id	sid	tid	token	lemma	pos
iajs-3322	1	1	359	359	NUM
iajs-3322	1	2	©	©	ADP
iajs-3322	1	3	2025	2025	NUM
iajs-3322	1	4	the	the	DET
iajs-3322	1	5	author(s	author(s	NOUN
iajs-3322	1	6	)	)	PUNCT
iajs-3322	1	7	.	.	PUNCT
iajs-3322	2	1	published	publish	VERB
iajs-3322	2	2	by	by	ADP
iajs-3322	2	3	college	college	NOUN
iajs-3322	2	4	of	of	ADP
iajs-3322	2	5	education	education	NOUN
iajs-3322	2	6	for	for	ADP
iajs-3322	2	7	pure	pure	ADJ
iajs-3322	2	8	science	science	NOUN
iajs-3322	2	9	(	(	PUNCT
iajs-3322	2	10	ibn	ibn	PROPN
iajs-3322	2	11	al	al	PROPN
iajs-3322	2	12	-	-	PUNCT
iajs-3322	2	13	haitham	haitham	PROPN
iajs-3322	2	14	)	)	PUNCT
iajs-3322	2	15	,	,	PUNCT
iajs-3322	2	16	university	university	NOUN
iajs-3322	2	17	of	of	ADP
iajs-3322	2	18	baghdad	baghdad	PROPN
iajs-3322	2	19	.	.	PUNCT
iajs-3322	3	1	this	this	PRON
iajs-3322	3	2	is	be	AUX
iajs-3322	3	3	an	an	DET
iajs-3322	3	4	open	open	ADJ
iajs-3322	3	5	-	-	PUNCT
iajs-3322	3	6	access	access	NOUN
iajs-3322	3	7	article	article	NOUN
iajs-3322	3	8	distributed	distribute	VERB
iajs-3322	3	9	under	under	ADP
iajs-3322	3	10	the	the	DET
iajs-3322	3	11	terms	term	NOUN
iajs-3322	3	12	of	of	ADP
iajs-3322	3	13	the	the	DET
iajs-3322	3	14	creative	creative	ADJ
iajs-3322	3	15	commons	common	NOUN
iajs-3322	3	16	attribution	attribution	NOUN
iajs-3322	3	17	4.0	4.0	NUM
iajs-3322	3	18	international	international	ADJ
iajs-3322	3	19	license	license	NOUN
iajs-3322	3	20	on	on	ADP
iajs-3322	3	21	ƞǥ_ş	ƞǥ_ş	NOUN
iajs-3322	3	22	-	-	PUNCT
iajs-3322	3	23	compactness	compactness	NOUN
iajs-3322	3	24	ahmed	ahmed	PROPN
iajs-3322	3	25	sh	sh	PROPN
iajs-3322	3	26	.	.	PUNCT
iajs-3322	3	27	mohamed1	mohamed1	PROPN
iajs-3322	3	28	*	*	PROPN
iajs-3322	3	29	,	,	PUNCT
iajs-3322	3	30	r.	r.	PROPN
iajs-3322	3	31	b.	b.	PROPN
iajs-3322	3	32	esmaeel2	esmaeel2	PROPN
iajs-3322	3	33	and	and	CCONJ
iajs-3322	3	34	abdelaziz	abdelaziz	PROPN
iajs-3322	3	35	e.	e.	PROPN
iajs-3322	3	36	radwan3	radwan3	PROPN
iajs-3322	3	37	1department	1department	NUM
iajs-3322	3	38	of	of	ADP
iajs-3322	3	39	mathematics	mathematic	NOUN
iajs-3322	3	40	,	,	PUNCT
iajs-3322	3	41	college	college	NOUN
iajs-3322	3	42	of	of	ADP
iajs-3322	3	43	education	education	NOUN
iajs-3322	3	44	for	for	ADP
iajs-3322	3	45	pure	pure	ADJ
iajs-3322	3	46	science	science	NOUN
iajs-3322	3	47	(	(	PUNCT
iajs-3322	3	48	ibn	ibn	NOUN
iajs-3322	3	49	al	al	PROPN
iajs-3322	3	50	haitham	haitham	PROPN
iajs-3322	3	51	)	)	PUNCT
iajs-3322	3	52	,	,	PUNCT
iajs-3322	3	53	university	university	NOUN
iajs-3322	3	54	of	of	ADP
iajs-3322	3	55	baghdad	baghdad	PROPN
iajs-3322	3	56	,	,	PUNCT
iajs-3322	3	57	baghdad	baghdad	PROPN
iajs-3322	3	58	,	,	PUNCT
iajs-3322	3	59	iraq	iraq	PROPN
iajs-3322	3	60	.	.	PUNCT
iajs-3322	4	1	2	2	NUM
iajs-3322	4	2	department	department	NOUN
iajs-3322	4	3	of	of	ADP
iajs-3322	4	4	mathematics	mathematic	NOUN
iajs-3322	4	5	,	,	PUNCT
iajs-3322	4	6	college	college	NOUN
iajs-3322	4	7	of	of	ADP
iajs-3322	4	8	education	education	NOUN
iajs-3322	4	9	for	for	ADP
iajs-3322	4	10	pure	pure	ADJ
iajs-3322	4	11	science	science	NOUN
iajs-3322	4	12	(	(	PUNCT
iajs-3322	4	13	ibn	ibn	NOUN
iajs-3322	4	14	al	al	PROPN
iajs-3322	4	15	haitham	haitham	PROPN
iajs-3322	4	16	)	)	PUNCT
iajs-3322	4	17	,	,	PUNCT
iajs-3322	4	18	university	university	NOUN
iajs-3322	4	19	of	of	ADP
iajs-3322	4	20	baghdad	baghdad	PROPN
iajs-3322	4	21	,	,	PUNCT
iajs-3322	4	22	baghdad	baghdad	PROPN
iajs-3322	4	23	,	,	PUNCT
iajs-3322	4	24	iraq	iraq	PROPN
iajs-3322	4	25	.	.	PUNCT
iajs-3322	5	1	3	3	NUM
iajs-3322	5	2	department	department	NOUN
iajs-3322	5	3	of	of	ADP
iajs-3322	5	4	mathematics	mathematics	PROPN
iajs-3322	5	5	faculty	faculty	NOUN
iajs-3322	5	6	of	of	ADP
iajs-3322	5	7	science	science	NOUN
iajs-3322	5	8	ain	ain	PROPN
iajs-3322	5	9	shams	shams	PROPN
iajs-3322	5	10	university	university	PROPN
iajs-3322	5	11	,	,	PUNCT
iajs-3322	5	12	cairo	cairo	PROPN
iajs-3322	5	13	,	,	PUNCT
iajs-3322	5	14	egypt	egypt	PROPN
iajs-3322	5	15	.	.	PUNCT
iajs-3322	6	1	corresponding	correspond	VERB
iajs-3322	6	2	author	author	NOUN
iajs-3322	6	3	*	*	PUNCT
iajs-3322	6	4	received	receive	VERB
iajs-3322	6	5	:	:	PUNCT
iajs-3322	6	6	11	11	NUM
iajs-3322	6	7	march	march	NOUN
iajs-3322	6	8	2023	2023	NUM
iajs-3322	6	9	accepted:12	accepted:12	X
iajs-3322	6	10	july	july	PROPN
iajs-3322	6	11	2023	2023	NUM
iajs-3322	6	12	published	publish	VERB
iajs-3322	6	13	:	:	PUNCT
iajs-3322	6	14	20	20	NUM
iajs-3322	6	15	january	january	PROPN
iajs-3322	6	16	2025	2025	NUM
iajs-3322	6	17	doi.org/10.30526/38.1.3322	doi.org/10.30526/38.1.3322	PROPN
iajs-3322	6	18	abstract	abstract	ADJ
iajs-3322	6	19	open	open	ADJ
iajs-3322	6	20	sets	set	NOUN
iajs-3322	6	21	may	may	AUX
iajs-3322	6	22	be	be	AUX
iajs-3322	6	23	viewed	view	VERB
iajs-3322	6	24	as	as	ADP
iajs-3322	6	25	an	an	DET
iajs-3322	6	26	extension	extension	NOUN
iajs-3322	6	27	of	of	ADP
iajs-3322	6	28	semi	semi	ADJ
iajs-3322	6	29	-	-	ADJ
iajs-3322	6	30	open	open	ADJ
iajs-3322	6	31	sets	set	NOUN
iajs-3322	6	32	by	by	ADP
iajs-3322	6	33	applying	apply	VERB
iajs-3322	6	34	the	the	DET
iajs-3322	6	35	notions	notion	NOUN
iajs-3322	6	36	of	of	ADP
iajs-3322	6	37	semiopen	semiopen	ADJ
iajs-3322	6	38	sets	set	NOUN
iajs-3322	6	39	and	and	CCONJ
iajs-3322	6	40	grill	grill	NOUN
iajs-3322	6	41	nano	nano	NOUN
iajs-3322	6	42	to	to	ADP
iajs-3322	6	43	ngs	ng	NOUN
iajs-3322	6	44	-	-	PUNCT
iajs-3322	6	45	open	open	ADJ
iajs-3322	6	46	sets	set	NOUN
iajs-3322	6	47	,	,	PUNCT
iajs-3322	6	48	with	with	ADP
iajs-3322	6	49	the	the	DET
iajs-3322	6	50	following	follow	VERB
iajs-3322	6	51	four	four	NUM
iajs-3322	6	52	goals	goal	NOUN
iajs-3322	6	53	in	in	ADP
iajs-3322	6	54	mind	mind	NOUN
iajs-3322	6	55	:	:	PUNCT
iajs-3322	6	56	the	the	DET
iajs-3322	6	57	objective	objective	NOUN
iajs-3322	6	58	is	be	AUX
iajs-3322	6	59	to	to	PART
iajs-3322	6	60	characterize	characterize	VERB
iajs-3322	6	61	ngs	ng	NOUN
iajs-3322	6	62	-	-	PUNCT
iajs-3322	6	63	open	open	ADJ
iajs-3322	6	64	sets	set	NOUN
iajs-3322	6	65	by	by	ADP
iajs-3322	6	66	examining	examine	VERB
iajs-3322	6	67	and	and	CCONJ
iajs-3322	6	68	proving	prove	VERB
iajs-3322	6	69	numerous	numerous	ADJ
iajs-3322	6	70	of	of	ADP
iajs-3322	6	71	its	its	PRON
iajs-3322	6	72	attributes	attribute	NOUN
iajs-3322	6	73	and	and	CCONJ
iajs-3322	6	74	comments	comment	NOUN
iajs-3322	6	75	.	.	PUNCT
iajs-3322	7	1	and	and	CCONJ
iajs-3322	7	2	investigate	investigate	VERB
iajs-3322	7	3	and	and	CCONJ
iajs-3322	7	4	define	define	VERB
iajs-3322	7	5	new	new	ADJ
iajs-3322	7	6	kinds	kind	NOUN
iajs-3322	7	7	of	of	ADP
iajs-3322	7	8	functions	function	NOUN
iajs-3322	7	9	based	base	VERB
iajs-3322	7	10	on	on	ADP
iajs-3322	7	11	the	the	DET
iajs-3322	7	12	concept	concept	NOUN
iajs-3322	7	13	of	of	ADP
iajs-3322	7	14	ngs	ng	NOUN
iajs-3322	7	15	-	-	PUNCT
iajs-3322	7	16	open	open	ADJ
iajs-3322	7	17	sets	set	NOUN
iajs-3322	7	18	,	,	PUNCT
iajs-3322	7	19	using	use	VERB
iajs-3322	7	20	sets	set	NOUN
iajs-3322	7	21	of	of	ADP
iajs-3322	7	22	ngs	ng	NOUN
iajs-3322	7	23	-	-	PUNCT
iajs-3322	7	24	open	open	ADJ
iajs-3322	7	25	sets	set	NOUN
iajs-3322	7	26	,	,	PUNCT
iajs-3322	7	27	we	we	PRON
iajs-3322	7	28	will	will	AUX
iajs-3322	7	29	define	define	VERB
iajs-3322	7	30	a	a	DET
iajs-3322	7	31	new	new	ADJ
iajs-3322	7	32	type	type	NOUN
iajs-3322	7	33	of	of	ADP
iajs-3322	7	34	compact	compact	ADJ
iajs-3322	7	35	type	type	NOUN
iajs-3322	7	36	and	and	CCONJ
iajs-3322	7	37	call	call	VERB
iajs-3322	7	38	it	it	PRON
iajs-3322	7	39	ngs	ng	VERB
iajs-3322	7	40	-	-	PUNCT
iajs-3322	7	41	open	open	ADJ
iajs-3322	7	42	compact	compact	NOUN
iajs-3322	7	43	then	then	ADV
iajs-3322	7	44	we	we	PRON
iajs-3322	7	45	will	will	AUX
iajs-3322	7	46	find	find	VERB
iajs-3322	7	47	the	the	DET
iajs-3322	7	48	relationship	relationship	NOUN
iajs-3322	7	49	between	between	ADP
iajs-3322	7	50	these	these	DET
iajs-3322	7	51	new	new	ADJ
iajs-3322	7	52	types	type	NOUN
iajs-3322	7	53	of	of	ADP
iajs-3322	7	54	compact	compact	ADJ
iajs-3322	7	55	type	type	NOUN
iajs-3322	7	56	with	with	ADP
iajs-3322	7	57	nano	nano	NOUN
iajs-3322	7	58	compact	compact	NOUN
iajs-3322	7	59	.	.	PUNCT
iajs-3322	8	1	we	we	PRON
iajs-3322	8	2	will	will	AUX
iajs-3322	8	3	also	also	ADV
iajs-3322	8	4	talk	talk	VERB
iajs-3322	8	5	about	about	ADP
iajs-3322	8	6	the	the	DET
iajs-3322	8	7	relationship	relationship	NOUN
iajs-3322	8	8	between	between	ADP
iajs-3322	8	9	nano	nano	NOUN
iajs-3322	8	10	grill	grill	NOUN
iajs-3322	8	11	semi	semi	ADJ
iajs-3322	8	12	-	-	ADJ
iajs-3322	8	13	open	open	ADJ
iajs-3322	8	14	sets	set	NOUN
iajs-3322	8	15	and	and	CCONJ
iajs-3322	8	16	continuous	continuous	ADJ
iajs-3322	8	17	functions	function	NOUN
iajs-3322	8	18	and	and	CCONJ
iajs-3322	8	19	the	the	DET
iajs-3322	8	20	relationship	relationship	NOUN
iajs-3322	8	21	between	between	ADP
iajs-3322	8	22	nano	nano	NOUN
iajs-3322	8	23	grill	grill	NOUN
iajs-3322	8	24	semi	semi	ADJ
iajs-3322	8	25	-	-	ADJ
iajs-3322	8	26	open	open	ADJ
iajs-3322	8	27	sets	set	NOUN
iajs-3322	8	28	and	and	CCONJ
iajs-3322	8	29	irresolute	irresolute	ADJ
iajs-3322	8	30	function	function	NOUN
iajs-3322	8	31	as	as	ADV
iajs-3322	8	32	well	well	ADV
iajs-3322	8	33	we	we	PRON
iajs-3322	8	34	give	give	VERB
iajs-3322	8	35	some	some	DET
iajs-3322	8	36	examples	example	NOUN
iajs-3322	8	37	,	,	PUNCT
iajs-3322	8	38	proofs	proof	NOUN
iajs-3322	8	39	and	and	CCONJ
iajs-3322	8	40	observations	observation	NOUN
iajs-3322	8	41	about	about	ADP
iajs-3322	8	42	the	the	DET
iajs-3322	8	43	relationship	relationship	NOUN
iajs-3322	8	44	between	between	ADP
iajs-3322	8	45	nano	nano	NOUN
iajs-3322	8	46	grill	grill	NOUN
iajs-3322	8	47	semi	semi	ADJ
iajs-3322	8	48	-	-	ADJ
iajs-3322	8	49	open	open	ADJ
iajs-3322	8	50	sets	set	NOUN
iajs-3322	8	51	and	and	CCONJ
iajs-3322	8	52	functions	function	NOUN
iajs-3322	8	53	and	and	CCONJ
iajs-3322	8	54	their	their	PRON
iajs-3322	8	55	relation	relation	NOUN
iajs-3322	8	56	to	to	ADP
iajs-3322	8	57	nano	nano	NOUN
iajs-3322	8	58	compact	compact	ADJ
iajs-3322	8	59	.	.	PUNCT
iajs-3322	9	1	keywords	keyword	NOUN
iajs-3322	9	2	:	:	PUNCT
iajs-3322	9	3	nano	nano	NOUN
iajs-3322	9	4	grill	grill	NOUN
iajs-3322	9	5	semi	semi	ADJ
iajs-3322	9	6	-	-	ADJ
iajs-3322	9	7	open	open	ADJ
iajs-3322	9	8	compact	compact	ADJ
iajs-3322	9	9	space	space	NOUN
iajs-3322	9	10	,	,	PUNCT
iajs-3322	9	11	ƞǥ_ş	ƞǥ_ş	NUM
iajs-3322	9	12	ỏ	ỏ	NUM
iajs-3322	9	13	-	-	PUNCT
iajs-3322	9	14	semi	semi	ADJ
iajs-3322	9	15	-	-	ADJ
iajs-3322	9	16	open	open	ADJ
iajs-3322	9	17	compact	compact	ADJ
iajs-3322	9	18	.	.	PUNCT
iajs-3322	9	19	,	,	PUNCT
iajs-3322	9	20	nano	nano	NOUN
iajs-3322	9	21	compact	compact	NOUN
iajs-3322	9	22	.	.	PUNCT
iajs-3322	10	1	1	1	X
iajs-3322	10	2	.	.	X
iajs-3322	10	3	introduction	introduction	NOUN
iajs-3322	10	4	the	the	DET
iajs-3322	10	5	concept	concept	NOUN
iajs-3322	10	6	for	for	ADP
iajs-3322	10	7	grill	grill	ADJ
iajs-3322	10	8	topological	topological	ADJ
iajs-3322	10	9	spaces	space	NOUN
iajs-3322	10	10	rests	rest	VERB
iajs-3322	10	11	on	on	ADP
iajs-3322	10	12	the	the	DET
iajs-3322	10	13	use	use	NOUN
iajs-3322	10	14	of	of	ADP
iajs-3322	10	15	two	two	NUM
iajs-3322	10	16	operators	operator	NOUN
iajs-3322	10	17	:	:	PUNCT
iajs-3322	10	18	and	and	CCONJ
iajs-3322	10	19	.	.	PUNCT
iajs-3322	11	1	the	the	DET
iajs-3322	11	2	pioneer	pioneer	NOUN
iajs-3322	11	3	of	of	ADP
iajs-3322	11	4	this	this	DET
iajs-3322	11	5	concept	concept	NOUN
iajs-3322	11	6	was	be	AUX
iajs-3322	11	7	choquet	choquet	NOUN
iajs-3322	11	8	)	)	PUNCT
iajs-3322	11	9	1	1	NUM
iajs-3322	11	10	)	)	PUNCT
iajs-3322	11	11	.	.	PUNCT
iajs-3322	12	1	some	some	DET
iajs-3322	12	2	parallels	parallel	NOUN
iajs-3322	12	3	between	between	ADP
iajs-3322	12	4	the	the	DET
iajs-3322	12	5	choquat	choquat	ADJ
iajs-3322	12	6	idea	idea	NOUN
iajs-3322	12	7	and	and	CCONJ
iajs-3322	12	8	ideas	idea	NOUN
iajs-3322	12	9	,	,	PUNCT
iajs-3322	12	10	nets	net	NOUN
iajs-3322	12	11	and	and	CCONJ
iajs-3322	12	12	filters	filter	NOUN
iajs-3322	12	13	have	have	AUX
iajs-3322	12	14	been	be	AUX
iajs-3322	12	15	discovered	discover	VERB
iajs-3322	12	16	.	.	PUNCT
iajs-3322	13	1	several	several	ADJ
iajs-3322	13	2	hypotheses	hypothesis	NOUN
iajs-3322	13	3	and	and	CCONJ
iajs-3322	13	4	characteristics	characteristic	NOUN
iajs-3322	13	5	have	have	AUX
iajs-3322	13	6	been	be	AUX
iajs-3322	13	7	discussed	discuss	VERB
iajs-3322	13	8	in	in	ADP
iajs-3322	13	9	)	)	PUNCT
iajs-3322	13	10	2–5	2–5	PROPN
iajs-3322	13	11	(	(	PUNCT
iajs-3322	13	12	.	.	PUNCT
iajs-3322	14	1	it	it	PRON
iajs-3322	14	2	allows	allow	VERB
iajs-3322	14	3	for	for	ADP
iajs-3322	14	4	the	the	DET
iajs-3322	14	5	growth	growth	NOUN
iajs-3322	14	6	of	of	ADP
iajs-3322	14	7	the	the	DET
iajs-3322	14	8	topological	topological	ADJ
iajs-3322	14	9	assembly	assembly	NOUN
iajs-3322	14	10	utilized	utilize	VERB
iajs-3322	14	11	to	to	PART
iajs-3322	14	12	account	account	VERB
iajs-3322	14	13	for	for	ADP
iajs-3322	14	14	intangibles	intangible	NOUN
iajs-3322	14	15	like	like	ADP
iajs-3322	14	16	love	love	NOUN
iajs-3322	14	17	,	,	PUNCT
iajs-3322	14	18	intelligence	intelligence	NOUN
iajs-3322	14	19	,	,	PUNCT
iajs-3322	14	20	beauty	beauty	NOUN
iajs-3322	14	21	,	,	PUNCT
iajs-3322	14	22	instructional	instructional	ADJ
iajs-3322	14	23	quality	quality	NOUN
iajs-3322	14	24	,	,	PUNCT
iajs-3322	14	25	etc	etc	X
iajs-3322	14	26	.	.	X
iajs-3322	14	27	additionally	additionally	ADV
iajs-3322	14	28	,	,	PUNCT
iajs-3322	14	29	it	it	PRON
iajs-3322	14	30	broadens	broaden	VERB
iajs-3322	14	31	the	the	DET
iajs-3322	14	32	frontiers	frontier	NOUN
iajs-3322	14	33	of	of	ADP
iajs-3322	14	34	nano	nano	NOUN
iajs-3322	14	35	topological	topological	ADJ
iajs-3322	14	36	spaces	space	NOUN
iajs-3322	14	37	by	by	ADP
iajs-3322	14	38	employing	employ	VERB
iajs-3322	14	39	the	the	DET
iajs-3322	14	40	concept	concept	NOUN
iajs-3322	14	41	of	of	ADP
iajs-3322	14	42	grill	grill	ADJ
iajs-3322	14	43	modifications	modification	NOUN
iajs-3322	14	44	in	in	ADP
iajs-3322	14	45	the	the	DET
iajs-3322	14	46	lower	low	ADJ
iajs-3322	14	47	approximation	approximation	NOUN
iajs-3322	14	48	,	,	PUNCT
iajs-3322	14	49	the	the	DET
iajs-3322	14	50	upper	upper	ADJ
iajs-3322	14	51	approximation	approximation	NOUN
iajs-3322	14	52	,	,	PUNCT
iajs-3322	14	53	and	and	CCONJ
iajs-3322	14	54	the	the	DET
iajs-3322	14	55	boundary	boundary	ADJ
iajs-3322	14	56	region	region	NOUN
iajs-3322	14	57	.	.	PUNCT
iajs-3322	15	1	first	first	ADV
iajs-3322	15	2	proposed	propose	VERB
iajs-3322	15	3	in	in	ADP
iajs-3322	15	4	1970	1970	NUM
iajs-3322	15	5	by	by	ADP
iajs-3322	15	6	levine	levine	PROPN
iajs-3322	15	7	(	(	PUNCT
iajs-3322	15	8	6	6	NUM
iajs-3322	15	9	)	)	PUNCT
iajs-3322	15	10	,	,	PUNCT
iajs-3322	15	11	the	the	DET
iajs-3322	15	12	concept	concept	NOUN
iajs-3322	15	13	of	of	ADP
iajs-3322	15	14	enlarging	enlarge	VERB
iajs-3322	15	15	closed	closed	ADJ
iajs-3322	15	16	sets	set	NOUN
iajs-3322	15	17	is	be	AUX
iajs-3322	15	18	widely	widely	ADV
iajs-3322	15	19	credited	credit	VERB
iajs-3322	15	20	as	as	ADP
iajs-3322	15	21	a	a	DET
iajs-3322	15	22	breakthrough	breakthrough	NOUN
iajs-3322	15	23	in	in	ADP
iajs-3322	15	24	the	the	DET
iajs-3322	15	25	field	field	NOUN
iajs-3322	15	26	.	.	PUNCT
iajs-3322	16	1	lower	low	ADJ
iajs-3322	16	2	,	,	PUNCT
iajs-3322	16	3	higher	high	ADJ
iajs-3322	16	4	,	,	PUNCT
iajs-3322	16	5	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3322	16	6	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3322	16	7	https://doi.org/10.30526/38.1.3501	https://doi.org/10.30526/38.1.3501	NUM
iajs-3322	16	8	https://orcid.org/0009-0000-9139-257x	https://orcid.org/0009-0000-9139-257x	PROPN
iajs-3322	16	9	mailto:shakr3394@gmail.com	mailto:shakr3394@gmail.com	X
iajs-3322	16	10	https://orcid.org/0000-0002-4743-6034	https://orcid.org/0000-0002-4743-6034	ADJ
iajs-3322	16	11	mailto:ranamumosa@yahoo.com	mailto:ranamumosa@yahoo.com	NOUN
iajs-3322	16	12	https://orcid.org/	https://orcid.org/	NOUN
iajs-3322	16	13	mailto:zezoradwan@yahoo.com	mailto:zezoradwan@yahoo.com	PROPN
iajs-3322	16	14	ihjpas	ihjpas	PROPN
iajs-3322	16	15	.	.	PUNCT
iajs-3322	17	1	2025	2025	NUM
iajs-3322	17	2	,	,	PUNCT
iajs-3322	17	3	38	38	NUM
iajs-3322	17	4	(	(	PUNCT
iajs-3322	17	5	1	1	NUM
iajs-3322	17	6	)	)	PUNCT
iajs-3322	17	7	360	360	NUM
iajs-3322	17	8	and	and	CCONJ
iajs-3322	17	9	boundary	boundary	ADJ
iajs-3322	17	10	estimates	estimate	NOUN
iajs-3322	17	11	of	of	ADP
iajs-3322	17	12	a	a	DET
iajs-3322	17	13	subset	subset	NOUN
iajs-3322	17	14	of	of	ADP
iajs-3322	17	15	a	a	DET
iajs-3322	17	16	cosmic	cosmic	ADJ
iajs-3322	17	17	set	set	NOUN
iajs-3322	17	18	with	with	ADP
iajs-3322	17	19	an	an	DET
iajs-3322	17	20	important	important	ADJ
iajs-3322	17	21	basis	basis	NOUN
iajs-3322	17	22	to	to	ADP
iajs-3322	17	23	it	it	PRON
iajs-3322	17	24	are	be	AUX
iajs-3322	17	25	the	the	DET
iajs-3322	17	26	foundation	foundation	NOUN
iajs-3322	17	27	on	on	ADP
iajs-3322	17	28	which	which	PRON
iajs-3322	17	29	the	the	DET
iajs-3322	17	30	idea	idea	NOUN
iajs-3322	17	31	of	of	ADP
iajs-3322	17	32	nano	nano	NOUN
iajs-3322	17	33	topological	topological	ADJ
iajs-3322	17	34	assemblage	assemblage	NOUN
iajs-3322	17	35	rests	rest	NOUN
iajs-3322	17	36	.	.	PUNCT
iajs-3322	18	1	also	also	ADV
iajs-3322	18	2	,	,	PUNCT
iajs-3322	18	3	the	the	DET
iajs-3322	18	4	concept	concept	NOUN
iajs-3322	18	5	of	of	ADP
iajs-3322	18	6	nano	nano	NOUN
iajs-3322	18	7	is	be	AUX
iajs-3322	18	8	used	use	VERB
iajs-3322	18	9	to	to	PART
iajs-3322	18	10	introduce	introduce	VERB
iajs-3322	18	11	the	the	DET
iajs-3322	18	12	definitions	definition	NOUN
iajs-3322	18	13	of	of	ADP
iajs-3322	18	14	the	the	DET
iajs-3322	18	15	closed	closed	ADJ
iajs-3322	18	16	set	set	NOUN
iajs-3322	18	17	,	,	PUNCT
iajs-3322	18	18	the	the	DET
iajs-3322	18	19	interior	interior	ADJ
iajs-3322	18	20	set	set	NOUN
iajs-3322	18	21	,	,	PUNCT
iajs-3322	18	22	and	and	CCONJ
iajs-3322	18	23	the	the	DET
iajs-3322	18	24	closure	closure	NOUN
iajs-3322	18	25	set	set	NOUN
iajs-3322	18	26	.	.	PUNCT
iajs-3322	19	1	lellis	lellis	PROPN
iajs-3322	19	2	(	(	PUNCT
iajs-3322	19	3	7	7	NUM
iajs-3322	19	4	)	)	PUNCT
iajs-3322	19	5	first	first	ADV
iajs-3322	19	6	developed	develop	VERB
iajs-3322	19	7	this	this	DET
iajs-3322	19	8	concept	concept	NOUN
iajs-3322	19	9	in	in	ADP
iajs-3322	19	10	2013	2013	NUM
iajs-3322	19	11	.	.	PUNCT
iajs-3322	20	1	the	the	DET
iajs-3322	20	2	primary	primary	ADJ
iajs-3322	20	3	objective	objective	NOUN
iajs-3322	20	4	of	of	ADP
iajs-3322	20	5	this	this	DET
iajs-3322	20	6	study	study	NOUN
iajs-3322	20	7	is	be	AUX
iajs-3322	20	8	to	to	PART
iajs-3322	20	9	incorporate	incorporate	VERB
iajs-3322	20	10	a	a	DET
iajs-3322	20	11	grill	grill	NOUN
iajs-3322	20	12	into	into	ADP
iajs-3322	20	13	a	a	DET
iajs-3322	20	14	space	space	NOUN
iajs-3322	20	15	containing	contain	VERB
iajs-3322	20	16	a	a	DET
iajs-3322	20	17	generalized	generalize	VERB
iajs-3322	20	18	closed	closed	ADJ
iajs-3322	20	19	nano	nano	NOUN
iajs-3322	20	20	topology	topology	NOUN
iajs-3322	20	21	.	.	PUNCT
iajs-3322	21	1	we	we	PRON
iajs-3322	21	2	've	have	AUX
iajs-3322	21	3	established	establish	VERB
iajs-3322	21	4	contact	contact	NOUN
iajs-3322	21	5	with	with	ADP
iajs-3322	21	6	some	some	DET
iajs-3322	21	7	very	very	ADV
iajs-3322	21	8	important	important	ADJ
iajs-3322	21	9	people	people	NOUN
iajs-3322	21	10	.	.	PUNCT
iajs-3322	22	1	2	2	X
iajs-3322	22	2	.	.	NUM
iajs-3322	22	3	preliminaries	preliminary	NOUN
iajs-3322	22	4	definition	definition	NOUN
iajs-3322	22	5	2.1:(4	2.1:(4	NUM
iajs-3322	22	6	)	)	PUNCT
iajs-3322	22	7	,	,	PUNCT
iajs-3322	22	8	(	(	PUNCT
iajs-3322	22	9	8)	8)	NUM
iajs-3322	22	10	ⱥ	ⱥ	NOUN
iajs-3322	22	11	grill	grill	NOUN
iajs-3322	22	12	is	be	AUX
iajs-3322	22	13	a	a	DET
iajs-3322	22	14	nonempty	nonempty	ADJ
iajs-3322	22	15	collection	collection	NOUN
iajs-3322	22	16	of	of	ADP
iajs-3322	22	17	nonempty	nonempty	ADJ
iajs-3322	22	18	subsets	subset	NOUN
iajs-3322	22	19	of	of	ADP
iajs-3322	22	20	a	a	DET
iajs-3322	22	21	topological	topological	ADJ
iajs-3322	22	22	space	space	NOUN
iajs-3322	22	23	ꭓ	ꭓ	PRON
iajs-3322	22	24	i.	i.	NOUN
iajs-3322	22	25	ⱥ∈	ⱥ∈	PROPN
iajs-3322	22	26	ǥ	ǥ	PROPN
iajs-3322	22	27	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3322	22	28	ⱥ	ⱥ	PROPN
iajs-3322	22	29	⊆	⊆	NUM
iajs-3322	22	30	ɓ	ɓ	DET
iajs-3322	22	31	⊆	⊆	NUM
iajs-3322	22	32	ꭓ	ꭓ	NOUN
iajs-3322	22	33	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
iajs-3322	22	34	ɓ	ɓ	PRON
iajs-3322	22	35	∈	∈	PROPN
iajs-3322	22	36	ǥ	ǥ	PRON
iajs-3322	22	37	ii	ii	PROPN
iajs-3322	22	38	.	.	PUNCT
iajs-3322	23	1	ⱥ	ⱥ	X
iajs-3322	23	2	,	,	PUNCT
iajs-3322	23	3	ɓ	ɓ	PRON
iajs-3322	23	4	⊆	⊆	NUM
iajs-3322	23	5	ꭓ	ꭓ	NUM
iajs-3322	23	6	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3322	23	7	ⱥ	ⱥ	NOUN
iajs-3322	23	8	∪	∪	ADP
iajs-3322	23	9	ɓ	ɓ	PRON
iajs-3322	23	10	∈	∈	NOUN
iajs-3322	23	11	ǥ	ǥ	NOUN
iajs-3322	23	12	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
iajs-3322	23	13	ⱥ	ⱥ	X
iajs-3322	23	14	∈	∈	NOUN
iajs-3322	23	15	ǥ	ǥ	NOUN
iajs-3322	23	16	𝑜𝑟	𝑜𝑟	VERB
iajs-3322	23	17	ɓ	ɓ	DET
iajs-3322	23	18	∈	∈	PROPN
iajs-3322	23	19	ǥ	ǥ	NOUN
iajs-3322	23	20	.	.	PUNCT
iajs-3322	24	1	(	(	PUNCT
iajs-3322	24	2	9	9	NUM
iajs-3322	24	3	)	)	PUNCT
iajs-3322	24	4	,	,	PUNCT
iajs-3322	24	5	(	(	PUNCT
iajs-3322	24	6	10	10	NUM
iajs-3322	24	7	)	)	PUNCT
iajs-3322	24	8	assuming	assume	VERB
iajs-3322	24	9	that	that	SCONJ
iajs-3322	24	10	ꭓ	ꭓ	PROPN
iajs-3322	24	11	is	be	AUX
iajs-3322	24	12	a	a	DET
iajs-3322	24	13	non	non	ADJ
iajs-3322	24	14	-	-	ADJ
iajs-3322	24	15	empty	empty	ADJ
iajs-3322	24	16	set	set	NOUN
iajs-3322	24	17	,	,	PUNCT
iajs-3322	24	18	the	the	DET
iajs-3322	24	19	following	follow	VERB
iajs-3322	24	20	sets	set	NOUN
iajs-3322	24	21	are	be	AUX
iajs-3322	24	22	grills	grill	NOUN
iajs-3322	24	23	on	on	ADP
iajs-3322	24	24	ꭓ.(11	ꭓ.(11	NOUN
iajs-3322	24	25	)	)	PUNCT
iajs-3322	24	26	,	,	PUNCT
iajs-3322	24	27	(	(	PUNCT
iajs-3322	24	28	12	12	NUM
iajs-3322	24	29	)	)	PUNCT
iajs-3322	24	30	•	•	NUM
iajs-3322	24	31	ø	ø	PROPN
iajs-3322	24	32	&	&	CCONJ
iajs-3322	24	33	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	24	34	)	)	PUNCT
iajs-3322	24	35	∖	∖	X
iajs-3322	24	36	{	{	PUNCT
iajs-3322	24	37	ø	ø	NOUN
iajs-3322	24	38	}	}	PUNCT
iajs-3322	24	39	are	be	AUX
iajs-3322	24	40	examples	example	NOUN
iajs-3322	24	41	of	of	ADP
iajs-3322	24	42	trivial	trivial	ADJ
iajs-3322	24	43	grills	grill	NOUN
iajs-3322	24	44	on	on	ADP
iajs-3322	24	45	ꭓ	ꭓ	PROPN
iajs-3322	24	46	.	.	NOUN
iajs-3322	24	47	•	•	NOUN
iajs-3322	24	48	ǥ∞	ǥ∞	PRON
iajs-3322	24	49	is	be	AUX
iajs-3322	24	50	the	the	DET
iajs-3322	24	51	grill	grill	NOUN
iajs-3322	24	52	of	of	ADP
iajs-3322	24	53	all	all	DET
iajs-3322	24	54	infinite	infinite	ADJ
iajs-3322	24	55	subset	subset	NOUN
iajs-3322	24	56	of	of	ADP
iajs-3322	24	57	ꭓ	ꭓ	PROPN
iajs-3322	24	58	.	.	NOUN
iajs-3322	24	59	•	•	NOUN
iajs-3322	24	60	ǥҫỏ	ǥҫỏ	NOUN
iajs-3322	24	61	is	be	VERB
iajs-3322	24	62	the	the	DET
iajs-3322	24	63	grill	grill	NOUN
iajs-3322	24	64	of	of	ADP
iajs-3322	24	65	all	all	DET
iajs-3322	24	66	uncountable	uncountable	ADJ
iajs-3322	24	67	subsets	subset	NOUN
iajs-3322	24	68	of	of	ADP
iajs-3322	24	69	ꭓ	ꭓ	PROPN
iajs-3322	24	70	.	.	NOUN
iajs-3322	24	71	•	•	NUM
iajs-3322	24	72	ǥꝕ	ǥꝕ	VERB
iajs-3322	24	73	=	=	X
iajs-3322	24	74	{	{	PUNCT
iajs-3322	24	75	ⱥ	ⱥ	X
iajs-3322	24	76	:	:	PUNCT
iajs-3322	24	77	ⱥ	ⱥ	PROPN
iajs-3322	24	78	∈	∈	PROPN
iajs-3322	24	79	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	24	80	)	)	PUNCT
iajs-3322	24	81	,	,	PUNCT
iajs-3322	24	82	ꝕ	ꝕ	PROPN
iajs-3322	24	83	∈	∈	PROPN
iajs-3322	24	84	ⱥ	ⱥ	AUX
iajs-3322	24	85	}	}	PUNCT
iajs-3322	24	86	is	be	AUX
iajs-3322	24	87	a	a	DET
iajs-3322	24	88	certain	certain	ADJ
iajs-3322	24	89	point	point	NOUN
iajs-3322	24	90	grill	grill	NOUN
iajs-3322	24	91	on	on	ADP
iajs-3322	24	92	ꭓ	ꭓ	PROPN
iajs-3322	24	93	.	.	NOUN
iajs-3322	24	94	•	•	NUM
iajs-3322	25	1	ǥⱥ	ǥⱥ	NOUN
iajs-3322	25	2	=	=	PRON
iajs-3322	25	3	{	{	PUNCT
iajs-3322	25	4	ɓ	ɓ	X
iajs-3322	25	5	:	:	PUNCT
iajs-3322	25	6	ɓ	ɓ	DET
iajs-3322	25	7	∈	∈	PROPN
iajs-3322	25	8	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	25	9	)	)	PUNCT
iajs-3322	25	10	,	,	PUNCT
iajs-3322	25	11	ɓ	ɓ	DET
iajs-3322	25	12	∩	∩	NOUN
iajs-3322	25	13	ⱥҫ	ⱥҫ	VERB
iajs-3322	25	14	≠	≠	PROPN
iajs-3322	25	15	ø	ø	NOUN
iajs-3322	25	16	}	}	PUNCT
iajs-3322	25	17	.	.	PUNCT
iajs-3322	26	1	⁎	⁎	NUM
iajs-3322	26	2	if	if	SCONJ
iajs-3322	26	3	(	(	PUNCT
iajs-3322	26	4	ꭓ	ꭓ	X
iajs-3322	26	5	,	,	PUNCT
iajs-3322	26	6	ʈ	ʈ	ADJ
iajs-3322	26	7	)	)	PUNCT
iajs-3322	26	8	is	be	AUX
iajs-3322	26	9	a	a	DET
iajs-3322	26	10	topological	topological	ADJ
iajs-3322	26	11	space	space	NOUN
iajs-3322	26	12	,	,	PUNCT
iajs-3322	26	13	and	and	CCONJ
iajs-3322	26	14	so	so	ADV
iajs-3322	26	15	the	the	DET
iajs-3322	26	16	set	set	NOUN
iajs-3322	26	17	of	of	ADP
iajs-3322	26	18	the	the	DET
iajs-3322	26	19	all	all	DET
iajs-3322	26	20	dense	dense	ADJ
iajs-3322	26	21	subset	subset	NOUN
iajs-3322	26	22	that	that	PRON
iajs-3322	26	23	does	do	AUX
iajs-3322	26	24	not	not	PART
iajs-3322	26	25	already	already	ADV
iajs-3322	26	26	exist	exist	VERB
iajs-3322	26	27	here	here	ADV
iajs-3322	26	28	is	be	AUX
iajs-3322	26	29	known	know	VERB
iajs-3322	26	30	as	as	ADP
iajs-3322	26	31	ǥ=	ǥ=	X
iajs-3322	26	32	{	{	PUNCT
iajs-3322	26	33	ⱥ	ⱥ	X
iajs-3322	26	34	:	:	PUNCT
iajs-3322	26	35	𝑖ƞʈ(ҫ𝑙(ⱥ	𝑖ƞʈ(ҫ𝑙(ⱥ	PROPN
iajs-3322	26	36	)	)	PUNCT
iajs-3322	26	37	)	)	PUNCT
iajs-3322	27	1	≠	≠	PROPN
iajs-3322	27	2	ǿ	ǿ	X
iajs-3322	27	3	}	}	PUNCT
iajs-3322	27	4	is	be	AUX
iajs-3322	27	5	one	one	NUM
iajs-3322	27	6	kind	kind	NOUN
iajs-3322	27	7	of	of	ADP
iajs-3322	27	8	grill	grill	NOUN
iajs-3322	27	9	on	on	ADP
iajs-3322	27	10	ꭓ	ꭓ	PROPN
iajs-3322	27	11	(	(	PUNCT
iajs-3322	27	12	4	4	NUM
iajs-3322	27	13	)	)	PUNCT
iajs-3322	27	14	.	.	PUNCT
iajs-3322	28	1	⁎	⁎	NOUN
iajs-3322	28	2	suppose	suppose	VERB
iajs-3322	28	3	that	that	SCONJ
iajs-3322	28	4	ǥ	ǥ	PROPN
iajs-3322	28	5	a	a	DET
iajs-3322	28	6	grill	grill	NOUN
iajs-3322	28	7	on	on	ADP
iajs-3322	28	8	(	(	PUNCT
iajs-3322	28	9	ꭓ	ꭓ	X
iajs-3322	28	10	,	,	PUNCT
iajs-3322	28	11	ʈ	ʈ	NOUN
iajs-3322	28	12	)	)	PUNCT
iajs-3322	28	13	.	.	PUNCT
iajs-3322	29	1	a	a	DET
iajs-3322	29	2	mapping	mapping	NOUN
iajs-3322	29	3	∯:ꝕ(ꭓ	∯:ꝕ(ꭓ	PROPN
iajs-3322	29	4	)	)	PUNCT
iajs-3322	29	5	→	→	SYM
iajs-3322	29	6	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	29	7	)	)	PUNCT
iajs-3322	29	8	is	be	AUX
iajs-3322	29	9	referred	refer	VERB
iajs-3322	29	10	to	to	ADP
iajs-3322	29	11	as	as	ADP
iajs-3322	29	12	∯	∯	PROPN
iajs-3322	29	13	(	(	PUNCT
iajs-3322	29	14	ⱥ	ⱥ	X
iajs-3322	29	15	)	)	PUNCT
iajs-3322	29	16	=	=	NOUN
iajs-3322	29	17	{	{	PUNCT
iajs-3322	29	18	ꭓ	ꭓ	PROPN
iajs-3322	29	19	∈	∈	PROPN
iajs-3322	29	20	ꭓ	ꭓ	X
iajs-3322	29	21	:	:	PUNCT
iajs-3322	29	22	ⱥ	ⱥ	X
iajs-3322	29	23	∩	∩	NOUN
iajs-3322	29	24	ȗ∈	ȗ∈	PROPN
iajs-3322	29	25	ǥ	ǥ	NOUN
iajs-3322	29	26	for	for	ADP
iajs-3322	29	27	every	every	DET
iajs-3322	29	28	ȗ	ȗ	PROPN
iajs-3322	29	29	∈	∈	PROPN
iajs-3322	29	30	ʈ	ʈ	NOUN
iajs-3322	29	31	;	;	PUNCT
iajs-3322	29	32	ꭓ	ꭓ	PRON
iajs-3322	29	33	∈	∈	NOUN
iajs-3322	29	34	ȗ	ȗ	X
iajs-3322	29	35	}	}	PUNCT
iajs-3322	29	36	for	for	ADP
iajs-3322	29	37	every	every	DET
iajs-3322	29	38	ⱥ	ⱥ	PRON
iajs-3322	29	39	∈	∈	NOUN
iajs-3322	29	40	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	29	41	)	)	PUNCT
iajs-3322	29	42	.	.	PUNCT
iajs-3322	30	1	a	a	DET
iajs-3322	30	2	mapping	mapping	NOUN
iajs-3322	30	3	ψ	ψ	NOUN
iajs-3322	30	4	:	:	PUNCT
iajs-3322	30	5	ꝕ(ꭓ	ꝕ(ꭓ	NUM
iajs-3322	30	6	)	)	PUNCT
iajs-3322	30	7	→ꝕ(ꭓ	→ꝕ(ꭓ	PROPN
iajs-3322	30	8	)	)	PUNCT
iajs-3322	30	9	is	be	AUX
iajs-3322	30	10	referred	refer	VERB
iajs-3322	30	11	to	to	ADP
iajs-3322	30	12	as	as	ADP
iajs-3322	30	13	ψ	ψ	X
iajs-3322	30	14	(	(	PUNCT
iajs-3322	30	15	ⱥ	ⱥ	X
iajs-3322	30	16	)	)	PUNCT
iajs-3322	30	17	=	=	SYM
iajs-3322	31	1	ⱥ	ⱥ	X
iajs-3322	31	2	∪	∪	X
iajs-3322	31	3	∯	∯	X
iajs-3322	31	4	(	(	PUNCT
iajs-3322	31	5	ⱥ	ⱥ	X
iajs-3322	31	6	)	)	PUNCT
iajs-3322	31	7	for	for	SCONJ
iajs-3322	31	8	every	every	DET
iajs-3322	31	9	ⱥ	ⱥ	PROPN
iajs-3322	31	10	∈	∈	PROPN
iajs-3322	31	11	ꝕ(ꭓ).(13	ꝕ(ꭓ).(13	PROPN
iajs-3322	31	12	)	)	PUNCT
iajs-3322	31	13	kuratowski	kuratowski	PROPN
iajs-3322	31	14	's	's	PART
iajs-3322	31	15	axioms	axiom	NOUN
iajs-3322	31	16	of	of	ADP
iajs-3322	31	17	closure	closure	NOUN
iajs-3322	31	18	for	for	ADP
iajs-3322	31	19	the	the	DET
iajs-3322	31	20	map	map	NOUN
iajs-3322	31	21	ψ	ψ	NOUN
iajs-3322	31	22	are	be	AUX
iajs-3322	31	23	verified	verify	VERB
iajs-3322	31	24	:	:	PUNCT
iajs-3322	31	25	(	(	PUNCT
iajs-3322	31	26	13	13	NUM
iajs-3322	31	27	)	)	PUNCT
iajs-3322	31	28	,	,	PUNCT
iajs-3322	31	29	(	(	PUNCT
iajs-3322	31	30	14	14	NUM
iajs-3322	31	31	)	)	PUNCT
iajs-3322	31	32	,	,	PUNCT
iajs-3322	31	33	(	(	PUNCT
iajs-3322	31	34	15	15	X
iajs-3322	31	35	)	)	PUNCT
iajs-3322	31	36	i.	i.	NOUN
iajs-3322	31	37	ψ	ψ	PROPN
iajs-3322	31	38	(	(	PUNCT
iajs-3322	31	39	ø	ø	NOUN
iajs-3322	31	40	)	)	PUNCT
iajs-3322	31	41	=	=	SYM
iajs-3322	31	42	ø	ø	PROPN
iajs-3322	31	43	,	,	PUNCT
iajs-3322	31	44	ii	ii	PROPN
iajs-3322	31	45	.	.	PUNCT
iajs-3322	32	1	when	when	SCONJ
iajs-3322	32	2	ⱥ	ⱥ	PROPN
iajs-3322	32	3	⊆	⊆	NUM
iajs-3322	32	4	ɓ	ɓ	NOUN
iajs-3322	32	5	,	,	PUNCT
iajs-3322	32	6	then	then	ADV
iajs-3322	32	7	ψ	ψ	X
iajs-3322	32	8	(	(	PUNCT
iajs-3322	32	9	ⱥ	ⱥ	X
iajs-3322	32	10	)	)	PUNCT
iajs-3322	32	11	⊆	⊆	NUM
iajs-3322	32	12	ψ	ψ	X
iajs-3322	32	13	(	(	PUNCT
iajs-3322	32	14	ɓ	ɓ	NOUN
iajs-3322	32	15	)	)	PUNCT
iajs-3322	32	16	,	,	PUNCT
iajs-3322	32	17	iii	iii	X
iajs-3322	32	18	.	.	PUNCT
iajs-3322	33	1	when	when	SCONJ
iajs-3322	33	2	ⱥ	ⱥ	X
iajs-3322	33	3	⊆	⊆	NUM
iajs-3322	33	4	ꭓ	ꭓ	NUM
iajs-3322	33	5	,	,	PUNCT
iajs-3322	33	6	then	then	ADV
iajs-3322	33	7	ψ	ψ	X
iajs-3322	33	8	(	(	PUNCT
iajs-3322	33	9	ψ	ψ	X
iajs-3322	33	10	(	(	PUNCT
iajs-3322	33	11	ⱥ))=	ⱥ))=	PROPN
iajs-3322	33	12	ψ	ψ	X
iajs-3322	33	13	(	(	PUNCT
iajs-3322	33	14	ⱥ	ⱥ	X
iajs-3322	33	15	)	)	PUNCT
iajs-3322	33	16	,	,	PUNCT
iajs-3322	33	17	iv	iv	X
iajs-3322	33	18	.	.	PUNCT
iajs-3322	34	1	when	when	SCONJ
iajs-3322	34	2	ⱥ	ⱥ	X
iajs-3322	34	3	,	,	PUNCT
iajs-3322	34	4	ɓ	ɓ	PRON
iajs-3322	34	5	⊆	⊆	NUM
iajs-3322	34	6	ꭓ	ꭓ	NUM
iajs-3322	34	7	,	,	PUNCT
iajs-3322	34	8	then	then	ADV
iajs-3322	34	9	ψ	ψ	X
iajs-3322	34	10	(	(	PUNCT
iajs-3322	34	11	ⱥ	ⱥ	X
iajs-3322	34	12	∪	∪	X
iajs-3322	34	13	ɓ)=	ɓ)=	ADJ
iajs-3322	34	14	ψ	ψ	X
iajs-3322	34	15	(	(	PUNCT
iajs-3322	34	16	ⱥ	ⱥ	X
iajs-3322	34	17	)	)	PUNCT
iajs-3322	34	18	∪	∪	NOUN
iajs-3322	34	19	ψ	ψ	X
iajs-3322	34	20	(	(	PUNCT
iajs-3322	34	21	ɓ	ɓ	NOUN
iajs-3322	34	22	)	)	PUNCT
iajs-3322	34	23	.	.	PUNCT
iajs-3322	35	1	definition	definition	NOUN
iajs-3322	35	2	2.2	2.2	NUM
iajs-3322	35	3	:	:	PUNCT
iajs-3322	35	4	(	(	PUNCT
iajs-3322	35	5	13	13	NUM
iajs-3322	35	6	)	)	PUNCT
iajs-3322	35	7	there	there	PRON
iajs-3322	35	8	exists	exist	VERB
iajs-3322	35	9	a	a	DET
iajs-3322	35	10	special	special	ADJ
iajs-3322	35	11	topology	topology	NOUN
iajs-3322	35	12	ʈǥ	ʈǥ	ADV
iajs-3322	35	13	=	=	PUNCT
iajs-3322	35	14	{	{	PUNCT
iajs-3322	35	15	ȗ	ȗ	PRON
iajs-3322	35	16	⊆	⊆	NUM
iajs-3322	35	17	ꭓ	ꭓ	NUM
iajs-3322	35	18	:	:	PUNCT
iajs-3322	35	19	ψ	ψ	X
iajs-3322	35	20	(	(	PUNCT
iajs-3322	35	21	ꭓ	ꭓ	DET
iajs-3322	35	22	−	−	PROPN
iajs-3322	35	23	ȗ	ȗ	NOUN
iajs-3322	35	24	)	)	PUNCT
iajs-3322	35	25	=	=	SYM
iajs-3322	35	26	(	(	PUNCT
iajs-3322	35	27	ꭓ	ꭓ	DET
iajs-3322	35	28	−	−	NOUN
iajs-3322	35	29	ȗ	ȗ	NOUN
iajs-3322	35	30	)	)	PUNCT
iajs-3322	35	31	}	}	PUNCT
iajs-3322	35	32	,	,	PUNCT
iajs-3322	35	33	when	when	SCONJ
iajs-3322	35	34	for	for	ADP
iajs-3322	35	35	any	any	DET
iajs-3322	35	36	ⱥ	ⱥ	PROPN
iajs-3322	35	37	⊆	⊆	NUM
iajs-3322	35	38	ꭓ	ꭓ	NUM
iajs-3322	35	39	that	that	PRON
iajs-3322	35	40	corresponds	correspond	VERB
iajs-3322	35	41	inside	inside	ADP
iajs-3322	35	42	the	the	DET
iajs-3322	35	43	topological	topological	ADJ
iajs-3322	35	44	space	space	NOUN
iajs-3322	35	45	,	,	PUNCT
iajs-3322	35	46	to	to	ADP
iajs-3322	35	47	a	a	DET
iajs-3322	35	48	grill	grill	NOUN
iajs-3322	35	49	ǥ	ǥ	ADP
iajs-3322	35	50	(	(	PUNCT
iajs-3322	35	51	ꭓ	ꭓ	X
iajs-3322	35	52	,	,	PUNCT
iajs-3322	35	53	ʈ	ʈ	NOUN
iajs-3322	35	54	)	)	PUNCT
iajs-3322	35	55	.	.	PUNCT
iajs-3322	36	1	ψ	ψ	X
iajs-3322	36	2	(	(	PUNCT
iajs-3322	36	3	ⱥ	ⱥ	X
iajs-3322	36	4	)	)	PUNCT
iajs-3322	36	5	=	=	SYM
iajs-3322	36	6	ⱥ	ⱥ	X
iajs-3322	36	7	∪	∪	X
iajs-3322	36	8	∯(ⱥ	∯(ⱥ	PROPN
iajs-3322	36	9	)	)	PUNCT
iajs-3322	36	10	=	=	PRON
iajs-3322	36	11	ʈǥҫ𝑙	ʈǥҫ𝑙	ADJ
iajs-3322	36	12	(	(	PUNCT
iajs-3322	36	13	ⱥ	ⱥ	X
iajs-3322	36	14	)	)	PUNCT
iajs-3322	36	15	and	and	CCONJ
iajs-3322	36	16	ʈ	ʈ	ADP
iajs-3322	36	17	⊆	⊆	NUM
iajs-3322	36	18	ʈǥ	ʈǥ	NOUN
iajs-3322	36	19	.	.	PUNCT
iajs-3322	36	20	remark	remark	VERB
iajs-3322	36	21	2.3	2.3	NUM
iajs-3322	36	22	:	:	PUNCT
iajs-3322	36	23	(	(	PUNCT
iajs-3322	36	24	4	4	X
iajs-3322	36	25	)	)	PUNCT
iajs-3322	36	26	if	if	SCONJ
iajs-3322	36	27	ǥ	ǥ	NOUN
iajs-3322	36	28	=	=	SYM
iajs-3322	37	1	ꝕ(ꭓ)/{ǿ	ꝕ(ꭓ)/{ǿ	NUM
iajs-3322	37	2	}	}	PUNCT
iajs-3322	37	3	,	,	PUNCT
iajs-3322	37	4	then	then	ADV
iajs-3322	37	5	ʈǥ.=	ʈǥ.=	PROPN
iajs-3322	37	6	ʈ	ʈ	PROPN
iajs-3322	37	7	.	.	PUNCT
iajs-3322	37	8	remark	remark	NOUN
iajs-3322	37	9	2.4	2.4	NUM
iajs-3322	37	10	:	:	PUNCT
iajs-3322	37	11	(	(	PUNCT
iajs-3322	37	12	2	2	X
iajs-3322	37	13	)	)	PUNCT
iajs-3322	37	14	we	we	PRON
iajs-3322	37	15	can	can	AUX
iajs-3322	37	16	find	find	VERB
iajs-3322	37	17	ʈǥ	ʈǥ	ADV
iajs-3322	37	18	by	by	ADP
iajs-3322	37	19	using	use	VERB
iajs-3322	37	20	the	the	DET
iajs-3322	37	21	base	base	NOUN
iajs-3322	37	22	as	as	SCONJ
iajs-3322	37	23	follows	follow	VERB
iajs-3322	37	24	ℬ(ʈǥ	ℬ(ʈǥ	NOUN
iajs-3322	37	25	,	,	PUNCT
iajs-3322	37	26	ʈ	ʈ	NOUN
iajs-3322	37	27	)	)	PUNCT
iajs-3322	37	28	=	=	SYM
iajs-3322	37	29	{	{	PUNCT
iajs-3322	37	30	ⱱ	ⱱ	PROPN
iajs-3322	37	31	−	−	PROPN
iajs-3322	37	32	ⱥ	ⱥ	NOUN
iajs-3322	37	33	;	;	PUNCT
iajs-3322	37	34	ⱱ	ⱱ	PROPN
iajs-3322	37	35	∈	∈	PROPN
iajs-3322	37	36	ʈ	ʈ	AUX
iajs-3322	37	37	,	,	PUNCT
iajs-3322	37	38	ⱥ	ⱥ	PROPN
iajs-3322	37	39	∉	∉	PROPN
iajs-3322	37	40	ǥ	ǥ	PROPN
iajs-3322	37	41	}	}	PUNCT
iajs-3322	37	42	definition	definition	NOUN
iajs-3322	37	43	2.5:(13	2.5:(13	NUM
iajs-3322	37	44	)	)	PUNCT
iajs-3322	37	45	let	let	VERB
iajs-3322	37	46	ꭓ	ꭓ	PRON
iajs-3322	37	47	≠	≠	PROPN
iajs-3322	37	48	ǿ	ǿ	NOUN
iajs-3322	37	49	and	and	CCONJ
iajs-3322	37	50	ɽ	ɽ	NOUN
iajs-3322	37	51	be	be	VERB
iajs-3322	37	52	an	an	DET
iajs-3322	37	53	equivalence	equivalence	NOUN
iajs-3322	37	54	relation	relation	NOUN
iajs-3322	37	55	on	on	ADP
iajs-3322	37	56	ꭓ	ꭓ	NUM
iajs-3322	37	57	,	,	PUNCT
iajs-3322	37	58	ⱥ	ⱥ	PROPN
iajs-3322	38	1	⊆	⊆	NUM
iajs-3322	38	2	ꭓ	ꭓ	PROPN
iajs-3322	38	3	.	.	PUNCT
iajs-3322	38	4	i.	i.	PROPN
iajs-3322	38	5	the	the	DET
iajs-3322	38	6	upper	upper	ADJ
iajs-3322	38	7	approximation	approximation	NOUN
iajs-3322	38	8	of	of	ADP
iajs-3322	38	9	ⱥ	ⱥ	PRON
iajs-3322	38	10	for	for	ADP
iajs-3322	38	11	ɽ	ɽ	NOUN
iajs-3322	38	12	is	be	AUX
iajs-3322	38	13	denoted	denote	VERB
iajs-3322	38	14	by	by	ADP
iajs-3322	38	15	ɽⱳ	ɽⱳ	PROPN
iajs-3322	38	16	̅̅	̅̅	PROPN
iajs-3322	38	17	̅̅	̅̅	PROPN
iajs-3322	38	18	(	(	PUNCT
iajs-3322	38	19	ⱥ	ⱥ	X
iajs-3322	38	20	)	)	PUNCT
iajs-3322	38	21	,	,	PUNCT
iajs-3322	38	22	where	where	SCONJ
iajs-3322	38	23	ɽⱳ	ɽⱳ	PROPN
iajs-3322	38	24	̅̅	̅̅	PROPN
iajs-3322	38	25	̅̅	̅̅	PROPN
iajs-3322	38	26	(	(	PUNCT
iajs-3322	38	27	ⱥ	ⱥ	X
iajs-3322	38	28	)	)	PUNCT
iajs-3322	38	29	=	=	SYM
iajs-3322	38	30	∪ꭓ∈ꭓ	∪ꭓ∈ꭓ	NOUN
iajs-3322	38	31	{	{	PUNCT
iajs-3322	38	32	ɽ(ꭓ	ɽ(ꭓ	NOUN
iajs-3322	38	33	):	):	PUNCT
iajs-3322	38	34	ɽ(ꭓ	ɽ(ꭓ	NOUN
iajs-3322	38	35	)	)	PUNCT
iajs-3322	38	36	∩	∩	NOUN
iajs-3322	38	37	ⱥ	ⱥ	PROPN
iajs-3322	38	38	≠	≠	PROPN
iajs-3322	38	39	ǿ	ǿ	PROPN
iajs-3322	38	40	}	}	PUNCT
iajs-3322	38	41	.	.	PUNCT
iajs-3322	39	1	ihjpas	ihjpas	PROPN
iajs-3322	39	2	.	.	PUNCT
iajs-3322	40	1	2025	2025	NUM
iajs-3322	40	2	,	,	PUNCT
iajs-3322	40	3	38	38	NUM
iajs-3322	40	4	(	(	PUNCT
iajs-3322	40	5	1	1	NUM
iajs-3322	40	6	)	)	PUNCT
iajs-3322	40	7	361	361	NUM
iajs-3322	40	8	ii	ii	NOUN
iajs-3322	40	9	.	.	PUNCT
iajs-3322	41	1	the	the	DET
iajs-3322	41	2	lower	low	ADJ
iajs-3322	41	3	approximation	approximation	NOUN
iajs-3322	41	4	of	of	ADP
iajs-3322	41	5	ⱥ	ⱥ	PRON
iajs-3322	41	6	for	for	ADP
iajs-3322	41	7	ɽ	ɽ	NOUN
iajs-3322	41	8	is	be	AUX
iajs-3322	41	9	denoted	denote	VERB
iajs-3322	41	10	by	by	ADP
iajs-3322	41	11	ɽⱳ(ⱥ	ɽⱳ(ⱥ	NOUN
iajs-3322	41	12	)	)	PUNCT
iajs-3322	41	13	,	,	PUNCT
iajs-3322	41	14	where	where	SCONJ
iajs-3322	41	15	ɽⱳ(ⱥ	ɽⱳ(ⱥ	PUNCT
iajs-3322	41	16	)	)	PUNCT
iajs-3322	41	17	=	=	SYM
iajs-3322	41	18	∪ꭓ∈ꭓ	∪ꭓ∈ꭓ	NOUN
iajs-3322	41	19	{	{	PUNCT
iajs-3322	41	20	ɽ(ꭓ	ɽ(ꭓ	NOUN
iajs-3322	41	21	):	):	PUNCT
iajs-3322	41	22	ɽ(ꭓ	ɽ(ꭓ	PROPN
iajs-3322	41	23	)	)	PUNCT
iajs-3322	41	24	⊆	⊆	NUM
iajs-3322	41	25	ⱥ	ⱥ	X
iajs-3322	41	26	}	}	PUNCT
iajs-3322	41	27	.	.	PUNCT
iajs-3322	42	1	iii	iii	X
iajs-3322	42	2	.	.	PUNCT
iajs-3322	43	1	the	the	DET
iajs-3322	43	2	boundary	boundary	ADJ
iajs-3322	43	3	region	region	NOUN
iajs-3322	43	4	of	of	ADP
iajs-3322	43	5	ⱥ	ⱥ	PROPN
iajs-3322	43	6	for	for	ADP
iajs-3322	43	7	ɽ	ɽ	NOUN
iajs-3322	43	8	is	be	AUX
iajs-3322	43	9	denoted	denote	VERB
iajs-3322	43	10	by	by	ADP
iajs-3322	43	11	ᴃⱳ(ⱥ	ᴃⱳ(ⱥ	NOUN
iajs-3322	43	12	)	)	PUNCT
iajs-3322	43	13	,	,	PUNCT
iajs-3322	43	14	where	where	SCONJ
iajs-3322	43	15	ᴃⱳ(ⱥ	ᴃⱳ(ⱥ	NUM
iajs-3322	43	16	)	)	PUNCT
iajs-3322	43	17	=	=	SYM
iajs-3322	43	18	ɽⱳ	ɽⱳ	PROPN
iajs-3322	43	19	̅̅	̅̅	PROPN
iajs-3322	43	20	̅̅	̅̅	PROPN
iajs-3322	43	21	(	(	PUNCT
iajs-3322	43	22	ⱥ	ⱥ	NOUN
iajs-3322	43	23	)	)	PUNCT
iajs-3322	43	24	−	−	NOUN
iajs-3322	43	25	ɽⱳ(ⱥ	ɽⱳ(ⱥ	PUNCT
iajs-3322	43	26	)	)	PUNCT
iajs-3322	43	27	.	.	PUNCT
iajs-3322	44	1	definition	definition	NOUN
iajs-3322	44	2	2.6:(7	2.6:(7	NUM
iajs-3322	44	3	)	)	PUNCT
iajs-3322	44	4	,	,	PUNCT
iajs-3322	44	5	(	(	PUNCT
iajs-3322	44	6	16	16	X
iajs-3322	44	7	)	)	PUNCT
iajs-3322	44	8	let	let	AUX
iajs-3322	44	9	ꭓ≠	ꭓ≠	VERB
iajs-3322	44	10	ǿ	ǿ	NOUN
iajs-3322	44	11	and	and	CCONJ
iajs-3322	44	12	ɽ	ɽ	NOUN
iajs-3322	44	13	be	be	AUX
iajs-3322	44	14	an	an	DET
iajs-3322	44	15	equivalence	equivalence	NOUN
iajs-3322	44	16	relation	relation	NOUN
iajs-3322	44	17	on	on	ADP
iajs-3322	44	18	ꭓ	ꭓ	NUM
iajs-3322	44	19	and	and	CCONJ
iajs-3322	44	20	ʈⱳ(ⱥ	ʈⱳ(ⱥ	NUM
iajs-3322	44	21	)	)	PUNCT
iajs-3322	44	22	=	=	PRON
iajs-3322	44	23	{	{	PUNCT
iajs-3322	44	24	ꭓ	ꭓ	PROPN
iajs-3322	44	25	,	,	PUNCT
iajs-3322	44	26	ǿ	ǿ	PROPN
iajs-3322	44	27	,	,	PUNCT
iajs-3322	44	28	ɽⱳ	ɽⱳ	PROPN
iajs-3322	44	29	̅̅	̅̅	PROPN
iajs-3322	44	30	̅̅	̅̅	PROPN
iajs-3322	44	31	(	(	PUNCT
iajs-3322	44	32	ⱥ	ⱥ	NOUN
iajs-3322	44	33	)	)	PUNCT
iajs-3322	44	34	,	,	PUNCT
iajs-3322	44	35	ɽⱳ(ⱥ	ɽⱳ(ⱥ	PROPN
iajs-3322	44	36	)	)	PUNCT
iajs-3322	44	37	,	,	PUNCT
iajs-3322	44	38	ᴃⱳ(ⱥ	ᴃⱳ(ⱥ	NUM
iajs-3322	44	39	)	)	PUNCT
iajs-3322	44	40	}	}	PUNCT
iajs-3322	44	41	,	,	PUNCT
iajs-3322	44	42	where	where	SCONJ
iajs-3322	44	43	ⱥ	ⱥ	PROPN
iajs-3322	44	44	⊆	⊆	NUM
iajs-3322	44	45	ꭓ	ꭓ	PROPN
iajs-3322	44	46	.	.	PUNCT
iajs-3322	45	1	then	then	ADV
iajs-3322	45	2	ʈⱳ(ⱥ	ʈⱳ(ⱥ	NUM
iajs-3322	45	3	)	)	PUNCT
iajs-3322	45	4	is	be	AUX
iajs-3322	45	5	a	a	DET
iajs-3322	45	6	topology	topology	NOUN
iajs-3322	45	7	on	on	ADP
iajs-3322	45	8	ꭓ	ꭓ	PROPN
iajs-3322	45	9	named	name	VERB
iajs-3322	45	10	nano	nano	NOUN
iajs-3322	45	11	topology	topology	NOUN
iajs-3322	45	12	for	for	ADP
iajs-3322	45	13	ⱥ	ⱥ	PROPN
iajs-3322	45	14	(	(	PUNCT
iajs-3322	45	15	ꭓ	ꭓ	NUM
iajs-3322	45	16	,	,	PUNCT
iajs-3322	45	17	ʈⱳ(ⱥ	ʈⱳ(ⱥ	NUM
iajs-3322	45	18	)	)	PUNCT
iajs-3322	45	19	space	space	NOUN
iajs-3322	45	20	is	be	AUX
iajs-3322	45	21	known	know	VERB
iajs-3322	45	22	as	as	ADP
iajs-3322	45	23	nano	nano	NOUN
iajs-3322	45	24	topological	topological	ADJ
iajs-3322	45	25	.	.	PUNCT
iajs-3322	46	1	the	the	DET
iajs-3322	46	2	components	component	NOUN
iajs-3322	46	3	of	of	ADP
iajs-3322	46	4	ʈⱳ(ⱥ	ʈⱳ(ⱥ	NOUN
iajs-3322	46	5	)	)	PUNCT
iajs-3322	46	6	are	be	AUX
iajs-3322	46	7	named	name	VERB
iajs-3322	46	8	nano	nano	NOUN
iajs-3322	46	9	-	-	PUNCT
iajs-3322	46	10	open	open	ADJ
iajs-3322	46	11	sets	set	NOUN
iajs-3322	46	12	denoted	denote	VERB
iajs-3322	46	13	by	by	ADP
iajs-3322	46	14	ƞ	ƞ	NOUN
iajs-3322	46	15	−	−	PROPN
iajs-3322	46	16	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	46	17	𝑠𝑒𝑡𝑠.	𝑠𝑒𝑡𝑠.	VERB
iajs-3322	46	18	the	the	DET
iajs-3322	46	19	complement	complement	NOUN
iajs-3322	46	20	of	of	ADP
iajs-3322	46	21	a	a	DET
iajs-3322	46	22	ƞ	ƞ	NOUN
iajs-3322	46	23	−	−	PROPN
iajs-3322	46	24	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	46	25	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	NOUN
iajs-3322	46	26	is	be	AUX
iajs-3322	46	27	named	name	VERB
iajs-3322	46	28	a	a	DET
iajs-3322	46	29	nano	nano	NOUN
iajs-3322	46	30	-	-	PUNCT
iajs-3322	46	31	closed	close	VERB
iajs-3322	46	32	set	set	NOUN
iajs-3322	46	33	denoted	denote	VERB
iajs-3322	46	34	by	by	ADP
iajs-3322	46	35	ƞ	ƞ	PRON
iajs-3322	46	36	−	−	PROPN
iajs-3322	46	37	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-3322	46	38	𝑠𝑒𝑡𝑠.	𝑠𝑒𝑡𝑠.	NOUN
iajs-3322	46	39	definition	definition	NOUN
iajs-3322	46	40	2.7:(7	2.7:(7	NOUN
iajs-3322	46	41	)	)	PUNCT
iajs-3322	46	42	let	let	VERB
iajs-3322	46	43	(	(	PUNCT
iajs-3322	46	44	ꭓ	ꭓ	NUM
iajs-3322	46	45	,	,	PUNCT
iajs-3322	46	46	ʈⱳ	ʈⱳ	NOUN
iajs-3322	46	47	)	)	PUNCT
iajs-3322	46	48	be	be	VERB
iajs-3322	46	49	n.t.s	n.t.s	ADJ
iajs-3322	46	50	(	(	PUNCT
iajs-3322	46	51	nano	nano	NOUN
iajs-3322	46	52	topological	topological	ADJ
iajs-3322	46	53	space	space	NOUN
iajs-3322	46	54	)	)	PUNCT
iajs-3322	46	55	and	and	CCONJ
iajs-3322	46	56	ⱥ	ⱥ	VERB
iajs-3322	46	57	⊆	⊆	NUM
iajs-3322	46	58	ꭓ	ꭓ	NOUN
iajs-3322	46	59	.	.	PUNCT
iajs-3322	47	1	the	the	DET
iajs-3322	47	2	nano	nano	NOUN
iajs-3322	47	3	closure	closure	NOUN
iajs-3322	47	4	(	(	PUNCT
iajs-3322	47	5	respectively	respectively	ADV
iajs-3322	47	6	,	,	PUNCT
iajs-3322	47	7	nano	nano	NOUN
iajs-3322	47	8	interior	interior	NOUN
iajs-3322	47	9	)	)	PUNCT
iajs-3322	47	10	of	of	ADP
iajs-3322	47	11	ⱥ	ⱥ	PRON
iajs-3322	47	12	which	which	PRON
iajs-3322	47	13	is	be	AUX
iajs-3322	47	14	short	short	ADJ
iajs-3322	47	15	ƞҫ𝑙ⱳ(ⱥ	ƞҫ𝑙ⱳ(ⱥ	NOUN
iajs-3322	47	16	)	)	PUNCT
iajs-3322	47	17	(	(	PUNCT
iajs-3322	47	18	respectively	respectively	ADV
iajs-3322	47	19	,	,	PUNCT
iajs-3322	47	20	ƞ𝑖𝑛𝑡ⱳ(ⱥ	ƞ𝑖𝑛𝑡ⱳ(ⱥ	NOUN
iajs-3322	47	21	)	)	PUNCT
iajs-3322	47	22	)	)	PUNCT
iajs-3322	47	23	is	be	AUX
iajs-3322	47	24	defined	define	VERB
iajs-3322	47	25	by	by	ADP
iajs-3322	47	26	;	;	PUNCT
iajs-3322	47	27	ƞҫ𝑙ⱳ(ⱥ	ƞҫ𝑙ⱳ(ⱥ	NUM
iajs-3322	47	28	)	)	PUNCT
iajs-3322	47	29	=	=	NOUN
iajs-3322	47	30	∩	∩	NOUN
iajs-3322	47	31	{	{	PUNCT
iajs-3322	47	32	ℱ	ℱ	PROPN
iajs-3322	47	33	,	,	PUNCT
iajs-3322	47	34	ℱҫ	ℱҫ	PROPN
iajs-3322	47	35	∈	∈	PROPN
iajs-3322	47	36	ʈⱳ	ʈⱳ	PROPN
iajs-3322	47	37	,	,	PUNCT
iajs-3322	47	38	ⱥ	ⱥ	PROPN
iajs-3322	47	39	⊆	⊆	NUM
iajs-3322	47	40	ℱ	ℱ	PROPN
iajs-3322	47	41	}	}	PUNCT
iajs-3322	47	42	,	,	PUNCT
iajs-3322	47	43	(	(	PUNCT
iajs-3322	47	44	resp	resp	NOUN
iajs-3322	47	45	.	.	PUNCT
iajs-3322	47	46	,	,	PUNCT
iajs-3322	47	47	ƞ𝑖𝑛𝑡ⱳ(ⱥ	ƞ𝑖𝑛𝑡ⱳ(ⱥ	NOUN
iajs-3322	47	48	)	)	PUNCT
iajs-3322	47	49	)	)	PUNCT
iajs-3322	48	1	=	=	SYM
iajs-3322	48	2	ƞ𝑖𝑛𝑡ⱳ(ⱥ	ƞ𝑖𝑛𝑡ⱳ(ⱥ	NOUN
iajs-3322	48	3	)	)	PUNCT
iajs-3322	48	4	=	=	SYM
iajs-3322	48	5	{	{	PUNCT
iajs-3322	48	6	ȗ	ȗ	PROPN
iajs-3322	48	7	;	;	PUNCT
iajs-3322	48	8	ȗ	ȗ	PROPN
iajs-3322	48	9	∈	∈	PROPN
iajs-3322	48	10	ʈⱳ	ʈⱳ	PROPN
iajs-3322	48	11	,	,	PUNCT
iajs-3322	48	12	ȗ	ȗ	PRON
iajs-3322	48	13	∈	∈	PROPN
iajs-3322	48	14	ⱥ	ⱥ	X
iajs-3322	48	15	}	}	PUNCT
iajs-3322	48	16	.	.	PUNCT
iajs-3322	49	1	note	note	VERB
iajs-3322	49	2	8	8	NUM
iajs-3322	49	3	:	:	PUNCT
iajs-3322	49	4	we	we	PRON
iajs-3322	49	5	said	say	VERB
iajs-3322	49	6	the	the	DET
iajs-3322	49	7	triple	triple	ADJ
iajs-3322	49	8	(	(	PUNCT
iajs-3322	49	9	ꭓ	ꭓ	NUM
iajs-3322	49	10	,	,	PUNCT
iajs-3322	49	11	ʈⱳ	ʈⱳ	NOUN
iajs-3322	49	12	,	,	PUNCT
iajs-3322	49	13	ǥ	ǥ	NOUN
iajs-3322	49	14	)	)	PUNCT
iajs-3322	49	15	g.n.t.s	g.n.t.s	NOUN
iajs-3322	49	16	(	(	PUNCT
iajs-3322	49	17	grill	grill	NOUN
iajs-3322	49	18	nano	nano	NOUN
iajs-3322	49	19	topological	topological	ADJ
iajs-3322	49	20	space	space	NOUN
iajs-3322	49	21	)	)	PUNCT
iajs-3322	49	22	..	..	PUNCT
iajs-3322	50	1	definition	definition	NOUN
iajs-3322	50	2	2.9:(7	2.9:(7	NUM
iajs-3322	50	3	)	)	PUNCT
iajs-3322	50	4	let	let	VERB
iajs-3322	50	5	(	(	PUNCT
iajs-3322	50	6	ꭓ	ꭓ	NUM
iajs-3322	50	7	,	,	PUNCT
iajs-3322	50	8	ʈⱳ	ʈⱳ	NOUN
iajs-3322	50	9	)	)	PUNCT
iajs-3322	50	10	be	be	VERB
iajs-3322	50	11	an	an	DET
iajs-3322	50	12	n.t.s	n.t.s	NOUN
iajs-3322	50	13	,	,	PUNCT
iajs-3322	50	14	a	a	DET
iajs-3322	50	15	subset	subset	NOUN
iajs-3322	50	16	ⱥ	ⱥ	X
iajs-3322	50	17	of	of	ADP
iajs-3322	50	18	ꭓ	ꭓ	PROPN
iajs-3322	50	19	is	be	AUX
iajs-3322	50	20	named	name	VERB
iajs-3322	50	21	n.s.o	n.s.o	ADJ
iajs-3322	50	22	(	(	PUNCT
iajs-3322	50	23	nano	nano	NOUN
iajs-3322	50	24	semi	semi	ADJ
iajs-3322	50	25	-	-	ADJ
iajs-3322	50	26	open	open	ADJ
iajs-3322	50	27	set	set	NOUN
iajs-3322	50	28	)	)	PUNCT
iajs-3322	50	29	ⱥ	ⱥ	PROPN
iajs-3322	50	30	⊆	⊆	NUM
iajs-3322	50	31	ƞҫ𝑙ⱳ(ƞ𝑖𝑛𝑡ⱳ(ⱥ	ƞҫ𝑙ⱳ(ƞ𝑖𝑛𝑡ⱳ(ⱥ	NUM
iajs-3322	50	32	)	)	PUNCT
iajs-3322	50	33	)	)	PUNCT
iajs-3322	51	1	⟺	⟺	DET
iajs-3322	51	2	∃ȗ	∃ȗ	PROPN
iajs-3322	51	3	∈	∈	PROPN
iajs-3322	51	4	ʈⱳ	ʈⱳ	NOUN
iajs-3322	51	5	;	;	PUNCT
iajs-3322	51	6	ȗ	ȗ	PRON
iajs-3322	51	7	⊆	⊆	NUM
iajs-3322	51	8	ⱥ	ⱥ	PROPN
iajs-3322	51	9	⊆	⊆	NUM
iajs-3322	51	10	ƞҫ𝑙ⱳ(ȗ	ƞҫ𝑙ⱳ(ȗ	NOUN
iajs-3322	51	11	)	)	PUNCT
iajs-3322	51	12	.	.	PUNCT
iajs-3322	52	1	ⱥ	ⱥ	PROPN
iajs-3322	52	2	subset	subset	VERB
iajs-3322	52	3	ɓ	ɓ	PRON
iajs-3322	52	4	of	of	ADP
iajs-3322	52	5	ꭓ	ꭓ	PROPN
iajs-3322	52	6	is	be	AUX
iajs-3322	52	7	called	call	VERB
iajs-3322	52	8	𝑛𝑎𝑛𝑜	𝑛𝑎𝑛𝑜	ADJ
iajs-3322	52	9	semi	semi	ADV
iajs-3322	52	10	-	-	ADJ
iajs-3322	52	11	closed	closed	ADJ
iajs-3322	52	12	if	if	SCONJ
iajs-3322	52	13	(	(	PUNCT
iajs-3322	52	14	ꭓ	ꭓ	NUM
iajs-3322	52	15	-	-	PUNCT
iajs-3322	52	16	ɓ	ɓ	NOUN
iajs-3322	52	17	)	)	PUNCT
iajs-3322	52	18	is	be	AUX
iajs-3322	52	19	n.s.o	n.s.o	NOUN
iajs-3322	52	20	set	set	VERB
iajs-3322	52	21	the	the	DET
iajs-3322	52	22	collection	collection	NOUN
iajs-3322	52	23	of	of	ADP
iajs-3322	52	24	all	all	DET
iajs-3322	52	25	n.s.o	n.s.o	ADJ
iajs-3322	52	26	(	(	PUNCT
iajs-3322	52	27	respectively	respectively	ADV
iajs-3322	52	28	,	,	PUNCT
iajs-3322	52	29	n.s.c	n.s.c	ADJ
iajs-3322	52	30	)	)	PUNCT
iajs-3322	52	31	sets	set	NOUN
iajs-3322	52	32	in	in	ADP
iajs-3322	52	33	a	a	DET
iajs-3322	52	34	nano	nano	ADJ
iajs-3322	52	35	topological	topological	ADJ
iajs-3322	52	36	space	space	NOUN
iajs-3322	52	37	(	(	PUNCT
iajs-3322	52	38	ꭓ	ꭓ	PROPN
iajs-3322	52	39	,	,	PUNCT
iajs-3322	52	40	ʈⱳ	ʈⱳ	NOUN
iajs-3322	52	41	)	)	PUNCT
iajs-3322	52	42	.	.	PUNCT
iajs-3322	53	1	will	will	AUX
iajs-3322	53	2	be	be	AUX
iajs-3322	53	3	symbolized	symbolize	VERB
iajs-3322	53	4	by	by	ADP
iajs-3322	53	5	ƞşỏ(ꭓ	ƞşỏ(ꭓ	PROPN
iajs-3322	53	6	)	)	PUNCT
iajs-3322	53	7	(	(	PUNCT
iajs-3322	53	8	respectively	respectively	ADV
iajs-3322	53	9	,	,	PUNCT
iajs-3322	53	10	ƞǥşҫ(ꭓ	ƞǥşҫ(ꭓ	NOUN
iajs-3322	53	11	)	)	PUNCT
iajs-3322	53	12	.	.	PUNCT
iajs-3322	54	1	definition	definition	NOUN
iajs-3322	54	2	2.10:(17	2.10:(17	NUM
iajs-3322	54	3	)	)	PUNCT
iajs-3322	54	4	there	there	PRON
iajs-3322	54	5	exists	exist	VERB
iajs-3322	54	6	a	a	DET
iajs-3322	54	7	special	special	ADJ
iajs-3322	54	8	topology	topology	NOUN
iajs-3322	54	9	ƞʈⱳǥ	ƞʈⱳǥ	NOUN
iajs-3322	54	10	=	=	PRON
iajs-3322	54	11	{	{	PUNCT
iajs-3322	54	12	ȗ	ȗ	PROPN
iajs-3322	54	13	⊆	⊆	NUM
iajs-3322	54	14	ꭓ	ꭓ	NUM
iajs-3322	54	15	:	:	PUNCT
iajs-3322	54	16	ψ	ψ	X
iajs-3322	54	17	(	(	PUNCT
iajs-3322	54	18	ꭓ	ꭓ	DET
iajs-3322	54	19	−	−	PROPN
iajs-3322	54	20	ȗ	ȗ	NOUN
iajs-3322	54	21	)	)	PUNCT
iajs-3322	54	22	=	=	SYM
iajs-3322	54	23	(	(	PUNCT
iajs-3322	54	24	ꭓ	ꭓ	DET
iajs-3322	54	25	−	−	NOUN
iajs-3322	54	26	ȗ	ȗ	NOUN
iajs-3322	54	27	)	)	PUNCT
iajs-3322	54	28	}	}	PUNCT
iajs-3322	54	29	,	,	PUNCT
iajs-3322	54	30	when	when	SCONJ
iajs-3322	54	31	for	for	ADP
iajs-3322	54	32	any	any	DET
iajs-3322	54	33	ⱥ	ⱥ	PROPN
iajs-3322	54	34	⊆	⊆	NUM
iajs-3322	54	35	ꭓ	ꭓ	PROPN
iajs-3322	54	36	that	that	PRON
iajs-3322	54	37	corresponds	correspond	VERB
iajs-3322	54	38	to	to	ADP
iajs-3322	54	39	a	a	DET
iajs-3322	54	40	nano	nano	NOUN
iajs-3322	54	41	grill	grill	NOUN
iajs-3322	54	42	ǥ	ǥ	ADP
iajs-3322	54	43	on	on	ADP
iajs-3322	54	44	the	the	DET
iajs-3322	54	45	topological	topological	ADJ
iajs-3322	54	46	space	space	NOUN
iajs-3322	54	47	(	(	PUNCT
iajs-3322	54	48	ꭓ	ꭓ	PROPN
iajs-3322	54	49	,	,	PUNCT
iajs-3322	54	50	ʈⱳ	ʈⱳ	NOUN
iajs-3322	54	51	)	)	PUNCT
iajs-3322	54	52	.	.	PUNCT
iajs-3322	55	1	ψ	ψ	X
iajs-3322	55	2	(	(	PUNCT
iajs-3322	55	3	ⱥ	ⱥ	X
iajs-3322	55	4	)	)	PUNCT
iajs-3322	55	5	=	=	SYM
iajs-3322	55	6	ⱥ	ⱥ	X
iajs-3322	55	7	∪	∪	X
iajs-3322	55	8	∯(ⱥ	∯(ⱥ	PROPN
iajs-3322	55	9	)	)	PUNCT
iajs-3322	56	1	=	=	SYM
iajs-3322	56	2	ƞʈⱳǥҫ𝑙	ƞʈⱳǥҫ𝑙	NOUN
iajs-3322	56	3	(	(	PUNCT
iajs-3322	56	4	ⱥ	ⱥ	X
iajs-3322	56	5	)	)	PUNCT
iajs-3322	56	6	and	and	CCONJ
iajs-3322	56	7	ʈⱳ	ʈⱳ	X
iajs-3322	56	8	⊆	⊆	NUM
iajs-3322	56	9	ƞʈⱳǥ	ƞʈⱳǥ	NOUN
iajs-3322	56	10	.	.	PUNCT
iajs-3322	57	1	definition	definition	NOUN
iajs-3322	57	2	2.11	2.11	NUM
iajs-3322	57	3	:	:	PUNCT
iajs-3322	57	4	let	let	AUX
iajs-3322	57	5	(	(	PUNCT
iajs-3322	57	6	ꭓ	ꭓ	NUM
iajs-3322	57	7	,	,	PUNCT
iajs-3322	57	8	ʈⱳ	ʈⱳ	NOUN
iajs-3322	57	9	)	)	PUNCT
iajs-3322	57	10	be	be	AUX
iajs-3322	57	11	n.t.s	n.t.s	ADJ
iajs-3322	57	12	and	and	CCONJ
iajs-3322	57	13	ⱥ	ⱥ	PRON
iajs-3322	57	14	⊆	⊆	NUM
iajs-3322	57	15	ꭓ	ꭓ	NOUN
iajs-3322	57	16	.	.	PUNCT
iajs-3322	58	1	the	the	DET
iajs-3322	58	2	nano	nano	NOUN
iajs-3322	58	3	closure	closure	NOUN
iajs-3322	58	4	(	(	PUNCT
iajs-3322	58	5	respectively	respectively	ADV
iajs-3322	58	6	,	,	PUNCT
iajs-3322	58	7	nano	nano	NOUN
iajs-3322	58	8	interior	interior	NOUN
iajs-3322	58	9	)	)	PUNCT
iajs-3322	58	10	of	of	ADP
iajs-3322	58	11	ⱥ	ⱥ	PRON
iajs-3322	58	12	which	which	PRON
iajs-3322	58	13	is	be	AUX
iajs-3322	58	14	short	short	ADJ
iajs-3322	58	15	ƞҫ𝑙ⱳ(ⱥ	ƞҫ𝑙ⱳ(ⱥ	NOUN
iajs-3322	58	16	)	)	PUNCT
iajs-3322	58	17	(	(	PUNCT
iajs-3322	58	18	respectively	respectively	ADV
iajs-3322	58	19	,	,	PUNCT
iajs-3322	58	20	ƞ𝑖𝑛𝑡ⱳ(ⱥ	ƞ𝑖𝑛𝑡ⱳ(ⱥ	NOUN
iajs-3322	58	21	)	)	PUNCT
iajs-3322	58	22	)	)	PUNCT
iajs-3322	58	23	is	be	AUX
iajs-3322	58	24	defined	define	VERB
iajs-3322	58	25	by	by	ADP
iajs-3322	58	26	;	;	PUNCT
iajs-3322	58	27	ƞҫ𝑙ⱳǥ(ⱥ	ƞҫ𝑙ⱳǥ(ⱥ	NUM
iajs-3322	58	28	)	)	PUNCT
iajs-3322	58	29	=	=	NOUN
iajs-3322	58	30	∩	∩	NOUN
iajs-3322	58	31	{	{	PUNCT
iajs-3322	58	32	ℱ	ℱ	PROPN
iajs-3322	58	33	,	,	PUNCT
iajs-3322	58	34	ℱҫ	ℱҫ	PROPN
iajs-3322	58	35	∈	∈	PROPN
iajs-3322	58	36	ʈⱳ	ʈⱳ	PROPN
iajs-3322	58	37	,	,	PUNCT
iajs-3322	58	38	ⱥ	ⱥ	PROPN
iajs-3322	58	39	⊆	⊆	NUM
iajs-3322	58	40	ℱ	ℱ	PROPN
iajs-3322	58	41	}	}	PUNCT
iajs-3322	58	42	,	,	PUNCT
iajs-3322	58	43	(	(	PUNCT
iajs-3322	58	44	resp	resp	NOUN
iajs-3322	58	45	.	.	PUNCT
iajs-3322	58	46	,	,	PUNCT
iajs-3322	58	47	ƞ𝑖𝑛𝑡ⱳǥ(ⱥ	ƞ𝑖𝑛𝑡ⱳǥ(ⱥ	PROPN
iajs-3322	58	48	)	)	PUNCT
iajs-3322	58	49	)	)	PUNCT
iajs-3322	59	1	=	=	SYM
iajs-3322	59	2	ƞ𝑖𝑛𝑡ⱳǥ(ⱥ	ƞ𝑖𝑛𝑡ⱳǥ(ⱥ	PROPN
iajs-3322	59	3	)	)	PUNCT
iajs-3322	59	4	=	=	PUNCT
iajs-3322	59	5	{	{	PUNCT
iajs-3322	59	6	ȗ	ȗ	PROPN
iajs-3322	59	7	;	;	PUNCT
iajs-3322	59	8	ȗ	ȗ	PROPN
iajs-3322	59	9	∈	∈	PROPN
iajs-3322	59	10	ʈⱳ	ʈⱳ	PROPN
iajs-3322	59	11	,	,	PUNCT
iajs-3322	59	12	ȗ	ȗ	PRON
iajs-3322	59	13	∈	∈	PROPN
iajs-3322	59	14	ⱥ	ⱥ	X
iajs-3322	59	15	}	}	PUNCT
iajs-3322	59	16	.	.	PUNCT
iajs-3322	60	1	definition	definition	NOUN
iajs-3322	60	2	2.12	2.12	NUM
iajs-3322	60	3	:	:	PUNCT
iajs-3322	60	4	(	(	PUNCT
iajs-3322	60	5	18	18	NUM
iajs-3322	60	6	)	)	PUNCT
iajs-3322	60	7	,	,	PUNCT
iajs-3322	60	8	(	(	PUNCT
iajs-3322	60	9	19	19	NUM
iajs-3322	60	10	)	)	PUNCT
iajs-3322	60	11	,	,	PUNCT
iajs-3322	60	12	(	(	PUNCT
iajs-3322	60	13	20	20	X
iajs-3322	60	14	)	)	PUNCT
iajs-3322	60	15	a	a	DET
iajs-3322	60	16	topological	topological	ADJ
iajs-3322	60	17	spaces	space	NOUN
iajs-3322	60	18	(	(	PUNCT
iajs-3322	60	19	ꭓ	ꭓ	NUM
iajs-3322	60	20	,	,	PUNCT
iajs-3322	60	21	ʈⱳ	ʈⱳ	NOUN
iajs-3322	60	22	,	,	PUNCT
iajs-3322	60	23	ǥ	ǥ	NOUN
iajs-3322	60	24	)	)	PUNCT
iajs-3322	60	25	is	be	AUX
iajs-3322	60	26	named	name	VERB
iajs-3322	60	27	nano	nano	ADJ
iajs-3322	60	28	compact	compact	ADJ
iajs-3322	60	29	space	space	NOUN
iajs-3322	60	30	if	if	SCONJ
iajs-3322	60	31	and	and	CCONJ
iajs-3322	60	32	only	only	ADV
iajs-3322	60	33	if	if	SCONJ
iajs-3322	60	34	all	all	DET
iajs-3322	60	35	nano	nano	VERB
iajs-3322	60	36	open	open	ADJ
iajs-3322	60	37	cover	cover	NOUN
iajs-3322	60	38	of	of	ADP
iajs-3322	60	39	ꭓ	ꭓ	PROPN
iajs-3322	60	40	has	have	VERB
iajs-3322	60	41	a	a	DET
iajs-3322	60	42	finite	finite	ADJ
iajs-3322	60	43	subcover	subcover	PROPN
iajs-3322	60	44	..	..	PROPN
iajs-3322	61	1	3	3	X
iajs-3322	61	2	.	.	X
iajs-3322	61	3	nano	nano	NOUN
iajs-3322	61	4	gr𝐢ll	gr𝐢ll	VERB
iajs-3322	61	5	sem𝐢-open	sem𝐢-open	ADJ
iajs-3322	61	6	sets	set	NOUN
iajs-3322	61	7	in	in	ADP
iajs-3322	61	8	nano	nano	NOUN
iajs-3322	61	9	c𝐨mpact	c𝐨mpact	NOUN
iajs-3322	61	10	space	space	NOUN
iajs-3322	61	11	definition	definition	NOUN
iajs-3322	61	12	3.𝟏	3.𝟏	NUM
iajs-3322	61	13	:	:	PUNCT
iajs-3322	61	14	for	for	ADP
iajs-3322	61	15	any	any	DET
iajs-3322	61	16	grill	grill	ADJ
iajs-3322	61	17	topological	topological	ADJ
iajs-3322	61	18	space	space	NOUN
iajs-3322	61	19	(	(	PUNCT
iajs-3322	61	20	ꭓ	ꭓ	NUM
iajs-3322	61	21	,	,	PUNCT
iajs-3322	61	22	ʈ𝐺	ʈ𝐺	NOUN
iajs-3322	61	23	)	)	PUNCT
iajs-3322	61	24	and	and	CCONJ
iajs-3322	61	25	ⱥ⊑	ⱥ⊑	NOUN
iajs-3322	61	26	ꭓ	ꭓ	X
iajs-3322	61	27	;	;	PUNCT
iajs-3322	61	28	ⱥis	ⱥis	NOUN
iajs-3322	61	29	said	say	VERB
iajs-3322	61	30	to	to	PART
iajs-3322	61	31	be	be	AUX
iajs-3322	61	32	nano	nano	NOUN
iajs-3322	61	33	grill	grill	NOUN
iajs-3322	61	34	semi	semi	ADJ
iajs-3322	61	35	-	-	ADJ
iajs-3322	61	36	open	open	ADJ
iajs-3322	61	37	if	if	SCONJ
iajs-3322	61	38	there	there	PRON
iajs-3322	61	39	exists	exist	VERB
iajs-3322	61	40	ȗ	ȗ	SYM
iajs-3322	61	41	∈	∈	PROPN
iajs-3322	61	42	ʈⱳ	ʈⱳ	X
iajs-3322	61	43	;	;	PUNCT
iajs-3322	61	44	ȗ	ȗ	PROPN
iajs-3322	61	45	−	−	PROPN
iajs-3322	61	46	ⱥ	ⱥ	X
iajs-3322	61	47	∉	∉	X
iajs-3322	61	48	ǥ	ǥ	PROPN
iajs-3322	61	49	and	and	CCONJ
iajs-3322	61	50	ⱥ	ⱥ	X
iajs-3322	61	51	−	−	PROPN
iajs-3322	61	52	ƞҫ𝑙ⱳǥ(ȗ	ƞҫ𝑙ⱳǥ(ȗ	PROPN
iajs-3322	61	53	)	)	PUNCT
iajs-3322	61	54	∉	∉	PROPN
iajs-3322	62	1	ǥ	ǥ	ADP
iajs-3322	62	2	.and	.and	PUNCT
iajs-3322	63	1	ⱥ	ⱥ	PROPN
iajs-3322	63	2	denoted	denote	VERB
iajs-3322	63	3	by	by	ADP
iajs-3322	63	4	ƞǥş	ƞǥş	NOUN
iajs-3322	63	5	-	-	PUNCT
iajs-3322	63	6	open	open	ADJ
iajs-3322	63	7	.	.	PUNCT
iajs-3322	64	1	ꭓ	ꭓ	PRON
iajs-3322	64	2	−	−	NOUN
iajs-3322	64	3	ⱥ	ⱥ	PROPN
iajs-3322	64	4	is	be	AUX
iajs-3322	64	5	a	a	DET
iajs-3322	64	6	nano	nano	NOUN
iajs-3322	64	7	grill	grill	NOUN
iajs-3322	64	8	semi	semi	ADJ
iajs-3322	64	9	-	-	ADJ
iajs-3322	64	10	closed	closed	ADJ
iajs-3322	64	11	and	and	CCONJ
iajs-3322	64	12	denoted	denote	VERB
iajs-3322	64	13	by	by	ADP
iajs-3322	64	14	ƞǥş	ƞǥş	NOUN
iajs-3322	64	15	-semi	-semi	NOUN
iajs-3322	64	16	-	-	PUNCT
iajs-3322	64	17	closed	close	VERB
iajs-3322	64	18	and	and	CCONJ
iajs-3322	64	19	the	the	DET
iajs-3322	64	20	set	set	NOUN
iajs-3322	64	21	of	of	ADP
iajs-3322	64	22	all	all	DET
iajs-3322	64	23	ƞǥş	ƞǥş	NOUN
iajs-3322	64	24	-open	-open	NOUN
iajs-3322	64	25	presently	presently	ADV
iajs-3322	64	26	by	by	ADP
iajs-3322	64	27	ihjpas	ihjpa	NOUN
iajs-3322	64	28	.	.	PUNCT
iajs-3322	65	1	2025	2025	NUM
iajs-3322	65	2	,	,	PUNCT
iajs-3322	65	3	38	38	NUM
iajs-3322	65	4	(	(	PUNCT
iajs-3322	65	5	1	1	NUM
iajs-3322	65	6	)	)	PUNCT
iajs-3322	65	7	362	362	NUM
iajs-3322	65	8	ƞǥşỏ	ƞǥşỏ	NOUN
iajs-3322	65	9	(	(	PUNCT
iajs-3322	65	10	ꭓ	ꭓ	X
iajs-3322	65	11	)	)	PUNCT
iajs-3322	65	12	and	and	CCONJ
iajs-3322	65	13	the	the	DET
iajs-3322	65	14	set	set	NOUN
iajs-3322	65	15	of	of	ADP
iajs-3322	65	16	all	all	DET
iajs-3322	65	17	ƞǥş	ƞǥş	NOUN
iajs-3322	65	18	-	-	PUNCT
iajs-3322	65	19	semi	semi	ADV
iajs-3322	65	20	-	-	ADJ
iajs-3322	65	21	closed	closed	ADJ
iajs-3322	65	22	presently	presently	ADV
iajs-3322	65	23	by	by	ADP
iajs-3322	65	24	ƞǥşҫ(ꭓ	ƞǥşҫ(ꭓ	NOUN
iajs-3322	65	25	)	)	PUNCT
iajs-3322	65	26	.	.	PUNCT
iajs-3322	66	1	eҳample	eҳample	ADJ
iajs-3322	66	2	3.2	3.2	NUM
iajs-3322	66	3	:	:	PUNCT
iajs-3322	66	4	let	let	AUX
iajs-3322	66	5	(	(	PUNCT
iajs-3322	66	6	ꭓ	ꭓ	NUM
iajs-3322	66	7	,	,	PUNCT
iajs-3322	66	8	ʈⱳ	ʈⱳ	NOUN
iajs-3322	66	9	,	,	PUNCT
iajs-3322	66	10	ǥ	ǥ	NOUN
iajs-3322	66	11	)	)	PUNCT
iajs-3322	66	12	be	be	AUX
iajs-3322	66	13	a	a	DET
iajs-3322	66	14	nano	nano	NOUN
iajs-3322	66	15	grill	grill	NOUN
iajs-3322	66	16	topological	topological	ADJ
iajs-3322	66	17	space	space	NOUN
iajs-3322	66	18	to	to	PART
iajs-3322	66	19	be	be	AUX
iajs-3322	66	20	a	a	DET
iajs-3322	66	21	nano	nano	NOUN
iajs-3322	66	22	𝑔𝑟ill	𝑔𝑟ill	NOUN
iajs-3322	66	23	and	and	CCONJ
iajs-3322	66	24	ꭓ={ꭓ	ꭓ={ꭓ	ADJ
iajs-3322	66	25	1	1	NUM
iajs-3322	66	26	,	,	PUNCT
iajs-3322	66	27	ꭓ	ꭓ	PROPN
iajs-3322	66	28	2	2	NUM
iajs-3322	66	29	,	,	PUNCT
iajs-3322	66	30	ꭓ	ꭓ	PROPN
iajs-3322	66	31	3	3	NUM
iajs-3322	66	32	,	,	PUNCT
iajs-3322	66	33	ꭓ	ꭓ	PROPN
iajs-3322	66	34	4	4	NUM
iajs-3322	66	35	}	}	PUNCT
iajs-3322	66	36	ǥ	ǥ	NOUN
iajs-3322	66	37	=	=	PUNCT
iajs-3322	66	38	{	{	PUNCT
iajs-3322	66	39	ȗ	ȗ	PROPN
iajs-3322	66	40	⊑	⊑	PROPN
iajs-3322	66	41	ꭓ	ꭓ	X
iajs-3322	66	42	;	;	PUNCT
iajs-3322	66	43	ꭓ	ꭓ	NUM
iajs-3322	66	44	2	2	NUM
iajs-3322	66	45	∈	∈	PROPN
iajs-3322	66	46	ȗ	ȗ	NOUN
iajs-3322	66	47	}	}	SYM
iajs-3322	66	48	ǥ	ǥ	NOUN
iajs-3322	66	49	=	=	PRON
iajs-3322	66	50	{	{	PUNCT
iajs-3322	66	51	{	{	PUNCT
iajs-3322	66	52	ꭓ	ꭓ	PROPN
iajs-3322	66	53	2	2	NUM
iajs-3322	66	54	}	}	PUNCT
iajs-3322	66	55	,	,	PUNCT
iajs-3322	66	56	{	{	PUNCT
iajs-3322	66	57	ꭓ	ꭓ	NOUN
iajs-3322	66	58	1	1	NUM
iajs-3322	66	59	,	,	PUNCT
iajs-3322	66	60	ꭓ	ꭓ	PROPN
iajs-3322	66	61	2	2	NUM
iajs-3322	66	62	}	}	PUNCT
iajs-3322	66	63	,	,	PUNCT
iajs-3322	66	64	{	{	PUNCT
iajs-3322	66	65	ꭓ	ꭓ	NOUN
iajs-3322	66	66	3	3	NUM
iajs-3322	66	67	,	,	PUNCT
iajs-3322	66	68	ꭓ	ꭓ	PROPN
iajs-3322	66	69	2	2	NUM
iajs-3322	66	70	}	}	PUNCT
iajs-3322	66	71	,	,	PUNCT
iajs-3322	66	72	{	{	PUNCT
iajs-3322	66	73	ꭓ	ꭓ	NOUN
iajs-3322	66	74	4	4	NUM
iajs-3322	66	75	,	,	PUNCT
iajs-3322	66	76	ꭓ	ꭓ	PROPN
iajs-3322	66	77	2	2	NUM
iajs-3322	66	78	}	}	PUNCT
iajs-3322	66	79	,	,	PUNCT
iajs-3322	66	80	{	{	PUNCT
iajs-3322	66	81	ꭓ	ꭓ	NOUN
iajs-3322	66	82	1	1	NUM
iajs-3322	66	83	,	,	PUNCT
iajs-3322	66	84	ꭓ	ꭓ	PROPN
iajs-3322	66	85	2	2	NUM
iajs-3322	66	86	,	,	PUNCT
iajs-3322	66	87	ꭓ	ꭓ	PROPN
iajs-3322	66	88	3	3	NUM
iajs-3322	66	89	}	}	PUNCT
iajs-3322	66	90	,	,	PUNCT
iajs-3322	66	91	{	{	PUNCT
iajs-3322	66	92	ꭓ	ꭓ	NOUN
iajs-3322	66	93	1	1	NUM
iajs-3322	66	94	,	,	PUNCT
iajs-3322	66	95	ꭓ	ꭓ	PROPN
iajs-3322	66	96	2	2	NUM
iajs-3322	66	97	,	,	PUNCT
iajs-3322	66	98	ꭓ	ꭓ	PROPN
iajs-3322	66	99	4	4	NUM
iajs-3322	66	100	}	}	PUNCT
iajs-3322	66	101	,	,	PUNCT
iajs-3322	66	102	{	{	PUNCT
iajs-3322	66	103	ꭓ	ꭓ	PROPN
iajs-3322	66	104	2	2	NUM
iajs-3322	66	105	,	,	PUNCT
iajs-3322	66	106	ꭓ	ꭓ	PROPN
iajs-3322	66	107	3	3	NUM
iajs-3322	66	108	,	,	PUNCT
iajs-3322	66	109	ꭓ	ꭓ	PROPN
iajs-3322	66	110	4	4	NUM
iajs-3322	66	111	}	}	PUNCT
iajs-3322	66	112	,	,	PUNCT
iajs-3322	66	113	ꭓ	ꭓ	X
iajs-3322	66	114	}	}	PUNCT
iajs-3322	66	115	ɽ={(ꭓ	ɽ={(ꭓ	PROPN
iajs-3322	66	116	1	1	NUM
iajs-3322	66	117	,	,	PUNCT
iajs-3322	66	118	ꭓ	ꭓ	PROPN
iajs-3322	66	119	1	1	NUM
iajs-3322	66	120	)	)	PUNCT
iajs-3322	66	121	,	,	PUNCT
iajs-3322	66	122	(	(	PUNCT
iajs-3322	66	123	ꭓ	ꭓ	PROPN
iajs-3322	66	124	2	2	NUM
iajs-3322	66	125	,	,	PUNCT
iajs-3322	66	126	ꭓ	ꭓ	PROPN
iajs-3322	66	127	2	2	NUM
iajs-3322	66	128	)	)	PUNCT
iajs-3322	66	129	,	,	PUNCT
iajs-3322	66	130	(	(	PUNCT
iajs-3322	66	131	ꭓ	ꭓ	NOUN
iajs-3322	66	132	3	3	NUM
iajs-3322	66	133	,	,	PUNCT
iajs-3322	66	134	ꭓ	ꭓ	PROPN
iajs-3322	66	135	3	3	NUM
iajs-3322	66	136	)	)	PUNCT
iajs-3322	66	137	,	,	PUNCT
iajs-3322	66	138	(	(	PUNCT
iajs-3322	66	139	ꭓ	ꭓ	NOUN
iajs-3322	66	140	4	4	NUM
iajs-3322	66	141	,	,	PUNCT
iajs-3322	66	142	ꭓ	ꭓ	PROPN
iajs-3322	66	143	4	4	NUM
iajs-3322	66	144	)	)	PUNCT
iajs-3322	66	145	,	,	PUNCT
iajs-3322	66	146	(	(	PUNCT
iajs-3322	66	147	ꭓ	ꭓ	PROPN
iajs-3322	66	148	2	2	NUM
iajs-3322	66	149	,	,	PUNCT
iajs-3322	66	150	ꭓ	ꭓ	PROPN
iajs-3322	66	151	4	4	NUM
iajs-3322	66	152	)	)	PUNCT
iajs-3322	66	153	,	,	PUNCT
iajs-3322	66	154	(	(	PUNCT
iajs-3322	66	155	ꭓ	ꭓ	NOUN
iajs-3322	66	156	4	4	NUM
iajs-3322	66	157	,	,	PUNCT
iajs-3322	66	158	ꭓ	ꭓ	PROPN
iajs-3322	66	159	2	2	NUM
iajs-3322	66	160	)	)	PUNCT
iajs-3322	66	161	}	}	PUNCT
iajs-3322	66	162	ɽ	ɽ	NOUN
iajs-3322	66	163	∖	∖	NOUN
iajs-3322	67	1	[	[	X
iajs-3322	67	2	ꭓ	ꭓ	X
iajs-3322	67	3	]	]	X
iajs-3322	67	4	=	=	X
iajs-3322	67	5	{	{	PUNCT
iajs-3322	67	6	{	{	PUNCT
iajs-3322	67	7	ꭓ	ꭓ	NOUN
iajs-3322	67	8	1	1	NUM
iajs-3322	67	9	}	}	PUNCT
iajs-3322	67	10	,	,	PUNCT
iajs-3322	67	11	{	{	PUNCT
iajs-3322	67	12	ꭓ	ꭓ	PROPN
iajs-3322	67	13	2	2	NUM
iajs-3322	67	14	,	,	PUNCT
iajs-3322	67	15	ꭓ	ꭓ	PROPN
iajs-3322	67	16	4	4	NUM
iajs-3322	67	17	}	}	PUNCT
iajs-3322	67	18	,	,	PUNCT
iajs-3322	67	19	{	{	PUNCT
iajs-3322	67	20	ꭓ	ꭓ	NOUN
iajs-3322	67	21	3	3	NUM
iajs-3322	67	22	}	}	PUNCT
iajs-3322	67	23	ⱳ	ⱳ	X
iajs-3322	67	24	⊑	⊑	PROPN
iajs-3322	67	25	ꭓ	ꭓ	NUM
iajs-3322	67	26	,	,	PUNCT
iajs-3322	67	27	ⱳ	ⱳ	X
iajs-3322	67	28	=	=	PUNCT
iajs-3322	67	29	{	{	PUNCT
iajs-3322	67	30	2,3	2,3	NUM
iajs-3322	67	31	}	}	PUNCT
iajs-3322	67	32	,	,	PUNCT
iajs-3322	67	33	ʈⱳ	ʈⱳ	X
iajs-3322	67	34	=	=	X
iajs-3322	67	35	{	{	PUNCT
iajs-3322	67	36	ꭓ	ꭓ	PROPN
iajs-3322	67	37	,	,	PUNCT
iajs-3322	67	38	ǿ	ǿ	PRON
iajs-3322	67	39	,	,	PUNCT
iajs-3322	67	40	{	{	PUNCT
iajs-3322	67	41	3	3	NUM
iajs-3322	67	42	}	}	PUNCT
iajs-3322	67	43	,	,	PUNCT
iajs-3322	67	44	{	{	PUNCT
iajs-3322	67	45	2,4	2,4	NUM
iajs-3322	67	46	}	}	PUNCT
iajs-3322	67	47	,	,	PUNCT
iajs-3322	67	48	{	{	PUNCT
iajs-3322	67	49	2,3,4	2,3,4	NUM
iajs-3322	67	50	}	}	PUNCT
iajs-3322	67	51	}	}	PUNCT
iajs-3322	67	52	ℬ	ℬ	NOUN
iajs-3322	67	53	=	=	PRON
iajs-3322	67	54	{	{	PUNCT
iajs-3322	67	55	ⱱ	ⱱ	PROPN
iajs-3322	67	56	−	−	PROPN
iajs-3322	67	57	ⱥ	ⱥ	NOUN
iajs-3322	67	58	;	;	PUNCT
iajs-3322	67	59	ⱱ	ⱱ	PROPN
iajs-3322	67	60	∈	∈	PROPN
iajs-3322	67	61	ʈⱳ	ʈⱳ	ADP
iajs-3322	67	62	∧	∧	PROPN
iajs-3322	67	63	ⱥ	ⱥ	PROPN
iajs-3322	67	64	∉	∉	X
iajs-3322	67	65	ǥ	ǥ	ADP
iajs-3322	67	66	}	}	PUNCT
iajs-3322	67	67	ℬ	ℬ	NOUN
iajs-3322	67	68	=	=	SYM
iajs-3322	67	69	{	{	PUNCT
iajs-3322	67	70	ꭓ	ꭓ	PROPN
iajs-3322	67	71	,	,	PUNCT
iajs-3322	67	72	ǿ	ǿ	PRON
iajs-3322	67	73	,	,	PUNCT
iajs-3322	67	74	{	{	PUNCT
iajs-3322	67	75	ꭓ	ꭓ	NOUN
iajs-3322	67	76	1	1	NUM
iajs-3322	67	77	,	,	PUNCT
iajs-3322	67	78	ꭓ	ꭓ	PROPN
iajs-3322	67	79	2	2	NUM
iajs-3322	67	80	,	,	PUNCT
iajs-3322	67	81	ꭓ	ꭓ	PROPN
iajs-3322	67	82	4	4	NUM
iajs-3322	67	83	}	}	PUNCT
iajs-3322	67	84	,	,	PUNCT
iajs-3322	67	85	{	{	PUNCT
iajs-3322	67	86	ꭓ	ꭓ	NOUN
iajs-3322	67	87	1	1	NUM
iajs-3322	67	88	,	,	PUNCT
iajs-3322	67	89	ꭓ	ꭓ	PROPN
iajs-3322	67	90	2	2	NUM
iajs-3322	67	91	,	,	PUNCT
iajs-3322	67	92	ꭓ	ꭓ	PROPN
iajs-3322	67	93	3	3	NUM
iajs-3322	67	94	}	}	PUNCT
iajs-3322	67	95	,	,	PUNCT
iajs-3322	67	96	{	{	PUNCT
iajs-3322	67	97	ꭓ	ꭓ	PROPN
iajs-3322	67	98	2	2	NUM
iajs-3322	67	99	,	,	PUNCT
iajs-3322	67	100	ꭓ	ꭓ	PROPN
iajs-3322	67	101	3	3	NUM
iajs-3322	67	102	,	,	PUNCT
iajs-3322	67	103	ꭓ	ꭓ	PROPN
iajs-3322	67	104	4	4	NUM
iajs-3322	67	105	}	}	PUNCT
iajs-3322	67	106	,	,	PUNCT
iajs-3322	67	107	{	{	PUNCT
iajs-3322	67	108	ꭓ	ꭓ	PROPN
iajs-3322	67	109	2	2	NUM
iajs-3322	67	110	,	,	PUNCT
iajs-3322	67	111	ꭓ	ꭓ	PROPN
iajs-3322	67	112	3	3	NUM
iajs-3322	67	113	}	}	PUNCT
iajs-3322	67	114	,	,	PUNCT
iajs-3322	67	115	{	{	PUNCT
iajs-3322	67	116	ꭓ	ꭓ	PROPN
iajs-3322	67	117	2	2	NUM
iajs-3322	67	118	,	,	PUNCT
iajs-3322	67	119	ꭓ	ꭓ	PROPN
iajs-3322	67	120	4	4	NUM
iajs-3322	67	121	}	}	PUNCT
iajs-3322	67	122	,	,	PUNCT
iajs-3322	67	123	{	{	PUNCT
iajs-3322	67	124	ꭓ	ꭓ	NOUN
iajs-3322	67	125	1	1	NUM
iajs-3322	67	126	,	,	PUNCT
iajs-3322	67	127	ꭓ	ꭓ	PROPN
iajs-3322	67	128	2	2	NUM
iajs-3322	67	129	}	}	PUNCT
iajs-3322	67	130	,	,	PUNCT
iajs-3322	67	131	{	{	PUNCT
iajs-3322	67	132	ꭓ	ꭓ	PROPN
iajs-3322	67	133	2	2	NUM
iajs-3322	67	134	}	}	PUNCT
iajs-3322	67	135	,	,	PUNCT
iajs-3322	67	136	{	{	PUNCT
iajs-3322	67	137	ꭓ	ꭓ	NOUN
iajs-3322	67	138	3	3	NUM
iajs-3322	67	139	}	}	PUNCT
iajs-3322	67	140	}	}	PUNCT
iajs-3322	67	141	=	=	SYM
iajs-3322	67	142	ʈⱳǥ	ʈⱳǥ	PROPN
iajs-3322	67	143	∴	∴	PROPN
iajs-3322	67	144	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	PROPN
iajs-3322	67	145	)	)	PUNCT
iajs-3322	67	146	=	=	SYM
iajs-3322	67	147	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	67	148	)	)	PUNCT
iajs-3322	67	149	.	.	PUNCT
iajs-3322	68	1	proposition	proposition	NOUN
iajs-3322	68	2	3.3	3.3	NUM
iajs-3322	68	3	:	:	PUNCT
iajs-3322	68	4	i.	i.	NOUN
iajs-3322	68	5	every	every	DET
iajs-3322	68	6	nano	nano	NOUN
iajs-3322	68	7	open	open	ADJ
iajs-3322	68	8	set	set	NOUN
iajs-3322	68	9	is	be	AUX
iajs-3322	68	10	a	a	DET
iajs-3322	68	11	ƞǥş	ƞǥş	NOUN
iajs-3322	68	12	-open	-open	NOUN
iajs-3322	68	13	sets	set	NOUN
iajs-3322	68	14	.	.	PUNCT
iajs-3322	69	1	ii	ii	X
iajs-3322	69	2	.	.	PUNCT
iajs-3322	70	1	every	every	DET
iajs-3322	70	2	nano	nano	NOUN
iajs-3322	70	3	closed	close	VERB
iajs-3322	70	4	set	set	NOUN
iajs-3322	70	5	is	be	AUX
iajs-3322	70	6	a	a	DET
iajs-3322	70	7	ƞǥş	ƞǥş	NOUN
iajs-3322	70	8	-closed	-close	VERB
iajs-3322	70	9	.	.	PUNCT
iajs-3322	70	10	example	example	NOUN
iajs-3322	70	11	3.2	3.2	NUM
iajs-3322	70	12	demonstrates	demonstrate	VERB
iajs-3322	70	13	that	that	SCONJ
iajs-3322	70	14	the	the	DET
iajs-3322	70	15	converse	converse	NOUN
iajs-3322	70	16	of	of	ADP
iajs-3322	70	17	remark	remark	NOUN
iajs-3322	70	18	3.3(i)(ii	3.3(i)(ii	NUM
iajs-3322	70	19	)	)	PUNCT
iajs-3322	70	20	is	be	AUX
iajs-3322	70	21	not	not	PART
iajs-3322	70	22	true	true	ADJ
iajs-3322	70	23	.	.	PUNCT
iajs-3322	71	1	definition	definition	NOUN
iajs-3322	71	2	3.4	3.4	NUM
iajs-3322	71	3	:	:	PUNCT
iajs-3322	71	4	let	let	VERB
iajs-3322	71	5	(	(	PUNCT
iajs-3322	71	6	ꭓ	ꭓ	NUM
iajs-3322	71	7	,	,	PUNCT
iajs-3322	71	8	ʈⱳ	ʈⱳ	NOUN
iajs-3322	71	9	,	,	PUNCT
iajs-3322	71	10	ǥ	ǥ	NOUN
iajs-3322	71	11	)	)	PUNCT
iajs-3322	71	12	be	be	AUX
iajs-3322	71	13	a	a	DET
iajs-3322	71	14	nano	nano	ADJ
iajs-3322	71	15	gr𝑖ll	gr𝑖ll	NOUN
iajs-3322	71	16	topological	topological	ADJ
iajs-3322	71	17	space	space	NOUN
iajs-3322	71	18	.	.	PUNCT
iajs-3322	72	1	by	by	ADP
iajs-3322	72	2	a	a	DET
iajs-3322	72	3	ƞǥş	ƞǥş	NOUN
iajs-3322	72	4	−	−	NOUN
iajs-3322	72	5	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	72	6	𝑐𝑜𝑣𝑒𝑟	𝑐𝑜𝑣𝑒𝑟	NOUN
iajs-3322	72	7	𝑜𝑓	𝑜𝑓	ADP
iajs-3322	72	8	ꭓ	ꭓ	PRON
iajs-3322	72	9	we	we	PRON
iajs-3322	72	10	mean	mean	VERB
iajs-3322	72	11	a	a	DET
iajs-3322	72	12	subfamily	subfamily	NOUN
iajs-3322	72	13	of	of	ADP
iajs-3322	72	14	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	NOUN
iajs-3322	72	15	)	)	PUNCT
iajs-3322	72	16	wich	wich	PRON
iajs-3322	72	17	cover	cover	VERB
iajs-3322	72	18	ꭓ	ꭓ	DET
iajs-3322	72	19	definition	definition	NOUN
iajs-3322	72	20	3.5	3.5	NUM
iajs-3322	72	21	:	:	PUNCT
iajs-3322	72	22	a	a	DET
iajs-3322	72	23	nano	nano	NOUN
iajs-3322	72	24	grill	grill	NOUN
iajs-3322	72	25	topological	topological	ADJ
iajs-3322	72	26	space	space	NOUN
iajs-3322	72	27	(	(	PUNCT
iajs-3322	72	28	ꭓ	ꭓ	X
iajs-3322	72	29	,	,	PUNCT
iajs-3322	72	30	ʈⱳ	ʈⱳ	NOUN
iajs-3322	72	31	,	,	PUNCT
iajs-3322	72	32	ǥ	ǥ	NOUN
iajs-3322	72	33	)	)	PUNCT
iajs-3322	72	34	is	be	AUX
iajs-3322	72	35	said	say	VERB
iajs-3322	72	36	to	to	PART
iajs-3322	72	37	be	be	AUX
iajs-3322	72	38	ƞǥş	ƞǥş	NOUN
iajs-3322	72	39	−	−	NOUN
iajs-3322	72	40	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	72	41	𝑠𝑝𝑎𝑐𝑒if	𝑠𝑝𝑎𝑐𝑒if	NOUN
iajs-3322	72	42	every	every	DET
iajs-3322	72	43	ƞǥş	ƞǥş	NOUN
iajs-3322	72	44	−	−	PROPN
iajs-3322	72	45	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	72	46	𝑐𝑜𝑣𝑒𝑟	𝑐𝑜𝑣𝑒𝑟	NOUN
iajs-3322	72	47	for	for	SCONJ
iajs-3322	72	48	ꭓ	ꭓ	PROPN
iajs-3322	72	49	has	have	VERB
iajs-3322	72	50	a	a	DET
iajs-3322	72	51	finite	finite	ADJ
iajs-3322	72	52	subcover	subcover	NOUN
iajs-3322	72	53	.	.	PUNCT
iajs-3322	73	1	theorem3.6	theorem3.6	NUM
iajs-3322	73	2	:	:	PUNCT
iajs-3322	73	3	a	a	DET
iajs-3322	73	4	nano	nano	NOUN
iajs-3322	73	5	grill	grill	NOUN
iajs-3322	73	6	topological	topological	ADJ
iajs-3322	73	7	space	space	NOUN
iajs-3322	73	8	(	(	PUNCT
iajs-3322	73	9	ꭓ	ꭓ	X
iajs-3322	73	10	,	,	PUNCT
iajs-3322	73	11	ʈⱳ	ʈⱳ	NOUN
iajs-3322	73	12	,	,	PUNCT
iajs-3322	73	13	ǥ	ǥ	NOUN
iajs-3322	73	14	)	)	PUNCT
iajs-3322	73	15	is	be	AUX
iajs-3322	73	16	be	be	AUX
iajs-3322	73	17	ƞǥş	ƞǥş	NOUN
iajs-3322	73	18	−	−	NOUN
iajs-3322	73	19	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	73	20	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-3322	73	21	if	if	SCONJ
iajs-3322	73	22	and	and	CCONJ
iajs-3322	73	23	only	only	ADV
iajs-3322	73	24	if	if	SCONJ
iajs-3322	73	25	every	every	DET
iajs-3322	73	26	family	family	NOUN
iajs-3322	73	27	of	of	ADP
iajs-3322	73	28	ƞǥş	ƞǥş	NOUN
iajs-3322	73	29	−	−	PROPN
iajs-3322	73	30	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-3322	73	31	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	NOUN
iajs-3322	73	32	of	of	ADP
iajs-3322	73	33	ꭓ	ꭓ	PROPN
iajs-3322	73	34	with	with	ADP
iajs-3322	73	35	finite	finite	ADJ
iajs-3322	73	36	intersection	intersection	NOUN
iajs-3322	73	37	property	property	NOUN
iajs-3322	73	38	has	have	VERB
iajs-3322	73	39	a	a	DET
iajs-3322	73	40	non	non	ADJ
iajs-3322	73	41	-	-	ADJ
iajs-3322	73	42	empty	empty	ADJ
iajs-3322	73	43	intersection	intersection	NOUN
iajs-3322	73	44	.	.	PUNCT
iajs-3322	74	1	proof	proof	NOUN
iajs-3322	74	2	:	:	PUNCT
iajs-3322	74	3	suppose	suppose	VERB
iajs-3322	74	4	that	that	SCONJ
iajs-3322	74	5	ꭓ	ꭓ	PROPN
iajs-3322	74	6	is	be	AUX
iajs-3322	74	7	ƞǥş	ƞǥş	NOUN
iajs-3322	74	8	−	−	PROPN
iajs-3322	74	9	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	74	10	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-3322	74	11	and	and	CCONJ
iajs-3322	74	12	let	let	VERB
iajs-3322	74	13	{	{	PUNCT
iajs-3322	74	14	₣	₣	NUM
iajs-3322	74	15	𝑖	𝑖	NUM
iajs-3322	74	16	:	:	PUNCT
iajs-3322	74	17	𝑖	𝑖	SYM
iajs-3322	74	18	∈	∈	PROPN
iajs-3322	74	19	λ	λ	NOUN
iajs-3322	74	20	}	}	PUNCT
iajs-3322	74	21	be	be	VERB
iajs-3322	74	22	a	a	DET
iajs-3322	74	23	family	family	NOUN
iajs-3322	74	24	of	of	ADP
iajs-3322	74	25	ƞǥş	ƞǥş	NOUN
iajs-3322	74	26	−	−	PROPN
iajs-3322	74	27	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-3322	74	28	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	NOUN
iajs-3322	74	29	of	of	ADP
iajs-3322	74	30	ꭓ	ꭓ	PROPN
iajs-3322	74	31	with	with	ADP
iajs-3322	74	32	(	(	PUNCT
iajs-3322	74	33	f.i.p	f.i.p	ADJ
iajs-3322	74	34	)	)	PUNCT
iajs-3322	74	35	.	.	PUNCT
iajs-3322	75	1	assume	assume	VERB
iajs-3322	75	2	that	that	SCONJ
iajs-3322	75	3	∩𝑖∈λ	∩𝑖∈λ	VERB
iajs-3322	75	4	₣	₣	PRON
iajs-3322	75	5	𝑖	𝑖	SYM
iajs-3322	75	6	=	=	SYM
iajs-3322	75	7	ø	ø	PROPN
iajs-3322	75	8	,	,	PUNCT
iajs-3322	75	9	then	then	ADV
iajs-3322	75	10	∪𝑖∈λ	∪𝑖∈λ	VERB
iajs-3322	76	1	₣	₣	X
iajs-3322	76	2	𝑐	𝑐	NOUN
iajs-3322	76	3	𝑖	𝑖	NOUN
iajs-3322	76	4	=	=	PUNCT
iajs-3322	76	5	ꭓ	ꭓ	PROPN
iajs-3322	76	6	,	,	PUNCT
iajs-3322	76	7	where	where	SCONJ
iajs-3322	76	8	{	{	PUNCT
iajs-3322	76	9	₣	₣	PROPN
iajs-3322	76	10	𝑐	𝑐	NOUN
iajs-3322	76	11	𝑖	𝑖	NUM
iajs-3322	76	12	:	:	PUNCT
iajs-3322	76	13	𝑖	𝑖	ADP
iajs-3322	76	14	∈	∈	PROPN
iajs-3322	76	15	λ	λ	NOUN
iajs-3322	76	16	}	}	PUNCT
iajs-3322	76	17	is	be	AUX
iajs-3322	76	18	a	a	DET
iajs-3322	76	19	ƞǥş	ƞǥş	NOUN
iajs-3322	76	20	−	−	NOUN
iajs-3322	76	21	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	76	22	𝑐𝑜𝑣𝑒𝑟of	𝑐𝑜𝑣𝑒𝑟of	NOUN
iajs-3322	76	23	ꭓ	ꭓ	PRON
iajs-3322	76	24	which	which	PRON
iajs-3322	76	25	is	be	AUX
iajs-3322	76	26	a	a	DET
iajs-3322	76	27	ƞǥş	ƞǥş	NOUN
iajs-3322	76	28	−	−	PROPN
iajs-3322	76	29	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	76	30	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-3322	76	31	,	,	PUNCT
iajs-3322	76	32	if	if	SCONJ
iajs-3322	76	33	follows	follow	VERB
iajs-3322	76	34	that	that	SCONJ
iajs-3322	76	35	there	there	PRON
iajs-3322	76	36	exists	exist	VERB
iajs-3322	76	37	a	a	DET
iajs-3322	76	38	finite	finite	ADJ
iajs-3322	76	39	subcover	subcover	PROPN
iajs-3322	76	40	{	{	PUNCT
iajs-3322	76	41	₣	₣	PROPN
iajs-3322	76	42	𝑐	𝑐	X
iajs-3322	76	43	𝑖}𝑛	𝑖}𝑛	PROPN
iajs-3322	76	44	𝑖=1	𝑖=1	PUNCT
iajs-3322	76	45	such	such	ADJ
iajs-3322	76	46	that	that	SCONJ
iajs-3322	76	47	ꭓ	ꭓ	PROPN
iajs-3322	76	48	=	=	PUNCT
iajs-3322	76	49	⋃	⋃	NOUN
iajs-3322	76	50	₣	₣	SYM
iajs-3322	76	51	𝑐	𝑐	NOUN
iajs-3322	76	52	𝑖	𝑖	X
iajs-3322	76	53	𝑛	𝑛	NOUN
iajs-3322	76	54	𝑖=1	𝑖=1	PUNCT
iajs-3322	76	55	,	,	PUNCT
iajs-3322	76	56	then	then	ADV
iajs-3322	76	57	⋃	⋃	PROPN
iajs-3322	76	58	₣	₣	SYM
iajs-3322	76	59	𝑖	𝑖	SYM
iajs-3322	76	60	𝑛	𝑛	PRON
iajs-3322	76	61	𝑖=1	𝑖=1	PUNCT
iajs-3322	76	62	=	=	NOUN
iajs-3322	76	63	∅	∅	NOUN
iajs-3322	76	64	which	which	PRON
iajs-3322	76	65	is	be	AUX
iajs-3322	76	66	a	a	DET
iajs-3322	76	67	contradiction	contradiction	NOUN
iajs-3322	76	68	.	.	PUNCT
iajs-3322	77	1	since₣𝑖	since₣𝑖	NUM
iajs-3322	77	2	:	:	PUNCT
iajs-3322	78	1	𝑖	𝑖	SYM
iajs-3322	78	2	∈	∈	PROPN
iajs-3322	78	3	λ}hasaf.i.p	λ}hasaf.i.p	PROPN
iajs-3322	78	4	.	.	PUNCT
iajs-3322	79	1	now	now	ADV
iajs-3322	79	2	,	,	PUNCT
iajs-3322	79	3	suppose	suppose	VERB
iajs-3322	79	4	that	that	SCONJ
iajs-3322	79	5	every	every	DET
iajs-3322	79	6	family	family	NOUN
iajs-3322	79	7	of	of	ADP
iajs-3322	79	8	ƞǥş	ƞǥş	NOUN
iajs-3322	79	9	−	−	PROPN
iajs-3322	79	10	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-3322	79	11	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	NOUN
iajs-3322	79	12	of	of	ADP
iajs-3322	79	13	ꭓ	ꭓ	PROPN
iajs-3322	79	14	with	with	ADP
iajs-3322	79	15	(	(	PUNCT
iajs-3322	79	16	f.i.p	f.i.p	ADV
iajs-3322	79	17	)	)	PUNCT
iajs-3322	79	18	has	have	VERB
iajs-3322	79	19	a	a	DET
iajs-3322	79	20	non	non	ADJ
iajs-3322	79	21	-	-	ADJ
iajs-3322	79	22	empty	empty	ADJ
iajs-3322	79	23	intersection	intersection	NOUN
iajs-3322	79	24	.	.	PUNCT
iajs-3322	80	1	assume	assume	VERB
iajs-3322	80	2	that	that	SCONJ
iajs-3322	80	3	ꭓ	ꭓ	PROPN
iajs-3322	80	4	is	be	AUX
iajs-3322	80	5	not	not	PART
iajs-3322	80	6	ƞǥş	ƞǥş	NOUN
iajs-3322	80	7	−	−	PROPN
iajs-3322	80	8	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	80	9	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-3322	80	10	,	,	PUNCT
iajs-3322	80	11	let	let	VERB
iajs-3322	80	12	{	{	PUNCT
iajs-3322	80	13	𝑢𝛼	𝑢𝛼	ADJ
iajs-3322	80	14	:	:	PUNCT
iajs-3322	80	15	𝛼	𝛼	PROPN
iajs-3322	80	16	∈	∈	PROPN
iajs-3322	80	17	λ	λ	PROPN
iajs-3322	80	18	}	}	PUNCT
iajs-3322	80	19	be	be	VERB
iajs-3322	80	20	a	a	DET
iajs-3322	80	21	ƞǥş	ƞǥş	NOUN
iajs-3322	80	22	−	−	NOUN
iajs-3322	80	23	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	80	24	𝑐𝑜𝑣𝑒𝑟of	𝑐𝑜𝑣𝑒𝑟of	NOUN
iajs-3322	80	25	ꭓ	ꭓ	PROPN
iajs-3322	80	26	and	and	CCONJ
iajs-3322	80	27	suppose	suppose	VERB
iajs-3322	80	28	if	if	SCONJ
iajs-3322	80	29	possible	possible	ADJ
iajs-3322	80	30	,	,	PUNCT
iajs-3322	80	31	{	{	PUNCT
iajs-3322	80	32	𝑢𝛼	𝑢𝛼	X
iajs-3322	80	33	:	:	PUNCT
iajs-3322	80	34	𝛼	𝛼	PROPN
iajs-3322	80	35	∈	∈	PROPN
iajs-3322	80	36	λ	λ	PROPN
iajs-3322	80	37	}	}	PUNCT
iajs-3322	80	38	has	have	VERB
iajs-3322	80	39	no	no	DET
iajs-3322	80	40	finite	finite	PROPN
iajs-3322	80	41	subcover	subcover	PROPN
iajs-3322	80	42	.	.	PUNCT
iajs-3322	81	1	the	the	DET
iajs-3322	81	2	collection	collection	NOUN
iajs-3322	81	3	{	{	PUNCT
iajs-3322	81	4	𝑢𝑐	𝑢𝑐	NOUN
iajs-3322	81	5	𝛼	𝛼	NOUN
iajs-3322	81	6	:	:	PUNCT
iajs-3322	81	7	𝛼	𝛼	PROPN
iajs-3322	81	8	∈	∈	PROPN
iajs-3322	81	9	λ	λ	PROPN
iajs-3322	81	10	}	}	PUNCT
iajs-3322	81	11	has	have	VERB
iajs-3322	81	12	the	the	DET
iajs-3322	81	13	f.i.p	f.i.p	ADJ
iajs-3322	81	14	,	,	PUNCT
iajs-3322	81	15	if	if	SCONJ
iajs-3322	81	16	but	but	CCONJ
iajs-3322	81	17	{	{	PUNCT
iajs-3322	81	18	𝑢𝑐	𝑢𝑐	NOUN
iajs-3322	81	19	𝛼	𝛼	NOUN
iajs-3322	81	20	:	:	PUNCT
iajs-3322	81	21	𝛼	𝛼	PROPN
iajs-3322	81	22	∈	∈	PROPN
iajs-3322	81	23	λ	λ	PROPN
iajs-3322	81	24	}	}	PUNCT
iajs-3322	81	25	is	be	AUX
iajs-3322	81	26	a	a	DET
iajs-3322	81	27	family	family	NOUN
iajs-3322	81	28	of	of	ADP
iajs-3322	81	29	ƞǥş	ƞǥş	NOUN
iajs-3322	82	1	−	−	PROPN
iajs-3322	82	2	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-3322	82	3	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	NOUN
iajs-3322	82	4	,	,	PUNCT
iajs-3322	82	5	so	so	ADV
iajs-3322	82	6	ihjpas	ihjpa	NOUN
iajs-3322	82	7	.	.	PUNCT
iajs-3322	83	1	2025	2025	NUM
iajs-3322	83	2	,	,	PUNCT
iajs-3322	83	3	38	38	NUM
iajs-3322	83	4	(	(	PUNCT
iajs-3322	83	5	1	1	NUM
iajs-3322	83	6	)	)	SYM
iajs-3322	83	7	363	363	NUM
iajs-3322	83	8	∩𝛼∈λ	∩𝛼∈λ	NOUN
iajs-3322	83	9	𝑢𝑐	𝑢𝑐	VERB
iajs-3322	83	10	𝛼	𝛼	PRON
iajs-3322	83	11	≠	≠	PROPN
iajs-3322	83	12	∅	∅	NOUN
iajs-3322	83	13	,	,	PUNCT
iajs-3322	83	14	it	it	PRON
iajs-3322	83	15	follows	follow	VERB
iajs-3322	83	16	that	that	SCONJ
iajs-3322	83	17	∪𝛼∈λ	∪𝛼∈λ	VERB
iajs-3322	83	18	𝑢𝛼	𝑢𝛼	ADP
iajs-3322	83	19	≠	≠	PROPN
iajs-3322	83	20	ꭓ	ꭓ	NUM
iajs-3322	83	21	which	which	PRON
iajs-3322	83	22	is	be	AUX
iajs-3322	83	23	contradiction	contradiction	NOUN
iajs-3322	83	24	since	since	SCONJ
iajs-3322	83	25	{	{	PUNCT
iajs-3322	83	26	𝑢𝛼	𝑢𝛼	NOUN
iajs-3322	83	27	:	:	PUNCT
iajs-3322	83	28	𝛼	𝛼	PROPN
iajs-3322	83	29	∈	∈	PROPN
iajs-3322	83	30	λ	λ	PROPN
iajs-3322	83	31	}	}	PUNCT
iajs-3322	83	32	is	be	AUX
iajs-3322	83	33	a	a	DET
iajs-3322	83	34	ƞǥş	ƞǥş	NOUN
iajs-3322	83	35	−	−	NOUN
iajs-3322	83	36	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	83	37	𝑐𝑜𝑣𝑒𝑟of	𝑐𝑜𝑣𝑒𝑟of	NOUN
iajs-3322	83	38	ꭓ	ꭓ	PROPN
iajs-3322	83	39	.	.	PUNCT
iajs-3322	84	1	theorem	theorem	VERB
iajs-3322	84	2	3.7	3.7	NUM
iajs-3322	84	3	:	:	PUNCT
iajs-3322	84	4	every	every	DET
iajs-3322	84	5	ƞǥş	ƞǥş	NOUN
iajs-3322	84	6	−	−	PROPN
iajs-3322	84	7	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	84	8	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-3322	84	9	is	be	AUX
iajs-3322	84	10	a	a	DET
iajs-3322	84	11	nano	nano	ADJ
iajs-3322	84	12	compact	compact	ADJ
iajs-3322	84	13	space	space	NOUN
iajs-3322	84	14	.	.	PUNCT
iajs-3322	85	1	proof	proof	NOUN
iajs-3322	85	2	:	:	PUNCT
iajs-3322	85	3	let	let	VERB
iajs-3322	85	4	𝑈	𝑈	PROPN
iajs-3322	85	5	=	=	PRON
iajs-3322	85	6	{	{	PUNCT
iajs-3322	85	7	𝑢	𝑢	X
iajs-3322	85	8	i	i	PRON
iajs-3322	85	9	,	,	PUNCT
iajs-3322	85	10	i	i	PROPN
iajs-3322	85	11	∈	∈	PROPN
iajs-3322	85	12	ᴧ	ᴧ	PROPN
iajs-3322	85	13	;	;	PUNCT
iajs-3322	86	1	𝑢	𝑢	PROPN
iajs-3322	86	2	i	i	PROPN
iajs-3322	86	3	∈	∈	PROPN
iajs-3322	86	4	ʈⱳ	ʈⱳ	X
iajs-3322	86	5	∀	∀	X
iajs-3322	86	6	i	i	PRON
iajs-3322	86	7	}	}	PUNCT
iajs-3322	86	8	is	be	AUX
iajs-3322	86	9	an	an	DET
iajs-3322	86	10	open	open	ADJ
iajs-3322	86	11	cover	cover	NOUN
iajs-3322	86	12	for	for	ADP
iajs-3322	86	13	ꭓ	ꭓ	PRON
iajs-3322	86	14	such	such	ADJ
iajs-3322	86	15	that	that	SCONJ
iajs-3322	86	16	ꭓ	ꭓ	PROPN
iajs-3322	86	17	=	=	X
iajs-3322	86	18	⋃	⋃	ADP
iajs-3322	86	19	𝑢	𝑢	NOUN
iajs-3322	86	20	ii∈ᴧ	ii∈ᴧ	NOUN
iajs-3322	86	21	and	and	CCONJ
iajs-3322	86	22	since	since	SCONJ
iajs-3322	86	23	every	every	DET
iajs-3322	86	24	open	open	ADJ
iajs-3322	86	25	set	set	NOUN
iajs-3322	86	26	is	be	AUX
iajs-3322	86	27	a	a	DET
iajs-3322	86	28	ƞǥş	ƞǥş	NOUN
iajs-3322	86	29	−	−	NOUN
iajs-3322	86	30	open	open	ADJ
iajs-3322	86	31	sets	set	NOUN
iajs-3322	86	32	.so	.so	PRON
iajs-3322	86	33	,	,	PUNCT
iajs-3322	86	34	𝑈	𝑈	PROPN
iajs-3322	86	35	is	be	AUX
iajs-3322	86	36	a	a	DET
iajs-3322	86	37	ƞǥş	ƞǥş	NOUN
iajs-3322	86	38	−	−	NOUN
iajs-3322	86	39	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	86	40	𝑐𝑜𝑣𝑒𝑟	𝑐𝑜𝑣𝑒𝑟	NOUN
iajs-3322	86	41	for	for	ADP
iajs-3322	86	42	ꭓ	ꭓ	NUM
iajs-3322	86	43	,	,	PUNCT
iajs-3322	86	44	and	and	CCONJ
iajs-3322	86	45	since	since	SCONJ
iajs-3322	86	46	ӽ	ӽ	PRON
iajs-3322	86	47	is	be	AUX
iajs-3322	86	48	a	a	DET
iajs-3322	86	49	not	not	PART
iajs-3322	86	50	ƞǥş	ƞǥş	NOUN
iajs-3322	86	51	−	−	NOUN
iajs-3322	86	52	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	86	53	set	set	NOUN
iajs-3322	86	54	.so	.so	PUNCT
iajs-3322	86	55	,	,	PUNCT
iajs-3322	86	56	there	there	PRON
iajs-3322	86	57	exist	exist	VERB
iajs-3322	86	58	a	a	DET
iajs-3322	86	59	finite	finite	ADJ
iajs-3322	86	60	subcover	subcover	PROPN
iajs-3322	86	61	say	say	VERB
iajs-3322	86	62	𝑈	𝑈	PROPN
iajs-3322	86	63	=	=	SYM
iajs-3322	86	64	{	{	PUNCT
iajs-3322	86	65	𝑢1	𝑢1	PROPN
iajs-3322	86	66	,	,	PUNCT
iajs-3322	86	67	𝑢2	𝑢2	PROPN
iajs-3322	86	68	,	,	PUNCT
iajs-3322	86	69	…	…	PUNCT
iajs-3322	86	70	,	,	PUNCT
iajs-3322	86	71	𝑢𝑛	𝑢𝑛	X
iajs-3322	86	72	}	}	PUNCT
iajs-3322	87	1	such	such	ADJ
iajs-3322	87	2	that	that	SCONJ
iajs-3322	87	3	ꭓ	ꭓ	PROPN
iajs-3322	87	4	=	=	X
iajs-3322	87	5	⋃	⋃	ADP
iajs-3322	87	6	𝑢	𝑢	X
iajs-3322	87	7	i	i	PRON
iajs-3322	87	8	𝑛	𝑛	VERB
iajs-3322	87	9	i=1	i=1	PROPN
iajs-3322	87	10	.therefore	.therefore	NOUN
iajs-3322	87	11	,	,	PUNCT
iajs-3322	87	12	ꭓ	ꭓ	PROPN
iajs-3322	87	13	is	be	AUX
iajs-3322	87	14	a	a	DET
iajs-3322	87	15	nano	nano	ADJ
iajs-3322	87	16	compact	compact	ADJ
iajs-3322	87	17	space	space	NOUN
iajs-3322	87	18	.	.	PUNCT
iajs-3322	88	1	definition	definition	NOUN
iajs-3322	88	2	3.8	3.8	NUM
iajs-3322	88	3	:	:	PUNCT
iajs-3322	88	4	let	let	VERB
iajs-3322	88	5	ℱ	ℱ	PROPN
iajs-3322	88	6	:	:	PUNCT
iajs-3322	88	7	(	(	PUNCT
iajs-3322	88	8	ꭓ	ꭓ	X
iajs-3322	88	9	,	,	PUNCT
iajs-3322	88	10	ʈⱳ	ʈⱳ	NOUN
iajs-3322	88	11	,	,	PUNCT
iajs-3322	88	12	ǥ	ǥ	NOUN
iajs-3322	88	13	)	)	PUNCT
iajs-3322	88	14	→	→	SYM
iajs-3322	88	15	(	(	PUNCT
iajs-3322	88	16	ƴ	ƴ	PROPN
iajs-3322	88	17	,	,	PUNCT
iajs-3322	88	18	ʈⱳ	ʈⱳ	PROPN
iajs-3322	88	19	′	′	PROPN
iajs-3322	88	20	,	,	PUNCT
iajs-3322	88	21	ǥ′	ǥ′	PROPN
iajs-3322	88	22	)	)	PUNCT
iajs-3322	88	23	be	be	VERB
iajs-3322	88	24	a	a	DET
iajs-3322	88	25	function	function	NOUN
iajs-3322	88	26	then	then	ADV
iajs-3322	88	27	ℱ	ℱ	PROPN
iajs-3322	88	28	believed	believe	VERB
iajs-3322	88	29	to	to	PART
iajs-3322	88	30	be	be	AUX
iajs-3322	88	31	;	;	PUNCT
iajs-3322	88	32	1	1	X
iajs-3322	88	33	.	.	PUNCT
iajs-3322	88	34	ƞǥ	ƞǥ	PROPN
iajs-3322	88	35	𝑠𝑒𝑚𝑖	𝑠𝑒𝑚𝑖	PROPN
iajs-3322	88	36	−continuous	−continuous	PROPN
iajs-3322	88	37	function	function	NOUN
iajs-3322	88	38	,	,	PUNCT
iajs-3322	88	39	denoted	denote	VERB
iajs-3322	88	40	b𝑦	b𝑦	PROPN
iajs-3322	88	41	ƞǥş	ƞǥş	NOUN
iajs-3322	88	42	-	-	PUNCT
iajs-3322	88	43	continuous	continuous	ADJ
iajs-3322	88	44	function	function	NOUN
iajs-3322	88	45	if	if	SCONJ
iajs-3322	88	46	ℱ−1(u	ℱ−1(u	NUM
iajs-3322	88	47	)	)	PUNCT
iajs-3322	88	48	∈	∈	NOUN
iajs-3322	88	49	ƞǥşỏ(ꭓ)for	ƞǥşỏ(ꭓ)for	ADP
iajs-3322	88	50	all	all	DET
iajs-3322	88	51	u	u	PROPN
iajs-3322	88	52	∈	∈	PROPN
iajs-3322	88	53	ʈⱳ	ʈⱳ	PROPN
iajs-3322	88	54	.	.	PROPN
iajs-3322	88	55	2	2	NUM
iajs-3322	88	56	.	.	PUNCT
iajs-3322	88	57	strongly	strongly	ADV
iajs-3322	88	58	ƞǥ	ƞǥ	VERB
iajs-3322	88	59	𝑠𝑒𝑚𝑖	𝑠𝑒𝑚𝑖	PROPN
iajs-3322	88	60	−continuous	−continuous	PROPN
iajs-3322	88	61	function	function	NOUN
iajs-3322	88	62	,	,	PUNCT
iajs-3322	88	63	denoted	denote	VERB
iajs-3322	88	64	by	by	ADP
iajs-3322	88	65	"	"	PUNCT
iajs-3322	88	66	.	.	PUNCT
iajs-3322	89	1	𝑆𝑡𝑟𝑜𝑛𝑔𝑙𝑦	𝑆𝑡𝑟𝑜𝑛𝑔𝑙𝑦	NOUN
iajs-3322	89	2	ƞǥş	ƞǥş	NOUN
iajs-3322	89	3	-	-	PUNCT
iajs-3322	89	4	continuous	continuous	ADJ
iajs-3322	89	5	function	function	NOUN
iajs-3322	89	6	"	"	PUNCT
iajs-3322	89	7	𝑖𝑓	𝑖𝑓	ADP
iajs-3322	89	8	ℱ−1(u	ℱ−1(u	PROPN
iajs-3322	89	9	)	)	PUNCT
iajs-3322	89	10	∈	∈	PROPN
iajs-3322	90	1	ʈⱳ	ʈⱳ	PROPN
iajs-3322	90	2	,	,	PUNCT
iajs-3322	90	3	fore	fore	NOUN
iajs-3322	90	4	all	all	DET
iajs-3322	90	5	u	u	NOUN
iajs-3322	90	6	∈	∈	PROPN
iajs-3322	90	7	ƞǥşỏ(ƴ	ƞǥşỏ(ƴ	PROPN
iajs-3322	90	8	)	)	PUNCT
iajs-3322	90	9	.	.	PUNCT
iajs-3322	91	1	3	3	X
iajs-3322	91	2	.	.	NUM
iajs-3322	91	3	ƞǥ	ƞǥ	PROPN
iajs-3322	91	4	𝑠𝑒𝑚𝑖-irresolute	𝑠𝑒𝑚𝑖-irresolute	ADJ
iajs-3322	91	5	function	function	NOUN
iajs-3322	91	6	,	,	PUNCT
iajs-3322	91	7	denoted	denote	VERB
iajs-3322	91	8	by	by	ADP
iajs-3322	91	9	ƞǥş	ƞǥş	NOUN
iajs-3322	91	10	-irresolute	-irresolute	ADJ
iajs-3322	91	11	function	function	NOUN
iajs-3322	91	12	if	if	SCONJ
iajs-3322	91	13	ℱ−1(u	ℱ−1(u	NUM
iajs-3322	91	14	)	)	PUNCT
iajs-3322	91	15	∈	∈	PROPN
iajs-3322	91	16	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	PROPN
iajs-3322	91	17	)	)	PUNCT
iajs-3322	91	18	,	,	PUNCT
iajs-3322	91	19	for	for	ADP
iajs-3322	91	20	all	all	DET
iajs-3322	91	21	u	u	PRON
iajs-3322	91	22	∈	∈	PROPN
iajs-3322	91	23	ƞǥşỏ(ƴ	ƞǥşỏ(ƴ	PROPN
iajs-3322	91	24	)	)	PUNCT
iajs-3322	91	25	.	.	PUNCT
iajs-3322	92	1	proposition	proposition	NOUN
iajs-3322	92	2	3.9	3.9	NUM
iajs-3322	92	3	:	:	PUNCT
iajs-3322	92	4	let	let	VERB
iajs-3322	92	5	ℱ	ℱ	PROPN
iajs-3322	92	6	:	:	PUNCT
iajs-3322	92	7	(	(	PUNCT
iajs-3322	92	8	ꭓ	ꭓ	X
iajs-3322	92	9	,	,	PUNCT
iajs-3322	92	10	ʈⱳ	ʈⱳ	NOUN
iajs-3322	92	11	,	,	PUNCT
iajs-3322	92	12	ǥ	ǥ	NOUN
iajs-3322	92	13	)	)	PUNCT
iajs-3322	92	14	→	→	SYM
iajs-3322	92	15	(	(	PUNCT
iajs-3322	92	16	ƴ	ƴ	PROPN
iajs-3322	92	17	,	,	PUNCT
iajs-3322	92	18	ʈⱳ	ʈⱳ	PROPN
iajs-3322	92	19	′	′	PROPN
iajs-3322	92	20	,	,	PUNCT
iajs-3322	92	21	ǥ′	ǥ′	PROPN
iajs-3322	92	22	)	)	PUNCT
iajs-3322	92	23	be	be	VERB
iajs-3322	92	24	a	a	DET
iajs-3322	92	25	function	function	NOUN
iajs-3322	92	26	.	.	PUNCT
iajs-3322	93	1	1	1	X
iajs-3322	93	2	.	.	X
iajs-3322	93	3	ℱ	ℱ	PROPN
iajs-3322	93	4	is	be	AUX
iajs-3322	93	5	ƞǥş	ƞǥş	NOUN
iajs-3322	93	6	-irresolute	-irresolute	ADJ
iajs-3322	93	7	function	function	NOUN
iajs-3322	93	8	whenever	whenever	SCONJ
iajs-3322	93	9	ℱ	ℱ	PROPN
iajs-3322	93	10	is	be	AUX
iajs-3322	93	11	strongly	strongly	ADV
iajs-3322	93	12	ƞǥş	ƞǥş	NOUN
iajs-3322	93	13	-	-	PUNCT
iajs-3322	93	14	continuous	continuous	ADJ
iajs-3322	93	15	function	function	NOUN
iajs-3322	93	16	.	.	PUNCT
iajs-3322	94	1	2	2	X
iajs-3322	94	2	.	.	X
iajs-3322	94	3	if	if	SCONJ
iajs-3322	94	4	ℱ	ℱ	PROPN
iajs-3322	94	5	is	be	AUX
iajs-3322	94	6	a	a	DET
iajs-3322	94	7	strongly	strongly	ADV
iajs-3322	94	8	ƞǥş	ƞǥş	NOUN
iajs-3322	94	9	-	-	PUNCT
iajs-3322	94	10	continuous	continuous	ADJ
iajs-3322	94	11	function	function	NOUN
iajs-3322	94	12	then	then	ADV
iajs-3322	94	13	ℱ	ℱ	PROPN
iajs-3322	94	14	is	be	AUX
iajs-3322	94	15	a	a	DET
iajs-3322	94	16	continuous	continuous	ADJ
iajs-3322	94	17	function	function	NOUN
iajs-3322	94	18	.	.	PUNCT
iajs-3322	95	1	3	3	X
iajs-3322	95	2	.	.	PUNCT
iajs-3322	95	3	"	"	PUNCT
iajs-3322	96	1	𝑊ℎ𝑒𝑛	𝑊ℎ𝑒𝑛	NOUN
iajs-3322	96	2	ℱ	ℱ	PROPN
iajs-3322	96	3	𝑖𝑠	𝑖𝑠	CCONJ
iajs-3322	96	4	𝑎	𝑎	DET
iajs-3322	96	5	𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠	𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠	NOUN
iajs-3322	96	6	𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛	𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛	ADP
iajs-3322	96	7	“	"	PUNCT
iajs-3322	96	8	then	then	ADV
iajs-3322	96	9	ℱisƞǥş	ℱisƞǥş	NOUN
iajs-3322	96	10	-	-	PUNCT
iajs-3322	96	11	continuous	continuous	ADJ
iajs-3322	96	12	function	function	NOUN
iajs-3322	96	13	.	.	PUNCT
iajs-3322	97	1	4	4	X
iajs-3322	97	2	.	.	X
iajs-3322	97	3	ℱ	ℱ	PROPN
iajs-3322	97	4	isƞǥş	isƞǥş	NOUN
iajs-3322	97	5	-	-	PUNCT
iajs-3322	97	6	continuous	continuous	ADJ
iajs-3322	97	7	function	function	NOUN
iajs-3322	97	8	whenever	whenever	SCONJ
iajs-3322	97	9	ℱ	ℱ	PROPN
iajs-3322	97	10	is	be	AUX
iajs-3322	97	11	a	a	DET
iajs-3322	97	12	ƞǥş	ƞǥş	NOUN
iajs-3322	97	13	-irresolute	-irresolute	ADJ
iajs-3322	97	14	function	function	NOUN
iajs-3322	97	15	.	.	PUNCT
iajs-3322	98	1	in	in	ADP
iajs-3322	98	2	general	general	ADJ
iajs-3322	98	3	,	,	PUNCT
iajs-3322	98	4	the	the	DET
iajs-3322	98	5	opposite	opposite	NOUN
iajs-3322	98	6	of	of	ADP
iajs-3322	98	7	(	(	PUNCT
iajs-3322	98	8	proposition	proposition	NOUN
iajs-3322	98	9	3.9	3.9	NUM
iajs-3322	98	10	)	)	PUNCT
iajs-3322	98	11	is	be	AUX
iajs-3322	98	12	not	not	PART
iajs-3322	98	13	supported	support	VERB
iajs-3322	98	14	by	by	ADP
iajs-3322	98	15	the	the	DET
iajs-3322	98	16	following	follow	VERB
iajs-3322	98	17	examples	example	NOUN
iajs-3322	98	18	.	.	PUNCT
iajs-3322	99	1	example	example	NOUN
iajs-3322	99	2	3.10	3.10	NUM
iajs-3322	99	3	:	:	PUNCT
iajs-3322	99	4	let	let	VERB
iajs-3322	99	5	ℱ	ℱ	PROPN
iajs-3322	99	6	:	:	PUNCT
iajs-3322	99	7	(	(	PUNCT
iajs-3322	99	8	ꭓ	ꭓ	X
iajs-3322	99	9	,	,	PUNCT
iajs-3322	99	10	ʈⱳ	ʈⱳ	NOUN
iajs-3322	99	11	,	,	PUNCT
iajs-3322	99	12	ǥ	ǥ	NOUN
iajs-3322	99	13	)	)	PUNCT
iajs-3322	99	14	→	→	SYM
iajs-3322	99	15	(	(	PUNCT
iajs-3322	99	16	ꭓ	ꭓ	NUM
iajs-3322	99	17	,	,	PUNCT
iajs-3322	99	18	ʈⱳ	ʈⱳ	ADJ
iajs-3322	99	19	,	,	PUNCT
iajs-3322	99	20	ǥ~	ǥ~	NUM
iajs-3322	99	21	)	)	PUNCT
iajs-3322	99	22	be	be	VERB
iajs-3322	99	23	a	a	DET
iajs-3322	99	24	function	function	NOUN
iajs-3322	99	25	such	such	ADJ
iajs-3322	99	26	that	that	PRON
iajs-3322	99	27	ℱ(ꭓ	ℱ(ꭓ	ADP
iajs-3322	99	28	)	)	PUNCT
iajs-3322	99	29	=	=	SYM
iajs-3322	100	1	ꭓ	ꭓ	PROPN
iajs-3322	100	2	for	for	ADP
iajs-3322	100	3	each	each	DET
iajs-3322	100	4	ꭓ	ꭓ	PRON
iajs-3322	100	5	∈	∈	NOUN
iajs-3322	100	6	ꭓ	ꭓ	NUM
iajs-3322	100	7	where	where	SCONJ
iajs-3322	100	8	ꭓ	ꭓ	NOUN
iajs-3322	100	9	=	=	PUNCT
iajs-3322	100	10	{	{	PUNCT
iajs-3322	100	11	ӽ1	ӽ1	PROPN
iajs-3322	100	12	,	,	PUNCT
iajs-3322	100	13	ӽ2	ӽ2	PROPN
iajs-3322	100	14	,	,	PUNCT
iajs-3322	100	15	ӽ3	ӽ3	ADJ
iajs-3322	100	16	}	}	PUNCT
iajs-3322	100	17	,	,	PUNCT
iajs-3322	100	18	ǥ	ǥ	PROPN
iajs-3322	100	19	=	=	SYM
iajs-3322	100	20	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	100	21	)	)	PUNCT
iajs-3322	100	22	∖	∖	X
iajs-3322	100	23	{	{	PUNCT
iajs-3322	100	24	ǿ	ǿ	NOUN
iajs-3322	100	25	}	}	PUNCT
iajs-3322	100	26	ɽ	ɽ	NOUN
iajs-3322	100	27	=	=	SYM
iajs-3322	100	28	{	{	PUNCT
iajs-3322	100	29	(	(	PUNCT
iajs-3322	100	30	ꭓ	ꭓ	PROPN
iajs-3322	100	31	1	1	NUM
iajs-3322	100	32	,	,	PUNCT
iajs-3322	100	33	ꭓ	ꭓ	PROPN
iajs-3322	100	34	1	1	NUM
iajs-3322	100	35	)	)	PUNCT
iajs-3322	100	36	,	,	PUNCT
iajs-3322	100	37	(	(	PUNCT
iajs-3322	100	38	ꭓ	ꭓ	PROPN
iajs-3322	100	39	2	2	NUM
iajs-3322	100	40	,	,	PUNCT
iajs-3322	100	41	ꭓ	ꭓ	PROPN
iajs-3322	100	42	2	2	NUM
iajs-3322	100	43	)	)	PUNCT
iajs-3322	100	44	,	,	PUNCT
iajs-3322	100	45	(	(	PUNCT
iajs-3322	100	46	ꭓ	ꭓ	NOUN
iajs-3322	100	47	3	3	NUM
iajs-3322	100	48	,	,	PUNCT
iajs-3322	100	49	ꭓ	ꭓ	PROPN
iajs-3322	100	50	3	3	NUM
iajs-3322	100	51	)	)	PUNCT
iajs-3322	100	52	,	,	PUNCT
iajs-3322	100	53	(	(	PUNCT
iajs-3322	100	54	ꭓ	ꭓ	PROPN
iajs-3322	100	55	2	2	NUM
iajs-3322	100	56	,	,	PUNCT
iajs-3322	100	57	ꭓ	ꭓ	PROPN
iajs-3322	100	58	3	3	NUM
iajs-3322	100	59	)	)	PUNCT
iajs-3322	100	60	,	,	PUNCT
iajs-3322	100	61	(	(	PUNCT
iajs-3322	100	62	ꭓ	ꭓ	NOUN
iajs-3322	100	63	3	3	NUM
iajs-3322	100	64	,	,	PUNCT
iajs-3322	100	65	ꭓ	ꭓ	PROPN
iajs-3322	100	66	2	2	NUM
iajs-3322	100	67	)	)	PUNCT
iajs-3322	100	68	}	}	PUNCT
iajs-3322	100	69	ɽ	ɽ	NOUN
iajs-3322	100	70	∖	∖	NOUN
iajs-3322	101	1	[	[	X
iajs-3322	101	2	ꭓ	ꭓ	X
iajs-3322	101	3	]	]	X
iajs-3322	101	4	=	=	X
iajs-3322	101	5	{	{	PUNCT
iajs-3322	101	6	{	{	PUNCT
iajs-3322	101	7	ꭓ	ꭓ	PROPN
iajs-3322	101	8	2	2	NUM
iajs-3322	101	9	,	,	PUNCT
iajs-3322	101	10	ꭓ	ꭓ	PROPN
iajs-3322	101	11	3	3	NUM
iajs-3322	101	12	}	}	PUNCT
iajs-3322	101	13	,	,	PUNCT
iajs-3322	101	14	{	{	PUNCT
iajs-3322	101	15	ꭓ	ꭓ	NOUN
iajs-3322	101	16	1	1	NUM
iajs-3322	101	17	}	}	PUNCT
iajs-3322	101	18	}	}	PUNCT
iajs-3322	101	19	,	,	PUNCT
iajs-3322	101	20	ⱳ	ⱳ	X
iajs-3322	101	21	=	=	SYM
iajs-3322	101	22	{	{	PUNCT
iajs-3322	101	23	ꭓ	ꭓ	PROPN
iajs-3322	101	24	1	1	NUM
iajs-3322	101	25	}	}	PUNCT
iajs-3322	101	26	ʈⱳ	ʈⱳ	X
iajs-3322	101	27	=	=	X
iajs-3322	101	28	{	{	PUNCT
iajs-3322	101	29	ꭓ	ꭓ	PROPN
iajs-3322	101	30	,	,	PUNCT
iajs-3322	101	31	ǿ	ǿ	PRON
iajs-3322	101	32	,	,	PUNCT
iajs-3322	101	33	{	{	PUNCT
iajs-3322	101	34	ꭓ	ꭓ	NOUN
iajs-3322	101	35	1	1	NUM
iajs-3322	101	36	}	}	PUNCT
iajs-3322	101	37	}	}	PUNCT
iajs-3322	101	38	ǥ~	ǥ~	PROPN
iajs-3322	101	39	=	=	SYM
iajs-3322	101	40	{	{	PUNCT
iajs-3322	101	41	u	u	NOUN
iajs-3322	101	42	;	;	PUNCT
iajs-3322	101	43	ꭓ	ꭓ	PROPN
iajs-3322	101	44	1	1	NUM
iajs-3322	101	45	∈	∈	NOUN
iajs-3322	101	46	u	u	NOUN
iajs-3322	101	47	}	}	PUNCT
iajs-3322	101	48	,	,	PUNCT
iajs-3322	101	49	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	NUM
iajs-3322	101	50	)	)	PUNCT
iajs-3322	101	51	=	=	PRON
iajs-3322	101	52	{	{	PUNCT
iajs-3322	101	53	u	u	NOUN
iajs-3322	101	54	;	;	PUNCT
iajs-3322	101	55	ꭓ	ꭓ	NUM
iajs-3322	101	56	1	1	NUM
iajs-3322	101	57	∈	∈	NOUN
iajs-3322	101	58	u	u	NOUN
iajs-3322	101	59	}	}	PUNCT
iajs-3322	101	60	∪	∪	VERB
iajs-3322	101	61	{	{	PUNCT
iajs-3322	101	62	ø	ø	NOUN
iajs-3322	101	63	}	}	PUNCT
iajs-3322	101	64	,	,	PUNCT
iajs-3322	101	65	ƞǥş	ƞǥş	NOUN
iajs-3322	101	66	~ỏ(ꭓ	~ỏ(ꭓ	NOUN
iajs-3322	101	67	)	)	PUNCT
iajs-3322	101	68	=	=	SYM
iajs-3322	101	69	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	101	70	)	)	PUNCT
iajs-3322	101	71	.	.	PUNCT
iajs-3322	102	1	so	so	ADV
iajs-3322	102	2	that	that	SCONJ
iajs-3322	102	3	,	,	PUNCT
iajs-3322	102	4	,	,	PUNCT
iajs-3322	102	5	ℱ	ℱ	PROPN
iajs-3322	102	6	isƞǥş	isƞǥş	NOUN
iajs-3322	102	7	-	-	PUNCT
iajs-3322	102	8	continuous	continuous	ADJ
iajs-3322	102	9	function	function	NOUN
iajs-3322	102	10	and	and	CCONJ
iajs-3322	102	11	continuous	continuous	ADJ
iajs-3322	102	12	function	function	NOUN
iajs-3322	102	13	but	but	CCONJ
iajs-3322	102	14	it	it	PRON
iajs-3322	102	15	's	be	AUX
iajs-3322	102	16	not	not	PART
iajs-3322	102	17	ƞǥş	ƞǥş	NOUN
iajs-3322	102	18	-irresolute	-irresolute	ADJ
iajs-3322	102	19	function	function	NOUN
iajs-3322	103	1	and	and	CCONJ
iajs-3322	103	2	it	it	PRON
iajs-3322	103	3	's	be	AUX
iajs-3322	103	4	not	not	PART
iajs-3322	103	5	strongly	strongly	ADV
iajs-3322	103	6	ƞǥş	ƞǥş	NOUN
iajs-3322	103	7	-	-	PUNCT
iajs-3322	103	8	continuous	continuous	ADJ
iajs-3322	103	9	function	function	NOUN
iajs-3322	103	10	.	.	PUNCT
iajs-3322	104	1	example	example	NOUN
iajs-3322	105	1	3.11	3.11	NUM
iajs-3322	105	2	:	:	PUNCT
iajs-3322	105	3	the	the	DET
iajs-3322	105	4	function	function	NOUN
iajs-3322	105	5	ℱ	ℱ	PROPN
iajs-3322	105	6	:	:	PUNCT
iajs-3322	105	7	(	(	PUNCT
iajs-3322	105	8	ꭓ	ꭓ	X
iajs-3322	105	9	,	,	PUNCT
iajs-3322	105	10	ʈⱳ	ʈⱳ	NOUN
iajs-3322	105	11	,	,	PUNCT
iajs-3322	105	12	ǥ	ǥ	NOUN
iajs-3322	105	13	)	)	PUNCT
iajs-3322	105	14	→	→	SYM
iajs-3322	105	15	(	(	PUNCT
iajs-3322	105	16	ꭓ	ꭓ	NUM
iajs-3322	105	17	,	,	PUNCT
iajs-3322	105	18	ʈⱳ	ʈⱳ	ADJ
iajs-3322	105	19	,	,	PUNCT
iajs-3322	105	20	ǥ~	ǥ~	NUM
iajs-3322	105	21	)	)	PUNCT
iajs-3322	105	22	such	such	ADJ
iajs-3322	105	23	that	that	SCONJ
iajs-3322	105	24	ℱ({ꭓ	ℱ({ꭓ	NOUN
iajs-3322	105	25	2	2	NUM
iajs-3322	105	26	}	}	PUNCT
iajs-3322	105	27	)	)	PUNCT
iajs-3322	105	28	=	=	PRON
iajs-3322	105	29	{	{	PUNCT
iajs-3322	105	30	ꭓ	ꭓ	NOUN
iajs-3322	105	31	1	1	NUM
iajs-3322	105	32	}	}	PUNCT
iajs-3322	105	33	,	,	PUNCT
iajs-3322	105	34	ℱ({ꭓ	ℱ({ꭓ	ADV
iajs-3322	105	35	1	1	NUM
iajs-3322	105	36	}	}	PUNCT
iajs-3322	105	37	)	)	PUNCT
iajs-3322	105	38	=	=	PRON
iajs-3322	105	39	{	{	PUNCT
iajs-3322	105	40	ꭓ	ꭓ	PROPN
iajs-3322	105	41	2	2	NUM
iajs-3322	105	42	}	}	PUNCT
iajs-3322	105	43	,	,	PUNCT
iajs-3322	105	44	ℱ({ꭓ	ℱ({ꭓ	ADP
iajs-3322	105	45	3	3	NUM
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iajs-3322	105	47	)	)	PUNCT
iajs-3322	106	1	=	=	PRON
iajs-3322	106	2	{	{	PUNCT
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iajs-3322	106	4	3	3	NUM
iajs-3322	106	5	}	}	PUNCT
iajs-3322	106	6	,	,	PUNCT
iajs-3322	106	7	ihjpas	ihjpas	PROPN
iajs-3322	106	8	.	.	PUNCT
iajs-3322	107	1	2025	2025	NUM
iajs-3322	107	2	,	,	PUNCT
iajs-3322	107	3	38	38	NUM
iajs-3322	107	4	(	(	PUNCT
iajs-3322	107	5	1	1	NUM
iajs-3322	107	6	)	)	PUNCT
iajs-3322	107	7	364	364	NUM
iajs-3322	107	8	where	where	SCONJ
iajs-3322	107	9	ꭓ	ꭓ	NOUN
iajs-3322	107	10	=	=	PRON
iajs-3322	107	11	{	{	PUNCT
iajs-3322	107	12	ꭓ	ꭓ	PROPN
iajs-3322	107	13	1	1	NUM
iajs-3322	107	14	,	,	PUNCT
iajs-3322	107	15	ꭓ	ꭓ	PROPN
iajs-3322	107	16	2	2	NUM
iajs-3322	107	17	,	,	PUNCT
iajs-3322	107	18	ꭓ	ꭓ	PROPN
iajs-3322	107	19	3	3	NUM
iajs-3322	107	20	}	}	PUNCT
iajs-3322	107	21	,	,	PUNCT
iajs-3322	107	22	ǥ~	ǥ~	PROPN
iajs-3322	107	23	=	=	SYM
iajs-3322	107	24	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	107	25	)	)	PUNCT
iajs-3322	107	26	∖	∖	X
iajs-3322	107	27	{	{	PUNCT
iajs-3322	107	28	ǿ	ǿ	NOUN
iajs-3322	107	29	}	}	PUNCT
iajs-3322	107	30	}	}	PUNCT
iajs-3322	107	31	ɽ	ɽ	NOUN
iajs-3322	107	32	=	=	SYM
iajs-3322	107	33	{	{	PUNCT
iajs-3322	107	34	(	(	PUNCT
iajs-3322	107	35	ꭓ	ꭓ	PROPN
iajs-3322	107	36	1	1	NUM
iajs-3322	107	37	,	,	PUNCT
iajs-3322	107	38	ꭓ	ꭓ	PROPN
iajs-3322	107	39	1	1	NUM
iajs-3322	107	40	)	)	PUNCT
iajs-3322	107	41	,	,	PUNCT
iajs-3322	107	42	(	(	PUNCT
iajs-3322	107	43	ꭓ	ꭓ	PROPN
iajs-3322	107	44	2	2	NUM
iajs-3322	107	45	,	,	PUNCT
iajs-3322	107	46	ꭓ	ꭓ	PROPN
iajs-3322	107	47	2	2	NUM
iajs-3322	107	48	)	)	PUNCT
iajs-3322	107	49	,	,	PUNCT
iajs-3322	107	50	(	(	PUNCT
iajs-3322	107	51	ꭓ	ꭓ	NOUN
iajs-3322	107	52	3	3	NUM
iajs-3322	107	53	,	,	PUNCT
iajs-3322	107	54	ꭓ	ꭓ	PROPN
iajs-3322	107	55	3	3	NUM
iajs-3322	107	56	)	)	PUNCT
iajs-3322	107	57	,	,	PUNCT
iajs-3322	107	58	(	(	PUNCT
iajs-3322	107	59	ꭓ	ꭓ	PROPN
iajs-3322	107	60	2	2	NUM
iajs-3322	107	61	,	,	PUNCT
iajs-3322	107	62	ꭓ	ꭓ	PROPN
iajs-3322	107	63	3	3	NUM
iajs-3322	107	64	)	)	PUNCT
iajs-3322	107	65	,	,	PUNCT
iajs-3322	107	66	(	(	PUNCT
iajs-3322	107	67	ꭓ	ꭓ	NOUN
iajs-3322	107	68	3	3	NUM
iajs-3322	107	69	,	,	PUNCT
iajs-3322	107	70	ꭓ	ꭓ	PROPN
iajs-3322	107	71	2	2	NUM
iajs-3322	107	72	)	)	PUNCT
iajs-3322	107	73	}	}	PUNCT
iajs-3322	108	1	ɽ	ɽ	NOUN
iajs-3322	108	2	∖	∖	NOUN
iajs-3322	109	1	[	[	X
iajs-3322	109	2	ꭓ	ꭓ	X
iajs-3322	109	3	]	]	X
iajs-3322	109	4	=	=	X
iajs-3322	109	5	{	{	PUNCT
iajs-3322	109	6	{	{	PUNCT
iajs-3322	109	7	ꭓ	ꭓ	PROPN
iajs-3322	109	8	2	2	NUM
iajs-3322	109	9	,	,	PUNCT
iajs-3322	109	10	ꭓ	ꭓ	PROPN
iajs-3322	109	11	3	3	NUM
iajs-3322	109	12	}	}	PUNCT
iajs-3322	109	13	,	,	PUNCT
iajs-3322	109	14	{	{	PUNCT
iajs-3322	109	15	ꭓ	ꭓ	NOUN
iajs-3322	109	16	1	1	NUM
iajs-3322	109	17	}	}	PUNCT
iajs-3322	109	18	}	}	PUNCT
iajs-3322	109	19	,	,	PUNCT
iajs-3322	109	20	ⱳ	ⱳ	X
iajs-3322	109	21	=	=	SYM
iajs-3322	109	22	{	{	PUNCT
iajs-3322	109	23	ꭓ	ꭓ	PROPN
iajs-3322	109	24	1	1	NUM
iajs-3322	109	25	}	}	PUNCT
iajs-3322	109	26	ʈⱳ	ʈⱳ	X
iajs-3322	109	27	=	=	X
iajs-3322	109	28	{	{	PUNCT
iajs-3322	109	29	ꭓ	ꭓ	PROPN
iajs-3322	109	30	,	,	PUNCT
iajs-3322	109	31	ǿ	ǿ	PRON
iajs-3322	109	32	,	,	PUNCT
iajs-3322	109	33	{	{	PUNCT
iajs-3322	109	34	ꭓ	ꭓ	NOUN
iajs-3322	109	35	1	1	NUM
iajs-3322	109	36	}	}	PUNCT
iajs-3322	109	37	}	}	PUNCT
iajs-3322	109	38	,	,	PUNCT
iajs-3322	109	39	ǥ	ǥ	NOUN
iajs-3322	109	40	=	=	PRON
iajs-3322	109	41	{	{	PUNCT
iajs-3322	109	42	u	u	NOUN
iajs-3322	109	43	;	;	PUNCT
iajs-3322	109	44	ꭓ	ꭓ	PROPN
iajs-3322	109	45	1	1	NUM
iajs-3322	109	46	∈	∈	NOUN
iajs-3322	109	47	u	u	NOUN
iajs-3322	109	48	}	}	PUNCT
iajs-3322	109	49	,	,	PUNCT
iajs-3322	109	50	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	NUM
iajs-3322	109	51	)	)	PUNCT
iajs-3322	109	52	=	=	SYM
iajs-3322	109	53	ꝕ(ꭓ	ꝕ(ꭓ	PROPN
iajs-3322	109	54	)	)	PUNCT
iajs-3322	109	55	∖	∖	X
iajs-3322	109	56	{	{	PUNCT
iajs-3322	109	57	ǿ	ǿ	NOUN
iajs-3322	109	58	}	}	PUNCT
iajs-3322	109	59	,	,	PUNCT
iajs-3322	109	60	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	NOUN
iajs-3322	109	61	)	)	PUNCT
iajs-3322	109	62	=	=	PRON
iajs-3322	109	63	{	{	PUNCT
iajs-3322	109	64	u	u	NOUN
iajs-3322	109	65	;	;	PUNCT
iajs-3322	109	66	ꭓ	ꭓ	NUM
iajs-3322	109	67	1	1	NUM
iajs-3322	109	68	∈	∈	NOUN
iajs-3322	109	69	u	u	NOUN
iajs-3322	109	70	}	}	PUNCT
iajs-3322	109	71	∪	∪	VERB
iajs-3322	109	72	{	{	PUNCT
iajs-3322	109	73	ø	ø	NOUN
iajs-3322	109	74	}	}	PUNCT
iajs-3322	109	75	,	,	PUNCT
iajs-3322	109	76	ℱ	ℱ	PROPN
iajs-3322	109	77	𝑖𝑠	𝑖𝑠	NOUN
iajs-3322	109	78	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	NOUN
iajs-3322	109	79	)	)	PUNCT
iajs-3322	109	80	continuous	continuous	ADJ
iajs-3322	109	81	function	function	NOUN
iajs-3322	109	82	and	and	CCONJ
iajs-3322	109	83	ƞǥş	ƞǥş	NOUN
iajs-3322	109	84	-irresolute	-irresolute	NOUN
iajs-3322	109	85	function	function	NOUN
iajs-3322	110	1	but	but	CCONJ
iajs-3322	110	2	it	it	PRON
iajs-3322	110	3	is	be	AUX
iajs-3322	110	4	n't	not	PART
iajs-3322	110	5	continuous	continuous	ADJ
iajs-3322	110	6	function	function	NOUN
iajs-3322	110	7	and	and	CCONJ
iajs-3322	110	8	not	not	PART
iajs-3322	110	9	strongly	strongly	ADV
iajs-3322	110	10	ƞǥş	ƞǥş	NOUN
iajs-3322	110	11	-	-	PUNCT
iajs-3322	110	12	continuous	continuous	ADJ
iajs-3322	110	13	function	function	NOUN
iajs-3322	110	14	it	it	PRON
iajs-3322	110	15	's	be	AUX
iajs-3322	110	16	not	not	PART
iajs-3322	110	17	since	since	SCONJ
iajs-3322	110	18	ℱ−1(ꭓ	ℱ−1(ꭓ	X
iajs-3322	110	19	1	1	X
iajs-3322	110	20	)	)	PUNCT
iajs-3322	110	21	=	=	PRON
iajs-3322	111	1	{	{	PUNCT
iajs-3322	111	2	ꭓ	ꭓ	PROPN
iajs-3322	111	3	2	2	NUM
iajs-3322	111	4	}	}	PUNCT
iajs-3322	111	5	∉	∉	PROPN
iajs-3322	111	6	ʈⱳ	ʈⱳ	PROPN
iajs-3322	111	7	.	.	PROPN
iajs-3322	111	8	diagram1	diagram1	PROPN
iajs-3322	111	9	.	.	PUNCT
iajs-3322	112	1	continuous	continuous	ADJ
iajs-3322	112	2	functions	function	NOUN
iajs-3322	112	3	via	via	ADP
iajs-3322	112	4	ƞǥşopen	ƞǥşopen	NOUN
iajs-3322	112	5	proposition	proposition	NOUN
iajs-3322	112	6	12	12	NUM
iajs-3322	112	7	:	:	PUNCT
iajs-3322	112	8	i.	i.	NOUN
iajs-3322	112	9	the	the	DET
iajs-3322	112	10	ƞǥşirresolute	ƞǥşirresolute	ADJ
iajs-3322	112	11	image	image	NOUN
iajs-3322	112	12	function	function	NOUN
iajs-3322	112	13	ƞǥş	ƞǥş	NOUN
iajs-3322	112	14	−	−	PROPN
iajs-3322	112	15	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	112	16	𝑠𝑝𝑎𝑐𝑒is	𝑠𝑝𝑎𝑐𝑒is	NOUN
iajs-3322	112	17	a	a	DET
iajs-3322	112	18	ƞǥş	ƞǥş	NOUN
iajs-3322	112	19	−	−	PROPN
iajs-3322	112	20	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	112	21	𝑠𝑝𝑎𝑐𝑒.	𝑠𝑝𝑎𝑐𝑒.	PROPN
iajs-3322	112	22	ii	ii	PROPN
iajs-3322	112	23	.	.	PUNCT
iajs-3322	113	1	in	in	ADP
iajs-3322	113	2	strongly	strongly	ADV
iajs-3322	113	3	ƞǥş	ƞǥş	NOUN
iajs-3322	113	4	−	−	NOUN
iajs-3322	113	5	continuous	continuous	ADJ
iajs-3322	113	6	the	the	DET
iajs-3322	113	7	image	image	NOUN
iajs-3322	113	8	of	of	ADP
iajs-3322	113	9	nano	nano	ADJ
iajs-3322	113	10	compact	compact	ADJ
iajs-3322	113	11	space	space	NOUN
iajs-3322	113	12	is	be	AUX
iajs-3322	113	13	a	a	DET
iajs-3322	113	14	ƞǥş	ƞǥş	NOUN
iajs-3322	113	15	−	−	NOUN
iajs-3322	113	16	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	113	17	𝑠𝑝𝑎𝑐𝑒.	𝑠𝑝𝑎𝑐𝑒.	PROPN
iajs-3322	113	18	iii	iii	PROPN
iajs-3322	113	19	.	.	PUNCT
iajs-3322	114	1	the	the	DET
iajs-3322	114	2	ƞǥş	ƞǥş	NOUN
iajs-3322	114	3	−	−	NOUN
iajs-3322	114	4	continuous	continuous	ADJ
iajs-3322	114	5	function	function	NOUN
iajs-3322	114	6	the	the	DET
iajs-3322	114	7	image	image	NOUN
iajs-3322	114	8	function	function	NOUN
iajs-3322	114	9	of	of	ADP
iajs-3322	114	10	ƞǥş	ƞǥş	NOUN
iajs-3322	114	11	−	−	PROPN
iajs-3322	114	12	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	114	13	is	be	AUX
iajs-3322	114	14	a	a	DET
iajs-3322	114	15	nano	nano	ADJ
iajs-3322	114	16	compact	compact	NOUN
iajs-3322	114	17	.	.	PUNCT
iajs-3322	115	1	proposition	proposition	NOUN
iajs-3322	115	2	3.13	3.13	NUM
iajs-3322	115	3	:	:	PUNCT
iajs-3322	115	4	a	a	DET
iajs-3322	115	5	ƞǥş	ƞǥş	NOUN
iajs-3322	115	6	−	−	NOUN
iajs-3322	115	7	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-3322	115	8	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	𝑠𝑢𝑏𝑠𝑒𝑡𝑠	NOUN
iajs-3322	115	9	of	of	ADP
iajs-3322	115	10	ƞǥş	ƞǥş	NOUN
iajs-3322	115	11	−	−	PROPN
iajs-3322	115	12	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	115	13	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-3322	115	14	is	be	AUX
iajs-3322	115	15	ƞǥş	ƞǥş	NOUN
iajs-3322	115	16	−	−	PROPN
iajs-3322	115	17	𝑐𝑜𝑚𝑝𝑎𝑐𝑡.	𝑐𝑜𝑚𝑝𝑎𝑐𝑡.	NOUN
iajs-3322	115	18	theorem	theorem	VERB
iajs-3322	115	19	3.14	3.14	NUM
iajs-3322	115	20	:	:	PUNCT
iajs-3322	115	21	if	if	SCONJ
iajs-3322	115	22	a	a	PRON
iajs-3322	115	23	&	&	CCONJ
iajs-3322	115	24	b	b	PROPN
iajs-3322	115	25	are	be	AUX
iajs-3322	115	26	ƞǥş	ƞǥş	NOUN
iajs-3322	115	27	−	−	PROPN
iajs-3322	115	28	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	115	29	,	,	PUNCT
iajs-3322	115	30	then	then	ADV
iajs-3322	115	31	a∪	a∪	PROPN
iajs-3322	115	32	b	b	NOUN
iajs-3322	115	33	is	be	AUX
iajs-3322	115	34	a	a	DET
iajs-3322	115	35	ƞǥş	ƞǥş	NOUN
iajs-3322	115	36	−	−	NOUN
iajs-3322	115	37	𝑐𝑜𝑚𝑝𝑎𝑐𝑡.	𝑐𝑜𝑚𝑝𝑎𝑐𝑡.	NOUN
iajs-3322	115	38	proposition	proposition	NOUN
iajs-3322	115	39	3.15	3.15	NUM
iajs-3322	115	40	:	:	PUNCT
iajs-3322	115	41	every	every	DET
iajs-3322	115	42	ƞǥş	ƞǥş	NOUN
iajs-3322	115	43	−	−	PROPN
iajs-3322	115	44	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	115	45	is	be	AUX
iajs-3322	115	46	a	a	DET
iajs-3322	115	47	nano	nano	ADJ
iajs-3322	115	48	compact	compact	NOUN
iajs-3322	115	49	.	.	PUNCT
iajs-3322	116	1	example	example	NOUN
iajs-3322	117	1	3.16	3.16	NUM
iajs-3322	117	2	:	:	PUNCT
iajs-3322	117	3	let	let	VERB
iajs-3322	117	4	(	(	PUNCT
iajs-3322	117	5	℟	℟	PROPN
iajs-3322	117	6	,	,	PUNCT
iajs-3322	117	7	ꭓ	ꭓ	PROPN
iajs-3322	117	8	,	,	PUNCT
iajs-3322	117	9	ʈⱳ	ʈⱳ	NOUN
iajs-3322	117	10	)	)	PUNCT
iajs-3322	117	11	be	be	VERB
iajs-3322	117	12	any	any	DET
iajs-3322	117	13	nano	nano	ADJ
iajs-3322	117	14	topological	topological	ADJ
iajs-3322	117	15	space	space	NOUN
iajs-3322	117	16	such	such	ADJ
iajs-3322	117	17	that	that	SCONJ
iajs-3322	117	18	℟	℟	PROPN
iajs-3322	117	19	is	be	AUX
iajs-3322	117	20	the	the	DET
iajs-3322	117	21	set	set	NOUN
iajs-3322	117	22	of	of	ADP
iajs-3322	117	23	all	all	DET
iajs-3322	117	24	real	real	ADJ
iajs-3322	117	25	numbers	number	NOUN
iajs-3322	117	26	and	and	CCONJ
iajs-3322	117	27	ɽ	ɽ	NOUN
iajs-3322	117	28	=	=	NOUN
iajs-3322	117	29	ƞǥş	ƞǥş	NOUN
iajs-3322	117	30	-irresolute	-irresolute	ADJ
iajs-3322	117	31	function	function	NOUN
iajs-3322	117	32	ƞǥş	ƞǥş	NOUN
iajs-3322	117	33	-	-	PUNCT
iajs-3322	117	34	continuous	continuous	ADJ
iajs-3322	117	35	function	function	NOUN
iajs-3322	117	36	strongly	strongly	ADV
iajs-3322	117	37	ƞǥş	ƞǥş	NOUN
iajs-3322	117	38	-	-	PUNCT
iajs-3322	117	39	continuous	continuous	ADJ
iajs-3322	117	40	function	function	NOUN
iajs-3322	117	41	continuous	continuous	ADJ
iajs-3322	117	42	function	function	NOUN
iajs-3322	117	43	ihjpas	ihjpa	NOUN
iajs-3322	117	44	.	.	PUNCT
iajs-3322	118	1	2025	2025	NUM
iajs-3322	118	2	,	,	PUNCT
iajs-3322	118	3	38	38	NUM
iajs-3322	118	4	(	(	PUNCT
iajs-3322	118	5	1	1	NUM
iajs-3322	118	6	)	)	PUNCT
iajs-3322	118	7	365	365	NUM
iajs-3322	118	8	{	{	PUNCT
iajs-3322	118	9	(	(	PUNCT
iajs-3322	118	10	r	r	NOUN
iajs-3322	118	11	,	,	PUNCT
iajs-3322	118	12	r	r	NOUN
iajs-3322	118	13	)	)	PUNCT
iajs-3322	118	14	,	,	PUNCT
iajs-3322	118	15	r	r	NOUN
iajs-3322	118	16	∈	∈	PROPN
iajs-3322	118	17	℟	℟	PROPN
iajs-3322	118	18	}	}	PUNCT
iajs-3322	118	19	so	so	ADV
iajs-3322	118	20	,	,	PUNCT
iajs-3322	118	21	ɽ	ɽ	NOUN
iajs-3322	118	22	∖	∖	X
iajs-3322	119	1	[	[	X
iajs-3322	119	2	𝑟	𝑟	X
iajs-3322	119	3	]	]	X
iajs-3322	119	4	=	=	X
iajs-3322	119	5	{	{	PUNCT
iajs-3322	119	6	{	{	PUNCT
iajs-3322	119	7	r	r	NOUN
iajs-3322	119	8	}	}	PUNCT
iajs-3322	119	9	,	,	PUNCT
iajs-3322	119	10	r	r	PROPN
iajs-3322	119	11	∈	∈	PROPN
iajs-3322	119	12	℟	℟	PROPN
iajs-3322	119	13	}	}	PUNCT
iajs-3322	119	14	.	.	PUNCT
iajs-3322	120	1	now	now	ADV
iajs-3322	120	2	,	,	PUNCT
iajs-3322	120	3	if	if	SCONJ
iajs-3322	120	4	ⱳ=	ⱳ=	PRON
iajs-3322	120	5	{	{	PUNCT
iajs-3322	120	6	1	1	NUM
iajs-3322	120	7	}	}	PUNCT
iajs-3322	120	8	and	and	CCONJ
iajs-3322	120	9	ǥ	ǥ	NOUN
iajs-3322	120	10	=	=	SYM
iajs-3322	120	11	ꝕ	ꝕ	PROPN
iajs-3322	120	12	[	[	X
iajs-3322	120	13	℟	℟	PROPN
iajs-3322	120	14	]	]	PUNCT
iajs-3322	120	15	∖	∖	PROPN
iajs-3322	120	16	ø	ø	PROPN
iajs-3322	120	17	,	,	PUNCT
iajs-3322	120	18	then	then	ADV
iajs-3322	120	19	ɽⱳ	ɽⱳ	PROPN
iajs-3322	120	20	̅̅	̅̅	PROPN
iajs-3322	120	21	̅̅	̅̅	PROPN
iajs-3322	120	22	=	=	PUNCT
iajs-3322	120	23	{	{	PUNCT
iajs-3322	120	24	1	1	NUM
iajs-3322	120	25	}	}	PUNCT
iajs-3322	120	26	=	=	SYM
iajs-3322	120	27	ɽⱳ	ɽⱳ	NOUN
iajs-3322	120	28	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
iajs-3322	120	29	ᴃⱳ	ᴃⱳ	ADP
iajs-3322	120	30	=	=	SYM
iajs-3322	120	31	ø	ø	PROPN
iajs-3322	121	1	so	so	ADV
iajs-3322	121	2	,	,	PUNCT
iajs-3322	121	3	ʈⱳ	ʈⱳ	NOUN
iajs-3322	121	4	=	=	NOUN
iajs-3322	121	5	ƞʈⱳǥ	ƞʈⱳǥ	NOUN
iajs-3322	121	6	=	=	SYM
iajs-3322	121	7	{	{	PUNCT
iajs-3322	121	8	℟	℟	PROPN
iajs-3322	121	9	,	,	PUNCT
iajs-3322	121	10	ø	ø	PROPN
iajs-3322	121	11	,	,	PUNCT
iajs-3322	121	12	{	{	PUNCT
iajs-3322	121	13	1	1	NUM
iajs-3322	121	14	}	}	PUNCT
iajs-3322	121	15	}	}	PUNCT
iajs-3322	121	16	and	and	CCONJ
iajs-3322	121	17	ƞǥşỏ	ƞǥşỏ	PROPN
iajs-3322	121	18	(	(	PUNCT
iajs-3322	121	19	℟	℟	PROPN
iajs-3322	121	20	)	)	PUNCT
iajs-3322	121	21	=	=	PRON
iajs-3322	121	22	{	{	PUNCT
iajs-3322	121	23	ȗ⊆	ȗ⊆	PROPN
iajs-3322	121	24	℟	℟	PROPN
iajs-3322	121	25	;	;	PUNCT
iajs-3322	121	26	1	1	NUM
iajs-3322	121	27	∈	∈	PROPN
iajs-3322	121	28	ȗ	ȗ	NOUN
iajs-3322	121	29	}	}	PUNCT
iajs-3322	121	30	∪	∪	VERB
iajs-3322	121	31	ø	ø	PROPN
iajs-3322	121	32	.this	.this	PRON
iajs-3322	121	33	much	much	ADJ
iajs-3322	121	34	is	be	AUX
iajs-3322	121	35	clear	clear	ADJ
iajs-3322	121	36	:	:	PUNCT
iajs-3322	121	37	(	(	PUNCT
iajs-3322	121	38	℟	℟	PROPN
iajs-3322	121	39	,	,	PUNCT
iajs-3322	121	40	ʈⱳ	ʈⱳ	NOUN
iajs-3322	121	41	,	,	PUNCT
iajs-3322	121	42	ǥ	ǥ	NOUN
iajs-3322	121	43	)	)	PUNCT
iajs-3322	121	44	is	be	AUX
iajs-3322	121	45	a	a	DET
iajs-3322	121	46	nano	nano	ADJ
iajs-3322	121	47	compact	compact	NOUN
iajs-3322	121	48	which	which	PRON
iajs-3322	121	49	is	be	AUX
iajs-3322	121	50	not	not	PART
iajs-3322	121	51	ƞǥş	ƞǥş	NOUN
iajs-3322	121	52	−	−	PROPN
iajs-3322	121	53	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	𝑐𝑜𝑚𝑝𝑎𝑐𝑡	NOUN
iajs-3322	121	54	since	since	SCONJ
iajs-3322	121	55	l	l	PROPN
iajs-3322	121	56	=	=	PUNCT
iajs-3322	121	57	{	{	PUNCT
iajs-3322	121	58	{	{	PUNCT
iajs-3322	121	59	1,r	1,r	NUM
iajs-3322	121	60	}	}	PUNCT
iajs-3322	121	61	,	,	PUNCT
iajs-3322	121	62	r	r	PROPN
iajs-3322	121	63	∈	∈	PROPN
iajs-3322	121	64	℟	℟	PROPN
iajs-3322	121	65	}	}	PUNCT
iajs-3322	121	66	is	be	AUX
iajs-3322	121	67	ƞǥş	ƞǥş	NOUN
iajs-3322	121	68	−	−	NOUN
iajs-3322	121	69	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	121	70	𝑐𝑜𝑣𝑒𝑟	𝑐𝑜𝑣𝑒𝑟	NOUN
iajs-3322	121	71	has	have	VERB
iajs-3322	121	72	no	no	DET
iajs-3322	121	73	finite	finite	PROPN
iajs-3322	121	74	subcover	subcover	PROPN
iajs-3322	121	75	.	.	PUNCT
iajs-3322	122	1	4	4	X
iajs-3322	122	2	.	.	X
iajs-3322	122	3	conclusion	conclusion	NOUN
iajs-3322	122	4	in	in	ADP
iajs-3322	122	5	this	this	DET
iajs-3322	122	6	work	work	NOUN
iajs-3322	122	7	,	,	PUNCT
iajs-3322	122	8	a	a	DET
iajs-3322	122	9	new	new	ADJ
iajs-3322	122	10	type	type	NOUN
iajs-3322	122	11	of	of	ADP
iajs-3322	122	12	open	open	ADJ
iajs-3322	122	13	set	set	NOUN
iajs-3322	122	14	was	be	AUX
iajs-3322	122	15	studied	study	VERB
iajs-3322	122	16	using	use	VERB
iajs-3322	122	17	the	the	DET
iajs-3322	122	18	concept	concept	NOUN
iajs-3322	122	19	of	of	ADP
iajs-3322	122	20	nano	nano	NOUN
iajs-3322	122	21	-	-	PUNCT
iajs-3322	122	22	topology	topology	NOUN
iajs-3322	122	23	,	,	PUNCT
iajs-3322	122	24	grill	grill	NOUN
iajs-3322	122	25	and	and	CCONJ
iajs-3322	122	26	nano	nano	NOUN
iajs-3322	122	27	compact	compact	NOUN
iajs-3322	122	28	which	which	PRON
iajs-3322	122	29	is	be	AUX
iajs-3322	122	30	called	call	VERB
iajs-3322	122	31	ƞǥş	ƞǥş	NOUN
iajs-3322	122	32	−	−	NOUN
iajs-3322	122	33	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-3322	122	34	𝑠𝑒𝑡𝑠.	𝑠𝑒𝑡𝑠.	VERB
iajs-3322	122	35	the	the	DET
iajs-3322	122	36	properties	property	NOUN
iajs-3322	122	37	of	of	ADP
iajs-3322	122	38	this	this	DET
iajs-3322	122	39	set	set	NOUN
iajs-3322	122	40	were	be	AUX
iajs-3322	122	41	studied	study	VERB
iajs-3322	122	42	.	.	PUNCT
iajs-3322	123	1	it	it	PRON
iajs-3322	123	2	was	be	AUX
iajs-3322	123	3	found	find	VERB
iajs-3322	123	4	that	that	SCONJ
iajs-3322	123	5	ƞǥşỏ(ꭓ	ƞǥşỏ(ꭓ	NOUN
iajs-3322	123	6	)	)	PUNCT
iajs-3322	123	7	represents	represent	VERB
iajs-3322	123	8	a	a	DET
iajs-3322	123	9	supra	supra	ADJ
iajs-3322	123	10	-	-	PUNCT
iajs-3322	123	11	topology	topology	NOUN
iajs-3322	123	12	space	space	NOUN
iajs-3322	123	13	.	.	PUNCT
iajs-3322	124	1	new	new	ADJ
iajs-3322	124	2	forms	form	NOUN
iajs-3322	124	3	of	of	ADP
iajs-3322	124	4	functionality	functionality	NOUN
iajs-3322	124	5	were	be	AUX
iajs-3322	124	6	defined	define	VERB
iajs-3322	124	7	by	by	ADP
iajs-3322	124	8	applying	apply	VERB
iajs-3322	124	9	this	this	DET
iajs-3322	124	10	notion	notion	NOUN
iajs-3322	124	11	,	,	PUNCT
iajs-3322	124	12	and	and	CCONJ
iajs-3322	124	13	the	the	DET
iajs-3322	124	14	relationship	relationship	NOUN
iajs-3322	124	15	between	between	ADP
iajs-3322	124	16	these	these	DET
iajs-3322	124	17	functions	function	NOUN
iajs-3322	124	18	was	be	AUX
iajs-3322	124	19	found	find	VERB
iajs-3322	124	20	.	.	PUNCT
iajs-3322	125	1	acknowledgment	acknowledgment	NOUN
iajs-3322	125	2	our	our	PRON
iajs-3322	125	3	researcher	researcher	NOUN
iajs-3322	125	4	extends	extend	VERB
iajs-3322	125	5	his	his	PRON
iajs-3322	125	6	sincere	sincere	ADJ
iajs-3322	125	7	thanks	thank	NOUN
iajs-3322	125	8	to	to	ADP
iajs-3322	125	9	the	the	DET
iajs-3322	125	10	editor	editor	NOUN
iajs-3322	125	11	and	and	CCONJ
iajs-3322	125	12	members	member	NOUN
iajs-3322	125	13	of	of	ADP
iajs-3322	125	14	the	the	DET
iajs-3322	125	15	preparatory	preparatory	PROPN
iajs-3322	125	16	committee	committee	NOUN
iajs-3322	125	17	of	of	ADP
iajs-3322	125	18	the	the	DET
iajs-3322	125	19	ibn	ibn	PROPN
iajs-3322	125	20	al	al	PROPN
iajs-3322	125	21	-	-	PUNCT
iajs-3322	125	22	haitham	haitham	PROPN
iajs-3322	125	23	journal	journal	PROPN
iajs-3322	125	24	of	of	ADP
iajs-3322	125	25	pure	pure	ADJ
iajs-3322	125	26	and	and	CCONJ
iajs-3322	125	27	applied	applied	ADJ
iajs-3322	125	28	sciences	science	NOUN
iajs-3322	125	29	.	.	PUNCT
iajs-3322	126	1	conflict	conflict	NOUN
iajs-3322	126	2	of	of	ADP
iajs-3322	126	3	interest	interest	NOUN
iajs-3322	126	4	there	there	PRON
iajs-3322	126	5	are	be	VERB
iajs-3322	126	6	no	no	DET
iajs-3322	126	7	conflicts	conflict	NOUN
iajs-3322	126	8	of	of	ADP
iajs-3322	126	9	interest	interest	NOUN
iajs-3322	126	10	.	.	PUNCT
iajs-3322	127	1	fundinsg	fundinsg	PROPN
iajs-3322	127	2	there	there	PRON
iajs-3322	127	3	is	be	VERB
iajs-3322	127	4	no	no	DET
iajs-3322	127	5	funding	funding	NOUN
iajs-3322	127	6	for	for	ADP
iajs-3322	127	7	the	the	DET
iajs-3322	127	8	article	article	NOUN
iajs-3322	127	9	.	.	PUNCT
iajs-3322	128	1	references	reference	NOUN
iajs-3322	128	2	1	1	NUM
iajs-3322	128	3	.	.	PUNCT
iajs-3322	128	4	choquet	choquet	PROPN
iajs-3322	128	5	g.	g.	PROPN
iajs-3322	128	6	sur	sur	PROPN
iajs-3322	128	7	les	les	PROPN
iajs-3322	128	8	notions	notion	NOUN
iajs-3322	128	9	de	de	X
iajs-3322	128	10	filtre	filtre	NOUN
iajs-3322	128	11	et	et	NOUN
iajs-3322	128	12	de	de	NOUN
iajs-3322	128	13	grille	grille	NOUN
iajs-3322	128	14	.	.	PUNCT
iajs-3322	129	1	comptes	compte	VERB
iajs-3322	129	2	rendus	rendus	PROPN
iajs-3322	129	3	acad	acad	PROPN
iajs-3322	129	4	sci	sci	PROPN
iajs-3322	129	5	paris	paris	PROPN
iajs-3322	129	6	.	.	PUNCT
iajs-3322	130	1	1947;224:171	1947;224:171	NUM
iajs-3322	130	2	-	-	SYM
iajs-3322	130	3	3	3	NUM
iajs-3322	130	4	.	.	NOUN
iajs-3322	131	1	2	2	NUM
iajs-3322	131	2	.	.	X
iajs-3322	132	1	al	al	PROPN
iajs-3322	132	2	-	-	PUNCT
iajs-3322	132	3	omari	omari	PROPN
iajs-3322	132	4	a	a	X
iajs-3322	132	5	,	,	PUNCT
iajs-3322	132	6	noiri	noiri	NOUN
iajs-3322	132	7	t.	t.	NOUN
iajs-3322	132	8	decomposition	decomposition	NOUN
iajs-3322	132	9	of	of	ADP
iajs-3322	132	10	continuity	continuity	NOUN
iajs-3322	132	11	via	via	ADP
iajs-3322	132	12	grilles	grille	NOUN
iajs-3322	132	13	.	.	PUNCT
iajs-3322	133	1	jordan	jordan	PROPN
iajs-3322	133	2	j	j	PROPN
iajs-3322	133	3	math	math	PROPN
iajs-3322	133	4	stat	stat	PROPN
iajs-3322	133	5	.	.	PUNCT
iajs-3322	134	1	2011;4(1):33	2011;4(1):33	NUM
iajs-3322	134	2	-	-	SYM
iajs-3322	134	3	46	46	NUM
iajs-3322	134	4	.	.	PUNCT
iajs-3322	135	1	3	3	X
iajs-3322	135	2	.	.	X
iajs-3322	135	3	mustafa	mustafa	PROPN
iajs-3322	135	4	mo	mo	PROPN
iajs-3322	135	5	,	,	PUNCT
iajs-3322	135	6	esmaeel	esmaeel	VERB
iajs-3322	135	7	rb	rb	NOUN
iajs-3322	135	8	.	.	PUNCT
iajs-3322	136	1	some	some	DET
iajs-3322	136	2	properties	property	NOUN
iajs-3322	136	3	in	in	ADP
iajs-3322	136	4	grill	grill	ADJ
iajs-3322	136	5	–	–	PUNCT
iajs-3322	136	6	topological	topological	ADJ
iajs-3322	136	7	open	open	ADJ
iajs-3322	136	8	and	and	CCONJ
iajs-3322	136	9	closed	closed	ADJ
iajs-3322	136	10	sets	set	NOUN
iajs-3322	136	11	.	.	PUNCT
iajs-3322	137	1	j	j	PROPN
iajs-3322	137	2	phys	phys	PROPN
iajs-3322	137	3	conf	conf	NOUN
iajs-3322	137	4	ser	ser	PROPN
iajs-3322	137	5	.	.	PUNCT
iajs-3322	137	6	2021;012038	2021;012038	NUM
iajs-3322	137	7	.	.	PUNCT
iajs-3322	138	1	https://doi.org/10.1088/1742-6596/1879/1/012038	https://doi.org/10.1088/1742-6596/1879/1/012038	NOUN
iajs-3322	138	2	.	.	PUNCT
iajs-3322	139	1	4	4	NUM
iajs-3322	139	2	.	.	X
iajs-3322	139	3	choquet	choquet	PROPN
iajs-3322	139	4	g.	g.	PROPN
iajs-3322	139	5	sur	sur	PROPN
iajs-3322	139	6	les	les	PROPN
iajs-3322	139	7	notions	notion	NOUN
iajs-3322	139	8	de	de	X
iajs-3322	139	9	filtre	filtre	NOUN
iajs-3322	139	10	et	et	NOUN
iajs-3322	139	11	de	de	NOUN
iajs-3322	139	12	grille	grille	NOUN
iajs-3322	139	13	.	.	PUNCT
iajs-3322	140	1	comptes	compte	VERB
iajs-3322	140	2	rendus	rendus	PROPN
iajs-3322	140	3	acad	acad	PROPN
iajs-3322	140	4	sci	sci	PROPN
iajs-3322	140	5	paris	paris	PROPN
iajs-3322	140	6	.	.	PUNCT
iajs-3322	141	1	1947;224:171	1947;224:171	NUM
iajs-3322	141	2	-	-	SYM
iajs-3322	141	3	3	3	NUM
iajs-3322	141	4	.	.	NOUN
iajs-3322	141	5	5	5	NUM
iajs-3322	141	6	.	.	X
iajs-3322	141	7	crossley	crossley	PROPN
iajs-3322	141	8	sg	sg	AUX
iajs-3322	141	9	.	.	PUNCT
iajs-3322	141	10	semi	semi	ADJ
iajs-3322	141	11	-	-	NOUN
iajs-3322	141	12	closure	closure	ADJ
iajs-3322	141	13	.	.	PUNCT
iajs-3322	142	1	texas	texas	PROPN
iajs-3322	142	2	j	j	PROPN
iajs-3322	142	3	sci	sci	PROPN
iajs-3322	142	4	.	.	PROPN
iajs-3322	142	5	1971;22:99	1971;22:99	NUM
iajs-3322	142	6	-	-	SYM
iajs-3322	142	7	112	112	NUM
iajs-3322	142	8	.	.	PUNCT
iajs-3322	143	1	6	6	NUM
iajs-3322	143	2	.	.	X
iajs-3322	143	3	levine	levine	PROPN
iajs-3322	143	4	n.	n.	PROPN
iajs-3322	143	5	generalized	generalize	VERB
iajs-3322	143	6	closed	closed	ADJ
iajs-3322	143	7	sets	set	NOUN
iajs-3322	143	8	in	in	ADP
iajs-3322	143	9	topology	topology	NOUN
iajs-3322	143	10	.	.	PUNCT
iajs-3322	144	1	rend	rend	VERB
iajs-3322	144	2	circ	circ	PROPN
iajs-3322	144	3	mat	mat	NOUN
iajs-3322	144	4	palermo	palermo	NOUN
iajs-3322	144	5	.	.	PUNCT
iajs-3322	145	1	1970;19:89	1970;19:89	NUM
iajs-3322	145	2	-	-	SYM
iajs-3322	145	3	96	96	NUM
iajs-3322	145	4	.	.	PUNCT
iajs-3322	146	1	7	7	X
iajs-3322	146	2	.	.	X
iajs-3322	146	3	thivagar	thivagar	PROPN
iajs-3322	146	4	ml	ml	PROPN
iajs-3322	146	5	,	,	PUNCT
iajs-3322	146	6	richard	richard	PROPN
iajs-3322	146	7	c.	c.	PROPN
iajs-3322	146	8	on	on	ADP
iajs-3322	146	9	nano	nano	NOUN
iajs-3322	146	10	forms	form	NOUN
iajs-3322	146	11	of	of	ADP
iajs-3322	146	12	weakly	weakly	ADJ
iajs-3322	146	13	open	open	ADJ
iajs-3322	146	14	sets	set	NOUN
iajs-3322	146	15	.	.	PUNCT
iajs-3322	147	1	int	int	NOUN
iajs-3322	147	2	j	j	PROPN
iajs-3322	147	3	math	math	PROPN
iajs-3322	147	4	stat	stat	PROPN
iajs-3322	147	5	invent	invent	NOUN
iajs-3322	147	6	.	.	PUNCT
iajs-3322	148	1	2013;1(1):317	2013;1(1):317	NUM
iajs-3322	148	2	.	.	NOUN
iajs-3322	148	3	8	8	NUM
iajs-3322	148	4	.	.	PUNCT
iajs-3322	149	1	thron	thron	PROPN
iajs-3322	149	2	wj	wj	PROPN
iajs-3322	149	3	.	.	PUNCT
iajs-3322	150	1	proximity	proximity	NOUN
iajs-3322	150	2	structures	structure	NOUN
iajs-3322	150	3	and	and	CCONJ
iajs-3322	150	4	grills	grill	NOUN
iajs-3322	150	5	.	.	PUNCT
iajs-3322	151	1	math	math	PROPN
iajs-3322	151	2	ann	ann	PROPN
iajs-3322	151	3	.	.	PUNCT
iajs-3322	152	1	1973;206:35	1973;206:35	NUM
iajs-3322	152	2	-	-	SYM
iajs-3322	152	3	62	62	NUM
iajs-3322	152	4	.	.	PUNCT
iajs-3322	153	1	9	9	NUM
iajs-3322	153	2	.	.	PUNCT
iajs-3322	153	3	mahmood	mahmood	PROPN
iajs-3322	153	4	aj	aj	PROPN
iajs-3322	153	5	,	,	PUNCT
iajs-3322	153	6	naser	naser	PROPN
iajs-3322	153	7	ai	ai	PROPN
iajs-3322	153	8	.	.	PUNCT
iajs-3322	153	9	connectedness	connectedness	NOUN
iajs-3322	153	10	via	via	ADP
iajs-3322	153	11	generalizations	generalization	NOUN
iajs-3322	153	12	of	of	ADP
iajs-3322	153	13	semi	semi	ADJ
iajs-3322	153	14	-	-	ADJ
iajs-3322	153	15	open	open	ADJ
iajs-3322	153	16	sets	set	NOUN
iajs-3322	153	17	.	.	PUNCT
iajs-3322	154	1	ibn	ibn	PROPN
iajs-3322	154	2	al	al	PROPN
iajs-3322	154	3	-	-	PUNCT
iajs-3322	154	4	haitham	haitham	PROPN
iajs-3322	154	5	j	j	PROPN
iajs-3322	154	6	pure	pure	PROPN
iajs-3322	154	7	appl	appl	PROPN
iajs-3322	154	8	sci	sci	PROPN
iajs-3322	154	9	.	.	PUNCT
iajs-3322	155	1	2022;35(4):235	2022;35(4):235	PROPN
iajs-3322	155	2	-	-	SYM
iajs-3322	155	3	40	40	NUM
iajs-3322	155	4	.	.	PUNCT
iajs-3322	156	1	10	10	NUM
iajs-3322	156	2	.	.	PUNCT
iajs-3322	157	1	suliman	suliman	PROPN
iajs-3322	157	2	ss	ss	PROPN
iajs-3322	157	3	,	,	PUNCT
iajs-3322	157	4	esmaeel	esmaeel	VERB
iajs-3322	157	5	rb	rb	NOUN
iajs-3322	157	6	.	.	PUNCT
iajs-3322	158	1	some	some	DET
iajs-3322	158	2	properties	property	NOUN
iajs-3322	158	3	of	of	ADP
iajs-3322	158	4	connectedness	connectedness	NOUN
iajs-3322	158	5	in	in	ADP
iajs-3322	158	6	grill	grill	ADJ
iajs-3322	158	7	topological	topological	ADJ
iajs-3322	158	8	spaces	space	NOUN
iajs-3322	158	9	.	.	PUNCT
iajs-3322	159	1	ibn	ibn	PROPN
iajs-3322	159	2	alhaitham	alhaitham	PROPN
iajs-3322	159	3	j	j	PROPN
iajs-3322	159	4	pure	pure	PROPN
iajs-3322	159	5	appl	appl	PROPN
iajs-3322	159	6	sci	sci	PROPN
iajs-3322	159	7	.	.	PUNCT
iajs-3322	160	1	2022;35(4):213	2022;35(4):213	PROPN
iajs-3322	160	2	-	-	SYM
iajs-3322	160	3	9	9	NUM
iajs-3322	160	4	.	.	NOUN
iajs-3322	160	5	11	11	NUM
iajs-3322	160	6	.	.	PUNCT
iajs-3322	161	1	roy	roy	PROPN
iajs-3322	161	2	b	b	PROPN
iajs-3322	161	3	,	,	PUNCT
iajs-3322	161	4	mukherjee	mukherjee	PROPN
iajs-3322	161	5	mn	mn	PROPN
iajs-3322	161	6	.	.	PROPN
iajs-3322	162	1	on	on	ADP
iajs-3322	162	2	a	a	DET
iajs-3322	162	3	typical	typical	ADJ
iajs-3322	162	4	topology	topology	NOUN
iajs-3322	162	5	induced	induce	VERB
iajs-3322	162	6	by	by	ADP
iajs-3322	162	7	a	a	DET
iajs-3322	162	8	grill	grill	NOUN
iajs-3322	162	9	.	.	PUNCT
iajs-3322	163	1	soochow	soochow	PROPN
iajs-3322	163	2	j	j	PROPN
iajs-3322	163	3	math	math	PROPN
iajs-3322	163	4	.	.	PUNCT
iajs-3322	164	1	2007;33(4):771	2007;33(4):771	NOUN
iajs-3322	164	2	.	.	PUNCT
iajs-3322	165	1	12	12	NUM
iajs-3322	165	2	.	.	PUNCT
iajs-3322	166	1	mandal	mandal	PROPN
iajs-3322	166	2	d	d	PROPN
iajs-3322	166	3	,	,	PUNCT
iajs-3322	166	4	mukherjee	mukherjee	PROPN
iajs-3322	166	5	mn	mn	PROPN
iajs-3322	166	6	.	.	PROPN
iajs-3322	167	1	on	on	ADP
iajs-3322	167	2	a	a	DET
iajs-3322	167	3	class	class	NOUN
iajs-3322	167	4	of	of	ADP
iajs-3322	167	5	sets	set	NOUN
iajs-3322	167	6	via	via	ADP
iajs-3322	167	7	grill	grill	NOUN
iajs-3322	167	8	:	:	PUNCT
iajs-3322	167	9	a	a	DET
iajs-3322	167	10	decomposition	decomposition	NOUN
iajs-3322	167	11	of	of	ADP
iajs-3322	167	12	continuity	continuity	NOUN
iajs-3322	167	13	.	.	PUNCT
iajs-3322	168	1	an	an	DET
iajs-3322	168	2	stiint	stiint	ADJ
iajs-3322	168	3	univ	univ	PROPN
iajs-3322	168	4	ovidius	ovidius	PROPN
iajs-3322	168	5	constanta	constanta	PROPN
iajs-3322	168	6	ser	ser	PROPN
iajs-3322	168	7	mat	mat	PROPN
iajs-3322	168	8	.	.	PUNCT
iajs-3322	169	1	2012;20(1):307	2012;20(1):307	NUM
iajs-3322	169	2	-	-	SYM
iajs-3322	169	3	16	16	NUM
iajs-3322	169	4	.	.	PUNCT
iajs-3322	169	5	13	13	NUM
iajs-3322	169	6	.	.	PUNCT
iajs-3322	170	1	pawlak	pawlak	PROPN
iajs-3322	170	2	z.	z.	PROPN
iajs-3322	170	3	rough	rough	ADJ
iajs-3322	170	4	sets	set	NOUN
iajs-3322	170	5	.	.	PUNCT
iajs-3322	171	1	int	int	NOUN
iajs-3322	171	2	j	j	PROPN
iajs-3322	171	3	comput	comput	PROPN
iajs-3322	171	4	inf	inf	PROPN
iajs-3322	171	5	sci	sci	PROPN
iajs-3322	171	6	.	.	PUNCT
iajs-3322	172	1	1982;11:341	1982;11:341	NUM
iajs-3322	172	2	-	-	SYM
iajs-3322	172	3	56	56	NUM
iajs-3322	172	4	.	.	PUNCT
iajs-3322	173	1	https://doi.org/10.1007/bf01001956	https://doi.org/10.1007/bf01001956	PRON
iajs-3322	173	2	14	14	NUM
iajs-3322	173	3	.	.	PUNCT
iajs-3322	174	1	esmaeel	esmaeel	VERB
iajs-3322	174	2	rb	rb	PROPN
iajs-3322	174	3	,	,	PUNCT
iajs-3322	174	4	saeed	saeed	PROPN
iajs-3322	174	5	sg	sg	PROPN
iajs-3322	174	6	.	.	PUNCT
iajs-3322	175	1	nano	nano	VERB
iajs-3322	175	2	αg	αg	ADP
iajs-3322	175	3	ị	ị	DET
iajs-3322	175	4	-	-	ADJ
iajs-3322	175	5	open	open	ADJ
iajs-3322	175	6	set	set	NOUN
iajs-3322	175	7	.	.	PUNCT
iajs-3322	176	1	j	j	PROPN
iajs-3322	176	2	phys	phys	PROPN
iajs-3322	176	3	conf	conf	NOUN
iajs-3322	176	4	ser	ser	PROPN
iajs-3322	176	5	.	.	PUNCT
iajs-3322	177	1	2021;012031	2021;012031	NUM
iajs-3322	177	2	.	.	PUNCT
iajs-3322	178	1	https://doi.org/10.1088/1742-6596/1879/1/012031	https://doi.org/10.1088/1742-6596/1879/1/012031	PROPN
iajs-3322	178	2	15	15	NUM
iajs-3322	178	3	.	.	PUNCT
iajs-3322	179	1	hatir	hatir	PROPN
iajs-3322	179	2	e	e	PROPN
iajs-3322	179	3	,	,	PUNCT
iajs-3322	179	4	jafari	jafari	PROPN
iajs-3322	179	5	s.	s.	PROPN
iajs-3322	179	6	on	on	ADP
iajs-3322	179	7	some	some	DET
iajs-3322	179	8	new	new	ADJ
iajs-3322	179	9	classes	class	NOUN
iajs-3322	179	10	of	of	ADP
iajs-3322	179	11	sets	set	NOUN
iajs-3322	179	12	and	and	CCONJ
iajs-3322	179	13	a	a	DET
iajs-3322	179	14	new	new	ADJ
iajs-3322	179	15	decomposition	decomposition	NOUN
iajs-3322	179	16	of	of	ADP
iajs-3322	179	17	continuity	continuity	NOUN
iajs-3322	179	18	via	via	ADP
iajs-3322	179	19	grills	grill	NOUN
iajs-3322	179	20	.	.	PUNCT
iajs-3322	180	1	j	j	PROPN
iajs-3322	180	2	https://doi.org/10.1088/1742-6596/1879/1/012031	https://doi.org/10.1088/1742-6596/1879/1/012031	PROPN
iajs-3322	180	3	ihjpas	ihjpas	PROPN
iajs-3322	180	4	.	.	PUNCT
iajs-3322	181	1	2025	2025	NUM
iajs-3322	181	2	,	,	PUNCT
iajs-3322	181	3	38	38	NUM
iajs-3322	181	4	(	(	PUNCT
iajs-3322	181	5	1	1	NUM
iajs-3322	181	6	)	)	PUNCT
iajs-3322	181	7	366	366	NUM
iajs-3322	181	8	adv	adv	PROPN
iajs-3322	181	9	math	math	NOUN
iajs-3322	181	10	stud	stud	NOUN
iajs-3322	181	11	.	.	PUNCT
iajs-3322	182	1	2010;3(1):33	2010;3(1):33	NUM
iajs-3322	182	2	-	-	SYM
iajs-3322	182	3	41	41	NUM
iajs-3322	182	4	.	.	PUNCT
iajs-3322	183	1	16	16	NUM
iajs-3322	183	2	.	.	PUNCT
iajs-3322	184	1	njåstad	njåstad	PROPN
iajs-3322	184	2	o.	o.	PROPN
iajs-3322	184	3	on	on	ADP
iajs-3322	184	4	some	some	DET
iajs-3322	184	5	classes	class	NOUN
iajs-3322	184	6	of	of	ADP
iajs-3322	184	7	nearly	nearly	ADV
iajs-3322	184	8	open	open	ADJ
iajs-3322	184	9	sets	set	NOUN
iajs-3322	184	10	.	.	PUNCT
iajs-3322	185	1	pac	pac	PROPN
iajs-3322	185	2	j	j	PROPN
iajs-3322	185	3	math	math	NOUN
iajs-3322	185	4	.	.	PUNCT
iajs-3322	186	1	1965;15(3):961	1965;15(3):961	NUM
iajs-3322	186	2	-	-	PUNCT
iajs-3322	186	3	70	70	NUM
iajs-3322	186	4	.	.	PUNCT
iajs-3322	187	1	17	17	NUM
iajs-3322	187	2	.	.	PUNCT
iajs-3322	188	1	noori	noori	PROPN
iajs-3322	188	2	s	s	PROPN
iajs-3322	188	3	,	,	PUNCT
iajs-3322	188	4	yousif	yousif	PROPN
iajs-3322	188	5	yy	yy	PROPN
iajs-3322	188	6	.	.	PUNCT
iajs-3322	188	7	soft	soft	ADJ
iajs-3322	188	8	simply	simply	ADV
iajs-3322	188	9	compact	compact	ADJ
iajs-3322	188	10	spaces	space	NOUN
iajs-3322	188	11	.	.	PUNCT
iajs-3322	189	1	iraqi	iraqi	PROPN
iajs-3322	189	2	j	j	PROPN
iajs-3322	189	3	sci	sci	PROPN
iajs-3322	189	4	.	.	PROPN
iajs-3322	189	5	2020;108	2020;108	PROPN
iajs-3322	189	6	-	-	SYM
iajs-3322	189	7	13	13	NUM
iajs-3322	189	8	.	.	NOUN
iajs-3322	189	9	18	18	NUM
iajs-3322	189	10	.	.	PUNCT
iajs-3322	190	1	krishnaprakash	krishnaprakash	PROPN
iajs-3322	190	2	s	s	PROPN
iajs-3322	190	3	,	,	PUNCT
iajs-3322	190	4	ramesh	ramesh	PROPN
iajs-3322	190	5	r	r	PROPN
iajs-3322	190	6	,	,	PUNCT
iajs-3322	190	7	suresh	suresh	PROPN
iajs-3322	190	8	r.	r.	PROPN
iajs-3322	190	9	nano	nano	PROPN
iajs-3322	190	10	-	-	PUNCT
iajs-3322	190	11	compactness	compactness	NOUN
iajs-3322	190	12	and	and	CCONJ
iajs-3322	190	13	nano	nano	NOUN
iajs-3322	190	14	-	-	PUNCT
iajs-3322	190	15	connectedness	connectedness	NOUN
iajs-3322	190	16	in	in	ADP
iajs-3322	190	17	nano	nano	ADJ
iajs-3322	190	18	topological	topological	ADJ
iajs-3322	190	19	spaces	space	NOUN
iajs-3322	190	20	.	.	PUNCT
iajs-3322	191	1	int	int	NOUN
iajs-3322	191	2	j	j	PROPN
iajs-3322	191	3	pure	pure	ADJ
iajs-3322	191	4	appl	appl	PROPN
iajs-3322	191	5	math	math	NOUN
iajs-3322	191	6	.	.	PUNCT
iajs-3322	192	1	2018;119(13):107	2018;119(13):107	NUM
iajs-3322	192	2	-	-	SYM
iajs-3322	192	3	15	15	NUM
iajs-3322	192	4	.	.	NOUN
iajs-3322	192	5	19	19	NUM
iajs-3322	192	6	.	.	PUNCT
iajs-3322	193	1	noori	noori	PROPN
iajs-3322	193	2	s	s	PROPN
iajs-3322	193	3	,	,	PUNCT
iajs-3322	193	4	yousif	yousif	PROPN
iajs-3322	193	5	yy	yy	PROPN
iajs-3322	193	6	.	.	PUNCT
iajs-3322	193	7	soft	soft	ADJ
iajs-3322	193	8	simply	simply	ADV
iajs-3322	193	9	compact	compact	ADJ
iajs-3322	193	10	spaces	space	NOUN
iajs-3322	193	11	.	.	PUNCT
iajs-3322	194	1	iraqi	iraqi	PROPN
iajs-3322	194	2	j	j	PROPN
iajs-3322	194	3	sci	sci	PROPN
iajs-3322	194	4	.	.	PROPN
iajs-3322	194	5	2020;108	2020;108	PROPN
iajs-3322	194	6	-	-	SYM
iajs-3322	194	7	13	13	NUM
iajs-3322	194	8	.	.	NOUN
iajs-3322	194	9	20	20	NUM
iajs-3322	194	10	.	.	PUNCT
iajs-3322	195	1	ryll	ryll	NOUN
iajs-3322	195	2	-	-	PUNCT
iajs-3322	195	3	nardzewski	nardzewski	ADJ
iajs-3322	195	4	c.	c.	PROPN
iajs-3322	195	5	a	a	DET
iajs-3322	195	6	remark	remark	NOUN
iajs-3322	195	7	on	on	ADP
iajs-3322	195	8	the	the	DET
iajs-3322	195	9	cartesian	cartesian	ADJ
iajs-3322	195	10	product	product	NOUN
iajs-3322	195	11	of	of	ADP
iajs-3322	195	12	two	two	NUM
iajs-3322	195	13	compact	compact	ADJ
iajs-3322	195	14	spaces	space	NOUN
iajs-3322	195	15	.	.	PUNCT
iajs-3322	196	1	bull	bull	NOUN
iajs-3322	196	2	acad	acad	PROPN
iajs-3322	196	3	polon	polon	NOUN
iajs-3322	196	4	sci	sci	PROPN
iajs-3322	196	5	cl	cl	PROPN
iajs-3322	196	6	iii	iii	PROPN
iajs-3322	196	7	.	.	PUNCT
iajs-3322	197	1	1954;2:265	1954;2:265	NUM
iajs-3322	197	2	-	-	SYM
iajs-3322	197	3	6	6	NUM
iajs-3322	197	4	.	.	PUNCT