id	sid	tid	token	lemma	pos
iajs-2707	1	1	108	108	NUM
iajs-2707	1	2	some	some	DET
iajs-2707	1	3	results	result	NOUN
iajs-2707	1	4	via	via	ADP
iajs-2707	1	5	gril	gril	NOUN
iajs-2707	1	6	semi	semi	ADV
iajs-2707	1	7	–	–	PUNCT
iajs-2707	1	8	p	p	ADJ
iajs-2707	1	9	-	-	PUNCT
iajs-2707	1	10	open	open	ADJ
iajs-2707	1	11	set	set	NOUN
iajs-2707	1	12	abstract	abstract	NOUN
iajs-2707	1	13	the	the	DET
iajs-2707	1	14	significance	significance	NOUN
iajs-2707	1	15	of	of	ADP
iajs-2707	1	16	the	the	DET
iajs-2707	1	17	work	work	NOUN
iajs-2707	1	18	is	be	AUX
iajs-2707	1	19	to	to	PART
iajs-2707	1	20	introduce	introduce	VERB
iajs-2707	1	21	the	the	DET
iajs-2707	1	22	new	new	ADJ
iajs-2707	1	23	class	class	NOUN
iajs-2707	1	24	of	of	ADP
iajs-2707	1	25	open	open	ADJ
iajs-2707	1	26	sets	set	NOUN
iajs-2707	1	27	,	,	PUNCT
iajs-2707	1	28	which	which	PRON
iajs-2707	1	29	is	be	AUX
iajs-2707	1	30	said	say	VERB
iajs-2707	1	31	ǥ𝑠𝑝-open	ǥ𝑠𝑝-open	ADJ
iajs-2707	1	32	set	set	NOUN
iajs-2707	1	33	with	with	ADP
iajs-2707	1	34	some	some	PRON
iajs-2707	1	35	of	of	ADP
iajs-2707	1	36	properties	property	NOUN
iajs-2707	1	37	.	.	PUNCT
iajs-2707	2	1	then	then	ADV
iajs-2707	2	2	clarify	clarify	VERB
iajs-2707	2	3	how	how	SCONJ
iajs-2707	2	4	to	to	PART
iajs-2707	2	5	calculate	calculate	VERB
iajs-2707	2	6	the	the	DET
iajs-2707	2	7	boundary	boundary	ADJ
iajs-2707	2	8	area	area	NOUN
iajs-2707	2	9	for	for	ADP
iajs-2707	2	10	these	these	DET
iajs-2707	2	11	sets	set	NOUN
iajs-2707	2	12	using	use	VERB
iajs-2707	2	13	the	the	DET
iajs-2707	2	14	upper	upper	ADJ
iajs-2707	2	15	and	and	CCONJ
iajs-2707	2	16	lower	low	ADJ
iajs-2707	2	17	approximation	approximation	NOUN
iajs-2707	2	18	and	and	CCONJ
iajs-2707	2	19	obtain	obtain	VERB
iajs-2707	2	20	the	the	DET
iajs-2707	2	21	best	good	ADJ
iajs-2707	2	22	accuracy	accuracy	NOUN
iajs-2707	2	23	.	.	PUNCT
iajs-2707	3	1	keywords	keyword	NOUN
iajs-2707	3	2	.	.	PUNCT
iajs-2707	4	1	ǥ	ǥ	X
iajs-2707	4	2	-	-	PUNCT
iajs-2707	4	3	semi	semi	ADJ
iajs-2707	4	4	-	-	ADJ
iajs-2707	4	5	p	p	ADJ
iajs-2707	4	6	open	open	ADJ
iajs-2707	4	7	set	set	NOUN
iajs-2707	4	8	,	,	PUNCT
iajs-2707	4	9	ǥsemi	ǥsemi	ADV
iajs-2707	4	10	-	-	PUNCT
iajs-2707	4	11	p	p	ADJ
iajs-2707	4	12	closed	closed	ADJ
iajs-2707	4	13	set	set	VERB
iajs-2707	4	14	,	,	PUNCT
iajs-2707	4	15	𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦	𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦	ADJ
iajs-2707	4	16	𝑠𝑒𝑎𝑠𝑢𝑟𝑒	𝑠𝑒𝑎𝑠𝑢𝑟𝑒	NOUN
iajs-2707	4	17	𝔐(μ	𝔐(μ	NUM
iajs-2707	4	18	)	)	PUNCT
iajs-2707	4	19	.	.	PUNCT
iajs-2707	5	1	1.introduction	1.introduction	NUM
iajs-2707	5	2	a	a	DET
iajs-2707	5	3	nonempty	nonempty	ADJ
iajs-2707	5	4	family	family	NOUN
iajs-2707	5	5	g	g	NOUN
iajs-2707	5	6	𝑜𝑓	𝑜𝑓	ADP
iajs-2707	5	7	𝑎	𝑎	X
iajs-2707	5	8	𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙	𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙	ADJ
iajs-2707	5	9	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2707	5	10	ẋ	ẋ	NOUN
iajs-2707	5	11	is	be	AUX
iajs-2707	5	12	named	name	VERB
iajs-2707	5	13	𝑎	𝑎	PRON
iajs-2707	5	14	𝐺𝑟𝑖𝑙𝑙	𝐺𝑟𝑖𝑙𝑙	PROPN
iajs-2707	5	15	whenever	whenever	SCONJ
iajs-2707	5	16	i.	i.	PROPN
iajs-2707	5	17	μ	μ	PROPN
iajs-2707	5	18	∈	∈	PROPN
iajs-2707	5	19	ǥ	ǥ	ADP
iajs-2707	5	20	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2707	5	21	μ	μ	PROPN
iajs-2707	5	22	⊆	⊆	NUM
iajs-2707	5	23	ѕ	ѕ	PROPN
iajs-2707	5	24	⊆	⊆	NUM
iajs-2707	5	25	ẋ	ẋ	NOUN
iajs-2707	5	26	then	then	ADV
iajs-2707	5	27	ѕ	ѕ	PROPN
iajs-2707	5	28	∈	∈	PROPN
iajs-2707	5	29	ǥ	ǥ	PROPN
iajs-2707	5	30	.	.	PUNCT
iajs-2707	5	31	ii	ii	PROPN
iajs-2707	5	32	.	.	PUNCT
iajs-2707	6	1	μ	μ	PROPN
iajs-2707	6	2	,	,	PUNCT
iajs-2707	6	3	ѕ	ѕ	PROPN
iajs-2707	6	4	⊆	⊆	NUM
iajs-2707	6	5	ẋ	ẋ	DET
iajs-2707	6	6	∧	∧	PROPN
iajs-2707	6	7	μ	μ	PROPN
iajs-2707	6	8	∪	∪	ADP
iajs-2707	6	9	ѕ	ѕ	PROPN
iajs-2707	6	10	∈	∈	PROPN
iajs-2707	6	11	ǥ	ǥ	NOUN
iajs-2707	6	12	then	then	ADV
iajs-2707	6	13	μ	μ	PROPN
iajs-2707	6	14	∈	∈	PROPN
iajs-2707	6	15	ǥ	ǥ	ADP
iajs-2707	6	16	∨	∨	NUM
iajs-2707	6	17	ѕ	ѕ	PROPN
iajs-2707	6	18	∈	∈	PROPN
iajs-2707	6	19	ǥ	ǥ	NOUN
iajs-2707	6	20	.	.	PUNCT
iajs-2707	7	1	[	[	X
iajs-2707	7	2	1	1	X
iajs-2707	7	3	]	]	PUNCT
iajs-2707	7	4	suppose	suppose	VERB
iajs-2707	7	5	that	that	SCONJ
iajs-2707	7	6	ẋ	ẋ	NOUN
iajs-2707	7	7	is	be	AUX
iajs-2707	7	8	a	a	DET
iajs-2707	7	9	nonempty	nonempty	ADJ
iajs-2707	7	10	set	set	NOUN
iajs-2707	7	11	,	,	PUNCT
iajs-2707	7	12	then	then	ADV
iajs-2707	7	13	the	the	DET
iajs-2707	7	14	following	follow	VERB
iajs-2707	7	15	families	family	NOUN
iajs-2707	7	16	are	be	AUX
iajs-2707	7	17	grills	grill	NOUN
iajs-2707	7	18	on	on	ADP
iajs-2707	7	19	ẋ	ẋ	NOUN
iajs-2707	7	20	.	.	PUNCT
iajs-2707	8	1	[	[	X
iajs-2707	8	2	1	1	NUM
iajs-2707	8	3	-	-	SYM
iajs-2707	8	4	3	3	NUM
iajs-2707	8	5	]	]	SYM
iajs-2707	8	6	∅	∅	NOUN
iajs-2707	8	7	and	and	CCONJ
iajs-2707	8	8	p(ẋ	p(ẋ	PROPN
iajs-2707	8	9	)	)	PUNCT
iajs-2707	8	10	\	\	NOUN
iajs-2707	8	11	{	{	PUNCT
iajs-2707	8	12	∅	∅	NOUN
iajs-2707	8	13	}	}	PUNCT
iajs-2707	8	14	are	be	AUX
iajs-2707	8	15	trivial	trivial	ADJ
iajs-2707	8	16	examples	example	NOUN
iajs-2707	8	17	of	of	ADP
iajs-2707	8	18	a	a	DET
iajs-2707	8	19	grill	grill	NOUN
iajs-2707	8	20	on	on	ADP
iajs-2707	8	21	ẋ	ẋ	DET
iajs-2707	8	22	ǥ∞which	ǥ∞which	PROPN
iajs-2707	8	23	is	be	AUX
iajs-2707	8	24	the	the	DET
iajs-2707	8	25	collection	collection	NOUN
iajs-2707	8	26	of	of	ADP
iajs-2707	8	27	all	all	DET
iajs-2707	8	28	infinite	infinite	ADJ
iajs-2707	8	29	subsets	subset	NOUN
iajs-2707	8	30	of	of	ADP
iajs-2707	8	31	ẋ	ẋ	PROPN
iajs-2707	8	32	.	.	PROPN
iajs-2707	8	33	ǥ𝑐𝑜which	ǥ𝑐𝑜which	PROPN
iajs-2707	8	34	is	be	AUX
iajs-2707	8	35	the	the	DET
iajs-2707	8	36	collection	collection	NOUN
iajs-2707	8	37	of	of	ADP
iajs-2707	8	38	all	all	DET
iajs-2707	8	39	uncountable	uncountable	ADJ
iajs-2707	8	40	subsets	subset	NOUN
iajs-2707	8	41	of	of	ADP
iajs-2707	8	42	ẋ	ẋ	PROPN
iajs-2707	8	43	.	.	PUNCT
iajs-2707	8	44	ǥ𝑝=	ǥ𝑝=	PROPN
iajs-2707	8	45	{	{	PUNCT
iajs-2707	8	46	ʌ	ʌ	PROPN
iajs-2707	8	47	:	:	PUNCT
iajs-2707	8	48	ʌ∈	ʌ∈	PROPN
iajs-2707	8	49	p(ẋ	p(ẋ	PROPN
iajs-2707	8	50	)	)	PUNCT
iajs-2707	8	51	,	,	PUNCT
iajs-2707	8	52	p	p	NOUN
iajs-2707	8	53	⊆	⊆	NUM
iajs-2707	8	54	ʌ	ʌ	PROPN
iajs-2707	8	55	}	}	PUNCT
iajs-2707	8	56	is	be	AUX
iajs-2707	8	57	a	a	DET
iajs-2707	8	58	specific	specific	ADJ
iajs-2707	8	59	point	point	NOUN
iajs-2707	8	60	grill	grill	NOUN
iajs-2707	8	61	on	on	ADP
iajs-2707	8	62	ẋ	ẋ	PROPN
iajs-2707	8	63	.	.	PUNCT
iajs-2707	8	64	ǥά=	ǥά=	PROPN
iajs-2707	8	65	{	{	PUNCT
iajs-2707	8	66	ѕ	ѕ	NOUN
iajs-2707	8	67	:	:	PUNCT
iajs-2707	8	68	ѕ∈p(ẋ	ѕ∈p(ẋ	PROPN
iajs-2707	8	69	)	)	PUNCT
iajs-2707	8	70	,	,	PUNCT
iajs-2707	8	71	ѕ∩μ	ѕ∩μ	ADJ
iajs-2707	8	72	≠	≠	PROPN
iajs-2707	8	73	∅	∅	NOUN
iajs-2707	8	74	}	}	PUNCT
iajs-2707	8	75	,	,	PUNCT
iajs-2707	8	76	and	and	CCONJ
iajs-2707	8	77	if	if	SCONJ
iajs-2707	8	78	(	(	PUNCT
iajs-2707	8	79	ẋ	ẋ	X
iajs-2707	8	80	,	,	PUNCT
iajs-2707	8	81	𝒯	𝒯	PROPN
iajs-2707	8	82	)	)	PUNCT
iajs-2707	8	83	is	be	AUX
iajs-2707	8	84	a	a	DET
iajs-2707	8	85	topological	topological	ADJ
iajs-2707	8	86	space	space	NOUN
iajs-2707	8	87	,	,	PUNCT
iajs-2707	8	88	then	then	ADV
iajs-2707	8	89	the	the	DET
iajs-2707	8	90	family	family	NOUN
iajs-2707	8	91	of	of	ADP
iajs-2707	8	92	all	all	DET
iajs-2707	8	93	non	non	ADJ
iajs-2707	8	94	-	-	ADJ
iajs-2707	8	95	nowhere	nowhere	ADJ
iajs-2707	8	96	dense	dense	ADJ
iajs-2707	8	97	subsets	subset	NOUN
iajs-2707	8	98	called	call	VERB
iajs-2707	8	99	ǥ=	ǥ=	INTJ
iajs-2707	8	100	{	{	PUNCT
iajs-2707	8	101	μ:𝑖𝑛𝑡𝒯	μ:𝑖𝑛𝑡𝒯	PROPN
iajs-2707	8	102	𝑐𝑙𝒯(𝛭	𝑐𝑙𝒯(𝛭	PROPN
iajs-2707	8	103	)	)	PUNCT
iajs-2707	8	104	≠	≠	PROPN
iajs-2707	8	105	∅	∅	NOUN
iajs-2707	8	106	}	}	PUNCT
iajs-2707	8	107	is	be	AUX
iajs-2707	8	108	the	the	DET
iajs-2707	8	109	one	one	NUM
iajs-2707	8	110	of	of	ADP
iajs-2707	8	111	kinds	kind	NOUN
iajs-2707	8	112	of	of	ADP
iajs-2707	8	113	a	a	DET
iajs-2707	8	114	grill	grill	NOUN
iajs-2707	8	115	on	on	ADP
iajs-2707	8	116	ẋ	ẋ	PRON
iajs-2707	8	117	.	.	PUNCT
iajs-2707	8	118	suppose	suppose	VERB
iajs-2707	8	119	that	that	SCONJ
iajs-2707	8	120	ǥ	ǥ	PROPN
iajs-2707	8	121	is	be	AUX
iajs-2707	8	122	a	a	DET
iajs-2707	8	123	grill	grill	NOUN
iajs-2707	8	124	on	on	ADP
iajs-2707	8	125	(	(	PUNCT
iajs-2707	8	126	ẋ,𝒯	ẋ,𝒯	NOUN
iajs-2707	8	127	)	)	PUNCT
iajs-2707	8	128	the	the	DET
iajs-2707	8	129	operator	operator	NOUN
iajs-2707	8	130	ǿ	ǿ	NOUN
iajs-2707	8	131	:	:	PUNCT
iajs-2707	8	132	p(ẋ)→p(ẋ	p(ẋ)→p(ẋ	PROPN
iajs-2707	8	133	)	)	PUNCT
iajs-2707	8	134	is	be	AUX
iajs-2707	8	135	defined	define	VERB
iajs-2707	8	136	by	by	ADP
iajs-2707	8	137	ǿ	ǿ	PROPN
iajs-2707	8	138	(	(	PUNCT
iajs-2707	8	139	μ)={x	μ)={x	NOUN
iajs-2707	8	140	∈	∈	PROPN
iajs-2707	8	141	ẋ\	ẋ\	PUNCT
iajs-2707	8	142	ủ	ủ	PROPN
iajs-2707	8	143	∩	∩	NOUN
iajs-2707	8	144	μ	μ	NOUN
iajs-2707	8	145	∈	∈	PROPN
iajs-2707	8	146	ǥ	ǥ	NOUN
iajs-2707	8	147	,	,	PUNCT
iajs-2707	8	148	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2707	8	149	𝑎𝑙𝑙	𝑎𝑙𝑙	VERB
iajs-2707	8	150	ủ	ủ	PROPN
iajs-2707	8	151	∈	∈	PROPN
iajs-2707	8	152	𝒯(ẋ)},𝒯(ẋ	𝒯(ẋ)},𝒯(ẋ	NOUN
iajs-2707	8	153	)	)	PUNCT
iajs-2707	8	154	indicate	indicate	VERB
iajs-2707	8	155	the	the	DET
iajs-2707	8	156	neighborhood	neighborhood	NOUN
iajs-2707	8	157	of	of	ADP
iajs-2707	8	158	x.	x.	NOUN
iajs-2707	8	159	a	a	DET
iajs-2707	8	160	mapping	mapping	NOUN
iajs-2707	8	161	ѱ	ѱ	NOUN
iajs-2707	8	162	:	:	PUNCT
iajs-2707	8	163	p(ẋ)→p(ẋ	p(ẋ)→p(ẋ	PROPN
iajs-2707	8	164	)	)	PUNCT
iajs-2707	8	165	is	be	AUX
iajs-2707	8	166	defined	define	VERB
iajs-2707	8	167	as	as	ADP
iajs-2707	8	168	ѱ	ѱ	PROPN
iajs-2707	8	169	(	(	PUNCT
iajs-2707	8	170	μ	μ	NOUN
iajs-2707	8	171	)	)	PUNCT
iajs-2707	9	1	=	=	SYM
iajs-2707	9	2	μ	μ	PROPN
iajs-2707	9	3	∪	∪	VERB
iajs-2707	9	4	ǿ	ǿ	PROPN
iajs-2707	9	5	(	(	PUNCT
iajs-2707	9	6	μ	μ	NOUN
iajs-2707	9	7	)	)	PUNCT
iajs-2707	9	8	for	for	ADP
iajs-2707	9	9	all	all	DET
iajs-2707	9	10	μ	μ	PROPN
iajs-2707	9	11	∈	∈	PROPN
iajs-2707	9	12	p(ẋ).[4,5	p(ẋ).[4,5	VERB
iajs-2707	9	13	]	]	X
iajs-2707	9	14	𝑇ℎ𝑒	𝑇ℎ𝑒	PROPN
iajs-2707	9	15	𝑠𝑎𝑝	𝑠𝑎𝑝	VERB
iajs-2707	9	16	ѱ	ѱ	NOUN
iajs-2707	9	17	satisfies	satisfie	NOUN
iajs-2707	9	18	kuratowski	kuratowski	PROPN
iajs-2707	9	19	closure	closure	NOUN
iajs-2707	9	20	axioms	axiom	NOUN
iajs-2707	9	21	:	:	PUNCT
iajs-2707	10	1	[	[	X
iajs-2707	10	2	3,4	3,4	NUM
iajs-2707	10	3	]	]	SYM
iajs-2707	10	4	1	1	NUM
iajs-2707	10	5	.	.	PUNCT
iajs-2707	10	6	ѱ	ѱ	NOUN
iajs-2707	10	7	(	(	PUNCT
iajs-2707	10	8	∅	∅	NOUN
iajs-2707	10	9	)	)	PUNCT
iajs-2707	10	10	=	=	NOUN
iajs-2707	10	11	∅	∅	NOUN
iajs-2707	10	12	doi	doi	NOUN
iajs-2707	10	13	:	:	PUNCT
iajs-2707	10	14	10.30526/34.4.2707	10.30526/34.4.2707	NUM
iajs-2707	10	15	article	article	NOUN
iajs-2707	10	16	history	history	NOUN
iajs-2707	10	17	:	:	PUNCT
iajs-2707	10	18	received	receive	VERB
iajs-2707	10	19	9	9	NUM
iajs-2707	10	20	,	,	PUNCT
iajs-2707	10	21	april,2021	april,2021	NOUN
iajs-2707	10	22	,	,	PUNCT
iajs-2707	10	23	accepted	accept	VERB
iajs-2707	10	24	29,june,2021	29,june,2021	NUM
iajs-2707	10	25	,	,	PUNCT
iajs-2707	10	26	published	publish	VERB
iajs-2707	10	27	in	in	ADP
iajs-2707	10	28	october	october	PROPN
iajs-2707	10	29	2021	2021	NUM
iajs-2707	10	30	.	.	PUNCT
iajs-2707	11	1	ibn	ibn	PROPN
iajs-2707	11	2	al	al	PROPN
iajs-2707	11	3	haitham	haitham	PROPN
iajs-2707	11	4	journal	journal	PROPN
iajs-2707	11	5	for	for	ADP
iajs-2707	11	6	pure	pure	ADJ
iajs-2707	11	7	and	and	CCONJ
iajs-2707	11	8	applied	apply	VERB
iajs-2707	11	9	science	science	NOUN
iajs-2707	11	10	journal	journal	PROPN
iajs-2707	11	11	homepage	homepage	NOUN
iajs-2707	11	12	:	:	PUNCT
iajs-2707	11	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2707	11	14	esmaeel	esmaeel	NOUN
iajs-2707	11	15	r.b	r.b	PROPN
iajs-2707	11	16	.	.	PROPN
iajs-2707	11	17	department	department	PROPN
iajs-2707	11	18	of	of	ADP
iajs-2707	11	19	mathematics	mathematics	PROPN
iajs-2707	11	20	,	,	PUNCT
iajs-2707	11	21	college	college	NOUN
iajs-2707	11	22	of	of	ADP
iajs-2707	11	23	education	education	NOUN
iajs-2707	11	24	for	for	ADP
iajs-2707	11	25	pure	pure	ADJ
iajs-2707	11	26	science	science	NOUN
iajs-2707	11	27	ibn	ibn	PROPN
iajs-2707	11	28	alhaitham	alhaitham	PROPN
iajs-2707	11	29	university	university	PROPN
iajs-2707	11	30	of	of	ADP
iajs-2707	11	31	baghdad	baghdad	PROPN
iajs-2707	11	32	,	,	PUNCT
iajs-2707	11	33	iraq	iraq	PROPN
iajs-2707	11	34	.	.	PUNCT
iajs-2707	12	1	ranamumosa@yahoo.com	ranamumosa@yahoo.com	X
iajs-2707	12	2	shahadhuh	shahadhuh	PROPN
iajs-2707	13	1	n.m	n.m	PROPN
iajs-2707	13	2	.	.	PROPN
iajs-2707	13	3	department	department	PROPN
iajs-2707	13	4	of	of	ADP
iajs-2707	13	5	mathematics	mathematics	PROPN
iajs-2707	13	6	,	,	PUNCT
iajs-2707	13	7	college	college	NOUN
iajs-2707	13	8	of	of	ADP
iajs-2707	13	9	education	education	NOUN
iajs-2707	13	10	for	for	ADP
iajs-2707	13	11	pure	pure	ADJ
iajs-2707	13	12	science	science	NOUN
iajs-2707	13	13	ibn	ibn	PROPN
iajs-2707	13	14	al	al	PROPN
iajs-2707	13	15	-	-	PUNCT
iajs-2707	13	16	haitham	haitham	PROPN
iajs-2707	13	17	university	university	PROPN
iajs-2707	13	18	of	of	ADP
iajs-2707	13	19	baghdad	baghdad	PROPN
iajs-2707	13	20	,	,	PUNCT
iajs-2707	13	21	iraq	iraq	PROPN
iajs-2707	13	22	.	.	PUNCT
iajs-2707	14	1	noora1993327@gmail.com	noora1993327@gmail.com	X
iajs-2707	15	1	mailto:ranamumosa@yahoo.com	mailto:ranamumosa@yahoo.com	X
iajs-2707	16	1	mailto:noora1993327@gmail.com	mailto:noora1993327@gmail.com	X
iajs-2707	16	2	ibn	ibn	PROPN
iajs-2707	16	3	al	al	PROPN
iajs-2707	16	4	-	-	PUNCT
iajs-2707	16	5	haitham	haitham	PROPN
iajs-2707	16	6	jour	jour	X
iajs-2707	16	7	.	.	PROPN
iajs-2707	16	8	for	for	ADP
iajs-2707	16	9	pure	pure	ADJ
iajs-2707	16	10	&	&	CCONJ
iajs-2707	16	11	appl	appl	PROPN
iajs-2707	16	12	.	.	PUNCT
iajs-2707	17	1	sci	sci	PROPN
iajs-2707	17	2	.	.	PROPN
iajs-2707	18	1	34(4)2021	34(4)2021	NUM
iajs-2707	18	2	109	109	NUM
iajs-2707	18	3	2	2	NUM
iajs-2707	18	4	.	.	PUNCT
iajs-2707	19	1	if	if	SCONJ
iajs-2707	19	2	μ	μ	PROPN
iajs-2707	19	3	⊆ѕ	⊆ѕ	PROPN
iajs-2707	19	4	,	,	PUNCT
iajs-2707	19	5	then	then	ADV
iajs-2707	19	6	ѱ	ѱ	PROPN
iajs-2707	19	7	(	(	PUNCT
iajs-2707	19	8	μ	μ	NOUN
iajs-2707	19	9	)	)	PUNCT
iajs-2707	19	10	⊆	⊆	NUM
iajs-2707	19	11	ѱ(ѕ	ѱ(ѕ	NOUN
iajs-2707	19	12	)	)	PUNCT
iajs-2707	19	13	,	,	PUNCT
iajs-2707	19	14	3	3	X
iajs-2707	19	15	.	.	PUNCT
iajs-2707	20	1	if	if	SCONJ
iajs-2707	20	2	μ	μ	PROPN
iajs-2707	20	3	⊆	⊆	NUM
iajs-2707	20	4	ẋ	ẋ	NOUN
iajs-2707	20	5	,	,	PUNCT
iajs-2707	20	6	then	then	ADV
iajs-2707	20	7	ѱ	ѱ	PROPN
iajs-2707	20	8	(	(	PUNCT
iajs-2707	20	9	ѱ	ѱ	PROPN
iajs-2707	20	10	(	(	PUNCT
iajs-2707	20	11	μ	μ	NOUN
iajs-2707	20	12	)	)	PUNCT
iajs-2707	20	13	)	)	PUNCT
iajs-2707	21	1	=	=	X
iajs-2707	21	2	ѱ	ѱ	X
iajs-2707	21	3	(	(	PUNCT
iajs-2707	21	4	μ	μ	NOUN
iajs-2707	21	5	)	)	PUNCT
iajs-2707	21	6	,	,	PUNCT
iajs-2707	21	7	4	4	X
iajs-2707	21	8	.	.	PUNCT
iajs-2707	22	1	if	if	SCONJ
iajs-2707	22	2	μ	μ	PROPN
iajs-2707	22	3	,	,	PUNCT
iajs-2707	22	4	ѕ	ѕ	PROPN
iajs-2707	22	5	⊆	⊆	NUM
iajs-2707	22	6	ẋ	ẋ	NOUN
iajs-2707	22	7	,	,	PUNCT
iajs-2707	22	8	then	then	ADV
iajs-2707	22	9	ѱ	ѱ	PROPN
iajs-2707	22	10	(	(	PUNCT
iajs-2707	22	11	μ	μ	PROPN
iajs-2707	22	12	∪	∪	X
iajs-2707	22	13	ѕ	ѕ	PROPN
iajs-2707	22	14	)	)	PUNCT
iajs-2707	23	1	=	=	NOUN
iajs-2707	23	2	ѱ	ѱ	X
iajs-2707	23	3	(	(	PUNCT
iajs-2707	23	4	𝛭	𝛭	PROPN
iajs-2707	23	5	)	)	PUNCT
iajs-2707	23	6	∪	∪	NOUN
iajs-2707	23	7	ѱ	ѱ	PROPN
iajs-2707	23	8	(	(	PUNCT
iajs-2707	23	9	ѕ	ѕ	PROPN
iajs-2707	23	10	)	)	PUNCT
iajs-2707	23	11	.	.	PUNCT
iajs-2707	24	1	a	a	DET
iajs-2707	24	2	subset	subset	NOUN
iajs-2707	24	3	μ	μ	PROPN
iajs-2707	24	4	of	of	ADP
iajs-2707	24	5	(	(	PUNCT
iajs-2707	24	6	ẋ,𝒯	ẋ,𝒯	NOUN
iajs-2707	24	7	)	)	PUNCT
iajs-2707	24	8	is	be	AUX
iajs-2707	24	9	a	a	DET
iajs-2707	24	10	preopen	preopen	ADJ
iajs-2707	24	11	set	set	VERB
iajs-2707	24	12	if	if	SCONJ
iajs-2707	24	13	𝛭	𝛭	PROPN
iajs-2707	24	14	⊆	⊆	NUM
iajs-2707	24	15	intcl	intcl	NOUN
iajs-2707	24	16	𝛭	𝛭	VERB
iajs-2707	24	17	the	the	DET
iajs-2707	24	18	complement	complement	NOUN
iajs-2707	24	19	of	of	ADP
iajs-2707	24	20	a	a	DET
iajs-2707	24	21	preopen	preopen	ADJ
iajs-2707	24	22	set	set	NOUN
iajs-2707	24	23	is	be	AUX
iajs-2707	24	24	named	name	VERB
iajs-2707	24	25	preclosed	preclose	VERB
iajs-2707	24	26	set	set	NOUN
iajs-2707	24	27	.	.	PUNCT
iajs-2707	25	1	the	the	DET
iajs-2707	25	2	collection	collection	NOUN
iajs-2707	25	3	of	of	ADP
iajs-2707	25	4	all	all	DET
iajs-2707	25	5	preopen	preopen	ADJ
iajs-2707	25	6	sets	set	NOUN
iajs-2707	25	7	of	of	ADP
iajs-2707	25	8	ẋ	ẋ	NOUN
iajs-2707	25	9	is	be	AUX
iajs-2707	25	10	indicate	indicate	ADJ
iajs-2707	25	11	by	by	ADP
iajs-2707	25	12	po(ẋ	po(ẋ	NOUN
iajs-2707	25	13	)	)	PUNCT
iajs-2707	25	14	.	.	PUNCT
iajs-2707	26	1	the	the	DET
iajs-2707	26	2	collection	collection	NOUN
iajs-2707	26	3	of	of	ADP
iajs-2707	26	4	all	all	DET
iajs-2707	26	5	preclosed	preclose	VERB
iajs-2707	26	6	sets	set	NOUN
iajs-2707	26	7	of	of	ADP
iajs-2707	26	8	ẋ	ẋ	NOUN
iajs-2707	26	9	is	be	AUX
iajs-2707	26	10	indicate	indicate	ADJ
iajs-2707	26	11	by	by	ADP
iajs-2707	26	12	pc(ẋ).[7	pc(ẋ).[7	NOUN
iajs-2707	26	13	]	]	X
iajs-2707	26	14	now	now	ADV
iajs-2707	26	15	,	,	PUNCT
iajs-2707	26	16	pcl=∩	pcl=∩	PROPN
iajs-2707	26	17	{	{	PUNCT
iajs-2707	26	18	μ	μ	PROPN
iajs-2707	26	19	⊆	⊆	NUM
iajs-2707	26	20	ẋ	ẋ	NOUN
iajs-2707	26	21	;	;	PUNCT
iajs-2707	26	22	ủ	ủ	PROPN
iajs-2707	26	23	⊆	⊆	NUM
iajs-2707	26	24	μ	μ	NOUN
iajs-2707	26	25	whenever	whenever	SCONJ
iajs-2707	26	26	μ𝑐	μ𝑐	PROPN
iajs-2707	26	27	∈	∈	PROPN
iajs-2707	26	28	𝑃𝑂(ẋ	𝑃𝑂(ẋ	PROPN
iajs-2707	26	29	)	)	PUNCT
iajs-2707	26	30	}	}	PUNCT
iajs-2707	26	31	.	.	PUNCT
iajs-2707	27	1	[	[	X
iajs-2707	27	2	7	7	X
iajs-2707	27	3	]	]	X
iajs-2707	27	4	a	a	DET
iajs-2707	27	5	subset	subset	NOUN
iajs-2707	27	6	μ	μ	PROPN
iajs-2707	27	7	of	of	ADP
iajs-2707	27	8	(	(	PUNCT
iajs-2707	27	9	ẋ	ẋ	X
iajs-2707	27	10	,	,	PUNCT
iajs-2707	27	11	𝒯	𝒯	PROPN
iajs-2707	27	12	)	)	PUNCT
iajs-2707	27	13	𝑖𝑠	𝑖𝑠	NOUN
iajs-2707	27	14	named	name	VERB
iajs-2707	27	15	semi	semi	ADJ
iajs-2707	27	16	-	-	ADJ
iajs-2707	27	17	p	p	ADJ
iajs-2707	27	18	-	-	PUNCT
iajs-2707	27	19	open	open	NOUN
iajs-2707	27	20	set	set	NOUN
iajs-2707	27	21	,	,	PUNCT
iajs-2707	27	22	if	if	SCONJ
iajs-2707	27	23	and	and	CCONJ
iajs-2707	27	24	only	only	ADV
iajs-2707	27	25	if	if	SCONJ
iajs-2707	27	26	there	there	PRON
iajs-2707	27	27	exists	exist	VERB
iajs-2707	27	28	a	a	DET
iajs-2707	27	29	preopen	preopen	ADJ
iajs-2707	27	30	set	set	NOUN
iajs-2707	27	31	in	in	ADP
iajs-2707	27	32	ẋ	ẋ	PRON
iajs-2707	27	33	say	say	NOUN
iajs-2707	27	34	ụ	ụ	PRON
iajs-2707	27	35	such	such	ADJ
iajs-2707	27	36	that	that	SCONJ
iajs-2707	27	37	ụ	ụ	PROPN
iajs-2707	27	38	⊆	⊆	NUM
iajs-2707	27	39	μ	μ	PROPN
iajs-2707	27	40	⊆	⊆	NUM
iajs-2707	27	41	pcl	pcl	PROPN
iajs-2707	27	42	ụ	ụ	PROPN
iajs-2707	27	43	.	.	PUNCT
iajs-2707	28	1	the	the	DET
iajs-2707	28	2	collection	collection	NOUN
iajs-2707	28	3	of	of	ADP
iajs-2707	28	4	all	all	DET
iajs-2707	28	5	semi	semi	ADJ
iajs-2707	28	6	-	-	ADJ
iajs-2707	28	7	p	p	ADJ
iajs-2707	28	8	-	-	PUNCT
iajs-2707	28	9	open	open	ADJ
iajs-2707	28	10	sets	set	NOUN
iajs-2707	28	11	of	of	ADP
iajs-2707	28	12	ẋ	ẋ	NOUN
iajs-2707	28	13	is	be	AUX
iajs-2707	28	14	indicated	indicate	VERB
iajs-2707	28	15	by	by	ADP
iajs-2707	28	16	s	s	NOUN
iajs-2707	28	17	-	-	PUNCT
iajs-2707	28	18	po(ẋ	po(ẋ	NOUN
iajs-2707	28	19	)	)	PUNCT
iajs-2707	28	20	.	.	PUNCT
iajs-2707	29	1	the	the	DET
iajs-2707	29	2	complement	complement	NOUN
iajs-2707	29	3	of	of	ADP
iajs-2707	29	4	a	a	DET
iajs-2707	29	5	semi	semi	ADJ
iajs-2707	29	6	-	-	ADJ
iajs-2707	29	7	pclosed	pclosed	ADJ
iajs-2707	29	8	set	set	NOUN
iajs-2707	29	9	.	.	PUNCT
iajs-2707	30	1	the	the	DET
iajs-2707	30	2	family	family	NOUN
iajs-2707	30	3	of	of	ADP
iajs-2707	30	4	all	all	DET
iajs-2707	30	5	semi	semi	ADJ
iajs-2707	30	6	-	-	ADJ
iajs-2707	30	7	p	p	ADJ
iajs-2707	30	8	-	-	PUNCT
iajs-2707	30	9	closed	close	VERB
iajs-2707	30	10	sets	set	NOUN
iajs-2707	30	11	of	of	ADP
iajs-2707	30	12	ẋ	ẋ	NOUN
iajs-2707	30	13	is	be	AUX
iajs-2707	30	14	indicate	indicate	NOUN
iajs-2707	30	15	by	by	ADP
iajs-2707	30	16	s	s	NOUN
iajs-2707	30	17	-	-	PUNCT
iajs-2707	30	18	pc(ẋ	pc(ẋ	NOUN
iajs-2707	30	19	)	)	PUNCT
iajs-2707	30	20	.	.	PUNCT
iajs-2707	31	1	[	[	X
iajs-2707	31	2	7	7	X
iajs-2707	31	3	]	]	PUNCT
iajs-2707	31	4	it	it	PRON
iajs-2707	31	5	is	be	AUX
iajs-2707	31	6	clear	clear	ADJ
iajs-2707	31	7	that	that	SCONJ
iajs-2707	31	8	every	every	DET
iajs-2707	31	9	preopen	preopen	ADJ
iajs-2707	31	10	set	set	NOUN
iajs-2707	31	11	is	be	AUX
iajs-2707	31	12	a	a	DET
iajs-2707	31	13	s	s	NOUN
iajs-2707	31	14	-	-	PUNCT
iajs-2707	31	15	po	po	NOUN
iajs-2707	31	16	set	set	NOUN
iajs-2707	31	17	[	[	X
iajs-2707	31	18	7	7	NUM
iajs-2707	31	19	]	]	PUNCT
iajs-2707	31	20	.	.	PUNCT
iajs-2707	32	1	2.preliminaries	2.preliminaries	NUM
iajs-2707	32	2	.	.	PUNCT
iajs-2707	33	1	definition	definition	NOUN
iajs-2707	33	2	2.1	2.1	NUM
iajs-2707	33	3	:	:	PUNCT
iajs-2707	34	1	[	[	X
iajs-2707	34	2	8	8	NUM
iajs-2707	34	3	]	]	PUNCT
iajs-2707	34	4	let	let	VERB
iajs-2707	34	5	ẋ	ẋ	PRON
iajs-2707	34	6	be	be	AUX
iajs-2707	34	7	a	a	DET
iajs-2707	34	8	nonempty	nonempty	ADV
iajs-2707	34	9	set	set	VERB
iajs-2707	34	10	and	and	CCONJ
iajs-2707	34	11	ř	ř	INTJ
iajs-2707	34	12	be	be	AUX
iajs-2707	34	13	an	an	DET
iajs-2707	34	14	equivalence	equivalence	NOUN
iajs-2707	34	15	relation	relation	NOUN
iajs-2707	34	16	on	on	ADP
iajs-2707	34	17	ẋ	ẋ	NOUN
iajs-2707	34	18	,	,	PUNCT
iajs-2707	34	19	ḿ	ḿ	ADP
iajs-2707	34	20	⊆	⊆	NUM
iajs-2707	34	21	ẋ	ẋ	NOUN
iajs-2707	34	22	;	;	PUNCT
iajs-2707	34	23	the	the	DET
iajs-2707	34	24	upper	upper	ADJ
iajs-2707	34	25	approximation	approximation	NOUN
iajs-2707	34	26	of	of	ADP
iajs-2707	34	27	ḿ	ḿ	NOUN
iajs-2707	34	28	for	for	ADP
iajs-2707	34	29	ř	ř	PROPN
iajs-2707	34	30	is	be	AUX
iajs-2707	34	31	denoted	denote	VERB
iajs-2707	34	32	by	by	ADP
iajs-2707	34	33	ữ(ḿ	ữ(ḿ	PROPN
iajs-2707	34	34	)	)	PUNCT
iajs-2707	34	35	,	,	PUNCT
iajs-2707	34	36	which	which	PRON
iajs-2707	34	37	is	be	AUX
iajs-2707	34	38	,	,	PUNCT
iajs-2707	34	39	ữ	ữ	NOUN
iajs-2707	34	40	(	(	PUNCT
iajs-2707	34	41	ḿ	ḿ	NOUN
iajs-2707	34	42	)	)	PUNCT
iajs-2707	34	43	=	=	SYM
iajs-2707	35	1	⋃	⋃	NOUN
iajs-2707	35	2	{	{	PUNCT
iajs-2707	35	3	𝑥∈ẋ	𝑥∈ẋ	NUM
iajs-2707	35	4	ř	ř	PROPN
iajs-2707	35	5	(	(	PUNCT
iajs-2707	35	6	x	x	X
iajs-2707	35	7	):	):	PUNCT
iajs-2707	35	8	ř	ř	X
iajs-2707	35	9	(	(	PUNCT
iajs-2707	35	10	x	x	NOUN
iajs-2707	35	11	)	)	PUNCT
iajs-2707	35	12	∩	∩	NOUN
iajs-2707	35	13	ḿ	ḿ	ADP
iajs-2707	35	14	≠	≠	PROPN
iajs-2707	35	15	∅	∅	NOUN
iajs-2707	35	16	}	}	PUNCT
iajs-2707	35	17	such	such	ADJ
iajs-2707	35	18	that	that	SCONJ
iajs-2707	35	19	ř	ř	PROPN
iajs-2707	35	20	(	(	PUNCT
iajs-2707	35	21	x	x	X
iajs-2707	35	22	)	)	PUNCT
iajs-2707	35	23	𝑖𝑠	𝑖𝑠	NOUN
iajs-2707	35	24	𝑡ℎ𝑒	𝑡ℎ𝑒	PROPN
iajs-2707	35	25	𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑐𝑒	𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑐𝑒	NOUN
iajs-2707	35	26	𝑐𝑙𝑎𝑠𝑠	𝑐𝑙𝑎𝑠𝑠	NOUN
iajs-2707	35	27	𝑜𝑓	𝑜𝑓	ADP
iajs-2707	35	28	𝑥	𝑥	PROPN
iajs-2707	35	29	and	and	CCONJ
iajs-2707	35	30	the	the	DET
iajs-2707	35	31	lower	low	ADJ
iajs-2707	35	32	approximation	approximation	NOUN
iajs-2707	35	33	of	of	ADP
iajs-2707	35	34	m	m	PROPN
iajs-2707	35	35	for	for	ADP
iajs-2707	35	36	ř	ř	PROPN
iajs-2707	35	37	is	be	AUX
iajs-2707	35	38	denoted	denote	VERB
iajs-2707	35	39	by	by	ADP
iajs-2707	35	40	₤	₤	PROPN
iajs-2707	35	41	(	(	PUNCT
iajs-2707	35	42	ḿ	ḿ	NOUN
iajs-2707	35	43	)	)	PUNCT
iajs-2707	35	44	,	,	PUNCT
iajs-2707	35	45	which	which	PRON
iajs-2707	35	46	is	be	AUX
iajs-2707	35	47	,	,	PUNCT
iajs-2707	35	48	₤	₤	PROPN
iajs-2707	35	49	(	(	PUNCT
iajs-2707	35	50	ḿ	ḿ	NOUN
iajs-2707	35	51	)	)	PUNCT
iajs-2707	35	52	=	=	SYM
iajs-2707	35	53	⋃	⋃	NOUN
iajs-2707	35	54	{	{	PUNCT
iajs-2707	35	55	𝑥∈ẋ	𝑥∈ẋ	NUM
iajs-2707	35	56	ř	ř	PROPN
iajs-2707	35	57	(	(	PUNCT
iajs-2707	35	58	x	x	X
iajs-2707	35	59	):	):	PUNCT
iajs-2707	35	60	ř	ř	X
iajs-2707	35	61	(	(	PUNCT
iajs-2707	35	62	x	x	NOUN
iajs-2707	35	63	)	)	PUNCT
iajs-2707	35	64	⊆	⊆	NUM
iajs-2707	35	65	ḿ	ḿ	NOUN
iajs-2707	35	66	}	}	PUNCT
iajs-2707	35	67	.	.	PUNCT
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iajs-2707	36	2	boundary	boundary	ADJ
iajs-2707	36	3	region	region	NOUN
iajs-2707	36	4	of	of	ADP
iajs-2707	36	5	m	m	PROPN
iajs-2707	36	6	for	for	ADP
iajs-2707	36	7	ℛ	ℛ	PROPN
iajs-2707	36	8	is	be	AUX
iajs-2707	36	9	denoted	denote	VERB
iajs-2707	36	10	by	by	ADP
iajs-2707	36	11	ℬ(m	ℬ(m	NUM
iajs-2707	36	12	)	)	PUNCT
iajs-2707	36	13	,	,	PUNCT
iajs-2707	36	14	which	which	PRON
iajs-2707	36	15	is	be	AUX
iajs-2707	36	16	,	,	PUNCT
iajs-2707	36	17	ℬ	ℬ	PROPN
iajs-2707	36	18	(	(	PUNCT
iajs-2707	36	19	ḿ	ḿ	NOUN
iajs-2707	36	20	)	)	PUNCT
iajs-2707	36	21	=	=	SYM
iajs-2707	36	22	ữ	ữ	NOUN
iajs-2707	36	23	(	(	PUNCT
iajs-2707	36	24	ḿ	ḿ	NOUN
iajs-2707	36	25	)	)	PUNCT
iajs-2707	36	26	−	−	NOUN
iajs-2707	36	27	₤	₤	PROPN
iajs-2707	36	28	(	(	PUNCT
iajs-2707	36	29	ḿ	ḿ	NOUN
iajs-2707	36	30	)	)	PUNCT
iajs-2707	36	31	.	.	PUNCT
iajs-2707	37	1	proposition	proposition	NOUN
iajs-2707	37	2	2.2	2.2	NUM
iajs-2707	37	3	:	:	PUNCT
iajs-2707	38	1	[	[	X
iajs-2707	38	2	9,10	9,10	X
iajs-2707	38	3	]	]	X
iajs-2707	38	4	if	if	SCONJ
iajs-2707	38	5	ḿ	ḿ	PROPN
iajs-2707	38	6	,	,	PUNCT
iajs-2707	38	7	ỷ	ỷ	PROPN
iajs-2707	38	8	⊆	⊆	NUM
iajs-2707	38	9	ẋ	ẋ	DET
iajs-2707	38	10	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
iajs-2707	38	11	𝑡ℎ𝑒	𝑡ℎ𝑒	PROPN
iajs-2707	38	12	𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔	𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔	PROPN
iajs-2707	38	13	𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑖𝑒𝑠	𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑖𝑒𝑠	PROPN
iajs-2707	38	14	𝑎𝑟𝑒	𝑎𝑟𝑒	PROPN
iajs-2707	38	15	𝑟𝑒𝑎𝑙𝑖𝑧𝑒𝑑	𝑟𝑒𝑎𝑙𝑖𝑧𝑒𝑑	PROPN
iajs-2707	38	16	1	1	NUM
iajs-2707	38	17	.	.	PUNCT
iajs-2707	38	18	₤	₤	PROPN
iajs-2707	38	19	(	(	PUNCT
iajs-2707	38	20	ḿ	ḿ	NOUN
iajs-2707	38	21	)	)	PUNCT
iajs-2707	39	1	⊆	⊆	NUM
iajs-2707	39	2	m	m	NUM
iajs-2707	39	3	⊆	⊆	NUM
iajs-2707	39	4	ữ	ữ	NOUN
iajs-2707	39	5	(	(	PUNCT
iajs-2707	39	6	ḿ	ḿ	NOUN
iajs-2707	39	7	)	)	PUNCT
iajs-2707	39	8	.	.	PUNCT
iajs-2707	40	1	2	2	X
iajs-2707	40	2	.	.	X
iajs-2707	40	3	ḿ	ḿ	ADP
iajs-2707	40	4	⊆	⊆	NUM
iajs-2707	40	5	ỷ	ỷ	PROPN
iajs-2707	40	6	,	,	PUNCT
iajs-2707	40	7	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
iajs-2707	40	8	₤	₤	PROPN
iajs-2707	40	9	(	(	PUNCT
iajs-2707	40	10	ḿ	ḿ	NOUN
iajs-2707	40	11	)	)	PUNCT
iajs-2707	40	12	⊆	⊆	NUM
iajs-2707	40	13	₤	₤	NOUN
iajs-2707	40	14	(	(	PUNCT
iajs-2707	40	15	s	s	NOUN
iajs-2707	40	16	)	)	PUNCT
iajs-2707	40	17	and	and	CCONJ
iajs-2707	40	18	(	(	PUNCT
iajs-2707	40	19	ữḿ	ữḿ	NOUN
iajs-2707	40	20	)	)	PUNCT
iajs-2707	40	21	⊆	⊆	NUM
iajs-2707	40	22	ữ(ỷ	ữ(ỷ	NOUN
iajs-2707	40	23	)	)	PUNCT
iajs-2707	40	24	.	.	PUNCT
iajs-2707	41	1	3	3	X
iajs-2707	41	2	.	.	X
iajs-2707	41	3	₤	₤	PROPN
iajs-2707	41	4	(	(	PUNCT
iajs-2707	41	5	∅	∅	NOUN
iajs-2707	41	6	)	)	PUNCT
iajs-2707	41	7	=	=	SYM
iajs-2707	41	8	ữ(∅	ữ(∅	NOUN
iajs-2707	41	9	)	)	PUNCT
iajs-2707	41	10	=	=	SYM
iajs-2707	41	11	∅	∅	NOUN
iajs-2707	41	12	𝑎𝑛𝑑₤	𝑎𝑛𝑑₤	PROPN
iajs-2707	41	13	(	(	PUNCT
iajs-2707	41	14	ẋ	ẋ	NOUN
iajs-2707	41	15	)	)	PUNCT
iajs-2707	41	16	=	=	SYM
iajs-2707	41	17	ữ(ẋ	ữ(ẋ	X
iajs-2707	41	18	)	)	PUNCT
iajs-2707	41	19	=	=	SYM
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iajs-2707	42	2	.	.	NOUN
iajs-2707	42	3	4	4	X
iajs-2707	42	4	.	.	PUNCT
iajs-2707	43	1	ữ(ḿ	ữ(ḿ	PROPN
iajs-2707	43	2	∪	∪	ADP
iajs-2707	43	3	ỷ	ỷ	PROPN
iajs-2707	43	4	)	)	PUNCT
iajs-2707	43	5	=	=	SYM
iajs-2707	43	6	ữ(ḿ	ữ(ḿ	NOUN
iajs-2707	43	7	)	)	PUNCT
iajs-2707	43	8	∪	∪	ADP
iajs-2707	43	9	ữ(ỷ	ữ(ỷ	PROPN
iajs-2707	43	10	)	)	PUNCT
iajs-2707	43	11	.	.	PUNCT
iajs-2707	44	1	5.ữ(ḿ	5.ữ(ḿ	NUM
iajs-2707	44	2	∩	∩	NOUN
iajs-2707	44	3	ỷ	ỷ	X
iajs-2707	44	4	)	)	PUNCT
iajs-2707	44	5	⊆	⊆	NUM
iajs-2707	44	6	ữ(ḿ	ữ(ḿ	NOUN
iajs-2707	44	7	)	)	PUNCT
iajs-2707	44	8	∩	∩	NOUN
iajs-2707	44	9	ữ(ỷ	ữ(ỷ	NOUN
iajs-2707	44	10	)	)	PUNCT
iajs-2707	44	11	.	.	PUNCT
iajs-2707	45	1	6	6	X
iajs-2707	45	2	.	.	X
iajs-2707	45	3	₤	₤	PROPN
iajs-2707	45	4	(	(	PUNCT
iajs-2707	45	5	ḿ	ḿ	ADP
iajs-2707	45	6	∪	∪	ADP
iajs-2707	45	7	ỷ	ỷ	PROPN
iajs-2707	45	8	)	)	PUNCT
iajs-2707	45	9	⊇	⊇	PROPN
iajs-2707	45	10	₤	₤	PROPN
iajs-2707	45	11	(	(	PUNCT
iajs-2707	45	12	ḿ	ḿ	NOUN
iajs-2707	45	13	)	)	PUNCT
iajs-2707	45	14	∪	∪	NOUN
iajs-2707	45	15	₤	₤	PROPN
iajs-2707	45	16	(	(	PUNCT
iajs-2707	45	17	ỷ	ỷ	NOUN
iajs-2707	45	18	)	)	PUNCT
iajs-2707	45	19	7	7	NUM
iajs-2707	45	20	.	.	PUNCT
iajs-2707	46	1	₤	₤	PROPN
iajs-2707	46	2	(	(	PUNCT
iajs-2707	46	3	ḿ	ḿ	PROPN
iajs-2707	46	4	∩	∩	X
iajs-2707	46	5	ỷ	ỷ	PART
iajs-2707	46	6	)	)	PUNCT
iajs-2707	46	7	⊆	⊆	NUM
iajs-2707	46	8	₤	₤	NOUN
iajs-2707	46	9	(	(	PUNCT
iajs-2707	46	10	ḿ	ḿ	NOUN
iajs-2707	46	11	)	)	PUNCT
iajs-2707	46	12	∩	∩	NOUN
iajs-2707	46	13	₤	₤	PROPN
iajs-2707	46	14	(	(	PUNCT
iajs-2707	46	15	ỷ	ỷ	NOUN
iajs-2707	46	16	)	)	PUNCT
iajs-2707	46	17	.	.	PUNCT
iajs-2707	47	1	8.ữ(ữ(ḿ	8.ữ(ữ(ḿ	NUM
iajs-2707	47	2	)	)	PUNCT
iajs-2707	47	3	)	)	PUNCT
iajs-2707	48	1	=	=	SYM
iajs-2707	48	2	₤	₤	PROPN
iajs-2707	48	3	(	(	PUNCT
iajs-2707	48	4	ữ(ḿ	ữ(ḿ	NOUN
iajs-2707	48	5	)	)	PUNCT
iajs-2707	48	6	)	)	PUNCT
iajs-2707	48	7	=	=	SYM
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iajs-2707	48	9	)	)	PUNCT
iajs-2707	48	10	.	.	PUNCT
iajs-2707	49	1	9	9	X
iajs-2707	49	2	.	.	X
iajs-2707	49	3	₤	₤	PROPN
iajs-2707	49	4	(	(	PUNCT
iajs-2707	49	5	₤	₤	PROPN
iajs-2707	49	6	(	(	PUNCT
iajs-2707	49	7	ḿ	ḿ	NOUN
iajs-2707	49	8	)	)	PUNCT
iajs-2707	49	9	)	)	PUNCT
iajs-2707	49	10	=	=	PUNCT
iajs-2707	49	11	ữ(₤(ḿ	ữ(₤(ḿ	X
iajs-2707	49	12	)	)	PUNCT
iajs-2707	49	13	)	)	PUNCT
iajs-2707	50	1	=	=	PUNCT
iajs-2707	50	2	₤	₤	PROPN
iajs-2707	50	3	(	(	PUNCT
iajs-2707	50	4	ḿ	ḿ	NOUN
iajs-2707	50	5	)	)	PUNCT
iajs-2707	50	6	.	.	PUNCT
iajs-2707	51	1	example	example	NOUN
iajs-2707	51	2	2.3	2.3	NUM
iajs-2707	51	3	:	:	PUNCT
iajs-2707	51	4	let	let	VERB
iajs-2707	51	5	ẋ=	ẋ=	ADV
iajs-2707	51	6	{	{	PUNCT
iajs-2707	51	7	ϼ1	ϼ1	ADJ
iajs-2707	51	8	,	,	PUNCT
iajs-2707	51	9	ϼ2	ϼ2	NOUN
iajs-2707	51	10	,	,	PUNCT
iajs-2707	51	11	ϼ3	ϼ3	NOUN
iajs-2707	51	12	,	,	PUNCT
iajs-2707	51	13	ϼ4	ϼ4	ADJ
iajs-2707	51	14	}	}	PUNCT
iajs-2707	51	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2707	51	16	ǥ=	ǥ=	X
iajs-2707	51	17	p(ẋ	p(ẋ	PROPN
iajs-2707	51	18	)	)	PUNCT
iajs-2707	51	19	\	\	PROPN
iajs-2707	51	20	{	{	PUNCT
iajs-2707	51	21	∅	∅	NOUN
iajs-2707	51	22	}	}	PUNCT
iajs-2707	51	23	,	,	PUNCT
iajs-2707	52	1	ř	ř	X
iajs-2707	52	2	=	=	SYM
iajs-2707	52	3	{	{	PUNCT
iajs-2707	52	4	(	(	PUNCT
iajs-2707	52	5	ϼ1	ϼ1	PROPN
iajs-2707	52	6	,	,	PUNCT
iajs-2707	52	7	ϼ1	ϼ1	ADJ
iajs-2707	52	8	)	)	PUNCT
iajs-2707	52	9	,	,	PUNCT
iajs-2707	52	10	(	(	PUNCT
iajs-2707	52	11	ϼ2	ϼ2	NOUN
iajs-2707	52	12	,	,	PUNCT
iajs-2707	52	13	ϼ2	ϼ2	NOUN
iajs-2707	52	14	)	)	PUNCT
iajs-2707	52	15	,	,	PUNCT
iajs-2707	52	16	(	(	PUNCT
iajs-2707	52	17	ϼ3	ϼ3	NOUN
iajs-2707	52	18	,	,	PUNCT
iajs-2707	52	19	ϼ3	ϼ3	NOUN
iajs-2707	52	20	)	)	PUNCT
iajs-2707	52	21	,	,	PUNCT
iajs-2707	52	22	(	(	PUNCT
iajs-2707	52	23	ϼ4	ϼ4	ADV
iajs-2707	52	24	,	,	PUNCT
iajs-2707	52	25	ϼ4	ϼ4	ADJ
iajs-2707	52	26	)	)	PUNCT
iajs-2707	52	27	,	,	PUNCT
iajs-2707	52	28	(	(	PUNCT
iajs-2707	52	29	ϼ1	ϼ1	PROPN
iajs-2707	52	30	,	,	PUNCT
iajs-2707	52	31	ϼ2	ϼ2	NOUN
iajs-2707	52	32	)	)	PUNCT
iajs-2707	52	33	,	,	PUNCT
iajs-2707	52	34	(	(	PUNCT
iajs-2707	52	35	ϼ2	ϼ2	NOUN
iajs-2707	52	36	,	,	PUNCT
iajs-2707	52	37	ϼ1	ϼ1	ADJ
iajs-2707	52	38	)	)	PUNCT
iajs-2707	52	39	}	}	PUNCT
iajs-2707	52	40	,	,	PUNCT
iajs-2707	52	41	ř	ř	PROPN
iajs-2707	52	42	(	(	PUNCT
iajs-2707	52	43	ϼ1)=	ϼ1)=	X
iajs-2707	52	44	{	{	PUNCT
iajs-2707	52	45	ϼ1	ϼ1	PROPN
iajs-2707	52	46	,	,	PUNCT
iajs-2707	52	47	ϼ2	ϼ2	NOUN
iajs-2707	52	48	}	}	PUNCT
iajs-2707	52	49	=	=	SYM
iajs-2707	52	50	ř	ř	PROPN
iajs-2707	52	51	(	(	PUNCT
iajs-2707	52	52	ϼ2	ϼ2	PROPN
iajs-2707	52	53	)	)	PUNCT
iajs-2707	52	54	ř	ř	PROPN
iajs-2707	52	55	(	(	PUNCT
iajs-2707	52	56	ϼ3	ϼ3	NOUN
iajs-2707	52	57	)	)	PUNCT
iajs-2707	52	58	=	=	SYM
iajs-2707	52	59	{	{	PUNCT
iajs-2707	52	60	ϼ3	ϼ3	NOUN
iajs-2707	52	61	}	}	PUNCT
iajs-2707	52	62	,	,	PUNCT
iajs-2707	52	63	ř	ř	PROPN
iajs-2707	52	64	(	(	PUNCT
iajs-2707	52	65	ϼ4)=	ϼ4)=	PROPN
iajs-2707	52	66	{	{	PUNCT
iajs-2707	52	67	ϼ4	ϼ4	ADJ
iajs-2707	52	68	}	}	PUNCT
iajs-2707	52	69	ibn	ibn	PROPN
iajs-2707	52	70	al	al	PROPN
iajs-2707	52	71	-	-	PUNCT
iajs-2707	52	72	haitham	haitham	PROPN
iajs-2707	52	73	jour	jour	X
iajs-2707	52	74	.	.	PROPN
iajs-2707	53	1	for	for	ADP
iajs-2707	53	2	pure	pure	ADJ
iajs-2707	53	3	&	&	CCONJ
iajs-2707	53	4	appl	appl	PROPN
iajs-2707	53	5	.	.	PUNCT
iajs-2707	54	1	sci	sci	PROPN
iajs-2707	54	2	.	.	PROPN
iajs-2707	55	1	34(4)2021	34(4)2021	NUM
iajs-2707	55	2	110	110	NUM
iajs-2707	55	3	table	table	NOUN
iajs-2707	55	4	2.1	2.1	NUM
iajs-2707	55	5	.	.	PUNCT
iajs-2707	56	1	the	the	DET
iajs-2707	56	2	boundary	boundary	ADJ
iajs-2707	56	3	region	region	NOUN
iajs-2707	56	4	p(ẋ	p(ẋ	PROPN
iajs-2707	56	5	)	)	PUNCT
iajs-2707	56	6	ữ	ữ	NOUN
iajs-2707	56	7	(	(	PUNCT
iajs-2707	56	8	ḿ	ḿ	NOUN
iajs-2707	56	9	)	)	PUNCT
iajs-2707	56	10	₤	₤	PROPN
iajs-2707	56	11	(	(	PUNCT
iajs-2707	56	12	ḿ	ḿ	NOUN
iajs-2707	56	13	)	)	PUNCT
iajs-2707	56	14	ℬ	ℬ	NOUN
iajs-2707	56	15	(	(	PUNCT
iajs-2707	56	16	ḿ	ḿ	NOUN
iajs-2707	56	17	)	)	PUNCT
iajs-2707	56	18	∅	∅	NOUN
iajs-2707	56	19	∅	∅	NOUN
iajs-2707	56	20	∅	∅	NOUN
iajs-2707	56	21	∅	∅	NOUN
iajs-2707	56	22	{	{	PUNCT
iajs-2707	56	23	ϼ1	ϼ1	PROPN
iajs-2707	56	24	}	}	PUNCT
iajs-2707	56	25	{	{	PUNCT
iajs-2707	56	26	ϼ1	ϼ1	PROPN
iajs-2707	56	27	,	,	PUNCT
iajs-2707	56	28	ϼ2	ϼ2	NOUN
iajs-2707	56	29	}	}	PUNCT
iajs-2707	56	30	∅	∅	NOUN
iajs-2707	56	31	{	{	PUNCT
iajs-2707	56	32	ϼ1	ϼ1	PROPN
iajs-2707	56	33	,	,	PUNCT
iajs-2707	56	34	ϼ2	ϼ2	NOUN
iajs-2707	56	35	}	}	PUNCT
iajs-2707	56	36	{	{	PUNCT
iajs-2707	56	37	ϼ2	ϼ2	NOUN
iajs-2707	56	38	}	}	PUNCT
iajs-2707	56	39	{	{	PUNCT
iajs-2707	56	40	ϼ1	ϼ1	PROPN
iajs-2707	56	41	,	,	PUNCT
iajs-2707	56	42	ϼ2	ϼ2	NOUN
iajs-2707	56	43	}	}	PUNCT
iajs-2707	56	44	∅	∅	NOUN
iajs-2707	56	45	{	{	PUNCT
iajs-2707	56	46	ϼ1	ϼ1	PROPN
iajs-2707	56	47	,	,	PUNCT
iajs-2707	56	48	ϼ2	ϼ2	NOUN
iajs-2707	56	49	}	}	PUNCT
iajs-2707	56	50	{	{	PUNCT
iajs-2707	56	51	ϼ3	ϼ3	NOUN
iajs-2707	56	52	}	}	PUNCT
iajs-2707	56	53	{	{	PUNCT
iajs-2707	56	54	ϼ3	ϼ3	NOUN
iajs-2707	56	55	}	}	PUNCT
iajs-2707	56	56	{	{	PUNCT
iajs-2707	56	57	ϼ3	ϼ3	NOUN
iajs-2707	56	58	}	}	PUNCT
iajs-2707	56	59	∅	∅	NOUN
iajs-2707	56	60	{	{	PUNCT
iajs-2707	56	61	ϼ4	ϼ4	ADV
iajs-2707	56	62	}	}	PUNCT
iajs-2707	56	63	{	{	PUNCT
iajs-2707	56	64	ϼ4	ϼ4	ADV
iajs-2707	56	65	}	}	PUNCT
iajs-2707	56	66	{	{	PUNCT
iajs-2707	56	67	ϼ4	ϼ4	ADJ
iajs-2707	56	68	}	}	PUNCT
iajs-2707	56	69	∅	∅	NOUN
iajs-2707	56	70	{	{	PUNCT
iajs-2707	56	71	ϼ1	ϼ1	PROPN
iajs-2707	56	72	,	,	PUNCT
iajs-2707	56	73	ϼ2	ϼ2	NOUN
iajs-2707	56	74	}	}	PUNCT
iajs-2707	56	75	{	{	PUNCT
iajs-2707	56	76	ϼ1	ϼ1	PROPN
iajs-2707	56	77	,	,	PUNCT
iajs-2707	56	78	ϼ2	ϼ2	NOUN
iajs-2707	56	79	}	}	PUNCT
iajs-2707	56	80	{	{	PUNCT
iajs-2707	56	81	ϼ1	ϼ1	PROPN
iajs-2707	56	82	,	,	PUNCT
iajs-2707	56	83	ϼ2	ϼ2	NOUN
iajs-2707	56	84	}	}	PUNCT
iajs-2707	56	85	∅	∅	NOUN
iajs-2707	56	86	{	{	PUNCT
iajs-2707	56	87	ϼ1	ϼ1	ADJ
iajs-2707	56	88	,	,	PUNCT
iajs-2707	56	89	ϼ3	ϼ3	NOUN
iajs-2707	56	90	}	}	PUNCT
iajs-2707	56	91	{	{	PUNCT
iajs-2707	56	92	ϼ1	ϼ1	PROPN
iajs-2707	56	93	,	,	PUNCT
iajs-2707	56	94	ϼ2	ϼ2	NOUN
iajs-2707	56	95	,	,	PUNCT
iajs-2707	56	96	ϼ3	ϼ3	NOUN
iajs-2707	56	97	}	}	PUNCT
iajs-2707	56	98	{	{	PUNCT
iajs-2707	56	99	ϼ3	ϼ3	NOUN
iajs-2707	56	100	}	}	PUNCT
iajs-2707	56	101	{	{	PUNCT
iajs-2707	56	102	ϼ1	ϼ1	PROPN
iajs-2707	56	103	,	,	PUNCT
iajs-2707	56	104	ϼ2	ϼ2	NOUN
iajs-2707	56	105	}	}	PUNCT
iajs-2707	56	106	{	{	PUNCT
iajs-2707	56	107	ϼ1	ϼ1	PROPN
iajs-2707	56	108	,	,	PUNCT
iajs-2707	56	109	ϼ4	ϼ4	ADJ
iajs-2707	56	110	}	}	PUNCT
iajs-2707	56	111	{	{	PUNCT
iajs-2707	56	112	𝑠ϼ1	𝑠ϼ1	PROPN
iajs-2707	56	113	,	,	PUNCT
iajs-2707	56	114	ϼ2	ϼ2	NOUN
iajs-2707	56	115	,	,	PUNCT
iajs-2707	56	116	ϼ4	ϼ4	ADV
iajs-2707	56	117	}	}	PUNCT
iajs-2707	56	118	{	{	PUNCT
iajs-2707	56	119	ϼ4	ϼ4	ADV
iajs-2707	56	120	}	}	PUNCT
iajs-2707	56	121	{	{	PUNCT
iajs-2707	56	122	ϼ1	ϼ1	PROPN
iajs-2707	56	123	,	,	PUNCT
iajs-2707	56	124	ϼ2	ϼ2	NOUN
iajs-2707	56	125	}	}	PUNCT
iajs-2707	56	126	{	{	PUNCT
iajs-2707	56	127	ϼ2	ϼ2	NOUN
iajs-2707	56	128	,	,	PUNCT
iajs-2707	56	129	ϼ3	ϼ3	NOUN
iajs-2707	56	130	}	}	PUNCT
iajs-2707	56	131	{	{	PUNCT
iajs-2707	56	132	ϼ1	ϼ1	PROPN
iajs-2707	56	133	,	,	PUNCT
iajs-2707	56	134	ϼ2	ϼ2	NOUN
iajs-2707	56	135	,	,	PUNCT
iajs-2707	56	136	ϼ3	ϼ3	NOUN
iajs-2707	56	137	}	}	PUNCT
iajs-2707	56	138	{	{	PUNCT
iajs-2707	56	139	ϼ3	ϼ3	NOUN
iajs-2707	56	140	}	}	PUNCT
iajs-2707	56	141	{	{	PUNCT
iajs-2707	56	142	ϼ1	ϼ1	PROPN
iajs-2707	56	143	,	,	PUNCT
iajs-2707	56	144	ϼ2	ϼ2	NOUN
iajs-2707	56	145	}	}	PUNCT
iajs-2707	56	146	{	{	PUNCT
iajs-2707	56	147	ϼ2	ϼ2	NOUN
iajs-2707	56	148	,	,	PUNCT
iajs-2707	56	149	ϼ4	ϼ4	ADV
iajs-2707	56	150	}	}	PUNCT
iajs-2707	56	151	{	{	PUNCT
iajs-2707	56	152	ϼ1	ϼ1	PROPN
iajs-2707	56	153	,	,	PUNCT
iajs-2707	56	154	ϼ2	ϼ2	NOUN
iajs-2707	56	155	,	,	PUNCT
iajs-2707	56	156	ϼ4	ϼ4	ADV
iajs-2707	56	157	}	}	PUNCT
iajs-2707	56	158	{	{	PUNCT
iajs-2707	56	159	ϼ4	ϼ4	ADV
iajs-2707	56	160	}	}	PUNCT
iajs-2707	56	161	{	{	PUNCT
iajs-2707	56	162	ϼ1	ϼ1	PROPN
iajs-2707	56	163	,	,	PUNCT
iajs-2707	56	164	ϼ2	ϼ2	NOUN
iajs-2707	56	165	}	}	PUNCT
iajs-2707	56	166	{	{	PUNCT
iajs-2707	56	167	ϼ3	ϼ3	NOUN
iajs-2707	56	168	,	,	PUNCT
iajs-2707	56	169	ϼ4	ϼ4	ADV
iajs-2707	56	170	}	}	PUNCT
iajs-2707	56	171	{	{	PUNCT
iajs-2707	56	172	ϼ3	ϼ3	NOUN
iajs-2707	56	173	,	,	PUNCT
iajs-2707	56	174	ϼ4	ϼ4	ADV
iajs-2707	56	175	}	}	PUNCT
iajs-2707	56	176	{	{	PUNCT
iajs-2707	56	177	ϼ3	ϼ3	NOUN
iajs-2707	56	178	,	,	PUNCT
iajs-2707	56	179	ϼ4	ϼ4	ADJ
iajs-2707	56	180	}	}	PUNCT
iajs-2707	56	181	∅	∅	NOUN
iajs-2707	56	182	{	{	PUNCT
iajs-2707	56	183	ϼ1	ϼ1	PROPN
iajs-2707	56	184	,	,	PUNCT
iajs-2707	56	185	ϼ2	ϼ2	NOUN
iajs-2707	56	186	,	,	PUNCT
iajs-2707	56	187	ϼ3	ϼ3	NOUN
iajs-2707	56	188	}	}	PUNCT
iajs-2707	56	189	{	{	PUNCT
iajs-2707	56	190	ϼ1	ϼ1	PROPN
iajs-2707	56	191	,	,	PUNCT
iajs-2707	56	192	ϼ2	ϼ2	NOUN
iajs-2707	56	193	,	,	PUNCT
iajs-2707	56	194	ϼ3	ϼ3	NOUN
iajs-2707	56	195	}	}	PUNCT
iajs-2707	56	196	{	{	PUNCT
iajs-2707	56	197	ϼ1	ϼ1	PROPN
iajs-2707	56	198	,	,	PUNCT
iajs-2707	56	199	ϼ2	ϼ2	NOUN
iajs-2707	56	200	,	,	PUNCT
iajs-2707	56	201	ϼ3	ϼ3	NOUN
iajs-2707	56	202	}	}	PUNCT
iajs-2707	56	203	∅	∅	NOUN
iajs-2707	56	204	{	{	PUNCT
iajs-2707	56	205	ϼ1	ϼ1	PROPN
iajs-2707	56	206	,	,	PUNCT
iajs-2707	56	207	ϼ2	ϼ2	NOUN
iajs-2707	56	208	,	,	PUNCT
iajs-2707	56	209	ϼ4	ϼ4	ADV
iajs-2707	56	210	}	}	PUNCT
iajs-2707	56	211	{	{	PUNCT
iajs-2707	56	212	ϼ1	ϼ1	PROPN
iajs-2707	56	213	,	,	PUNCT
iajs-2707	56	214	ϼ2	ϼ2	NOUN
iajs-2707	56	215	,	,	PUNCT
iajs-2707	56	216	ϼ4	ϼ4	ADV
iajs-2707	56	217	}	}	PUNCT
iajs-2707	56	218	{	{	PUNCT
iajs-2707	56	219	ϼ1	ϼ1	PROPN
iajs-2707	56	220	,	,	PUNCT
iajs-2707	56	221	ϼ2	ϼ2	NOUN
iajs-2707	56	222	,	,	PUNCT
iajs-2707	56	223	ϼ4	ϼ4	ADJ
iajs-2707	56	224	}	}	PUNCT
iajs-2707	56	225	∅	∅	NOUN
iajs-2707	56	226	{	{	PUNCT
iajs-2707	56	227	ϼ2	ϼ2	NOUN
iajs-2707	56	228	,	,	PUNCT
iajs-2707	56	229	ϼ3	ϼ3	NOUN
iajs-2707	56	230	,	,	PUNCT
iajs-2707	56	231	ϼ4	ϼ4	ADV
iajs-2707	56	232	}	}	PUNCT
iajs-2707	56	233	{	{	PUNCT
iajs-2707	56	234	ϼ1	ϼ1	PROPN
iajs-2707	56	235	,	,	PUNCT
iajs-2707	56	236	ϼ2	ϼ2	NOUN
iajs-2707	56	237	,	,	PUNCT
iajs-2707	56	238	ϼ3	ϼ3	NOUN
iajs-2707	56	239	,	,	PUNCT
iajs-2707	56	240	ϼ4	ϼ4	ADV
iajs-2707	56	241	}	}	PUNCT
iajs-2707	56	242	{	{	PUNCT
iajs-2707	56	243	ϼ3	ϼ3	NOUN
iajs-2707	56	244	,	,	PUNCT
iajs-2707	56	245	ϼ4	ϼ4	ADV
iajs-2707	56	246	}	}	PUNCT
iajs-2707	56	247	{	{	PUNCT
iajs-2707	56	248	ϼ1	ϼ1	PROPN
iajs-2707	56	249	,	,	PUNCT
iajs-2707	56	250	ϼ2	ϼ2	NOUN
iajs-2707	56	251	}	}	PUNCT
iajs-2707	56	252	{	{	PUNCT
iajs-2707	56	253	ϼ1	ϼ1	ADJ
iajs-2707	56	254	,	,	PUNCT
iajs-2707	56	255	ϼ3	ϼ3	NOUN
iajs-2707	56	256	,	,	PUNCT
iajs-2707	56	257	ϼ4	ϼ4	ADV
iajs-2707	56	258	}	}	PUNCT
iajs-2707	56	259	{	{	PUNCT
iajs-2707	56	260	ϼ1	ϼ1	PROPN
iajs-2707	56	261	,	,	PUNCT
iajs-2707	56	262	ϼ2	ϼ2	NOUN
iajs-2707	56	263	,	,	PUNCT
iajs-2707	56	264	ϼ3	ϼ3	NOUN
iajs-2707	56	265	,	,	PUNCT
iajs-2707	56	266	ϼ4	ϼ4	ADV
iajs-2707	56	267	}	}	PUNCT
iajs-2707	56	268	{	{	PUNCT
iajs-2707	56	269	ϼ3	ϼ3	NOUN
iajs-2707	56	270	,	,	PUNCT
iajs-2707	56	271	ϼ4	ϼ4	ADV
iajs-2707	56	272	}	}	PUNCT
iajs-2707	56	273	{	{	PUNCT
iajs-2707	56	274	ϼ1	ϼ1	PROPN
iajs-2707	56	275	,	,	PUNCT
iajs-2707	56	276	ϼ2	ϼ2	NOUN
iajs-2707	56	277	}	}	PUNCT
iajs-2707	56	278	{	{	PUNCT
iajs-2707	56	279	ϼ1	ϼ1	PROPN
iajs-2707	56	280	,	,	PUNCT
iajs-2707	56	281	ϼ2	ϼ2	NOUN
iajs-2707	56	282	,	,	PUNCT
iajs-2707	56	283	ϼ3	ϼ3	NOUN
iajs-2707	56	284	,	,	PUNCT
iajs-2707	56	285	ϼ4	ϼ4	ADV
iajs-2707	56	286	}	}	PUNCT
iajs-2707	56	287	{	{	PUNCT
iajs-2707	56	288	ϼ1	ϼ1	PROPN
iajs-2707	56	289	,	,	PUNCT
iajs-2707	56	290	ϼ2	ϼ2	NOUN
iajs-2707	56	291	,	,	PUNCT
iajs-2707	56	292	ϼ3	ϼ3	NOUN
iajs-2707	56	293	,	,	PUNCT
iajs-2707	56	294	ϼ4	ϼ4	ADV
iajs-2707	56	295	}	}	PUNCT
iajs-2707	56	296	{	{	PUNCT
iajs-2707	56	297	ϼ1	ϼ1	PROPN
iajs-2707	56	298	,	,	PUNCT
iajs-2707	56	299	ϼ2	ϼ2	NOUN
iajs-2707	56	300	,	,	PUNCT
iajs-2707	56	301	ϼ3	ϼ3	NOUN
iajs-2707	56	302	,	,	PUNCT
iajs-2707	56	303	ϼ4	ϼ4	ADV
iajs-2707	56	304	}	}	PUNCT
iajs-2707	56	305	∅	∅	NOUN
iajs-2707	56	306	definition	definition	NOUN
iajs-2707	56	307	2.4:[11	2.4:[11	NUM
iajs-2707	56	308	]	]	PUNCT
iajs-2707	56	309	let	let	VERB
iajs-2707	56	310	ẋ	ẋ	PRON
iajs-2707	56	311	be	be	AUX
iajs-2707	56	312	a	a	DET
iajs-2707	56	313	nonempty	nonempty	ADV
iajs-2707	56	314	set	set	VERB
iajs-2707	56	315	and	and	CCONJ
iajs-2707	56	316	ḿ	ḿ	ADP
iajs-2707	56	317	⊆	⊆	NUM
iajs-2707	56	318	ẋ	ẋ	DET
iajs-2707	56	319	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	NOUN
iajs-2707	56	320	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	PROPN
iajs-2707	56	321	ř	ř	PROPN
iajs-2707	56	322	is	be	AUX
iajs-2707	56	323	any	any	DET
iajs-2707	56	324	relation	relation	NOUN
iajs-2707	56	325	on	on	ADP
iajs-2707	56	326	ẋ	ẋ	NOUN
iajs-2707	56	327	so	so	ADV
iajs-2707	56	328	,	,	PUNCT
iajs-2707	56	329	by	by	ADP
iajs-2707	56	330	using	use	VERB
iajs-2707	56	331	the	the	DET
iajs-2707	56	332	concepts	concept	NOUN
iajs-2707	56	333	of	of	ADP
iajs-2707	56	334	lower	low	ADJ
iajs-2707	56	335	and	and	CCONJ
iajs-2707	56	336	upper	upper	ADJ
iajs-2707	56	337	approximation	approximation	NOUN
iajs-2707	56	338	.	.	PUNCT
iajs-2707	57	1	𝔐(ḿ	𝔐(ḿ	NUM
iajs-2707	57	2	)	)	PUNCT
iajs-2707	57	3	=	=	PUNCT
iajs-2707	58	1	|₤(ḿ)|	|₤(ḿ)|	NUM
iajs-2707	58	2	|ữ(ḿ)|	|ữ(ḿ)|	PROPN
iajs-2707	58	3	,	,	PUNCT
iajs-2707	58	4	|	|	ADV
iajs-2707	58	5	₤	₤	PROPN
iajs-2707	58	6	(	(	PUNCT
iajs-2707	58	7	ḿ)|	ḿ)|	PROPN
iajs-2707	58	8	≠	≠	PROPN
iajs-2707	58	9	∅	∅	NOUN
iajs-2707	58	10	we	we	PRON
iajs-2707	58	11	can	can	AUX
iajs-2707	58	12	define	define	VERB
iajs-2707	58	13	the	the	DET
iajs-2707	58	14	second	second	ADJ
iajs-2707	58	15	accuracy	accuracy	NOUN
iajs-2707	58	16	measure	measure	NOUN
iajs-2707	58	17	of	of	ADP
iajs-2707	58	18	ḿ	ḿ	ADP
iajs-2707	58	19	which	which	PRON
iajs-2707	58	20	is	be	AUX
iajs-2707	58	21	called	call	VERB
iajs-2707	58	22	a	a	DET
iajs-2707	58	23	semi	semi	ADJ
iajs-2707	58	24	-	-	ADJ
iajs-2707	58	25	accuracy	accuracy	ADJ
iajs-2707	58	26	measure	measure	NOUN
iajs-2707	58	27	of	of	ADP
iajs-2707	58	28	approximation	approximation	NOUN
iajs-2707	58	29	.	.	PUNCT
iajs-2707	59	1	𝔐𝜉(ḿ	𝔐𝜉(ḿ	NOUN
iajs-2707	59	2	)	)	PUNCT
iajs-2707	59	3	=	=	SYM
iajs-2707	60	1	|ữ(₤(ḿ))|	|ữ(₤(ḿ))|	PROPN
iajs-2707	60	2	|ữ(ḿ)|	|ữ(ḿ)|	PROPN
iajs-2707	60	3	,	,	PUNCT
iajs-2707	60	4	|	|	ADV
iajs-2707	60	5	₤	₤	PROPN
iajs-2707	60	6	(	(	PUNCT
iajs-2707	60	7	ḿ)|	ḿ)|	PROPN
iajs-2707	60	8	≠	≠	PROPN
iajs-2707	60	9	∅	∅	VERB
iajs-2707	60	10	the	the	DET
iajs-2707	60	11	third	third	ADJ
iajs-2707	60	12	measure	measure	NOUN
iajs-2707	60	13	is	be	AUX
iajs-2707	60	14	called	call	VERB
iajs-2707	60	15	pre	pre	ADJ
iajs-2707	60	16	–	–	PUNCT
iajs-2707	60	17	accuracy	accuracy	NOUN
iajs-2707	60	18	measure	measure	NOUN
iajs-2707	60	19	of	of	ADP
iajs-2707	60	20	approximation	approximation	NOUN
iajs-2707	60	21	.	.	PUNCT
iajs-2707	61	1	𝔐𝑝(ḿ	𝔐𝑝(ḿ	X
iajs-2707	61	2	)	)	PUNCT
iajs-2707	61	3	=	=	SYM
iajs-2707	61	4	|₤(ữḿ)|	|₤(ữḿ)|	PUNCT
iajs-2707	61	5	|ữ(ḿ)|	|ữ(ḿ)|	PROPN
iajs-2707	61	6	,	,	PUNCT
iajs-2707	61	7	|	|	ADV
iajs-2707	61	8	₤	₤	PROPN
iajs-2707	61	9	(	(	PUNCT
iajs-2707	61	10	ḿ)|	ḿ)|	PROPN
iajs-2707	61	11	≠	≠	PROPN
iajs-2707	61	12	∅	∅	NOUN
iajs-2707	61	13	example	example	NOUN
iajs-2707	61	14	2	2	NUM
iajs-2707	61	15	.	.	NOUN
iajs-2707	61	16	5	5	NUM
iajs-2707	61	17	:	:	PUNCT
iajs-2707	61	18	let	let	VERB
iajs-2707	61	19	ẋ	ẋ	X
iajs-2707	61	20	=	=	SYM
iajs-2707	61	21	{	{	PUNCT
iajs-2707	61	22	ϼ1	ϼ1	PROPN
iajs-2707	61	23	,	,	PUNCT
iajs-2707	61	24	ϼ2	ϼ2	NOUN
iajs-2707	61	25	,	,	PUNCT
iajs-2707	61	26	ϼ3	ϼ3	NOUN
iajs-2707	61	27	,	,	PUNCT
iajs-2707	61	28	ϼ4	ϼ4	ADV
iajs-2707	61	29	}	}	PUNCT
iajs-2707	61	30	and	and	CCONJ
iajs-2707	61	31	,	,	PUNCT
iajs-2707	61	32	ǥ=	ǥ=	CCONJ
iajs-2707	62	1	p(ẋ	p(ẋ	PROPN
iajs-2707	62	2	)	)	PUNCT
iajs-2707	62	3	\	\	PROPN
iajs-2707	62	4	{	{	PUNCT
iajs-2707	62	5	∅	∅	NOUN
iajs-2707	62	6	}	}	PUNCT
iajs-2707	62	7	,	,	PUNCT
iajs-2707	62	8	ř=	ř=	VERB
iajs-2707	62	9	{	{	PUNCT
iajs-2707	62	10	(	(	PUNCT
iajs-2707	62	11	ϼ1	ϼ1	PROPN
iajs-2707	62	12	,	,	PUNCT
iajs-2707	62	13	ϼ1	ϼ1	ADJ
iajs-2707	62	14	)	)	PUNCT
iajs-2707	62	15	,	,	PUNCT
iajs-2707	62	16	(	(	PUNCT
iajs-2707	62	17	ϼ2	ϼ2	NOUN
iajs-2707	62	18	,	,	PUNCT
iajs-2707	62	19	ϼ2	ϼ2	NOUN
iajs-2707	62	20	)	)	PUNCT
iajs-2707	62	21	,	,	PUNCT
iajs-2707	62	22	(	(	PUNCT
iajs-2707	62	23	ϼ3	ϼ3	NOUN
iajs-2707	62	24	,	,	PUNCT
iajs-2707	62	25	ϼ3	ϼ3	NOUN
iajs-2707	62	26	)	)	PUNCT
iajs-2707	62	27	,	,	PUNCT
iajs-2707	62	28	(	(	PUNCT
iajs-2707	62	29	ϼ4	ϼ4	ADV
iajs-2707	62	30	,	,	PUNCT
iajs-2707	62	31	ϼ4	ϼ4	ADJ
iajs-2707	62	32	)	)	PUNCT
iajs-2707	62	33	,	,	PUNCT
iajs-2707	62	34	(	(	PUNCT
iajs-2707	62	35	ϼ2	ϼ2	NOUN
iajs-2707	62	36	,	,	PUNCT
iajs-2707	62	37	ϼ3	ϼ3	NOUN
iajs-2707	62	38	)	)	PUNCT
iajs-2707	62	39	,	,	PUNCT
iajs-2707	62	40	(	(	PUNCT
iajs-2707	62	41	ϼ3	ϼ3	NOUN
iajs-2707	62	42	,	,	PUNCT
iajs-2707	62	43	ϼ2	ϼ2	NOUN
iajs-2707	62	44	)	)	PUNCT
iajs-2707	62	45	}	}	PUNCT
iajs-2707	62	46	ř	ř	PROPN
iajs-2707	62	47	(	(	PUNCT
iajs-2707	62	48	ϼ1)=	ϼ1)=	X
iajs-2707	62	49	{	{	PUNCT
iajs-2707	62	50	ϼ1	ϼ1	PROPN
iajs-2707	62	51	}	}	PUNCT
iajs-2707	62	52	,	,	PUNCT
iajs-2707	62	53	ř	ř	PROPN
iajs-2707	62	54	(	(	PUNCT
iajs-2707	62	55	ϼ2	ϼ2	NOUN
iajs-2707	62	56	)	)	PUNCT
iajs-2707	62	57	=	=	SYM
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iajs-2707	68	269	ẋ	ẋ	ADJ
iajs-2707	68	270	{	{	PUNCT
iajs-2707	68	271	ϼ1	ϼ1	PROPN
iajs-2707	68	272	,	,	PUNCT
iajs-2707	68	273	ϼ4	ϼ4	ADJ
iajs-2707	68	274	}	}	PUNCT
iajs-2707	68	275	{	{	PUNCT
iajs-2707	68	276	ϼ2	ϼ2	NOUN
iajs-2707	68	277	,	,	PUNCT
iajs-2707	68	278	ϼ3	ϼ3	NOUN
iajs-2707	68	279	,	,	PUNCT
iajs-2707	68	280	ϼ4	ϼ4	ADV
iajs-2707	68	281	}	}	PUNCT
iajs-2707	68	282	{	{	PUNCT
iajs-2707	68	283	ϼ2	ϼ2	NOUN
iajs-2707	68	284	,	,	PUNCT
iajs-2707	68	285	ϼ3	ϼ3	NOUN
iajs-2707	68	286	,	,	PUNCT
iajs-2707	68	287	ϼ4	ϼ4	ADV
iajs-2707	68	288	}	}	PUNCT
iajs-2707	68	289	{	{	PUNCT
iajs-2707	68	290	ϼ2	ϼ2	NOUN
iajs-2707	68	291	,	,	PUNCT
iajs-2707	68	292	ϼ3	ϼ3	NOUN
iajs-2707	68	293	,	,	PUNCT
iajs-2707	68	294	ϼ4	ϼ4	ADJ
iajs-2707	68	295	}	}	PUNCT
iajs-2707	68	296	∅	∅	NOUN
iajs-2707	68	297	{	{	PUNCT
iajs-2707	68	298	ϼ2	ϼ2	NOUN
iajs-2707	68	299	,	,	PUNCT
iajs-2707	68	300	ϼ3	ϼ3	NOUN
iajs-2707	68	301	,	,	PUNCT
iajs-2707	68	302	ϼ4	ϼ4	ADV
iajs-2707	68	303	}	}	PUNCT
iajs-2707	68	304	{	{	PUNCT
iajs-2707	68	305	ϼ2	ϼ2	NOUN
iajs-2707	68	306	,	,	PUNCT
iajs-2707	68	307	ϼ3	ϼ3	NOUN
iajs-2707	68	308	,	,	PUNCT
iajs-2707	68	309	ϼ4	ϼ4	ADJ
iajs-2707	68	310	}	}	PUNCT
iajs-2707	68	311	table	table	NOUN
iajs-2707	68	312	2	2	NUM
iajs-2707	68	313	.	.	SYM
iajs-2707	68	314	3	3	NUM
iajs-2707	68	315	accuracy	accuracy	NOUN
iajs-2707	68	316	measure	measure	NOUN
iajs-2707	68	317	of	of	ADP
iajs-2707	68	318	approximation	approximation	NOUN
iajs-2707	68	319	.	.	PUNCT
iajs-2707	69	1	p(ẋ	p(ẋ	PROPN
iajs-2707	69	2	)	)	PUNCT
iajs-2707	69	3	𝔐(ḿ	𝔐(ḿ	PROPN
iajs-2707	69	4	)	)	PUNCT
iajs-2707	69	5	𝔐𝜉(ḿ	𝔐𝜉(ḿ	NOUN
iajs-2707	69	6	)	)	PUNCT
iajs-2707	69	7	𝔐𝑝(ḿ	𝔐𝑝(ḿ	NOUN
iajs-2707	69	8	)	)	PUNCT
iajs-2707	69	9	ẋ	ẋ	NOUN
iajs-2707	69	10	1	1	NUM
iajs-2707	69	11	1	1	NUM
iajs-2707	69	12	1	1	NUM
iajs-2707	69	13	∅	∅	NOUN
iajs-2707	69	14	1	1	NUM
iajs-2707	69	15	1	1	NUM
iajs-2707	69	16	1	1	NUM
iajs-2707	69	17	{	{	PUNCT
iajs-2707	69	18	ϼ1	ϼ1	PROPN
iajs-2707	69	19	}	}	PUNCT
iajs-2707	69	20	0	0	NUM
iajs-2707	69	21	0	0	NUM
iajs-2707	69	22	1	1	NUM
iajs-2707	69	23	{	{	PUNCT
iajs-2707	69	24	ϼ2	ϼ2	NOUN
iajs-2707	69	25	}	}	PUNCT
iajs-2707	69	26	0	0	NUM
iajs-2707	69	27	0	0	NUM
iajs-2707	69	28	1	1	NUM
iajs-2707	69	29	{	{	PUNCT
iajs-2707	69	30	ϼ3	ϼ3	NOUN
iajs-2707	69	31	}	}	PUNCT
iajs-2707	69	32	1	1	NUM
iajs-2707	69	33	1	1	NUM
iajs-2707	69	34	1	1	NUM
iajs-2707	69	35	{	{	PUNCT
iajs-2707	69	36	ϼ4	ϼ4	ADV
iajs-2707	69	37	}	}	PUNCT
iajs-2707	69	38	1/3	1/3	NUM
iajs-2707	69	39	1/3	1/3	NUM
iajs-2707	69	40	1	1	NUM
iajs-2707	69	41	{	{	PUNCT
iajs-2707	69	42	ϼ1	ϼ1	PROPN
iajs-2707	69	43	,	,	PUNCT
iajs-2707	69	44	ϼ2	ϼ2	NOUN
iajs-2707	69	45	}	}	PUNCT
iajs-2707	69	46	1/3	1/3	NUM
iajs-2707	69	47	1/3	1/3	NUM
iajs-2707	69	48	1	1	NUM
iajs-2707	69	49	{	{	PUNCT
iajs-2707	69	50	ϼ1	ϼ1	ADJ
iajs-2707	69	51	,	,	PUNCT
iajs-2707	69	52	ϼ3	ϼ3	NOUN
iajs-2707	69	53	}	}	PUNCT
iajs-2707	69	54	1	1	NUM
iajs-2707	69	55	1	1	NUM
iajs-2707	69	56	1	1	NUM
iajs-2707	69	57	{	{	PUNCT
iajs-2707	69	58	ϼ1	ϼ1	PROPN
iajs-2707	69	59	,	,	PUNCT
iajs-2707	69	60	ϼ4	ϼ4	ADJ
iajs-2707	69	61	}	}	PUNCT
iajs-2707	69	62	1	1	NUM
iajs-2707	69	63	1	1	NUM
iajs-2707	69	64	1	1	NUM
iajs-2707	69	65	{	{	PUNCT
iajs-2707	69	66	ϼ2	ϼ2	NOUN
iajs-2707	69	67	,	,	PUNCT
iajs-2707	69	68	ϼ3	ϼ3	NOUN
iajs-2707	69	69	}	}	PUNCT
iajs-2707	69	70	1/3	1/3	NUM
iajs-2707	69	71	1/3	1/3	NUM
iajs-2707	69	72	1	1	NUM
iajs-2707	69	73	{	{	PUNCT
iajs-2707	69	74	ϼ2	ϼ2	NOUN
iajs-2707	69	75	,	,	PUNCT
iajs-2707	69	76	ϼ4	ϼ4	ADJ
iajs-2707	69	77	}	}	PUNCT
iajs-2707	69	78	1/3	1/3	NUM
iajs-2707	69	79	1/3	1/3	NUM
iajs-2707	69	80	1	1	NUM
iajs-2707	69	81	{	{	PUNCT
iajs-2707	69	82	ϼ3	ϼ3	NOUN
iajs-2707	69	83	,	,	PUNCT
iajs-2707	69	84	ϼ4	ϼ4	ADV
iajs-2707	69	85	}	}	PUNCT
iajs-2707	69	86	1	1	NUM
iajs-2707	69	87	1	1	NUM
iajs-2707	69	88	1	1	NUM
iajs-2707	69	89	{	{	PUNCT
iajs-2707	69	90	ϼ1	ϼ1	PROPN
iajs-2707	69	91	,	,	PUNCT
iajs-2707	69	92	ϼ2	ϼ2	NOUN
iajs-2707	69	93	,	,	PUNCT
iajs-2707	69	94	ϼ3	ϼ3	NOUN
iajs-2707	69	95	}	}	PUNCT
iajs-2707	69	96	½	½	NOUN
iajs-2707	69	97	½	½	NOUN
iajs-2707	69	98	1	1	NUM
iajs-2707	69	99	{	{	PUNCT
iajs-2707	69	100	ϼ1	ϼ1	PROPN
iajs-2707	69	101	,	,	PUNCT
iajs-2707	69	102	ϼ2	ϼ2	NOUN
iajs-2707	69	103	,	,	PUNCT
iajs-2707	69	104	ϼ4	ϼ4	ADJ
iajs-2707	69	105	}	}	PUNCT
iajs-2707	69	106	½	½	NOUN
iajs-2707	69	107	½	½	NOUN
iajs-2707	69	108	1	1	NUM
iajs-2707	69	109	{	{	PUNCT
iajs-2707	69	110	ϼ1	ϼ1	ADJ
iajs-2707	69	111	,	,	PUNCT
iajs-2707	69	112	ϼ3	ϼ3	NOUN
iajs-2707	69	113	,	,	PUNCT
iajs-2707	69	114	ϼ4	ϼ4	ADV
iajs-2707	69	115	}	}	PUNCT
iajs-2707	69	116	1	1	NUM
iajs-2707	69	117	1	1	NUM
iajs-2707	69	118	1	1	NUM
iajs-2707	69	119	{	{	PUNCT
iajs-2707	69	120	ϼ2	ϼ2	NOUN
iajs-2707	69	121	,	,	PUNCT
iajs-2707	69	122	ϼ3	ϼ3	NOUN
iajs-2707	69	123	,	,	PUNCT
iajs-2707	69	124	ϼ4	ϼ4	ADV
iajs-2707	69	125	}	}	PUNCT
iajs-2707	69	126	1	1	NUM
iajs-2707	69	127	1	1	NUM
iajs-2707	69	128	1	1	NUM
iajs-2707	69	129	3	3	NUM
iajs-2707	69	130	.	.	PUNCT
iajs-2707	69	131	grill	grill	NOUN
iajs-2707	69	132	semi	semi	ADJ
iajs-2707	69	133	-	-	ADJ
iajs-2707	69	134	p	p	ADJ
iajs-2707	69	135	-	-	PUNCT
iajs-2707	69	136	open	open	ADJ
iajs-2707	69	137	sets	set	NOUN
iajs-2707	69	138	definition	definition	NOUN
iajs-2707	69	139	3.1	3.1	NUM
iajs-2707	69	140	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-2707	69	141	(	(	PUNCT
iajs-2707	69	142	ẋ	ẋ	X
iajs-2707	69	143	,	,	PUNCT
iajs-2707	69	144	𝒯	𝒯	PROPN
iajs-2707	69	145	,	,	PUNCT
iajs-2707	69	146	ǥ)𝑏𝑒	ǥ)𝑏𝑒	PROPN
iajs-2707	69	147	𝑎	𝑎	PRON
iajs-2707	69	148	𝑔𝑟𝑖𝑙𝑙	𝑔𝑟𝑖𝑙𝑙	ADV
iajs-2707	69	149	𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙	𝑡𝑜𝑝𝑜𝑙𝑜𝑔𝑖𝑐𝑎𝑙	ADJ
iajs-2707	69	150	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	NOUN
iajs-2707	69	151	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-2707	69	152	μ	μ	PROPN
iajs-2707	69	153	⊆	⊆	NUM
iajs-2707	69	154	ẋ	ẋ	NOUN
iajs-2707	69	155	,	,	PUNCT
iajs-2707	69	156	then	then	ADV
iajs-2707	69	157	μ	μ	PROPN
iajs-2707	69	158	is	be	AUX
iajs-2707	69	159	called	call	VERB
iajs-2707	69	160	grill	grill	NOUN
iajs-2707	69	161	semi	semi	ADJ
iajs-2707	69	162	-	-	ADJ
iajs-2707	69	163	popen	popen	ADJ
iajs-2707	69	164	set	set	NOUN
iajs-2707	69	165	denoted	denote	VERB
iajs-2707	69	166	by	by	ADP
iajs-2707	69	167	"	"	PUNCT
iajs-2707	69	168	ǥ	ǥ	NOUN
iajs-2707	69	169	-	-	PUNCT
iajs-2707	69	170	spo	spo	NOUN
iajs-2707	69	171	set	set	VERB
iajs-2707	69	172	"	"	PUNCT
iajs-2707	69	173	if	if	SCONJ
iajs-2707	69	174	∃	∃	PROPN
iajs-2707	69	175	v	v	PROPN
iajs-2707	69	176	∈	∈	PROPN
iajs-2707	69	177	po(ẋ	po(ẋ	NOUN
iajs-2707	69	178	)	)	PUNCT
iajs-2707	69	179	such	such	ADJ
iajs-2707	69	180	that	that	SCONJ
iajs-2707	69	181	v	v	NOUN
iajs-2707	69	182	-	-	PUNCT
iajs-2707	69	183	μ	μ	NOUN
iajs-2707	69	184	ǥ	ǥ	NOUN
iajs-2707	69	185	∧	∧	PROPN
iajs-2707	69	186	𝛭-pcl(v	𝛭-pcl(v	NOUN
iajs-2707	69	187	)	)	PUNCT
iajs-2707	69	188	∉ǥ	∉ǥ	NOUN
iajs-2707	69	189	.	.	PUNCT
iajs-2707	70	1	the	the	DET
iajs-2707	70	2	set	set	NOUN
iajs-2707	70	3	of	of	ADP
iajs-2707	70	4	all	all	DET
iajs-2707	70	5	ǥspo	ǥspo	PROPN
iajs-2707	70	6	sets	set	VERB
iajs-2707	70	7	is	be	AUX
iajs-2707	70	8	denoted	denote	VERB
iajs-2707	70	9	by	by	ADP
iajs-2707	70	10	ǥ	ǥ	NOUN
iajs-2707	70	11	-	-	PUNCT
iajs-2707	70	12	spo(ẋ	spo(ẋ	NOUN
iajs-2707	70	13	)	)	PUNCT
iajs-2707	70	14	.	.	PUNCT
iajs-2707	71	1	example3.2	example3.2	NOUN
iajs-2707	71	2	let	let	VERB
iajs-2707	71	3	ẋ=	ẋ=	VERB
iajs-2707	71	4	{	{	PUNCT
iajs-2707	71	5	ϼ1	ϼ1	ADJ
iajs-2707	71	6	,	,	PUNCT
iajs-2707	71	7	ϼ2	ϼ2	NOUN
iajs-2707	71	8	,	,	PUNCT
iajs-2707	71	9	ϼ3	ϼ3	NOUN
iajs-2707	71	10	}	}	PUNCT
iajs-2707	71	11	,	,	PUNCT
iajs-2707	71	12	𝒯=	𝒯=	PROPN
iajs-2707	71	13	{	{	PUNCT
iajs-2707	71	14	ẋ,∅,{ϼ1	ẋ,∅,{ϼ1	ADJ
iajs-2707	71	15	}	}	PUNCT
iajs-2707	71	16	}	}	PUNCT
iajs-2707	71	17	po(ẋ)=	po(ẋ)=	PROPN
iajs-2707	71	18	{	{	PUNCT
iajs-2707	71	19	ủ	ủ	PROPN
iajs-2707	71	20	⊆	⊆	NUM
iajs-2707	71	21	ẋ	ẋ	NOUN
iajs-2707	71	22	;	;	PUNCT
iajs-2707	71	23	ϼ1	ϼ1	PROPN
iajs-2707	71	24	∈	∈	PROPN
iajs-2707	71	25	ủ	ủ	X
iajs-2707	71	26	}	}	PUNCT
iajs-2707	71	27	∪	∪	ADJ
iajs-2707	71	28	∅	∅	NOUN
iajs-2707	71	29	,	,	PUNCT
iajs-2707	71	30	pc(ẋ	pc(ẋ	ADV
iajs-2707	71	31	)	)	PUNCT
iajs-2707	72	1	=	=	SYM
iajs-2707	72	2	{	{	PUNCT
iajs-2707	72	3	ℱ	ℱ	PROPN
iajs-2707	72	4	⊆	⊆	NUM
iajs-2707	72	5	ẋ	ẋ	NOUN
iajs-2707	72	6	;	;	PUNCT
iajs-2707	72	7	ϼ1	ϼ1	PROPN
iajs-2707	72	8	∉	∉	PROPN
iajs-2707	72	9	ℱ	ℱ	PROPN
iajs-2707	72	10	}	}	PUNCT
iajs-2707	72	11	∪	∪	VERB
iajs-2707	72	12	ẋ	ẋ	NOUN
iajs-2707	72	13	.	.	PUNCT
iajs-2707	73	1	then	then	ADV
iajs-2707	73	2	ǥ	ǥ	ADV
iajs-2707	73	3	-	-	PUNCT
iajs-2707	73	4	spo	spo	NOUN
iajs-2707	73	5	(	(	PUNCT
iajs-2707	73	6	ẋ	ẋ	NOUN
iajs-2707	73	7	)	)	PUNCT
iajs-2707	73	8	=	=	SYM
iajs-2707	73	9	𝑝(ẋ	𝑝(ẋ	PROPN
iajs-2707	73	10	)	)	PUNCT
iajs-2707	73	11	.	.	PUNCT
iajs-2707	74	1	example	example	NOUN
iajs-2707	74	2	3.3	3.3	NUM
iajs-2707	74	3	:	:	PUNCT
iajs-2707	74	4	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-2707	74	5	ẋ	ẋ	NOUN
iajs-2707	74	6	=	=	SYM
iajs-2707	74	7	{	{	PUNCT
iajs-2707	74	8	ϼ1	ϼ1	PROPN
iajs-2707	74	9	,	,	PUNCT
iajs-2707	74	10	ϼ2	ϼ2	NOUN
iajs-2707	74	11	,	,	PUNCT
iajs-2707	74	12	ϼ3	ϼ3	NOUN
iajs-2707	74	13	,	,	PUNCT
iajs-2707	74	14	ϼ4	ϼ4	ADV
iajs-2707	74	15	}	}	PUNCT
iajs-2707	74	16	,	,	PUNCT
iajs-2707	75	1	𝒯	𝒯	PROPN
iajs-2707	75	2	=	=	PUNCT
iajs-2707	75	3	{	{	PUNCT
iajs-2707	75	4	ẋ	ẋ	X
iajs-2707	75	5	,	,	PUNCT
iajs-2707	75	6	∅	∅	NOUN
iajs-2707	75	7	,	,	PUNCT
iajs-2707	75	8	{	{	PUNCT
iajs-2707	75	9	ϼ1	ϼ1	ADJ
iajs-2707	75	10	}	}	PUNCT
iajs-2707	75	11	,	,	PUNCT
iajs-2707	75	12	{	{	PUNCT
iajs-2707	75	13	ϼ4	ϼ4	ADV
iajs-2707	75	14	}	}	PUNCT
iajs-2707	75	15	,	,	PUNCT
iajs-2707	75	16	{	{	PUNCT
iajs-2707	75	17	ϼ1	ϼ1	PROPN
iajs-2707	75	18	,	,	PUNCT
iajs-2707	75	19	ϼ4}},ǥ=	ϼ4}},ǥ=	PROPN
iajs-2707	75	20	p(ẋ	p(ẋ	PROPN
iajs-2707	75	21	)	)	PUNCT
iajs-2707	75	22	\	\	PROPN
iajs-2707	75	23	{	{	PUNCT
iajs-2707	75	24	∅	∅	NOUN
iajs-2707	75	25	}	}	PUNCT
iajs-2707	75	26	,	,	PUNCT
iajs-2707	75	27	po(ẋ	po(ẋ	NOUN
iajs-2707	75	28	)	)	PUNCT
iajs-2707	75	29	=	=	SYM
iajs-2707	76	1	{	{	PUNCT
iajs-2707	76	2	ẋ,∅	ẋ,∅	ADJ
iajs-2707	76	3	,	,	PUNCT
iajs-2707	76	4	{	{	PUNCT
iajs-2707	76	5	ϼ1	ϼ1	ADJ
iajs-2707	76	6	}	}	PUNCT
iajs-2707	76	7	,	,	PUNCT
iajs-2707	76	8	{	{	PUNCT
iajs-2707	76	9	ϼ4	ϼ4	ADV
iajs-2707	76	10	}	}	PUNCT
iajs-2707	76	11	,	,	PUNCT
iajs-2707	76	12	{	{	PUNCT
iajs-2707	76	13	ϼ1	ϼ1	ADJ
iajs-2707	76	14	,	,	PUNCT
iajs-2707	76	15	ϼ4	ϼ4	ADJ
iajs-2707	76	16	}	}	PUNCT
iajs-2707	76	17	,	,	PUNCT
iajs-2707	76	18	{	{	PUNCT
iajs-2707	76	19	ϼ1	ϼ1	PROPN
iajs-2707	76	20	,	,	PUNCT
iajs-2707	76	21	ϼ2	ϼ2	NOUN
iajs-2707	76	22	,	,	PUNCT
iajs-2707	76	23	ϼ4	ϼ4	ADV
iajs-2707	76	24	}	}	PUNCT
iajs-2707	76	25	,	,	PUNCT
iajs-2707	76	26	{	{	PUNCT
iajs-2707	76	27	ϼ1	ϼ1	ADJ
iajs-2707	76	28	,	,	PUNCT
iajs-2707	76	29	ϼ3	ϼ3	NOUN
iajs-2707	76	30	,	,	PUNCT
iajs-2707	76	31	ϼ4	ϼ4	ADV
iajs-2707	76	32	}	}	PUNCT
iajs-2707	76	33	}	}	PUNCT
iajs-2707	76	34	.	.	PUNCT
iajs-2707	77	1	pc(ẋ	pc(ẋ	NOUN
iajs-2707	77	2	)	)	PUNCT
iajs-2707	78	1	=	=	PRON
iajs-2707	78	2	{	{	PUNCT
iajs-2707	78	3	ẋ	ẋ	NOUN
iajs-2707	78	4	,	,	PUNCT
iajs-2707	78	5	∅	∅	NOUN
iajs-2707	78	6	,	,	PUNCT
iajs-2707	78	7	{	{	PUNCT
iajs-2707	78	8	ϼ2	ϼ2	NOUN
iajs-2707	78	9	,	,	PUNCT
iajs-2707	78	10	ϼ3	ϼ3	NOUN
iajs-2707	78	11	,	,	PUNCT
iajs-2707	78	12	ϼ4	ϼ4	ADV
iajs-2707	78	13	}	}	PUNCT
iajs-2707	78	14	,	,	PUNCT
iajs-2707	78	15	{	{	PUNCT
iajs-2707	78	16	ϼ1	ϼ1	PROPN
iajs-2707	78	17	,	,	PUNCT
iajs-2707	78	18	ϼ2	ϼ2	NOUN
iajs-2707	78	19	,	,	PUNCT
iajs-2707	78	20	ϼ3	ϼ3	NOUN
iajs-2707	78	21	}	}	PUNCT
iajs-2707	78	22	,	,	PUNCT
iajs-2707	78	23	{	{	PUNCT
iajs-2707	78	24	ϼ2	ϼ2	NOUN
iajs-2707	78	25	,	,	PUNCT
iajs-2707	78	26	ϼ3	ϼ3	NOUN
iajs-2707	78	27	}	}	PUNCT
iajs-2707	78	28	,	,	PUNCT
iajs-2707	78	29	{	{	PUNCT
iajs-2707	78	30	ϼ3	ϼ3	NOUN
iajs-2707	78	31	}	}	PUNCT
iajs-2707	78	32	,	,	PUNCT
iajs-2707	78	33	{	{	PUNCT
iajs-2707	78	34	ϼ2	ϼ2	NOUN
iajs-2707	78	35	}	}	PUNCT
iajs-2707	78	36	}	}	PUNCT
iajs-2707	78	37	,	,	PUNCT
iajs-2707	78	38	then	then	ADV
iajs-2707	78	39	ǥ	ǥ	X
iajs-2707	78	40	-	-	PUNCT
iajs-2707	78	41	spo(ẋ)=	spo(ẋ)=	NOUN
iajs-2707	78	42	{	{	PUNCT
iajs-2707	78	43	ẋ,∅,{ϼ1	ẋ,∅,{ϼ1	NOUN
iajs-2707	78	44	}	}	PUNCT
iajs-2707	78	45	,	,	PUNCT
iajs-2707	78	46	{	{	PUNCT
iajs-2707	78	47	ϼ4	ϼ4	ADV
iajs-2707	78	48	}	}	PUNCT
iajs-2707	78	49	,	,	PUNCT
iajs-2707	78	50	{	{	PUNCT
iajs-2707	78	51	ϼ1	ϼ1	PROPN
iajs-2707	78	52	,	,	PUNCT
iajs-2707	78	53	ϼ2	ϼ2	NOUN
iajs-2707	78	54	}	}	PUNCT
iajs-2707	78	55	,	,	PUNCT
iajs-2707	78	56	{	{	PUNCT
iajs-2707	78	57	ϼ1	ϼ1	ADJ
iajs-2707	78	58	,	,	PUNCT
iajs-2707	78	59	ϼ3	ϼ3	NOUN
iajs-2707	78	60	}	}	PUNCT
iajs-2707	78	61	,	,	PUNCT
iajs-2707	78	62	{	{	PUNCT
iajs-2707	78	63	ϼ1	ϼ1	ADJ
iajs-2707	78	64	,	,	PUNCT
iajs-2707	78	65	ϼ4	ϼ4	ADJ
iajs-2707	78	66	}	}	PUNCT
iajs-2707	78	67	,	,	PUNCT
iajs-2707	78	68	{	{	PUNCT
iajs-2707	78	69	ϼ2	ϼ2	NOUN
iajs-2707	78	70	,	,	PUNCT
iajs-2707	78	71	ϼ4	ϼ4	ADV
iajs-2707	78	72	}	}	PUNCT
iajs-2707	78	73	,	,	PUNCT
iajs-2707	78	74	{	{	PUNCT
iajs-2707	78	75	ϼ3	ϼ3	NOUN
iajs-2707	78	76	,	,	PUNCT
iajs-2707	78	77	ϼ4	ϼ4	ADV
iajs-2707	78	78	}	}	PUNCT
iajs-2707	78	79	,	,	PUNCT
iajs-2707	78	80	{	{	PUNCT
iajs-2707	78	81	ϼ1	ϼ1	PROPN
iajs-2707	78	82	,	,	PUNCT
iajs-2707	78	83	ϼ2	ϼ2	NOUN
iajs-2707	78	84	,	,	PUNCT
iajs-2707	78	85	ϼ3	ϼ3	NOUN
iajs-2707	78	86	}	}	PUNCT
iajs-2707	78	87	,	,	PUNCT
iajs-2707	78	88	{	{	PUNCT
iajs-2707	78	89	ϼ1	ϼ1	PROPN
iajs-2707	78	90	,	,	PUNCT
iajs-2707	78	91	ϼ2	ϼ2	NOUN
iajs-2707	78	92	,	,	PUNCT
iajs-2707	78	93	ϼ4	ϼ4	ADV
iajs-2707	78	94	}	}	PUNCT
iajs-2707	78	95	,	,	PUNCT
iajs-2707	78	96	{	{	PUNCT
iajs-2707	78	97	ϼ2	ϼ2	NOUN
iajs-2707	78	98	,	,	PUNCT
iajs-2707	78	99	ϼ3	ϼ3	NOUN
iajs-2707	78	100	,	,	PUNCT
iajs-2707	78	101	ϼ4	ϼ4	ADV
iajs-2707	78	102	}	}	PUNCT
iajs-2707	78	103	,	,	PUNCT
iajs-2707	78	104	{	{	PUNCT
iajs-2707	78	105	ϼ1	ϼ1	ADJ
iajs-2707	78	106	,	,	PUNCT
iajs-2707	78	107	ϼ3	ϼ3	NOUN
iajs-2707	78	108	,	,	PUNCT
iajs-2707	78	109	ϼ4	ϼ4	ADV
iajs-2707	78	110	}	}	PUNCT
iajs-2707	78	111	.	.	PUNCT
iajs-2707	79	1	remark	remark	VERB
iajs-2707	79	2	3.4	3.4	NUM
iajs-2707	79	3	:	:	PUNCT
iajs-2707	80	1	[	[	X
iajs-2707	80	2	7	7	X
iajs-2707	80	3	]	]	X
iajs-2707	80	4	⋃	⋃	NOUN
iajs-2707	80	5	𝑃𝐶𝐿(ủ𝑖	𝑃𝐶𝐿(ủ𝑖	NOUN
iajs-2707	80	6	)	)	PUNCT
iajs-2707	80	7	⊆	⊆	NUM
iajs-2707	80	8	𝑃𝐶𝐿(⋃	𝑃𝐶𝐿(⋃	PROPN
iajs-2707	80	9	ủ𝑖)𝑖∈∧𝑖∈∧	ủ𝑖)𝑖∈∧𝑖∈∧	PROPN
iajs-2707	80	10	.	.	PUNCT
iajs-2707	81	1	proposition	proposition	NOUN
iajs-2707	81	2	3.5	3.5	NUM
iajs-2707	81	3	:	:	PUNCT
iajs-2707	81	4	if	if	SCONJ
iajs-2707	81	5	μ𝑖	μ𝑖	VERB
iajs-2707	81	6	∈	∈	PROPN
iajs-2707	81	7	ǥ	ǥ	NOUN
iajs-2707	81	8	-	-	PUNCT
iajs-2707	81	9	spo(ẋ	spo(ẋ	NOUN
iajs-2707	81	10	)	)	PUNCT
iajs-2707	81	11	∀	∀	PUNCT
iajs-2707	81	12	𝑖	𝑖	SYM
iajs-2707	81	13	∈	∈	PROPN
iajs-2707	81	14	∧	∧	PROPN
iajs-2707	81	15	,	,	PUNCT
iajs-2707	81	16	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
iajs-2707	81	17	⋃	⋃	VERB
iajs-2707	81	18	μ𝑖𝑖𝜖∧	μ𝑖𝑖𝜖∧	PROPN
iajs-2707	81	19	∈	∈	PROPN
iajs-2707	81	20	ǥ	ǥ	NOUN
iajs-2707	81	21	-	-	PUNCT
iajs-2707	81	22	spo(ẋ	spo(ẋ	NOUN
iajs-2707	81	23	)	)	PUNCT
iajs-2707	81	24	.	.	PUNCT
iajs-2707	82	1	ibn	ibn	PROPN
iajs-2707	82	2	al	al	PROPN
iajs-2707	82	3	-	-	PUNCT
iajs-2707	82	4	haitham	haitham	PROPN
iajs-2707	82	5	jour	jour	X
iajs-2707	82	6	.	.	PROPN
iajs-2707	82	7	for	for	ADP
iajs-2707	82	8	pure	pure	ADJ
iajs-2707	82	9	&	&	CCONJ
iajs-2707	82	10	appl	appl	PROPN
iajs-2707	82	11	.	.	PUNCT
iajs-2707	83	1	sci	sci	PROPN
iajs-2707	83	2	.	.	PROPN
iajs-2707	84	1	34(4)2021	34(4)2021	NUM
iajs-2707	84	2	112	112	NUM
iajs-2707	84	3	proof	proof	NOUN
iajs-2707	84	4	:	:	PUNCT
iajs-2707	84	5	let	let	VERB
iajs-2707	84	6	μ𝑖	μ𝑖	VERB
iajs-2707	84	7	∈	∈	NOUN
iajs-2707	84	8	ǥ	ǥ	NOUN
iajs-2707	84	9	-	-	PUNCT
iajs-2707	84	10	spo(ẋ	spo(ẋ	NOUN
iajs-2707	84	11	)	)	PUNCT
iajs-2707	84	12	,	,	PUNCT
iajs-2707	84	13	∃	∃	PROPN
iajs-2707	84	14	ủ	ủ	PROPN
iajs-2707	84	15	∈	∈	PROPN
iajs-2707	84	16	po(ẋ	po(ẋ	NOUN
iajs-2707	84	17	)	)	PUNCT
iajs-2707	84	18	,	,	PUNCT
iajs-2707	84	19	(	(	PUNCT
iajs-2707	84	20	ủ𝑖	ủ𝑖	X
iajs-2707	84	21	−	−	PROPN
iajs-2707	84	22	μ	μ	PROPN
iajs-2707	84	23	𝑖	𝑖	PROPN
iajs-2707	84	24	)	)	PUNCT
iajs-2707	85	1	∉ǥ	∉ǥ	PROPN
iajs-2707	85	2	∧	∧	PROPN
iajs-2707	85	3	(	(	PUNCT
iajs-2707	85	4	μ𝑖	μ𝑖	NOUN
iajs-2707	85	5	−pcl	−pcl	NOUN
iajs-2707	85	6	(	(	PUNCT
iajs-2707	85	7	ủ𝑖	ủ𝑖	X
iajs-2707	85	8	)	)	PUNCT
iajs-2707	85	9	)	)	PUNCT
iajs-2707	85	10	∉	∉	PROPN
iajs-2707	85	11	ǥ∀	ǥ∀	PROPN
iajs-2707	85	12	𝑖	𝑖	SYM
iajs-2707	85	13	∈∧	∈∧	PROPN
iajs-2707	85	14	.	.	PUNCT
iajs-2707	86	1	this	this	PRON
iajs-2707	86	2	implies	imply	VERB
iajs-2707	86	3	,	,	PUNCT
iajs-2707	86	4	⋃	⋃	PROPN
iajs-2707	86	5	(	(	PUNCT
iajs-2707	86	6	ủ𝑖𝑖	ủ𝑖𝑖	X
iajs-2707	86	7	𝛭𝑖	𝛭𝑖	PROPN
iajs-2707	86	8	)	)	PUNCT
iajs-2707	86	9	∉	∉	PROPN
iajs-2707	87	1	ǥ	ǥ	PROPN
iajs-2707	87	2	,	,	PUNCT
iajs-2707	87	3	𝑠𝑜	𝑠𝑜	X
iajs-2707	87	4	(	(	PUNCT
iajs-2707	87	5	⋃	⋃	PROPN
iajs-2707	87	6	ủ𝑖	ủ𝑖	PRON
iajs-2707	87	7	−	−	PROPN
iajs-2707	87	8	⋃	⋃	NOUN
iajs-2707	87	9	𝛭𝑖)𝑖𝑖	𝛭𝑖)𝑖𝑖	NOUN
iajs-2707	87	10	⊆	⊆	NUM
iajs-2707	87	11	⋃	⋃	PROPN
iajs-2707	87	12	(	(	PUNCT
iajs-2707	87	13	ủ𝑖	ủ𝑖	PRON
iajs-2707	87	14	−	−	PROPN
iajs-2707	87	15	𝛭𝑖	𝛭𝑖	PROPN
iajs-2707	87	16	)	)	PUNCT
iajs-2707	87	17	𝑖	𝑖	PROPN
iajs-2707	87	18	∉	∉	PROPN
iajs-2707	87	19	ǥ	ǥ	PROPN
iajs-2707	87	20	,	,	PUNCT
iajs-2707	87	21	therefore	therefore	ADV
iajs-2707	87	22	,	,	PUNCT
iajs-2707	87	23	(	(	PUNCT
iajs-2707	87	24	⋃	⋃	PUNCT
iajs-2707	87	25	ủ𝑖𝑖	ủ𝑖𝑖	NOUN
iajs-2707	87	26	−	−	PROPN
iajs-2707	87	27	⋃	⋃	PROPN
iajs-2707	87	28	μ𝑖	μ𝑖	NUM
iajs-2707	87	29	)	)	PUNCT
iajs-2707	87	30	∉	∉	PROPN
iajs-2707	87	31	𝑖	𝑖	SYM
iajs-2707	87	32	ǥ	ǥ	NOUN
iajs-2707	87	33	,	,	PUNCT
iajs-2707	87	34	on	on	ADP
iajs-2707	87	35	the	the	DET
iajs-2707	87	36	other	other	ADJ
iajs-2707	87	37	hands	hand	NOUN
iajs-2707	87	38	,	,	PUNCT
iajs-2707	87	39	(	(	PUNCT
iajs-2707	87	40	μ𝑖	μ𝑖	ADP
iajs-2707	87	41	−	−	PROPN
iajs-2707	87	42	pcl	pcl	PROPN
iajs-2707	87	43	(	(	PUNCT
iajs-2707	87	44	ủ𝑖	ủ𝑖	NOUN
iajs-2707	87	45	)	)	PUNCT
iajs-2707	87	46	)	)	PUNCT
iajs-2707	87	47	∉	∉	PROPN
iajs-2707	88	1	ǥ	ǥ	ADP
iajs-2707	88	2	∀	∀	NOUN
iajs-2707	88	3	𝑖	𝑖	SYM
iajs-2707	88	4	∈	∈	PROPN
iajs-2707	88	5	∧	∧	NOUN
iajs-2707	88	6	,	,	PUNCT
iajs-2707	88	7	⋃	⋃	PROPN
iajs-2707	88	8	(	(	PUNCT
iajs-2707	88	9	μ𝑖	μ𝑖	NOUN
iajs-2707	88	10	−	−	NOUN
iajs-2707	88	11	𝑃𝐶𝐿(ủ𝑖))𝑖	𝑃𝐶𝐿(ủ𝑖))𝑖	ADJ
iajs-2707	88	12	∉	∉	PROPN
iajs-2707	88	13	ǥ	ǥ	PROPN
iajs-2707	88	14	,	,	PUNCT
iajs-2707	88	15	(	(	PUNCT
iajs-2707	88	16	⋃	⋃	ADV
iajs-2707	88	17	μ𝑖	μ𝑖	ADP
iajs-2707	88	18	−	−	NOUN
iajs-2707	88	19	⋃	⋃	NOUN
iajs-2707	88	20	𝑃𝐶𝐿	𝑃𝐶𝐿	PROPN
iajs-2707	88	21	(	(	PUNCT
iajs-2707	88	22	ủ𝑖	ủ𝑖	NOUN
iajs-2707	88	23	)	)	PUNCT
iajs-2707	88	24	)	)	PUNCT
iajs-2707	89	1	⊆	⊆	NUM
iajs-2707	89	2	⋃	⋃	PROPN
iajs-2707	89	3	(	(	PUNCT
iajs-2707	89	4	μ𝑖	μ𝑖	ADP
iajs-2707	89	5	−	−	PROPN
iajs-2707	89	6	𝑃𝐶𝐿(ủ𝑖	𝑃𝐶𝐿(ủ𝑖	PROPN
iajs-2707	89	7	)	)	PUNCT
iajs-2707	89	8	)	)	PUNCT
iajs-2707	89	9	∉	∉	PROPN
iajs-2707	89	10	ǥ𝑖𝑖𝑖	ǥ𝑖𝑖𝑖	NOUN
iajs-2707	89	11	so	so	ADV
iajs-2707	89	12	,	,	PUNCT
iajs-2707	89	13	⋃	⋃	PROPN
iajs-2707	89	14	μ𝑖	μ𝑖	ADP
iajs-2707	89	15	−	−	NOUN
iajs-2707	89	16	⋃	⋃	PROPN
iajs-2707	89	17	(	(	PUNCT
iajs-2707	89	18	𝑃𝐶𝐿(ủ𝑖	𝑃𝐶𝐿(ủ𝑖	PROPN
iajs-2707	89	19	)	)	PUNCT
iajs-2707	89	20	)	)	PUNCT
iajs-2707	89	21	∉	∉	PROPN
iajs-2707	89	22	ǥ𝑖𝑖	ǥ𝑖𝑖	NOUN
iajs-2707	89	23	,	,	PUNCT
iajs-2707	89	24	since	since	SCONJ
iajs-2707	89	25	⋃	⋃	PROPN
iajs-2707	89	26	𝑃𝐶𝐿(ủ𝑖	𝑃𝐶𝐿(ủ𝑖	PROPN
iajs-2707	89	27	)	)	PUNCT
iajs-2707	89	28	⊆	⊆	NUM
iajs-2707	89	29	𝑃𝐶𝐿(⋃	𝑃𝐶𝐿(⋃	ADJ
iajs-2707	89	30	ủ𝑖𝐼	ủ𝑖𝐼	NOUN
iajs-2707	89	31	)	)	PUNCT
iajs-2707	89	32	,	,	PUNCT
iajs-2707	89	33	𝑖	𝑖	X
iajs-2707	89	34	there	there	ADV
iajs-2707	89	35	for	for	ADP
iajs-2707	89	36	(	(	PUNCT
iajs-2707	89	37	⋃	⋃	PROPN
iajs-2707	89	38	μ𝑖	μ𝑖	NOUN
iajs-2707	89	39	−	−	NOUN
iajs-2707	89	40	𝑃𝐶𝐿(⋃	𝑃𝐶𝐿(⋃	ADJ
iajs-2707	89	41	ủ𝑖	ủ𝑖	NOUN
iajs-2707	89	42	)	)	PUNCT
iajs-2707	89	43	)	)	PUNCT
iajs-2707	90	1	⊆	⊆	NUM
iajs-2707	90	2	(	(	PUNCT
iajs-2707	90	3	⋃	⋃	NOUN
iajs-2707	90	4	μ𝑖	μ𝑖	ADP
iajs-2707	90	5	−	−	NOUN
iajs-2707	90	6	⋃	⋃	NOUN
iajs-2707	90	7	𝑃𝐶𝐿(ủ𝑖))𝑖𝑖	𝑃𝐶𝐿(ủ𝑖))𝑖𝑖	NUM
iajs-2707	90	8	∉	∉	X
iajs-2707	90	9	ǥ𝑖𝑖∈∧	ǥ𝑖𝑖∈∧	PROPN
iajs-2707	90	10	so,(⋃	so,(⋃	NOUN
iajs-2707	90	11	μ𝑖	μ𝑖	ADP
iajs-2707	90	12	−	−	NOUN
iajs-2707	90	13	𝑃𝐶𝐿(⋃	𝑃𝐶𝐿(⋃	PROPN
iajs-2707	90	14	ủ𝑖	ủ𝑖	NOUN
iajs-2707	90	15	)	)	PUNCT
iajs-2707	90	16	)	)	PUNCT
iajs-2707	91	1	∉	∉	PROPN
iajs-2707	91	2	ǥ𝑖𝑖	ǥ𝑖𝑖	NOUN
iajs-2707	91	3	.	.	PUNCT
iajs-2707	92	1	corollary	corollary	ADJ
iajs-2707	92	2	3.6	3.6	NUM
iajs-2707	92	3	:	:	PUNCT
iajs-2707	92	4	if	if	SCONJ
iajs-2707	92	5	ℱ𝑖	ℱ𝑖	NUM
iajs-2707	92	6	∈	∈	PROPN
iajs-2707	92	7	ǥ	ǥ	NOUN
iajs-2707	92	8	-	-	PUNCT
iajs-2707	92	9	spc(ẋ	spc(ẋ	PROPN
iajs-2707	92	10	)	)	PUNCT
iajs-2707	92	11	,	,	PUNCT
iajs-2707	92	12	then	then	ADV
iajs-2707	92	13	⋂	⋂	PROPN
iajs-2707	92	14	ℱ𝑖𝑖	ℱ𝑖𝑖	PROPN
iajs-2707	92	15	∈	∈	PROPN
iajs-2707	92	16	ǥ	ǥ	NOUN
iajs-2707	92	17	-	-	PUNCT
iajs-2707	92	18	spc(ẋ	spc(ẋ	PROPN
iajs-2707	92	19	)	)	PUNCT
iajs-2707	92	20	.	.	PUNCT
iajs-2707	93	1	remark	remark	VERB
iajs-2707	93	2	3.7	3.7	NUM
iajs-2707	93	3	:	:	PUNCT
iajs-2707	93	4	𝑙𝑒𝑡	𝑙𝑒𝑡	PROPN
iajs-2707	93	5	𝛭	𝛭	PROPN
iajs-2707	93	6	,	,	PUNCT
iajs-2707	93	7	𝑆	𝑆	PROPN
iajs-2707	93	8	∈	∈	PROPN
iajs-2707	93	9	ǥ	ǥ	NOUN
iajs-2707	93	10	-spo(ẋ	-spo(ẋ	PROPN
iajs-2707	93	11	)	)	PUNCT
iajs-2707	93	12	then	then	ADV
iajs-2707	93	13	μ	μ	PROPN
iajs-2707	93	14	∩	∩	ADJ
iajs-2707	93	15	𝑆	𝑆	PROPN
iajs-2707	93	16	need	need	VERB
iajs-2707	93	17	not	not	PART
iajs-2707	93	18	to	to	PART
iajs-2707	93	19	be	be	AUX
iajs-2707	93	20	a	a	DET
iajs-2707	93	21	ǥ	ǥ	NOUN
iajs-2707	93	22	-	-	PUNCT
iajs-2707	93	23	spo	spo	NOUN
iajs-2707	93	24	set	set	PROPN
iajs-2707	93	25	.	.	PUNCT
iajs-2707	94	1	example	example	NOUN
iajs-2707	94	2	3.8	3.8	NUM
iajs-2707	94	3	:	:	PUNCT
iajs-2707	94	4	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-2707	94	5	ẋ	ẋ	NOUN
iajs-2707	94	6	=	=	SYM
iajs-2707	94	7	{	{	PUNCT
iajs-2707	94	8	ϼ1	ϼ1	PROPN
iajs-2707	94	9	,	,	PUNCT
iajs-2707	94	10	ϼ2	ϼ2	NOUN
iajs-2707	94	11	,	,	PUNCT
iajs-2707	94	12	ϼ3	ϼ3	NOUN
iajs-2707	94	13	,	,	PUNCT
iajs-2707	94	14	ϼ4	ϼ4	ADV
iajs-2707	94	15	}	}	PUNCT
iajs-2707	94	16	,	,	PUNCT
iajs-2707	94	17	𝒯	𝒯	PROPN
iajs-2707	94	18	=	=	PUNCT
iajs-2707	94	19	{	{	PUNCT
iajs-2707	94	20	ẋ	ẋ	X
iajs-2707	94	21	,	,	PUNCT
iajs-2707	94	22	∅	∅	NOUN
iajs-2707	94	23	,	,	PUNCT
iajs-2707	94	24	{	{	PUNCT
iajs-2707	94	25	ϼ1	ϼ1	ADJ
iajs-2707	94	26	}	}	PUNCT
iajs-2707	94	27	,	,	PUNCT
iajs-2707	94	28	{	{	PUNCT
iajs-2707	94	29	ϼ4	ϼ4	ADV
iajs-2707	94	30	}	}	PUNCT
iajs-2707	94	31	,	,	PUNCT
iajs-2707	94	32	{	{	PUNCT
iajs-2707	94	33	ϼ1	ϼ1	ADJ
iajs-2707	94	34	,	,	PUNCT
iajs-2707	94	35	ϼ4	ϼ4	ADJ
iajs-2707	94	36	}	}	PUNCT
iajs-2707	94	37	}	}	PUNCT
iajs-2707	94	38	.	.	PUNCT
iajs-2707	95	1	𝑇ℎ𝑒𝑛	𝑇ℎ𝑒𝑛	NOUN
iajs-2707	95	2	𝑃𝑂(ẋ	𝑃𝑂(ẋ	PROPN
iajs-2707	95	3	)	)	PUNCT
iajs-2707	96	1	=	=	PRON
iajs-2707	96	2	{	{	PUNCT
iajs-2707	96	3	ẋ	ẋ	X
iajs-2707	96	4	,	,	PUNCT
iajs-2707	96	5	∅	∅	NOUN
iajs-2707	96	6	,	,	PUNCT
iajs-2707	96	7	{	{	PUNCT
iajs-2707	96	8	ϼ1	ϼ1	PROPN
iajs-2707	96	9	}	}	PUNCT
iajs-2707	96	10	,	,	PUNCT
iajs-2707	96	11	{	{	PUNCT
iajs-2707	96	12	ϼ4	ϼ4	ADV
iajs-2707	96	13	}	}	PUNCT
iajs-2707	96	14	,	,	PUNCT
iajs-2707	96	15	{	{	PUNCT
iajs-2707	96	16	ϼ1	ϼ1	ADJ
iajs-2707	96	17	,	,	PUNCT
iajs-2707	96	18	ϼ4	ϼ4	ADJ
iajs-2707	96	19	}	}	PUNCT
iajs-2707	96	20	,	,	PUNCT
iajs-2707	96	21	{	{	PUNCT
iajs-2707	96	22	ϼ1	ϼ1	PROPN
iajs-2707	96	23	,	,	PUNCT
iajs-2707	96	24	ϼ2	ϼ2	NOUN
iajs-2707	96	25	,	,	PUNCT
iajs-2707	96	26	ϼ4	ϼ4	ADV
iajs-2707	96	27	}	}	PUNCT
iajs-2707	96	28	,	,	PUNCT
iajs-2707	96	29	{	{	PUNCT
iajs-2707	96	30	ϼ1	ϼ1	ADJ
iajs-2707	96	31	,	,	PUNCT
iajs-2707	96	32	ϼ3	ϼ3	NOUN
iajs-2707	96	33	,	,	PUNCT
iajs-2707	96	34	ϼ4	ϼ4	ADV
iajs-2707	96	35	}	}	PUNCT
iajs-2707	96	36	}	}	PUNCT
iajs-2707	96	37	,	,	PUNCT
iajs-2707	96	38	𝑃𝐶(ẋ	𝑃𝐶(ẋ	PROPN
iajs-2707	96	39	)	)	PUNCT
iajs-2707	96	40	=	=	PRON
iajs-2707	96	41	{	{	PUNCT
iajs-2707	96	42	ẋ	ẋ	NOUN
iajs-2707	96	43	,	,	PUNCT
iajs-2707	96	44	∅	∅	NOUN
iajs-2707	96	45	,	,	PUNCT
iajs-2707	96	46	{	{	PUNCT
iajs-2707	96	47	ϼ2	ϼ2	NOUN
iajs-2707	96	48	,	,	PUNCT
iajs-2707	96	49	ϼ3	ϼ3	NOUN
iajs-2707	96	50	,	,	PUNCT
iajs-2707	96	51	ϼ4	ϼ4	ADV
iajs-2707	96	52	}	}	PUNCT
iajs-2707	96	53	,	,	PUNCT
iajs-2707	96	54	{	{	PUNCT
iajs-2707	96	55	ϼ1	ϼ1	PROPN
iajs-2707	96	56	,	,	PUNCT
iajs-2707	96	57	ϼ2	ϼ2	NOUN
iajs-2707	96	58	,	,	PUNCT
iajs-2707	96	59	ϼ3	ϼ3	NOUN
iajs-2707	96	60	}	}	PUNCT
iajs-2707	96	61	,	,	PUNCT
iajs-2707	96	62	{	{	PUNCT
iajs-2707	96	63	ϼ2	ϼ2	NOUN
iajs-2707	96	64	,	,	PUNCT
iajs-2707	96	65	ϼ3	ϼ3	NOUN
iajs-2707	96	66	}	}	PUNCT
iajs-2707	96	67	,	,	PUNCT
iajs-2707	96	68	{	{	PUNCT
iajs-2707	96	69	ϼ3	ϼ3	NOUN
iajs-2707	96	70	}	}	PUNCT
iajs-2707	96	71	,	,	PUNCT
iajs-2707	96	72	{	{	PUNCT
iajs-2707	96	73	ϼ2	ϼ2	NOUN
iajs-2707	96	74	}	}	PUNCT
iajs-2707	96	75	}	}	PUNCT
iajs-2707	96	76	,	,	PUNCT
iajs-2707	96	77	when	when	SCONJ
iajs-2707	96	78	ǥ	ǥ	ADP
iajs-2707	96	79	=	=	NOUN
iajs-2707	96	80	p(ẋ)\	p(ẋ)\	NOUN
iajs-2707	96	81	{	{	PUNCT
iajs-2707	96	82	∅	∅	NOUN
iajs-2707	96	83	}	}	PUNCT
iajs-2707	96	84	,	,	PUNCT
iajs-2707	96	85	𝐻𝑒𝑛𝑐𝑒	𝐻𝑒𝑛𝑐𝑒	PROPN
iajs-2707	96	86	ǥ-𝑆𝑃𝑂(ẋ	ǥ-𝑆𝑃𝑂(ẋ	PROPN
iajs-2707	96	87	)	)	PUNCT
iajs-2707	96	88	=	=	PRON
iajs-2707	96	89	{	{	PUNCT
iajs-2707	96	90	ẋ	ẋ	NOUN
iajs-2707	96	91	,	,	PUNCT
iajs-2707	96	92	∅	∅	NOUN
iajs-2707	96	93	,	,	PUNCT
iajs-2707	96	94	{	{	PUNCT
iajs-2707	96	95	ϼ1	ϼ1	ADJ
iajs-2707	96	96	}	}	PUNCT
iajs-2707	96	97	,	,	PUNCT
iajs-2707	96	98	{	{	PUNCT
iajs-2707	96	99	ϼ4	ϼ4	ADV
iajs-2707	96	100	}	}	PUNCT
iajs-2707	96	101	,	,	PUNCT
iajs-2707	96	102	{	{	PUNCT
iajs-2707	96	103	ϼ1	ϼ1	PROPN
iajs-2707	96	104	,	,	PUNCT
iajs-2707	96	105	ϼ2	ϼ2	NOUN
iajs-2707	96	106	}	}	PUNCT
iajs-2707	96	107	,	,	PUNCT
iajs-2707	96	108	{	{	PUNCT
iajs-2707	96	109	ϼ1	ϼ1	ADJ
iajs-2707	96	110	,	,	PUNCT
iajs-2707	96	111	ϼ3	ϼ3	NOUN
iajs-2707	96	112	}	}	PUNCT
iajs-2707	96	113	,	,	PUNCT
iajs-2707	96	114	{	{	PUNCT
iajs-2707	96	115	ϼ1	ϼ1	ADJ
iajs-2707	96	116	,	,	PUNCT
iajs-2707	96	117	ϼ4	ϼ4	ADJ
iajs-2707	96	118	}	}	PUNCT
iajs-2707	96	119	,	,	PUNCT
iajs-2707	96	120	{	{	PUNCT
iajs-2707	96	121	ϼ2	ϼ2	NOUN
iajs-2707	96	122	,	,	PUNCT
iajs-2707	96	123	ϼ4	ϼ4	ADV
iajs-2707	96	124	}	}	PUNCT
iajs-2707	96	125	,	,	PUNCT
iajs-2707	96	126	{	{	PUNCT
iajs-2707	96	127	ϼ3	ϼ3	NOUN
iajs-2707	96	128	,	,	PUNCT
iajs-2707	96	129	ϼ4	ϼ4	ADV
iajs-2707	96	130	}	}	PUNCT
iajs-2707	96	131	,	,	PUNCT
iajs-2707	96	132	{	{	PUNCT
iajs-2707	96	133	ϼ1	ϼ1	PROPN
iajs-2707	96	134	,	,	PUNCT
iajs-2707	96	135	ϼ2	ϼ2	NOUN
iajs-2707	96	136	,	,	PUNCT
iajs-2707	96	137	ϼ3	ϼ3	NOUN
iajs-2707	96	138	}	}	PUNCT
iajs-2707	96	139	,	,	PUNCT
iajs-2707	96	140	{	{	PUNCT
iajs-2707	96	141	ϼ1	ϼ1	PROPN
iajs-2707	96	142	,	,	PUNCT
iajs-2707	96	143	ϼ2	ϼ2	NOUN
iajs-2707	96	144	,	,	PUNCT
iajs-2707	96	145	ϼ4	ϼ4	ADV
iajs-2707	96	146	}	}	PUNCT
iajs-2707	96	147	,	,	PUNCT
iajs-2707	96	148	{	{	PUNCT
iajs-2707	96	149	ϼ2	ϼ2	NOUN
iajs-2707	96	150	,	,	PUNCT
iajs-2707	96	151	ϼ3	ϼ3	NOUN
iajs-2707	96	152	,	,	PUNCT
iajs-2707	96	153	ϼ4	ϼ4	ADV
iajs-2707	96	154	}	}	PUNCT
iajs-2707	96	155	,	,	PUNCT
iajs-2707	96	156	{	{	PUNCT
iajs-2707	96	157	ϼ1	ϼ1	ADJ
iajs-2707	96	158	,	,	PUNCT
iajs-2707	96	159	ϼ3	ϼ3	NOUN
iajs-2707	96	160	,	,	PUNCT
iajs-2707	96	161	ϼ4	ϼ4	ADV
iajs-2707	96	162	}	}	PUNCT
iajs-2707	96	163	}	}	PUNCT
iajs-2707	96	164	,	,	PUNCT
iajs-2707	96	165	𝑙𝑒𝑡	𝑙𝑒𝑡	PROPN
iajs-2707	96	166	𝛭	𝛭	PROPN
iajs-2707	96	167	=	=	SYM
iajs-2707	96	168	{	{	PUNCT
iajs-2707	96	169	ϼ1	ϼ1	PROPN
iajs-2707	96	170	,	,	PUNCT
iajs-2707	96	171	ϼ2	ϼ2	NOUN
iajs-2707	96	172	,	,	PUNCT
iajs-2707	96	173	ϼ3	ϼ3	NOUN
iajs-2707	96	174	}	}	PUNCT
iajs-2707	96	175	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-2707	97	1	ѕ	ѕ	PROPN
iajs-2707	97	2	=	=	PUNCT
iajs-2707	97	3	{	{	PUNCT
iajs-2707	97	4	ϼ2	ϼ2	NOUN
iajs-2707	97	5	,	,	PUNCT
iajs-2707	97	6	ϼ4	ϼ4	ADV
iajs-2707	97	7	}	}	PUNCT
iajs-2707	97	8	,	,	PUNCT
iajs-2707	97	9	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
iajs-2707	97	10	𝛭	𝛭	VERB
iajs-2707	97	11	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2707	97	12	ѕ	ѕ	PROPN
iajs-2707	97	13	are	be	AUX
iajs-2707	97	14	ǥ	ǥ	ADV
iajs-2707	97	15	-	-	PUNCT
iajs-2707	97	16	spo(ẋ	spo(ẋ	NOUN
iajs-2707	97	17	)	)	PUNCT
iajs-2707	97	18	but	but	CCONJ
iajs-2707	97	19	𝛭∩ѕ	𝛭∩ѕ	PROPN
iajs-2707	97	20	=	=	SYM
iajs-2707	97	21	{	{	PUNCT
iajs-2707	97	22	ϼ2},which	ϼ2},which	NOUN
iajs-2707	97	23	is	be	AUX
iajs-2707	97	24	not	not	PART
iajs-2707	97	25	a	a	DET
iajs-2707	97	26	ǥ	ǥ	NOUN
iajs-2707	97	27	-	-	PUNCT
iajs-2707	97	28	spo(ẋ	spo(ẋ	NOUN
iajs-2707	97	29	)	)	PUNCT
iajs-2707	97	30	.	.	PUNCT
iajs-2707	98	1	remark	remark	VERB
iajs-2707	98	2	3.9	3.9	NUM
iajs-2707	98	3	:	:	PUNCT
iajs-2707	98	4	let	let	VERB
iajs-2707	98	5	μ	μ	NOUN
iajs-2707	98	6	,	,	PUNCT
iajs-2707	98	7	𝑆	𝑆	PROPN
iajs-2707	98	8	∈	∈	PROPN
iajs-2707	98	9	ǥ	ǥ	ADP
iajs-2707	98	10	-spc(ẋ	-spc(ẋ	NOUN
iajs-2707	98	11	)	)	PUNCT
iajs-2707	98	12	then	then	ADV
iajs-2707	98	13	μ	μ	PROPN
iajs-2707	98	14	∪	∪	PROPN
iajs-2707	98	15	𝑆	𝑆	PROPN
iajs-2707	98	16	need	need	AUX
iajs-2707	98	17	not	not	PART
iajs-2707	98	18	be	be	AUX
iajs-2707	98	19	a	a	DET
iajs-2707	98	20	ǥ	ǥ	NOUN
iajs-2707	98	21	-	-	PUNCT
iajs-2707	98	22	spc	spc	NOUN
iajs-2707	98	23	set	set	NOUN
iajs-2707	98	24	.	.	PUNCT
iajs-2707	99	1	see	see	VERB
iajs-2707	99	2	example	example	NOUN
iajs-2707	99	3	2.8	2.8	NUM
iajs-2707	99	4	,	,	PUNCT
iajs-2707	99	5	𝑙𝑒𝑡	𝑙𝑒𝑡	PROPN
iajs-2707	99	6	𝛭	𝛭	PROPN
iajs-2707	99	7	=	=	SYM
iajs-2707	99	8	{	{	PUNCT
iajs-2707	99	9	ϼ1	ϼ1	PROPN
iajs-2707	99	10	,	,	PUNCT
iajs-2707	99	11	ϼ2	ϼ2	NOUN
iajs-2707	99	12	,	,	PUNCT
iajs-2707	99	13	ϼ3	ϼ3	NOUN
iajs-2707	99	14	}	}	PUNCT
iajs-2707	99	15	,	,	PUNCT
iajs-2707	100	1	ѕ	ѕ	PROPN
iajs-2707	100	2	=	=	PRON
iajs-2707	100	3	{	{	PUNCT
iajs-2707	100	4	ϼ2	ϼ2	NOUN
iajs-2707	100	5	,	,	PUNCT
iajs-2707	100	6	ϼ4	ϼ4	ADV
iajs-2707	100	7	}	}	PUNCT
iajs-2707	100	8	,	,	PUNCT
iajs-2707	100	9	𝛭𝑐	𝛭𝑐	PROPN
iajs-2707	100	10	=	=	PUNCT
iajs-2707	100	11	{	{	PUNCT
iajs-2707	100	12	ϼ4	ϼ4	ADV
iajs-2707	100	13	}	}	PUNCT
iajs-2707	100	14	,	,	PUNCT
iajs-2707	100	15	ѕ𝑐	ѕ𝑐	INTJ
iajs-2707	100	16	=	=	NOUN
iajs-2707	100	17	{	{	PUNCT
iajs-2707	100	18	ϼ2	ϼ2	NOUN
iajs-2707	100	19	,	,	PUNCT
iajs-2707	100	20	ϼ3	ϼ3	NOUN
iajs-2707	100	21	}	}	PUNCT
iajs-2707	100	22	,	,	PUNCT
iajs-2707	100	23	μ𝑐	μ𝑐	INTJ
iajs-2707	100	24	,	,	PUNCT
iajs-2707	100	25	𝑆𝑐	𝑆𝑐	PROPN
iajs-2707	100	26	𝑎𝑟𝑒	𝑎𝑟𝑒	NOUN
iajs-2707	100	27	ǥ𝑆𝑃𝐶(ẋ	ǥ𝑆𝑃𝐶(ẋ	PROPN
iajs-2707	100	28	)	)	PUNCT
iajs-2707	100	29	,	,	PUNCT
iajs-2707	100	30	and	and	CCONJ
iajs-2707	100	31	μ𝑐	μ𝑐	X
iajs-2707	100	32	∪	∪	NOUN
iajs-2707	100	33	ѕ𝑐	ѕ𝑐	INTJ
iajs-2707	100	34	=	=	PUNCT
iajs-2707	100	35	{	{	PUNCT
iajs-2707	100	36	ϼ1	ϼ1	ADJ
iajs-2707	100	37	,	,	PUNCT
iajs-2707	100	38	ϼ3	ϼ3	NOUN
iajs-2707	100	39	,	,	PUNCT
iajs-2707	100	40	ϼ4	ϼ4	ADV
iajs-2707	100	41	}	}	PUNCT
iajs-2707	100	42	which	which	PRON
iajs-2707	100	43	is	be	AUX
iajs-2707	100	44	not	not	PART
iajs-2707	100	45	a	a	DET
iajs-2707	100	46	ǥ	ǥ	NOUN
iajs-2707	100	47	-	-	PUNCT
iajs-2707	100	48	spc(ẋ	spc(ẋ	PROPN
iajs-2707	100	49	)	)	PUNCT
iajs-2707	100	50	.	.	PUNCT
iajs-2707	101	1	remark	remark	VERB
iajs-2707	101	2	3.10	3.10	NUM
iajs-2707	101	3	:	:	PUNCT
iajs-2707	102	1	[	[	X
iajs-2707	102	2	7	7	X
iajs-2707	102	3	]	]	X
iajs-2707	102	4	each	each	DET
iajs-2707	102	5	open	open	ADJ
iajs-2707	102	6	set	set	NOUN
iajs-2707	102	7	is	be	AUX
iajs-2707	102	8	a	a	DET
iajs-2707	102	9	preopen	preopen	ADJ
iajs-2707	102	10	set	set	NOUN
iajs-2707	102	11	.	.	PUNCT
iajs-2707	103	1	proposition	proposition	NOUN
iajs-2707	103	2	3.11	3.11	NUM
iajs-2707	103	3	:	:	PUNCT
iajs-2707	103	4	each	each	DET
iajs-2707	103	5	open	open	ADJ
iajs-2707	103	6	set	set	NOUN
iajs-2707	103	7	is	be	AUX
iajs-2707	103	8	a	a	DET
iajs-2707	103	9	ǥ	ǥ	NOUN
iajs-2707	103	10	-spo	-spo	NOUN
iajs-2707	103	11	set	set	NOUN
iajs-2707	103	12	.	.	PUNCT
iajs-2707	104	1	proof	proof	NOUN
iajs-2707	104	2	:	:	PUNCT
iajs-2707	104	3	let	let	VERB
iajs-2707	104	4	𝛭	𝛭	PROPN
iajs-2707	104	5	∈	∈	PROPN
iajs-2707	104	6	𝒯	𝒯	PROPN
iajs-2707	104	7	by	by	ADP
iajs-2707	104	8	remark	remark	NOUN
iajs-2707	104	9	2.4	2.4	NUM
iajs-2707	104	10	,	,	PUNCT
iajs-2707	104	11	so	so	CCONJ
iajs-2707	104	12	𝛭	𝛭	PROPN
iajs-2707	104	13	is	be	AUX
iajs-2707	104	14	a	a	DET
iajs-2707	104	15	preopen	preopen	ADJ
iajs-2707	104	16	set	set	NOUN
iajs-2707	104	17	;	;	PUNCT
iajs-2707	104	18	∃𝛭	∃𝛭	PROPN
iajs-2707	104	19	∈	∈	PROPN
iajs-2707	104	20	𝑝𝑜(ẋ	𝑝𝑜(ẋ	PRON
iajs-2707	104	21	)	)	PUNCT
iajs-2707	104	22	,	,	PUNCT
iajs-2707	104	23	such	such	ADJ
iajs-2707	104	24	that	that	SCONJ
iajs-2707	104	25	,	,	PUNCT
iajs-2707	104	26	𝛭-𝛭	𝛭-𝛭	NOUN
iajs-2707	104	27	=	=	SYM
iajs-2707	104	28	{	{	PUNCT
iajs-2707	104	29	∅	∅	NOUN
iajs-2707	104	30	}	}	PUNCT
iajs-2707	104	31	∉	∉	PROPN
iajs-2707	104	32	ǥ	ǥ	PROPN
iajs-2707	104	33	,	,	PUNCT
iajs-2707	104	34	and	and	CCONJ
iajs-2707	104	35	𝛭-pcl	𝛭-pcl	NOUN
iajs-2707	104	36	(	(	PUNCT
iajs-2707	104	37	𝛭	𝛭	PROPN
iajs-2707	104	38	)	)	PUNCT
iajs-2707	104	39	=	=	PRON
iajs-2707	104	40	{	{	PUNCT
iajs-2707	104	41	∅	∅	NOUN
iajs-2707	104	42	}	}	PUNCT
iajs-2707	104	43	∉	∉	PROPN
iajs-2707	104	44	ǥ	ǥ	ADP
iajs-2707	104	45	,	,	PUNCT
iajs-2707	104	46	𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟	𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟	ADJ
iajs-2707	104	47	𝛭	𝛭	PROPN
iajs-2707	104	48	is	be	AUX
iajs-2707	104	49	a	a	DET
iajs-2707	104	50	ǥ	ǥ	NOUN
iajs-2707	104	51	-	-	PUNCT
iajs-2707	104	52	spo	spo	NOUN
iajs-2707	104	53	set	set	VERB
iajs-2707	104	54	.	.	PUNCT
iajs-2707	105	1	corollary	corollary	ADJ
iajs-2707	105	2	3.12	3.12	NUM
iajs-2707	105	3	:	:	PUNCT
iajs-2707	105	4	if	if	SCONJ
iajs-2707	105	5	f	f	PROPN
iajs-2707	105	6	is	be	AUX
iajs-2707	105	7	a	a	DET
iajs-2707	105	8	closed	closed	ADJ
iajs-2707	105	9	set	set	NOUN
iajs-2707	105	10	,	,	PUNCT
iajs-2707	105	11	then	then	ADV
iajs-2707	105	12	f	f	PROPN
iajs-2707	105	13	is	be	AUX
iajs-2707	105	14	a	a	DET
iajs-2707	105	15	ǥ	ǥ	NOUN
iajs-2707	105	16	-	-	PUNCT
iajs-2707	105	17	spc	spc	NOUN
iajs-2707	105	18	set	set	NOUN
iajs-2707	105	19	.	.	PUNCT
iajs-2707	106	1	proposition	proposition	NOUN
iajs-2707	106	2	3.13	3.13	NUM
iajs-2707	106	3	:	:	PUNCT
iajs-2707	106	4	every	every	DET
iajs-2707	106	5	semi	semi	ADJ
iajs-2707	106	6	-	-	ADJ
iajs-2707	106	7	po	po	ADJ
iajs-2707	106	8	set	set	NOUN
iajs-2707	106	9	is	be	AUX
iajs-2707	106	10	a	a	DET
iajs-2707	106	11	ǥ	ǥ	NOUN
iajs-2707	106	12	-	-	PUNCT
iajs-2707	106	13	spo	spo	NOUN
iajs-2707	106	14	set	set	NOUN
iajs-2707	106	15	.	.	PUNCT
iajs-2707	107	1	proof	proof	NOUN
iajs-2707	107	2	:	:	PUNCT
iajs-2707	107	3	let	let	VERB
iajs-2707	107	4	𝛭	𝛭	VERB
iajs-2707	107	5	∈	∈	PROPN
iajs-2707	107	6	s	s	NOUN
iajs-2707	107	7	-	-	PUNCT
iajs-2707	107	8	po(ẋ	po(ẋ	NOUN
iajs-2707	107	9	)	)	PUNCT
iajs-2707	107	10	for	for	ADP
iajs-2707	107	11	that	that	DET
iajs-2707	107	12	∃ủ	∃ủ	PROPN
iajs-2707	107	13	∈	∈	PROPN
iajs-2707	107	14	𝑃𝑂(ẋ	𝑃𝑂(ẋ	PROPN
iajs-2707	107	15	)	)	PUNCT
iajs-2707	107	16	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	NOUN
iajs-2707	107	17	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	PROPN
iajs-2707	107	18	ủ	ủ	CCONJ
iajs-2707	107	19	⊆	⊆	NUM
iajs-2707	107	20	μ	μ	NUM
iajs-2707	107	21	⊂	⊂	PROPN
iajs-2707	107	22	𝑃𝐶𝐿(μ	𝑃𝐶𝐿(μ	NUM
iajs-2707	107	23	)	)	PUNCT
iajs-2707	107	24	,	,	PUNCT
iajs-2707	107	25	further	far	ADV
iajs-2707	107	26	more	more	ADV
iajs-2707	107	27	ủ	ủ	PRON
iajs-2707	107	28	μ=	μ=	NOUN
iajs-2707	107	29	{	{	PUNCT
iajs-2707	107	30	∅	∅	NOUN
iajs-2707	107	31	}	}	PUNCT
iajs-2707	107	32	∉	∉	NOUN
iajs-2707	107	33	ǥ	ǥ	ADP
iajs-2707	107	34	∧	∧	PROPN
iajs-2707	107	35	𝛭-𝑃𝐶𝐿(𝛭	𝛭-𝑃𝐶𝐿(𝛭	PROPN
iajs-2707	107	36	)	)	PUNCT
iajs-2707	107	37	=	=	SYM
iajs-2707	107	38	{	{	PUNCT
iajs-2707	107	39	∅	∅	NOUN
iajs-2707	107	40	}	}	PUNCT
iajs-2707	107	41	∉	∉	PROPN
iajs-2707	107	42	ǥ	ǥ	SYM
iajs-2707	107	43	.	.	PUNCT
iajs-2707	108	1	hence	hence	ADV
iajs-2707	108	2	,	,	PUNCT
iajs-2707	108	3	μ	μ	PROPN
iajs-2707	108	4	is	be	AUX
iajs-2707	108	5	a	a	DET
iajs-2707	108	6	ǥ	ǥ	NOUN
iajs-2707	108	7	-	-	PUNCT
iajs-2707	108	8	spo	spo	NOUN
iajs-2707	108	9	set	set	VERB
iajs-2707	108	10	.	.	PUNCT
iajs-2707	109	1	as	as	ADP
iajs-2707	109	2	for	for	ADP
iajs-2707	109	3	the	the	DET
iajs-2707	109	4	reverse	reverse	ADJ
iajs-2707	109	5	proposition	proposition	NOUN
iajs-2707	109	6	(	(	PUNCT
iajs-2707	109	7	2.13	2.13	NUM
iajs-2707	109	8	)	)	PUNCT
iajs-2707	109	9	,	,	PUNCT
iajs-2707	109	10	it	it	PRON
iajs-2707	109	11	is	be	AUX
iajs-2707	109	12	not	not	PART
iajs-2707	109	13	necessarily	necessarily	ADV
iajs-2707	109	14	to	to	PART
iajs-2707	109	15	be	be	AUX
iajs-2707	109	16	achieved	achieve	VERB
iajs-2707	109	17	.	.	PUNCT
iajs-2707	109	18	example	example	NOUN
iajs-2707	110	1	3.14	3.14	NUM
iajs-2707	110	2	:	:	PUNCT
iajs-2707	110	3	suppose	suppose	VERB
iajs-2707	110	4	that	that	SCONJ
iajs-2707	110	5	ẋ	ẋ	X
iajs-2707	110	6	=	=	SYM
iajs-2707	110	7	{	{	PUNCT
iajs-2707	110	8	ϼ1	ϼ1	PROPN
iajs-2707	110	9	,	,	PUNCT
iajs-2707	110	10	ϼ2	ϼ2	NOUN
iajs-2707	110	11	,	,	PUNCT
iajs-2707	110	12	ϼ3	ϼ3	NOUN
iajs-2707	110	13	,	,	PUNCT
iajs-2707	110	14	ϼ4	ϼ4	ADV
iajs-2707	110	15	}	}	PUNCT
iajs-2707	110	16	,	,	PUNCT
iajs-2707	110	17	𝒯	𝒯	PROPN
iajs-2707	110	18	=	=	PUNCT
iajs-2707	110	19	{	{	PUNCT
iajs-2707	110	20	ẋ	ẋ	X
iajs-2707	110	21	,	,	PUNCT
iajs-2707	110	22	∅	∅	NOUN
iajs-2707	110	23	,	,	PUNCT
iajs-2707	110	24	{	{	PUNCT
iajs-2707	110	25	ϼ1	ϼ1	ADJ
iajs-2707	110	26	}	}	PUNCT
iajs-2707	110	27	,	,	PUNCT
iajs-2707	110	28	{	{	PUNCT
iajs-2707	110	29	ϼ4	ϼ4	ADV
iajs-2707	110	30	}	}	PUNCT
iajs-2707	110	31	,	,	PUNCT
iajs-2707	110	32	{	{	PUNCT
iajs-2707	110	33	ϼ1	ϼ1	ADJ
iajs-2707	110	34	,	,	PUNCT
iajs-2707	110	35	ϼ4	ϼ4	ADJ
iajs-2707	110	36	}	}	PUNCT
iajs-2707	110	37	}	}	PUNCT
iajs-2707	110	38	,	,	PUNCT
iajs-2707	110	39	ǥ=	ǥ=	CCONJ
iajs-2707	110	40	∅	∅	NOUN
iajs-2707	110	41	,	,	PUNCT
iajs-2707	110	42	𝑃𝑂(ẋ	𝑃𝑂(ẋ	PROPN
iajs-2707	110	43	)	)	PUNCT
iajs-2707	111	1	=	=	PRON
iajs-2707	111	2	{	{	PUNCT
iajs-2707	111	3	ẋ	ẋ	X
iajs-2707	111	4	,	,	PUNCT
iajs-2707	111	5	∅	∅	NOUN
iajs-2707	111	6	,	,	PUNCT
iajs-2707	111	7	{	{	PUNCT
iajs-2707	111	8	ϼ1	ϼ1	ADJ
iajs-2707	111	9	}	}	PUNCT
iajs-2707	111	10	,	,	PUNCT
iajs-2707	111	11	{	{	PUNCT
iajs-2707	111	12	ϼ4	ϼ4	ADV
iajs-2707	111	13	}	}	PUNCT
iajs-2707	111	14	,	,	PUNCT
iajs-2707	111	15	{	{	PUNCT
iajs-2707	111	16	ϼ1	ϼ1	ADJ
iajs-2707	111	17	,	,	PUNCT
iajs-2707	111	18	ϼ4	ϼ4	ADJ
iajs-2707	111	19	}	}	PUNCT
iajs-2707	111	20	,	,	PUNCT
iajs-2707	111	21	{	{	PUNCT
iajs-2707	111	22	ϼ1	ϼ1	PROPN
iajs-2707	111	23	,	,	PUNCT
iajs-2707	111	24	ϼ2	ϼ2	NOUN
iajs-2707	111	25	,	,	PUNCT
iajs-2707	111	26	ϼ4	ϼ4	ADV
iajs-2707	111	27	}	}	PUNCT
iajs-2707	111	28	,	,	PUNCT
iajs-2707	111	29	{	{	PUNCT
iajs-2707	111	30	ϼ1	ϼ1	ADJ
iajs-2707	111	31	,	,	PUNCT
iajs-2707	111	32	ϼ3	ϼ3	NOUN
iajs-2707	111	33	,	,	PUNCT
iajs-2707	111	34	ϼ4	ϼ4	ADV
iajs-2707	111	35	}	}	PUNCT
iajs-2707	111	36	}	}	PUNCT
iajs-2707	111	37	,	,	PUNCT
iajs-2707	111	38	𝑃𝐶(ẋ	𝑃𝐶(ẋ	PROPN
iajs-2707	111	39	)	)	PUNCT
iajs-2707	111	40	=	=	PRON
iajs-2707	111	41	{	{	PUNCT
iajs-2707	111	42	ẋ	ẋ	NOUN
iajs-2707	111	43	,	,	PUNCT
iajs-2707	111	44	∅	∅	NOUN
iajs-2707	111	45	,	,	PUNCT
iajs-2707	111	46	{	{	PUNCT
iajs-2707	111	47	ϼ2	ϼ2	NOUN
iajs-2707	111	48	,	,	PUNCT
iajs-2707	111	49	ϼ3	ϼ3	NOUN
iajs-2707	111	50	,	,	PUNCT
iajs-2707	111	51	ϼ4	ϼ4	ADV
iajs-2707	111	52	}	}	PUNCT
iajs-2707	111	53	,	,	PUNCT
iajs-2707	111	54	{	{	PUNCT
iajs-2707	111	55	ϼ1	ϼ1	PROPN
iajs-2707	111	56	,	,	PUNCT
iajs-2707	111	57	ϼ2	ϼ2	NOUN
iajs-2707	111	58	,	,	PUNCT
iajs-2707	111	59	ϼ3	ϼ3	NOUN
iajs-2707	111	60	}	}	PUNCT
iajs-2707	111	61	,	,	PUNCT
iajs-2707	111	62	{	{	PUNCT
iajs-2707	111	63	ϼ2	ϼ2	NOUN
iajs-2707	111	64	,	,	PUNCT
iajs-2707	111	65	ϼ3	ϼ3	NOUN
iajs-2707	111	66	}	}	PUNCT
iajs-2707	111	67	,	,	PUNCT
iajs-2707	111	68	{	{	PUNCT
iajs-2707	111	69	ϼ3	ϼ3	NOUN
iajs-2707	111	70	}	}	PUNCT
iajs-2707	111	71	,	,	PUNCT
iajs-2707	111	72	{	{	PUNCT
iajs-2707	111	73	ϼ2	ϼ2	NOUN
iajs-2707	111	74	}	}	PUNCT
iajs-2707	111	75	}	}	PUNCT
iajs-2707	111	76	,	,	PUNCT
iajs-2707	111	77	ǥ	ǥ	NOUN
iajs-2707	111	78	-	-	PUNCT
iajs-2707	111	79	spo(ẋ)=p(ẋ	spo(ẋ)=p(ẋ	PROPN
iajs-2707	111	80	)	)	PUNCT
iajs-2707	111	81	.	.	PUNCT
iajs-2707	112	1	then	then	ADV
iajs-2707	112	2	{	{	PUNCT
iajs-2707	112	3	ϼ2}∈	ϼ2}∈	PROPN
iajs-2707	112	4	ǥ-𝑆𝑃𝑂(ẋ),but	ǥ-𝑆𝑃𝑂(ẋ),but	PROPN
iajs-2707	112	5	{	{	PUNCT
iajs-2707	112	6	ϼ2	ϼ2	PROPN
iajs-2707	112	7	}	}	PUNCT
iajs-2707	112	8	∉	∉	PROPN
iajs-2707	112	9	ǥ	ǥ	ADP
iajs-2707	112	10	-spo(ẋ	-spo(ẋ	PROPN
iajs-2707	112	11	)	)	PUNCT
iajs-2707	112	12	.	.	PUNCT
iajs-2707	113	1	corollary	corollary	ADJ
iajs-2707	113	2	3.15	3.15	NUM
iajs-2707	113	3	:	:	PUNCT
iajs-2707	113	4	the	the	DET
iajs-2707	113	5	set	set	NOUN
iajs-2707	113	6	of	of	ADP
iajs-2707	113	7	all	all	DET
iajs-2707	113	8	ǥ	ǥ	NOUN
iajs-2707	113	9	-	-	PUNCT
iajs-2707	113	10	spo	spo	NOUN
iajs-2707	113	11	is	be	AUX
iajs-2707	113	12	a	a	DET
iajs-2707	113	13	supra	supra	ADJ
iajs-2707	113	14	topological	topological	ADJ
iajs-2707	113	15	space	space	NOUN
iajs-2707	113	16	.	.	PUNCT
iajs-2707	114	1	now	now	ADV
iajs-2707	114	2	,	,	PUNCT
iajs-2707	114	3	let	let	VERB
iajs-2707	114	4	's	us	PRON
iajs-2707	114	5	calculate	calculate	VERB
iajs-2707	114	6	the	the	DET
iajs-2707	114	7	following	follow	VERB
iajs-2707	114	8	example	example	NOUN
iajs-2707	114	9	;	;	PUNCT
iajs-2707	114	10	example	example	NOUN
iajs-2707	115	1	3.16	3.16	NUM
iajs-2707	115	2	:	:	PUNCT
iajs-2707	115	3	let	let	VERB
iajs-2707	115	4	ẋ=	ẋ=	ADV
iajs-2707	115	5	{	{	PUNCT
iajs-2707	115	6	ϼ1	ϼ1	ADJ
iajs-2707	115	7	,	,	PUNCT
iajs-2707	115	8	ϼ2	ϼ2	NOUN
iajs-2707	115	9	,	,	PUNCT
iajs-2707	115	10	ϼ3	ϼ3	NOUN
iajs-2707	115	11	}	}	PUNCT
iajs-2707	115	12	,	,	PUNCT
iajs-2707	115	13	𝒯=	𝒯=	PROPN
iajs-2707	115	14	{	{	PUNCT
iajs-2707	115	15	ẋ,∅,{ϼ1	ẋ,∅,{ϼ1	NOUN
iajs-2707	115	16	}	}	PUNCT
iajs-2707	115	17	}	}	PUNCT
iajs-2707	115	18	then	then	ADV
iajs-2707	115	19	ǥ	ǥ	X
iajs-2707	115	20	-	-	PUNCT
iajs-2707	115	21	spo	spo	NOUN
iajs-2707	115	22	(	(	PUNCT
iajs-2707	115	23	ẋ	ẋ	NOUN
iajs-2707	115	24	)	)	PUNCT
iajs-2707	115	25	=	=	SYM
iajs-2707	115	26	𝑝(ẋ	𝑝(ẋ	PROPN
iajs-2707	115	27	)	)	PUNCT
iajs-2707	115	28	and	and	CCONJ
iajs-2707	115	29	ř	ř	X
iajs-2707	115	30	=	=	PUNCT
iajs-2707	115	31	{	{	PUNCT
iajs-2707	115	32	(	(	PUNCT
iajs-2707	115	33	ϼ1	ϼ1	PROPN
iajs-2707	115	34	,	,	PUNCT
iajs-2707	115	35	ϼ1	ϼ1	ADJ
iajs-2707	115	36	)	)	PUNCT
iajs-2707	115	37	,	,	PUNCT
iajs-2707	115	38	(	(	PUNCT
iajs-2707	115	39	ϼ2	ϼ2	NOUN
iajs-2707	115	40	,	,	PUNCT
iajs-2707	115	41	ϼ2	ϼ2	PROPN
iajs-2707	115	42	)	)	PUNCT
iajs-2707	115	43	,	,	PUNCT
iajs-2707	115	44	(	(	PUNCT
iajs-2707	115	45	ϼ3	ϼ3	NOUN
iajs-2707	115	46	,	,	PUNCT
iajs-2707	115	47	ϼ3	ϼ3	NOUN
iajs-2707	115	48	)	)	PUNCT
iajs-2707	115	49	}	}	PUNCT
iajs-2707	115	50	ř	ř	PROPN
iajs-2707	115	51	(	(	PUNCT
iajs-2707	115	52	ϼ1)={ϼ1	ϼ1)={ϼ1	PROPN
iajs-2707	115	53	}	}	PUNCT
iajs-2707	115	54	,	,	PUNCT
iajs-2707	115	55	ř(ϼ2)={ϼ2	ř(ϼ2)={ϼ2	ADV
iajs-2707	115	56	}	}	PUNCT
iajs-2707	115	57	,	,	PUNCT
iajs-2707	115	58	ř	ř	X
iajs-2707	115	59	(	(	PUNCT
iajs-2707	115	60	ϼ3	ϼ3	NOUN
iajs-2707	115	61	)	)	PUNCT
iajs-2707	115	62	=	=	SYM
iajs-2707	115	63	{	{	PUNCT
iajs-2707	115	64	ϼ3	ϼ3	NOUN
iajs-2707	115	65	}	}	PUNCT
iajs-2707	115	66	.	.	PUNCT
iajs-2707	116	1	ibn	ibn	PROPN
iajs-2707	116	2	al	al	PROPN
iajs-2707	116	3	-	-	PUNCT
iajs-2707	116	4	haitham	haitham	PROPN
iajs-2707	116	5	jour	jour	X
iajs-2707	116	6	.	.	PROPN
iajs-2707	116	7	for	for	ADP
iajs-2707	116	8	pure	pure	ADJ
iajs-2707	116	9	&	&	CCONJ
iajs-2707	116	10	appl	appl	PROPN
iajs-2707	116	11	.	.	PUNCT
iajs-2707	117	1	sci	sci	PROPN
iajs-2707	117	2	.	.	PROPN
iajs-2707	118	1	34(4)2021	34(4)2021	NUM
iajs-2707	118	2	113	113	NUM
iajs-2707	118	3	table	table	NOUN
iajs-2707	118	4	3	3	NUM
iajs-2707	118	5	.	.	NOUN
iajs-2707	118	6	1	1	NUM
iajs-2707	118	7	grill	grill	NOUN
iajs-2707	118	8	of	of	ADP
iajs-2707	118	9	accuracy	accuracy	NOUN
iajs-2707	118	10	measure	measure	NOUN
iajs-2707	118	11	of	of	ADP
iajs-2707	118	12	approximation	approximation	NOUN
iajs-2707	118	13	ǥ	ǥ	NOUN
iajs-2707	118	14	-	-	PUNCT
iajs-2707	118	15	spo(ẋ	spo(ẋ	NOUN
iajs-2707	118	16	)	)	PUNCT
iajs-2707	118	17	ữ	ữ	NOUN
iajs-2707	118	18	(	(	PUNCT
iajs-2707	118	19	ǥspo(ẋ	ǥspo(ẋ	PROPN
iajs-2707	118	20	)	)	PUNCT
iajs-2707	118	21	)	)	PUNCT
iajs-2707	118	22	₤	₤	PROPN
iajs-2707	118	23	(	(	PUNCT
iajs-2707	118	24	ǥspo(ẋ	ǥspo(ẋ	NOUN
iajs-2707	118	25	)	)	PUNCT
iajs-2707	118	26	)	)	PUNCT
iajs-2707	118	27	𝓑(ǥspo(ẋ	𝓑(ǥspo(ẋ	PROPN
iajs-2707	118	28	)	)	PUNCT
iajs-2707	118	29	)	)	PUNCT
iajs-2707	118	30	₤	₤	PROPN
iajs-2707	118	31	(	(	PUNCT
iajs-2707	118	32	ữ	ữ	NOUN
iajs-2707	118	33	(	(	PUNCT
iajs-2707	118	34	ǥspo(ẋ	ǥspo(ẋ	PROPN
iajs-2707	118	35	)	)	PUNCT
iajs-2707	118	36	₤	₤	PROPN
iajs-2707	118	37	(	(	PUNCT
iajs-2707	118	38	ǥ	ǥ	NOUN
iajs-2707	118	39	-	-	PUNCT
iajs-2707	118	40	spo(ẋ	spo(ẋ	NOUN
iajs-2707	118	41	)	)	PUNCT
iajs-2707	118	42	ẋ	ẋ	NOUN
iajs-2707	118	43	ẋ	ẋ	NOUN
iajs-2707	118	44	ẋ	ẋ	NOUN
iajs-2707	118	45	∅	∅	NOUN
iajs-2707	118	46	ẋ	ẋ	DET
iajs-2707	118	47	ẋ	ẋ	NOUN
iajs-2707	118	48	∅	∅	NOUN
iajs-2707	118	49	∅	∅	NOUN
iajs-2707	118	50	∅	∅	NOUN
iajs-2707	118	51	∅	∅	NOUN
iajs-2707	118	52	∅	∅	NOUN
iajs-2707	118	53	∅	∅	NOUN
iajs-2707	118	54	{	{	PUNCT
iajs-2707	118	55	ϼ𝟏	ϼ𝟏	PROPN
iajs-2707	118	56	}	}	PUNCT
iajs-2707	118	57	{	{	PUNCT
iajs-2707	118	58	ϼ1	ϼ1	PROPN
iajs-2707	118	59	}	}	PUNCT
iajs-2707	118	60	{	{	PUNCT
iajs-2707	118	61	ϼ1	ϼ1	PROPN
iajs-2707	118	62	}	}	PUNCT
iajs-2707	118	63	∅	∅	NOUN
iajs-2707	118	64	{	{	PUNCT
iajs-2707	118	65	ϼ1	ϼ1	PROPN
iajs-2707	118	66	}	}	PUNCT
iajs-2707	118	67	{	{	PUNCT
iajs-2707	118	68	ϼ1	ϼ1	PROPN
iajs-2707	118	69	}	}	PUNCT
iajs-2707	118	70	{	{	PUNCT
iajs-2707	118	71	ϼ𝟐	ϼ𝟐	PROPN
iajs-2707	118	72	}	}	PUNCT
iajs-2707	118	73	{	{	PUNCT
iajs-2707	118	74	ϼ2	ϼ2	NOUN
iajs-2707	118	75	}	}	PUNCT
iajs-2707	118	76	{	{	PUNCT
iajs-2707	118	77	ϼ2	ϼ2	NOUN
iajs-2707	118	78	}	}	PUNCT
iajs-2707	118	79	∅	∅	NOUN
iajs-2707	118	80	{	{	PUNCT
iajs-2707	118	81	ϼ2	ϼ2	NOUN
iajs-2707	118	82	}	}	PUNCT
iajs-2707	118	83	{	{	PUNCT
iajs-2707	118	84	ϼ2	ϼ2	NOUN
iajs-2707	118	85	}	}	PUNCT
iajs-2707	118	86	{	{	PUNCT
iajs-2707	118	87	ϼ𝟑	ϼ𝟑	NOUN
iajs-2707	118	88	}	}	PUNCT
iajs-2707	118	89	{	{	PUNCT
iajs-2707	118	90	ϼ3	ϼ3	NOUN
iajs-2707	118	91	}	}	PUNCT
iajs-2707	118	92	{	{	PUNCT
iajs-2707	118	93	ϼ3	ϼ3	NOUN
iajs-2707	118	94	}	}	PUNCT
iajs-2707	118	95	∅	∅	NOUN
iajs-2707	118	96	{	{	PUNCT
iajs-2707	118	97	ϼ3	ϼ3	NOUN
iajs-2707	118	98	}	}	PUNCT
iajs-2707	118	99	{	{	PUNCT
iajs-2707	118	100	ϼ3	ϼ3	NOUN
iajs-2707	118	101	}	}	PUNCT
iajs-2707	118	102	{	{	PUNCT
iajs-2707	118	103	ϼ𝟏	ϼ𝟏	PROPN
iajs-2707	118	104	,	,	PUNCT
iajs-2707	118	105	ϼ𝟐	ϼ𝟐	PROPN
iajs-2707	118	106	}	}	PUNCT
iajs-2707	118	107	{	{	PUNCT
iajs-2707	118	108	ϼ1	ϼ1	PROPN
iajs-2707	118	109	,	,	PUNCT
iajs-2707	118	110	ϼ2	ϼ2	NOUN
iajs-2707	118	111	}	}	PUNCT
iajs-2707	118	112	{	{	PUNCT
iajs-2707	118	113	ϼ1	ϼ1	PROPN
iajs-2707	118	114	,	,	PUNCT
iajs-2707	118	115	ϼ2	ϼ2	NOUN
iajs-2707	118	116	}	}	PUNCT
iajs-2707	118	117	∅	∅	NOUN
iajs-2707	118	118	{	{	PUNCT
iajs-2707	118	119	ϼ1	ϼ1	PROPN
iajs-2707	118	120	,	,	PUNCT
iajs-2707	118	121	ϼ2	ϼ2	NOUN
iajs-2707	118	122	}	}	PUNCT
iajs-2707	118	123	{	{	PUNCT
iajs-2707	118	124	ϼ1	ϼ1	PROPN
iajs-2707	118	125	,	,	PUNCT
iajs-2707	118	126	ϼ2	ϼ2	NOUN
iajs-2707	118	127	}	}	PUNCT
iajs-2707	118	128	{	{	PUNCT
iajs-2707	118	129	ϼ𝟏	ϼ𝟏	PROPN
iajs-2707	118	130	,	,	PUNCT
iajs-2707	118	131	ϼ𝟑	ϼ𝟑	NOUN
iajs-2707	118	132	}	}	PUNCT
iajs-2707	118	133	{	{	PUNCT
iajs-2707	118	134	ϼ1	ϼ1	ADJ
iajs-2707	118	135	,	,	PUNCT
iajs-2707	118	136	ϼ3	ϼ3	NOUN
iajs-2707	118	137	}	}	PUNCT
iajs-2707	118	138	{	{	PUNCT
iajs-2707	118	139	ϼ1	ϼ1	ADJ
iajs-2707	118	140	,	,	PUNCT
iajs-2707	118	141	ϼ3	ϼ3	NOUN
iajs-2707	118	142	}	}	PUNCT
iajs-2707	118	143	∅	∅	NOUN
iajs-2707	118	144	{	{	PUNCT
iajs-2707	118	145	ϼ1	ϼ1	ADJ
iajs-2707	118	146	,	,	PUNCT
iajs-2707	118	147	ϼ3	ϼ3	NOUN
iajs-2707	118	148	}	}	PUNCT
iajs-2707	118	149	{	{	PUNCT
iajs-2707	118	150	ϼ1	ϼ1	ADJ
iajs-2707	118	151	,	,	PUNCT
iajs-2707	118	152	ϼ3	ϼ3	NOUN
iajs-2707	118	153	}	}	PUNCT
iajs-2707	118	154	{	{	PUNCT
iajs-2707	118	155	ϼ𝟐	ϼ𝟐	PROPN
iajs-2707	118	156	,	,	PUNCT
iajs-2707	118	157	ϼ𝟑	ϼ𝟑	NOUN
iajs-2707	118	158	}	}	PUNCT
iajs-2707	118	159	{	{	PUNCT
iajs-2707	118	160	ϼ2	ϼ2	NOUN
iajs-2707	118	161	,	,	PUNCT
iajs-2707	118	162	ϼ3	ϼ3	NOUN
iajs-2707	118	163	}	}	PUNCT
iajs-2707	118	164	{	{	PUNCT
iajs-2707	118	165	ϼ2	ϼ2	NOUN
iajs-2707	118	166	,	,	PUNCT
iajs-2707	118	167	ϼ3	ϼ3	NOUN
iajs-2707	118	168	}	}	PUNCT
iajs-2707	118	169	∅	∅	NOUN
iajs-2707	118	170	{	{	PUNCT
iajs-2707	118	171	ϼ2	ϼ2	NOUN
iajs-2707	118	172	,	,	PUNCT
iajs-2707	118	173	ϼ3	ϼ3	NOUN
iajs-2707	118	174	}	}	PUNCT
iajs-2707	118	175	{	{	PUNCT
iajs-2707	118	176	ϼ2	ϼ2	NOUN
iajs-2707	118	177	,	,	PUNCT
iajs-2707	118	178	ϼ3	ϼ3	NOUN
iajs-2707	118	179	}	}	PUNCT
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iajs-2707	118	181	3	3	NUM
iajs-2707	118	182	.	.	SYM
iajs-2707	118	183	2	2	NUM
iajs-2707	118	184	grill	grill	NOUN
iajs-2707	118	185	of	of	ADP
iajs-2707	118	186	accuracy	accuracy	NOUN
iajs-2707	118	187	measure	measure	NOUN
iajs-2707	118	188	of	of	ADP
iajs-2707	118	189	approximation	approximation	NOUN
iajs-2707	118	190	ǥ	ǥ	NOUN
iajs-2707	118	191	-	-	PUNCT
iajs-2707	118	192	spo(ẋ	spo(ẋ	NOUN
iajs-2707	118	193	)	)	PUNCT
iajs-2707	118	194	𝔐(ǥ	𝔐(ǥ	NOUN
iajs-2707	118	195	−	−	PUNCT
iajs-2707	118	196	spo(ẋ	spo(ẋ	NOUN
iajs-2707	118	197	)	)	PUNCT
iajs-2707	118	198	)	)	PUNCT
iajs-2707	119	1	𝔐𝜉(ǥ	𝔐𝜉(ǥ	NOUN
iajs-2707	119	2	−	−	PROPN
iajs-2707	119	3	spo(ẋ	spo(ẋ	NOUN
iajs-2707	119	4	)	)	PUNCT
iajs-2707	119	5	)	)	PUNCT
iajs-2707	120	1	𝔐𝑝(ǥ	𝔐𝑝(ǥ	ADP
iajs-2707	120	2	−	−	PROPN
iajs-2707	120	3	spo(ẋ	spo(ẋ	NOUN
iajs-2707	120	4	)	)	PUNCT
iajs-2707	120	5	)	)	PUNCT
iajs-2707	120	6	ẋ	ẋ	X
iajs-2707	120	7	1	1	NUM
iajs-2707	120	8	1	1	NUM
iajs-2707	120	9	1	1	NUM
iajs-2707	120	10	∅	∅	NOUN
iajs-2707	120	11	1	1	NUM
iajs-2707	120	12	1	1	NUM
iajs-2707	120	13	1	1	NUM
iajs-2707	120	14	{	{	PUNCT
iajs-2707	120	15	ϼ1	ϼ1	PROPN
iajs-2707	120	16	}	}	PUNCT
iajs-2707	120	17	1	1	NUM
iajs-2707	120	18	1	1	NUM
iajs-2707	120	19	1	1	NUM
iajs-2707	120	20	{	{	PUNCT
iajs-2707	120	21	ϼ2	ϼ2	NOUN
iajs-2707	120	22	}	}	PUNCT
iajs-2707	120	23	1	1	NUM
iajs-2707	120	24	1	1	NUM
iajs-2707	120	25	1	1	NUM
iajs-2707	120	26	{	{	PUNCT
iajs-2707	120	27	ϼ3	ϼ3	NOUN
iajs-2707	120	28	}	}	PUNCT
iajs-2707	120	29	1	1	NUM
iajs-2707	120	30	1	1	NUM
iajs-2707	120	31	1	1	NUM
iajs-2707	120	32	{	{	PUNCT
iajs-2707	120	33	ϼ1	ϼ1	PROPN
iajs-2707	120	34	,	,	PUNCT
iajs-2707	120	35	ϼ2	ϼ2	NOUN
iajs-2707	120	36	}	}	PUNCT
iajs-2707	120	37	1	1	NUM
iajs-2707	120	38	1	1	NUM
iajs-2707	120	39	1	1	NUM
iajs-2707	120	40	{	{	PUNCT
iajs-2707	120	41	ϼ1	ϼ1	ADJ
iajs-2707	120	42	,	,	PUNCT
iajs-2707	120	43	ϼ3	ϼ3	NOUN
iajs-2707	120	44	}	}	PUNCT
iajs-2707	120	45	1	1	NUM
iajs-2707	120	46	1	1	NUM
iajs-2707	120	47	1	1	NUM
iajs-2707	120	48	{	{	PUNCT
iajs-2707	120	49	ϼ2	ϼ2	NOUN
iajs-2707	120	50	,	,	PUNCT
iajs-2707	120	51	ϼ3	ϼ3	NOUN
iajs-2707	120	52	}	}	PUNCT
iajs-2707	120	53	1	1	NUM
iajs-2707	120	54	1	1	NUM
iajs-2707	120	55	1	1	NUM
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iajs-2707	120	57	example	example	NOUN
iajs-2707	120	58	3.3	3.3	NUM
iajs-2707	120	59	ǥ	ǥ	NOUN
iajs-2707	120	60	-	-	PUNCT
iajs-2707	120	61	spo(ẋ)=	spo(ẋ)=	NOUN
iajs-2707	120	62	{	{	PUNCT
iajs-2707	120	63	ẋ	ẋ	NOUN
iajs-2707	120	64	,	,	PUNCT
iajs-2707	120	65	∅	∅	NOUN
iajs-2707	120	66	,	,	PUNCT
iajs-2707	120	67	{	{	PUNCT
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iajs-2707	120	69	}	}	PUNCT
iajs-2707	120	70	,	,	PUNCT
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iajs-2707	120	73	}	}	PUNCT
iajs-2707	120	74	,	,	PUNCT
iajs-2707	120	75	{	{	PUNCT
iajs-2707	120	76	ϼ1	ϼ1	PROPN
iajs-2707	120	77	,	,	PUNCT
iajs-2707	120	78	ϼ2	ϼ2	NOUN
iajs-2707	120	79	}	}	PUNCT
iajs-2707	120	80	,	,	PUNCT
iajs-2707	120	81	{	{	PUNCT
iajs-2707	120	82	ϼ1	ϼ1	ADJ
iajs-2707	120	83	,	,	PUNCT
iajs-2707	120	84	ϼ3	ϼ3	NOUN
iajs-2707	120	85	}	}	PUNCT
iajs-2707	120	86	,	,	PUNCT
iajs-2707	120	87	{	{	PUNCT
iajs-2707	120	88	ϼ1	ϼ1	ADJ
iajs-2707	120	89	,	,	PUNCT
iajs-2707	120	90	ϼ4	ϼ4	ADJ
iajs-2707	120	91	}	}	PUNCT
iajs-2707	120	92	,	,	PUNCT
iajs-2707	120	93	{	{	PUNCT
iajs-2707	120	94	ϼ2	ϼ2	NOUN
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iajs-2707	120	96	ϼ4	ϼ4	ADV
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iajs-2707	120	98	,	,	PUNCT
iajs-2707	120	99	{	{	PUNCT
iajs-2707	120	100	ϼ3	ϼ3	NOUN
iajs-2707	120	101	,	,	PUNCT
iajs-2707	120	102	ϼ4	ϼ4	ADV
iajs-2707	120	103	}	}	PUNCT
iajs-2707	120	104	,	,	PUNCT
iajs-2707	120	105	{	{	PUNCT
iajs-2707	120	106	ϼ1	ϼ1	PROPN
iajs-2707	120	107	,	,	PUNCT
iajs-2707	120	108	ϼ2	ϼ2	NOUN
iajs-2707	120	109	,	,	PUNCT
iajs-2707	120	110	ϼ3	ϼ3	NOUN
iajs-2707	120	111	}	}	PUNCT
iajs-2707	120	112	,	,	PUNCT
iajs-2707	120	113	{	{	PUNCT
iajs-2707	120	114	ϼ1	ϼ1	PROPN
iajs-2707	120	115	,	,	PUNCT
iajs-2707	120	116	ϼ2	ϼ2	NOUN
iajs-2707	120	117	,	,	PUNCT
iajs-2707	120	118	ϼ4	ϼ4	ADV
iajs-2707	120	119	}	}	PUNCT
iajs-2707	120	120	,	,	PUNCT
iajs-2707	120	121	{	{	PUNCT
iajs-2707	120	122	ϼ2	ϼ2	NOUN
iajs-2707	120	123	,	,	PUNCT
iajs-2707	120	124	ϼ3	ϼ3	NOUN
iajs-2707	120	125	,	,	PUNCT
iajs-2707	120	126	ϼ4	ϼ4	ADV
iajs-2707	120	127	}	}	PUNCT
iajs-2707	120	128	,	,	PUNCT
iajs-2707	120	129	{	{	PUNCT
iajs-2707	120	130	{	{	PUNCT
iajs-2707	120	131	ϼ1	ϼ1	ADJ
iajs-2707	120	132	,	,	PUNCT
iajs-2707	120	133	ϼ3	ϼ3	NOUN
iajs-2707	120	134	,	,	PUNCT
iajs-2707	120	135	ϼ4	ϼ4	ADV
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iajs-2707	120	137	}	}	PUNCT
iajs-2707	120	138	.	.	PUNCT
iajs-2707	121	1	ř	ř	X
iajs-2707	121	2	=	=	PUNCT
iajs-2707	121	3	{	{	PUNCT
iajs-2707	121	4	(	(	PUNCT
iajs-2707	121	5	ϼ1	ϼ1	PROPN
iajs-2707	121	6	,	,	PUNCT
iajs-2707	121	7	ϼ1	ϼ1	ADJ
iajs-2707	121	8	)	)	PUNCT
iajs-2707	121	9	,	,	PUNCT
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iajs-2707	121	11	ϼ2	ϼ2	NOUN
iajs-2707	121	12	,	,	PUNCT
iajs-2707	121	13	ϼ2	ϼ2	NOUN
iajs-2707	121	14	)	)	PUNCT
iajs-2707	121	15	,	,	PUNCT
iajs-2707	121	16	(	(	PUNCT
iajs-2707	121	17	ϼ3	ϼ3	NOUN
iajs-2707	121	18	,	,	PUNCT
iajs-2707	121	19	ϼ3	ϼ3	NOUN
iajs-2707	121	20	)	)	PUNCT
iajs-2707	121	21	,	,	PUNCT
iajs-2707	121	22	(	(	PUNCT
iajs-2707	121	23	ϼ4	ϼ4	ADV
iajs-2707	121	24	,	,	PUNCT
iajs-2707	121	25	ϼ4	ϼ4	ADJ
iajs-2707	121	26	)	)	PUNCT
iajs-2707	121	27	,	,	PUNCT
iajs-2707	121	28	(	(	PUNCT
iajs-2707	121	29	ϼ3	ϼ3	NOUN
iajs-2707	121	30	,	,	PUNCT
iajs-2707	121	31	ϼ4	ϼ4	ADJ
iajs-2707	121	32	)	)	PUNCT
iajs-2707	121	33	,	,	PUNCT
iajs-2707	121	34	(	(	PUNCT
iajs-2707	121	35	ϼ4	ϼ4	ADV
iajs-2707	121	36	,	,	PUNCT
iajs-2707	121	37	ϼ3	ϼ3	NOUN
iajs-2707	121	38	)	)	PUNCT
iajs-2707	121	39	}	}	PUNCT
iajs-2707	121	40	ř	ř	PROPN
iajs-2707	121	41	(	(	PUNCT
iajs-2707	121	42	ϼ1)=	ϼ1)=	X
iajs-2707	121	43	{	{	PUNCT
iajs-2707	121	44	ϼ1	ϼ1	PROPN
iajs-2707	121	45	}	}	PUNCT
iajs-2707	121	46	,	,	PUNCT
iajs-2707	121	47	ř(ϼ2)={ϼ2	ř(ϼ2)={ϼ2	ADV
iajs-2707	121	48	}	}	PUNCT
iajs-2707	121	49	,	,	PUNCT
iajs-2707	121	50	ř(ϼ4	ř(ϼ4	ADV
iajs-2707	121	51	)	)	PUNCT
iajs-2707	121	52	,	,	PUNCT
iajs-2707	121	53	ř(ϼ	ř(ϼ	PROPN
iajs-2707	121	54	3	3	NUM
iajs-2707	121	55	)	)	PUNCT
iajs-2707	121	56	=	=	NOUN
iajs-2707	121	57	{	{	PUNCT
iajs-2707	121	58	ϼ4	ϼ4	ADV
iajs-2707	121	59	,	,	PUNCT
iajs-2707	121	60	ϼ3	ϼ3	NOUN
iajs-2707	121	61	}	}	PUNCT
iajs-2707	121	62	.	.	PUNCT
iajs-2707	122	1	table	table	NOUN
iajs-2707	122	2	3.3	3.3	NUM
iajs-2707	122	3	gspo	gspo	NOUN
iajs-2707	122	4	of	of	ADP
iajs-2707	122	5	accuracy	accuracy	NOUN
iajs-2707	122	6	measure	measure	NOUN
iajs-2707	122	7	of	of	ADP
iajs-2707	122	8	approximation	approximation	NOUN
iajs-2707	122	9	ǥ	ǥ	NOUN
iajs-2707	122	10	-	-	PUNCT
iajs-2707	122	11	spo(ẋ	spo(ẋ	NOUN
iajs-2707	122	12	)	)	PUNCT
iajs-2707	122	13	ữ(ǥ	ữ(ǥ	NOUN
iajs-2707	122	14	-	-	PUNCT
iajs-2707	122	15	spo(ẋ	spo(ẋ	NOUN
iajs-2707	122	16	)	)	PUNCT
iajs-2707	122	17	)	)	PUNCT
iajs-2707	123	1	₤	₤	PROPN
iajs-2707	123	2	(	(	PUNCT
iajs-2707	123	3	ǥ	ǥ	NOUN
iajs-2707	123	4	-	-	PUNCT
iajs-2707	123	5	spo(ẋ	spo(ẋ	NOUN
iajs-2707	123	6	)	)	PUNCT
iajs-2707	123	7	)	)	PUNCT
iajs-2707	123	8	ℬ(ǥ	ℬ(ǥ	PROPN
iajs-2707	123	9	-	-	PUNCT
iajs-2707	123	10	spo(ẋ	spo(ẋ	NOUN
iajs-2707	123	11	)	)	PUNCT
iajs-2707	123	12	)	)	PUNCT
iajs-2707	124	1	₤	₤	NOUN
iajs-2707	124	2	(	(	PUNCT
iajs-2707	124	3	ữ	ữ	NOUN
iajs-2707	124	4	(	(	PUNCT
iajs-2707	124	5	ǥ	ǥ	NOUN
iajs-2707	124	6	-	-	PUNCT
iajs-2707	124	7	spo(ẋ	spo(ẋ	NOUN
iajs-2707	124	8	)	)	PUNCT
iajs-2707	124	9	ữ(₤	ữ(₤	NOUN
iajs-2707	124	10	(	(	PUNCT
iajs-2707	124	11	ǥspo(ẋ	ǥspo(ẋ	NOUN
iajs-2707	124	12	)	)	PUNCT
iajs-2707	124	13	ẋ	ẋ	NOUN
iajs-2707	124	14	ẋ	ẋ	NOUN
iajs-2707	124	15	ẋ	ẋ	NOUN
iajs-2707	124	16	∅	∅	NOUN
iajs-2707	124	17	ẋ	ẋ	DET
iajs-2707	124	18	ẋ	ẋ	NOUN
iajs-2707	124	19	∅	∅	NOUN
iajs-2707	124	20	∅	∅	NOUN
iajs-2707	124	21	∅	∅	NOUN
iajs-2707	124	22	∅	∅	NOUN
iajs-2707	124	23	∅	∅	NOUN
iajs-2707	124	24	∅	∅	NOUN
iajs-2707	124	25	{	{	PUNCT
iajs-2707	124	26	ϼ1	ϼ1	PROPN
iajs-2707	124	27	}	}	PUNCT
iajs-2707	124	28	{	{	PUNCT
iajs-2707	124	29	ϼ1	ϼ1	PROPN
iajs-2707	124	30	}	}	PUNCT
iajs-2707	124	31	{	{	PUNCT
iajs-2707	124	32	ϼ1	ϼ1	PROPN
iajs-2707	124	33	}	}	PUNCT
iajs-2707	124	34	∅	∅	NOUN
iajs-2707	124	35	{	{	PUNCT
iajs-2707	124	36	ϼ1	ϼ1	PROPN
iajs-2707	124	37	}	}	PUNCT
iajs-2707	124	38	{	{	PUNCT
iajs-2707	124	39	ϼ1	ϼ1	PROPN
iajs-2707	124	40	}	}	PUNCT
iajs-2707	124	41	{	{	PUNCT
iajs-2707	124	42	ϼ4	ϼ4	ADV
iajs-2707	124	43	}	}	PUNCT
iajs-2707	124	44	{	{	PUNCT
iajs-2707	124	45	ϼ3	ϼ3	NOUN
iajs-2707	124	46	,	,	PUNCT
iajs-2707	124	47	ϼ4	ϼ4	ADJ
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iajs-2707	124	49	∅	∅	NOUN
iajs-2707	124	50	{	{	PUNCT
iajs-2707	124	51	ϼ3	ϼ3	NOUN
iajs-2707	124	52	,	,	PUNCT
iajs-2707	124	53	ϼ4	ϼ4	ADV
iajs-2707	124	54	}	}	PUNCT
iajs-2707	124	55	{	{	PUNCT
iajs-2707	124	56	ϼ3	ϼ3	NOUN
iajs-2707	124	57	,	,	PUNCT
iajs-2707	124	58	ϼ4	ϼ4	ADJ
iajs-2707	124	59	}	}	PUNCT
iajs-2707	124	60	∅	∅	NOUN
iajs-2707	124	61	{	{	PUNCT
iajs-2707	124	62	ϼ1	ϼ1	PROPN
iajs-2707	124	63	,	,	PUNCT
iajs-2707	124	64	ϼ2	ϼ2	NOUN
iajs-2707	124	65	}	}	PUNCT
iajs-2707	124	66	{	{	PUNCT
iajs-2707	124	67	ϼ1	ϼ1	PROPN
iajs-2707	124	68	,	,	PUNCT
iajs-2707	124	69	ϼ2	ϼ2	NOUN
iajs-2707	124	70	}	}	PUNCT
iajs-2707	124	71	{	{	PUNCT
iajs-2707	124	72	ϼ1	ϼ1	PROPN
iajs-2707	124	73	,	,	PUNCT
iajs-2707	124	74	ϼ2	ϼ2	NOUN
iajs-2707	124	75	}	}	PUNCT
iajs-2707	124	76	∅	∅	NOUN
iajs-2707	124	77	{	{	PUNCT
iajs-2707	124	78	ϼ1	ϼ1	PROPN
iajs-2707	124	79	,	,	PUNCT
iajs-2707	124	80	ϼ2	ϼ2	NOUN
iajs-2707	124	81	}	}	PUNCT
iajs-2707	124	82	{	{	PUNCT
iajs-2707	124	83	ϼ1	ϼ1	PROPN
iajs-2707	124	84	,	,	PUNCT
iajs-2707	124	85	ϼ2	ϼ2	NOUN
iajs-2707	124	86	}	}	PUNCT
iajs-2707	124	87	{	{	PUNCT
iajs-2707	124	88	ϼ1	ϼ1	ADJ
iajs-2707	124	89	,	,	PUNCT
iajs-2707	124	90	ϼ3	ϼ3	NOUN
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iajs-2707	124	92	{	{	PUNCT
iajs-2707	124	93	ϼ1	ϼ1	ADJ
iajs-2707	124	94	,	,	PUNCT
iajs-2707	124	95	ϼ3	ϼ3	NOUN
iajs-2707	124	96	,	,	PUNCT
iajs-2707	124	97	ϼ4	ϼ4	ADV
iajs-2707	124	98	}	}	PUNCT
iajs-2707	124	99	{	{	PUNCT
iajs-2707	124	100	ϼ1	ϼ1	PROPN
iajs-2707	124	101	}	}	PUNCT
iajs-2707	124	102	{	{	PUNCT
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iajs-2707	124	104	,	,	PUNCT
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iajs-2707	124	107	{	{	PUNCT
iajs-2707	124	108	ϼ1	ϼ1	ADJ
iajs-2707	124	109	,	,	PUNCT
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iajs-2707	124	111	,	,	PUNCT
iajs-2707	124	112	ϼ4	ϼ4	ADV
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iajs-2707	124	116	}	}	PUNCT
iajs-2707	124	117	{	{	PUNCT
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iajs-2707	124	119	,	,	PUNCT
iajs-2707	124	120	ϼ4	ϼ4	ADJ
iajs-2707	124	121	}	}	PUNCT
iajs-2707	124	122	{	{	PUNCT
iajs-2707	124	123	ϼ1	ϼ1	ADJ
iajs-2707	124	124	,	,	PUNCT
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iajs-2707	124	126	,	,	PUNCT
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iajs-2707	124	130	ϼ1	ϼ1	PROPN
iajs-2707	124	131	}	}	PUNCT
iajs-2707	124	132	{	{	PUNCT
iajs-2707	124	133	ϼ3	ϼ3	NOUN
iajs-2707	124	134	,	,	PUNCT
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iajs-2707	124	138	ϼ1	ϼ1	ADJ
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iajs-2707	124	146	}	}	PUNCT
iajs-2707	124	147	{	{	PUNCT
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iajs-2707	124	149	,	,	PUNCT
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iajs-2707	124	152	{	{	PUNCT
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iajs-2707	124	161	}	}	PUNCT
iajs-2707	124	162	{	{	PUNCT
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iajs-2707	124	174	{	{	PUNCT
iajs-2707	124	175	ϼ2	ϼ2	NOUN
iajs-2707	124	176	}	}	PUNCT
iajs-2707	124	177	{	{	PUNCT
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iajs-2707	124	194	ϼ3	ϼ3	NOUN
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iajs-2707	124	200	,	,	PUNCT
iajs-2707	124	201	ϼ4	ϼ4	ADV
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iajs-2707	124	204	ϼ1	ϼ1	PROPN
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iajs-2707	124	210	ẋ	ẋ	ADJ
iajs-2707	124	211	{	{	PUNCT
iajs-2707	124	212	ϼ1	ϼ1	PROPN
iajs-2707	124	213	,	,	PUNCT
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iajs-2707	124	215	}	}	PUNCT
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iajs-2707	124	228	ϼ1	ϼ1	PROPN
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iajs-2707	124	253	,	,	PUNCT
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iajs-2707	128	7	ǥ	ǥ	NOUN
iajs-2707	128	8	-	-	PUNCT
iajs-2707	128	9	spo(ẋ	spo(ẋ	NOUN
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iajs-2707	128	12	−	−	PUNCT
iajs-2707	128	13	spo(ẋ	spo(ẋ	NOUN
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iajs-2707	129	1	𝔐𝜉(ǥ	𝔐𝜉(ǥ	NOUN
iajs-2707	129	2	−	−	PROPN
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iajs-2707	130	1	𝔐𝑝(ǥ	𝔐𝑝(ǥ	ADP
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iajs-2707	130	3	spo(ẋ	spo(ẋ	NOUN
iajs-2707	130	4	)	)	PUNCT
iajs-2707	130	5	)	)	PUNCT
iajs-2707	130	6	ẋ	ẋ	X
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iajs-2707	130	8	1	1	NUM
iajs-2707	130	9	1	1	NUM
iajs-2707	130	10	∅	∅	NOUN
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iajs-2707	130	35	ϼ𝑠1	ϼ𝑠1	NOUN
iajs-2707	130	36	,	,	PUNCT
iajs-2707	130	37	ϼ3	ϼ3	NOUN
iajs-2707	130	38	}	}	PUNCT
iajs-2707	130	39	1/3	1/3	NUM
iajs-2707	130	40	1/3	1/3	NUM
iajs-2707	130	41	1	1	NUM
iajs-2707	130	42	{	{	PUNCT
iajs-2707	130	43	ϼ1	ϼ1	PROPN
iajs-2707	130	44	,	,	PUNCT
iajs-2707	130	45	ϼ4	ϼ4	ADJ
iajs-2707	130	46	}	}	PUNCT
iajs-2707	130	47	1/3	1/3	NUM
iajs-2707	130	48	1/3	1/3	NUM
iajs-2707	130	49	1	1	NUM
iajs-2707	130	50	{	{	PUNCT
iajs-2707	130	51	ϼ2	ϼ2	NOUN
iajs-2707	130	52	,	,	PUNCT
iajs-2707	130	53	ϼ4	ϼ4	ADJ
iajs-2707	130	54	}	}	PUNCT
iajs-2707	130	55	1	1	NUM
iajs-2707	130	56	1	1	NUM
iajs-2707	130	57	1	1	NUM
iajs-2707	130	58	{	{	PUNCT
iajs-2707	130	59	ϼ3	ϼ3	NOUN
iajs-2707	130	60	,	,	PUNCT
iajs-2707	130	61	ϼ4	ϼ4	ADJ
iajs-2707	130	62	}	}	PUNCT
iajs-2707	130	63	½	½	NOUN
iajs-2707	130	64	½	½	NOUN
iajs-2707	130	65	1	1	NUM
iajs-2707	130	66	{	{	PUNCT
iajs-2707	130	67	ϼ1	ϼ1	PROPN
iajs-2707	130	68	,	,	PUNCT
iajs-2707	130	69	ϼ2	ϼ2	NOUN
iajs-2707	130	70	,	,	PUNCT
iajs-2707	130	71	ϼ3	ϼ3	NOUN
iajs-2707	130	72	}	}	PUNCT
iajs-2707	130	73	½	½	NOUN
iajs-2707	130	74	½	½	NOUN
iajs-2707	130	75	1	1	NUM
iajs-2707	130	76	{	{	PUNCT
iajs-2707	130	77	ϼ1	ϼ1	PROPN
iajs-2707	130	78	,	,	PUNCT
iajs-2707	130	79	ϼ2	ϼ2	NOUN
iajs-2707	130	80	,	,	PUNCT
iajs-2707	130	81	ϼ4	ϼ4	ADJ
iajs-2707	130	82	}	}	PUNCT
iajs-2707	130	83	1	1	NUM
iajs-2707	130	84	1	1	NUM
iajs-2707	130	85	1	1	NUM
iajs-2707	130	86	{	{	PUNCT
iajs-2707	130	87	ϼ2	ϼ2	NOUN
iajs-2707	130	88	,	,	PUNCT
iajs-2707	130	89	ϼ3	ϼ3	NOUN
iajs-2707	130	90	,	,	PUNCT
iajs-2707	130	91	ϼ4	ϼ4	ADV
iajs-2707	130	92	}	}	PUNCT
iajs-2707	130	93	1	1	NUM
iajs-2707	130	94	1	1	NUM
iajs-2707	130	95	1	1	NUM
iajs-2707	130	96	{	{	PUNCT
iajs-2707	130	97	ϼ1	ϼ1	ADJ
iajs-2707	130	98	,	,	PUNCT
iajs-2707	130	99	ϼ3	ϼ3	NOUN
iajs-2707	130	100	,	,	PUNCT
iajs-2707	130	101	ϼ4	ϼ4	ADV
iajs-2707	130	102	}	}	PUNCT
iajs-2707	130	103	1	1	NUM
iajs-2707	130	104	1	1	NUM
iajs-2707	130	105	1	1	NUM
iajs-2707	130	106	4	4	NUM
iajs-2707	130	107	.	.	PUNCT
iajs-2707	130	108	conclusion	conclusion	NOUN
iajs-2707	130	109	the	the	DET
iajs-2707	130	110	aim	aim	NOUN
iajs-2707	130	111	of	of	ADP
iajs-2707	130	112	our	our	PRON
iajs-2707	130	113	study	study	NOUN
iajs-2707	130	114	is	be	AUX
iajs-2707	130	115	to	to	PART
iajs-2707	130	116	define	define	VERB
iajs-2707	130	117	the	the	DET
iajs-2707	130	118	ǥ-𝑆𝑃𝑂	ǥ-𝑆𝑃𝑂	NOUN
iajs-2707	130	119	sets	set	NOUN
iajs-2707	130	120	and	and	CCONJ
iajs-2707	130	121	study	study	VERB
iajs-2707	130	122	some	some	PRON
iajs-2707	130	123	of	of	ADP
iajs-2707	130	124	the	the	DET
iajs-2707	130	125	properties	property	NOUN
iajs-2707	130	126	of	of	ADP
iajs-2707	130	127	these	these	DET
iajs-2707	130	128	sets	set	NOUN
iajs-2707	130	129	,	,	PUNCT
iajs-2707	130	130	and	and	CCONJ
iajs-2707	130	131	then	then	ADV
iajs-2707	130	132	find	find	VERB
iajs-2707	130	133	the	the	DET
iajs-2707	130	134	boundary	boundary	ADJ
iajs-2707	130	135	area	area	NOUN
iajs-2707	130	136	for	for	ADP
iajs-2707	130	137	the	the	DET
iajs-2707	130	138	family	family	NOUN
iajs-2707	130	139	of	of	ADP
iajs-2707	130	140	ǥ-𝑆𝑃𝑂	ǥ-𝑆𝑃𝑂	PROPN
iajs-2707	130	141	(	(	PUNCT
iajs-2707	130	142	ẋ	ẋ	NOUN
iajs-2707	130	143	)	)	PUNCT
iajs-2707	130	144	.	.	PUNCT
iajs-2707	131	1	and	and	CCONJ
iajs-2707	131	2	try	try	VERB
iajs-2707	131	3	to	to	PART
iajs-2707	131	4	get	get	VERB
iajs-2707	131	5	the	the	DET
iajs-2707	131	6	best	good	ADJ
iajs-2707	131	7	accuracy	accuracy	NOUN
iajs-2707	131	8	for	for	ADP
iajs-2707	131	9	the	the	DET
iajs-2707	131	10	set	set	NOUN
iajs-2707	131	11	when	when	SCONJ
iajs-2707	131	12	it	it	PRON
iajs-2707	131	13	equals	equal	VERB
iajs-2707	131	14	1	1	NUM
iajs-2707	131	15	for	for	ADP
iajs-2707	131	16	most	most	ADJ
iajs-2707	131	17	of	of	ADP
iajs-2707	131	18	m	m	PROPN
iajs-2707	131	19	∈	∈	NOUN
iajs-2707	131	20	ǥ-𝑆𝑃𝑂	ǥ-𝑆𝑃𝑂	NOUN
iajs-2707	131	21	(	(	PUNCT
iajs-2707	131	22	ẋ	ẋ	NOUN
iajs-2707	131	23	)	)	PUNCT
iajs-2707	131	24	.	.	PUNCT
iajs-2707	132	1	references	reference	NOUN
iajs-2707	132	2	1	1	NUM
iajs-2707	132	3	.	.	PUNCT
iajs-2707	132	4	choquet	choquet	PROPN
iajs-2707	132	5	,	,	PUNCT
iajs-2707	132	6	g.	g.	PROPN
iajs-2707	132	7	sur	sur	PROPN
iajs-2707	132	8	les	les	PROPN
iajs-2707	132	9	notions	notion	NOUN
iajs-2707	132	10	de	de	ADP
iajs-2707	132	11	filter	filter	NOUN
iajs-2707	132	12	et	et	NOUN
iajs-2707	132	13	grille	grille	NOUN
iajs-2707	132	14	,	,	PUNCT
iajs-2707	132	15	comptes	compte	VERB
iajs-2707	132	16	rendus	rendus	PROPN
iajs-2707	132	17	acad	acad	PROPN
iajs-2707	132	18	.	.	PUNCT
iajs-2707	133	1	sci	sci	PROPN
iajs-2707	133	2	.	.	PROPN
iajs-2707	133	3	paris	paris	PROPN
iajs-2707	133	4	,	,	PUNCT
iajs-2707	133	5	1947	1947	NUM
iajs-2707	133	6	,	,	PUNCT
iajs-2707	133	7	224,171	224,171	NUM
iajs-2707	133	8	-	-	SYM
iajs-2707	133	9	173	173	NUM
iajs-2707	133	10	.	.	NOUN
iajs-2707	134	1	2	2	NUM
iajs-2707	134	2	.	.	X
iajs-2707	134	3	roy	roy	PROPN
iajs-2707	134	4	,	,	PUNCT
iajs-2707	134	5	b	b	PROPN
iajs-2707	134	6	.	.	PUNCT
iajs-2707	134	7	;	;	PUNCT
iajs-2707	134	8	mukherjee	mukherjee	PROPN
iajs-2707	134	9	,	,	PUNCT
iajs-2707	134	10	m	m	VERB
iajs-2707	134	11	n	n	ADJ
iajs-2707	134	12	.on	.on	PUNCT
iajs-2707	134	13	a	a	DET
iajs-2707	134	14	type	type	NOUN
iajs-2707	134	15	of	of	ADP
iajs-2707	134	16	compactness	compactness	NOUN
iajs-2707	134	17	via	via	ADP
iajs-2707	134	18	grills	grill	NOUN
iajs-2707	134	19	matematicki	matematicki	NOUN
iajs-2707	134	20	vesnik	vesnik	NOUN
iajs-2707	134	21	.	.	PUNCT
iajs-2707	135	1	2007	2007	NUM
iajs-2707	135	2	,	,	PUNCT
iajs-2707	135	3	59	59	NUM
iajs-2707	135	4	,	,	PUNCT
iajs-2707	135	5	113	113	NUM
iajs-2707	135	6	-	-	SYM
iajs-2707	135	7	120	120	NUM
iajs-2707	135	8	.	.	PUNCT
iajs-2707	136	1	3	3	X
iajs-2707	136	2	.	.	X
iajs-2707	136	3	roy	roy	PROPN
iajs-2707	136	4	,	,	PUNCT
iajs-2707	136	5	b	b	PROPN
iajs-2707	136	6	.	.	PUNCT
iajs-2707	136	7	;	;	PUNCT
iajs-2707	136	8	mukherjee	mukherjee	PROPN
iajs-2707	136	9	,	,	PUNCT
iajs-2707	136	10	m	m	VERB
iajs-2707	136	11	n.	n.	ADJ
iajs-2707	136	12	on	on	ADP
iajs-2707	136	13	a	a	DET
iajs-2707	136	14	typical	typical	ADJ
iajs-2707	136	15	topology	topology	NOUN
iajs-2707	136	16	induced	induce	VERB
iajs-2707	136	17	by	by	ADP
iajs-2707	136	18	a	a	DET
iajs-2707	136	19	grill	grill	NOUN
iajs-2707	136	20	soochow	soochow	NOUN
iajs-2707	136	21	j	j	PROPN
iajs-2707	136	22	ath	ath	NOUN
iajs-2707	136	23	.	.	PUNCT
iajs-2707	137	1	2007,33	2007,33	NUM
iajs-2707	137	2	,	,	PUNCT
iajs-2707	137	3	4	4	NUM
iajs-2707	137	4	,	,	PUNCT
iajs-2707	137	5	,	,	PUNCT
iajs-2707	137	6	771	771	NUM
iajs-2707	137	7	-	-	SYM
iajs-2707	137	8	786	786	NUM
iajs-2707	137	9	.	.	PUNCT
iajs-2707	138	1	ibn	ibn	PROPN
iajs-2707	138	2	al	al	PROPN
iajs-2707	138	3	-	-	PUNCT
iajs-2707	138	4	haitham	haitham	PROPN
iajs-2707	138	5	jour	jour	X
iajs-2707	138	6	.	.	PROPN
iajs-2707	138	7	for	for	ADP
iajs-2707	138	8	pure	pure	ADJ
iajs-2707	138	9	&	&	CCONJ
iajs-2707	138	10	appl	appl	PROPN
iajs-2707	138	11	.	.	PUNCT
iajs-2707	139	1	sci	sci	PROPN
iajs-2707	139	2	.	.	PROPN
iajs-2707	140	1	34(4)2021	34(4)2021	NUM
iajs-2707	140	2	115	115	NUM
iajs-2707	140	3	4	4	NUM
iajs-2707	140	4	.	.	PUNCT
iajs-2707	140	5	shawqi	shawqi	ADJ
iajs-2707	140	6	a	a	DET
iajs-2707	140	7	hazza	hazza	NOUN
iajs-2707	140	8	;	;	PUNCT
iajs-2707	140	9	sobhy	sobhy	VERB
iajs-2707	140	10	a	a	DET
iajs-2707	140	11	el	el	PROPN
iajs-2707	140	12	-	-	PUNCT
iajs-2707	140	13	sheikh	sheikh	PROPN
iajs-2707	140	14	ali	ali	PROPN
iajs-2707	140	15	kandil	kandil	PROPN
iajs-2707	140	16	and	and	CCONJ
iajs-2707	140	17	mohamed	mohamed	PROPN
iajs-2707	140	18	ahmed	ahmed	PROPN
iajs-2707	140	19	abdelhakem	abdelhakem	PROPN
iajs-2707	140	20	on	on	ADP
iajs-2707	140	21	ideals	ideal	NOUN
iajs-2707	140	22	and	and	CCONJ
iajs-2707	140	23	grills	grill	NOUN
iajs-2707	140	24	in	in	ADP
iajs-2707	140	25	topological	topological	ADJ
iajs-2707	140	26	spaces	space	NOUN
iajs-2707	140	27	south	south	VERB
iajs-2707	140	28	a	a	DET
iajs-2707	140	29	sian	sian	ADJ
iajs-2707	140	30	journal	journal	NOUN
iajs-2707	140	31	of	of	ADP
iajs-2707	140	32	mathematics	mathematic	NOUN
iajs-2707	140	33	.	.	PUNCT
iajs-2707	141	1	2015	2015	NUM
iajs-2707	141	2	,	,	PUNCT
iajs-2707	141	3	5	5	NUM
iajs-2707	141	4	,	,	PUNCT
iajs-2707	141	5	6	6	NUM
iajs-2707	141	6	,	,	PUNCT
iajs-2707	141	7	233238	233238	NUM
iajs-2707	141	8	.	.	PUNCT
iajs-2707	142	1	5	5	NUM
iajs-2707	142	2	.	.	X
iajs-2707	142	3	thenmozhi	thenmozhi	PROPN
iajs-2707	142	4	,	,	PUNCT
iajs-2707	142	5	p.	p.	NOUN
iajs-2707	142	6	;	;	PUNCT
iajs-2707	142	7	kaleeswari	kaleeswari	NOUN
iajs-2707	142	8	,	,	PUNCT
iajs-2707	142	9	m.	m.	NOUN
iajs-2707	142	10	;	;	PUNCT
iajs-2707	142	11	maheswari	maheswari	PROPN
iajs-2707	142	12	,	,	PUNCT
iajs-2707	142	13	n.	n.	PROPN
iajs-2707	142	14	regular	regular	ADJ
iajs-2707	142	15	generalized	generalize	VERB
iajs-2707	142	16	closed	close	VERB
iajs-2707	142	17	sets	set	NOUN
iajs-2707	142	18	in	in	ADP
iajs-2707	142	19	grill	grill	ADJ
iajs-2707	142	20	topological	topological	ADJ
iajs-2707	142	21	spaces	space	NOUN
iajs-2707	142	22	,	,	PUNCT
iajs-2707	142	23	international	international	ADJ
iajs-2707	142	24	journal	journal	NOUN
iajs-2707	142	25	of	of	ADP
iajs-2707	142	26	science	science	PROPN
iajs-2707	142	27	research	research	PROPN
iajs-2707	142	28	issn	issn	PROPN
iajs-2707	142	29	,	,	PUNCT
iajs-2707	142	30	2015	2015	NUM
iajs-2707	142	31	,	,	PUNCT
iajs-2707	142	32	23197064	23197064	NUM
iajs-2707	142	33	.	.	PUNCT
iajs-2707	143	1	6	6	NUM
iajs-2707	143	2	.	.	X
iajs-2707	144	1	chaudhary	chaudhary	PROPN
iajs-2707	144	2	,	,	PUNCT
iajs-2707	144	3	m	m	VERB
iajs-2707	144	4	p	p	ADJ
iajs-2707	144	5	.	.	PUNCT
iajs-2707	144	6	;	;	PUNCT
iajs-2707	144	7	vinesh	vinesh	PROPN
iajs-2707	144	8	kumar	kumar	PROPN
iajs-2707	144	9	on	on	ADP
iajs-2707	144	10	g	g	NOUN
iajs-2707	144	11	-	-	PUNCT
iajs-2707	144	12	closed	close	VERB
iajs-2707	144	13	sets	set	NOUN
iajs-2707	144	14	in	in	ADP
iajs-2707	144	15	a	a	DET
iajs-2707	144	16	topological	topological	ADJ
iajs-2707	144	17	space	space	NOUN
iajs-2707	144	18	global	global	ADJ
iajs-2707	144	19	journal	journal	PROPN
iajs-2707	144	20	of	of	ADP
iajs-2707	144	21	science	science	PROPN
iajs-2707	144	22	frontier	frontier	NOUN
iajs-2707	144	23	research	research	PROPN
iajs-2707	144	24	.2010	.2010	PROPN
iajs-2707	144	25	,	,	PUNCT
iajs-2707	144	26	10	10	NUM
iajs-2707	144	27	,	,	PUNCT
iajs-2707	144	28	2	2	NUM
iajs-2707	144	29	,	,	PUNCT
iajs-2707	144	30	10	10	NUM
iajs-2707	144	31	-	-	SYM
iajs-2707	144	32	12	12	NUM
iajs-2707	144	33	.	.	PUNCT
iajs-2707	145	1	7	7	X
iajs-2707	145	2	.	.	X
iajs-2707	145	3	r	r	NOUN
iajs-2707	145	4	b.	b.	PROPN
iajs-2707	145	5	esmaeel	esmaeel	NOUN
iajs-2707	145	6	,	,	PUNCT
iajs-2707	145	7	on	on	ADP
iajs-2707	145	8	semi	semi	ADJ
iajs-2707	145	9	-	-	ADJ
iajs-2707	145	10	p	p	ADJ
iajs-2707	145	11	-	-	PUNCT
iajs-2707	145	12	open	open	ADJ
iajs-2707	145	13	sets	set	NOUN
iajs-2707	145	14	m	m	VERB
iajs-2707	145	15	s	s	NOUN
iajs-2707	145	16	,	,	PUNCT
iajs-2707	145	17	college	college	NOUN
iajs-2707	145	18	of	of	ADP
iajs-2707	145	19	education	education	PROPN
iajs-2707	145	20	ibn	ibn	PROPN
iajs-2707	145	21	alhaithatham	alhaithatham	PROPN
iajs-2707	145	22	university	university	PROPN
iajs-2707	145	23	of	of	ADP
iajs-2707	145	24	baghdad	baghdad	PROPN
iajs-2707	145	25	,	,	PUNCT
iajs-2707	145	26	2004	2004	NUM
iajs-2707	145	27	.	.	PUNCT
iajs-2707	146	1	8	8	NUM
iajs-2707	146	2	.	.	PUNCT
iajs-2707	147	1	pawlak	pawlak	PROPN
iajs-2707	147	2	,	,	PUNCT
iajs-2707	147	3	z.	z.	PROPN
iajs-2707	147	4	,	,	PUNCT
iajs-2707	147	5	rough	rough	ADJ
iajs-2707	147	6	sets	set	NOUN
iajs-2707	147	7	,	,	PUNCT
iajs-2707	147	8	international	international	ADJ
iajs-2707	147	9	journal	journal	NOUN
iajs-2707	147	10	of	of	ADP
iajs-2707	147	11	computer	computer	NOUN
iajs-2707	147	12	and	and	CCONJ
iajs-2707	147	13	information	information	NOUN
iajs-2707	147	14	sciences	science	NOUN
iajs-2707	147	15	.	.	PUNCT
iajs-2707	148	1	1982	1982	NUM
iajs-2707	148	2	.	.	PUNCT
iajs-2707	149	1	11	11	NUM
iajs-2707	149	2	,	,	PUNCT
iajs-2707	149	3	341	341	NUM
iajs-2707	149	4	-	-	SYM
iajs-2707	149	5	356	356	NUM
iajs-2707	149	6	.	.	PUNCT
iajs-2707	150	1	9	9	NUM
iajs-2707	150	2	.	.	X
iajs-2707	150	3	lellis	lellis	PROPN
iajs-2707	150	4	thivagar	thivagar	NOUN
iajs-2707	150	5	,	,	PUNCT
iajs-2707	150	6	m.	m.	NOUN
iajs-2707	150	7	;	;	PUNCT
iajs-2707	150	8	carmel	carmel	PROPN
iajs-2707	150	9	richard	richard	PROPN
iajs-2707	150	10	,	,	PUNCT
iajs-2707	150	11	on	on	ADP
iajs-2707	150	12	nano	nano	NOUN
iajs-2707	150	13	forms	form	NOUN
iajs-2707	150	14	of	of	ADP
iajs-2707	150	15	weakly	weakly	ADJ
iajs-2707	150	16	open	open	ADJ
iajs-2707	150	17	sets	set	NOUN
iajs-2707	150	18	,	,	PUNCT
iajs-2707	150	19	international	international	ADJ
iajs-2707	150	20	journal	journal	NOUN
iajs-2707	150	21	of	of	ADP
iajs-2707	150	22	mathematics	mathematics	PROPN
iajs-2707	150	23	and	and	CCONJ
iajs-2707	150	24	statistics	statistic	NOUN
iajs-2707	150	25	invention	invention	NOUN
iajs-2707	150	26	.	.	PUNCT
iajs-2707	151	1	2013	2013	NUM
iajs-2707	151	2	.	.	PUNCT
iajs-2707	152	1	1	1	NUM
iajs-2707	152	2	,	,	PUNCT
iajs-2707	152	3	1	1	NUM
iajs-2707	152	4	,	,	PUNCT
iajs-2707	152	5	31	31	NUM
iajs-2707	152	6	-	-	SYM
iajs-2707	152	7	37	37	NUM
iajs-2707	152	8	.	.	PUNCT
iajs-2707	153	1	10	10	NUM
iajs-2707	153	2	.	.	PUNCT
iajs-2707	154	1	lellis	lellis	PROPN
iajs-2707	154	2	thivagar	thivagar	NOUN
iajs-2707	154	3	,	,	PUNCT
iajs-2707	154	4	m.	m.	PROPN
iajs-2707	154	5	carmel	carmel	PROPN
iajs-2707	154	6	richard	richard	PROPN
iajs-2707	154	7	,	,	PUNCT
iajs-2707	154	8	note	note	VERB
iajs-2707	154	9	on	on	ADP
iajs-2707	154	10	nano	nano	NOUN
iajs-2707	154	11	topological	topological	ADJ
iajs-2707	154	12	space	space	NOUN
iajs-2707	154	13	(	(	PUNCT
iajs-2707	154	14	communicated	communicate	VERB
iajs-2707	154	15	)	)	PUNCT
iajs-2707	154	16	11	11	NUM
iajs-2707	154	17	.	.	PUNCT
iajs-2707	155	1	nayle	nayle	NOUN
iajs-2707	155	2	,	,	PUNCT
iajs-2707	155	3	m.	m.	NOUN
iajs-2707	155	4	s.	s.	PROPN
iajs-2707	155	5	;	;	PUNCT
iajs-2707	155	6	nasir	nasir	PROPN
iajs-2707	155	7	a.	a.	PROPN
iajs-2707	155	8	i.	i.	PROPN
iajs-2707	155	9	some	some	DET
iajs-2707	155	10	rough	rough	ADJ
iajs-2707	155	11	sets	set	NOUN
iajs-2707	155	12	properties	property	NOUN
iajs-2707	155	13	on	on	ADP
iajs-2707	155	14	simple	simple	ADJ
iajs-2707	155	15	graphs	graph	NOUN
iajs-2707	155	16	,	,	PUNCT
iajs-2707	155	17	australian	australian	ADJ
iajs-2707	155	18	journal	journal	NOUN
iajs-2707	155	19	of	of	ADP
iajs-2707	155	20	basic	basic	ADJ
iajs-2707	155	21	and	and	CCONJ
iajs-2707	155	22	applied	apply	VERB
iajs-2707	155	23	science	science	NOUN
iajs-2707	155	24	.	.	PUNCT
iajs-2707	156	1	2011	2011	NUM
iajs-2707	156	2	.	.	PUNCT
iajs-2707	157	1	5	5	NUM
iajs-2707	157	2	,	,	PUNCT
iajs-2707	157	3	12	12	NUM
iajs-2707	157	4	,	,	PUNCT
iajs-2707	157	5	1824	1824	NUM
iajs-2707	157	6	-	-	SYM
iajs-2707	157	7	1829	1829	NUM
iajs-2707	157	8	.	.	PUNCT