id	sid	tid	token	lemma	pos
iajs-2517	1	1	ibn	ibn	PROPN
iajs-2517	1	2	al	al	PROPN
iajs-2517	1	3	-	-	PUNCT
iajs-2517	1	4	haitham	haitham	PROPN
iajs-2517	1	5	jour	jour	X
iajs-2517	1	6	.	.	PROPN
iajs-2517	1	7	for	for	ADP
iajs-2517	1	8	pure	pure	ADJ
iajs-2517	1	9	&	&	CCONJ
iajs-2517	1	10	appl	appl	PROPN
iajs-2517	1	11	.	.	PUNCT
iajs-2517	2	1	sci	sci	PROPN
iajs-2517	2	2	.	.	PROPN
iajs-2517	3	1	33	33	NUM
iajs-2517	3	2	(	(	PUNCT
iajs-2517	3	3	4	4	NUM
iajs-2517	3	4	)	)	PUNCT
iajs-2517	3	5	2020	2020	NUM
iajs-2517	3	6	122	122	NUM
iajs-2517	3	7	new	new	ADJ
iajs-2517	3	8	games	game	NOUN
iajs-2517	3	9	via	via	ADP
iajs-2517	3	10	soft-𝓘-𝐒𝐞𝐦𝐢-𝐠-separation	soft-𝓘-𝐒𝐞𝐦𝐢-𝐠-separation	NOUN
iajs-2517	3	11	axioms	axioms	PROPN
iajs-2517	3	12	r.j	r.j	PROPN
iajs-2517	3	13	.	.	PROPN
iajs-2517	3	14	mohammad	mohammad	PROPN
iajs-2517	3	15	r.b	r.b	PROPN
iajs-2517	3	16	.	.	PROPN
iajs-2517	3	17	esmaeel	esmaeel	PROPN
iajs-2517	3	18	department	department	PROPN
iajs-2517	3	19	of	of	ADP
iajs-2517	3	20	mathematics	mathematics	PROPN
iajs-2517	3	21	,	,	PUNCT
iajs-2517	3	22	college	college	NOUN
iajs-2517	3	23	of	of	ADP
iajs-2517	3	24	education	education	NOUN
iajs-2517	3	25	for	for	ADP
iajs-2517	3	26	pure	pure	ADJ
iajs-2517	3	27	sciences	science	NOUN
iajs-2517	3	28	,	,	PUNCT
iajs-2517	3	29	ibn	ibn	PROPN
iajs-2517	3	30	al	al	PROPN
iajs-2517	3	31	-	-	PUNCT
iajs-2517	3	32	haitham	haitham	PROPN
iajs-2517	3	33	,	,	PUNCT
iajs-2517	3	34	university	university	PROPN
iajs-2517	3	35	of	of	ADP
iajs-2517	3	36	baghdad	baghdad	PROPN
iajs-2517	3	37	,	,	PUNCT
iajs-2517	3	38	baghdad	baghdad	PROPN
iajs-2517	3	39	,	,	PUNCT
iajs-2517	3	40	iraq	iraq	PROPN
iajs-2517	3	41	.	.	PUNCT
iajs-2517	4	1	raf44456@gmail.com	raf44456@gmail.com	X
iajs-2517	5	1	ranamumosa@yahoo.com	ranamumosa@yahoo.com	X
iajs-2517	5	2	abstract	abstract	ADJ
iajs-2517	5	3	in	in	ADP
iajs-2517	5	4	this	this	DET
iajs-2517	5	5	article	article	NOUN
iajs-2517	5	6	,	,	PUNCT
iajs-2517	5	7	the	the	DET
iajs-2517	5	8	notions	notion	NOUN
iajs-2517	5	9	of	of	ADP
iajs-2517	5	10	soft	soft	ADJ
iajs-2517	5	11	closed	closed	ADJ
iajs-2517	5	12	sets	set	NOUN
iajs-2517	5	13	are	be	AUX
iajs-2517	5	14	introduced	introduce	VERB
iajs-2517	5	15	by	by	ADP
iajs-2517	5	16	using	use	VERB
iajs-2517	5	17	soft	soft	ADJ
iajs-2517	5	18	ideal	ideal	ADJ
iajs-2517	5	19	and	and	CCONJ
iajs-2517	5	20	soft	soft	ADJ
iajs-2517	5	21	semi	semi	ADJ
iajs-2517	5	22	-	-	ADJ
iajs-2517	5	23	open	open	ADJ
iajs-2517	5	24	sets	set	NOUN
iajs-2517	5	25	,	,	PUNCT
iajs-2517	5	26	which	which	PRON
iajs-2517	5	27	are	be	AUX
iajs-2517	5	28	soft-ℐ-semi	soft-ℐ-semi	PROPN
iajs-2517	5	29	-	-	PUNCT
iajs-2517	5	30	g	g	NOUN
iajs-2517	5	31	-	-	PUNCT
iajs-2517	5	32	closed	close	VERB
iajs-2517	5	33	sets	set	NOUN
iajs-2517	5	34	"	"	PUNCT
iajs-2517	5	35	sℐsg	sℐsg	PROPN
iajs-2517	5	36	-	-	PUNCT
iajs-2517	5	37	closed	close	VERB
iajs-2517	5	38	"	"	PUNCT
iajs-2517	5	39	where	where	SCONJ
iajs-2517	5	40	many	many	ADJ
iajs-2517	5	41	of	of	ADP
iajs-2517	5	42	the	the	DET
iajs-2517	5	43	properties	property	NOUN
iajs-2517	5	44	of	of	ADP
iajs-2517	5	45	these	these	DET
iajs-2517	5	46	sets	set	NOUN
iajs-2517	5	47	are	be	AUX
iajs-2517	5	48	clarified	clarify	VERB
iajs-2517	5	49	.	.	PUNCT
iajs-2517	6	1	some	some	DET
iajs-2517	6	2	games	game	NOUN
iajs-2517	6	3	by	by	ADP
iajs-2517	6	4	using	use	VERB
iajs-2517	6	5	softℐ-semi	softℐ-semi	NOUN
iajs-2517	6	6	,	,	PUNCT
iajs-2517	6	7	soft	soft	ADJ
iajs-2517	6	8	separation	separation	NOUN
iajs-2517	6	9	axioms	axiom	NOUN
iajs-2517	6	10	:	:	PUNCT
iajs-2517	6	11	like	like	ADP
iajs-2517	6	12	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	6	13	,	,	PUNCT
iajs-2517	6	14	χ	χ	X
iajs-2517	6	15	)	)	PUNCT
iajs-2517	6	16	,	,	PUNCT
iajs-2517	6	17	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	6	18	,	,	PUNCT
iajs-2517	6	19	ℐ	ℐ	PROPN
iajs-2517	6	20	)	)	PUNCT
iajs-2517	6	21	.	.	PUNCT
iajs-2517	7	1	using	use	VERB
iajs-2517	7	2	many	many	ADJ
iajs-2517	7	3	figures	figure	NOUN
iajs-2517	7	4	and	and	CCONJ
iajs-2517	7	5	proposition	proposition	NOUN
iajs-2517	7	6	to	to	PART
iajs-2517	7	7	study	study	VERB
iajs-2517	7	8	the	the	DET
iajs-2517	7	9	relationships	relationship	NOUN
iajs-2517	7	10	among	among	ADP
iajs-2517	7	11	these	these	DET
iajs-2517	7	12	kinds	kind	NOUN
iajs-2517	7	13	of	of	ADP
iajs-2517	7	14	games	game	NOUN
iajs-2517	7	15	with	with	ADP
iajs-2517	7	16	some	some	DET
iajs-2517	7	17	examples	example	NOUN
iajs-2517	7	18	are	be	AUX
iajs-2517	7	19	explained	explain	VERB
iajs-2517	7	20	.	.	PUNCT
iajs-2517	8	1	keywords	keyword	NOUN
iajs-2517	8	2	:	:	PUNCT
iajs-2517	8	3	soft	soft	ADJ
iajs-2517	8	4	ideal	ideal	NOUN
iajs-2517	8	5	,	,	PUNCT
iajs-2517	8	6	soft-𝒯𝑖-𝑠𝑝𝑎𝑐𝑒	soft-𝒯𝑖-𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	8	7	,	,	PUNCT
iajs-2517	8	8	soft-ℐ-semi-𝑔-𝒯𝑖-𝑠𝑝𝑎𝑐𝑒	soft-ℐ-semi-𝑔-𝒯𝑖-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	8	9	,	,	PUNCT
iajs-2517	8	10	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	NOUN
iajs-2517	8	11	,	,	PUNCT
iajs-2517	8	12	χ	χ	X
iajs-2517	8	13	)	)	PUNCT
iajs-2517	8	14	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	NOUN
iajs-2517	8	15	,	,	PUNCT
iajs-2517	8	16	ℐ	ℐ	PROPN
iajs-2517	8	17	)	)	PUNCT
iajs-2517	8	18	.	.	PUNCT
iajs-2517	9	1	where	where	SCONJ
iajs-2517	9	2	𝑖	𝑖	ADV
iajs-2517	9	3	=	=	PUNCT
iajs-2517	9	4	{	{	PUNCT
iajs-2517	9	5	0,1,2	0,1,2	NOUN
iajs-2517	9	6	}	}	PUNCT
iajs-2517	9	7	.	.	PUNCT
iajs-2517	10	1	1.introduction	1.introduction	NUM
iajs-2517	10	2	in	in	ADP
iajs-2517	10	3	2011	2011	NUM
iajs-2517	10	4	,	,	PUNCT
iajs-2517	10	5	shaber	shaber	NOUN
iajs-2517	10	6	[	[	X
iajs-2517	10	7	1	1	X
iajs-2517	10	8	]	]	PUNCT
iajs-2517	10	9	introduced	introduce	VERB
iajs-2517	10	10	soft	soft	ADJ
iajs-2517	10	11	topological	topological	ADJ
iajs-2517	10	12	spaces	space	NOUN
iajs-2517	10	13	.	.	PUNCT
iajs-2517	11	1	shaber	shaber	PROPN
iajs-2517	11	2	have	have	AUX
iajs-2517	11	3	been	be	AUX
iajs-2517	11	4	introduced	introduce	VERB
iajs-2517	11	5	to	to	PART
iajs-2517	11	6	study	study	VERB
iajs-2517	11	7	many	many	ADJ
iajs-2517	11	8	topological	topological	ADJ
iajs-2517	11	9	properties	property	NOUN
iajs-2517	11	10	by	by	ADP
iajs-2517	11	11	using	use	VERB
iajs-2517	11	12	soft	soft	ADJ
iajs-2517	11	13	set	set	NOUN
iajs-2517	11	14	like	like	ADP
iajs-2517	11	15	derived	derive	VERB
iajs-2517	11	16	sets	set	NOUN
iajs-2517	11	17	,	,	PUNCT
iajs-2517	11	18	compactness	compactness	NOUN
iajs-2517	11	19	,	,	PUNCT
iajs-2517	11	20	separation	separation	NOUN
iajs-2517	11	21	axioms	axiom	NOUN
iajs-2517	11	22	and	and	CCONJ
iajs-2517	11	23	other	other	ADJ
iajs-2517	11	24	properties	property	NOUN
iajs-2517	11	25	.	.	PUNCT
iajs-2517	12	1	[	[	X
iajs-2517	12	2	2	2	NUM
iajs-2517	12	3	-	-	SYM
iajs-2517	12	4	4	4	NUM
iajs-2517	12	5	]	]	PUNCT
iajs-2517	12	6	.	.	PUNCT
iajs-2517	13	1	also	also	ADV
iajs-2517	13	2	,	,	PUNCT
iajs-2517	13	3	kandil	kandil	PROPN
iajs-2517	13	4	used	use	VERB
iajs-2517	13	5	the	the	DET
iajs-2517	13	6	soft	soft	ADJ
iajs-2517	13	7	ideal	ideal	NOUN
iajs-2517	13	8	which	which	PRON
iajs-2517	13	9	is	be	AUX
iajs-2517	13	10	a	a	DET
iajs-2517	13	11	family	family	NOUN
iajs-2517	13	12	of	of	ADP
iajs-2517	13	13	soft	soft	ADJ
iajs-2517	13	14	sets	set	NOUN
iajs-2517	13	15	that	that	PRON
iajs-2517	13	16	meet	meet	VERB
iajs-2517	13	17	hereditary	hereditary	NOUN
iajs-2517	13	18	and	and	CCONJ
iajs-2517	13	19	finite	finite	VERB
iajs-2517	13	20	additively	additively	ADV
iajs-2517	13	21	property	property	NOUN
iajs-2517	13	22	of	of	ADP
iajs-2517	13	23	χ	χ	NOUN
iajs-2517	13	24	to	to	PART
iajs-2517	13	25	study	study	VERB
iajs-2517	13	26	the	the	DET
iajs-2517	13	27	notion	notion	NOUN
iajs-2517	13	28	of	of	ADP
iajs-2517	13	29	soft	soft	ADJ
iajs-2517	13	30	logical	logical	ADJ
iajs-2517	13	31	function	function	NOUN
iajs-2517	13	32	[	[	X
iajs-2517	13	33	5	5	NUM
iajs-2517	13	34	]	]	PUNCT
iajs-2517	13	35	,	,	PUNCT
iajs-2517	13	36	which	which	PRON
iajs-2517	13	37	was	be	AUX
iajs-2517	13	38	the	the	DET
iajs-2517	13	39	starting	starting	NOUN
iajs-2517	13	40	point	point	NOUN
iajs-2517	13	41	for	for	ADP
iajs-2517	13	42	studying	study	VERB
iajs-2517	13	43	the	the	DET
iajs-2517	13	44	properties	property	NOUN
iajs-2517	13	45	of	of	ADP
iajs-2517	13	46	soft	soft	ADJ
iajs-2517	13	47	ideal	ideal	ADJ
iajs-2517	13	48	topological	topological	ADJ
iajs-2517	13	49	spaces	space	NOUN
iajs-2517	13	50	(	(	PUNCT
iajs-2517	13	51	χ	χ	X
iajs-2517	13	52	,	,	PUNCT
iajs-2517	13	53	𝒯	𝒯	PROPN
iajs-2517	13	54	,	,	PUNCT
iajs-2517	13	55	ℋ	ℋ	PROPN
iajs-2517	13	56	,	,	PUNCT
iajs-2517	13	57	ℐ	ℐ	NUM
iajs-2517	13	58	)	)	PUNCT
iajs-2517	13	59	and	and	CCONJ
iajs-2517	13	60	defined	define	VERB
iajs-2517	13	61	new	new	ADJ
iajs-2517	13	62	types	type	NOUN
iajs-2517	13	63	of	of	ADP
iajs-2517	13	64	near	near	ADP
iajs-2517	13	65	open	open	ADJ
iajs-2517	13	66	soft	soft	ADJ
iajs-2517	13	67	sets	set	NOUN
iajs-2517	13	68	and	and	CCONJ
iajs-2517	13	69	studied	study	VERB
iajs-2517	13	70	their	their	PRON
iajs-2517	13	71	properties	property	NOUN
iajs-2517	13	72	as	as	ADP
iajs-2517	13	73	[	[	X
iajs-2517	13	74	6	6	NUM
iajs-2517	13	75	-	-	SYM
iajs-2517	13	76	8	8	NUM
iajs-2517	13	77	]	]	PUNCT
iajs-2517	13	78	.	.	PUNCT
iajs-2517	14	1	2.preliminaries	2.preliminaries	NUM
iajs-2517	14	2	.	.	PUNCT
iajs-2517	15	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	NOUN
iajs-2517	15	2	𝟐.	𝟐.	PUNCT
iajs-2517	15	3	𝟏.	𝟏.	PUNCT
iajs-2517	16	1	[	[	X
iajs-2517	16	2	9	9	NUM
iajs-2517	16	3	]	]	PUNCT
iajs-2517	16	4	let	let	VERB
iajs-2517	16	5	𝜒	𝜒	DET
iajs-2517	16	6	≠	≠	ADJ
iajs-2517	16	7	∅	∅	NOUN
iajs-2517	16	8	and	and	CCONJ
iajs-2517	16	9	ℋ	ℋ	PROPN
iajs-2517	16	10	be	be	VERB
iajs-2517	16	11	a	a	DET
iajs-2517	16	12	set	set	NOUN
iajs-2517	16	13	of	of	ADP
iajs-2517	16	14	parameters	parameter	NOUN
iajs-2517	16	15	.	.	PUNCT
iajs-2517	17	1	such	such	ADJ
iajs-2517	17	2	that	that	PRON
iajs-2517	17	3	is	be	AUX
iajs-2517	17	4	𝓅(𝜒	𝓅(𝜒	PROPN
iajs-2517	17	5	)	)	PUNCT
iajs-2517	18	1	the	the	DET
iajs-2517	18	2	power	power	NOUN
iajs-2517	18	3	set	set	NOUN
iajs-2517	18	4	of	of	ADP
iajs-2517	18	5	𝜒	𝜒	NOUN
iajs-2517	18	6	and	and	CCONJ
iajs-2517	18	7	𝓟	𝓟	PROPN
iajs-2517	18	8	⫋	⫋	NOUN
iajs-2517	18	9	ℋ.	ℋ.	PROPN
iajs-2517	18	10	a	a	DET
iajs-2517	18	11	pair	pair	NOUN
iajs-2517	18	12	(	(	PUNCT
iajs-2517	18	13	г	г	PROPN
iajs-2517	18	14	,	,	PUNCT
iajs-2517	18	15	ℋ	ℋ	PROPN
iajs-2517	18	16	)	)	PUNCT
iajs-2517	18	17	(	(	PUNCT
iajs-2517	18	18	briefly	briefly	ADV
iajs-2517	18	19	г𝓗	г𝓗	NUM
iajs-2517	18	20	)	)	PUNCT
iajs-2517	18	21	is	be	AUX
iajs-2517	18	22	a	a	DET
iajs-2517	18	23	soft	soft	ADJ
iajs-2517	18	24	set	set	NOUN
iajs-2517	18	25	over	over	ADP
iajs-2517	18	26	𝜒	𝜒	NOUN
iajs-2517	18	27	where	where	SCONJ
iajs-2517	18	28	,	,	PUNCT
iajs-2517	18	29	г	г	PROPN
iajs-2517	18	30	is	be	AUX
iajs-2517	18	31	a	a	DET
iajs-2517	18	32	ibn	ibn	PROPN
iajs-2517	18	33	al	al	PROPN
iajs-2517	18	34	haitham	haitham	PROPN
iajs-2517	18	35	journal	journal	PROPN
iajs-2517	18	36	for	for	ADP
iajs-2517	18	37	pure	pure	ADJ
iajs-2517	18	38	and	and	CCONJ
iajs-2517	18	39	applied	apply	VERB
iajs-2517	18	40	science	science	NOUN
iajs-2517	18	41	journal	journal	PROPN
iajs-2517	18	42	homepage	homepage	NOUN
iajs-2517	18	43	:	:	PUNCT
iajs-2517	18	44	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2517	18	45	doi	doi	NOUN
iajs-2517	18	46	:	:	PUNCT
iajs-2517	18	47	10.30526/33.4.2517	10.30526/33.4.2517	PROPN
iajs-2517	18	48	article	article	NOUN
iajs-2517	18	49	history	history	NOUN
iajs-2517	18	50	:	:	PUNCT
iajs-2517	18	51	received	receive	VERB
iajs-2517	18	52	9	9	NUM
iajs-2517	18	53	february	february	NOUN
iajs-2517	18	54	2020	2020	NUM
iajs-2517	18	55	,	,	PUNCT
iajs-2517	18	56	accepted	accept	VERB
iajs-2517	18	57	20	20	NUM
iajs-2517	18	58	july	july	NOUN
iajs-2517	18	59	2020	2020	NUM
iajs-2517	18	60	,	,	PUNCT
iajs-2517	18	61	published	publish	VERB
iajs-2517	18	62	in	in	ADP
iajs-2517	18	63	october	october	PROPN
iajs-2517	18	64	2020	2020	NUM
iajs-2517	18	65	mailto:raf44456@gmail.com	mailto:raf44456@gmail.com	X
iajs-2517	18	66	mailto:ranamumosa@yahoo.com	mailto:ranamumosa@yahoo.com	PROPN
iajs-2517	18	67	123	123	NUM
iajs-2517	19	1	ibn	ibn	PROPN
iajs-2517	19	2	al	al	PROPN
iajs-2517	19	3	-	-	PUNCT
iajs-2517	19	4	haitham	haitham	PROPN
iajs-2517	19	5	jour	jour	X
iajs-2517	19	6	.	.	PROPN
iajs-2517	19	7	for	for	ADP
iajs-2517	19	8	pure	pure	ADJ
iajs-2517	19	9	&	&	CCONJ
iajs-2517	19	10	appl	appl	PROPN
iajs-2517	19	11	.	.	PUNCT
iajs-2517	20	1	sci	sci	PROPN
iajs-2517	20	2	.	.	PROPN
iajs-2517	21	1	33	33	NUM
iajs-2517	21	2	(	(	PUNCT
iajs-2517	21	3	4	4	NUM
iajs-2517	21	4	)	)	PUNCT
iajs-2517	21	5	2020	2020	NUM
iajs-2517	21	6	function	function	NOUN
iajs-2517	21	7	given	give	VERB
iajs-2517	21	8	by	by	ADP
iajs-2517	21	9	г	г	PROPN
iajs-2517	21	10	∶	∶	PROPN
iajs-2517	21	11	ℋ	ℋ	PROPN
iajs-2517	21	12	→	→	SYM
iajs-2517	21	13	𝓅(𝜒	𝓅(𝜒	PROPN
iajs-2517	21	14	)	)	PUNCT
iajs-2517	21	15	.	.	PUNCT
iajs-2517	22	1	so	so	ADV
iajs-2517	22	2	,	,	PUNCT
iajs-2517	22	3	г𝓗	г𝓗	PROPN
iajs-2517	22	4	=	=	SYM
iajs-2517	22	5	{	{	PUNCT
iajs-2517	22	6	г(𝒽	г(𝒽	NOUN
iajs-2517	22	7	):	):	PUNCT
iajs-2517	22	8	𝒽	𝒽	DET
iajs-2517	22	9	∈	∈	NOUN
iajs-2517	22	10	𝓟	𝓟	PROPN
iajs-2517	22	11	⊆	⊆	NUM
iajs-2517	22	12	ℋ	ℋ	PROPN
iajs-2517	22	13	,	,	PUNCT
iajs-2517	22	14	г	г	PROPN
iajs-2517	22	15	∶	∶	PROPN
iajs-2517	22	16	ℋ	ℋ	PROPN
iajs-2517	22	17	→	→	SYM
iajs-2517	22	18	𝓅(𝜒	𝓅(𝜒	PROPN
iajs-2517	22	19	)	)	PUNCT
iajs-2517	22	20	}	}	PUNCT
iajs-2517	22	21	.the	.the	PRON
iajs-2517	22	22	family	family	NOUN
iajs-2517	22	23	of	of	ADP
iajs-2517	22	24	all	all	DET
iajs-2517	22	25	soft	soft	ADJ
iajs-2517	22	26	sets	set	NOUN
iajs-2517	22	27	(	(	PUNCT
iajs-2517	22	28	is	be	AUX
iajs-2517	22	29	denoted	denote	VERB
iajs-2517	22	30	by	by	ADP
iajs-2517	22	31	şş(𝜒)𝓗	şş(𝜒)𝓗	NOUN
iajs-2517	22	32	)	)	PUNCT
iajs-2517	22	33	.	.	PUNCT
iajs-2517	23	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	NOUN
iajs-2517	23	2	𝟐.	𝟐.	PUNCT
iajs-2517	24	1	𝟐.	𝟐.	X
iajs-2517	24	2	[	[	X
iajs-2517	24	3	9	9	NUM
iajs-2517	24	4	]	]	X
iajs-2517	24	5	let	let	VERB
iajs-2517	24	6	(	(	PUNCT
iajs-2517	24	7	г	г	NOUN
iajs-2517	24	8	,	,	PUNCT
iajs-2517	24	9	ℋ	ℋ	PROPN
iajs-2517	24	10	)	)	PUNCT
iajs-2517	24	11	,	,	PUNCT
iajs-2517	24	12	(	(	PUNCT
iajs-2517	24	13	𝒢	𝒢	PROPN
iajs-2517	24	14	,	,	PUNCT
iajs-2517	24	15	ℋ	ℋ	PROPN
iajs-2517	24	16	)	)	PUNCT
iajs-2517	24	17	∈	∈	PROPN
iajs-2517	24	18	şş(χ)𝓗.	şş(χ)𝓗.	VERB
iajs-2517	24	19	then	then	ADV
iajs-2517	24	20	(	(	PUNCT
iajs-2517	24	21	г	г	PROPN
iajs-2517	24	22	,	,	PUNCT
iajs-2517	24	23	ℋ	ℋ	PROPN
iajs-2517	24	24	)	)	PUNCT
iajs-2517	24	25	is	be	AUX
iajs-2517	24	26	a	a	DET
iajs-2517	24	27	soft	soft	ADJ
iajs-2517	24	28	subset	subset	NOUN
iajs-2517	24	29	of	of	ADP
iajs-2517	24	30	,	,	PUNCT
iajs-2517	24	31	(	(	PUNCT
iajs-2517	24	32	𝒢	𝒢	PROPN
iajs-2517	24	33	,	,	PUNCT
iajs-2517	24	34	ℋ	ℋ	PROPN
iajs-2517	24	35	)	)	PUNCT
iajs-2517	24	36	,	,	PUNCT
iajs-2517	24	37	(	(	PUNCT
iajs-2517	24	38	briefly(г	briefly(г	NOUN
iajs-2517	24	39	,	,	PUNCT
iajs-2517	24	40	ℋ	ℋ	NOUN
iajs-2517	24	41	)	)	PUNCT
iajs-2517	24	42	⊆̃	⊆̃	NOUN
iajs-2517	24	43	,	,	PUNCT
iajs-2517	24	44	(	(	PUNCT
iajs-2517	24	45	𝒢	𝒢	PROPN
iajs-2517	24	46	,	,	PUNCT
iajs-2517	24	47	ℋ	ℋ	PROPN
iajs-2517	24	48	)	)	PUNCT
iajs-2517	24	49	)	)	PUNCT
iajs-2517	24	50	,	,	PUNCT
iajs-2517	24	51	if	if	SCONJ
iajs-2517	24	52	г(𝒽	г(𝒽	NOUN
iajs-2517	24	53	)	)	PUNCT
iajs-2517	24	54	⊆̃	⊆̃	NOUN
iajs-2517	24	55	𝒢(𝒽	𝒢(𝒽	PRON
iajs-2517	24	56	)	)	PUNCT
iajs-2517	24	57	,	,	PUNCT
iajs-2517	24	58	for	for	ADP
iajs-2517	24	59	all	all	PRON
iajs-2517	24	60	𝒽	𝒽	DET
iajs-2517	24	61	∈	∈	PROPN
iajs-2517	24	62	ℋ	ℋ	PROPN
iajs-2517	24	63	.	.	PUNCT
iajs-2517	25	1	now	now	ADV
iajs-2517	25	2	(	(	PUNCT
iajs-2517	25	3	г	г	PROPN
iajs-2517	25	4	,	,	PUNCT
iajs-2517	25	5	ℋ	ℋ	PROPN
iajs-2517	25	6	)	)	PUNCT
iajs-2517	25	7	is	be	AUX
iajs-2517	25	8	a	a	DET
iajs-2517	25	9	soft	soft	ADJ
iajs-2517	25	10	subset	subset	NOUN
iajs-2517	25	11	of	of	ADP
iajs-2517	25	12	,	,	PUNCT
iajs-2517	25	13	(	(	PUNCT
iajs-2517	25	14	𝒢	𝒢	PROPN
iajs-2517	25	15	,	,	PUNCT
iajs-2517	25	16	ℋ	ℋ	PROPN
iajs-2517	25	17	)	)	PUNCT
iajs-2517	25	18	and	and	CCONJ
iajs-2517	25	19	,	,	PUNCT
iajs-2517	25	20	(	(	PUNCT
iajs-2517	25	21	𝒢	𝒢	PROPN
iajs-2517	25	22	,	,	PUNCT
iajs-2517	25	23	ℋ	ℋ	PROPN
iajs-2517	25	24	)	)	PUNCT
iajs-2517	25	25	is	be	AUX
iajs-2517	25	26	a	a	DET
iajs-2517	25	27	soft	soft	ADJ
iajs-2517	25	28	super	super	ADJ
iajs-2517	25	29	set	set	NOUN
iajs-2517	25	30	of	of	ADP
iajs-2517	25	31	(	(	PUNCT
iajs-2517	25	32	г	г	PROPN
iajs-2517	25	33	,	,	PUNCT
iajs-2517	25	34	ℋ	ℋ	PROPN
iajs-2517	25	35	)	)	PUNCT
iajs-2517	25	36	,	,	PUNCT
iajs-2517	25	37	(	(	PUNCT
iajs-2517	25	38	г	г	PROPN
iajs-2517	25	39	,	,	PUNCT
iajs-2517	25	40	ℋ	ℋ	NOUN
iajs-2517	25	41	)	)	PUNCT
iajs-2517	25	42	⊆̃	⊆̃	PROPN
iajs-2517	25	43	(	(	PUNCT
iajs-2517	25	44	𝒢	𝒢	PROPN
iajs-2517	25	45	,	,	PUNCT
iajs-2517	25	46	ℋ	ℋ	PROPN
iajs-2517	25	47	)	)	PUNCT
iajs-2517	25	48	.	.	PUNCT
iajs-2517	26	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	NOUN
iajs-2517	26	2	𝟐.	𝟐.	PUNCT
iajs-2517	26	3	𝟑.	𝟑.	PUNCT
iajs-2517	26	4	[	[	X
iajs-2517	26	5	10	10	NUM
iajs-2517	26	6	]	]	PUNCT
iajs-2517	26	7	the	the	DET
iajs-2517	26	8	complement	complement	NOUN
iajs-2517	26	9	of	of	ADP
iajs-2517	26	10	a	a	DET
iajs-2517	26	11	soft	soft	ADJ
iajs-2517	26	12	set	set	NOUN
iajs-2517	26	13	(	(	PUNCT
iajs-2517	26	14	г	г	PROPN
iajs-2517	26	15	,	,	PUNCT
iajs-2517	26	16	ℋ	ℋ	PROPN
iajs-2517	26	17	)	)	PUNCT
iajs-2517	26	18	(	(	PUNCT
iajs-2517	26	19	is	be	AUX
iajs-2517	26	20	denoted	denote	VERB
iajs-2517	26	21	by	by	ADP
iajs-2517	26	22	(	(	PUNCT
iajs-2517	26	23	г	г	PROPN
iajs-2517	26	24	,	,	PUNCT
iajs-2517	26	25	ℋ)′	ℋ)′	PROPN
iajs-2517	26	26	)	)	PUNCT
iajs-2517	26	27	and	and	CCONJ
iajs-2517	26	28	(	(	PUNCT
iajs-2517	26	29	г	г	PROPN
iajs-2517	26	30	,	,	PUNCT
iajs-2517	26	31	ℋ)′	ℋ)′	PROPN
iajs-2517	26	32	=	=	SYM
iajs-2517	26	33	(	(	PUNCT
iajs-2517	26	34	г′	г′	X
iajs-2517	26	35	,	,	PUNCT
iajs-2517	26	36	ℋ	ℋ	NOUN
iajs-2517	26	37	)	)	PUNCT
iajs-2517	26	38	where	where	SCONJ
iajs-2517	26	39	г′	г′	ADP
iajs-2517	26	40	:	:	PUNCT
iajs-2517	26	41	ℋ	ℋ	PROPN
iajs-2517	26	42	→	→	SYM
iajs-2517	26	43	𝓅(𝜒	𝓅(𝜒	PROPN
iajs-2517	26	44	)	)	PUNCT
iajs-2517	26	45	is	be	AUX
iajs-2517	26	46	a	a	DET
iajs-2517	26	47	function	function	NOUN
iajs-2517	26	48	such	such	ADJ
iajs-2517	26	49	that	that	DET
iajs-2517	26	50	г′(𝒽	г′(𝒽	NOUN
iajs-2517	26	51	)	)	PUNCT
iajs-2517	26	52	=	=	SYM
iajs-2517	26	53	𝜒	𝜒	X
iajs-2517	26	54	‒	‒	X
iajs-2517	26	55	г(𝒽	г(𝒽	NOUN
iajs-2517	26	56	)	)	PUNCT
iajs-2517	26	57	,	,	PUNCT
iajs-2517	26	58	for	for	SCONJ
iajs-2517	26	59	each	each	DET
iajs-2517	26	60	𝒽	𝒽	DET
iajs-2517	26	61	∈	∈	PROPN
iajs-2517	26	62	ℋ	ℋ	PROPN
iajs-2517	26	63	and	and	CCONJ
iajs-2517	26	64	г′	г′	NOUN
iajs-2517	26	65	is	be	AUX
iajs-2517	26	66	a	a	DET
iajs-2517	26	67	soft	soft	ADJ
iajs-2517	26	68	complement	complement	NOUN
iajs-2517	26	69	of	of	ADP
iajs-2517	26	70	г	г	PROPN
iajs-2517	26	71	.	.	PUNCT
iajs-2517	27	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	NOUN
iajs-2517	27	2	𝟐.	𝟐.	PUNCT
iajs-2517	27	3	𝟒.	𝟒.	PUNCT
iajs-2517	27	4	[	[	X
iajs-2517	27	5	1	1	NUM
iajs-2517	27	6	]	]	X
iajs-2517	27	7	let	let	VERB
iajs-2517	27	8	(	(	PUNCT
iajs-2517	27	9	г	г	NOUN
iajs-2517	27	10	,	,	PUNCT
iajs-2517	27	11	ℋ	ℋ	PROPN
iajs-2517	27	12	)	)	PUNCT
iajs-2517	27	13	be	be	VERB
iajs-2517	27	14	a	a	DET
iajs-2517	27	15	soft	soft	ADJ
iajs-2517	27	16	over	over	ADP
iajs-2517	27	17	χ	χ	NOUN
iajs-2517	27	18	and	and	CCONJ
iajs-2517	27	19	𝓍	𝓍	DET
iajs-2517	27	20	∈	∈	PROPN
iajs-2517	27	21	𝜒.	𝜒.	NOUN
iajs-2517	27	22	then	then	ADV
iajs-2517	27	23	𝓍	𝓍	X
iajs-2517	27	24	∈̃	∈̃	PROPN
iajs-2517	27	25	(	(	PUNCT
iajs-2517	27	26	г	г	PROPN
iajs-2517	27	27	,	,	PUNCT
iajs-2517	27	28	ℋ	ℋ	NOUN
iajs-2517	27	29	)	)	PUNCT
iajs-2517	27	30	whenever	whenever	SCONJ
iajs-2517	27	31	,	,	PUNCT
iajs-2517	27	32	𝓍	𝓍	DET
iajs-2517	27	33	∈	∈	PROPN
iajs-2517	27	34	г(𝒽	г(𝒽	NOUN
iajs-2517	27	35	)	)	PUNCT
iajs-2517	27	36	for	for	ADP
iajs-2517	27	37	each	each	DET
iajs-2517	27	38	𝒽	𝒽	DET
iajs-2517	27	39	∈	∈	PROPN
iajs-2517	27	40	ℋ.	ℋ.	PROPN
iajs-2517	27	41	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	PROPN
iajs-2517	27	42	𝟐.	𝟐.	PUNCT
iajs-2517	28	1	𝟓.	𝟓.	PUNCT
iajs-2517	28	2	[	[	X
iajs-2517	28	3	1	1	NUM
iajs-2517	28	4	]	]	PUNCT
iajs-2517	28	5	(	(	PUNCT
iajs-2517	28	6	г	г	PROPN
iajs-2517	28	7	,	,	PUNCT
iajs-2517	28	8	ℋ	ℋ	NOUN
iajs-2517	28	9	)	)	PUNCT
iajs-2517	28	10	χ	χ	NOUN
iajs-2517	28	11	is	be	AUX
iajs-2517	28	12	a	a	DET
iajs-2517	28	13	null	null	ADJ
iajs-2517	28	14	soft	soft	ADJ
iajs-2517	28	15	set	set	NOUN
iajs-2517	28	16	(	(	PUNCT
iajs-2517	28	17	briefly	briefly	NOUN
iajs-2517	28	18	∅	∅	CCONJ
iajs-2517	28	19	̃or	̃or	X
iajs-2517	28	20	ø𝓗	ø𝓗	PROPN
iajs-2517	28	21	)	)	PUNCT
iajs-2517	28	22	if	if	SCONJ
iajs-2517	28	23	for	for	ADP
iajs-2517	28	24	each	each	DET
iajs-2517	28	25	𝒽	𝒽	DET
iajs-2517	28	26	∈	∈	PROPN
iajs-2517	28	27	ℋ	ℋ	PROPN
iajs-2517	28	28	,	,	PUNCT
iajs-2517	28	29	г(𝒽	г(𝒽	NOUN
iajs-2517	28	30	)	)	PUNCT
iajs-2517	29	1	=	=	SYM
iajs-2517	29	2	ø	ø	PROPN
iajs-2517	29	3	(	(	PUNCT
iajs-2517	29	4	null	null	ADJ
iajs-2517	29	5	set	set	NOUN
iajs-2517	29	6	)	)	PUNCT
iajs-2517	29	7	.	.	PUNCT
iajs-2517	30	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	NOUN
iajs-2517	30	2	𝟐.	𝟐.	PUNCT
iajs-2517	30	3	𝟔.	𝟔.	X
iajs-2517	30	4	[	[	X
iajs-2517	30	5	1	1	X
iajs-2517	30	6	]	]	PUNCT
iajs-2517	30	7	a	a	DET
iajs-2517	30	8	soft	soft	ADJ
iajs-2517	30	9	set	set	NOUN
iajs-2517	30	10	(	(	PUNCT
iajs-2517	30	11	г	г	PROPN
iajs-2517	30	12	,	,	PUNCT
iajs-2517	30	13	ℋ	ℋ	NOUN
iajs-2517	30	14	)	)	PUNCT
iajs-2517	30	15	over	over	ADP
iajs-2517	30	16	χ	χ	PROPN
iajs-2517	30	17	is	be	AUX
iajs-2517	30	18	an	an	DET
iajs-2517	30	19	absolute	absolute	ADJ
iajs-2517	30	20	soft	soft	ADJ
iajs-2517	30	21	set	set	NOUN
iajs-2517	30	22	(	(	PUNCT
iajs-2517	30	23	briefly	briefly	NOUN
iajs-2517	30	24	�	�	PROPN
iajs-2517	30	25	̃	̃	PROPN
iajs-2517	30	26	�	�	PROPN
iajs-2517	30	27	or	or	CCONJ
iajs-2517	30	28	χ𝓗	χ𝓗	PROPN
iajs-2517	30	29	)	)	PUNCT
iajs-2517	30	30	if	if	SCONJ
iajs-2517	30	31	for	for	ADP
iajs-2517	30	32	each	each	DET
iajs-2517	30	33	𝒽	𝒽	DET
iajs-2517	30	34	∈	∈	PROPN
iajs-2517	30	35	ℋ	ℋ	PROPN
iajs-2517	30	36	,	,	PUNCT
iajs-2517	30	37	г(𝒽	г(𝒽	NOUN
iajs-2517	30	38	)	)	PUNCT
iajs-2517	30	39	=	=	SYM
iajs-2517	30	40	χ	χ	NOUN
iajs-2517	30	41	.	.	PUNCT
iajs-2517	31	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	NOUN
iajs-2517	31	2	𝟐.	𝟐.	PUNCT
iajs-2517	32	1	𝟕.	𝟕.	X
iajs-2517	32	2	[	[	X
iajs-2517	32	3	1	1	X
iajs-2517	32	4	]	]	PUNCT
iajs-2517	32	5	let	let	VERB
iajs-2517	32	6	𝒯	𝒯	PROPN
iajs-2517	32	7	be	be	AUX
iajs-2517	32	8	a	a	DET
iajs-2517	32	9	collection	collection	NOUN
iajs-2517	32	10	of	of	ADP
iajs-2517	32	11	soft	soft	ADJ
iajs-2517	32	12	sets	set	NOUN
iajs-2517	32	13	over	over	ADP
iajs-2517	32	14	χ	χ	NOUN
iajs-2517	32	15	with	with	ADP
iajs-2517	32	16	same	same	ADJ
iajs-2517	32	17	ℋ	ℋ	PROPN
iajs-2517	32	18	,	,	PUNCT
iajs-2517	32	19	then	then	ADV
iajs-2517	32	20	𝒯	𝒯	PROPN
iajs-2517	32	21	∈	∈	PROPN
iajs-2517	32	22	şş(χ)𝓗	şş(χ)𝓗	VERB
iajs-2517	32	23	is	be	AUX
iajs-2517	32	24	a	a	DET
iajs-2517	32	25	soft	soft	ADJ
iajs-2517	32	26	topology	topology	NOUN
iajs-2517	32	27	on	on	ADP
iajs-2517	32	28	χ	χ	X
iajs-2517	32	29	if	if	SCONJ
iajs-2517	32	30	;	;	PUNCT
iajs-2517	32	31	i.	i.	PROPN
iajs-2517	32	32	χ̃	χ̃	PROPN
iajs-2517	32	33	,	,	PUNCT
iajs-2517	32	34	∅̃	∅̃	NOUN
iajs-2517	32	35	∈	∈	PROPN
iajs-2517	32	36	𝒯	𝒯	PROPN
iajs-2517	33	1	where	where	SCONJ
iajs-2517	33	2	,	,	PUNCT
iajs-2517	33	3	∅̃(𝒽	∅̃(𝒽	NUM
iajs-2517	33	4	)	)	PUNCT
iajs-2517	33	5	=	=	SYM
iajs-2517	33	6	ø	ø	PROPN
iajs-2517	33	7	and	and	CCONJ
iajs-2517	33	8	χ̃(𝒽	χ̃(𝒽	PROPN
iajs-2517	33	9	)	)	PUNCT
iajs-2517	34	1	=	=	SYM
iajs-2517	34	2	χ	χ	X
iajs-2517	34	3	,	,	PUNCT
iajs-2517	34	4	for	for	ADP
iajs-2517	34	5	each	each	DET
iajs-2517	34	6	𝒽	𝒽	PRON
iajs-2517	34	7	∈	∈	PROPN
iajs-2517	34	8	ℋ	ℋ	PROPN
iajs-2517	34	9	,	,	PUNCT
iajs-2517	34	10	ii	ii	PROPN
iajs-2517	34	11	.	.	PUNCT
iajs-2517	35	1	⋃	⋃	VERB
iajs-2517	35	2	͠	͠	NOUN
iajs-2517	35	3	α∈ʌ	α∈ʌ	NOUN
iajs-2517	35	4	(	(	PUNCT
iajs-2517	35	5	ơα	ơα	NOUN
iajs-2517	35	6	,	,	PUNCT
iajs-2517	35	7	ℋ	ℋ	PROPN
iajs-2517	35	8	)	)	PUNCT
iajs-2517	35	9	∈	∈	PROPN
iajs-2517	35	10	𝒯	𝒯	PROPN
iajs-2517	35	11	whenever	whenever	ADV
iajs-2517	35	12	,	,	PUNCT
iajs-2517	35	13	(	(	PUNCT
iajs-2517	35	14	ơα	ơα	NOUN
iajs-2517	35	15	,	,	PUNCT
iajs-2517	35	16	ℋ	ℋ	PROPN
iajs-2517	35	17	)	)	PUNCT
iajs-2517	35	18	∈	∈	PROPN
iajs-2517	35	19	𝒯	𝒯	PROPN
iajs-2517	35	20	∀	∀	X
iajs-2517	35	21	α	α	PRON
iajs-2517	35	22	∈	∈	PROPN
iajs-2517	35	23	ʌ	ʌ	PROPN
iajs-2517	35	24	,	,	PUNCT
iajs-2517	35	25	iii	iii	PROPN
iajs-2517	35	26	.	.	PUNCT
iajs-2517	36	1	(	(	PUNCT
iajs-2517	36	2	(	(	PUNCT
iajs-2517	36	3	г	г	PROPN
iajs-2517	36	4	,	,	PUNCT
iajs-2517	36	5	ℋ	ℋ	NOUN
iajs-2517	36	6	)	)	PUNCT
iajs-2517	36	7	∩	∩	NOUN
iajs-2517	36	8	̃(𝒢	̃(𝒢	PROPN
iajs-2517	36	9	,	,	PUNCT
iajs-2517	36	10	ℋ	ℋ	NOUN
iajs-2517	36	11	)	)	PUNCT
iajs-2517	36	12	)	)	PUNCT
iajs-2517	37	1	∈	∈	PROPN
iajs-2517	37	2	𝒯	𝒯	PROPN
iajs-2517	37	3	for	for	ADP
iajs-2517	37	4	each	each	PRON
iajs-2517	37	5	(	(	PUNCT
iajs-2517	37	6	г	г	PROPN
iajs-2517	37	7	,	,	PUNCT
iajs-2517	37	8	ℋ	ℋ	PROPN
iajs-2517	37	9	)	)	PUNCT
iajs-2517	37	10	,	,	PUNCT
iajs-2517	37	11	(	(	PUNCT
iajs-2517	37	12	𝒢	𝒢	PROPN
iajs-2517	37	13	,	,	PUNCT
iajs-2517	37	14	ℋ	ℋ	PROPN
iajs-2517	37	15	)	)	PUNCT
iajs-2517	37	16	∈	∈	PROPN
iajs-2517	37	17	𝒯.	𝒯.	PROPN
iajs-2517	37	18	(	(	PUNCT
iajs-2517	37	19	χ	χ	X
iajs-2517	37	20	,	,	PUNCT
iajs-2517	37	21	𝒯	𝒯	PROPN
iajs-2517	37	22	,	,	PUNCT
iajs-2517	37	23	ℋ	ℋ	PROPN
iajs-2517	37	24	)	)	PUNCT
iajs-2517	37	25	is	be	AUX
iajs-2517	37	26	a	a	DET
iajs-2517	37	27	soft	soft	ADJ
iajs-2517	37	28	topological	topological	ADJ
iajs-2517	37	29	space	space	NOUN
iajs-2517	37	30	if	if	SCONJ
iajs-2517	37	31	(	(	PUNCT
iajs-2517	37	32	ơ	ơ	PROPN
iajs-2517	37	33	,	,	PUNCT
iajs-2517	37	34	ℋ	ℋ	PROPN
iajs-2517	37	35	)	)	PUNCT
iajs-2517	37	36	∈	∈	PROPN
iajs-2517	37	37	𝒯	𝒯	PROPN
iajs-2517	37	38	then	then	ADV
iajs-2517	37	39	(	(	PUNCT
iajs-2517	37	40	ơ	ơ	PROPN
iajs-2517	37	41	,	,	PUNCT
iajs-2517	37	42	ℋ	ℋ	PROPN
iajs-2517	37	43	)	)	PUNCT
iajs-2517	37	44	is	be	AUX
iajs-2517	37	45	an	an	DET
iajs-2517	37	46	open	open	ADJ
iajs-2517	37	47	soft	soft	ADJ
iajs-2517	37	48	set	set	NOUN
iajs-2517	37	49	.	.	PUNCT
iajs-2517	38	1	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧	PROPN
iajs-2517	38	2	𝟐.	𝟐.	PUNCT
iajs-2517	38	3	𝟖.	𝟖.	PUNCT
iajs-2517	39	1	[	[	X
iajs-2517	39	2	11	11	NUM
iajs-2517	39	3	]	]	X
iajs-2517	39	4	let	let	VERB
iajs-2517	39	5	(	(	PUNCT
iajs-2517	39	6	𝜒	𝜒	X
iajs-2517	39	7	,	,	PUNCT
iajs-2517	39	8	𝒯	𝒯	PROPN
iajs-2517	39	9	,	,	PUNCT
iajs-2517	39	10	ℋ	ℋ	PROPN
iajs-2517	39	11	)	)	PUNCT
iajs-2517	39	12	be	be	VERB
iajs-2517	39	13	a	a	DET
iajs-2517	39	14	soft	soft	ADJ
iajs-2517	39	15	topological	topological	ADJ
iajs-2517	39	16	space	space	NOUN
iajs-2517	39	17	.	.	PUNCT
iajs-2517	40	1	a	a	DET
iajs-2517	40	2	soft	soft	ADJ
iajs-2517	40	3	set	set	NOUN
iajs-2517	40	4	(	(	PUNCT
iajs-2517	40	5	г	г	PROPN
iajs-2517	40	6	,	,	PUNCT
iajs-2517	40	7	ℋ	ℋ	NOUN
iajs-2517	40	8	)	)	PUNCT
iajs-2517	40	9	over	over	ADP
iajs-2517	40	10	χ	χ	PROPN
iajs-2517	40	11	is	be	AUX
iajs-2517	40	12	a	a	DET
iajs-2517	40	13	soft	soft	ADJ
iajs-2517	40	14	closed	closed	ADJ
iajs-2517	40	15	set	set	NOUN
iajs-2517	40	16	in	in	ADP
iajs-2517	40	17	χ	χ	ADP
iajs-2517	40	18	,	,	PUNCT
iajs-2517	40	19	if	if	SCONJ
iajs-2517	40	20	its	its	PRON
iajs-2517	40	21	complement	complement	NOUN
iajs-2517	40	22	(	(	PUNCT
iajs-2517	40	23	г	г	PROPN
iajs-2517	40	24	,	,	PUNCT
iajs-2517	40	25	ℋ)′	ℋ)′	PROPN
iajs-2517	40	26	∈	∈	PROPN
iajs-2517	40	27	𝒯	𝒯	PROPN
iajs-2517	40	28	,	,	PUNCT
iajs-2517	40	29	the	the	DET
iajs-2517	40	30	family	family	NOUN
iajs-2517	40	31	of	of	ADP
iajs-2517	40	32	all	all	DET
iajs-2517	40	33	soft	soft	ADJ
iajs-2517	40	34	closed	closed	ADJ
iajs-2517	40	35	sets	set	NOUN
iajs-2517	40	36	(	(	PUNCT
iajs-2517	40	37	is	be	AUX
iajs-2517	40	38	denoted	denote	VERB
iajs-2517	40	39	by	by	ADP
iajs-2517	40	40	şc(χ	şc(χ	NOUN
iajs-2517	40	41	)	)	PUNCT
iajs-2517	40	42	𝓗	𝓗	NOUN
iajs-2517	40	43	)	)	PUNCT
iajs-2517	40	44	.	.	PUNCT
iajs-2517	41	1	definition	definition	NOUN
iajs-2517	41	2	2.9	2.9	NUM
iajs-2517	41	3	.	.	PUNCT
iajs-2517	42	1	[	[	X
iajs-2517	42	2	11	11	NUM
iajs-2517	42	3	]	]	PUNCT
iajs-2517	42	4	for	for	ADP
iajs-2517	42	5	any	any	PRON
iajs-2517	42	6	(	(	PUNCT
iajs-2517	42	7	χ	χ	NOUN
iajs-2517	42	8	,	,	PUNCT
iajs-2517	42	9	𝒯	𝒯	PROPN
iajs-2517	42	10	,	,	PUNCT
iajs-2517	42	11	ℋ	ℋ	PROPN
iajs-2517	42	12	)	)	PUNCT
iajs-2517	42	13	.	.	PUNCT
iajs-2517	43	1	let	let	VERB
iajs-2517	43	2	(	(	PUNCT
iajs-2517	43	3	г	г	PROPN
iajs-2517	43	4	,	,	PUNCT
iajs-2517	43	5	ℋ)′	ℋ)′	PROPN
iajs-2517	43	6	∈̃	∈̃	PROPN
iajs-2517	43	7	�	�	PROPN
iajs-2517	43	8	̃	̃	PROPN
iajs-2517	43	9	�	�	PROPN
iajs-2517	43	10	,	,	PUNCT
iajs-2517	43	11	then	then	ADV
iajs-2517	43	12	the	the	DET
iajs-2517	43	13	soft	soft	ADJ
iajs-2517	43	14	closure	closure	NOUN
iajs-2517	43	15	of	of	ADP
iajs-2517	43	16	(	(	PUNCT
iajs-2517	43	17	г	г	PROPN
iajs-2517	43	18	,	,	PUNCT
iajs-2517	43	19	ℋ)′	ℋ)′	PROPN
iajs-2517	43	20	,	,	PUNCT
iajs-2517	43	21	(	(	PUNCT
iajs-2517	43	22	briefly	briefly	ADV
iajs-2517	43	23	cl	cl	INTJ
iajs-2517	43	24	(	(	PUNCT
iajs-2517	43	25	г	г	PROPN
iajs-2517	43	26	,	,	PUNCT
iajs-2517	43	27	ℋ	ℋ	NOUN
iajs-2517	43	28	)	)	PUNCT
iajs-2517	43	29	)	)	PUNCT
iajs-2517	43	30	,	,	PUNCT
iajs-2517	43	31	(	(	PUNCT
iajs-2517	43	32	is	be	AUX
iajs-2517	43	33	defined	define	VERB
iajs-2517	43	34	as	as	ADP
iajs-2517	43	35	cl((г	cl((г	NOUN
iajs-2517	43	36	,	,	PUNCT
iajs-2517	43	37	ℋ	ℋ	NOUN
iajs-2517	43	38	)	)	PUNCT
iajs-2517	43	39	)	)	PUNCT
iajs-2517	43	40	)	)	PUNCT
iajs-2517	44	1	=	=	SYM
iajs-2517	44	2	∩̃	∩̃	PUNCT
iajs-2517	44	3	{	{	PUNCT
iajs-2517	44	4	(	(	PUNCT
iajs-2517	44	5	𝒢	𝒢	PROPN
iajs-2517	44	6	,	,	PUNCT
iajs-2517	44	7	ℋ	ℋ	PROPN
iajs-2517	44	8	)	)	PUNCT
iajs-2517	44	9	∶	∶	NOUN
iajs-2517	44	10	(	(	PUNCT
iajs-2517	44	11	𝒢	𝒢	PROPN
iajs-2517	44	12	,	,	PUNCT
iajs-2517	44	13	ℋ	ℋ	PROPN
iajs-2517	44	14	)	)	PUNCT
iajs-2517	44	15	∈	∈	PROPN
iajs-2517	44	16	şc(χ)𝓗	şc(χ)𝓗	VERB
iajs-2517	44	17	,	,	PUNCT
iajs-2517	44	18	(	(	PUNCT
iajs-2517	44	19	г	г	PROPN
iajs-2517	44	20	,	,	PUNCT
iajs-2517	44	21	ℋ	ℋ	NOUN
iajs-2517	44	22	)	)	PUNCT
iajs-2517	44	23	⊆̃	⊆̃	PROPN
iajs-2517	44	24	(	(	PUNCT
iajs-2517	44	25	𝒢	𝒢	PROPN
iajs-2517	44	26	,	,	PUNCT
iajs-2517	44	27	ℋ	ℋ	PROPN
iajs-2517	44	28	)	)	PUNCT
iajs-2517	44	29	}	}	PUNCT
iajs-2517	44	30	.	.	PUNCT
iajs-2517	45	1	definition	definition	NOUN
iajs-2517	45	2	2.10	2.10	NUM
iajs-2517	45	3	.	.	PUNCT
iajs-2517	46	1	[	[	X
iajs-2517	46	2	11	11	NUM
iajs-2517	46	3	]	]	PUNCT
iajs-2517	46	4	for	for	ADP
iajs-2517	46	5	any	any	PRON
iajs-2517	46	6	(	(	PUNCT
iajs-2517	46	7	𝜒	𝜒	NOUN
iajs-2517	46	8	,	,	PUNCT
iajs-2517	46	9	𝒯	𝒯	PROPN
iajs-2517	46	10	,	,	PUNCT
iajs-2517	46	11	ℋ	ℋ	PROPN
iajs-2517	46	12	)	)	PUNCT
iajs-2517	46	13	.	.	PUNCT
iajs-2517	47	1	let(г	let(г	PROPN
iajs-2517	47	2	,	,	PUNCT
iajs-2517	47	3	ℋ	ℋ	PROPN
iajs-2517	47	4	)	)	PUNCT
iajs-2517	47	5	∈	∈	PROPN
iajs-2517	47	6	şş(χ	şş(χ	NUM
iajs-2517	47	7	)	)	PUNCT
iajs-2517	47	8	𝓗	𝓗	PROPN
iajs-2517	47	9	,	,	PUNCT
iajs-2517	47	10	then	then	ADV
iajs-2517	47	11	the	the	DET
iajs-2517	47	12	soft	soft	ADJ
iajs-2517	47	13	interior	interior	NOUN
iajs-2517	47	14	of	of	ADP
iajs-2517	47	15	(	(	PUNCT
iajs-2517	47	16	г	г	PROPN
iajs-2517	47	17	,	,	PUNCT
iajs-2517	47	18	ℋ	ℋ	PROPN
iajs-2517	47	19	)	)	PUNCT
iajs-2517	47	20	,	,	PUNCT
iajs-2517	47	21	(	(	PUNCT
iajs-2517	47	22	briefly	briefly	ADV
iajs-2517	47	23	int(г	int(г	PROPN
iajs-2517	47	24	,	,	PUNCT
iajs-2517	47	25	ℋ	ℋ	NOUN
iajs-2517	47	26	)	)	PUNCT
iajs-2517	47	27	)	)	PUNCT
iajs-2517	47	28	,	,	PUNCT
iajs-2517	47	29	(	(	PUNCT
iajs-2517	47	30	is	be	AUX
iajs-2517	47	31	defined	define	VERB
iajs-2517	47	32	as	as	ADP
iajs-2517	47	33	int((г	int((г	NOUN
iajs-2517	47	34	,	,	PUNCT
iajs-2517	47	35	ℋ	ℋ	NOUN
iajs-2517	47	36	)	)	PUNCT
iajs-2517	47	37	)	)	PUNCT
iajs-2517	47	38	)	)	PUNCT
iajs-2517	48	1	=	=	SYM
iajs-2517	48	2	∪̃	∪̃	PROPN
iajs-2517	48	3	{	{	PUNCT
iajs-2517	48	4	(	(	PUNCT
iajs-2517	48	5	𝒢	𝒢	PROPN
iajs-2517	48	6	,	,	PUNCT
iajs-2517	48	7	ℋ	ℋ	PROPN
iajs-2517	48	8	):	):	PUNCT
iajs-2517	48	9	(	(	PUNCT
iajs-2517	48	10	𝒢	𝒢	PROPN
iajs-2517	48	11	,	,	PUNCT
iajs-2517	48	12	ℋ	ℋ	PROPN
iajs-2517	48	13	)	)	PUNCT
iajs-2517	48	14	∈	∈	PROPN
iajs-2517	48	15	𝒯	𝒯	PROPN
iajs-2517	48	16	,	,	PUNCT
iajs-2517	48	17	(	(	PUNCT
iajs-2517	48	18	𝒢	𝒢	PROPN
iajs-2517	48	19	,	,	PUNCT
iajs-2517	48	20	ℋ	ℋ	NOUN
iajs-2517	48	21	)	)	PUNCT
iajs-2517	48	22	⊆̃	⊆̃	PROPN
iajs-2517	48	23	(	(	PUNCT
iajs-2517	48	24	г	г	PROPN
iajs-2517	48	25	,	,	PUNCT
iajs-2517	48	26	ℋ	ℋ	NOUN
iajs-2517	48	27	)	)	PUNCT
iajs-2517	48	28	}	}	PUNCT
iajs-2517	48	29	.	.	PUNCT
iajs-2517	49	1	definition	definition	NOUN
iajs-2517	49	2	2.11	2.11	NUM
iajs-2517	49	3	.	.	PUNCT
iajs-2517	50	1	[	[	X
iajs-2517	50	2	2	2	NUM
iajs-2517	50	3	]	]	PUNCT
iajs-2517	50	4	two	two	NUM
iajs-2517	50	5	soft	soft	ADJ
iajs-2517	50	6	sets	set	NOUN
iajs-2517	50	7	(	(	PUNCT
iajs-2517	50	8	𝒵	𝒵	PROPN
iajs-2517	50	9	,	,	PUNCT
iajs-2517	50	10	ℋ	ℋ	PROPN
iajs-2517	50	11	)	)	PUNCT
iajs-2517	50	12	,	,	PUNCT
iajs-2517	50	13	(	(	PUNCT
iajs-2517	50	14	𝒩	𝒩	PROPN
iajs-2517	50	15	,	,	PUNCT
iajs-2517	50	16	ℋ	ℋ	PROPN
iajs-2517	50	17	)	)	PUNCT
iajs-2517	50	18	in	in	ADP
iajs-2517	50	19	şş(𝜒)𝓗.	şş(𝜒)𝓗.	PROPN
iajs-2517	50	20	are	be	AUX
iajs-2517	50	21	said	say	VERB
iajs-2517	50	22	to	to	PART
iajs-2517	50	23	be	be	AUX
iajs-2517	50	24	soft	soft	ADJ
iajs-2517	50	25	disjoint	disjoint	NOUN
iajs-2517	50	26	,	,	PUNCT
iajs-2517	50	27	if	if	SCONJ
iajs-2517	50	28	(	(	PUNCT
iajs-2517	50	29	𝒵	𝒵	PROPN
iajs-2517	50	30	,	,	PUNCT
iajs-2517	50	31	ℋ	ℋ	PROPN
iajs-2517	50	32	)	)	PUNCT
iajs-2517	50	33	∩̃	∩̃	PUNCT
iajs-2517	50	34	(	(	PUNCT
iajs-2517	50	35	𝒩	𝒩	PROPN
iajs-2517	50	36	,	,	PUNCT
iajs-2517	50	37	ℋ	ℋ	PROPN
iajs-2517	50	38	)	)	PUNCT
iajs-2517	50	39	=	=	SYM
iajs-2517	50	40	∅̃	∅̃	NOUN
iajs-2517	50	41	written	write	VERB
iajs-2517	50	42	𝒵(𝒽	𝒵(𝒽	NOUN
iajs-2517	50	43	)	)	PUNCT
iajs-2517	50	44	∩	∩	NOUN
iajs-2517	50	45	𝒩(𝒽	𝒩(𝒽	X
iajs-2517	50	46	)	)	PUNCT
iajs-2517	50	47	=	=	NOUN
iajs-2517	50	48	{	{	PUNCT
iajs-2517	50	49	∅	∅	NOUN
iajs-2517	50	50	}	}	PUNCT
iajs-2517	50	51	,	,	PUNCT
iajs-2517	50	52	for	for	ADP
iajs-2517	50	53	each	each	DET
iajs-2517	50	54	𝒽	𝒽	PRON
iajs-2517	50	55	∈	∈	PROPN
iajs-2517	50	56	ℋ.	ℋ.	PROPN
iajs-2517	50	57	(	(	PUNCT
iajs-2517	50	58	ℳ	ℳ	PROPN
iajs-2517	50	59	,	,	PUNCT
iajs-2517	50	60	ℋ	ℋ	PROPN
iajs-2517	50	61	)	)	PUNCT
iajs-2517	50	62	∃	∃	NOUN
iajs-2517	50	63	,	,	PUNCT
iajs-2517	50	64	if	if	SCONJ
iajs-2517	50	65	𝓝𝒽	𝓝𝒽	PROPN
iajs-2517	50	66	≠	≠	PROPN
iajs-2517	50	67	𝓜𝒽are	𝓜𝒽are	PROPN
iajs-2517	50	68	distinct	distinct	NOUN
iajs-2517	50	69	,	,	PUNCT
iajs-2517	50	70	written	write	VERB
iajs-2517	50	71	�	�	PROPN
iajs-2517	50	72	̃	̃	PROPN
iajs-2517	50	73	�	�	PROPN
iajs-2517	50	74	∈̃	∈̃	PROPN
iajs-2517	50	75	𝓝𝒽	𝓝𝒽	PROPN
iajs-2517	50	76	,	,	PUNCT
iajs-2517	50	77	𝓜	𝓜	PROPN
iajs-2517	50	78	𝒽[2	𝒽[2	PROPN
iajs-2517	50	79	]	]	X
iajs-2517	50	80	two	two	NUM
iajs-2517	50	81	soft	soft	ADJ
iajs-2517	50	82	pointdefinition	pointdefinition	NOUN
iajs-2517	50	83	2.12	2.12	NUM
iajs-2517	50	84	.	.	PUNCT
iajs-2517	50	85	.∈̃	.∈̃	PUNCT
iajs-2517	51	1	(	(	PUNCT
iajs-2517	51	2	𝒩	𝒩	PROPN
iajs-2517	51	3	,	,	PUNCT
iajs-2517	51	4	ℋ	ℋ	PROPN
iajs-2517	51	5	)	)	PUNCT
iajs-2517	51	6	∈̃	∈̃	PROPN
iajs-2517	51	7	(	(	PUNCT
iajs-2517	51	8	ℳ	ℳ	PROPN
iajs-2517	51	9	,	,	PUNCT
iajs-2517	51	10	ℋ)𝑎𝑛𝑑	ℋ)𝑎𝑛𝑑	NUM
iajs-2517	51	11	𝒽	𝒽	DET
iajs-2517	51	12	𝓜𝒽soft	𝓜𝒽soft	PROPN
iajs-2517	51	13	disjoint	disjoint	NOUN
iajs-2517	51	14	sets	set	NOUN
iajs-2517	51	15	,	,	PUNCT
iajs-2517	51	16	such	such	ADJ
iajs-2517	51	17	that	that	PRON
iajs-2517	51	18	are	be	AUX
iajs-2517	51	19	two	two	NUM
iajs-2517	51	20	(	(	PUNCT
iajs-2517	51	21	𝒩	𝒩	PROPN
iajs-2517	51	22	,	,	PUNCT
iajs-2517	51	23	ℋ	ℋ	PROPN
iajs-2517	51	24	)	)	PUNCT
iajs-2517	51	25	and	and	CCONJ
iajs-2517	51	26	124	124	NUM
iajs-2517	51	27	ibn	ibn	PROPN
iajs-2517	51	28	al	al	PROPN
iajs-2517	51	29	-	-	PUNCT
iajs-2517	51	30	haitham	haitham	PROPN
iajs-2517	51	31	jour	jour	X
iajs-2517	51	32	.	.	PROPN
iajs-2517	52	1	for	for	ADP
iajs-2517	52	2	pure	pure	ADJ
iajs-2517	52	3	&	&	CCONJ
iajs-2517	52	4	appl	appl	PROPN
iajs-2517	52	5	.	.	PUNCT
iajs-2517	53	1	sci	sci	PROPN
iajs-2517	53	2	.	.	PROPN
iajs-2517	54	1	33	33	NUM
iajs-2517	54	2	(	(	PUNCT
iajs-2517	54	3	4	4	NUM
iajs-2517	54	4	)	)	PUNCT
iajs-2517	54	5	2020	2020	NUM
iajs-2517	54	6	definition	definition	NOUN
iajs-2517	54	7	2.13	2.13	NUM
iajs-2517	54	8	.	.	PUNCT
iajs-2517	55	1	[	[	X
iajs-2517	55	2	5	5	X
iajs-2517	55	3	]	]	PUNCT
iajs-2517	55	4	let	let	VERB
iajs-2517	55	5	ℐ	ℐ	PRON
iajs-2517	55	6	be	be	AUX
iajs-2517	55	7	a	a	DET
iajs-2517	55	8	non	non	ADJ
iajs-2517	55	9	-	-	ADJ
iajs-2517	55	10	null	null	ADJ
iajs-2517	55	11	family	family	NOUN
iajs-2517	55	12	of	of	ADP
iajs-2517	55	13	soft	soft	ADJ
iajs-2517	55	14	sets	set	NOUN
iajs-2517	55	15	over	over	ADP
iajs-2517	55	16	χ	χ	NOUN
iajs-2517	55	17	with	with	ADP
iajs-2517	55	18	parameter	parameter	NOUN
iajs-2517	55	19	ℋ	ℋ	PROPN
iajs-2517	55	20	,	,	PUNCT
iajs-2517	55	21	then	then	ADV
iajs-2517	55	22	ℐ	ℐ	PRON
iajs-2517	55	23	⊆̃	⊆̃	VERB
iajs-2517	55	24	şş	şş	PRON
iajs-2517	55	25	(	(	PUNCT
iajs-2517	55	26	χ	χ	X
iajs-2517	55	27	)	)	PUNCT
iajs-2517	55	28	𝓗	𝓗	NOUN
iajs-2517	55	29	is	be	AUX
iajs-2517	55	30	a	a	DET
iajs-2517	55	31	soft	soft	ADJ
iajs-2517	55	32	ideal	ideal	NOUN
iajs-2517	55	33	whenever	whenever	SCONJ
iajs-2517	55	34	,	,	PUNCT
iajs-2517	55	35	(	(	PUNCT
iajs-2517	55	36	1	1	X
iajs-2517	55	37	)	)	PUNCT
iajs-2517	55	38	if	if	SCONJ
iajs-2517	55	39	(	(	PUNCT
iajs-2517	55	40	г	г	PROPN
iajs-2517	55	41	,	,	PUNCT
iajs-2517	55	42	ℋ	ℋ	NOUN
iajs-2517	55	43	)	)	PUNCT
iajs-2517	55	44	∈̃	∈̃	PROPN
iajs-2517	55	45	ℐ	ℐ	PROPN
iajs-2517	55	46	and	and	CCONJ
iajs-2517	55	47	(	(	PUNCT
iajs-2517	55	48	𝒢	𝒢	PROPN
iajs-2517	55	49	,	,	PUNCT
iajs-2517	55	50	ℋ	ℋ	PROPN
iajs-2517	55	51	)	)	PUNCT
iajs-2517	55	52	∈̃	∈̃	PROPN
iajs-2517	55	53	ℐ	ℐ	PROPN
iajs-2517	55	54	implies,(г	implies,(г	PROPN
iajs-2517	55	55	,	,	PUNCT
iajs-2517	55	56	ℋ	ℋ	PROPN
iajs-2517	55	57	)	)	PUNCT
iajs-2517	55	58	∪̃	∪̃	PROPN
iajs-2517	55	59	(	(	PUNCT
iajs-2517	55	60	𝒢	𝒢	PROPN
iajs-2517	55	61	,	,	PUNCT
iajs-2517	55	62	ℋ	ℋ	PROPN
iajs-2517	55	63	)	)	PUNCT
iajs-2517	55	64	∈̃	∈̃	PROPN
iajs-2517	55	65	ℐ.	ℐ.	PROPN
iajs-2517	55	66	(	(	PUNCT
iajs-2517	55	67	2	2	NUM
iajs-2517	55	68	)	)	PUNCT
iajs-2517	55	69	if	if	SCONJ
iajs-2517	55	70	(	(	PUNCT
iajs-2517	55	71	г	г	PROPN
iajs-2517	55	72	,	,	PUNCT
iajs-2517	55	73	ℋ	ℋ	NOUN
iajs-2517	55	74	)	)	PUNCT
iajs-2517	55	75	∈̃	∈̃	PROPN
iajs-2517	55	76	ℐ	ℐ	PROPN
iajs-2517	55	77	and	and	CCONJ
iajs-2517	55	78	(	(	PUNCT
iajs-2517	55	79	𝒢	𝒢	PROPN
iajs-2517	55	80	,	,	PUNCT
iajs-2517	55	81	ℋ	ℋ	NOUN
iajs-2517	55	82	)	)	PUNCT
iajs-2517	55	83	⊆̃	⊆̃	PROPN
iajs-2517	55	84	(	(	PUNCT
iajs-2517	55	85	г	г	PROPN
iajs-2517	55	86	,	,	PUNCT
iajs-2517	55	87	ℋ	ℋ	NOUN
iajs-2517	55	88	)	)	PUNCT
iajs-2517	55	89	implies	imply	VERB
iajs-2517	55	90	(	(	PUNCT
iajs-2517	55	91	𝒢	𝒢	PROPN
iajs-2517	55	92	,	,	PUNCT
iajs-2517	55	93	ℋ	ℋ	PROPN
iajs-2517	55	94	)	)	PUNCT
iajs-2517	55	95	∈̃	∈̃	PROPN
iajs-2517	55	96	ℐ	ℐ	PROPN
iajs-2517	55	97	.	.	PUNCT
iajs-2517	56	1	any	any	PRON
iajs-2517	56	2	(	(	PUNCT
iajs-2517	56	3	𝜒	𝜒	NOUN
iajs-2517	56	4	,	,	PUNCT
iajs-2517	56	5	𝒯	𝒯	PROPN
iajs-2517	56	6	,	,	PUNCT
iajs-2517	56	7	ℋ	ℋ	PROPN
iajs-2517	56	8	)	)	PUNCT
iajs-2517	56	9	with	with	ADP
iajs-2517	56	10	a	a	DET
iajs-2517	56	11	soft	soft	ADJ
iajs-2517	56	12	ideal	ideal	NOUN
iajs-2517	56	13	ℐ	ℐ	PRON
iajs-2517	56	14	is	be	AUX
iajs-2517	56	15	a	a	DET
iajs-2517	56	16	soft	soft	ADJ
iajs-2517	56	17	ideal	ideal	ADJ
iajs-2517	56	18	topological	topological	ADJ
iajs-2517	56	19	space	space	NOUN
iajs-2517	56	20	(	(	PUNCT
iajs-2517	56	21	briefly	briefly	ADV
iajs-2517	56	22	(	(	PUNCT
iajs-2517	56	23	𝜒	𝜒	X
iajs-2517	56	24	,	,	PUNCT
iajs-2517	56	25	𝒯	𝒯	PROPN
iajs-2517	56	26	,	,	PUNCT
iajs-2517	56	27	ℋ	ℋ	PROPN
iajs-2517	56	28	,	,	PUNCT
iajs-2517	56	29	ℐ	ℐ	PROPN
iajs-2517	56	30	)	)	PUNCT
iajs-2517	56	31	)	)	PUNCT
iajs-2517	56	32	.	.	PUNCT
iajs-2517	57	1	definition	definition	NOUN
iajs-2517	57	2	2.14	2.14	NUM
iajs-2517	57	3	.	.	PUNCT
iajs-2517	58	1	[	[	X
iajs-2517	58	2	5	5	X
iajs-2517	58	3	]	]	X
iajs-2517	58	4	any	any	PRON
iajs-2517	58	5	(	(	PUNCT
iajs-2517	58	6	χ	χ	X
iajs-2517	58	7	,	,	PUNCT
iajs-2517	58	8	𝒯	𝒯	PROPN
iajs-2517	58	9	,	,	PUNCT
iajs-2517	58	10	ℋ	ℋ	PROPN
iajs-2517	58	11	)	)	PUNCT
iajs-2517	58	12	with	with	ADP
iajs-2517	58	13	a	a	DET
iajs-2517	58	14	soft	soft	ADJ
iajs-2517	58	15	ideal	ideal	NOUN
iajs-2517	58	16	ℐ	ℐ	PRON
iajs-2517	58	17	is	be	AUX
iajs-2517	58	18	namelya	namelya	ADV
iajs-2517	58	19	soft	soft	ADJ
iajs-2517	58	20	ideal	ideal	ADJ
iajs-2517	58	21	topological	topological	ADJ
iajs-2517	58	22	space	space	NOUN
iajs-2517	58	23	(	(	PUNCT
iajs-2517	58	24	briefly	briefly	ADV
iajs-2517	58	25	(	(	PUNCT
iajs-2517	58	26	χ	χ	X
iajs-2517	58	27	,	,	PUNCT
iajs-2517	58	28	𝒯	𝒯	PROPN
iajs-2517	58	29	,	,	PUNCT
iajs-2517	58	30	ℋ	ℋ	PROPN
iajs-2517	58	31	,	,	PUNCT
iajs-2517	58	32	ℐ	ℐ	PROPN
iajs-2517	58	33	)	)	PUNCT
iajs-2517	58	34	)	)	PUNCT
iajs-2517	58	35	.	.	PUNCT
iajs-2517	59	1	definition	definition	NOUN
iajs-2517	59	2	2.15	2.15	NUM
iajs-2517	59	3	.	.	PUNCT
iajs-2517	60	1	[	[	X
iajs-2517	60	2	12	12	NUM
iajs-2517	60	3	]	]	PUNCT
iajs-2517	60	4	for	for	ADP
iajs-2517	60	5	any	any	DET
iajs-2517	60	6	(	(	PUNCT
iajs-2517	60	7	𝜒	𝜒	NOUN
iajs-2517	60	8	,	,	PUNCT
iajs-2517	60	9	𝒯	𝒯	PROPN
iajs-2517	60	10	,	,	PUNCT
iajs-2517	60	11	ℋ	ℋ	PROPN
iajs-2517	60	12	)	)	PUNCT
iajs-2517	60	13	,	,	PUNCT
iajs-2517	60	14	then	then	ADV
iajs-2517	60	15	(	(	PUNCT
iajs-2517	60	16	г	г	PROPN
iajs-2517	60	17	,	,	PUNCT
iajs-2517	60	18	ℋ	ℋ	PROPN
iajs-2517	60	19	)	)	PUNCT
iajs-2517	60	20	is	be	AUX
iajs-2517	60	21	a	a	DET
iajs-2517	60	22	soft	soft	ADJ
iajs-2517	60	23	semi	semi	ADJ
iajs-2517	60	24	-	-	ADJ
iajs-2517	60	25	open	open	ADJ
iajs-2517	60	26	set	set	NOUN
iajs-2517	60	27	(	(	PUNCT
iajs-2517	60	28	briefly	briefly	ADV
iajs-2517	60	29	şş𝑜𝑝𝑒𝑛	şş𝑜𝑝𝑒𝑛	NOUN
iajs-2517	60	30	𝑠𝑒𝑡	𝑠𝑒𝑡	NOUN
iajs-2517	60	31	)	)	PUNCT
iajs-2517	60	32	if	if	SCONJ
iajs-2517	60	33	(	(	PUNCT
iajs-2517	60	34	г	г	PROPN
iajs-2517	60	35	,	,	PUNCT
iajs-2517	60	36	ℋ	ℋ	NOUN
iajs-2517	60	37	)	)	PUNCT
iajs-2517	60	38	⊆̃	⊆̃	NOUN
iajs-2517	60	39	cl(int(г	cl(int(г	NOUN
iajs-2517	60	40	,	,	PUNCT
iajs-2517	60	41	ℋ	ℋ	NOUN
iajs-2517	60	42	)	)	PUNCT
iajs-2517	60	43	)	)	PUNCT
iajs-2517	60	44	.	.	PUNCT
iajs-2517	61	1	a	a	DET
iajs-2517	61	2	complement	complement	NOUN
iajs-2517	61	3	of	of	ADP
iajs-2517	61	4	a	a	DET
iajs-2517	61	5	soft	soft	ADJ
iajs-2517	61	6	semi	semi	ADJ
iajs-2517	61	7	-	-	ADJ
iajs-2517	61	8	open	open	ADJ
iajs-2517	61	9	set	set	NOUN
iajs-2517	61	10	is	be	AUX
iajs-2517	61	11	a	a	DET
iajs-2517	61	12	soft	soft	ADJ
iajs-2517	61	13	semiclosed	semiclose	VERB
iajs-2517	61	14	(	(	PUNCT
iajs-2517	61	15	briefly	briefly	ADV
iajs-2517	61	16	𝑠𝑠-closed	𝑠𝑠-close	VERB
iajs-2517	61	17	𝑒𝑡	𝑒𝑡	NOUN
iajs-2517	61	18	)	)	PUNCT
iajs-2517	61	19	.	.	PUNCT
iajs-2517	62	1	the	the	DET
iajs-2517	62	2	collection	collection	NOUN
iajs-2517	62	3	of	of	ADP
iajs-2517	62	4	each	each	DET
iajs-2517	62	5	soft	soft	ADJ
iajs-2517	62	6	semi	semi	ADJ
iajs-2517	62	7	-open	-open	ADJ
iajs-2517	62	8	sets	set	NOUN
iajs-2517	62	9	in	in	ADP
iajs-2517	62	10	(	(	PUNCT
iajs-2517	62	11	𝜒	𝜒	X
iajs-2517	62	12	,	,	PUNCT
iajs-2517	62	13	𝒯	𝒯	PROPN
iajs-2517	62	14	,	,	PUNCT
iajs-2517	62	15	ℋ	ℋ	PROPN
iajs-2517	62	16	)	)	PUNCT
iajs-2517	62	17	(	(	PUNCT
iajs-2517	62	18	briefly	briefly	ADV
iajs-2517	62	19	şş𝑂(χ	şş𝑂(χ	PROPN
iajs-2517	62	20	)	)	PUNCT
iajs-2517	62	21	)	)	PUNCT
iajs-2517	62	22	.	.	PUNCT
iajs-2517	63	1	the	the	DET
iajs-2517	63	2	collection	collection	NOUN
iajs-2517	63	3	of	of	ADP
iajs-2517	63	4	each	each	DET
iajs-2517	63	5	soft	soft	ADJ
iajs-2517	63	6	semi	semi	ADJ
iajs-2517	63	7	-	-	ADJ
iajs-2517	63	8	closed	closed	ADJ
iajs-2517	63	9	sets	set	NOUN
iajs-2517	63	10	(	(	PUNCT
iajs-2517	63	11	briefly	briefly	NOUN
iajs-2517	63	12	şş𝐶(χ	şş𝐶(χ	NUM
iajs-2517	63	13	)	)	PUNCT
iajs-2517	63	14	𝓗	𝓗	NOUN
iajs-2517	63	15	)	)	PUNCT
iajs-2517	63	16	.	.	PUNCT
iajs-2517	64	1	definition	definition	NOUN
iajs-2517	64	2	2.16	2.16	NUM
iajs-2517	64	3	.	.	PUNCT
iajs-2517	65	1	[	[	X
iajs-2517	65	2	2	2	X
iajs-2517	65	3	]	]	PUNCT
iajs-2517	65	4	a	a	DET
iajs-2517	65	5	soft	soft	ADJ
iajs-2517	65	6	topological	topological	ADJ
iajs-2517	65	7	space	space	NOUN
iajs-2517	65	8	(	(	PUNCT
iajs-2517	65	9	𝜒	𝜒	X
iajs-2517	65	10	,	,	PUNCT
iajs-2517	65	11	𝒯	𝒯	PROPN
iajs-2517	65	12	,	,	PUNCT
iajs-2517	65	13	ℋ	ℋ	PROPN
iajs-2517	65	14	)	)	PUNCT
iajs-2517	65	15	over	over	ADP
iajs-2517	65	16	χ	χ	PROPN
iajs-2517	65	17	is	be	AUX
iajs-2517	65	18	a	a	DET
iajs-2517	65	19	soft𝒯0	soft𝒯0	NOUN
iajs-2517	65	20	-	-	PUNCT
iajs-2517	65	21	space	space	NOUN
iajs-2517	65	22	if	if	SCONJ
iajs-2517	65	23	for	for	ADP
iajs-2517	65	24	each	each	DET
iajs-2517	65	25	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	65	26	,	,	PUNCT
iajs-2517	65	27	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	65	28	∈̃	∈̃	PROPN
iajs-2517	65	29	�	�	PROPN
iajs-2517	65	30	̃	̃	PROPN
iajs-2517	65	31	�	�	NOUN
iajs-2517	65	32	such	such	ADJ
iajs-2517	65	33	that	that	DET
iajs-2517	65	34	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	65	35	≠	≠	PROPN
iajs-2517	65	36	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	65	37	,	,	PUNCT
iajs-2517	65	38	there	there	PRON
iajs-2517	65	39	exists	exist	VERB
iajs-2517	65	40	a	a	DET
iajs-2517	65	41	soft	soft	ADJ
iajs-2517	65	42	open	open	ADJ
iajs-2517	65	43	set	set	NOUN
iajs-2517	65	44	(	(	PUNCT
iajs-2517	65	45	ϣ	ϣ	NOUN
iajs-2517	65	46	,	,	PUNCT
iajs-2517	65	47	ℋ	ℋ	NOUN
iajs-2517	65	48	)	)	PUNCT
iajs-2517	65	49	such	such	ADJ
iajs-2517	66	1	that	that	SCONJ
iajs-2517	66	2	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	66	3	∈̃	∈̃	NOUN
iajs-2517	66	4	(	(	PUNCT
iajs-2517	66	5	ϣ	ϣ	NOUN
iajs-2517	66	6	,	,	PUNCT
iajs-2517	66	7	ℋ	ℋ	NOUN
iajs-2517	66	8	)	)	PUNCT
iajs-2517	66	9	and	and	CCONJ
iajs-2517	66	10	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	66	11	∉̃	∉̃	ADJ
iajs-2517	66	12	(	(	PUNCT
iajs-2517	66	13	ϣ	ϣ	PROPN
iajs-2517	66	14	,	,	PUNCT
iajs-2517	66	15	ℋ	ℋ	NOUN
iajs-2517	66	16	)	)	PUNCT
iajs-2517	66	17	or	or	CCONJ
iajs-2517	66	18	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	66	19	∉̃	∉̃	ADJ
iajs-2517	66	20	(	(	PUNCT
iajs-2517	66	21	ϣ	ϣ	NOUN
iajs-2517	66	22	,	,	PUNCT
iajs-2517	66	23	ℋ	ℋ	NOUN
iajs-2517	66	24	)	)	PUNCT
iajs-2517	66	25	and	and	CCONJ
iajs-2517	66	26	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	66	27	∈̃	∈̃	PROPN
iajs-2517	66	28	(	(	PUNCT
iajs-2517	66	29	ϣ	ϣ	PROPN
iajs-2517	66	30	,	,	PUNCT
iajs-2517	66	31	ℋ	ℋ	PROPN
iajs-2517	66	32	)	)	PUNCT
iajs-2517	66	33	.	.	PUNCT
iajs-2517	66	34	theorem	theorem	VERB
iajs-2517	66	35	2.17	2.17	NUM
iajs-2517	66	36	.	.	PUNCT
iajs-2517	67	1	[	[	X
iajs-2517	67	2	2	2	X
iajs-2517	67	3	]	]	PUNCT
iajs-2517	67	4	a	a	DET
iajs-2517	67	5	soft	soft	ADJ
iajs-2517	67	6	topological	topological	ADJ
iajs-2517	67	7	space	space	NOUN
iajs-2517	67	8	(	(	PUNCT
iajs-2517	67	9	𝜒	𝜒	X
iajs-2517	67	10	,	,	PUNCT
iajs-2517	67	11	𝒯	𝒯	PROPN
iajs-2517	67	12	,	,	PUNCT
iajs-2517	67	13	ℋ	ℋ	PROPN
iajs-2517	67	14	)	)	PUNCT
iajs-2517	67	15	over	over	ADP
iajs-2517	67	16	χ	χ	PROPN
iajs-2517	67	17	is	be	AUX
iajs-2517	67	18	a	a	DET
iajs-2517	67	19	soft𝒯0	soft𝒯0	NOUN
iajs-2517	67	20	-	-	PUNCT
iajs-2517	67	21	space	space	NOUN
iajs-2517	67	22	if	if	SCONJ
iajs-2517	67	23	and	and	CCONJ
iajs-2517	67	24	only	only	ADV
iajs-2517	67	25	if	if	SCONJ
iajs-2517	67	26	for	for	ADP
iajs-2517	67	27	each	each	DET
iajs-2517	67	28	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	67	29	,	,	PUNCT
iajs-2517	67	30	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	67	31	∈̃	∈̃	PROPN
iajs-2517	67	32	𝜒	𝜒	PRON
iajs-2517	67	33	such	such	ADJ
iajs-2517	67	34	that	that	DET
iajs-2517	67	35	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	67	36	≠	≠	PROPN
iajs-2517	67	37	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	67	38	,	,	PUNCT
iajs-2517	67	39	there	there	PRON
iajs-2517	67	40	exists	exist	VERB
iajs-2517	67	41	a	a	DET
iajs-2517	67	42	soft	soft	ADJ
iajs-2517	67	43	closed	closed	ADJ
iajs-2517	67	44	set	set	NOUN
iajs-2517	67	45	(	(	PUNCT
iajs-2517	67	46	𝒱	𝒱	PROPN
iajs-2517	67	47	,	,	PUNCT
iajs-2517	67	48	ℋ	ℋ	PROPN
iajs-2517	67	49	)	)	PUNCT
iajs-2517	67	50	such	such	ADJ
iajs-2517	67	51	that	that	SCONJ
iajs-2517	67	52	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	67	53	∈̃	∈̃	PROPN
iajs-2517	67	54	(	(	PUNCT
iajs-2517	67	55	𝒱	𝒱	PROPN
iajs-2517	67	56	,	,	PUNCT
iajs-2517	67	57	ℋ	ℋ	PROPN
iajs-2517	67	58	)	)	PUNCT
iajs-2517	67	59	,	,	PUNCT
iajs-2517	67	60	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	67	61	∉̃	∉̃	PROPN
iajs-2517	67	62	(	(	PUNCT
iajs-2517	67	63	𝒱	𝒱	PROPN
iajs-2517	67	64	,	,	PUNCT
iajs-2517	67	65	ℋ	ℋ	PROPN
iajs-2517	67	66	)	)	PUNCT
iajs-2517	67	67	or	or	CCONJ
iajs-2517	67	68	𝒽	𝒽	PRON
iajs-2517	67	69	∉̃	∉̃	ADJ
iajs-2517	67	70	(	(	PUNCT
iajs-2517	67	71	𝒱	𝒱	PROPN
iajs-2517	67	72	,	,	PUNCT
iajs-2517	67	73	ℋ	ℋ	PROPN
iajs-2517	67	74	)	)	PUNCT
iajs-2517	67	75	,	,	PUNCT
iajs-2517	67	76	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	67	77	∈̃	∈̃	PROPN
iajs-2517	67	78	(	(	PUNCT
iajs-2517	67	79	𝒱	𝒱	PROPN
iajs-2517	67	80	,	,	PUNCT
iajs-2517	67	81	ℋ	ℋ	PROPN
iajs-2517	67	82	)	)	PUNCT
iajs-2517	67	83	.	.	PUNCT
iajs-2517	68	1	definition	definition	NOUN
iajs-2517	68	2	2.18	2.18	NUM
iajs-2517	68	3	.	.	PUNCT
iajs-2517	69	1	[	[	X
iajs-2517	69	2	2	2	X
iajs-2517	69	3	]	]	PUNCT
iajs-2517	69	4	a	a	DET
iajs-2517	69	5	soft	soft	ADJ
iajs-2517	69	6	topological	topological	ADJ
iajs-2517	69	7	space	space	NOUN
iajs-2517	69	8	(	(	PUNCT
iajs-2517	69	9	𝜒	𝜒	X
iajs-2517	69	10	,	,	PUNCT
iajs-2517	69	11	𝒯	𝒯	PROPN
iajs-2517	69	12	,	,	PUNCT
iajs-2517	69	13	ℋ	ℋ	PROPN
iajs-2517	69	14	)	)	PUNCT
iajs-2517	69	15	over	over	ADP
iajs-2517	69	16	χ	χ	PROPN
iajs-2517	69	17	is	be	AUX
iajs-2517	69	18	a	a	DET
iajs-2517	69	19	soft-𝒯1	soft-𝒯1	NOUN
iajs-2517	69	20	-	-	NOUN
iajs-2517	69	21	space	space	NOUN
iajs-2517	69	22	if	if	SCONJ
iajs-2517	69	23	for	for	ADP
iajs-2517	69	24	each	each	DET
iajs-2517	69	25	𝒽	𝒽	NOUN
iajs-2517	69	26	,	,	PUNCT
iajs-2517	69	27	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	69	28	∈̃	∈̃	PROPN
iajs-2517	69	29	𝜒	𝜒	PRON
iajs-2517	69	30	such	such	ADJ
iajs-2517	69	31	that	that	DET
iajs-2517	69	32	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	69	33	≠	≠	PROPN
iajs-2517	69	34	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	69	35	∃	∃	PROPN
iajs-2517	69	36	(	(	PUNCT
iajs-2517	69	37	𝒫	𝒫	PROPN
iajs-2517	69	38	,	,	PUNCT
iajs-2517	69	39	ℋ	ℋ	PROPN
iajs-2517	69	40	)	)	PUNCT
iajs-2517	69	41	,	,	PUNCT
iajs-2517	69	42	(	(	PUNCT
iajs-2517	69	43	ϣ	ϣ	X
iajs-2517	69	44	,	,	PUNCT
iajs-2517	69	45	ℋ	ℋ	NOUN
iajs-2517	69	46	)	)	PUNCT
iajs-2517	69	47	∈	∈	PROPN
iajs-2517	69	48	𝒯	𝒯	PROPN
iajs-2517	69	49	whenever	whenever	ADV
iajs-2517	69	50	,	,	PUNCT
iajs-2517	69	51	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	69	52	∈̃	∈̃	NOUN
iajs-2517	69	53	(	(	PUNCT
iajs-2517	69	54	𝒫	𝒫	NOUN
iajs-2517	69	55	,	,	PUNCT
iajs-2517	69	56	ℋ	ℋ	PROPN
iajs-2517	69	57	)	)	PUNCT
iajs-2517	69	58	,	,	PUNCT
iajs-2517	69	59	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	69	60	∉̃	∉̃	NOUN
iajs-2517	69	61	(	(	PUNCT
iajs-2517	69	62	𝒫	𝒫	PROPN
iajs-2517	69	63	,	,	PUNCT
iajs-2517	69	64	ℋ	ℋ	NOUN
iajs-2517	69	65	)	)	PUNCT
iajs-2517	69	66	and	and	CCONJ
iajs-2517	69	67	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	69	68	∉̃	∉̃	ADJ
iajs-2517	69	69	(	(	PUNCT
iajs-2517	69	70	ϣ	ϣ	NOUN
iajs-2517	69	71	,	,	PUNCT
iajs-2517	69	72	ℋ	ℋ	NOUN
iajs-2517	69	73	)	)	PUNCT
iajs-2517	69	74	,	,	PUNCT
iajs-2517	69	75	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	69	76	∈̃	∈̃	PROPN
iajs-2517	69	77	(	(	PUNCT
iajs-2517	69	78	ϣ	ϣ	PROPN
iajs-2517	69	79	,	,	PUNCT
iajs-2517	69	80	ℋ	ℋ	PROPN
iajs-2517	69	81	)	)	PUNCT
iajs-2517	69	82	.	.	PUNCT
iajs-2517	70	1	theorem	theorem	VERB
iajs-2517	70	2	2.19	2.19	NUM
iajs-2517	70	3	.	.	PUNCT
iajs-2517	71	1	[	[	X
iajs-2517	71	2	2	2	X
iajs-2517	71	3	]	]	PUNCT
iajs-2517	71	4	a	a	DET
iajs-2517	71	5	space	space	NOUN
iajs-2517	71	6	(	(	PUNCT
iajs-2517	71	7	𝜒	𝜒	X
iajs-2517	71	8	,	,	PUNCT
iajs-2517	71	9	𝒯	𝒯	PROPN
iajs-2517	71	10	,	,	PUNCT
iajs-2517	71	11	ℋ	ℋ	PROPN
iajs-2517	71	12	)	)	PUNCT
iajs-2517	71	13	is	be	AUX
iajs-2517	71	14	a	a	DET
iajs-2517	71	15	soft-𝒯1	soft-𝒯1	NOUN
iajs-2517	71	16	-	-	NOUN
iajs-2517	71	17	space	space	NOUN
iajs-2517	71	18	if	if	SCONJ
iajs-2517	71	19	and	and	CCONJ
iajs-2517	71	20	only	only	ADV
iajs-2517	71	21	if	if	SCONJ
iajs-2517	71	22	for	for	ADP
iajs-2517	71	23	all	all	DET
iajs-2517	71	24	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	71	25	,	,	PUNCT
iajs-2517	71	26	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	71	27	∈̃	∈̃	PROPN
iajs-2517	71	28	�	�	PROPN
iajs-2517	71	29	̃	̃	PROPN
iajs-2517	71	30	�	�	NOUN
iajs-2517	71	31	such	such	ADJ
iajs-2517	71	32	that	that	PRON
iajs-2517	71	33	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	71	34	≠	≠	PROPN
iajs-2517	71	35	𝒽𝓝.	𝒽𝓝.	ADJ
iajs-2517	71	36	∃	∃	NOUN
iajs-2517	71	37	(	(	PUNCT
iajs-2517	71	38	𝒫	𝒫	PROPN
iajs-2517	71	39	,	,	PUNCT
iajs-2517	71	40	ℋ	ℋ	PROPN
iajs-2517	71	41	)	)	PUNCT
iajs-2517	71	42	,	,	PUNCT
iajs-2517	71	43	(	(	PUNCT
iajs-2517	71	44	𝒱	𝒱	PROPN
iajs-2517	71	45	,	,	PUNCT
iajs-2517	71	46	ℋ	ℋ	PROPN
iajs-2517	71	47	)	)	PUNCT
iajs-2517	71	48	are	be	AUX
iajs-2517	71	49	two	two	NUM
iajs-2517	71	50	soft	soft	ADJ
iajs-2517	71	51	closed	closed	ADJ
iajs-2517	71	52	sets	set	NOUN
iajs-2517	71	53	whenever	whenever	ADV
iajs-2517	71	54	,	,	PUNCT
iajs-2517	71	55	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	71	56	∈̃	∈̃	NOUN
iajs-2517	71	57	(	(	PUNCT
iajs-2517	71	58	𝒫	𝒫	NOUN
iajs-2517	71	59	,	,	PUNCT
iajs-2517	71	60	ℋ	ℋ	PROPN
iajs-2517	71	61	)	)	PUNCT
iajs-2517	71	62	,	,	PUNCT
iajs-2517	71	63	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	71	64	∉̃	∉̃	NOUN
iajs-2517	71	65	(	(	PUNCT
iajs-2517	71	66	𝒫	𝒫	PROPN
iajs-2517	71	67	,	,	PUNCT
iajs-2517	71	68	ℋ	ℋ	NOUN
iajs-2517	71	69	)	)	PUNCT
iajs-2517	71	70	and	and	CCONJ
iajs-2517	71	71	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	71	72	∉̃	∉̃	ADJ
iajs-2517	71	73	(	(	PUNCT
iajs-2517	71	74	𝒱	𝒱	PROPN
iajs-2517	71	75	,	,	PUNCT
iajs-2517	71	76	ℋ	ℋ	PROPN
iajs-2517	71	77	)	)	PUNCT
iajs-2517	71	78	,	,	PUNCT
iajs-2517	71	79	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	71	80	∈̃	∈̃	PROPN
iajs-2517	71	81	(	(	PUNCT
iajs-2517	71	82	𝒱	𝒱	PROPN
iajs-2517	71	83	,	,	PUNCT
iajs-2517	71	84	ℋ	ℋ	PROPN
iajs-2517	71	85	)	)	PUNCT
iajs-2517	71	86	.	.	PUNCT
iajs-2517	72	1	definition	definition	NOUN
iajs-2517	72	2	2.20	2.20	NUM
iajs-2517	72	3	.	.	PUNCT
iajs-2517	73	1	[	[	X
iajs-2517	73	2	2	2	X
iajs-2517	73	3	]	]	X
iajs-2517	73	4	let	let	VERB
iajs-2517	73	5	(	(	PUNCT
iajs-2517	73	6	𝜒	𝜒	X
iajs-2517	73	7	,	,	PUNCT
iajs-2517	73	8	𝒯	𝒯	PROPN
iajs-2517	73	9	,	,	PUNCT
iajs-2517	73	10	ℋ	ℋ	PROPN
iajs-2517	73	11	)	)	PUNCT
iajs-2517	73	12	be	be	VERB
iajs-2517	73	13	a	a	DET
iajs-2517	73	14	soft	soft	ADJ
iajs-2517	73	15	topological	topological	ADJ
iajs-2517	73	16	space	space	NOUN
iajs-2517	73	17	over	over	ADP
iajs-2517	73	18	χ	χ	PROPN
iajs-2517	73	19	is	be	AUX
iajs-2517	73	20	said	say	VERB
iajs-2517	73	21	to	to	PART
iajs-2517	73	22	be	be	AUX
iajs-2517	73	23	soft-𝒯2space	soft-𝒯2space	NOUN
iajs-2517	73	24	if	if	SCONJ
iajs-2517	73	25	,	,	PUNCT
iajs-2517	73	26	for	for	ADP
iajs-2517	73	27	each	each	DET
iajs-2517	73	28	𝒽	𝒽	NOUN
iajs-2517	73	29	,	,	PUNCT
iajs-2517	73	30	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	73	31	∈̃	∈̃	PROPN
iajs-2517	73	32	�	�	PROPN
iajs-2517	73	33	̃	̃	PROPN
iajs-2517	73	34	�	�	NOUN
iajs-2517	73	35	such	such	ADJ
iajs-2517	73	36	that	that	DET
iajs-2517	73	37	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	73	38	≠	≠	PROPN
iajs-2517	73	39	𝒽𝓝.	𝒽𝓝.	ADJ
iajs-2517	73	40	∃	∃	NOUN
iajs-2517	73	41	(	(	PUNCT
iajs-2517	73	42	𝒫	𝒫	PROPN
iajs-2517	73	43	,	,	PUNCT
iajs-2517	73	44	ℋ	ℋ	PROPN
iajs-2517	73	45	)	)	PUNCT
iajs-2517	73	46	,	,	PUNCT
iajs-2517	73	47	(	(	PUNCT
iajs-2517	73	48	ϣ	ϣ	X
iajs-2517	73	49	,	,	PUNCT
iajs-2517	73	50	ℋ	ℋ	NOUN
iajs-2517	73	51	)	)	PUNCT
iajs-2517	73	52	∈	∈	PROPN
iajs-2517	73	53	𝒯	𝒯	PROPN
iajs-2517	73	54	whenever	whenever	ADV
iajs-2517	73	55	,	,	PUNCT
iajs-2517	73	56	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	73	57	∈̃	∈̃	NOUN
iajs-2517	73	58	(	(	PUNCT
iajs-2517	73	59	𝒫	𝒫	NOUN
iajs-2517	73	60	,	,	PUNCT
iajs-2517	73	61	ℋ)𝒽𝓜	ℋ)𝒽𝓜	NOUN
iajs-2517	73	62	,	,	PUNCT
iajs-2517	73	63	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	73	64	∈̃	∈̃	PROPN
iajs-2517	73	65	(	(	PUNCT
iajs-2517	73	66	ϣ	ϣ	PROPN
iajs-2517	73	67	,	,	PUNCT
iajs-2517	73	68	ℋ	ℋ	NOUN
iajs-2517	73	69	)	)	PUNCT
iajs-2517	73	70	and	and	CCONJ
iajs-2517	73	71	(	(	PUNCT
iajs-2517	73	72	𝒫	𝒫	NOUN
iajs-2517	73	73	,	,	PUNCT
iajs-2517	73	74	ℋ	ℋ	PROPN
iajs-2517	73	75	)	)	PUNCT
iajs-2517	73	76	∩̃	∩̃	PUNCT
iajs-2517	73	77	(	(	PUNCT
iajs-2517	73	78	ϣ	ϣ	PROPN
iajs-2517	73	79	,	,	PUNCT
iajs-2517	73	80	ℋ	ℋ	PROPN
iajs-2517	73	81	)	)	PUNCT
iajs-2517	73	82	=	=	SYM
iajs-2517	73	83	{	{	PUNCT
iajs-2517	73	84	∅̃	∅̃	NOUN
iajs-2517	73	85	}	}	PUNCT
iajs-2517	73	86	.	.	PUNCT
iajs-2517	74	1	proposition	proposition	NOUN
iajs-2517	74	2	2.21	2.21	NUM
iajs-2517	74	3	.	.	PUNCT
iajs-2517	75	1	[	[	X
iajs-2517	75	2	2	2	X
iajs-2517	75	3	]	]	PUNCT
iajs-2517	75	4	for	for	ADP
iajs-2517	75	5	all	all	DET
iajs-2517	75	6	soft𝒯𝑖+1	soft𝒯𝑖+1	NOUN
iajs-2517	75	7	-	-	PUNCT
iajs-2517	75	8	space	space	NOUN
iajs-2517	75	9	is	be	AUX
iajs-2517	75	10	a	a	DET
iajs-2517	75	11	soft𝒯𝑖-space	soft𝒯𝑖-space	NOUN
iajs-2517	75	12	and	and	CCONJ
iajs-2517	76	1	i	i	PRON
iajs-2517	76	2	∈	∈	PROPN
iajs-2517	76	3	{	{	PUNCT
iajs-2517	76	4	0,1,2	0,1,2	NOUN
iajs-2517	76	5	}	}	PUNCT
iajs-2517	76	6	𝐏𝐫𝐨𝐨𝐟.	𝐏𝐫𝐨𝐨𝐟.	NOUN
iajs-2517	76	7	obvious	obvious	ADJ
iajs-2517	76	8	.	.	PUNCT
iajs-2517	77	1	note	note	VERB
iajs-2517	77	2	that	that	SCONJ
iajs-2517	77	3	for	for	ADP
iajs-2517	77	4	all	all	DET
iajs-2517	77	5	soft𝒯1	soft𝒯1	NOUN
iajs-2517	77	6	-	-	PUNCT
iajs-2517	77	7	space	space	NOUN
iajs-2517	77	8	is	be	AUX
iajs-2517	77	9	a	a	DET
iajs-2517	77	10	soft𝒯0	soft𝒯0	NOUN
iajs-2517	77	11	-	-	PUNCT
iajs-2517	77	12	space	space	NOUN
iajs-2517	77	13	and	and	CCONJ
iajs-2517	77	14	for	for	ADP
iajs-2517	77	15	all	all	DET
iajs-2517	77	16	a	a	DET
iajs-2517	77	17	soft𝒯2	soft𝒯2	NOUN
iajs-2517	77	18	-	-	PUNCT
iajs-2517	77	19	space	space	NOUN
iajs-2517	77	20	is	be	AUX
iajs-2517	77	21	a	a	DET
iajs-2517	77	22	soft𝒯1space	soft𝒯1space	NOUN
iajs-2517	77	23	.	.	PUNCT
iajs-2517	78	1	the	the	DET
iajs-2517	78	2	converse	converse	NOUN
iajs-2517	78	3	is	be	AUX
iajs-2517	78	4	not	not	PART
iajs-2517	78	5	true	true	ADJ
iajs-2517	78	6	hold	hold	NOUN
iajs-2517	78	7	in	in	ADP
iajs-2517	78	8	general	general	ADJ
iajs-2517	78	9	.	.	PUNCT
iajs-2517	79	1	3	3	X
iajs-2517	79	2	.	.	X
iajs-2517	79	3	on	on	ADP
iajs-2517	79	4	𝐬𝐨𝐟𝐭	𝐬𝐨𝐟𝐭	PROPN
iajs-2517	79	5	𝐢𝐝𝐞𝐚𝐥	𝐢𝐝𝐞𝐚𝐥	NOUN
iajs-2517	79	6	𝐬𝐞𝐦𝐢-𝐠-𝐜𝐥𝐨𝐬𝐞𝐝	𝐬𝐞𝐦𝐢-𝐠-𝐜𝐥𝐨𝐬𝐞𝐝	PROPN
iajs-2517	79	7	𝐬𝐞𝐭.	𝐬𝐞𝐭.	NUM
iajs-2517	79	8	definition	definition	NOUN
iajs-2517	79	9	3.1	3.1	NUM
iajs-2517	79	10	:	:	PUNCT
iajs-2517	79	11	in	in	ADP
iajs-2517	79	12	soft	soft	ADJ
iajs-2517	79	13	ideal	ideal	ADJ
iajs-2517	79	14	topological	topological	ADJ
iajs-2517	79	15	space	space	NOUN
iajs-2517	79	16	(	(	PUNCT
iajs-2517	79	17	χ	χ	X
iajs-2517	79	18	,	,	PUNCT
iajs-2517	79	19	𝒯	𝒯	PROPN
iajs-2517	79	20	,	,	PUNCT
iajs-2517	79	21	ℋ	ℋ	PROPN
iajs-2517	79	22	,	,	PUNCT
iajs-2517	79	23	ℐ	ℐ	PROPN
iajs-2517	79	24	)	)	PUNCT
iajs-2517	79	25	,	,	PUNCT
iajs-2517	79	26	let	let	VERB
iajs-2517	79	27	(	(	PUNCT
iajs-2517	79	28	г	г	NOUN
iajs-2517	79	29	,	,	PUNCT
iajs-2517	79	30	ℋ	ℋ	PROPN
iajs-2517	79	31	)	)	PUNCT
iajs-2517	79	32	∈	∈	PROPN
iajs-2517	79	33	şşo(χ	şşo(χ	PROPN
iajs-2517	79	34	)	)	PUNCT
iajs-2517	79	35	,	,	PUNCT
iajs-2517	79	36	then	then	ADV
iajs-2517	79	37	(	(	PUNCT
iajs-2517	79	38	г	г	PROPN
iajs-2517	79	39	,	,	PUNCT
iajs-2517	79	40	ℋ	ℋ	PROPN
iajs-2517	79	41	)	)	PUNCT
iajs-2517	79	42	is	be	AUX
iajs-2517	79	43	a	a	DET
iajs-2517	79	44	soft-ℐ-semi	soft-ℐ-semi	PROPN
iajs-2517	79	45	-	-	PUNCT
iajs-2517	79	46	g	g	NOUN
iajs-2517	79	47	-	-	PUNCT
iajs-2517	79	48	closed	close	VERB
iajs-2517	79	49	set	set	NOUN
iajs-2517	79	50	(	(	PUNCT
iajs-2517	79	51	briefly	briefly	ADV
iajs-2517	79	52	sℐsg	sℐsg	PROPN
iajs-2517	79	53	-	-	PUNCT
iajs-2517	79	54	closed	closed	ADJ
iajs-2517	79	55	)	)	PUNCT
iajs-2517	79	56	.	.	PUNCT
iajs-2517	80	1	if	if	SCONJ
iajs-2517	80	2	cl(г	cl(г	NUM
iajs-2517	80	3	,	,	PUNCT
iajs-2517	80	4	ℋ	ℋ	NOUN
iajs-2517	80	5	)	)	PUNCT
iajs-2517	80	6	−	−	PROPN
iajs-2517	80	7	(	(	PUNCT
iajs-2517	80	8	ơ	ơ	PROPN
iajs-2517	80	9	,	,	PUNCT
iajs-2517	80	10	ℋ	ℋ	PROPN
iajs-2517	80	11	)	)	PUNCT
iajs-2517	80	12	∈	∈	NOUN
iajs-2517	80	13	ℐ	ℐ	PRON
iajs-2517	80	14	whenever	whenever	ADV
iajs-2517	80	15	,	,	PUNCT
iajs-2517	80	16	(	(	PUNCT
iajs-2517	80	17	г	г	PROPN
iajs-2517	80	18	,	,	PUNCT
iajs-2517	80	19	ℋ	ℋ	PROPN
iajs-2517	80	20	)	)	PUNCT
iajs-2517	80	21	–	–	PUNCT
iajs-2517	80	22	(	(	PUNCT
iajs-2517	80	23	ơ	ơ	PROPN
iajs-2517	80	24	,	,	PUNCT
iajs-2517	80	25	ℋ	ℋ	PROPN
iajs-2517	80	26	)	)	PUNCT
iajs-2517	80	27	∈	∈	PROPN
iajs-2517	80	28	ℐ	ℐ	PROPN
iajs-2517	80	29	and	and	CCONJ
iajs-2517	80	30	(	(	PUNCT
iajs-2517	80	31	ơ	ơ	PROPN
iajs-2517	80	32	,	,	PUNCT
iajs-2517	80	33	ℋ	ℋ	PROPN
iajs-2517	80	34	)	)	PUNCT
iajs-2517	80	35	∈	∈	PROPN
iajs-2517	80	36	şşo(χ	şşo(χ	PROPN
iajs-2517	80	37	)	)	PUNCT
iajs-2517	80	38	.	.	PUNCT
iajs-2517	81	1	χ̃	χ̃	PROPN
iajs-2517	81	2	−	−	PROPN
iajs-2517	81	3	(	(	PUNCT
iajs-2517	81	4	г	г	PROPN
iajs-2517	81	5	,	,	PUNCT
iajs-2517	81	6	ℋ	ℋ	PROPN
iajs-2517	81	7	)	)	PUNCT
iajs-2517	81	8	is	be	AUX
iajs-2517	81	9	a	a	DET
iajs-2517	81	10	soft-ℐ-semi	soft-ℐ-semi	PROPN
iajs-2517	81	11	-	-	PUNCT
iajs-2517	81	12	g	g	NOUN
iajs-2517	81	13	-	-	PUNCT
iajs-2517	81	14	open	open	ADJ
iajs-2517	81	15	set	set	NOUN
iajs-2517	81	16	(	(	PUNCT
iajs-2517	81	17	briefly	briefly	ADV
iajs-2517	81	18	sℐsg	sℐsg	NOUN
iajs-2517	81	19	-	-	PUNCT
iajs-2517	81	20	open	open	ADJ
iajs-2517	81	21	set	set	NOUN
iajs-2517	81	22	)	)	PUNCT
iajs-2517	81	23	.	.	PUNCT
iajs-2517	82	1	the	the	DET
iajs-2517	82	2	family	family	NOUN
iajs-2517	82	3	of	of	ADP
iajs-2517	82	4	each	each	DET
iajs-2517	82	5	sℐsgclosed	sℐsgclosed	PROPN
iajs-2517	82	6	sets	set	NOUN
iajs-2517	82	7	(	(	PUNCT
iajs-2517	82	8	briefly	briefly	ADV
iajs-2517	82	9	sℐsgc(χ	sℐsgc(χ	NUM
iajs-2517	82	10	)	)	PUNCT
iajs-2517	82	11	)	)	PUNCT
iajs-2517	83	1	.the	.the	PRON
iajs-2517	84	1	family	family	NOUN
iajs-2517	84	2	of	of	ADP
iajs-2517	84	3	each	each	DET
iajs-2517	84	4	sℐsg	sℐsg	PROPN
iajs-2517	84	5	-	-	PUNCT
iajs-2517	84	6	open	open	ADJ
iajs-2517	84	7	soft	soft	ADJ
iajs-2517	84	8	sets	set	NOUN
iajs-2517	84	9	(	(	PUNCT
iajs-2517	84	10	briefly	briefly	ADV
iajs-2517	84	11	sℐsgo(χ)𝓗	sℐsgo(χ)𝓗	VERB
iajs-2517	84	12	)	)	PUNCT
iajs-2517	84	13	.	.	PUNCT
iajs-2517	85	1	125	125	NUM
iajs-2517	85	2	ibn	ibn	PROPN
iajs-2517	85	3	al	al	PROPN
iajs-2517	85	4	-	-	PUNCT
iajs-2517	85	5	haitham	haitham	PROPN
iajs-2517	85	6	jour	jour	X
iajs-2517	85	7	.	.	PROPN
iajs-2517	85	8	for	for	ADP
iajs-2517	85	9	pure	pure	ADJ
iajs-2517	85	10	&	&	CCONJ
iajs-2517	85	11	appl	appl	PROPN
iajs-2517	85	12	.	.	PUNCT
iajs-2517	86	1	sci	sci	PROPN
iajs-2517	86	2	.	.	PROPN
iajs-2517	87	1	33	33	NUM
iajs-2517	87	2	(	(	PUNCT
iajs-2517	87	3	4	4	NUM
iajs-2517	87	4	)	)	PUNCT
iajs-2517	87	5	2020	2020	NUM
iajs-2517	87	6	example	example	NOUN
iajs-2517	87	7	3.2	3.2	NUM
iajs-2517	87	8	:	:	PUNCT
iajs-2517	87	9	for	for	ADP
iajs-2517	87	10	any	any	DET
iajs-2517	87	11	space	space	NOUN
iajs-2517	87	12	(	(	PUNCT
iajs-2517	87	13	χ	χ	X
iajs-2517	87	14	,	,	PUNCT
iajs-2517	87	15	𝒯	𝒯	PROPN
iajs-2517	87	16	,	,	PUNCT
iajs-2517	87	17	ℋ	ℋ	PROPN
iajs-2517	87	18	,	,	PUNCT
iajs-2517	87	19	ℐ	ℐ	PROPN
iajs-2517	87	20	)	)	PUNCT
iajs-2517	87	21	,	,	PUNCT
iajs-2517	87	22	where	where	SCONJ
iajs-2517	87	23	χ	χ	X
iajs-2517	87	24	=	=	PUNCT
iajs-2517	87	25	{	{	PUNCT
iajs-2517	87	26	1,2	1,2	NUM
iajs-2517	87	27	}	}	PUNCT
iajs-2517	87	28	,	,	PUNCT
iajs-2517	87	29	ℋ	ℋ	PROPN
iajs-2517	87	30	=	=	SYM
iajs-2517	87	31	{	{	PUNCT
iajs-2517	87	32	𝒽1	𝒽1	PROPN
iajs-2517	87	33	,	,	PUNCT
iajs-2517	87	34	𝒽2	𝒽2	PROPN
iajs-2517	87	35	}	}	PUNCT
iajs-2517	87	36	,	,	PUNCT
iajs-2517	87	37	𝒯	𝒯	PROPN
iajs-2517	87	38	=	=	PRON
iajs-2517	87	39	{	{	PUNCT
iajs-2517	87	40	∅̃,x̃,г	∅̃,x̃,г	NOUN
iajs-2517	87	41	}	}	PUNCT
iajs-2517	87	42	,	,	PUNCT
iajs-2517	87	43	ℐ	ℐ	PRON
iajs-2517	87	44	=	=	PRON
iajs-2517	87	45	{	{	PUNCT
iajs-2517	87	46	∅̃	∅̃	NOUN
iajs-2517	87	47	,	,	PUNCT
iajs-2517	87	48	𝒦	𝒦	PROPN
iajs-2517	87	49	}	}	PUNCT
iajs-2517	87	50	such	such	ADJ
iajs-2517	87	51	that	that	SCONJ
iajs-2517	87	52	(	(	PUNCT
iajs-2517	87	53	г	г	PROPN
iajs-2517	87	54	,	,	PUNCT
iajs-2517	87	55	ℋ	ℋ	PROPN
iajs-2517	87	56	)	)	PUNCT
iajs-2517	87	57	=	=	SYM
iajs-2517	87	58	{	{	PUNCT
iajs-2517	87	59	(	(	PUNCT
iajs-2517	87	60	𝒽1	𝒽1	PROPN
iajs-2517	87	61	,	,	PUNCT
iajs-2517	87	62	{	{	PUNCT
iajs-2517	87	63	2	2	NUM
iajs-2517	87	64	}	}	PUNCT
iajs-2517	87	65	)	)	PUNCT
iajs-2517	87	66	,	,	PUNCT
iajs-2517	87	67	(	(	PUNCT
iajs-2517	87	68	𝒽2	𝒽2	NOUN
iajs-2517	87	69	,	,	PUNCT
iajs-2517	87	70	χ	χ	NOUN
iajs-2517	87	71	)	)	PUNCT
iajs-2517	87	72	}	}	PUNCT
iajs-2517	87	73	and	and	CCONJ
iajs-2517	87	74	(	(	PUNCT
iajs-2517	87	75	𝒦	𝒦	PROPN
iajs-2517	87	76	,	,	PUNCT
iajs-2517	87	77	ℋ	ℋ	PROPN
iajs-2517	87	78	)	)	PUNCT
iajs-2517	87	79	=	=	SYM
iajs-2517	87	80	{	{	PUNCT
iajs-2517	87	81	(	(	PUNCT
iajs-2517	87	82	𝒽1	𝒽1	PROPN
iajs-2517	87	83	,	,	PUNCT
iajs-2517	87	84	{	{	PUNCT
iajs-2517	87	85	ø	ø	NOUN
iajs-2517	87	86	}	}	PUNCT
iajs-2517	87	87	)	)	PUNCT
iajs-2517	87	88	,	,	PUNCT
iajs-2517	87	89	(	(	PUNCT
iajs-2517	87	90	𝒽2	𝒽2	NOUN
iajs-2517	87	91	,	,	PUNCT
iajs-2517	87	92	{	{	PUNCT
iajs-2517	87	93	1	1	NUM
iajs-2517	87	94	}	}	PUNCT
iajs-2517	87	95	)	)	PUNCT
iajs-2517	87	96	}	}	PUNCT
iajs-2517	87	97	then	then	ADV
iajs-2517	87	98	şşo(χ	şşo(χ	PROPN
iajs-2517	87	99	)	)	PUNCT
iajs-2517	87	100	=	=	SYM
iajs-2517	87	101	𝒯	𝒯	PROPN
iajs-2517	87	102	,	,	PUNCT
iajs-2517	87	103	sℐsg	sℐsg	PROPN
iajs-2517	87	104	-	-	PUNCT
iajs-2517	87	105	c(χ)𝓗	c(χ)𝓗	PROPN
iajs-2517	87	106	=	=	PUNCT
iajs-2517	87	107	{	{	PUNCT
iajs-2517	87	108	∅̃	∅̃	NOUN
iajs-2517	87	109	,	,	PUNCT
iajs-2517	87	110	χ̃	χ̃	PROPN
iajs-2517	87	111	,	,	PUNCT
iajs-2517	87	112	(	(	PUNCT
iajs-2517	87	113	𝒫	𝒫	NOUN
iajs-2517	87	114	,	,	PUNCT
iajs-2517	87	115	ℋ	ℋ	PROPN
iajs-2517	87	116	)	)	PUNCT
iajs-2517	87	117	,	,	PUNCT
iajs-2517	87	118	(	(	PUNCT
iajs-2517	87	119	ϣ	ϣ	X
iajs-2517	87	120	,	,	PUNCT
iajs-2517	87	121	ℋ	ℋ	PROPN
iajs-2517	87	122	)	)	PUNCT
iajs-2517	87	123	,	,	PUNCT
iajs-2517	87	124	(	(	PUNCT
iajs-2517	87	125	𝒵	𝒵	PROPN
iajs-2517	87	126	,	,	PUNCT
iajs-2517	87	127	ℋ	ℋ	PROPN
iajs-2517	87	128	)	)	PUNCT
iajs-2517	87	129	,	,	PUNCT
iajs-2517	87	130	(	(	PUNCT
iajs-2517	87	131	𝒟	𝒟	PROPN
iajs-2517	87	132	,	,	PUNCT
iajs-2517	87	133	ℋ	ℋ	PROPN
iajs-2517	87	134	)	)	PUNCT
iajs-2517	87	135	,	,	PUNCT
iajs-2517	87	136	(	(	PUNCT
iajs-2517	87	137	ℰ	ℰ	PROPN
iajs-2517	87	138	,	,	PUNCT
iajs-2517	87	139	ℋ	ℋ	PROPN
iajs-2517	87	140	)	)	PUNCT
iajs-2517	87	141	,	,	PUNCT
iajs-2517	87	142	(	(	PUNCT
iajs-2517	87	143	𝒩	𝒩	PROPN
iajs-2517	87	144	,	,	PUNCT
iajs-2517	87	145	ℋ	ℋ	PROPN
iajs-2517	87	146	)	)	PUNCT
iajs-2517	87	147	,	,	PUNCT
iajs-2517	87	148	(	(	PUNCT
iajs-2517	87	149	𝒢	𝒢	PROPN
iajs-2517	87	150	,	,	PUNCT
iajs-2517	87	151	ℋ	ℋ	NOUN
iajs-2517	87	152	)	)	PUNCT
iajs-2517	87	153	}	}	PUNCT
iajs-2517	87	154	such	such	ADJ
iajs-2517	87	155	that	that	SCONJ
iajs-2517	87	156	(	(	PUNCT
iajs-2517	87	157	𝒫	𝒫	NOUN
iajs-2517	87	158	,	,	PUNCT
iajs-2517	87	159	ℋ)={(𝒽1,{1}),(𝒽2,{1})},(ϣ	ℋ)={(𝒽1,{1}),(𝒽2,{1})},(ϣ	NOUN
iajs-2517	87	160	,	,	PUNCT
iajs-2517	87	161	ℋ)={(𝒽1,χ),(𝒽2,{ø})},(𝒵	ℋ)={(𝒽1,χ),(𝒽2,{ø})},(𝒵	NOUN
iajs-2517	87	162	,	,	PUNCT
iajs-2517	87	163	ℋ)={(𝒽1,χ),(𝒽2,{1})},(𝒟	ℋ)={(𝒽1,χ),(𝒽2,{1})},(𝒟	PROPN
iajs-2517	87	164	,	,	PUNCT
iajs-2517	87	165	ℋ	ℋ	PROPN
iajs-2517	87	166	)	)	PUNCT
iajs-2517	87	167	=	=	SYM
iajs-2517	87	168	{	{	PUNCT
iajs-2517	87	169	(	(	PUNCT
iajs-2517	87	170	𝒽1	𝒽1	PROPN
iajs-2517	87	171	,	,	PUNCT
iajs-2517	87	172	χ	χ	NOUN
iajs-2517	87	173	)	)	PUNCT
iajs-2517	87	174	,	,	PUNCT
iajs-2517	87	175	(	(	PUNCT
iajs-2517	87	176	𝒽2	𝒽2	NOUN
iajs-2517	87	177	,	,	PUNCT
iajs-2517	87	178	{	{	PUNCT
iajs-2517	87	179	2})},(ℰ	2})},(ℰ	NUM
iajs-2517	87	180	,	,	PUNCT
iajs-2517	87	181	ℋ)={(𝒽1,{1}),(𝒽2,{ø})},(𝒩	ℋ)={(𝒽1,{1}),(𝒽2,{ø})},(𝒩	ADV
iajs-2517	87	182	,	,	PUNCT
iajs-2517	87	183	ℋ)={(𝒽1,{1}),(𝒽2,{2	ℋ)={(𝒽1,{1}),(𝒽2,{2	ADV
iajs-2517	87	184	}	}	PUNCT
iajs-2517	87	185	)	)	PUNCT
iajs-2517	87	186	}	}	PUNCT
iajs-2517	87	187	and	and	CCONJ
iajs-2517	87	188	(	(	PUNCT
iajs-2517	87	189	𝒢	𝒢	PROPN
iajs-2517	87	190	,	,	PUNCT
iajs-2517	87	191	ℋ)=	ℋ)=	NUM
iajs-2517	87	192	{	{	PUNCT
iajs-2517	87	193	(	(	PUNCT
iajs-2517	87	194	𝒽1,{1	𝒽1,{1	NOUN
iajs-2517	87	195	}	}	PUNCT
iajs-2517	87	196	)	)	PUNCT
iajs-2517	87	197	,	,	PUNCT
iajs-2517	87	198	(	(	PUNCT
iajs-2517	87	199	𝒽2,χ	𝒽2,χ	NOUN
iajs-2517	87	200	)	)	PUNCT
iajs-2517	87	201	}	}	PUNCT
iajs-2517	87	202	.	.	PUNCT
iajs-2517	88	1	remark	remark	VERB
iajs-2517	88	2	3.3	3.3	NUM
iajs-2517	88	3	:	:	PUNCT
iajs-2517	88	4	for	for	ADP
iajs-2517	88	5	any	any	DET
iajs-2517	88	6	(	(	PUNCT
iajs-2517	88	7	χ	χ	NOUN
iajs-2517	88	8	,	,	PUNCT
iajs-2517	88	9	𝒯	𝒯	PROPN
iajs-2517	88	10	,	,	PUNCT
iajs-2517	88	11	ℋ	ℋ	PROPN
iajs-2517	88	12	,	,	PUNCT
iajs-2517	88	13	ℐ	ℐ	PROPN
iajs-2517	88	14	)	)	PUNCT
iajs-2517	88	15	then	then	ADV
iajs-2517	88	16	i.	i.	PROPN
iajs-2517	88	17	each	each	DET
iajs-2517	88	18	closed	close	VERB
iajs-2517	88	19	soft	soft	ADJ
iajs-2517	88	20	set	set	NOUN
iajs-2517	88	21	is	be	AUX
iajs-2517	88	22	a	a	DET
iajs-2517	88	23	sℐsg	sℐsg	PROPN
iajs-2517	88	24	-	-	PUNCT
iajs-2517	88	25	closed	close	VERB
iajs-2517	88	26	.	.	PUNCT
iajs-2517	89	1	ii	ii	X
iajs-2517	89	2	.	.	PUNCT
iajs-2517	90	1	each	each	DET
iajs-2517	90	2	open	open	ADJ
iajs-2517	90	3	soft	soft	ADJ
iajs-2517	90	4	set	set	NOUN
iajs-2517	90	5	is	be	AUX
iajs-2517	90	6	a	a	DET
iajs-2517	90	7	sℐsg	sℐsg	PROPN
iajs-2517	90	8	-	-	PUNCT
iajs-2517	90	9	open	open	ADJ
iajs-2517	90	10	.	.	PUNCT
iajs-2517	91	1	proof	proof	NOUN
iajs-2517	91	2	(	(	PUNCT
iajs-2517	91	3	i	i	NOUN
iajs-2517	91	4	)	)	PUNCT
iajs-2517	91	5	let	let	VERB
iajs-2517	91	6	(	(	PUNCT
iajs-2517	91	7	𝒫	𝒫	NOUN
iajs-2517	91	8	,	,	PUNCT
iajs-2517	91	9	ℋ	ℋ	PROPN
iajs-2517	91	10	)	)	PUNCT
iajs-2517	91	11	be	be	VERB
iajs-2517	91	12	any	any	DET
iajs-2517	91	13	closed	closed	ADJ
iajs-2517	91	14	soft	soft	ADJ
iajs-2517	91	15	set	set	NOUN
iajs-2517	91	16	in	in	ADP
iajs-2517	91	17	(	(	PUNCT
iajs-2517	91	18	χ	χ	X
iajs-2517	91	19	,	,	PUNCT
iajs-2517	91	20	𝒯	𝒯	PROPN
iajs-2517	91	21	,	,	PUNCT
iajs-2517	91	22	ℋ	ℋ	PROPN
iajs-2517	91	23	,	,	PUNCT
iajs-2517	91	24	ℐ	ℐ	PROPN
iajs-2517	91	25	)	)	PUNCT
iajs-2517	91	26	and	and	CCONJ
iajs-2517	91	27	(	(	PUNCT
iajs-2517	91	28	ơ	ơ	PROPN
iajs-2517	91	29	,	,	PUNCT
iajs-2517	91	30	ℋ	ℋ	PROPN
iajs-2517	91	31	)	)	PUNCT
iajs-2517	91	32	be	be	VERB
iajs-2517	91	33	a	a	DET
iajs-2517	91	34	soft	soft	ADJ
iajs-2517	91	35	semi	semi	ADJ
iajs-2517	91	36	-	-	ADJ
iajs-2517	91	37	open	open	ADJ
iajs-2517	91	38	set	set	NOUN
iajs-2517	91	39	such	such	ADJ
iajs-2517	91	40	that	that	SCONJ
iajs-2517	91	41	(	(	PUNCT
iajs-2517	91	42	𝒫	𝒫	NOUN
iajs-2517	91	43	,	,	PUNCT
iajs-2517	91	44	ℋ	ℋ	PROPN
iajs-2517	91	45	)	)	PUNCT
iajs-2517	91	46	–	–	PUNCT
iajs-2517	91	47	(	(	PUNCT
iajs-2517	91	48	ơ	ơ	PROPN
iajs-2517	91	49	,	,	PUNCT
iajs-2517	91	50	ℋ	ℋ	PROPN
iajs-2517	91	51	)	)	PUNCT
iajs-2517	91	52	∈	∈	PROPN
iajs-2517	91	53	ℐ	ℐ	PROPN
iajs-2517	91	54	,	,	PUNCT
iajs-2517	91	55	but	but	CCONJ
iajs-2517	91	56	cl(𝒫	cl(𝒫	NOUN
iajs-2517	91	57	,	,	PUNCT
iajs-2517	91	58	ℋ	ℋ	PROPN
iajs-2517	91	59	)	)	PUNCT
iajs-2517	91	60	=	=	SYM
iajs-2517	91	61	(	(	PUNCT
iajs-2517	91	62	𝒫	𝒫	PROPN
iajs-2517	91	63	,	,	PUNCT
iajs-2517	91	64	ℋ	ℋ	PROPN
iajs-2517	91	65	)	)	PUNCT
iajs-2517	91	66	,	,	PUNCT
iajs-2517	91	67	since	since	SCONJ
iajs-2517	91	68	(	(	PUNCT
iajs-2517	91	69	𝒫	𝒫	NOUN
iajs-2517	91	70	,	,	PUNCT
iajs-2517	91	71	ℋ	ℋ	PROPN
iajs-2517	91	72	)	)	PUNCT
iajs-2517	91	73	is	be	AUX
iajs-2517	91	74	a	a	DET
iajs-2517	91	75	closed	closed	ADJ
iajs-2517	91	76	soft	soft	ADJ
iajs-2517	91	77	set	set	NOUN
iajs-2517	91	78	so	so	ADV
iajs-2517	91	79	,	,	PUNCT
iajs-2517	91	80	cl(𝒫	cl(𝒫	NOUN
iajs-2517	91	81	,	,	PUNCT
iajs-2517	91	82	ℋ	ℋ	PROPN
iajs-2517	91	83	)	)	PUNCT
iajs-2517	91	84	(	(	PUNCT
iajs-2517	91	85	ơ	ơ	PROPN
iajs-2517	91	86	,	,	PUNCT
iajs-2517	91	87	ℋ	ℋ	PROPN
iajs-2517	91	88	)	)	PUNCT
iajs-2517	91	89	=	=	SYM
iajs-2517	91	90	(	(	PUNCT
iajs-2517	91	91	𝒫	𝒫	PROPN
iajs-2517	91	92	,	,	PUNCT
iajs-2517	91	93	ℋ	ℋ	PROPN
iajs-2517	91	94	)	)	PUNCT
iajs-2517	91	95	–	–	PUNCT
iajs-2517	91	96	(	(	PUNCT
iajs-2517	91	97	ơ	ơ	PROPN
iajs-2517	91	98	,	,	PUNCT
iajs-2517	91	99	ℋ	ℋ	PROPN
iajs-2517	91	100	)	)	PUNCT
iajs-2517	91	101	∈	∈	PROPN
iajs-2517	91	102	ℐ.	ℐ.	PROPN
iajs-2517	91	103	this	this	PRON
iajs-2517	91	104	implies	imply	VERB
iajs-2517	91	105	(	(	PUNCT
iajs-2517	91	106	𝒫	𝒫	NOUN
iajs-2517	91	107	,	,	PUNCT
iajs-2517	91	108	ℋ	ℋ	PROPN
iajs-2517	91	109	)	)	PUNCT
iajs-2517	91	110	is	be	AUX
iajs-2517	91	111	a	a	DET
iajs-2517	91	112	soft-ℐ-semi	soft-ℐ-semi	PROPN
iajs-2517	91	113	-	-	PUNCT
iajs-2517	91	114	g	g	NOUN
iajs-2517	91	115	-	-	PUNCT
iajs-2517	91	116	closed	close	VERB
iajs-2517	91	117	soft	soft	ADJ
iajs-2517	91	118	set	set	NOUN
iajs-2517	91	119	.	.	PUNCT
iajs-2517	92	1	(	(	PUNCT
iajs-2517	92	2	ii)let	ii)let	PROPN
iajs-2517	92	3	(	(	PUNCT
iajs-2517	92	4	ơ	ơ	PROPN
iajs-2517	92	5	,	,	PUNCT
iajs-2517	92	6	ℋ	ℋ	PROPN
iajs-2517	92	7	)	)	PUNCT
iajs-2517	92	8	be	be	VERB
iajs-2517	92	9	any	any	DET
iajs-2517	92	10	open	open	ADJ
iajs-2517	92	11	soft	soft	ADJ
iajs-2517	92	12	set	set	NOUN
iajs-2517	92	13	in	in	ADP
iajs-2517	92	14	(	(	PUNCT
iajs-2517	92	15	χ	χ	X
iajs-2517	92	16	,	,	PUNCT
iajs-2517	92	17	𝒯	𝒯	PROPN
iajs-2517	92	18	,	,	PUNCT
iajs-2517	92	19	ℋ	ℋ	PROPN
iajs-2517	92	20	,	,	PUNCT
iajs-2517	92	21	ℐ	ℐ	PROPN
iajs-2517	92	22	)	)	PUNCT
iajs-2517	92	23	then	then	ADV
iajs-2517	92	24	χ̃	χ̃	PROPN
iajs-2517	92	25	–	–	PUNCT
iajs-2517	92	26	(	(	PUNCT
iajs-2517	92	27	ơ	ơ	PROPN
iajs-2517	92	28	,	,	PUNCT
iajs-2517	92	29	ℋ)is	ℋ)is	VERB
iajs-2517	92	30	a	a	DET
iajs-2517	92	31	closed	closed	ADJ
iajs-2517	92	32	soft	soft	ADJ
iajs-2517	92	33	set	set	NOUN
iajs-2517	92	34	.	.	PUNCT
iajs-2517	93	1	by	by	ADP
iajs-2517	93	2	(	(	PUNCT
iajs-2517	93	3	i	i	NOUN
iajs-2517	93	4	)	)	PUNCT
iajs-2517	93	5	(	(	PUNCT
iajs-2517	93	6	χ	χ	X
iajs-2517	93	7	̃	̃	PROPN
iajs-2517	93	8	(	(	PUNCT
iajs-2517	93	9	ơ	ơ	PROPN
iajs-2517	93	10	,	,	PUNCT
iajs-2517	93	11	ℋ	ℋ	PROPN
iajs-2517	93	12	)	)	PUNCT
iajs-2517	93	13	)	)	PUNCT
iajs-2517	93	14	is	be	AUX
iajs-2517	93	15	a	a	DET
iajs-2517	93	16	sℐsg	sℐsg	PROPN
iajs-2517	93	17	-	-	PUNCT
iajs-2517	93	18	closed	close	VERB
iajs-2517	93	19	set	set	NOUN
iajs-2517	93	20	thus	thus	ADV
iajs-2517	93	21	(	(	PUNCT
iajs-2517	93	22	ơ	ơ	PROPN
iajs-2517	93	23	,	,	PUNCT
iajs-2517	93	24	ℋ)is	ℋ)is	VERB
iajs-2517	93	25	a	a	DET
iajs-2517	93	26	sℐsg	sℐsg	PROPN
iajs-2517	93	27	-	-	PUNCT
iajs-2517	93	28	open	open	ADJ
iajs-2517	93	29	soft	soft	ADJ
iajs-2517	93	30	set	set	NOUN
iajs-2517	93	31	.	.	PUNCT
iajs-2517	94	1	the	the	DET
iajs-2517	94	2	converse	converse	NOUN
iajs-2517	94	3	of	of	ADP
iajs-2517	94	4	remark	remark	NOUN
iajs-2517	94	5	3.3	3.3	NUM
iajs-2517	94	6	is	be	AUX
iajs-2517	94	7	not	not	PART
iajs-2517	94	8	hold	hold	ADJ
iajs-2517	94	9	.	.	PUNCT
iajs-2517	95	1	see	see	VERB
iajs-2517	95	2	example	example	NOUN
iajs-2517	95	3	3	3	NUM
iajs-2517	95	4	.	.	SYM
iajs-2517	95	5	2	2	NUM
iajs-2517	95	6	i.	i.	NOUN
iajs-2517	95	7	let	let	VERB
iajs-2517	95	8	(	(	PUNCT
iajs-2517	95	9	𝒫	𝒫	NOUN
iajs-2517	95	10	,	,	PUNCT
iajs-2517	95	11	ℋ	ℋ	PROPN
iajs-2517	95	12	)	)	PUNCT
iajs-2517	95	13	=	=	SYM
iajs-2517	95	14	{	{	PUNCT
iajs-2517	95	15	(	(	PUNCT
iajs-2517	95	16	𝒽1	𝒽1	PROPN
iajs-2517	95	17	,	,	PUNCT
iajs-2517	95	18	{	{	PUNCT
iajs-2517	95	19	1	1	NUM
iajs-2517	95	20	}	}	PUNCT
iajs-2517	95	21	)	)	PUNCT
iajs-2517	95	22	,	,	PUNCT
iajs-2517	95	23	(	(	PUNCT
iajs-2517	95	24	𝒽2	𝒽2	NOUN
iajs-2517	95	25	,	,	PUNCT
iajs-2517	95	26	{	{	PUNCT
iajs-2517	95	27	1	1	NUM
iajs-2517	95	28	}	}	PUNCT
iajs-2517	95	29	)	)	PUNCT
iajs-2517	95	30	}	}	PUNCT
iajs-2517	95	31	is	be	AUX
iajs-2517	95	32	a	a	DET
iajs-2517	95	33	sℐsg	sℐsg	PROPN
iajs-2517	95	34	-	-	PUNCT
iajs-2517	95	35	closed	close	VERB
iajs-2517	95	36	set	set	NOUN
iajs-2517	95	37	,	,	PUNCT
iajs-2517	95	38	but	but	CCONJ
iajs-2517	95	39	(	(	PUNCT
iajs-2517	95	40	𝒫	𝒫	NOUN
iajs-2517	95	41	,	,	PUNCT
iajs-2517	95	42	ℋ	ℋ	PROPN
iajs-2517	95	43	)	)	PUNCT
iajs-2517	95	44	is	be	AUX
iajs-2517	95	45	not	not	PART
iajs-2517	95	46	closed	close	VERB
iajs-2517	95	47	soft	soft	ADJ
iajs-2517	95	48	set	set	NOUN
iajs-2517	95	49	.	.	PUNCT
iajs-2517	96	1	ii	ii	PROPN
iajs-2517	96	2	.	.	PUNCT
iajs-2517	97	1	let	let	VERB
iajs-2517	97	2	(	(	PUNCT
iajs-2517	97	3	𝒫	𝒫	NOUN
iajs-2517	97	4	,	,	PUNCT
iajs-2517	97	5	ℋ)=	ℋ)=	NUM
iajs-2517	97	6	{	{	PUNCT
iajs-2517	97	7	(	(	PUNCT
iajs-2517	97	8	𝒽1	𝒽1	PROPN
iajs-2517	97	9	,	,	PUNCT
iajs-2517	97	10	{	{	PUNCT
iajs-2517	97	11	2	2	NUM
iajs-2517	97	12	}	}	PUNCT
iajs-2517	97	13	)	)	PUNCT
iajs-2517	97	14	,	,	PUNCT
iajs-2517	97	15	(	(	PUNCT
iajs-2517	97	16	𝒽2	𝒽2	NOUN
iajs-2517	97	17	,	,	PUNCT
iajs-2517	97	18	{	{	PUNCT
iajs-2517	97	19	2	2	NUM
iajs-2517	97	20	}	}	PUNCT
iajs-2517	97	21	)	)	PUNCT
iajs-2517	97	22	}	}	PUNCT
iajs-2517	97	23	is	be	AUX
iajs-2517	97	24	a	a	DET
iajs-2517	97	25	sℐsg	sℐsg	PROPN
iajs-2517	97	26	-	-	PUNCT
iajs-2517	97	27	open	open	NOUN
iajs-2517	97	28	set	set	NOUN
iajs-2517	97	29	,	,	PUNCT
iajs-2517	97	30	but	but	CCONJ
iajs-2517	97	31	(	(	PUNCT
iajs-2517	97	32	𝒫	𝒫	NOUN
iajs-2517	97	33	,	,	PUNCT
iajs-2517	97	34	ℋ	ℋ	PROPN
iajs-2517	97	35	)	)	PUNCT
iajs-2517	97	36	∉	∉	PROPN
iajs-2517	97	37	𝓣.	𝓣.	PROPN
iajs-2517	97	38	4	4	NUM
iajs-2517	97	39	.	.	PUNCT
iajs-2517	98	1	separation	separation	NOUN
iajs-2517	98	2	axioms	axiom	NOUN
iajs-2517	98	3	with	with	ADP
iajs-2517	98	4	soft-𝓘semi	soft-𝓘semi	ADJ
iajs-2517	98	5	-	-	ADJ
iajs-2517	98	6	g	g	NOUN
iajs-2517	98	7	-	-	PUNCT
iajs-2517	98	8	open	open	ADJ
iajs-2517	98	9	sets	set	NOUN
iajs-2517	98	10	definition	definition	NOUN
iajs-2517	98	11	4.1	4.1	NUM
iajs-2517	98	12	.	.	PUNCT
iajs-2517	99	1	a	a	DET
iajs-2517	99	2	space	space	NOUN
iajs-2517	99	3	(	(	PUNCT
iajs-2517	99	4	𝜒	𝜒	X
iajs-2517	99	5	,	,	PUNCT
iajs-2517	99	6	𝒯	𝒯	PROPN
iajs-2517	99	7	,	,	PUNCT
iajs-2517	99	8	ℋ	ℋ	PROPN
iajs-2517	99	9	,	,	PUNCT
iajs-2517	99	10	ℐ	ℐ	PROPN
iajs-2517	99	11	)	)	PUNCT
iajs-2517	99	12	is	be	AUX
iajs-2517	99	13	a	a	DET
iajs-2517	99	14	soft-ℐ-semi-𝑔-𝒯0	soft-ℐ-semi-𝑔-𝒯0	NOUN
iajs-2517	99	15	-	-	PUNCT
iajs-2517	99	16	space	space	NOUN
iajs-2517	99	17	(	(	PUNCT
iajs-2517	99	18	briefly	briefly	ADV
iajs-2517	99	19	𝑠ℐ𝑠𝑔-𝒯0	𝑠ℐ𝑠𝑔-𝒯0	ADJ
iajs-2517	99	20	-	-	PUNCT
iajs-2517	99	21	space	space	NOUN
iajs-2517	99	22	)	)	PUNCT
iajs-2517	99	23	,	,	PUNCT
iajs-2517	99	24	if	if	SCONJ
iajs-2517	99	25	for	for	ADP
iajs-2517	99	26	each	each	DET
iajs-2517	99	27	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	99	28	≠	≠	PROPN
iajs-2517	99	29	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	99	30	and	and	CCONJ
iajs-2517	99	31	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	99	32	,	,	PUNCT
iajs-2517	99	33	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	99	34	∈̃	∈̃	PROPN
iajs-2517	99	35	�	�	PROPN
iajs-2517	99	36	̃	̃	PROPN
iajs-2517	99	37	�	�	PROPN
iajs-2517	99	38	,	,	PUNCT
iajs-2517	99	39	∃	∃	PROPN
iajs-2517	99	40	(	(	PUNCT
iajs-2517	99	41	𝔒	𝔒	PROPN
iajs-2517	99	42	,	,	PUNCT
iajs-2517	99	43	ℋ	ℋ	PROPN
iajs-2517	99	44	)	)	PUNCT
iajs-2517	99	45	∈	∈	NOUN
iajs-2517	99	46	sℐs𝑔-o(χ)𝓗	sℐs𝑔-o(χ)𝓗	VERB
iajs-2517	99	47	whenever	whenever	ADV
iajs-2517	99	48	,	,	PUNCT
iajs-2517	99	49	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	99	50	∈̃	∈̃	NOUN
iajs-2517	99	51	(	(	PUNCT
iajs-2517	99	52	𝔒	𝔒	PROPN
iajs-2517	99	53	,	,	PUNCT
iajs-2517	99	54	ℋ	ℋ	PROPN
iajs-2517	99	55	)	)	PUNCT
iajs-2517	99	56	,	,	PUNCT
iajs-2517	99	57	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	99	58	∉̃	∉̃	PROPN
iajs-2517	99	59	(	(	PUNCT
iajs-2517	99	60	𝔒	𝔒	PROPN
iajs-2517	99	61	,	,	PUNCT
iajs-2517	99	62	ℋ	ℋ	NOUN
iajs-2517	99	63	)	)	PUNCT
iajs-2517	99	64	or	or	CCONJ
iajs-2517	99	65	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	99	66	∉̃	∉̃	ADJ
iajs-2517	99	67	(	(	PUNCT
iajs-2517	99	68	𝔒	𝔒	PROPN
iajs-2517	99	69	,	,	PUNCT
iajs-2517	99	70	ℋ	ℋ	PROPN
iajs-2517	99	71	)	)	PUNCT
iajs-2517	99	72	,	,	PUNCT
iajs-2517	99	73	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	99	74	∈̃	∈̃	PROPN
iajs-2517	99	75	(	(	PUNCT
iajs-2517	99	76	𝔒	𝔒	PROPN
iajs-2517	99	77	,	,	PUNCT
iajs-2517	99	78	ℋ	ℋ	PROPN
iajs-2517	99	79	)	)	PUNCT
iajs-2517	99	80	.	.	PUNCT
iajs-2517	100	1	example	example	NOUN
iajs-2517	100	2	4.2	4.2	NUM
iajs-2517	100	3	.	.	PUNCT
iajs-2517	101	1	in	in	ADP
iajs-2517	101	2	(	(	PUNCT
iajs-2517	101	3	𝜒	𝜒	X
iajs-2517	101	4	,	,	PUNCT
iajs-2517	101	5	𝒯	𝒯	PROPN
iajs-2517	101	6	,	,	PUNCT
iajs-2517	101	7	ℋ	ℋ	PROPN
iajs-2517	101	8	,	,	PUNCT
iajs-2517	101	9	ℐ	ℐ	NUM
iajs-2517	101	10	)	)	PUNCT
iajs-2517	101	11	let	let	VERB
iajs-2517	101	12	χ	χ	X
iajs-2517	101	13	=	=	PUNCT
iajs-2517	101	14	{	{	PUNCT
iajs-2517	101	15	1,2,3	1,2,3	NUM
iajs-2517	101	16	}	}	PUNCT
iajs-2517	101	17	,	,	PUNCT
iajs-2517	101	18	ℋ	ℋ	PROPN
iajs-2517	101	19	=	=	SYM
iajs-2517	101	20	{	{	PUNCT
iajs-2517	101	21	𝒽1	𝒽1	PROPN
iajs-2517	101	22	,	,	PUNCT
iajs-2517	101	23	𝒽2	𝒽2	PROPN
iajs-2517	101	24	}	}	PUNCT
iajs-2517	101	25	,	,	PUNCT
iajs-2517	101	26	𝒯	𝒯	PROPN
iajs-2517	101	27	=	=	PRON
iajs-2517	101	28	{	{	PUNCT
iajs-2517	101	29	∅̃	∅̃	NOUN
iajs-2517	101	30	,	,	PUNCT
iajs-2517	101	31	�	�	PROPN
iajs-2517	101	32	̃	̃	PROPN
iajs-2517	101	33	�	�	PROPN
iajs-2517	101	34	,	,	PUNCT
iajs-2517	101	35	(	(	PUNCT
iajs-2517	101	36	𝓟	𝓟	PROPN
iajs-2517	101	37	,	,	PUNCT
iajs-2517	101	38	ℋ	ℋ	PROPN
iajs-2517	101	39	)	)	PUNCT
iajs-2517	101	40	,	,	PUNCT
iajs-2517	101	41	(	(	PUNCT
iajs-2517	101	42	ϣ	ϣ	X
iajs-2517	101	43	,	,	PUNCT
iajs-2517	101	44	ℋ	ℋ	NOUN
iajs-2517	101	45	)	)	PUNCT
iajs-2517	101	46	}	}	PUNCT
iajs-2517	102	1	where	where	SCONJ
iajs-2517	102	2	,	,	PUNCT
iajs-2517	102	3	(	(	PUNCT
iajs-2517	102	4	𝓟	𝓟	PROPN
iajs-2517	102	5	,	,	PUNCT
iajs-2517	102	6	ℋ	ℋ	PROPN
iajs-2517	102	7	)	)	PUNCT
iajs-2517	102	8	=	=	SYM
iajs-2517	102	9	{	{	PUNCT
iajs-2517	102	10	(	(	PUNCT
iajs-2517	102	11	𝒽1,{1	𝒽1,{1	NOUN
iajs-2517	102	12	}	}	PUNCT
iajs-2517	102	13	)	)	PUNCT
iajs-2517	102	14	,	,	PUNCT
iajs-2517	102	15	(	(	PUNCT
iajs-2517	102	16	𝒽2	𝒽2	NOUN
iajs-2517	102	17	,	,	PUNCT
iajs-2517	102	18	{	{	PUNCT
iajs-2517	102	19	1})},(ϣ	1})},(ϣ	NUM
iajs-2517	102	20	,	,	PUNCT
iajs-2517	102	21	ℋ	ℋ	PROPN
iajs-2517	102	22	)	)	PUNCT
iajs-2517	102	23	=	=	PRON
iajs-2517	102	24	{	{	PUNCT
iajs-2517	102	25	(	(	PUNCT
iajs-2517	102	26	𝒽1,{1,2	𝒽1,{1,2	ADJ
iajs-2517	102	27	}	}	PUNCT
iajs-2517	102	28	)	)	PUNCT
iajs-2517	102	29	,	,	PUNCT
iajs-2517	102	30	(	(	PUNCT
iajs-2517	102	31	𝒽2	𝒽2	NOUN
iajs-2517	102	32	,	,	PUNCT
iajs-2517	102	33	{	{	PUNCT
iajs-2517	102	34	1,2	1,2	NUM
iajs-2517	102	35	}	}	PUNCT
iajs-2517	102	36	)	)	PUNCT
iajs-2517	102	37	and	and	CCONJ
iajs-2517	102	38	ℐ	ℐ	PRON
iajs-2517	102	39	=	=	NOUN
iajs-2517	102	40	{	{	PUNCT
iajs-2517	102	41	∅̃	∅̃	NOUN
iajs-2517	102	42	}	}	PUNCT
iajs-2517	102	43	.	.	PUNCT
iajs-2517	103	1	then	then	ADV
iajs-2517	103	2	şş𝑂(𝜒)𝓗	şş𝑂(𝜒)𝓗	ADV
iajs-2517	103	3	=	=	PRON
iajs-2517	103	4	{	{	PUNCT
iajs-2517	103	5	(	(	PUNCT
iajs-2517	103	6	г	г	PROPN
iajs-2517	103	7	,	,	PUNCT
iajs-2517	103	8	ℋ	ℋ	PROPN
iajs-2517	103	9	)	)	PUNCT
iajs-2517	103	10	;	;	PUNCT
iajs-2517	103	11	1	1	NUM
iajs-2517	103	12	∈̃	∈̃	PROPN
iajs-2517	103	13	(	(	PUNCT
iajs-2517	103	14	г	г	PROPN
iajs-2517	103	15	,	,	PUNCT
iajs-2517	103	16	ℋ	ℋ	NOUN
iajs-2517	103	17	)	)	PUNCT
iajs-2517	103	18	}	}	PUNCT
iajs-2517	103	19	.	.	PUNCT
iajs-2517	104	1	so	so	ADV
iajs-2517	104	2	,	,	PUNCT
iajs-2517	104	3	𝑠ℐ𝑠𝑔-𝑐(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑐(𝜒)𝓗	NOUN
iajs-2517	104	4	=	=	NOUN
iajs-2517	104	5	{	{	PUNCT
iajs-2517	104	6	∅̃	∅̃	NOUN
iajs-2517	104	7	,	,	PUNCT
iajs-2517	104	8	𝜒	𝜒	PROPN
iajs-2517	104	9	̃,(𝓟′	̃,(𝓟′	PROPN
iajs-2517	104	10	,	,	PUNCT
iajs-2517	104	11	ℋ	ℋ	PROPN
iajs-2517	104	12	)	)	PUNCT
iajs-2517	104	13	,	,	PUNCT
iajs-2517	104	14	(	(	PUNCT
iajs-2517	104	15	ϣ′	ϣ′	NOUN
iajs-2517	104	16	,	,	PUNCT
iajs-2517	104	17	ℋ	ℋ	NOUN
iajs-2517	104	18	)	)	PUNCT
iajs-2517	104	19	}	}	PUNCT
iajs-2517	104	20	and	and	CCONJ
iajs-2517	104	21	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	NUM
iajs-2517	104	22	=	=	SYM
iajs-2517	104	23	𝒯	𝒯	PROPN
iajs-2517	104	24	,	,	PUNCT
iajs-2517	104	25	hence	hence	ADV
iajs-2517	104	26	(	(	PUNCT
iajs-2517	104	27	𝜒	𝜒	X
iajs-2517	104	28	,	,	PUNCT
iajs-2517	104	29	𝒯	𝒯	PROPN
iajs-2517	104	30	,	,	PUNCT
iajs-2517	104	31	ℋ	ℋ	PROPN
iajs-2517	104	32	,	,	PUNCT
iajs-2517	104	33	ℐ	ℐ	NUM
iajs-2517	104	34	)	)	PUNCT
iajs-2517	104	35	is	be	AUX
iajs-2517	104	36	a	a	DET
iajs-2517	104	37	𝑠ℐ𝑠𝑔-𝒯0	𝑠ℐ𝑠𝑔-𝒯0	ADJ
iajs-2517	104	38	-	-	PUNCT
iajs-2517	104	39	space	space	NOUN
iajs-2517	104	40	.	.	PUNCT
iajs-2517	105	1	since	since	SCONJ
iajs-2517	105	2	∀	∀	NOUN
iajs-2517	105	3	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	105	4	≠	≠	PROPN
iajs-2517	105	5	𝒽	𝒽	X
iajs-2517	105	6	,	,	PUNCT
iajs-2517	105	7	∃	∃	PROPN
iajs-2517	105	8	(	(	PUNCT
iajs-2517	105	9	𝔒	𝔒	PROPN
iajs-2517	105	10	,	,	PUNCT
iajs-2517	105	11	ℋ	ℋ	PROPN
iajs-2517	105	12	)	)	PUNCT
iajs-2517	105	13	∈	∈	NOUN
iajs-2517	105	14	sℐs𝑔-o(χ)𝓗	sℐs𝑔-o(χ)𝓗	VERB
iajs-2517	105	15	whenever	whenever	ADV
iajs-2517	105	16	,	,	PUNCT
iajs-2517	105	17	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	105	18	∈̃	∈̃	NOUN
iajs-2517	105	19	(	(	PUNCT
iajs-2517	105	20	𝔒	𝔒	PROPN
iajs-2517	105	21	,	,	PUNCT
iajs-2517	105	22	ℋ	ℋ	PROPN
iajs-2517	105	23	)	)	PUNCT
iajs-2517	105	24	,	,	PUNCT
iajs-2517	105	25	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	105	26	∉̃	∉̃	PROPN
iajs-2517	105	27	(	(	PUNCT
iajs-2517	105	28	𝔒	𝔒	PROPN
iajs-2517	105	29	,	,	PUNCT
iajs-2517	105	30	ℋ	ℋ	NOUN
iajs-2517	105	31	)	)	PUNCT
iajs-2517	105	32	or	or	CCONJ
iajs-2517	105	33	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	105	34	∉̃	∉̃	ADJ
iajs-2517	105	35	(	(	PUNCT
iajs-2517	105	36	𝔒	𝔒	PROPN
iajs-2517	105	37	,	,	PUNCT
iajs-2517	105	38	ℋ	ℋ	PROPN
iajs-2517	105	39	)	)	PUNCT
iajs-2517	105	40	,	,	PUNCT
iajs-2517	105	41	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	105	42	∈̃	∈̃	PROPN
iajs-2517	105	43	(	(	PUNCT
iajs-2517	105	44	𝔒	𝔒	PROPN
iajs-2517	105	45	,	,	PUNCT
iajs-2517	105	46	ℋ	ℋ	PROPN
iajs-2517	105	47	)	)	PUNCT
iajs-2517	105	48	.	.	PUNCT
iajs-2517	106	1	proposition	proposition	NOUN
iajs-2517	106	2	4.3.if	4.3.if	INTJ
iajs-2517	107	1	(	(	PUNCT
iajs-2517	107	2	𝜒	𝜒	X
iajs-2517	107	3	,	,	PUNCT
iajs-2517	107	4	𝒯	𝒯	PROPN
iajs-2517	107	5	,	,	PUNCT
iajs-2517	107	6	ℋ	ℋ	PROPN
iajs-2517	107	7	)	)	PUNCT
iajs-2517	107	8	is	be	AUX
iajs-2517	107	9	a	a	DET
iajs-2517	107	10	soft-𝒯0	soft-𝒯0	PROPN
iajs-2517	107	11	-	-	PUNCT
iajs-2517	107	12	space	space	NOUN
iajs-2517	107	13	then	then	ADV
iajs-2517	107	14	(	(	PUNCT
iajs-2517	107	15	𝜒	𝜒	X
iajs-2517	107	16	,	,	PUNCT
iajs-2517	107	17	𝒯	𝒯	PROPN
iajs-2517	107	18	,	,	PUNCT
iajs-2517	107	19	ℋ	ℋ	PROPN
iajs-2517	107	20	,	,	PUNCT
iajs-2517	107	21	ℐ	ℐ	NUM
iajs-2517	107	22	)	)	PUNCT
iajs-2517	107	23	is	be	AUX
iajs-2517	107	24	a	a	DET
iajs-2517	107	25	𝑠ℐ𝑠𝑔-𝒯0	𝑠ℐ𝑠𝑔-𝒯0	ADJ
iajs-2517	107	26	-	-	PUNCT
iajs-2517	107	27	space	space	NOUN
iajs-2517	107	28	.	.	PUNCT
iajs-2517	108	1	proof	proof	NOUN
iajs-2517	108	2	:	:	PUNCT
iajs-2517	108	3	let	let	VERB
iajs-2517	108	4	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	108	5	,	,	PUNCT
iajs-2517	108	6	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	108	7	∈̃	∈̃	PROPN
iajs-2517	108	8	�	�	PROPN
iajs-2517	108	9	̃	̃	PROPN
iajs-2517	108	10	�	�	NOUN
iajs-2517	108	11	such	such	ADJ
iajs-2517	108	12	that	that	DET
iajs-2517	108	13	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	108	14	≠	≠	PROPN
iajs-2517	108	15	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	108	16	since	since	SCONJ
iajs-2517	108	17	(	(	PUNCT
iajs-2517	108	18	𝜒	𝜒	X
iajs-2517	108	19	,	,	PUNCT
iajs-2517	108	20	𝒯	𝒯	PROPN
iajs-2517	108	21	,	,	PUNCT
iajs-2517	108	22	ℋ	ℋ	PROPN
iajs-2517	108	23	)	)	PUNCT
iajs-2517	108	24	is	be	AUX
iajs-2517	108	25	a	a	DET
iajs-2517	108	26	soft-𝒯0	soft-𝒯0	PROPN
iajs-2517	108	27	-	-	PUNCT
iajs-2517	108	28	space	space	NOUN
iajs-2517	108	29	,	,	PUNCT
iajs-2517	108	30	then	then	ADV
iajs-2517	108	31	∃	∃	PROPN
iajs-2517	108	32	(	(	PUNCT
iajs-2517	108	33	𝔒	𝔒	PROPN
iajs-2517	108	34	,	,	PUNCT
iajs-2517	108	35	ℋ	ℋ	PROPN
iajs-2517	108	36	)	)	PUNCT
iajs-2517	108	37	∈	∈	PROPN
iajs-2517	108	38	𝒯	𝒯	PROPN
iajs-2517	108	39	whenever	whenever	ADV
iajs-2517	108	40	,	,	PUNCT
iajs-2517	108	41	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	108	42	∈̃	∈̃	NOUN
iajs-2517	108	43	(	(	PUNCT
iajs-2517	108	44	𝔒	𝔒	PROPN
iajs-2517	108	45	,	,	PUNCT
iajs-2517	108	46	ℋ	ℋ	PROPN
iajs-2517	108	47	)	)	PUNCT
iajs-2517	108	48	,	,	PUNCT
iajs-2517	108	49	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	108	50	∉̃	∉̃	PROPN
iajs-2517	108	51	(	(	PUNCT
iajs-2517	108	52	𝔒	𝔒	PROPN
iajs-2517	108	53	,	,	PUNCT
iajs-2517	108	54	ℋ	ℋ	NOUN
iajs-2517	108	55	)	)	PUNCT
iajs-2517	108	56	or	or	CCONJ
iajs-2517	108	57	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	108	58	∉̃	∉̃	ADJ
iajs-2517	108	59	(	(	PUNCT
iajs-2517	108	60	𝔒	𝔒	PROPN
iajs-2517	108	61	,	,	PUNCT
iajs-2517	108	62	ℋ	ℋ	PROPN
iajs-2517	108	63	)	)	PUNCT
iajs-2517	108	64	,	,	PUNCT
iajs-2517	108	65	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	108	66	∈̃	∈̃	PROPN
iajs-2517	108	67	(	(	PUNCT
iajs-2517	108	68	𝔒	𝔒	PROPN
iajs-2517	108	69	,	,	PUNCT
iajs-2517	108	70	ℋ	ℋ	PROPN
iajs-2517	108	71	)	)	PUNCT
iajs-2517	108	72	.	.	PUNCT
iajs-2517	109	1	by	by	ADP
iajs-2517	109	2	remark	remark	NOUN
iajs-2517	109	3	2.3	2.3	NUM
iajs-2517	109	4	,	,	PUNCT
iajs-2517	109	5	(	(	PUNCT
iajs-2517	109	6	𝔒	𝔒	PROPN
iajs-2517	109	7	,	,	PUNCT
iajs-2517	109	8	ℋ	ℋ	PROPN
iajs-2517	109	9	)	)	PUNCT
iajs-2517	109	10	is	be	AUX
iajs-2517	109	11	a	a	DET
iajs-2517	109	12	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	109	13	set	set	NOUN
iajs-2517	109	14	such	such	ADJ
iajs-2517	109	15	that	that	DET
iajs-2517	109	16	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	109	17	∈̃	∈̃	PROPN
iajs-2517	109	18	(	(	PUNCT
iajs-2517	109	19	𝔒	𝔒	PROPN
iajs-2517	109	20	,	,	PUNCT
iajs-2517	109	21	ℋ	ℋ	PROPN
iajs-2517	109	22	)	)	PUNCT
iajs-2517	109	23	and	and	CCONJ
iajs-2517	109	24	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	109	25	∉̃	∉̃	PROPN
iajs-2517	109	26	(	(	PUNCT
iajs-2517	109	27	𝔒	𝔒	PROPN
iajs-2517	109	28	,	,	PUNCT
iajs-2517	109	29	ℋ	ℋ	NOUN
iajs-2517	109	30	)	)	PUNCT
iajs-2517	109	31	or	or	CCONJ
iajs-2517	109	32	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	109	33	∉̃	∉̃	ADJ
iajs-2517	109	34	(	(	PUNCT
iajs-2517	109	35	𝔒	𝔒	PROPN
iajs-2517	109	36	,	,	PUNCT
iajs-2517	109	37	ℋ	ℋ	PROPN
iajs-2517	109	38	)	)	PUNCT
iajs-2517	109	39	and	and	CCONJ
iajs-2517	109	40	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	109	41	∈̃	∈̃	PROPN
iajs-2517	109	42	(	(	PUNCT
iajs-2517	109	43	𝔒	𝔒	PROPN
iajs-2517	109	44	,	,	PUNCT
iajs-2517	109	45	ℋ	ℋ	PROPN
iajs-2517	109	46	)	)	PUNCT
iajs-2517	109	47	.	.	PUNCT
iajs-2517	110	1	theorem	theorem	VERB
iajs-2517	110	2	4.4	4.4	NUM
iajs-2517	110	3	(	(	PUNCT
iajs-2517	110	4	𝜒	𝜒	X
iajs-2517	110	5	,	,	PUNCT
iajs-2517	110	6	𝒯	𝒯	PROPN
iajs-2517	110	7	,	,	PUNCT
iajs-2517	110	8	ℋ	ℋ	PROPN
iajs-2517	110	9	,	,	PUNCT
iajs-2517	110	10	ℐ	ℐ	NUM
iajs-2517	110	11	)	)	PUNCT
iajs-2517	110	12	is	be	AUX
iajs-2517	110	13	a	a	DET
iajs-2517	110	14	𝑠ℐ𝑠𝑔-𝒯0	𝑠ℐ𝑠𝑔-𝒯0	ADJ
iajs-2517	110	15	-	-	PUNCT
iajs-2517	110	16	space	space	NOUN
iajs-2517	110	17	if	if	SCONJ
iajs-2517	110	18	and	and	CCONJ
iajs-2517	110	19	only	only	ADV
iajs-2517	110	20	if	if	SCONJ
iajs-2517	110	21	for	for	ADP
iajs-2517	110	22	each	each	DET
iajs-2517	110	23	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	110	24	≠	≠	PROPN
iajs-2517	110	25	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	110	26	there	there	PRON
iajs-2517	110	27	is	be	VERB
iajs-2517	110	28	a	a	DET
iajs-2517	110	29	𝑠ℐ𝑠𝑔-closed	𝑠ℐ𝑠𝑔-close	VERB
iajs-2517	110	30	set	set	NOUN
iajs-2517	110	31	(	(	PUNCT
iajs-2517	110	32	ѵ	ѵ	NOUN
iajs-2517	110	33	,	,	PUNCT
iajs-2517	110	34	ℋ	ℋ	NOUN
iajs-2517	110	35	)	)	PUNCT
iajs-2517	110	36	such	such	ADJ
iajs-2517	110	37	that	that	SCONJ
iajs-2517	110	38	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	110	39	∈̃	∈̃	NOUN
iajs-2517	110	40	(	(	PUNCT
iajs-2517	110	41	ѵ	ѵ	NOUN
iajs-2517	110	42	,	,	PUNCT
iajs-2517	110	43	ℋ	ℋ	PROPN
iajs-2517	110	44	)	)	PUNCT
iajs-2517	110	45	,	,	PUNCT
iajs-2517	110	46	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	110	47	∉̃	∉̃	NOUN
iajs-2517	110	48	(	(	PUNCT
iajs-2517	110	49	ѵ	ѵ	PROPN
iajs-2517	110	50	,	,	PUNCT
iajs-2517	110	51	ℋ	ℋ	NOUN
iajs-2517	110	52	)	)	PUNCT
iajs-2517	110	53	or	or	CCONJ
iajs-2517	110	54	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	110	55	∉̃	∉̃	ADJ
iajs-2517	110	56	(	(	PUNCT
iajs-2517	110	57	ѵ	ѵ	NOUN
iajs-2517	110	58	,	,	PUNCT
iajs-2517	110	59	ℋ	ℋ	PROPN
iajs-2517	110	60	)	)	PUNCT
iajs-2517	110	61	,	,	PUNCT
iajs-2517	110	62	𝒽	𝒽	DET
iajs-2517	110	63	∈̃	∈̃	PROPN
iajs-2517	110	64	(	(	PUNCT
iajs-2517	110	65	ѵ	ѵ	NOUN
iajs-2517	110	66	,	,	PUNCT
iajs-2517	110	67	ℋ	ℋ	PROPN
iajs-2517	110	68	)	)	PUNCT
iajs-2517	110	69	.	.	PUNCT
iajs-2517	111	1	proof	proof	NOUN
iajs-2517	111	2	:(	:(	PUNCT
iajs-2517	111	3	⇒	⇒	NOUN
iajs-2517	111	4	)	)	PUNCT
iajs-2517	111	5	let	let	VERB
iajs-2517	111	6	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	111	7	,	,	PUNCT
iajs-2517	111	8	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	111	9	∈̃	∈̃	PROPN
iajs-2517	111	10	�	�	PROPN
iajs-2517	111	11	̃	̃	PROPN
iajs-2517	111	12	�	�	NOUN
iajs-2517	111	13	such	such	ADJ
iajs-2517	111	14	that	that	DET
iajs-2517	111	15	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	111	16	≠	≠	PROPN
iajs-2517	111	17	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	111	18	since	since	SCONJ
iajs-2517	111	19	χ	χ	NOUN
iajs-2517	111	20	is	be	AUX
iajs-2517	111	21	a	a	DET
iajs-2517	111	22	𝑠ℐ𝑠𝑔-𝒯0	𝑠ℐ𝑠𝑔-𝒯0	ADJ
iajs-2517	111	23	-	-	PUNCT
iajs-2517	111	24	space	space	NOUN
iajs-2517	111	25	,	,	PUNCT
iajs-2517	111	26	then	then	ADV
iajs-2517	111	27	∃	∃	PROPN
iajs-2517	111	28	(	(	PUNCT
iajs-2517	111	29	𝔒	𝔒	PROPN
iajs-2517	111	30	,	,	PUNCT
iajs-2517	111	31	ℋ	ℋ	PROPN
iajs-2517	111	32	)	)	PUNCT
iajs-2517	111	33	∈	∈	NOUN
iajs-2517	111	34	sℐs𝑔-o(χ)𝓗	sℐs𝑔-o(χ)𝓗	VERB
iajs-2517	111	35	whenever	whenever	ADV
iajs-2517	111	36	,	,	PUNCT
iajs-2517	111	37	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	111	38	∈̃	∈̃	NOUN
iajs-2517	111	39	(	(	PUNCT
iajs-2517	111	40	𝔒	𝔒	PROPN
iajs-2517	111	41	,	,	PUNCT
iajs-2517	111	42	ℋ	ℋ	PROPN
iajs-2517	111	43	)	)	PUNCT
iajs-2517	111	44	and	and	CCONJ
iajs-2517	111	45	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	111	46	∉̃	∉̃	NOUN
iajs-2517	111	47	(	(	PUNCT
iajs-2517	111	48	(	(	PUNCT
iajs-2517	111	49	𝔒	𝔒	PROPN
iajs-2517	111	50	,	,	PUNCT
iajs-2517	111	51	ℋ	ℋ	NOUN
iajs-2517	111	52	)	)	PUNCT
iajs-2517	111	53	or	or	CCONJ
iajs-2517	111	54	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	111	55	∉̃	∉̃	ADJ
iajs-2517	111	56	126	126	NUM
iajs-2517	111	57	ibn	ibn	PROPN
iajs-2517	111	58	al	al	PROPN
iajs-2517	111	59	-	-	PUNCT
iajs-2517	111	60	haitham	haitham	PROPN
iajs-2517	111	61	jour	jour	X
iajs-2517	111	62	.	.	PROPN
iajs-2517	112	1	for	for	ADP
iajs-2517	112	2	pure	pure	ADJ
iajs-2517	112	3	&	&	CCONJ
iajs-2517	112	4	appl	appl	PROPN
iajs-2517	112	5	.	.	PUNCT
iajs-2517	113	1	sci	sci	PROPN
iajs-2517	113	2	.	.	PROPN
iajs-2517	114	1	33	33	NUM
iajs-2517	114	2	(	(	PUNCT
iajs-2517	114	3	4	4	NUM
iajs-2517	114	4	)	)	PUNCT
iajs-2517	114	5	2020	2020	NUM
iajs-2517	114	6	(	(	PUNCT
iajs-2517	114	7	𝔒	𝔒	PROPN
iajs-2517	114	8	,	,	PUNCT
iajs-2517	114	9	ℋ	ℋ	PROPN
iajs-2517	114	10	)	)	PUNCT
iajs-2517	114	11	and	and	CCONJ
iajs-2517	114	12	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	114	13	∈̃	∈̃	PROPN
iajs-2517	114	14	(	(	PUNCT
iajs-2517	114	15	𝔒	𝔒	PROPN
iajs-2517	114	16	,	,	PUNCT
iajs-2517	114	17	ℋ	ℋ	PROPN
iajs-2517	114	18	)	)	PUNCT
iajs-2517	114	19	,	,	PUNCT
iajs-2517	114	20	then	then	ADV
iajs-2517	114	21	∃	∃	PROPN
iajs-2517	114	22	(	(	PUNCT
iajs-2517	114	23	ѵ	ѵ	PROPN
iajs-2517	114	24	,	,	PUNCT
iajs-2517	114	25	ℋ	ℋ	PROPN
iajs-2517	114	26	)	)	PUNCT
iajs-2517	114	27	∈	∈	NOUN
iajs-2517	114	28	sℐs𝑔-c(χ)𝓗	sℐs𝑔-c(χ)𝓗	VERB
iajs-2517	114	29	whenever	whenever	SCONJ
iajs-2517	114	30	,	,	PUNCT
iajs-2517	114	31	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	114	32	∈̃	∈̃	NOUN
iajs-2517	114	33	(	(	PUNCT
iajs-2517	114	34	ѵ	ѵ	NOUN
iajs-2517	114	35	,	,	PUNCT
iajs-2517	114	36	ℋ	ℋ	NOUN
iajs-2517	114	37	)	)	PUNCT
iajs-2517	114	38	and	and	CCONJ
iajs-2517	114	39	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	114	40	∉̃	∉̃	NOUN
iajs-2517	114	41	(	(	PUNCT
iajs-2517	114	42	ѵ	ѵ	PROPN
iajs-2517	114	43	,	,	PUNCT
iajs-2517	114	44	ℋ	ℋ	NOUN
iajs-2517	114	45	)	)	PUNCT
iajs-2517	114	46	or	or	CCONJ
iajs-2517	114	47	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	114	48	∉̃	∉̃	ADJ
iajs-2517	114	49	(	(	PUNCT
iajs-2517	114	50	ѵ	ѵ	NOUN
iajs-2517	114	51	,	,	PUNCT
iajs-2517	114	52	ℋ	ℋ	PROPN
iajs-2517	114	53	)	)	PUNCT
iajs-2517	114	54	,	,	PUNCT
iajs-2517	114	55	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	114	56	∈̃	∈̃	PROPN
iajs-2517	114	57	(	(	PUNCT
iajs-2517	114	58	ơ	ơ	PROPN
iajs-2517	114	59	,	,	PUNCT
iajs-2517	114	60	ℋ	ℋ	PROPN
iajs-2517	114	61	)	)	PUNCT
iajs-2517	114	62	where	where	SCONJ
iajs-2517	114	63	,	,	PUNCT
iajs-2517	114	64	(	(	PUNCT
iajs-2517	114	65	�	�	PROPN
iajs-2517	114	66	̃	̃	NOUN
iajs-2517	114	67	�	�	PROPN
iajs-2517	114	68	–	–	PUNCT
iajs-2517	114	69	(	(	PUNCT
iajs-2517	114	70	ơ	ơ	PROPN
iajs-2517	114	71	,	,	PUNCT
iajs-2517	114	72	ℋ	ℋ	PROPN
iajs-2517	114	73	)	)	PUNCT
iajs-2517	114	74	)	)	PUNCT
iajs-2517	114	75	=	=	SYM
iajs-2517	114	76	(	(	PUNCT
iajs-2517	114	77	ѵ	ѵ	NOUN
iajs-2517	114	78	,	,	PUNCT
iajs-2517	114	79	ℋ	ℋ	PROPN
iajs-2517	114	80	)	)	PUNCT
iajs-2517	114	81	.	.	PUNCT
iajs-2517	115	1	(	(	PUNCT
iajs-2517	115	2	⇐	⇐	PROPN
iajs-2517	115	3	)	)	PUNCT
iajs-2517	115	4	let	let	VERB
iajs-2517	115	5	𝒽	𝒽	PRON
iajs-2517	115	6	,	,	PUNCT
iajs-2517	115	7	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	115	8	∈̃	∈̃	PROPN
iajs-2517	115	9	�	�	PROPN
iajs-2517	115	10	̃	̃	PROPN
iajs-2517	115	11	�	�	NOUN
iajs-2517	115	12	such	such	ADJ
iajs-2517	115	13	that	that	DET
iajs-2517	115	14	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	115	15	≠	≠	PROPN
iajs-2517	115	16	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	115	17	and	and	CCONJ
iajs-2517	115	18	there	there	PRON
iajs-2517	115	19	is	be	VERB
iajs-2517	115	20	a	a	DET
iajs-2517	115	21	𝑠ℐ𝑠𝑔-closed	𝑠ℐ𝑠𝑔-close	VERB
iajs-2517	115	22	set	set	NOUN
iajs-2517	115	23	(	(	PUNCT
iajs-2517	115	24	ѵ	ѵ	NOUN
iajs-2517	115	25	,	,	PUNCT
iajs-2517	115	26	ℋ	ℋ	NOUN
iajs-2517	115	27	)	)	PUNCT
iajs-2517	115	28	such	such	ADJ
iajs-2517	115	29	that	that	SCONJ
iajs-2517	115	30	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	115	31	∈̃	∈̃	NOUN
iajs-2517	115	32	(	(	PUNCT
iajs-2517	115	33	ѵ	ѵ	NOUN
iajs-2517	115	34	,	,	PUNCT
iajs-2517	115	35	ℋ	ℋ	PROPN
iajs-2517	115	36	)	)	PUNCT
iajs-2517	115	37	,	,	PUNCT
iajs-2517	115	38	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	115	39	∉̃	∉̃	NOUN
iajs-2517	115	40	(	(	PUNCT
iajs-2517	115	41	ѵ	ѵ	PROPN
iajs-2517	115	42	,	,	PUNCT
iajs-2517	115	43	ℋ	ℋ	NOUN
iajs-2517	115	44	)	)	PUNCT
iajs-2517	115	45	or	or	CCONJ
iajs-2517	115	46	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	115	47	∉̃	∉̃	ADJ
iajs-2517	115	48	(	(	PUNCT
iajs-2517	115	49	ѵ	ѵ	NOUN
iajs-2517	115	50	,	,	PUNCT
iajs-2517	115	51	ℋ	ℋ	PROPN
iajs-2517	115	52	)	)	PUNCT
iajs-2517	115	53	,	,	PUNCT
iajs-2517	115	54	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	115	55	∈̃	∈̃	PROPN
iajs-2517	115	56	(	(	PUNCT
iajs-2517	115	57	𝔒	𝔒	PROPN
iajs-2517	115	58	,	,	PUNCT
iajs-2517	115	59	ℋ	ℋ	PROPN
iajs-2517	115	60	)	)	PUNCT
iajs-2517	115	61	.	.	PUNCT
iajs-2517	116	1	then	then	ADV
iajs-2517	116	2	there	there	PRON
iajs-2517	116	3	is	be	VERB
iajs-2517	116	4	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	116	5	set	set	NOUN
iajs-2517	116	6	(	(	PUNCT
iajs-2517	116	7	𝜒	𝜒	X
iajs-2517	116	8	–	–	PUNCT
iajs-2517	116	9	(	(	PUNCT
iajs-2517	116	10	ѵ	ѵ	NOUN
iajs-2517	116	11	,	,	PUNCT
iajs-2517	116	12	ℋ	ℋ	NOUN
iajs-2517	116	13	)	)	PUNCT
iajs-2517	116	14	)	)	PUNCT
iajs-2517	117	1	=	=	SYM
iajs-2517	117	2	(	(	PUNCT
iajs-2517	117	3	𝔒	𝔒	PROPN
iajs-2517	117	4	,	,	PUNCT
iajs-2517	117	5	ℋ	ℋ	PROPN
iajs-2517	117	6	)	)	PUNCT
iajs-2517	117	7	such	such	ADJ
iajs-2517	117	8	that	that	SCONJ
iajs-2517	117	9	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	117	10	∈̃	∈̃	NOUN
iajs-2517	117	11	(	(	PUNCT
iajs-2517	117	12	𝔒	𝔒	PROPN
iajs-2517	117	13	,	,	PUNCT
iajs-2517	117	14	ℋ	ℋ	PROPN
iajs-2517	117	15	)	)	PUNCT
iajs-2517	117	16	,	,	PUNCT
iajs-2517	117	17	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	117	18	∉̃	∉̃	PROPN
iajs-2517	117	19	(	(	PUNCT
iajs-2517	117	20	𝔒	𝔒	PROPN
iajs-2517	117	21	,	,	PUNCT
iajs-2517	117	22	ℋ	ℋ	NOUN
iajs-2517	117	23	)	)	PUNCT
iajs-2517	117	24	or	or	CCONJ
iajs-2517	117	25	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	117	26	∉̃	∉̃	ADJ
iajs-2517	117	27	(	(	PUNCT
iajs-2517	117	28	𝔒	𝔒	PROPN
iajs-2517	117	29	,	,	PUNCT
iajs-2517	117	30	ℋ	ℋ	PROPN
iajs-2517	117	31	)	)	PUNCT
iajs-2517	117	32	,	,	PUNCT
iajs-2517	117	33	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	117	34	∈̃	∈̃	PROPN
iajs-2517	117	35	(	(	PUNCT
iajs-2517	117	36	𝔒	𝔒	PROPN
iajs-2517	117	37	,	,	PUNCT
iajs-2517	117	38	ℋ	ℋ	PROPN
iajs-2517	117	39	)	)	PUNCT
iajs-2517	117	40	.	.	PUNCT
iajs-2517	118	1	definition	definition	NOUN
iajs-2517	118	2	4.5	4.5	NUM
iajs-2517	118	3	.	.	PUNCT
iajs-2517	119	1	(	(	PUNCT
iajs-2517	119	2	𝜒	𝜒	X
iajs-2517	119	3	,	,	PUNCT
iajs-2517	119	4	𝒯	𝒯	PROPN
iajs-2517	119	5	,	,	PUNCT
iajs-2517	119	6	ℋ	ℋ	PROPN
iajs-2517	119	7	,	,	PUNCT
iajs-2517	119	8	ℐ	ℐ	PROPN
iajs-2517	119	9	)	)	PUNCT
iajs-2517	119	10	is	be	AUX
iajs-2517	119	11	a	a	DET
iajs-2517	119	12	soft-ℐ-semi-𝑔-𝒯1	soft-ℐ-semi-𝑔-𝒯1	NOUN
iajs-2517	119	13	-	-	PUNCT
iajs-2517	119	14	space	space	NOUN
iajs-2517	119	15	(	(	PUNCT
iajs-2517	119	16	briefly	briefly	ADV
iajs-2517	119	17	𝑠ℐ𝑠𝑔-𝒯1	𝑠ℐ𝑠𝑔-𝒯1	NOUN
iajs-2517	119	18	-	-	PRON
iajs-2517	119	19	space),if	space),if	NOUN
iajs-2517	119	20	for	for	ADP
iajs-2517	119	21	each	each	DET
iajs-2517	119	22	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	119	23	,	,	PUNCT
iajs-2517	119	24	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	119	25	∈̃	∈̃	PROPN
iajs-2517	119	26	�	�	PROPN
iajs-2517	119	27	̃	̃	PROPN
iajs-2517	119	28	�	�	PROPN
iajs-2517	119	29	and	and	CCONJ
iajs-2517	119	30	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	119	31	≠	≠	PROPN
iajs-2517	119	32	𝒽𝓝.	𝒽𝓝.	NOUN
iajs-2517	119	33	then	then	ADV
iajs-2517	119	34	there	there	PRON
iajs-2517	119	35	are	be	VERB
iajs-2517	119	36	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	119	37	sets	set	NOUN
iajs-2517	119	38	(	(	PUNCT
iajs-2517	119	39	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	119	40	)	)	PUNCT
iajs-2517	119	41	,	,	PUNCT
iajs-2517	119	42	(	(	PUNCT
iajs-2517	119	43	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	119	44	)	)	PUNCT
iajs-2517	119	45	whenever	whenever	SCONJ
iajs-2517	119	46	,	,	PUNCT
iajs-2517	119	47	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	119	48	∈̃	∈̃	NOUN
iajs-2517	119	49	(	(	PUNCT
iajs-2517	119	50	(	(	PUNCT
iajs-2517	119	51	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	119	52	)	)	PUNCT
iajs-2517	119	53	–	–	PUNCT
iajs-2517	119	54	(	(	PUNCT
iajs-2517	119	55	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	119	56	)	)	PUNCT
iajs-2517	119	57	)	)	PUNCT
iajs-2517	119	58	and	and	CCONJ
iajs-2517	119	59	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	119	60	∈̃	∈̃	PROPN
iajs-2517	119	61	(	(	PUNCT
iajs-2517	119	62	(	(	PUNCT
iajs-2517	119	63	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	119	64	)	)	PUNCT
iajs-2517	119	65	–	–	PUNCT
iajs-2517	119	66	(	(	PUNCT
iajs-2517	119	67	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	119	68	)	)	PUNCT
iajs-2517	119	69	)	)	PUNCT
iajs-2517	119	70	.	.	PUNCT
iajs-2517	120	1	example	example	NOUN
iajs-2517	121	1	4.6	4.6	NUM
iajs-2517	121	2	.	.	PUNCT
iajs-2517	122	1	a	a	DET
iajs-2517	122	2	space	space	NOUN
iajs-2517	122	3	(	(	PUNCT
iajs-2517	122	4	𝜒	𝜒	X
iajs-2517	122	5	,	,	PUNCT
iajs-2517	122	6	𝒯	𝒯	PROPN
iajs-2517	122	7	,	,	PUNCT
iajs-2517	122	8	ℋ	ℋ	PROPN
iajs-2517	122	9	,	,	PUNCT
iajs-2517	122	10	ℐ	ℐ	PROPN
iajs-2517	122	11	)	)	PUNCT
iajs-2517	122	12	when	when	SCONJ
iajs-2517	122	13	χ	χ	X
iajs-2517	122	14	=	=	PUNCT
iajs-2517	122	15	ℋ=	ℋ=	NOUN
iajs-2517	122	16	ℕ	ℕ	PROPN
iajs-2517	122	17	the	the	DET
iajs-2517	122	18	set	set	NOUN
iajs-2517	122	19	of	of	ADP
iajs-2517	122	20	all	all	DET
iajs-2517	122	21	natural	natural	ADJ
iajs-2517	122	22	number	number	NOUN
iajs-2517	122	23	𝒯	𝒯	PROPN
iajs-2517	122	24	=	=	SYM
iajs-2517	122	25	𝒯scof	𝒯scof	PROPN
iajs-2517	122	26	=	=	PUNCT
iajs-2517	122	27	{	{	PUNCT
iajs-2517	122	28	г𝓐	г𝓐	NOUN
iajs-2517	122	29	:	:	PUNCT
iajs-2517	122	30	г′(𝓱	г′(𝓱	X
iajs-2517	122	31	)	)	PUNCT
iajs-2517	122	32	is	be	AUX
iajs-2517	122	33	finite	finite	NOUN
iajs-2517	122	34	set	set	VERB
iajs-2517	122	35	∀	∀	X
iajs-2517	122	36	𝓱	𝓱	X
iajs-2517	122	37	}	}	PUNCT
iajs-2517	122	38	⋃̃	⋃̃	PROPN
iajs-2517	122	39	{	{	PUNCT
iajs-2517	122	40	∅̃	∅̃	NOUN
iajs-2517	122	41	}	}	PUNCT
iajs-2517	122	42	and	and	CCONJ
iajs-2517	122	43	ℐ	ℐ	PROPN
iajs-2517	122	44	=	=	NOUN
iajs-2517	122	45	{	{	PUNCT
iajs-2517	122	46	∅̃	∅̃	NOUN
iajs-2517	122	47	}	}	PUNCT
iajs-2517	122	48	.	.	PUNCT
iajs-2517	123	1	so	so	ADV
iajs-2517	123	2	,	,	PUNCT
iajs-2517	123	3	(	(	PUNCT
iajs-2517	123	4	𝜒	𝜒	X
iajs-2517	123	5	,	,	PUNCT
iajs-2517	123	6	𝒯	𝒯	PROPN
iajs-2517	123	7	,	,	PUNCT
iajs-2517	123	8	ℋ	ℋ	PROPN
iajs-2517	123	9	,	,	PUNCT
iajs-2517	123	10	ℐ	ℐ	PROPN
iajs-2517	123	11	)	)	PUNCT
iajs-2517	123	12	is	be	AUX
iajs-2517	123	13	a	a	DET
iajs-2517	123	14	𝑠ℐ𝑠𝑔-𝒯1	𝑠ℐ𝑠𝑔-𝒯1	NOUN
iajs-2517	123	15	-	-	NOUN
iajs-2517	123	16	space	space	NOUN
iajs-2517	123	17	.	.	PUNCT
iajs-2517	124	1	if	if	SCONJ
iajs-2517	124	2	for	for	ADP
iajs-2517	124	3	each	each	DET
iajs-2517	124	4	𝒽	𝒽	NOUN
iajs-2517	124	5	,	,	PUNCT
iajs-2517	124	6	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	124	7	∈̃	∈̃	PROPN
iajs-2517	124	8	�	�	PROPN
iajs-2517	124	9	̃	̃	PROPN
iajs-2517	124	10	�	�	PROPN
iajs-2517	124	11	and	and	CCONJ
iajs-2517	124	12	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	124	13	≠	≠	PROPN
iajs-2517	124	14	𝒽𝓝.	𝒽𝓝.	NOUN
iajs-2517	124	15	then	then	ADV
iajs-2517	124	16	there	there	PRON
iajs-2517	124	17	are	be	VERB
iajs-2517	124	18	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	124	19	sets	set	NOUN
iajs-2517	124	20	(	(	PUNCT
iajs-2517	124	21	�	�	PROPN
iajs-2517	124	22	̃	̃	NOUN
iajs-2517	124	23	�	�	PROPN
iajs-2517	124	24	–	–	PUNCT
iajs-2517	124	25	𝒰	𝒰	PROPN
iajs-2517	124	26	)	)	PUNCT
iajs-2517	124	27	,	,	PUNCT
iajs-2517	124	28	(	(	PUNCT
iajs-2517	124	29	�	�	PROPN
iajs-2517	124	30	̃	̃	NOUN
iajs-2517	124	31	�	�	PROPN
iajs-2517	124	32	–	–	PUNCT
iajs-2517	124	33	𝒱	𝒱	PROPN
iajs-2517	124	34	)	)	PUNCT
iajs-2517	124	35	such	such	ADJ
iajs-2517	124	36	that	that	SCONJ
iajs-2517	124	37	𝒰	𝒰	PROPN
iajs-2517	124	38	⊆	⊆	NUM
iajs-2517	124	39	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	124	40	,	,	PUNCT
iajs-2517	124	41	𝒱	𝒱	PROPN
iajs-2517	124	42	⊆	⊆	NUM
iajs-2517	124	43	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	124	44	and	and	CCONJ
iajs-2517	124	45	𝒰	𝒰	PROPN
iajs-2517	124	46	,	,	PUNCT
iajs-2517	124	47	𝒱	𝒱	PROPN
iajs-2517	124	48	are	be	AUX
iajs-2517	124	49	two	two	NUM
iajs-2517	124	50	finite	finite	NOUN
iajs-2517	124	51	sets	set	NOUN
iajs-2517	124	52	whenever	whenever	ADV
iajs-2517	124	53	,	,	PUNCT
iajs-2517	124	54	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	124	55	∈̃	∈̃	PROPN
iajs-2517	124	56	(	(	PUNCT
iajs-2517	124	57	�	�	PROPN
iajs-2517	124	58	̃	̃	NOUN
iajs-2517	124	59	�	�	PROPN
iajs-2517	124	60	–	–	PUNCT
iajs-2517	124	61	𝒱	𝒱	PROPN
iajs-2517	124	62	)	)	PUNCT
iajs-2517	124	63	,	,	PUNCT
iajs-2517	124	64	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	124	65	∉	∉	PROPN
iajs-2517	124	66	(	(	PUNCT
iajs-2517	124	67	�	�	PROPN
iajs-2517	124	68	̃	̃	PROPN
iajs-2517	124	69	�	�	PROPN
iajs-2517	124	70	–	–	PUNCT
iajs-2517	124	71	𝒱	𝒱	PROPN
iajs-2517	124	72	)	)	PUNCT
iajs-2517	124	73	and	and	CCONJ
iajs-2517	124	74	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	124	75	∉	∉	PROPN
iajs-2517	124	76	(	(	PUNCT
iajs-2517	124	77	�	�	PROPN
iajs-2517	124	78	̃	̃	PROPN
iajs-2517	124	79	�	�	PROPN
iajs-2517	124	80	–	–	PUNCT
iajs-2517	124	81	𝒰	𝒰	PROPN
iajs-2517	124	82	)	)	PUNCT
iajs-2517	124	83	,	,	PUNCT
iajs-2517	124	84	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	124	85	∈̃	∈̃	PROPN
iajs-2517	124	86	(	(	PUNCT
iajs-2517	124	87	�	�	PROPN
iajs-2517	124	88	̃	̃	NOUN
iajs-2517	124	89	�	�	PROPN
iajs-2517	124	90	–	–	PUNCT
iajs-2517	124	91	𝒰	𝒰	PROPN
iajs-2517	124	92	)	)	PUNCT
iajs-2517	124	93	and	and	CCONJ
iajs-2517	124	94	(	(	PUNCT
iajs-2517	124	95	𝜒	𝜒	X
iajs-2517	124	96	–	–	PUNCT
iajs-2517	124	97	𝒱	𝒱	NOUN
iajs-2517	124	98	)	)	PUNCT
iajs-2517	124	99	⋂	⋂	PROPN
iajs-2517	124	100	(	(	PUNCT
iajs-2517	124	101	�	�	PROPN
iajs-2517	124	102	̃	̃	PROPN
iajs-2517	124	103	�	�	PROPN
iajs-2517	124	104	–	–	PUNCT
iajs-2517	124	105	𝒰	𝒰	PROPN
iajs-2517	124	106	)	)	PUNCT
iajs-2517	124	107	≠	≠	PROPN
iajs-2517	124	108	{	{	PUNCT
iajs-2517	124	109	∅	∅	NOUN
iajs-2517	124	110	}	}	PUNCT
iajs-2517	124	111	.	.	PUNCT
iajs-2517	125	1	proposition	proposition	NOUN
iajs-2517	125	2	4.7	4.7	NUM
iajs-2517	125	3	.	.	PUNCT
iajs-2517	126	1	if	if	SCONJ
iajs-2517	126	2	(	(	PUNCT
iajs-2517	126	3	𝜒	𝜒	X
iajs-2517	126	4	,	,	PUNCT
iajs-2517	126	5	𝒯	𝒯	PROPN
iajs-2517	126	6	,	,	PUNCT
iajs-2517	126	7	ℋ	ℋ	PROPN
iajs-2517	126	8	)	)	PUNCT
iajs-2517	126	9	is	be	AUX
iajs-2517	126	10	a	a	DET
iajs-2517	126	11	soft-𝒯1	soft-𝒯1	NOUN
iajs-2517	126	12	-	-	NOUN
iajs-2517	126	13	space	space	NOUN
iajs-2517	126	14	then	then	ADV
iajs-2517	126	15	(	(	PUNCT
iajs-2517	126	16	𝜒	𝜒	X
iajs-2517	126	17	,	,	PUNCT
iajs-2517	126	18	𝒯	𝒯	PROPN
iajs-2517	126	19	,	,	PUNCT
iajs-2517	126	20	ℋ	ℋ	PROPN
iajs-2517	126	21	,	,	PUNCT
iajs-2517	126	22	ℐ	ℐ	PROPN
iajs-2517	126	23	)	)	PUNCT
iajs-2517	126	24	is	be	AUX
iajs-2517	126	25	a	a	DET
iajs-2517	126	26	soft-ℐ-semi-𝑔-𝒯1space	soft-ℐ-semi-𝑔-𝒯1space	NOUN
iajs-2517	126	27	.	.	PUNCT
iajs-2517	127	1	proof	proof	NOUN
iajs-2517	127	2	:	:	PUNCT
iajs-2517	127	3	let	let	VERB
iajs-2517	127	4	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	127	5	,	,	PUNCT
iajs-2517	127	6	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	127	7	∈̃	∈̃	PROPN
iajs-2517	127	8	𝜒	𝜒	PRON
iajs-2517	127	9	such	such	ADJ
iajs-2517	127	10	that	that	DET
iajs-2517	127	11	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	127	12	≠	≠	PROPN
iajs-2517	127	13	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	127	14	since	since	SCONJ
iajs-2517	127	15	(	(	PUNCT
iajs-2517	127	16	𝜒	𝜒	X
iajs-2517	127	17	,	,	PUNCT
iajs-2517	127	18	𝒯	𝒯	PROPN
iajs-2517	127	19	,	,	PUNCT
iajs-2517	127	20	ℋ	ℋ	PROPN
iajs-2517	127	21	)	)	PUNCT
iajs-2517	127	22	is	be	AUX
iajs-2517	127	23	a	a	DET
iajs-2517	127	24	soft-𝒯1	soft-𝒯1	NOUN
iajs-2517	127	25	-	-	NOUN
iajs-2517	127	26	space	space	NOUN
iajs-2517	127	27	,	,	PUNCT
iajs-2517	127	28	then	then	ADV
iajs-2517	127	29	∃	∃	PROPN
iajs-2517	127	30	(	(	PUNCT
iajs-2517	127	31	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	127	32	)	)	PUNCT
iajs-2517	127	33	,	,	PUNCT
iajs-2517	127	34	(	(	PUNCT
iajs-2517	127	35	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	127	36	)	)	PUNCT
iajs-2517	127	37	∈	∈	PROPN
iajs-2517	128	1	𝒯such	𝒯such	PROPN
iajs-2517	128	2	that	that	SCONJ
iajs-2517	128	3	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	128	4	∈̃	∈̃	NOUN
iajs-2517	128	5	(	(	PUNCT
iajs-2517	128	6	(	(	PUNCT
iajs-2517	128	7	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	128	8	)	)	PUNCT
iajs-2517	128	9	–	–	PUNCT
iajs-2517	128	10	(	(	PUNCT
iajs-2517	128	11	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	128	12	)	)	PUNCT
iajs-2517	128	13	)	)	PUNCT
iajs-2517	128	14	and	and	CCONJ
iajs-2517	128	15	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	128	16	∈̃	∈̃	PROPN
iajs-2517	128	17	(	(	PUNCT
iajs-2517	128	18	(	(	PUNCT
iajs-2517	128	19	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	128	20	)	)	PUNCT
iajs-2517	128	21	–	–	PUNCT
iajs-2517	128	22	(	(	PUNCT
iajs-2517	128	23	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	128	24	)	)	PUNCT
iajs-2517	128	25	)	)	PUNCT
iajs-2517	128	26	.	.	PUNCT
iajs-2517	129	1	by	by	ADP
iajs-2517	129	2	remark	remark	NOUN
iajs-2517	129	3	3.3	3.3	NUM
iajs-2517	129	4	,	,	PUNCT
iajs-2517	129	5	(	(	PUNCT
iajs-2517	129	6	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	129	7	)	)	PUNCT
iajs-2517	129	8	and	and	CCONJ
iajs-2517	129	9	(	(	PUNCT
iajs-2517	129	10	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	129	11	)	)	PUNCT
iajs-2517	129	12	are	be	AUX
iajs-2517	129	13	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	129	14	sets	set	NOUN
iajs-2517	129	15	,	,	PUNCT
iajs-2517	129	16	and	and	CCONJ
iajs-2517	129	17	the	the	DET
iajs-2517	129	18	proof	proof	NOUN
iajs-2517	129	19	is	be	AUX
iajs-2517	129	20	over	over	ADV
iajs-2517	129	21	.	.	PUNCT
iajs-2517	130	1	proposition	proposition	NOUN
iajs-2517	130	2	4.8	4.8	NUM
iajs-2517	130	3	.	.	PUNCT
iajs-2517	131	1	if	if	SCONJ
iajs-2517	131	2	(	(	PUNCT
iajs-2517	131	3	𝜒	𝜒	X
iajs-2517	131	4	,	,	PUNCT
iajs-2517	131	5	𝒯	𝒯	PROPN
iajs-2517	131	6	,	,	PUNCT
iajs-2517	131	7	ℋ	ℋ	PROPN
iajs-2517	131	8	,	,	PUNCT
iajs-2517	131	9	ℐ	ℐ	PROPN
iajs-2517	131	10	)	)	PUNCT
iajs-2517	131	11	is	be	AUX
iajs-2517	131	12	a	a	DET
iajs-2517	131	13	𝑠ℐ𝑠𝑔-𝒯1	𝑠ℐ𝑠𝑔-𝒯1	NOUN
iajs-2517	131	14	-	-	NOUN
iajs-2517	131	15	space	space	NOUN
iajs-2517	131	16	then	then	ADV
iajs-2517	131	17	it	it	PRON
iajs-2517	131	18	is	be	AUX
iajs-2517	131	19	a	a	DET
iajs-2517	131	20	𝑠ℐ𝑠𝑔-𝒯0-𝑠𝑝𝑎𝑐𝑒.	𝑠ℐ𝑠𝑔-𝒯0-𝑠𝑝𝑎𝑐𝑒.	ADJ
iajs-2517	131	21	proof	proof	NOUN
iajs-2517	131	22	:	:	PUNCT
iajs-2517	131	23	let	let	VERB
iajs-2517	131	24	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	131	25	,	,	PUNCT
iajs-2517	131	26	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	131	27	∈̃	∈̃	PROPN
iajs-2517	131	28	�	�	PROPN
iajs-2517	131	29	̃	̃	PROPN
iajs-2517	131	30	�	�	NOUN
iajs-2517	131	31	such	such	ADJ
iajs-2517	131	32	that	that	DET
iajs-2517	131	33	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	131	34	≠	≠	PROPN
iajs-2517	131	35	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	131	36	since	since	SCONJ
iajs-2517	131	37	(	(	PUNCT
iajs-2517	131	38	𝜒	𝜒	X
iajs-2517	131	39	,	,	PUNCT
iajs-2517	131	40	𝒯	𝒯	PROPN
iajs-2517	131	41	,	,	PUNCT
iajs-2517	131	42	ℋ	ℋ	PROPN
iajs-2517	131	43	,	,	PUNCT
iajs-2517	131	44	ℐ	ℐ	PROPN
iajs-2517	131	45	)	)	PUNCT
iajs-2517	131	46	is	be	AUX
iajs-2517	131	47	a	a	DET
iajs-2517	131	48	𝑠ℐ𝑠𝑔-𝒯1-𝑠𝑝𝑎𝑐𝑒	𝑠ℐ𝑠𝑔-𝒯1-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	131	49	,	,	PUNCT
iajs-2517	131	50	then	then	ADV
iajs-2517	131	51	∃	∃	PROPN
iajs-2517	131	52	(	(	PUNCT
iajs-2517	131	53	ơ1	ơ1	PROPN
iajs-2517	131	54	,	,	PUNCT
iajs-2517	131	55	ℋ	ℋ	NOUN
iajs-2517	131	56	)	)	PUNCT
iajs-2517	131	57	,	,	PUNCT
iajs-2517	131	58	(	(	PUNCT
iajs-2517	131	59	ơ2	ơ2	NOUN
iajs-2517	131	60	,	,	PUNCT
iajs-2517	131	61	ℋ	ℋ	PROPN
iajs-2517	131	62	)	)	PUNCT
iajs-2517	131	63	∈	∈	NOUN
iajs-2517	131	64	sℐs𝑔-o(χ)𝓗	sℐs𝑔-o(χ)𝓗	VERB
iajs-2517	131	65	such	such	ADJ
iajs-2517	131	66	that	that	PRON
iajs-2517	131	67	,	,	PUNCT
iajs-2517	131	68	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	131	69	∈̃	∈̃	NOUN
iajs-2517	131	70	(	(	PUNCT
iajs-2517	131	71	(	(	PUNCT
iajs-2517	131	72	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	131	73	)	)	PUNCT
iajs-2517	131	74	–	–	PUNCT
iajs-2517	131	75	(	(	PUNCT
iajs-2517	131	76	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	131	77	)	)	PUNCT
iajs-2517	131	78	)	)	PUNCT
iajs-2517	131	79	and	and	CCONJ
iajs-2517	131	80	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	131	81	∈̃	∈̃	PROPN
iajs-2517	131	82	(	(	PUNCT
iajs-2517	131	83	(	(	PUNCT
iajs-2517	131	84	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	131	85	)	)	PUNCT
iajs-2517	131	86	–	–	PUNCT
iajs-2517	131	87	(	(	PUNCT
iajs-2517	131	88	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	131	89	)	)	PUNCT
iajs-2517	131	90	)	)	PUNCT
iajs-2517	131	91	.	.	PUNCT
iajs-2517	132	1	then	then	ADV
iajs-2517	132	2	∃	∃	PROPN
iajs-2517	132	3	(	(	PUNCT
iajs-2517	132	4	ơ	ơ	PROPN
iajs-2517	132	5	,	,	PUNCT
iajs-2517	132	6	ℋ	ℋ	PROPN
iajs-2517	132	7	)	)	PUNCT
iajs-2517	132	8	∈	∈	PROPN
iajs-2517	132	9	sℐs𝑔-o(χ)𝓗	sℐs𝑔-o(χ)𝓗	VERB
iajs-2517	132	10	-open	-open	NOUN
iajs-2517	132	11	set	set	VERB
iajs-2517	132	12	whenever	whenever	ADV
iajs-2517	132	13	,	,	PUNCT
iajs-2517	132	14	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	132	15	∈̃	∈̃	NOUN
iajs-2517	132	16	(	(	PUNCT
iajs-2517	132	17	ơ,ℋ	ơ,ℋ	PROPN
iajs-2517	132	18	)	)	PUNCT
iajs-2517	132	19	,	,	PUNCT
iajs-2517	132	20	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	132	21	∉̃	∉̃	PROPN
iajs-2517	132	22	(	(	PUNCT
iajs-2517	132	23	ơ,ℋ	ơ,ℋ	PROPN
iajs-2517	132	24	)	)	PUNCT
iajs-2517	132	25	or	or	CCONJ
iajs-2517	132	26	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	132	27	∉̃	∉̃	ADJ
iajs-2517	132	28	(	(	PUNCT
iajs-2517	132	29	ơ,ℋ	ơ,ℋ	PROPN
iajs-2517	132	30	)	)	PUNCT
iajs-2517	132	31	,	,	PUNCT
iajs-2517	132	32	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	132	33	∈̃	∈̃	PROPN
iajs-2517	132	34	(	(	PUNCT
iajs-2517	132	35	ơ,ℋ	ơ,ℋ	PROPN
iajs-2517	132	36	)	)	PUNCT
iajs-2517	132	37	.	.	PUNCT
iajs-2517	133	1	the	the	DET
iajs-2517	133	2	conclusions	conclusion	NOUN
iajs-2517	133	3	in	in	ADP
iajs-2517	133	4	proposition	proposition	NOUN
iajs-2517	133	5	4.8	4.8	NUM
iajs-2517	133	6	,	,	PUNCT
iajs-2517	133	7	is	be	AUX
iajs-2517	133	8	not	not	PART
iajs-2517	133	9	reversible	reversible	ADJ
iajs-2517	133	10	by	by	ADP
iajs-2517	133	11	example	example	NOUN
iajs-2517	133	12	4.2	4.2	NUM
iajs-2517	133	13	.	.	PUNCT
iajs-2517	134	1	(	(	PUNCT
iajs-2517	134	2	𝜒	𝜒	X
iajs-2517	134	3	,	,	PUNCT
iajs-2517	134	4	𝒯	𝒯	PROPN
iajs-2517	134	5	,	,	PUNCT
iajs-2517	134	6	ℋ	ℋ	PROPN
iajs-2517	134	7	,	,	PUNCT
iajs-2517	134	8	ℐ	ℐ	NUM
iajs-2517	134	9	)	)	PUNCT
iajs-2517	134	10	is	be	AUX
iajs-2517	134	11	a	a	DET
iajs-2517	134	12	𝑠ℐ𝑠𝑔-𝒯0	𝑠ℐ𝑠𝑔-𝒯0	ADJ
iajs-2517	134	13	-	-	PUNCT
iajs-2517	134	14	space	space	NOUN
iajs-2517	134	15	,	,	PUNCT
iajs-2517	134	16	but	but	CCONJ
iajs-2517	134	17	is	be	AUX
iajs-2517	134	18	not	not	PART
iajs-2517	134	19	𝑠ℐ𝑠𝑔-𝒯1	𝑠ℐ𝑠𝑔-𝒯1	NOUN
iajs-2517	134	20	-	-	NOUN
iajs-2517	134	21	space	space	NOUN
iajs-2517	134	22	.	.	PUNCT
iajs-2517	135	1	since	since	SCONJ
iajs-2517	135	2	∃	∃	PROPN
iajs-2517	135	3	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	135	4	≠	≠	PROPN
iajs-2517	135	5	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	135	6	;	;	PUNCT
iajs-2517	135	7	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	135	8	=	=	SYM
iajs-2517	135	9	{	{	PUNCT
iajs-2517	135	10	1,2	1,2	NUM
iajs-2517	135	11	}	}	PUNCT
iajs-2517	135	12	and	and	CCONJ
iajs-2517	135	13	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	135	14	=	=	PUNCT
iajs-2517	135	15	{	{	PUNCT
iajs-2517	135	16	3	3	NUM
iajs-2517	135	17	}	}	PUNCT
iajs-2517	135	18	there	there	PRON
iajs-2517	135	19	is	be	VERB
iajs-2517	135	20	no	no	DET
iajs-2517	135	21	(	(	PUNCT
iajs-2517	135	22	𝒰,ℋ	𝒰,ℋ	NOUN
iajs-2517	135	23	)	)	PUNCT
iajs-2517	135	24	and	and	CCONJ
iajs-2517	135	25	(	(	PUNCT
iajs-2517	135	26	𝒱,ℋ	𝒱,ℋ	INTJ
iajs-2517	135	27	)	)	PUNCT
iajs-2517	135	28	such	such	ADJ
iajs-2517	135	29	that	that	SCONJ
iajs-2517	135	30	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	135	31	∈̃	∈̃	NOUN
iajs-2517	135	32	(	(	PUNCT
iajs-2517	135	33	𝒰,ℋ	𝒰,ℋ	NOUN
iajs-2517	135	34	)	)	PUNCT
iajs-2517	135	35	,	,	PUNCT
iajs-2517	135	36	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	135	37	∉̃	∉̃	NOUN
iajs-2517	135	38	(	(	PUNCT
iajs-2517	135	39	𝒰,ℋ	𝒰,ℋ	NOUN
iajs-2517	135	40	)	)	PUNCT
iajs-2517	135	41	and	and	CCONJ
iajs-2517	135	42	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	135	43	∈̃	∈̃	PROPN
iajs-2517	135	44	(	(	PUNCT
iajs-2517	135	45	𝒱,ℋ	𝒱,ℋ	NOUN
iajs-2517	135	46	)	)	PUNCT
iajs-2517	135	47	,	,	PUNCT
iajs-2517	135	48	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	135	49	∉̃	∉̃	ADJ
iajs-2517	135	50	(	(	PUNCT
iajs-2517	135	51	𝒱,ℋ	𝒱,ℋ	NOUN
iajs-2517	135	52	)	)	PUNCT
iajs-2517	135	53	.	.	PUNCT
iajs-2517	136	1	theorem	theorem	VERB
iajs-2517	136	2	4.9	4.9	NUM
iajs-2517	136	3	.	.	PUNCT
iajs-2517	137	1	a	a	DET
iajs-2517	137	2	space	space	NOUN
iajs-2517	137	3	(	(	PUNCT
iajs-2517	137	4	𝜒	𝜒	X
iajs-2517	137	5	,	,	PUNCT
iajs-2517	137	6	𝒯	𝒯	PROPN
iajs-2517	137	7	,	,	PUNCT
iajs-2517	137	8	ℋ	ℋ	PROPN
iajs-2517	137	9	,	,	PUNCT
iajs-2517	137	10	ℐ	ℐ	PROPN
iajs-2517	137	11	)	)	PUNCT
iajs-2517	137	12	is	be	AUX
iajs-2517	137	13	a	a	DET
iajs-2517	137	14	𝑠ℐ𝑠𝑔-𝒯1	𝑠ℐ𝑠𝑔-𝒯1	NOUN
iajs-2517	137	15	-	-	NOUN
iajs-2517	137	16	space	space	NOUN
iajs-2517	137	17	if	if	SCONJ
iajs-2517	137	18	and	and	CCONJ
iajs-2517	137	19	only	only	ADV
iajs-2517	137	20	if	if	SCONJ
iajs-2517	137	21	for	for	ADP
iajs-2517	137	22	each	each	DET
iajs-2517	137	23	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	137	24	,	,	PUNCT
iajs-2517	137	25	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	137	26	∈̃	∈̃	PROPN
iajs-2517	137	27	�	�	PROPN
iajs-2517	137	28	̃	̃	PROPN
iajs-2517	137	29	�	�	PROPN
iajs-2517	137	30	and	and	CCONJ
iajs-2517	137	31	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	137	32	≠	≠	PROPN
iajs-2517	137	33	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	137	34	there	there	PRON
iajs-2517	137	35	are	be	VERB
iajs-2517	137	36	two	two	NUM
iajs-2517	137	37	𝑠ℐ𝑠𝑔-closed	𝑠ℐ𝑠𝑔-close	VERB
iajs-2517	137	38	sets	set	NOUN
iajs-2517	137	39	(	(	PUNCT
iajs-2517	137	40	𝒱1	𝒱1	NOUN
iajs-2517	137	41	,	,	PUNCT
iajs-2517	137	42	ℋ	ℋ	PROPN
iajs-2517	137	43	)	)	PUNCT
iajs-2517	137	44	,	,	PUNCT
iajs-2517	137	45	(	(	PUNCT
iajs-2517	137	46	𝒱2	𝒱2	NOUN
iajs-2517	137	47	,	,	PUNCT
iajs-2517	137	48	ℋ	ℋ	NOUN
iajs-2517	137	49	)	)	PUNCT
iajs-2517	137	50	such	such	ADJ
iajs-2517	137	51	that	that	SCONJ
iajs-2517	137	52	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	137	53	∈̃	∈̃	NOUN
iajs-2517	137	54	(	(	PUNCT
iajs-2517	137	55	(	(	PUNCT
iajs-2517	137	56	𝒱1	𝒱1	NOUN
iajs-2517	137	57	,	,	PUNCT
iajs-2517	137	58	ℋ	ℋ	NOUN
iajs-2517	137	59	)	)	PUNCT
iajs-2517	137	60	∩	∩	NOUN
iajs-2517	137	61	(	(	PUNCT
iajs-2517	137	62	𝒱2′	𝒱2′	ADJ
iajs-2517	137	63	,	,	PUNCT
iajs-2517	137	64	ℋ	ℋ	NOUN
iajs-2517	137	65	)	)	PUNCT
iajs-2517	137	66	)	)	PUNCT
iajs-2517	137	67	and	and	CCONJ
iajs-2517	137	68	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	137	69	∈̃	∈̃	PROPN
iajs-2517	137	70	(	(	PUNCT
iajs-2517	137	71	(	(	PUNCT
iajs-2517	137	72	𝒱2	𝒱2	NOUN
iajs-2517	137	73	,	,	PUNCT
iajs-2517	137	74	ℋ	ℋ	NOUN
iajs-2517	137	75	)	)	PUNCT
iajs-2517	137	76	∩	∩	NOUN
iajs-2517	137	77	(	(	PUNCT
iajs-2517	137	78	𝒱1′	𝒱1′	PROPN
iajs-2517	137	79	,	,	PUNCT
iajs-2517	137	80	ℋ	ℋ	NOUN
iajs-2517	137	81	)	)	PUNCT
iajs-2517	137	82	)	)	PUNCT
iajs-2517	137	83	.	.	PUNCT
iajs-2517	138	1	proof	proof	NOUN
iajs-2517	138	2	:	:	PUNCT
iajs-2517	138	3	(	(	PUNCT
iajs-2517	138	4	⇒	⇒	NOUN
iajs-2517	138	5	)	)	PUNCT
iajs-2517	138	6	let	let	VERB
iajs-2517	138	7	𝒽	𝒽	PRON
iajs-2517	138	8	,	,	PUNCT
iajs-2517	138	9	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	138	10	∈̃	∈̃	PROPN
iajs-2517	138	11	�	�	PROPN
iajs-2517	138	12	̃	̃	PROPN
iajs-2517	138	13	�	�	NOUN
iajs-2517	138	14	such	such	ADJ
iajs-2517	138	15	that	that	DET
iajs-2517	138	16	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	138	17	≠	≠	PROPN
iajs-2517	138	18	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	138	19	since	since	SCONJ
iajs-2517	138	20	(	(	PUNCT
iajs-2517	138	21	𝜒	𝜒	X
iajs-2517	138	22	,	,	PUNCT
iajs-2517	138	23	𝒯	𝒯	PROPN
iajs-2517	138	24	,	,	PUNCT
iajs-2517	138	25	ℋ	ℋ	PROPN
iajs-2517	138	26	,	,	PUNCT
iajs-2517	138	27	ℐ	ℐ	PROPN
iajs-2517	138	28	)	)	PUNCT
iajs-2517	138	29	is	be	AUX
iajs-2517	138	30	a	a	DET
iajs-2517	138	31	soft𝒯1-𝑠𝑝𝑎𝑐𝑒	soft𝒯1-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	138	32	,	,	PUNCT
iajs-2517	138	33	then	then	ADV
iajs-2517	138	34	∃	∃	PROPN
iajs-2517	138	35	(	(	PUNCT
iajs-2517	138	36	ơ1	ơ1	PROPN
iajs-2517	138	37	,	,	PUNCT
iajs-2517	138	38	ℋ	ℋ	NOUN
iajs-2517	138	39	)	)	PUNCT
iajs-2517	138	40	,	,	PUNCT
iajs-2517	138	41	(	(	PUNCT
iajs-2517	138	42	ơ2	ơ2	NOUN
iajs-2517	138	43	,	,	PUNCT
iajs-2517	138	44	ℋ	ℋ	PROPN
iajs-2517	138	45	)	)	PUNCT
iajs-2517	138	46	∈	∈	NOUN
iajs-2517	138	47	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	NUM
iajs-2517	138	48	whenever	whenever	ADV
iajs-2517	138	49	,	,	PUNCT
iajs-2517	138	50	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	138	51	∈̃	∈̃	NOUN
iajs-2517	138	52	(	(	PUNCT
iajs-2517	138	53	(	(	PUNCT
iajs-2517	138	54	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	138	55	)	)	PUNCT
iajs-2517	138	56	–	–	PUNCT
iajs-2517	138	57	(	(	PUNCT
iajs-2517	138	58	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	138	59	)	)	PUNCT
iajs-2517	138	60	)	)	PUNCT
iajs-2517	138	61	and	and	CCONJ
iajs-2517	138	62	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	138	63	∈̃	∈̃	PROPN
iajs-2517	138	64	(	(	PUNCT
iajs-2517	138	65	(	(	PUNCT
iajs-2517	138	66	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	138	67	)	)	PUNCT
iajs-2517	138	68	–	–	PUNCT
iajs-2517	138	69	(	(	PUNCT
iajs-2517	138	70	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	138	71	)	)	PUNCT
iajs-2517	138	72	)	)	PUNCT
iajs-2517	138	73	.	.	PUNCT
iajs-2517	139	1	then	then	ADV
iajs-2517	139	2	there	there	PRON
iajs-2517	139	3	is	be	VERB
iajs-2517	139	4	a	a	DET
iajs-2517	139	5	𝑠ℐ𝑠𝑔-closed	𝑠ℐ𝑠𝑔-close	VERB
iajs-2517	139	6	sets	set	NOUN
iajs-2517	139	7	(	(	PUNCT
iajs-2517	139	8	𝒱1	𝒱1	NOUN
iajs-2517	139	9	,	,	PUNCT
iajs-2517	139	10	ℋ	ℋ	PROPN
iajs-2517	139	11	)	)	PUNCT
iajs-2517	139	12	,	,	PUNCT
iajs-2517	139	13	(	(	PUNCT
iajs-2517	139	14	𝒱2	𝒱2	NOUN
iajs-2517	139	15	,	,	PUNCT
iajs-2517	139	16	ℋ	ℋ	NOUN
iajs-2517	139	17	)	)	PUNCT
iajs-2517	139	18	whenever	whenever	ADV
iajs-2517	139	19	,	,	PUNCT
iajs-2517	139	20	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	139	21	∈̃	∈̃	NOUN
iajs-2517	139	22	(	(	PUNCT
iajs-2517	139	23	(	(	PUNCT
iajs-2517	139	24	𝒱1	𝒱1	NOUN
iajs-2517	139	25	,	,	PUNCT
iajs-2517	139	26	ℋ	ℋ	PROPN
iajs-2517	139	27	)	)	PUNCT
iajs-2517	139	28	–	–	PUNCT
iajs-2517	139	29	(	(	PUNCT
iajs-2517	139	30	𝒱2	𝒱2	NOUN
iajs-2517	139	31	,	,	PUNCT
iajs-2517	139	32	ℋ	ℋ	NOUN
iajs-2517	139	33	)	)	PUNCT
iajs-2517	139	34	)	)	PUNCT
iajs-2517	139	35	and	and	CCONJ
iajs-2517	139	36	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	139	37	∈̃	∈̃	PROPN
iajs-2517	139	38	(	(	PUNCT
iajs-2517	139	39	(	(	PUNCT
iajs-2517	139	40	𝒱2	𝒱2	NOUN
iajs-2517	139	41	,	,	PUNCT
iajs-2517	139	42	ℋ	ℋ	PROPN
iajs-2517	139	43	)	)	PUNCT
iajs-2517	139	44	–	–	PUNCT
iajs-2517	139	45	(	(	PUNCT
iajs-2517	139	46	𝒱1	𝒱1	NOUN
iajs-2517	139	47	,	,	PUNCT
iajs-2517	139	48	ℋ	ℋ	PROPN
iajs-2517	139	49	)	)	PUNCT
iajs-2517	139	50	)	)	PUNCT
iajs-2517	139	51	where	where	SCONJ
iajs-2517	139	52	,	,	PUNCT
iajs-2517	139	53	(	(	PUNCT
iajs-2517	139	54	𝜒	𝜒	X
iajs-2517	139	55	̃	̃	NOUN
iajs-2517	139	56	–	–	PUNCT
iajs-2517	139	57	(	(	PUNCT
iajs-2517	139	58	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	139	59	)	)	PUNCT
iajs-2517	139	60	)	)	PUNCT
iajs-2517	140	1	=	=	PRON
iajs-2517	140	2	(	(	PUNCT
iajs-2517	140	3	𝒱2	𝒱2	NOUN
iajs-2517	140	4	,	,	PUNCT
iajs-2517	140	5	ℋ	ℋ	PROPN
iajs-2517	140	6	)	)	PUNCT
iajs-2517	140	7	and	and	CCONJ
iajs-2517	140	8	(	(	PUNCT
iajs-2517	140	9	𝜒	𝜒	X
iajs-2517	140	10	̃	̃	PROPN
iajs-2517	140	11	–	–	PUNCT
iajs-2517	140	12	(	(	PUNCT
iajs-2517	140	13	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	140	14	)	)	PUNCT
iajs-2517	140	15	)	)	PUNCT
iajs-2517	140	16	127	127	NUM
iajs-2517	140	17	ibn	ibn	PROPN
iajs-2517	140	18	al	al	PROPN
iajs-2517	140	19	-	-	PUNCT
iajs-2517	140	20	haitham	haitham	PROPN
iajs-2517	140	21	jour	jour	X
iajs-2517	140	22	.	.	PROPN
iajs-2517	141	1	for	for	ADP
iajs-2517	141	2	pure	pure	ADJ
iajs-2517	141	3	&	&	CCONJ
iajs-2517	141	4	appl	appl	PROPN
iajs-2517	141	5	.	.	PUNCT
iajs-2517	142	1	sci	sci	PROPN
iajs-2517	142	2	.	.	PROPN
iajs-2517	143	1	33	33	NUM
iajs-2517	143	2	(	(	PUNCT
iajs-2517	143	3	4	4	NUM
iajs-2517	143	4	)	)	PUNCT
iajs-2517	143	5	2020	2020	NUM
iajs-2517	143	6	=	=	SYM
iajs-2517	143	7	(	(	PUNCT
iajs-2517	143	8	𝒱1	𝒱1	PROPN
iajs-2517	143	9	,	,	PUNCT
iajs-2517	143	10	ℋ	ℋ	PROPN
iajs-2517	143	11	)	)	PUNCT
iajs-2517	143	12	.	.	PUNCT
iajs-2517	144	1	then	then	ADV
iajs-2517	144	2	there	there	PRON
iajs-2517	144	3	are	be	VERB
iajs-2517	144	4	two	two	NUM
iajs-2517	144	5	𝑠ℐ𝑠𝑔-closed	𝑠ℐ𝑠𝑔-close	VERB
iajs-2517	144	6	sets	set	NOUN
iajs-2517	144	7	(	(	PUNCT
iajs-2517	144	8	𝒱1	𝒱1	NOUN
iajs-2517	144	9	,	,	PUNCT
iajs-2517	144	10	ℋ	ℋ	PROPN
iajs-2517	144	11	)	)	PUNCT
iajs-2517	144	12	,	,	PUNCT
iajs-2517	144	13	(	(	PUNCT
iajs-2517	144	14	𝒱2	𝒱2	NOUN
iajs-2517	144	15	,	,	PUNCT
iajs-2517	144	16	ℋ	ℋ	NOUN
iajs-2517	144	17	)	)	PUNCT
iajs-2517	144	18	such	such	ADJ
iajs-2517	144	19	that	that	SCONJ
iajs-2517	144	20	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	144	21	∈̃	∈̃	NOUN
iajs-2517	144	22	(	(	PUNCT
iajs-2517	144	23	(	(	PUNCT
iajs-2517	144	24	𝒱1	𝒱1	NOUN
iajs-2517	144	25	,	,	PUNCT
iajs-2517	144	26	ℋ	ℋ	NOUN
iajs-2517	144	27	)	)	PUNCT
iajs-2517	144	28	∩	∩	NOUN
iajs-2517	144	29	(	(	PUNCT
iajs-2517	144	30	𝒱2′	𝒱2′	ADJ
iajs-2517	144	31	,	,	PUNCT
iajs-2517	144	32	ℋ	ℋ	NOUN
iajs-2517	144	33	)	)	PUNCT
iajs-2517	144	34	)	)	PUNCT
iajs-2517	144	35	and	and	CCONJ
iajs-2517	144	36	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	144	37	∈̃	∈̃	PROPN
iajs-2517	144	38	(	(	PUNCT
iajs-2517	144	39	(	(	PUNCT
iajs-2517	144	40	𝒱2	𝒱2	NOUN
iajs-2517	144	41	,	,	PUNCT
iajs-2517	144	42	ℋ	ℋ	NOUN
iajs-2517	144	43	)	)	PUNCT
iajs-2517	144	44	∩	∩	NOUN
iajs-2517	144	45	(	(	PUNCT
iajs-2517	144	46	𝒱1′	𝒱1′	PROPN
iajs-2517	144	47	,	,	PUNCT
iajs-2517	144	48	ℋ	ℋ	NOUN
iajs-2517	144	49	)	)	PUNCT
iajs-2517	144	50	)	)	PUNCT
iajs-2517	144	51	.	.	PUNCT
iajs-2517	145	1	(	(	PUNCT
iajs-2517	145	2	⇐	⇐	INTJ
iajs-2517	145	3	)	)	PUNCT
iajs-2517	145	4	let	let	VERB
iajs-2517	145	5	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	145	6	,	,	PUNCT
iajs-2517	145	7	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	145	8	∈̃	∈̃	PROPN
iajs-2517	145	9	�	�	PROPN
iajs-2517	145	10	̃	̃	PROPN
iajs-2517	145	11	�	�	NOUN
iajs-2517	145	12	such	such	ADJ
iajs-2517	145	13	that	that	DET
iajs-2517	145	14	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	145	15	≠	≠	PROPN
iajs-2517	145	16	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	145	17	and	and	CCONJ
iajs-2517	145	18	there	there	PRON
iajs-2517	145	19	are	be	VERB
iajs-2517	145	20	two	two	NUM
iajs-2517	145	21	𝑠ℐ𝑠𝑔-closed	𝑠ℐ𝑠𝑔-close	VERB
iajs-2517	145	22	sets	set	NOUN
iajs-2517	145	23	(	(	PUNCT
iajs-2517	145	24	𝒱1	𝒱1	NOUN
iajs-2517	145	25	,	,	PUNCT
iajs-2517	145	26	ℋ	ℋ	PROPN
iajs-2517	145	27	)	)	PUNCT
iajs-2517	145	28	,	,	PUNCT
iajs-2517	145	29	(	(	PUNCT
iajs-2517	145	30	𝒱2	𝒱2	NOUN
iajs-2517	145	31	,	,	PUNCT
iajs-2517	145	32	ℋ	ℋ	NOUN
iajs-2517	145	33	)	)	PUNCT
iajs-2517	145	34	such	such	ADJ
iajs-2517	145	35	that	that	SCONJ
iajs-2517	145	36	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	145	37	∈̃	∈̃	NOUN
iajs-2517	145	38	(	(	PUNCT
iajs-2517	145	39	(	(	PUNCT
iajs-2517	145	40	𝒱1	𝒱1	NOUN
iajs-2517	145	41	,	,	PUNCT
iajs-2517	145	42	ℋ	ℋ	PROPN
iajs-2517	145	43	)	)	PUNCT
iajs-2517	145	44	∩̃	∩̃	PUNCT
iajs-2517	145	45	(	(	PUNCT
iajs-2517	145	46	𝒱2′	𝒱2′	ADJ
iajs-2517	145	47	,	,	PUNCT
iajs-2517	145	48	ℋ	ℋ	NOUN
iajs-2517	145	49	)	)	PUNCT
iajs-2517	145	50	)	)	PUNCT
iajs-2517	145	51	and	and	CCONJ
iajs-2517	145	52	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	145	53	∈̃	∈̃	PROPN
iajs-2517	145	54	(	(	PUNCT
iajs-2517	145	55	(	(	PUNCT
iajs-2517	145	56	𝒱2	𝒱2	NOUN
iajs-2517	145	57	,	,	PUNCT
iajs-2517	145	58	ℋ	ℋ	PROPN
iajs-2517	145	59	)	)	PUNCT
iajs-2517	145	60	∩̃	∩̃	PUNCT
iajs-2517	145	61	(	(	PUNCT
iajs-2517	145	62	𝒱1′	𝒱1′	PROPN
iajs-2517	145	63	,	,	PUNCT
iajs-2517	145	64	ℋ	ℋ	NOUN
iajs-2517	145	65	)	)	PUNCT
iajs-2517	145	66	)	)	PUNCT
iajs-2517	145	67	.then	.then	VERB
iajs-2517	146	1	there	there	PRON
iajs-2517	146	2	are	be	VERB
iajs-2517	146	3	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	146	4	sets	set	NOUN
iajs-2517	146	5	(	(	PUNCT
iajs-2517	146	6	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	146	7	)	)	PUNCT
iajs-2517	146	8	,	,	PUNCT
iajs-2517	146	9	(	(	PUNCT
iajs-2517	146	10	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	146	11	)	)	PUNCT
iajs-2517	146	12	whenever	whenever	SCONJ
iajs-2517	146	13	,	,	PUNCT
iajs-2517	146	14	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	146	15	∈̃	∈̃	NOUN
iajs-2517	146	16	(	(	PUNCT
iajs-2517	146	17	(	(	PUNCT
iajs-2517	146	18	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	146	19	)	)	PUNCT
iajs-2517	146	20	–	–	PUNCT
iajs-2517	146	21	(	(	PUNCT
iajs-2517	146	22	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	146	23	)	)	PUNCT
iajs-2517	146	24	)	)	PUNCT
iajs-2517	146	25	and	and	CCONJ
iajs-2517	146	26	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	146	27	∈̃	∈̃	PROPN
iajs-2517	146	28	(	(	PUNCT
iajs-2517	146	29	(	(	PUNCT
iajs-2517	146	30	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	146	31	)	)	PUNCT
iajs-2517	146	32	–	–	PUNCT
iajs-2517	146	33	(	(	PUNCT
iajs-2517	146	34	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	146	35	)	)	PUNCT
iajs-2517	146	36	)	)	PUNCT
iajs-2517	146	37	where	where	SCONJ
iajs-2517	146	38	,	,	PUNCT
iajs-2517	146	39	(	(	PUNCT
iajs-2517	146	40	𝜒	𝜒	X
iajs-2517	146	41	̃	̃	NOUN
iajs-2517	146	42	–	–	PUNCT
iajs-2517	146	43	(	(	PUNCT
iajs-2517	146	44	𝒱2	𝒱2	NOUN
iajs-2517	146	45	,	,	PUNCT
iajs-2517	146	46	ℋ	ℋ	NOUN
iajs-2517	146	47	)	)	PUNCT
iajs-2517	146	48	)	)	PUNCT
iajs-2517	147	1	=	=	PRON
iajs-2517	147	2	(	(	PUNCT
iajs-2517	147	3	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	147	4	)	)	PUNCT
iajs-2517	147	5	and	and	CCONJ
iajs-2517	147	6	(	(	PUNCT
iajs-2517	147	7	𝜒	𝜒	X
iajs-2517	147	8	̃	̃	PROPN
iajs-2517	147	9	–	–	PUNCT
iajs-2517	147	10	(	(	PUNCT
iajs-2517	147	11	𝒱1	𝒱1	NOUN
iajs-2517	147	12	,	,	PUNCT
iajs-2517	147	13	ℋ	ℋ	PROPN
iajs-2517	147	14	)	)	PUNCT
iajs-2517	147	15	)	)	PUNCT
iajs-2517	147	16	=	=	SYM
iajs-2517	147	17	(	(	PUNCT
iajs-2517	147	18	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	147	19	)	)	PUNCT
iajs-2517	147	20	.	.	PUNCT
iajs-2517	148	1	definition	definition	NOUN
iajs-2517	148	2	4.10	4.10	NUM
iajs-2517	148	3	.	.	PUNCT
iajs-2517	149	1	(	(	PUNCT
iajs-2517	149	2	𝜒	𝜒	X
iajs-2517	149	3	,	,	PUNCT
iajs-2517	149	4	𝒯	𝒯	PROPN
iajs-2517	149	5	,	,	PUNCT
iajs-2517	149	6	ℋ	ℋ	PROPN
iajs-2517	149	7	,	,	PUNCT
iajs-2517	149	8	ℐ	ℐ	NUM
iajs-2517	149	9	)	)	PUNCT
iajs-2517	149	10	is	be	AUX
iajs-2517	149	11	a	a	DET
iajs-2517	149	12	soft-ℐ-semi-𝑔-𝒯2	soft-ℐ-semi-𝑔-𝒯2	NOUN
iajs-2517	149	13	-	-	NOUN
iajs-2517	149	14	space	space	NOUN
iajs-2517	149	15	(	(	PUNCT
iajs-2517	149	16	briefly	briefly	ADV
iajs-2517	149	17	𝑠ℐ𝑠𝑔-𝒯2	𝑠ℐ𝑠𝑔-𝒯2	NOUN
iajs-2517	149	18	-	-	PUNCT
iajs-2517	149	19	space	space	NOUN
iajs-2517	149	20	)	)	PUNCT
iajs-2517	149	21	.if	.if	PUNCT
iajs-2517	150	1	for	for	ADP
iajs-2517	150	2	any	any	DET
iajs-2517	150	3	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	150	4	≠	≠	PROPN
iajs-2517	150	5	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	150	6	there	there	PRON
iajs-2517	150	7	are	be	VERB
iajs-2517	150	8	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	150	9	sets	set	NOUN
iajs-2517	150	10	(	(	PUNCT
iajs-2517	150	11	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	150	12	)	)	PUNCT
iajs-2517	150	13	,	,	PUNCT
iajs-2517	150	14	(	(	PUNCT
iajs-2517	150	15	𝔒2,ℋ	𝔒2,ℋ	NOUN
iajs-2517	150	16	)	)	PUNCT
iajs-2517	150	17	such	such	ADJ
iajs-2517	150	18	that	that	DET
iajs-2517	150	19	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	150	20	∈̃	∈̃	NOUN
iajs-2517	150	21	(	(	PUNCT
iajs-2517	150	22	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	150	23	)	)	PUNCT
iajs-2517	150	24	,	,	PUNCT
iajs-2517	150	25	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	150	26	∈̃	∈̃	PROPN
iajs-2517	150	27	(	(	PUNCT
iajs-2517	150	28	𝔒2,ℋ	𝔒2,ℋ	PROPN
iajs-2517	150	29	)	)	PUNCT
iajs-2517	150	30	and	and	CCONJ
iajs-2517	150	31	(	(	PUNCT
iajs-2517	150	32	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	150	33	)	)	PUNCT
iajs-2517	150	34	∩(𝔒2,ℋ	∩(𝔒2,ℋ	NUM
iajs-2517	150	35	)	)	PUNCT
iajs-2517	151	1	=	=	NOUN
iajs-2517	151	2	{	{	PUNCT
iajs-2517	151	3	∅̃	∅̃	NOUN
iajs-2517	151	4	}	}	PUNCT
iajs-2517	151	5	.	.	PUNCT
iajs-2517	152	1	example	example	NOUN
iajs-2517	153	1	4.11	4.11	NUM
iajs-2517	153	2	.	.	PUNCT
iajs-2517	154	1	a	a	DET
iajs-2517	154	2	space	space	NOUN
iajs-2517	154	3	(	(	PUNCT
iajs-2517	154	4	𝜒	𝜒	X
iajs-2517	154	5	,	,	PUNCT
iajs-2517	154	6	𝒯	𝒯	PROPN
iajs-2517	154	7	,	,	PUNCT
iajs-2517	154	8	ℋ	ℋ	PROPN
iajs-2517	154	9	,	,	PUNCT
iajs-2517	154	10	ℐ	ℐ	PROPN
iajs-2517	154	11	)	)	PUNCT
iajs-2517	154	12	;	;	PUNCT
iajs-2517	154	13	χ	χ	X
iajs-2517	154	14	=	=	PUNCT
iajs-2517	154	15	{	{	PUNCT
iajs-2517	154	16	1	1	NUM
iajs-2517	154	17	,	,	PUNCT
iajs-2517	154	18	2	2	NUM
iajs-2517	154	19	,	,	PUNCT
iajs-2517	154	20	3	3	NUM
iajs-2517	154	21	}	}	PUNCT
iajs-2517	154	22	,	,	PUNCT
iajs-2517	154	23	𝒯	𝒯	PROPN
iajs-2517	154	24	=	=	PRON
iajs-2517	154	25	{	{	PUNCT
iajs-2517	154	26	∅̃	∅̃	NOUN
iajs-2517	154	27	,	,	PUNCT
iajs-2517	154	28	�	�	PROPN
iajs-2517	154	29	̃	̃	PROPN
iajs-2517	154	30	�	�	PROPN
iajs-2517	154	31	}	}	PUNCT
iajs-2517	154	32	and	and	CCONJ
iajs-2517	154	33	ℐ	ℐ	NOUN
iajs-2517	154	34	=	=	PUNCT
iajs-2517	154	35	şş(χ)𝓗	şş(χ)𝓗	VERB
iajs-2517	154	36	.then	.then	PUNCT
iajs-2517	155	1	şş𝑂(𝜒)𝓗	şş𝑂(𝜒)𝓗	PROPN
iajs-2517	155	2	=	=	PROPN
iajs-2517	155	3	𝒯.	𝒯.	PROPN
iajs-2517	155	4	so	so	ADV
iajs-2517	155	5	,	,	PUNCT
iajs-2517	155	6	𝑠ℐ𝑠𝑔-𝑐(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑐(𝜒)𝓗	NOUN
iajs-2517	155	7	=	=	NOUN
iajs-2517	155	8	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	PROPN
iajs-2517	155	9	=	=	PUNCT
iajs-2517	155	10	şş(𝜒)𝓗.	şş(𝜒)𝓗.	PROPN
iajs-2517	155	11	then	then	ADV
iajs-2517	155	12	(	(	PUNCT
iajs-2517	155	13	𝜒	𝜒	X
iajs-2517	155	14	,	,	PUNCT
iajs-2517	155	15	𝒯	𝒯	PROPN
iajs-2517	155	16	,	,	PUNCT
iajs-2517	155	17	ℋ	ℋ	PROPN
iajs-2517	155	18	,	,	PUNCT
iajs-2517	155	19	ℐ	ℐ	PROPN
iajs-2517	155	20	)	)	PUNCT
iajs-2517	155	21	is	be	AUX
iajs-2517	155	22	a	a	DET
iajs-2517	155	23	𝑠ℐ𝑠𝑔-𝒯2space	𝑠ℐ𝑠𝑔-𝒯2space	NOUN
iajs-2517	155	24	.	.	PUNCT
iajs-2517	156	1	remark	remark	PROPN
iajs-2517	156	2	4.12	4.12	NUM
iajs-2517	156	3	.	.	PUNCT
iajs-2517	157	1	if	if	SCONJ
iajs-2517	157	2	(	(	PUNCT
iajs-2517	157	3	𝜒	𝜒	X
iajs-2517	157	4	,	,	PUNCT
iajs-2517	157	5	𝒯	𝒯	PROPN
iajs-2517	157	6	,	,	PUNCT
iajs-2517	157	7	ℋ	ℋ	PROPN
iajs-2517	157	8	)	)	PUNCT
iajs-2517	157	9	is	be	AUX
iajs-2517	157	10	a	a	DET
iajs-2517	157	11	soft-𝒯2-𝑠𝑝𝑎𝑐𝑒	soft-𝒯2-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	157	12	,	,	PUNCT
iajs-2517	157	13	then	then	ADV
iajs-2517	157	14	(	(	PUNCT
iajs-2517	157	15	𝜒	𝜒	X
iajs-2517	157	16	,	,	PUNCT
iajs-2517	157	17	𝒯	𝒯	PROPN
iajs-2517	157	18	,	,	PUNCT
iajs-2517	157	19	ℋ	ℋ	PROPN
iajs-2517	157	20	,	,	PUNCT
iajs-2517	157	21	ℐ	ℐ	NUM
iajs-2517	157	22	)	)	PUNCT
iajs-2517	157	23	is	be	AUX
iajs-2517	157	24	a	a	DET
iajs-2517	157	25	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒.	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒.	ADJ
iajs-2517	157	26	proof	proof	NOUN
iajs-2517	157	27	:	:	PUNCT
iajs-2517	157	28	let	let	VERB
iajs-2517	157	29	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	157	30	,	,	PUNCT
iajs-2517	157	31	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	157	32	∈̃	∈̃	PROPN
iajs-2517	157	33	�	�	PROPN
iajs-2517	157	34	̃	̃	PROPN
iajs-2517	157	35	�	�	NOUN
iajs-2517	157	36	whenever	whenever	ADV
iajs-2517	157	37	,	,	PUNCT
iajs-2517	157	38	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	157	39	≠	≠	PROPN
iajs-2517	157	40	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	157	41	since	since	SCONJ
iajs-2517	157	42	(	(	PUNCT
iajs-2517	157	43	𝜒	𝜒	X
iajs-2517	157	44	,	,	PUNCT
iajs-2517	157	45	𝒯	𝒯	PROPN
iajs-2517	157	46	,	,	PUNCT
iajs-2517	157	47	ℋ	ℋ	PROPN
iajs-2517	157	48	,	,	PUNCT
iajs-2517	157	49	ℐ	ℐ	NUM
iajs-2517	157	50	)	)	PUNCT
iajs-2517	157	51	is	be	AUX
iajs-2517	157	52	a	a	DET
iajs-2517	157	53	soft-𝒯2-𝑠𝑝𝑎𝑐𝑒	soft-𝒯2-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	157	54	,	,	PUNCT
iajs-2517	157	55	then	then	ADV
iajs-2517	157	56	∃	∃	PROPN
iajs-2517	157	57	(	(	PUNCT
iajs-2517	157	58	𝔒1,ℋ),(𝔒2,ℋ	𝔒1,ℋ),(𝔒2,ℋ	NOUN
iajs-2517	157	59	)	)	PUNCT
iajs-2517	158	1	∈	∈	PROPN
iajs-2517	158	2	𝒯	𝒯	PROPN
iajs-2517	158	3	such	such	ADJ
iajs-2517	158	4	that	that	DET
iajs-2517	158	5	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	158	6	∈̃	∈̃	NOUN
iajs-2517	158	7	(	(	PUNCT
iajs-2517	158	8	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	158	9	)	)	PUNCT
iajs-2517	158	10	,	,	PUNCT
iajs-2517	158	11	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	158	12	∈̃	∈̃	PROPN
iajs-2517	158	13	(	(	PUNCT
iajs-2517	158	14	𝔒2,ℋ	𝔒2,ℋ	PROPN
iajs-2517	158	15	)	)	PUNCT
iajs-2517	158	16	and	and	CCONJ
iajs-2517	158	17	(	(	PUNCT
iajs-2517	158	18	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	158	19	)	)	PUNCT
iajs-2517	158	20	∩̃(𝔒2,ℋ	∩̃(𝔒2,ℋ	NOUN
iajs-2517	158	21	)	)	PUNCT
iajs-2517	159	1	=	=	PRON
iajs-2517	159	2	{	{	PUNCT
iajs-2517	159	3	∅̃	∅̃	NOUN
iajs-2517	159	4	}	}	PUNCT
iajs-2517	159	5	,	,	PUNCT
iajs-2517	159	6	by	by	ADP
iajs-2517	159	7	remark	remark	NOUN
iajs-2517	159	8	3.3	3.3	NUM
iajs-2517	159	9	,	,	PUNCT
iajs-2517	159	10	there	there	PRON
iajs-2517	159	11	are	be	VERB
iajs-2517	159	12	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	159	13	sets	set	NOUN
iajs-2517	159	14	(	(	PUNCT
iajs-2517	159	15	𝔒1,ℋ),(ơ2,ℋ	𝔒1,ℋ),(ơ2,ℋ	NUM
iajs-2517	159	16	)	)	PUNCT
iajs-2517	159	17	,	,	PUNCT
iajs-2517	159	18	such	such	ADJ
iajs-2517	159	19	that	that	SCONJ
iajs-2517	159	20	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	159	21	∈̃	∈̃	NOUN
iajs-2517	159	22	(	(	PUNCT
iajs-2517	159	23	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	159	24	)	)	PUNCT
iajs-2517	159	25	,	,	PUNCT
iajs-2517	159	26	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	159	27	∈̃	∈̃	PROPN
iajs-2517	159	28	(	(	PUNCT
iajs-2517	159	29	𝔒2,ℋ	𝔒2,ℋ	PROPN
iajs-2517	159	30	)	)	PUNCT
iajs-2517	159	31	and	and	CCONJ
iajs-2517	159	32	(	(	PUNCT
iajs-2517	159	33	𝔒1,ℋ	𝔒1,ℋ	NUM
iajs-2517	159	34	)	)	PUNCT
iajs-2517	159	35	∩̃(𝔒2,ℋ	∩̃(𝔒2,ℋ	NOUN
iajs-2517	159	36	)	)	PUNCT
iajs-2517	160	1	=	=	PRON
iajs-2517	160	2	{	{	PUNCT
iajs-2517	160	3	∅̃	∅̃	NOUN
iajs-2517	160	4	}	}	PUNCT
iajs-2517	160	5	.	.	PUNCT
iajs-2517	161	1	remark	remark	NOUN
iajs-2517	161	2	4.13	4.13	NUM
iajs-2517	161	3	.	.	PUNCT
iajs-2517	162	1	if	if	SCONJ
iajs-2517	162	2	(	(	PUNCT
iajs-2517	162	3	𝜒	𝜒	X
iajs-2517	162	4	,	,	PUNCT
iajs-2517	162	5	𝒯	𝒯	PROPN
iajs-2517	162	6	,	,	PUNCT
iajs-2517	162	7	ℋ	ℋ	PROPN
iajs-2517	162	8	,	,	PUNCT
iajs-2517	162	9	ℐ	ℐ	PROPN
iajs-2517	162	10	)	)	PUNCT
iajs-2517	162	11	is	be	AUX
iajs-2517	162	12	a	a	DET
iajs-2517	162	13	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	162	14	then	then	ADV
iajs-2517	162	15	it	it	PRON
iajs-2517	162	16	is	be	AUX
iajs-2517	162	17	a	a	DET
iajs-2517	162	18	𝑠ℐ𝑠𝑔-𝒯1-𝑠𝑝𝑎𝑐𝑒.	𝑠ℐ𝑠𝑔-𝒯1-𝑠𝑝𝑎𝑐𝑒.	ADJ
iajs-2517	162	19	proof	proof	NOUN
iajs-2517	162	20	:	:	PUNCT
iajs-2517	162	21	let	let	VERB
iajs-2517	162	22	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	162	23	,	,	PUNCT
iajs-2517	162	24	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	162	25	∈̃	∈̃	PROPN
iajs-2517	162	26	�	�	PROPN
iajs-2517	162	27	̃	̃	PROPN
iajs-2517	162	28	�	�	NOUN
iajs-2517	162	29	whenever	whenever	ADV
iajs-2517	162	30	,	,	PUNCT
iajs-2517	162	31	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	162	32	≠	≠	PROPN
iajs-2517	162	33	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	162	34	since	since	SCONJ
iajs-2517	162	35	(	(	PUNCT
iajs-2517	162	36	𝜒	𝜒	X
iajs-2517	162	37	,	,	PUNCT
iajs-2517	162	38	𝒯	𝒯	PROPN
iajs-2517	162	39	,	,	PUNCT
iajs-2517	162	40	ℋ	ℋ	PROPN
iajs-2517	162	41	,	,	PUNCT
iajs-2517	162	42	ℐ	ℐ	PROPN
iajs-2517	162	43	)	)	PUNCT
iajs-2517	162	44	is	be	AUX
iajs-2517	162	45	a	a	DET
iajs-2517	162	46	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	162	47	,	,	PUNCT
iajs-2517	162	48	then	then	ADV
iajs-2517	162	49	there	there	PRON
iajs-2517	162	50	are	be	VERB
iajs-2517	162	51	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	162	52	sets	set	NOUN
iajs-2517	162	53	(	(	PUNCT
iajs-2517	162	54	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	162	55	)	)	PUNCT
iajs-2517	162	56	,	,	PUNCT
iajs-2517	162	57	(	(	PUNCT
iajs-2517	162	58	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	162	59	)	)	PUNCT
iajs-2517	162	60	such	such	ADJ
iajs-2517	162	61	that	that	SCONJ
iajs-2517	162	62	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	162	63	∈̃	∈̃	PROPN
iajs-2517	162	64	(	(	PUNCT
iajs-2517	162	65	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	162	66	)	)	PUNCT
iajs-2517	162	67	,	,	PUNCT
iajs-2517	162	68	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	162	69	∈̃	∈̃	PROPN
iajs-2517	162	70	(	(	PUNCT
iajs-2517	162	71	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	162	72	)	)	PUNCT
iajs-2517	162	73	and	and	CCONJ
iajs-2517	162	74	(	(	PUNCT
iajs-2517	162	75	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	162	76	)	)	PUNCT
iajs-2517	162	77	∩(ơ2,ℋ	∩(ơ2,ℋ	NUM
iajs-2517	162	78	)	)	PUNCT
iajs-2517	163	1	=	=	PRON
iajs-2517	163	2	{	{	PUNCT
iajs-2517	163	3	∅̃	∅̃	NOUN
iajs-2517	163	4	}	}	PUNCT
iajs-2517	163	5	.	.	PUNCT
iajs-2517	164	1	implies	implie	NOUN
iajs-2517	164	2	,	,	PUNCT
iajs-2517	164	3	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	164	4	∈̃	∈̃	NOUN
iajs-2517	164	5	(	(	PUNCT
iajs-2517	164	6	(	(	PUNCT
iajs-2517	164	7	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	164	8	)	)	PUNCT
iajs-2517	164	9	–	–	PUNCT
iajs-2517	164	10	(	(	PUNCT
iajs-2517	164	11	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	164	12	)	)	PUNCT
iajs-2517	164	13	)	)	PUNCT
iajs-2517	164	14	and	and	CCONJ
iajs-2517	164	15	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	164	16	∈̃	∈̃	PROPN
iajs-2517	164	17	(	(	PUNCT
iajs-2517	164	18	(	(	PUNCT
iajs-2517	164	19	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	164	20	)	)	PUNCT
iajs-2517	164	21	–	–	PUNCT
iajs-2517	164	22	(	(	PUNCT
iajs-2517	164	23	ơ1,ℋ	ơ1,ℋ	NOUN
iajs-2517	164	24	)	)	PUNCT
iajs-2517	164	25	)	)	PUNCT
iajs-2517	164	26	.	.	PUNCT
iajs-2517	165	1	the	the	DET
iajs-2517	165	2	conclusions	conclusion	NOUN
iajs-2517	165	3	in	in	ADP
iajs-2517	165	4	remark	remark	NOUN
iajs-2517	165	5	4.13	4.13	NUM
iajs-2517	165	6	,	,	PUNCT
iajs-2517	165	7	is	be	AUX
iajs-2517	165	8	not	not	PART
iajs-2517	165	9	reversible	reversible	ADJ
iajs-2517	165	10	by	by	ADP
iajs-2517	165	11	example	example	NOUN
iajs-2517	165	12	3.6	3.6	NUM
iajs-2517	165	13	.	.	PUNCT
iajs-2517	166	1	a	a	DET
iajs-2517	166	2	space	space	NOUN
iajs-2517	166	3	(	(	PUNCT
iajs-2517	166	4	𝜒	𝜒	X
iajs-2517	166	5	,	,	PUNCT
iajs-2517	166	6	𝒯	𝒯	PROPN
iajs-2517	166	7	,	,	PUNCT
iajs-2517	166	8	ℋ	ℋ	PROPN
iajs-2517	166	9	,	,	PUNCT
iajs-2517	166	10	ℐ	ℐ	PROPN
iajs-2517	166	11	)	)	PUNCT
iajs-2517	166	12	is	be	AUX
iajs-2517	166	13	a	a	DET
iajs-2517	166	14	𝑠ℐ𝑠𝑔-𝒯1	𝑠ℐ𝑠𝑔-𝒯1	NOUN
iajs-2517	166	15	-	-	NOUN
iajs-2517	166	16	space	space	NOUN
iajs-2517	166	17	.	.	PUNCT
iajs-2517	167	1	if	if	SCONJ
iajs-2517	167	2	for	for	ADP
iajs-2517	167	3	each	each	DET
iajs-2517	167	4	𝒽	𝒽	NOUN
iajs-2517	167	5	,	,	PUNCT
iajs-2517	167	6	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	167	7	∈̃	∈̃	PROPN
iajs-2517	167	8	�	�	PROPN
iajs-2517	167	9	̃	̃	PROPN
iajs-2517	167	10	�	�	PROPN
iajs-2517	167	11	and	and	CCONJ
iajs-2517	167	12	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	167	13	≠	≠	PROPN
iajs-2517	167	14	𝒽𝓝.	𝒽𝓝.	NOUN
iajs-2517	167	15	then	then	ADV
iajs-2517	167	16	there	there	PRON
iajs-2517	167	17	are	be	VERB
iajs-2517	167	18	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	167	19	sets	set	NOUN
iajs-2517	167	20	(	(	PUNCT
iajs-2517	167	21	�	�	PROPN
iajs-2517	167	22	̃	̃	NOUN
iajs-2517	167	23	�	�	PROPN
iajs-2517	167	24	–	–	PUNCT
iajs-2517	167	25	𝒰	𝒰	PROPN
iajs-2517	167	26	)	)	PUNCT
iajs-2517	167	27	,	,	PUNCT
iajs-2517	167	28	(	(	PUNCT
iajs-2517	167	29	�	�	PROPN
iajs-2517	167	30	̃	̃	NOUN
iajs-2517	167	31	�	�	PROPN
iajs-2517	167	32	–	–	PUNCT
iajs-2517	167	33	𝒱	𝒱	PROPN
iajs-2517	167	34	)	)	PUNCT
iajs-2517	167	35	whenever	whenever	ADV
iajs-2517	167	36	,	,	PUNCT
iajs-2517	167	37	,	,	PUNCT
iajs-2517	167	38	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	167	39	∈̃	∈̃	PROPN
iajs-2517	167	40	(	(	PUNCT
iajs-2517	167	41	�	�	PROPN
iajs-2517	167	42	̃	̃	NOUN
iajs-2517	167	43	�	�	PROPN
iajs-2517	167	44	–	–	PUNCT
iajs-2517	167	45	𝒱	𝒱	PROPN
iajs-2517	167	46	)	)	PUNCT
iajs-2517	167	47	,	,	PUNCT
iajs-2517	167	48	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	167	49	∉	∉	PROPN
iajs-2517	167	50	(	(	PUNCT
iajs-2517	167	51	�	�	PROPN
iajs-2517	167	52	̃	̃	PROPN
iajs-2517	167	53	�	�	PROPN
iajs-2517	167	54	–	–	PUNCT
iajs-2517	167	55	𝒱	𝒱	PROPN
iajs-2517	167	56	)	)	PUNCT
iajs-2517	167	57	and	and	CCONJ
iajs-2517	167	58	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	167	59	∉	∉	PROPN
iajs-2517	167	60	(	(	PUNCT
iajs-2517	167	61	�	�	PROPN
iajs-2517	167	62	̃	̃	PROPN
iajs-2517	167	63	�	�	PROPN
iajs-2517	167	64	–	–	PUNCT
iajs-2517	167	65	𝒰	𝒰	PROPN
iajs-2517	167	66	)	)	PUNCT
iajs-2517	167	67	,	,	PUNCT
iajs-2517	167	68	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	167	69	∈̃	∈̃	PROPN
iajs-2517	167	70	(	(	PUNCT
iajs-2517	167	71	�	�	PROPN
iajs-2517	167	72	̃	̃	NOUN
iajs-2517	167	73	�	�	PROPN
iajs-2517	167	74	–	–	PUNCT
iajs-2517	167	75	𝒰	𝒰	PROPN
iajs-2517	167	76	)	)	PUNCT
iajs-2517	167	77	and	and	CCONJ
iajs-2517	167	78	(	(	PUNCT
iajs-2517	167	79	�	�	PROPN
iajs-2517	167	80	̃	̃	PROPN
iajs-2517	167	81	�	�	PROPN
iajs-2517	167	82	–	–	PUNCT
iajs-2517	167	83	𝒱	𝒱	PROPN
iajs-2517	167	84	)	)	PUNCT
iajs-2517	167	85	⋂	⋂	PROPN
iajs-2517	167	86	(	(	PUNCT
iajs-2517	167	87	�	�	PROPN
iajs-2517	167	88	̃	̃	PROPN
iajs-2517	167	89	�	�	PROPN
iajs-2517	167	90	–	–	PUNCT
iajs-2517	167	91	𝒰	𝒰	PROPN
iajs-2517	167	92	)	)	PUNCT
iajs-2517	167	93	≠	≠	PROPN
iajs-2517	167	94	{	{	PUNCT
iajs-2517	167	95	∅}.which	∅}.which	PROPN
iajs-2517	167	96	is	be	AUX
iajs-2517	167	97	not	not	PART
iajs-2517	167	98	𝑠ℐ𝑠𝑔𝒯2	𝑠ℐ𝑠𝑔𝒯2	ADJ
iajs-2517	167	99	-	-	PUNCT
iajs-2517	167	100	space	space	NOUN
iajs-2517	167	101	.	.	PUNCT
iajs-2517	168	1	since	since	SCONJ
iajs-2517	168	2	for	for	ADP
iajs-2517	168	3	any	any	DET
iajs-2517	168	4	two	two	NUM
iajs-2517	168	5	𝑠ℐ𝑠𝑔-open	𝑠ℐ𝑠𝑔-open	ADJ
iajs-2517	168	6	sets	set	NOUN
iajs-2517	168	7	(	(	PUNCT
iajs-2517	168	8	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	168	9	)	)	PUNCT
iajs-2517	168	10	,	,	PUNCT
iajs-2517	168	11	(	(	PUNCT
iajs-2517	168	12	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	168	13	)	)	PUNCT
iajs-2517	168	14	such	such	ADJ
iajs-2517	168	15	that	that	SCONJ
iajs-2517	168	16	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	168	17	∈̃	∈̃	PROPN
iajs-2517	168	18	(	(	PUNCT
iajs-2517	168	19	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	168	20	)	)	PUNCT
iajs-2517	168	21	,	,	PUNCT
iajs-2517	168	22	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	168	23	∈̃	∈̃	PROPN
iajs-2517	168	24	(	(	PUNCT
iajs-2517	168	25	ơ2,ℋ	ơ2,ℋ	NOUN
iajs-2517	168	26	)	)	PUNCT
iajs-2517	168	27	then	then	ADV
iajs-2517	168	28	(	(	PUNCT
iajs-2517	168	29	ơ1,ℋ	ơ1,ℋ	PROPN
iajs-2517	168	30	)	)	PUNCT
iajs-2517	168	31	∩(ơ2,ℋ	∩(ơ2,ℋ	PROPN
iajs-2517	168	32	)	)	PUNCT
iajs-2517	168	33	≠	≠	PROPN
iajs-2517	168	34	∅̃	∅̃	NOUN
iajs-2517	168	35	.	.	PUNCT
iajs-2517	169	1	we	we	PRON
iajs-2517	169	2	have	have	AUX
iajs-2517	169	3	previously	previously	ADV
iajs-2517	169	4	noted	note	VERB
iajs-2517	169	5	that	that	SCONJ
iajs-2517	169	6	χ	χ	PROPN
iajs-2517	169	7	is	be	AUX
iajs-2517	169	8	a	a	PRON
iajs-2517	169	9	𝑠ℐ𝑠𝑔𝒯i-𝑠𝑝𝑎𝑐𝑒	𝑠ℐ𝑠𝑔𝒯i-𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	169	10	whenever	whenever	SCONJ
iajs-2517	169	11	it	it	PRON
iajs-2517	169	12	is	be	AUX
iajs-2517	169	13	a	a	DET
iajs-2517	169	14	𝒯i+1-𝑠𝑝𝑎𝑐𝑒	𝒯i+1-𝑠𝑝𝑎𝑐𝑒	ADJ
iajs-2517	169	15	(	(	PUNCT
iajs-2517	169	16	∀	∀	NOUN
iajs-2517	169	17	𝑖	𝑖	SYM
iajs-2517	169	18	=	=	NOUN
iajs-2517	169	19	0	0	NUM
iajs-2517	169	20	,	,	PUNCT
iajs-2517	169	21	1	1	NUM
iajs-2517	169	22	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2517	169	23	2	2	NUM
iajs-2517	169	24	)	)	PUNCT
iajs-2517	169	25	.	.	PUNCT
iajs-2517	170	1	the	the	DET
iajs-2517	170	2	opposite	opposite	NOUN
iajs-2517	170	3	is	be	AUX
iajs-2517	170	4	not	not	PART
iajs-2517	170	5	generally	generally	ADV
iajs-2517	170	6	achieved	achieve	VERB
iajs-2517	170	7	by	by	ADP
iajs-2517	170	8	example	example	NOUN
iajs-2517	170	9	below	below	ADV
iajs-2517	170	10	.	.	PUNCT
iajs-2517	171	1	example	example	NOUN
iajs-2517	171	2	4.14	4.14	NUM
iajs-2517	171	3	.	.	PUNCT
iajs-2517	172	1	(	(	PUNCT
iajs-2517	172	2	𝜒	𝜒	X
iajs-2517	172	3	,	,	PUNCT
iajs-2517	172	4	𝒯	𝒯	PROPN
iajs-2517	172	5	,	,	PUNCT
iajs-2517	172	6	ℋ	ℋ	PROPN
iajs-2517	172	7	,	,	PUNCT
iajs-2517	172	8	ℐ	ℐ	NUM
iajs-2517	172	9	)	)	PUNCT
iajs-2517	172	10	is	be	AUX
iajs-2517	172	11	a	a	DET
iajs-2517	172	12	𝑠ℐ𝑠𝑔-𝒯i	𝑠ℐ𝑠𝑔-𝒯i	NOUN
iajs-2517	172	13	-𝑠𝑝𝑎𝑐𝑒	-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	172	14	(	(	PUNCT
iajs-2517	172	15	𝑖	𝑖	SYM
iajs-2517	172	16	∈	∈	PROPN
iajs-2517	172	17	{	{	PUNCT
iajs-2517	172	18	0,1,2	0,1,2	NOUN
iajs-2517	172	19	}	}	PUNCT
iajs-2517	172	20	)	)	PUNCT
iajs-2517	172	21	,	,	PUNCT
iajs-2517	172	22	where	where	SCONJ
iajs-2517	172	23	,	,	PUNCT
iajs-2517	172	24	χ	χ	X
iajs-2517	172	25	=	=	PUNCT
iajs-2517	172	26	{	{	PUNCT
iajs-2517	172	27	1,2,3	1,2,3	NUM
iajs-2517	172	28	}	}	PUNCT
iajs-2517	172	29	,	,	PUNCT
iajs-2517	172	30	𝒯	𝒯	PROPN
iajs-2517	172	31	=	=	PRON
iajs-2517	172	32	{	{	PUNCT
iajs-2517	172	33	∅̃	∅̃	NOUN
iajs-2517	172	34	,	,	PUNCT
iajs-2517	172	35	�	�	PROPN
iajs-2517	172	36	̃	̃	PROPN
iajs-2517	172	37	�	�	PROPN
iajs-2517	172	38	}	}	PUNCT
iajs-2517	172	39	and	and	CCONJ
iajs-2517	172	40	ℐ	ℐ	NOUN
iajs-2517	172	41	=	=	NOUN
iajs-2517	172	42	şş(𝜒)𝓗	şş(𝜒)𝓗	NOUN
iajs-2517	172	43	.	.	PUNCT
iajs-2517	173	1	since	since	SCONJ
iajs-2517	173	2	,	,	PUNCT
iajs-2517	173	3	𝑠ℐ𝑠𝑔-𝑐(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑐(𝜒)𝓗	NOUN
iajs-2517	173	4	=	=	NOUN
iajs-2517	173	5	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	𝑠ℐ𝑠𝑔-𝑜(𝜒)𝓗	PROPN
iajs-2517	173	6	=	=	PUNCT
iajs-2517	173	7	şş(𝜒)𝓗.	şş(𝜒)𝓗.	NOUN
iajs-2517	173	8	but	but	CCONJ
iajs-2517	173	9	the	the	DET
iajs-2517	173	10	space	space	NOUN
iajs-2517	173	11	(	(	PUNCT
iajs-2517	173	12	𝜒	𝜒	X
iajs-2517	173	13	,	,	PUNCT
iajs-2517	173	14	𝒯	𝒯	PROPN
iajs-2517	173	15	,	,	PUNCT
iajs-2517	173	16	ℋ	ℋ	PROPN
iajs-2517	173	17	)	)	PUNCT
iajs-2517	173	18	is	be	AUX
iajs-2517	173	19	not	not	PART
iajs-2517	173	20	soft𝒯i-𝑠𝑝𝑎𝑐𝑒	soft𝒯i-𝑠𝑝𝑎𝑐𝑒	ADJ
iajs-2517	173	21	(	(	PUNCT
iajs-2517	173	22	i	i	PRON
iajs-2517	173	23	∈	∈	PROPN
iajs-2517	173	24	{	{	PUNCT
iajs-2517	173	25	0,1,2	0,1,2	NOUN
iajs-2517	173	26	}	}	PUNCT
iajs-2517	173	27	)	)	PUNCT
iajs-2517	173	28	.	.	PUNCT
iajs-2517	174	1	the	the	DET
iajs-2517	174	2	following	follow	VERB
iajs-2517	174	3	chart	chart	NOUN
iajs-2517	174	4	shows	show	VERB
iajs-2517	174	5	the	the	DET
iajs-2517	174	6	relationships	relationship	NOUN
iajs-2517	174	7	among	among	ADP
iajs-2517	174	8	the	the	DET
iajs-2517	174	9	various	various	ADJ
iajs-2517	174	10	types	type	NOUN
iajs-2517	174	11	of	of	ADP
iajs-2517	174	12	notions	notion	NOUN
iajs-2517	174	13	of	of	ADP
iajs-2517	174	14	our	our	PRON
iajs-2517	174	15	previously	previously	ADV
iajs-2517	174	16	mentioned	mention	VERB
iajs-2517	174	17	.	.	PUNCT
iajs-2517	175	1	128	128	NUM
iajs-2517	175	2	ibn	ibn	PROPN
iajs-2517	175	3	al	al	PROPN
iajs-2517	175	4	-	-	PUNCT
iajs-2517	175	5	haitham	haitham	PROPN
iajs-2517	175	6	jour	jour	X
iajs-2517	175	7	.	.	PROPN
iajs-2517	175	8	for	for	ADP
iajs-2517	175	9	pure	pure	ADJ
iajs-2517	175	10	&	&	CCONJ
iajs-2517	175	11	appl	appl	PROPN
iajs-2517	175	12	.	.	PUNCT
iajs-2517	176	1	sci	sci	PROPN
iajs-2517	176	2	.	.	PROPN
iajs-2517	177	1	33	33	NUM
iajs-2517	177	2	(	(	PUNCT
iajs-2517	177	3	4	4	NUM
iajs-2517	177	4	)	)	PUNCT
iajs-2517	177	5	2020	2020	NUM
iajs-2517	177	6	figure	figure	VERB
iajs-2517	177	7	1	1	NUM
iajs-2517	177	8	:	:	PUNCT
iajs-2517	177	9	soft𝒯i-𝑠𝑝𝑎𝑐𝑒	soft𝒯i-𝑠𝑝𝑎𝑐𝑒	PROPN
iajs-2517	177	10	5	5	NUM
iajs-2517	177	11	.	.	PUNCT
iajs-2517	177	12	games	game	NOUN
iajs-2517	177	13	in	in	ADP
iajs-2517	177	14	soft	soft	ADJ
iajs-2517	177	15	ideal	ideal	ADJ
iajs-2517	177	16	topological	topological	ADJ
iajs-2517	177	17	spaces	space	NOUN
iajs-2517	177	18	in	in	ADP
iajs-2517	177	19	this	this	DET
iajs-2517	177	20	section	section	NOUN
iajs-2517	177	21	,	,	PUNCT
iajs-2517	177	22	a	a	DET
iajs-2517	177	23	new	new	ADJ
iajs-2517	177	24	game	game	NOUN
iajs-2517	177	25	by	by	ADP
iajs-2517	177	26	linking	link	VERB
iajs-2517	177	27	them	they	PRON
iajs-2517	177	28	with	with	ADP
iajs-2517	177	29	soft	soft	ADJ
iajs-2517	177	30	separation	separation	NOUN
iajs-2517	177	31	axioms	axiom	NOUN
iajs-2517	177	32	via	via	ADP
iajs-2517	177	33	open	open	ADJ
iajs-2517	177	34	(	(	PUNCT
iajs-2517	177	35	respectively	respectively	ADV
iajs-2517	177	36	,	,	PUNCT
iajs-2517	177	37	sℐsg	sℐsg	PROPN
iajs-2517	177	38	-	-	PUNCT
iajs-2517	177	39	open	open	ADJ
iajs-2517	177	40	)	)	PUNCT
iajs-2517	177	41	sets	set	NOUN
iajs-2517	177	42	was	be	AUX
iajs-2517	177	43	inserted	insert	VERB
iajs-2517	177	44	.	.	PUNCT
iajs-2517	178	1	(	(	PUNCT
iajs-2517	178	2	respectively	respectively	ADV
iajs-2517	178	3	,	,	PUNCT
iajs-2517	178	4	χ	χ	NOUN
iajs-2517	178	5	)	)	PUNCT
iajs-2517	178	6	0𝒯(ş𝒢	0𝒯(ş𝒢	NUM
iajs-2517	178	7	,	,	PUNCT
iajs-2517	178	8	determane	determane	NOUN
iajs-2517	178	9	a	a	DET
iajs-2517	178	10	game	game	NOUN
iajs-2517	178	11	(	(	PUNCT
iajs-2517	178	12	χ	χ	NOUN
iajs-2517	178	13	,	,	PUNCT
iajs-2517	178	14	𝒯	𝒯	PROPN
iajs-2517	178	15	,	,	PUNCT
iajs-2517	178	16	ℋ	ℋ	PROPN
iajs-2517	178	17	,	,	PUNCT
iajs-2517	178	18	ℐ)for	ℐ)for	ADP
iajs-2517	178	19	a	a	DET
iajs-2517	178	20	soft	soft	ADJ
iajs-2517	178	21	ideal	ideal	ADJ
iajs-2517	178	22	space	space	NOUN
iajs-2517	178	23	definition	definition	NOUN
iajs-2517	178	24	5.1	5.1	NUM
iajs-2517	178	25	.	.	PUNCT
iajs-2517	179	1	as	as	SCONJ
iajs-2517	179	2	follows	follow	VERB
iajs-2517	179	3	:	:	PUNCT
iajs-2517	179	4	,	,	PUNCT
iajs-2517	179	5	ℐ	ℐ	PROPN
iajs-2517	179	6	)	)	PUNCT
iajs-2517	179	7	)	)	PUNCT
iajs-2517	180	1	0𝒯(ş𝒢	0𝒯(ş𝒢	NUM
iajs-2517	181	1	player	player	NOUN
iajs-2517	181	2	ⅰ	ⅰ	NOUN
iajs-2517	181	3	and	and	CCONJ
iajs-2517	181	4	player	player	NOUN
iajs-2517	181	5	ⅱ	ⅱ	PROPN
iajs-2517	181	6	are	be	AUX
iajs-2517	181	7	play	play	VERB
iajs-2517	181	8	an	an	DET
iajs-2517	181	9	inning	inning	NOUN
iajs-2517	181	10	for	for	SCONJ
iajs-2517	181	11	each	each	DET
iajs-2517	181	12	positive	positive	ADJ
iajs-2517	181	13	integer	integer	NOUN
iajs-2517	181	14	numbers	number	NOUN
iajs-2517	181	15	in	in	ADP
iajs-2517	181	16	the	the	DET
iajs-2517	181	17	𝑟-𝑡ℎ	𝑟-𝑡ℎ	PROPN
iajs-2517	181	18	inning	inne	VERB
iajs-2517	181	19	:	:	PUNCT
iajs-2517	181	20	the	the	DET
iajs-2517	181	21	first	first	ADJ
iajs-2517	181	22	step	step	NOUN
iajs-2517	181	23	,	,	PUNCT
iajs-2517	181	24	player	player	NOUN
iajs-2517	181	25	ⅰ	ⅰ	X
iajs-2517	181	26	choose	choose	VERB
iajs-2517	181	27	(	(	PUNCT
iajs-2517	181	28	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	181	29	≠	≠	PROPN
iajs-2517	181	30	(	(	PUNCT
iajs-2517	181	31	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	181	32	where	where	SCONJ
iajs-2517	181	33	,	,	PUNCT
iajs-2517	181	34	(	(	PUNCT
iajs-2517	181	35	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	181	36	,	,	PUNCT
iajs-2517	181	37	(	(	PUNCT
iajs-2517	181	38	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	181	39	∈̃	∈̃	PROPN
iajs-2517	181	40	𝜒	𝜒	NOUN
iajs-2517	181	41	.	.	PUNCT
iajs-2517	182	1	in	in	ADP
iajs-2517	182	2	the	the	DET
iajs-2517	182	3	second	second	ADJ
iajs-2517	182	4	step	step	NOUN
iajs-2517	182	5	,	,	PUNCT
iajs-2517	182	6	player	player	NOUN
iajs-2517	182	7	ⅱ	ⅱ	PROPN
iajs-2517	182	8	chooses	choose	VERB
iajs-2517	182	9	ℬ𝑟	ℬ𝑟	PROPN
iajs-2517	182	10	a	a	DET
iajs-2517	182	11	soft	soft	ADJ
iajs-2517	182	12	open	open	ADJ
iajs-2517	182	13	(	(	PUNCT
iajs-2517	182	14	respectively	respectively	ADV
iajs-2517	182	15	sℐsg	sℐsg	PROPN
iajs-2517	182	16	-	-	PUNCT
iajs-2517	182	17	open	open	ADJ
iajs-2517	182	18	set	set	NOUN
iajs-2517	182	19	)	)	PUNCT
iajs-2517	182	20	containing	contain	VERB
iajs-2517	182	21	only	only	ADV
iajs-2517	182	22	one	one	NUM
iajs-2517	182	23	of	of	ADP
iajs-2517	182	24	the	the	DET
iajs-2517	182	25	two	two	NUM
iajs-2517	182	26	elements	element	NOUN
iajs-2517	182	27	(	(	PUNCT
iajs-2517	182	28	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	182	29	,	,	PUNCT
iajs-2517	182	30	(	(	PUNCT
iajs-2517	182	31	𝒽𝒩)𝑟.	𝒽𝒩)𝑟.	NOUN
iajs-2517	182	32	3	3	NUM
iajs-2517	182	33	ℬ,2	ℬ,2	NOUN
iajs-2517	182	34	ℬ,1	ℬ,1	NUM
iajs-2517	182	35	ℬ=	ℬ=	PROPN
iajs-2517	182	36	{	{	PUNCT
iajs-2517	182	37	ℬif	ℬif	PROPN
iajs-2517	182	38	,	,	PUNCT
iajs-2517	182	39	ℐ	ℐ	NUM
iajs-2517	182	40	)	)	PUNCT
iajs-2517	182	41	0𝒯(𝑆𝒢(respectively	0𝒯(𝑆𝒢(respectively	ADV
iajs-2517	182	42	,	,	PUNCT
iajs-2517	182	43	χ	χ	X
iajs-2517	182	44	)	)	PUNCT
iajs-2517	182	45	0𝒯(ş𝒢wins	0𝒯(ş𝒢wins	NUM
iajs-2517	182	46	in	in	ADP
iajs-2517	182	47	the	the	DET
iajs-2517	182	48	soft	soft	ADJ
iajs-2517	182	49	game	game	NOUN
iajs-2517	182	50	ⅱthen	ⅱthen	NOUN
iajs-2517	182	51	player	player	NOUN
iajs-2517	182	52	,	,	PUNCT
iajs-2517	182	53	…	…	PUNCT
iajs-2517	182	54	ℬ𝑟	ℬ𝑟	NOUN
iajs-2517	182	55	,	,	PUNCT
iajs-2517	182	56	…	…	PUNCT
iajs-2517	182	57	..	..	PUNCT
iajs-2517	182	58	}	}	PUNCT
iajs-2517	182	59	be	be	AUX
iajs-2517	182	60	a	a	DET
iajs-2517	182	61	collection	collection	NOUN
iajs-2517	182	62	of	of	ADP
iajs-2517	182	63	a	a	DET
iajs-2517	182	64	soft	soft	ADJ
iajs-2517	182	65	open	open	ADJ
iajs-2517	182	66	set	set	NOUN
iajs-2517	182	67	(	(	PUNCT
iajs-2517	182	68	respectively	respectively	ADV
iajs-2517	182	69	,	,	PUNCT
iajs-2517	182	70	s𝒥sg	s𝒥sg	NOUN
iajs-2517	182	71	-	-	PUNCT
iajs-2517	182	72	open	open	ADJ
iajs-2517	182	73	)	)	PUNCT
iajs-2517	182	74	set	set	VERB
iajs-2517	182	75	in	in	ADP
iajs-2517	182	76	χ	χ	PRON
iajs-2517	182	77	such	such	ADJ
iajs-2517	182	78	that	that	DET
iajs-2517	182	79	∀	∀	NOUN
iajs-2517	182	80	,	,	PUNCT
iajs-2517	182	81	(	(	PUNCT
iajs-2517	182	82	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	182	83	,	,	PUNCT
iajs-2517	182	84	(	(	PUNCT
iajs-2517	182	85	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	182	86	∈̃	∈̃	PROPN
iajs-2517	182	87	𝜒	𝜒	NUM
iajs-2517	182	88	,	,	PUNCT
iajs-2517	182	89	∃	∃	PROPN
iajs-2517	182	90	ℬ𝑟	ℬ𝑟	PROPN
iajs-2517	182	91	∈	∈	PROPN
iajs-2517	182	92	ℬ	ℬ	NOUN
iajs-2517	182	93	containing	contain	VERB
iajs-2517	182	94	only	only	ADV
iajs-2517	182	95	one	one	NUM
iajs-2517	182	96	of	of	ADP
iajs-2517	182	97	two	two	NUM
iajs-2517	182	98	element	element	NOUN
iajs-2517	182	99	(	(	PUNCT
iajs-2517	182	100	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	182	101	,	,	PUNCT
iajs-2517	182	102	(	(	PUNCT
iajs-2517	182	103	𝒽𝒩)𝑟.	𝒽𝒩)𝑟.	NOUN
iajs-2517	182	104	otherwise	otherwise	ADV
iajs-2517	182	105	,	,	PUNCT
iajs-2517	182	106	player	player	NOUN
iajs-2517	182	107	ⅰ	ⅰ	NOUN
iajs-2517	182	108	wins	win	VERB
iajs-2517	182	109	.	.	PUNCT
iajs-2517	183	1	,	,	PUNCT
iajs-2517	183	2	χ	χ	X
iajs-2517	183	3	=	=	PUNCT
iajs-2517	183	4	{	{	PUNCT
iajs-2517	183	5	1,2,3}be	1,2,3}be	NUM
iajs-2517	183	6	a	a	DET
iajs-2517	183	7	soft	soft	ADJ
iajs-2517	183	8	game	game	NOUN
iajs-2517	183	9	where	where	SCONJ
iajs-2517	183	10	,	,	PUNCT
iajs-2517	183	11	,	,	PUNCT
iajs-2517	183	12	ℐ	ℐ	PROPN
iajs-2517	183	13	)	)	PUNCT
iajs-2517	183	14	)	)	PUNCT
iajs-2517	184	1	0𝒯(ş𝒢(respectively	0𝒯(ş𝒢(respectively	ADV
iajs-2517	184	2	,	,	PUNCT
iajs-2517	184	3	χ	χ	X
iajs-2517	184	4	)	)	PUNCT
iajs-2517	184	5	0𝒯(ş𝒢let	0𝒯(ş𝒢let	NOUN
iajs-2517	184	6	example	example	NOUN
iajs-2517	185	1	5.2	5.2	NUM
iajs-2517	185	2	.	.	PUNCT
iajs-2517	185	3	,	,	PUNCT
iajs-2517	185	4	{	{	PUNCT
iajs-2517	185	5	1})}2𝒽,{1}),(1𝒽	1})}2𝒽,{1}),(1𝒽	NUM
iajs-2517	185	6	{	{	PUNCT
iajs-2517	185	7	(	(	PUNCT
iajs-2517	185	8	=	=	SYM
iajs-2517	185	9	(	(	PUNCT
iajs-2517	185	10	𝒫	𝒫	PROPN
iajs-2517	185	11	,	,	PUNCT
iajs-2517	185	12	ℋ	ℋ	PROPN
iajs-2517	185	13	)	)	PUNCT
iajs-2517	185	14	}	}	PUNCT
iajs-2517	185	15	where	where	SCONJ
iajs-2517	185	16	,	,	PUNCT
iajs-2517	185	17	ℋ),𝒵	ℋ),𝒵	NOUN
iajs-2517	185	18	,	,	PUNCT
iajs-2517	185	19	(	(	PUNCT
iajs-2517	185	20	ℋ),ϣ	ℋ),ϣ	X
iajs-2517	185	21	,	,	PUNCT
iajs-2517	185	22	(	(	PUNCT
iajs-2517	185	23	ℋ),𝒫	ℋ),𝒫	PROPN
iajs-2517	185	24	,	,	PUNCT
iajs-2517	185	25	(	(	PUNCT
iajs-2517	185	26	χ̃	χ̃	PROPN
iajs-2517	185	27	,	,	PUNCT
iajs-2517	185	28	∅̃	∅̃	NOUN
iajs-2517	185	29	=	=	SYM
iajs-2517	185	30	{	{	PUNCT
iajs-2517	185	31	𝒯	𝒯	PROPN
iajs-2517	185	32	,	,	PUNCT
iajs-2517	185	33	}	}	PUNCT
iajs-2517	185	34	2	2	NUM
iajs-2517	185	35	𝒽,1	𝒽,1	NUM
iajs-2517	185	36	𝒽	𝒽	X
iajs-2517	185	37	{	{	PUNCT
iajs-2517	185	38	ℋ	ℋ	NOUN
iajs-2517	185	39	=	=	PUNCT
iajs-2517	185	40	,	,	PUNCT
iajs-2517	185	41	(	(	PUNCT
iajs-2517	185	42	ϣ	ϣ	NOUN
iajs-2517	185	43	,	,	PUNCT
iajs-2517	185	44	ℋ	ℋ	PROPN
iajs-2517	185	45	)	)	PUNCT
iajs-2517	185	46	=	=	SYM
iajs-2517	185	47	{	{	PUNCT
iajs-2517	185	48	(	(	PUNCT
iajs-2517	185	49	𝒽1,{3}),(𝒽2,{3	𝒽1,{3}),(𝒽2,{3	PROPN
iajs-2517	185	50	}	}	PUNCT
iajs-2517	185	51	)	)	PUNCT
iajs-2517	185	52	}	}	PUNCT
iajs-2517	185	53	,	,	PUNCT
iajs-2517	185	54	(	(	PUNCT
iajs-2517	185	55	𝒵	𝒵	PROPN
iajs-2517	185	56	,	,	PUNCT
iajs-2517	185	57	ℋ	ℋ	PROPN
iajs-2517	185	58	)	)	PUNCT
iajs-2517	185	59	=	=	SYM
iajs-2517	185	60	{	{	PUNCT
iajs-2517	185	61	(	(	PUNCT
iajs-2517	185	62	𝒽1,{1,3}),(𝒽2,{1,3	𝒽1,{1,3}),(𝒽2,{1,3	NOUN
iajs-2517	185	63	}	}	PUNCT
iajs-2517	185	64	)	)	PUNCT
iajs-2517	185	65	}	}	PUNCT
iajs-2517	185	66	and	and	CCONJ
iajs-2517	185	67	ℐ	ℐ	PROPN
iajs-2517	185	68	=	=	NOUN
iajs-2517	185	69	{	{	PUNCT
iajs-2517	185	70	∅̃	∅̃	NOUN
iajs-2517	185	71	}	}	PUNCT
iajs-2517	185	72	.	.	PUNCT
iajs-2517	186	1	then	then	ADV
iajs-2517	186	2	şşo(χ	şşo(χ	PROPN
iajs-2517	186	3	)	)	PUNCT
iajs-2517	186	4	=	=	PRON
iajs-2517	186	5	{	{	PUNCT
iajs-2517	186	6	{	{	PUNCT
iajs-2517	186	7	1	1	NUM
iajs-2517	186	8	}	}	PUNCT
iajs-2517	186	9	∈̃	∈̃	PROPN
iajs-2517	186	10	(	(	PUNCT
iajs-2517	186	11	г	г	PROPN
iajs-2517	186	12	,	,	PUNCT
iajs-2517	186	13	ℋ	ℋ	NOUN
iajs-2517	186	14	)	)	PUNCT
iajs-2517	186	15	and	and	CCONJ
iajs-2517	186	16	{	{	PUNCT
iajs-2517	186	17	3	3	NUM
iajs-2517	186	18	}	}	PUNCT
iajs-2517	186	19	∉̃	∉̃	ADJ
iajs-2517	186	20	г	г	PROPN
iajs-2517	186	21	(	(	PUNCT
iajs-2517	186	22	𝒽	𝒽	NOUN
iajs-2517	186	23	)	)	PUNCT
iajs-2517	186	24	∀𝒽	∀𝒽	NOUN
iajs-2517	186	25	,	,	PUNCT
iajs-2517	186	26	{	{	PUNCT
iajs-2517	186	27	3	3	NUM
iajs-2517	186	28	}	}	PUNCT
iajs-2517	186	29	∈̃	∈̃	PROPN
iajs-2517	186	30	(	(	PUNCT
iajs-2517	186	31	г	г	PROPN
iajs-2517	186	32	,	,	PUNCT
iajs-2517	186	33	ℋ	ℋ	NOUN
iajs-2517	186	34	)	)	PUNCT
iajs-2517	186	35	and	and	CCONJ
iajs-2517	186	36	{	{	PUNCT
iajs-2517	186	37	1	1	NUM
iajs-2517	186	38	}	}	PUNCT
iajs-2517	186	39	∉̃	∉̃	ADJ
iajs-2517	186	40	г	г	PROPN
iajs-2517	186	41	(	(	PUNCT
iajs-2517	186	42	𝒽	𝒽	NOUN
iajs-2517	186	43	)	)	PUNCT
iajs-2517	186	44	∀𝒽	∀𝒽	NOUN
iajs-2517	186	45	,	,	PUNCT
iajs-2517	186	46	{	{	PUNCT
iajs-2517	186	47	1,3	1,3	NUM
iajs-2517	186	48	}	}	PUNCT
iajs-2517	186	49	∈̃	∈̃	PROPN
iajs-2517	186	50	(	(	PUNCT
iajs-2517	186	51	г	г	PROPN
iajs-2517	186	52	,	,	PUNCT
iajs-2517	186	53	ℋ)}∪	ℋ)}∪	NOUN
iajs-2517	186	54	{	{	PUNCT
iajs-2517	186	55	∅̃	∅̃	NOUN
iajs-2517	186	56	}	}	PUNCT
iajs-2517	186	57	,	,	PUNCT
iajs-2517	186	58	then	then	ADV
iajs-2517	186	59	sℐsgc(χ)𝓗	sℐsgc(χ)𝓗	ADJ
iajs-2517	186	60	=	=	SYM
iajs-2517	186	61	sc(χ)𝓗	sc(χ)𝓗	NOUN
iajs-2517	186	62	and	and	CCONJ
iajs-2517	186	63	sℐsgo(χ)𝓗	sℐsgo(χ)𝓗	ADJ
iajs-2517	186	64	=	=	PROPN
iajs-2517	186	65	𝒯.	𝒯.	PROPN
iajs-2517	186	66	then	then	ADV
iajs-2517	186	67	in	in	ADP
iajs-2517	186	68	the	the	DET
iajs-2517	186	69	first	first	ADJ
iajs-2517	186	70	inning	inning	NOUN
iajs-2517	186	71	:	:	PUNCT
iajs-2517	187	1	=	=	SYM
iajs-2517	187	2	𝒩𝒽=	𝒩𝒽=	PROPN
iajs-2517	187	3	{	{	PUNCT
iajs-2517	187	4	1	1	NUM
iajs-2517	187	5	}	}	PUNCT
iajs-2517	187	6	and	and	CCONJ
iajs-2517	187	7	𝓜𝒽such	𝓜𝒽such	PROPN
iajs-2517	187	8	that	that	PRON
iajs-2517	187	9	∈̃	∈̃	PROPN
iajs-2517	187	10	�	�	PROPN
iajs-2517	187	11	̃	̃	PROPN
iajs-2517	187	12	�	�	PROPN
iajs-2517	187	13	𝒩𝒽	𝒩𝒽	PROPN
iajs-2517	187	14	,	,	PUNCT
iajs-2517	187	15	𝒽where	𝒽where	ADV
iajs-2517	187	16	,	,	PUNCT
iajs-2517	187	17	𝒩𝒽	𝒩𝒽	PROPN
iajs-2517	187	18	≠	≠	PROPN
iajs-2517	187	19	𝓜𝒽choose	𝓜𝒽choose	PROPN
iajs-2517	187	20	ⅰthe	ⅰthe	DET
iajs-2517	187	21	first	first	ADJ
iajs-2517	187	22	step	step	NOUN
iajs-2517	187	23	,	,	PUNCT
iajs-2517	187	24	player	player	NOUN
iajs-2517	187	25	{	{	PUNCT
iajs-2517	187	26	2	2	NUM
iajs-2517	187	27	}	}	PUNCT
iajs-2517	187	28	.	.	PUNCT
iajs-2517	188	1	in	in	ADP
iajs-2517	188	2	the	the	DET
iajs-2517	188	3	second	second	ADJ
iajs-2517	188	4	step	step	NOUN
iajs-2517	188	5	,	,	PUNCT
iajs-2517	188	6	player	player	NOUN
iajs-2517	188	7	ⅱ	ⅱ	PROPN
iajs-2517	188	8	choose	choose	VERB
iajs-2517	188	9	(	(	PUNCT
iajs-2517	188	10	𝒫	𝒫	NOUN
iajs-2517	188	11	,	,	PUNCT
iajs-2517	188	12	ℋ	ℋ	PROPN
iajs-2517	188	13	)	)	PUNCT
iajs-2517	188	14	=	=	SYM
iajs-2517	188	15	{	{	PUNCT
iajs-2517	188	16	(	(	PUNCT
iajs-2517	188	17	𝒽1,{1}),(𝒽2,{1	𝒽1,{1}),(𝒽2,{1	NUM
iajs-2517	188	18	}	}	PUNCT
iajs-2517	188	19	)	)	PUNCT
iajs-2517	188	20	}	}	PUNCT
iajs-2517	188	21	a	a	DET
iajs-2517	188	22	soft	soft	ADJ
iajs-2517	188	23	open	open	ADJ
iajs-2517	188	24	(	(	PUNCT
iajs-2517	188	25	respectively	respectively	ADV
iajs-2517	188	26	,	,	PUNCT
iajs-2517	188	27	sℐsg	sℐsg	PROPN
iajs-2517	188	28	-	-	PUNCT
iajs-2517	188	29	open	open	ADJ
iajs-2517	188	30	set	set	NOUN
iajs-2517	188	31	)	)	PUNCT
iajs-2517	188	32	)	)	PUNCT
iajs-2517	188	33	.	.	PUNCT
iajs-2517	189	1	in	in	ADP
iajs-2517	189	2	the	the	DET
iajs-2517	189	3	second	second	ADJ
iajs-2517	189	4	inning	inning	NOUN
iajs-2517	189	5	:	:	PUNCT
iajs-2517	189	6	the	the	DET
iajs-2517	189	7	first	first	ADJ
iajs-2517	189	8	step	step	NOUN
iajs-2517	189	9	,	,	PUNCT
iajs-2517	189	10	player	player	NOUN
iajs-2517	189	11	ⅰ	ⅰ	PROPN
iajs-2517	189	12	chooses	choose	VERB
iajs-2517	189	13	𝒽	𝒽	DET
iajs-2517	189	14	𝓜	𝓜	PROPN
iajs-2517	189	15	≠	≠	PROPN
iajs-2517	189	16	𝒽𝓞	𝒽𝓞	ADJ
iajs-2517	189	17	where	where	SCONJ
iajs-2517	189	18	,	,	PUNCT
iajs-2517	189	19	𝒽	𝒽	DET
iajs-2517	189	20	𝓜	𝓜	PROPN
iajs-2517	189	21	,	,	PUNCT
iajs-2517	189	22	𝒽𝓞	𝒽𝓞	ADJ
iajs-2517	189	23	∈̃	∈̃	PROPN
iajs-2517	189	24	�	�	PROPN
iajs-2517	189	25	̃	̃	PROPN
iajs-2517	189	26	�	�	NOUN
iajs-2517	189	27	such	such	ADJ
iajs-2517	189	28	that	that	DET
iajs-2517	189	29	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	189	30	=	=	SYM
iajs-2517	189	31	{	{	PUNCT
iajs-2517	189	32	1	1	NUM
iajs-2517	189	33	}	}	PUNCT
iajs-2517	189	34	and	and	CCONJ
iajs-2517	189	35	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	189	36	=	=	SYM
iajs-2517	189	37	{	{	PUNCT
iajs-2517	189	38	3	3	NUM
iajs-2517	189	39	}	}	PUNCT
iajs-2517	189	40	.	.	PUNCT
iajs-2517	190	1	in	in	ADP
iajs-2517	190	2	the	the	DET
iajs-2517	190	3	second	second	ADJ
iajs-2517	190	4	step	step	NOUN
iajs-2517	190	5	,	,	PUNCT
iajs-2517	190	6	player	player	NOUN
iajs-2517	190	7	ⅱ	ⅱ	PROPN
iajs-2517	190	8	choose	choose	VERB
iajs-2517	190	9	(	(	PUNCT
iajs-2517	190	10	ϣ	ϣ	NOUN
iajs-2517	190	11	,	,	PUNCT
iajs-2517	190	12	ℋ	ℋ	PROPN
iajs-2517	190	13	)	)	PUNCT
iajs-2517	190	14	=	=	SYM
iajs-2517	190	15	{	{	PUNCT
iajs-2517	190	16	(	(	PUNCT
iajs-2517	190	17	𝒽1,{3}),(𝒽2,{3	𝒽1,{3}),(𝒽2,{3	PROPN
iajs-2517	190	18	}	}	PUNCT
iajs-2517	190	19	)	)	PUNCT
iajs-2517	190	20	}	}	PUNCT
iajs-2517	190	21	which	which	PRON
iajs-2517	190	22	is	be	AUX
iajs-2517	190	23	a	a	DET
iajs-2517	190	24	soft	soft	ADJ
iajs-2517	190	25	open	open	ADJ
iajs-2517	190	26	(	(	PUNCT
iajs-2517	190	27	respectively	respectively	ADV
iajs-2517	190	28	,	,	PUNCT
iajs-2517	190	29	sℐsg	sℐsg	PROPN
iajs-2517	190	30	-	-	PUNCT
iajs-2517	190	31	open	open	ADJ
iajs-2517	190	32	set	set	NOUN
iajs-2517	190	33	)	)	PUNCT
iajs-2517	190	34	.	.	PUNCT
iajs-2517	191	1	(	(	PUNCT
iajs-2517	191	2	𝜒	𝜒	X
iajs-2517	191	3	,	,	PUNCT
iajs-2517	191	4	𝒯	𝒯	PROPN
iajs-2517	191	5	,	,	PUNCT
iajs-2517	191	6	ℋ	ℋ	PROPN
iajs-2517	191	7	)	)	PUNCT
iajs-2517	191	8	is	be	AUX
iajs-2517	191	9	𝑎𝑠𝑝𝑎𝑐𝑒-2𝒯-soft	𝑎𝑠𝑝𝑎𝑐𝑒-2𝒯-soft	PROPN
iajs-2517	191	10	(	(	PUNCT
iajs-2517	191	11	𝜒	𝜒	X
iajs-2517	191	12	,	,	PUNCT
iajs-2517	191	13	𝒯	𝒯	PROPN
iajs-2517	191	14	,	,	PUNCT
iajs-2517	191	15	ℋ	ℋ	PROPN
iajs-2517	191	16	)	)	PUNCT
iajs-2517	191	17	is	be	AUX
iajs-2517	191	18	𝑎𝑠𝑝𝑎𝑐𝑒-0𝒯-soft	𝑎𝑠𝑝𝑎𝑐𝑒-0𝒯-soft	ADJ
iajs-2517	191	19	(	(	PUNCT
iajs-2517	191	20	𝜒	𝜒	X
iajs-2517	191	21	,	,	PUNCT
iajs-2517	191	22	𝒯	𝒯	PROPN
iajs-2517	191	23	,	,	PUNCT
iajs-2517	191	24	ℋ)is	ℋ)is	PROPN
iajs-2517	191	25	𝑎𝑠𝑝𝑎𝑐𝑒-1𝒯-soft	𝑎𝑠𝑝𝑎𝑐𝑒-1𝒯-soft	ADV
iajs-2517	191	26	(	(	PUNCT
iajs-2517	191	27	𝜒	𝜒	X
iajs-2517	191	28	,	,	PUNCT
iajs-2517	191	29	𝒯	𝒯	PROPN
iajs-2517	191	30	,	,	PUNCT
iajs-2517	191	31	ℋ	ℋ	PROPN
iajs-2517	191	32	,	,	PUNCT
iajs-2517	191	33	ℐ	ℐ	NUM
iajs-2517	191	34	)	)	PUNCT
iajs-2517	191	35	is	be	AUX
iajs-2517	191	36	𝑎	𝑎	PRON
iajs-2517	191	37	𝑠ℐ𝑠𝑔𝑠𝑝𝑎𝑐𝑒-2𝒯	𝑠ℐ𝑠𝑔𝑠𝑝𝑎𝑐𝑒-2𝒯	ADJ
iajs-2517	191	38	(	(	PUNCT
iajs-2517	191	39	𝜒	𝜒	X
iajs-2517	191	40	,	,	PUNCT
iajs-2517	191	41	𝒯	𝒯	PROPN
iajs-2517	191	42	,	,	PUNCT
iajs-2517	191	43	ℋ	ℋ	PROPN
iajs-2517	191	44	,	,	PUNCT
iajs-2517	191	45	ℐ)is	ℐ)is	PROPN
iajs-2517	191	46	𝑎	𝑎	DET
iajs-2517	191	47	𝑠ℐ𝑠𝑔𝑠𝑝𝑎𝑐𝑒-1𝒯	𝑠ℐ𝑠𝑔𝑠𝑝𝑎𝑐𝑒-1𝒯	NOUN
iajs-2517	191	48	(	(	PUNCT
iajs-2517	191	49	𝜒	𝜒	X
iajs-2517	191	50	,	,	PUNCT
iajs-2517	191	51	𝒯	𝒯	PROPN
iajs-2517	191	52	,	,	PUNCT
iajs-2517	191	53	ℋ	ℋ	PROPN
iajs-2517	191	54	,	,	PUNCT
iajs-2517	191	55	ℐ)is	ℐ)is	PROPN
iajs-2517	191	56	𝑎	𝑎	PRON
iajs-2517	191	57	𝑠ℐ𝑠𝑔𝑠𝑝𝑎𝑐𝑒-0𝒯	𝑠ℐ𝑠𝑔𝑠𝑝𝑎𝑐𝑒-0𝒯	NOUN
iajs-2517	191	58	129	129	NUM
iajs-2517	191	59	ibn	ibn	PROPN
iajs-2517	191	60	al	al	PROPN
iajs-2517	191	61	-	-	PUNCT
iajs-2517	191	62	haitham	haitham	PROPN
iajs-2517	191	63	jour	jour	X
iajs-2517	191	64	.	.	PROPN
iajs-2517	192	1	for	for	ADP
iajs-2517	192	2	pure	pure	ADJ
iajs-2517	192	3	&	&	CCONJ
iajs-2517	192	4	appl	appl	PROPN
iajs-2517	192	5	.	.	PUNCT
iajs-2517	193	1	sci	sci	PROPN
iajs-2517	193	2	.	.	PROPN
iajs-2517	194	1	33	33	NUM
iajs-2517	194	2	(	(	PUNCT
iajs-2517	194	3	4	4	NUM
iajs-2517	194	4	)	)	PUNCT
iajs-2517	194	5	2020	2020	NUM
iajs-2517	195	1	in	in	ADP
iajs-2517	195	2	the	the	DET
iajs-2517	195	3	third	third	ADJ
iajs-2517	195	4	inning	inning	NOUN
iajs-2517	195	5	:	:	PUNCT
iajs-2517	195	6	the	the	DET
iajs-2517	195	7	first	first	ADJ
iajs-2517	195	8	step	step	NOUN
iajs-2517	195	9	,	,	PUNCT
iajs-2517	195	10	player	player	NOUN
iajs-2517	195	11	ⅰ	ⅰ	PROPN
iajs-2517	195	12	choose	choose	VERB
iajs-2517	195	13	𝒽	𝒽	DET
iajs-2517	195	14	𝓝	𝓝	PROPN
iajs-2517	195	15	≠	≠	PROPN
iajs-2517	195	16	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	195	17	where	where	SCONJ
iajs-2517	195	18	,	,	PUNCT
iajs-2517	195	19	𝒽	𝒽	X
iajs-2517	195	20	,	,	PUNCT
iajs-2517	195	21	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	195	22	∈̃	∈̃	PROPN
iajs-2517	195	23	�	�	PROPN
iajs-2517	195	24	̃	̃	PROPN
iajs-2517	195	25	�	�	PROPN
iajs-2517	195	26	such	such	ADJ
iajs-2517	195	27	that	that	SCONJ
iajs-2517	195	28	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	195	29	=	=	PUNCT
iajs-2517	195	30	{	{	PUNCT
iajs-2517	195	31	2	2	NUM
iajs-2517	195	32	}	}	PUNCT
iajs-2517	195	33	and	and	CCONJ
iajs-2517	195	34	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	195	35	=	=	SYM
iajs-2517	195	36	{	{	PUNCT
iajs-2517	195	37	3	3	NUM
iajs-2517	195	38	}	}	PUNCT
iajs-2517	195	39	.	.	PUNCT
iajs-2517	196	1	in	in	ADP
iajs-2517	196	2	the	the	DET
iajs-2517	196	3	second	second	ADJ
iajs-2517	196	4	step	step	NOUN
iajs-2517	196	5	,	,	PUNCT
iajs-2517	196	6	player	player	NOUN
iajs-2517	196	7	ⅱ	ⅱ	PROPN
iajs-2517	196	8	choose	choose	VERB
iajs-2517	196	9	(	(	PUNCT
iajs-2517	196	10	ϣ	ϣ	NOUN
iajs-2517	196	11	,	,	PUNCT
iajs-2517	196	12	ℋ	ℋ	PROPN
iajs-2517	196	13	)	)	PUNCT
iajs-2517	196	14	=	=	SYM
iajs-2517	196	15	{	{	PUNCT
iajs-2517	196	16	(	(	PUNCT
iajs-2517	196	17	𝒽1,{3}),(𝒽2,{3	𝒽1,{3}),(𝒽2,{3	PROPN
iajs-2517	196	18	}	}	PUNCT
iajs-2517	196	19	)	)	PUNCT
iajs-2517	196	20	}	}	PUNCT
iajs-2517	196	21	which	which	PRON
iajs-2517	196	22	is	be	AUX
iajs-2517	196	23	a	a	DET
iajs-2517	196	24	soft	soft	ADJ
iajs-2517	196	25	open	open	ADJ
iajs-2517	196	26	(	(	PUNCT
iajs-2517	196	27	respectively	respectively	ADV
iajs-2517	196	28	,	,	PUNCT
iajs-2517	196	29	sℐsg	sℐsg	PROPN
iajs-2517	196	30	-	-	PUNCT
iajs-2517	196	31	open	open	ADJ
iajs-2517	196	32	set	set	NOUN
iajs-2517	196	33	)	)	PUNCT
iajs-2517	196	34	)	)	PUNCT
iajs-2517	196	35	.	.	PUNCT
iajs-2517	197	1	in	in	ADP
iajs-2517	197	2	the	the	DET
iajs-2517	197	3	fourth	fourth	ADJ
iajs-2517	197	4	inning	inning	NOUN
iajs-2517	197	5	:	:	PUNCT
iajs-2517	197	6	the	the	DET
iajs-2517	197	7	first	first	ADJ
iajs-2517	197	8	step	step	NOUN
iajs-2517	197	9	,	,	PUNCT
iajs-2517	197	10	player	player	NOUN
iajs-2517	197	11	ⅰ	ⅰ	NOUN
iajs-2517	197	12	choose	choose	VERB
iajs-2517	197	13	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	197	14	≠	≠	PROPN
iajs-2517	197	15	𝒽𝓡	𝒽𝓡	NOUN
iajs-2517	197	16	where	where	SCONJ
iajs-2517	197	17	,	,	PUNCT
iajs-2517	197	18	𝒽	𝒽	X
iajs-2517	197	19	,	,	PUNCT
iajs-2517	197	20	𝒽𝓡	𝒽𝓡	PROPN
iajs-2517	197	21	∈̃	∈̃	PROPN
iajs-2517	197	22	�	�	PROPN
iajs-2517	197	23	̃	̃	PROPN
iajs-2517	197	24	�	�	NOUN
iajs-2517	197	25	such	such	ADJ
iajs-2517	197	26	that	that	PRON
iajs-2517	197	27	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	197	28	=	=	SYM
iajs-2517	197	29	{	{	PUNCT
iajs-2517	197	30	1	1	NUM
iajs-2517	197	31	}	}	PUNCT
iajs-2517	197	32	and	and	CCONJ
iajs-2517	197	33	𝒽𝓡	𝒽𝓡	NOUN
iajs-2517	197	34	=	=	X
iajs-2517	197	35	{	{	PUNCT
iajs-2517	197	36	2,3	2,3	NUM
iajs-2517	197	37	}	}	PUNCT
iajs-2517	197	38	.	.	PUNCT
iajs-2517	198	1	in	in	ADP
iajs-2517	198	2	the	the	DET
iajs-2517	198	3	second	second	ADJ
iajs-2517	198	4	step	step	NOUN
iajs-2517	198	5	,	,	PUNCT
iajs-2517	198	6	player	player	NOUN
iajs-2517	198	7	ⅱ	ⅱ	PROPN
iajs-2517	198	8	choose	choose	VERB
iajs-2517	198	9	(	(	PUNCT
iajs-2517	198	10	𝒫	𝒫	NOUN
iajs-2517	198	11	,	,	PUNCT
iajs-2517	198	12	ℋ	ℋ	PROPN
iajs-2517	198	13	)	)	PUNCT
iajs-2517	198	14	=	=	SYM
iajs-2517	198	15	{	{	PUNCT
iajs-2517	198	16	(	(	PUNCT
iajs-2517	198	17	𝒽1,{1}),(𝒽2,{1	𝒽1,{1}),(𝒽2,{1	NUM
iajs-2517	198	18	}	}	PUNCT
iajs-2517	198	19	)	)	PUNCT
iajs-2517	198	20	}	}	PUNCT
iajs-2517	198	21	which	which	PRON
iajs-2517	198	22	is	be	AUX
iajs-2517	198	23	a	a	DET
iajs-2517	198	24	soft	soft	ADJ
iajs-2517	198	25	open	open	ADJ
iajs-2517	198	26	(	(	PUNCT
iajs-2517	198	27	respectively	respectively	ADV
iajs-2517	198	28	,	,	PUNCT
iajs-2517	198	29	sℐsg	sℐsg	PROPN
iajs-2517	198	30	-	-	PUNCT
iajs-2517	198	31	open	open	ADJ
iajs-2517	198	32	set	set	NOUN
iajs-2517	198	33	)	)	PUNCT
iajs-2517	198	34	)	)	PUNCT
iajs-2517	198	35	.	.	PUNCT
iajs-2517	199	1	in	in	ADP
iajs-2517	199	2	the	the	DET
iajs-2517	199	3	fifth	fifth	ADJ
iajs-2517	199	4	inning	inning	NOUN
iajs-2517	199	5	:	:	PUNCT
iajs-2517	199	6	the	the	DET
iajs-2517	199	7	first	first	ADJ
iajs-2517	199	8	step	step	NOUN
iajs-2517	199	9	,	,	PUNCT
iajs-2517	199	10	player	player	NOUN
iajs-2517	199	11	ⅰ	ⅰ	PRON
iajs-2517	199	12	choose	choose	VERB
iajs-2517	199	13	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	199	14	≠	≠	PROPN
iajs-2517	199	15	𝒽𝓢	𝒽𝓢	NOUN
iajs-2517	199	16	where	where	SCONJ
iajs-2517	199	17	,	,	PUNCT
iajs-2517	199	18	𝒽	𝒽	X
iajs-2517	199	19	,	,	PUNCT
iajs-2517	199	20	𝒽𝓢	𝒽𝓢	NOUN
iajs-2517	199	21	∈̃	∈̃	PROPN
iajs-2517	199	22	�	�	PROPN
iajs-2517	199	23	̃	̃	PROPN
iajs-2517	199	24	�	�	PROPN
iajs-2517	199	25	such	such	ADJ
iajs-2517	199	26	that	that	SCONJ
iajs-2517	199	27	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	199	28	=	=	PUNCT
iajs-2517	199	29	{	{	PUNCT
iajs-2517	199	30	2	2	NUM
iajs-2517	199	31	}	}	PUNCT
iajs-2517	199	32	and	and	CCONJ
iajs-2517	199	33	𝒽𝓢	𝒽𝓢	NOUN
iajs-2517	199	34	=	=	SYM
iajs-2517	199	35	{	{	PUNCT
iajs-2517	199	36	1,3	1,3	NUM
iajs-2517	199	37	}	}	PUNCT
iajs-2517	199	38	.	.	PUNCT
iajs-2517	200	1	in	in	ADP
iajs-2517	200	2	the	the	DET
iajs-2517	200	3	second	second	ADJ
iajs-2517	200	4	step	step	NOUN
iajs-2517	200	5	,	,	PUNCT
iajs-2517	200	6	player	player	NOUN
iajs-2517	200	7	ⅱ	ⅱ	PROPN
iajs-2517	200	8	choose	choose	VERB
iajs-2517	200	9	(	(	PUNCT
iajs-2517	200	10	𝒵	𝒵	PROPN
iajs-2517	200	11	,	,	PUNCT
iajs-2517	200	12	ℋ	ℋ	PROPN
iajs-2517	200	13	)	)	PUNCT
iajs-2517	200	14	=	=	SYM
iajs-2517	200	15	{	{	PUNCT
iajs-2517	200	16	(	(	PUNCT
iajs-2517	200	17	𝒽1,{1,3}),(𝒽2,{1,3	𝒽1,{1,3}),(𝒽2,{1,3	NOUN
iajs-2517	200	18	}	}	PUNCT
iajs-2517	200	19	)	)	PUNCT
iajs-2517	200	20	}	}	PUNCT
iajs-2517	200	21	which	which	PRON
iajs-2517	200	22	is	be	AUX
iajs-2517	200	23	a	a	DET
iajs-2517	200	24	soft	soft	ADJ
iajs-2517	200	25	open	open	ADJ
iajs-2517	200	26	(	(	PUNCT
iajs-2517	200	27	respectively	respectively	ADV
iajs-2517	200	28	,	,	PUNCT
iajs-2517	200	29	sℐsg	sℐsg	PROPN
iajs-2517	200	30	-	-	PUNCT
iajs-2517	200	31	open	open	ADJ
iajs-2517	200	32	set	set	NOUN
iajs-2517	200	33	)	)	PUNCT
iajs-2517	200	34	)	)	PUNCT
iajs-2517	200	35	.	.	PUNCT
iajs-2517	201	1	in	in	ADP
iajs-2517	201	2	the	the	DET
iajs-2517	201	3	sixth	sixth	ADJ
iajs-2517	201	4	inning	inning	NOUN
iajs-2517	201	5	:	:	PUNCT
iajs-2517	201	6	the	the	DET
iajs-2517	201	7	first	first	ADJ
iajs-2517	201	8	step	step	NOUN
iajs-2517	201	9	,	,	PUNCT
iajs-2517	201	10	player	player	NOUN
iajs-2517	201	11	ⅰ	ⅰ	PRON
iajs-2517	201	12	choose	choose	VERB
iajs-2517	201	13	𝒽𝓞	𝒽𝓞	ADJ
iajs-2517	201	14	≠	≠	PROPN
iajs-2517	201	15	𝒽𝓛	𝒽𝓛	ADP
iajs-2517	201	16	where	where	SCONJ
iajs-2517	201	17	,	,	PUNCT
iajs-2517	201	18	𝒽	𝒽	X
iajs-2517	201	19	,	,	PUNCT
iajs-2517	201	20	𝒽𝓛	𝒽𝓛	PROPN
iajs-2517	201	21	∈̃	∈̃	PROPN
iajs-2517	201	22	�	�	PROPN
iajs-2517	201	23	̃	̃	PROPN
iajs-2517	201	24	�	�	PROPN
iajs-2517	201	25	such	such	ADJ
iajs-2517	201	26	that	that	SCONJ
iajs-2517	201	27	𝒽𝒪	𝒽𝒪	NOUN
iajs-2517	201	28	=	=	SYM
iajs-2517	201	29	{	{	PUNCT
iajs-2517	201	30	3	3	NUM
iajs-2517	201	31	}	}	PUNCT
iajs-2517	201	32	and	and	CCONJ
iajs-2517	201	33	𝒽𝓛	𝒽𝓛	ADP
iajs-2517	201	34	=	=	SYM
iajs-2517	201	35	{	{	PUNCT
iajs-2517	201	36	1,2	1,2	NUM
iajs-2517	201	37	}	}	PUNCT
iajs-2517	201	38	.	.	PUNCT
iajs-2517	202	1	in	in	ADP
iajs-2517	202	2	the	the	DET
iajs-2517	202	3	second	second	ADJ
iajs-2517	202	4	step	step	NOUN
iajs-2517	202	5	,	,	PUNCT
iajs-2517	202	6	player	player	NOUN
iajs-2517	202	7	ⅱ	ⅱ	PROPN
iajs-2517	202	8	choose	choose	VERB
iajs-2517	202	9	(	(	PUNCT
iajs-2517	202	10	ϣ	ϣ	NOUN
iajs-2517	202	11	,	,	PUNCT
iajs-2517	202	12	ℋ	ℋ	PROPN
iajs-2517	202	13	)	)	PUNCT
iajs-2517	202	14	=	=	SYM
iajs-2517	202	15	{	{	PUNCT
iajs-2517	202	16	(	(	PUNCT
iajs-2517	202	17	𝒽1,{3}),(𝒽2,{3	𝒽1,{3}),(𝒽2,{3	PROPN
iajs-2517	202	18	}	}	PUNCT
iajs-2517	202	19	)	)	PUNCT
iajs-2517	202	20	}	}	PUNCT
iajs-2517	202	21	which	which	PRON
iajs-2517	202	22	is	be	AUX
iajs-2517	202	23	a	a	DET
iajs-2517	202	24	soft	soft	ADJ
iajs-2517	202	25	open	open	ADJ
iajs-2517	202	26	(	(	PUNCT
iajs-2517	202	27	respectively	respectively	ADV
iajs-2517	202	28	,	,	PUNCT
iajs-2517	202	29	sℐsg	sℐsg	PROPN
iajs-2517	202	30	-	-	PUNCT
iajs-2517	202	31	open	open	ADJ
iajs-2517	202	32	set	set	NOUN
iajs-2517	202	33	)	)	PUNCT
iajs-2517	202	34	)	)	PUNCT
iajs-2517	202	35	.	.	PUNCT
iajs-2517	203	1	then	then	ADV
iajs-2517	203	2	ℬ	ℬ	NOUN
iajs-2517	203	3	=	=	PRON
iajs-2517	203	4	{	{	PUNCT
iajs-2517	203	5	,	,	PUNCT
iajs-2517	203	6	(	(	PUNCT
iajs-2517	203	7	𝒫	𝒫	NOUN
iajs-2517	203	8	,	,	PUNCT
iajs-2517	203	9	ℋ	ℋ	PROPN
iajs-2517	203	10	)	)	PUNCT
iajs-2517	203	11	,	,	PUNCT
iajs-2517	203	12	(	(	PUNCT
iajs-2517	203	13	ϣ	ϣ	X
iajs-2517	203	14	,	,	PUNCT
iajs-2517	203	15	ℋ	ℋ	NOUN
iajs-2517	203	16	)	)	PUNCT
iajs-2517	203	17	,	,	PUNCT
iajs-2517	203	18	(	(	PUNCT
iajs-2517	203	19	𝒵	𝒵	PROPN
iajs-2517	203	20	,	,	PUNCT
iajs-2517	203	21	ℋ	ℋ	NOUN
iajs-2517	203	22	)	)	PUNCT
iajs-2517	203	23	}	}	PUNCT
iajs-2517	203	24	is	be	AUX
iajs-2517	203	25	the	the	DET
iajs-2517	203	26	winning	win	VERB
iajs-2517	203	27	strategy	strategy	NOUN
iajs-2517	203	28	for	for	ADP
iajs-2517	203	29	player	player	NOUN
iajs-2517	203	30	ⅱ	ⅱ	PROPN
iajs-2517	203	31	in	in	ADP
iajs-2517	203	32	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	203	33	,	,	PUNCT
iajs-2517	203	34	χ	χ	X
iajs-2517	203	35	)	)	PUNCT
iajs-2517	203	36	(	(	PUNCT
iajs-2517	203	37	respectively	respectively	ADV
iajs-2517	203	38	ş𝒢(𝒯0	ş𝒢(𝒯0	ADJ
iajs-2517	203	39	,	,	PUNCT
iajs-2517	203	40	ℐ	ℐ	PROPN
iajs-2517	203	41	)	)	PUNCT
iajs-2517	203	42	)	)	PUNCT
iajs-2517	203	43	.	.	PUNCT
iajs-2517	204	1	hence	hence	ADV
iajs-2517	204	2	player	player	NOUN
iajs-2517	204	3	ⅱ	ⅱ	PROPN
iajs-2517	204	4	↑	↑	PROPN
iajs-2517	204	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	204	6	,	,	PUNCT
iajs-2517	204	7	χ	χ	X
iajs-2517	204	8	)	)	PUNCT
iajs-2517	204	9	(	(	PUNCT
iajs-2517	204	10	respectively	respectively	ADV
iajs-2517	204	11	ş𝒢(𝒯0	ş𝒢(𝒯0	ADJ
iajs-2517	204	12	,	,	PUNCT
iajs-2517	204	13	ℐ	ℐ	PROPN
iajs-2517	204	14	)	)	PUNCT
iajs-2517	204	15	)	)	PUNCT
iajs-2517	204	16	.	.	PUNCT
iajs-2517	205	1	ℋ	ℋ	PROPN
iajs-2517	205	2	=	=	PROPN
iajs-2517	205	3	,	,	PUNCT
iajs-2517	205	4	χ	χ	NOUN
iajs-2517	205	5	=	=	PUNCT
iajs-2517	205	6	{	{	PUNCT
iajs-2517	205	7	1,2,3}is	1,2,3}is	NUM
iajs-2517	205	8	a	a	DET
iajs-2517	205	9	game	game	NOUN
iajs-2517	205	10	where	where	SCONJ
iajs-2517	205	11	,	,	PUNCT
iajs-2517	205	12	,	,	PUNCT
iajs-2517	205	13	ℐ	ℐ	PROPN
iajs-2517	205	14	)	)	PUNCT
iajs-2517	205	15	)	)	PUNCT
iajs-2517	206	1	0𝒯(ş𝒢(respectively	0𝒯(ş𝒢(respectively	ADV
iajs-2517	206	2	,	,	PUNCT
iajs-2517	206	3	χ	χ	X
iajs-2517	206	4	)	)	PUNCT
iajs-2517	206	5	0𝒯	0𝒯	NOUN
iajs-2517	206	6	(	(	PUNCT
iajs-2517	206	7	ş𝒢let	ş𝒢let	PROPN
iajs-2517	206	8	example	example	NOUN
iajs-2517	206	9	5.3	5.3	NUM
iajs-2517	206	10	.	.	PUNCT
iajs-2517	207	1	then	then	ADV
iajs-2517	207	2	ℐ	ℐ	PRON
iajs-2517	207	3	=	=	NOUN
iajs-2517	207	4	{	{	PUNCT
iajs-2517	207	5	∅̃},{3	∅̃},{3	NOUN
iajs-2517	207	6	}	}	PUNCT
iajs-2517	207	7	)	)	PUNCT
iajs-2517	207	8	}	}	PUNCT
iajs-2517	207	9	and	and	CCONJ
iajs-2517	207	10	2𝒽,{3}),(1𝒽=	2𝒽,{3}),(1𝒽=	NUM
iajs-2517	207	11	{	{	PUNCT
iajs-2517	207	12	(	(	PUNCT
iajs-2517	207	13	(	(	PUNCT
iajs-2517	207	14	ϣ	ϣ	INTJ
iajs-2517	207	15	,	,	PUNCT
iajs-2517	207	16	ℋ)where	ℋ)where	ADV
iajs-2517	207	17	,	,	PUNCT
iajs-2517	207	18	ℋ)},ϣ	ℋ)},ϣ	PRON
iajs-2517	207	19	,	,	PUNCT
iajs-2517	207	20	(	(	PUNCT
iajs-2517	207	21	χ̃	χ̃	PROPN
iajs-2517	207	22	,	,	PUNCT
iajs-2517	207	23	∅̃	∅̃	NOUN
iajs-2517	207	24	=	=	SYM
iajs-2517	207	25	{	{	PUNCT
iajs-2517	207	26	𝒯	𝒯	PROPN
iajs-2517	207	27	,	,	PUNCT
iajs-2517	207	28	}	}	PUNCT
iajs-2517	207	29	2	2	NUM
iajs-2517	207	30	𝒽,1𝒽	𝒽,1𝒽	PROPN
iajs-2517	207	31	{	{	PUNCT
iajs-2517	207	32	.𝒯=	.𝒯=	NOUN
iajs-2517	208	1	𝓗sℐsgo(χ)and	𝓗sℐsgo(χ)and	PRON
iajs-2517	208	2	𝓗(χ)=	𝓗(χ)=	PROPN
iajs-2517	208	3	sc	sc	PROPN
iajs-2517	208	4	𝓗	𝓗	PROPN
iajs-2517	208	5	sℐsgc(χ	sℐsgc(χ	PROPN
iajs-2517	208	6	)	)	PUNCT
iajs-2517	209	1	in	in	ADP
iajs-2517	209	2	the	the	DET
iajs-2517	209	3	first	first	ADJ
iajs-2517	209	4	inning	inning	NOUN
iajs-2517	209	5	:	:	PUNCT
iajs-2517	209	6	the	the	DET
iajs-2517	209	7	first	first	ADJ
iajs-2517	209	8	step	step	NOUN
iajs-2517	209	9	,	,	PUNCT
iajs-2517	209	10	player	player	NOUN
iajs-2517	209	11	ⅰ	ⅰ	NOUN
iajs-2517	209	12	choose	choose	VERB
iajs-2517	209	13	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	209	14	≠	≠	PUNCT
iajs-2517	209	15	𝒽𝒩	𝒽𝒩	NUM
iajs-2517	209	16	where	where	SCONJ
iajs-2517	209	17	,	,	PUNCT
iajs-2517	209	18	𝒽	𝒽	PRON
iajs-2517	209	19	,	,	PUNCT
iajs-2517	209	20	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	209	21	∈̃	∈̃	PROPN
iajs-2517	209	22	�	�	PROPN
iajs-2517	209	23	̃	̃	PROPN
iajs-2517	209	24	�	�	PROPN
iajs-2517	209	25	since	since	SCONJ
iajs-2517	209	26	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	209	27	=	=	SYM
iajs-2517	209	28	{	{	PUNCT
iajs-2517	209	29	1	1	NUM
iajs-2517	209	30	}	}	PUNCT
iajs-2517	209	31	and	and	CCONJ
iajs-2517	209	32	𝒽𝒩	𝒽𝒩	NOUN
iajs-2517	209	33	=	=	PUNCT
iajs-2517	209	34	{	{	PUNCT
iajs-2517	209	35	2	2	NUM
iajs-2517	209	36	}	}	PUNCT
iajs-2517	209	37	.	.	PUNCT
iajs-2517	210	1	in	in	ADP
iajs-2517	210	2	the	the	DET
iajs-2517	210	3	second	second	ADJ
iajs-2517	210	4	step	step	NOUN
iajs-2517	210	5	,	,	PUNCT
iajs-2517	210	6	player	player	NOUN
iajs-2517	210	7	ⅱ	ⅱ	PROPN
iajs-2517	210	8	can	can	AUX
iajs-2517	210	9	not	not	PART
iajs-2517	210	10	find	find	VERB
iajs-2517	210	11	(	(	PUNCT
iajs-2517	210	12	ơ	ơ	PROPN
iajs-2517	210	13	,	,	PUNCT
iajs-2517	210	14	ℋ	ℋ	PROPN
iajs-2517	210	15	)	)	PUNCT
iajs-2517	210	16	which	which	PRON
iajs-2517	210	17	is	be	AUX
iajs-2517	210	18	a	a	DET
iajs-2517	210	19	soft	soft	ADJ
iajs-2517	210	20	open	open	ADJ
iajs-2517	210	21	(	(	PUNCT
iajs-2517	210	22	respectively	respectively	ADV
iajs-2517	210	23	,	,	PUNCT
iajs-2517	210	24	sℐsg	sℐsg	PROPN
iajs-2517	210	25	-	-	PUNCT
iajs-2517	210	26	open	open	ADJ
iajs-2517	210	27	set	set	NOUN
iajs-2517	210	28	)	)	PUNCT
iajs-2517	210	29	)	)	PUNCT
iajs-2517	210	30	containing	contain	VERB
iajs-2517	210	31	one	one	NUM
iajs-2517	210	32	of	of	ADP
iajs-2517	210	33	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	210	34	,	,	PUNCT
iajs-2517	210	35	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	210	36	.	.	PUNCT
iajs-2517	211	1	hence	hence	ADV
iajs-2517	211	2	player	player	NOUN
iajs-2517	211	3	ⅰ	ⅰ	PROPN
iajs-2517	211	4	↑	↑	X
iajs-2517	211	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	211	6	,	,	PUNCT
iajs-2517	211	7	χ	χ	X
iajs-2517	211	8	)	)	PUNCT
iajs-2517	211	9	(	(	PUNCT
iajs-2517	211	10	respectively	respectively	ADV
iajs-2517	211	11	ş𝒢(𝒯0	ş𝒢(𝒯0	ADJ
iajs-2517	211	12	,	,	PUNCT
iajs-2517	211	13	ℐ	ℐ	PROPN
iajs-2517	211	14	)	)	PUNCT
iajs-2517	211	15	)	)	PUNCT
iajs-2517	211	16	.	.	PUNCT
iajs-2517	212	1	remark	remark	PROPN
iajs-2517	212	2	5.4	5.4	NUM
iajs-2517	212	3	.	.	PUNCT
iajs-2517	213	1	for	for	ADP
iajs-2517	213	2	a	a	DET
iajs-2517	213	3	space	space	NOUN
iajs-2517	213	4	(	(	PUNCT
iajs-2517	213	5	χ	χ	X
iajs-2517	213	6	,	,	PUNCT
iajs-2517	213	7	𝒯	𝒯	PROPN
iajs-2517	213	8	,	,	PUNCT
iajs-2517	213	9	ℋ	ℋ	PROPN
iajs-2517	213	10	,	,	PUNCT
iajs-2517	213	11	ℐ	ℐ	PROPN
iajs-2517	213	12	):	):	PUNCT
iajs-2517	213	13	i.	i.	NOUN
iajs-2517	213	14	if	if	SCONJ
iajs-2517	213	15	player	player	NOUN
iajs-2517	213	16	ⅱ	ⅱ	PROPN
iajs-2517	213	17	↑	↑	PROPN
iajs-2517	213	18	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	213	19	,	,	PUNCT
iajs-2517	213	20	χ	χ	X
iajs-2517	213	21	)	)	PUNCT
iajs-2517	213	22	then	then	ADV
iajs-2517	213	23	player	player	NOUN
iajs-2517	213	24	ⅱ	ⅱ	PROPN
iajs-2517	213	25	↑	↑	PROPN
iajs-2517	213	26	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	213	27	,	,	PUNCT
iajs-2517	213	28	ℐ	ℐ	PROPN
iajs-2517	213	29	)	)	PUNCT
iajs-2517	213	30	.	.	PUNCT
iajs-2517	214	1	ii	ii	PROPN
iajs-2517	214	2	.	.	PUNCT
iajs-2517	215	1	if	if	SCONJ
iajs-2517	215	2	player	player	NOUN
iajs-2517	215	3	ⅰ	ⅰ	PROPN
iajs-2517	215	4	↑	↑	X
iajs-2517	215	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	215	6	,	,	PUNCT
iajs-2517	215	7	χ	χ	X
iajs-2517	215	8	)	)	PUNCT
iajs-2517	215	9	then	then	ADV
iajs-2517	215	10	player	player	NOUN
iajs-2517	215	11	ⅰ	ⅰ	PROPN
iajs-2517	215	12	↑	↑	PROPN
iajs-2517	215	13	ş𝒢	ş𝒢	PROPN
iajs-2517	215	14	(	(	PUNCT
iajs-2517	215	15	𝒯0	𝒯0	NOUN
iajs-2517	215	16	,	,	PUNCT
iajs-2517	215	17	ℐ	ℐ	PROPN
iajs-2517	215	18	)	)	PUNCT
iajs-2517	215	19	.	.	PUNCT
iajs-2517	216	1	remark	remark	VERB
iajs-2517	216	2	5.5	5.5	NUM
iajs-2517	216	3	.	.	PUNCT
iajs-2517	217	1	for	for	ADP
iajs-2517	217	2	a	a	DET
iajs-2517	217	3	space	space	NOUN
iajs-2517	217	4	(	(	PUNCT
iajs-2517	217	5	χ	χ	X
iajs-2517	217	6	,	,	PUNCT
iajs-2517	217	7	𝒯	𝒯	PROPN
iajs-2517	217	8	,	,	PUNCT
iajs-2517	217	9	ℋ	ℋ	PROPN
iajs-2517	217	10	,	,	PUNCT
iajs-2517	217	11	ℐ	ℐ	PROPN
iajs-2517	217	12	)	)	PUNCT
iajs-2517	217	13	,	,	PUNCT
iajs-2517	217	14	if	if	SCONJ
iajs-2517	217	15	player	player	NOUN
iajs-2517	217	16	ⅱ	ⅱ	PROPN
iajs-2517	217	17	↓	↓	PROPN
iajs-2517	217	18	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	217	19	,	,	PUNCT
iajs-2517	217	20	χ	χ	X
iajs-2517	217	21	)	)	PUNCT
iajs-2517	217	22	then	then	ADV
iajs-2517	217	23	player	player	NOUN
iajs-2517	217	24	ⅱ	ⅱ	PROPN
iajs-2517	217	25	↓	↓	PROPN
iajs-2517	217	26	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	217	27	,	,	PUNCT
iajs-2517	217	28	ℐ	ℐ	PROPN
iajs-2517	217	29	)	)	PUNCT
iajs-2517	217	30	.	.	PUNCT
iajs-2517	218	1	theorem	theorem	VERB
iajs-2517	218	2	5.6	5.6	NUM
iajs-2517	218	3	.	.	PUNCT
iajs-2517	219	1	a	a	DET
iajs-2517	219	2	space	space	NOUN
iajs-2517	219	3	(	(	PUNCT
iajs-2517	219	4	χ	χ	X
iajs-2517	219	5	,	,	PUNCT
iajs-2517	219	6	𝒯	𝒯	PROPN
iajs-2517	219	7	,	,	PUNCT
iajs-2517	219	8	ℋ	ℋ	PROPN
iajs-2517	219	9	)	)	PUNCT
iajs-2517	219	10	(	(	PUNCT
iajs-2517	219	11	respectively	respectively	ADV
iajs-2517	219	12	(	(	PUNCT
iajs-2517	219	13	χ	χ	X
iajs-2517	219	14	,	,	PUNCT
iajs-2517	219	15	𝒯	𝒯	PROPN
iajs-2517	219	16	,	,	PUNCT
iajs-2517	219	17	ℋ	ℋ	PROPN
iajs-2517	219	18	,	,	PUNCT
iajs-2517	219	19	ℐ	ℐ	NOUN
iajs-2517	219	20	)	)	PUNCT
iajs-2517	219	21	)	)	PUNCT
iajs-2517	219	22	is	be	AUX
iajs-2517	219	23	𝒯0	𝒯0	NOUN
iajs-2517	219	24	-	-	PUNCT
iajs-2517	219	25	space	space	NOUN
iajs-2517	219	26	(	(	PUNCT
iajs-2517	219	27	respectively	respectively	ADV
iajs-2517	219	28	,	,	PUNCT
iajs-2517	219	29	sℐsg𝒯0	sℐsg𝒯0	NOUN
iajs-2517	219	30	-	-	PUNCT
iajs-2517	219	31	space	space	NOUN
iajs-2517	219	32	)	)	PUNCT
iajs-2517	220	1	if	if	SCONJ
iajs-2517	220	2	and	and	CCONJ
iajs-2517	220	3	only	only	ADV
iajs-2517	220	4	if	if	SCONJ
iajs-2517	220	5	player	player	NOUN
iajs-2517	220	6	ⅱ	ⅱ	PROPN
iajs-2517	220	7	↑	↑	PROPN
iajs-2517	220	8	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	220	9	,	,	PUNCT
iajs-2517	220	10	χ	χ	X
iajs-2517	220	11	)	)	PUNCT
iajs-2517	220	12	(	(	PUNCT
iajs-2517	220	13	respectively	respectively	ADV
iajs-2517	220	14	,	,	PUNCT
iajs-2517	220	15	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	220	16	,	,	PUNCT
iajs-2517	220	17	ℐ	ℐ	NOUN
iajs-2517	220	18	)	)	PUNCT
iajs-2517	220	19	)	)	PUNCT
iajs-2517	220	20	.	.	PUNCT
iajs-2517	221	1	proof	proof	NOUN
iajs-2517	221	2	:	:	PUNCT
iajs-2517	221	3	(	(	PUNCT
iajs-2517	221	4	⇒	⇒	NOUN
iajs-2517	221	5	)	)	PUNCT
iajs-2517	221	6	in	in	ADP
iajs-2517	221	7	the	the	DET
iajs-2517	221	8	𝑟-𝑡ℎ	𝑟-𝑡ℎ	PROPN
iajs-2517	221	9	inning	inne	VERB
iajs-2517	221	10	player	player	NOUN
iajs-2517	221	11	in	in	ADP
iajs-2517	221	12	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	221	13	,	,	PUNCT
iajs-2517	221	14	χ	χ	X
iajs-2517	221	15	)	)	PUNCT
iajs-2517	221	16	(	(	PUNCT
iajs-2517	221	17	respectively	respectively	ADV
iajs-2517	221	18	,	,	PUNCT
iajs-2517	221	19	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	221	20	,	,	PUNCT
iajs-2517	221	21	ℐ	ℐ	NOUN
iajs-2517	221	22	)	)	PUNCT
iajs-2517	221	23	)	)	PUNCT
iajs-2517	222	1	choose	choose	VERB
iajs-2517	222	2	(	(	PUNCT
iajs-2517	222	3	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	222	4	≠	≠	PROPN
iajs-2517	222	5	(	(	PUNCT
iajs-2517	222	6	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	222	7	where	where	SCONJ
iajs-2517	222	8	,	,	PUNCT
iajs-2517	222	9	(	(	PUNCT
iajs-2517	222	10	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	222	11	,	,	PUNCT
iajs-2517	222	12	(	(	PUNCT
iajs-2517	222	13	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	222	14	∈̃	∈̃	PROPN
iajs-2517	222	15	�	�	PROPN
iajs-2517	222	16	̃	̃	PROPN
iajs-2517	222	17	�	�	PROPN
iajs-2517	222	18	,	,	PUNCT
iajs-2517	222	19	player	player	NOUN
iajs-2517	222	20	in	in	ADP
iajs-2517	222	21	ⅱ	ⅱ	PROPN
iajs-2517	222	22	in	in	ADP
iajs-2517	222	23	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	222	24	,	,	PUNCT
iajs-2517	222	25	χ	χ	X
iajs-2517	222	26	)	)	PUNCT
iajs-2517	222	27	(	(	PUNCT
iajs-2517	222	28	respectively	respectively	ADV
iajs-2517	222	29	,	,	PUNCT
iajs-2517	222	30	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	222	31	,	,	PUNCT
iajs-2517	222	32	ℐ	ℐ	NOUN
iajs-2517	222	33	)	)	PUNCT
iajs-2517	222	34	)	)	PUNCT
iajs-2517	223	1	choose	choose	VERB
iajs-2517	223	2	(	(	PUNCT
iajs-2517	223	3	ơ𝑟	ơ𝑟	NOUN
iajs-2517	223	4	,	,	PUNCT
iajs-2517	223	5	ℋ	ℋ	PROPN
iajs-2517	223	6	)	)	PUNCT
iajs-2517	223	7	is	be	AUX
iajs-2517	223	8	a	a	DET
iajs-2517	223	9	soft	soft	ADJ
iajs-2517	223	10	open	open	ADJ
iajs-2517	223	11	(	(	PUNCT
iajs-2517	223	12	respectively	respectively	ADV
iajs-2517	223	13	,	,	PUNCT
iajs-2517	223	14	sℐsg	sℐsg	PROPN
iajs-2517	223	15	-	-	PUNCT
iajs-2517	223	16	open	open	ADJ
iajs-2517	223	17	set	set	NOUN
iajs-2517	223	18	)	)	PUNCT
iajs-2517	223	19	containing	contain	VERB
iajs-2517	223	20	only	only	ADV
iajs-2517	223	21	one	one	NUM
iajs-2517	223	22	of	of	ADP
iajs-2517	223	23	the	the	DET
iajs-2517	223	24	two	two	NUM
iajs-2517	223	25	elements	element	NOUN
iajs-2517	223	26	(	(	PUNCT
iajs-2517	223	27	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	223	28	,	,	PUNCT
iajs-2517	223	29	(	(	PUNCT
iajs-2517	223	30	𝒽𝒩)𝑟.	𝒽𝒩)𝑟.	NOUN
iajs-2517	223	31	since	since	SCONJ
iajs-2517	223	32	(	(	PUNCT
iajs-2517	223	33	χ	χ	X
iajs-2517	223	34	,	,	PUNCT
iajs-2517	223	35	𝒯	𝒯	PROPN
iajs-2517	223	36	,	,	PUNCT
iajs-2517	223	37	ℋ	ℋ	PROPN
iajs-2517	223	38	)	)	PUNCT
iajs-2517	223	39	is	be	AUX
iajs-2517	223	40	a	a	DET
iajs-2517	223	41	soft	soft	ADJ
iajs-2517	223	42	𝒯0	𝒯0	NOUN
iajs-2517	223	43	-	-	PUNCT
iajs-2517	223	44	space	space	NOUN
iajs-2517	223	45	(	(	PUNCT
iajs-2517	223	46	respectively	respectively	ADV
iajs-2517	223	47	,	,	PUNCT
iajs-2517	223	48	sℐsg-𝒯0	sℐsg-𝒯0	PROPN
iajs-2517	223	49	-	-	PUNCT
iajs-2517	223	50	space	space	NOUN
iajs-2517	223	51	)	)	PUNCT
iajs-2517	223	52	.	.	PUNCT
iajs-2517	224	1	then	then	ADV
iajs-2517	224	2	if	if	SCONJ
iajs-2517	224	3	ℬ	ℬ	NOUN
iajs-2517	224	4	=	=	PRON
iajs-2517	224	5	{	{	PUNCT
iajs-2517	224	6	(	(	PUNCT
iajs-2517	224	7	ơ1	ơ1	NOUN
iajs-2517	224	8	,	,	PUNCT
iajs-2517	224	9	ℋ	ℋ	NOUN
iajs-2517	224	10	)	)	PUNCT
iajs-2517	224	11	,	,	PUNCT
iajs-2517	224	12	(	(	PUNCT
iajs-2517	224	13	ơ2	ơ2	NOUN
iajs-2517	224	14	,	,	PUNCT
iajs-2517	224	15	ℋ	ℋ	PROPN
iajs-2517	224	16	)	)	PUNCT
iajs-2517	224	17	,	,	PUNCT
iajs-2517	224	18	(	(	PUNCT
iajs-2517	224	19	ơ3	ơ3	NOUN
iajs-2517	224	20	,	,	PUNCT
iajs-2517	224	21	ℋ	ℋ	PROPN
iajs-2517	224	22	)	)	PUNCT
iajs-2517	224	23	,	,	PUNCT
iajs-2517	224	24	…	…	PUNCT
iajs-2517	224	25	,	,	PUNCT
iajs-2517	224	26	(	(	PUNCT
iajs-2517	224	27	ơ𝑟	ơ𝑟	ADP
iajs-2517	224	28	,	,	PUNCT
iajs-2517	224	29	ℋ	ℋ	PROPN
iajs-2517	224	30	)	)	PUNCT
iajs-2517	224	31	,	,	PUNCT
iajs-2517	224	32	...	...	PUNCT
iajs-2517	224	33	}	}	PUNCT
iajs-2517	224	34	is	be	AUX
iajs-2517	224	35	the	the	DET
iajs-2517	224	36	winning	win	VERB
iajs-2517	224	37	strategy	strategy	NOUN
iajs-2517	224	38	for	for	ADP
iajs-2517	224	39	player	player	NOUN
iajs-2517	224	40	in	in	ADP
iajs-2517	224	41	ⅱ	ⅱ	PROPN
iajs-2517	224	42	in	in	ADP
iajs-2517	224	43	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	224	44	,	,	PUNCT
iajs-2517	224	45	χ	χ	X
iajs-2517	224	46	)	)	PUNCT
iajs-2517	224	47	(	(	PUNCT
iajs-2517	224	48	respectively	respectively	ADV
iajs-2517	224	49	,	,	PUNCT
iajs-2517	224	50	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	224	51	,	,	PUNCT
iajs-2517	224	52	ℐ	ℐ	NOUN
iajs-2517	224	53	)	)	PUNCT
iajs-2517	224	54	)	)	PUNCT
iajs-2517	224	55	.	.	PUNCT
iajs-2517	225	1	hence	hence	ADV
iajs-2517	225	2	player	player	NOUN
iajs-2517	225	3	ⅱ	ⅱ	PROPN
iajs-2517	225	4	↑	↑	PROPN
iajs-2517	225	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	225	6	,	,	PUNCT
iajs-2517	225	7	χ	χ	X
iajs-2517	225	8	)	)	PUNCT
iajs-2517	225	9	(	(	PUNCT
iajs-2517	225	10	respectively	respectively	ADV
iajs-2517	225	11	,	,	PUNCT
iajs-2517	225	12	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	225	13	,	,	PUNCT
iajs-2517	225	14	ℐ	ℐ	NOUN
iajs-2517	225	15	)	)	PUNCT
iajs-2517	225	16	)	)	PUNCT
iajs-2517	225	17	.	.	PUNCT
iajs-2517	226	1	(	(	PUNCT
iajs-2517	226	2	⇐	⇐	INTJ
iajs-2517	226	3	)	)	PUNCT
iajs-2517	226	4	clear	clear	ADJ
iajs-2517	226	5	.	.	PUNCT
iajs-2517	227	1	130	130	NUM
iajs-2517	227	2	ibn	ibn	PROPN
iajs-2517	227	3	al	al	PROPN
iajs-2517	227	4	-	-	PUNCT
iajs-2517	227	5	haitham	haitham	PROPN
iajs-2517	227	6	jour	jour	X
iajs-2517	227	7	.	.	PROPN
iajs-2517	227	8	for	for	ADP
iajs-2517	227	9	pure	pure	ADJ
iajs-2517	227	10	&	&	CCONJ
iajs-2517	227	11	appl	appl	PROPN
iajs-2517	227	12	.	.	PUNCT
iajs-2517	228	1	sci	sci	PROPN
iajs-2517	228	2	.	.	PROPN
iajs-2517	229	1	33	33	NUM
iajs-2517	229	2	(	(	PUNCT
iajs-2517	229	3	4	4	NUM
iajs-2517	229	4	)	)	PUNCT
iajs-2517	229	5	2020	2020	NUM
iajs-2517	229	6	corollary	corollary	ADJ
iajs-2517	229	7	5.7	5.7	NUM
iajs-2517	229	8	.	.	PUNCT
iajs-2517	230	1	for	for	ADP
iajs-2517	230	2	a	a	DET
iajs-2517	230	3	space	space	NOUN
iajs-2517	230	4	(	(	PUNCT
iajs-2517	230	5	χ	χ	X
iajs-2517	230	6	,	,	PUNCT
iajs-2517	230	7	𝒯	𝒯	PROPN
iajs-2517	230	8	,	,	PUNCT
iajs-2517	230	9	ℋ	ℋ	PROPN
iajs-2517	230	10	):	):	PUNCT
iajs-2517	230	11	iplayer	iplayer	PROPN
iajs-2517	230	12	ⅱ	ⅱ	PROPN
iajs-2517	230	13	↑	↑	PROPN
iajs-2517	230	14	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	230	15	,	,	PUNCT
iajs-2517	230	16	χ	χ	X
iajs-2517	230	17	)	)	PUNCT
iajs-2517	230	18	if	if	SCONJ
iajs-2517	230	19	and	and	CCONJ
iajs-2517	230	20	only	only	ADV
iajs-2517	230	21	if	if	SCONJ
iajs-2517	230	22	∀	∀	NOUN
iajs-2517	230	23	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	230	24	≠	≠	PROPN
iajs-2517	230	25	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	230	26	where	where	SCONJ
iajs-2517	230	27	,	,	PUNCT
iajs-2517	230	28	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	230	29	,	,	PUNCT
iajs-2517	230	30	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	230	31	∈̃	∈̃	PROPN
iajs-2517	230	32	𝜒	𝜒	X
iajs-2517	230	33	∃	∃	PROPN
iajs-2517	230	34	(	(	PUNCT
iajs-2517	230	35	𝒜	𝒜	PROPN
iajs-2517	230	36	,	,	PUNCT
iajs-2517	230	37	ℋ	ℋ	PROPN
iajs-2517	230	38	)	)	PUNCT
iajs-2517	230	39	is	be	AUX
iajs-2517	230	40	a	a	DET
iajs-2517	230	41	𝑐𝑙𝑜𝑠𝑒𝑑	𝑐𝑙𝑜𝑠𝑒𝑑	NOUN
iajs-2517	230	42	set	set	NOUN
iajs-2517	230	43	where	where	SCONJ
iajs-2517	230	44	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	230	45	∈̃	∈̃	NOUN
iajs-2517	230	46	(	(	PUNCT
iajs-2517	230	47	𝒜	𝒜	NOUN
iajs-2517	230	48	,	,	PUNCT
iajs-2517	230	49	ℋ	ℋ	NOUN
iajs-2517	230	50	)	)	PUNCT
iajs-2517	230	51	and	and	CCONJ
iajs-2517	230	52	𝒽𝒩	𝒽𝒩	ADP
iajs-2517	230	53	∉̃	∉̃	ADJ
iajs-2517	230	54	(	(	PUNCT
iajs-2517	230	55	𝒜	𝒜	NOUN
iajs-2517	230	56	,	,	PUNCT
iajs-2517	230	57	ℋ	ℋ	PROPN
iajs-2517	230	58	)	)	PUNCT
iajs-2517	230	59	.	.	PUNCT
iajs-2517	231	1	iiplayer	iiplayer	NOUN
iajs-2517	231	2	ⅱ	ⅱ	PROPN
iajs-2517	231	3	↑	↑	PROPN
iajs-2517	231	4	ş𝒢(𝒯0	ş𝒢(𝒯0	PROPN
iajs-2517	231	5	,	,	PUNCT
iajs-2517	231	6	ℐ	ℐ	NOUN
iajs-2517	231	7	)	)	PUNCT
iajs-2517	232	1	if	if	SCONJ
iajs-2517	232	2	and	and	CCONJ
iajs-2517	232	3	only	only	ADV
iajs-2517	232	4	if	if	SCONJ
iajs-2517	232	5	∀	∀	NOUN
iajs-2517	232	6	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	232	7	≠	≠	PROPN
iajs-2517	232	8	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	232	9	where	where	SCONJ
iajs-2517	232	10	,	,	PUNCT
iajs-2517	232	11	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	232	12	,	,	PUNCT
iajs-2517	232	13	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	232	14	∈̃	∈̃	PROPN
iajs-2517	232	15	𝜒	𝜒	X
iajs-2517	232	16	∃	∃	PROPN
iajs-2517	232	17	(	(	PUNCT
iajs-2517	232	18	ℬ	ℬ	PROPN
iajs-2517	232	19	,	,	PUNCT
iajs-2517	232	20	ℋ	ℋ	PROPN
iajs-2517	232	21	)	)	PUNCT
iajs-2517	232	22	is	be	AUX
iajs-2517	232	23	a	a	DET
iajs-2517	232	24	sℐsg	sℐsg	PROPN
iajs-2517	232	25	-	-	PUNCT
iajs-2517	232	26	closed	close	VERB
iajs-2517	232	27	set	set	NOUN
iajs-2517	232	28	where	where	SCONJ
iajs-2517	232	29	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	232	30	∈̃	∈̃	NOUN
iajs-2517	232	31	(	(	PUNCT
iajs-2517	232	32	ℬ	ℬ	X
iajs-2517	232	33	,	,	PUNCT
iajs-2517	232	34	ℋ	ℋ	NOUN
iajs-2517	232	35	)	)	PUNCT
iajs-2517	232	36	and	and	CCONJ
iajs-2517	232	37	𝒽𝒩	𝒽𝒩	ADP
iajs-2517	232	38	∉̃	∉̃	ADJ
iajs-2517	232	39	(	(	PUNCT
iajs-2517	232	40	ℬ	ℬ	NOUN
iajs-2517	232	41	,	,	PUNCT
iajs-2517	232	42	ℋ	ℋ	PROPN
iajs-2517	232	43	)	)	PUNCT
iajs-2517	233	1	.	.	PUNCT
iajs-2517	234	1	proof	proof	NOUN
iajs-2517	234	2	:	:	PUNCT
iajs-2517	234	3	i.	i.	PROPN
iajs-2517	234	4	(	(	PUNCT
iajs-2517	234	5	⟹	⟹	X
iajs-2517	234	6	)	)	PUNCT
iajs-2517	234	7	let	let	VERB
iajs-2517	234	8	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	234	9	≠	≠	PROPN
iajs-2517	234	10	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	234	11	where	where	SCONJ
iajs-2517	234	12	,	,	PUNCT
iajs-2517	234	13	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	234	14	,	,	PUNCT
iajs-2517	234	15	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	234	16	∈̃	∈̃	NOUN
iajs-2517	234	17	𝜒	𝜒	X
iajs-2517	234	18	.	.	PUNCT
iajs-2517	235	1	since	since	SCONJ
iajs-2517	235	2	player	player	NOUN
iajs-2517	235	3	ⅱ	ⅱ	PROPN
iajs-2517	235	4	↑	↑	PROPN
iajs-2517	235	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	235	6	,	,	PUNCT
iajs-2517	235	7	χ	χ	X
iajs-2517	235	8	)	)	PUNCT
iajs-2517	235	9	,	,	PUNCT
iajs-2517	235	10	then	then	ADV
iajs-2517	235	11	by	by	ADP
iajs-2517	235	12	theorem	theorem	NOUN
iajs-2517	235	13	5.6	5.6	NUM
iajs-2517	235	14	,	,	PUNCT
iajs-2517	235	15	the	the	DET
iajs-2517	235	16	space	space	NOUN
iajs-2517	235	17	(	(	PUNCT
iajs-2517	235	18	χ	χ	X
iajs-2517	235	19	,	,	PUNCT
iajs-2517	235	20	𝒯	𝒯	PROPN
iajs-2517	235	21	,	,	PUNCT
iajs-2517	235	22	ℋ	ℋ	PROPN
iajs-2517	235	23	)	)	PUNCT
iajs-2517	235	24	is	be	AUX
iajs-2517	235	25	a	a	DET
iajs-2517	235	26	soft𝒯0­space	soft𝒯0­space	NOUN
iajs-2517	235	27	.	.	PUNCT
iajs-2517	236	1	then	then	ADV
iajs-2517	236	2	theorem	theorem	VERB
iajs-2517	236	3	1.17	1.17	NUM
iajs-2517	236	4	,	,	PUNCT
iajs-2517	236	5	is	be	AUX
iajs-2517	236	6	applicable	applicable	ADJ
iajs-2517	236	7	.	.	PUNCT
iajs-2517	237	1	(	(	PUNCT
iajs-2517	237	2	⟸	⟸	NOUN
iajs-2517	237	3	)	)	PUNCT
iajs-2517	237	4	by	by	ADP
iajs-2517	237	5	theorem	theorem	NOUN
iajs-2517	237	6	2.17	2.17	NUM
iajs-2517	237	7	,	,	PUNCT
iajs-2517	237	8	the	the	DET
iajs-2517	237	9	space	space	NOUN
iajs-2517	237	10	(	(	PUNCT
iajs-2517	237	11	χ	χ	X
iajs-2517	237	12	,	,	PUNCT
iajs-2517	237	13	𝒯	𝒯	PROPN
iajs-2517	237	14	,	,	PUNCT
iajs-2517	237	15	ℋ	ℋ	PROPN
iajs-2517	237	16	)	)	PUNCT
iajs-2517	237	17	is	be	AUX
iajs-2517	237	18	a	a	DET
iajs-2517	237	19	soft𝒯0­space	soft𝒯0­space	NOUN
iajs-2517	237	20	.	.	PUNCT
iajs-2517	238	1	then	then	ADV
iajs-2517	238	2	theorem	theorem	VERB
iajs-2517	238	3	4.6	4.6	NUM
iajs-2517	238	4	,	,	PUNCT
iajs-2517	238	5	is	be	AUX
iajs-2517	238	6	applicable	applicable	ADJ
iajs-2517	238	7	.	.	PUNCT
iajs-2517	239	1	ii	ii	X
iajs-2517	239	2	.	.	PUNCT
iajs-2517	240	1	(	(	PUNCT
iajs-2517	240	2	⟹	⟹	X
iajs-2517	240	3	)	)	PUNCT
iajs-2517	240	4	let	let	VERB
iajs-2517	240	5	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	240	6	≠	≠	PROPN
iajs-2517	240	7	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	240	8	where	where	SCONJ
iajs-2517	240	9	,	,	PUNCT
iajs-2517	240	10	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	240	11	,	,	PUNCT
iajs-2517	240	12	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	240	13	∈̃	∈̃	NOUN
iajs-2517	240	14	𝜒	𝜒	X
iajs-2517	240	15	.	.	PUNCT
iajs-2517	241	1	since	since	SCONJ
iajs-2517	241	2	player	player	NOUN
iajs-2517	241	3	ⅱ	ⅱ	PROPN
iajs-2517	241	4	↑	↑	PROPN
iajs-2517	241	5	ş𝒢(𝒯0	ş𝒢(𝒯0	PROPN
iajs-2517	241	6	,	,	PUNCT
iajs-2517	241	7	ℐ	ℐ	PROPN
iajs-2517	241	8	)	)	PUNCT
iajs-2517	241	9	,	,	PUNCT
iajs-2517	241	10	then	then	ADV
iajs-2517	241	11	by	by	ADP
iajs-2517	241	12	theorem	theorem	PROPN
iajs-2517	241	13	4.1.6	4.1.6	PROPN
iajs-2517	241	14	,	,	PUNCT
iajs-2517	241	15	the	the	DET
iajs-2517	241	16	space	space	NOUN
iajs-2517	241	17	(	(	PUNCT
iajs-2517	241	18	χ	χ	X
iajs-2517	241	19	,	,	PUNCT
iajs-2517	241	20	𝒯	𝒯	PROPN
iajs-2517	241	21	,	,	PUNCT
iajs-2517	241	22	ℋ	ℋ	PROPN
iajs-2517	241	23	)	)	PUNCT
iajs-2517	241	24	is	be	AUX
iajs-2517	241	25	a	a	DET
iajs-2517	241	26	sℐsg-𝒯0­space	sℐsg-𝒯0­space	NOUN
iajs-2517	241	27	.	.	PUNCT
iajs-2517	242	1	then	then	ADV
iajs-2517	242	2	theorem	theorem	VERB
iajs-2517	242	3	4.4	4.4	NUM
iajs-2517	242	4	,	,	PUNCT
iajs-2517	242	5	is	be	AUX
iajs-2517	242	6	applicable	applicable	ADJ
iajs-2517	242	7	.	.	PUNCT
iajs-2517	243	1	(	(	PUNCT
iajs-2517	243	2	⟸	⟸	NOUN
iajs-2517	243	3	)	)	PUNCT
iajs-2517	243	4	by	by	ADP
iajs-2517	243	5	theorem	theorem	NOUN
iajs-2517	243	6	4.4	4.4	NUM
iajs-2517	243	7	,	,	PUNCT
iajs-2517	243	8	the	the	DET
iajs-2517	243	9	space	space	NOUN
iajs-2517	243	10	(	(	PUNCT
iajs-2517	243	11	χ	χ	X
iajs-2517	243	12	,	,	PUNCT
iajs-2517	243	13	𝒯	𝒯	PROPN
iajs-2517	243	14	,	,	PUNCT
iajs-2517	243	15	ℋ	ℋ	PROPN
iajs-2517	243	16	)	)	PUNCT
iajs-2517	243	17	is	be	AUX
iajs-2517	243	18	a	a	DET
iajs-2517	243	19	sℐsg-𝒯0­space	sℐsg-𝒯0­space	NOUN
iajs-2517	243	20	.	.	PUNCT
iajs-2517	244	1	then	then	ADV
iajs-2517	244	2	theorem	theorem	VERB
iajs-2517	244	3	4.6	4.6	NUM
iajs-2517	244	4	,	,	PUNCT
iajs-2517	244	5	is	be	AUX
iajs-2517	244	6	applicable	applicable	ADJ
iajs-2517	244	7	.	.	PUNCT
iajs-2517	245	1	corollary	corollary	ADJ
iajs-2517	245	2	5.8	5.8	NUM
iajs-2517	245	3	.	.	PUNCT
iajs-2517	246	1	ia	ia	PROPN
iajs-2517	246	2	space	space	NOUN
iajs-2517	246	3	(	(	PUNCT
iajs-2517	246	4	χ	χ	X
iajs-2517	246	5	,	,	PUNCT
iajs-2517	246	6	𝒯	𝒯	PROPN
iajs-2517	246	7	,	,	PUNCT
iajs-2517	246	8	ℋ	ℋ	PROPN
iajs-2517	246	9	)	)	PUNCT
iajs-2517	246	10	is	be	AUX
iajs-2517	246	11	a	a	DET
iajs-2517	246	12	soft-𝒯0­space	soft-𝒯0­space	NOUN
iajs-2517	246	13	if	if	SCONJ
iajs-2517	247	1	and	and	CCONJ
iajs-2517	247	2	only	only	ADV
iajs-2517	247	3	if	if	SCONJ
iajs-2517	247	4	player	player	NOUN
iajs-2517	247	5	ⅰ	ⅰ	X
iajs-2517	247	6	⤉	⤉	VERB
iajs-2517	247	7	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	247	8	,	,	PUNCT
iajs-2517	247	9	χ	χ	X
iajs-2517	247	10	)	)	PUNCT
iajs-2517	247	11	.	.	PUNCT
iajs-2517	248	1	iia	iia	NOUN
iajs-2517	248	2	space	space	NOUN
iajs-2517	248	3	(	(	PUNCT
iajs-2517	248	4	χ	χ	X
iajs-2517	248	5	,	,	PUNCT
iajs-2517	248	6	𝒯	𝒯	PROPN
iajs-2517	248	7	,	,	PUNCT
iajs-2517	248	8	ℋ	ℋ	PROPN
iajs-2517	248	9	,	,	PUNCT
iajs-2517	248	10	ℐ	ℐ	NUM
iajs-2517	248	11	)	)	PUNCT
iajs-2517	248	12	is	be	AUX
iajs-2517	248	13	a	a	DET
iajs-2517	248	14	sℐsg-𝒯0­space	sℐsg-𝒯0­space	PROPN
iajs-2517	248	15	if	if	SCONJ
iajs-2517	249	1	and	and	CCONJ
iajs-2517	249	2	only	only	ADV
iajs-2517	249	3	if	if	SCONJ
iajs-2517	249	4	player	player	NOUN
iajs-2517	249	5	ⅰ	ⅰ	PRON
iajs-2517	249	6	⤉	⤉	VERB
iajs-2517	249	7	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	249	8	,	,	PUNCT
iajs-2517	249	9	ℐ	ℐ	NOUN
iajs-2517	249	10	)	)	PUNCT
iajs-2517	249	11	.	.	PUNCT
iajs-2517	250	1	proof	proof	NOUN
iajs-2517	250	2	:	:	PUNCT
iajs-2517	250	3	by	by	ADP
iajs-2517	250	4	theorem	theorem	NOUN
iajs-2517	250	5	5.6	5.6	NUM
iajs-2517	250	6	,	,	PUNCT
iajs-2517	250	7	the	the	DET
iajs-2517	250	8	proof	proof	NOUN
iajs-2517	250	9	is	be	AUX
iajs-2517	250	10	over	over	ADV
iajs-2517	250	11	.	.	PUNCT
iajs-2517	251	1	theorem	theorem	VERB
iajs-2517	251	2	5.9	5.9	NUM
iajs-2517	251	3	.	.	PUNCT
iajs-2517	252	1	for	for	ADP
iajs-2517	252	2	a	a	DET
iajs-2517	252	3	space	space	NOUN
iajs-2517	252	4	(	(	PUNCT
iajs-2517	252	5	χ	χ	X
iajs-2517	252	6	,	,	PUNCT
iajs-2517	252	7	𝒯	𝒯	PROPN
iajs-2517	252	8	,	,	PUNCT
iajs-2517	252	9	ℋ	ℋ	PROPN
iajs-2517	252	10	,	,	PUNCT
iajs-2517	252	11	ℐ	ℐ	PROPN
iajs-2517	252	12	)	)	PUNCT
iajs-2517	252	13	:	:	PUNCT
iajs-2517	252	14	ia	ia	PROPN
iajs-2517	252	15	space	space	NOUN
iajs-2517	252	16	(	(	PUNCT
iajs-2517	252	17	χ	χ	X
iajs-2517	252	18	,	,	PUNCT
iajs-2517	252	19	𝒯	𝒯	PROPN
iajs-2517	252	20	,	,	PUNCT
iajs-2517	252	21	ℋ	ℋ	PROPN
iajs-2517	252	22	)	)	PUNCT
iajs-2517	252	23	is	be	AUX
iajs-2517	252	24	not	not	PART
iajs-2517	252	25	soft-𝒯0­space	soft-𝒯0­space	NOUN
iajs-2517	252	26	if	if	SCONJ
iajs-2517	253	1	and	and	CCONJ
iajs-2517	253	2	only	only	ADV
iajs-2517	253	3	if	if	SCONJ
iajs-2517	253	4	player	player	NOUN
iajs-2517	253	5	ⅰ	ⅰ	X
iajs-2517	253	6	↑	↑	X
iajs-2517	253	7	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	253	8	,	,	PUNCT
iajs-2517	253	9	χ	χ	X
iajs-2517	253	10	)	)	PUNCT
iajs-2517	253	11	.	.	PUNCT
iajs-2517	254	1	iia	iia	NOUN
iajs-2517	254	2	space	space	NOUN
iajs-2517	254	3	(	(	PUNCT
iajs-2517	254	4	χ	χ	X
iajs-2517	254	5	,	,	PUNCT
iajs-2517	254	6	𝒯	𝒯	PROPN
iajs-2517	254	7	,	,	PUNCT
iajs-2517	254	8	ℋ	ℋ	PROPN
iajs-2517	254	9	,	,	PUNCT
iajs-2517	254	10	ℐ	ℐ	NUM
iajs-2517	254	11	)	)	PUNCT
iajs-2517	254	12	is	be	AUX
iajs-2517	254	13	not	not	PART
iajs-2517	254	14	sℐsg-𝒯0­space	sℐsg-𝒯0­space	NOUN
iajs-2517	254	15	if	if	SCONJ
iajs-2517	255	1	and	and	CCONJ
iajs-2517	255	2	only	only	ADV
iajs-2517	255	3	if	if	SCONJ
iajs-2517	255	4	playerⅰ	playerⅰ	PROPN
iajs-2517	255	5	↑	↑	PROPN
iajs-2517	255	6	ş𝒢(𝒯0	ş𝒢(𝒯0	VERB
iajs-2517	255	7	,	,	PUNCT
iajs-2517	255	8	ℐ	ℐ	NOUN
iajs-2517	255	9	)	)	PUNCT
iajs-2517	255	10	.	.	PUNCT
iajs-2517	256	1	proof	proof	NOUN
iajs-2517	256	2	:	:	PUNCT
iajs-2517	256	3	i(⟹	i(⟹	NOUN
iajs-2517	256	4	)	)	PUNCT
iajs-2517	256	5	in	in	ADP
iajs-2517	256	6	the	the	DET
iajs-2517	256	7	𝑟-th	𝑟-th	NOUN
iajs-2517	256	8	inning	inning	NOUN
iajs-2517	256	9	player	player	NOUN
iajs-2517	256	10	ⅰ	ⅰ	NUM
iajs-2517	256	11	in	in	ADP
iajs-2517	256	12	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	256	13	,	,	PUNCT
iajs-2517	256	14	χ	χ	X
iajs-2517	256	15	)	)	PUNCT
iajs-2517	256	16	choose	choose	VERB
iajs-2517	256	17	(	(	PUNCT
iajs-2517	256	18	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	256	19	≠	≠	PROPN
iajs-2517	256	20	(	(	PUNCT
iajs-2517	256	21	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	256	22	where	where	SCONJ
iajs-2517	256	23	,	,	PUNCT
iajs-2517	256	24	(	(	PUNCT
iajs-2517	256	25	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	256	26	,	,	PUNCT
iajs-2517	256	27	(	(	PUNCT
iajs-2517	256	28	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	256	29	∈̃	∈̃	PROPN
iajs-2517	256	30	�	�	PROPN
iajs-2517	256	31	̃	̃	PROPN
iajs-2517	256	32	�	�	PROPN
iajs-2517	256	33	,	,	PUNCT
iajs-2517	256	34	player	player	NOUN
iajs-2517	256	35	ⅱ	ⅱ	PROPN
iajs-2517	256	36	in	in	ADP
iajs-2517	256	37	ş𝒢(𝒯0	ş𝒢(𝒯0	PRON
iajs-2517	256	38	,	,	PUNCT
iajs-2517	256	39	χ	χ	X
iajs-2517	256	40	)	)	PUNCT
iajs-2517	256	41	can	can	AUX
iajs-2517	256	42	not	not	PART
iajs-2517	256	43	find	find	VERB
iajs-2517	256	44	(	(	PUNCT
iajs-2517	256	45	ơ𝑟,ℋ	ơ𝑟,ℋ	NUM
iajs-2517	256	46	)	)	PUNCT
iajs-2517	256	47	is	be	AUX
iajs-2517	256	48	a	a	DET
iajs-2517	256	49	soft	soft	ADJ
iajs-2517	256	50	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-2517	256	51	set	set	NOUN
iajs-2517	256	52	(	(	PUNCT
iajs-2517	256	53	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	256	54	∈̃	∈̃	PROPN
iajs-2517	256	55	(	(	PUNCT
iajs-2517	256	56	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	256	57	)	)	PUNCT
iajs-2517	256	58	,	,	PUNCT
iajs-2517	256	59	(	(	PUNCT
iajs-2517	256	60	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	256	61	∉̃	∉̃	PROPN
iajs-2517	256	62	(	(	PUNCT
iajs-2517	256	63	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	256	64	)	)	PUNCT
iajs-2517	256	65	or	or	CCONJ
iajs-2517	256	66	(	(	PUNCT
iajs-2517	256	67	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	256	68	∉̃	∉̃	NOUN
iajs-2517	256	69	(	(	PUNCT
iajs-2517	256	70	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	256	71	)	)	PUNCT
iajs-2517	256	72	,	,	PUNCT
iajs-2517	256	73	(	(	PUNCT
iajs-2517	257	1	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	257	2	∈̃	∈̃	PROPN
iajs-2517	257	3	(	(	PUNCT
iajs-2517	257	4	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	257	5	)	)	PUNCT
iajs-2517	257	6	.	.	PUNCT
iajs-2517	258	1	(	(	PUNCT
iajs-2517	258	2	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	258	3	,	,	PUNCT
iajs-2517	258	4	(	(	PUNCT
iajs-2517	258	5	𝒽𝒩)r	𝒽𝒩)r	ADP
iajs-2517	258	6	,	,	PUNCT
iajs-2517	258	7	because	because	SCONJ
iajs-2517	258	8	(	(	PUNCT
iajs-2517	258	9	χ	χ	X
iajs-2517	258	10	,	,	PUNCT
iajs-2517	258	11	𝒯	𝒯	PROPN
iajs-2517	258	12	,	,	PUNCT
iajs-2517	258	13	ℋ	ℋ	PROPN
iajs-2517	258	14	)	)	PUNCT
iajs-2517	258	15	is	be	AUX
iajs-2517	258	16	not	not	PART
iajs-2517	258	17	soft-𝒯0­space	soft-𝒯0­space	NOUN
iajs-2517	258	18	.	.	PUNCT
iajs-2517	259	1	hence	hence	ADV
iajs-2517	259	2	player	player	NOUN
iajs-2517	259	3	ⅰ	ⅰ	PROPN
iajs-2517	259	4	↑	↑	X
iajs-2517	259	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	259	6	,	,	PUNCT
iajs-2517	259	7	χ	χ	X
iajs-2517	259	8	)	)	PUNCT
iajs-2517	259	9	.	.	PUNCT
iajs-2517	260	1	(	(	PUNCT
iajs-2517	260	2	⟸	⟸	ADJ
iajs-2517	260	3	)	)	PUNCT
iajs-2517	260	4	clear	clear	ADJ
iajs-2517	260	5	.	.	PUNCT
iajs-2517	261	1	ii(⟹	ii(⟹	VERB
iajs-2517	261	2	)	)	PUNCT
iajs-2517	262	1	in	in	ADP
iajs-2517	262	2	the	the	DET
iajs-2517	262	3	𝑟-th	𝑟-th	NOUN
iajs-2517	262	4	inning	inning	NOUN
iajs-2517	262	5	player	player	NOUN
iajs-2517	262	6	ⅰ	ⅰ	NUM
iajs-2517	262	7	in	in	ADP
iajs-2517	262	8	ş𝒢(𝒯0	ş𝒢(𝒯0	PROPN
iajs-2517	262	9	,	,	PUNCT
iajs-2517	262	10	ℐ	ℐ	PRON
iajs-2517	262	11	)	)	PUNCT
iajs-2517	262	12	choose	choose	VERB
iajs-2517	262	13	(	(	PUNCT
iajs-2517	262	14	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	262	15	≠	≠	PROPN
iajs-2517	262	16	(	(	PUNCT
iajs-2517	262	17	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	262	18	where	where	SCONJ
iajs-2517	262	19	,	,	PUNCT
iajs-2517	262	20	(	(	PUNCT
iajs-2517	262	21	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	262	22	,	,	PUNCT
iajs-2517	262	23	(	(	PUNCT
iajs-2517	262	24	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	262	25	∈̃	∈̃	PROPN
iajs-2517	262	26	�	�	PROPN
iajs-2517	262	27	̃	̃	PROPN
iajs-2517	262	28	�	�	PROPN
iajs-2517	262	29	,	,	PUNCT
iajs-2517	262	30	player	player	NOUN
iajs-2517	262	31	ⅱ	ⅱ	PROPN
iajs-2517	262	32	in	in	ADP
iajs-2517	262	33	ş𝒢(𝒯0	ş𝒢(𝒯0	PROPN
iajs-2517	262	34	,	,	PUNCT
iajs-2517	262	35	ℐ	ℐ	X
iajs-2517	262	36	)	)	PUNCT
iajs-2517	262	37	can	can	AUX
iajs-2517	262	38	not	not	PART
iajs-2517	262	39	find	find	VERB
iajs-2517	262	40	(	(	PUNCT
iajs-2517	262	41	ơ𝑟,ℋ	ơ𝑟,ℋ	NUM
iajs-2517	262	42	)	)	PUNCT
iajs-2517	262	43	is	be	AUX
iajs-2517	262	44	a	a	DET
iajs-2517	262	45	sℐsg	sℐsg	PROPN
iajs-2517	262	46	𝑜𝑝𝑒𝑛	𝑜𝑝𝑒𝑛	NOUN
iajs-2517	262	47	set	set	NOUN
iajs-2517	262	48	(	(	PUNCT
iajs-2517	262	49	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	262	50	∈̃	∈̃	PROPN
iajs-2517	262	51	(	(	PUNCT
iajs-2517	262	52	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	262	53	)	)	PUNCT
iajs-2517	262	54	,	,	PUNCT
iajs-2517	262	55	(	(	PUNCT
iajs-2517	262	56	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	262	57	∉̃	∉̃	PROPN
iajs-2517	262	58	(	(	PUNCT
iajs-2517	262	59	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	262	60	)	)	PUNCT
iajs-2517	262	61	or	or	CCONJ
iajs-2517	262	62	(	(	PUNCT
iajs-2517	262	63	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	262	64	∉̃	∉̃	NOUN
iajs-2517	262	65	(	(	PUNCT
iajs-2517	262	66	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	262	67	)	)	PUNCT
iajs-2517	262	68	,	,	PUNCT
iajs-2517	262	69	(	(	PUNCT
iajs-2517	262	70	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	262	71	∈̃	∈̃	PROPN
iajs-2517	262	72	(	(	PUNCT
iajs-2517	262	73	ơ𝑟,ℋ	ơ𝑟,ℋ	PROPN
iajs-2517	262	74	)	)	PUNCT
iajs-2517	262	75	,	,	PUNCT
iajs-2517	262	76	because	because	SCONJ
iajs-2517	262	77	(	(	PUNCT
iajs-2517	262	78	χ	χ	X
iajs-2517	262	79	,	,	PUNCT
iajs-2517	262	80	𝒯	𝒯	PROPN
iajs-2517	262	81	,	,	PUNCT
iajs-2517	262	82	ℋ	ℋ	PROPN
iajs-2517	262	83	)	)	PUNCT
iajs-2517	262	84	is	be	AUX
iajs-2517	262	85	not	not	PART
iajs-2517	262	86	sℐsg-𝒯0­space	sℐsg-𝒯0­space	NOUN
iajs-2517	262	87	.	.	PUNCT
iajs-2517	263	1	hence	hence	ADV
iajs-2517	263	2	player	player	NOUN
iajs-2517	263	3	ⅰ	ⅰ	PROPN
iajs-2517	263	4	↑	↑	X
iajs-2517	263	5	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	263	6	,	,	PUNCT
iajs-2517	263	7	ℐ	ℐ	NOUN
iajs-2517	263	8	)	)	PUNCT
iajs-2517	263	9	.	.	PUNCT
iajs-2517	264	1	(	(	PUNCT
iajs-2517	264	2	⟸	⟸	ADJ
iajs-2517	264	3	)	)	PUNCT
iajs-2517	264	4	clear	clear	ADJ
iajs-2517	264	5	.	.	PUNCT
iajs-2517	265	1	corollary	corollary	ADJ
iajs-2517	265	2	5.10	5.10	NUM
iajs-2517	265	3	.	.	PUNCT
iajs-2517	266	1	ia	ia	PROPN
iajs-2517	266	2	space	space	NOUN
iajs-2517	266	3	(	(	PUNCT
iajs-2517	266	4	χ	χ	X
iajs-2517	266	5	,	,	PUNCT
iajs-2517	266	6	𝒯	𝒯	PROPN
iajs-2517	266	7	,	,	PUNCT
iajs-2517	266	8	ℋ	ℋ	PROPN
iajs-2517	266	9	)	)	PUNCT
iajs-2517	266	10	is	be	AUX
iajs-2517	266	11	not	not	PART
iajs-2517	266	12	soft-𝒯0­space	soft-𝒯0­space	NOUN
iajs-2517	266	13	if	if	SCONJ
iajs-2517	267	1	and	and	CCONJ
iajs-2517	267	2	only	only	ADV
iajs-2517	267	3	if	if	SCONJ
iajs-2517	267	4	player	player	NOUN
iajs-2517	267	5	ⅱ	ⅱ	NOUN
iajs-2517	267	6	⤉	⤉	VERB
iajs-2517	267	7	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	267	8	,	,	PUNCT
iajs-2517	267	9	χ	χ	X
iajs-2517	267	10	)	)	PUNCT
iajs-2517	267	11	.	.	PUNCT
iajs-2517	268	1	iia	iia	NOUN
iajs-2517	268	2	space	space	NOUN
iajs-2517	268	3	(	(	PUNCT
iajs-2517	268	4	χ	χ	X
iajs-2517	268	5	,	,	PUNCT
iajs-2517	268	6	𝒯	𝒯	PROPN
iajs-2517	268	7	,	,	PUNCT
iajs-2517	268	8	ℋ	ℋ	PROPN
iajs-2517	268	9	,	,	PUNCT
iajs-2517	268	10	ℐ	ℐ	NUM
iajs-2517	268	11	)	)	PUNCT
iajs-2517	268	12	is	be	AUX
iajs-2517	268	13	not	not	PART
iajs-2517	268	14	sℐsg-𝒯0­space	sℐsg-𝒯0­space	NOUN
iajs-2517	268	15	if	if	SCONJ
iajs-2517	269	1	and	and	CCONJ
iajs-2517	269	2	only	only	ADV
iajs-2517	269	3	if	if	SCONJ
iajs-2517	269	4	player	player	NOUN
iajs-2517	269	5	ⅱ	ⅱ	PROPN
iajs-2517	269	6	⤉	⤉	VERB
iajs-2517	269	7	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	269	8	,	,	PUNCT
iajs-2517	269	9	ℐ	ℐ	NOUN
iajs-2517	269	10	)	)	PUNCT
iajs-2517	269	11	.	.	PUNCT
iajs-2517	270	1	proof	proof	NOUN
iajs-2517	270	2	:	:	PUNCT
iajs-2517	270	3	by	by	ADP
iajs-2517	270	4	theorem	theorem	NOUN
iajs-2517	270	5	5.9	5.9	NUM
iajs-2517	270	6	,	,	PUNCT
iajs-2517	270	7	the	the	DET
iajs-2517	270	8	proof	proof	NOUN
iajs-2517	270	9	is	be	AUX
iajs-2517	270	10	over	over	ADV
iajs-2517	270	11	.	.	PUNCT
iajs-2517	271	1	definition	definition	NOUN
iajs-2517	271	2	5.11	5.11	NUM
iajs-2517	271	3	.	.	PUNCT
iajs-2517	272	1	for	for	ADP
iajs-2517	272	2	a	a	DET
iajs-2517	272	3	soft	soft	ADJ
iajs-2517	272	4	ideal	ideal	ADJ
iajs-2517	272	5	space	space	NOUN
iajs-2517	272	6	(	(	PUNCT
iajs-2517	272	7	χ	χ	X
iajs-2517	272	8	,	,	PUNCT
iajs-2517	272	9	𝒯	𝒯	PROPN
iajs-2517	272	10	,	,	PUNCT
iajs-2517	272	11	ℋ	ℋ	PROPN
iajs-2517	272	12	,	,	PUNCT
iajs-2517	272	13	ℐ	ℐ	PROPN
iajs-2517	272	14	)	)	PUNCT
iajs-2517	272	15	,	,	PUNCT
iajs-2517	272	16	determine	determine	VERB
iajs-2517	272	17	a	a	DET
iajs-2517	272	18	game	game	NOUN
iajs-2517	272	19	ş𝒢(𝒯1	ş𝒢(𝒯1	NOUN
iajs-2517	272	20	,	,	PUNCT
iajs-2517	272	21	χ	χ	X
iajs-2517	272	22	)	)	PUNCT
iajs-2517	272	23	(	(	PUNCT
iajs-2517	272	24	respectively	respectively	ADV
iajs-2517	272	25	,	,	PUNCT
iajs-2517	272	26	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	272	27	,	,	PUNCT
iajs-2517	272	28	ℐ	ℐ	NUM
iajs-2517	272	29	)	)	PUNCT
iajs-2517	272	30	)	)	PUNCT
iajs-2517	272	31	as	as	SCONJ
iajs-2517	272	32	follows	follow	VERB
iajs-2517	272	33	:	:	PUNCT
iajs-2517	272	34	player	player	NOUN
iajs-2517	272	35	ⅰ	ⅰ	NOUN
iajs-2517	272	36	and	and	CCONJ
iajs-2517	272	37	player	player	NOUN
iajs-2517	272	38	ⅱ	ⅱ	PROPN
iajs-2517	272	39	are	be	AUX
iajs-2517	272	40	play	play	VERB
iajs-2517	272	41	an	an	DET
iajs-2517	272	42	inning	inning	NOUN
iajs-2517	272	43	with	with	ADP
iajs-2517	272	44	each	each	DET
iajs-2517	272	45	positive	positive	ADJ
iajs-2517	272	46	integer	integer	NOUN
iajs-2517	272	47	numbers	number	NOUN
iajs-2517	272	48	in	in	ADP
iajs-2517	272	49	the	the	DET
iajs-2517	272	50	𝑟	𝑟	NOUN
iajs-2517	272	51	𝑡ℎ	𝑡ℎ	NOUN
iajs-2517	272	52	inning	inning	NOUN
iajs-2517	272	53	:	:	PUNCT
iajs-2517	272	54	the	the	DET
iajs-2517	272	55	first	first	ADJ
iajs-2517	272	56	step	step	NOUN
iajs-2517	272	57	,	,	PUNCT
iajs-2517	272	58	player	player	NOUN
iajs-2517	272	59	ⅰ	ⅰ	X
iajs-2517	272	60	choose	choose	VERB
iajs-2517	272	61	(	(	PUNCT
iajs-2517	272	62	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	272	63	≠	≠	PROPN
iajs-2517	272	64	(	(	PUNCT
iajs-2517	272	65	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	272	66	where	where	SCONJ
iajs-2517	272	67	,	,	PUNCT
iajs-2517	272	68	(	(	PUNCT
iajs-2517	272	69	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	272	70	,	,	PUNCT
iajs-2517	272	71	(	(	PUNCT
iajs-2517	272	72	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	272	73	∈̃	∈̃	PROPN
iajs-2517	272	74	�	�	PROPN
iajs-2517	272	75	̃	̃	PROPN
iajs-2517	272	76	�	�	PROPN
iajs-2517	272	77	.	.	PUNCT
iajs-2517	273	1	in	in	ADP
iajs-2517	273	2	the	the	DET
iajs-2517	273	3	second	second	ADJ
iajs-2517	273	4	step	step	NOUN
iajs-2517	273	5	,	,	PUNCT
iajs-2517	273	6	player	player	NOUN
iajs-2517	273	7	ⅱ	ⅱ	PROPN
iajs-2517	273	8	choose	choose	VERB
iajs-2517	273	9	(	(	PUNCT
iajs-2517	273	10	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	273	11	)	)	PUNCT
iajs-2517	273	12	,	,	PUNCT
iajs-2517	273	13	(	(	PUNCT
iajs-2517	273	14	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	273	15	)	)	PUNCT
iajs-2517	273	16	are	be	AUX
iajs-2517	273	17	two	two	NUM
iajs-2517	273	18	soft	soft	ADJ
iajs-2517	273	19	open	open	ADJ
iajs-2517	273	20	(	(	PUNCT
iajs-2517	273	21	respectively	respectively	ADV
iajs-2517	273	22	,	,	PUNCT
iajs-2517	273	23	sℐsg𝑜𝑝𝑒𝑛	sℐsg𝑜𝑝𝑒𝑛	PROPN
iajs-2517	273	24	)	)	PUNCT
iajs-2517	273	25	sets	set	VERB
iajs-2517	273	26	such	such	ADJ
iajs-2517	273	27	that	that	SCONJ
iajs-2517	273	28	(	(	PUNCT
iajs-2517	273	29	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	273	30	∈̃	∈̃	PROPN
iajs-2517	273	31	(	(	PUNCT
iajs-2517	273	32	(	(	PUNCT
iajs-2517	273	33	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	273	34	)	)	PUNCT
iajs-2517	273	35	‒	‒	NOUN
iajs-2517	273	36	(	(	PUNCT
iajs-2517	273	37	ℬ𝑟,ℋ))and	ℬ𝑟,ℋ))and	NOUN
iajs-2517	273	38	(	(	PUNCT
iajs-2517	273	39	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	273	40	∈̃	∈̃	PROPN
iajs-2517	273	41	(	(	PUNCT
iajs-2517	273	42	(	(	PUNCT
iajs-2517	273	43	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	273	44	)	)	PUNCT
iajs-2517	273	45	‒	‒	NOUN
iajs-2517	273	46	(	(	PUNCT
iajs-2517	273	47	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	273	48	)	)	PUNCT
iajs-2517	273	49	)	)	PUNCT
iajs-2517	273	50	.	.	PUNCT
iajs-2517	274	1	then	then	ADV
iajs-2517	274	2	player	player	NOUN
iajs-2517	274	3	ⅱ	ⅱ	PROPN
iajs-2517	274	4	wins	win	VERB
iajs-2517	274	5	in	in	ADP
iajs-2517	274	6	the	the	DET
iajs-2517	274	7	soft	soft	ADJ
iajs-2517	274	8	game	game	NOUN
iajs-2517	274	9	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	274	10	,	,	PUNCT
iajs-2517	274	11	χ	χ	X
iajs-2517	274	12	)	)	PUNCT
iajs-2517	274	13	(	(	PUNCT
iajs-2517	274	14	respectively	respectively	ADV
iajs-2517	274	15	,	,	PUNCT
iajs-2517	274	16	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	274	17	,	,	PUNCT
iajs-2517	274	18	ℐ	ℐ	NOUN
iajs-2517	274	19	)	)	PUNCT
iajs-2517	274	20	)	)	PUNCT
iajs-2517	275	1	131	131	NUM
iajs-2517	275	2	ibn	ibn	PROPN
iajs-2517	275	3	al	al	PROPN
iajs-2517	275	4	-	-	PUNCT
iajs-2517	275	5	haitham	haitham	PROPN
iajs-2517	275	6	jour	jour	X
iajs-2517	275	7	.	.	PROPN
iajs-2517	275	8	for	for	ADP
iajs-2517	275	9	pure	pure	ADJ
iajs-2517	275	10	&	&	CCONJ
iajs-2517	275	11	appl	appl	PROPN
iajs-2517	275	12	.	.	PUNCT
iajs-2517	276	1	sci	sci	PROPN
iajs-2517	276	2	.	.	PROPN
iajs-2517	277	1	33	33	NUM
iajs-2517	277	2	(	(	PUNCT
iajs-2517	277	3	4	4	NUM
iajs-2517	277	4	)	)	PUNCT
iajs-2517	277	5	2020	2020	NUM
iajs-2517	277	6	if	if	SCONJ
iajs-2517	277	7	ℬ	ℬ	NOUN
iajs-2517	277	8	=	=	PRON
iajs-2517	277	9	{	{	PUNCT
iajs-2517	277	10	{	{	PUNCT
iajs-2517	277	11	(	(	PUNCT
iajs-2517	277	12	𝒜1,ℋ	𝒜1,ℋ	PROPN
iajs-2517	277	13	)	)	PUNCT
iajs-2517	277	14	,	,	PUNCT
iajs-2517	277	15	(	(	PUNCT
iajs-2517	277	16	ℬ1,ℋ	ℬ1,ℋ	NOUN
iajs-2517	277	17	)	)	PUNCT
iajs-2517	277	18	}	}	PUNCT
iajs-2517	277	19	,	,	PUNCT
iajs-2517	277	20	{	{	PUNCT
iajs-2517	277	21	(	(	PUNCT
iajs-2517	277	22	𝒜2,ℋ	𝒜2,ℋ	NOUN
iajs-2517	277	23	)	)	PUNCT
iajs-2517	277	24	,	,	PUNCT
iajs-2517	277	25	(	(	PUNCT
iajs-2517	277	26	ℬ2,ℋ	ℬ2,ℋ	NOUN
iajs-2517	277	27	)	)	PUNCT
iajs-2517	277	28	}	}	PUNCT
iajs-2517	277	29	,	,	PUNCT
iajs-2517	277	30	…	…	PUNCT
iajs-2517	277	31	,	,	PUNCT
iajs-2517	277	32	{	{	PUNCT
iajs-2517	277	33	(	(	PUNCT
iajs-2517	277	34	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	277	35	)	)	PUNCT
iajs-2517	277	36	,	,	PUNCT
iajs-2517	277	37	(	(	PUNCT
iajs-2517	277	38	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	277	39	)	)	PUNCT
iajs-2517	277	40	}	}	PUNCT
iajs-2517	277	41	,	,	PUNCT
iajs-2517	277	42	…	…	PUNCT
iajs-2517	277	43	}	}	PUNCT
iajs-2517	277	44	be	be	AUX
iajs-2517	277	45	a	a	DET
iajs-2517	277	46	collection	collection	NOUN
iajs-2517	277	47	of	of	ADP
iajs-2517	277	48	a	a	DET
iajs-2517	277	49	soft	soft	ADJ
iajs-2517	277	50	open	open	NOUN
iajs-2517	277	51	(	(	PUNCT
iajs-2517	277	52	respectively	respectively	ADV
iajs-2517	277	53	,	,	PUNCT
iajs-2517	277	54	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	277	55	)	)	PUNCT
iajs-2517	277	56	sets	set	VERB
iajs-2517	277	57	in	in	ADP
iajs-2517	277	58	χ	χ	PRON
iajs-2517	277	59	such	such	ADJ
iajs-2517	277	60	that	that	DET
iajs-2517	277	61	∀	∀	X
iajs-2517	277	62	(	(	PUNCT
iajs-2517	277	63	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	277	64	≠	≠	PROPN
iajs-2517	277	65	(	(	PUNCT
iajs-2517	277	66	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	277	67	where	where	SCONJ
iajs-2517	277	68	,	,	PUNCT
iajs-2517	277	69	(	(	PUNCT
iajs-2517	277	70	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	277	71	,	,	PUNCT
iajs-2517	277	72	(	(	PUNCT
iajs-2517	277	73	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	277	74	∈̃	∈̃	PROPN
iajs-2517	277	75	�	�	PROPN
iajs-2517	277	76	̃	̃	PROPN
iajs-2517	277	77	�	�	PROPN
iajs-2517	277	78	,	,	PUNCT
iajs-2517	277	79	∃{(𝒜𝑟,ℋ	∃{(𝒜𝑟,ℋ	PROPN
iajs-2517	277	80	)	)	PUNCT
iajs-2517	277	81	,	,	PUNCT
iajs-2517	278	1	(	(	PUNCT
iajs-2517	278	2	ℬ𝑟,ℋ	ℬ𝑟,ℋ	ADJ
iajs-2517	278	3	)	)	PUNCT
iajs-2517	278	4	}	}	PUNCT
iajs-2517	278	5	∈	∈	NOUN
iajs-2517	278	6	ℬ	ℬ	NOUN
iajs-2517	278	7	such	such	ADJ
iajs-2517	278	8	that	that	SCONJ
iajs-2517	278	9	(	(	PUNCT
iajs-2517	278	10	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	278	11	∈̃	∈̃	PROPN
iajs-2517	278	12	(	(	PUNCT
iajs-2517	278	13	(	(	PUNCT
iajs-2517	278	14	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	278	15	)	)	PUNCT
iajs-2517	278	16	‒	‒	NOUN
iajs-2517	278	17	(	(	PUNCT
iajs-2517	278	18	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	278	19	)	)	PUNCT
iajs-2517	278	20	)	)	PUNCT
iajs-2517	278	21	and	and	CCONJ
iajs-2517	278	22	(	(	PUNCT
iajs-2517	278	23	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	278	24	∈̃	∈̃	PROPN
iajs-2517	278	25	(	(	PUNCT
iajs-2517	278	26	(	(	PUNCT
iajs-2517	278	27	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	278	28	)	)	PUNCT
iajs-2517	278	29	‒	‒	NOUN
iajs-2517	278	30	(	(	PUNCT
iajs-2517	278	31	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	278	32	)	)	PUNCT
iajs-2517	278	33	)	)	PUNCT
iajs-2517	278	34	.	.	PUNCT
iajs-2517	279	1	otherwise	otherwise	ADV
iajs-2517	279	2	,	,	PUNCT
iajs-2517	279	3	playerⅰ	playerⅰ	PROPN
iajs-2517	279	4	wins	win	VERB
iajs-2517	279	5	in	in	ADP
iajs-2517	279	6	the	the	DET
iajs-2517	279	7	soft	soft	ADJ
iajs-2517	279	8	game	game	NOUN
iajs-2517	279	9	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	279	10	,	,	PUNCT
iajs-2517	279	11	χ	χ	X
iajs-2517	279	12	)	)	PUNCT
iajs-2517	279	13	(	(	PUNCT
iajs-2517	279	14	respectively	respectively	ADV
iajs-2517	279	15	,	,	PUNCT
iajs-2517	279	16	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	279	17	,	,	PUNCT
iajs-2517	279	18	ℐ	ℐ	NOUN
iajs-2517	279	19	)	)	PUNCT
iajs-2517	279	20	)	)	PUNCT
iajs-2517	279	21	.	.	PUNCT
iajs-2517	280	1	example	example	NOUN
iajs-2517	281	1	5.12	5.12	NUM
iajs-2517	281	2	.	.	PUNCT
iajs-2517	282	1	let	let	VERB
iajs-2517	282	2	a	a	DET
iajs-2517	282	3	game	game	NOUN
iajs-2517	282	4	ş𝒢(𝒯1	ş𝒢(𝒯1	NOUN
iajs-2517	282	5	,	,	PUNCT
iajs-2517	282	6	χ	χ	X
iajs-2517	282	7	)	)	PUNCT
iajs-2517	282	8	(	(	PUNCT
iajs-2517	282	9	respectively	respectively	ADV
iajs-2517	282	10	,	,	PUNCT
iajs-2517	282	11	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	282	12	,	,	PUNCT
iajs-2517	282	13	ℐ	ℐ	NOUN
iajs-2517	282	14	)	)	PUNCT
iajs-2517	282	15	)	)	PUNCT
iajs-2517	283	1	be	be	AUX
iajs-2517	283	2	a	a	DET
iajs-2517	283	3	game	game	NOUN
iajs-2517	283	4	where	where	SCONJ
iajs-2517	283	5	,	,	PUNCT
iajs-2517	283	6	χ	χ	X
iajs-2517	283	7	=	=	PUNCT
iajs-2517	283	8	{	{	PUNCT
iajs-2517	283	9	1,2,3	1,2,3	NUM
iajs-2517	283	10	}	}	PUNCT
iajs-2517	283	11	,	,	PUNCT
iajs-2517	283	12	ℋ	ℋ	PROPN
iajs-2517	283	13	=	=	SYM
iajs-2517	283	14	{	{	PUNCT
iajs-2517	283	15	𝒽1	𝒽1	PROPN
iajs-2517	283	16	,	,	PUNCT
iajs-2517	283	17	𝒽2	𝒽2	PROPN
iajs-2517	283	18	}	}	PUNCT
iajs-2517	283	19	,	,	PUNCT
iajs-2517	283	20	𝒯	𝒯	PROPN
iajs-2517	283	21	=	=	PUNCT
iajs-2517	283	22	şş(χ)𝓗	şş(χ)𝓗	PROPN
iajs-2517	283	23	,	,	PUNCT
iajs-2517	283	24	ℐ	ℐ	PRON
iajs-2517	283	25	=	=	NOUN
iajs-2517	283	26	{	{	PUNCT
iajs-2517	283	27	∅̃	∅̃	NOUN
iajs-2517	283	28	}	}	PUNCT
iajs-2517	283	29	.	.	PUNCT
iajs-2517	284	1	then	then	ADV
iajs-2517	284	2	şş𝑂(ჯ	şş𝑂(ჯ	PROPN
iajs-2517	284	3	)	)	PUNCT
iajs-2517	284	4	=	=	SYM
iajs-2517	285	1	sℐsg­𝑐(χ)𝓗	sℐsg­𝑐(χ)𝓗	VERB
iajs-2517	285	2	=	=	NUM
iajs-2517	285	3	sℐsg­𝑜(χ)𝓗	sℐsg­𝑜(χ)𝓗	VERB
iajs-2517	285	4	=	=	PUNCT
iajs-2517	285	5	şş(χ)𝓗.	şş(χ)𝓗.	VERB
iajs-2517	285	6	in	in	ADP
iajs-2517	285	7	the	the	DET
iajs-2517	285	8	first	first	ADJ
iajs-2517	285	9	inning	inning	NOUN
iajs-2517	285	10	:	:	PUNCT
iajs-2517	285	11	the	the	DET
iajs-2517	285	12	first	first	ADJ
iajs-2517	285	13	step	step	NOUN
iajs-2517	285	14	,	,	PUNCT
iajs-2517	285	15	player	player	NOUN
iajs-2517	285	16	ⅰ	ⅰ	PROPN
iajs-2517	285	17	chooses	choose	VERB
iajs-2517	285	18	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	285	19	≠	≠	PROPN
iajs-2517	285	20	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	286	1	where	where	SCONJ
iajs-2517	286	2	,	,	PUNCT
iajs-2517	286	3	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	286	4	,	,	PUNCT
iajs-2517	286	5	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	286	6	∈̃	∈̃	PROPN
iajs-2517	286	7	�	�	PROPN
iajs-2517	286	8	̃	̃	PROPN
iajs-2517	286	9	�	�	NOUN
iajs-2517	286	10	such	such	ADJ
iajs-2517	286	11	that	that	PRON
iajs-2517	286	12	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	286	13	=	=	SYM
iajs-2517	286	14	{	{	PUNCT
iajs-2517	286	15	1	1	NUM
iajs-2517	286	16	}	}	PUNCT
iajs-2517	286	17	and	and	CCONJ
iajs-2517	286	18	𝒽𝒩	𝒽𝒩	NOUN
iajs-2517	286	19	=	=	PUNCT
iajs-2517	286	20	{	{	PUNCT
iajs-2517	286	21	2	2	NUM
iajs-2517	286	22	}	}	PUNCT
iajs-2517	286	23	in	in	ADP
iajs-2517	286	24	the	the	DET
iajs-2517	286	25	second	second	ADJ
iajs-2517	286	26	step	step	NOUN
iajs-2517	286	27	,	,	PUNCT
iajs-2517	286	28	player	player	NOUN
iajs-2517	286	29	ⅱ	ⅱ	PROPN
iajs-2517	286	30	choose	choose	VERB
iajs-2517	286	31	(	(	PUNCT
iajs-2517	286	32	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	286	33	)	)	PUNCT
iajs-2517	286	34	,	,	PUNCT
iajs-2517	286	35	(	(	PUNCT
iajs-2517	286	36	ℬ,ℋ	ℬ,ℋ	INTJ
iajs-2517	286	37	)	)	PUNCT
iajs-2517	286	38	such	such	ADJ
iajs-2517	286	39	that	that	SCONJ
iajs-2517	286	40	𝒜(𝒽	𝒜(𝒽	PUNCT
iajs-2517	286	41	)	)	PUNCT
iajs-2517	286	42	=	=	SYM
iajs-2517	286	43	{	{	PUNCT
iajs-2517	286	44	1	1	NUM
iajs-2517	286	45	}	}	PUNCT
iajs-2517	286	46	,	,	PUNCT
iajs-2517	286	47	ℬ(𝒽	ℬ(𝒽	NUM
iajs-2517	286	48	)	)	PUNCT
iajs-2517	286	49	=	=	NOUN
iajs-2517	286	50	{	{	PUNCT
iajs-2517	286	51	2	2	NUM
iajs-2517	286	52	}	}	PUNCT
iajs-2517	286	53	∀	∀	NUM
iajs-2517	286	54	𝒽	𝒽	PRON
iajs-2517	286	55	which	which	PRON
iajs-2517	286	56	are	be	AUX
iajs-2517	286	57	soft	soft	ADJ
iajs-2517	286	58	open	open	ADJ
iajs-2517	286	59	(	(	PUNCT
iajs-2517	286	60	respectively	respectively	ADV
iajs-2517	286	61	,	,	PUNCT
iajs-2517	286	62	sℐsg­𝑜𝑝𝑒𝑛	sℐsg­𝑜𝑝𝑒𝑛	NOUN
iajs-2517	286	63	)	)	PUNCT
iajs-2517	286	64	sets	set	NOUN
iajs-2517	286	65	.	.	PUNCT
iajs-2517	287	1	in	in	ADP
iajs-2517	287	2	the	the	DET
iajs-2517	287	3	second	second	ADJ
iajs-2517	287	4	inning	inning	NOUN
iajs-2517	287	5	:	:	PUNCT
iajs-2517	287	6	the	the	DET
iajs-2517	287	7	first	first	ADJ
iajs-2517	287	8	step	step	NOUN
iajs-2517	287	9	,	,	PUNCT
iajs-2517	287	10	player	player	NOUN
iajs-2517	287	11	ⅰ	ⅰ	NOUN
iajs-2517	287	12	choose	choose	VERB
iajs-2517	287	13	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	287	14	≠	≠	PROPN
iajs-2517	287	15	𝒽𝓞	𝒽𝓞	VERB
iajs-2517	287	16	where	where	SCONJ
iajs-2517	287	17	,	,	PUNCT
iajs-2517	287	18	𝒽	𝒽	PRON
iajs-2517	287	19	,	,	PUNCT
iajs-2517	287	20	𝒽𝓞	𝒽𝓞	ADJ
iajs-2517	287	21	∈̃	∈̃	PROPN
iajs-2517	287	22	�	�	PROPN
iajs-2517	287	23	̃	̃	PROPN
iajs-2517	287	24	�	�	NOUN
iajs-2517	287	25	such	such	ADJ
iajs-2517	287	26	that	that	DET
iajs-2517	287	27	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	287	28	=	=	SYM
iajs-2517	287	29	{	{	PUNCT
iajs-2517	287	30	2	2	NUM
iajs-2517	287	31	}	}	PUNCT
iajs-2517	287	32	and	and	CCONJ
iajs-2517	287	33	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	287	34	=	=	SYM
iajs-2517	287	35	{	{	PUNCT
iajs-2517	287	36	3	3	NUM
iajs-2517	287	37	}	}	PUNCT
iajs-2517	287	38	.	.	PUNCT
iajs-2517	288	1	in	in	ADP
iajs-2517	288	2	the	the	DET
iajs-2517	288	3	second	second	ADJ
iajs-2517	288	4	step	step	NOUN
iajs-2517	288	5	,	,	PUNCT
iajs-2517	288	6	player	player	NOUN
iajs-2517	288	7	ⅱ	ⅱ	PROPN
iajs-2517	288	8	choose	choose	VERB
iajs-2517	288	9	(	(	PUNCT
iajs-2517	288	10	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	288	11	)	)	PUNCT
iajs-2517	288	12	,	,	PUNCT
iajs-2517	288	13	(	(	PUNCT
iajs-2517	288	14	𝒞,ℋ	𝒞,ℋ	ADV
iajs-2517	288	15	)	)	PUNCT
iajs-2517	288	16	such	such	ADJ
iajs-2517	288	17	that	that	PRON
iajs-2517	288	18	ℬ(𝒽	ℬ(𝒽	X
iajs-2517	288	19	)	)	PUNCT
iajs-2517	288	20	=	=	NOUN
iajs-2517	288	21	{	{	PUNCT
iajs-2517	288	22	2	2	NUM
iajs-2517	288	23	}	}	PUNCT
iajs-2517	288	24	,	,	PUNCT
iajs-2517	288	25	𝒞(𝒽	𝒞(𝒽	NUM
iajs-2517	288	26	)	)	PUNCT
iajs-2517	288	27	=	=	NOUN
iajs-2517	288	28	{	{	PUNCT
iajs-2517	288	29	3	3	NUM
iajs-2517	288	30	}	}	PUNCT
iajs-2517	288	31	∀	∀	NUM
iajs-2517	288	32	𝒽	𝒽	PRON
iajs-2517	288	33	which	which	PRON
iajs-2517	288	34	are	be	AUX
iajs-2517	288	35	soft	soft	ADJ
iajs-2517	288	36	open	open	ADJ
iajs-2517	288	37	(	(	PUNCT
iajs-2517	288	38	respectively	respectively	ADV
iajs-2517	288	39	,	,	PUNCT
iajs-2517	288	40	sℐsg­𝑜𝑝𝑒𝑛	sℐsg­𝑜𝑝𝑒𝑛	NOUN
iajs-2517	288	41	)	)	PUNCT
iajs-2517	288	42	sets	set	NOUN
iajs-2517	288	43	.	.	PUNCT
iajs-2517	289	1	in	in	ADP
iajs-2517	289	2	the	the	DET
iajs-2517	289	3	third	third	ADJ
iajs-2517	289	4	inning	inning	NOUN
iajs-2517	289	5	:	:	PUNCT
iajs-2517	289	6	the	the	DET
iajs-2517	289	7	first	first	ADJ
iajs-2517	289	8	step	step	NOUN
iajs-2517	289	9	,	,	PUNCT
iajs-2517	289	10	player	player	NOUN
iajs-2517	289	11	ⅰ	ⅰ	PRON
iajs-2517	289	12	choose	choose	VERB
iajs-2517	289	13	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	289	14	≠	≠	PROPN
iajs-2517	289	15	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	289	16	where	where	SCONJ
iajs-2517	289	17	,	,	PUNCT
iajs-2517	289	18	𝒽	𝒽	X
iajs-2517	289	19	,	,	PUNCT
iajs-2517	289	20	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	289	21	∈̃	∈̃	PROPN
iajs-2517	289	22	�	�	PROPN
iajs-2517	289	23	̃	̃	PROPN
iajs-2517	289	24	�	�	PROPN
iajs-2517	289	25	such	such	ADJ
iajs-2517	289	26	that	that	SCONJ
iajs-2517	289	27	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	289	28	=	=	PUNCT
iajs-2517	289	29	{	{	PUNCT
iajs-2517	289	30	1	1	NUM
iajs-2517	289	31	}	}	PUNCT
iajs-2517	289	32	and	and	CCONJ
iajs-2517	289	33	𝒽𝒪	𝒽𝒪	PROPN
iajs-2517	289	34	=	=	SYM
iajs-2517	289	35	{	{	PUNCT
iajs-2517	289	36	3	3	NUM
iajs-2517	289	37	}	}	PUNCT
iajs-2517	289	38	.	.	PUNCT
iajs-2517	290	1	in	in	ADP
iajs-2517	290	2	the	the	DET
iajs-2517	290	3	second	second	ADJ
iajs-2517	290	4	step	step	NOUN
iajs-2517	290	5	,	,	PUNCT
iajs-2517	290	6	player	player	NOUN
iajs-2517	290	7	ⅱ	ⅱ	PROPN
iajs-2517	290	8	choose	choose	VERB
iajs-2517	290	9	(	(	PUNCT
iajs-2517	290	10	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	290	11	)	)	PUNCT
iajs-2517	290	12	,	,	PUNCT
iajs-2517	290	13	(	(	PUNCT
iajs-2517	290	14	𝒞,ℋ	𝒞,ℋ	ADV
iajs-2517	290	15	)	)	PUNCT
iajs-2517	290	16	such	such	ADJ
iajs-2517	290	17	that	that	SCONJ
iajs-2517	290	18	𝒜(𝒽	𝒜(𝒽	PUNCT
iajs-2517	290	19	)	)	PUNCT
iajs-2517	290	20	=	=	SYM
iajs-2517	290	21	{	{	PUNCT
iajs-2517	290	22	1	1	NUM
iajs-2517	290	23	}	}	PUNCT
iajs-2517	290	24	,	,	PUNCT
iajs-2517	290	25	𝒞(𝒽	𝒞(𝒽	NUM
iajs-2517	290	26	)	)	PUNCT
iajs-2517	290	27	=	=	NOUN
iajs-2517	290	28	{	{	PUNCT
iajs-2517	290	29	3	3	NUM
iajs-2517	290	30	}	}	PUNCT
iajs-2517	290	31	∀	∀	NUM
iajs-2517	290	32	𝒽	𝒽	PRON
iajs-2517	290	33	which	which	PRON
iajs-2517	290	34	are	be	AUX
iajs-2517	290	35	soft	soft	ADJ
iajs-2517	290	36	open	open	ADJ
iajs-2517	290	37	(	(	PUNCT
iajs-2517	290	38	respectively	respectively	ADV
iajs-2517	290	39	,	,	PUNCT
iajs-2517	290	40	sℐsg­𝑜𝑝𝑒𝑛	sℐsg­𝑜𝑝𝑒𝑛	NOUN
iajs-2517	290	41	)	)	PUNCT
iajs-2517	290	42	sets	set	NOUN
iajs-2517	290	43	.	.	PUNCT
iajs-2517	291	1	in	in	ADP
iajs-2517	291	2	the	the	DET
iajs-2517	291	3	fourth	fourth	ADJ
iajs-2517	291	4	inning	inning	NOUN
iajs-2517	291	5	:	:	PUNCT
iajs-2517	291	6	the	the	DET
iajs-2517	291	7	first	first	ADJ
iajs-2517	291	8	step	step	NOUN
iajs-2517	291	9	,	,	PUNCT
iajs-2517	291	10	player	player	NOUN
iajs-2517	291	11	ⅰ	ⅰ	NOUN
iajs-2517	291	12	choose	choose	VERB
iajs-2517	291	13	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	291	14	≠	≠	PROPN
iajs-2517	291	15	𝒽𝓡	𝒽𝓡	NOUN
iajs-2517	291	16	where	where	SCONJ
iajs-2517	291	17	,	,	PUNCT
iajs-2517	291	18	𝒽	𝒽	X
iajs-2517	291	19	,	,	PUNCT
iajs-2517	291	20	𝒽𝓡	𝒽𝓡	PROPN
iajs-2517	291	21	∈̃	∈̃	PROPN
iajs-2517	291	22	�	�	PROPN
iajs-2517	291	23	̃	̃	PROPN
iajs-2517	291	24	�	�	NOUN
iajs-2517	291	25	such	such	ADJ
iajs-2517	291	26	that	that	PRON
iajs-2517	291	27	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	291	28	=	=	SYM
iajs-2517	291	29	{	{	PUNCT
iajs-2517	291	30	1	1	NUM
iajs-2517	291	31	}	}	PUNCT
iajs-2517	291	32	and	and	CCONJ
iajs-2517	291	33	𝒽𝓡	𝒽𝓡	NOUN
iajs-2517	291	34	=	=	X
iajs-2517	291	35	{	{	PUNCT
iajs-2517	291	36	2,3	2,3	NUM
iajs-2517	291	37	}	}	PUNCT
iajs-2517	291	38	.	.	PUNCT
iajs-2517	292	1	in	in	ADP
iajs-2517	292	2	the	the	DET
iajs-2517	292	3	second	second	ADJ
iajs-2517	292	4	step	step	NOUN
iajs-2517	292	5	,	,	PUNCT
iajs-2517	292	6	player	player	NOUN
iajs-2517	292	7	ⅱ	ⅱ	PROPN
iajs-2517	292	8	choose	choose	VERB
iajs-2517	292	9	(	(	PUNCT
iajs-2517	292	10	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	292	11	)	)	PUNCT
iajs-2517	292	12	,	,	PUNCT
iajs-2517	292	13	(	(	PUNCT
iajs-2517	292	14	𝒟,ℋ	𝒟,ℋ	INTJ
iajs-2517	292	15	)	)	PUNCT
iajs-2517	292	16	such	such	ADJ
iajs-2517	292	17	that	that	SCONJ
iajs-2517	292	18	𝒜(𝒽	𝒜(𝒽	PUNCT
iajs-2517	292	19	)	)	PUNCT
iajs-2517	292	20	=	=	SYM
iajs-2517	292	21	{	{	PUNCT
iajs-2517	292	22	1	1	NUM
iajs-2517	292	23	}	}	PUNCT
iajs-2517	292	24	,	,	PUNCT
iajs-2517	292	25	𝒟(𝒽	𝒟(𝒽	X
iajs-2517	292	26	)	)	PUNCT
iajs-2517	292	27	=	=	PRON
iajs-2517	292	28	{	{	PUNCT
iajs-2517	292	29	2,3	2,3	NUM
iajs-2517	292	30	}	}	NUM
iajs-2517	292	31	∀	∀	NOUN
iajs-2517	292	32	𝒽	𝒽	NOUN
iajs-2517	292	33	which	which	PRON
iajs-2517	292	34	are	be	AUX
iajs-2517	292	35	soft	soft	ADJ
iajs-2517	292	36	open	open	ADJ
iajs-2517	292	37	(	(	PUNCT
iajs-2517	292	38	respectively	respectively	ADV
iajs-2517	292	39	,	,	PUNCT
iajs-2517	292	40	sℐsg­𝑜𝑝𝑒𝑛	sℐsg­𝑜𝑝𝑒𝑛	NOUN
iajs-2517	292	41	)	)	PUNCT
iajs-2517	292	42	sets	set	NOUN
iajs-2517	292	43	.	.	PUNCT
iajs-2517	293	1	in	in	ADP
iajs-2517	293	2	the	the	DET
iajs-2517	293	3	fifth	fifth	ADJ
iajs-2517	293	4	inning	inning	NOUN
iajs-2517	293	5	:	:	PUNCT
iajs-2517	293	6	the	the	DET
iajs-2517	293	7	first	first	ADJ
iajs-2517	293	8	step	step	NOUN
iajs-2517	293	9	,	,	PUNCT
iajs-2517	293	10	player	player	NOUN
iajs-2517	293	11	ⅰ	ⅰ	PRON
iajs-2517	293	12	choose	choose	VERB
iajs-2517	293	13	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	293	14	≠	≠	PROPN
iajs-2517	293	15	𝒽𝓢	𝒽𝓢	NOUN
iajs-2517	293	16	where	where	SCONJ
iajs-2517	293	17	,	,	PUNCT
iajs-2517	293	18	𝒽	𝒽	X
iajs-2517	293	19	,	,	PUNCT
iajs-2517	293	20	𝒽𝓢	𝒽𝓢	NOUN
iajs-2517	293	21	∈̃	∈̃	PROPN
iajs-2517	293	22	�	�	PROPN
iajs-2517	293	23	̃	̃	PROPN
iajs-2517	293	24	�	�	PROPN
iajs-2517	293	25	such	such	ADJ
iajs-2517	293	26	that	that	SCONJ
iajs-2517	293	27	𝒽𝓝	𝒽𝓝	PROPN
iajs-2517	293	28	=	=	PUNCT
iajs-2517	293	29	{	{	PUNCT
iajs-2517	293	30	2	2	NUM
iajs-2517	293	31	}	}	PUNCT
iajs-2517	293	32	and	and	CCONJ
iajs-2517	293	33	𝒽𝓢	𝒽𝓢	NOUN
iajs-2517	293	34	=	=	SYM
iajs-2517	293	35	{	{	PUNCT
iajs-2517	293	36	1,3	1,3	NUM
iajs-2517	293	37	}	}	PUNCT
iajs-2517	293	38	.	.	PUNCT
iajs-2517	294	1	in	in	ADP
iajs-2517	294	2	the	the	DET
iajs-2517	294	3	second	second	ADJ
iajs-2517	294	4	step	step	NOUN
iajs-2517	294	5	,	,	PUNCT
iajs-2517	294	6	player	player	NOUN
iajs-2517	294	7	ⅱ	ⅱ	PROPN
iajs-2517	294	8	choose	choose	VERB
iajs-2517	294	9	(	(	PUNCT
iajs-2517	294	10	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	294	11	)	)	PUNCT
iajs-2517	294	12	,	,	PUNCT
iajs-2517	294	13	(	(	PUNCT
iajs-2517	294	14	ℰ,ℋ	ℰ,ℋ	NOUN
iajs-2517	294	15	)	)	PUNCT
iajs-2517	294	16	such	such	ADJ
iajs-2517	294	17	that	that	PRON
iajs-2517	294	18	ℬ(𝒽	ℬ(𝒽	X
iajs-2517	294	19	)	)	PUNCT
iajs-2517	294	20	=	=	NOUN
iajs-2517	294	21	{	{	PUNCT
iajs-2517	294	22	2	2	NUM
iajs-2517	294	23	}	}	PUNCT
iajs-2517	294	24	,	,	PUNCT
iajs-2517	294	25	ℰ(𝒽	ℰ(𝒽	NUM
iajs-2517	294	26	)	)	PUNCT
iajs-2517	294	27	=	=	SYM
iajs-2517	294	28	{	{	PUNCT
iajs-2517	294	29	1,3	1,3	NUM
iajs-2517	294	30	}	}	PUNCT
iajs-2517	294	31	∀	∀	PUNCT
iajs-2517	294	32	𝒽	𝒽	NOUN
iajs-2517	294	33	which	which	PRON
iajs-2517	294	34	are	be	AUX
iajs-2517	294	35	soft	soft	ADJ
iajs-2517	294	36	open	open	ADJ
iajs-2517	294	37	(	(	PUNCT
iajs-2517	294	38	respectively	respectively	ADV
iajs-2517	294	39	,	,	PUNCT
iajs-2517	294	40	sℐsg­𝑜𝑝𝑒𝑛	sℐsg­𝑜𝑝𝑒𝑛	NOUN
iajs-2517	294	41	)	)	PUNCT
iajs-2517	294	42	sets	set	NOUN
iajs-2517	294	43	.	.	PUNCT
iajs-2517	295	1	in	in	ADP
iajs-2517	295	2	the	the	DET
iajs-2517	295	3	sixth	sixth	ADJ
iajs-2517	295	4	inning	inning	NOUN
iajs-2517	295	5	:	:	PUNCT
iajs-2517	295	6	the	the	DET
iajs-2517	295	7	first	first	ADJ
iajs-2517	295	8	step	step	NOUN
iajs-2517	295	9	,	,	PUNCT
iajs-2517	295	10	player	player	NOUN
iajs-2517	295	11	ⅰ	ⅰ	PRON
iajs-2517	295	12	choose	choose	VERB
iajs-2517	295	13	𝒽𝓞	𝒽𝓞	ADJ
iajs-2517	295	14	≠	≠	PROPN
iajs-2517	295	15	𝒽𝓛	𝒽𝓛	ADP
iajs-2517	295	16	where	where	SCONJ
iajs-2517	295	17	,	,	PUNCT
iajs-2517	295	18	𝒽	𝒽	X
iajs-2517	295	19	,	,	PUNCT
iajs-2517	295	20	𝒽𝓛	𝒽𝓛	PROPN
iajs-2517	295	21	∈̃	∈̃	PROPN
iajs-2517	295	22	�	�	PROPN
iajs-2517	295	23	̃	̃	PROPN
iajs-2517	295	24	�	�	PROPN
iajs-2517	295	25	such	such	ADJ
iajs-2517	295	26	that	that	SCONJ
iajs-2517	295	27	𝒽𝒪	𝒽𝒪	NOUN
iajs-2517	295	28	=	=	SYM
iajs-2517	295	29	{	{	PUNCT
iajs-2517	295	30	3	3	NUM
iajs-2517	295	31	}	}	PUNCT
iajs-2517	295	32	and	and	CCONJ
iajs-2517	295	33	𝒽𝓛	𝒽𝓛	ADP
iajs-2517	295	34	=	=	SYM
iajs-2517	295	35	{	{	PUNCT
iajs-2517	295	36	1,2	1,2	NUM
iajs-2517	295	37	}	}	PUNCT
iajs-2517	295	38	.	.	PUNCT
iajs-2517	296	1	in	in	ADP
iajs-2517	296	2	the	the	DET
iajs-2517	296	3	second	second	ADJ
iajs-2517	296	4	step	step	NOUN
iajs-2517	296	5	,	,	PUNCT
iajs-2517	296	6	player	player	NOUN
iajs-2517	296	7	ⅱ	ⅱ	PROPN
iajs-2517	296	8	choose	choose	VERB
iajs-2517	296	9	(	(	PUNCT
iajs-2517	296	10	𝒞,ℋ	𝒞,ℋ	NOUN
iajs-2517	296	11	)	)	PUNCT
iajs-2517	296	12	,	,	PUNCT
iajs-2517	296	13	(	(	PUNCT
iajs-2517	296	14	ℱ,ℋ	ℱ,ℋ	NOUN
iajs-2517	296	15	)	)	PUNCT
iajs-2517	296	16	such	such	ADJ
iajs-2517	296	17	that	that	SCONJ
iajs-2517	296	18	𝒞(𝒽	𝒞(𝒽	NOUN
iajs-2517	296	19	)	)	PUNCT
iajs-2517	296	20	=	=	NOUN
iajs-2517	296	21	{	{	PUNCT
iajs-2517	296	22	3	3	NUM
iajs-2517	296	23	}	}	PUNCT
iajs-2517	296	24	,	,	PUNCT
iajs-2517	296	25	ℱ(𝒽	ℱ(𝒽	NUM
iajs-2517	296	26	)	)	PUNCT
iajs-2517	296	27	=	=	SYM
iajs-2517	296	28	{	{	PUNCT
iajs-2517	296	29	1,2	1,2	NUM
iajs-2517	296	30	}	}	PUNCT
iajs-2517	296	31	∀	∀	PUNCT
iajs-2517	296	32	𝒽	𝒽	NOUN
iajs-2517	296	33	which	which	PRON
iajs-2517	296	34	are	be	AUX
iajs-2517	296	35	soft	soft	ADJ
iajs-2517	296	36	open	open	ADJ
iajs-2517	296	37	(	(	PUNCT
iajs-2517	296	38	respectively	respectively	ADV
iajs-2517	296	39	,	,	PUNCT
iajs-2517	296	40	sℐsg­𝑜𝑝𝑒𝑛	sℐsg­𝑜𝑝𝑒𝑛	NOUN
iajs-2517	296	41	)	)	PUNCT
iajs-2517	296	42	sets	set	NOUN
iajs-2517	296	43	.	.	PUNCT
iajs-2517	297	1	then	then	ADV
iajs-2517	297	2	ℬ	ℬ	NOUN
iajs-2517	297	3	=	=	PRON
iajs-2517	297	4	{	{	PUNCT
iajs-2517	297	5	{	{	PUNCT
iajs-2517	297	6	(	(	PUNCT
iajs-2517	297	7	𝒜	𝒜	NOUN
iajs-2517	297	8	,	,	PUNCT
iajs-2517	297	9	ℋ	ℋ	PROPN
iajs-2517	297	10	)	)	PUNCT
iajs-2517	297	11	,	,	PUNCT
iajs-2517	297	12	(	(	PUNCT
iajs-2517	297	13	ℬ	ℬ	X
iajs-2517	297	14	,	,	PUNCT
iajs-2517	297	15	ℋ	ℋ	NOUN
iajs-2517	297	16	)	)	PUNCT
iajs-2517	297	17	}	}	PUNCT
iajs-2517	297	18	,	,	PUNCT
iajs-2517	297	19	{	{	PUNCT
iajs-2517	297	20	(	(	PUNCT
iajs-2517	297	21	ℬ	ℬ	X
iajs-2517	297	22	,	,	PUNCT
iajs-2517	297	23	ℋ	ℋ	PROPN
iajs-2517	297	24	)	)	PUNCT
iajs-2517	297	25	,	,	PUNCT
iajs-2517	297	26	(	(	PUNCT
iajs-2517	297	27	𝒞	𝒞	PROPN
iajs-2517	297	28	,	,	PUNCT
iajs-2517	297	29	ℋ	ℋ	PROPN
iajs-2517	297	30	)	)	PUNCT
iajs-2517	297	31	}	}	PUNCT
iajs-2517	297	32	,	,	PUNCT
iajs-2517	297	33	{	{	PUNCT
iajs-2517	297	34	(	(	PUNCT
iajs-2517	297	35	𝒜	𝒜	NOUN
iajs-2517	297	36	,	,	PUNCT
iajs-2517	297	37	ℋ	ℋ	PROPN
iajs-2517	297	38	)	)	PUNCT
iajs-2517	297	39	,	,	PUNCT
iajs-2517	297	40	(	(	PUNCT
iajs-2517	297	41	𝒞	𝒞	PROPN
iajs-2517	297	42	,	,	PUNCT
iajs-2517	297	43	ℋ	ℋ	PROPN
iajs-2517	297	44	)	)	PUNCT
iajs-2517	297	45	}	}	PUNCT
iajs-2517	297	46	,	,	PUNCT
iajs-2517	297	47	{	{	PUNCT
iajs-2517	297	48	(	(	PUNCT
iajs-2517	297	49	𝒜	𝒜	NOUN
iajs-2517	297	50	,	,	PUNCT
iajs-2517	297	51	ℋ	ℋ	PROPN
iajs-2517	297	52	)	)	PUNCT
iajs-2517	297	53	,	,	PUNCT
iajs-2517	297	54	(	(	PUNCT
iajs-2517	297	55	𝒟	𝒟	PROPN
iajs-2517	297	56	,	,	PUNCT
iajs-2517	297	57	ℋ	ℋ	PROPN
iajs-2517	297	58	)	)	PUNCT
iajs-2517	297	59	}	}	PUNCT
iajs-2517	297	60	,	,	PUNCT
iajs-2517	297	61	{	{	PUNCT
iajs-2517	297	62	(	(	PUNCT
iajs-2517	297	63	ℬ	ℬ	X
iajs-2517	297	64	,	,	PUNCT
iajs-2517	297	65	ℋ	ℋ	PROPN
iajs-2517	297	66	)	)	PUNCT
iajs-2517	297	67	,	,	PUNCT
iajs-2517	297	68	(	(	PUNCT
iajs-2517	297	69	ℰ	ℰ	PROPN
iajs-2517	297	70	,	,	PUNCT
iajs-2517	297	71	ℋ	ℋ	PROPN
iajs-2517	297	72	)	)	PUNCT
iajs-2517	297	73	}	}	PUNCT
iajs-2517	297	74	,	,	PUNCT
iajs-2517	297	75	{	{	PUNCT
iajs-2517	297	76	(	(	PUNCT
iajs-2517	297	77	𝒞	𝒞	PROPN
iajs-2517	297	78	,	,	PUNCT
iajs-2517	297	79	ℋ	ℋ	PROPN
iajs-2517	297	80	)	)	PUNCT
iajs-2517	297	81	,	,	PUNCT
iajs-2517	297	82	(	(	PUNCT
iajs-2517	297	83	ℱ	ℱ	PROPN
iajs-2517	297	84	,	,	PUNCT
iajs-2517	297	85	ℋ	ℋ	PROPN
iajs-2517	297	86	)	)	PUNCT
iajs-2517	297	87	}	}	PUNCT
iajs-2517	297	88	}	}	PUNCT
iajs-2517	297	89	is	be	AUX
iajs-2517	297	90	the	the	DET
iajs-2517	297	91	winning	win	VERB
iajs-2517	297	92	strategy	strategy	NOUN
iajs-2517	297	93	for	for	ADP
iajs-2517	297	94	player	player	NOUN
iajs-2517	297	95	ⅱ	ⅱ	NOUN
iajs-2517	297	96	in	in	ADP
iajs-2517	297	97	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	297	98	,	,	PUNCT
iajs-2517	297	99	χ	χ	X
iajs-2517	297	100	)	)	PUNCT
iajs-2517	297	101	(	(	PUNCT
iajs-2517	297	102	respectively	respectively	ADV
iajs-2517	297	103	,	,	PUNCT
iajs-2517	297	104	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	297	105	,	,	PUNCT
iajs-2517	297	106	ℐ	ℐ	NOUN
iajs-2517	297	107	)	)	PUNCT
iajs-2517	297	108	)	)	PUNCT
iajs-2517	297	109	.	.	PUNCT
iajs-2517	298	1	hence	hence	ADV
iajs-2517	298	2	player	player	NOUN
iajs-2517	298	3	ⅱ	ⅱ	PROPN
iajs-2517	298	4	↑	↑	PROPN
iajs-2517	298	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	298	6	,	,	PUNCT
iajs-2517	298	7	χ	χ	X
iajs-2517	298	8	)	)	PUNCT
iajs-2517	298	9	(	(	PUNCT
iajs-2517	298	10	respectively	respectively	ADV
iajs-2517	298	11	,	,	PUNCT
iajs-2517	298	12	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	298	13	,	,	PUNCT
iajs-2517	298	14	ℐ	ℐ	NOUN
iajs-2517	298	15	)	)	PUNCT
iajs-2517	298	16	)	)	PUNCT
iajs-2517	298	17	.	.	PUNCT
iajs-2517	299	1	by	by	ADP
iajs-2517	299	2	the	the	DET
iajs-2517	299	3	same	same	ADJ
iajs-2517	299	4	way	way	NOUN
iajs-2517	299	5	in	in	ADP
iajs-2517	299	6	example	example	NOUN
iajs-2517	299	7	4.3	4.3	NUM
iajs-2517	299	8	,	,	PUNCT
iajs-2517	299	9	player	player	NOUN
iajs-2517	299	10	ⅰ	ⅰ	X
iajs-2517	299	11	↑	↑	NOUN
iajs-2517	299	12	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	299	13	,	,	PUNCT
iajs-2517	299	14	χ	χ	NOUN
iajs-2517	299	15	)	)	PUNCT
iajs-2517	299	16	and	and	CCONJ
iajs-2517	299	17	player	player	NOUN
iajs-2517	299	18	ⅰ	ⅰ	PROPN
iajs-2517	299	19	↑	↑	PROPN
iajs-2517	299	20	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	299	21	,	,	PUNCT
iajs-2517	299	22	ℐ	ℐ	NOUN
iajs-2517	299	23	)	)	PUNCT
iajs-2517	299	24	.	.	PUNCT
iajs-2517	299	25	remark	remark	PROPN
iajs-2517	299	26	5.13	5.13	NUM
iajs-2517	299	27	.	.	PUNCT
iajs-2517	300	1	for	for	ADP
iajs-2517	300	2	a	a	DET
iajs-2517	300	3	space	space	NOUN
iajs-2517	300	4	(	(	PUNCT
iajs-2517	300	5	χ	χ	X
iajs-2517	300	6	,	,	PUNCT
iajs-2517	300	7	𝒯	𝒯	PROPN
iajs-2517	300	8	,	,	PUNCT
iajs-2517	300	9	ℋ	ℋ	PROPN
iajs-2517	300	10	,	,	PUNCT
iajs-2517	300	11	ℐ	ℐ	PROPN
iajs-2517	300	12	)	)	PUNCT
iajs-2517	300	13	:	:	PUNCT
iajs-2517	300	14	iif	iif	PROPN
iajs-2517	300	15	player	player	NOUN
iajs-2517	300	16	ⅱ	ⅱ	PROPN
iajs-2517	300	17	↑	↑	PROPN
iajs-2517	300	18	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	300	19	,	,	PUNCT
iajs-2517	300	20	χ	χ	X
iajs-2517	300	21	)	)	PUNCT
iajs-2517	300	22	then	then	ADV
iajs-2517	300	23	player	player	NOUN
iajs-2517	300	24	ⅱ	ⅱ	PROPN
iajs-2517	300	25	↑	↑	PROPN
iajs-2517	300	26	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	300	27	,	,	PUNCT
iajs-2517	300	28	ℐ	ℐ	NOUN
iajs-2517	300	29	)	)	PUNCT
iajs-2517	300	30	.	.	PUNCT
iajs-2517	301	1	iiif	iiif	PROPN
iajs-2517	301	2	player	player	PROPN
iajs-2517	301	3	ⅰ	ⅰ	PROPN
iajs-2517	301	4	↑	↑	PROPN
iajs-2517	301	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	301	6	,	,	PUNCT
iajs-2517	301	7	ℐ)then	ℐ)then	ADP
iajs-2517	301	8	player	player	NOUN
iajs-2517	301	9	ⅰ	ⅰ	PROPN
iajs-2517	301	10	↑	↑	PROPN
iajs-2517	301	11	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	301	12	,	,	PUNCT
iajs-2517	301	13	χ	χ	X
iajs-2517	301	14	)	)	PUNCT
iajs-2517	301	15	.	.	PUNCT
iajs-2517	302	1	remark	remark	VERB
iajs-2517	302	2	5.14	5.14	NUM
iajs-2517	302	3	.	.	PUNCT
iajs-2517	303	1	for	for	ADP
iajs-2517	303	2	a	a	DET
iajs-2517	303	3	space	space	NOUN
iajs-2517	303	4	(	(	PUNCT
iajs-2517	303	5	χ	χ	X
iajs-2517	303	6	,	,	PUNCT
iajs-2517	303	7	𝒯	𝒯	PROPN
iajs-2517	303	8	,	,	PUNCT
iajs-2517	303	9	ℋ	ℋ	PROPN
iajs-2517	303	10	,	,	PUNCT
iajs-2517	303	11	ℐ	ℐ	PROPN
iajs-2517	303	12	)	)	PUNCT
iajs-2517	303	13	,	,	PUNCT
iajs-2517	303	14	if	if	SCONJ
iajs-2517	303	15	player	player	NOUN
iajs-2517	303	16	ⅱ	ⅱ	PROPN
iajs-2517	303	17	↓	↓	PROPN
iajs-2517	303	18	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	303	19	,	,	PUNCT
iajs-2517	303	20	χ	χ	X
iajs-2517	303	21	)	)	PUNCT
iajs-2517	303	22	then	then	ADV
iajs-2517	303	23	player	player	NOUN
iajs-2517	303	24	ⅱ	ⅱ	PROPN
iajs-2517	303	25	↓	↓	PROPN
iajs-2517	303	26	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	303	27	,	,	PUNCT
iajs-2517	303	28	ℐ	ℐ	NOUN
iajs-2517	303	29	)	)	PUNCT
iajs-2517	303	30	.	.	PUNCT
iajs-2517	304	1	132	132	NUM
iajs-2517	304	2	ibn	ibn	PROPN
iajs-2517	304	3	al	al	PROPN
iajs-2517	304	4	-	-	PUNCT
iajs-2517	304	5	haitham	haitham	PROPN
iajs-2517	304	6	jour	jour	X
iajs-2517	304	7	.	.	PROPN
iajs-2517	304	8	for	for	ADP
iajs-2517	304	9	pure	pure	ADJ
iajs-2517	304	10	&	&	CCONJ
iajs-2517	304	11	appl	appl	PROPN
iajs-2517	304	12	.	.	PUNCT
iajs-2517	305	1	sci	sci	PROPN
iajs-2517	305	2	.	.	PROPN
iajs-2517	306	1	33	33	NUM
iajs-2517	306	2	(	(	PUNCT
iajs-2517	306	3	4	4	NUM
iajs-2517	306	4	)	)	PUNCT
iajs-2517	306	5	2020	2020	NUM
iajs-2517	306	6	theorem	theorem	VERB
iajs-2517	306	7	5.15	5.15	NUM
iajs-2517	306	8	.	.	PUNCT
iajs-2517	307	1	a	a	DET
iajs-2517	307	2	space	space	NOUN
iajs-2517	307	3	(	(	PUNCT
iajs-2517	307	4	χ	χ	X
iajs-2517	307	5	,	,	PUNCT
iajs-2517	307	6	𝒯	𝒯	PROPN
iajs-2517	307	7	,	,	PUNCT
iajs-2517	307	8	ℋ	ℋ	PROPN
iajs-2517	307	9	)	)	PUNCT
iajs-2517	307	10	(	(	PUNCT
iajs-2517	307	11	respectively	respectively	ADV
iajs-2517	307	12	,	,	PUNCT
iajs-2517	307	13	(	(	PUNCT
iajs-2517	307	14	χ	χ	X
iajs-2517	307	15	,	,	PUNCT
iajs-2517	307	16	𝒯	𝒯	PROPN
iajs-2517	307	17	,	,	PUNCT
iajs-2517	307	18	ℋ	ℋ	PROPN
iajs-2517	307	19	,	,	PUNCT
iajs-2517	307	20	ℐ	ℐ	NOUN
iajs-2517	307	21	)	)	PUNCT
iajs-2517	307	22	)	)	PUNCT
iajs-2517	307	23	is	be	AUX
iajs-2517	307	24	a	a	DET
iajs-2517	307	25	soft-𝒯1	soft-𝒯1	PROPN
iajs-2517	307	26	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	307	27	(	(	PUNCT
iajs-2517	307	28	respectively	respectively	ADV
iajs-2517	307	29	,	,	PUNCT
iajs-2517	307	30	sℐsg-𝒯1­space	sℐsg-𝒯1­space	PROPN
iajs-2517	307	31	)	)	PUNCT
iajs-2517	307	32	if	if	SCONJ
iajs-2517	307	33	and	and	CCONJ
iajs-2517	307	34	only	only	ADV
iajs-2517	307	35	if	if	SCONJ
iajs-2517	307	36	player	player	NOUN
iajs-2517	307	37	ⅱ	ⅱ	PROPN
iajs-2517	307	38	↑	↑	PROPN
iajs-2517	307	39	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	307	40	,	,	PUNCT
iajs-2517	307	41	χ	χ	X
iajs-2517	307	42	)	)	PUNCT
iajs-2517	307	43	(	(	PUNCT
iajs-2517	307	44	respectively	respectively	ADV
iajs-2517	307	45	,	,	PUNCT
iajs-2517	307	46	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	307	47	,	,	PUNCT
iajs-2517	307	48	ℐ	ℐ	NOUN
iajs-2517	307	49	)	)	PUNCT
iajs-2517	307	50	)	)	PUNCT
iajs-2517	307	51	.	.	PUNCT
iajs-2517	308	1	proof	proof	NOUN
iajs-2517	308	2	:	:	PUNCT
iajs-2517	308	3	(	(	PUNCT
iajs-2517	308	4	⟹	⟹	X
iajs-2517	308	5	)	)	PUNCT
iajs-2517	308	6	in	in	ADP
iajs-2517	308	7	the	the	DET
iajs-2517	308	8	𝑟-th	𝑟-th	NOUN
iajs-2517	308	9	inning	inning	NOUN
iajs-2517	308	10	player	player	NOUN
iajs-2517	308	11	ⅰ	ⅰ	NUM
iajs-2517	308	12	in	in	ADP
iajs-2517	308	13	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	308	14	,	,	PUNCT
iajs-2517	308	15	χ	χ	X
iajs-2517	308	16	)	)	PUNCT
iajs-2517	308	17	(	(	PUNCT
iajs-2517	308	18	respectively	respectively	ADV
iajs-2517	308	19	,	,	PUNCT
iajs-2517	308	20	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	308	21	,	,	PUNCT
iajs-2517	308	22	ℐ	ℐ	NOUN
iajs-2517	308	23	)	)	PUNCT
iajs-2517	308	24	)	)	PUNCT
iajs-2517	308	25	choose	choose	VERB
iajs-2517	308	26	∀	∀	X
iajs-2517	308	27	(	(	PUNCT
iajs-2517	308	28	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	308	29	≠	≠	PROPN
iajs-2517	308	30	(	(	PUNCT
iajs-2517	308	31	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	308	32	where	where	SCONJ
iajs-2517	308	33	,	,	PUNCT
iajs-2517	308	34	(	(	PUNCT
iajs-2517	308	35	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	308	36	,	,	PUNCT
iajs-2517	308	37	(	(	PUNCT
iajs-2517	308	38	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	308	39	∈̃	∈̃	PROPN
iajs-2517	308	40	�	�	PROPN
iajs-2517	308	41	̃	̃	PROPN
iajs-2517	308	42	�	�	PROPN
iajs-2517	308	43	,	,	PUNCT
iajs-2517	308	44	player	player	NOUN
iajs-2517	308	45	ⅱ	ⅱ	NOUN
iajs-2517	308	46	in	in	ADP
iajs-2517	308	47	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	308	48	,	,	PUNCT
iajs-2517	308	49	χ	χ	X
iajs-2517	308	50	)	)	PUNCT
iajs-2517	308	51	(	(	PUNCT
iajs-2517	308	52	respectively	respectively	ADV
iajs-2517	308	53	,	,	PUNCT
iajs-2517	308	54	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	308	55	,	,	PUNCT
iajs-2517	308	56	ℐ	ℐ	NOUN
iajs-2517	308	57	)	)	PUNCT
iajs-2517	308	58	)	)	PUNCT
iajs-2517	309	1	choose	choose	VERB
iajs-2517	309	2	(	(	PUNCT
iajs-2517	309	3	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	309	4	)	)	PUNCT
iajs-2517	309	5	,	,	PUNCT
iajs-2517	309	6	(	(	PUNCT
iajs-2517	309	7	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	309	8	)	)	PUNCT
iajs-2517	309	9	are	be	AUX
iajs-2517	309	10	two	two	NUM
iajs-2517	309	11	soft	soft	ADJ
iajs-2517	309	12	open	open	ADJ
iajs-2517	309	13	(	(	PUNCT
iajs-2517	309	14	respectively	respectively	ADV
iajs-2517	309	15	,	,	PUNCT
iajs-2517	309	16	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	309	17	)	)	PUNCT
iajs-2517	309	18	sets	set	VERB
iajs-2517	309	19	such	such	ADJ
iajs-2517	309	20	that	that	SCONJ
iajs-2517	309	21	(	(	PUNCT
iajs-2517	309	22	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	309	23	∈̃	∈̃	PROPN
iajs-2517	309	24	(	(	PUNCT
iajs-2517	309	25	(	(	PUNCT
iajs-2517	309	26	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	309	27	)	)	PUNCT
iajs-2517	309	28	‒	‒	NOUN
iajs-2517	309	29	(	(	PUNCT
iajs-2517	309	30	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	309	31	)	)	PUNCT
iajs-2517	309	32	)	)	PUNCT
iajs-2517	309	33	and	and	CCONJ
iajs-2517	309	34	(	(	PUNCT
iajs-2517	309	35	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	309	36	∈̃	∈̃	PROPN
iajs-2517	309	37	(	(	PUNCT
iajs-2517	309	38	(	(	PUNCT
iajs-2517	309	39	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	309	40	)	)	PUNCT
iajs-2517	309	41	‒	‒	NOUN
iajs-2517	309	42	(	(	PUNCT
iajs-2517	309	43	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	309	44	)	)	PUNCT
iajs-2517	309	45	)	)	PUNCT
iajs-2517	309	46	.	.	PUNCT
iajs-2517	310	1	since	since	SCONJ
iajs-2517	310	2	(	(	PUNCT
iajs-2517	310	3	χ	χ	X
iajs-2517	310	4	,	,	PUNCT
iajs-2517	310	5	𝒯	𝒯	PROPN
iajs-2517	310	6	,	,	PUNCT
iajs-2517	310	7	ℋ	ℋ	PROPN
iajs-2517	310	8	)	)	PUNCT
iajs-2517	310	9	a	a	DET
iajs-2517	310	10	soft-𝒯1	soft-𝒯1	PROPN
iajs-2517	310	11	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	310	12	(	(	PUNCT
iajs-2517	310	13	respectively	respectively	ADV
iajs-2517	310	14	,	,	PUNCT
iajs-2517	310	15	sℐsg-𝒯1­space).then	sℐsg-𝒯1­space).then	ADV
iajs-2517	310	16	ℬ	ℬ	NOUN
iajs-2517	310	17	=	=	PRON
iajs-2517	310	18	{	{	PUNCT
iajs-2517	310	19	{	{	PUNCT
iajs-2517	310	20	(	(	PUNCT
iajs-2517	310	21	𝒜1,ℋ	𝒜1,ℋ	PROPN
iajs-2517	310	22	)	)	PUNCT
iajs-2517	310	23	,	,	PUNCT
iajs-2517	310	24	(	(	PUNCT
iajs-2517	310	25	ℬ1,ℋ	ℬ1,ℋ	NOUN
iajs-2517	310	26	)	)	PUNCT
iajs-2517	310	27	}	}	PUNCT
iajs-2517	310	28	,	,	PUNCT
iajs-2517	310	29	{	{	PUNCT
iajs-2517	310	30	(	(	PUNCT
iajs-2517	310	31	𝒜2,ℋ	𝒜2,ℋ	NOUN
iajs-2517	310	32	)	)	PUNCT
iajs-2517	310	33	,	,	PUNCT
iajs-2517	310	34	(	(	PUNCT
iajs-2517	310	35	ℬ2,ℋ	ℬ2,ℋ	NOUN
iajs-2517	310	36	)	)	PUNCT
iajs-2517	310	37	}	}	PUNCT
iajs-2517	310	38	,	,	PUNCT
iajs-2517	310	39	…	…	PUNCT
iajs-2517	310	40	,	,	PUNCT
iajs-2517	310	41	{	{	PUNCT
iajs-2517	310	42	(	(	PUNCT
iajs-2517	310	43	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	310	44	)	)	PUNCT
iajs-2517	310	45	,	,	PUNCT
iajs-2517	310	46	(	(	PUNCT
iajs-2517	310	47	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	310	48	)	)	PUNCT
iajs-2517	310	49	}	}	PUNCT
iajs-2517	310	50	,	,	PUNCT
iajs-2517	310	51	…	…	PUNCT
iajs-2517	310	52	}	}	PUNCT
iajs-2517	310	53	is	be	AUX
iajs-2517	310	54	the	the	DET
iajs-2517	310	55	winning	win	VERB
iajs-2517	310	56	strategy	strategy	NOUN
iajs-2517	310	57	for	for	ADP
iajs-2517	310	58	player	player	NOUN
iajs-2517	310	59	ⅱ	ⅱ	NOUN
iajs-2517	310	60	in	in	ADP
iajs-2517	310	61	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	310	62	,	,	PUNCT
iajs-2517	310	63	χ	χ	X
iajs-2517	310	64	)	)	PUNCT
iajs-2517	310	65	(	(	PUNCT
iajs-2517	310	66	respectively	respectively	ADV
iajs-2517	310	67	,	,	PUNCT
iajs-2517	310	68	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	310	69	,	,	PUNCT
iajs-2517	310	70	ℐ	ℐ	NOUN
iajs-2517	310	71	)	)	PUNCT
iajs-2517	310	72	)	)	PUNCT
iajs-2517	310	73	.	.	PUNCT
iajs-2517	311	1	hence	hence	ADV
iajs-2517	311	2	player	player	NOUN
iajs-2517	311	3	ⅱ	ⅱ	PROPN
iajs-2517	311	4	↑	↑	PROPN
iajs-2517	311	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	311	6	,	,	PUNCT
iajs-2517	311	7	χ	χ	X
iajs-2517	311	8	)	)	PUNCT
iajs-2517	311	9	(	(	PUNCT
iajs-2517	311	10	respectively	respectively	ADV
iajs-2517	311	11	,	,	PUNCT
iajs-2517	311	12	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	311	13	,	,	PUNCT
iajs-2517	311	14	ℐ	ℐ	NOUN
iajs-2517	311	15	)	)	PUNCT
iajs-2517	311	16	)	)	PUNCT
iajs-2517	311	17	.	.	PUNCT
iajs-2517	312	1	(	(	PUNCT
iajs-2517	312	2	⟸	⟸	ADJ
iajs-2517	312	3	)	)	PUNCT
iajs-2517	312	4	clear	clear	ADJ
iajs-2517	312	5	.	.	PUNCT
iajs-2517	313	1	corollary	corollary	ADJ
iajs-2517	313	2	5.16	5.16	NUM
iajs-2517	313	3	.	.	PUNCT
iajs-2517	314	1	for	for	ADP
iajs-2517	314	2	a	a	DET
iajs-2517	314	3	space	space	NOUN
iajs-2517	314	4	(	(	PUNCT
iajs-2517	314	5	χ	χ	X
iajs-2517	314	6	,	,	PUNCT
iajs-2517	314	7	𝒯	𝒯	PROPN
iajs-2517	314	8	,	,	PUNCT
iajs-2517	314	9	ℋ	ℋ	PROPN
iajs-2517	314	10	,	,	PUNCT
iajs-2517	314	11	ℐ	ℐ	PROPN
iajs-2517	314	12	):	):	PUNCT
iajs-2517	314	13	iplayer	iplayer	PROPN
iajs-2517	314	14	ⅱ	ⅱ	PROPN
iajs-2517	314	15	↑	↑	PROPN
iajs-2517	314	16	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	314	17	,	,	PUNCT
iajs-2517	314	18	χ	χ	X
iajs-2517	314	19	)	)	PUNCT
iajs-2517	314	20	if	if	SCONJ
iajs-2517	314	21	∀	∀	NOUN
iajs-2517	314	22	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	314	23	≠	≠	PROPN
iajs-2517	314	24	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	314	25	where	where	SCONJ
iajs-2517	314	26	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	314	27	,	,	PUNCT
iajs-2517	314	28	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	314	29	∈̃	∈̃	PROPN
iajs-2517	314	30	�	�	PROPN
iajs-2517	314	31	̃	̃	PROPN
iajs-2517	314	32	�	�	PROPN
iajs-2517	314	33	,	,	PUNCT
iajs-2517	314	34	∃	∃	PROPN
iajs-2517	314	35	(	(	PUNCT
iajs-2517	314	36	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	314	37	)	)	PUNCT
iajs-2517	314	38	,	,	PUNCT
iajs-2517	314	39	(	(	PUNCT
iajs-2517	314	40	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	314	41	)	)	PUNCT
iajs-2517	314	42	are	be	AUX
iajs-2517	314	43	two	two	NUM
iajs-2517	314	44	closed	closed	ADJ
iajs-2517	314	45	sets	set	NOUN
iajs-2517	314	46	such	such	ADJ
iajs-2517	314	47	that	that	DET
iajs-2517	314	48	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	314	49	∈̃	∈̃	NOUN
iajs-2517	314	50	(	(	PUNCT
iajs-2517	314	51	(	(	PUNCT
iajs-2517	314	52	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	314	53	)	)	PUNCT
iajs-2517	314	54	‒	‒	NOUN
iajs-2517	314	55	(	(	PUNCT
iajs-2517	314	56	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	314	57	)	)	PUNCT
iajs-2517	314	58	)	)	PUNCT
iajs-2517	314	59	and	and	CCONJ
iajs-2517	314	60	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	314	61	∈̃	∈̃	PROPN
iajs-2517	314	62	(	(	PUNCT
iajs-2517	314	63	(	(	PUNCT
iajs-2517	314	64	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	314	65	)	)	PUNCT
iajs-2517	314	66	‒	‒	NOUN
iajs-2517	314	67	(	(	PUNCT
iajs-2517	314	68	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	314	69	)	)	PUNCT
iajs-2517	314	70	)	)	PUNCT
iajs-2517	314	71	.	.	PUNCT
iajs-2517	315	1	iiplayer	iiplayer	NOUN
iajs-2517	315	2	ⅱ	ⅱ	PROPN
iajs-2517	315	3	↑	↑	PROPN
iajs-2517	315	4	𝒢(𝒯1	𝒢(𝒯1	PROPN
iajs-2517	315	5	,	,	PUNCT
iajs-2517	315	6	ℐ	ℐ	NUM
iajs-2517	315	7	)	)	PUNCT
iajs-2517	315	8	if	if	SCONJ
iajs-2517	315	9	∀	∀	NOUN
iajs-2517	315	10	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	315	11	≠	≠	PROPN
iajs-2517	315	12	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	315	13	where	where	SCONJ
iajs-2517	315	14	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	315	15	,	,	PUNCT
iajs-2517	315	16	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	315	17	∈̃	∈̃	PROPN
iajs-2517	315	18	𝜒	𝜒	NUM
iajs-2517	315	19	,	,	PUNCT
iajs-2517	315	20	∃	∃	PROPN
iajs-2517	315	21	(	(	PUNCT
iajs-2517	315	22	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	315	23	)	)	PUNCT
iajs-2517	315	24	,	,	PUNCT
iajs-2517	315	25	(	(	PUNCT
iajs-2517	315	26	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	315	27	)	)	PUNCT
iajs-2517	315	28	}	}	PUNCT
iajs-2517	315	29	are	be	AUX
iajs-2517	315	30	two	two	NUM
iajs-2517	315	31	sℐsg	sℐsg	PROPN
iajs-2517	315	32	-	-	PUNCT
iajs-2517	315	33	closed	close	VERB
iajs-2517	315	34	sets	set	NOUN
iajs-2517	315	35	where	where	SCONJ
iajs-2517	315	36	,	,	PUNCT
iajs-2517	315	37	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	315	38	∈̃	∈̃	NOUN
iajs-2517	315	39	(	(	PUNCT
iajs-2517	315	40	(	(	PUNCT
iajs-2517	315	41	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	315	42	)	)	PUNCT
iajs-2517	315	43	‒	‒	NOUN
iajs-2517	315	44	(	(	PUNCT
iajs-2517	315	45	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	315	46	)	)	PUNCT
iajs-2517	315	47	)	)	PUNCT
iajs-2517	315	48	and	and	CCONJ
iajs-2517	315	49	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	315	50	∈̃	∈̃	PROPN
iajs-2517	315	51	(	(	PUNCT
iajs-2517	315	52	(	(	PUNCT
iajs-2517	315	53	ℬ,ℋ	ℬ,ℋ	ADJ
iajs-2517	315	54	)	)	PUNCT
iajs-2517	315	55	‒	‒	NOUN
iajs-2517	315	56	(	(	PUNCT
iajs-2517	315	57	𝒜,ℋ	𝒜,ℋ	NOUN
iajs-2517	315	58	)	)	PUNCT
iajs-2517	315	59	)	)	PUNCT
iajs-2517	315	60	.	.	PUNCT
iajs-2517	316	1	proof	proof	NOUN
iajs-2517	316	2	:	:	PUNCT
iajs-2517	316	3	i.	i.	PROPN
iajs-2517	316	4	(	(	PUNCT
iajs-2517	316	5	⟹	⟹	X
iajs-2517	316	6	)	)	PUNCT
iajs-2517	316	7	let	let	VERB
iajs-2517	316	8	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	316	9	≠	≠	PUNCT
iajs-2517	316	10	𝒽𝒩	𝒽𝒩	NOUN
iajs-2517	316	11	where	where	SCONJ
iajs-2517	316	12	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	316	13	,	,	PUNCT
iajs-2517	316	14	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	316	15	∈̃	∈̃	PROPN
iajs-2517	316	16	�	�	PROPN
iajs-2517	316	17	̃	̃	PROPN
iajs-2517	316	18	�	�	PROPN
iajs-2517	316	19	.	.	PUNCT
iajs-2517	317	1	since	since	SCONJ
iajs-2517	317	2	player	player	NOUN
iajs-2517	317	3	ⅱ	ⅱ	PROPN
iajs-2517	317	4	↑	↑	PROPN
iajs-2517	317	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	317	6	,	,	PUNCT
iajs-2517	317	7	χ	χ	X
iajs-2517	317	8	)	)	PUNCT
iajs-2517	317	9	,	,	PUNCT
iajs-2517	317	10	then	then	ADV
iajs-2517	317	11	by	by	ADP
iajs-2517	317	12	theorem	theorem	ADJ
iajs-2517	317	13	4.1.15	4.1.15	NUM
iajs-2517	317	14	,	,	PUNCT
iajs-2517	317	15	the	the	DET
iajs-2517	317	16	space	space	NOUN
iajs-2517	317	17	(	(	PUNCT
iajs-2517	317	18	χ	χ	X
iajs-2517	317	19	,	,	PUNCT
iajs-2517	317	20	𝒯	𝒯	PROPN
iajs-2517	317	21	,	,	PUNCT
iajs-2517	317	22	ℋ	ℋ	PROPN
iajs-2517	317	23	)	)	PUNCT
iajs-2517	317	24	is	be	AUX
iajs-2517	317	25	a	a	DET
iajs-2517	317	26	soft-𝒯1	soft-𝒯1	NOUN
iajs-2517	317	27	𝑠𝑝𝑎𝑐𝑒.	𝑠𝑝𝑎𝑐𝑒.	NOUN
iajs-2517	317	28	then	then	ADV
iajs-2517	317	29	theorem	theorem	VERB
iajs-2517	317	30	2.19	2.19	NUM
iajs-2517	317	31	,	,	PUNCT
iajs-2517	317	32	is	be	AUX
iajs-2517	317	33	applicable	applicable	ADJ
iajs-2517	317	34	.	.	PUNCT
iajs-2517	318	1	(	(	PUNCT
iajs-2517	318	2	⟸	⟸	NOUN
iajs-2517	318	3	)	)	PUNCT
iajs-2517	318	4	by	by	ADP
iajs-2517	318	5	theorem	theorem	NOUN
iajs-2517	318	6	2.19	2.19	NUM
iajs-2517	318	7	,	,	PUNCT
iajs-2517	318	8	the	the	DET
iajs-2517	318	9	space	space	NOUN
iajs-2517	318	10	(	(	PUNCT
iajs-2517	318	11	χ	χ	X
iajs-2517	318	12	,	,	PUNCT
iajs-2517	318	13	𝒯	𝒯	PROPN
iajs-2517	318	14	,	,	PUNCT
iajs-2517	318	15	ℋ	ℋ	PROPN
iajs-2517	318	16	)	)	PUNCT
iajs-2517	318	17	is	be	AUX
iajs-2517	318	18	a	a	DET
iajs-2517	318	19	soft-𝒯1	soft-𝒯1	NOUN
iajs-2517	318	20	𝑠𝑝𝑎𝑐𝑒.	𝑠𝑝𝑎𝑐𝑒.	NOUN
iajs-2517	318	21	then	then	ADV
iajs-2517	318	22	theorem	theorem	VERB
iajs-2517	318	23	5.15	5.15	NUM
iajs-2517	318	24	,	,	PUNCT
iajs-2517	318	25	is	be	AUX
iajs-2517	318	26	applicable	applicable	ADJ
iajs-2517	318	27	.	.	PUNCT
iajs-2517	319	1	ii	ii	X
iajs-2517	319	2	.	.	PUNCT
iajs-2517	320	1	(	(	PUNCT
iajs-2517	320	2	⟹)let	⟹)let	NOUN
iajs-2517	320	3	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	320	4	≠	≠	PUNCT
iajs-2517	320	5	𝒽𝒩	𝒽𝒩	NOUN
iajs-2517	320	6	where	where	SCONJ
iajs-2517	320	7	𝒽𝓜	𝒽𝓜	NOUN
iajs-2517	320	8	,	,	PUNCT
iajs-2517	320	9	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	320	10	∈̃	∈̃	PROPN
iajs-2517	320	11	�	�	PROPN
iajs-2517	320	12	̃	̃	PROPN
iajs-2517	320	13	�	�	PROPN
iajs-2517	320	14	.	.	PUNCT
iajs-2517	321	1	since	since	SCONJ
iajs-2517	321	2	player	player	NOUN
iajs-2517	321	3	ⅱ	ⅱ	PROPN
iajs-2517	321	4	↑	↑	PROPN
iajs-2517	321	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	321	6	,	,	PUNCT
iajs-2517	321	7	ℐ	ℐ	NUM
iajs-2517	321	8	)	)	PUNCT
iajs-2517	321	9	,	,	PUNCT
iajs-2517	321	10	then	then	ADV
iajs-2517	321	11	by	by	ADP
iajs-2517	321	12	theorem	theorem	NOUN
iajs-2517	321	13	5.15	5.15	NUM
iajs-2517	321	14	,	,	PUNCT
iajs-2517	321	15	the	the	DET
iajs-2517	321	16	space	space	NOUN
iajs-2517	321	17	(	(	PUNCT
iajs-2517	321	18	χ	χ	X
iajs-2517	321	19	,	,	PUNCT
iajs-2517	321	20	𝒯	𝒯	PROPN
iajs-2517	321	21	,	,	PUNCT
iajs-2517	321	22	ℋ	ℋ	PROPN
iajs-2517	321	23	)	)	PUNCT
iajs-2517	321	24	is	be	AUX
iajs-2517	321	25	a	a	DET
iajs-2517	321	26	sℐsg-𝒯1­space	sℐsg-𝒯1­space	PROPN
iajs-2517	321	27	.	.	PUNCT
iajs-2517	322	1	then	then	ADV
iajs-2517	322	2	theorem	theorem	VERB
iajs-2517	322	3	4.9	4.9	NUM
iajs-2517	322	4	,	,	PUNCT
iajs-2517	322	5	is	be	AUX
iajs-2517	322	6	applicable	applicable	ADJ
iajs-2517	322	7	.	.	PUNCT
iajs-2517	323	1	(	(	PUNCT
iajs-2517	323	2	⟸	⟸	NOUN
iajs-2517	323	3	)	)	PUNCT
iajs-2517	323	4	by	by	ADP
iajs-2517	323	5	theorem	theorem	NOUN
iajs-2517	323	6	4.9	4.9	NUM
iajs-2517	323	7	,	,	PUNCT
iajs-2517	323	8	the	the	DET
iajs-2517	323	9	space	space	NOUN
iajs-2517	323	10	(	(	PUNCT
iajs-2517	323	11	χ	χ	X
iajs-2517	323	12	,	,	PUNCT
iajs-2517	323	13	𝒯	𝒯	PROPN
iajs-2517	323	14	,	,	PUNCT
iajs-2517	323	15	ℋ	ℋ	PROPN
iajs-2517	323	16	)	)	PUNCT
iajs-2517	323	17	is	be	AUX
iajs-2517	323	18	a	a	DET
iajs-2517	323	19	sℐsg-𝒯1­space	sℐsg-𝒯1­space	PROPN
iajs-2517	323	20	.	.	PUNCT
iajs-2517	324	1	then	then	ADV
iajs-2517	324	2	theorem	theorem	VERB
iajs-2517	324	3	5.15	5.15	NUM
iajs-2517	324	4	,	,	PUNCT
iajs-2517	324	5	is	be	AUX
iajs-2517	324	6	applicable	applicable	ADJ
iajs-2517	324	7	.	.	PUNCT
iajs-2517	325	1	corollary	corollary	ADJ
iajs-2517	325	2	5.17	5.17	NUM
iajs-2517	325	3	.	.	PUNCT
iajs-2517	326	1	ia	ia	PROPN
iajs-2517	326	2	space	space	NOUN
iajs-2517	326	3	(	(	PUNCT
iajs-2517	326	4	χ	χ	X
iajs-2517	326	5	,	,	PUNCT
iajs-2517	326	6	𝒯	𝒯	PROPN
iajs-2517	326	7	,	,	PUNCT
iajs-2517	326	8	ℋ	ℋ	PROPN
iajs-2517	326	9	)	)	PUNCT
iajs-2517	326	10	is	be	AUX
iajs-2517	326	11	a	a	DET
iajs-2517	326	12	soft-𝒯1­space	soft-𝒯1­space	NOUN
iajs-2517	326	13	if	if	SCONJ
iajs-2517	327	1	and	and	CCONJ
iajs-2517	327	2	only	only	ADV
iajs-2517	327	3	if	if	SCONJ
iajs-2517	327	4	player	player	NOUN
iajs-2517	327	5	ⅰ	ⅰ	PRON
iajs-2517	327	6	⤉	⤉	VERB
iajs-2517	327	7	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	327	8	,	,	PUNCT
iajs-2517	327	9	χ	χ	NOUN
iajs-2517	327	10	)	)	PUNCT
iajs-2517	327	11	.	.	PUNCT
iajs-2517	328	1	iia	iia	NOUN
iajs-2517	328	2	space	space	NOUN
iajs-2517	328	3	(	(	PUNCT
iajs-2517	328	4	χ	χ	X
iajs-2517	328	5	,	,	PUNCT
iajs-2517	328	6	𝒯	𝒯	PROPN
iajs-2517	328	7	,	,	PUNCT
iajs-2517	328	8	ℋ	ℋ	PROPN
iajs-2517	328	9	,	,	PUNCT
iajs-2517	328	10	ℐ	ℐ	NUM
iajs-2517	328	11	)	)	PUNCT
iajs-2517	328	12	is	be	AUX
iajs-2517	328	13	a	a	DET
iajs-2517	328	14	sℐsg-𝒯1­space	sℐsg-𝒯1­space	PROPN
iajs-2517	328	15	if	if	SCONJ
iajs-2517	329	1	and	and	CCONJ
iajs-2517	329	2	only	only	ADV
iajs-2517	329	3	if	if	SCONJ
iajs-2517	329	4	player	player	NOUN
iajs-2517	329	5	ⅰ	ⅰ	PRON
iajs-2517	329	6	⤉	⤉	VERB
iajs-2517	329	7	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	329	8	,	,	PUNCT
iajs-2517	329	9	ℐ	ℐ	NOUN
iajs-2517	329	10	)	)	PUNCT
iajs-2517	329	11	.	.	PUNCT
iajs-2517	330	1	proof	proof	NOUN
iajs-2517	330	2	:	:	PUNCT
iajs-2517	330	3	by	by	ADP
iajs-2517	330	4	theorem	theorem	NOUN
iajs-2517	330	5	5.15	5.15	NUM
iajs-2517	330	6	,	,	PUNCT
iajs-2517	330	7	the	the	DET
iajs-2517	330	8	proof	proof	NOUN
iajs-2517	330	9	is	be	AUX
iajs-2517	330	10	over	over	ADV
iajs-2517	330	11	.	.	PUNCT
iajs-2517	331	1	theorem	theorem	VERB
iajs-2517	331	2	5.18	5.18	NUM
iajs-2517	331	3	.	.	PUNCT
iajs-2517	332	1	for	for	ADP
iajs-2517	332	2	a	a	DET
iajs-2517	332	3	space	space	NOUN
iajs-2517	332	4	(	(	PUNCT
iajs-2517	332	5	χ	χ	X
iajs-2517	332	6	,	,	PUNCT
iajs-2517	332	7	𝒯	𝒯	PROPN
iajs-2517	332	8	,	,	PUNCT
iajs-2517	332	9	ℋ	ℋ	PROPN
iajs-2517	332	10	,	,	PUNCT
iajs-2517	332	11	ℐ	ℐ	PROPN
iajs-2517	332	12	):	):	PUNCT
iajs-2517	332	13	ia	ia	PROPN
iajs-2517	332	14	space	space	NOUN
iajs-2517	332	15	(	(	PUNCT
iajs-2517	332	16	χ	χ	X
iajs-2517	332	17	,	,	PUNCT
iajs-2517	332	18	𝒯	𝒯	PROPN
iajs-2517	332	19	,	,	PUNCT
iajs-2517	332	20	ℋ	ℋ	PROPN
iajs-2517	332	21	)	)	PUNCT
iajs-2517	332	22	is	be	AUX
iajs-2517	332	23	not	not	PART
iajs-2517	332	24	soft-𝒯1­space	soft-𝒯1­space	NOUN
iajs-2517	332	25	if	if	SCONJ
iajs-2517	333	1	and	and	CCONJ
iajs-2517	333	2	only	only	ADV
iajs-2517	333	3	if	if	SCONJ
iajs-2517	333	4	player	player	NOUN
iajs-2517	333	5	ⅰ	ⅰ	X
iajs-2517	333	6	↑	↑	PROPN
iajs-2517	333	7	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	333	8	,	,	PUNCT
iajs-2517	333	9	χ	χ	NOUN
iajs-2517	333	10	)	)	PUNCT
iajs-2517	333	11	.	.	PUNCT
iajs-2517	334	1	iia	iia	NOUN
iajs-2517	334	2	space	space	NOUN
iajs-2517	334	3	(	(	PUNCT
iajs-2517	334	4	χ	χ	X
iajs-2517	334	5	,	,	PUNCT
iajs-2517	334	6	𝒯	𝒯	PROPN
iajs-2517	334	7	,	,	PUNCT
iajs-2517	334	8	ℋ	ℋ	PROPN
iajs-2517	334	9	,	,	PUNCT
iajs-2517	334	10	ℐ	ℐ	NUM
iajs-2517	334	11	)	)	PUNCT
iajs-2517	334	12	is	be	AUX
iajs-2517	334	13	not	not	PART
iajs-2517	334	14	sℐsg-𝒯1­space	sℐsg-𝒯1­space	PROPN
iajs-2517	334	15	if	if	SCONJ
iajs-2517	335	1	and	and	CCONJ
iajs-2517	335	2	only	only	ADV
iajs-2517	335	3	if	if	SCONJ
iajs-2517	335	4	player	player	NOUN
iajs-2517	335	5	ⅰ	ⅰ	X
iajs-2517	335	6	↑	↑	PROPN
iajs-2517	335	7	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	335	8	,	,	PUNCT
iajs-2517	335	9	ℐ	ℐ	NOUN
iajs-2517	335	10	)	)	PUNCT
iajs-2517	335	11	.	.	PUNCT
iajs-2517	336	1	proof	proof	NOUN
iajs-2517	336	2	:	:	PUNCT
iajs-2517	336	3	i.	i.	PROPN
iajs-2517	336	4	(	(	PUNCT
iajs-2517	336	5	⟹	⟹	X
iajs-2517	336	6	)	)	PUNCT
iajs-2517	336	7	in	in	ADP
iajs-2517	336	8	the	the	DET
iajs-2517	336	9	𝑟-th	𝑟-th	NOUN
iajs-2517	336	10	inning	inning	NOUN
iajs-2517	336	11	player	player	NOUN
iajs-2517	336	12	ⅰ	ⅰ	NUM
iajs-2517	336	13	in	in	ADP
iajs-2517	336	14	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	336	15	,	,	PUNCT
iajs-2517	336	16	χ	χ	X
iajs-2517	336	17	)	)	PUNCT
iajs-2517	336	18	choose	choose	VERB
iajs-2517	336	19	(	(	PUNCT
iajs-2517	336	20	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	336	21	≠	≠	PROPN
iajs-2517	336	22	(	(	PUNCT
iajs-2517	336	23	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	336	24	where	where	SCONJ
iajs-2517	336	25	,	,	PUNCT
iajs-2517	336	26	(	(	PUNCT
iajs-2517	336	27	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	336	28	,	,	PUNCT
iajs-2517	336	29	(	(	PUNCT
iajs-2517	336	30	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	336	31	∈̃	∈̃	PROPN
iajs-2517	336	32	�	�	PROPN
iajs-2517	336	33	̃	̃	PROPN
iajs-2517	336	34	�	�	PROPN
iajs-2517	336	35	,	,	PUNCT
iajs-2517	336	36	player	player	NOUN
iajs-2517	336	37	ⅱ	ⅱ	PROPN
iajs-2517	336	38	in	in	ADP
iajs-2517	336	39	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	336	40	,	,	PUNCT
iajs-2517	336	41	χ	χ	X
iajs-2517	336	42	)	)	PUNCT
iajs-2517	336	43	can	can	AUX
iajs-2517	336	44	not	not	PART
iajs-2517	336	45	find	find	VERB
iajs-2517	336	46	(	(	PUNCT
iajs-2517	336	47	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	336	48	)	)	PUNCT
iajs-2517	336	49	,	,	PUNCT
iajs-2517	336	50	(	(	PUNCT
iajs-2517	336	51	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	336	52	)	)	PUNCT
iajs-2517	336	53	are	be	AUX
iajs-2517	336	54	two	two	NUM
iajs-2517	336	55	soft	soft	ADJ
iajs-2517	336	56	open	open	ADJ
iajs-2517	336	57	sets	set	NOUN
iajs-2517	336	58	such	such	ADJ
iajs-2517	336	59	that	that	SCONJ
iajs-2517	336	60	(	(	PUNCT
iajs-2517	336	61	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	336	62	∈̃	∈̃	PROPN
iajs-2517	336	63	(	(	PUNCT
iajs-2517	336	64	(	(	PUNCT
iajs-2517	336	65	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	336	66	)	)	PUNCT
iajs-2517	336	67	‒	‒	NOUN
iajs-2517	336	68	(	(	PUNCT
iajs-2517	336	69	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	336	70	)	)	PUNCT
iajs-2517	336	71	)	)	PUNCT
iajs-2517	336	72	and	and	CCONJ
iajs-2517	336	73	(	(	PUNCT
iajs-2517	336	74	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	336	75	∈̃	∈̃	PROPN
iajs-2517	336	76	(	(	PUNCT
iajs-2517	336	77	(	(	PUNCT
iajs-2517	336	78	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	336	79	)	)	PUNCT
iajs-2517	336	80	‒	‒	NOUN
iajs-2517	336	81	(	(	PUNCT
iajs-2517	336	82	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	336	83	)	)	PUNCT
iajs-2517	336	84	)	)	PUNCT
iajs-2517	336	85	,	,	PUNCT
iajs-2517	336	86	because	because	SCONJ
iajs-2517	336	87	(	(	PUNCT
iajs-2517	336	88	χ	χ	X
iajs-2517	336	89	,	,	PUNCT
iajs-2517	336	90	𝒯	𝒯	PROPN
iajs-2517	336	91	,	,	PUNCT
iajs-2517	336	92	ℋ	ℋ	PROPN
iajs-2517	336	93	)	)	PUNCT
iajs-2517	336	94	is	be	AUX
iajs-2517	336	95	not	not	PART
iajs-2517	336	96	soft-𝒯1­space	soft-𝒯1­space	NUM
iajs-2517	336	97	.	.	PUNCT
iajs-2517	337	1	hence	hence	ADV
iajs-2517	337	2	player	player	NOUN
iajs-2517	337	3	ⅰ	ⅰ	PROPN
iajs-2517	337	4	↑	↑	PROPN
iajs-2517	337	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	337	6	,	,	PUNCT
iajs-2517	337	7	χ	χ	NOUN
iajs-2517	337	8	)	)	PUNCT
iajs-2517	337	9	.	.	PUNCT
iajs-2517	338	1	(	(	PUNCT
iajs-2517	338	2	⟸	⟸	ADJ
iajs-2517	338	3	)	)	PUNCT
iajs-2517	338	4	clear	clear	ADJ
iajs-2517	338	5	.	.	PUNCT
iajs-2517	339	1	ii	ii	X
iajs-2517	339	2	.	.	PUNCT
iajs-2517	340	1	(	(	PUNCT
iajs-2517	340	2	⟹	⟹	X
iajs-2517	340	3	)	)	PUNCT
iajs-2517	340	4	in	in	ADP
iajs-2517	340	5	the	the	DET
iajs-2517	340	6	𝑟-th	𝑟-th	NOUN
iajs-2517	340	7	inning	inning	NOUN
iajs-2517	340	8	player	player	NOUN
iajs-2517	340	9	ⅰ	ⅰ	NUM
iajs-2517	340	10	in	in	ADP
iajs-2517	340	11	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	340	12	,	,	PUNCT
iajs-2517	340	13	ℐ	ℐ	X
iajs-2517	340	14	)	)	PUNCT
iajs-2517	340	15	choose	choose	VERB
iajs-2517	340	16	(	(	PUNCT
iajs-2517	340	17	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	340	18	≠	≠	PROPN
iajs-2517	340	19	(	(	PUNCT
iajs-2517	340	20	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	340	21	where	where	SCONJ
iajs-2517	340	22	,	,	PUNCT
iajs-2517	340	23	(	(	PUNCT
iajs-2517	340	24	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	340	25	,	,	PUNCT
iajs-2517	340	26	(	(	PUNCT
iajs-2517	340	27	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	340	28	∈̃	∈̃	PROPN
iajs-2517	340	29	�	�	PROPN
iajs-2517	340	30	̃	̃	PROPN
iajs-2517	340	31	�	�	PROPN
iajs-2517	340	32	,	,	PUNCT
iajs-2517	340	33	player	player	NOUN
iajs-2517	340	34	ⅱ	ⅱ	PROPN
iajs-2517	340	35	in	in	ADP
iajs-2517	340	36	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	340	37	,	,	PUNCT
iajs-2517	340	38	ℐ	ℐ	X
iajs-2517	340	39	)	)	PUNCT
iajs-2517	340	40	can	can	AUX
iajs-2517	340	41	not	not	PART
iajs-2517	340	42	find	find	VERB
iajs-2517	340	43	(	(	PUNCT
iajs-2517	340	44	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	340	45	)	)	PUNCT
iajs-2517	340	46	,	,	PUNCT
iajs-2517	340	47	(	(	PUNCT
iajs-2517	340	48	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	340	49	)	)	PUNCT
iajs-2517	340	50	are	be	AUX
iajs-2517	340	51	two	two	NUM
iajs-2517	340	52	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	340	53	sets	set	VERB
iajs-2517	340	54	such	such	ADJ
iajs-2517	340	55	that	that	SCONJ
iajs-2517	340	56	(	(	PUNCT
iajs-2517	340	57	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	340	58	∈̃	∈̃	PROPN
iajs-2517	340	59	(	(	PUNCT
iajs-2517	340	60	(	(	PUNCT
iajs-2517	340	61	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	340	62	)	)	PUNCT
iajs-2517	340	63	‒	‒	NOUN
iajs-2517	340	64	(	(	PUNCT
iajs-2517	340	65	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	340	66	)	)	PUNCT
iajs-2517	340	67	)	)	PUNCT
iajs-2517	340	68	and	and	CCONJ
iajs-2517	340	69	(	(	PUNCT
iajs-2517	340	70	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	340	71	∈̃	∈̃	PROPN
iajs-2517	340	72	(	(	PUNCT
iajs-2517	340	73	(	(	PUNCT
iajs-2517	340	74	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	340	75	)	)	PUNCT
iajs-2517	340	76	‒	‒	NOUN
iajs-2517	340	77	(	(	PUNCT
iajs-2517	340	78	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	340	79	)	)	PUNCT
iajs-2517	340	80	)	)	PUNCT
iajs-2517	340	81	,	,	PUNCT
iajs-2517	340	82	because	because	SCONJ
iajs-2517	340	83	(	(	PUNCT
iajs-2517	340	84	χ	χ	X
iajs-2517	340	85	,	,	PUNCT
iajs-2517	340	86	𝒯	𝒯	PROPN
iajs-2517	340	87	,	,	PUNCT
iajs-2517	340	88	ℋ	ℋ	PROPN
iajs-2517	340	89	)	)	PUNCT
iajs-2517	340	90	is	be	AUX
iajs-2517	340	91	not	not	PART
iajs-2517	340	92	soft𝒯1­space	soft𝒯1­space	NOUN
iajs-2517	340	93	.	.	PUNCT
iajs-2517	341	1	hence	hence	ADV
iajs-2517	341	2	player	player	NOUN
iajs-2517	341	3	ⅰ	ⅰ	PROPN
iajs-2517	341	4	↑	↑	PROPN
iajs-2517	341	5	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	341	6	,	,	PUNCT
iajs-2517	341	7	ℐ	ℐ	NOUN
iajs-2517	341	8	)	)	PUNCT
iajs-2517	341	9	.	.	PUNCT
iajs-2517	342	1	133	133	NUM
iajs-2517	342	2	ibn	ibn	PROPN
iajs-2517	342	3	al	al	PROPN
iajs-2517	342	4	-	-	PUNCT
iajs-2517	342	5	haitham	haitham	PROPN
iajs-2517	342	6	jour	jour	X
iajs-2517	342	7	.	.	PROPN
iajs-2517	342	8	for	for	ADP
iajs-2517	342	9	pure	pure	ADJ
iajs-2517	342	10	&	&	CCONJ
iajs-2517	342	11	appl	appl	PROPN
iajs-2517	342	12	.	.	PUNCT
iajs-2517	343	1	sci	sci	PROPN
iajs-2517	343	2	.	.	PROPN
iajs-2517	344	1	33	33	NUM
iajs-2517	344	2	(	(	PUNCT
iajs-2517	344	3	4	4	NUM
iajs-2517	344	4	)	)	PUNCT
iajs-2517	344	5	2020	2020	NUM
iajs-2517	344	6	(	(	PUNCT
iajs-2517	344	7	⟸	⟸	ADJ
iajs-2517	344	8	)	)	PUNCT
iajs-2517	344	9	clear	clear	ADJ
iajs-2517	344	10	.	.	PUNCT
iajs-2517	345	1	corollary	corollary	ADJ
iajs-2517	345	2	5.19	5.19	NUM
iajs-2517	345	3	.	.	PUNCT
iajs-2517	346	1	iif	iif	VERB
iajs-2517	346	2	a	a	DET
iajs-2517	346	3	space	space	NOUN
iajs-2517	346	4	(	(	PUNCT
iajs-2517	346	5	χ	χ	X
iajs-2517	346	6	,	,	PUNCT
iajs-2517	346	7	𝒯	𝒯	PROPN
iajs-2517	346	8	,	,	PUNCT
iajs-2517	346	9	ℋ	ℋ	PROPN
iajs-2517	346	10	)	)	PUNCT
iajs-2517	346	11	is	be	AUX
iajs-2517	346	12	not	not	PART
iajs-2517	346	13	soft𝒯1­space	soft𝒯1­space	NOUN
iajs-2517	346	14	if	if	SCONJ
iajs-2517	347	1	and	and	CCONJ
iajs-2517	347	2	only	only	ADV
iajs-2517	347	3	if	if	SCONJ
iajs-2517	347	4	player	player	NOUN
iajs-2517	347	5	ⅱ	ⅱ	PROPN
iajs-2517	347	6	⤉	⤉	VERB
iajs-2517	347	7	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	347	8	,	,	PUNCT
iajs-2517	347	9	𝜒	𝜒	NOUN
iajs-2517	347	10	)	)	PUNCT
iajs-2517	347	11	.	.	PUNCT
iajs-2517	348	1	iiif	iiif	PROPN
iajs-2517	348	2	a	a	DET
iajs-2517	348	3	space	space	NOUN
iajs-2517	348	4	(	(	PUNCT
iajs-2517	348	5	χ	χ	X
iajs-2517	348	6	,	,	PUNCT
iajs-2517	348	7	𝒯	𝒯	PROPN
iajs-2517	348	8	,	,	PUNCT
iajs-2517	348	9	ℋ	ℋ	PROPN
iajs-2517	348	10	,	,	PUNCT
iajs-2517	348	11	ℐ	ℐ	NUM
iajs-2517	348	12	)	)	PUNCT
iajs-2517	348	13	is	be	AUX
iajs-2517	348	14	not	not	PART
iajs-2517	348	15	sℐsg-𝒯1­space	sℐsg-𝒯1­space	PROPN
iajs-2517	349	1	if	if	SCONJ
iajs-2517	350	1	and	and	CCONJ
iajs-2517	350	2	only	only	ADV
iajs-2517	350	3	if	if	SCONJ
iajs-2517	350	4	player	player	NOUN
iajs-2517	350	5	ⅱ	ⅱ	PROPN
iajs-2517	350	6	⤉	⤉	VERB
iajs-2517	350	7	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	350	8	,	,	PUNCT
iajs-2517	350	9	ℐ	ℐ	NOUN
iajs-2517	350	10	)	)	PUNCT
iajs-2517	350	11	.	.	PUNCT
iajs-2517	351	1	proof	proof	NOUN
iajs-2517	351	2	:	:	PUNCT
iajs-2517	351	3	similar	similar	ADJ
iajs-2517	351	4	way	way	NOUN
iajs-2517	351	5	of	of	ADP
iajs-2517	351	6	proof	proof	NOUN
iajs-2517	351	7	theorem	theorem	VERB
iajs-2517	351	8	5.18	5.18	NUM
iajs-2517	351	9	.	.	PUNCT
iajs-2517	352	1	definition	definition	NOUN
iajs-2517	352	2	5.20	5.20	NUM
iajs-2517	352	3	.	.	PUNCT
iajs-2517	353	1	for	for	ADP
iajs-2517	353	2	a	a	DET
iajs-2517	353	3	soft	soft	ADJ
iajs-2517	353	4	ideal	ideal	ADJ
iajs-2517	353	5	space	space	NOUN
iajs-2517	353	6	(	(	PUNCT
iajs-2517	353	7	χ	χ	X
iajs-2517	353	8	,	,	PUNCT
iajs-2517	353	9	𝒯	𝒯	PROPN
iajs-2517	353	10	,	,	PUNCT
iajs-2517	353	11	ℋ	ℋ	PROPN
iajs-2517	353	12	,	,	PUNCT
iajs-2517	353	13	ℐ	ℐ	PROPN
iajs-2517	353	14	)	)	PUNCT
iajs-2517	353	15	,	,	PUNCT
iajs-2517	353	16	determine	determine	VERB
iajs-2517	353	17	a	a	DET
iajs-2517	353	18	game	game	NOUN
iajs-2517	353	19	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	353	20	,	,	PUNCT
iajs-2517	353	21	χ	χ	X
iajs-2517	353	22	)	)	PUNCT
iajs-2517	353	23	(	(	PUNCT
iajs-2517	353	24	respectively	respectively	ADV
iajs-2517	353	25	,	,	PUNCT
iajs-2517	353	26	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	353	27	,	,	PUNCT
iajs-2517	353	28	ℐ	ℐ	NOUN
iajs-2517	353	29	)	)	PUNCT
iajs-2517	353	30	)	)	PUNCT
iajs-2517	353	31	as	as	SCONJ
iajs-2517	353	32	follows	follow	VERB
iajs-2517	353	33	:	:	PUNCT
iajs-2517	353	34	player	player	NOUN
iajs-2517	353	35	ⅰ	ⅰ	NOUN
iajs-2517	353	36	and	and	CCONJ
iajs-2517	353	37	playerⅱ	playerⅱ	NOUN
iajs-2517	353	38	are	be	AUX
iajs-2517	353	39	play	play	VERB
iajs-2517	353	40	an	an	DET
iajs-2517	353	41	inning	inning	NOUN
iajs-2517	353	42	with	with	ADP
iajs-2517	353	43	each	each	DET
iajs-2517	353	44	positive	positive	ADJ
iajs-2517	353	45	integer	integer	NOUN
iajs-2517	353	46	numbers	number	NOUN
iajs-2517	353	47	in	in	ADP
iajs-2517	353	48	the	the	DET
iajs-2517	353	49	𝑟	𝑟	NOUN
iajs-2517	353	50	𝑡ℎ	𝑡ℎ	NOUN
iajs-2517	353	51	inning	inning	NOUN
iajs-2517	353	52	:	:	PUNCT
iajs-2517	353	53	the	the	DET
iajs-2517	353	54	first	first	ADJ
iajs-2517	353	55	step	step	NOUN
iajs-2517	353	56	,	,	PUNCT
iajs-2517	353	57	player	player	NOUN
iajs-2517	353	58	ⅰ	ⅰ	X
iajs-2517	353	59	choose	choose	VERB
iajs-2517	353	60	(	(	PUNCT
iajs-2517	353	61	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	353	62	≠	≠	PROPN
iajs-2517	353	63	(	(	PUNCT
iajs-2517	353	64	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	353	65	where	where	SCONJ
iajs-2517	353	66	,	,	PUNCT
iajs-2517	353	67	(	(	PUNCT
iajs-2517	353	68	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	353	69	,	,	PUNCT
iajs-2517	353	70	(	(	PUNCT
iajs-2517	353	71	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	353	72	∈̃	∈̃	PROPN
iajs-2517	353	73	�	�	PROPN
iajs-2517	353	74	̃	̃	PROPN
iajs-2517	353	75	�	�	PROPN
iajs-2517	353	76	.	.	PUNCT
iajs-2517	354	1	in	in	ADP
iajs-2517	354	2	the	the	DET
iajs-2517	354	3	second	second	ADJ
iajs-2517	354	4	step	step	NOUN
iajs-2517	354	5	,	,	PUNCT
iajs-2517	354	6	player	player	NOUN
iajs-2517	354	7	ⅱ	ⅱ	PROPN
iajs-2517	354	8	choose	choose	VERB
iajs-2517	354	9	(	(	PUNCT
iajs-2517	354	10	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	354	11	)	)	PUNCT
iajs-2517	354	12	,	,	PUNCT
iajs-2517	354	13	(	(	PUNCT
iajs-2517	354	14	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	354	15	)	)	PUNCT
iajs-2517	354	16	are	be	AUX
iajs-2517	354	17	two	two	NUM
iajs-2517	354	18	soft	soft	ADJ
iajs-2517	354	19	open	open	ADJ
iajs-2517	354	20	(	(	PUNCT
iajs-2517	354	21	respectively	respectively	ADV
iajs-2517	354	22	,	,	PUNCT
iajs-2517	354	23	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	354	24	)	)	PUNCT
iajs-2517	354	25	sets	set	VERB
iajs-2517	354	26	such	such	ADJ
iajs-2517	354	27	that	that	SCONJ
iajs-2517	354	28	(	(	PUNCT
iajs-2517	354	29	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	354	30	∈̃	∈̃	PROPN
iajs-2517	354	31	(	(	PUNCT
iajs-2517	354	32	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	354	33	)	)	PUNCT
iajs-2517	354	34	,	,	PUNCT
iajs-2517	354	35	(	(	PUNCT
iajs-2517	354	36	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	354	37	∈̃	∈̃	PROPN
iajs-2517	354	38	(	(	PUNCT
iajs-2517	354	39	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	354	40	)	)	PUNCT
iajs-2517	354	41	and	and	CCONJ
iajs-2517	354	42	(	(	PUNCT
iajs-2517	354	43	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	354	44	)	)	PUNCT
iajs-2517	354	45	∩̃	∩̃	PUNCT
iajs-2517	354	46	(	(	PUNCT
iajs-2517	354	47	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	354	48	)	)	PUNCT
iajs-2517	354	49	=	=	PRON
iajs-2517	354	50	{	{	PUNCT
iajs-2517	354	51	∅̃	∅̃	NOUN
iajs-2517	354	52	}	}	PUNCT
iajs-2517	354	53	.	.	PUNCT
iajs-2517	355	1	then	then	ADV
iajs-2517	355	2	player	player	NOUN
iajs-2517	355	3	ⅱ	ⅱ	PROPN
iajs-2517	355	4	wins	win	VERB
iajs-2517	355	5	in	in	ADP
iajs-2517	355	6	the	the	DET
iajs-2517	355	7	game	game	NOUN
iajs-2517	355	8	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	355	9	,	,	PUNCT
iajs-2517	355	10	χ	χ	X
iajs-2517	355	11	)	)	PUNCT
iajs-2517	355	12	(	(	PUNCT
iajs-2517	355	13	respectively	respectively	ADV
iajs-2517	355	14	,	,	PUNCT
iajs-2517	355	15	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	355	16	,	,	PUNCT
iajs-2517	355	17	ℐ	ℐ	NUM
iajs-2517	355	18	)	)	PUNCT
iajs-2517	355	19	)	)	PUNCT
iajs-2517	356	1	if	if	SCONJ
iajs-2517	356	2	ℬ	ℬ	NOUN
iajs-2517	356	3	=	=	PRON
iajs-2517	356	4	{	{	PUNCT
iajs-2517	356	5	{	{	PUNCT
iajs-2517	356	6	(	(	PUNCT
iajs-2517	356	7	𝒜	𝒜	NOUN
iajs-2517	356	8	,	,	PUNCT
iajs-2517	356	9	ℋ	ℋ	PROPN
iajs-2517	356	10	)	)	PUNCT
iajs-2517	356	11	,	,	PUNCT
iajs-2517	356	12	(	(	PUNCT
iajs-2517	356	13	ℬ	ℬ	X
iajs-2517	356	14	,	,	PUNCT
iajs-2517	356	15	ℋ	ℋ	NOUN
iajs-2517	356	16	)	)	PUNCT
iajs-2517	356	17	}	}	PUNCT
iajs-2517	356	18	,	,	PUNCT
iajs-2517	356	19	{	{	PUNCT
iajs-2517	356	20	(	(	PUNCT
iajs-2517	356	21	ℬ	ℬ	X
iajs-2517	356	22	,	,	PUNCT
iajs-2517	356	23	ℋ	ℋ	PROPN
iajs-2517	356	24	)	)	PUNCT
iajs-2517	356	25	,	,	PUNCT
iajs-2517	356	26	(	(	PUNCT
iajs-2517	356	27	𝒞	𝒞	PROPN
iajs-2517	356	28	,	,	PUNCT
iajs-2517	356	29	ℋ	ℋ	PROPN
iajs-2517	356	30	)	)	PUNCT
iajs-2517	356	31	}	}	PUNCT
iajs-2517	356	32	,	,	PUNCT
iajs-2517	356	33	{	{	PUNCT
iajs-2517	356	34	(	(	PUNCT
iajs-2517	356	35	𝒜	𝒜	NOUN
iajs-2517	356	36	,	,	PUNCT
iajs-2517	356	37	ℋ	ℋ	PROPN
iajs-2517	356	38	)	)	PUNCT
iajs-2517	356	39	,	,	PUNCT
iajs-2517	356	40	(	(	PUNCT
iajs-2517	356	41	𝒞	𝒞	PROPN
iajs-2517	356	42	,	,	PUNCT
iajs-2517	356	43	ℋ	ℋ	PROPN
iajs-2517	356	44	)	)	PUNCT
iajs-2517	356	45	}	}	PUNCT
iajs-2517	356	46	}	}	PUNCT
iajs-2517	356	47	be	be	AUX
iajs-2517	356	48	a	a	DET
iajs-2517	356	49	collection	collection	NOUN
iajs-2517	356	50	of	of	ADP
iajs-2517	356	51	a	a	DET
iajs-2517	356	52	soft	soft	ADJ
iajs-2517	356	53	open	open	ADJ
iajs-2517	356	54	(	(	PUNCT
iajs-2517	356	55	respectively	respectively	ADV
iajs-2517	356	56	,	,	PUNCT
iajs-2517	356	57	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	356	58	)	)	PUNCT
iajs-2517	356	59	sets	set	VERB
iajs-2517	356	60	in	in	ADP
iajs-2517	356	61	𝜒	𝜒	NOUN
iajs-2517	356	62	such	such	ADJ
iajs-2517	356	63	that	that	PRON
iajs-2517	356	64	∀	∀	X
iajs-2517	356	65	(	(	PUNCT
iajs-2517	356	66	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	356	67	≠	≠	PROPN
iajs-2517	356	68	(	(	PUNCT
iajs-2517	356	69	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	356	70	where	where	SCONJ
iajs-2517	356	71	,	,	PUNCT
iajs-2517	356	72	(	(	PUNCT
iajs-2517	356	73	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	356	74	,	,	PUNCT
iajs-2517	356	75	(	(	PUNCT
iajs-2517	356	76	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	356	77	∈̃	∈̃	PROPN
iajs-2517	356	78	�	�	PROPN
iajs-2517	356	79	̃	̃	PROPN
iajs-2517	356	80	�	�	PROPN
iajs-2517	356	81	,	,	PUNCT
iajs-2517	356	82	∃{(𝒜𝑟,ℋ	∃{(𝒜𝑟,ℋ	PROPN
iajs-2517	356	83	)	)	PUNCT
iajs-2517	356	84	,	,	PUNCT
iajs-2517	356	85	(	(	PUNCT
iajs-2517	356	86	ℬ𝑟,ℋ	ℬ𝑟,ℋ	ADJ
iajs-2517	356	87	)	)	PUNCT
iajs-2517	356	88	}	}	PUNCT
iajs-2517	356	89	∈	∈	NOUN
iajs-2517	356	90	ℬ	ℬ	NOUN
iajs-2517	357	1	such	such	ADJ
iajs-2517	357	2	that	that	SCONJ
iajs-2517	357	3	(	(	PUNCT
iajs-2517	357	4	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	357	5	∈̃	∈̃	PROPN
iajs-2517	357	6	(	(	PUNCT
iajs-2517	357	7	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	357	8	)	)	PUNCT
iajs-2517	357	9	and	and	CCONJ
iajs-2517	357	10	(	(	PUNCT
iajs-2517	357	11	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	357	12	∈̃	∈̃	PROPN
iajs-2517	357	13	(	(	PUNCT
iajs-2517	357	14	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	357	15	)	)	PUNCT
iajs-2517	357	16	and	and	CCONJ
iajs-2517	357	17	(	(	PUNCT
iajs-2517	357	18	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	357	19	)	)	PUNCT
iajs-2517	357	20	∩̃	∩̃	PUNCT
iajs-2517	357	21	(	(	PUNCT
iajs-2517	357	22	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	357	23	)	)	PUNCT
iajs-2517	357	24	=	=	PRON
iajs-2517	357	25	{	{	PUNCT
iajs-2517	357	26	∅̃	∅̃	NOUN
iajs-2517	357	27	}	}	PUNCT
iajs-2517	357	28	.	.	PUNCT
iajs-2517	358	1	otherwise	otherwise	ADV
iajs-2517	358	2	,	,	PUNCT
iajs-2517	358	3	playerⅰ	playerⅰ	PROPN
iajs-2517	358	4	wins	win	VERB
iajs-2517	358	5	in	in	ADP
iajs-2517	358	6	the	the	DET
iajs-2517	358	7	game	game	NOUN
iajs-2517	358	8	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	358	9	,	,	PUNCT
iajs-2517	358	10	χ	χ	X
iajs-2517	358	11	)	)	PUNCT
iajs-2517	358	12	(	(	PUNCT
iajs-2517	358	13	respectively	respectively	ADV
iajs-2517	358	14	,	,	PUNCT
iajs-2517	358	15	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	358	16	,	,	PUNCT
iajs-2517	358	17	ℐ	ℐ	NOUN
iajs-2517	358	18	)	)	PUNCT
iajs-2517	358	19	)	)	PUNCT
iajs-2517	358	20	.	.	PUNCT
iajs-2517	359	1	by	by	ADP
iajs-2517	359	2	example	example	NOUN
iajs-2517	359	3	5.12	5.12	NUM
iajs-2517	359	4	.	.	PUNCT
iajs-2517	359	5	∀	∀	NOUN
iajs-2517	359	6	𝒽𝓜	𝒽𝓜	ADP
iajs-2517	359	7	≠	≠	PROPN
iajs-2517	359	8	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	359	9	where	where	SCONJ
iajs-2517	359	10	,	,	PUNCT
iajs-2517	359	11	𝒽𝓜	𝒽𝓜	PROPN
iajs-2517	359	12	,	,	PUNCT
iajs-2517	359	13	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	359	14	∈̃	∈̃	PROPN
iajs-2517	359	15	�	�	PROPN
iajs-2517	359	16	̃	̃	PROPN
iajs-2517	359	17	�	�	PROPN
iajs-2517	359	18	there	there	PRON
iajs-2517	359	19	exist	exist	VERB
iajs-2517	359	20	(	(	PUNCT
iajs-2517	359	21	ℳ	ℳ	PROPN
iajs-2517	359	22	,	,	PUNCT
iajs-2517	359	23	ℋ	ℋ	PROPN
iajs-2517	359	24	)	)	PUNCT
iajs-2517	359	25	,	,	PUNCT
iajs-2517	359	26	(	(	PUNCT
iajs-2517	359	27	𝒩	𝒩	PROPN
iajs-2517	359	28	,	,	PUNCT
iajs-2517	359	29	ℋ	ℋ	PROPN
iajs-2517	359	30	)	)	PUNCT
iajs-2517	359	31	are	be	AUX
iajs-2517	359	32	soft	soft	ADJ
iajs-2517	359	33	𝒽𝓜	𝒽𝓜	ADJ
iajs-2517	359	34	∈̃	∈̃	NOUN
iajs-2517	359	35	(	(	PUNCT
iajs-2517	359	36	ℳ	ℳ	PROPN
iajs-2517	359	37	,	,	PUNCT
iajs-2517	359	38	ℋ	ℋ	PROPN
iajs-2517	359	39	)	)	PUNCT
iajs-2517	359	40	and	and	CCONJ
iajs-2517	359	41	𝒽𝒩	𝒽𝒩	PROPN
iajs-2517	359	42	∈̃	∈̃	PROPN
iajs-2517	359	43	(	(	PUNCT
iajs-2517	359	44	𝒩	𝒩	PROPN
iajs-2517	359	45	,	,	PUNCT
iajs-2517	359	46	ℋ	ℋ	PROPN
iajs-2517	359	47	)	)	PUNCT
iajs-2517	359	48	such	such	ADJ
iajs-2517	359	49	that	that	SCONJ
iajs-2517	359	50	(	(	PUNCT
iajs-2517	359	51	ℳ	ℳ	PROPN
iajs-2517	359	52	,	,	PUNCT
iajs-2517	359	53	ℋ	ℋ	PROPN
iajs-2517	359	54	)	)	PUNCT
iajs-2517	359	55	∩̃	∩̃	PUNCT
iajs-2517	359	56	(	(	PUNCT
iajs-2517	359	57	𝒩	𝒩	PROPN
iajs-2517	359	58	,	,	PUNCT
iajs-2517	359	59	ℋ	ℋ	PROPN
iajs-2517	359	60	)	)	PUNCT
iajs-2517	359	61	=	=	SYM
iajs-2517	359	62	{	{	PUNCT
iajs-2517	359	63	∅̃	∅̃	NOUN
iajs-2517	359	64	}	}	PUNCT
iajs-2517	359	65	.	.	PUNCT
iajs-2517	360	1	so	so	ADV
iajs-2517	360	2	,	,	PUNCT
iajs-2517	360	3	then	then	ADV
iajs-2517	360	4	ℬ	ℬ	NOUN
iajs-2517	360	5	=	=	PRON
iajs-2517	360	6	{	{	PUNCT
iajs-2517	360	7	{	{	PUNCT
iajs-2517	360	8	(	(	PUNCT
iajs-2517	360	9	𝒜	𝒜	NOUN
iajs-2517	360	10	,	,	PUNCT
iajs-2517	360	11	ℋ	ℋ	PROPN
iajs-2517	360	12	)	)	PUNCT
iajs-2517	360	13	,	,	PUNCT
iajs-2517	360	14	(	(	PUNCT
iajs-2517	360	15	ℬ	ℬ	X
iajs-2517	360	16	,	,	PUNCT
iajs-2517	360	17	ℋ	ℋ	NOUN
iajs-2517	360	18	)	)	PUNCT
iajs-2517	360	19	}	}	PUNCT
iajs-2517	360	20	,	,	PUNCT
iajs-2517	360	21	{	{	PUNCT
iajs-2517	360	22	(	(	PUNCT
iajs-2517	360	23	ℬ	ℬ	X
iajs-2517	360	24	,	,	PUNCT
iajs-2517	360	25	ℋ	ℋ	PROPN
iajs-2517	360	26	)	)	PUNCT
iajs-2517	360	27	,	,	PUNCT
iajs-2517	360	28	(	(	PUNCT
iajs-2517	360	29	𝒞	𝒞	PROPN
iajs-2517	360	30	,	,	PUNCT
iajs-2517	360	31	ℋ	ℋ	PROPN
iajs-2517	360	32	)	)	PUNCT
iajs-2517	360	33	}	}	PUNCT
iajs-2517	360	34	,	,	PUNCT
iajs-2517	360	35	{	{	PUNCT
iajs-2517	360	36	(	(	PUNCT
iajs-2517	360	37	𝒜	𝒜	NOUN
iajs-2517	360	38	,	,	PUNCT
iajs-2517	360	39	ℋ	ℋ	PROPN
iajs-2517	360	40	)	)	PUNCT
iajs-2517	360	41	,	,	PUNCT
iajs-2517	360	42	(	(	PUNCT
iajs-2517	360	43	𝒞	𝒞	PROPN
iajs-2517	360	44	,	,	PUNCT
iajs-2517	360	45	ℋ	ℋ	PROPN
iajs-2517	360	46	)	)	PUNCT
iajs-2517	360	47	}	}	PUNCT
iajs-2517	360	48	,	,	PUNCT
iajs-2517	360	49	{	{	PUNCT
iajs-2517	360	50	(	(	PUNCT
iajs-2517	360	51	𝒜	𝒜	NOUN
iajs-2517	360	52	,	,	PUNCT
iajs-2517	360	53	ℋ	ℋ	PROPN
iajs-2517	360	54	)	)	PUNCT
iajs-2517	360	55	,	,	PUNCT
iajs-2517	360	56	(	(	PUNCT
iajs-2517	360	57	𝒟	𝒟	PROPN
iajs-2517	360	58	,	,	PUNCT
iajs-2517	360	59	ℋ	ℋ	PROPN
iajs-2517	360	60	)	)	PUNCT
iajs-2517	360	61	}	}	PUNCT
iajs-2517	360	62	,	,	PUNCT
iajs-2517	360	63	{	{	PUNCT
iajs-2517	360	64	(	(	PUNCT
iajs-2517	360	65	ℬ	ℬ	X
iajs-2517	360	66	,	,	PUNCT
iajs-2517	360	67	ℋ	ℋ	PROPN
iajs-2517	360	68	)	)	PUNCT
iajs-2517	360	69	,	,	PUNCT
iajs-2517	360	70	(	(	PUNCT
iajs-2517	360	71	ℰ	ℰ	PROPN
iajs-2517	360	72	,	,	PUNCT
iajs-2517	360	73	ℋ	ℋ	PROPN
iajs-2517	360	74	)	)	PUNCT
iajs-2517	360	75	}	}	PUNCT
iajs-2517	360	76	,	,	PUNCT
iajs-2517	360	77	{	{	PUNCT
iajs-2517	360	78	(	(	PUNCT
iajs-2517	360	79	𝒞	𝒞	PROPN
iajs-2517	360	80	,	,	PUNCT
iajs-2517	360	81	ℋ	ℋ	PROPN
iajs-2517	360	82	)	)	PUNCT
iajs-2517	360	83	,	,	PUNCT
iajs-2517	360	84	(	(	PUNCT
iajs-2517	360	85	ℱ	ℱ	PROPN
iajs-2517	360	86	,	,	PUNCT
iajs-2517	360	87	ℋ	ℋ	PROPN
iajs-2517	360	88	)	)	PUNCT
iajs-2517	360	89	}	}	PUNCT
iajs-2517	360	90	}	}	PUNCT
iajs-2517	360	91	.	.	PUNCT
iajs-2517	361	1	is	be	AUX
iajs-2517	361	2	the	the	DET
iajs-2517	361	3	winning	win	VERB
iajs-2517	361	4	strategy	strategy	NOUN
iajs-2517	361	5	for	for	ADP
iajs-2517	361	6	player	player	NOUN
iajs-2517	361	7	ⅱ	ⅱ	NOUN
iajs-2517	361	8	in	in	ADP
iajs-2517	361	9	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	361	10	,	,	PUNCT
iajs-2517	361	11	χ	χ	X
iajs-2517	361	12	)	)	PUNCT
iajs-2517	361	13	(	(	PUNCT
iajs-2517	361	14	respectively	respectively	ADV
iajs-2517	361	15	,	,	PUNCT
iajs-2517	361	16	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	361	17	,	,	PUNCT
iajs-2517	361	18	ℐ	ℐ	NOUN
iajs-2517	361	19	)	)	PUNCT
iajs-2517	361	20	)	)	PUNCT
iajs-2517	361	21	.	.	PUNCT
iajs-2517	362	1	hence	hence	ADV
iajs-2517	362	2	player	player	NOUN
iajs-2517	362	3	ⅱ	ⅱ	PROPN
iajs-2517	362	4	↑	↑	PROPN
iajs-2517	362	5	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	362	6	,	,	PUNCT
iajs-2517	362	7	χ	χ	X
iajs-2517	362	8	)	)	PUNCT
iajs-2517	362	9	(	(	PUNCT
iajs-2517	362	10	respectively	respectively	ADV
iajs-2517	362	11	,	,	PUNCT
iajs-2517	362	12	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	362	13	,	,	PUNCT
iajs-2517	362	14	ℐ	ℐ	NOUN
iajs-2517	362	15	)	)	PUNCT
iajs-2517	362	16	)	)	PUNCT
iajs-2517	362	17	.	.	PUNCT
iajs-2517	363	1	by	by	ADP
iajs-2517	363	2	the	the	DET
iajs-2517	363	3	same	same	ADJ
iajs-2517	363	4	way	way	NOUN
iajs-2517	363	5	in	in	ADP
iajs-2517	363	6	example	example	NOUN
iajs-2517	363	7	5.3	5.3	NUM
iajs-2517	363	8	,	,	PUNCT
iajs-2517	363	9	player	player	NOUN
iajs-2517	363	10	ⅰ	ⅰ	X
iajs-2517	363	11	↑	↑	PROPN
iajs-2517	363	12	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	363	13	,	,	PUNCT
iajs-2517	363	14	χ	χ	NOUN
iajs-2517	363	15	)	)	PUNCT
iajs-2517	363	16	and	and	CCONJ
iajs-2517	363	17	player	player	NOUN
iajs-2517	363	18	ⅰ	ⅰ	PROPN
iajs-2517	363	19	↑	↑	PROPN
iajs-2517	363	20	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	363	21	,	,	PUNCT
iajs-2517	363	22	ℐ	ℐ	NOUN
iajs-2517	363	23	)	)	PUNCT
iajs-2517	363	24	.	.	PUNCT
iajs-2517	364	1	remark	remark	PROPN
iajs-2517	364	2	5.21	5.21	NUM
iajs-2517	364	3	.	.	PUNCT
iajs-2517	365	1	for	for	ADP
iajs-2517	365	2	a	a	DET
iajs-2517	365	3	space	space	NOUN
iajs-2517	365	4	(	(	PUNCT
iajs-2517	365	5	χ	χ	X
iajs-2517	365	6	,	,	PUNCT
iajs-2517	365	7	𝒯	𝒯	PROPN
iajs-2517	365	8	,	,	PUNCT
iajs-2517	365	9	ℋ	ℋ	PROPN
iajs-2517	365	10	,	,	PUNCT
iajs-2517	365	11	ℐ	ℐ	PROPN
iajs-2517	365	12	):	):	PUNCT
iajs-2517	365	13	iif	iif	PROPN
iajs-2517	365	14	player	player	NOUN
iajs-2517	365	15	ⅱ	ⅱ	PROPN
iajs-2517	365	16	↑	↑	PROPN
iajs-2517	365	17	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	365	18	,	,	PUNCT
iajs-2517	365	19	χ	χ	X
iajs-2517	365	20	)	)	PUNCT
iajs-2517	365	21	then	then	ADV
iajs-2517	365	22	player	player	NOUN
iajs-2517	365	23	ⅱ	ⅱ	PROPN
iajs-2517	365	24	↑	↑	PROPN
iajs-2517	365	25	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	365	26	,	,	PUNCT
iajs-2517	365	27	ℐ	ℐ	NOUN
iajs-2517	365	28	)	)	PUNCT
iajs-2517	365	29	.	.	PUNCT
iajs-2517	366	1	iiif	iiif	PROPN
iajs-2517	366	2	player	player	PROPN
iajs-2517	366	3	ⅰ	ⅰ	PROPN
iajs-2517	366	4	↑	↑	PROPN
iajs-2517	366	5	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	366	6	,	,	PUNCT
iajs-2517	366	7	ℐ	ℐ	NUM
iajs-2517	366	8	)	)	PUNCT
iajs-2517	366	9	then	then	ADV
iajs-2517	366	10	player	player	NOUN
iajs-2517	366	11	ⅰ	ⅰ	PROPN
iajs-2517	366	12	↑	↑	PROPN
iajs-2517	366	13	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	366	14	,	,	PUNCT
iajs-2517	366	15	χ	χ	NOUN
iajs-2517	366	16	)	)	PUNCT
iajs-2517	366	17	.	.	PUNCT
iajs-2517	367	1	remark	remark	PROPN
iajs-2517	367	2	5.22	5.22	NUM
iajs-2517	367	3	.	.	PUNCT
iajs-2517	368	1	for	for	ADP
iajs-2517	368	2	a	a	DET
iajs-2517	368	3	space	space	NOUN
iajs-2517	368	4	(	(	PUNCT
iajs-2517	368	5	(	(	PUNCT
iajs-2517	368	6	χ	χ	X
iajs-2517	368	7	,	,	PUNCT
iajs-2517	368	8	𝒯	𝒯	PROPN
iajs-2517	368	9	,	,	PUNCT
iajs-2517	368	10	ℋ	ℋ	PROPN
iajs-2517	368	11	,	,	PUNCT
iajs-2517	368	12	ℐ	ℐ	PROPN
iajs-2517	368	13	)	)	PUNCT
iajs-2517	368	14	,	,	PUNCT
iajs-2517	368	15	if	if	SCONJ
iajs-2517	368	16	playerⅱ	playerⅱ	ADV
iajs-2517	368	17	↓	↓	PROPN
iajs-2517	368	18	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	368	19	,	,	PUNCT
iajs-2517	368	20	χ	χ	X
iajs-2517	368	21	)	)	PUNCT
iajs-2517	368	22	then	then	ADV
iajs-2517	368	23	player	player	NOUN
iajs-2517	368	24	ⅱ	ⅱ	PROPN
iajs-2517	368	25	↓	↓	PROPN
iajs-2517	368	26	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	368	27	,	,	PUNCT
iajs-2517	368	28	ℐ	ℐ	NOUN
iajs-2517	368	29	)	)	PUNCT
iajs-2517	368	30	.	.	PUNCT
iajs-2517	369	1	theorem	theorem	VERB
iajs-2517	369	2	5.23	5.23	NUM
iajs-2517	369	3	.	.	PUNCT
iajs-2517	370	1	a	a	DET
iajs-2517	370	2	space	space	NOUN
iajs-2517	370	3	(	(	PUNCT
iajs-2517	370	4	χ	χ	X
iajs-2517	370	5	,	,	PUNCT
iajs-2517	370	6	𝒯	𝒯	PROPN
iajs-2517	370	7	,	,	PUNCT
iajs-2517	370	8	ℋ	ℋ	PROPN
iajs-2517	370	9	)	)	PUNCT
iajs-2517	370	10	(	(	PUNCT
iajs-2517	370	11	respectively	respectively	ADV
iajs-2517	370	12	,	,	PUNCT
iajs-2517	370	13	(	(	PUNCT
iajs-2517	370	14	χ	χ	X
iajs-2517	370	15	,	,	PUNCT
iajs-2517	370	16	𝒯	𝒯	PROPN
iajs-2517	370	17	,	,	PUNCT
iajs-2517	370	18	ℋ	ℋ	PROPN
iajs-2517	370	19	,	,	PUNCT
iajs-2517	370	20	ℐ	ℐ	NOUN
iajs-2517	370	21	)	)	PUNCT
iajs-2517	370	22	)	)	PUNCT
iajs-2517	370	23	is	be	AUX
iajs-2517	370	24	a	a	DET
iajs-2517	370	25	soft-𝒯2-𝑠𝑝𝑎𝑐𝑒	soft-𝒯2-𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	370	26	(	(	PUNCT
iajs-2517	370	27	respectively	respectively	ADV
iajs-2517	370	28	,	,	PUNCT
iajs-2517	370	29	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒	𝑠ℐ𝑠𝑔-𝒯2-𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	370	30	)	)	PUNCT
iajs-2517	370	31	if	if	SCONJ
iajs-2517	371	1	and	and	CCONJ
iajs-2517	371	2	only	only	ADV
iajs-2517	371	3	if	if	SCONJ
iajs-2517	371	4	player	player	NOUN
iajs-2517	371	5	ⅱ	ⅱ	PROPN
iajs-2517	371	6	↑	↑	PROPN
iajs-2517	371	7	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	371	8	,	,	PUNCT
iajs-2517	371	9	χ	χ	X
iajs-2517	371	10	)	)	PUNCT
iajs-2517	371	11	(	(	PUNCT
iajs-2517	371	12	respectively	respectively	ADV
iajs-2517	371	13	,	,	PUNCT
iajs-2517	371	14	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	371	15	,	,	PUNCT
iajs-2517	371	16	ℐ	ℐ	NOUN
iajs-2517	371	17	)	)	PUNCT
iajs-2517	371	18	)	)	PUNCT
iajs-2517	371	19	.	.	PUNCT
iajs-2517	372	1	proof	proof	NOUN
iajs-2517	372	2	:	:	PUNCT
iajs-2517	372	3	(	(	PUNCT
iajs-2517	372	4	⟹	⟹	X
iajs-2517	372	5	)	)	PUNCT
iajs-2517	372	6	in	in	ADP
iajs-2517	372	7	the	the	DET
iajs-2517	372	8	𝑟-th	𝑟-th	NOUN
iajs-2517	372	9	inning	inning	NOUN
iajs-2517	372	10	player	player	NOUN
iajs-2517	372	11	ⅰ	ⅰ	NUM
iajs-2517	372	12	in	in	ADP
iajs-2517	372	13	ş𝒢(𝒯2	ş𝒢(𝒯2	ADP
iajs-2517	372	14	,	,	PUNCT
iajs-2517	372	15	χ	χ	X
iajs-2517	372	16	)	)	PUNCT
iajs-2517	372	17	(	(	PUNCT
iajs-2517	372	18	respectively	respectively	ADV
iajs-2517	372	19	,	,	PUNCT
iajs-2517	372	20	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	372	21	,	,	PUNCT
iajs-2517	372	22	ℐ	ℐ	NOUN
iajs-2517	372	23	)	)	PUNCT
iajs-2517	372	24	)	)	PUNCT
iajs-2517	373	1	choose	choose	VERB
iajs-2517	373	2	(	(	PUNCT
iajs-2517	373	3	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	373	4	≠	≠	PROPN
iajs-2517	373	5	(	(	PUNCT
iajs-2517	373	6	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	373	7	where	where	SCONJ
iajs-2517	373	8	,	,	PUNCT
iajs-2517	373	9	(	(	PUNCT
iajs-2517	373	10	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	373	11	,	,	PUNCT
iajs-2517	373	12	(	(	PUNCT
iajs-2517	373	13	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	373	14	∈̃	∈̃	PROPN
iajs-2517	373	15	�	�	PROPN
iajs-2517	373	16	̃	̃	PROPN
iajs-2517	373	17	�	�	PROPN
iajs-2517	373	18	,	,	PUNCT
iajs-2517	373	19	player	player	NOUN
iajs-2517	373	20	ⅱ	ⅱ	PROPN
iajs-2517	373	21	in	in	ADP
iajs-2517	373	22	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	373	23	,	,	PUNCT
iajs-2517	373	24	χ	χ	X
iajs-2517	373	25	)	)	PUNCT
iajs-2517	373	26	(	(	PUNCT
iajs-2517	373	27	respectively	respectively	ADV
iajs-2517	373	28	,	,	PUNCT
iajs-2517	373	29	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	373	30	,	,	PUNCT
iajs-2517	373	31	ℐ	ℐ	NOUN
iajs-2517	373	32	)	)	PUNCT
iajs-2517	373	33	)	)	PUNCT
iajs-2517	374	1	choose	choose	VERB
iajs-2517	374	2	(	(	PUNCT
iajs-2517	374	3	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	374	4	)	)	PUNCT
iajs-2517	374	5	,	,	PUNCT
iajs-2517	374	6	(	(	PUNCT
iajs-2517	374	7	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	374	8	)	)	PUNCT
iajs-2517	374	9	are	be	AUX
iajs-2517	374	10	two	two	NUM
iajs-2517	374	11	soft	soft	ADJ
iajs-2517	374	12	open	open	ADJ
iajs-2517	374	13	(	(	PUNCT
iajs-2517	374	14	respectively	respectively	ADV
iajs-2517	374	15	,	,	PUNCT
iajs-2517	374	16	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	374	17	)	)	PUNCT
iajs-2517	374	18	sets	set	VERB
iajs-2517	374	19	such	such	ADJ
iajs-2517	374	20	that	that	SCONJ
iajs-2517	374	21	(	(	PUNCT
iajs-2517	374	22	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	374	23	∈̃	∈̃	PROPN
iajs-2517	374	24	(	(	PUNCT
iajs-2517	374	25	(	(	PUNCT
iajs-2517	374	26	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	374	27	)	)	PUNCT
iajs-2517	374	28	and	and	CCONJ
iajs-2517	374	29	(	(	PUNCT
iajs-2517	374	30	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	374	31	∈̃	∈̃	PROPN
iajs-2517	374	32	(	(	PUNCT
iajs-2517	374	33	(	(	PUNCT
iajs-2517	374	34	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	374	35	)	)	PUNCT
iajs-2517	374	36	and	and	CCONJ
iajs-2517	374	37	(	(	PUNCT
iajs-2517	374	38	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	374	39	)	)	PUNCT
iajs-2517	374	40	∩̃	∩̃	PUNCT
iajs-2517	374	41	(	(	PUNCT
iajs-2517	374	42	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	374	43	)	)	PUNCT
iajs-2517	374	44	=	=	PRON
iajs-2517	374	45	{	{	PUNCT
iajs-2517	374	46	∅̃	∅̃	NOUN
iajs-2517	374	47	}	}	PUNCT
iajs-2517	374	48	.	.	PUNCT
iajs-2517	375	1	since	since	SCONJ
iajs-2517	375	2	(	(	PUNCT
iajs-2517	375	3	χ	χ	X
iajs-2517	375	4	,	,	PUNCT
iajs-2517	375	5	𝒯	𝒯	PROPN
iajs-2517	375	6	,	,	PUNCT
iajs-2517	375	7	ℋ	ℋ	PROPN
iajs-2517	375	8	)	)	PUNCT
iajs-2517	375	9	a	a	DET
iajs-2517	375	10	soft-𝒯2	soft-𝒯2	NOUN
iajs-2517	375	11	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	375	12	(	(	PUNCT
iajs-2517	375	13	respectively	respectively	ADV
iajs-2517	375	14	,	,	PUNCT
iajs-2517	375	15	sℐsg-𝒯1­space).then	sℐsg-𝒯1­space).then	ADV
iajs-2517	375	16	ℬ	ℬ	NOUN
iajs-2517	375	17	=	=	PRON
iajs-2517	375	18	{	{	PUNCT
iajs-2517	375	19	{	{	PUNCT
iajs-2517	375	20	(	(	PUNCT
iajs-2517	375	21	𝒜1,ℋ	𝒜1,ℋ	PROPN
iajs-2517	375	22	)	)	PUNCT
iajs-2517	375	23	,	,	PUNCT
iajs-2517	375	24	(	(	PUNCT
iajs-2517	375	25	ℬ1,ℋ	ℬ1,ℋ	NOUN
iajs-2517	375	26	)	)	PUNCT
iajs-2517	375	27	}	}	PUNCT
iajs-2517	375	28	,	,	PUNCT
iajs-2517	375	29	{	{	PUNCT
iajs-2517	375	30	(	(	PUNCT
iajs-2517	375	31	𝒜2,ℋ	𝒜2,ℋ	NOUN
iajs-2517	375	32	)	)	PUNCT
iajs-2517	375	33	,	,	PUNCT
iajs-2517	375	34	(	(	PUNCT
iajs-2517	375	35	ℬ2,ℋ	ℬ2,ℋ	NOUN
iajs-2517	375	36	)	)	PUNCT
iajs-2517	375	37	}	}	PUNCT
iajs-2517	375	38	,	,	PUNCT
iajs-2517	375	39	…	…	PUNCT
iajs-2517	375	40	,	,	PUNCT
iajs-2517	375	41	{	{	PUNCT
iajs-2517	375	42	(	(	PUNCT
iajs-2517	375	43	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	375	44	)	)	PUNCT
iajs-2517	375	45	,	,	PUNCT
iajs-2517	375	46	(	(	PUNCT
iajs-2517	375	47	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	375	48	)	)	PUNCT
iajs-2517	375	49	}	}	PUNCT
iajs-2517	375	50	,	,	PUNCT
iajs-2517	375	51	…	…	PUNCT
iajs-2517	375	52	}	}	PUNCT
iajs-2517	375	53	is	be	AUX
iajs-2517	375	54	the	the	DET
iajs-2517	375	55	winning	win	VERB
iajs-2517	375	56	strategy	strategy	NOUN
iajs-2517	375	57	for	for	ADP
iajs-2517	375	58	player	player	NOUN
iajs-2517	375	59	ⅱ	ⅱ	NOUN
iajs-2517	375	60	in	in	ADP
iajs-2517	375	61	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	375	62	,	,	PUNCT
iajs-2517	375	63	χ	χ	X
iajs-2517	375	64	)	)	PUNCT
iajs-2517	375	65	(	(	PUNCT
iajs-2517	375	66	respectively	respectively	ADV
iajs-2517	375	67	,	,	PUNCT
iajs-2517	375	68	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	375	69	,	,	PUNCT
iajs-2517	375	70	ℐ	ℐ	NOUN
iajs-2517	375	71	)	)	PUNCT
iajs-2517	375	72	)	)	PUNCT
iajs-2517	375	73	.	.	PUNCT
iajs-2517	376	1	hence	hence	ADV
iajs-2517	376	2	player	player	NOUN
iajs-2517	376	3	ⅱ	ⅱ	PROPN
iajs-2517	376	4	↑	↑	PROPN
iajs-2517	376	5	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	376	6	,	,	PUNCT
iajs-2517	376	7	χ	χ	X
iajs-2517	376	8	)	)	PUNCT
iajs-2517	376	9	(	(	PUNCT
iajs-2517	376	10	respectively	respectively	ADV
iajs-2517	376	11	,	,	PUNCT
iajs-2517	376	12	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	376	13	,	,	PUNCT
iajs-2517	376	14	ℐ	ℐ	NOUN
iajs-2517	376	15	)	)	PUNCT
iajs-2517	376	16	)	)	PUNCT
iajs-2517	376	17	.	.	PUNCT
iajs-2517	377	1	(	(	PUNCT
iajs-2517	377	2	⟸	⟸	ADJ
iajs-2517	377	3	)	)	PUNCT
iajs-2517	377	4	clear	clear	ADJ
iajs-2517	377	5	.	.	PUNCT
iajs-2517	378	1	corollary	corollary	ADJ
iajs-2517	378	2	5.24	5.24	NUM
iajs-2517	378	3	.	.	PUNCT
iajs-2517	379	1	ia	ia	PROPN
iajs-2517	379	2	space	space	NOUN
iajs-2517	379	3	(	(	PUNCT
iajs-2517	379	4	χ	χ	X
iajs-2517	379	5	,	,	PUNCT
iajs-2517	379	6	𝒯	𝒯	PROPN
iajs-2517	379	7	,	,	PUNCT
iajs-2517	379	8	ℋ	ℋ	PROPN
iajs-2517	379	9	)	)	PUNCT
iajs-2517	379	10	is	be	AUX
iajs-2517	379	11	a	a	DET
iajs-2517	379	12	soft-𝒯2	soft-𝒯2	NOUN
iajs-2517	379	13	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	379	14	if	if	SCONJ
iajs-2517	380	1	and	and	CCONJ
iajs-2517	380	2	only	only	ADV
iajs-2517	380	3	if	if	SCONJ
iajs-2517	380	4	player	player	NOUN
iajs-2517	380	5	ⅰ	ⅰ	X
iajs-2517	380	6	⤉	⤉	VERB
iajs-2517	380	7	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	380	8	,	,	PUNCT
iajs-2517	380	9	χ	χ	NOUN
iajs-2517	380	10	)	)	PUNCT
iajs-2517	380	11	.	.	PUNCT
iajs-2517	381	1	134	134	NUM
iajs-2517	381	2	ibn	ibn	PROPN
iajs-2517	381	3	al	al	PROPN
iajs-2517	381	4	-	-	PUNCT
iajs-2517	381	5	haitham	haitham	PROPN
iajs-2517	381	6	jour	jour	X
iajs-2517	381	7	.	.	PROPN
iajs-2517	381	8	for	for	ADP
iajs-2517	381	9	pure	pure	ADJ
iajs-2517	381	10	&	&	CCONJ
iajs-2517	381	11	appl	appl	PROPN
iajs-2517	381	12	.	.	PUNCT
iajs-2517	382	1	sci	sci	PROPN
iajs-2517	382	2	.	.	PROPN
iajs-2517	383	1	33	33	NUM
iajs-2517	383	2	(	(	PUNCT
iajs-2517	383	3	4	4	NUM
iajs-2517	383	4	)	)	PUNCT
iajs-2517	383	5	2020	2020	NUM
iajs-2517	383	6	iia	iia	NOUN
iajs-2517	383	7	space	space	NOUN
iajs-2517	383	8	(	(	PUNCT
iajs-2517	383	9	χ	χ	X
iajs-2517	383	10	,	,	PUNCT
iajs-2517	383	11	𝒯	𝒯	PROPN
iajs-2517	383	12	,	,	PUNCT
iajs-2517	383	13	ℋ	ℋ	PROPN
iajs-2517	383	14	,	,	PUNCT
iajs-2517	383	15	ℐ	ℐ	NUM
iajs-2517	383	16	)	)	PUNCT
iajs-2517	383	17	is	be	AUX
iajs-2517	383	18	a	a	DET
iajs-2517	383	19	sℐsg-𝒯2­space	sℐsg-𝒯2­space	PROPN
iajs-2517	383	20	if	if	SCONJ
iajs-2517	384	1	and	and	CCONJ
iajs-2517	384	2	only	only	ADV
iajs-2517	384	3	if	if	SCONJ
iajs-2517	384	4	player	player	NOUN
iajs-2517	384	5	ⅰ	ⅰ	X
iajs-2517	384	6	⤉	⤉	VERB
iajs-2517	384	7	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	384	8	,	,	PUNCT
iajs-2517	384	9	ℐ	ℐ	NOUN
iajs-2517	384	10	)	)	PUNCT
iajs-2517	384	11	.	.	PUNCT
iajs-2517	385	1	proof	proof	NOUN
iajs-2517	385	2	:	:	PUNCT
iajs-2517	385	3	by	by	SCONJ
iajs-2517	385	4	theorem	theorem	NOUN
iajs-2517	385	5	4.23	4.23	NUM
iajs-2517	385	6	,	,	PUNCT
iajs-2517	385	7	the	the	DET
iajs-2517	385	8	proof	proof	NOUN
iajs-2517	385	9	is	be	AUX
iajs-2517	385	10	over	over	ADV
iajs-2517	385	11	.	.	PUNCT
iajs-2517	386	1	theorem	theorem	ADJ
iajs-2517	386	2	5	5	NUM
iajs-2517	386	3	.	.	NUM
iajs-2517	386	4	25	25	NUM
iajs-2517	386	5	.	.	PUNCT
iajs-2517	387	1	for	for	ADP
iajs-2517	387	2	a	a	DET
iajs-2517	387	3	space	space	NOUN
iajs-2517	387	4	(	(	PUNCT
iajs-2517	387	5	χ	χ	X
iajs-2517	387	6	,	,	PUNCT
iajs-2517	387	7	𝒯	𝒯	PROPN
iajs-2517	387	8	,	,	PUNCT
iajs-2517	387	9	ℋ	ℋ	PROPN
iajs-2517	387	10	,	,	PUNCT
iajs-2517	387	11	ℐ	ℐ	PROPN
iajs-2517	387	12	):	):	PUNCT
iajs-2517	387	13	ia	ia	PROPN
iajs-2517	387	14	space	space	NOUN
iajs-2517	387	15	(	(	PUNCT
iajs-2517	387	16	χ	χ	X
iajs-2517	387	17	,	,	PUNCT
iajs-2517	387	18	𝒯	𝒯	PROPN
iajs-2517	387	19	,	,	PUNCT
iajs-2517	387	20	ℋ	ℋ	PROPN
iajs-2517	387	21	)	)	PUNCT
iajs-2517	387	22	is	be	AUX
iajs-2517	387	23	not	not	PART
iajs-2517	387	24	soft-𝒯2­space	soft-𝒯2­space	ADJ
iajs-2517	387	25	if	if	SCONJ
iajs-2517	388	1	and	and	CCONJ
iajs-2517	388	2	only	only	ADV
iajs-2517	388	3	if	if	SCONJ
iajs-2517	388	4	player	player	NOUN
iajs-2517	388	5	ⅰ	ⅰ	X
iajs-2517	388	6	↑	↑	PROPN
iajs-2517	388	7	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	388	8	,	,	PUNCT
iajs-2517	388	9	χ	χ	NOUN
iajs-2517	388	10	)	)	PUNCT
iajs-2517	388	11	.	.	PUNCT
iajs-2517	389	1	iia	iia	NOUN
iajs-2517	389	2	space	space	NOUN
iajs-2517	389	3	(	(	PUNCT
iajs-2517	389	4	χ	χ	X
iajs-2517	389	5	,	,	PUNCT
iajs-2517	389	6	𝒯	𝒯	PROPN
iajs-2517	389	7	,	,	PUNCT
iajs-2517	389	8	ℋ	ℋ	PROPN
iajs-2517	389	9	,	,	PUNCT
iajs-2517	389	10	ℐ	ℐ	NUM
iajs-2517	389	11	)	)	PUNCT
iajs-2517	389	12	is	be	AUX
iajs-2517	389	13	not	not	PART
iajs-2517	389	14	a	a	DET
iajs-2517	389	15	sℐsg-𝒯2­space	sℐsg-𝒯2­space	PROPN
iajs-2517	389	16	if	if	SCONJ
iajs-2517	390	1	and	and	CCONJ
iajs-2517	390	2	only	only	ADV
iajs-2517	390	3	if	if	SCONJ
iajs-2517	390	4	player	player	NOUN
iajs-2517	390	5	ⅰ	ⅰ	X
iajs-2517	390	6	↑	↑	PROPN
iajs-2517	390	7	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	390	8	,	,	PUNCT
iajs-2517	390	9	ℐ	ℐ	NOUN
iajs-2517	390	10	)	)	PUNCT
iajs-2517	390	11	.	.	PUNCT
iajs-2517	391	1	proof	proof	NOUN
iajs-2517	391	2	:	:	PUNCT
iajs-2517	391	3	i(⟹	i(⟹	NOUN
iajs-2517	391	4	)	)	PUNCT
iajs-2517	391	5	in	in	ADP
iajs-2517	391	6	the	the	DET
iajs-2517	391	7	𝑟-th	𝑟-th	NOUN
iajs-2517	391	8	inning	inning	NOUN
iajs-2517	391	9	player	player	NOUN
iajs-2517	391	10	ⅰ	ⅰ	NUM
iajs-2517	391	11	in	in	ADP
iajs-2517	391	12	ş𝒢(𝒯2	ş𝒢(𝒯2	ADP
iajs-2517	391	13	,	,	PUNCT
iajs-2517	391	14	χ	χ	X
iajs-2517	391	15	)	)	PUNCT
iajs-2517	391	16	choose	choose	VERB
iajs-2517	391	17	(	(	PUNCT
iajs-2517	391	18	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADP
iajs-2517	391	19	≠	≠	PROPN
iajs-2517	391	20	(	(	PUNCT
iajs-2517	391	21	𝒽𝒩)𝑟	𝒽𝒩)𝑟	VERB
iajs-2517	391	22	where	where	SCONJ
iajs-2517	391	23	,	,	PUNCT
iajs-2517	391	24	(	(	PUNCT
iajs-2517	391	25	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	391	26	,	,	PUNCT
iajs-2517	391	27	(	(	PUNCT
iajs-2517	391	28	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	391	29	∈̃	∈̃	PROPN
iajs-2517	391	30	�	�	PROPN
iajs-2517	391	31	̃	̃	PROPN
iajs-2517	391	32	�	�	PROPN
iajs-2517	391	33	,	,	PUNCT
iajs-2517	391	34	player	player	NOUN
iajs-2517	391	35	ⅱ	ⅱ	PROPN
iajs-2517	391	36	in	in	ADP
iajs-2517	391	37	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	391	38	,	,	PUNCT
iajs-2517	391	39	χ	χ	X
iajs-2517	391	40	)	)	PUNCT
iajs-2517	391	41	can	can	AUX
iajs-2517	391	42	not	not	PART
iajs-2517	391	43	find	find	VERB
iajs-2517	391	44	(	(	PUNCT
iajs-2517	391	45	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	391	46	)	)	PUNCT
iajs-2517	391	47	,	,	PUNCT
iajs-2517	391	48	(	(	PUNCT
iajs-2517	391	49	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	391	50	)	)	PUNCT
iajs-2517	391	51	are	be	AUX
iajs-2517	391	52	two	two	NUM
iajs-2517	391	53	soft-𝑜𝑝𝑒𝑛	soft-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	391	54	sets	set	VERB
iajs-2517	391	55	such	such	ADJ
iajs-2517	391	56	that	that	SCONJ
iajs-2517	391	57	(	(	PUNCT
iajs-2517	391	58	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	391	59	∈̃	∈̃	PROPN
iajs-2517	391	60	(	(	PUNCT
iajs-2517	391	61	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	391	62	)	)	PUNCT
iajs-2517	391	63	,	,	PUNCT
iajs-2517	391	64	(	(	PUNCT
iajs-2517	392	1	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	392	2	∈̃	∈̃	PROPN
iajs-2517	392	3	(	(	PUNCT
iajs-2517	392	4	(	(	PUNCT
iajs-2517	392	5	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	392	6	)	)	PUNCT
iajs-2517	392	7	and	and	CCONJ
iajs-2517	392	8	(	(	PUNCT
iajs-2517	392	9	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	392	10	)	)	PUNCT
iajs-2517	392	11	∩̃	∩̃	PUNCT
iajs-2517	392	12	(	(	PUNCT
iajs-2517	392	13	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	392	14	)	)	PUNCT
iajs-2517	392	15	=	=	SYM
iajs-2517	392	16	{	{	PUNCT
iajs-2517	392	17	∅̃	∅̃	NOUN
iajs-2517	392	18	}	}	PUNCT
iajs-2517	392	19	,	,	PUNCT
iajs-2517	392	20	because	because	SCONJ
iajs-2517	392	21	(	(	PUNCT
iajs-2517	392	22	χ	χ	X
iajs-2517	392	23	,	,	PUNCT
iajs-2517	392	24	𝒯	𝒯	PROPN
iajs-2517	392	25	,	,	PUNCT
iajs-2517	392	26	ℋ	ℋ	PROPN
iajs-2517	392	27	)	)	PUNCT
iajs-2517	392	28	is	be	AUX
iajs-2517	392	29	not	not	PART
iajs-2517	392	30	soft-𝒯2­space	soft-𝒯2­space	PROPN
iajs-2517	392	31	.	.	PUNCT
iajs-2517	393	1	hence	hence	ADV
iajs-2517	393	2	playerⅰ	playerⅰ	PROPN
iajs-2517	393	3	↑	↑	PROPN
iajs-2517	393	4	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	393	5	,	,	PUNCT
iajs-2517	393	6	χ	χ	NOUN
iajs-2517	393	7	)	)	PUNCT
iajs-2517	393	8	.	.	PUNCT
iajs-2517	394	1	(	(	PUNCT
iajs-2517	394	2	⟸	⟸	ADJ
iajs-2517	394	3	)	)	PUNCT
iajs-2517	394	4	clear	clear	ADJ
iajs-2517	394	5	.	.	PUNCT
iajs-2517	395	1	ii(⟹	ii(⟹	VERB
iajs-2517	395	2	)	)	PUNCT
iajs-2517	396	1	in	in	ADP
iajs-2517	396	2	the	the	DET
iajs-2517	396	3	𝑟-th	𝑟-th	NOUN
iajs-2517	396	4	inning	inne	VERB
iajs-2517	396	5	playerⅰ	playerⅰ	NOUN
iajs-2517	396	6	in	in	ADP
iajs-2517	396	7	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	396	8	,	,	PUNCT
iajs-2517	396	9	ℐ	ℐ	PRON
iajs-2517	396	10	)	)	PUNCT
iajs-2517	396	11	choose	choose	VERB
iajs-2517	396	12	(	(	PUNCT
iajs-2517	396	13	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	396	14	≠	≠	PROPN
iajs-2517	396	15	(	(	PUNCT
iajs-2517	396	16	𝒽𝒩)𝑟where	𝒽𝒩)𝑟where	ADV
iajs-2517	396	17	,	,	PUNCT
iajs-2517	396	18	(	(	PUNCT
iajs-2517	396	19	𝒽ℳ)𝑟	𝒽ℳ)𝑟	ADV
iajs-2517	396	20	,	,	PUNCT
iajs-2517	396	21	(	(	PUNCT
iajs-2517	396	22	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	396	23	∈̃	∈̃	PROPN
iajs-2517	396	24	𝜒	𝜒	NUM
iajs-2517	396	25	,	,	PUNCT
iajs-2517	396	26	player	player	NOUN
iajs-2517	396	27	ⅱ	ⅱ	NOUN
iajs-2517	396	28	in	in	ADP
iajs-2517	396	29	ş𝒢(𝒯2	ş𝒢(𝒯2	ADP
iajs-2517	396	30	,	,	PUNCT
iajs-2517	396	31	ℐ	ℐ	NUM
iajs-2517	396	32	)	)	PUNCT
iajs-2517	396	33	can	can	AUX
iajs-2517	396	34	not	not	PART
iajs-2517	396	35	find	find	VERB
iajs-2517	396	36	(	(	PUNCT
iajs-2517	396	37	𝒜𝑟,ℋ	𝒜𝑟,ℋ	NOUN
iajs-2517	396	38	)	)	PUNCT
iajs-2517	396	39	,	,	PUNCT
iajs-2517	396	40	(	(	PUNCT
iajs-2517	396	41	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	396	42	)	)	PUNCT
iajs-2517	396	43	are	be	AUX
iajs-2517	396	44	two	two	NUM
iajs-2517	396	45	sℐsg-𝑜𝑝𝑒𝑛	sℐsg-𝑜𝑝𝑒𝑛	NOUN
iajs-2517	396	46	sets	set	VERB
iajs-2517	396	47	such	such	ADJ
iajs-2517	396	48	that	that	SCONJ
iajs-2517	396	49	(	(	PUNCT
iajs-2517	396	50	𝒽ℳ)𝑟	𝒽ℳ)𝑟	PROPN
iajs-2517	396	51	∈̃	∈̃	PROPN
iajs-2517	396	52	(	(	PUNCT
iajs-2517	396	53	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	396	54	)	)	PUNCT
iajs-2517	396	55	,	,	PUNCT
iajs-2517	396	56	(	(	PUNCT
iajs-2517	396	57	𝒽𝒩)𝑟	𝒽𝒩)𝑟	PROPN
iajs-2517	396	58	∈̃	∈̃	PROPN
iajs-2517	396	59	(	(	PUNCT
iajs-2517	396	60	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	396	61	)	)	PUNCT
iajs-2517	396	62	and	and	CCONJ
iajs-2517	396	63	(	(	PUNCT
iajs-2517	396	64	𝒜𝑟,ℋ	𝒜𝑟,ℋ	PROPN
iajs-2517	396	65	)	)	PUNCT
iajs-2517	396	66	∩̃	∩̃	PUNCT
iajs-2517	396	67	(	(	PUNCT
iajs-2517	396	68	ℬ𝑟,ℋ	ℬ𝑟,ℋ	PROPN
iajs-2517	396	69	)	)	PUNCT
iajs-2517	396	70	=	=	SYM
iajs-2517	396	71	{	{	PUNCT
iajs-2517	396	72	∅̃	∅̃	NOUN
iajs-2517	396	73	}	}	PUNCT
iajs-2517	396	74	,	,	PUNCT
iajs-2517	396	75	because	because	SCONJ
iajs-2517	396	76	(	(	PUNCT
iajs-2517	396	77	χ	χ	X
iajs-2517	396	78	,	,	PUNCT
iajs-2517	396	79	𝒯	𝒯	PROPN
iajs-2517	396	80	,	,	PUNCT
iajs-2517	396	81	ℋ	ℋ	PROPN
iajs-2517	396	82	)	)	PUNCT
iajs-2517	396	83	is	be	AUX
iajs-2517	396	84	a	a	PRON
iajs-2517	396	85	not	not	PART
iajs-2517	396	86	soft-𝒯2	soft-𝒯2	PRON
iajs-2517	396	87	𝑠𝑝𝑎𝑐𝑒.	𝑠𝑝𝑎𝑐𝑒.	ADJ
iajs-2517	396	88	hence	hence	ADV
iajs-2517	396	89	playerⅰ	playerⅰ	PROPN
iajs-2517	396	90	↑	↑	PROPN
iajs-2517	396	91	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	396	92	,	,	PUNCT
iajs-2517	396	93	ℐ	ℐ	NOUN
iajs-2517	396	94	)	)	PUNCT
iajs-2517	396	95	.	.	PUNCT
iajs-2517	397	1	(	(	PUNCT
iajs-2517	397	2	⟸	⟸	ADJ
iajs-2517	397	3	)	)	PUNCT
iajs-2517	397	4	clear	clear	ADJ
iajs-2517	397	5	.	.	PUNCT
iajs-2517	398	1	corollary	corollary	ADJ
iajs-2517	398	2	5.26	5.26	NUM
iajs-2517	398	3	.	.	PUNCT
iajs-2517	399	1	ia	ia	PROPN
iajs-2517	399	2	space	space	NOUN
iajs-2517	399	3	(	(	PUNCT
iajs-2517	399	4	χ	χ	X
iajs-2517	399	5	,	,	PUNCT
iajs-2517	399	6	𝒯	𝒯	PROPN
iajs-2517	399	7	,	,	PUNCT
iajs-2517	399	8	ℋ	ℋ	PROPN
iajs-2517	399	9	)	)	PUNCT
iajs-2517	399	10	is	be	AUX
iajs-2517	399	11	a	a	DET
iajs-2517	399	12	not	not	PART
iajs-2517	399	13	soft-𝒯2	soft-𝒯2	X
iajs-2517	399	14	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	399	15	if	if	SCONJ
iajs-2517	400	1	and	and	CCONJ
iajs-2517	400	2	only	only	ADV
iajs-2517	400	3	if	if	SCONJ
iajs-2517	400	4	player	player	NOUN
iajs-2517	400	5	ⅱ	ⅱ	PROPN
iajs-2517	400	6	⤉	⤉	VERB
iajs-2517	400	7	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	400	8	,	,	PUNCT
iajs-2517	400	9	χ	χ	NOUN
iajs-2517	400	10	)	)	PUNCT
iajs-2517	400	11	.	.	PUNCT
iajs-2517	401	1	iia	iia	NOUN
iajs-2517	401	2	space	space	NOUN
iajs-2517	401	3	(	(	PUNCT
iajs-2517	401	4	χ	χ	X
iajs-2517	401	5	,	,	PUNCT
iajs-2517	401	6	𝒯	𝒯	PROPN
iajs-2517	401	7	,	,	PUNCT
iajs-2517	401	8	ℋ	ℋ	PROPN
iajs-2517	401	9	,	,	PUNCT
iajs-2517	401	10	ℐ	ℐ	NUM
iajs-2517	401	11	)	)	PUNCT
iajs-2517	401	12	is	be	AUX
iajs-2517	401	13	not	not	PART
iajs-2517	401	14	a	a	DET
iajs-2517	401	15	sℐsg-𝒯2­space	sℐsg-𝒯2­space	PROPN
iajs-2517	401	16	if	if	SCONJ
iajs-2517	401	17	and	and	CCONJ
iajs-2517	401	18	only	only	ADV
iajs-2517	401	19	if	if	SCONJ
iajs-2517	401	20	player	player	NOUN
iajs-2517	401	21	ⅱ	ⅱ	PROPN
iajs-2517	401	22	⤉	⤉	VERB
iajs-2517	401	23	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	401	24	,	,	PUNCT
iajs-2517	401	25	ℐ	ℐ	NOUN
iajs-2517	401	26	)	)	PUNCT
iajs-2517	401	27	.	.	PUNCT
iajs-2517	402	1	proof	proof	NOUN
iajs-2517	402	2	:	:	PUNCT
iajs-2517	402	3	by	by	ADP
iajs-2517	402	4	theorem	theorem	NOUN
iajs-2517	402	5	5.25	5.25	NUM
iajs-2517	402	6	,	,	PUNCT
iajs-2517	402	7	the	the	DET
iajs-2517	402	8	proof	proof	NOUN
iajs-2517	402	9	is	be	AUX
iajs-2517	402	10	over	over	ADV
iajs-2517	402	11	.	.	PUNCT
iajs-2517	403	1	remark	remark	PROPN
iajs-2517	403	2	5.27	5.27	NUM
iajs-2517	403	3	.	.	PUNCT
iajs-2517	404	1	for	for	ADP
iajs-2517	404	2	a	a	DET
iajs-2517	404	3	space	space	NOUN
iajs-2517	404	4	(	(	PUNCT
iajs-2517	404	5	χ	χ	X
iajs-2517	404	6	,	,	PUNCT
iajs-2517	404	7	𝒯	𝒯	PROPN
iajs-2517	404	8	,	,	PUNCT
iajs-2517	404	9	ℋ	ℋ	PROPN
iajs-2517	404	10	,	,	PUNCT
iajs-2517	404	11	ℐ	ℐ	PROPN
iajs-2517	404	12	):	):	PUNCT
iajs-2517	404	13	i.	i.	NOUN
iajs-2517	404	14	if	if	SCONJ
iajs-2517	404	15	player	player	NOUN
iajs-2517	404	16	ⅱ	ⅱ	PROPN
iajs-2517	404	17	↑	↑	PROPN
iajs-2517	404	18	ş𝒢(𝒯𝑖+1	ş𝒢(𝒯𝑖+1	NOUN
iajs-2517	404	19	,	,	PUNCT
iajs-2517	404	20	𝜒	𝜒	X
iajs-2517	404	21	)	)	PUNCT
iajs-2517	404	22	(	(	PUNCT
iajs-2517	404	23	respectively	respectively	ADV
iajs-2517	404	24	,	,	PUNCT
iajs-2517	404	25	ş𝒢(𝒯𝑖+1	ş𝒢(𝒯𝑖+1	NOUN
iajs-2517	404	26	,	,	PUNCT
iajs-2517	404	27	ℐ	ℐ	NUM
iajs-2517	404	28	)	)	PUNCT
iajs-2517	404	29	)	)	PUNCT
iajs-2517	404	30	then	then	ADV
iajs-2517	404	31	player	player	NOUN
iajs-2517	404	32	ⅱ	ⅱ	PROPN
iajs-2517	404	33	↑	↑	PROPN
iajs-2517	404	34	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	ADV
iajs-2517	404	35	,	,	PUNCT
iajs-2517	404	36	𝜒	𝜒	X
iajs-2517	404	37	)	)	PUNCT
iajs-2517	404	38	(	(	PUNCT
iajs-2517	404	39	respectively	respectively	ADV
iajs-2517	404	40	,	,	PUNCT
iajs-2517	404	41	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	NOUN
iajs-2517	404	42	,	,	PUNCT
iajs-2517	404	43	ℐ	ℐ	NOUN
iajs-2517	404	44	)	)	PUNCT
iajs-2517	404	45	)	)	PUNCT
iajs-2517	404	46	,	,	PUNCT
iajs-2517	404	47	where	where	SCONJ
iajs-2517	404	48	𝑖	𝑖	ADP
iajs-2517	404	49	=	=	SYM
iajs-2517	404	50	{	{	PUNCT
iajs-2517	404	51	0,1	0,1	NUM
iajs-2517	404	52	}	}	PUNCT
iajs-2517	404	53	.	.	PUNCT
iajs-2517	405	1	ii	ii	PROPN
iajs-2517	405	2	.	.	PUNCT
iajs-2517	406	1	if	if	SCONJ
iajs-2517	406	2	player	player	NOUN
iajs-2517	406	3	ⅱ	ⅱ	PROPN
iajs-2517	406	4	↑	↑	PROPN
iajs-2517	406	5	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	ADV
iajs-2517	406	6	,	,	PUNCT
iajs-2517	406	7	𝜒	𝜒	X
iajs-2517	406	8	)	)	PUNCT
iajs-2517	406	9	;	;	PUNCT
iajs-2517	406	10	then	then	ADV
iajs-2517	406	11	player	player	NOUN
iajs-2517	406	12	ⅱ	ⅱ	PROPN
iajs-2517	406	13	↑	↑	PROPN
iajs-2517	406	14	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	ADV
iajs-2517	406	15	,	,	PUNCT
iajs-2517	406	16	ℐ	ℐ	PROPN
iajs-2517	406	17	)	)	PUNCT
iajs-2517	406	18	,	,	PUNCT
iajs-2517	406	19	where	where	SCONJ
iajs-2517	406	20	𝑖	𝑖	ADP
iajs-2517	406	21	=	=	PUNCT
iajs-2517	406	22	{	{	PUNCT
iajs-2517	406	23	0,1,2	0,1,2	NOUN
iajs-2517	406	24	}	}	PUNCT
iajs-2517	406	25	.	.	PUNCT
iajs-2517	407	1	the	the	DET
iajs-2517	407	2	following	follow	VERB
iajs-2517	407	3	(	(	PUNCT
iajs-2517	407	4	figure	figure	NOUN
iajs-2517	407	5	)	)	PUNCT
iajs-2517	407	6	clarifies	clarify	VERB
iajs-2517	407	7	a	a	DET
iajs-2517	407	8	relationships	relationship	NOUN
iajs-2517	407	9	in	in	ADP
iajs-2517	407	10	theorem	theorem	ADJ
iajs-2517	407	11	5.6	5.6	NUM
iajs-2517	407	12	,	,	PUNCT
iajs-2517	407	13	theorem	theorem	VERB
iajs-2517	407	14	5.15	5.15	NUM
iajs-2517	407	15	,	,	PUNCT
iajs-2517	407	16	theorem	theorem	VERB
iajs-2517	407	17	5.23	5.23	NUM
iajs-2517	407	18	and	and	CCONJ
iajs-2517	407	19	remark	remark	NOUN
iajs-2517	407	20	5.27	5.27	NUM
iajs-2517	407	21	.	.	PUNCT
iajs-2517	408	1	player	player	NOUN
iajs-2517	408	2	ⅱ	ⅱ	PROPN
iajs-2517	408	3	↑	↑	PROPN
iajs-2517	408	4	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	408	5	,	,	PUNCT
iajs-2517	408	6	χ	χ	X
iajs-2517	408	7	)	)	PUNCT
iajs-2517	408	8	player	player	NOUN
iajs-2517	408	9	ⅱ	ⅱ	PROPN
iajs-2517	408	10	↑	↑	PROPN
iajs-2517	408	11	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	408	12	,	,	PUNCT
iajs-2517	408	13	χ	χ	X
iajs-2517	408	14	)	)	PUNCT
iajs-2517	408	15	player	player	NOUN
iajs-2517	408	16	ⅱ	ⅱ	PROPN
iajs-2517	408	17	↑	↑	PROPN
iajs-2517	408	18	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	408	19	,	,	PUNCT
iajs-2517	408	20	χ	χ	X
iajs-2517	408	21	)	)	PUNCT
iajs-2517	408	22	(	(	PUNCT
iajs-2517	408	23	𝜒	𝜒	X
iajs-2517	408	24	,	,	PUNCT
iajs-2517	408	25	𝒯	𝒯	PROPN
iajs-2517	408	26	,	,	PUNCT
iajs-2517	408	27	ℋ	ℋ	PROPN
iajs-2517	408	28	)	)	PUNCT
iajs-2517	408	29	is	be	AUX
iajs-2517	408	30	a	a	DET
iajs-2517	408	31	soft-𝒯2	soft-𝒯2	X
iajs-2517	408	32	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	408	33	(	(	PUNCT
iajs-2517	408	34	𝜒	𝜒	X
iajs-2517	408	35	,	,	PUNCT
iajs-2517	408	36	𝒯	𝒯	PROPN
iajs-2517	408	37	,	,	PUNCT
iajs-2517	408	38	ℋ	ℋ	PROPN
iajs-2517	408	39	)	)	PUNCT
iajs-2517	408	40	is	be	AUX
iajs-2517	408	41	a	a	DET
iajs-2517	408	42	soft-𝒯1	soft-𝒯1	PROPN
iajs-2517	408	43	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	408	44	(	(	PUNCT
iajs-2517	408	45	𝜒	𝜒	X
iajs-2517	408	46	,	,	PUNCT
iajs-2517	408	47	𝒯	𝒯	PROPN
iajs-2517	408	48	,	,	PUNCT
iajs-2517	408	49	ℋ	ℋ	PROPN
iajs-2517	408	50	)	)	PUNCT
iajs-2517	408	51	is	be	AUX
iajs-2517	408	52	a	a	DET
iajs-2517	408	53	soft-𝒯0	soft-𝒯0	PROPN
iajs-2517	408	54	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	408	55	(	(	PUNCT
iajs-2517	408	56	𝜒	𝜒	X
iajs-2517	408	57	,	,	PUNCT
iajs-2517	408	58	𝒯	𝒯	PROPN
iajs-2517	408	59	,	,	PUNCT
iajs-2517	408	60	ℋ	ℋ	PROPN
iajs-2517	408	61	,	,	PUNCT
iajs-2517	408	62	ℐ	ℐ	NUM
iajs-2517	408	63	)	)	PUNCT
iajs-2517	408	64	is	be	AUX
iajs-2517	408	65	𝑠ℐ𝑠𝑔	𝑠ℐ𝑠𝑔	PROPN
iajs-2517	408	66	𝒯2	𝒯2	NOUN
iajs-2517	408	67	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	408	68	(	(	PUNCT
iajs-2517	408	69	𝜒	𝜒	X
iajs-2517	408	70	,	,	PUNCT
iajs-2517	408	71	𝒯	𝒯	PROPN
iajs-2517	408	72	,	,	PUNCT
iajs-2517	408	73	ℋ	ℋ	PROPN
iajs-2517	408	74	,	,	PUNCT
iajs-2517	408	75	ℐ	ℐ	NUM
iajs-2517	408	76	)	)	PUNCT
iajs-2517	408	77	is	be	AUX
iajs-2517	408	78	𝑠ℐ𝑠𝑔	𝑠ℐ𝑠𝑔	PROPN
iajs-2517	408	79	𝒯1	𝒯1	NOUN
iajs-2517	408	80	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	408	81	(	(	PUNCT
iajs-2517	408	82	𝜒	𝜒	X
iajs-2517	408	83	,	,	PUNCT
iajs-2517	408	84	𝒯	𝒯	PROPN
iajs-2517	408	85	,	,	PUNCT
iajs-2517	408	86	ℋ	ℋ	PROPN
iajs-2517	408	87	,	,	PUNCT
iajs-2517	408	88	ℐ	ℐ	NUM
iajs-2517	408	89	)	)	PUNCT
iajs-2517	408	90	is	be	AUX
iajs-2517	408	91	𝑠ℐ𝑠𝑔	𝑠ℐ𝑠𝑔	PROPN
iajs-2517	408	92	𝒯0	𝒯0	NOUN
iajs-2517	408	93	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	408	94	player	player	NOUN
iajs-2517	408	95	ⅰ	ⅰ	X
iajs-2517	408	96	⤉	⤉	VERB
iajs-2517	408	97	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	408	98	,	,	PUNCT
iajs-2517	408	99	χ	χ	X
iajs-2517	408	100	)	)	PUNCT
iajs-2517	408	101	player	player	NOUN
iajs-2517	408	102	ⅰ	ⅰ	PROPN
iajs-2517	408	103	⤉	⤉	VERB
iajs-2517	408	104	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	408	105	,	,	PUNCT
iajs-2517	408	106	χ	χ	X
iajs-2517	408	107	)	)	PUNCT
iajs-2517	408	108	player	player	NOUN
iajs-2517	408	109	ⅰ	ⅰ	NOUN
iajs-2517	408	110	⤉	⤉	VERB
iajs-2517	408	111	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	408	112	,	,	PUNCT
iajs-2517	408	113	χ	χ	X
iajs-2517	408	114	)	)	PUNCT
iajs-2517	408	115	135	135	NUM
iajs-2517	408	116	ibn	ibn	PROPN
iajs-2517	408	117	al	al	PROPN
iajs-2517	408	118	-	-	PUNCT
iajs-2517	408	119	haitham	haitham	PROPN
iajs-2517	408	120	jour	jour	X
iajs-2517	408	121	.	.	PROPN
iajs-2517	409	1	for	for	ADP
iajs-2517	409	2	pure	pure	ADJ
iajs-2517	409	3	&	&	CCONJ
iajs-2517	409	4	appl	appl	PROPN
iajs-2517	409	5	.	.	PUNCT
iajs-2517	410	1	sci	sci	PROPN
iajs-2517	410	2	.	.	PROPN
iajs-2517	411	1	33	33	NUM
iajs-2517	411	2	(	(	PUNCT
iajs-2517	411	3	4	4	NUM
iajs-2517	411	4	)	)	PUNCT
iajs-2517	411	5	2020	2020	NUM
iajs-2517	411	6	figure	figure	VERB
iajs-2517	411	7	2	2	NUM
iajs-2517	411	8	:	:	PUNCT
iajs-2517	411	9	the	the	DET
iajs-2517	411	10	winning	win	VERB
iajs-2517	411	11	strategy	strategy	NOUN
iajs-2517	411	12	for	for	ADP
iajs-2517	411	13	player	player	NOUN
iajs-2517	411	14	ⅱ	ⅱ	PROPN
iajs-2517	411	15	remark	remark	NOUN
iajs-2517	411	16	5.28	5.28	NUM
iajs-2517	411	17	.	.	PUNCT
iajs-2517	412	1	for	for	ADP
iajs-2517	412	2	a	a	DET
iajs-2517	412	3	space	space	NOUN
iajs-2517	412	4	(	(	PUNCT
iajs-2517	412	5	𝜒	𝜒	X
iajs-2517	412	6	,	,	PUNCT
iajs-2517	412	7	𝒯	𝒯	PROPN
iajs-2517	412	8	,	,	PUNCT
iajs-2517	412	9	ℐ	ℐ	PROPN
iajs-2517	412	10	):	):	PUNCT
iajs-2517	412	11	iif	iif	PROPN
iajs-2517	412	12	player	player	NOUN
iajs-2517	412	13	ⅰ	ⅰ	PROPN
iajs-2517	412	14	↑	↑	PROPN
iajs-2517	412	15	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	ADV
iajs-2517	412	16	,	,	PUNCT
iajs-2517	412	17	𝜒	𝜒	X
iajs-2517	412	18	)	)	PUNCT
iajs-2517	412	19	(	(	PUNCT
iajs-2517	412	20	respectively	respectively	ADV
iajs-2517	412	21	,	,	PUNCT
iajs-2517	412	22	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	NOUN
iajs-2517	412	23	,	,	PUNCT
iajs-2517	412	24	ℐ	ℐ	PROPN
iajs-2517	412	25	)	)	PUNCT
iajs-2517	412	26	)	)	PUNCT
iajs-2517	412	27	then	then	ADV
iajs-2517	412	28	player	player	NOUN
iajs-2517	412	29	ⅰ	ⅰ	PROPN
iajs-2517	412	30	↑	↑	PROPN
iajs-2517	412	31	ş𝒢(𝒯𝑖+1	ş𝒢(𝒯𝑖+1	X
iajs-2517	412	32	,	,	PUNCT
iajs-2517	412	33	𝜒	𝜒	X
iajs-2517	412	34	)	)	PUNCT
iajs-2517	412	35	(	(	PUNCT
iajs-2517	412	36	respectively	respectively	ADV
iajs-2517	412	37	,	,	PUNCT
iajs-2517	412	38	ş𝒢(𝒯𝑖+1	ş𝒢(𝒯𝑖+1	NOUN
iajs-2517	412	39	,	,	PUNCT
iajs-2517	412	40	ℐ	ℐ	NUM
iajs-2517	412	41	)	)	PUNCT
iajs-2517	412	42	)	)	PUNCT
iajs-2517	412	43	,	,	PUNCT
iajs-2517	412	44	where	where	SCONJ
iajs-2517	412	45	𝑖	𝑖	ADP
iajs-2517	412	46	=	=	SYM
iajs-2517	412	47	{	{	PUNCT
iajs-2517	412	48	0,1	0,1	NUM
iajs-2517	412	49	}	}	PUNCT
iajs-2517	412	50	.	.	PUNCT
iajs-2517	413	1	iiif	iiif	PROPN
iajs-2517	413	2	player	player	PROPN
iajs-2517	413	3	ⅰ	ⅰ	PROPN
iajs-2517	413	4	↑	↑	PROPN
iajs-2517	413	5	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	ADV
iajs-2517	413	6	,	,	PUNCT
iajs-2517	413	7	ℐ	ℐ	X
iajs-2517	413	8	)	)	PUNCT
iajs-2517	413	9	then	then	ADV
iajs-2517	413	10	player	player	NOUN
iajs-2517	413	11	ⅰ	ⅰ	PROPN
iajs-2517	413	12	↑	↑	PROPN
iajs-2517	413	13	ş𝒢(𝒯𝑖	ş𝒢(𝒯𝑖	ADV
iajs-2517	413	14	,	,	PUNCT
iajs-2517	413	15	𝜒	𝜒	X
iajs-2517	413	16	)	)	PUNCT
iajs-2517	413	17	,	,	PUNCT
iajs-2517	413	18	where	where	SCONJ
iajs-2517	413	19	𝑖	𝑖	ADP
iajs-2517	413	20	=	=	PUNCT
iajs-2517	413	21	{	{	PUNCT
iajs-2517	413	22	0,1,2	0,1,2	NOUN
iajs-2517	413	23	}	}	PUNCT
iajs-2517	413	24	.	.	PUNCT
iajs-2517	414	1	the	the	DET
iajs-2517	414	2	following	follow	VERB
iajs-2517	414	3	(	(	PUNCT
iajs-2517	414	4	figure	figure	NOUN
iajs-2517	414	5	)	)	PUNCT
iajs-2517	414	6	clarifies	clarify	VERB
iajs-2517	414	7	a	a	DET
iajs-2517	414	8	relationships	relationship	NOUN
iajs-2517	414	9	in	in	ADP
iajs-2517	414	10	theorem	theorem	ADJ
iajs-2517	414	11	5.9	5.9	NUM
iajs-2517	414	12	,	,	PUNCT
iajs-2517	414	13	theorem	theorem	VERB
iajs-2517	414	14	5.18	5.18	NUM
iajs-2517	414	15	,	,	PUNCT
iajs-2517	414	16	theorem	theorem	VERB
iajs-2517	414	17	5.26	5.26	NUM
iajs-2517	414	18	and	and	CCONJ
iajs-2517	414	19	remark	remark	NOUN
iajs-2517	414	20	5.28	5.28	NUM
iajs-2517	414	21	.	.	PUNCT
iajs-2517	415	1	figure	figure	NOUN
iajs-2517	415	2	3	3	NUM
iajs-2517	415	3	:	:	PUNCT
iajs-2517	415	4	the	the	DET
iajs-2517	415	5	winning	win	VERB
iajs-2517	415	6	strategy	strategy	NOUN
iajs-2517	415	7	for	for	ADP
iajs-2517	415	8	player	player	NOUN
iajs-2517	415	9	ⅰ	ⅰ	PROPN
iajs-2517	415	10	player	player	NOUN
iajs-2517	415	11	ⅱ	ⅱ	PROPN
iajs-2517	415	12	↑	↑	PROPN
iajs-2517	415	13	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	415	14	,	,	PUNCT
iajs-2517	415	15	ℐ	ℐ	X
iajs-2517	415	16	)	)	PUNCT
iajs-2517	415	17	player	player	NOUN
iajs-2517	415	18	ⅱ	ⅱ	PROPN
iajs-2517	415	19	↑	↑	PROPN
iajs-2517	415	20	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	415	21	,	,	PUNCT
iajs-2517	415	22	ℐ	ℐ	X
iajs-2517	415	23	)	)	PUNCT
iajs-2517	415	24	player	player	NOUN
iajs-2517	415	25	ⅱ	ⅱ	PROPN
iajs-2517	415	26	↑	↑	PROPN
iajs-2517	415	27	ş𝒢(𝒯0	ş𝒢(𝒯0	PROPN
iajs-2517	415	28	,	,	PUNCT
iajs-2517	415	29	ℐ	ℐ	X
iajs-2517	415	30	)	)	PUNCT
iajs-2517	415	31	player	player	NOUN
iajs-2517	415	32	ⅱ	ⅱ	PROPN
iajs-2517	415	33	⤉	⤉	VERB
iajs-2517	415	34	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	415	35	,	,	PUNCT
iajs-2517	415	36	χ	χ	X
iajs-2517	415	37	)	)	PUNCT
iajs-2517	415	38	player	player	NOUN
iajs-2517	415	39	ⅱ	ⅱ	PROPN
iajs-2517	415	40	⤉	⤉	VERB
iajs-2517	415	41	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	415	42	,	,	PUNCT
iajs-2517	415	43	χ	χ	X
iajs-2517	415	44	)	)	PUNCT
iajs-2517	415	45	player	player	NOUN
iajs-2517	415	46	ⅱ	ⅱ	PROPN
iajs-2517	415	47	⤉	⤉	VERB
iajs-2517	415	48	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	415	49	,	,	PUNCT
iajs-2517	415	50	χ	χ	X
iajs-2517	415	51	)	)	PUNCT
iajs-2517	415	52	player	player	NOUN
iajs-2517	415	53	ⅰ	ⅰ	PROPN
iajs-2517	415	54	⤉	⤉	VERB
iajs-2517	415	55	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	415	56	,	,	PUNCT
iajs-2517	415	57	ℐ	ℐ	NOUN
iajs-2517	415	58	)	)	PUNCT
iajs-2517	415	59	player	player	NOUN
iajs-2517	415	60	ⅰ	ⅰ	PROPN
iajs-2517	415	61	⤉	⤉	VERB
iajs-2517	415	62	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	415	63	,	,	PUNCT
iajs-2517	415	64	ℐ	ℐ	NUM
iajs-2517	415	65	)	)	PUNCT
iajs-2517	415	66	player	player	NOUN
iajs-2517	415	67	ⅰ	ⅰ	NOUN
iajs-2517	415	68	⤉	⤉	VERB
iajs-2517	415	69	ş𝒢(𝒯0	ş𝒢(𝒯0	VERB
iajs-2517	415	70	,	,	PUNCT
iajs-2517	415	71	ℐ	ℐ	X
iajs-2517	415	72	)	)	PUNCT
iajs-2517	415	73	player	player	NOUN
iajs-2517	415	74	ⅰ	ⅰ	PROPN
iajs-2517	415	75	↑	↑	PROPN
iajs-2517	415	76	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	415	77	,	,	PUNCT
iajs-2517	415	78	χ	χ	X
iajs-2517	415	79	)	)	PUNCT
iajs-2517	415	80	player	player	NOUN
iajs-2517	415	81	ⅰ	ⅰ	PROPN
iajs-2517	415	82	↑	↑	PROPN
iajs-2517	415	83	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	415	84	,	,	PUNCT
iajs-2517	415	85	χ	χ	X
iajs-2517	415	86	)	)	PUNCT
iajs-2517	415	87	player	player	NOUN
iajs-2517	415	88	ⅰ	ⅰ	PROPN
iajs-2517	415	89	↑	↑	X
iajs-2517	415	90	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	415	91	,	,	PUNCT
iajs-2517	415	92	χ	χ	X
iajs-2517	415	93	)	)	PUNCT
iajs-2517	415	94	player	player	NOUN
iajs-2517	415	95	ⅰ	ⅰ	PROPN
iajs-2517	415	96	↑	↑	PROPN
iajs-2517	415	97	ş𝒢(𝒯2	ş𝒢(𝒯2	PROPN
iajs-2517	415	98	,	,	PUNCT
iajs-2517	415	99	ℐ	ℐ	X
iajs-2517	415	100	)	)	PUNCT
iajs-2517	415	101	player	player	NOUN
iajs-2517	415	102	ⅰ	ⅰ	PROPN
iajs-2517	415	103	↑	↑	PROPN
iajs-2517	415	104	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	415	105	,	,	PUNCT
iajs-2517	415	106	ℐ	ℐ	X
iajs-2517	415	107	)	)	PUNCT
iajs-2517	415	108	player	player	NOUN
iajs-2517	415	109	ⅰ	ⅰ	PROPN
iajs-2517	415	110	↑	↑	X
iajs-2517	415	111	ş𝒢(𝒯0	ş𝒢(𝒯0	X
iajs-2517	415	112	,	,	PUNCT
iajs-2517	415	113	ℐ	ℐ	NUM
iajs-2517	415	114	)	)	PUNCT
iajs-2517	415	115	(	(	PUNCT
iajs-2517	415	116	𝜒	𝜒	X
iajs-2517	415	117	,	,	PUNCT
iajs-2517	415	118	𝒯	𝒯	PROPN
iajs-2517	415	119	,	,	PUNCT
iajs-2517	415	120	ℋ	ℋ	PROPN
iajs-2517	415	121	)	)	PUNCT
iajs-2517	415	122	is	be	AUX
iajs-2517	415	123	not	not	PART
iajs-2517	415	124	a	a	DET
iajs-2517	415	125	soft-𝒯2	soft-𝒯2	X
iajs-2517	415	126	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	415	127	(	(	PUNCT
iajs-2517	415	128	𝜒	𝜒	X
iajs-2517	415	129	,	,	PUNCT
iajs-2517	415	130	𝒯	𝒯	PROPN
iajs-2517	415	131	,	,	PUNCT
iajs-2517	415	132	ℋ	ℋ	PROPN
iajs-2517	415	133	)	)	PUNCT
iajs-2517	415	134	is	be	AUX
iajs-2517	415	135	not	not	PART
iajs-2517	415	136	a	a	DET
iajs-2517	415	137	soft-𝒯1	soft-𝒯1	PROPN
iajs-2517	415	138	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	415	139	(	(	PUNCT
iajs-2517	415	140	𝜒	𝜒	X
iajs-2517	415	141	,	,	PUNCT
iajs-2517	415	142	𝒯	𝒯	PROPN
iajs-2517	415	143	,	,	PUNCT
iajs-2517	415	144	ℋ	ℋ	PROPN
iajs-2517	415	145	)	)	PUNCT
iajs-2517	415	146	is	be	AUX
iajs-2517	415	147	not	not	PART
iajs-2517	415	148	a	a	DET
iajs-2517	415	149	soft-𝒯0	soft-𝒯0	PROPN
iajs-2517	415	150	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	415	151	(	(	PUNCT
iajs-2517	415	152	𝜒	𝜒	X
iajs-2517	415	153	,	,	PUNCT
iajs-2517	415	154	𝒯	𝒯	PROPN
iajs-2517	415	155	,	,	PUNCT
iajs-2517	415	156	ℋ	ℋ	PROPN
iajs-2517	415	157	,	,	PUNCT
iajs-2517	415	158	ℐ	ℐ	NUM
iajs-2517	415	159	)	)	PUNCT
iajs-2517	415	160	is	be	AUX
iajs-2517	415	161	not	not	PART
iajs-2517	415	162	a	a	DET
iajs-2517	415	163	sℐsg	sℐsg	PROPN
iajs-2517	415	164	𝒯2	𝒯2	PROPN
iajs-2517	415	165	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	415	166	(	(	PUNCT
iajs-2517	415	167	𝜒	𝜒	X
iajs-2517	415	168	,	,	PUNCT
iajs-2517	415	169	𝒯	𝒯	PROPN
iajs-2517	415	170	,	,	PUNCT
iajs-2517	415	171	ℋ	ℋ	PROPN
iajs-2517	415	172	,	,	PUNCT
iajs-2517	415	173	ℐ)is	ℐ)is	PROPN
iajs-2517	415	174	not	not	PART
iajs-2517	415	175	a	a	DET
iajs-2517	415	176	sℐsg	sℐsg	PROPN
iajs-2517	415	177	𝒯1	𝒯1	NOUN
iajs-2517	415	178	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	ADV
iajs-2517	415	179	(	(	PUNCT
iajs-2517	415	180	𝜒	𝜒	X
iajs-2517	415	181	,	,	PUNCT
iajs-2517	415	182	𝒯	𝒯	PROPN
iajs-2517	415	183	,	,	PUNCT
iajs-2517	415	184	ℋ	ℋ	PROPN
iajs-2517	415	185	,	,	PUNCT
iajs-2517	415	186	ℐ)is	ℐ)is	PROPN
iajs-2517	415	187	not	not	PART
iajs-2517	415	188	a	a	DET
iajs-2517	415	189	sℐsg	sℐsg	PROPN
iajs-2517	415	190	𝒯0	𝒯0	PROPN
iajs-2517	415	191	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2517	415	192	player	player	NOUN
iajs-2517	415	193	ⅱ	ⅱ	PROPN
iajs-2517	415	194	⤉	⤉	VERB
iajs-2517	415	195	ş𝒢(𝒯2	ş𝒢(𝒯2	NOUN
iajs-2517	415	196	,	,	PUNCT
iajs-2517	415	197	ℐ	ℐ	NOUN
iajs-2517	415	198	)	)	PUNCT
iajs-2517	415	199	player	player	NOUN
iajs-2517	415	200	ⅱ	ⅱ	PROPN
iajs-2517	415	201	⤉	⤉	VERB
iajs-2517	415	202	ş𝒢(𝒯1	ş𝒢(𝒯1	PROPN
iajs-2517	415	203	,	,	PUNCT
iajs-2517	415	204	ℐ	ℐ	NUM
iajs-2517	415	205	)	)	PUNCT
iajs-2517	415	206	player	player	NOUN
iajs-2517	415	207	ⅱ	ⅱ	PROPN
iajs-2517	415	208	⤉	⤉	VERB
iajs-2517	415	209	ş𝒢(𝒯0	ş𝒢(𝒯0	NOUN
iajs-2517	415	210	,	,	PUNCT
iajs-2517	415	211	ℐ	ℐ	NOUN
iajs-2517	415	212	)	)	PUNCT
iajs-2517	415	213	136	136	NUM
iajs-2517	415	214	ibn	ibn	PROPN
iajs-2517	415	215	al	al	PROPN
iajs-2517	415	216	-	-	PUNCT
iajs-2517	415	217	haitham	haitham	PROPN
iajs-2517	415	218	jour	jour	X
iajs-2517	415	219	.	.	PROPN
iajs-2517	416	1	for	for	ADP
iajs-2517	416	2	pure	pure	ADJ
iajs-2517	416	3	&	&	CCONJ
iajs-2517	416	4	appl	appl	PROPN
iajs-2517	416	5	.	.	PUNCT
iajs-2517	417	1	sci	sci	PROPN
iajs-2517	417	2	.	.	PROPN
iajs-2517	418	1	33	33	NUM
iajs-2517	418	2	(	(	PUNCT
iajs-2517	418	3	4	4	NUM
iajs-2517	418	4	)	)	PUNCT
iajs-2517	418	5	2020	2020	NUM
iajs-2517	418	6	references	reference	NOUN
iajs-2517	418	7	1	1	NUM
iajs-2517	418	8	.	.	PUNCT
iajs-2517	419	1	shabir	shabir	PROPN
iajs-2517	419	2	,	,	PUNCT
iajs-2517	419	3	m.	m.	NOUN
iajs-2517	419	4	;	;	PUNCT
iajs-2517	419	5	naz	naz	PROPN
iajs-2517	419	6	,	,	PUNCT
iajs-2517	419	7	m.	m.	NOUN
iajs-2517	419	8	on	on	ADP
iajs-2517	419	9	soft	soft	ADJ
iajs-2517	419	10	to	to	ADP
iajs-2517	419	11	topological	topological	ADJ
iajs-2517	419	12	spaces	space	NOUN
iajs-2517	419	13	.	.	PUNCT
iajs-2517	420	1	com	com	NOUN
iajs-2517	420	2	put	put	VERB
iajs-2517	420	3	math	math	NOUN
iajs-2517	420	4	.	.	PUNCT
iajs-2517	421	1	appl	appl	PROPN
iajs-2517	421	2	.	.	PUNCT
iajs-2517	422	1	2011	2011	NUM
iajs-2517	422	2	,	,	PUNCT
iajs-2517	422	3	61,1786	61,1786	NUM
iajs-2517	422	4	-	-	SYM
iajs-2517	422	5	1799	1799	NUM
iajs-2517	422	6	.	.	PUNCT
iajs-2517	423	1	2	2	NUM
iajs-2517	423	2	.	.	X
iajs-2517	423	3	hussain	hussain	PROPN
iajs-2517	423	4	,	,	PUNCT
iajs-2517	423	5	s.	s.	PROPN
iajs-2517	423	6	;	;	PUNCT
iajs-2517	423	7	ahmad	ahmad	PROPN
iajs-2517	423	8	,	,	PUNCT
iajs-2517	423	9	b.	b.	PROPN
iajs-2517	423	10	soft	soft	ADJ
iajs-2517	423	11	separation	separation	NOUN
iajs-2517	423	12	axioms	axiom	NOUN
iajs-2517	423	13	in	in	ADP
iajs-2517	423	14	soft	soft	ADJ
iajs-2517	423	15	topological	topological	ADJ
iajs-2517	423	16	spaces	space	NOUN
iajs-2517	423	17	.	.	PUNCT
iajs-2517	424	1	hjms	hjms	NOUN
iajs-2517	424	2	.	.	PUNCT
iajs-2517	425	1	2015	2015	NUM
iajs-2517	425	2	,	,	PUNCT
iajs-2517	425	3	44,3	44,3	NUM
iajs-2517	425	4	,	,	PUNCT
iajs-2517	425	5	559	559	NUM
iajs-2517	425	6	-	-	SYM
iajs-2517	425	7	568	568	NUM
iajs-2517	425	8	.	.	PUNCT
iajs-2517	426	1	3	3	X
iajs-2517	426	2	.	.	X
iajs-2517	426	3	kadil	kadil	PROPN
iajs-2517	426	4	,	,	PUNCT
iajs-2517	426	5	a.	a.	NOUN
iajs-2517	426	6	;	;	PUNCT
iajs-2517	426	7	tantawy	tantawy	NUM
iajs-2517	426	8	,	,	PUNCT
iajs-2517	426	9	o.	o.	NOUN
iajs-2517	426	10	a.	a.	PROPN
iajs-2517	426	11	;	;	PUNCT
iajs-2517	426	12	el	el	PROPN
iajs-2517	426	13	-	-	PUNCT
iajs-2517	426	14	sheikn	sheikn	PROPN
iajs-2517	426	15	,	,	PUNCT
iajs-2517	426	16	s.	s.	PROPN
iajs-2517	426	17	a.	a.	PROPN
iajs-2517	426	18	;	;	PUNCT
iajs-2517	426	19	abd	abd	PROPN
iajs-2517	426	20	el	el	PROPN
iajs-2517	426	21	-	-	PROPN
iajs-2517	426	22	latif	latif	PROPN
iajs-2517	426	23	,	,	PUNCT
iajs-2517	426	24	a.	a.	NOUN
iajs-2517	426	25	m.	m.	NOUN
iajs-2517	426	26	yoperation	yoperation	NOUN
iajs-2517	426	27	and	and	CCONJ
iajs-2517	426	28	decompositions	decomposition	NOUN
iajs-2517	426	29	of	of	ADP
iajs-2517	426	30	some	some	DET
iajs-2517	426	31	forms	form	NOUN
iajs-2517	426	32	of	of	ADP
iajs-2517	426	33	soft	soft	ADJ
iajs-2517	426	34	continuity	continuity	NOUN
iajs-2517	426	35	in	in	ADP
iajs-2517	426	36	soft	soft	ADJ
iajs-2517	426	37	topological	topological	ADJ
iajs-2517	426	38	spaces	space	NOUN
iajs-2517	426	39	.	.	PUNCT
iajs-2517	427	1	afmi	afmi	PROPN
iajs-2517	427	2	.	.	PUNCT
iajs-2517	428	1	2014	2014	NUM
iajs-2517	428	2	,	,	PUNCT
iajs-2517	428	3	7,181	7,181	NUM
iajs-2517	428	4	-	-	SYM
iajs-2517	428	5	196	196	NUM
iajs-2517	428	6	.	.	PUNCT
iajs-2517	429	1	4	4	X
iajs-2517	429	2	.	.	X
iajs-2517	429	3	abd	abd	PROPN
iajs-2517	429	4	el	el	PROPN
iajs-2517	429	5	-	-	PROPN
iajs-2517	429	6	latif	latif	PROPN
iajs-2517	429	7	,	,	PUNCT
iajs-2517	429	8	a.m.	a.m.	PROPN
iajs-2517	429	9	supra	supra	PROPN
iajs-2517	429	10	soft	soft	ADJ
iajs-2517	429	11	topological	topological	ADJ
iajs-2517	429	12	spaces	space	NOUN
iajs-2517	429	13	.	.	PUNCT
iajs-2517	430	1	jo	jo	PROPN
iajs-2517	430	2	̈	̈	PROPN
iajs-2517	430	3	kull	kull	PROPN
iajs-2517	430	4	journal	journal	PROPN
iajs-2517	430	5	.	.	PUNCT
iajs-2517	431	1	2014	2014	NUM
iajs-2517	431	2	,	,	PUNCT
iajs-2517	431	3	8	8	NUM
iajs-2517	431	4	,	,	PUNCT
iajs-2517	431	5	4	4	NUM
iajs-2517	431	6	,	,	PUNCT
iajs-2517	431	7	17311740	17311740	NUM
iajs-2517	431	8	.	.	PUNCT
iajs-2517	432	1	5	5	NUM
iajs-2517	432	2	.	.	X
iajs-2517	432	3	kandil	kandil	PROPN
iajs-2517	432	4	,	,	PUNCT
iajs-2517	432	5	a.	a.	NOUN
iajs-2517	432	6	;	;	PUNCT
iajs-2517	432	7	tantawy	tantawy	NUM
iajs-2517	432	8	,	,	PUNCT
iajs-2517	432	9	o.	o.	PROPN
iajs-2517	432	10	a.	a.	PROPN
iajs-2517	432	11	e.	e.	PROPN
iajs-2517	432	12	;	;	PUNCT
iajs-2517	432	13	el	el	PROPN
iajs-2517	432	14	-	-	PUNCT
iajs-2517	432	15	sheikh	sheikh	PROPN
iajs-2517	432	16	,	,	PUNCT
iajs-2517	432	17	s.	s.	PROPN
iajs-2517	432	18	a	a	PROPN
iajs-2517	432	19	;	;	PUNCT
iajs-2517	432	20	abd	abd	PROPN
iajs-2517	432	21	el	el	PROPN
iajs-2517	432	22	-	-	PROPN
iajs-2517	432	23	latif	latif	PROPN
iajs-2517	432	24	,	,	PUNCT
iajs-2517	432	25	a.	a.	NOUN
iajs-2517	432	26	m.	m.	NOUN
iajs-2517	432	27	soft	soft	ADJ
iajs-2517	432	28	ideal	ideal	PROPN
iajs-2517	432	29	theory	theory	NOUN
iajs-2517	432	30	,	,	PUNCT
iajs-2517	432	31	soft	soft	ADJ
iajs-2517	432	32	local	local	ADJ
iajs-2517	432	33	function	function	NOUN
iajs-2517	432	34	and	and	CCONJ
iajs-2517	432	35	generated	generate	VERB
iajs-2517	432	36	soft	soft	ADJ
iajs-2517	432	37	topological	topological	ADJ
iajs-2517	432	38	spaces	space	NOUN
iajs-2517	432	39	.	.	PUNCT
iajs-2517	433	1	appl	appl	PROPN
iajs-2517	433	2	.	.	PROPN
iajs-2517	433	3	math	math	PROPN
iajs-2517	433	4	.	.	PUNCT
iajs-2517	434	1	inf.sci	inf.sci	X
iajs-2517	434	2	.	.	PUNCT
iajs-2517	434	3	2014	2014	NUM
iajs-2517	434	4	,	,	PUNCT
iajs-2517	434	5	8,4	8,4	NUM
iajs-2517	434	6	,	,	PUNCT
iajs-2517	434	7	1595	1595	NUM
iajs-2517	434	8	-	-	SYM
iajs-2517	434	9	1603	1603	NUM
iajs-2517	434	10	.	.	PUNCT
iajs-2517	435	1	6	6	NUM
iajs-2517	435	2	.	.	X
iajs-2517	435	3	nasaf	nasaf	PROPN
iajs-2517	435	4	,	,	PUNCT
iajs-2517	435	5	a.	a.	NOUN
iajs-2517	435	6	a.	a.	NOUN
iajs-2517	435	7	;	;	PUNCT
iajs-2517	436	1	radwan	radwan	NOUN
iajs-2517	436	2	,	,	PUNCT
iajs-2517	436	3	a.	a.	PROPN
iajs-2517	436	4	e.	e.	PROPN
iajs-2517	436	5	;	;	PUNCT
iajs-2517	436	6	ibrahem	ibrahem	PROPN
iajs-2517	436	7	,	,	PUNCT
iajs-2517	436	8	f.	f.	PROPN
iajs-2517	436	9	;	;	PUNCT
iajs-2517	436	10	esmaeel	esmaeel	VERB
iajs-2517	436	11	,	,	PUNCT
iajs-2517	436	12	r.	r.	PROPN
iajs-2517	436	13	b.	b.	PROPN
iajs-2517	436	14	soft	soft	ADJ
iajs-2517	436	15	α	α	NOUN
iajs-2517	436	16	-	-	NOUN
iajs-2517	436	17	compactness	compactness	NOUN
iajs-2517	436	18	via	via	ADP
iajs-2517	436	19	soft	soft	ADJ
iajs-2517	436	20	ideals	ideal	NOUN
iajs-2517	436	21	.	.	PUNCT
iajs-2517	437	1	jou	jou	INTJ
iajs-2517	437	2	.	.	PROPN
iajs-2517	437	3	of	of	ADP
iajs-2517	437	4	advances	advance	NOUN
iajs-2517	437	5	in	in	ADP
iajs-2517	437	6	math	math	NOUN
iajs-2517	437	7	.	.	PUNCT
iajs-2517	438	1	2016	2016	NUM
iajs-2517	438	2	,	,	PUNCT
iajs-2517	438	3	12,4	12,4	NUM
iajs-2517	438	4	,	,	PUNCT
iajs-2517	438	5	6178	6178	NUM
iajs-2517	438	6	-	-	SYM
iajs-2517	438	7	6184	6184	NUM
iajs-2517	438	8	.	.	PUNCT
iajs-2517	439	1	7	7	X
iajs-2517	439	2	.	.	X
iajs-2517	439	3	esmaeel	esmaeel	PROPN
iajs-2517	439	4	,	,	PUNCT
iajs-2517	439	5	r.	r.	PROPN
iajs-2517	439	6	b.	b.	PROPN
iajs-2517	439	7	;	;	PUNCT
iajs-2517	439	8	naser	naser	PROPN
iajs-2517	439	9	,	,	PUNCT
iajs-2517	439	10	a.	a.	NOUN
iajs-2517	439	11	i.	i.	PROPN
iajs-2517	439	12	some	some	DET
iajs-2517	439	13	properties	property	NOUN
iajs-2517	439	14	of	of	ADP
iajs-2517	439	15	-	-	PUNCT
iajs-2517	439	16	ĩ	ĩ	NOUN
iajs-2517	439	17	-	-	PUNCT
iajs-2517	439	18	semi	semi	ADV
iajs-2517	439	19	open	open	ADJ
iajs-2517	439	20	soft	soft	ADJ
iajs-2517	439	21	sets	set	NOUN
iajs-2517	439	22	with	with	ADP
iajs-2517	439	23	respect	respect	NOUN
iajs-2517	439	24	to	to	ADP
iajs-2517	439	25	soft	soft	ADJ
iajs-2517	439	26	ideals	ideal	NOUN
iajs-2517	439	27	.	.	PUNCT
iajs-2517	440	1	ijpam	ijpam	NOUN
iajs-2517	440	2	.	.	PUNCT
iajs-2517	441	1	2016	2016	NUM
iajs-2517	441	2	,	,	PUNCT
iajs-2517	441	3	4	4	NUM
iajs-2517	441	4	,	,	PUNCT
iajs-2517	441	5	545	545	NUM
iajs-2517	441	6	-	-	SYM
iajs-2517	441	7	561	561	NUM
iajs-2517	441	8	.	.	NOUN
iajs-2517	442	1	8	8	NUM
iajs-2517	442	2	.	.	X
iajs-2517	442	3	esmaeel	esmaeel	PROPN
iajs-2517	442	4	,	,	PUNCT
iajs-2517	442	5	r.	r.	PROPN
iajs-2517	442	6	b.	b.	PROPN
iajs-2517	442	7	;	;	PUNCT
iajs-2517	443	1	nasir	nasir	PROPN
iajs-2517	443	2	,	,	PUNCT
iajs-2517	443	3	a.	a.	PROPN
iajs-2517	443	4	i	i	PROPN
iajs-2517	443	5	;	;	PUNCT
iajs-2517	443	6	bayda	bayda	VERB
iajs-2517	443	7	atiya	atiya	PROPN
iajs-2517	443	8	kalaf	kalaf	PROPN
iajs-2517	443	9	.	.	PUNCT
iajs-2517	444	1	on	on	ADP
iajs-2517	444	2	α	α	PROPN
iajs-2517	444	3	-	-	PUNCT
iajs-2517	444	4	gĩ	gĩ	PRON
iajs-2517	444	5	-	-	PUNCT
iajs-2517	444	6	closed	close	VERB
iajs-2517	444	7	soft	soft	ADJ
iajs-2517	444	8	sets	set	NOUN
iajs-2517	444	9	.	.	PUNCT
iajs-2517	445	1	sci	sci	PROPN
iajs-2517	445	2	.	.	PUNCT
iajs-2517	445	3	inter	inter	PROPN
iajs-2517	445	4	.	.	PUNCT
iajs-2517	446	1	(	(	PUNCT
iajs-2517	446	2	lahore	lahore	NOUN
iajs-2517	446	3	)	)	PUNCT
iajs-2517	446	4	.	.	PUNCT
iajs-2517	447	1	2018	2018	NUM
iajs-2517	447	2	,	,	PUNCT
iajs-2517	447	3	30,5	30,5	NOUN
iajs-2517	447	4	,	,	PUNCT
iajs-2517	447	5	703	703	NUM
iajs-2517	447	6	-	-	SYM
iajs-2517	447	7	705	705	NUM
iajs-2517	447	8	.	.	PUNCT
iajs-2517	448	1	9	9	NUM
iajs-2517	448	2	.	.	X
iajs-2517	448	3	maji	maji	PROPN
iajs-2517	448	4	,	,	PUNCT
iajs-2517	448	5	p.	p.	PROPN
iajs-2517	448	6	k.	k.	PROPN
iajs-2517	448	7	;	;	PUNCT
iajs-2517	449	1	biswas	biswas	PROPN
iajs-2517	449	2	,	,	PUNCT
iajs-2517	449	3	r	r	PROPN
iajs-2517	449	4	;	;	PUNCT
iajs-2517	449	5	roy	roy	PROPN
iajs-2517	449	6	,	,	PUNCT
iajs-2517	449	7	a.r	a.r	PROPN
iajs-2517	449	8	.	.	PROPN
iajs-2517	449	9	soft	soft	ADJ
iajs-2517	449	10	set	set	NOUN
iajs-2517	449	11	theory	theory	NOUN
iajs-2517	449	12	.	.	PUNCT
iajs-2517	449	13	com	com	PROPN
iajs-2517	450	1	put	put	PROPN
iajs-2517	450	2	.	.	PUNCT
iajs-2517	451	1	math	math	NOUN
iajs-2517	451	2	.	.	PUNCT
iajs-2517	452	1	appl	appl	PROPN
iajs-2517	452	2	.	.	PROPN
iajs-2517	453	1	2003	2003	NUM
iajs-2517	453	2	,	,	PUNCT
iajs-2517	453	3	45	45	NUM
iajs-2517	453	4	,	,	PUNCT
iajs-2517	453	5	555562	555562	NUM
iajs-2517	453	6	.	.	PUNCT
iajs-2517	454	1	10	10	NUM
iajs-2517	454	2	.	.	X
iajs-2517	454	3	ali	ali	PROPN
iajs-2517	454	4	,	,	PUNCT
iajs-2517	454	5	m.	m.	NOUN
iajs-2517	454	6	i.	i.	PROPN
iajs-2517	454	7	;	;	PUNCT
iajs-2517	454	8	feng	feng	PROPN
iajs-2517	454	9	,	,	PUNCT
iajs-2517	454	10	f.	f.	PROPN
iajs-2517	454	11	;	;	PUNCT
iajs-2517	454	12	liu	liu	PROPN
iajs-2517	454	13	,	,	PUNCT
iajs-2517	454	14	x.	x.	PROPN
iajs-2517	454	15	;	;	PUNCT
iajs-2517	454	16	min	min	PROPN
iajs-2517	454	17	,	,	PUNCT
iajs-2517	454	18	w.	w.	PROPN
iajs-2517	454	19	k	k	PROPN
iajs-2517	454	20	;	;	PUNCT
iajs-2517	454	21	shaber	shaber	NOUN
iajs-2517	454	22	,	,	PUNCT
iajs-2517	454	23	m.	m.	NOUN
iajs-2517	454	24	on	on	ADP
iajs-2517	454	25	some	some	DET
iajs-2517	454	26	new	new	ADJ
iajs-2517	454	27	operations	operation	NOUN
iajs-2517	454	28	in	in	ADP
iajs-2517	454	29	soft	soft	ADJ
iajs-2517	454	30	set	set	NOUN
iajs-2517	454	31	theory	theory	NOUN
iajs-2517	454	32	.com	.com	PROPN
iajs-2517	454	33	put	put	VERB
iajs-2517	454	34	.	.	PUNCT
iajs-2517	455	1	math	math	NOUN
iajs-2517	455	2	.	.	PUNCT
iajs-2517	456	1	apple	apple	NOUN
iajs-2517	456	2	.	.	PUNCT
iajs-2517	457	1	2009	2009	NUM
iajs-2517	457	2	,	,	PUNCT
iajs-2517	457	3	57,9	57,9	NUM
iajs-2517	457	4	,	,	PUNCT
iajs-2517	457	5	1547	1547	NUM
iajs-2517	457	6	-	-	SYM
iajs-2517	457	7	1553	1553	NUM
iajs-2517	457	8	.	.	PUNCT
iajs-2517	458	1	11	11	NUM
iajs-2517	458	2	.	.	X
iajs-2517	459	1	zorlutuna	zorlutuna	PROPN
iajs-2517	459	2	,	,	PUNCT
iajs-2517	459	3	i.	i.	PROPN
iajs-2517	459	4	;	;	PUNCT
iajs-2517	459	5	akdag	akdag	PROPN
iajs-2517	459	6	,	,	PUNCT
iajs-2517	459	7	m.	m.	NOUN
iajs-2517	459	8	;	;	PUNCT
iajs-2517	459	9	min	min	PROPN
iajs-2517	459	10	,	,	PUNCT
iajs-2517	459	11	w.	w.	PROPN
iajs-2517	459	12	k	k	PROPN
iajs-2517	459	13	;	;	PUNCT
iajs-2517	459	14	atmaca	atmaca	PROPN
iajs-2517	459	15	,	,	PUNCT
iajs-2517	459	16	s.	s.	PROPN
iajs-2517	459	17	remark	remark	VERB
iajs-2517	459	18	on	on	ADP
iajs-2517	459	19	soft	soft	ADJ
iajs-2517	459	20	topological	topological	ADJ
iajs-2517	459	21	spaces	space	NOUN
iajs-2517	459	22	,	,	PUNCT
iajs-2517	459	23	ann	ann	PROPN
iajs-2517	459	24	.	.	PROPN
iajs-2517	459	25	fuzzy	fuzzy	ADJ
iajs-2517	459	26	math	math	NOUN
iajs-2517	459	27	.	.	PUNCT
iajs-2517	460	1	in	in	ADP
iajs-2517	460	2	form	form	NOUN
iajs-2517	460	3	.	.	PUNCT
iajs-2517	461	1	2012	2012	NUM
iajs-2517	461	2	,	,	PUNCT
iajs-2517	461	3	3,2	3,2	NUM
iajs-2517	461	4	,	,	PUNCT
iajs-2517	461	5	171	171	NUM
iajs-2517	461	6	-	-	SYM
iajs-2517	461	7	185	185	NUM
iajs-2517	461	8	.	.	PUNCT
iajs-2517	462	1	12	12	NUM
iajs-2517	462	2	.	.	PUNCT
iajs-2517	462	3	saziye	saziye	PROPN
iajs-2517	462	4	yuksel	yuksel	PROPN
iajs-2517	462	5	.	.	PUNCT
iajs-2517	462	6	;	;	PUNCT
iajs-2517	463	1	naime	naime	PROPN
iajs-2517	463	2	tozlu	tozlu	PROPN
iajs-2517	463	3	.	.	PUNCT
iajs-2517	463	4	;	;	PUNCT
iajs-2517	463	5	zehra	zehra	PROPN
iajs-2517	463	6	guzel	guzel	PROPN
iajs-2517	463	7	ergul	ergul	NOUN
iajs-2517	463	8	.	.	PUNCT
iajs-2517	464	1	soft	soft	ADJ
iajs-2517	464	2	regular	regular	ADJ
iajs-2517	464	3	generalized	generalized	ADJ
iajs-2517	464	4	closed	close	VERB
iajs-2517	464	5	sets	set	NOUN
iajs-2517	464	6	in	in	ADP
iajs-2517	464	7	soft	soft	ADJ
iajs-2517	464	8	topological	topological	ADJ
iajs-2517	464	9	spaces	space	NOUN
iajs-2517	464	10	.	.	PUNCT
iajs-2517	465	1	int	int	NOUN
iajs-2517	465	2	.	.	PUNCT
iajs-2517	466	1	journal	journal	PROPN
iajs-2517	466	2	of	of	ADP
iajs-2517	466	3	math	math	NOUN
iajs-2517	466	4	.	.	PUNCT
iajs-2517	467	1	analysis	analysis	NOUN
iajs-2517	467	2	.	.	PUNCT
iajs-2517	468	1	2014	2014	NUM
iajs-2517	468	2	,	,	PUNCT
iajs-2517	468	3	8	8	NUM
iajs-2517	468	4	,	,	PUNCT
iajs-2517	468	5	8	8	NUM
iajs-2517	468	6	,	,	PUNCT
iajs-2517	468	7	355	355	NUM
iajs-2517	468	8	-	-	SYM
iajs-2517	468	9	367	367	NUM
iajs-2517	468	10	.	.	PUNCT