id	sid	tid	token	lemma	pos
ejpam-6339	1	1	european	european	PROPN
ejpam-6339	1	2	journal	journal	PROPN
ejpam-6339	1	3	of	of	ADP
ejpam-6339	1	4	pure	pure	ADJ
ejpam-6339	1	5	and	and	CCONJ
ejpam-6339	1	6	applied	applied	ADJ
ejpam-6339	1	7	mathematics	mathematic	NOUN
ejpam-6339	1	8	2025	2025	NUM
ejpam-6339	1	9	,	,	PUNCT
ejpam-6339	1	10	vol	vol	NOUN
ejpam-6339	1	11	.	.	PROPN
ejpam-6339	1	12	18	18	NUM
ejpam-6339	1	13	,	,	PUNCT
ejpam-6339	1	14	issue	issue	NOUN
ejpam-6339	1	15	3	3	NUM
ejpam-6339	1	16	,	,	PUNCT
ejpam-6339	1	17	article	article	NOUN
ejpam-6339	1	18	number	number	NOUN
ejpam-6339	1	19	6339	6339	NUM
ejpam-6339	1	20	issn	issn	PROPN
ejpam-6339	1	21	1307	1307	NUM
ejpam-6339	1	22	-	-	SYM
ejpam-6339	1	23	5543	5543	NUM
ejpam-6339	1	24	–	–	PUNCT
ejpam-6339	1	25	ejpam.com	ejpam.com	X
ejpam-6339	1	26	published	publish	VERB
ejpam-6339	1	27	by	by	ADP
ejpam-6339	1	28	new	new	PROPN
ejpam-6339	1	29	york	york	PROPN
ejpam-6339	1	30	business	business	PROPN
ejpam-6339	1	31	global	global	PROPN
ejpam-6339	1	32	an	an	DET
ejpam-6339	1	33	approach	approach	NOUN
ejpam-6339	1	34	to	to	ADP
ejpam-6339	1	35	closure	closure	NOUN
ejpam-6339	1	36	and	and	CCONJ
ejpam-6339	1	37	kernel	kernel	PROPN
ejpam-6339	1	38	defined	define	VERB
ejpam-6339	1	39	through	through	ADP
ejpam-6339	1	40	n	n	CCONJ
ejpam-6339	1	41	-	-	PUNCT
ejpam-6339	1	42	points	point	NOUN
ejpam-6339	1	43	josé	josé	ADJ
ejpam-6339	1	44	sanabria1,∗	sanabria1,∗	PROPN
ejpam-6339	1	45	,	,	PUNCT
ejpam-6339	1	46	ennis	ennis	PROPN
ejpam-6339	1	47	rosas2	rosas2	PROPN
ejpam-6339	1	48	,	,	PUNCT
ejpam-6339	1	49	carlos	carlos	PROPN
ejpam-6339	1	50	granados3	granados3	PROPN
ejpam-6339	1	51	1	1	NUM
ejpam-6339	1	52	departamento	departamento	NOUN
ejpam-6339	1	53	de	de	PROPN
ejpam-6339	1	54	matemáticas	matemáticas	PROPN
ejpam-6339	1	55	,	,	PUNCT
ejpam-6339	1	56	facultad	facultad	PROPN
ejpam-6339	1	57	de	de	PROPN
ejpam-6339	1	58	educación	educación	PROPN
ejpam-6339	1	59	y	y	PROPN
ejpam-6339	1	60	ciencias	ciencias	PROPN
ejpam-6339	1	61	,	,	PUNCT
ejpam-6339	1	62	universidad	universidad	PROPN
ejpam-6339	1	63	de	de	X
ejpam-6339	1	64	sucre	sucre	PROPN
ejpam-6339	1	65	,	,	PUNCT
ejpam-6339	1	66	sincelejo	sincelejo	ADJ
ejpam-6339	1	67	,	,	PUNCT
ejpam-6339	1	68	colombia	colombia	PROPN
ejpam-6339	1	69	2	2	NUM
ejpam-6339	1	70	departamento	departamento	PROPN
ejpam-6339	1	71	de	de	PROPN
ejpam-6339	1	72	ciencias	ciencias	PROPN
ejpam-6339	1	73	naturales	naturales	PROPN
ejpam-6339	1	74	y	y	PROPN
ejpam-6339	1	75	exactas	exactas	PROPN
ejpam-6339	1	76	,	,	PUNCT
ejpam-6339	1	77	universidad	universidad	PROPN
ejpam-6339	1	78	de	de	PROPN
ejpam-6339	1	79	la	la	PROPN
ejpam-6339	1	80	costa	costa	PROPN
ejpam-6339	1	81	,	,	PUNCT
ejpam-6339	1	82	barranquilla	barranquilla	PROPN
ejpam-6339	1	83	,	,	PUNCT
ejpam-6339	1	84	colombia	colombia	PROPN
ejpam-6339	1	85	3	3	NUM
ejpam-6339	1	86	escuela	escuela	PROPN
ejpam-6339	1	87	de	de	PROPN
ejpam-6339	1	88	ciencias	ciencias	PROPN
ejpam-6339	1	89	de	de	X
ejpam-6339	1	90	la	la	PROPN
ejpam-6339	1	91	educación	educación	PROPN
ejpam-6339	1	92	,	,	PUNCT
ejpam-6339	1	93	universidad	universidad	PROPN
ejpam-6339	1	94	nacional	nacional	PROPN
ejpam-6339	1	95	abierta	abierta	PROPN
ejpam-6339	1	96	y	y	PROPN
ejpam-6339	1	97	a	a	DET
ejpam-6339	1	98	distancia	distancia	PROPN
ejpam-6339	1	99	,	,	PUNCT
ejpam-6339	1	100	barranquilla	barranquilla	PROPN
ejpam-6339	1	101	,	,	PUNCT
ejpam-6339	1	102	colombia	colombia	PROPN
ejpam-6339	1	103	abstract	abstract	NOUN
ejpam-6339	1	104	.	.	PUNCT
ejpam-6339	2	1	in	in	ADP
ejpam-6339	2	2	this	this	DET
ejpam-6339	2	3	paper	paper	NOUN
ejpam-6339	2	4	,	,	PUNCT
ejpam-6339	2	5	we	we	PRON
ejpam-6339	2	6	introduce	introduce	VERB
ejpam-6339	2	7	novel	novel	ADJ
ejpam-6339	2	8	definitions	definition	NOUN
ejpam-6339	2	9	of	of	ADP
ejpam-6339	2	10	closure	closure	NOUN
ejpam-6339	2	11	and	and	CCONJ
ejpam-6339	2	12	kernel	kernel	NOUN
ejpam-6339	2	13	of	of	ADP
ejpam-6339	2	14	a	a	DET
ejpam-6339	2	15	neutrosophic	neutrosophic	ADJ
ejpam-6339	2	16	set	set	NOUN
ejpam-6339	2	17	(	(	PUNCT
ejpam-6339	2	18	abbreviated	abbreviate	VERB
ejpam-6339	2	19	as	as	ADP
ejpam-6339	2	20	n	n	PROPN
ejpam-6339	2	21	-set	-set	NUM
ejpam-6339	2	22	)	)	PUNCT
ejpam-6339	2	23	based	base	VERB
ejpam-6339	2	24	on	on	ADP
ejpam-6339	2	25	the	the	DET
ejpam-6339	2	26	newly	newly	ADV
ejpam-6339	2	27	formulated	formulate	VERB
ejpam-6339	2	28	concept	concept	NOUN
ejpam-6339	2	29	of	of	ADP
ejpam-6339	2	30	a	a	DET
ejpam-6339	2	31	n	n	X
ejpam-6339	2	32	-point	-point	NOUN
ejpam-6339	2	33	.	.	PUNCT
ejpam-6339	3	1	building	build	VERB
ejpam-6339	3	2	upon	upon	SCONJ
ejpam-6339	3	3	these	these	DET
ejpam-6339	3	4	foundational	foundational	ADJ
ejpam-6339	3	5	ideas	idea	NOUN
ejpam-6339	3	6	,	,	PUNCT
ejpam-6339	3	7	we	we	PRON
ejpam-6339	3	8	develop	develop	VERB
ejpam-6339	3	9	and	and	CCONJ
ejpam-6339	3	10	analyze	analyze	VERB
ejpam-6339	3	11	the	the	DET
ejpam-6339	3	12	key	key	ADJ
ejpam-6339	3	13	properties	property	NOUN
ejpam-6339	3	14	of	of	ADP
ejpam-6339	3	15	these	these	DET
ejpam-6339	3	16	new	new	ADJ
ejpam-6339	3	17	notions	notion	NOUN
ejpam-6339	3	18	,	,	PUNCT
ejpam-6339	3	19	which	which	PRON
ejpam-6339	3	20	naturally	naturally	ADV
ejpam-6339	3	21	lead	lead	VERB
ejpam-6339	3	22	to	to	ADP
ejpam-6339	3	23	the	the	DET
ejpam-6339	3	24	construction	construction	NOUN
ejpam-6339	3	25	of	of	ADP
ejpam-6339	3	26	two	two	NUM
ejpam-6339	3	27	previously	previously	ADV
ejpam-6339	3	28	unstudied	unstudied	ADJ
ejpam-6339	3	29	n	n	PRON
ejpam-6339	3	30	-topologies	-topologie	NOUN
ejpam-6339	3	31	.	.	PUNCT
ejpam-6339	4	1	these	these	DET
ejpam-6339	4	2	contributions	contribution	NOUN
ejpam-6339	4	3	offer	offer	VERB
ejpam-6339	4	4	fresh	fresh	ADJ
ejpam-6339	4	5	insights	insight	NOUN
ejpam-6339	4	6	into	into	ADP
ejpam-6339	4	7	the	the	DET
ejpam-6339	4	8	topological	topological	ADJ
ejpam-6339	4	9	behavior	behavior	NOUN
ejpam-6339	4	10	of	of	ADP
ejpam-6339	4	11	neutrosophic	neutrosophic	ADJ
ejpam-6339	4	12	structures	structure	NOUN
ejpam-6339	4	13	.	.	PUNCT
ejpam-6339	5	1	we	we	PRON
ejpam-6339	5	2	believe	believe	VERB
ejpam-6339	5	3	that	that	SCONJ
ejpam-6339	5	4	the	the	DET
ejpam-6339	5	5	proposed	propose	VERB
ejpam-6339	5	6	framework	framework	NOUN
ejpam-6339	5	7	not	not	PART
ejpam-6339	5	8	only	only	ADV
ejpam-6339	5	9	deepens	deepen	VERB
ejpam-6339	5	10	the	the	DET
ejpam-6339	5	11	theoretical	theoretical	ADJ
ejpam-6339	5	12	understanding	understanding	NOUN
ejpam-6339	5	13	of	of	ADP
ejpam-6339	5	14	n	n	DET
ejpam-6339	5	15	-sets	-set	NOUN
ejpam-6339	5	16	but	but	CCONJ
ejpam-6339	5	17	also	also	ADV
ejpam-6339	5	18	opens	open	VERB
ejpam-6339	5	19	new	new	ADJ
ejpam-6339	5	20	avenues	avenue	NOUN
ejpam-6339	5	21	for	for	ADP
ejpam-6339	5	22	their	their	PRON
ejpam-6339	5	23	application	application	NOUN
ejpam-6339	5	24	in	in	ADP
ejpam-6339	5	25	various	various	ADJ
ejpam-6339	5	26	fields	field	NOUN
ejpam-6339	5	27	involving	involve	VERB
ejpam-6339	5	28	uncertainty	uncertainty	NOUN
ejpam-6339	5	29	,	,	PUNCT
ejpam-6339	5	30	imprecision	imprecision	NOUN
ejpam-6339	5	31	,	,	PUNCT
ejpam-6339	5	32	and	and	CCONJ
ejpam-6339	5	33	indeterminacy	indeterminacy	NOUN
ejpam-6339	5	34	.	.	PUNCT
ejpam-6339	6	1	2020	2020	NUM
ejpam-6339	6	2	mathematics	mathematic	NOUN
ejpam-6339	6	3	subject	subject	NOUN
ejpam-6339	6	4	classifications	classification	NOUN
ejpam-6339	6	5	:	:	PUNCT
ejpam-6339	6	6	03e72	03e72	NUM
ejpam-6339	6	7	,	,	PUNCT
ejpam-6339	6	8	54a40	54a40	NUM
ejpam-6339	6	9	.	.	PUNCT
ejpam-6339	7	1	key	key	ADJ
ejpam-6339	7	2	words	word	NOUN
ejpam-6339	7	3	and	and	CCONJ
ejpam-6339	7	4	phrases	phrase	NOUN
ejpam-6339	7	5	:	:	PUNCT
ejpam-6339	7	6	neutrosophic	neutrosophic	ADJ
ejpam-6339	7	7	set	set	NOUN
ejpam-6339	7	8	,	,	PUNCT
ejpam-6339	7	9	neutrosophic	neutrosophic	ADJ
ejpam-6339	7	10	point	point	NOUN
ejpam-6339	7	11	,	,	PUNCT
ejpam-6339	7	12	neutrosophic	neutrosophic	ADJ
ejpam-6339	7	13	topological	topological	ADJ
ejpam-6339	7	14	space	space	NOUN
ejpam-6339	7	15	1	1	NUM
ejpam-6339	7	16	.	.	PUNCT
ejpam-6339	7	17	introduction	introduction	NOUN
ejpam-6339	7	18	neutrosophic	neutrosophic	ADJ
ejpam-6339	7	19	sets	set	NOUN
ejpam-6339	7	20	(	(	PUNCT
ejpam-6339	7	21	briefly	briefly	NOUN
ejpam-6339	7	22	n	n	PRON
ejpam-6339	7	23	-sets	-set	NOUN
ejpam-6339	7	24	)	)	PUNCT
ejpam-6339	7	25	were	be	AUX
ejpam-6339	7	26	introduced	introduce	VERB
ejpam-6339	7	27	by	by	ADP
ejpam-6339	7	28	f.	f.	PROPN
ejpam-6339	7	29	smarandache	smarandache	PROPN
ejpam-6339	7	30	in	in	ADP
ejpam-6339	7	31	2010	2010	NUM
ejpam-6339	8	1	[	[	X
ejpam-6339	8	2	1	1	X
ejpam-6339	8	3	]	]	PUNCT
ejpam-6339	8	4	as	as	ADP
ejpam-6339	8	5	a	a	DET
ejpam-6339	8	6	generalization	generalization	NOUN
ejpam-6339	8	7	of	of	ADP
ejpam-6339	8	8	classical	classical	ADJ
ejpam-6339	8	9	and	and	CCONJ
ejpam-6339	8	10	intuitionistic	intuitionistic	ADJ
ejpam-6339	8	11	fuzzy	fuzzy	ADJ
ejpam-6339	8	12	sets	set	NOUN
ejpam-6339	8	13	.	.	PUNCT
ejpam-6339	9	1	unlike	unlike	ADP
ejpam-6339	9	2	their	their	PRON
ejpam-6339	9	3	predecessors	predecessor	NOUN
ejpam-6339	9	4	,	,	PUNCT
ejpam-6339	9	5	n	n	PRON
ejpam-6339	9	6	sets	set	NOUN
ejpam-6339	9	7	are	be	AUX
ejpam-6339	9	8	characterized	characterize	VERB
ejpam-6339	9	9	by	by	ADP
ejpam-6339	9	10	the	the	DET
ejpam-6339	9	11	presence	presence	NOUN
ejpam-6339	9	12	of	of	ADP
ejpam-6339	9	13	three	three	NUM
ejpam-6339	9	14	independent	independent	ADJ
ejpam-6339	9	15	membership	membership	NOUN
ejpam-6339	9	16	functions	function	NOUN
ejpam-6339	9	17	:	:	PUNCT
ejpam-6339	9	18	truth	truth	NOUN
ejpam-6339	9	19	(	(	PUNCT
ejpam-6339	9	20	t	t	NOUN
ejpam-6339	9	21	)	)	PUNCT
ejpam-6339	9	22	,	,	PUNCT
ejpam-6339	9	23	indeterminacy	indeterminacy	NOUN
ejpam-6339	9	24	(	(	PUNCT
ejpam-6339	9	25	i	i	NOUN
ejpam-6339	9	26	)	)	PUNCT
ejpam-6339	9	27	,	,	PUNCT
ejpam-6339	9	28	and	and	CCONJ
ejpam-6339	9	29	falsity	falsity	NOUN
ejpam-6339	9	30	(	(	PUNCT
ejpam-6339	9	31	f	f	PROPN
ejpam-6339	9	32	)	)	PUNCT
ejpam-6339	9	33	,	,	PUNCT
ejpam-6339	9	34	each	each	PRON
ejpam-6339	9	35	of	of	ADP
ejpam-6339	9	36	which	which	PRON
ejpam-6339	9	37	varies	vary	VERB
ejpam-6339	9	38	independently	independently	ADV
ejpam-6339	9	39	within	within	ADP
ejpam-6339	9	40	the	the	DET
ejpam-6339	9	41	unit	unit	NOUN
ejpam-6339	9	42	interval	interval	NOUN
ejpam-6339	9	43	[	[	X
ejpam-6339	9	44	0	0	NUM
ejpam-6339	9	45	,	,	PUNCT
ejpam-6339	9	46	1	1	NUM
ejpam-6339	9	47	]	]	PUNCT
ejpam-6339	9	48	.	.	PUNCT
ejpam-6339	10	1	this	this	PRON
ejpam-6339	10	2	allows	allow	VERB
ejpam-6339	10	3	n	n	PRON
ejpam-6339	10	4	-sets	-set	NOUN
ejpam-6339	10	5	to	to	PART
ejpam-6339	10	6	effectively	effectively	ADV
ejpam-6339	10	7	model	model	VERB
ejpam-6339	10	8	uncertainty	uncertainty	NOUN
ejpam-6339	10	9	,	,	PUNCT
ejpam-6339	10	10	inconsistency	inconsistency	NOUN
ejpam-6339	10	11	,	,	PUNCT
ejpam-6339	10	12	and	and	CCONJ
ejpam-6339	10	13	incompleteness	incompleteness	NOUN
ejpam-6339	10	14	in	in	ADP
ejpam-6339	10	15	a	a	DET
ejpam-6339	10	16	way	way	NOUN
ejpam-6339	10	17	that	that	SCONJ
ejpam-6339	10	18	classical	classical	ADJ
ejpam-6339	10	19	and	and	CCONJ
ejpam-6339	10	20	intuitionistic	intuitionistic	ADJ
ejpam-6339	10	21	frameworks	framework	NOUN
ejpam-6339	10	22	can	can	AUX
ejpam-6339	10	23	not	not	PART
ejpam-6339	10	24	,	,	PUNCT
ejpam-6339	10	25	making	make	VERB
ejpam-6339	10	26	them	they	PRON
ejpam-6339	10	27	particularly	particularly	ADV
ejpam-6339	10	28	suitable	suitable	ADJ
ejpam-6339	10	29	for	for	ADP
ejpam-6339	10	30	complex	complex	ADJ
ejpam-6339	10	31	real	real	ADJ
ejpam-6339	10	32	-	-	PUNCT
ejpam-6339	10	33	world	world	NOUN
ejpam-6339	10	34	applications	application	NOUN
ejpam-6339	10	35	in	in	ADP
ejpam-6339	10	36	decision	decision	NOUN
ejpam-6339	10	37	-	-	PUNCT
ejpam-6339	10	38	making	making	NOUN
ejpam-6339	10	39	,	,	PUNCT
ejpam-6339	10	40	artificial	artificial	ADJ
ejpam-6339	10	41	intelligence	intelligence	NOUN
ejpam-6339	10	42	,	,	PUNCT
ejpam-6339	10	43	and	and	CCONJ
ejpam-6339	10	44	information	information	NOUN
ejpam-6339	10	45	systems	system	NOUN
ejpam-6339	10	46	.	.	PUNCT
ejpam-6339	11	1	today	today	NOUN
ejpam-6339	11	2	,	,	PUNCT
ejpam-6339	11	3	researchers	researcher	NOUN
ejpam-6339	11	4	have	have	AUX
ejpam-6339	11	5	contributed	contribute	VERB
ejpam-6339	11	6	significantly	significantly	ADV
ejpam-6339	11	7	to	to	ADP
ejpam-6339	11	8	neutrosophic	neutrosophic	ADJ
ejpam-6339	11	9	theory	theory	NOUN
ejpam-6339	11	10	,	,	PUNCT
ejpam-6339	11	11	driving	drive	VERB
ejpam-6339	11	12	the	the	DET
ejpam-6339	11	13	development	development	NOUN
ejpam-6339	11	14	of	of	ADP
ejpam-6339	11	15	new	new	ADJ
ejpam-6339	11	16	concepts	concept	NOUN
ejpam-6339	11	17	such	such	ADJ
ejpam-6339	11	18	as	as	ADP
ejpam-6339	11	19	neutrosophic	neutrosophic	ADJ
ejpam-6339	11	20	∗corresponding	∗corresponding	NOUN
ejpam-6339	11	21	author	author	NOUN
ejpam-6339	11	22	.	.	PUNCT
ejpam-6339	12	1	doi	doi	NOUN
ejpam-6339	12	2	:	:	PUNCT
ejpam-6339	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6339	https://doi.org/10.29020/nybg.ejpam.v18i3.6339	ADJ
ejpam-6339	12	4	email	email	NOUN
ejpam-6339	12	5	addresses	address	NOUN
ejpam-6339	12	6	:	:	PUNCT
ejpam-6339	12	7	jesanabri@gmail.com	jesanabri@gmail.com	PROPN
ejpam-6339	12	8	(	(	PUNCT
ejpam-6339	12	9	j.	j.	PROPN
ejpam-6339	12	10	sanabria	sanabria	PROPN
ejpam-6339	12	11	)	)	PUNCT
ejpam-6339	12	12	,	,	PUNCT
ejpam-6339	12	13	ennisrafael@gmail.com	ennisrafael@gmail.com	X
ejpam-6339	12	14	(	(	PUNCT
ejpam-6339	12	15	e.	e.	PROPN
ejpam-6339	12	16	rosas	rosas	PROPN
ejpam-6339	12	17	)	)	PUNCT
ejpam-6339	12	18	,	,	PUNCT
ejpam-6339	12	19	carlosgranadosortiz@outlook.es	carlosgranadosortiz@outlook.es	PROPN
ejpam-6339	12	20	(	(	PUNCT
ejpam-6339	12	21	c.	c.	PROPN
ejpam-6339	12	22	granados	granados	PROPN
ejpam-6339	12	23	)	)	PUNCT
ejpam-6339	12	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6339	13	1	1	1	NUM
ejpam-6339	13	2	copyright	copyright	NOUN
ejpam-6339	13	3	:	:	PUNCT
ejpam-6339	13	4	©	©	PROPN
ejpam-6339	13	5	2025	2025	NUM
ejpam-6339	13	6	the	the	DET
ejpam-6339	13	7	author(s	author(s	NOUN
ejpam-6339	13	8	)	)	PUNCT
ejpam-6339	13	9	.	.	PUNCT
ejpam-6339	14	1	(	(	PUNCT
ejpam-6339	14	2	cc	cc	NOUN
ejpam-6339	14	3	by	by	ADP
ejpam-6339	14	4	-	-	PUNCT
ejpam-6339	14	5	nc	nc	PROPN
ejpam-6339	14	6	4.0	4.0	NUM
ejpam-6339	14	7	)	)	PUNCT
ejpam-6339	14	8	j.	j.	PROPN
ejpam-6339	14	9	sanabria	sanabria	PROPN
ejpam-6339	14	10	,	,	PUNCT
ejpam-6339	14	11	e.	e.	PROPN
ejpam-6339	14	12	rosas	rosas	PROPN
ejpam-6339	14	13	,	,	PUNCT
ejpam-6339	14	14	c.	c.	PROPN
ejpam-6339	14	15	granados	granados	PROPN
ejpam-6339	14	16	/	/	PUNCT
ejpam-6339	14	17	eur	eur	PROPN
ejpam-6339	14	18	.	.	PUNCT
ejpam-6339	15	1	j.	j.	PROPN
ejpam-6339	15	2	pure	pure	PROPN
ejpam-6339	15	3	appl	appl	PROPN
ejpam-6339	15	4	.	.	PROPN
ejpam-6339	15	5	math	math	PROPN
ejpam-6339	15	6	,	,	PUNCT
ejpam-6339	15	7	18	18	NUM
ejpam-6339	15	8	(	(	PUNCT
ejpam-6339	15	9	3	3	NUM
ejpam-6339	15	10	)	)	PUNCT
ejpam-6339	15	11	(	(	PUNCT
ejpam-6339	15	12	2025	2025	NUM
ejpam-6339	15	13	)	)	PUNCT
ejpam-6339	15	14	,	,	PUNCT
ejpam-6339	15	15	6339	6339	NUM
ejpam-6339	15	16	2	2	NUM
ejpam-6339	15	17	of	of	ADP
ejpam-6339	15	18	15	15	NUM
ejpam-6339	15	19	convex	convex	NOUN
ejpam-6339	15	20	structures	structure	NOUN
ejpam-6339	15	21	[	[	X
ejpam-6339	15	22	2	2	NUM
ejpam-6339	15	23	]	]	PUNCT
ejpam-6339	15	24	and	and	CCONJ
ejpam-6339	15	25	pythagorean	pythagorean	PROPN
ejpam-6339	15	26	neutrosophic	neutrosophic	ADJ
ejpam-6339	15	27	closure	closure	NOUN
ejpam-6339	16	1	[	[	X
ejpam-6339	16	2	3	3	NUM
ejpam-6339	16	3	]	]	PUNCT
ejpam-6339	16	4	,	,	PUNCT
ejpam-6339	16	5	among	among	ADP
ejpam-6339	16	6	others	other	NOUN
ejpam-6339	16	7	.	.	PUNCT
ejpam-6339	17	1	for	for	ADP
ejpam-6339	17	2	the	the	DET
ejpam-6339	17	3	above	above	ADJ
ejpam-6339	17	4	,	,	PUNCT
ejpam-6339	17	5	neutrosophic	neutrosophic	ADJ
ejpam-6339	17	6	set	set	NOUN
ejpam-6339	17	7	theory	theory	NOUN
ejpam-6339	17	8	represents	represent	VERB
ejpam-6339	17	9	a	a	DET
ejpam-6339	17	10	field	field	NOUN
ejpam-6339	17	11	of	of	ADP
ejpam-6339	17	12	research	research	NOUN
ejpam-6339	17	13	in	in	ADP
ejpam-6339	17	14	constant	constant	ADJ
ejpam-6339	17	15	and	and	CCONJ
ejpam-6339	17	16	rapid	rapid	ADJ
ejpam-6339	17	17	growth	growth	NOUN
ejpam-6339	17	18	.	.	PUNCT
ejpam-6339	18	1	following	follow	VERB
ejpam-6339	18	2	the	the	DET
ejpam-6339	18	3	introduction	introduction	NOUN
ejpam-6339	18	4	of	of	ADP
ejpam-6339	18	5	n	n	DET
ejpam-6339	18	6	-sets	-set	NOUN
ejpam-6339	18	7	,	,	PUNCT
ejpam-6339	18	8	researchers	researcher	NOUN
ejpam-6339	18	9	began	begin	VERB
ejpam-6339	18	10	exploring	explore	VERB
ejpam-6339	18	11	their	their	PRON
ejpam-6339	18	12	topological	topological	ADJ
ejpam-6339	18	13	aspects	aspect	NOUN
ejpam-6339	18	14	.	.	PUNCT
ejpam-6339	19	1	in	in	ADP
ejpam-6339	19	2	particular	particular	ADJ
ejpam-6339	19	3	,	,	PUNCT
ejpam-6339	19	4	salama	salama	NOUN
ejpam-6339	19	5	and	and	CCONJ
ejpam-6339	19	6	alblowi	alblowi	NOUN
ejpam-6339	19	7	[	[	X
ejpam-6339	19	8	4	4	X
ejpam-6339	19	9	]	]	PUNCT
ejpam-6339	19	10	introduced	introduce	VERB
ejpam-6339	19	11	the	the	DET
ejpam-6339	19	12	concept	concept	NOUN
ejpam-6339	19	13	of	of	ADP
ejpam-6339	19	14	n	n	PRON
ejpam-6339	19	15	-topological	-topological	ADJ
ejpam-6339	19	16	spaces	space	NOUN
ejpam-6339	19	17	,	,	PUNCT
ejpam-6339	19	18	laying	lay	VERB
ejpam-6339	19	19	the	the	DET
ejpam-6339	19	20	groundwork	groundwork	NOUN
ejpam-6339	19	21	for	for	ADP
ejpam-6339	19	22	a	a	DET
ejpam-6339	19	23	new	new	ADJ
ejpam-6339	19	24	branch	branch	NOUN
ejpam-6339	19	25	of	of	ADP
ejpam-6339	19	26	neutrosophic	neutrosophic	ADJ
ejpam-6339	19	27	topology	topology	NOUN
ejpam-6339	19	28	.	.	PUNCT
ejpam-6339	20	1	this	this	DET
ejpam-6339	20	2	development	development	NOUN
ejpam-6339	20	3	has	have	AUX
ejpam-6339	20	4	stimulated	stimulate	VERB
ejpam-6339	20	5	a	a	DET
ejpam-6339	20	6	growing	grow	VERB
ejpam-6339	20	7	body	body	NOUN
ejpam-6339	20	8	of	of	ADP
ejpam-6339	20	9	research	research	NOUN
ejpam-6339	20	10	aiming	aim	VERB
ejpam-6339	20	11	to	to	PART
ejpam-6339	20	12	extend	extend	VERB
ejpam-6339	20	13	classical	classical	ADJ
ejpam-6339	20	14	topological	topological	ADJ
ejpam-6339	20	15	concepts	concept	NOUN
ejpam-6339	20	16	such	such	ADJ
ejpam-6339	20	17	as	as	ADP
ejpam-6339	20	18	open	open	ADJ
ejpam-6339	20	19	and	and	CCONJ
ejpam-6339	20	20	closed	closed	ADJ
ejpam-6339	20	21	sets	set	NOUN
ejpam-6339	20	22	,	,	PUNCT
ejpam-6339	20	23	continuity	continuity	NOUN
ejpam-6339	20	24	,	,	PUNCT
ejpam-6339	20	25	and	and	CCONJ
ejpam-6339	20	26	convergence	convergence	NOUN
ejpam-6339	20	27	into	into	ADP
ejpam-6339	20	28	the	the	DET
ejpam-6339	20	29	neutrosophic	neutrosophic	ADJ
ejpam-6339	20	30	setting	setting	NOUN
ejpam-6339	20	31	.	.	PUNCT
ejpam-6339	21	1	subsequent	subsequent	ADJ
ejpam-6339	21	2	contributions	contribution	NOUN
ejpam-6339	21	3	by	by	ADP
ejpam-6339	21	4	ray	ray	NOUN
ejpam-6339	22	1	[	[	X
ejpam-6339	22	2	5	5	NUM
ejpam-6339	22	3	]	]	PUNCT
ejpam-6339	22	4	,	,	PUNCT
ejpam-6339	22	5	subasree	subasree	NOUN
ejpam-6339	22	6	and	and	CCONJ
ejpam-6339	22	7	basari	basari	ADJ
ejpam-6339	23	1	[	[	X
ejpam-6339	23	2	6	6	NUM
ejpam-6339	23	3	,	,	PUNCT
ejpam-6339	23	4	7	7	NUM
ejpam-6339	23	5	]	]	PUNCT
ejpam-6339	23	6	,	,	PUNCT
ejpam-6339	23	7	among	among	ADP
ejpam-6339	23	8	others	other	NOUN
ejpam-6339	23	9	,	,	PUNCT
ejpam-6339	23	10	have	have	AUX
ejpam-6339	23	11	enriched	enrich	VERB
ejpam-6339	23	12	this	this	DET
ejpam-6339	23	13	field	field	NOUN
ejpam-6339	23	14	by	by	ADP
ejpam-6339	23	15	proposing	propose	VERB
ejpam-6339	23	16	new	new	ADJ
ejpam-6339	23	17	forms	form	NOUN
ejpam-6339	23	18	of	of	ADP
ejpam-6339	23	19	neutrosophic	neutrosophic	ADJ
ejpam-6339	23	20	continuity	continuity	NOUN
ejpam-6339	23	21	,	,	PUNCT
ejpam-6339	23	22	compactness	compactness	NOUN
ejpam-6339	23	23	,	,	PUNCT
ejpam-6339	23	24	separation	separation	NOUN
ejpam-6339	23	25	axioms	axiom	NOUN
ejpam-6339	23	26	,	,	PUNCT
ejpam-6339	23	27	and	and	CCONJ
ejpam-6339	23	28	bases	basis	NOUN
ejpam-6339	23	29	for	for	ADP
ejpam-6339	23	30	neutrosophic	neutrosophic	ADJ
ejpam-6339	23	31	topologies	topology	NOUN
ejpam-6339	23	32	(	(	PUNCT
ejpam-6339	23	33	briefly	briefly	NOUN
ejpam-6339	23	34	n	n	PRON
ejpam-6339	23	35	-topologies	-topologie	NOUN
ejpam-6339	23	36	)	)	PUNCT
ejpam-6339	23	37	.	.	PUNCT
ejpam-6339	24	1	recently	recently	ADV
ejpam-6339	24	2	,	,	PUNCT
ejpam-6339	24	3	in	in	ADP
ejpam-6339	24	4	2024	2024	NUM
ejpam-6339	24	5	,	,	PUNCT
ejpam-6339	24	6	açikgöz	açikgöz	PROPN
ejpam-6339	24	7	and	and	CCONJ
ejpam-6339	24	8	esenbel	esenbel	VERB
ejpam-6339	24	9	[	[	X
ejpam-6339	24	10	8	8	NUM
ejpam-6339	24	11	]	]	PUNCT
ejpam-6339	24	12	introduced	introduce	VERB
ejpam-6339	24	13	the	the	DET
ejpam-6339	24	14	concept	concept	NOUN
ejpam-6339	24	15	of	of	ADP
ejpam-6339	24	16	neutrosophic	neutrosophic	ADJ
ejpam-6339	24	17	preclosure	preclosure	ADJ
ejpam-6339	24	18	and	and	CCONJ
ejpam-6339	24	19	neutrosophic	neutrosophic	ADJ
ejpam-6339	24	20	strong	strong	ADJ
ejpam-6339	24	21	semiclosure	semiclosure	NOUN
ejpam-6339	24	22	to	to	PART
ejpam-6339	24	23	study	study	VERB
ejpam-6339	24	24	new	new	ADJ
ejpam-6339	24	25	classes	class	NOUN
ejpam-6339	24	26	of	of	ADP
ejpam-6339	24	27	open	open	ADJ
ejpam-6339	24	28	sets	set	NOUN
ejpam-6339	24	29	and	and	CCONJ
ejpam-6339	24	30	explore	explore	VERB
ejpam-6339	24	31	the	the	DET
ejpam-6339	24	32	properties	property	NOUN
ejpam-6339	24	33	of	of	ADP
ejpam-6339	24	34	modifications	modification	NOUN
ejpam-6339	24	35	of	of	ADP
ejpam-6339	24	36	key	key	ADJ
ejpam-6339	24	37	topological	topological	ADJ
ejpam-6339	24	38	notions	notion	NOUN
ejpam-6339	24	39	such	such	ADJ
ejpam-6339	24	40	as	as	ADP
ejpam-6339	24	41	connectivity	connectivity	NOUN
ejpam-6339	24	42	and	and	CCONJ
ejpam-6339	24	43	continuity	continuity	NOUN
ejpam-6339	24	44	in	in	ADP
ejpam-6339	24	45	neutrosophic	neutrosophic	ADJ
ejpam-6339	24	46	topological	topological	ADJ
ejpam-6339	24	47	spaces	space	NOUN
ejpam-6339	24	48	(	(	PUNCT
ejpam-6339	24	49	briefly	briefly	NOUN
ejpam-6339	24	50	n	n	CCONJ
ejpam-6339	24	51	-topological	-topological	ADJ
ejpam-6339	24	52	spaces	space	NOUN
ejpam-6339	24	53	)	)	PUNCT
ejpam-6339	24	54	.	.	PUNCT
ejpam-6339	25	1	in	in	ADP
ejpam-6339	25	2	this	this	DET
ejpam-6339	25	3	year	year	NOUN
ejpam-6339	25	4	,	,	PUNCT
ejpam-6339	25	5	tyagi	tyagi	PROPN
ejpam-6339	25	6	and	and	CCONJ
ejpam-6339	25	7	kumar	kumar	PROPN
ejpam-6339	25	8	gupta	gupta	PROPN
ejpam-6339	26	1	[	[	X
ejpam-6339	26	2	9	9	NUM
ejpam-6339	26	3	]	]	PUNCT
ejpam-6339	26	4	studied	study	VERB
ejpam-6339	26	5	the	the	DET
ejpam-6339	26	6	neutrosophic	neutrosophic	ADJ
ejpam-6339	26	7	λ	λ	PROPN
ejpam-6339	26	8	-	-	ADJ
ejpam-6339	26	9	closed	closed	ADJ
ejpam-6339	26	10	sets	set	NOUN
ejpam-6339	26	11	,	,	PUNCT
ejpam-6339	26	12	generalizing	generalize	VERB
ejpam-6339	26	13	closed	closed	ADJ
ejpam-6339	26	14	and	and	CCONJ
ejpam-6339	26	15	pre	pre	ADJ
ejpam-6339	26	16	-	-	ADJ
ejpam-6339	26	17	closed	closed	ADJ
ejpam-6339	26	18	neutrosophic	neutrosophic	ADJ
ejpam-6339	26	19	sets	set	NOUN
ejpam-6339	26	20	within	within	ADP
ejpam-6339	26	21	n	n	CCONJ
ejpam-6339	26	22	-topological	-topological	ADJ
ejpam-6339	26	23	spaces	space	NOUN
ejpam-6339	26	24	,	,	PUNCT
ejpam-6339	26	25	along	along	ADP
ejpam-6339	26	26	with	with	ADP
ejpam-6339	26	27	relevant	relevant	ADJ
ejpam-6339	26	28	concepts	concept	NOUN
ejpam-6339	26	29	and	and	CCONJ
ejpam-6339	26	30	its	its	PRON
ejpam-6339	26	31	properties	property	NOUN
ejpam-6339	26	32	.	.	PUNCT
ejpam-6339	27	1	despite	despite	SCONJ
ejpam-6339	27	2	this	this	DET
ejpam-6339	27	3	progress	progress	NOUN
ejpam-6339	27	4	,	,	PUNCT
ejpam-6339	27	5	certain	certain	ADJ
ejpam-6339	27	6	fundamental	fundamental	ADJ
ejpam-6339	27	7	constructs	construct	NOUN
ejpam-6339	27	8	in	in	ADP
ejpam-6339	27	9	topology	topology	NOUN
ejpam-6339	27	10	,	,	PUNCT
ejpam-6339	27	11	such	such	ADJ
ejpam-6339	27	12	as	as	ADP
ejpam-6339	27	13	the	the	DET
ejpam-6339	27	14	closure	closure	NOUN
ejpam-6339	27	15	and	and	CCONJ
ejpam-6339	27	16	kernel	kernel	PROPN
ejpam-6339	27	17	operators	operator	NOUN
ejpam-6339	27	18	,	,	PUNCT
ejpam-6339	27	19	have	have	AUX
ejpam-6339	27	20	not	not	PART
ejpam-6339	27	21	been	be	AUX
ejpam-6339	27	22	thoroughly	thoroughly	ADV
ejpam-6339	27	23	studied	study	VERB
ejpam-6339	27	24	in	in	ADP
ejpam-6339	27	25	the	the	DET
ejpam-6339	27	26	context	context	NOUN
ejpam-6339	27	27	of	of	ADP
ejpam-6339	27	28	n	n	PRON
ejpam-6339	27	29	-topological	-topological	ADJ
ejpam-6339	27	30	spaces	space	NOUN
ejpam-6339	27	31	.	.	PUNCT
ejpam-6339	28	1	closure	closure	NOUN
ejpam-6339	28	2	and	and	CCONJ
ejpam-6339	28	3	kernel	kernel	PROPN
ejpam-6339	28	4	play	play	VERB
ejpam-6339	28	5	pivotal	pivotal	ADJ
ejpam-6339	28	6	roles	role	NOUN
ejpam-6339	28	7	in	in	ADP
ejpam-6339	28	8	classical	classical	ADJ
ejpam-6339	28	9	and	and	CCONJ
ejpam-6339	28	10	fuzzy	fuzzy	ADJ
ejpam-6339	28	11	topology	topology	NOUN
ejpam-6339	28	12	by	by	ADP
ejpam-6339	28	13	characterizing	characterize	VERB
ejpam-6339	28	14	the	the	DET
ejpam-6339	28	15	boundaries	boundary	NOUN
ejpam-6339	28	16	and	and	CCONJ
ejpam-6339	28	17	interior	interior	ADJ
ejpam-6339	28	18	structures	structure	NOUN
ejpam-6339	28	19	of	of	ADP
ejpam-6339	28	20	sets	set	NOUN
ejpam-6339	28	21	,	,	PUNCT
ejpam-6339	28	22	as	as	ADV
ejpam-6339	28	23	well	well	ADV
ejpam-6339	28	24	as	as	ADP
ejpam-6339	28	25	influencing	influence	VERB
ejpam-6339	28	26	the	the	DET
ejpam-6339	28	27	properties	property	NOUN
ejpam-6339	28	28	of	of	ADP
ejpam-6339	28	29	continuity	continuity	NOUN
ejpam-6339	28	30	,	,	PUNCT
ejpam-6339	28	31	connectedness	connectedness	NOUN
ejpam-6339	28	32	,	,	PUNCT
ejpam-6339	28	33	and	and	CCONJ
ejpam-6339	28	34	compactness	compactness	NOUN
ejpam-6339	28	35	.	.	PUNCT
ejpam-6339	29	1	their	their	PRON
ejpam-6339	29	2	proper	proper	ADJ
ejpam-6339	29	3	generalization	generalization	NOUN
ejpam-6339	29	4	to	to	ADP
ejpam-6339	29	5	n	n	PRON
ejpam-6339	29	6	-sets	-set	NOUN
ejpam-6339	29	7	is	be	AUX
ejpam-6339	29	8	therefore	therefore	ADV
ejpam-6339	29	9	essential	essential	ADJ
ejpam-6339	29	10	for	for	ADP
ejpam-6339	29	11	a	a	DET
ejpam-6339	29	12	deeper	deep	ADJ
ejpam-6339	29	13	understanding	understanding	NOUN
ejpam-6339	29	14	of	of	ADP
ejpam-6339	29	15	neutrosophic	neutrosophic	ADJ
ejpam-6339	29	16	topological	topological	ADJ
ejpam-6339	29	17	behavior	behavior	NOUN
ejpam-6339	29	18	.	.	PUNCT
ejpam-6339	30	1	in	in	ADP
ejpam-6339	30	2	this	this	DET
ejpam-6339	30	3	paper	paper	NOUN
ejpam-6339	30	4	,	,	PUNCT
ejpam-6339	30	5	we	we	PRON
ejpam-6339	30	6	introduce	introduce	VERB
ejpam-6339	30	7	novel	novel	ADJ
ejpam-6339	30	8	definitions	definition	NOUN
ejpam-6339	30	9	of	of	ADP
ejpam-6339	30	10	closure	closure	NOUN
ejpam-6339	30	11	and	and	CCONJ
ejpam-6339	30	12	kernel	kernel	NOUN
ejpam-6339	30	13	for	for	ADP
ejpam-6339	30	14	n	n	PRON
ejpam-6339	30	15	-sets	-set	NOUN
ejpam-6339	30	16	,	,	PUNCT
ejpam-6339	30	17	employing	employ	VERB
ejpam-6339	30	18	the	the	DET
ejpam-6339	30	19	concept	concept	NOUN
ejpam-6339	30	20	of	of	ADP
ejpam-6339	30	21	a	a	DET
ejpam-6339	30	22	n	n	ADV
ejpam-6339	30	23	-point	-point	NOUN
ejpam-6339	30	24	as	as	ADP
ejpam-6339	30	25	the	the	DET
ejpam-6339	30	26	central	central	ADJ
ejpam-6339	30	27	building	building	NOUN
ejpam-6339	30	28	block	block	NOUN
ejpam-6339	30	29	.	.	PUNCT
ejpam-6339	31	1	we	we	PRON
ejpam-6339	31	2	then	then	ADV
ejpam-6339	31	3	systematically	systematically	ADV
ejpam-6339	31	4	explore	explore	VERB
ejpam-6339	31	5	the	the	DET
ejpam-6339	31	6	fundamental	fundamental	ADJ
ejpam-6339	31	7	properties	property	NOUN
ejpam-6339	31	8	of	of	ADP
ejpam-6339	31	9	these	these	DET
ejpam-6339	31	10	new	new	ADJ
ejpam-6339	31	11	notions	notion	NOUN
ejpam-6339	31	12	and	and	CCONJ
ejpam-6339	31	13	demonstrate	demonstrate	VERB
ejpam-6339	31	14	how	how	SCONJ
ejpam-6339	31	15	they	they	PRON
ejpam-6339	31	16	lead	lead	VERB
ejpam-6339	31	17	to	to	ADP
ejpam-6339	31	18	the	the	DET
ejpam-6339	31	19	construction	construction	NOUN
ejpam-6339	31	20	of	of	ADP
ejpam-6339	31	21	two	two	NUM
ejpam-6339	31	22	previously	previously	ADV
ejpam-6339	31	23	unexamined	unexamined	ADJ
ejpam-6339	31	24	n	n	PRON
ejpam-6339	31	25	-topologies	-topologie	NOUN
ejpam-6339	31	26	.	.	PUNCT
ejpam-6339	32	1	in	in	ADP
ejpam-6339	32	2	comparison	comparison	NOUN
ejpam-6339	32	3	with	with	ADP
ejpam-6339	32	4	most	most	ADJ
ejpam-6339	32	5	of	of	ADP
ejpam-6339	32	6	the	the	DET
ejpam-6339	32	7	studies	study	NOUN
ejpam-6339	32	8	carried	carry	VERB
ejpam-6339	32	9	out	out	ADP
ejpam-6339	32	10	in	in	ADP
ejpam-6339	32	11	n	n	PRON
ejpam-6339	32	12	-topological	-topological	ADJ
ejpam-6339	32	13	spaces	space	NOUN
ejpam-6339	32	14	,	,	PUNCT
ejpam-6339	32	15	where	where	SCONJ
ejpam-6339	32	16	variations	variation	NOUN
ejpam-6339	32	17	of	of	ADP
ejpam-6339	32	18	the	the	DET
ejpam-6339	32	19	closure	closure	NOUN
ejpam-6339	32	20	and	and	CCONJ
ejpam-6339	32	21	kernel	kernel	PROPN
ejpam-6339	32	22	operators	operator	NOUN
ejpam-6339	32	23	have	have	AUX
ejpam-6339	32	24	been	be	AUX
ejpam-6339	32	25	defined	define	VERB
ejpam-6339	32	26	by	by	ADP
ejpam-6339	32	27	means	mean	NOUN
ejpam-6339	32	28	of	of	ADP
ejpam-6339	32	29	global	global	ADJ
ejpam-6339	32	30	tools	tool	NOUN
ejpam-6339	32	31	,	,	PUNCT
ejpam-6339	32	32	our	our	PRON
ejpam-6339	32	33	study	study	NOUN
ejpam-6339	32	34	incorporates	incorporate	VERB
ejpam-6339	32	35	the	the	DET
ejpam-6339	32	36	novelty	novelty	NOUN
ejpam-6339	32	37	of	of	ADP
ejpam-6339	32	38	defining	define	VERB
ejpam-6339	32	39	these	these	DET
ejpam-6339	32	40	operators	operator	NOUN
ejpam-6339	32	41	by	by	ADP
ejpam-6339	32	42	means	mean	NOUN
ejpam-6339	32	43	of	of	ADP
ejpam-6339	32	44	a	a	DET
ejpam-6339	32	45	local	local	ADJ
ejpam-6339	32	46	tool	tool	NOUN
ejpam-6339	32	47	such	such	ADJ
ejpam-6339	32	48	as	as	ADP
ejpam-6339	32	49	the	the	DET
ejpam-6339	32	50	notion	notion	NOUN
ejpam-6339	32	51	of	of	ADP
ejpam-6339	32	52	n	n	DET
ejpam-6339	32	53	-point	-point	NOUN
ejpam-6339	32	54	.	.	PUNCT
ejpam-6339	33	1	with	with	ADP
ejpam-6339	33	2	this	this	PRON
ejpam-6339	33	3	,	,	PUNCT
ejpam-6339	33	4	we	we	PRON
ejpam-6339	33	5	intend	intend	VERB
ejpam-6339	33	6	to	to	PART
ejpam-6339	33	7	fill	fill	VERB
ejpam-6339	33	8	the	the	DET
ejpam-6339	33	9	gap	gap	NOUN
ejpam-6339	33	10	in	in	ADP
ejpam-6339	33	11	the	the	DET
ejpam-6339	33	12	existing	exist	VERB
ejpam-6339	33	13	literature	literature	NOUN
ejpam-6339	33	14	and	and	CCONJ
ejpam-6339	33	15	bring	bring	VERB
ejpam-6339	33	16	new	new	ADJ
ejpam-6339	33	17	perspectives	perspective	NOUN
ejpam-6339	33	18	to	to	ADP
ejpam-6339	33	19	the	the	DET
ejpam-6339	33	20	theory	theory	NOUN
ejpam-6339	33	21	of	of	ADP
ejpam-6339	33	22	n	n	CCONJ
ejpam-6339	33	23	-topological	-topological	ADJ
ejpam-6339	33	24	spaces	space	NOUN
ejpam-6339	33	25	.	.	PUNCT
ejpam-6339	34	1	our	our	PRON
ejpam-6339	34	2	results	result	NOUN
ejpam-6339	34	3	not	not	PART
ejpam-6339	34	4	only	only	ADV
ejpam-6339	34	5	enrich	enrich	VERB
ejpam-6339	34	6	the	the	DET
ejpam-6339	34	7	mathematical	mathematical	ADJ
ejpam-6339	34	8	framework	framework	NOUN
ejpam-6339	34	9	of	of	ADP
ejpam-6339	34	10	n	n	DET
ejpam-6339	34	11	-sets	-set	NOUN
ejpam-6339	34	12	,	,	PUNCT
ejpam-6339	34	13	but	but	CCONJ
ejpam-6339	34	14	also	also	ADV
ejpam-6339	34	15	offer	offer	VERB
ejpam-6339	34	16	potential	potential	NOUN
ejpam-6339	34	17	for	for	ADP
ejpam-6339	34	18	future	future	ADJ
ejpam-6339	34	19	applications	application	NOUN
ejpam-6339	34	20	in	in	ADP
ejpam-6339	34	21	areas	area	NOUN
ejpam-6339	34	22	where	where	SCONJ
ejpam-6339	34	23	uncertainty	uncertainty	NOUN
ejpam-6339	34	24	and	and	CCONJ
ejpam-6339	34	25	indeterminacy	indeterminacy	NOUN
ejpam-6339	34	26	play	play	VERB
ejpam-6339	34	27	a	a	DET
ejpam-6339	34	28	central	central	ADJ
ejpam-6339	34	29	role	role	NOUN
ejpam-6339	34	30	.	.	PUNCT
ejpam-6339	35	1	2	2	X
ejpam-6339	35	2	.	.	NUM
ejpam-6339	35	3	neutrosophic	neutrosophic	ADJ
ejpam-6339	35	4	sets	set	NOUN
ejpam-6339	35	5	throughout	throughout	ADP
ejpam-6339	35	6	this	this	DET
ejpam-6339	35	7	paper	paper	NOUN
ejpam-6339	35	8	,	,	PUNCT
ejpam-6339	35	9	let	let	VERB
ejpam-6339	35	10	x	x	PRON
ejpam-6339	35	11	be	be	AUX
ejpam-6339	35	12	a	a	DET
ejpam-6339	35	13	nonempty	nonempty	ADJ
ejpam-6339	35	14	set	set	NOUN
ejpam-6339	35	15	,	,	PUNCT
ejpam-6339	35	16	called	call	VERB
ejpam-6339	35	17	universe	universe	NOUN
ejpam-6339	35	18	of	of	ADP
ejpam-6339	35	19	discourse	discourse	NOUN
ejpam-6339	35	20	.	.	PUNCT
ejpam-6339	36	1	definition	definition	NOUN
ejpam-6339	36	2	1	1	NUM
ejpam-6339	36	3	.	.	PUNCT
ejpam-6339	37	1	[	[	X
ejpam-6339	37	2	1	1	X
ejpam-6339	37	3	]	]	PUNCT
ejpam-6339	37	4	a	a	DET
ejpam-6339	37	5	neutrosophic	neutrosophic	ADJ
ejpam-6339	37	6	set	set	NOUN
ejpam-6339	37	7	(	(	PUNCT
ejpam-6339	37	8	briefly	briefly	NOUN
ejpam-6339	37	9	n	n	PRON
ejpam-6339	37	10	-set	-set	NUM
ejpam-6339	37	11	)	)	PUNCT
ejpam-6339	37	12	n	n	CCONJ
ejpam-6339	37	13	on	on	ADP
ejpam-6339	37	14	x	x	X
ejpam-6339	37	15	is	be	AUX
ejpam-6339	37	16	an	an	DET
ejpam-6339	37	17	object	object	NOUN
ejpam-6339	37	18	of	of	ADP
ejpam-6339	37	19	the	the	DET
ejpam-6339	37	20	form	form	NOUN
ejpam-6339	37	21	n	n	NOUN
ejpam-6339	37	22	=	=	PRON
ejpam-6339	37	23	{	{	PUNCT
ejpam-6339	37	24	⟨x	⟨x	NUM
ejpam-6339	37	25	,	,	PUNCT
ejpam-6339	37	26	µn	µn	PROPN
ejpam-6339	37	27	(	(	PUNCT
ejpam-6339	37	28	x	x	NOUN
ejpam-6339	37	29	)	)	PUNCT
ejpam-6339	37	30	,	,	PUNCT
ejpam-6339	37	31	σn	σn	X
ejpam-6339	37	32	(	(	PUNCT
ejpam-6339	37	33	x	x	NOUN
ejpam-6339	37	34	)	)	PUNCT
ejpam-6339	37	35	,	,	PUNCT
ejpam-6339	37	36	γn	γn	X
ejpam-6339	37	37	(	(	PUNCT
ejpam-6339	37	38	x)⟩	x)⟩	NOUN
ejpam-6339	37	39	:	:	PUNCT
ejpam-6339	37	40	x	x	SYM
ejpam-6339	37	41	∈	∈	NOUN
ejpam-6339	37	42	x	x	X
ejpam-6339	37	43	}	}	PUNCT
ejpam-6339	37	44	,	,	PUNCT
ejpam-6339	37	45	where	where	SCONJ
ejpam-6339	37	46	µn	µn	PROPN
ejpam-6339	37	47	,	,	PUNCT
ejpam-6339	37	48	σn	σn	X
ejpam-6339	37	49	,	,	PUNCT
ejpam-6339	37	50	γn	γn	NOUN
ejpam-6339	37	51	are	be	AUX
ejpam-6339	37	52	functions	function	NOUN
ejpam-6339	37	53	from	from	ADP
ejpam-6339	37	54	x	x	PUNCT
ejpam-6339	37	55	to	to	ADP
ejpam-6339	37	56	[	[	X
ejpam-6339	37	57	0	0	NUM
ejpam-6339	37	58	,	,	PUNCT
ejpam-6339	37	59	1	1	NUM
ejpam-6339	37	60	]	]	PUNCT
ejpam-6339	37	61	.	.	PUNCT
ejpam-6339	38	1	we	we	PRON
ejpam-6339	38	2	denote	denote	VERB
ejpam-6339	38	3	by	by	ADP
ejpam-6339	38	4	n	n	PROPN
ejpam-6339	38	5	(	(	PUNCT
ejpam-6339	38	6	x	x	X
ejpam-6339	38	7	)	)	PUNCT
ejpam-6339	38	8	the	the	DET
ejpam-6339	38	9	collection	collection	NOUN
ejpam-6339	38	10	of	of	ADP
ejpam-6339	38	11	all	all	DET
ejpam-6339	38	12	n	n	PRON
ejpam-6339	38	13	-sets	-set	NOUN
ejpam-6339	38	14	over	over	ADP
ejpam-6339	38	15	x.	x.	PROPN
ejpam-6339	38	16	j.	j.	PROPN
ejpam-6339	38	17	sanabria	sanabria	PROPN
ejpam-6339	38	18	,	,	PUNCT
ejpam-6339	38	19	e.	e.	PROPN
ejpam-6339	38	20	rosas	rosas	PROPN
ejpam-6339	38	21	,	,	PUNCT
ejpam-6339	38	22	c.	c.	PROPN
ejpam-6339	38	23	granados	granados	PROPN
ejpam-6339	38	24	/	/	PUNCT
ejpam-6339	38	25	eur	eur	PROPN
ejpam-6339	38	26	.	.	PUNCT
ejpam-6339	39	1	j.	j.	PROPN
ejpam-6339	39	2	pure	pure	PROPN
ejpam-6339	39	3	appl	appl	PROPN
ejpam-6339	39	4	.	.	PROPN
ejpam-6339	39	5	math	math	PROPN
ejpam-6339	39	6	,	,	PUNCT
ejpam-6339	39	7	18	18	NUM
ejpam-6339	39	8	(	(	PUNCT
ejpam-6339	39	9	3	3	NUM
ejpam-6339	39	10	)	)	PUNCT
ejpam-6339	39	11	(	(	PUNCT
ejpam-6339	39	12	2025	2025	NUM
ejpam-6339	39	13	)	)	PUNCT
ejpam-6339	39	14	,	,	PUNCT
ejpam-6339	39	15	6339	6339	NUM
ejpam-6339	39	16	3	3	NUM
ejpam-6339	39	17	of	of	ADP
ejpam-6339	39	18	15	15	NUM
ejpam-6339	39	19	definition	definition	NOUN
ejpam-6339	39	20	2	2	NUM
ejpam-6339	39	21	.	.	PUNCT
ejpam-6339	40	1	[	[	X
ejpam-6339	40	2	10	10	NUM
ejpam-6339	40	3	]	]	PUNCT
ejpam-6339	40	4	for	for	ADP
ejpam-6339	40	5	n	n	CCONJ
ejpam-6339	40	6	,	,	PUNCT
ejpam-6339	40	7	m	m	VERB
ejpam-6339	40	8	∈	∈	ADJ
ejpam-6339	40	9	n	n	CCONJ
ejpam-6339	40	10	(	(	PUNCT
ejpam-6339	40	11	x	x	X
ejpam-6339	40	12	)	)	PUNCT
ejpam-6339	40	13	we	we	PRON
ejpam-6339	40	14	define	define	VERB
ejpam-6339	40	15	the	the	DET
ejpam-6339	40	16	following	following	NOUN
ejpam-6339	40	17	:	:	PUNCT
ejpam-6339	40	18	(	(	PUNCT
ejpam-6339	40	19	1	1	X
ejpam-6339	40	20	)	)	PUNCT
ejpam-6339	40	21	(	(	PUNCT
ejpam-6339	40	22	inclusion	inclusion	NOUN
ejpam-6339	40	23	)	)	PUNCT
ejpam-6339	40	24	n	n	CCONJ
ejpam-6339	40	25	is	be	AUX
ejpam-6339	40	26	called	call	VERB
ejpam-6339	40	27	a	a	DET
ejpam-6339	40	28	neutrosophic	neutrosophic	ADJ
ejpam-6339	40	29	subset	subset	NOUN
ejpam-6339	40	30	of	of	ADP
ejpam-6339	40	31	m	m	PROPN
ejpam-6339	40	32	,	,	PUNCT
ejpam-6339	40	33	denoted	denote	VERB
ejpam-6339	40	34	by	by	ADP
ejpam-6339	40	35	n	n	PROPN
ejpam-6339	40	36	⊑	⊑	X
ejpam-6339	40	37	m	m	VERB
ejpam-6339	40	38	,	,	PUNCT
ejpam-6339	40	39	if	if	SCONJ
ejpam-6339	40	40	µn	µn	PROPN
ejpam-6339	40	41	(	(	PUNCT
ejpam-6339	40	42	x	x	NOUN
ejpam-6339	40	43	)	)	PUNCT
ejpam-6339	40	44	≤	≤	NOUN
ejpam-6339	40	45	µm	µm	ADP
ejpam-6339	40	46	(	(	PUNCT
ejpam-6339	40	47	x	x	NOUN
ejpam-6339	40	48	)	)	PUNCT
ejpam-6339	40	49	,	,	PUNCT
ejpam-6339	40	50	σn	σn	X
ejpam-6339	40	51	(	(	PUNCT
ejpam-6339	40	52	x	x	NOUN
ejpam-6339	40	53	)	)	PUNCT
ejpam-6339	40	54	≥	≥	NOUN
ejpam-6339	40	55	σm	σm	INTJ
ejpam-6339	40	56	(	(	PUNCT
ejpam-6339	40	57	x	x	NOUN
ejpam-6339	40	58	)	)	PUNCT
ejpam-6339	40	59	and	and	CCONJ
ejpam-6339	40	60	γn	γn	X
ejpam-6339	40	61	(	(	PUNCT
ejpam-6339	40	62	x	x	X
ejpam-6339	40	63	)	)	PUNCT
ejpam-6339	40	64	≥	≥	NOUN
ejpam-6339	40	65	γm	γm	X
ejpam-6339	40	66	(	(	PUNCT
ejpam-6339	40	67	x	x	X
ejpam-6339	40	68	)	)	PUNCT
ejpam-6339	40	69	for	for	ADP
ejpam-6339	40	70	all	all	PRON
ejpam-6339	40	71	x	x	SYM
ejpam-6339	40	72	∈	∈	NOUN
ejpam-6339	40	73	x.	x.	NOUN
ejpam-6339	41	1	also	also	ADV
ejpam-6339	41	2	,	,	PUNCT
ejpam-6339	41	3	we	we	PRON
ejpam-6339	41	4	can	can	AUX
ejpam-6339	41	5	say	say	VERB
ejpam-6339	41	6	that	that	SCONJ
ejpam-6339	41	7	m	m	PROPN
ejpam-6339	41	8	is	be	AUX
ejpam-6339	41	9	a	a	DET
ejpam-6339	41	10	neutrosophic	neutrosophic	ADJ
ejpam-6339	41	11	super	super	ADJ
ejpam-6339	41	12	set	set	NOUN
ejpam-6339	41	13	of	of	ADP
ejpam-6339	41	14	n	n	PROPN
ejpam-6339	41	15	.	.	PUNCT
ejpam-6339	42	1	(	(	PUNCT
ejpam-6339	42	2	2	2	X
ejpam-6339	42	3	)	)	PUNCT
ejpam-6339	42	4	(	(	PUNCT
ejpam-6339	42	5	equality	equality	NOUN
ejpam-6339	42	6	)	)	PUNCT
ejpam-6339	42	7	n	n	CCONJ
ejpam-6339	42	8	is	be	AUX
ejpam-6339	42	9	called	call	VERB
ejpam-6339	42	10	neutrosophic	neutrosophic	ADJ
ejpam-6339	42	11	equal	equal	ADJ
ejpam-6339	42	12	to	to	ADP
ejpam-6339	42	13	m	m	PROPN
ejpam-6339	42	14	,	,	PUNCT
ejpam-6339	42	15	denoted	denote	VERB
ejpam-6339	42	16	by	by	ADP
ejpam-6339	42	17	n	n	PROPN
ejpam-6339	42	18	=	=	NOUN
ejpam-6339	42	19	m	m	ADJ
ejpam-6339	42	20	,	,	PUNCT
ejpam-6339	42	21	if	if	SCONJ
ejpam-6339	42	22	n	n	CCONJ
ejpam-6339	42	23	⊑	⊑	X
ejpam-6339	42	24	m	m	VERB
ejpam-6339	42	25	and	and	CCONJ
ejpam-6339	42	26	m	m	VERB
ejpam-6339	42	27	⊑	⊑	PRON
ejpam-6339	42	28	n	n	X
ejpam-6339	42	29	.	.	PUNCT
ejpam-6339	43	1	(	(	PUNCT
ejpam-6339	43	2	3	3	X
ejpam-6339	43	3	)	)	PUNCT
ejpam-6339	43	4	(	(	PUNCT
ejpam-6339	43	5	universal	universal	ADJ
ejpam-6339	43	6	set	set	NOUN
ejpam-6339	43	7	)	)	PUNCT
ejpam-6339	43	8	n	n	CCONJ
ejpam-6339	43	9	is	be	AUX
ejpam-6339	43	10	called	call	VERB
ejpam-6339	43	11	the	the	DET
ejpam-6339	43	12	neutrosophic	neutrosophic	ADJ
ejpam-6339	43	13	universal	universal	ADJ
ejpam-6339	43	14	set	set	NOUN
ejpam-6339	43	15	,	,	PUNCT
ejpam-6339	43	16	denoted	denote	VERB
ejpam-6339	43	17	by	by	ADP
ejpam-6339	43	18	x̃	x̃	PROPN
ejpam-6339	43	19	,	,	PUNCT
ejpam-6339	43	20	if	if	SCONJ
ejpam-6339	43	21	µn	µn	PROPN
ejpam-6339	43	22	(	(	PUNCT
ejpam-6339	43	23	x	x	NOUN
ejpam-6339	43	24	)	)	PUNCT
ejpam-6339	43	25	=	=	SYM
ejpam-6339	43	26	1	1	NUM
ejpam-6339	43	27	,	,	PUNCT
ejpam-6339	43	28	σn	σn	X
ejpam-6339	43	29	(	(	PUNCT
ejpam-6339	43	30	x	x	NOUN
ejpam-6339	43	31	)	)	PUNCT
ejpam-6339	43	32	=	=	SYM
ejpam-6339	43	33	0	0	NUM
ejpam-6339	43	34	and	and	CCONJ
ejpam-6339	43	35	γn	γn	X
ejpam-6339	43	36	(	(	PUNCT
ejpam-6339	43	37	x	x	X
ejpam-6339	43	38	)	)	PUNCT
ejpam-6339	43	39	=	=	SYM
ejpam-6339	43	40	0	0	NUM
ejpam-6339	43	41	for	for	ADP
ejpam-6339	43	42	all	all	PRON
ejpam-6339	43	43	x	x	SYM
ejpam-6339	43	44	∈	∈	ADJ
ejpam-6339	43	45	x.	x.	NOUN
ejpam-6339	43	46	(	(	PUNCT
ejpam-6339	43	47	4	4	NUM
ejpam-6339	43	48	)	)	PUNCT
ejpam-6339	43	49	(	(	PUNCT
ejpam-6339	43	50	empty	empty	ADJ
ejpam-6339	43	51	set	set	NOUN
ejpam-6339	43	52	)	)	PUNCT
ejpam-6339	43	53	n	n	CCONJ
ejpam-6339	43	54	is	be	AUX
ejpam-6339	43	55	called	call	VERB
ejpam-6339	43	56	neutrosophic	neutrosophic	ADJ
ejpam-6339	43	57	empty	empty	ADJ
ejpam-6339	43	58	set	set	NOUN
ejpam-6339	43	59	,	,	PUNCT
ejpam-6339	43	60	denoted	denote	VERB
ejpam-6339	43	61	by	by	ADP
ejpam-6339	43	62	∅̃	∅̃	NOUN
ejpam-6339	43	63	,	,	PUNCT
ejpam-6339	43	64	if	if	SCONJ
ejpam-6339	43	65	µn	µn	PROPN
ejpam-6339	43	66	(	(	PUNCT
ejpam-6339	43	67	x	x	NOUN
ejpam-6339	43	68	)	)	PUNCT
ejpam-6339	43	69	=	=	SYM
ejpam-6339	43	70	0	0	NUM
ejpam-6339	43	71	,	,	PUNCT
ejpam-6339	43	72	σn	σn	X
ejpam-6339	43	73	(	(	PUNCT
ejpam-6339	43	74	x	x	NOUN
ejpam-6339	43	75	)	)	PUNCT
ejpam-6339	43	76	=	=	SYM
ejpam-6339	43	77	1	1	NUM
ejpam-6339	43	78	and	and	CCONJ
ejpam-6339	43	79	γn	γn	NOUN
ejpam-6339	43	80	(	(	PUNCT
ejpam-6339	43	81	x	x	X
ejpam-6339	43	82	)	)	PUNCT
ejpam-6339	43	83	=	=	SYM
ejpam-6339	43	84	1	1	NUM
ejpam-6339	43	85	for	for	ADP
ejpam-6339	43	86	all	all	PRON
ejpam-6339	43	87	x	x	SYM
ejpam-6339	43	88	∈	∈	ADJ
ejpam-6339	43	89	x.	x.	NOUN
ejpam-6339	43	90	(	(	PUNCT
ejpam-6339	43	91	5	5	NUM
ejpam-6339	43	92	)	)	PUNCT
ejpam-6339	43	93	(	(	PUNCT
ejpam-6339	43	94	intersection	intersection	NOUN
ejpam-6339	43	95	)	)	PUNCT
ejpam-6339	43	96	the	the	DET
ejpam-6339	43	97	neutrosophic	neutrosophic	ADJ
ejpam-6339	43	98	intersection	intersection	NOUN
ejpam-6339	43	99	of	of	ADP
ejpam-6339	43	100	n	n	DET
ejpam-6339	43	101	andm	andm	NOUN
ejpam-6339	43	102	,	,	PUNCT
ejpam-6339	43	103	denoted	denote	VERB
ejpam-6339	43	104	by	by	ADP
ejpam-6339	43	105	n⊓m	n⊓m	PROPN
ejpam-6339	43	106	,	,	PUNCT
ejpam-6339	43	107	is	be	AUX
ejpam-6339	43	108	defined	define	VERB
ejpam-6339	43	109	as	as	ADP
ejpam-6339	43	110	n	n	NOUN
ejpam-6339	43	111	⊓m	⊓m	NOUN
ejpam-6339	43	112	=	=	PUNCT
ejpam-6339	43	113	{	{	PUNCT
ejpam-6339	43	114	(	(	PUNCT
ejpam-6339	43	115	x	x	NOUN
ejpam-6339	43	116	,	,	PUNCT
ejpam-6339	43	117	µn	µn	PROPN
ejpam-6339	43	118	(	(	PUNCT
ejpam-6339	43	119	x	x	NOUN
ejpam-6339	43	120	)	)	PUNCT
ejpam-6339	43	121	∧	∧	PROPN
ejpam-6339	43	122	µm	µm	ADP
ejpam-6339	43	123	(	(	PUNCT
ejpam-6339	43	124	x	x	NOUN
ejpam-6339	43	125	)	)	PUNCT
ejpam-6339	43	126	,	,	PUNCT
ejpam-6339	43	127	σn	σn	X
ejpam-6339	43	128	(	(	PUNCT
ejpam-6339	43	129	x	x	NOUN
ejpam-6339	43	130	)	)	PUNCT
ejpam-6339	43	131	∨	∨	NUM
ejpam-6339	43	132	σm	σm	X
ejpam-6339	43	133	(	(	PUNCT
ejpam-6339	43	134	x	x	NOUN
ejpam-6339	43	135	)	)	PUNCT
ejpam-6339	43	136	,	,	PUNCT
ejpam-6339	43	137	γn	γn	PART
ejpam-6339	43	138	(	(	PUNCT
ejpam-6339	43	139	x	x	NOUN
ejpam-6339	43	140	)	)	PUNCT
ejpam-6339	43	141	∨	∨	NUM
ejpam-6339	43	142	γm	γm	X
ejpam-6339	43	143	(	(	PUNCT
ejpam-6339	43	144	x)⟩	x)⟩	NOUN
ejpam-6339	43	145	:	:	PUNCT
ejpam-6339	43	146	x	x	SYM
ejpam-6339	43	147	∈	∈	NOUN
ejpam-6339	43	148	x	x	X
ejpam-6339	43	149	}	}	PUNCT
ejpam-6339	43	150	.	.	PUNCT
ejpam-6339	44	1	(	(	PUNCT
ejpam-6339	44	2	6	6	NUM
ejpam-6339	44	3	)	)	PUNCT
ejpam-6339	44	4	(	(	PUNCT
ejpam-6339	44	5	union	union	NOUN
ejpam-6339	44	6	)	)	PUNCT
ejpam-6339	44	7	the	the	DET
ejpam-6339	44	8	neutrosophic	neutrosophic	PROPN
ejpam-6339	44	9	union	union	NOUN
ejpam-6339	44	10	of	of	ADP
ejpam-6339	44	11	n	n	PROPN
ejpam-6339	44	12	and	and	CCONJ
ejpam-6339	44	13	m	m	PROPN
ejpam-6339	44	14	,	,	PUNCT
ejpam-6339	44	15	denoted	denote	VERB
ejpam-6339	44	16	by	by	ADP
ejpam-6339	44	17	n	n	PROPN
ejpam-6339	44	18	⊔m	⊔m	NUM
ejpam-6339	44	19	,	,	PUNCT
ejpam-6339	44	20	is	be	AUX
ejpam-6339	44	21	defined	define	VERB
ejpam-6339	44	22	as	as	ADP
ejpam-6339	44	23	n	n	PROPN
ejpam-6339	44	24	⊔m	⊔m	NUM
ejpam-6339	44	25	=	=	NOUN
ejpam-6339	44	26	{	{	PUNCT
ejpam-6339	44	27	⟨x	⟨x	NUM
ejpam-6339	44	28	,	,	PUNCT
ejpam-6339	44	29	µn	µn	PROPN
ejpam-6339	44	30	(	(	PUNCT
ejpam-6339	44	31	x	x	NOUN
ejpam-6339	44	32	)	)	PUNCT
ejpam-6339	44	33	∨	∨	NUM
ejpam-6339	44	34	µm	µm	X
ejpam-6339	44	35	(	(	PUNCT
ejpam-6339	44	36	x	x	NOUN
ejpam-6339	44	37	)	)	PUNCT
ejpam-6339	44	38	,	,	PUNCT
ejpam-6339	44	39	σn	σn	X
ejpam-6339	44	40	(	(	PUNCT
ejpam-6339	44	41	x	x	NOUN
ejpam-6339	44	42	)	)	PUNCT
ejpam-6339	44	43	∧	∧	NOUN
ejpam-6339	44	44	σm	σm	INTJ
ejpam-6339	44	45	(	(	PUNCT
ejpam-6339	44	46	x	x	NOUN
ejpam-6339	44	47	)	)	PUNCT
ejpam-6339	44	48	,	,	PUNCT
ejpam-6339	44	49	γn	γn	PART
ejpam-6339	44	50	(	(	PUNCT
ejpam-6339	44	51	x	x	X
ejpam-6339	44	52	)	)	PUNCT
ejpam-6339	44	53	∧	∧	NOUN
ejpam-6339	44	54	γm	γm	X
ejpam-6339	44	55	(	(	PUNCT
ejpam-6339	44	56	x)⟩	x)⟩	NOUN
ejpam-6339	44	57	:	:	PUNCT
ejpam-6339	44	58	x	x	SYM
ejpam-6339	44	59	∈	∈	NOUN
ejpam-6339	44	60	x	x	X
ejpam-6339	44	61	}	}	PUNCT
ejpam-6339	44	62	.	.	PUNCT
ejpam-6339	45	1	(	(	PUNCT
ejpam-6339	45	2	7	7	NUM
ejpam-6339	45	3	)	)	PUNCT
ejpam-6339	45	4	(	(	PUNCT
ejpam-6339	45	5	complement	complement	NOUN
ejpam-6339	45	6	)	)	PUNCT
ejpam-6339	45	7	the	the	DET
ejpam-6339	45	8	neutrosophic	neutrosophic	ADJ
ejpam-6339	45	9	complement	complement	NOUN
ejpam-6339	45	10	of	of	ADP
ejpam-6339	45	11	n	n	PROPN
ejpam-6339	45	12	,	,	PUNCT
ejpam-6339	45	13	denoted	denote	VERB
ejpam-6339	45	14	by	by	ADP
ejpam-6339	45	15	n	n	PRON
ejpam-6339	45	16	c	c	NOUN
ejpam-6339	45	17	,	,	PUNCT
ejpam-6339	45	18	is	be	AUX
ejpam-6339	45	19	defined	define	VERB
ejpam-6339	45	20	as	as	ADP
ejpam-6339	45	21	n	n	X
ejpam-6339	45	22	c	c	NOUN
ejpam-6339	45	23	=	=	PUNCT
ejpam-6339	45	24	{	{	PUNCT
ejpam-6339	45	25	⟨x	⟨x	NUM
ejpam-6339	45	26	,	,	PUNCT
ejpam-6339	45	27	γn	γn	X
ejpam-6339	45	28	(	(	PUNCT
ejpam-6339	45	29	x	x	NOUN
ejpam-6339	45	30	)	)	PUNCT
ejpam-6339	45	31	,	,	PUNCT
ejpam-6339	45	32	1−	1−	NUM
ejpam-6339	45	33	σn	σn	NOUN
ejpam-6339	45	34	(	(	PUNCT
ejpam-6339	45	35	x	x	NOUN
ejpam-6339	45	36	)	)	PUNCT
ejpam-6339	45	37	,	,	PUNCT
ejpam-6339	45	38	µn	µn	PROPN
ejpam-6339	45	39	(	(	PUNCT
ejpam-6339	45	40	x)⟩	x)⟩	NOUN
ejpam-6339	45	41	:	:	PUNCT
ejpam-6339	45	42	x	x	SYM
ejpam-6339	45	43	∈	∈	NOUN
ejpam-6339	45	44	x	x	X
ejpam-6339	45	45	}	}	PUNCT
ejpam-6339	45	46	.	.	PUNCT
ejpam-6339	46	1	proposition	proposition	NOUN
ejpam-6339	46	2	1	1	NUM
ejpam-6339	46	3	.	.	PUNCT
ejpam-6339	47	1	[	[	X
ejpam-6339	47	2	10	10	NUM
ejpam-6339	47	3	]	]	X
ejpam-6339	47	4	if	if	SCONJ
ejpam-6339	47	5	n	n	CCONJ
ejpam-6339	47	6	,	,	PUNCT
ejpam-6339	47	7	m	m	VERB
ejpam-6339	47	8	∈	∈	ADJ
ejpam-6339	47	9	n	n	CCONJ
ejpam-6339	47	10	(	(	PUNCT
ejpam-6339	47	11	x	x	NOUN
ejpam-6339	47	12	)	)	PUNCT
ejpam-6339	47	13	,	,	PUNCT
ejpam-6339	47	14	then	then	ADV
ejpam-6339	47	15	we	we	PRON
ejpam-6339	47	16	have	have	VERB
ejpam-6339	47	17	the	the	DET
ejpam-6339	47	18	following	follow	VERB
ejpam-6339	47	19	properties	property	NOUN
ejpam-6339	47	20	:	:	PUNCT
ejpam-6339	47	21	(	(	PUNCT
ejpam-6339	47	22	1	1	X
ejpam-6339	47	23	)	)	PUNCT
ejpam-6339	47	24	n	n	NOUN
ejpam-6339	47	25	⊓n	⊓n	NOUN
ejpam-6339	48	1	=	=	PUNCT
ejpam-6339	48	2	n	n	PROPN
ejpam-6339	48	3	and	and	CCONJ
ejpam-6339	48	4	n	n	PRON
ejpam-6339	48	5	⊔n	⊔n	NUM
ejpam-6339	48	6	=	=	SYM
ejpam-6339	48	7	n	n	NOUN
ejpam-6339	48	8	.	.	PUNCT
ejpam-6339	49	1	(	(	PUNCT
ejpam-6339	49	2	2	2	X
ejpam-6339	49	3	)	)	PUNCT
ejpam-6339	49	4	n	n	NOUN
ejpam-6339	49	5	⊓m	⊓m	NOUN
ejpam-6339	50	1	=	=	NOUN
ejpam-6339	50	2	m	m	VERB
ejpam-6339	50	3	⊓n	⊓n	ADJ
ejpam-6339	50	4	and	and	CCONJ
ejpam-6339	50	5	n	n	PRON
ejpam-6339	50	6	⊔m	⊔m	NUM
ejpam-6339	50	7	=	=	PRON
ejpam-6339	50	8	m	m	NOUN
ejpam-6339	50	9	⊔n	⊔n	NUM
ejpam-6339	50	10	.	.	PUNCT
ejpam-6339	51	1	(	(	PUNCT
ejpam-6339	51	2	3	3	X
ejpam-6339	51	3	)	)	PUNCT
ejpam-6339	51	4	n	n	PRON
ejpam-6339	51	5	⊓	⊓	PROPN
ejpam-6339	51	6	∅̃	∅̃	NOUN
ejpam-6339	51	7	=	=	SYM
ejpam-6339	51	8	∅̃	∅̃	NOUN
ejpam-6339	51	9	and	and	CCONJ
ejpam-6339	51	10	n	n	PRON
ejpam-6339	51	11	⊓	⊓	PROPN
ejpam-6339	51	12	x̃	x̃	PROPN
ejpam-6339	51	13	=	=	PUNCT
ejpam-6339	51	14	n	n	PROPN
ejpam-6339	51	15	.	.	PUNCT
ejpam-6339	52	1	(	(	PUNCT
ejpam-6339	52	2	4	4	X
ejpam-6339	52	3	)	)	PUNCT
ejpam-6339	52	4	n	n	CCONJ
ejpam-6339	52	5	⊔	⊔	NUM
ejpam-6339	52	6	∅̃	∅̃	NOUN
ejpam-6339	52	7	=	=	PUNCT
ejpam-6339	52	8	n	n	PROPN
ejpam-6339	52	9	and	and	CCONJ
ejpam-6339	52	10	n	n	PRON
ejpam-6339	53	1	⊔	⊔	NUM
ejpam-6339	53	2	x̃	x̃	PROPN
ejpam-6339	54	1	=	=	PUNCT
ejpam-6339	54	2	x̃.	x̃.	ADJ
ejpam-6339	54	3	(	(	PUNCT
ejpam-6339	54	4	5	5	NUM
ejpam-6339	54	5	)	)	PUNCT
ejpam-6339	54	6	n	n	PRON
ejpam-6339	54	7	⊓	⊓	PROPN
ejpam-6339	54	8	(	(	PUNCT
ejpam-6339	54	9	m	m	PROPN
ejpam-6339	54	10	⊓o	⊓o	PROPN
ejpam-6339	54	11	)	)	PUNCT
ejpam-6339	54	12	=	=	SYM
ejpam-6339	54	13	(	(	PUNCT
ejpam-6339	54	14	n	n	X
ejpam-6339	54	15	⊓m	⊓m	NOUN
ejpam-6339	54	16	)	)	PUNCT
ejpam-6339	54	17	⊓o	⊓o	NOUN
ejpam-6339	54	18	and	and	CCONJ
ejpam-6339	54	19	n	n	DET
ejpam-6339	54	20	⊔	⊔	PROPN
ejpam-6339	54	21	(	(	PUNCT
ejpam-6339	54	22	m	m	PROPN
ejpam-6339	54	23	⊔o	⊔o	PRON
ejpam-6339	54	24	)	)	PUNCT
ejpam-6339	54	25	=	=	PUNCT
ejpam-6339	54	26	(	(	PUNCT
ejpam-6339	54	27	n	n	X
ejpam-6339	54	28	⊔m	⊔m	PROPN
ejpam-6339	54	29	)	)	PUNCT
ejpam-6339	54	30	⊔o	⊔o	NUM
ejpam-6339	54	31	.	.	PUNCT
ejpam-6339	55	1	(	(	PUNCT
ejpam-6339	55	2	6	6	NUM
ejpam-6339	55	3	)	)	PUNCT
ejpam-6339	55	4	(	(	PUNCT
ejpam-6339	55	5	n	n	X
ejpam-6339	55	6	c)c	c)c	NOUN
ejpam-6339	55	7	=	=	SYM
ejpam-6339	55	8	n	n	X
ejpam-6339	55	9	.	.	PUNCT
ejpam-6339	56	1	the	the	DET
ejpam-6339	56	2	union	union	NOUN
ejpam-6339	56	3	and	and	CCONJ
ejpam-6339	56	4	intersection	intersection	NOUN
ejpam-6339	56	5	operations	operation	NOUN
ejpam-6339	56	6	given	give	VERB
ejpam-6339	56	7	in	in	ADP
ejpam-6339	56	8	definition	definition	NOUN
ejpam-6339	56	9	2	2	NUM
ejpam-6339	56	10	can	can	AUX
ejpam-6339	56	11	be	be	AUX
ejpam-6339	56	12	extended	extend	VERB
ejpam-6339	56	13	as	as	SCONJ
ejpam-6339	56	14	follows	follow	VERB
ejpam-6339	56	15	.	.	PUNCT
ejpam-6339	57	1	definition	definition	NOUN
ejpam-6339	57	2	3	3	NUM
ejpam-6339	57	3	.	.	PUNCT
ejpam-6339	58	1	[	[	X
ejpam-6339	58	2	4	4	X
ejpam-6339	58	3	]	]	PUNCT
ejpam-6339	58	4	for	for	ADP
ejpam-6339	58	5	{	{	PUNCT
ejpam-6339	58	6	nj	nj	PROPN
ejpam-6339	58	7	:	:	PUNCT
ejpam-6339	58	8	j	j	PROPN
ejpam-6339	58	9	∈	∈	PROPN
ejpam-6339	58	10	j	j	PROPN
ejpam-6339	58	11	}	}	PUNCT
ejpam-6339	58	12	⊆	⊆	NUM
ejpam-6339	58	13	n	n	NUM
ejpam-6339	58	14	(	(	PUNCT
ejpam-6339	58	15	x	x	X
ejpam-6339	58	16	)	)	PUNCT
ejpam-6339	58	17	we	we	PRON
ejpam-6339	58	18	define	define	VERB
ejpam-6339	58	19	the	the	DET
ejpam-6339	58	20	following	follow	VERB
ejpam-6339	58	21	operations	operation	NOUN
ejpam-6339	58	22	:	:	PUNCT
ejpam-6339	58	23	j.	j.	PROPN
ejpam-6339	58	24	sanabria	sanabria	PROPN
ejpam-6339	58	25	,	,	PUNCT
ejpam-6339	58	26	e.	e.	PROPN
ejpam-6339	58	27	rosas	rosas	PROPN
ejpam-6339	58	28	,	,	PUNCT
ejpam-6339	58	29	c.	c.	PROPN
ejpam-6339	58	30	granados	granados	PROPN
ejpam-6339	58	31	/	/	PUNCT
ejpam-6339	58	32	eur	eur	PROPN
ejpam-6339	58	33	.	.	PUNCT
ejpam-6339	59	1	j.	j.	PROPN
ejpam-6339	59	2	pure	pure	PROPN
ejpam-6339	59	3	appl	appl	PROPN
ejpam-6339	59	4	.	.	PROPN
ejpam-6339	59	5	math	math	PROPN
ejpam-6339	59	6	,	,	PUNCT
ejpam-6339	59	7	18	18	NUM
ejpam-6339	59	8	(	(	PUNCT
ejpam-6339	59	9	3	3	NUM
ejpam-6339	59	10	)	)	PUNCT
ejpam-6339	59	11	(	(	PUNCT
ejpam-6339	59	12	2025	2025	NUM
ejpam-6339	59	13	)	)	PUNCT
ejpam-6339	59	14	,	,	PUNCT
ejpam-6339	59	15	6339	6339	NUM
ejpam-6339	59	16	4	4	NUM
ejpam-6339	59	17	of	of	ADP
ejpam-6339	59	18	15	15	NUM
ejpam-6339	59	19	(	(	PUNCT
ejpam-6339	59	20	1	1	NUM
ejpam-6339	59	21	)	)	PUNCT
ejpam-6339	59	22	(	(	PUNCT
ejpam-6339	59	23	arbitrary	arbitrary	ADJ
ejpam-6339	59	24	intersection	intersection	NOUN
ejpam-6339	59	25	)	)	PUNCT
ejpam-6339	59	26	the	the	DET
ejpam-6339	59	27	arbitrary	arbitrary	ADJ
ejpam-6339	59	28	neutrosophic	neutrosophic	ADJ
ejpam-6339	59	29	intersection	intersection	NOUN
ejpam-6339	59	30	of	of	ADP
ejpam-6339	59	31	the	the	DET
ejpam-6339	59	32	collection	collection	NOUN
ejpam-6339	59	33	{	{	PUNCT
ejpam-6339	59	34	nj	nj	PROPN
ejpam-6339	59	35	:	:	PUNCT
ejpam-6339	60	1	j	j	PROPN
ejpam-6339	60	2	∈	∈	PROPN
ejpam-6339	60	3	j	j	PROPN
ejpam-6339	60	4	}	}	PUNCT
ejpam-6339	60	5	,	,	PUNCT
ejpam-6339	60	6	denoted	denote	VERB
ejpam-6339	60	7	by	by	ADP
ejpam-6339	60	8	l	l	PROPN
ejpam-6339	60	9	j∈j	j∈j	PROPN
ejpam-6339	60	10	nj	nj	PROPN
ejpam-6339	60	11	,	,	PUNCT
ejpam-6339	60	12	is	be	AUX
ejpam-6339	60	13	defined	define	VERB
ejpam-6339	60	14	as	as	ADP
ejpam-6339	60	15	l	l	PROPN
ejpam-6339	60	16	j∈j	j∈j	NOUN
ejpam-6339	60	17	nj	nj	PROPN
ejpam-6339	61	1	=	=	PUNCT
ejpam-6339	61	2	{	{	PUNCT
ejpam-6339	61	3	〈	〈	PROPN
ejpam-6339	61	4	x	x	PROPN
ejpam-6339	61	5	,	,	PUNCT
ejpam-6339	61	6	inf	inf	PROPN
ejpam-6339	61	7	j∈j	j∈j	NOUN
ejpam-6339	61	8	µnj	µnj	PROPN
ejpam-6339	61	9	(	(	PUNCT
ejpam-6339	61	10	x	x	NOUN
ejpam-6339	61	11	)	)	PUNCT
ejpam-6339	61	12	,	,	PUNCT
ejpam-6339	61	13	sup	sup	NOUN
ejpam-6339	61	14	j∈j	j∈j	NOUN
ejpam-6339	61	15	σnj	σnj	ADJ
ejpam-6339	61	16	(	(	PUNCT
ejpam-6339	61	17	x	x	NOUN
ejpam-6339	61	18	)	)	PUNCT
ejpam-6339	61	19	,	,	PUNCT
ejpam-6339	61	20	sup	sup	NOUN
ejpam-6339	61	21	j∈j	j∈j	NOUN
ejpam-6339	61	22	γnj	γnj	PROPN
ejpam-6339	61	23	(	(	PUNCT
ejpam-6339	61	24	x	x	NOUN
ejpam-6339	61	25	)	)	PUNCT
ejpam-6339	61	26	〉	〉	NOUN
ejpam-6339	61	27	:	:	PUNCT
ejpam-6339	61	28	x	x	X
ejpam-6339	61	29	∈	∈	NOUN
ejpam-6339	61	30	x	x	PUNCT
ejpam-6339	61	31	}	}	PUNCT
ejpam-6339	61	32	.	.	PUNCT
ejpam-6339	62	1	(	(	PUNCT
ejpam-6339	62	2	2	2	X
ejpam-6339	62	3	)	)	PUNCT
ejpam-6339	62	4	(	(	PUNCT
ejpam-6339	62	5	arbitrary	arbitrary	ADJ
ejpam-6339	62	6	union	union	NOUN
ejpam-6339	62	7	)	)	PUNCT
ejpam-6339	62	8	the	the	DET
ejpam-6339	62	9	arbitrary	arbitrary	ADJ
ejpam-6339	62	10	neutrosophic	neutrosophic	ADJ
ejpam-6339	62	11	union	union	NOUN
ejpam-6339	62	12	of	of	ADP
ejpam-6339	62	13	the	the	DET
ejpam-6339	62	14	collection	collection	NOUN
ejpam-6339	62	15	{	{	PUNCT
ejpam-6339	62	16	nj	nj	PROPN
ejpam-6339	62	17	:	:	PUNCT
ejpam-6339	63	1	j	j	PROPN
ejpam-6339	63	2	∈	∈	PROPN
ejpam-6339	63	3	j	j	PROPN
ejpam-6339	63	4	}	}	PUNCT
ejpam-6339	63	5	,	,	PUNCT
ejpam-6339	63	6	denoted	denote	VERB
ejpam-6339	63	7	by	by	ADP
ejpam-6339	63	8	⊔	⊔	PROPN
ejpam-6339	63	9	j∈j	j∈j	PROPN
ejpam-6339	63	10	nj	nj	PROPN
ejpam-6339	63	11	,	,	PUNCT
ejpam-6339	63	12	is	be	AUX
ejpam-6339	63	13	defined	define	VERB
ejpam-6339	63	14	as	as	ADP
ejpam-6339	63	15	⊔	⊔	PROPN
ejpam-6339	63	16	j∈j	j∈j	NOUN
ejpam-6339	63	17	nj	nj	PROPN
ejpam-6339	64	1	=	=	PUNCT
ejpam-6339	64	2	{	{	PUNCT
ejpam-6339	64	3	〈	〈	PROPN
ejpam-6339	64	4	x	x	PROPN
ejpam-6339	64	5	,	,	PUNCT
ejpam-6339	64	6	sup	sup	PROPN
ejpam-6339	64	7	j∈j	j∈j	NOUN
ejpam-6339	64	8	µnj	µnj	PROPN
ejpam-6339	64	9	(	(	PUNCT
ejpam-6339	64	10	x	x	NOUN
ejpam-6339	64	11	)	)	PUNCT
ejpam-6339	64	12	,	,	PUNCT
ejpam-6339	64	13	inf	inf	PROPN
ejpam-6339	64	14	j∈j	j∈j	PROPN
ejpam-6339	64	15	σnj	σnj	PROPN
ejpam-6339	64	16	(	(	PUNCT
ejpam-6339	64	17	x	x	NOUN
ejpam-6339	64	18	)	)	PUNCT
ejpam-6339	64	19	,	,	PUNCT
ejpam-6339	64	20	inf	inf	PROPN
ejpam-6339	64	21	j∈j	j∈j	NOUN
ejpam-6339	64	22	γnj	γnj	PROPN
ejpam-6339	64	23	(	(	PUNCT
ejpam-6339	64	24	x	x	X
ejpam-6339	64	25	)	)	PUNCT
ejpam-6339	64	26	〉	〉	NOUN
ejpam-6339	64	27	:	:	PUNCT
ejpam-6339	64	28	x	x	X
ejpam-6339	64	29	∈	∈	NOUN
ejpam-6339	64	30	x	x	PUNCT
ejpam-6339	64	31	}	}	PUNCT
ejpam-6339	64	32	.	.	PUNCT
ejpam-6339	65	1	proposition	proposition	NOUN
ejpam-6339	65	2	2	2	NUM
ejpam-6339	65	3	.	.	PUNCT
ejpam-6339	66	1	[	[	X
ejpam-6339	66	2	10	10	NUM
ejpam-6339	66	3	]	]	X
ejpam-6339	66	4	if	if	SCONJ
ejpam-6339	66	5	{	{	PUNCT
ejpam-6339	66	6	nj	nj	NOUN
ejpam-6339	66	7	:	:	PUNCT
ejpam-6339	67	1	j	j	PROPN
ejpam-6339	67	2	∈	∈	PROPN
ejpam-6339	67	3	j	j	PROPN
ejpam-6339	67	4	}	}	PUNCT
ejpam-6339	67	5	⊆	⊆	NUM
ejpam-6339	67	6	n	n	NUM
ejpam-6339	67	7	(	(	PUNCT
ejpam-6339	67	8	x	x	NOUN
ejpam-6339	67	9	)	)	PUNCT
ejpam-6339	67	10	and	and	CCONJ
ejpam-6339	67	11	m	m	PROPN
ejpam-6339	67	12	∈	∈	PROPN
ejpam-6339	67	13	n	n	CCONJ
ejpam-6339	67	14	(	(	PUNCT
ejpam-6339	67	15	x	x	NOUN
ejpam-6339	67	16	)	)	PUNCT
ejpam-6339	67	17	,	,	PUNCT
ejpam-6339	67	18	then	then	ADV
ejpam-6339	67	19	we	we	PRON
ejpam-6339	67	20	have	have	VERB
ejpam-6339	67	21	the	the	DET
ejpam-6339	67	22	following	follow	VERB
ejpam-6339	67	23	properties	property	NOUN
ejpam-6339	67	24	:	:	PUNCT
ejpam-6339	67	25	(	(	PUNCT
ejpam-6339	67	26	1	1	X
ejpam-6339	67	27	)	)	PUNCT
ejpam-6339	67	28	m	m	VERB
ejpam-6339	67	29	⊓	⊓	NOUN
ejpam-6339	67	30	⊔	⊔	NOUN
ejpam-6339	67	31	j∈j	j∈j	NOUN
ejpam-6339	67	32	nj	nj	PROPN
ejpam-6339	67	33			PROPN
ejpam-6339	67	34	=	=	SYM
ejpam-6339	67	35	⊔	⊔	PROPN
ejpam-6339	67	36	j∈j	j∈j	NOUN
ejpam-6339	67	37	(	(	PUNCT
ejpam-6339	67	38	m	m	PROPN
ejpam-6339	67	39	⊓nj	⊓nj	X
ejpam-6339	67	40	)	)	PUNCT
ejpam-6339	67	41	.	.	PUNCT
ejpam-6339	68	1	(	(	PUNCT
ejpam-6339	68	2	2	2	X
ejpam-6339	68	3	)	)	PUNCT
ejpam-6339	68	4	m	m	VERB
ejpam-6339	68	5	⊔	⊔	PROPN
ejpam-6339	68	6	l	l	PROPN
ejpam-6339	68	7	j∈j	j∈j	NOUN
ejpam-6339	68	8	nj	nj	NOUN
ejpam-6339	68	9			PROPN
ejpam-6339	68	10	=	=	SYM
ejpam-6339	68	11	l	l	PROPN
ejpam-6339	68	12	j∈j	j∈j	NOUN
ejpam-6339	68	13	(	(	PUNCT
ejpam-6339	68	14	m	m	NOUN
ejpam-6339	68	15	⊔nj	⊔nj	PROPN
ejpam-6339	68	16	)	)	PUNCT
ejpam-6339	68	17	.	.	PUNCT
ejpam-6339	69	1	(	(	PUNCT
ejpam-6339	69	2	3	3	X
ejpam-6339	69	3	)	)	PUNCT
ejpam-6339	69	4	l	l	NOUN
ejpam-6339	69	5	j∈j	j∈j	PROPN
ejpam-6339	69	6	nj	nj	PROPN
ejpam-6339	69	7	c	c	PUNCT
ejpam-6339	70	1	=	=	PUNCT
ejpam-6339	70	2	⊔	⊔	PROPN
ejpam-6339	70	3	j∈j	j∈j	NOUN
ejpam-6339	70	4	n	n	PROPN
ejpam-6339	70	5	c	c	PROPN
ejpam-6339	70	6	j	j	PROPN
ejpam-6339	70	7	.	.	PUNCT
ejpam-6339	71	1	(	(	PUNCT
ejpam-6339	71	2	4	4	X
ejpam-6339	71	3	)	)	PUNCT
ejpam-6339	71	4	⊔	⊔	NOUN
ejpam-6339	71	5	j∈j	j∈j	NOUN
ejpam-6339	71	6	nj	nj	PROPN
ejpam-6339	71	7	c	c	PUNCT
ejpam-6339	72	1	=	=	PUNCT
ejpam-6339	72	2	l	l	NOUN
ejpam-6339	72	3	j∈j	j∈j	NOUN
ejpam-6339	72	4	n	n	PROPN
ejpam-6339	72	5	c	c	PROPN
ejpam-6339	72	6	j	j	PROPN
ejpam-6339	72	7	.	.	PUNCT
ejpam-6339	73	1	definition	definition	NOUN
ejpam-6339	73	2	4	4	NUM
ejpam-6339	73	3	.	.	PUNCT
ejpam-6339	74	1	[	[	X
ejpam-6339	74	2	10	10	NUM
ejpam-6339	74	3	]	]	X
ejpam-6339	74	4	a	a	DET
ejpam-6339	74	5	neutrosophic	neutrosophic	ADJ
ejpam-6339	74	6	topology	topology	NOUN
ejpam-6339	74	7	(	(	PUNCT
ejpam-6339	74	8	briefly	briefly	NOUN
ejpam-6339	74	9	n	n	PRON
ejpam-6339	74	10	-topology	-topology	NOUN
ejpam-6339	74	11	)	)	PUNCT
ejpam-6339	74	12	on	on	ADP
ejpam-6339	74	13	a	a	DET
ejpam-6339	74	14	set	set	NOUN
ejpam-6339	74	15	x	x	PUNCT
ejpam-6339	74	16	is	be	AUX
ejpam-6339	74	17	a	a	DET
ejpam-6339	74	18	collection	collection	NOUN
ejpam-6339	74	19	τ	τ	X
ejpam-6339	74	20	⊆	⊆	NUM
ejpam-6339	74	21	n	n	PRON
ejpam-6339	74	22	(	(	PUNCT
ejpam-6339	74	23	x	x	X
ejpam-6339	74	24	)	)	PUNCT
ejpam-6339	74	25	which	which	PRON
ejpam-6339	74	26	satisfies	satisfy	VERB
ejpam-6339	74	27	the	the	DET
ejpam-6339	74	28	following	follow	VERB
ejpam-6339	74	29	conditions	condition	NOUN
ejpam-6339	74	30	:	:	PUNCT
ejpam-6339	74	31	(	(	PUNCT
ejpam-6339	74	32	1	1	X
ejpam-6339	74	33	)	)	PUNCT
ejpam-6339	74	34	∅̃	∅̃	NOUN
ejpam-6339	74	35	and	and	CCONJ
ejpam-6339	74	36	x̃	x̃	PROPN
ejpam-6339	74	37	are	be	AUX
ejpam-6339	74	38	in	in	ADP
ejpam-6339	74	39	τ	τ	PROPN
ejpam-6339	74	40	.	.	PUNCT
ejpam-6339	75	1	(	(	PUNCT
ejpam-6339	75	2	2	2	X
ejpam-6339	75	3	)	)	PUNCT
ejpam-6339	75	4	the	the	DET
ejpam-6339	75	5	intersection	intersection	NOUN
ejpam-6339	75	6	of	of	ADP
ejpam-6339	75	7	two	two	NUM
ejpam-6339	75	8	n	n	PRON
ejpam-6339	75	9	-sets	-set	NOUN
ejpam-6339	75	10	belonging	belong	VERB
ejpam-6339	75	11	to	to	ADP
ejpam-6339	75	12	τ	τ	PROPN
ejpam-6339	75	13	is	be	AUX
ejpam-6339	75	14	in	in	ADP
ejpam-6339	75	15	τ	τ	PROPN
ejpam-6339	75	16	.	.	PUNCT
ejpam-6339	76	1	(	(	PUNCT
ejpam-6339	76	2	3	3	X
ejpam-6339	76	3	)	)	PUNCT
ejpam-6339	76	4	the	the	DET
ejpam-6339	76	5	union	union	NOUN
ejpam-6339	76	6	of	of	ADP
ejpam-6339	76	7	any	any	DET
ejpam-6339	76	8	collection	collection	NOUN
ejpam-6339	76	9	of	of	ADP
ejpam-6339	76	10	n	n	DET
ejpam-6339	76	11	-sets	-set	NOUN
ejpam-6339	76	12	belonging	belong	VERB
ejpam-6339	76	13	to	to	ADP
ejpam-6339	76	14	τ	τ	PROPN
ejpam-6339	76	15	is	be	AUX
ejpam-6339	76	16	in	in	ADP
ejpam-6339	76	17	τ	τ	PROPN
ejpam-6339	76	18	.	.	PUNCT
ejpam-6339	77	1	a	a	DET
ejpam-6339	77	2	set	set	NOUN
ejpam-6339	77	3	x	x	PUNCT
ejpam-6339	77	4	for	for	ADP
ejpam-6339	77	5	which	which	PRON
ejpam-6339	77	6	a	a	DET
ejpam-6339	77	7	n	n	PRON
ejpam-6339	77	8	-topology	-topology	NOUN
ejpam-6339	77	9	τ	τ	PROPN
ejpam-6339	77	10	has	have	AUX
ejpam-6339	77	11	been	be	AUX
ejpam-6339	77	12	defined	define	VERB
ejpam-6339	77	13	is	be	AUX
ejpam-6339	77	14	called	call	VERB
ejpam-6339	77	15	a	a	DET
ejpam-6339	77	16	n	n	NUM
ejpam-6339	77	17	-topological	-topological	ADJ
ejpam-6339	77	18	space	space	NOUN
ejpam-6339	77	19	and	and	CCONJ
ejpam-6339	77	20	is	be	AUX
ejpam-6339	77	21	denoted	denote	VERB
ejpam-6339	77	22	as	as	ADP
ejpam-6339	77	23	a	a	DET
ejpam-6339	77	24	pair	pair	NOUN
ejpam-6339	77	25	(	(	PUNCT
ejpam-6339	77	26	x	x	X
ejpam-6339	77	27	,	,	PUNCT
ejpam-6339	77	28	τ	τ	PROPN
ejpam-6339	77	29	)	)	PUNCT
ejpam-6339	77	30	.	.	PUNCT
ejpam-6339	78	1	if	if	SCONJ
ejpam-6339	78	2	n	n	PRON
ejpam-6339	78	3	∈	∈	PROPN
ejpam-6339	78	4	τ	τ	X
ejpam-6339	78	5	,	,	PUNCT
ejpam-6339	78	6	then	then	ADV
ejpam-6339	78	7	n	n	CCONJ
ejpam-6339	78	8	is	be	AUX
ejpam-6339	78	9	called	call	VERB
ejpam-6339	78	10	a	a	DET
ejpam-6339	78	11	n	n	ADV
ejpam-6339	78	12	-open	-open	NOUN
ejpam-6339	78	13	set	set	NOUN
ejpam-6339	78	14	and	and	CCONJ
ejpam-6339	78	15	if	if	SCONJ
ejpam-6339	78	16	n	n	PRON
ejpam-6339	78	17	c	c	NOUN
ejpam-6339	78	18	∈	∈	PROPN
ejpam-6339	78	19	τ	τ	X
ejpam-6339	78	20	,	,	PUNCT
ejpam-6339	78	21	then	then	ADV
ejpam-6339	78	22	n	n	CCONJ
ejpam-6339	78	23	is	be	AUX
ejpam-6339	78	24	called	call	VERB
ejpam-6339	78	25	a	a	DET
ejpam-6339	78	26	n	n	ADV
ejpam-6339	78	27	-closed	-close	VERB
ejpam-6339	78	28	set	set	NOUN
ejpam-6339	78	29	.	.	PUNCT
ejpam-6339	79	1	we	we	PRON
ejpam-6339	79	2	denote	denote	VERB
ejpam-6339	79	3	by	by	ADP
ejpam-6339	79	4	τ	τ	PROPN
ejpam-6339	79	5	c	c	NOUN
ejpam-6339	79	6	the	the	DET
ejpam-6339	79	7	collection	collection	NOUN
ejpam-6339	79	8	of	of	ADP
ejpam-6339	79	9	all	all	DET
ejpam-6339	79	10	n	n	ADV
ejpam-6339	79	11	-closed	-close	VERB
ejpam-6339	79	12	sets	set	NOUN
ejpam-6339	79	13	in	in	ADP
ejpam-6339	79	14	the	the	DET
ejpam-6339	79	15	n	n	CCONJ
ejpam-6339	79	16	-topological	-topological	ADJ
ejpam-6339	79	17	space	space	NOUN
ejpam-6339	79	18	(	(	PUNCT
ejpam-6339	79	19	x	x	X
ejpam-6339	79	20	,	,	PUNCT
ejpam-6339	79	21	τ	τ	PROPN
ejpam-6339	79	22	)	)	PUNCT
ejpam-6339	79	23	.	.	PUNCT
ejpam-6339	80	1	j.	j.	PROPN
ejpam-6339	80	2	sanabria	sanabria	PROPN
ejpam-6339	80	3	,	,	PUNCT
ejpam-6339	80	4	e.	e.	PROPN
ejpam-6339	80	5	rosas	rosas	PROPN
ejpam-6339	80	6	,	,	PUNCT
ejpam-6339	80	7	c.	c.	PROPN
ejpam-6339	80	8	granados	granados	PROPN
ejpam-6339	80	9	/	/	PUNCT
ejpam-6339	80	10	eur	eur	PROPN
ejpam-6339	80	11	.	.	PUNCT
ejpam-6339	81	1	j.	j.	PROPN
ejpam-6339	81	2	pure	pure	PROPN
ejpam-6339	81	3	appl	appl	PROPN
ejpam-6339	81	4	.	.	PROPN
ejpam-6339	81	5	math	math	PROPN
ejpam-6339	81	6	,	,	PUNCT
ejpam-6339	81	7	18	18	NUM
ejpam-6339	81	8	(	(	PUNCT
ejpam-6339	81	9	3	3	NUM
ejpam-6339	81	10	)	)	PUNCT
ejpam-6339	81	11	(	(	PUNCT
ejpam-6339	81	12	2025	2025	NUM
ejpam-6339	81	13	)	)	PUNCT
ejpam-6339	81	14	,	,	PUNCT
ejpam-6339	81	15	6339	6339	NUM
ejpam-6339	81	16	5	5	NUM
ejpam-6339	81	17	of	of	ADP
ejpam-6339	81	18	15	15	NUM
ejpam-6339	81	19	proposition	proposition	NOUN
ejpam-6339	81	20	3	3	NUM
ejpam-6339	81	21	.	.	PUNCT
ejpam-6339	82	1	[	[	X
ejpam-6339	82	2	10	10	NUM
ejpam-6339	82	3	]	]	X
ejpam-6339	82	4	let	let	VERB
ejpam-6339	82	5	(	(	PUNCT
ejpam-6339	82	6	x	x	NOUN
ejpam-6339	82	7	,	,	PUNCT
ejpam-6339	82	8	τ	τ	X
ejpam-6339	82	9	)	)	PUNCT
ejpam-6339	82	10	be	be	VERB
ejpam-6339	82	11	a	a	DET
ejpam-6339	82	12	n	n	CCONJ
ejpam-6339	82	13	-topological	-topological	ADJ
ejpam-6339	82	14	space	space	NOUN
ejpam-6339	82	15	.	.	PUNCT
ejpam-6339	83	1	then	then	ADV
ejpam-6339	83	2	,	,	PUNCT
ejpam-6339	83	3	the	the	DET
ejpam-6339	83	4	following	follow	VERB
ejpam-6339	83	5	conditions	condition	NOUN
ejpam-6339	83	6	hold	hold	VERB
ejpam-6339	83	7	:	:	PUNCT
ejpam-6339	83	8	(	(	PUNCT
ejpam-6339	83	9	1	1	X
ejpam-6339	83	10	)	)	PUNCT
ejpam-6339	83	11	∅̃	∅̃	NOUN
ejpam-6339	83	12	and	and	CCONJ
ejpam-6339	83	13	x̃	x̃	PROPN
ejpam-6339	83	14	are	be	AUX
ejpam-6339	83	15	in	in	ADP
ejpam-6339	83	16	τ	τ	PROPN
ejpam-6339	83	17	c.	c.	PROPN
ejpam-6339	83	18	(	(	PUNCT
ejpam-6339	83	19	2	2	X
ejpam-6339	83	20	)	)	PUNCT
ejpam-6339	83	21	the	the	DET
ejpam-6339	83	22	union	union	NOUN
ejpam-6339	83	23	of	of	ADP
ejpam-6339	83	24	two	two	NUM
ejpam-6339	83	25	n	n	PRON
ejpam-6339	83	26	-sets	-set	NOUN
ejpam-6339	83	27	belonging	belong	VERB
ejpam-6339	83	28	to	to	ADP
ejpam-6339	83	29	τ	τ	PROPN
ejpam-6339	83	30	c	c	PROPN
ejpam-6339	83	31	is	be	AUX
ejpam-6339	83	32	in	in	ADP
ejpam-6339	83	33	τ	τ	PROPN
ejpam-6339	83	34	c.	c.	PROPN
ejpam-6339	83	35	(	(	PUNCT
ejpam-6339	83	36	3	3	X
ejpam-6339	83	37	)	)	PUNCT
ejpam-6339	83	38	the	the	DET
ejpam-6339	83	39	intersection	intersection	NOUN
ejpam-6339	83	40	of	of	ADP
ejpam-6339	83	41	any	any	DET
ejpam-6339	83	42	collection	collection	NOUN
ejpam-6339	83	43	of	of	ADP
ejpam-6339	83	44	n	n	DET
ejpam-6339	83	45	-sets	-set	NOUN
ejpam-6339	83	46	belonging	belong	VERB
ejpam-6339	83	47	to	to	ADP
ejpam-6339	83	48	τ	τ	PROPN
ejpam-6339	83	49	c	c	PROPN
ejpam-6339	83	50	is	be	AUX
ejpam-6339	83	51	in	in	ADP
ejpam-6339	83	52	τ	τ	PROPN
ejpam-6339	83	53	c.	c.	PROPN
ejpam-6339	83	54	definition	definition	NOUN
ejpam-6339	83	55	5	5	NUM
ejpam-6339	83	56	.	.	PUNCT
ejpam-6339	84	1	[	[	X
ejpam-6339	84	2	10	10	NUM
ejpam-6339	84	3	]	]	X
ejpam-6339	84	4	let	let	VERB
ejpam-6339	84	5	(	(	PUNCT
ejpam-6339	84	6	x	x	NOUN
ejpam-6339	84	7	,	,	PUNCT
ejpam-6339	84	8	τ	τ	X
ejpam-6339	84	9	)	)	PUNCT
ejpam-6339	84	10	be	be	VERB
ejpam-6339	84	11	a	a	DET
ejpam-6339	84	12	n	n	CCONJ
ejpam-6339	84	13	-topological	-topological	ADJ
ejpam-6339	84	14	space	space	NOUN
ejpam-6339	84	15	and	and	CCONJ
ejpam-6339	84	16	n	n	CCONJ
ejpam-6339	84	17	∈	∈	PROPN
ejpam-6339	84	18	n	n	CCONJ
ejpam-6339	84	19	(	(	PUNCT
ejpam-6339	84	20	x	x	NOUN
ejpam-6339	84	21	)	)	PUNCT
ejpam-6339	84	22	.	.	PUNCT
ejpam-6339	85	1	the	the	DET
ejpam-6339	85	2	n	n	PRON
ejpam-6339	85	3	-closure	-closure	NOUN
ejpam-6339	85	4	of	of	ADP
ejpam-6339	85	5	n	n	PROPN
ejpam-6339	85	6	,	,	PUNCT
ejpam-6339	85	7	denoted	denote	VERB
ejpam-6339	85	8	by	by	ADP
ejpam-6339	85	9	cl(n	cl(n	NOUN
ejpam-6339	85	10	)	)	PUNCT
ejpam-6339	85	11	,	,	PUNCT
ejpam-6339	85	12	is	be	AUX
ejpam-6339	85	13	defined	define	VERB
ejpam-6339	85	14	as	as	ADP
ejpam-6339	85	15	cl(n	cl(n	NOUN
ejpam-6339	85	16	)	)	PUNCT
ejpam-6339	86	1	=	=	PUNCT
ejpam-6339	86	2	l	l	NOUN
ejpam-6339	86	3	{	{	PUNCT
ejpam-6339	86	4	f	f	PROPN
ejpam-6339	86	5	∈	∈	PROPN
ejpam-6339	86	6	n	n	PRON
ejpam-6339	86	7	(	(	PUNCT
ejpam-6339	86	8	x	x	X
ejpam-6339	86	9	)	)	PUNCT
ejpam-6339	86	10	:	:	PUNCT
ejpam-6339	87	1	n	n	CCONJ
ejpam-6339	87	2	⊑	⊑	PRON
ejpam-6339	87	3	f	f	PROPN
ejpam-6339	87	4	and	and	CCONJ
ejpam-6339	87	5	f	f	PROPN
ejpam-6339	87	6	∈	∈	PROPN
ejpam-6339	87	7	τ	τ	X
ejpam-6339	87	8	c	c	NOUN
ejpam-6339	87	9	}	}	PUNCT
ejpam-6339	87	10	.	.	PUNCT
ejpam-6339	88	1	proposition	proposition	NOUN
ejpam-6339	88	2	4	4	NUM
ejpam-6339	88	3	.	.	PUNCT
ejpam-6339	89	1	[	[	X
ejpam-6339	89	2	10	10	NUM
ejpam-6339	89	3	]	]	X
ejpam-6339	89	4	let	let	VERB
ejpam-6339	89	5	(	(	PUNCT
ejpam-6339	89	6	x	x	NOUN
ejpam-6339	89	7	,	,	PUNCT
ejpam-6339	89	8	τ	τ	X
ejpam-6339	89	9	)	)	PUNCT
ejpam-6339	89	10	be	be	VERB
ejpam-6339	89	11	a	a	DET
ejpam-6339	89	12	n	n	CCONJ
ejpam-6339	89	13	-topological	-topological	ADJ
ejpam-6339	89	14	space	space	NOUN
ejpam-6339	89	15	and	and	CCONJ
ejpam-6339	89	16	n	n	CCONJ
ejpam-6339	89	17	,	,	PUNCT
ejpam-6339	89	18	m	m	VERB
ejpam-6339	89	19	∈	∈	ADJ
ejpam-6339	89	20	n	n	CCONJ
ejpam-6339	89	21	(	(	PUNCT
ejpam-6339	89	22	x	x	NOUN
ejpam-6339	89	23	)	)	PUNCT
ejpam-6339	89	24	.	.	PUNCT
ejpam-6339	90	1	then	then	ADV
ejpam-6339	90	2	,	,	PUNCT
ejpam-6339	90	3	the	the	DET
ejpam-6339	90	4	following	follow	VERB
ejpam-6339	90	5	conditions	condition	NOUN
ejpam-6339	90	6	hold	hold	VERB
ejpam-6339	90	7	:	:	PUNCT
ejpam-6339	90	8	(	(	PUNCT
ejpam-6339	90	9	1	1	X
ejpam-6339	90	10	)	)	PUNCT
ejpam-6339	90	11	n	n	CCONJ
ejpam-6339	90	12	⊑	⊑	PRON
ejpam-6339	90	13	cl(n	cl(n	NUM
ejpam-6339	90	14	)	)	PUNCT
ejpam-6339	90	15	.	.	PUNCT
ejpam-6339	91	1	(	(	PUNCT
ejpam-6339	91	2	2	2	X
ejpam-6339	91	3	)	)	PUNCT
ejpam-6339	91	4	cl(cl(n	cl(cl(n	PROPN
ejpam-6339	91	5	)	)	PUNCT
ejpam-6339	91	6	)	)	PUNCT
ejpam-6339	92	1	=	=	SYM
ejpam-6339	92	2	cl(n	cl(n	X
ejpam-6339	92	3	)	)	PUNCT
ejpam-6339	92	4	.	.	PUNCT
ejpam-6339	93	1	(	(	PUNCT
ejpam-6339	93	2	3	3	X
ejpam-6339	93	3	)	)	PUNCT
ejpam-6339	93	4	cl(n	cl(n	PUNCT
ejpam-6339	93	5	⊔m	⊔m	NOUN
ejpam-6339	93	6	)	)	PUNCT
ejpam-6339	94	1	=	=	SYM
ejpam-6339	94	2	cl(n	cl(n	X
ejpam-6339	94	3	)	)	PUNCT
ejpam-6339	94	4	⊔	⊔	NUM
ejpam-6339	94	5	cl(m	cl(m	NOUN
ejpam-6339	94	6	)	)	PUNCT
ejpam-6339	94	7	.	.	PUNCT
ejpam-6339	95	1	(	(	PUNCT
ejpam-6339	95	2	4	4	X
ejpam-6339	95	3	)	)	PUNCT
ejpam-6339	95	4	cl(∅̃	cl(∅̃	PROPN
ejpam-6339	95	5	)	)	PUNCT
ejpam-6339	96	1	=	=	PUNCT
ejpam-6339	96	2	∅̃.	∅̃.	NOUN
ejpam-6339	96	3	(	(	PUNCT
ejpam-6339	96	4	5	5	NUM
ejpam-6339	96	5	)	)	PUNCT
ejpam-6339	96	6	cl(x̃	cl(x̃	PROPN
ejpam-6339	96	7	)	)	PUNCT
ejpam-6339	96	8	=	=	SYM
ejpam-6339	97	1	x̃.	x̃.	ADJ
ejpam-6339	97	2	(	(	PUNCT
ejpam-6339	97	3	6	6	NUM
ejpam-6339	97	4	)	)	PUNCT
ejpam-6339	97	5	if	if	SCONJ
ejpam-6339	97	6	n	n	PRON
ejpam-6339	97	7	⊑m	⊑m	NOUN
ejpam-6339	97	8	,	,	PUNCT
ejpam-6339	97	9	then	then	ADV
ejpam-6339	97	10	cl(n	cl(n	NOUN
ejpam-6339	97	11	)	)	PUNCT
ejpam-6339	97	12	⊑	⊑	PRON
ejpam-6339	97	13	cl(m	cl(m	PROPN
ejpam-6339	97	14	)	)	PUNCT
ejpam-6339	97	15	.	.	PUNCT
ejpam-6339	98	1	(	(	PUNCT
ejpam-6339	98	2	7	7	NUM
ejpam-6339	98	3	)	)	PUNCT
ejpam-6339	98	4	cl(n	cl(n	PUNCT
ejpam-6339	98	5	⊓m	⊓m	NOUN
ejpam-6339	98	6	)	)	PUNCT
ejpam-6339	98	7	⊑	⊑	PRON
ejpam-6339	98	8	cl(n	cl(n	X
ejpam-6339	98	9	)	)	PUNCT
ejpam-6339	98	10	⊓	⊓	PROPN
ejpam-6339	98	11	cl(m	cl(m	NUM
ejpam-6339	98	12	)	)	PUNCT
ejpam-6339	98	13	.	.	PUNCT
ejpam-6339	99	1	(	(	PUNCT
ejpam-6339	99	2	8)	8)	NUM
ejpam-6339	99	3	n	n	PRON
ejpam-6339	99	4	∈	∈	NOUN
ejpam-6339	99	5	τ	τ	X
ejpam-6339	99	6	c	c	NOUN
ejpam-6339	100	1	if	if	SCONJ
ejpam-6339	101	1	and	and	CCONJ
ejpam-6339	101	2	only	only	ADV
ejpam-6339	101	3	if	if	SCONJ
ejpam-6339	101	4	n	n	X
ejpam-6339	101	5	=	=	SYM
ejpam-6339	101	6	cl(n	cl(n	X
ejpam-6339	101	7	)	)	PUNCT
ejpam-6339	101	8	.	.	PUNCT
ejpam-6339	102	1	definition	definition	NOUN
ejpam-6339	102	2	6	6	NUM
ejpam-6339	102	3	.	.	PUNCT
ejpam-6339	103	1	[	[	X
ejpam-6339	103	2	5	5	NUM
ejpam-6339	103	3	]	]	PUNCT
ejpam-6339	103	4	a	a	DET
ejpam-6339	103	5	n	n	ADV
ejpam-6339	103	6	-set	-set	NOUN
ejpam-6339	103	7	m	m	VERB
ejpam-6339	103	8	=	=	NOUN
ejpam-6339	103	9	{	{	PUNCT
ejpam-6339	103	10	⟨x	⟨x	VERB
ejpam-6339	103	11	,	,	PUNCT
ejpam-6339	103	12	µm	µm	ADP
ejpam-6339	103	13	(	(	PUNCT
ejpam-6339	103	14	x	x	NOUN
ejpam-6339	103	15	)	)	PUNCT
ejpam-6339	103	16	,	,	PUNCT
ejpam-6339	103	17	σm	σm	X
ejpam-6339	103	18	(	(	PUNCT
ejpam-6339	103	19	x	x	NOUN
ejpam-6339	103	20	)	)	PUNCT
ejpam-6339	103	21	,	,	PUNCT
ejpam-6339	103	22	γm	γm	X
ejpam-6339	103	23	(	(	PUNCT
ejpam-6339	103	24	x)⟩	x)⟩	NOUN
ejpam-6339	103	25	:	:	PUNCT
ejpam-6339	103	26	x	x	SYM
ejpam-6339	103	27	∈	∈	PROPN
ejpam-6339	103	28	x	x	VERB
ejpam-6339	103	29	}	}	PUNCT
ejpam-6339	103	30	is	be	AUX
ejpam-6339	103	31	called	call	VERB
ejpam-6339	103	32	a	a	DET
ejpam-6339	103	33	n	n	NUM
ejpam-6339	103	34	-point	-point	NOUN
ejpam-6339	103	35	if	if	SCONJ
ejpam-6339	103	36	for	for	ADP
ejpam-6339	103	37	any	any	DET
ejpam-6339	103	38	element	element	NOUN
ejpam-6339	103	39	y	y	PROPN
ejpam-6339	103	40	∈	∈	PROPN
ejpam-6339	103	41	x	x	X
ejpam-6339	103	42	,	,	PUNCT
ejpam-6339	103	43	µm	µm	ADP
ejpam-6339	103	44	(	(	PUNCT
ejpam-6339	103	45	y	y	NOUN
ejpam-6339	103	46	)	)	PUNCT
ejpam-6339	103	47	=	=	SYM
ejpam-6339	103	48	a	a	PROPN
ejpam-6339	103	49	,	,	PUNCT
ejpam-6339	103	50	σm	σm	INTJ
ejpam-6339	103	51	(	(	PUNCT
ejpam-6339	103	52	y	y	NOUN
ejpam-6339	103	53	)	)	PUNCT
ejpam-6339	103	54	=	=	SYM
ejpam-6339	103	55	b	b	NOUN
ejpam-6339	103	56	,	,	PUNCT
ejpam-6339	103	57	γm	γm	ADJ
ejpam-6339	103	58	(	(	PUNCT
ejpam-6339	103	59	y	y	NOUN
ejpam-6339	103	60	)	)	PUNCT
ejpam-6339	104	1	=	=	SYM
ejpam-6339	105	1	c	c	PROPN
ejpam-6339	105	2	for	for	ADP
ejpam-6339	105	3	y	y	PROPN
ejpam-6339	105	4	=	=	PUNCT
ejpam-6339	105	5	x	x	PROPN
ejpam-6339	105	6	and	and	CCONJ
ejpam-6339	105	7	µm	µm	ADP
ejpam-6339	105	8	(	(	PUNCT
ejpam-6339	105	9	y	y	NOUN
ejpam-6339	105	10	)	)	PUNCT
ejpam-6339	105	11	=	=	SYM
ejpam-6339	106	1	0	0	NUM
ejpam-6339	106	2	,	,	PUNCT
ejpam-6339	106	3	σm	σm	INTJ
ejpam-6339	106	4	(	(	PUNCT
ejpam-6339	106	5	y	y	NOUN
ejpam-6339	106	6	)	)	PUNCT
ejpam-6339	106	7	=	=	SYM
ejpam-6339	106	8	1	1	NUM
ejpam-6339	106	9	,	,	PUNCT
ejpam-6339	106	10	γm	γm	ADJ
ejpam-6339	106	11	(	(	PUNCT
ejpam-6339	106	12	y	y	NOUN
ejpam-6339	106	13	)	)	PUNCT
ejpam-6339	106	14	=	=	SYM
ejpam-6339	106	15	1	1	NUM
ejpam-6339	106	16	for	for	ADP
ejpam-6339	106	17	y	y	PROPN
ejpam-6339	106	18	̸=	̸=	PROPN
ejpam-6339	106	19	x	x	NUM
ejpam-6339	106	20	,	,	PUNCT
ejpam-6339	106	21	where	where	SCONJ
ejpam-6339	106	22	a	a	DET
ejpam-6339	106	23	∈	∈	NOUN
ejpam-6339	106	24	(	(	PUNCT
ejpam-6339	106	25	0	0	NUM
ejpam-6339	106	26	,	,	PUNCT
ejpam-6339	106	27	1	1	NUM
ejpam-6339	106	28	]	]	PUNCT
ejpam-6339	106	29	and	and	CCONJ
ejpam-6339	106	30	b	b	NOUN
ejpam-6339	106	31	,	,	PUNCT
ejpam-6339	106	32	c	c	PROPN
ejpam-6339	106	33	∈	∈	PROPN
ejpam-6339	107	1	[	[	X
ejpam-6339	107	2	0	0	NUM
ejpam-6339	107	3	,	,	PUNCT
ejpam-6339	107	4	1	1	NUM
ejpam-6339	107	5	)	)	PUNCT
ejpam-6339	107	6	.	.	PUNCT
ejpam-6339	108	1	in	in	ADP
ejpam-6339	108	2	this	this	DET
ejpam-6339	108	3	case	case	NOUN
ejpam-6339	108	4	,	,	PUNCT
ejpam-6339	108	5	the	the	DET
ejpam-6339	108	6	n	n	PRON
ejpam-6339	108	7	-point	-point	NOUN
ejpam-6339	108	8	m	m	VERB
ejpam-6339	108	9	is	be	AUX
ejpam-6339	108	10	denoted	denote	VERB
ejpam-6339	108	11	by	by	ADP
ejpam-6339	108	12	mx	mx	PROPN
ejpam-6339	108	13	a	a	PRON
ejpam-6339	108	14	,	,	PUNCT
ejpam-6339	108	15	b	b	NOUN
ejpam-6339	108	16	,	,	PUNCT
ejpam-6339	108	17	c	c	NOUN
ejpam-6339	108	18	or	or	CCONJ
ejpam-6339	108	19	simply	simply	ADV
ejpam-6339	108	20	by	by	ADP
ejpam-6339	108	21	xa	xa	PROPN
ejpam-6339	108	22	,	,	PUNCT
ejpam-6339	108	23	b	b	PROPN
ejpam-6339	108	24	,	,	PUNCT
ejpam-6339	108	25	c.	c.	PROPN
ejpam-6339	108	26	also	also	ADV
ejpam-6339	108	27	,	,	PUNCT
ejpam-6339	108	28	x	x	VERB
ejpam-6339	108	29	is	be	AUX
ejpam-6339	108	30	called	call	VERB
ejpam-6339	108	31	the	the	DET
ejpam-6339	108	32	support	support	NOUN
ejpam-6339	108	33	of	of	ADP
ejpam-6339	108	34	the	the	DET
ejpam-6339	108	35	n	n	PROPN
ejpam-6339	108	36	-point	-point	PROPN
ejpam-6339	108	37	xa	xa	PROPN
ejpam-6339	108	38	,	,	PUNCT
ejpam-6339	108	39	b	b	PROPN
ejpam-6339	108	40	,	,	PUNCT
ejpam-6339	108	41	c.	c.	PROPN
ejpam-6339	108	42	the	the	DET
ejpam-6339	108	43	n	n	NUM
ejpam-6339	108	44	-point	-point	NOUN
ejpam-6339	108	45	x1,0,0	x1,0,0	PROPN
ejpam-6339	108	46	is	be	AUX
ejpam-6339	108	47	called	call	VERB
ejpam-6339	108	48	a	a	DET
ejpam-6339	108	49	n	n	NUM
ejpam-6339	108	50	-crisp	-crisp	NOUN
ejpam-6339	108	51	point	point	NOUN
ejpam-6339	108	52	.	.	PUNCT
ejpam-6339	109	1	definition	definition	NOUN
ejpam-6339	109	2	7	7	NUM
ejpam-6339	109	3	.	.	PUNCT
ejpam-6339	110	1	[	[	X
ejpam-6339	110	2	5	5	NUM
ejpam-6339	110	3	]	]	PUNCT
ejpam-6339	110	4	let	let	VERB
ejpam-6339	110	5	n	n	PRON
ejpam-6339	110	6	∈	∈	PROPN
ejpam-6339	110	7	n	n	CCONJ
ejpam-6339	110	8	(	(	PUNCT
ejpam-6339	110	9	x	x	NOUN
ejpam-6339	110	10	)	)	PUNCT
ejpam-6339	110	11	.	.	PUNCT
ejpam-6339	111	1	a	a	PRON
ejpam-6339	111	2	n	n	CCONJ
ejpam-6339	111	3	-point	-point	PROPN
ejpam-6339	111	4	xa	xa	PROPN
ejpam-6339	111	5	,	,	PUNCT
ejpam-6339	111	6	b	b	PROPN
ejpam-6339	111	7	,	,	PUNCT
ejpam-6339	111	8	c	c	PROPN
ejpam-6339	111	9	is	be	AUX
ejpam-6339	111	10	said	say	VERB
ejpam-6339	111	11	to	to	PART
ejpam-6339	111	12	belong	belong	VERB
ejpam-6339	111	13	to	to	ADP
ejpam-6339	111	14	n	n	PROPN
ejpam-6339	111	15	,	,	PUNCT
ejpam-6339	111	16	denoted	denote	VERB
ejpam-6339	111	17	by	by	ADP
ejpam-6339	111	18	xa	xa	PROPN
ejpam-6339	111	19	,	,	PUNCT
ejpam-6339	111	20	b	b	PROPN
ejpam-6339	111	21	,	,	PUNCT
ejpam-6339	111	22	c	c	PROPN
ejpam-6339	111	23	∈	∈	PROPN
ejpam-6339	111	24	n	n	CCONJ
ejpam-6339	111	25	,	,	PUNCT
ejpam-6339	111	26	if	if	SCONJ
ejpam-6339	111	27	µn	µn	PROPN
ejpam-6339	111	28	(	(	PUNCT
ejpam-6339	111	29	x	x	NOUN
ejpam-6339	111	30	)	)	PUNCT
ejpam-6339	111	31	≥	≥	NOUN
ejpam-6339	111	32	a	a	NOUN
ejpam-6339	111	33	,	,	PUNCT
ejpam-6339	111	34	σn	σn	X
ejpam-6339	111	35	(	(	PUNCT
ejpam-6339	111	36	x	x	NOUN
ejpam-6339	111	37	)	)	PUNCT
ejpam-6339	111	38	≤	≤	NUM
ejpam-6339	111	39	b	b	PROPN
ejpam-6339	111	40	and	and	CCONJ
ejpam-6339	111	41	γn	γn	NOUN
ejpam-6339	111	42	(	(	PUNCT
ejpam-6339	111	43	x	x	NOUN
ejpam-6339	111	44	)	)	PUNCT
ejpam-6339	111	45	≤	≤	ADJ
ejpam-6339	111	46	c.	c.	NOUN
ejpam-6339	111	47	remark	remark	NOUN
ejpam-6339	111	48	1	1	NUM
ejpam-6339	111	49	.	.	PUNCT
ejpam-6339	112	1	it	it	PRON
ejpam-6339	112	2	is	be	AUX
ejpam-6339	112	3	important	important	ADJ
ejpam-6339	112	4	to	to	PART
ejpam-6339	112	5	note	note	VERB
ejpam-6339	112	6	that	that	SCONJ
ejpam-6339	112	7	∅̃	∅̃	NOUN
ejpam-6339	112	8	is	be	AUX
ejpam-6339	112	9	not	not	PART
ejpam-6339	112	10	the	the	DET
ejpam-6339	112	11	only	only	ADJ
ejpam-6339	112	12	n	n	NUM
ejpam-6339	112	13	-set	-set	PUNCT
ejpam-6339	112	14	that	that	PRON
ejpam-6339	112	15	does	do	AUX
ejpam-6339	112	16	not	not	PART
ejpam-6339	112	17	have	have	VERB
ejpam-6339	112	18	points	point	NOUN
ejpam-6339	112	19	belonging	belong	VERB
ejpam-6339	112	20	to	to	ADP
ejpam-6339	112	21	it	it	PRON
ejpam-6339	112	22	.	.	PUNCT
ejpam-6339	113	1	for	for	ADP
ejpam-6339	113	2	example	example	NOUN
ejpam-6339	113	3	,	,	PUNCT
ejpam-6339	113	4	if	if	SCONJ
ejpam-6339	113	5	x	x	X
ejpam-6339	113	6	=	=	PRON
ejpam-6339	113	7	{	{	PUNCT
ejpam-6339	113	8	x	x	PROPN
ejpam-6339	113	9	,	,	PUNCT
ejpam-6339	113	10	y	y	PROPN
ejpam-6339	113	11	}	}	PUNCT
ejpam-6339	113	12	,	,	PUNCT
ejpam-6339	113	13	then	then	ADV
ejpam-6339	113	14	n	n	CCONJ
ejpam-6339	113	15	=	=	NOUN
ejpam-6339	113	16	{	{	PUNCT
ejpam-6339	113	17	⟨x	⟨x	VERB
ejpam-6339	113	18	,	,	PUNCT
ejpam-6339	113	19	0	0	NUM
ejpam-6339	113	20	,	,	PUNCT
ejpam-6339	113	21	0.5	0.5	NUM
ejpam-6339	113	22	,	,	PUNCT
ejpam-6339	113	23	1⟩	1⟩	NUM
ejpam-6339	113	24	,	,	PUNCT
ejpam-6339	113	25	⟨y	⟨y	X
ejpam-6339	113	26	,	,	PUNCT
ejpam-6339	113	27	0	0	NUM
ejpam-6339	113	28	,	,	PUNCT
ejpam-6339	113	29	0.4	0.4	NUM
ejpam-6339	113	30	,	,	PUNCT
ejpam-6339	113	31	1⟩	1⟩	NUM
ejpam-6339	113	32	}	}	PUNCT
ejpam-6339	113	33	is	be	AUX
ejpam-6339	113	34	a	a	DET
ejpam-6339	113	35	n	n	ADV
ejpam-6339	113	36	-set	-set	PUNCT
ejpam-6339	113	37	over	over	ADP
ejpam-6339	113	38	x	x	PUNCT
ejpam-6339	113	39	for	for	ADP
ejpam-6339	113	40	which	which	PRON
ejpam-6339	113	41	there	there	PRON
ejpam-6339	113	42	are	be	VERB
ejpam-6339	113	43	not	not	PART
ejpam-6339	113	44	n	n	PRON
ejpam-6339	113	45	-points	-point	NOUN
ejpam-6339	113	46	belonging	belong	VERB
ejpam-6339	113	47	to	to	ADP
ejpam-6339	113	48	it	it	PRON
ejpam-6339	113	49	.	.	PUNCT
ejpam-6339	114	1	lemma	lemma	PROPN
ejpam-6339	114	2	1	1	NUM
ejpam-6339	114	3	.	.	PUNCT
ejpam-6339	115	1	[	[	X
ejpam-6339	115	2	5	5	NUM
ejpam-6339	115	3	]	]	X
ejpam-6339	115	4	let	let	VERB
ejpam-6339	115	5	n	n	PRON
ejpam-6339	115	6	,	,	PUNCT
ejpam-6339	115	7	m	m	VERB
ejpam-6339	115	8	∈	∈	ADJ
ejpam-6339	115	9	n	n	CCONJ
ejpam-6339	115	10	(	(	PUNCT
ejpam-6339	115	11	x	x	NOUN
ejpam-6339	115	12	)	)	PUNCT
ejpam-6339	115	13	.	.	PUNCT
ejpam-6339	116	1	then	then	ADV
ejpam-6339	116	2	,	,	PUNCT
ejpam-6339	116	3	we	we	PRON
ejpam-6339	116	4	have	have	VERB
ejpam-6339	116	5	:	:	PUNCT
ejpam-6339	116	6	(	(	PUNCT
ejpam-6339	116	7	1	1	X
ejpam-6339	116	8	)	)	PUNCT
ejpam-6339	116	9	n	n	NOUN
ejpam-6339	116	10	=	=	SYM
ejpam-6339	116	11	⊔	⊔	PROPN
ejpam-6339	116	12	{	{	PUNCT
ejpam-6339	116	13	xa	xa	PROPN
ejpam-6339	116	14	,	,	PUNCT
ejpam-6339	116	15	b	b	PROPN
ejpam-6339	116	16	,	,	PUNCT
ejpam-6339	116	17	c	c	NOUN
ejpam-6339	116	18	:	:	PUNCT
ejpam-6339	116	19	xa	xa	PROPN
ejpam-6339	116	20	,	,	PUNCT
ejpam-6339	116	21	b	b	PROPN
ejpam-6339	116	22	,	,	PUNCT
ejpam-6339	116	23	c	c	PROPN
ejpam-6339	116	24	∈	∈	PROPN
ejpam-6339	116	25	n	n	CCONJ
ejpam-6339	116	26	}	}	PUNCT
ejpam-6339	116	27	.	.	PUNCT
ejpam-6339	117	1	j.	j.	PROPN
ejpam-6339	117	2	sanabria	sanabria	PROPN
ejpam-6339	117	3	,	,	PUNCT
ejpam-6339	117	4	e.	e.	PROPN
ejpam-6339	117	5	rosas	rosas	PROPN
ejpam-6339	117	6	,	,	PUNCT
ejpam-6339	117	7	c.	c.	PROPN
ejpam-6339	117	8	granados	granados	PROPN
ejpam-6339	117	9	/	/	PUNCT
ejpam-6339	117	10	eur	eur	PROPN
ejpam-6339	117	11	.	.	PUNCT
ejpam-6339	118	1	j.	j.	PROPN
ejpam-6339	118	2	pure	pure	PROPN
ejpam-6339	118	3	appl	appl	PROPN
ejpam-6339	118	4	.	.	PROPN
ejpam-6339	118	5	math	math	PROPN
ejpam-6339	118	6	,	,	PUNCT
ejpam-6339	118	7	18	18	NUM
ejpam-6339	118	8	(	(	PUNCT
ejpam-6339	118	9	3	3	NUM
ejpam-6339	118	10	)	)	PUNCT
ejpam-6339	118	11	(	(	PUNCT
ejpam-6339	118	12	2025	2025	NUM
ejpam-6339	118	13	)	)	PUNCT
ejpam-6339	118	14	,	,	PUNCT
ejpam-6339	118	15	6339	6339	NUM
ejpam-6339	118	16	6	6	NUM
ejpam-6339	118	17	of	of	ADP
ejpam-6339	118	18	15	15	NUM
ejpam-6339	118	19	(	(	PUNCT
ejpam-6339	118	20	2	2	NUM
ejpam-6339	118	21	)	)	PUNCT
ejpam-6339	118	22	if	if	SCONJ
ejpam-6339	118	23	xa	xa	PROPN
ejpam-6339	118	24	,	,	PUNCT
ejpam-6339	118	25	b	b	PROPN
ejpam-6339	118	26	,	,	PUNCT
ejpam-6339	118	27	c	c	PROPN
ejpam-6339	118	28	∈	∈	PROPN
ejpam-6339	118	29	n	n	NOUN
ejpam-6339	118	30	and	and	CCONJ
ejpam-6339	118	31	n	n	CCONJ
ejpam-6339	118	32	⊑m	⊑m	NOUN
ejpam-6339	118	33	,	,	PUNCT
ejpam-6339	118	34	then	then	ADV
ejpam-6339	118	35	xa	xa	PROPN
ejpam-6339	118	36	,	,	PUNCT
ejpam-6339	118	37	b	b	PROPN
ejpam-6339	118	38	,	,	PUNCT
ejpam-6339	118	39	c	c	NOUN
ejpam-6339	118	40	∈m	∈m	NOUN
ejpam-6339	118	41	.	.	PUNCT
ejpam-6339	119	1	definition	definition	NOUN
ejpam-6339	119	2	8	8	NUM
ejpam-6339	119	3	.	.	PUNCT
ejpam-6339	120	1	[	[	X
ejpam-6339	120	2	11	11	NUM
ejpam-6339	120	3	]	]	PUNCT
ejpam-6339	120	4	a	a	PRON
ejpam-6339	120	5	n	n	ADV
ejpam-6339	120	6	-ideal	-ideal	NOUN
ejpam-6339	120	7	on	on	ADP
ejpam-6339	120	8	a	a	DET
ejpam-6339	120	9	set	set	NOUN
ejpam-6339	120	10	x	x	PUNCT
ejpam-6339	120	11	is	be	AUX
ejpam-6339	120	12	a	a	DET
ejpam-6339	120	13	nonempty	nonempty	ADJ
ejpam-6339	120	14	collection	collection	NOUN
ejpam-6339	120	15	l	l	NOUN
ejpam-6339	120	16	⊆	⊆	NUM
ejpam-6339	120	17	n	n	SYM
ejpam-6339	120	18	(	(	PUNCT
ejpam-6339	120	19	x	x	NOUN
ejpam-6339	120	20	)	)	PUNCT
ejpam-6339	120	21	,	,	PUNCT
ejpam-6339	120	22	which	which	PRON
ejpam-6339	120	23	satisfies	satisfy	VERB
ejpam-6339	120	24	the	the	DET
ejpam-6339	120	25	following	follow	VERB
ejpam-6339	120	26	conditions	condition	NOUN
ejpam-6339	120	27	:	:	PUNCT
ejpam-6339	120	28	(	(	PUNCT
ejpam-6339	120	29	1	1	X
ejpam-6339	120	30	)	)	PUNCT
ejpam-6339	120	31	n	n	DET
ejpam-6339	120	32	∈	∈	NOUN
ejpam-6339	120	33	l	l	NOUN
ejpam-6339	120	34	and	and	CCONJ
ejpam-6339	120	35	m	m	PRON
ejpam-6339	120	36	⊑	⊑	X
ejpam-6339	120	37	n	n	ADV
ejpam-6339	120	38	imply	imply	VERB
ejpam-6339	120	39	that	that	SCONJ
ejpam-6339	120	40	m	m	PROPN
ejpam-6339	120	41	∈	∈	PROPN
ejpam-6339	120	42	l.	l.	NOUN
ejpam-6339	120	43	(	(	PUNCT
ejpam-6339	120	44	hereditary	hereditary	ADJ
ejpam-6339	120	45	property	property	NOUN
ejpam-6339	120	46	)	)	PUNCT
ejpam-6339	120	47	(	(	PUNCT
ejpam-6339	120	48	2	2	NUM
ejpam-6339	120	49	)	)	PUNCT
ejpam-6339	120	50	n	n	CCONJ
ejpam-6339	120	51	,	,	PUNCT
ejpam-6339	120	52	m	m	PROPN
ejpam-6339	120	53	∈	∈	NOUN
ejpam-6339	120	54	l	l	NOUN
ejpam-6339	120	55	imply	imply	VERB
ejpam-6339	120	56	that	that	SCONJ
ejpam-6339	120	57	n	n	X
ejpam-6339	120	58	⊔m	⊔m	NUM
ejpam-6339	120	59	∈	∈	PROPN
ejpam-6339	120	60	l.	l.	PROPN
ejpam-6339	120	61	(	(	PUNCT
ejpam-6339	120	62	finite	finite	VERB
ejpam-6339	120	63	additivity	additivity	NOUN
ejpam-6339	120	64	property	property	NOUN
ejpam-6339	120	65	)	)	PUNCT
ejpam-6339	120	66	given	give	VERB
ejpam-6339	120	67	a	a	DET
ejpam-6339	120	68	n	n	CCONJ
ejpam-6339	120	69	-topological	-topological	ADJ
ejpam-6339	120	70	space	space	NOUN
ejpam-6339	120	71	(	(	PUNCT
ejpam-6339	120	72	x	x	X
ejpam-6339	120	73	,	,	PUNCT
ejpam-6339	120	74	τ	τ	PROPN
ejpam-6339	120	75	)	)	PUNCT
ejpam-6339	120	76	,	,	PUNCT
ejpam-6339	120	77	a	a	DET
ejpam-6339	120	78	n	n	CCONJ
ejpam-6339	120	79	-ideal	-ideal	ADJ
ejpam-6339	120	80	l	l	NOUN
ejpam-6339	120	81	on	on	ADP
ejpam-6339	120	82	x	x	X
ejpam-6339	120	83	and	and	CCONJ
ejpam-6339	120	84	n	n	CCONJ
ejpam-6339	120	85	∈	∈	PROPN
ejpam-6339	120	86	n	n	CCONJ
ejpam-6339	120	87	(	(	PUNCT
ejpam-6339	120	88	x	x	NOUN
ejpam-6339	120	89	)	)	PUNCT
ejpam-6339	120	90	,	,	PUNCT
ejpam-6339	120	91	the	the	DET
ejpam-6339	120	92	n	n	CCONJ
ejpam-6339	120	93	-local	-local	ADJ
ejpam-6339	120	94	function	function	NOUN
ejpam-6339	120	95	[	[	X
ejpam-6339	120	96	12	12	NUM
ejpam-6339	120	97	]	]	PUNCT
ejpam-6339	120	98	of	of	ADP
ejpam-6339	120	99	n	n	PROPN
ejpam-6339	120	100	,	,	PUNCT
ejpam-6339	120	101	denoted	denote	VERB
ejpam-6339	120	102	by	by	ADP
ejpam-6339	120	103	n⋆(l	n⋆(l	PROPN
ejpam-6339	120	104	,	,	PUNCT
ejpam-6339	120	105	τ	τ	PROPN
ejpam-6339	120	106	)	)	PUNCT
ejpam-6339	120	107	,	,	PUNCT
ejpam-6339	120	108	is	be	AUX
ejpam-6339	120	109	defined	define	VERB
ejpam-6339	120	110	as	as	ADP
ejpam-6339	120	111	n⋆(l	n⋆(l	NOUN
ejpam-6339	120	112	,	,	PUNCT
ejpam-6339	120	113	τ	τ	X
ejpam-6339	120	114	)	)	PUNCT
ejpam-6339	120	115	=	=	SYM
ejpam-6339	120	116	⊔	⊔	PROPN
ejpam-6339	120	117	{	{	PUNCT
ejpam-6339	120	118	xa	xa	PROPN
ejpam-6339	120	119	,	,	PUNCT
ejpam-6339	120	120	b	b	PROPN
ejpam-6339	120	121	,	,	PUNCT
ejpam-6339	120	122	c	c	PROPN
ejpam-6339	120	123	∈	∈	PROPN
ejpam-6339	120	124	n	n	CCONJ
ejpam-6339	120	125	(	(	PUNCT
ejpam-6339	120	126	x	x	X
ejpam-6339	120	127	)	)	PUNCT
ejpam-6339	120	128	:	:	PUNCT
ejpam-6339	121	1	u	u	NOUN
ejpam-6339	121	2	⊓n	⊓n	NOUN
ejpam-6339	121	3	/∈	/∈	PUNCT
ejpam-6339	121	4	l	l	NOUN
ejpam-6339	122	1	for	for	ADP
ejpam-6339	122	2	every	every	DET
ejpam-6339	122	3	u	u	PROPN
ejpam-6339	122	4	∈	∈	PROPN
ejpam-6339	122	5	τ(xa	τ(xa	NUM
ejpam-6339	122	6	,	,	PUNCT
ejpam-6339	122	7	b	b	NOUN
ejpam-6339	122	8	,	,	PUNCT
ejpam-6339	122	9	c	c	NOUN
ejpam-6339	122	10	)	)	PUNCT
ejpam-6339	122	11	}	}	PUNCT
ejpam-6339	122	12	,	,	PUNCT
ejpam-6339	122	13	where	where	SCONJ
ejpam-6339	122	14	τ(xa	τ(xa	NUM
ejpam-6339	122	15	,	,	PUNCT
ejpam-6339	122	16	b	b	NOUN
ejpam-6339	122	17	,	,	PUNCT
ejpam-6339	122	18	c	c	NOUN
ejpam-6339	122	19	)	)	PUNCT
ejpam-6339	122	20	=	=	PRON
ejpam-6339	122	21	{	{	PUNCT
ejpam-6339	122	22	u	u	X
ejpam-6339	122	23	∈	∈	PROPN
ejpam-6339	122	24	τ	τ	X
ejpam-6339	122	25	:	:	PUNCT
ejpam-6339	122	26	xa	xa	PROPN
ejpam-6339	122	27	,	,	PUNCT
ejpam-6339	122	28	b	b	PROPN
ejpam-6339	122	29	,	,	PUNCT
ejpam-6339	122	30	c	c	PROPN
ejpam-6339	122	31	∈	∈	PROPN
ejpam-6339	122	32	u	u	NOUN
ejpam-6339	122	33	}	}	PUNCT
ejpam-6339	122	34	.	.	PUNCT
ejpam-6339	123	1	we	we	PRON
ejpam-6339	123	2	will	will	AUX
ejpam-6339	123	3	denote	denote	VERB
ejpam-6339	123	4	n⋆(l	n⋆(l	PROPN
ejpam-6339	123	5	,	,	PUNCT
ejpam-6339	123	6	τ	τ	X
ejpam-6339	123	7	)	)	PUNCT
ejpam-6339	123	8	by	by	ADP
ejpam-6339	123	9	n⋆	n⋆	PRON
ejpam-6339	123	10	or	or	CCONJ
ejpam-6339	123	11	n⋆(l	n⋆(l	NOUN
ejpam-6339	123	12	)	)	PUNCT
ejpam-6339	123	13	.	.	PUNCT
ejpam-6339	124	1	theorem	theorem	NOUN
ejpam-6339	124	2	1	1	NUM
ejpam-6339	124	3	.	.	PUNCT
ejpam-6339	125	1	[	[	X
ejpam-6339	125	2	12	12	NUM
ejpam-6339	125	3	]	]	X
ejpam-6339	125	4	let	let	AUX
ejpam-6339	125	5	(	(	PUNCT
ejpam-6339	125	6	x	x	NOUN
ejpam-6339	125	7	,	,	PUNCT
ejpam-6339	125	8	τ	τ	X
ejpam-6339	125	9	)	)	PUNCT
ejpam-6339	125	10	be	be	VERB
ejpam-6339	125	11	a	a	DET
ejpam-6339	125	12	n	n	CCONJ
ejpam-6339	125	13	-topological	-topological	ADJ
ejpam-6339	125	14	space	space	NOUN
ejpam-6339	125	15	with	with	ADP
ejpam-6339	125	16	two	two	NUM
ejpam-6339	125	17	n	n	NUM
ejpam-6339	125	18	-ideals	-ideal	NOUN
ejpam-6339	125	19	l	l	NOUN
ejpam-6339	125	20	,	,	PUNCT
ejpam-6339	125	21	l′	l′	VERB
ejpam-6339	125	22	on	on	ADP
ejpam-6339	125	23	x.	x.	NOUN
ejpam-6339	125	24	if	if	SCONJ
ejpam-6339	125	25	n	n	X
ejpam-6339	125	26	,	,	PUNCT
ejpam-6339	125	27	m	m	VERB
ejpam-6339	125	28	∈	∈	ADJ
ejpam-6339	125	29	n	n	CCONJ
ejpam-6339	125	30	(	(	PUNCT
ejpam-6339	125	31	x	x	NOUN
ejpam-6339	125	32	)	)	PUNCT
ejpam-6339	125	33	,	,	PUNCT
ejpam-6339	125	34	then	then	ADV
ejpam-6339	125	35	the	the	DET
ejpam-6339	125	36	following	follow	VERB
ejpam-6339	125	37	properties	property	NOUN
ejpam-6339	125	38	hold	hold	VERB
ejpam-6339	125	39	:	:	PUNCT
ejpam-6339	125	40	(	(	PUNCT
ejpam-6339	125	41	1	1	X
ejpam-6339	125	42	)	)	PUNCT
ejpam-6339	125	43	if	if	SCONJ
ejpam-6339	125	44	n	n	PRON
ejpam-6339	125	45	⊑m	⊑m	VERB
ejpam-6339	125	46	,	,	PUNCT
ejpam-6339	125	47	then	then	ADV
ejpam-6339	125	48	n⋆	n⋆	ADJ
ejpam-6339	125	49	⊑m⋆.	⊑m⋆.	X
ejpam-6339	125	50	(	(	PUNCT
ejpam-6339	125	51	2	2	NUM
ejpam-6339	125	52	)	)	PUNCT
ejpam-6339	125	53	if	if	SCONJ
ejpam-6339	125	54	l	l	NOUN
ejpam-6339	125	55	⊆	⊆	NUM
ejpam-6339	125	56	l′	l′	NOUN
ejpam-6339	125	57	,	,	PUNCT
ejpam-6339	125	58	then	then	ADV
ejpam-6339	125	59	n⋆(l′	n⋆(l′	NOUN
ejpam-6339	125	60	)	)	PUNCT
ejpam-6339	125	61	⊑	⊑	PROPN
ejpam-6339	125	62	n⋆(l	n⋆(l	PROPN
ejpam-6339	125	63	)	)	PUNCT
ejpam-6339	125	64	.	.	PUNCT
ejpam-6339	126	1	(	(	PUNCT
ejpam-6339	126	2	3	3	X
ejpam-6339	126	3	)	)	PUNCT
ejpam-6339	126	4	n⋆	n⋆	X
ejpam-6339	126	5	=	=	SYM
ejpam-6339	126	6	cl(n⋆	cl(n⋆	PROPN
ejpam-6339	126	7	)	)	PUNCT
ejpam-6339	127	1	⊑	⊑	PRON
ejpam-6339	127	2	cl(n	cl(n	NUM
ejpam-6339	127	3	)	)	PUNCT
ejpam-6339	127	4	(	(	PUNCT
ejpam-6339	127	5	n⋆	n⋆	X
ejpam-6339	127	6	is	be	AUX
ejpam-6339	127	7	a	a	DET
ejpam-6339	127	8	n	n	ADV
ejpam-6339	127	9	-closed	-close	VERB
ejpam-6339	127	10	set	set	NOUN
ejpam-6339	127	11	)	)	PUNCT
ejpam-6339	127	12	.	.	PUNCT
ejpam-6339	128	1	(	(	PUNCT
ejpam-6339	128	2	4	4	X
ejpam-6339	128	3	)	)	PUNCT
ejpam-6339	128	4	(	(	PUNCT
ejpam-6339	128	5	n⋆)⋆	n⋆)⋆	ADP
ejpam-6339	128	6	⊑	⊑	PROPN
ejpam-6339	128	7	n⋆.	n⋆.	PROPN
ejpam-6339	128	8	(	(	PUNCT
ejpam-6339	128	9	5	5	NUM
ejpam-6339	128	10	)	)	PUNCT
ejpam-6339	128	11	(	(	PUNCT
ejpam-6339	128	12	n	n	X
ejpam-6339	128	13	⊔m)⋆	⊔m)⋆	NOUN
ejpam-6339	129	1	=	=	X
ejpam-6339	129	2	n⋆	n⋆	X
ejpam-6339	129	3	⊔m⋆.	⊔m⋆.	PROPN
ejpam-6339	129	4	(	(	PUNCT
ejpam-6339	129	5	6	6	NUM
ejpam-6339	129	6	)	)	PUNCT
ejpam-6339	129	7	(	(	PUNCT
ejpam-6339	129	8	n	n	X
ejpam-6339	129	9	⊓m)⋆	⊓m)⋆	ADP
ejpam-6339	129	10	⊑	⊑	X
ejpam-6339	129	11	n⋆	n⋆	X
ejpam-6339	129	12	⊓m⋆.	⊓m⋆.	X
ejpam-6339	129	13	(	(	PUNCT
ejpam-6339	129	14	7	7	NUM
ejpam-6339	129	15	)	)	PUNCT
ejpam-6339	129	16	if	if	SCONJ
ejpam-6339	129	17	m	m	VERB
ejpam-6339	129	18	∈	∈	PROPN
ejpam-6339	129	19	l	l	NOUN
ejpam-6339	129	20	,	,	PUNCT
ejpam-6339	129	21	then	then	ADV
ejpam-6339	129	22	(	(	PUNCT
ejpam-6339	129	23	n	n	X
ejpam-6339	129	24	⊔m)⋆	⊔m)⋆	NOUN
ejpam-6339	129	25	=	=	SYM
ejpam-6339	129	26	n⋆.	n⋆.	PROPN
ejpam-6339	129	27	3	3	NUM
ejpam-6339	129	28	.	.	NUM
ejpam-6339	129	29	n	n	CCONJ
ejpam-6339	129	30	-	-	PUNCT
ejpam-6339	129	31	point	point	NOUN
ejpam-6339	129	32	-	-	PUNCT
ejpam-6339	129	33	closure	closure	NOUN
ejpam-6339	129	34	the	the	DET
ejpam-6339	129	35	concept	concept	NOUN
ejpam-6339	129	36	of	of	ADP
ejpam-6339	129	37	n	n	PRON
ejpam-6339	129	38	-closure	-closure	NOUN
ejpam-6339	129	39	introduced	introduce	VERB
ejpam-6339	129	40	by	by	ADP
ejpam-6339	129	41	karatas	karata	NOUN
ejpam-6339	129	42	and	and	CCONJ
ejpam-6339	129	43	kuru	kuru	NOUN
ejpam-6339	129	44	[	[	X
ejpam-6339	129	45	10	10	NUM
ejpam-6339	129	46	]	]	PUNCT
ejpam-6339	129	47	has	have	AUX
ejpam-6339	129	48	inspired	inspire	VERB
ejpam-6339	129	49	recent	recent	ADJ
ejpam-6339	129	50	research	research	NOUN
ejpam-6339	129	51	in	in	ADP
ejpam-6339	129	52	the	the	DET
ejpam-6339	129	53	neutrosophic	neutrosophic	ADJ
ejpam-6339	129	54	environment	environment	NOUN
ejpam-6339	129	55	,	,	PUNCT
ejpam-6339	129	56	which	which	PRON
ejpam-6339	129	57	has	have	AUX
ejpam-6339	129	58	extended	extend	VERB
ejpam-6339	129	59	the	the	DET
ejpam-6339	129	60	related	relate	VERB
ejpam-6339	129	61	theory	theory	NOUN
ejpam-6339	129	62	of	of	ADP
ejpam-6339	129	63	neutrosophic	neutrosophic	ADJ
ejpam-6339	129	64	topological	topological	ADJ
ejpam-6339	129	65	spaces	space	NOUN
ejpam-6339	129	66	to	to	ADP
ejpam-6339	129	67	other	other	ADJ
ejpam-6339	129	68	contexts	contexts	NOUN
ejpam-6339	129	69	,	,	PUNCT
ejpam-6339	129	70	some	some	PRON
ejpam-6339	129	71	of	of	ADP
ejpam-6339	129	72	which	which	PRON
ejpam-6339	129	73	can	can	AUX
ejpam-6339	129	74	be	be	AUX
ejpam-6339	129	75	found	find	VERB
ejpam-6339	129	76	in	in	ADP
ejpam-6339	129	77	references	reference	NOUN
ejpam-6339	129	78	[	[	X
ejpam-6339	129	79	8	8	NUM
ejpam-6339	129	80	]	]	PUNCT
ejpam-6339	129	81	and	and	CCONJ
ejpam-6339	129	82	[	[	X
ejpam-6339	129	83	3	3	NUM
ejpam-6339	129	84	]	]	PUNCT
ejpam-6339	129	85	.	.	PUNCT
ejpam-6339	130	1	motivated	motivate	VERB
ejpam-6339	130	2	by	by	ADP
ejpam-6339	130	3	these	these	DET
ejpam-6339	130	4	recent	recent	ADJ
ejpam-6339	130	5	advances	advance	NOUN
ejpam-6339	130	6	,	,	PUNCT
ejpam-6339	130	7	in	in	ADP
ejpam-6339	130	8	this	this	DET
ejpam-6339	130	9	section	section	NOUN
ejpam-6339	130	10	,	,	PUNCT
ejpam-6339	130	11	we	we	PRON
ejpam-6339	130	12	introduce	introduce	VERB
ejpam-6339	130	13	and	and	CCONJ
ejpam-6339	130	14	investigate	investigate	VERB
ejpam-6339	130	15	the	the	DET
ejpam-6339	130	16	concept	concept	NOUN
ejpam-6339	130	17	of	of	ADP
ejpam-6339	130	18	n	n	DET
ejpam-6339	130	19	-point	-point	NOUN
ejpam-6339	130	20	-	-	PUNCT
ejpam-6339	130	21	closure	closure	NOUN
ejpam-6339	130	22	using	use	VERB
ejpam-6339	130	23	n	n	DET
ejpam-6339	130	24	-points	-point	NOUN
ejpam-6339	130	25	,	,	PUNCT
ejpam-6339	130	26	which	which	PRON
ejpam-6339	130	27	is	be	AUX
ejpam-6339	130	28	independent	independent	ADJ
ejpam-6339	130	29	of	of	ADP
ejpam-6339	130	30	the	the	DET
ejpam-6339	130	31	concept	concept	NOUN
ejpam-6339	130	32	of	of	ADP
ejpam-6339	130	33	n	n	DET
ejpam-6339	130	34	-closure	-closure	NOUN
ejpam-6339	130	35	,	,	PUNCT
ejpam-6339	130	36	as	as	SCONJ
ejpam-6339	130	37	we	we	PRON
ejpam-6339	130	38	show	show	VERB
ejpam-6339	130	39	in	in	ADP
ejpam-6339	130	40	two	two	NUM
ejpam-6339	130	41	examples	example	NOUN
ejpam-6339	130	42	below	below	ADV
ejpam-6339	130	43	.	.	PUNCT
ejpam-6339	131	1	first	first	ADV
ejpam-6339	131	2	,	,	PUNCT
ejpam-6339	131	3	we	we	PRON
ejpam-6339	131	4	establish	establish	VERB
ejpam-6339	131	5	new	new	ADJ
ejpam-6339	131	6	results	result	NOUN
ejpam-6339	131	7	related	relate	VERB
ejpam-6339	131	8	to	to	ADP
ejpam-6339	131	9	the	the	DET
ejpam-6339	131	10	concepts	concept	NOUN
ejpam-6339	131	11	of	of	ADP
ejpam-6339	131	12	n	n	CCONJ
ejpam-6339	131	13	-points	-point	NOUN
ejpam-6339	131	14	and	and	CCONJ
ejpam-6339	131	15	n	n	PRON
ejpam-6339	131	16	-closure	-closure	NOUN
ejpam-6339	131	17	.	.	PUNCT
ejpam-6339	132	1	proposition	proposition	NOUN
ejpam-6339	132	2	5	5	NUM
ejpam-6339	132	3	.	.	PUNCT
ejpam-6339	133	1	let	let	VERB
ejpam-6339	133	2	n	n	PRON
ejpam-6339	133	3	,	,	PUNCT
ejpam-6339	133	4	m	m	VERB
ejpam-6339	133	5	∈	∈	ADJ
ejpam-6339	133	6	n	n	CCONJ
ejpam-6339	133	7	(	(	PUNCT
ejpam-6339	133	8	x	x	NOUN
ejpam-6339	133	9	)	)	PUNCT
ejpam-6339	133	10	.	.	PUNCT
ejpam-6339	134	1	if	if	SCONJ
ejpam-6339	134	2	n	n	PRON
ejpam-6339	134	3	⊓m	⊓m	NOUN
ejpam-6339	134	4	=	=	SYM
ejpam-6339	134	5	∅̃	∅̃	PROPN
ejpam-6339	134	6	,	,	PUNCT
ejpam-6339	134	7	then	then	ADV
ejpam-6339	134	8	m	m	VERB
ejpam-6339	134	9	⊑	⊑	PRON
ejpam-6339	134	10	n	n	PRON
ejpam-6339	134	11	c	c	NOUN
ejpam-6339	134	12	and	and	CCONJ
ejpam-6339	134	13	n	n	CCONJ
ejpam-6339	134	14	⊑m	⊑m	NOUN
ejpam-6339	134	15	c.	c.	NOUN
ejpam-6339	134	16	proof	proof	NOUN
ejpam-6339	134	17	.	.	PUNCT
ejpam-6339	135	1	we	we	PRON
ejpam-6339	135	2	will	will	AUX
ejpam-6339	135	3	only	only	ADV
ejpam-6339	135	4	show	show	VERB
ejpam-6339	135	5	the	the	DET
ejpam-6339	135	6	neutrosophic	neutrosophic	ADJ
ejpam-6339	135	7	inclusion	inclusion	NOUN
ejpam-6339	135	8	m	m	VERB
ejpam-6339	135	9	⊑	⊑	X
ejpam-6339	135	10	n	n	PROPN
ejpam-6339	135	11	c	c	NOUN
ejpam-6339	135	12	,	,	PUNCT
ejpam-6339	135	13	because	because	SCONJ
ejpam-6339	135	14	the	the	DET
ejpam-6339	135	15	other	other	ADJ
ejpam-6339	135	16	neutrosophic	neutrosophic	ADJ
ejpam-6339	135	17	inclusion	inclusion	NOUN
ejpam-6339	135	18	is	be	AUX
ejpam-6339	135	19	shown	show	VERB
ejpam-6339	135	20	in	in	ADP
ejpam-6339	135	21	the	the	DET
ejpam-6339	135	22	same	same	ADJ
ejpam-6339	135	23	way	way	NOUN
ejpam-6339	135	24	.	.	PUNCT
ejpam-6339	136	1	assume	assume	VERB
ejpam-6339	136	2	that	that	SCONJ
ejpam-6339	136	3	n	n	NOUN
ejpam-6339	136	4	⊓m	⊓m	NOUN
ejpam-6339	136	5	=	=	PUNCT
ejpam-6339	136	6	∅̃.	∅̃.	NOUN
ejpam-6339	136	7	then	then	ADV
ejpam-6339	136	8	,	,	PUNCT
ejpam-6339	136	9	{	{	PUNCT
ejpam-6339	136	10	⟨x	⟨x	VERB
ejpam-6339	136	11	,	,	PUNCT
ejpam-6339	136	12	µn	µn	PROPN
ejpam-6339	136	13	(	(	PUNCT
ejpam-6339	136	14	x	x	NOUN
ejpam-6339	136	15	)	)	PUNCT
ejpam-6339	136	16	∧	∧	PROPN
ejpam-6339	136	17	µm	µm	ADP
ejpam-6339	136	18	(	(	PUNCT
ejpam-6339	136	19	x	x	NOUN
ejpam-6339	136	20	)	)	PUNCT
ejpam-6339	136	21	,	,	PUNCT
ejpam-6339	136	22	σn	σn	X
ejpam-6339	136	23	(	(	PUNCT
ejpam-6339	136	24	x	x	NOUN
ejpam-6339	136	25	)	)	PUNCT
ejpam-6339	136	26	∨	∨	NUM
ejpam-6339	136	27	σm	σm	X
ejpam-6339	136	28	(	(	PUNCT
ejpam-6339	136	29	x	x	NOUN
ejpam-6339	136	30	)	)	PUNCT
ejpam-6339	136	31	,	,	PUNCT
ejpam-6339	136	32	γn	γn	PART
ejpam-6339	136	33	(	(	PUNCT
ejpam-6339	136	34	x	x	NOUN
ejpam-6339	136	35	)	)	PUNCT
ejpam-6339	136	36	∨	∨	NUM
ejpam-6339	136	37	γm	γm	X
ejpam-6339	136	38	(	(	PUNCT
ejpam-6339	136	39	x)⟩	x)⟩	NOUN
ejpam-6339	136	40	:	:	PUNCT
ejpam-6339	137	1	x	x	SYM
ejpam-6339	137	2	∈	∈	NOUN
ejpam-6339	137	3	x	x	X
ejpam-6339	137	4	}	}	PUNCT
ejpam-6339	137	5	=	=	SYM
ejpam-6339	137	6	∅̃	∅̃	PROPN
ejpam-6339	137	7	,	,	PUNCT
ejpam-6339	137	8	j.	j.	PROPN
ejpam-6339	137	9	sanabria	sanabria	PROPN
ejpam-6339	137	10	,	,	PUNCT
ejpam-6339	137	11	e.	e.	PROPN
ejpam-6339	137	12	rosas	rosas	PROPN
ejpam-6339	137	13	,	,	PUNCT
ejpam-6339	137	14	c.	c.	PROPN
ejpam-6339	137	15	granados	granados	PROPN
ejpam-6339	137	16	/	/	PUNCT
ejpam-6339	137	17	eur	eur	PROPN
ejpam-6339	137	18	.	.	PUNCT
ejpam-6339	138	1	j.	j.	PROPN
ejpam-6339	138	2	pure	pure	PROPN
ejpam-6339	138	3	appl	appl	PROPN
ejpam-6339	138	4	.	.	PROPN
ejpam-6339	138	5	math	math	PROPN
ejpam-6339	138	6	,	,	PUNCT
ejpam-6339	138	7	18	18	NUM
ejpam-6339	138	8	(	(	PUNCT
ejpam-6339	138	9	3	3	NUM
ejpam-6339	138	10	)	)	PUNCT
ejpam-6339	138	11	(	(	PUNCT
ejpam-6339	138	12	2025	2025	NUM
ejpam-6339	138	13	)	)	PUNCT
ejpam-6339	138	14	,	,	PUNCT
ejpam-6339	138	15	6339	6339	NUM
ejpam-6339	138	16	7	7	NUM
ejpam-6339	138	17	of	of	ADP
ejpam-6339	138	18	15	15	NUM
ejpam-6339	138	19	so	so	SCONJ
ejpam-6339	138	20	the	the	DET
ejpam-6339	138	21	following	follow	VERB
ejpam-6339	138	22	equalities	equality	NOUN
ejpam-6339	138	23	hold	hold	VERB
ejpam-6339	138	24	:	:	PUNCT
ejpam-6339	138	25	(	(	PUNCT
ejpam-6339	138	26	1	1	X
ejpam-6339	138	27	)	)	PUNCT
ejpam-6339	138	28	µn	µn	PROPN
ejpam-6339	138	29	(	(	PUNCT
ejpam-6339	138	30	x	x	NOUN
ejpam-6339	138	31	)	)	PUNCT
ejpam-6339	138	32	∧	∧	PROPN
ejpam-6339	138	33	µm	µm	ADP
ejpam-6339	138	34	(	(	PUNCT
ejpam-6339	138	35	x	x	NOUN
ejpam-6339	138	36	)	)	PUNCT
ejpam-6339	138	37	=	=	SYM
ejpam-6339	138	38	0	0	NUM
ejpam-6339	138	39	,	,	PUNCT
ejpam-6339	138	40	∀x	∀x	X
ejpam-6339	138	41	∈	∈	PROPN
ejpam-6339	138	42	x.	x.	NOUN
ejpam-6339	138	43	(	(	PUNCT
ejpam-6339	138	44	2	2	NUM
ejpam-6339	138	45	)	)	PUNCT
ejpam-6339	138	46	σn	σn	NOUN
ejpam-6339	138	47	(	(	PUNCT
ejpam-6339	138	48	x	x	NOUN
ejpam-6339	138	49	)	)	PUNCT
ejpam-6339	138	50	∨	∨	NUM
ejpam-6339	138	51	σm	σm	X
ejpam-6339	138	52	(	(	PUNCT
ejpam-6339	138	53	x	x	X
ejpam-6339	138	54	)	)	PUNCT
ejpam-6339	138	55	=	=	SYM
ejpam-6339	138	56	1	1	NUM
ejpam-6339	138	57	,	,	PUNCT
ejpam-6339	138	58	∀x	∀x	X
ejpam-6339	138	59	∈	∈	PROPN
ejpam-6339	138	60	x.	x.	NOUN
ejpam-6339	138	61	(	(	PUNCT
ejpam-6339	138	62	3	3	NUM
ejpam-6339	138	63	)	)	PUNCT
ejpam-6339	138	64	γn	γn	NOUN
ejpam-6339	138	65	(	(	PUNCT
ejpam-6339	138	66	x	x	NOUN
ejpam-6339	138	67	)	)	PUNCT
ejpam-6339	138	68	∨	∨	NUM
ejpam-6339	138	69	γm	γm	X
ejpam-6339	138	70	(	(	PUNCT
ejpam-6339	138	71	x	x	NOUN
ejpam-6339	138	72	)	)	PUNCT
ejpam-6339	138	73	=	=	SYM
ejpam-6339	138	74	1	1	NUM
ejpam-6339	138	75	,	,	PUNCT
ejpam-6339	138	76	∀x	∀x	X
ejpam-6339	138	77	∈	∈	PROPN
ejpam-6339	138	78	x.	x.	NOUN
ejpam-6339	138	79	from	from	ADP
ejpam-6339	138	80	equality	equality	NOUN
ejpam-6339	138	81	(	(	PUNCT
ejpam-6339	138	82	1	1	NUM
ejpam-6339	138	83	)	)	PUNCT
ejpam-6339	138	84	,	,	PUNCT
ejpam-6339	138	85	we	we	PRON
ejpam-6339	138	86	have	have	VERB
ejpam-6339	138	87	γn	γn	NUM
ejpam-6339	138	88	(	(	PUNCT
ejpam-6339	138	89	x	x	NOUN
ejpam-6339	138	90	)	)	PUNCT
ejpam-6339	138	91	=	=	SYM
ejpam-6339	138	92	1−	1−	NUM
ejpam-6339	138	93	µn	µn	PROPN
ejpam-6339	138	94	(	(	PUNCT
ejpam-6339	138	95	x	x	NOUN
ejpam-6339	138	96	)	)	PUNCT
ejpam-6339	138	97	≥	≥	X
ejpam-6339	138	98	µm	µm	X
ejpam-6339	138	99	(	(	PUNCT
ejpam-6339	138	100	x	x	NOUN
ejpam-6339	138	101	)	)	PUNCT
ejpam-6339	138	102	,	,	PUNCT
ejpam-6339	138	103	∀x	∀x	X
ejpam-6339	138	104	∈	∈	PROPN
ejpam-6339	138	105	x.	x.	NOUN
ejpam-6339	138	106	from	from	ADP
ejpam-6339	138	107	equality	equality	NOUN
ejpam-6339	138	108	(	(	PUNCT
ejpam-6339	138	109	2	2	NUM
ejpam-6339	138	110	)	)	PUNCT
ejpam-6339	138	111	,	,	PUNCT
ejpam-6339	138	112	let	let	VERB
ejpam-6339	138	113	us	we	PRON
ejpam-6339	138	114	observe	observe	VERB
ejpam-6339	138	115	that	that	SCONJ
ejpam-6339	138	116	one	one	NUM
ejpam-6339	138	117	of	of	ADP
ejpam-6339	138	118	the	the	DET
ejpam-6339	138	119	quantities	quantity	NOUN
ejpam-6339	138	120	σn	σn	X
ejpam-6339	138	121	(	(	PUNCT
ejpam-6339	138	122	x	x	NOUN
ejpam-6339	138	123	)	)	PUNCT
ejpam-6339	138	124	or	or	CCONJ
ejpam-6339	138	125	σm	σm	X
ejpam-6339	138	126	(	(	PUNCT
ejpam-6339	138	127	x	x	X
ejpam-6339	138	128	)	)	PUNCT
ejpam-6339	138	129	is	be	AUX
ejpam-6339	138	130	equal	equal	ADJ
ejpam-6339	138	131	to	to	ADP
ejpam-6339	138	132	1	1	NUM
ejpam-6339	138	133	for	for	ADP
ejpam-6339	138	134	an	an	DET
ejpam-6339	138	135	arbitrary	arbitrary	ADJ
ejpam-6339	138	136	x	x	SYM
ejpam-6339	138	137	∈	∈	PROPN
ejpam-6339	138	138	x.	x.	NOUN
ejpam-6339	138	139	since	since	SCONJ
ejpam-6339	138	140	0	0	NUM
ejpam-6339	138	141	≤	≤	NUM
ejpam-6339	138	142	σn	σn	NOUN
ejpam-6339	138	143	(	(	PUNCT
ejpam-6339	138	144	x	x	NOUN
ejpam-6339	138	145	)	)	PUNCT
ejpam-6339	138	146	≤	≤	NUM
ejpam-6339	138	147	1	1	NUM
ejpam-6339	138	148	and	and	CCONJ
ejpam-6339	138	149	0	0	NUM
ejpam-6339	138	150	≤	≤	NUM
ejpam-6339	138	151	σm	σm	X
ejpam-6339	138	152	(	(	PUNCT
ejpam-6339	138	153	x	x	NOUN
ejpam-6339	138	154	)	)	PUNCT
ejpam-6339	138	155	≤	≤	NUM
ejpam-6339	138	156	1	1	NUM
ejpam-6339	138	157	,	,	PUNCT
ejpam-6339	138	158	∀x	∀x	VERB
ejpam-6339	138	159	∈	∈	PROPN
ejpam-6339	138	160	x	x	PRON
ejpam-6339	138	161	,	,	PUNCT
ejpam-6339	138	162	it	it	PRON
ejpam-6339	138	163	follows	follow	VERB
ejpam-6339	138	164	that	that	SCONJ
ejpam-6339	138	165	σn	σn	PROPN
ejpam-6339	138	166	(	(	PUNCT
ejpam-6339	138	167	x	x	NOUN
ejpam-6339	138	168	)	)	PUNCT
ejpam-6339	139	1	+	+	NUM
ejpam-6339	139	2	σm	σm	ADJ
ejpam-6339	139	3	(	(	PUNCT
ejpam-6339	139	4	x	x	X
ejpam-6339	139	5	)	)	PUNCT
ejpam-6339	139	6	≥	≥	NOUN
ejpam-6339	139	7	1	1	NUM
ejpam-6339	139	8	,	,	PUNCT
ejpam-6339	139	9	∀x	∀x	X
ejpam-6339	139	10	∈	∈	PROPN
ejpam-6339	139	11	x.	x.	NOUN
ejpam-6339	139	12	thus	thus	ADV
ejpam-6339	139	13	,	,	PUNCT
ejpam-6339	139	14	σm	σm	INTJ
ejpam-6339	139	15	(	(	PUNCT
ejpam-6339	139	16	x	x	X
ejpam-6339	139	17	)	)	PUNCT
ejpam-6339	139	18	≥	≥	NOUN
ejpam-6339	139	19	1−	1−	NUM
ejpam-6339	139	20	σn	σn	NOUN
ejpam-6339	139	21	(	(	PUNCT
ejpam-6339	139	22	x	x	NOUN
ejpam-6339	139	23	)	)	PUNCT
ejpam-6339	139	24	,	,	PUNCT
ejpam-6339	139	25	∀x	∀x	X
ejpam-6339	139	26	∈	∈	NOUN
ejpam-6339	139	27	x.	x.	NOUN
ejpam-6339	139	28	using	use	VERB
ejpam-6339	139	29	a	a	DET
ejpam-6339	139	30	similar	similar	ADJ
ejpam-6339	139	31	reasoning	reasoning	NOUN
ejpam-6339	139	32	from	from	ADP
ejpam-6339	139	33	equality	equality	NOUN
ejpam-6339	139	34	(	(	PUNCT
ejpam-6339	139	35	3	3	NUM
ejpam-6339	139	36	)	)	PUNCT
ejpam-6339	139	37	,	,	PUNCT
ejpam-6339	139	38	we	we	PRON
ejpam-6339	139	39	show	show	VERB
ejpam-6339	139	40	that	that	SCONJ
ejpam-6339	139	41	γm	γm	ADJ
ejpam-6339	139	42	(	(	PUNCT
ejpam-6339	139	43	x	x	NOUN
ejpam-6339	139	44	)	)	PUNCT
ejpam-6339	139	45	≥	≥	NOUN
ejpam-6339	139	46	1−	1−	NUM
ejpam-6339	139	47	γn	γn	NOUN
ejpam-6339	139	48	(	(	PUNCT
ejpam-6339	139	49	x	x	NOUN
ejpam-6339	139	50	)	)	PUNCT
ejpam-6339	139	51	=	=	SYM
ejpam-6339	139	52	µn	µn	PROPN
ejpam-6339	139	53	(	(	PUNCT
ejpam-6339	139	54	x	x	NOUN
ejpam-6339	139	55	)	)	PUNCT
ejpam-6339	139	56	,	,	PUNCT
ejpam-6339	139	57	∀x	∀x	X
ejpam-6339	139	58	∈	∈	PROPN
ejpam-6339	139	59	x.	x.	NOUN
ejpam-6339	139	60	therefore	therefore	ADV
ejpam-6339	139	61	,	,	PUNCT
ejpam-6339	139	62	m	m	VERB
ejpam-6339	139	63	=	=	NOUN
ejpam-6339	139	64	{	{	PUNCT
ejpam-6339	139	65	⟨x	⟨x	VERB
ejpam-6339	139	66	,	,	PUNCT
ejpam-6339	139	67	µm	µm	ADP
ejpam-6339	139	68	(	(	PUNCT
ejpam-6339	139	69	x	x	NOUN
ejpam-6339	139	70	)	)	PUNCT
ejpam-6339	139	71	,	,	PUNCT
ejpam-6339	139	72	σm	σm	X
ejpam-6339	139	73	(	(	PUNCT
ejpam-6339	139	74	x	x	NOUN
ejpam-6339	139	75	)	)	PUNCT
ejpam-6339	139	76	,	,	PUNCT
ejpam-6339	139	77	γm	γm	X
ejpam-6339	139	78	(	(	PUNCT
ejpam-6339	139	79	x)⟩	x)⟩	NOUN
ejpam-6339	139	80	:	:	PUNCT
ejpam-6339	139	81	x	x	SYM
ejpam-6339	139	82	∈	∈	NOUN
ejpam-6339	139	83	x	x	X
ejpam-6339	139	84	}	}	PUNCT
ejpam-6339	139	85	⊑	⊑	X
ejpam-6339	139	86	{	{	PUNCT
ejpam-6339	139	87	⟨x	⟨x	NUM
ejpam-6339	139	88	,	,	PUNCT
ejpam-6339	139	89	γn	γn	X
ejpam-6339	139	90	(	(	PUNCT
ejpam-6339	139	91	x	x	NOUN
ejpam-6339	139	92	)	)	PUNCT
ejpam-6339	139	93	,	,	PUNCT
ejpam-6339	139	94	1−	1−	NUM
ejpam-6339	139	95	σn	σn	NOUN
ejpam-6339	139	96	(	(	PUNCT
ejpam-6339	139	97	x	x	NOUN
ejpam-6339	139	98	)	)	PUNCT
ejpam-6339	139	99	,	,	PUNCT
ejpam-6339	139	100	µn	µn	PROPN
ejpam-6339	139	101	(	(	PUNCT
ejpam-6339	139	102	x)⟩	x)⟩	NOUN
ejpam-6339	139	103	:	:	PUNCT
ejpam-6339	139	104	x	x	SYM
ejpam-6339	139	105	∈	∈	NOUN
ejpam-6339	139	106	x	x	X
ejpam-6339	139	107	}	}	PUNCT
ejpam-6339	139	108	=	=	SYM
ejpam-6339	139	109	n	n	DET
ejpam-6339	139	110	c.	c.	NOUN
ejpam-6339	139	111	in	in	ADP
ejpam-6339	139	112	the	the	DET
ejpam-6339	139	113	following	follow	VERB
ejpam-6339	139	114	example	example	NOUN
ejpam-6339	139	115	,	,	PUNCT
ejpam-6339	139	116	we	we	PRON
ejpam-6339	139	117	show	show	VERB
ejpam-6339	139	118	that	that	SCONJ
ejpam-6339	139	119	the	the	DET
ejpam-6339	139	120	converse	converse	NOUN
ejpam-6339	139	121	of	of	ADP
ejpam-6339	139	122	proposition	proposition	NOUN
ejpam-6339	139	123	5	5	NUM
ejpam-6339	139	124	,	,	PUNCT
ejpam-6339	139	125	in	in	ADP
ejpam-6339	139	126	general	general	ADJ
ejpam-6339	139	127	,	,	PUNCT
ejpam-6339	139	128	is	be	AUX
ejpam-6339	139	129	not	not	PART
ejpam-6339	139	130	true	true	ADJ
ejpam-6339	139	131	.	.	PUNCT
ejpam-6339	140	1	example	example	NOUN
ejpam-6339	141	1	1	1	NUM
ejpam-6339	141	2	.	.	PUNCT
ejpam-6339	141	3	let	let	VERB
ejpam-6339	141	4	x	x	PUNCT
ejpam-6339	141	5	=	=	PRON
ejpam-6339	141	6	{	{	PUNCT
ejpam-6339	141	7	x	x	PROPN
ejpam-6339	141	8	,	,	PUNCT
ejpam-6339	141	9	y	y	NOUN
ejpam-6339	141	10	}	}	PUNCT
ejpam-6339	141	11	and	and	CCONJ
ejpam-6339	141	12	o	o	NOUN
ejpam-6339	141	13	,	,	PUNCT
ejpam-6339	141	14	u	u	PROPN
ejpam-6339	141	15	∈	∈	PROPN
ejpam-6339	141	16	n	n	CCONJ
ejpam-6339	141	17	(	(	PUNCT
ejpam-6339	141	18	x	x	X
ejpam-6339	141	19	)	)	PUNCT
ejpam-6339	141	20	such	such	ADJ
ejpam-6339	141	21	that	that	SCONJ
ejpam-6339	141	22	n	n	NOUN
ejpam-6339	141	23	=	=	PRON
ejpam-6339	141	24	{	{	PUNCT
ejpam-6339	141	25	⟨x	⟨x	VERB
ejpam-6339	141	26	,	,	PUNCT
ejpam-6339	141	27	0.4	0.4	NUM
ejpam-6339	141	28	,	,	PUNCT
ejpam-6339	141	29	0.8	0.8	NUM
ejpam-6339	141	30	,	,	PUNCT
ejpam-6339	141	31	0.6⟩	0.6⟩	NUM
ejpam-6339	141	32	,	,	PUNCT
ejpam-6339	141	33	⟨y	⟨y	X
ejpam-6339	141	34	,	,	PUNCT
ejpam-6339	141	35	0.6	0.6	NUM
ejpam-6339	141	36	,	,	PUNCT
ejpam-6339	141	37	0.7	0.7	NUM
ejpam-6339	141	38	,	,	PUNCT
ejpam-6339	141	39	0.4⟩	0.4⟩	NUM
ejpam-6339	141	40	}	}	PUNCT
ejpam-6339	141	41	,	,	PUNCT
ejpam-6339	141	42	m	m	VERB
ejpam-6339	141	43	=	=	NOUN
ejpam-6339	141	44	{	{	PUNCT
ejpam-6339	141	45	⟨x	⟨x	VERB
ejpam-6339	141	46	,	,	PUNCT
ejpam-6339	141	47	0.3	0.3	NUM
ejpam-6339	141	48	,	,	PUNCT
ejpam-6339	141	49	0.3	0.3	NUM
ejpam-6339	141	50	,	,	PUNCT
ejpam-6339	141	51	0.7⟩	0.7⟩	NOUN
ejpam-6339	141	52	,	,	PUNCT
ejpam-6339	141	53	⟨y	⟨y	NOUN
ejpam-6339	141	54	,	,	PUNCT
ejpam-6339	141	55	0.4	0.4	NUM
ejpam-6339	141	56	,	,	PUNCT
ejpam-6339	141	57	0.3	0.3	NUM
ejpam-6339	141	58	,	,	PUNCT
ejpam-6339	141	59	0.6⟩	0.6⟩	NUM
ejpam-6339	141	60	}	}	PUNCT
ejpam-6339	141	61	.	.	PUNCT
ejpam-6339	142	1	then	then	ADV
ejpam-6339	142	2	,	,	PUNCT
ejpam-6339	142	3	m	m	VERB
ejpam-6339	142	4	⊑	⊑	X
ejpam-6339	142	5	n	n	X
ejpam-6339	142	6	c	c	NOUN
ejpam-6339	142	7	=	=	PUNCT
ejpam-6339	142	8	{	{	PUNCT
ejpam-6339	142	9	⟨x	⟨x	VERB
ejpam-6339	142	10	,	,	PUNCT
ejpam-6339	142	11	0.6	0.6	NUM
ejpam-6339	142	12	,	,	PUNCT
ejpam-6339	142	13	0.2	0.2	NUM
ejpam-6339	142	14	,	,	PUNCT
ejpam-6339	142	15	0.4⟩	0.4⟩	NUM
ejpam-6339	142	16	,	,	PUNCT
ejpam-6339	142	17	⟨y	⟨y	X
ejpam-6339	142	18	,	,	PUNCT
ejpam-6339	142	19	0.4	0.4	NUM
ejpam-6339	142	20	,	,	PUNCT
ejpam-6339	142	21	0.3	0.3	NUM
ejpam-6339	142	22	,	,	PUNCT
ejpam-6339	142	23	0.6⟩	0.6⟩	NUM
ejpam-6339	142	24	}	}	PUNCT
ejpam-6339	142	25	,	,	PUNCT
ejpam-6339	142	26	but	but	CCONJ
ejpam-6339	142	27	n	n	PRON
ejpam-6339	142	28	⊓m	⊓m	NOUN
ejpam-6339	142	29	=	=	X
ejpam-6339	142	30	{	{	PUNCT
ejpam-6339	142	31	⟨x	⟨x	NUM
ejpam-6339	142	32	,	,	PUNCT
ejpam-6339	142	33	0.3	0.3	NUM
ejpam-6339	142	34	,	,	PUNCT
ejpam-6339	142	35	0.8	0.8	NUM
ejpam-6339	142	36	,	,	PUNCT
ejpam-6339	142	37	0.7⟩	0.7⟩	NOUN
ejpam-6339	142	38	,	,	PUNCT
ejpam-6339	142	39	⟨y	⟨y	NOUN
ejpam-6339	142	40	,	,	PUNCT
ejpam-6339	142	41	0.4	0.4	NUM
ejpam-6339	142	42	,	,	PUNCT
ejpam-6339	142	43	0.7	0.7	NUM
ejpam-6339	142	44	,	,	PUNCT
ejpam-6339	142	45	0.6⟩	0.6⟩	NUM
ejpam-6339	142	46	}	}	PUNCT
ejpam-6339	142	47	=	=	X
ejpam-6339	142	48	̸	̸	CCONJ
ejpam-6339	142	49	∅̃.	∅̃.	NOUN
ejpam-6339	142	50	remark	remark	NOUN
ejpam-6339	142	51	2	2	NUM
ejpam-6339	142	52	.	.	PUNCT
ejpam-6339	143	1	in	in	ADP
ejpam-6339	143	2	example	example	NOUN
ejpam-6339	143	3	1	1	NUM
ejpam-6339	143	4	,	,	PUNCT
ejpam-6339	143	5	we	we	PRON
ejpam-6339	143	6	have	have	VERB
ejpam-6339	143	7	n	n	NUM
ejpam-6339	143	8	⊔n	⊔n	NUM
ejpam-6339	143	9	c	c	NOUN
ejpam-6339	143	10	=	=	PUNCT
ejpam-6339	143	11	{	{	PUNCT
ejpam-6339	143	12	⟨x	⟨x	VERB
ejpam-6339	143	13	,	,	PUNCT
ejpam-6339	143	14	0.6	0.6	NUM
ejpam-6339	143	15	,	,	PUNCT
ejpam-6339	143	16	0.2	0.2	NUM
ejpam-6339	143	17	,	,	PUNCT
ejpam-6339	143	18	0.4⟩	0.4⟩	NUM
ejpam-6339	143	19	,	,	PUNCT
ejpam-6339	143	20	⟨y	⟨y	NOUN
ejpam-6339	143	21	,	,	PUNCT
ejpam-6339	143	22	0.6	0.6	NUM
ejpam-6339	143	23	,	,	PUNCT
ejpam-6339	143	24	0.3	0.3	NUM
ejpam-6339	143	25	,	,	PUNCT
ejpam-6339	143	26	0.4⟩	0.4⟩	NUM
ejpam-6339	143	27	}	}	PUNCT
ejpam-6339	143	28	=	=	NUM
ejpam-6339	143	29	̸	̸	ADV
ejpam-6339	143	30	x̃	x̃	PROPN
ejpam-6339	143	31	and	and	CCONJ
ejpam-6339	143	32	n	n	CCONJ
ejpam-6339	143	33	⊓	⊓	PROPN
ejpam-6339	143	34	n	n	PRON
ejpam-6339	143	35	c	c	NOUN
ejpam-6339	143	36	=	=	PUNCT
ejpam-6339	143	37	{	{	PUNCT
ejpam-6339	143	38	⟨x	⟨x	VERB
ejpam-6339	143	39	,	,	PUNCT
ejpam-6339	143	40	0.4	0.4	NUM
ejpam-6339	143	41	,	,	PUNCT
ejpam-6339	143	42	0.8	0.8	NUM
ejpam-6339	143	43	,	,	PUNCT
ejpam-6339	143	44	0.6⟩	0.6⟩	NUM
ejpam-6339	143	45	,	,	PUNCT
ejpam-6339	143	46	⟨y	⟨y	X
ejpam-6339	143	47	,	,	PUNCT
ejpam-6339	143	48	0.4	0.4	NUM
ejpam-6339	143	49	,	,	PUNCT
ejpam-6339	143	50	0.7	0.7	NUM
ejpam-6339	143	51	,	,	PUNCT
ejpam-6339	143	52	0.6⟩	0.6⟩	NUM
ejpam-6339	143	53	}	}	PUNCT
ejpam-6339	143	54	=	=	X
ejpam-6339	143	55	̸	̸	PUNCT
ejpam-6339	143	56	∅̃.	∅̃.	NOUN
ejpam-6339	143	57	thus	thus	ADV
ejpam-6339	143	58	,	,	PUNCT
ejpam-6339	143	59	we	we	PRON
ejpam-6339	143	60	deduce	deduce	VERB
ejpam-6339	143	61	that	that	SCONJ
ejpam-6339	143	62	the	the	DET
ejpam-6339	143	63	equalities	equality	NOUN
ejpam-6339	143	64	n	n	NOUN
ejpam-6339	143	65	⊔n	⊔n	NUM
ejpam-6339	143	66	c	c	X
ejpam-6339	143	67	=	=	SYM
ejpam-6339	143	68	x̃	x̃	PROPN
ejpam-6339	143	69	and	and	CCONJ
ejpam-6339	143	70	n	n	CCONJ
ejpam-6339	143	71	⊓n	⊓n	NOUN
ejpam-6339	144	1	c	c	NOUN
ejpam-6339	144	2	=	=	PUNCT
ejpam-6339	144	3	∅̃	∅̃	NOUN
ejpam-6339	144	4	are	be	AUX
ejpam-6339	144	5	not	not	PART
ejpam-6339	144	6	satisfied	satisfied	ADJ
ejpam-6339	144	7	,	,	PUNCT
ejpam-6339	144	8	in	in	ADP
ejpam-6339	144	9	general	general	ADJ
ejpam-6339	144	10	.	.	PUNCT
ejpam-6339	145	1	proposition	proposition	NOUN
ejpam-6339	145	2	6	6	NUM
ejpam-6339	145	3	.	.	PUNCT
ejpam-6339	146	1	let	let	VERB
ejpam-6339	146	2	n	n	PRON
ejpam-6339	146	3	,	,	PUNCT
ejpam-6339	146	4	m	m	VERB
ejpam-6339	146	5	∈	∈	ADJ
ejpam-6339	146	6	n	n	CCONJ
ejpam-6339	146	7	(	(	PUNCT
ejpam-6339	146	8	x	x	NOUN
ejpam-6339	146	9	)	)	PUNCT
ejpam-6339	146	10	.	.	PUNCT
ejpam-6339	147	1	then	then	ADV
ejpam-6339	147	2	,	,	PUNCT
ejpam-6339	147	3	the	the	DET
ejpam-6339	147	4	following	follow	VERB
ejpam-6339	147	5	properties	property	NOUN
ejpam-6339	147	6	are	be	AUX
ejpam-6339	147	7	equivalent	equivalent	ADJ
ejpam-6339	147	8	:	:	PUNCT
ejpam-6339	147	9	(	(	PUNCT
ejpam-6339	147	10	1	1	X
ejpam-6339	147	11	)	)	PUNCT
ejpam-6339	147	12	n	n	CCONJ
ejpam-6339	147	13	⊑m	⊑m	NOUN
ejpam-6339	147	14	.	.	PUNCT
ejpam-6339	148	1	(	(	PUNCT
ejpam-6339	148	2	2	2	X
ejpam-6339	148	3	)	)	PUNCT
ejpam-6339	148	4	xa	xa	PROPN
ejpam-6339	148	5	,	,	PUNCT
ejpam-6339	148	6	b	b	PROPN
ejpam-6339	148	7	,	,	PUNCT
ejpam-6339	148	8	c	c	PROPN
ejpam-6339	148	9	∈	∈	PROPN
ejpam-6339	148	10	n	n	PRON
ejpam-6339	148	11	implies	imply	VERB
ejpam-6339	148	12	that	that	SCONJ
ejpam-6339	148	13	xa	xa	PROPN
ejpam-6339	148	14	,	,	PUNCT
ejpam-6339	148	15	b	b	PROPN
ejpam-6339	148	16	,	,	PUNCT
ejpam-6339	148	17	c	c	NOUN
ejpam-6339	148	18	∈m	∈m	NOUN
ejpam-6339	148	19	.	.	PUNCT
ejpam-6339	149	1	proof	proof	NOUN
ejpam-6339	149	2	.	.	PUNCT
ejpam-6339	150	1	the	the	DET
ejpam-6339	150	2	proof	proof	NOUN
ejpam-6339	150	3	follows	follow	VERB
ejpam-6339	150	4	directly	directly	ADV
ejpam-6339	150	5	from	from	ADP
ejpam-6339	150	6	lemma	lemma	PROPN
ejpam-6339	150	7	1	1	NUM
ejpam-6339	150	8	.	.	PUNCT
ejpam-6339	150	9	definition	definition	NOUN
ejpam-6339	150	10	9	9	NUM
ejpam-6339	150	11	.	.	PUNCT
ejpam-6339	151	1	an	an	DET
ejpam-6339	151	2	application	application	NOUN
ejpam-6339	151	3	υ	υ	NOUN
ejpam-6339	151	4	:	:	PUNCT
ejpam-6339	151	5	n	n	PROPN
ejpam-6339	151	6	(	(	PUNCT
ejpam-6339	151	7	x	x	X
ejpam-6339	151	8	)	)	PUNCT
ejpam-6339	151	9	→	→	SYM
ejpam-6339	151	10	n	n	CCONJ
ejpam-6339	151	11	(	(	PUNCT
ejpam-6339	151	12	x	x	X
ejpam-6339	151	13	)	)	PUNCT
ejpam-6339	151	14	is	be	AUX
ejpam-6339	151	15	called	call	VERB
ejpam-6339	151	16	a	a	DET
ejpam-6339	151	17	n	n	CCONJ
ejpam-6339	151	18	-closure	-closure	NOUN
ejpam-6339	151	19	operator	operator	NOUN
ejpam-6339	151	20	if	if	SCONJ
ejpam-6339	151	21	it	it	PRON
ejpam-6339	151	22	satisfies	satisfy	VERB
ejpam-6339	151	23	the	the	DET
ejpam-6339	151	24	following	follow	VERB
ejpam-6339	151	25	conditions	condition	NOUN
ejpam-6339	151	26	:	:	PUNCT
ejpam-6339	151	27	(	(	PUNCT
ejpam-6339	151	28	1	1	X
ejpam-6339	151	29	)	)	PUNCT
ejpam-6339	151	30	n	n	CCONJ
ejpam-6339	151	31	⊑	⊑	DET
ejpam-6339	151	32	υ(n	υ(n	PROPN
ejpam-6339	151	33	)	)	PUNCT
ejpam-6339	151	34	,	,	PUNCT
ejpam-6339	151	35	(	(	PUNCT
ejpam-6339	151	36	expansivity	expansivity	NOUN
ejpam-6339	151	37	)	)	PUNCT
ejpam-6339	151	38	j.	j.	PROPN
ejpam-6339	151	39	sanabria	sanabria	PROPN
ejpam-6339	151	40	,	,	PUNCT
ejpam-6339	151	41	e.	e.	PROPN
ejpam-6339	151	42	rosas	rosas	PROPN
ejpam-6339	151	43	,	,	PUNCT
ejpam-6339	151	44	c.	c.	PROPN
ejpam-6339	151	45	granados	granados	PROPN
ejpam-6339	151	46	/	/	PUNCT
ejpam-6339	151	47	eur	eur	PROPN
ejpam-6339	151	48	.	.	PUNCT
ejpam-6339	152	1	j.	j.	PROPN
ejpam-6339	152	2	pure	pure	PROPN
ejpam-6339	152	3	appl	appl	PROPN
ejpam-6339	152	4	.	.	PROPN
ejpam-6339	152	5	math	math	PROPN
ejpam-6339	152	6	,	,	PUNCT
ejpam-6339	152	7	18	18	NUM
ejpam-6339	152	8	(	(	PUNCT
ejpam-6339	152	9	3	3	NUM
ejpam-6339	152	10	)	)	PUNCT
ejpam-6339	152	11	(	(	PUNCT
ejpam-6339	152	12	2025	2025	NUM
ejpam-6339	152	13	)	)	PUNCT
ejpam-6339	152	14	,	,	PUNCT
ejpam-6339	152	15	6339	6339	NUM
ejpam-6339	152	16	8	8	NUM
ejpam-6339	152	17	of	of	ADP
ejpam-6339	152	18	15	15	NUM
ejpam-6339	152	19	(	(	PUNCT
ejpam-6339	152	20	2	2	NUM
ejpam-6339	152	21	)	)	PUNCT
ejpam-6339	152	22	υ(υ(n	υ(υ(n	PROPN
ejpam-6339	152	23	)	)	PUNCT
ejpam-6339	152	24	)	)	PUNCT
ejpam-6339	153	1	=	=	SYM
ejpam-6339	153	2	υ(n	υ(n	PROPN
ejpam-6339	153	3	)	)	PUNCT
ejpam-6339	153	4	,	,	PUNCT
ejpam-6339	153	5	(	(	PUNCT
ejpam-6339	153	6	idempotency	idempotency	NOUN
ejpam-6339	153	7	)	)	PUNCT
ejpam-6339	153	8	(	(	PUNCT
ejpam-6339	153	9	3	3	X
ejpam-6339	153	10	)	)	PUNCT
ejpam-6339	153	11	υ(n	υ(n	PROPN
ejpam-6339	153	12	⊔m	⊔m	PROPN
ejpam-6339	153	13	)	)	PUNCT
ejpam-6339	153	14	=	=	SYM
ejpam-6339	153	15	υ(n	υ(n	PROPN
ejpam-6339	153	16	)	)	PUNCT
ejpam-6339	153	17	⊔υ(m	⊔υ(m	PROPN
ejpam-6339	153	18	)	)	PUNCT
ejpam-6339	153	19	,	,	PUNCT
ejpam-6339	153	20	(	(	PUNCT
ejpam-6339	153	21	additivity	additivity	NOUN
ejpam-6339	153	22	)	)	PUNCT
ejpam-6339	153	23	(	(	PUNCT
ejpam-6339	153	24	4	4	X
ejpam-6339	153	25	)	)	PUNCT
ejpam-6339	153	26	υ(∅̃	υ(∅̃	NOUN
ejpam-6339	153	27	)	)	PUNCT
ejpam-6339	153	28	=	=	SYM
ejpam-6339	153	29	∅̃	∅̃	NOUN
ejpam-6339	153	30	,	,	PUNCT
ejpam-6339	153	31	(	(	PUNCT
ejpam-6339	153	32	non	non	ADJ
ejpam-6339	153	33	-	-	ADJ
ejpam-6339	153	34	spontaneous	spontaneous	ADJ
ejpam-6339	153	35	creation	creation	NOUN
ejpam-6339	153	36	)	)	PUNCT
ejpam-6339	153	37	whenever	whenever	SCONJ
ejpam-6339	153	38	m	m	X
ejpam-6339	153	39	,	,	PUNCT
ejpam-6339	153	40	n	n	PROPN
ejpam-6339	153	41	∈	∈	PROPN
ejpam-6339	153	42	n	n	CCONJ
ejpam-6339	153	43	(	(	PUNCT
ejpam-6339	153	44	x	x	NOUN
ejpam-6339	153	45	)	)	PUNCT
ejpam-6339	153	46	.	.	PUNCT
ejpam-6339	154	1	proposition	proposition	NOUN
ejpam-6339	154	2	7	7	NUM
ejpam-6339	154	3	.	.	PUNCT
ejpam-6339	155	1	if	if	SCONJ
ejpam-6339	155	2	υ	υ	NOUN
ejpam-6339	155	3	:	:	PUNCT
ejpam-6339	155	4	n	n	CCONJ
ejpam-6339	155	5	(	(	PUNCT
ejpam-6339	155	6	x	x	X
ejpam-6339	155	7	)	)	PUNCT
ejpam-6339	155	8	→	→	SYM
ejpam-6339	155	9	n	n	CCONJ
ejpam-6339	155	10	(	(	PUNCT
ejpam-6339	155	11	x	x	X
ejpam-6339	155	12	)	)	PUNCT
ejpam-6339	155	13	is	be	AUX
ejpam-6339	155	14	a	a	DET
ejpam-6339	155	15	n	n	CCONJ
ejpam-6339	155	16	-closure	-closure	NOUN
ejpam-6339	155	17	operator	operator	NOUN
ejpam-6339	155	18	,	,	PUNCT
ejpam-6339	155	19	then	then	ADV
ejpam-6339	155	20	the	the	DET
ejpam-6339	155	21	collection	collection	NOUN
ejpam-6339	155	22	τ(υ	τ(υ	NOUN
ejpam-6339	155	23	)	)	PUNCT
ejpam-6339	155	24	=	=	SYM
ejpam-6339	155	25	{	{	PUNCT
ejpam-6339	155	26	n	n	NOUN
ejpam-6339	155	27	∈	∈	PROPN
ejpam-6339	155	28	n	n	CCONJ
ejpam-6339	155	29	(	(	PUNCT
ejpam-6339	155	30	x	x	X
ejpam-6339	155	31	)	)	PUNCT
ejpam-6339	155	32	:	:	PUNCT
ejpam-6339	156	1	υ(n	υ(n	PROPN
ejpam-6339	156	2	c	c	PROPN
ejpam-6339	156	3	)	)	PUNCT
ejpam-6339	156	4	=	=	SYM
ejpam-6339	157	1	n	n	PROPN
ejpam-6339	157	2	c	c	X
ejpam-6339	157	3	}	}	PUNCT
ejpam-6339	157	4	is	be	AUX
ejpam-6339	157	5	a	a	DET
ejpam-6339	157	6	n	n	PRON
ejpam-6339	157	7	-topology	-topology	NOUN
ejpam-6339	157	8	on	on	ADP
ejpam-6339	157	9	x	x	PUNCT
ejpam-6339	157	10	and	and	CCONJ
ejpam-6339	157	11	υ	υ	PROPN
ejpam-6339	157	12	is	be	AUX
ejpam-6339	157	13	the	the	PRON
ejpam-6339	157	14	n	n	ADV
ejpam-6339	157	15	-closure	-closure	NOUN
ejpam-6339	157	16	in	in	ADP
ejpam-6339	157	17	the	the	DET
ejpam-6339	157	18	n	n	NUM
ejpam-6339	157	19	-topological	-topological	ADJ
ejpam-6339	157	20	space	space	NOUN
ejpam-6339	157	21	(	(	PUNCT
ejpam-6339	157	22	x	x	NOUN
ejpam-6339	157	23	,	,	PUNCT
ejpam-6339	157	24	τ(υ	τ(υ	NOUN
ejpam-6339	157	25	)	)	PUNCT
ejpam-6339	157	26	)	)	PUNCT
ejpam-6339	157	27	.	.	PUNCT
ejpam-6339	158	1	proof	proof	NOUN
ejpam-6339	158	2	.	.	PUNCT
ejpam-6339	159	1	we	we	PRON
ejpam-6339	159	2	verify	verify	VERB
ejpam-6339	159	3	that	that	SCONJ
ejpam-6339	159	4	τ(υ	τ(υ	NOUN
ejpam-6339	159	5	)	)	PUNCT
ejpam-6339	159	6	satisfies	satisfy	VERB
ejpam-6339	159	7	the	the	DET
ejpam-6339	159	8	conditions	condition	NOUN
ejpam-6339	159	9	of	of	ADP
ejpam-6339	160	1	a	a	DET
ejpam-6339	160	2	n	n	PRON
ejpam-6339	160	3	-topology	-topology	NOUN
ejpam-6339	160	4	on	on	ADP
ejpam-6339	160	5	x.	x.	NOUN
ejpam-6339	160	6	indeed	indeed	ADV
ejpam-6339	160	7	:	:	PUNCT
ejpam-6339	160	8	(	(	PUNCT
ejpam-6339	160	9	1	1	X
ejpam-6339	160	10	)	)	PUNCT
ejpam-6339	160	11	x̃	x̃	PROPN
ejpam-6339	160	12	∈	∈	PROPN
ejpam-6339	160	13	τ(υ	τ(υ	NOUN
ejpam-6339	160	14	)	)	PUNCT
ejpam-6339	160	15	because	because	SCONJ
ejpam-6339	160	16	by	by	ADP
ejpam-6339	160	17	the	the	DET
ejpam-6339	160	18	non	non	ADJ
ejpam-6339	160	19	-	-	ADJ
ejpam-6339	160	20	spontaneous	spontaneous	ADJ
ejpam-6339	160	21	creation	creation	NOUN
ejpam-6339	160	22	of	of	ADP
ejpam-6339	160	23	υ	υ	PROPN
ejpam-6339	160	24	,	,	PUNCT
ejpam-6339	160	25	we	we	PRON
ejpam-6339	160	26	have	have	VERB
ejpam-6339	160	27	υ(x̃c	υ(x̃c	PROPN
ejpam-6339	160	28	)	)	PUNCT
ejpam-6339	160	29	=	=	SYM
ejpam-6339	160	30	υ(∅̃	υ(∅̃	NOUN
ejpam-6339	160	31	)	)	PUNCT
ejpam-6339	160	32	=	=	SYM
ejpam-6339	160	33	∅̃	∅̃	NOUN
ejpam-6339	160	34	=	=	PUNCT
ejpam-6339	160	35	x̃c	x̃c	PROPN
ejpam-6339	160	36	.	.	PUNCT
ejpam-6339	161	1	also	also	ADV
ejpam-6339	161	2	,	,	PUNCT
ejpam-6339	161	3	∅̃	∅̃	NOUN
ejpam-6339	161	4	∈	∈	NOUN
ejpam-6339	161	5	τ(υ	τ(υ	NOUN
ejpam-6339	161	6	)	)	PUNCT
ejpam-6339	161	7	because	because	SCONJ
ejpam-6339	161	8	x̃	x̃	PROPN
ejpam-6339	161	9	⊑	⊑	PRON
ejpam-6339	161	10	υ(x̃	υ(x̃	PROPN
ejpam-6339	161	11	)	)	PUNCT
ejpam-6339	161	12	⊑	⊑	X
ejpam-6339	161	13	x̃	x̃	PROPN
ejpam-6339	161	14	by	by	ADP
ejpam-6339	161	15	expansivity	expansivity	NOUN
ejpam-6339	161	16	of	of	ADP
ejpam-6339	161	17	υ	υ	PROPN
ejpam-6339	161	18	and	and	CCONJ
ejpam-6339	161	19	the	the	DET
ejpam-6339	161	20	fact	fact	NOUN
ejpam-6339	161	21	that	that	SCONJ
ejpam-6339	161	22	υ(x̃	υ(x̃	NOUN
ejpam-6339	161	23	)	)	PUNCT
ejpam-6339	161	24	∈	∈	PROPN
ejpam-6339	161	25	n	n	CCONJ
ejpam-6339	161	26	(	(	PUNCT
ejpam-6339	161	27	x	x	NOUN
ejpam-6339	161	28	)	)	PUNCT
ejpam-6339	161	29	.	.	PUNCT
ejpam-6339	162	1	(	(	PUNCT
ejpam-6339	162	2	2	2	X
ejpam-6339	162	3	)	)	PUNCT
ejpam-6339	162	4	let	let	VERB
ejpam-6339	162	5	{	{	PUNCT
ejpam-6339	162	6	mj	mj	NOUN
ejpam-6339	162	7	:	:	PUNCT
ejpam-6339	162	8	j	j	PROPN
ejpam-6339	162	9	∈	∈	PROPN
ejpam-6339	162	10	j	j	PROPN
ejpam-6339	162	11	}	}	PUNCT
ejpam-6339	162	12	⊆	⊆	NUM
ejpam-6339	162	13	n	n	NUM
ejpam-6339	162	14	(	(	PUNCT
ejpam-6339	162	15	x	x	NOUN
ejpam-6339	162	16	)	)	PUNCT
ejpam-6339	162	17	.	.	PUNCT
ejpam-6339	163	1	then	then	ADV
ejpam-6339	163	2	,	,	PUNCT
ejpam-6339	163	3	υ(m	υ(m	PROPN
ejpam-6339	163	4	c	c	PROPN
ejpam-6339	163	5	j	j	PROPN
ejpam-6339	163	6	)	)	PUNCT
ejpam-6339	164	1	=	=	NOUN
ejpam-6339	164	2	m	m	PROPN
ejpam-6339	164	3	c	c	NOUN
ejpam-6339	164	4	j	j	PROPN
ejpam-6339	164	5	for	for	ADP
ejpam-6339	164	6	each	each	DET
ejpam-6339	164	7	j	j	PROPN
ejpam-6339	164	8	∈	∈	PROPN
ejpam-6339	164	9	j	j	PROPN
ejpam-6339	164	10	.	.	PUNCT
ejpam-6339	165	1	by	by	ADP
ejpam-6339	165	2	expansivity	expansivity	PROPN
ejpam-6339	165	3	υ	υ	PROPN
ejpam-6339	165	4	,	,	PUNCT
ejpam-6339	165	5	we	we	PRON
ejpam-6339	165	6	have	have	VERB
ejpam-6339	165	7	⊔	⊔	NOUN
ejpam-6339	165	8	j∈j	j∈j	NOUN
ejpam-6339	165	9	mj	mj	PROPN
ejpam-6339	165	10	c	c	PROPN
ejpam-6339	165	11	⊑	⊑	PRON
ejpam-6339	165	12	υ	υ	PROPN
ejpam-6339	165	13	⊔	⊔	NOUN
ejpam-6339	165	14	j∈j	j∈j	NOUN
ejpam-6339	165	15	mj	mj	PROPN
ejpam-6339	165	16	c.	c.	PROPN
ejpam-6339	165	17	for	for	ADP
ejpam-6339	165	18	other	other	ADJ
ejpam-6339	165	19	neutrosophic	neutrosophic	ADJ
ejpam-6339	165	20	inclusion	inclusion	NOUN
ejpam-6339	165	21	,	,	PUNCT
ejpam-6339	165	22	let	let	VERB
ejpam-6339	165	23	us	we	PRON
ejpam-6339	165	24	note	note	VERB
ejpam-6339	165	25	that⊔	that⊔	NOUN
ejpam-6339	165	26	j∈j	j∈j	PROPN
ejpam-6339	165	27	mj	mj	PROPN
ejpam-6339	165	28	c	c	PUNCT
ejpam-6339	165	29	⊑m	⊑m	PROPN
ejpam-6339	165	30	c	c	PROPN
ejpam-6339	165	31	j	j	PROPN
ejpam-6339	165	32	,	,	PUNCT
ejpam-6339	165	33	for	for	ADP
ejpam-6339	165	34	each	each	DET
ejpam-6339	165	35	j	j	PROPN
ejpam-6339	165	36	∈	∈	PROPN
ejpam-6339	165	37	j	j	PROPN
ejpam-6339	165	38	.	.	PUNCT
ejpam-6339	166	1	by	by	ADP
ejpam-6339	166	2	idempotency	idempotency	NOUN
ejpam-6339	166	3	of	of	ADP
ejpam-6339	166	4	υ	υ	NOUN
ejpam-6339	166	5	,	,	PUNCT
ejpam-6339	166	6	it	it	PRON
ejpam-6339	166	7	follows	follow	VERB
ejpam-6339	166	8	that	that	SCONJ
ejpam-6339	166	9	υ	υ	PROPN
ejpam-6339	166	10	⊔	⊔	PROPN
ejpam-6339	166	11	j∈j	j∈j	NOUN
ejpam-6339	166	12	mi	mi	PROPN
ejpam-6339	166	13	c	c	VERB
ejpam-6339	166	14	⊑	⊑	PRON
ejpam-6339	166	15	υ(m	υ(m	PROPN
ejpam-6339	166	16	c	c	PROPN
ejpam-6339	166	17	j	j	PROPN
ejpam-6339	166	18	)	)	PUNCT
ejpam-6339	167	1	=	=	NOUN
ejpam-6339	167	2	m	m	PROPN
ejpam-6339	167	3	c	c	NOUN
ejpam-6339	167	4	j	j	PROPN
ejpam-6339	167	5	for	for	ADP
ejpam-6339	167	6	each	each	DET
ejpam-6339	167	7	j	j	PROPN
ejpam-6339	167	8	∈	∈	PROPN
ejpam-6339	167	9	j	j	PROPN
ejpam-6339	167	10	.	.	PUNCT
ejpam-6339	168	1	thus	thus	ADV
ejpam-6339	168	2	,	,	PUNCT
ejpam-6339	168	3	υ	υ	PROPN
ejpam-6339	168	4	⊔	⊔	PROPN
ejpam-6339	168	5	j∈j	j∈j	NOUN
ejpam-6339	168	6	mj	mj	PROPN
ejpam-6339	168	7	c	c	VERB
ejpam-6339	168	8	⊑	⊑	PROPN
ejpam-6339	168	9	l	l	PROPN
ejpam-6339	168	10	j∈j	j∈j	PROPN
ejpam-6339	168	11	m	m	PROPN
ejpam-6339	168	12	c	c	NOUN
ejpam-6339	168	13	j	j	PROPN
ejpam-6339	168	14	=	=	SYM
ejpam-6339	168	15	⊔	⊔	PROPN
ejpam-6339	168	16	j∈j	j∈j	NOUN
ejpam-6339	168	17	mj	mj	PROPN
ejpam-6339	168	18	c	c	PROPN
ejpam-6339	168	19	and	and	CCONJ
ejpam-6339	168	20	hence	hence	ADV
ejpam-6339	168	21	,	,	PUNCT
ejpam-6339	168	22	υ	υ	PROPN
ejpam-6339	168	23	⊔	⊔	PROPN
ejpam-6339	168	24	j∈j	j∈j	NOUN
ejpam-6339	168	25	mj	mj	PROPN
ejpam-6339	168	26	c	c	VERB
ejpam-6339	169	1	=	=	NOUN
ejpam-6339	169	2	⊔	⊔	X
ejpam-6339	169	3	j∈j	j∈j	NOUN
ejpam-6339	169	4	mj	mj	PROPN
ejpam-6339	169	5	c	c	PROPN
ejpam-6339	169	6	.	.	PUNCT
ejpam-6339	170	1	this	this	PRON
ejpam-6339	170	2	shows	show	VERB
ejpam-6339	170	3	that	that	SCONJ
ejpam-6339	170	4	⊔	⊔	PROPN
ejpam-6339	170	5	j∈j	j∈j	NOUN
ejpam-6339	170	6	mj	mj	PROPN
ejpam-6339	170	7	belongs	belong	VERB
ejpam-6339	170	8	to	to	ADP
ejpam-6339	170	9	τ(υ	τ(υ	NOUN
ejpam-6339	170	10	)	)	PUNCT
ejpam-6339	170	11	.	.	PUNCT
ejpam-6339	171	1	(	(	PUNCT
ejpam-6339	171	2	3	3	X
ejpam-6339	171	3	)	)	PUNCT
ejpam-6339	171	4	suppose	suppose	VERB
ejpam-6339	171	5	that	that	SCONJ
ejpam-6339	171	6	n	n	CCONJ
ejpam-6339	171	7	,	,	PUNCT
ejpam-6339	171	8	m	m	VERB
ejpam-6339	171	9	∈	∈	ADJ
ejpam-6339	171	10	n	n	CCONJ
ejpam-6339	171	11	(	(	PUNCT
ejpam-6339	171	12	x	x	NOUN
ejpam-6339	171	13	)	)	PUNCT
ejpam-6339	171	14	.	.	PUNCT
ejpam-6339	172	1	then	then	ADV
ejpam-6339	172	2	,	,	PUNCT
ejpam-6339	172	3	υ(n	υ(n	PROPN
ejpam-6339	172	4	c	c	PROPN
ejpam-6339	172	5	)	)	PUNCT
ejpam-6339	172	6	=	=	SYM
ejpam-6339	172	7	n	n	PROPN
ejpam-6339	172	8	c	c	NOUN
ejpam-6339	172	9	and	and	CCONJ
ejpam-6339	172	10	υ(m	υ(m	PROPN
ejpam-6339	172	11	c	c	PROPN
ejpam-6339	172	12	)	)	PUNCT
ejpam-6339	172	13	=	=	PUNCT
ejpam-6339	173	1	m	m	VERB
ejpam-6339	173	2	c	c	NOUN
ejpam-6339	173	3	and	and	CCONJ
ejpam-6339	173	4	so	so	ADV
ejpam-6339	173	5	,	,	PUNCT
ejpam-6339	173	6	by	by	ADP
ejpam-6339	173	7	additivity	additivity	NOUN
ejpam-6339	173	8	of	of	ADP
ejpam-6339	173	9	υ	υ	NOUN
ejpam-6339	173	10	,	,	PUNCT
ejpam-6339	173	11	we	we	PRON
ejpam-6339	173	12	get	get	VERB
ejpam-6339	173	13	that	that	DET
ejpam-6339	173	14	υ((n	υ((n	NOUN
ejpam-6339	173	15	⊓m)c	⊓m)c	ADJ
ejpam-6339	173	16	)	)	PUNCT
ejpam-6339	174	1	=	=	PUNCT
ejpam-6339	174	2	υ(n	υ(n	PROPN
ejpam-6339	174	3	c	c	PROPN
ejpam-6339	174	4	⊔m	⊔m	NUM
ejpam-6339	174	5	c	c	NOUN
ejpam-6339	174	6	)	)	PUNCT
ejpam-6339	174	7	=	=	SYM
ejpam-6339	174	8	υ(n	υ(n	PROPN
ejpam-6339	174	9	c)⊔υ(m	c)⊔υ(m	NOUN
ejpam-6339	174	10	c	c	X
ejpam-6339	174	11	)	)	PUNCT
ejpam-6339	174	12	=	=	SYM
ejpam-6339	174	13	n	n	PROPN
ejpam-6339	174	14	c	c	NOUN
ejpam-6339	174	15	⊔m	⊔m	NUM
ejpam-6339	174	16	c	c	NOUN
ejpam-6339	174	17	=	=	SYM
ejpam-6339	174	18	(	(	PUNCT
ejpam-6339	174	19	n	n	CCONJ
ejpam-6339	174	20	⊓m)c	⊓m)c	NOUN
ejpam-6339	174	21	,	,	PUNCT
ejpam-6339	174	22	which	which	PRON
ejpam-6339	174	23	proves	prove	VERB
ejpam-6339	174	24	that	that	SCONJ
ejpam-6339	174	25	n	n	ADV
ejpam-6339	174	26	⊓m	⊓m	NOUN
ejpam-6339	174	27	belongs	belong	VERB
ejpam-6339	174	28	to	to	ADP
ejpam-6339	174	29	τ(υ	τ(υ	NOUN
ejpam-6339	174	30	)	)	PUNCT
ejpam-6339	174	31	.	.	PUNCT
ejpam-6339	175	1	from	from	ADP
ejpam-6339	175	2	(	(	PUNCT
ejpam-6339	175	3	1)-(3	1)-(3	NUM
ejpam-6339	175	4	)	)	PUNCT
ejpam-6339	175	5	,	,	PUNCT
ejpam-6339	175	6	we	we	PRON
ejpam-6339	175	7	conclude	conclude	VERB
ejpam-6339	175	8	that	that	SCONJ
ejpam-6339	175	9	τ(υ	τ(υ	NOUN
ejpam-6339	175	10	)	)	PUNCT
ejpam-6339	175	11	is	be	AUX
ejpam-6339	175	12	a	a	DET
ejpam-6339	175	13	n	n	PRON
ejpam-6339	175	14	-topology	-topology	NOUN
ejpam-6339	175	15	on	on	ADP
ejpam-6339	175	16	x.	x.	NOUN
ejpam-6339	175	17	now	now	ADV
ejpam-6339	175	18	,	,	PUNCT
ejpam-6339	175	19	we	we	PRON
ejpam-6339	175	20	will	will	AUX
ejpam-6339	175	21	prove	prove	VERB
ejpam-6339	175	22	the	the	DET
ejpam-6339	175	23	remainder	remainder	NOUN
ejpam-6339	175	24	of	of	ADP
ejpam-6339	175	25	the	the	DET
ejpam-6339	175	26	statement	statement	NOUN
ejpam-6339	175	27	.	.	PUNCT
ejpam-6339	176	1	first	first	ADV
ejpam-6339	176	2	,	,	PUNCT
ejpam-6339	176	3	υ(n	υ(n	PROPN
ejpam-6339	176	4	)	)	PUNCT
ejpam-6339	176	5	∈	∈	PROPN
ejpam-6339	176	6	τ	τ	PROPN
ejpam-6339	176	7	c(υ	c(υ	PROPN
ejpam-6339	176	8	)	)	PUNCT
ejpam-6339	176	9	,	,	PUNCT
ejpam-6339	176	10	because	because	SCONJ
ejpam-6339	176	11	υ(n	υ(n	PROPN
ejpam-6339	176	12	)	)	PUNCT
ejpam-6339	176	13	=	=	SYM
ejpam-6339	176	14	υ(υ(n	υ(υ(n	PROPN
ejpam-6339	176	15	)	)	PUNCT
ejpam-6339	176	16	)	)	PUNCT
ejpam-6339	176	17	by	by	ADP
ejpam-6339	176	18	(	(	PUNCT
ejpam-6339	176	19	2	2	NUM
ejpam-6339	176	20	)	)	PUNCT
ejpam-6339	176	21	.	.	PUNCT
ejpam-6339	177	1	since	since	SCONJ
ejpam-6339	177	2	n	n	PROPN
ejpam-6339	177	3	⊑	⊑	DET
ejpam-6339	177	4	υ(n	υ(n	PROPN
ejpam-6339	177	5	)	)	PUNCT
ejpam-6339	177	6	and	and	CCONJ
ejpam-6339	177	7	cl(n	cl(n	NUM
ejpam-6339	177	8	)	)	PUNCT
ejpam-6339	177	9	is	be	AUX
ejpam-6339	177	10	the	the	DET
ejpam-6339	177	11	smallest	small	ADJ
ejpam-6339	177	12	n	n	ADP
ejpam-6339	177	13	-τ(υ)-closed	-τ(υ)-close	VERB
ejpam-6339	177	14	set	set	NOUN
ejpam-6339	177	15	containing	contain	VERB
ejpam-6339	177	16	n	n	PRON
ejpam-6339	177	17	,	,	PUNCT
ejpam-6339	177	18	it	it	PRON
ejpam-6339	177	19	follows	follow	VERB
ejpam-6339	177	20	that	that	PRON
ejpam-6339	177	21	cl(n	cl(n	VERB
ejpam-6339	177	22	)	)	PUNCT
ejpam-6339	177	23	⊑	⊑	PRON
ejpam-6339	177	24	υ(n	υ(n	PROPN
ejpam-6339	177	25	)	)	PUNCT
ejpam-6339	177	26	.	.	PUNCT
ejpam-6339	178	1	secondly	secondly	ADV
ejpam-6339	178	2	,	,	PUNCT
ejpam-6339	178	3	n	n	PROPN
ejpam-6339	178	4	⊑	⊑	DET
ejpam-6339	178	5	cl(n	cl(n	X
ejpam-6339	178	6	)	)	PUNCT
ejpam-6339	178	7	and	and	CCONJ
ejpam-6339	178	8	cl(n	cl(n	NOUN
ejpam-6339	178	9	)	)	PUNCT
ejpam-6339	178	10	⊑	⊑	PRON
ejpam-6339	178	11	υ(n	υ(n	PROPN
ejpam-6339	178	12	)	)	PUNCT
ejpam-6339	178	13	imply	imply	VERB
ejpam-6339	178	14	that	that	PRON
ejpam-6339	178	15	cl(n	cl(n	VERB
ejpam-6339	178	16	)	)	PUNCT
ejpam-6339	178	17	⊑	⊑	PRON
ejpam-6339	178	18	υ(cl(n	υ(cl(n	PROPN
ejpam-6339	178	19	)	)	PUNCT
ejpam-6339	178	20	)	)	PUNCT
ejpam-6339	179	1	=	=	SYM
ejpam-6339	179	2	cl(n	cl(n	X
ejpam-6339	179	3	)	)	PUNCT
ejpam-6339	179	4	.	.	PUNCT
ejpam-6339	180	1	therefore	therefore	ADV
ejpam-6339	180	2	,	,	PUNCT
ejpam-6339	180	3	υ(n	υ(n	PROPN
ejpam-6339	180	4	)	)	PUNCT
ejpam-6339	180	5	=	=	SYM
ejpam-6339	180	6	cl(n	cl(n	X
ejpam-6339	180	7	)	)	PUNCT
ejpam-6339	180	8	whatever	whatever	PRON
ejpam-6339	180	9	is	be	AUX
ejpam-6339	180	10	n	n	PRON
ejpam-6339	180	11	∈	∈	PROPN
ejpam-6339	180	12	n	n	CCONJ
ejpam-6339	180	13	(	(	PUNCT
ejpam-6339	180	14	x	x	NOUN
ejpam-6339	180	15	)	)	PUNCT
ejpam-6339	180	16	.	.	PUNCT
ejpam-6339	181	1	let	let	VERB
ejpam-6339	181	2	np(x	np(x	PRON
ejpam-6339	181	3	)	)	PUNCT
ejpam-6339	181	4	=	=	PRON
ejpam-6339	181	5	{	{	PUNCT
ejpam-6339	181	6	n	n	NOUN
ejpam-6339	181	7	∈	∈	PROPN
ejpam-6339	181	8	n	n	CCONJ
ejpam-6339	181	9	(	(	PUNCT
ejpam-6339	181	10	x	x	X
ejpam-6339	181	11	)	)	PUNCT
ejpam-6339	181	12	:	:	PUNCT
ejpam-6339	181	13	there	there	PRON
ejpam-6339	181	14	exists	exist	VERB
ejpam-6339	181	15	a	a	DET
ejpam-6339	181	16	n	n	CCONJ
ejpam-6339	181	17	-point	-point	PROPN
ejpam-6339	181	18	xa	xa	PROPN
ejpam-6339	181	19	,	,	PUNCT
ejpam-6339	181	20	b	b	PROPN
ejpam-6339	181	21	,	,	PUNCT
ejpam-6339	181	22	c	c	PROPN
ejpam-6339	181	23	∈	∈	PROPN
ejpam-6339	181	24	n	n	CCONJ
ejpam-6339	181	25	}	}	PUNCT
ejpam-6339	181	26	and	and	CCONJ
ejpam-6339	181	27	let	let	VERB
ejpam-6339	181	28	n	n	PRON
ejpam-6339	181	29	′(x	′(x	VERB
ejpam-6339	181	30	)	)	PUNCT
ejpam-6339	182	1	=	=	PRON
ejpam-6339	182	2	{	{	PUNCT
ejpam-6339	182	3	∅̃	∅̃	NOUN
ejpam-6339	182	4	}	}	PUNCT
ejpam-6339	182	5	∪	∪	NOUN
ejpam-6339	182	6	np(x	np(x	NOUN
ejpam-6339	182	7	)	)	PUNCT
ejpam-6339	182	8	.	.	PUNCT
ejpam-6339	183	1	in	in	ADP
ejpam-6339	183	2	the	the	DET
ejpam-6339	183	3	remainder	remainder	NOUN
ejpam-6339	183	4	of	of	ADP
ejpam-6339	183	5	this	this	DET
ejpam-6339	183	6	paper	paper	NOUN
ejpam-6339	183	7	,	,	PUNCT
ejpam-6339	183	8	we	we	PRON
ejpam-6339	183	9	will	will	AUX
ejpam-6339	183	10	use	use	VERB
ejpam-6339	183	11	the	the	DET
ejpam-6339	183	12	definitions	definition	NOUN
ejpam-6339	183	13	and	and	CCONJ
ejpam-6339	183	14	results	result	NOUN
ejpam-6339	183	15	described	describe	VERB
ejpam-6339	183	16	in	in	ADP
ejpam-6339	183	17	the	the	DET
ejpam-6339	183	18	previous	previous	ADJ
ejpam-6339	183	19	section	section	NOUN
ejpam-6339	183	20	,	,	PUNCT
ejpam-6339	183	21	restricted	restrict	VERB
ejpam-6339	183	22	to	to	ADP
ejpam-6339	183	23	the	the	DET
ejpam-6339	183	24	collection	collection	NOUN
ejpam-6339	183	25	n	n	PRON
ejpam-6339	183	26	′(x	′(x	NOUN
ejpam-6339	183	27	)	)	PUNCT
ejpam-6339	183	28	.	.	PUNCT
ejpam-6339	184	1	j.	j.	PROPN
ejpam-6339	184	2	sanabria	sanabria	PROPN
ejpam-6339	184	3	,	,	PUNCT
ejpam-6339	184	4	e.	e.	PROPN
ejpam-6339	184	5	rosas	rosas	PROPN
ejpam-6339	184	6	,	,	PUNCT
ejpam-6339	184	7	c.	c.	PROPN
ejpam-6339	184	8	granados	granados	PROPN
ejpam-6339	184	9	/	/	PUNCT
ejpam-6339	184	10	eur	eur	PROPN
ejpam-6339	184	11	.	.	PUNCT
ejpam-6339	185	1	j.	j.	PROPN
ejpam-6339	185	2	pure	pure	PROPN
ejpam-6339	185	3	appl	appl	PROPN
ejpam-6339	185	4	.	.	PROPN
ejpam-6339	185	5	math	math	PROPN
ejpam-6339	185	6	,	,	PUNCT
ejpam-6339	185	7	18	18	NUM
ejpam-6339	185	8	(	(	PUNCT
ejpam-6339	185	9	3	3	NUM
ejpam-6339	185	10	)	)	PUNCT
ejpam-6339	185	11	(	(	PUNCT
ejpam-6339	185	12	2025	2025	NUM
ejpam-6339	185	13	)	)	PUNCT
ejpam-6339	185	14	,	,	PUNCT
ejpam-6339	185	15	6339	6339	NUM
ejpam-6339	185	16	9	9	NUM
ejpam-6339	185	17	of	of	ADP
ejpam-6339	185	18	15	15	NUM
ejpam-6339	185	19	definition	definition	NOUN
ejpam-6339	185	20	10	10	NUM
ejpam-6339	185	21	.	.	PUNCT
ejpam-6339	186	1	let	let	VERB
ejpam-6339	186	2	(	(	PUNCT
ejpam-6339	186	3	x	x	NOUN
ejpam-6339	186	4	,	,	PUNCT
ejpam-6339	186	5	τ	τ	X
ejpam-6339	186	6	)	)	PUNCT
ejpam-6339	186	7	be	be	VERB
ejpam-6339	186	8	a	a	DET
ejpam-6339	186	9	n	n	CCONJ
ejpam-6339	186	10	-topological	-topological	ADJ
ejpam-6339	186	11	space	space	NOUN
ejpam-6339	186	12	and	and	CCONJ
ejpam-6339	186	13	n	n	CCONJ
ejpam-6339	186	14	∈	∈	PROPN
ejpam-6339	186	15	n	n	PRON
ejpam-6339	186	16	′(x	′(x	NOUN
ejpam-6339	186	17	)	)	PUNCT
ejpam-6339	186	18	.	.	PUNCT
ejpam-6339	187	1	the	the	DET
ejpam-6339	187	2	n	n	CCONJ
ejpam-6339	187	3	-point	-point	NOUN
ejpam-6339	187	4	-	-	PUNCT
ejpam-6339	187	5	closure	closure	NOUN
ejpam-6339	187	6	of	of	ADP
ejpam-6339	187	7	n	n	PROPN
ejpam-6339	187	8	,	,	PUNCT
ejpam-6339	187	9	denoted	denote	VERB
ejpam-6339	187	10	by	by	ADP
ejpam-6339	187	11	clp(n	clp(n	PROPN
ejpam-6339	187	12	)	)	PUNCT
ejpam-6339	187	13	,	,	PUNCT
ejpam-6339	187	14	is	be	AUX
ejpam-6339	187	15	defined	define	VERB
ejpam-6339	187	16	as	as	ADP
ejpam-6339	187	17	clp(n	clp(n	PROPN
ejpam-6339	187	18	)	)	PUNCT
ejpam-6339	188	1	=	=	SYM
ejpam-6339	188	2	⊔	⊔	PROPN
ejpam-6339	188	3	{	{	PUNCT
ejpam-6339	188	4	xa	xa	PROPN
ejpam-6339	188	5	,	,	PUNCT
ejpam-6339	188	6	b	b	PROPN
ejpam-6339	188	7	,	,	PUNCT
ejpam-6339	188	8	c	c	PROPN
ejpam-6339	188	9	∈	∈	PROPN
ejpam-6339	188	10	n	n	PRON
ejpam-6339	188	11	′(x	′(x	NOUN
ejpam-6339	188	12	)	)	PUNCT
ejpam-6339	188	13	:	:	PUNCT
ejpam-6339	189	1	u	u	NOUN
ejpam-6339	189	2	⊓n	⊓n	VERB
ejpam-6339	189	3	̸=	̸=	PROPN
ejpam-6339	189	4	∅̃	∅̃	NOUN
ejpam-6339	189	5	for	for	ADP
ejpam-6339	189	6	every	every	DET
ejpam-6339	189	7	u	u	PROPN
ejpam-6339	189	8	∈	∈	PROPN
ejpam-6339	189	9	τ(xa	τ(xa	NUM
ejpam-6339	189	10	,	,	PUNCT
ejpam-6339	189	11	b	b	NOUN
ejpam-6339	189	12	,	,	PUNCT
ejpam-6339	189	13	c	c	NOUN
ejpam-6339	189	14	)	)	PUNCT
ejpam-6339	189	15	}	}	PUNCT
ejpam-6339	189	16	.	.	PUNCT
ejpam-6339	190	1	remark	remark	NOUN
ejpam-6339	190	2	3	3	NUM
ejpam-6339	190	3	.	.	PUNCT
ejpam-6339	191	1	in	in	ADP
ejpam-6339	191	2	general	general	ADJ
ejpam-6339	191	3	,	,	PUNCT
ejpam-6339	191	4	it	it	PRON
ejpam-6339	191	5	is	be	AUX
ejpam-6339	191	6	not	not	PART
ejpam-6339	191	7	true	true	ADJ
ejpam-6339	191	8	that	that	SCONJ
ejpam-6339	191	9	cl(n	cl(n	VERB
ejpam-6339	191	10	)	)	PUNCT
ejpam-6339	191	11	=	=	SYM
ejpam-6339	191	12	clp(n	clp(n	PROPN
ejpam-6339	191	13	)	)	PUNCT
ejpam-6339	191	14	for	for	ADP
ejpam-6339	191	15	eachn	eachn	PROPN
ejpam-6339	191	16	∈	∈	PROPN
ejpam-6339	191	17	n	n	PRON
ejpam-6339	191	18	′(x	′(x	NOUN
ejpam-6339	191	19	)	)	PUNCT
ejpam-6339	191	20	.	.	PUNCT
ejpam-6339	192	1	moreover	moreover	ADV
ejpam-6339	192	2	,	,	PUNCT
ejpam-6339	192	3	none	none	NOUN
ejpam-6339	192	4	of	of	ADP
ejpam-6339	192	5	the	the	DET
ejpam-6339	192	6	neutrosophic	neutrosophic	ADJ
ejpam-6339	192	7	inclusions	inclusion	NOUN
ejpam-6339	192	8	cl(n	cl(n	NOUN
ejpam-6339	192	9	)	)	PUNCT
ejpam-6339	192	10	⊑	⊑	PRON
ejpam-6339	192	11	clp(n	clp(n	PROPN
ejpam-6339	192	12	)	)	PUNCT
ejpam-6339	192	13	and	and	CCONJ
ejpam-6339	192	14	clp(n	clp(n	PROPN
ejpam-6339	192	15	)	)	PUNCT
ejpam-6339	192	16	⊑	⊑	PRON
ejpam-6339	192	17	cl(n	cl(n	X
ejpam-6339	192	18	)	)	PUNCT
ejpam-6339	192	19	is	be	AUX
ejpam-6339	192	20	true	true	ADJ
ejpam-6339	192	21	in	in	ADP
ejpam-6339	192	22	general	general	ADJ
ejpam-6339	192	23	,	,	PUNCT
ejpam-6339	192	24	as	as	SCONJ
ejpam-6339	192	25	we	we	PRON
ejpam-6339	192	26	can	can	AUX
ejpam-6339	192	27	see	see	VERB
ejpam-6339	192	28	in	in	ADP
ejpam-6339	192	29	the	the	DET
ejpam-6339	192	30	following	follow	VERB
ejpam-6339	192	31	two	two	NUM
ejpam-6339	192	32	examples	example	NOUN
ejpam-6339	192	33	.	.	PUNCT
ejpam-6339	193	1	example	example	NOUN
ejpam-6339	194	1	2	2	NUM
ejpam-6339	194	2	.	.	PUNCT
ejpam-6339	194	3	let	let	VERB
ejpam-6339	194	4	x	x	PUNCT
ejpam-6339	194	5	=	=	PRON
ejpam-6339	194	6	{	{	PUNCT
ejpam-6339	194	7	x	x	PROPN
ejpam-6339	194	8	,	,	PUNCT
ejpam-6339	194	9	y	y	NOUN
ejpam-6339	194	10	}	}	PUNCT
ejpam-6339	194	11	and	and	CCONJ
ejpam-6339	194	12	o	o	NOUN
ejpam-6339	194	13	,	,	PUNCT
ejpam-6339	194	14	u	u	PROPN
ejpam-6339	194	15	∈	∈	PROPN
ejpam-6339	194	16	n	n	PRON
ejpam-6339	194	17	′(x	′(x	NOUN
ejpam-6339	194	18	)	)	PUNCT
ejpam-6339	194	19	such	such	ADJ
ejpam-6339	194	20	that	that	DET
ejpam-6339	194	21	o	o	NOUN
ejpam-6339	194	22	=	=	PUNCT
ejpam-6339	194	23	{	{	PUNCT
ejpam-6339	194	24	⟨x	⟨x	VERB
ejpam-6339	194	25	,	,	PUNCT
ejpam-6339	194	26	0.5	0.5	NUM
ejpam-6339	194	27	,	,	PUNCT
ejpam-6339	194	28	0.5	0.5	NUM
ejpam-6339	194	29	,	,	PUNCT
ejpam-6339	194	30	0.5⟩	0.5⟩	NOUN
ejpam-6339	194	31	,	,	PUNCT
ejpam-6339	194	32	⟨y	⟨y	NOUN
ejpam-6339	194	33	,	,	PUNCT
ejpam-6339	194	34	0.4	0.4	NUM
ejpam-6339	194	35	,	,	PUNCT
ejpam-6339	194	36	0.4	0.4	NUM
ejpam-6339	194	37	,	,	PUNCT
ejpam-6339	194	38	0.6⟩	0.6⟩	NUM
ejpam-6339	194	39	}	}	PUNCT
ejpam-6339	194	40	,	,	PUNCT
ejpam-6339	194	41	u	u	NOUN
ejpam-6339	194	42	=	=	PUNCT
ejpam-6339	194	43	{	{	PUNCT
ejpam-6339	194	44	⟨x	⟨x	VERB
ejpam-6339	194	45	,	,	PUNCT
ejpam-6339	194	46	0.6	0.6	NUM
ejpam-6339	194	47	,	,	PUNCT
ejpam-6339	194	48	0.6	0.6	NUM
ejpam-6339	194	49	,	,	PUNCT
ejpam-6339	194	50	0.4⟩	0.4⟩	NUM
ejpam-6339	194	51	,	,	PUNCT
ejpam-6339	194	52	⟨y	⟨y	X
ejpam-6339	194	53	,	,	PUNCT
ejpam-6339	194	54	0.3	0.3	NUM
ejpam-6339	194	55	,	,	PUNCT
ejpam-6339	194	56	0.3	0.3	NUM
ejpam-6339	194	57	,	,	PUNCT
ejpam-6339	194	58	0.7⟩	0.7⟩	NUM
ejpam-6339	194	59	}	}	PUNCT
ejpam-6339	194	60	.	.	PUNCT
ejpam-6339	195	1	observe	observe	VERB
ejpam-6339	195	2	that	that	SCONJ
ejpam-6339	195	3	τ	τ	PROPN
ejpam-6339	195	4	=	=	PRON
ejpam-6339	195	5	{	{	PUNCT
ejpam-6339	195	6	∅̃	∅̃	NOUN
ejpam-6339	195	7	,	,	PUNCT
ejpam-6339	195	8	x̃	x̃	PROPN
ejpam-6339	195	9	,	,	PUNCT
ejpam-6339	195	10	o	o	NOUN
ejpam-6339	195	11	,	,	PUNCT
ejpam-6339	195	12	u	u	NOUN
ejpam-6339	195	13	,	,	PUNCT
ejpam-6339	195	14	o	o	NOUN
ejpam-6339	195	15	⊓	⊓	PROPN
ejpam-6339	195	16	u	u	NOUN
ejpam-6339	195	17	,	,	PUNCT
ejpam-6339	195	18	o	o	PROPN
ejpam-6339	195	19	⊔	⊔	NUM
ejpam-6339	195	20	u	u	NOUN
ejpam-6339	195	21	}	}	PUNCT
ejpam-6339	195	22	is	be	AUX
ejpam-6339	195	23	a	a	DET
ejpam-6339	195	24	n	n	PRON
ejpam-6339	195	25	-topology	-topology	NOUN
ejpam-6339	195	26	on	on	ADP
ejpam-6339	195	27	x.	x.	NOUN
ejpam-6339	195	28	then	then	ADV
ejpam-6339	195	29	,	,	PUNCT
ejpam-6339	195	30	the	the	DET
ejpam-6339	195	31	collection	collection	NOUN
ejpam-6339	195	32	of	of	ADP
ejpam-6339	195	33	all	all	DET
ejpam-6339	195	34	n	n	ADV
ejpam-6339	195	35	-closed	-close	VERB
ejpam-6339	195	36	sets	set	NOUN
ejpam-6339	195	37	on	on	ADP
ejpam-6339	195	38	x	x	X
ejpam-6339	195	39	is	be	AUX
ejpam-6339	195	40	τ	τ	X
ejpam-6339	195	41	c	c	NOUN
ejpam-6339	195	42	=	=	PUNCT
ejpam-6339	195	43	{	{	PUNCT
ejpam-6339	195	44	x̃	x̃	PROPN
ejpam-6339	195	45	,	,	PUNCT
ejpam-6339	195	46	∅̃	∅̃	NOUN
ejpam-6339	195	47	,	,	PUNCT
ejpam-6339	195	48	oc	oc	NOUN
ejpam-6339	195	49	,	,	PUNCT
ejpam-6339	195	50	u	u	NOUN
ejpam-6339	195	51	c	c	NOUN
ejpam-6339	195	52	,	,	PUNCT
ejpam-6339	195	53	(	(	PUNCT
ejpam-6339	195	54	o	o	X
ejpam-6339	195	55	⊓	⊓	NOUN
ejpam-6339	195	56	u)c	u)c	X
ejpam-6339	195	57	,	,	PUNCT
ejpam-6339	195	58	(	(	PUNCT
ejpam-6339	195	59	o	o	X
ejpam-6339	195	60	⊔	⊔	INTJ
ejpam-6339	195	61	u)c	u)c	PROPN
ejpam-6339	195	62	}	}	PUNCT
ejpam-6339	195	63	,	,	PUNCT
ejpam-6339	195	64	where	where	SCONJ
ejpam-6339	195	65	oc	oc	PART
ejpam-6339	195	66	=	=	X
ejpam-6339	195	67	{	{	PUNCT
ejpam-6339	195	68	⟨x	⟨x	VERB
ejpam-6339	195	69	,	,	PUNCT
ejpam-6339	195	70	0.5	0.5	NUM
ejpam-6339	195	71	,	,	PUNCT
ejpam-6339	195	72	0.5	0.5	NUM
ejpam-6339	195	73	,	,	PUNCT
ejpam-6339	195	74	0.5⟩	0.5⟩	NOUN
ejpam-6339	195	75	,	,	PUNCT
ejpam-6339	195	76	⟨y	⟨y	NOUN
ejpam-6339	195	77	,	,	PUNCT
ejpam-6339	195	78	0.6	0.6	NUM
ejpam-6339	195	79	,	,	PUNCT
ejpam-6339	195	80	0.6	0.6	NUM
ejpam-6339	195	81	,	,	PUNCT
ejpam-6339	195	82	0.4⟩	0.4⟩	NUM
ejpam-6339	195	83	}	}	PUNCT
ejpam-6339	195	84	,	,	PUNCT
ejpam-6339	195	85	u	u	NOUN
ejpam-6339	195	86	c	c	NOUN
ejpam-6339	195	87	=	=	PUNCT
ejpam-6339	195	88	{	{	PUNCT
ejpam-6339	195	89	⟨x	⟨x	VERB
ejpam-6339	195	90	,	,	PUNCT
ejpam-6339	195	91	0.4	0.4	NUM
ejpam-6339	195	92	,	,	PUNCT
ejpam-6339	195	93	0.4	0.4	NUM
ejpam-6339	195	94	,	,	PUNCT
ejpam-6339	195	95	0.6⟩	0.6⟩	NUM
ejpam-6339	195	96	,	,	PUNCT
ejpam-6339	195	97	⟨y	⟨y	X
ejpam-6339	195	98	,	,	PUNCT
ejpam-6339	195	99	0.7	0.7	NUM
ejpam-6339	195	100	,	,	PUNCT
ejpam-6339	195	101	0.7	0.7	NUM
ejpam-6339	195	102	,	,	PUNCT
ejpam-6339	195	103	0.3⟩	0.3⟩	NUM
ejpam-6339	195	104	}	}	PUNCT
ejpam-6339	195	105	,	,	PUNCT
ejpam-6339	195	106	(	(	PUNCT
ejpam-6339	195	107	o	o	NOUN
ejpam-6339	195	108	⊓	⊓	PROPN
ejpam-6339	195	109	u)c	u)c	X
ejpam-6339	195	110	=	=	PUNCT
ejpam-6339	195	111	{	{	PUNCT
ejpam-6339	195	112	⟨x	⟨x	VERB
ejpam-6339	195	113	,	,	PUNCT
ejpam-6339	195	114	0.5	0.5	NUM
ejpam-6339	195	115	,	,	PUNCT
ejpam-6339	195	116	0.4	0.4	NUM
ejpam-6339	195	117	,	,	PUNCT
ejpam-6339	195	118	0.5⟩	0.5⟩	NOUN
ejpam-6339	195	119	,	,	PUNCT
ejpam-6339	195	120	⟨y	⟨y	NOUN
ejpam-6339	195	121	,	,	PUNCT
ejpam-6339	195	122	0.7	0.7	NUM
ejpam-6339	195	123	,	,	PUNCT
ejpam-6339	195	124	0.6	0.6	NUM
ejpam-6339	195	125	,	,	PUNCT
ejpam-6339	195	126	0.3⟩	0.3⟩	NUM
ejpam-6339	195	127	}	}	PUNCT
ejpam-6339	195	128	,	,	PUNCT
ejpam-6339	195	129	(	(	PUNCT
ejpam-6339	195	130	o	o	X
ejpam-6339	195	131	⊔	⊔	X
ejpam-6339	195	132	u)c	u)c	X
ejpam-6339	195	133	=	=	X
ejpam-6339	195	134	{	{	PUNCT
ejpam-6339	195	135	⟨x	⟨x	VERB
ejpam-6339	195	136	,	,	PUNCT
ejpam-6339	195	137	0.4	0.4	NUM
ejpam-6339	195	138	,	,	PUNCT
ejpam-6339	195	139	0.5	0.5	NUM
ejpam-6339	195	140	,	,	PUNCT
ejpam-6339	195	141	0.6⟩	0.6⟩	NUM
ejpam-6339	195	142	,	,	PUNCT
ejpam-6339	195	143	⟨y	⟨y	X
ejpam-6339	195	144	,	,	PUNCT
ejpam-6339	195	145	0.6	0.6	NUM
ejpam-6339	195	146	,	,	PUNCT
ejpam-6339	195	147	0.7	0.7	NUM
ejpam-6339	195	148	,	,	PUNCT
ejpam-6339	195	149	0.4⟩	0.4⟩	NUM
ejpam-6339	195	150	}	}	PUNCT
ejpam-6339	195	151	.	.	PUNCT
ejpam-6339	196	1	consider	consider	VERB
ejpam-6339	196	2	the	the	DET
ejpam-6339	196	3	n	n	NOUN
ejpam-6339	196	4	-set	-set	ADJ
ejpam-6339	196	5	n	n	NOUN
ejpam-6339	196	6	=	=	PRON
ejpam-6339	196	7	{	{	PUNCT
ejpam-6339	196	8	⟨x	⟨x	VERB
ejpam-6339	196	9	,	,	PUNCT
ejpam-6339	196	10	0.1	0.1	NUM
ejpam-6339	196	11	,	,	PUNCT
ejpam-6339	196	12	0.8	0.8	NUM
ejpam-6339	196	13	,	,	PUNCT
ejpam-6339	196	14	0.9⟩	0.9⟩	NUM
ejpam-6339	196	15	,	,	PUNCT
ejpam-6339	196	16	⟨y	⟨y	X
ejpam-6339	196	17	,	,	PUNCT
ejpam-6339	196	18	0.4	0.4	NUM
ejpam-6339	196	19	,	,	PUNCT
ejpam-6339	196	20	0.9	0.9	NUM
ejpam-6339	196	21	,	,	PUNCT
ejpam-6339	196	22	0.6⟩	0.6⟩	NUM
ejpam-6339	196	23	}	}	PUNCT
ejpam-6339	196	24	and	and	CCONJ
ejpam-6339	196	25	the	the	DET
ejpam-6339	196	26	n	n	CCONJ
ejpam-6339	196	27	-point	-point	PROPN
ejpam-6339	196	28	x0.4,0.3,0.6	x0.4,0.3,0.6	NOUN
ejpam-6339	196	29	.	.	PUNCT
ejpam-6339	197	1	then	then	ADV
ejpam-6339	197	2	,	,	PUNCT
ejpam-6339	197	3	cl(n	cl(n	X
ejpam-6339	197	4	)	)	PUNCT
ejpam-6339	197	5	=	=	PUNCT
ejpam-6339	197	6	(	(	PUNCT
ejpam-6339	197	7	o	o	X
ejpam-6339	197	8	⊔u)c	⊔u)c	NOUN
ejpam-6339	197	9	and	and	CCONJ
ejpam-6339	197	10	x̃	x̃	PROPN
ejpam-6339	197	11	is	be	AUX
ejpam-6339	197	12	the	the	DET
ejpam-6339	197	13	only	only	ADJ
ejpam-6339	197	14	n	n	NUM
ejpam-6339	197	15	-open	-open	NOUN
ejpam-6339	197	16	set	set	VERB
ejpam-6339	197	17	to	to	PART
ejpam-6339	197	18	which	which	PRON
ejpam-6339	197	19	x0.4,0.3,0.6	x0.4,0.3,0.6	NOUN
ejpam-6339	197	20	belongs	belong	VERB
ejpam-6339	197	21	.	.	PUNCT
ejpam-6339	198	1	since	since	SCONJ
ejpam-6339	198	2	x̃	x̃	PROPN
ejpam-6339	198	3	⊓n	⊓n	PROPN
ejpam-6339	198	4	̸=	̸=	PROPN
ejpam-6339	198	5	∅̃	∅̃	NOUN
ejpam-6339	198	6	,	,	PUNCT
ejpam-6339	198	7	it	it	PRON
ejpam-6339	198	8	follows	follow	VERB
ejpam-6339	198	9	that	that	SCONJ
ejpam-6339	198	10	x0.4,0.3,0.6	x0.4,0.3,0.6	PROPN
ejpam-6339	198	11	belongs	belong	VERB
ejpam-6339	198	12	to	to	ADP
ejpam-6339	198	13	clp(n	clp(n	PROPN
ejpam-6339	198	14	)	)	PUNCT
ejpam-6339	198	15	,	,	PUNCT
ejpam-6339	198	16	but	but	CCONJ
ejpam-6339	198	17	x0.4,0.3,0.6	x0.4,0.3,0.6	PROPN
ejpam-6339	198	18	does	do	AUX
ejpam-6339	198	19	not	not	PART
ejpam-6339	198	20	belong	belong	VERB
ejpam-6339	198	21	to	to	ADP
ejpam-6339	198	22	cl(n	cl(n	NOUN
ejpam-6339	198	23	)	)	PUNCT
ejpam-6339	198	24	=	=	PRON
ejpam-6339	198	25	{	{	PUNCT
ejpam-6339	198	26	⟨x	⟨x	NUM
ejpam-6339	198	27	,	,	PUNCT
ejpam-6339	198	28	0.4	0.4	NUM
ejpam-6339	198	29	,	,	PUNCT
ejpam-6339	198	30	0.5	0.5	NUM
ejpam-6339	198	31	,	,	PUNCT
ejpam-6339	198	32	0.6⟩	0.6⟩	NUM
ejpam-6339	198	33	,	,	PUNCT
ejpam-6339	198	34	⟨y	⟨y	X
ejpam-6339	198	35	,	,	PUNCT
ejpam-6339	198	36	0.6	0.6	NUM
ejpam-6339	198	37	,	,	PUNCT
ejpam-6339	198	38	0.7	0.7	NUM
ejpam-6339	198	39	,	,	PUNCT
ejpam-6339	198	40	0.4⟩	0.4⟩	NUM
ejpam-6339	198	41	}	}	PUNCT
ejpam-6339	198	42	.	.	PUNCT
ejpam-6339	199	1	example	example	NOUN
ejpam-6339	200	1	3	3	X
ejpam-6339	200	2	.	.	PUNCT
ejpam-6339	200	3	let	let	VERB
ejpam-6339	200	4	x	x	PUNCT
ejpam-6339	200	5	=	=	PRON
ejpam-6339	200	6	{	{	PUNCT
ejpam-6339	200	7	x	x	PROPN
ejpam-6339	200	8	,	,	PUNCT
ejpam-6339	200	9	y	y	NOUN
ejpam-6339	200	10	}	}	PUNCT
ejpam-6339	200	11	and	and	CCONJ
ejpam-6339	200	12	o	o	NOUN
ejpam-6339	200	13	,	,	PUNCT
ejpam-6339	200	14	u	u	PROPN
ejpam-6339	200	15	∈	∈	PROPN
ejpam-6339	200	16	n	n	PRON
ejpam-6339	200	17	′(x	′(x	NOUN
ejpam-6339	200	18	)	)	PUNCT
ejpam-6339	200	19	such	such	ADJ
ejpam-6339	200	20	that	that	DET
ejpam-6339	200	21	o	o	NOUN
ejpam-6339	200	22	=	=	PUNCT
ejpam-6339	200	23	{	{	PUNCT
ejpam-6339	200	24	⟨x	⟨x	VERB
ejpam-6339	200	25	,	,	PUNCT
ejpam-6339	200	26	0.2	0.2	NUM
ejpam-6339	200	27	,	,	PUNCT
ejpam-6339	200	28	0.4	0.4	NUM
ejpam-6339	200	29	,	,	PUNCT
ejpam-6339	200	30	0.8⟩	0.8⟩	NUM
ejpam-6339	200	31	,	,	PUNCT
ejpam-6339	200	32	⟨y	⟨y	X
ejpam-6339	200	33	,	,	PUNCT
ejpam-6339	200	34	0.4	0.4	NUM
ejpam-6339	200	35	,	,	PUNCT
ejpam-6339	200	36	0.6	0.6	NUM
ejpam-6339	200	37	,	,	PUNCT
ejpam-6339	200	38	0.6⟩	0.6⟩	NUM
ejpam-6339	200	39	}	}	PUNCT
ejpam-6339	200	40	,	,	PUNCT
ejpam-6339	200	41	u	u	NOUN
ejpam-6339	200	42	=	=	PUNCT
ejpam-6339	200	43	{	{	PUNCT
ejpam-6339	200	44	⟨x	⟨x	VERB
ejpam-6339	200	45	,	,	PUNCT
ejpam-6339	200	46	0	0	NUM
ejpam-6339	200	47	,	,	PUNCT
ejpam-6339	200	48	0.3	0.3	NUM
ejpam-6339	200	49	,	,	PUNCT
ejpam-6339	200	50	1⟩	1⟩	NUM
ejpam-6339	200	51	,	,	PUNCT
ejpam-6339	200	52	⟨y	⟨y	NOUN
ejpam-6339	200	53	,	,	PUNCT
ejpam-6339	200	54	0.1	0.1	NUM
ejpam-6339	200	55	,	,	PUNCT
ejpam-6339	200	56	1	1	NUM
ejpam-6339	200	57	,	,	PUNCT
ejpam-6339	200	58	0.9⟩	0.9⟩	NUM
ejpam-6339	200	59	}	}	PUNCT
ejpam-6339	200	60	.	.	PUNCT
ejpam-6339	201	1	consider	consider	VERB
ejpam-6339	201	2	the	the	DET
ejpam-6339	201	3	n	n	PRON
ejpam-6339	201	4	-topology	-topology	NOUN
ejpam-6339	201	5	on	on	ADP
ejpam-6339	201	6	x	x	PUNCT
ejpam-6339	201	7	given	give	VERB
ejpam-6339	201	8	by	by	ADP
ejpam-6339	201	9	τ	τ	X
ejpam-6339	201	10	=	=	SYM
ejpam-6339	201	11	{	{	PUNCT
ejpam-6339	201	12	∅̃	∅̃	NOUN
ejpam-6339	201	13	,	,	PUNCT
ejpam-6339	201	14	x̃	x̃	PROPN
ejpam-6339	201	15	,	,	PUNCT
ejpam-6339	201	16	o	o	NOUN
ejpam-6339	201	17	,	,	PUNCT
ejpam-6339	201	18	u	u	NOUN
ejpam-6339	201	19	,	,	PUNCT
ejpam-6339	201	20	o	o	NOUN
ejpam-6339	201	21	⊓	⊓	PROPN
ejpam-6339	201	22	u	u	NOUN
ejpam-6339	201	23	,	,	PUNCT
ejpam-6339	201	24	o	o	PROPN
ejpam-6339	201	25	⊔	⊔	NUM
ejpam-6339	201	26	u	u	NOUN
ejpam-6339	201	27	}	}	PUNCT
ejpam-6339	201	28	.	.	PUNCT
ejpam-6339	202	1	the	the	DET
ejpam-6339	202	2	collection	collection	NOUN
ejpam-6339	202	3	of	of	ADP
ejpam-6339	202	4	all	all	DET
ejpam-6339	202	5	n	n	ADV
ejpam-6339	202	6	-closed	-close	VERB
ejpam-6339	202	7	sets	set	NOUN
ejpam-6339	202	8	on	on	ADP
ejpam-6339	202	9	x	x	X
ejpam-6339	202	10	is	be	AUX
ejpam-6339	202	11	τ	τ	X
ejpam-6339	202	12	c	c	NOUN
ejpam-6339	202	13	=	=	PUNCT
ejpam-6339	202	14	{	{	PUNCT
ejpam-6339	202	15	x̃	x̃	PROPN
ejpam-6339	202	16	,	,	PUNCT
ejpam-6339	202	17	∅̃	∅̃	NOUN
ejpam-6339	202	18	,	,	PUNCT
ejpam-6339	202	19	oc	oc	NOUN
ejpam-6339	202	20	,	,	PUNCT
ejpam-6339	202	21	u	u	NOUN
ejpam-6339	202	22	c	c	NOUN
ejpam-6339	202	23	,	,	PUNCT
ejpam-6339	202	24	(	(	PUNCT
ejpam-6339	202	25	o	o	X
ejpam-6339	202	26	⊓	⊓	NOUN
ejpam-6339	202	27	u)c	u)c	X
ejpam-6339	202	28	,	,	PUNCT
ejpam-6339	202	29	(	(	PUNCT
ejpam-6339	202	30	o	o	X
ejpam-6339	202	31	⊔	⊔	X
ejpam-6339	202	32	u)c	u)c	PROPN
ejpam-6339	202	33	}	}	PUNCT
ejpam-6339	202	34	,	,	PUNCT
ejpam-6339	202	35	j.	j.	PROPN
ejpam-6339	202	36	sanabria	sanabria	PROPN
ejpam-6339	202	37	,	,	PUNCT
ejpam-6339	202	38	e.	e.	PROPN
ejpam-6339	202	39	rosas	rosas	PROPN
ejpam-6339	202	40	,	,	PUNCT
ejpam-6339	202	41	c.	c.	PROPN
ejpam-6339	202	42	granados	granados	PROPN
ejpam-6339	202	43	/	/	PUNCT
ejpam-6339	202	44	eur	eur	PROPN
ejpam-6339	202	45	.	.	PUNCT
ejpam-6339	203	1	j.	j.	PROPN
ejpam-6339	203	2	pure	pure	PROPN
ejpam-6339	203	3	appl	appl	PROPN
ejpam-6339	203	4	.	.	PROPN
ejpam-6339	203	5	math	math	PROPN
ejpam-6339	203	6	,	,	PUNCT
ejpam-6339	203	7	18	18	NUM
ejpam-6339	203	8	(	(	PUNCT
ejpam-6339	203	9	3	3	NUM
ejpam-6339	203	10	)	)	PUNCT
ejpam-6339	203	11	(	(	PUNCT
ejpam-6339	203	12	2025	2025	NUM
ejpam-6339	203	13	)	)	PUNCT
ejpam-6339	203	14	,	,	PUNCT
ejpam-6339	203	15	6339	6339	NUM
ejpam-6339	203	16	10	10	NUM
ejpam-6339	203	17	of	of	ADP
ejpam-6339	203	18	15	15	NUM
ejpam-6339	203	19	where	where	SCONJ
ejpam-6339	203	20	oc	oc	NOUN
ejpam-6339	203	21	=	=	X
ejpam-6339	203	22	{	{	PUNCT
ejpam-6339	203	23	⟨x	⟨x	VERB
ejpam-6339	203	24	,	,	PUNCT
ejpam-6339	203	25	0.8	0.8	NUM
ejpam-6339	203	26	,	,	PUNCT
ejpam-6339	203	27	0.6	0.6	NUM
ejpam-6339	203	28	,	,	PUNCT
ejpam-6339	203	29	0.2⟩	0.2⟩	NUM
ejpam-6339	203	30	,	,	PUNCT
ejpam-6339	203	31	⟨y	⟨y	NOUN
ejpam-6339	203	32	,	,	PUNCT
ejpam-6339	203	33	0.6	0.6	NUM
ejpam-6339	203	34	,	,	PUNCT
ejpam-6339	203	35	0.4	0.4	NUM
ejpam-6339	203	36	,	,	PUNCT
ejpam-6339	203	37	0.4⟩	0.4⟩	NUM
ejpam-6339	203	38	}	}	PUNCT
ejpam-6339	203	39	,	,	PUNCT
ejpam-6339	203	40	u	u	NOUN
ejpam-6339	203	41	c	c	NOUN
ejpam-6339	203	42	=	=	PUNCT
ejpam-6339	203	43	{	{	PUNCT
ejpam-6339	203	44	⟨x	⟨x	VERB
ejpam-6339	203	45	,	,	PUNCT
ejpam-6339	203	46	1	1	NUM
ejpam-6339	203	47	,	,	PUNCT
ejpam-6339	203	48	0.7	0.7	NUM
ejpam-6339	203	49	,	,	PUNCT
ejpam-6339	203	50	0⟩	0⟩	PROPN
ejpam-6339	203	51	,	,	PUNCT
ejpam-6339	203	52	⟨y	⟨y	X
ejpam-6339	203	53	,	,	PUNCT
ejpam-6339	203	54	0.9	0.9	NUM
ejpam-6339	203	55	,	,	PUNCT
ejpam-6339	203	56	0	0	NUM
ejpam-6339	203	57	,	,	PUNCT
ejpam-6339	203	58	0.1⟩	0.1⟩	NUM
ejpam-6339	203	59	}	}	PUNCT
ejpam-6339	203	60	,	,	PUNCT
ejpam-6339	203	61	(	(	PUNCT
ejpam-6339	203	62	o	o	NOUN
ejpam-6339	203	63	⊓	⊓	PROPN
ejpam-6339	203	64	u)c	u)c	X
ejpam-6339	203	65	=	=	PUNCT
ejpam-6339	203	66	{	{	PUNCT
ejpam-6339	203	67	⟨x	⟨x	VERB
ejpam-6339	203	68	,	,	PUNCT
ejpam-6339	203	69	1	1	NUM
ejpam-6339	203	70	,	,	PUNCT
ejpam-6339	203	71	0.6	0.6	NUM
ejpam-6339	203	72	,	,	PUNCT
ejpam-6339	203	73	0⟩	0⟩	PROPN
ejpam-6339	203	74	,	,	PUNCT
ejpam-6339	203	75	⟨y	⟨y	X
ejpam-6339	203	76	,	,	PUNCT
ejpam-6339	203	77	0.9	0.9	NUM
ejpam-6339	203	78	,	,	PUNCT
ejpam-6339	203	79	0	0	NUM
ejpam-6339	203	80	,	,	PUNCT
ejpam-6339	203	81	0.1⟩	0.1⟩	NUM
ejpam-6339	203	82	}	}	PUNCT
ejpam-6339	203	83	,	,	PUNCT
ejpam-6339	203	84	(	(	PUNCT
ejpam-6339	203	85	o	o	X
ejpam-6339	203	86	⊔	⊔	X
ejpam-6339	203	87	u)c	u)c	X
ejpam-6339	203	88	=	=	X
ejpam-6339	203	89	{	{	PUNCT
ejpam-6339	203	90	⟨x	⟨x	VERB
ejpam-6339	203	91	,	,	PUNCT
ejpam-6339	203	92	0.8	0.8	NUM
ejpam-6339	203	93	,	,	PUNCT
ejpam-6339	203	94	0.7	0.7	NUM
ejpam-6339	203	95	,	,	PUNCT
ejpam-6339	203	96	0.2⟩	0.2⟩	NUM
ejpam-6339	203	97	,	,	PUNCT
ejpam-6339	203	98	⟨y	⟨y	NOUN
ejpam-6339	203	99	,	,	PUNCT
ejpam-6339	203	100	0.6	0.6	NUM
ejpam-6339	203	101	,	,	PUNCT
ejpam-6339	203	102	0.4	0.4	NUM
ejpam-6339	203	103	,	,	PUNCT
ejpam-6339	203	104	0.4⟩	0.4⟩	NUM
ejpam-6339	203	105	}	}	PUNCT
ejpam-6339	203	106	.	.	PUNCT
ejpam-6339	204	1	consider	consider	VERB
ejpam-6339	204	2	the	the	DET
ejpam-6339	204	3	n	n	NOUN
ejpam-6339	204	4	-set	-set	ADJ
ejpam-6339	204	5	n	n	NOUN
ejpam-6339	204	6	=	=	PRON
ejpam-6339	204	7	{	{	PUNCT
ejpam-6339	204	8	⟨x	⟨x	VERB
ejpam-6339	204	9	,	,	PUNCT
ejpam-6339	204	10	0.1	0.1	NUM
ejpam-6339	204	11	,	,	PUNCT
ejpam-6339	204	12	1	1	NUM
ejpam-6339	204	13	,	,	PUNCT
ejpam-6339	204	14	0.9⟩	0.9⟩	NUM
ejpam-6339	204	15	,	,	PUNCT
ejpam-6339	204	16	⟨y	⟨y	NOUN
ejpam-6339	204	17	,	,	PUNCT
ejpam-6339	204	18	0	0	NUM
ejpam-6339	204	19	,	,	PUNCT
ejpam-6339	204	20	0.3	0.3	NUM
ejpam-6339	204	21	,	,	PUNCT
ejpam-6339	204	22	1⟩	1⟩	NUM
ejpam-6339	204	23	}	}	PUNCT
ejpam-6339	204	24	and	and	CCONJ
ejpam-6339	204	25	the	the	DET
ejpam-6339	204	26	n	n	PRON
ejpam-6339	204	27	-point	-point	PROPN
ejpam-6339	204	28	y0.1,1,0.9	y0.1,1,0.9	NOUN
ejpam-6339	204	29	.	.	PUNCT
ejpam-6339	205	1	then	then	ADV
ejpam-6339	205	2	,	,	PUNCT
ejpam-6339	205	3	y0.1,1,0.9	y0.1,1,0.9	NOUN
ejpam-6339	205	4	∈	∈	NOUN
ejpam-6339	205	5	cl(n	cl(n	NOUN
ejpam-6339	205	6	)	)	PUNCT
ejpam-6339	206	1	=	=	SYM
ejpam-6339	206	2	u	u	NOUN
ejpam-6339	206	3	c	c	NOUN
ejpam-6339	206	4	,	,	PUNCT
ejpam-6339	206	5	but	but	CCONJ
ejpam-6339	206	6	u	u	NOUN
ejpam-6339	206	7	∈	∈	PROPN
ejpam-6339	206	8	τ(y0.1,1,0.9	τ(y0.1,1,0.9	NOUN
ejpam-6339	206	9	)	)	PUNCT
ejpam-6339	206	10	and	and	CCONJ
ejpam-6339	206	11	u	u	NOUN
ejpam-6339	206	12	⊓	⊓	PROPN
ejpam-6339	206	13	n	n	PROPN
ejpam-6339	206	14	=	=	SYM
ejpam-6339	206	15	∅̃	∅̃	NOUN
ejpam-6339	206	16	,	,	PUNCT
ejpam-6339	206	17	which	which	PRON
ejpam-6339	206	18	implies	imply	VERB
ejpam-6339	206	19	that	that	SCONJ
ejpam-6339	206	20	y0.1,1,0.9	y0.1,1,0.9	NOUN
ejpam-6339	206	21	does	do	AUX
ejpam-6339	206	22	not	not	PART
ejpam-6339	206	23	belong	belong	VERB
ejpam-6339	206	24	to	to	ADP
ejpam-6339	206	25	clp(n	clp(n	PROPN
ejpam-6339	206	26	)	)	PUNCT
ejpam-6339	206	27	.	.	PUNCT
ejpam-6339	207	1	proposition	proposition	NOUN
ejpam-6339	207	2	8	8	NUM
ejpam-6339	207	3	.	.	PUNCT
ejpam-6339	208	1	let	let	VERB
ejpam-6339	208	2	(	(	PUNCT
ejpam-6339	208	3	x	x	NOUN
ejpam-6339	208	4	,	,	PUNCT
ejpam-6339	208	5	τ	τ	X
ejpam-6339	208	6	)	)	PUNCT
ejpam-6339	208	7	be	be	VERB
ejpam-6339	208	8	a	a	DET
ejpam-6339	208	9	n	n	CCONJ
ejpam-6339	208	10	-topological	-topological	ADJ
ejpam-6339	208	11	space	space	NOUN
ejpam-6339	208	12	and	and	CCONJ
ejpam-6339	208	13	n	n	CCONJ
ejpam-6339	208	14	,	,	PUNCT
ejpam-6339	208	15	m	m	VERB
ejpam-6339	208	16	∈	∈	PROPN
ejpam-6339	208	17	n	n	PRON
ejpam-6339	208	18	′(x	′(x	NOUN
ejpam-6339	208	19	)	)	PUNCT
ejpam-6339	208	20	.	.	PUNCT
ejpam-6339	209	1	then	then	ADV
ejpam-6339	209	2	,	,	PUNCT
ejpam-6339	209	3	the	the	DET
ejpam-6339	209	4	following	follow	VERB
ejpam-6339	209	5	conditions	condition	NOUN
ejpam-6339	209	6	hold	hold	VERB
ejpam-6339	209	7	:	:	PUNCT
ejpam-6339	209	8	(	(	PUNCT
ejpam-6339	209	9	1	1	X
ejpam-6339	209	10	)	)	PUNCT
ejpam-6339	209	11	n	n	CCONJ
ejpam-6339	209	12	⊑	⊑	DET
ejpam-6339	209	13	clp(n	clp(n	PROPN
ejpam-6339	209	14	)	)	PUNCT
ejpam-6339	209	15	.	.	PUNCT
ejpam-6339	210	1	(	(	PUNCT
ejpam-6339	210	2	2	2	X
ejpam-6339	210	3	)	)	PUNCT
ejpam-6339	210	4	clp(clp(n	clp(clp(n	PROPN
ejpam-6339	210	5	)	)	PUNCT
ejpam-6339	210	6	)	)	PUNCT
ejpam-6339	211	1	=	=	PUNCT
ejpam-6339	211	2	clp(n	clp(n	PROPN
ejpam-6339	211	3	)	)	PUNCT
ejpam-6339	211	4	.	.	PUNCT
ejpam-6339	212	1	(	(	PUNCT
ejpam-6339	212	2	3	3	X
ejpam-6339	212	3	)	)	PUNCT
ejpam-6339	212	4	if	if	SCONJ
ejpam-6339	212	5	n	n	ADV
ejpam-6339	212	6	⊑m	⊑m	NOUN
ejpam-6339	212	7	,	,	PUNCT
ejpam-6339	212	8	then	then	ADV
ejpam-6339	212	9	clp(n	clp(n	PROPN
ejpam-6339	212	10	)	)	PUNCT
ejpam-6339	213	1	⊑	⊑	PRON
ejpam-6339	213	2	clp(m	clp(m	PROPN
ejpam-6339	213	3	)	)	PUNCT
ejpam-6339	213	4	.	.	PUNCT
ejpam-6339	214	1	(	(	PUNCT
ejpam-6339	214	2	4	4	X
ejpam-6339	214	3	)	)	PUNCT
ejpam-6339	214	4	clp(n	clp(n	PROPN
ejpam-6339	214	5	⊓m	⊓m	NOUN
ejpam-6339	214	6	)	)	PUNCT
ejpam-6339	214	7	⊑	⊑	PROPN
ejpam-6339	214	8	clp(n	clp(n	PROPN
ejpam-6339	214	9	)	)	PUNCT
ejpam-6339	214	10	⊓	⊓	PROPN
ejpam-6339	214	11	clp(m	clp(m	NOUN
ejpam-6339	214	12	)	)	PUNCT
ejpam-6339	214	13	.	.	PUNCT
ejpam-6339	215	1	(	(	PUNCT
ejpam-6339	215	2	5	5	X
ejpam-6339	215	3	)	)	PUNCT
ejpam-6339	215	4	clp(n	clp(n	PROPN
ejpam-6339	215	5	⊔m	⊔m	PROPN
ejpam-6339	215	6	)	)	PUNCT
ejpam-6339	216	1	=	=	SYM
ejpam-6339	216	2	clp(n	clp(n	PROPN
ejpam-6339	216	3	)	)	PUNCT
ejpam-6339	216	4	⊔	⊔	NUM
ejpam-6339	216	5	clp(m	clp(m	NOUN
ejpam-6339	216	6	)	)	PUNCT
ejpam-6339	216	7	.	.	PUNCT
ejpam-6339	217	1	(	(	PUNCT
ejpam-6339	217	2	6	6	NUM
ejpam-6339	217	3	)	)	PUNCT
ejpam-6339	217	4	clp(∅̃	clp(∅̃	NOUN
ejpam-6339	217	5	)	)	PUNCT
ejpam-6339	217	6	=	=	PUNCT
ejpam-6339	218	1	∅̃.	∅̃.	NOUN
ejpam-6339	218	2	(	(	PUNCT
ejpam-6339	218	3	7	7	NUM
ejpam-6339	218	4	)	)	PUNCT
ejpam-6339	218	5	clp(x̃	clp(x̃	NOUN
ejpam-6339	218	6	)	)	PUNCT
ejpam-6339	218	7	=	=	SYM
ejpam-6339	219	1	x̃.	x̃.	ADJ
ejpam-6339	219	2	proof	proof	NOUN
ejpam-6339	219	3	.	.	PUNCT
ejpam-6339	220	1	(	(	PUNCT
ejpam-6339	220	2	1	1	X
ejpam-6339	220	3	)	)	PUNCT
ejpam-6339	220	4	it	it	PRON
ejpam-6339	220	5	is	be	AUX
ejpam-6339	220	6	obvious	obvious	ADJ
ejpam-6339	220	7	from	from	ADP
ejpam-6339	220	8	definition	definition	NOUN
ejpam-6339	220	9	10	10	NUM
ejpam-6339	220	10	.	.	PUNCT
ejpam-6339	221	1	(	(	PUNCT
ejpam-6339	221	2	2	2	X
ejpam-6339	221	3	)	)	PUNCT
ejpam-6339	221	4	the	the	DET
ejpam-6339	221	5	inclusion	inclusion	NOUN
ejpam-6339	221	6	clp(n	clp(n	PROPN
ejpam-6339	221	7	)	)	PUNCT
ejpam-6339	221	8	⊑	⊑	PROPN
ejpam-6339	221	9	clp(clp(n	clp(clp(n	PROPN
ejpam-6339	221	10	)	)	PUNCT
ejpam-6339	221	11	)	)	PUNCT
ejpam-6339	221	12	is	be	AUX
ejpam-6339	221	13	an	an	DET
ejpam-6339	221	14	immediate	immediate	ADJ
ejpam-6339	221	15	consequence	consequence	NOUN
ejpam-6339	221	16	of	of	ADP
ejpam-6339	221	17	part	part	NOUN
ejpam-6339	221	18	(	(	PUNCT
ejpam-6339	221	19	1	1	NUM
ejpam-6339	221	20	)	)	PUNCT
ejpam-6339	221	21	.	.	PUNCT
ejpam-6339	222	1	for	for	ADP
ejpam-6339	222	2	the	the	DET
ejpam-6339	222	3	other	other	ADJ
ejpam-6339	222	4	inclusion	inclusion	NOUN
ejpam-6339	222	5	,	,	PUNCT
ejpam-6339	222	6	suppose	suppose	VERB
ejpam-6339	222	7	that	that	SCONJ
ejpam-6339	222	8	xa	xa	PROPN
ejpam-6339	222	9	,	,	PUNCT
ejpam-6339	222	10	b	b	PROPN
ejpam-6339	222	11	,	,	PUNCT
ejpam-6339	222	12	c	c	PROPN
ejpam-6339	222	13	∈	∈	PROPN
ejpam-6339	222	14	clp(clp(n	clp(clp(n	PROPN
ejpam-6339	222	15	)	)	PUNCT
ejpam-6339	222	16	)	)	PUNCT
ejpam-6339	222	17	and	and	CCONJ
ejpam-6339	222	18	let	let	VERB
ejpam-6339	222	19	o	o	PROPN
ejpam-6339	222	20	∈	∈	PROPN
ejpam-6339	222	21	τ(xa	τ(xa	NUM
ejpam-6339	222	22	,	,	PUNCT
ejpam-6339	222	23	b	b	NOUN
ejpam-6339	222	24	,	,	PUNCT
ejpam-6339	222	25	c	c	NOUN
ejpam-6339	222	26	)	)	PUNCT
ejpam-6339	222	27	.	.	PUNCT
ejpam-6339	223	1	then	then	ADV
ejpam-6339	223	2	,	,	PUNCT
ejpam-6339	223	3	o	o	PROPN
ejpam-6339	223	4	⊓	⊓	PROPN
ejpam-6339	223	5	clp(n	clp(n	PROPN
ejpam-6339	223	6	)	)	PUNCT
ejpam-6339	223	7	̸=	̸=	PROPN
ejpam-6339	223	8	∅̃	∅̃	NOUN
ejpam-6339	223	9	,	,	PUNCT
ejpam-6339	223	10	which	which	PRON
ejpam-6339	223	11	implies	imply	VERB
ejpam-6339	223	12	that	that	SCONJ
ejpam-6339	223	13	there	there	PRON
ejpam-6339	223	14	exists	exist	VERB
ejpam-6339	223	15	a	a	DET
ejpam-6339	223	16	n	n	CCONJ
ejpam-6339	223	17	-point	-point	PROPN
ejpam-6339	223	18	yu	yu	PROPN
ejpam-6339	223	19	,	,	PUNCT
ejpam-6339	223	20	v	v	NOUN
ejpam-6339	223	21	,	,	PUNCT
ejpam-6339	223	22	w	w	PROPN
ejpam-6339	223	23	∈	∈	PROPN
ejpam-6339	223	24	clp(n	clp(n	PROPN
ejpam-6339	223	25	)	)	PUNCT
ejpam-6339	223	26	and	and	CCONJ
ejpam-6339	223	27	o	o	PROPN
ejpam-6339	223	28	∈	∈	PROPN
ejpam-6339	223	29	τ(yu	τ(yu	NUM
ejpam-6339	223	30	,	,	PUNCT
ejpam-6339	223	31	v	v	NOUN
ejpam-6339	223	32	,	,	PUNCT
ejpam-6339	223	33	w	w	NOUN
ejpam-6339	223	34	)	)	PUNCT
ejpam-6339	223	35	.	.	PUNCT
ejpam-6339	224	1	thus	thus	ADV
ejpam-6339	224	2	,	,	PUNCT
ejpam-6339	224	3	o	o	INTJ
ejpam-6339	224	4	⊓n	⊓n	INTJ
ejpam-6339	224	5	̸=	̸=	PROPN
ejpam-6339	224	6	∅̃	∅̃	NOUN
ejpam-6339	224	7	and	and	CCONJ
ejpam-6339	224	8	hence	hence	ADV
ejpam-6339	224	9	,	,	PUNCT
ejpam-6339	224	10	xa	xa	PROPN
ejpam-6339	224	11	,	,	PUNCT
ejpam-6339	224	12	b	b	PROPN
ejpam-6339	224	13	,	,	PUNCT
ejpam-6339	224	14	c	c	PROPN
ejpam-6339	224	15	∈	∈	PROPN
ejpam-6339	224	16	clp(n	clp(n	PROPN
ejpam-6339	224	17	)	)	PUNCT
ejpam-6339	224	18	.	.	PUNCT
ejpam-6339	225	1	(	(	PUNCT
ejpam-6339	225	2	3	3	X
ejpam-6339	225	3	)	)	PUNCT
ejpam-6339	225	4	suppose	suppose	VERB
ejpam-6339	225	5	that	that	SCONJ
ejpam-6339	225	6	n	n	CCONJ
ejpam-6339	225	7	,	,	PUNCT
ejpam-6339	225	8	m	m	VERB
ejpam-6339	225	9	∈	∈	PROPN
ejpam-6339	225	10	n	n	PRON
ejpam-6339	225	11	′(x	′(x	NOUN
ejpam-6339	225	12	)	)	PUNCT
ejpam-6339	225	13	are	be	AUX
ejpam-6339	225	14	such	such	ADJ
ejpam-6339	225	15	that	that	SCONJ
ejpam-6339	225	16	n	n	PROPN
ejpam-6339	225	17	⊑	⊑	X
ejpam-6339	225	18	m	m	VERB
ejpam-6339	225	19	.	.	PUNCT
ejpam-6339	226	1	if	if	SCONJ
ejpam-6339	226	2	xa	xa	PROPN
ejpam-6339	226	3	,	,	PUNCT
ejpam-6339	226	4	b	b	PROPN
ejpam-6339	226	5	,	,	PUNCT
ejpam-6339	226	6	c	c	NOUN
ejpam-6339	226	7	/∈	/∈	PUNCT
ejpam-6339	226	8	clp(m	clp(m	NOUN
ejpam-6339	226	9	)	)	PUNCT
ejpam-6339	226	10	,	,	PUNCT
ejpam-6339	226	11	then	then	ADV
ejpam-6339	226	12	there	there	PRON
ejpam-6339	226	13	exists	exist	VERB
ejpam-6339	226	14	u	u	PROPN
ejpam-6339	226	15	∈	∈	PROPN
ejpam-6339	226	16	τ(xa	τ(xa	NUM
ejpam-6339	226	17	,	,	PUNCT
ejpam-6339	226	18	b	b	NOUN
ejpam-6339	226	19	,	,	PUNCT
ejpam-6339	226	20	c	c	NOUN
ejpam-6339	226	21	)	)	PUNCT
ejpam-6339	227	1	such	such	ADJ
ejpam-6339	227	2	that	that	SCONJ
ejpam-6339	227	3	u	u	NOUN
ejpam-6339	227	4	⊓m	⊓m	NOUN
ejpam-6339	227	5	=	=	SYM
ejpam-6339	227	6	∅̃	∅̃	PROPN
ejpam-6339	227	7	,	,	PUNCT
ejpam-6339	227	8	which	which	PRON
ejpam-6339	227	9	implies	imply	VERB
ejpam-6339	227	10	that	that	SCONJ
ejpam-6339	227	11	u	u	PRON
ejpam-6339	227	12	⊓	⊓	PROPN
ejpam-6339	227	13	n	n	CCONJ
ejpam-6339	227	14	⊑	⊑	X
ejpam-6339	227	15	u	u	NOUN
ejpam-6339	228	1	⊓m	⊓m	NOUN
ejpam-6339	228	2	=	=	PUNCT
ejpam-6339	228	3	∅̃	∅̃	NOUN
ejpam-6339	229	1	and	and	CCONJ
ejpam-6339	229	2	so	so	ADV
ejpam-6339	229	3	,	,	PUNCT
ejpam-6339	229	4	u	u	NOUN
ejpam-6339	229	5	⊓n	⊓n	NOUN
ejpam-6339	230	1	=	=	SYM
ejpam-6339	231	1	∅̃	∅̃	PROPN
ejpam-6339	231	2	,	,	PUNCT
ejpam-6339	231	3	which	which	PRON
ejpam-6339	231	4	proves	prove	VERB
ejpam-6339	231	5	that	that	SCONJ
ejpam-6339	231	6	xa	xa	PROPN
ejpam-6339	231	7	,	,	PUNCT
ejpam-6339	231	8	b	b	PROPN
ejpam-6339	231	9	,	,	PUNCT
ejpam-6339	231	10	c	c	PROPN
ejpam-6339	231	11	/∈	/∈	PUNCT
ejpam-6339	231	12	clp(n	clp(n	PROPN
ejpam-6339	231	13	)	)	PUNCT
ejpam-6339	231	14	.	.	PUNCT
ejpam-6339	232	1	therefore	therefore	ADV
ejpam-6339	232	2	,	,	PUNCT
ejpam-6339	232	3	clp(n	clp(n	PROPN
ejpam-6339	232	4	)	)	PUNCT
ejpam-6339	232	5	⊑	⊑	X
ejpam-6339	232	6	clp(m	clp(m	PROPN
ejpam-6339	232	7	)	)	PUNCT
ejpam-6339	232	8	whenever	whenever	SCONJ
ejpam-6339	232	9	n	n	PRON
ejpam-6339	232	10	⊑m	⊑m	NOUN
ejpam-6339	232	11	.	.	PUNCT
ejpam-6339	233	1	(	(	PUNCT
ejpam-6339	233	2	4	4	X
ejpam-6339	233	3	)	)	PUNCT
ejpam-6339	233	4	the	the	DET
ejpam-6339	233	5	proof	proof	NOUN
ejpam-6339	233	6	follows	follow	VERB
ejpam-6339	233	7	from	from	ADP
ejpam-6339	233	8	part	part	NOUN
ejpam-6339	233	9	(	(	PUNCT
ejpam-6339	233	10	3	3	NUM
ejpam-6339	233	11	)	)	PUNCT
ejpam-6339	233	12	.	.	PUNCT
ejpam-6339	234	1	(	(	PUNCT
ejpam-6339	234	2	5	5	X
ejpam-6339	234	3	)	)	PUNCT
ejpam-6339	234	4	the	the	DET
ejpam-6339	234	5	inclusion	inclusion	NOUN
ejpam-6339	234	6	clp(n	clp(n	PROPN
ejpam-6339	234	7	)	)	PUNCT
ejpam-6339	234	8	⊔	⊔	PROPN
ejpam-6339	234	9	clp(m	clp(m	PROPN
ejpam-6339	234	10	)	)	PUNCT
ejpam-6339	234	11	⊑	⊑	PART
ejpam-6339	234	12	clp(n	clp(n	PROPN
ejpam-6339	234	13	⊔m	⊔m	PROPN
ejpam-6339	234	14	)	)	PUNCT
ejpam-6339	234	15	is	be	AUX
ejpam-6339	234	16	an	an	DET
ejpam-6339	234	17	immediate	immediate	ADJ
ejpam-6339	234	18	consequence	consequence	NOUN
ejpam-6339	234	19	of	of	ADP
ejpam-6339	234	20	part	part	NOUN
ejpam-6339	234	21	(	(	PUNCT
ejpam-6339	234	22	1	1	NUM
ejpam-6339	234	23	)	)	PUNCT
ejpam-6339	234	24	.	.	PUNCT
ejpam-6339	235	1	suppose	suppose	VERB
ejpam-6339	236	1	that	that	SCONJ
ejpam-6339	236	2	xa	xa	PROPN
ejpam-6339	236	3	,	,	PUNCT
ejpam-6339	236	4	b	b	PROPN
ejpam-6339	236	5	,	,	PUNCT
ejpam-6339	236	6	c	c	NOUN
ejpam-6339	236	7	/∈	/∈	PUNCT
ejpam-6339	236	8	clp(n	clp(n	PROPN
ejpam-6339	236	9	)	)	PUNCT
ejpam-6339	236	10	⊔	⊔	NUM
ejpam-6339	236	11	clp(m	clp(m	NOUN
ejpam-6339	236	12	)	)	PUNCT
ejpam-6339	236	13	.	.	PUNCT
ejpam-6339	237	1	then	then	ADV
ejpam-6339	237	2	,	,	PUNCT
ejpam-6339	237	3	there	there	PRON
ejpam-6339	237	4	exist	exist	VERB
ejpam-6339	237	5	o	o	NOUN
ejpam-6339	237	6	,	,	PUNCT
ejpam-6339	237	7	u	u	PROPN
ejpam-6339	237	8	∈	∈	PROPN
ejpam-6339	237	9	τ(xa	τ(xa	NUM
ejpam-6339	237	10	,	,	PUNCT
ejpam-6339	237	11	b	b	NOUN
ejpam-6339	237	12	,	,	PUNCT
ejpam-6339	237	13	c	c	NOUN
ejpam-6339	237	14	)	)	PUNCT
ejpam-6339	238	1	such	such	ADJ
ejpam-6339	238	2	that	that	DET
ejpam-6339	238	3	o	o	INTJ
ejpam-6339	238	4	⊓n	⊓n	NOUN
ejpam-6339	238	5	=	=	PUNCT
ejpam-6339	239	1	∅̃	∅̃	NOUN
ejpam-6339	239	2	and	and	CCONJ
ejpam-6339	239	3	u	u	NOUN
ejpam-6339	239	4	⊓m	⊓m	NOUN
ejpam-6339	239	5	=	=	PUNCT
ejpam-6339	239	6	∅̃.	∅̃.	NOUN
ejpam-6339	239	7	putting	put	VERB
ejpam-6339	239	8	v	v	NOUN
ejpam-6339	239	9	=	=	NOUN
ejpam-6339	239	10	o	o	X
ejpam-6339	239	11	⊓	⊓	PROPN
ejpam-6339	239	12	u	u	NOUN
ejpam-6339	239	13	,	,	PUNCT
ejpam-6339	239	14	we	we	PRON
ejpam-6339	239	15	have	have	VERB
ejpam-6339	239	16	v	v	NUM
ejpam-6339	239	17	∈	∈	PROPN
ejpam-6339	239	18	τ(xa	τ(xa	NUM
ejpam-6339	239	19	,	,	PUNCT
ejpam-6339	239	20	b	b	NOUN
ejpam-6339	239	21	,	,	PUNCT
ejpam-6339	239	22	c	c	NOUN
ejpam-6339	239	23	)	)	PUNCT
ejpam-6339	239	24	and	and	CCONJ
ejpam-6339	239	25	v	v	X
ejpam-6339	239	26	⊓	⊓	PROPN
ejpam-6339	239	27	(	(	PUNCT
ejpam-6339	239	28	n	n	NOUN
ejpam-6339	239	29	⊔m	⊔m	PROPN
ejpam-6339	239	30	)	)	PUNCT
ejpam-6339	239	31	=	=	PUNCT
ejpam-6339	239	32	(	(	PUNCT
ejpam-6339	239	33	v	v	NUM
ejpam-6339	239	34	⊓n	⊓n	NOUN
ejpam-6339	239	35	)	)	PUNCT
ejpam-6339	239	36	⊔	⊔	PROPN
ejpam-6339	239	37	(	(	PUNCT
ejpam-6339	239	38	v	v	NOUN
ejpam-6339	239	39	⊓m	⊓m	NOUN
ejpam-6339	239	40	)	)	PUNCT
ejpam-6339	240	1	=	=	PUNCT
ejpam-6339	241	1	(	(	PUNCT
ejpam-6339	241	2	o	o	X
ejpam-6339	241	3	⊓	⊓	PROPN
ejpam-6339	241	4	u	u	NOUN
ejpam-6339	241	5	⊓n	⊓n	PROPN
ejpam-6339	241	6	)	)	PUNCT
ejpam-6339	241	7	⊔	⊔	PROPN
ejpam-6339	241	8	(	(	PUNCT
ejpam-6339	241	9	o	o	NOUN
ejpam-6339	241	10	⊓	⊓	PROPN
ejpam-6339	241	11	u	u	NOUN
ejpam-6339	241	12	⊓m	⊓m	NOUN
ejpam-6339	241	13	)	)	PUNCT
ejpam-6339	241	14	⊑	⊑	X
ejpam-6339	241	15	(	(	PUNCT
ejpam-6339	241	16	o	o	X
ejpam-6339	241	17	⊓n	⊓n	PROPN
ejpam-6339	241	18	)	)	PUNCT
ejpam-6339	241	19	⊔	⊔	PROPN
ejpam-6339	241	20	(	(	PUNCT
ejpam-6339	241	21	u	u	NOUN
ejpam-6339	241	22	⊓m	⊓m	NOUN
ejpam-6339	241	23	)	)	PUNCT
ejpam-6339	241	24	=	=	SYM
ejpam-6339	241	25	∅̃	∅̃	NOUN
ejpam-6339	241	26	⊔	⊔	NUM
ejpam-6339	241	27	∅̃	∅̃	NOUN
ejpam-6339	241	28	=	=	SYM
ejpam-6339	241	29	∅̃	∅̃	NOUN
ejpam-6339	241	30	,	,	PUNCT
ejpam-6339	241	31	which	which	PRON
ejpam-6339	241	32	implies	imply	VERB
ejpam-6339	241	33	that	that	SCONJ
ejpam-6339	241	34	v	v	X
ejpam-6339	241	35	⊓	⊓	PROPN
ejpam-6339	241	36	(	(	PUNCT
ejpam-6339	241	37	n	n	NOUN
ejpam-6339	241	38	⊔m	⊔m	PROPN
ejpam-6339	241	39	)	)	PUNCT
ejpam-6339	241	40	=	=	SYM
ejpam-6339	241	41	∅̃	∅̃	NOUN
ejpam-6339	241	42	and	and	CCONJ
ejpam-6339	241	43	hence	hence	ADV
ejpam-6339	241	44	,	,	PUNCT
ejpam-6339	241	45	xa	xa	PROPN
ejpam-6339	241	46	,	,	PUNCT
ejpam-6339	241	47	b	b	PROPN
ejpam-6339	241	48	,	,	PUNCT
ejpam-6339	241	49	c	c	PROPN
ejpam-6339	241	50	/∈	/∈	PUNCT
ejpam-6339	241	51	clp(n	clp(n	PROPN
ejpam-6339	241	52	⊔m	⊔m	NOUN
ejpam-6339	241	53	)	)	PUNCT
ejpam-6339	241	54	.	.	PUNCT
ejpam-6339	242	1	(	(	PUNCT
ejpam-6339	242	2	6	6	NUM
ejpam-6339	242	3	)	)	PUNCT
ejpam-6339	242	4	and	and	CCONJ
ejpam-6339	242	5	(	(	PUNCT
ejpam-6339	242	6	7	7	X
ejpam-6339	242	7	)	)	PUNCT
ejpam-6339	242	8	are	be	AUX
ejpam-6339	242	9	deduced	deduce	VERB
ejpam-6339	242	10	from	from	ADP
ejpam-6339	242	11	the	the	DET
ejpam-6339	242	12	definition	definition	NOUN
ejpam-6339	242	13	10	10	NUM
ejpam-6339	242	14	.	.	PUNCT
ejpam-6339	243	1	j.	j.	PROPN
ejpam-6339	243	2	sanabria	sanabria	PROPN
ejpam-6339	243	3	,	,	PUNCT
ejpam-6339	243	4	e.	e.	PROPN
ejpam-6339	243	5	rosas	rosas	PROPN
ejpam-6339	243	6	,	,	PUNCT
ejpam-6339	243	7	c.	c.	PROPN
ejpam-6339	243	8	granados	granados	PROPN
ejpam-6339	243	9	/	/	PUNCT
ejpam-6339	243	10	eur	eur	PROPN
ejpam-6339	243	11	.	.	PUNCT
ejpam-6339	244	1	j.	j.	PROPN
ejpam-6339	244	2	pure	pure	PROPN
ejpam-6339	244	3	appl	appl	PROPN
ejpam-6339	244	4	.	.	PROPN
ejpam-6339	244	5	math	math	PROPN
ejpam-6339	244	6	,	,	PUNCT
ejpam-6339	244	7	18	18	NUM
ejpam-6339	244	8	(	(	PUNCT
ejpam-6339	244	9	3	3	NUM
ejpam-6339	244	10	)	)	PUNCT
ejpam-6339	244	11	(	(	PUNCT
ejpam-6339	244	12	2025	2025	NUM
ejpam-6339	244	13	)	)	PUNCT
ejpam-6339	244	14	,	,	PUNCT
ejpam-6339	244	15	6339	6339	NUM
ejpam-6339	244	16	11	11	NUM
ejpam-6339	244	17	of	of	ADP
ejpam-6339	244	18	15	15	NUM
ejpam-6339	244	19	in	in	ADP
ejpam-6339	244	20	the	the	DET
ejpam-6339	244	21	following	follow	VERB
ejpam-6339	244	22	example	example	NOUN
ejpam-6339	245	1	,	,	PUNCT
ejpam-6339	245	2	we	we	PRON
ejpam-6339	245	3	show	show	VERB
ejpam-6339	245	4	that	that	SCONJ
ejpam-6339	245	5	the	the	DET
ejpam-6339	245	6	converse	converse	NOUN
ejpam-6339	245	7	of	of	ADP
ejpam-6339	245	8	the	the	DET
ejpam-6339	245	9	part	part	NOUN
ejpam-6339	245	10	(	(	PUNCT
ejpam-6339	245	11	4	4	NUM
ejpam-6339	245	12	)	)	PUNCT
ejpam-6339	245	13	of	of	ADP
ejpam-6339	245	14	proposition	proposition	NOUN
ejpam-6339	245	15	8	8	NUM
ejpam-6339	245	16	is	be	AUX
ejpam-6339	245	17	not	not	PART
ejpam-6339	245	18	true	true	ADJ
ejpam-6339	245	19	in	in	ADP
ejpam-6339	245	20	general	general	ADJ
ejpam-6339	245	21	.	.	PUNCT
ejpam-6339	246	1	example	example	NOUN
ejpam-6339	247	1	4	4	X
ejpam-6339	247	2	.	.	PUNCT
ejpam-6339	248	1	let	let	AUX
ejpam-6339	248	2	(	(	PUNCT
ejpam-6339	248	3	x	x	NOUN
ejpam-6339	248	4	,	,	PUNCT
ejpam-6339	248	5	τ	τ	X
ejpam-6339	248	6	)	)	PUNCT
ejpam-6339	248	7	be	be	VERB
ejpam-6339	248	8	the	the	DET
ejpam-6339	248	9	n	n	CCONJ
ejpam-6339	248	10	-topological	-topological	ADJ
ejpam-6339	248	11	space	space	NOUN
ejpam-6339	248	12	given	give	VERB
ejpam-6339	248	13	in	in	ADP
ejpam-6339	248	14	example	example	NOUN
ejpam-6339	248	15	3	3	NUM
ejpam-6339	248	16	.	.	X
ejpam-6339	249	1	consider	consider	VERB
ejpam-6339	249	2	the	the	DET
ejpam-6339	249	3	n	n	NUM
ejpam-6339	249	4	-sets	-set	NOUN
ejpam-6339	249	5	n	n	NOUN
ejpam-6339	249	6	=	=	PRON
ejpam-6339	249	7	{	{	PUNCT
ejpam-6339	249	8	⟨x	⟨x	VERB
ejpam-6339	249	9	,	,	PUNCT
ejpam-6339	249	10	0.1	0.1	NUM
ejpam-6339	249	11	,	,	PUNCT
ejpam-6339	249	12	1	1	NUM
ejpam-6339	249	13	,	,	PUNCT
ejpam-6339	249	14	0.9⟩	0.9⟩	NUM
ejpam-6339	249	15	,	,	PUNCT
ejpam-6339	249	16	⟨y	⟨y	NOUN
ejpam-6339	249	17	,	,	PUNCT
ejpam-6339	249	18	0	0	NUM
ejpam-6339	249	19	,	,	PUNCT
ejpam-6339	249	20	0.3	0.3	NUM
ejpam-6339	249	21	,	,	PUNCT
ejpam-6339	249	22	1⟩	1⟩	NUM
ejpam-6339	249	23	}	}	PUNCT
ejpam-6339	249	24	and	and	CCONJ
ejpam-6339	249	25	m	m	PROPN
ejpam-6339	249	26	=	=	NOUN
ejpam-6339	249	27	{	{	PUNCT
ejpam-6339	249	28	⟨x	⟨x	VERB
ejpam-6339	249	29	,	,	PUNCT
ejpam-6339	249	30	0	0	NUM
ejpam-6339	249	31	,	,	PUNCT
ejpam-6339	249	32	0.3	0.3	NUM
ejpam-6339	249	33	,	,	PUNCT
ejpam-6339	249	34	1⟩	1⟩	NUM
ejpam-6339	249	35	,	,	PUNCT
ejpam-6339	249	36	⟨y	⟨y	NOUN
ejpam-6339	249	37	,	,	PUNCT
ejpam-6339	249	38	0.1	0.1	NUM
ejpam-6339	249	39	,	,	PUNCT
ejpam-6339	249	40	1	1	NUM
ejpam-6339	249	41	,	,	PUNCT
ejpam-6339	249	42	0.9⟩	0.9⟩	NUM
ejpam-6339	249	43	}	}	PUNCT
ejpam-6339	249	44	.	.	PUNCT
ejpam-6339	250	1	then	then	ADV
ejpam-6339	250	2	,	,	PUNCT
ejpam-6339	250	3	m	m	VERB
ejpam-6339	250	4	⊓n	⊓n	NOUN
ejpam-6339	250	5	=	=	PUNCT
ejpam-6339	250	6	∅̃	∅̃	NOUN
ejpam-6339	250	7	and	and	CCONJ
ejpam-6339	250	8	so	so	ADV
ejpam-6339	250	9	(	(	PUNCT
ejpam-6339	250	10	by	by	ADP
ejpam-6339	250	11	part	part	NOUN
ejpam-6339	250	12	(	(	PUNCT
ejpam-6339	250	13	6	6	NUM
ejpam-6339	250	14	)	)	PUNCT
ejpam-6339	250	15	of	of	ADP
ejpam-6339	250	16	proposition	proposition	NOUN
ejpam-6339	250	17	8)	8)	NUM
ejpam-6339	250	18	clp(m	clp(m	NUM
ejpam-6339	250	19	⊓n	⊓n	NOUN
ejpam-6339	250	20	)	)	PUNCT
ejpam-6339	250	21	=	=	PUNCT
ejpam-6339	250	22	∅̃.	∅̃.	NOUN
ejpam-6339	250	23	on	on	ADP
ejpam-6339	250	24	the	the	DET
ejpam-6339	250	25	other	other	ADJ
ejpam-6339	250	26	hand	hand	NOUN
ejpam-6339	250	27	,	,	PUNCT
ejpam-6339	250	28	as	as	SCONJ
ejpam-6339	250	29	x̃	x̃	PROPN
ejpam-6339	250	30	is	be	AUX
ejpam-6339	250	31	the	the	DET
ejpam-6339	250	32	only	only	ADJ
ejpam-6339	250	33	n	n	NUM
ejpam-6339	250	34	-open	-open	NOUN
ejpam-6339	250	35	set	set	VERB
ejpam-6339	250	36	to	to	PART
ejpam-6339	250	37	which	which	PRON
ejpam-6339	250	38	the	the	DET
ejpam-6339	250	39	n	n	PRON
ejpam-6339	250	40	-point	-point	NOUN
ejpam-6339	250	41	x0.3,1,0.7	x0.3,1,0.7	NOUN
ejpam-6339	250	42	belongs	belong	VERB
ejpam-6339	250	43	and	and	CCONJ
ejpam-6339	250	44	x̃⊓n	x̃⊓n	PROPN
ejpam-6339	250	45	̸=	̸=	PROPN
ejpam-6339	250	46	∅̃	∅̃	NOUN
ejpam-6339	250	47	,	,	PUNCT
ejpam-6339	250	48	x̃⊓m	x̃⊓m	PROPN
ejpam-6339	250	49	̸=	̸=	PROPN
ejpam-6339	250	50	∅̃	∅̃	NOUN
ejpam-6339	250	51	,	,	PUNCT
ejpam-6339	250	52	we	we	PRON
ejpam-6339	250	53	obtain	obtain	VERB
ejpam-6339	250	54	that	that	DET
ejpam-6339	250	55	x0.3,1,0.7	x0.3,1,0.7	NOUN
ejpam-6339	250	56	∈	∈	PROPN
ejpam-6339	250	57	clp(m	clp(m	NOUN
ejpam-6339	250	58	)	)	PUNCT
ejpam-6339	250	59	⊓	⊓	PROPN
ejpam-6339	250	60	clp(n	clp(n	PROPN
ejpam-6339	250	61	)	)	PUNCT
ejpam-6339	250	62	,	,	PUNCT
ejpam-6339	250	63	which	which	PRON
ejpam-6339	250	64	implies	imply	VERB
ejpam-6339	250	65	that	that	SCONJ
ejpam-6339	250	66	clp(m	clp(m	NOUN
ejpam-6339	250	67	)	)	PUNCT
ejpam-6339	250	68	⊓	⊓	PROPN
ejpam-6339	250	69	clp(n	clp(n	PROPN
ejpam-6339	250	70	)	)	PUNCT
ejpam-6339	250	71	̸=	̸=	PROPN
ejpam-6339	250	72	∅̃.	∅̃.	VERB
ejpam-6339	250	73	therefore	therefore	ADV
ejpam-6339	250	74	,	,	PUNCT
ejpam-6339	250	75	the	the	DET
ejpam-6339	250	76	inclusion	inclusion	NOUN
ejpam-6339	250	77	clp(m	clp(m	NOUN
ejpam-6339	250	78	)	)	PUNCT
ejpam-6339	250	79	⊓	⊓	PROPN
ejpam-6339	250	80	clp(n	clp(n	PROPN
ejpam-6339	250	81	)	)	PUNCT
ejpam-6339	250	82	⊑	⊑	PRON
ejpam-6339	250	83	clp(m	clp(m	PROPN
ejpam-6339	250	84	⊓n	⊓n	NOUN
ejpam-6339	250	85	)	)	PUNCT
ejpam-6339	250	86	is	be	AUX
ejpam-6339	250	87	not	not	PART
ejpam-6339	250	88	satisfied	satisfied	ADJ
ejpam-6339	250	89	.	.	PUNCT
ejpam-6339	251	1	remark	remark	VERB
ejpam-6339	251	2	4	4	NUM
ejpam-6339	251	3	.	.	PUNCT
ejpam-6339	251	4	from	from	ADP
ejpam-6339	251	5	proposition	proposition	NOUN
ejpam-6339	251	6	8	8	NUM
ejpam-6339	251	7	we	we	PRON
ejpam-6339	251	8	infer	infer	VERB
ejpam-6339	251	9	that	that	SCONJ
ejpam-6339	251	10	clp	clp	PROPN
ejpam-6339	251	11	satisfies	satisfy	VERB
ejpam-6339	251	12	the	the	DET
ejpam-6339	251	13	conditions	condition	NOUN
ejpam-6339	251	14	of	of	ADP
ejpam-6339	251	15	definition	definition	NOUN
ejpam-6339	251	16	9	9	NUM
ejpam-6339	251	17	.	.	PUNCT
ejpam-6339	252	1	thus	thus	ADV
ejpam-6339	252	2	,	,	PUNCT
ejpam-6339	252	3	by	by	ADP
ejpam-6339	252	4	proposition	proposition	NOUN
ejpam-6339	252	5	7	7	NUM
ejpam-6339	252	6	,	,	PUNCT
ejpam-6339	252	7	we	we	PRON
ejpam-6339	252	8	get	get	VERB
ejpam-6339	252	9	that	that	SCONJ
ejpam-6339	252	10	the	the	DET
ejpam-6339	252	11	collection	collection	NOUN
ejpam-6339	252	12	τp	τp	NOUN
ejpam-6339	252	13	=	=	PUNCT
ejpam-6339	252	14	{	{	PUNCT
ejpam-6339	252	15	n	n	NOUN
ejpam-6339	252	16	∈	∈	PROPN
ejpam-6339	252	17	n	n	PRON
ejpam-6339	252	18	′(x	′(x	NOUN
ejpam-6339	252	19	)	)	PUNCT
ejpam-6339	252	20	:	:	PUNCT
ejpam-6339	253	1	clp(n	clp(n	PROPN
ejpam-6339	253	2	c	c	NOUN
ejpam-6339	253	3	)	)	PUNCT
ejpam-6339	253	4	=	=	SYM
ejpam-6339	254	1	n	n	PROPN
ejpam-6339	254	2	c	c	X
ejpam-6339	254	3	}	}	PUNCT
ejpam-6339	254	4	is	be	AUX
ejpam-6339	254	5	a	a	DET
ejpam-6339	254	6	n	n	PRON
ejpam-6339	254	7	-topology	-topology	NOUN
ejpam-6339	254	8	on	on	ADP
ejpam-6339	254	9	x	x	PUNCT
ejpam-6339	254	10	and	and	CCONJ
ejpam-6339	254	11	clp	clp	PROPN
ejpam-6339	254	12	is	be	AUX
ejpam-6339	254	13	the	the	PRON
ejpam-6339	254	14	n	n	ADV
ejpam-6339	254	15	-closure	-closure	NOUN
ejpam-6339	254	16	in	in	ADP
ejpam-6339	254	17	the	the	DET
ejpam-6339	254	18	n	n	NUM
ejpam-6339	254	19	-topological	-topological	ADJ
ejpam-6339	254	20	space	space	NOUN
ejpam-6339	254	21	(	(	PUNCT
ejpam-6339	254	22	x	x	NOUN
ejpam-6339	254	23	,	,	PUNCT
ejpam-6339	254	24	τp	τp	NOUN
ejpam-6339	254	25	)	)	PUNCT
ejpam-6339	254	26	.	.	PUNCT
ejpam-6339	255	1	we	we	PRON
ejpam-6339	255	2	say	say	VERB
ejpam-6339	255	3	that	that	SCONJ
ejpam-6339	255	4	a	a	DET
ejpam-6339	255	5	n	n	NOUN
ejpam-6339	255	6	-set	-set	NUM
ejpam-6339	255	7	n	n	CCONJ
ejpam-6339	255	8	is	be	AUX
ejpam-6339	255	9	n	n	PRON
ejpam-6339	255	10	-τp	-τp	ADV
ejpam-6339	255	11	-	-	PUNCT
ejpam-6339	255	12	open	open	ADJ
ejpam-6339	255	13	if	if	SCONJ
ejpam-6339	255	14	n	n	NOUN
ejpam-6339	255	15	∈	∈	PROPN
ejpam-6339	255	16	τp	τp	NOUN
ejpam-6339	255	17	.	.	PUNCT
ejpam-6339	256	1	the	the	DET
ejpam-6339	256	2	complement	complement	NOUN
ejpam-6339	256	3	of	of	ADP
ejpam-6339	256	4	a	a	DET
ejpam-6339	256	5	n	n	PRON
ejpam-6339	256	6	-τp	-τp	ADV
ejpam-6339	256	7	-	-	PUNCT
ejpam-6339	256	8	open	open	ADJ
ejpam-6339	256	9	set	set	NOUN
ejpam-6339	256	10	,	,	PUNCT
ejpam-6339	256	11	we	we	PRON
ejpam-6339	256	12	will	will	AUX
ejpam-6339	256	13	call	call	VERB
ejpam-6339	256	14	it	it	PRON
ejpam-6339	256	15	a	a	DET
ejpam-6339	256	16	n	n	PRON
ejpam-6339	256	17	-τp	-τp	ADV
ejpam-6339	256	18	-	-	PUNCT
ejpam-6339	256	19	closed	close	VERB
ejpam-6339	256	20	set	set	NOUN
ejpam-6339	256	21	.	.	PUNCT
ejpam-6339	257	1	observe	observe	VERB
ejpam-6339	257	2	that	that	SCONJ
ejpam-6339	257	3	a	a	DET
ejpam-6339	257	4	n	n	NOUN
ejpam-6339	257	5	-set	-set	NOUN
ejpam-6339	257	6	m	m	VERB
ejpam-6339	257	7	is	be	AUX
ejpam-6339	257	8	τp	τp	ADV
ejpam-6339	257	9	-	-	PUNCT
ejpam-6339	257	10	closed	close	VERB
ejpam-6339	257	11	if	if	SCONJ
ejpam-6339	257	12	and	and	CCONJ
ejpam-6339	257	13	only	only	ADV
ejpam-6339	257	14	if	if	SCONJ
ejpam-6339	257	15	clp(m	clp(m	NOUN
ejpam-6339	257	16	)	)	PUNCT
ejpam-6339	257	17	=	=	NOUN
ejpam-6339	257	18	m	m	NOUN
ejpam-6339	257	19	.	.	PUNCT
ejpam-6339	258	1	remark	remark	PROPN
ejpam-6339	258	2	5	5	NUM
ejpam-6339	258	3	.	.	PUNCT
ejpam-6339	259	1	if	if	SCONJ
ejpam-6339	259	2	we	we	PRON
ejpam-6339	259	3	restrict	restrict	VERB
ejpam-6339	259	4	the	the	DET
ejpam-6339	259	5	definition	definition	NOUN
ejpam-6339	259	6	of	of	ADP
ejpam-6339	259	7	n	n	DET
ejpam-6339	259	8	-ideal	-ideal	ADJ
ejpam-6339	259	9	to	to	ADP
ejpam-6339	259	10	the	the	DET
ejpam-6339	259	11	collection	collection	NOUN
ejpam-6339	259	12	n	n	PRON
ejpam-6339	259	13	′(x	′(x	NOUN
ejpam-6339	259	14	)	)	PUNCT
ejpam-6339	259	15	,	,	PUNCT
ejpam-6339	259	16	then	then	ADV
ejpam-6339	259	17	we	we	PRON
ejpam-6339	259	18	can	can	AUX
ejpam-6339	259	19	correct	correct	VERB
ejpam-6339	259	20	some	some	DET
ejpam-6339	259	21	results	result	NOUN
ejpam-6339	259	22	given	give	VERB
ejpam-6339	259	23	in	in	ADP
ejpam-6339	259	24	[	[	X
ejpam-6339	259	25	12	12	NUM
ejpam-6339	259	26	]	]	PUNCT
ejpam-6339	259	27	,	,	PUNCT
ejpam-6339	259	28	as	as	SCONJ
ejpam-6339	259	29	we	we	PRON
ejpam-6339	259	30	show	show	VERB
ejpam-6339	259	31	in	in	ADP
ejpam-6339	259	32	the	the	DET
ejpam-6339	259	33	following	following	NOUN
ejpam-6339	259	34	:	:	PUNCT
ejpam-6339	259	35	(	(	PUNCT
ejpam-6339	259	36	1	1	X
ejpam-6339	259	37	)	)	PUNCT
ejpam-6339	259	38	if	if	SCONJ
ejpam-6339	259	39	(	(	PUNCT
ejpam-6339	259	40	x	x	NOUN
ejpam-6339	259	41	,	,	PUNCT
ejpam-6339	259	42	τ	τ	X
ejpam-6339	259	43	)	)	PUNCT
ejpam-6339	259	44	is	be	AUX
ejpam-6339	259	45	a	a	DET
ejpam-6339	259	46	n	n	CCONJ
ejpam-6339	259	47	-topological	-topological	ADJ
ejpam-6339	259	48	space	space	NOUN
ejpam-6339	259	49	and	and	CCONJ
ejpam-6339	259	50	l	l	NOUN
ejpam-6339	259	51	is	be	AUX
ejpam-6339	259	52	a	a	DET
ejpam-6339	259	53	n	n	ADV
ejpam-6339	259	54	-ideal	-ideal	NOUN
ejpam-6339	259	55	on	on	ADP
ejpam-6339	259	56	x	x	NOUN
ejpam-6339	259	57	,	,	PUNCT
ejpam-6339	259	58	then	then	ADV
ejpam-6339	259	59	∅̃⋆	∅̃⋆	NOUN
ejpam-6339	259	60	=	=	SYM
ejpam-6339	259	61	∅̃	∅̃	NOUN
ejpam-6339	259	62	,	,	PUNCT
ejpam-6339	259	63	because	because	SCONJ
ejpam-6339	259	64	for	for	ADP
ejpam-6339	259	65	every	every	DET
ejpam-6339	259	66	n	n	CCONJ
ejpam-6339	259	67	-point	-point	PROPN
ejpam-6339	259	68	xa	xa	PROPN
ejpam-6339	259	69	,	,	PUNCT
ejpam-6339	259	70	b	b	PROPN
ejpam-6339	259	71	,	,	PUNCT
ejpam-6339	259	72	c	c	PROPN
ejpam-6339	259	73	∈	∈	PROPN
ejpam-6339	259	74	n	n	PRON
ejpam-6339	259	75	′(x	′(x	NOUN
ejpam-6339	259	76	)	)	PUNCT
ejpam-6339	259	77	and	and	CCONJ
ejpam-6339	259	78	every	every	DET
ejpam-6339	259	79	u	u	PROPN
ejpam-6339	259	80	∈	∈	PROPN
ejpam-6339	259	81	τ(xa	τ(xa	NUM
ejpam-6339	259	82	,	,	PUNCT
ejpam-6339	259	83	b	b	NOUN
ejpam-6339	259	84	,	,	PUNCT
ejpam-6339	259	85	c	c	NOUN
ejpam-6339	259	86	)	)	PUNCT
ejpam-6339	259	87	,	,	PUNCT
ejpam-6339	259	88	∅̃	∅̃	NOUN
ejpam-6339	259	89	⊓	⊓	PROPN
ejpam-6339	259	90	u	u	NOUN
ejpam-6339	259	91	=	=	PROPN
ejpam-6339	259	92	∅̃	∅̃	PROPN
ejpam-6339	259	93	∈	∈	PROPN
ejpam-6339	259	94	l.	l.	NOUN
ejpam-6339	259	95	(	(	PUNCT
ejpam-6339	259	96	2	2	NUM
ejpam-6339	259	97	)	)	PUNCT
ejpam-6339	259	98	for	for	ADP
ejpam-6339	259	99	each	each	DET
ejpam-6339	259	100	n	n	PRON
ejpam-6339	259	101	∈	∈	PROPN
ejpam-6339	259	102	n	n	PRON
ejpam-6339	259	103	′(x	′(x	NOUN
ejpam-6339	259	104	)	)	PUNCT
ejpam-6339	259	105	,	,	PUNCT
ejpam-6339	259	106	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	259	107	)	)	PUNCT
ejpam-6339	259	108	is	be	AUX
ejpam-6339	259	109	defined	define	VERB
ejpam-6339	259	110	as	as	ADP
ejpam-6339	259	111	the	the	DET
ejpam-6339	259	112	neutrosophic	neutrosophic	ADJ
ejpam-6339	259	113	union	union	NOUN
ejpam-6339	259	114	of	of	ADP
ejpam-6339	259	115	n	n	PROPN
ejpam-6339	259	116	with	with	ADP
ejpam-6339	259	117	n⋆	n⋆	NOUN
ejpam-6339	259	118	;	;	PUNCT
ejpam-6339	259	119	that	that	PRON
ejpam-6339	259	120	is	is	ADV
ejpam-6339	259	121	,	,	PUNCT
ejpam-6339	259	122	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	259	123	)	)	PUNCT
ejpam-6339	259	124	=	=	SYM
ejpam-6339	260	1	n	n	CCONJ
ejpam-6339	260	2	⊔	⊔	NOUN
ejpam-6339	260	3	n⋆	n⋆	X
ejpam-6339	260	4	(	(	PUNCT
ejpam-6339	260	5	see	see	VERB
ejpam-6339	260	6	[	[	X
ejpam-6339	260	7	12	12	NUM
ejpam-6339	260	8	]	]	PUNCT
ejpam-6339	260	9	)	)	PUNCT
ejpam-6339	260	10	.	.	PUNCT
ejpam-6339	261	1	observe	observe	VERB
ejpam-6339	261	2	that	that	SCONJ
ejpam-6339	261	3	,	,	PUNCT
ejpam-6339	261	4	by	by	ADP
ejpam-6339	261	5	proposition	proposition	NOUN
ejpam-6339	261	6	7	7	NUM
ejpam-6339	261	7	,	,	PUNCT
ejpam-6339	261	8	we	we	PRON
ejpam-6339	261	9	have	have	VERB
ejpam-6339	261	10	cl⋆	cl⋆	PROPN
ejpam-6339	261	11	is	be	AUX
ejpam-6339	261	12	a	a	DET
ejpam-6339	261	13	n	n	CCONJ
ejpam-6339	261	14	-closure	-closure	NOUN
ejpam-6339	261	15	operator	operator	NOUN
ejpam-6339	261	16	.	.	PUNCT
ejpam-6339	262	1	using	use	VERB
ejpam-6339	262	2	this	this	DET
ejpam-6339	262	3	fact	fact	NOUN
ejpam-6339	262	4	,	,	PUNCT
ejpam-6339	262	5	we	we	PRON
ejpam-6339	262	6	denote	denote	VERB
ejpam-6339	262	7	by	by	ADP
ejpam-6339	262	8	τ⋆	τ⋆	ADJ
ejpam-6339	262	9	(	(	PUNCT
ejpam-6339	262	10	or	or	CCONJ
ejpam-6339	262	11	τ⋆(l	τ⋆(l	PROPN
ejpam-6339	262	12	)	)	PUNCT
ejpam-6339	262	13	)	)	PUNCT
ejpam-6339	262	14	to	to	ADP
ejpam-6339	262	15	the	the	DET
ejpam-6339	262	16	n	n	PRON
ejpam-6339	262	17	-topology	-topology	NOUN
ejpam-6339	262	18	generated	generate	VERB
ejpam-6339	262	19	by	by	ADP
ejpam-6339	262	20	cl⋆	cl⋆	PROPN
ejpam-6339	262	21	,	,	PUNCT
ejpam-6339	262	22	that	that	ADV
ejpam-6339	262	23	is	be	AUX
ejpam-6339	262	24	,	,	PUNCT
ejpam-6339	262	25	τ⋆	τ⋆	ADV
ejpam-6339	262	26	=	=	PUNCT
ejpam-6339	262	27	{	{	PUNCT
ejpam-6339	262	28	n	n	NOUN
ejpam-6339	262	29	∈	∈	PROPN
ejpam-6339	262	30	n	n	PRON
ejpam-6339	262	31	′(x	′(x	NOUN
ejpam-6339	262	32	)	)	PUNCT
ejpam-6339	262	33	:	:	PUNCT
ejpam-6339	262	34	cl⋆(n	cl⋆(n	VERB
ejpam-6339	262	35	c	c	NOUN
ejpam-6339	262	36	)	)	PUNCT
ejpam-6339	262	37	=	=	SYM
ejpam-6339	263	1	n	n	PROPN
ejpam-6339	263	2	c	c	NOUN
ejpam-6339	263	3	}	}	PUNCT
ejpam-6339	263	4	.	.	PUNCT
ejpam-6339	264	1	(	(	PUNCT
ejpam-6339	264	2	3	3	X
ejpam-6339	264	3	)	)	PUNCT
ejpam-6339	264	4	if	if	SCONJ
ejpam-6339	264	5	l	l	NOUN
ejpam-6339	264	6	=	=	SYM
ejpam-6339	264	7	{	{	PUNCT
ejpam-6339	264	8	∅̃	∅̃	NOUN
ejpam-6339	264	9	}	}	PUNCT
ejpam-6339	264	10	,	,	PUNCT
ejpam-6339	264	11	then	then	ADV
ejpam-6339	264	12	for	for	ADP
ejpam-6339	264	13	each	each	DET
ejpam-6339	264	14	n	n	PRON
ejpam-6339	264	15	∈	∈	PROPN
ejpam-6339	264	16	n	n	PRON
ejpam-6339	264	17	′(x	′(x	NOUN
ejpam-6339	264	18	)	)	PUNCT
ejpam-6339	264	19	,	,	PUNCT
ejpam-6339	264	20	n⋆	n⋆	X
ejpam-6339	264	21	=	=	ADJ
ejpam-6339	264	22	clp(n	clp(n	PROPN
ejpam-6339	264	23	)	)	PUNCT
ejpam-6339	264	24	and	and	CCONJ
ejpam-6339	264	25	hence	hence	ADV
ejpam-6339	264	26	,	,	PUNCT
ejpam-6339	264	27	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	264	28	)	)	PUNCT
ejpam-6339	264	29	=	=	PUNCT
ejpam-6339	265	1	n	n	CCONJ
ejpam-6339	265	2	⊔n⋆	⊔n⋆	NOUN
ejpam-6339	265	3	=	=	SYM
ejpam-6339	265	4	n	n	CCONJ
ejpam-6339	265	5	⊔	⊔	PROPN
ejpam-6339	265	6	clp(n	clp(n	PROPN
ejpam-6339	265	7	)	)	PUNCT
ejpam-6339	265	8	=	=	PUNCT
ejpam-6339	266	1	clp(n	clp(n	PROPN
ejpam-6339	266	2	)	)	PUNCT
ejpam-6339	266	3	,	,	PUNCT
ejpam-6339	266	4	i.e.	i.e.	X
ejpam-6339	266	5	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	266	6	)	)	PUNCT
ejpam-6339	267	1	=	=	SYM
ejpam-6339	267	2	clp(n	clp(n	PROPN
ejpam-6339	267	3	)	)	PUNCT
ejpam-6339	267	4	.	.	PUNCT
ejpam-6339	268	1	therefore	therefore	ADV
ejpam-6339	268	2	,	,	PUNCT
ejpam-6339	268	3	τ⋆({∅̃	τ⋆({∅̃	ADP
ejpam-6339	268	4	}	}	PUNCT
ejpam-6339	268	5	)	)	PUNCT
ejpam-6339	269	1	=	=	SYM
ejpam-6339	269	2	τp	τp	PROPN
ejpam-6339	269	3	.	.	PUNCT
ejpam-6339	269	4	(	(	PUNCT
ejpam-6339	269	5	4	4	NUM
ejpam-6339	269	6	)	)	PUNCT
ejpam-6339	269	7	by	by	ADP
ejpam-6339	269	8	using	use	VERB
ejpam-6339	269	9	the	the	DET
ejpam-6339	269	10	result	result	NOUN
ejpam-6339	269	11	of	of	ADP
ejpam-6339	269	12	the	the	DET
ejpam-6339	269	13	previous	previous	ADJ
ejpam-6339	269	14	part	part	NOUN
ejpam-6339	269	15	,	,	PUNCT
ejpam-6339	269	16	we	we	PRON
ejpam-6339	269	17	correct	correct	VERB
ejpam-6339	269	18	part	part	NOUN
ejpam-6339	269	19	(	(	PUNCT
ejpam-6339	269	20	3	3	NUM
ejpam-6339	269	21	)	)	PUNCT
ejpam-6339	269	22	of	of	ADP
ejpam-6339	269	23	theorem	theorem	NOUN
ejpam-6339	269	24	1	1	NUM
ejpam-6339	269	25	as	as	SCONJ
ejpam-6339	269	26	follows	follow	VERB
ejpam-6339	269	27	:	:	PUNCT
ejpam-6339	269	28	n⋆	n⋆	X
ejpam-6339	269	29	=	=	SYM
ejpam-6339	269	30	clp(n	clp(n	PROPN
ejpam-6339	269	31	⋆	⋆	NOUN
ejpam-6339	269	32	)	)	PUNCT
ejpam-6339	269	33	⊑	⊑	PRON
ejpam-6339	269	34	clp(n	clp(n	PROPN
ejpam-6339	269	35	)	)	PUNCT
ejpam-6339	269	36	(	(	PUNCT
ejpam-6339	269	37	n⋆	n⋆	X
ejpam-6339	269	38	is	be	AUX
ejpam-6339	269	39	a	a	DET
ejpam-6339	269	40	n	n	PRON
ejpam-6339	269	41	-τp	-τp	ADV
ejpam-6339	269	42	-	-	PUNCT
ejpam-6339	269	43	closed	closed	ADJ
ejpam-6339	269	44	set	set	NOUN
ejpam-6339	269	45	)	)	PUNCT
ejpam-6339	269	46	.	.	PUNCT
ejpam-6339	270	1	the	the	DET
ejpam-6339	270	2	following	follow	VERB
ejpam-6339	270	3	is	be	AUX
ejpam-6339	270	4	the	the	DET
ejpam-6339	270	5	proof	proof	NOUN
ejpam-6339	270	6	of	of	ADP
ejpam-6339	270	7	the	the	DET
ejpam-6339	270	8	above	above	ADJ
ejpam-6339	270	9	statement	statement	NOUN
ejpam-6339	270	10	.	.	PUNCT
ejpam-6339	271	1	since	since	SCONJ
ejpam-6339	271	2	{	{	PUNCT
ejpam-6339	271	3	∅̃	∅̃	NOUN
ejpam-6339	271	4	}	}	PUNCT
ejpam-6339	271	5	⊆	⊆	NUM
ejpam-6339	271	6	l	l	NOUN
ejpam-6339	271	7	for	for	ADP
ejpam-6339	271	8	each	each	DET
ejpam-6339	271	9	n	n	PRON
ejpam-6339	271	10	-ideal	-ideal	ADJ
ejpam-6339	271	11	l	l	NOUN
ejpam-6339	271	12	on	on	ADP
ejpam-6339	271	13	x	x	SYM
ejpam-6339	271	14	,	,	PUNCT
ejpam-6339	271	15	we	we	PRON
ejpam-6339	271	16	have	have	VERB
ejpam-6339	271	17	n⋆(l	n⋆(l	NOUN
ejpam-6339	271	18	)	)	PUNCT
ejpam-6339	271	19	⊆	⊆	NUM
ejpam-6339	271	20	n⋆({∅̃	n⋆({∅̃	PROPN
ejpam-6339	271	21	}	}	PUNCT
ejpam-6339	271	22	)	)	PUNCT
ejpam-6339	272	1	=	=	SYM
ejpam-6339	272	2	clp(n	clp(n	PROPN
ejpam-6339	272	3	)	)	PUNCT
ejpam-6339	272	4	for	for	ADP
ejpam-6339	272	5	each	each	DET
ejpam-6339	272	6	n	n	PRON
ejpam-6339	272	7	∈	∈	PROPN
ejpam-6339	272	8	n	n	PRON
ejpam-6339	272	9	′(x	′(x	NOUN
ejpam-6339	272	10	)	)	PUNCT
ejpam-6339	272	11	.	.	PUNCT
ejpam-6339	272	12	suppose	suppose	VERB
ejpam-6339	272	13	that	that	SCONJ
ejpam-6339	272	14	xa	xa	PROPN
ejpam-6339	272	15	,	,	PUNCT
ejpam-6339	272	16	b	b	PROPN
ejpam-6339	272	17	,	,	PUNCT
ejpam-6339	272	18	c	c	PROPN
ejpam-6339	272	19	∈	∈	PROPN
ejpam-6339	272	20	clp(n	clp(n	PROPN
ejpam-6339	272	21	⋆	⋆	NOUN
ejpam-6339	272	22	)	)	PUNCT
ejpam-6339	272	23	and	and	CCONJ
ejpam-6339	272	24	let	let	VERB
ejpam-6339	272	25	u	u	PRON
ejpam-6339	272	26	∈	∈	PROPN
ejpam-6339	272	27	τ(xa	τ(xa	NUM
ejpam-6339	272	28	,	,	PUNCT
ejpam-6339	272	29	b	b	NOUN
ejpam-6339	272	30	,	,	PUNCT
ejpam-6339	272	31	c	c	NOUN
ejpam-6339	272	32	)	)	PUNCT
ejpam-6339	272	33	arbitrary	arbitrary	ADJ
ejpam-6339	272	34	.	.	PUNCT
ejpam-6339	273	1	then	then	ADV
ejpam-6339	273	2	,	,	PUNCT
ejpam-6339	273	3	u	u	PROPN
ejpam-6339	273	4	⊓n⋆	⊓n⋆	VERB
ejpam-6339	273	5	̸=	̸=	PROPN
ejpam-6339	273	6	∅̃	∅̃	NOUN
ejpam-6339	273	7	and	and	CCONJ
ejpam-6339	273	8	so	so	ADV
ejpam-6339	273	9	,	,	PUNCT
ejpam-6339	273	10	there	there	PRON
ejpam-6339	273	11	exists	exist	VERB
ejpam-6339	273	12	a	a	DET
ejpam-6339	273	13	n	n	CCONJ
ejpam-6339	273	14	-point	-point	PROPN
ejpam-6339	273	15	yu	yu	PROPN
ejpam-6339	273	16	,	,	PUNCT
ejpam-6339	273	17	v	v	NOUN
ejpam-6339	273	18	,	,	PUNCT
ejpam-6339	273	19	w	w	PROPN
ejpam-6339	273	20	∈	∈	PROPN
ejpam-6339	273	21	u	u	NOUN
ejpam-6339	273	22	⊓	⊓	NOUN
ejpam-6339	273	23	n⋆	n⋆	NOUN
ejpam-6339	273	24	,	,	PUNCT
ejpam-6339	273	25	which	which	PRON
ejpam-6339	273	26	implies	imply	VERB
ejpam-6339	273	27	that	that	SCONJ
ejpam-6339	273	28	yu	yu	PROPN
ejpam-6339	273	29	,	,	PUNCT
ejpam-6339	273	30	v	v	NOUN
ejpam-6339	273	31	,	,	PUNCT
ejpam-6339	273	32	w	w	PROPN
ejpam-6339	273	33	∈	∈	PROPN
ejpam-6339	273	34	u	u	NOUN
ejpam-6339	273	35	and	and	CCONJ
ejpam-6339	273	36	yu	yu	PROPN
ejpam-6339	273	37	,	,	PUNCT
ejpam-6339	273	38	v	v	NOUN
ejpam-6339	273	39	,	,	PUNCT
ejpam-6339	273	40	w	w	PROPN
ejpam-6339	273	41	∈	∈	PROPN
ejpam-6339	273	42	n⋆.	n⋆.	NOUN
ejpam-6339	273	43	since	since	SCONJ
ejpam-6339	273	44	u	u	NOUN
ejpam-6339	273	45	∈	∈	PROPN
ejpam-6339	273	46	τ(yu	τ(yu	NUM
ejpam-6339	273	47	,	,	PUNCT
ejpam-6339	273	48	v	v	NOUN
ejpam-6339	273	49	,	,	PUNCT
ejpam-6339	273	50	w	w	NOUN
ejpam-6339	273	51	)	)	PUNCT
ejpam-6339	273	52	,	,	PUNCT
ejpam-6339	273	53	it	it	PRON
ejpam-6339	273	54	follows	follow	VERB
ejpam-6339	273	55	that	that	SCONJ
ejpam-6339	273	56	u	u	PRON
ejpam-6339	273	57	⊓n	⊓n	X
ejpam-6339	273	58	̸∈	̸∈	PROPN
ejpam-6339	273	59	l	l	PROPN
ejpam-6339	273	60	and	and	CCONJ
ejpam-6339	273	61	so	so	ADV
ejpam-6339	273	62	xa	xa	PROPN
ejpam-6339	273	63	,	,	PUNCT
ejpam-6339	273	64	b	b	PROPN
ejpam-6339	273	65	,	,	PUNCT
ejpam-6339	273	66	c	c	PROPN
ejpam-6339	273	67	∈	∈	PROPN
ejpam-6339	273	68	n⋆.	n⋆.	NOUN
ejpam-6339	273	69	on	on	ADP
ejpam-6339	273	70	the	the	DET
ejpam-6339	273	71	other	other	ADJ
ejpam-6339	273	72	hand	hand	NOUN
ejpam-6339	273	73	,	,	PUNCT
ejpam-6339	273	74	since	since	SCONJ
ejpam-6339	273	75	n⋆	n⋆	ADJ
ejpam-6339	273	76	⊑	⊑	DET
ejpam-6339	273	77	clp(n	clp(n	PROPN
ejpam-6339	273	78	⋆	⋆	NOUN
ejpam-6339	273	79	)	)	PUNCT
ejpam-6339	273	80	,	,	PUNCT
ejpam-6339	273	81	we	we	PRON
ejpam-6339	273	82	conclude	conclude	VERB
ejpam-6339	273	83	that	that	SCONJ
ejpam-6339	273	84	n⋆	n⋆	PUNCT
ejpam-6339	273	85	=	=	ADJ
ejpam-6339	273	86	clp(n	clp(n	PROPN
ejpam-6339	273	87	⋆	⋆	NOUN
ejpam-6339	273	88	)	)	PUNCT
ejpam-6339	273	89	.	.	PUNCT
ejpam-6339	274	1	(	(	PUNCT
ejpam-6339	274	2	5	5	X
ejpam-6339	274	3	)	)	PUNCT
ejpam-6339	274	4	if	if	SCONJ
ejpam-6339	274	5	l	l	NOUN
ejpam-6339	274	6	=	=	PUNCT
ejpam-6339	274	7	n	n	PRON
ejpam-6339	274	8	′(x	′(x	NOUN
ejpam-6339	274	9	)	)	PUNCT
ejpam-6339	274	10	,	,	PUNCT
ejpam-6339	274	11	then	then	ADV
ejpam-6339	274	12	for	for	ADP
ejpam-6339	274	13	any	any	DET
ejpam-6339	274	14	n	n	PRON
ejpam-6339	274	15	∈	∈	PROPN
ejpam-6339	274	16	n	n	PRON
ejpam-6339	274	17	′(x	′(x	NOUN
ejpam-6339	274	18	)	)	PUNCT
ejpam-6339	274	19	,	,	PUNCT
ejpam-6339	274	20	n⋆	n⋆	X
ejpam-6339	274	21	=	=	PUNCT
ejpam-6339	274	22	∅̃	∅̃	NOUN
ejpam-6339	274	23	and	and	CCONJ
ejpam-6339	274	24	so	so	ADV
ejpam-6339	274	25	,	,	PUNCT
ejpam-6339	274	26	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	274	27	)	)	PUNCT
ejpam-6339	274	28	=	=	SYM
ejpam-6339	275	1	n	n	DET
ejpam-6339	275	2	⊔	⊔	NUM
ejpam-6339	275	3	∅̃	∅̃	NOUN
ejpam-6339	275	4	=	=	NOUN
ejpam-6339	275	5	n	n	PROPN
ejpam-6339	275	6	.	.	PUNCT
ejpam-6339	276	1	therefore	therefore	ADV
ejpam-6339	276	2	,	,	PUNCT
ejpam-6339	276	3	τ⋆(n	τ⋆(n	NOUN
ejpam-6339	276	4	′(x	′(x	NOUN
ejpam-6339	276	5	)	)	PUNCT
ejpam-6339	276	6	)	)	PUNCT
ejpam-6339	277	1	=	=	SYM
ejpam-6339	277	2	n	n	PRON
ejpam-6339	277	3	′(x	′(x	NOUN
ejpam-6339	277	4	)	)	PUNCT
ejpam-6339	277	5	.	.	PUNCT
ejpam-6339	278	1	j.	j.	PROPN
ejpam-6339	278	2	sanabria	sanabria	PROPN
ejpam-6339	278	3	,	,	PUNCT
ejpam-6339	278	4	e.	e.	PROPN
ejpam-6339	278	5	rosas	rosas	PROPN
ejpam-6339	278	6	,	,	PUNCT
ejpam-6339	278	7	c.	c.	PROPN
ejpam-6339	278	8	granados	granados	PROPN
ejpam-6339	278	9	/	/	PUNCT
ejpam-6339	278	10	eur	eur	PROPN
ejpam-6339	278	11	.	.	PUNCT
ejpam-6339	279	1	j.	j.	PROPN
ejpam-6339	279	2	pure	pure	PROPN
ejpam-6339	279	3	appl	appl	PROPN
ejpam-6339	279	4	.	.	PROPN
ejpam-6339	279	5	math	math	PROPN
ejpam-6339	279	6	,	,	PUNCT
ejpam-6339	279	7	18	18	NUM
ejpam-6339	279	8	(	(	PUNCT
ejpam-6339	279	9	3	3	NUM
ejpam-6339	279	10	)	)	PUNCT
ejpam-6339	279	11	(	(	PUNCT
ejpam-6339	279	12	2025	2025	NUM
ejpam-6339	279	13	)	)	PUNCT
ejpam-6339	279	14	,	,	PUNCT
ejpam-6339	279	15	6339	6339	NUM
ejpam-6339	279	16	12	12	NUM
ejpam-6339	279	17	of	of	ADP
ejpam-6339	279	18	15	15	NUM
ejpam-6339	279	19	(	(	PUNCT
ejpam-6339	279	20	6	6	NUM
ejpam-6339	279	21	)	)	PUNCT
ejpam-6339	279	22	since	since	SCONJ
ejpam-6339	279	23	n⋆	n⋆	ADJ
ejpam-6339	279	24	=	=	SYM
ejpam-6339	279	25	clp(n	clp(n	PROPN
ejpam-6339	279	26	⋆	⋆	NOUN
ejpam-6339	279	27	)	)	PUNCT
ejpam-6339	279	28	⊑	⊑	PRON
ejpam-6339	279	29	clp(n	clp(n	PROPN
ejpam-6339	279	30	)	)	PUNCT
ejpam-6339	279	31	,	,	PUNCT
ejpam-6339	279	32	we	we	PRON
ejpam-6339	279	33	have	have	AUX
ejpam-6339	279	34	cl⋆(n	cl⋆(n	VERB
ejpam-6339	279	35	)	)	PUNCT
ejpam-6339	280	1	⊑	⊑	PROPN
ejpam-6339	280	2	clp(n	clp(n	PROPN
ejpam-6339	280	3	)	)	PUNCT
ejpam-6339	280	4	for	for	ADP
ejpam-6339	280	5	each	each	DET
ejpam-6339	280	6	n	n	PRON
ejpam-6339	280	7	∈	∈	PROPN
ejpam-6339	280	8	n	n	PRON
ejpam-6339	280	9	′(x	′(x	NOUN
ejpam-6339	280	10	)	)	PUNCT
ejpam-6339	280	11	.	.	PUNCT
ejpam-6339	281	1	hence	hence	ADV
ejpam-6339	281	2	,	,	PUNCT
ejpam-6339	281	3	if	if	SCONJ
ejpam-6339	281	4	n	n	PRON
ejpam-6339	281	5	is	be	AUX
ejpam-6339	281	6	a	a	DET
ejpam-6339	281	7	n	n	PRON
ejpam-6339	281	8	-τp	-τp	ADV
ejpam-6339	281	9	-	-	PUNCT
ejpam-6339	281	10	closed	close	VERB
ejpam-6339	281	11	set	set	NOUN
ejpam-6339	281	12	,	,	PUNCT
ejpam-6339	281	13	then	then	ADV
ejpam-6339	281	14	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	281	15	)	)	PUNCT
ejpam-6339	281	16	⊑	⊑	PROPN
ejpam-6339	281	17	clp(n	clp(n	PROPN
ejpam-6339	281	18	)	)	PUNCT
ejpam-6339	281	19	=	=	SYM
ejpam-6339	281	20	n	n	PROPN
ejpam-6339	281	21	,	,	PUNCT
ejpam-6339	281	22	which	which	PRON
ejpam-6339	281	23	implies	imply	VERB
ejpam-6339	281	24	that	that	DET
ejpam-6339	281	25	cl⋆(n	cl⋆(n	NOUN
ejpam-6339	281	26	)	)	PUNCT
ejpam-6339	281	27	=	=	SYM
ejpam-6339	281	28	n	n	PROPN
ejpam-6339	281	29	and	and	CCONJ
ejpam-6339	281	30	so	so	ADV
ejpam-6339	281	31	,	,	PUNCT
ejpam-6339	281	32	n	n	PRON
ejpam-6339	281	33	is	be	AUX
ejpam-6339	281	34	n	n	ADV
ejpam-6339	281	35	-τ⋆-closed	-τ⋆-closed	ADJ
ejpam-6339	281	36	.	.	PUNCT
ejpam-6339	282	1	thus	thus	ADV
ejpam-6339	282	2	,	,	PUNCT
ejpam-6339	282	3	every	every	DET
ejpam-6339	282	4	n	n	NOUN
ejpam-6339	282	5	-τp	-τp	ADV
ejpam-6339	282	6	-	-	PUNCT
ejpam-6339	282	7	open	open	ADJ
ejpam-6339	282	8	set	set	NOUN
ejpam-6339	282	9	is	be	AUX
ejpam-6339	282	10	n	n	PRON
ejpam-6339	282	11	-τ⋆-open	-τ⋆-open	ADJ
ejpam-6339	282	12	;	;	PUNCT
ejpam-6339	282	13	i.e.	i.e.	X
ejpam-6339	282	14	τp	τp	DET
ejpam-6339	282	15	⊆	⊆	NUM
ejpam-6339	282	16	τ⋆.	τ⋆.	SYM
ejpam-6339	282	17	4	4	NUM
ejpam-6339	282	18	.	.	NUM
ejpam-6339	282	19	n	n	CCONJ
ejpam-6339	282	20	-	-	PUNCT
ejpam-6339	282	21	point	point	NOUN
ejpam-6339	282	22	-	-	PUNCT
ejpam-6339	282	23	kernel	kernel	NOUN
ejpam-6339	282	24	in	in	ADP
ejpam-6339	282	25	2017	2017	NUM
ejpam-6339	282	26	,	,	PUNCT
ejpam-6339	282	27	s.	s.	PROPN
ejpam-6339	282	28	jafari	jafari	PROPN
ejpam-6339	282	29	and	and	CCONJ
ejpam-6339	282	30	n.	n.	PROPN
ejpam-6339	282	31	rajesh	rajesh	PROPN
ejpam-6339	283	1	[	[	X
ejpam-6339	283	2	13	13	NUM
ejpam-6339	283	3	]	]	PUNCT
ejpam-6339	283	4	introduced	introduce	VERB
ejpam-6339	283	5	the	the	DET
ejpam-6339	283	6	notion	notion	NOUN
ejpam-6339	283	7	of	of	ADP
ejpam-6339	283	8	n	n	DET
ejpam-6339	283	9	-kernel	-kernel	NOUN
ejpam-6339	283	10	in	in	ADP
ejpam-6339	283	11	a	a	DET
ejpam-6339	283	12	n	n	CCONJ
ejpam-6339	283	13	topological	topological	ADJ
ejpam-6339	283	14	space	space	NOUN
ejpam-6339	283	15	(	(	PUNCT
ejpam-6339	283	16	x	x	X
ejpam-6339	283	17	,	,	PUNCT
ejpam-6339	283	18	τ	τ	X
ejpam-6339	283	19	)	)	PUNCT
ejpam-6339	283	20	as	as	SCONJ
ejpam-6339	283	21	follows	follow	VERB
ejpam-6339	283	22	:	:	PUNCT
ejpam-6339	283	23	the	the	DET
ejpam-6339	283	24	n	n	PRON
ejpam-6339	283	25	-kernel	-kernel	NOUN
ejpam-6339	283	26	of	of	ADP
ejpam-6339	283	27	n	n	NOUN
ejpam-6339	283	28	∈	∈	PROPN
ejpam-6339	283	29	n	n	CCONJ
ejpam-6339	283	30	(	(	PUNCT
ejpam-6339	283	31	x	x	NOUN
ejpam-6339	283	32	)	)	PUNCT
ejpam-6339	283	33	,	,	PUNCT
ejpam-6339	283	34	denoted	denote	VERB
ejpam-6339	283	35	by	by	ADP
ejpam-6339	283	36	ker(n	ker(n	NOUN
ejpam-6339	283	37	)	)	PUNCT
ejpam-6339	283	38	,	,	PUNCT
ejpam-6339	283	39	is	be	AUX
ejpam-6339	283	40	defined	define	VERB
ejpam-6339	283	41	as	as	ADP
ejpam-6339	283	42	ker(n	ker(n	X
ejpam-6339	283	43	)	)	PUNCT
ejpam-6339	284	1	=	=	SYM
ejpam-6339	284	2	l	l	NOUN
ejpam-6339	284	3	{	{	PUNCT
ejpam-6339	284	4	u	u	NOUN
ejpam-6339	284	5	∈	∈	PROPN
ejpam-6339	284	6	n	n	CCONJ
ejpam-6339	284	7	(	(	PUNCT
ejpam-6339	284	8	x	x	X
ejpam-6339	284	9	)	)	PUNCT
ejpam-6339	284	10	:	:	PUNCT
ejpam-6339	285	1	n	n	CCONJ
ejpam-6339	285	2	⊑	⊑	PRON
ejpam-6339	285	3	u	u	NOUN
ejpam-6339	285	4	and	and	CCONJ
ejpam-6339	285	5	u	u	PROPN
ejpam-6339	285	6	∈	∈	PROPN
ejpam-6339	285	7	τ	τ	PROPN
ejpam-6339	285	8	}	}	PUNCT
ejpam-6339	285	9	.	.	PUNCT
ejpam-6339	286	1	in	in	ADP
ejpam-6339	286	2	this	this	DET
ejpam-6339	286	3	section	section	NOUN
ejpam-6339	286	4	,	,	PUNCT
ejpam-6339	286	5	we	we	PRON
ejpam-6339	286	6	introduce	introduce	VERB
ejpam-6339	286	7	and	and	CCONJ
ejpam-6339	286	8	study	study	VERB
ejpam-6339	286	9	the	the	DET
ejpam-6339	286	10	concept	concept	NOUN
ejpam-6339	286	11	of	of	ADP
ejpam-6339	286	12	n	n	DET
ejpam-6339	286	13	-point	-point	NOUN
ejpam-6339	286	14	-	-	PUNCT
ejpam-6339	286	15	kernel	kernel	NOUN
ejpam-6339	286	16	of	of	ADP
ejpam-6339	286	17	n	n	PROPN
ejpam-6339	286	18	∈	∈	PROPN
ejpam-6339	286	19	n	n	PRON
ejpam-6339	286	20	′(x	′(x	NOUN
ejpam-6339	286	21	)	)	PUNCT
ejpam-6339	286	22	by	by	ADP
ejpam-6339	286	23	using	use	VERB
ejpam-6339	286	24	n	n	DET
ejpam-6339	286	25	-points	-point	NOUN
ejpam-6339	286	26	,	,	PUNCT
ejpam-6339	286	27	which	which	PRON
ejpam-6339	286	28	is	be	AUX
ejpam-6339	286	29	distinct	distinct	ADJ
ejpam-6339	286	30	from	from	ADP
ejpam-6339	286	31	the	the	DET
ejpam-6339	286	32	notion	notion	NOUN
ejpam-6339	286	33	given	give	VERB
ejpam-6339	286	34	in	in	ADP
ejpam-6339	286	35	[	[	PUNCT
ejpam-6339	286	36	13	13	NUM
ejpam-6339	286	37	]	]	PUNCT
ejpam-6339	286	38	,	,	PUNCT
ejpam-6339	286	39	as	as	SCONJ
ejpam-6339	286	40	we	we	PRON
ejpam-6339	286	41	can	can	AUX
ejpam-6339	286	42	see	see	VERB
ejpam-6339	286	43	in	in	ADP
ejpam-6339	286	44	examples	example	NOUN
ejpam-6339	286	45	5	5	NUM
ejpam-6339	286	46	and	and	CCONJ
ejpam-6339	286	47	6	6	NUM
ejpam-6339	286	48	below	below	ADV
ejpam-6339	286	49	.	.	PUNCT
ejpam-6339	287	1	definition	definition	NOUN
ejpam-6339	287	2	11	11	NUM
ejpam-6339	287	3	.	.	PUNCT
ejpam-6339	288	1	let	let	VERB
ejpam-6339	288	2	(	(	PUNCT
ejpam-6339	288	3	x	x	NOUN
ejpam-6339	288	4	,	,	PUNCT
ejpam-6339	288	5	τ	τ	X
ejpam-6339	288	6	)	)	PUNCT
ejpam-6339	288	7	be	be	VERB
ejpam-6339	288	8	a	a	DET
ejpam-6339	288	9	n	n	CCONJ
ejpam-6339	288	10	-topological	-topological	ADJ
ejpam-6339	288	11	space	space	NOUN
ejpam-6339	288	12	and	and	CCONJ
ejpam-6339	288	13	n	n	CCONJ
ejpam-6339	288	14	∈	∈	PROPN
ejpam-6339	288	15	n	n	PRON
ejpam-6339	288	16	′(x	′(x	NOUN
ejpam-6339	288	17	)	)	PUNCT
ejpam-6339	288	18	.	.	PUNCT
ejpam-6339	289	1	the	the	DET
ejpam-6339	289	2	n	n	CCONJ
ejpam-6339	289	3	-point	-point	PROPN
ejpam-6339	289	4	-	-	PUNCT
ejpam-6339	289	5	kernel	kernel	NOUN
ejpam-6339	289	6	of	of	ADP
ejpam-6339	289	7	n	n	PROPN
ejpam-6339	289	8	,	,	PUNCT
ejpam-6339	289	9	denoted	denote	VERB
ejpam-6339	289	10	by	by	ADP
ejpam-6339	289	11	kerp(n	kerp(n	PROPN
ejpam-6339	289	12	)	)	PUNCT
ejpam-6339	289	13	,	,	PUNCT
ejpam-6339	289	14	is	be	AUX
ejpam-6339	289	15	defined	define	VERB
ejpam-6339	289	16	as	as	ADP
ejpam-6339	289	17	kerp(n	kerp(n	NOUN
ejpam-6339	289	18	)	)	PUNCT
ejpam-6339	290	1	=	=	SYM
ejpam-6339	290	2	⊔	⊔	PROPN
ejpam-6339	290	3	{	{	PUNCT
ejpam-6339	290	4	xa	xa	PROPN
ejpam-6339	290	5	,	,	PUNCT
ejpam-6339	290	6	b	b	PROPN
ejpam-6339	290	7	,	,	PUNCT
ejpam-6339	290	8	c	c	PROPN
ejpam-6339	290	9	∈	∈	PROPN
ejpam-6339	290	10	n	n	PRON
ejpam-6339	290	11	′(x	′(x	NOUN
ejpam-6339	290	12	)	)	PUNCT
ejpam-6339	290	13	:	:	PUNCT
ejpam-6339	291	1	f	f	X
ejpam-6339	291	2	⊓n	⊓n	VERB
ejpam-6339	291	3	̸=	̸=	PROPN
ejpam-6339	291	4	∅̃	∅̃	NOUN
ejpam-6339	291	5	for	for	ADP
ejpam-6339	291	6	every	every	DET
ejpam-6339	291	7	f	f	PROPN
ejpam-6339	291	8	∈	∈	PROPN
ejpam-6339	291	9	τ	τ	PROPN
ejpam-6339	291	10	c(xa	c(xa	PROPN
ejpam-6339	291	11	,	,	PUNCT
ejpam-6339	291	12	b	b	NOUN
ejpam-6339	291	13	,	,	PUNCT
ejpam-6339	291	14	c	c	NOUN
ejpam-6339	291	15	)	)	PUNCT
ejpam-6339	291	16	}	}	PUNCT
ejpam-6339	291	17	,	,	PUNCT
ejpam-6339	291	18	where	where	SCONJ
ejpam-6339	291	19	τ	τ	PROPN
ejpam-6339	291	20	c(xa	c(xa	PROPN
ejpam-6339	291	21	,	,	PUNCT
ejpam-6339	291	22	b	b	NOUN
ejpam-6339	291	23	,	,	PUNCT
ejpam-6339	291	24	c	c	NOUN
ejpam-6339	291	25	)	)	PUNCT
ejpam-6339	291	26	=	=	PRON
ejpam-6339	291	27	{	{	PUNCT
ejpam-6339	291	28	f	f	PROPN
ejpam-6339	291	29	∈	∈	PROPN
ejpam-6339	291	30	τ	τ	X
ejpam-6339	291	31	c	c	NOUN
ejpam-6339	291	32	:	:	PUNCT
ejpam-6339	291	33	xa	xa	PROPN
ejpam-6339	291	34	,	,	PUNCT
ejpam-6339	291	35	b	b	PROPN
ejpam-6339	291	36	,	,	PUNCT
ejpam-6339	291	37	c	c	PROPN
ejpam-6339	291	38	∈	∈	PROPN
ejpam-6339	291	39	f	f	X
ejpam-6339	291	40	}	}	PUNCT
ejpam-6339	291	41	.	.	PUNCT
ejpam-6339	292	1	remark	remark	PROPN
ejpam-6339	292	2	6	6	NUM
ejpam-6339	292	3	.	.	PUNCT
ejpam-6339	293	1	givenn	givenn	PROPN
ejpam-6339	293	2	∈	∈	PROPN
ejpam-6339	293	3	n	n	PRON
ejpam-6339	293	4	′(x	′(x	NOUN
ejpam-6339	293	5	)	)	PUNCT
ejpam-6339	293	6	we	we	PRON
ejpam-6339	293	7	can	can	AUX
ejpam-6339	293	8	see	see	VERB
ejpam-6339	293	9	that	that	PRON
ejpam-6339	293	10	,	,	PUNCT
ejpam-6339	293	11	in	in	ADP
ejpam-6339	293	12	general	general	ADJ
ejpam-6339	293	13	,	,	PUNCT
ejpam-6339	293	14	is	be	AUX
ejpam-6339	293	15	not	not	PART
ejpam-6339	293	16	trueker(n	trueker(n	PROPN
ejpam-6339	293	17	)	)	PUNCT
ejpam-6339	293	18	̸=	̸=	PROPN
ejpam-6339	293	19	kerp(n	kerp(n	PROPN
ejpam-6339	293	20	)	)	PUNCT
ejpam-6339	293	21	.	.	PUNCT
ejpam-6339	294	1	example	example	NOUN
ejpam-6339	295	1	5	5	NUM
ejpam-6339	295	2	.	.	PUNCT
ejpam-6339	296	1	let	let	VERB
ejpam-6339	296	2	(	(	PUNCT
ejpam-6339	296	3	x	x	NOUN
ejpam-6339	296	4	,	,	PUNCT
ejpam-6339	296	5	τ	τ	X
ejpam-6339	296	6	)	)	PUNCT
ejpam-6339	296	7	be	be	VERB
ejpam-6339	296	8	the	the	DET
ejpam-6339	296	9	n	n	CCONJ
ejpam-6339	296	10	-topological	-topological	ADJ
ejpam-6339	296	11	space	space	NOUN
ejpam-6339	296	12	given	give	VERB
ejpam-6339	296	13	in	in	ADP
ejpam-6339	296	14	example	example	NOUN
ejpam-6339	296	15	2	2	NUM
ejpam-6339	296	16	.	.	X
ejpam-6339	297	1	consider	consider	VERB
ejpam-6339	297	2	the	the	DET
ejpam-6339	297	3	n	n	NOUN
ejpam-6339	297	4	set	set	NOUN
ejpam-6339	297	5	n	n	NOUN
ejpam-6339	297	6	=	=	PRON
ejpam-6339	297	7	{	{	PUNCT
ejpam-6339	297	8	⟨x	⟨x	VERB
ejpam-6339	297	9	,	,	PUNCT
ejpam-6339	297	10	0.1	0.1	NUM
ejpam-6339	297	11	,	,	PUNCT
ejpam-6339	297	12	0.8	0.8	NUM
ejpam-6339	297	13	,	,	PUNCT
ejpam-6339	297	14	0.9⟩	0.9⟩	NUM
ejpam-6339	297	15	,	,	PUNCT
ejpam-6339	297	16	⟨y	⟨y	X
ejpam-6339	297	17	,	,	PUNCT
ejpam-6339	297	18	0.4	0.4	NUM
ejpam-6339	297	19	,	,	PUNCT
ejpam-6339	297	20	0.9	0.9	NUM
ejpam-6339	297	21	,	,	PUNCT
ejpam-6339	297	22	0.6⟩	0.6⟩	NUM
ejpam-6339	297	23	}	}	PUNCT
ejpam-6339	297	24	and	and	CCONJ
ejpam-6339	297	25	the	the	DET
ejpam-6339	297	26	n	n	CCONJ
ejpam-6339	297	27	-point	-point	PROPN
ejpam-6339	297	28	x0.4,0.3,0.6	x0.4,0.3,0.6	NOUN
ejpam-6339	297	29	.	.	PUNCT
ejpam-6339	298	1	then	then	ADV
ejpam-6339	298	2	,	,	PUNCT
ejpam-6339	298	3	ker(n	ker(n	PROPN
ejpam-6339	298	4	)	)	PUNCT
ejpam-6339	298	5	=	=	SYM
ejpam-6339	298	6	o	o	NOUN
ejpam-6339	298	7	and	and	CCONJ
ejpam-6339	298	8	x̃	x̃	PROPN
ejpam-6339	298	9	is	be	AUX
ejpam-6339	298	10	the	the	DET
ejpam-6339	298	11	only	only	ADJ
ejpam-6339	298	12	n	n	PRON
ejpam-6339	298	13	-closed	-close	VERB
ejpam-6339	298	14	set	set	NOUN
ejpam-6339	298	15	to	to	PART
ejpam-6339	298	16	which	which	PRON
ejpam-6339	298	17	x0.4,0.3,0.6	x0.4,0.3,0.6	NOUN
ejpam-6339	298	18	belongs	belong	VERB
ejpam-6339	298	19	.	.	PUNCT
ejpam-6339	299	1	since	since	SCONJ
ejpam-6339	299	2	x̃	x̃	PROPN
ejpam-6339	299	3	⊓	⊓	PROPN
ejpam-6339	299	4	n	n	PRON
ejpam-6339	299	5	̸=	̸=	PROPN
ejpam-6339	299	6	∅̃	∅̃	NOUN
ejpam-6339	299	7	,	,	PUNCT
ejpam-6339	299	8	it	it	PRON
ejpam-6339	299	9	follows	follow	VERB
ejpam-6339	299	10	that	that	SCONJ
ejpam-6339	299	11	x0.4,0.3,0.6	x0.4,0.3,0.6	PROPN
ejpam-6339	299	12	belongs	belong	VERB
ejpam-6339	299	13	to	to	ADP
ejpam-6339	299	14	kerp(n	kerp(n	PROPN
ejpam-6339	299	15	)	)	PUNCT
ejpam-6339	299	16	,	,	PUNCT
ejpam-6339	299	17	but	but	CCONJ
ejpam-6339	299	18	x0.4,0.3,0.6	x0.4,0.3,0.6	PROPN
ejpam-6339	299	19	does	do	AUX
ejpam-6339	299	20	not	not	PART
ejpam-6339	299	21	belong	belong	VERB
ejpam-6339	299	22	to	to	ADP
ejpam-6339	299	23	ker(n	ker(n	NOUN
ejpam-6339	299	24	)	)	PUNCT
ejpam-6339	299	25	=	=	PRON
ejpam-6339	299	26	{	{	PUNCT
ejpam-6339	299	27	⟨x	⟨x	VERB
ejpam-6339	299	28	,	,	PUNCT
ejpam-6339	299	29	0.5	0.5	NUM
ejpam-6339	299	30	,	,	PUNCT
ejpam-6339	299	31	0.5	0.5	NUM
ejpam-6339	299	32	,	,	PUNCT
ejpam-6339	299	33	0.5⟩	0.5⟩	NOUN
ejpam-6339	299	34	,	,	PUNCT
ejpam-6339	299	35	⟨y	⟨y	NOUN
ejpam-6339	299	36	,	,	PUNCT
ejpam-6339	299	37	0.4	0.4	NUM
ejpam-6339	299	38	,	,	PUNCT
ejpam-6339	299	39	0.4	0.4	NUM
ejpam-6339	299	40	,	,	PUNCT
ejpam-6339	299	41	0.6⟩	0.6⟩	NUM
ejpam-6339	299	42	}	}	PUNCT
ejpam-6339	299	43	.	.	PUNCT
ejpam-6339	300	1	example	example	NOUN
ejpam-6339	301	1	6	6	NUM
ejpam-6339	301	2	.	.	PUNCT
ejpam-6339	302	1	let	let	VERB
ejpam-6339	302	2	x	x	PUNCT
ejpam-6339	302	3	=	=	PRON
ejpam-6339	302	4	{	{	PUNCT
ejpam-6339	302	5	x	x	PROPN
ejpam-6339	302	6	,	,	PUNCT
ejpam-6339	302	7	y	y	NOUN
ejpam-6339	302	8	}	}	PUNCT
ejpam-6339	302	9	and	and	CCONJ
ejpam-6339	302	10	o	o	NOUN
ejpam-6339	302	11	,	,	PUNCT
ejpam-6339	302	12	u	u	PROPN
ejpam-6339	302	13	∈	∈	PROPN
ejpam-6339	302	14	n	n	PRON
ejpam-6339	302	15	′(x	′(x	NOUN
ejpam-6339	302	16	)	)	PUNCT
ejpam-6339	302	17	such	such	ADJ
ejpam-6339	302	18	that	that	DET
ejpam-6339	302	19	o	o	NOUN
ejpam-6339	302	20	=	=	PUNCT
ejpam-6339	302	21	{	{	PUNCT
ejpam-6339	302	22	⟨x	⟨x	VERB
ejpam-6339	302	23	,	,	PUNCT
ejpam-6339	302	24	0.8	0.8	NUM
ejpam-6339	302	25	,	,	PUNCT
ejpam-6339	302	26	0.6	0.6	NUM
ejpam-6339	302	27	,	,	PUNCT
ejpam-6339	302	28	0.2⟩	0.2⟩	NUM
ejpam-6339	302	29	,	,	PUNCT
ejpam-6339	302	30	⟨y	⟨y	NOUN
ejpam-6339	302	31	,	,	PUNCT
ejpam-6339	302	32	0.6	0.6	NUM
ejpam-6339	302	33	,	,	PUNCT
ejpam-6339	302	34	0.4	0.4	NUM
ejpam-6339	302	35	,	,	PUNCT
ejpam-6339	302	36	0.4⟩	0.4⟩	NUM
ejpam-6339	302	37	}	}	PUNCT
ejpam-6339	302	38	,	,	PUNCT
ejpam-6339	302	39	u	u	NOUN
ejpam-6339	302	40	=	=	PUNCT
ejpam-6339	302	41	{	{	PUNCT
ejpam-6339	302	42	⟨x	⟨x	VERB
ejpam-6339	302	43	,	,	PUNCT
ejpam-6339	302	44	1	1	NUM
ejpam-6339	302	45	,	,	PUNCT
ejpam-6339	302	46	0.7	0.7	NUM
ejpam-6339	302	47	,	,	PUNCT
ejpam-6339	302	48	0⟩	0⟩	PROPN
ejpam-6339	302	49	,	,	PUNCT
ejpam-6339	302	50	⟨y	⟨y	X
ejpam-6339	302	51	,	,	PUNCT
ejpam-6339	302	52	0.9	0.9	NUM
ejpam-6339	302	53	,	,	PUNCT
ejpam-6339	302	54	0	0	NUM
ejpam-6339	302	55	,	,	PUNCT
ejpam-6339	302	56	0.1⟩	0.1⟩	NUM
ejpam-6339	302	57	}	}	PUNCT
ejpam-6339	302	58	.	.	PUNCT
ejpam-6339	303	1	consider	consider	VERB
ejpam-6339	303	2	the	the	DET
ejpam-6339	303	3	n	n	PRON
ejpam-6339	303	4	-topology	-topology	NOUN
ejpam-6339	303	5	on	on	ADP
ejpam-6339	303	6	x	x	PUNCT
ejpam-6339	303	7	given	give	VERB
ejpam-6339	303	8	by	by	ADP
ejpam-6339	303	9	τ	τ	X
ejpam-6339	303	10	=	=	SYM
ejpam-6339	303	11	{	{	PUNCT
ejpam-6339	303	12	∅̃	∅̃	NOUN
ejpam-6339	303	13	,	,	PUNCT
ejpam-6339	303	14	x̃	x̃	PROPN
ejpam-6339	303	15	,	,	PUNCT
ejpam-6339	303	16	o	o	NOUN
ejpam-6339	303	17	,	,	PUNCT
ejpam-6339	303	18	u	u	NOUN
ejpam-6339	303	19	,	,	PUNCT
ejpam-6339	303	20	o	o	NOUN
ejpam-6339	303	21	⊓	⊓	PROPN
ejpam-6339	303	22	u	u	NOUN
ejpam-6339	303	23	,	,	PUNCT
ejpam-6339	303	24	o	o	PROPN
ejpam-6339	303	25	⊔	⊔	NUM
ejpam-6339	303	26	u	u	NOUN
ejpam-6339	303	27	}	}	PUNCT
ejpam-6339	303	28	.	.	PUNCT
ejpam-6339	304	1	the	the	DET
ejpam-6339	304	2	collection	collection	NOUN
ejpam-6339	304	3	of	of	ADP
ejpam-6339	304	4	all	all	DET
ejpam-6339	304	5	n	n	ADV
ejpam-6339	304	6	-closed	-close	VERB
ejpam-6339	304	7	sets	set	NOUN
ejpam-6339	304	8	on	on	ADP
ejpam-6339	304	9	x	x	X
ejpam-6339	304	10	is	be	AUX
ejpam-6339	304	11	τ	τ	X
ejpam-6339	304	12	c	c	NOUN
ejpam-6339	304	13	=	=	PUNCT
ejpam-6339	304	14	{	{	PUNCT
ejpam-6339	304	15	x̃	x̃	PROPN
ejpam-6339	304	16	,	,	PUNCT
ejpam-6339	304	17	∅̃	∅̃	NOUN
ejpam-6339	304	18	,	,	PUNCT
ejpam-6339	304	19	oc	oc	NOUN
ejpam-6339	304	20	,	,	PUNCT
ejpam-6339	304	21	u	u	NOUN
ejpam-6339	304	22	c	c	NOUN
ejpam-6339	304	23	,	,	PUNCT
ejpam-6339	304	24	(	(	PUNCT
ejpam-6339	304	25	o	o	X
ejpam-6339	304	26	⊓	⊓	NOUN
ejpam-6339	304	27	u)c	u)c	X
ejpam-6339	304	28	,	,	PUNCT
ejpam-6339	304	29	(	(	PUNCT
ejpam-6339	304	30	o	o	X
ejpam-6339	304	31	⊔	⊔	INTJ
ejpam-6339	304	32	u)c	u)c	PROPN
ejpam-6339	304	33	}	}	PUNCT
ejpam-6339	304	34	,	,	PUNCT
ejpam-6339	304	35	where	where	SCONJ
ejpam-6339	304	36	oc	oc	PART
ejpam-6339	304	37	=	=	X
ejpam-6339	304	38	{	{	PUNCT
ejpam-6339	304	39	⟨x	⟨x	VERB
ejpam-6339	304	40	,	,	PUNCT
ejpam-6339	304	41	0.2	0.2	NUM
ejpam-6339	304	42	,	,	PUNCT
ejpam-6339	304	43	0.4	0.4	NUM
ejpam-6339	304	44	,	,	PUNCT
ejpam-6339	304	45	0.8⟩	0.8⟩	NUM
ejpam-6339	304	46	,	,	PUNCT
ejpam-6339	304	47	⟨y	⟨y	X
ejpam-6339	304	48	,	,	PUNCT
ejpam-6339	304	49	0.4	0.4	NUM
ejpam-6339	304	50	,	,	PUNCT
ejpam-6339	304	51	0.6	0.6	NUM
ejpam-6339	304	52	,	,	PUNCT
ejpam-6339	304	53	0.6⟩	0.6⟩	NUM
ejpam-6339	304	54	}	}	PUNCT
ejpam-6339	304	55	,	,	PUNCT
ejpam-6339	304	56	u	u	NOUN
ejpam-6339	304	57	c	c	NOUN
ejpam-6339	304	58	=	=	PUNCT
ejpam-6339	304	59	{	{	PUNCT
ejpam-6339	304	60	⟨x	⟨x	VERB
ejpam-6339	304	61	,	,	PUNCT
ejpam-6339	304	62	0	0	NUM
ejpam-6339	304	63	,	,	PUNCT
ejpam-6339	304	64	0.3	0.3	NUM
ejpam-6339	304	65	,	,	PUNCT
ejpam-6339	304	66	1⟩	1⟩	NUM
ejpam-6339	304	67	,	,	PUNCT
ejpam-6339	304	68	⟨y	⟨y	NOUN
ejpam-6339	304	69	,	,	PUNCT
ejpam-6339	304	70	0.1	0.1	NUM
ejpam-6339	304	71	,	,	PUNCT
ejpam-6339	304	72	1	1	NUM
ejpam-6339	304	73	,	,	PUNCT
ejpam-6339	304	74	0.9⟩	0.9⟩	NUM
ejpam-6339	304	75	}	}	PUNCT
ejpam-6339	304	76	,	,	PUNCT
ejpam-6339	304	77	(	(	PUNCT
ejpam-6339	304	78	o	o	NOUN
ejpam-6339	304	79	⊓	⊓	PROPN
ejpam-6339	304	80	u)c	u)c	X
ejpam-6339	304	81	=	=	PUNCT
ejpam-6339	304	82	{	{	PUNCT
ejpam-6339	304	83	⟨x	⟨x	VERB
ejpam-6339	304	84	,	,	PUNCT
ejpam-6339	304	85	0.2	0.2	NUM
ejpam-6339	304	86	,	,	PUNCT
ejpam-6339	304	87	0.3	0.3	NUM
ejpam-6339	304	88	,	,	PUNCT
ejpam-6339	304	89	0.8⟩	0.8⟩	NUM
ejpam-6339	304	90	,	,	PUNCT
ejpam-6339	304	91	⟨y	⟨y	X
ejpam-6339	304	92	,	,	PUNCT
ejpam-6339	304	93	0.4	0.4	NUM
ejpam-6339	304	94	,	,	PUNCT
ejpam-6339	304	95	0.6	0.6	NUM
ejpam-6339	304	96	,	,	PUNCT
ejpam-6339	304	97	0.6⟩	0.6⟩	NUM
ejpam-6339	304	98	}	}	PUNCT
ejpam-6339	304	99	,	,	PUNCT
ejpam-6339	304	100	(	(	PUNCT
ejpam-6339	304	101	o	o	X
ejpam-6339	304	102	⊔	⊔	X
ejpam-6339	304	103	u)c	u)c	X
ejpam-6339	304	104	=	=	X
ejpam-6339	304	105	{	{	PUNCT
ejpam-6339	304	106	⟨x	⟨x	VERB
ejpam-6339	304	107	,	,	PUNCT
ejpam-6339	304	108	0	0	NUM
ejpam-6339	304	109	,	,	PUNCT
ejpam-6339	304	110	0.4	0.4	NUM
ejpam-6339	304	111	,	,	PUNCT
ejpam-6339	304	112	1⟩	1⟩	NUM
ejpam-6339	304	113	,	,	PUNCT
ejpam-6339	304	114	⟨y	⟨y	NOUN
ejpam-6339	304	115	,	,	PUNCT
ejpam-6339	304	116	0.1	0.1	NUM
ejpam-6339	304	117	,	,	PUNCT
ejpam-6339	304	118	1	1	NUM
ejpam-6339	304	119	,	,	PUNCT
ejpam-6339	304	120	0.9⟩	0.9⟩	NUM
ejpam-6339	304	121	}	}	PUNCT
ejpam-6339	304	122	.	.	PUNCT
ejpam-6339	305	1	j.	j.	PROPN
ejpam-6339	305	2	sanabria	sanabria	PROPN
ejpam-6339	305	3	,	,	PUNCT
ejpam-6339	305	4	e.	e.	PROPN
ejpam-6339	305	5	rosas	rosas	PROPN
ejpam-6339	305	6	,	,	PUNCT
ejpam-6339	305	7	c.	c.	PROPN
ejpam-6339	305	8	granados	granados	PROPN
ejpam-6339	305	9	/	/	PUNCT
ejpam-6339	305	10	eur	eur	PROPN
ejpam-6339	305	11	.	.	PUNCT
ejpam-6339	306	1	j.	j.	PROPN
ejpam-6339	306	2	pure	pure	PROPN
ejpam-6339	306	3	appl	appl	PROPN
ejpam-6339	306	4	.	.	PROPN
ejpam-6339	306	5	math	math	PROPN
ejpam-6339	306	6	,	,	PUNCT
ejpam-6339	306	7	18	18	NUM
ejpam-6339	306	8	(	(	PUNCT
ejpam-6339	306	9	3	3	NUM
ejpam-6339	306	10	)	)	PUNCT
ejpam-6339	306	11	(	(	PUNCT
ejpam-6339	306	12	2025	2025	NUM
ejpam-6339	306	13	)	)	PUNCT
ejpam-6339	306	14	,	,	PUNCT
ejpam-6339	306	15	6339	6339	NUM
ejpam-6339	306	16	13	13	NUM
ejpam-6339	306	17	of	of	ADP
ejpam-6339	306	18	15	15	NUM
ejpam-6339	306	19	consider	consider	VERB
ejpam-6339	306	20	the	the	DET
ejpam-6339	306	21	n	n	NOUN
ejpam-6339	306	22	-set	-set	ADJ
ejpam-6339	306	23	n	n	NOUN
ejpam-6339	306	24	=	=	PRON
ejpam-6339	306	25	{	{	PUNCT
ejpam-6339	306	26	⟨x	⟨x	VERB
ejpam-6339	306	27	,	,	PUNCT
ejpam-6339	306	28	0.1	0.1	NUM
ejpam-6339	306	29	,	,	PUNCT
ejpam-6339	306	30	1	1	NUM
ejpam-6339	306	31	,	,	PUNCT
ejpam-6339	306	32	0.9⟩	0.9⟩	NUM
ejpam-6339	306	33	,	,	PUNCT
ejpam-6339	306	34	⟨y	⟨y	NOUN
ejpam-6339	306	35	,	,	PUNCT
ejpam-6339	306	36	0	0	NUM
ejpam-6339	306	37	,	,	PUNCT
ejpam-6339	306	38	0.3	0.3	NUM
ejpam-6339	306	39	,	,	PUNCT
ejpam-6339	306	40	1⟩	1⟩	NUM
ejpam-6339	306	41	}	}	PUNCT
ejpam-6339	306	42	and	and	CCONJ
ejpam-6339	306	43	the	the	DET
ejpam-6339	306	44	n	n	PRON
ejpam-6339	306	45	-point	-point	PROPN
ejpam-6339	306	46	y0.1,1,0.9	y0.1,1,0.9	NOUN
ejpam-6339	306	47	.	.	PUNCT
ejpam-6339	307	1	then	then	ADV
ejpam-6339	307	2	,	,	PUNCT
ejpam-6339	307	3	y0.1,1,0.9	y0.1,1,0.9	NOUN
ejpam-6339	307	4	∈	∈	PROPN
ejpam-6339	307	5	ker(n	ker(n	PROPN
ejpam-6339	307	6	)	)	PUNCT
ejpam-6339	307	7	=	=	SYM
ejpam-6339	307	8	u	u	NOUN
ejpam-6339	307	9	,	,	PUNCT
ejpam-6339	307	10	but	but	CCONJ
ejpam-6339	307	11	u	u	NOUN
ejpam-6339	307	12	c	c	PROPN
ejpam-6339	307	13	∈	∈	PROPN
ejpam-6339	307	14	τ	τ	X
ejpam-6339	307	15	c(y0.1,1,0.9	c(y0.1,1,0.9	NOUN
ejpam-6339	307	16	)	)	PUNCT
ejpam-6339	307	17	and	and	CCONJ
ejpam-6339	307	18	u	u	NOUN
ejpam-6339	307	19	c	c	PROPN
ejpam-6339	307	20	⊓	⊓	PROPN
ejpam-6339	307	21	n	n	PROPN
ejpam-6339	307	22	=	=	SYM
ejpam-6339	307	23	∅̃	∅̃	NOUN
ejpam-6339	307	24	,	,	PUNCT
ejpam-6339	307	25	which	which	PRON
ejpam-6339	307	26	implies	imply	VERB
ejpam-6339	307	27	that	that	SCONJ
ejpam-6339	307	28	y0.1,1,0.9	y0.1,1,0.9	NOUN
ejpam-6339	307	29	does	do	AUX
ejpam-6339	307	30	not	not	PART
ejpam-6339	307	31	belong	belong	VERB
ejpam-6339	307	32	to	to	ADP
ejpam-6339	307	33	kerp(n	kerp(n	NOUN
ejpam-6339	307	34	)	)	PUNCT
ejpam-6339	307	35	.	.	PUNCT
ejpam-6339	308	1	proposition	proposition	NOUN
ejpam-6339	308	2	9	9	NUM
ejpam-6339	308	3	.	.	PUNCT
ejpam-6339	309	1	let	let	VERB
ejpam-6339	309	2	n	n	PRON
ejpam-6339	309	3	,	,	PUNCT
ejpam-6339	309	4	m	m	VERB
ejpam-6339	309	5	∈	∈	PROPN
ejpam-6339	309	6	n	n	PRON
ejpam-6339	309	7	′(x	′(x	NOUN
ejpam-6339	309	8	)	)	PUNCT
ejpam-6339	309	9	and	and	CCONJ
ejpam-6339	309	10	{	{	PUNCT
ejpam-6339	309	11	nα	nα	X
ejpam-6339	309	12	:	:	PUNCT
ejpam-6339	309	13	α	α	NOUN
ejpam-6339	309	14	∈	∈	NOUN
ejpam-6339	309	15	∆	∆	X
ejpam-6339	309	16	}	}	PUNCT
ejpam-6339	309	17	⊆	⊆	NUM
ejpam-6339	309	18	n	n	PRON
ejpam-6339	309	19	′(x	′(x	NOUN
ejpam-6339	309	20	)	)	PUNCT
ejpam-6339	309	21	.	.	PUNCT
ejpam-6339	310	1	then	then	ADV
ejpam-6339	310	2	,	,	PUNCT
ejpam-6339	310	3	the	the	DET
ejpam-6339	310	4	following	follow	VERB
ejpam-6339	310	5	properties	property	NOUN
ejpam-6339	310	6	hold	hold	VERB
ejpam-6339	310	7	:	:	PUNCT
ejpam-6339	310	8	(	(	PUNCT
ejpam-6339	310	9	1	1	X
ejpam-6339	310	10	)	)	PUNCT
ejpam-6339	310	11	n	n	CCONJ
ejpam-6339	310	12	⊑	⊑	DET
ejpam-6339	310	13	kerp(n	kerp(n	PROPN
ejpam-6339	310	14	)	)	PUNCT
ejpam-6339	310	15	.	.	PUNCT
ejpam-6339	311	1	(	(	PUNCT
ejpam-6339	311	2	2	2	X
ejpam-6339	311	3	)	)	PUNCT
ejpam-6339	311	4	si	si	PROPN
ejpam-6339	311	5	n	n	ADV
ejpam-6339	311	6	⊑m	⊑m	NOUN
ejpam-6339	311	7	,	,	PUNCT
ejpam-6339	311	8	entonces	entonces	PROPN
ejpam-6339	311	9	kerp(n	kerp(n	PROPN
ejpam-6339	311	10	)	)	PUNCT
ejpam-6339	311	11	⊑	⊑	PRON
ejpam-6339	311	12	kerp(m	kerp(m	PROPN
ejpam-6339	311	13	)	)	PUNCT
ejpam-6339	311	14	.	.	PUNCT
ejpam-6339	312	1	(	(	PUNCT
ejpam-6339	312	2	3	3	X
ejpam-6339	312	3	)	)	PUNCT
ejpam-6339	312	4	kerp(kerp(n	kerp(kerp(n	NUM
ejpam-6339	312	5	)	)	PUNCT
ejpam-6339	312	6	)	)	PUNCT
ejpam-6339	313	1	=	=	SYM
ejpam-6339	313	2	kerp(n	kerp(n	PROPN
ejpam-6339	313	3	)	)	PUNCT
ejpam-6339	313	4	.	.	PUNCT
ejpam-6339	314	1	(	(	PUNCT
ejpam-6339	314	2	4	4	X
ejpam-6339	314	3	)	)	PUNCT
ejpam-6339	314	4	kerp	kerp	NOUN
ejpam-6339	314	5	(	(	PUNCT
ejpam-6339	314	6	⊔	⊔	NOUN
ejpam-6339	314	7	α∈∆	α∈∆	PROPN
ejpam-6339	314	8	nα	nα	NOUN
ejpam-6339	314	9	)	)	PUNCT
ejpam-6339	314	10	=	=	PUNCT
ejpam-6339	315	1	⊔	⊔	NUM
ejpam-6339	315	2	α∈∆	α∈∆	PROPN
ejpam-6339	315	3	kerp	kerp	X
ejpam-6339	315	4	(	(	PUNCT
ejpam-6339	315	5	nα	nα	NOUN
ejpam-6339	315	6	)	)	PUNCT
ejpam-6339	315	7	.	.	PUNCT
ejpam-6339	316	1	(	(	PUNCT
ejpam-6339	316	2	5	5	X
ejpam-6339	316	3	)	)	PUNCT
ejpam-6339	316	4	kerp	kerp	NOUN
ejpam-6339	316	5	(	(	PUNCT
ejpam-6339	316	6	d	d	NOUN
ejpam-6339	316	7	α∈∆	α∈∆	PROPN
ejpam-6339	316	8	nα	nα	NOUN
ejpam-6339	316	9	)	)	PUNCT
ejpam-6339	316	10	⊑	⊑	X
ejpam-6339	317	1	d	d	X
ejpam-6339	317	2	α∈∆	α∈∆	PROPN
ejpam-6339	317	3	kerp	kerp	X
ejpam-6339	317	4	(	(	PUNCT
ejpam-6339	317	5	nα	nα	NOUN
ejpam-6339	317	6	)	)	PUNCT
ejpam-6339	317	7	.	.	PUNCT
ejpam-6339	318	1	(	(	PUNCT
ejpam-6339	318	2	6	6	NUM
ejpam-6339	318	3	)	)	PUNCT
ejpam-6339	318	4	kerp(∅̃	kerp(∅̃	PROPN
ejpam-6339	318	5	)	)	PUNCT
ejpam-6339	319	1	=	=	PUNCT
ejpam-6339	319	2	∅̃.	∅̃.	NOUN
ejpam-6339	319	3	(	(	PUNCT
ejpam-6339	319	4	7	7	X
ejpam-6339	319	5	)	)	PUNCT
ejpam-6339	319	6	kerp(x̃	kerp(x̃	NOUN
ejpam-6339	319	7	)	)	PUNCT
ejpam-6339	319	8	=	=	PUNCT
ejpam-6339	320	1	x̃.	x̃.	ADJ
ejpam-6339	320	2	proof	proof	NOUN
ejpam-6339	320	3	.	.	PUNCT
ejpam-6339	321	1	(	(	PUNCT
ejpam-6339	321	2	1	1	X
ejpam-6339	321	3	)	)	PUNCT
ejpam-6339	321	4	it	it	PRON
ejpam-6339	321	5	is	be	AUX
ejpam-6339	321	6	clear	clear	ADJ
ejpam-6339	321	7	from	from	ADP
ejpam-6339	321	8	definition	definition	NOUN
ejpam-6339	321	9	11	11	NUM
ejpam-6339	321	10	.	.	PUNCT
ejpam-6339	322	1	(	(	PUNCT
ejpam-6339	322	2	2	2	X
ejpam-6339	322	3	)	)	PUNCT
ejpam-6339	322	4	suppose	suppose	VERB
ejpam-6339	323	1	that	that	SCONJ
ejpam-6339	323	2	xa	xa	PROPN
ejpam-6339	323	3	,	,	PUNCT
ejpam-6339	323	4	b	b	PROPN
ejpam-6339	323	5	,	,	PUNCT
ejpam-6339	323	6	c	c	NOUN
ejpam-6339	323	7	/∈	/∈	PUNCT
ejpam-6339	323	8	kerp(m	kerp(m	ADP
ejpam-6339	323	9	)	)	PUNCT
ejpam-6339	323	10	.	.	PUNCT
ejpam-6339	324	1	then	then	ADV
ejpam-6339	324	2	,	,	PUNCT
ejpam-6339	324	3	there	there	PRON
ejpam-6339	324	4	exists	exist	VERB
ejpam-6339	324	5	f	f	PROPN
ejpam-6339	324	6	∈	∈	PROPN
ejpam-6339	324	7	τ	τ	PROPN
ejpam-6339	324	8	c(xa	c(xa	PROPN
ejpam-6339	324	9	,	,	PUNCT
ejpam-6339	324	10	b	b	NOUN
ejpam-6339	324	11	,	,	PUNCT
ejpam-6339	324	12	c	c	NOUN
ejpam-6339	324	13	)	)	PUNCT
ejpam-6339	325	1	such	such	ADJ
ejpam-6339	325	2	that	that	SCONJ
ejpam-6339	325	3	f	f	PROPN
ejpam-6339	325	4	⊓m	⊓m	NOUN
ejpam-6339	325	5	=	=	PUNCT
ejpam-6339	325	6	∅̃.	∅̃.	NOUN
ejpam-6339	325	7	sincen	sincen	VERB
ejpam-6339	325	8	⊑m	⊑m	NOUN
ejpam-6339	326	1	,	,	PUNCT
ejpam-6339	326	2	we	we	PRON
ejpam-6339	326	3	have	have	VERB
ejpam-6339	326	4	f⊓n	f⊓n	NUM
ejpam-6339	326	5	⊑	⊑	PRON
ejpam-6339	326	6	f⊓m	f⊓m	PROPN
ejpam-6339	326	7	=	=	SYM
ejpam-6339	326	8	∅̃	∅̃	NOUN
ejpam-6339	326	9	and	and	CCONJ
ejpam-6339	326	10	so	so	ADV
ejpam-6339	326	11	,	,	PUNCT
ejpam-6339	326	12	f⊓n	f⊓n	PROPN
ejpam-6339	326	13	=	=	NOUN
ejpam-6339	326	14	∅̃.	∅̃.	PROPN
ejpam-6339	326	15	therefore	therefore	ADV
ejpam-6339	326	16	,	,	PUNCT
ejpam-6339	326	17	xa	xa	PROPN
ejpam-6339	326	18	,	,	PUNCT
ejpam-6339	326	19	b	b	PROPN
ejpam-6339	326	20	,	,	PUNCT
ejpam-6339	326	21	c	c	PROPN
ejpam-6339	326	22	/∈	/∈	PUNCT
ejpam-6339	326	23	kerp(n	kerp(n	PROPN
ejpam-6339	326	24	)	)	PUNCT
ejpam-6339	326	25	.	.	PUNCT
ejpam-6339	327	1	(	(	PUNCT
ejpam-6339	327	2	3	3	X
ejpam-6339	327	3	)	)	PUNCT
ejpam-6339	327	4	by	by	ADP
ejpam-6339	327	5	part	part	NOUN
ejpam-6339	327	6	(	(	PUNCT
ejpam-6339	327	7	1	1	NUM
ejpam-6339	327	8	)	)	PUNCT
ejpam-6339	327	9	,	,	PUNCT
ejpam-6339	327	10	we	we	PRON
ejpam-6339	327	11	have	have	AUX
ejpam-6339	327	12	kerp(n	kerp(n	VERB
ejpam-6339	327	13	)	)	PUNCT
ejpam-6339	327	14	⊑	⊑	PRON
ejpam-6339	327	15	kerp(kerp(n	kerp(kerp(n	PROPN
ejpam-6339	327	16	)	)	PUNCT
ejpam-6339	327	17	)	)	PUNCT
ejpam-6339	327	18	.	.	PUNCT
ejpam-6339	328	1	to	to	PART
ejpam-6339	328	2	demonstrate	demonstrate	VERB
ejpam-6339	328	3	the	the	DET
ejpam-6339	328	4	opposite	opposite	ADJ
ejpam-6339	328	5	inclusion	inclusion	NOUN
ejpam-6339	328	6	,	,	PUNCT
ejpam-6339	328	7	suppose	suppose	VERB
ejpam-6339	328	8	that	that	SCONJ
ejpam-6339	328	9	xa	xa	PROPN
ejpam-6339	328	10	,	,	PUNCT
ejpam-6339	328	11	b	b	PROPN
ejpam-6339	328	12	,	,	PUNCT
ejpam-6339	328	13	c	c	PROPN
ejpam-6339	328	14	∈	∈	PROPN
ejpam-6339	328	15	kerp(kerp(n	kerp(kerp(n	PROPN
ejpam-6339	328	16	)	)	PUNCT
ejpam-6339	328	17	)	)	PUNCT
ejpam-6339	328	18	and	and	CCONJ
ejpam-6339	328	19	let	let	VERB
ejpam-6339	328	20	f	f	PROPN
ejpam-6339	328	21	∈	∈	PROPN
ejpam-6339	328	22	τ	τ	PROPN
ejpam-6339	328	23	c(xa	c(xa	PROPN
ejpam-6339	328	24	,	,	PUNCT
ejpam-6339	328	25	b	b	NOUN
ejpam-6339	328	26	,	,	PUNCT
ejpam-6339	328	27	c	c	NOUN
ejpam-6339	328	28	)	)	PUNCT
ejpam-6339	328	29	.	.	PUNCT
ejpam-6339	329	1	then	then	ADV
ejpam-6339	329	2	,	,	PUNCT
ejpam-6339	329	3	f	f	PROPN
ejpam-6339	329	4	⊓kerp(n	⊓kerp(n	PROPN
ejpam-6339	329	5	)	)	PUNCT
ejpam-6339	329	6	̸=	̸=	PROPN
ejpam-6339	329	7	∅̃	∅̃	NOUN
ejpam-6339	329	8	,	,	PUNCT
ejpam-6339	329	9	which	which	PRON
ejpam-6339	329	10	implies	imply	VERB
ejpam-6339	329	11	that	that	SCONJ
ejpam-6339	329	12	there	there	PRON
ejpam-6339	329	13	exists	exist	VERB
ejpam-6339	329	14	a	a	DET
ejpam-6339	329	15	n	n	CCONJ
ejpam-6339	329	16	-point	-point	PROPN
ejpam-6339	329	17	yu	yu	PROPN
ejpam-6339	329	18	,	,	PUNCT
ejpam-6339	329	19	v	v	NOUN
ejpam-6339	329	20	,	,	PUNCT
ejpam-6339	329	21	w	w	PROPN
ejpam-6339	329	22	∈	∈	PROPN
ejpam-6339	329	23	kerp(n	kerp(n	PROPN
ejpam-6339	329	24	)	)	PUNCT
ejpam-6339	329	25	and	and	CCONJ
ejpam-6339	329	26	f	f	PROPN
ejpam-6339	329	27	∈	∈	PROPN
ejpam-6339	329	28	τ	τ	X
ejpam-6339	329	29	c(yu	c(yu	NUM
ejpam-6339	329	30	,	,	PUNCT
ejpam-6339	329	31	v	v	NOUN
ejpam-6339	329	32	,	,	PUNCT
ejpam-6339	329	33	w	w	NOUN
ejpam-6339	329	34	)	)	PUNCT
ejpam-6339	329	35	.	.	PUNCT
ejpam-6339	330	1	thus	thus	ADV
ejpam-6339	330	2	,	,	PUNCT
ejpam-6339	330	3	f	f	PROPN
ejpam-6339	330	4	⊓n	⊓n	VERB
ejpam-6339	330	5	̸=	̸=	PROPN
ejpam-6339	330	6	∅̃	∅̃	NOUN
ejpam-6339	330	7	and	and	CCONJ
ejpam-6339	330	8	hence	hence	ADV
ejpam-6339	330	9	,	,	PUNCT
ejpam-6339	330	10	xa	xa	PROPN
ejpam-6339	330	11	,	,	PUNCT
ejpam-6339	330	12	b	b	PROPN
ejpam-6339	330	13	,	,	PUNCT
ejpam-6339	330	14	c	c	PROPN
ejpam-6339	330	15	∈	∈	PROPN
ejpam-6339	330	16	kerp(n	kerp(n	PROPN
ejpam-6339	330	17	)	)	PUNCT
ejpam-6339	330	18	.	.	PUNCT
ejpam-6339	331	1	(	(	PUNCT
ejpam-6339	331	2	4	4	X
ejpam-6339	331	3	)	)	PUNCT
ejpam-6339	331	4	sincenα	sincenα	NOUN
ejpam-6339	331	5	⊑	⊑	X
ejpam-6339	331	6	⊔	⊔	PROPN
ejpam-6339	331	7	α∈∆	α∈∆	PROPN
ejpam-6339	331	8	nα	nα	VERB
ejpam-6339	331	9	for	for	ADP
ejpam-6339	331	10	each	each	DET
ejpam-6339	331	11	α	α	PROPN
ejpam-6339	331	12	∈	∈	PROPN
ejpam-6339	331	13	△	△	PROPN
ejpam-6339	331	14	,	,	PUNCT
ejpam-6339	331	15	by	by	ADP
ejpam-6339	331	16	part	part	NOUN
ejpam-6339	331	17	(	(	PUNCT
ejpam-6339	331	18	2	2	X
ejpam-6339	331	19	)	)	PUNCT
ejpam-6339	331	20	it	it	PRON
ejpam-6339	331	21	follows	follow	VERB
ejpam-6339	331	22	thatkerp(nα	thatkerp(nα	PROPN
ejpam-6339	331	23	)	)	PUNCT
ejpam-6339	331	24	⊑	⊑	PROPN
ejpam-6339	331	25	kerp	kerp	PROPN
ejpam-6339	331	26	(	(	PUNCT
ejpam-6339	331	27	⊔	⊔	NOUN
ejpam-6339	331	28	α∈∆	α∈∆	PROPN
ejpam-6339	331	29	nα	nα	VERB
ejpam-6339	331	30	)	)	PUNCT
ejpam-6339	331	31	for	for	ADP
ejpam-6339	331	32	each	each	DET
ejpam-6339	331	33	α	α	PROPN
ejpam-6339	331	34	∈	∈	PROPN
ejpam-6339	331	35	△	△	PROPN
ejpam-6339	331	36	.	.	PUNCT
ejpam-6339	332	1	therefore	therefore	ADV
ejpam-6339	332	2	,	,	PUNCT
ejpam-6339	332	3	⊔	⊔	PROPN
ejpam-6339	332	4	α∈∆	α∈∆	PROPN
ejpam-6339	332	5	kerp(nα	kerp(nα	PROPN
ejpam-6339	332	6	)	)	PUNCT
ejpam-6339	332	7	⊑	⊑	PROPN
ejpam-6339	332	8	kerp	kerp	PROPN
ejpam-6339	332	9	(	(	PUNCT
ejpam-6339	332	10	⊔	⊔	NOUN
ejpam-6339	332	11	α∈∆	α∈∆	PROPN
ejpam-6339	332	12	nα	nα	NOUN
ejpam-6339	332	13	)	)	PUNCT
ejpam-6339	332	14	.	.	PUNCT
ejpam-6339	333	1	for	for	ADP
ejpam-6339	333	2	the	the	DET
ejpam-6339	333	3	other	other	ADJ
ejpam-6339	333	4	inclusion	inclusion	NOUN
ejpam-6339	333	5	,	,	PUNCT
ejpam-6339	333	6	suppose	suppose	VERB
ejpam-6339	333	7	that	that	SCONJ
ejpam-6339	333	8	xa	xa	PROPN
ejpam-6339	333	9	,	,	PUNCT
ejpam-6339	333	10	b	b	PROPN
ejpam-6339	333	11	,	,	PUNCT
ejpam-6339	333	12	c	c	NOUN
ejpam-6339	333	13	/∈	/∈	PUNCT
ejpam-6339	334	1	⊔	⊔	INTJ
ejpam-6339	334	2	α∈∆	α∈∆	PROPN
ejpam-6339	334	3	kerp(nα	kerp(nα	PROPN
ejpam-6339	334	4	)	)	PUNCT
ejpam-6339	334	5	.	.	PUNCT
ejpam-6339	335	1	then	then	ADV
ejpam-6339	335	2	,	,	PUNCT
ejpam-6339	335	3	x	x	PROPN
ejpam-6339	335	4	/∈	/∈	PUNCT
ejpam-6339	335	5	kerp(nα	kerp(nα	PROPN
ejpam-6339	335	6	)	)	PUNCT
ejpam-6339	335	7	for	for	ADP
ejpam-6339	335	8	every	every	DET
ejpam-6339	335	9	α	α	PROPN
ejpam-6339	335	10	∈	∈	NOUN
ejpam-6339	335	11	∆	∆	PROPN
ejpam-6339	335	12	and	and	CCONJ
ejpam-6339	335	13	so	so	ADV
ejpam-6339	335	14	,	,	PUNCT
ejpam-6339	335	15	there	there	PRON
ejpam-6339	335	16	exists	exist	VERB
ejpam-6339	335	17	fα	fα	ADP
ejpam-6339	335	18	∈	∈	PROPN
ejpam-6339	335	19	τ	τ	X
ejpam-6339	335	20	c(xa	c(xa	PROPN
ejpam-6339	335	21	,	,	PUNCT
ejpam-6339	335	22	b	b	NOUN
ejpam-6339	335	23	,	,	PUNCT
ejpam-6339	335	24	c	c	NOUN
ejpam-6339	335	25	)	)	PUNCT
ejpam-6339	335	26	such	such	ADJ
ejpam-6339	335	27	that	that	PRON
ejpam-6339	335	28	fα	fα	ADP
ejpam-6339	335	29	⊓	⊓	PROPN
ejpam-6339	335	30	nα	nα	NOUN
ejpam-6339	335	31	=	=	PUNCT
ejpam-6339	335	32	∅̃	∅̃	NOUN
ejpam-6339	335	33	for	for	ADP
ejpam-6339	335	34	each	each	DET
ejpam-6339	335	35	α	α	NOUN
ejpam-6339	335	36	∈	∈	PROPN
ejpam-6339	336	1	∆.	∆.	NOUN
ejpam-6339	336	2	putting	put	VERB
ejpam-6339	336	3	f	f	X
ejpam-6339	336	4	=	=	PUNCT
ejpam-6339	336	5	l	l	NOUN
ejpam-6339	336	6	α∈∆	α∈∆	PUNCT
ejpam-6339	336	7	fα	fα	NOUN
ejpam-6339	336	8	,	,	PUNCT
ejpam-6339	336	9	we	we	PRON
ejpam-6339	336	10	have	have	VERB
ejpam-6339	336	11	f	f	PROPN
ejpam-6339	336	12	∈	∈	PROPN
ejpam-6339	336	13	τ	τ	PROPN
ejpam-6339	336	14	c(xa	c(xa	PROPN
ejpam-6339	336	15	,	,	PUNCT
ejpam-6339	336	16	b	b	NOUN
ejpam-6339	336	17	,	,	PUNCT
ejpam-6339	336	18	c	c	NOUN
ejpam-6339	336	19	)	)	PUNCT
ejpam-6339	336	20	and	and	CCONJ
ejpam-6339	336	21	f	f	X
ejpam-6339	336	22	⊓	⊓	PROPN
ejpam-6339	336	23	(	(	PUNCT
ejpam-6339	336	24	⊔	⊔	NOUN
ejpam-6339	336	25	α∈∆	α∈∆	PROPN
ejpam-6339	336	26	nα	nα	NOUN
ejpam-6339	336	27	)	)	PUNCT
ejpam-6339	336	28	=	=	PUNCT
ejpam-6339	337	1	⊔	⊔	VERB
ejpam-6339	337	2	α∈∆	α∈∆	PUNCT
ejpam-6339	337	3	(	(	PUNCT
ejpam-6339	337	4	f	f	X
ejpam-6339	337	5	⊓nα	⊓nα	PROPN
ejpam-6339	337	6	)	)	PUNCT
ejpam-6339	337	7	⊑	⊑	X
ejpam-6339	338	1	⊔	⊔	X
ejpam-6339	338	2	α∈∆	α∈∆	X
ejpam-6339	338	3	(	(	PUNCT
ejpam-6339	338	4	fα⊓nα	fα⊓nα	NUM
ejpam-6339	338	5	)	)	PUNCT
ejpam-6339	338	6	=	=	PRON
ejpam-6339	338	7	∅̃.	∅̃.	NOUN
ejpam-6339	338	8	thus	thus	ADV
ejpam-6339	338	9	,	,	PUNCT
ejpam-6339	338	10	f	f	PROPN
ejpam-6339	338	11	⊓	⊓	PROPN
ejpam-6339	338	12	(	(	PUNCT
ejpam-6339	338	13	⊔	⊔	NOUN
ejpam-6339	338	14	α∈∆	α∈∆	PROPN
ejpam-6339	338	15	nα	nα	NOUN
ejpam-6339	338	16	)	)	PUNCT
ejpam-6339	338	17	=	=	SYM
ejpam-6339	338	18	∅̃	∅̃	NOUN
ejpam-6339	338	19	and	and	CCONJ
ejpam-6339	338	20	hence	hence	ADV
ejpam-6339	338	21	,	,	PUNCT
ejpam-6339	338	22	xa	xa	PROPN
ejpam-6339	338	23	,	,	PUNCT
ejpam-6339	338	24	b	b	PROPN
ejpam-6339	338	25	,	,	PUNCT
ejpam-6339	338	26	c	c	PROPN
ejpam-6339	338	27	/∈	/∈	PUNCT
ejpam-6339	338	28	kerp	kerp	PROPN
ejpam-6339	338	29	(	(	PUNCT
ejpam-6339	338	30	⊔	⊔	NOUN
ejpam-6339	338	31	α∈∆	α∈∆	PROPN
ejpam-6339	338	32	nα	nα	NOUN
ejpam-6339	338	33	)	)	PUNCT
ejpam-6339	338	34	,	,	PUNCT
ejpam-6339	338	35	which	which	PRON
ejpam-6339	338	36	shows	show	VERB
ejpam-6339	338	37	that	that	SCONJ
ejpam-6339	338	38	kerp	kerp	PROPN
ejpam-6339	338	39	(	(	PUNCT
ejpam-6339	338	40	⊔	⊔	NOUN
ejpam-6339	338	41	α∈∆	α∈∆	PROPN
ejpam-6339	338	42	nα	nα	NOUN
ejpam-6339	338	43	)	)	PUNCT
ejpam-6339	338	44	⊑	⊑	X
ejpam-6339	339	1	⊔	⊔	PROPN
ejpam-6339	339	2	α∈∆	α∈∆	PROPN
ejpam-6339	339	3	kerp(nα	kerp(nα	PROPN
ejpam-6339	339	4	)	)	PUNCT
ejpam-6339	339	5	.	.	PUNCT
ejpam-6339	340	1	j.	j.	PROPN
ejpam-6339	340	2	sanabria	sanabria	PROPN
ejpam-6339	340	3	,	,	PUNCT
ejpam-6339	340	4	e.	e.	PROPN
ejpam-6339	340	5	rosas	rosas	PROPN
ejpam-6339	340	6	,	,	PUNCT
ejpam-6339	340	7	c.	c.	PROPN
ejpam-6339	340	8	granados	granados	PROPN
ejpam-6339	340	9	/	/	PUNCT
ejpam-6339	340	10	eur	eur	PROPN
ejpam-6339	340	11	.	.	PUNCT
ejpam-6339	341	1	j.	j.	PROPN
ejpam-6339	341	2	pure	pure	PROPN
ejpam-6339	341	3	appl	appl	PROPN
ejpam-6339	341	4	.	.	PROPN
ejpam-6339	341	5	math	math	PROPN
ejpam-6339	341	6	,	,	PUNCT
ejpam-6339	341	7	18	18	NUM
ejpam-6339	341	8	(	(	PUNCT
ejpam-6339	341	9	3	3	NUM
ejpam-6339	341	10	)	)	PUNCT
ejpam-6339	341	11	(	(	PUNCT
ejpam-6339	341	12	2025	2025	NUM
ejpam-6339	341	13	)	)	PUNCT
ejpam-6339	341	14	,	,	PUNCT
ejpam-6339	341	15	6339	6339	NUM
ejpam-6339	341	16	14	14	NUM
ejpam-6339	341	17	of	of	ADP
ejpam-6339	341	18	15	15	NUM
ejpam-6339	341	19	(	(	PUNCT
ejpam-6339	341	20	5	5	NUM
ejpam-6339	341	21	)	)	PUNCT
ejpam-6339	341	22	since	since	SCONJ
ejpam-6339	341	23	l	l	NOUN
ejpam-6339	341	24	α∈∆	α∈∆	NOUN
ejpam-6339	341	25	nα	nα	ADP
ejpam-6339	341	26	⊑	⊑	PRON
ejpam-6339	341	27	nα	nα	VERB
ejpam-6339	341	28	for	for	ADP
ejpam-6339	341	29	each	each	DET
ejpam-6339	341	30	α	α	NOUN
ejpam-6339	341	31	∈	∈	NOUN
ejpam-6339	341	32	∆	∆	PROPN
ejpam-6339	341	33	,	,	PUNCT
ejpam-6339	341	34	by	by	ADP
ejpam-6339	341	35	using	use	VERB
ejpam-6339	341	36	part	part	NOUN
ejpam-6339	341	37	(	(	PUNCT
ejpam-6339	341	38	2	2	NUM
ejpam-6339	341	39	)	)	PUNCT
ejpam-6339	341	40	,	,	PUNCT
ejpam-6339	341	41	we	we	PRON
ejpam-6339	341	42	have	have	VERB
ejpam-6339	341	43	kerp	kerp	NOUN
ejpam-6339	341	44	(	(	PUNCT
ejpam-6339	341	45	l	l	NOUN
ejpam-6339	341	46	α∈∆	α∈∆	AUX
ejpam-6339	341	47	nα	nα	VERB
ejpam-6339	341	48	)	)	PUNCT
ejpam-6339	342	1	⊑	⊑	DET
ejpam-6339	342	2	kerp(nα	kerp(nα	PROPN
ejpam-6339	342	3	)	)	PUNCT
ejpam-6339	342	4	for	for	ADP
ejpam-6339	342	5	each	each	DET
ejpam-6339	342	6	α	α	NOUN
ejpam-6339	342	7	∈	∈	PROPN
ejpam-6339	342	8	∆	∆	PROPN
ejpam-6339	342	9	,	,	PUNCT
ejpam-6339	342	10	which	which	PRON
ejpam-6339	342	11	implies	imply	VERB
ejpam-6339	342	12	that	that	SCONJ
ejpam-6339	342	13	kerp	kerp	PROPN
ejpam-6339	342	14	(	(	PUNCT
ejpam-6339	342	15	l	l	NOUN
ejpam-6339	342	16	α∈∆	α∈∆	AUX
ejpam-6339	342	17	nα	nα	NOUN
ejpam-6339	342	18	)	)	PUNCT
ejpam-6339	342	19	⊑	⊑	X
ejpam-6339	342	20	l	l	X
ejpam-6339	342	21	α∈∆	α∈∆	PROPN
ejpam-6339	342	22	kerp	kerp	X
ejpam-6339	342	23	(	(	PUNCT
ejpam-6339	342	24	nα	nα	NOUN
ejpam-6339	342	25	)	)	PUNCT
ejpam-6339	342	26	.	.	PUNCT
ejpam-6339	343	1	(	(	PUNCT
ejpam-6339	343	2	6	6	NUM
ejpam-6339	343	3	)	)	PUNCT
ejpam-6339	343	4	and	and	CCONJ
ejpam-6339	343	5	(	(	PUNCT
ejpam-6339	343	6	7	7	X
ejpam-6339	343	7	)	)	PUNCT
ejpam-6339	343	8	are	be	AUX
ejpam-6339	343	9	immediate	immediate	ADJ
ejpam-6339	343	10	consequences	consequence	NOUN
ejpam-6339	343	11	of	of	ADP
ejpam-6339	343	12	definition	definition	NOUN
ejpam-6339	343	13	11	11	NUM
ejpam-6339	343	14	.	.	PUNCT
ejpam-6339	344	1	in	in	ADP
ejpam-6339	344	2	the	the	DET
ejpam-6339	344	3	following	follow	VERB
ejpam-6339	344	4	example	example	NOUN
ejpam-6339	344	5	,	,	PUNCT
ejpam-6339	344	6	we	we	PRON
ejpam-6339	344	7	show	show	VERB
ejpam-6339	344	8	that	that	SCONJ
ejpam-6339	344	9	the	the	DET
ejpam-6339	344	10	converse	converse	NOUN
ejpam-6339	344	11	of	of	ADP
ejpam-6339	344	12	the	the	DET
ejpam-6339	344	13	part	part	NOUN
ejpam-6339	344	14	(	(	PUNCT
ejpam-6339	344	15	4	4	NUM
ejpam-6339	344	16	)	)	PUNCT
ejpam-6339	344	17	of	of	ADP
ejpam-6339	344	18	proposition	proposition	NOUN
ejpam-6339	344	19	9	9	NUM
ejpam-6339	344	20	is	be	AUX
ejpam-6339	344	21	not	not	PART
ejpam-6339	344	22	true	true	ADJ
ejpam-6339	344	23	in	in	ADP
ejpam-6339	344	24	general	general	ADJ
ejpam-6339	344	25	.	.	PUNCT
ejpam-6339	345	1	example	example	NOUN
ejpam-6339	346	1	7	7	X
ejpam-6339	346	2	.	.	X
ejpam-6339	347	1	let	let	AUX
ejpam-6339	347	2	(	(	PUNCT
ejpam-6339	347	3	x	x	NOUN
ejpam-6339	347	4	,	,	PUNCT
ejpam-6339	347	5	τ	τ	X
ejpam-6339	347	6	)	)	PUNCT
ejpam-6339	347	7	be	be	VERB
ejpam-6339	347	8	the	the	DET
ejpam-6339	347	9	n	n	CCONJ
ejpam-6339	347	10	-topological	-topological	ADJ
ejpam-6339	347	11	space	space	NOUN
ejpam-6339	347	12	given	give	VERB
ejpam-6339	347	13	in	in	ADP
ejpam-6339	347	14	example	example	NOUN
ejpam-6339	347	15	5	5	NUM
ejpam-6339	347	16	.	.	PUNCT
ejpam-6339	348	1	consider	consider	VERB
ejpam-6339	348	2	the	the	DET
ejpam-6339	348	3	n	n	NUM
ejpam-6339	348	4	-sets	-set	NOUN
ejpam-6339	348	5	n	n	NOUN
ejpam-6339	348	6	=	=	PRON
ejpam-6339	348	7	{	{	PUNCT
ejpam-6339	348	8	⟨x	⟨x	VERB
ejpam-6339	348	9	,	,	PUNCT
ejpam-6339	348	10	0.1	0.1	NUM
ejpam-6339	348	11	,	,	PUNCT
ejpam-6339	348	12	1	1	NUM
ejpam-6339	348	13	,	,	PUNCT
ejpam-6339	348	14	0.9⟩	0.9⟩	NUM
ejpam-6339	348	15	,	,	PUNCT
ejpam-6339	348	16	⟨y	⟨y	NOUN
ejpam-6339	348	17	,	,	PUNCT
ejpam-6339	348	18	0	0	NUM
ejpam-6339	348	19	,	,	PUNCT
ejpam-6339	348	20	0.3	0.3	NUM
ejpam-6339	348	21	,	,	PUNCT
ejpam-6339	348	22	1⟩	1⟩	NUM
ejpam-6339	348	23	}	}	PUNCT
ejpam-6339	348	24	and	and	CCONJ
ejpam-6339	348	25	m	m	PROPN
ejpam-6339	348	26	=	=	NOUN
ejpam-6339	348	27	{	{	PUNCT
ejpam-6339	348	28	⟨x	⟨x	VERB
ejpam-6339	348	29	,	,	PUNCT
ejpam-6339	348	30	0	0	NUM
ejpam-6339	348	31	,	,	PUNCT
ejpam-6339	348	32	0.3	0.3	NUM
ejpam-6339	348	33	,	,	PUNCT
ejpam-6339	348	34	1⟩	1⟩	NUM
ejpam-6339	348	35	,	,	PUNCT
ejpam-6339	348	36	⟨y	⟨y	NOUN
ejpam-6339	348	37	,	,	PUNCT
ejpam-6339	348	38	0.1	0.1	NUM
ejpam-6339	348	39	,	,	PUNCT
ejpam-6339	348	40	1	1	NUM
ejpam-6339	348	41	,	,	PUNCT
ejpam-6339	348	42	0.9⟩	0.9⟩	NUM
ejpam-6339	348	43	}	}	PUNCT
ejpam-6339	348	44	.	.	PUNCT
ejpam-6339	349	1	then	then	ADV
ejpam-6339	349	2	,	,	PUNCT
ejpam-6339	349	3	m⊓n	m⊓n	PROPN
ejpam-6339	349	4	=	=	PUNCT
ejpam-6339	349	5	∅̃	∅̃	NOUN
ejpam-6339	349	6	and	and	CCONJ
ejpam-6339	349	7	so	so	ADV
ejpam-6339	349	8	(	(	PUNCT
ejpam-6339	349	9	by	by	ADP
ejpam-6339	349	10	part	part	NOUN
ejpam-6339	349	11	(	(	PUNCT
ejpam-6339	349	12	6	6	NUM
ejpam-6339	349	13	)	)	PUNCT
ejpam-6339	349	14	of	of	ADP
ejpam-6339	349	15	proposition	proposition	NOUN
ejpam-6339	349	16	9)kerp(m⊓n	9)kerp(m⊓n	NUM
ejpam-6339	349	17	)	)	PUNCT
ejpam-6339	349	18	=	=	PUNCT
ejpam-6339	349	19	∅̃.	∅̃.	NOUN
ejpam-6339	349	20	on	on	ADP
ejpam-6339	349	21	the	the	DET
ejpam-6339	349	22	other	other	ADJ
ejpam-6339	349	23	hand	hand	NOUN
ejpam-6339	349	24	,	,	PUNCT
ejpam-6339	349	25	as	as	SCONJ
ejpam-6339	349	26	x̃	x̃	PROPN
ejpam-6339	349	27	is	be	AUX
ejpam-6339	349	28	the	the	DET
ejpam-6339	349	29	only	only	ADJ
ejpam-6339	349	30	n	n	PRON
ejpam-6339	349	31	-closed	-close	VERB
ejpam-6339	349	32	set	set	NOUN
ejpam-6339	349	33	to	to	PART
ejpam-6339	349	34	which	which	PRON
ejpam-6339	349	35	the	the	DET
ejpam-6339	349	36	n	n	PRON
ejpam-6339	349	37	-point	-point	NOUN
ejpam-6339	349	38	x0.3,1,0.7	x0.3,1,0.7	NOUN
ejpam-6339	349	39	belongs	belong	VERB
ejpam-6339	349	40	and	and	CCONJ
ejpam-6339	349	41	x̃⊓n	x̃⊓n	PROPN
ejpam-6339	349	42	̸=	̸=	PROPN
ejpam-6339	349	43	∅̃	∅̃	NOUN
ejpam-6339	349	44	,	,	PUNCT
ejpam-6339	349	45	x̃⊓m	x̃⊓m	PROPN
ejpam-6339	349	46	̸=	̸=	PROPN
ejpam-6339	349	47	∅̃	∅̃	NOUN
ejpam-6339	349	48	,	,	PUNCT
ejpam-6339	349	49	we	we	PRON
ejpam-6339	349	50	obtain	obtain	VERB
ejpam-6339	349	51	that	that	DET
ejpam-6339	349	52	x0.3,1,0.7	x0.3,1,0.7	NOUN
ejpam-6339	350	1	∈	∈	PROPN
ejpam-6339	350	2	kerp(m)⊓kerp(n	kerp(m)⊓kerp(n	PROPN
ejpam-6339	350	3	)	)	PUNCT
ejpam-6339	350	4	,	,	PUNCT
ejpam-6339	350	5	which	which	PRON
ejpam-6339	350	6	implies	imply	VERB
ejpam-6339	350	7	that	that	SCONJ
ejpam-6339	350	8	kerp(m)⊓kerp(n	kerp(m)⊓kerp(n	NOUN
ejpam-6339	350	9	)	)	PUNCT
ejpam-6339	350	10	̸=	̸=	PROPN
ejpam-6339	350	11	∅̃.	∅̃.	NOUN
ejpam-6339	350	12	therefore	therefore	ADV
ejpam-6339	350	13	,	,	PUNCT
ejpam-6339	350	14	the	the	DET
ejpam-6339	350	15	inclusion	inclusion	NOUN
ejpam-6339	350	16	kerp(m	kerp(m	PROPN
ejpam-6339	350	17	)	)	PUNCT
ejpam-6339	350	18	⊓kerp(n	⊓kerp(n	PROPN
ejpam-6339	350	19	)	)	PUNCT
ejpam-6339	350	20	⊑	⊑	PROPN
ejpam-6339	350	21	kerp(m	kerp(m	PROPN
ejpam-6339	350	22	⊓n	⊓n	PROPN
ejpam-6339	350	23	)	)	PUNCT
ejpam-6339	350	24	is	be	AUX
ejpam-6339	350	25	not	not	PART
ejpam-6339	350	26	satisfied	satisfied	ADJ
ejpam-6339	350	27	.	.	PUNCT
ejpam-6339	351	1	remark	remark	VERB
ejpam-6339	351	2	7	7	NUM
ejpam-6339	351	3	.	.	PUNCT
ejpam-6339	351	4	by	by	ADP
ejpam-6339	351	5	proposition	proposition	NOUN
ejpam-6339	351	6	9	9	NUM
ejpam-6339	351	7	,	,	PUNCT
ejpam-6339	351	8	we	we	PRON
ejpam-6339	351	9	have	have	VERB
ejpam-6339	351	10	kerp	kerp	NOUN
ejpam-6339	351	11	satisfies	satisfie	NOUN
ejpam-6339	351	12	the	the	DET
ejpam-6339	351	13	conditions	condition	NOUN
ejpam-6339	351	14	of	of	ADP
ejpam-6339	351	15	definition	definition	NOUN
ejpam-6339	351	16	9	9	NUM
ejpam-6339	351	17	and	and	CCONJ
ejpam-6339	351	18	by	by	ADP
ejpam-6339	351	19	proposition	proposition	NOUN
ejpam-6339	351	20	7	7	NUM
ejpam-6339	351	21	,	,	PUNCT
ejpam-6339	351	22	we	we	PRON
ejpam-6339	351	23	conclude	conclude	VERB
ejpam-6339	351	24	that	that	SCONJ
ejpam-6339	351	25	τk	τk	ADP
ejpam-6339	351	26	=	=	PUNCT
ejpam-6339	351	27	{	{	PUNCT
ejpam-6339	351	28	n	n	CCONJ
ejpam-6339	351	29	∈	∈	PROPN
ejpam-6339	351	30	n	n	PRON
ejpam-6339	351	31	′(x	′(x	NOUN
ejpam-6339	351	32	)	)	PUNCT
ejpam-6339	351	33	:	:	PUNCT
ejpam-6339	352	1	kerp(n	kerp(n	NOUN
ejpam-6339	352	2	c	c	NOUN
ejpam-6339	352	3	)	)	PUNCT
ejpam-6339	352	4	=	=	SYM
ejpam-6339	353	1	n	n	PROPN
ejpam-6339	353	2	c	c	X
ejpam-6339	353	3	}	}	PUNCT
ejpam-6339	353	4	is	be	AUX
ejpam-6339	353	5	a	a	DET
ejpam-6339	353	6	n	n	PRON
ejpam-6339	353	7	-topology	-topology	NOUN
ejpam-6339	353	8	on	on	ADP
ejpam-6339	353	9	x	x	PUNCT
ejpam-6339	353	10	and	and	CCONJ
ejpam-6339	353	11	kerp	kerp	PROPN
ejpam-6339	353	12	is	be	AUX
ejpam-6339	354	1	the	the	DET
ejpam-6339	354	2	n	n	ADV
ejpam-6339	354	3	-closure	-closure	NOUN
ejpam-6339	354	4	in	in	ADP
ejpam-6339	354	5	the	the	DET
ejpam-6339	354	6	n	n	NUM
ejpam-6339	354	7	-topological	-topological	ADJ
ejpam-6339	354	8	space	space	NOUN
ejpam-6339	354	9	(	(	PUNCT
ejpam-6339	354	10	x	x	NOUN
ejpam-6339	354	11	,	,	PUNCT
ejpam-6339	354	12	τk	τk	ADP
ejpam-6339	354	13	)	)	PUNCT
ejpam-6339	354	14	.	.	PUNCT
ejpam-6339	355	1	the	the	DET
ejpam-6339	355	2	elements	element	NOUN
ejpam-6339	355	3	of	of	ADP
ejpam-6339	355	4	τk	τk	NOUN
ejpam-6339	355	5	are	be	AUX
ejpam-6339	355	6	called	call	VERB
ejpam-6339	355	7	n	n	CCONJ
ejpam-6339	355	8	-τk	-τk	ADJ
ejpam-6339	355	9	-	-	PUNCT
ejpam-6339	355	10	open	open	ADJ
ejpam-6339	355	11	sets	set	NOUN
ejpam-6339	355	12	and	and	CCONJ
ejpam-6339	355	13	their	their	PRON
ejpam-6339	355	14	complements	complement	NOUN
ejpam-6339	355	15	are	be	AUX
ejpam-6339	355	16	said	say	VERB
ejpam-6339	355	17	to	to	PART
ejpam-6339	355	18	be	be	AUX
ejpam-6339	355	19	n	n	DET
ejpam-6339	355	20	-τk	-τk	ADJ
ejpam-6339	355	21	-	-	PUNCT
ejpam-6339	355	22	closed	closed	ADJ
ejpam-6339	355	23	sets	set	NOUN
ejpam-6339	355	24	.	.	PUNCT
ejpam-6339	356	1	it	it	PRON
ejpam-6339	356	2	is	be	AUX
ejpam-6339	356	3	clear	clear	ADJ
ejpam-6339	356	4	that	that	SCONJ
ejpam-6339	356	5	m	m	NOUN
ejpam-6339	356	6	is	be	AUX
ejpam-6339	356	7	n	n	PRON
ejpam-6339	356	8	-τk	-τk	ADV
ejpam-6339	356	9	-	-	PUNCT
ejpam-6339	356	10	closed	closed	ADJ
ejpam-6339	356	11	if	if	SCONJ
ejpam-6339	356	12	and	and	CCONJ
ejpam-6339	356	13	only	only	ADV
ejpam-6339	356	14	if	if	SCONJ
ejpam-6339	356	15	kerp(m	kerp(m	ADJ
ejpam-6339	356	16	)	)	PUNCT
ejpam-6339	356	17	=	=	NOUN
ejpam-6339	356	18	m	m	NOUN
ejpam-6339	356	19	.	.	PUNCT
ejpam-6339	357	1	5	5	X
ejpam-6339	357	2	.	.	X
ejpam-6339	357	3	conclusion	conclusion	NOUN
ejpam-6339	357	4	the	the	DET
ejpam-6339	357	5	concept	concept	NOUN
ejpam-6339	357	6	ofn	ofn	PROPN
ejpam-6339	357	7	-set	-set	X
ejpam-6339	357	8	has	have	AUX
ejpam-6339	357	9	been	be	AUX
ejpam-6339	357	10	the	the	DET
ejpam-6339	357	11	cornerstone	cornerstone	NOUN
ejpam-6339	357	12	of	of	ADP
ejpam-6339	357	13	neutrosophic	neutrosophic	ADJ
ejpam-6339	357	14	science	science	NOUN
ejpam-6339	357	15	,	,	PUNCT
ejpam-6339	357	16	which	which	PRON
ejpam-6339	357	17	has	have	AUX
ejpam-6339	357	18	found	find	VERB
ejpam-6339	357	19	its	its	PRON
ejpam-6339	357	20	place	place	NOUN
ejpam-6339	357	21	in	in	ADP
ejpam-6339	357	22	contemporary	contemporary	ADJ
ejpam-6339	357	23	research	research	NOUN
ejpam-6339	357	24	,	,	PUNCT
ejpam-6339	357	25	since	since	SCONJ
ejpam-6339	357	26	this	this	DET
ejpam-6339	357	27	science	science	NOUN
ejpam-6339	357	28	means	mean	VERB
ejpam-6339	357	29	development	development	NOUN
ejpam-6339	357	30	and	and	CCONJ
ejpam-6339	357	31	applications	application	NOUN
ejpam-6339	357	32	of	of	ADP
ejpam-6339	357	33	neutrosophic	neutrosophic	ADJ
ejpam-6339	357	34	logic	logic	NOUN
ejpam-6339	357	35	,	,	PUNCT
ejpam-6339	357	36	set	set	NOUN
ejpam-6339	357	37	,	,	PUNCT
ejpam-6339	357	38	measure	measure	NOUN
ejpam-6339	357	39	,	,	PUNCT
ejpam-6339	357	40	integral	integral	ADJ
ejpam-6339	357	41	,	,	PUNCT
ejpam-6339	357	42	probability	probability	NOUN
ejpam-6339	357	43	,	,	PUNCT
ejpam-6339	357	44	etc	etc	X
ejpam-6339	357	45	.	.	X
ejpam-6339	357	46	,	,	PUNCT
ejpam-6339	357	47	and	and	CCONJ
ejpam-6339	357	48	their	their	PRON
ejpam-6339	357	49	applications	application	NOUN
ejpam-6339	357	50	in	in	ADP
ejpam-6339	357	51	any	any	DET
ejpam-6339	357	52	field	field	NOUN
ejpam-6339	357	53	of	of	ADP
ejpam-6339	357	54	knowledge	knowledge	NOUN
ejpam-6339	357	55	.	.	PUNCT
ejpam-6339	358	1	in	in	ADP
ejpam-6339	358	2	this	this	DET
ejpam-6339	358	3	research	research	NOUN
ejpam-6339	358	4	it	it	PRON
ejpam-6339	358	5	was	be	AUX
ejpam-6339	358	6	possible	possible	ADJ
ejpam-6339	358	7	to	to	PART
ejpam-6339	358	8	verify	verify	VERB
ejpam-6339	358	9	that	that	SCONJ
ejpam-6339	358	10	,	,	PUNCT
ejpam-6339	358	11	in	in	ADP
ejpam-6339	358	12	some	some	DET
ejpam-6339	358	13	cases	case	NOUN
ejpam-6339	358	14	,	,	PUNCT
ejpam-6339	358	15	neutrosophic	neutrosophic	ADJ
ejpam-6339	358	16	set	set	NOUN
ejpam-6339	358	17	theory	theory	NOUN
ejpam-6339	358	18	does	do	AUX
ejpam-6339	358	19	not	not	PART
ejpam-6339	358	20	behave	behave	VERB
ejpam-6339	358	21	like	like	ADP
ejpam-6339	358	22	classical	classical	ADJ
ejpam-6339	358	23	set	set	NOUN
ejpam-6339	358	24	theory	theory	NOUN
ejpam-6339	358	25	;	;	PUNCT
ejpam-6339	358	26	for	for	ADP
ejpam-6339	358	27	example	example	NOUN
ejpam-6339	358	28	,	,	PUNCT
ejpam-6339	358	29	the	the	DET
ejpam-6339	358	30	union	union	NOUN
ejpam-6339	358	31	of	of	ADP
ejpam-6339	358	32	a	a	DET
ejpam-6339	358	33	n	n	NOUN
ejpam-6339	358	34	-set	-set	PUNCT
ejpam-6339	358	35	with	with	ADP
ejpam-6339	358	36	its	its	PRON
ejpam-6339	358	37	neutrosophic	neutrosophic	ADJ
ejpam-6339	358	38	complement	complement	NOUN
ejpam-6339	358	39	is	be	AUX
ejpam-6339	358	40	not	not	PART
ejpam-6339	358	41	equal	equal	ADJ
ejpam-6339	358	42	to	to	ADP
ejpam-6339	358	43	the	the	DET
ejpam-6339	358	44	neutrosophic	neutrosophic	ADJ
ejpam-6339	358	45	universe	universe	NOUN
ejpam-6339	358	46	and	and	CCONJ
ejpam-6339	358	47	the	the	DET
ejpam-6339	358	48	neutrosophic	neutrosophic	ADJ
ejpam-6339	358	49	empty	empty	ADJ
ejpam-6339	358	50	set	set	NOUN
ejpam-6339	358	51	is	be	AUX
ejpam-6339	358	52	not	not	PART
ejpam-6339	358	53	the	the	DET
ejpam-6339	358	54	only	only	ADJ
ejpam-6339	358	55	n	n	NUM
ejpam-6339	358	56	-set	-set	PUNCT
ejpam-6339	358	57	that	that	PRON
ejpam-6339	358	58	does	do	AUX
ejpam-6339	358	59	not	not	PART
ejpam-6339	358	60	contain	contain	VERB
ejpam-6339	358	61	n	n	DET
ejpam-6339	358	62	-points	-point	NOUN
ejpam-6339	358	63	.	.	PUNCT
ejpam-6339	359	1	also	also	ADV
ejpam-6339	359	2	,	,	PUNCT
ejpam-6339	359	3	the	the	DET
ejpam-6339	359	4	notions	notion	NOUN
ejpam-6339	359	5	of	of	ADP
ejpam-6339	359	6	closure	closure	NOUN
ejpam-6339	359	7	and	and	CCONJ
ejpam-6339	359	8	kernel	kernel	NOUN
ejpam-6339	359	9	of	of	ADP
ejpam-6339	359	10	an	an	DET
ejpam-6339	359	11	n	n	PRON
ejpam-6339	359	12	-set	-set	NUM
ejpam-6339	359	13	were	be	AUX
ejpam-6339	359	14	introduced	introduce	VERB
ejpam-6339	359	15	by	by	ADP
ejpam-6339	359	16	means	mean	NOUN
ejpam-6339	359	17	of	of	ADP
ejpam-6339	359	18	the	the	DET
ejpam-6339	359	19	concept	concept	NOUN
ejpam-6339	359	20	of	of	ADP
ejpam-6339	359	21	n	n	DET
ejpam-6339	359	22	-point	-point	NOUN
ejpam-6339	359	23	,	,	PUNCT
ejpam-6339	359	24	the	the	DET
ejpam-6339	359	25	main	main	ADJ
ejpam-6339	359	26	properties	property	NOUN
ejpam-6339	359	27	of	of	ADP
ejpam-6339	359	28	these	these	DET
ejpam-6339	359	29	notions	notion	NOUN
ejpam-6339	359	30	were	be	AUX
ejpam-6339	359	31	discussed	discuss	VERB
ejpam-6339	359	32	and	and	CCONJ
ejpam-6339	359	33	two	two	NUM
ejpam-6339	359	34	new	new	ADJ
ejpam-6339	359	35	n	n	PRON
ejpam-6339	359	36	-topologies	-topologie	NOUN
ejpam-6339	359	37	related	relate	VERB
ejpam-6339	359	38	to	to	ADP
ejpam-6339	359	39	the	the	DET
ejpam-6339	359	40	introduced	introduce	VERB
ejpam-6339	359	41	notions	notion	NOUN
ejpam-6339	359	42	were	be	AUX
ejpam-6339	359	43	generated	generate	VERB
ejpam-6339	359	44	.	.	PUNCT
ejpam-6339	360	1	the	the	DET
ejpam-6339	360	2	results	result	NOUN
ejpam-6339	360	3	presented	present	VERB
ejpam-6339	360	4	here	here	ADV
ejpam-6339	360	5	constitute	constitute	VERB
ejpam-6339	360	6	a	a	DET
ejpam-6339	360	7	contribution	contribution	NOUN
ejpam-6339	360	8	to	to	ADP
ejpam-6339	360	9	the	the	DET
ejpam-6339	360	10	theory	theory	NOUN
ejpam-6339	360	11	of	of	ADP
ejpam-6339	360	12	n	n	CCONJ
ejpam-6339	360	13	-topological	-topological	ADJ
ejpam-6339	360	14	spaces	space	NOUN
ejpam-6339	360	15	and	and	CCONJ
ejpam-6339	360	16	may	may	AUX
ejpam-6339	360	17	be	be	AUX
ejpam-6339	360	18	useful	useful	ADJ
ejpam-6339	360	19	to	to	PART
ejpam-6339	360	20	extend	extend	VERB
ejpam-6339	360	21	this	this	DET
ejpam-6339	360	22	area	area	NOUN
ejpam-6339	360	23	of	of	ADP
ejpam-6339	360	24	knowledge	knowledge	NOUN
ejpam-6339	360	25	by	by	ADP
ejpam-6339	360	26	developing	develop	VERB
ejpam-6339	360	27	new	new	ADJ
ejpam-6339	360	28	investigations	investigation	NOUN
ejpam-6339	360	29	involving	involve	VERB
ejpam-6339	360	30	n	n	DET
ejpam-6339	360	31	-functions	-function	NOUN
ejpam-6339	360	32	as	as	SCONJ
ejpam-6339	360	33	has	have	AUX
ejpam-6339	360	34	been	be	AUX
ejpam-6339	360	35	done	do	VERB
ejpam-6339	360	36	in	in	ADP
ejpam-6339	360	37	the	the	DET
ejpam-6339	360	38	works	work	NOUN
ejpam-6339	360	39	of	of	ADP
ejpam-6339	360	40	s.	s.	PROPN
ejpam-6339	360	41	das	das	PROPN
ejpam-6339	360	42	and	and	CCONJ
ejpam-6339	360	43	b.c	b.c	PROPN
ejpam-6339	360	44	.	.	PROPN
ejpam-6339	360	45	tripathy	tripathy	PROPN
ejpam-6339	361	1	[	[	X
ejpam-6339	361	2	14	14	NUM
ejpam-6339	361	3	]	]	X
ejpam-6339	361	4	,	,	PUNCT
ejpam-6339	361	5	s.	s.	PROPN
ejpam-6339	361	6	f.	f.	PROPN
ejpam-6339	361	7	matar	matar	PROPN
ejpam-6339	361	8	and	and	CCONJ
ejpam-6339	361	9	a.a	a.a	PROPN
ejpam-6339	361	10	.	.	PROPN
ejpam-6339	361	11	hijab	hijab	PROPN
ejpam-6339	362	1	[	[	X
ejpam-6339	362	2	15	15	NUM
ejpam-6339	362	3	]	]	PUNCT
ejpam-6339	362	4	,	,	PUNCT
ejpam-6339	362	5	p.	p.	NOUN
ejpam-6339	362	6	basker	basker	PROPN
ejpam-6339	362	7	and	and	CCONJ
ejpam-6339	362	8	b.	b.	PROPN
ejpam-6339	362	9	said	say	VERB
ejpam-6339	363	1	[	[	X
ejpam-6339	363	2	16	16	NUM
ejpam-6339	363	3	]	]	PUNCT
ejpam-6339	363	4	.	.	PUNCT
ejpam-6339	364	1	references	reference	NOUN
ejpam-6339	364	2	[	[	X
ejpam-6339	364	3	1	1	NUM
ejpam-6339	364	4	]	]	PUNCT
ejpam-6339	364	5	f.	f.	PROPN
ejpam-6339	364	6	smarandache	smarandache	PROPN
ejpam-6339	364	7	.	.	PUNCT
ejpam-6339	365	1	neutrosophic	neutrosophic	PROPN
ejpam-6339	365	2	set	set	VERB
ejpam-6339	365	3	a	a	DET
ejpam-6339	365	4	generalization	generalization	NOUN
ejpam-6339	365	5	of	of	ADP
ejpam-6339	365	6	the	the	DET
ejpam-6339	365	7	intuitionistic	intuitionistic	ADJ
ejpam-6339	365	8	fuzzy	fuzzy	ADJ
ejpam-6339	365	9	set	set	NOUN
ejpam-6339	365	10	.	.	PUNCT
ejpam-6339	366	1	journal	journal	PROPN
ejpam-6339	366	2	of	of	ADP
ejpam-6339	366	3	defense	defense	PROPN
ejpam-6339	366	4	resources	resource	NOUN
ejpam-6339	366	5	management	management	NOUN
ejpam-6339	366	6	,	,	PUNCT
ejpam-6339	366	7	1(1):107–116	1(1):107–116	NUM
ejpam-6339	366	8	,	,	PUNCT
ejpam-6339	366	9	2010	2010	NUM
ejpam-6339	366	10	.	.	PUNCT
ejpam-6339	367	1	j.	j.	PROPN
ejpam-6339	367	2	sanabria	sanabria	PROPN
ejpam-6339	367	3	,	,	PUNCT
ejpam-6339	367	4	e.	e.	PROPN
ejpam-6339	367	5	rosas	rosas	PROPN
ejpam-6339	367	6	,	,	PUNCT
ejpam-6339	367	7	c.	c.	PROPN
ejpam-6339	367	8	granados	granados	PROPN
ejpam-6339	367	9	/	/	PUNCT
ejpam-6339	367	10	eur	eur	PROPN
ejpam-6339	367	11	.	.	PUNCT
ejpam-6339	368	1	j.	j.	PROPN
ejpam-6339	368	2	pure	pure	PROPN
ejpam-6339	368	3	appl	appl	PROPN
ejpam-6339	368	4	.	.	PROPN
ejpam-6339	368	5	math	math	PROPN
ejpam-6339	368	6	,	,	PUNCT
ejpam-6339	368	7	18	18	NUM
ejpam-6339	368	8	(	(	PUNCT
ejpam-6339	368	9	3	3	NUM
ejpam-6339	368	10	)	)	PUNCT
ejpam-6339	368	11	(	(	PUNCT
ejpam-6339	368	12	2025	2025	NUM
ejpam-6339	368	13	)	)	PUNCT
ejpam-6339	368	14	,	,	PUNCT
ejpam-6339	368	15	6339	6339	NUM
ejpam-6339	368	16	15	15	NUM
ejpam-6339	368	17	of	of	ADP
ejpam-6339	368	18	15	15	NUM
ejpam-6339	368	19	[	[	SYM
ejpam-6339	368	20	2	2	NUM
ejpam-6339	368	21	]	]	PUNCT
ejpam-6339	368	22	e.	e.	PROPN
ejpam-6339	368	23	rosas	rosas	PROPN
ejpam-6339	368	24	j.	j.	PROPN
ejpam-6339	368	25	sanabria	sanabria	PROPN
ejpam-6339	368	26	and	and	CCONJ
ejpam-6339	368	27	e.	e.	PROPN
ejpam-6339	368	28	aponte	aponte	PROPN
ejpam-6339	368	29	.	.	PUNCT
ejpam-6339	369	1	foundations	foundation	NOUN
ejpam-6339	369	2	of	of	ADP
ejpam-6339	369	3	neutrosophic	neutrosophic	ADJ
ejpam-6339	369	4	convex	convex	NOUN
ejpam-6339	369	5	structures	structure	NOUN
ejpam-6339	369	6	.	.	PUNCT
ejpam-6339	370	1	international	international	ADJ
ejpam-6339	370	2	journal	journal	PROPN
ejpam-6339	370	3	of	of	ADP
ejpam-6339	370	4	neutrosophic	neutrosophic	ADJ
ejpam-6339	370	5	science	science	NOUN
ejpam-6339	370	6	,	,	PUNCT
ejpam-6339	370	7	24(2):163–175	24(2):163–175	PROPN
ejpam-6339	370	8	,	,	PUNCT
ejpam-6339	370	9	2024	2024	NUM
ejpam-6339	370	10	.	.	PUNCT
ejpam-6339	371	1	[	[	X
ejpam-6339	371	2	3	3	X
ejpam-6339	371	3	]	]	X
ejpam-6339	371	4	s.	s.	PROPN
ejpam-6339	371	5	bhuvaneshwari	bhuvaneshwari	PROPN
ejpam-6339	371	6	and	and	CCONJ
ejpam-6339	371	7	c.	c.	PROPN
ejpam-6339	371	8	a.	a.	PROPN
ejpam-6339	371	9	c.	c.	PROPN
ejpam-6339	371	10	sweety	sweety	PROPN
ejpam-6339	371	11	.	.	PUNCT
ejpam-6339	372	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	372	2	over	over	ADP
ejpam-6339	372	3	topological	topological	ADJ
ejpam-6339	372	4	spaces	space	NOUN
ejpam-6339	372	5	.	.	PUNCT
ejpam-6339	373	1	boletim	boletim	PROPN
ejpam-6339	373	2	da	da	PROPN
ejpam-6339	373	3	sociedade	sociedade	PROPN
ejpam-6339	373	4	paranaense	paranaense	PROPN
ejpam-6339	373	5	de	de	PROPN
ejpam-6339	373	6	matematica	matematica	PROPN
ejpam-6339	373	7	,	,	PUNCT
ejpam-6339	373	8	43:1–11	43:1–11	NUM
ejpam-6339	373	9	,	,	PUNCT
ejpam-6339	373	10	2025	2025	NUM
ejpam-6339	373	11	.	.	PUNCT
ejpam-6339	374	1	[	[	X
ejpam-6339	374	2	4	4	NUM
ejpam-6339	374	3	]	]	PUNCT
ejpam-6339	374	4	a.	a.	NOUN
ejpam-6339	374	5	a.	a.	NOUN
ejpam-6339	374	6	salama	salama	PROPN
ejpam-6339	374	7	and	and	CCONJ
ejpam-6339	374	8	s.	s.	PROPN
ejpam-6339	374	9	a.	a.	PROPN
ejpam-6339	374	10	alblowi	alblowi	PROPN
ejpam-6339	374	11	.	.	PUNCT
ejpam-6339	375	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	375	2	set	set	NOUN
ejpam-6339	375	3	and	and	CCONJ
ejpam-6339	375	4	neutrosophic	neutrosophic	ADJ
ejpam-6339	375	5	topological	topological	ADJ
ejpam-6339	375	6	spaces	space	NOUN
ejpam-6339	375	7	.	.	PUNCT
ejpam-6339	376	1	iosr	iosr	ADJ
ejpam-6339	376	2	journal	journal	PROPN
ejpam-6339	376	3	of	of	ADP
ejpam-6339	376	4	mathematics	mathematic	NOUN
ejpam-6339	376	5	,	,	PUNCT
ejpam-6339	376	6	3(4):31–35	3(4):31–35	NUM
ejpam-6339	376	7	,	,	PUNCT
ejpam-6339	376	8	2012	2012	NUM
ejpam-6339	376	9	.	.	PUNCT
ejpam-6339	377	1	[	[	X
ejpam-6339	377	2	5	5	X
ejpam-6339	377	3	]	]	PUNCT
ejpam-6339	377	4	g.	g.	PROPN
ejpam-6339	377	5	c.	c.	PROPN
ejpam-6339	377	6	ray	ray	PROPN
ejpam-6339	377	7	and	and	CCONJ
ejpam-6339	377	8	s.	s.	PROPN
ejpam-6339	377	9	dey	dey	PROPN
ejpam-6339	377	10	.	.	PROPN
ejpam-6339	377	11	neutrosophic	neutrosophic	ADJ
ejpam-6339	377	12	point	point	NOUN
ejpam-6339	377	13	and	and	CCONJ
ejpam-6339	377	14	its	its	PRON
ejpam-6339	377	15	neighbourhood	neighbourhood	NOUN
ejpam-6339	377	16	structure	structure	NOUN
ejpam-6339	377	17	.	.	PUNCT
ejpam-6339	378	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	378	2	sets	set	NOUN
ejpam-6339	378	3	and	and	CCONJ
ejpam-6339	378	4	systems	system	NOUN
ejpam-6339	378	5	,	,	PUNCT
ejpam-6339	378	6	43:156–168	43:156–168	NOUN
ejpam-6339	378	7	,	,	PUNCT
ejpam-6339	378	8	2021	2021	NUM
ejpam-6339	378	9	.	.	PUNCT
ejpam-6339	379	1	[	[	X
ejpam-6339	379	2	6	6	NUM
ejpam-6339	379	3	]	]	PUNCT
ejpam-6339	379	4	r.	r.	PROPN
ejpam-6339	379	5	subasree	subasree	PROPN
ejpam-6339	379	6	and	and	CCONJ
ejpam-6339	379	7	k.	k.	PROPN
ejpam-6339	379	8	k.	k.	PROPN
ejpam-6339	379	9	basari	basari	PROPN
ejpam-6339	379	10	.	.	PUNCT
ejpam-6339	380	1	on	on	ADP
ejpam-6339	380	2	nβ∗-closed	nβ∗-close	VERB
ejpam-6339	380	3	sets	set	NOUN
ejpam-6339	380	4	in	in	ADP
ejpam-6339	380	5	neutrosophic	neutrosophic	ADJ
ejpam-6339	380	6	topological	topological	ADJ
ejpam-6339	380	7	spaces	space	NOUN
ejpam-6339	380	8	.	.	PUNCT
ejpam-6339	381	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	381	2	sets	set	NOUN
ejpam-6339	381	3	and	and	CCONJ
ejpam-6339	381	4	systems	system	NOUN
ejpam-6339	381	5	,	,	PUNCT
ejpam-6339	381	6	50(1):372–378	50(1):372–378	NOUN
ejpam-6339	381	7	,	,	PUNCT
ejpam-6339	381	8	2022	2022	NUM
ejpam-6339	381	9	.	.	PUNCT
ejpam-6339	382	1	[	[	X
ejpam-6339	382	2	7	7	X
ejpam-6339	382	3	]	]	X
ejpam-6339	382	4	r.	r.	PROPN
ejpam-6339	382	5	subasree	subasree	PROPN
ejpam-6339	382	6	and	and	CCONJ
ejpam-6339	382	7	k.	k.	PROPN
ejpam-6339	382	8	k.	k.	PROPN
ejpam-6339	382	9	basari	basari	PROPN
ejpam-6339	382	10	.	.	PUNCT
ejpam-6339	383	1	a	a	DET
ejpam-6339	383	2	study	study	NOUN
ejpam-6339	383	3	on	on	ADP
ejpam-6339	383	4	nψβ	nψβ	ADJ
ejpam-6339	383	5	and	and	CCONJ
ejpam-6339	383	6	nβψ	nβψ	ADV
ejpam-6339	383	7	-	-	PUNCT
ejpam-6339	383	8	closed	closed	ADJ
ejpam-6339	383	9	sets	set	NOUN
ejpam-6339	383	10	in	in	ADP
ejpam-6339	383	11	neutrosophic	neutrosophic	ADJ
ejpam-6339	383	12	topological	topological	ADJ
ejpam-6339	383	13	spaces	space	NOUN
ejpam-6339	383	14	.	.	PUNCT
ejpam-6339	384	1	baghdad	baghdad	PROPN
ejpam-6339	384	2	science	science	PROPN
ejpam-6339	384	3	journal	journal	PROPN
ejpam-6339	384	4	,	,	PUNCT
ejpam-6339	384	5	20(1	20(1	NUM
ejpam-6339	384	6	special	special	ADJ
ejpam-6339	384	7	issue	issue	NOUN
ejpam-6339	384	8	icaam):283–287	icaam):283–287	PROPN
ejpam-6339	384	9	,	,	PUNCT
ejpam-6339	384	10	2023	2023	NUM
ejpam-6339	384	11	.	.	PUNCT
ejpam-6339	385	1	[	[	X
ejpam-6339	385	2	8	8	NUM
ejpam-6339	385	3	]	]	PUNCT
ejpam-6339	385	4	a.	a.	NOUN
ejpam-6339	385	5	açikgöz	açikgöz	PROPN
ejpam-6339	385	6	and	and	CCONJ
ejpam-6339	385	7	f.	f.	PROPN
ejpam-6339	385	8	esenbel	esenbel	PROPN
ejpam-6339	385	9	.	.	PUNCT
ejpam-6339	386	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	386	2	strongly	strongly	ADV
ejpam-6339	386	3	preopen	preopen	ADJ
ejpam-6339	386	4	sets	set	NOUN
ejpam-6339	386	5	and	and	CCONJ
ejpam-6339	386	6	neutrosophic	neutrosophic	ADJ
ejpam-6339	386	7	strong	strong	ADJ
ejpam-6339	386	8	precontinuity	precontinuity	NOUN
ejpam-6339	386	9	.	.	PUNCT
ejpam-6339	387	1	axioms	axiom	NOUN
ejpam-6339	387	2	,	,	PUNCT
ejpam-6339	387	3	13(12):865	13(12):865	NUM
ejpam-6339	387	4	,	,	PUNCT
ejpam-6339	387	5	2024	2024	NUM
ejpam-6339	387	6	.	.	PUNCT
ejpam-6339	388	1	[	[	X
ejpam-6339	388	2	9	9	NUM
ejpam-6339	388	3	]	]	X
ejpam-6339	388	4	s.	s.	PROPN
ejpam-6339	388	5	tyagi	tyagi	PROPN
ejpam-6339	388	6	and	and	CCONJ
ejpam-6339	388	7	m.	m.	PROPN
ejpam-6339	388	8	kumar	kumar	PROPN
ejpam-6339	388	9	gupta	gupta	PROPN
ejpam-6339	388	10	.	.	PUNCT
ejpam-6339	388	11	neutrosophic	neutrosophic	PROPN
ejpam-6339	388	12	λ	λ	PROPN
ejpam-6339	388	13	-	-	ADJ
ejpam-6339	388	14	closed	closed	ADJ
ejpam-6339	388	15	set	set	VERB
ejpam-6339	388	16	and	and	CCONJ
ejpam-6339	388	17	related	related	ADJ
ejpam-6339	388	18	mappings	mapping	NOUN
ejpam-6339	388	19	in	in	ADP
ejpam-6339	388	20	neutrosophic	neutrosophic	ADJ
ejpam-6339	388	21	topological	topological	ADJ
ejpam-6339	388	22	spaces	space	NOUN
ejpam-6339	388	23	.	.	PUNCT
ejpam-6339	389	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	389	2	sets	set	NOUN
ejpam-6339	389	3	and	and	CCONJ
ejpam-6339	389	4	systems	system	NOUN
ejpam-6339	389	5	,	,	PUNCT
ejpam-6339	389	6	82:911–923	82:911–923	NUM
ejpam-6339	389	7	,	,	PUNCT
ejpam-6339	389	8	2025	2025	NUM
ejpam-6339	389	9	.	.	PUNCT
ejpam-6339	390	1	[	[	X
ejpam-6339	390	2	10	10	NUM
ejpam-6339	390	3	]	]	X
ejpam-6339	390	4	s.	s.	PROPN
ejpam-6339	390	5	karatas	karatas	PROPN
ejpam-6339	390	6	and	and	CCONJ
ejpam-6339	390	7	c.	c.	PROPN
ejpam-6339	390	8	kuru	kuru	PROPN
ejpam-6339	390	9	.	.	PUNCT
ejpam-6339	390	10	neutrosophic	neutrosophic	ADJ
ejpam-6339	390	11	topology	topology	NOUN
ejpam-6339	390	12	.	.	PUNCT
ejpam-6339	391	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	391	2	sets	set	NOUN
ejpam-6339	391	3	and	and	CCONJ
ejpam-6339	391	4	systems	system	NOUN
ejpam-6339	391	5	,	,	PUNCT
ejpam-6339	391	6	13:90–95	13:90–95	NUM
ejpam-6339	391	7	,	,	PUNCT
ejpam-6339	391	8	2016	2016	NUM
ejpam-6339	391	9	.	.	PUNCT
ejpam-6339	392	1	[	[	X
ejpam-6339	392	2	11	11	NUM
ejpam-6339	392	3	]	]	PUNCT
ejpam-6339	392	4	a.	a.	NOUN
ejpam-6339	392	5	a.	a.	NOUN
ejpam-6339	392	6	salama	salama	PROPN
ejpam-6339	392	7	s.	s.	PROPN
ejpam-6339	392	8	a.	a.	PROPN
ejpam-6339	392	9	alblowi	alblowi	PROPN
ejpam-6339	392	10	and	and	CCONJ
ejpam-6339	392	11	m.	m.	NOUN
ejpam-6339	392	12	eisa	eisa	PROPN
ejpam-6339	392	13	.	.	PUNCT
ejpam-6339	393	1	new	new	ADJ
ejpam-6339	393	2	concepts	concept	NOUN
ejpam-6339	393	3	of	of	ADP
ejpam-6339	393	4	neutrosophic	neutrosophic	ADJ
ejpam-6339	393	5	sets	set	NOUN
ejpam-6339	393	6	.	.	PUNCT
ejpam-6339	394	1	international	international	ADJ
ejpam-6339	394	2	journal	journal	NOUN
ejpam-6339	394	3	of	of	ADP
ejpam-6339	394	4	mathematics	mathematics	PROPN
ejpam-6339	394	5	and	and	CCONJ
ejpam-6339	394	6	computer	computer	NOUN
ejpam-6339	394	7	applications	application	NOUN
ejpam-6339	394	8	research	research	NOUN
ejpam-6339	394	9	,	,	PUNCT
ejpam-6339	394	10	3(4):95–102	3(4):95–102	NUM
ejpam-6339	394	11	,	,	PUNCT
ejpam-6339	394	12	2013	2013	NUM
ejpam-6339	394	13	.	.	PUNCT
ejpam-6339	395	1	[	[	X
ejpam-6339	395	2	12	12	NUM
ejpam-6339	395	3	]	]	PUNCT
ejpam-6339	395	4	a.	a.	NOUN
ejpam-6339	395	5	a.	a.	NOUN
ejpam-6339	395	6	salama	salama	PROPN
ejpam-6339	395	7	and	and	CCONJ
ejpam-6339	395	8	f.	f.	PROPN
ejpam-6339	395	9	smarandache	smarandache	PROPN
ejpam-6339	395	10	.	.	PUNCT
ejpam-6339	396	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	396	2	local	local	ADJ
ejpam-6339	396	3	function	function	NOUN
ejpam-6339	396	4	and	and	CCONJ
ejpam-6339	396	5	generated	generate	VERB
ejpam-6339	396	6	neutrosophic	neutrosophic	ADJ
ejpam-6339	396	7	topology	topology	NOUN
ejpam-6339	396	8	.	.	PUNCT
ejpam-6339	397	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	397	2	knowledge	knowledge	NOUN
ejpam-6339	397	3	,	,	PUNCT
ejpam-6339	397	4	1:1–6	1:1–6	NUM
ejpam-6339	397	5	,	,	PUNCT
ejpam-6339	397	6	2020	2020	NUM
ejpam-6339	397	7	.	.	PUNCT
ejpam-6339	398	1	[	[	X
ejpam-6339	398	2	13	13	NUM
ejpam-6339	398	3	]	]	PUNCT
ejpam-6339	398	4	s.	s.	PROPN
ejpam-6339	398	5	jafari	jafari	PROPN
ejpam-6339	398	6	and	and	CCONJ
ejpam-6339	398	7	n.	n.	PROPN
ejpam-6339	398	8	rajesh	rajesh	PROPN
ejpam-6339	398	9	.	.	PUNCT
ejpam-6339	399	1	neutrosophic	neutrosophic	PROPN
ejpam-6339	399	2	contra	contra	ADJ
ejpam-6339	399	3	-	-	ADJ
ejpam-6339	399	4	continuous	continuous	ADJ
ejpam-6339	399	5	multi	multi	NOUN
ejpam-6339	399	6	-	-	NOUN
ejpam-6339	399	7	functions	function	NOUN
ejpam-6339	399	8	.	.	PUNCT
ejpam-6339	400	1	in	in	ADP
ejpam-6339	400	2	florentin	florentin	PROPN
ejpam-6339	400	3	smarandache	smarandache	NOUN
ejpam-6339	400	4	and	and	CCONJ
ejpam-6339	400	5	surpati	surpati	NOUN
ejpam-6339	400	6	pramanik	pramanik	PROPN
ejpam-6339	400	7	,	,	PUNCT
ejpam-6339	400	8	editors	editor	NOUN
ejpam-6339	400	9	,	,	PUNCT
ejpam-6339	400	10	new	new	ADJ
ejpam-6339	400	11	trends	trend	NOUN
ejpam-6339	400	12	in	in	ADP
ejpam-6339	400	13	neutrosophic	neutrosophic	ADJ
ejpam-6339	400	14	theory	theory	NOUN
ejpam-6339	400	15	and	and	CCONJ
ejpam-6339	400	16	applications	application	NOUN
ejpam-6339	400	17	.	.	PUNCT
ejpam-6339	400	18	,	,	PUNCT
ejpam-6339	400	19	volume	volume	NOUN
ejpam-6339	400	20	2	2	NUM
ejpam-6339	400	21	,	,	PUNCT
ejpam-6339	400	22	pages	page	NOUN
ejpam-6339	400	23	299–307	299–307	NUM
ejpam-6339	400	24	,	,	PUNCT
ejpam-6339	400	25	brussels	brussel	NOUN
ejpam-6339	400	26	,	,	PUNCT
ejpam-6339	400	27	2017	2017	NUM
ejpam-6339	400	28	.	.	PUNCT
ejpam-6339	401	1	pons	pon	NOUN
ejpam-6339	401	2	editions	edition	NOUN
ejpam-6339	401	3	.	.	PUNCT
ejpam-6339	402	1	[	[	X
ejpam-6339	402	2	14	14	NUM
ejpam-6339	402	3	]	]	X
ejpam-6339	402	4	s.	s.	PROPN
ejpam-6339	402	5	das	das	PROPN
ejpam-6339	402	6	and	and	CCONJ
ejpam-6339	402	7	b.	b.	PROPN
ejpam-6339	402	8	c.	c.	PROPN
ejpam-6339	402	9	tripathy	tripathy	PROPN
ejpam-6339	402	10	.	.	PUNCT
ejpam-6339	403	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	403	2	simply	simply	ADV
ejpam-6339	403	3	b	b	X
ejpam-6339	403	4	-	-	PUNCT
ejpam-6339	403	5	open	open	ADJ
ejpam-6339	403	6	set	set	NOUN
ejpam-6339	403	7	in	in	ADP
ejpam-6339	403	8	neutrosophic	neutrosophic	ADJ
ejpam-6339	403	9	topological	topological	ADJ
ejpam-6339	403	10	spaces	space	NOUN
ejpam-6339	403	11	.	.	PUNCT
ejpam-6339	404	1	iraqi	iraqi	ADJ
ejpam-6339	404	2	journal	journal	PROPN
ejpam-6339	404	3	of	of	ADP
ejpam-6339	404	4	science	science	NOUN
ejpam-6339	404	5	,	,	PUNCT
ejpam-6339	404	6	62(12):4830–4838	62(12):4830–4838	NUM
ejpam-6339	404	7	,	,	PUNCT
ejpam-6339	404	8	2021	2021	NUM
ejpam-6339	404	9	.	.	PUNCT
ejpam-6339	405	1	[	[	X
ejpam-6339	405	2	15	15	NUM
ejpam-6339	405	3	]	]	X
ejpam-6339	405	4	s.	s.	PROPN
ejpam-6339	405	5	f.	f.	PROPN
ejpam-6339	405	6	matar	matar	PROPN
ejpam-6339	405	7	and	and	CCONJ
ejpam-6339	405	8	a.	a.	NOUN
ejpam-6339	405	9	a.	a.	PROPN
ejpam-6339	405	10	hijab	hijab	PROPN
ejpam-6339	405	11	.	.	PUNCT
ejpam-6339	406	1	some	some	DET
ejpam-6339	406	2	properties	property	NOUN
ejpam-6339	406	3	of	of	ADP
ejpam-6339	406	4	fuzzy	fuzzy	ADJ
ejpam-6339	406	5	neutrosophic	neutrosophic	ADJ
ejpam-6339	406	6	generalized	generalize	VERB
ejpam-6339	406	7	semi	semi	ADJ
ejpam-6339	406	8	continuous	continuous	ADJ
ejpam-6339	406	9	mapping	mapping	NOUN
ejpam-6339	406	10	and	and	CCONJ
ejpam-6339	406	11	alpha	alpha	NOUN
ejpam-6339	406	12	generalized	generalize	VERB
ejpam-6339	406	13	continuous	continuous	ADJ
ejpam-6339	406	14	mapping	mapping	NOUN
ejpam-6339	406	15	.	.	PUNCT
ejpam-6339	407	1	baghdad	baghdad	PROPN
ejpam-6339	407	2	science	science	PROPN
ejpam-6339	407	3	journal	journal	PROPN
ejpam-6339	407	4	,	,	PUNCT
ejpam-6339	407	5	19(3):536–541	19(3):536–541	PROPN
ejpam-6339	407	6	,	,	PUNCT
ejpam-6339	407	7	2022	2022	NUM
ejpam-6339	407	8	.	.	PUNCT
ejpam-6339	408	1	[	[	X
ejpam-6339	408	2	16	16	NUM
ejpam-6339	408	3	]	]	PUNCT
ejpam-6339	408	4	p.	p.	NOUN
ejpam-6339	408	5	basker	basker	PROPN
ejpam-6339	408	6	and	and	CCONJ
ejpam-6339	408	7	b.	b.	PROPN
ejpam-6339	408	8	said	say	VERB
ejpam-6339	408	9	.	.	PUNCT
ejpam-6339	409	1	on	on	ADP
ejpam-6339	409	2	neutrosophic	neutrosophic	ADJ
ejpam-6339	409	3	homeomorphisms	homeomorphism	NOUN
ejpam-6339	409	4	via	via	ADP
ejpam-6339	409	5	neutrosophic	neutrosophic	ADJ
ejpam-6339	409	6	functions	function	NOUN
ejpam-6339	409	7	.	.	PUNCT
ejpam-6339	410	1	neutrosophic	neutrosophic	ADJ
ejpam-6339	410	2	sets	set	NOUN
ejpam-6339	410	3	and	and	CCONJ
ejpam-6339	410	4	systems	system	NOUN
ejpam-6339	410	5	,	,	PUNCT
ejpam-6339	410	6	55(1):403–414	55(1):403–414	NUM
ejpam-6339	410	7	,	,	PUNCT
ejpam-6339	410	8	2023	2023	NUM
ejpam-6339	410	9	.	.	PUNCT