id	sid	tid	token	lemma	pos
iajs-2877	1	1	ihjpas	ihjpas	PROPN
iajs-2877	1	2	.	.	PUNCT
iajs-2877	2	1	53	53	NUM
iajs-2877	2	2	(	(	PUNCT
iajs-2877	2	3	4)2022	4)2022	NOUN
iajs-2877	2	4	235	235	NUM
iajs-2877	2	5	this	this	DET
iajs-2877	2	6	work	work	NOUN
iajs-2877	2	7	is	be	AUX
iajs-2877	2	8	licensed	license	VERB
iajs-2877	2	9	under	under	ADP
iajs-2877	2	10	a	a	DET
iajs-2877	2	11	creative	creative	ADJ
iajs-2877	2	12	commons	common	NOUN
iajs-2877	2	13	attribution	attribution	NOUN
iajs-2877	2	14	4.0	4.0	NUM
iajs-2877	2	15	international	international	ADJ
iajs-2877	2	16	license	license	NOUN
iajs-2877	2	17	.	.	PUNCT
iajs-2877	3	1	connectedness	connectedness	NOUN
iajs-2877	3	2	via	via	ADP
iajs-2877	3	3	generalizations	generalization	NOUN
iajs-2877	3	4	of	of	ADP
iajs-2877	3	5	semi	semi	ADJ
iajs-2877	3	6	-	-	ADJ
iajs-2877	3	7	open	open	ADJ
iajs-2877	3	8	sets	set	NOUN
iajs-2877	3	9	abstract	abstract	NOUN
iajs-2877	3	10	we	we	PRON
iajs-2877	3	11	use	use	VERB
iajs-2877	3	12	the	the	DET
iajs-2877	3	13	idea	idea	NOUN
iajs-2877	3	14	of	of	ADP
iajs-2877	3	15	the	the	DET
iajs-2877	3	16	grill	grill	NOUN
iajs-2877	3	17	.	.	PUNCT
iajs-2877	4	1	this	this	DET
iajs-2877	4	2	study	study	NOUN
iajs-2877	4	3	generalized	generalize	VERB
iajs-2877	4	4	a	a	DET
iajs-2877	4	5	new	new	ADJ
iajs-2877	4	6	sort	sort	NOUN
iajs-2877	4	7	of	of	ADP
iajs-2877	4	8	linked	link	VERB
iajs-2877	4	9	space	space	NOUN
iajs-2877	4	10	like	like	ADP
iajs-2877	4	11	₲	₲	NOUN
iajs-2877	4	12	∗	∗	NOUN
iajs-2877	4	13	𝑠𝑜-connected	𝑠𝑜-connecte	VERB
iajs-2877	4	14	and	and	CCONJ
iajs-2877	4	15	₲	₲	NOUN
iajs-2877	4	16	∗𝑠𝑜-hyperconnected	∗𝑠𝑜-hyperconnecte	VERB
iajs-2877	4	17	and	and	CCONJ
iajs-2877	4	18	investigated	investigate	VERB
iajs-2877	4	19	its	its	PRON
iajs-2877	4	20	features	feature	NOUN
iajs-2877	4	21	,	,	PUNCT
iajs-2877	4	22	as	as	ADV
iajs-2877	4	23	well	well	ADV
iajs-2877	4	24	as	as	ADP
iajs-2877	4	25	the	the	DET
iajs-2877	4	26	relationship	relationship	NOUN
iajs-2877	4	27	between	between	ADP
iajs-2877	4	28	it	it	PRON
iajs-2877	4	29	and	and	CCONJ
iajs-2877	4	30	previously	previously	ADV
iajs-2877	4	31	described	describe	VERB
iajs-2877	4	32	notions	notion	NOUN
iajs-2877	4	33	.	.	PUNCT
iajs-2877	5	1	it	it	PRON
iajs-2877	5	2	also	also	ADV
iajs-2877	5	3	developed	develop	VERB
iajs-2877	5	4	new	new	ADJ
iajs-2877	5	5	sorts	sort	NOUN
iajs-2877	5	6	of	of	ADP
iajs-2877	5	7	functions	function	NOUN
iajs-2877	5	8	,	,	PUNCT
iajs-2877	5	9	such	such	ADJ
iajs-2877	5	10	as	as	ADP
iajs-2877	5	11	hyperconnected	hyperconnecte	VERB
iajs-2877	5	12	space	space	NOUN
iajs-2877	5	13	,	,	PUNCT
iajs-2877	5	14	and	and	CCONJ
iajs-2877	5	15	identified	identify	VERB
iajs-2877	5	16	their	their	PRON
iajs-2877	5	17	relationship	relationship	NOUN
iajs-2877	5	18	by	by	ADP
iajs-2877	5	19	offering	offer	VERB
iajs-2877	5	20	numerous	numerous	ADJ
iajs-2877	5	21	instances	instance	NOUN
iajs-2877	5	22	and	and	CCONJ
iajs-2877	5	23	attributes	attribute	NOUN
iajs-2877	5	24	that	that	PRON
iajs-2877	5	25	belong	belong	VERB
iajs-2877	5	26	to	to	ADP
iajs-2877	5	27	this	this	DET
iajs-2877	5	28	set	set	NOUN
iajs-2877	5	29	.	.	PUNCT
iajs-2877	6	1	this	this	DET
iajs-2877	6	2	set	set	NOUN
iajs-2877	6	3	will	will	AUX
iajs-2877	6	4	serve	serve	VERB
iajs-2877	6	5	as	as	ADP
iajs-2877	6	6	a	a	DET
iajs-2877	6	7	starting	starting	NOUN
iajs-2877	6	8	point	point	NOUN
iajs-2877	6	9	for	for	ADP
iajs-2877	6	10	further	further	ADJ
iajs-2877	6	11	research	research	NOUN
iajs-2877	6	12	into	into	ADP
iajs-2877	6	13	the	the	DET
iajs-2877	6	14	set	set	NOUN
iajs-2877	6	15	many	many	ADJ
iajs-2877	6	16	future	future	ADJ
iajs-2877	6	17	possibilities	possibility	NOUN
iajs-2877	6	18	.	.	PUNCT
iajs-2877	7	1	we	we	PRON
iajs-2877	7	2	also	also	ADV
iajs-2877	7	3	use	use	VERB
iajs-2877	7	4	some	some	DET
iajs-2877	7	5	theorems	theorem	NOUN
iajs-2877	7	6	and	and	CCONJ
iajs-2877	7	7	observations	observation	NOUN
iajs-2877	7	8	previously	previously	ADV
iajs-2877	7	9	studied	study	VERB
iajs-2877	7	10	and	and	CCONJ
iajs-2877	7	11	related	relate	VERB
iajs-2877	7	12	to	to	ADP
iajs-2877	7	13	the	the	DET
iajs-2877	7	14	grill	grill	NOUN
iajs-2877	7	15	and	and	CCONJ
iajs-2877	7	16	the	the	DET
iajs-2877	7	17	semi	semi	ADJ
iajs-2877	7	18	-	-	ADJ
iajs-2877	7	19	open	open	ADJ
iajs-2877	7	20	to	to	PART
iajs-2877	7	21	obtain	obtain	VERB
iajs-2877	7	22	results	result	NOUN
iajs-2877	7	23	in	in	ADP
iajs-2877	7	24	this	this	DET
iajs-2877	7	25	research	research	NOUN
iajs-2877	7	26	.	.	PUNCT
iajs-2877	8	1	we	we	PRON
iajs-2877	8	2	applied	apply	VERB
iajs-2877	8	3	the	the	DET
iajs-2877	8	4	concept	concept	NOUN
iajs-2877	8	5	of	of	ADP
iajs-2877	8	6	connected	connect	VERB
iajs-2877	8	7	to	to	ADP
iajs-2877	8	8	them	they	PRON
iajs-2877	8	9	and	and	CCONJ
iajs-2877	8	10	obtained	obtain	VERB
iajs-2877	8	11	results	result	NOUN
iajs-2877	8	12	related	relate	VERB
iajs-2877	8	13	to	to	AUX
iajs-2877	8	14	connected	connect	VERB
iajs-2877	8	15	.	.	PUNCT
iajs-2877	9	1	the	the	DET
iajs-2877	9	2	sources	source	NOUN
iajs-2877	9	3	related	relate	VERB
iajs-2877	9	4	to	to	ADP
iajs-2877	9	5	the	the	DET
iajs-2877	9	6	connected	connected	ADJ
iajs-2877	9	7	and	and	CCONJ
iajs-2877	9	8	semi	semi	ADJ
iajs-2877	9	9	-	-	ADJ
iajs-2877	9	10	open	open	ADJ
iajs-2877	9	11	where	where	SCONJ
iajs-2877	9	12	considered	consider	VERB
iajs-2877	9	13	as	as	ADP
iajs-2877	9	14	starting	start	VERB
iajs-2877	9	15	points	point	NOUN
iajs-2877	9	16	and	and	CCONJ
iajs-2877	9	17	an	an	DET
iajs-2877	9	18	important	important	ADJ
iajs-2877	9	19	basis	basis	NOUN
iajs-2877	9	20	in	in	ADP
iajs-2877	9	21	this	this	DET
iajs-2877	9	22	research	research	NOUN
iajs-2877	9	23	.	.	PUNCT
iajs-2877	10	1	keywords	keyword	NOUN
iajs-2877	10	2	:	:	PUNCT
iajs-2877	10	3	grill	grill	ADJ
iajs-2877	10	4	topological	topological	ADJ
iajs-2877	10	5	space	space	NOUN
iajs-2877	10	6	,	,	PUNCT
iajs-2877	10	7	₲	₲	NOUN
iajs-2877	10	8	*	*	PUNCT
iajs-2877	10	9	s	s	X
iajs-2877	10	10	-	-	PUNCT
iajs-2877	10	11	connected	connect	VERB
iajs-2877	10	12	,	,	PUNCT
iajs-2877	10	13	₲	₲	NOUN
iajs-2877	10	14	*	*	NUM
iajs-2877	10	15	s-𝑑𝑖𝑠connected	s-𝑑𝑖𝑠connecte	VERB
iajs-2877	10	16	,	,	PUNCT
iajs-2877	10	17	₲	₲	NOUN
iajs-2877	10	18	∗	∗	NOUN
iajs-2877	10	19	-semi	-semi	NOUN
iajs-2877	10	20	-	-	PUNCT
iajs-2877	10	21	open	open	ADJ
iajs-2877	10	22	sets	set	NOUN
iajs-2877	10	23	.	.	PUNCT
iajs-2877	11	1	1	1	X
iajs-2877	11	2	.	.	X
iajs-2877	11	3	introduction	introduction	NOUN
iajs-2877	11	4	in	in	ADP
iajs-2877	11	5	[	[	X
iajs-2877	11	6	1,2	1,2	NUM
iajs-2877	11	7	]	]	PUNCT
iajs-2877	11	8	found	find	VERB
iajs-2877	11	9	a	a	DET
iajs-2877	11	10	topological	topological	ADJ
iajs-2877	11	11	area	area	NOUN
iajs-2877	11	12	where	where	SCONJ
iajs-2877	11	13	the	the	DET
iajs-2877	11	14	concept	concept	NOUN
iajs-2877	11	15	of	of	ADP
iajs-2877	11	16	the	the	DET
iajs-2877	11	17	grill	grill	NOUN
iajs-2877	11	18	,	,	PUNCT
iajs-2877	11	19	and	and	CCONJ
iajs-2877	11	20	the	the	DET
iajs-2877	11	21	grill	grill	NOUN
iajs-2877	11	22	has	have	AUX
iajs-2877	11	23	shown	show	VERB
iajs-2877	11	24	to	to	PART
iajs-2877	11	25	be	be	AUX
iajs-2877	11	26	an	an	DET
iajs-2877	11	27	effective	effective	ADJ
iajs-2877	11	28	tool	tool	NOUN
iajs-2877	11	29	for	for	ADP
iajs-2877	11	30	learning	learn	VERB
iajs-2877	11	31	a	a	DET
iajs-2877	11	32	variety	variety	NOUN
iajs-2877	11	33	of	of	ADP
iajs-2877	11	34	topological	topological	ADJ
iajs-2877	11	35	concerns	concern	NOUN
iajs-2877	11	36	.	.	PUNCT
iajs-2877	12	1	subsets	subset	NOUN
iajs-2877	12	2	of	of	ADP
iajs-2877	12	3	a	a	DET
iajs-2877	12	4	topological	topological	ADJ
iajs-2877	12	5	space	space	NOUN
iajs-2877	12	6	(	(	PUNCT
iajs-2877	12	7	ӽ	ӽ	X
iajs-2877	12	8	,	,	PUNCT
iajs-2877	12	9	𝜏	𝜏	NOUN
iajs-2877	12	10	)	)	PUNCT
iajs-2877	12	11	which	which	PRON
iajs-2877	12	12	is	be	AUX
iajs-2877	12	13	a	a	DET
iajs-2877	12	14	non	non	ADJ
iajs-2877	12	15	-	-	ADJ
iajs-2877	12	16	empty	empty	ADJ
iajs-2877	12	17	collection	collection	NOUN
iajs-2877	12	18	₲	₲	NOUN
iajs-2877	12	19	and	and	CCONJ
iajs-2877	12	20	is	be	AUX
iajs-2877	12	21	referred	refer	VERB
iajs-2877	12	22	to	to	PART
iajs-2877	12	23	be	be	AUX
iajs-2877	12	24	a	a	DET
iajs-2877	12	25	grill	grill	NOUN
iajs-2877	12	26	whenever	whenever	SCONJ
iajs-2877	12	27	(	(	PUNCT
iajs-2877	12	28	a	a	X
iajs-2877	12	29	)	)	PUNCT
iajs-2877	12	30	ѧ	ѧ	PROPN
iajs-2877	12	31	∈₲	∈₲	NOUN
iajs-2877	12	32	and	and	CCONJ
iajs-2877	12	33	ѧ	ѧ	PRON
iajs-2877	12	34	⊆	⊆	NUM
iajs-2877	12	35	ƀ	ƀ	PRON
iajs-2877	12	36	implying	implying	ADJ
iajs-2877	12	37	ƀ∈₲.	ƀ∈₲.	NOUN
iajs-2877	12	38	(	(	PUNCT
iajs-2877	12	39	b	b	NOUN
iajs-2877	12	40	)	)	PUNCT
iajs-2877	12	41	ӽ	ӽ	NOUN
iajs-2877	12	42	has	have	AUX
iajs-2877	12	43	a	a	DET
iajs-2877	12	44	subset	subset	NOUN
iajs-2877	12	45	ѧ	ѧ	NOUN
iajs-2877	12	46	and	and	CCONJ
iajs-2877	12	47	ƀ	ƀ	PRON
iajs-2877	12	48	also	also	ADV
iajs-2877	12	49	ѧ	ѧ	X
iajs-2877	12	50	∪	∪	ADJ
iajs-2877	12	51	ƀ∈₲	ƀ∈₲	PROPN
iajs-2877	12	52	lead	lead	NOUN
iajs-2877	12	53	to	to	ADP
iajs-2877	12	54	ѧ	ѧ	DET
iajs-2877	12	55	∈₲	∈₲	NOUN
iajs-2877	12	56	or	or	CCONJ
iajs-2877	12	57	ƀ∈₲.	ƀ∈₲.	NOUN
iajs-2877	12	58	a	a	DET
iajs-2877	12	59	triple	triple	ADJ
iajs-2877	12	60	(	(	PUNCT
iajs-2877	12	61	ӽ	ӽ	NOUN
iajs-2877	12	62	,	,	PUNCT
iajs-2877	12	63	𝜏	𝜏	NOUN
iajs-2877	12	64	,	,	PUNCT
iajs-2877	12	65	₲	₲	NOUN
iajs-2877	12	66	)	)	PUNCT
iajs-2877	12	67	topological	topological	ADJ
iajs-2877	12	68	space	space	NOUN
iajs-2877	12	69	with	with	ADP
iajs-2877	12	70	grills	grill	NOUN
iajs-2877	12	71	is	be	AUX
iajs-2877	12	72	one	one	NUM
iajs-2877	12	73	type	type	NOUN
iajs-2877	12	74	of	of	ADP
iajs-2877	12	75	the	the	DET
iajs-2877	12	76	topological	topological	ADJ
iajs-2877	12	77	space	space	NOUN
iajs-2877	12	78	.	.	PUNCT
iajs-2877	13	1	[	[	X
iajs-2877	13	2	3	3	X
iajs-2877	13	3	]	]	PUNCT
iajs-2877	13	4	created	create	VERB
iajs-2877	13	5	a	a	DET
iajs-2877	13	6	distinctive	distinctive	ADJ
iajs-2877	13	7	topology	topology	NOUN
iajs-2877	13	8	with	with	ADP
iajs-2877	13	9	a	a	DET
iajs-2877	13	10	grill	grill	NOUN
iajs-2877	13	11	and	and	CCONJ
iajs-2877	13	12	investigated	investigate	VERB
iajs-2877	13	13	topological	topological	ADJ
iajs-2877	13	14	notions	notion	NOUN
iajs-2877	13	15	.	.	PUNCT
iajs-2877	14	1	for	for	ADP
iajs-2877	14	2	every	every	DET
iajs-2877	14	3	topological	topological	ADJ
iajs-2877	14	4	space	space	NOUN
iajs-2877	14	5	(	(	PUNCT
iajs-2877	14	6	ӽ	ӽ	X
iajs-2877	14	7	,	,	PUNCT
iajs-2877	14	8	𝜏	𝜏	NOUN
iajs-2877	14	9	)	)	PUNCT
iajs-2877	14	10	point	point	NOUN
iajs-2877	14	11	ӽ	ӽ	NOUN
iajs-2877	14	12	,	,	PUNCT
iajs-2877	14	13	neighborhoods	neighborhood	NOUN
iajs-2877	14	14	are	be	AUX
iajs-2877	14	15	open	open	ADJ
iajs-2877	14	16	of	of	ADP
iajs-2877	14	17	ӽ	ӽ	NOUN
iajs-2877	14	18	,	,	PUNCT
iajs-2877	14	19	and	and	CCONJ
iajs-2877	14	20	embodied	embody	VERB
iajs-2877	14	21	by	by	ADP
iajs-2877	14	22	𝜏(ӽ	𝜏(ӽ	NOUN
iajs-2877	14	23	)	)	PUNCT
iajs-2877	14	24	.	.	PUNCT
iajs-2877	15	1	a	a	DET
iajs-2877	15	2	mapping	mapping	NOUN
iajs-2877	15	3	ψ:ℙ(ӽ	ψ:ℙ(ӽ	NUM
iajs-2877	15	4	)	)	PUNCT
iajs-2877	15	5	→	→	SYM
iajs-2877	15	6	ℙ(ӽ	ℙ(ӽ	CCONJ
iajs-2877	15	7	)	)	PUNCT
iajs-2877	15	8	is	be	AUX
iajs-2877	15	9	referred	refer	VERB
iajs-2877	15	10	to	to	ADP
iajs-2877	15	11	as	as	ADP
iajs-2877	15	12	∮	∮	NUM
iajs-2877	15	13	(	(	PUNCT
iajs-2877	15	14	ѧ	ѧ	NOUN
iajs-2877	15	15	)	)	PUNCT
iajs-2877	15	16	=	=	SYM
iajs-2877	15	17	{	{	PUNCT
iajs-2877	15	18	ӽ	ӽ	X
iajs-2877	15	19	∈	∈	PROPN
iajs-2877	15	20	ӽ	ӽ	NOUN
iajs-2877	15	21	:	:	PUNCT
iajs-2877	15	22	ѧ	ѧ	NOUN
iajs-2877	15	23	∩	∩	NOUN
iajs-2877	15	24	ữ	ữ	PROPN
iajs-2877	15	25	∈	∈	PROPN
iajs-2877	15	26	₲	₲	NOUN
iajs-2877	15	27	,	,	PUNCT
iajs-2877	15	28	∀	∀	X
iajs-2877	15	29	ữ	ữ	NOUN
iajs-2877	15	30	∈	∈	PROPN
iajs-2877	15	31	τ(ӽ	τ(ӽ	PROPN
iajs-2877	15	32	)	)	PUNCT
iajs-2877	15	33	and	and	CCONJ
iajs-2877	15	34	ѧ	ѧ	DET
iajs-2877	15	35	∈	∈	PROPN
iajs-2877	15	36	ℙ(ӽ	ℙ(ӽ	PROPN
iajs-2877	15	37	)	)	PUNCT
iajs-2877	15	38	}	}	PUNCT
iajs-2877	15	39	.	.	PUNCT
iajs-2877	16	1	a	a	DET
iajs-2877	16	2	mapping	mapping	NOUN
iajs-2877	16	3	ψ	ψ	NOUN
iajs-2877	16	4	:	:	PUNCT
iajs-2877	16	5	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	16	6	)	)	PUNCT
iajs-2877	16	7	→ℙ(ӽ	→ℙ(ӽ	NUM
iajs-2877	16	8	)	)	PUNCT
iajs-2877	16	9	is	be	AUX
iajs-2877	16	10	referred	refer	VERB
iajs-2877	16	11	to	to	ADP
iajs-2877	16	12	as	as	ADP
iajs-2877	16	13	ψ	ψ	X
iajs-2877	16	14	(	(	PUNCT
iajs-2877	16	15	ѧ	ѧ	NOUN
iajs-2877	16	16	)	)	PUNCT
iajs-2877	16	17	=	=	SYM
iajs-2877	17	1	ѧ	ѧ	PROPN
iajs-2877	17	2	∪	∪	ADP
iajs-2877	17	3	∮	∮	PRON
iajs-2877	17	4	(	(	PUNCT
iajs-2877	17	5	ѧ	ѧ	NOUN
iajs-2877	17	6	)	)	PUNCT
iajs-2877	17	7	for	for	ADP
iajs-2877	17	8	every	every	DET
iajs-2877	17	9	ѧ	ѧ	PROPN
iajs-2877	17	10	∈	∈	PROPN
iajs-2877	17	11	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	17	12	)	)	PUNCT
iajs-2877	17	13	.	.	PUNCT
iajs-2877	18	1	the	the	DET
iajs-2877	18	2	map	map	NOUN
iajs-2877	18	3	ψ	ψ	ADP
iajs-2877	18	4	kuratowski	kuratowski	ADJ
iajs-2877	18	5	closure	closure	NOUN
iajs-2877	18	6	axioms	axiom	NOUN
iajs-2877	18	7	are	be	AUX
iajs-2877	18	8	met	meet	VERB
iajs-2877	18	9	:	:	PUNCT
iajs-2877	18	10	(	(	PUNCT
iajs-2877	18	11	a	a	X
iajs-2877	18	12	)	)	PUNCT
iajs-2877	18	13	ψ	ψ	NOUN
iajs-2877	18	14	(	(	PUNCT
iajs-2877	18	15	∅)=∅	∅)=∅	NOUN
iajs-2877	18	16	,	,	PUNCT
iajs-2877	18	17	doi	doi	NOUN
iajs-2877	18	18	:	:	PUNCT
iajs-2877	18	19	10.30526/35.4.2877	10.30526/35.4.2877	NUM
iajs-2877	18	20	article	article	NOUN
iajs-2877	18	21	history	history	NOUN
iajs-2877	18	22	:	:	PUNCT
iajs-2877	18	23	received	receive	VERB
iajs-2877	18	24	12	12	NUM
iajs-2877	18	25	june	june	PROPN
iajs-2877	18	26	,	,	PUNCT
iajs-2877	18	27	2022	2022	NUM
iajs-2877	18	28	,	,	PUNCT
iajs-2877	18	29	accepted	accept	VERB
iajs-2877	18	30	21	21	NUM
iajs-2877	18	31	august	august	PROPN
iajs-2877	18	32	2022	2022	NUM
iajs-2877	18	33	,	,	PUNCT
iajs-2877	18	34	published	publish	VERB
iajs-2877	18	35	in	in	ADP
iajs-2877	18	36	october	october	PROPN
iajs-2877	18	37	2022	2022	NUM
iajs-2877	18	38	.	.	PUNCT
iajs-2877	19	1	ibn	ibn	PROPN
iajs-2877	19	2	al	al	PROPN
iajs-2877	19	3	-	-	PUNCT
iajs-2877	19	4	haitham	haitham	PROPN
iajs-2877	19	5	journal	journal	PROPN
iajs-2877	19	6	for	for	ADP
iajs-2877	19	7	pure	pure	ADJ
iajs-2877	19	8	and	and	CCONJ
iajs-2877	19	9	applied	applied	ADJ
iajs-2877	19	10	sciences	sciences	PROPN
iajs-2877	19	11	journal	journal	PROPN
iajs-2877	19	12	homepage	homepage	NOUN
iajs-2877	19	13	:	:	PUNCT
iajs-2877	19	14	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2877	19	15	ali	ali	PROPN
iajs-2877	19	16	j.	j.	PROPN
iajs-2877	19	17	mahmood	mahmood	PROPN
iajs-2877	19	18	department	department	PROPN
iajs-2877	19	19	of	of	ADP
iajs-2877	19	20	mathematics	mathematics	PROPN
iajs-2877	19	21	,	,	PUNCT
iajs-2877	19	22	college	college	NOUN
iajs-2877	19	23	of	of	ADP
iajs-2877	19	24	education	education	NOUN
iajs-2877	19	25	for	for	ADP
iajs-2877	19	26	pure	pure	ADJ
iajs-2877	19	27	science	science	NOUN
iajs-2877	19	28	,	,	PUNCT
iajs-2877	19	29	ibn	ibn	PROPN
iajs-2877	19	30	al	al	PROPN
iajs-2877	19	31	haitham	haitham	PROPN
iajs-2877	19	32	,	,	PUNCT
iajs-2877	19	33	university	university	PROPN
iajs-2877	19	34	of	of	ADP
iajs-2877	19	35	baghdad	baghdad	PROPN
iajs-2877	19	36	,	,	PUNCT
iajs-2877	19	37	iraq	iraq	PROPN
iajs-2877	19	38	.	.	PUNCT
iajs-2877	20	1	ali.jamal1203a@ihcoedu.uobaghdad.edu.iq	ali.jamal1203a@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-2877	20	2	naser	naser	PROPN
iajs-2877	20	3	a.i	a.i	PROPN
iajs-2877	20	4	.	.	PROPN
iajs-2877	20	5	department	department	PROPN
iajs-2877	20	6	of	of	ADP
iajs-2877	20	7	mathematics	mathematics	PROPN
iajs-2877	20	8	,	,	PUNCT
iajs-2877	20	9	college	college	NOUN
iajs-2877	20	10	of	of	ADP
iajs-2877	20	11	education	education	NOUN
iajs-2877	20	12	for	for	ADP
iajs-2877	20	13	pure	pure	ADJ
iajs-2877	20	14	science	science	NOUN
iajs-2877	20	15	,	,	PUNCT
iajs-2877	20	16	ibn	ibn	PROPN
iajs-2877	20	17	al	al	PROPN
iajs-2877	20	18	haitham	haitham	PROPN
iajs-2877	20	19	,	,	PUNCT
iajs-2877	20	20	university	university	PROPN
iajs-2877	20	21	of	of	ADP
iajs-2877	20	22	baghdad	baghdad	PROPN
iajs-2877	20	23	,	,	PUNCT
iajs-2877	20	24	iraq	iraq	PROPN
iajs-2877	20	25	.	.	PUNCT
iajs-2877	21	1	ahmed_math06@yahoo.com	ahmed_math06@yahoo.com	X
iajs-2877	21	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2877	21	3	mailto:ali.jamal.1203a@ihcoedu.uobaghdad.edu.iq	mailto:ali.jamal.1203a@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-2877	21	4	mailto:ahmed_math06@yahoo.com	mailto:ahmed_math06@yahoo.com	PROPN
iajs-2877	21	5	ihjpas	ihjpas	PROPN
iajs-2877	21	6	.	.	PUNCT
iajs-2877	22	1	53	53	NUM
iajs-2877	22	2	(	(	PUNCT
iajs-2877	22	3	4)2022	4)2022	NOUN
iajs-2877	22	4	236	236	NUM
iajs-2877	22	5	(	(	PUNCT
iajs-2877	22	6	b	b	NOUN
iajs-2877	22	7	)	)	PUNCT
iajs-2877	22	8	as	as	ADV
iajs-2877	22	9	soon	soon	ADV
iajs-2877	22	10	as	as	ADP
iajs-2877	22	11	ѧ	ѧ	DET
iajs-2877	22	12	⊆	⊆	NUM
iajs-2877	22	13	ƀ	ƀ	NOUN
iajs-2877	22	14	,	,	PUNCT
iajs-2877	22	15	so	so	SCONJ
iajs-2877	22	16	ψ	ψ	X
iajs-2877	22	17	(	(	PUNCT
iajs-2877	22	18	ѧ	ѧ	NOUN
iajs-2877	22	19	)	)	PUNCT
iajs-2877	22	20	⊆	⊆	NUM
iajs-2877	22	21	ψ	ψ	X
iajs-2877	22	22	(	(	PUNCT
iajs-2877	22	23	ƀ	ƀ	NOUN
iajs-2877	22	24	)	)	PUNCT
iajs-2877	22	25	,	,	PUNCT
iajs-2877	22	26	(	(	PUNCT
iajs-2877	22	27	c	c	X
iajs-2877	22	28	)	)	PUNCT
iajs-2877	22	29	as	as	ADV
iajs-2877	22	30	soon	soon	ADV
iajs-2877	22	31	as	as	ADP
iajs-2877	22	32	ѧ	ѧ	DET
iajs-2877	22	33	⊆	⊆	NUM
iajs-2877	22	34	ӽ	ӽ	NOUN
iajs-2877	22	35	,	,	PUNCT
iajs-2877	22	36	so	so	SCONJ
iajs-2877	22	37	ψ	ψ	X
iajs-2877	22	38	(	(	PUNCT
iajs-2877	22	39	ψ	ψ	X
iajs-2877	22	40	(	(	PUNCT
iajs-2877	22	41	ѧ))=	ѧ))=	PROPN
iajs-2877	22	42	ψ	ψ	X
iajs-2877	22	43	(	(	PUNCT
iajs-2877	22	44	ѧ	ѧ	NOUN
iajs-2877	22	45	)	)	PUNCT
iajs-2877	22	46	,	,	PUNCT
iajs-2877	22	47	(	(	PUNCT
iajs-2877	22	48	d	d	X
iajs-2877	22	49	)	)	PUNCT
iajs-2877	22	50	as	as	ADV
iajs-2877	22	51	soon	soon	ADV
iajs-2877	22	52	as	as	ADP
iajs-2877	22	53	ѧ	ѧ	NOUN
iajs-2877	22	54	,	,	PUNCT
iajs-2877	22	55	ƀ⊆	ƀ⊆	PROPN
iajs-2877	22	56	ӽ	ӽ	NOUN
iajs-2877	22	57	,	,	PUNCT
iajs-2877	22	58	so	so	SCONJ
iajs-2877	22	59	ψ	ψ	X
iajs-2877	22	60	(	(	PUNCT
iajs-2877	22	61	ѧ	ѧ	X
iajs-2877	22	62	∪	∪	ADJ
iajs-2877	22	63	ƀ)=	ƀ)=	NOUN
iajs-2877	22	64	ψ	ψ	X
iajs-2877	22	65	(	(	PUNCT
iajs-2877	22	66	ѧ	ѧ	NOUN
iajs-2877	22	67	)	)	PUNCT
iajs-2877	22	68	∪	∪	NOUN
iajs-2877	22	69	ψ	ψ	X
iajs-2877	22	70	(	(	PUNCT
iajs-2877	22	71	ƀ	ƀ	NOUN
iajs-2877	22	72	)	)	PUNCT
iajs-2877	22	73	.	.	PUNCT
iajs-2877	23	1	grill	grill	PROPN
iajs-2877	23	2	topological	topological	ADJ
iajs-2877	23	3	spaces	space	NOUN
iajs-2877	23	4	come	come	VERB
iajs-2877	23	5	in	in	ADP
iajs-2877	23	6	various	various	ADJ
iajs-2877	23	7	shapes	shape	NOUN
iajs-2877	23	8	,	,	PUNCT
iajs-2877	23	9	sizes	size	NOUN
iajs-2877	23	10	,	,	PUNCT
iajs-2877	23	11	as	as	ADP
iajs-2877	23	12	a	a	DET
iajs-2877	23	13	discrete	discrete	ADJ
iajs-2877	23	14	topology	topology	NOUN
iajs-2877	23	15	,	,	PUNCT
iajs-2877	23	16	and	and	CCONJ
iajs-2877	23	17	a	a	DET
iajs-2877	23	18	coffinite	coffinite	ADJ
iajs-2877	23	19	topology	topology	NOUN
iajs-2877	23	20	.	.	PUNCT
iajs-2877	24	1	on	on	ADP
iajs-2877	24	2	a	a	DET
iajs-2877	24	3	space	space	NOUN
iajs-2877	24	4	(	(	PUNCT
iajs-2877	24	5	ӽ	ӽ	X
iajs-2877	24	6	,	,	PUNCT
iajs-2877	24	7	𝜏	𝜏	NOUN
iajs-2877	24	8	)	)	PUNCT
iajs-2877	24	9	;	;	PUNCT
iajs-2877	24	10	this	this	PRON
iajs-2877	24	11	agrees	agree	VERB
iajs-2877	24	12	to	to	ADP
iajs-2877	24	13	a	a	DET
iajs-2877	24	14	grill	grill	NOUN
iajs-2877	24	15	₲	₲	NOUN
iajs-2877	24	16	a	a	DET
iajs-2877	24	17	topology	topology	NOUN
iajs-2877	24	18	exists	exist	VERB
iajs-2877	24	19	𝜏₲	𝜏₲	PROPN
iajs-2877	24	20	on	on	ADP
iajs-2877	24	21	ӽ	ӽ	NOUN
iajs-2877	24	22	that	that	PRON
iajs-2877	24	23	is	be	AUX
iajs-2877	24	24	given	give	VERB
iajs-2877	24	25	by	by	ADP
iajs-2877	24	26	no	no	DET
iajs-2877	24	27	one	one	NOUN
iajs-2877	24	28	else	else	ADV
iajs-2877	24	29	by	by	ADP
iajs-2877	24	30	𝜏₲	𝜏₲	PROPN
iajs-2877	25	1	=	=	PRON
iajs-2877	25	2	{	{	PUNCT
iajs-2877	25	3	ữ	ữ	NOUN
iajs-2877	25	4	⊆ӽ	⊆ӽ	NOUN
iajs-2877	25	5	:	:	PUNCT
iajs-2877	25	6	ψ	ψ	X
iajs-2877	25	7	(	(	PUNCT
iajs-2877	25	8	ӽ	ӽ	X
iajs-2877	25	9	–	–	PUNCT
iajs-2877	25	10	ữ	ữ	NOUN
iajs-2877	25	11	)	)	PUNCT
iajs-2877	25	12	=	=	SYM
iajs-2877	25	13	ӽ	ӽ	X
iajs-2877	25	14	–	–	PUNCT
iajs-2877	25	15	ữ	ữ	NOUN
iajs-2877	25	16	}	}	PUNCT
iajs-2877	25	17	,	,	PUNCT
iajs-2877	25	18	consequently	consequently	ADV
iajs-2877	25	19	,	,	PUNCT
iajs-2877	25	20	ѧ	ѧ	PRON
iajs-2877	25	21	⊆	⊆	NUM
iajs-2877	25	22	ӽ	ӽ	NOUN
iajs-2877	25	23	,	,	PUNCT
iajs-2877	25	24	ψ	ψ	X
iajs-2877	25	25	(	(	PUNCT
iajs-2877	25	26	ѧ	ѧ	NOUN
iajs-2877	25	27	)	)	PUNCT
iajs-2877	25	28	=	=	SYM
iajs-2877	25	29	ѧ	ѧ	PROPN
iajs-2877	25	30	∪	∪	ADP
iajs-2877	25	31	∮	∮	PRON
iajs-2877	25	32	(	(	PUNCT
iajs-2877	25	33	ѧ	ѧ	NOUN
iajs-2877	25	34	)	)	PUNCT
iajs-2877	26	1	[	[	X
iajs-2877	26	2	4,5	4,5	NUM
iajs-2877	26	3	]	]	PUNCT
iajs-2877	26	4	.	.	PUNCT
iajs-2877	27	1	τ	τ	PROPN
iajs-2877	27	2	⊆	⊆	NUM
iajs-2877	27	3	𝜏₲	𝜏₲	PROPN
iajs-2877	27	4	and	and	CCONJ
iajs-2877	27	5	ψ	ψ	X
iajs-2877	27	6	(	(	PUNCT
iajs-2877	27	7	ѧ	ѧ	NOUN
iajs-2877	27	8	)	)	PUNCT
iajs-2877	27	9	=	=	NOUN
iajs-2877	27	10	𝑐𝜄(ѧ	𝑐𝜄(ѧ	NOUN
iajs-2877	27	11	)	)	PUNCT
iajs-2877	27	12	.	.	PUNCT
iajs-2877	28	1	using	use	VERB
iajs-2877	28	2	the	the	DET
iajs-2877	28	3	following	following	NOUN
iajs-2877	28	4	as	as	ADP
iajs-2877	28	5	a	a	DET
iajs-2877	28	6	basis	basis	NOUN
iajs-2877	28	7	,	,	PUNCT
iajs-2877	28	8	we	we	PRON
iajs-2877	28	9	can	can	AUX
iajs-2877	28	10	locate	locate	VERB
iajs-2877	28	11	𝜏₲	𝜏₲	PROPN
iajs-2877	28	12	on	on	ADP
iajs-2877	28	13	ӽ	ӽ	NOUN
iajs-2877	28	14	by	by	ADP
iajs-2877	28	15	supplying	supply	VERB
iajs-2877	28	16	𝜏₲	𝜏₲	PROPN
iajs-2877	28	17	through	through	ADP
iajs-2877	28	18	𝛽(𝜏₲	𝛽(𝜏₲	PROPN
iajs-2877	28	19	,	,	PUNCT
iajs-2877	28	20	ӽ	ӽ	X
iajs-2877	28	21	)	)	PUNCT
iajs-2877	28	22	=	=	SYM
iajs-2877	28	23	{	{	PUNCT
iajs-2877	28	24	ƴ	ƴ	PROPN
iajs-2877	28	25	−	−	PROPN
iajs-2877	28	26	ѧ	ѧ	NOUN
iajs-2877	28	27	;	;	PUNCT
iajs-2877	28	28	ƴ	ƴ	PROPN
iajs-2877	28	29	∈	∈	PROPN
iajs-2877	28	30	𝜏	𝜏	PROPN
iajs-2877	28	31	,	,	PUNCT
iajs-2877	28	32	ѧ	ѧ	PRON
iajs-2877	28	33	∉₲	∉₲	NOUN
iajs-2877	28	34	}	}	PUNCT
iajs-2877	28	35	.	.	PUNCT
iajs-2877	29	1	on	on	ADP
iajs-2877	29	2	a	a	DET
iajs-2877	29	3	space	space	NOUN
iajs-2877	29	4	(	(	PUNCT
iajs-2877	29	5	ӽ	ӽ	X
iajs-2877	29	6	,	,	PUNCT
iajs-2877	29	7	𝜏	𝜏	NOUN
iajs-2877	29	8	)	)	PUNCT
iajs-2877	29	9	,	,	PUNCT
iajs-2877	29	10	there	there	PRON
iajs-2877	29	11	is	be	VERB
iajs-2877	29	12	a	a	DET
iajs-2877	29	13	grill	grill	NOUN
iajs-2877	29	14	₲	₲	NOUN
iajs-2877	29	15	,	,	PUNCT
iajs-2877	29	16	𝜏	𝜏	NOUN
iajs-2877	29	17	⊆	⊆	NUM
iajs-2877	29	18	𝛽(₲	𝛽(₲	NOUN
iajs-2877	29	19	,	,	PUNCT
iajs-2877	29	20	τ	τ	X
iajs-2877	29	21	)	)	PUNCT
iajs-2877	29	22	⊆	⊆	NUM
iajs-2877	29	23	𝜏₲	𝜏₲	PROPN
iajs-2877	29	24	,	,	PUNCT
iajs-2877	29	25	where	where	SCONJ
iajs-2877	29	26	𝛽(₲	𝛽(₲	NOUN
iajs-2877	29	27	,	,	PUNCT
iajs-2877	29	28	τ	τ	NOUN
iajs-2877	29	29	)	)	PUNCT
iajs-2877	29	30	basis	basis	NOUN
iajs-2877	29	31	for	for	ADP
iajs-2877	29	32	𝜏₲[6	𝜏₲[6	PROPN
iajs-2877	29	33	]	]	PUNCT
iajs-2877	29	34	.	.	PUNCT
iajs-2877	30	1	as	as	ADP
iajs-2877	30	2	an	an	DET
iajs-2877	30	3	example	example	NOUN
iajs-2877	30	4	,	,	PUNCT
iajs-2877	30	5	to	to	PART
iajs-2877	30	6	exist	exist	VERB
iajs-2877	30	7	in	in	ADP
iajs-2877	30	8	a	a	DET
iajs-2877	30	9	space	space	NOUN
iajs-2877	30	10	(	(	PUNCT
iajs-2877	30	11	ӽ	ӽ	X
iajs-2877	30	12	,	,	PUNCT
iajs-2877	30	13	𝜏	𝜏	NOUN
iajs-2877	30	14	)	)	PUNCT
iajs-2877	30	15	,	,	PUNCT
iajs-2877	30	16	𝜏₲	𝜏₲	PROPN
iajs-2877	31	1	=	=	PUNCT
iajs-2877	31	2	𝜏	𝜏	X
iajs-2877	31	3	whenever	whenever	SCONJ
iajs-2877	31	4	₲	₲	NOUN
iajs-2877	31	5	=	=	SYM
iajs-2877	31	6	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	31	7	)	)	PUNCT
iajs-2877	31	8	∖	∖	NOUN
iajs-2877	31	9	{	{	PUNCT
iajs-2877	31	10	ø	ø	AUX
iajs-2877	31	11	}	}	PUNCT
iajs-2877	31	12	implying	imply	VERB
iajs-2877	31	13	𝜏₲	𝜏₲	PROPN
iajs-2877	32	1	=	=	PUNCT
iajs-2877	33	1	τ	τ	PROPN
iajs-2877	34	1	[	[	X
iajs-2877	34	2	7].the	7].the	DET
iajs-2877	34	3	family	family	NOUN
iajs-2877	34	4	of	of	ADP
iajs-2877	34	5	all	all	DET
iajs-2877	34	6	semi	semi	ADJ
iajs-2877	34	7	-	-	ADJ
iajs-2877	34	8	open	open	ADJ
iajs-2877	34	9	set	set	NOUN
iajs-2877	34	10	is	be	AUX
iajs-2877	34	11	showed	show	VERB
iajs-2877	34	12	by	by	ADP
iajs-2877	34	13	𝜏𝑠.	𝜏𝑠.	X
iajs-2877	34	14	semi	semi	ADJ
iajs-2877	34	15	-	-	ADJ
iajs-2877	34	16	open	open	ADJ
iajs-2877	34	17	is	be	AUX
iajs-2877	34	18	a	a	DET
iajs-2877	34	19	subset	subset	NOUN
iajs-2877	34	20	ѧ	ѧ	NOUN
iajs-2877	34	21	of	of	ADP
iajs-2877	34	22	a	a	DET
iajs-2877	34	23	space	space	NOUN
iajs-2877	34	24	(	(	PUNCT
iajs-2877	34	25	ӽ	ӽ	NOUN
iajs-2877	34	26	,	,	PUNCT
iajs-2877	34	27	𝜏	𝜏	NOUN
iajs-2877	34	28	)	)	PUNCT
iajs-2877	34	29	,	,	PUNCT
iajs-2877	34	30	if	if	SCONJ
iajs-2877	34	31	ѧ	ѧ	PROPN
iajs-2877	34	32	⊆	⊆	NUM
iajs-2877	34	33	𝑐𝜄(ḭ𝑛ţ(ѧ))[8	𝑐𝜄(ḭ𝑛ţ(ѧ))[8	ADP
iajs-2877	34	34	]	]	PUNCT
iajs-2877	34	35	.	.	PUNCT
iajs-2877	35	1	let	let	VERB
iajs-2877	35	2	(	(	PUNCT
iajs-2877	35	3	ӽ	ӽ	X
iajs-2877	35	4	,	,	PUNCT
iajs-2877	35	5	τ	τ	NOUN
iajs-2877	35	6	,	,	PUNCT
iajs-2877	35	7	₲	₲	NOUN
iajs-2877	35	8	)	)	PUNCT
iajs-2877	35	9	be	be	AUX
iajs-2877	35	10	topological	topological	ADJ
iajs-2877	35	11	space	space	NOUN
iajs-2877	35	12	.	.	PUNCT
iajs-2877	36	1	the	the	DET
iajs-2877	36	2	subset	subset	NOUN
iajs-2877	36	3	ѧ	ѧ	NOUN
iajs-2877	36	4	in	in	ADP
iajs-2877	36	5	ӽ	ӽ	NOUN
iajs-2877	36	6	is	be	AUX
iajs-2877	36	7	known	know	VERB
iajs-2877	36	8	as	as	ADP
iajs-2877	36	9	₲	₲	NOUN
iajs-2877	36	10	-semi	-semi	NOUN
iajs-2877	36	11	-	-	PUNCT
iajs-2877	36	12	open	open	ADJ
iajs-2877	36	13	if	if	SCONJ
iajs-2877	36	14	ѧ	ѧ	DET
iajs-2877	36	15	⊆	⊆	NUM
iajs-2877	36	16	ψ(ḭnţ(ѧ	ψ(ḭnţ(ѧ	NOUN
iajs-2877	36	17	)	)	PUNCT
iajs-2877	36	18	)	)	PUNCT
iajs-2877	36	19	,	,	PUNCT
iajs-2877	36	20	and	and	CCONJ
iajs-2877	36	21	every	every	DET
iajs-2877	36	22	ψ	ψ	NOUN
iajs-2877	36	23	-	-	ADJ
iajs-2877	36	24	semi	semi	ADJ
iajs-2877	36	25	-	-	ADJ
iajs-2877	36	26	open	open	ADJ
iajs-2877	36	27	is	be	AUX
iajs-2877	36	28	a	a	DET
iajs-2877	36	29	semi	semi	ADJ
iajs-2877	36	30	-	-	ADJ
iajs-2877	36	31	open	open	ADJ
iajs-2877	36	32	.	.	PUNCT
iajs-2877	37	1	various	various	ADJ
iajs-2877	37	2	academics	academic	NOUN
iajs-2877	37	3	have	have	AUX
iajs-2877	37	4	made	make	VERB
iajs-2877	37	5	generalizations	generalization	NOUN
iajs-2877	37	6	using	use	VERB
iajs-2877	37	7	these	these	DET
iajs-2877	37	8	combinations	combination	NOUN
iajs-2877	37	9	[	[	X
iajs-2877	37	10	9	9	NUM
iajs-2877	37	11	,	,	PUNCT
iajs-2877	37	12	10	10	NUM
iajs-2877	37	13	]	]	PUNCT
iajs-2877	37	14	.	.	PUNCT
iajs-2877	38	1	the	the	DET
iajs-2877	38	2	symbol	symbol	NOUN
iajs-2877	38	3	ḭ𝑛ţ(ѧ	ḭ𝑛ţ(ѧ	NOUN
iajs-2877	38	4	)	)	PUNCT
iajs-2877	38	5	to	to	ADP
iajs-2877	38	6	the	the	DET
iajs-2877	38	7	set	set	ADJ
iajs-2877	38	8	interior	interior	ADJ
iajs-2877	38	9	ѧ	ѧ	NOUN
iajs-2877	38	10	,	,	PUNCT
iajs-2877	38	11	as	as	ADV
iajs-2877	38	12	well	well	ADV
iajs-2877	38	13	as	as	ADP
iajs-2877	38	14	the	the	DET
iajs-2877	38	15	sign	sign	NOUN
iajs-2877	38	16	𝑐𝜄(ѧ	𝑐𝜄(ѧ	PUNCT
iajs-2877	38	17	)	)	PUNCT
iajs-2877	38	18	is	be	AUX
iajs-2877	38	19	the	the	DET
iajs-2877	38	20	closure	closure	NOUN
iajs-2877	38	21	of	of	ADP
iajs-2877	38	22	ѧ	ѧ	PROPN
iajs-2877	38	23	is	be	AUX
iajs-2877	38	24	utilized	utilize	VERB
iajs-2877	38	25	in	in	ADP
iajs-2877	38	26	this	this	DET
iajs-2877	38	27	paper	paper	NOUN
iajs-2877	38	28	.	.	PUNCT
iajs-2877	39	1	the	the	DET
iajs-2877	39	2	space	space	NOUN
iajs-2877	39	3	(	(	PUNCT
iajs-2877	39	4	ӽ	ӽ	NOUN
iajs-2877	39	5	,	,	PUNCT
iajs-2877	39	6			NOUN
iajs-2877	39	7	)	)	PUNCT
iajs-2877	39	8	is	be	AUX
iajs-2877	39	9	disconnected	disconnect	VERB
iajs-2877	39	10	if	if	SCONJ
iajs-2877	39	11	and	and	CCONJ
iajs-2877	39	12	only	only	ADV
iajs-2877	39	13	if	if	SCONJ
iajs-2877	39	14	there	there	PRON
iajs-2877	39	15	exists	exist	VERB
iajs-2877	39	16	two	two	NUM
iajs-2877	39	17	open	open	ADJ
iajs-2877	39	18	disjoint	disjoint	NOUN
iajs-2877	39	19	nonempty	nonempty	NOUN
iajs-2877	39	20	sets	set	VERB
iajs-2877	39	21	ѧ	ѧ	PROPN
iajs-2877	39	22	and	and	CCONJ
iajs-2877	39	23	ƀ	ƀ	PROPN
iajs-2877	39	24	,	,	PUNCT
iajs-2877	39	25	such	such	ADJ
iajs-2877	39	26	that	that	SCONJ
iajs-2877	39	27	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	39	28	=	=	SYM
iajs-2877	39	29	ӽ.	ӽ.	NOUN
iajs-2877	39	30	i.e.	i.e.	X
iajs-2877	39	31	,	,	PUNCT
iajs-2877	39	32	ӽ	ӽ	PRON
iajs-2877	39	33	is	be	AUX
iajs-2877	39	34	disconnected	disconnect	VERB
iajs-2877	39	35	if	if	SCONJ
iajs-2877	39	36	and	and	CCONJ
iajs-2877	39	37	only	only	ADV
iajs-2877	39	38	if	if	SCONJ
iajs-2877	39	39	ӽ=ѧ⋃ƀ	ӽ=ѧ⋃ƀ	PROPN
iajs-2877	39	40	,	,	PUNCT
iajs-2877	39	41	ѧ	ѧ	NOUN
iajs-2877	39	42	,	,	PUNCT
iajs-2877	39	43	ƀ	ƀ	PROPN
iajs-2877	39	44	∈	∈	PROPN
iajs-2877	39	45			NOUN
iajs-2877	39	46	,	,	PUNCT
iajs-2877	39	47	and	and	CCONJ
iajs-2877	39	48	ѧ	ѧ	DET
iajs-2877	39	49	⋂	⋂	PROPN
iajs-2877	39	50	ƀ	ƀ	NOUN
iajs-2877	39	51	=	=	SYM
iajs-2877	39	52			NOUN
iajs-2877	39	53	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-2877	39	54	ѧ	ѧ	PROPN
iajs-2877	39	55	,	,	PUNCT
iajs-2877	39	56	ƀ	ƀ	PROPN
iajs-2877	39	57	.	.	VERB
iajs-2877	39	58	the	the	DET
iajs-2877	39	59	sets	set	NOUN
iajs-2877	39	60	ѧ	ѧ	PROPN
iajs-2877	39	61	and	and	CCONJ
iajs-2877	39	62	ƀ	ƀ	PRON
iajs-2877	39	63	form	form	VERB
iajs-2877	39	64	a	a	DET
iajs-2877	39	65	separation	separation	NOUN
iajs-2877	39	66	of	of	ADP
iajs-2877	39	67	ӽ.	ӽ.	NOUN
iajs-2877	39	68	the	the	DET
iajs-2877	39	69	space	space	NOUN
iajs-2877	39	70	(	(	PUNCT
iajs-2877	39	71	x	x	X
iajs-2877	39	72	,	,	PUNCT
iajs-2877	39	73			PROPN
iajs-2877	39	74	)	)	PUNCT
iajs-2877	39	75	is	be	AUX
iajs-2877	39	76	connected	connect	VERB
iajs-2877	39	77	if	if	SCONJ
iajs-2877	39	78	and	and	CCONJ
iajs-2877	39	79	only	only	ADV
iajs-2877	39	80	if	if	SCONJ
iajs-2877	39	81	it	it	PRON
iajs-2877	39	82	is	be	AUX
iajs-2877	39	83	not	not	PART
iajs-2877	39	84	disconnected	disconnect	VERB
iajs-2877	39	85	.	.	PUNCT
iajs-2877	40	1	ӽ	ӽ	NOUN
iajs-2877	40	2	is	be	AUX
iajs-2877	40	3	connected	connect	VERB
iajs-2877	40	4	if	if	SCONJ
iajs-2877	40	5	and	and	CCONJ
iajs-2877	40	6	only	only	ADV
iajs-2877	40	7	if	if	SCONJ
iajs-2877	40	8	ӽ	ӽ	PRON
iajs-2877	40	9			VERB
iajs-2877	40	10	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	40	11	,	,	PUNCT
iajs-2877	40	12	ѧ	ѧ	PROPN
iajs-2877	40	13	,	,	PUNCT
iajs-2877	40	14	ƀ	ƀ	PROPN
iajs-2877	40	15	∈	∈	NOUN
iajs-2877	40	16			NOUN
iajs-2877	40	17	,	,	PUNCT
iajs-2877	40	18	ѧ	ѧ	PROPN
iajs-2877	40	19	⋂	⋂	PROPN
iajs-2877	40	20	ƀ	ƀ	NOUN
iajs-2877	40	21	=	=	SYM
iajs-2877	40	22			NOUN
iajs-2877	40	23	,	,	PUNCT
iajs-2877	40	24	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	40	25	ѧ	ѧ	PROPN
iajs-2877	40	26	,	,	PUNCT
iajs-2877	40	27	ƀ	ƀ	PROPN
iajs-2877	40	28	.	.	PART
iajs-2877	40	29	2	2	NUM
iajs-2877	40	30	.	.	PUNCT
iajs-2877	40	31	grill	grill	NOUN
iajs-2877	40	32	semi	semi	ADJ
iajs-2877	40	33	-	-	ADJ
iajs-2877	40	34	open	open	ADJ
iajs-2877	40	35	sets	set	NOUN
iajs-2877	40	36	definition	definition	NOUN
iajs-2877	40	37	2.1	2.1	NUM
iajs-2877	40	38	.	.	PUNCT
iajs-2877	41	1	[	[	X
iajs-2877	41	2	2	2	NUM
iajs-2877	41	3	]	]	PUNCT
iajs-2877	41	4	:	:	PUNCT
iajs-2877	41	5	ѧ	ѧ	PRON
iajs-2877	41	6	is	be	AUX
iajs-2877	41	7	the	the	DET
iajs-2877	41	8	set	set	NOUN
iajs-2877	41	9	that	that	PRON
iajs-2877	41	10	will	will	AUX
iajs-2877	41	11	be	be	AUX
iajs-2877	41	12	𝐺rill	𝐺rill	PROPN
iajs-2877	41	13	semi	semi	ADJ
iajs-2877	41	14	-	-	ADJ
iajs-2877	41	15	open	open	ADJ
iajs-2877	41	16	when	when	SCONJ
iajs-2877	41	17	∃	∃	PROPN
iajs-2877	41	18	ữ	ữ	NOUN
iajs-2877	41	19	∈	∈	PROPN
iajs-2877	41	20	𝜏	𝜏	NOUN
iajs-2877	41	21	;	;	PUNCT
iajs-2877	41	22	ữ	ữ	NOUN
iajs-2877	41	23	−	−	PROPN
iajs-2877	41	24	ѧ	ѧ	X
iajs-2877	41	25	∉	∉	PROPN
iajs-2877	41	26	₲	₲	NOUN
iajs-2877	41	27	and	and	CCONJ
iajs-2877	41	28	ѧ	ѧ	DET
iajs-2877	41	29	−	−	PROPN
iajs-2877	41	30	𝑐𝜄₲(ữ	𝑐𝜄₲(ữ	NOUN
iajs-2877	41	31	)	)	PUNCT
iajs-2877	41	32	∉	∉	PROPN
iajs-2877	41	33	₲	₲	NOUN
iajs-2877	41	34	.	.	PUNCT
iajs-2877	42	1	and	and	CCONJ
iajs-2877	42	2	it	it	PRON
iajs-2877	42	3	is	be	AUX
iajs-2877	42	4	described	describe	VERB
iajs-2877	42	5	by	by	ADP
iajs-2877	42	6	₲	₲	NOUN
iajs-2877	42	7	∗	∗	NOUN
iajs-2877	42	8	-semi	-semi	NOUN
iajs-2877	42	9	-	-	PUNCT
iajs-2877	42	10	open	open	ADJ
iajs-2877	42	11	.	.	PUNCT
iajs-2877	43	1	ӽ	ӽ	PRON
iajs-2877	43	2	−	−	NOUN
iajs-2877	43	3	₲	₲	NOUN
iajs-2877	43	4	∗	∗	NOUN
iajs-2877	43	5	-semi	-semi	PROPN
iajs-2877	43	6	-	-	PUNCT
iajs-2877	43	7	open	open	ADJ
iajs-2877	43	8	is	be	AUX
iajs-2877	43	9	a	a	DET
iajs-2877	43	10	₲	₲	NOUN
iajs-2877	43	11	∗	∗	NOUN
iajs-2877	43	12	-semi	-semi	PROPN
iajs-2877	43	13	-	-	PUNCT
iajs-2877	43	14	cl𝑜sed	cl𝑜se	VERB
iajs-2877	43	15	,	,	PUNCT
iajs-2877	43	16	as	as	ADV
iajs-2877	43	17	well	well	ADV
iajs-2877	43	18	as	as	ADP
iajs-2877	43	19	the	the	DET
iajs-2877	43	20	set	set	NOUN
iajs-2877	43	21	of	of	ADP
iajs-2877	43	22	all	all	DET
iajs-2877	43	23	₲	₲	NOUN
iajs-2877	43	24	∗	∗	NOUN
iajs-2877	43	25	semi	semi	ADV
iajs-2877	43	26	-	-	ADJ
iajs-2877	43	27	open	open	ADJ
iajs-2877	43	28	at	at	ADP
iajs-2877	43	29	the	the	DET
iajs-2877	43	30	moment	moment	NOUN
iajs-2877	43	31	by	by	ADP
iajs-2877	43	32	₲	₲	NOUN
iajs-2877	43	33	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	43	34	)	)	PUNCT
iajs-2877	43	35	a𝑛d	a𝑛d	VERB
iajs-2877	43	36	the	the	DET
iajs-2877	43	37	collection	collection	NOUN
iajs-2877	43	38	of	of	ADP
iajs-2877	43	39	every	every	DET
iajs-2877	43	40	₲	₲	NOUN
iajs-2877	43	41	∗	∗	NOUN
iajs-2877	43	42	-semi-𝑐𝑙osed	-semi-𝑐𝑙ose	VERB
iajs-2877	43	43	at	at	ADP
iajs-2877	43	44	the	the	DET
iajs-2877	43	45	moment	moment	NOUN
iajs-2877	43	46	by	by	ADP
iajs-2877	43	47	₲	₲	NOUN
iajs-2877	43	48	∗𝑠𝑐(ӽ	∗𝑠𝑐(ӽ	NOUN
iajs-2877	43	49	)	)	PUNCT
iajs-2877	43	50	.	.	PUNCT
iajs-2877	44	1	.	.	PUNCT
iajs-2877	45	1	example	example	NOUN
iajs-2877	45	2	2.2	2.2	NUM
iajs-2877	45	3	.	.	PUNCT
iajs-2877	46	1	let	let	VERB
iajs-2877	46	2	(	(	PUNCT
iajs-2877	46	3	ӽ	ӽ	X
iajs-2877	46	4	,	,	PUNCT
iajs-2877	46	5	τ	τ	NOUN
iajs-2877	46	6	,	,	PUNCT
iajs-2877	46	7	₲	₲	NOUN
iajs-2877	46	8	)	)	PUNCT
iajs-2877	46	9	topological	topological	ADJ
iajs-2877	46	10	space	space	NOUN
iajs-2877	46	11	to	to	PART
iajs-2877	46	12	be	be	AUX
iajs-2877	46	13	a	a	DET
iajs-2877	46	14	grill	grill	NOUN
iajs-2877	46	15	and	and	CCONJ
iajs-2877	46	16	ӽ	ӽ	NOUN
iajs-2877	46	17	=	=	X
iajs-2877	46	18	{	{	PUNCT
iajs-2877	46	19	ӽ1	ӽ1	PROPN
iajs-2877	46	20	,	,	PUNCT
iajs-2877	46	21	ӽ2	ӽ2	PROPN
iajs-2877	46	22	,	,	PUNCT
iajs-2877	46	23	ӽ3	ӽ3	ADJ
iajs-2877	46	24	}	}	PUNCT
iajs-2877	46	25	,	,	PUNCT
iajs-2877	46	26	𝜏	𝜏	X
iajs-2877	46	27	=	=	SYM
iajs-2877	46	28	{	{	PUNCT
iajs-2877	46	29	ӽ	ӽ	X
iajs-2877	46	30	,	,	PUNCT
iajs-2877	46	31	ø	ø	PROPN
iajs-2877	46	32	,	,	PUNCT
iajs-2877	46	33	{	{	PUNCT
iajs-2877	46	34	ӽ1	ӽ1	NOUN
iajs-2877	46	35	}	}	PUNCT
iajs-2877	46	36	,	,	PUNCT
iajs-2877	46	37	{	{	PUNCT
iajs-2877	46	38	ӽ1	ӽ1	NOUN
iajs-2877	46	39	,	,	PUNCT
iajs-2877	46	40	ӽ2	ӽ2	PROPN
iajs-2877	46	41	}	}	PUNCT
iajs-2877	46	42	}	}	PUNCT
iajs-2877	46	43	,	,	PUNCT
iajs-2877	46	44	ℱ	ℱ	PROPN
iajs-2877	46	45	=	=	SYM
iajs-2877	46	46	{	{	PUNCT
iajs-2877	46	47	ӽ	ӽ	X
iajs-2877	46	48	,	,	PUNCT
iajs-2877	46	49	ø	ø	PROPN
iajs-2877	46	50	,	,	PUNCT
iajs-2877	46	51	{	{	PUNCT
iajs-2877	46	52	ӽ3	ӽ3	ADJ
iajs-2877	46	53	}	}	PUNCT
iajs-2877	46	54	,	,	PUNCT
iajs-2877	46	55	{	{	PUNCT
iajs-2877	46	56	ӽ3	ӽ3	ADJ
iajs-2877	46	57	,	,	PUNCT
iajs-2877	46	58	ӽ2	ӽ2	PROPN
iajs-2877	46	59	}	}	PUNCT
iajs-2877	46	60	}	}	PUNCT
iajs-2877	46	61	,	,	PUNCT
iajs-2877	46	62	₲	₲	NOUN
iajs-2877	46	63	=	=	PRON
iajs-2877	46	64	{	{	PUNCT
iajs-2877	46	65	ữ	ữ	NOUN
iajs-2877	46	66	⊆	⊆	NUM
iajs-2877	46	67	ӽ	ӽ	NOUN
iajs-2877	46	68	;	;	PUNCT
iajs-2877	46	69	ӽ2	ӽ2	PROPN
iajs-2877	46	70	∊	∊	PROPN
iajs-2877	46	71	ữ	ữ	NOUN
iajs-2877	46	72	}	}	PUNCT
iajs-2877	46	73	,	,	PUNCT
iajs-2877	46	74	∮	∮	PRON
iajs-2877	46	75	:	:	PUNCT
iajs-2877	46	76	ℙ(ӽ	ℙ(ӽ	X
iajs-2877	46	77	)	)	PUNCT
iajs-2877	46	78	⇾	⇾	PROPN
iajs-2877	46	79	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	46	80	)	)	PUNCT
iajs-2877	46	81	,	,	PUNCT
iajs-2877	46	82	∮	∮	PRON
iajs-2877	46	83	(	(	PUNCT
iajs-2877	46	84	ѧ	ѧ	NOUN
iajs-2877	46	85	)	)	PUNCT
iajs-2877	46	86	=	=	SYM
iajs-2877	46	87	{	{	PUNCT
iajs-2877	46	88	ӽ	ӽ	X
iajs-2877	46	89	∈	∈	PROPN
iajs-2877	46	90	ӽ	ӽ	NOUN
iajs-2877	46	91	;	;	PUNCT
iajs-2877	46	92	∀ữ	∀ữ	NUM
iajs-2877	46	93	∈	∈	NOUN
iajs-2877	46	94	𝜏ӽ	𝜏ӽ	NOUN
iajs-2877	46	95	;	;	PUNCT
iajs-2877	47	1	ữ	ữ	NOUN
iajs-2877	47	2	∩	∩	ADJ
iajs-2877	47	3	ѧ	ѧ	PROPN
iajs-2877	47	4	∈	∈	PROPN
iajs-2877	47	5	₲	₲	NOUN
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iajs-2877	47	7	,	,	PUNCT
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iajs-2877	48	4	,	,	PUNCT
iajs-2877	48	5	τ₲	τ₲	PUNCT
iajs-2877	48	6	=	=	PRON
iajs-2877	48	7	{	{	PUNCT
iajs-2877	48	8	ӽ	ӽ	X
iajs-2877	48	9	,	,	PUNCT
iajs-2877	48	10	ø	ø	PROPN
iajs-2877	48	11	,	,	PUNCT
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iajs-2877	48	32	ӽ	ӽ	X
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iajs-2877	48	88	ӽ2	ӽ2	PROPN
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iajs-2877	50	2	10	10	NUM
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iajs-2877	52	2	10	10	NUM
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iajs-2877	52	10	-	-	PUNCT
iajs-2877	52	11	open	open	ADJ
iajs-2877	52	12	sets	set	NOUN
iajs-2877	52	13	intersecting	intersecting	NOUN
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iajs-2877	54	2	10	10	NUM
iajs-2877	54	3	]	]	PUNCT
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iajs-2877	54	6	family	family	NOUN
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iajs-2877	54	12	-	-	PUNCT
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iajs-2877	56	2	10	10	NUM
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iajs-2877	56	10	₲	₲	NOUN
iajs-2877	56	11	∗	∗	NOUN
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iajs-2877	56	13	-	-	PUNCT
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iajs-2877	56	16	.	.	PUNCT
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iajs-2877	58	1	every	every	DET
iajs-2877	58	2	closed	close	VERB
iajs-2877	58	3	is	be	AUX
iajs-2877	58	4	a	a	DET
iajs-2877	58	5	₲	₲	NOUN
iajs-2877	58	6	∗	∗	NOUN
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iajs-2877	58	8	-	-	PUNCT
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iajs-2877	60	3	4)2022	4)2022	SYM
iajs-2877	60	4	237	237	NUM
iajs-2877	60	5	theorem	theorem	VERB
iajs-2877	60	6	2.7	2.7	NUM
iajs-2877	60	7	.	.	PUNCT
iajs-2877	61	1	[	[	X
iajs-2877	61	2	10	10	NUM
iajs-2877	61	3	]	]	X
iajs-2877	61	4	:	:	PUNCT
iajs-2877	61	5	every	every	DET
iajs-2877	61	6	₲	₲	NOUN
iajs-2877	61	7	-semi	-semi	NOUN
iajs-2877	61	8	-	-	PUNCT
iajs-2877	61	9	open	open	ADJ
iajs-2877	61	10	is	be	AUX
iajs-2877	61	11	a	a	DET
iajs-2877	61	12	₲	₲	NOUN
iajs-2877	61	13	∗	∗	NOUN
iajs-2877	61	14	-semi	-semi	NOUN
iajs-2877	61	15	-	-	PUNCT
iajs-2877	61	16	open	open	ADJ
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iajs-2877	63	2	10	10	NUM
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iajs-2877	63	9	ӽ,τ,₲	ӽ,τ,₲	PROPN
iajs-2877	63	10	)	)	PUNCT
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iajs-2877	63	17	-	-	PUNCT
iajs-2877	63	18	open	open	NOUN
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iajs-2877	63	21	and	and	CCONJ
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iajs-2877	63	23	if	if	SCONJ
iajs-2877	63	24	ѧ	ѧ	PRON
iajs-2877	63	25	is	be	AUX
iajs-2877	63	26	a	a	DET
iajs-2877	63	27	₲	₲	NOUN
iajs-2877	63	28	∗	∗	NOUN
iajs-2877	63	29	-semi	-semi	NOUN
iajs-2877	63	30	-	-	PUNCT
iajs-2877	63	31	open	open	ADJ
iajs-2877	63	32	sets	set	NOUN
iajs-2877	63	33	whenever	whenever	SCONJ
iajs-2877	63	34	₲	₲	NOUN
iajs-2877	63	35	=	=	SYM
iajs-2877	63	36	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	63	37	)	)	PUNCT
iajs-2877	63	38	∖	∖	NOUN
iajs-2877	63	39	{	{	PUNCT
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iajs-2877	63	42	.	.	PUNCT
iajs-2877	64	1	remark	remark	PROPN
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iajs-2877	64	3	.	.	PUNCT
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iajs-2877	65	2	10	10	NUM
iajs-2877	65	3	]	]	X
iajs-2877	65	4	:	:	PUNCT
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iajs-2877	65	6	concepts	concept	NOUN
iajs-2877	65	7	₲	₲	NOUN
iajs-2877	65	8	∗	∗	NOUN
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iajs-2877	65	10	-	-	PUNCT
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iajs-2877	65	12	sets	set	NOUN
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iajs-2877	65	14	the	the	DET
iajs-2877	65	15	semi	semi	ADJ
iajs-2877	65	16	-	-	ADJ
iajs-2877	65	17	open	open	ADJ
iajs-2877	65	18	set	set	NOUN
iajs-2877	65	19	are	be	AUX
iajs-2877	65	20	independent	independent	ADJ
iajs-2877	65	21	.	.	PUNCT
iajs-2877	66	1	definition	definition	NOUN
iajs-2877	66	2	2.10	2.10	NUM
iajs-2877	66	3	.	.	PUNCT
iajs-2877	67	1	[	[	X
iajs-2877	67	2	10	10	NUM
iajs-2877	67	3	]	]	PUNCT
iajs-2877	67	4	:	:	PUNCT
iajs-2877	67	5	the	the	DET
iajs-2877	67	6	function	function	NOUN
iajs-2877	67	7	ḟ	ḟ	X
iajs-2877	67	8	:	:	PUNCT
iajs-2877	67	9	(	(	PUNCT
iajs-2877	67	10	ӽ	ӽ	X
iajs-2877	67	11	,	,	PUNCT
iajs-2877	67	12	τ	τ	NOUN
iajs-2877	67	13	,	,	PUNCT
iajs-2877	67	14	₲	₲	NOUN
iajs-2877	67	15	)	)	PUNCT
iajs-2877	67	16	→	→	SYM
iajs-2877	67	17	(	(	PUNCT
iajs-2877	67	18	ƴ	ƴ	PROPN
iajs-2877	67	19	,	,	PUNCT
iajs-2877	67	20	𝜏′	𝜏′	PROPN
iajs-2877	67	21	,	,	PUNCT
iajs-2877	67	22	₲	₲	NOUN
iajs-2877	67	23	)	)	PUNCT
iajs-2877	67	24	is	be	AUX
iajs-2877	67	25	known	know	VERB
iajs-2877	67	26	as	as	ADP
iajs-2877	67	27	:	:	PUNCT
iajs-2877	67	28	1	1	NUM
iajs-2877	67	29	.	.	NOUN
iajs-2877	67	30	₲	₲	NOUN
iajs-2877	67	31	∗	∗	NOUN
iajs-2877	67	32	-semi	-semi	NOUN
iajs-2877	67	33	-	-	PUNCT
iajs-2877	67	34	open	open	ADJ
iajs-2877	67	35	function	function	NOUN
iajs-2877	67	36	,	,	PUNCT
iajs-2877	67	37	currently	currently	ADV
iajs-2877	67	38	"	"	PUNCT
iajs-2877	67	39	₲	₲	NOUN
iajs-2877	67	40	∗	∗	NOUN
iajs-2877	67	41	-ᵴ	-ᵴ	NUM
iajs-2877	67	42	-	-	PUNCT
iajs-2877	67	43	o	o	NOUN
iajs-2877	67	44	function	function	NOUN
iajs-2877	67	45	"	"	PUNCT
iajs-2877	67	46	if	if	SCONJ
iajs-2877	67	47	ḟ(ữ	ḟ(ữ	NUM
iajs-2877	67	48	)	)	PUNCT
iajs-2877	67	49	∈	∈	PROPN
iajs-2877	67	50	₲	₲	NOUN
iajs-2877	67	51	∗𝑠𝑜(ƴ	∗𝑠𝑜(ƴ	NOUN
iajs-2877	67	52	)	)	PUNCT
iajs-2877	67	53	,	,	PUNCT
iajs-2877	67	54	whenever	whenever	SCONJ
iajs-2877	67	55	ữ	ữ	PROPN
iajs-2877	67	56	∈	∈	PROPN
iajs-2877	67	57	₲	₲	NOUN
iajs-2877	67	58	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	NOUN
iajs-2877	67	59	)	)	PUNCT
iajs-2877	67	60	.	.	PUNCT
iajs-2877	68	1	2	2	NUM
iajs-2877	68	2	.	.	NUM
iajs-2877	68	3	₲	₲	NOUN
iajs-2877	69	1	∗∗	∗∗	PROPN
iajs-2877	69	2	-semi	-semi	PROPN
iajs-2877	69	3	-	-	PUNCT
iajs-2877	69	4	open	open	ADJ
iajs-2877	69	5	function	function	NOUN
iajs-2877	69	6	,	,	PUNCT
iajs-2877	69	7	currently	currently	ADV
iajs-2877	69	8	"	"	PUNCT
iajs-2877	69	9	₲	₲	NOUN
iajs-2877	69	10	∗∗	∗∗	PROPN
iajs-2877	69	11	-ᵴ	-ᵴ	NUM
iajs-2877	69	12	-	-	PUNCT
iajs-2877	69	13	o	o	NOUN
iajs-2877	69	14	function	function	NOUN
iajs-2877	69	15	"	"	PUNCT
iajs-2877	69	16	if	if	SCONJ
iajs-2877	69	17	ḟ(ữ	ḟ(ữ	NUM
iajs-2877	69	18	)	)	PUNCT
iajs-2877	69	19	∈	∈	PROPN
iajs-2877	69	20	₲	₲	NOUN
iajs-2877	69	21	∗𝑠𝑜(ƴ	∗𝑠𝑜(ƴ	NOUN
iajs-2877	69	22	)	)	PUNCT
iajs-2877	69	23	whenever	whenever	SCONJ
iajs-2877	69	24	ữ	ữ	PROPN
iajs-2877	69	25	∈	∈	PROPN
iajs-2877	69	26	𝜏	𝜏	X
iajs-2877	69	27	.	.	PUNCT
iajs-2877	70	1	3	3	NUM
iajs-2877	70	2	.	.	NOUN
iajs-2877	70	3	₲	₲	NOUN
iajs-2877	70	4	∗∗∗	∗∗∗	NUM
iajs-2877	70	5	-semi	-semi	NOUN
iajs-2877	70	6	-	-	PUNCT
iajs-2877	70	7	open	open	ADJ
iajs-2877	70	8	function	function	NOUN
iajs-2877	70	9	,	,	PUNCT
iajs-2877	70	10	currently	currently	ADV
iajs-2877	70	11	"	"	PUNCT
iajs-2877	70	12	₲	₲	NOUN
iajs-2877	70	13	∗∗∗	∗∗∗	ADV
iajs-2877	70	14	-ᵴ	-ᵴ	NUM
iajs-2877	70	15	-	-	PUNCT
iajs-2877	70	16	o	o	NOUN
iajs-2877	70	17	function	function	NOUN
iajs-2877	70	18	"	"	PUNCT
iajs-2877	70	19	if	if	SCONJ
iajs-2877	70	20	ḟ(ữ	ḟ(ữ	NUM
iajs-2877	70	21	)	)	PUNCT
iajs-2877	70	22	∈	∈	PROPN
iajs-2877	70	23	𝜏′	𝜏′	ADJ
iajs-2877	70	24	whenever	whenever	SCONJ
iajs-2877	70	25	ữ	ữ	PROPN
iajs-2877	70	26	∈	∈	PROPN
iajs-2877	70	27	₲	₲	NOUN
iajs-2877	70	28	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	70	29	)	)	PUNCT
iajs-2877	70	30	.	.	PUNCT
iajs-2877	71	1	definition	definition	NOUN
iajs-2877	71	2	2.11	2.11	NUM
iajs-2877	71	3	.	.	PUNCT
iajs-2877	72	1	[	[	X
iajs-2877	72	2	2	2	NUM
iajs-2877	72	3	]	]	PUNCT
iajs-2877	72	4	:	:	PUNCT
iajs-2877	72	5	a	a	DET
iajs-2877	72	6	function	function	NOUN
iajs-2877	72	7	ḟ	ḟ	PROPN
iajs-2877	72	8	∶	∶	NOUN
iajs-2877	72	9	(	(	PUNCT
iajs-2877	72	10	ӽ	ӽ	X
iajs-2877	72	11	,	,	PUNCT
iajs-2877	72	12	τ	τ	NOUN
iajs-2877	72	13	,	,	PUNCT
iajs-2877	72	14	₲	₲	NOUN
iajs-2877	72	15	)	)	PUNCT
iajs-2877	72	16	→	→	SYM
iajs-2877	72	17	(	(	PUNCT
iajs-2877	72	18	ƴ	ƴ	PROPN
iajs-2877	72	19	,	,	PUNCT
iajs-2877	72	20	𝜏′	𝜏′	PROPN
iajs-2877	72	21	,	,	PUNCT
iajs-2877	72	22	₲	₲	NOUN
iajs-2877	72	23	)	)	PUNCT
iajs-2877	72	24	is	be	AUX
iajs-2877	72	25	said	say	VERB
iajs-2877	72	26	to	to	PART
iajs-2877	72	27	be	be	AUX
iajs-2877	72	28	;	;	PUNCT
iajs-2877	72	29	1	1	NUM
iajs-2877	72	30	.	.	X
iajs-2877	72	31	₲	₲	NOUN
iajs-2877	73	1	∗𝑠continuous	∗𝑠continuous	PROPN
iajs-2877	73	2	function	function	NOUN
iajs-2877	73	3	,	,	PUNCT
iajs-2877	73	4	currently	currently	ADV
iajs-2877	73	5	"	"	PUNCT
iajs-2877	73	6	₲	₲	NOUN
iajs-2877	73	7	*	*	PUNCT
iajs-2877	73	8	s	s	X
iajs-2877	73	9	-	-	ADJ
iajs-2877	73	10	continuous	continuous	ADJ
iajs-2877	73	11	function	function	NOUN
iajs-2877	73	12	"	"	PUNCT
iajs-2877	73	13	𝑖𝑓	𝑖𝑓	ADP
iajs-2877	73	14	ḟ−1(ữ	ḟ−1(ữ	NOUN
iajs-2877	73	15	)	)	PUNCT
iajs-2877	73	16	∈	∈	PROPN
iajs-2877	73	17	₲	₲	NOUN
iajs-2877	73	18	∗𝑠𝑜(ӽ)for	∗𝑠𝑜(ӽ)for	ADP
iajs-2877	73	19	all	all	DET
iajs-2877	73	20	ữ	ữ	NOUN
iajs-2877	73	21	∈	∈	NOUN
iajs-2877	73	22	𝜏.	𝜏.	NOUN
iajs-2877	73	23	2	2	NUM
iajs-2877	73	24	.	.	PUNCT
iajs-2877	73	25	strongly	strongly	ADV
iajs-2877	73	26	₲	₲	NOUN
iajs-2877	73	27	∗𝑠-continuous	∗𝑠-continuous	ADJ
iajs-2877	73	28	function	function	NOUN
iajs-2877	73	29	,	,	PUNCT
iajs-2877	73	30	currently	currently	ADV
iajs-2877	73	31	“	"	PUNCT
iajs-2877	73	32	strongly	strongly	ADV
iajs-2877	73	33	₲	₲	NOUN
iajs-2877	73	34	*	*	SYM
iajs-2877	73	35	s	s	X
iajs-2877	73	36	-	-	ADJ
iajs-2877	73	37	continuous	continuous	ADJ
iajs-2877	73	38	function	function	NOUN
iajs-2877	73	39	”	"	PUNCT
iajs-2877	73	40	𝑖𝑓	𝑖𝑓	ADP
iajs-2877	73	41	ḟ−1(ữ	ḟ−1(ữ	NOUN
iajs-2877	73	42	)	)	PUNCT
iajs-2877	73	43	∈	∈	PROPN
iajs-2877	73	44	𝜏	𝜏	NOUN
iajs-2877	73	45	,	,	PUNCT
iajs-2877	73	46	fore	fore	NOUN
iajs-2877	73	47	ever	ever	ADV
iajs-2877	73	48	ữ	ữ	NOUN
iajs-2877	73	49	∈	∈	PROPN
iajs-2877	73	50	₲	₲	NOUN
iajs-2877	73	51	∗𝑠𝑜(ƴ	∗𝑠𝑜(ƴ	NOUN
iajs-2877	73	52	)	)	PUNCT
iajs-2877	73	53	.	.	PUNCT
iajs-2877	74	1	3	3	X
iajs-2877	74	2	.	.	NOUN
iajs-2877	74	3	₲	₲	NOUN
iajs-2877	74	4	∗𝑠-irresolute	∗𝑠-irresolute	NOUN
iajs-2877	74	5	function	function	NOUN
iajs-2877	74	6	,	,	PUNCT
iajs-2877	74	7	presently	presently	ADV
iajs-2877	74	8	"	"	PUNCT
iajs-2877	74	9	₲	₲	NOUN
iajs-2877	74	10	*	*	PUNCT
iajs-2877	74	11	s	s	X
iajs-2877	74	12	-	-	PUNCT
iajs-2877	74	13	irresolute	irresolute	ADJ
iajs-2877	74	14	function	function	NOUN
iajs-2877	74	15	"	"	PUNCT
iajs-2877	74	16	if	if	SCONJ
iajs-2877	74	17	ḟ−1(ữ	ḟ−1(ữ	NOUN
iajs-2877	74	18	)	)	PUNCT
iajs-2877	74	19	∈	∈	PROPN
iajs-2877	74	20	₲	₲	NOUN
iajs-2877	74	21	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	74	22	)	)	PUNCT
iajs-2877	74	23	,	,	PUNCT
iajs-2877	74	24	fore	fore	NOUN
iajs-2877	74	25	ever	ever	ADV
iajs-2877	74	26	ữ	ữ	NOUN
iajs-2877	74	27	∈	∈	PROPN
iajs-2877	74	28	₲	₲	NOUN
iajs-2877	74	29	∗	∗	NOUN
iajs-2877	74	30	𝑠𝑜(ƴ	𝑠𝑜(ƴ	NOUN
iajs-2877	74	31	)	)	PUNCT
iajs-2877	74	32	.	.	PUNCT
iajs-2877	75	1	3	3	X
iajs-2877	75	2	.	.	X
iajs-2877	75	3	grill	grill	NOUN
iajs-2877	75	4	semi	semi	ADJ
iajs-2877	75	5	-	-	ADJ
iajs-2877	75	6	open	open	ADJ
iajs-2877	75	7	sets	set	NOUN
iajs-2877	75	8	in	in	ADP
iajs-2877	75	9	grill	grill	NOUN
iajs-2877	75	10	connected	connect	VERB
iajs-2877	75	11	space	space	NOUN
iajs-2877	75	12	definition	definition	NOUN
iajs-2877	75	13	3.1	3.1	NUM
iajs-2877	75	14	:	:	PUNCT
iajs-2877	75	15	the	the	DET
iajs-2877	75	16	space	space	NOUN
iajs-2877	75	17	(	(	PUNCT
iajs-2877	75	18	ӽ	ӽ	X
iajs-2877	75	19	,	,	PUNCT
iajs-2877	75	20	τ	τ	NOUN
iajs-2877	75	21	,	,	PUNCT
iajs-2877	75	22	₲	₲	NOUN
iajs-2877	75	23	)	)	PUNCT
iajs-2877	75	24	is	be	AUX
iajs-2877	75	25	a	a	DET
iajs-2877	75	26	₲	₲	NOUN
iajs-2877	75	27	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	75	28	if	if	SCONJ
iajs-2877	75	29	and	and	CCONJ
iajs-2877	75	30	only	only	ADV
iajs-2877	75	31	if	if	SCONJ
iajs-2877	75	32	there	there	PRON
iajs-2877	75	33	exists	exist	VERB
iajs-2877	75	34	two	two	NUM
iajs-2877	75	35	₲	₲	NOUN
iajs-2877	75	36	∗𝑠-open	∗𝑠-open	VERB
iajs-2877	75	37	disjoint	disjoint	NOUN
iajs-2877	75	38	nonempty	nonempty	NOUN
iajs-2877	75	39	sets	set	VERB
iajs-2877	75	40	ѧ	ѧ	PROPN
iajs-2877	75	41	and	and	CCONJ
iajs-2877	75	42	ƀ	ƀ	PRON
iajs-2877	75	43	such	such	ADJ
iajs-2877	75	44	that	that	DET
iajs-2877	75	45	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	75	46	=	=	SYM
iajs-2877	75	47	ӽ.	ӽ.	NOUN
iajs-2877	75	48	i.e.	i.e.	X
iajs-2877	75	49	,	,	PUNCT
iajs-2877	75	50	ӽ	ӽ	PRON
iajs-2877	75	51	is	be	AUX
iajs-2877	75	52	a	a	DET
iajs-2877	75	53	₲	₲	NOUN
iajs-2877	75	54	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	75	55	if	if	SCONJ
iajs-2877	75	56	and	and	CCONJ
iajs-2877	75	57	only	only	ADV
iajs-2877	75	58	if	if	SCONJ
iajs-2877	75	59	ӽ	ӽ	NOUN
iajs-2877	75	60	=	=	NOUN
iajs-2877	75	61	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	75	62	,	,	PUNCT
iajs-2877	75	63	ѧ	ѧ	PROPN
iajs-2877	75	64	,	,	PUNCT
iajs-2877	75	65	ƀ	ƀ	PROPN
iajs-2877	75	66	∈	∈	PROPN
iajs-2877	75	67	₲	₲	NOUN
iajs-2877	75	68	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	75	69	)	)	PUNCT
iajs-2877	75	70	,	,	PUNCT
iajs-2877	75	71	and	and	CCONJ
iajs-2877	75	72	ѧ	ѧ	DET
iajs-2877	75	73	⋂	⋂	PROPN
iajs-2877	75	74	ƀ	ƀ	NOUN
iajs-2877	75	75	=	=	SYM
iajs-2877	75	76			NOUN
iajs-2877	75	77	.	.	PUNCT
iajs-2877	76	1	the	the	DET
iajs-2877	76	2	sets	set	NOUN
iajs-2877	76	3	ѧ	ѧ	PROPN
iajs-2877	76	4	and	and	CCONJ
iajs-2877	76	5	ƀ	ƀ	PRON
iajs-2877	76	6	form	form	VERB
iajs-2877	76	7	a	a	DET
iajs-2877	76	8	₲	₲	NOUN
iajs-2877	76	9	∗𝑠𝑜-separation	∗𝑠𝑜-separation	PROPN
iajs-2877	76	10	of	of	ADP
iajs-2877	76	11	ӽ.	ӽ.	NOUN
iajs-2877	76	12	the	the	DET
iajs-2877	76	13	space	space	NOUN
iajs-2877	76	14	(	(	PUNCT
iajs-2877	76	15	ӽ	ӽ	X
iajs-2877	76	16	,	,	PUNCT
iajs-2877	76	17	τ	τ	NOUN
iajs-2877	76	18	,	,	PUNCT
iajs-2877	76	19	₲	₲	NOUN
iajs-2877	76	20	)	)	PUNCT
iajs-2877	76	21	is	be	AUX
iajs-2877	76	22	a	a	DET
iajs-2877	76	23	₲	₲	NOUN
iajs-2877	76	24	∗𝑠𝑜connected	∗𝑠𝑜connecte	VERB
iajs-2877	76	25	if	if	SCONJ
iajs-2877	76	26	and	and	CCONJ
iajs-2877	76	27	only	only	ADV
iajs-2877	76	28	if	if	SCONJ
iajs-2877	76	29	it	it	PRON
iajs-2877	76	30	is	be	AUX
iajs-2877	76	31	not	not	PART
iajs-2877	76	32	₲	₲	NOUN
iajs-2877	76	33	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	76	34	.	.	PUNCT
iajs-2877	77	1	ӽ	ӽ	PRON
iajs-2877	77	2	is	be	AUX
iajs-2877	77	3	a	a	DET
iajs-2877	77	4	₲	₲	NOUN
iajs-2877	77	5	∗𝑠𝑜connected	∗𝑠𝑜connecte	VERB
iajs-2877	77	6	if	if	SCONJ
iajs-2877	77	7	and	and	CCONJ
iajs-2877	77	8	only	only	ADV
iajs-2877	77	9	if	if	SCONJ
iajs-2877	77	10	ӽ	ӽ	PRON
iajs-2877	77	11			VERB
iajs-2877	77	12	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	77	13	,	,	PUNCT
iajs-2877	77	14	ѧ	ѧ	PROPN
iajs-2877	77	15	,	,	PUNCT
iajs-2877	77	16	ƀ	ƀ	PROPN
iajs-2877	77	17	∈	∈	PROPN
iajs-2877	77	18	₲	₲	NOUN
iajs-2877	77	19	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	77	20	)	)	PUNCT
iajs-2877	77	21	,	,	PUNCT
iajs-2877	77	22	ѧ	ѧ	PROPN
iajs-2877	77	23	⋂	⋂	PROPN
iajs-2877	77	24	ƀ	ƀ	NOUN
iajs-2877	77	25	=	=	SYM
iajs-2877	77	26			NOUN
iajs-2877	77	27	,	,	PUNCT
iajs-2877	77	28	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	77	29	ѧ	ѧ	PROPN
iajs-2877	77	30	,	,	PUNCT
iajs-2877	77	31	ƀ	ƀ	PROPN
iajs-2877	77	32	.	.	PART
iajs-2877	77	33	example	example	NOUN
iajs-2877	77	34	3.2	3.2	NUM
iajs-2877	77	35	.	.	PUNCT
iajs-2877	78	1	let	let	VERB
iajs-2877	78	2	(	(	PUNCT
iajs-2877	78	3	ӽ	ӽ	X
iajs-2877	78	4	,	,	PUNCT
iajs-2877	78	5	τ	τ	NOUN
iajs-2877	78	6	,	,	PUNCT
iajs-2877	78	7	₲	₲	NOUN
iajs-2877	78	8	)	)	PUNCT
iajs-2877	78	9	topològical	topològical	ADJ
iajs-2877	78	10	𝑠pace	𝑠pace	NOUN
iajs-2877	78	11	to	to	PART
iajs-2877	78	12	be	be	AUX
iajs-2877	78	13	a	a	DET
iajs-2877	78	14	grill	grill	NOUN
iajs-2877	78	15	a𝑛d	a𝑛d	NOUN
iajs-2877	78	16	ӽ	ӽ	NOUN
iajs-2877	78	17	=	=	PUNCT
iajs-2877	78	18	{	{	PUNCT
iajs-2877	78	19	ӽ1	ӽ1	PROPN
iajs-2877	78	20	,	,	PUNCT
iajs-2877	78	21	ӽ2	ӽ2	PROPN
iajs-2877	78	22	,	,	PUNCT
iajs-2877	78	23	ӽ3	ӽ3	ADJ
iajs-2877	78	24	}	}	PUNCT
iajs-2877	78	25	,	,	PUNCT
iajs-2877	78	26	𝜏	𝜏	NOUN
iajs-2877	78	27	=	=	SYM
iajs-2877	78	28	𝜏₲	𝜏₲	X
iajs-2877	78	29	=	=	SYM
iajs-2877	78	30	{	{	PUNCT
iajs-2877	78	31	ӽ	ӽ	X
iajs-2877	78	32	,	,	PUNCT
iajs-2877	78	33	ø	ø	PROPN
iajs-2877	78	34	,	,	PUNCT
iajs-2877	78	35	{	{	PUNCT
iajs-2877	78	36	ӽ2	ӽ2	PROPN
iajs-2877	78	37	}	}	PUNCT
iajs-2877	78	38	,	,	PUNCT
iajs-2877	78	39	{	{	PUNCT
iajs-2877	78	40	ӽ3	ӽ3	ADJ
iajs-2877	78	41	}	}	PUNCT
iajs-2877	78	42	}	}	PUNCT
iajs-2877	78	43	,	,	PUNCT
iajs-2877	78	44	₲	₲	NOUN
iajs-2877	78	45	=	=	SYM
iajs-2877	78	46	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	78	47	)	)	PUNCT
iajs-2877	78	48	∖	∖	NOUN
iajs-2877	78	49	{	{	PUNCT
iajs-2877	78	50	ø	ø	NOUN
iajs-2877	78	51	}	}	PUNCT
iajs-2877	78	52	is	be	AUX
iajs-2877	78	53	a	a	DET
iajs-2877	78	54	₲	₲	NOUN
iajs-2877	78	55	∗𝑠𝑜connected	∗𝑠𝑜connected	ADJ
iajs-2877	78	56	space	space	NOUN
iajs-2877	78	57	.	.	PUNCT
iajs-2877	79	1	remark	remark	VERB
iajs-2877	79	2	3.3	3.3	NUM
iajs-2877	79	3	.	.	PUNCT
iajs-2877	80	1	every	every	DET
iajs-2877	80	2	disconnected	disconnected	ADJ
iajs-2877	80	3	set	set	NOUN
iajs-2877	80	4	is	be	AUX
iajs-2877	80	5	a	a	DET
iajs-2877	80	6	₲	₲	NOUN
iajs-2877	80	7	∗𝑠𝑜-disconnected	∗𝑠𝑜-disconnecte	VERB
iajs-2877	80	8	.	.	PUNCT
iajs-2877	81	1	proof	proof	NOUN
iajs-2877	81	2	.	.	PUNCT
iajs-2877	82	1	let	let	AUX
iajs-2877	82	2	(	(	PUNCT
iajs-2877	82	3	ӽ	ӽ	X
iajs-2877	82	4	,	,	PUNCT
iajs-2877	82	5	₲	₲	NOUN
iajs-2877	82	6	)	)	PUNCT
iajs-2877	82	7	be	be	AUX
iajs-2877	82	8	a	a	DET
iajs-2877	82	9	disconnected	disconnected	ADJ
iajs-2877	82	10	space	space	NOUN
iajs-2877	82	11	,	,	PUNCT
iajs-2877	82	12	then	then	ADV
iajs-2877	82	13	there	there	PRON
iajs-2877	82	14	exists	exist	VERB
iajs-2877	82	15	≠	≠	PROPN
iajs-2877	82	16	∅	∅	NOUN
iajs-2877	82	17	,	,	PUNCT
iajs-2877	82	18	𝒵	𝒵	PROPN
iajs-2877	82	19	≠	≠	PROPN
iajs-2877	82	20	∅	∅	NOUN
iajs-2877	82	21	,	,	PUNCT
iajs-2877	82	22	𝒲	𝒲	NOUN
iajs-2877	82	23	,	,	PUNCT
iajs-2877	82	24	𝒵	𝒵	PROPN
iajs-2877	82	25	∈	∈	PROPN
iajs-2877	82	26	τ	τ	X
iajs-2877	82	27	,	,	PUNCT
iajs-2877	82	28	𝒲	𝒲	PROPN
iajs-2877	82	29	⋂	⋂	PROPN
iajs-2877	82	30	𝒵	𝒵	NOUN
iajs-2877	82	31	=	=	PUNCT
iajs-2877	82	32	∅	∅	NOUN
iajs-2877	82	33	,	,	PUNCT
iajs-2877	82	34	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	82	35	𝒲	𝒲	PROPN
iajs-2877	82	36	⋃	⋃	NOUN
iajs-2877	82	37	𝒵	𝒵	NOUN
iajs-2877	82	38	=	=	SYM
iajs-2877	82	39	ӽ	ӽ	NOUN
iajs-2877	82	40	,	,	PUNCT
iajs-2877	82	41	since	since	SCONJ
iajs-2877	82	42	every	every	DET
iajs-2877	82	43	open	open	ADJ
iajs-2877	82	44	set	set	NOUN
iajs-2877	82	45	is	be	AUX
iajs-2877	82	46	₲	₲	NOUN
iajs-2877	82	47	∗𝑠-open	∗𝑠-open	VERB
iajs-2877	82	48	set	set	VERB
iajs-2877	82	49	.	.	PUNCT
iajs-2877	83	1	therefore	therefore	ADV
iajs-2877	83	2	,	,	PUNCT
iajs-2877	83	3	ӽ	ӽ	PRON
iajs-2877	83	4	is	be	AUX
iajs-2877	83	5	₲	₲	NOUN
iajs-2877	83	6	∗𝑠𝑜-disconnected	∗𝑠𝑜-disconnecte	VERB
iajs-2877	83	7	.	.	PUNCT
iajs-2877	84	1	remark	remark	NOUN
iajs-2877	84	2	3.4	3.4	NUM
iajs-2877	84	3	.	.	PUNCT
iajs-2877	85	1	ihjpas	ihjpas	PROPN
iajs-2877	85	2	.	.	PUNCT
iajs-2877	86	1	53	53	NUM
iajs-2877	86	2	(	(	PUNCT
iajs-2877	86	3	4)2022	4)2022	NOUN
iajs-2877	86	4	238	238	NUM
iajs-2877	86	5	the	the	DET
iajs-2877	86	6	space	space	NOUN
iajs-2877	86	7	(	(	PUNCT
iajs-2877	86	8	ӽ	ӽ	X
iajs-2877	86	9	,	,	PUNCT
iajs-2877	86	10	τ	τ	NOUN
iajs-2877	86	11	,	,	PUNCT
iajs-2877	86	12	₲	₲	NOUN
iajs-2877	86	13	)	)	PUNCT
iajs-2877	86	14	is	be	AUX
iajs-2877	86	15	a	a	DET
iajs-2877	86	16	₲	₲	NOUN
iajs-2877	86	17	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	86	18	with	with	ADP
iajs-2877	86	19	any	any	DET
iajs-2877	86	20	grill	grill	NOUN
iajs-2877	86	21	and	and	CCONJ
iajs-2877	86	22	₲	₲	NOUN
iajs-2877	86	23	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	86	24	)	)	PUNCT
iajs-2877	86	25	=	=	SYM
iajs-2877	87	1	ℙ(ӽ	ℙ(ӽ	X
iajs-2877	87	2	)	)	PUNCT
iajs-2877	87	3	if	if	SCONJ
iajs-2877	87	4	ӽ	ӽ	NOUN
iajs-2877	87	5	contains	contain	VERB
iajs-2877	87	6	more	more	ADJ
iajs-2877	87	7	than	than	ADP
iajs-2877	87	8	one	one	NUM
iajs-2877	87	9	element	element	NOUN
iajs-2877	87	10	since	since	SCONJ
iajs-2877	87	11	there	there	PRON
iajs-2877	87	12	exists	exist	VERB
iajs-2877	87	13	ѧ	ѧ	PROPN
iajs-2877	87	14	and	and	CCONJ
iajs-2877	87	15	ѧ𝑐	ѧ𝑐	ADP
iajs-2877	87	16	∈	∈	PROPN
iajs-2877	87	17	₲	₲	NOUN
iajs-2877	87	18	∗	∗	NOUN
iajs-2877	87	19	𝑠𝑜(ӽ),ѧ	𝑠𝑜(ӽ),ѧ	NUM
iajs-2877	87	20	⋃ƀ	⋃ƀ	PROPN
iajs-2877	87	21	=	=	SYM
iajs-2877	87	22	ӽ	ӽ	NOUN
iajs-2877	87	23	,	,	PUNCT
iajs-2877	87	24	ѧ	ѧ	PROPN
iajs-2877	87	25	⋂	⋂	PROPN
iajs-2877	87	26	ƀ	ƀ	NOUN
iajs-2877	87	27	=	=	SYM
iajs-2877	87	28			NOUN
iajs-2877	87	29	,	,	PUNCT
iajs-2877	87	30	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	87	31	ѧ	ѧ	PROPN
iajs-2877	87	32	,	,	PUNCT
iajs-2877	87	33	ƀ	ƀ	PROPN
iajs-2877	87	34	.	.	PUNCT
iajs-2877	87	35	remark	remark	VERB
iajs-2877	87	36	3.5	3.5	NUM
iajs-2877	87	37	.	.	PUNCT
iajs-2877	88	1	the	the	DET
iajs-2877	88	2	space	space	NOUN
iajs-2877	88	3	(	(	PUNCT
iajs-2877	88	4	ӽ	ӽ	X
iajs-2877	88	5	,	,	PUNCT
iajs-2877	88	6	τ	τ	NOUN
iajs-2877	88	7	,	,	PUNCT
iajs-2877	88	8	₲	₲	NOUN
iajs-2877	88	9	)	)	PUNCT
iajs-2877	88	10	is	be	AUX
iajs-2877	88	11	a	a	DET
iajs-2877	88	12	₲	₲	NOUN
iajs-2877	88	13	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	88	14	,	,	PUNCT
iajs-2877	88	15	₲	₲	NOUN
iajs-2877	88	16	=	=	SYM
iajs-2877	88	17	∅	∅	NOUN
iajs-2877	88	18	,	,	PUNCT
iajs-2877	88	19	and	and	CCONJ
iajs-2877	88	20	𝜏₲	𝜏₲	PROPN
iajs-2877	88	21	=	=	PRON
iajs-2877	88	22	{	{	PUNCT
iajs-2877	88	23	ӽ	ӽ	X
iajs-2877	88	24	,	,	PUNCT
iajs-2877	88	25	ø	ø	NOUN
iajs-2877	88	26	}	}	PUNCT
iajs-2877	88	27	,	,	PUNCT
iajs-2877	88	28	so	so	ADV
iajs-2877	88	29	₲	₲	NOUN
iajs-2877	88	30	∗𝑠𝑜connected	∗𝑠𝑜connected	ADJ
iajs-2877	88	31	space	space	NOUN
iajs-2877	88	32	.	.	PUNCT
iajs-2877	89	1	remark	remark	NOUN
iajs-2877	89	2	3.6	3.6	NUM
iajs-2877	89	3	.	.	PUNCT
iajs-2877	90	1	if	if	SCONJ
iajs-2877	90	2	𝜏₲	𝜏₲	PROPN
iajs-2877	90	3	=	=	SYM
iajs-2877	90	4	ℱ₲	ℱ₲	PROPN
iajs-2877	90	5	and	and	CCONJ
iajs-2877	90	6	𝜏₲	𝜏₲	PROPN
iajs-2877	90	7	≠	≠	PROPN
iajs-2877	91	1	ι	ι	X
iajs-2877	91	2	indiscrete	indiscrete	ADJ
iajs-2877	91	3	,	,	PUNCT
iajs-2877	91	4	when	when	SCONJ
iajs-2877	91	5	₲	₲	NOUN
iajs-2877	91	6	=	=	SYM
iajs-2877	91	7	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	91	8	)	)	PUNCT
iajs-2877	91	9	∖	∖	NOUN
iajs-2877	91	10	{	{	PUNCT
iajs-2877	91	11	ø	ø	NOUN
iajs-2877	91	12	}	}	PUNCT
iajs-2877	91	13	,	,	PUNCT
iajs-2877	91	14	that	that	PRON
iajs-2877	91	15	is	be	AUX
iajs-2877	91	16	mean	mean	ADJ
iajs-2877	91	17	(	(	PUNCT
iajs-2877	91	18	ӽ	ӽ	X
iajs-2877	91	19	,	,	PUNCT
iajs-2877	91	20	τ	τ	NOUN
iajs-2877	91	21	,	,	PUNCT
iajs-2877	91	22	₲	₲	NOUN
iajs-2877	91	23	)	)	PUNCT
iajs-2877	91	24	is	be	AUX
iajs-2877	91	25	a	a	DET
iajs-2877	91	26	₲	₲	NOUN
iajs-2877	91	27	∗𝑠𝑜	∗𝑠𝑜	PUNCT
iajs-2877	91	28	disconnected	disconnected	ADJ
iajs-2877	91	29	.	.	PUNCT
iajs-2877	92	1	theorem	theorem	VERB
iajs-2877	92	2	3.7	3.7	NUM
iajs-2877	92	3	.	.	PUNCT
iajs-2877	93	1	the	the	DET
iajs-2877	93	2	space	space	NOUN
iajs-2877	93	3	(	(	PUNCT
iajs-2877	93	4	ӽ	ӽ	X
iajs-2877	93	5	,	,	PUNCT
iajs-2877	93	6	τ	τ	NOUN
iajs-2877	93	7	,	,	PUNCT
iajs-2877	93	8	₲	₲	NOUN
iajs-2877	93	9	)	)	PUNCT
iajs-2877	93	10	is	be	AUX
iajs-2877	93	11	a	a	DET
iajs-2877	93	12	₲	₲	NOUN
iajs-2877	93	13	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	93	14	if	if	SCONJ
iajs-2877	93	15	and	and	CCONJ
iajs-2877	93	16	only	only	ADV
iajs-2877	93	17	ӽ	ӽ	PRON
iajs-2877	93	18	can	can	AUX
iajs-2877	93	19	not	not	PART
iajs-2877	93	20	be	be	AUX
iajs-2877	93	21	written	write	VERB
iajs-2877	93	22	as	as	ADP
iajs-2877	93	23	union	union	NOUN
iajs-2877	93	24	of	of	ADP
iajs-2877	93	25	two	two	NUM
iajs-2877	93	26	nonempty	nonempty	ADJ
iajs-2877	93	27	disjoint	disjoint	NOUN
iajs-2877	93	28	closed	close	VERB
iajs-2877	93	29	set	set	NOUN
iajs-2877	93	30	's	's	PART
iajs-2877	93	31	.	.	PUNCT
iajs-2877	94	1	proof	proof	NOUN
iajs-2877	94	2	.	.	PUNCT
iajs-2877	95	1	let	let	VERB
iajs-2877	95	2	ӽ	ӽ	NOUN
iajs-2877	95	3	is	be	AUX
iajs-2877	95	4	a	a	DET
iajs-2877	95	5	₲	₲	NOUN
iajs-2877	95	6	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	95	7	if	if	SCONJ
iajs-2877	95	8	ӽ	ӽ	X
iajs-2877	95	9	=	=	SYM
iajs-2877	95	10	ѧ	ѧ	NUM
iajs-2877	95	11	⋃ƀ	⋃ƀ	NUM
iajs-2877	95	12	such	such	ADJ
iajs-2877	95	13	that	that	SCONJ
iajs-2877	95	14	ѧ	ѧ	NOUN
iajs-2877	95	15	,	,	PUNCT
iajs-2877	95	16	ƀ	ƀ	PROPN
iajs-2877	95	17	∈	∈	PROPN
iajs-2877	95	18	₲	₲	NOUN
iajs-2877	95	19	∗𝑠𝑐(ӽ	∗𝑠𝑐(ӽ	NOUN
iajs-2877	95	20	)	)	PUNCT
iajs-2877	95	21	,	,	PUNCT
iajs-2877	95	22	ѧ	ѧ	PROPN
iajs-2877	95	23	⋂	⋂	PROPN
iajs-2877	95	24	ƀ	ƀ	X
iajs-2877	95	25	=	=	SYM
iajs-2877	95	26			NOUN
iajs-2877	95	27	,	,	PUNCT
iajs-2877	95	28	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	95	29	ѧ	ѧ	PROPN
iajs-2877	95	30	,	,	PUNCT
iajs-2877	95	31	ƀ	ƀ	PROPN
iajs-2877	95	32	.	.	X
iajs-2877	96	1	so	so	SCONJ
iajs-2877	96	2	ѧ	ѧ	PROPN
iajs-2877	96	3	=	=	PUNCT
iajs-2877	96	4	ƀ𝑐	ƀ𝑐	NOUN
iajs-2877	96	5	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
iajs-2877	96	6	ƀ	ƀ	PROPN
iajs-2877	96	7	=	=	SYM
iajs-2877	96	8	ѧ𝑐	ѧ𝑐	PROPN
iajs-2877	96	9	,	,	PUNCT
iajs-2877	96	10	then	then	ADV
iajs-2877	96	11	ӽ	ӽ	X
iajs-2877	96	12	=	=	SYM
iajs-2877	96	13	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	96	14	,	,	PUNCT
iajs-2877	96	15	ѧ	ѧ	PROPN
iajs-2877	96	16	,	,	PUNCT
iajs-2877	96	17	ƀ	ƀ	PROPN
iajs-2877	96	18	∈	∈	PROPN
iajs-2877	96	19	₲	₲	NOUN
iajs-2877	96	20	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	96	21	)	)	PUNCT
iajs-2877	96	22	,	,	PUNCT
iajs-2877	96	23	ѧ	ѧ	PROPN
iajs-2877	96	24	⋂	⋂	PROPN
iajs-2877	96	25	ƀ	ƀ	X
iajs-2877	96	26	=	=	SYM
iajs-2877	96	27			NOUN
iajs-2877	96	28	,	,	PUNCT
iajs-2877	96	29	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	96	30	ѧ	ѧ	NOUN
iajs-2877	96	31	,	,	PUNCT
iajs-2877	96	32	ƀ	ƀ	PROPN
iajs-2877	96	33			NOUN
iajs-2877	96	34	,	,	PUNCT
iajs-2877	96	35	that	that	PRON
iajs-2877	96	36	's	be	AUX
iajs-2877	96	37	mean	mean	ADJ
iajs-2877	96	38	ӽ	ӽ	PRON
iajs-2877	96	39	is	be	AUX
iajs-2877	96	40	a	a	DET
iajs-2877	96	41	₲	₲	NOUN
iajs-2877	96	42	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	96	43	.	.	PUNCT
iajs-2877	97	1	that	that	PRON
iajs-2877	97	2	's	be	AUX
iajs-2877	97	3	contradiction	contradiction	NOUN
iajs-2877	97	4	.	.	PUNCT
iajs-2877	98	1	therefore	therefore	ADV
iajs-2877	98	2	,	,	PUNCT
iajs-2877	98	3	ӽ	ӽ	PRON
iajs-2877	98	4	can	can	AUX
iajs-2877	98	5	not	not	PART
iajs-2877	98	6	be	be	AUX
iajs-2877	98	7	written	write	VERB
iajs-2877	98	8	as	as	ADP
iajs-2877	98	9	a	a	DET
iajs-2877	98	10	union	union	NOUN
iajs-2877	98	11	of	of	ADP
iajs-2877	98	12	two	two	NUM
iajs-2877	98	13	non	non	ADJ
iajs-2877	98	14	-	-	ADJ
iajs-2877	98	15	empty	empty	ADJ
iajs-2877	98	16	disjoint	disjoint	NOUN
iajs-2877	98	17	closed	close	VERB
iajs-2877	98	18	set	set	NOUN
iajs-2877	98	19	.	.	PUNCT
iajs-2877	99	1	now	now	ADV
iajs-2877	99	2	,	,	PUNCT
iajs-2877	99	3	if	if	SCONJ
iajs-2877	99	4	ӽ	ӽ	PRON
iajs-2877	99	5	is	be	AUX
iajs-2877	99	6	a	a	DET
iajs-2877	99	7	₲	₲	NOUN
iajs-2877	99	8	∗𝑠𝑜disconnected	∗𝑠𝑜disconnecte	VERB
iajs-2877	99	9	space	space	NOUN
iajs-2877	99	10	,	,	PUNCT
iajs-2877	99	11	so	so	SCONJ
iajs-2877	99	12	ӽ=	ӽ=	PROPN
iajs-2877	99	13	ѧ	ѧ	PROPN
iajs-2877	99	14	⋃ƀ	⋃ƀ	PROPN
iajs-2877	99	15	;	;	PUNCT
iajs-2877	99	16	ѧ	ѧ	X
iajs-2877	99	17	,	,	PUNCT
iajs-2877	99	18	ƀ	ƀ	PROPN
iajs-2877	99	19	∈	∈	PROPN
iajs-2877	99	20	₲	₲	NOUN
iajs-2877	99	21	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	99	22	)	)	PUNCT
iajs-2877	99	23	,	,	PUNCT
iajs-2877	99	24	ѧ	ѧ	PROPN
iajs-2877	99	25	⋂	⋂	PROPN
iajs-2877	99	26	ƀ	ƀ	X
iajs-2877	99	27	=	=	SYM
iajs-2877	99	28			NOUN
iajs-2877	99	29	,	,	PUNCT
iajs-2877	99	30	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	99	31	ѧ	ѧ	PROPN
iajs-2877	99	32	,	,	PUNCT
iajs-2877	99	33	ƀ	ƀ	PROPN
iajs-2877	99	34	.	.	X
iajs-2877	100	1	so	so	SCONJ
iajs-2877	100	2	ѧ	ѧ	PROPN
iajs-2877	100	3	=	=	PUNCT
iajs-2877	100	4	ƀ𝑐	ƀ𝑐	NOUN
iajs-2877	100	5	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
iajs-2877	100	6	ƀ	ƀ	PROPN
iajs-2877	100	7	=	=	SYM
iajs-2877	100	8	ѧ𝑐	ѧ𝑐	PROPN
iajs-2877	100	9	,	,	PUNCT
iajs-2877	100	10	then	then	ADV
iajs-2877	100	11	ѧ	ѧ	PROPN
iajs-2877	100	12	and	and	CCONJ
iajs-2877	100	13	ƀ	ƀ	PROPN
iajs-2877	100	14	∈	∈	PROPN
iajs-2877	100	15	₲	₲	NOUN
iajs-2877	100	16	∗𝑠𝑐(𝑥	∗𝑠𝑐(𝑥	NOUN
iajs-2877	100	17	)	)	PUNCT
iajs-2877	100	18	,	,	PUNCT
iajs-2877	100	19	but	but	CCONJ
iajs-2877	100	20	that	that	PRON
iajs-2877	100	21	is	be	AUX
iajs-2877	100	22	contradiction	contradiction	NOUN
iajs-2877	100	23	.	.	PUNCT
iajs-2877	101	1	therefore	therefore	ADV
iajs-2877	101	2	,	,	PUNCT
iajs-2877	101	3	ӽ	ӽ	PRON
iajs-2877	101	4	is	be	AUX
iajs-2877	101	5	a	a	DET
iajs-2877	101	6	₲	₲	NOUN
iajs-2877	101	7	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	101	8	space	space	NOUN
iajs-2877	101	9	.	.	PUNCT
iajs-2877	102	1	theorem	theorem	VERB
iajs-2877	102	2	3.8	3.8	NUM
iajs-2877	102	3	.	.	PUNCT
iajs-2877	103	1	the	the	DET
iajs-2877	103	2	space	space	NOUN
iajs-2877	103	3	(	(	PUNCT
iajs-2877	103	4	ӽ	ӽ	X
iajs-2877	103	5	,	,	PUNCT
iajs-2877	103	6	τ	τ	NOUN
iajs-2877	103	7	,	,	PUNCT
iajs-2877	103	8	₲	₲	NOUN
iajs-2877	103	9	)	)	PUNCT
iajs-2877	103	10	is	be	AUX
iajs-2877	103	11	a	a	DET
iajs-2877	103	12	₲	₲	NOUN
iajs-2877	103	13	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	103	14	if	if	SCONJ
iajs-2877	103	15	and	and	CCONJ
iajs-2877	103	16	only	only	ADV
iajs-2877	103	17	if	if	SCONJ
iajs-2877	103	18	the	the	DET
iajs-2877	103	19	only	only	ADJ
iajs-2877	103	20	subsets	subset	NOUN
iajs-2877	103	21	of	of	ADP
iajs-2877	103	22	the	the	DET
iajs-2877	103	23	space	space	NOUN
iajs-2877	103	24	ӽ	ӽ	NOUN
iajs-2877	103	25	which	which	PRON
iajs-2877	103	26	are	be	AUX
iajs-2877	103	27	₲	₲	NOUN
iajs-2877	103	28	∗𝑠-open	∗𝑠-open	VERB
iajs-2877	103	29	and	and	CCONJ
iajs-2877	103	30	₲	₲	NOUN
iajs-2877	103	31	∗𝑠-closed	∗𝑠-close	VERB
iajs-2877	103	32	are	be	AUX
iajs-2877	103	33	ӽ	ӽ	NOUN
iajs-2877	103	34	and	and	CCONJ
iajs-2877	103	35	ø	ø	NOUN
iajs-2877	103	36	.	.	PUNCT
iajs-2877	104	1	proof	proof	NOUN
iajs-2877	104	2	.	.	PUNCT
iajs-2877	105	1	let	let	VERB
iajs-2877	105	2	ѧ	ѧ	NOUN
iajs-2877	105	3	,	,	PUNCT
iajs-2877	105	4	ѧ𝑐	ѧ𝑐	PROPN
iajs-2877	105	5	∈	∈	PROPN
iajs-2877	105	6	₲	₲	NOUN
iajs-2877	105	7	∗𝑠𝑜(𝑥	∗𝑠𝑜(𝑥	NOUN
iajs-2877	105	8	)	)	PUNCT
iajs-2877	105	9	,	,	PUNCT
iajs-2877	105	10	ѧ	ѧ	PROPN
iajs-2877	105	11	≠	≠	PROPN
iajs-2877	105	12	ӽ	ӽ	X
iajs-2877	105	13	,	,	PUNCT
iajs-2877	105	14	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	105	15	ѧ	ѧ	PROPN
iajs-2877	105	16	≠	≠	PROPN
iajs-2877	105	17	ø	ø	PROPN
iajs-2877	105	18	,	,	PUNCT
iajs-2877	105	19	so	so	SCONJ
iajs-2877	105	20	ӽ	ӽ	X
iajs-2877	105	21	=	=	SYM
iajs-2877	105	22	ѧ⋃ѧ𝑐	ѧ⋃ѧ𝑐	INTJ
iajs-2877	105	23	,	,	PUNCT
iajs-2877	105	24	ѧ	ѧ	PROPN
iajs-2877	105	25	⋂	⋂	PROPN
iajs-2877	105	26	ѧ𝑐	ѧ𝑐	NOUN
iajs-2877	105	27	=	=	SYM
iajs-2877	105	28			NOUN
iajs-2877	105	29	,	,	PUNCT
iajs-2877	105	30	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2877	105	31	ѧ	ѧ	PROPN
iajs-2877	105	32	,	,	PUNCT
iajs-2877	105	33	ѧ𝑐	ѧ𝑐	ADP
iajs-2877	105	34	≠	≠	PROPN
iajs-2877	105	35	.	.	PUNCT
iajs-2877	105	36	then	then	ADV
iajs-2877	105	37	,	,	PUNCT
iajs-2877	105	38	ӽ	ӽ	PRON
iajs-2877	105	39	is	be	AUX
iajs-2877	105	40	a	a	DET
iajs-2877	105	41	₲	₲	NOUN
iajs-2877	105	42	∗𝑠𝑜-disconnected	∗𝑠𝑜-disconnecte	VERB
iajs-2877	105	43	and	and	CCONJ
iajs-2877	105	44	that	that	PRON
iajs-2877	105	45	is	be	AUX
iajs-2877	105	46	a	a	DET
iajs-2877	105	47	contradiction	contradiction	NOUN
iajs-2877	105	48	.	.	PUNCT
iajs-2877	106	1	so	so	ADV
iajs-2877	106	2	,	,	PUNCT
iajs-2877	106	3	where	where	SCONJ
iajs-2877	106	4	ѧ	ѧ	PRON
iajs-2877	106	5	⊆	⊆	NUM
iajs-2877	106	6	ӽ	ӽ	NOUN
iajs-2877	106	7	,	,	PUNCT
iajs-2877	106	8	ѧ	ѧ	NOUN
iajs-2877	106	9	,	,	PUNCT
iajs-2877	106	10	ѧ𝑐	ѧ𝑐	PROPN
iajs-2877	106	11	∈	∈	PROPN
iajs-2877	106	12	₲	₲	NOUN
iajs-2877	106	13	∗𝑠𝑜(𝑥	∗𝑠𝑜(𝑥	NOUN
iajs-2877	106	14	)	)	PUNCT
iajs-2877	106	15	,	,	PUNCT
iajs-2877	106	16	then	then	ADV
iajs-2877	106	17	,	,	PUNCT
iajs-2877	106	18	ѧ	ѧ	PROPN
iajs-2877	106	19	=	=	PUNCT
iajs-2877	106	20	ӽ	ӽ	NOUN
iajs-2877	106	21	or	or	CCONJ
iajs-2877	106	22	ѧ	ѧ	NOUN
iajs-2877	106	23	=	=	SYM
iajs-2877	106	24	ø	ø	PROPN
iajs-2877	106	25	.	.	PUNCT
iajs-2877	107	1	conversely	conversely	ADV
iajs-2877	107	2	ӽ	ӽ	PRON
iajs-2877	107	3	is	be	AUX
iajs-2877	107	4	a	a	DET
iajs-2877	107	5	₲	₲	NOUN
iajs-2877	107	6	∗𝑠𝑜-disconnected	∗𝑠𝑜-disconnecte	VERB
iajs-2877	107	7	space	space	NOUN
iajs-2877	107	8	;	;	PUNCT
iajs-2877	107	9	this	this	PRON
iajs-2877	107	10	means	mean	VERB
iajs-2877	107	11	that	that	SCONJ
iajs-2877	107	12	ӽ	ӽ	NOUN
iajs-2877	107	13	=	=	X
iajs-2877	107	14	𝒲⋃𝒵	𝒲⋃𝒵	PROPN
iajs-2877	107	15	,	,	PUNCT
iajs-2877	107	16	𝒲	𝒲	PROPN
iajs-2877	107	17	,	,	PUNCT
iajs-2877	107	18	𝒵	𝒵	PROPN
iajs-2877	107	19	∈	∈	PROPN
iajs-2877	107	20	₲	₲	NOUN
iajs-2877	107	21	∗𝑠𝑜(𝑥	∗𝑠𝑜(𝑥	NOUN
iajs-2877	107	22	)	)	PUNCT
iajs-2877	107	23	,	,	PUNCT
iajs-2877	107	24	𝒲	𝒲	PROPN
iajs-2877	107	25	⋂	⋂	PROPN
iajs-2877	107	26	𝒵	𝒵	NOUN
iajs-2877	107	27	=	=	PUNCT
iajs-2877	107	28			NOUN
iajs-2877	107	29	,	,	PUNCT
iajs-2877	107	30	and	and	CCONJ
iajs-2877	107	31	𝒲	𝒲	PROPN
iajs-2877	107	32	,	,	PUNCT
iajs-2877	107	33	𝒵	𝒵	PROPN
iajs-2877	107	34	≠	≠	PROPN
iajs-2877	107	35	ø	ø	PROPN
iajs-2877	107	36	implies	imply	VERB
iajs-2877	107	37	that	that	SCONJ
iajs-2877	107	38	𝒲	𝒲	NOUN
iajs-2877	107	39	=	=	SYM
iajs-2877	107	40	𝒵𝑐	𝒵𝑐	PROPN
iajs-2877	107	41	and	and	CCONJ
iajs-2877	107	42	𝒵	𝒵	PROPN
iajs-2877	107	43	=	=	SYM
iajs-2877	107	44	𝒲𝑐.	𝒲𝑐.	PROPN
iajs-2877	107	45	so	so	ADV
iajs-2877	107	46	𝒲	𝒲	PROPN
iajs-2877	107	47	,	,	PUNCT
iajs-2877	107	48	𝒵	𝒵	PROPN
iajs-2877	107	49	∈	∈	PROPN
iajs-2877	107	50	₲	₲	NOUN
iajs-2877	107	51	∗𝑠𝑐(𝑥	∗𝑠𝑐(𝑥	NOUN
iajs-2877	107	52	)	)	PUNCT
iajs-2877	107	53	(	(	PUNCT
iajs-2877	107	54	that	that	PRON
iajs-2877	107	55	is	be	AUX
iajs-2877	107	56	a	a	DET
iajs-2877	107	57	contradiction).therefore	contradiction).therefore	NOUN
iajs-2877	107	58	,	,	PUNCT
iajs-2877	107	59	ӽ	ӽ	PRON
iajs-2877	107	60	is	be	AUX
iajs-2877	107	61	a	a	DET
iajs-2877	107	62	₲	₲	NOUN
iajs-2877	107	63	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	107	64	space	space	NOUN
iajs-2877	107	65	.	.	PUNCT
iajs-2877	108	1	remark	remark	VERB
iajs-2877	108	2	3.9	3.9	NUM
iajs-2877	108	3	.	.	PUNCT
iajs-2877	109	1	if	if	SCONJ
iajs-2877	109	2	ḟ	ḟ	PRON
iajs-2877	109	3	∶	∶	NOUN
iajs-2877	109	4	(	(	PUNCT
iajs-2877	109	5	ӽ	ӽ	X
iajs-2877	109	6	,	,	PUNCT
iajs-2877	109	7	τ	τ	NOUN
iajs-2877	109	8	,	,	PUNCT
iajs-2877	109	9	₲	₲	NOUN
iajs-2877	109	10	)	)	PUNCT
iajs-2877	109	11	→	→	SYM
iajs-2877	109	12	(	(	PUNCT
iajs-2877	109	13	ƴ	ƴ	PROPN
iajs-2877	109	14	,	,	PUNCT
iajs-2877	109	15	𝜏′	𝜏′	PROPN
iajs-2877	109	16	,	,	PUNCT
iajs-2877	109	17	₲	₲	NOUN
iajs-2877	109	18	)	)	PUNCT
iajs-2877	109	19	is	be	AUX
iajs-2877	109	20	a	a	DET
iajs-2877	109	21	₲	₲	NOUN
iajs-2877	109	22	∗𝑠𝑜-𝑖𝑟𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑒	∗𝑠𝑜-𝑖𝑟𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑒	PROPN
iajs-2877	109	23	and	and	CCONJ
iajs-2877	109	24	onto	onto	ADP
iajs-2877	109	25	function	function	NOUN
iajs-2877	109	26	and	and	CCONJ
iajs-2877	109	27	ƴ	ƴ	PRON
iajs-2877	109	28	is	be	AUX
iajs-2877	109	29	a	a	DET
iajs-2877	109	30	₲	₲	NOUN
iajs-2877	110	1	∗𝑠𝑜-𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑	∗𝑠𝑜-𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑	PROPN
iajs-2877	110	2	space	space	NOUN
iajs-2877	110	3	,	,	PUNCT
iajs-2877	110	4	then	then	ADV
iajs-2877	110	5	ӽ	ӽ	PRON
iajs-2877	110	6	is	be	AUX
iajs-2877	110	7	not	not	PART
iajs-2877	110	8	necessary	necessary	ADJ
iajs-2877	110	9	₲	₲	NOUN
iajs-2877	110	10	∗𝑠𝑜-𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑	∗𝑠𝑜-𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑	PROPN
iajs-2877	110	11	space	space	NOUN
iajs-2877	110	12	.	.	PUNCT
iajs-2877	110	13	example	example	NOUN
iajs-2877	111	1	3.10	3.10	NUM
iajs-2877	111	2	.	.	PUNCT
iajs-2877	112	1	let	let	VERB
iajs-2877	112	2	ḟ	ḟ	PRON
iajs-2877	112	3	∶	∶	NOUN
iajs-2877	112	4	(	(	PUNCT
iajs-2877	112	5	ℝ	ℝ	PROPN
iajs-2877	112	6	,	,	PUNCT
iajs-2877	112	7	d	d	NOUN
iajs-2877	112	8	,	,	PUNCT
iajs-2877	112	9	₲	₲	NOUN
iajs-2877	112	10	)	)	PUNCT
iajs-2877	112	11	→	→	SYM
iajs-2877	112	12	(	(	PUNCT
iajs-2877	112	13	ℝ	ℝ	PROPN
iajs-2877	112	14	,	,	PUNCT
iajs-2877	112	15	ι	ι	NOUN
iajs-2877	112	16	,	,	PUNCT
iajs-2877	112	17	₲	₲	NOUN
iajs-2877	112	18	)	)	PUNCT
iajs-2877	112	19	,	,	PUNCT
iajs-2877	112	20	such	such	ADJ
iajs-2877	112	21	that	that	SCONJ
iajs-2877	112	22	ḟ(ӽ	ḟ(ӽ	PROPN
iajs-2877	112	23	)	)	PUNCT
iajs-2877	113	1	=	=	SYM
iajs-2877	113	2	ӽ	ӽ	NOUN
iajs-2877	113	3	,	,	PUNCT
iajs-2877	113	4	for	for	ADP
iajs-2877	113	5	all	all	PRON
iajs-2877	113	6	ӽ	ӽ	DET
iajs-2877	113	7	∈	∈	PROPN
iajs-2877	113	8	ℝ	ℝ	PROPN
iajs-2877	113	9	,	,	PUNCT
iajs-2877	113	10	and	and	CCONJ
iajs-2877	113	11	₲	₲	NOUN
iajs-2877	113	12	=	=	SYM
iajs-2877	113	13	ℙ(ӽ	ℙ(ӽ	NUM
iajs-2877	113	14	)	)	PUNCT
iajs-2877	113	15	∖	∖	NOUN
iajs-2877	113	16	{	{	PUNCT
iajs-2877	113	17	ø	ø	NOUN
iajs-2877	113	18	}	}	PUNCT
iajs-2877	113	19	,	,	PUNCT
iajs-2877	113	20	so	so	CCONJ
iajs-2877	113	21	ḟ	ḟ	PROPN
iajs-2877	113	22	is	be	AUX
iajs-2877	113	23	a	a	DET
iajs-2877	113	24	₲	₲	NOUN
iajs-2877	113	25	∗𝑠𝑜𝑖𝑟𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑒	∗𝑠𝑜𝑖𝑟𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑒	PROPN
iajs-2877	113	26	and	and	CCONJ
iajs-2877	113	27	onto	onto	ADP
iajs-2877	113	28	function	function	NOUN
iajs-2877	113	29	,	,	PUNCT
iajs-2877	113	30	(	(	PUNCT
iajs-2877	113	31	ℝ	ℝ	PROPN
iajs-2877	113	32	,	,	PUNCT
iajs-2877	113	33	ι	ι	X
iajs-2877	113	34	,	,	PUNCT
iajs-2877	113	35	₲	₲	NOUN
iajs-2877	113	36	)	)	PUNCT
iajs-2877	113	37	is	be	AUX
iajs-2877	113	38	a	a	DET
iajs-2877	113	39	₲	₲	NOUN
iajs-2877	113	40	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	113	41	space	space	NOUN
iajs-2877	113	42	,	,	PUNCT
iajs-2877	113	43	and	and	CCONJ
iajs-2877	113	44	(	(	PUNCT
iajs-2877	113	45	ℝ	ℝ	PROPN
iajs-2877	113	46	,	,	PUNCT
iajs-2877	113	47	d	d	NOUN
iajs-2877	113	48	,	,	PUNCT
iajs-2877	113	49	₲	₲	NOUN
iajs-2877	113	50	)	)	PUNCT
iajs-2877	113	51	is	be	AUX
iajs-2877	113	52	a	a	DET
iajs-2877	113	53	₲	₲	NOUN
iajs-2877	113	54	∗𝑠𝑜disconnected	∗𝑠𝑜disconnected	ADJ
iajs-2877	113	55	space	space	NOUN
iajs-2877	113	56	.	.	PUNCT
iajs-2877	114	1	theorem	theorem	VERB
iajs-2877	114	2	3.11	3.11	NUM
iajs-2877	114	3	.	.	PUNCT
iajs-2877	115	1	if	if	SCONJ
iajs-2877	115	2	ѧ	ѧ	PROPN
iajs-2877	115	3	and	and	CCONJ
iajs-2877	115	4	ƀ	ƀ	PRON
iajs-2877	115	5	are	be	AUX
iajs-2877	115	6	a	a	DET
iajs-2877	115	7	₲	₲	NOUN
iajs-2877	115	8	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	115	9	spaces	space	NOUN
iajs-2877	115	10	of	of	ADP
iajs-2877	115	11	(	(	PUNCT
iajs-2877	115	12	ӽ	ӽ	X
iajs-2877	115	13	,	,	PUNCT
iajs-2877	115	14	τ	τ	NOUN
iajs-2877	115	15	,	,	PUNCT
iajs-2877	115	16	₲	₲	NOUN
iajs-2877	115	17	)	)	PUNCT
iajs-2877	115	18	and	and	CCONJ
iajs-2877	115	19	ѧ	ѧ	PRON
iajs-2877	115	20	⋂	⋂	PROPN
iajs-2877	115	21	ƀ	ƀ	PRON
iajs-2877	115	22	≠	≠	PROPN
iajs-2877	115	23			NOUN
iajs-2877	115	24	,	,	PUNCT
iajs-2877	115	25	then	then	ADV
iajs-2877	115	26	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	115	27	is	be	AUX
iajs-2877	115	28	a	a	DET
iajs-2877	115	29	₲	₲	NOUN
iajs-2877	115	30	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	115	31	space	space	NOUN
iajs-2877	115	32	.	.	PUNCT
iajs-2877	116	1	proof	proof	NOUN
iajs-2877	116	2	.	.	PUNCT
iajs-2877	117	1	let	let	VERB
iajs-2877	117	2	(	(	PUNCT
iajs-2877	117	3	ӽ	ӽ	X
iajs-2877	117	4	,	,	PUNCT
iajs-2877	117	5	τ	τ	NOUN
iajs-2877	117	6	,	,	PUNCT
iajs-2877	117	7	₲	₲	NOUN
iajs-2877	117	8	)	)	PUNCT
iajs-2877	117	9	be	be	VERB
iajs-2877	117	10	a	a	DET
iajs-2877	117	11	grill	grill	ADJ
iajs-2877	117	12	topological	topological	ADJ
iajs-2877	117	13	space	space	NOUN
iajs-2877	117	14	and	and	CCONJ
iajs-2877	117	15	ѧ	ѧ	NOUN
iajs-2877	117	16	,	,	PUNCT
iajs-2877	117	17	ƀ	ƀ	PROPN
iajs-2877	117	18	⊆	⊆	NUM
iajs-2877	117	19	ӽ	ӽ	NOUN
iajs-2877	117	20	;	;	PUNCT
iajs-2877	117	21	ѧ	ѧ	X
iajs-2877	117	22	,	,	PUNCT
iajs-2877	117	23	ƀ	ƀ	PROPN
iajs-2877	117	24	is	be	AUX
iajs-2877	117	25	a	a	DET
iajs-2877	117	26	₲	₲	NOUN
iajs-2877	117	27	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	117	28	space	space	NOUN
iajs-2877	117	29	.	.	PUNCT
iajs-2877	118	1	now	now	ADV
iajs-2877	118	2	,	,	PUNCT
iajs-2877	118	3	if	if	SCONJ
iajs-2877	118	4	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	118	5	is	be	AUX
iajs-2877	118	6	a	a	DET
iajs-2877	118	7	₲	₲	NOUN
iajs-2877	118	8	∗𝑠𝑜-disconnected	∗𝑠𝑜-disconnecte	VERB
iajs-2877	118	9	space	space	NOUN
iajs-2877	118	10	,	,	PUNCT
iajs-2877	118	11	so	so	ADV
iajs-2877	118	12	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	118	13	=	=	PROPN
iajs-2877	118	14	𝒲⋃𝒵	𝒲⋃𝒵	PROPN
iajs-2877	118	15	,	,	PUNCT
iajs-2877	118	16	𝒲	𝒲	PROPN
iajs-2877	118	17	,	,	PUNCT
iajs-2877	118	18	𝒵	𝒵	PROPN
iajs-2877	118	19	∈	∈	PROPN
iajs-2877	118	20	₲	₲	NOUN
iajs-2877	118	21	∗	∗	NOUN
iajs-2877	118	22	𝑠𝑜(𝑥)(ѧ⋃ƀ	𝑠𝑜(𝑥)(ѧ⋃ƀ	NUM
iajs-2877	118	23	)	)	PUNCT
iajs-2877	118	24	,	,	PUNCT
iajs-2877	118	25	𝒲	𝒲	PROPN
iajs-2877	118	26	⋂	⋂	PROPN
iajs-2877	118	27	𝒵	𝒵	NOUN
iajs-2877	118	28	=	=	PUNCT
iajs-2877	118	29			NOUN
iajs-2877	118	30	,	,	PUNCT
iajs-2877	118	31	and	and	CCONJ
iajs-2877	118	32	𝒲	𝒲	PROPN
iajs-2877	118	33	,	,	PUNCT
iajs-2877	118	34	𝒵	𝒵	PROPN
iajs-2877	118	35	≠	≠	PROPN
iajs-2877	118	36	ø	ø	PROPN
iajs-2877	118	37	,	,	PUNCT
iajs-2877	118	38	then	then	ADV
iajs-2877	118	39	ѧ	ѧ	PROPN
iajs-2877	118	40	⊆	⊆	NUM
iajs-2877	118	41	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	118	42	,	,	PUNCT
iajs-2877	118	43	ѧ	ѧ	PROPN
iajs-2877	118	44	⊆	⊆	NUM
iajs-2877	118	45	𝒲⋃𝒵	𝒲⋃𝒵	PROPN
iajs-2877	118	46	,	,	PUNCT
iajs-2877	118	47	ѧ	ѧ	PRON
iajs-2877	118	48	⊆	⊆	NUM
iajs-2877	118	49	𝒲	𝒲	PROPN
iajs-2877	118	50	𝑜𝑟	𝑜𝑟	ADP
iajs-2877	118	51	ѧ	ѧ	DET
iajs-2877	118	52	⊆	⊆	NUM
iajs-2877	118	53	𝒵.	𝒵.	PROPN
iajs-2877	118	54	ihjpas	ihjpa	NOUN
iajs-2877	118	55	.	.	PUNCT
iajs-2877	119	1	53	53	NUM
iajs-2877	119	2	(	(	PUNCT
iajs-2877	119	3	4)2022	4)2022	NOUN
iajs-2877	119	4	239	239	NUM
iajs-2877	119	5	similarly	similarly	ADV
iajs-2877	119	6	,	,	PUNCT
iajs-2877	119	7	ƀ	ƀ	PRON
iajs-2877	119	8	leads	lead	VERB
iajs-2877	119	9	to	to	ADP
iajs-2877	119	10	either	either	CCONJ
iajs-2877	119	11	ѧ	ѧ	PROPN
iajs-2877	119	12	⊆	⊆	NUM
iajs-2877	119	13	𝒲	𝒲	PROPN
iajs-2877	119	14	and	and	CCONJ
iajs-2877	119	15	ƀ	ƀ	PRON
iajs-2877	119	16	⊆	⊆	NUM
iajs-2877	119	17	𝒲	𝒲	PROPN
iajs-2877	119	18	then	then	ADV
iajs-2877	119	19	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	119	20	⊆	⊆	NUM
iajs-2877	119	21	𝒲	𝒲	PROPN
iajs-2877	119	22	then	then	ADV
iajs-2877	119	23	𝒵	𝒵	PROPN
iajs-2877	119	24	=	=	NOUN
iajs-2877	120	1	ø	ø	NOUN
iajs-2877	120	2	c	c	X
iajs-2877	120	3	!	!	PUNCT
iajs-2877	121	1	or	or	CCONJ
iajs-2877	121	2	ѧ	ѧ	DET
iajs-2877	121	3	⊆	⊆	NUM
iajs-2877	121	4	𝒵	𝒵	PROPN
iajs-2877	121	5	and	and	CCONJ
iajs-2877	121	6	ƀ	ƀ	PRON
iajs-2877	121	7	⊆	⊆	NUM
iajs-2877	121	8	𝒵	𝒵	PROPN
iajs-2877	121	9	then	then	ADV
iajs-2877	121	10	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	121	11	⊆	⊆	NUM
iajs-2877	121	12	𝒵	𝒵	PROPN
iajs-2877	121	13	then	then	ADV
iajs-2877	121	14	𝒲	𝒲	PROPN
iajs-2877	121	15	=	=	PUNCT
iajs-2877	121	16	ø	ø	NOUN
iajs-2877	121	17	c	c	X
iajs-2877	121	18	!	!	PUNCT
iajs-2877	121	19	or	or	CCONJ
iajs-2877	121	20	ѧ	ѧ	DET
iajs-2877	121	21	⊆	⊆	NUM
iajs-2877	121	22	𝒲	𝒲	PROPN
iajs-2877	121	23	and	and	CCONJ
iajs-2877	121	24	ƀ	ƀ	PRON
iajs-2877	121	25	⊆	⊆	NUM
iajs-2877	121	26	𝒵	𝒵	PROPN
iajs-2877	121	27	then	then	ADV
iajs-2877	121	28	ѧ	ѧ	PROPN
iajs-2877	121	29	∩	∩	PROPN
iajs-2877	121	30	ƀ	ƀ	PROPN
iajs-2877	121	31	⊆	⊆	NUM
iajs-2877	121	32	𝒲	𝒲	PROPN
iajs-2877	121	33	∩	∩	ADJ
iajs-2877	121	34	𝒵	𝒵	PROPN
iajs-2877	121	35	then	then	ADV
iajs-2877	121	36	ѧ	ѧ	PROPN
iajs-2877	121	37	∩	∩	PROPN
iajs-2877	121	38	ƀ	ƀ	X
iajs-2877	121	39	=	=	SYM
iajs-2877	121	40	ø	ø	PROPN
iajs-2877	121	41	that	that	PRON
iajs-2877	121	42	’s	’	VERB
iajs-2877	121	43	contradiction	contradiction	NOUN
iajs-2877	121	44	or	or	CCONJ
iajs-2877	121	45	ѧ	ѧ	PRON
iajs-2877	121	46	⊆	⊆	NUM
iajs-2877	121	47	𝒵	𝒵	PROPN
iajs-2877	121	48	and	and	CCONJ
iajs-2877	121	49	ƀ	ƀ	PRON
iajs-2877	121	50	⊆	⊆	NUM
iajs-2877	121	51	𝒲	𝒲	PROPN
iajs-2877	121	52	then	then	ADV
iajs-2877	121	53	ѧ	ѧ	PROPN
iajs-2877	121	54	∩	∩	PROPN
iajs-2877	121	55	ƀ	ƀ	PROPN
iajs-2877	121	56	⊆	⊆	NUM
iajs-2877	121	57	𝒲	𝒲	PROPN
iajs-2877	121	58	∩	∩	ADJ
iajs-2877	121	59	𝒵	𝒵	PROPN
iajs-2877	121	60	then	then	ADV
iajs-2877	121	61	ѧ	ѧ	PROPN
iajs-2877	121	62	∩	∩	PROPN
iajs-2877	121	63	ƀ	ƀ	X
iajs-2877	121	64	=	=	SYM
iajs-2877	121	65	ø	ø	PROPN
iajs-2877	121	66	(	(	PUNCT
iajs-2877	121	67	that	that	PRON
iajs-2877	121	68	’s	’	VERB
iajs-2877	121	69	contradiction	contradiction	NOUN
iajs-2877	121	70	!	!	PUNCT
iajs-2877	121	71	)	)	PUNCT
iajs-2877	121	72	.	.	PUNCT
iajs-2877	122	1	so	so	ADV
iajs-2877	122	2	,	,	PUNCT
iajs-2877	122	3	ѧ⋃ƀ	ѧ⋃ƀ	PROPN
iajs-2877	122	4	is	be	AUX
iajs-2877	122	5	a	a	DET
iajs-2877	122	6	₲	₲	NOUN
iajs-2877	122	7	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	122	8	space	space	NOUN
iajs-2877	122	9	.	.	PUNCT
iajs-2877	123	1	remark	remark	PROPN
iajs-2877	123	2	3.12	3.12	NUM
iajs-2877	123	3	.	.	PUNCT
iajs-2877	124	1	we	we	PRON
iajs-2877	124	2	can	can	AUX
iajs-2877	124	3	generalize	generalize	VERB
iajs-2877	124	4	theorem	theorem	VERB
iajs-2877	124	5	3.11	3.11	NUM
iajs-2877	124	6	.	.	PUNCT
iajs-2877	125	1	to	to	ADP
iajs-2877	125	2	a	a	DET
iajs-2877	125	3	family	family	NOUN
iajs-2877	125	4	of	of	ADP
iajs-2877	125	5	a	a	DET
iajs-2877	125	6	₲	₲	NOUN
iajs-2877	125	7	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	125	8	sets	set	NOUN
iajs-2877	125	9	as	as	SCONJ
iajs-2877	125	10	follows	follow	VERB
iajs-2877	125	11	:	:	PUNCT
iajs-2877	125	12	let	let	VERB
iajs-2877	125	13	{	{	PUNCT
iajs-2877	125	14	ѧ∝}∝∈∧	ѧ∝}∝∈∧	X
iajs-2877	125	15	be	be	AUX
iajs-2877	125	16	a	a	DET
iajs-2877	125	17	family	family	NOUN
iajs-2877	125	18	of	of	ADP
iajs-2877	125	19	a	a	DET
iajs-2877	125	20	₲	₲	NOUN
iajs-2877	125	21	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	125	22	subsets	subset	NOUN
iajs-2877	125	23	of	of	ADP
iajs-2877	125	24	a	a	DET
iajs-2877	125	25	space	space	NOUN
iajs-2877	125	26	(	(	PUNCT
iajs-2877	125	27	ӽ	ӽ	X
iajs-2877	125	28	,	,	PUNCT
iajs-2877	125	29	τ	τ	NOUN
iajs-2877	125	30	,	,	PUNCT
iajs-2877	125	31	₲	₲	NOUN
iajs-2877	125	32	)	)	PUNCT
iajs-2877	125	33	and	and	CCONJ
iajs-2877	125	34	⋂	⋂	PROPN
iajs-2877	125	35	ѧ∝	ѧ∝	VERB
iajs-2877	125	36	≠	≠	PROPN
iajs-2877	125	37	ø∝∈∧	ø∝∈∧	PROPN
iajs-2877	125	38	,	,	PUNCT
iajs-2877	125	39	then	then	ADV
iajs-2877	125	40	⋃	⋃	PUNCT
iajs-2877	125	41	ѧ∝∝∈∧	ѧ∝∝∈∧	PRON
iajs-2877	125	42	is	be	AUX
iajs-2877	125	43	a	a	DET
iajs-2877	125	44	₲	₲	NOUN
iajs-2877	125	45	∗𝑠𝑜-connected	∗𝑠𝑜-connecte	VERB
iajs-2877	125	46	set	set	NOUN
iajs-2877	125	47	.	.	PUNCT
iajs-2877	126	1	4	4	X
iajs-2877	126	2	.	.	X
iajs-2877	126	3	grill	grill	NOUN
iajs-2877	126	4	semi	semi	ADJ
iajs-2877	126	5	-	-	ADJ
iajs-2877	126	6	open	open	ADJ
iajs-2877	126	7	sets	set	NOUN
iajs-2877	126	8	in	in	ADP
iajs-2877	126	9	grill	grill	NOUN
iajs-2877	126	10	connected	connect	VERB
iajs-2877	126	11	space	space	NOUN
iajs-2877	126	12	hyperconnected	hyperconnecte	VERB
iajs-2877	126	13	definition	definition	NOUN
iajs-2877	126	14	4.1	4.1	NUM
iajs-2877	126	15	.	.	PUNCT
iajs-2877	127	1	in	in	ADP
iajs-2877	127	2	any	any	DET
iajs-2877	127	3	grill	grill	ADJ
iajs-2877	127	4	topological	topological	ADJ
iajs-2877	127	5	space	space	NOUN
iajs-2877	127	6	(	(	PUNCT
iajs-2877	127	7	ӽ	ӽ	X
iajs-2877	127	8	,	,	PUNCT
iajs-2877	127	9	τ	τ	NOUN
iajs-2877	127	10	,	,	PUNCT
iajs-2877	127	11	₲	₲	NOUN
iajs-2877	127	12	)	)	PUNCT
iajs-2877	127	13	is	be	AUX
iajs-2877	127	14	said	say	VERB
iajs-2877	127	15	to	to	PART
iajs-2877	127	16	be	be	AUX
iajs-2877	127	17	:	:	PUNCT
iajs-2877	127	18	1	1	X
iajs-2877	127	19	.	.	X
iajs-2877	127	20	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2877	127	21	if	if	SCONJ
iajs-2877	127	22	ѧ	ѧ	PRON
iajs-2877	127	23	is	be	AUX
iajs-2877	127	24	τ₲-dense	τ₲-dense	ADJ
iajs-2877	127	25	(	(	PUNCT
iajs-2877	127	26	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	127	27	)	)	PUNCT
iajs-2877	127	28	=	=	SYM
iajs-2877	128	1	ӽ	ӽ	X
iajs-2877	128	2	)	)	PUNCT
iajs-2877	128	3	for	for	ADP
iajs-2877	128	4	every	every	DET
iajs-2877	128	5	non	non	ADJ
iajs-2877	128	6	-	-	ADJ
iajs-2877	128	7	empty	empty	ADJ
iajs-2877	128	8	open	open	ADJ
iajs-2877	128	9	subset	subset	NOUN
iajs-2877	128	10	ѧ	ѧ	NOUN
iajs-2877	128	11	of	of	ADP
iajs-2877	128	12	ӽ.	ӽ.	NOUN
iajs-2877	128	13	2	2	NUM
iajs-2877	128	14	.	.	NOUN
iajs-2877	129	1	₲	₲	NOUN
iajs-2877	129	2	∗	∗	NOUN
iajs-2877	129	3	-hyperconnected	-hyperconnecte	VERB
iajs-2877	129	4	if	if	SCONJ
iajs-2877	129	5	ӽ	ӽ	PRON
iajs-2877	129	6	−	−	NOUN
iajs-2877	129	7	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	129	8	)	)	PUNCT
iajs-2877	129	9	∉	∉	PROPN
iajs-2877	129	10	₲	₲	NOUN
iajs-2877	129	11	for	for	ADP
iajs-2877	129	12	every	every	DET
iajs-2877	129	13	non	non	ADJ
iajs-2877	129	14	-	-	ADJ
iajs-2877	129	15	empty	empty	ADJ
iajs-2877	129	16	open	open	ADJ
iajs-2877	129	17	subset	subset	NOUN
iajs-2877	129	18	ѧ	ѧ	NOUN
iajs-2877	129	19	of	of	ADP
iajs-2877	129	20	ӽ.	ӽ.	NOUN
iajs-2877	129	21	3	3	NUM
iajs-2877	129	22	.	.	NOUN
iajs-2877	129	23	₲	₲	NOUN
iajs-2877	129	24	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	129	25	if	if	SCONJ
iajs-2877	129	26	ӽ	ӽ	PRON
iajs-2877	129	27	−	−	NOUN
iajs-2877	129	28	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	129	29	)	)	PUNCT
iajs-2877	129	30	∉	∉	PROPN
iajs-2877	129	31	₲	₲	NOUN
iajs-2877	129	32	for	for	ADP
iajs-2877	129	33	every	every	DET
iajs-2877	129	34	non	non	ADJ
iajs-2877	129	35	-	-	ADJ
iajs-2877	129	36	empty	empty	ADJ
iajs-2877	129	37	₲	₲	NOUN
iajs-2877	129	38	∗𝑠-𝑜𝑝𝑒𝑛	∗𝑠-𝑜𝑝𝑒𝑛	NOUN
iajs-2877	129	39	subset	subset	VERB
iajs-2877	129	40	ѧ	ѧ	NOUN
iajs-2877	129	41	of	of	ADP
iajs-2877	129	42	ӽ.	ӽ.	NOUN
iajs-2877	129	43	4	4	NUM
iajs-2877	129	44	.	.	NOUN
iajs-2877	129	45	₲	₲	NOUN
iajs-2877	129	46	∗𝑠𝑜-hyperconnected	∗𝑠𝑜-hyperconnecte	VERB
iajs-2877	129	47	if	if	SCONJ
iajs-2877	129	48	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	129	49	)	)	PUNCT
iajs-2877	130	1	=	=	SYM
iajs-2877	130	2	ӽ	ӽ	NOUN
iajs-2877	130	3	for	for	ADP
iajs-2877	130	4	all	all	DET
iajs-2877	130	5	ѧ	ѧ	PROPN
iajs-2877	130	6	∈	∈	PROPN
iajs-2877	130	7	₲	₲	NOUN
iajs-2877	130	8	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	130	9	)	)	PUNCT
iajs-2877	130	10	.	.	PUNCT
iajs-2877	131	1	proposition	proposition	NOUN
iajs-2877	131	2	4.2	4.2	NUM
iajs-2877	131	3	.	.	PUNCT
iajs-2877	132	1	1	1	NUM
iajs-2877	132	2	.	.	X
iajs-2877	133	1	every	every	DET
iajs-2877	133	2	₲	₲	NOUN
iajs-2877	133	3	∗𝑠𝑜-hyperconnected	∗𝑠𝑜-hyperconnected	PROPN
iajs-2877	133	4	is	be	AUX
iajs-2877	133	5	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2877	133	6	.	.	PUNCT
iajs-2877	134	1	2	2	X
iajs-2877	134	2	.	.	X
iajs-2877	134	3	every	every	DET
iajs-2877	134	4	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2877	134	5	is	be	AUX
iajs-2877	134	6	₲	₲	NOUN
iajs-2877	134	7	∗	∗	NOUN
iajs-2877	134	8	-hyperconnected	-hyperconnecte	VERB
iajs-2877	134	9	.	.	PUNCT
iajs-2877	135	1	3	3	X
iajs-2877	135	2	.	.	X
iajs-2877	135	3	every	every	DET
iajs-2877	135	4	₲	₲	NOUN
iajs-2877	135	5	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	135	6	is	be	AUX
iajs-2877	135	7	₲	₲	NOUN
iajs-2877	135	8	∗	∗	NOUN
iajs-2877	135	9	-hyperconnected	-hyperconnecte	VERB
iajs-2877	135	10	.	.	PUNCT
iajs-2877	136	1	4	4	X
iajs-2877	136	2	.	.	X
iajs-2877	136	3	every	every	DET
iajs-2877	136	4	₲	₲	NOUN
iajs-2877	136	5	∗𝑠𝑜-hyperconnected	∗𝑠𝑜-hyperconnected	PROPN
iajs-2877	136	6	is	be	AUX
iajs-2877	136	7	₲	₲	NOUN
iajs-2877	136	8	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	136	9	.	.	PUNCT
iajs-2877	137	1	proof	proof	NOUN
iajs-2877	137	2	.	.	PUNCT
iajs-2877	138	1	1	1	X
iajs-2877	138	2	.	.	X
iajs-2877	138	3	let	let	VERB
iajs-2877	138	4	ѧ	ѧ	PRON
iajs-2877	138	5	be	be	AUX
iajs-2877	138	6	a	a	DET
iajs-2877	138	7	₲	₲	NOUN
iajs-2877	138	8	∗𝑠𝑜-hyperconnected	∗𝑠𝑜-hyperconnected	NUM
iajs-2877	138	9	,	,	PUNCT
iajs-2877	138	10	then	then	ADV
iajs-2877	138	11	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	138	12	)	)	PUNCT
iajs-2877	139	1	=	=	SYM
iajs-2877	140	1	ӽ	ӽ	NOUN
iajs-2877	140	2	,	,	PUNCT
iajs-2877	140	3	then	then	ADV
iajs-2877	140	4	ѧ	ѧ	PROPN
iajs-2877	140	5	is	be	AUX
iajs-2877	140	6	a	a	DET
iajs-2877	140	7	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2877	140	8	(	(	PUNCT
iajs-2877	140	9	since	since	SCONJ
iajs-2877	140	10	ѧ	ѧ	PROPN
iajs-2877	140	11	∈	∈	PROPN
iajs-2877	140	12	₲	₲	NOUN
iajs-2877	140	13	∗𝑠𝑜(ӽ	∗𝑠𝑜(ӽ	PROPN
iajs-2877	140	14	)	)	PUNCT
iajs-2877	140	15	then	then	ADV
iajs-2877	140	16	ѧ	ѧ	PROPN
iajs-2877	140	17	∈	∈	PROPN
iajs-2877	140	18	τ	τ	PROPN
iajs-2877	140	19	)	)	PUNCT
iajs-2877	140	20	.	.	PUNCT
iajs-2877	141	1	2	2	X
iajs-2877	141	2	.	.	X
iajs-2877	141	3	let	let	VERB
iajs-2877	141	4	ѧ	ѧ	PRON
iajs-2877	141	5	be	be	AUX
iajs-2877	141	6	a	a	DET
iajs-2877	141	7	∗-hyperconnected	∗-hyperconnected	NOUN
iajs-2877	141	8	.	.	PUNCT
iajs-2877	142	1	this	this	PRON
iajs-2877	142	2	means	mean	VERB
iajs-2877	142	3	that	that	SCONJ
iajs-2877	142	4	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	142	5	)	)	PUNCT
iajs-2877	143	1	=	=	SYM
iajs-2877	143	2	ӽ.	ӽ.	NOUN
iajs-2877	144	1	so	so	ADV
iajs-2877	144	2	,	,	PUNCT
iajs-2877	144	3	ӽ	ӽ	DET
iajs-2877	144	4	−	−	NOUN
iajs-2877	144	5	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	144	6	)	)	PUNCT
iajs-2877	145	1	=	=	SYM
iajs-2877	145	2	∅	∅	NOUN
iajs-2877	145	3	∉	∉	PROPN
iajs-2877	145	4	₲	₲	NOUN
iajs-2877	145	5	.	.	PUNCT
iajs-2877	146	1	therefore	therefore	ADV
iajs-2877	146	2	,	,	PUNCT
iajs-2877	146	3	ѧ	ѧ	PROPN
iajs-2877	146	4	is	be	AUX
iajs-2877	146	5	a	a	DET
iajs-2877	146	6	₲	₲	NOUN
iajs-2877	146	7	∗	∗	NOUN
iajs-2877	146	8	-hyperconnected	-hyperconnecte	VERB
iajs-2877	146	9	.	.	PUNCT
iajs-2877	147	1	3	3	X
iajs-2877	147	2	.	.	X
iajs-2877	147	3	let	let	VERB
iajs-2877	147	4	ѧ	ѧ	PRON
iajs-2877	147	5	be	be	AUX
iajs-2877	147	6	an	an	DET
iajs-2877	147	7	open	open	NOUN
iajs-2877	147	8	in	in	ADP
iajs-2877	147	9	₲	₲	NOUN
iajs-2877	147	10	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	147	11	.	.	PUNCT
iajs-2877	148	1	this	this	PRON
iajs-2877	148	2	means	mean	VERB
iajs-2877	148	3	that	that	SCONJ
iajs-2877	148	4	ӽ	ӽ	DET
iajs-2877	148	5	−	−	NOUN
iajs-2877	148	6	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	148	7	)	)	PUNCT
iajs-2877	148	8	∉	∉	PROPN
iajs-2877	149	1	₲	₲	NOUN
iajs-2877	149	2	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	149	3	(	(	PUNCT
iajs-2877	149	4	since	since	SCONJ
iajs-2877	149	5	every	every	DET
iajs-2877	149	6	open	open	ADJ
iajs-2877	149	7	set	set	VERB
iajs-2877	149	8	in	in	ADP
iajs-2877	149	9	₲	₲	NOUN
iajs-2877	149	10	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	149	11	is	be	AUX
iajs-2877	149	12	an	an	DET
iajs-2877	149	13	open	open	ADJ
iajs-2877	149	14	set	set	NOUN
iajs-2877	149	15	in	in	ADP
iajs-2877	149	16	₲	₲	NOUN
iajs-2877	149	17	∗	∗	NOUN
iajs-2877	149	18	-hyperconnected	-hyperconnecte	VERB
iajs-2877	149	19	.	.	PUNCT
iajs-2877	150	1	so	so	ADV
iajs-2877	150	2	,	,	PUNCT
iajs-2877	150	3	ӽ	ӽ	DET
iajs-2877	150	4	−	−	NOUN
iajs-2877	150	5	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	150	6	)	)	PUNCT
iajs-2877	150	7	∉	∉	PROPN
iajs-2877	150	8	₲	₲	NOUN
iajs-2877	150	9	.therefore	.therefore	NOUN
iajs-2877	150	10	,	,	PUNCT
iajs-2877	150	11	ѧ	ѧ	PROPN
iajs-2877	150	12	is	be	AUX
iajs-2877	150	13	a	a	DET
iajs-2877	150	14	₲	₲	NOUN
iajs-2877	150	15	∗	∗	NOUN
iajs-2877	150	16	-hyperconnected	-hyperconnecte	VERB
iajs-2877	150	17	.	.	PUNCT
iajs-2877	151	1	4	4	X
iajs-2877	151	2	.	.	X
iajs-2877	151	3	let	let	VERB
iajs-2877	151	4	ѧ	ѧ	PRON
iajs-2877	151	5	be	be	AUX
iajs-2877	151	6	an	an	DET
iajs-2877	151	7	open	open	ADJ
iajs-2877	151	8	set	set	NOUN
iajs-2877	151	9	in	in	ADP
iajs-2877	151	10	₲	₲	NOUN
iajs-2877	151	11	∗𝑠𝑜-hyperconnected	∗𝑠𝑜-hyperconnected	NUM
iajs-2877	151	12	.	.	PUNCT
iajs-2877	152	1	this	this	PRON
iajs-2877	152	2	means	mean	VERB
iajs-2877	152	3	that	that	SCONJ
iajs-2877	152	4	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	152	5	)	)	PUNCT
iajs-2877	153	1	=	=	SYM
iajs-2877	153	2	ӽ.	ӽ.	NOUN
iajs-2877	154	1	so	so	ADV
iajs-2877	154	2	,	,	PUNCT
iajs-2877	154	3	ӽ	ӽ	DET
iajs-2877	154	4	−	−	NOUN
iajs-2877	154	5	𝑐𝜄₲(ѧ	𝑐𝜄₲(ѧ	NUM
iajs-2877	154	6	)	)	PUNCT
iajs-2877	154	7	∉	∉	PROPN
iajs-2877	154	8	₲	₲	NOUN
iajs-2877	154	9	.	.	PUNCT
iajs-2877	155	1	therefore	therefore	ADV
iajs-2877	155	2	,	,	PUNCT
iajs-2877	155	3	ѧ	ѧ	PROPN
iajs-2877	155	4	is	be	AUX
iajs-2877	155	5	a	a	DET
iajs-2877	155	6	₲	₲	NOUN
iajs-2877	155	7	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	155	8	.	.	PUNCT
iajs-2877	156	1	the	the	DET
iajs-2877	156	2	following	follow	VERB
iajs-2877	156	3	diagram	diagram	NOUN
iajs-2877	156	4	shows	show	VERB
iajs-2877	156	5	the	the	DET
iajs-2877	156	6	relationship	relationship	NOUN
iajs-2877	156	7	between	between	ADP
iajs-2877	156	8	the	the	DET
iajs-2877	156	9	types	type	NOUN
iajs-2877	156	10	of	of	ADP
iajs-2877	156	11	hyperconnected	hyperconnecte	VERB
iajs-2877	156	12	.	.	PUNCT
iajs-2877	157	1	∗hyperconnected	∗hyperconnecte	VERB
iajs-2877	157	2	₲	₲	NOUN
iajs-2877	157	3	∗𝑠𝑜hyperconnected	∗𝑠𝑜hyperconnecte	VERB
iajs-2877	157	4	₲	₲	NOUN
iajs-2877	157	5	∗	∗	NOUN
iajs-2877	157	6	hyperconnected	hyperconnecte	VERB
iajs-2877	157	7	₲	₲	NOUN
iajs-2877	157	8	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2877	157	9	diagram	diagram	NOUN
iajs-2877	157	10	1	1	NUM
iajs-2877	157	11	hyperconnected	hyperconnecte	VERB
iajs-2877	157	12	space	space	NOUN
iajs-2877	157	13	via	via	ADP
iajs-2877	157	14	grill	grill	ADJ
iajs-2877	157	15	space	space	NOUN
iajs-2877	157	16	4	4	NUM
iajs-2877	157	17	.	.	PUNCT
iajs-2877	158	1	conclusion	conclusion	NOUN
iajs-2877	158	2	ihjpas	ihjpa	VERB
iajs-2877	158	3	.	.	PUNCT
iajs-2877	159	1	53	53	NUM
iajs-2877	159	2	(	(	PUNCT
iajs-2877	159	3	4)2022	4)2022	NOUN
iajs-2877	159	4	240	240	NUM
iajs-2877	159	5	in	in	ADP
iajs-2877	159	6	this	this	DET
iajs-2877	159	7	research	research	NOUN
iajs-2877	159	8	,	,	PUNCT
iajs-2877	159	9	we	we	PRON
iajs-2877	159	10	studied	study	VERB
iajs-2877	159	11	a	a	DET
iajs-2877	159	12	connect	connect	ADJ
iajs-2877	159	13	space	space	NOUN
iajs-2877	159	14	in	in	ADP
iajs-2877	159	15	the	the	DET
iajs-2877	159	16	grill	grill	NOUN
iajs-2877	159	17	semi	semi	ADJ
iajs-2877	159	18	-	-	ADJ
iajs-2877	159	19	open	open	ADJ
iajs-2877	159	20	topological	topological	ADJ
iajs-2877	159	21	spaces	space	NOUN
iajs-2877	159	22	,	,	PUNCT
iajs-2877	159	23	some	some	DET
iajs-2877	159	24	examples	example	NOUN
iajs-2877	159	25	are	be	AUX
iajs-2877	159	26	showed	show	VERB
iajs-2877	159	27	,	,	PUNCT
iajs-2877	159	28	and	and	CCONJ
iajs-2877	159	29	some	some	DET
iajs-2877	159	30	theorems	theorem	NOUN
iajs-2877	159	31	are	be	AUX
iajs-2877	159	32	applied	apply	VERB
iajs-2877	159	33	for	for	ADP
iajs-2877	159	34	these	these	DET
iajs-2877	159	35	new	new	ADJ
iajs-2877	159	36	sets	set	NOUN
iajs-2877	159	37	.	.	PUNCT
iajs-2877	160	1	we	we	PRON
iajs-2877	160	2	also	also	ADV
iajs-2877	160	3	found	find	VERB
iajs-2877	160	4	some	some	DET
iajs-2877	160	5	new	new	ADJ
iajs-2877	160	6	properties	property	NOUN
iajs-2877	160	7	of	of	ADP
iajs-2877	160	8	these	these	DET
iajs-2877	160	9	sets	set	NOUN
iajs-2877	160	10	.	.	PUNCT
iajs-2877	161	1	references	reference	NOUN
iajs-2877	161	2	1	1	NUM
iajs-2877	161	3	.	.	PUNCT
iajs-2877	161	4	choquet	choquet	PROPN
iajs-2877	161	5	,	,	PUNCT
iajs-2877	161	6	g.	g.	PROPN
iajs-2877	161	7	sur	sur	PROPN
iajs-2877	161	8	les	les	PROPN
iajs-2877	161	9	notions	notion	NOUN
iajs-2877	161	10	de	de	X
iajs-2877	161	11	filtre	filtre	NOUN
iajs-2877	161	12	et	et	NOUN
iajs-2877	161	13	grille	grille	NOUN
iajs-2877	161	14	,	,	PUNCT
iajs-2877	161	15	comptes	compte	VERB
iajs-2877	161	16	rendus	rendus	PROPN
iajs-2877	161	17	acad	acad	PROPN
iajs-2877	161	18	.	.	PUNCT
iajs-2877	162	1	sci	sci	PROPN
iajs-2877	162	2	.	.	PROPN
iajs-2877	162	3	paris	paris	PROPN
iajs-2877	162	4	,	,	PUNCT
iajs-2877	162	5	1947	1947	NUM
iajs-2877	162	6	,	,	PUNCT
iajs-2877	162	7	224	224	NUM
iajs-2877	162	8	,	,	PUNCT
iajs-2877	162	9	171	171	NUM
iajs-2877	162	10	-	-	SYM
iajs-2877	162	11	173	173	NUM
iajs-2877	162	12	.	.	PUNCT
iajs-2877	163	1	2.esmaeel	2.esmaeel	NUM
iajs-2877	163	2	,	,	PUNCT
iajs-2877	163	3	r.b	r.b	PROPN
iajs-2877	163	4	.	.	PROPN
iajs-2877	163	5	;	;	PUNCT
iajs-2877	163	6	mohammad	mohammad	PROPN
iajs-2877	163	7	,	,	PUNCT
iajs-2877	163	8	r.j	r.j	PROPN
iajs-2877	163	9	.	.	PUNCT
iajs-2877	164	1	on	on	ADP
iajs-2877	164	2	nano	nano	PROPN
iajs-2877	164	3	soft	soft	ADJ
iajs-2877	164	4	j	j	NOUN
iajs-2877	164	5	-	-	PUNCT
iajs-2877	164	6	semi	semi	ADJ
iajs-2877	164	7	-	-	ADJ
iajs-2877	164	8	g	g	ADV
iajs-2877	164	9	-	-	PUNCT
iajs-2877	164	10	closed	close	VERB
iajs-2877	164	11	sets	set	NOUN
iajs-2877	164	12	,	,	PUNCT
iajs-2877	164	13	j.	j.	PROPN
iajs-2877	164	14	phys	phys	PROPN
iajs-2877	164	15	.	.	PUNCT
iajs-2877	164	16	conf	conf	PROPN
iajs-2877	164	17	.	.	PUNCT
iajs-2877	165	1	ser	ser	NOUN
iajs-2877	165	2	.	.	PUNCT
iajs-2877	166	1	2020,159(1	2020,159(1	NUM
iajs-2877	166	2	)	)	PUNCT
iajs-2877	166	3	012071	012071	NUM
iajs-2877	166	4	.	.	PUNCT
iajs-2877	167	1	3.esmaeel	3.esmaeel	NUM
iajs-2877	167	2	,	,	PUNCT
iajs-2877	167	3	r.	r.	PROPN
iajs-2877	167	4	b	b	PROPN
iajs-2877	167	5	;	;	PUNCT
iajs-2877	167	6	nasir	nasir	PROPN
iajs-2877	167	7	,	,	PUNCT
iajs-2877	167	8	a.	a.	PROPN
iajs-2877	167	9	i	i	PROPN
iajs-2877	167	10	;	;	PUNCT
iajs-2877	167	11	kalaf	kalaf	PROPN
iajs-2877	167	12	,	,	PUNCT
iajs-2877	167	13	b.a	b.a	PROPN
iajs-2877	167	14	.	.	PROPN
iajs-2877	168	1	on	on	ADP
iajs-2877	168	2	αĩ	αĩ	ADP
iajs-2877	168	3	-	-	PUNCT
iajs-2877	168	4	closed	close	VERB
iajs-2877	168	5	soft	soft	ADJ
iajs-2877	168	6	sets	set	NOUN
iajs-2877	168	7	.	.	PUNCT
iajs-2877	169	1	sci	sci	PROPN
iajs-2877	169	2	.	.	PUNCT
iajs-2877	169	3	inter	inter	PROPN
iajs-2877	169	4	.	.	PUNCT
iajs-2877	170	1	(	(	PUNCT
iajs-2877	170	2	lahore	lahore	NOUN
iajs-2877	170	3	)	)	PUNCT
iajs-2877	170	4	.	.	PUNCT
iajs-2877	171	1	2018	2018	NUM
iajs-2877	171	2	.	.	PUNCT
iajs-2877	172	1	30(5	30(5	NUM
iajs-2877	172	2	):	):	PUNCT
iajs-2877	172	3	703705	703705	NUM
iajs-2877	172	4	.	.	PUNCT
iajs-2877	173	1	4.levine	4.levine	NUM
iajs-2877	173	2	,	,	PUNCT
iajs-2877	173	3	n.	n.	NOUN
iajs-2877	173	4	semi	semi	ADJ
iajs-2877	173	5	-	-	ADJ
iajs-2877	173	6	open	open	ADJ
iajs-2877	173	7	sets	set	NOUN
iajs-2877	173	8	and	and	CCONJ
iajs-2877	173	9	semi	semi	ADJ
iajs-2877	173	10	-	-	NOUN
iajs-2877	173	11	continuity	continuity	NOUN
iajs-2877	173	12	in	in	ADP
iajs-2877	173	13	topological	topological	ADJ
iajs-2877	173	14	spaces	space	NOUN
iajs-2877	173	15	,	,	PUNCT
iajs-2877	173	16	amer	amer	PROPN
iajs-2877	173	17	math	math	PROPN
iajs-2877	173	18	.	.	PUNCT
iajs-2877	174	1	monthly	monthly	ADJ
iajs-2877	174	2	,	,	PUNCT
iajs-2877	174	3	1963	1963	NUM
iajs-2877	174	4	,	,	PUNCT
iajs-2877	174	5	70	70	NUM
iajs-2877	174	6	,	,	PUNCT
iajs-2877	174	7	36	36	NUM
iajs-2877	174	8	-	-	SYM
iajs-2877	174	9	41	41	NUM
iajs-2877	174	10	.	.	PUNCT
iajs-2877	175	1	5	5	NUM
iajs-2877	175	2	.	.	X
iajs-2877	176	1	al	al	PROPN
iajs-2877	176	2	-	-	PUNCT
iajs-2877	176	3	omary	omary	PROPN
iajs-2877	176	4	,	,	PUNCT
iajs-2877	176	5	a	a	PRON
iajs-2877	176	6	;	;	PUNCT
iajs-2877	176	7	noiri	noiri	PROPN
iajs-2877	176	8	,	,	PUNCT
iajs-2877	176	9	t.	t.	NOUN
iajs-2877	176	10	decompositions	decomposition	NOUN
iajs-2877	176	11	of	of	ADP
iajs-2877	176	12	continuity	continuity	NOUN
iajs-2877	176	13	via	via	ADP
iajs-2877	176	14	grills	grill	NOUN
iajs-2877	176	15	,	,	PUNCT
iajs-2877	176	16	jordan	jordan	PROPN
iajs-2877	176	17	journal	journal	PROPN
iajs-2877	176	18	mathematics	mathematics	PROPN
iajs-2877	176	19	and	and	CCONJ
iajs-2877	176	20	statistics	statistic	NOUN
iajs-2877	176	21	(	(	PUNCT
iajs-2877	176	22	jjms	jjms	PROPN
iajs-2877	176	23	)	)	PUNCT
iajs-2877	176	24	.2011	.2011	PROPN
iajs-2877	176	25	,	,	PUNCT
iajs-2877	176	26	4(1),33	4(1),33	NUM
iajs-2877	176	27	-	-	SYM
iajs-2877	176	28	46	46	NUM
iajs-2877	176	29	6	6	NUM
iajs-2877	176	30	.	.	PUNCT
iajs-2877	176	31	saravanakumar	saravanakumar	PROPN
iajs-2877	176	32	,	,	PUNCT
iajs-2877	176	33	d.	d.	PROPN
iajs-2877	176	34	;	;	PUNCT
iajs-2877	176	35	kalaivani	kalaivani	PROPN
iajs-2877	176	36	,	,	PUNCT
iajs-2877	176	37	n.	n.	NOUN
iajs-2877	176	38	on	on	ADP
iajs-2877	176	39	grill	grill	NOUN
iajs-2877	176	40	spopen	spopen	NOUN
iajs-2877	176	41	set	set	VERB
iajs-2877	176	42	in	in	ADP
iajs-2877	176	43	grill	grill	ADJ
iajs-2877	176	44	topological	topological	ADJ
iajs-2877	176	45	spaces	space	NOUN
iajs-2877	176	46	,	,	PUNCT
iajs-2877	176	47	journal	journal	NOUN
iajs-2877	176	48	of	of	ADP
iajs-2877	176	49	new	new	ADJ
iajs-2877	176	50	theory	theory	NOUN
iajs-2877	176	51	,	,	PUNCT
iajs-2877	176	52	2018	2018	NUM
iajs-2877	176	53	,	,	PUNCT
iajs-2877	176	54	23	23	NUM
iajs-2877	176	55	,	,	PUNCT
iajs-2877	176	56	85	85	NUM
iajs-2877	176	57	-	-	SYM
iajs-2877	176	58	92	92	NUM
iajs-2877	176	59	.	.	PUNCT
iajs-2877	177	1	7.mustafa	7.mustafa	NUM
iajs-2877	177	2	,	,	PUNCT
iajs-2877	177	3	m.o	m.o	PROPN
iajs-2877	177	4	.	.	PROPN
iajs-2877	177	5	;	;	PUNCT
iajs-2877	177	6	esmaeel	esmaeel	VERB
iajs-2877	177	7	,	,	PUNCT
iajs-2877	177	8	r.b	r.b	PROPN
iajs-2877	177	9	.	.	PROPN
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iajs-2877	177	11	axioms	axiom	NOUN
iajs-2877	177	12	with	with	ADP
iajs-2877	177	13	grill	grill	ADJ
iajs-2877	177	14	-	-	PUNCT
iajs-2877	177	15	toplogical	toplogical	ADJ
iajs-2877	177	16	open	open	ADJ
iajs-2877	177	17	set	set	NOUN
iajs-2877	177	18	,	,	PUNCT
iajs-2877	177	19	j.	j.	PROPN
iajs-2877	177	20	phys	phys	PROPN
iajs-2877	177	21	.	.	PUNCT
iajs-2877	178	1	2021	2021	NUM
iajs-2877	178	2	,	,	PUNCT
iajs-2877	178	3	1879,2	1879,2	NUM
iajs-2877	178	4	,	,	PUNCT
iajs-2877	178	5	022107	022107	NUM
iajs-2877	178	6	.	.	PUNCT
iajs-2877	179	1	8	8	NUM
iajs-2877	179	2	.	.	X
iajs-2877	179	3	arkhangel'skii	arkhangel'skii	PROPN
iajs-2877	179	4	,	,	PUNCT
iajs-2877	179	5	a.v	a.v	PROPN
iajs-2877	179	6	.	.	PROPN
iajs-2877	179	7	;	;	PUNCT
iajs-2877	179	8	ponomar''ev	ponomar''ev	PROPN
iajs-2877	179	9	.	.	PUNCT
iajs-2877	180	1	v.i	v.i	PROPN
iajs-2877	180	2	.	.	PROPN
iajs-2877	180	3	fundamentals	fundamental	NOUN
iajs-2877	180	4	of	of	ADP
iajs-2877	180	5	general	general	ADJ
iajs-2877	180	6	topology	topology	NOUN
iajs-2877	180	7	-	-	PUNCT
iajs-2877	180	8	problems	problem	NOUN
iajs-2877	180	9	and	and	CCONJ
iajs-2877	180	10	exercises	exercise	NOUN
iajs-2877	180	11	,	,	PUNCT
iajs-2877	180	12	hindustan	hindustan	PROPN
iajs-2877	180	13	pub.corporation	pub.corporation	NOUN
iajs-2877	180	14	,	,	PUNCT
iajs-2877	180	15	delhi	delhi	PROPN
iajs-2877	180	16	,	,	PUNCT
iajs-2877	180	17	1966	1966	NUM
iajs-2877	180	18	.	.	PUNCT
iajs-2877	181	1	9	9	X
iajs-2877	181	2	.	.	X
iajs-2877	181	3	roy	roy	PROPN
iajs-2877	181	4	,	,	PUNCT
iajs-2877	181	5	b.	b.	PROPN
iajs-2877	181	6	;	;	PUNCT
iajs-2877	181	7	mukherjee	mukherjee	PROPN
iajs-2877	181	8	,	,	PUNCT
iajs-2877	181	9	m.	m.	NOUN
iajs-2877	181	10	n.	n.	PROPN
iajs-2877	181	11	on	on	ADP
iajs-2877	181	12	a	a	DET
iajs-2877	181	13	typical	typical	ADJ
iajs-2877	181	14	topology	topology	NOUN
iajs-2877	181	15	induced	induce	VERB
iajs-2877	181	16	by	by	ADP
iajs-2877	181	17	a	a	DET
iajs-2877	181	18	grill	grill	NOUN
iajs-2877	181	19	,	,	PUNCT
iajs-2877	181	20	soochow	soochow	PROPN
iajs-2877	181	21	j.	j.	PROPN
iajs-2877	181	22	math	math	PROPN
iajs-2877	181	23	.	.	PUNCT
iajs-2877	181	24	,	,	PUNCT
iajs-2877	181	25	2007,33	2007,33	NUM
iajs-2877	181	26	(	(	PUNCT
iajs-2877	181	27	4	4	NUM
iajs-2877	181	28	)	)	PUNCT
iajs-2877	181	29	,	,	PUNCT
iajs-2877	181	30	771	771	NUM
iajs-2877	181	31	-	-	SYM
iajs-2877	181	32	786	786	NUM
iajs-2877	181	33	.	.	PUNCT
iajs-2877	181	34	10	10	NUM
iajs-2877	181	35	.	.	PUNCT
iajs-2877	182	1	suliman	suliman	NOUN
iajs-2877	182	2	,	,	PUNCT
iajs-2877	182	3	s.s	s.s	PROPN
iajs-2877	182	4	;	;	PUNCT
iajs-2877	182	5	esmaeel	esmaeel	PROPN
iajs-2877	182	6	,	,	PUNCT
iajs-2877	182	7	r.	r.	PROPN
iajs-2877	182	8	b.	b.	PROPN
iajs-2877	183	1	on	on	ADP
iajs-2877	183	2	some	some	DET
iajs-2877	183	3	topology	topology	NOUN
iajs-2877	183	4	concepts	concept	NOUN
iajs-2877	183	5	via	via	ADP
iajs-2877	183	6	grill	grill	NOUN
iajs-2877	183	7	,	,	PUNCT
iajs-2877	183	8	int	int	NOUN
iajs-2877	183	9	.	.	PUNCT
iajs-2877	184	1	j.	j.	PROPN
iajs-2877	184	2	nonlinear	nonlinear	PROPN
iajs-2877	184	3	anal	anal	PROPN
iajs-2877	184	4	.	.	PUNCT
iajs-2877	185	1	appl	appl	PROPN
iajs-2877	185	2	.	.	PUNCT
iajs-2877	186	1	2022	2022	NUM
iajs-2877	186	2	,	,	PUNCT
iajs-2877	186	3	13	13	NUM
iajs-2877	186	4	1	1	NUM
iajs-2877	186	5	,	,	PUNCT
iajs-2877	186	6	3765	3765	NUM
iajs-2877	186	7	–	–	PUNCT
iajs-2877	186	8	3772	3772	NUM
iajs-2877	186	9	.	.	PUNCT