id	sid	tid	token	lemma	pos
iajs-2878	1	1	ihjpas	ihjpas	PROPN
iajs-2878	1	2	.	.	PUNCT
iajs-2878	2	1	53	53	NUM
iajs-2878	2	2	(	(	PUNCT
iajs-2878	2	3	4)2022	4)2022	NOUN
iajs-2878	2	4	213	213	NUM
iajs-2878	2	5	this	this	DET
iajs-2878	2	6	work	work	NOUN
iajs-2878	2	7	is	be	AUX
iajs-2878	2	8	licensed	license	VERB
iajs-2878	2	9	under	under	ADP
iajs-2878	2	10	a	a	DET
iajs-2878	2	11	creative	creative	ADJ
iajs-2878	2	12	commons	common	NOUN
iajs-2878	2	13	attribution	attribution	NOUN
iajs-2878	2	14	4.0	4.0	NUM
iajs-2878	2	15	international	international	ADJ
iajs-2878	2	16	license	license	NOUN
iajs-2878	2	17	.	.	PUNCT
iajs-2878	3	1	some	some	DET
iajs-2878	3	2	properties	property	NOUN
iajs-2878	3	3	of	of	ADP
iajs-2878	3	4	connectedness	connectedness	NOUN
iajs-2878	3	5	in	in	ADP
iajs-2878	3	6	grill	grill	ADJ
iajs-2878	3	7	topological	topological	ADJ
iajs-2878	3	8	spaces	space	NOUN
iajs-2878	3	9	abstract	abstract	NOUN
iajs-2878	3	10	we	we	PRON
iajs-2878	3	11	use	use	VERB
iajs-2878	3	12	the	the	DET
iajs-2878	3	13	idea	idea	NOUN
iajs-2878	3	14	of	of	ADP
iajs-2878	3	15	grill	grill	NOUN
iajs-2878	3	16	,	,	PUNCT
iajs-2878	3	17	this	this	DET
iajs-2878	3	18	study	study	NOUN
iajs-2878	3	19	generalized	generalize	VERB
iajs-2878	3	20	a	a	DET
iajs-2878	3	21	new	new	ADJ
iajs-2878	3	22	sort	sort	NOUN
iajs-2878	3	23	of	of	ADP
iajs-2878	3	24	linked	link	VERB
iajs-2878	3	25	space	space	NOUN
iajs-2878	3	26	like	like	ADP
iajs-2878	3	27	–	–	PUNCT
iajs-2878	3	28	connected	connected	ADJ
iajs-2878	3	29	–	–	PUNCT
iajs-2878	3	30	hyperconnected	hyperconnecte	VERB
iajs-2878	3	31	and	and	CCONJ
iajs-2878	3	32	investigated	investigate	VERB
iajs-2878	3	33	its	its	PRON
iajs-2878	3	34	features	feature	NOUN
iajs-2878	3	35	,	,	PUNCT
iajs-2878	3	36	as	as	ADV
iajs-2878	3	37	well	well	ADV
iajs-2878	3	38	as	as	ADP
iajs-2878	3	39	the	the	DET
iajs-2878	3	40	relationship	relationship	NOUN
iajs-2878	3	41	between	between	ADP
iajs-2878	3	42	it	it	PRON
iajs-2878	3	43	and	and	CCONJ
iajs-2878	3	44	previously	previously	ADV
iajs-2878	3	45	described	describe	VERB
iajs-2878	3	46	notation	notation	NOUN
iajs-2878	3	47	.	.	PUNCT
iajs-2878	4	1	it	it	PRON
iajs-2878	4	2	also	also	ADV
iajs-2878	4	3	developed	develop	VERB
iajs-2878	4	4	new	new	ADJ
iajs-2878	4	5	sorts	sort	NOUN
iajs-2878	4	6	of	of	ADP
iajs-2878	4	7	functions	function	NOUN
iajs-2878	4	8	,	,	PUNCT
iajs-2878	4	9	such	such	ADJ
iajs-2878	4	10	as	as	ADP
iajs-2878	4	11	hyperconnected	hyperconnecte	VERB
iajs-2878	4	12	space	space	NOUN
iajs-2878	4	13	,	,	PUNCT
iajs-2878	4	14	and	and	CCONJ
iajs-2878	4	15	identifying	identify	VERB
iajs-2878	4	16	their	their	PRON
iajs-2878	4	17	relationship	relationship	NOUN
iajs-2878	4	18	,	,	PUNCT
iajs-2878	4	19	by	by	ADP
iajs-2878	4	20	offering	offer	VERB
iajs-2878	4	21	numerous	numerous	ADJ
iajs-2878	4	22	instance	instance	NOUN
iajs-2878	4	23	and	and	CCONJ
iajs-2878	4	24	attributes	attribute	NOUN
iajs-2878	4	25	that	that	PRON
iajs-2878	4	26	belong	belong	VERB
iajs-2878	4	27	to	to	ADP
iajs-2878	4	28	this	this	DET
iajs-2878	4	29	set	set	NOUN
iajs-2878	4	30	.	.	PUNCT
iajs-2878	5	1	this	this	DET
iajs-2878	5	2	set	set	NOUN
iajs-2878	5	3	will	will	AUX
iajs-2878	5	4	serve	serve	VERB
iajs-2878	5	5	as	as	ADP
iajs-2878	5	6	a	a	DET
iajs-2878	5	7	starting	starting	NOUN
iajs-2878	5	8	point	point	NOUN
iajs-2878	5	9	for	for	ADP
iajs-2878	5	10	further	further	ADJ
iajs-2878	5	11	research	research	NOUN
iajs-2878	5	12	into	into	ADP
iajs-2878	5	13	the	the	DET
iajs-2878	5	14	sets	set	NOUN
iajs-2878	5	15	many	many	ADJ
iajs-2878	5	16	future	future	ADJ
iajs-2878	5	17	possibilities	possibility	NOUN
iajs-2878	5	18	.	.	PUNCT
iajs-2878	6	1	also	also	ADV
iajs-2878	6	2	,	,	PUNCT
iajs-2878	6	3	we	we	PRON
iajs-2878	6	4	use	use	VERB
iajs-2878	6	5	some	some	PRON
iajs-2878	6	6	of	of	ADP
iajs-2878	6	7	the	the	DET
iajs-2878	6	8	theorems	theorem	NOUN
iajs-2878	6	9	and	and	CCONJ
iajs-2878	6	10	observations	observation	NOUN
iajs-2878	6	11	previously	previously	ADV
iajs-2878	6	12	studied	study	VERB
iajs-2878	6	13	and	and	CCONJ
iajs-2878	6	14	relate	relate	VERB
iajs-2878	6	15	them	they	PRON
iajs-2878	6	16	to	to	ADP
iajs-2878	6	17	the	the	DET
iajs-2878	6	18	grill	grill	NOUN
iajs-2878	6	19	and	and	CCONJ
iajs-2878	6	20	the	the	DET
iajs-2878	6	21	alpha	alpha	NOUN
iajs-2878	6	22	group	group	NOUN
iajs-2878	6	23	,	,	PUNCT
iajs-2878	6	24	and	and	CCONJ
iajs-2878	6	25	benefit	benefit	VERB
iajs-2878	6	26	from	from	ADP
iajs-2878	6	27	them	they	PRON
iajs-2878	6	28	in	in	ADP
iajs-2878	6	29	order	order	NOUN
iajs-2878	6	30	to	to	PART
iajs-2878	6	31	obtain	obtain	VERB
iajs-2878	6	32	new	new	ADJ
iajs-2878	6	33	results	result	NOUN
iajs-2878	6	34	in	in	ADP
iajs-2878	6	35	this	this	DET
iajs-2878	6	36	research	research	NOUN
iajs-2878	6	37	.	.	PUNCT
iajs-2878	7	1	we	we	PRON
iajs-2878	7	2	applied	apply	VERB
iajs-2878	7	3	the	the	DET
iajs-2878	7	4	concept	concept	NOUN
iajs-2878	7	5	of	of	ADP
iajs-2878	7	6	connected	connect	VERB
iajs-2878	7	7	to	to	ADP
iajs-2878	7	8	them	they	PRON
iajs-2878	7	9	and	and	CCONJ
iajs-2878	7	10	obtained	obtain	VERB
iajs-2878	7	11	results	result	NOUN
iajs-2878	7	12	related	relate	VERB
iajs-2878	7	13	to	to	AUX
iajs-2878	7	14	connected	connect	VERB
iajs-2878	7	15	.	.	PUNCT
iajs-2878	8	1	the	the	DET
iajs-2878	8	2	sources	source	NOUN
iajs-2878	8	3	related	relate	VERB
iajs-2878	8	4	to	to	ADP
iajs-2878	8	5	the	the	DET
iajs-2878	8	6	connected	connected	ADJ
iajs-2878	8	7	and	and	CCONJ
iajs-2878	8	8	alpha	alpha	NOUN
iajs-2878	8	9	were	be	AUX
iajs-2878	8	10	considered	consider	VERB
iajs-2878	8	11	as	as	ADP
iajs-2878	8	12	starting	start	VERB
iajs-2878	8	13	points	point	NOUN
iajs-2878	8	14	and	and	CCONJ
iajs-2878	8	15	an	an	DET
iajs-2878	8	16	important	important	ADJ
iajs-2878	8	17	basis	basis	NOUN
iajs-2878	8	18	in	in	ADP
iajs-2878	8	19	this	this	DET
iajs-2878	8	20	research	research	NOUN
iajs-2878	8	21	.	.	PUNCT
iajs-2878	9	1	keywords	keyword	NOUN
iajs-2878	9	2	:	:	PUNCT
iajs-2878	9	3	grill	grill	ADJ
iajs-2878	9	4	,	,	PUNCT
iajs-2878	9	5	₢	₢	ADP
iajs-2878	9	6	*	*	PUNCT
iajs-2878	9	7	𝛼-connected	𝛼-connecte	VERB
iajs-2878	9	8	,	,	PUNCT
iajs-2878	9	9	₢	₢	ADP
iajs-2878	9	10	*	*	X
iajs-2878	9	11	𝛼-𝑑𝑖𝑠connected	𝛼-𝑑𝑖𝑠connecte	VERB
iajs-2878	9	12	,	,	PUNCT
iajs-2878	9	13	₢	₢	ADP
iajs-2878	9	14	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	9	15	)	)	PUNCT
iajs-2878	9	16	,	,	PUNCT
iajs-2878	9	17	₢	₢	ADP
iajs-2878	9	18	∗	∗	X
iajs-2878	9	19	𝛼	𝛼	X
iajs-2878	9	20	-open	-open	NOUN
iajs-2878	9	21	.	.	PUNCT
iajs-2878	10	1	1	1	NUM
iajs-2878	10	2	.	.	X
iajs-2878	10	3	introduction	introduction	NOUN
iajs-2878	11	1	[	[	X
iajs-2878	11	2	1	1	NUM
iajs-2878	11	3	]	]	PUNCT
iajs-2878	11	4	,	,	PUNCT
iajs-2878	11	5	[	[	X
iajs-2878	11	6	2	2	NUM
iajs-2878	11	7	]	]	PUNCT
iajs-2878	11	8	established	establish	VERB
iajs-2878	11	9	a	a	DET
iajs-2878	11	10	grill	grill	NOUN
iajs-2878	11	11	notion	notion	NOUN
iajs-2878	11	12	in	in	ADP
iajs-2878	11	13	a	a	DET
iajs-2878	11	14	topological	topological	ADJ
iajs-2878	11	15	space	space	NOUN
iajs-2878	11	16	,	,	PUNCT
iajs-2878	11	17	and	and	CCONJ
iajs-2878	11	18	the	the	DET
iajs-2878	11	19	grill	grill	NOUN
iajs-2878	11	20	has	have	AUX
iajs-2878	11	21	shown	show	VERB
iajs-2878	11	22	to	to	PART
iajs-2878	11	23	be	be	AUX
iajs-2878	11	24	an	an	DET
iajs-2878	11	25	effective	effective	ADJ
iajs-2878	11	26	tool	tool	NOUN
iajs-2878	11	27	for	for	ADP
iajs-2878	11	28	learning	learn	VERB
iajs-2878	11	29	a	a	DET
iajs-2878	11	30	variety	variety	NOUN
iajs-2878	11	31	of	of	ADP
iajs-2878	11	32	topological	topological	ADJ
iajs-2878	11	33	concerns	concern	NOUN
iajs-2878	11	34	.	.	PUNCT
iajs-2878	12	1	a	a	DET
iajs-2878	12	2	subset	subset	NOUN
iajs-2878	12	3	of	of	ADP
iajs-2878	12	4	a	a	DET
iajs-2878	12	5	topological	topological	ADJ
iajs-2878	12	6	space	space	NOUN
iajs-2878	12	7	(	(	PUNCT
iajs-2878	12	8	ꝡ	ꝡ	NOUN
iajs-2878	12	9	,	,	PUNCT
iajs-2878	12	10	𝜏	𝜏	NOUN
iajs-2878	12	11	)	)	PUNCT
iajs-2878	12	12	which	which	PRON
iajs-2878	12	13	is	be	AUX
iajs-2878	12	14	a	a	DET
iajs-2878	12	15	non	non	ADJ
iajs-2878	12	16	-	-	ADJ
iajs-2878	12	17	empty	empty	ADJ
iajs-2878	12	18	collection	collection	NOUN
iajs-2878	12	19	₢	₢	PROPN
iajs-2878	12	20	is	be	AUX
iajs-2878	12	21	referred	refer	VERB
iajs-2878	12	22	to	to	PART
iajs-2878	12	23	be	be	AUX
iajs-2878	12	24	a	a	DET
iajs-2878	12	25	grill	grill	NOUN
iajs-2878	12	26	whenever	whenever	SCONJ
iajs-2878	12	27	(	(	PUNCT
iajs-2878	12	28	a	a	NOUN
iajs-2878	12	29	)	)	PUNCT
iajs-2878	12	30	ⱥ	ⱥ	NOUN
iajs-2878	12	31	∈₢	∈₢	NOUN
iajs-2878	12	32	and	and	CCONJ
iajs-2878	12	33	ⱥ	ⱥ	X
iajs-2878	12	34	⊆	⊆	NUM
iajs-2878	12	35	ӎ	ӎ	X
iajs-2878	12	36	implying	imply	VERB
iajs-2878	12	37	ɓ∈₢.	ɓ∈₢.	NOUN
iajs-2878	12	38	(	(	PUNCT
iajs-2878	12	39	b	b	NOUN
iajs-2878	12	40	)	)	PUNCT
iajs-2878	12	41	ꝡ	ꝡ	PROPN
iajs-2878	12	42	has	have	VERB
iajs-2878	12	43	a	a	DET
iajs-2878	12	44	subset	subset	NOUN
iajs-2878	12	45	ⱥ	ⱥ	X
iajs-2878	12	46	and	and	CCONJ
iajs-2878	12	47	ӎ	ӎ	X
iajs-2878	12	48	also	also	ADV
iajs-2878	12	49	ⱥ	ⱥ	X
iajs-2878	12	50	∪	∪	X
iajs-2878	12	51	ɓ∈₢	ɓ∈₢	NUM
iajs-2878	12	52	lead	lead	VERB
iajs-2878	12	53	to	to	ADP
iajs-2878	12	54	ⱥ	ⱥ	PROPN
iajs-2878	12	55	∈₢	∈₢	NOUN
iajs-2878	12	56	or	or	CCONJ
iajs-2878	12	57	ɓ∈₢.	ɓ∈₢.	PROPN
iajs-2878	12	58	a	a	DET
iajs-2878	12	59	triple	triple	ADJ
iajs-2878	12	60	(	(	PUNCT
iajs-2878	12	61	ꝡ	ꝡ	NOUN
iajs-2878	12	62	,	,	PUNCT
iajs-2878	12	63	𝜏	𝜏	NOUN
iajs-2878	12	64	,	,	PUNCT
iajs-2878	12	65	₢	₢	ADP
iajs-2878	12	66	)	)	PUNCT
iajs-2878	12	67	topological	topological	ADJ
iajs-2878	12	68	space	space	NOUN
iajs-2878	12	69	with	with	ADP
iajs-2878	12	70	grills	grill	NOUN
iajs-2878	12	71	is	be	AUX
iajs-2878	12	72	one	one	NUM
iajs-2878	12	73	type	type	NOUN
iajs-2878	12	74	of	of	ADP
iajs-2878	12	75	topological	topological	ADJ
iajs-2878	12	76	space	space	NOUN
iajs-2878	12	77	.	.	PUNCT
iajs-2878	13	1	mukherjee	mukherjee	PROPN
iajs-2878	13	2	and	and	CCONJ
iajs-2878	13	3	roy	roy	PROPN
iajs-2878	14	1	[	[	X
iajs-2878	14	2	3	3	NUM
iajs-2878	14	3	]	]	PUNCT
iajs-2878	14	4	created	create	VERB
iajs-2878	14	5	a	a	DET
iajs-2878	14	6	distinctive	distinctive	ADJ
iajs-2878	14	7	topology	topology	NOUN
iajs-2878	14	8	with	with	ADP
iajs-2878	14	9	a	a	DET
iajs-2878	14	10	grill	grill	NOUN
iajs-2878	14	11	and	and	CCONJ
iajs-2878	14	12	investigated	investigate	VERB
iajs-2878	14	13	topological	topological	ADJ
iajs-2878	14	14	notions	notion	NOUN
iajs-2878	14	15	.	.	PUNCT
iajs-2878	15	1	for	for	ADP
iajs-2878	15	2	every	every	DET
iajs-2878	15	3	topological	topological	ADJ
iajs-2878	15	4	space	space	NOUN
iajs-2878	15	5	(	(	PUNCT
iajs-2878	15	6	ꝡ	ꝡ	NOUN
iajs-2878	15	7	,	,	PUNCT
iajs-2878	15	8	𝜏	𝜏	NOUN
iajs-2878	15	9	)	)	PUNCT
iajs-2878	15	10	point	point	NOUN
iajs-2878	15	11	ꝡ	ꝡ	PROPN
iajs-2878	15	12	,	,	PUNCT
iajs-2878	15	13	neighborhoods	neighborhood	NOUN
iajs-2878	15	14	are	be	AUX
iajs-2878	15	15	open	open	ADJ
iajs-2878	15	16	of	of	ADP
iajs-2878	15	17	ꝡ	ꝡ	NOUN
iajs-2878	15	18	embodied	embodied	ADJ
iajs-2878	15	19	doi	doi	NOUN
iajs-2878	15	20	:	:	PUNCT
iajs-2878	15	21	10.30526/35.4.2878	10.30526/35.4.2878	ADJ
iajs-2878	15	22	article	article	NOUN
iajs-2878	15	23	history	history	NOUN
iajs-2878	15	24	:	:	PUNCT
iajs-2878	15	25	received	receive	VERB
iajs-2878	15	26	12	12	NUM
iajs-2878	15	27	june	june	PROPN
iajs-2878	15	28	2022	2022	NUM
iajs-2878	15	29	,	,	PUNCT
iajs-2878	15	30	accepted	accept	VERB
iajs-2878	15	31	21	21	NUM
iajs-2878	15	32	august	august	PROPN
iajs-2878	15	33	2022	2022	NUM
iajs-2878	15	34	,	,	PUNCT
iajs-2878	15	35	published	publish	VERB
iajs-2878	15	36	in	in	ADP
iajs-2878	15	37	october	october	PROPN
iajs-2878	15	38	2022	2022	NUM
iajs-2878	15	39	.	.	PUNCT
iajs-2878	16	1	ibn	ibn	PROPN
iajs-2878	16	2	al	al	PROPN
iajs-2878	16	3	haitham	haitham	PROPN
iajs-2878	16	4	journal	journal	PROPN
iajs-2878	16	5	for	for	ADP
iajs-2878	16	6	pure	pure	ADJ
iajs-2878	16	7	and	and	CCONJ
iajs-2878	16	8	applied	applied	ADJ
iajs-2878	16	9	sciences	sciences	PROPN
iajs-2878	16	10	journal	journal	PROPN
iajs-2878	16	11	homepage	homepage	NOUN
iajs-2878	16	12	:	:	PUNCT
iajs-2878	16	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2878	16	14	saad	saad	PROPN
iajs-2878	16	15	s.	s.	PROPN
iajs-2878	16	16	suliman	suliman	PROPN
iajs-2878	16	17	department	department	PROPN
iajs-2878	16	18	of	of	ADP
iajs-2878	16	19	mathematics	mathematics	PROPN
iajs-2878	16	20	,	,	PUNCT
iajs-2878	16	21	college	college	NOUN
iajs-2878	16	22	of	of	ADP
iajs-2878	16	23	education	education	NOUN
iajs-2878	16	24	for	for	ADP
iajs-2878	16	25	pure	pure	ADJ
iajs-2878	16	26	science	science	NOUN
iajs-2878	16	27	,	,	PUNCT
iajs-2878	16	28	ibn	ibn	PROPN
iajs-2878	16	29	al	al	PROPN
iajs-2878	16	30	haitham	haitham	PROPN
iajs-2878	16	31	,	,	PUNCT
iajs-2878	16	32	university	university	PROPN
iajs-2878	16	33	of	of	ADP
iajs-2878	16	34	baghdad	baghdad	PROPN
iajs-2878	16	35	,	,	PUNCT
iajs-2878	16	36	iraq	iraq	PROPN
iajs-2878	16	37	.	.	PUNCT
iajs-2878	17	1	saadsadeq05@gmail.com	saadsadeq05@gmail.com	X
iajs-2878	17	2	esmaeel	esmaeel	NOUN
iajs-2878	17	3	r.b	r.b	PROPN
iajs-2878	17	4	.	.	PROPN
iajs-2878	17	5	department	department	PROPN
iajs-2878	17	6	of	of	ADP
iajs-2878	17	7	mathematics	mathematics	PROPN
iajs-2878	17	8	,	,	PUNCT
iajs-2878	17	9	college	college	NOUN
iajs-2878	17	10	of	of	ADP
iajs-2878	17	11	education	education	NOUN
iajs-2878	17	12	for	for	ADP
iajs-2878	17	13	pure	pure	ADJ
iajs-2878	17	14	science	science	NOUN
iajs-2878	17	15	,	,	PUNCT
iajs-2878	17	16	ibn	ibn	PROPN
iajs-2878	17	17	al	al	PROPN
iajs-2878	17	18	haitham	haitham	PROPN
iajs-2878	17	19	,	,	PUNCT
iajs-2878	17	20	university	university	PROPN
iajs-2878	17	21	of	of	ADP
iajs-2878	17	22	baghdad	baghdad	PROPN
iajs-2878	17	23	,	,	PUNCT
iajs-2878	17	24	iraq	iraq	PROPN
iajs-2878	17	25	.	.	PUNCT
iajs-2878	18	1	ranamumosa@yahoo.com	ranamumosa@yahoo.com	X
iajs-2878	18	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2878	19	1	mailto:saadsadeq05@gmail.com	mailto:saadsadeq05@gmail.com	PROPN
iajs-2878	19	2	mailto:ranamumosa@yahoo.com	mailto:ranamumosa@yahoo.com	PROPN
iajs-2878	19	3	ihjpas	ihjpas	PROPN
iajs-2878	19	4	.	.	PUNCT
iajs-2878	20	1	53	53	NUM
iajs-2878	20	2	(	(	PUNCT
iajs-2878	20	3	4)2022	4)2022	NOUN
iajs-2878	20	4	214	214	NUM
iajs-2878	20	5	by	by	ADP
iajs-2878	20	6	𝜏(ꝡ	𝜏(ꝡ	NOUN
iajs-2878	20	7	)	)	PUNCT
iajs-2878	20	8	.	.	PUNCT
iajs-2878	21	1	a	a	DET
iajs-2878	21	2	mapping	mapping	NOUN
iajs-2878	21	3	ѱ:ℙ(ꝡ	ѱ:ℙ(ꝡ	NOUN
iajs-2878	21	4	)	)	PUNCT
iajs-2878	21	5	→	→	SYM
iajs-2878	21	6	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	21	7	)	)	PUNCT
iajs-2878	21	8	is	be	AUX
iajs-2878	21	9	referred	refer	VERB
iajs-2878	21	10	to	to	ADP
iajs-2878	21	11	as	as	ADP
iajs-2878	21	12	∮	∮	NUM
iajs-2878	21	13	(	(	PUNCT
iajs-2878	21	14	ⱥ	ⱥ	X
iajs-2878	21	15	)	)	PUNCT
iajs-2878	21	16	=	=	SYM
iajs-2878	21	17	{	{	PUNCT
iajs-2878	21	18	ꝡ	ꝡ	PROPN
iajs-2878	21	19	∈	∈	PROPN
iajs-2878	21	20	ꝡ	ꝡ	PROPN
iajs-2878	21	21	:	:	PUNCT
iajs-2878	21	22	ⱥ	ⱥ	X
iajs-2878	21	23	∩	∩	X
iajs-2878	21	24	ữ	ữ	ADP
iajs-2878	21	25	∈	∈	PROPN
iajs-2878	21	26	₢	₢	ADP
iajs-2878	21	27	apiece	apiece	ADP
iajs-2878	21	28	ữ	ữ	PROPN
iajs-2878	21	29	∈	∈	PROPN
iajs-2878	21	30	τ(ꝡ	τ(ꝡ	PROPN
iajs-2878	21	31	)	)	PUNCT
iajs-2878	21	32	}	}	PUNCT
iajs-2878	21	33	for	for	ADP
iajs-2878	21	34	every	every	DET
iajs-2878	21	35	ⱥ	ⱥ	PROPN
iajs-2878	21	36	∈	∈	PROPN
iajs-2878	21	37	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	21	38	)	)	PUNCT
iajs-2878	21	39	.	.	PUNCT
iajs-2878	22	1	a	a	DET
iajs-2878	22	2	mapping	mapping	NOUN
iajs-2878	22	3	ѱ	ѱ	NOUN
iajs-2878	22	4	:	:	PUNCT
iajs-2878	22	5	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	22	6	)	)	PUNCT
iajs-2878	22	7	→ℙ(ꝡ	→ℙ(ꝡ	NOUN
iajs-2878	22	8	)	)	PUNCT
iajs-2878	22	9	is	be	AUX
iajs-2878	22	10	referred	refer	VERB
iajs-2878	22	11	to	to	ADP
iajs-2878	22	12	as	as	ADP
iajs-2878	22	13	ѱ	ѱ	PROPN
iajs-2878	22	14	(	(	PUNCT
iajs-2878	22	15	ⱥ	ⱥ	X
iajs-2878	22	16	)	)	PUNCT
iajs-2878	22	17	=	=	PUNCT
iajs-2878	22	18	ⱥ	ⱥ	X
iajs-2878	22	19	∪	∪	VERB
iajs-2878	22	20	∮	∮	PRON
iajs-2878	22	21	(	(	PUNCT
iajs-2878	22	22	ⱥ	ⱥ	X
iajs-2878	22	23	)	)	PUNCT
iajs-2878	22	24	for	for	ADP
iajs-2878	22	25	every	every	DET
iajs-2878	22	26	ⱥ	ⱥ	PROPN
iajs-2878	22	27	∈	∈	PROPN
iajs-2878	22	28	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	22	29	)	)	PUNCT
iajs-2878	22	30	.	.	PUNCT
iajs-2878	23	1	the	the	DET
iajs-2878	23	2	map	map	NOUN
iajs-2878	23	3	ѱ	ѱ	PROPN
iajs-2878	23	4	kuratowski	kuratowski	PROPN
iajs-2878	23	5	closure	closure	NOUN
iajs-2878	23	6	axioms	axiom	NOUN
iajs-2878	23	7	are	be	AUX
iajs-2878	23	8	met	meet	VERB
iajs-2878	23	9	:	:	PUNCT
iajs-2878	23	10	(	(	PUNCT
iajs-2878	23	11	𝑎	𝑎	NOUN
iajs-2878	23	12	)	)	PUNCT
iajs-2878	23	13	ѱ	ѱ	NOUN
iajs-2878	23	14	(	(	PUNCT
iajs-2878	23	15	∅	∅	NOUN
iajs-2878	23	16	)	)	PUNCT
iajs-2878	23	17	=	=	NOUN
iajs-2878	23	18	∅	∅	NOUN
iajs-2878	23	19	,	,	PUNCT
iajs-2878	23	20	(	(	PUNCT
iajs-2878	23	21	𝑏	𝑏	NOUN
iajs-2878	23	22	)	)	PUNCT
iajs-2878	23	23	𝑤ℎ𝑒𝑛	𝑤ℎ𝑒𝑛	VERB
iajs-2878	23	24	ⱥ	ⱥ	PROPN
iajs-2878	23	25	⊆	⊆	NUM
iajs-2878	23	26	ɓ	ɓ	NOUN
iajs-2878	23	27	,	,	PUNCT
iajs-2878	23	28	𝑠𝑜	𝑠𝑜	INTJ
iajs-2878	23	29	ѱ	ѱ	PROPN
iajs-2878	23	30	(	(	PUNCT
iajs-2878	23	31	ⱥ	ⱥ	X
iajs-2878	23	32	)	)	PUNCT
iajs-2878	23	33	⊆	⊆	NUM
iajs-2878	23	34	ѱ	ѱ	NOUN
iajs-2878	23	35	(	(	PUNCT
iajs-2878	23	36	ɓ	ɓ	NOUN
iajs-2878	23	37	)	)	PUNCT
iajs-2878	23	38	,	,	PUNCT
iajs-2878	23	39	(	(	PUNCT
iajs-2878	23	40	𝑐	𝑐	X
iajs-2878	23	41	)	)	PUNCT
iajs-2878	23	42	𝑤ℎ𝑒𝑛	𝑤ℎ𝑒𝑛	VERB
iajs-2878	23	43	ⱥ	ⱥ	PROPN
iajs-2878	23	44	⊆	⊆	NUM
iajs-2878	23	45	ꝡ	ꝡ	PROPN
iajs-2878	23	46	,	,	PUNCT
iajs-2878	23	47	𝑠𝑜	𝑠𝑜	ADP
iajs-2878	23	48	ѱ	ѱ	PROPN
iajs-2878	23	49	(	(	PUNCT
iajs-2878	23	50	ѱ	ѱ	PROPN
iajs-2878	23	51	(	(	PUNCT
iajs-2878	23	52	ⱥ	ⱥ	NOUN
iajs-2878	23	53	)	)	PUNCT
iajs-2878	23	54	)	)	PUNCT
iajs-2878	24	1	=	=	SYM
iajs-2878	24	2	ѱ	ѱ	PROPN
iajs-2878	24	3	(	(	PUNCT
iajs-2878	24	4	ⱥ	ⱥ	PROPN
iajs-2878	24	5	)	)	PUNCT
iajs-2878	24	6	,	,	PUNCT
iajs-2878	24	7	(	(	PUNCT
iajs-2878	24	8	𝑑	𝑑	NOUN
iajs-2878	24	9	)	)	PUNCT
iajs-2878	24	10	𝑤ℎ𝑒𝑛	𝑤ℎ𝑒𝑛	VERB
iajs-2878	24	11	ⱥ	ⱥ	PRON
iajs-2878	24	12	,	,	PUNCT
iajs-2878	24	13	ɓ	ɓ	PRON
iajs-2878	24	14	⊆	⊆	NUM
iajs-2878	24	15	ꝡ	ꝡ	NOUN
iajs-2878	24	16	,	,	PUNCT
iajs-2878	24	17	𝑠𝑜	𝑠𝑜	ADP
iajs-2878	24	18	ѱ	ѱ	PROPN
iajs-2878	24	19	(	(	PUNCT
iajs-2878	24	20	ⱥ	ⱥ	X
iajs-2878	24	21	∪	∪	X
iajs-2878	24	22	ɓ	ɓ	PROPN
iajs-2878	24	23	)	)	PUNCT
iajs-2878	24	24	=	=	SYM
iajs-2878	24	25	ѱ	ѱ	PROPN
iajs-2878	24	26	(	(	PUNCT
iajs-2878	24	27	ⱥ	ⱥ	X
iajs-2878	24	28	)	)	PUNCT
iajs-2878	24	29	∪	∪	PROPN
iajs-2878	24	30	ѱ	ѱ	PROPN
iajs-2878	24	31	(	(	PUNCT
iajs-2878	24	32	ɓ	ɓ	NOUN
iajs-2878	24	33	)	)	PUNCT
iajs-2878	24	34	.	.	PUNCT
iajs-2878	25	1	grill	grill	PROPN
iajs-2878	25	2	topological	topological	ADJ
iajs-2878	25	3	spaces	space	NOUN
iajs-2878	25	4	come	come	VERB
iajs-2878	25	5	in	in	ADP
iajs-2878	25	6	a	a	DET
iajs-2878	25	7	variety	variety	NOUN
iajs-2878	25	8	of	of	ADP
iajs-2878	25	9	shapes	shape	NOUN
iajs-2878	25	10	and	and	CCONJ
iajs-2878	25	11	size	size	NOUN
iajs-2878	25	12	as	as	ADP
iajs-2878	25	13	a	a	DET
iajs-2878	25	14	discrete	discrete	ADJ
iajs-2878	25	15	topology	topology	NOUN
iajs-2878	25	16	and	and	CCONJ
iajs-2878	25	17	a	a	DET
iajs-2878	25	18	complement	complement	NOUN
iajs-2878	25	19	finite	finite	NOUN
iajs-2878	25	20	topology	topology	NOUN
iajs-2878	25	21	.	.	PUNCT
iajs-2878	26	1	[	[	X
iajs-2878	26	2	4	4	X
iajs-2878	26	3	]	]	X
iajs-2878	26	4	[	[	X
iajs-2878	26	5	5	5	NUM
iajs-2878	26	6	]	]	PUNCT
iajs-2878	26	7	on	on	ADP
iajs-2878	26	8	a	a	DET
iajs-2878	26	9	space	space	NOUN
iajs-2878	26	10	(	(	PUNCT
iajs-2878	26	11	ꝡ	ꝡ	NOUN
iajs-2878	26	12	,	,	PUNCT
iajs-2878	26	13	𝜏	𝜏	NOUN
iajs-2878	26	14	)	)	PUNCT
iajs-2878	26	15	,	,	PUNCT
iajs-2878	26	16	this	this	PRON
iajs-2878	26	17	agrees	agree	VERB
iajs-2878	26	18	to	to	ADP
iajs-2878	26	19	a	a	DET
iajs-2878	26	20	grill	grill	NOUN
iajs-2878	26	21	₢	₢	ADP
iajs-2878	26	22	a	a	DET
iajs-2878	26	23	topology	topology	NOUN
iajs-2878	26	24	exists	exist	VERB
iajs-2878	26	25	𝜏₢	𝜏₢	NOUN
iajs-2878	26	26	on	on	ADP
iajs-2878	26	27	ꝡ	ꝡ	PROPN
iajs-2878	26	28	that	that	PRON
iajs-2878	26	29	is	be	AUX
iajs-2878	26	30	given	give	VERB
iajs-2878	26	31	by	by	ADP
iajs-2878	26	32	no	no	DET
iajs-2878	26	33	one	one	NOUN
iajs-2878	26	34	else	else	ADV
iajs-2878	26	35	by	by	ADP
iajs-2878	26	36	𝜏₢	𝜏₢	X
iajs-2878	26	37	=	=	PUNCT
iajs-2878	26	38	{	{	PUNCT
iajs-2878	26	39	ữ	ữ	NOUN
iajs-2878	26	40	⊆ꝡ	⊆ꝡ	X
iajs-2878	26	41	:	:	PUNCT
iajs-2878	26	42	ѱ	ѱ	PROPN
iajs-2878	26	43	(	(	PUNCT
iajs-2878	26	44	ꝡ	ꝡ	PROPN
iajs-2878	26	45	–	–	PUNCT
iajs-2878	26	46	ữ	ữ	NOUN
iajs-2878	26	47	)	)	PUNCT
iajs-2878	26	48	=	=	SYM
iajs-2878	26	49	ꝡ	ꝡ	PROPN
iajs-2878	26	50	–	–	PUNCT
iajs-2878	26	51	ữ	ữ	NOUN
iajs-2878	26	52	}	}	PUNCT
iajs-2878	26	53	,	,	PUNCT
iajs-2878	26	54	consequently	consequently	ADV
iajs-2878	26	55	,	,	PUNCT
iajs-2878	26	56	ⱥ	ⱥ	PROPN
iajs-2878	26	57	⊆	⊆	NUM
iajs-2878	26	58	ꝡ	ꝡ	PROPN
iajs-2878	26	59	,	,	PUNCT
iajs-2878	26	60	ѱ	ѱ	PROPN
iajs-2878	26	61	(	(	PUNCT
iajs-2878	26	62	ⱥ	ⱥ	X
iajs-2878	26	63	)	)	PUNCT
iajs-2878	26	64	=	=	SYM
iajs-2878	26	65	ⱥ	ⱥ	X
iajs-2878	26	66	∪	∪	ADP
iajs-2878	26	67	∮	∮	PRON
iajs-2878	26	68	(	(	PUNCT
iajs-2878	26	69	ⱥ	ⱥ	NOUN
iajs-2878	26	70	)	)	PUNCT
iajs-2878	26	71	.	.	PUNCT
iajs-2878	27	1	τ	τ	PROPN
iajs-2878	27	2	⊆	⊆	NUM
iajs-2878	27	3	𝜏₢	𝜏₢	PROPN
iajs-2878	27	4	and	and	CCONJ
iajs-2878	27	5	ѱ	ѱ	PROPN
iajs-2878	27	6	(	(	PUNCT
iajs-2878	27	7	ⱥ	ⱥ	X
iajs-2878	27	8	)	)	PUNCT
iajs-2878	27	9	=	=	SYM
iajs-2878	27	10	𝑐𝜄(ⱥ	𝑐𝜄(ⱥ	X
iajs-2878	27	11	)	)	PUNCT
iajs-2878	27	12	.	.	PUNCT
iajs-2878	28	1	using	use	VERB
iajs-2878	28	2	the	the	DET
iajs-2878	28	3	following	following	NOUN
iajs-2878	28	4	as	as	ADP
iajs-2878	28	5	a	a	DET
iajs-2878	28	6	basis	basis	NOUN
iajs-2878	28	7	,	,	PUNCT
iajs-2878	28	8	we	we	PRON
iajs-2878	28	9	are	be	AUX
iajs-2878	28	10	able	able	ADJ
iajs-2878	28	11	to	to	PART
iajs-2878	28	12	locate	locate	VERB
iajs-2878	28	13	𝜏₢	𝜏₢	PROPN
iajs-2878	28	14	on	on	ADP
iajs-2878	28	15	ꝡ	ꝡ	NOUN
iajs-2878	28	16	by	by	ADP
iajs-2878	28	17	supplying	supply	VERB
iajs-2878	28	18	𝜏₢	𝜏₢	NOUN
iajs-2878	28	19	through	through	ADP
iajs-2878	28	20	using	use	VERB
iajs-2878	28	21	the	the	DET
iajs-2878	28	22	following	following	NOUN
iajs-2878	28	23	as	as	ADP
iajs-2878	28	24	a	a	DET
iajs-2878	28	25	basis	basis	NOUN
iajs-2878	28	26	𝛽	𝛽	PROPN
iajs-2878	28	27	(	(	PUNCT
iajs-2878	28	28	𝜏₢	𝜏₢	PROPN
iajs-2878	28	29	,	,	PUNCT
iajs-2878	28	30	ꝡ	ꝡ	NOUN
iajs-2878	28	31	)	)	PUNCT
iajs-2878	28	32	=	=	PUNCT
iajs-2878	28	33	{	{	PUNCT
iajs-2878	28	34	ƴ	ƴ	PROPN
iajs-2878	28	35	−	−	NOUN
iajs-2878	28	36	ⱥ	ⱥ	NOUN
iajs-2878	28	37	;	;	PUNCT
iajs-2878	28	38	ƴ	ƴ	PROPN
iajs-2878	28	39	∈	∈	PROPN
iajs-2878	28	40	𝜏	𝜏	PROPN
iajs-2878	28	41	,	,	PUNCT
iajs-2878	28	42	ⱥ	ⱥ	X
iajs-2878	28	43	∉	∉	PROPN
iajs-2878	28	44	₢	₢	ADP
iajs-2878	28	45	}	}	PUNCT
iajs-2878	28	46	.	.	PUNCT
iajs-2878	29	1	[	[	X
iajs-2878	29	2	6	6	NUM
iajs-2878	29	3	]	]	PUNCT
iajs-2878	29	4	.	.	PUNCT
iajs-2878	30	1	on	on	ADP
iajs-2878	30	2	a	a	DET
iajs-2878	30	3	space	space	NOUN
iajs-2878	30	4	(	(	PUNCT
iajs-2878	30	5	ꝡ	ꝡ	NOUN
iajs-2878	30	6	,	,	PUNCT
iajs-2878	30	7	𝜏	𝜏	NOUN
iajs-2878	30	8	)	)	PUNCT
iajs-2878	30	9	,	,	PUNCT
iajs-2878	30	10	there	there	PRON
iajs-2878	30	11	is	be	VERB
iajs-2878	30	12	a	a	DET
iajs-2878	30	13	grill	grill	NOUN
iajs-2878	30	14	₢	₢	ADP
iajs-2878	30	15	,	,	PUNCT
iajs-2878	30	16	𝜏	𝜏	PROPN
iajs-2878	30	17	⊆	⊆	NUM
iajs-2878	30	18	𝛽(₢	𝛽(₢	PROPN
iajs-2878	30	19	,	,	PUNCT
iajs-2878	30	20	τ	τ	PROPN
iajs-2878	30	21	)	)	PUNCT
iajs-2878	30	22	⊆	⊆	NUM
iajs-2878	30	23	𝜏₢	𝜏₢	NOUN
iajs-2878	30	24	,	,	PUNCT
iajs-2878	30	25	where	where	SCONJ
iajs-2878	30	26	𝛽(₢	𝛽(₢	PROPN
iajs-2878	30	27	,	,	PUNCT
iajs-2878	30	28	τ	τ	NOUN
iajs-2878	30	29	)	)	PUNCT
iajs-2878	30	30	basis	basis	NOUN
iajs-2878	30	31	for	for	ADP
iajs-2878	30	32	𝜏₢.	𝜏₢.	NOUN
iajs-2878	30	33	as	as	ADP
iajs-2878	30	34	an	an	DET
iajs-2878	30	35	example	example	NOUN
iajs-2878	30	36	,	,	PUNCT
iajs-2878	30	37	[	[	X
iajs-2878	30	38	7	7	X
iajs-2878	30	39	]	]	PUNCT
iajs-2878	30	40	to	to	PART
iajs-2878	30	41	exist	exist	VERB
iajs-2878	30	42	in	in	ADP
iajs-2878	30	43	a	a	DET
iajs-2878	30	44	space	space	NOUN
iajs-2878	30	45	(	(	PUNCT
iajs-2878	30	46	ꝡ	ꝡ	NOUN
iajs-2878	30	47	,	,	PUNCT
iajs-2878	30	48	𝜏	𝜏	NOUN
iajs-2878	30	49	)	)	PUNCT
iajs-2878	30	50	,	,	PUNCT
iajs-2878	30	51	𝜏₢	𝜏₢	X
iajs-2878	30	52	=	=	NOUN
iajs-2878	30	53	𝜏	𝜏	X
iajs-2878	30	54	whenever	whenever	SCONJ
iajs-2878	30	55	₢	₢	X
iajs-2878	30	56	=	=	SYM
iajs-2878	30	57	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	30	58	)	)	PUNCT
iajs-2878	30	59	∖	∖	NOUN
iajs-2878	30	60	{	{	PUNCT
iajs-2878	30	61	ø	ø	NOUN
iajs-2878	30	62	}	}	PUNCT
iajs-2878	30	63	implying	imply	VERB
iajs-2878	30	64	𝜏₢	𝜏₢	NOUN
iajs-2878	30	65	=	=	SYM
iajs-2878	30	66	τ	τ	PROPN
iajs-2878	30	67	.	.	PUNCT
iajs-2878	31	1	the	the	DET
iajs-2878	31	2	family	family	NOUN
iajs-2878	31	3	of	of	ADP
iajs-2878	31	4	all	all	DET
iajs-2878	31	5	𝛼	𝛼	PRON
iajs-2878	31	6	-open	-open	ADJ
iajs-2878	31	7	set	set	NOUN
iajs-2878	31	8	is	be	AUX
iajs-2878	31	9	showed	show	VERB
iajs-2878	31	10	by	by	ADP
iajs-2878	31	11	𝜏𝑠.	𝜏𝑠.	X
iajs-2878	31	12	𝛼	𝛼	X
iajs-2878	31	13	-𝑜𝑝𝑒𝑛	-𝑜𝑝𝑒𝑛	NOUN
iajs-2878	31	14	𝑖𝑠	𝑖𝑠	ADP
iajs-2878	31	15	𝑎	𝑎	DET
iajs-2878	31	16	𝑠𝑢𝑏𝑠𝑒𝑡	𝑠𝑢𝑏𝑠𝑒𝑡	NOUN
iajs-2878	31	17	ⱥ	ⱥ	X
iajs-2878	31	18	𝑜𝑓	𝑜𝑓	ADP
iajs-2878	31	19	𝑎	𝑎	PRON
iajs-2878	31	20	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2878	31	21	(	(	PUNCT
iajs-2878	31	22	ꝡ	ꝡ	NOUN
iajs-2878	31	23	,	,	PUNCT
iajs-2878	31	24	𝜏	𝜏	NOUN
iajs-2878	31	25	)	)	PUNCT
iajs-2878	31	26	,	,	PUNCT
iajs-2878	32	1	[	[	X
iajs-2878	32	2	8	8	NUM
iajs-2878	32	3	]	]	PUNCT
iajs-2878	32	4	𝑖𝑓	𝑖𝑓	ADP
iajs-2878	32	5	ⱥ	ⱥ	NOUN
iajs-2878	32	6	⊆	⊆	NUM
iajs-2878	32	7	𝜍𝑙(ᶩ𝑛𝑡(ⱥ	𝜍𝑙(ᶩ𝑛𝑡(ⱥ	NOUN
iajs-2878	32	8	)	)	PUNCT
iajs-2878	32	9	)	)	PUNCT
iajs-2878	32	10	,	,	PUNCT
iajs-2878	32	11	let	let	VERB
iajs-2878	32	12	(	(	PUNCT
iajs-2878	32	13	ꝡ	ꝡ	NOUN
iajs-2878	32	14	,	,	PUNCT
iajs-2878	32	15	τ	τ	PROPN
iajs-2878	32	16	,	,	PUNCT
iajs-2878	32	17	₢	₢	ADP
iajs-2878	32	18	)	)	PUNCT
iajs-2878	32	19	be	be	AUX
iajs-2878	32	20	topological	topological	ADJ
iajs-2878	32	21	space	space	NOUN
iajs-2878	32	22	.	.	PUNCT
iajs-2878	33	1	the	the	DET
iajs-2878	33	2	subset	subset	NOUN
iajs-2878	33	3	ⱥ	ⱥ	X
iajs-2878	33	4	in	in	ADP
iajs-2878	33	5	ꝡ	ꝡ	PROPN
iajs-2878	33	6	is	be	AUX
iajs-2878	33	7	known	know	VERB
iajs-2878	33	8	as	as	ADP
iajs-2878	33	9	₢	₢	X
iajs-2878	33	10	𝛼	𝛼	PRON
iajs-2878	33	11	-open	-open	ADJ
iajs-2878	33	12	if	if	SCONJ
iajs-2878	33	13	ⱥ	ⱥ	PROPN
iajs-2878	33	14	⊆	⊆	NUM
iajs-2878	33	15	ѱ(ᶩ𝑛𝑡(ⱥ	ѱ(ᶩ𝑛𝑡(ⱥ	NOUN
iajs-2878	33	16	)	)	PUNCT
iajs-2878	33	17	)	)	PUNCT
iajs-2878	33	18	,	,	PUNCT
iajs-2878	33	19	and	and	CCONJ
iajs-2878	33	20	every	every	DET
iajs-2878	33	21	ѱ	ѱ	NOUN
iajs-2878	33	22	𝛼	𝛼	NOUN
iajs-2878	33	23	-open	-open	NOUN
iajs-2878	33	24	is	be	AUX
iajs-2878	33	25	an	an	DET
iajs-2878	33	26	𝛼	𝛼	NOUN
iajs-2878	33	27	-open	-open	NOUN
iajs-2878	33	28	.	.	PUNCT
iajs-2878	34	1	many	many	ADJ
iajs-2878	34	2	researchers	researcher	NOUN
iajs-2878	34	3	have	have	AUX
iajs-2878	34	4	generalized	generalize	VERB
iajs-2878	34	5	using	use	VERB
iajs-2878	34	6	these	these	PRON
iajs-2878	35	1	[	[	X
iajs-2878	35	2	9	9	NUM
iajs-2878	35	3	]	]	X
iajs-2878	35	4	[	[	X
iajs-2878	35	5	10	10	NUM
iajs-2878	35	6	]	]	PUNCT
iajs-2878	35	7	.	.	PUNCT
iajs-2878	36	1	the	the	DET
iajs-2878	36	2	symbol	symbol	NOUN
iajs-2878	36	3	ᶩ𝑛𝑡(ⱥ	ᶩ𝑛𝑡(ⱥ	NUM
iajs-2878	36	4	)	)	PUNCT
iajs-2878	36	5	is	be	AUX
iajs-2878	36	6	the	the	DET
iajs-2878	36	7	interior	interior	ADJ
iajs-2878	36	8	set	set	NOUN
iajs-2878	36	9	of	of	ADP
iajs-2878	36	10	ⱥ	ⱥ	PROPN
iajs-2878	36	11	and	and	CCONJ
iajs-2878	36	12	𝜍𝑙(ⱥ	𝜍𝑙(ⱥ	PUNCT
iajs-2878	36	13	)	)	PUNCT
iajs-2878	36	14	denotes	denote	VERB
iajs-2878	36	15	the	the	DET
iajs-2878	36	16	closure	closure	NOUN
iajs-2878	36	17	of	of	ADP
iajs-2878	36	18	ⱥ	ⱥ	ADJ
iajs-2878	36	19	.	.	PUNCT
iajs-2878	36	20	combinations	combination	NOUN
iajs-2878	36	21	the	the	DET
iajs-2878	36	22	space	space	NOUN
iajs-2878	36	23	(	(	PUNCT
iajs-2878	36	24	ꝡ	ꝡ	NOUN
iajs-2878	36	25	,	,	PUNCT
iajs-2878	36	26			PROPN
iajs-2878	36	27	)	)	PUNCT
iajs-2878	36	28	is	be	AUX
iajs-2878	36	29	disconnected	disconnect	VERB
iajs-2878	36	30	if	if	SCONJ
iajs-2878	36	31	and	and	CCONJ
iajs-2878	36	32	only	only	ADV
iajs-2878	36	33	if	if	SCONJ
iajs-2878	36	34	there	there	PRON
iajs-2878	36	35	exist	exist	VERB
iajs-2878	36	36	two	two	NUM
iajs-2878	36	37	open	open	ADJ
iajs-2878	36	38	disjoint	disjoint	NOUN
iajs-2878	36	39	nonempty	nonempty	NOUN
iajs-2878	36	40	sets	set	VERB
iajs-2878	36	41	ⱥ	ⱥ	PROPN
iajs-2878	36	42	and	and	CCONJ
iajs-2878	36	43	ɓ	ɓ	DET
iajs-2878	36	44	such	such	ADJ
iajs-2878	36	45	that	that	DET
iajs-2878	36	46	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	36	47	=	=	SYM
iajs-2878	36	48	ꝡ	ꝡ	NOUN
iajs-2878	36	49	.	.	PUNCT
iajs-2878	37	1	i.e.	i.e.	X
iajs-2878	37	2	,	,	PUNCT
iajs-2878	37	3	ꝡ	ꝡ	PROPN
iajs-2878	37	4	is	be	AUX
iajs-2878	37	5	disconnected	disconnect	VERB
iajs-2878	37	6	𝑖𝑓	𝑖𝑓	ADP
iajs-2878	37	7	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-2878	37	8	𝑜𝑛𝑙𝑦	𝑜𝑛𝑙𝑦	ADV
iajs-2878	37	9	𝑖𝑓	𝑖𝑓	ADP
iajs-2878	37	10	ꝡ	ꝡ	NOUN
iajs-2878	37	11	=	=	PUNCT
iajs-2878	37	12	⋃ɓ	⋃ɓ	PROPN
iajs-2878	37	13	;	;	PUNCT
iajs-2878	37	14	ⱥ	ⱥ	X
iajs-2878	37	15	,	,	PUNCT
iajs-2878	37	16	ɓ	ɓ	DET
iajs-2878	37	17	∈	∈	NOUN
iajs-2878	37	18			NOUN
iajs-2878	37	19	,	,	PUNCT
iajs-2878	37	20	ⱥ	ⱥ	PROPN
iajs-2878	37	21	⋂	⋂	PROPN
iajs-2878	37	22	ɓ	ɓ	X
iajs-2878	37	23	=	=	NOUN
iajs-2878	37	24			NOUN
iajs-2878	37	25	,	,	PUNCT
iajs-2878	37	26	ⱥ	ⱥ	X
iajs-2878	37	27	,	,	PUNCT
iajs-2878	37	28	ɓ	ɓ	PROPN
iajs-2878	37	29	.	.	X
iajs-2878	37	30	the	the	DET
iajs-2878	37	31	sets	set	NOUN
iajs-2878	37	32	ⱥ	ⱥ	PROPN
iajs-2878	37	33	and	and	CCONJ
iajs-2878	37	34	ɓ	ɓ	DET
iajs-2878	37	35	form	form	NOUN
iajs-2878	37	36	a	a	DET
iajs-2878	37	37	separation	separation	NOUN
iajs-2878	37	38	of	of	ADP
iajs-2878	37	39	ꝡ	ꝡ	PROPN
iajs-2878	37	40	.	.	PUNCT
iajs-2878	38	1	the	the	DET
iajs-2878	38	2	space	space	NOUN
iajs-2878	38	3	(	(	PUNCT
iajs-2878	38	4	ꝡ	ꝡ	NOUN
iajs-2878	38	5	,	,	PUNCT
iajs-2878	38	6			PROPN
iajs-2878	38	7	)	)	PUNCT
iajs-2878	38	8	is	be	AUX
iajs-2878	38	9	connected	connect	VERB
iajs-2878	38	10	if	if	SCONJ
iajs-2878	38	11	and	and	CCONJ
iajs-2878	38	12	only	only	ADV
iajs-2878	38	13	if	if	SCONJ
iajs-2878	38	14	it	it	PRON
iajs-2878	38	15	is	be	AUX
iajs-2878	38	16	not	not	PART
iajs-2878	38	17	disconnectaaed	disconnectaae	VERB
iajs-2878	38	18	.	.	PUNCT
iajs-2878	39	1	ꝡ	ꝡ	PROPN
iajs-2878	39	2	is	be	AUX
iajs-2878	39	3	connected	connect	VERB
iajs-2878	39	4	if	if	SCONJ
iajs-2878	39	5	and	and	CCONJ
iajs-2878	39	6	only	only	ADV
iajs-2878	39	7	if	if	SCONJ
iajs-2878	39	8	ꝡ	ꝡ	PROPN
iajs-2878	39	9			VERB
iajs-2878	39	10	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	39	11	;	;	PUNCT
iajs-2878	39	12	ⱥ	ⱥ	X
iajs-2878	39	13	,	,	PUNCT
iajs-2878	39	14	ɓ	ɓ	DET
iajs-2878	39	15	∈	∈	NOUN
iajs-2878	39	16			NOUN
iajs-2878	39	17	,	,	PUNCT
iajs-2878	39	18	ⱥ	ⱥ	X
iajs-2878	39	19	⋂ɓ	⋂ɓ	NOUN
iajs-2878	39	20	=	=	SYM
iajs-2878	39	21			NOUN
iajs-2878	39	22	,	,	PUNCT
iajs-2878	39	23	ⱥ	ⱥ	X
iajs-2878	39	24	,	,	PUNCT
iajs-2878	39	25	ɓ	ɓ	PROPN
iajs-2878	39	26	.	.	NUM
iajs-2878	39	27	2	2	NUM
iajs-2878	39	28	.	.	NOUN
iajs-2878	39	29	grill	grill	NOUN
iajs-2878	39	30	𝜶	𝜶	ADP
iajs-2878	39	31	-open	-open	ADJ
iajs-2878	39	32	sets	set	NOUN
iajs-2878	39	33	definition	definition	NOUN
iajs-2878	39	34	2.1	2.1	NUM
iajs-2878	39	35	.	.	PUNCT
iajs-2878	40	1	in	in	ADP
iajs-2878	40	2	[	[	X
iajs-2878	40	3	10	10	NUM
iajs-2878	40	4	]	]	PUNCT
iajs-2878	40	5	,	,	PUNCT
iajs-2878	40	6	the	the	DET
iajs-2878	40	7	set	set	NOUN
iajs-2878	40	8	ⱥ	ⱥ	NOUN
iajs-2878	40	9	is	be	AUX
iajs-2878	40	10	referred	refer	VERB
iajs-2878	40	11	to	to	ADP
iajs-2878	40	12	as	as	ADP
iajs-2878	40	13	grill	grill	NOUN
iajs-2878	40	14	α	α	NOUN
iajs-2878	40	15	-	-	NOUN
iajs-2878	40	16	open	open	ADJ
iajs-2878	40	17	if	if	SCONJ
iajs-2878	40	18	ᶊ	ᶊ	PROPN
iajs-2878	40	19	∈	∈	PROPN
iajs-2878	40	20	𝜏	𝜏	X
iajs-2878	40	21	;	;	PUNCT
iajs-2878	40	22	ᶊ	ᶊ	PRON
iajs-2878	40	23	−	−	PROPN
iajs-2878	40	24	ⱥ	ⱥ	X
iajs-2878	40	25	∉	∉	X
iajs-2878	40	26	₢	₢	X
iajs-2878	40	27	and	and	CCONJ
iajs-2878	40	28	ⱥ	ⱥ	ADJ
iajs-2878	40	29	−	−	PROPN
iajs-2878	40	30	ᶩ𝑛𝑡𝜍𝑙₢(ᶊ	ᶩ𝑛𝑡𝜍𝑙₢(ᶊ	NOUN
iajs-2878	40	31	)	)	PUNCT
iajs-2878	40	32	∉	∉	PROPN
iajs-2878	40	33	₢	₢	PROPN
iajs-2878	40	34	.	.	PUNCT
iajs-2878	41	1	as	as	SCONJ
iajs-2878	41	2	stated	state	VERB
iajs-2878	41	3	by	by	ADP
iajs-2878	41	4	₢	₢	ADP
iajs-2878	41	5	∗α	∗α	NOUN
iajs-2878	41	6	−	−	NOUN
iajs-2878	41	7	open	open	ADJ
iajs-2878	41	8	,	,	PUNCT
iajs-2878	41	9	the	the	DET
iajs-2878	41	10	complment	complment	NOUN
iajs-2878	41	11	of	of	ADP
iajs-2878	41	12	₢	₢	ADP
iajs-2878	41	13	∗	∗	NOUN
iajs-2878	42	1	α	α	PRON
iajs-2878	42	2	−	−	PROPN
iajs-2878	42	3	open	open	ADJ
iajs-2878	42	4	is	be	AUX
iajs-2878	42	5	₢	₢	ADP
iajs-2878	42	6	∗α	∗α	NOUN
iajs-2878	42	7	−	−	PROPN
iajs-2878	42	8	closed	close	VERB
iajs-2878	42	9	.	.	PUNCT
iajs-2878	43	1	the	the	DET
iajs-2878	43	2	set	set	NOUN
iajs-2878	43	3	of	of	ADP
iajs-2878	43	4	all	all	DET
iajs-2878	43	5	₢	₢	NOUN
iajs-2878	43	6	∗α	∗α	NOUN
iajs-2878	43	7	−	−	PROPN
iajs-2878	43	8	open	open	ADJ
iajs-2878	43	9	is	be	AUX
iajs-2878	43	10	represented	represent	VERB
iajs-2878	43	11	by	by	ADP
iajs-2878	43	12	₢	₢	NOUN
iajs-2878	43	13	∗α𝑜(ꝡ	∗α𝑜(ꝡ	PROPN
iajs-2878	43	14	)	)	PUNCT
iajs-2878	43	15	,	,	PUNCT
iajs-2878	43	16	and	and	CCONJ
iajs-2878	43	17	₢	₢	ADP
iajs-2878	43	18	∗α	∗α	NOUN
iajs-2878	43	19	−	−	PROPN
iajs-2878	43	20	closed	close	VERB
iajs-2878	43	21	is	be	AUX
iajs-2878	43	22	denoted	denote	VERB
iajs-2878	43	23	by	by	ADP
iajs-2878	43	24	₢	₢	NOUN
iajs-2878	43	25	∗α𝑐(ꝡ	∗α𝑐(ꝡ	NOUN
iajs-2878	43	26	)	)	PUNCT
iajs-2878	43	27	.	.	PUNCT
iajs-2878	44	1	a	a	DET
iajs-2878	44	2	example	example	NOUN
iajs-2878	44	3	2.2	2.2	NUM
iajs-2878	44	4	.	.	PUNCT
iajs-2878	45	1	[	[	X
iajs-2878	45	2	10	10	NUM
iajs-2878	45	3	]	]	X
iajs-2878	45	4	let	let	ADJ
iajs-2878	45	5	(	(	PUNCT
iajs-2878	45	6	ꝡ,ꚍ	ꝡ,ꚍ	NOUN
iajs-2878	45	7	,	,	PUNCT
iajs-2878	45	8	₢	₢	X
iajs-2878	45	9	)	)	PUNCT
iajs-2878	45	10	is	be	AUX
iajs-2878	45	11	a	a	DET
iajs-2878	45	12	topological	topological	ADJ
iajs-2878	45	13	space	space	NOUN
iajs-2878	45	14	of	of	ADP
iajs-2878	45	15	the	the	DET
iajs-2878	45	16	grill	grill	NOUN
iajs-2878	45	17	,	,	PUNCT
iajs-2878	45	18	and	and	CCONJ
iajs-2878	45	19	let	let	VERB
iajs-2878	45	20	ꝡ	ꝡ	NOUN
iajs-2878	45	21	=	=	PUNCT
iajs-2878	45	22	{	{	PUNCT
iajs-2878	45	23	ꝡ	ꝡ	PROPN
iajs-2878	45	24	1	1	NUM
iajs-2878	45	25	,	,	PUNCT
iajs-2878	45	26	ꝡ	ꝡ	PROPN
iajs-2878	45	27	2	2	NUM
iajs-2878	45	28	,	,	PUNCT
iajs-2878	45	29	ꝡ	ꝡ	PROPN
iajs-2878	45	30	3	3	NUM
iajs-2878	45	31	}	}	PUNCT
iajs-2878	45	32	,	,	PUNCT
iajs-2878	45	33	𝜏	𝜏	X
iajs-2878	45	34	=	=	SYM
iajs-2878	45	35	{	{	PUNCT
iajs-2878	45	36	ꝡ	ꝡ	PROPN
iajs-2878	45	37	,	,	PUNCT
iajs-2878	45	38	ø	ø	PROPN
iajs-2878	45	39	,	,	PUNCT
iajs-2878	45	40	{	{	PUNCT
iajs-2878	45	41	ꝡ	ꝡ	NOUN
iajs-2878	45	42	1	1	NUM
iajs-2878	45	43	}	}	PUNCT
iajs-2878	45	44	,	,	PUNCT
iajs-2878	45	45	{	{	PUNCT
iajs-2878	45	46	ꝡ	ꝡ	NOUN
iajs-2878	45	47	1	1	NUM
iajs-2878	45	48	,	,	PUNCT
iajs-2878	45	49	ꝡ	ꝡ	PROPN
iajs-2878	45	50	2	2	NUM
iajs-2878	45	51	}	}	PUNCT
iajs-2878	45	52	}	}	PUNCT
iajs-2878	45	53	,	,	PUNCT
iajs-2878	45	54	ℱ	ℱ	PROPN
iajs-2878	45	55	=	=	SYM
iajs-2878	45	56	{	{	PUNCT
iajs-2878	45	57	ꝡ	ꝡ	PROPN
iajs-2878	45	58	,	,	PUNCT
iajs-2878	45	59	ø	ø	PROPN
iajs-2878	45	60	,	,	PUNCT
iajs-2878	45	61	{	{	PUNCT
iajs-2878	45	62	ꝡ	ꝡ	NOUN
iajs-2878	45	63	3	3	NUM
iajs-2878	45	64	}	}	PUNCT
iajs-2878	45	65	,	,	PUNCT
iajs-2878	45	66	{	{	PUNCT
iajs-2878	45	67	ꝡ	ꝡ	NOUN
iajs-2878	45	68	2	2	NUM
iajs-2878	45	69	,	,	PUNCT
iajs-2878	45	70	ꝡ	ꝡ	PROPN
iajs-2878	45	71	3	3	NUM
iajs-2878	45	72	}	}	PUNCT
iajs-2878	45	73	}	}	PUNCT
iajs-2878	45	74	,	,	PUNCT
iajs-2878	45	75	₢	₢	PROPN
iajs-2878	45	76	=	=	PUNCT
iajs-2878	45	77	{	{	PUNCT
iajs-2878	45	78	ᶊ	ᶊ	NOUN
iajs-2878	45	79	⊆	⊆	NUM
iajs-2878	45	80	ꝡ;ꝡ	ꝡ;ꝡ	ADP
iajs-2878	45	81	2	2	NUM
iajs-2878	45	82	∊	∊	NUM
iajs-2878	45	83	ᶊ	ᶊ	NOUN
iajs-2878	45	84	}	}	PUNCT
iajs-2878	45	85	,	,	PUNCT
iajs-2878	45	86	ø	ø	NOUN
iajs-2878	45	87	:	:	PUNCT
iajs-2878	45	88	p(ꝡ	p(ꝡ	ADJ
iajs-2878	45	89	)	)	PUNCT
iajs-2878	45	90	⇾	⇾	VERB
iajs-2878	45	91	p(ꝡ	p(ꝡ	NOUN
iajs-2878	45	92	)	)	PUNCT
iajs-2878	45	93	,	,	PUNCT
iajs-2878	45	94	}	}	PUNCT
iajs-2878	45	95	}	}	PUNCT
iajs-2878	45	96	ꝡ	ꝡ	ADP
iajs-2878	45	97	2	2	NUM
iajs-2878	45	98	}	}	PUNCT
iajs-2878	45	99	,	,	PUNCT
iajs-2878	45	100	{	{	PUNCT
iajs-2878	45	101	ꝡ	ꝡ	PROPN
iajs-2878	45	102	2	2	NUM
iajs-2878	45	103	,	,	PUNCT
iajs-2878	45	104	ꝡ	ꝡ	PROPN
iajs-2878	45	105	3	3	NUM
iajs-2878	45	106	}	}	PUNCT
iajs-2878	45	107	,	,	PUNCT
iajs-2878	45	108	{	{	PUNCT
iajs-2878	45	109	ꝡ	ꝡ	NOUN
iajs-2878	45	110	1	1	NUM
iajs-2878	45	111	,	,	PUNCT
iajs-2878	45	112	ꝡ	ꝡ	PROPN
iajs-2878	45	113	2	2	NUM
iajs-2878	45	114	,	,	PUNCT
iajs-2878	45	115	{	{	PUNCT
iajs-2878	45	116	ø	ø	NOUN
iajs-2878	45	117	,	,	PUNCT
iajs-2878	45	118	ꝡ=	ꝡ=	PROPN
iajs-2878	45	119	{	{	PUNCT
iajs-2878	45	120	₢	₢	ADP
iajs-2878	45	121	τ	τ	X
iajs-2878	45	122	,	,	PUNCT
iajs-2878	45	123	ø	ø	PROPN
iajs-2878	45	124	∪	∪	X
iajs-2878	45	125	ⱥ	ⱥ	X
iajs-2878	45	126	=	=	SYM
iajs-2878	45	127	)	)	PUNCT
iajs-2878	45	128	ⱥ	ⱥ	PROPN
iajs-2878	45	129	(	(	PUNCT
iajs-2878	45	130	ѱ	ѱ	NOUN
iajs-2878	45	131	,	,	PUNCT
iajs-2878	45	132	ø(ⱥ	ø(ⱥ	PROPN
iajs-2878	45	133	)	)	PUNCT
iajs-2878	45	134	=	=	PRON
iajs-2878	46	1	{	{	PUNCT
iajs-2878	46	2	ꝡ	ꝡ	PROPN
iajs-2878	46	3	∈	∈	PROPN
iajs-2878	46	4	ꝡ	ꝡ	PROPN
iajs-2878	46	5	;	;	PUNCT
iajs-2878	46	6	∀ᶊ	∀ᶊ	X
iajs-2878	46	7	∈	∈	PROPN
iajs-2878	46	8	𝜏𝑥	𝜏𝑥	PROPN
iajs-2878	46	9	;	;	PUNCT
iajs-2878	46	10	ᶊ	ᶊ	NOUN
iajs-2878	46	11	∩	∩	NOUN
iajs-2878	46	12	ⱥ	ⱥ	X
iajs-2878	46	13	∈	∈	NOUN
iajs-2878	46	14	₢	₢	ADP
iajs-2878	46	15	}	}	PUNCT
iajs-2878	46	16	,	,	PUNCT
iajs-2878	46	17	ℱ₢	ℱ₢	PROPN
iajs-2878	46	18	=	=	PRON
iajs-2878	46	19	{	{	PUNCT
iajs-2878	46	20	ꝡ	ꝡ	PROPN
iajs-2878	46	21	,	,	PUNCT
iajs-2878	46	22	ø	ø	PROPN
iajs-2878	46	23	,	,	PUNCT
iajs-2878	46	24	{	{	PUNCT
iajs-2878	46	25	ꝡ	ꝡ	NOUN
iajs-2878	46	26	3	3	NUM
iajs-2878	46	27	}	}	PUNCT
iajs-2878	46	28	,	,	PUNCT
iajs-2878	46	29	{	{	PUNCT
iajs-2878	46	30	ꝡ	ꝡ	NOUN
iajs-2878	46	31	1	1	NUM
iajs-2878	46	32	}	}	PUNCT
iajs-2878	46	33	,	,	PUNCT
iajs-2878	46	34	{	{	PUNCT
iajs-2878	46	35	ꝡ	ꝡ	NOUN
iajs-2878	46	36	2	2	NUM
iajs-2878	46	37	,	,	PUNCT
iajs-2878	46	38	ꝡ	ꝡ	PROPN
iajs-2878	46	39	3	3	NUM
iajs-2878	46	40	}	}	PUNCT
iajs-2878	46	41	}	}	PUNCT
iajs-2878	46	42	,	,	PUNCT
iajs-2878	46	43	so	so	SCONJ
iajs-2878	46	44	₢	₢	ADP
iajs-2878	46	45	∗α𝑜(ꝡ	∗α𝑜(ꝡ	ADJ
iajs-2878	46	46	)	)	PUNCT
iajs-2878	46	47	=	=	PRON
iajs-2878	46	48	{	{	PUNCT
iajs-2878	46	49	ꝡ	ꝡ	PROPN
iajs-2878	46	50	,	,	PUNCT
iajs-2878	46	51	ø	ø	PROPN
iajs-2878	46	52	,	,	PUNCT
iajs-2878	46	53	{	{	PUNCT
iajs-2878	46	54	ꝡ	ꝡ	NOUN
iajs-2878	46	55	3	3	NUM
iajs-2878	46	56	}	}	PUNCT
iajs-2878	46	57	,	,	PUNCT
iajs-2878	46	58	{	{	PUNCT
iajs-2878	46	59	ꝡ	ꝡ	NOUN
iajs-2878	46	60	2	2	NUM
iajs-2878	46	61	}	}	PUNCT
iajs-2878	46	62	,	,	PUNCT
iajs-2878	46	63	{	{	PUNCT
iajs-2878	46	64	ꝡ	ꝡ	NOUN
iajs-2878	46	65	1	1	NUM
iajs-2878	46	66	}	}	PUNCT
iajs-2878	46	67	,	,	PUNCT
iajs-2878	46	68	{	{	PUNCT
iajs-2878	46	69	ꝡ	ꝡ	NOUN
iajs-2878	46	70	2	2	NUM
iajs-2878	46	71	,	,	PUNCT
iajs-2878	46	72	ꝡ	ꝡ	PROPN
iajs-2878	46	73	3	3	NUM
iajs-2878	46	74	}	}	PUNCT
iajs-2878	46	75	,	,	PUNCT
iajs-2878	46	76	{	{	PUNCT
iajs-2878	46	77	ꝡ	ꝡ	NOUN
iajs-2878	46	78	1	1	NUM
iajs-2878	46	79	,	,	PUNCT
iajs-2878	46	80	ꝡ	ꝡ	PROPN
iajs-2878	46	81	2	2	NUM
iajs-2878	46	82	}	}	PUNCT
iajs-2878	46	83	,	,	PUNCT
iajs-2878	46	84	{	{	PUNCT
iajs-2878	46	85	ꝡ	ꝡ	NOUN
iajs-2878	46	86	3	3	NUM
iajs-2878	46	87	,	,	PUNCT
iajs-2878	46	88	ꝡ	ꝡ	PROPN
iajs-2878	46	89	1	1	NUM
iajs-2878	46	90	}	}	PUNCT
iajs-2878	46	91	}	}	PUNCT
iajs-2878	46	92	.	.	PUNCT
iajs-2878	47	1	ihjpas	ihjpas	PROPN
iajs-2878	47	2	.	.	PUNCT
iajs-2878	48	1	53	53	NUM
iajs-2878	48	2	(	(	PUNCT
iajs-2878	48	3	4)2022	4)2022	NOUN
iajs-2878	48	4	215	215	NUM
iajs-2878	48	5	theorem	theorem	VERB
iajs-2878	48	6	2.3	2.3	NUM
iajs-2878	48	7	.	.	PUNCT
iajs-2878	49	1	[	[	X
iajs-2878	49	2	10	10	NUM
iajs-2878	49	3	]	]	PUNCT
iajs-2878	49	4	the	the	DET
iajs-2878	49	5	union	union	NOUN
iajs-2878	49	6	of	of	ADP
iajs-2878	49	7	any	any	DET
iajs-2878	49	8	family	family	NOUN
iajs-2878	49	9	of	of	ADP
iajs-2878	49	10	₢	₢	ADP
iajs-2878	49	11	∗	∗	NOUN
iajs-2878	49	12	−	−	NOUN
iajs-2878	49	13	𝛼	𝛼	PRON
iajs-2878	49	14	open	open	ADJ
iajs-2878	49	15	set	set	NOUN
iajs-2878	49	16	is	be	AUX
iajs-2878	49	17	a	a	DET
iajs-2878	49	18	₢	₢	ADP
iajs-2878	49	19	∗	∗	NOUN
iajs-2878	49	20	−	−	NOUN
iajs-2878	49	21	𝛼	𝛼	NOUN
iajs-2878	49	22	open	open	ADJ
iajs-2878	49	23	set	set	NOUN
iajs-2878	49	24	.	.	PUNCT
iajs-2878	50	1	remark	remark	PROPN
iajs-2878	50	2	2.4	2.4	NUM
iajs-2878	50	3	.	.	PUNCT
iajs-2878	51	1	[	[	X
iajs-2878	51	2	10	10	NUM
iajs-2878	51	3	]	]	PUNCT
iajs-2878	51	4	both	both	DET
iajs-2878	51	5	ideas	idea	NOUN
iajs-2878	51	6	are	be	AUX
iajs-2878	51	7	related	relate	VERB
iajs-2878	51	8	₢	₢	ADP
iajs-2878	51	9	∗α	∗α	NOUN
iajs-2878	51	10	−	−	PROPN
iajs-2878	51	11	open	open	ADJ
iajs-2878	51	12	set	set	NOUN
iajs-2878	51	13	,	,	PUNCT
iajs-2878	51	14	α	α	PRON
iajs-2878	51	15	−	−	PROPN
iajs-2878	51	16	open	open	ADJ
iajs-2878	51	17	set	set	NOUN
iajs-2878	51	18	are	be	AUX
iajs-2878	51	19	independent	independent	ADJ
iajs-2878	51	20	.	.	PUNCT
iajs-2878	52	1	remark	remark	PROPN
iajs-2878	52	2	2.5	2.5	NUM
iajs-2878	52	3	.	.	PUNCT
iajs-2878	53	1	[	[	X
iajs-2878	53	2	10	10	NUM
iajs-2878	53	3	]	]	X
iajs-2878	53	4	supra	supra	ADJ
iajs-2878	53	5	topology	topology	NOUN
iajs-2878	53	6	refers	refer	VERB
iajs-2878	53	7	to	to	ADP
iajs-2878	53	8	the	the	DET
iajs-2878	53	9	collection	collection	NOUN
iajs-2878	53	10	of	of	ADP
iajs-2878	53	11	all	all	DET
iajs-2878	53	12	₢	₢	ADP
iajs-2878	53	13	∗α	∗α	NOUN
iajs-2878	53	14	-	-	PUNCT
iajs-2878	53	15	open	open	ADJ
iajs-2878	53	16	sets	set	NOUN
iajs-2878	53	17	.	.	PUNCT
iajs-2878	54	1	remark	remark	VERB
iajs-2878	54	2	2.6	2.6	NUM
iajs-2878	55	1	[	[	SYM
iajs-2878	55	2	10	10	NUM
iajs-2878	55	3	]	]	X
iajs-2878	55	4	i.	i.	NOUN
iajs-2878	55	5	the	the	DET
iajs-2878	55	6	open	open	ADJ
iajs-2878	55	7	set	set	NOUN
iajs-2878	55	8	leads	lead	VERB
iajs-2878	55	9	to	to	ADP
iajs-2878	55	10	₢	₢	ADP
iajs-2878	55	11	∗αopen	∗αopen	PROPN
iajs-2878	55	12	set	set	VERB
iajs-2878	55	13	.	.	PUNCT
iajs-2878	56	1	ii	ii	PROPN
iajs-2878	56	2	.	.	PUNCT
iajs-2878	57	1	the	the	DET
iajs-2878	57	2	closed	closed	ADJ
iajs-2878	57	3	set	set	NOUN
iajs-2878	57	4	leads	lead	VERB
iajs-2878	57	5	to	to	ADP
iajs-2878	57	6	₢	₢	ADP
iajs-2878	57	7	∗αclosed	∗αclosed	ADJ
iajs-2878	57	8	set	set	NOUN
iajs-2878	57	9	.	.	PUNCT
iajs-2878	58	1	theorem	theorem	VERB
iajs-2878	58	2	2.7	2.7	NUM
iajs-2878	58	3	.	.	PUNCT
iajs-2878	59	1	[	[	X
iajs-2878	59	2	10	10	NUM
iajs-2878	59	3	]	]	X
iajs-2878	59	4	the	the	DET
iajs-2878	59	5	₢	₢	ADP
iajs-2878	59	6	α	α	X
iajs-2878	59	7	-	-	ADJ
iajs-2878	59	8	open	open	ADJ
iajs-2878	59	9	leads	lead	VERB
iajs-2878	59	10	to	to	ADP
iajs-2878	59	11	₢	₢	ADP
iajs-2878	59	12	∗α	∗α	NOUN
iajs-2878	59	13	-	-	PUNCT
iajs-2878	59	14	open	open	ADJ
iajs-2878	59	15	.	.	PUNCT
iajs-2878	60	1	proposition	proposition	NOUN
iajs-2878	60	2	2.8	2.8	NUM
iajs-2878	60	3	.	.	PUNCT
iajs-2878	61	1	[	[	X
iajs-2878	61	2	10	10	NUM
iajs-2878	61	3	]	]	PUNCT
iajs-2878	61	4	for	for	ADP
iajs-2878	61	5	any	any	DET
iajs-2878	61	6	grill	grill	NOUN
iajs-2878	61	7	topology	topology	NOUN
iajs-2878	61	8	(	(	PUNCT
iajs-2878	61	9	ꝡ	ꝡ	NOUN
iajs-2878	61	10	,	,	PUNCT
iajs-2878	61	11	τ	τ	PROPN
iajs-2878	61	12	,	,	PUNCT
iajs-2878	61	13	₢	₢	ADP
iajs-2878	61	14	)	)	PUNCT
iajs-2878	61	15	,	,	PUNCT
iajs-2878	61	16	ⱥ	ⱥ	X
iajs-2878	61	17	is	be	AUX
iajs-2878	61	18	a	a	DET
iajs-2878	61	19	₢	₢	ADP
iajs-2878	61	20	α	α	X
iajs-2878	61	21	-	-	ADJ
iajs-2878	61	22	open	open	ADJ
iajs-2878	61	23	set	set	NOUN
iajs-2878	61	24	if	if	SCONJ
iajs-2878	61	25	and	and	CCONJ
iajs-2878	61	26	only	only	ADV
iajs-2878	61	27	if	if	SCONJ
iajs-2878	61	28	ⱥ	ⱥ	PROPN
iajs-2878	61	29	𝑖𝑠	𝑖𝑠	X
iajs-2878	61	30	𝑎	𝑎	VERB
iajs-2878	61	31	₢	₢	NOUN
iajs-2878	61	32	∗α	∗α	NOUN
iajs-2878	61	33	-	-	PUNCT
iajs-2878	61	34	open	open	NOUN
iajs-2878	61	35	set	set	VERB
iajs-2878	61	36	whenever	whenever	SCONJ
iajs-2878	61	37	₢	₢	X
iajs-2878	61	38	=	=	SYM
iajs-2878	61	39	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	61	40	)	)	PUNCT
iajs-2878	61	41	∖	∖	NOUN
iajs-2878	61	42	{	{	PUNCT
iajs-2878	61	43	∅	∅	NOUN
iajs-2878	61	44	}	}	PUNCT
iajs-2878	61	45	.	.	PUNCT
iajs-2878	62	1	definition	definition	NOUN
iajs-2878	62	2	2.9	2.9	NUM
iajs-2878	62	3	.	.	PUNCT
iajs-2878	63	1	[	[	X
iajs-2878	63	2	10	10	NUM
iajs-2878	63	3	]	]	PUNCT
iajs-2878	63	4	the	the	DET
iajs-2878	63	5	function	function	NOUN
iajs-2878	63	6	ᶂ	ᶂ	NOUN
iajs-2878	63	7	:	:	PUNCT
iajs-2878	63	8	(	(	PUNCT
iajs-2878	63	9	ꝡ	ꝡ	NOUN
iajs-2878	63	10	,	,	PUNCT
iajs-2878	63	11	τ	τ	PROPN
iajs-2878	63	12	,	,	PUNCT
iajs-2878	63	13	₢	₢	ADP
iajs-2878	63	14	)	)	PUNCT
iajs-2878	63	15	)	)	PUNCT
iajs-2878	63	16	→	→	PUNCT
iajs-2878	63	17	(	(	PUNCT
iajs-2878	63	18	ꝡ	ꝡ	NOUN
iajs-2878	63	19	,	,	PUNCT
iajs-2878	63	20	𝜏′	𝜏′	PROPN
iajs-2878	63	21	,	,	PUNCT
iajs-2878	63	22	₢	₢	NOUN
iajs-2878	63	23	)	)	PUNCT
iajs-2878	63	24	is	be	AUX
iajs-2878	63	25	referred	refer	VERB
iajs-2878	63	26	to	to	ADP
iajs-2878	63	27	as	as	ADP
iajs-2878	63	28	:	:	PUNCT
iajs-2878	63	29	1	1	NUM
iajs-2878	63	30	.	.	X
iajs-2878	63	31	₢	₢	ADP
iajs-2878	63	32	∗α	∗α	NOUN
iajs-2878	63	33	-	-	PUNCT
iajs-2878	63	34	open	open	ADJ
iajs-2878	63	35	function	function	NOUN
iajs-2878	63	36	,	,	PUNCT
iajs-2878	63	37	shortly	shortly	ADV
iajs-2878	63	38	"	"	PUNCT
iajs-2878	63	39	₢	₢	ADP
iajs-2878	63	40	∗α	∗α	NOUN
iajs-2878	63	41	-	-	PUNCT
iajs-2878	63	42	o	o	NOUN
iajs-2878	63	43	function	function	NOUN
iajs-2878	63	44	"	"	PUNCT
iajs-2878	63	45	if	if	SCONJ
iajs-2878	63	46	ᶂ(ᶊ	ᶂ(ᶊ	NOUN
iajs-2878	63	47	)	)	PUNCT
iajs-2878	63	48	∈	∈	PROPN
iajs-2878	63	49	₢	₢	ADP
iajs-2878	63	50	∗𝛼𝑜(𝑦	∗𝛼𝑜(𝑦	NOUN
iajs-2878	63	51	)	)	PUNCT
iajs-2878	63	52	when	when	SCONJ
iajs-2878	63	53	ᶊ	ᶊ	PROPN
iajs-2878	63	54	∈	∈	PROPN
iajs-2878	63	55	₢	₢	ADP
iajs-2878	63	56	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	63	57	)	)	PUNCT
iajs-2878	63	58	.	.	PUNCT
iajs-2878	64	1	2	2	X
iajs-2878	64	2	.	.	X
iajs-2878	64	3	₢	₢	ADP
iajs-2878	64	4	∗∗αopen	∗∗αopen	PROPN
iajs-2878	64	5	function	function	NOUN
iajs-2878	64	6	,	,	PUNCT
iajs-2878	64	7	shortly	shortly	ADV
iajs-2878	64	8	"	"	PUNCT
iajs-2878	64	9	₢	₢	ADP
iajs-2878	64	10	∗∗α	∗∗α	ADJ
iajs-2878	64	11	-	-	PUNCT
iajs-2878	64	12	o	o	NOUN
iajs-2878	64	13	function	function	NOUN
iajs-2878	64	14	"	"	PUNCT
iajs-2878	64	15	if	if	SCONJ
iajs-2878	64	16	ᶂ(ᶊ	ᶂ(ᶊ	NOUN
iajs-2878	64	17	)	)	PUNCT
iajs-2878	64	18	∈	∈	PROPN
iajs-2878	64	19	₢	₢	ADP
iajs-2878	64	20	∗𝛼𝑜(𝑦	∗𝛼𝑜(𝑦	NOUN
iajs-2878	64	21	)	)	PUNCT
iajs-2878	64	22	when	when	SCONJ
iajs-2878	64	23	ᶊ	ᶊ	PROPN
iajs-2878	64	24	∈	∈	PROPN
iajs-2878	64	25	𝜏	𝜏	X
iajs-2878	64	26	.	.	PUNCT
iajs-2878	65	1	3	3	X
iajs-2878	65	2	.	.	X
iajs-2878	65	3	₢	₢	ADP
iajs-2878	65	4	∗∗∗αopen	∗∗∗αopen	ADJ
iajs-2878	65	5	function	function	NOUN
iajs-2878	65	6	,	,	PUNCT
iajs-2878	65	7	shortly	shortly	ADV
iajs-2878	65	8	"	"	PUNCT
iajs-2878	65	9	₢	₢	ADP
iajs-2878	65	10	∗∗∗α	∗∗∗α	ADV
iajs-2878	65	11	-	-	PUNCT
iajs-2878	65	12	o	o	NOUN
iajs-2878	65	13	function	function	NOUN
iajs-2878	65	14	"	"	PUNCT
iajs-2878	65	15	if	if	SCONJ
iajs-2878	65	16	ᶂ(ᶊ	ᶂ(ᶊ	NOUN
iajs-2878	65	17	)	)	PUNCT
iajs-2878	65	18	∈	∈	NOUN
iajs-2878	65	19	𝜏′	𝜏′	NOUN
iajs-2878	65	20	whenever	whenever	SCONJ
iajs-2878	65	21	ᶊ	ᶊ	PRON
iajs-2878	65	22	∈	∈	PROPN
iajs-2878	65	23	₢	₢	ADP
iajs-2878	65	24	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	NUM
iajs-2878	65	25	)	)	PUNCT
iajs-2878	65	26	.	.	PUNCT
iajs-2878	66	1	definition	definition	NOUN
iajs-2878	66	2	2.10	2.10	NUM
iajs-2878	66	3	the	the	DET
iajs-2878	66	4	function	function	NOUN
iajs-2878	66	5	ᶂ	ᶂ	PROPN
iajs-2878	66	6	∶	∶	NOUN
iajs-2878	66	7	(	(	PUNCT
iajs-2878	66	8	ҳ	ҳ	NOUN
iajs-2878	66	9	,	,	PUNCT
iajs-2878	66	10	𝜏	𝜏	NOUN
iajs-2878	66	11	,	,	PUNCT
iajs-2878	66	12	₢	₢	ADP
iajs-2878	66	13	)	)	PUNCT
iajs-2878	66	14	→	→	SYM
iajs-2878	66	15	(	(	PUNCT
iajs-2878	66	16	ꝡ	ꝡ	NOUN
iajs-2878	66	17	,	,	PUNCT
iajs-2878	66	18	𝜏′	𝜏′	PROPN
iajs-2878	66	19	,	,	PUNCT
iajs-2878	66	20	₢	₢	NOUN
iajs-2878	66	21	)	)	PUNCT
iajs-2878	66	22	is	be	AUX
iajs-2878	66	23	called	call	VERB
iajs-2878	66	24	;	;	PUNCT
iajs-2878	66	25	1	1	X
iajs-2878	66	26	.	.	X
iajs-2878	67	1	₢	₢	ADP
iajs-2878	67	2	∗𝛼	∗𝛼	PROPN
iajs-2878	67	3	−continuose	−continuose	NUM
iajs-2878	67	4	function	function	NOUN
iajs-2878	67	5	,	,	PUNCT
iajs-2878	67	6	shortly	shortly	ADV
iajs-2878	67	7	"	"	PUNCT
iajs-2878	67	8	₢	₢	X
iajs-2878	67	9	*	*	PUNCT
iajs-2878	67	10	α-"continuous	α-"continuous	ADJ
iajs-2878	67	11	function\	function\	NOUN
iajs-2878	67	12	"	"	PUNCT
iajs-2878	67	13	"	"	PUNCT
iajs-2878	67	14	if	if	SCONJ
iajs-2878	67	15	ᶂ−1(ᶊ	ᶂ−1(ᶊ	PROPN
iajs-2878	67	16	)	)	PUNCT
iajs-2878	67	17	∈	∈	PROPN
iajs-2878	67	18	₢	₢	ADP
iajs-2878	67	19	∗𝛼𝑂(ҳ	∗𝛼𝑂(ҳ	NUM
iajs-2878	67	20	)	)	PUNCT
iajs-2878	67	21	for	for	ADP
iajs-2878	67	22	all	all	PRON
iajs-2878	67	23	ᶊ	ᶊ	PRON
iajs-2878	67	24	∈	∈	PROPN
iajs-2878	67	25	𝜏′.	𝜏′.	NOUN
iajs-2878	67	26	2	2	NUM
iajs-2878	67	27	.	.	PUNCT
iajs-2878	67	28	strongly	strongly	ADV
iajs-2878	67	29	₢	₢	ADP
iajs-2878	67	30	∗𝛼	∗𝛼	PROPN
iajs-2878	67	31	−	−	PROPN
iajs-2878	67	32	𝑐ontinuose	𝑐ontinuose	NOUN
iajs-2878	67	33	function	function	NOUN
iajs-2878	67	34	shortly	shortly	ADV
iajs-2878	67	35	"	"	PUNCT
iajs-2878	67	36	strongly	strongly	ADV
iajs-2878	67	37	₢	₢	ADP
iajs-2878	67	38	*	*	DET
iajs-2878	67	39	α	α	PRON
iajs-2878	67	40	-	-	ADJ
iajs-2878	67	41	continuous	continuous	ADJ
iajs-2878	67	42	function	function	NOUN
iajs-2878	67	43	"	"	PUNCT
iajs-2878	67	44	if	if	SCONJ
iajs-2878	67	45	ᶂ−1(ᶊ	ᶂ−1(ᶊ	PROPN
iajs-2878	67	46	)	)	PUNCT
iajs-2878	67	47	∈	∈	PROPN
iajs-2878	67	48	𝜏	𝜏	NOUN
iajs-2878	67	49	,	,	PUNCT
iajs-2878	67	50	fore	fore	NOUN
iajs-2878	67	51	every	every	DET
iajs-2878	67	52	ᶊ	ᶊ	PROPN
iajs-2878	67	53	∈	∈	PROPN
iajs-2878	67	54	₢	₢	ADP
iajs-2878	67	55	∗𝛼𝑂(ꝡ	∗𝛼𝑂(ꝡ	NUM
iajs-2878	67	56	)	)	PUNCT
iajs-2878	67	57	.	.	PUNCT
iajs-2878	68	1	3	3	X
iajs-2878	68	2	.	.	X
iajs-2878	68	3	₢	₢	ADP
iajs-2878	68	4	∗𝛼	∗𝛼	PROPN
iajs-2878	68	5	−irresolute	−irresolute	NOUN
iajs-2878	68	6	function	function	NOUN
iajs-2878	68	7	,	,	PUNCT
iajs-2878	68	8	shortly	shortly	ADV
iajs-2878	68	9	"	"	PUNCT
iajs-2878	68	10	₢	₢	X
iajs-2878	68	11	*	*	PUNCT
iajs-2878	68	12	α	α	X
iajs-2878	68	13	-	-	PUNCT
iajs-2878	68	14	irresolute	irresolute	ADJ
iajs-2878	68	15	function	function	NOUN
iajs-2878	68	16	"	"	PUNCT
iajs-2878	68	17	if	if	SCONJ
iajs-2878	68	18	ᶂ−1(ᶊ	ᶂ−1(ᶊ	PROPN
iajs-2878	68	19	)	)	PUNCT
iajs-2878	68	20	∈	∈	PROPN
iajs-2878	68	21	₢	₢	ADP
iajs-2878	68	22	∗𝛼𝑂(ҳ	∗𝛼𝑂(ҳ	NUM
iajs-2878	68	23	)	)	PUNCT
iajs-2878	68	24	,	,	PUNCT
iajs-2878	68	25	for	for	ADP
iajs-2878	68	26	every	every	DET
iajs-2878	68	27	ᶊ	ᶊ	PROPN
iajs-2878	68	28	∈	∈	PROPN
iajs-2878	68	29	₢	₢	ADP
iajs-2878	68	30	∗𝛼𝑂(ꝡ	∗𝛼𝑂(ꝡ	X
iajs-2878	68	31	)	)	PUNCT
iajs-2878	68	32	3	3	NUM
iajs-2878	68	33	.	.	X
iajs-2878	68	34	grill	grill	NOUN
iajs-2878	68	35	𝜶	𝜶	ADP
iajs-2878	68	36	-open	-open	ADJ
iajs-2878	68	37	sets	set	NOUN
iajs-2878	68	38	in	in	ADP
iajs-2878	68	39	grill	grill	NOUN
iajs-2878	68	40	connected	connect	VERB
iajs-2878	68	41	space	space	NOUN
iajs-2878	68	42	definition	definition	NOUN
iajs-2878	68	43	3.1	3.1	NUM
iajs-2878	68	44	:	:	PUNCT
iajs-2878	68	45	the	the	DET
iajs-2878	68	46	space	space	NOUN
iajs-2878	68	47	(	(	PUNCT
iajs-2878	68	48	ꝡ	ꝡ	NOUN
iajs-2878	68	49	,	,	PUNCT
iajs-2878	68	50	τ	τ	PROPN
iajs-2878	68	51	,	,	PUNCT
iajs-2878	68	52	₢	₢	ADP
iajs-2878	68	53	)	)	PUNCT
iajs-2878	68	54	is	be	AUX
iajs-2878	68	55	a	a	DET
iajs-2878	68	56	₢	₢	ADP
iajs-2878	68	57	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	68	58	if	if	SCONJ
iajs-2878	69	1	and	and	CCONJ
iajs-2878	69	2	only	only	ADV
iajs-2878	69	3	if	if	SCONJ
iajs-2878	69	4	there	there	PRON
iajs-2878	69	5	exist	exist	VERB
iajs-2878	69	6	two	two	NUM
iajs-2878	69	7	₢	₢	NOUN
iajs-2878	69	8	∗𝛼-open	∗𝛼-open	X
iajs-2878	69	9	disjoint	disjoint	NOUN
iajs-2878	69	10	nonempty	nonempty	NOUN
iajs-2878	69	11	sets	set	VERB
iajs-2878	69	12	ⱥ	ⱥ	PROPN
iajs-2878	69	13	and	and	CCONJ
iajs-2878	69	14	ɓ	ɓ	DET
iajs-2878	69	15	such	such	ADJ
iajs-2878	69	16	that	that	DET
iajs-2878	69	17	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	69	18	=	=	SYM
iajs-2878	69	19	ꝡ	ꝡ	NOUN
iajs-2878	69	20	.	.	PUNCT
iajs-2878	70	1	i.e.	i.e.	X
iajs-2878	70	2	,ꝡ	,ꝡ	PUNCT
iajs-2878	70	3	is	be	AUX
iajs-2878	70	4	a	a	DET
iajs-2878	70	5	₢	₢	ADP
iajs-2878	70	6	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	70	7	if	if	SCONJ
iajs-2878	70	8	and	and	CCONJ
iajs-2878	70	9	only	only	ADV
iajs-2878	70	10	if	if	SCONJ
iajs-2878	70	11	ꝡ	ꝡ	PROPN
iajs-2878	70	12	=	=	NOUN
iajs-2878	70	13	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	70	14	;	;	PUNCT
iajs-2878	70	15	ⱥ	ⱥ	X
iajs-2878	70	16	,	,	PUNCT
iajs-2878	70	17	ɓ	ɓ	PRON
iajs-2878	70	18	∈	∈	NOUN
iajs-2878	70	19	₢	₢	ADP
iajs-2878	70	20	∗𝑠𝑜(ꝡ	∗𝑠𝑜(ꝡ	PROPN
iajs-2878	70	21	)	)	PUNCT
iajs-2878	70	22	,	,	PUNCT
iajs-2878	70	23	ⱥ	ⱥ	PROPN
iajs-2878	70	24	⋂	⋂	PROPN
iajs-2878	70	25	ɓ	ɓ	X
iajs-2878	70	26	=	=	NOUN
iajs-2878	70	27			NOUN
iajs-2878	70	28	.	.	PUNCT
iajs-2878	71	1	the	the	DET
iajs-2878	71	2	s𝑒ts	s𝑒t	NOUN
iajs-2878	71	3	ⱥ	ⱥ	PROPN
iajs-2878	71	4	and	and	CCONJ
iajs-2878	71	5	ɓ	ɓ	DET
iajs-2878	71	6	form	form	NOUN
iajs-2878	71	7	a	a	DET
iajs-2878	71	8	₢	₢	ADP
iajs-2878	71	9	∗𝑠𝑜-separation	∗𝑠𝑜-separation	PROPN
iajs-2878	71	10	of	of	ADP
iajs-2878	71	11	ꝡ	ꝡ	PROPN
iajs-2878	71	12	.	.	PUNCT
iajs-2878	72	1	the	the	DET
iajs-2878	72	2	space	space	NOUN
iajs-2878	72	3	(	(	PUNCT
iajs-2878	72	4	ꝡ	ꝡ	NOUN
iajs-2878	72	5	,	,	PUNCT
iajs-2878	72	6	τ	τ	PROPN
iajs-2878	72	7	,	,	PUNCT
iajs-2878	72	8	₢	₢	ADP
iajs-2878	72	9	)	)	PUNCT
iajs-2878	72	10	is	be	AUX
iajs-2878	72	11	a	a	DET
iajs-2878	72	12	₢	₢	ADP
iajs-2878	72	13	∗𝑠𝑜connected	∗𝑠𝑜connecte	VERB
iajs-2878	72	14	if	if	SCONJ
iajs-2878	72	15	and	and	CCONJ
iajs-2878	72	16	ihjpas	ihjpa	VERB
iajs-2878	72	17	.	.	PUNCT
iajs-2878	73	1	53	53	NUM
iajs-2878	73	2	(	(	PUNCT
iajs-2878	73	3	4)2022	4)2022	NOUN
iajs-2878	73	4	216	216	NUM
iajs-2878	73	5	only	only	ADV
iajs-2878	73	6	if	if	SCONJ
iajs-2878	73	7	it	it	PRON
iajs-2878	73	8	is	be	AUX
iajs-2878	73	9	not	not	PART
iajs-2878	73	10	₢	₢	AUX
iajs-2878	73	11	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	73	12	.	.	PUNCT
iajs-2878	74	1	ꝡ	ꝡ	PROPN
iajs-2878	74	2	is	be	AUX
iajs-2878	74	3	a	a	DET
iajs-2878	74	4	₢	₢	ADP
iajs-2878	74	5	∗𝛼𝑜connected	∗𝛼𝑜connecte	VERB
iajs-2878	74	6	if	if	SCONJ
iajs-2878	74	7	and	and	CCONJ
iajs-2878	74	8	only	only	ADV
iajs-2878	74	9	if	if	SCONJ
iajs-2878	74	10	ꝡ	ꝡ	PROPN
iajs-2878	74	11			VERB
iajs-2878	74	12	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	74	13	;	;	PUNCT
iajs-2878	74	14	ⱥ	ⱥ	X
iajs-2878	74	15	,	,	PUNCT
iajs-2878	74	16	ɓ	ɓ	PRON
iajs-2878	74	17	∈	∈	NOUN
iajs-2878	74	18	₢	₢	ADP
iajs-2878	74	19	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	74	20	)	)	PUNCT
iajs-2878	74	21	,	,	PUNCT
iajs-2878	74	22	ⱥ	ⱥ	PROPN
iajs-2878	74	23	⋂	⋂	PROPN
iajs-2878	74	24	ɓ	ɓ	X
iajs-2878	74	25	=	=	NOUN
iajs-2878	74	26			NOUN
iajs-2878	74	27	,	,	PUNCT
iajs-2878	74	28	ⱥ	ⱥ	X
iajs-2878	74	29	,	,	PUNCT
iajs-2878	74	30	ɓ	ɓ	PROPN
iajs-2878	74	31	.	.	PART
iajs-2878	74	32	example	example	NOUN
iajs-2878	74	33	3.2	3.2	NUM
iajs-2878	74	34	.	.	PUNCT
iajs-2878	75	1	l𝑒t	l𝑒t	VERB
iajs-2878	75	2	(	(	PUNCT
iajs-2878	75	3	ꝡ	ꝡ	PROPN
iajs-2878	75	4	,	,	PUNCT
iajs-2878	75	5	τ	τ	PROPN
iajs-2878	75	6	,	,	PUNCT
iajs-2878	75	7	₢	₢	ADP
iajs-2878	75	8	)	)	PUNCT
iajs-2878	75	9	topological	topological	ADJ
iajs-2878	75	10	𝑠pace	𝑠pace	NOUN
iajs-2878	75	11	b𝑒	b𝑒	ADP
iajs-2878	75	12	a	a	DET
iajs-2878	75	13	𝑔𝑟ill	𝑔𝑟ill	NOUN
iajs-2878	75	14	a𝑛d	a𝑛d	VERB
iajs-2878	75	15	ꝡ	ꝡ	NOUN
iajs-2878	75	16	=	=	PUNCT
iajs-2878	75	17	{	{	PUNCT
iajs-2878	75	18	ꝡ	ꝡ	PROPN
iajs-2878	75	19	1	1	NUM
iajs-2878	75	20	,	,	PUNCT
iajs-2878	75	21	ꝡ	ꝡ	PROPN
iajs-2878	75	22	2	2	NUM
iajs-2878	75	23	,	,	PUNCT
iajs-2878	75	24	ꝡ	ꝡ	PROPN
iajs-2878	75	25	3	3	NUM
iajs-2878	75	26	}	}	PUNCT
iajs-2878	75	27	,	,	PUNCT
iajs-2878	75	28	𝜏	𝜏	NOUN
iajs-2878	75	29	=	=	SYM
iajs-2878	75	30	𝜏₢	𝜏₢	NOUN
iajs-2878	75	31	=	=	SYM
iajs-2878	75	32	{	{	PUNCT
iajs-2878	75	33	ꝡ	ꝡ	PROPN
iajs-2878	75	34	,	,	PUNCT
iajs-2878	75	35	ø	ø	PROPN
iajs-2878	75	36	,	,	PUNCT
iajs-2878	75	37	{	{	PUNCT
iajs-2878	75	38	ꝡ	ꝡ	NOUN
iajs-2878	75	39	2	2	NUM
iajs-2878	75	40	}	}	PUNCT
iajs-2878	75	41	,	,	PUNCT
iajs-2878	75	42	{	{	PUNCT
iajs-2878	75	43	ꝡ	ꝡ	NOUN
iajs-2878	75	44	3	3	NUM
iajs-2878	75	45	}	}	PUNCT
iajs-2878	75	46	}	}	PUNCT
iajs-2878	75	47	,	,	PUNCT
iajs-2878	75	48	₢	₢	ADP
iajs-2878	75	49	=	=	SYM
iajs-2878	75	50	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	75	51	)	)	PUNCT
iajs-2878	75	52	∖	∖	NOUN
iajs-2878	75	53	{	{	PUNCT
iajs-2878	75	54	ø	ø	NOUN
iajs-2878	75	55	}	}	PUNCT
iajs-2878	75	56	is	be	AUX
iajs-2878	75	57	a	a	DET
iajs-2878	75	58	₢	₢	ADP
iajs-2878	75	59	∗𝛼𝑜connected	∗𝛼𝑜connecte	VERB
iajs-2878	75	60	space	space	NOUN
iajs-2878	75	61	.	.	PUNCT
iajs-2878	76	1	remark	remark	VERB
iajs-2878	76	2	3.3	3.3	NUM
iajs-2878	76	3	every	every	DET
iajs-2878	76	4	disconnected	disconnected	ADJ
iajs-2878	76	5	set	set	NOUN
iajs-2878	76	6	is	be	AUX
iajs-2878	76	7	a	a	DET
iajs-2878	76	8	₢	₢	ADP
iajs-2878	76	9	∗𝛼𝑜-disconnected	∗𝛼𝑜-disconnecte	VERB
iajs-2878	76	10	.	.	PUNCT
iajs-2878	77	1	proof	proof	NOUN
iajs-2878	77	2	.	.	PUNCT
iajs-2878	78	1	let	let	VERB
iajs-2878	78	2	ꝡ	ꝡ	NOUN
iajs-2878	78	3	is	be	AUX
iajs-2878	78	4	disconnected	disconnect	VERB
iajs-2878	78	5	set	set	NOUN
iajs-2878	78	6	,	,	PUNCT
iajs-2878	78	7	then	then	ADV
iajs-2878	78	8	the	the	DET
iajs-2878	78	9	exist	exist	ADJ
iajs-2878	78	10	𝒲	𝒲	NOUN
iajs-2878	78	11	≠	≠	PROPN
iajs-2878	78	12	∅	∅	NOUN
iajs-2878	78	13	,	,	PUNCT
iajs-2878	78	14	𝒵	𝒵	PROPN
iajs-2878	78	15	≠	≠	PROPN
iajs-2878	78	16	∅	∅	NOUN
iajs-2878	78	17	and	and	CCONJ
iajs-2878	78	18	𝒲	𝒲	NOUN
iajs-2878	78	19	,	,	PUNCT
iajs-2878	78	20	𝒵	𝒵	PROPN
iajs-2878	78	21	∈	∈	PROPN
iajs-2878	78	22	τ	τ	X
iajs-2878	78	23	;	;	PUNCT
iajs-2878	78	24	𝒲	𝒲	PROPN
iajs-2878	78	25	⋂	⋂	PROPN
iajs-2878	78	26	𝒵	𝒵	NOUN
iajs-2878	78	27	=	=	NOUN
iajs-2878	78	28	∅	∅	NOUN
iajs-2878	78	29	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2878	78	30	𝒲	𝒲	PROPN
iajs-2878	78	31	⋃	⋃	PROPN
iajs-2878	78	32	𝒵	𝒵	NOUN
iajs-2878	78	33	=	=	SYM
iajs-2878	78	34	ꝡ	ꝡ	PROPN
iajs-2878	78	35	since	since	SCONJ
iajs-2878	78	36	every	every	DET
iajs-2878	78	37	open	open	ADJ
iajs-2878	78	38	set	set	NOUN
iajs-2878	78	39	in	in	ADP
iajs-2878	78	40	₢	₢	ADP
iajs-2878	78	41	∗𝛼-open	∗𝛼-open	ADV
iajs-2878	78	42	set	set	VERB
iajs-2878	78	43	.	.	PUNCT
iajs-2878	79	1	therefore	therefore	ADV
iajs-2878	79	2	,	,	PUNCT
iajs-2878	79	3	ꝡ	ꝡ	PROPN
iajs-2878	79	4	is	be	AUX
iajs-2878	79	5	₢	₢	AUX
iajs-2878	79	6	∗𝛼𝑜-disconnected	∗𝛼𝑜-disconnecte	VERB
iajs-2878	79	7	.	.	PUNCT
iajs-2878	80	1	remark	remark	PROPN
iajs-2878	80	2	3.4	3.4	NUM
iajs-2878	80	3	.	.	PUNCT
iajs-2878	81	1	the	the	DET
iajs-2878	81	2	space	space	NOUN
iajs-2878	81	3	(	(	PUNCT
iajs-2878	81	4	ꝡ	ꝡ	NOUN
iajs-2878	81	5	,	,	PUNCT
iajs-2878	81	6	τ	τ	PROPN
iajs-2878	81	7	,	,	PUNCT
iajs-2878	81	8	₢	₢	ADP
iajs-2878	81	9	)	)	PUNCT
iajs-2878	81	10	is	be	AUX
iajs-2878	81	11	a	a	DET
iajs-2878	81	12	₢	₢	ADP
iajs-2878	81	13	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	81	14	with	with	ADP
iajs-2878	81	15	any	any	DET
iajs-2878	81	16	grill	grill	NOUN
iajs-2878	81	17	and	and	CCONJ
iajs-2878	81	18	₢	₢	ADP
iajs-2878	81	19	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	NUM
iajs-2878	81	20	)	)	PUNCT
iajs-2878	81	21	=	=	SYM
iajs-2878	82	1	ℙ(ꝡ	ℙ(ꝡ	PROPN
iajs-2878	82	2	)	)	PUNCT
iajs-2878	82	3	if	if	SCONJ
iajs-2878	82	4	ꝡ	ꝡ	PROPN
iajs-2878	82	5	contained	contain	VERB
iajs-2878	82	6	more	more	ADJ
iajs-2878	82	7	than	than	ADP
iajs-2878	82	8	one	one	NUM
iajs-2878	82	9	element	element	NOUN
iajs-2878	82	10	since	since	SCONJ
iajs-2878	82	11	there	there	PRON
iajs-2878	82	12	exist	exist	VERB
iajs-2878	82	13	ⱥ	ⱥ	PRON
iajs-2878	82	14	and	and	CCONJ
iajs-2878	82	15	ⱥ𝑐	ⱥ𝑐	ADP
iajs-2878	82	16	∈	∈	PROPN
iajs-2878	82	17	₢	₢	ADP
iajs-2878	82	18	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	82	19	)	)	PUNCT
iajs-2878	82	20	;	;	PUNCT
iajs-2878	82	21	ⱥ	ⱥ	X
iajs-2878	82	22	⋃ɓ	⋃ɓ	PROPN
iajs-2878	82	23	=	=	SYM
iajs-2878	82	24	ꝡ	ꝡ	PROPN
iajs-2878	82	25	,	,	PUNCT
iajs-2878	82	26	ⱥ	ⱥ	PROPN
iajs-2878	82	27	⋂	⋂	PROPN
iajs-2878	82	28	ɓ	ɓ	X
iajs-2878	82	29	=	=	SYM
iajs-2878	82	30			NOUN
iajs-2878	82	31	,	,	PUNCT
iajs-2878	82	32	ⱥ	ⱥ	X
iajs-2878	82	33	,	,	PUNCT
iajs-2878	82	34	ɓ	ɓ	PROPN
iajs-2878	82	35	.	.	PUNCT
iajs-2878	82	36	remark	remark	NOUN
iajs-2878	82	37	3.5	3.5	NUM
iajs-2878	82	38	.	.	PUNCT
iajs-2878	83	1	the	the	DET
iajs-2878	83	2	space	space	NOUN
iajs-2878	83	3	(	(	PUNCT
iajs-2878	83	4	ꝡ	ꝡ	NOUN
iajs-2878	83	5	,	,	PUNCT
iajs-2878	83	6	τ	τ	PROPN
iajs-2878	83	7	,	,	PUNCT
iajs-2878	83	8	₢	₢	ADP
iajs-2878	83	9	)	)	PUNCT
iajs-2878	83	10	is	be	AUX
iajs-2878	83	11	a	a	DET
iajs-2878	83	12	₢	₢	ADP
iajs-2878	83	13	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	83	14	and	and	CCONJ
iajs-2878	83	15	₢	₢	ADP
iajs-2878	83	16	=	=	SYM
iajs-2878	83	17	∅	∅	NOUN
iajs-2878	83	18	and	and	CCONJ
iajs-2878	83	19	𝜏₢	𝜏₢	NOUN
iajs-2878	83	20	=	=	SYM
iajs-2878	83	21	{	{	PUNCT
iajs-2878	83	22	ꝡ	ꝡ	PROPN
iajs-2878	83	23	,	,	PUNCT
iajs-2878	83	24	ø	ø	NOUN
iajs-2878	83	25	}	}	PUNCT
iajs-2878	83	26	,	,	PUNCT
iajs-2878	83	27	so	so	ADV
iajs-2878	83	28	₢	₢	ADP
iajs-2878	83	29	∗𝛼𝑜connected	∗𝛼𝑜connecte	VERB
iajs-2878	83	30	space	space	NOUN
iajs-2878	83	31	.	.	PUNCT
iajs-2878	84	1	remark	remark	NOUN
iajs-2878	84	2	3.6	3.6	NUM
iajs-2878	84	3	.	.	PUNCT
iajs-2878	85	1	if	if	SCONJ
iajs-2878	85	2	𝜏₢	𝜏₢	X
iajs-2878	85	3	=	=	SYM
iajs-2878	85	4	ℱ₢	ℱ₢	PROPN
iajs-2878	85	5	and	and	CCONJ
iajs-2878	85	6	𝜏₢	𝜏₢	NOUN
iajs-2878	85	7	≠	≠	PROPN
iajs-2878	85	8	ι𝑛𝑑𝑖𝑠𝑐𝑟𝑒𝑡	ι𝑛𝑑𝑖𝑠𝑐𝑟𝑒𝑡	NOUN
iajs-2878	85	9	,	,	PUNCT
iajs-2878	85	10	when	when	SCONJ
iajs-2878	85	11	₢	₢	X
iajs-2878	85	12	=	=	SYM
iajs-2878	85	13	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	85	14	)	)	PUNCT
iajs-2878	85	15	∖	∖	NOUN
iajs-2878	85	16	{	{	PUNCT
iajs-2878	85	17	ø	ø	NOUN
iajs-2878	85	18	}	}	PUNCT
iajs-2878	85	19	.	.	PUNCT
iajs-2878	86	1	this	this	PRON
iajs-2878	86	2	means	mean	VERB
iajs-2878	86	3	that	that	SCONJ
iajs-2878	86	4	(	(	PUNCT
iajs-2878	86	5	ꝡ	ꝡ	NOUN
iajs-2878	86	6	,	,	PUNCT
iajs-2878	86	7	τ	τ	PROPN
iajs-2878	86	8	,	,	PUNCT
iajs-2878	86	9	₢	₢	ADP
iajs-2878	86	10	)	)	PUNCT
iajs-2878	86	11	is	be	AUX
iajs-2878	86	12	a	a	DET
iajs-2878	86	13	₢	₢	ADP
iajs-2878	86	14	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	86	15	.	.	PUNCT
iajs-2878	87	1	theorem	theorem	VERB
iajs-2878	87	2	3.7	3.7	NUM
iajs-2878	87	3	.	.	PUNCT
iajs-2878	88	1	the	the	DET
iajs-2878	88	2	space	space	NOUN
iajs-2878	88	3	(	(	PUNCT
iajs-2878	88	4	ꝡ	ꝡ	NOUN
iajs-2878	88	5	,	,	PUNCT
iajs-2878	88	6	τ	τ	PROPN
iajs-2878	88	7	,	,	PUNCT
iajs-2878	88	8	₢	₢	ADP
iajs-2878	88	9	)	)	PUNCT
iajs-2878	88	10	is	be	AUX
iajs-2878	88	11	a	a	DET
iajs-2878	88	12	₢	₢	ADP
iajs-2878	88	13	∗𝛼𝑜-connected	∗𝛼𝑜-connecte	VERB
iajs-2878	88	14	if	if	SCONJ
iajs-2878	88	15	and	and	CCONJ
iajs-2878	88	16	only	only	ADV
iajs-2878	88	17	ꝡ	ꝡ	PROPN
iajs-2878	88	18	can	can	AUX
iajs-2878	88	19	not	not	PART
iajs-2878	88	20	be	be	AUX
iajs-2878	88	21	written	write	VERB
iajs-2878	88	22	as	as	ADP
iajs-2878	88	23	a	a	DET
iajs-2878	88	24	union	union	NOUN
iajs-2878	88	25	of	of	ADP
iajs-2878	88	26	two	two	NUM
iajs-2878	88	27	non	non	ADJ
iajs-2878	88	28	-	-	ADJ
iajs-2878	88	29	empty	empty	ADJ
iajs-2878	88	30	disjoint	disjoint	ADJ
iajs-2878	88	31	closed	close	VERB
iajs-2878	88	32	sets	set	NOUN
iajs-2878	88	33	.	.	PUNCT
iajs-2878	89	1	proof	proof	NOUN
iajs-2878	89	2	.	.	PUNCT
iajs-2878	90	1	let	let	VERB
iajs-2878	90	2	ꝡ	ꝡ	NOUN
iajs-2878	90	3	be	be	AUX
iajs-2878	90	4	a	a	DET
iajs-2878	90	5	₢	₢	NOUN
iajs-2878	90	6	∗𝛼𝑜-connected	∗𝛼𝑜-connecte	VERB
iajs-2878	90	7	if	if	SCONJ
iajs-2878	90	8	ꝡ	ꝡ	PROPN
iajs-2878	90	9	=	=	VERB
iajs-2878	90	10	ⱥ	ⱥ	X
iajs-2878	90	11	⋃ɓ	⋃ɓ	NUM
iajs-2878	90	12	,	,	PUNCT
iajs-2878	90	13	such	such	ADJ
iajs-2878	90	14	that	that	PRON
iajs-2878	90	15	;	;	PUNCT
iajs-2878	90	16	ⱥ	ⱥ	X
iajs-2878	90	17	and	and	CCONJ
iajs-2878	90	18	ɓ	ɓ	DET
iajs-2878	90	19	∈	∈	NOUN
iajs-2878	90	20	₢	₢	ADP
iajs-2878	90	21	∗𝛼𝑐(ꝡ	∗𝛼𝑐(ꝡ	NOUN
iajs-2878	90	22	)	)	PUNCT
iajs-2878	90	23	,	,	PUNCT
iajs-2878	90	24	ⱥ	ⱥ	PROPN
iajs-2878	90	25	⋂	⋂	PROPN
iajs-2878	90	26	ɓ	ɓ	X
iajs-2878	90	27	=	=	SYM
iajs-2878	90	28			NOUN
iajs-2878	90	29	,	,	PUNCT
iajs-2878	90	30	ⱥ	ⱥ	X
iajs-2878	90	31	,	,	PUNCT
iajs-2878	90	32	ɓ	ɓ	NOUN
iajs-2878	90	33			NOUN
iajs-2878	90	34	,	,	PUNCT
iajs-2878	90	35	so	so	ADV
iajs-2878	90	36	.	.	PUNCT
iajs-2878	91	1	ⱥ	ⱥ	X
iajs-2878	92	1	=	=	X
iajs-2878	92	2	ɓ𝑐	ɓ𝑐	X
iajs-2878	92	3	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2878	92	4	ɓ	ɓ	PROPN
iajs-2878	92	5	=	=	X
iajs-2878	92	6	ⱥ𝑐	ⱥ𝑐	PROPN
iajs-2878	92	7	,	,	PUNCT
iajs-2878	92	8	then	then	ADV
iajs-2878	92	9	ꝡ	ꝡ	NOUN
iajs-2878	92	10	=	=	SYM
iajs-2878	92	11	ⱥ⋃ɓ	ⱥ⋃ɓ	PROPN
iajs-2878	92	12	;	;	PUNCT
iajs-2878	92	13	ⱥ	ⱥ	X
iajs-2878	92	14	and	and	CCONJ
iajs-2878	92	15	ɓ	ɓ	DET
iajs-2878	92	16	∈	∈	NOUN
iajs-2878	92	17	₢	₢	ADP
iajs-2878	92	18	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	92	19	)	)	PUNCT
iajs-2878	92	20	,	,	PUNCT
iajs-2878	92	21	ⱥ	ⱥ	PROPN
iajs-2878	92	22	⋂	⋂	PROPN
iajs-2878	92	23	ɓ	ɓ	X
iajs-2878	92	24	=	=	SYM
iajs-2878	92	25			NOUN
iajs-2878	92	26	,	,	PUNCT
iajs-2878	92	27	ⱥ	ⱥ	X
iajs-2878	92	28	,	,	PUNCT
iajs-2878	92	29	ɓ	ɓ	NOUN
iajs-2878	92	30			NOUN
iajs-2878	92	31	,	,	PUNCT
iajs-2878	92	32	that	that	PRON
iajs-2878	92	33	is	is	ADV
iajs-2878	92	34	mean	mean	VERB
iajs-2878	92	35	that	that	SCONJ
iajs-2878	92	36	ꝡ	ꝡ	PROPN
iajs-2878	92	37	is	be	AUX
iajs-2878	92	38	a	a	DET
iajs-2878	92	39	₢	₢	NUM
iajs-2878	92	40	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	92	41	.	.	PUNCT
iajs-2878	93	1	that	that	PRON
iajs-2878	93	2	is	be	AUX
iajs-2878	93	3	contradiction	contradiction	NOUN
iajs-2878	93	4	.	.	PUNCT
iajs-2878	94	1	therefore	therefore	ADV
iajs-2878	94	2	,	,	PUNCT
iajs-2878	94	3	ꝡ	ꝡ	PROPN
iajs-2878	94	4	can	can	AUX
iajs-2878	94	5	not	not	PART
iajs-2878	94	6	be	be	AUX
iajs-2878	94	7	written	write	VERB
iajs-2878	94	8	as	as	ADP
iajs-2878	94	9	a	a	DET
iajs-2878	94	10	union	union	NOUN
iajs-2878	94	11	of	of	ADP
iajs-2878	94	12	two	two	NUM
iajs-2878	94	13	non	non	ADJ
iajs-2878	94	14	-	-	ADJ
iajs-2878	94	15	empty	empty	ADJ
iajs-2878	94	16	disjoint	disjoint	NOUN
iajs-2878	94	17	closed	close	VERB
iajs-2878	94	18	set	set	NOUN
iajs-2878	94	19	.	.	PUNCT
iajs-2878	95	1	now	now	ADV
iajs-2878	95	2	,	,	PUNCT
iajs-2878	95	3	if	if	SCONJ
iajs-2878	95	4	ꝡ	ꝡ	PROPN
iajs-2878	95	5	is	be	AUX
iajs-2878	95	6	a	a	DET
iajs-2878	95	7	₢	₢	ADP
iajs-2878	95	8	∗𝛼𝑜	∗𝛼𝑜	PART
iajs-2878	95	9	disconnected	disconnected	ADJ
iajs-2878	95	10	space	space	NOUN
iajs-2878	95	11	,	,	PUNCT
iajs-2878	95	12	so	so	ADV
iajs-2878	95	13	.	.	PUNCT
iajs-2878	96	1	ꝡ=	ꝡ=	NOUN
iajs-2878	96	2	ⱥ	ⱥ	PROPN
iajs-2878	96	3	⋃ɓ	⋃ɓ	NUM
iajs-2878	96	4	;	;	PUNCT
iajs-2878	96	5	ⱥ	ⱥ	X
iajs-2878	96	6	and	and	CCONJ
iajs-2878	96	7	ɓ	ɓ	DET
iajs-2878	96	8	∈	∈	NOUN
iajs-2878	96	9	₢	₢	ADP
iajs-2878	96	10	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	96	11	)	)	PUNCT
iajs-2878	96	12	,	,	PUNCT
iajs-2878	96	13	ⱥ	ⱥ	PROPN
iajs-2878	96	14	⋂	⋂	PROPN
iajs-2878	96	15	ɓ	ɓ	X
iajs-2878	96	16	=	=	SYM
iajs-2878	96	17			NOUN
iajs-2878	96	18	,	,	PUNCT
iajs-2878	96	19	ⱥ	ⱥ	X
iajs-2878	96	20	,	,	PUNCT
iajs-2878	96	21	ɓ	ɓ	NOUN
iajs-2878	96	22			NOUN
iajs-2878	96	23	,	,	PUNCT
iajs-2878	96	24	so	so	CCONJ
iajs-2878	96	25	ⱥ	ⱥ	X
iajs-2878	96	26	=	=	X
iajs-2878	96	27	ɓ𝑐	ɓ𝑐	X
iajs-2878	96	28	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2878	96	29	ɓ	ɓ	PROPN
iajs-2878	96	30	=	=	X
iajs-2878	96	31	ⱥ𝑐	ⱥ𝑐	PROPN
iajs-2878	96	32	,	,	PUNCT
iajs-2878	96	33	then	then	ADV
iajs-2878	96	34	ⱥ	ⱥ	X
iajs-2878	96	35	and	and	CCONJ
iajs-2878	96	36	ɓ	ɓ	DET
iajs-2878	96	37	∈	∈	NOUN
iajs-2878	96	38	₢	₢	ADP
iajs-2878	96	39	∗𝛼𝑐(𝑥	∗𝛼𝑐(𝑥	PROPN
iajs-2878	96	40	)	)	PUNCT
iajs-2878	96	41	,	,	PUNCT
iajs-2878	96	42	but	but	CCONJ
iajs-2878	96	43	that	that	PRON
iajs-2878	96	44	is	be	AUX
iajs-2878	96	45	a	a	DET
iajs-2878	96	46	contradiction	contradiction	NOUN
iajs-2878	96	47	.	.	PUNCT
iajs-2878	97	1	therefore	therefore	ADV
iajs-2878	97	2	,	,	PUNCT
iajs-2878	97	3	ꝡ	ꝡ	PROPN
iajs-2878	97	4	is	be	AUX
iajs-2878	97	5	a	a	DET
iajs-2878	97	6	₢	₢	ADP
iajs-2878	97	7	∗𝛼𝑜connected	∗𝛼𝑜connecte	VERB
iajs-2878	97	8	space	space	NOUN
iajs-2878	97	9	.	.	PUNCT
iajs-2878	98	1	theorem	theorem	VERB
iajs-2878	98	2	3.8	3.8	NUM
iajs-2878	98	3	.	.	PUNCT
iajs-2878	99	1	the	the	DET
iajs-2878	99	2	space	space	NOUN
iajs-2878	99	3	(	(	PUNCT
iajs-2878	99	4	ꝡ	ꝡ	NOUN
iajs-2878	99	5	,	,	PUNCT
iajs-2878	99	6	τ	τ	PROPN
iajs-2878	99	7	,	,	PUNCT
iajs-2878	99	8	₢	₢	ADP
iajs-2878	99	9	)	)	PUNCT
iajs-2878	99	10	is	be	AUX
iajs-2878	99	11	a	a	DET
iajs-2878	99	12	₢	₢	ADP
iajs-2878	99	13	∗𝛼𝑜-connected	∗𝛼𝑜-connecte	VERB
iajs-2878	99	14	if	if	SCONJ
iajs-2878	99	15	and	and	CCONJ
iajs-2878	99	16	only	only	ADV
iajs-2878	99	17	if	if	SCONJ
iajs-2878	99	18	the	the	DET
iajs-2878	99	19	only	only	ADJ
iajs-2878	99	20	the	the	DET
iajs-2878	99	21	subsets	subset	NOUN
iajs-2878	99	22	of	of	ADP
iajs-2878	99	23	the	the	DET
iajs-2878	99	24	space	space	NOUN
iajs-2878	99	25	ꝡ	ꝡ	NOUN
iajs-2878	99	26	which	which	PRON
iajs-2878	99	27	are	be	AUX
iajs-2878	99	28	₢	₢	NOUN
iajs-2878	99	29	∗𝛼-open	∗𝛼-open	ADJ
iajs-2878	99	30	and	and	CCONJ
iajs-2878	99	31	₢	₢	NOUN
iajs-2878	99	32	∗𝛼-closed	∗𝛼-close	VERB
iajs-2878	99	33	are	be	AUX
iajs-2878	99	34	ꝡ	ꝡ	PROPN
iajs-2878	99	35	and	and	CCONJ
iajs-2878	99	36	ø	ø	PROPN
iajs-2878	99	37	.	.	PUNCT
iajs-2878	100	1	ihjpas	ihjpas	PROPN
iajs-2878	100	2	.	.	PUNCT
iajs-2878	101	1	53	53	NUM
iajs-2878	101	2	(	(	PUNCT
iajs-2878	101	3	4)2022	4)2022	NOUN
iajs-2878	101	4	217	217	NUM
iajs-2878	101	5	proof	proof	NOUN
iajs-2878	101	6	.	.	PUNCT
iajs-2878	102	1	let	let	VERB
iajs-2878	102	2	ⱥ	ⱥ	NOUN
iajs-2878	102	3	and	and	CCONJ
iajs-2878	102	4	ⱥ𝑐	ⱥ𝑐	ADP
iajs-2878	102	5	∈	∈	PROPN
iajs-2878	102	6	₢	₢	ADP
iajs-2878	102	7	∗𝛼𝑜(𝑥	∗𝛼𝑜(𝑥	NOUN
iajs-2878	102	8	)	)	PUNCT
iajs-2878	102	9	and	and	CCONJ
iajs-2878	102	10	ⱥ	ⱥ	PROPN
iajs-2878	102	11	≠	≠	PROPN
iajs-2878	102	12	ꝡ	ꝡ	PROPN
iajs-2878	102	13	,	,	PUNCT
iajs-2878	102	14	ⱥ	ⱥ	PROPN
iajs-2878	102	15	≠	≠	PROPN
iajs-2878	102	16	ø	ø	PROPN
iajs-2878	102	17	,	,	PUNCT
iajs-2878	102	18	so	so	ADV
iajs-2878	102	19	ꝡ	ꝡ	PROPN
iajs-2878	102	20	=	=	SYM
iajs-2878	102	21	ⱥ⋃ⱥ𝑐	ⱥ⋃ⱥ𝑐	PROPN
iajs-2878	102	22	;	;	PUNCT
iajs-2878	102	23	ⱥ	ⱥ	X
iajs-2878	102	24	⋂	⋂	PROPN
iajs-2878	102	25	ⱥ𝑐	ⱥ𝑐	NOUN
iajs-2878	102	26	=	=	SYM
iajs-2878	102	27			NOUN
iajs-2878	102	28	,	,	PUNCT
iajs-2878	102	29	ⱥ	ⱥ	X
iajs-2878	102	30	,	,	PUNCT
iajs-2878	102	31	ⱥ𝑐	ⱥ𝑐	ADP
iajs-2878	102	32	≠	≠	PROPN
iajs-2878	102	33	.	.	PUNCT
iajs-2878	102	34	then	then	ADV
iajs-2878	102	35	,	,	PUNCT
iajs-2878	102	36	ꝡ	ꝡ	PROPN
iajs-2878	102	37	is	be	AUX
iajs-2878	102	38	a	a	DET
iajs-2878	102	39	₢	₢	ADP
iajs-2878	102	40	∗𝛼𝑜-disconnected	∗𝛼𝑜-disconnecte	VERB
iajs-2878	102	41	,	,	PUNCT
iajs-2878	102	42	and	and	CCONJ
iajs-2878	102	43	that	that	PRON
iajs-2878	102	44	is	be	AUX
iajs-2878	102	45	a	a	DET
iajs-2878	102	46	contradiction	contradiction	NOUN
iajs-2878	102	47	.	.	PUNCT
iajs-2878	103	1	so	so	ADV
iajs-2878	103	2	,	,	PUNCT
iajs-2878	103	3	where	where	SCONJ
iajs-2878	103	4	ⱥ	ⱥ	PROPN
iajs-2878	103	5	⊆	⊆	NUM
iajs-2878	103	6	ꝡ	ꝡ	PROPN
iajs-2878	103	7	,	,	PUNCT
iajs-2878	103	8	ⱥ	ⱥ	X
iajs-2878	103	9	,	,	PUNCT
iajs-2878	103	10	ⱥ𝑐	ⱥ𝑐	PROPN
iajs-2878	103	11	∈	∈	PROPN
iajs-2878	103	12	₢	₢	ADP
iajs-2878	103	13	∗𝛼𝑜(𝑥	∗𝛼𝑜(𝑥	NOUN
iajs-2878	103	14	)	)	PUNCT
iajs-2878	103	15	,	,	PUNCT
iajs-2878	103	16	then	then	ADV
iajs-2878	103	17	ⱥ	ⱥ	PROPN
iajs-2878	103	18	=	=	SYM
iajs-2878	103	19	ꝡ	ꝡ	PROPN
iajs-2878	103	20	or	or	CCONJ
iajs-2878	103	21	ⱥ	ⱥ	X
iajs-2878	103	22	=	=	SYM
iajs-2878	103	23	ø	ø	PROPN
iajs-2878	103	24	,	,	PUNCT
iajs-2878	103	25	let	let	VERB
iajs-2878	103	26	ꝡ	ꝡ	PART
iajs-2878	103	27	be	be	AUX
iajs-2878	103	28	a	a	DET
iajs-2878	103	29	₢	₢	NUM
iajs-2878	103	30	∗𝛼𝑜-disconnected	∗𝛼𝑜-disconnecte	VERB
iajs-2878	103	31	space	space	NOUN
iajs-2878	103	32	.	.	PUNCT
iajs-2878	104	1	this	this	PRON
iajs-2878	104	2	means	mean	VERB
iajs-2878	104	3	that	that	SCONJ
iajs-2878	104	4	ꝡ	ꝡ	PROPN
iajs-2878	104	5	=	=	SYM
iajs-2878	104	6	𝒲⋃𝒵	𝒲⋃𝒵	PROPN
iajs-2878	104	7	;	;	PUNCT
iajs-2878	104	8	𝒲	𝒲	PROPN
iajs-2878	104	9	,	,	PUNCT
iajs-2878	104	10	𝒵	𝒵	PROPN
iajs-2878	104	11	∈	∈	PROPN
iajs-2878	104	12	₢	₢	ADP
iajs-2878	104	13	∗𝛼𝑜(𝑥	∗𝛼𝑜(𝑥	NOUN
iajs-2878	104	14	)	)	PUNCT
iajs-2878	104	15	,	,	PUNCT
iajs-2878	104	16	𝒲	𝒲	PROPN
iajs-2878	104	17	⋂	⋂	PROPN
iajs-2878	104	18	𝒵	𝒵	NOUN
iajs-2878	104	19	=	=	PUNCT
iajs-2878	104	20			NOUN
iajs-2878	104	21	and	and	CCONJ
iajs-2878	104	22	𝒲	𝒲	NOUN
iajs-2878	104	23	,	,	PUNCT
iajs-2878	104	24	𝒵	𝒵	PROPN
iajs-2878	104	25	≠	≠	PROPN
iajs-2878	104	26	ø	ø	PROPN
iajs-2878	104	27	implies	imply	VERB
iajs-2878	104	28	that	that	SCONJ
iajs-2878	104	29	𝒲	𝒲	NOUN
iajs-2878	104	30	=	=	SYM
iajs-2878	104	31	𝒵𝑐	𝒵𝑐	PROPN
iajs-2878	104	32	and	and	CCONJ
iajs-2878	104	33	𝒵	𝒵	PROPN
iajs-2878	104	34	=	=	SYM
iajs-2878	104	35	𝒲𝑐.	𝒲𝑐.	PROPN
iajs-2878	104	36	so	so	ADV
iajs-2878	104	37	𝒲	𝒲	PROPN
iajs-2878	104	38	,	,	PUNCT
iajs-2878	104	39	𝒵	𝒵	PROPN
iajs-2878	104	40	∈	∈	PROPN
iajs-2878	104	41	₢	₢	ADP
iajs-2878	104	42	∗𝛼𝑐(𝑥	∗𝛼𝑐(𝑥	PROPN
iajs-2878	104	43	)	)	PUNCT
iajs-2878	104	44	(	(	PUNCT
iajs-2878	104	45	that	that	PRON
iajs-2878	104	46	is	be	AUX
iajs-2878	104	47	contradiction	contradiction	NOUN
iajs-2878	104	48	)	)	PUNCT
iajs-2878	104	49	therefore	therefore	ADV
iajs-2878	104	50	,	,	PUNCT
iajs-2878	104	51	ꝡ	ꝡ	PROPN
iajs-2878	104	52	is	be	AUX
iajs-2878	104	53	a	a	DET
iajs-2878	104	54	₢	₢	ADP
iajs-2878	104	55	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	104	56	space	space	NOUN
iajs-2878	104	57	.	.	PUNCT
iajs-2878	105	1	remark	remark	PROPN
iajs-2878	105	2	3.9	3.9	NUM
iajs-2878	105	3	.	.	PUNCT
iajs-2878	106	1	if	if	SCONJ
iajs-2878	106	2	ᶂ	ᶂ	PROPN
iajs-2878	106	3	∶	∶	NOUN
iajs-2878	106	4	(	(	PUNCT
iajs-2878	106	5	ꝡ	ꝡ	PROPN
iajs-2878	106	6	,	,	PUNCT
iajs-2878	106	7	τ	τ	PROPN
iajs-2878	106	8	,	,	PUNCT
iajs-2878	106	9	₢	₢	ADP
iajs-2878	106	10	)	)	PUNCT
iajs-2878	106	11	→	→	SYM
iajs-2878	106	12	(	(	PUNCT
iajs-2878	106	13	ƴ	ƴ	PROPN
iajs-2878	106	14	,	,	PUNCT
iajs-2878	106	15	𝜏′	𝜏′	PROPN
iajs-2878	106	16	,	,	PUNCT
iajs-2878	106	17	₢	₢	NOUN
iajs-2878	106	18	)	)	PUNCT
iajs-2878	106	19	is	be	AUX
iajs-2878	106	20	a	a	DET
iajs-2878	106	21	₢	₢	NOUN
iajs-2878	106	22	∗𝛼𝑜-irresolute	∗𝛼𝑜-irresolute	NOUN
iajs-2878	106	23	and	and	CCONJ
iajs-2878	106	24	onto	onto	ADP
iajs-2878	106	25	function	function	NOUN
iajs-2878	106	26	and	and	CCONJ
iajs-2878	106	27	ƴ	ƴ	PROPN
iajs-2878	106	28	is	be	AUX
iajs-2878	106	29	a	a	DET
iajs-2878	106	30	₢	₢	NUM
iajs-2878	106	31	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	106	32	space	space	NOUN
iajs-2878	106	33	then	then	ADV
iajs-2878	106	34	ꝡ	ꝡ	PROPN
iajs-2878	106	35	is	be	AUX
iajs-2878	106	36	not	not	PART
iajs-2878	106	37	necessary	necessary	ADJ
iajs-2878	106	38	₢	₢	ADP
iajs-2878	106	39	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	106	40	space	space	NOUN
iajs-2878	106	41	.	.	PUNCT
iajs-2878	107	1	example	example	NOUN
iajs-2878	108	1	3.10	3.10	NUM
iajs-2878	108	2	.	.	PUNCT
iajs-2878	109	1	let	let	VERB
iajs-2878	109	2	ᶂ	ᶂ	PRON
iajs-2878	109	3	∶	∶	NOUN
iajs-2878	109	4	(	(	PUNCT
iajs-2878	109	5	ℝ	ℝ	PROPN
iajs-2878	109	6	,	,	PUNCT
iajs-2878	109	7	d	d	NOUN
iajs-2878	109	8	,	,	PUNCT
iajs-2878	109	9	₢	₢	ADP
iajs-2878	109	10	)	)	PUNCT
iajs-2878	109	11	→	→	SYM
iajs-2878	109	12	(	(	PUNCT
iajs-2878	109	13	ℝ	ℝ	PROPN
iajs-2878	109	14	,	,	PUNCT
iajs-2878	109	15	ι	ι	PROPN
iajs-2878	109	16	,	,	PUNCT
iajs-2878	109	17	₢	₢	ADP
iajs-2878	109	18	)	)	PUNCT
iajs-2878	109	19	;	;	PUNCT
iajs-2878	109	20	ḟ(ꝡ	ḟ(ꝡ	X
iajs-2878	109	21	)	)	PUNCT
iajs-2878	110	1	=	=	SYM
iajs-2878	110	2	ꝡ	ꝡ	PROPN
iajs-2878	110	3	for	for	ADP
iajs-2878	110	4	all	all	PRON
iajs-2878	110	5	ꝡ	ꝡ	PROPN
iajs-2878	110	6	∈	∈	PROPN
iajs-2878	110	7	ℝ	ℝ	PROPN
iajs-2878	110	8	and	and	CCONJ
iajs-2878	110	9	₢	₢	NOUN
iajs-2878	110	10	=	=	SYM
iajs-2878	110	11	ℙ(ꝡ	ℙ(ꝡ	NUM
iajs-2878	110	12	)	)	PUNCT
iajs-2878	110	13	∖	∖	NOUN
iajs-2878	110	14	{	{	PUNCT
iajs-2878	110	15	ø	ø	NOUN
iajs-2878	110	16	}	}	PUNCT
iajs-2878	110	17	,	,	PUNCT
iajs-2878	110	18	so	so	CCONJ
iajs-2878	110	19	ḟ	ḟ	PROPN
iajs-2878	110	20	is	be	AUX
iajs-2878	110	21	a	a	DET
iajs-2878	110	22	₢	₢	NOUN
iajs-2878	110	23	∗𝛼𝑜	∗𝛼𝑜	NOUN
iajs-2878	110	24	𝑖𝑟𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑒	𝑖𝑟𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑒	NOUN
iajs-2878	110	25	and	and	CCONJ
iajs-2878	110	26	onto	onto	ADP
iajs-2878	110	27	function	function	NOUN
iajs-2878	110	28	and	and	CCONJ
iajs-2878	110	29	(	(	PUNCT
iajs-2878	110	30	ℝ	ℝ	PROPN
iajs-2878	110	31	,	,	PUNCT
iajs-2878	110	32	ι	ι	PROPN
iajs-2878	110	33	,	,	PUNCT
iajs-2878	110	34	₢	₢	ADP
iajs-2878	110	35	)	)	PUNCT
iajs-2878	110	36	is	be	AUX
iajs-2878	110	37	a	a	DET
iajs-2878	110	38	₢	₢	ADP
iajs-2878	110	39	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	110	40	space	space	NOUN
iajs-2878	110	41	and	and	CCONJ
iajs-2878	110	42	(	(	PUNCT
iajs-2878	110	43	ℝ	ℝ	PROPN
iajs-2878	110	44	,	,	PUNCT
iajs-2878	110	45	d	d	NOUN
iajs-2878	110	46	,	,	PUNCT
iajs-2878	110	47	₢	₢	NOUN
iajs-2878	110	48	)	)	PUNCT
iajs-2878	110	49	is	be	AUX
iajs-2878	110	50	a	a	DET
iajs-2878	110	51	₢	₢	ADP
iajs-2878	110	52	∗𝛼𝑜disconnected	∗𝛼𝑜disconnecte	VERB
iajs-2878	110	53	space	space	NOUN
iajs-2878	110	54	.	.	PUNCT
iajs-2878	111	1	theorem	theorem	NOUN
iajs-2878	111	2	3.11	3.11	NUM
iajs-2878	111	3	.	.	PUNCT
iajs-2878	112	1	if	if	SCONJ
iajs-2878	112	2	ⱥ	ⱥ	PROPN
iajs-2878	112	3	and	and	CCONJ
iajs-2878	112	4	ɓ	ɓ	PRON
iajs-2878	112	5	are	be	AUX
iajs-2878	112	6	a	a	DET
iajs-2878	112	7	₢	₢	NUM
iajs-2878	112	8	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	112	9	spaces	space	NOUN
iajs-2878	112	10	of	of	ADP
iajs-2878	112	11	(	(	PUNCT
iajs-2878	112	12	ꝡ	ꝡ	PROPN
iajs-2878	112	13	,	,	PUNCT
iajs-2878	112	14	τ	τ	PROPN
iajs-2878	112	15	,	,	PUNCT
iajs-2878	112	16	₢	₢	ADP
iajs-2878	112	17	)	)	PUNCT
iajs-2878	112	18	and	and	CCONJ
iajs-2878	112	19	ⱥ	ⱥ	X
iajs-2878	112	20	⋂	⋂	PROPN
iajs-2878	112	21	ɓ	ɓ	DET
iajs-2878	112	22	≠	≠	PROPN
iajs-2878	112	23			NOUN
iajs-2878	112	24	,	,	PUNCT
iajs-2878	112	25	then	then	ADV
iajs-2878	112	26	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	112	27	is	be	AUX
iajs-2878	112	28	a	a	DET
iajs-2878	112	29	₢	₢	ADP
iajs-2878	112	30	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	112	31	space	space	NOUN
iajs-2878	112	32	.	.	PUNCT
iajs-2878	113	1	proof	proof	NOUN
iajs-2878	113	2	.	.	PUNCT
iajs-2878	114	1	let	let	VERB
iajs-2878	114	2	(	(	PUNCT
iajs-2878	114	3	ꝡ	ꝡ	NOUN
iajs-2878	114	4	,	,	PUNCT
iajs-2878	114	5	τ	τ	PROPN
iajs-2878	114	6	,	,	PUNCT
iajs-2878	114	7	₢	₢	ADP
iajs-2878	114	8	)	)	PUNCT
iajs-2878	114	9	be	be	VERB
iajs-2878	114	10	a	a	DET
iajs-2878	114	11	grill	grill	ADJ
iajs-2878	114	12	topological	topological	ADJ
iajs-2878	114	13	space	space	NOUN
iajs-2878	114	14	and	and	CCONJ
iajs-2878	114	15	ⱥ	ⱥ	X
iajs-2878	114	16	,	,	PUNCT
iajs-2878	114	17	ɓ	ɓ	PROPN
iajs-2878	114	18	⊆	⊆	NUM
iajs-2878	114	19	ꝡ	ꝡ	NOUN
iajs-2878	114	20	;	;	PUNCT
iajs-2878	114	21	ⱥ	ⱥ	X
iajs-2878	114	22	,	,	PUNCT
iajs-2878	114	23	ɓ	ɓ	PRON
iajs-2878	114	24	be	be	AUX
iajs-2878	114	25	a	a	DET
iajs-2878	114	26	₢	₢	ADP
iajs-2878	114	27	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	114	28	space	space	NOUN
iajs-2878	114	29	.	.	PUNCT
iajs-2878	115	1	now	now	ADV
iajs-2878	115	2	,	,	PUNCT
iajs-2878	115	3	if	if	SCONJ
iajs-2878	115	4	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	115	5	is	be	AUX
iajs-2878	115	6	a	a	DET
iajs-2878	115	7	₢	₢	ADP
iajs-2878	115	8	∗𝛼𝑜-disconnected	∗𝛼𝑜-disconnecte	VERB
iajs-2878	115	9	space	space	NOUN
iajs-2878	115	10	,	,	PUNCT
iajs-2878	115	11	so	so	ADV
iajs-2878	115	12	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	115	13	=	=	SYM
iajs-2878	115	14	𝒲⋃𝒵	𝒲⋃𝒵	NOUN
iajs-2878	115	15	;	;	PUNCT
iajs-2878	115	16	𝒲	𝒲	PROPN
iajs-2878	115	17	,	,	PUNCT
iajs-2878	115	18	𝒵	𝒵	PROPN
iajs-2878	115	19	∈	∈	PROPN
iajs-2878	115	20	₢	₢	ADP
iajs-2878	115	21	∗𝛼𝑜(𝑥)(ⱥ⋃ɓ	∗𝛼𝑜(𝑥)(ⱥ⋃ɓ	NOUN
iajs-2878	115	22	)	)	PUNCT
iajs-2878	115	23	,	,	PUNCT
iajs-2878	115	24	𝒲	𝒲	PROPN
iajs-2878	115	25	⋂	⋂	PROPN
iajs-2878	115	26	𝒵	𝒵	NOUN
iajs-2878	115	27	=	=	PUNCT
iajs-2878	115	28			NOUN
iajs-2878	115	29	and	and	CCONJ
iajs-2878	115	30	𝒲	𝒲	NOUN
iajs-2878	115	31	,	,	PUNCT
iajs-2878	115	32	𝒵	𝒵	PROPN
iajs-2878	115	33	≠	≠	PROPN
iajs-2878	115	34	ø	ø	PROPN
iajs-2878	115	35	,	,	PUNCT
iajs-2878	115	36	then	then	ADV
iajs-2878	115	37	ⱥ	ⱥ	X
iajs-2878	115	38	⊆	⊆	NUM
iajs-2878	115	39	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	115	40	,	,	PUNCT
iajs-2878	115	41	ⱥ	ⱥ	PROPN
iajs-2878	115	42	⊆	⊆	NUM
iajs-2878	115	43	𝒲⋃𝒵	𝒲⋃𝒵	NOUN
iajs-2878	115	44	,	,	PUNCT
iajs-2878	115	45	ⱥ	ⱥ	PROPN
iajs-2878	115	46	⊆	⊆	NUM
iajs-2878	115	47	𝒲	𝒲	NOUN
iajs-2878	115	48	𝑜𝑟	𝑜𝑟	NOUN
iajs-2878	115	49	ⱥ	ⱥ	PRON
iajs-2878	115	50	⊆	⊆	NUM
iajs-2878	115	51	𝒵.	𝒵.	PROPN
iajs-2878	115	52	similarly	similarly	ADV
iajs-2878	115	53	,	,	PUNCT
iajs-2878	115	54	ɓ	ɓ	PRON
iajs-2878	115	55	leads	lead	VERB
iajs-2878	115	56	to	to	ADP
iajs-2878	115	57	either	either	CCONJ
iajs-2878	115	58	ⱥ	ⱥ	PROPN
iajs-2878	115	59	⊆	⊆	NUM
iajs-2878	115	60	𝒲	𝒲	PROPN
iajs-2878	115	61	and	and	CCONJ
iajs-2878	115	62	ɓ	ɓ	DET
iajs-2878	115	63	⊆	⊆	NUM
iajs-2878	115	64	𝒲	𝒲	NOUN
iajs-2878	115	65	,	,	PUNCT
iajs-2878	115	66	then	then	ADV
iajs-2878	115	67	ⱥ⋃ɓ	ⱥ⋃ɓ	VERB
iajs-2878	115	68	⊆	⊆	NUM
iajs-2878	115	69	𝒲	𝒲	NOUN
iajs-2878	115	70	,	,	PUNCT
iajs-2878	115	71	then	then	ADV
iajs-2878	115	72	𝒵	𝒵	PROPN
iajs-2878	115	73	=	=	NOUN
iajs-2878	115	74	ø	ø	NOUN
iajs-2878	115	75	contradiction	contradiction	NOUN
iajs-2878	115	76	.	.	PUNCT
iajs-2878	116	1	or	or	CCONJ
iajs-2878	116	2	,	,	PUNCT
iajs-2878	116	3	ⱥ	ⱥ	PROPN
iajs-2878	116	4	⊆	⊆	NUM
iajs-2878	116	5	𝒵	𝒵	PROPN
iajs-2878	116	6	and	and	CCONJ
iajs-2878	116	7	ɓ	ɓ	DET
iajs-2878	116	8	⊆	⊆	NUM
iajs-2878	116	9	𝒵	𝒵	NOUN
iajs-2878	116	10	,	,	PUNCT
iajs-2878	116	11	then	then	ADV
iajs-2878	116	12	ⱥ⋃ɓ	ⱥ⋃ɓ	VERB
iajs-2878	116	13	⊆	⊆	NUM
iajs-2878	116	14	𝒵	𝒵	PROPN
iajs-2878	116	15	,	,	PUNCT
iajs-2878	116	16	then	then	ADV
iajs-2878	116	17	𝒲	𝒲	PROPN
iajs-2878	116	18	=	=	PUNCT
iajs-2878	116	19	ø	ø	NOUN
iajs-2878	116	20	c	c	X
iajs-2878	116	21	!	!	PUNCT
iajs-2878	116	22	or	or	CCONJ
iajs-2878	116	23	ⱥ	ⱥ	X
iajs-2878	116	24	⊆	⊆	NUM
iajs-2878	116	25	𝒲	𝒲	PROPN
iajs-2878	116	26	and	and	CCONJ
iajs-2878	116	27	ɓ	ɓ	DET
iajs-2878	116	28	⊆	⊆	NUM
iajs-2878	116	29	𝒵	𝒵	PROPN
iajs-2878	116	30	,	,	PUNCT
iajs-2878	116	31	then	then	ADV
iajs-2878	116	32	ⱥ	ⱥ	X
iajs-2878	116	33	∩	∩	NOUN
iajs-2878	116	34	ɓ	ɓ	PRON
iajs-2878	116	35	⊆	⊆	NUM
iajs-2878	116	36	𝒲	𝒲	PROPN
iajs-2878	116	37	∩	∩	ADJ
iajs-2878	116	38	𝒵	𝒵	PROPN
iajs-2878	116	39	,	,	PUNCT
iajs-2878	116	40	then	then	ADV
iajs-2878	116	41	ⱥ	ⱥ	X
iajs-2878	116	42	∩	∩	NOUN
iajs-2878	116	43	ɓ	ɓ	X
iajs-2878	116	44	=	=	SYM
iajs-2878	116	45	ø	ø	NOUN
iajs-2878	116	46	c	c	X
iajs-2878	116	47	!	!	PUNCT
iajs-2878	116	48	or	or	CCONJ
iajs-2878	116	49	ⱥ	ⱥ	X
iajs-2878	116	50	⊆	⊆	NUM
iajs-2878	116	51	𝒵	𝒵	PROPN
iajs-2878	116	52	and	and	CCONJ
iajs-2878	116	53	ɓ	ɓ	DET
iajs-2878	116	54	⊆	⊆	NUM
iajs-2878	116	55	𝒲	𝒲	NOUN
iajs-2878	116	56	,	,	PUNCT
iajs-2878	116	57	then	then	ADV
iajs-2878	116	58	ⱥ	ⱥ	X
iajs-2878	116	59	∩	∩	NOUN
iajs-2878	116	60	ɓ	ɓ	PRON
iajs-2878	116	61	⊆	⊆	NUM
iajs-2878	116	62	𝒲	𝒲	PROPN
iajs-2878	116	63	∩	∩	ADJ
iajs-2878	116	64	𝒵	𝒵	PROPN
iajs-2878	116	65	,	,	PUNCT
iajs-2878	116	66	then	then	ADV
iajs-2878	116	67	ⱥ	ⱥ	X
iajs-2878	116	68	∩	∩	ADJ
iajs-2878	116	69	ɓ	ɓ	X
iajs-2878	116	70	=	=	SYM
iajs-2878	116	71	ø	ø	PROPN
iajs-2878	116	72	.	.	PUNCT
iajs-2878	117	1	this	this	PRON
iajs-2878	117	2	is	be	AUX
iajs-2878	117	3	a	a	DET
iajs-2878	117	4	contradiction	contradiction	NOUN
iajs-2878	117	5	.	.	PUNCT
iajs-2878	118	1	so	so	ADV
iajs-2878	118	2	,	,	PUNCT
iajs-2878	118	3	ⱥ⋃ɓ	ⱥ⋃ɓ	NOUN
iajs-2878	118	4	is	be	AUX
iajs-2878	118	5	a	a	DET
iajs-2878	118	6	₢	₢	ADP
iajs-2878	118	7	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	118	8	space	space	NOUN
iajs-2878	118	9	.	.	PUNCT
iajs-2878	119	1	remark	remark	PROPN
iajs-2878	119	2	3.12	3.12	NUM
iajs-2878	119	3	.	.	PUNCT
iajs-2878	120	1	we	we	PRON
iajs-2878	120	2	can	can	AUX
iajs-2878	120	3	generalize	generalize	VERB
iajs-2878	120	4	theorem	theorem	VERB
iajs-2878	120	5	3.11	3.11	NUM
iajs-2878	120	6	to	to	ADP
iajs-2878	120	7	a	a	DET
iajs-2878	120	8	family	family	NOUN
iajs-2878	120	9	of	of	ADP
iajs-2878	120	10	a	a	DET
iajs-2878	120	11	₢	₢	NUM
iajs-2878	120	12	∗𝛼𝑜-connected	∗𝛼𝑜-connecte	VERB
iajs-2878	120	13	sets	set	NOUN
iajs-2878	120	14	as	as	SCONJ
iajs-2878	120	15	follows	follow	VERB
iajs-2878	120	16	:	:	PUNCT
iajs-2878	120	17	let	let	VERB
iajs-2878	120	18	{	{	PUNCT
iajs-2878	120	19	ⱥ∝}∝∈∧	ⱥ∝}∝∈∧	PROPN
iajs-2878	120	20	be	be	AUX
iajs-2878	120	21	a	a	DET
iajs-2878	120	22	family	family	NOUN
iajs-2878	120	23	of	of	ADP
iajs-2878	120	24	a	a	DET
iajs-2878	120	25	₢	₢	NUM
iajs-2878	120	26	∗𝛼𝑜-connected	∗𝛼𝑜-connected	ADJ
iajs-2878	120	27	subsets	subset	NOUN
iajs-2878	120	28	of	of	ADP
iajs-2878	120	29	a	a	DET
iajs-2878	120	30	space	space	NOUN
iajs-2878	120	31	(	(	PUNCT
iajs-2878	120	32	ꝡ	ꝡ	NOUN
iajs-2878	120	33	,	,	PUNCT
iajs-2878	120	34	τ	τ	PROPN
iajs-2878	120	35	,	,	PUNCT
iajs-2878	120	36	₢	₢	ADP
iajs-2878	120	37	)	)	PUNCT
iajs-2878	120	38	and	and	CCONJ
iajs-2878	120	39	⋂	⋂	PROPN
iajs-2878	120	40	ⱥ∝	ⱥ∝	PROPN
iajs-2878	120	41	≠	≠	PROPN
iajs-2878	120	42	ø∝∈∧	ø∝∈∧	PROPN
iajs-2878	120	43	,	,	PUNCT
iajs-2878	120	44	then	then	ADV
iajs-2878	120	45	⋃	⋃	NOUN
iajs-2878	120	46	ⱥ∝∝∈∧	ⱥ∝∝∈∧	NOUN
iajs-2878	120	47	is	be	AUX
iajs-2878	120	48	a	a	DET
iajs-2878	120	49	₢	₢	NUM
iajs-2878	120	50	∗𝛼𝑜-connected	∗𝛼𝑜-connecte	VERB
iajs-2878	120	51	set	set	NOUN
iajs-2878	120	52	.	.	PUNCT
iajs-2878	121	1	4	4	X
iajs-2878	121	2	.	.	X
iajs-2878	121	3	grill	grill	NOUN
iajs-2878	121	4	𝜶-open	𝜶-open	ADJ
iajs-2878	121	5	sets	set	NOUN
iajs-2878	121	6	in	in	ADP
iajs-2878	121	7	grill	grill	NOUN
iajs-2878	121	8	connected	connect	VERB
iajs-2878	121	9	space	space	NOUN
iajs-2878	121	10	hyperconnected	hyperconnecte	VERB
iajs-2878	121	11	definition	definition	NOUN
iajs-2878	121	12	4.1	4.1	NUM
iajs-2878	121	13	.	.	PUNCT
iajs-2878	122	1	in	in	ADP
iajs-2878	122	2	any	any	DET
iajs-2878	122	3	grill	grill	ADJ
iajs-2878	122	4	topological	topological	ADJ
iajs-2878	122	5	space	space	NOUN
iajs-2878	122	6	,	,	PUNCT
iajs-2878	122	7	(	(	PUNCT
iajs-2878	122	8	ꝡ	ꝡ	NOUN
iajs-2878	122	9	,	,	PUNCT
iajs-2878	122	10	τ	τ	PROPN
iajs-2878	122	11	,	,	PUNCT
iajs-2878	122	12	₢	₢	ADP
iajs-2878	122	13	)	)	PUNCT
iajs-2878	122	14	is	be	AUX
iajs-2878	122	15	said	say	VERB
iajs-2878	122	16	to	to	PART
iajs-2878	122	17	be	be	AUX
iajs-2878	122	18	:	:	PUNCT
iajs-2878	122	19	1	1	X
iajs-2878	122	20	.	.	X
iajs-2878	122	21	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	122	22	if	if	SCONJ
iajs-2878	122	23	ⱥ	ⱥ	X
iajs-2878	122	24	is	be	AUX
iajs-2878	122	25	τ₢-dense	τ₢-dense	PROPN
iajs-2878	122	26	(	(	PUNCT
iajs-2878	122	27	𝜍𝑙₢(ⱥ	𝜍𝑙₢(ⱥ	X
iajs-2878	122	28	)	)	PUNCT
iajs-2878	122	29	=	=	SYM
iajs-2878	122	30	ꝡ	ꝡ	NOUN
iajs-2878	122	31	)	)	PUNCT
iajs-2878	122	32	for	for	ADP
iajs-2878	122	33	every	every	DET
iajs-2878	122	34	non	non	ADJ
iajs-2878	122	35	-	-	ADJ
iajs-2878	122	36	empty	empty	ADJ
iajs-2878	122	37	open	open	ADJ
iajs-2878	122	38	subset	subset	NOUN
iajs-2878	122	39	ⱥ	ⱥ	PROPN
iajs-2878	122	40	of	of	ADP
iajs-2878	122	41	ꝡ	ꝡ	PROPN
iajs-2878	122	42	.	.	PROPN
iajs-2878	122	43	2	2	NUM
iajs-2878	122	44	.	.	X
iajs-2878	123	1	₢	₢	NOUN
iajs-2878	123	2	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	123	3	if	if	SCONJ
iajs-2878	123	4	ꝡ	ꝡ	PROPN
iajs-2878	123	5	−	−	PROPN
iajs-2878	123	6	𝜍𝑙₢(ⱥ	𝜍𝑙₢(ⱥ	NOUN
iajs-2878	123	7	)	)	PUNCT
iajs-2878	123	8	∉	∉	PROPN
iajs-2878	123	9	₢	₢	ADP
iajs-2878	123	10	for	for	ADP
iajs-2878	123	11	every	every	DET
iajs-2878	123	12	non	non	ADJ
iajs-2878	123	13	-	-	ADJ
iajs-2878	123	14	empty	empty	ADJ
iajs-2878	123	15	open	open	ADJ
iajs-2878	123	16	subset	subset	NOUN
iajs-2878	123	17	ⱥ	ⱥ	PROPN
iajs-2878	123	18	of	of	ADP
iajs-2878	123	19	ꝡ	ꝡ	PROPN
iajs-2878	123	20	.	.	PROPN
iajs-2878	123	21	3	3	NUM
iajs-2878	123	22	.	.	X
iajs-2878	123	23	₢	₢	NOUN
iajs-2878	123	24	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	123	25	if	if	SCONJ
iajs-2878	123	26	ꝡ	ꝡ	PROPN
iajs-2878	123	27	−	−	PROPN
iajs-2878	123	28	𝜍𝑙₢(ⱥ	𝜍𝑙₢(ⱥ	NOUN
iajs-2878	123	29	)	)	PUNCT
iajs-2878	123	30	∉	∉	PROPN
iajs-2878	123	31	₢	₢	ADP
iajs-2878	123	32	for	for	ADP
iajs-2878	123	33	every	every	DET
iajs-2878	123	34	non	non	ADJ
iajs-2878	123	35	-	-	ADJ
iajs-2878	123	36	empty	empty	ADJ
iajs-2878	123	37	₢	₢	ADP
iajs-2878	123	38	∗𝛼-𝑜𝑝𝑒𝑛	∗𝛼-𝑜𝑝𝑒𝑛	NOUN
iajs-2878	123	39	subset	subset	VERB
iajs-2878	123	40	ⱥ	ⱥ	PROPN
iajs-2878	123	41	of	of	ADP
iajs-2878	123	42	ꝡ	ꝡ	PROPN
iajs-2878	123	43	.	.	PROPN
iajs-2878	123	44	4	4	NUM
iajs-2878	123	45	.	.	X
iajs-2878	124	1	₢	₢	ADP
iajs-2878	124	2	∗𝛼𝑜-hyperconnected	∗𝛼𝑜-hyperconnecte	VERB
iajs-2878	124	3	if	if	SCONJ
iajs-2878	124	4	𝜍𝑙₢(ⱥ	𝜍𝑙₢(ⱥ	NOUN
iajs-2878	124	5	)	)	PUNCT
iajs-2878	124	6	=	=	SYM
iajs-2878	124	7	ꝡ	ꝡ	PROPN
iajs-2878	124	8	for	for	ADP
iajs-2878	124	9	all	all	DET
iajs-2878	124	10	ⱥ	ⱥ	PRON
iajs-2878	124	11	∈	∈	NOUN
iajs-2878	124	12	₢	₢	ADP
iajs-2878	124	13	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	PROPN
iajs-2878	124	14	)	)	PUNCT
iajs-2878	124	15	.	.	PUNCT
iajs-2878	125	1	ihjpas	ihjpas	PROPN
iajs-2878	125	2	.	.	PUNCT
iajs-2878	126	1	53	53	NUM
iajs-2878	126	2	(	(	PUNCT
iajs-2878	126	3	4)2022	4)2022	SYM
iajs-2878	126	4	218	218	NUM
iajs-2878	126	5	proposition	proposition	NOUN
iajs-2878	126	6	4.2	4.2	NUM
iajs-2878	126	7	.	.	PUNCT
iajs-2878	127	1	1.every	1.every	NUM
iajs-2878	127	2	₢	₢	ADP
iajs-2878	127	3	∗𝛼𝑜-hyperconnected	∗𝛼𝑜-hyperconnected	PROPN
iajs-2878	127	4	is	be	AUX
iajs-2878	127	5	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	127	6	.	.	PUNCT
iajs-2878	128	1	2	2	X
iajs-2878	128	2	.	.	X
iajs-2878	128	3	every	every	DET
iajs-2878	128	4	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	128	5	is	be	AUX
iajs-2878	128	6	₢	₢	NOUN
iajs-2878	128	7	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	128	8	.	.	PUNCT
iajs-2878	129	1	3	3	X
iajs-2878	129	2	.	.	X
iajs-2878	129	3	every	every	DET
iajs-2878	129	4	₢	₢	NUM
iajs-2878	129	5	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	129	6	is	be	AUX
iajs-2878	129	7	₢	₢	NOUN
iajs-2878	129	8	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	129	9	.	.	PUNCT
iajs-2878	130	1	4	4	X
iajs-2878	130	2	.	.	X
iajs-2878	130	3	every	every	DET
iajs-2878	130	4	₢	₢	NUM
iajs-2878	130	5	∗𝛼𝑜-hyperconnected	∗𝛼𝑜-hyperconnected	PROPN
iajs-2878	130	6	is	be	AUX
iajs-2878	130	7	₢	₢	ADP
iajs-2878	130	8	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	130	9	.	.	PUNCT
iajs-2878	131	1	proof	proof	NOUN
iajs-2878	131	2	.	.	PUNCT
iajs-2878	132	1	1	1	X
iajs-2878	132	2	.	.	X
iajs-2878	132	3	let	let	VERB
iajs-2878	132	4	ⱥ	ⱥ	PRON
iajs-2878	132	5	is	be	AUX
iajs-2878	132	6	a	a	DET
iajs-2878	132	7	₢	₢	ADP
iajs-2878	132	8	∗𝛼𝑜-hyperconnected	∗𝛼𝑜-hyperconnected	ADJ
iajs-2878	132	9	,	,	PUNCT
iajs-2878	132	10	then	then	ADV
iajs-2878	132	11	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	ADP
iajs-2878	132	12	)	)	PUNCT
iajs-2878	132	13	=	=	SYM
iajs-2878	133	1	ꝡ	ꝡ	PROPN
iajs-2878	133	2	then	then	ADV
iajs-2878	133	3	ⱥ	ⱥ	X
iajs-2878	133	4	is	be	AUX
iajs-2878	133	5	a	a	DET
iajs-2878	133	6	∗-hyperconnected	∗-hyperconnecte	VERB
iajs-2878	133	7	(	(	PUNCT
iajs-2878	133	8	since	since	SCONJ
iajs-2878	133	9	ⱥ	ⱥ	PROPN
iajs-2878	133	10	∈	∈	PROPN
iajs-2878	133	11	₢	₢	ADP
iajs-2878	133	12	∗𝛼𝑜(ꝡ	∗𝛼𝑜(ꝡ	NUM
iajs-2878	133	13	)	)	PUNCT
iajs-2878	133	14	.	.	PUNCT
iajs-2878	134	1	then	then	ADV
iajs-2878	134	2	ⱥ	ⱥ	PROPN
iajs-2878	134	3	∈	∈	PROPN
iajs-2878	134	4	τ	τ	PROPN
iajs-2878	134	5	)	)	PUNCT
iajs-2878	134	6	.	.	PUNCT
iajs-2878	135	1	2	2	X
iajs-2878	135	2	.	.	X
iajs-2878	135	3	let	let	VERB
iajs-2878	135	4	ⱥ	ⱥ	PRON
iajs-2878	135	5	be	be	AUX
iajs-2878	135	6	a	a	DET
iajs-2878	135	7	∗-hyperconnected	∗-hyperconnected	NOUN
iajs-2878	135	8	.	.	PUNCT
iajs-2878	136	1	this	this	PRON
iajs-2878	136	2	means	mean	VERB
iajs-2878	136	3	that	that	SCONJ
iajs-2878	136	4	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	ADP
iajs-2878	136	5	)	)	PUNCT
iajs-2878	136	6	=	=	SYM
iajs-2878	136	7	ꝡ	ꝡ	NOUN
iajs-2878	136	8	.	.	PUNCT
iajs-2878	137	1	so	so	ADV
iajs-2878	137	2	,	,	PUNCT
iajs-2878	137	3	ꝡ	ꝡ	PROPN
iajs-2878	137	4	−	−	NOUN
iajs-2878	137	5	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	NOUN
iajs-2878	137	6	)	)	PUNCT
iajs-2878	137	7	=	=	SYM
iajs-2878	137	8	∅	∅	NOUN
iajs-2878	137	9	∉	∉	ADJ
iajs-2878	137	10	₢	₢	PROPN
iajs-2878	137	11	.	.	PUNCT
iajs-2878	138	1	therefore	therefore	ADV
iajs-2878	138	2	,	,	PUNCT
iajs-2878	138	3	ⱥ	ⱥ	X
iajs-2878	138	4	is	be	AUX
iajs-2878	138	5	a	a	DET
iajs-2878	138	6	₢	₢	NOUN
iajs-2878	138	7	∗-hyperconnected	∗-hyperconnected	ADJ
iajs-2878	138	8	.	.	PUNCT
iajs-2878	139	1	3	3	X
iajs-2878	139	2	.	.	X
iajs-2878	139	3	let	let	VERB
iajs-2878	139	4	ⱥ	ⱥ	PRON
iajs-2878	139	5	be	be	AUX
iajs-2878	139	6	an	an	DET
iajs-2878	139	7	open	open	ADJ
iajs-2878	139	8	in	in	ADP
iajs-2878	139	9	₢	₢	ADP
iajs-2878	139	10	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	139	11	that	that	PRON
iajs-2878	139	12	's	be	AUX
iajs-2878	139	13	mean	mean	VERB
iajs-2878	139	14	that	that	SCONJ
iajs-2878	139	15	ꝡ	ꝡ	PROPN
iajs-2878	139	16	−	−	PROPN
iajs-2878	139	17	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	NOUN
iajs-2878	139	18	)	)	PUNCT
iajs-2878	139	19	∉	∉	PROPN
iajs-2878	140	1	₢	₢	ADP
iajs-2878	140	2	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	140	3	(	(	PUNCT
iajs-2878	140	4	since	since	SCONJ
iajs-2878	140	5	every	every	DET
iajs-2878	140	6	open	open	ADJ
iajs-2878	140	7	set	set	NOUN
iajs-2878	140	8	in	in	ADP
iajs-2878	140	9	₢	₢	NOUN
iajs-2878	140	10	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	140	11	is	be	AUX
iajs-2878	140	12	an	an	DET
iajs-2878	140	13	open	open	ADJ
iajs-2878	140	14	set	set	NOUN
iajs-2878	140	15	in	in	ADP
iajs-2878	140	16	₢	₢	ADP
iajs-2878	140	17	∗-hyperconnected	∗-hyperconnected	ADJ
iajs-2878	140	18	.	.	PUNCT
iajs-2878	141	1	so	so	ADV
iajs-2878	141	2	,	,	PUNCT
iajs-2878	141	3	ꝡ	ꝡ	PROPN
iajs-2878	141	4	−	−	PROPN
iajs-2878	141	5	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	NOUN
iajs-2878	141	6	)	)	PUNCT
iajs-2878	141	7	∉	∉	PROPN
iajs-2878	141	8	₢	₢	ADP
iajs-2878	141	9	.therefore	.therefore	NOUN
iajs-2878	141	10	,	,	PUNCT
iajs-2878	141	11	ⱥ	ⱥ	X
iajs-2878	141	12	is	be	AUX
iajs-2878	141	13	a	a	DET
iajs-2878	141	14	₢	₢	NOUN
iajs-2878	141	15	∗-hyperconnected	∗-hyperconnected	ADJ
iajs-2878	141	16	.	.	PUNCT
iajs-2878	142	1	4	4	X
iajs-2878	142	2	.	.	X
iajs-2878	142	3	let	let	VERB
iajs-2878	142	4	ⱥ	ⱥ	PRON
iajs-2878	142	5	be	be	AUX
iajs-2878	142	6	an	an	DET
iajs-2878	142	7	open	open	NOUN
iajs-2878	142	8	in	in	ADP
iajs-2878	142	9	₢	₢	ADP
iajs-2878	142	10	∗𝛼𝑜-hyperconnected	∗𝛼𝑜-hyperconnected	PROPN
iajs-2878	142	11	.	.	PUNCT
iajs-2878	143	1	this	this	PRON
iajs-2878	143	2	means	mean	VERB
iajs-2878	143	3	that	that	SCONJ
iajs-2878	143	4	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	ADP
iajs-2878	143	5	)	)	PUNCT
iajs-2878	143	6	=	=	SYM
iajs-2878	143	7	ꝡ	ꝡ	NOUN
iajs-2878	143	8	.	.	PUNCT
iajs-2878	144	1	so	so	ADV
iajs-2878	144	2	,	,	PUNCT
iajs-2878	144	3	ꝡ	ꝡ	PROPN
iajs-2878	144	4	−	−	PROPN
iajs-2878	144	5	𝑐𝜄₢(ⱥ	𝑐𝜄₢(ⱥ	NOUN
iajs-2878	144	6	)	)	PUNCT
iajs-2878	144	7	∉	∉	PROPN
iajs-2878	144	8	₢	₢	PROPN
iajs-2878	144	9	.	.	PUNCT
iajs-2878	145	1	therefore	therefore	ADV
iajs-2878	145	2	,	,	PUNCT
iajs-2878	145	3	ⱥ	ⱥ	X
iajs-2878	145	4	is	be	AUX
iajs-2878	145	5	a	a	DET
iajs-2878	145	6	₢	₢	NUM
iajs-2878	145	7	∗𝑠-hyperconnected	∗𝑠-hyperconnecte	VERB
iajs-2878	145	8	.	.	PUNCT
iajs-2878	146	1	the	the	DET
iajs-2878	146	2	following	follow	VERB
iajs-2878	146	3	diagram	diagram	NOUN
iajs-2878	146	4	shows	show	VERB
iajs-2878	146	5	the	the	DET
iajs-2878	146	6	relationship	relationship	NOUN
iajs-2878	146	7	between	between	ADP
iajs-2878	146	8	the	the	DET
iajs-2878	146	9	types	type	NOUN
iajs-2878	146	10	of	of	ADP
iajs-2878	146	11	hyperconnected	hyperconnecte	VERB
iajs-2878	146	12	.	.	PUNCT
iajs-2878	147	1	∗-hyperconn𝑒cted	∗-hyperconn𝑒cte	VERB
iajs-2878	147	2	₢	₢	ADP
iajs-2878	147	3	∗𝛼𝑜-hyperconn𝑒cted	∗𝛼𝑜-hyperconn𝑒cte	VERB
iajs-2878	147	4	₢	₢	ADP
iajs-2878	147	5	∗-hyperconn𝑒cted	∗-hyperconn𝑒cte	VERB
iajs-2878	147	6	₢	₢	NUM
iajs-2878	147	7	∗𝛼-hyperconnected	∗𝛼-hyperconnecte	VERB
iajs-2878	147	8	diagram	diagram	NOUN
iajs-2878	147	9	1	1	NUM
iajs-2878	147	10	hyperconnected	hyperconnecte	VERB
iajs-2878	147	11	space	space	NOUN
iajs-2878	147	12	via	via	ADP
iajs-2878	147	13	grill	grill	ADJ
iajs-2878	147	14	space	space	NOUN
iajs-2878	147	15	.	.	PUNCT
iajs-2878	148	1	conclusion4	conclusion4	NOUN
iajs-2878	149	1	in	in	ADP
iajs-2878	149	2	this	this	DET
iajs-2878	149	3	research	research	NOUN
iajs-2878	149	4	we	we	PRON
iajs-2878	149	5	studied	study	VERB
iajs-2878	149	6	a	a	DET
iajs-2878	149	7	connect	connect	ADJ
iajs-2878	149	8	space	space	NOUN
iajs-2878	149	9	in	in	ADP
iajs-2878	149	10	the	the	DET
iajs-2878	149	11	grill	grill	NOUN
iajs-2878	149	12	α	α	PROPN
iajs-2878	149	13	-open	-open	PROPN
iajs-2878	149	14	topological	topological	ADJ
iajs-2878	149	15	spaces	space	NOUN
iajs-2878	149	16	,	,	PUNCT
iajs-2878	149	17	we	we	PRON
iajs-2878	149	18	showed	show	VERB
iajs-2878	149	19	some	some	DET
iajs-2878	149	20	examples	example	NOUN
iajs-2878	149	21	and	and	CCONJ
iajs-2878	149	22	applied	apply	VERB
iajs-2878	149	23	some	some	DET
iajs-2878	149	24	theorems	theorem	NOUN
iajs-2878	149	25	for	for	ADP
iajs-2878	149	26	this	this	DET
iajs-2878	149	27	new	new	ADJ
iajs-2878	149	28	sets	set	NOUN
iajs-2878	149	29	.	.	PUNCT
iajs-2878	150	1	we	we	PRON
iajs-2878	150	2	also	also	ADV
iajs-2878	150	3	found	find	VERB
iajs-2878	150	4	some	some	DET
iajs-2878	150	5	new	new	ADJ
iajs-2878	150	6	properties	property	NOUN
iajs-2878	150	7	of	of	ADP
iajs-2878	150	8	these	these	DET
iajs-2878	150	9	sets	set	NOUN
iajs-2878	150	10	.	.	PUNCT
iajs-2878	151	1	ihjpas	ihjpas	PROPN
iajs-2878	151	2	.	.	PUNCT
iajs-2878	152	1	53	53	NUM
iajs-2878	152	2	(	(	PUNCT
iajs-2878	152	3	4)2022	4)2022	NOUN
iajs-2878	152	4	219	219	NUM
iajs-2878	152	5	references	reference	NOUN
iajs-2878	152	6	1	1	NUM
iajs-2878	152	7	.	.	PUNCT
iajs-2878	152	8	choquet	choquet	PROPN
iajs-2878	152	9	.	.	PUNCT
iajs-2878	153	1	g.	g.	PROPN
iajs-2878	153	2	sur	sur	PROPN
iajs-2878	153	3	les	les	PROPN
iajs-2878	153	4	notions	notion	NOUN
iajs-2878	153	5	de	de	X
iajs-2878	153	6	filtre	filtre	NOUN
iajs-2878	153	7	et	et	NOUN
iajs-2878	153	8	grille	grille	NOUN
iajs-2878	153	9	,	,	PUNCT
iajs-2878	153	10	comptes	compte	VERB
iajs-2878	153	11	rendus	rendus	PROPN
iajs-2878	153	12	acad	acad	PROPN
iajs-2878	153	13	.	.	PUNCT
iajs-2878	154	1	sci	sci	PROPN
iajs-2878	154	2	.	.	PROPN
iajs-2878	154	3	paris	paris	PROPN
iajs-2878	154	4	,	,	PUNCT
iajs-2878	154	5	224	224	NUM
iajs-2878	154	6	1947	1947	NUM
iajs-2878	154	7	,	,	PUNCT
iajs-2878	154	8	171173	171173	NUM
iajs-2878	154	9	.	.	PUNCT
iajs-2878	155	1	2	2	X
iajs-2878	155	2	.	.	X
iajs-2878	155	3	esmaeel	esmaeel	NOUN
iajs-2878	155	4	,	,	PUNCT
iajs-2878	155	5	r.b	r.b	PROPN
iajs-2878	155	6	.	.	PROPN
iajs-2878	155	7	;	;	PUNCT
iajs-2878	156	1	mohammad	mohammad	PROPN
iajs-2878	156	2	.	.	PUNCT
iajs-2878	157	1	r.j	r.j	AUX
iajs-2878	157	2	on	on	ADP
iajs-2878	157	3	nano	nano	PROPN
iajs-2878	157	4	soft	soft	ADJ
iajs-2878	157	5	j	j	NOUN
iajs-2878	157	6	-	-	PUNCT
iajs-2878	157	7	semi	semi	ADJ
iajs-2878	157	8	-	-	ADJ
iajs-2878	157	9	g	g	ADV
iajs-2878	157	10	-	-	PUNCT
iajs-2878	157	11	closed	close	VERB
iajs-2878	157	12	sets	set	NOUN
iajs-2878	157	13	,	,	PUNCT
iajs-2878	157	14	j.	j.	PROPN
iajs-2878	157	15	phys	phys	PROPN
iajs-2878	157	16	.	.	PUNCT
iajs-2878	157	17	conf	conf	PROPN
iajs-2878	157	18	.	.	PUNCT
iajs-2878	158	1	ser	ser	PROPN
iajs-2878	158	2	.	.	PROPN
iajs-2878	159	1	2020	2020	NUM
iajs-2878	159	2	,	,	PUNCT
iajs-2878	159	3	159(1	159(1	NUM
iajs-2878	159	4	)	)	PUNCT
iajs-2878	159	5	,	,	PUNCT
iajs-2878	159	6	012071	012071	NUM
iajs-2878	159	7	.	.	PUNCT
iajs-2878	160	1	3	3	X
iajs-2878	160	2	.	.	X
iajs-2878	160	3	esmaeel	esmaeel	PROPN
iajs-2878	160	4	,	,	PUNCT
iajs-2878	160	5	r.	r.	PROPN
iajs-2878	160	6	b	b	PROPN
iajs-2878	160	7	;	;	PUNCT
iajs-2878	160	8	nasir	nasir	PROPN
iajs-2878	160	9	.	.	PUNCT
iajs-2878	161	1	a.	a.	PROPN
iajs-2878	161	2	i	i	PRON
iajs-2878	161	3	;	;	PUNCT
iajs-2878	161	4	bayda	bayda	VERB
iajs-2878	161	5	atiya	atiya	PROPN
iajs-2878	161	6	kalaf	kalaf	PROPN
iajs-2878	161	7	.	.	PUNCT
iajs-2878	162	1	on	on	ADP
iajs-2878	162	2	αĩ	αĩ	ADP
iajs-2878	162	3	-	-	PUNCT
iajs-2878	162	4	closed	close	VERB
iajs-2878	162	5	soft	soft	ADJ
iajs-2878	162	6	sets	set	NOUN
iajs-2878	162	7	.	.	PUNCT
iajs-2878	163	1	sci	sci	PROPN
iajs-2878	163	2	.	.	PUNCT
iajs-2878	163	3	inter	inter	PROPN
iajs-2878	163	4	.	.	PUNCT
iajs-2878	164	1	(	(	PUNCT
iajs-2878	164	2	lahore	lahore	NOUN
iajs-2878	164	3	)	)	PUNCT
iajs-2878	164	4	.	.	PUNCT
iajs-2878	165	1	2018	2018	NUM
iajs-2878	165	2	.	.	PUNCT
iajs-2878	166	1	30(5	30(5	NUM
iajs-2878	166	2	):	):	PUNCT
iajs-2878	166	3	703	703	NUM
iajs-2878	166	4	-	-	SYM
iajs-2878	166	5	705	705	NUM
iajs-2878	166	6	.	.	NOUN
iajs-2878	166	7	4	4	NUM
iajs-2878	166	8	.	.	X
iajs-2878	166	9	levine	levine	PROPN
iajs-2878	166	10	,	,	PUNCT
iajs-2878	166	11	n.	n.	PROPN
iajs-2878	166	12	semi	semi	ADJ
iajs-2878	166	13	-	-	ADJ
iajs-2878	166	14	open	open	ADJ
iajs-2878	166	15	sets	set	NOUN
iajs-2878	166	16	and	and	CCONJ
iajs-2878	166	17	semi	semi	ADJ
iajs-2878	166	18	-	-	NOUN
iajs-2878	166	19	continuity	continuity	NOUN
iajs-2878	166	20	in	in	ADP
iajs-2878	166	21	topological	topological	ADJ
iajs-2878	166	22	spaces	space	NOUN
iajs-2878	166	23	,	,	PUNCT
iajs-2878	166	24	amer	amer	PROPN
iajs-2878	166	25	math	math	PROPN
iajs-2878	166	26	.	.	PUNCT
iajs-2878	167	1	monthly	monthly	ADJ
iajs-2878	167	2	,	,	PUNCT
iajs-2878	167	3	1963,70	1963,70	NUM
iajs-2878	167	4	,	,	PUNCT
iajs-2878	167	5	36	36	NUM
iajs-2878	167	6	-	-	SYM
iajs-2878	167	7	41	41	NUM
iajs-2878	167	8	.	.	PUNCT
iajs-2878	168	1	5	5	NUM
iajs-2878	168	2	.	.	PUNCT
iajs-2878	168	3	ahmed	ahmed	PROPN
iajs-2878	168	4	al	al	PROPN
iajs-2878	168	5	-	-	PROPN
iajs-2878	168	6	omary	omary	NOUN
iajs-2878	168	7	;	;	PUNCT
iajs-2878	168	8	takasi	takasi	PROPN
iajs-2878	168	9	noiri	noiri	PROPN
iajs-2878	168	10	.	.	PUNCT
iajs-2878	169	1	decompositions	decomposition	NOUN
iajs-2878	169	2	of	of	ADP
iajs-2878	169	3	continuity	continuity	NOUN
iajs-2878	169	4	via	via	ADP
iajs-2878	169	5	grills	grill	NOUN
iajs-2878	169	6	,	,	PUNCT
iajs-2878	169	7	jordan	jordan	PROPN
iajs-2878	169	8	journal	journal	PROPN
iajs-2878	169	9	mathematics	mathematics	PROPN
iajs-2878	169	10	and	and	CCONJ
iajs-2878	169	11	statistics	statistic	NOUN
iajs-2878	169	12	(	(	PUNCT
iajs-2878	169	13	jjms	jjms	PROPN
iajs-2878	169	14	)	)	PUNCT
iajs-2878	169	15	,	,	PUNCT
iajs-2878	169	16	2011,4(1	2011,4(1	NUM
iajs-2878	169	17	)	)	PUNCT
iajs-2878	169	18	,	,	PUNCT
iajs-2878	169	19	33	33	NUM
iajs-2878	169	20	-	-	SYM
iajs-2878	169	21	46	46	NUM
iajs-2878	169	22	6	6	NUM
iajs-2878	169	23	.	.	PUNCT
iajs-2878	169	24	dhanabal	dhanabal	ADJ
iajs-2878	169	25	saravanakumar	saravanakumar	PROPN
iajs-2878	169	26	;	;	PUNCT
iajs-2878	169	27	nagarajan	nagarajan	NOUN
iajs-2878	169	28	kalaivani	kalaivani	PROPN
iajs-2878	169	29	.	.	PUNCT
iajs-2878	170	1	on	on	ADP
iajs-2878	170	2	grill	grill	NOUN
iajs-2878	170	3	spopen	spopen	NOUN
iajs-2878	170	4	set	set	VERB
iajs-2878	170	5	in	in	ADP
iajs-2878	170	6	grill	grill	ADJ
iajs-2878	170	7	topological	topological	ADJ
iajs-2878	170	8	spaces	space	NOUN
iajs-2878	170	9	,	,	PUNCT
iajs-2878	170	10	journal	journal	NOUN
iajs-2878	170	11	of	of	ADP
iajs-2878	170	12	new	new	ADJ
iajs-2878	170	13	theory	theory	NOUN
iajs-2878	170	14	,	,	PUNCT
iajs-2878	170	15	2018	2018	NUM
iajs-2878	170	16	,	,	PUNCT
iajs-2878	170	17	23,85	23,85	NUM
iajs-2878	170	18	-	-	SYM
iajs-2878	170	19	92	92	NUM
iajs-2878	170	20	.	.	PUNCT
iajs-2878	170	21	7	7	X
iajs-2878	170	22	.	.	X
iajs-2878	170	23	mustafa	mustafa	PROPN
iajs-2878	170	24	,	,	PUNCT
iajs-2878	170	25	m.o	m.o	PROPN
iajs-2878	170	26	.	.	PROPN
iajs-2878	170	27	;	;	PUNCT
iajs-2878	170	28	esmaeel	esmaeel	VERB
iajs-2878	170	29	,	,	PUNCT
iajs-2878	170	30	r.b	r.b	PROPN
iajs-2878	170	31	.	.	PROPN
iajs-2878	170	32	.	.	PUNCT
iajs-2878	171	1	separation	separation	NOUN
iajs-2878	171	2	axioms	axiom	VERB
iajs-2878	171	3	with	with	ADP
iajs-2878	171	4	grill	grill	ADJ
iajs-2878	171	5	-	-	PUNCT
iajs-2878	171	6	topological	topological	ADJ
iajs-2878	171	7	open	open	ADJ
iajs-2878	171	8	set	set	NOUN
iajs-2878	171	9	,	,	PUNCT
iajs-2878	171	10	j.	j.	PROPN
iajs-2878	171	11	phys	phys	PROPN
iajs-2878	171	12	.	.	PUNCT
iajs-2878	172	1	2021	2021	NUM
iajs-2878	172	2	,	,	PUNCT
iajs-2878	172	3	1879,2	1879,2	NUM
iajs-2878	172	4	,	,	PUNCT
iajs-2878	172	5	022107	022107	NUM
iajs-2878	172	6	.	.	PUNCT
iajs-2878	173	1	8	8	NUM
iajs-2878	173	2	.	.	X
iajs-2878	173	3	arkhangel'skii	arkhangel'skii	PROPN
iajs-2878	173	4	,	,	PUNCT
iajs-2878	173	5	a.v	a.v	PROPN
iajs-2878	173	6	.	.	PROPN
iajs-2878	173	7	;	;	PUNCT
iajs-2878	173	8	ponomar''ev	ponomar''ev	PROPN
iajs-2878	173	9	,	,	PUNCT
iajs-2878	173	10	v.i	v.i	PROPN
iajs-2878	173	11	.	.	PROPN
iajs-2878	173	12	fundamentals	fundamental	NOUN
iajs-2878	173	13	of	of	ADP
iajs-2878	173	14	general	general	ADJ
iajs-2878	173	15	topology	topology	NOUN
iajs-2878	173	16	-	-	PUNCT
iajs-2878	173	17	problems	problem	NOUN
iajs-2878	173	18	and	and	CCONJ
iajs-2878	173	19	exercises	exercise	NOUN
iajs-2878	173	20	,	,	PUNCT
iajs-2878	173	21	hindustan	hindustan	PROPN
iajs-2878	173	22	pub.corporation	pub.corporation	NOUN
iajs-2878	173	23	,	,	PUNCT
iajs-2878	173	24	delhi	delhi	PROPN
iajs-2878	173	25	,	,	PUNCT
iajs-2878	173	26	1966	1966	NUM
iajs-2878	173	27	.	.	PUNCT
iajs-2878	174	1	9	9	NUM
iajs-2878	174	2	.	.	X
iajs-2878	174	3	b.	b.	PROPN
iajs-2878	174	4	roy	roy	PROPN
iajs-2878	174	5	;	;	PUNCT
iajs-2878	174	6	m.	m.	PROPN
iajs-2878	174	7	n.	n.	PROPN
iajs-2878	174	8	mukherjee	mukherjee	PROPN
iajs-2878	174	9	.	.	PUNCT
iajs-2878	175	1	on	on	ADP
iajs-2878	175	2	a	a	DET
iajs-2878	175	3	typical	typical	ADJ
iajs-2878	175	4	topology	topology	NOUN
iajs-2878	175	5	induced	induce	VERB
iajs-2878	175	6	by	by	ADP
iajs-2878	175	7	a	a	DET
iajs-2878	175	8	grill	grill	NOUN
iajs-2878	175	9	,	,	PUNCT
iajs-2878	175	10	soochow	soochow	PROPN
iajs-2878	175	11	j.	j.	PROPN
iajs-2878	175	12	math	math	PROPN
iajs-2878	175	13	.	.	PUNCT
iajs-2878	175	14	,	,	PUNCT
iajs-2878	175	15	2007	2007	NUM
iajs-2878	175	16	,	,	PUNCT
iajs-2878	175	17	33	33	NUM
iajs-2878	175	18	(	(	PUNCT
iajs-2878	175	19	4	4	NUM
iajs-2878	175	20	)	)	PUNCT
iajs-2878	175	21	,	,	PUNCT
iajs-2878	175	22	771	771	NUM
iajs-2878	175	23	-	-	SYM
iajs-2878	175	24	786	786	NUM
iajs-2878	175	25	.	.	PUNCT
iajs-2878	176	1	10	10	NUM
iajs-2878	176	2	.	.	PUNCT
iajs-2878	177	1	saad	saad	PROPN
iajs-2878	177	2	,	,	PUNCT
iajs-2878	177	3	s.	s.	PROPN
iajs-2878	177	4	suliman	suliman	PROPN
iajs-2878	177	5	;	;	PUNCT
iajs-2878	177	6	r.	r.	PROPN
iajs-2878	177	7	b.	b.	PROPN
iajs-2878	177	8	esmaeel	esmaeel	PROPN
iajs-2878	177	9	.	.	PUNCT
iajs-2878	178	1	on	on	ADP
iajs-2878	178	2	some	some	DET
iajs-2878	178	3	topology	topology	NOUN
iajs-2878	178	4	concepts	concept	NOUN
iajs-2878	178	5	via	via	ADP
iajs-2878	178	6	grill	grill	NOUN
iajs-2878	178	7	,	,	PUNCT
iajs-2878	178	8	int	int	NOUN
iajs-2878	178	9	.	.	PUNCT
iajs-2878	179	1	j.	j.	PROPN
iajs-2878	179	2	nonlinear	nonlinear	PROPN
iajs-2878	179	3	anal	anal	PROPN
iajs-2878	179	4	.	.	PUNCT
iajs-2878	180	1	2022	2022	NUM
iajs-2878	180	2	,	,	PUNCT
iajs-2878	180	3	appl	appl	NOUN
iajs-2878	180	4	.	.	PROPN
iajs-2878	180	5	13	13	NUM
iajs-2878	180	6	,	,	PUNCT
iajs-2878	180	7	1	1	NUM
iajs-2878	180	8	,	,	PUNCT
iajs-2878	180	9	3765	3765	NUM
iajs-2878	180	10	–	–	PUNCT
iajs-2878	180	11	3772	3772	NUM
iajs-2878	180	12	.	.	PUNCT