB
american_scientific_journal-2676	166	2	3.1	3.1	NUM
american_scientific_journal-2676	166	3	let	let	NOUN
american_scientific_journal-2676	166	4	)	)	PUNCT
american_scientific_journal-2676	166	5	,	,	PUNCT
american_scientific_journal-2676	166	6	,	,	PUNCT
american_scientific_journal-2676	166	7	,	,	PUNCT
american_scientific_journal-2676	166	8	(	(	PUNCT
american_scientific_journal-2676	166	9	21	21	NUM
american_scientific_journal-2676	166	10	ex	ex	X
american_scientific_journal-2676	166	11	ηη	ηη	PROPN
american_scientific_journal-2676	166	12	be	be	AUX
american_scientific_journal-2676	166	13	a	a	DET
american_scientific_journal-2676	166	14	sbts	sbts	ADJ
american_scientific_journal-2676	166	15	and	and	CCONJ
american_scientific_journal-2676	166	16	exsseg	exsseg	ADJ
american_scientific_journal-2676	166	17	)	)	PUNCT
american_scientific_journal-2676	166	18	(	(	PUNCT
american_scientific_journal-2676	166	19	)	)	PUNCT
american_scientific_journal-2676	166	20	,	,	PUNCT
american_scientific_journal-2676	166	21	(	(	PUNCT
american_scientific_journal-2676	166	22	∈	∈	PROPN
american_scientific_journal-2676	166	23	.	.	PUNCT
american_scientific_journal-2676	167	1	the	the	DET
american_scientific_journal-2676	167	2	arbitrary	arbitrary	ADJ
american_scientific_journal-2676	167	3	intersection	intersection	NOUN
american_scientific_journal-2676	167	4	of	of	ADP
american_scientific_journal-2676	167	5	λp	λp	ADV
american_scientific_journal-2676	167	6	-closed	-close	VERB
american_scientific_journal-2676	167	7	soft	soft	ADJ
american_scientific_journal-2676	167	8	sets	set	NOUN
american_scientific_journal-2676	167	9	is	be	AUX
american_scientific_journal-2676	167	10	a	a	DET
american_scientific_journal-2676	167	11	λp	λp	ADV
american_scientific_journal-2676	167	12	-closed	-close	VERB
american_scientific_journal-2676	167	13	soft	soft	ADJ
american_scientific_journal-2676	167	14	set	set	NOUN
american_scientific_journal-2676	167	15	.	.	PUNCT
american_scientific_journal-2676	168	1	proof	proof	NOUN
american_scientific_journal-2676	168	2	.	.	PUNCT
american_scientific_journal-2676	169	1	let	let	VERB
american_scientific_journal-2676	169	2	ei	ei	NOUN
american_scientific_journal-2676	169	3	xcspieg	xcspieg	NOUN
american_scientific_journal-2676	169	4	)	)	PUNCT
american_scientific_journal-2676	169	5	,	,	PUNCT
american_scientific_journal-2676	169	6	,	,	PUNCT
american_scientific_journal-2676	169	7	(	(	PUNCT
american_scientific_journal-2676	169	8	}	}	PUNCT
american_scientific_journal-2676	169	9	:)	:)	NOUN
american_scientific_journal-2676	169	10	,	,	PUNCT
american_scientific_journal-2676	169	11	{	{	PUNCT
american_scientific_journal-2676	169	12	(	(	PUNCT
american_scientific_journal-2676	169	13	21	21	NUM
american_scientific_journal-2676	169	14	ηηλ⊆∆∈	ηηλ⊆∆∈	NOUN
american_scientific_journal-2676	169	15	.	.	PUNCT
american_scientific_journal-2676	170	1	then	then	ADV
american_scientific_journal-2676	170	2	,	,	PUNCT
american_scientific_journal-2676	170	3	∆∈∀∈	∆∈∀∈	ADJ
american_scientific_journal-2676	170	4	ixcspeg	ixcspeg	NOUN
american_scientific_journal-2676	170	5	ei	ei	PROPN
american_scientific_journal-2676	170	6	)	)	PUNCT
american_scientific_journal-2676	170	7	,	,	PUNCT
american_scientific_journal-2676	170	8	,	,	PUNCT
american_scientific_journal-2676	170	9	(	(	PUNCT
american_scientific_journal-2676	170	10	)	)	PUNCT
american_scientific_journal-2676	170	11	,	,	PUNCT
american_scientific_journal-2676	170	12	(	(	PUNCT
american_scientific_journal-2676	170	13	21	21	NUM
american_scientific_journal-2676	170	14	ηηλ	ηηλ	NOUN
american_scientific_journal-2676	170	15	.	.	PUNCT
american_scientific_journal-2676	171	1	thus	thus	ADV
american_scientific_journal-2676	171	2	,	,	PUNCT
american_scientific_journal-2676	171	3	for	for	ADP
american_scientific_journal-2676	171	4	all	all	DET
american_scientific_journal-2676	171	5	∆∈i	∆∈i	NOUN
american_scientific_journal-2676	171	6	there	there	PRON
american_scientific_journal-2676	171	7	exist	exist	VERB
american_scientific_journal-2676	171	8	c	c	NOUN
american_scientific_journal-2676	171	9	i	i	PRON
american_scientific_journal-2676	171	10	ef	ef	VERB
american_scientific_journal-2676	171	11	12	12	NUM
american_scientific_journal-2676	171	12	)	)	PUNCT
american_scientific_journal-2676	171	13	,	,	PUNCT
american_scientific_journal-2676	171	14	(	(	PUNCT
american_scientific_journal-2676	171	15	η∈	η∈	PROPN
american_scientific_journal-2676	171	16	and	and	CCONJ
american_scientific_journal-2676	171	17	λ∈	λ∈	PROPN
american_scientific_journal-2676	171	18	pi	pi	NOUN
american_scientific_journal-2676	171	19	eh	eh	INTJ
american_scientific_journal-2676	171	20	η	η	PROPN
american_scientific_journal-2676	171	21	)	)	PUNCT
american_scientific_journal-2676	171	22	,	,	PUNCT
american_scientific_journal-2676	171	23	(	(	PUNCT
american_scientific_journal-2676	171	24	such	such	ADJ
american_scientific_journal-2676	171	25	that	that	PRON
american_scientific_journal-2676	171	26	)	)	PUNCT
american_scientific_journal-2676	171	27	,	,	PUNCT
american_scientific_journal-2676	171	28	(	(	PUNCT
american_scientific_journal-2676	171	29	~),(=	~),(=	NUM
american_scientific_journal-2676	171	30	)	)	PUNCT
american_scientific_journal-2676	171	31	,	,	PUNCT
american_scientific_journal-2676	171	32	(	(	PUNCT
american_scientific_journal-2676	171	33	ehefeg	ehefeg	PROPN
american_scientific_journal-2676	171	34	iii	iii	PROPN
american_scientific_journal-2676	171	35	∩	∩	PROPN
american_scientific_journal-2676	171	36	⇒	⇒	NOUN
american_scientific_journal-2676	171	37	=)	=)	PROPN
american_scientific_journal-2676	171	38	,	,	PUNCT
american_scientific_journal-2676	171	39	(	(	PUNCT
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american_scientific_journal-2676	171	41	∆∈	∆∈	NOUN
american_scientific_journal-2676	171	42	)	)	PUNCT
american_scientific_journal-2676	171	43	]	]	PUNCT
american_scientific_journal-2676	171	44	,	,	PUNCT
american_scientific_journal-2676	171	45	(	(	PUNCT
american_scientific_journal-2676	171	46	~	~	NOUN
american_scientific_journal-2676	171	47	)	)	PUNCT
american_scientific_journal-2676	171	48	,	,	PUNCT
american_scientific_journal-2676	172	1	[	[	X
american_scientific_journal-2676	172	2	(	(	PUNCT
american_scientific_journal-2676	172	3	ehef	ehef	PROPN
american_scientific_journal-2676	172	4	iii	iii	NUM
american_scientific_journal-2676	172	5	∩	∩	ADJ
american_scientific_journal-2676	172	6	∆∈	∆∈	NOUN
american_scientific_journal-2676	172	7	)	)	PUNCT
american_scientific_journal-2676	172	8	]	]	PUNCT
american_scientific_journal-2676	172	9	,	,	PUNCT
american_scientific_journal-2676	172	10	(	(	PUNCT
american_scientific_journal-2676	172	11	[	[	X
american_scientific_journal-2676	172	12	)	)	PUNCT
american_scientific_journal-2676	172	13	]	]	PUNCT
american_scientific_journal-2676	172	14	,	,	PUNCT
american_scientific_journal-2676	172	15	(	(	PUNCT
american_scientific_journal-2676	172	16	[=	[=	X
american_scientific_journal-2676	172	17	ehef	ehef	PROPN
american_scientific_journal-2676	172	18	iiii	iiii	NOUN
american_scientific_journal-2676	172	19	∆∈∆∈	∆∈∆∈	X
american_scientific_journal-2676	172	20			PROPN
american_scientific_journal-2676	172	21	.	.	PUNCT
american_scientific_journal-2676	173	1	since	since	SCONJ
american_scientific_journal-2676	173	2	∆∈∀∈	∆∈∀∈	PROPN
american_scientific_journal-2676	173	3	ief	ief	PROPN
american_scientific_journal-2676	173	4	c	c	PROPN
american_scientific_journal-2676	173	5	i	i	PRON
american_scientific_journal-2676	173	6	12	12	NUM
american_scientific_journal-2676	173	7	)	)	PUNCT
american_scientific_journal-2676	173	8	,	,	PUNCT
american_scientific_journal-2676	173	9	(	(	PUNCT
american_scientific_journal-2676	173	10	η	η	PROPN
american_scientific_journal-2676	173	11	,	,	PUNCT
american_scientific_journal-2676	173	12	then	then	ADV
american_scientific_journal-2676	173	13	c	c	PROPN
american_scientific_journal-2676	173	14	ii	ii	PROPN
american_scientific_journal-2676	173	15	ef	ef	PROPN
american_scientific_journal-2676	173	16	12	12	NUM
american_scientific_journal-2676	173	17	)	)	PUNCT
american_scientific_journal-2676	173	18	,	,	PUNCT
american_scientific_journal-2676	173	19	(	(	PUNCT
american_scientific_journal-2676	173	20	η∈	η∈	PROPN
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american_scientific_journal-2676	173	22	.	.	PUNCT
american_scientific_journal-2676	174	1	also	also	ADV
american_scientific_journal-2676	174	2	,	,	PUNCT
american_scientific_journal-2676	174	3	since	since	SCONJ
american_scientific_journal-2676	174	4	∆∈∀∈	∆∈∀∈	ADJ
american_scientific_journal-2676	174	5	λ	λ	PROPN
american_scientific_journal-2676	174	6	ieh	ieh	NOUN
american_scientific_journal-2676	174	7	pi	pi	PROPN
american_scientific_journal-2676	174	8	η	η	PROPN
american_scientific_journal-2676	174	9	)	)	PUNCT
american_scientific_journal-2676	174	10	,	,	PUNCT
american_scientific_journal-2676	174	11	(	(	PUNCT
american_scientific_journal-2676	174	12	,	,	PUNCT
american_scientific_journal-2676	174	13	then	then	ADV
american_scientific_journal-2676	174	14	λ∆∈	λ∆∈	PROPN
american_scientific_journal-2676	174	15	∈	∈	PROPN
american_scientific_journal-2676	174	16	pii	pii	NOUN
american_scientific_journal-2676	174	17	eh	eh	INTJ
american_scientific_journal-2676	174	18	η),(	η),(	NOUN
american_scientific_journal-2676	174	19	[	[	PUNCT
american_scientific_journal-2676	174	20	for	for	ADP
american_scientific_journal-2676	174	21	λpη	λpη	ADJ
american_scientific_journal-2676	174	22	is	be	AUX
american_scientific_journal-2676	174	23	an	an	DET
american_scientific_journal-2676	174	24	alexandroff	alexandroff	NOUN
american_scientific_journal-2676	174	25	soft	soft	ADJ
american_scientific_journal-2676	174	26	topology	topology	NOUN
american_scientific_journal-2676	174	27	]	]	PUNCT
american_scientific_journal-2676	174	28	.	.	PUNCT
american_scientific_journal-2676	175	1	therefore	therefore	ADV
american_scientific_journal-2676	175	2	,	,	PUNCT
american_scientific_journal-2676	175	3	)	)	PUNCT
american_scientific_journal-2676	175	4	,	,	PUNCT
american_scientific_journal-2676	175	5	(	(	PUNCT
american_scientific_journal-2676	175	6	egii	egii	NOUN
american_scientific_journal-2676	175	7	∆∈	∆∈	NOUN
american_scientific_journal-2676	175	8	is	be	AUX
american_scientific_journal-2676	175	9	a	a	DET
american_scientific_journal-2676	175	10	λp	λp	ADV
american_scientific_journal-2676	175	11	-closed	-close	VERB
american_scientific_journal-2676	175	12	soft	soft	ADJ
american_scientific_journal-2676	175	13	set	set	NOUN
american_scientific_journal-2676	175	14	.	.	PUNCT
american_scientific_journal-2676	176	1	remark	remark	PROPN
american_scientific_journal-2676	176	2	3.1	3.1	NUM
american_scientific_journal-2676	176	3	the	the	DET
american_scientific_journal-2676	176	4	union	union	NOUN
american_scientific_journal-2676	176	5	of	of	ADP
american_scientific_journal-2676	176	6	any	any	DET
american_scientific_journal-2676	176	7	two	two	NUM
american_scientific_journal-2676	176	8	λp	λp	ADV
american_scientific_journal-2676	176	9	-closed	-close	VERB
american_scientific_journal-2676	176	10	soft	soft	ADJ
american_scientific_journal-2676	176	11	sets	set	NOUN
american_scientific_journal-2676	176	12	may	may	AUX
american_scientific_journal-2676	176	13	not	not	PART
american_scientific_journal-2676	176	14	be	be	AUX
american_scientific_journal-2676	176	15	a	a	DET
american_scientific_journal-2676	176	16	λp	λp	ADV
american_scientific_journal-2676	176	17	-closed	-close	VERB
american_scientific_journal-2676	176	18	soft	soft	ADJ
american_scientific_journal-2676	176	19	set	set	NOUN
american_scientific_journal-2676	176	20	as	as	SCONJ
american_scientific_journal-2676	176	21	shown	show	VERB
american_scientific_journal-2676	176	22	in	in	ADP
american_scientific_journal-2676	176	23	the	the	DET
american_scientific_journal-2676	176	24	following	follow	VERB
american_scientific_journal-2676	176	25	example	example	NOUN
american_scientific_journal-2676	176	26	.	.	PUNCT
american_scientific_journal-2676	177	1	example	example	NOUN
american_scientific_journal-2676	177	2	3.1	3.1	NUM
american_scientific_journal-2676	177	3	let	let	VERB
american_scientific_journal-2676	177	4	}	}	PUNCT
american_scientific_journal-2676	177	5	,	,	PUNCT
american_scientific_journal-2676	177	6	{	{	PUNCT
american_scientific_journal-2676	177	7	=	=	PUNCT
american_scientific_journal-2676	177	8	yxx	yxx	NOUN
american_scientific_journal-2676	177	9	,	,	PUNCT
american_scientific_journal-2676	177	10	}	}	PUNCT
american_scientific_journal-2676	177	11	,	,	PUNCT
american_scientific_journal-2676	177	12	{	{	PUNCT
american_scientific_journal-2676	177	13	=	=	NOUN
american_scientific_journal-2676	177	14	21	21	NUM
american_scientific_journal-2676	177	15	eee	eee	NOUN
american_scientific_journal-2676	177	16	and	and	CCONJ
american_scientific_journal-2676	177	17	let	let	VERB
american_scientific_journal-2676	177	18	)	)	PUNCT
american_scientific_journal-2676	177	19	}	}	PUNCT
american_scientific_journal-2676	177	20	,	,	PUNCT
american_scientific_journal-2676	177	21	(	(	PUNCT
american_scientific_journal-2676	177	22	)	)	PUNCT
american_scientific_journal-2676	177	23	,	,	PUNCT
american_scientific_journal-2676	177	24	,	,	PUNCT
american_scientific_journal-2676	177	25	(	(	PUNCT
american_scientific_journal-2676	177	26	)	)	PUNCT
american_scientific_journal-2676	177	27	,	,	PUNCT
american_scientific_journal-2676	177	28	,	,	PUNCT
american_scientific_journal-2676	177	29	~(),,~{(=	~(),,~{(=	ADJ
american_scientific_journal-2676	177	30	211	211	NUM
american_scientific_journal-2676	177	31	egegexeφη	egegexeφη	NOUN
american_scientific_journal-2676	177	32	,	,	PUNCT
american_scientific_journal-2676	177	33	)	)	PUNCT
american_scientific_journal-2676	177	34	}	}	PUNCT
american_scientific_journal-2676	177	35	,	,	PUNCT
american_scientific_journal-2676	177	36	(	(	PUNCT
american_scientific_journal-2676	177	37	)	)	PUNCT
american_scientific_journal-2676	177	38	,	,	PUNCT
american_scientific_journal-2676	177	39	,	,	PUNCT
american_scientific_journal-2676	177	40	~(),,~{(=2	~(),,~{(=2	PROPN
american_scientific_journal-2676	177	41	ehexeφη	ehexeφη	NOUN
american_scientific_journal-2676	177	42	,	,	PUNCT
american_scientific_journal-2676	177	43	where	where	SCONJ
american_scientific_journal-2676	177	44	}	}	PUNCT
american_scientific_journal-2676	177	45	)	)	PUNCT
american_scientific_journal-2676	177	46	}	}	PUNCT
american_scientific_journal-2676	177	47	{	{	PUNCT
american_scientific_journal-2676	177	48	,	,	PUNCT
american_scientific_journal-2676	177	49	(	(	PUNCT
american_scientific_journal-2676	177	50	}	}	PUNCT
american_scientific_journal-2676	177	51	)	)	PUNCT
american_scientific_journal-2676	177	52	,	,	PUNCT
american_scientific_journal-2676	177	53	{	{	PUNCT
american_scientific_journal-2676	177	54	,	,	PUNCT
american_scientific_journal-2676	177	55	{	{	PUNCT
american_scientific_journal-2676	177	56	(=	(=	NOUN
american_scientific_journal-2676	177	57	)	)	PUNCT
american_scientific_journal-2676	177	58	,	,	PUNCT
american_scientific_journal-2676	177	59	(	(	PUNCT
american_scientific_journal-2676	177	60	211	211	NUM
american_scientific_journal-2676	177	61	yexeeg	yexeeg	NOUN
american_scientific_journal-2676	177	62	,	,	PUNCT
american_scientific_journal-2676	177	63	american	american	PROPN
american_scientific_journal-2676	177	64	scientific	scientific	ADJ
american_scientific_journal-2676	177	65	research	research	NOUN
american_scientific_journal-2676	177	66	journal	journal	NOUN
american_scientific_journal-2676	177	67	for	for	ADP
american_scientific_journal-2676	177	68	engineering	engineering	NOUN
american_scientific_journal-2676	177	69	,	,	PUNCT
american_scientific_journal-2676	177	70	technology	technology	NOUN
american_scientific_journal-2676	177	71	,	,	PUNCT
american_scientific_journal-2676	177	72	and	and	CCONJ
american_scientific_journal-2676	177	73	sciences	science	NOUN
american_scientific_journal-2676	177	74	(	(	PUNCT
american_scientific_journal-2676	177	75	asrjets	asrjet	NOUN
american_scientific_journal-2676	177	76	)	)	PUNCT
american_scientific_journal-2676	177	77	(	(	PUNCT
american_scientific_journal-2676	177	78	2017	2017	NUM
american_scientific_journal-2676	177	79	)	)	PUNCT
american_scientific_journal-2676	177	80	volume	volume	NOUN
american_scientific_journal-2676	177	81	28	28	NUM
american_scientific_journal-2676	177	82	,	,	PUNCT
american_scientific_journal-2676	177	83	no	no	DET
american_scientific_journal-2676	177	84	1	1	NUM
american_scientific_journal-2676	177	85	,	,	PUNCT
american_scientific_journal-2676	177	86	pp	pp	ADV
american_scientific_journal-2676	177	87	225	225	NUM
american_scientific_journal-2676	177	88	-	-	SYM
american_scientific_journal-2676	177	89	247	247	NUM
american_scientific_journal-2676	177	90	233	233	NUM
american_scientific_journal-2676	177	91	}	}	PUNCT
american_scientific_journal-2676	177	92	)	)	PUNCT
american_scientific_journal-2676	177	93	}	}	PUNCT
american_scientific_journal-2676	177	94	{	{	PUNCT
american_scientific_journal-2676	177	95	,	,	PUNCT
american_scientific_journal-2676	177	96	(	(	PUNCT
american_scientific_journal-2676	177	97	}	}	PUNCT
american_scientific_journal-2676	177	98	)	)	PUNCT
american_scientific_journal-2676	177	99	,	,	PUNCT
american_scientific_journal-2676	177	100	{	{	PUNCT
american_scientific_journal-2676	177	101	,	,	PUNCT
american_scientific_journal-2676	177	102	{	{	PUNCT
american_scientific_journal-2676	177	103	(=	(=	NOUN
american_scientific_journal-2676	177	104	)	)	PUNCT
american_scientific_journal-2676	177	105	,	,	PUNCT
american_scientific_journal-2676	177	106	(	(	PUNCT
american_scientific_journal-2676	177	107	212	212	NUM
american_scientific_journal-2676	177	108	xeyeeg	xeyeeg	NOUN
american_scientific_journal-2676	177	109	,	,	PUNCT
american_scientific_journal-2676	177	110	}	}	PUNCT
american_scientific_journal-2676	177	111	)	)	PUNCT
american_scientific_journal-2676	177	112	}	}	PUNCT
american_scientific_journal-2676	177	113	{	{	PUNCT
american_scientific_journal-2676	177	114	,	,	PUNCT
american_scientific_journal-2676	177	115	(	(	PUNCT
american_scientific_journal-2676	177	116	}	}	PUNCT
american_scientific_journal-2676	177	117	)	)	PUNCT
american_scientific_journal-2676	177	118	,	,	PUNCT
american_scientific_journal-2676	177	119	{	{	PUNCT
american_scientific_journal-2676	177	120	,	,	PUNCT
american_scientific_journal-2676	177	121	{	{	PUNCT
american_scientific_journal-2676	177	122	(=	(=	NOUN
american_scientific_journal-2676	177	123	)	)	PUNCT
american_scientific_journal-2676	177	124	,	,	PUNCT
american_scientific_journal-2676	177	125	(	(	PUNCT
american_scientific_journal-2676	177	126	21	21	NUM
american_scientific_journal-2676	177	127	xexeeh	xexeeh	NOUN
american_scientific_journal-2676	177	128	.	.	PUNCT
american_scientific_journal-2676	178	1	then	then	ADV
american_scientific_journal-2676	178	2	,	,	PUNCT
american_scientific_journal-2676	178	3	)	)	PUNCT
american_scientific_journal-2676	178	4	,	,	PUNCT
american_scientific_journal-2676	178	5	,	,	PUNCT
american_scientific_journal-2676	178	6	,	,	PUNCT
american_scientific_journal-2676	178	7	(	(	PUNCT
american_scientific_journal-2676	178	8	21	21	NUM
american_scientific_journal-2676	178	9	ex	ex	X
american_scientific_journal-2676	178	10	ηη	ηη	PROPN
american_scientific_journal-2676	178	11	is	be	AUX
american_scientific_journal-2676	178	12	a	a	DET
american_scientific_journal-2676	178	13	sbts	sbts	ADJ
american_scientific_journal-2676	178	14	.	.	PUNCT
american_scientific_journal-2676	179	1	consequently	consequently	ADV
american_scientific_journal-2676	179	2	,	,	PUNCT
american_scientific_journal-2676	179	3	)	)	PUNCT
american_scientific_journal-2676	179	4	}	}	PUNCT
american_scientific_journal-2676	179	5	,	,	PUNCT
american_scientific_journal-2676	179	6	(	(	PUNCT
american_scientific_journal-2676	179	7	)	)	PUNCT
american_scientific_journal-2676	179	8	,	,	PUNCT
american_scientific_journal-2676	179	9	,	,	PUNCT
american_scientific_journal-2676	179	10	(	(	PUNCT
american_scientific_journal-2676	179	11	)	)	PUNCT
american_scientific_journal-2676	179	12	,	,	PUNCT
american_scientific_journal-2676	179	13	,	,	PUNCT
american_scientific_journal-2676	179	14	(	(	PUNCT
american_scientific_journal-2676	179	15	)	)	PUNCT
american_scientific_journal-2676	179	16	,	,	PUNCT
american_scientific_journal-2676	179	17	,	,	PUNCT
american_scientific_journal-2676	179	18	(	(	PUNCT
american_scientific_journal-2676	179	19	)	)	PUNCT
american_scientific_journal-2676	179	20	,	,	PUNCT
american_scientific_journal-2676	179	21	,	,	PUNCT
american_scientific_journal-2676	179	22	(	(	PUNCT
american_scientific_journal-2676	179	23	)	)	PUNCT
american_scientific_journal-2676	179	24	,	,	PUNCT
american_scientific_journal-2676	179	25	,	,	PUNCT
american_scientific_journal-2676	179	26	~(),,~{(=	~(),,~{(=	ADJ
american_scientific_journal-2676	179	27	212112	212112	NUM
american_scientific_journal-2676	179	28	epepehegegexeφη	epepehegegexeφη	NOUN
american_scientific_journal-2676	179	29	,	,	PUNCT
american_scientific_journal-2676	179	30	where	where	SCONJ
american_scientific_journal-2676	179	31	)	)	PUNCT
american_scientific_journal-2676	179	32	}	}	PUNCT
american_scientific_journal-2676	179	33	,	,	PUNCT
american_scientific_journal-2676	179	34	(	(	PUNCT
american_scientific_journal-2676	179	35	}	}	PUNCT
american_scientific_journal-2676	179	36	)	)	PUNCT
american_scientific_journal-2676	179	37	,	,	PUNCT
american_scientific_journal-2676	179	38	{	{	PUNCT
american_scientific_journal-2676	179	39	,	,	PUNCT
american_scientific_journal-2676	179	40	{	{	PUNCT
american_scientific_journal-2676	179	41	(=	(=	NOUN
american_scientific_journal-2676	179	42	)	)	PUNCT
american_scientific_journal-2676	179	43	,	,	PUNCT
american_scientific_journal-2676	179	44	(	(	PUNCT
american_scientific_journal-2676	179	45	211	211	NUM
american_scientific_journal-2676	179	46	xexeep	xexeep	NOUN
american_scientific_journal-2676	179	47	,	,	PUNCT
american_scientific_journal-2676	179	48	}	}	PUNCT
american_scientific_journal-2676	179	49	)	)	PUNCT
american_scientific_journal-2676	179	50	}	}	PUNCT
american_scientific_journal-2676	179	51	{	{	PUNCT
american_scientific_journal-2676	179	52	,	,	PUNCT
american_scientific_journal-2676	179	53	(	(	PUNCT
american_scientific_journal-2676	179	54	)	)	PUNCT
american_scientific_journal-2676	179	55	,	,	PUNCT
american_scientific_journal-2676	179	56	,	,	PUNCT
american_scientific_journal-2676	179	57	{	{	PUNCT
american_scientific_journal-2676	179	58	(=	(=	NOUN
american_scientific_journal-2676	179	59	)	)	PUNCT
american_scientific_journal-2676	179	60	,	,	PUNCT
american_scientific_journal-2676	179	61	(	(	PUNCT
american_scientific_journal-2676	179	62	212	212	NUM
american_scientific_journal-2676	179	63	xexeep	xexeep	NOUN
american_scientific_journal-2676	179	64	.	.	PUNCT
american_scientific_journal-2676	180	1	it	it	PRON
american_scientific_journal-2676	180	2	is	be	AUX
american_scientific_journal-2676	180	3	easy	easy	ADJ
american_scientific_journal-2676	180	4	to	to	PART
american_scientific_journal-2676	180	5	prove	prove	VERB
american_scientific_journal-2676	180	6	that	that	PRON
american_scientific_journal-2676	180	7	)	)	PUNCT
american_scientific_journal-2676	180	8	}	}	PUNCT
american_scientific_journal-2676	180	9	,	,	PUNCT
american_scientific_journal-2676	180	10	(	(	PUNCT
american_scientific_journal-2676	180	11	)	)	PUNCT
american_scientific_journal-2676	180	12	,	,	PUNCT
american_scientific_journal-2676	180	13	,	,	PUNCT
american_scientific_journal-2676	180	14	{	{	PUNCT
american_scientific_journal-2676	180	15	(=	(=	NOUN
american_scientific_journal-2676	180	16	2112	2112	NUM
american_scientific_journal-2676	180	17	ememp	ememp	NOUN
american_scientific_journal-2676	180	18	ηη	ηη	PROPN
american_scientific_journal-2676	180	19	λ	λ	PROPN
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american_scientific_journal-2676	180	21	)	)	PUNCT
american_scientific_journal-2676	180	22	}	}	PUNCT
american_scientific_journal-2676	180	23	,	,	PUNCT
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american_scientific_journal-2676	180	26	)	)	PUNCT
american_scientific_journal-2676	180	27	,	,	PUNCT
american_scientific_journal-2676	180	28	{	{	PUNCT
american_scientific_journal-2676	180	29	,	,	PUNCT
american_scientific_journal-2676	180	30	{	{	PUNCT
american_scientific_journal-2676	180	31	(=	(=	NOUN
american_scientific_journal-2676	180	32	)	)	PUNCT
american_scientific_journal-2676	180	33	,	,	PUNCT
american_scientific_journal-2676	180	34	(	(	PUNCT
american_scientific_journal-2676	180	35	211	211	NUM
american_scientific_journal-2676	180	36	φexeem	φexeem	NOUN
american_scientific_journal-2676	180	37	,	,	PUNCT
american_scientific_journal-2676	180	38	}	}	PUNCT
american_scientific_journal-2676	180	39	)	)	PUNCT
american_scientific_journal-2676	180	40	}	}	PUNCT
american_scientific_journal-2676	180	41	{	{	PUNCT
american_scientific_journal-2676	180	42	,	,	PUNCT
american_scientific_journal-2676	180	43	(	(	PUNCT
american_scientific_journal-2676	180	44	)	)	PUNCT
american_scientific_journal-2676	180	45	,	,	PUNCT
american_scientific_journal-2676	180	46	,	,	PUNCT
american_scientific_journal-2676	180	47	{	{	PUNCT
american_scientific_journal-2676	180	48	(=	(=	NOUN
american_scientific_journal-2676	180	49	)	)	PUNCT
american_scientific_journal-2676	180	50	,	,	PUNCT
american_scientific_journal-2676	180	51	(	(	PUNCT
american_scientific_journal-2676	180	52	212	212	NUM
american_scientific_journal-2676	180	53	xeeem	xeeem	NOUN
american_scientific_journal-2676	180	54	φ	φ	PROPN
american_scientific_journal-2676	180	55	.	.	PUNCT
american_scientific_journal-2676	181	1	let	let	VERB
american_scientific_journal-2676	181	2	}	}	PUNCT
american_scientific_journal-2676	181	3	)	)	PUNCT
american_scientific_journal-2676	181	4	}	}	PUNCT
american_scientific_journal-2676	181	5	{	{	PUNCT
american_scientific_journal-2676	181	6	,	,	PUNCT
american_scientific_journal-2676	181	7	(	(	PUNCT
american_scientific_journal-2676	181	8	)	)	PUNCT
american_scientific_journal-2676	181	9	,	,	PUNCT
american_scientific_journal-2676	181	10	,	,	PUNCT
american_scientific_journal-2676	181	11	{	{	PUNCT
american_scientific_journal-2676	181	12	(=	(=	NOUN
american_scientific_journal-2676	181	13	)	)	PUNCT
american_scientific_journal-2676	181	14	,	,	PUNCT
american_scientific_journal-2676	181	15	(	(	PUNCT
american_scientific_journal-2676	181	16	21	21	NUM
american_scientific_journal-2676	181	17	yeeek	yeeek	NOUN
american_scientific_journal-2676	181	18	φ	φ	PROPN
american_scientific_journal-2676	181	19	,	,	PUNCT
american_scientific_journal-2676	181	20	then	then	ADV
american_scientific_journal-2676	181	21	)	)	PUNCT
american_scientific_journal-2676	181	22	,	,	PUNCT
american_scientific_journal-2676	181	23	(	(	PUNCT
american_scientific_journal-2676	181	24	ek	ek	PROPN
american_scientific_journal-2676	181	25	is	be	AUX
american_scientific_journal-2676	181	26	a	a	DET
american_scientific_journal-2676	181	27	p	p	NOUN
american_scientific_journal-2676	181	28	-closed	-close	VERB
american_scientific_journal-2676	181	29	soft	soft	ADJ
american_scientific_journal-2676	181	30	set	set	NOUN
american_scientific_journal-2676	181	31	.	.	PUNCT
american_scientific_journal-2676	182	1	it	it	PRON
american_scientific_journal-2676	182	2	is	be	AUX
american_scientific_journal-2676	182	3	clear	clear	ADJ
american_scientific_journal-2676	182	4	that	that	SCONJ
american_scientific_journal-2676	182	5	)	)	PUNCT
american_scientific_journal-2676	182	6	,	,	PUNCT
american_scientific_journal-2676	182	7	(	(	PUNCT
american_scientific_journal-2676	182	8	ek	ek	NOUN
american_scientific_journal-2676	182	9	and	and	CCONJ
american_scientific_journal-2676	182	10	)	)	PUNCT
american_scientific_journal-2676	182	11	,	,	PUNCT
american_scientific_journal-2676	182	12	(	(	PUNCT
american_scientific_journal-2676	182	13	2	2	NUM
american_scientific_journal-2676	182	14	eg	eg	NOUN
american_scientific_journal-2676	182	15	are	be	AUX
american_scientific_journal-2676	182	16	λp	λp	X
american_scientific_journal-2676	182	17	-closed	-close	VERB
american_scientific_journal-2676	182	18	soft	soft	ADJ
american_scientific_journal-2676	182	19	sets	set	NOUN
american_scientific_journal-2676	182	20	but	but	CCONJ
american_scientific_journal-2676	182	21	)	)	PUNCT
american_scientific_journal-2676	182	22	}	}	PUNCT
american_scientific_journal-2676	182	23	,	,	PUNCT
american_scientific_journal-2676	182	24	(	(	PUNCT
american_scientific_journal-2676	182	25	}	}	PUNCT
american_scientific_journal-2676	182	26	)	)	PUNCT
american_scientific_journal-2676	182	27	,	,	PUNCT
american_scientific_journal-2676	182	28	{	{	PUNCT
american_scientific_journal-2676	182	29	,	,	PUNCT
american_scientific_journal-2676	182	30	{	{	PUNCT
american_scientific_journal-2676	182	31	(=	(=	NOUN
american_scientific_journal-2676	182	32	)	)	PUNCT
american_scientific_journal-2676	182	33	,	,	PUNCT
american_scientific_journal-2676	182	34	(	(	PUNCT
american_scientific_journal-2676	182	35	~	~	NOUN
american_scientific_journal-2676	182	36	)	)	PUNCT
american_scientific_journal-2676	182	37	,	,	PUNCT
american_scientific_journal-2676	182	38	(	(	PUNCT
american_scientific_journal-2676	182	39	212	212	NUM
american_scientific_journal-2676	182	40	xeyeegek	xeyeegek	PROPN
american_scientific_journal-2676	182	41	∪	∪	NOUN
american_scientific_journal-2676	182	42	is	be	AUX
american_scientific_journal-2676	182	43	not	not	PART
american_scientific_journal-2676	182	44	λp	λp	ADV
american_scientific_journal-2676	182	45	-closed	-close	VERB
american_scientific_journal-2676	182	46	soft	soft	ADJ
american_scientific_journal-2676	182	47	set	set	NOUN
american_scientific_journal-2676	182	48	.	.	PUNCT
american_scientific_journal-2676	183	1	moreover	moreover	ADV
american_scientific_journal-2676	183	2	,	,	PUNCT
american_scientific_journal-2676	183	3	)	)	PUNCT
american_scientific_journal-2676	183	4	}	}	PUNCT
american_scientific_journal-2676	183	5	,	,	PUNCT
american_scientific_journal-2676	183	6	(	(	PUNCT
american_scientific_journal-2676	183	7	)	)	PUNCT
american_scientific_journal-2676	183	8	,	,	PUNCT
american_scientific_journal-2676	183	9	,	,	PUNCT
american_scientific_journal-2676	183	10	{	{	PUNCT
american_scientific_journal-2676	183	11	(=	(=	ADJ
american_scientific_journal-2676	183	12	)	)	PUNCT
american_scientific_journal-2676	183	13	,	,	PUNCT
american_scientific_journal-2676	183	14	,	,	PUNCT
american_scientific_journal-2676	183	15	(	(	PUNCT
american_scientific_journal-2676	183	16	21121221	21121221	NUM
american_scientific_journal-2676	183	17	ememxcsp	ememxcsp	NOUN
american_scientific_journal-2676	183	18	c	c	NOUN
american_scientific_journal-2676	183	19	e	e	X
american_scientific_journal-2676	183	20	ηηηηλ	ηηηηλ	PROPN
american_scientific_journal-2676	183	21	.	.	PUNCT
american_scientific_journal-2676	184	1	lemma	lemma	PROPN
american_scientific_journal-2676	184	2	3.1	3.1	NUM
american_scientific_journal-2676	184	3	let	let	NOUN
american_scientific_journal-2676	184	4	)	)	PUNCT
american_scientific_journal-2676	184	5	,	,	PUNCT
american_scientific_journal-2676	184	6	,	,	PUNCT
american_scientific_journal-2676	184	7	,	,	PUNCT
american_scientific_journal-2676	184	8	(	(	PUNCT
american_scientific_journal-2676	184	9	21	21	NUM
american_scientific_journal-2676	184	10	ex	ex	X
american_scientific_journal-2676	184	11	ηη	ηη	PROPN
american_scientific_journal-2676	184	12	be	be	AUX
american_scientific_journal-2676	184	13	a	a	DET
american_scientific_journal-2676	184	14	sbts	sbts	ADJ
american_scientific_journal-2676	184	15	and	and	CCONJ
american_scientific_journal-2676	184	16	let	let	VERB
american_scientific_journal-2676	184	17	)	)	PUNCT
american_scientific_journal-2676	184	18	,	,	PUNCT
american_scientific_journal-2676	184	19	(	(	PUNCT
american_scientific_journal-2676	184	20	exe	exe	NOUN
american_scientific_journal-2676	184	21	be	be	AUX
american_scientific_journal-2676	184	22	a	a	DET
american_scientific_journal-2676	184	23	soft	soft	ADJ
american_scientific_journal-2676	184	24	point	point	NOUN
american_scientific_journal-2676	184	25	in	in	ADP
american_scientific_journal-2676	184	26	)	)	PUNCT
american_scientific_journal-2676	184	27	,	,	PUNCT
american_scientific_journal-2676	184	28	~	~	PUNCT
american_scientific_journal-2676	184	29	(	(	PUNCT
american_scientific_journal-2676	184	30	ex	ex	X
american_scientific_journal-2676	184	31	.	.	PUNCT
american_scientific_journal-2676	185	1	if	if	SCONJ
american_scientific_journal-2676	185	2	c	c	PROPN
american_scientific_journal-2676	185	3	e	e	X
american_scientific_journal-2676	185	4	c	c	X
american_scientific_journal-2676	185	5	e	e	X
american_scientific_journal-2676	185	6	exexsker	exexsker	NOUN
american_scientific_journal-2676	185	7	)	)	PUNCT
american_scientific_journal-2676	185	8	,	,	PUNCT
american_scientific_journal-2676	185	9	(=	(=	ADV
american_scientific_journal-2676	185	10	)	)	PUNCT
american_scientific_journal-2676	185	11	,	,	PUNCT
american_scientific_journal-2676	185	12	(	(	PUNCT
american_scientific_journal-2676	185	13	12	12	NUM
american_scientific_journal-2676	185	14	,	,	PUNCT
american_scientific_journal-2676	185	15	then	then	ADV
american_scientific_journal-2676	185	16	c	c	PROPN
american_scientific_journal-2676	185	17	e	e	X
american_scientific_journal-2676	185	18	ex	ex	X
american_scientific_journal-2676	185	19	)	)	PUNCT
american_scientific_journal-2676	185	20	,	,	PUNCT
american_scientific_journal-2676	185	21	(	(	PUNCT
american_scientific_journal-2676	185	22	is	be	AUX
american_scientific_journal-2676	185	23	a	a	DET
american_scientific_journal-2676	185	24	p	p	X
american_scientific_journal-2676	185	25	-open	-open	ADJ
american_scientific_journal-2676	185	26	soft	soft	ADJ
american_scientific_journal-2676	185	27	set	set	NOUN
american_scientific_journal-2676	185	28	.	.	PUNCT
american_scientific_journal-2676	186	1	proof	proof	NOUN
american_scientific_journal-2676	186	2	.	.	PUNCT
american_scientific_journal-2676	187	1	assume	assume	VERB
american_scientific_journal-2676	187	2	that	that	SCONJ
american_scientific_journal-2676	187	3	c	c	PROPN
american_scientific_journal-2676	187	4	e	e	X
american_scientific_journal-2676	187	5	ex	ex	X
american_scientific_journal-2676	187	6	)	)	PUNCT
american_scientific_journal-2676	187	7	,	,	PUNCT
american_scientific_journal-2676	187	8	(	(	PUNCT
american_scientific_journal-2676	187	9	is	be	AUX
american_scientific_journal-2676	187	10	not	not	PART
american_scientific_journal-2676	187	11	a	a	DET
american_scientific_journal-2676	187	12	p	p	NOUN
american_scientific_journal-2676	187	13	-open	-open	ADJ
american_scientific_journal-2676	187	14	soft	soft	ADJ
american_scientific_journal-2676	187	15	set	set	NOUN
american_scientific_journal-2676	187	16	,	,	PUNCT
american_scientific_journal-2676	187	17	then	then	ADV
american_scientific_journal-2676	187	18	the	the	DET
american_scientific_journal-2676	187	19	only	only	ADJ
american_scientific_journal-2676	187	20	p	p	NOUN
american_scientific_journal-2676	187	21	-open	-open	ADJ
american_scientific_journal-2676	187	22	soft	soft	ADJ
american_scientific_journal-2676	187	23	superset	superset	NOUN
american_scientific_journal-2676	187	24	of	of	ADP
american_scientific_journal-2676	187	25	c	c	PROPN
american_scientific_journal-2676	187	26	e	e	X
american_scientific_journal-2676	187	27	ex	ex	X
american_scientific_journal-2676	187	28	)	)	PUNCT
american_scientific_journal-2676	187	29	,	,	PUNCT
american_scientific_journal-2676	187	30	(	(	PUNCT
american_scientific_journal-2676	187	31	is	be	AUX
american_scientific_journal-2676	187	32	)	)	PUNCT
american_scientific_journal-2676	187	33	,	,	PUNCT
american_scientific_journal-2676	188	1	~	~	PUNCT
american_scientific_journal-2676	188	2	(	(	PUNCT
american_scientific_journal-2676	188	3	ex	ex	X
american_scientific_journal-2676	188	4	.	.	PUNCT
american_scientific_journal-2676	189	1	therefore	therefore	ADV
american_scientific_journal-2676	189	2	,	,	PUNCT
american_scientific_journal-2676	189	3	)	)	PUNCT
american_scientific_journal-2676	189	4	,	,	PUNCT
american_scientific_journal-2676	189	5	~(=),(12	~(=),(12	NOUN
american_scientific_journal-2676	189	6	exexsker	exexsker	NOUN
american_scientific_journal-2676	189	7	c	c	PROPN
american_scientific_journal-2676	189	8	e	e	X
american_scientific_journal-2676	189	9	,	,	PUNCT
american_scientific_journal-2676	189	10	a	a	DET
american_scientific_journal-2676	189	11	contradiction	contradiction	NOUN
american_scientific_journal-2676	189	12	.	.	PUNCT
american_scientific_journal-2676	190	1	theorem	theorem	ADJ
american_scientific_journal-2676	190	2	3.2	3.2	NUM
american_scientific_journal-2676	190	3	let	let	NOUN
american_scientific_journal-2676	190	4	)	)	PUNCT
american_scientific_journal-2676	190	5	,	,	PUNCT
american_scientific_journal-2676	190	6	,	,	PUNCT
american_scientific_journal-2676	190	7	,	,	PUNCT
american_scientific_journal-2676	190	8	(	(	PUNCT
american_scientific_journal-2676	190	9	21	21	NUM
american_scientific_journal-2676	190	10	ex	ex	X
american_scientific_journal-2676	190	11	ηη	ηη	PROPN
american_scientific_journal-2676	190	12	be	be	AUX
american_scientific_journal-2676	190	13	a	a	DET
american_scientific_journal-2676	190	14	sbts	sbts	ADJ
american_scientific_journal-2676	190	15	.	.	PUNCT
american_scientific_journal-2676	191	1	then	then	ADV
american_scientific_journal-2676	191	2	)	)	PUNCT
american_scientific_journal-2676	191	3	,	,	PUNCT
american_scientific_journal-2676	191	4	,	,	PUNCT
american_scientific_journal-2676	191	5	,	,	PUNCT
american_scientific_journal-2676	191	6	(	(	PUNCT
american_scientific_journal-2676	191	7	21	21	NUM
american_scientific_journal-2676	191	8	ex	ex	X
american_scientific_journal-2676	191	9	ηη	ηη	PROPN
american_scientific_journal-2676	191	10	is	be	AUX
american_scientific_journal-2676	191	11	a	a	DET
american_scientific_journal-2676	191	12	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	191	13	2	2	NUM
american_scientific_journal-2676	191	14	�	�	PROPN
american_scientific_journal-2676	191	15	∗	∗	NOUN
american_scientific_journal-2676	191	16	iff	iff	VERB
american_scientific_journal-2676	191	17	every	every	DET
american_scientific_journal-2676	191	18	soft	soft	ADJ
american_scientific_journal-2676	191	19	set	set	NOUN
american_scientific_journal-2676	191	20	on	on	ADP
american_scientific_journal-2676	191	21	x	x	SYM
american_scientific_journal-2676	191	22	is	be	AUX
american_scientific_journal-2676	191	23	a	a	DET
american_scientific_journal-2676	191	24	λp	λp	ADV
american_scientific_journal-2676	191	25	-closed	-close	VERB
american_scientific_journal-2676	191	26	soft	soft	ADJ
american_scientific_journal-2676	191	27	set	set	NOUN
american_scientific_journal-2676	191	28	.	.	PUNCT
american_scientific_journal-2676	192	1	american	american	PROPN
american_scientific_journal-2676	192	2	scientific	scientific	ADJ
american_scientific_journal-2676	192	3	research	research	PROPN
american_scientific_journal-2676	192	4	journal	journal	NOUN
american_scientific_journal-2676	192	5	for	for	ADP
american_scientific_journal-2676	192	6	engineering	engineering	NOUN
american_scientific_journal-2676	192	7	,	,	PUNCT
american_scientific_journal-2676	192	8	technology	technology	NOUN
american_scientific_journal-2676	192	9	,	,	PUNCT
american_scientific_journal-2676	192	10	and	and	CCONJ
american_scientific_journal-2676	192	11	sciences	science	NOUN
american_scientific_journal-2676	192	12	(	(	PUNCT
american_scientific_journal-2676	192	13	asrjets	asrjet	NOUN
american_scientific_journal-2676	192	14	)	)	PUNCT
american_scientific_journal-2676	192	15	(	(	PUNCT
american_scientific_journal-2676	192	16	2017	2017	NUM
american_scientific_journal-2676	192	17	)	)	PUNCT
american_scientific_journal-2676	192	18	volume	volume	NOUN
american_scientific_journal-2676	192	19	28	28	NUM
american_scientific_journal-2676	192	20	,	,	PUNCT
american_scientific_journal-2676	192	21	no	no	DET
american_scientific_journal-2676	192	22	1	1	NUM
american_scientific_journal-2676	192	23	,	,	PUNCT
american_scientific_journal-2676	192	24	pp	pp	ADV
american_scientific_journal-2676	192	25	225	225	NUM
american_scientific_journal-2676	192	26	-	-	SYM
american_scientific_journal-2676	192	27	247	247	NUM
american_scientific_journal-2676	192	28	234	234	NUM
american_scientific_journal-2676	192	29	proof	proof	NOUN
american_scientific_journal-2676	192	30	.	.	PUNCT
american_scientific_journal-2676	193	1	for	for	ADP
american_scientific_journal-2676	193	2	any	any	DET
american_scientific_journal-2676	193	3	soft	soft	ADJ
american_scientific_journal-2676	193	4	set	set	NOUN
american_scientific_journal-2676	193	5	)	)	PUNCT
american_scientific_journal-2676	193	6	,	,	PUNCT
american_scientific_journal-2676	193	7	(	(	PUNCT
american_scientific_journal-2676	193	8	eg	eg	NOUN
american_scientific_journal-2676	193	9	over	over	ADP
american_scientific_journal-2676	193	10	x	x	PRON
american_scientific_journal-2676	193	11	,	,	PUNCT
american_scientific_journal-2676	193	12	let	let	VERB
american_scientific_journal-2676	193	13	}	}	PUNCT
american_scientific_journal-2676	193	14	)	)	PUNCT
american_scientific_journal-2676	193	15	,	,	PUNCT
american_scientific_journal-2676	193	16	(	(	PUNCT
american_scientific_journal-2676	193	17	~:),{(=	~:),{(=	ADJ
american_scientific_journal-2676	193	18	)	)	PUNCT
american_scientific_journal-2676	193	19	,	,	PUNCT
american_scientific_journal-2676	193	20	(	(	PUNCT
american_scientific_journal-2676	193	21	12	12	NUM
american_scientific_journal-2676	193	22	c	c	NOUN
american_scientific_journal-2676	193	23	ee	ee	PROPN
american_scientific_journal-2676	193	24	egxexem	egxexem	ADV
american_scientific_journal-2676	193	25	∈∈η	∈∈η	PROPN
american_scientific_journal-2676	193	26	.	.	PUNCT
american_scientific_journal-2676	194	1	then	then	ADV
american_scientific_journal-2676	194	2	,	,	PUNCT
american_scientific_journal-2676	194	3	)	)	PUNCT
american_scientific_journal-2676	194	4	,	,	PUNCT
american_scientific_journal-2676	194	5	(	(	PUNCT
american_scientific_journal-2676	194	6	em	em	PRON
american_scientific_journal-2676	194	7	is	be	AUX
american_scientific_journal-2676	194	8	a	a	DET
american_scientific_journal-2676	194	9	p	p	NOUN
american_scientific_journal-2676	194	10	-open	-open	ADJ
american_scientific_journal-2676	194	11	soft	soft	ADJ
american_scientific_journal-2676	194	12	set	set	NOUN
american_scientific_journal-2676	194	13	.	.	PUNCT
american_scientific_journal-2676	195	1	moreover	moreover	ADV
american_scientific_journal-2676	195	2	,	,	PUNCT
american_scientific_journal-2676	195	3	every	every	DET
american_scientific_journal-2676	195	4	soft	soft	ADJ
american_scientific_journal-2676	195	5	point	point	NOUN
american_scientific_journal-2676	195	6	in	in	ADP
american_scientific_journal-2676	195	7	)	)	PUNCT
american_scientific_journal-2676	195	8	,	,	PUNCT
american_scientific_journal-2676	195	9	(	(	PUNCT
american_scientific_journal-2676	195	10	em	em	PRON
american_scientific_journal-2676	195	11	is	be	AUX
american_scientific_journal-2676	195	12	a	a	DET
american_scientific_journal-2676	195	13	p	p	NOUN
american_scientific_journal-2676	195	14	-open	-open	ADJ
american_scientific_journal-2676	195	15	soft	soft	ADJ
american_scientific_journal-2676	195	16	set	set	NOUN
american_scientific_journal-2676	195	17	.	.	PUNCT
american_scientific_journal-2676	196	1	we	we	PRON
american_scientific_journal-2676	196	2	set	set	VERB
american_scientific_journal-2676	196	3	)	)	PUNCT
american_scientific_journal-2676	196	4	}	}	PUNCT
american_scientific_journal-2676	196	5	,	,	PUNCT
american_scientific_journal-2676	196	6	(	(	PUNCT
american_scientific_journal-2676	196	7	~:),{(=	~:),{(=	ADJ
american_scientific_journal-2676	196	8	)	)	PUNCT
american_scientific_journal-2676	196	9	,	,	PUNCT
american_scientific_journal-2676	196	10	(	(	PUNCT
american_scientific_journal-2676	196	11	emyeyef	emyeyef	PROPN
american_scientific_journal-2676	196	12	c	c	PROPN
american_scientific_journal-2676	196	13	∈αα	∈αα	PROPN
american_scientific_journal-2676	196	14	,	,	PUNCT
american_scientific_journal-2676	196	15	then	then	ADV
american_scientific_journal-2676	196	16	)	)	PUNCT
american_scientific_journal-2676	196	17	,	,	PUNCT
american_scientific_journal-2676	196	18	(	(	PUNCT
american_scientific_journal-2676	196	19	ef	ef	PROPN
american_scientific_journal-2676	196	20	is	be	AUX
american_scientific_journal-2676	196	21	a	a	DET
american_scientific_journal-2676	196	22	p	p	NOUN
american_scientific_journal-2676	196	23	-closed	-close	VERB
american_scientific_journal-2676	196	24	soft	soft	ADJ
american_scientific_journal-2676	196	25	set	set	NOUN
american_scientific_journal-2676	196	26	.	.	PUNCT
american_scientific_journal-2676	197	1	now	now	ADV
american_scientific_journal-2676	197	2	,	,	PUNCT
american_scientific_journal-2676	197	3	we	we	PRON
american_scientific_journal-2676	197	4	take	take	VERB
american_scientific_journal-2676	197	5	cc	cc	NOUN
american_scientific_journal-2676	197	6	emegen	emegen	NOUN
american_scientific_journal-2676	197	7	)	)	PUNCT
american_scientific_journal-2676	197	8	,	,	PUNCT
american_scientific_journal-2676	197	9	(	(	PUNCT
american_scientific_journal-2676	197	10	~),(=	~),(=	NUM
american_scientific_journal-2676	197	11	)	)	PUNCT
american_scientific_journal-2676	197	12	,	,	PUNCT
american_scientific_journal-2676	197	13	(	(	PUNCT
american_scientific_journal-2676	197	14	∩	∩	NOUN
american_scientific_journal-2676	197	15	.	.	PUNCT
american_scientific_journal-2676	198	1	let	let	VERB
american_scientific_journal-2676	198	2	)	)	PUNCT
american_scientific_journal-2676	198	3	,	,	PUNCT
american_scientific_journal-2676	198	4	(	(	PUNCT
american_scientific_journal-2676	198	5	~	~	PUNCT
american_scientific_journal-2676	198	6	enw	enw	PROPN
american_scientific_journal-2676	198	7	∈γ	∈γ	PROPN
american_scientific_journal-2676	198	8	.	.	PUNCT
american_scientific_journal-2676	199	1	then	then	ADV
american_scientific_journal-2676	199	2	cegw	cegw	X
american_scientific_journal-2676	199	3	)	)	PUNCT
american_scientific_journal-2676	199	4	,	,	PUNCT
american_scientific_journal-2676	199	5	(	(	PUNCT
american_scientific_journal-2676	199	6	~∈γ	~∈γ	X
american_scientific_journal-2676	199	7	and	and	CCONJ
american_scientific_journal-2676	199	8	cemw	cemw	PROPN
american_scientific_journal-2676	199	9	)	)	PUNCT
american_scientific_journal-2676	199	10	,	,	PUNCT
american_scientific_journal-2676	199	11	(	(	PUNCT
american_scientific_journal-2676	199	12	~∈γ	~∈γ	X
american_scientific_journal-2676	199	13	.	.	PUNCT
american_scientific_journal-2676	200	1	therefore	therefore	ADV
american_scientific_journal-2676	200	2	,	,	PUNCT
american_scientific_journal-2676	200	3	)	)	PUNCT
american_scientific_journal-2676	200	4	,	,	PUNCT
american_scientific_journal-2676	200	5	(	(	PUNCT
american_scientific_journal-2676	200	6	ewγ	ewγ	NOUN
american_scientific_journal-2676	200	7	is	be	AUX
american_scientific_journal-2676	200	8	a	a	DET
american_scientific_journal-2676	200	9	p	p	ADV
american_scientific_journal-2676	200	10	-closed	-close	VERB
american_scientific_journal-2676	200	11	soft	soft	ADJ
american_scientific_journal-2676	200	12	set	set	NOUN
american_scientific_journal-2676	200	13	because	because	SCONJ
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american_scientific_journal-2676	200	15	)	)	PUNCT
american_scientific_journal-2676	200	16	,	,	PUNCT
american_scientific_journal-2676	200	17	(	(	PUNCT
american_scientific_journal-2676	200	18	ewγ	ewγ	NOUN
american_scientific_journal-2676	200	19	is	be	AUX
american_scientific_journal-2676	200	20	not	not	PART
american_scientific_journal-2676	200	21	p	p	NOUN
american_scientific_journal-2676	200	22	-closed	-close	VERB
american_scientific_journal-2676	200	23	soft	soft	ADJ
american_scientific_journal-2676	200	24	set	set	NOUN
american_scientific_journal-2676	200	25	,	,	PUNCT
american_scientific_journal-2676	200	26	then	then	ADV
american_scientific_journal-2676	200	27	by	by	ADP
american_scientific_journal-2676	200	28	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	200	29	2	2	NUM
american_scientific_journal-2676	200	30	�	�	PROPN
american_scientific_journal-2676	200	31	∗	∗	NOUN
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american_scientific_journal-2676	200	33	and	and	CCONJ
american_scientific_journal-2676	200	34	theorem	theorem	VERB
american_scientific_journal-2676	200	35	2.9	2.9	NUM
american_scientific_journal-2676	200	36	we	we	PRON
american_scientific_journal-2676	200	37	conclude	conclude	VERB
american_scientific_journal-2676	200	38	that	that	PRON
american_scientific_journal-2676	200	39	)	)	PUNCT
american_scientific_journal-2676	200	40	,	,	PUNCT
american_scientific_journal-2676	200	41	(	(	PUNCT
american_scientific_journal-2676	200	42	ewγ	ewγ	NOUN
american_scientific_journal-2676	200	43	is	be	AUX
american_scientific_journal-2676	200	44	p	p	NOUN
american_scientific_journal-2676	200	45	-open	-open	ADJ
american_scientific_journal-2676	200	46	soft	soft	ADJ
american_scientific_journal-2676	200	47	set	set	NOUN
american_scientific_journal-2676	200	48	.	.	PUNCT
american_scientific_journal-2676	201	1	it	it	PRON
american_scientific_journal-2676	201	2	follows	follow	VERB
american_scientific_journal-2676	201	3	that	that	PRON
american_scientific_journal-2676	201	4	)	)	PUNCT
american_scientific_journal-2676	201	5	,	,	PUNCT
american_scientific_journal-2676	201	6	(	(	PUNCT
american_scientific_journal-2676	201	7	~	~	NOUN
american_scientific_journal-2676	201	8	)	)	PUNCT
american_scientific_journal-2676	201	9	,	,	PUNCT
american_scientific_journal-2676	201	10	(	(	PUNCT
american_scientific_journal-2676	201	11	emew	emew	NOUN
american_scientific_journal-2676	201	12	⊆γ	⊆γ	NOUN
american_scientific_journal-2676	201	13	which	which	PRON
american_scientific_journal-2676	201	14	contradicts	contradict	VERB
american_scientific_journal-2676	201	15	with	with	ADP
american_scientific_journal-2676	201	16	cemw	cemw	NOUN
american_scientific_journal-2676	201	17	)	)	PUNCT
american_scientific_journal-2676	201	18	,	,	PUNCT
american_scientific_journal-2676	201	19	(	(	PUNCT
american_scientific_journal-2676	201	20	~∈γ	~∈γ	X
american_scientific_journal-2676	201	21	.	.	PUNCT
american_scientific_journal-2676	202	1	consequently	consequently	ADV
american_scientific_journal-2676	202	2	,	,	PUNCT
american_scientific_journal-2676	202	3	every	every	DET
american_scientific_journal-2676	202	4	soft	soft	ADJ
american_scientific_journal-2676	202	5	point	point	NOUN
american_scientific_journal-2676	202	6	in	in	ADP
american_scientific_journal-2676	202	7	)	)	PUNCT
american_scientific_journal-2676	202	8	,	,	PUNCT
american_scientific_journal-2676	202	9	(	(	PUNCT
american_scientific_journal-2676	202	10	en	en	X
american_scientific_journal-2676	202	11	is	be	AUX
american_scientific_journal-2676	202	12	a	a	DET
american_scientific_journal-2676	202	13	p	p	NOUN
american_scientific_journal-2676	202	14	-closed	-close	VERB
american_scientific_journal-2676	202	15	soft	soft	ADJ
american_scientific_journal-2676	202	16	set	set	NOUN
american_scientific_journal-2676	202	17	.	.	PUNCT
american_scientific_journal-2676	203	1	put	put	VERB
american_scientific_journal-2676	203	2	)	)	PUNCT
american_scientific_journal-2676	203	3	}	}	PUNCT
american_scientific_journal-2676	203	4	,	,	PUNCT
american_scientific_journal-2676	203	5	(	(	PUNCT
american_scientific_journal-2676	203	6	~:),{(=	~:),{(=	ADJ
american_scientific_journal-2676	203	7	)	)	PUNCT
american_scientific_journal-2676	203	8	,	,	PUNCT
american_scientific_journal-2676	203	9	(	(	PUNCT
american_scientific_journal-2676	203	10	enzezeh	enzezeh	NOUN
american_scientific_journal-2676	203	11	c	c	NOUN
american_scientific_journal-2676	203	12	∈ββ	∈ββ	NOUN
american_scientific_journal-2676	203	13	implies	imply	VERB
american_scientific_journal-2676	203	14	)	)	PUNCT
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american_scientific_journal-2676	203	16	]	]	PUNCT
american_scientific_journal-2676	203	17	,	,	PUNCT
american_scientific_journal-2676	203	18	(	(	PUNCT
american_scientific_journal-2676	203	19	~:),{([=	~:),{([=	NOUN
american_scientific_journal-2676	203	20	)	)	PUNCT
american_scientific_journal-2676	203	21	,	,	PUNCT
american_scientific_journal-2676	203	22	(	(	PUNCT
american_scientific_journal-2676	203	23	1212	1212	NUM
american_scientific_journal-2676	203	24	enzezskerehsker	enzezskerehsker	NOUN
american_scientific_journal-2676	203	25	c	c	NOUN
american_scientific_journal-2676	203	26	∈ββ	∈ββ	VERB
american_scientific_journal-2676	203	27	)	)	PUNCT
american_scientific_journal-2676	203	28	}	}	PUNCT
american_scientific_journal-2676	203	29	,	,	PUNCT
american_scientific_journal-2676	203	30	(	(	PUNCT
american_scientific_journal-2676	203	31	~:),({=	~:),({=	PUNCT
american_scientific_journal-2676	203	32	12	12	NUM
american_scientific_journal-2676	203	33	enzezsker	enzezsker	NOUN
american_scientific_journal-2676	203	34	c	c	NOUN
american_scientific_journal-2676	203	35	∈ββ	∈ββ	VERB
american_scientific_journal-2676	203	36	[	[	PUNCT
american_scientific_journal-2676	203	37	by	by	ADP
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american_scientific_journal-2676	203	39	3.32	3.32	NUM
american_scientific_journal-2676	203	40	in	in	ADP
american_scientific_journal-2676	203	41	[	[	X
american_scientific_journal-2676	203	42	10	10	NUM
american_scientific_journal-2676	203	43	]	]	X
american_scientific_journal-2676	203	44	]	]	PUNCT
american_scientific_journal-2676	203	45	)	)	PUNCT
american_scientific_journal-2676	203	46	}	}	PUNCT
american_scientific_journal-2676	203	47	,	,	PUNCT
american_scientific_journal-2676	203	48	(	(	PUNCT
american_scientific_journal-2676	203	49	~:),{(=	~:),{(=	PRON
american_scientific_journal-2676	203	50	enzez	enzez	VERB
american_scientific_journal-2676	203	51	c	c	NOUN
american_scientific_journal-2676	203	52	∈ββ	∈ββ	NOUN
american_scientific_journal-2676	203	53	[	[	X
american_scientific_journal-2676	203	54	for	for	ADP
american_scientific_journal-2676	203	55	cez	cez	NOUN
american_scientific_journal-2676	203	56	)	)	PUNCT
american_scientific_journal-2676	203	57	,	,	PUNCT
american_scientific_journal-2676	203	58	(	(	PUNCT
american_scientific_journal-2676	203	59	β	β	X
american_scientific_journal-2676	203	60	is	be	AUX
american_scientific_journal-2676	203	61	p	p	X
american_scientific_journal-2676	203	62	-open	-open	ADJ
american_scientific_journal-2676	203	63	soft	soft	ADJ
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american_scientific_journal-2676	203	65	]	]	PUNCT
american_scientific_journal-2676	203	66	)	)	PUNCT
american_scientific_journal-2676	203	67	,	,	PUNCT
american_scientific_journal-2676	203	68	(=	(=	INTJ
american_scientific_journal-2676	203	69	eh	eh	INTJ
american_scientific_journal-2676	203	70	.	.	PUNCT
american_scientific_journal-2676	204	1	hence	hence	ADV
american_scientific_journal-2676	204	2	,	,	PUNCT
american_scientific_journal-2676	204	3	)	)	PUNCT
american_scientific_journal-2676	204	4	,	,	PUNCT
american_scientific_journal-2676	204	5	(	(	PUNCT
american_scientific_journal-2676	204	6	eh	eh	INTJ
american_scientific_journal-2676	204	7	is	be	AUX
american_scientific_journal-2676	204	8	a	a	DET
american_scientific_journal-2676	204	9	λp	λp	ADP
american_scientific_journal-2676	204	10	-soft	-soft	ADJ
american_scientific_journal-2676	204	11	set	set	NOUN
american_scientific_journal-2676	204	12	.	.	PUNCT
american_scientific_journal-2676	205	1	now	now	ADV
american_scientific_journal-2676	205	2	,	,	PUNCT
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american_scientific_journal-2676	205	4	cegem	cegem	PROPN
american_scientific_journal-2676	205	5	)	)	PUNCT
american_scientific_journal-2676	205	6	,	,	PUNCT
american_scientific_journal-2676	205	7	(	(	PUNCT
american_scientific_journal-2676	205	8	~	~	NOUN
american_scientific_journal-2676	205	9	)	)	PUNCT
american_scientific_journal-2676	205	10	,	,	PUNCT
american_scientific_journal-2676	205	11	(	(	PUNCT
american_scientific_journal-2676	205	12	⊆	⊆	NUM
american_scientific_journal-2676	205	13	,	,	PUNCT
american_scientific_journal-2676	205	14	then	then	ADV
american_scientific_journal-2676	205	15	cegy	cegy	PROPN
american_scientific_journal-2676	205	16	)	)	PUNCT
american_scientific_journal-2676	205	17	,	,	PUNCT
american_scientific_journal-2676	205	18	(	(	PUNCT
american_scientific_journal-2676	205	19	~∈α	~∈α	X
american_scientific_journal-2676	205	20	)	)	PUNCT
american_scientific_journal-2676	205	21	,	,	PUNCT
american_scientific_journal-2676	205	22	(	(	PUNCT
american_scientific_journal-2676	205	23	~	~	PUNCT
american_scientific_journal-2676	205	24	emy	emy	PROPN
american_scientific_journal-2676	205	25	∈∀	∈∀	PROPN
american_scientific_journal-2676	205	26	α	α	PROPN
american_scientific_journal-2676	205	27	implies	imply	VERB
american_scientific_journal-2676	205	28	ceyeg	ceyeg	NOUN
american_scientific_journal-2676	205	29	)	)	PUNCT
american_scientific_journal-2676	205	30	,	,	PUNCT
american_scientific_journal-2676	205	31	(	(	PUNCT
american_scientific_journal-2676	205	32	~	~	NOUN
american_scientific_journal-2676	205	33	)	)	PUNCT
american_scientific_journal-2676	205	34	,	,	PUNCT
american_scientific_journal-2676	205	35	(	(	PUNCT
american_scientific_journal-2676	205	36	α⊆	α⊆	NOUN
american_scientific_journal-2676	205	37	)	)	PUNCT
american_scientific_journal-2676	205	38	,	,	PUNCT
american_scientific_journal-2676	205	39	(	(	PUNCT
american_scientific_journal-2676	205	40	~	~	PUNCT
american_scientific_journal-2676	205	41	emy	emy	PROPN
american_scientific_journal-2676	205	42	∈∀	∈∀	PROPN
american_scientific_journal-2676	205	43	α	α	PROPN
american_scientific_journal-2676	205	44	.	.	PUNCT
american_scientific_journal-2676	206	1	it	it	PRON
american_scientific_journal-2676	206	2	follows	follow	VERB
american_scientific_journal-2676	206	3	that	that	PRON
american_scientific_journal-2676	206	4	)	)	PUNCT
american_scientific_journal-2676	206	5	,	,	PUNCT
american_scientific_journal-2676	206	6	(	(	PUNCT
american_scientific_journal-2676	206	7	~	~	NOUN
american_scientific_journal-2676	206	8	)	)	PUNCT
american_scientific_journal-2676	206	9	,	,	PUNCT
american_scientific_journal-2676	206	10	(	(	PUNCT
american_scientific_journal-2676	206	11	efeg	efeg	VERB
american_scientific_journal-2676	206	12	⊆	⊆	NUM
american_scientific_journal-2676	206	13	.	.	PUNCT
american_scientific_journal-2676	207	1	similarly	similarly	ADV
american_scientific_journal-2676	207	2	,	,	PUNCT
american_scientific_journal-2676	207	3	since	since	SCONJ
american_scientific_journal-2676	207	4	cegen	cegen	NOUN
american_scientific_journal-2676	207	5	)	)	PUNCT
american_scientific_journal-2676	207	6	,	,	PUNCT
american_scientific_journal-2676	207	7	(	(	PUNCT
american_scientific_journal-2676	207	8	~	~	NOUN
american_scientific_journal-2676	207	9	)	)	PUNCT
american_scientific_journal-2676	207	10	,	,	PUNCT
american_scientific_journal-2676	207	11	(	(	PUNCT
american_scientific_journal-2676	207	12	⊆	⊆	NUM
american_scientific_journal-2676	207	13	,	,	PUNCT
american_scientific_journal-2676	207	14	then	then	ADV
american_scientific_journal-2676	207	15	)	)	PUNCT
american_scientific_journal-2676	207	16	,	,	PUNCT
american_scientific_journal-2676	207	17	(	(	PUNCT
american_scientific_journal-2676	207	18	~	~	NOUN
american_scientific_journal-2676	207	19	)	)	PUNCT
american_scientific_journal-2676	207	20	,	,	PUNCT
american_scientific_journal-2676	207	21	(	(	PUNCT
american_scientific_journal-2676	207	22	eheg	eheg	VERB
american_scientific_journal-2676	207	23	⊆	⊆	NUM
american_scientific_journal-2676	207	24	.	.	PUNCT
american_scientific_journal-2676	208	1	consequently	consequently	ADV
american_scientific_journal-2676	208	2	,	,	PUNCT
american_scientific_journal-2676	208	3	)	)	PUNCT
american_scientific_journal-2676	208	4	,	,	PUNCT
american_scientific_journal-2676	208	5	(	(	PUNCT
american_scientific_journal-2676	208	6	~),(~	~),(~	NUM
american_scientific_journal-2676	208	7	)	)	PUNCT
american_scientific_journal-2676	208	8	,	,	PUNCT
american_scientific_journal-2676	208	9	(	(	PUNCT
american_scientific_journal-2676	208	10	efeheg	efeheg	AUX
american_scientific_journal-2676	208	11	∩⊆	∩⊆	NOUN
american_scientific_journal-2676	208	12	.	.	PUNCT
american_scientific_journal-2676	209	1	on	on	ADP
american_scientific_journal-2676	209	2	the	the	DET
american_scientific_journal-2676	209	3	other	other	ADJ
american_scientific_journal-2676	209	4	hand	hand	NOUN
american_scientific_journal-2676	209	5	,	,	PUNCT
american_scientific_journal-2676	209	6	let	let	VERB
american_scientific_journal-2676	209	7	)	)	PUNCT
american_scientific_journal-2676	209	8	,	,	PUNCT
american_scientific_journal-2676	209	9	(	(	PUNCT
american_scientific_journal-2676	209	10	~),(~	~),(~	NUM
american_scientific_journal-2676	209	11	efehze	efehze	NOUN
american_scientific_journal-2676	209	12	∩∈	∩∈	NUM
american_scientific_journal-2676	209	13	.	.	PUNCT
american_scientific_journal-2676	210	1	assume	assume	VERB
american_scientific_journal-2676	210	2	that	that	PRON
american_scientific_journal-2676	210	3	)	)	PUNCT
american_scientific_journal-2676	210	4	,	,	PUNCT
american_scientific_journal-2676	211	1	(	(	PUNCT
american_scientific_journal-2676	211	2	~	~	PUNCT
american_scientific_journal-2676	211	3	egze	egze	NOUN
american_scientific_journal-2676	211	4	∈/	∈/	PROPN
american_scientific_journal-2676	211	5	,	,	PUNCT
american_scientific_journal-2676	211	6	then	then	ADV
american_scientific_journal-2676	211	7	c	c	PROPN
american_scientific_journal-2676	211	8	e	e	X
american_scientific_journal-2676	211	9	egz	egz	NOUN
american_scientific_journal-2676	211	10	)	)	PUNCT
american_scientific_journal-2676	211	11	,	,	PUNCT
american_scientific_journal-2676	211	12	(	(	PUNCT
american_scientific_journal-2676	211	13	~∈	~∈	PUNCT
american_scientific_journal-2676	211	14	.	.	PUNCT
american_scientific_journal-2676	212	1	we	we	PRON
american_scientific_journal-2676	212	2	have	have	VERB
american_scientific_journal-2676	212	3	two	two	NUM
american_scientific_journal-2676	212	4	cases	case	NOUN
american_scientific_journal-2676	212	5	:	:	PUNCT
american_scientific_journal-2676	212	6	case(1	case(1	PROPN
american_scientific_journal-2676	212	7	):	):	PUNCT
american_scientific_journal-2676	212	8	if	if	SCONJ
american_scientific_journal-2676	212	9	)	)	PUNCT
american_scientific_journal-2676	212	10	,	,	PUNCT
american_scientific_journal-2676	212	11	(	(	PUNCT
american_scientific_journal-2676	212	12	eze	eze	PROPN
american_scientific_journal-2676	212	13	is	be	AUX
american_scientific_journal-2676	212	14	p	p	NOUN
american_scientific_journal-2676	212	15	-open	-open	ADJ
american_scientific_journal-2676	212	16	soft	soft	ADJ
american_scientific_journal-2676	212	17	point	point	NOUN
american_scientific_journal-2676	212	18	,	,	PUNCT
american_scientific_journal-2676	212	19	then	then	ADV
american_scientific_journal-2676	212	20	)	)	PUNCT
american_scientific_journal-2676	212	21	,	,	PUNCT
american_scientific_journal-2676	212	22	(	(	PUNCT
american_scientific_journal-2676	212	23	~	~	PUNCT
american_scientific_journal-2676	212	24	emze	emze	ADJ
american_scientific_journal-2676	212	25	∈	∈	PROPN
american_scientific_journal-2676	212	26	it	it	PRON
american_scientific_journal-2676	212	27	follows	follow	VERB
american_scientific_journal-2676	212	28	that	that	SCONJ
american_scientific_journal-2676	212	29	c	c	PROPN
american_scientific_journal-2676	212	30	e	e	NOUN
american_scientific_journal-2676	212	31	ezef	ezef	PROPN
american_scientific_journal-2676	212	32	)	)	PUNCT
american_scientific_journal-2676	212	33	,	,	PUNCT
american_scientific_journal-2676	212	34	(	(	PUNCT
american_scientific_journal-2676	212	35	~	~	NOUN
american_scientific_journal-2676	212	36	)	)	PUNCT
american_scientific_journal-2676	212	37	,	,	PUNCT
american_scientific_journal-2676	212	38	(	(	PUNCT
american_scientific_journal-2676	212	39	⊆	⊆	NUM
american_scientific_journal-2676	212	40	which	which	PRON
american_scientific_journal-2676	212	41	contradicts	contradict	VERB
american_scientific_journal-2676	212	42	with	with	ADP
american_scientific_journal-2676	212	43	)	)	PUNCT
american_scientific_journal-2676	212	44	,	,	PUNCT
american_scientific_journal-2676	212	45	(	(	PUNCT
american_scientific_journal-2676	212	46	~	~	PUNCT
american_scientific_journal-2676	212	47	efze	efze	VERB
american_scientific_journal-2676	212	48	∈	∈	PROPN
american_scientific_journal-2676	212	49	.	.	PUNCT
american_scientific_journal-2676	213	1	case(2	case(2	NOUN
american_scientific_journal-2676	213	2	):	):	PUNCT
american_scientific_journal-2676	213	3	if	if	SCONJ
american_scientific_journal-2676	213	4	)	)	PUNCT
american_scientific_journal-2676	213	5	,	,	PUNCT
american_scientific_journal-2676	213	6	(	(	PUNCT
american_scientific_journal-2676	213	7	eze	eze	X
american_scientific_journal-2676	213	8	is	be	AUX
american_scientific_journal-2676	213	9	not	not	PART
american_scientific_journal-2676	213	10	p	p	NOUN
american_scientific_journal-2676	213	11	-open	-open	ADJ
american_scientific_journal-2676	213	12	soft	soft	ADJ
american_scientific_journal-2676	213	13	point	point	NOUN
american_scientific_journal-2676	213	14	,	,	PUNCT
american_scientific_journal-2676	213	15	then	then	ADV
american_scientific_journal-2676	213	16	)	)	PUNCT
american_scientific_journal-2676	213	17	,	,	PUNCT
american_scientific_journal-2676	213	18	(	(	PUNCT
american_scientific_journal-2676	213	19	~	~	PUNCT
american_scientific_journal-2676	213	20	emze	emze	ADJ
american_scientific_journal-2676	213	21	∈/	∈/	PROPN
american_scientific_journal-2676	213	22	it	it	PRON
american_scientific_journal-2676	213	23	follows	follow	VERB
american_scientific_journal-2676	213	24	that	that	SCONJ
american_scientific_journal-2676	213	25	c	c	PROPN
american_scientific_journal-2676	213	26	e	e	PROPN
american_scientific_journal-2676	213	27	emz	emz	PROPN
american_scientific_journal-2676	213	28	)	)	PUNCT
american_scientific_journal-2676	213	29	,	,	PUNCT
american_scientific_journal-2676	213	30	(	(	PUNCT
american_scientific_journal-2676	213	31	~∈	~∈	PUNCT
american_scientific_journal-2676	213	32	.	.	PUNCT
american_scientific_journal-2676	214	1	therefore	therefore	ADV
american_scientific_journal-2676	214	2	,	,	PUNCT
american_scientific_journal-2676	214	3	)	)	PUNCT
american_scientific_journal-2676	214	4	,	,	PUNCT
american_scientific_journal-2676	214	5	(	(	PUNCT
american_scientific_journal-2676	214	6	~	~	PUNCT
american_scientific_journal-2676	214	7	enze	enze	NOUN
american_scientific_journal-2676	214	8	∈	∈	PROPN
american_scientific_journal-2676	214	9	which	which	PRON
american_scientific_journal-2676	214	10	implies	imply	VERB
american_scientific_journal-2676	214	11	that	that	SCONJ
american_scientific_journal-2676	214	12	c	c	PROPN
american_scientific_journal-2676	214	13	e	e	X
american_scientific_journal-2676	214	14	ezeh	ezeh	ADV
american_scientific_journal-2676	214	15	)	)	PUNCT
american_scientific_journal-2676	214	16	,	,	PUNCT
american_scientific_journal-2676	214	17	(	(	PUNCT
american_scientific_journal-2676	214	18	~	~	NOUN
american_scientific_journal-2676	214	19	)	)	PUNCT
american_scientific_journal-2676	214	20	,	,	PUNCT
american_scientific_journal-2676	214	21	(	(	PUNCT
american_scientific_journal-2676	214	22	⊆	⊆	NUM
american_scientific_journal-2676	214	23	which	which	PRON
american_scientific_journal-2676	214	24	contradicts	contradict	VERB
american_scientific_journal-2676	214	25	with	with	ADP
american_scientific_journal-2676	214	26	)	)	PUNCT
american_scientific_journal-2676	214	27	,	,	PUNCT
american_scientific_journal-2676	214	28	(	(	PUNCT
american_scientific_journal-2676	214	29	~	~	PUNCT
american_scientific_journal-2676	214	30	ehze	ehze	PROPN
american_scientific_journal-2676	214	31	∈	∈	PROPN
american_scientific_journal-2676	214	32	.	.	PUNCT
american_scientific_journal-2676	215	1	in	in	ADP
american_scientific_journal-2676	215	2	both	both	DET
american_scientific_journal-2676	215	3	cases	case	NOUN
american_scientific_journal-2676	215	4	we	we	PRON
american_scientific_journal-2676	215	5	have	have	VERB
american_scientific_journal-2676	215	6	a	a	DET
american_scientific_journal-2676	215	7	contradiction	contradiction	NOUN
american_scientific_journal-2676	215	8	.	.	PUNCT
american_scientific_journal-2676	216	1	hence	hence	ADV
american_scientific_journal-2676	216	2	,	,	PUNCT
american_scientific_journal-2676	216	3	)	)	PUNCT
american_scientific_journal-2676	216	4	,	,	PUNCT
american_scientific_journal-2676	216	5	(	(	PUNCT
american_scientific_journal-2676	216	6	~	~	PUNCT
american_scientific_journal-2676	216	7	egze	egze	ADJ
american_scientific_journal-2676	216	8	∈	∈	PROPN
american_scientific_journal-2676	216	9	.	.	PUNCT
american_scientific_journal-2676	217	1	consequently	consequently	ADV
american_scientific_journal-2676	217	2	,	,	PUNCT
american_scientific_journal-2676	217	3	)	)	PUNCT
american_scientific_journal-2676	217	4	,	,	PUNCT
american_scientific_journal-2676	217	5	(	(	PUNCT
american_scientific_journal-2676	217	6	~),(=	~),(=	NUM
american_scientific_journal-2676	217	7	)	)	PUNCT
american_scientific_journal-2676	217	8	,	,	PUNCT
american_scientific_journal-2676	217	9	(	(	PUNCT
american_scientific_journal-2676	217	10	efeheg	efeheg	NOUN
american_scientific_journal-2676	217	11	∩	∩	NOUN
american_scientific_journal-2676	217	12	.	.	PUNCT
american_scientific_journal-2676	218	1	from	from	ADP
american_scientific_journal-2676	218	2	the	the	DET
american_scientific_journal-2676	218	3	above	above	ADV
american_scientific_journal-2676	218	4	we	we	PRON
american_scientific_journal-2676	218	5	conclude	conclude	VERB
american_scientific_journal-2676	218	6	that	that	PRON
american_scientific_journal-2676	218	7	,	,	PUNCT
american_scientific_journal-2676	218	8	)	)	PUNCT
american_scientific_journal-2676	218	9	,	,	PUNCT
american_scientific_journal-2676	218	10	(	(	PUNCT
american_scientific_journal-2676	218	11	eg	eg	NOUN
american_scientific_journal-2676	218	12	is	be	AUX
american_scientific_journal-2676	218	13	a	a	DET
american_scientific_journal-2676	218	14	λp	λp	ADV
american_scientific_journal-2676	218	15	-closed	-close	VERB
american_scientific_journal-2676	218	16	soft	soft	ADJ
american_scientific_journal-2676	218	17	set	set	NOUN
american_scientific_journal-2676	218	18	.	.	PUNCT
american_scientific_journal-2676	219	1	conversely	conversely	ADV
american_scientific_journal-2676	219	2	,	,	PUNCT
american_scientific_journal-2676	219	3	let	let	VERB
american_scientific_journal-2676	219	4	)	)	PUNCT
american_scientific_journal-2676	219	5	,	,	PUNCT
american_scientific_journal-2676	219	6	(	(	PUNCT
american_scientific_journal-2676	219	7	exe	exe	NOUN
american_scientific_journal-2676	219	8	be	be	AUX
american_scientific_journal-2676	219	9	a	a	DET
american_scientific_journal-2676	219	10	soft	soft	ADJ
american_scientific_journal-2676	219	11	point	point	NOUN
american_scientific_journal-2676	219	12	in	in	ADP
american_scientific_journal-2676	219	13	x	x	X
american_scientific_journal-2676	219	14	.	.	PUNCT
american_scientific_journal-2676	220	1	then	then	ADV
american_scientific_journal-2676	220	2	,	,	PUNCT
american_scientific_journal-2676	220	3	c	c	PROPN
american_scientific_journal-2676	220	4	e	e	X
american_scientific_journal-2676	220	5	ex	ex	X
american_scientific_journal-2676	220	6	)	)	PUNCT
american_scientific_journal-2676	220	7	,	,	PUNCT
american_scientific_journal-2676	220	8	(	(	PUNCT
american_scientific_journal-2676	220	9	is	be	AUX
american_scientific_journal-2676	220	10	a	a	DET
american_scientific_journal-2676	220	11	soft	soft	ADJ
american_scientific_journal-2676	220	12	set	set	NOUN
american_scientific_journal-2676	220	13	over	over	ADP
american_scientific_journal-2676	220	14	x	x	PROPN
american_scientific_journal-2676	220	15	.	.	PUNCT
american_scientific_journal-2676	221	1	therefore	therefore	ADV
american_scientific_journal-2676	221	2	,	,	PUNCT
american_scientific_journal-2676	221	3	by	by	ADP
american_scientific_journal-2676	221	4	hypothesis	hypothesis	NOUN
american_scientific_journal-2676	221	5	,	,	PUNCT
american_scientific_journal-2676	221	6	c	c	NOUN
american_scientific_journal-2676	221	7	e	e	X
american_scientific_journal-2676	221	8	ex	ex	X
american_scientific_journal-2676	221	9	)	)	PUNCT
american_scientific_journal-2676	221	10	,	,	PUNCT
american_scientific_journal-2676	221	11	(	(	PUNCT
american_scientific_journal-2676	221	12	is	be	AUX
american_scientific_journal-2676	221	13	a	a	DET
american_scientific_journal-2676	221	14	λp	λp	ADV
american_scientific_journal-2676	221	15	-closed	-close	VERB
american_scientific_journal-2676	221	16	soft	soft	ADJ
american_scientific_journal-2676	221	17	set	set	NOUN
american_scientific_journal-2676	221	18	.	.	PUNCT
american_scientific_journal-2676	222	1	now	now	ADV
american_scientific_journal-2676	222	2	,	,	PUNCT
american_scientific_journal-2676	222	3	if	if	SCONJ
american_scientific_journal-2676	222	4	)	)	PUNCT
american_scientific_journal-2676	222	5	,	,	PUNCT
american_scientific_journal-2676	222	6	(	(	PUNCT
american_scientific_journal-2676	222	7	exe	exe	NOUN
american_scientific_journal-2676	222	8	is	be	AUX
american_scientific_journal-2676	222	9	a	a	DET
american_scientific_journal-2676	222	10	p	p	NOUN
american_scientific_journal-2676	222	11	-open	-open	ADJ
american_scientific_journal-2676	222	12	soft	soft	ADJ
american_scientific_journal-2676	222	13	set	set	NOUN
american_scientific_journal-2676	222	14	,	,	PUNCT
american_scientific_journal-2676	222	15	then	then	ADV
american_scientific_journal-2676	222	16	we	we	PRON
american_scientific_journal-2676	222	17	are	be	AUX
american_scientific_journal-2676	222	18	done	do	VERB
american_scientific_journal-2676	222	19	.	.	PUNCT
american_scientific_journal-2676	223	1	if	if	SCONJ
american_scientific_journal-2676	223	2	)	)	PUNCT
american_scientific_journal-2676	223	3	,	,	PUNCT
american_scientific_journal-2676	223	4	(	(	PUNCT
american_scientific_journal-2676	223	5	exe	exe	NOUN
american_scientific_journal-2676	223	6	is	be	AUX
american_scientific_journal-2676	223	7	not	not	PART
american_scientific_journal-2676	223	8	american	american	ADJ
american_scientific_journal-2676	223	9	scientific	scientific	ADJ
american_scientific_journal-2676	223	10	research	research	NOUN
american_scientific_journal-2676	223	11	journal	journal	NOUN
american_scientific_journal-2676	223	12	for	for	ADP
american_scientific_journal-2676	223	13	engineering	engineering	NOUN
american_scientific_journal-2676	223	14	,	,	PUNCT
american_scientific_journal-2676	223	15	technology	technology	NOUN
american_scientific_journal-2676	223	16	,	,	PUNCT
american_scientific_journal-2676	223	17	and	and	CCONJ
american_scientific_journal-2676	223	18	sciences	science	NOUN
american_scientific_journal-2676	223	19	(	(	PUNCT
american_scientific_journal-2676	223	20	asrjets	asrjet	NOUN
american_scientific_journal-2676	223	21	)	)	PUNCT
american_scientific_journal-2676	223	22	(	(	PUNCT
american_scientific_journal-2676	223	23	2017	2017	NUM
american_scientific_journal-2676	223	24	)	)	PUNCT
american_scientific_journal-2676	223	25	volume	volume	NOUN
american_scientific_journal-2676	223	26	28	28	NUM
american_scientific_journal-2676	223	27	,	,	PUNCT
american_scientific_journal-2676	223	28	no	no	DET
american_scientific_journal-2676	223	29	1	1	NUM
american_scientific_journal-2676	223	30	,	,	PUNCT
american_scientific_journal-2676	223	31	pp	pp	ADV
american_scientific_journal-2676	223	32	225	225	NUM
american_scientific_journal-2676	223	33	-	-	SYM
american_scientific_journal-2676	223	34	247	247	NUM
american_scientific_journal-2676	223	35	235	235	NUM
american_scientific_journal-2676	223	36	p	p	NOUN
american_scientific_journal-2676	223	37	-open	-open	ADJ
american_scientific_journal-2676	223	38	soft	soft	ADJ
american_scientific_journal-2676	223	39	set	set	NOUN
american_scientific_journal-2676	223	40	,	,	PUNCT
american_scientific_journal-2676	223	41	then	then	ADV
american_scientific_journal-2676	223	42	c	c	PROPN
american_scientific_journal-2676	223	43	e	e	X
american_scientific_journal-2676	223	44	ex	ex	X
american_scientific_journal-2676	223	45	)	)	PUNCT
american_scientific_journal-2676	223	46	,	,	PUNCT
american_scientific_journal-2676	223	47	(	(	PUNCT
american_scientific_journal-2676	223	48	is	be	AUX
american_scientific_journal-2676	223	49	not	not	PART
american_scientific_journal-2676	223	50	p	p	NOUN
american_scientific_journal-2676	223	51	-closed	-close	VERB
american_scientific_journal-2676	223	52	soft	soft	ADJ
american_scientific_journal-2676	223	53	set	set	NOUN
american_scientific_journal-2676	223	54	.	.	PUNCT
american_scientific_journal-2676	224	1	but	but	CCONJ
american_scientific_journal-2676	224	2	c	c	NOUN
american_scientific_journal-2676	224	3	e	e	X
american_scientific_journal-2676	224	4	ex	ex	X
american_scientific_journal-2676	224	5	)	)	PUNCT
american_scientific_journal-2676	224	6	,	,	PUNCT
american_scientific_journal-2676	224	7	(	(	PUNCT
american_scientific_journal-2676	224	8	is	be	AUX
american_scientific_journal-2676	224	9	a	a	DET
american_scientific_journal-2676	224	10	λp	λp	ADV
american_scientific_journal-2676	224	11	-closed	-close	VERB
american_scientific_journal-2676	224	12	soft	soft	ADJ
american_scientific_journal-2676	224	13	set	set	NOUN
american_scientific_journal-2676	224	14	,	,	PUNCT
american_scientific_journal-2676	224	15	then	then	ADV
american_scientific_journal-2676	224	16	there	there	PRON
american_scientific_journal-2676	224	17	exist	exist	VERB
american_scientific_journal-2676	224	18	a	a	DET
american_scientific_journal-2676	224	19	λp	λp	ADP
american_scientific_journal-2676	224	20	-soft	-soft	ADJ
american_scientific_journal-2676	224	21	set	set	NOUN
american_scientific_journal-2676	224	22	)	)	PUNCT
american_scientific_journal-2676	224	23	,	,	PUNCT
american_scientific_journal-2676	224	24	(	(	PUNCT
american_scientific_journal-2676	224	25	eh	eh	INTJ
american_scientific_journal-2676	224	26	and	and	CCONJ
american_scientific_journal-2676	224	27	a	a	DET
american_scientific_journal-2676	224	28	p	p	NOUN
american_scientific_journal-2676	224	29	-closed	-close	VERB
american_scientific_journal-2676	224	30	soft	soft	ADJ
american_scientific_journal-2676	224	31	set	set	NOUN
american_scientific_journal-2676	224	32	)	)	PUNCT
american_scientific_journal-2676	224	33	,	,	PUNCT
american_scientific_journal-2676	224	34	(	(	PUNCT
american_scientific_journal-2676	224	35	ef	ef	ADP
american_scientific_journal-2676	224	36	such	such	ADJ
american_scientific_journal-2676	224	37	that	that	PRON
american_scientific_journal-2676	224	38	)	)	PUNCT
american_scientific_journal-2676	224	39	,	,	PUNCT
american_scientific_journal-2676	224	40	(	(	PUNCT
american_scientific_journal-2676	224	41	~),(=	~),(=	NUM
american_scientific_journal-2676	224	42	)	)	PUNCT
american_scientific_journal-2676	224	43	,	,	PUNCT
american_scientific_journal-2676	224	44	(	(	PUNCT
american_scientific_journal-2676	224	45	efehex	efehex	PROPN
american_scientific_journal-2676	224	46	c	c	PROPN
american_scientific_journal-2676	224	47	e	e	PROPN
american_scientific_journal-2676	224	48	∩	∩	X
american_scientific_journal-2676	224	49	.	.	PUNCT
american_scientific_journal-2676	225	1	but	but	CCONJ
american_scientific_journal-2676	225	2	the	the	DET
american_scientific_journal-2676	225	3	only	only	ADJ
american_scientific_journal-2676	225	4	p	p	NOUN
american_scientific_journal-2676	225	5	-closed	-close	VERB
american_scientific_journal-2676	225	6	soft	soft	ADJ
american_scientific_journal-2676	225	7	superset	superset	NOUN
american_scientific_journal-2676	225	8	of	of	ADP
american_scientific_journal-2676	225	9	c	c	PROPN
american_scientific_journal-2676	225	10	e	e	X
american_scientific_journal-2676	225	11	ex	ex	X
american_scientific_journal-2676	225	12	)	)	PUNCT
american_scientific_journal-2676	225	13	,	,	PUNCT
american_scientific_journal-2676	225	14	(	(	PUNCT
american_scientific_journal-2676	225	15	is	be	AUX
american_scientific_journal-2676	225	16	)	)	PUNCT
american_scientific_journal-2676	225	17	,	,	PUNCT
american_scientific_journal-2676	226	1	~	~	PUNCT
american_scientific_journal-2676	226	2	(	(	PUNCT
american_scientific_journal-2676	226	3	ex	ex	X
american_scientific_journal-2676	226	4	.	.	PUNCT
american_scientific_journal-2676	227	1	therefore	therefore	ADV
american_scientific_journal-2676	227	2	,	,	PUNCT
american_scientific_journal-2676	227	3	)	)	PUNCT
american_scientific_journal-2676	227	4	,	,	PUNCT
american_scientific_journal-2676	227	5	(	(	PUNCT
american_scientific_journal-2676	227	6	=)	=)	INTJ
american_scientific_journal-2676	227	7	,	,	PUNCT
american_scientific_journal-2676	227	8	(	(	PUNCT
american_scientific_journal-2676	227	9	ehex	ehex	PROPN
american_scientific_journal-2676	227	10	c	c	PROPN
american_scientific_journal-2676	227	11	e	e	X
american_scientific_journal-2676	227	12	.	.	PUNCT
american_scientific_journal-2676	228	1	consequently	consequently	ADV
american_scientific_journal-2676	228	2	,	,	PUNCT
american_scientific_journal-2676	228	3	c	c	PROPN
american_scientific_journal-2676	228	4	e	e	X
american_scientific_journal-2676	228	5	c	c	X
american_scientific_journal-2676	228	6	e	e	X
american_scientific_journal-2676	228	7	exexsker	exexsker	NOUN
american_scientific_journal-2676	228	8	)	)	PUNCT
american_scientific_journal-2676	228	9	,	,	PUNCT
american_scientific_journal-2676	228	10	(=	(=	ADV
american_scientific_journal-2676	228	11	)	)	PUNCT
american_scientific_journal-2676	228	12	,	,	PUNCT
american_scientific_journal-2676	228	13	(	(	PUNCT
american_scientific_journal-2676	228	14	12	12	NUM
american_scientific_journal-2676	228	15	.	.	PUNCT
american_scientific_journal-2676	229	1	hence	hence	ADV
american_scientific_journal-2676	229	2	,	,	PUNCT
american_scientific_journal-2676	229	3	by	by	ADP
american_scientific_journal-2676	229	4	lemma	lemma	PROPN
american_scientific_journal-2676	229	5	3.1	3.1	NUM
american_scientific_journal-2676	229	6	,	,	PUNCT
american_scientific_journal-2676	229	7	c	c	PROPN
american_scientific_journal-2676	229	8	e	e	X
american_scientific_journal-2676	229	9	ex	ex	X
american_scientific_journal-2676	229	10	)	)	PUNCT
american_scientific_journal-2676	229	11	,	,	PUNCT
american_scientific_journal-2676	229	12	(	(	PUNCT
american_scientific_journal-2676	229	13	is	be	AUX
american_scientific_journal-2676	229	14	a	a	DET
american_scientific_journal-2676	229	15	p	p	X
american_scientific_journal-2676	229	16	-open	-open	ADJ
american_scientific_journal-2676	229	17	soft	soft	ADJ
american_scientific_journal-2676	229	18	set	set	NOUN
american_scientific_journal-2676	229	19	.	.	PUNCT
american_scientific_journal-2676	230	1	therefore	therefore	ADV
american_scientific_journal-2676	230	2	,	,	PUNCT
american_scientific_journal-2676	230	3	)	)	PUNCT
american_scientific_journal-2676	230	4	,	,	PUNCT
american_scientific_journal-2676	230	5	(	(	PUNCT
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american_scientific_journal-2676	230	7	is	be	AUX
american_scientific_journal-2676	230	8	a	a	DET
american_scientific_journal-2676	230	9	p	p	ADV
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american_scientific_journal-2676	230	13	.	.	PUNCT
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american_scientific_journal-2676	231	2	3.1	3.1	NUM
american_scientific_journal-2676	231	3	a	a	DET
american_scientific_journal-2676	231	4	soft	soft	ADJ
american_scientific_journal-2676	231	5	topological	topological	ADJ
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american_scientific_journal-2676	231	7	)	)	PUNCT
american_scientific_journal-2676	231	8	,	,	PUNCT
american_scientific_journal-2676	231	9	,	,	PUNCT
american_scientific_journal-2676	231	10	(	(	PUNCT
american_scientific_journal-2676	231	11	ex	ex	X
american_scientific_journal-2676	231	12	η	η	PROPN
american_scientific_journal-2676	231	13	is	be	AUX
american_scientific_journal-2676	231	14	said	say	VERB
american_scientific_journal-2676	231	15	to	to	PART
american_scientific_journal-2676	231	16	be	be	AUX
american_scientific_journal-2676	231	17	a	a	DET
american_scientific_journal-2676	231	18	soft	soft	ADJ
american_scientific_journal-2676	231	19	𝑇𝑇1	𝑇𝑇1	NOUN
american_scientific_journal-2676	231	20	4	4	NUM
american_scientific_journal-2676	231	21	�	�	NOUN
american_scientific_journal-2676	231	22	[	[	X
american_scientific_journal-2676	231	23	briefly	briefly	ADV
american_scientific_journal-2676	231	24	,	,	PUNCT
american_scientific_journal-2676	231	25	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	231	26	4	4	NUM
american_scientific_journal-2676	231	27	�	�	PROPN
american_scientific_journal-2676	231	28	]	]	PUNCT
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american_scientific_journal-2676	231	33	soft	soft	ADJ
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american_scientific_journal-2676	231	35	)	)	PUNCT
american_scientific_journal-2676	231	36	,	,	PUNCT
american_scientific_journal-2676	231	37	(	(	PUNCT
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american_scientific_journal-2676	231	39	over	over	ADP
american_scientific_journal-2676	231	40	x	x	PUNCT
american_scientific_journal-2676	231	41	and	and	CCONJ
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american_scientific_journal-2676	231	43	)	)	PUNCT
american_scientific_journal-2676	231	44	,	,	PUNCT
american_scientific_journal-2676	231	45	(	(	PUNCT
american_scientific_journal-2676	231	46	~	~	PUNCT
american_scientific_journal-2676	231	47	egxe	egxe	NOUN
american_scientific_journal-2676	231	48	∈/	∈/	NOUN
american_scientific_journal-2676	231	49	,	,	PUNCT
american_scientific_journal-2676	231	50	there	there	PRON
american_scientific_journal-2676	231	51	exists	exist	VERB
american_scientific_journal-2676	231	52	a	a	DET
american_scientific_journal-2676	231	53	soft	soft	ADJ
american_scientific_journal-2676	231	54	set	set	NOUN
american_scientific_journal-2676	231	55	cex	cex	NOUN
american_scientific_journal-2676	231	56	em	em	PRON
american_scientific_journal-2676	231	57	ηη∈	ηη∈	PROPN
american_scientific_journal-2676	231	58	)	)	PUNCT
american_scientific_journal-2676	231	59	,	,	PUNCT
american_scientific_journal-2676	231	60	(	(	PUNCT
american_scientific_journal-2676	231	61	such	such	ADJ
american_scientific_journal-2676	231	62	that	that	PRON
american_scientific_journal-2676	231	63	)	)	PUNCT
american_scientific_journal-2676	231	64	,	,	PUNCT
american_scientific_journal-2676	231	65	(	(	PUNCT
american_scientific_journal-2676	231	66	~	~	PUNCT
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american_scientific_journal-2676	231	68	ex	ex	ADJ
american_scientific_journal-2676	231	69	e	e	NOUN
american_scientific_journal-2676	231	70	∈/	∈/	PROPN
american_scientific_journal-2676	231	71	and	and	CCONJ
american_scientific_journal-2676	231	72	)	)	PUNCT
american_scientific_journal-2676	231	73	,	,	PUNCT
american_scientific_journal-2676	231	74	(	(	PUNCT
american_scientific_journal-2676	231	75	~	~	NOUN
american_scientific_journal-2676	231	76	)	)	PUNCT
american_scientific_journal-2676	231	77	,	,	PUNCT
american_scientific_journal-2676	231	78	(	(	PUNCT
american_scientific_journal-2676	231	79	emeg	emeg	NOUN
american_scientific_journal-2676	231	80	ex⊆	ex⊆	NOUN
american_scientific_journal-2676	231	81	.	.	PUNCT
american_scientific_journal-2676	232	1	example	example	NOUN
american_scientific_journal-2676	232	2	3.2	3.2	NUM
american_scientific_journal-2676	232	3	let	let	VERB
american_scientific_journal-2676	232	4	zx	zx	PROPN
american_scientific_journal-2676	232	5	=	=	PUNCT
american_scientific_journal-2676	232	6	,	,	PUNCT
american_scientific_journal-2676	232	7	where	where	SCONJ
american_scientific_journal-2676	232	8	z	z	NOUN
american_scientific_journal-2676	232	9	denote	denote	VERB
american_scientific_journal-2676	232	10	the	the	DET
american_scientific_journal-2676	232	11	set	set	NOUN
american_scientific_journal-2676	232	12	of	of	ADP
american_scientific_journal-2676	232	13	all	all	DET
american_scientific_journal-2676	232	14	integer	integer	NOUN
american_scientific_journal-2676	232	15	numbers	number	NOUN
american_scientific_journal-2676	232	16	,	,	PUNCT
american_scientific_journal-2676	232	17	e	e	X
american_scientific_journal-2676	232	18	be	be	VERB
american_scientific_journal-2676	232	19	a	a	DET
american_scientific_journal-2676	232	20	non	non	ADJ
american_scientific_journal-2676	232	21	-	-	ADJ
american_scientific_journal-2676	232	22	empty	empty	ADJ
american_scientific_journal-2676	232	23	set	set	NOUN
american_scientific_journal-2676	232	24	of	of	ADP
american_scientific_journal-2676	232	25	parameters	parameter	NOUN
american_scientific_journal-2676	232	26	such	such	ADJ
american_scientific_journal-2676	232	27	that	that	SCONJ
american_scientific_journal-2676	232	28	}	}	PUNCT
american_scientific_journal-2676	232	29	{	{	PUNCT
american_scientific_journal-2676	232	30	=	=	SYM
american_scientific_journal-2676	232	31	1	1	NUM
american_scientific_journal-2676	232	32	dee	dee	PROPN
american_scientific_journal-2676	232	33	∪	∪	NOUN
american_scientific_journal-2676	232	34	and	and	CCONJ
american_scientific_journal-2676	232	35	1ed	1ed	ADJ
american_scientific_journal-2676	232	36	∈/	∈/	PROPN
american_scientific_journal-2676	232	37	and	and	CCONJ
american_scientific_journal-2676	232	38	let	let	VERB
american_scientific_journal-2676	232	39	}	}	PUNCT
american_scientific_journal-2676	232	40	)	)	PUNCT
american_scientific_journal-2676	232	41	,	,	PUNCT
american_scientific_journal-2676	232	42	(	(	PUNCT
american_scientific_journal-2676	232	43	)	)	PUNCT
american_scientific_journal-2676	232	44	,	,	PUNCT
american_scientific_journal-2676	232	45	(	(	PUNCT
american_scientific_journal-2676	232	46	~0:)(),{()},~{(=	~0:)(),{()},~{(=	NUM
american_scientific_journal-2676	232	47	setsoftfiniteisegandegzssege	setsoftfiniteisegandegzssege	NOUN
american_scientific_journal-2676	232	48	c	c	PROPN
american_scientific_journal-2676	232	49	ded	de	VERB
american_scientific_journal-2676	232	50	∈∈φη	∈∈φη	ADJ
american_scientific_journal-2676	232	51	.	.	PUNCT
american_scientific_journal-2676	233	1	it	it	PRON
american_scientific_journal-2676	233	2	is	be	AUX
american_scientific_journal-2676	233	3	easy	easy	ADJ
american_scientific_journal-2676	233	4	to	to	PART
american_scientific_journal-2676	233	5	prove	prove	VERB
american_scientific_journal-2676	233	6	that	that	SCONJ
american_scientific_journal-2676	233	7	dη	dη	NOUN
american_scientific_journal-2676	233	8	is	be	AUX
american_scientific_journal-2676	233	9	a	a	DET
american_scientific_journal-2676	233	10	soft	soft	ADJ
american_scientific_journal-2676	233	11	topology	topology	NOUN
american_scientific_journal-2676	233	12	on	on	ADP
american_scientific_journal-2676	233	13	z	z	PROPN
american_scientific_journal-2676	233	14	.	.	PUNCT
american_scientific_journal-2676	234	1	now	now	ADV
american_scientific_journal-2676	234	2	,	,	PUNCT
american_scientific_journal-2676	234	3	let	let	VERB
american_scientific_journal-2676	234	4	)	)	PUNCT
american_scientific_journal-2676	234	5	,	,	PUNCT
american_scientific_journal-2676	234	6	(	(	PUNCT
american_scientific_journal-2676	234	7	ef	ef	X
american_scientific_journal-2676	234	8	be	be	AUX
american_scientific_journal-2676	234	9	a	a	DET
american_scientific_journal-2676	234	10	finite	finite	ADJ
american_scientific_journal-2676	234	11	soft	soft	ADJ
american_scientific_journal-2676	234	12	set	set	NOUN
american_scientific_journal-2676	234	13	and	and	CCONJ
american_scientific_journal-2676	234	14	)	)	PUNCT
american_scientific_journal-2676	234	15	,	,	PUNCT
american_scientific_journal-2676	234	16	(	(	PUNCT
american_scientific_journal-2676	234	17	~	~	PUNCT
american_scientific_journal-2676	234	18	efxe	efxe	NOUN
american_scientific_journal-2676	234	19	∈/	∈/	PROPN
american_scientific_journal-2676	234	20	,	,	PUNCT
american_scientific_journal-2676	234	21	then	then	ADV
american_scientific_journal-2676	234	22	we	we	PRON
american_scientific_journal-2676	234	23	have	have	VERB
american_scientific_journal-2676	234	24	four	four	NUM
american_scientific_journal-2676	234	25	cases	case	NOUN
american_scientific_journal-2676	234	26	:	:	PUNCT
american_scientific_journal-2676	234	27	case(1	case(1	PROPN
american_scientific_journal-2676	234	28	):	):	PUNCT
american_scientific_journal-2676	234	29	dex	dex	NOUN
american_scientific_journal-2676	234	30	0≠	0≠	NUM
american_scientific_journal-2676	234	31	,	,	PUNCT
american_scientific_journal-2676	234	32	0≠x	0≠x	NUM
american_scientific_journal-2676	234	33	and	and	CCONJ
american_scientific_journal-2676	234	34	)	)	PUNCT
american_scientific_journal-2676	234	35	,	,	PUNCT
american_scientific_journal-2676	234	36	(	(	PUNCT
american_scientific_journal-2676	234	37	~0	~0	NUM
american_scientific_journal-2676	234	38	efd	efd	PROPN
american_scientific_journal-2676	234	39	∈/	∈/	PROPN
american_scientific_journal-2676	234	40	.	.	PUNCT
american_scientific_journal-2676	235	1	in	in	ADP
american_scientific_journal-2676	235	2	this	this	DET
american_scientific_journal-2676	235	3	case	case	NOUN
american_scientific_journal-2676	235	4	,	,	PUNCT
american_scientific_journal-2676	235	5	we	we	PRON
american_scientific_journal-2676	235	6	have	have	VERB
american_scientific_journal-2676	235	7	c	c	NOUN
american_scientific_journal-2676	235	8	d	d	X
american_scientific_journal-2676	235	9	ef	ef	PROPN
american_scientific_journal-2676	235	10	)	)	PUNCT
american_scientific_journal-2676	235	11	,	,	PUNCT
american_scientific_journal-2676	235	12	(	(	PUNCT
american_scientific_journal-2676	235	13	~0	~0	NUM
american_scientific_journal-2676	235	14	∈	∈	NOUN
american_scientific_journal-2676	235	15	.	.	PUNCT
american_scientific_journal-2676	236	1	but	but	CCONJ
american_scientific_journal-2676	236	2	,	,	PUNCT
american_scientific_journal-2676	236	3	)	)	PUNCT
american_scientific_journal-2676	236	4	,	,	PUNCT
american_scientific_journal-2676	236	5	(	(	PUNCT
american_scientific_journal-2676	236	6	ef	ef	PROPN
american_scientific_journal-2676	236	7	is	be	AUX
american_scientific_journal-2676	236	8	finite	finite	ADJ
american_scientific_journal-2676	236	9	soft	soft	ADJ
american_scientific_journal-2676	236	10	set	set	NOUN
american_scientific_journal-2676	236	11	,	,	PUNCT
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american_scientific_journal-2676	236	13	cef	cef	PROPN
american_scientific_journal-2676	236	14	)	)	PUNCT
american_scientific_journal-2676	236	15	,	,	PUNCT
american_scientific_journal-2676	236	16	(	(	PUNCT
american_scientific_journal-2676	236	17	is	be	AUX
american_scientific_journal-2676	236	18	an	an	DET
american_scientific_journal-2676	236	19	open	open	ADJ
american_scientific_journal-2676	236	20	soft	soft	ADJ
american_scientific_journal-2676	236	21	set	set	NOUN
american_scientific_journal-2676	236	22	.	.	PUNCT
american_scientific_journal-2676	237	1	it	it	PRON
american_scientific_journal-2676	237	2	follows	follow	VERB
american_scientific_journal-2676	237	3	that	that	PRON
american_scientific_journal-2676	237	4	)	)	PUNCT
american_scientific_journal-2676	237	5	,	,	PUNCT
american_scientific_journal-2676	237	6	(	(	PUNCT
american_scientific_journal-2676	237	7	ef	ef	PROPN
american_scientific_journal-2676	237	8	is	be	AUX
american_scientific_journal-2676	237	9	a	a	DET
american_scientific_journal-2676	237	10	closed	closed	ADJ
american_scientific_journal-2676	237	11	soft	soft	ADJ
american_scientific_journal-2676	237	12	set	set	NOUN
american_scientific_journal-2676	237	13	.	.	PUNCT
american_scientific_journal-2676	238	1	take	take	VERB
american_scientific_journal-2676	238	2	)	)	PUNCT
american_scientific_journal-2676	238	3	,	,	PUNCT
american_scientific_journal-2676	238	4	(	(	PUNCT
american_scientific_journal-2676	238	5	=)	=)	INTJ
american_scientific_journal-2676	238	6	,	,	PUNCT
american_scientific_journal-2676	238	7	(	(	PUNCT
american_scientific_journal-2676	238	8	efem	efem	PROPN
american_scientific_journal-2676	238	9	ex	ex	X
american_scientific_journal-2676	238	10	.	.	PUNCT
american_scientific_journal-2676	239	1	case(2	case(2	NOUN
american_scientific_journal-2676	239	2	):	):	PUNCT
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american_scientific_journal-2676	239	4	0≠	0≠	NUM
american_scientific_journal-2676	239	5	,	,	PUNCT
american_scientific_journal-2676	239	6	0≠x	0≠x	NUM
american_scientific_journal-2676	239	7	and	and	CCONJ
american_scientific_journal-2676	239	8	)	)	PUNCT
american_scientific_journal-2676	239	9	,	,	PUNCT
american_scientific_journal-2676	239	10	(	(	PUNCT
american_scientific_journal-2676	239	11	~0	~0	NUM
american_scientific_journal-2676	239	12	efd	efd	PROPN
american_scientific_journal-2676	239	13	∈	∈	PROPN
american_scientific_journal-2676	239	14	.	.	PUNCT
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american_scientific_journal-2676	240	3	case	case	NOUN
american_scientific_journal-2676	240	4	,	,	PUNCT
american_scientific_journal-2676	240	5	we	we	PRON
american_scientific_journal-2676	240	6	have	have	VERB
american_scientific_journal-2676	240	7	c	c	NOUN
american_scientific_journal-2676	240	8	ed	ed	NOUN
american_scientific_journal-2676	240	9	ex	ex	X
american_scientific_journal-2676	240	10	)	)	PUNCT
american_scientific_journal-2676	240	11	,	,	PUNCT
american_scientific_journal-2676	240	12	(	(	PUNCT
american_scientific_journal-2676	240	13	~0	~0	NUM
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american_scientific_journal-2676	240	15	.	.	PUNCT
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american_scientific_journal-2676	241	2	,	,	PUNCT
american_scientific_journal-2676	241	3	c	c	PROPN
american_scientific_journal-2676	241	4	e	e	X
american_scientific_journal-2676	241	5	ex	ex	X
american_scientific_journal-2676	241	6	)	)	PUNCT
american_scientific_journal-2676	241	7	,	,	PUNCT
american_scientific_journal-2676	241	8	(	(	PUNCT
american_scientific_journal-2676	241	9	is	be	AUX
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american_scientific_journal-2676	241	11	open	open	ADJ
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american_scientific_journal-2676	241	14	,	,	PUNCT
american_scientific_journal-2676	241	15	c	c	PROPN
american_scientific_journal-2676	241	16	e	e	NOUN
american_scientific_journal-2676	241	17	exef	exef	PROPN
american_scientific_journal-2676	241	18	)	)	PUNCT
american_scientific_journal-2676	241	19	,	,	PUNCT
american_scientific_journal-2676	241	20	(	(	PUNCT
american_scientific_journal-2676	241	21	~	~	NOUN
american_scientific_journal-2676	241	22	)	)	PUNCT
american_scientific_journal-2676	241	23	,	,	PUNCT
american_scientific_journal-2676	241	24	(	(	PUNCT
american_scientific_journal-2676	241	25	⊆	⊆	NUM
american_scientific_journal-2676	241	26	and	and	CCONJ
american_scientific_journal-2676	241	27	c	c	PROPN
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american_scientific_journal-2676	241	29	exx	exx	PROPN
american_scientific_journal-2676	241	30	)	)	PUNCT
american_scientific_journal-2676	241	31	,	,	PUNCT
american_scientific_journal-2676	241	32	(	(	PUNCT
american_scientific_journal-2676	241	33	~∈/	~∈/	ADV
american_scientific_journal-2676	241	34	.	.	PUNCT
american_scientific_journal-2676	242	1	take	take	VERB
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american_scientific_journal-2676	242	3	e	e	X
american_scientific_journal-2676	242	4	ex	ex	X
american_scientific_journal-2676	242	5	exem	exem	ADJ
american_scientific_journal-2676	242	6	)	)	PUNCT
american_scientific_journal-2676	242	7	,	,	PUNCT
american_scientific_journal-2676	242	8	(	(	PUNCT
american_scientific_journal-2676	242	9	=)	=)	INTJ
american_scientific_journal-2676	242	10	,	,	PUNCT
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american_scientific_journal-2676	243	4	0≠	0≠	NUM
american_scientific_journal-2676	243	5	,	,	PUNCT
american_scientific_journal-2676	243	6	0	0	PUNCT
american_scientific_journal-2676	243	7	=	=	NOUN
american_scientific_journal-2676	243	8	x	x	X
american_scientific_journal-2676	243	9	.	.	PUNCT
american_scientific_journal-2676	244	1	in	in	ADP
american_scientific_journal-2676	244	2	this	this	DET
american_scientific_journal-2676	244	3	case	case	NOUN
american_scientific_journal-2676	244	4	,	,	PUNCT
american_scientific_journal-2676	244	5	we	we	PRON
american_scientific_journal-2676	244	6	have	have	VERB
american_scientific_journal-2676	244	7	de	de	ADP
american_scientific_journal-2676	244	8	≠	≠	PROPN
american_scientific_journal-2676	244	9	.	.	PUNCT
american_scientific_journal-2676	245	1	so	so	ADV
american_scientific_journal-2676	245	2	,	,	PUNCT
american_scientific_journal-2676	245	3	c	c	PROPN
american_scientific_journal-2676	245	4	ed	ed	NOUN
american_scientific_journal-2676	245	5	ex	ex	X
american_scientific_journal-2676	245	6	)	)	PUNCT
american_scientific_journal-2676	245	7	,	,	PUNCT
american_scientific_journal-2676	245	8	(	(	PUNCT
american_scientific_journal-2676	245	9	~0	~0	NUM
american_scientific_journal-2676	245	10	∈	∈	NOUN
american_scientific_journal-2676	245	11	.	.	PUNCT
american_scientific_journal-2676	246	1	therefore	therefore	ADV
american_scientific_journal-2676	246	2	,	,	PUNCT
american_scientific_journal-2676	246	3	c	c	PROPN
american_scientific_journal-2676	246	4	e	e	X
american_scientific_journal-2676	246	5	ex	ex	X
american_scientific_journal-2676	246	6	)	)	PUNCT
american_scientific_journal-2676	246	7	,	,	PUNCT
american_scientific_journal-2676	246	8	(	(	PUNCT
american_scientific_journal-2676	246	9	is	be	AUX
american_scientific_journal-2676	246	10	an	an	DET
american_scientific_journal-2676	246	11	open	open	ADJ
american_scientific_journal-2676	246	12	soft	soft	ADJ
american_scientific_journal-2676	246	13	set	set	NOUN
american_scientific_journal-2676	246	14	.	.	PUNCT
american_scientific_journal-2676	247	1	take	take	VERB
american_scientific_journal-2676	247	2	c	c	NOUN
american_scientific_journal-2676	247	3	e	e	X
american_scientific_journal-2676	247	4	ex	ex	X
american_scientific_journal-2676	247	5	exem	exem	ADJ
american_scientific_journal-2676	247	6	)	)	PUNCT
american_scientific_journal-2676	247	7	,	,	PUNCT
american_scientific_journal-2676	247	8	(	(	PUNCT
american_scientific_journal-2676	247	9	=)	=)	INTJ
american_scientific_journal-2676	247	10	,	,	PUNCT
american_scientific_journal-2676	247	11	(	(	PUNCT
american_scientific_journal-2676	247	12	.	.	PUNCT
american_scientific_journal-2676	248	1	case(4	case(4	PROPN
american_scientific_journal-2676	248	2	):	):	PUNCT
american_scientific_journal-2676	248	3	dex	dex	NOUN
american_scientific_journal-2676	248	4	0=	0=	NOUN
american_scientific_journal-2676	248	5	.	.	PUNCT
american_scientific_journal-2676	249	1	in	in	ADP
american_scientific_journal-2676	249	2	this	this	DET
american_scientific_journal-2676	249	3	case	case	NOUN
american_scientific_journal-2676	249	4	,	,	PUNCT
american_scientific_journal-2676	249	5	we	we	PRON
american_scientific_journal-2676	249	6	have	have	VERB
american_scientific_journal-2676	249	7	de	de	X
american_scientific_journal-2676	249	8	=	=	X
american_scientific_journal-2676	249	9	and	and	CCONJ
american_scientific_journal-2676	249	10	0	0	NUM
american_scientific_journal-2676	249	11	=	=	NOUN
american_scientific_journal-2676	249	12	x	x	NOUN
american_scientific_journal-2676	249	13	implies	imply	VERB
american_scientific_journal-2676	249	14	)	)	PUNCT
american_scientific_journal-2676	249	15	,	,	PUNCT
american_scientific_journal-2676	249	16	(	(	PUNCT
american_scientific_journal-2676	249	17	~0	~0	NUM
american_scientific_journal-2676	249	18	efd	efd	PROPN
american_scientific_journal-2676	249	19	∈/	∈/	PROPN
american_scientific_journal-2676	249	20	.	.	PUNCT
american_scientific_journal-2676	250	1	therefore	therefore	ADV
american_scientific_journal-2676	250	2	,	,	PUNCT
american_scientific_journal-2676	250	3	cef	cef	PROPN
american_scientific_journal-2676	250	4	)	)	PUNCT
american_scientific_journal-2676	250	5	,	,	PUNCT
american_scientific_journal-2676	250	6	(	(	PUNCT
american_scientific_journal-2676	250	7	is	be	AUX
american_scientific_journal-2676	250	8	an	an	DET
american_scientific_journal-2676	250	9	open	open	ADJ
american_scientific_journal-2676	250	10	soft	soft	ADJ
american_scientific_journal-2676	250	11	set	set	NOUN
american_scientific_journal-2676	250	12	.	.	PUNCT
american_scientific_journal-2676	251	1	it	it	PRON
american_scientific_journal-2676	251	2	follows	follow	VERB
american_scientific_journal-2676	251	3	that	that	PRON
american_scientific_journal-2676	251	4	)	)	PUNCT
american_scientific_journal-2676	251	5	,	,	PUNCT
american_scientific_journal-2676	251	6	(	(	PUNCT
american_scientific_journal-2676	251	7	ef	ef	PROPN
american_scientific_journal-2676	251	8	is	be	AUX
american_scientific_journal-2676	251	9	a	a	DET
american_scientific_journal-2676	251	10	closed	closed	ADJ
american_scientific_journal-2676	251	11	soft	soft	ADJ
american_scientific_journal-2676	251	12	set	set	NOUN
american_scientific_journal-2676	251	13	.	.	PUNCT
american_scientific_journal-2676	252	1	take	take	VERB
american_scientific_journal-2676	252	2	)	)	PUNCT
american_scientific_journal-2676	252	3	,	,	PUNCT
american_scientific_journal-2676	252	4	(	(	PUNCT
american_scientific_journal-2676	252	5	=)	=)	INTJ
american_scientific_journal-2676	252	6	,	,	PUNCT
american_scientific_journal-2676	252	7	(	(	PUNCT
american_scientific_journal-2676	252	8	efem	efem	PROPN
american_scientific_journal-2676	252	9	ex	ex	X
american_scientific_journal-2676	252	10	.	.	PUNCT
american_scientific_journal-2676	253	1	consequently	consequently	ADV
american_scientific_journal-2676	253	2	,	,	PUNCT
american_scientific_journal-2676	253	3	)	)	PUNCT
american_scientific_journal-2676	253	4	,	,	PUNCT
american_scientific_journal-2676	253	5	,	,	PUNCT
american_scientific_journal-2676	253	6	(	(	PUNCT
american_scientific_journal-2676	253	7	ez	ez	X
american_scientific_journal-2676	253	8	dη	dη	NOUN
american_scientific_journal-2676	253	9	is	be	AUX
american_scientific_journal-2676	253	10	a	a	DET
american_scientific_journal-2676	253	11	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	253	12	4	4	NUM
american_scientific_journal-2676	253	13	�	�	PROPN
american_scientific_journal-2676	253	14	.	.	PUNCT
american_scientific_journal-2676	254	1	theorem	theorem	VERB
american_scientific_journal-2676	254	2	3.3	3.3	NUM
american_scientific_journal-2676	254	3	let	let	NOUN
american_scientific_journal-2676	254	4	)	)	PUNCT
american_scientific_journal-2676	254	5	,	,	PUNCT
american_scientific_journal-2676	254	6	,	,	PUNCT
american_scientific_journal-2676	254	7	(	(	PUNCT
american_scientific_journal-2676	254	8	ex	ex	X
american_scientific_journal-2676	254	9	η	η	PROPN
american_scientific_journal-2676	254	10	be	be	AUX
american_scientific_journal-2676	254	11	a	a	DET
american_scientific_journal-2676	254	12	soft	soft	ADJ
american_scientific_journal-2676	254	13	topological	topological	ADJ
american_scientific_journal-2676	254	14	space	space	NOUN
american_scientific_journal-2676	254	15	.	.	PUNCT
american_scientific_journal-2676	255	1	then	then	ADV
american_scientific_journal-2676	255	2	,	,	PUNCT
american_scientific_journal-2676	255	3	american	american	ADJ
american_scientific_journal-2676	255	4	scientific	scientific	ADJ
american_scientific_journal-2676	255	5	research	research	NOUN
american_scientific_journal-2676	255	6	journal	journal	NOUN
american_scientific_journal-2676	255	7	for	for	ADP
american_scientific_journal-2676	255	8	engineering	engineering	NOUN
american_scientific_journal-2676	255	9	,	,	PUNCT
american_scientific_journal-2676	255	10	technology	technology	NOUN
american_scientific_journal-2676	255	11	,	,	PUNCT
american_scientific_journal-2676	255	12	and	and	CCONJ
american_scientific_journal-2676	255	13	sciences	science	NOUN
american_scientific_journal-2676	255	14	(	(	PUNCT
american_scientific_journal-2676	255	15	asrjets	asrjet	NOUN
american_scientific_journal-2676	255	16	)	)	PUNCT
american_scientific_journal-2676	255	17	(	(	PUNCT
american_scientific_journal-2676	255	18	2017	2017	NUM
american_scientific_journal-2676	255	19	)	)	PUNCT
american_scientific_journal-2676	255	20	volume	volume	NOUN
american_scientific_journal-2676	255	21	28	28	NUM
american_scientific_journal-2676	255	22	,	,	PUNCT
american_scientific_journal-2676	255	23	no	no	DET
american_scientific_journal-2676	255	24	1	1	NUM
american_scientific_journal-2676	255	25	,	,	PUNCT
american_scientific_journal-2676	255	26	pp	pp	ADV
american_scientific_journal-2676	255	27	225	225	NUM
american_scientific_journal-2676	255	28	-	-	SYM
american_scientific_journal-2676	255	29	247	247	NUM
american_scientific_journal-2676	255	30	236	236	NUM
american_scientific_journal-2676	255	31	1	1	NUM
american_scientific_journal-2676	255	32	)	)	PUNCT
american_scientific_journal-2676	255	33	if	if	SCONJ
american_scientific_journal-2676	255	34	)	)	PUNCT
american_scientific_journal-2676	255	35	,	,	PUNCT
american_scientific_journal-2676	255	36	,	,	PUNCT
american_scientific_journal-2676	255	37	(	(	PUNCT
american_scientific_journal-2676	255	38	ex	ex	X
american_scientific_journal-2676	255	39	η	η	PROPN
american_scientific_journal-2676	255	40	is	be	AUX
american_scientific_journal-2676	255	41	a	a	DET
american_scientific_journal-2676	255	42	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	255	43	4	4	NUM
american_scientific_journal-2676	255	44	�	�	PROPN
american_scientific_journal-2676	255	45	,	,	PUNCT
american_scientific_journal-2676	255	46	then	then	ADV
american_scientific_journal-2676	255	47	it	it	PRON
american_scientific_journal-2676	255	48	is	be	AUX
american_scientific_journal-2676	255	49	0st	0st	ADJ
american_scientific_journal-2676	255	50	.	.	PUNCT
american_scientific_journal-2676	256	1	2	2	X
american_scientific_journal-2676	256	2	)	)	PUNCT
american_scientific_journal-2676	256	3	if	if	SCONJ
american_scientific_journal-2676	256	4	)	)	PUNCT
american_scientific_journal-2676	256	5	,	,	PUNCT
american_scientific_journal-2676	256	6	,	,	PUNCT
american_scientific_journal-2676	256	7	(	(	PUNCT
american_scientific_journal-2676	256	8	ex	ex	X
american_scientific_journal-2676	256	9	η	η	PROPN
american_scientific_journal-2676	256	10	is	be	AUX
american_scientific_journal-2676	256	11	a	a	DET
american_scientific_journal-2676	256	12	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	256	13	2	2	NUM
american_scientific_journal-2676	256	14	�	�	PROPN
american_scientific_journal-2676	256	15	,	,	PUNCT
american_scientific_journal-2676	256	16	then	then	ADV
american_scientific_journal-2676	256	17	it	it	PRON
american_scientific_journal-2676	256	18	is	be	AUX
american_scientific_journal-2676	256	19	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	256	20	4	4	NUM
american_scientific_journal-2676	256	21	�	�	PROPN
american_scientific_journal-2676	256	22	.	.	PUNCT
american_scientific_journal-2676	257	1	proof	proof	NOUN
american_scientific_journal-2676	257	2	.	.	PUNCT
american_scientific_journal-2676	258	1	straightforward	straightforward	ADJ
american_scientific_journal-2676	258	2	.	.	PUNCT
american_scientific_journal-2676	259	1	definition	definition	NOUN
american_scientific_journal-2676	259	2	3.2	3.2	NUM
american_scientific_journal-2676	259	3	a	a	DET
american_scientific_journal-2676	259	4	sbts	sbts	ADJ
american_scientific_journal-2676	259	5	)	)	PUNCT
american_scientific_journal-2676	259	6	,	,	PUNCT
american_scientific_journal-2676	259	7	,	,	PUNCT
american_scientific_journal-2676	259	8	,	,	PUNCT
american_scientific_journal-2676	259	9	(	(	PUNCT
american_scientific_journal-2676	259	10	21	21	NUM
american_scientific_journal-2676	259	11	ex	ex	X
american_scientific_journal-2676	259	12	ηη	ηη	PROPN
american_scientific_journal-2676	259	13	is	be	AUX
american_scientific_journal-2676	259	14	said	say	VERB
american_scientific_journal-2676	259	15	to	to	PART
american_scientific_journal-2676	259	16	be	be	AUX
american_scientific_journal-2676	259	17	a	a	DET
american_scientific_journal-2676	259	18	pairwise	pairwise	NOUN
american_scientific_journal-2676	259	19	soft	soft	ADJ
american_scientific_journal-2676	259	20	𝑇𝑇1	𝑇𝑇1	PROPN
american_scientific_journal-2676	259	21	4	4	NUM
american_scientific_journal-2676	259	22	�	�	NOUN
american_scientific_journal-2676	259	23	∗	∗	NOUN
american_scientific_journal-2676	259	24	[	[	X
american_scientific_journal-2676	259	25	briefly	briefly	NOUN
american_scientific_journal-2676	259	26	,	,	PUNCT
american_scientific_journal-2676	259	27	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	259	28	4	4	NUM
american_scientific_journal-2676	259	29	�	�	PROPN
american_scientific_journal-2676	259	30	∗	∗	NOUN
american_scientific_journal-2676	259	31	]	]	PUNCT
american_scientific_journal-2676	259	32	if	if	SCONJ
american_scientific_journal-2676	259	33	for	for	ADP
american_scientific_journal-2676	259	34	every	every	DET
american_scientific_journal-2676	259	35	finite	finite	ADJ
american_scientific_journal-2676	259	36	soft	soft	ADJ
american_scientific_journal-2676	259	37	set	set	NOUN
american_scientific_journal-2676	259	38	)	)	PUNCT
american_scientific_journal-2676	259	39	,	,	PUNCT
american_scientific_journal-2676	259	40	(	(	PUNCT
american_scientific_journal-2676	259	41	eg	eg	NOUN
american_scientific_journal-2676	259	42	over	over	ADP
american_scientific_journal-2676	259	43	x	x	PUNCT
american_scientific_journal-2676	259	44	and	and	CCONJ
american_scientific_journal-2676	259	45	every	every	PRON
american_scientific_journal-2676	259	46	)	)	PUNCT
american_scientific_journal-2676	259	47	,	,	PUNCT
american_scientific_journal-2676	259	48	(	(	PUNCT
american_scientific_journal-2676	259	49	~	~	PUNCT
american_scientific_journal-2676	259	50	egxe	egxe	NOUN
american_scientific_journal-2676	259	51	∈/	∈/	NOUN
american_scientific_journal-2676	259	52	,	,	PUNCT
american_scientific_journal-2676	259	53	there	there	PRON
american_scientific_journal-2676	259	54	exists	exist	VERB
american_scientific_journal-2676	259	55	a	a	DET
american_scientific_journal-2676	259	56	soft	soft	ADJ
american_scientific_journal-2676	259	57	set	set	NOUN
american_scientific_journal-2676	259	58	cex	cex	NOUN
american_scientific_journal-2676	259	59	em	em	PRON
american_scientific_journal-2676	259	60	1212	1212	NUM
american_scientific_journal-2676	259	61	)	)	PUNCT
american_scientific_journal-2676	259	62	,	,	PUNCT
american_scientific_journal-2676	259	63	(	(	PUNCT
american_scientific_journal-2676	259	64	ηη	ηη	PROPN
american_scientific_journal-2676	259	65	∈	∈	PROPN
american_scientific_journal-2676	259	66	such	such	ADJ
american_scientific_journal-2676	259	67	that	that	PRON
american_scientific_journal-2676	259	68	)	)	PUNCT
american_scientific_journal-2676	259	69	,	,	PUNCT
american_scientific_journal-2676	259	70	(	(	PUNCT
american_scientific_journal-2676	259	71	~	~	PUNCT
american_scientific_journal-2676	259	72	emx	emx	NOUN
american_scientific_journal-2676	259	73	ex	ex	ADJ
american_scientific_journal-2676	259	74	e	e	NOUN
american_scientific_journal-2676	259	75	∈/	∈/	PROPN
american_scientific_journal-2676	259	76	and	and	CCONJ
american_scientific_journal-2676	259	77	)	)	PUNCT
american_scientific_journal-2676	259	78	,	,	PUNCT
american_scientific_journal-2676	259	79	(	(	PUNCT
american_scientific_journal-2676	259	80	~	~	NOUN
american_scientific_journal-2676	259	81	)	)	PUNCT
american_scientific_journal-2676	259	82	,	,	PUNCT
american_scientific_journal-2676	259	83	(	(	PUNCT
american_scientific_journal-2676	259	84	emeg	emeg	NOUN
american_scientific_journal-2676	259	85	ex⊆	ex⊆	NOUN
american_scientific_journal-2676	259	86	.	.	PUNCT
american_scientific_journal-2676	260	1	theorem	theorem	VERB
american_scientific_journal-2676	260	2	3.4	3.4	NUM
american_scientific_journal-2676	260	3	let	let	NOUN
american_scientific_journal-2676	260	4	)	)	PUNCT
american_scientific_journal-2676	260	5	,	,	PUNCT
american_scientific_journal-2676	260	6	,	,	PUNCT
american_scientific_journal-2676	260	7	,	,	PUNCT
american_scientific_journal-2676	260	8	(	(	PUNCT
american_scientific_journal-2676	260	9	21	21	NUM
american_scientific_journal-2676	260	10	ex	ex	X
american_scientific_journal-2676	260	11	ηη	ηη	PROPN
american_scientific_journal-2676	260	12	be	be	AUX
american_scientific_journal-2676	260	13	a	a	DET
american_scientific_journal-2676	260	14	sbts	sbts	ADJ
american_scientific_journal-2676	260	15	.	.	PUNCT
american_scientific_journal-2676	261	1	then	then	ADV
american_scientific_journal-2676	261	2	,	,	PUNCT
american_scientific_journal-2676	261	3	)	)	PUNCT
american_scientific_journal-2676	261	4	,	,	PUNCT
american_scientific_journal-2676	261	5	,	,	PUNCT
american_scientific_journal-2676	261	6	,	,	PUNCT
american_scientific_journal-2676	261	7	(	(	PUNCT
american_scientific_journal-2676	261	8	21	21	NUM
american_scientific_journal-2676	261	9	ex	ex	X
american_scientific_journal-2676	261	10	ηη	ηη	PROPN
american_scientific_journal-2676	261	11	is	be	AUX
american_scientific_journal-2676	261	12	a	a	DET
american_scientific_journal-2676	261	13	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	261	14	4	4	NUM
american_scientific_journal-2676	261	15	�	�	PROPN
american_scientific_journal-2676	261	16	∗	∗	NOUN
american_scientific_journal-2676	261	17	iff	iff	VERB
american_scientific_journal-2676	261	18	every	every	DET
american_scientific_journal-2676	261	19	finite	finite	PROPN
american_scientific_journal-2676	261	20	soft	soft	ADJ
american_scientific_journal-2676	261	21	set	set	NOUN
american_scientific_journal-2676	261	22	is	be	AUX
american_scientific_journal-2676	261	23	a	a	DET
american_scientific_journal-2676	261	24	λp	λp	ADV
american_scientific_journal-2676	261	25	-closed	-close	VERB
american_scientific_journal-2676	261	26	soft	soft	ADJ
american_scientific_journal-2676	261	27	set	set	NOUN
american_scientific_journal-2676	261	28	.	.	PUNCT
american_scientific_journal-2676	262	1	proof	proof	NOUN
american_scientific_journal-2676	262	2	.	.	PUNCT
american_scientific_journal-2676	263	1	let	let	VERB
american_scientific_journal-2676	263	2	)	)	PUNCT
american_scientific_journal-2676	263	3	,	,	PUNCT
american_scientific_journal-2676	263	4	(	(	PUNCT
american_scientific_journal-2676	263	5	eg	eg	NOUN
american_scientific_journal-2676	263	6	be	be	AUX
american_scientific_journal-2676	263	7	a	a	DET
american_scientific_journal-2676	263	8	finite	finite	NOUN
american_scientific_journal-2676	263	9	soft	soft	ADJ
american_scientific_journal-2676	263	10	set	set	NOUN
american_scientific_journal-2676	263	11	over	over	ADP
american_scientific_journal-2676	263	12	x	x	PROPN
american_scientific_journal-2676	263	13	.	.	PUNCT
american_scientific_journal-2676	264	1	since	since	SCONJ
american_scientific_journal-2676	264	2	,	,	PUNCT
american_scientific_journal-2676	264	3	)	)	PUNCT
american_scientific_journal-2676	264	4	,	,	PUNCT
american_scientific_journal-2676	264	5	,	,	PUNCT
american_scientific_journal-2676	264	6	,	,	PUNCT
american_scientific_journal-2676	264	7	(	(	PUNCT
american_scientific_journal-2676	264	8	21	21	NUM
american_scientific_journal-2676	264	9	ex	ex	X
american_scientific_journal-2676	264	10	ηη	ηη	PROPN
american_scientific_journal-2676	264	11	is	be	AUX
american_scientific_journal-2676	264	12	a	a	DET
american_scientific_journal-2676	264	13	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	264	14	4	4	NUM
american_scientific_journal-2676	264	15	�	�	PROPN
american_scientific_journal-2676	264	16	∗	∗	NOUN
american_scientific_journal-2676	264	17	,	,	PUNCT
american_scientific_journal-2676	264	18	then	then	ADV
american_scientific_journal-2676	264	19	for	for	ADP
american_scientific_journal-2676	264	20	every	every	PRON
american_scientific_journal-2676	264	21	)	)	PUNCT
american_scientific_journal-2676	264	22	,	,	PUNCT
american_scientific_journal-2676	264	23	(	(	PUNCT
american_scientific_journal-2676	264	24	~	~	PUNCT
american_scientific_journal-2676	264	25	egxe	egxe	NOUN
american_scientific_journal-2676	264	26	∈/	∈/	NOUN
american_scientific_journal-2676	264	27	there	there	PRON
american_scientific_journal-2676	264	28	exist	exist	VERB
american_scientific_journal-2676	264	29	cex	cex	NOUN
american_scientific_journal-2676	264	30	em	em	PRON
american_scientific_journal-2676	264	31	1212	1212	NUM
american_scientific_journal-2676	264	32	)	)	PUNCT
american_scientific_journal-2676	264	33	,	,	PUNCT
american_scientific_journal-2676	264	34	(	(	PUNCT
american_scientific_journal-2676	264	35	ηη	ηη	PROPN
american_scientific_journal-2676	264	36	∈	∈	PROPN
american_scientific_journal-2676	264	37	such	such	ADJ
american_scientific_journal-2676	264	38	that	that	PRON
american_scientific_journal-2676	264	39	)	)	PUNCT
american_scientific_journal-2676	264	40	,	,	PUNCT
american_scientific_journal-2676	264	41	(	(	PUNCT
american_scientific_journal-2676	264	42	~	~	PUNCT
american_scientific_journal-2676	264	43	emx	emx	NOUN
american_scientific_journal-2676	264	44	ex	ex	ADJ
american_scientific_journal-2676	264	45	e	e	NOUN
american_scientific_journal-2676	264	46	∈/	∈/	PROPN
american_scientific_journal-2676	264	47	and	and	CCONJ
american_scientific_journal-2676	264	48	)	)	PUNCT
american_scientific_journal-2676	264	49	,	,	PUNCT
american_scientific_journal-2676	264	50	(	(	PUNCT
american_scientific_journal-2676	264	51	~	~	NOUN
american_scientific_journal-2676	264	52	)	)	PUNCT
american_scientific_journal-2676	264	53	,	,	PUNCT
american_scientific_journal-2676	264	54	(	(	PUNCT
american_scientific_journal-2676	264	55	emeg	emeg	NOUN
american_scientific_journal-2676	264	56	ex⊆	ex⊆	NOUN
american_scientific_journal-2676	264	57	.	.	PUNCT
american_scientific_journal-2676	265	1	set	set	VERB
american_scientific_journal-2676	265	2	)	)	PUNCT
american_scientific_journal-2676	265	3	}	}	PUNCT
american_scientific_journal-2676	265	4	,	,	PUNCT
american_scientific_journal-2676	265	5	(	(	PUNCT
american_scientific_journal-2676	265	6	~),(),,(~:),{(=	~),(),,(~:),{(=	NUM
american_scientific_journal-2676	265	7	)	)	PUNCT
american_scientific_journal-2676	265	8	,	,	PUNCT
american_scientific_journal-2676	265	9	(	(	PUNCT
american_scientific_journal-2676	265	10	12),(~	12),(~	NUM
american_scientific_journal-2676	265	11	emegemxemeh	emegemxemeh	NOUN
american_scientific_journal-2676	265	12	exex	exex	NOUN
american_scientific_journal-2676	265	13	e	e	PROPN
american_scientific_journal-2676	265	14	ex	ex	NOUN
american_scientific_journal-2676	265	15	egex	egex	NOUN
american_scientific_journal-2676	265	16	⊆∈/∈	⊆∈/∈	VERB
american_scientific_journal-2676	265	17	∈/	∈/	PROPN
american_scientific_journal-2676	265	18	η	η	PROPN
american_scientific_journal-2676	265	19	and	and	CCONJ
american_scientific_journal-2676	265	20	)	)	PUNCT
american_scientific_journal-2676	265	21	}	}	PUNCT
american_scientific_journal-2676	265	22	,	,	PUNCT
american_scientific_journal-2676	265	23	(	(	PUNCT
american_scientific_journal-2676	265	24	~),(),,(~:),{(=	~),(),,(~:),{(=	NUM
american_scientific_journal-2676	265	25	)	)	PUNCT
american_scientific_journal-2676	265	26	,	,	PUNCT
american_scientific_journal-2676	265	27	(	(	PUNCT
american_scientific_journal-2676	265	28	12),(~	12),(~	NUM
american_scientific_journal-2676	265	29	emegemxemef	emegemxemef	NOUN
american_scientific_journal-2676	265	30	exex	exex	PROPN
american_scientific_journal-2676	265	31	e	e	PROPN
american_scientific_journal-2676	265	32	cex	cex	PROPN
american_scientific_journal-2676	265	33	egex	egex	NOUN
american_scientific_journal-2676	265	34	⊆∈/∈	⊆∈/∈	VERB
american_scientific_journal-2676	265	35	∈/	∈/	PROPN
american_scientific_journal-2676	265	36	η	η	PROPN
american_scientific_journal-2676	265	37	.	.	PUNCT
american_scientific_journal-2676	266	1	it	it	PRON
american_scientific_journal-2676	266	2	is	be	AUX
american_scientific_journal-2676	266	3	clear	clear	ADJ
american_scientific_journal-2676	266	4	that	that	SCONJ
american_scientific_journal-2676	266	5	)	)	PUNCT
american_scientific_journal-2676	266	6	,	,	PUNCT
american_scientific_journal-2676	266	7	(	(	PUNCT
american_scientific_journal-2676	266	8	eh	eh	INTJ
american_scientific_journal-2676	266	9	is	be	AUX
american_scientific_journal-2676	266	10	a	a	DET
american_scientific_journal-2676	266	11	λp	λp	X
american_scientific_journal-2676	266	12	-soft	-soft	NOUN
american_scientific_journal-2676	266	13	set	set	VERB
american_scientific_journal-2676	266	14	and	and	CCONJ
american_scientific_journal-2676	266	15	)	)	PUNCT
american_scientific_journal-2676	266	16	,	,	PUNCT
american_scientific_journal-2676	266	17	(	(	PUNCT
american_scientific_journal-2676	266	18	ef	ef	PROPN
american_scientific_journal-2676	266	19	is	be	AUX
american_scientific_journal-2676	266	20	a	a	DET
american_scientific_journal-2676	266	21	p	p	NOUN
american_scientific_journal-2676	266	22	-closed	-close	VERB
american_scientific_journal-2676	266	23	soft	soft	ADJ
american_scientific_journal-2676	266	24	set	set	NOUN
american_scientific_journal-2676	266	25	.	.	PUNCT
american_scientific_journal-2676	267	1	moreover	moreover	ADV
american_scientific_journal-2676	267	2	,	,	PUNCT
american_scientific_journal-2676	267	3	)	)	PUNCT
american_scientific_journal-2676	267	4	,	,	PUNCT
american_scientific_journal-2676	267	5	(	(	PUNCT
american_scientific_journal-2676	267	6	~),(=	~),(=	NUM
american_scientific_journal-2676	267	7	)	)	PUNCT
american_scientific_journal-2676	267	8	,	,	PUNCT
american_scientific_journal-2676	267	9	(	(	PUNCT
american_scientific_journal-2676	267	10	efeheg	efeheg	NOUN
american_scientific_journal-2676	267	11	∩	∩	NOUN
american_scientific_journal-2676	267	12	,	,	PUNCT
american_scientific_journal-2676	267	13	therefore	therefore	ADV
american_scientific_journal-2676	267	14	,	,	PUNCT
american_scientific_journal-2676	267	15	)	)	PUNCT
american_scientific_journal-2676	267	16	,	,	PUNCT
american_scientific_journal-2676	267	17	(	(	PUNCT
american_scientific_journal-2676	267	18	eg	eg	NOUN
american_scientific_journal-2676	267	19	is	be	AUX
american_scientific_journal-2676	267	20	a	a	DET
american_scientific_journal-2676	267	21	λp	λp	ADV
american_scientific_journal-2676	267	22	-closed	-close	VERB
american_scientific_journal-2676	267	23	soft	soft	ADJ
american_scientific_journal-2676	267	24	set	set	NOUN
american_scientific_journal-2676	267	25	.	.	PUNCT
american_scientific_journal-2676	268	1	conversely	conversely	ADV
american_scientific_journal-2676	268	2	,	,	PUNCT
american_scientific_journal-2676	268	3	let	let	VERB
american_scientific_journal-2676	268	4	)	)	PUNCT
american_scientific_journal-2676	268	5	,	,	PUNCT
american_scientific_journal-2676	268	6	(	(	PUNCT
american_scientific_journal-2676	268	7	eg	eg	NOUN
american_scientific_journal-2676	268	8	be	be	AUX
american_scientific_journal-2676	268	9	a	a	DET
american_scientific_journal-2676	268	10	finite	finite	NOUN
american_scientific_journal-2676	268	11	soft	soft	ADJ
american_scientific_journal-2676	268	12	set	set	NOUN
american_scientific_journal-2676	268	13	over	over	ADP
american_scientific_journal-2676	268	14	x	x	PUNCT
american_scientific_journal-2676	268	15	and	and	CCONJ
american_scientific_journal-2676	268	16	let	let	VERB
american_scientific_journal-2676	268	17	)	)	PUNCT
american_scientific_journal-2676	268	18	,	,	PUNCT
american_scientific_journal-2676	268	19	(	(	PUNCT
american_scientific_journal-2676	268	20	~	~	PUNCT
american_scientific_journal-2676	268	21	egxe	egxe	NOUN
american_scientific_journal-2676	268	22	∈/	∈/	PROPN
american_scientific_journal-2676	268	23	.	.	PUNCT
american_scientific_journal-2676	269	1	since	since	SCONJ
american_scientific_journal-2676	269	2	)	)	PUNCT
american_scientific_journal-2676	269	3	,	,	PUNCT
american_scientific_journal-2676	269	4	(	(	PUNCT
american_scientific_journal-2676	269	5	eg	eg	NOUN
american_scientific_journal-2676	269	6	is	be	AUX
american_scientific_journal-2676	269	7	a	a	DET
american_scientific_journal-2676	269	8	λp	λp	ADV
american_scientific_journal-2676	269	9	-closed	-close	VERB
american_scientific_journal-2676	269	10	soft	soft	ADJ
american_scientific_journal-2676	269	11	set	set	NOUN
american_scientific_journal-2676	269	12	,	,	PUNCT
american_scientific_journal-2676	269	13	then	then	ADV
american_scientific_journal-2676	269	14	)	)	PUNCT
american_scientific_journal-2676	269	15	,	,	PUNCT
american_scientific_journal-2676	269	16	(	(	PUNCT
american_scientific_journal-2676	269	17	~),(=	~),(=	NUM
american_scientific_journal-2676	269	18	)	)	PUNCT
american_scientific_journal-2676	269	19	,	,	PUNCT
american_scientific_journal-2676	269	20	(	(	PUNCT
american_scientific_journal-2676	269	21	efeheg	efeheg	NOUN
american_scientific_journal-2676	269	22	∩	∩	NOUN
american_scientific_journal-2676	269	23	,	,	PUNCT
american_scientific_journal-2676	269	24	where	where	SCONJ
american_scientific_journal-2676	269	25	)	)	PUNCT
american_scientific_journal-2676	269	26	,	,	PUNCT
american_scientific_journal-2676	269	27	(	(	PUNCT
american_scientific_journal-2676	269	28	eh	eh	INTJ
american_scientific_journal-2676	269	29	is	be	AUX
american_scientific_journal-2676	269	30	a	a	DET
american_scientific_journal-2676	269	31	λp	λp	X
american_scientific_journal-2676	269	32	-soft	-soft	NOUN
american_scientific_journal-2676	269	33	set	set	VERB
american_scientific_journal-2676	269	34	and	and	CCONJ
american_scientific_journal-2676	269	35	)	)	PUNCT
american_scientific_journal-2676	269	36	,	,	PUNCT
american_scientific_journal-2676	269	37	(	(	PUNCT
american_scientific_journal-2676	269	38	ef	ef	PROPN
american_scientific_journal-2676	269	39	is	be	AUX
american_scientific_journal-2676	269	40	a	a	DET
american_scientific_journal-2676	269	41	p	p	NOUN
american_scientific_journal-2676	269	42	-closed	-close	VERB
american_scientific_journal-2676	269	43	soft	soft	ADJ
american_scientific_journal-2676	269	44	set	set	NOUN
american_scientific_journal-2676	269	45	.	.	PUNCT
american_scientific_journal-2676	270	1	so	so	ADV
american_scientific_journal-2676	270	2	,	,	PUNCT
american_scientific_journal-2676	270	3	)	)	PUNCT
american_scientific_journal-2676	270	4	,	,	PUNCT
american_scientific_journal-2676	270	5	(	(	PUNCT
american_scientific_journal-2676	270	6	~	~	PUNCT
american_scientific_journal-2676	270	7	ehxe	ehxe	ADJ
american_scientific_journal-2676	270	8	∈/	∈/	PROPN
american_scientific_journal-2676	270	9	or	or	CCONJ
american_scientific_journal-2676	270	10	)	)	PUNCT
american_scientific_journal-2676	270	11	,	,	PUNCT
american_scientific_journal-2676	270	12	(	(	PUNCT
american_scientific_journal-2676	270	13	~	~	PUNCT
american_scientific_journal-2676	270	14	efxe	efxe	NOUN
american_scientific_journal-2676	270	15	∈/	∈/	PROPN
american_scientific_journal-2676	270	16	.	.	PUNCT
american_scientific_journal-2676	271	1	if	if	SCONJ
american_scientific_journal-2676	271	2	)	)	PUNCT
american_scientific_journal-2676	271	3	,	,	PUNCT
american_scientific_journal-2676	271	4	(	(	PUNCT
american_scientific_journal-2676	271	5	~	~	PUNCT
american_scientific_journal-2676	271	6	ehxe	ehxe	ADJ
american_scientific_journal-2676	271	7	∈/	∈/	NOUN
american_scientific_journal-2676	271	8	,	,	PUNCT
american_scientific_journal-2676	271	9	then	then	ADV
american_scientific_journal-2676	271	10	)	)	PUNCT
american_scientific_journal-2676	271	11	,	,	PUNCT
american_scientific_journal-2676	271	12	(	(	PUNCT
american_scientific_journal-2676	271	13	~	~	PUNCT
american_scientific_journal-2676	271	14	12	12	NUM
american_scientific_journal-2676	271	15	ehskerxe	ehskerxe	NOUN
american_scientific_journal-2676	271	16	∈/	∈/	PROPN
american_scientific_journal-2676	271	17	.	.	PUNCT
american_scientific_journal-2676	272	1	it	it	PRON
american_scientific_journal-2676	272	2	follows	follow	VERB
american_scientific_journal-2676	272	3	that	that	SCONJ
american_scientific_journal-2676	272	4	there	there	PRON
american_scientific_journal-2676	272	5	exists	exist	VERB
american_scientific_journal-2676	272	6	a	a	DET
american_scientific_journal-2676	272	7	p	p	NOUN
american_scientific_journal-2676	272	8	-open	-open	ADJ
american_scientific_journal-2676	272	9	soft	soft	ADJ
american_scientific_journal-2676	272	10	set	set	NOUN
american_scientific_journal-2676	272	11	)	)	PUNCT
american_scientific_journal-2676	272	12	,	,	PUNCT
american_scientific_journal-2676	272	13	(	(	PUNCT
american_scientific_journal-2676	272	14	en	en	ADP
american_scientific_journal-2676	272	15	such	such	ADJ
american_scientific_journal-2676	272	16	that	that	PRON
american_scientific_journal-2676	272	17	)	)	PUNCT
american_scientific_journal-2676	272	18	,	,	PUNCT
american_scientific_journal-2676	272	19	(	(	PUNCT
american_scientific_journal-2676	272	20	~	~	NOUN
american_scientific_journal-2676	272	21	)	)	PUNCT
american_scientific_journal-2676	272	22	,	,	PUNCT
american_scientific_journal-2676	272	23	(	(	PUNCT
american_scientific_journal-2676	272	24	eneh	eneh	NOUN
american_scientific_journal-2676	272	25	⊆	⊆	NUM
american_scientific_journal-2676	272	26	and	and	CCONJ
american_scientific_journal-2676	272	27	)	)	PUNCT
american_scientific_journal-2676	272	28	,	,	PUNCT
american_scientific_journal-2676	272	29	(	(	PUNCT
american_scientific_journal-2676	272	30	~	~	PUNCT
american_scientific_journal-2676	272	31	enxe	enxe	PROPN
american_scientific_journal-2676	272	32	∈/	∈/	PROPN
american_scientific_journal-2676	272	33	,	,	PUNCT
american_scientific_journal-2676	272	34	in	in	ADP
american_scientific_journal-2676	272	35	this	this	DET
american_scientific_journal-2676	272	36	case	case	NOUN
american_scientific_journal-2676	272	37	take	take	NOUN
american_scientific_journal-2676	272	38	)	)	PUNCT
american_scientific_journal-2676	272	39	,	,	PUNCT
american_scientific_journal-2676	272	40	(=	(=	NOUN
american_scientific_journal-2676	272	41	)	)	PUNCT
american_scientific_journal-2676	272	42	,	,	PUNCT
american_scientific_journal-2676	272	43	enem	enem	PROPN
american_scientific_journal-2676	273	1	ex	ex	X
american_scientific_journal-2676	273	2	.	.	PUNCT
american_scientific_journal-2676	274	1	if	if	SCONJ
american_scientific_journal-2676	274	2	)	)	PUNCT
american_scientific_journal-2676	274	3	,	,	PUNCT
american_scientific_journal-2676	274	4	(	(	PUNCT
american_scientific_journal-2676	274	5	~	~	PUNCT
american_scientific_journal-2676	274	6	efxe	efxe	NOUN
american_scientific_journal-2676	274	7	∈/	∈/	PROPN
american_scientific_journal-2676	274	8	,	,	PUNCT
american_scientific_journal-2676	274	9	take	take	VERB
american_scientific_journal-2676	274	10	)	)	PUNCT
american_scientific_journal-2676	274	11	,	,	PUNCT
american_scientific_journal-2676	274	12	(=	(=	ADV
american_scientific_journal-2676	274	13	)	)	PUNCT
american_scientific_journal-2676	274	14	,	,	PUNCT
american_scientific_journal-2676	274	15	efem	efem	PROPN
american_scientific_journal-2676	274	16	ex	ex	X
american_scientific_journal-2676	274	17	.	.	PUNCT
american_scientific_journal-2676	275	1	consequently	consequently	ADV
american_scientific_journal-2676	275	2	,	,	PUNCT
american_scientific_journal-2676	275	3	)	)	PUNCT
american_scientific_journal-2676	275	4	,	,	PUNCT
american_scientific_journal-2676	275	5	,	,	PUNCT
american_scientific_journal-2676	275	6	,	,	PUNCT
american_scientific_journal-2676	275	7	(	(	PUNCT
american_scientific_journal-2676	275	8	21	21	NUM
american_scientific_journal-2676	275	9	ex	ex	X
american_scientific_journal-2676	275	10	ηη	ηη	PROPN
american_scientific_journal-2676	275	11	is	be	AUX
american_scientific_journal-2676	275	12	a	a	DET
american_scientific_journal-2676	275	13	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	275	14	4	4	NUM
american_scientific_journal-2676	275	15	�	�	PROPN
american_scientific_journal-2676	275	16	∗	∗	NOUN
american_scientific_journal-2676	275	17	.	.	PUNCT
american_scientific_journal-2676	276	1	theorem	theorem	VERB
american_scientific_journal-2676	276	2	3.5	3.5	NUM
american_scientific_journal-2676	276	3	let	let	NOUN
american_scientific_journal-2676	276	4	)	)	PUNCT
american_scientific_journal-2676	276	5	,	,	PUNCT
american_scientific_journal-2676	276	6	,	,	PUNCT
american_scientific_journal-2676	276	7	,	,	PUNCT
american_scientific_journal-2676	276	8	(	(	PUNCT
american_scientific_journal-2676	276	9	21	21	NUM
american_scientific_journal-2676	276	10	ex	ex	X
american_scientific_journal-2676	276	11	ηη	ηη	PROPN
american_scientific_journal-2676	276	12	be	be	AUX
american_scientific_journal-2676	276	13	a	a	DET
american_scientific_journal-2676	276	14	sbts	sbts	ADJ
american_scientific_journal-2676	276	15	.	.	PUNCT
american_scientific_journal-2676	277	1	then	then	ADV
american_scientific_journal-2676	277	2	,	,	PUNCT
american_scientific_journal-2676	277	3	1	1	X
american_scientific_journal-2676	277	4	)	)	PUNCT
american_scientific_journal-2676	277	5	if	if	SCONJ
american_scientific_journal-2676	277	6	)	)	PUNCT
american_scientific_journal-2676	277	7	,	,	PUNCT
american_scientific_journal-2676	277	8	,	,	PUNCT
american_scientific_journal-2676	277	9	(	(	PUNCT
american_scientific_journal-2676	277	10	1	1	NUM
american_scientific_journal-2676	277	11	ex	ex	X
american_scientific_journal-2676	277	12	η	η	PROPN
american_scientific_journal-2676	277	13	or	or	CCONJ
american_scientific_journal-2676	277	14	)	)	PUNCT
american_scientific_journal-2676	277	15	,	,	PUNCT
american_scientific_journal-2676	277	16	,	,	PUNCT
american_scientific_journal-2676	277	17	(	(	PUNCT
american_scientific_journal-2676	277	18	1	1	NUM
american_scientific_journal-2676	277	19	ex	ex	X
american_scientific_journal-2676	277	20	η	η	PROPN
american_scientific_journal-2676	277	21	is	be	AUX
american_scientific_journal-2676	277	22	a	a	DET
american_scientific_journal-2676	277	23	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	277	24	4	4	NUM
american_scientific_journal-2676	277	25	�	�	PROPN
american_scientific_journal-2676	277	26	,	,	PUNCT
american_scientific_journal-2676	277	27	then	then	ADV
american_scientific_journal-2676	277	28	)	)	PUNCT
american_scientific_journal-2676	277	29	,	,	PUNCT
american_scientific_journal-2676	277	30	,	,	PUNCT
american_scientific_journal-2676	277	31	,	,	PUNCT
american_scientific_journal-2676	277	32	(	(	PUNCT
american_scientific_journal-2676	277	33	21	21	NUM
american_scientific_journal-2676	277	34	ex	ex	X
american_scientific_journal-2676	277	35	ηη	ηη	PROPN
american_scientific_journal-2676	277	36	is	be	AUX
american_scientific_journal-2676	277	37	a	a	DET
american_scientific_journal-2676	277	38	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	277	39	4	4	NUM
american_scientific_journal-2676	277	40	�	�	PROPN
american_scientific_journal-2676	277	41	∗	∗	NOUN
american_scientific_journal-2676	277	42	.	.	PUNCT
american_scientific_journal-2676	278	1	2	2	X
american_scientific_journal-2676	278	2	)	)	PUNCT
american_scientific_journal-2676	278	3	if	if	SCONJ
american_scientific_journal-2676	278	4	)	)	PUNCT
american_scientific_journal-2676	278	5	,	,	PUNCT
american_scientific_journal-2676	278	6	,	,	PUNCT
american_scientific_journal-2676	278	7	,	,	PUNCT
american_scientific_journal-2676	278	8	(	(	PUNCT
american_scientific_journal-2676	278	9	21	21	NUM
american_scientific_journal-2676	278	10	ex	ex	X
american_scientific_journal-2676	278	11	ηη	ηη	PROPN
american_scientific_journal-2676	278	12	is	be	AUX
american_scientific_journal-2676	278	13	a	a	DET
american_scientific_journal-2676	278	14	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	278	15	4	4	NUM
american_scientific_journal-2676	278	16	�	�	PROPN
american_scientific_journal-2676	278	17	∗	∗	NOUN
american_scientific_journal-2676	278	18	,	,	PUNCT
american_scientific_journal-2676	278	19	then	then	ADV
american_scientific_journal-2676	278	20	)	)	PUNCT
american_scientific_journal-2676	278	21	,	,	PUNCT
american_scientific_journal-2676	278	22	,	,	PUNCT
american_scientific_journal-2676	278	23	(	(	PUNCT
american_scientific_journal-2676	278	24	ex	ex	X
american_scientific_journal-2676	278	25	pλη	pλη	NOUN
american_scientific_journal-2676	278	26	is	be	AUX
american_scientific_journal-2676	278	27	a	a	DET
american_scientific_journal-2676	278	28	𝑃𝑃𝑇𝑇1	𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	278	29	4	4	NUM
american_scientific_journal-2676	278	30	�	�	PROPN
american_scientific_journal-2676	278	31	.	.	PUNCT
american_scientific_journal-2676	279	1	proof	proof	NOUN
american_scientific_journal-2676	279	2	.	.	PUNCT
american_scientific_journal-2676	280	1	straightforward	straightforward	ADJ
american_scientific_journal-2676	280	2	.	.	PUNCT
american_scientific_journal-2676	281	1	american	american	ADJ
american_scientific_journal-2676	281	2	scientific	scientific	ADJ
american_scientific_journal-2676	281	3	research	research	PROPN
american_scientific_journal-2676	281	4	journal	journal	NOUN
american_scientific_journal-2676	281	5	for	for	ADP
american_scientific_journal-2676	281	6	engineering	engineering	NOUN
american_scientific_journal-2676	281	7	,	,	PUNCT
american_scientific_journal-2676	281	8	technology	technology	NOUN
american_scientific_journal-2676	281	9	,	,	PUNCT
american_scientific_journal-2676	281	10	and	and	CCONJ
american_scientific_journal-2676	281	11	sciences	science	NOUN
american_scientific_journal-2676	281	12	(	(	PUNCT
american_scientific_journal-2676	281	13	asrjets	asrjet	NOUN
american_scientific_journal-2676	281	14	)	)	PUNCT
american_scientific_journal-2676	281	15	(	(	PUNCT
american_scientific_journal-2676	281	16	2017	2017	NUM
american_scientific_journal-2676	281	17	)	)	PUNCT
american_scientific_journal-2676	281	18	volume	volume	NOUN
american_scientific_journal-2676	281	19	28	28	NUM
american_scientific_journal-2676	281	20	,	,	PUNCT
american_scientific_journal-2676	281	21	no	no	DET
american_scientific_journal-2676	281	22	1	1	NUM
american_scientific_journal-2676	281	23	,	,	PUNCT
american_scientific_journal-2676	281	24	pp	pp	ADV
american_scientific_journal-2676	281	25	225	225	NUM
american_scientific_journal-2676	281	26	-	-	SYM
american_scientific_journal-2676	281	27	247	247	NUM
american_scientific_journal-2676	281	28	237	237	NUM
american_scientific_journal-2676	281	29	theorem	theorem	VERB
american_scientific_journal-2676	281	30	3.6	3.6	NUM
american_scientific_journal-2676	281	31	let	let	NOUN
american_scientific_journal-2676	281	32	)	)	PUNCT
american_scientific_journal-2676	281	33	,	,	PUNCT
american_scientific_journal-2676	281	34	,	,	PUNCT
american_scientific_journal-2676	281	35	,	,	PUNCT
american_scientific_journal-2676	281	36	(	(	PUNCT
american_scientific_journal-2676	281	37	21	21	NUM
american_scientific_journal-2676	281	38	ex	ex	X
american_scientific_journal-2676	281	39	ηη	ηη	PROPN
american_scientific_journal-2676	281	40	be	be	AUX
american_scientific_journal-2676	281	41	a	a	DET
american_scientific_journal-2676	281	42	sbts	sbts	ADJ
american_scientific_journal-2676	281	43	.	.	PUNCT
american_scientific_journal-2676	282	1	then	then	ADV
american_scientific_journal-2676	282	2	,	,	PUNCT
american_scientific_journal-2676	282	3	1	1	X
american_scientific_journal-2676	282	4	)	)	PUNCT
american_scientific_journal-2676	282	5	if	if	SCONJ
american_scientific_journal-2676	282	6	)	)	PUNCT
american_scientific_journal-2676	282	7	,	,	PUNCT
american_scientific_journal-2676	282	8	,	,	PUNCT
american_scientific_journal-2676	282	9	,	,	PUNCT
american_scientific_journal-2676	282	10	(	(	PUNCT
american_scientific_journal-2676	282	11	21	21	NUM
american_scientific_journal-2676	282	12	ex	ex	X
american_scientific_journal-2676	282	13	ηη	ηη	PROPN
american_scientific_journal-2676	282	14	is	be	AUX
american_scientific_journal-2676	282	15	a	a	DET
american_scientific_journal-2676	282	16	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	282	17	4	4	NUM
american_scientific_journal-2676	282	18	�	�	PROPN
american_scientific_journal-2676	282	19	∗	∗	NOUN
american_scientific_journal-2676	282	20	,	,	PUNCT
american_scientific_journal-2676	282	21	then	then	ADV
american_scientific_journal-2676	282	22	it	it	PRON
american_scientific_journal-2676	282	23	is	be	AUX
american_scientific_journal-2676	282	24	𝑃𝑃𝑃𝑃𝑇𝑇0∗.	𝑃𝑃𝑃𝑃𝑇𝑇0∗.	PROPN
american_scientific_journal-2676	282	25	2	2	NUM
american_scientific_journal-2676	282	26	)	)	PUNCT
american_scientific_journal-2676	282	27	if	if	SCONJ
american_scientific_journal-2676	282	28	)	)	PUNCT
american_scientific_journal-2676	282	29	,	,	PUNCT
american_scientific_journal-2676	282	30	,	,	PUNCT
american_scientific_journal-2676	282	31	,	,	PUNCT
american_scientific_journal-2676	282	32	(	(	PUNCT
american_scientific_journal-2676	282	33	21	21	NUM
american_scientific_journal-2676	282	34	ex	ex	X
american_scientific_journal-2676	282	35	ηη	ηη	PROPN
american_scientific_journal-2676	282	36	is	be	AUX
american_scientific_journal-2676	282	37	a	a	DET
american_scientific_journal-2676	282	38	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	282	39	2	2	NUM
american_scientific_journal-2676	282	40	�	�	PROPN
american_scientific_journal-2676	282	41	∗	∗	NOUN
american_scientific_journal-2676	282	42	,	,	PUNCT
american_scientific_journal-2676	282	43	then	then	ADV
american_scientific_journal-2676	282	44	it	it	PRON
american_scientific_journal-2676	282	45	is	be	AUX
american_scientific_journal-2676	282	46	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	282	47	4	4	NUM
american_scientific_journal-2676	282	48	�	�	PROPN
american_scientific_journal-2676	282	49	∗	∗	NOUN
american_scientific_journal-2676	282	50	.	.	PUNCT
american_scientific_journal-2676	283	1	proof	proof	NOUN
american_scientific_journal-2676	283	2	.	.	PUNCT
american_scientific_journal-2676	284	1	(	(	PUNCT
american_scientific_journal-2676	284	2	1	1	NUM
american_scientific_journal-2676	284	3	)	)	PUNCT
american_scientific_journal-2676	284	4	:	:	PUNCT
american_scientific_journal-2676	284	5	let	let	VERB
american_scientific_journal-2676	284	6	exyx	exyx	ADJ
american_scientific_journal-2676	284	7	)	)	PUNCT
american_scientific_journal-2676	284	8	(	(	PUNCT
american_scientific_journal-2676	284	9	,	,	PUNCT
american_scientific_journal-2676	284	10	ξβα	ξβα	NOUN
american_scientific_journal-2676	284	11	∈	∈	PRON
american_scientific_journal-2676	284	12	such	such	ADJ
american_scientific_journal-2676	284	13	that	that	PRON
american_scientific_journal-2676	284	14	βα	βα	PROPN
american_scientific_journal-2676	284	15	yx	yx	NUM
american_scientific_journal-2676	284	16	≠	≠	PROPN
american_scientific_journal-2676	284	17	.	.	PUNCT
american_scientific_journal-2676	285	1	since	since	SCONJ
american_scientific_journal-2676	285	2	)	)	PUNCT
american_scientific_journal-2676	285	3	,	,	PUNCT
american_scientific_journal-2676	285	4	(	(	PUNCT
american_scientific_journal-2676	285	5	exα	exα	PROPN
american_scientific_journal-2676	285	6	is	be	AUX
american_scientific_journal-2676	285	7	a	a	DET
american_scientific_journal-2676	285	8	finite	finite	ADJ
american_scientific_journal-2676	285	9	soft	soft	ADJ
american_scientific_journal-2676	285	10	set	set	NOUN
american_scientific_journal-2676	285	11	and	and	CCONJ
american_scientific_journal-2676	285	12	)	)	PUNCT
american_scientific_journal-2676	285	13	,	,	PUNCT
american_scientific_journal-2676	285	14	(	(	PUNCT
american_scientific_journal-2676	285	15	~	~	PUNCT
american_scientific_journal-2676	285	16	exy	exy	ADJ
american_scientific_journal-2676	285	17	αβ	αβ	INTJ
american_scientific_journal-2676	285	18	∈/	∈/	NOUN
american_scientific_journal-2676	285	19	,	,	PUNCT
american_scientific_journal-2676	285	20	then	then	ADV
american_scientific_journal-2676	285	21	by	by	ADP
american_scientific_journal-2676	285	22	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	285	23	4	4	NUM
american_scientific_journal-2676	285	24	�	�	PROPN
american_scientific_journal-2676	285	25	∗	∗	NOUN
american_scientific_journal-2676	285	26	property	property	NOUN
american_scientific_journal-2676	285	27	there	there	PRON
american_scientific_journal-2676	285	28	exists	exist	VERB
american_scientific_journal-2676	285	29	ceg	ceg	NOUN
american_scientific_journal-2676	285	30	1212	1212	NUM
american_scientific_journal-2676	285	31	)	)	PUNCT
american_scientific_journal-2676	285	32	,	,	PUNCT
american_scientific_journal-2676	285	33	(	(	PUNCT
american_scientific_journal-2676	285	34	ηη	ηη	PRON
american_scientific_journal-2676	285	35	∪∈	∪∈	VERB
american_scientific_journal-2676	285	36	such	such	ADJ
american_scientific_journal-2676	285	37	that	that	PRON
american_scientific_journal-2676	285	38	)	)	PUNCT
american_scientific_journal-2676	285	39	,	,	PUNCT
american_scientific_journal-2676	285	40	(	(	PUNCT
american_scientific_journal-2676	285	41	~	~	NOUN
american_scientific_journal-2676	285	42	)	)	PUNCT
american_scientific_journal-2676	285	43	,	,	PUNCT
american_scientific_journal-2676	285	44	(	(	PUNCT
american_scientific_journal-2676	285	45	egex	egex	NOUN
american_scientific_journal-2676	285	46	⊆α	⊆α	NOUN
american_scientific_journal-2676	285	47	and	and	CCONJ
american_scientific_journal-2676	285	48	)	)	PUNCT
american_scientific_journal-2676	285	49	,	,	PUNCT
american_scientific_journal-2676	285	50	(	(	PUNCT
american_scientific_journal-2676	285	51	~	~	PUNCT
american_scientific_journal-2676	285	52	egy	egy	PROPN
american_scientific_journal-2676	285	53	∈/β	∈/β	PROPN
american_scientific_journal-2676	285	54	.	.	PUNCT
american_scientific_journal-2676	286	1	it	it	PRON
american_scientific_journal-2676	286	2	follows	follow	VERB
american_scientific_journal-2676	286	3	that	that	PRON
american_scientific_journal-2676	286	4	)	)	PUNCT
american_scientific_journal-2676	286	5	,	,	PUNCT
american_scientific_journal-2676	286	6	(	(	PUNCT
american_scientific_journal-2676	286	7	~	~	PUNCT
american_scientific_journal-2676	286	8	egx	egx	X
american_scientific_journal-2676	286	9	∈α	∈α	PROPN
american_scientific_journal-2676	286	10	and	and	CCONJ
american_scientific_journal-2676	286	11	)	)	PUNCT
american_scientific_journal-2676	286	12	,	,	PUNCT
american_scientific_journal-2676	286	13	(	(	PUNCT
american_scientific_journal-2676	286	14	~	~	PUNCT
american_scientific_journal-2676	286	15	egy	egy	PROPN
american_scientific_journal-2676	286	16	∈/β	∈/β	PROPN
american_scientific_journal-2676	286	17	.	.	PUNCT
american_scientific_journal-2676	287	1	therefore	therefore	ADV
american_scientific_journal-2676	287	2	,	,	PUNCT
american_scientific_journal-2676	287	3	by	by	ADP
american_scientific_journal-2676	287	4	lemma	lemma	PROPN
american_scientific_journal-2676	287	5	2.1	2.1	NUM
american_scientific_journal-2676	287	6	,	,	PUNCT
american_scientific_journal-2676	287	7	)	)	PUNCT
american_scientific_journal-2676	287	8	,	,	PUNCT
american_scientific_journal-2676	287	9	,	,	PUNCT
american_scientific_journal-2676	287	10	,	,	PUNCT
american_scientific_journal-2676	287	11	(	(	PUNCT
american_scientific_journal-2676	287	12	21	21	NUM
american_scientific_journal-2676	287	13	ex	ex	X
american_scientific_journal-2676	287	14	ηη	ηη	PROPN
american_scientific_journal-2676	287	15	is	be	AUX
american_scientific_journal-2676	287	16	a	a	DET
american_scientific_journal-2676	287	17	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	287	18	4	4	NUM
american_scientific_journal-2676	287	19	�	�	PROPN
american_scientific_journal-2676	287	20	∗	∗	NOUN
american_scientific_journal-2676	287	21	.	.	PUNCT
american_scientific_journal-2676	288	1	(	(	PUNCT
american_scientific_journal-2676	288	2	2	2	NUM
american_scientific_journal-2676	288	3	)	)	PUNCT
american_scientific_journal-2676	288	4	:	:	PUNCT
american_scientific_journal-2676	288	5	it	it	PRON
american_scientific_journal-2676	288	6	follows	follow	VERB
american_scientific_journal-2676	288	7	from	from	ADP
american_scientific_journal-2676	288	8	theorems	theorem	NOUN
american_scientific_journal-2676	288	9	3.2	3.2	NUM
american_scientific_journal-2676	288	10	and	and	CCONJ
american_scientific_journal-2676	288	11	3.4	3.4	NUM
american_scientific_journal-2676	288	12	.	.	PUNCT
american_scientific_journal-2676	289	1	remark	remark	NOUN
american_scientific_journal-2676	289	2	3.2	3.2	NUM
american_scientific_journal-2676	289	3	the	the	DET
american_scientific_journal-2676	289	4	following	follow	VERB
american_scientific_journal-2676	289	5	examples	example	NOUN
american_scientific_journal-2676	289	6	shows	show	VERB
american_scientific_journal-2676	289	7	that	that	SCONJ
american_scientific_journal-2676	289	8	the	the	DET
american_scientific_journal-2676	289	9	converse	converse	NOUN
american_scientific_journal-2676	289	10	of	of	ADP
american_scientific_journal-2676	289	11	items	item	NOUN
american_scientific_journal-2676	289	12	(	(	PUNCT
american_scientific_journal-2676	289	13	1	1	NUM
american_scientific_journal-2676	289	14	)	)	PUNCT
american_scientific_journal-2676	289	15	and	and	CCONJ
american_scientific_journal-2676	289	16	(	(	PUNCT
american_scientific_journal-2676	289	17	2	2	X
american_scientific_journal-2676	289	18	)	)	PUNCT
american_scientific_journal-2676	289	19	in	in	ADP
american_scientific_journal-2676	289	20	theorem	theorem	ADJ
american_scientific_journal-2676	289	21	3.6	3.6	NUM
american_scientific_journal-2676	289	22	are	be	AUX
american_scientific_journal-2676	289	23	not	not	PART
american_scientific_journal-2676	289	24	true	true	ADJ
american_scientific_journal-2676	289	25	in	in	ADP
american_scientific_journal-2676	289	26	general	general	ADJ
american_scientific_journal-2676	289	27	.	.	PUNCT
american_scientific_journal-2676	290	1	example	example	NOUN
american_scientific_journal-2676	290	2	3.3	3.3	NUM
american_scientific_journal-2676	290	3	in	in	ADP
american_scientific_journal-2676	290	4	example	example	NOUN
american_scientific_journal-2676	290	5	3.1	3.1	NUM
american_scientific_journal-2676	290	6	,	,	PUNCT
american_scientific_journal-2676	290	7	it	it	PRON
american_scientific_journal-2676	290	8	is	be	AUX
american_scientific_journal-2676	290	9	easy	easy	ADJ
american_scientific_journal-2676	290	10	to	to	PART
american_scientific_journal-2676	290	11	prove	prove	VERB
american_scientific_journal-2676	290	12	that	that	PRON
american_scientific_journal-2676	290	13	)	)	PUNCT
american_scientific_journal-2676	290	14	,	,	PUNCT
american_scientific_journal-2676	290	15	,	,	PUNCT
american_scientific_journal-2676	290	16	,	,	PUNCT
american_scientific_journal-2676	290	17	(	(	PUNCT
american_scientific_journal-2676	290	18	21	21	NUM
american_scientific_journal-2676	290	19	ex	ex	X
american_scientific_journal-2676	290	20	ηη	ηη	PROPN
american_scientific_journal-2676	290	21	is	be	AUX
american_scientific_journal-2676	290	22	a	a	DET
american_scientific_journal-2676	290	23	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	NOUN
american_scientific_journal-2676	290	24	.	.	PUNCT
american_scientific_journal-2676	291	1	let	let	VERB
american_scientific_journal-2676	291	2	)	)	PUNCT
american_scientific_journal-2676	291	3	}	}	PUNCT
american_scientific_journal-2676	291	4	,	,	PUNCT
american_scientific_journal-2676	291	5	(	(	PUNCT
american_scientific_journal-2676	291	6	}	}	PUNCT
american_scientific_journal-2676	291	7	)	)	PUNCT
american_scientific_journal-2676	291	8	,	,	PUNCT
american_scientific_journal-2676	291	9	{	{	PUNCT
american_scientific_journal-2676	291	10	,	,	PUNCT
american_scientific_journal-2676	291	11	{	{	PUNCT
american_scientific_journal-2676	291	12	(=	(=	NOUN
american_scientific_journal-2676	291	13	)	)	PUNCT
american_scientific_journal-2676	291	14	,	,	PUNCT
american_scientific_journal-2676	291	15	(	(	PUNCT
american_scientific_journal-2676	291	16	21	21	NUM
american_scientific_journal-2676	291	17	xeyeef	xeyeef	NOUN
american_scientific_journal-2676	291	18	.	.	PUNCT
american_scientific_journal-2676	292	1	we	we	PRON
american_scientific_journal-2676	292	2	note	note	VERB
american_scientific_journal-2676	292	3	that	that	PRON
american_scientific_journal-2676	292	4	)	)	PUNCT
american_scientific_journal-2676	292	5	,	,	PUNCT
american_scientific_journal-2676	292	6	(	(	PUNCT
american_scientific_journal-2676	292	7	~	~	SYM
american_scientific_journal-2676	292	8	1	1	NUM
american_scientific_journal-2676	292	9	efxe	efxe	NOUN
american_scientific_journal-2676	292	10	∈/	∈/	PROPN
american_scientific_journal-2676	292	11	and	and	CCONJ
american_scientific_journal-2676	292	12	)	)	PUNCT
american_scientific_journal-2676	292	13	,	,	PUNCT
american_scientific_journal-2676	292	14	(	(	PUNCT
american_scientific_journal-2676	292	15	ef	ef	PROPN
american_scientific_journal-2676	292	16	is	be	AUX
american_scientific_journal-2676	292	17	finite	finite	ADJ
american_scientific_journal-2676	292	18	soft	soft	ADJ
american_scientific_journal-2676	292	19	set	set	NOUN
american_scientific_journal-2676	292	20	.	.	PUNCT
american_scientific_journal-2676	293	1	but	but	CCONJ
american_scientific_journal-2676	293	2	,	,	PUNCT
american_scientific_journal-2676	293	3	there	there	PRON
american_scientific_journal-2676	293	4	is	be	VERB
american_scientific_journal-2676	293	5	no	no	DET
american_scientific_journal-2676	293	6	p	p	NOUN
american_scientific_journal-2676	293	7	open	open	ADJ
american_scientific_journal-2676	293	8	or	or	CCONJ
american_scientific_journal-2676	293	9	p	p	NOUN
american_scientific_journal-2676	293	10	-closed	-close	VERB
american_scientific_journal-2676	293	11	soft	soft	ADJ
american_scientific_journal-2676	293	12	set	set	NOUN
american_scientific_journal-2676	293	13	)	)	PUNCT
american_scientific_journal-2676	293	14	,	,	PUNCT
american_scientific_journal-2676	293	15	(	(	PUNCT
american_scientific_journal-2676	293	16	em	em	PRON
american_scientific_journal-2676	293	17	such	such	ADJ
american_scientific_journal-2676	293	18	that	that	PRON
american_scientific_journal-2676	293	19	)	)	PUNCT
american_scientific_journal-2676	293	20	,	,	PUNCT
american_scientific_journal-2676	293	21	(	(	PUNCT
american_scientific_journal-2676	293	22	~	~	NOUN
american_scientific_journal-2676	293	23	)	)	PUNCT
american_scientific_journal-2676	293	24	,	,	PUNCT
american_scientific_journal-2676	293	25	(	(	PUNCT
american_scientific_journal-2676	293	26	emef	emef	NOUN
american_scientific_journal-2676	293	27	⊆	⊆	NUM
american_scientific_journal-2676	293	28	and	and	CCONJ
american_scientific_journal-2676	293	29	)	)	PUNCT
american_scientific_journal-2676	293	30	,	,	PUNCT
american_scientific_journal-2676	293	31	(	(	PUNCT
american_scientific_journal-2676	293	32	~	~	PUNCT
american_scientific_journal-2676	293	33	1	1	NUM
american_scientific_journal-2676	293	34	emxe	emxe	NOUN
american_scientific_journal-2676	293	35	∈/	∈/	PROPN
american_scientific_journal-2676	293	36	.	.	PUNCT
american_scientific_journal-2676	294	1	hence	hence	ADV
american_scientific_journal-2676	294	2	,	,	PUNCT
american_scientific_journal-2676	294	3	)	)	PUNCT
american_scientific_journal-2676	294	4	,	,	PUNCT
american_scientific_journal-2676	294	5	,	,	PUNCT
american_scientific_journal-2676	294	6	,	,	PUNCT
american_scientific_journal-2676	294	7	(	(	PUNCT
american_scientific_journal-2676	294	8	21	21	NUM
american_scientific_journal-2676	294	9	ex	ex	NOUN
american_scientific_journal-2676	294	10	ηη	ηη	PROPN
american_scientific_journal-2676	294	11	is	be	AUX
american_scientific_journal-2676	294	12	not	not	PART
american_scientific_journal-2676	294	13	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	294	14	4	4	NUM
american_scientific_journal-2676	294	15	�	�	PROPN
american_scientific_journal-2676	294	16	∗	∗	NOUN
american_scientific_journal-2676	294	17	.	.	PUNCT
american_scientific_journal-2676	295	1	example	example	NOUN
american_scientific_journal-2676	295	2	3.4	3.4	NUM
american_scientific_journal-2676	295	3	from	from	ADP
american_scientific_journal-2676	295	4	example	example	NOUN
american_scientific_journal-2676	295	5	3.2	3.2	NUM
american_scientific_journal-2676	295	6	and	and	CCONJ
american_scientific_journal-2676	295	7	theorem	theorem	VERB
american_scientific_journal-2676	295	8	3.3	3.3	NUM
american_scientific_journal-2676	295	9	,	,	PUNCT
american_scientific_journal-2676	295	10	we	we	PRON
american_scientific_journal-2676	295	11	have	have	VERB
american_scientific_journal-2676	295	12	)	)	PUNCT
american_scientific_journal-2676	295	13	,	,	PUNCT
american_scientific_journal-2676	295	14	,	,	PUNCT
american_scientific_journal-2676	295	15	,	,	PUNCT
american_scientific_journal-2676	295	16	(	(	PUNCT
american_scientific_journal-2676	295	17	ez	ez	X
american_scientific_journal-2676	295	18	dd	dd	VERB
american_scientific_journal-2676	295	19	ηη	ηη	PROPN
american_scientific_journal-2676	295	20	is	be	AUX
american_scientific_journal-2676	295	21	a	a	DET
american_scientific_journal-2676	295	22	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	295	23	4	4	NUM
american_scientific_journal-2676	295	24	�	�	PROPN
american_scientific_journal-2676	295	25	∗	∗	NOUN
american_scientific_journal-2676	295	26	,	,	PUNCT
american_scientific_journal-2676	295	27	but	but	CCONJ
american_scientific_journal-2676	295	28	it	it	PRON
american_scientific_journal-2676	295	29	is	be	AUX
american_scientific_journal-2676	295	30	not	not	PART
american_scientific_journal-2676	295	31	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	295	32	2	2	NUM
american_scientific_journal-2676	295	33	�	�	PROPN
american_scientific_journal-2676	295	34	∗	∗	NOUN
american_scientific_journal-2676	295	35	because	because	SCONJ
american_scientific_journal-2676	295	36	)	)	PUNCT
american_scientific_journal-2676	295	37	,	,	PUNCT
american_scientific_journal-2676	295	38	(	(	PUNCT
american_scientific_journal-2676	295	39	0	0	NUM
american_scientific_journal-2676	295	40	ed	ed	NOUN
american_scientific_journal-2676	295	41	is	be	AUX
american_scientific_journal-2676	295	42	a	a	DET
american_scientific_journal-2676	295	43	soft	soft	ADJ
american_scientific_journal-2676	295	44	point	point	NOUN
american_scientific_journal-2676	295	45	in	in	ADP
american_scientific_journal-2676	295	46	z	z	NOUN
american_scientific_journal-2676	296	1	but	but	CCONJ
american_scientific_journal-2676	296	2	it	it	PRON
american_scientific_journal-2676	296	3	is	be	AUX
american_scientific_journal-2676	296	4	neither	neither	CCONJ
american_scientific_journal-2676	296	5	p	p	NOUN
american_scientific_journal-2676	296	6	-open	-open	ADJ
american_scientific_journal-2676	296	7	nor	nor	CCONJ
american_scientific_journal-2676	296	8	p	p	NOUN
american_scientific_journal-2676	296	9	-closed	-close	VERB
american_scientific_journal-2676	296	10	soft	soft	ADJ
american_scientific_journal-2676	296	11	set	set	NOUN
american_scientific_journal-2676	296	12	.	.	PUNCT
american_scientific_journal-2676	297	1	corollary	corollary	ADJ
american_scientific_journal-2676	297	2	3.1	3.1	NUM
american_scientific_journal-2676	297	3	if	if	SCONJ
american_scientific_journal-2676	297	4	x	x	PRON
american_scientific_journal-2676	297	5	is	be	AUX
american_scientific_journal-2676	297	6	a	a	DET
american_scientific_journal-2676	297	7	finite	finite	ADJ
american_scientific_journal-2676	297	8	set	set	NOUN
american_scientific_journal-2676	297	9	,	,	PUNCT
american_scientific_journal-2676	297	10	then	then	ADV
american_scientific_journal-2676	297	11	)	)	PUNCT
american_scientific_journal-2676	297	12	,	,	PUNCT
american_scientific_journal-2676	297	13	,	,	PUNCT
american_scientific_journal-2676	297	14	,	,	PUNCT
american_scientific_journal-2676	297	15	(	(	PUNCT
american_scientific_journal-2676	297	16	21	21	NUM
american_scientific_journal-2676	297	17	ex	ex	X
american_scientific_journal-2676	297	18	ηη	ηη	PROPN
american_scientific_journal-2676	297	19	is	be	AUX
american_scientific_journal-2676	297	20	a	a	DET
american_scientific_journal-2676	297	21	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	297	22	2	2	NUM
american_scientific_journal-2676	297	23	�	�	PROPN
american_scientific_journal-2676	297	24	∗	∗	NOUN
american_scientific_journal-2676	297	25	iff	iff	PROPN
american_scientific_journal-2676	297	26	it	it	PRON
american_scientific_journal-2676	297	27	is	be	AUX
american_scientific_journal-2676	297	28	a	a	DET
american_scientific_journal-2676	297	29	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	297	30	4	4	NUM
american_scientific_journal-2676	297	31	�	�	PROPN
american_scientific_journal-2676	297	32	∗	∗	NOUN
american_scientific_journal-2676	297	33	.	.	PUNCT
american_scientific_journal-2676	298	1	4	4	X
american_scientific_journal-2676	298	2	.	.	X
american_scientific_journal-2676	298	3	pairwise	pairwise	NOUN
american_scientific_journal-2676	298	4	locally	locally	ADV
american_scientific_journal-2676	298	5	closed	close	VERB
american_scientific_journal-2676	298	6	soft	soft	ADJ
american_scientific_journal-2676	298	7	sets	set	NOUN
american_scientific_journal-2676	298	8	in	in	ADP
american_scientific_journal-2676	298	9	this	this	DET
american_scientific_journal-2676	298	10	section	section	NOUN
american_scientific_journal-2676	298	11	,	,	PUNCT
american_scientific_journal-2676	298	12	we	we	PRON
american_scientific_journal-2676	298	13	introduce	introduce	VERB
american_scientific_journal-2676	298	14	the	the	DET
american_scientific_journal-2676	298	15	notion	notion	NOUN
american_scientific_journal-2676	298	16	of	of	ADP
american_scientific_journal-2676	298	17	pairwise	pairwise	NOUN
american_scientific_journal-2676	298	18	locally	locally	ADV
american_scientific_journal-2676	298	19	closed	close	VERB
american_scientific_journal-2676	298	20	soft	soft	ADJ
american_scientific_journal-2676	298	21	sets	set	NOUN
american_scientific_journal-2676	298	22	.	.	PUNCT
american_scientific_journal-2676	299	1	some	some	DET
american_scientific_journal-2676	299	2	basic	basic	ADJ
american_scientific_journal-2676	299	3	properties	property	NOUN
american_scientific_journal-2676	299	4	of	of	ADP
american_scientific_journal-2676	299	5	them	they	PRON
american_scientific_journal-2676	299	6	and	and	CCONJ
american_scientific_journal-2676	299	7	their	their	PRON
american_scientific_journal-2676	299	8	relationships	relationship	NOUN
american_scientific_journal-2676	299	9	with	with	ADP
american_scientific_journal-2676	299	10	different	different	ADJ
american_scientific_journal-2676	299	11	types	type	NOUN
american_scientific_journal-2676	299	12	of	of	ADP
american_scientific_journal-2676	299	13	soft	soft	ADJ
american_scientific_journal-2676	299	14	sets	set	NOUN
american_scientific_journal-2676	299	15	are	be	AUX
american_scientific_journal-2676	299	16	studied	study	VERB
american_scientific_journal-2676	299	17	.	.	PUNCT
american_scientific_journal-2676	300	1	definition	definition	NOUN
american_scientific_journal-2676	300	2	4.1	4.1	NUM
american_scientific_journal-2676	300	3	a	a	DET
american_scientific_journal-2676	300	4	soft	soft	ADJ
american_scientific_journal-2676	300	5	set	set	NOUN
american_scientific_journal-2676	300	6	)	)	PUNCT
american_scientific_journal-2676	300	7	,	,	PUNCT
american_scientific_journal-2676	300	8	(	(	PUNCT
american_scientific_journal-2676	300	9	eg	eg	NOUN
american_scientific_journal-2676	300	10	is	be	AUX
american_scientific_journal-2676	300	11	said	say	VERB
american_scientific_journal-2676	300	12	to	to	PART
american_scientific_journal-2676	300	13	be	be	AUX
american_scientific_journal-2676	300	14	a	a	DET
american_scientific_journal-2676	300	15	pairwise	pairwise	NOUN
american_scientific_journal-2676	300	16	locally	locally	ADV
american_scientific_journal-2676	300	17	closed	close	VERB
american_scientific_journal-2676	300	18	soft	soft	ADJ
american_scientific_journal-2676	300	19	set	set	NOUN
american_scientific_journal-2676	300	20	in	in	ADP
american_scientific_journal-2676	300	21	a	a	DET
american_scientific_journal-2676	300	22	soft	soft	ADJ
american_scientific_journal-2676	300	23	bitopological	bitopological	ADJ
american_scientific_journal-2676	300	24	space	space	NOUN
american_scientific_journal-2676	300	25	)	)	PUNCT
american_scientific_journal-2676	300	26	,	,	PUNCT
american_scientific_journal-2676	300	27	,	,	PUNCT
american_scientific_journal-2676	300	28	,	,	PUNCT
american_scientific_journal-2676	300	29	(	(	PUNCT
american_scientific_journal-2676	300	30	21	21	NUM
american_scientific_journal-2676	300	31	ex	ex	NOUN
american_scientific_journal-2676	300	32	ηη	ηη	NOUN
american_scientific_journal-2676	301	1	[	[	X
american_scientific_journal-2676	301	2	briefly	briefly	ADV
american_scientific_journal-2676	301	3	,	,	PUNCT
american_scientific_journal-2676	301	4	p	p	PRON
american_scientific_journal-2676	301	5	locally	locally	ADV
american_scientific_journal-2676	301	6	-closed	-close	VERB
american_scientific_journal-2676	301	7	soft	soft	ADJ
american_scientific_journal-2676	301	8	set	set	NOUN
american_scientific_journal-2676	301	9	]	]	PUNCT
american_scientific_journal-2676	301	10	if	if	SCONJ
american_scientific_journal-2676	301	11	)	)	PUNCT
american_scientific_journal-2676	301	12	,	,	PUNCT
american_scientific_journal-2676	301	13	(	(	PUNCT
american_scientific_journal-2676	301	14	~),(=	~),(=	NUM
american_scientific_journal-2676	301	15	)	)	PUNCT
american_scientific_journal-2676	301	16	,	,	PUNCT
american_scientific_journal-2676	301	17	(	(	PUNCT
american_scientific_journal-2676	301	18	ehefeg	ehefeg	PROPN
american_scientific_journal-2676	301	19	∩	∩	NOUN
american_scientific_journal-2676	301	20	,	,	PUNCT
american_scientific_journal-2676	301	21	where	where	SCONJ
american_scientific_journal-2676	301	22	)	)	PUNCT
american_scientific_journal-2676	301	23	,	,	PUNCT
american_scientific_journal-2676	301	24	(	(	PUNCT
american_scientific_journal-2676	301	25	ef	ef	PROPN
american_scientific_journal-2676	301	26	is	be	AUX
american_scientific_journal-2676	301	27	a	a	DET
american_scientific_journal-2676	301	28	p	p	NOUN
american_scientific_journal-2676	301	29	closed	closed	ADJ
american_scientific_journal-2676	301	30	soft	soft	ADJ
american_scientific_journal-2676	301	31	set	set	NOUN
american_scientific_journal-2676	301	32	and	and	CCONJ
american_scientific_journal-2676	301	33	)	)	PUNCT
american_scientific_journal-2676	301	34	,	,	PUNCT
american_scientific_journal-2676	301	35	(	(	PUNCT
american_scientific_journal-2676	301	36	eh	eh	INTJ
american_scientific_journal-2676	301	37	is	be	AUX
american_scientific_journal-2676	301	38	a	a	DET
american_scientific_journal-2676	301	39	p	p	NOUN
american_scientific_journal-2676	301	40	-open	-open	ADJ
american_scientific_journal-2676	301	41	soft	soft	ADJ
american_scientific_journal-2676	301	42	set	set	NOUN
american_scientific_journal-2676	301	43	.	.	PUNCT
american_scientific_journal-2676	302	1	the	the	DET
american_scientific_journal-2676	302	2	family	family	NOUN
american_scientific_journal-2676	302	3	of	of	ADP
american_scientific_journal-2676	302	4	all	all	PRON
american_scientific_journal-2676	302	5	p	p	NOUN
american_scientific_journal-2676	302	6	locally	locally	ADV
american_scientific_journal-2676	302	7	closed	close	VERB
american_scientific_journal-2676	302	8	soft	soft	ADJ
american_scientific_journal-2676	302	9	sets	set	NOUN
american_scientific_journal-2676	302	10	we	we	PRON
american_scientific_journal-2676	302	11	denoted	denote	VERB
american_scientific_journal-2676	302	12	by	by	ADP
american_scientific_journal-2676	302	13	explcs	explcs	NOUN
american_scientific_journal-2676	302	14	)	)	PUNCT
american_scientific_journal-2676	302	15	,	,	PUNCT
american_scientific_journal-2676	302	16	,	,	PUNCT
american_scientific_journal-2676	302	17	(	(	PUNCT
american_scientific_journal-2676	302	18	21	21	NUM
american_scientific_journal-2676	302	19	ηη	ηη	PRON
american_scientific_journal-2676	302	20	.	.	PUNCT
american_scientific_journal-2676	303	1	theorem	theorem	VERB
american_scientific_journal-2676	303	2	4.1	4.1	NUM
american_scientific_journal-2676	303	3	let	let	NOUN
american_scientific_journal-2676	303	4	)	)	PUNCT
american_scientific_journal-2676	303	5	,	,	PUNCT
american_scientific_journal-2676	303	6	,	,	PUNCT
american_scientific_journal-2676	303	7	,	,	PUNCT
american_scientific_journal-2676	303	8	(	(	PUNCT
american_scientific_journal-2676	303	9	21	21	NUM
american_scientific_journal-2676	303	10	ex	ex	X
american_scientific_journal-2676	303	11	ηη	ηη	PROPN
american_scientific_journal-2676	303	12	be	be	AUX
american_scientific_journal-2676	303	13	a	a	DET
american_scientific_journal-2676	303	14	sbts	sbts	ADJ
american_scientific_journal-2676	303	15	.	.	PUNCT
american_scientific_journal-2676	304	1	then	then	ADV
american_scientific_journal-2676	304	2	,	,	PUNCT
american_scientific_journal-2676	304	3	american	american	ADJ
american_scientific_journal-2676	304	4	scientific	scientific	ADJ
american_scientific_journal-2676	304	5	research	research	NOUN
american_scientific_journal-2676	304	6	journal	journal	NOUN
american_scientific_journal-2676	304	7	for	for	ADP
american_scientific_journal-2676	304	8	engineering	engineering	NOUN
american_scientific_journal-2676	304	9	,	,	PUNCT
american_scientific_journal-2676	304	10	technology	technology	NOUN
american_scientific_journal-2676	304	11	,	,	PUNCT
american_scientific_journal-2676	304	12	and	and	CCONJ
american_scientific_journal-2676	304	13	sciences	science	NOUN
american_scientific_journal-2676	304	14	(	(	PUNCT
american_scientific_journal-2676	304	15	asrjets	asrjet	NOUN
american_scientific_journal-2676	304	16	)	)	PUNCT
american_scientific_journal-2676	304	17	(	(	PUNCT
american_scientific_journal-2676	304	18	2017	2017	NUM
american_scientific_journal-2676	304	19	)	)	PUNCT
american_scientific_journal-2676	304	20	volume	volume	NOUN
american_scientific_journal-2676	304	21	28	28	NUM
american_scientific_journal-2676	304	22	,	,	PUNCT
american_scientific_journal-2676	304	23	no	no	DET
american_scientific_journal-2676	304	24	1	1	NUM
american_scientific_journal-2676	304	25	,	,	PUNCT
american_scientific_journal-2676	304	26	pp	pp	ADV
american_scientific_journal-2676	304	27	225	225	NUM
american_scientific_journal-2676	304	28	-	-	SYM
american_scientific_journal-2676	304	29	247	247	NUM
american_scientific_journal-2676	304	30	238	238	NUM
american_scientific_journal-2676	304	31	every	every	DET
american_scientific_journal-2676	304	32	p	p	NOUN
american_scientific_journal-2676	304	33	-open	-open	NOUN
american_scientific_journal-2676	304	34	(	(	PUNCT
american_scientific_journal-2676	304	35	p	p	NOUN
american_scientific_journal-2676	304	36	-closed	-closed	ADJ
american_scientific_journal-2676	304	37	)	)	PUNCT
american_scientific_journal-2676	304	38	soft	soft	ADJ
american_scientific_journal-2676	304	39	set	set	NOUN
american_scientific_journal-2676	304	40	is	be	AUX
american_scientific_journal-2676	304	41	p	p	NOUN
american_scientific_journal-2676	304	42	-locally	-locally	ADV
american_scientific_journal-2676	304	43	closed	close	VERB
american_scientific_journal-2676	304	44	soft	soft	ADJ
american_scientific_journal-2676	304	45	set	set	NOUN
american_scientific_journal-2676	304	46	.	.	PUNCT
american_scientific_journal-2676	305	1	proof	proof	NOUN
american_scientific_journal-2676	305	2	.	.	PUNCT
american_scientific_journal-2676	306	1	immediate	immediate	ADJ
american_scientific_journal-2676	306	2	from	from	ADP
american_scientific_journal-2676	306	3	definition	definition	NOUN
american_scientific_journal-2676	306	4	.	.	PUNCT
american_scientific_journal-2676	307	1	remark	remark	VERB
american_scientific_journal-2676	307	2	4.1	4.1	NUM
american_scientific_journal-2676	307	3	the	the	DET
american_scientific_journal-2676	307	4	union	union	NOUN
american_scientific_journal-2676	307	5	(	(	PUNCT
american_scientific_journal-2676	307	6	intersection	intersection	NOUN
american_scientific_journal-2676	307	7	)	)	PUNCT
american_scientific_journal-2676	307	8	of	of	ADP
american_scientific_journal-2676	307	9	two	two	NUM
american_scientific_journal-2676	307	10	p	p	NOUN
american_scientific_journal-2676	307	11	locally	locally	ADV
american_scientific_journal-2676	307	12	closed	close	VERB
american_scientific_journal-2676	307	13	soft	soft	ADJ
american_scientific_journal-2676	307	14	sets	set	NOUN
american_scientific_journal-2676	307	15	need	need	AUX
american_scientific_journal-2676	307	16	not	not	PART
american_scientific_journal-2676	307	17	be	be	AUX
american_scientific_journal-2676	307	18	a	a	DET
american_scientific_journal-2676	307	19	p	p	NOUN
american_scientific_journal-2676	307	20	-locally	-locally	ADV
american_scientific_journal-2676	307	21	closed	close	VERB
american_scientific_journal-2676	307	22	soft	soft	ADJ
american_scientific_journal-2676	307	23	set	set	NOUN
american_scientific_journal-2676	307	24	as	as	SCONJ
american_scientific_journal-2676	307	25	shown	show	VERB
american_scientific_journal-2676	307	26	in	in	ADP
american_scientific_journal-2676	307	27	the	the	DET
american_scientific_journal-2676	307	28	following	follow	VERB
american_scientific_journal-2676	307	29	example	example	NOUN
american_scientific_journal-2676	307	30	example	example	NOUN
american_scientific_journal-2676	307	31	4.1	4.1	NUM
american_scientific_journal-2676	307	32	in	in	ADP
american_scientific_journal-2676	307	33	example	example	NOUN
american_scientific_journal-2676	307	34	3.1	3.1	NUM
american_scientific_journal-2676	307	35	,	,	PUNCT
american_scientific_journal-2676	307	36	it	it	PRON
american_scientific_journal-2676	307	37	is	be	AUX
american_scientific_journal-2676	307	38	clear	clear	ADJ
american_scientific_journal-2676	307	39	that	that	SCONJ
american_scientific_journal-2676	307	40	)	)	PUNCT
american_scientific_journal-2676	307	41	,	,	PUNCT
american_scientific_journal-2676	307	42	(	(	PUNCT
american_scientific_journal-2676	307	43	2	2	NUM
american_scientific_journal-2676	307	44	eg	eg	NOUN
american_scientific_journal-2676	307	45	and	and	CCONJ
american_scientific_journal-2676	307	46	)	)	PUNCT
american_scientific_journal-2676	307	47	,	,	PUNCT
american_scientific_journal-2676	307	48	(	(	PUNCT
american_scientific_journal-2676	307	49	ek	ek	PROPN
american_scientific_journal-2676	307	50	are	be	AUX
american_scientific_journal-2676	307	51	p	p	NOUN
american_scientific_journal-2676	307	52	-locally	-locally	ADV
american_scientific_journal-2676	307	53	closed	close	VERB
american_scientific_journal-2676	307	54	soft	soft	ADJ
american_scientific_journal-2676	307	55	sets	set	NOUN
american_scientific_journal-2676	307	56	[	[	X
american_scientific_journal-2676	307	57	by	by	ADP
american_scientific_journal-2676	307	58	proposition	proposition	NOUN
american_scientific_journal-2676	307	59	4.1	4.1	NUM
american_scientific_journal-2676	307	60	]	]	PUNCT
american_scientific_journal-2676	307	61	but	but	CCONJ
american_scientific_journal-2676	307	62	)	)	PUNCT
american_scientific_journal-2676	307	63	,	,	PUNCT
american_scientific_journal-2676	307	64	(	(	PUNCT
american_scientific_journal-2676	307	65	~	~	NOUN
american_scientific_journal-2676	307	66	)	)	PUNCT
american_scientific_journal-2676	307	67	,	,	PUNCT
american_scientific_journal-2676	307	68	(	(	PUNCT
american_scientific_journal-2676	307	69	2	2	NUM
american_scientific_journal-2676	307	70	ekeg	ekeg	NOUN
american_scientific_journal-2676	307	71	∪	∪	ADJ
american_scientific_journal-2676	307	72	is	be	AUX
american_scientific_journal-2676	307	73	not	not	PART
american_scientific_journal-2676	307	74	p	p	NOUN
american_scientific_journal-2676	307	75	-locally	-locally	ADV
american_scientific_journal-2676	307	76	closed	close	VERB
american_scientific_journal-2676	307	77	soft	soft	ADJ
american_scientific_journal-2676	307	78	set	set	NOUN
american_scientific_journal-2676	307	79	.	.	PUNCT
american_scientific_journal-2676	308	1	proposition	proposition	NOUN
american_scientific_journal-2676	308	2	4.1	4.1	NUM
american_scientific_journal-2676	308	3	let	let	NOUN
american_scientific_journal-2676	308	4	)	)	PUNCT
american_scientific_journal-2676	308	5	,	,	PUNCT
american_scientific_journal-2676	308	6	,	,	PUNCT
american_scientific_journal-2676	308	7	,	,	PUNCT
american_scientific_journal-2676	308	8	(	(	PUNCT
american_scientific_journal-2676	308	9	21	21	NUM
american_scientific_journal-2676	308	10	ex	ex	X
american_scientific_journal-2676	308	11	ηη	ηη	PROPN
american_scientific_journal-2676	308	12	be	be	AUX
american_scientific_journal-2676	308	13	a	a	DET
american_scientific_journal-2676	308	14	sbts	sbts	ADJ
american_scientific_journal-2676	308	15	.	.	PUNCT
american_scientific_journal-2676	309	1	then	then	ADV
american_scientific_journal-2676	309	2	,	,	PUNCT
american_scientific_journal-2676	309	3	every	every	DET
american_scientific_journal-2676	309	4	p	p	NOUN
american_scientific_journal-2676	309	5	-locally	-locally	ADV
american_scientific_journal-2676	309	6	closed	closed	ADJ
american_scientific_journal-2676	309	7	soft	soft	ADJ
american_scientific_journal-2676	309	8	set	set	NOUN
american_scientific_journal-2676	309	9	is	be	AUX
american_scientific_journal-2676	309	10	λp	λp	X
american_scientific_journal-2676	309	11	-closed	-close	VERB
american_scientific_journal-2676	309	12	soft	soft	ADJ
american_scientific_journal-2676	309	13	set	set	NOUN
american_scientific_journal-2676	309	14	.	.	PUNCT
american_scientific_journal-2676	310	1	proof	proof	NOUN
american_scientific_journal-2676	310	2	.	.	PUNCT
american_scientific_journal-2676	311	1	straightforward	straightforward	ADJ
american_scientific_journal-2676	311	2	theorem	theorem	VERB
american_scientific_journal-2676	311	3	4.2	4.2	NUM
american_scientific_journal-2676	311	4	a	a	DET
american_scientific_journal-2676	311	5	soft	soft	ADJ
american_scientific_journal-2676	311	6	set	set	NOUN
american_scientific_journal-2676	311	7	)	)	PUNCT
american_scientific_journal-2676	311	8	,	,	PUNCT
american_scientific_journal-2676	311	9	(	(	PUNCT
american_scientific_journal-2676	311	10	eg	eg	NOUN
american_scientific_journal-2676	311	11	in	in	ADP
american_scientific_journal-2676	311	12	a	a	DET
american_scientific_journal-2676	311	13	sbts	sbts	ADJ
american_scientific_journal-2676	311	14	)	)	PUNCT
american_scientific_journal-2676	311	15	,	,	PUNCT
american_scientific_journal-2676	311	16	,	,	PUNCT
american_scientific_journal-2676	311	17	,	,	PUNCT
american_scientific_journal-2676	311	18	(	(	PUNCT
american_scientific_journal-2676	311	19	21	21	NUM
american_scientific_journal-2676	311	20	ex	ex	X
american_scientific_journal-2676	311	21	ηη	ηη	PROPN
american_scientific_journal-2676	311	22	is	be	AUX
american_scientific_journal-2676	311	23	a	a	DET
american_scientific_journal-2676	311	24	p	p	NOUN
american_scientific_journal-2676	311	25	-locally	-locally	ADV
american_scientific_journal-2676	311	26	closed	closed	ADJ
american_scientific_journal-2676	311	27	soft	soft	ADJ
american_scientific_journal-2676	311	28	set	set	ADJ
american_scientific_journal-2676	311	29	iff	iff	PROPN
american_scientific_journal-2676	311	30	)	)	PUNCT
american_scientific_journal-2676	311	31	,	,	PUNCT
american_scientific_journal-2676	311	32	(	(	PUNCT
american_scientific_journal-2676	311	33	~),(=	~),(=	NUM
american_scientific_journal-2676	311	34	)	)	PUNCT
american_scientific_journal-2676	311	35	,	,	PUNCT
american_scientific_journal-2676	311	36	(	(	PUNCT
american_scientific_journal-2676	311	37	12	12	NUM
american_scientific_journal-2676	311	38	ehegscleg	ehegscleg	NOUN
american_scientific_journal-2676	311	39	∩	∩	NOUN
american_scientific_journal-2676	311	40	for	for	ADP
american_scientific_journal-2676	311	41	some	some	DET
american_scientific_journal-2676	311	42	12	12	NUM
american_scientific_journal-2676	311	43	)	)	PUNCT
american_scientific_journal-2676	311	44	,	,	PUNCT
american_scientific_journal-2676	311	45	(	(	PUNCT
american_scientific_journal-2676	311	46	η∈eh	η∈eh	NOUN
american_scientific_journal-2676	311	47	.	.	PUNCT
american_scientific_journal-2676	312	1	proof	proof	NOUN
american_scientific_journal-2676	312	2	.	.	PUNCT
american_scientific_journal-2676	313	1	let	let	VERB
american_scientific_journal-2676	313	2	)	)	PUNCT
american_scientific_journal-2676	313	3	,	,	PUNCT
american_scientific_journal-2676	313	4	(	(	PUNCT
american_scientific_journal-2676	313	5	el	el	PROPN
american_scientific_journal-2676	313	6	be	be	AUX
american_scientific_journal-2676	313	7	a	a	DET
american_scientific_journal-2676	313	8	p	p	NOUN
american_scientific_journal-2676	313	9	-locally	-locally	ADV
american_scientific_journal-2676	313	10	closed	close	VERB
american_scientific_journal-2676	313	11	soft	soft	ADJ
american_scientific_journal-2676	313	12	set	set	NOUN
american_scientific_journal-2676	313	13	.	.	PUNCT
american_scientific_journal-2676	314	1	then	then	ADV
american_scientific_journal-2676	314	2	,	,	PUNCT
american_scientific_journal-2676	314	3	there	there	PRON
american_scientific_journal-2676	314	4	exist	exist	VERB
american_scientific_journal-2676	314	5	p	p	X
american_scientific_journal-2676	314	6	-closed	-close	VERB
american_scientific_journal-2676	314	7	soft	soft	ADJ
american_scientific_journal-2676	314	8	set	set	NOUN
american_scientific_journal-2676	314	9	)	)	PUNCT
american_scientific_journal-2676	314	10	,	,	PUNCT
american_scientific_journal-2676	314	11	(	(	PUNCT
american_scientific_journal-2676	314	12	ef	ef	X
american_scientific_journal-2676	314	13	and	and	CCONJ
american_scientific_journal-2676	314	14	p	p	NOUN
american_scientific_journal-2676	314	15	-open	-open	ADJ
american_scientific_journal-2676	314	16	soft	soft	ADJ
american_scientific_journal-2676	314	17	set	set	NOUN
american_scientific_journal-2676	314	18	)	)	PUNCT
american_scientific_journal-2676	314	19	,	,	PUNCT
american_scientific_journal-2676	314	20	(	(	PUNCT
american_scientific_journal-2676	314	21	eh	eh	INTJ
american_scientific_journal-2676	314	22	such	such	ADJ
american_scientific_journal-2676	314	23	that	that	PRON
american_scientific_journal-2676	314	24	)	)	PUNCT
american_scientific_journal-2676	314	25	,	,	PUNCT
american_scientific_journal-2676	314	26	(	(	PUNCT
american_scientific_journal-2676	314	27	~),(=	~),(=	NUM
american_scientific_journal-2676	314	28	)	)	PUNCT
american_scientific_journal-2676	314	29	,	,	PUNCT
american_scientific_journal-2676	314	30	(	(	PUNCT
american_scientific_journal-2676	314	31	egefel	egefel	NOUN
american_scientific_journal-2676	314	32	∩	∩	NOUN
american_scientific_journal-2676	314	33	.	.	PUNCT
american_scientific_journal-2676	315	1	it	it	PRON
american_scientific_journal-2676	315	2	follows	follow	VERB
american_scientific_journal-2676	315	3	that	that	PRON
american_scientific_journal-2676	315	4	)	)	PUNCT
american_scientific_journal-2676	315	5	,	,	PUNCT
american_scientific_journal-2676	315	6	(	(	PUNCT
american_scientific_journal-2676	315	7	~),(~	~),(~	NUM
american_scientific_journal-2676	315	8	)	)	PUNCT
american_scientific_journal-2676	315	9	,	,	PUNCT
american_scientific_journal-2676	315	10	(	(	PUNCT
american_scientific_journal-2676	315	11	1212	1212	NUM
american_scientific_journal-2676	315	12	egsclefelscl	egsclefelscl	NOUN
american_scientific_journal-2676	315	13	∩⊆	∩⊆	NOUN
american_scientific_journal-2676	315	14	which	which	PRON
american_scientific_journal-2676	315	15	implies	imply	VERB
american_scientific_journal-2676	315	16	that	that	PRON
american_scientific_journal-2676	315	17	)	)	PUNCT
american_scientific_journal-2676	315	18	,	,	PUNCT
american_scientific_journal-2676	315	19	(	(	PUNCT
american_scientific_journal-2676	315	20	~),(12	~),(12	ADP
american_scientific_journal-2676	315	21	efelscl	efelscl	NOUN
american_scientific_journal-2676	315	22	⊆	⊆	NUM
american_scientific_journal-2676	315	23	and	and	CCONJ
american_scientific_journal-2676	315	24	so	so	ADV
american_scientific_journal-2676	315	25	)	)	PUNCT
american_scientific_journal-2676	315	26	,	,	PUNCT
american_scientific_journal-2676	315	27	(	(	PUNCT
american_scientific_journal-2676	315	28	~),(~),(~),(12	~),(~),(~),(12	NUM
american_scientific_journal-2676	315	29	egefegelscl	egefegelscl	PROPN
american_scientific_journal-2676	315	30	∩⊆∩	∩⊆∩	PROPN
american_scientific_journal-2676	315	31	.	.	PUNCT
american_scientific_journal-2676	316	1	therefore	therefore	ADV
american_scientific_journal-2676	316	2	,	,	PUNCT
american_scientific_journal-2676	316	3	)	)	PUNCT
american_scientific_journal-2676	316	4	,	,	PUNCT
american_scientific_journal-2676	316	5	(	(	PUNCT
american_scientific_journal-2676	316	6	~),(~),(12	~),(~),(12	VERB
american_scientific_journal-2676	316	7	elegelscl	elegelscl	NOUN
american_scientific_journal-2676	316	8	⊆∩	⊆∩	VERB
american_scientific_journal-2676	316	9	.	.	PUNCT
american_scientific_journal-2676	317	1	on	on	ADP
american_scientific_journal-2676	317	2	the	the	DET
american_scientific_journal-2676	317	3	other	other	ADJ
american_scientific_journal-2676	317	4	hand	hand	NOUN
american_scientific_journal-2676	317	5	,	,	PUNCT
american_scientific_journal-2676	317	6	since	since	SCONJ
american_scientific_journal-2676	317	7	)	)	PUNCT
american_scientific_journal-2676	317	8	,	,	PUNCT
american_scientific_journal-2676	317	9	(	(	PUNCT
american_scientific_journal-2676	317	10	~	~	NOUN
american_scientific_journal-2676	317	11	)	)	PUNCT
american_scientific_journal-2676	317	12	,	,	PUNCT
american_scientific_journal-2676	317	13	(	(	PUNCT
american_scientific_journal-2676	317	14	12	12	NUM
american_scientific_journal-2676	317	15	elsclel	elsclel	NOUN
american_scientific_journal-2676	317	16	⊆	⊆	NUM
american_scientific_journal-2676	317	17	,	,	PUNCT
american_scientific_journal-2676	317	18	then	then	ADV
american_scientific_journal-2676	317	19	)	)	PUNCT
american_scientific_journal-2676	317	20	,	,	PUNCT
american_scientific_journal-2676	317	21	(	(	PUNCT
american_scientific_journal-2676	317	22	~),(~),(~	~),(~),(~	NUM
american_scientific_journal-2676	317	23	)	)	PUNCT
american_scientific_journal-2676	317	24	,	,	PUNCT
american_scientific_journal-2676	317	25	(	(	PUNCT
american_scientific_journal-2676	317	26	12	12	NUM
american_scientific_journal-2676	317	27	egelsclegel	egelsclegel	NOUN
american_scientific_journal-2676	317	28	∩⊆∩	∩⊆∩	PROPN
american_scientific_journal-2676	317	29	.	.	PUNCT
american_scientific_journal-2676	318	1	it	it	PRON
american_scientific_journal-2676	318	2	follows	follow	VERB
american_scientific_journal-2676	318	3	that	that	PRON
american_scientific_journal-2676	318	4	)	)	PUNCT
american_scientific_journal-2676	318	5	,	,	PUNCT
american_scientific_journal-2676	318	6	(	(	PUNCT
american_scientific_journal-2676	318	7	~),(~	~),(~	NUM
american_scientific_journal-2676	318	8	)	)	PUNCT
american_scientific_journal-2676	318	9	,	,	PUNCT
american_scientific_journal-2676	318	10	(	(	PUNCT
american_scientific_journal-2676	318	11	12	12	NUM
american_scientific_journal-2676	318	12	egelsclel	egelsclel	ADJ
american_scientific_journal-2676	318	13	∩⊆	∩⊆	NOUN
american_scientific_journal-2676	318	14	.	.	PUNCT
american_scientific_journal-2676	319	1	consequently	consequently	ADV
american_scientific_journal-2676	319	2	,	,	PUNCT
american_scientific_journal-2676	319	3	)	)	PUNCT
american_scientific_journal-2676	319	4	,	,	PUNCT
american_scientific_journal-2676	319	5	(	(	PUNCT
american_scientific_journal-2676	319	6	~),(=	~),(=	NUM
american_scientific_journal-2676	319	7	)	)	PUNCT
american_scientific_journal-2676	319	8	,	,	PUNCT
american_scientific_journal-2676	319	9	(	(	PUNCT
american_scientific_journal-2676	319	10	12	12	NUM
american_scientific_journal-2676	319	11	egelsclel	egelsclel	ADJ
american_scientific_journal-2676	319	12	∩	∩	NOUN
american_scientific_journal-2676	319	13	.	.	PUNCT
american_scientific_journal-2676	320	1	the	the	DET
american_scientific_journal-2676	320	2	sufficiency	sufficiency	NOUN
american_scientific_journal-2676	320	3	of	of	ADP
american_scientific_journal-2676	320	4	the	the	DET
american_scientific_journal-2676	320	5	theorem	theorem	NOUN
american_scientific_journal-2676	320	6	is	be	AUX
american_scientific_journal-2676	320	7	clear	clear	ADJ
american_scientific_journal-2676	320	8	.	.	PUNCT
american_scientific_journal-2676	321	1	definition	definition	NOUN
american_scientific_journal-2676	321	2	4.2	4.2	NUM
american_scientific_journal-2676	321	3	a	a	DET
american_scientific_journal-2676	321	4	sbts	sbts	ADJ
american_scientific_journal-2676	321	5	)	)	PUNCT
american_scientific_journal-2676	321	6	,	,	PUNCT
american_scientific_journal-2676	321	7	,	,	PUNCT
american_scientific_journal-2676	321	8	,	,	PUNCT
american_scientific_journal-2676	321	9	(	(	PUNCT
american_scientific_journal-2676	321	10	21	21	NUM
american_scientific_journal-2676	321	11	ex	ex	X
american_scientific_journal-2676	321	12	ηη	ηη	PROPN
american_scientific_journal-2676	321	13	is	be	AUX
american_scientific_journal-2676	321	14	said	say	VERB
american_scientific_journal-2676	321	15	to	to	PART
american_scientific_journal-2676	321	16	be	be	AUX
american_scientific_journal-2676	321	17	a	a	DET
american_scientific_journal-2676	321	18	pairwise	pairwise	NOUN
american_scientific_journal-2676	321	19	soft	soft	ADJ
american_scientific_journal-2676	321	20	𝑇𝑇𝐿𝐿∗	𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	322	1	[	[	X
american_scientific_journal-2676	322	2	briefly	briefly	ADV
american_scientific_journal-2676	322	3	,	,	PUNCT
american_scientific_journal-2676	322	4	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	322	5	]	]	PUNCT
american_scientific_journal-2676	322	6	if	if	SCONJ
american_scientific_journal-2676	322	7	every	every	DET
american_scientific_journal-2676	322	8	soft	soft	ADJ
american_scientific_journal-2676	322	9	point	point	NOUN
american_scientific_journal-2676	322	10	in	in	ADP
american_scientific_journal-2676	322	11	x	x	PROPN
american_scientific_journal-2676	322	12	is	be	AUX
american_scientific_journal-2676	322	13	a	a	DET
american_scientific_journal-2676	322	14	p	p	NOUN
american_scientific_journal-2676	322	15	-locally	-locally	ADV
american_scientific_journal-2676	322	16	closed	close	VERB
american_scientific_journal-2676	322	17	soft	soft	ADJ
american_scientific_journal-2676	322	18	set	set	NOUN
american_scientific_journal-2676	322	19	.	.	PUNCT
american_scientific_journal-2676	323	1	theorem	theorem	VERB
american_scientific_journal-2676	323	2	4.3	4.3	NUM
american_scientific_journal-2676	323	3	let	let	NOUN
american_scientific_journal-2676	323	4	)	)	PUNCT
american_scientific_journal-2676	323	5	,	,	PUNCT
american_scientific_journal-2676	323	6	,	,	PUNCT
american_scientific_journal-2676	323	7	,	,	PUNCT
american_scientific_journal-2676	323	8	(	(	PUNCT
american_scientific_journal-2676	323	9	21	21	NUM
american_scientific_journal-2676	323	10	ex	ex	X
american_scientific_journal-2676	323	11	ηη	ηη	PROPN
american_scientific_journal-2676	323	12	be	be	AUX
american_scientific_journal-2676	323	13	a	a	DET
american_scientific_journal-2676	323	14	sbts	sbts	ADJ
american_scientific_journal-2676	323	15	.	.	PUNCT
american_scientific_journal-2676	324	1	then	then	ADV
american_scientific_journal-2676	324	2	1	1	X
american_scientific_journal-2676	324	3	)	)	PUNCT
american_scientific_journal-2676	324	4	if	if	SCONJ
american_scientific_journal-2676	324	5	)	)	PUNCT
american_scientific_journal-2676	324	6	,	,	PUNCT
american_scientific_journal-2676	324	7	,	,	PUNCT
american_scientific_journal-2676	324	8	,	,	PUNCT
american_scientific_journal-2676	324	9	(	(	PUNCT
american_scientific_journal-2676	324	10	21	21	NUM
american_scientific_journal-2676	324	11	ex	ex	X
american_scientific_journal-2676	324	12	ηη	ηη	PROPN
american_scientific_journal-2676	324	13	is	be	AUX
american_scientific_journal-2676	324	14	a	a	DET
american_scientific_journal-2676	324	15	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	324	16	2	2	NUM
american_scientific_journal-2676	324	17	�	�	PROPN
american_scientific_journal-2676	324	18	∗	∗	NOUN
american_scientific_journal-2676	324	19	,	,	PUNCT
american_scientific_journal-2676	324	20	then	then	ADV
american_scientific_journal-2676	324	21	it	it	PRON
american_scientific_journal-2676	324	22	is	be	AUX
american_scientific_journal-2676	324	23	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗.	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗.	NOUN
american_scientific_journal-2676	324	24	2	2	NUM
american_scientific_journal-2676	324	25	)	)	PUNCT
american_scientific_journal-2676	324	26	if	if	SCONJ
american_scientific_journal-2676	324	27	)	)	PUNCT
american_scientific_journal-2676	324	28	,	,	PUNCT
american_scientific_journal-2676	324	29	,	,	PUNCT
american_scientific_journal-2676	324	30	,	,	PUNCT
american_scientific_journal-2676	324	31	(	(	PUNCT
american_scientific_journal-2676	324	32	21	21	NUM
american_scientific_journal-2676	324	33	ex	ex	X
american_scientific_journal-2676	324	34	ηη	ηη	PROPN
american_scientific_journal-2676	324	35	is	be	AUX
american_scientific_journal-2676	324	36	a	a	DET
american_scientific_journal-2676	324	37	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	324	38	,	,	PUNCT
american_scientific_journal-2676	324	39	then	then	ADV
american_scientific_journal-2676	324	40	it	it	PRON
american_scientific_journal-2676	324	41	is	be	AUX
american_scientific_journal-2676	324	42	𝑃𝑃𝑃𝑃𝑇𝑇0∗.	𝑃𝑃𝑃𝑃𝑇𝑇0∗.	PROPN
american_scientific_journal-2676	324	43	american	american	ADJ
american_scientific_journal-2676	324	44	scientific	scientific	ADJ
american_scientific_journal-2676	324	45	research	research	NOUN
american_scientific_journal-2676	324	46	journal	journal	NOUN
american_scientific_journal-2676	324	47	for	for	ADP
american_scientific_journal-2676	324	48	engineering	engineering	NOUN
american_scientific_journal-2676	324	49	,	,	PUNCT
american_scientific_journal-2676	324	50	technology	technology	NOUN
american_scientific_journal-2676	324	51	,	,	PUNCT
american_scientific_journal-2676	324	52	and	and	CCONJ
american_scientific_journal-2676	324	53	sciences	science	NOUN
american_scientific_journal-2676	324	54	(	(	PUNCT
american_scientific_journal-2676	324	55	asrjets	asrjet	NOUN
american_scientific_journal-2676	324	56	)	)	PUNCT
american_scientific_journal-2676	324	57	(	(	PUNCT
american_scientific_journal-2676	324	58	2017	2017	NUM
american_scientific_journal-2676	324	59	)	)	PUNCT
american_scientific_journal-2676	324	60	volume	volume	NOUN
american_scientific_journal-2676	324	61	28	28	NUM
american_scientific_journal-2676	324	62	,	,	PUNCT
american_scientific_journal-2676	324	63	no	no	DET
american_scientific_journal-2676	324	64	1	1	NUM
american_scientific_journal-2676	324	65	,	,	PUNCT
american_scientific_journal-2676	324	66	pp	pp	ADV
american_scientific_journal-2676	324	67	225	225	NUM
american_scientific_journal-2676	324	68	-	-	SYM
american_scientific_journal-2676	324	69	247	247	NUM
american_scientific_journal-2676	324	70	239	239	NUM
american_scientific_journal-2676	324	71	proof	proof	NOUN
american_scientific_journal-2676	324	72	.	.	PUNCT
american_scientific_journal-2676	325	1	(	(	PUNCT
american_scientific_journal-2676	325	2	1	1	NUM
american_scientific_journal-2676	325	3	)	)	PUNCT
american_scientific_journal-2676	325	4	:	:	PUNCT
american_scientific_journal-2676	325	5	since	since	SCONJ
american_scientific_journal-2676	325	6	)	)	PUNCT
american_scientific_journal-2676	325	7	,	,	PUNCT
american_scientific_journal-2676	325	8	,	,	PUNCT
american_scientific_journal-2676	325	9	,	,	PUNCT
american_scientific_journal-2676	325	10	(	(	PUNCT
american_scientific_journal-2676	325	11	21	21	NUM
american_scientific_journal-2676	325	12	ex	ex	X
american_scientific_journal-2676	325	13	ηη	ηη	PROPN
american_scientific_journal-2676	325	14	is	be	AUX
american_scientific_journal-2676	325	15	a	a	DET
american_scientific_journal-2676	325	16	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	325	17	2	2	NUM
american_scientific_journal-2676	325	18	�	�	PROPN
american_scientific_journal-2676	325	19	∗	∗	NOUN
american_scientific_journal-2676	325	20	,	,	PUNCT
american_scientific_journal-2676	325	21	then	then	ADV
american_scientific_journal-2676	325	22	every	every	DET
american_scientific_journal-2676	325	23	soft	soft	ADJ
american_scientific_journal-2676	325	24	point	point	NOUN
american_scientific_journal-2676	325	25	is	be	AUX
american_scientific_journal-2676	325	26	a	a	DET
american_scientific_journal-2676	325	27	p	p	NOUN
american_scientific_journal-2676	325	28	-open	-open	ADJ
american_scientific_journal-2676	325	29	soft	soft	ADJ
american_scientific_journal-2676	325	30	set	set	NOUN
american_scientific_journal-2676	325	31	or	or	CCONJ
american_scientific_journal-2676	325	32	a	a	DET
american_scientific_journal-2676	325	33	p	p	NOUN
american_scientific_journal-2676	325	34	-closed	-close	VERB
american_scientific_journal-2676	325	35	soft	soft	ADJ
american_scientific_journal-2676	325	36	set	set	NOUN
american_scientific_journal-2676	325	37	.	.	PUNCT
american_scientific_journal-2676	326	1	it	it	PRON
american_scientific_journal-2676	326	2	follows	follow	VERB
american_scientific_journal-2676	326	3	that	that	SCONJ
american_scientific_journal-2676	326	4	,	,	PUNCT
american_scientific_journal-2676	326	5	by	by	ADP
american_scientific_journal-2676	326	6	proposition	proposition	NOUN
american_scientific_journal-2676	326	7	4.1	4.1	NUM
american_scientific_journal-2676	326	8	,	,	PUNCT
american_scientific_journal-2676	326	9	every	every	DET
american_scientific_journal-2676	326	10	soft	soft	ADJ
american_scientific_journal-2676	326	11	point	point	NOUN
american_scientific_journal-2676	326	12	is	be	AUX
american_scientific_journal-2676	326	13	a	a	DET
american_scientific_journal-2676	326	14	p	p	NOUN
american_scientific_journal-2676	326	15	-locally	-locally	ADV
american_scientific_journal-2676	326	16	closed	close	VERB
american_scientific_journal-2676	326	17	soft	soft	ADJ
american_scientific_journal-2676	326	18	set	set	NOUN
american_scientific_journal-2676	326	19	.	.	PUNCT
american_scientific_journal-2676	327	1	consequently	consequently	ADV
american_scientific_journal-2676	327	2	,	,	PUNCT
american_scientific_journal-2676	327	3	)	)	PUNCT
american_scientific_journal-2676	327	4	,	,	PUNCT
american_scientific_journal-2676	327	5	,	,	PUNCT
american_scientific_journal-2676	327	6	,	,	PUNCT
american_scientific_journal-2676	327	7	(	(	PUNCT
american_scientific_journal-2676	327	8	21	21	NUM
american_scientific_journal-2676	327	9	ex	ex	X
american_scientific_journal-2676	327	10	ηη	ηη	PROPN
american_scientific_journal-2676	327	11	is	be	AUX
american_scientific_journal-2676	327	12	a	a	DET
american_scientific_journal-2676	327	13	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗.	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗.	NOUN
american_scientific_journal-2676	327	14	(	(	PUNCT
american_scientific_journal-2676	327	15	2	2	NUM
american_scientific_journal-2676	327	16	)	)	PUNCT
american_scientific_journal-2676	327	17	:	:	PUNCT
american_scientific_journal-2676	327	18	since	since	SCONJ
american_scientific_journal-2676	327	19	)	)	PUNCT
american_scientific_journal-2676	327	20	,	,	PUNCT
american_scientific_journal-2676	327	21	,	,	PUNCT
american_scientific_journal-2676	327	22	,	,	PUNCT
american_scientific_journal-2676	327	23	(	(	PUNCT
american_scientific_journal-2676	327	24	21	21	NUM
american_scientific_journal-2676	327	25	ex	ex	X
american_scientific_journal-2676	327	26	ηη	ηη	PROPN
american_scientific_journal-2676	327	27	is	be	AUX
american_scientific_journal-2676	327	28	a	a	DET
american_scientific_journal-2676	327	29	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	327	30	,	,	PUNCT
american_scientific_journal-2676	327	31	then	then	ADV
american_scientific_journal-2676	327	32	every	every	DET
american_scientific_journal-2676	327	33	soft	soft	ADJ
american_scientific_journal-2676	327	34	point	point	NOUN
american_scientific_journal-2676	327	35	is	be	AUX
american_scientific_journal-2676	327	36	a	a	DET
american_scientific_journal-2676	327	37	p	p	NOUN
american_scientific_journal-2676	327	38	-locally	-locally	ADV
american_scientific_journal-2676	327	39	closed	close	VERB
american_scientific_journal-2676	327	40	soft	soft	ADJ
american_scientific_journal-2676	327	41	set	set	NOUN
american_scientific_journal-2676	327	42	.	.	PUNCT
american_scientific_journal-2676	328	1	it	it	PRON
american_scientific_journal-2676	328	2	follows	follow	VERB
american_scientific_journal-2676	328	3	that	that	SCONJ
american_scientific_journal-2676	328	4	,	,	PUNCT
american_scientific_journal-2676	328	5	by	by	ADP
american_scientific_journal-2676	328	6	proposition	proposition	NOUN
american_scientific_journal-2676	328	7	4.1	4.1	NUM
american_scientific_journal-2676	328	8	,	,	PUNCT
american_scientific_journal-2676	328	9	every	every	DET
american_scientific_journal-2676	328	10	soft	soft	ADJ
american_scientific_journal-2676	328	11	point	point	NOUN
american_scientific_journal-2676	328	12	is	be	AUX
american_scientific_journal-2676	328	13	a	a	DET
american_scientific_journal-2676	328	14	λp	λp	ADV
american_scientific_journal-2676	328	15	-closed	-close	VERB
american_scientific_journal-2676	328	16	soft	soft	ADJ
american_scientific_journal-2676	328	17	set	set	NOUN
american_scientific_journal-2676	328	18	.	.	PUNCT
american_scientific_journal-2676	329	1	therefore	therefore	ADV
american_scientific_journal-2676	329	2	,	,	PUNCT
american_scientific_journal-2676	329	3	)	)	PUNCT
american_scientific_journal-2676	329	4	,	,	PUNCT
american_scientific_journal-2676	329	5	,	,	PUNCT
american_scientific_journal-2676	329	6	,	,	PUNCT
american_scientific_journal-2676	329	7	(	(	PUNCT
american_scientific_journal-2676	329	8	21	21	NUM
american_scientific_journal-2676	329	9	ex	ex	X
american_scientific_journal-2676	329	10	ηη	ηη	PROPN
american_scientific_journal-2676	329	11	is	be	AUX
american_scientific_journal-2676	329	12	a	a	DET
american_scientific_journal-2676	329	13	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	ADJ
american_scientific_journal-2676	329	14	[	[	PUNCT
american_scientific_journal-2676	329	15	by	by	SCONJ
american_scientific_journal-2676	329	16	theorem	theorem	ADJ
american_scientific_journal-2676	329	17	2.8	2.8	NUM
american_scientific_journal-2676	329	18	]	]	PUNCT
american_scientific_journal-2676	329	19	.	.	PUNCT
american_scientific_journal-2676	330	1	remark	remark	VERB
american_scientific_journal-2676	330	2	4.2	4.2	NUM
american_scientific_journal-2676	330	3	the	the	DET
american_scientific_journal-2676	330	4	converse	converse	NOUN
american_scientific_journal-2676	330	5	of	of	ADP
american_scientific_journal-2676	330	6	items	item	NOUN
american_scientific_journal-2676	330	7	(	(	PUNCT
american_scientific_journal-2676	330	8	1	1	NUM
american_scientific_journal-2676	330	9	)	)	PUNCT
american_scientific_journal-2676	330	10	and	and	CCONJ
american_scientific_journal-2676	330	11	(	(	PUNCT
american_scientific_journal-2676	330	12	2	2	X
american_scientific_journal-2676	330	13	)	)	PUNCT
american_scientific_journal-2676	330	14	in	in	ADP
american_scientific_journal-2676	330	15	the	the	DET
american_scientific_journal-2676	330	16	above	above	ADJ
american_scientific_journal-2676	330	17	theorem	theorem	NOUN
american_scientific_journal-2676	330	18	is	be	AUX
american_scientific_journal-2676	330	19	not	not	PART
american_scientific_journal-2676	330	20	true	true	ADJ
american_scientific_journal-2676	330	21	in	in	ADP
american_scientific_journal-2676	330	22	general	general	ADJ
american_scientific_journal-2676	330	23	which	which	PRON
american_scientific_journal-2676	330	24	is	be	AUX
american_scientific_journal-2676	330	25	shown	show	VERB
american_scientific_journal-2676	330	26	in	in	ADP
american_scientific_journal-2676	330	27	the	the	DET
american_scientific_journal-2676	330	28	following	follow	VERB
american_scientific_journal-2676	330	29	example	example	NOUN
american_scientific_journal-2676	330	30	.	.	PUNCT
american_scientific_journal-2676	331	1	example	example	NOUN
american_scientific_journal-2676	331	2	4.2	4.2	NUM
american_scientific_journal-2676	331	3	let	let	NOUN
american_scientific_journal-2676	331	4	)	)	PUNCT
american_scientific_journal-2676	331	5	,	,	PUNCT
american_scientific_journal-2676	331	6	,	,	PUNCT
american_scientific_journal-2676	331	7	,	,	PUNCT
american_scientific_journal-2676	331	8	(	(	PUNCT
american_scientific_journal-2676	331	9	21	21	NUM
american_scientific_journal-2676	331	10	ex	ex	X
american_scientific_journal-2676	331	11	ηη	ηη	PROPN
american_scientific_journal-2676	331	12	be	be	AUX
american_scientific_journal-2676	331	13	the	the	DET
american_scientific_journal-2676	331	14	same	same	ADJ
american_scientific_journal-2676	331	15	in	in	ADP
american_scientific_journal-2676	331	16	example	example	NOUN
american_scientific_journal-2676	331	17	3.1	3.1	NUM
american_scientific_journal-2676	331	18	.	.	PUNCT
american_scientific_journal-2676	332	1	since	since	SCONJ
american_scientific_journal-2676	332	2	)	)	PUNCT
american_scientific_journal-2676	332	3	,	,	PUNCT
american_scientific_journal-2676	332	4	(	(	PUNCT
american_scientific_journal-2676	332	5	=)	=)	INTJ
american_scientific_journal-2676	332	6	,	,	PUNCT
american_scientific_journal-2676	332	7	(	(	PUNCT
american_scientific_journal-2676	332	8	11	11	NUM
american_scientific_journal-2676	332	9	eyep	eyep	NOUN
american_scientific_journal-2676	332	10	e	e	PROPN
american_scientific_journal-2676	332	11	c	c	PROPN
american_scientific_journal-2676	332	12	,	,	PUNCT
american_scientific_journal-2676	332	13	then	then	ADV
american_scientific_journal-2676	332	14	)	)	PUNCT
american_scientific_journal-2676	332	15	,	,	PUNCT
american_scientific_journal-2676	332	16	(	(	PUNCT
american_scientific_journal-2676	332	17	1	1	NUM
american_scientific_journal-2676	332	18	eye	eye	NOUN
american_scientific_journal-2676	332	19	is	be	AUX
american_scientific_journal-2676	332	20	a	a	DET
american_scientific_journal-2676	332	21	p	p	NOUN
american_scientific_journal-2676	332	22	-closed	-close	VERB
american_scientific_journal-2676	332	23	soft	soft	ADJ
american_scientific_journal-2676	332	24	set	set	NOUN
american_scientific_journal-2676	332	25	.	.	PUNCT
american_scientific_journal-2676	333	1	it	it	PRON
american_scientific_journal-2676	333	2	follows	follow	VERB
american_scientific_journal-2676	333	3	that	that	PRON
american_scientific_journal-2676	333	4	)	)	PUNCT
american_scientific_journal-2676	333	5	,	,	PUNCT
american_scientific_journal-2676	333	6	(	(	PUNCT
american_scientific_journal-2676	333	7	1	1	NUM
american_scientific_journal-2676	333	8	eye	eye	NOUN
american_scientific_journal-2676	333	9	is	be	AUX
american_scientific_journal-2676	333	10	a	a	DET
american_scientific_journal-2676	333	11	p	p	NOUN
american_scientific_journal-2676	333	12	-locally	-locally	ADV
american_scientific_journal-2676	333	13	closed	close	VERB
american_scientific_journal-2676	333	14	soft	soft	ADJ
american_scientific_journal-2676	333	15	set	set	NOUN
american_scientific_journal-2676	333	16	.	.	PUNCT
american_scientific_journal-2676	334	1	also	also	ADV
american_scientific_journal-2676	334	2	,	,	PUNCT
american_scientific_journal-2676	334	3	)	)	PUNCT
american_scientific_journal-2676	334	4	,	,	PUNCT
american_scientific_journal-2676	334	5	(	(	PUNCT
american_scientific_journal-2676	334	6	=)	=)	INTJ
american_scientific_journal-2676	334	7	,	,	PUNCT
american_scientific_journal-2676	334	8	(	(	PUNCT
american_scientific_journal-2676	334	9	22	22	NUM
american_scientific_journal-2676	334	10	eyep	eyep	NOUN
american_scientific_journal-2676	334	11	e	e	X
american_scientific_journal-2676	334	12	c	c	PROPN
american_scientific_journal-2676	334	13	is	be	AUX
american_scientific_journal-2676	334	14	a	a	DET
american_scientific_journal-2676	334	15	p	p	NOUN
american_scientific_journal-2676	334	16	locally	locally	ADV
american_scientific_journal-2676	334	17	closed	close	VERB
american_scientific_journal-2676	334	18	soft	soft	ADJ
american_scientific_journal-2676	334	19	set	set	NOUN
american_scientific_journal-2676	334	20	.	.	PUNCT
american_scientific_journal-2676	335	1	now	now	ADV
american_scientific_journal-2676	335	2	,	,	PUNCT
american_scientific_journal-2676	335	3	since	since	SCONJ
american_scientific_journal-2676	335	4	c	c	PROPN
american_scientific_journal-2676	335	5	e	e	PROPN
american_scientific_journal-2676	335	6	egehex	egehex	PROPN
american_scientific_journal-2676	335	7	)	)	PUNCT
american_scientific_journal-2676	335	8	,	,	PUNCT
american_scientific_journal-2676	335	9	(	(	PUNCT
american_scientific_journal-2676	335	10	~),(=	~),(=	NUM
american_scientific_journal-2676	335	11	)	)	PUNCT
american_scientific_journal-2676	335	12	,	,	PUNCT
american_scientific_journal-2676	335	13	(	(	PUNCT
american_scientific_journal-2676	335	14	21	21	NUM
american_scientific_journal-2676	335	15	∩	∩	NOUN
american_scientific_journal-2676	335	16	,	,	PUNCT
american_scientific_journal-2676	335	17	then	then	ADV
american_scientific_journal-2676	335	18	)	)	PUNCT
american_scientific_journal-2676	335	19	,	,	PUNCT
american_scientific_journal-2676	335	20	(	(	PUNCT
american_scientific_journal-2676	335	21	1	1	NUM
american_scientific_journal-2676	335	22	exe	exe	NOUN
american_scientific_journal-2676	335	23	is	be	AUX
american_scientific_journal-2676	335	24	a	a	DET
american_scientific_journal-2676	335	25	p	p	NOUN
american_scientific_journal-2676	335	26	-locally	-locally	ADV
american_scientific_journal-2676	335	27	closed	close	VERB
american_scientific_journal-2676	335	28	soft	soft	ADJ
american_scientific_journal-2676	335	29	set	set	NOUN
american_scientific_journal-2676	335	30	.	.	PUNCT
american_scientific_journal-2676	336	1	also	also	ADV
american_scientific_journal-2676	336	2	,	,	PUNCT
american_scientific_journal-2676	336	3	c	c	PROPN
american_scientific_journal-2676	336	4	e	e	PRON
american_scientific_journal-2676	336	5	egehex	egehex	PROPN
american_scientific_journal-2676	336	6	)	)	PUNCT
american_scientific_journal-2676	336	7	,	,	PUNCT
american_scientific_journal-2676	336	8	(	(	PUNCT
american_scientific_journal-2676	336	9	~),(=	~),(=	NUM
american_scientific_journal-2676	336	10	)	)	PUNCT
american_scientific_journal-2676	336	11	,	,	PUNCT
american_scientific_journal-2676	336	12	(	(	PUNCT
american_scientific_journal-2676	336	13	12	12	NUM
american_scientific_journal-2676	336	14	∩	∩	NOUN
american_scientific_journal-2676	336	15	.	.	PUNCT
american_scientific_journal-2676	337	1	it	it	PRON
american_scientific_journal-2676	337	2	follows	follow	VERB
american_scientific_journal-2676	337	3	that	that	PRON
american_scientific_journal-2676	337	4	)	)	PUNCT
american_scientific_journal-2676	337	5	,	,	PUNCT
american_scientific_journal-2676	337	6	(	(	PUNCT
american_scientific_journal-2676	337	7	2	2	NUM
american_scientific_journal-2676	337	8	exe	exe	NOUN
american_scientific_journal-2676	337	9	is	be	AUX
american_scientific_journal-2676	337	10	a	a	DET
american_scientific_journal-2676	337	11	a	a	DET
american_scientific_journal-2676	337	12	p	p	NOUN
american_scientific_journal-2676	337	13	-locally	-locally	ADV
american_scientific_journal-2676	337	14	closed	close	VERB
american_scientific_journal-2676	337	15	soft	soft	ADJ
american_scientific_journal-2676	337	16	set	set	NOUN
american_scientific_journal-2676	337	17	.	.	PUNCT
american_scientific_journal-2676	338	1	therefore	therefore	ADV
american_scientific_journal-2676	338	2	,	,	PUNCT
american_scientific_journal-2676	338	3	every	every	DET
american_scientific_journal-2676	338	4	soft	soft	ADJ
american_scientific_journal-2676	338	5	point	point	NOUN
american_scientific_journal-2676	338	6	in	in	ADP
american_scientific_journal-2676	338	7	x	x	PROPN
american_scientific_journal-2676	338	8	is	be	AUX
american_scientific_journal-2676	338	9	a	a	DET
american_scientific_journal-2676	338	10	p	p	NOUN
american_scientific_journal-2676	338	11	-locally	-locally	ADV
american_scientific_journal-2676	338	12	closed	close	VERB
american_scientific_journal-2676	338	13	soft	soft	ADJ
american_scientific_journal-2676	338	14	set	set	NOUN
american_scientific_journal-2676	338	15	.	.	PUNCT
american_scientific_journal-2676	339	1	hence	hence	ADV
american_scientific_journal-2676	339	2	,	,	PUNCT
american_scientific_journal-2676	339	3	)	)	PUNCT
american_scientific_journal-2676	339	4	,	,	PUNCT
american_scientific_journal-2676	339	5	,	,	PUNCT
american_scientific_journal-2676	339	6	,	,	PUNCT
american_scientific_journal-2676	339	7	(	(	PUNCT
american_scientific_journal-2676	339	8	21	21	NUM
american_scientific_journal-2676	339	9	ex	ex	X
american_scientific_journal-2676	339	10	ηη	ηη	PROPN
american_scientific_journal-2676	339	11	is	be	AUX
american_scientific_journal-2676	339	12	a	a	DET
american_scientific_journal-2676	339	13	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗.	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗.	NOUN
american_scientific_journal-2676	339	14	on	on	ADP
american_scientific_journal-2676	339	15	the	the	DET
american_scientific_journal-2676	339	16	other	other	ADJ
american_scientific_journal-2676	339	17	hand	hand	NOUN
american_scientific_journal-2676	339	18	,	,	PUNCT
american_scientific_journal-2676	339	19	)	)	PUNCT
american_scientific_journal-2676	339	20	,	,	PUNCT
american_scientific_journal-2676	339	21	,	,	PUNCT
american_scientific_journal-2676	339	22	,	,	PUNCT
american_scientific_journal-2676	339	23	(	(	PUNCT
american_scientific_journal-2676	339	24	21	21	NUM
american_scientific_journal-2676	339	25	ex	ex	NOUN
american_scientific_journal-2676	339	26	ηη	ηη	PROPN
american_scientific_journal-2676	339	27	is	be	AUX
american_scientific_journal-2676	339	28	not	not	PART
american_scientific_journal-2676	339	29	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	339	30	2	2	NUM
american_scientific_journal-2676	339	31	�	�	PROPN
american_scientific_journal-2676	339	32	∗	∗	NOUN
american_scientific_journal-2676	339	33	because	because	SCONJ
american_scientific_journal-2676	339	34	)	)	PUNCT
american_scientific_journal-2676	339	35	,	,	PUNCT
american_scientific_journal-2676	339	36	(	(	PUNCT
american_scientific_journal-2676	339	37	1	1	NUM
american_scientific_journal-2676	339	38	exe	exe	VERB
american_scientific_journal-2676	339	39	neither	neither	CCONJ
american_scientific_journal-2676	339	40	p	p	NOUN
american_scientific_journal-2676	339	41	-open	-open	ADJ
american_scientific_journal-2676	339	42	nor	nor	CCONJ
american_scientific_journal-2676	339	43	p	p	NOUN
american_scientific_journal-2676	339	44	-closed	-close	VERB
american_scientific_journal-2676	339	45	soft	soft	ADJ
american_scientific_journal-2676	339	46	set	set	NOUN
american_scientific_journal-2676	339	47	.	.	PUNCT
american_scientific_journal-2676	340	1	remark	remark	VERB
american_scientific_journal-2676	340	2	4.3	4.3	NUM
american_scientific_journal-2676	340	3	the	the	DET
american_scientific_journal-2676	340	4	concepts	concept	NOUN
american_scientific_journal-2676	340	5	of	of	ADP
american_scientific_journal-2676	340	6	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	340	7	and	and	CCONJ
american_scientific_journal-2676	340	8	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	340	9	4	4	NUM
american_scientific_journal-2676	340	10	�	�	PROPN
american_scientific_journal-2676	340	11	∗	∗	NOUN
american_scientific_journal-2676	340	12	are	be	AUX
american_scientific_journal-2676	340	13	independent	independent	ADJ
american_scientific_journal-2676	340	14	as	as	SCONJ
american_scientific_journal-2676	340	15	shown	show	VERB
american_scientific_journal-2676	340	16	in	in	ADP
american_scientific_journal-2676	340	17	the	the	DET
american_scientific_journal-2676	340	18	following	follow	VERB
american_scientific_journal-2676	340	19	example	example	NOUN
american_scientific_journal-2676	340	20	.	.	PUNCT
american_scientific_journal-2676	341	1	example	example	NOUN
american_scientific_journal-2676	341	2	4.3	4.3	NUM
american_scientific_journal-2676	341	3	in	in	ADP
american_scientific_journal-2676	341	4	example	example	NOUN
american_scientific_journal-2676	341	5	4.2	4.2	NUM
american_scientific_journal-2676	341	6	,	,	PUNCT
american_scientific_journal-2676	341	7	we	we	PRON
american_scientific_journal-2676	341	8	have	have	VERB
american_scientific_journal-2676	341	9	)	)	PUNCT
american_scientific_journal-2676	341	10	,	,	PUNCT
american_scientific_journal-2676	341	11	,	,	PUNCT
american_scientific_journal-2676	341	12	,	,	PUNCT
american_scientific_journal-2676	341	13	(	(	PUNCT
american_scientific_journal-2676	341	14	21	21	NUM
american_scientific_journal-2676	341	15	ex	ex	X
american_scientific_journal-2676	341	16	ηη	ηη	PROPN
american_scientific_journal-2676	341	17	is	be	AUX
american_scientific_journal-2676	341	18	a	a	DET
american_scientific_journal-2676	341	19	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	PROPN
american_scientific_journal-2676	341	20	but	but	CCONJ
american_scientific_journal-2676	341	21	it	it	PRON
american_scientific_journal-2676	341	22	is	be	AUX
american_scientific_journal-2676	341	23	not	not	PART
american_scientific_journal-2676	341	24	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	341	25	2	2	NUM
american_scientific_journal-2676	341	26	�	�	PROPN
american_scientific_journal-2676	341	27	∗	∗	NOUN
american_scientific_journal-2676	341	28	which	which	PRON
american_scientific_journal-2676	341	29	implies	imply	VERB
american_scientific_journal-2676	341	30	that	that	PRON
american_scientific_journal-2676	341	31	)	)	PUNCT
american_scientific_journal-2676	341	32	,	,	PUNCT
american_scientific_journal-2676	341	33	,	,	PUNCT
american_scientific_journal-2676	341	34	,	,	PUNCT
american_scientific_journal-2676	341	35	(	(	PUNCT
american_scientific_journal-2676	341	36	21	21	NUM
american_scientific_journal-2676	341	37	ex	ex	NOUN
american_scientific_journal-2676	341	38	ηη	ηη	PROPN
american_scientific_journal-2676	341	39	is	be	AUX
american_scientific_journal-2676	341	40	not	not	PART
american_scientific_journal-2676	341	41	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	341	42	4	4	NUM
american_scientific_journal-2676	341	43	�	�	PROPN
american_scientific_journal-2676	341	44	∗	∗	NOUN
american_scientific_journal-2676	341	45	[	[	PUNCT
american_scientific_journal-2676	341	46	by	by	ADP
american_scientific_journal-2676	341	47	corollary	corollary	ADJ
american_scientific_journal-2676	341	48	3.1	3.1	NUM
american_scientific_journal-2676	341	49	]	]	PUNCT
american_scientific_journal-2676	341	50	.	.	PUNCT
american_scientific_journal-2676	342	1	from	from	ADP
american_scientific_journal-2676	342	2	examples	example	NOUN
american_scientific_journal-2676	342	3	3.2	3.2	NUM
american_scientific_journal-2676	342	4	and	and	CCONJ
american_scientific_journal-2676	342	5	3.4	3.4	NUM
american_scientific_journal-2676	342	6	,	,	PUNCT
american_scientific_journal-2676	342	7	we	we	PRON
american_scientific_journal-2676	342	8	have	have	VERB
american_scientific_journal-2676	342	9	)	)	PUNCT
american_scientific_journal-2676	342	10	,	,	PUNCT
american_scientific_journal-2676	342	11	,	,	PUNCT
american_scientific_journal-2676	342	12	,	,	PUNCT
american_scientific_journal-2676	342	13	(	(	PUNCT
american_scientific_journal-2676	342	14	ex	ex	X
american_scientific_journal-2676	342	15	dd	dd	VERB
american_scientific_journal-2676	342	16	ηη	ηη	PRON
american_scientific_journal-2676	342	17	is	be	AUX
american_scientific_journal-2676	342	18	a	a	DET
american_scientific_journal-2676	342	19	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	342	20	4	4	NUM
american_scientific_journal-2676	342	21	�	�	PROPN
american_scientific_journal-2676	342	22	∗	∗	NOUN
american_scientific_journal-2676	342	23	but	but	CCONJ
american_scientific_journal-2676	342	24	it	it	PRON
american_scientific_journal-2676	342	25	is	be	AUX
american_scientific_journal-2676	342	26	not	not	PART
american_scientific_journal-2676	342	27	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	𝑃𝑃𝑃𝑃𝑇𝑇𝐿𝐿∗	VERB
american_scientific_journal-2676	342	28	for	for	ADP
american_scientific_journal-2676	342	29	)	)	PUNCT
american_scientific_journal-2676	342	30	,	,	PUNCT
american_scientific_journal-2676	342	31	(	(	PUNCT
american_scientific_journal-2676	342	32	0	0	NUM
american_scientific_journal-2676	342	33	ed	ed	NOUN
american_scientific_journal-2676	342	34	is	be	AUX
american_scientific_journal-2676	342	35	not	not	PART
american_scientific_journal-2676	342	36	p	p	PRON
american_scientific_journal-2676	342	37	-locally	-locally	ADV
american_scientific_journal-2676	342	38	closed	close	VERB
american_scientific_journal-2676	342	39	soft	soft	ADJ
american_scientific_journal-2676	342	40	set	set	NOUN
american_scientific_journal-2676	342	41	.	.	PUNCT
american_scientific_journal-2676	343	1	5	5	X
american_scientific_journal-2676	343	2	.	.	X
american_scientific_journal-2676	343	3	on	on	ADP
american_scientific_journal-2676	343	4	λp	λp	ADP
american_scientific_journal-2676	343	5	open	open	ADJ
american_scientific_journal-2676	343	6	soft	soft	ADJ
american_scientific_journal-2676	343	7	sets	set	NOUN
american_scientific_journal-2676	343	8	in	in	ADP
american_scientific_journal-2676	343	9	this	this	DET
american_scientific_journal-2676	343	10	section	section	NOUN
american_scientific_journal-2676	343	11	,	,	PUNCT
american_scientific_journal-2676	343	12	we	we	PRON
american_scientific_journal-2676	343	13	introduce	introduce	VERB
american_scientific_journal-2676	343	14	the	the	DET
american_scientific_journal-2676	343	15	notion	notion	NOUN
american_scientific_journal-2676	343	16	of	of	ADP
american_scientific_journal-2676	343	17	pairwise	pairwise	NOUN
american_scientific_journal-2676	343	18	λ	λ	NOUN
american_scientific_journal-2676	343	19	-open	-open	NOUN
american_scientific_journal-2676	343	20	soft	soft	ADJ
american_scientific_journal-2676	343	21	sets	set	NOUN
american_scientific_journal-2676	343	22	.	.	PUNCT
american_scientific_journal-2676	344	1	some	some	DET
american_scientific_journal-2676	344	2	basic	basic	ADJ
american_scientific_journal-2676	344	3	properties	property	NOUN
american_scientific_journal-2676	344	4	of	of	ADP
american_scientific_journal-2676	344	5	them	they	PRON
american_scientific_journal-2676	344	6	and	and	CCONJ
american_scientific_journal-2676	344	7	their	their	PRON
american_scientific_journal-2676	344	8	relationships	relationship	NOUN
american_scientific_journal-2676	344	9	with	with	ADP
american_scientific_journal-2676	344	10	different	different	ADJ
american_scientific_journal-2676	344	11	types	type	NOUN
american_scientific_journal-2676	344	12	of	of	ADP
american_scientific_journal-2676	344	13	soft	soft	ADJ
american_scientific_journal-2676	344	14	sets	set	NOUN
american_scientific_journal-2676	344	15	are	be	AUX
american_scientific_journal-2676	344	16	studied	study	VERB
american_scientific_journal-2676	344	17	.	.	PUNCT
american_scientific_journal-2676	345	1	definition	definition	NOUN
american_scientific_journal-2676	345	2	5.1	5.1	NUM
american_scientific_journal-2676	345	3	a	a	DET
american_scientific_journal-2676	345	4	soft	soft	ADJ
american_scientific_journal-2676	345	5	set	set	NOUN
american_scientific_journal-2676	345	6	)	)	PUNCT
american_scientific_journal-2676	345	7	,	,	PUNCT
american_scientific_journal-2676	345	8	(	(	PUNCT
american_scientific_journal-2676	345	9	eg	eg	NOUN
american_scientific_journal-2676	345	10	in	in	ADP
american_scientific_journal-2676	345	11	a	a	DET
american_scientific_journal-2676	345	12	sbts	sbts	ADJ
american_scientific_journal-2676	345	13	)	)	PUNCT
american_scientific_journal-2676	345	14	,	,	PUNCT
american_scientific_journal-2676	345	15	,	,	PUNCT
american_scientific_journal-2676	345	16	,	,	PUNCT
american_scientific_journal-2676	345	17	(	(	PUNCT
american_scientific_journal-2676	345	18	21	21	NUM
american_scientific_journal-2676	345	19	ex	ex	X
american_scientific_journal-2676	345	20	ηη	ηη	PROPN
american_scientific_journal-2676	345	21	is	be	AUX
american_scientific_journal-2676	345	22	said	say	VERB
american_scientific_journal-2676	345	23	to	to	PART
american_scientific_journal-2676	345	24	be	be	AUX
american_scientific_journal-2676	345	25	a	a	DET
american_scientific_journal-2676	345	26	pairwise	pairwise	NOUN
american_scientific_journal-2676	345	27	λ	λ	NOUN
american_scientific_journal-2676	345	28	-open	-open	NOUN
american_scientific_journal-2676	345	29	soft	soft	ADJ
american_scientific_journal-2676	345	30	set[briefly	set[briefly	NOUN
american_scientific_journal-2676	345	31	,	,	PUNCT
american_scientific_journal-2676	345	32	λp	λp	X
american_scientific_journal-2676	345	33	-open	-open	VERB
american_scientific_journal-2676	345	34	soft	soft	ADJ
american_scientific_journal-2676	345	35	set	set	NOUN
american_scientific_journal-2676	345	36	]	]	PUNCT
american_scientific_journal-2676	345	37	if	if	SCONJ
american_scientific_journal-2676	345	38	its	its	PRON
american_scientific_journal-2676	345	39	complement	complement	NOUN
american_scientific_journal-2676	345	40	is	be	AUX
american_scientific_journal-2676	345	41	a	a	DET
american_scientific_journal-2676	345	42	λp	λp	ADV
american_scientific_journal-2676	345	43	-closed	-close	VERB
american_scientific_journal-2676	345	44	soft	soft	ADJ
american_scientific_journal-2676	345	45	set	set	NOUN
american_scientific_journal-2676	345	46	.	.	PUNCT
american_scientific_journal-2676	346	1	clearly	clearly	ADV
american_scientific_journal-2676	346	2	,	,	PUNCT
american_scientific_journal-2676	346	3	)	)	PUNCT
american_scientific_journal-2676	346	4	,	,	PUNCT
american_scientific_journal-2676	346	5	(	(	PUNCT
american_scientific_journal-2676	346	6	eg	eg	NOUN
american_scientific_journal-2676	346	7	is	be	AUX
american_scientific_journal-2676	346	8	a	a	DET
american_scientific_journal-2676	346	9	λp	λp	X
american_scientific_journal-2676	346	10	-open	-open	ADJ
american_scientific_journal-2676	346	11	soft	soft	ADJ
american_scientific_journal-2676	346	12	set	set	ADJ
american_scientific_journal-2676	346	13	iff	iff	PROPN
american_scientific_journal-2676	346	14	)	)	PUNCT
american_scientific_journal-2676	346	15	,	,	PUNCT
american_scientific_journal-2676	346	16	(	(	PUNCT
american_scientific_journal-2676	346	17	~),(=	~),(=	NUM
american_scientific_journal-2676	346	18	)	)	PUNCT
american_scientific_journal-2676	346	19	,	,	PUNCT
american_scientific_journal-2676	346	20	(	(	PUNCT
american_scientific_journal-2676	346	21	emeheg	emeheg	X
american_scientific_journal-2676	346	22	∪	∪	NOUN
american_scientific_journal-2676	346	23	,	,	PUNCT
american_scientific_journal-2676	346	24	where	where	SCONJ
american_scientific_journal-2676	346	25	12	12	NUM
american_scientific_journal-2676	346	26	)	)	PUNCT
american_scientific_journal-2676	346	27	,	,	PUNCT
american_scientific_journal-2676	346	28	(	(	PUNCT
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american_scientific_journal-2676	346	30	and	and	CCONJ
american_scientific_journal-2676	346	31	∨λ∈	∨λ∈	X
american_scientific_journal-2676	346	32	p	p	PROPN
american_scientific_journal-2676	346	33	c	c	NOUN
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american_scientific_journal-2676	346	35	ηη	ηη	PROPN
american_scientific_journal-2676	346	36	=)	=)	PROPN
american_scientific_journal-2676	346	37	,	,	PUNCT
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american_scientific_journal-2676	346	39	.	.	PUNCT
american_scientific_journal-2676	347	1	we	we	PRON
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american_scientific_journal-2676	347	5	of	of	ADP
american_scientific_journal-2676	347	6	all	all	DET
american_scientific_journal-2676	347	7	λp	λp	ADP
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american_scientific_journal-2676	347	9	soft	soft	ADJ
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american_scientific_journal-2676	347	13	)	)	PUNCT
american_scientific_journal-2676	347	14	,	,	PUNCT
american_scientific_journal-2676	347	15	,	,	PUNCT
american_scientific_journal-2676	347	16	(	(	PUNCT
american_scientific_journal-2676	347	17	21	21	NUM
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american_scientific_journal-2676	347	19	.	.	PUNCT
american_scientific_journal-2676	348	1	american	american	PROPN
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american_scientific_journal-2676	348	3	research	research	PROPN
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american_scientific_journal-2676	348	7	,	,	PUNCT
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american_scientific_journal-2676	348	9	,	,	PUNCT
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american_scientific_journal-2676	348	12	(	(	PUNCT
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american_scientific_journal-2676	348	14	)	)	PUNCT
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american_scientific_journal-2676	348	16	2017	2017	NUM
american_scientific_journal-2676	348	17	)	)	PUNCT
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american_scientific_journal-2676	348	20	,	,	PUNCT
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american_scientific_journal-2676	348	22	1	1	NUM
american_scientific_journal-2676	348	23	,	,	PUNCT
american_scientific_journal-2676	348	24	pp	pp	ADV
american_scientific_journal-2676	348	25	225	225	NUM
american_scientific_journal-2676	348	26	-	-	SYM
american_scientific_journal-2676	348	27	247	247	NUM
american_scientific_journal-2676	348	28	240	240	NUM
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american_scientific_journal-2676	348	30	5.1	5.1	NUM
american_scientific_journal-2676	348	31	let	let	NOUN
american_scientific_journal-2676	348	32	)	)	PUNCT
american_scientific_journal-2676	348	33	,	,	PUNCT
american_scientific_journal-2676	348	34	,	,	PUNCT
american_scientific_journal-2676	348	35	,	,	PUNCT
american_scientific_journal-2676	348	36	(	(	PUNCT
american_scientific_journal-2676	348	37	21	21	NUM
american_scientific_journal-2676	348	38	ex	ex	X
american_scientific_journal-2676	348	39	ηη	ηη	PROPN
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american_scientific_journal-2676	348	45	)	)	PUNCT
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american_scientific_journal-2676	348	47	)	)	PUNCT
american_scientific_journal-2676	348	48	,	,	PUNCT
american_scientific_journal-2676	348	49	(	(	PUNCT
american_scientific_journal-2676	348	50	∈	∈	PROPN
american_scientific_journal-2676	348	51	.	.	PUNCT
american_scientific_journal-2676	349	1	then	then	ADV
american_scientific_journal-2676	349	2	:	:	PUNCT
american_scientific_journal-2676	349	3	1	1	X
american_scientific_journal-2676	349	4	)	)	PUNCT
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american_scientific_journal-2676	349	8	)	)	PUNCT
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american_scientific_journal-2676	349	13	λp	λp	X
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american_scientific_journal-2676	349	17	.	.	PUNCT
american_scientific_journal-2676	350	1	2	2	X
american_scientific_journal-2676	350	2	)	)	PUNCT
american_scientific_journal-2676	350	3	every	every	DET
american_scientific_journal-2676	350	4	∨p	∨p	NOUN
american_scientific_journal-2676	350	5	-soft	-soft	NOUN
american_scientific_journal-2676	350	6	set	set	NOUN
american_scientific_journal-2676	350	7	is	be	AUX
american_scientific_journal-2676	350	8	a	a	DET
american_scientific_journal-2676	350	9	λp	λp	X
american_scientific_journal-2676	350	10	-open	-open	ADJ
american_scientific_journal-2676	350	11	soft	soft	ADJ
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american_scientific_journal-2676	350	13	.	.	PUNCT
american_scientific_journal-2676	351	1	3	3	X
american_scientific_journal-2676	351	2	)	)	PUNCT
american_scientific_journal-2676	351	3	an	an	DET
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american_scientific_journal-2676	351	7	λp	λp	X
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american_scientific_journal-2676	351	12	a	a	DET
american_scientific_journal-2676	351	13	λp	λp	ADV
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american_scientific_journal-2676	352	2	.	.	PUNCT
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american_scientific_journal-2676	353	2	.	.	PUNCT
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american_scientific_journal-2676	354	2	5.1	5.1	NUM
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american_scientific_journal-2676	354	7	λp	λp	ADP
american_scientific_journal-2676	354	8	-open	-open	ADJ
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american_scientific_journal-2676	354	10	sets	set	NOUN
american_scientific_journal-2676	354	11	is	be	AUX
american_scientific_journal-2676	354	12	a	a	DET
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american_scientific_journal-2676	354	14	soft	soft	ADJ
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american_scientific_journal-2676	354	16	.	.	PUNCT
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american_scientific_journal-2676	355	2	.	.	PUNCT
american_scientific_journal-2676	356	1	the	the	DET
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american_scientific_journal-2676	356	3	is	be	AUX
american_scientific_journal-2676	356	4	direct	direct	ADJ
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american_scientific_journal-2676	356	7	5.1	5.1	NUM
american_scientific_journal-2676	356	8	.	.	PUNCT
american_scientific_journal-2676	357	1	remark	remark	VERB
american_scientific_journal-2676	357	2	5.1	5.1	NUM
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american_scientific_journal-2676	357	4	family	family	NOUN
american_scientific_journal-2676	357	5	of	of	ADP
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american_scientific_journal-2676	357	7	λp	λp	ADP
american_scientific_journal-2676	357	8	-open	-open	ADJ
american_scientific_journal-2676	357	9	soft	soft	ADJ
american_scientific_journal-2676	357	10	sets	set	NOUN
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american_scientific_journal-2676	357	13	be	be	AUX
american_scientific_journal-2676	357	14	a	a	DET
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american_scientific_journal-2676	357	23	.	.	PUNCT
american_scientific_journal-2676	358	1	example	example	NOUN
american_scientific_journal-2676	358	2	5.1	5.1	NUM
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american_scientific_journal-2676	358	4	example	example	NOUN
american_scientific_journal-2676	358	5	3.1	3.1	NUM
american_scientific_journal-2676	358	6	,	,	PUNCT
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american_scientific_journal-2676	358	9	1,	1,	NUM
american_scientific_journal-2676	358	10	...	...	PUNCT
american_scientific_journal-2676	358	11	,6}=:),{(=	,6}=:),{(=	PUNCT
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american_scientific_journal-2676	358	35	211	211	NUM
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american_scientific_journal-2676	358	45	,	,	PUNCT
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american_scientific_journal-2676	358	48	(=	(=	NOUN
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american_scientific_journal-2676	358	50	,	,	PUNCT
american_scientific_journal-2676	358	51	(	(	PUNCT
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american_scientific_journal-2676	358	84	214	214	NUM
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american_scientific_journal-2676	359	20	65121221	65121221	NUM
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american_scientific_journal-2676	360	14	,	,	PUNCT
american_scientific_journal-2676	360	15	,	,	PUNCT
american_scientific_journal-2676	360	16	(	(	PUNCT
american_scientific_journal-2676	360	17	2112	2112	NUM
american_scientific_journal-2676	360	18	ηηλ∈	ηηλ∈	NUM
american_scientific_journal-2676	360	19	but	but	CCONJ
american_scientific_journal-2676	360	20	)	)	PUNCT
american_scientific_journal-2676	360	21	,	,	PUNCT
american_scientific_journal-2676	360	22	(=	(=	ADV
american_scientific_journal-2676	360	23	)	)	PUNCT
american_scientific_journal-2676	360	24	,	,	PUNCT
american_scientific_journal-2676	360	25	(	(	PUNCT
american_scientific_journal-2676	360	26	~	~	NOUN
american_scientific_journal-2676	360	27	)	)	PUNCT
american_scientific_journal-2676	360	28	,	,	PUNCT
american_scientific_journal-2676	360	29	(	(	PUNCT
american_scientific_journal-2676	360	30	112	112	NUM
american_scientific_journal-2676	360	31	emegep	emegep	NOUN
american_scientific_journal-2676	360	32	∩	∩	NOUN
american_scientific_journal-2676	360	33	which	which	PRON
american_scientific_journal-2676	360	34	is	be	AUX
american_scientific_journal-2676	360	35	not	not	PART
american_scientific_journal-2676	360	36	λp	λp	DET
american_scientific_journal-2676	360	37	open	open	ADJ
american_scientific_journal-2676	360	38	soft	soft	ADJ
american_scientific_journal-2676	360	39	set	set	NOUN
american_scientific_journal-2676	360	40	.	.	PUNCT
american_scientific_journal-2676	361	1	theorem	theorem	VERB
american_scientific_journal-2676	361	2	5.2	5.2	NUM
american_scientific_journal-2676	361	3	let	let	NOUN
american_scientific_journal-2676	361	4	)	)	PUNCT
american_scientific_journal-2676	361	5	,	,	PUNCT
american_scientific_journal-2676	361	6	,	,	PUNCT
american_scientific_journal-2676	361	7	,	,	PUNCT
american_scientific_journal-2676	361	8	(	(	PUNCT
american_scientific_journal-2676	361	9	21	21	NUM
american_scientific_journal-2676	361	10	ex	ex	X
american_scientific_journal-2676	361	11	ηη	ηη	PROPN
american_scientific_journal-2676	361	12	be	be	AUX
american_scientific_journal-2676	361	13	a	a	DET
american_scientific_journal-2676	361	14	sbts	sbts	ADJ
american_scientific_journal-2676	361	15	and	and	CCONJ
american_scientific_journal-2676	361	16	exsseg	exsseg	ADJ
american_scientific_journal-2676	361	17	)	)	PUNCT
american_scientific_journal-2676	361	18	(	(	PUNCT
american_scientific_journal-2676	361	19	)	)	PUNCT
american_scientific_journal-2676	361	20	,	,	PUNCT
american_scientific_journal-2676	361	21	(	(	PUNCT
american_scientific_journal-2676	361	22	∈	∈	PROPN
american_scientific_journal-2676	361	23	.	.	PUNCT
american_scientific_journal-2676	362	1	the	the	DET
american_scientific_journal-2676	362	2	following	follow	VERB
american_scientific_journal-2676	362	3	statements	statement	NOUN
american_scientific_journal-2676	362	4	are	be	AUX
american_scientific_journal-2676	362	5	equivalent	equivalent	ADJ
american_scientific_journal-2676	362	6	.	.	PUNCT
american_scientific_journal-2676	363	1	1	1	NUM
american_scientific_journal-2676	363	2	)	)	PUNCT
american_scientific_journal-2676	363	3	)	)	PUNCT
american_scientific_journal-2676	363	4	,	,	PUNCT
american_scientific_journal-2676	363	5	(	(	PUNCT
american_scientific_journal-2676	363	6	eg	eg	NOUN
american_scientific_journal-2676	363	7	is	be	AUX
american_scientific_journal-2676	363	8	a	a	DET
american_scientific_journal-2676	363	9	λp	λp	X
american_scientific_journal-2676	363	10	-open	-open	ADJ
american_scientific_journal-2676	363	11	soft	soft	ADJ
american_scientific_journal-2676	363	12	set	set	NOUN
american_scientific_journal-2676	363	13	.	.	PUNCT
american_scientific_journal-2676	364	1	2	2	NUM
american_scientific_journal-2676	364	2	)	)	PUNCT
american_scientific_journal-2676	364	3	)	)	PUNCT
american_scientific_journal-2676	364	4	,	,	PUNCT
american_scientific_journal-2676	364	5	(	(	PUNCT
american_scientific_journal-2676	364	6	~),(=	~),(=	NUM
american_scientific_journal-2676	364	7	)	)	PUNCT
american_scientific_journal-2676	364	8	,	,	PUNCT
american_scientific_journal-2676	364	9	(	(	PUNCT
american_scientific_journal-2676	364	10	emeheg	emeheg	X
american_scientific_journal-2676	364	11	∪	∪	NOUN
american_scientific_journal-2676	364	12	,	,	PUNCT
american_scientific_journal-2676	364	13	where	where	SCONJ
american_scientific_journal-2676	364	14	12	12	NUM
american_scientific_journal-2676	364	15	)	)	PUNCT
american_scientific_journal-2676	364	16	,	,	PUNCT
american_scientific_journal-2676	364	17	(	(	PUNCT
american_scientific_journal-2676	364	18	η∈eh	η∈eh	NOUN
american_scientific_journal-2676	364	19	,	,	PUNCT
american_scientific_journal-2676	364	20	∨∈	∨∈	PROPN
american_scientific_journal-2676	364	21	pem	pem	NOUN
american_scientific_journal-2676	364	22	η	η	NOUN
american_scientific_journal-2676	364	23	)	)	PUNCT
american_scientific_journal-2676	364	24	,	,	PUNCT
american_scientific_journal-2676	364	25	(	(	PUNCT
american_scientific_journal-2676	364	26	.	.	PUNCT
american_scientific_journal-2676	365	1	3	3	X
american_scientific_journal-2676	365	2	)	)	PUNCT
american_scientific_journal-2676	365	3	)	)	PUNCT
american_scientific_journal-2676	365	4	,	,	PUNCT
american_scientific_journal-2676	365	5	(	(	PUNCT
american_scientific_journal-2676	365	6	~),(=	~),(=	NUM
american_scientific_journal-2676	365	7	)	)	PUNCT
american_scientific_journal-2676	365	8	,	,	PUNCT
american_scientific_journal-2676	365	9	(	(	PUNCT
american_scientific_journal-2676	365	10	12	12	NUM
american_scientific_journal-2676	365	11	emegsinteg	emegsinteg	PROPN
american_scientific_journal-2676	365	12	∪	∪	NOUN
american_scientific_journal-2676	365	13	,	,	PUNCT
american_scientific_journal-2676	365	14	where	where	SCONJ
american_scientific_journal-2676	365	15	∨∈	∨∈	ADJ
american_scientific_journal-2676	365	16	pem	pem	NOUN
american_scientific_journal-2676	365	17	η	η	NOUN
american_scientific_journal-2676	365	18	)	)	PUNCT
american_scientific_journal-2676	365	19	,	,	PUNCT
american_scientific_journal-2676	365	20	(	(	PUNCT
american_scientific_journal-2676	365	21	.	.	PUNCT
american_scientific_journal-2676	365	22	4	4	NUM
american_scientific_journal-2676	365	23	)	)	PUNCT
american_scientific_journal-2676	365	24	)	)	PUNCT
american_scientific_journal-2676	365	25	,	,	PUNCT
american_scientific_journal-2676	365	26	(	(	PUNCT
american_scientific_journal-2676	365	27	~),(=	~),(=	NUM
american_scientific_journal-2676	365	28	)	)	PUNCT
american_scientific_journal-2676	365	29	,	,	PUNCT
american_scientific_journal-2676	365	30	(	(	PUNCT
american_scientific_journal-2676	365	31	*	*	SYM
american_scientific_journal-2676	365	32	1212	1212	NUM
american_scientific_journal-2676	365	33	egskeregsinteg	egskeregsinteg	NOUN
american_scientific_journal-2676	365	34	∪	∪	NOUN
american_scientific_journal-2676	365	35	.	.	PUNCT
american_scientific_journal-2676	366	1	american	american	ADJ
american_scientific_journal-2676	366	2	scientific	scientific	ADJ
american_scientific_journal-2676	366	3	research	research	PROPN
american_scientific_journal-2676	366	4	journal	journal	NOUN
american_scientific_journal-2676	366	5	for	for	ADP
american_scientific_journal-2676	366	6	engineering	engineering	NOUN
american_scientific_journal-2676	366	7	,	,	PUNCT
american_scientific_journal-2676	366	8	technology	technology	NOUN
american_scientific_journal-2676	366	9	,	,	PUNCT
american_scientific_journal-2676	366	10	and	and	CCONJ
american_scientific_journal-2676	366	11	sciences	science	NOUN
american_scientific_journal-2676	366	12	(	(	PUNCT
american_scientific_journal-2676	366	13	asrjets	asrjet	NOUN
american_scientific_journal-2676	366	14	)	)	PUNCT
american_scientific_journal-2676	366	15	(	(	PUNCT
american_scientific_journal-2676	366	16	2017	2017	NUM
american_scientific_journal-2676	366	17	)	)	PUNCT
american_scientific_journal-2676	366	18	volume	volume	NOUN
american_scientific_journal-2676	366	19	28	28	NUM
american_scientific_journal-2676	366	20	,	,	PUNCT
american_scientific_journal-2676	366	21	no	no	DET
american_scientific_journal-2676	366	22	1	1	NUM
american_scientific_journal-2676	366	23	,	,	PUNCT
american_scientific_journal-2676	366	24	pp	pp	ADV
american_scientific_journal-2676	366	25	225	225	NUM
american_scientific_journal-2676	366	26	-	-	SYM
american_scientific_journal-2676	366	27	247	247	NUM
american_scientific_journal-2676	366	28	241	241	NUM
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american_scientific_journal-2676	366	30	.	.	PUNCT
american_scientific_journal-2676	367	1	(	(	PUNCT
american_scientific_journal-2676	367	2	2)(1)⇒	2)(1)⇒	NUM
american_scientific_journal-2676	367	3	:	:	PUNCT
american_scientific_journal-2676	367	4	let	let	VERB
american_scientific_journal-2676	367	5	)	)	PUNCT
american_scientific_journal-2676	367	6	,	,	PUNCT
american_scientific_journal-2676	367	7	(	(	PUNCT
american_scientific_journal-2676	367	8	eg	eg	NOUN
american_scientific_journal-2676	367	9	be	be	AUX
american_scientific_journal-2676	367	10	a	a	DET
american_scientific_journal-2676	367	11	λp	λp	ADV
american_scientific_journal-2676	367	12	-open	-open	ADJ
american_scientific_journal-2676	367	13	soft	soft	ADJ
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american_scientific_journal-2676	367	15	.	.	PUNCT
american_scientific_journal-2676	368	1	then	then	ADV
american_scientific_journal-2676	368	2	,	,	PUNCT
american_scientific_journal-2676	368	3	)	)	PUNCT
american_scientific_journal-2676	368	4	,	,	PUNCT
american_scientific_journal-2676	368	5	(	(	PUNCT
american_scientific_journal-2676	368	6	~),(=	~),(=	NUM
american_scientific_journal-2676	368	7	)	)	PUNCT
american_scientific_journal-2676	368	8	,	,	PUNCT
american_scientific_journal-2676	368	9	(	(	PUNCT
american_scientific_journal-2676	368	10	emeheg	emeheg	X
american_scientific_journal-2676	368	11	∪	∪	NOUN
american_scientific_journal-2676	368	12	,	,	PUNCT
american_scientific_journal-2676	368	13	where	where	SCONJ
american_scientific_journal-2676	368	14	12	12	NUM
american_scientific_journal-2676	368	15	)	)	PUNCT
american_scientific_journal-2676	368	16	,	,	PUNCT
american_scientific_journal-2676	368	17	(	(	PUNCT
american_scientific_journal-2676	368	18	η∈eh	η∈eh	NOUN
american_scientific_journal-2676	368	19	,	,	PUNCT
american_scientific_journal-2676	368	20	c	c	NOUN
american_scientific_journal-2676	368	21	pem	pem	NOUN
american_scientific_journal-2676	368	22	λ∈η	λ∈η	VERB
american_scientific_journal-2676	368	23	)	)	PUNCT
american_scientific_journal-2676	368	24	,	,	PUNCT
american_scientific_journal-2676	368	25	(	(	PUNCT
american_scientific_journal-2676	368	26	,	,	PUNCT
american_scientific_journal-2676	368	27	but	but	CCONJ
american_scientific_journal-2676	368	28	∨λ	∨λ	NOUN
american_scientific_journal-2676	368	29	p	p	PROPN
american_scientific_journal-2676	368	30	c	c	PROPN
american_scientific_journal-2676	368	31	p	p	NOUN
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american_scientific_journal-2676	368	33	=	=	PUNCT
american_scientific_journal-2676	369	1	[	[	X
american_scientific_journal-2676	369	2	by	by	ADP
american_scientific_journal-2676	369	3	theorem	theorem	NOUN
american_scientific_journal-2676	369	4	2.7	2.7	NUM
american_scientific_journal-2676	369	5	]	]	PUNCT
american_scientific_journal-2676	369	6	,	,	PUNCT
american_scientific_journal-2676	369	7	then	then	ADV
american_scientific_journal-2676	369	8	(	(	PUNCT
american_scientific_journal-2676	369	9	2	2	X
american_scientific_journal-2676	369	10	)	)	PUNCT
american_scientific_journal-2676	369	11	holds	hold	VERB
american_scientific_journal-2676	369	12	.	.	PUNCT
american_scientific_journal-2676	370	1	(	(	PUNCT
american_scientific_journal-2676	370	2	3)(2)⇒	3)(2)⇒	NUM
american_scientific_journal-2676	370	3	:	:	PUNCT
american_scientific_journal-2676	370	4	let	let	VERB
american_scientific_journal-2676	370	5	)	)	PUNCT
american_scientific_journal-2676	370	6	,	,	PUNCT
american_scientific_journal-2676	370	7	(	(	PUNCT
american_scientific_journal-2676	370	8	~),(=	~),(=	NUM
american_scientific_journal-2676	370	9	)	)	PUNCT
american_scientific_journal-2676	370	10	,	,	PUNCT
american_scientific_journal-2676	370	11	(	(	PUNCT
american_scientific_journal-2676	370	12	emeheg	emeheg	X
american_scientific_journal-2676	370	13	∪	∪	NOUN
american_scientific_journal-2676	370	14	,	,	PUNCT
american_scientific_journal-2676	370	15	where	where	SCONJ
american_scientific_journal-2676	370	16	12	12	NUM
american_scientific_journal-2676	370	17	)	)	PUNCT
american_scientific_journal-2676	370	18	,	,	PUNCT
american_scientific_journal-2676	370	19	(	(	PUNCT
american_scientific_journal-2676	370	20	η∈eh	η∈eh	NOUN
american_scientific_journal-2676	370	21	,	,	PUNCT
american_scientific_journal-2676	370	22	∨∈	∨∈	PROPN
american_scientific_journal-2676	370	23	pem	pem	NOUN
american_scientific_journal-2676	370	24	η	η	NOUN
american_scientific_journal-2676	370	25	)	)	PUNCT
american_scientific_journal-2676	370	26	,	,	PUNCT
american_scientific_journal-2676	370	27	(	(	PUNCT
american_scientific_journal-2676	370	28	.	.	PUNCT
american_scientific_journal-2676	371	1	since	since	SCONJ
american_scientific_journal-2676	371	2	)	)	PUNCT
american_scientific_journal-2676	371	3	,	,	PUNCT
american_scientific_journal-2676	371	4	(	(	PUNCT
american_scientific_journal-2676	371	5	~	~	NOUN
american_scientific_journal-2676	371	6	)	)	PUNCT
american_scientific_journal-2676	371	7	,	,	PUNCT
american_scientific_journal-2676	371	8	(	(	PUNCT
american_scientific_journal-2676	371	9	egeh	egeh	VERB
american_scientific_journal-2676	371	10	⊆	⊆	NUM
american_scientific_journal-2676	371	11	,	,	PUNCT
american_scientific_journal-2676	371	12	then	then	ADV
american_scientific_journal-2676	371	13	)	)	PUNCT
american_scientific_journal-2676	371	14	,	,	PUNCT
american_scientific_journal-2676	371	15	(	(	PUNCT
american_scientific_journal-2676	371	16	~	~	NOUN
american_scientific_journal-2676	371	17	)	)	PUNCT
american_scientific_journal-2676	371	18	,	,	PUNCT
american_scientific_journal-2676	371	19	(	(	PUNCT
american_scientific_journal-2676	371	20	1212	1212	NUM
american_scientific_journal-2676	371	21	egsintehsint	egsintehsint	NOUN
american_scientific_journal-2676	371	22	⊆	⊆	NUM
american_scientific_journal-2676	371	23	.	.	PUNCT
american_scientific_journal-2676	372	1	therefore	therefore	ADV
american_scientific_journal-2676	372	2	,	,	PUNCT
american_scientific_journal-2676	372	3	)	)	PUNCT
american_scientific_journal-2676	372	4	,	,	PUNCT
american_scientific_journal-2676	372	5	(	(	PUNCT
american_scientific_journal-2676	372	6	~	~	NOUN
american_scientific_journal-2676	372	7	)	)	PUNCT
american_scientific_journal-2676	372	8	,	,	PUNCT
american_scientific_journal-2676	372	9	(	(	PUNCT
american_scientific_journal-2676	372	10	12	12	NUM
american_scientific_journal-2676	372	11	egsinteh	egsinteh	NOUN
american_scientific_journal-2676	372	12	⊆	⊆	NUM
american_scientific_journal-2676	372	13	.	.	PUNCT
american_scientific_journal-2676	373	1	it	it	PRON
american_scientific_journal-2676	373	2	follows	follow	VERB
american_scientific_journal-2676	373	3	that	that	PRON
american_scientific_journal-2676	373	4	)	)	PUNCT
american_scientific_journal-2676	373	5	,	,	PUNCT
american_scientific_journal-2676	373	6	(	(	PUNCT
american_scientific_journal-2676	373	7	~),(~),(~	~),(~),(~	NUM
american_scientific_journal-2676	373	8	)	)	PUNCT
american_scientific_journal-2676	373	9	,	,	PUNCT
american_scientific_journal-2676	373	10	(	(	PUNCT
american_scientific_journal-2676	373	11	12	12	NUM
american_scientific_journal-2676	373	12	emegsintemeh	emegsintemeh	NOUN
american_scientific_journal-2676	373	13	∪⊆∪	∪⊆∪	PROPN
american_scientific_journal-2676	373	14	.	.	PUNCT
american_scientific_journal-2676	374	1	so	so	ADV
american_scientific_journal-2676	374	2	,	,	PUNCT
american_scientific_journal-2676	374	3	)	)	PUNCT
american_scientific_journal-2676	374	4	,	,	PUNCT
american_scientific_journal-2676	374	5	(	(	PUNCT
american_scientific_journal-2676	374	6	~),(~	~),(~	NUM
american_scientific_journal-2676	374	7	)	)	PUNCT
american_scientific_journal-2676	374	8	,	,	PUNCT
american_scientific_journal-2676	374	9	(	(	PUNCT
american_scientific_journal-2676	374	10	12	12	NUM
american_scientific_journal-2676	374	11	emegsinteg	emegsinteg	PROPN
american_scientific_journal-2676	374	12	∪⊆	∪⊆	X
american_scientific_journal-2676	374	13	,	,	PUNCT
american_scientific_journal-2676	374	14	but	but	CCONJ
american_scientific_journal-2676	374	15	)	)	PUNCT
american_scientific_journal-2676	374	16	,	,	PUNCT
american_scientific_journal-2676	374	17	(	(	PUNCT
american_scientific_journal-2676	374	18	~),(12	~),(12	ADP
american_scientific_journal-2676	374	19	egegsint	egegsint	NOUN
american_scientific_journal-2676	374	20	⊆	⊆	NUM
american_scientific_journal-2676	374	21	and	and	CCONJ
american_scientific_journal-2676	374	22	)	)	PUNCT
american_scientific_journal-2676	374	23	,	,	PUNCT
american_scientific_journal-2676	374	24	(	(	PUNCT
american_scientific_journal-2676	374	25	~	~	NOUN
american_scientific_journal-2676	374	26	)	)	PUNCT
american_scientific_journal-2676	374	27	,	,	PUNCT
american_scientific_journal-2676	374	28	(	(	PUNCT
american_scientific_journal-2676	374	29	egem	egem	NOUN
american_scientific_journal-2676	374	30	⊆	⊆	NUM
american_scientific_journal-2676	374	31	then	then	ADV
american_scientific_journal-2676	374	32	)	)	PUNCT
american_scientific_journal-2676	374	33	,	,	PUNCT
american_scientific_journal-2676	374	34	(	(	PUNCT
american_scientific_journal-2676	374	35	~),(~),(12	~),(~),(12	X
american_scientific_journal-2676	374	36	egemegsint	egemegsint	NOUN
american_scientific_journal-2676	374	37	⊆∪	⊆∪	NUM
american_scientific_journal-2676	374	38	.	.	PUNCT
american_scientific_journal-2676	375	1	therefore	therefore	ADV
american_scientific_journal-2676	375	2	,	,	PUNCT
american_scientific_journal-2676	375	3	)	)	PUNCT
american_scientific_journal-2676	375	4	,	,	PUNCT
american_scientific_journal-2676	375	5	(	(	PUNCT
american_scientific_journal-2676	375	6	~),(=	~),(=	NUM
american_scientific_journal-2676	375	7	)	)	PUNCT
american_scientific_journal-2676	375	8	,	,	PUNCT
american_scientific_journal-2676	375	9	(	(	PUNCT
american_scientific_journal-2676	375	10	12	12	NUM
american_scientific_journal-2676	375	11	emegsinteg	emegsinteg	PROPN
american_scientific_journal-2676	375	12	∪	∪	NOUN
american_scientific_journal-2676	375	13	.	.	PUNCT
american_scientific_journal-2676	376	1	hence	hence	ADV
american_scientific_journal-2676	376	2	,	,	PUNCT
american_scientific_journal-2676	376	3	(	(	PUNCT
american_scientific_journal-2676	376	4	3	3	X
american_scientific_journal-2676	376	5	)	)	PUNCT
american_scientific_journal-2676	376	6	holds	hold	VERB
american_scientific_journal-2676	376	7	.	.	PUNCT
american_scientific_journal-2676	377	1	(	(	PUNCT
american_scientific_journal-2676	377	2	3)⇒	3)⇒	NUM
american_scientific_journal-2676	377	3	(	(	PUNCT
american_scientific_journal-2676	377	4	4	4	NUM
american_scientific_journal-2676	377	5	):	):	PUNCT
american_scientific_journal-2676	377	6	let	let	NOUN
american_scientific_journal-2676	377	7	)	)	PUNCT
american_scientific_journal-2676	377	8	,	,	PUNCT
american_scientific_journal-2676	377	9	(	(	PUNCT
american_scientific_journal-2676	377	10	~),(=	~),(=	NUM
american_scientific_journal-2676	377	11	)	)	PUNCT
american_scientific_journal-2676	377	12	,	,	PUNCT
american_scientific_journal-2676	377	13	(	(	PUNCT
american_scientific_journal-2676	377	14	12	12	NUM
american_scientific_journal-2676	377	15	emegsinteg	emegsinteg	PROPN
american_scientific_journal-2676	377	16	∪	∪	NOUN
american_scientific_journal-2676	377	17	,	,	PUNCT
american_scientific_journal-2676	377	18	where	where	SCONJ
american_scientific_journal-2676	377	19	∨∈	∨∈	ADJ
american_scientific_journal-2676	377	20	pem	pem	NOUN
american_scientific_journal-2676	377	21	η	η	NOUN
american_scientific_journal-2676	377	22	)	)	PUNCT
american_scientific_journal-2676	377	23	,	,	PUNCT
american_scientific_journal-2676	377	24	(	(	PUNCT
american_scientific_journal-2676	377	25	.	.	PUNCT
american_scientific_journal-2676	378	1	then	then	ADV
american_scientific_journal-2676	378	2	∪~),(=	∪~),(=	NUM
american_scientific_journal-2676	378	3	)	)	PUNCT
american_scientific_journal-2676	378	4	,	,	PUNCT
american_scientific_journal-2676	378	5	(	(	PUNCT
american_scientific_journal-2676	378	6	12	12	NUM
american_scientific_journal-2676	378	7	egsinteg	egsinteg	NOUN
american_scientific_journal-2676	378	8	)	)	PUNCT
american_scientific_journal-2676	378	9	,	,	PUNCT
american_scientific_journal-2676	378	10	(	(	PUNCT
american_scientific_journal-2676	378	11	*	*	PUNCT
american_scientific_journal-2676	378	12	12	12	NUM
american_scientific_journal-2676	378	13	emsker	emsker	NOUN
american_scientific_journal-2676	378	14	.	.	PUNCT
american_scientific_journal-2676	379	1	since	since	SCONJ
american_scientific_journal-2676	379	2	)	)	PUNCT
american_scientific_journal-2676	379	3	,	,	PUNCT
american_scientific_journal-2676	379	4	(	(	PUNCT
american_scientific_journal-2676	379	5	~	~	NOUN
american_scientific_journal-2676	379	6	)	)	PUNCT
american_scientific_journal-2676	379	7	,	,	PUNCT
american_scientific_journal-2676	379	8	(	(	PUNCT
american_scientific_journal-2676	379	9	egem	egem	NOUN
american_scientific_journal-2676	379	10	⊆	⊆	NUM
american_scientific_journal-2676	379	11	,	,	PUNCT
american_scientific_journal-2676	379	12	then	then	ADV
american_scientific_journal-2676	379	13	)	)	PUNCT
american_scientific_journal-2676	379	14	,	,	PUNCT
american_scientific_journal-2676	379	15	(	(	PUNCT
american_scientific_journal-2676	379	16	~	~	NOUN
american_scientific_journal-2676	379	17	)	)	PUNCT
american_scientific_journal-2676	379	18	,	,	PUNCT
american_scientific_journal-2676	379	19	(	(	PUNCT
american_scientific_journal-2676	379	20	*	*	PUNCT
american_scientific_journal-2676	379	21	12	12	NUM
american_scientific_journal-2676	379	22	*	*	SYM
american_scientific_journal-2676	379	23	12	12	NUM
american_scientific_journal-2676	379	24	egskeremsker	egskeremsker	NOUN
american_scientific_journal-2676	379	25	⊆	⊆	NUM
american_scientific_journal-2676	379	26	which	which	PRON
american_scientific_journal-2676	379	27	implies	imply	VERB
american_scientific_journal-2676	379	28	that	that	PRON
american_scientific_journal-2676	379	29	)	)	PUNCT
american_scientific_journal-2676	379	30	,	,	PUNCT
american_scientific_journal-2676	379	31	(	(	PUNCT
american_scientific_journal-2676	379	32	~),(~),(~	~),(~),(~	NUM
american_scientific_journal-2676	379	33	)	)	PUNCT
american_scientific_journal-2676	379	34	,	,	PUNCT
american_scientific_journal-2676	379	35	(	(	PUNCT
american_scientific_journal-2676	379	36	*	*	VERB
american_scientific_journal-2676	379	37	1212	1212	NUM
american_scientific_journal-2676	379	38	*	*	SYM
american_scientific_journal-2676	379	39	1212	1212	NUM
american_scientific_journal-2676	379	40	egskeregsintemskeregsint	egskeregsintemskeregsint	NOUN
american_scientific_journal-2676	379	41	∪⊆∪	∪⊆∪	PROPN
american_scientific_journal-2676	379	42	.	.	PUNCT
american_scientific_journal-2676	380	1	it	it	PRON
american_scientific_journal-2676	380	2	follows	follow	VERB
american_scientific_journal-2676	380	3	that	that	PRON
american_scientific_journal-2676	380	4	)	)	PUNCT
american_scientific_journal-2676	380	5	,	,	PUNCT
american_scientific_journal-2676	380	6	(	(	PUNCT
american_scientific_journal-2676	380	7	~),(~	~),(~	NUM
american_scientific_journal-2676	380	8	)	)	PUNCT
american_scientific_journal-2676	380	9	,	,	PUNCT
american_scientific_journal-2676	380	10	(	(	PUNCT
american_scientific_journal-2676	380	11	*	*	SYM
american_scientific_journal-2676	380	12	1212	1212	NUM
american_scientific_journal-2676	380	13	egskeregsinteg	egskeregsinteg	NOUN
american_scientific_journal-2676	380	14	∪⊆	∪⊆	X
american_scientific_journal-2676	380	15	,	,	PUNCT
american_scientific_journal-2676	380	16	but	but	CCONJ
american_scientific_journal-2676	380	17	)	)	PUNCT
american_scientific_journal-2676	380	18	,	,	PUNCT
american_scientific_journal-2676	380	19	(	(	PUNCT
american_scientific_journal-2676	380	20	~),(12	~),(12	ADP
american_scientific_journal-2676	380	21	egegsint	egegsint	NOUN
american_scientific_journal-2676	380	22	⊆	⊆	NUM
american_scientific_journal-2676	380	23	and	and	CCONJ
american_scientific_journal-2676	380	24	)	)	PUNCT
american_scientific_journal-2676	380	25	,	,	PUNCT
american_scientific_journal-2676	380	26	(	(	PUNCT
american_scientific_journal-2676	380	27	~	~	NOUN
american_scientific_journal-2676	380	28	)	)	PUNCT
american_scientific_journal-2676	380	29	,	,	PUNCT
american_scientific_journal-2676	380	30	(	(	PUNCT
american_scientific_journal-2676	380	31	*	*	SYM
american_scientific_journal-2676	380	32	12	12	NUM
american_scientific_journal-2676	380	33	egegsker	egegsker	NOUN
american_scientific_journal-2676	380	34	⊆	⊆	NUM
american_scientific_journal-2676	380	35	,	,	PUNCT
american_scientific_journal-2676	380	36	then	then	ADV
american_scientific_journal-2676	380	37	)	)	PUNCT
american_scientific_journal-2676	380	38	,	,	PUNCT
american_scientific_journal-2676	380	39	(	(	PUNCT
american_scientific_journal-2676	380	40	~),(~	~),(~	NUM
american_scientific_journal-2676	380	41	)	)	PUNCT
american_scientific_journal-2676	380	42	,	,	PUNCT
american_scientific_journal-2676	380	43	(	(	PUNCT
american_scientific_journal-2676	380	44	*	*	SYM
american_scientific_journal-2676	380	45	1212	1212	NUM
american_scientific_journal-2676	380	46	egegskeregsint	egegskeregsint	NOUN
american_scientific_journal-2676	380	47	⊆∪	⊆∪	NUM
american_scientific_journal-2676	380	48	.	.	PUNCT
american_scientific_journal-2676	381	1	therefore	therefore	ADV
american_scientific_journal-2676	381	2	,	,	PUNCT
american_scientific_journal-2676	381	3	)	)	PUNCT
american_scientific_journal-2676	381	4	,	,	PUNCT
american_scientific_journal-2676	381	5	(	(	PUNCT
american_scientific_journal-2676	381	6	~),(=	~),(=	NUM
american_scientific_journal-2676	381	7	)	)	PUNCT
american_scientific_journal-2676	381	8	,	,	PUNCT
american_scientific_journal-2676	381	9	(	(	PUNCT
american_scientific_journal-2676	381	10	*	*	SYM
american_scientific_journal-2676	381	11	1212	1212	NUM
american_scientific_journal-2676	381	12	egskeregsinteg	egskeregsinteg	NOUN
american_scientific_journal-2676	381	13	∪	∪	NOUN
american_scientific_journal-2676	381	14	.	.	PUNCT
american_scientific_journal-2676	382	1	hence	hence	ADV
american_scientific_journal-2676	382	2	,	,	PUNCT
american_scientific_journal-2676	382	3	(	(	PUNCT
american_scientific_journal-2676	382	4	4	4	X
american_scientific_journal-2676	382	5	)	)	PUNCT
american_scientific_journal-2676	382	6	holds	hold	VERB
american_scientific_journal-2676	382	7	.	.	PUNCT
american_scientific_journal-2676	383	1	(	(	PUNCT
american_scientific_journal-2676	383	2	1)(4)⇒	1)(4)⇒	NUM
american_scientific_journal-2676	383	3	:	:	PUNCT
american_scientific_journal-2676	383	4	since	since	SCONJ
american_scientific_journal-2676	383	5	1212	1212	NUM
american_scientific_journal-2676	383	6	)	)	PUNCT
american_scientific_journal-2676	383	7	,	,	PUNCT
american_scientific_journal-2676	383	8	(	(	PUNCT
american_scientific_journal-2676	383	9	η∈egsint	η∈egsint	NOUN
american_scientific_journal-2676	383	10	,	,	PUNCT
american_scientific_journal-2676	383	11	∨∈	∨∈	PROPN
american_scientific_journal-2676	383	12	pegsker	pegsker	NOUN
american_scientific_journal-2676	383	13	η	η	PROPN
american_scientific_journal-2676	383	14	)	)	PUNCT
american_scientific_journal-2676	383	15	,	,	PUNCT
american_scientific_journal-2676	383	16	(	(	PUNCT
american_scientific_journal-2676	383	17	*	*	NOUN
american_scientific_journal-2676	383	18	12	12	NUM
american_scientific_journal-2676	383	19	,	,	PUNCT
american_scientific_journal-2676	383	20	then	then	ADV
american_scientific_journal-2676	383	21	)	)	PUNCT
american_scientific_journal-2676	383	22	,	,	PUNCT
american_scientific_journal-2676	383	23	(	(	PUNCT
american_scientific_journal-2676	383	24	eg	eg	NOUN
american_scientific_journal-2676	383	25	is	be	AUX
american_scientific_journal-2676	383	26	a	a	DET
american_scientific_journal-2676	383	27	λp	λp	X
american_scientific_journal-2676	383	28	-open	-open	ADJ
american_scientific_journal-2676	383	29	soft	soft	ADJ
american_scientific_journal-2676	383	30	set	set	NOUN
american_scientific_journal-2676	383	31	.	.	PUNCT
american_scientific_journal-2676	384	1	hence	hence	ADV
american_scientific_journal-2676	384	2	,	,	PUNCT
american_scientific_journal-2676	384	3	(	(	PUNCT
american_scientific_journal-2676	384	4	1	1	X
american_scientific_journal-2676	384	5	)	)	PUNCT
american_scientific_journal-2676	384	6	holds	hold	VERB
american_scientific_journal-2676	384	7	.	.	PUNCT
american_scientific_journal-2676	385	1	definition	definition	NOUN
american_scientific_journal-2676	385	2	5.2	5.2	NUM
american_scientific_journal-2676	385	3	let	let	VERB
american_scientific_journal-2676	385	4	)	)	PUNCT
american_scientific_journal-2676	385	5	,	,	PUNCT
american_scientific_journal-2676	385	6	,	,	PUNCT
american_scientific_journal-2676	385	7	,	,	PUNCT
american_scientific_journal-2676	385	8	(	(	PUNCT
american_scientific_journal-2676	385	9	21	21	NUM
american_scientific_journal-2676	385	10	ex	ex	X
american_scientific_journal-2676	385	11	ηη	ηη	PROPN
american_scientific_journal-2676	385	12	be	be	AUX
american_scientific_journal-2676	385	13	a	a	DET
american_scientific_journal-2676	385	14	sbts	sbts	ADJ
american_scientific_journal-2676	385	15	,	,	PUNCT
american_scientific_journal-2676	385	16	and	and	CCONJ
american_scientific_journal-2676	385	17	let	let	VERB
american_scientific_journal-2676	385	18	exsseg	exsseg	ADJ
american_scientific_journal-2676	385	19	)	)	PUNCT
american_scientific_journal-2676	385	20	(	(	PUNCT
american_scientific_journal-2676	385	21	)	)	PUNCT
american_scientific_journal-2676	385	22	,	,	PUNCT
american_scientific_journal-2676	385	23	(	(	PUNCT
american_scientific_journal-2676	385	24	∈	∈	PROPN
american_scientific_journal-2676	385	25	.	.	PUNCT
american_scientific_journal-2676	386	1	the	the	DET
american_scientific_journal-2676	386	2	λp	λp	ADP
american_scientific_journal-2676	386	3	-soft	-soft	ADJ
american_scientific_journal-2676	386	4	closure	closure	NOUN
american_scientific_journal-2676	386	5	of	of	ADP
american_scientific_journal-2676	386	6	)	)	PUNCT
american_scientific_journal-2676	386	7	,	,	PUNCT
american_scientific_journal-2676	386	8	(	(	PUNCT
american_scientific_journal-2676	386	9	eg	eg	NOUN
american_scientific_journal-2676	386	10	,	,	PUNCT
american_scientific_journal-2676	386	11	denoted	denote	VERB
american_scientific_journal-2676	386	12	by	by	ADP
american_scientific_journal-2676	386	13	)	)	PUNCT
american_scientific_journal-2676	386	14	,	,	PUNCT
american_scientific_journal-2676	386	15	(	(	PUNCT
american_scientific_journal-2676	386	16	egsclpλ	egsclpλ	PROPN
american_scientific_journal-2676	386	17	,	,	PUNCT
american_scientific_journal-2676	386	18	is	be	AUX
american_scientific_journal-2676	386	19	defined	define	VERB
american_scientific_journal-2676	386	20	by	by	ADP
american_scientific_journal-2676	386	21	)	)	PUNCT
american_scientific_journal-2676	386	22	}	}	PUNCT
american_scientific_journal-2676	386	23	,	,	PUNCT
american_scientific_journal-2676	386	24	(	(	PUNCT
american_scientific_journal-2676	386	25	~),(:),,(),{(=	~),(:),,(),{(=	ADJ
american_scientific_journal-2676	386	26	)	)	PUNCT
american_scientific_journal-2676	386	27	,	,	PUNCT
american_scientific_journal-2676	386	28	(	(	PUNCT
american_scientific_journal-2676	386	29	21	21	NUM
american_scientific_journal-2676	386	30	efegxcspefegscl	efegxcspefegscl	NOUN
american_scientific_journal-2676	386	31	ep	ep	PROPN
american_scientific_journal-2676	386	32	⊆∈	⊆∈	NUM
american_scientific_journal-2676	386	33	ηηλλ	ηηλλ	NOUN
american_scientific_journal-2676	386	34			NOUN
american_scientific_journal-2676	386	35	.	.	PUNCT
american_scientific_journal-2676	387	1	lemma	lemma	PROPN
american_scientific_journal-2676	387	2	5.1	5.1	NUM
american_scientific_journal-2676	387	3	let	let	NOUN
american_scientific_journal-2676	387	4	)	)	PUNCT
american_scientific_journal-2676	387	5	,	,	PUNCT
american_scientific_journal-2676	387	6	,	,	PUNCT
american_scientific_journal-2676	387	7	,	,	PUNCT
american_scientific_journal-2676	387	8	(	(	PUNCT
american_scientific_journal-2676	387	9	21	21	NUM
american_scientific_journal-2676	387	10	ex	ex	X
american_scientific_journal-2676	387	11	ηη	ηη	PROPN
american_scientific_journal-2676	387	12	be	be	AUX
american_scientific_journal-2676	387	13	a	a	DET
american_scientific_journal-2676	387	14	sbts	sbts	ADJ
american_scientific_journal-2676	387	15	and	and	CCONJ
american_scientific_journal-2676	387	16	exsseg	exsseg	ADJ
american_scientific_journal-2676	387	17	)	)	PUNCT
american_scientific_journal-2676	387	18	(	(	PUNCT
american_scientific_journal-2676	387	19	)	)	PUNCT
american_scientific_journal-2676	387	20	,	,	PUNCT
american_scientific_journal-2676	387	21	(	(	PUNCT
american_scientific_journal-2676	387	22	∈	∈	PROPN
american_scientific_journal-2676	387	23	.	.	PUNCT
american_scientific_journal-2676	388	1	the	the	DET
american_scientific_journal-2676	388	2	λp	λp	ADP
american_scientific_journal-2676	388	3	-soft	-soft	ADJ
american_scientific_journal-2676	388	4	closure	closure	NOUN
american_scientific_journal-2676	388	5	of	of	ADP
american_scientific_journal-2676	388	6	)	)	PUNCT
american_scientific_journal-2676	388	7	,	,	PUNCT
american_scientific_journal-2676	388	8	(	(	PUNCT
american_scientific_journal-2676	388	9	eg	eg	NOUN
american_scientific_journal-2676	388	10	is	be	AUX
american_scientific_journal-2676	388	11	the	the	DET
american_scientific_journal-2676	388	12	smallest	small	ADJ
american_scientific_journal-2676	388	13	λp	λp	ADP
american_scientific_journal-2676	388	14	-closed	-close	VERB
american_scientific_journal-2676	388	15	soft	soft	ADJ
american_scientific_journal-2676	388	16	superset	superset	NOUN
american_scientific_journal-2676	388	17	of	of	ADP
american_scientific_journal-2676	388	18	)	)	PUNCT
american_scientific_journal-2676	388	19	,	,	PUNCT
american_scientific_journal-2676	388	20	(	(	PUNCT
american_scientific_journal-2676	388	21	eg	eg	NOUN
american_scientific_journal-2676	388	22	.	.	PUNCT
american_scientific_journal-2676	389	1	proof	proof	NOUN
american_scientific_journal-2676	389	2	.	.	PUNCT
american_scientific_journal-2676	390	1	immediate	immediate	ADJ
american_scientific_journal-2676	390	2	from	from	ADP
american_scientific_journal-2676	390	3	theorem	theorem	ADJ
american_scientific_journal-2676	390	4	3.1	3.1	NUM
american_scientific_journal-2676	390	5	.	.	PUNCT
american_scientific_journal-2676	391	1	theorem	theorem	VERB
american_scientific_journal-2676	391	2	5.3	5.3	NUM
american_scientific_journal-2676	391	3	let	let	VERB
american_scientific_journal-2676	391	4	)	)	PUNCT
american_scientific_journal-2676	391	5	,	,	PUNCT
american_scientific_journal-2676	391	6	,	,	PUNCT
american_scientific_journal-2676	391	7	,	,	PUNCT
american_scientific_journal-2676	391	8	(	(	PUNCT
american_scientific_journal-2676	391	9	21	21	NUM
american_scientific_journal-2676	391	10	ex	ex	X
american_scientific_journal-2676	391	11	ηη	ηη	PROPN
american_scientific_journal-2676	391	12	be	be	AUX
american_scientific_journal-2676	391	13	a	a	DET
american_scientific_journal-2676	391	14	sbts	sbts	ADJ
american_scientific_journal-2676	391	15	and	and	CCONJ
american_scientific_journal-2676	391	16	let	let	VERB
american_scientific_journal-2676	391	17	exsseheg	exsseheg	ADJ
american_scientific_journal-2676	391	18	)	)	PUNCT
american_scientific_journal-2676	391	19	(	(	PUNCT
american_scientific_journal-2676	391	20	)	)	PUNCT
american_scientific_journal-2676	391	21	,	,	PUNCT
american_scientific_journal-2676	391	22	(	(	PUNCT
american_scientific_journal-2676	391	23	)	)	PUNCT
american_scientific_journal-2676	391	24	,	,	PUNCT
american_scientific_journal-2676	391	25	,	,	PUNCT
american_scientific_journal-2676	391	26	(	(	PUNCT
american_scientific_journal-2676	391	27	∈	∈	PROPN
american_scientific_journal-2676	391	28	.	.	PUNCT
american_scientific_journal-2676	392	1	then	then	ADV
american_scientific_journal-2676	392	2	1	1	NUM
american_scientific_journal-2676	392	3	)	)	PUNCT
american_scientific_journal-2676	392	4	)	)	PUNCT
american_scientific_journal-2676	392	5	,	,	PUNCT
american_scientific_journal-2676	392	6	~(=),~	~(=),~	PROPN
american_scientific_journal-2676	392	7	(	(	PUNCT
american_scientific_journal-2676	392	8	exexsclpλ	exexsclpλ	ADJ
american_scientific_journal-2676	392	9	;	;	PUNCT
american_scientific_journal-2676	392	10	)	)	PUNCT
american_scientific_journal-2676	392	11	,	,	PUNCT
american_scientific_journal-2676	392	12	~(=),~	~(=),~	PROPN
american_scientific_journal-2676	392	13	(	(	PUNCT
american_scientific_journal-2676	392	14	eesclp	eesclp	PROPN
american_scientific_journal-2676	392	15	φφλ	φφλ	PROPN
american_scientific_journal-2676	392	16	.	.	PUNCT
american_scientific_journal-2676	393	1	american	american	PROPN
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american_scientific_journal-2676	393	3	research	research	PROPN
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american_scientific_journal-2676	393	7	,	,	PUNCT
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american_scientific_journal-2676	393	9	,	,	PUNCT
american_scientific_journal-2676	393	10	and	and	CCONJ
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american_scientific_journal-2676	393	12	(	(	PUNCT
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american_scientific_journal-2676	393	14	)	)	PUNCT
american_scientific_journal-2676	393	15	(	(	PUNCT
american_scientific_journal-2676	393	16	2017	2017	NUM
american_scientific_journal-2676	393	17	)	)	PUNCT
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american_scientific_journal-2676	393	20	,	,	PUNCT
american_scientific_journal-2676	393	21	no	no	DET
american_scientific_journal-2676	393	22	1	1	NUM
american_scientific_journal-2676	393	23	,	,	PUNCT
american_scientific_journal-2676	393	24	pp	pp	ADV
american_scientific_journal-2676	393	25	225	225	NUM
american_scientific_journal-2676	393	26	-	-	SYM
american_scientific_journal-2676	393	27	247	247	NUM
american_scientific_journal-2676	393	28	242	242	NUM
american_scientific_journal-2676	393	29	2	2	NUM
american_scientific_journal-2676	393	30	)	)	PUNCT
american_scientific_journal-2676	393	31	)	)	PUNCT
american_scientific_journal-2676	393	32	,	,	PUNCT
american_scientific_journal-2676	393	33	(	(	PUNCT
american_scientific_journal-2676	393	34	~	~	NOUN
american_scientific_journal-2676	393	35	)	)	PUNCT
american_scientific_journal-2676	393	36	,	,	PUNCT
american_scientific_journal-2676	393	37	(	(	PUNCT
american_scientific_journal-2676	393	38	egscleg	egscleg	NOUN
american_scientific_journal-2676	393	39	pλ⊆	pλ⊆	ADJ
american_scientific_journal-2676	393	40	.	.	PUNCT
american_scientific_journal-2676	394	1	3	3	X
american_scientific_journal-2676	394	2	)	)	PUNCT
american_scientific_journal-2676	394	3	)	)	PUNCT
american_scientific_journal-2676	395	1	,	,	PUNCT
american_scientific_journal-2676	395	2	(	(	PUNCT
american_scientific_journal-2676	395	3	~),(),(~	~),(),(~	NOUN
american_scientific_journal-2676	395	4	)	)	PUNCT
american_scientific_journal-2676	395	5	,	,	PUNCT
american_scientific_journal-2676	395	6	(	(	PUNCT
american_scientific_journal-2676	395	7	ehsclegscleheg	ehsclegscleheg	NOUN
american_scientific_journal-2676	395	8	pp	pp	ADV
american_scientific_journal-2676	395	9	λλ	λλ	ADP
american_scientific_journal-2676	395	10	⊆⇒⊆	⊆⇒⊆	NUM
american_scientific_journal-2676	395	11	.	.	PUNCT
american_scientific_journal-2676	396	1	4	4	NUM
american_scientific_journal-2676	396	2	)	)	PUNCT
american_scientific_journal-2676	396	3	)	)	PUNCT
american_scientific_journal-2676	396	4	,	,	PUNCT
american_scientific_journal-2676	396	5	(	(	PUNCT
american_scientific_journal-2676	396	6	eg	eg	NOUN
american_scientific_journal-2676	396	7	is	be	AUX
american_scientific_journal-2676	396	8	a	a	DET
american_scientific_journal-2676	396	9	λp	λp	ADV
american_scientific_journal-2676	396	10	-closed	-close	VERB
american_scientific_journal-2676	396	11	soft	soft	ADJ
american_scientific_journal-2676	396	12	set	set	NOUN
american_scientific_journal-2676	396	13	)	)	PUNCT
american_scientific_journal-2676	396	14	,	,	PUNCT
american_scientific_journal-2676	396	15	(	(	PUNCT
american_scientific_journal-2676	396	16	=)	=)	INTJ
american_scientific_journal-2676	396	17	,	,	PUNCT
american_scientific_journal-2676	396	18	(	(	PUNCT
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american_scientific_journal-2676	396	20	.	.	PUNCT
american_scientific_journal-2676	397	1	5	5	NUM
american_scientific_journal-2676	397	2	)	)	PUNCT
american_scientific_journal-2676	397	3	)	)	PUNCT
american_scientific_journal-2676	398	1	]	]	PUNCT
american_scientific_journal-2676	398	2	,	,	PUNCT
american_scientific_journal-2676	398	3	(	(	PUNCT
american_scientific_journal-2676	398	4	~),[(~),(~	~),[(~),(~	NUM
american_scientific_journal-2676	398	5	)	)	PUNCT
american_scientific_journal-2676	398	6	,	,	PUNCT
american_scientific_journal-2676	398	7	(	(	PUNCT
american_scientific_journal-2676	398	8	ehegsclehsclegscl	ehegsclehsclegscl	NOUN
american_scientific_journal-2676	398	9	ppp	ppp	PROPN
american_scientific_journal-2676	398	10	∪⊆∪	∪⊆∪	PROPN
american_scientific_journal-2676	398	11	λλλ	λλλ	PROPN
american_scientific_journal-2676	398	12	.	.	PUNCT
american_scientific_journal-2676	398	13	6	6	NUM
american_scientific_journal-2676	398	14	)	)	PUNCT
american_scientific_journal-2676	398	15	)	)	PUNCT
american_scientific_journal-2676	398	16	,	,	PUNCT
american_scientific_journal-2676	398	17	(	(	PUNCT
american_scientific_journal-2676	398	18	=)	=)	PROPN
american_scientific_journal-2676	398	19	]	]	X
american_scientific_journal-2676	398	20	,	,	PUNCT
american_scientific_journal-2676	398	21	(	(	PUNCT
american_scientific_journal-2676	398	22	[	[	PUNCT
american_scientific_journal-2676	398	23	egsclegsclscl	egsclegsclscl	NOUN
american_scientific_journal-2676	398	24	ppp	ppp	PROPN
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american_scientific_journal-2676	398	26	.	.	PUNCT
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american_scientific_journal-2676	399	2	.	.	PUNCT
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american_scientific_journal-2676	400	2	.	.	PUNCT
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american_scientific_journal-2676	401	2	5.2	5.2	NUM
american_scientific_journal-2676	401	3	λpscl	λpscl	NOUN
american_scientific_journal-2676	401	4	is	be	AUX
american_scientific_journal-2676	401	5	a	a	DET
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american_scientific_journal-2676	401	11	it	it	PRON
american_scientific_journal-2676	401	12	is	be	AUX
american_scientific_journal-2676	401	13	induced	induce	VERB
american_scientific_journal-2676	401	14	a	a	DET
american_scientific_journal-2676	401	15	supra	supra	ADJ
american_scientific_journal-2676	401	16	soft	soft	ADJ
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american_scientific_journal-2676	401	21	)	)	PUNCT
american_scientific_journal-2676	401	22	,	,	PUNCT
american_scientific_journal-2676	401	23	(=	(=	ADV
american_scientific_journal-2676	401	24	)	)	PUNCT
american_scientific_journal-2676	401	25	,	,	PUNCT
american_scientific_journal-2676	401	26	(:	(:	PROPN
american_scientific_journal-2676	401	27	)	)	PUNCT
american_scientific_journal-2676	401	28	(	(	PUNCT
american_scientific_journal-2676	401	29	)	)	PUNCT
american_scientific_journal-2676	401	30	,	,	PUNCT
american_scientific_journal-2676	401	31	{	{	PUNCT
american_scientific_journal-2676	401	32	(=	(=	SCONJ
american_scientific_journal-2676	401	33	cc	cc	X
american_scientific_journal-2676	401	34	pep	pep	PROPN
american_scientific_journal-2676	401	35	egegsclxsseg	egegsclxsseg	VERB
american_scientific_journal-2676	401	36	λλη	λλη	PROPN
american_scientific_journal-2676	401	37	∈	∈	PROPN
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american_scientific_journal-2676	401	42	)	)	PUNCT
american_scientific_journal-2676	401	43	,	,	PUNCT
american_scientific_journal-2676	401	44	,	,	PUNCT
american_scientific_journal-2676	401	45	(	(	PUNCT
american_scientific_journal-2676	401	46	21	21	NUM
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american_scientific_journal-2676	401	48	.	.	PUNCT
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american_scientific_journal-2676	402	2	5.2	5.2	NUM
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american_scientific_journal-2676	402	7	5.3	5.3	NUM
american_scientific_journal-2676	402	8	(	(	PUNCT
american_scientific_journal-2676	402	9	5	5	NUM
american_scientific_journal-2676	402	10	)	)	PUNCT
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american_scientific_journal-2676	402	21	.	.	PUNCT
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american_scientific_journal-2676	403	2	5.2	5.2	NUM
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american_scientific_journal-2676	403	7	,	,	PUNCT
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american_scientific_journal-2676	403	9	ceh	ceh	PROPN
american_scientific_journal-2676	403	10	)	)	PUNCT
american_scientific_journal-2676	403	11	,	,	PUNCT
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american_scientific_journal-2676	403	14	)	)	PUNCT
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american_scientific_journal-2676	403	16	)	)	PUNCT
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american_scientific_journal-2676	403	18	,	,	PUNCT
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american_scientific_journal-2676	403	21	)	)	PUNCT
american_scientific_journal-2676	403	22	,	,	PUNCT
american_scientific_journal-2676	403	23	{	{	PUNCT
american_scientific_journal-2676	403	24	,	,	PUNCT
american_scientific_journal-2676	403	25	{	{	PUNCT
american_scientific_journal-2676	403	26	(	(	PUNCT
american_scientific_journal-2676	403	27	(=	(=	NOUN
american_scientific_journal-2676	403	28	21	21	NUM
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american_scientific_journal-2676	403	30	is	be	AUX
american_scientific_journal-2676	403	31	p	p	X
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american_scientific_journal-2676	403	35	,	,	PUNCT
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american_scientific_journal-2676	403	37	ceh	ceh	PROPN
american_scientific_journal-2676	403	38	)	)	PUNCT
american_scientific_journal-2676	403	39	,	,	PUNCT
american_scientific_journal-2676	403	40	(	(	PUNCT
american_scientific_journal-2676	403	41	is	be	AUX
american_scientific_journal-2676	403	42	a	a	DET
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american_scientific_journal-2676	403	44	-closed	-close	VERB
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american_scientific_journal-2676	403	47	.	.	PUNCT
american_scientific_journal-2676	404	1	therefore	therefore	ADV
american_scientific_journal-2676	404	2	,	,	PUNCT
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american_scientific_journal-2676	404	4	p	p	PROPN
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american_scientific_journal-2676	404	6	)	)	PUNCT
american_scientific_journal-2676	404	7	,	,	PUNCT
american_scientific_journal-2676	404	8	(=	(=	ADV
american_scientific_journal-2676	404	9	)	)	PUNCT
american_scientific_journal-2676	404	10	,	,	PUNCT
american_scientific_journal-2676	404	11	(	(	PUNCT
american_scientific_journal-2676	404	12	λ	λ	X
american_scientific_journal-2676	404	13	[	[	PUNCT
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american_scientific_journal-2676	405	2	,	,	PUNCT
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american_scientific_journal-2676	405	7	,	,	PUNCT
american_scientific_journal-2676	405	8	(	(	PUNCT
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american_scientific_journal-2676	405	10	,	,	PUNCT
american_scientific_journal-2676	405	11	(	(	PUNCT
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american_scientific_journal-2676	405	13	.	.	PUNCT
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american_scientific_journal-2676	406	5	)	)	PUNCT
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american_scientific_journal-2676	406	7	{	{	PUNCT
american_scientific_journal-2676	406	8	,	,	PUNCT
american_scientific_journal-2676	406	9	(	(	PUNCT
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american_scientific_journal-2676	406	11	)	)	PUNCT
american_scientific_journal-2676	406	12	,	,	PUNCT
american_scientific_journal-2676	406	13	{	{	PUNCT
american_scientific_journal-2676	406	14	,	,	PUNCT
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american_scientific_journal-2676	406	18	,	,	PUNCT
american_scientific_journal-2676	406	19	(	(	PUNCT
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american_scientific_journal-2676	406	21	)	)	PUNCT
american_scientific_journal-2676	406	22	,	,	PUNCT
american_scientific_journal-2676	406	23	(	(	PUNCT
american_scientific_journal-2676	406	24	211	211	NUM
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american_scientific_journal-2676	408	4	λλ	λλ	SCONJ
american_scientific_journal-2676	408	5	∪	∪	ADV
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american_scientific_journal-2676	409	5	,	,	PUNCT
american_scientific_journal-2676	409	6	)	)	PUNCT
american_scientific_journal-2676	409	7	,	,	PUNCT
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american_scientific_journal-2676	409	11	[	[	X
american_scientific_journal-2676	409	12	(	(	PUNCT
american_scientific_journal-2676	409	13	211	211	NUM
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american_scientific_journal-2676	409	18	λλ	λλ	SCONJ
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american_scientific_journal-2676	409	20	.	.	PUNCT
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american_scientific_journal-2676	410	17	(	(	PUNCT
american_scientific_journal-2676	410	18	11	11	NUM
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american_scientific_journal-2676	410	30	21	21	NUM
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american_scientific_journal-2676	410	35	sbts	sbts	ADJ
american_scientific_journal-2676	410	36	and	and	CCONJ
american_scientific_journal-2676	410	37	exsseg	exsseg	ADJ
american_scientific_journal-2676	410	38	)	)	PUNCT
american_scientific_journal-2676	410	39	(	(	PUNCT
american_scientific_journal-2676	410	40	)	)	PUNCT
american_scientific_journal-2676	410	41	,	,	PUNCT
american_scientific_journal-2676	410	42	(	(	PUNCT
american_scientific_journal-2676	410	43	∈	∈	PROPN
american_scientific_journal-2676	410	44	.	.	PUNCT
american_scientific_journal-2676	411	1	then	then	ADV
american_scientific_journal-2676	411	2	,	,	PUNCT
american_scientific_journal-2676	411	3	)	)	PUNCT
american_scientific_journal-2676	411	4	,	,	PUNCT
american_scientific_journal-2676	411	5	,	,	PUNCT
american_scientific_journal-2676	411	6	~(),(~),(),(~	~(),(~),(),(~	NUM
american_scientific_journal-2676	411	7	eegeoegsclx	eegeoegsclx	ADJ
american_scientific_journal-2676	411	8	expe	expe	NOUN
american_scientific_journal-2676	411	9	φλ	φλ	ADP
american_scientific_journal-2676	411	10	≠∩⇔∈	≠∩⇔∈	NOUN
american_scientific_journal-2676	411	11	)	)	PUNCT
american_scientific_journal-2676	411	12	,	,	PUNCT
american_scientific_journal-2676	411	13	(	(	PUNCT
american_scientific_journal-2676	411	14	eo	eo	X
american_scientific_journal-2676	411	15	ex∀	ex∀	PROPN
american_scientific_journal-2676	411	16	,	,	PUNCT
american_scientific_journal-2676	411	17	where	where	SCONJ
american_scientific_journal-2676	411	18	)	)	PUNCT
american_scientific_journal-2676	411	19	,	,	PUNCT
american_scientific_journal-2676	411	20	(	(	PUNCT
american_scientific_journal-2676	411	21	eo	eo	X
american_scientific_journal-2676	411	22	ex	ex	PROPN
american_scientific_journal-2676	411	23	is	be	AUX
american_scientific_journal-2676	411	24	a	a	DET
american_scientific_journal-2676	411	25	λp	λp	ADV
american_scientific_journal-2676	411	26	-open	-open	ADJ
american_scientific_journal-2676	411	27	soft	soft	ADJ
american_scientific_journal-2676	411	28	set	set	NOUN
american_scientific_journal-2676	411	29	containing	contain	VERB
american_scientific_journal-2676	411	30	ex	ex	PRON
american_scientific_journal-2676	411	31	.	.	PUNCT
american_scientific_journal-2676	412	1	proof	proof	NOUN
american_scientific_journal-2676	412	2	.	.	PUNCT
american_scientific_journal-2676	413	1	let	let	VERB
american_scientific_journal-2676	413	2	)	)	PUNCT
american_scientific_journal-2676	413	3	,	,	PUNCT
american_scientific_journal-2676	413	4	(	(	PUNCT
american_scientific_journal-2676	413	5	~	~	PUNCT
american_scientific_journal-2676	413	6	egsclx	egsclx	ADJ
american_scientific_journal-2676	413	7	pe	pe	X
american_scientific_journal-2676	413	8	λ∈	λ∈	PROPN
american_scientific_journal-2676	413	9	and	and	CCONJ
american_scientific_journal-2676	413	10	assume	assume	VERB
american_scientific_journal-2676	413	11	that	that	SCONJ
american_scientific_journal-2676	413	12	there	there	PRON
american_scientific_journal-2676	413	13	exists	exist	VERB
american_scientific_journal-2676	413	14	12	12	NUM
american_scientific_journal-2676	413	15	)	)	PUNCT
american_scientific_journal-2676	413	16	,	,	PUNCT
american_scientific_journal-2676	413	17	(	(	PUNCT
american_scientific_journal-2676	413	18	η∈eo	η∈eo	NOUN
american_scientific_journal-2676	413	19	ex	ex	PRON
american_scientific_journal-2676	413	20	such	such	ADJ
american_scientific_journal-2676	413	21	that	that	PRON
american_scientific_journal-2676	413	22	)	)	PUNCT
american_scientific_journal-2676	413	23	,	,	PUNCT
american_scientific_journal-2676	413	24	~(=),(~	~(=),(~	NUM
american_scientific_journal-2676	413	25	)	)	PUNCT
american_scientific_journal-2676	413	26	,	,	PUNCT
american_scientific_journal-2676	413	27	(	(	PUNCT
american_scientific_journal-2676	413	28	eegeo	eegeo	NOUN
american_scientific_journal-2676	413	29	ex	ex	X
american_scientific_journal-2676	413	30	φ∩	φ∩	NOUN
american_scientific_journal-2676	413	31	.	.	PUNCT
american_scientific_journal-2676	414	1	then	then	ADV
american_scientific_journal-2676	414	2	c	c	PROPN
american_scientific_journal-2676	414	3	ex	ex	X
american_scientific_journal-2676	414	4	eoeg	eoeg	NOUN
american_scientific_journal-2676	414	5	)	)	PUNCT
american_scientific_journal-2676	414	6	,	,	PUNCT
american_scientific_journal-2676	414	7	(	(	PUNCT
american_scientific_journal-2676	414	8	~	~	NOUN
american_scientific_journal-2676	414	9	)	)	PUNCT
american_scientific_journal-2676	414	10	,	,	PUNCT
american_scientific_journal-2676	414	11	(	(	PUNCT
american_scientific_journal-2676	414	12	⊆	⊆	NUM
american_scientific_journal-2676	414	13	which	which	PRON
american_scientific_journal-2676	414	14	implies	imply	VERB
american_scientific_journal-2676	414	15	that	that	SCONJ
american_scientific_journal-2676	414	16	c	c	PROPN
american_scientific_journal-2676	414	17	ex	ex	ADJ
american_scientific_journal-2676	414	18	c	c	X
american_scientific_journal-2676	414	19	expp	expp	VERB
american_scientific_journal-2676	414	20	eoeosclegscl	eoeosclegscl	NOUN
american_scientific_journal-2676	414	21	)	)	PUNCT
american_scientific_journal-2676	414	22	,	,	PUNCT
american_scientific_journal-2676	414	23	(=	(=	ADV
american_scientific_journal-2676	414	24	)	)	PUNCT
american_scientific_journal-2676	414	25	,	,	PUNCT
american_scientific_journal-2676	414	26	(	(	PUNCT
american_scientific_journal-2676	414	27	~	~	NOUN
american_scientific_journal-2676	414	28	)	)	PUNCT
american_scientific_journal-2676	414	29	,	,	PUNCT
american_scientific_journal-2676	414	30	(	(	PUNCT
american_scientific_journal-2676	414	31	λλ	λλ	ADP
american_scientific_journal-2676	414	32	⊆	⊆	NUM
american_scientific_journal-2676	414	33	,	,	PUNCT
american_scientific_journal-2676	414	34	therefor	therefor	ADP
american_scientific_journal-2676	414	35	)	)	PUNCT
american_scientific_journal-2676	414	36	,	,	PUNCT
american_scientific_journal-2676	414	37	~(=),(~	~(=),(~	NUM
american_scientific_journal-2676	414	38	)	)	PUNCT
american_scientific_journal-2676	414	39	,	,	PUNCT
american_scientific_journal-2676	414	40	(	(	PUNCT
american_scientific_journal-2676	414	41	eeoegscl	eeoegscl	PROPN
american_scientific_journal-2676	414	42	exp	exp	NOUN
american_scientific_journal-2676	414	43	φλ	φλ	ADP
american_scientific_journal-2676	414	44	∩	∩	PROPN
american_scientific_journal-2676	414	45	,	,	PUNCT
american_scientific_journal-2676	414	46	a	a	DET
american_scientific_journal-2676	414	47	contradiction	contradiction	NOUN
american_scientific_journal-2676	414	48	.	.	PUNCT
american_scientific_journal-2676	415	1	conversely	conversely	ADV
american_scientific_journal-2676	415	2	,	,	PUNCT
american_scientific_journal-2676	415	3	assume	assume	VERB
american_scientific_journal-2676	415	4	that	that	SCONJ
american_scientific_journal-2676	415	5	)	)	PUNCT
american_scientific_journal-2676	415	6	,	,	PUNCT
american_scientific_journal-2676	415	7	(	(	PUNCT
american_scientific_journal-2676	415	8	~	~	PUNCT
american_scientific_journal-2676	415	9	egsclx	egsclx	ADJ
american_scientific_journal-2676	415	10	pe	pe	PROPN
american_scientific_journal-2676	415	11	λ∈/	λ∈/	NOUN
american_scientific_journal-2676	415	12	.	.	PUNCT
american_scientific_journal-2676	416	1	then	then	ADV
american_scientific_journal-2676	416	2	c	c	PROPN
american_scientific_journal-2676	416	3	pe	pe	PROPN
american_scientific_journal-2676	416	4	egsclx	egsclx	ADJ
american_scientific_journal-2676	416	5	)	)	PUNCT
american_scientific_journal-2676	417	1	]	]	PUNCT
american_scientific_journal-2676	417	2	,	,	PUNCT
american_scientific_journal-2676	417	3	(	(	PUNCT
american_scientific_journal-2676	417	4	[	[	X
american_scientific_journal-2676	417	5	~	~	PUNCT
american_scientific_journal-2676	417	6	λ∈	λ∈	NOUN
american_scientific_journal-2676	417	7	it	it	PRON
american_scientific_journal-2676	417	8	follows	follow	VERB
american_scientific_journal-2676	417	9	tha	tha	PROPN
american_scientific_journal-2676	417	10	cegscl	cegscl	PROPN
american_scientific_journal-2676	417	11	)	)	PUNCT
american_scientific_journal-2676	418	1	]	]	PUNCT
american_scientific_journal-2676	418	2	,	,	PUNCT
american_scientific_journal-2676	418	3	(	(	PUNCT
american_scientific_journal-2676	418	4	[	[	PUNCT
american_scientific_journal-2676	418	5	12	12	NUM
american_scientific_journal-2676	418	6	is	be	AUX
american_scientific_journal-2676	418	7	a	a	DET
american_scientific_journal-2676	418	8	λp	λp	ADV
american_scientific_journal-2676	418	9	-open	-open	ADJ
american_scientific_journal-2676	418	10	soft	soft	ADJ
american_scientific_journal-2676	418	11	set	set	NOUN
american_scientific_journal-2676	418	12	containing	contain	VERB
american_scientific_journal-2676	418	13	ex	ex	PRON
american_scientific_journal-2676	418	14	.	.	PUNCT
american_scientific_journal-2676	419	1	thus	thus	ADV
american_scientific_journal-2676	419	2	,	,	PUNCT
american_scientific_journal-2676	419	3	by	by	ADP
american_scientific_journal-2676	419	4	hypothesis	hypothesis	NOUN
american_scientific_journal-2676	419	5	)	)	PUNCT
american_scientific_journal-2676	419	6	,	,	PUNCT
american_scientific_journal-2676	419	7	~(),(~	~(),(~	PROPN
american_scientific_journal-2676	419	8	)	)	PUNCT
american_scientific_journal-2676	419	9	]	]	PUNCT
american_scientific_journal-2676	419	10	,	,	PUNCT
american_scientific_journal-2676	419	11	(	(	PUNCT
american_scientific_journal-2676	419	12	[	[	PUNCT
american_scientific_journal-2676	419	13	12	12	NUM
american_scientific_journal-2676	419	14	eegegscl	eegegscl	NOUN
american_scientific_journal-2676	419	15	c	c	NOUN
american_scientific_journal-2676	419	16	φ≠∩	φ≠∩	NOUN
american_scientific_journal-2676	419	17	which	which	PRON
american_scientific_journal-2676	419	18	contradicts	contradict	VERB
american_scientific_journal-2676	419	19	american	american	ADJ
american_scientific_journal-2676	419	20	scientific	scientific	ADJ
american_scientific_journal-2676	419	21	research	research	NOUN
american_scientific_journal-2676	419	22	journal	journal	NOUN
american_scientific_journal-2676	419	23	for	for	ADP
american_scientific_journal-2676	419	24	engineering	engineering	NOUN
american_scientific_journal-2676	419	25	,	,	PUNCT
american_scientific_journal-2676	419	26	technology	technology	NOUN
american_scientific_journal-2676	419	27	,	,	PUNCT
american_scientific_journal-2676	419	28	and	and	CCONJ
american_scientific_journal-2676	419	29	sciences	science	NOUN
american_scientific_journal-2676	419	30	(	(	PUNCT
american_scientific_journal-2676	419	31	asrjets	asrjet	NOUN
american_scientific_journal-2676	419	32	)	)	PUNCT
american_scientific_journal-2676	419	33	(	(	PUNCT
american_scientific_journal-2676	419	34	2017	2017	NUM
american_scientific_journal-2676	419	35	)	)	PUNCT
american_scientific_journal-2676	419	36	volume	volume	NOUN
american_scientific_journal-2676	419	37	28	28	NUM
american_scientific_journal-2676	419	38	,	,	PUNCT
american_scientific_journal-2676	419	39	no	no	DET
american_scientific_journal-2676	419	40	1	1	NUM
american_scientific_journal-2676	419	41	,	,	PUNCT
american_scientific_journal-2676	419	42	pp	pp	ADV
american_scientific_journal-2676	419	43	225	225	NUM
american_scientific_journal-2676	419	44	-	-	SYM
american_scientific_journal-2676	419	45	247	247	NUM
american_scientific_journal-2676	419	46	243	243	NUM
american_scientific_journal-2676	419	47	with	with	ADP
american_scientific_journal-2676	419	48	)	)	PUNCT
american_scientific_journal-2676	419	49	,	,	PUNCT
american_scientific_journal-2676	419	50	(	(	PUNCT
american_scientific_journal-2676	419	51	~	~	NOUN
american_scientific_journal-2676	419	52	)	)	PUNCT
american_scientific_journal-2676	419	53	,	,	PUNCT
american_scientific_journal-2676	419	54	(	(	PUNCT
american_scientific_journal-2676	419	55	egscleg	egscleg	NOUN
american_scientific_journal-2676	419	56	pλ⊆	pλ⊆	X
american_scientific_journal-2676	419	57	.	.	PUNCT
american_scientific_journal-2676	420	1	corollary	corollary	ADJ
american_scientific_journal-2676	420	2	5.3	5.3	NUM
american_scientific_journal-2676	420	3	let	let	NOUN
american_scientific_journal-2676	420	4	)	)	PUNCT
american_scientific_journal-2676	420	5	,	,	PUNCT
american_scientific_journal-2676	420	6	,	,	PUNCT
american_scientific_journal-2676	420	7	,	,	PUNCT
american_scientific_journal-2676	420	8	(	(	PUNCT
american_scientific_journal-2676	420	9	21	21	NUM
american_scientific_journal-2676	420	10	ex	ex	X
american_scientific_journal-2676	420	11	ηη	ηη	PROPN
american_scientific_journal-2676	420	12	be	be	AUX
american_scientific_journal-2676	420	13	a	a	DET
american_scientific_journal-2676	420	14	sbts	sbts	ADJ
american_scientific_journal-2676	420	15	.	.	PUNCT
american_scientific_journal-2676	421	1	then	then	ADV
american_scientific_journal-2676	421	2	,	,	PUNCT
american_scientific_journal-2676	421	3	epp	epp	PROPN
american_scientific_journal-2676	421	4	c	c	PROPN
american_scientific_journal-2676	421	5	xss	xss	PROPN
american_scientific_journal-2676	421	6	)	)	PUNCT
american_scientific_journal-2676	421	7	(	(	PUNCT
american_scientific_journal-2676	421	8	12	12	NUM
american_scientific_journal-2676	421	9	⊆⊆⊆	⊆⊆⊆	PROPN
american_scientific_journal-2676	421	10	∨	∨	NUM
american_scientific_journal-2676	421	11	ληηη	ληηη	NOUN
american_scientific_journal-2676	421	12	.	.	PUNCT
american_scientific_journal-2676	422	1	proof	proof	NOUN
american_scientific_journal-2676	422	2	.	.	PUNCT
american_scientific_journal-2676	423	1	straightforward	straightforward	ADJ
american_scientific_journal-2676	423	2	.	.	PUNCT
american_scientific_journal-2676	424	1	remark	remark	VERB
american_scientific_journal-2676	424	2	5.3	5.3	NUM
american_scientific_journal-2676	424	3	the	the	DET
american_scientific_journal-2676	424	4	equality	equality	NOUN
american_scientific_journal-2676	424	5	in	in	ADP
american_scientific_journal-2676	424	6	corollary	corollary	ADJ
american_scientific_journal-2676	424	7	5.3	5.3	NUM
american_scientific_journal-2676	424	8	may	may	AUX
american_scientific_journal-2676	424	9	not	not	PART
american_scientific_journal-2676	424	10	be	be	AUX
american_scientific_journal-2676	424	11	satisfied	satisfied	ADJ
american_scientific_journal-2676	424	12	as	as	SCONJ
american_scientific_journal-2676	424	13	shown	show	VERB
american_scientific_journal-2676	424	14	in	in	ADP
american_scientific_journal-2676	424	15	the	the	DET
american_scientific_journal-2676	424	16	following	follow	VERB
american_scientific_journal-2676	424	17	example	example	NOUN
american_scientific_journal-2676	424	18	.	.	PUNCT
american_scientific_journal-2676	425	1	example	example	NOUN
american_scientific_journal-2676	425	2	5.3	5.3	NUM
american_scientific_journal-2676	425	3	in	in	ADP
american_scientific_journal-2676	425	4	example	example	NOUN
american_scientific_journal-2676	425	5	5.1	5.1	NUM
american_scientific_journal-2676	425	6	,	,	PUNCT
american_scientific_journal-2676	425	7	clear	clear	ADJ
american_scientific_journal-2676	425	8	that	that	SCONJ
american_scientific_journal-2676	425	9	ep	ep	PROPN
american_scientific_journal-2676	425	10	xss	xss	PROPN
american_scientific_journal-2676	425	11	)	)	PUNCT
american_scientific_journal-2676	425	12	(	(	PUNCT
american_scientific_journal-2676	425	13	≠λη	≠λη	NOUN
american_scientific_journal-2676	425	14	.	.	PUNCT
american_scientific_journal-2676	426	1	also	also	ADV
american_scientific_journal-2676	426	2	,	,	PUNCT
american_scientific_journal-2676	426	3	we	we	PRON
american_scientific_journal-2676	426	4	have	have	VERB
american_scientific_journal-2676	426	5	λη	λη	X
american_scientific_journal-2676	426	6	pep	pep	NOUN
american_scientific_journal-2676	426	7	∈	∈	PROPN
american_scientific_journal-2676	426	8	)	)	PUNCT
american_scientific_journal-2676	426	9	,	,	PUNCT
american_scientific_journal-2676	426	10	(	(	PUNCT
american_scientific_journal-2676	426	11	1	1	NUM
american_scientific_journal-2676	426	12	but	but	CCONJ
american_scientific_journal-2676	426	13	∨∈/	∨∈/	PROPN
american_scientific_journal-2676	426	14	pep	pep	NOUN
american_scientific_journal-2676	426	15	η	η	NOUN
american_scientific_journal-2676	426	16	)	)	PUNCT
american_scientific_journal-2676	426	17	,	,	PUNCT
american_scientific_journal-2676	426	18	(	(	PUNCT
american_scientific_journal-2676	426	19	1	1	NUM
american_scientific_journal-2676	426	20	because	because	SCONJ
american_scientific_journal-2676	426	21	)	)	PUNCT
american_scientific_journal-2676	426	22	,	,	PUNCT
american_scientific_journal-2676	426	23	(	(	PUNCT
american_scientific_journal-2676	426	24	}	}	PUNCT
american_scientific_journal-2676	426	25	)	)	PUNCT
american_scientific_journal-2676	426	26	}	}	PUNCT
american_scientific_journal-2676	426	27	{	{	PUNCT
american_scientific_journal-2676	426	28	,	,	PUNCT
american_scientific_journal-2676	426	29	(	(	PUNCT
american_scientific_journal-2676	426	30	}	}	PUNCT
american_scientific_journal-2676	426	31	)	)	PUNCT
american_scientific_journal-2676	426	32	,	,	PUNCT
american_scientific_journal-2676	426	33	{	{	PUNCT
american_scientific_journal-2676	426	34	,	,	PUNCT
american_scientific_journal-2676	426	35	{	{	PUNCT
american_scientific_journal-2676	426	36	(=	(=	NOUN
american_scientific_journal-2676	426	37	)	)	PUNCT
american_scientific_journal-2676	426	38	,	,	PUNCT
american_scientific_journal-2676	426	39	(	(	PUNCT
american_scientific_journal-2676	426	40	1111	1111	NUM
american_scientific_journal-2676	426	41	*	*	SYM
american_scientific_journal-2676	426	42	12	12	NUM
american_scientific_journal-2676	426	43	epyexeepsker	epyexeepsker	NOUN
american_scientific_journal-2676	426	44	≠	≠	PROPN
american_scientific_journal-2676	426	45	.	.	PUNCT
american_scientific_journal-2676	427	1	hence	hence	ADV
american_scientific_journal-2676	427	2	,	,	PUNCT
american_scientific_journal-2676	427	3	ληη	ληη	INTJ
american_scientific_journal-2676	427	4	pp	pp	ADP
american_scientific_journal-2676	427	5	≠∨	≠∨	PROPN
american_scientific_journal-2676	427	6	.	.	PUNCT
american_scientific_journal-2676	428	1	lemma	lemma	PROPN
american_scientific_journal-2676	428	2	5.2	5.2	NUM
american_scientific_journal-2676	428	3	let	let	NOUN
american_scientific_journal-2676	428	4	)	)	PUNCT
american_scientific_journal-2676	428	5	,	,	PUNCT
american_scientific_journal-2676	428	6	,	,	PUNCT
american_scientific_journal-2676	428	7	,	,	PUNCT
american_scientific_journal-2676	428	8	(	(	PUNCT
american_scientific_journal-2676	428	9	21	21	NUM
american_scientific_journal-2676	428	10	ex	ex	X
american_scientific_journal-2676	428	11	ηη	ηη	PROPN
american_scientific_journal-2676	428	12	be	be	AUX
american_scientific_journal-2676	428	13	a	a	DET
american_scientific_journal-2676	428	14	sbts	sbts	ADJ
american_scientific_journal-2676	428	15	.	.	PUNCT
american_scientific_journal-2676	429	1	then	then	ADV
american_scientific_journal-2676	429	2	,	,	PUNCT
american_scientific_journal-2676	429	3	the	the	DET
american_scientific_journal-2676	429	4	supra	supra	PROPN
american_scientific_journal-2676	429	5	soft	soft	ADJ
american_scientific_journal-2676	429	6	topology	topology	NOUN
american_scientific_journal-2676	429	7	λη	λη	ADP
american_scientific_journal-2676	429	8	p	p	NOUN
american_scientific_journal-2676	429	9	is	be	AUX
american_scientific_journal-2676	429	10	a	a	DET
american_scientific_journal-2676	429	11	soft	soft	ADJ
american_scientific_journal-2676	429	12	topology	topology	NOUN
american_scientific_journal-2676	429	13	on	on	ADP
american_scientific_journal-2676	429	14	x	x	SYM
american_scientific_journal-2676	429	15	iff	iff	PROPN
american_scientific_journal-2676	429	16	the	the	DET
american_scientific_journal-2676	429	17	finite	finite	ADJ
american_scientific_journal-2676	429	18	intersection	intersection	NOUN
american_scientific_journal-2676	429	19	of	of	ADP
american_scientific_journal-2676	429	20	λp	λp	PUNCT
american_scientific_journal-2676	429	21	-open	-open	ADJ
american_scientific_journal-2676	429	22	soft	soft	ADJ
american_scientific_journal-2676	429	23	sets	set	NOUN
american_scientific_journal-2676	429	24	is	be	AUX
american_scientific_journal-2676	429	25	a	a	DET
american_scientific_journal-2676	429	26	λp	λp	ADV
american_scientific_journal-2676	429	27	-open	-open	ADJ
american_scientific_journal-2676	429	28	soft	soft	ADJ
american_scientific_journal-2676	429	29	set	set	NOUN
american_scientific_journal-2676	429	30	or	or	CCONJ
american_scientific_journal-2676	429	31	equivalently	equivalently	ADV
american_scientific_journal-2676	429	32	,	,	PUNCT
american_scientific_journal-2676	429	33	the	the	DET
american_scientific_journal-2676	429	34	finite	finite	PROPN
american_scientific_journal-2676	429	35	union	union	PROPN
american_scientific_journal-2676	429	36	of	of	ADP
american_scientific_journal-2676	429	37	λp	λp	ADV
american_scientific_journal-2676	429	38	-closed	-close	VERB
american_scientific_journal-2676	429	39	soft	soft	ADJ
american_scientific_journal-2676	429	40	sets	set	NOUN
american_scientific_journal-2676	429	41	is	be	AUX
american_scientific_journal-2676	429	42	a	a	DET
american_scientific_journal-2676	429	43	λp	λp	ADV
american_scientific_journal-2676	429	44	-closed	-close	VERB
american_scientific_journal-2676	429	45	soft	soft	ADJ
american_scientific_journal-2676	429	46	set	set	NOUN
american_scientific_journal-2676	429	47	.	.	PUNCT
american_scientific_journal-2676	430	1	proof	proof	NOUN
american_scientific_journal-2676	430	2	.	.	PUNCT
american_scientific_journal-2676	431	1	suppose	suppose	VERB
american_scientific_journal-2676	431	2	that	that	SCONJ
american_scientific_journal-2676	431	3	λη	λη	PRON
american_scientific_journal-2676	431	4	p	p	X
american_scientific_journal-2676	431	5	is	be	AUX
american_scientific_journal-2676	431	6	a	a	DET
american_scientific_journal-2676	431	7	soft	soft	ADJ
american_scientific_journal-2676	431	8	topology	topology	NOUN
american_scientific_journal-2676	431	9	on	on	ADP
american_scientific_journal-2676	431	10	x	x	X
american_scientific_journal-2676	431	11	.	.	PUNCT
american_scientific_journal-2676	432	1	let	let	VERB
american_scientific_journal-2676	432	2	)	)	PUNCT
american_scientific_journal-2676	432	3	,	,	PUNCT
american_scientific_journal-2676	432	4	(	(	PUNCT
american_scientific_journal-2676	432	5	eg	eg	NOUN
american_scientific_journal-2676	432	6	and	and	CCONJ
american_scientific_journal-2676	432	7	)	)	PUNCT
american_scientific_journal-2676	432	8	,	,	PUNCT
american_scientific_journal-2676	432	9	(	(	PUNCT
american_scientific_journal-2676	432	10	eh	eh	INTJ
american_scientific_journal-2676	432	11	be	be	AUX
american_scientific_journal-2676	432	12	two	two	NUM
american_scientific_journal-2676	432	13	λp	λp	ADV
american_scientific_journal-2676	432	14	-closed	-close	VERB
american_scientific_journal-2676	432	15	soft	soft	ADJ
american_scientific_journal-2676	432	16	sets	set	NOUN
american_scientific_journal-2676	432	17	.	.	PUNCT
american_scientific_journal-2676	433	1	then	then	ADV
american_scientific_journal-2676	433	2	,	,	PUNCT
american_scientific_journal-2676	433	3	ceg	ceg	PROPN
american_scientific_journal-2676	433	4	)	)	PUNCT
american_scientific_journal-2676	433	5	,	,	PUNCT
american_scientific_journal-2676	433	6	(	(	PUNCT
american_scientific_journal-2676	433	7	and	and	CCONJ
american_scientific_journal-2676	433	8	ceh	ceh	PROPN
american_scientific_journal-2676	433	9	)	)	PUNCT
american_scientific_journal-2676	433	10	,	,	PUNCT
american_scientific_journal-2676	433	11	(	(	PUNCT
american_scientific_journal-2676	433	12	are	be	AUX
american_scientific_journal-2676	433	13	λp	λp	X
american_scientific_journal-2676	433	14	-open	-open	ADJ
american_scientific_journal-2676	433	15	soft	soft	ADJ
american_scientific_journal-2676	433	16	sets	set	NOUN
american_scientific_journal-2676	433	17	.	.	PUNCT
american_scientific_journal-2676	434	1	therefore	therefore	ADV
american_scientific_journal-2676	434	2	,	,	PUNCT
american_scientific_journal-2676	434	3	cc	cc	PROPN
american_scientific_journal-2676	434	4	eheg	eheg	PROPN
american_scientific_journal-2676	434	5	)	)	PUNCT
american_scientific_journal-2676	434	6	,	,	PUNCT
american_scientific_journal-2676	434	7	(	(	PUNCT
american_scientific_journal-2676	434	8	~	~	NOUN
american_scientific_journal-2676	434	9	)	)	PUNCT
american_scientific_journal-2676	434	10	,	,	PUNCT
american_scientific_journal-2676	434	11	(	(	PUNCT
american_scientific_journal-2676	434	12	∩	∩	NOUN
american_scientific_journal-2676	434	13	is	be	AUX
american_scientific_journal-2676	434	14	a	a	DET
american_scientific_journal-2676	434	15	λp	λp	X
american_scientific_journal-2676	434	16	-open	-open	PROPN
american_scientific_journal-2676	434	17	soft	soft	ADJ
american_scientific_journal-2676	434	18	set[for	set[for	ADP
american_scientific_journal-2676	434	19	λη	λη	PROPN
american_scientific_journal-2676	434	20	p	p	NOUN
american_scientific_journal-2676	434	21	is	be	AUX
american_scientific_journal-2676	434	22	a	a	DET
american_scientific_journal-2676	434	23	soft	soft	ADJ
american_scientific_journal-2676	434	24	topology	topology	NOUN
american_scientific_journal-2676	434	25	]	]	PUNCT
american_scientific_journal-2676	434	26	.	.	PUNCT
american_scientific_journal-2676	435	1	consequently	consequently	ADV
american_scientific_journal-2676	435	2	,	,	PUNCT
american_scientific_journal-2676	435	3	)	)	PUNCT
american_scientific_journal-2676	435	4	,	,	PUNCT
american_scientific_journal-2676	435	5	(	(	PUNCT
american_scientific_journal-2676	435	6	~	~	NOUN
american_scientific_journal-2676	435	7	)	)	PUNCT
american_scientific_journal-2676	435	8	,	,	PUNCT
american_scientific_journal-2676	435	9	(	(	PUNCT
american_scientific_journal-2676	435	10	eheg	eheg	PROPN
american_scientific_journal-2676	435	11	∪	∪	NOUN
american_scientific_journal-2676	435	12	is	be	AUX
american_scientific_journal-2676	435	13	a	a	DET
american_scientific_journal-2676	435	14	λp	λp	ADV
american_scientific_journal-2676	435	15	-closed	-close	VERB
american_scientific_journal-2676	435	16	soft	soft	ADJ
american_scientific_journal-2676	435	17	set	set	NOUN
american_scientific_journal-2676	435	18	.	.	PUNCT
american_scientific_journal-2676	436	1	conversely	conversely	ADV
american_scientific_journal-2676	436	2	,	,	PUNCT
american_scientific_journal-2676	436	3	it	it	PRON
american_scientific_journal-2676	436	4	is	be	AUX
american_scientific_journal-2676	436	5	obvious	obvious	ADJ
american_scientific_journal-2676	436	6	.	.	PUNCT
american_scientific_journal-2676	437	1	definition	definition	NOUN
american_scientific_journal-2676	437	2	5.3	5.3	NUM
american_scientific_journal-2676	437	3	a	a	DET
american_scientific_journal-2676	437	4	sbts	sbts	ADJ
american_scientific_journal-2676	437	5	)	)	PUNCT
american_scientific_journal-2676	437	6	,	,	PUNCT
american_scientific_journal-2676	437	7	,	,	PUNCT
american_scientific_journal-2676	437	8	,	,	PUNCT
american_scientific_journal-2676	437	9	(	(	PUNCT
american_scientific_journal-2676	437	10	21	21	NUM
american_scientific_journal-2676	437	11	ex	ex	NOUN
american_scientific_journal-2676	437	12	ηη	ηη	PROPN
american_scientific_journal-2676	437	13	is	be	AUX
american_scientific_journal-2676	437	14	called	call	VERB
american_scientific_journal-2676	437	15	a	a	DET
american_scientific_journal-2676	437	16	pairwise	pairwise	NOUN
american_scientific_journal-2676	437	17	soft	soft	ADJ
american_scientific_journal-2676	437	18	𝑇𝑇𝜆𝜆∗	𝑇𝑇𝜆𝜆∗	PROPN
american_scientific_journal-2676	438	1	[	[	X
american_scientific_journal-2676	438	2	briefly	briefly	ADV
american_scientific_journal-2676	438	3	,	,	PUNCT
american_scientific_journal-2676	438	4	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	X
american_scientific_journal-2676	438	5	]	]	PUNCT
american_scientific_journal-2676	438	6	if	if	SCONJ
american_scientific_journal-2676	438	7	λη	λη	PROPN
american_scientific_journal-2676	438	8	p	p	NOUN
american_scientific_journal-2676	438	9	is	be	AUX
american_scientific_journal-2676	438	10	a	a	DET
american_scientific_journal-2676	438	11	soft	soft	ADJ
american_scientific_journal-2676	438	12	topology	topology	NOUN
american_scientific_journal-2676	438	13	on	on	ADP
american_scientific_journal-2676	438	14	x	x	X
american_scientific_journal-2676	438	15	.	.	PUNCT
american_scientific_journal-2676	439	1	theorem	theorem	VERB
american_scientific_journal-2676	439	2	5.5	5.5	NUM
american_scientific_journal-2676	439	3	every	every	DET
american_scientific_journal-2676	439	4	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	439	5	2	2	NUM
american_scientific_journal-2676	439	6	�	�	PROPN
american_scientific_journal-2676	439	7	∗	∗	NOUN
american_scientific_journal-2676	439	8	is	be	AUX
american_scientific_journal-2676	439	9	a	a	DET
american_scientific_journal-2676	439	10	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗.	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗.	PROPN
american_scientific_journal-2676	439	11	proof	proof	NOUN
american_scientific_journal-2676	439	12	.	.	PUNCT
american_scientific_journal-2676	440	1	let	let	VERB
american_scientific_journal-2676	440	2	)	)	PUNCT
american_scientific_journal-2676	440	3	,	,	PUNCT
american_scientific_journal-2676	440	4	,	,	PUNCT
american_scientific_journal-2676	440	5	,	,	PUNCT
american_scientific_journal-2676	440	6	(	(	PUNCT
american_scientific_journal-2676	440	7	21	21	NUM
american_scientific_journal-2676	440	8	ex	ex	X
american_scientific_journal-2676	440	9	ηη	ηη	PROPN
american_scientific_journal-2676	440	10	be	be	AUX
american_scientific_journal-2676	440	11	a	a	DET
american_scientific_journal-2676	440	12	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	440	13	2	2	NUM
american_scientific_journal-2676	440	14	�	�	PROPN
american_scientific_journal-2676	440	15	∗	∗	NOUN
american_scientific_journal-2676	440	16	space	space	NOUN
american_scientific_journal-2676	440	17	.	.	PUNCT
american_scientific_journal-2676	441	1	then	then	ADV
american_scientific_journal-2676	441	2	,	,	PUNCT
american_scientific_journal-2676	441	3	by	by	ADP
american_scientific_journal-2676	441	4	theorem	theorem	NOUN
american_scientific_journal-2676	441	5	3.2	3.2	NUM
american_scientific_journal-2676	441	6	,	,	PUNCT
american_scientific_journal-2676	441	7	every	every	DET
american_scientific_journal-2676	441	8	soft	soft	ADJ
american_scientific_journal-2676	441	9	set	set	NOUN
american_scientific_journal-2676	441	10	is	be	AUX
american_scientific_journal-2676	441	11	a	a	DET
american_scientific_journal-2676	441	12	λp	λp	ADV
american_scientific_journal-2676	441	13	-closed	-close	VERB
american_scientific_journal-2676	441	14	soft	soft	ADJ
american_scientific_journal-2676	441	15	set	set	NOUN
american_scientific_journal-2676	441	16	.	.	PUNCT
american_scientific_journal-2676	442	1	consequently	consequently	ADV
american_scientific_journal-2676	442	2	,	,	PUNCT
american_scientific_journal-2676	442	3	the	the	DET
american_scientific_journal-2676	442	4	union	union	NOUN
american_scientific_journal-2676	442	5	of	of	ADP
american_scientific_journal-2676	442	6	any	any	DET
american_scientific_journal-2676	442	7	two	two	NUM
american_scientific_journal-2676	442	8	λp	λp	ADV
american_scientific_journal-2676	442	9	-closed	-close	VERB
american_scientific_journal-2676	442	10	soft	soft	ADJ
american_scientific_journal-2676	442	11	sets	set	NOUN
american_scientific_journal-2676	442	12	is	be	AUX
american_scientific_journal-2676	442	13	a	a	DET
american_scientific_journal-2676	442	14	λp	λp	ADV
american_scientific_journal-2676	442	15	-closed	-close	VERB
american_scientific_journal-2676	442	16	soft	soft	ADJ
american_scientific_journal-2676	442	17	set	set	NOUN
american_scientific_journal-2676	442	18	.	.	PUNCT
american_scientific_journal-2676	443	1	hence	hence	ADV
american_scientific_journal-2676	443	2	,	,	PUNCT
american_scientific_journal-2676	443	3	by	by	ADP
american_scientific_journal-2676	443	4	lemma	lemma	PROPN
american_scientific_journal-2676	443	5	5.2	5.2	NUM
american_scientific_journal-2676	443	6	,	,	PUNCT
american_scientific_journal-2676	443	7	λη	λη	ADP
american_scientific_journal-2676	443	8	p	p	NOUN
american_scientific_journal-2676	443	9	is	be	AUX
american_scientific_journal-2676	443	10	a	a	DET
american_scientific_journal-2676	443	11	soft	soft	ADJ
american_scientific_journal-2676	443	12	topology	topology	NOUN
american_scientific_journal-2676	443	13	on	on	ADP
american_scientific_journal-2676	443	14	x	x	X
american_scientific_journal-2676	443	15	.	.	PUNCT
american_scientific_journal-2676	444	1	hence	hence	ADV
american_scientific_journal-2676	444	2	,	,	PUNCT
american_scientific_journal-2676	444	3	)	)	PUNCT
american_scientific_journal-2676	444	4	,	,	PUNCT
american_scientific_journal-2676	444	5	,	,	PUNCT
american_scientific_journal-2676	444	6	,	,	PUNCT
american_scientific_journal-2676	444	7	(	(	PUNCT
american_scientific_journal-2676	444	8	21	21	NUM
american_scientific_journal-2676	444	9	ex	ex	X
american_scientific_journal-2676	444	10	ηη	ηη	PROPN
american_scientific_journal-2676	444	11	is	be	AUX
american_scientific_journal-2676	444	12	a	a	DET
american_scientific_journal-2676	444	13	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗.	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗.	PROPN
american_scientific_journal-2676	444	14	remark	remark	NOUN
american_scientific_journal-2676	444	15	5.4	5.4	NUM
american_scientific_journal-2676	444	16	a	a	DET
american_scientific_journal-2676	444	17	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	NOUN
american_scientific_journal-2676	444	18	need	need	AUX
american_scientific_journal-2676	444	19	not	not	PART
american_scientific_journal-2676	444	20	be	be	AUX
american_scientific_journal-2676	444	21	a	a	DET
american_scientific_journal-2676	444	22	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	444	23	2	2	NUM
american_scientific_journal-2676	444	24	�	�	PROPN
american_scientific_journal-2676	444	25	∗	∗	NOUN
american_scientific_journal-2676	444	26	or	or	CCONJ
american_scientific_journal-2676	444	27	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	NOUN
american_scientific_journal-2676	444	28	as	as	SCONJ
american_scientific_journal-2676	444	29	shown	show	VERB
american_scientific_journal-2676	444	30	by	by	ADP
american_scientific_journal-2676	444	31	the	the	DET
american_scientific_journal-2676	444	32	following	follow	VERB
american_scientific_journal-2676	444	33	example	example	NOUN
american_scientific_journal-2676	444	34	.	.	PUNCT
american_scientific_journal-2676	445	1	example	example	NOUN
american_scientific_journal-2676	445	2	5.4	5.4	NUM
american_scientific_journal-2676	445	3	let	let	VERB
american_scientific_journal-2676	445	4	}	}	PUNCT
american_scientific_journal-2676	445	5	,	,	PUNCT
american_scientific_journal-2676	445	6	,	,	PUNCT
american_scientific_journal-2676	445	7	{	{	PUNCT
american_scientific_journal-2676	445	8	=	=	X
american_scientific_journal-2676	445	9	zyxx	zyxx	PROPN
american_scientific_journal-2676	445	10	,	,	PUNCT
american_scientific_journal-2676	445	11	}	}	PUNCT
american_scientific_journal-2676	445	12	,	,	PUNCT
american_scientific_journal-2676	445	13	{	{	PUNCT
american_scientific_journal-2676	445	14	=	=	NOUN
american_scientific_journal-2676	445	15	21	21	NUM
american_scientific_journal-2676	445	16	eee	eee	NOUN
american_scientific_journal-2676	445	17	and	and	CCONJ
american_scientific_journal-2676	445	18	let	let	VERB
american_scientific_journal-2676	445	19	american	american	PROPN
american_scientific_journal-2676	445	20	scientific	scientific	ADJ
american_scientific_journal-2676	445	21	research	research	NOUN
american_scientific_journal-2676	445	22	journal	journal	NOUN
american_scientific_journal-2676	445	23	for	for	ADP
american_scientific_journal-2676	445	24	engineering	engineering	NOUN
american_scientific_journal-2676	445	25	,	,	PUNCT
american_scientific_journal-2676	445	26	technology	technology	NOUN
american_scientific_journal-2676	445	27	,	,	PUNCT
american_scientific_journal-2676	445	28	and	and	CCONJ
american_scientific_journal-2676	445	29	sciences	science	NOUN
american_scientific_journal-2676	445	30	(	(	PUNCT
american_scientific_journal-2676	445	31	asrjets	asrjet	NOUN
american_scientific_journal-2676	445	32	)	)	PUNCT
american_scientific_journal-2676	445	33	(	(	PUNCT
american_scientific_journal-2676	445	34	2017	2017	NUM
american_scientific_journal-2676	445	35	)	)	PUNCT
american_scientific_journal-2676	445	36	volume	volume	NOUN
american_scientific_journal-2676	445	37	28	28	NUM
american_scientific_journal-2676	445	38	,	,	PUNCT
american_scientific_journal-2676	445	39	no	no	DET
american_scientific_journal-2676	445	40	1	1	NUM
american_scientific_journal-2676	445	41	,	,	PUNCT
american_scientific_journal-2676	445	42	pp	pp	ADV
american_scientific_journal-2676	445	43	225	225	NUM
american_scientific_journal-2676	445	44	-	-	SYM
american_scientific_journal-2676	445	45	247	247	NUM
american_scientific_journal-2676	445	46	244	244	NUM
american_scientific_journal-2676	445	47	)	)	PUNCT
american_scientific_journal-2676	445	48	}	}	PUNCT
american_scientific_journal-2676	445	49	,	,	PUNCT
american_scientific_journal-2676	445	50	(	(	PUNCT
american_scientific_journal-2676	445	51	)	)	PUNCT
american_scientific_journal-2676	445	52	,	,	PUNCT
american_scientific_journal-2676	445	53	,	,	PUNCT
american_scientific_journal-2676	445	54	(	(	PUNCT
american_scientific_journal-2676	445	55	)	)	PUNCT
american_scientific_journal-2676	445	56	,	,	PUNCT
american_scientific_journal-2676	445	57	,	,	PUNCT
american_scientific_journal-2676	445	58	(	(	PUNCT
american_scientific_journal-2676	445	59	)	)	PUNCT
american_scientific_journal-2676	445	60	,	,	PUNCT
american_scientific_journal-2676	445	61	,	,	PUNCT
american_scientific_journal-2676	445	62	~(),,~{(=	~(),,~{(=	ADJ
american_scientific_journal-2676	445	63	3211	3211	NUM
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american_scientific_journal-2676	445	65	,	,	PUNCT
american_scientific_journal-2676	445	66	)	)	PUNCT
american_scientific_journal-2676	445	67	}	}	PUNCT
american_scientific_journal-2676	445	68	,	,	PUNCT
american_scientific_journal-2676	445	69	(	(	PUNCT
american_scientific_journal-2676	445	70	)	)	PUNCT
american_scientific_journal-2676	445	71	,	,	PUNCT
american_scientific_journal-2676	445	72	,	,	PUNCT
american_scientific_journal-2676	445	73	(	(	PUNCT
american_scientific_journal-2676	445	74	)	)	PUNCT
american_scientific_journal-2676	445	75	,	,	PUNCT
american_scientific_journal-2676	445	76	,	,	PUNCT
american_scientific_journal-2676	445	77	(	(	PUNCT
american_scientific_journal-2676	445	78	)	)	PUNCT
american_scientific_journal-2676	445	79	,	,	PUNCT
american_scientific_journal-2676	445	80	,	,	PUNCT
american_scientific_journal-2676	445	81	~(),,~{(=	~(),,~{(=	ADJ
american_scientific_journal-2676	445	82	3212	3212	NUM
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american_scientific_journal-2676	445	84	,	,	PUNCT
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american_scientific_journal-2676	445	87	}	}	PUNCT
american_scientific_journal-2676	445	88	)	)	PUNCT
american_scientific_journal-2676	445	89	}	}	PUNCT
american_scientific_journal-2676	445	90	,	,	PUNCT
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american_scientific_journal-2676	445	92	,	,	PUNCT
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american_scientific_journal-2676	445	94	}	}	PUNCT
american_scientific_journal-2676	445	95	)	)	PUNCT
american_scientific_journal-2676	445	96	,	,	PUNCT
american_scientific_journal-2676	445	97	,	,	PUNCT
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american_scientific_journal-2676	445	99	,	,	PUNCT
american_scientific_journal-2676	445	100	{	{	PUNCT
american_scientific_journal-2676	445	101	(=	(=	NOUN
american_scientific_journal-2676	445	102	)	)	PUNCT
american_scientific_journal-2676	445	103	,	,	PUNCT
american_scientific_journal-2676	445	104	(	(	PUNCT
american_scientific_journal-2676	445	105	211	211	NUM
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american_scientific_journal-2676	445	107	,	,	PUNCT
american_scientific_journal-2676	445	108	}	}	PUNCT
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american_scientific_journal-2676	445	111	,	,	PUNCT
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american_scientific_journal-2676	445	116	)	)	PUNCT
american_scientific_journal-2676	445	117	,	,	PUNCT
american_scientific_journal-2676	445	118	,	,	PUNCT
american_scientific_journal-2676	445	119	{	{	PUNCT
american_scientific_journal-2676	445	120	,	,	PUNCT
american_scientific_journal-2676	445	121	{	{	PUNCT
american_scientific_journal-2676	445	122	(=	(=	NOUN
american_scientific_journal-2676	445	123	)	)	PUNCT
american_scientific_journal-2676	445	124	,	,	PUNCT
american_scientific_journal-2676	445	125	(	(	PUNCT
american_scientific_journal-2676	445	126	212	212	NUM
american_scientific_journal-2676	445	127	zyezyeeg	zyezyeeg	NOUN
american_scientific_journal-2676	445	128	,	,	PUNCT
american_scientific_journal-2676	445	129	}	}	PUNCT
american_scientific_journal-2676	445	130	)	)	PUNCT
american_scientific_journal-2676	445	131	}	}	PUNCT
american_scientific_journal-2676	445	132	{	{	PUNCT
american_scientific_journal-2676	445	133	,	,	PUNCT
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american_scientific_journal-2676	445	135	}	}	PUNCT
american_scientific_journal-2676	445	136	)	)	PUNCT
american_scientific_journal-2676	445	137	,	,	PUNCT
american_scientific_journal-2676	445	138	{	{	PUNCT
american_scientific_journal-2676	445	139	,	,	PUNCT
american_scientific_journal-2676	445	140	{	{	PUNCT
american_scientific_journal-2676	445	141	(=	(=	NOUN
american_scientific_journal-2676	445	142	)	)	PUNCT
american_scientific_journal-2676	445	143	,	,	PUNCT
american_scientific_journal-2676	445	144	(	(	PUNCT
american_scientific_journal-2676	445	145	213	213	NUM
american_scientific_journal-2676	445	146	yezeeg	yezeeg	NOUN
american_scientific_journal-2676	445	147	,	,	PUNCT
american_scientific_journal-2676	445	148	}	}	PUNCT
american_scientific_journal-2676	445	149	)	)	PUNCT
american_scientific_journal-2676	445	150	}	}	PUNCT
american_scientific_journal-2676	445	151	,	,	PUNCT
american_scientific_journal-2676	445	152	{	{	PUNCT
american_scientific_journal-2676	445	153	,	,	PUNCT
american_scientific_journal-2676	445	154	(	(	PUNCT
american_scientific_journal-2676	445	155	}	}	PUNCT
american_scientific_journal-2676	445	156	)	)	PUNCT
american_scientific_journal-2676	445	157	,	,	PUNCT
american_scientific_journal-2676	445	158	,	,	PUNCT
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american_scientific_journal-2676	445	160	,	,	PUNCT
american_scientific_journal-2676	445	161	{	{	PUNCT
american_scientific_journal-2676	445	162	(=	(=	NOUN
american_scientific_journal-2676	445	163	)	)	PUNCT
american_scientific_journal-2676	445	164	,	,	PUNCT
american_scientific_journal-2676	445	165	(	(	PUNCT
american_scientific_journal-2676	445	166	211	211	NUM
american_scientific_journal-2676	445	167	zxeyxeeh	zxeyxeeh	NOUN
american_scientific_journal-2676	445	168	,	,	PUNCT
american_scientific_journal-2676	445	169	}	}	PUNCT
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american_scientific_journal-2676	445	171	}	}	PUNCT
american_scientific_journal-2676	445	172	,	,	PUNCT
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american_scientific_journal-2676	445	174	,	,	PUNCT
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american_scientific_journal-2676	445	177	)	)	PUNCT
american_scientific_journal-2676	445	178	,	,	PUNCT
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american_scientific_journal-2676	445	180	,	,	PUNCT
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american_scientific_journal-2676	445	183	)	)	PUNCT
american_scientific_journal-2676	445	184	,	,	PUNCT
american_scientific_journal-2676	445	185	(	(	PUNCT
american_scientific_journal-2676	445	186	212	212	NUM
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american_scientific_journal-2676	445	188	,	,	PUNCT
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american_scientific_journal-2676	445	196	,	,	PUNCT
american_scientific_journal-2676	445	197	,	,	PUNCT
american_scientific_journal-2676	445	198	{	{	PUNCT
american_scientific_journal-2676	445	199	(=	(=	NOUN
american_scientific_journal-2676	445	200	)	)	PUNCT
american_scientific_journal-2676	445	201	,	,	PUNCT
american_scientific_journal-2676	445	202	(	(	PUNCT
american_scientific_journal-2676	445	203	213	213	NUM
american_scientific_journal-2676	445	204	xeeeh	xeeeh	ADJ
american_scientific_journal-2676	445	205	φ	φ	NOUN
american_scientific_journal-2676	445	206	.	.	PUNCT
american_scientific_journal-2676	446	1	it	it	PRON
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american_scientific_journal-2676	446	6	)	)	PUNCT
american_scientific_journal-2676	446	7	,	,	PUNCT
american_scientific_journal-2676	446	8	,	,	PUNCT
american_scientific_journal-2676	446	9	,	,	PUNCT
american_scientific_journal-2676	446	10	(	(	PUNCT
american_scientific_journal-2676	446	11	21	21	NUM
american_scientific_journal-2676	446	12	ex	ex	X
american_scientific_journal-2676	446	13	ηη	ηη	PROPN
american_scientific_journal-2676	446	14	is	be	AUX
american_scientific_journal-2676	446	15	a	a	DET
american_scientific_journal-2676	446	16	sbts	sbts	ADJ
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american_scientific_journal-2676	446	18	)	)	PUNCT
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american_scientific_journal-2676	446	20	,	,	PUNCT
american_scientific_journal-2676	446	21	(	(	PUNCT
american_scientific_journal-2676	446	22	)	)	PUNCT
american_scientific_journal-2676	446	23	,	,	PUNCT
american_scientific_journal-2676	446	24	,	,	PUNCT
american_scientific_journal-2676	446	25	(	(	PUNCT
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american_scientific_journal-2676	446	27	,	,	PUNCT
american_scientific_journal-2676	446	28	,	,	PUNCT
american_scientific_journal-2676	446	29	(	(	PUNCT
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american_scientific_journal-2676	446	31	,	,	PUNCT
american_scientific_journal-2676	446	32	,	,	PUNCT
american_scientific_journal-2676	446	33	(	(	PUNCT
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american_scientific_journal-2676	446	35	,	,	PUNCT
american_scientific_journal-2676	446	36	,	,	PUNCT
american_scientific_journal-2676	446	37	(	(	PUNCT
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american_scientific_journal-2676	446	39	,	,	PUNCT
american_scientific_journal-2676	446	40	,	,	PUNCT
american_scientific_journal-2676	446	41	(	(	PUNCT
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american_scientific_journal-2676	446	43	,	,	PUNCT
american_scientific_journal-2676	446	44	,	,	PUNCT
american_scientific_journal-2676	446	45	(	(	PUNCT
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american_scientific_journal-2676	446	47	,	,	PUNCT
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american_scientific_journal-2676	446	49	~(),,~{(=	~(),,~{(=	NUM
american_scientific_journal-2676	446	50	32132112	32132112	NUM
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american_scientific_journal-2676	446	52	,	,	PUNCT
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american_scientific_journal-2676	446	56	,	,	PUNCT
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american_scientific_journal-2676	446	59	)	)	PUNCT
american_scientific_journal-2676	446	60	,	,	PUNCT
american_scientific_journal-2676	446	61	,	,	PUNCT
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american_scientific_journal-2676	446	64	{	{	PUNCT
american_scientific_journal-2676	446	65	(=	(=	NOUN
american_scientific_journal-2676	446	66	)	)	PUNCT
american_scientific_journal-2676	446	67	,	,	PUNCT
american_scientific_journal-2676	446	68	(	(	PUNCT
american_scientific_journal-2676	446	69	21	21	NUM
american_scientific_journal-2676	446	70	xezyeep	xezyeep	NOUN
american_scientific_journal-2676	446	71	.	.	PUNCT
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american_scientific_journal-2676	447	2	,	,	PUNCT
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american_scientific_journal-2676	447	4	)	)	PUNCT
american_scientific_journal-2676	447	5	,	,	PUNCT
american_scientific_journal-2676	447	6	(	(	PUNCT
american_scientific_journal-2676	447	7	,	,	PUNCT
american_scientific_journal-2676	447	8	)	)	PUNCT
american_scientific_journal-2676	447	9	,	,	PUNCT
american_scientific_journal-2676	447	10	{	{	PUNCT
american_scientific_journal-2676	447	11	(=	(=	NOUN
american_scientific_journal-2676	447	12	2112	2112	NUM
american_scientific_journal-2676	447	13	cc	cc	ADP
american_scientific_journal-2676	447	14	p	p	X
american_scientific_journal-2676	447	15	egegηη	egegηη	PROPN
american_scientific_journal-2676	447	16	λ	λ	PROPN
american_scientific_journal-2676	447	17	.	.	PUNCT
american_scientific_journal-2676	448	1	by	by	ADP
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american_scientific_journal-2676	448	4	soft	soft	ADJ
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american_scientific_journal-2676	448	8	50}1,2,3,	50}1,2,3,	NUM
american_scientific_journal-2676	448	9	...	...	PUNCT
american_scientific_journal-2676	448	10	,=:),{(=	,=:),{(=	PUNCT
american_scientific_journal-2676	448	11	)	)	PUNCT
american_scientific_journal-2676	448	12	(	(	PUNCT
american_scientific_journal-2676	448	13	1212	1212	NUM
american_scientific_journal-2676	448	14	iemxss	iemxss	NOUN
american_scientific_journal-2676	449	1	i	i	PRON
american_scientific_journal-2676	449	2	c	c	NOUN
american_scientific_journal-2676	449	3	e	e	X
american_scientific_journal-2676	449	4	ηη	ηη	VERB
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american_scientific_journal-2676	449	6	found	find	VERB
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american_scientific_journal-2676	449	8	:	:	PUNCT
american_scientific_journal-2676	449	9	c	c	NOUN
american_scientific_journal-2676	449	10	excsp	excsp	NOUN
american_scientific_journal-2676	449	11	121221	121221	NUM
american_scientific_journal-2676	449	12	=)	=)	NOUN
american_scientific_journal-2676	449	13	,	,	PUNCT
american_scientific_journal-2676	449	14	,	,	PUNCT
american_scientific_journal-2676	449	15	(	(	PUNCT
american_scientific_journal-2676	449	16	ηηηηλ	ηηηηλ	NOUN
american_scientific_journal-2676	449	17			ADV
american_scientific_journal-2676	449	18	.	.	PUNCT
american_scientific_journal-2676	450	1	moreover	moreover	ADV
american_scientific_journal-2676	450	2	,	,	PUNCT
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american_scientific_journal-2676	450	6	,	,	PUNCT
american_scientific_journal-2676	450	7	,	,	PUNCT
american_scientific_journal-2676	450	8	(	(	PUNCT
american_scientific_journal-2676	450	9	21	21	NUM
american_scientific_journal-2676	450	10	.	.	PUNCT
american_scientific_journal-2676	451	1	now	now	ADV
american_scientific_journal-2676	451	2	,	,	PUNCT
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american_scientific_journal-2676	451	4	λη	λη	PRON
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american_scientific_journal-2676	451	6	∈	∈	PROPN
american_scientific_journal-2676	451	7	)	)	PUNCT
american_scientific_journal-2676	451	8	,	,	PUNCT
american_scientific_journal-2676	451	9	(	(	PUNCT
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american_scientific_journal-2676	451	11	,	,	PUNCT
american_scientific_journal-2676	451	12	,	,	PUNCT
american_scientific_journal-2676	451	13	(	(	PUNCT
american_scientific_journal-2676	451	14	,	,	PUNCT
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american_scientific_journal-2676	451	17	)	)	PUNCT
american_scientific_journal-2676	451	18	,	,	PUNCT
american_scientific_journal-2676	451	19	,	,	PUNCT
american_scientific_journal-2676	451	20	(	(	PUNCT
american_scientific_journal-2676	451	21	)	)	PUNCT
american_scientific_journal-2676	451	22	,	,	PUNCT
american_scientific_journal-2676	451	23	(	(	PUNCT
american_scientific_journal-2676	451	24	)	)	PUNCT
american_scientific_journal-2676	451	25	,	,	PUNCT
american_scientific_journal-2676	451	26	,	,	PUNCT
american_scientific_journal-2676	451	27	(	(	PUNCT
american_scientific_journal-2676	451	28	21	21	NUM
american_scientific_journal-2676	451	29	ηηλ∈	ηηλ∈	NOUN
american_scientific_journal-2676	451	30	.	.	PUNCT
american_scientific_journal-2676	452	1	therefore	therefore	ADV
american_scientific_journal-2676	452	2	,	,	PUNCT
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american_scientific_journal-2676	452	4	)	)	PUNCT
american_scientific_journal-2676	452	5	,	,	PUNCT
american_scientific_journal-2676	452	6	,	,	PUNCT
american_scientific_journal-2676	452	7	(	(	PUNCT
american_scientific_journal-2676	452	8	)	)	PUNCT
american_scientific_journal-2676	452	9	,	,	PUNCT
american_scientific_journal-2676	452	10	(	(	PUNCT
american_scientific_journal-2676	452	11	~	~	NOUN
american_scientific_journal-2676	452	12	)	)	PUNCT
american_scientific_journal-2676	452	13	,	,	PUNCT
american_scientific_journal-2676	452	14	(	(	PUNCT
american_scientific_journal-2676	452	15	21	21	NUM
american_scientific_journal-2676	452	16	ηηλ∈∩	ηηλ∈∩	PROPN
american_scientific_journal-2676	452	17	[	[	PUNCT
american_scientific_journal-2676	452	18	by	by	ADP
american_scientific_journal-2676	452	19	theorem	theorem	NOUN
american_scientific_journal-2676	452	20	3.1	3.1	NUM
american_scientific_journal-2676	452	21	]	]	PUNCT
american_scientific_journal-2676	452	22	.	.	PUNCT
american_scientific_journal-2676	453	1	hence	hence	ADV
american_scientific_journal-2676	453	2	,	,	PUNCT
american_scientific_journal-2676	453	3	λη	λη	ADP
american_scientific_journal-2676	453	4	peken	peken	VERB
american_scientific_journal-2676	453	5	∈∩	∈∩	PROPN
american_scientific_journal-2676	453	6	)	)	PUNCT
american_scientific_journal-2676	453	7	,	,	PUNCT
american_scientific_journal-2676	453	8	(	(	PUNCT
american_scientific_journal-2676	453	9	~	~	NOUN
american_scientific_journal-2676	453	10	)	)	PUNCT
american_scientific_journal-2676	453	11	,	,	PUNCT
american_scientific_journal-2676	453	12	(	(	PUNCT
american_scientific_journal-2676	453	13	.	.	PUNCT
american_scientific_journal-2676	454	1	therefore	therefore	ADV
american_scientific_journal-2676	454	2	,	,	PUNCT
american_scientific_journal-2676	454	3	λη	λη	PROPN
american_scientific_journal-2676	454	4	p	p	NOUN
american_scientific_journal-2676	454	5	is	be	AUX
american_scientific_journal-2676	454	6	a	a	DET
american_scientific_journal-2676	454	7	soft	soft	ADJ
american_scientific_journal-2676	454	8	topology	topology	NOUN
american_scientific_journal-2676	454	9	.	.	PUNCT
american_scientific_journal-2676	455	1	consequently	consequently	ADV
american_scientific_journal-2676	455	2	,	,	PUNCT
american_scientific_journal-2676	455	3	)	)	PUNCT
american_scientific_journal-2676	455	4	,	,	PUNCT
american_scientific_journal-2676	455	5	,	,	PUNCT
american_scientific_journal-2676	455	6	,	,	PUNCT
american_scientific_journal-2676	455	7	(	(	PUNCT
american_scientific_journal-2676	455	8	21	21	NUM
american_scientific_journal-2676	455	9	ex	ex	X
american_scientific_journal-2676	455	10	ηη	ηη	PROPN
american_scientific_journal-2676	455	11	is	be	AUX
american_scientific_journal-2676	455	12	a	a	DET
american_scientific_journal-2676	455	13	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	NOUN
american_scientific_journal-2676	455	14	but	but	CCONJ
american_scientific_journal-2676	455	15	it	it	PRON
american_scientific_journal-2676	455	16	is	be	AUX
american_scientific_journal-2676	455	17	not	not	PART
american_scientific_journal-2676	455	18	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	455	19	2	2	NUM
american_scientific_journal-2676	455	20	�	�	PROPN
american_scientific_journal-2676	455	21	∗	∗	NOUN
american_scientific_journal-2676	455	22	because	because	SCONJ
american_scientific_journal-2676	455	23	)	)	PUNCT
american_scientific_journal-2676	455	24	,	,	PUNCT
american_scientific_journal-2676	455	25	(	(	PUNCT
american_scientific_journal-2676	455	26	1	1	NUM
american_scientific_journal-2676	455	27	eye	eye	NOUN
american_scientific_journal-2676	455	28	neither	neither	CCONJ
american_scientific_journal-2676	455	29	p	p	NOUN
american_scientific_journal-2676	455	30	-open	-open	ADJ
american_scientific_journal-2676	455	31	soft	soft	ADJ
american_scientific_journal-2676	455	32	set	set	NOUN
american_scientific_journal-2676	455	33	nor	nor	CCONJ
american_scientific_journal-2676	455	34	p	p	NOUN
american_scientific_journal-2676	455	35	-closed	-close	VERB
american_scientific_journal-2676	455	36	soft	soft	ADJ
american_scientific_journal-2676	455	37	set	set	NOUN
american_scientific_journal-2676	455	38	.	.	PUNCT
american_scientific_journal-2676	456	1	also	also	ADV
american_scientific_journal-2676	456	2	,	,	PUNCT
american_scientific_journal-2676	456	3	)	)	PUNCT
american_scientific_journal-2676	456	4	,	,	PUNCT
american_scientific_journal-2676	456	5	,	,	PUNCT
american_scientific_journal-2676	456	6	,	,	PUNCT
american_scientific_journal-2676	456	7	(	(	PUNCT
american_scientific_journal-2676	456	8	21	21	NUM
american_scientific_journal-2676	456	9	ex	ex	NOUN
american_scientific_journal-2676	456	10	ηη	ηη	PROPN
american_scientific_journal-2676	456	11	is	be	AUX
american_scientific_journal-2676	456	12	not	not	PART
american_scientific_journal-2676	456	13	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	NOUN
american_scientific_journal-2676	456	14	for	for	ADP
american_scientific_journal-2676	456	15	21	21	NUM
american_scientific_journal-2676	456	16	ee	ee	NOUN
american_scientific_journal-2676	456	17	zy	zy	PROPN
american_scientific_journal-2676	456	18	≠	≠	PROPN
american_scientific_journal-2676	456	19	but	but	CCONJ
american_scientific_journal-2676	456	20	there	there	PRON
american_scientific_journal-2676	456	21	is	be	VERB
american_scientific_journal-2676	456	22	no	no	DET
american_scientific_journal-2676	456	23	p	p	NOUN
american_scientific_journal-2676	456	24	-open	-open	ADJ
american_scientific_journal-2676	456	25	soft	soft	ADJ
american_scientific_journal-2676	456	26	set	set	NOUN
american_scientific_journal-2676	456	27	contains	contain	VERB
american_scientific_journal-2676	456	28	one	one	NUM
american_scientific_journal-2676	456	29	of	of	ADP
american_scientific_journal-2676	456	30	them	they	PRON
american_scientific_journal-2676	456	31	but	but	CCONJ
american_scientific_journal-2676	456	32	not	not	PART
american_scientific_journal-2676	456	33	american	american	ADJ
american_scientific_journal-2676	456	34	scientific	scientific	ADJ
american_scientific_journal-2676	456	35	research	research	NOUN
american_scientific_journal-2676	456	36	journal	journal	NOUN
american_scientific_journal-2676	456	37	for	for	ADP
american_scientific_journal-2676	456	38	engineering	engineering	NOUN
american_scientific_journal-2676	456	39	,	,	PUNCT
american_scientific_journal-2676	456	40	technology	technology	NOUN
american_scientific_journal-2676	456	41	,	,	PUNCT
american_scientific_journal-2676	456	42	and	and	CCONJ
american_scientific_journal-2676	456	43	sciences	science	NOUN
american_scientific_journal-2676	456	44	(	(	PUNCT
american_scientific_journal-2676	456	45	asrjets	asrjet	NOUN
american_scientific_journal-2676	456	46	)	)	PUNCT
american_scientific_journal-2676	456	47	(	(	PUNCT
american_scientific_journal-2676	456	48	2017	2017	NUM
american_scientific_journal-2676	456	49	)	)	PUNCT
american_scientific_journal-2676	456	50	volume	volume	NOUN
american_scientific_journal-2676	456	51	28	28	NUM
american_scientific_journal-2676	456	52	,	,	PUNCT
american_scientific_journal-2676	456	53	no	no	DET
american_scientific_journal-2676	456	54	1	1	NUM
american_scientific_journal-2676	456	55	,	,	PUNCT
american_scientific_journal-2676	456	56	pp	pp	ADV
american_scientific_journal-2676	456	57	225	225	NUM
american_scientific_journal-2676	456	58	-	-	SYM
american_scientific_journal-2676	456	59	247	247	NUM
american_scientific_journal-2676	456	60	245	245	NUM
american_scientific_journal-2676	456	61	contains	contain	VERB
american_scientific_journal-2676	456	62	the	the	DET
american_scientific_journal-2676	456	63	other	other	ADJ
american_scientific_journal-2676	456	64	.	.	PUNCT
american_scientific_journal-2676	457	1	theorem	theorem	VERB
american_scientific_journal-2676	457	2	5.6	5.6	NUM
american_scientific_journal-2676	457	3	a	a	DET
american_scientific_journal-2676	457	4	sbts	sbts	ADJ
american_scientific_journal-2676	457	5	)	)	PUNCT
american_scientific_journal-2676	457	6	,	,	PUNCT
american_scientific_journal-2676	457	7	,	,	PUNCT
american_scientific_journal-2676	457	8	,	,	PUNCT
american_scientific_journal-2676	457	9	(	(	PUNCT
american_scientific_journal-2676	457	10	21	21	NUM
american_scientific_journal-2676	457	11	ex	ex	X
american_scientific_journal-2676	457	12	ηη	ηη	PROPN
american_scientific_journal-2676	457	13	is	be	AUX
american_scientific_journal-2676	457	14	a	a	DET
american_scientific_journal-2676	457	15	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	457	16	4	4	NUM
american_scientific_journal-2676	457	17	�	�	PROPN
american_scientific_journal-2676	457	18	∗	∗	NOUN
american_scientific_journal-2676	457	19	if	if	SCONJ
american_scientific_journal-2676	457	20	it	it	PRON
american_scientific_journal-2676	457	21	is	be	AUX
american_scientific_journal-2676	457	22	a	a	DET
american_scientific_journal-2676	457	23	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	ADJ
american_scientific_journal-2676	457	24	and	and	CCONJ
american_scientific_journal-2676	457	25	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗.	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗.	PROPN
american_scientific_journal-2676	457	26	proof	proof	NOUN
american_scientific_journal-2676	457	27	.	.	PUNCT
american_scientific_journal-2676	458	1	suppose	suppose	VERB
american_scientific_journal-2676	458	2	that	that	PRON
american_scientific_journal-2676	458	3	)	)	PUNCT
american_scientific_journal-2676	458	4	,	,	PUNCT
american_scientific_journal-2676	458	5	,	,	PUNCT
american_scientific_journal-2676	458	6	,	,	PUNCT
american_scientific_journal-2676	458	7	(	(	PUNCT
american_scientific_journal-2676	458	8	21	21	NUM
american_scientific_journal-2676	458	9	ex	ex	X
american_scientific_journal-2676	458	10	ηη	ηη	PROPN
american_scientific_journal-2676	458	11	is	be	AUX
american_scientific_journal-2676	458	12	a	a	DET
american_scientific_journal-2676	458	13	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	NOUN
american_scientific_journal-2676	458	14	and	and	CCONJ
american_scientific_journal-2676	458	15	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	NOUN
american_scientific_journal-2676	458	16	.	.	PUNCT
american_scientific_journal-2676	459	1	let	let	VERB
american_scientific_journal-2676	459	2	)	)	PUNCT
american_scientific_journal-2676	459	3	,	,	PUNCT
american_scientific_journal-2676	459	4	(	(	PUNCT
american_scientific_journal-2676	459	5	ef	ef	X
american_scientific_journal-2676	459	6	be	be	AUX
american_scientific_journal-2676	459	7	a	a	DET
american_scientific_journal-2676	459	8	finite	finite	ADJ
american_scientific_journal-2676	459	9	soft	soft	ADJ
american_scientific_journal-2676	459	10	set	set	NOUN
american_scientific_journal-2676	459	11	.	.	PUNCT
american_scientific_journal-2676	460	1	then	then	ADV
american_scientific_journal-2676	460	2	)	)	PUNCT
american_scientific_journal-2676	460	3	}	}	PUNCT
american_scientific_journal-2676	460	4	,	,	PUNCT
american_scientific_journal-2676	460	5	(	(	PUNCT
american_scientific_journal-2676	460	6	~:),{(=	~:),{(=	ADJ
american_scientific_journal-2676	460	7	)	)	PUNCT
american_scientific_journal-2676	460	8	,	,	PUNCT
american_scientific_journal-2676	460	9	(	(	PUNCT
american_scientific_journal-2676	460	10	efxexef	efxexef	PROPN
american_scientific_journal-2676	460	11	ee	ee	PROPN
american_scientific_journal-2676	460	12	∈	∈	NOUN
american_scientific_journal-2676	460	13	[	[	PUNCT
american_scientific_journal-2676	460	14	by	by	ADP
american_scientific_journal-2676	460	15	proposition	proposition	NOUN
american_scientific_journal-2676	460	16	2.1	2.1	NUM
american_scientific_journal-2676	460	17	]	]	PUNCT
american_scientific_journal-2676	460	18	.	.	PUNCT
american_scientific_journal-2676	461	1	since	since	SCONJ
american_scientific_journal-2676	461	2	)	)	PUNCT
american_scientific_journal-2676	461	3	,	,	PUNCT
american_scientific_journal-2676	461	4	,	,	PUNCT
american_scientific_journal-2676	461	5	,	,	PUNCT
american_scientific_journal-2676	461	6	(	(	PUNCT
american_scientific_journal-2676	461	7	21	21	NUM
american_scientific_journal-2676	461	8	ex	ex	X
american_scientific_journal-2676	461	9	ηη	ηη	PROPN
american_scientific_journal-2676	461	10	is	be	AUX
american_scientific_journal-2676	461	11	a	a	DET
american_scientific_journal-2676	461	12	𝑃𝑃𝑃𝑃𝑇𝑇0∗	𝑃𝑃𝑃𝑃𝑇𝑇0∗	NOUN
american_scientific_journal-2676	461	13	,	,	PUNCT
american_scientific_journal-2676	461	14	then	then	ADV
american_scientific_journal-2676	461	15	)	)	PUNCT
american_scientific_journal-2676	461	16	,	,	PUNCT
american_scientific_journal-2676	461	17	(	(	PUNCT
american_scientific_journal-2676	461	18	exe	exe	NOUN
american_scientific_journal-2676	461	19	is	be	AUX
american_scientific_journal-2676	461	20	a	a	DET
american_scientific_journal-2676	461	21	𝑝𝑝𝑝𝑝-closed	𝑝𝑝𝑝𝑝-closed	ADJ
american_scientific_journal-2676	461	22	soft	soft	ADJ
american_scientific_journal-2676	461	23	set	set	NOUN
american_scientific_journal-2676	461	24	for	for	ADP
american_scientific_journal-2676	461	25	all	all	PRON
american_scientific_journal-2676	461	26	)	)	PUNCT
american_scientific_journal-2676	461	27	,	,	PUNCT
american_scientific_journal-2676	461	28	(	(	PUNCT
american_scientific_journal-2676	461	29	~	~	PUNCT
american_scientific_journal-2676	461	30	efxe	efxe	NOUN
american_scientific_journal-2676	461	31	∈	∈	NOUN
american_scientific_journal-2676	461	32	.	.	PUNCT
american_scientific_journal-2676	462	1	but	but	CCONJ
american_scientific_journal-2676	462	2	,	,	PUNCT
american_scientific_journal-2676	462	3	)	)	PUNCT
american_scientific_journal-2676	462	4	,	,	PUNCT
american_scientific_journal-2676	462	5	,	,	PUNCT
american_scientific_journal-2676	462	6	,	,	PUNCT
american_scientific_journal-2676	462	7	(	(	PUNCT
american_scientific_journal-2676	462	8	21	21	NUM
american_scientific_journal-2676	462	9	ex	ex	X
american_scientific_journal-2676	462	10	ηη	ηη	PROPN
american_scientific_journal-2676	462	11	is	be	AUX
american_scientific_journal-2676	462	12	a	a	DET
american_scientific_journal-2676	462	13	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	𝑃𝑃𝑃𝑃𝑇𝑇𝜆𝜆∗	NOUN
american_scientific_journal-2676	462	14	,	,	PUNCT
american_scientific_journal-2676	462	15	then	then	ADV
american_scientific_journal-2676	462	16	𝜂𝜂𝑝𝑝𝜆𝜆	𝜂𝜂𝑝𝑝𝜆𝜆	NOUN
american_scientific_journal-2676	462	17	is	be	AUX
american_scientific_journal-2676	462	18	a	a	DET
american_scientific_journal-2676	462	19	soft	soft	ADJ
american_scientific_journal-2676	462	20	topology	topology	NOUN
american_scientific_journal-2676	462	21	on	on	ADP
american_scientific_journal-2676	462	22	x	x	X
american_scientific_journal-2676	462	23	.	.	PUNCT
american_scientific_journal-2676	463	1	it	it	PRON
american_scientific_journal-2676	463	2	follows	follow	VERB
american_scientific_journal-2676	463	3	that	that	SCONJ
american_scientific_journal-2676	463	4	,	,	PUNCT
american_scientific_journal-2676	463	5	by	by	ADP
american_scientific_journal-2676	463	6	lemma	lemma	PROPN
american_scientific_journal-2676	463	7	5.2,the	5.2,the	DET
american_scientific_journal-2676	463	8	finite	finite	PROPN
american_scientific_journal-2676	463	9	union	union	PROPN
american_scientific_journal-2676	463	10	of	of	ADP
american_scientific_journal-2676	463	11	λp	λp	ADV
american_scientific_journal-2676	463	12	-closed	-close	VERB
american_scientific_journal-2676	463	13	soft	soft	ADJ
american_scientific_journal-2676	463	14	sets	set	NOUN
american_scientific_journal-2676	463	15	is	be	AUX
american_scientific_journal-2676	463	16	a	a	DET
american_scientific_journal-2676	463	17	λp	λp	ADV
american_scientific_journal-2676	463	18	-closed	-close	VERB
american_scientific_journal-2676	463	19	soft	soft	ADJ
american_scientific_journal-2676	463	20	set	set	NOUN
american_scientific_journal-2676	463	21	.	.	PUNCT
american_scientific_journal-2676	464	1	consequently	consequently	ADV
american_scientific_journal-2676	464	2	,	,	PUNCT
american_scientific_journal-2676	464	3	)	)	PUNCT
american_scientific_journal-2676	464	4	}	}	PUNCT
american_scientific_journal-2676	464	5	,	,	PUNCT
american_scientific_journal-2676	464	6	(	(	PUNCT
american_scientific_journal-2676	464	7	~	~	PUNCT
american_scientific_journal-2676	464	8	:)	:)	INTJ
american_scientific_journal-2676	464	9	,	,	PUNCT
american_scientific_journal-2676	464	10	{	{	PUNCT
american_scientific_journal-2676	464	11	(	(	PUNCT
american_scientific_journal-2676	464	12	efxex	efxex	ADJ
american_scientific_journal-2676	464	13	ee	ee	ADP
american_scientific_journal-2676	464	14	∈	∈	NOUN
american_scientific_journal-2676	464	15	is	be	AUX
american_scientific_journal-2676	464	16	a	a	DET
american_scientific_journal-2676	464	17	λp	λp	ADV
american_scientific_journal-2676	464	18	-closed	-close	VERB
american_scientific_journal-2676	464	19	soft	soft	ADJ
american_scientific_journal-2676	464	20	set	set	NOUN
american_scientific_journal-2676	464	21	.	.	PUNCT
american_scientific_journal-2676	465	1	therefore	therefore	ADV
american_scientific_journal-2676	465	2	,	,	PUNCT
american_scientific_journal-2676	465	3	)	)	PUNCT
american_scientific_journal-2676	465	4	,	,	PUNCT
american_scientific_journal-2676	465	5	(	(	PUNCT
american_scientific_journal-2676	465	6	ef	ef	PROPN
american_scientific_journal-2676	465	7	is	be	AUX
american_scientific_journal-2676	465	8	a	a	DET
american_scientific_journal-2676	465	9	λp	λp	ADV
american_scientific_journal-2676	465	10	-closed	-close	VERB
american_scientific_journal-2676	465	11	soft	soft	ADJ
american_scientific_journal-2676	465	12	set	set	NOUN
american_scientific_journal-2676	465	13	.	.	PUNCT
american_scientific_journal-2676	466	1	hence	hence	ADV
american_scientific_journal-2676	466	2	,	,	PUNCT
american_scientific_journal-2676	466	3	by	by	ADP
american_scientific_journal-2676	466	4	theorem	theorem	NOUN
american_scientific_journal-2676	466	5	3.4	3.4	NUM
american_scientific_journal-2676	466	6	we	we	PRON
american_scientific_journal-2676	466	7	conclude	conclude	VERB
american_scientific_journal-2676	466	8	that	that	PRON
american_scientific_journal-2676	466	9	)	)	PUNCT
american_scientific_journal-2676	466	10	,	,	PUNCT
american_scientific_journal-2676	466	11	,	,	PUNCT
american_scientific_journal-2676	466	12	,	,	PUNCT
american_scientific_journal-2676	466	13	(	(	PUNCT
american_scientific_journal-2676	466	14	21	21	NUM
american_scientific_journal-2676	466	15	ex	ex	X
american_scientific_journal-2676	466	16	ηη	ηη	PROPN
american_scientific_journal-2676	466	17	is	be	AUX
american_scientific_journal-2676	466	18	a	a	DET
american_scientific_journal-2676	466	19	𝑃𝑃𝑃𝑃𝑇𝑇1	𝑃𝑃𝑃𝑃𝑇𝑇1	PROPN
american_scientific_journal-2676	466	20	4	4	NUM
american_scientific_journal-2676	466	21	�	�	PROPN
american_scientific_journal-2676	466	22	∗	∗	NOUN
american_scientific_journal-2676	466	23	.	.	PUNCT
american_scientific_journal-2676	467	1	remark	remark	VERB
american_scientific_journal-2676	467	2	5.5	5.5	NUM
american_scientific_journal-2676	467	3	a	a	DET
american_scientific_journal-2676	467	4	𝐏𝐏𝐏𝐏𝐓𝐓𝛌𝛌∗	𝐏𝐏𝐏𝐏𝐓𝐓𝛌𝛌∗	NUM
american_scientific_journal-2676	467	5	space	space	NOUN
american_scientific_journal-2676	467	6	need	need	AUX
american_scientific_journal-2676	467	7	not	not	PART
american_scientific_journal-2676	467	8	be	be	AUX
american_scientific_journal-2676	467	9	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	PROPN
american_scientific_journal-2676	467	10	𝟒𝟒	𝟒𝟒	NUM
american_scientific_journal-2676	467	11	�	�	PROPN
american_scientific_journal-2676	467	12	∗	∗	NOUN
american_scientific_journal-2676	467	13	.	.	PUNCT
american_scientific_journal-2676	468	1	in	in	ADP
american_scientific_journal-2676	468	2	example	example	NOUN
american_scientific_journal-2676	468	3	5.4	5.4	NUM
american_scientific_journal-2676	468	4	,	,	PUNCT
american_scientific_journal-2676	468	5	we	we	PRON
american_scientific_journal-2676	468	6	proved	prove	VERB
american_scientific_journal-2676	468	7	that	that	PRON
american_scientific_journal-2676	468	8	)	)	PUNCT
american_scientific_journal-2676	468	9	,	,	PUNCT
american_scientific_journal-2676	468	10	,	,	PUNCT
american_scientific_journal-2676	468	11	,	,	PUNCT
american_scientific_journal-2676	468	12	(	(	PUNCT
american_scientific_journal-2676	468	13	21	21	NUM
american_scientific_journal-2676	468	14	ex	ex	X
american_scientific_journal-2676	468	15	ηη	ηη	PROPN
american_scientific_journal-2676	468	16	is	be	AUX
american_scientific_journal-2676	468	17	a	a	DET
american_scientific_journal-2676	468	18	𝑷𝑷𝑷𝑷𝑻𝑻𝝀𝝀∗	𝑷𝑷𝑷𝑷𝑻𝑻𝝀𝝀∗	PROPN
american_scientific_journal-2676	468	19	.	.	PUNCT
american_scientific_journal-2676	469	1	since	since	SCONJ
american_scientific_journal-2676	469	2	x	x	PRON
american_scientific_journal-2676	469	3	is	be	AUX
american_scientific_journal-2676	469	4	a	a	DET
american_scientific_journal-2676	469	5	finite	finite	NOUN
american_scientific_journal-2676	469	6	set	set	NOUN
american_scientific_journal-2676	469	7	and	and	CCONJ
american_scientific_journal-2676	469	8	)	)	PUNCT
american_scientific_journal-2676	469	9	,	,	PUNCT
american_scientific_journal-2676	469	10	,	,	PUNCT
american_scientific_journal-2676	469	11	,	,	PUNCT
american_scientific_journal-2676	469	12	(	(	PUNCT
american_scientific_journal-2676	469	13	21	21	NUM
american_scientific_journal-2676	469	14	ex	ex	NOUN
american_scientific_journal-2676	469	15	ηη	ηη	PROPN
american_scientific_journal-2676	469	16	is	be	AUX
american_scientific_journal-2676	469	17	not	not	PART
american_scientific_journal-2676	469	18	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	NUM
american_scientific_journal-2676	469	19	𝟐𝟐	𝟐𝟐	NUM
american_scientific_journal-2676	469	20	�	�	PROPN
american_scientific_journal-2676	469	21	∗	∗	NOUN
american_scientific_journal-2676	469	22	,	,	PUNCT
american_scientific_journal-2676	469	23	then	then	ADV
american_scientific_journal-2676	469	24	by	by	ADP
american_scientific_journal-2676	469	25	corollary	corollary	ADJ
american_scientific_journal-2676	469	26	3.1	3.1	NUM
american_scientific_journal-2676	469	27	we	we	PRON
american_scientific_journal-2676	469	28	conclude	conclude	VERB
american_scientific_journal-2676	469	29	that	that	PRON
american_scientific_journal-2676	469	30	)	)	PUNCT
american_scientific_journal-2676	469	31	,	,	PUNCT
american_scientific_journal-2676	469	32	,	,	PUNCT
american_scientific_journal-2676	469	33	,	,	PUNCT
american_scientific_journal-2676	469	34	(	(	PUNCT
american_scientific_journal-2676	469	35	21	21	NUM
american_scientific_journal-2676	469	36	ex	ex	NOUN
american_scientific_journal-2676	469	37	ηη	ηη	PROPN
american_scientific_journal-2676	469	38	is	be	AUX
american_scientific_journal-2676	469	39	not	not	PART
american_scientific_journal-2676	469	40	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	NUM
american_scientific_journal-2676	469	41	𝟒𝟒	𝟒𝟒	NUM
american_scientific_journal-2676	469	42	�	�	PROPN
american_scientific_journal-2676	469	43	∗	∗	NOUN
american_scientific_journal-2676	469	44	.	.	PUNCT
american_scientific_journal-2676	470	1	6	6	X
american_scientific_journal-2676	470	2	.	.	X
american_scientific_journal-2676	470	3	conclusion	conclusion	NOUN
american_scientific_journal-2676	470	4	the	the	DET
american_scientific_journal-2676	470	5	notions	notion	NOUN
american_scientific_journal-2676	470	6	of	of	ADP
american_scientific_journal-2676	470	7	pairwise	pairwise	NOUN
american_scientific_journal-2676	470	8	λ	λ	SYM
american_scientific_journal-2676	470	9	-closed	-close	VERB
american_scientific_journal-2676	470	10	soft	soft	ADJ
american_scientific_journal-2676	470	11	sets	set	NOUN
american_scientific_journal-2676	470	12	,	,	PUNCT
american_scientific_journal-2676	470	13	pairwise	pairwise	NOUN
american_scientific_journal-2676	470	14	λ	λ	NOUN
american_scientific_journal-2676	470	15	-open	-open	NOUN
american_scientific_journal-2676	470	16	soft	soft	ADJ
american_scientific_journal-2676	470	17	sets	set	NOUN
american_scientific_journal-2676	470	18	and	and	CCONJ
american_scientific_journal-2676	470	19	pairwise	pairwise	NOUN
american_scientific_journal-2676	470	20	locally	locally	ADV
american_scientific_journal-2676	470	21	closed	close	VERB
american_scientific_journal-2676	470	22	soft	soft	ADJ
american_scientific_journal-2676	470	23	sets	set	NOUN
american_scientific_journal-2676	470	24	are	be	AUX
american_scientific_journal-2676	470	25	turn	turn	VERB
american_scientific_journal-2676	470	26	out	out	ADP
american_scientific_journal-2676	470	27	to	to	PART
american_scientific_journal-2676	470	28	be	be	AUX
american_scientific_journal-2676	470	29	useful	useful	ADJ
american_scientific_journal-2676	470	30	in	in	ADP
american_scientific_journal-2676	470	31	the	the	DET
american_scientific_journal-2676	470	32	study	study	NOUN
american_scientific_journal-2676	470	33	of	of	ADP
american_scientific_journal-2676	470	34	some	some	DET
american_scientific_journal-2676	470	35	soft	soft	ADJ
american_scientific_journal-2676	470	36	bitopologies	bitopologie	NOUN
american_scientific_journal-2676	470	37	which	which	PRON
american_scientific_journal-2676	470	38	are	be	AUX
american_scientific_journal-2676	470	39	not	not	PART
american_scientific_journal-2676	470	40	*	*	PROPN
american_scientific_journal-2676	470	41	1pst	1pst	NUM
american_scientific_journal-2676	470	42	.	.	PUNCT
american_scientific_journal-2676	471	1	in	in	ADP
american_scientific_journal-2676	471	2	this	this	DET
american_scientific_journal-2676	471	3	paper	paper	NOUN
american_scientific_journal-2676	471	4	,	,	PUNCT
american_scientific_journal-2676	471	5	we	we	PRON
american_scientific_journal-2676	471	6	introduce	introduce	VERB
american_scientific_journal-2676	471	7	new	new	ADJ
american_scientific_journal-2676	471	8	classes	class	NOUN
american_scientific_journal-2676	471	9	of	of	ADP
american_scientific_journal-2676	471	10	soft	soft	ADJ
american_scientific_journal-2676	471	11	sets	set	NOUN
american_scientific_journal-2676	471	12	called	call	VERB
american_scientific_journal-2676	471	13	λp	λp	ADP
american_scientific_journal-2676	471	14	-closed	-close	VERB
american_scientific_journal-2676	471	15	soft	soft	ADJ
american_scientific_journal-2676	471	16	sets	set	NOUN
american_scientific_journal-2676	471	17	,	,	PUNCT
american_scientific_journal-2676	471	18	λp	λp	X
american_scientific_journal-2676	471	19	-open	-open	VERB
american_scientific_journal-2676	471	20	soft	soft	ADJ
american_scientific_journal-2676	471	21	sets	set	NOUN
american_scientific_journal-2676	471	22	and	and	CCONJ
american_scientific_journal-2676	471	23	p	p	NOUN
american_scientific_journal-2676	471	24	-locally	-locally	ADV
american_scientific_journal-2676	471	25	closed	close	VERB
american_scientific_journal-2676	471	26	soft	soft	ADJ
american_scientific_journal-2676	471	27	sets	set	NOUN
american_scientific_journal-2676	471	28	in	in	ADP
american_scientific_journal-2676	471	29	soft	soft	ADJ
american_scientific_journal-2676	471	30	bitopological	bitopological	ADJ
american_scientific_journal-2676	471	31	spaces	space	NOUN
american_scientific_journal-2676	471	32	.	.	PUNCT
american_scientific_journal-2676	472	1	it	it	PRON
american_scientific_journal-2676	472	2	turn	turn	VERB
american_scientific_journal-2676	472	3	out	out	ADP
american_scientific_journal-2676	472	4	that	that	SCONJ
american_scientific_journal-2676	472	5	λp	λp	ADP
american_scientific_journal-2676	472	6	-closed	-close	VERB
american_scientific_journal-2676	472	7	soft	soft	ADJ
american_scientific_journal-2676	472	8	sets	set	NOUN
american_scientific_journal-2676	472	9	,	,	PUNCT
american_scientific_journal-2676	472	10	λp	λp	X
american_scientific_journal-2676	472	11	-open	-open	VERB
american_scientific_journal-2676	472	12	soft	soft	ADJ
american_scientific_journal-2676	472	13	sets	set	NOUN
american_scientific_journal-2676	472	14	and	and	CCONJ
american_scientific_journal-2676	472	15	p	p	NOUN
american_scientific_journal-2676	472	16	-locally	-locally	ADV
american_scientific_journal-2676	472	17	closed	close	VERB
american_scientific_journal-2676	472	18	soft	soft	ADJ
american_scientific_journal-2676	472	19	sets	set	NOUN
american_scientific_journal-2676	472	20	are	be	AUX
american_scientific_journal-2676	472	21	weaker	weak	ADJ
american_scientific_journal-2676	472	22	forms	form	NOUN
american_scientific_journal-2676	472	23	of	of	ADP
american_scientific_journal-2676	472	24	p	p	NOUN
american_scientific_journal-2676	472	25	-open(closed	-open(closed	ADJ
american_scientific_journal-2676	472	26	)	)	PUNCT
american_scientific_journal-2676	472	27	soft	soft	ADJ
american_scientific_journal-2676	472	28	sets	set	NOUN
american_scientific_journal-2676	472	29	.	.	PUNCT
american_scientific_journal-2676	473	1	we	we	PRON
american_scientific_journal-2676	473	2	also	also	ADV
american_scientific_journal-2676	473	3	conclude	conclude	VERB
american_scientific_journal-2676	473	4	several	several	ADJ
american_scientific_journal-2676	473	5	important	important	ADJ
american_scientific_journal-2676	473	6	properties	property	NOUN
american_scientific_journal-2676	473	7	of	of	ADP
american_scientific_journal-2676	473	8	such	such	ADJ
american_scientific_journal-2676	473	9	soft	soft	ADJ
american_scientific_journal-2676	473	10	sets	set	NOUN
american_scientific_journal-2676	473	11	.	.	PUNCT
american_scientific_journal-2676	474	1	moreover	moreover	ADV
american_scientific_journal-2676	474	2	,	,	PUNCT
american_scientific_journal-2676	474	3	we	we	PRON
american_scientific_journal-2676	474	4	introduce	introduce	VERB
american_scientific_journal-2676	474	5	and	and	CCONJ
american_scientific_journal-2676	474	6	study	study	VERB
american_scientific_journal-2676	474	7	a	a	DET
american_scientific_journal-2676	474	8	related	relate	VERB
american_scientific_journal-2676	474	9	pairwise	pairwise	NOUN
american_scientific_journal-2676	474	10	soft	soft	ADJ
american_scientific_journal-2676	474	11	separation	separation	NOUN
american_scientific_journal-2676	474	12	axioms	axiom	NOUN
american_scientific_journal-2676	474	13	,	,	PUNCT
american_scientific_journal-2676	474	14	namely	namely	ADV
american_scientific_journal-2676	474	15	,	,	PUNCT
american_scientific_journal-2676	474	16	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	𝑷𝑷𝑷𝑷𝑻𝑻𝟏𝟏	PROPN
american_scientific_journal-2676	474	17	𝟒𝟒	𝟒𝟒	NUM
american_scientific_journal-2676	474	18	�	�	PROPN
american_scientific_journal-2676	474	19	∗	∗	NOUN
american_scientific_journal-2676	474	20	,	,	PUNCT
american_scientific_journal-2676	474	21	𝑷𝑷𝑷𝑷𝑻𝑻𝑳𝑳∗	𝑷𝑷𝑷𝑷𝑻𝑻𝑳𝑳∗	PROPN
american_scientific_journal-2676	474	22	and	and	CCONJ
american_scientific_journal-2676	474	23	𝑷𝑷𝑷𝑷𝑻𝑻𝝀𝝀∗	𝑷𝑷𝑷𝑷𝑻𝑻𝝀𝝀∗	PROPN
american_scientific_journal-2676	474	24	.	.	PUNCT
american_scientific_journal-2676	475	1	we	we	PRON
american_scientific_journal-2676	475	2	studied	study	VERB
american_scientific_journal-2676	475	3	the	the	DET
american_scientific_journal-2676	475	4	relationships	relationship	NOUN
american_scientific_journal-2676	475	5	between	between	ADP
american_scientific_journal-2676	475	6	these	these	DET
american_scientific_journal-2676	475	7	types	type	NOUN
american_scientific_journal-2676	475	8	of	of	ADP
american_scientific_journal-2676	475	9	separation	separation	NOUN
american_scientific_journal-2676	475	10	axioms	axiom	NOUN
american_scientific_journal-2676	475	11	.	.	PUNCT
american_scientific_journal-2676	476	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-2676	476	2	the	the	DET
american_scientific_journal-2676	476	3	authors	author	NOUN
american_scientific_journal-2676	476	4	express	express	VERB
american_scientific_journal-2676	476	5	their	their	PRON
american_scientific_journal-2676	476	6	sincere	sincere	ADJ
american_scientific_journal-2676	476	7	thanks	thank	NOUN
american_scientific_journal-2676	476	8	to	to	ADP
american_scientific_journal-2676	476	9	the	the	DET
american_scientific_journal-2676	476	10	reviewers	reviewer	NOUN
american_scientific_journal-2676	476	11	for	for	ADP
american_scientific_journal-2676	476	12	their	their	PRON
american_scientific_journal-2676	476	13	valuable	valuable	ADJ
american_scientific_journal-2676	476	14	suggestions	suggestion	NOUN
american_scientific_journal-2676	476	15	.	.	PUNCT
american_scientific_journal-2676	477	1	the	the	DET
american_scientific_journal-2676	477	2	authors	author	NOUN
american_scientific_journal-2676	477	3	are	be	AUX
american_scientific_journal-2676	477	4	also	also	ADV
american_scientific_journal-2676	477	5	thankful	thankful	ADJ
american_scientific_journal-2676	477	6	to	to	ADP
american_scientific_journal-2676	477	7	the	the	DET
american_scientific_journal-2676	477	8	editors	editor	NOUN
american_scientific_journal-2676	477	9	-	-	PUNCT
american_scientific_journal-2676	477	10	in	in	ADP
american_scientific_journal-2676	477	11	-	-	PUNCT
american_scientific_journal-2676	477	12	chief	chief	NOUN
american_scientific_journal-2676	477	13	and	and	CCONJ
american_scientific_journal-2676	477	14	managing	manage	VERB
american_scientific_journal-2676	477	15	editors	editor	NOUN
american_scientific_journal-2676	477	16	for	for	ADP
american_scientific_journal-2676	477	17	their	their	PRON
american_scientific_journal-2676	477	18	important	important	ADJ
american_scientific_journal-2676	477	19	comments	comment	NOUN
american_scientific_journal-2676	477	20	which	which	PRON
american_scientific_journal-2676	477	21	helped	help	VERB
american_scientific_journal-2676	477	22	to	to	PART
american_scientific_journal-2676	477	23	improve	improve	VERB
american_scientific_journal-2676	477	24	the	the	DET
american_scientific_journal-2676	477	25	presentation	presentation	NOUN
american_scientific_journal-2676	477	26	of	of	ADP
american_scientific_journal-2676	477	27	the	the	DET
american_scientific_journal-2676	477	28	paper	paper	NOUN
american_scientific_journal-2676	477	29	.	.	PUNCT
american_scientific_journal-2676	478	1	references	reference	NOUN
american_scientific_journal-2676	478	2	[	[	X
american_scientific_journal-2676	478	3	1	1	NUM
american_scientific_journal-2676	478	4	]	]	PUNCT
american_scientific_journal-2676	478	5	a.	a.	NOUN
american_scientific_journal-2676	478	6	aygunoglu	aygunoglu	PROPN
american_scientific_journal-2676	478	7	and	and	CCONJ
american_scientific_journal-2676	478	8	h.	h.	PROPN
american_scientific_journal-2676	478	9	aygun	aygun	PROPN
american_scientific_journal-2676	478	10	,	,	PUNCT
american_scientific_journal-2676	478	11	some	some	DET
american_scientific_journal-2676	478	12	notes	note	NOUN
american_scientific_journal-2676	478	13	on	on	ADP
american_scientific_journal-2676	478	14	soft	soft	ADJ
american_scientific_journal-2676	478	15	topological	topological	ADJ
american_scientific_journal-2676	478	16	spaces	space	NOUN
american_scientific_journal-2676	478	17	,	,	PUNCT
american_scientific_journal-2676	478	18	neural	neural	ADJ
american_scientific_journal-2676	478	19	comput	comput	NOUN
american_scientific_journal-2676	478	20	.	.	PUNCT
american_scientific_journal-2676	479	1	applic	applic	PROPN
american_scientific_journal-2676	479	2	.	.	PUNCT
american_scientific_journal-2676	480	1	,	,	PUNCT
american_scientific_journal-2676	480	2	vol	vol	NOUN
american_scientific_journal-2676	480	3	.	.	PROPN
american_scientific_journal-2676	480	4	21	21	NUM
american_scientific_journal-2676	480	5	(	(	PUNCT
american_scientific_journal-2676	480	6	suppl	suppl	NOUN
american_scientific_journal-2676	480	7	1	1	NUM
american_scientific_journal-2676	480	8	)	)	PUNCT
american_scientific_journal-2676	480	9	,	,	PUNCT
american_scientific_journal-2676	480	10	pp	pp	PROPN
american_scientific_journal-2676	480	11	.	.	PUNCT
american_scientific_journal-2676	481	1	s113−s119	s113−s119	PROPN
american_scientific_journal-2676	481	2	,	,	PUNCT
american_scientific_journal-2676	481	3	2012	2012	NUM
american_scientific_journal-2676	481	4	.	.	PUNCT
american_scientific_journal-2676	482	1	[	[	X
american_scientific_journal-2676	482	2	2	2	NUM
american_scientific_journal-2676	482	3	]	]	PUNCT
american_scientific_journal-2676	482	4	basavaraj	basavaraj	PROPN
american_scientific_journal-2676	482	5	ittanagi	ittanagi	VERB
american_scientific_journal-2676	482	6	,	,	PUNCT
american_scientific_journal-2676	482	7	soft	soft	ADJ
american_scientific_journal-2676	482	8	bitopological	bitopological	ADJ
american_scientific_journal-2676	482	9	spaces	space	NOUN
american_scientific_journal-2676	482	10	,	,	PUNCT
american_scientific_journal-2676	482	11	international	international	ADJ
american_scientific_journal-2676	482	12	journal	journal	NOUN
american_scientific_journal-2676	482	13	of	of	ADP
american_scientific_journal-2676	482	14	computer	computer	NOUN
american_scientific_journal-2676	482	15	applications	application	NOUN
american_scientific_journal-2676	482	16	,	,	PUNCT
american_scientific_journal-2676	482	17	vol	vol	NOUN
american_scientific_journal-2676	482	18	.	.	PROPN
american_scientific_journal-2676	482	19	107	107	NUM
american_scientific_journal-2676	482	20	american	american	PROPN
american_scientific_journal-2676	482	21	scientific	scientific	ADJ
american_scientific_journal-2676	482	22	research	research	NOUN
american_scientific_journal-2676	482	23	journal	journal	NOUN
american_scientific_journal-2676	482	24	for	for	ADP
american_scientific_journal-2676	482	25	engineering	engineering	NOUN
american_scientific_journal-2676	482	26	,	,	PUNCT
american_scientific_journal-2676	482	27	technology	technology	NOUN
american_scientific_journal-2676	482	28	,	,	PUNCT
american_scientific_journal-2676	482	29	and	and	CCONJ
american_scientific_journal-2676	482	30	sciences	science	NOUN
american_scientific_journal-2676	482	31	(	(	PUNCT
american_scientific_journal-2676	482	32	asrjets	asrjet	NOUN
american_scientific_journal-2676	482	33	)	)	PUNCT
american_scientific_journal-2676	482	34	(	(	PUNCT
american_scientific_journal-2676	482	35	2017	2017	NUM
american_scientific_journal-2676	482	36	)	)	PUNCT
american_scientific_journal-2676	482	37	volume	volume	NOUN
american_scientific_journal-2676	482	38	28	28	NUM
american_scientific_journal-2676	482	39	,	,	PUNCT
american_scientific_journal-2676	482	40	no	no	DET
american_scientific_journal-2676	482	41	1	1	NUM
american_scientific_journal-2676	482	42	,	,	PUNCT
american_scientific_journal-2676	482	43	pp	pp	ADV
american_scientific_journal-2676	482	44	225	225	NUM
american_scientific_journal-2676	482	45	-	-	SYM
american_scientific_journal-2676	482	46	247	247	NUM
american_scientific_journal-2676	482	47	246	246	NUM
american_scientific_journal-2676	482	48	no	no	NOUN
american_scientific_journal-2676	482	49	.	.	PROPN
american_scientific_journal-2676	483	1	7	7	NUM
american_scientific_journal-2676	483	2	,	,	PUNCT
american_scientific_journal-2676	483	3	pp	pp	ADJ
american_scientific_journal-2676	483	4	.	.	PUNCT
american_scientific_journal-2676	484	1	1−	1−	NUM
american_scientific_journal-2676	484	2	4	4	NUM
american_scientific_journal-2676	484	3	,	,	PUNCT
american_scientific_journal-2676	484	4	2011	2011	NUM
american_scientific_journal-2676	484	5	.	.	PUNCT
american_scientific_journal-2676	485	1	[	[	X
american_scientific_journal-2676	485	2	3	3	X
american_scientific_journal-2676	485	3	]	]	X
american_scientific_journal-2676	485	4	n.	n.	PROPN
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american_scientific_journal-2676	485	6	,	,	PUNCT
american_scientific_journal-2676	485	7	s.	s.	PROPN
american_scientific_journal-2676	485	8	karatas	karatas	PROPN
american_scientific_journal-2676	485	9	and	and	CCONJ
american_scientific_journal-2676	485	10	s.	s.	PROPN
american_scientific_journal-2676	485	11	enginoglu	enginoglu	PROPN
american_scientific_journal-2676	485	12	,	,	PUNCT
american_scientific_journal-2676	485	13	soft	soft	ADJ
american_scientific_journal-2676	485	14	topology	topology	NOUN
american_scientific_journal-2676	485	15	,	,	PUNCT
american_scientific_journal-2676	485	16	comput	comput	NOUN
american_scientific_journal-2676	485	17	.	.	PUNCT
american_scientific_journal-2676	486	1	math	math	NOUN
american_scientific_journal-2676	486	2	.	.	PUNCT
american_scientific_journal-2676	487	1	appl	appl	PROPN
american_scientific_journal-2676	487	2	.	.	PROPN
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american_scientific_journal-2676	488	2	.	.	PROPN
american_scientific_journal-2676	489	1	62	62	NUM
american_scientific_journal-2676	489	2	,	,	PUNCT
american_scientific_journal-2676	489	3	pp	pp	ADV
american_scientific_journal-2676	489	4	.	.	PUNCT
american_scientific_journal-2676	490	1	351−	351−	NUM
american_scientific_journal-2676	490	2	358	358	NUM
american_scientific_journal-2676	490	3	,	,	PUNCT
american_scientific_journal-2676	490	4	2011	2011	NUM
american_scientific_journal-2676	490	5	.	.	PUNCT
american_scientific_journal-2676	491	1	[	[	X
american_scientific_journal-2676	491	2	4	4	X
american_scientific_journal-2676	491	3	]	]	PUNCT
american_scientific_journal-2676	491	4	s.	s.	PROPN
american_scientific_journal-2676	491	5	a.	a.	PROPN
american_scientific_journal-2676	491	6	el	el	PROPN
american_scientific_journal-2676	491	7	-	-	PUNCT
american_scientific_journal-2676	491	8	sheikh	sheikh	PROPN
american_scientific_journal-2676	491	9	and	and	CCONJ
american_scientific_journal-2676	491	10	a.	a.	NOUN
american_scientific_journal-2676	491	11	m.	m.	NOUN
american_scientific_journal-2676	491	12	abd	abd	PROPN
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american_scientific_journal-2676	491	14	-	-	PROPN
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american_scientific_journal-2676	491	16	,	,	PUNCT
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american_scientific_journal-2676	491	18	of	of	ADP
american_scientific_journal-2676	491	19	some	some	DET
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american_scientific_journal-2676	491	24	sets	set	NOUN
american_scientific_journal-2676	491	25	and	and	CCONJ
american_scientific_journal-2676	491	26	soft	soft	ADJ
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american_scientific_journal-2676	491	28	,	,	PUNCT
american_scientific_journal-2676	491	29	international	international	ADJ
american_scientific_journal-2676	491	30	journal	journal	NOUN
american_scientific_journal-2676	491	31	of	of	ADP
american_scientific_journal-2676	491	32	mathematics	mathematics	NOUN
american_scientific_journal-2676	491	33	trends	trend	NOUN
american_scientific_journal-2676	491	34	and	and	CCONJ
american_scientific_journal-2676	491	35	technology	technology	NOUN
american_scientific_journal-2676	491	36	,	,	PUNCT
american_scientific_journal-2676	491	37	vol	vol	NOUN
american_scientific_journal-2676	491	38	.	.	PROPN
american_scientific_journal-2676	491	39	9	9	NUM
american_scientific_journal-2676	491	40	,	,	PUNCT
american_scientific_journal-2676	491	41	no	no	INTJ
american_scientific_journal-2676	491	42	.	.	NOUN
american_scientific_journal-2676	491	43	1	1	NUM
american_scientific_journal-2676	491	44	,	,	PUNCT
american_scientific_journal-2676	491	45	pp	pp	ADJ
american_scientific_journal-2676	491	46	.	.	PUNCT
american_scientific_journal-2676	492	1	37−56	37−56	NUM
american_scientific_journal-2676	492	2	,	,	PUNCT
american_scientific_journal-2676	492	3	2014	2014	NUM
american_scientific_journal-2676	492	4	.	.	PUNCT
american_scientific_journal-2676	493	1	[	[	X
american_scientific_journal-2676	493	2	5	5	X
american_scientific_journal-2676	493	3	]	]	PUNCT
american_scientific_journal-2676	493	4	d.	d.	PROPN
american_scientific_journal-2676	493	5	n.	n.	PROPN
american_scientific_journal-2676	493	6	georgiou	georgiou	PROPN
american_scientific_journal-2676	493	7	a	a	DET
american_scientific_journal-2676	493	8	and	and	CCONJ
american_scientific_journal-2676	493	9	a.	a.	PROPN
american_scientific_journal-2676	493	10	c.	c.	PROPN
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american_scientific_journal-2676	493	12	,	,	PUNCT
american_scientific_journal-2676	493	13	soft	soft	ADJ
american_scientific_journal-2676	493	14	set	set	NOUN
american_scientific_journal-2676	493	15	theory	theory	NOUN
american_scientific_journal-2676	493	16	and	and	CCONJ
american_scientific_journal-2676	493	17	topology	topology	NOUN
american_scientific_journal-2676	493	18	,	,	PUNCT
american_scientific_journal-2676	493	19	appl	appl	PROPN
american_scientific_journal-2676	493	20	.	.	PUNCT
american_scientific_journal-2676	494	1	gen	gen	PROPN
american_scientific_journal-2676	494	2	.	.	PROPN
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american_scientific_journal-2676	494	4	.	.	PUNCT
american_scientific_journal-2676	495	1	,	,	PUNCT
american_scientific_journal-2676	495	2	vol	vol	NOUN
american_scientific_journal-2676	495	3	.	.	PROPN
american_scientific_journal-2676	496	1	15	15	NUM
american_scientific_journal-2676	496	2	,	,	PUNCT
american_scientific_journal-2676	496	3	no	no	INTJ
american_scientific_journal-2676	496	4	.	.	NOUN
american_scientific_journal-2676	496	5	1	1	NUM
american_scientific_journal-2676	496	6	,	,	PUNCT
american_scientific_journal-2676	496	7	pp	pp	ADJ
american_scientific_journal-2676	496	8	.	.	PUNCT
american_scientific_journal-2676	497	1	93−109	93−109	NUM
american_scientific_journal-2676	497	2	,	,	PUNCT
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american_scientific_journal-2676	497	4	.	.	PUNCT
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american_scientific_journal-2676	498	2	6	6	NUM
american_scientific_journal-2676	498	3	]	]	PUNCT
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american_scientific_journal-2676	498	6	,	,	PUNCT
american_scientific_journal-2676	498	7	p.	p.	PROPN
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american_scientific_journal-2676	498	9	and	and	CCONJ
american_scientific_journal-2676	498	10	s.	s.	PROPN
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american_scientific_journal-2676	498	12	,	,	PUNCT
american_scientific_journal-2676	498	13	soft	soft	ADJ
american_scientific_journal-2676	498	14	topology	topology	NOUN
american_scientific_journal-2676	498	15	,	,	PUNCT
american_scientific_journal-2676	498	16	fuzzy	fuzzy	ADJ
american_scientific_journal-2676	498	17	inform	inform	NOUN
american_scientific_journal-2676	498	18	.	.	PUNCT
american_scientific_journal-2676	499	1	eng	eng	PROPN
american_scientific_journal-2676	499	2	.	.	PROPN
american_scientific_journal-2676	499	3	,	,	PUNCT
american_scientific_journal-2676	499	4	vol	vol	NOUN
american_scientific_journal-2676	499	5	.	.	PROPN
american_scientific_journal-2676	499	6	4	4	NUM
american_scientific_journal-2676	499	7	,	,	PUNCT
american_scientific_journal-2676	499	8	no	no	INTJ
american_scientific_journal-2676	499	9	.	.	NOUN
american_scientific_journal-2676	499	10	1	1	NUM
american_scientific_journal-2676	499	11	,	,	PUNCT
american_scientific_journal-2676	499	12	pp.105−	pp.105−	ADV
american_scientific_journal-2676	499	13	115	115	NUM
american_scientific_journal-2676	499	14	,	,	PUNCT
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american_scientific_journal-2676	499	16	.	.	PUNCT
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american_scientific_journal-2676	500	2	7	7	X
american_scientific_journal-2676	500	3	]	]	PUNCT
american_scientific_journal-2676	500	4	s.	s.	PROPN
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american_scientific_journal-2676	500	6	and	and	CCONJ
american_scientific_journal-2676	500	7	b.	b.	PROPN
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american_scientific_journal-2676	500	9	,	,	PUNCT
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american_scientific_journal-2676	500	12	of	of	ADP
american_scientific_journal-2676	500	13	soft	soft	ADJ
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american_scientific_journal-2676	500	16	,	,	PUNCT
american_scientific_journal-2676	500	17	comput	comput	NOUN
american_scientific_journal-2676	500	18	.	.	PUNCT
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american_scientific_journal-2676	500	20	.	.	PUNCT
american_scientific_journal-2676	501	1	appl	appl	PROPN
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american_scientific_journal-2676	501	3	,	,	PUNCT
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american_scientific_journal-2676	501	5	.	.	PROPN
american_scientific_journal-2676	502	1	62	62	NUM
american_scientific_journal-2676	502	2	,	,	PUNCT
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american_scientific_journal-2676	502	4	.	.	PUNCT
american_scientific_journal-2676	503	1	4058−	4058−	NUM
american_scientific_journal-2676	503	2	4067	4067	NUM
american_scientific_journal-2676	503	3	,	,	PUNCT
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american_scientific_journal-2676	503	5	.	.	PUNCT
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american_scientific_journal-2676	504	4	m.	m.	PROPN
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american_scientific_journal-2676	504	7	,	,	PUNCT
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american_scientific_journal-2676	504	23	,	,	PUNCT
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american_scientific_journal-2676	504	25	.	.	PUNCT
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american_scientific_journal-2676	505	2	.	.	PUNCT
american_scientific_journal-2676	506	1	appl	appl	PROPN
american_scientific_journal-2676	506	2	.	.	PROPN
american_scientific_journal-2676	506	3	,	,	PUNCT
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american_scientific_journal-2676	506	5	.	.	PROPN
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american_scientific_journal-2676	506	7	,	,	PUNCT
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american_scientific_journal-2676	506	9	.	.	PUNCT
american_scientific_journal-2676	507	1	2647−	2647−	NUM
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american_scientific_journal-2676	507	3	,	,	PUNCT
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american_scientific_journal-2676	507	5	.	.	PUNCT
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american_scientific_journal-2676	508	6	,	,	PUNCT
american_scientific_journal-2676	508	7	o.	o.	PROPN
american_scientific_journal-2676	508	8	a.	a.	PROPN
american_scientific_journal-2676	508	9	e.	e.	PROPN
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american_scientific_journal-2676	508	11	,	,	PUNCT
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american_scientific_journal-2676	508	13	a.	a.	PROPN
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american_scientific_journal-2676	508	15	-	-	PUNCT
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american_scientific_journal-2676	509	1	,	,	PUNCT
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american_scientific_journal-2676	510	2	,	,	PUNCT
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american_scientific_journal-2676	510	5	2	2	NUM
american_scientific_journal-2676	510	6	,	,	PUNCT
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american_scientific_journal-2676	510	8	.	.	PUNCT
american_scientific_journal-2676	510	9	,	,	PUNCT
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american_scientific_journal-2676	511	2	10	10	NUM
american_scientific_journal-2676	511	3	]	]	X
american_scientific_journal-2676	511	4	a.	a.	NOUN
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american_scientific_journal-2676	511	6	,	,	PUNCT
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american_scientific_journal-2676	511	11	,	,	PUNCT
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american_scientific_journal-2676	511	15	-	-	PUNCT
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american_scientific_journal-2676	511	18	shawqi	shawqi	ADJ
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american_scientific_journal-2676	511	24	(	(	PUNCT
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american_scientific_journal-2676	511	39	.	.	PUNCT
american_scientific_journal-2676	512	1	inform	inform	NOUN
american_scientific_journal-2676	512	2	.	.	PUNCT
american_scientific_journal-2676	512	3	,	,	PUNCT
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american_scientific_journal-2676	513	2	,	,	PUNCT
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american_scientific_journal-2676	513	5	4	4	NUM
american_scientific_journal-2676	513	6	,	,	PUNCT
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american_scientific_journal-2676	513	8	.	.	PUNCT
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american_scientific_journal-2676	514	2	,	,	PUNCT
american_scientific_journal-2676	514	3	2016	2016	NUM
american_scientific_journal-2676	514	4	.	.	PUNCT
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american_scientific_journal-2676	515	2	11	11	NUM
american_scientific_journal-2676	515	3	]	]	PUNCT
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american_scientific_journal-2676	515	6	,	,	PUNCT
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american_scientific_journal-2676	515	8	a.	a.	PROPN
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american_scientific_journal-2676	515	35	.	.	PUNCT
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american_scientific_journal-2676	516	3	,	,	PUNCT
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american_scientific_journal-2676	517	2	,	,	PUNCT
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american_scientific_journal-2676	518	2	,	,	PUNCT
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american_scientific_journal-2676	518	4	.	.	PUNCT
american_scientific_journal-2676	519	1	1	1	NUM
american_scientific_journal-2676	519	2	-	-	SYM
american_scientific_journal-2676	519	3	20	20	NUM
american_scientific_journal-2676	519	4	,	,	PUNCT
american_scientific_journal-2676	519	5	2017	2017	NUM
american_scientific_journal-2676	519	6	.	.	PUNCT
american_scientific_journal-2676	520	1	[	[	X
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american_scientific_journal-2676	520	3	]	]	PUNCT
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american_scientific_journal-2676	520	5	kandil	kandil	PROPN
american_scientific_journal-2676	520	6	,	,	PUNCT
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american_scientific_journal-2676	520	15	-	-	PUNCT
american_scientific_journal-2676	520	16	sheikh	sheikh	PROPN
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american_scientific_journal-2676	520	18	shawqi	shawqi	ADJ
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american_scientific_journal-2676	520	21	,	,	PUNCT
american_scientific_journal-2676	520	22	some	some	DET
american_scientific_journal-2676	520	23	types	type	NOUN
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american_scientific_journal-2676	520	25	pairwise	pairwise	NOUN
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american_scientific_journal-2676	520	30	associated	associated	ADJ
american_scientific_journal-2676	520	31	soft	soft	ADJ
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american_scientific_journal-2676	520	33	,	,	PUNCT
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american_scientific_journal-2676	520	38	fuzzy	fuzzy	ADJ
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american_scientific_journal-2676	520	40	.	.	PUNCT
american_scientific_journal-2676	520	41	,	,	PUNCT
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american_scientific_journal-2676	520	45	,	,	PUNCT
american_scientific_journal-2676	520	46	no	no	INTJ
american_scientific_journal-2676	520	47	.	.	NOUN
american_scientific_journal-2676	520	48	2	2	NUM
american_scientific_journal-2676	520	49	,	,	PUNCT
american_scientific_journal-2676	520	50	pp	pp	ADJ
american_scientific_journal-2676	520	51	.	.	PUNCT
american_scientific_journal-2676	521	1	1007−	1007−	NUM
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american_scientific_journal-2676	521	3	,	,	PUNCT
american_scientific_journal-2676	521	4	2017	2017	NUM
american_scientific_journal-2676	521	5	.	.	PUNCT
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american_scientific_journal-2676	522	2	13	13	NUM
american_scientific_journal-2676	522	3	]	]	PUNCT
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american_scientific_journal-2676	522	6	,	,	PUNCT
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american_scientific_journal-2676	522	8	generalized	generalize	VERB
american_scientific_journal-2676	522	9	closed	closed	ADJ
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american_scientific_journal-2676	522	14	spaces	space	NOUN
american_scientific_journal-2676	522	15	,	,	PUNCT
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american_scientific_journal-2676	522	21	.	.	PUNCT
american_scientific_journal-2676	523	1	inform	inform	NOUN
american_scientific_journal-2676	523	2	.	.	PUNCT
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american_scientific_journal-2676	524	2	,	,	PUNCT
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american_scientific_journal-2676	524	4	.	.	PROPN
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american_scientific_journal-2676	525	2	,	,	PUNCT
american_scientific_journal-2676	525	3	no	no	INTJ
american_scientific_journal-2676	525	4	.	.	NOUN
american_scientific_journal-2676	525	5	1	1	NUM
american_scientific_journal-2676	525	6	,	,	PUNCT
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american_scientific_journal-2676	526	4	.	.	PUNCT
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american_scientific_journal-2676	527	2	14	14	NUM
american_scientific_journal-2676	527	3	]	]	X
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american_scientific_journal-2676	527	10	-	-	PUNCT
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american_scientific_journal-2676	527	13	,	,	PUNCT
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american_scientific_journal-2676	527	15	.	.	PUNCT
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american_scientific_journal-2676	527	17	.	.	PUNCT
american_scientific_journal-2676	528	1	appl	appl	PROPN
american_scientific_journal-2676	528	2	.	.	PROPN
american_scientific_journal-2676	528	3	,	,	PUNCT
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american_scientific_journal-2676	528	5	.	.	PROPN
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american_scientific_journal-2676	529	2	,	,	PUNCT
american_scientific_journal-2676	529	3	pp	pp	ADV
american_scientific_journal-2676	529	4	.	.	PUNCT
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american_scientific_journal-2676	530	2	31	31	NUM
american_scientific_journal-2676	530	3	,	,	PUNCT
american_scientific_journal-2676	530	4	1999	1999	NUM
american_scientific_journal-2676	530	5	.	.	PUNCT
american_scientific_journal-2676	531	1	[	[	X
american_scientific_journal-2676	531	2	15	15	NUM
american_scientific_journal-2676	531	3	]	]	X
american_scientific_journal-2676	531	4	sk	sk	X
american_scientific_journal-2676	531	5	.	.	PROPN
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american_scientific_journal-2676	531	8	s.	s.	PROPN
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american_scientific_journal-2676	531	17	spaces	space	NOUN
american_scientific_journal-2676	531	18	,	,	PUNCT
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american_scientific_journal-2676	531	23	.	.	PUNCT
american_scientific_journal-2676	532	1	inform	inform	NOUN
american_scientific_journal-2676	532	2	.	.	PUNCT
american_scientific_journal-2676	533	1	,	,	PUNCT
american_scientific_journal-2676	533	2	vol	vol	NOUN
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american_scientific_journal-2676	534	2	,	,	PUNCT
american_scientific_journal-2676	534	3	no	no	INTJ
american_scientific_journal-2676	534	4	.	.	NOUN
american_scientific_journal-2676	534	5	1	1	NUM
american_scientific_journal-2676	534	6	,	,	PUNCT
american_scientific_journal-2676	534	7	pp	pp	ADJ
american_scientific_journal-2676	534	8	.	.	PUNCT
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american_scientific_journal-2676	535	2	,	,	PUNCT
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american_scientific_journal-2676	535	4	.	.	PUNCT
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american_scientific_journal-2676	536	7	,	,	PUNCT
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american_scientific_journal-2676	536	9	,	,	PUNCT
american_scientific_journal-2676	536	10	and	and	CCONJ
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american_scientific_journal-2676	536	12	(	(	PUNCT
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american_scientific_journal-2676	536	20	,	,	PUNCT
american_scientific_journal-2676	536	21	no	no	DET
american_scientific_journal-2676	536	22	1	1	NUM
american_scientific_journal-2676	536	23	,	,	PUNCT
american_scientific_journal-2676	536	24	pp	pp	ADV
american_scientific_journal-2676	536	25	225	225	NUM
american_scientific_journal-2676	536	26	-	-	SYM
american_scientific_journal-2676	536	27	247	247	NUM
american_scientific_journal-2676	536	28	247	247	NUM
american_scientific_journal-2676	536	29	[	[	SYM
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american_scientific_journal-2676	536	31	]	]	PUNCT
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american_scientific_journal-2676	536	33	.	.	PROPN
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american_scientific_journal-2676	536	49	,	,	PUNCT
american_scientific_journal-2676	536	50	ann	ann	PROPN
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american_scientific_journal-2676	536	54	.	.	PUNCT
american_scientific_journal-2676	537	1	inform.m	inform.m	PROPN
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american_scientific_journal-2676	537	3	.	.	PROPN
american_scientific_journal-2676	538	1	8	8	NUM
american_scientific_journal-2676	538	2	,	,	PUNCT
american_scientific_journal-2676	538	3	no	no	INTJ
american_scientific_journal-2676	538	4	.	.	NOUN
american_scientific_journal-2676	538	5	4	4	NUM
american_scientific_journal-2676	538	6	,	,	PUNCT
american_scientific_journal-2676	538	7	pp	pp	ADJ
american_scientific_journal-2676	538	8	.	.	PUNCT
american_scientific_journal-2676	539	1	645−	645−	NUM
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american_scientific_journal-2676	539	3	,	,	PUNCT
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american_scientific_journal-2676	539	5	.	.	PUNCT
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american_scientific_journal-2676	540	5	xie	xie	PROPN
american_scientific_journal-2676	540	6	,	,	PUNCT
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american_scientific_journal-2676	540	16	,	,	PUNCT
american_scientific_journal-2676	540	17	ann	ann	PROPN
american_scientific_journal-2676	540	18	.	.	PROPN
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american_scientific_journal-2676	540	20	.	.	PUNCT
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american_scientific_journal-2676	541	2	.	.	PUNCT
american_scientific_journal-2676	542	1	inform	inform	NOUN
american_scientific_journal-2676	542	2	.	.	PUNCT
american_scientific_journal-2676	542	3	,	,	PUNCT
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american_scientific_journal-2676	542	5	.	.	PROPN
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american_scientific_journal-2676	543	2	,	,	PUNCT
american_scientific_journal-2676	543	3	no	no	INTJ
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american_scientific_journal-2676	543	5	2	2	NUM
american_scientific_journal-2676	543	6	,	,	PUNCT
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american_scientific_journal-2676	544	2	,	,	PUNCT
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american_scientific_journal-2676	545	4	e.	e.	PROPN
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american_scientific_journal-2676	545	17	,	,	PUNCT
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american_scientific_journal-2676	545	24	,	,	PUNCT
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american_scientific_journal-2676	545	28	,	,	PUNCT
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american_scientific_journal-2676	545	30	.	.	PUNCT
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american_scientific_journal-2676	546	2	,	,	PUNCT
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american_scientific_journal-2676	547	4	d.	d.	PROPN
american_scientific_journal-2676	547	5	pie	pie	PROPN
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american_scientific_journal-2676	547	7	d.	d.	PROPN
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american_scientific_journal-2676	547	25	,	,	PUNCT
american_scientific_journal-2676	547	26	vol	vol	NOUN
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american_scientific_journal-2676	548	5	.	.	PUNCT
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american_scientific_journal-2676	549	14	,	,	PUNCT
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american_scientific_journal-2676	552	5	.	.	PUNCT
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