id	sid	tid	token	lemma	pos
iajs-2289	1	1	165	165	NUM
iajs-2289	1	2	ibn	ibn	PROPN
iajs-2289	1	3	al	al	PROPN
iajs-2289	1	4	-	-	PUNCT
iajs-2289	1	5	haitham	haitham	PROPN
iajs-2289	1	6	jour	jour	X
iajs-2289	1	7	.	.	PROPN
iajs-2289	1	8	for	for	ADP
iajs-2289	1	9	pure	pure	ADJ
iajs-2289	1	10	&	&	CCONJ
iajs-2289	1	11	appl	appl	PROPN
iajs-2289	1	12	.	.	PUNCT
iajs-2289	2	1	sci	sci	PROPN
iajs-2289	2	2	.	.	PROPN
iajs-2289	2	3	32	32	NUM
iajs-2289	2	4	(	(	PUNCT
iajs-2289	2	5	3	3	NUM
iajs-2289	2	6	)	)	PUNCT
iajs-2289	2	7	2019	2019	NUM
iajs-2289	2	8	g.	g.	PROPN
iajs-2289	2	9	s.	s.	PROPN
iajs-2289	2	10	ashaea	ashaea	PROPN
iajs-2289	2	11	y.	y.	PROPN
iajs-2289	2	12	y.	y.	PROPN
iajs-2289	2	13	yousif	yousif	PROPN
iajs-2289	3	1	abstract	abstract	ADJ
iajs-2289	3	2	this	this	DET
iajs-2289	3	3	paper	paper	NOUN
iajs-2289	3	4	consist	consist	VERB
iajs-2289	3	5	some	some	DET
iajs-2289	3	6	new	new	ADJ
iajs-2289	3	7	generalizations	generalization	NOUN
iajs-2289	3	8	of	of	ADP
iajs-2289	3	9	some	some	DET
iajs-2289	3	10	definitions	definition	NOUN
iajs-2289	3	11	such	such	ADJ
iajs-2289	3	12	:	:	PUNCT
iajs-2289	3	13	j	j	PROPN
iajs-2289	3	14	-	-	PUNCT
iajs-2289	3	15	ω	ω	NOUN
iajs-2289	3	16	-	-	PUNCT
iajs-2289	3	17	closure	closure	NOUN
iajs-2289	3	18	converge	converge	NOUN
iajs-2289	3	19	to	to	ADP
iajs-2289	3	20	a	a	DET
iajs-2289	3	21	point	point	NOUN
iajs-2289	3	22	,	,	PUNCT
iajs-2289	3	23	j	j	PROPN
iajs-2289	3	24	-	-	PUNCT
iajs-2289	3	25	ω	ω	NOUN
iajs-2289	3	26	-	-	PUNCT
iajs-2289	3	27	closure	closure	NOUN
iajs-2289	3	28	directed	direct	VERB
iajs-2289	3	29	toward	toward	ADP
iajs-2289	3	30	a	a	DET
iajs-2289	3	31	set	set	NOUN
iajs-2289	3	32	,	,	PUNCT
iajs-2289	3	33	almost	almost	ADV
iajs-2289	3	34	j	j	PROPN
iajs-2289	3	35	-	-	PUNCT
iajs-2289	3	36	ω	ω	NOUN
iajs-2289	3	37	-	-	PUNCT
iajs-2289	3	38	converges	converge	NOUN
iajs-2289	3	39	to	to	ADP
iajs-2289	3	40	a	a	DET
iajs-2289	3	41	set	set	NOUN
iajs-2289	3	42	,	,	PUNCT
iajs-2289	3	43	almost	almost	ADV
iajs-2289	3	44	j	j	PROPN
iajs-2289	3	45	-	-	PUNCT
iajs-2289	3	46	ω	ω	VERB
iajs-2289	3	47	-	-	PUNCT
iajs-2289	3	48	cluster	cluster	NOUN
iajs-2289	3	49	point	point	NOUN
iajs-2289	3	50	,	,	PUNCT
iajs-2289	3	51	a	a	DET
iajs-2289	3	52	set	set	ADJ
iajs-2289	3	53	j	j	PROPN
iajs-2289	3	54	-	-	PUNCT
iajs-2289	3	55	ω	ω	VERB
iajs-2289	3	56	-	-	PUNCT
iajs-2289	3	57	h	h	NOUN
iajs-2289	3	58	-	-	PUNCT
iajs-2289	3	59	closed	closed	ADJ
iajs-2289	3	60	relative	relative	ADJ
iajs-2289	3	61	,	,	PUNCT
iajs-2289	3	62	j	j	PROPN
iajs-2289	3	63	-	-	PUNCT
iajs-2289	3	64	ω	ω	NOUN
iajs-2289	3	65	-	-	PUNCT
iajs-2289	3	66	closure	closure	NOUN
iajs-2289	3	67	continuous	continuous	ADJ
iajs-2289	3	68	mappings	mapping	NOUN
iajs-2289	3	69	,	,	PUNCT
iajs-2289	3	70	j	j	PROPN
iajs-2289	3	71	-	-	PUNCT
iajs-2289	3	72	ω	ω	VERB
iajs-2289	3	73	-	-	ADJ
iajs-2289	3	74	weakly	weakly	ADJ
iajs-2289	3	75	continuous	continuous	ADJ
iajs-2289	3	76	mappings	mapping	NOUN
iajs-2289	3	77	,	,	PUNCT
iajs-2289	3	78	j	j	PROPN
iajs-2289	3	79	-	-	PUNCT
iajs-2289	3	80	ω	ω	VERB
iajs-2289	3	81	-	-	ADJ
iajs-2289	3	82	compact	compact	ADJ
iajs-2289	3	83	mappings	mapping	NOUN
iajs-2289	3	84	,	,	PUNCT
iajs-2289	3	85	j	j	PROPN
iajs-2289	3	86	-	-	PUNCT
iajs-2289	3	87	ω	ω	NOUN
iajs-2289	3	88	-	-	NOUN
iajs-2289	3	89	rigid	rigid	ADJ
iajs-2289	3	90	a	a	DET
iajs-2289	3	91	set	set	NOUN
iajs-2289	3	92	,	,	PUNCT
iajs-2289	3	93	almost	almost	ADV
iajs-2289	3	94	j	j	PROPN
iajs-2289	3	95	-	-	PUNCT
iajs-2289	3	96	ω	ω	VERB
iajs-2289	3	97	-	-	PUNCT
iajs-2289	3	98	closed	close	VERB
iajs-2289	3	99	mappings	mapping	NOUN
iajs-2289	3	100	and	and	CCONJ
iajs-2289	3	101	j	j	PROPN
iajs-2289	3	102	-	-	PUNCT
iajs-2289	3	103	ω	ω	VERB
iajs-2289	3	104	-	-	PUNCT
iajs-2289	3	105	perfect	perfect	ADJ
iajs-2289	3	106	mappings	mapping	NOUN
iajs-2289	3	107	.	.	PUNCT
iajs-2289	4	1	also	also	ADV
iajs-2289	4	2	,	,	PUNCT
iajs-2289	4	3	we	we	PRON
iajs-2289	4	4	prove	prove	VERB
iajs-2289	4	5	several	several	ADJ
iajs-2289	4	6	results	result	NOUN
iajs-2289	4	7	concerning	concern	VERB
iajs-2289	4	8	it	it	PRON
iajs-2289	4	9	,	,	PUNCT
iajs-2289	4	10	where	where	SCONJ
iajs-2289	4	11	j	j	PROPN
iajs-2289	4	12	{	{	PROPN
iajs-2289	4	13	,	,	PUNCT
iajs-2289	4	14	δ,	δ,	X
iajs-2289	4	15	,	,	PUNCT
iajs-2289	4	16	pre	pre	ADJ
iajs-2289	4	17	,	,	PUNCT
iajs-2289	4	18	b	b	NOUN
iajs-2289	4	19	,	,	PUNCT
iajs-2289	4	20			NOUN
iajs-2289	4	21	}	}	PUNCT
iajs-2289	4	22	.	.	PUNCT
iajs-2289	5	1	keywords	keyword	NOUN
iajs-2289	5	2	:	:	PUNCT
iajs-2289	5	3	filter	filter	NOUN
iajs-2289	5	4	base	base	NOUN
iajs-2289	5	5	,	,	PUNCT
iajs-2289	5	6	j	j	PROPN
iajs-2289	5	7	-	-	PUNCT
iajs-2289	5	8	ω	ω	VERB
iajs-2289	5	9	-	-	PUNCT
iajs-2289	5	10	closure	closure	NOUN
iajs-2289	5	11	converge	converge	NOUN
iajs-2289	5	12	,	,	PUNCT
iajs-2289	5	13	almost	almost	ADV
iajs-2289	5	14	j	j	PROPN
iajs-2289	5	15	-	-	PUNCT
iajs-2289	5	16	ω	ω	NOUN
iajs-2289	5	17	-	-	PUNCT
iajs-2289	5	18	converges	converge	NOUN
iajs-2289	5	19	,	,	PUNCT
iajs-2289	5	20	almost	almost	ADV
iajs-2289	5	21	j	j	PROPN
iajs-2289	5	22	-	-	PUNCT
iajs-2289	5	23	ω	ω	NOUN
iajs-2289	5	24	-	-	PUNCT
iajs-2289	5	25	cluster	cluster	NOUN
iajs-2289	5	26	,	,	PUNCT
iajs-2289	5	27	j	j	NOUN
iajs-2289	5	28	-	-	NOUN
iajs-2289	5	29	ωrigid	ωrigid	PROPN
iajs-2289	5	30	a	a	DET
iajs-2289	5	31	set	set	NOUN
iajs-2289	5	32	,	,	PUNCT
iajs-2289	5	33	j	j	PROPN
iajs-2289	5	34	-	-	PUNCT
iajs-2289	5	35	ω	ω	VERB
iajs-2289	5	36	-	-	PUNCT
iajs-2289	5	37	perfect	perfect	ADJ
iajs-2289	5	38	mappings	mapping	NOUN
iajs-2289	5	39	.	.	PUNCT
iajs-2289	6	1	math	math	NOUN
iajs-2289	6	2	subject	subject	PROPN
iajs-2289	6	3	classification	classification	NOUN
iajs-2289	6	4	2010	2010	NUM
iajs-2289	6	5	:	:	PUNCT
iajs-2289	6	6	54c05	54c05	NUM
iajs-2289	6	7	,	,	PUNCT
iajs-2289	6	8	54c08	54c08	NUM
iajs-2289	6	9	,	,	PUNCT
iajs-2289	6	10	54c10	54c10	NUM
iajs-2289	6	11	.	.	X
iajs-2289	7	1	1	1	X
iajs-2289	7	2	.	.	X
iajs-2289	7	3	introduction	introduction	NOUN
iajs-2289	7	4	the	the	DET
iajs-2289	7	5	notion	notion	NOUN
iajs-2289	7	6	"	"	PUNCT
iajs-2289	7	7	filter	filter	NOUN
iajs-2289	7	8	"	"	PUNCT
iajs-2289	7	9	first	first	ADJ
iajs-2289	7	10	commence	commence	NOUN
iajs-2289	7	11	in	in	ADP
iajs-2289	7	12	riesz	riesz	NOUN
iajs-2289	7	13	[	[	X
iajs-2289	7	14	1	1	NUM
iajs-2289	7	15	]	]	PUNCT
iajs-2289	7	16	.	.	PUNCT
iajs-2289	8	1	and	and	CCONJ
iajs-2289	8	2	the	the	DET
iajs-2289	8	3	setting	setting	NOUN
iajs-2289	8	4	of	of	ADP
iajs-2289	8	5	convergence	convergence	NOUN
iajs-2289	8	6	in	in	ADP
iajs-2289	8	7	terms	term	NOUN
iajs-2289	8	8	of	of	ADP
iajs-2289	8	9	filters	filter	NOUN
iajs-2289	8	10	sketched	sketch	VERB
iajs-2289	8	11	by	by	ADP
iajs-2289	8	12	cartan	cartan	PROPN
iajs-2289	8	13	in	in	ADP
iajs-2289	8	14	[	[	X
iajs-2289	8	15	2	2	NUM
iajs-2289	8	16	,	,	PUNCT
iajs-2289	8	17	3	3	NUM
iajs-2289	8	18	]	]	PUNCT
iajs-2289	8	19	.	.	PUNCT
iajs-2289	9	1	and	and	CCONJ
iajs-2289	9	2	was	be	AUX
iajs-2289	9	3	sophisticatedly	sophisticatedly	ADV
iajs-2289	9	4	by	by	ADP
iajs-2289	9	5	bourbaki	bourbaki	NOUN
iajs-2289	9	6	in	in	ADP
iajs-2289	9	7	[	[	X
iajs-2289	9	8	4	4	NUM
iajs-2289	9	9	]	]	PUNCT
iajs-2289	9	10	.	.	PUNCT
iajs-2289	10	1	whyburn	whyburn	NOUN
iajs-2289	10	2	in	in	ADP
iajs-2289	10	3	[	[	X
iajs-2289	10	4	5	5	NUM
iajs-2289	10	5	]	]	PUNCT
iajs-2289	10	6	.	.	PUNCT
iajs-2289	11	1	introduces	introduce	VERB
iajs-2289	11	2	the	the	DET
iajs-2289	11	3	notion	notion	NOUN
iajs-2289	11	4	directed	direct	VERB
iajs-2289	11	5	toward	toward	ADP
iajs-2289	11	6	a	a	DET
iajs-2289	11	7	set	set	NOUN
iajs-2289	11	8	and	and	CCONJ
iajs-2289	11	9	the	the	DET
iajs-2289	11	10	generalization	generalization	NOUN
iajs-2289	11	11	of	of	ADP
iajs-2289	11	12	this	this	DET
iajs-2289	11	13	notion	notion	NOUN
iajs-2289	11	14	studied	study	VERB
iajs-2289	11	15	in	in	ADP
iajs-2289	11	16	section	section	NOUN
iajs-2289	11	17	2	2	NUM
iajs-2289	11	18	.	.	PUNCT
iajs-2289	11	19	dickman	dickman	PROPN
iajs-2289	11	20	and	and	CCONJ
iajs-2289	11	21	porter	porter	VERB
iajs-2289	11	22	in	in	ADP
iajs-2289	11	23	[	[	X
iajs-2289	11	24	6	6	NUM
iajs-2289	11	25	]	]	PUNCT
iajs-2289	11	26	.	.	PUNCT
iajs-2289	12	1	introduce	introduce	VERB
iajs-2289	12	2	the	the	DET
iajs-2289	12	3	notion	notion	NOUN
iajs-2289	12	4	almost	almost	ADV
iajs-2289	12	5	convergence	convergence	NOUN
iajs-2289	12	6	,	,	PUNCT
iajs-2289	12	7	porter	porter	NOUN
iajs-2289	12	8	and	and	CCONJ
iajs-2289	12	9	thomas	thomas	PROPN
iajs-2289	12	10	in	in	ADP
iajs-2289	12	11	[	[	X
iajs-2289	12	12	7	7	NUM
iajs-2289	12	13	]	]	PUNCT
iajs-2289	12	14	.	.	PUNCT
iajs-2289	13	1	introduce	introduce	VERB
iajs-2289	13	2	the	the	DET
iajs-2289	13	3	notion	notion	NOUN
iajs-2289	13	4	of	of	ADP
iajs-2289	13	5	quasi	quasi	ADJ
iajs-2289	13	6	-	-	ADJ
iajs-2289	13	7	h	h	ADJ
iajs-2289	13	8	-	-	PUNCT
iajs-2289	13	9	closed	close	VERB
iajs-2289	13	10	and	and	CCONJ
iajs-2289	13	11	the	the	DET
iajs-2289	13	12	analogues	analogue	NOUN
iajs-2289	13	13	of	of	ADP
iajs-2289	13	14	this	this	DET
iajs-2289	13	15	notions	notion	NOUN
iajs-2289	13	16	are	be	AUX
iajs-2289	13	17	studied	study	VERB
iajs-2289	13	18	in	in	ADP
iajs-2289	13	19	section	section	NOUN
iajs-2289	13	20	3	3	NUM
iajs-2289	13	21	.	.	PUNCT
iajs-2289	13	22	levine	levine	PROPN
iajs-2289	13	23	in	in	ADP
iajs-2289	13	24	[	[	X
iajs-2289	13	25	8	8	NUM
iajs-2289	13	26	]	]	PUNCT
iajs-2289	13	27	.	.	PUNCT
iajs-2289	14	1	introduce	introduce	VERB
iajs-2289	14	2	the	the	DET
iajs-2289	14	3	notion	notion	NOUN
iajs-2289	14	4	θ	θ	ADJ
iajs-2289	14	5	-	-	ADJ
iajs-2289	14	6	continuous	continuous	ADJ
iajs-2289	14	7	functions	function	NOUN
iajs-2289	14	8	,	,	PUNCT
iajs-2289	14	9	andrew	andrew	PROPN
iajs-2289	14	10	and	and	CCONJ
iajs-2289	14	11	whittlesy	whittlesy	VERB
iajs-2289	14	12	in	in	ADP
iajs-2289	14	13	[	[	X
iajs-2289	14	14	9	9	NUM
iajs-2289	14	15	]	]	PUNCT
iajs-2289	14	16	.	.	PUNCT
iajs-2289	15	1	introduce	introduce	VERB
iajs-2289	15	2	the	the	DET
iajs-2289	15	3	notion	notion	NOUN
iajs-2289	15	4	weakly	weakly	ADJ
iajs-2289	15	5	θ	θ	ADJ
iajs-2289	15	6	-	-	ADJ
iajs-2289	15	7	continuous	continuous	ADJ
iajs-2289	15	8	functions	function	NOUN
iajs-2289	15	9	,	,	PUNCT
iajs-2289	15	10	in	in	ADP
iajs-2289	15	11	dickman	dickman	NOUN
iajs-2289	15	12	[	[	X
iajs-2289	15	13	6	6	NUM
iajs-2289	15	14	]	]	PUNCT
iajs-2289	15	15	.	.	PUNCT
iajs-2289	16	1	introduce	introduce	VERB
iajs-2289	16	2	the	the	DET
iajs-2289	16	3	notions	notion	NOUN
iajs-2289	16	4	θ	θ	ADJ
iajs-2289	16	5	-	-	ADJ
iajs-2289	16	6	compact	compact	ADJ
iajs-2289	16	7	functions	function	NOUN
iajs-2289	16	8	,	,	PUNCT
iajs-2289	16	9	θ	θ	NOUN
iajs-2289	16	10	-	-	ADJ
iajs-2289	16	11	rigid	rigid	ADJ
iajs-2289	16	12	a	a	DET
iajs-2289	16	13	set	set	NOUN
iajs-2289	16	14	,	,	PUNCT
iajs-2289	16	15	almost	almost	ADV
iajs-2289	16	16	closed	close	VERB
iajs-2289	16	17	functions	function	NOUN
iajs-2289	16	18	and	and	CCONJ
iajs-2289	16	19	the	the	DET
iajs-2289	16	20	analogues	analogue	NOUN
iajs-2289	16	21	of	of	ADP
iajs-2289	16	22	this	this	DET
iajs-2289	16	23	notions	notion	NOUN
iajs-2289	16	24	are	be	AUX
iajs-2289	16	25	studied	study	VERB
iajs-2289	16	26	in	in	ADP
iajs-2289	16	27	section	section	NOUN
iajs-2289	16	28	4	4	NUM
iajs-2289	16	29	.	.	PUNCT
iajs-2289	17	1	in	in	ADP
iajs-2289	17	2	[	[	X
iajs-2289	17	3	5	5	NUM
iajs-2289	17	4	]	]	PUNCT
iajs-2289	17	5	.	.	PUNCT
iajs-2289	18	1	the	the	DET
iajs-2289	18	2	researcher	researcher	NOUN
iajs-2289	18	3	introduces	introduce	VERB
iajs-2289	18	4	the	the	DET
iajs-2289	18	5	notion	notion	NOUN
iajs-2289	18	6	of	of	ADP
iajs-2289	18	7	θ	θ	ADJ
iajs-2289	18	8	-	-	PUNCT
iajs-2289	18	9	perfect	perfect	ADJ
iajs-2289	18	10	functions	function	NOUN
iajs-2289	18	11	but	but	CCONJ
iajs-2289	18	12	the	the	DET
iajs-2289	18	13	analogue	analogue	NOUN
iajs-2289	18	14	of	of	ADP
iajs-2289	18	15	this	this	DET
iajs-2289	18	16	notion	notion	NOUN
iajs-2289	18	17	studied	study	VERB
iajs-2289	18	18	in	in	ADP
iajs-2289	18	19	section	section	NOUN
iajs-2289	18	20	5	5	NUM
iajs-2289	18	21	.	.	PUNCT
iajs-2289	19	1	the	the	DET
iajs-2289	19	2	neighborhood	neighborhood	NOUN
iajs-2289	19	3	denoted	denote	VERB
iajs-2289	19	4	by	by	ADP
iajs-2289	19	5	nbd	nbd	PROPN
iajs-2289	19	6	.	.	PUNCT
iajs-2289	20	1	the	the	DET
iajs-2289	20	2	closure	closure	NOUN
iajs-2289	20	3	(	(	PUNCT
iajs-2289	20	4	resp	resp	NOUN
iajs-2289	20	5	.	.	PUNCT
iajs-2289	20	6	interior	interior	NOUN
iajs-2289	20	7	)	)	PUNCT
iajs-2289	20	8	of	of	ADP
iajs-2289	20	9	a	a	DET
iajs-2289	20	10	subset	subset	NOUN
iajs-2289	20	11	k	k	NOUN
iajs-2289	20	12	of	of	ADP
iajs-2289	20	13	a	a	DET
iajs-2289	20	14	space	space	NOUN
iajs-2289	20	15	g	g	NOUN
iajs-2289	20	16	denoted	denote	VERB
iajs-2289	20	17	by	by	ADP
iajs-2289	20	18	cl	cl	NOUN
iajs-2289	20	19	(	(	PUNCT
iajs-2289	20	20	k	k	NOUN
iajs-2289	20	21	)	)	PUNCT
iajs-2289	20	22	(	(	PUNCT
iajs-2289	20	23	resp	resp	NOUN
iajs-2289	20	24	.	.	PROPN
iajs-2289	20	25	,	,	PUNCT
iajs-2289	20	26	int(k	int(k	PROPN
iajs-2289	20	27	)	)	PUNCT
iajs-2289	20	28	)	)	PUNCT
iajs-2289	20	29	.	.	PUNCT
iajs-2289	21	1	a	a	DET
iajs-2289	21	2	point	point	NOUN
iajs-2289	21	3	g	g	NOUN
iajs-2289	21	4	in	in	ADP
iajs-2289	21	5	g	g	PROPN
iajs-2289	21	6	is	be	AUX
iajs-2289	21	7	said	say	VERB
iajs-2289	21	8	to	to	PART
iajs-2289	21	9	be	be	AUX
iajs-2289	21	10	condensation	condensation	NOUN
iajs-2289	21	11	point	point	NOUN
iajs-2289	21	12	of	of	ADP
iajs-2289	21	13	k	k	PROPN
iajs-2289	21	14	⊆	⊆	NUM
iajs-2289	21	15	g	g	NOUN
iajs-2289	21	16	if	if	SCONJ
iajs-2289	21	17	every	every	PRON
iajs-2289	21	18	s	s	NOUN
iajs-2289	21	19	in	in	ADP
iajs-2289	21	20	τ	τ	PROPN
iajs-2289	21	21	with	with	ADP
iajs-2289	21	22	g	g	PROPN
iajs-2289	21	23			PROPN
iajs-2289	21	24	s	s	PART
iajs-2289	21	25	,	,	PUNCT
iajs-2289	21	26	the	the	DET
iajs-2289	21	27	set	set	NOUN
iajs-2289	21	28	k	k	PROPN
iajs-2289	21	29	∩	∩	PROPN
iajs-2289	21	30	s	s	PART
iajs-2289	21	31	is	be	AUX
iajs-2289	21	32	uncountable	uncountable	ADJ
iajs-2289	21	33	[	[	X
iajs-2289	21	34	10	10	NUM
iajs-2289	21	35	]	]	PUNCT
iajs-2289	21	36	.	.	PUNCT
iajs-2289	22	1	in	in	ADP
iajs-2289	22	2	1982	1982	NUM
iajs-2289	22	3	the	the	DET
iajs-2289	22	4	ω	ω	ADV
iajs-2289	22	5	-	-	PUNCT
iajs-2289	22	6	closed	closed	ADJ
iajs-2289	22	7	set	set	NOUN
iajs-2289	22	8	was	be	AUX
iajs-2289	22	9	first	first	ADV
iajs-2289	22	10	exhibiting	exhibit	VERB
iajs-2289	22	11	by	by	ADP
iajs-2289	22	12	hdeib	hdeib	NOUN
iajs-2289	22	13	in	in	ADP
iajs-2289	22	14	[	[	X
iajs-2289	22	15	10	10	NUM
iajs-2289	22	16	]	]	PUNCT
iajs-2289	22	17	.	.	PUNCT
iajs-2289	23	1	and	and	CCONJ
iajs-2289	23	2	he	he	PRON
iajs-2289	23	3	know	know	VERB
iajs-2289	23	4	it	it	PRON
iajs-2289	23	5	a	a	DET
iajs-2289	23	6	subset	subset	NOUN
iajs-2289	23	7	k	k	PROPN
iajs-2289	23	8	⊆	⊆	NUM
iajs-2289	23	9	g	g	PROPN
iajs-2289	23	10	is	be	AUX
iajs-2289	23	11	called	call	VERB
iajs-2289	23	12	ω	ω	NOUN
iajs-2289	23	13	-	-	PUNCT
iajs-2289	23	14	closed	closed	ADJ
iajs-2289	23	15	if	if	SCONJ
iajs-2289	23	16	it	it	PRON
iajs-2289	23	17	incorporates	incorporate	VERB
iajs-2289	23	18	each	each	DET
iajs-2289	23	19	its	its	PRON
iajs-2289	23	20	condensation	condensation	NOUN
iajs-2289	23	21	points	point	NOUN
iajs-2289	23	22	and	and	CCONJ
iajs-2289	23	23	the	the	DET
iajs-2289	23	24	ω	ω	NOUN
iajs-2289	23	25	-	-	ADJ
iajs-2289	23	26	open	open	ADJ
iajs-2289	23	27	set	set	NOUN
iajs-2289	23	28	is	be	AUX
iajs-2289	23	29	the	the	DET
iajs-2289	23	30	complement	complement	NOUN
iajs-2289	23	31	of	of	ADP
iajs-2289	23	32	the	the	DET
iajs-2289	23	33	ω	ω	ADV
iajs-2289	23	34	-	-	PUNCT
iajs-2289	23	35	closed	closed	ADJ
iajs-2289	23	36	set	set	NOUN
iajs-2289	23	37	[	[	X
iajs-2289	23	38	12	12	NUM
iajs-2289	23	39	]	]	PUNCT
iajs-2289	23	40	.	.	PUNCT
iajs-2289	24	1	the	the	DET
iajs-2289	24	2	ωinterior	ωinterior	NOUN
iajs-2289	24	3	of	of	ADP
iajs-2289	24	4	the	the	DET
iajs-2289	24	5	set	set	NOUN
iajs-2289	24	6	k	k	PROPN
iajs-2289	24	7	⊆	⊆	NUM
iajs-2289	24	8	g	g	NOUN
iajs-2289	24	9	defined	define	VERB
iajs-2289	24	10	as	as	ADP
iajs-2289	24	11	the	the	DET
iajs-2289	24	12	union	union	NOUN
iajs-2289	24	13	of	of	ADP
iajs-2289	24	14	all	all	DET
iajs-2289	24	15	ω	ω	ADJ
iajs-2289	24	16	-	-	ADJ
iajs-2289	24	17	open	open	ADJ
iajs-2289	24	18	sets	set	NOUN
iajs-2289	24	19	contain	contain	VERB
iajs-2289	24	20	in	in	ADP
iajs-2289	24	21	k	k	PROPN
iajs-2289	24	22	and	and	CCONJ
iajs-2289	24	23	is	be	AUX
iajs-2289	24	24	denoted	denote	VERB
iajs-2289	24	25	by	by	ADP
iajs-2289	24	26	intω(k	intω(k	PROPN
iajs-2289	24	27	)	)	PUNCT
iajs-2289	24	28	.	.	PUNCT
iajs-2289	25	1	a	a	DET
iajs-2289	25	2	point	point	NOUN
iajs-2289	25	3	g	g	ADP
iajs-2289	25	4			NOUN
iajs-2289	25	5	g	g	PROPN
iajs-2289	25	6	is	be	AUX
iajs-2289	25	7	said	say	VERB
iajs-2289	25	8	to	to	ADP
iajs-2289	25	9	θ	θ	NOUN
iajs-2289	25	10	-	-	PUNCT
iajs-2289	25	11	cluster	cluster	NOUN
iajs-2289	25	12	points	point	NOUN
iajs-2289	25	13	of	of	ADP
iajs-2289	25	14	k	k	PROPN
iajs-2289	25	15	⊆	⊆	NUM
iajs-2289	25	16	g	g	NOUN
iajs-2289	25	17	if	if	SCONJ
iajs-2289	25	18	cl(s	cl(s	NOUN
iajs-2289	25	19	)	)	PUNCT
iajs-2289	25	20	∩	∩	NOUN
iajs-2289	25	21	k	k	PROPN
iajs-2289	25	22	≠	≠	PROPN
iajs-2289	25	23	φ	φ	PROPN
iajs-2289	25	24	for	for	ADP
iajs-2289	25	25	each	each	DET
iajs-2289	25	26	open	open	ADJ
iajs-2289	25	27	set	set	NOUN
iajs-2289	25	28	s	s	PROPN
iajs-2289	25	29	ibn	ibn	PROPN
iajs-2289	25	30	al	al	PROPN
iajs-2289	25	31	haitham	haitham	PROPN
iajs-2289	25	32	journal	journal	PROPN
iajs-2289	25	33	for	for	ADP
iajs-2289	25	34	pure	pure	ADJ
iajs-2289	25	35	and	and	CCONJ
iajs-2289	25	36	applied	apply	VERB
iajs-2289	25	37	science	science	NOUN
iajs-2289	25	38	journal	journal	PROPN
iajs-2289	25	39	homepage	homepage	NOUN
iajs-2289	25	40	:	:	PUNCT
iajs-2289	25	41	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2289	25	42	doi:10.30526/32.3.2289	doi:10.30526/32.3.2289	ADJ
iajs-2289	25	43	filter	filter	NOUN
iajs-2289	25	44	bases	basis	NOUN
iajs-2289	25	45	and	and	CCONJ
iajs-2289	25	46	j	j	PROPN
iajs-2289	25	47	-	-	PUNCT
iajs-2289	25	48	ω	ω	VERB
iajs-2289	25	49	-	-	PUNCT
iajs-2289	25	50	perfect	perfect	ADJ
iajs-2289	25	51	mappings	mapping	NOUN
iajs-2289	25	52	department	department	NOUN
iajs-2289	25	53	of	of	ADP
iajs-2289	25	54	mathematics	mathematics	PROPN
iajs-2289	25	55	,	,	PUNCT
iajs-2289	25	56	college	college	NOUN
iajs-2289	25	57	of	of	ADP
iajs-2289	25	58	education	education	NOUN
iajs-2289	25	59	for	for	ADP
iajs-2289	25	60	pure	pure	ADJ
iajs-2289	25	61	sciences	science	NOUN
iajs-2289	25	62	,	,	PUNCT
iajs-2289	25	63	ibn	ibn	PROPN
iajs-2289	25	64	al	al	PROPN
iajs-2289	25	65	-	-	PUNCT
iajs-2289	25	66	haitham	haitham	PROPN
iajs-2289	25	67	,	,	PUNCT
iajs-2289	25	68	university	university	PROPN
iajs-2289	25	69	of	of	ADP
iajs-2289	25	70	baghdad	baghdad	PROPN
iajs-2289	25	71	dept	dept	PROPN
iajs-2289	25	72	.	.	PROPN
iajs-2289	26	1	of	of	ADP
iajs-2289	26	2	mathematics	mathematics	PROPN
iajs-2289	26	3	,	,	PUNCT
iajs-2289	26	4	college	college	NOUN
iajs-2289	26	5	of	of	ADP
iajs-2289	26	6	education	education	NOUN
iajs-2289	26	7	for	for	ADP
iajs-2289	26	8	pure	pure	ADJ
iajs-2289	26	9	sciences	science	NOUN
iajs-2289	26	10	,	,	PUNCT
iajs-2289	26	11	ibn	ibn	NOUN
iajs-2289	26	12	-alhaitham	-alhaitham	PROPN
iajs-2289	26	13	,	,	PUNCT
iajs-2289	26	14	university	university	NOUN
iajs-2289	26	15	of	of	ADP
iajs-2289	26	16	baghdad	baghdad	PROPN
iajs-2289	26	17	ghidaasadoon@gmail.com	ghidaasadoon@gmail.com	X
iajs-2289	27	1	yoyayousif@yahoo.com	yoyayousif@yahoo.com	PROPN
iajs-2289	27	2	article	article	NOUN
iajs-2289	27	3	history	history	NOUN
iajs-2289	27	4	:	:	PUNCT
iajs-2289	27	5	received	receive	VERB
iajs-2289	27	6	25	25	NUM
iajs-2289	27	7	march	march	NOUN
iajs-2289	27	8	2019	2019	NUM
iajs-2289	27	9	,	,	PUNCT
iajs-2289	27	10	accepted	accept	VERB
iajs-2289	27	11	26	26	NUM
iajs-2289	27	12	may	may	PROPN
iajs-2289	27	13	2019	2019	NUM
iajs-2289	27	14	,	,	PUNCT
iajs-2289	27	15	publish	publish	VERB
iajs-2289	27	16	september	september	PROPN
iajs-2289	27	17	2019	2019	NUM
iajs-2289	27	18	mailto:ghidaasadoon@gmail.com	mailto:ghidaasadoon@gmail.com	PROPN
iajs-2289	27	19	mailto	mailto	PROPN
iajs-2289	27	20	:	:	PUNCT
iajs-2289	27	21	yoyayousif@yahoo.com1	yoyayousif@yahoo.com1	NOUN
iajs-2289	27	22	166	166	NUM
iajs-2289	27	23	ibn	ibn	PROPN
iajs-2289	27	24	al	al	PROPN
iajs-2289	27	25	-	-	PUNCT
iajs-2289	27	26	haitham	haitham	PROPN
iajs-2289	27	27	jour	jour	X
iajs-2289	27	28	.	.	PROPN
iajs-2289	27	29	for	for	ADP
iajs-2289	27	30	pure	pure	ADJ
iajs-2289	27	31	&	&	CCONJ
iajs-2289	27	32	appl	appl	PROPN
iajs-2289	27	33	.	.	PUNCT
iajs-2289	28	1	sci	sci	PROPN
iajs-2289	28	2	.	.	PROPN
iajs-2289	28	3	32	32	NUM
iajs-2289	28	4	(	(	PUNCT
iajs-2289	28	5	3	3	NUM
iajs-2289	28	6	)	)	PUNCT
iajs-2289	28	7	2019	2019	NUM
iajs-2289	28	8	of	of	ADP
iajs-2289	28	9	g	g	PROPN
iajs-2289	28	10	containment	containment	NOUN
iajs-2289	28	11	g.	g.	PROPN
iajs-2289	28	12	the	the	DET
iajs-2289	28	13	set	set	NOUN
iajs-2289	28	14	of	of	ADP
iajs-2289	28	15	each	each	DET
iajs-2289	28	16	θ	θ	NOUN
iajs-2289	28	17	-	-	PUNCT
iajs-2289	28	18	cluster	cluster	NOUN
iajs-2289	28	19	points	point	NOUN
iajs-2289	28	20	of	of	ADP
iajs-2289	28	21	k	k	PROPN
iajs-2289	28	22	is	be	AUX
iajs-2289	28	23	called	call	VERB
iajs-2289	28	24	the	the	DET
iajs-2289	28	25	θ	θ	NOUN
iajs-2289	28	26	-	-	NOUN
iajs-2289	28	27	closure	closure	NOUN
iajs-2289	28	28	of	of	ADP
iajs-2289	28	29	k	k	PROPN
iajs-2289	28	30	and	and	CCONJ
iajs-2289	28	31	is	be	AUX
iajs-2289	28	32	denoted	denote	VERB
iajs-2289	28	33	by	by	ADP
iajs-2289	28	34	clθ(k	clθ(k	NOUN
iajs-2289	28	35	)	)	PUNCT
iajs-2289	28	36	.	.	PUNCT
iajs-2289	29	1	a	a	DET
iajs-2289	29	2	subset	subset	NOUN
iajs-2289	29	3	k	k	NOUN
iajs-2289	29	4	⊆	⊆	NUM
iajs-2289	29	5	g	g	NOUN
iajs-2289	29	6	is	be	AUX
iajs-2289	29	7	said	say	VERB
iajs-2289	29	8	to	to	PART
iajs-2289	29	9	be	be	AUX
iajs-2289	29	10	θ	θ	NOUN
iajs-2289	29	11	-	-	ADJ
iajs-2289	29	12	closed	closed	ADJ
iajs-2289	29	13	[	[	X
iajs-2289	29	14	11	11	NUM
iajs-2289	29	15	]	]	PUNCT
iajs-2289	29	16	.	.	PUNCT
iajs-2289	30	1	if	if	SCONJ
iajs-2289	30	2	k	k	PROPN
iajs-2289	30	3	=	=	SYM
iajs-2289	30	4	clθ(k	clθ(k	PROPN
iajs-2289	30	5	)	)	PUNCT
iajs-2289	30	6	.	.	PUNCT
iajs-2289	31	1	the	the	DET
iajs-2289	31	2	complement	complement	NOUN
iajs-2289	31	3	of	of	ADP
iajs-2289	31	4	θ	θ	PROPN
iajs-2289	31	5	-	-	PUNCT
iajs-2289	31	6	closed	closed	ADJ
iajs-2289	31	7	set	set	NOUN
iajs-2289	31	8	said	say	VERB
iajs-2289	31	9	to	to	PART
iajs-2289	31	10	be	be	AUX
iajs-2289	31	11	θ	θ	NOUN
iajs-2289	31	12	-	-	ADJ
iajs-2289	31	13	open	open	ADJ
iajs-2289	31	14	.	.	PUNCT
iajs-2289	32	1	a	a	DET
iajs-2289	32	2	point	point	NOUN
iajs-2289	32	3	g	g	PROPN
iajs-2289	32	4			NOUN
iajs-2289	32	5	g	g	PROPN
iajs-2289	32	6	said	say	VERB
iajs-2289	32	7	to	to	ADP
iajs-2289	32	8	θ	θ	PROPN
iajs-2289	32	9	-	-	PUNCT
iajs-2289	32	10	ω	ω	VERB
iajs-2289	32	11	-	-	PUNCT
iajs-2289	32	12	cluster	cluster	NOUN
iajs-2289	32	13	points	point	NOUN
iajs-2289	32	14	of	of	ADP
iajs-2289	32	15	k	k	PROPN
iajs-2289	32	16	⊆	⊆	NUM
iajs-2289	32	17	g	g	NOUN
iajs-2289	32	18	if	if	SCONJ
iajs-2289	32	19	ωclθ(s	ωclθ(s	NOUN
iajs-2289	32	20	)	)	PUNCT
iajs-2289	32	21	∩	∩	NOUN
iajs-2289	32	22	k	k	PROPN
iajs-2289	32	23	≠	≠	PROPN
iajs-2289	32	24	φ	φ	PROPN
iajs-2289	32	25	for	for	ADP
iajs-2289	32	26	each	each	DET
iajs-2289	32	27	ω	ω	NOUN
iajs-2289	32	28	-	-	ADJ
iajs-2289	32	29	open	open	ADJ
iajs-2289	32	30	set	set	NOUN
iajs-2289	32	31	s	s	PROPN
iajs-2289	32	32	of	of	ADP
iajs-2289	32	33	g	g	PROPN
iajs-2289	32	34	containment	containment	NOUN
iajs-2289	32	35	g.	g.	PROPN
iajs-2289	33	1	the	the	DET
iajs-2289	33	2	set	set	NOUN
iajs-2289	33	3	of	of	ADP
iajs-2289	33	4	each	each	DET
iajs-2289	33	5	θ	θ	PROPN
iajs-2289	33	6	-	-	PUNCT
iajs-2289	33	7	ω	ω	VERB
iajs-2289	33	8	-	-	PUNCT
iajs-2289	33	9	cluster	cluster	NOUN
iajs-2289	33	10	points	point	NOUN
iajs-2289	33	11	of	of	ADP
iajs-2289	33	12	k	k	PROPN
iajs-2289	33	13	is	be	AUX
iajs-2289	33	14	called	call	VERB
iajs-2289	33	15	the	the	DET
iajs-2289	33	16	θ	θ	PROPN
iajs-2289	33	17	-	-	PUNCT
iajs-2289	33	18	ω	ω	NOUN
iajs-2289	33	19	-	-	NOUN
iajs-2289	33	20	closure	closure	NOUN
iajs-2289	33	21	of	of	ADP
iajs-2289	33	22	k	k	PROPN
iajs-2289	33	23	and	and	CCONJ
iajs-2289	33	24	is	be	AUX
iajs-2289	33	25	denoted	denote	VERB
iajs-2289	33	26	by	by	ADP
iajs-2289	33	27	ωclθ(k	ωclθ(k	NOUN
iajs-2289	33	28	)	)	PUNCT
iajs-2289	33	29	.	.	PUNCT
iajs-2289	34	1	a	a	DET
iajs-2289	34	2	subset	subset	NOUN
iajs-2289	34	3	k	k	NOUN
iajs-2289	34	4	⊆	⊆	NUM
iajs-2289	34	5	g	g	NOUN
iajs-2289	34	6	is	be	AUX
iajs-2289	34	7	said	say	VERB
iajs-2289	34	8	to	to	PART
iajs-2289	34	9	be	be	AUX
iajs-2289	34	10	θ	θ	NOUN
iajs-2289	34	11	-	-	PUNCT
iajs-2289	34	12	ωclosed	ωclose	VERB
iajs-2289	34	13	[	[	X
iajs-2289	34	14	11	11	NUM
iajs-2289	34	15	]	]	PUNCT
iajs-2289	34	16	.	.	PUNCT
iajs-2289	35	1	if	if	SCONJ
iajs-2289	35	2	k	k	PROPN
iajs-2289	35	3	=	=	SYM
iajs-2289	35	4	ωclθ(k	ωclθ(k	PROPN
iajs-2289	35	5	)	)	PUNCT
iajs-2289	35	6	.	.	PUNCT
iajs-2289	36	1	the	the	DET
iajs-2289	36	2	complement	complement	NOUN
iajs-2289	36	3	of	of	ADP
iajs-2289	36	4	θ	θ	PROPN
iajs-2289	36	5	-	-	PUNCT
iajs-2289	36	6	ω	ω	VERB
iajs-2289	36	7	-	-	PUNCT
iajs-2289	36	8	closed	closed	ADJ
iajs-2289	36	9	set	set	NOUN
iajs-2289	36	10	said	say	VERB
iajs-2289	36	11	to	to	PART
iajs-2289	36	12	be	be	AUX
iajs-2289	36	13	θ	θ	PROPN
iajs-2289	36	14	-	-	PUNCT
iajs-2289	36	15	ω	ω	NOUN
iajs-2289	36	16	-	-	NOUN
iajs-2289	36	17	open	open	ADJ
iajs-2289	36	18	,	,	PUNCT
iajs-2289	36	19	δ	δ	NOUN
iajs-2289	36	20	-	-	PUNCT
iajs-2289	36	21	closed	close	VERB
iajs-2289	36	22	[	[	X
iajs-2289	36	23	12	12	NUM
iajs-2289	36	24	]	]	PUNCT
iajs-2289	36	25	.	.	PUNCT
iajs-2289	37	1	if	if	SCONJ
iajs-2289	37	2	k=	k=	X
iajs-2289	37	3	clδ(k	clδ(k	PROPN
iajs-2289	37	4	)	)	PUNCT
iajs-2289	37	5	=	=	PRON
iajs-2289	37	6	{	{	PUNCT
iajs-2289	37	7	g	g	PROPN
iajs-2289	37	8			NOUN
iajs-2289	37	9	g	g	PROPN
iajs-2289	37	10	:	:	PUNCT
iajs-2289	37	11	int(cl(s	int(cl(s	PROPN
iajs-2289	37	12	)	)	PUNCT
iajs-2289	37	13	)	)	PUNCT
iajs-2289	37	14	∩	∩	PROPN
iajs-2289	37	15	k	k	PROPN
iajs-2289	37	16	≠	≠	PROPN
iajs-2289	37	17	φ	φ	PROPN
iajs-2289	37	18	,	,	PUNCT
iajs-2289	37	19	s	s	PART
iajs-2289	37	20			PROPN
iajs-2289	37	21	τ	τ	PROPN
iajs-2289	37	22	and	and	CCONJ
iajs-2289	37	23	g	g	PROPN
iajs-2289	37	24			PROPN
iajs-2289	37	25	s	s	PART
iajs-2289	37	26	}	}	PUNCT
iajs-2289	37	27	.	.	PUNCT
iajs-2289	38	1	the	the	DET
iajs-2289	38	2	complement	complement	NOUN
iajs-2289	38	3	of	of	ADP
iajs-2289	38	4	δclosed	δclose	VERB
iajs-2289	38	5	said	say	VERB
iajs-2289	38	6	δ	δ	NOUN
iajs-2289	38	7	-	-	ADJ
iajs-2289	38	8	open	open	ADJ
iajs-2289	38	9	set	set	NOUN
iajs-2289	38	10	,	,	PUNCT
iajs-2289	38	11	δ	δ	PROPN
iajs-2289	38	12	-	-	PUNCT
iajs-2289	38	13	ω	ω	NOUN
iajs-2289	38	14	-	-	PUNCT
iajs-2289	38	15	closed	closed	ADJ
iajs-2289	38	16	if	if	SCONJ
iajs-2289	38	17	k	k	PROPN
iajs-2289	38	18	=	=	VERB
iajs-2289	38	19	ωclδ	ωclδ	NOUN
iajs-2289	38	20	(	(	PUNCT
iajs-2289	38	21	k	k	X
iajs-2289	38	22	)	)	PUNCT
iajs-2289	38	23	=	=	PRON
iajs-2289	38	24	{	{	PUNCT
iajs-2289	38	25	g	g	PROPN
iajs-2289	38	26			NOUN
iajs-2289	38	27	g	g	PROPN
iajs-2289	38	28	:	:	PUNCT
iajs-2289	38	29	intω(cl(s	intω(cl(	NOUN
iajs-2289	38	30	)	)	PUNCT
iajs-2289	38	31	)	)	PUNCT
iajs-2289	38	32	∩	∩	PROPN
iajs-2289	38	33	k	k	PROPN
iajs-2289	38	34	≠	≠	PROPN
iajs-2289	38	35	φ	φ	PROPN
iajs-2289	38	36	,	,	PUNCT
iajs-2289	38	37	s	s	PART
iajs-2289	38	38			PROPN
iajs-2289	38	39	τ	τ	PROPN
iajs-2289	38	40	and	and	CCONJ
iajs-2289	38	41	g	g	PROPN
iajs-2289	38	42			PROPN
iajs-2289	38	43	s	s	PART
iajs-2289	38	44	}	}	PUNCT
iajs-2289	38	45	.	.	PUNCT
iajs-2289	39	1	the	the	DET
iajs-2289	39	2	complement	complement	NOUN
iajs-2289	39	3	of	of	ADP
iajs-2289	39	4	δ	δ	PROPN
iajs-2289	39	5	-	-	PUNCT
iajs-2289	39	6	ω	ω	VERB
iajs-2289	39	7	-	-	PUNCT
iajs-2289	39	8	closed	closed	ADJ
iajs-2289	39	9	said	say	VERB
iajs-2289	39	10	δ	δ	PROPN
iajs-2289	39	11	-	-	PUNCT
iajs-2289	39	12	ω	ω	NOUN
iajs-2289	39	13	-	-	NOUN
iajs-2289	39	14	open	open	ADJ
iajs-2289	39	15	.	.	PUNCT
iajs-2289	40	1	2	2	X
iajs-2289	40	2	.	.	X
iajs-2289	40	3	filter	filter	NOUN
iajs-2289	40	4	in	in	ADP
iajs-2289	40	5	this	this	DET
iajs-2289	40	6	section	section	NOUN
iajs-2289	40	7	we	we	PRON
iajs-2289	40	8	introduce	introduce	VERB
iajs-2289	40	9	definition	definition	NOUN
iajs-2289	40	10	of	of	ADP
iajs-2289	40	11	filter	filter	NOUN
iajs-2289	40	12	,	,	PUNCT
iajs-2289	40	13	filter	filter	NOUN
iajs-2289	40	14	base	base	NOUN
iajs-2289	40	15	,	,	PUNCT
iajs-2289	40	16	nbd	nbd	PROPN
iajs-2289	40	17	filter	filter	PROPN
iajs-2289	40	18	,	,	PUNCT
iajs-2289	40	19	finer	fine	ADJ
iajs-2289	40	20	ultrafilter	ultrafilter	NOUN
iajs-2289	40	21	and	and	CCONJ
iajs-2289	40	22	some	some	DET
iajs-2289	40	23	other	other	ADJ
iajs-2289	40	24	related	related	ADJ
iajs-2289	40	25	concepts	concept	NOUN
iajs-2289	40	26	.	.	PUNCT
iajs-2289	41	1	definition	definition	NOUN
iajs-2289	41	2	1	1	NUM
iajs-2289	41	3	[	[	X
iajs-2289	41	4	4	4	NUM
iajs-2289	41	5	]	]	PUNCT
iajs-2289	41	6	.	.	PUNCT
iajs-2289	42	1	a	a	DET
iajs-2289	42	2	nonempty	nonempty	ADJ
iajs-2289	42	3	family	family	NOUN
iajs-2289	42	4			NOUN
iajs-2289	42	5	of	of	ADP
iajs-2289	42	6	nonempty	nonempty	ADJ
iajs-2289	42	7	subsets	subset	NOUN
iajs-2289	42	8	of	of	ADP
iajs-2289	42	9	g	g	NOUN
iajs-2289	42	10	called	call	VERB
iajs-2289	42	11	filter	filter	NOUN
iajs-2289	42	12	if	if	SCONJ
iajs-2289	42	13	it	it	PRON
iajs-2289	42	14	satisfies	satisfy	VERB
iajs-2289	42	15	the	the	DET
iajs-2289	42	16	following	follow	VERB
iajs-2289	42	17	conditions	condition	NOUN
iajs-2289	42	18	:	:	PUNCT
iajs-2289	42	19	(	(	PUNCT
iajs-2289	42	20	a	a	X
iajs-2289	42	21	)	)	PUNCT
iajs-2289	42	22	if	if	SCONJ
iajs-2289	42	23	m1	m1	PROPN
iajs-2289	42	24	,	,	PUNCT
iajs-2289	42	25	m2	m2	PROPN
iajs-2289	42	26			PROPN
iajs-2289	42	27			PROPN
iajs-2289	42	28	,	,	PUNCT
iajs-2289	42	29	then	then	ADV
iajs-2289	42	30	m1	m1	PROPN
iajs-2289	42	31	∩	∩	NOUN
iajs-2289	42	32	m2	m2	PROPN
iajs-2289	42	33			NOUN
iajs-2289	42	34	.	.	PROPN
iajs-2289	42	35	(	(	PUNCT
iajs-2289	42	36	b	b	NOUN
iajs-2289	42	37	)	)	PUNCT
iajs-2289	42	38	if	if	SCONJ
iajs-2289	42	39	m	m	VERB
iajs-2289	42	40			NOUN
iajs-2289	42	41			NOUN
iajs-2289	42	42	and	and	CCONJ
iajs-2289	42	43	m	m	NOUN
iajs-2289	42	44			PROPN
iajs-2289	42	45	m	m	PROPN
iajs-2289	42	46	*	*	PROPN
iajs-2289	42	47			PROPN
iajs-2289	42	48	g	g	PROPN
iajs-2289	42	49	,	,	PUNCT
iajs-2289	42	50	then	then	ADV
iajs-2289	42	51	m*	m*	NOUN
iajs-2289	42	52	.	.	PROPN
iajs-2289	42	53	definition	definition	NOUN
iajs-2289	42	54	2	2	NUM
iajs-2289	43	1	[	[	X
iajs-2289	43	2	4	4	NUM
iajs-2289	43	3	]	]	PUNCT
iajs-2289	43	4	.	.	PUNCT
iajs-2289	44	1	a	a	DET
iajs-2289	44	2	nonempty	nonempty	ADJ
iajs-2289	44	3	family	family	NOUN
iajs-2289	44	4			NOUN
iajs-2289	44	5	of	of	ADP
iajs-2289	44	6	nonempty	nonempty	ADJ
iajs-2289	44	7	subsets	subset	NOUN
iajs-2289	44	8	of	of	ADP
iajs-2289	44	9	g	g	PROPN
iajs-2289	44	10	is	be	AUX
iajs-2289	44	11	called	call	VERB
iajs-2289	44	12	filter	filter	NOUN
iajs-2289	44	13	base	base	NOUN
iajs-2289	44	14	if	if	SCONJ
iajs-2289	44	15	m1	m1	PROPN
iajs-2289	44	16	,	,	PUNCT
iajs-2289	44	17	m2	m2	PROPN
iajs-2289	44	18			PROPN
iajs-2289	44	19			PROPN
iajs-2289	44	20	then	then	ADV
iajs-2289	44	21	m3	m3	PROPN
iajs-2289	44	22			PROPN
iajs-2289	44	23	m1	m1	PROPN
iajs-2289	44	24	∩	∩	NOUN
iajs-2289	44	25	m2	m2	PROPN
iajs-2289	44	26	for	for	ADP
iajs-2289	44	27	some	some	DET
iajs-2289	44	28	m3	m3	PROPN
iajs-2289	44	29			NOUN
iajs-2289	44	30	.	.	PROPN
iajs-2289	44	31	the	the	DET
iajs-2289	44	32	filter	filter	NOUN
iajs-2289	44	33	generated	generate	VERB
iajs-2289	44	34	by	by	ADP
iajs-2289	44	35	a	a	DET
iajs-2289	44	36	filter	filter	NOUN
iajs-2289	44	37	base	base	NOUN
iajs-2289	44	38			NOUN
iajs-2289	44	39	consists	consist	VERB
iajs-2289	44	40	of	of	ADP
iajs-2289	44	41	all	all	DET
iajs-2289	44	42	supersets	superset	NOUN
iajs-2289	44	43	of	of	ADP
iajs-2289	44	44	elements	element	NOUN
iajs-2289	44	45	of	of	ADP
iajs-2289	44	46	.	.	PRON
iajs-2289	44	47	an	an	DET
iajs-2289	44	48	open	open	ADJ
iajs-2289	44	49	filter	filter	NOUN
iajs-2289	44	50	base	base	NOUN
iajs-2289	44	51	on	on	ADP
iajs-2289	44	52	a	a	DET
iajs-2289	44	53	space	space	NOUN
iajs-2289	44	54	g	g	NOUN
iajs-2289	44	55	is	be	AUX
iajs-2289	44	56	a	a	DET
iajs-2289	44	57	filter	filter	NOUN
iajs-2289	44	58	base	base	NOUN
iajs-2289	44	59	with	with	ADP
iajs-2289	44	60	open	open	ADJ
iajs-2289	44	61	members	member	NOUN
iajs-2289	44	62	.	.	PUNCT
iajs-2289	45	1	the	the	DET
iajs-2289	45	2	set	set	NOUN
iajs-2289	45	3	g	g	PROPN
iajs-2289	45	4	of	of	ADP
iajs-2289	45	5	all	all	DET
iajs-2289	45	6	nbds	nbds	NOUN
iajs-2289	45	7	of	of	ADP
iajs-2289	45	8	g	g	PROPN
iajs-2289	45	9			PROPN
iajs-2289	45	10	g	g	PROPN
iajs-2289	45	11	is	be	AUX
iajs-2289	45	12	a	a	DET
iajs-2289	45	13	filter	filter	NOUN
iajs-2289	45	14	on	on	ADP
iajs-2289	45	15	g	g	NOUN
iajs-2289	45	16	,	,	PUNCT
iajs-2289	45	17	and	and	CCONJ
iajs-2289	45	18	any	any	DET
iajs-2289	45	19	nbd	nbd	PROPN
iajs-2289	45	20	base	base	NOUN
iajs-2289	45	21	at	at	ADP
iajs-2289	45	22	g	g	PROPN
iajs-2289	45	23	is	be	AUX
iajs-2289	45	24	a	a	DET
iajs-2289	45	25	filter	filter	NOUN
iajs-2289	45	26	base	base	NOUN
iajs-2289	45	27	for	for	ADP
iajs-2289	45	28	g	g	PROPN
iajs-2289	45	29	.	.	PUNCT
iajs-2289	46	1	this	this	DET
iajs-2289	46	2	filter	filter	NOUN
iajs-2289	46	3	called	call	VERB
iajs-2289	46	4	the	the	DET
iajs-2289	46	5	nbd	nbd	PROPN
iajs-2289	46	6	filter	filter	NOUN
iajs-2289	46	7	at	at	ADP
iajs-2289	46	8	g.	g.	PROPN
iajs-2289	46	9	definition	definition	NOUN
iajs-2289	46	10	3	3	NUM
iajs-2289	46	11	[	[	X
iajs-2289	46	12	4	4	NUM
iajs-2289	46	13	]	]	PUNCT
iajs-2289	46	14	.	.	PUNCT
iajs-2289	47	1	let	let	VERB
iajs-2289	47	2			NOUN
iajs-2289	47	3	and	and	VERB
iajs-2289	47	4	be	be	AUX
iajs-2289	47	5	filter	filter	NOUN
iajs-2289	47	6	bases	basis	NOUN
iajs-2289	47	7	on	on	ADP
iajs-2289	47	8	g.	g.	PROPN
iajs-2289	47	9	thenis	thenis	PROPN
iajs-2289	47	10	called	call	VERB
iajs-2289	47	11	finer	fine	ADJ
iajs-2289	47	12	than	than	ADP
iajs-2289	47	13			NOUN
iajs-2289	47	14	(	(	PUNCT
iajs-2289	47	15	written	write	VERB
iajs-2289	47	16	as	as	ADP
iajs-2289	47	17			NOUN
iajs-2289	47	18	<	<	X
iajs-2289	47	19			NOUN
iajs-2289	47	20	)	)	PUNCT
iajs-2289	47	21	if	if	SCONJ
iajs-2289	47	22	for	for	ADP
iajs-2289	47	23	all	all	DET
iajs-2289	47	24	m	m	NOUN
iajs-2289	47	25			NOUN
iajs-2289	47	26			NOUN
iajs-2289	47	27	,	,	PUNCT
iajs-2289	47	28	there	there	PRON
iajs-2289	47	29	is	be	VERB
iajs-2289	47	30	g	g	PROPN
iajs-2289	47	31			NOUN
iajs-2289	47	32	such	such	NUM
iajs-2289	47	33	that	that	DET
iajs-2289	47	34	g	g	PROPN
iajs-2289	47	35			PROPN
iajs-2289	47	36	m	m	PROPN
iajs-2289	47	37	and	and	CCONJ
iajs-2289	47	38	that	that	SCONJ
iajs-2289	47	39			NOUN
iajs-2289	47	40	meets	meet	VERB
iajs-2289	47	41	g	g	NOUN
iajs-2289	47	42	if	if	SCONJ
iajs-2289	47	43	m	m	NOUN
iajs-2289	47	44	∩	∩	ADJ
iajs-2289	47	45	g	g	PROPN
iajs-2289	47	46			NOUN
iajs-2289	47	47			NOUN
iajs-2289	47	48	for	for	ADP
iajs-2289	47	49	all	all	DET
iajs-2289	47	50	m	m	PROPN
iajs-2289	47	51			NOUN
iajs-2289	47	52			NOUN
iajs-2289	47	53	and	and	CCONJ
iajs-2289	47	54	g	g	PROPN
iajs-2289	47	55	.	.	PROPN
iajs-2289	47	56	notice	notice	NOUN
iajs-2289	47	57	,	,	PUNCT
iajs-2289	47	58			NOUN
iajs-2289	47	59			NOUN
iajs-2289	47	60	g	g	PROPN
iajs-2289	47	61	iff	iff	PROPN
iajs-2289	47	62	g	g	X
iajs-2289	47	63	<	<	X
iajs-2289	47	64	.	.	PRON
iajs-2289	47	65	definition	definition	NOUN
iajs-2289	47	66	4	4	NUM
iajs-2289	47	67	[	[	X
iajs-2289	47	68	4	4	NUM
iajs-2289	47	69	]	]	PUNCT
iajs-2289	47	70	.	.	PUNCT
iajs-2289	48	1	a	a	DET
iajs-2289	48	2	filter	filter	NOUN
iajs-2289	48	3			NOUN
iajs-2289	48	4	is	be	AUX
iajs-2289	48	5	called	call	VERB
iajs-2289	48	6	an	an	DET
iajs-2289	48	7	ultrafilter	ultrafilter	NOUN
iajs-2289	48	8	if	if	SCONJ
iajs-2289	48	9	there	there	PRON
iajs-2289	48	10	is	be	VERB
iajs-2289	48	11	no	no	DET
iajs-2289	48	12	strictly	strictly	ADV
iajs-2289	48	13	finer	fine	ADJ
iajs-2289	48	14	filter	filter	NOUN
iajs-2289	48	15	than	than	ADP
iajs-2289	48	16	.	.	NOUN
iajs-2289	48	17	the	the	DET
iajs-2289	48	18	ultrafilter	ultrafilter	NOUN
iajs-2289	48	19	is	be	AUX
iajs-2289	48	20	the	the	DET
iajs-2289	48	21	maximal	maximal	ADJ
iajs-2289	48	22	filter	filter	NOUN
iajs-2289	48	23	.	.	PUNCT
iajs-2289	49	1	definition	definition	NOUN
iajs-2289	49	2	5	5	NUM
iajs-2289	49	3	[	[	X
iajs-2289	49	4	13	13	NUM
iajs-2289	49	5	]	]	PUNCT
iajs-2289	49	6	.	.	PUNCT
iajs-2289	50	1	a	a	DET
iajs-2289	50	2	subset	subset	NOUN
iajs-2289	50	3	k	k	NOUN
iajs-2289	50	4	of	of	ADP
iajs-2289	50	5	a	a	DET
iajs-2289	50	6	space	space	NOUN
iajs-2289	50	7	g	g	NOUN
iajs-2289	50	8	called	call	VERB
iajs-2289	50	9	:	:	PUNCT
iajs-2289	50	10	(	(	PUNCT
iajs-2289	50	11	a	a	X
iajs-2289	50	12	)	)	PUNCT
iajs-2289	50	13	-ω	-ω	NOUN
iajs-2289	50	14	-	-	PUNCT
iajs-2289	50	15	open	open	ADJ
iajs-2289	50	16	if	if	SCONJ
iajs-2289	50	17	k	k	PROPN
iajs-2289	50	18			PROPN
iajs-2289	50	19	intω(cl(intω(k	intω(cl(intω(k	PROPN
iajs-2289	50	20	)	)	PUNCT
iajs-2289	50	21	)	)	PUNCT
iajs-2289	50	22	)	)	PUNCT
iajs-2289	50	23	.	.	PUNCT
iajs-2289	51	1	(	(	PUNCT
iajs-2289	51	2	b	b	X
iajs-2289	51	3	)	)	PUNCT
iajs-2289	51	4	pre	pre	ADJ
iajs-2289	51	5	-	-	ADJ
iajs-2289	51	6	ω	ω	VERB
iajs-2289	51	7	-	-	NOUN
iajs-2289	51	8	open	open	ADJ
iajs-2289	51	9	if	if	SCONJ
iajs-2289	51	10	k	k	PROPN
iajs-2289	51	11			PROPN
iajs-2289	51	12	intω(cl(k	intω(cl(k	VERB
iajs-2289	51	13	)	)	PUNCT
iajs-2289	51	14	)	)	PUNCT
iajs-2289	51	15	.	.	PUNCT
iajs-2289	52	1	(	(	PUNCT
iajs-2289	52	2	c	c	X
iajs-2289	52	3	)	)	PUNCT
iajs-2289	52	4	b	b	X
iajs-2289	52	5	-	-	PUNCT
iajs-2289	52	6	ω	ω	NOUN
iajs-2289	52	7	-	-	NOUN
iajs-2289	52	8	open	open	ADJ
iajs-2289	52	9	if	if	SCONJ
iajs-2289	52	10	k	k	PROPN
iajs-2289	52	11			PROPN
iajs-2289	52	12	cl(intω(k	cl(intω(k	PROPN
iajs-2289	52	13	)	)	PUNCT
iajs-2289	52	14	)	)	PUNCT
iajs-2289	53	1			NOUN
iajs-2289	53	2	intω(cl(k	intω(cl(k	NOUN
iajs-2289	53	3	)	)	PUNCT
iajs-2289	53	4	)	)	PUNCT
iajs-2289	53	5	.	.	PUNCT
iajs-2289	54	1	(	(	PUNCT
iajs-2289	54	2	d	d	X
iajs-2289	54	3	)	)	PUNCT
iajs-2289	54	4	-ω	-ω	NOUN
iajs-2289	54	5	-	-	PUNCT
iajs-2289	54	6	open	open	ADJ
iajs-2289	54	7	if	if	SCONJ
iajs-2289	54	8	k	k	PROPN
iajs-2289	54	9			PROPN
iajs-2289	54	10	cl(intω(cl(k	cl(intω(cl(k	PROPN
iajs-2289	54	11	)	)	PUNCT
iajs-2289	54	12	)	)	PUNCT
iajs-2289	54	13	)	)	PUNCT
iajs-2289	54	14	.	.	PUNCT
iajs-2289	55	1	the	the	DET
iajs-2289	55	2	complement	complement	NOUN
iajs-2289	55	3	of	of	ADP
iajs-2289	55	4	an	an	DET
iajs-2289	55	5	(	(	PUNCT
iajs-2289	55	6	resp	resp	NOUN
iajs-2289	55	7	.	.	PUNCT
iajs-2289	56	1	-ω	-ω	X
iajs-2289	56	2	-	-	PUNCT
iajs-2289	56	3	open	open	ADJ
iajs-2289	56	4	,	,	PUNCT
iajs-2289	56	5	pre	pre	ADJ
iajs-2289	56	6	-	-	ADJ
iajs-2289	56	7	ω	ω	VERB
iajs-2289	56	8	-	-	ADJ
iajs-2289	56	9	open	open	ADJ
iajs-2289	56	10	,	,	PUNCT
iajs-2289	56	11	b	b	X
iajs-2289	56	12	-	-	PUNCT
iajs-2289	56	13	ω	ω	NOUN
iajs-2289	56	14	-	-	ADJ
iajs-2289	56	15	open	open	ADJ
iajs-2289	56	16	,	,	PUNCT
iajs-2289	56	17	-ω	-ω	NOUN
iajs-2289	56	18	-	-	PUNCT
iajs-2289	56	19	open	open	ADJ
iajs-2289	56	20	)	)	PUNCT
iajs-2289	57	1	called	call	VERB
iajs-2289	57	2	(	(	PUNCT
iajs-2289	57	3	resp	resp	NOUN
iajs-2289	57	4	.	.	PUNCT
iajs-2289	58	1	ω	ω	X
iajs-2289	58	2	-	-	PUNCT
iajs-2289	58	3	closed	closed	ADJ
iajs-2289	58	4	,	,	PUNCT
iajs-2289	58	5	pre	pre	ADJ
iajs-2289	58	6	-	-	ADJ
iajs-2289	58	7	ω	ω	ADJ
iajs-2289	58	8	-	-	PUNCT
iajs-2289	58	9	closed	closed	ADJ
iajs-2289	58	10	,	,	PUNCT
iajs-2289	58	11	b	b	X
iajs-2289	58	12	-	-	PUNCT
iajs-2289	58	13	ω	ω	NOUN
iajs-2289	58	14	-	-	PUNCT
iajs-2289	58	15	closed	closed	ADJ
iajs-2289	58	16	,	,	PUNCT
iajs-2289	58	17	-ω	-ω	NOUN
iajs-2289	58	18	-	-	PUNCT
iajs-2289	58	19	closed	closed	ADJ
iajs-2289	58	20	)	)	PUNCT
iajs-2289	58	21	.	.	PUNCT
iajs-2289	59	1	the	the	DET
iajs-2289	59	2	j	j	PROPN
iajs-2289	59	3	-	-	PUNCT
iajs-2289	59	4	ω	ω	NOUN
iajs-2289	59	5	-	-	NOUN
iajs-2289	59	6	closure	closure	NOUN
iajs-2289	59	7	of	of	ADP
iajs-2289	59	8	k	k	PROPN
iajs-2289	59	9			PROPN
iajs-2289	59	10	g	g	PROPN
iajs-2289	59	11	is	be	AUX
iajs-2289	59	12	denoted	denote	VERB
iajs-2289	59	13	by	by	ADP
iajs-2289	59	14	cl	cl	NOUN
iajs-2289	59	15	j	j	NOUN
iajs-2289	59	16	-	-	PUNCT
iajs-2289	59	17	ω-(k	ω-(k	ADV
iajs-2289	59	18	)	)	PUNCT
iajs-2289	59	19	and	and	CCONJ
iajs-2289	59	20	defined	define	VERB
iajs-2289	59	21	by	by	ADP
iajs-2289	59	22	cl	cl	NOUN
iajs-2289	59	23	j	j	NOUN
iajs-2289	59	24	-	-	PUNCT
iajs-2289	59	25	ω-(k	ω-(k	NOUN
iajs-2289	59	26	)	)	PUNCT
iajs-2289	59	27	=	=	PUNCT
iajs-2289	60	1	∩{m	∩{m	PROPN
iajs-2289	60	2			PROPN
iajs-2289	60	3	g	g	PROPN
iajs-2289	60	4	;	;	PUNCT
iajs-2289	60	5	g	g	PROPN
iajs-2289	60	6	is	be	AUX
iajs-2289	60	7	j	j	PROPN
iajs-2289	60	8	-	-	PUNCT
iajs-2289	60	9	ω	ω	NOUN
iajs-2289	60	10	-	-	PUNCT
iajs-2289	60	11	closed	closed	ADJ
iajs-2289	60	12	and	and	CCONJ
iajs-2289	60	13	k	k	PROPN
iajs-2289	60	14			PROPN
iajs-2289	60	15	m	m	PROPN
iajs-2289	60	16	}	}	PUNCT
iajs-2289	60	17	,	,	PUNCT
iajs-2289	60	18	where	where	SCONJ
iajs-2289	60	19	j{	j{	PROPN
iajs-2289	60	20	,	,	PUNCT
iajs-2289	60	21	δ	δ	PROPN
iajs-2289	60	22	,	,	PUNCT
iajs-2289	60	23			X
iajs-2289	60	24	,	,	PUNCT
iajs-2289	60	25	pre	pre	ADJ
iajs-2289	60	26	,	,	PUNCT
iajs-2289	60	27	b	b	NOUN
iajs-2289	60	28	,	,	PUNCT
iajs-2289	60	29			PROPN
iajs-2289	60	30	}	}	PUNCT
iajs-2289	60	31	.	.	PUNCT
iajs-2289	61	1	several	several	ADJ
iajs-2289	61	2	characterizations	characterization	NOUN
iajs-2289	61	3	of	of	ADP
iajs-2289	61	4	ω	ω	VERB
iajs-2289	61	5	-	-	PUNCT
iajs-2289	61	6	closed	closed	ADJ
iajs-2289	61	7	sets	set	NOUN
iajs-2289	61	8	were	be	AUX
iajs-2289	61	9	provided	provide	VERB
iajs-2289	61	10	in	in	ADP
iajs-2289	61	11	[	[	X
iajs-2289	61	12	11	11	NUM
iajs-2289	61	13	]	]	PUNCT
iajs-2289	61	14	,	,	PUNCT
iajs-2289	61	15	.	.	PUNCT
iajs-2289	62	1	[	[	X
iajs-2289	62	2	13	13	NUM
iajs-2289	62	3	-	-	SYM
iajs-2289	62	4	16	16	NUM
iajs-2289	62	5	]	]	PUNCT
iajs-2289	62	6	.	.	PUNCT
iajs-2289	63	1	furthermore	furthermore	ADV
iajs-2289	63	2	,	,	PUNCT
iajs-2289	63	3	we	we	PRON
iajs-2289	63	4	built	build	VERB
iajs-2289	63	5	some	some	DET
iajs-2289	63	6	results	result	NOUN
iajs-2289	63	7	about	about	ADP
iajs-2289	63	8	δ	δ	PROPN
iajs-2289	63	9	-	-	PUNCT
iajs-2289	63	10	ω	ω	NOUN
iajs-2289	63	11	-	-	PUNCT
iajs-2289	63	12	closed	closed	ADJ
iajs-2289	63	13	and	and	CCONJ
iajs-2289	63	14	δ	δ	PROPN
iajs-2289	63	15	-	-	PUNCT
iajs-2289	63	16	ω	ω	NOUN
iajs-2289	63	17	-	-	NOUN
iajs-2289	63	18	open	open	ADJ
iajs-2289	63	19	depending	depend	VERB
iajs-2289	63	20	on	on	ADP
iajs-2289	63	21	the	the	DET
iajs-2289	63	22	results	result	NOUN
iajs-2289	63	23	in	in	ADP
iajs-2289	63	24	[	[	PUNCT
iajs-2289	63	25	17	17	NUM
iajs-2289	63	26	-	-	SYM
iajs-2289	63	27	19	19	NUM
iajs-2289	63	28	]	]	PUNCT
iajs-2289	63	29	.	.	PUNCT
iajs-2289	64	1	167	167	NUM
iajs-2289	64	2	ibn	ibn	PROPN
iajs-2289	64	3	al	al	PROPN
iajs-2289	64	4	-	-	PUNCT
iajs-2289	64	5	haitham	haitham	PROPN
iajs-2289	64	6	jour	jour	X
iajs-2289	64	7	.	.	PROPN
iajs-2289	64	8	for	for	ADP
iajs-2289	64	9	pure	pure	ADJ
iajs-2289	64	10	&	&	CCONJ
iajs-2289	64	11	appl	appl	PROPN
iajs-2289	64	12	.	.	PUNCT
iajs-2289	65	1	sci	sci	PROPN
iajs-2289	65	2	.	.	PROPN
iajs-2289	65	3	32	32	NUM
iajs-2289	65	4	(	(	PUNCT
iajs-2289	65	5	3	3	NUM
iajs-2289	65	6	)	)	PUNCT
iajs-2289	65	7	2019	2019	NUM
iajs-2289	65	8	3	3	NUM
iajs-2289	65	9	.	.	PUNCT
iajs-2289	65	10	filter	filter	NOUN
iajs-2289	65	11	bases	basis	NOUN
iajs-2289	65	12	and	and	CCONJ
iajs-2289	65	13	j	j	PROPN
iajs-2289	65	14	-	-	PUNCT
iajs-2289	65	15	ω	ω	NOUN
iajs-2289	65	16	-	-	PUNCT
iajs-2289	65	17	closure	closure	NOUN
iajs-2289	65	18	directed	direct	VERB
iajs-2289	65	19	toward	toward	ADP
iajs-2289	65	20	a	a	DET
iajs-2289	65	21	set	set	NOUN
iajs-2289	65	22	in	in	ADP
iajs-2289	65	23	this	this	DET
iajs-2289	65	24	section	section	NOUN
iajs-2289	65	25	we	we	PRON
iajs-2289	65	26	defined	define	VERB
iajs-2289	65	27	filter	filter	NOUN
iajs-2289	65	28	bases	basis	NOUN
iajs-2289	65	29	and	and	CCONJ
iajs-2289	65	30	j	j	PROPN
iajs-2289	65	31	-	-	PUNCT
iajs-2289	65	32	ω	ω	NOUN
iajs-2289	65	33	-	-	PUNCT
iajs-2289	65	34	closure	closure	NOUN
iajs-2289	65	35	directed	direct	VERB
iajs-2289	65	36	toward	toward	ADP
iajs-2289	65	37	a	a	DET
iajs-2289	65	38	set	set	NOUN
iajs-2289	65	39	and	and	CCONJ
iajs-2289	65	40	the	the	DET
iajs-2289	65	41	some	some	DET
iajs-2289	65	42	theorems	theorem	NOUN
iajs-2289	65	43	concerning	concern	VERB
iajs-2289	65	44	of	of	ADP
iajs-2289	65	45	them	they	PRON
iajs-2289	65	46	.	.	PUNCT
iajs-2289	66	1	lemma	lemma	PROPN
iajs-2289	66	2	6	6	NUM
iajs-2289	67	1	[	[	X
iajs-2289	67	2	15	15	NUM
iajs-2289	67	3	]	]	PUNCT
iajs-2289	67	4	.	.	PUNCT
iajs-2289	68	1	let	let	VERB
iajs-2289	68	2			ADJ
iajs-2289	68	3	:	:	PUNCT
iajs-2289	68	4	(	(	PUNCT
iajs-2289	68	5	g	g	NOUN
iajs-2289	68	6	,	,	PUNCT
iajs-2289	68	7	τ	τ	NOUN
iajs-2289	68	8	)	)	PUNCT
iajs-2289	68	9			PUNCT
iajs-2289	69	1	(	(	PUNCT
iajs-2289	69	2	h	h	NOUN
iajs-2289	69	3	,	,	PUNCT
iajs-2289	69	4	σ	σ	PROPN
iajs-2289	69	5	)	)	PUNCT
iajs-2289	69	6	be	be	AUX
iajs-2289	69	7	an	an	DET
iajs-2289	69	8	injective	injective	ADJ
iajs-2289	69	9	mapping	mapping	NOUN
iajs-2289	69	10	.	.	PUNCT
iajs-2289	70	1	(	(	PUNCT
iajs-2289	70	2	a	a	X
iajs-2289	70	3	)	)	PUNCT
iajs-2289	70	4	if	if	SCONJ
iajs-2289	70	5			VERB
iajs-2289	70	6	=	=	PUNCT
iajs-2289	70	7	{	{	PUNCT
iajs-2289	70	8	m	m	NOUN
iajs-2289	70	9	:	:	PUNCT
iajs-2289	70	10	m	m	VERB
iajs-2289	70	11			ADJ
iajs-2289	70	12	g	g	PROPN
iajs-2289	70	13	}	}	PUNCT
iajs-2289	70	14	is	be	AUX
iajs-2289	70	15	a	a	DET
iajs-2289	70	16	filter	filter	NOUN
iajs-2289	70	17	base	base	NOUN
iajs-2289	70	18	in	in	ADP
iajs-2289	70	19	g	g	PROPN
iajs-2289	70	20	,	,	PUNCT
iajs-2289	70	21	then	then	ADV
iajs-2289	70	22	(	(	NUM
iajs-2289	70	23	)	)	PUNCT
iajs-2289	71	1	=	=	PRON
iajs-2289	71	2	{	{	PUNCT
iajs-2289	71	3	(m	(m	NOUN
iajs-2289	71	4	):	):	PUNCT
iajs-2289	71	5	m	m	VERB
iajs-2289	71	6			NOUN
iajs-2289	71	7			NOUN
iajs-2289	71	8	}	}	PUNCT
iajs-2289	71	9	is	be	AUX
iajs-2289	71	10	a	a	DET
iajs-2289	71	11	filter	filter	NOUN
iajs-2289	71	12	base	base	NOUN
iajs-2289	71	13	in	in	ADP
iajs-2289	71	14	h.	h.	PROPN
iajs-2289	71	15	(	(	PUNCT
iajs-2289	71	16	b	b	X
iajs-2289	71	17	)	)	PUNCT
iajs-2289	71	18	if	if	SCONJ
iajs-2289	71	19			NOUN
iajs-2289	71	20	=	=	SYM
iajs-2289	71	21	{	{	PUNCT
iajs-2289	71	22	g	g	NOUN
iajs-2289	71	23	:	:	PUNCT
iajs-2289	71	24	g	g	PROPN
iajs-2289	71	25			PROPN
iajs-2289	71	26	(g	(g	PROPN
iajs-2289	71	27	)	)	PUNCT
iajs-2289	71	28	}	}	PUNCT
iajs-2289	71	29	is	be	AUX
iajs-2289	71	30	a	a	DET
iajs-2289	71	31	filter	filter	NOUN
iajs-2289	71	32	base	base	NOUN
iajs-2289	71	33	in	in	ADP
iajs-2289	71	34	(g	(g	PROPN
iajs-2289	71	35	)	)	PUNCT
iajs-2289	71	36	,	,	PUNCT
iajs-2289	71	37			PROPN
iajs-2289	71	38	=	=	SYM
iajs-2289	71	39	{	{	PUNCT
iajs-2289	71	40	–1	–1	PROPN
iajs-2289	71	41	(	(	PUNCT
iajs-2289	71	42	g	g	NOUN
iajs-2289	71	43	):	):	PUNCT
iajs-2289	71	44	g	g	PROPN
iajs-2289	71	45			PROPN
iajs-2289	71	46			PROPN
iajs-2289	71	47	}	}	PUNCT
iajs-2289	71	48	is	be	AUX
iajs-2289	71	49	a	a	DET
iajs-2289	71	50	filter	filter	NOUN
iajs-2289	71	51	base	base	NOUN
iajs-2289	71	52	in	in	ADP
iajs-2289	71	53	g.	g.	PROPN
iajs-2289	71	54	for	for	ADP
iajs-2289	71	55	each	each	DET
iajs-2289	71	56			NOUN
iajs-2289	71	57			NOUN
iajs-2289	71	58	k	k	NOUN
iajs-2289	71	59			PROPN
iajs-2289	71	60	g	g	PROPN
iajs-2289	71	61	and	and	CCONJ
iajs-2289	71	62	any	any	DET
iajs-2289	71	63	filter	filter	NOUN
iajs-2289	71	64	base	base	NOUN
iajs-2289	71	65			NOUN
iajs-2289	71	66	in	in	ADP
iajs-2289	71	67	(k	(k	PROPN
iajs-2289	71	68	)	)	PUNCT
iajs-2289	71	69	,	,	PUNCT
iajs-2289	71	70	then	then	ADV
iajs-2289	71	71	{	{	PUNCT
iajs-2289	71	72	k	k	PROPN
iajs-2289	71	73	∩	∩	NOUN
iajs-2289	71	74	–1	–1	PROPN
iajs-2289	71	75	(	(	PUNCT
iajs-2289	71	76	g	g	NOUN
iajs-2289	71	77	):	):	PUNCT
iajs-2289	71	78	g	g	PROPN
iajs-2289	71	79			PROPN
iajs-2289	71	80			PROPN
iajs-2289	71	81	}	}	PUNCT
iajs-2289	71	82	is	be	AUX
iajs-2289	71	83	a	a	DET
iajs-2289	71	84	filter	filter	NOUN
iajs-2289	71	85	base	base	NOUN
iajs-2289	71	86	in	in	ADP
iajs-2289	71	87	k.	k.	PROPN
iajs-2289	71	88	(	(	PUNCT
iajs-2289	71	89	c	c	X
iajs-2289	71	90	)	)	PUNCT
iajs-2289	71	91	if	if	SCONJ
iajs-2289	71	92			NOUN
iajs-2289	71	93	=	=	PUNCT
iajs-2289	71	94	{	{	PUNCT
iajs-2289	71	95	m	m	NOUN
iajs-2289	71	96	:	:	PUNCT
iajs-2289	71	97	m	m	VERB
iajs-2289	71	98			ADJ
iajs-2289	71	99	g	g	PROPN
iajs-2289	71	100	}	}	PUNCT
iajs-2289	71	101	is	be	AUX
iajs-2289	71	102	a	a	DET
iajs-2289	71	103	filter	filter	NOUN
iajs-2289	71	104	base	base	NOUN
iajs-2289	71	105	in	in	ADP
iajs-2289	71	106	g	g	PROPN
iajs-2289	71	107	,	,	PUNCT
iajs-2289	71	108			NOUN
iajs-2289	71	109	=	=	SYM
iajs-2289	71	110	{	{	PUNCT
iajs-2289	71	111	(m	(m	NOUN
iajs-2289	71	112	)	)	PUNCT
iajs-2289	71	113	:	:	PUNCT
iajs-2289	71	114	m	m	VERB
iajs-2289	71	115			NOUN
iajs-2289	71	116			NOUN
iajs-2289	71	117	}	}	PUNCT
iajs-2289	71	118	,	,	PUNCT
iajs-2289	71	119	g	g	PROPN
iajs-2289	71	120	*	*	PUNCT
iajs-2289	71	121	is	be	AUX
iajs-2289	71	122	finer	fine	ADJ
iajs-2289	71	123	than	than	ADP
iajs-2289	71	124	g	g	NOUN
iajs-2289	71	125	,	,	PUNCT
iajs-2289	71	126	and	and	CCONJ
iajs-2289	71	127			NOUN
iajs-2289	71	128	*	*	PUNCT
iajs-2289	72	1	=	=	PUNCT
iajs-2289	72	2	{	{	PUNCT
iajs-2289	72	3	–1	–1	PROPN
iajs-2289	72	4	(	(	PUNCT
iajs-2289	72	5	g	g	NOUN
iajs-2289	72	6	*	*	PUNCT
iajs-2289	72	7	)	)	PUNCT
iajs-2289	72	8	:	:	PUNCT
iajs-2289	72	9	g	g	X
iajs-2289	72	10	*	*	PUNCT
iajs-2289	72	11			PROPN
iajs-2289	72	12			PROPN
iajs-2289	72	13	*	*	PUNCT
iajs-2289	72	14	}	}	PUNCT
iajs-2289	72	15	,	,	PUNCT
iajs-2289	72	16	then	then	ADV
iajs-2289	72	17	the	the	DET
iajs-2289	72	18	collection	collection	NOUN
iajs-2289	72	19	of	of	ADP
iajs-2289	72	20	sets	set	NOUN
iajs-2289	72	21			NOUN
iajs-2289	72	22	*	*	NOUN
iajs-2289	72	23	*	*	PUNCT
iajs-2289	72	24	=	=	PUNCT
iajs-2289	72	25	{	{	PUNCT
iajs-2289	72	26	m	m	PROPN
iajs-2289	72	27	∩	∩	NOUN
iajs-2289	72	28	m	m	VERB
iajs-2289	72	29	*	*	VERB
iajs-2289	72	30	for	for	ADP
iajs-2289	72	31	all	all	DET
iajs-2289	72	32	m	m	PROPN
iajs-2289	72	33			NOUN
iajs-2289	72	34			NOUN
iajs-2289	72	35	and	and	CCONJ
iajs-2289	72	36	m	m	PROPN
iajs-2289	72	37	*	*	NOUN
iajs-2289	72	38			NOUN
iajs-2289	72	39			NOUN
iajs-2289	72	40	*	*	PUNCT
iajs-2289	72	41	}	}	PUNCT
iajs-2289	72	42	is	be	AUX
iajs-2289	72	43	finer	fine	ADJ
iajs-2289	72	44	than	than	ADP
iajs-2289	72	45	both	both	PRON
iajs-2289	72	46	of	of	ADP
iajs-2289	72	47			NOUN
iajs-2289	72	48	and	and	CCONJ
iajs-2289	72	49			NOUN
iajs-2289	72	50	*	*	PUNCT
iajs-2289	72	51	.	.	PUNCT
iajs-2289	73	1	definition	definition	NOUN
iajs-2289	73	2	7	7	NUM
iajs-2289	73	3	[	[	X
iajs-2289	73	4	4	4	NUM
iajs-2289	73	5	]	]	PUNCT
iajs-2289	73	6	.	.	PUNCT
iajs-2289	74	1	let	let	VERB
iajs-2289	74	2			NOUN
iajs-2289	74	3	be	be	AUX
iajs-2289	74	4	a	a	DET
iajs-2289	74	5	filter	filter	NOUN
iajs-2289	74	6	base	base	NOUN
iajs-2289	74	7	on	on	ADP
iajs-2289	74	8	a	a	DET
iajs-2289	74	9	space	space	NOUN
iajs-2289	74	10	g.	g.	NOUN
iajs-2289	74	11	we	we	PRON
iajs-2289	74	12	say	say	VERB
iajs-2289	74	13	that	that	SCONJ
iajs-2289	74	14			NOUN
iajs-2289	74	15	converges	converge	VERB
iajs-2289	74	16	to	to	ADP
iajs-2289	74	17	g	g	PROPN
iajs-2289	74	18			PROPN
iajs-2289	74	19	g	g	PROPN
iajs-2289	74	20	(	(	PUNCT
iajs-2289	74	21	written	write	VERB
iajs-2289	74	22	as	as	ADP
iajs-2289	74	23			NOUN
iajs-2289	74	24			PUNCT
iajs-2289	74	25	g	g	NOUN
iajs-2289	74	26	)	)	PUNCT
iajs-2289	74	27	iff	iff	VERB
iajs-2289	74	28	each	each	DET
iajs-2289	74	29	open	open	ADJ
iajs-2289	74	30	set	set	NOUN
iajs-2289	74	31	s	s	PRON
iajs-2289	74	32	about	about	ADP
iajs-2289	74	33	g	g	PROPN
iajs-2289	74	34	contains	contain	VERB
iajs-2289	74	35	some	some	DET
iajs-2289	74	36	element	element	NOUN
iajs-2289	74	37	m	m	PROPN
iajs-2289	74	38			NOUN
iajs-2289	75	1	.	.	INTJ
iajs-2289	75	2	we	we	PRON
iajs-2289	75	3	say	say	VERB
iajs-2289	75	4			NOUN
iajs-2289	75	5	has	have	VERB
iajs-2289	75	6	g	g	NOUN
iajs-2289	75	7	as	as	ADP
iajs-2289	75	8	a	a	DET
iajs-2289	75	9	cluster	cluster	NOUN
iajs-2289	75	10	point	point	NOUN
iajs-2289	75	11	(	(	PUNCT
iajs-2289	75	12	or	or	CCONJ
iajs-2289	75	13			NOUN
iajs-2289	75	14	cluster	cluster	NOUN
iajs-2289	75	15	at	at	ADP
iajs-2289	75	16	g	g	NOUN
iajs-2289	75	17	)	)	PUNCT
iajs-2289	75	18	iff	iff	VERB
iajs-2289	75	19	each	each	DET
iajs-2289	75	20	open	open	ADJ
iajs-2289	75	21	set	set	NOUN
iajs-2289	75	22	s	s	PRON
iajs-2289	75	23	about	about	ADP
iajs-2289	75	24	g	g	PROPN
iajs-2289	75	25	meets	meet	VERB
iajs-2289	75	26	all	all	DET
iajs-2289	75	27	element	element	NOUN
iajs-2289	75	28	m	m	PROPN
iajs-2289	75	29			NOUN
iajs-2289	76	1	.	.	ADV
iajs-2289	76	2	clear	clear	ADJ
iajs-2289	76	3	that	that	SCONJ
iajs-2289	76	4	if	if	SCONJ
iajs-2289	76	5			NOUN
iajs-2289	76	6			VERB
iajs-2289	76	7	g	g	NOUN
iajs-2289	76	8	,	,	PUNCT
iajs-2289	76	9	then	then	ADV
iajs-2289	76	10			VERB
iajs-2289	76	11	cluster	cluster	NOUN
iajs-2289	76	12	at	at	ADP
iajs-2289	76	13	g.	g.	PROPN
iajs-2289	76	14	definition	definition	NOUN
iajs-2289	76	15	8	8	NUM
iajs-2289	76	16	[	[	X
iajs-2289	76	17	15	15	NUM
iajs-2289	76	18	]	]	PUNCT
iajs-2289	76	19	.	.	PUNCT
iajs-2289	77	1	let	let	VERB
iajs-2289	77	2			NOUN
iajs-2289	77	3	be	be	AUX
iajs-2289	77	4	a	a	DET
iajs-2289	77	5	filter	filter	NOUN
iajs-2289	77	6	base	base	NOUN
iajs-2289	77	7	on	on	ADP
iajs-2289	77	8	a	a	DET
iajs-2289	77	9	space	space	NOUN
iajs-2289	77	10	g.	g.	NOUN
iajs-2289	77	11	we	we	PRON
iajs-2289	77	12	say	say	VERB
iajs-2289	77	13	that	that	SCONJ
iajs-2289	77	14			NOUN
iajs-2289	77	15	directed	direct	VERB
iajs-2289	77	16	toward	toward	ADP
iajs-2289	77	17	(	(	PUNCT
iajs-2289	77	18	shortly	shortly	ADV
iajs-2289	77	19	,	,	PUNCT
iajs-2289	77	20	dir	dir	PROPN
iajs-2289	77	21	,	,	PUNCT
iajs-2289	77	22	tow	tow	NOUN
iajs-2289	77	23	)	)	PUNCT
iajs-2289	77	24	a	a	DET
iajs-2289	77	25	set	set	NOUN
iajs-2289	77	26	k	k	PROPN
iajs-2289	77	27			PROPN
iajs-2289	77	28	g	g	PROPN
iajs-2289	77	29	,	,	PUNCT
iajs-2289	77	30	provided	provide	VERB
iajs-2289	77	31	each	each	DET
iajs-2289	77	32	filter	filter	NOUN
iajs-2289	77	33	base	base	NOUN
iajs-2289	77	34	finer	fine	ADJ
iajs-2289	77	35	than	than	ADP
iajs-2289	77	36			NOUN
iajs-2289	77	37	has	have	VERB
iajs-2289	77	38	a	a	DET
iajs-2289	77	39	cluster	cluster	NOUN
iajs-2289	77	40	point	point	NOUN
iajs-2289	77	41	in	in	ADP
iajs-2289	77	42	k.	k.	PROPN
iajs-2289	77	43	(	(	PUNCT
iajs-2289	77	44	note	note	VERB
iajs-2289	77	45	:	:	PUNCT
iajs-2289	77	46	any	any	DET
iajs-2289	77	47	filter	filter	NOUN
iajs-2289	77	48	base	base	NOUN
iajs-2289	77	49	ca	can	AUX
iajs-2289	77	50	n't	not	PART
iajs-2289	77	51	be	be	AUX
iajs-2289	77	52	dir	dir	NOUN
iajs-2289	77	53	,	,	PUNCT
iajs-2289	77	54	tow	tow	VERB
iajs-2289	77	55	the	the	DET
iajs-2289	77	56	empty	empty	ADJ
iajs-2289	77	57	set	set	NOUN
iajs-2289	77	58	)	)	PUNCT
iajs-2289	77	59	.	.	PUNCT
iajs-2289	78	1	now	now	ADV
iajs-2289	78	2	,	,	PUNCT
iajs-2289	78	3	we	we	PRON
iajs-2289	78	4	will	will	AUX
iajs-2289	78	5	generalizations	generalization	NOUN
iajs-2289	78	6	definitions	definition	NOUN
iajs-2289	78	7	7	7	NUM
iajs-2289	78	8	and	and	CCONJ
iajs-2289	78	9	8	8	NUM
iajs-2289	78	10	as	as	SCONJ
iajs-2289	78	11	follows	follow	VERB
iajs-2289	78	12	.	.	PUNCT
iajs-2289	79	1	definition	definition	NOUN
iajs-2289	79	2	9	9	NUM
iajs-2289	79	3	let	let	VERB
iajs-2289	79	4			NOUN
iajs-2289	79	5	be	be	AUX
iajs-2289	79	6	a	a	DET
iajs-2289	79	7	filter	filter	NOUN
iajs-2289	79	8	base	base	NOUN
iajs-2289	79	9	on	on	ADP
iajs-2289	79	10	a	a	DET
iajs-2289	79	11	space	space	NOUN
iajs-2289	79	12	g.	g.	NOUN
iajs-2289	79	13	we	we	PRON
iajs-2289	79	14	say	say	VERB
iajs-2289	79	15	that	that	SCONJ
iajs-2289	79	16			VERB
iajs-2289	79	17	closure	closure	NOUN
iajs-2289	79	18	converges	converge	NOUN
iajs-2289	79	19	to	to	ADP
iajs-2289	79	20	g	g	PROPN
iajs-2289	79	21			PROPN
iajs-2289	79	22	g	g	PROPN
iajs-2289	79	23	(	(	PUNCT
iajs-2289	79	24	written	write	VERB
iajs-2289	79	25	as	as	ADP
iajs-2289	79	26			NOUN
iajs-2289	79	27	⇝	⇝	X
iajs-2289	79	28	g	g	NOUN
iajs-2289	79	29	)	)	PUNCT
iajs-2289	79	30	iff	iff	NOUN
iajs-2289	79	31	all	all	DET
iajs-2289	79	32	open	open	ADJ
iajs-2289	79	33	set	set	NOUN
iajs-2289	79	34	s	s	PRON
iajs-2289	79	35	about	about	ADP
iajs-2289	79	36	g	g	NOUN
iajs-2289	79	37	,	,	PUNCT
iajs-2289	79	38	the	the	DET
iajs-2289	79	39	cl(s	cl(s	NOUN
iajs-2289	79	40	)	)	PUNCT
iajs-2289	79	41	contains	contain	VERB
iajs-2289	79	42	some	some	DET
iajs-2289	79	43	element	element	NOUN
iajs-2289	79	44	m	m	PROPN
iajs-2289	79	45			NOUN
iajs-2289	80	1	.	.	INTJ
iajs-2289	80	2	we	we	PRON
iajs-2289	80	3	say	say	VERB
iajs-2289	80	4			NOUN
iajs-2289	80	5	has	have	VERB
iajs-2289	80	6	g	g	NOUN
iajs-2289	80	7	as	as	ADP
iajs-2289	80	8	a	a	DET
iajs-2289	80	9	closure	closure	NOUN
iajs-2289	80	10	cluster	cluster	NOUN
iajs-2289	80	11	point	point	NOUN
iajs-2289	80	12	(	(	PUNCT
iajs-2289	80	13	or	or	CCONJ
iajs-2289	80	14			VERB
iajs-2289	80	15	closure	closure	NOUN
iajs-2289	80	16	cluster	cluster	NOUN
iajs-2289	80	17	at	at	ADP
iajs-2289	80	18	g	g	NOUN
iajs-2289	80	19	)	)	PUNCT
iajs-2289	80	20	iff	iff	NOUN
iajs-2289	80	21	all	all	DET
iajs-2289	80	22	open	open	ADJ
iajs-2289	80	23	set	set	NOUN
iajs-2289	80	24	s	s	PRON
iajs-2289	80	25	about	about	ADP
iajs-2289	80	26	g	g	PROPN
iajs-2289	80	27	the	the	DET
iajs-2289	80	28	cl(s	cl(s	NOUN
iajs-2289	80	29	)	)	PUNCT
iajs-2289	80	30	meets	meet	VERB
iajs-2289	80	31	all	all	DET
iajs-2289	80	32	element	element	NOUN
iajs-2289	80	33	m	m	PROPN
iajs-2289	80	34			NOUN
iajs-2289	81	1	.	.	ADV
iajs-2289	81	2	clear	clear	ADJ
iajs-2289	81	3	that	that	SCONJ
iajs-2289	81	4	if	if	SCONJ
iajs-2289	81	5			NOUN
iajs-2289	81	6	⇝	⇝	NOUN
iajs-2289	81	7	g	g	NOUN
iajs-2289	81	8	,	,	PUNCT
iajs-2289	81	9	then	then	ADV
iajs-2289	81	10			VERB
iajs-2289	81	11	closure	closure	NOUN
iajs-2289	81	12	cluster	cluster	NOUN
iajs-2289	81	13	at	at	ADP
iajs-2289	81	14	g.	g.	PROPN
iajs-2289	81	15	cl	cl	PROPN
iajs-2289	81	16	(	(	PUNCT
iajs-2289	81	17	g	g	NUM
iajs-2289	81	18	)	)	PUNCT
iajs-2289	81	19	used	use	VERB
iajs-2289	81	20	to	to	PART
iajs-2289	81	21	denote	denote	VERB
iajs-2289	81	22	the	the	DET
iajs-2289	81	23	filter	filter	NOUN
iajs-2289	81	24	base	base	NOUN
iajs-2289	81	25	{	{	PUNCT
iajs-2289	81	26	cl(s	cl(s	NOUN
iajs-2289	81	27	):	):	PUNCT
iajs-2289	81	28	s	s	VERB
iajs-2289	81	29			NOUN
iajs-2289	81	30	g	g	NUM
iajs-2289	81	31	}	}	PUNCT
iajs-2289	81	32	.	.	PUNCT
iajs-2289	82	1	notice	notice	NOUN
iajs-2289	82	2	,	,	PUNCT
iajs-2289	82	3			X
iajs-2289	82	4	⇝	⇝	NOUN
iajs-2289	82	5	g	g	PROPN
iajs-2289	82	6	if	if	NOUN
iajs-2289	83	1	and	and	CCONJ
iajs-2289	83	2	only	only	ADV
iajs-2289	83	3	if	if	SCONJ
iajs-2289	83	4	cl	cl	INTJ
iajs-2289	83	5	(	(	PUNCT
iajs-2289	83	6	g	g	NUM
iajs-2289	83	7	)	)	PUNCT
iajs-2289	83	8	<	<	X
iajs-2289	84	1	.	.	PRON
iajs-2289	85	1	[	[	X
iajs-2289	85	2	10	10	NUM
iajs-2289	85	3	]	]	PUNCT
iajs-2289	85	4	.	.	PUNCT
iajs-2289	86	1	definition	definition	NOUN
iajs-2289	86	2	10	10	NUM
iajs-2289	86	3	let	let	VERB
iajs-2289	86	4			NOUN
iajs-2289	86	5	be	be	AUX
iajs-2289	86	6	a	a	DET
iajs-2289	86	7	filter	filter	NOUN
iajs-2289	86	8	base	base	NOUN
iajs-2289	86	9	on	on	ADP
iajs-2289	86	10	a	a	DET
iajs-2289	86	11	space	space	NOUN
iajs-2289	86	12	g.	g.	NOUN
iajs-2289	86	13	we	we	PRON
iajs-2289	86	14	say	say	VERB
iajs-2289	86	15	that	that	SCONJ
iajs-2289	86	16			VERB
iajs-2289	86	17	closure	closure	NOUN
iajs-2289	86	18	directed	direct	VERB
iajs-2289	86	19	toward	toward	ADP
iajs-2289	86	20	(	(	PUNCT
iajs-2289	86	21	shortly	shortly	ADV
iajs-2289	86	22	,	,	PUNCT
iajs-2289	86	23	cl	cl	NOUN
iajs-2289	86	24	dir	dir	NOUN
iajs-2289	86	25	,	,	PUNCT
iajs-2289	86	26	tow	tow	NOUN
iajs-2289	86	27	)	)	PUNCT
iajs-2289	86	28	a	a	DET
iajs-2289	86	29	set	set	NOUN
iajs-2289	86	30	k	k	PROPN
iajs-2289	86	31			PROPN
iajs-2289	86	32	g	g	PROPN
iajs-2289	86	33	,	,	PUNCT
iajs-2289	86	34	provided	provide	VERB
iajs-2289	86	35	each	each	DET
iajs-2289	86	36	filter	filter	NOUN
iajs-2289	86	37	base	base	NOUN
iajs-2289	86	38	finer	fine	ADJ
iajs-2289	86	39	than	than	ADP
iajs-2289	86	40			NOUN
iajs-2289	86	41	has	have	VERB
iajs-2289	86	42	a	a	DET
iajs-2289	86	43	closure	closure	NOUN
iajs-2289	86	44	cluster	cluster	NOUN
iajs-2289	86	45	point	point	NOUN
iajs-2289	86	46	in	in	ADP
iajs-2289	86	47	k.	k.	PROPN
iajs-2289	86	48	theorem	theorem	PROPN
iajs-2289	86	49	11	11	NUM
iajs-2289	86	50	let	let	VERB
iajs-2289	86	51			NOUN
iajs-2289	86	52	be	be	AUX
iajs-2289	86	53	a	a	DET
iajs-2289	86	54	filter	filter	NOUN
iajs-2289	86	55	base	base	NOUN
iajs-2289	86	56	on	on	ADP
iajs-2289	86	57	a	a	DET
iajs-2289	86	58	space	space	NOUN
iajs-2289	86	59	g.	g.	NOUN
iajs-2289	86	60			NOUN
iajs-2289	86	61	⇝	⇝	NOUN
iajs-2289	86	62	g	g	PROPN
iajs-2289	86	63			NOUN
iajs-2289	86	64	g	g	NOUN
iajs-2289	86	65	if	if	SCONJ
iajs-2289	87	1	and	and	CCONJ
iajs-2289	87	2	only	only	ADV
iajs-2289	87	3	if	if	SCONJ
iajs-2289	87	4			NOUN
iajs-2289	87	5	is	be	AUX
iajs-2289	87	6	cl	cl	NOUN
iajs-2289	87	7	dir	dir	NOUN
iajs-2289	87	8	,	,	PUNCT
iajs-2289	87	9	tow	tow	NOUN
iajs-2289	87	10	g.	g.	NOUN
iajs-2289	87	11	proof	proof	PROPN
iajs-2289	87	12	:	:	PUNCT
iajs-2289	87	13	(	(	PUNCT
iajs-2289	87	14			NOUN
iajs-2289	87	15	)	)	PUNCT
iajs-2289	87	16	assume	assume	VERB
iajs-2289	87	17			NOUN
iajs-2289	87	18	⇝	⇝	NOUN
iajs-2289	87	19	g	g	NOUN
iajs-2289	87	20	,	,	PUNCT
iajs-2289	87	21	all	all	PRON
iajs-2289	87	22	open	open	ADJ
iajs-2289	87	23	set	set	NOUN
iajs-2289	87	24	s	s	PRON
iajs-2289	87	25	about	about	ADP
iajs-2289	87	26	g	g	NOUN
iajs-2289	87	27	,	,	PUNCT
iajs-2289	87	28	cl(s	cl(s	NOUN
iajs-2289	87	29	)	)	PUNCT
iajs-2289	87	30	contains	contain	VERB
iajs-2289	87	31	an	an	DET
iajs-2289	87	32	element	element	NOUN
iajs-2289	87	33	of	of	ADP
iajs-2289	87	34			NOUN
iajs-2289	87	35	and	and	CCONJ
iajs-2289	87	36	thus	thus	ADV
iajs-2289	87	37	contains	contain	VERB
iajs-2289	87	38	an	an	DET
iajs-2289	87	39	element	element	NOUN
iajs-2289	87	40	of	of	ADP
iajs-2289	87	41	every	every	DET
iajs-2289	87	42	filter	filter	NOUN
iajs-2289	87	43	base	base	NOUN
iajs-2289	87	44			NOUN
iajs-2289	87	45	*	*	PUNCT
iajs-2289	87	46	<	<	X
iajs-2289	87	47			NOUN
iajs-2289	87	48	,	,	PUNCT
iajs-2289	87	49	therefore	therefore	ADV
iajs-2289	87	50			NOUN
iajs-2289	87	51	*	*	PUNCT
iajs-2289	87	52	actually	actually	ADV
iajs-2289	87	53	closure	closure	ADJ
iajs-2289	87	54	converges	converge	NOUN
iajs-2289	87	55	to	to	ADP
iajs-2289	87	56	g.	g.	PROPN
iajs-2289	87	57	(	(	PUNCT
iajs-2289	87	58			PROPN
iajs-2289	87	59	)	)	PUNCT
iajs-2289	87	60	assume	assume	VERB
iajs-2289	87	61			NOUN
iajs-2289	87	62	is	be	AUX
iajs-2289	87	63	cl	cl	NOUN
iajs-2289	87	64	dir	dir	NOUN
iajs-2289	87	65	,	,	PUNCT
iajs-2289	87	66	tow	tow	VERB
iajs-2289	87	67	g	g	NOUN
iajs-2289	87	68	,	,	PUNCT
iajs-2289	87	69	it	it	PRON
iajs-2289	87	70	must	must	AUX
iajs-2289	87	71			NOUN
iajs-2289	87	72	⇝	⇝	X
iajs-2289	87	73	g.	g.	NOUN
iajs-2289	87	74	for	for	ADP
iajs-2289	87	75	if	if	SCONJ
iajs-2289	87	76	not	not	PART
iajs-2289	87	77	,	,	PUNCT
iajs-2289	87	78	yond	yond	PROPN
iajs-2289	87	79	is	be	AUX
iajs-2289	87	80	an	an	DET
iajs-2289	87	81	open	open	ADJ
iajs-2289	87	82	set	set	NOUN
iajs-2289	87	83	s	s	NOUN
iajs-2289	87	84	in	in	ADP
iajs-2289	87	85	g	g	PROPN
iajs-2289	87	86	about	about	ADP
iajs-2289	87	87	g	g	PROPN
iajs-2289	87	88	such	such	ADJ
iajs-2289	87	89	that	that	DET
iajs-2289	87	90	cl(s	cl(s	NOUN
iajs-2289	87	91	)	)	PUNCT
iajs-2289	87	92	do	do	AUX
iajs-2289	87	93	n't	not	PART
iajs-2289	87	94	contains	contain	VERB
iajs-2289	87	95	an	an	DET
iajs-2289	87	96	element	element	NOUN
iajs-2289	87	97	of	of	ADP
iajs-2289	87	98	.	.	PRON
iajs-2289	87	99	denote	denote	VERB
iajs-2289	87	100	by	by	ADP
iajs-2289	87	101			NOUN
iajs-2289	87	102	*	*	PUNCT
iajs-2289	87	103	the	the	DET
iajs-2289	87	104	collection	collection	NOUN
iajs-2289	87	105	of	of	ADP
iajs-2289	87	106	sets	set	NOUN
iajs-2289	87	107	m	m	VERB
iajs-2289	87	108	*	*	PUNCT
iajs-2289	87	109	=	=	PUNCT
iajs-2289	87	110	m	m	NOUN
iajs-2289	87	111	∩	∩	NOUN
iajs-2289	87	112	(	(	PUNCT
iajs-2289	87	113	g	g	PROPN
iajs-2289	87	114			PROPN
iajs-2289	87	115	cl(s	cl(s	NOUN
iajs-2289	87	116	)	)	PUNCT
iajs-2289	87	117	)	)	PUNCT
iajs-2289	87	118	for	for	ADP
iajs-2289	87	119	m	m	PROPN
iajs-2289	87	120			NOUN
iajs-2289	87	121			NOUN
iajs-2289	87	122	,	,	PUNCT
iajs-2289	87	123	then	then	ADV
iajs-2289	87	124	the	the	DET
iajs-2289	87	125	sets	set	NOUN
iajs-2289	87	126	m	m	VERB
iajs-2289	87	127	*	*	VERB
iajs-2289	87	128	are	be	AUX
iajs-2289	87	129	nonempty	nonempty	X
iajs-2289	87	130	.	.	PUNCT
iajs-2289	88	1	and	and	CCONJ
iajs-2289	88	2			NOUN
iajs-2289	88	3	*	*	PUNCT
iajs-2289	88	4	is	be	AUX
iajs-2289	88	5	a	a	DET
iajs-2289	88	6	filter	filter	NOUN
iajs-2289	88	7	base	base	NOUN
iajs-2289	88	8	and	and	CCONJ
iajs-2289	88	9	indeed	indeed	ADV
iajs-2289	88	10			NOUN
iajs-2289	88	11	*	*	PUNCT
iajs-2289	88	12	<	<	X
iajs-2289	88	13			NOUN
iajs-2289	88	14	,	,	PUNCT
iajs-2289	88	15	because	because	SCONJ
iajs-2289	88	16	result	result	NOUN
iajs-2289	88	17	in	in	ADP
iajs-2289	88	18	m1	m1	PROPN
iajs-2289	88	19	*	*	PUNCT
iajs-2289	89	1	=	=	SYM
iajs-2289	89	2	m1	m1	PROPN
iajs-2289	89	3	∩	∩	NOUN
iajs-2289	89	4	(	(	PUNCT
iajs-2289	89	5	g	g	PROPN
iajs-2289	89	6			PROPN
iajs-2289	89	7	cl(s	cl(s	NOUN
iajs-2289	89	8	)	)	PUNCT
iajs-2289	89	9	)	)	PUNCT
iajs-2289	89	10	and	and	CCONJ
iajs-2289	89	11	m2	m2	PROPN
iajs-2289	89	12	*	*	PROPN
iajs-2289	89	13	=	=	PROPN
iajs-2289	89	14	m2	m2	PROPN
iajs-2289	89	15	∩	∩	NOUN
iajs-2289	89	16	(	(	PUNCT
iajs-2289	89	17	g	g	PROPN
iajs-2289	89	18			PROPN
iajs-2289	89	19	cl(s	cl(s	NOUN
iajs-2289	89	20	)	)	PUNCT
iajs-2289	89	21	)	)	PUNCT
iajs-2289	89	22	,	,	PUNCT
iajs-2289	89	23	so	so	CCONJ
iajs-2289	89	24	there	there	PRON
iajs-2289	89	25	is	be	VERB
iajs-2289	89	26	an	an	DET
iajs-2289	89	27	m3	m3	PROPN
iajs-2289	89	28			PROPN
iajs-2289	89	29	m1	m1	PROPN
iajs-2289	89	30	∩	∩	NOUN
iajs-2289	89	31	m2	m2	PROPN
iajs-2289	89	32	and	and	CCONJ
iajs-2289	89	33	this	this	DET
iajs-2289	89	34	perform	perform	NOUN
iajs-2289	89	35	to	to	ADP
iajs-2289	89	36	m3	m3	PROPN
iajs-2289	89	37	*	*	PUNCT
iajs-2289	89	38	=	=	SYM
iajs-2289	89	39	m3	m3	PROPN
iajs-2289	89	40	∩	∩	NOUN
iajs-2289	89	41	(	(	PUNCT
iajs-2289	89	42	g	g	PROPN
iajs-2289	89	43			PROPN
iajs-2289	89	44	cl(s	cl(s	NOUN
iajs-2289	89	45	)	)	PUNCT
iajs-2289	89	46	)	)	PUNCT
iajs-2289	89	47			PROPN
iajs-2289	89	48	m1	m1	PROPN
iajs-2289	89	49	∩	∩	NOUN
iajs-2289	89	50	m2	m2	PROPN
iajs-2289	89	51	∩	∩	NOUN
iajs-2289	89	52	(	(	PUNCT
iajs-2289	89	53	g	g	PROPN
iajs-2289	89	54			PROPN
iajs-2289	89	55	cl(s	cl(s	NOUN
iajs-2289	89	56	)	)	PUNCT
iajs-2289	89	57	)	)	PUNCT
iajs-2289	90	1	=	=	SYM
iajs-2289	90	2	m1	m1	PROPN
iajs-2289	90	3	∩	∩	NOUN
iajs-2289	90	4	(	(	PUNCT
iajs-2289	90	5	g	g	PROPN
iajs-2289	90	6			PROPN
iajs-2289	90	7	cl(s	cl(s	NOUN
iajs-2289	90	8	)	)	PUNCT
iajs-2289	90	9	)	)	PUNCT
iajs-2289	90	10	∩	∩	PROPN
iajs-2289	90	11	m2	m2	PROPN
iajs-2289	90	12	∩	∩	NOUN
iajs-2289	90	13	(	(	PUNCT
iajs-2289	90	14	g	g	PROPN
iajs-2289	90	15			PROPN
iajs-2289	90	16	cl(s	cl(s	NOUN
iajs-2289	90	17	)	)	PUNCT
iajs-2289	90	18	)	)	PUNCT
iajs-2289	90	19	.	.	PUNCT
iajs-2289	91	1	168	168	NUM
iajs-2289	91	2	ibn	ibn	PROPN
iajs-2289	91	3	al	al	PROPN
iajs-2289	91	4	-	-	PUNCT
iajs-2289	91	5	haitham	haitham	PROPN
iajs-2289	91	6	jour	jour	X
iajs-2289	91	7	.	.	PROPN
iajs-2289	91	8	for	for	ADP
iajs-2289	91	9	pure	pure	ADJ
iajs-2289	91	10	&	&	CCONJ
iajs-2289	91	11	appl	appl	PROPN
iajs-2289	91	12	.	.	PUNCT
iajs-2289	92	1	sci	sci	PROPN
iajs-2289	92	2	.	.	PROPN
iajs-2289	92	3	32	32	NUM
iajs-2289	92	4	(	(	PUNCT
iajs-2289	92	5	3	3	NUM
iajs-2289	92	6	)	)	PUNCT
iajs-2289	92	7	2019	2019	NUM
iajs-2289	92	8	by	by	ADP
iajs-2289	92	9	construction	construction	NOUN
iajs-2289	92	10	,	,	PUNCT
iajs-2289	92	11	g	g	PROPN
iajs-2289	92	12	is	be	AUX
iajs-2289	92	13	not	not	PART
iajs-2289	92	14	a	a	DET
iajs-2289	92	15	closure	closure	NOUN
iajs-2289	92	16	cluster	cluster	NOUN
iajs-2289	92	17	point	point	NOUN
iajs-2289	92	18	of	of	ADP
iajs-2289	92	19			NOUN
iajs-2289	92	20	*	*	PUNCT
iajs-2289	92	21	.	.	PUNCT
iajs-2289	93	1	this	this	DET
iajs-2289	93	2	contradiction	contradiction	NOUN
iajs-2289	93	3	crops	crop	VERB
iajs-2289	93	4	that	that	SCONJ
iajs-2289	93	5	,	,	PUNCT
iajs-2289	93	6			ADJ
iajs-2289	93	7	⇝	⇝	NOUN
iajs-2289	93	8	g.	g.	NOUN
iajs-2289	93	9	theorem	theorem	VERB
iajs-2289	93	10	12	12	NUM
iajs-2289	93	11	let	let	VERB
iajs-2289	93	12			X
iajs-2289	93	13	:	:	PUNCT
iajs-2289	93	14	(	(	PUNCT
iajs-2289	93	15	g	g	NOUN
iajs-2289	93	16	,	,	PUNCT
iajs-2289	93	17	τ	τ	NOUN
iajs-2289	93	18	)	)	PUNCT
iajs-2289	93	19			PUNCT
iajs-2289	94	1	(	(	PUNCT
iajs-2289	94	2	h	h	NOUN
iajs-2289	94	3	,	,	PUNCT
iajs-2289	94	4	σ	σ	PROPN
iajs-2289	94	5	)	)	PUNCT
iajs-2289	94	6	be	be	VERB
iajs-2289	94	7	an	an	DET
iajs-2289	94	8	injective	injective	ADJ
iajs-2289	94	9	mapping	mapping	NOUN
iajs-2289	94	10	and	and	CCONJ
iajs-2289	94	11	given	give	VERB
iajs-2289	94	12	l	l	PROPN
iajs-2289	94	13			PROPN
iajs-2289	94	14	h.	h.	PROPN
iajs-2289	94	15	if	if	SCONJ
iajs-2289	94	16	for	for	ADP
iajs-2289	94	17	each	each	DET
iajs-2289	94	18	filter	filter	NOUN
iajs-2289	94	19	base	base	NOUN
iajs-2289	94	20			NOUN
iajs-2289	94	21	in	in	ADP
iajs-2289	94	22	(g	(g	NOUN
iajs-2289	94	23	)	)	PUNCT
iajs-2289	94	24	cl	cl	NOUN
iajs-2289	94	25	dir	dir	NOUN
iajs-2289	94	26	,	,	PUNCT
iajs-2289	94	27	tow	tow	VERB
iajs-2289	94	28	a	a	DET
iajs-2289	94	29	point	point	NOUN
iajs-2289	94	30	h	h	NOUN
iajs-2289	94	31			PROPN
iajs-2289	94	32	l	l	NOUN
iajs-2289	94	33	,	,	PUNCT
iajs-2289	94	34	the	the	DET
iajs-2289	94	35	inverse	inverse	ADJ
iajs-2289	94	36	filter	filter	NOUN
iajs-2289	94	37	m	m	NOUN
iajs-2289	94	38	=	=	PUNCT
iajs-2289	94	39	{	{	PUNCT
iajs-2289	94	40	–1	–1	PROPN
iajs-2289	94	41	(	(	PUNCT
iajs-2289	94	42	g	g	NOUN
iajs-2289	94	43	)	)	PUNCT
iajs-2289	94	44	:	:	PUNCT
iajs-2289	94	45	g	g	PROPN
iajs-2289	94	46			ADV
iajs-2289	94	47	}	}	PUNCT
iajs-2289	94	48	is	be	AUX
iajs-2289	94	49	cl	cl	NOUN
iajs-2289	94	50	dir	dir	NOUN
iajs-2289	94	51	,	,	PUNCT
iajs-2289	94	52	tow	tow	NOUN
iajs-2289	94	53			X
iajs-2289	94	54	–	–	PUNCT
iajs-2289	94	55	1	1	NUM
iajs-2289	94	56	(	(	PUNCT
iajs-2289	94	57	h	h	NOUN
iajs-2289	94	58	)	)	PUNCT
iajs-2289	94	59	,	,	PUNCT
iajs-2289	94	60	then	then	ADV
iajs-2289	94	61	for	for	ADP
iajs-2289	94	62	any	any	DET
iajs-2289	94	63	filter	filter	NOUN
iajs-2289	94	64	base	base	NOUN
iajs-2289	94	65			NOUN
iajs-2289	94	66	in	in	ADP
iajs-2289	94	67	(g	(g	NOUN
iajs-2289	94	68	)	)	PUNCT
iajs-2289	94	69	cl	cl	NOUN
iajs-2289	94	70	dir	dir	NOUN
iajs-2289	94	71	,	,	PUNCT
iajs-2289	94	72	tow	tow	VERB
iajs-2289	94	73	a	a	DET
iajs-2289	94	74	set	set	NOUN
iajs-2289	94	75	l	l	NOUN
iajs-2289	94	76	,	,	PUNCT
iajs-2289	95	1	e	e	X
iajs-2289	95	2	=	=	PRON
iajs-2289	95	3	{	{	PUNCT
iajs-2289	95	4	–1	–1	PROPN
iajs-2289	95	5	(	(	PUNCT
iajs-2289	95	6	m	m	NOUN
iajs-2289	95	7	)	)	PUNCT
iajs-2289	95	8	:	:	PUNCT
iajs-2289	95	9	m	m	VERB
iajs-2289	95	10			NOUN
iajs-2289	95	11			NOUN
iajs-2289	95	12	}	}	PUNCT
iajs-2289	95	13	is	be	AUX
iajs-2289	95	14	cl	cl	NOUN
iajs-2289	95	15	dir	dir	NOUN
iajs-2289	95	16	,	,	PUNCT
iajs-2289	95	17	tow	tow	NOUN
iajs-2289	95	18	k	k	X
iajs-2289	96	1	=	=	PUNCT
iajs-2289	96	2	–1	–1	PROPN
iajs-2289	96	3	(	(	PUNCT
iajs-2289	96	4	l	l	NOUN
iajs-2289	96	5	)	)	PUNCT
iajs-2289	96	6	.	.	PUNCT
iajs-2289	97	1	proof	proof	NOUN
iajs-2289	97	2	:	:	PUNCT
iajs-2289	97	3	suppose	suppose	VERB
iajs-2289	97	4	that	that	SCONJ
iajs-2289	97	5	the	the	DET
iajs-2289	97	6	hypothesis	hypothesis	NOUN
iajs-2289	97	7	is	be	AUX
iajs-2289	97	8	true	true	ADJ
iajs-2289	97	9	and	and	CCONJ
iajs-2289	97	10	any	any	DET
iajs-2289	97	11	h	h	NOUN
iajs-2289	97	12			PROPN
iajs-2289	97	13	l	l	NOUN
iajs-2289	97	14	is	be	AUX
iajs-2289	97	15	a	a	DET
iajs-2289	97	16	closure	closure	NOUN
iajs-2289	97	17	cluster	cluster	NOUN
iajs-2289	97	18	point	point	NOUN
iajs-2289	97	19	of	of	ADP
iajs-2289	97	20	a	a	DET
iajs-2289	97	21	filter	filter	NOUN
iajs-2289	97	22	base	base	NOUN
iajs-2289	97	23	finer	fine	ADJ
iajs-2289	97	24	than	than	ADP
iajs-2289	97	25			NOUN
iajs-2289	97	26	must	must	AUX
iajs-2289	97	27	be	be	AUX
iajs-2289	97	28	in	in	ADP
iajs-2289	97	29	(g	(g	PROPN
iajs-2289	97	30	)	)	PUNCT
iajs-2289	97	31	.	.	PUNCT
iajs-2289	98	1	thus	thus	ADV
iajs-2289	98	2	l	l	NOUN
iajs-2289	98	3	∩	∩	ADJ
iajs-2289	98	4	(g	(g	NUM
iajs-2289	98	5	)	)	PUNCT
iajs-2289	98	6			NOUN
iajs-2289	98	7			NOUN
iajs-2289	98	8	,	,	PUNCT
iajs-2289	98	9	and	and	CCONJ
iajs-2289	98	10			NOUN
iajs-2289	98	11	is	be	AUX
iajs-2289	98	12	cl	cl	NOUN
iajs-2289	98	13	dir	dir	NOUN
iajs-2289	98	14	,	,	PUNCT
iajs-2289	98	15	tow	tow	NOUN
iajs-2289	98	16	l	l	NOUN
iajs-2289	98	17	∩	∩	X
iajs-2289	98	18			X
iajs-2289	98	19	(	(	PUNCT
iajs-2289	98	20	g	g	NOUN
iajs-2289	98	21	)	)	PUNCT
iajs-2289	98	22	.	.	PUNCT
iajs-2289	99	1	so	so	ADV
iajs-2289	99	2	we	we	PRON
iajs-2289	99	3	may	may	AUX
iajs-2289	99	4	assume	assume	VERB
iajs-2289	99	5	l	l	PROPN
iajs-2289	99	6			PROPN
iajs-2289	99	7	(g	(g	PROPN
iajs-2289	99	8	)	)	PUNCT
iajs-2289	99	9	.	.	PUNCT
iajs-2289	100	1	let	let	VERB
iajs-2289	100	2	m	m	PRON
iajs-2289	100	3	be	be	AUX
iajs-2289	100	4	a	a	DET
iajs-2289	100	5	filter	filter	NOUN
iajs-2289	100	6	base	base	NOUN
iajs-2289	100	7	finer	fine	ADJ
iajs-2289	100	8	than	than	ADP
iajs-2289	100	9	e.	e.	PROPN
iajs-2289	100	10	then	then	ADV
iajs-2289	100	11			PROPN
iajs-2289	100	12	=	=	SYM
iajs-2289	100	13	{	{	PUNCT
iajs-2289	100	14	(	(	PUNCT
iajs-2289	100	15			X
iajs-2289	100	16	(	(	PUNCT
iajs-2289	100	17	m	m	PROPN
iajs-2289	100	18	):	):	PUNCT
iajs-2289	100	19	m	m	PROPN
iajs-2289	100	20	m	m	PROPN
iajs-2289	100	21	}	}	PUNCT
iajs-2289	100	22	finer	fine	ADJ
iajs-2289	100	23	than	than	ADP
iajs-2289	100	24			NOUN
iajs-2289	100	25	by	by	ADP
iajs-2289	100	26	lemma	lemma	PROPN
iajs-2289	100	27	(	(	PUNCT
iajs-2289	100	28	6	6	NUM
iajs-2289	100	29	,	,	PUNCT
iajs-2289	100	30	a	a	PRON
iajs-2289	100	31	)	)	PUNCT
iajs-2289	100	32	.	.	PUNCT
iajs-2289	101	1	so	so	ADV
iajs-2289	101	2			PROPN
iajs-2289	101	3	has	have	VERB
iajs-2289	101	4	a	a	DET
iajs-2289	101	5	closure	closure	NOUN
iajs-2289	101	6	cluster	cluster	NOUN
iajs-2289	101	7	point	point	NOUN
iajs-2289	101	8	l	l	NOUN
iajs-2289	101	9	in	in	ADP
iajs-2289	101	10	l	l	PROPN
iajs-2289	101	11	and	and	CCONJ
iajs-2289	101	12	a	a	DET
iajs-2289	101	13	filter	filter	NOUN
iajs-2289	101	14	base	base	NOUN
iajs-2289	101	15			PROPN
iajs-2289	101	16	*	*	NOUN
iajs-2289	101	17	finer	fine	ADJ
iajs-2289	101	18	than	than	ADP
iajs-2289	101	19			NOUN
iajs-2289	101	20	closure	closure	NOUN
iajs-2289	101	21	converges	converge	NOUN
iajs-2289	101	22	to	to	ADP
iajs-2289	101	23	l	l	NOUN
iajs-2289	102	1	and	and	CCONJ
iajs-2289	102	2	so	so	ADV
iajs-2289	102	3	is	be	AUX
iajs-2289	102	4	cl	cl	NOUN
iajs-2289	102	5	dir	dir	NOUN
iajs-2289	102	6	,	,	PUNCT
iajs-2289	102	7	tow	tow	NOUN
iajs-2289	102	8	l.	l.	PROPN
iajs-2289	102	9	by	by	ADP
iajs-2289	102	10	supposition	supposition	PROPN
iajs-2289	102	11	m	m	PROPN
iajs-2289	102	12	*	*	PUNCT
iajs-2289	103	1	=	=	PUNCT
iajs-2289	103	2	{	{	PUNCT
iajs-2289	103	3	–1	–1	PROPN
iajs-2289	103	4	(	(	PUNCT
iajs-2289	103	5	g	g	NOUN
iajs-2289	103	6	*	*	NOUN
iajs-2289	103	7	):	):	PUNCT
iajs-2289	103	8	g	g	PROPN
iajs-2289	103	9	*	*	PUNCT
iajs-2289	103	10			VERB
iajs-2289	103	11	*	*	PUNCT
iajs-2289	103	12	}	}	PUNCT
iajs-2289	103	13	is	be	AUX
iajs-2289	103	14	cl	cl	NOUN
iajs-2289	103	15	dir	dir	NOUN
iajs-2289	103	16	,	,	PUNCT
iajs-2289	103	17	tow	tow	VERB
iajs-2289	103	18	–1	–1	PROPN
iajs-2289	103	19	(	(	PUNCT
iajs-2289	103	20	l	l	NOUN
iajs-2289	103	21	)	)	PUNCT
iajs-2289	103	22	.	.	PUNCT
iajs-2289	104	1	in	in	ADP
iajs-2289	104	2	addition	addition	NOUN
iajs-2289	104	3	,	,	PUNCT
iajs-2289	104	4	by	by	ADP
iajs-2289	104	5	lemma	lemma	PROPN
iajs-2289	104	6	(	(	PUNCT
iajs-2289	104	7	6	6	NUM
iajs-2289	104	8	,	,	PUNCT
iajs-2289	104	9	c	c	NOUN
iajs-2289	104	10	)	)	PUNCT
iajs-2289	104	11	,	,	PUNCT
iajs-2289	104	12	m	m	VERB
iajs-2289	104	13	and	and	CCONJ
iajs-2289	104	14	m	m	PROPN
iajs-2289	104	15	*	*	AUX
iajs-2289	104	16	have	have	VERB
iajs-2289	104	17	a	a	DET
iajs-2289	104	18	common	common	ADJ
iajs-2289	104	19	filter	filter	NOUN
iajs-2289	104	20	base	base	NOUN
iajs-2289	104	21	m	m	NOUN
iajs-2289	104	22	*	*	NOUN
iajs-2289	104	23	*	*	NOUN
iajs-2289	104	24	finer	fine	ADJ
iajs-2289	104	25	than	than	ADP
iajs-2289	104	26	of	of	ADP
iajs-2289	104	27	them	they	PRON
iajs-2289	104	28	.	.	PUNCT
iajs-2289	105	1	so	so	ADV
iajs-2289	105	2	m	m	VERB
iajs-2289	105	3	*	*	NOUN
iajs-2289	105	4	*	*	PUNCT
iajs-2289	105	5	has	have	VERB
iajs-2289	105	6	a	a	DET
iajs-2289	105	7	closure	closure	NOUN
iajs-2289	105	8	cluster	cluster	NOUN
iajs-2289	105	9	point	point	NOUN
iajs-2289	105	10	g	g	NOUN
iajs-2289	105	11	in	in	ADP
iajs-2289	105	12	–1	–1	PROPN
iajs-2289	105	13	(	(	PUNCT
iajs-2289	105	14	l	l	NOUN
iajs-2289	105	15	)	)	PUNCT
iajs-2289	105	16	.	.	PUNCT
iajs-2289	106	1	since	since	SCONJ
iajs-2289	106	2	g	g	PROPN
iajs-2289	106	3	is	be	AUX
iajs-2289	106	4	a	a	DET
iajs-2289	106	5	closure	closure	NOUN
iajs-2289	106	6	cluster	cluster	NOUN
iajs-2289	106	7	point	point	NOUN
iajs-2289	106	8	of	of	ADP
iajs-2289	106	9	m	m	PROPN
iajs-2289	106	10	and	and	CCONJ
iajs-2289	106	11	g	g	ADP
iajs-2289	106	12			NOUN
iajs-2289	106	13	–1	–1	PROPN
iajs-2289	106	14	(	(	PUNCT
iajs-2289	106	15	l	l	NOUN
iajs-2289	106	16	)	)	PUNCT
iajs-2289	106	17			PROPN
iajs-2289	106	18	k	k	NOUN
iajs-2289	106	19	,	,	PUNCT
iajs-2289	106	20	obtain	obtain	VERB
iajs-2289	106	21	result	result	NOUN
iajs-2289	106	22	follows	follow	VERB
iajs-2289	106	23	.	.	PUNCT
iajs-2289	107	1	theorem	theorem	ADJ
iajs-2289	107	2	13	13	NUM
iajs-2289	107	3	let	let	VERB
iajs-2289	107	4			ADJ
iajs-2289	107	5	:	:	PUNCT
iajs-2289	107	6	g	g	PROPN
iajs-2289	107	7			NOUN
iajs-2289	107	8	h	h	NOUN
iajs-2289	107	9	be	be	AUX
iajs-2289	107	10	closed	close	VERB
iajs-2289	107	11	mapping	mapping	NOUN
iajs-2289	107	12	and	and	CCONJ
iajs-2289	107	13	–1	–1	PROPN
iajs-2289	107	14	(	(	PUNCT
iajs-2289	107	15	h	h	NOUN
iajs-2289	107	16	)	)	PUNCT
iajs-2289	107	17	compact	compact	NOUN
iajs-2289	107	18	for	for	ADP
iajs-2289	107	19	every	every	DET
iajs-2289	107	20	h	h	NOUN
iajs-2289	107	21			PROPN
iajs-2289	107	22	h	h	PROPN
iajs-2289	107	23	iff	iff	PROPN
iajs-2289	107	24	for	for	ADP
iajs-2289	107	25	every	every	DET
iajs-2289	107	26	filter	filter	NOUN
iajs-2289	107	27	base	base	NOUN
iajs-2289	107	28			NOUN
iajs-2289	107	29	in	in	ADP
iajs-2289	107	30	(g	(g	NOUN
iajs-2289	107	31	)	)	PUNCT
iajs-2289	107	32	cl	cl	NOUN
iajs-2289	107	33	dir	dir	NOUN
iajs-2289	107	34	,	,	PUNCT
iajs-2289	107	35	tow	tow	VERB
iajs-2289	107	36	a	a	DET
iajs-2289	107	37	set	set	NOUN
iajs-2289	107	38	l	l	NOUN
iajs-2289	107	39			PROPN
iajs-2289	107	40	h	h	NOUN
iajs-2289	107	41	,	,	PUNCT
iajs-2289	107	42	the	the	DET
iajs-2289	107	43	collection	collection	NOUN
iajs-2289	107	44	e	e	NOUN
iajs-2289	107	45	=	=	PRON
iajs-2289	107	46	{	{	PUNCT
iajs-2289	107	47	–1	–1	PROPN
iajs-2289	107	48	(	(	PUNCT
iajs-2289	107	49	m	m	NOUN
iajs-2289	107	50	)	)	PUNCT
iajs-2289	107	51	:	:	PUNCT
iajs-2289	108	1	m	m	VERB
iajs-2289	108	2			NOUN
iajs-2289	108	3			NOUN
iajs-2289	108	4	}	}	PUNCT
iajs-2289	108	5	is	be	AUX
iajs-2289	108	6	cl	cl	NOUN
iajs-2289	108	7	dir	dir	NOUN
iajs-2289	108	8	,	,	PUNCT
iajs-2289	108	9	tow	tow	VERB
iajs-2289	108	10	–1	–1	PROPN
iajs-2289	108	11	(	(	PUNCT
iajs-2289	108	12	l	l	NOUN
iajs-2289	108	13	)	)	PUNCT
iajs-2289	108	14	.	.	PUNCT
iajs-2289	109	1	proof	proof	NOUN
iajs-2289	109	2	:	:	PUNCT
iajs-2289	109	3	(	(	PUNCT
iajs-2289	109	4			NOUN
iajs-2289	109	5	)	)	PUNCT
iajs-2289	109	6	suppose	suppose	VERB
iajs-2289	109	7	that	that	SCONJ
iajs-2289	109	8			NOUN
iajs-2289	109	9	is	be	AUX
iajs-2289	109	10	closed	close	VERB
iajs-2289	109	11	mapping	mapping	NOUN
iajs-2289	109	12	and	and	CCONJ
iajs-2289	109	13	–1	–1	PROPN
iajs-2289	109	14	(	(	PUNCT
iajs-2289	109	15	h	h	NOUN
iajs-2289	109	16	)	)	PUNCT
iajs-2289	109	17	compact	compact	NOUN
iajs-2289	109	18	for	for	ADP
iajs-2289	109	19	every	every	DET
iajs-2289	109	20	h	h	NOUN
iajs-2289	109	21			PROPN
iajs-2289	109	22	h.	h.	PROPN
iajs-2289	109	23	then	then	ADV
iajs-2289	109	24	by	by	ADP
iajs-2289	109	25	theorem	theorem	NOUN
iajs-2289	109	26	11	11	NUM
iajs-2289	109	27	and	and	CCONJ
iajs-2289	109	28	12	12	NUM
iajs-2289	109	29	it	it	PRON
iajs-2289	109	30	suffices	suffice	VERB
iajs-2289	109	31	to	to	PART
iajs-2289	109	32	prove	prove	VERB
iajs-2289	109	33	that	that	SCONJ
iajs-2289	109	34	if	if	SCONJ
iajs-2289	109	35			NOUN
iajs-2289	109	36	is	be	AUX
iajs-2289	109	37	a	a	DET
iajs-2289	109	38	filter	filter	NOUN
iajs-2289	109	39	base	base	NOUN
iajs-2289	109	40	in	in	ADP
iajs-2289	109	41			ADJ
iajs-2289	109	42	(	(	PUNCT
iajs-2289	109	43	g	g	NOUN
iajs-2289	109	44	)	)	PUNCT
iajs-2289	109	45	j	j	PROPN
iajs-2289	109	46	-	-	PUNCT
iajs-2289	109	47	ω	ω	NOUN
iajs-2289	109	48	-	-	PUNCT
iajs-2289	109	49	closure	closure	NOUN
iajs-2289	109	50	converging	converging	NOUN
iajs-2289	109	51	to	to	ADP
iajs-2289	109	52	h	h	PROPN
iajs-2289	109	53			PROPN
iajs-2289	109	54	l	l	NOUN
iajs-2289	109	55	,	,	PUNCT
iajs-2289	109	56	then	then	ADV
iajs-2289	109	57	m	m	VERB
iajs-2289	109	58	=	=	PUNCT
iajs-2289	109	59	{	{	PUNCT
iajs-2289	109	60	–1	–1	PROPN
iajs-2289	109	61	(	(	PUNCT
iajs-2289	109	62	g	g	NOUN
iajs-2289	109	63	)	)	PUNCT
iajs-2289	109	64	:	:	PUNCT
iajs-2289	109	65	g	g	PROPN
iajs-2289	109	66			ADV
iajs-2289	109	67	}	}	PUNCT
iajs-2289	109	68	is	be	AUX
iajs-2289	109	69	cl	cl	NOUN
iajs-2289	109	70	-	-	PUNCT
iajs-2289	109	71	d	d	NOUN
iajs-2289	109	72	-	-	PUNCT
iajs-2289	109	73	t	t	NOUN
iajs-2289	109	74	–1	–1	PROPN
iajs-2289	109	75	(	(	PUNCT
iajs-2289	109	76	h).in	h).in	X
iajs-2289	109	77	order	order	NOUN
iajs-2289	109	78	to	to	PART
iajs-2289	109	79	if	if	SCONJ
iajs-2289	109	80	not	not	PART
iajs-2289	109	81	,	,	PUNCT
iajs-2289	109	82	yond	yond	PROPN
iajs-2289	109	83	is	be	AUX
iajs-2289	109	84	a	a	DET
iajs-2289	109	85	filter	filter	NOUN
iajs-2289	109	86	base	base	NOUN
iajs-2289	109	87	m	m	PROPN
iajs-2289	109	88	*	*	X
iajs-2289	109	89	finer	fine	ADJ
iajs-2289	109	90	than	than	ADP
iajs-2289	109	91	m	m	PROPN
iajs-2289	109	92	,	,	PUNCT
iajs-2289	109	93	no	no	DET
iajs-2289	109	94	point	point	NOUN
iajs-2289	109	95	of	of	ADP
iajs-2289	109	96	–1	–1	PROPN
iajs-2289	109	97	(	(	PUNCT
iajs-2289	109	98	h	h	NOUN
iajs-2289	109	99	)	)	PUNCT
iajs-2289	109	100	is	be	AUX
iajs-2289	109	101	a	a	DET
iajs-2289	109	102	j	j	PROPN
iajs-2289	109	103	-	-	PUNCT
iajs-2289	109	104	ω	ω	VERB
iajs-2289	109	105	-	-	PUNCT
iajs-2289	109	106	closure	closure	NOUN
iajs-2289	109	107	cluster	cluster	NOUN
iajs-2289	109	108	point	point	NOUN
iajs-2289	109	109	of	of	ADP
iajs-2289	109	110	m	m	PROPN
iajs-2289	109	111	*	*	NOUN
iajs-2289	109	112	.	.	PUNCT
iajs-2289	110	1	for	for	ADP
iajs-2289	110	2	all	all	DET
iajs-2289	110	3	g	g	NOUN
iajs-2289	110	4			NOUN
iajs-2289	110	5	–1	–1	PROPN
iajs-2289	110	6	(	(	PUNCT
iajs-2289	110	7	h	h	NOUN
iajs-2289	110	8	)	)	PUNCT
iajs-2289	110	9	,	,	PUNCT
iajs-2289	110	10	by	by	ADP
iajs-2289	110	11	supposition	supposition	NOUN
iajs-2289	110	12	yond	yond	PROPN
iajs-2289	110	13	is	be	AUX
iajs-2289	110	14	an	an	DET
iajs-2289	110	15	open	open	ADJ
iajs-2289	110	16	set	set	NOUN
iajs-2289	110	17	sg	sg	NOUN
iajs-2289	110	18	about	about	ADP
iajs-2289	110	19	g	g	PROPN
iajs-2289	110	20	and	and	CCONJ
iajs-2289	110	21	m	m	PROPN
iajs-2289	110	22	*	*	PUNCT
iajs-2289	110	23	g	g	PROPN
iajs-2289	110	24			PROPN
iajs-2289	110	25	m	m	PROPN
iajs-2289	110	26	*	*	NOUN
iajs-2289	110	27	with	with	ADP
iajs-2289	110	28	m	m	PROPN
iajs-2289	110	29	*	*	PUNCT
iajs-2289	110	30	g	g	PROPN
iajs-2289	110	31	∩	∩	NOUN
iajs-2289	110	32	sg	sg	NOUN
iajs-2289	110	33	=	=	SYM
iajs-2289	110	34	.	.	X
iajs-2289	110	35	since	since	SCONJ
iajs-2289	110	36	–1	–1	PROPN
iajs-2289	110	37	(	(	PUNCT
iajs-2289	110	38	h	h	NOUN
iajs-2289	110	39	)	)	PUNCT
iajs-2289	110	40	is	be	AUX
iajs-2289	110	41	compact	compact	ADJ
iajs-2289	110	42	,	,	PUNCT
iajs-2289	110	43	yond	yond	PROPN
iajs-2289	110	44	are	be	AUX
iajs-2289	110	45	a	a	DET
iajs-2289	110	46	finite	finite	ADJ
iajs-2289	110	47	numbers	number	NOUN
iajs-2289	110	48	of	of	ADP
iajs-2289	110	49	open	open	ADJ
iajs-2289	110	50	sets	set	NOUN
iajs-2289	110	51	s	s	VERB
iajs-2289	110	52	ig	ig	PROPN
iajs-2289	110	53	such	such	ADJ
iajs-2289	110	54	that	that	SCONJ
iajs-2289	110	55	–1	–1	PROPN
iajs-2289	110	56	(	(	PUNCT
iajs-2289	110	57	h	h	NOUN
iajs-2289	110	58	)	)	PUNCT
iajs-2289	110	59			PROPN
iajs-2289	110	60	s	s	PART
iajs-2289	110	61	=	=	PROPN
iajs-2289	110	62			NOUN
iajs-2289	110	63	s	s	PART
iajs-2289	110	64	ig	ig	PROPN
iajs-2289	110	65	,	,	PUNCT
iajs-2289	110	66	suppose	suppose	VERB
iajs-2289	110	67	m	m	PROPN
iajs-2289	110	68	*	*	PROPN
iajs-2289	110	69			NOUN
iajs-2289	110	70	m	m	VERB
iajs-2289	110	71	*	*	PUNCT
iajs-2289	110	72	such	such	ADJ
iajs-2289	110	73	that	that	SCONJ
iajs-2289	110	74	m	m	PROPN
iajs-2289	110	75	*	*	ADJ
iajs-2289	110	76			PROPN
iajs-2289	110	77	∩	∩	NOUN
iajs-2289	110	78	m	m	PRON
iajs-2289	110	79	*	*	VERB
iajs-2289	110	80	ig	ig	PROPN
iajs-2289	110	81	and	and	CCONJ
iajs-2289	110	82	let	let	VERB
iajs-2289	110	83	t	t	NOUN
iajs-2289	110	84	=	=	PUNCT
iajs-2289	110	85	h	h	PROPN
iajs-2289	110	86			PROPN
iajs-2289	110	87			X
iajs-2289	110	88	(	(	PUNCT
iajs-2289	110	89	g	g	PROPN
iajs-2289	110	90			PROPN
iajs-2289	110	91	s	s	PART
iajs-2289	110	92	)	)	PUNCT
iajs-2289	110	93	be	be	AUX
iajs-2289	110	94	the	the	DET
iajs-2289	110	95	open	open	ADJ
iajs-2289	110	96	set	set	NOUN
iajs-2289	110	97	.	.	PUNCT
iajs-2289	111	1	then	then	ADV
iajs-2289	111	2	(m	(m	NOUN
iajs-2289	111	3	*	*	NOUN
iajs-2289	111	4	)	)	PUNCT
iajs-2289	111	5	∩	∩	NOUN
iajs-2289	111	6	t	t	NOUN
iajs-2289	111	7	=	=	SYM
iajs-2289	111	8			NOUN
iajs-2289	111	9	because	because	SCONJ
iajs-2289	111	10	of	of	ADP
iajs-2289	111	11	m	m	PROPN
iajs-2289	111	12	*	*	PROPN
iajs-2289	112	1			PROPN
iajs-2289	112	2	g	g	PROPN
iajs-2289	112	3			PROPN
iajs-2289	112	4	cl(s	cl(s	NOUN
iajs-2289	112	5	)	)	PUNCT
iajs-2289	112	6	.	.	PUNCT
iajs-2289	113	1	so	so	ADV
iajs-2289	113	2	since	since	SCONJ
iajs-2289	113	3	(m	(m	NOUN
iajs-2289	113	4	*	*	NOUN
iajs-2289	113	5	)	)	PUNCT
iajs-2289	113	6			PROPN
iajs-2289	113	7			PROPN
iajs-2289	113	8	*	*	PROPN
iajs-2289	113	9	,	,	PUNCT
iajs-2289	113	10			PROPN
iajs-2289	113	11	*	*	PUNCT
iajs-2289	113	12	can	can	AUX
iajs-2289	113	13	not	not	PART
iajs-2289	113	14	have	have	VERB
iajs-2289	113	15	h	h	NOUN
iajs-2289	113	16	as	as	ADP
iajs-2289	113	17	a	a	DET
iajs-2289	113	18	closure	closure	NOUN
iajs-2289	113	19	cluster	cluster	NOUN
iajs-2289	113	20	point	point	NOUN
iajs-2289	113	21	.	.	PUNCT
iajs-2289	114	1	(	(	PUNCT
iajs-2289	114	2			NOUN
iajs-2289	114	3	)	)	PUNCT
iajs-2289	114	4	suppose	suppose	VERB
iajs-2289	114	5	that	that	SCONJ
iajs-2289	114	6	the	the	DET
iajs-2289	114	7	hypothesis	hypothesis	NOUN
iajs-2289	114	8	is	be	AUX
iajs-2289	114	9	true	true	ADJ
iajs-2289	114	10	and	and	CCONJ
iajs-2289	114	11			ADJ
iajs-2289	114	12	is	be	AUX
iajs-2289	114	13	not	not	PART
iajs-2289	114	14	closed	closed	ADJ
iajs-2289	114	15	.	.	PUNCT
iajs-2289	115	1	let	let	VERB
iajs-2289	115	2	k	k	PROPN
iajs-2289	115	3			PROPN
iajs-2289	115	4	g	g	PROPN
iajs-2289	115	5	be	be	AUX
iajs-2289	115	6	a	a	DET
iajs-2289	115	7	closed	closed	ADJ
iajs-2289	115	8	set	set	NOUN
iajs-2289	115	9	and	and	CCONJ
iajs-2289	115	10	for	for	ADP
iajs-2289	115	11	some	some	DET
iajs-2289	115	12	h	h	NOUN
iajs-2289	115	13			PROPN
iajs-2289	115	14	h	h	PROPN
iajs-2289	115	15			PROPN
iajs-2289	115	16	(k	(k	PROPN
iajs-2289	115	17	)	)	PUNCT
iajs-2289	115	18	is	be	AUX
iajs-2289	115	19	a	a	DET
iajs-2289	115	20	closure	closure	NOUN
iajs-2289	115	21	cluster	cluster	NOUN
iajs-2289	115	22	point	point	NOUN
iajs-2289	115	23	of	of	ADP
iajs-2289	115	24	(k	(k	PROPN
iajs-2289	115	25	)	)	PUNCT
iajs-2289	115	26	.	.	PUNCT
iajs-2289	116	1	suppose	suppose	VERB
iajs-2289	116	2			PROPN
iajs-2289	116	3	be	be	VERB
iajs-2289	116	4	a	a	DET
iajs-2289	116	5	filter	filter	NOUN
iajs-2289	116	6	base	base	NOUN
iajs-2289	116	7	of	of	ADP
iajs-2289	116	8	sets	set	NOUN
iajs-2289	116	9	(k	(k	NOUN
iajs-2289	116	10	)	)	PUNCT
iajs-2289	116	11	∩	∩	NOUN
iajs-2289	116	12	t	t	NOUN
iajs-2289	116	13	for	for	ADP
iajs-2289	116	14	every	every	DET
iajs-2289	116	15	open	open	ADJ
iajs-2289	116	16	sets	set	NOUN
iajs-2289	116	17	t	t	PROPN
iajs-2289	116	18			PROPN
iajs-2289	116	19	h	h	PROPN
iajs-2289	116	20	such	such	ADJ
iajs-2289	116	21	that	that	SCONJ
iajs-2289	116	22	h	h	PROPN
iajs-2289	116	23			PROPN
iajs-2289	116	24	t	t	PROPN
iajs-2289	116	25	,	,	PUNCT
iajs-2289	116	26	then	then	ADV
iajs-2289	116	27	is	is	VERB
iajs-2289	116	28	a	a	DET
iajs-2289	116	29	filter	filter	NOUN
iajs-2289	116	30	base	base	NOUN
iajs-2289	116	31	in	in	ADP
iajs-2289	116	32			ADJ
iajs-2289	116	33	(	(	PUNCT
iajs-2289	116	34	g	g	NOUN
iajs-2289	116	35	)	)	PUNCT
iajs-2289	116	36	and	and	CCONJ
iajs-2289	116	37			NOUN
iajs-2289	116	38	⇝	⇝	PUNCT
iajs-2289	116	39	h.	h.	PROPN
iajs-2289	116	40	let	let	VERB
iajs-2289	116	41	m	m	VERB
iajs-2289	116	42	=	=	VERB
iajs-2289	116	43	{	{	PUNCT
iajs-2289	116	44	–1	–1	PROPN
iajs-2289	116	45	(	(	PUNCT
iajs-2289	116	46	g	g	NOUN
iajs-2289	116	47	):	):	PUNCT
iajs-2289	116	48	g	g	NOUN
iajs-2289	116	49			NOUN
iajs-2289	116	50	}	}	PUNCT
iajs-2289	116	51	and	and	CCONJ
iajs-2289	116	52	m	m	PROPN
iajs-2289	116	53	*	*	PUNCT
iajs-2289	116	54	=	=	SYM
iajs-2289	116	55	{	{	PUNCT
iajs-2289	116	56	k	k	X
iajs-2289	116	57	∩	∩	X
iajs-2289	116	58	m	m	VERB
iajs-2289	116	59	:	:	PUNCT
iajs-2289	116	60	m	m	VERB
iajs-2289	116	61			NOUN
iajs-2289	116	62	m	m	VERB
iajs-2289	116	63	}	}	PUNCT
iajs-2289	116	64	.	.	PUNCT
iajs-2289	117	1	it	it	PRON
iajs-2289	117	2	apparent	apparent	ADJ
iajs-2289	117	3	that	that	SCONJ
iajs-2289	117	4	m	m	VERB
iajs-2289	117	5	*	*	PUNCT
iajs-2289	117	6	<	<	X
iajs-2289	117	7	m.	m.	NOUN
iajs-2289	117	8	nevertheless	nevertheless	ADV
iajs-2289	117	9	,	,	PUNCT
iajs-2289	117	10	g	g	PROPN
iajs-2289	117	11			PROPN
iajs-2289	117	12	k	k	PROPN
iajs-2289	117	13	is	be	AUX
iajs-2289	117	14	open	open	ADJ
iajs-2289	117	15	and	and	CCONJ
iajs-2289	117	16	–1	–1	PROPN
iajs-2289	117	17	(	(	PUNCT
iajs-2289	117	18	h	h	NOUN
iajs-2289	117	19	)	)	PUNCT
iajs-2289	117	20			PROPN
iajs-2289	117	21	g	g	PROPN
iajs-2289	117	22			PROPN
iajs-2289	117	23	k	k	PROPN
iajs-2289	117	24	,	,	PUNCT
iajs-2289	117	25	m	m	VERB
iajs-2289	117	26	*	*	PUNCT
iajs-2289	117	27	has	have	VERB
iajs-2289	117	28	no	no	DET
iajs-2289	117	29	closure	closure	NOUN
iajs-2289	117	30	cluster	cluster	NOUN
iajs-2289	117	31	point	point	NOUN
iajs-2289	117	32	in	in	ADP
iajs-2289	117	33	–1	–1	PROPN
iajs-2289	117	34	(	(	PUNCT
iajs-2289	117	35	h	h	NOUN
iajs-2289	117	36	)	)	PUNCT
iajs-2289	117	37	.	.	PUNCT
iajs-2289	118	1	the	the	DET
iajs-2289	118	2	contradiction	contradiction	NOUN
iajs-2289	118	3	crops	crop	NOUN
iajs-2289	118	4	that	that	PRON
iajs-2289	118	5			ADJ
iajs-2289	118	6	be	be	VERB
iajs-2289	118	7	a	a	DET
iajs-2289	118	8	closed	closed	ADJ
iajs-2289	118	9	mapping	mapping	NOUN
iajs-2289	118	10	.	.	PUNCT
iajs-2289	119	1	finally	finally	ADV
iajs-2289	119	2	,	,	PUNCT
iajs-2289	119	3	to	to	PART
iajs-2289	119	4	prove	prove	VERB
iajs-2289	119	5	–1	–1	PROPN
iajs-2289	119	6	(	(	PUNCT
iajs-2289	119	7	h	h	NOUN
iajs-2289	119	8	)	)	PUNCT
iajs-2289	119	9	is	be	AUX
iajs-2289	119	10	compact	compact	ADJ
iajs-2289	119	11	,	,	PUNCT
iajs-2289	119	12	this	this	PRON
iajs-2289	119	13	is	be	AUX
iajs-2289	119	14	easy	easy	ADJ
iajs-2289	119	15	for	for	ADP
iajs-2289	119	16	h	h	PROPN
iajs-2289	119	17			PROPN
iajs-2289	119	18	h	h	PROPN
iajs-2289	119	19			PROPN
iajs-2289	119	20	(g	(g	NUM
iajs-2289	119	21	)	)	PUNCT
iajs-2289	119	22	.	.	PUNCT
iajs-2289	120	1	and	and	CCONJ
iajs-2289	120	2	for	for	ADP
iajs-2289	120	3	h	h	PROPN
iajs-2289	120	4			PROPN
iajs-2289	120	5	(g	(g	PROPN
iajs-2289	120	6	)	)	PUNCT
iajs-2289	120	7	,	,	PUNCT
iajs-2289	120	8	{	{	PUNCT
iajs-2289	120	9	h	h	NOUN
iajs-2289	120	10	}	}	PUNCT
iajs-2289	120	11	is	be	AUX
iajs-2289	120	12	a	a	DET
iajs-2289	120	13	filter	filter	NOUN
iajs-2289	120	14	base	base	NOUN
iajs-2289	120	15	in	in	ADP
iajs-2289	120	16	(g	(g	NOUN
iajs-2289	120	17	)	)	PUNCT
iajs-2289	120	18	cl	cl	NOUN
iajs-2289	120	19	dir	dir	NOUN
iajs-2289	120	20	,	,	PUNCT
iajs-2289	120	21	tow	tow	NOUN
iajs-2289	120	22	h.	h.	PROPN
iajs-2289	120	23	by	by	ADP
iajs-2289	120	24	supposition	supposition	PROPN
iajs-2289	120	25	,	,	PUNCT
iajs-2289	120	26	{	{	PUNCT
iajs-2289	120	27	–1	–1	NOUN
iajs-2289	120	28	(	(	PUNCT
iajs-2289	120	29	h	h	NOUN
iajs-2289	120	30	)	)	PUNCT
iajs-2289	120	31	}	}	PUNCT
iajs-2289	120	32	cl	cl	NOUN
iajs-2289	120	33	dir	dir	NOUN
iajs-2289	120	34	,	,	PUNCT
iajs-2289	120	35	tow	tow	VERB
iajs-2289	120	36	–1	–1	PROPN
iajs-2289	120	37	(	(	PUNCT
iajs-2289	120	38	h	h	NOUN
iajs-2289	120	39	)	)	PUNCT
iajs-2289	120	40	.	.	PUNCT
iajs-2289	121	1	this	this	PRON
iajs-2289	121	2	means	mean	VERB
iajs-2289	121	3	that	that	SCONJ
iajs-2289	121	4	every	every	DET
iajs-2289	121	5	filter	filter	NOUN
iajs-2289	121	6	base	base	NOUN
iajs-2289	121	7	in	in	ADP
iajs-2289	121	8	–1	–1	PROPN
iajs-2289	121	9	(	(	PUNCT
iajs-2289	121	10	h	h	NOUN
iajs-2289	121	11	)	)	PUNCT
iajs-2289	121	12	has	have	VERB
iajs-2289	121	13	a	a	DET
iajs-2289	121	14	closure	closure	NOUN
iajs-2289	121	15	cluster	cluster	NOUN
iajs-2289	121	16	point	point	NOUN
iajs-2289	121	17	in	in	ADP
iajs-2289	121	18	–1	–1	PROPN
iajs-2289	121	19	(	(	PUNCT
iajs-2289	121	20	h	h	NOUN
iajs-2289	121	21	)	)	PUNCT
iajs-2289	121	22	,	,	PUNCT
iajs-2289	121	23	so	so	SCONJ
iajs-2289	121	24	that	that	SCONJ
iajs-2289	121	25	–1	–1	PROPN
iajs-2289	121	26	(	(	PUNCT
iajs-2289	121	27	h	h	NOUN
iajs-2289	121	28	)	)	PUNCT
iajs-2289	121	29	is	be	AUX
iajs-2289	121	30	compact	compact	ADJ
iajs-2289	121	31	.	.	PUNCT
iajs-2289	122	1	corollary	corollary	ADJ
iajs-2289	122	2	14	14	NUM
iajs-2289	122	3	let	let	VERB
iajs-2289	122	4			ADJ
iajs-2289	122	5	:	:	PUNCT
iajs-2289	122	6	g	g	PROPN
iajs-2289	122	7			NOUN
iajs-2289	122	8	h	h	NOUN
iajs-2289	122	9	be	be	AUX
iajs-2289	122	10	closed	close	VERB
iajs-2289	122	11	mapping	mapping	NOUN
iajs-2289	122	12	and	and	CCONJ
iajs-2289	122	13	–1	–1	PROPN
iajs-2289	122	14	(	(	PUNCT
iajs-2289	122	15	h	h	NOUN
iajs-2289	122	16	)	)	PUNCT
iajs-2289	122	17	compact	compact	NOUN
iajs-2289	122	18	for	for	ADP
iajs-2289	122	19	every	every	DET
iajs-2289	122	20	h	h	NOUN
iajs-2289	123	1			NOUN
iajs-2289	123	2	h	h	NOUN
iajs-2289	124	1	if	if	SCONJ
iajs-2289	124	2	and	and	CCONJ
iajs-2289	124	3	only	only	ADV
iajs-2289	124	4	if	if	SCONJ
iajs-2289	124	5	each	each	DET
iajs-2289	124	6	filter	filter	NOUN
iajs-2289	124	7	base	base	NOUN
iajs-2289	124	8	in	in	ADP
iajs-2289	124	9	(g	(g	PROPN
iajs-2289	124	10	)	)	PUNCT
iajs-2289	124	11	⇝	⇝	PUNCT
iajs-2289	125	1	h	h	NOUN
iajs-2289	125	2			PROPN
iajs-2289	125	3	h	h	NOUN
iajs-2289	125	4	has	have	VERB
iajs-2289	125	5	pre	pre	ADJ
iajs-2289	125	6	-	-	ADJ
iajs-2289	125	7	image	image	ADJ
iajs-2289	125	8	filter	filter	NOUN
iajs-2289	125	9	base	base	NOUN
iajs-2289	125	10	cl	cl	NOUN
iajs-2289	125	11	dir	dir	NOUN
iajs-2289	125	12	,	,	PUNCT
iajs-2289	125	13	tow	tow	VERB
iajs-2289	125	14	–1	–1	PROPN
iajs-2289	125	15	(	(	PUNCT
iajs-2289	125	16	h	h	NOUN
iajs-2289	125	17	)	)	PUNCT
iajs-2289	125	18	.	.	PUNCT
iajs-2289	126	1	169	169	NUM
iajs-2289	126	2	ibn	ibn	PROPN
iajs-2289	126	3	al	al	PROPN
iajs-2289	126	4	-	-	PUNCT
iajs-2289	126	5	haitham	haitham	PROPN
iajs-2289	126	6	jour	jour	X
iajs-2289	126	7	.	.	PROPN
iajs-2289	126	8	for	for	ADP
iajs-2289	126	9	pure	pure	ADJ
iajs-2289	126	10	&	&	CCONJ
iajs-2289	126	11	appl	appl	PROPN
iajs-2289	126	12	.	.	PUNCT
iajs-2289	127	1	sci	sci	PROPN
iajs-2289	127	2	.	.	PROPN
iajs-2289	127	3	32	32	NUM
iajs-2289	127	4	(	(	PUNCT
iajs-2289	127	5	3	3	NUM
iajs-2289	127	6	)	)	SYM
iajs-2289	127	7	2019	2019	NUM
iajs-2289	127	8	corollary	corollary	NOUN
iajs-2289	127	9	15	15	NUM
iajs-2289	127	10	let	let	VERB
iajs-2289	127	11			ADJ
iajs-2289	127	12	:	:	PUNCT
iajs-2289	127	13	g	g	PROPN
iajs-2289	127	14			NOUN
iajs-2289	127	15	h	h	NOUN
iajs-2289	127	16	be	be	AUX
iajs-2289	127	17	closed	close	VERB
iajs-2289	127	18	mapping	mapping	NOUN
iajs-2289	127	19	and	and	CCONJ
iajs-2289	127	20	–1	–1	PROPN
iajs-2289	127	21	(	(	PUNCT
iajs-2289	127	22	h	h	NOUN
iajs-2289	127	23	)	)	PUNCT
iajs-2289	127	24	compact	compact	NOUN
iajs-2289	127	25	for	for	ADP
iajs-2289	127	26	every	every	DET
iajs-2289	127	27	h	h	NOUN
iajs-2289	127	28			NOUN
iajs-2289	127	29	y	y	PROPN
iajs-2289	127	30	,	,	PUNCT
iajs-2289	127	31	for	for	ADP
iajs-2289	127	32	every	every	DET
iajs-2289	127	33	compact	compact	ADJ
iajs-2289	127	34	set	set	NOUN
iajs-2289	127	35	w	w	PROPN
iajs-2289	127	36			PROPN
iajs-2289	127	37	h	h	NOUN
iajs-2289	127	38	,	,	PUNCT
iajs-2289	127	39	–1	–1	PROPN
iajs-2289	127	40	(	(	PUNCT
iajs-2289	127	41	w	w	NOUN
iajs-2289	127	42	)	)	PUNCT
iajs-2289	127	43	is	be	AUX
iajs-2289	127	44	compact	compact	ADJ
iajs-2289	127	45	.	.	PUNCT
iajs-2289	128	1	proof	proof	NOUN
iajs-2289	128	2	.	.	PUNCT
iajs-2289	129	1	let	let	VERB
iajs-2289	129	2	w	w	PROPN
iajs-2289	129	3			PROPN
iajs-2289	129	4	h	h	NOUN
iajs-2289	129	5	be	be	AUX
iajs-2289	129	6	a	a	DET
iajs-2289	129	7	compact	compact	ADJ
iajs-2289	129	8	set	set	NOUN
iajs-2289	129	9	and	and	CCONJ
iajs-2289	129	10			NOUN
iajs-2289	129	11	is	be	AUX
iajs-2289	129	12	a	a	DET
iajs-2289	129	13	filter	filter	NOUN
iajs-2289	129	14	base	base	NOUN
iajs-2289	129	15	in	in	ADP
iajs-2289	129	16	–1	–1	PROPN
iajs-2289	129	17	(	(	PUNCT
iajs-2289	129	18	w	w	NOUN
iajs-2289	129	19	)	)	PUNCT
iajs-2289	129	20	,	,	PUNCT
iajs-2289	129	21			NOUN
iajs-2289	129	22	=	=	SYM
iajs-2289	129	23	{	{	PUNCT
iajs-2289	129	24			X
iajs-2289	129	25	(	(	PUNCT
iajs-2289	129	26	m	m	PROPN
iajs-2289	129	27	):	):	PUNCT
iajs-2289	129	28	m	m	VERB
iajs-2289	129	29			NOUN
iajs-2289	129	30			NOUN
iajs-2289	129	31	}	}	PUNCT
iajs-2289	129	32	,	,	PUNCT
iajs-2289	129	33	is	be	AUX
iajs-2289	129	34	a	a	DET
iajs-2289	129	35	filter	filter	NOUN
iajs-2289	129	36	base	base	NOUN
iajs-2289	129	37	in	in	ADP
iajs-2289	129	38	w	w	PROPN
iajs-2289	129	39	and	and	CCONJ
iajs-2289	129	40	in	in	ADP
iajs-2289	129	41			ADJ
iajs-2289	129	42	(	(	PUNCT
iajs-2289	129	43	g	g	NOUN
iajs-2289	129	44	)	)	PUNCT
iajs-2289	129	45	and	and	CCONJ
iajs-2289	129	46	is	be	AUX
iajs-2289	129	47	cl	cl	NOUN
iajs-2289	129	48	dir	dir	NOUN
iajs-2289	129	49	,	,	PUNCT
iajs-2289	129	50	tow	tow	NOUN
iajs-2289	129	51	w.	w.	NOUN
iajs-2289	129	52	so	so	SCONJ
iajs-2289	129	53			NOUN
iajs-2289	129	54	*	*	PUNCT
iajs-2289	130	1	=	=	PUNCT
iajs-2289	130	2	{	{	PUNCT
iajs-2289	130	3	–1	–1	PROPN
iajs-2289	130	4	(	(	PUNCT
iajs-2289	130	5	g	g	NOUN
iajs-2289	130	6	):	):	PUNCT
iajs-2289	130	7	g	g	PROPN
iajs-2289	130	8			NOUN
iajs-2289	130	9	}	}	PUNCT
iajs-2289	130	10	is	be	AUX
iajs-2289	130	11	cl	cl	NOUN
iajs-2289	130	12	dir	dir	NOUN
iajs-2289	130	13	,	,	PUNCT
iajs-2289	130	14	tow	tow	NOUN
iajs-2289	130	15			X
iajs-2289	130	16	–	–	PUNCT
iajs-2289	130	17	1	1	NUM
iajs-2289	130	18	(	(	PUNCT
iajs-2289	130	19	w	w	NOUN
iajs-2289	130	20	)	)	PUNCT
iajs-2289	130	21	,	,	PUNCT
iajs-2289	130	22	so	so	SCONJ
iajs-2289	130	23	that	that	SCONJ
iajs-2289	130	24			NOUN
iajs-2289	130	25	*	*	PUNCT
iajs-2289	130	26	<	<	X
iajs-2289	130	27			NOUN
iajs-2289	130	28	and	and	CCONJ
iajs-2289	130	29			NOUN
iajs-2289	130	30	*	*	PUNCT
iajs-2289	130	31	has	have	VERB
iajs-2289	130	32	a	a	DET
iajs-2289	130	33	closure	closure	NOUN
iajs-2289	130	34	cluster	cluster	NOUN
iajs-2289	130	35	point	point	NOUN
iajs-2289	130	36	in	in	ADP
iajs-2289	130	37	–1	–1	PROPN
iajs-2289	130	38	(	(	PUNCT
iajs-2289	130	39	w	w	NOUN
iajs-2289	130	40	)	)	PUNCT
iajs-2289	130	41	.	.	PUNCT
iajs-2289	131	1	4	4	X
iajs-2289	131	2	.	.	X
iajs-2289	131	3	filter	filter	NOUN
iajs-2289	131	4	bases	basis	NOUN
iajs-2289	131	5	and	and	CCONJ
iajs-2289	131	6	almost	almost	ADV
iajs-2289	131	7	j	j	PROPN
iajs-2289	131	8	-	-	PUNCT
iajs-2289	131	9	ω	ω	NOUN
iajs-2289	131	10	-	-	NOUN
iajs-2289	131	11	convergence	convergence	NOUN
iajs-2289	131	12	in	in	ADP
iajs-2289	131	13	this	this	DET
iajs-2289	131	14	section	section	NOUN
iajs-2289	131	15	,	,	PUNCT
iajs-2289	131	16	we	we	PRON
iajs-2289	131	17	defined	define	VERB
iajs-2289	131	18	filter	filter	NOUN
iajs-2289	131	19	bases	basis	NOUN
iajs-2289	131	20	,	,	PUNCT
iajs-2289	131	21	almost	almost	ADV
iajs-2289	131	22	j	j	PROPN
iajs-2289	131	23	-	-	PUNCT
iajs-2289	131	24	ω	ω	NOUN
iajs-2289	131	25	-	-	NOUN
iajs-2289	131	26	closure	closure	NOUN
iajs-2289	131	27	,	,	PUNCT
iajs-2289	131	28	and	and	CCONJ
iajs-2289	131	29	the	the	DET
iajs-2289	131	30	some	some	DET
iajs-2289	131	31	theorems	theorem	NOUN
iajs-2289	131	32	about	about	ADP
iajs-2289	131	33	them	they	PRON
iajs-2289	131	34	.	.	PUNCT
iajs-2289	132	1	we	we	PRON
iajs-2289	132	2	now	now	ADV
iajs-2289	132	3	introduce	introduce	VERB
iajs-2289	132	4	the	the	DET
iajs-2289	132	5	definition	definition	NOUN
iajs-2289	132	6	of	of	ADP
iajs-2289	132	7	almost	almost	ADV
iajs-2289	132	8	j	j	PROPN
iajs-2289	132	9	-	-	PUNCT
iajs-2289	132	10	ω	ω	NOUN
iajs-2289	132	11	-	-	PUNCT
iajs-2289	132	12	closure	closure	NOUN
iajs-2289	132	13	,	,	PUNCT
iajs-2289	132	14	where	where	SCONJ
iajs-2289	132	15	j	j	PROPN
iajs-2289	132	16	{	{	PROPN
iajs-2289	132	17	,	,	PUNCT
iajs-2289	132	18	δ	δ	PROPN
iajs-2289	132	19	,	,	PUNCT
iajs-2289	132	20			NOUN
iajs-2289	132	21	,	,	PUNCT
iajs-2289	132	22	pre	pre	ADJ
iajs-2289	132	23	,	,	PUNCT
iajs-2289	132	24	b	b	NOUN
iajs-2289	132	25	,	,	PUNCT
iajs-2289	132	26			NOUN
iajs-2289	132	27	}	}	PUNCT
iajs-2289	132	28	.	.	PUNCT
iajs-2289	133	1	definition	definition	NOUN
iajs-2289	133	2	16	16	NUM
iajs-2289	133	3	let	let	VERB
iajs-2289	133	4			NOUN
iajs-2289	133	5	be	be	AUX
iajs-2289	133	6	a	a	DET
iajs-2289	133	7	filter	filter	NOUN
iajs-2289	133	8	base	base	NOUN
iajs-2289	133	9	on	on	ADP
iajs-2289	133	10	a	a	DET
iajs-2289	133	11	space	space	NOUN
iajs-2289	133	12	g.	g.	NOUN
iajs-2289	133	13	we	we	PRON
iajs-2289	133	14	say	say	VERB
iajs-2289	133	15			NOUN
iajs-2289	133	16	almost	almost	ADV
iajs-2289	133	17	j	j	PROPN
iajs-2289	133	18	-	-	PUNCT
iajs-2289	133	19	ω	ω	NOUN
iajs-2289	133	20	-	-	PUNCT
iajs-2289	133	21	converges	converge	NOUN
iajs-2289	133	22	to	to	ADP
iajs-2289	133	23	a	a	DET
iajs-2289	133	24	subset	subset	NOUN
iajs-2289	133	25	k	k	PROPN
iajs-2289	133	26			PROPN
iajs-2289	133	27	g	g	PROPN
iajs-2289	133	28	(	(	PUNCT
iajs-2289	133	29	written	write	VERB
iajs-2289	133	30	as	as	ADP
iajs-2289	133	31	j	j	PROPN
iajs-2289	133	32	-	-	PUNCT
iajs-2289	133	33	ω	ω	NOUN
iajs-2289	133	34	⇝	⇝	NOUN
iajs-2289	133	35	k	k	NOUN
iajs-2289	133	36	)	)	PUNCT
iajs-2289	133	37	if	if	SCONJ
iajs-2289	133	38	for	for	ADP
iajs-2289	133	39	each	each	DET
iajs-2289	133	40	cover	cover	NOUN
iajs-2289	133	41	k	k	PROPN
iajs-2289	133	42	of	of	ADP
iajs-2289	133	43	k	k	PROPN
iajs-2289	133	44	by	by	ADP
iajs-2289	133	45	subsets	subset	NOUN
iajs-2289	133	46	open	open	ADJ
iajs-2289	133	47	in	in	ADP
iajs-2289	133	48	g	g	NOUN
iajs-2289	133	49	,	,	PUNCT
iajs-2289	133	50	there	there	PRON
iajs-2289	133	51	is	be	VERB
iajs-2289	133	52	a	a	DET
iajs-2289	133	53	finite	finite	NOUN
iajs-2289	133	54	subfamily	subfamily	ADV
iajs-2289	133	55	l	l	NOUN
iajs-2289	133	56			PROPN
iajs-2289	133	57	k	k	PROPN
iajs-2289	133	58	and	and	CCONJ
iajs-2289	133	59	m	m	PROPN
iajs-2289	133	60			NOUN
iajs-2289	133	61			NOUN
iajs-2289	134	1	such	such	ADJ
iajs-2289	134	2	that	that	SCONJ
iajs-2289	134	3	m	m	PROPN
iajs-2289	134	4			PROPN
iajs-2289	134	5	{cl	{cl	PROPN
iajs-2289	134	6	(	(	PUNCT
iajs-2289	134	7	l	l	NOUN
iajs-2289	134	8	)	)	PUNCT
iajs-2289	134	9	:	:	PUNCT
iajs-2289	134	10	l	l	X
iajs-2289	134	11			PROPN
iajs-2289	134	12	l	l	NOUN
iajs-2289	134	13	}	}	PUNCT
iajs-2289	135	1	.	.	PUNCT
iajs-2289	136	1	we	we	PRON
iajs-2289	136	2	say	say	VERB
iajs-2289	136	3			NOUN
iajs-2289	136	4	almost	almost	ADV
iajs-2289	136	5	j	j	NOUN
iajs-2289	136	6	-	-	NOUN
iajs-2289	136	7	ωconverges	ωconverge	NOUN
iajs-2289	136	8	to	to	ADP
iajs-2289	136	9	g	g	PROPN
iajs-2289	136	10			PROPN
iajs-2289	136	11	g	g	PROPN
iajs-2289	136	12	(	(	PUNCT
iajs-2289	136	13	written	write	VERB
iajs-2289	136	14	as	as	ADP
iajs-2289	136	15			NOUN
iajs-2289	136	16	j	j	PROPN
iajs-2289	136	17	-	-	PUNCT
iajs-2289	136	18	ω	ω	PROPN
iajs-2289	136	19	⇝	⇝	NOUN
iajs-2289	136	20	g	g	NOUN
iajs-2289	136	21	)	)	PUNCT
iajs-2289	136	22	if	if	SCONJ
iajs-2289	136	23			VERB
iajs-2289	136	24	j	j	PROPN
iajs-2289	136	25	-	-	PUNCT
iajs-2289	136	26	ω	ω	PROPN
iajs-2289	136	27	⇝	⇝	NOUN
iajs-2289	136	28	{	{	PUNCT
iajs-2289	136	29	g	g	NOUN
iajs-2289	136	30	}	}	PUNCT
iajs-2289	136	31	.	.	PUNCT
iajs-2289	137	1	now	now	ADV
iajs-2289	137	2	,	,	PUNCT
iajs-2289	137	3	cl	cl	INTJ
iajs-2289	137	4	(	(	PUNCT
iajs-2289	137	5	g	g	NUM
iajs-2289	137	6	)	)	PUNCT
iajs-2289	137	7	⇝	⇝	NOUN
iajs-2289	137	8	g	g	NOUN
iajs-2289	137	9	,	,	PUNCT
iajs-2289	137	10	while	while	SCONJ
iajs-2289	137	11	,	,	PUNCT
iajs-2289	137	12	j	j	PROPN
iajs-2289	137	13	-	-	PUNCT
iajs-2289	137	14	ω	ω	NUM
iajs-2289	137	15	cl	cl	NOUN
iajs-2289	137	16	(	(	PUNCT
iajs-2289	137	17	g	g	NUM
iajs-2289	137	18	)	)	PUNCT
iajs-2289	137	19	j	j	PROPN
iajs-2289	137	20	-	-	PUNCT
iajs-2289	137	21	ω	ω	PROPN
iajs-2289	137	22	⇝	⇝	NOUN
iajs-2289	137	23	g	g	NOUN
iajs-2289	137	24	,	,	PUNCT
iajs-2289	137	25	where	where	SCONJ
iajs-2289	137	26	j	j	PROPN
iajs-2289	137	27	{	{	PROPN
iajs-2289	137	28	,	,	PUNCT
iajs-2289	137	29	δ	δ	PROPN
iajs-2289	137	30	,	,	PUNCT
iajs-2289	137	31			NOUN
iajs-2289	137	32	,	,	PUNCT
iajs-2289	137	33	pre	pre	ADJ
iajs-2289	137	34	,	,	PUNCT
iajs-2289	137	35	b	b	NOUN
iajs-2289	137	36	,	,	PUNCT
iajs-2289	137	37			NOUN
iajs-2289	137	38	}	}	PUNCT
iajs-2289	137	39	.	.	PUNCT
iajs-2289	138	1	also	also	ADV
iajs-2289	138	2	,	,	PUNCT
iajs-2289	138	3	we	we	PRON
iajs-2289	138	4	introduce	introduce	VERB
iajs-2289	138	5	the	the	DET
iajs-2289	138	6	definitions	definition	NOUN
iajs-2289	138	7	of	of	ADP
iajs-2289	138	8	almost	almost	ADV
iajs-2289	138	9	j	j	PROPN
iajs-2289	138	10	-	-	PUNCT
iajs-2289	138	11	ω	ω	VERB
iajs-2289	138	12	-	-	PUNCT
iajs-2289	138	13	cluster	cluster	NOUN
iajs-2289	138	14	point	point	NOUN
iajs-2289	138	15	,	,	PUNCT
iajs-2289	138	16	and	and	CCONJ
iajs-2289	138	17	quasi	quasi	ADJ
iajs-2289	138	18	-j	-j	PROPN
iajs-2289	138	19	-	-	PUNCT
iajs-2289	138	20	ω	ω	VERB
iajs-2289	138	21	-	-	PUNCT
iajs-2289	138	22	h	h	NOUN
iajs-2289	138	23	-	-	PUNCT
iajs-2289	138	24	closed	closed	ADJ
iajs-2289	138	25	set	set	NOUN
iajs-2289	138	26	where	where	SCONJ
iajs-2289	138	27	j	j	PROPN
iajs-2289	138	28	{	{	PROPN
iajs-2289	138	29	,	,	PUNCT
iajs-2289	138	30	δ	δ	PROPN
iajs-2289	138	31	,	,	PUNCT
iajs-2289	138	32			NOUN
iajs-2289	138	33	,	,	PUNCT
iajs-2289	138	34	pre	pre	ADJ
iajs-2289	138	35	,	,	PUNCT
iajs-2289	138	36	b	b	NOUN
iajs-2289	138	37	,	,	PUNCT
iajs-2289	138	38			NOUN
iajs-2289	138	39	}	}	PUNCT
iajs-2289	138	40	.	.	PUNCT
iajs-2289	139	1	definition	definition	NOUN
iajs-2289	139	2	17	17	NUM
iajs-2289	139	3	a	a	DET
iajs-2289	139	4	point	point	NOUN
iajs-2289	139	5	g	g	ADP
iajs-2289	139	6			NOUN
iajs-2289	139	7	g	g	PROPN
iajs-2289	139	8	is	be	AUX
iajs-2289	139	9	called	call	VERB
iajs-2289	139	10	an	an	DET
iajs-2289	139	11	almost	almost	ADV
iajs-2289	139	12	j	j	PROPN
iajs-2289	139	13	-	-	PUNCT
iajs-2289	139	14	ω	ω	VERB
iajs-2289	139	15	-	-	PUNCT
iajs-2289	139	16	cluster	cluster	NOUN
iajs-2289	139	17	point	point	NOUN
iajs-2289	139	18	of	of	ADP
iajs-2289	139	19	a	a	DET
iajs-2289	139	20	filter	filter	NOUN
iajs-2289	139	21	base	base	NOUN
iajs-2289	139	22			NOUN
iajs-2289	139	23	(	(	PUNCT
iajs-2289	139	24	written	write	VERB
iajs-2289	139	25	as	as	ADP
iajs-2289	139	26	g	g	PROPN
iajs-2289	139	27			PROPN
iajs-2289	139	28	(	(	PUNCT
iajs-2289	139	29	aljω	aljω	NOUN
iajs-2289	139	30	-	-	PUNCT
iajs-2289	139	31	cg)	cg)	X
iajs-2289	139	32	)	)	PUNCT
iajs-2289	139	33	if	if	SCONJ
iajs-2289	139	34			NOUN
iajs-2289	139	35	meets	meet	VERB
iajs-2289	139	36	cl	cl	NOUN
iajs-2289	139	37	j	j	PROPN
iajs-2289	139	38	-	-	PROPN
iajs-2289	139	39	ω-(g	ω-(g	PROPN
iajs-2289	139	40	)	)	PUNCT
iajs-2289	139	41	,	,	PUNCT
iajs-2289	139	42	where	where	SCONJ
iajs-2289	139	43	j	j	PROPN
iajs-2289	139	44	{	{	PROPN
iajs-2289	139	45	,	,	PUNCT
iajs-2289	139	46	δ	δ	PROPN
iajs-2289	139	47	,	,	PUNCT
iajs-2289	139	48			NOUN
iajs-2289	139	49	,	,	PUNCT
iajs-2289	139	50	pre	pre	AUX
iajs-2289	139	51	,	,	PUNCT
iajs-2289	139	52	b	b	NOUN
iajs-2289	139	53	,	,	PUNCT
iajs-2289	139	54			NOUN
iajs-2289	139	55	}	}	PUNCT
iajs-2289	139	56	.	.	PUNCT
iajs-2289	140	1	for	for	ADP
iajs-2289	140	2	a	a	DET
iajs-2289	140	3	set	set	NOUN
iajs-2289	140	4	k	k	PROPN
iajs-2289	140	5			PROPN
iajs-2289	140	6	g	g	PROPN
iajs-2289	140	7	,	,	PUNCT
iajs-2289	140	8	the	the	DET
iajs-2289	140	9	almost	almost	ADV
iajs-2289	140	10	j	j	PROPN
iajs-2289	140	11	-	-	PUNCT
iajs-2289	140	12	ω	ω	NOUN
iajs-2289	140	13	-	-	NOUN
iajs-2289	140	14	closure	closure	NOUN
iajs-2289	140	15	of	of	ADP
iajs-2289	140	16	k	k	NOUN
iajs-2289	140	17	,	,	PUNCT
iajs-2289	140	18	denoted	denote	VERB
iajs-2289	140	19	as	as	ADP
iajs-2289	140	20	(	(	PUNCT
iajs-2289	140	21	alj	alj	PROPN
iajs-2289	140	22	-	-	PUNCT
iajs-2289	140	23	ω	ω	NOUN
iajs-2289	140	24	-	-	NOUN
iajs-2289	140	25	cl	cl	NOUN
iajs-2289	140	26	(	(	PUNCT
iajs-2289	140	27	k	k	NOUN
iajs-2289	140	28	)	)	PUNCT
iajs-2289	140	29	)	)	PUNCT
iajs-2289	140	30	is	be	AUX
iajs-2289	140	31	al	al	PROPN
iajs-2289	140	32	j	j	PROPN
iajs-2289	140	33	-	-	PUNCT
iajs-2289	140	34	ω	ω	PROPN
iajs-2289	140	35	-	-	NOUN
iajs-2289	140	36	cg	cg	NOUN
iajs-2289	140	37	{	{	PUNCT
iajs-2289	140	38	k	k	NOUN
iajs-2289	140	39	}	}	PUNCT
iajs-2289	140	40	if	if	SCONJ
iajs-2289	140	41	k	k	PROPN
iajs-2289	140	42			VERB
iajs-2289	140	43			NOUN
iajs-2289	140	44	i.e.	i.e.	X
iajs-2289	140	45	{	{	PUNCT
iajs-2289	140	46	g	g	PROPN
iajs-2289	140	47			NOUN
iajs-2289	140	48	g	g	NOUN
iajs-2289	140	49	:	:	PUNCT
iajs-2289	140	50	every	every	DET
iajs-2289	140	51	j	j	PROPN
iajs-2289	140	52	-	-	PUNCT
iajs-2289	140	53	ω	ω	VERB
iajs-2289	140	54	-	-	PUNCT
iajs-2289	140	55	closed	close	VERB
iajs-2289	140	56	nbd	nbd	PROPN
iajs-2289	140	57	of	of	ADP
iajs-2289	140	58	g	g	PROPN
iajs-2289	140	59	meets	meet	VERB
iajs-2289	140	60	k	k	NOUN
iajs-2289	140	61	}	}	PUNCT
iajs-2289	140	62	and	and	CCONJ
iajs-2289	140	63	is	be	AUX
iajs-2289	140	64			NOUN
iajs-2289	140	65	if	if	SCONJ
iajs-2289	140	66	k	k	NOUN
iajs-2289	140	67	=	=	SYM
iajs-2289	140	68			NOUN
iajs-2289	140	69	;	;	PUNCT
iajs-2289	140	70	k	k	X
iajs-2289	140	71	is	be	AUX
iajs-2289	140	72	almost	almost	ADV
iajs-2289	140	73	j	j	PROPN
iajs-2289	140	74	-	-	PUNCT
iajs-2289	140	75	ω	ω	NOUN
iajs-2289	140	76	-	-	PUNCT
iajs-2289	140	77	closed	closed	ADJ
iajs-2289	140	78	if	if	SCONJ
iajs-2289	140	79	k	k	PROPN
iajs-2289	140	80	=	=	PRON
iajs-2289	140	81	(	(	PUNCT
iajs-2289	140	82	alj	alj	PROPN
iajs-2289	140	83	-	-	PUNCT
iajs-2289	140	84	ω	ω	NOUN
iajs-2289	140	85	-	-	NOUN
iajs-2289	140	86	cl(k	cl(k	NUM
iajs-2289	140	87	)	)	PUNCT
iajs-2289	140	88	)	)	PUNCT
iajs-2289	140	89	.	.	PUNCT
iajs-2289	141	1	correspondingly	correspondingly	ADV
iajs-2289	141	2	,	,	PUNCT
iajs-2289	141	3	the	the	DET
iajs-2289	141	4	almost	almost	ADV
iajs-2289	141	5	j	j	PROPN
iajs-2289	141	6	-	-	PUNCT
iajs-2289	141	7	ω	ω	NOUN
iajs-2289	141	8	-	-	NOUN
iajs-2289	141	9	interior	interior	NOUN
iajs-2289	141	10	of	of	ADP
iajs-2289	141	11	k	k	PROPN
iajs-2289	141	12	,	,	PUNCT
iajs-2289	141	13	denoted	denote	VERB
iajs-2289	141	14	as	as	ADP
iajs-2289	141	15	(	(	PUNCT
iajs-2289	141	16	alj	alj	PROPN
iajs-2289	141	17	-	-	PUNCT
iajs-2289	141	18	ω	ω	NOUN
iajs-2289	141	19	-	-	PUNCT
iajs-2289	141	20	intk	intk	NOUN
iajs-2289	141	21	)	)	PUNCT
iajs-2289	141	22	,	,	PUNCT
iajs-2289	141	23	is	be	AUX
iajs-2289	141	24	{	{	PUNCT
iajs-2289	141	25	g	g	PROPN
iajs-2289	141	26			NOUN
iajs-2289	141	27	g	g	ADP
iajs-2289	141	28	;	;	PUNCT
iajs-2289	141	29	cl	cl	NOUN
iajs-2289	141	30	j	j	NOUN
iajs-2289	141	31	-	-	PUNCT
iajs-2289	141	32	ω(s	ω(s	PROPN
iajs-2289	141	33	)	)	PUNCT
iajs-2289	141	34			PROPN
iajs-2289	141	35	k	k	PROPN
iajs-2289	141	36	for	for	SCONJ
iajs-2289	141	37	some	some	DET
iajs-2289	141	38	open	open	ADJ
iajs-2289	141	39	set	set	NOUN
iajs-2289	141	40	s	s	AUX
iajs-2289	141	41	containing	contain	VERB
iajs-2289	141	42	g	g	NOUN
iajs-2289	141	43	}	}	PUNCT
iajs-2289	141	44	;	;	PUNCT
iajs-2289	141	45	k	k	X
iajs-2289	141	46	is	be	AUX
iajs-2289	141	47	almost	almost	ADV
iajs-2289	141	48	j	j	PROPN
iajs-2289	141	49	-	-	PUNCT
iajs-2289	141	50	ω	ω	NOUN
iajs-2289	141	51	-	-	NOUN
iajs-2289	141	52	interior	interior	ADJ
iajs-2289	141	53	if	if	SCONJ
iajs-2289	141	54	k	k	PROPN
iajs-2289	141	55	=	=	PRON
iajs-2289	141	56	(	(	PUNCT
iajs-2289	141	57	al	al	PROPN
iajs-2289	141	58	j	j	PROPN
iajs-2289	141	59	-	-	PUNCT
iajs-2289	141	60	ω	ω	PROPN
iajs-2289	141	61	-	-	PUNCT
iajs-2289	141	62	int(k	int(k	PROPN
iajs-2289	141	63	)	)	PUNCT
iajs-2289	141	64	)	)	PUNCT
iajs-2289	141	65	,	,	PUNCT
iajs-2289	141	66	where	where	SCONJ
iajs-2289	141	67	j{	j{	PROPN
iajs-2289	141	68	,	,	PUNCT
iajs-2289	141	69	δ	δ	PROPN
iajs-2289	141	70	,	,	PUNCT
iajs-2289	141	71			NOUN
iajs-2289	141	72	,	,	PUNCT
iajs-2289	141	73	pre	pre	ADJ
iajs-2289	141	74	,	,	PUNCT
iajs-2289	141	75	b	b	NOUN
iajs-2289	141	76	,	,	PUNCT
iajs-2289	141	77			NOUN
iajs-2289	141	78	}	}	PUNCT
iajs-2289	141	79	.	.	PUNCT
iajs-2289	142	1	theorem	theorem	ADJ
iajs-2289	142	2	18	18	NUM
iajs-2289	142	3	let	let	VERB
iajs-2289	142	4			NOUN
iajs-2289	142	5	and	and	CCONJ
iajs-2289	142	6			NOUN
iajs-2289	142	7	be	be	VERB
iajs-2289	142	8	filter	filter	NOUN
iajs-2289	142	9	bases	basis	NOUN
iajs-2289	142	10	on	on	ADP
iajs-2289	142	11	a	a	DET
iajs-2289	142	12	space	space	NOUN
iajs-2289	142	13	g	g	NOUN
iajs-2289	142	14	,	,	PUNCT
iajs-2289	142	15	k	k	PROPN
iajs-2289	142	16			PROPN
iajs-2289	142	17	g	g	PROPN
iajs-2289	142	18	and	and	CCONJ
iajs-2289	142	19	g	g	PROPN
iajs-2289	142	20			PROPN
iajs-2289	142	21	g.	g.	PROPN
iajs-2289	142	22	(	(	PUNCT
iajs-2289	142	23	a	a	X
iajs-2289	142	24	)	)	PUNCT
iajs-2289	142	25	if	if	SCONJ
iajs-2289	142	26			VERB
iajs-2289	142	27	j	j	X
iajs-2289	142	28	-ω	-ω	PUNCT
iajs-2289	142	29	⇝	⇝	X
iajs-2289	143	1	k	k	NOUN
iajs-2289	143	2	,	,	PUNCT
iajs-2289	143	3	then	then	ADV
iajs-2289	143	4	cl	cl	INTJ
iajs-2289	143	5	j	j	PROPN
iajs-2289	143	6	-ω	-ω	X
iajs-2289	143	7	(	(	PUNCT
iajs-2289	143	8	k	k	NOUN
iajs-2289	143	9	)	)	PUNCT
iajs-2289	143	10	<	<	X
iajs-2289	144	1	.	.	PROPN
iajs-2289	144	2	(	(	PUNCT
iajs-2289	144	3	b	b	NOUN
iajs-2289	144	4	)	)	PUNCT
iajs-2289	144	5	if	if	SCONJ
iajs-2289	144	6			VERB
iajs-2289	144	7	j	j	X
iajs-2289	144	8	-ω	-ω	PUNCT
iajs-2289	144	9	⇝	⇝	NOUN
iajs-2289	144	10	g	g	NOUN
iajs-2289	144	11	,	,	PUNCT
iajs-2289	144	12	iff	iff	PROPN
iajs-2289	144	13	cl	cl	PROPN
iajs-2289	144	14	j	j	PROPN
iajs-2289	144	15	-ω	-ω	X
iajs-2289	144	16	(	(	PUNCT
iajs-2289	144	17	g	g	NUM
iajs-2289	144	18	)	)	PUNCT
iajs-2289	144	19	<	<	X
iajs-2289	145	1	.	.	PROPN
iajs-2289	145	2	(	(	PUNCT
iajs-2289	145	3	c	c	NOUN
iajs-2289	145	4	)	)	PUNCT
iajs-2289	145	5	if	if	SCONJ
iajs-2289	145	6			NOUN
iajs-2289	145	7	<	<	X
iajs-2289	145	8			NOUN
iajs-2289	145	9	,	,	PUNCT
iajs-2289	145	10	then	then	ADV
iajs-2289	145	11	(	(	PUNCT
iajs-2289	145	12	alj	alj	PROPN
iajs-2289	145	13	-ω	-ω	PROPN
iajs-2289	145	14	-cg	-cg	PROPN
iajs-2289	145	15	)	)	PUNCT
iajs-2289	145	16			PROPN
iajs-2289	145	17	(	(	PUNCT
iajs-2289	145	18	alj	alj	PROPN
iajs-2289	145	19	-ω	-ω	X
iajs-2289	145	20	cg	cg	PROPN
iajs-2289	145	21	)	)	PUNCT
iajs-2289	145	22	.	.	PUNCT
iajs-2289	146	1	(	(	PUNCT
iajs-2289	146	2	d	d	X
iajs-2289	146	3	)	)	PUNCT
iajs-2289	146	4	if	if	SCONJ
iajs-2289	146	5			NOUN
iajs-2289	146	6	<	<	X
iajs-2289	146	7			NOUN
iajs-2289	146	8	and	and	CCONJ
iajs-2289	146	9			NOUN
iajs-2289	146	10	j	j	PROPN
iajs-2289	146	11	-ω	-ω	PUNCT
iajs-2289	146	12	⇝	⇝	X
iajs-2289	146	13	k	k	X
iajs-2289	146	14	,	,	PUNCT
iajs-2289	146	15	then	then	ADV
iajs-2289	146	16			VERB
iajs-2289	146	17	j	j	PROPN
iajs-2289	146	18	-ω	-ω	PUNCT
iajs-2289	146	19	⇝	⇝	X
iajs-2289	146	20	k.	k.	PROPN
iajs-2289	146	21	(	(	PUNCT
iajs-2289	146	22	e	e	NOUN
iajs-2289	146	23	)	)	PUNCT
iajs-2289	146	24	(	(	PUNCT
iajs-2289	146	25	alj	alj	PROPN
iajs-2289	146	26	-ω	-ω	X
iajs-2289	146	27	cg	cg	PROPN
iajs-2289	146	28	)	)	PUNCT
iajs-2289	146	29	=	=	NOUN
iajs-2289	146	30	∩	∩	NOUN
iajs-2289	146	31	{	{	PUNCT
iajs-2289	146	32	cl	cl	INTJ
iajs-2289	146	33	j	j	PROPN
iajs-2289	146	34	-ω	-ω	X
iajs-2289	146	35	(	(	PUNCT
iajs-2289	146	36	m	m	PROPN
iajs-2289	146	37	):	):	PUNCT
iajs-2289	146	38	m	m	VERB
iajs-2289	146	39			NOUN
iajs-2289	146	40			NOUN
iajs-2289	146	41	}	}	PUNCT
iajs-2289	146	42	.	.	PUNCT
iajs-2289	147	1	(	(	PUNCT
iajs-2289	147	2	f	f	X
iajs-2289	147	3	)	)	PUNCT
iajs-2289	147	4	if	if	SCONJ
iajs-2289	147	5			VERB
iajs-2289	147	6	j	j	PROPN
iajs-2289	147	7	-ω	-ω	PUNCT
iajs-2289	147	8	⇝	⇝	NOUN
iajs-2289	147	9	g	g	NOUN
iajs-2289	147	10	and	and	CCONJ
iajs-2289	147	11	g	g	NOUN
iajs-2289	147	12			PROPN
iajs-2289	147	13	k	k	PROPN
iajs-2289	147	14	,	,	PUNCT
iajs-2289	147	15	then	then	ADV
iajs-2289	147	16			VERB
iajs-2289	147	17	j	j	PROPN
iajs-2289	147	18	-ω	-ω	PUNCT
iajs-2289	147	19	⇝	⇝	PROPN
iajs-2289	147	20	k.	k.	PROPN
iajs-2289	147	21	(	(	PUNCT
iajs-2289	147	22	g	g	NOUN
iajs-2289	147	23	)	)	PUNCT
iajs-2289	147	24	if	if	SCONJ
iajs-2289	147	25			VERB
iajs-2289	147	26	j	j	PROPN
iajs-2289	147	27	-ω	-ω	PUNCT
iajs-2289	147	28	⇝	⇝	PROPN
iajs-2289	147	29	k	k	PROPN
iajs-2289	147	30	iff	iff	PROPN
iajs-2289	147	31			VERB
iajs-2289	147	32	j	j	PROPN
iajs-2289	147	33	-ω	-ω	PUNCT
iajs-2289	147	34	⇝	⇝	PROPN
iajs-2289	147	35	k	k	PROPN
iajs-2289	147	36	∩	∩	X
iajs-2289	147	37	(	(	PUNCT
iajs-2289	147	38	alj	alj	PROPN
iajs-2289	147	39	-ω	-ω	PROPN
iajs-2289	147	40	-cg	-cg	PROPN
iajs-2289	147	41	)	)	PUNCT
iajs-2289	147	42	.	.	PUNCT
iajs-2289	148	1	(	(	PUNCT
iajs-2289	148	2	h	h	NOUN
iajs-2289	148	3	)	)	PUNCT
iajs-2289	148	4	if	if	SCONJ
iajs-2289	148	5			VERB
iajs-2289	148	6	j	j	PROPN
iajs-2289	148	7	-ω	-ω	PUNCT
iajs-2289	148	8	⇝	⇝	PROPN
iajs-2289	148	9	k	k	NOUN
iajs-2289	148	10	,	,	PUNCT
iajs-2289	148	11	then	then	ADV
iajs-2289	148	12	k	k	PROPN
iajs-2289	148	13	∩	∩	X
iajs-2289	148	14	(	(	PUNCT
iajs-2289	148	15	alj	alj	PROPN
iajs-2289	148	16	-ω	-ω	SYM
iajs-2289	148	17	cg	cg	PROPN
iajs-2289	148	18	)	)	PUNCT
iajs-2289	148	19			NOUN
iajs-2289	148	20	.	.	PUNCT
iajs-2289	148	21	(	(	PUNCT
iajs-2289	148	22	i	i	NOUN
iajs-2289	148	23	)	)	PUNCT
iajs-2289	148	24	if	if	SCONJ
iajs-2289	148	25	s	s	VERB
iajs-2289	148	26			PROPN
iajs-2289	148	27	g	g	PROPN
iajs-2289	148	28	is	be	AUX
iajs-2289	148	29	open	open	ADJ
iajs-2289	148	30	,	,	PUNCT
iajs-2289	148	31	then	then	ADV
iajs-2289	148	32	(	(	PUNCT
iajs-2289	148	33	alj	alj	PROPN
iajs-2289	148	34	-ω	-ω	X
iajs-2289	148	35	-cl(s	-cl(s	PROPN
iajs-2289	148	36	)	)	PUNCT
iajs-2289	148	37	)	)	PUNCT
iajs-2289	149	1	=	=	SYM
iajs-2289	149	2	cl(s	cl(s	NOUN
iajs-2289	149	3	)	)	PUNCT
iajs-2289	149	4	.	.	PUNCT
iajs-2289	150	1	(	(	PUNCT
iajs-2289	150	2	j	j	NOUN
iajs-2289	150	3	)	)	PUNCT
iajs-2289	150	4	if	if	SCONJ
iajs-2289	150	5			NOUN
iajs-2289	150	6	is	be	AUX
iajs-2289	150	7	a	a	DET
iajs-2289	150	8	open	open	ADJ
iajs-2289	150	9	filter	filter	NOUN
iajs-2289	150	10	base	base	NOUN
iajs-2289	150	11	,	,	PUNCT
iajs-2289	150	12	then	then	ADV
iajs-2289	150	13	(	(	PUNCT
iajs-2289	150	14	alj	alj	PROPN
iajs-2289	150	15	-ω	-ω	X
iajs-2289	150	16	cl	cl	PROPN
iajs-2289	150	17	)	)	PUNCT
iajs-2289	150	18	=	=	SYM
iajs-2289	151	1	(	(	PUNCT
iajs-2289	151	2	alj	alj	PROPN
iajs-2289	151	3	-ω	-ω	X
iajs-2289	151	4	cg	cg	PROPN
iajs-2289	151	5	)	)	PUNCT
iajs-2289	151	6	.	.	PUNCT
iajs-2289	152	1	if	if	SCONJ
iajs-2289	152	2	s	s	NOUN
iajs-2289	152	3	is	be	AUX
iajs-2289	152	4	an	an	DET
iajs-2289	152	5	open	open	ADJ
iajs-2289	152	6	ultrafilter	ultrafilter	NOUN
iajs-2289	152	7	on	on	ADP
iajs-2289	152	8	g.	g.	PROPN
iajs-2289	152	9	then	then	ADV
iajs-2289	152	10	s	s	VERB
iajs-2289	152	11	⇝	⇝	NOUN
iajs-2289	152	12	g	g	PROPN
iajs-2289	152	13	if	if	SCONJ
iajs-2289	153	1	and	and	CCONJ
iajs-2289	153	2	only	only	ADV
iajs-2289	153	3	if	if	SCONJ
iajs-2289	153	4	s	s	X
iajs-2289	153	5	j	j	PROPN
iajs-2289	153	6	-ω	-ω	PUNCT
iajs-2289	153	7	⇝	⇝	PROPN
iajs-2289	153	8	g	g	NOUN
iajs-2289	153	9	,	,	PUNCT
iajs-2289	153	10	where	where	SCONJ
iajs-2289	153	11	j	j	PROPN
iajs-2289	153	12	{	{	PROPN
iajs-2289	153	13	,	,	PUNCT
iajs-2289	153	14	δ	δ	PROPN
iajs-2289	153	15	,	,	PUNCT
iajs-2289	153	16			NOUN
iajs-2289	153	17	,	,	PUNCT
iajs-2289	153	18	pre	pre	ADJ
iajs-2289	153	19	,	,	PUNCT
iajs-2289	153	20	b,	b,	NOUN
iajs-2289	153	21	}	}	PUNCT
iajs-2289	153	22	.	.	PUNCT
iajs-2289	154	1	proof	proof	NOUN
iajs-2289	154	2	:	:	PUNCT
iajs-2289	154	3	the	the	DET
iajs-2289	154	4	proof	proof	NOUN
iajs-2289	154	5	is	be	AUX
iajs-2289	154	6	easy	easy	ADJ
iajs-2289	154	7	,	,	PUNCT
iajs-2289	154	8	so	so	ADV
iajs-2289	154	9	it	it	PRON
iajs-2289	154	10	omitted	omit	VERB
iajs-2289	154	11	.	.	PUNCT
iajs-2289	155	1	170	170	NUM
iajs-2289	155	2	ibn	ibn	PROPN
iajs-2289	155	3	al	al	PROPN
iajs-2289	155	4	-	-	PUNCT
iajs-2289	155	5	haitham	haitham	PROPN
iajs-2289	155	6	jour	jour	X
iajs-2289	155	7	.	.	PROPN
iajs-2289	155	8	for	for	ADP
iajs-2289	155	9	pure	pure	ADJ
iajs-2289	155	10	&	&	CCONJ
iajs-2289	155	11	appl	appl	PROPN
iajs-2289	155	12	.	.	PUNCT
iajs-2289	156	1	sci	sci	PROPN
iajs-2289	156	2	.	.	PROPN
iajs-2289	156	3	32	32	NUM
iajs-2289	156	4	(	(	PUNCT
iajs-2289	156	5	3	3	NUM
iajs-2289	156	6	)	)	SYM
iajs-2289	156	7	2019	2019	NUM
iajs-2289	156	8	definition	definition	NOUN
iajs-2289	156	9	19	19	NUM
iajs-2289	156	10	the	the	DET
iajs-2289	156	11	subset	subset	NOUN
iajs-2289	156	12	k	k	PROPN
iajs-2289	156	13	of	of	ADP
iajs-2289	156	14	a	a	DET
iajs-2289	156	15	space	space	NOUN
iajs-2289	156	16	g	g	NOUN
iajs-2289	156	17	is	be	AUX
iajs-2289	156	18	said	say	VERB
iajs-2289	156	19	to	to	PART
iajs-2289	156	20	be	be	AUX
iajs-2289	156	21	quasi	quasi	ADJ
iajs-2289	156	22	-j	-j	PROPN
iajs-2289	156	23	-	-	PUNCT
iajs-2289	156	24	ω	ω	VERB
iajs-2289	156	25	-	-	PUNCT
iajs-2289	156	26	h	h	NOUN
iajs-2289	156	27	-	-	PUNCT
iajs-2289	156	28	closed	closed	ADJ
iajs-2289	156	29	relative	relative	ADJ
iajs-2289	156	30	to	to	ADP
iajs-2289	156	31	g	g	NOUN
iajs-2289	156	32	if	if	SCONJ
iajs-2289	156	33	every	every	DET
iajs-2289	156	34	cover	cover	NOUN
iajs-2289	156	35	k	k	PROPN
iajs-2289	156	36	of	of	ADP
iajs-2289	156	37	k	k	PROPN
iajs-2289	156	38	by	by	ADP
iajs-2289	156	39	open	open	ADJ
iajs-2289	156	40	subsets	subset	NOUN
iajs-2289	156	41	of	of	ADP
iajs-2289	156	42	g	g	PROPN
iajs-2289	156	43	contains	contain	VERB
iajs-2289	156	44	a	a	DET
iajs-2289	156	45	finite	finite	NOUN
iajs-2289	156	46	subfamily	subfamily	ADV
iajs-2289	156	47	l	l	NOUN
iajs-2289	156	48			PROPN
iajs-2289	156	49	k	k	X
iajs-2289	156	50	such	such	ADJ
iajs-2289	156	51	that	that	SCONJ
iajs-2289	156	52	k	k	PROPN
iajs-2289	156	53			PROPN
iajs-2289	156	54	{cl	{cl	PROPN
iajs-2289	156	55	j	j	NOUN
iajs-2289	156	56	-	-	NOUN
iajs-2289	156	57	ω-(l	ω-(l	NOUN
iajs-2289	156	58	)	)	PUNCT
iajs-2289	156	59	:	:	PUNCT
iajs-2289	157	1	l	l	X
iajs-2289	157	2			NOUN
iajs-2289	157	3	b	b	X
iajs-2289	157	4	}	}	PUNCT
iajs-2289	157	5	.	.	PUNCT
iajs-2289	158	1	if	if	SCONJ
iajs-2289	158	2	g	g	PROPN
iajs-2289	158	3	is	be	AUX
iajs-2289	158	4	hausdorff	hausdorff	NOUN
iajs-2289	158	5	,	,	PUNCT
iajs-2289	158	6	we	we	PRON
iajs-2289	158	7	say	say	VERB
iajs-2289	158	8	that	that	SCONJ
iajs-2289	158	9	k	k	PROPN
iajs-2289	158	10	is	be	AUX
iajs-2289	158	11	j	j	PROPN
iajs-2289	158	12	-	-	PUNCT
iajs-2289	158	13	ω	ω	VERB
iajs-2289	158	14	-	-	PUNCT
iajs-2289	158	15	h	h	NOUN
iajs-2289	158	16	-	-	PUNCT
iajs-2289	158	17	closed	closed	ADJ
iajs-2289	158	18	relative	relative	ADJ
iajs-2289	158	19	to	to	ADP
iajs-2289	158	20	g.	g.	PROPN
iajs-2289	158	21	if	if	SCONJ
iajs-2289	158	22	g	g	PROPN
iajs-2289	158	23	is	be	AUX
iajs-2289	158	24	quasij	quasij	NOUN
iajs-2289	158	25	-	-	PUNCT
iajs-2289	158	26	ω	ω	NUM
iajs-2289	158	27	-	-	PUNCT
iajs-2289	158	28	h	h	NOUN
iajs-2289	158	29	-	-	PUNCT
iajs-2289	158	30	closed	closed	ADJ
iajs-2289	158	31	relative	relative	ADJ
iajs-2289	158	32	to	to	ADP
iajs-2289	158	33	itself	itself	PRON
iajs-2289	158	34	,	,	PUNCT
iajs-2289	158	35	then	then	ADV
iajs-2289	158	36	g	g	PROPN
iajs-2289	158	37	is	be	AUX
iajs-2289	158	38	said	say	VERB
iajs-2289	158	39	to	to	PART
iajs-2289	158	40	be	be	AUX
iajs-2289	158	41	quasij	quasij	NOUN
iajs-2289	158	42	-	-	PUNCT
iajs-2289	158	43	ω	ω	NUM
iajs-2289	158	44	-	-	PUNCT
iajs-2289	158	45	h	h	NOUN
iajs-2289	158	46	-	-	PUNCT
iajs-2289	158	47	closed	closed	ADJ
iajs-2289	158	48	(	(	PUNCT
iajs-2289	158	49	resp	resp	NOUN
iajs-2289	158	50	.	.	PUNCT
iajs-2289	159	1	j	j	PROPN
iajs-2289	159	2	-	-	PUNCT
iajs-2289	159	3	ω	ω	VERB
iajs-2289	159	4	-	-	PUNCT
iajs-2289	159	5	h	h	NOUN
iajs-2289	159	6	-	-	PUNCT
iajs-2289	159	7	closed	closed	ADJ
iajs-2289	159	8	)	)	PUNCT
iajs-2289	159	9	,	,	PUNCT
iajs-2289	159	10	where	where	SCONJ
iajs-2289	159	11	j	j	PROPN
iajs-2289	159	12	{	{	PROPN
iajs-2289	159	13	,	,	PUNCT
iajs-2289	159	14	δ	δ	PROPN
iajs-2289	159	15	,	,	PUNCT
iajs-2289	159	16			NOUN
iajs-2289	159	17	,	,	PUNCT
iajs-2289	159	18	pre	pre	ADJ
iajs-2289	159	19	,	,	PUNCT
iajs-2289	159	20	b	b	NOUN
iajs-2289	159	21	,	,	PUNCT
iajs-2289	159	22			NOUN
iajs-2289	159	23	}	}	PUNCT
iajs-2289	159	24	.	.	PUNCT
iajs-2289	160	1	theorem	theorem	VERB
iajs-2289	160	2	20	20	NUM
iajs-2289	160	3	the	the	DET
iajs-2289	160	4	following	following	NOUN
iajs-2289	160	5	are	be	AUX
iajs-2289	160	6	equivalent	equivalent	ADJ
iajs-2289	160	7	for	for	ADP
iajs-2289	160	8	a	a	DET
iajs-2289	160	9	subset	subset	NOUN
iajs-2289	160	10	k	k	PROPN
iajs-2289	160	11			PROPN
iajs-2289	161	1	g	g	PROPN
iajs-2289	161	2	:	:	PUNCT
iajs-2289	161	3	(	(	PUNCT
iajs-2289	161	4	a	a	X
iajs-2289	161	5	)	)	PUNCT
iajs-2289	161	6	k	k	NOUN
iajs-2289	161	7	is	be	AUX
iajs-2289	161	8	quasi	quasi	ADJ
iajs-2289	161	9	-	-	ADJ
iajs-2289	161	10	j	j	PROPN
iajs-2289	161	11	-	-	PUNCT
iajs-2289	161	12	ω	ω	VERB
iajs-2289	161	13	-	-	PUNCT
iajs-2289	161	14	h	h	NOUN
iajs-2289	161	15	-	-	PUNCT
iajs-2289	161	16	closed	closed	ADJ
iajs-2289	161	17	relative	relative	ADJ
iajs-2289	161	18	to	to	ADP
iajs-2289	161	19	g.	g.	PROPN
iajs-2289	161	20	(	(	PUNCT
iajs-2289	161	21	b	b	NOUN
iajs-2289	161	22	)	)	PUNCT
iajs-2289	161	23	for	for	ADP
iajs-2289	161	24	all	all	DET
iajs-2289	161	25	filter	filter	NOUN
iajs-2289	161	26	base	base	NOUN
iajs-2289	161	27			NOUN
iajs-2289	161	28	on	on	ADP
iajs-2289	161	29	k	k	X
iajs-2289	161	30	,	,	PUNCT
iajs-2289	161	31	j	j	PROPN
iajs-2289	161	32	-	-	PUNCT
iajs-2289	161	33	ω	ω	NUM
iajs-2289	161	34	⇝	⇝	PROPN
iajs-2289	161	35	k.	k.	PROPN
iajs-2289	161	36	(	(	PUNCT
iajs-2289	161	37	c	c	NOUN
iajs-2289	161	38	)	)	PUNCT
iajs-2289	161	39	for	for	ADP
iajs-2289	161	40	all	all	DET
iajs-2289	161	41	filter	filter	NOUN
iajs-2289	161	42	base	base	NOUN
iajs-2289	161	43			NOUN
iajs-2289	161	44	on	on	ADP
iajs-2289	161	45	k	k	PROPN
iajs-2289	161	46	,	,	PUNCT
iajs-2289	161	47	(	(	PUNCT
iajs-2289	161	48	al	al	PROPN
iajs-2289	161	49	-j	-j	PROPN
iajs-2289	161	50	-	-	PUNCT
iajs-2289	161	51	ω	ω	NUM
iajs-2289	161	52	cg	cg	NOUN
iajs-2289	161	53	)	)	PUNCT
iajs-2289	161	54	∩	∩	NOUN
iajs-2289	161	55	k	k	PROPN
iajs-2289	161	56			PROPN
iajs-2289	161	57	.	.	VERB
iajs-2289	161	58	where	where	SCONJ
iajs-2289	161	59	j	j	PROPN
iajs-2289	161	60	{	{	PROPN
iajs-2289	161	61	,	,	PUNCT
iajs-2289	161	62	δ	δ	PROPN
iajs-2289	161	63	,	,	PUNCT
iajs-2289	161	64			NOUN
iajs-2289	161	65	,	,	PUNCT
iajs-2289	161	66	pre	pre	ADJ
iajs-2289	161	67	,	,	PUNCT
iajs-2289	161	68	,	,	PUNCT
iajs-2289	161	69	b	b	X
iajs-2289	161	70	,	,	PUNCT
iajs-2289	161	71			NOUN
iajs-2289	161	72	}	}	PUNCT
iajs-2289	161	73	.	.	PUNCT
iajs-2289	162	1	proof	proof	NOUN
iajs-2289	162	2	:	:	PUNCT
iajs-2289	162	3	clearly	clearly	ADV
iajs-2289	162	4	(	(	PUNCT
iajs-2289	162	5	a	a	X
iajs-2289	162	6	)	)	PUNCT
iajs-2289	162	7			NOUN
iajs-2289	162	8	(	(	PUNCT
iajs-2289	162	9	b	b	NOUN
iajs-2289	162	10	)	)	PUNCT
iajs-2289	162	11	,	,	PUNCT
iajs-2289	162	12	and	and	CCONJ
iajs-2289	162	13	by	by	ADP
iajs-2289	162	14	theorem	theorem	NOUN
iajs-2289	162	15	(	(	PUNCT
iajs-2289	162	16	18	18	NUM
iajs-2289	162	17	,	,	PUNCT
iajs-2289	162	18	h	h	NOUN
iajs-2289	162	19	)	)	PUNCT
iajs-2289	162	20	,	,	PUNCT
iajs-2289	162	21	(	(	PUNCT
iajs-2289	162	22	b	b	X
iajs-2289	162	23	)	)	PUNCT
iajs-2289	162	24			NOUN
iajs-2289	162	25	(	(	PUNCT
iajs-2289	162	26	c	c	NOUN
iajs-2289	162	27	)	)	PUNCT
iajs-2289	162	28	.	.	PUNCT
iajs-2289	163	1	to	to	PART
iajs-2289	163	2	show	show	VERB
iajs-2289	163	3	(	(	PUNCT
iajs-2289	163	4	c	c	NOUN
iajs-2289	163	5	)	)	PUNCT
iajs-2289	163	6			NOUN
iajs-2289	163	7	(	(	PUNCT
iajs-2289	163	8	a	a	NOUN
iajs-2289	163	9	)	)	PUNCT
iajs-2289	163	10	,	,	PUNCT
iajs-2289	163	11	let	let	VERB
iajs-2289	163	12	k	k	PRON
iajs-2289	163	13	be	be	AUX
iajs-2289	163	14	a	a	DET
iajs-2289	163	15	cover	cover	NOUN
iajs-2289	163	16	of	of	ADP
iajs-2289	163	17	k	k	X
iajs-2289	163	18	by	by	ADP
iajs-2289	163	19	open	open	ADJ
iajs-2289	163	20	subsets	subset	NOUN
iajs-2289	163	21	of	of	ADP
iajs-2289	163	22	g	g	NOUN
iajs-2289	163	23	such	such	ADJ
iajs-2289	163	24	that	that	SCONJ
iajs-2289	163	25	the	the	DET
iajs-2289	163	26	j	j	PROPN
iajs-2289	163	27	-	-	PUNCT
iajs-2289	163	28	ω	ω	NOUN
iajs-2289	163	29	-	-	PUNCT
iajs-2289	163	30	closed	closed	NOUN
iajs-2289	163	31	of	of	ADP
iajs-2289	163	32	the	the	DET
iajs-2289	163	33	union	union	NOUN
iajs-2289	163	34	of	of	ADP
iajs-2289	163	35	any	any	DET
iajs-2289	163	36	finite	finite	NOUN
iajs-2289	163	37	subfamily	subfamily	ADV
iajs-2289	163	38	of	of	ADP
iajs-2289	163	39	k	k	PROPN
iajs-2289	163	40	is	be	AUX
iajs-2289	163	41	not	not	PART
iajs-2289	163	42	cover	cover	VERB
iajs-2289	163	43	k.	k.	NOUN
iajs-2289	163	44	then	then	ADV
iajs-2289	163	45			VERB
iajs-2289	163	46	=	=	SYM
iajs-2289	163	47	{	{	PUNCT
iajs-2289	163	48	k	k	X
iajs-2289	163	49			PROPN
iajs-2289	163	50	cl	cl	PROPN
iajs-2289	163	51	j	j	PROPN
iajs-2289	163	52	-	-	PUNCT
iajs-2289	163	53	ω	ω	PROPN
iajs-2289	163	54	-	-	PUNCT
iajs-2289	163	55	g(k	g(k	PROPN
iajs-2289	163	56	sk	sk	NOUN
iajs-2289	163	57	):	):	PUNCT
iajs-2289	163	58	k	k	PROPN
iajs-2289	163	59	is	be	AUX
iajs-2289	163	60	finite	finite	ADJ
iajs-2289	163	61	subfamily	subfamily	ADV
iajs-2289	163	62	of	of	ADP
iajs-2289	163	63	k	k	NOUN
iajs-2289	163	64	}	}	PUNCT
iajs-2289	163	65	is	be	AUX
iajs-2289	163	66	a	a	DET
iajs-2289	163	67	filter	filter	NOUN
iajs-2289	163	68	base	base	NOUN
iajs-2289	163	69	on	on	ADP
iajs-2289	163	70	k	k	PROPN
iajs-2289	163	71	and	and	CCONJ
iajs-2289	163	72	(	(	PUNCT
iajs-2289	163	73	al	al	PROPN
iajs-2289	163	74	-j	-j	PROPN
iajs-2289	163	75	-	-	PUNCT
iajs-2289	163	76	ω	ω	NOUN
iajs-2289	163	77	-	-	PUNCT
iajs-2289	163	78	cg	cg	NOUN
iajs-2289	163	79	)	)	PUNCT
iajs-2289	163	80	∩	∩	NOUN
iajs-2289	163	81	k	k	X
iajs-2289	163	82	=	=	PUNCT
iajs-2289	163	83	.	.	X
iajs-2289	163	84	this	this	DET
iajs-2289	163	85	contradiction	contradiction	NOUN
iajs-2289	163	86	crop	crop	NOUN
iajs-2289	163	87	s	s	VERB
iajs-2289	163	88	that	that	SCONJ
iajs-2289	163	89	k	k	PROPN
iajs-2289	163	90	is	be	AUX
iajs-2289	163	91	quasij	quasij	NOUN
iajs-2289	163	92	-	-	PUNCT
iajs-2289	163	93	ω	ω	NUM
iajs-2289	163	94	-	-	PUNCT
iajs-2289	163	95	h	h	NOUN
iajs-2289	163	96	-	-	PUNCT
iajs-2289	163	97	closed	closed	ADJ
iajs-2289	163	98	relative	relative	ADJ
iajs-2289	163	99	to	to	ADP
iajs-2289	163	100	g	g	NOUN
iajs-2289	163	101	,	,	PUNCT
iajs-2289	163	102	where	where	SCONJ
iajs-2289	163	103	j	j	PROPN
iajs-2289	163	104	{	{	PROPN
iajs-2289	163	105	,	,	PUNCT
iajs-2289	163	106	δ	δ	PROPN
iajs-2289	163	107	,	,	PUNCT
iajs-2289	163	108			NOUN
iajs-2289	163	109	,	,	PUNCT
iajs-2289	163	110	pre	pre	ADJ
iajs-2289	163	111	,	,	PUNCT
iajs-2289	163	112	b	b	NOUN
iajs-2289	163	113	,	,	PUNCT
iajs-2289	163	114			NOUN
iajs-2289	163	115	}	}	PUNCT
iajs-2289	163	116	.	.	PUNCT
iajs-2289	164	1	by	by	ADP
iajs-2289	164	2	concepts	concept	NOUN
iajs-2289	164	3	of	of	ADP
iajs-2289	164	4	closure	closure	NOUN
iajs-2289	164	5	directed	direct	VERB
iajs-2289	164	6	toward	toward	ADP
iajs-2289	164	7	a	a	DET
iajs-2289	164	8	set	set	NOUN
iajs-2289	164	9	,	,	PUNCT
iajs-2289	164	10	almost	almost	ADV
iajs-2289	164	11	j	j	PROPN
iajs-2289	164	12	-	-	PUNCT
iajs-2289	164	13	ω	ω	NOUN
iajs-2289	164	14	-	-	PUNCT
iajs-2289	164	15	convergence	convergence	NOUN
iajs-2289	164	16	characterized	characterize	VERB
iajs-2289	164	17	and	and	CCONJ
iajs-2289	164	18	related	relate	VERB
iajs-2289	164	19	in	in	ADP
iajs-2289	164	20	the	the	DET
iajs-2289	164	21	next	next	ADJ
iajs-2289	164	22	result	result	NOUN
iajs-2289	164	23	.	.	PUNCT
iajs-2289	165	1	theorem	theorem	ADJ
iajs-2289	165	2	21	21	NUM
iajs-2289	165	3	let	let	VERB
iajs-2289	165	4			NOUN
iajs-2289	165	5	be	be	AUX
iajs-2289	165	6	a	a	DET
iajs-2289	165	7	filter	filter	NOUN
iajs-2289	165	8	base	base	NOUN
iajs-2289	165	9	on	on	ADP
iajs-2289	165	10	a	a	DET
iajs-2289	165	11	space	space	NOUN
iajs-2289	165	12	g	g	NOUN
iajs-2289	165	13	and	and	CCONJ
iajs-2289	165	14	k	k	PROPN
iajs-2289	165	15			PROPN
iajs-2289	165	16	g	g	PROPN
iajs-2289	165	17	.	.	PUNCT
iajs-2289	166	1	then	then	ADV
iajs-2289	166	2	:	:	PUNCT
iajs-2289	166	3	(	(	PUNCT
iajs-2289	166	4	a	a	X
iajs-2289	166	5	)	)	PUNCT
iajs-2289	166	6			NOUN
iajs-2289	166	7	is	be	AUX
iajs-2289	166	8	cl	cl	NOUN
iajs-2289	166	9	-	-	PUNCT
iajs-2289	166	10	dir,-tow	dir,-tow	NOUN
iajs-2289	166	11	k	k	PROPN
iajs-2289	166	12	iff	iff	PROPN
iajs-2289	166	13	for	for	ADP
iajs-2289	166	14	each	each	DET
iajs-2289	166	15	cover	cover	NOUN
iajs-2289	166	16	k	k	PROPN
iajs-2289	166	17	of	of	ADP
iajs-2289	166	18	k	k	PROPN
iajs-2289	166	19	by	by	ADP
iajs-2289	166	20	open	open	ADJ
iajs-2289	166	21	subsets	subset	NOUN
iajs-2289	166	22	of	of	ADP
iajs-2289	166	23	g	g	NOUN
iajs-2289	166	24	,	,	PUNCT
iajs-2289	166	25	there	there	PRON
iajs-2289	166	26	is	be	VERB
iajs-2289	166	27	a	a	DET
iajs-2289	166	28	finite	finite	NOUN
iajs-2289	166	29	subfamily	subfamily	ADV
iajs-2289	166	30	l	l	NOUN
iajs-2289	166	31			PROPN
iajs-2289	166	32	k	k	PROPN
iajs-2289	166	33	and	and	CCONJ
iajs-2289	166	34	an	an	DET
iajs-2289	166	35	m	m	NOUN
iajs-2289	166	36			NOUN
iajs-2289	166	37			NOUN
iajs-2289	166	38	such	such	ADJ
iajs-2289	166	39	that	that	SCONJ
iajs-2289	166	40	m	m	PROPN
iajs-2289	166	41			PROPN
iajs-2289	166	42	{cl	{cl	PROPN
iajs-2289	166	43	j	j	NOUN
iajs-2289	166	44	-	-	NOUN
iajs-2289	166	45	ω-(l	ω-(l	NOUN
iajs-2289	166	46	)	)	PUNCT
iajs-2289	166	47	:	:	PUNCT
iajs-2289	167	1	l	l	PROPN
iajs-2289	167	2	b	b	PROPN
iajs-2289	167	3	}	}	PUNCT
iajs-2289	167	4	,	,	PUNCT
iajs-2289	167	5	where	where	SCONJ
iajs-2289	167	6	j	j	PROPN
iajs-2289	167	7	{	{	PUNCT
iajs-2289	167	8			PROPN
iajs-2289	167	9	,	,	PUNCT
iajs-2289	167	10	δ	δ	PROPN
iajs-2289	167	11	,	,	PUNCT
iajs-2289	167	12			NOUN
iajs-2289	167	13	,	,	PUNCT
iajs-2289	167	14	pre	pre	ADJ
iajs-2289	167	15	,	,	PUNCT
iajs-2289	167	16	,	,	PUNCT
iajs-2289	167	17	b	b	X
iajs-2289	167	18	,	,	PUNCT
iajs-2289	167	19			NOUN
iajs-2289	167	20	}	}	PUNCT
iajs-2289	167	21	.	.	PUNCT
iajs-2289	168	1	(	(	PUNCT
iajs-2289	168	2	b	b	X
iajs-2289	168	3	)	)	PUNCT
iajs-2289	168	4	for	for	ADP
iajs-2289	168	5	every	every	DET
iajs-2289	168	6	filter	filter	NOUN
iajs-2289	168	7	base	base	NOUN
iajs-2289	168	8	,	,	PUNCT
iajs-2289	168	9			VERB
iajs-2289	168	10	<	<	X
iajs-2289	168	11			NOUN
iajs-2289	168	12	implies	imply	VERB
iajs-2289	168	13	(	(	PUNCT
iajs-2289	168	14	alj	alj	PROPN
iajs-2289	168	15	-	-	PUNCT
iajs-2289	168	16	ω	ω	NOUN
iajs-2289	168	17	-	-	PUNCT
iajs-2289	168	18	cg	cg	NOUN
iajs-2289	168	19	)	)	PUNCT
iajs-2289	168	20	∩	∩	NOUN
iajs-2289	168	21	k	k	PROPN
iajs-2289	168	22			PROPN
iajs-2289	168	23			NOUN
iajs-2289	168	24	iff	iff	PROPN
iajs-2289	168	25	j	j	PROPN
iajs-2289	168	26	–	–	PUNCT
iajs-2289	168	27	ω	ω	PROPN
iajs-2289	168	28	⇝	⇝	X
iajs-2289	169	1	k	k	X
iajs-2289	169	2	,	,	PUNCT
iajs-2289	169	3	where	where	SCONJ
iajs-2289	169	4	j	j	PROPN
iajs-2289	169	5			NOUN
iajs-2289	169	6	{	{	PUNCT
iajs-2289	169	7			PROPN
iajs-2289	169	8	,	,	PUNCT
iajs-2289	169	9	δ	δ	PROPN
iajs-2289	169	10	,	,	PUNCT
iajs-2289	169	11			NOUN
iajs-2289	169	12	,	,	PUNCT
iajs-2289	169	13	pre	pre	ADJ
iajs-2289	169	14	,	,	PUNCT
iajs-2289	169	15	b	b	NOUN
iajs-2289	169	16	,	,	PUNCT
iajs-2289	169	17			NOUN
iajs-2289	169	18	}	}	PUNCT
iajs-2289	169	19	.	.	PUNCT
iajs-2289	170	1	proof	proof	NOUN
iajs-2289	170	2	:	:	PUNCT
iajs-2289	170	3	the	the	DET
iajs-2289	170	4	proofs	proof	NOUN
iajs-2289	170	5	of	of	ADP
iajs-2289	170	6	the	the	DET
iajs-2289	170	7	two	two	NUM
iajs-2289	170	8	facts	fact	NOUN
iajs-2289	170	9	are	be	AUX
iajs-2289	170	10	similar	similar	ADJ
iajs-2289	170	11	;	;	PUNCT
iajs-2289	170	12	so	so	ADV
iajs-2289	170	13	,	,	PUNCT
iajs-2289	170	14	we	we	PRON
iajs-2289	170	15	will	will	AUX
iajs-2289	170	16	only	only	ADV
iajs-2289	170	17	prove	prove	VERB
iajs-2289	170	18	the	the	DET
iajs-2289	170	19	fact	fact	NOUN
iajs-2289	170	20	(	(	PUNCT
iajs-2289	170	21	b	b	NOUN
iajs-2289	170	22	):	):	PUNCT
iajs-2289	170	23	(	(	PUNCT
iajs-2289	170	24			NOUN
iajs-2289	170	25	)	)	PUNCT
iajs-2289	170	26	suppose	suppose	VERB
iajs-2289	170	27	for	for	ADP
iajs-2289	170	28	every	every	DET
iajs-2289	170	29	filter	filter	NOUN
iajs-2289	170	30	base	base	NOUN
iajs-2289	170	31	,	,	PUNCT
iajs-2289	170	32			VERB
iajs-2289	170	33	<	<	X
iajs-2289	170	34			NOUN
iajs-2289	170	35	implies	imply	VERB
iajs-2289	170	36	(	(	PUNCT
iajs-2289	170	37	alj	alj	PROPN
iajs-2289	170	38	-	-	PUNCT
iajs-2289	170	39	ω	ω	NOUN
iajs-2289	170	40	-	-	PUNCT
iajs-2289	170	41	cg	cg	NOUN
iajs-2289	170	42	)	)	PUNCT
iajs-2289	170	43	∩	∩	NOUN
iajs-2289	170	44	k	k	PROPN
iajs-2289	170	45			PROPN
iajs-2289	170	46	.	.	PUNCT
iajs-2289	170	47	if	if	SCONJ
iajs-2289	170	48	j	j	PROPN
iajs-2289	170	49	–	–	PUNCT
iajs-2289	170	50	ω	ω	NUM
iajs-2289	170	51	⇝	⇝	NOUN
iajs-2289	170	52	g	g	NOUN
iajs-2289	170	53	for	for	ADP
iajs-2289	170	54	some	some	DET
iajs-2289	170	55	g	g	PROPN
iajs-2289	170	56			PROPN
iajs-2289	170	57	k	k	NOUN
iajs-2289	170	58	,	,	PUNCT
iajs-2289	170	59	then	then	ADV
iajs-2289	170	60	by	by	ADP
iajs-2289	170	61	theorem	theorem	NOUN
iajs-2289	170	62	(	(	PUNCT
iajs-2289	170	63	3.3	3.3	NUM
iajs-2289	170	64	,	,	PUNCT
iajs-2289	170	65	f	f	NOUN
iajs-2289	170	66	)	)	PUNCT
iajs-2289	170	67	,	,	PUNCT
iajs-2289	170	68	j	j	PROPN
iajs-2289	170	69	-	-	PUNCT
iajs-2289	170	70	ω	ω	NUM
iajs-2289	170	71	⇝	⇝	NOUN
iajs-2289	170	72	k.	k.	PROPN
iajs-2289	170	73	so	so	ADV
iajs-2289	170	74	,	,	PUNCT
iajs-2289	170	75	assume	assume	VERB
iajs-2289	170	76	that	that	SCONJ
iajs-2289	170	77	for	for	ADP
iajs-2289	170	78	each	each	DET
iajs-2289	170	79	g	g	PROPN
iajs-2289	170	80			PROPN
iajs-2289	170	81	k	k	PROPN
iajs-2289	170	82	,	,	PUNCT
iajs-2289	170	83			PROPN
iajs-2289	170	84	does	do	AUX
iajs-2289	170	85	not	not	PART
iajs-2289	170	86	j	j	PROPN
iajs-2289	170	87	-	-	PUNCT
iajs-2289	170	88	ω	ω	PROPN
iajs-2289	170	89	⇝	⇝	NOUN
iajs-2289	170	90	g.	g.	NOUN
iajs-2289	170	91	let	let	VERB
iajs-2289	170	92	k	k	PRON
iajs-2289	170	93	be	be	AUX
iajs-2289	170	94	a	a	DET
iajs-2289	170	95	cover	cover	NOUN
iajs-2289	170	96	of	of	ADP
iajs-2289	170	97	k	k	X
iajs-2289	170	98	by	by	ADP
iajs-2289	170	99	subsets	subset	NOUN
iajs-2289	170	100	open	open	ADJ
iajs-2289	170	101	in	in	ADP
iajs-2289	170	102	g.	g.	NOUN
iajs-2289	170	103	for	for	ADP
iajs-2289	170	104	every	every	DET
iajs-2289	170	105	g	g	PROPN
iajs-2289	170	106			PROPN
iajs-2289	170	107	k	k	PROPN
iajs-2289	170	108	,	,	PUNCT
iajs-2289	170	109	yond	yond	PROPN
iajs-2289	170	110	is	be	AUX
iajs-2289	170	111	an	an	DET
iajs-2289	170	112	open	open	ADJ
iajs-2289	170	113	set	set	NOUN
iajs-2289	170	114	sg	sg	NOUN
iajs-2289	170	115	containing	contain	VERB
iajs-2289	170	116	g	g	NOUN
iajs-2289	170	117	and	and	CCONJ
iajs-2289	170	118	tg	tg	PROPN
iajs-2289	170	119			PROPN
iajs-2289	170	120	k	k	PROPN
iajs-2289	170	121	such	such	ADJ
iajs-2289	170	122	that	that	SCONJ
iajs-2289	170	123	sg	sg	PROPN
iajs-2289	170	124			PROPN
iajs-2289	170	125	tg	tg	PROPN
iajs-2289	170	126	and	and	CCONJ
iajs-2289	170	127	m	m	NOUN
iajs-2289	170	128	cl	cl	INTJ
iajs-2289	170	129	j	j	PROPN
iajs-2289	170	130	-	-	PUNCT
iajs-2289	170	131	ω	ω	NOUN
iajs-2289	170	132	-	-	PUNCT
iajs-2289	170	133	g(sg	g(sg	NOUN
iajs-2289	170	134	)	)	PUNCT
iajs-2289	170	135			NOUN
iajs-2289	170	136			NOUN
iajs-2289	170	137	for	for	ADP
iajs-2289	170	138	every	every	DET
iajs-2289	170	139	m	m	NOUN
iajs-2289	170	140			NOUN
iajs-2289	171	1	.	.	NOUN
iajs-2289	172	1	so	so	ADV
iajs-2289	172	2	,	,	PUNCT
iajs-2289	172	3	g	g	NOUN
iajs-2289	172	4	=	=	SYM
iajs-2289	172	5	{	{	PUNCT
iajs-2289	172	6	m	m	PROPN
iajs-2289	172	7			PROPN
iajs-2289	172	8	cl	cl	PROPN
iajs-2289	172	9	j	j	PROPN
iajs-2289	172	10	-	-	PUNCT
iajs-2289	172	11	ω	ω	NOUN
iajs-2289	172	12	-	-	PUNCT
iajs-2289	172	13	g(sg	g(sg	NOUN
iajs-2289	172	14	)	)	PUNCT
iajs-2289	172	15	:	:	PUNCT
iajs-2289	172	16	m	m	VERB
iajs-2289	172	17			NOUN
iajs-2289	172	18			NOUN
iajs-2289	172	19	}	}	PUNCT
iajs-2289	172	20	is	be	AUX
iajs-2289	172	21	a	a	DET
iajs-2289	172	22	filter	filter	NOUN
iajs-2289	172	23	base	base	NOUN
iajs-2289	172	24	on	on	ADP
iajs-2289	172	25	g	g	NOUN
iajs-2289	172	26	and	and	CCONJ
iajs-2289	172	27			VERB
iajs-2289	172	28	<	<	X
iajs-2289	172	29	g	g	NOUN
iajs-2289	172	30	.	.	PUNCT
iajs-2289	173	1	now	now	ADV
iajs-2289	173	2	,	,	PUNCT
iajs-2289	173	3	g	g	PROPN
iajs-2289	173	4			PROPN
iajs-2289	173	5	(	(	PUNCT
iajs-2289	173	6	alj	alj	PROPN
iajs-2289	173	7	-	-	PUNCT
iajs-2289	173	8	ω	ω	NOUN
iajs-2289	173	9	-	-	NOUN
iajs-2289	173	10	cgg	cgg	NOUN
iajs-2289	173	11	)	)	PUNCT
iajs-2289	173	12	.	.	PUNCT
iajs-2289	174	1	assume	assume	VERB
iajs-2289	174	2	that	that	SCONJ
iajs-2289	174	3	{g	{g	ADP
iajs-2289	174	4	:	:	PUNCT
iajs-2289	174	5	g	g	PROPN
iajs-2289	174	6			PROPN
iajs-2289	174	7	k	k	NOUN
iajs-2289	174	8	}	}	PUNCT
iajs-2289	174	9	forms	form	VERB
iajs-2289	174	10	a	a	DET
iajs-2289	174	11	filter	filter	NOUN
iajs-2289	174	12	sub	sub	NOUN
iajs-2289	174	13	base	base	NOUN
iajs-2289	174	14	with	with	ADP
iajs-2289	174	15			NOUN
iajs-2289	174	16	denoting	denote	VERB
iajs-2289	174	17	the	the	DET
iajs-2289	174	18	generated	generate	VERB
iajs-2289	174	19	filter	filter	NOUN
iajs-2289	174	20	.	.	PUNCT
iajs-2289	175	1	then	then	ADV
iajs-2289	175	2			VERB
iajs-2289	175	3	<	<	X
iajs-2289	175	4			PROPN
iajs-2289	175	5	and	and	CCONJ
iajs-2289	175	6	(	(	PUNCT
iajs-2289	175	7	al	al	PROPN
iajs-2289	175	8	-j	-j	PROPN
iajs-2289	175	9	-	-	PUNCT
iajs-2289	175	10	ω	ω	NOUN
iajs-2289	175	11	-	-	PUNCT
iajs-2289	175	12	cg	cg	NOUN
iajs-2289	175	13	)	)	PUNCT
iajs-2289	175	14	∩	∩	NOUN
iajs-2289	175	15	k	k	PROPN
iajs-2289	175	16	=	=	PUNCT
iajs-2289	175	17	.	.	X
iajs-2289	175	18	this	this	DET
iajs-2289	175	19	contradiction	contradiction	NOUN
iajs-2289	175	20	implies	imply	VERB
iajs-2289	175	21	yond	yond	PROPN
iajs-2289	175	22	is	be	AUX
iajs-2289	175	23	a	a	DET
iajs-2289	175	24	finite	finite	NOUN
iajs-2289	175	25	subset	subset	NOUN
iajs-2289	175	26	l	l	PROPN
iajs-2289	175	27			PROPN
iajs-2289	175	28	k	k	PROPN
iajs-2289	175	29	and	and	CCONJ
iajs-2289	175	30	mg	mg	PROPN
iajs-2289	175	31			PROPN
iajs-2289	175	32			PROPN
iajs-2289	175	33	for	for	ADP
iajs-2289	175	34	g	g	PROPN
iajs-2289	175	35			PROPN
iajs-2289	175	36	l	l	NOUN
iajs-2289	175	37	such	such	ADJ
iajs-2289	175	38	that	that	SCONJ
iajs-2289	175	39	,	,	PUNCT
iajs-2289	175	40			NOUN
iajs-2289	175	41	=	=	SYM
iajs-2289	175	42	∩{mg	∩{mg	NUM
iajs-2289	175	43			PROPN
iajs-2289	175	44	cl	cl	PROPN
iajs-2289	175	45	j	j	PROPN
iajs-2289	175	46	-	-	PUNCT
iajs-2289	175	47	ω	ω	PROPN
iajs-2289	175	48	g(sg	g(sg	PROPN
iajs-2289	175	49	)	)	PUNCT
iajs-2289	175	50	:	:	PUNCT
iajs-2289	175	51	g	g	ADP
iajs-2289	175	52			NOUN
iajs-2289	175	53	l}.there	l}.there	NOUN
iajs-2289	175	54	is	be	AUX
iajs-2289	175	55	m	m	PROPN
iajs-2289	175	56			NOUN
iajs-2289	175	57			NOUN
iajs-2289	176	1	such	such	ADJ
iajs-2289	176	2	that	that	SCONJ
iajs-2289	176	3	m	m	VERB
iajs-2289	176	4			PROPN
iajs-2289	176	5	∩{mg	∩{mg	NUM
iajs-2289	176	6	:	:	PUNCT
iajs-2289	177	1	g	g	PROPN
iajs-2289	177	2			PROPN
iajs-2289	177	3	l	l	NOUN
iajs-2289	177	4	}	}	PUNCT
iajs-2289	177	5	.	.	PUNCT
iajs-2289	178	1	it	it	PRON
iajs-2289	178	2	easily	easily	ADV
iajs-2289	178	3	follows	follow	VERB
iajs-2289	178	4	that	that	SCONJ
iajs-2289	178	5			NOUN
iajs-2289	178	6	=	=	PUNCT
iajs-2289	178	7	∩{m	∩{m	NUM
iajs-2289	178	8			PROPN
iajs-2289	178	9	cl	cl	PROPN
iajs-2289	178	10	j	j	PROPN
iajs-2289	178	11	-	-	PUNCT
iajs-2289	178	12	ω	ω	NOUN
iajs-2289	178	13	-	-	PUNCT
iajs-2289	178	14	g(sg	g(sg	NOUN
iajs-2289	178	15	)	)	PUNCT
iajs-2289	178	16	:	:	PUNCT
iajs-2289	178	17	g	g	ADP
iajs-2289	178	18			PROPN
iajs-2289	178	19	l	l	PROPN
iajs-2289	178	20	and	and	CCONJ
iajs-2289	178	21	m	m	PROPN
iajs-2289	178	22			PROPN
iajs-2289	178	23	{cl	{cl	PROPN
iajs-2289	178	24	j	j	PROPN
iajs-2289	178	25	-	-	PUNCT
iajs-2289	178	26	ωg(tg	ωg(tg	PROPN
iajs-2289	178	27	):	):	PUNCT
iajs-2289	178	28	g	g	PROPN
iajs-2289	178	29			PROPN
iajs-2289	178	30	l	l	NOUN
iajs-2289	178	31	}	}	PUNCT
iajs-2289	178	32	.	.	PUNCT
iajs-2289	179	1	thus	thus	ADV
iajs-2289	179	2	j	j	NOUN
iajs-2289	179	3	-	-	PUNCT
iajs-2289	179	4	ω	ω	NUM
iajs-2289	179	5	⇝	⇝	PROPN
iajs-2289	179	6	k.	k.	PROPN
iajs-2289	179	7	(	(	PUNCT
iajs-2289	179	8			PROPN
iajs-2289	179	9	)	)	PUNCT
iajs-2289	179	10	suppose	suppose	VERB
iajs-2289	179	11	j	j	NOUN
iajs-2289	179	12	-	-	PUNCT
iajs-2289	179	13	ω	ω	NUM
iajs-2289	179	14	⇝	⇝	NOUN
iajs-2289	179	15	k	k	PROPN
iajs-2289	179	16	and	and	CCONJ
iajs-2289	179	17			PROPN
iajs-2289	179	18	is	be	AUX
iajs-2289	179	19	a	a	DET
iajs-2289	179	20	filter	filter	NOUN
iajs-2289	179	21	base	base	NOUN
iajs-2289	179	22	such	such	ADJ
iajs-2289	179	23	that	that	SCONJ
iajs-2289	179	24			NOUN
iajs-2289	179	25	<	<	X
iajs-2289	179	26	.	.	X
iajs-2289	179	27	by	by	ADP
iajs-2289	179	28	theorem	theorem	PROPN
iajs-2289	179	29	(	(	PUNCT
iajs-2289	179	30	18	18	NUM
iajs-2289	179	31	,	,	PUNCT
iajs-2289	179	32	d	d	NOUN
iajs-2289	179	33	)	)	PUNCT
iajs-2289	179	34	,	,	PUNCT
iajs-2289	179	35	j	j	PROPN
iajs-2289	179	36	-	-	PUNCT
iajs-2289	179	37	ω	ω	NOUN
iajs-2289	179	38	⇝	⇝	NOUN
iajs-2289	179	39	k	k	NOUN
iajs-2289	179	40	,	,	PUNCT
iajs-2289	179	41	and	and	CCONJ
iajs-2289	179	42	theorem	theorem	ADJ
iajs-2289	179	43	(	(	PUNCT
iajs-2289	179	44	18	18	NUM
iajs-2289	179	45	,	,	PUNCT
iajs-2289	179	46	h	h	NOUN
iajs-2289	179	47	)	)	PUNCT
iajs-2289	179	48	,	,	PUNCT
iajs-2289	179	49	(	(	PUNCT
iajs-2289	179	50	alj	alj	PROPN
iajs-2289	179	51	-	-	PUNCT
iajs-2289	179	52	ω	ω	NOUN
iajs-2289	179	53	-	-	PUNCT
iajs-2289	179	54	cg	cg	NOUN
iajs-2289	179	55	)	)	PUNCT
iajs-2289	179	56	∩	∩	NOUN
iajs-2289	179	57	k	k	PROPN
iajs-2289	179	58			PROPN
iajs-2289	179	59	.	.	NUM
iajs-2289	179	60	171	171	NUM
iajs-2289	179	61	ibn	ibn	PROPN
iajs-2289	179	62	al	al	PROPN
iajs-2289	179	63	-	-	PUNCT
iajs-2289	179	64	haitham	haitham	PROPN
iajs-2289	179	65	jour	jour	X
iajs-2289	179	66	.	.	PROPN
iajs-2289	179	67	for	for	ADP
iajs-2289	179	68	pure	pure	ADJ
iajs-2289	179	69	&	&	CCONJ
iajs-2289	179	70	appl	appl	PROPN
iajs-2289	179	71	.	.	PUNCT
iajs-2289	180	1	sci	sci	PROPN
iajs-2289	180	2	.	.	PROPN
iajs-2289	180	3	32	32	NUM
iajs-2289	180	4	(	(	PUNCT
iajs-2289	180	5	3	3	NUM
iajs-2289	180	6	)	)	PUNCT
iajs-2289	180	7	2019	2019	NUM
iajs-2289	180	8	5	5	NUM
iajs-2289	180	9	.	.	PUNCT
iajs-2289	181	1	filter	filter	NOUN
iajs-2289	181	2	bases	basis	NOUN
iajs-2289	181	3	and	and	CCONJ
iajs-2289	181	4	j	j	PROPN
iajs-2289	181	5	-	-	PUNCT
iajs-2289	181	6	ω	ω	NOUN
iajs-2289	181	7	-	-	NOUN
iajs-2289	181	8	rigidity	rigidity	NOUN
iajs-2289	181	9	in	in	ADP
iajs-2289	181	10	the	the	DET
iajs-2289	181	11	section	section	NOUN
iajs-2289	182	1	,	,	PUNCT
iajs-2289	182	2	we	we	PRON
iajs-2289	182	3	defined	define	VERB
iajs-2289	182	4	filter	filter	NOUN
iajs-2289	182	5	bases	basis	NOUN
iajs-2289	182	6	,	,	PUNCT
iajs-2289	182	7	j	j	PROPN
iajs-2289	182	8	-	-	PUNCT
iajs-2289	182	9	ω	ω	NOUN
iajs-2289	182	10	-	-	PUNCT
iajs-2289	182	11	rigidity	rigidity	NOUN
iajs-2289	182	12	,	,	PUNCT
iajs-2289	182	13	and	and	CCONJ
iajs-2289	182	14	the	the	DET
iajs-2289	182	15	some	some	DET
iajs-2289	182	16	theorems	theorem	NOUN
iajs-2289	182	17	concerning	concern	VERB
iajs-2289	182	18	of	of	ADP
iajs-2289	182	19	them	they	PRON
iajs-2289	182	20	.	.	PUNCT
iajs-2289	183	1	definition	definition	NOUN
iajs-2289	183	2	22	22	NUM
iajs-2289	183	3	a	a	DET
iajs-2289	183	4	mapping	mapping	NOUN
iajs-2289	183	5			ADJ
iajs-2289	183	6	:	:	PUNCT
iajs-2289	183	7	g	g	PROPN
iajs-2289	183	8			NOUN
iajs-2289	183	9	h	h	NOUN
iajs-2289	183	10	is	be	AUX
iajs-2289	183	11	said	say	VERB
iajs-2289	183	12	to	to	PART
iajs-2289	183	13	be	be	AUX
iajs-2289	183	14	j	j	PROPN
iajs-2289	183	15	-	-	PUNCT
iajs-2289	183	16	ω	ω	NOUN
iajs-2289	183	17	-	-	PUNCT
iajs-2289	183	18	closure	closure	NOUN
iajs-2289	183	19	continuous	continuous	ADJ
iajs-2289	183	20	(	(	PUNCT
iajs-2289	183	21	resp	resp	NOUN
iajs-2289	183	22	.	.	PUNCT
iajs-2289	184	1	j	j	PROPN
iajs-2289	184	2	-	-	PUNCT
iajs-2289	184	3	ω	ω	NOUN
iajs-2289	184	4	-	-	ADJ
iajs-2289	184	5	weakly	weakly	ADJ
iajs-2289	184	6	continuous	continuous	ADJ
iajs-2289	184	7	)	)	PUNCT
iajs-2289	184	8	if	if	SCONJ
iajs-2289	184	9	for	for	ADP
iajs-2289	184	10	every	every	DET
iajs-2289	184	11	g	g	NOUN
iajs-2289	184	12			NOUN
iajs-2289	184	13	g	g	PROPN
iajs-2289	184	14	and	and	CCONJ
iajs-2289	184	15	every	every	DET
iajs-2289	184	16	nbd	nbd	PROPN
iajs-2289	184	17	t	t	PROPN
iajs-2289	184	18	of	of	ADP
iajs-2289	184	19			X
iajs-2289	184	20	(	(	PUNCT
iajs-2289	184	21	g	g	NOUN
iajs-2289	184	22	)	)	PUNCT
iajs-2289	185	1	,	,	PUNCT
iajs-2289	185	2	there	there	PRON
iajs-2289	185	3	exists	exist	VERB
iajs-2289	185	4	a	a	DET
iajs-2289	185	5	nbd	nbd	PROPN
iajs-2289	185	6	s	s	PROPN
iajs-2289	185	7	of	of	ADP
iajs-2289	185	8	g	g	NOUN
iajs-2289	185	9	in	in	ADP
iajs-2289	185	10	g	g	PROPN
iajs-2289	185	11	such	such	ADJ
iajs-2289	185	12	that	that	SCONJ
iajs-2289	185	13	(cl	(cl	PROPN
iajs-2289	185	14	j	j	PROPN
iajs-2289	185	15	-	-	PUNCT
iajs-2289	185	16	ω(s	ω(s	PROPN
iajs-2289	185	17	)	)	PUNCT
iajs-2289	185	18	)	)	PUNCT
iajs-2289	186	1			PROPN
iajs-2289	186	2	cl	cl	INTJ
iajs-2289	186	3	j	j	NOUN
iajs-2289	186	4	-	-	PUNCT
iajs-2289	186	5	ω-(t	ω-(t	NUM
iajs-2289	186	6	)	)	PUNCT
iajs-2289	186	7	(	(	PUNCT
iajs-2289	186	8	resp	resp	NOUN
iajs-2289	186	9	.	.	PUNCT
iajs-2289	187	1	(s	(s	PRON
iajs-2289	187	2	)	)	PUNCT
iajs-2289	187	3			PROPN
iajs-2289	187	4	cl	cl	INTJ
iajs-2289	187	5	j	j	NOUN
iajs-2289	187	6	-	-	PUNCT
iajs-2289	187	7	ω-(t	ω-(t	NUM
iajs-2289	187	8	)	)	PUNCT
iajs-2289	187	9	)	)	PUNCT
iajs-2289	187	10	.	.	PUNCT
iajs-2289	188	1	clearly	clearly	ADV
iajs-2289	188	2	,	,	PUNCT
iajs-2289	188	3	every	every	DET
iajs-2289	188	4	continuous	continuous	ADJ
iajs-2289	188	5	mapping	mapping	NOUN
iajs-2289	188	6	is	be	AUX
iajs-2289	188	7	j	j	PROPN
iajs-2289	188	8	-	-	PUNCT
iajs-2289	188	9	ω	ω	VERB
iajs-2289	188	10	-	-	PUNCT
iajs-2289	188	11	closure	closure	NOUN
iajs-2289	188	12	continuous	continuous	ADJ
iajs-2289	188	13	,	,	PUNCT
iajs-2289	188	14	where	where	SCONJ
iajs-2289	188	15	j{	j{	PROPN
iajs-2289	188	16	,	,	PUNCT
iajs-2289	188	17	δ	δ	PROPN
iajs-2289	188	18	,	,	PUNCT
iajs-2289	188	19			NOUN
iajs-2289	188	20	,	,	PUNCT
iajs-2289	188	21	pre	pre	ADJ
iajs-2289	188	22	,	,	PUNCT
iajs-2289	188	23	b	b	NOUN
iajs-2289	188	24	,	,	PUNCT
iajs-2289	188	25			PROPN
iajs-2289	188	26	}	}	PUNCT
iajs-2289	188	27	.	.	PUNCT
iajs-2289	189	1	the	the	DET
iajs-2289	189	2	notions	notion	NOUN
iajs-2289	189	3	of	of	ADP
iajs-2289	189	4	almost	almost	ADV
iajs-2289	189	5	j	j	PROPN
iajs-2289	189	6	-	-	PUNCT
iajs-2289	189	7	ω	ω	NOUN
iajs-2289	189	8	-	-	PUNCT
iajs-2289	189	9	convergence	convergence	NOUN
iajs-2289	189	10	and	and	CCONJ
iajs-2289	189	11	almost	almost	ADV
iajs-2289	189	12	j	j	PROPN
iajs-2289	189	13	-	-	PUNCT
iajs-2289	189	14	ω	ω	NOUN
iajs-2289	189	15	-	-	PUNCT
iajs-2289	189	16	cluster	cluster	NOUN
iajs-2289	189	17	can	can	AUX
iajs-2289	189	18	used	use	VERB
iajs-2289	189	19	to	to	PART
iajs-2289	189	20	characterize	characterize	VERB
iajs-2289	189	21	j	j	PROPN
iajs-2289	189	22	-	-	PUNCT
iajs-2289	189	23	ωclosure	ωclosure	NOUN
iajs-2289	189	24	continuous	continuous	ADJ
iajs-2289	189	25	.	.	PUNCT
iajs-2289	190	1	theorem	theorem	ADJ
iajs-2289	190	2	23	23	NUM
iajs-2289	190	3	let	let	VERB
iajs-2289	190	4			ADJ
iajs-2289	190	5	:	:	PUNCT
iajs-2289	190	6	g	g	PROPN
iajs-2289	190	7			NOUN
iajs-2289	190	8	h	h	NOUN
iajs-2289	190	9	be	be	VERB
iajs-2289	190	10	a	a	DET
iajs-2289	190	11	mapping	mapping	NOUN
iajs-2289	190	12	.	.	PUNCT
iajs-2289	191	1	the	the	DET
iajs-2289	191	2	following	follow	VERB
iajs-2289	191	3	are	be	AUX
iajs-2289	191	4	equivalent	equivalent	ADJ
iajs-2289	191	5	:	:	PUNCT
iajs-2289	191	6	(	(	PUNCT
iajs-2289	191	7	a	a	X
iajs-2289	191	8	)	)	PUNCT
iajs-2289	191	9			X
iajs-2289	191	10	is	be	AUX
iajs-2289	191	11	j	j	PROPN
iajs-2289	191	12	-	-	PUNCT
iajs-2289	191	13	ω	ω	VERB
iajs-2289	191	14	-	-	PUNCT
iajs-2289	191	15	closure	closure	NOUN
iajs-2289	191	16	continuous	continuous	ADJ
iajs-2289	191	17	.	.	PUNCT
iajs-2289	192	1	(	(	PUNCT
iajs-2289	192	2	b	b	X
iajs-2289	192	3	)	)	PUNCT
iajs-2289	192	4	for	for	ADP
iajs-2289	192	5	all	all	DET
iajs-2289	192	6	filter	filter	NOUN
iajs-2289	192	7	base	base	NOUN
iajs-2289	192	8			NOUN
iajs-2289	192	9	on	on	ADP
iajs-2289	192	10	g	g	NOUN
iajs-2289	192	11	,	,	PUNCT
iajs-2289	192	12	j	j	PROPN
iajs-2289	192	13	-	-	PUNCT
iajs-2289	192	14	ω	ω	NOUN
iajs-2289	192	15	⇝	⇝	NOUN
iajs-2289	192	16	g	g	PROPN
iajs-2289	192	17	implies	imply	VERB
iajs-2289	192	18			ADJ
iajs-2289	192	19	(	(	PUNCT
iajs-2289	192	20			NOUN
iajs-2289	192	21	)	)	PUNCT
iajs-2289	192	22			NOUN
iajs-2289	192	23			ADJ
iajs-2289	192	24	(	(	PUNCT
iajs-2289	192	25	g	g	NOUN
iajs-2289	192	26	)	)	PUNCT
iajs-2289	192	27	.	.	PUNCT
iajs-2289	193	1	for	for	ADP
iajs-2289	193	2	all	all	DET
iajs-2289	193	3	filter	filter	NOUN
iajs-2289	193	4	base	base	NOUN
iajs-2289	193	5			NOUN
iajs-2289	193	6	on	on	ADP
iajs-2289	193	7	g	g	NOUN
iajs-2289	193	8	,	,	PUNCT
iajs-2289	193	9			X
iajs-2289	193	10	(	(	PUNCT
iajs-2289	193	11	alj	alj	PROPN
iajs-2289	193	12	-	-	PUNCT
iajs-2289	193	13	ω	ω	NOUN
iajs-2289	193	14	-	-	PUNCT
iajs-2289	193	15	c	c	NOUN
iajs-2289	193	16	)	)	PUNCT
iajs-2289	193	17			PROPN
iajs-2289	193	18	(	(	PUNCT
iajs-2289	193	19	alj	alj	PROPN
iajs-2289	193	20	-	-	PUNCT
iajs-2289	193	21	ω	ω	NOUN
iajs-2289	193	22	-	-	PUNCT
iajs-2289	193	23	c	c	NOUN
iajs-2289	193	24			X
iajs-2289	193	25	(	(	PUNCT
iajs-2289	193	26			NOUN
iajs-2289	193	27	)	)	PUNCT
iajs-2289	193	28	.	.	PUNCT
iajs-2289	194	1	for	for	ADP
iajs-2289	194	2	all	all	DET
iajs-2289	194	3	open	open	ADJ
iajs-2289	194	4	s	s	VERB
iajs-2289	194	5			PROPN
iajs-2289	194	6	h	h	NOUN
iajs-2289	194	7	,	,	PUNCT
iajs-2289	194	8	-1	-1	X
iajs-2289	194	9	(	(	PUNCT
iajs-2289	194	10	s	s	NOUN
iajs-2289	194	11	)	)	PUNCT
iajs-2289	194	12			PROPN
iajs-2289	194	13	(	(	PUNCT
iajs-2289	194	14	aljω	aljω	NOUN
iajs-2289	194	15	-	-	PUNCT
iajs-2289	194	16	int–1	int–1	NOUN
iajs-2289	194	17	(	(	PUNCT
iajs-2289	194	18	alj	alj	PROPN
iajs-2289	194	19	-	-	PUNCT
iajs-2289	194	20	ω	ω	NOUN
iajs-2289	194	21	-	-	PUNCT
iajs-2289	194	22	cl(s	cl(s	NOUN
iajs-2289	194	23	)	)	PUNCT
iajs-2289	194	24	)	)	PUNCT
iajs-2289	194	25	)	)	PUNCT
iajs-2289	194	26	.	.	PUNCT
iajs-2289	195	1	where	where	SCONJ
iajs-2289	195	2	j	j	PROPN
iajs-2289	195	3			PROPN
iajs-2289	195	4	{	{	PUNCT
iajs-2289	195	5			PROPN
iajs-2289	195	6	,	,	PUNCT
iajs-2289	195	7	δ	δ	PROPN
iajs-2289	195	8	,	,	PUNCT
iajs-2289	195	9			NOUN
iajs-2289	195	10	,	,	PUNCT
iajs-2289	195	11	pre	pre	ADJ
iajs-2289	195	12	,	,	PUNCT
iajs-2289	195	13	b	b	NOUN
iajs-2289	195	14	,	,	PUNCT
iajs-2289	195	15			NOUN
iajs-2289	195	16	}	}	PUNCT
iajs-2289	195	17	.	.	PUNCT
iajs-2289	196	1	proof	proof	NOUN
iajs-2289	196	2	:	:	PUNCT
iajs-2289	196	3	the	the	DET
iajs-2289	196	4	proof	proof	NOUN
iajs-2289	196	5	of	of	ADP
iajs-2289	196	6	the	the	DET
iajs-2289	196	7	equivalence	equivalence	NOUN
iajs-2289	196	8	of	of	ADP
iajs-2289	196	9	(	(	PUNCT
iajs-2289	196	10	a	a	NOUN
iajs-2289	196	11	)	)	PUNCT
iajs-2289	196	12	,	,	PUNCT
iajs-2289	196	13	(	(	PUNCT
iajs-2289	196	14	b	b	X
iajs-2289	196	15	)	)	PUNCT
iajs-2289	196	16	and	and	CCONJ
iajs-2289	196	17	(	(	PUNCT
iajs-2289	196	18	d	d	X
iajs-2289	196	19	)	)	PUNCT
iajs-2289	196	20	is	be	AUX
iajs-2289	196	21	straightforward	straightforward	ADJ
iajs-2289	196	22	.	.	PUNCT
iajs-2289	197	1	(	(	PUNCT
iajs-2289	197	2	a	a	X
iajs-2289	197	3	)	)	PUNCT
iajs-2289	197	4			NOUN
iajs-2289	197	5	(	(	PUNCT
iajs-2289	197	6	c	c	X
iajs-2289	197	7	)	)	PUNCT
iajs-2289	197	8	suppose	suppose	VERB
iajs-2289	197	9			NOUN
iajs-2289	197	10	is	be	AUX
iajs-2289	197	11	a	a	DET
iajs-2289	197	12	filter	filter	NOUN
iajs-2289	197	13	base	base	NOUN
iajs-2289	197	14	on	on	ADP
iajs-2289	197	15	g	g	PROPN
iajs-2289	197	16	,	,	PUNCT
iajs-2289	197	17	g	g	PROPN
iajs-2289	197	18			PROPN
iajs-2289	197	19	(	(	PUNCT
iajs-2289	197	20	alj	alj	PROPN
iajs-2289	197	21	-	-	PUNCT
iajs-2289	197	22	ω	ω	NOUN
iajs-2289	197	23	-	-	PROPN
iajs-2289	197	24	c	c	PROPN
iajs-2289	197	25	)	)	PUNCT
iajs-2289	197	26	,	,	PUNCT
iajs-2289	197	27	m	m	VERB
iajs-2289	197	28			NOUN
iajs-2289	197	29			NOUN
iajs-2289	197	30	and	and	CCONJ
iajs-2289	197	31	t	t	PROPN
iajs-2289	197	32	is	be	AUX
iajs-2289	197	33	a	a	DET
iajs-2289	197	34	nbd	nbd	PROPN
iajs-2289	197	35	of	of	ADP
iajs-2289	197	36			X
iajs-2289	197	37	(	(	PUNCT
iajs-2289	197	38	g	g	NOUN
iajs-2289	197	39	)	)	PUNCT
iajs-2289	197	40	,	,	PUNCT
iajs-2289	197	41	yond	yond	PROPN
iajs-2289	197	42	is	be	AUX
iajs-2289	197	43	a	a	DET
iajs-2289	197	44	nbd	nbd	PROPN
iajs-2289	197	45	s	s	PROPN
iajs-2289	197	46	of	of	ADP
iajs-2289	197	47	g	g	NOUN
iajs-2289	197	48	such	such	ADJ
iajs-2289	197	49	that	that	PRON
iajs-2289	197	50			ADJ
iajs-2289	197	51	(	(	PUNCT
iajs-2289	197	52	cl	cl	INTJ
iajs-2289	197	53	j	j	NOUN
iajs-2289	197	54	-	-	PUNCT
iajs-2289	197	55	ω(s	ω(s	PROPN
iajs-2289	197	56	)	)	PUNCT
iajs-2289	197	57	)	)	PUNCT
iajs-2289	198	1			PROPN
iajs-2289	198	2	cl	cl	INTJ
iajs-2289	198	3	j	j	NOUN
iajs-2289	198	4	-	-	PUNCT
iajs-2289	198	5	ω-(t	ω-(t	NUM
iajs-2289	198	6	)	)	PUNCT
iajs-2289	198	7	.	.	PUNCT
iajs-2289	199	1	since	since	SCONJ
iajs-2289	199	2	cl	cl	NOUN
iajs-2289	199	3	j	j	PROPN
iajs-2289	199	4	-	-	ADJ
iajs-2289	199	5	ω-(s	ω-(s	NUM
iajs-2289	199	6	)	)	PUNCT
iajs-2289	199	7	∩	∩	NOUN
iajs-2289	199	8	m	m	VERB
iajs-2289	199	9			NOUN
iajs-2289	199	10			NOUN
iajs-2289	199	11	,	,	PUNCT
iajs-2289	199	12	then	then	ADV
iajs-2289	199	13	cl	cl	NOUN
iajs-2289	199	14	jω-(t	jω-(t	NOUN
iajs-2289	199	15	)	)	PUNCT
iajs-2289	199	16	∩	∩	NOUN
iajs-2289	199	17			X
iajs-2289	199	18	(	(	PUNCT
iajs-2289	199	19	m	m	NOUN
iajs-2289	199	20	)	)	PUNCT
iajs-2289	199	21			NOUN
iajs-2289	199	22	.	.	PUNCT
iajs-2289	199	23	so	so	ADV
iajs-2289	199	24	,	,	PUNCT
iajs-2289	199	25			X
iajs-2289	199	26	(	(	PUNCT
iajs-2289	199	27	g	g	NOUN
iajs-2289	199	28	)	)	PUNCT
iajs-2289	199	29			NOUN
iajs-2289	199	30	(	(	PUNCT
iajs-2289	199	31	alj	alj	PROPN
iajs-2289	199	32	-	-	PUNCT
iajs-2289	199	33	ω	ω	PROPN
iajs-2289	199	34	-	-	PUNCT
iajs-2289	199	35	c	c	NOUN
iajs-2289	199	36	(	(	NOUN
iajs-2289	199	37	)	)	PUNCT
iajs-2289	199	38	)	)	PUNCT
iajs-2289	199	39	.	.	PUNCT
iajs-2289	200	1	this	this	PRON
iajs-2289	200	2	shows	show	VERB
iajs-2289	200	3	that	that	SCONJ
iajs-2289	200	4	(alj	(alj	NOUN
iajs-2289	200	5	-	-	PUNCT
iajs-2289	200	6	ω	ω	NOUN
iajs-2289	200	7	-	-	PUNCT
iajs-2289	200	8	c	c	NOUN
iajs-2289	200	9	)	)	PUNCT
iajs-2289	200	10			PROPN
iajs-2289	200	11	(	(	PUNCT
iajs-2289	200	12	alj	alj	PROPN
iajs-2289	200	13	-	-	PUNCT
iajs-2289	200	14	ω	ω	PROPN
iajs-2289	200	15	-	-	PUNCT
iajs-2289	200	16	c	c	NOUN
iajs-2289	200	17	(	(	NOUN
iajs-2289	200	18	)	)	PUNCT
iajs-2289	200	19	)	)	PUNCT
iajs-2289	200	20	.	.	PUNCT
iajs-2289	201	1	(	(	PUNCT
iajs-2289	201	2	c	c	X
iajs-2289	201	3	)	)	PUNCT
iajs-2289	201	4			NOUN
iajs-2289	201	5	(	(	PUNCT
iajs-2289	201	6	a	a	X
iajs-2289	201	7	)	)	PUNCT
iajs-2289	201	8	let	let	VERB
iajs-2289	201	9	s	s	PRON
iajs-2289	201	10	be	be	AUX
iajs-2289	201	11	an	an	DET
iajs-2289	201	12	ultrafilter	ultrafilter	NOUN
iajs-2289	201	13	containing	contain	VERB
iajs-2289	201	14	(cl	(cl	PROPN
iajs-2289	201	15	j	j	PROPN
iajs-2289	201	16	-	-	PUNCT
iajs-2289	201	17	ω-(g	ω-(g	PROPN
iajs-2289	201	18	)	)	PUNCT
iajs-2289	201	19	)	)	PUNCT
iajs-2289	201	20	.	.	PUNCT
iajs-2289	202	1	now	now	ADV
iajs-2289	202	2	,	,	PUNCT
iajs-2289	202	3	–1	–1	PROPN
iajs-2289	202	4	(	(	PUNCT
iajs-2289	202	5	s	s	X
iajs-2289	202	6	)	)	PUNCT
iajs-2289	202	7	is	be	AUX
iajs-2289	202	8	a	a	DET
iajs-2289	202	9	filter	filter	NOUN
iajs-2289	202	10	base	base	NOUN
iajs-2289	202	11	since	since	SCONJ
iajs-2289	202	12	(g	(g	PROPN
iajs-2289	202	13	)	)	PUNCT
iajs-2289	202	14			NOUN
iajs-2289	202	15	s	s	PART
iajs-2289	202	16	and	and	CCONJ
iajs-2289	202	17	–1	–1	PROPN
iajs-2289	202	18	(	(	PUNCT
iajs-2289	202	19	s	s	NOUN
iajs-2289	202	20	)	)	PUNCT
iajs-2289	202	21	meets	meet	VERB
iajs-2289	202	22	cl	cl	NOUN
iajs-2289	202	23	j	j	PROPN
iajs-2289	202	24	-	-	PROPN
iajs-2289	202	25	ω-(g	ω-(g	PROPN
iajs-2289	202	26	)	)	PUNCT
iajs-2289	202	27	.	.	PUNCT
iajs-2289	203	1	so	so	ADV
iajs-2289	203	2	,	,	PUNCT
iajs-2289	203	3	–1	–1	PROPN
iajs-2289	203	4	(	(	PUNCT
iajs-2289	203	5	s	s	NOUN
iajs-2289	203	6	)	)	PUNCT
iajs-2289	203	7			NOUN
iajs-2289	203	8	cl	cl	INTJ
iajs-2289	203	9	j	j	PROPN
iajs-2289	203	10	-	-	PUNCT
iajs-2289	203	11	ω-(g	ω-(g	PROPN
iajs-2289	203	12	)	)	PUNCT
iajs-2289	203	13	is	be	AUX
iajs-2289	203	14	contained	contain	VERB
iajs-2289	203	15	in	in	ADP
iajs-2289	203	16	some	some	DET
iajs-2289	203	17	ultrafilter	ultrafilter	NOUN
iajs-2289	203	18	t.	t.	NOUN
iajs-2289	203	19	now	now	ADV
iajs-2289	203	20	–1	–1	PROPN
iajs-2289	203	21	(	(	PUNCT
iajs-2289	203	22	s	s	X
iajs-2289	203	23	)	)	PUNCT
iajs-2289	203	24	is	be	AUX
iajs-2289	203	25	an	an	DET
iajs-2289	203	26	ultrafilter	ultrafilter	ADJ
iajs-2289	203	27	base	base	NOUN
iajs-2289	203	28	that	that	PRON
iajs-2289	203	29	generates	generate	VERB
iajs-2289	203	30	s.	s.	PROPN
iajs-2289	203	31	since	since	SCONJ
iajs-2289	203	32	–1	–1	PROPN
iajs-2289	203	33	(	(	PUNCT
iajs-2289	203	34	s	s	NOUN
iajs-2289	203	35	)	)	PUNCT
iajs-2289	203	36	<	<	X
iajs-2289	203	37	(t	(t	PROPN
iajs-2289	203	38	)	)	PUNCT
iajs-2289	203	39	,	,	PUNCT
iajs-2289	203	40	then	then	ADV
iajs-2289	203	41	(t	(t	NUM
iajs-2289	203	42	)	)	PUNCT
iajs-2289	203	43	also	also	ADV
iajs-2289	203	44	generates	generate	VERB
iajs-2289	203	45	s	s	NOUN
iajs-2289	203	46	;	;	PUNCT
iajs-2289	203	47	hence	hence	ADV
iajs-2289	203	48	(	(	PUNCT
iajs-2289	203	49	alj	alj	PROPN
iajs-2289	203	50	-	-	PUNCT
iajs-2289	203	51	ω	ω	NOUN
iajs-2289	203	52	-	-	PUNCT
iajs-2289	203	53	c(t	c(t	PROPN
iajs-2289	203	54	)	)	PUNCT
iajs-2289	203	55	)	)	PUNCT
iajs-2289	204	1	=	=	PRON
iajs-2289	204	2	(	(	PUNCT
iajs-2289	204	3	alj	alj	PROPN
iajs-2289	204	4	-	-	PUNCT
iajs-2289	204	5	ω	ω	NOUN
iajs-2289	204	6	-	-	PUNCT
iajs-2289	204	7	c	c	NOUN
iajs-2289	204	8	s	s	PART
iajs-2289	204	9	)	)	PUNCT
iajs-2289	204	10	.	.	PUNCT
iajs-2289	205	1	since	since	SCONJ
iajs-2289	205	2	g	g	PROPN
iajs-2289	205	3			PROPN
iajs-2289	205	4	(	(	PUNCT
iajs-2289	205	5	alj	alj	PROPN
iajs-2289	205	6	-	-	PUNCT
iajs-2289	205	7	ω	ω	NOUN
iajs-2289	205	8	-	-	PUNCT
iajs-2289	205	9	c(t	c(t	PROPN
iajs-2289	205	10	)	)	PUNCT
iajs-2289	205	11	)	)	PUNCT
iajs-2289	205	12	,	,	PUNCT
iajs-2289	205	13	then	then	ADV
iajs-2289	205	14	(g	(g	NUM
iajs-2289	205	15	)	)	PUNCT
iajs-2289	205	16			NOUN
iajs-2289	205	17	(al	(al	PROPN
iajs-2289	205	18	j	j	PROPN
iajs-2289	205	19	-	-	PUNCT
iajs-2289	205	20	ω	ω	PROPN
iajs-2289	205	21	-	-	PUNCT
iajs-2289	205	22	c	c	PROPN
iajs-2289	205	23	t	t	PROPN
iajs-2289	205	24	)	)	PUNCT
iajs-2289	205	25			PROPN
iajs-2289	205	26	(	(	PUNCT
iajs-2289	205	27	alj	alj	PROPN
iajs-2289	205	28	-	-	PUNCT
iajs-2289	205	29	ω	ω	NOUN
iajs-2289	205	30	-	-	PUNCT
iajs-2289	205	31	c	c	PROPN
iajs-2289	205	32	(t	(t	PROPN
iajs-2289	205	33	)	)	PUNCT
iajs-2289	205	34	)	)	PUNCT
iajs-2289	206	1	=	=	PRON
iajs-2289	206	2	(	(	PUNCT
iajs-2289	206	3	alj	alj	PROPN
iajs-2289	206	4	-	-	PUNCT
iajs-2289	206	5	ω	ω	NOUN
iajs-2289	206	6	-	-	PUNCT
iajs-2289	206	7	c	c	NOUN
iajs-2289	206	8	s	s	PART
iajs-2289	206	9	)	)	PUNCT
iajs-2289	206	10	.	.	PUNCT
iajs-2289	207	1	so	so	ADV
iajs-2289	207	2	,	,	PUNCT
iajs-2289	207	3	s	s	NOUN
iajs-2289	207	4	meets	meet	VERB
iajs-2289	207	5	cl	cl	X
iajs-2289	207	6	j	j	PROPN
iajs-2289	207	7	-	-	PROPN
iajs-2289	207	8	ω((g	ω((g	PROPN
iajs-2289	207	9	)	)	PUNCT
iajs-2289	207	10	)	)	PUNCT
iajs-2289	207	11	and	and	CCONJ
iajs-2289	207	12	cl	cl	NOUN
iajs-2289	207	13	j	j	PROPN
iajs-2289	207	14	-	-	PROPN
iajs-2289	207	15	ω((g	ω((g	PROPN
iajs-2289	207	16	)	)	PUNCT
iajs-2289	207	17	)	)	PUNCT
iajs-2289	208	1			PROPN
iajs-2289	208	2	∩	∩	PROPN
iajs-2289	208	3	{	{	PUNCT
iajs-2289	208	4	s	s	PART
iajs-2289	208	5	:	:	PUNCT
iajs-2289	208	6	s	s	NOUN
iajs-2289	208	7	ultrafilter	ultrafilter	NOUN
iajs-2289	208	8	,	,	PUNCT
iajs-2289	208	9	s	s	NOUN
iajs-2289	208	10			PROPN
iajs-2289	208	11	(cl	(cl	PROPN
iajs-2289	208	12	j	j	PROPN
iajs-2289	208	13	-	-	PUNCT
iajs-2289	208	14	ω-(g	ω-(g	PROPN
iajs-2289	208	15	)	)	PUNCT
iajs-2289	208	16	)	)	PUNCT
iajs-2289	208	17	}	}	PUNCT
iajs-2289	208	18	,	,	PUNCT
iajs-2289	208	19	(	(	PUNCT
iajs-2289	208	20	denote	denote	VERB
iajs-2289	208	21	this	this	DET
iajs-2289	208	22	intersection	intersection	NOUN
iajs-2289	208	23	by	by	ADP
iajs-2289	208	24			PROPN
iajs-2289	208	25	)	)	PUNCT
iajs-2289	208	26	.	.	PUNCT
iajs-2289	209	1	nevertheless	nevertheless	ADV
iajs-2289	209	2	,	,	PUNCT
iajs-2289	209	3			PROPN
iajs-2289	209	4	is	be	AUX
iajs-2289	209	5	the	the	DET
iajs-2289	209	6	filter	filter	NOUN
iajs-2289	209	7	generated	generate	VERB
iajs-2289	209	8	by	by	ADP
iajs-2289	209	9	(	(	PUNCT
iajs-2289	209	10	cl	cl	INTJ
iajs-2289	209	11	j	j	PROPN
iajs-2289	209	12	-	-	PUNCT
iajs-2289	209	13	ω-(g	ω-(g	PROPN
iajs-2289	209	14	)	)	PUNCT
iajs-2289	209	15	)	)	PUNCT
iajs-2289	209	16	(	(	PUNCT
iajs-2289	209	17	see	see	VERB
iajs-2289	209	18	[	[	X
iajs-2289	209	19	4	4	NUM
iajs-2289	209	20	]	]	PUNCT
iajs-2289	209	21	.	.	PUNCT
iajs-2289	210	1	proposition	proposition	NOUN
iajs-2289	210	2	i.6.6	i.6.6	ADJ
iajs-2289	210	3	)	)	PUNCT
iajs-2289	210	4	,	,	PUNCT
iajs-2289	211	1	so	so	SCONJ
iajs-2289	211	2	clj	clj	NOUN
iajs-2289	211	3	-	-	PUNCT
iajs-2289	211	4	ω	ω	PROPN
iajs-2289	211	5	(	(	PUNCT
iajs-2289	211	6	(g	(g	NOUN
iajs-2289	211	7	)	)	PUNCT
iajs-2289	211	8	)	)	PUNCT
iajs-2289	211	9	<	<	X
iajs-2289	212	1	(cl	(cl	PROPN
iajs-2289	212	2	j	j	PROPN
iajs-2289	212	3	-	-	PUNCT
iajs-2289	212	4	ω	ω	PROPN
iajs-2289	212	5	(	(	PUNCT
iajs-2289	212	6	g	g	PROPN
iajs-2289	212	7	)	)	PUNCT
iajs-2289	212	8	)	)	PUNCT
iajs-2289	212	9	.	.	PUNCT
iajs-2289	213	1	hence	hence	ADV
iajs-2289	213	2			PROPN
iajs-2289	213	3	is	be	AUX
iajs-2289	213	4	j	j	PROPN
iajs-2289	213	5	-	-	PUNCT
iajs-2289	213	6	ω	ω	NOUN
iajs-2289	213	7	-	-	PUNCT
iajs-2289	213	8	closure	closure	NOUN
iajs-2289	213	9	continuous	continuous	ADJ
iajs-2289	213	10	,	,	PUNCT
iajs-2289	213	11	where	where	SCONJ
iajs-2289	213	12	j{	j{	PROPN
iajs-2289	213	13	,	,	PUNCT
iajs-2289	213	14	δ	δ	PROPN
iajs-2289	213	15	,	,	PUNCT
iajs-2289	213	16			NOUN
iajs-2289	213	17	,	,	PUNCT
iajs-2289	213	18	pre	pre	AUX
iajs-2289	213	19	,	,	PUNCT
iajs-2289	213	20	b	b	NOUN
iajs-2289	213	21	,	,	PUNCT
iajs-2289	213	22			NOUN
iajs-2289	213	23	}	}	PUNCT
iajs-2289	213	24	.	.	PUNCT
iajs-2289	214	1	corollary	corollary	ADJ
iajs-2289	214	2	24	24	NUM
iajs-2289	214	3	if	if	SCONJ
iajs-2289	214	4			VERB
iajs-2289	214	5	:	:	PUNCT
iajs-2289	214	6	g	g	NOUN
iajs-2289	214	7			NOUN
iajs-2289	215	1	h	h	NOUN
iajs-2289	215	2	is	be	AUX
iajs-2289	215	3	j	j	PROPN
iajs-2289	215	4	-	-	PUNCT
iajs-2289	215	5	ω	ω	NOUN
iajs-2289	215	6	-	-	PUNCT
iajs-2289	215	7	closure	closure	NOUN
iajs-2289	215	8	continuous	continuous	ADJ
iajs-2289	215	9	and	and	CCONJ
iajs-2289	215	10	k	k	PROPN
iajs-2289	215	11			PROPN
iajs-2289	215	12	g	g	PROPN
iajs-2289	215	13	,	,	PUNCT
iajs-2289	215	14	then	then	ADV
iajs-2289	215	15	(alj	(alj	PROPN
iajs-2289	215	16	-	-	PUNCT
iajs-2289	215	17	ω	ω	NOUN
iajs-2289	215	18	-	-	NOUN
iajs-2289	215	19	cl(k	cl(k	NOUN
iajs-2289	215	20	)	)	PUNCT
iajs-2289	215	21	)	)	PUNCT
iajs-2289	216	1			PROPN
iajs-2289	216	2	(	(	PUNCT
iajs-2289	216	3	alj	alj	NOUN
iajs-2289	216	4	-	-	NOUN
iajs-2289	216	5	ωcl((k	ωcl((k	NUM
iajs-2289	216	6	)	)	PUNCT
iajs-2289	216	7	)	)	PUNCT
iajs-2289	216	8	,	,	PUNCT
iajs-2289	216	9	where	where	SCONJ
iajs-2289	216	10	j{	j{	PROPN
iajs-2289	216	11	,	,	PUNCT
iajs-2289	216	12	δ	δ	PROPN
iajs-2289	216	13	,	,	PUNCT
iajs-2289	216	14			NOUN
iajs-2289	216	15	,	,	PUNCT
iajs-2289	216	16	pre	pre	AUX
iajs-2289	216	17	,	,	PUNCT
iajs-2289	216	18	b	b	AUX
iajs-2289	216	19	,	,	PUNCT
iajs-2289	216	20			NOUN
iajs-2289	216	21	}	}	PUNCT
iajs-2289	216	22	.	.	PUNCT
iajs-2289	217	1	here	here	ADV
iajs-2289	217	2	are	be	AUX
iajs-2289	217	3	some	some	DET
iajs-2289	217	4	similarly	similarly	ADV
iajs-2289	217	5	proven	prove	VERB
iajs-2289	217	6	facts	fact	NOUN
iajs-2289	217	7	about	about	ADP
iajs-2289	217	8	j	j	PROPN
iajs-2289	217	9	-	-	PUNCT
iajs-2289	217	10	ω	ω	VERB
iajs-2289	217	11	-	-	ADJ
iajs-2289	217	12	weakly	weakly	ADJ
iajs-2289	217	13	continuous	continuous	ADJ
iajs-2289	217	14	mapping	mapping	NOUN
iajs-2289	217	15	.	.	PUNCT
iajs-2289	218	1	theorem	theorem	ADJ
iajs-2289	218	2	25	25	NUM
iajs-2289	218	3	let	let	VERB
iajs-2289	218	4			X
iajs-2289	218	5	:	:	PUNCT
iajs-2289	218	6	g	g	PROPN
iajs-2289	218	7			NOUN
iajs-2289	218	8	h	h	NOUN
iajs-2289	218	9	be	be	VERB
iajs-2289	218	10	a	a	DET
iajs-2289	218	11	mapping	mapping	NOUN
iajs-2289	218	12	.	.	PUNCT
iajs-2289	219	1	the	the	DET
iajs-2289	219	2	following	follow	VERB
iajs-2289	219	3	are	be	AUX
iajs-2289	219	4	equivalent	equivalent	ADJ
iajs-2289	219	5	:	:	PUNCT
iajs-2289	219	6	(	(	PUNCT
iajs-2289	219	7	a	a	X
iajs-2289	219	8	)	)	PUNCT
iajs-2289	219	9			X
iajs-2289	219	10	is	be	AUX
iajs-2289	219	11	j	j	PROPN
iajs-2289	219	12	-	-	PUNCT
iajs-2289	219	13	ω	ω	VERB
iajs-2289	219	14	-	-	ADJ
iajs-2289	219	15	weakly	weakly	ADJ
iajs-2289	219	16	continuous	continuous	ADJ
iajs-2289	219	17	.	.	PUNCT
iajs-2289	220	1	(	(	PUNCT
iajs-2289	220	2	b	b	X
iajs-2289	220	3	)	)	PUNCT
iajs-2289	220	4	for	for	ADP
iajs-2289	220	5	all	all	DET
iajs-2289	220	6	filter	filter	NOUN
iajs-2289	220	7	base	base	NOUN
iajs-2289	220	8			NOUN
iajs-2289	220	9	on	on	ADP
iajs-2289	220	10	g	g	NOUN
iajs-2289	220	11	,	,	PUNCT
iajs-2289	220	12			NOUN
iajs-2289	220	13			PRON
iajs-2289	220	14	g	g	NOUN
iajs-2289	220	15	implies	imply	VERB
iajs-2289	220	16	(	(	NOUN
iajs-2289	220	17	)	)	PUNCT
iajs-2289	220	18	j	j	PROPN
iajs-2289	220	19	-	-	PUNCT
iajs-2289	220	20	ω	ω	PROPN
iajs-2289	220	21	⇝	⇝	NOUN
iajs-2289	220	22	(g	(g	NUM
iajs-2289	220	23	)	)	PUNCT
iajs-2289	220	24	.	.	PUNCT
iajs-2289	221	1	(	(	PUNCT
iajs-2289	221	2	c	c	X
iajs-2289	221	3	)	)	PUNCT
iajs-2289	221	4	for	for	ADP
iajs-2289	221	5	all	all	DET
iajs-2289	221	6	filter	filter	NOUN
iajs-2289	221	7	base	base	NOUN
iajs-2289	221	8			NOUN
iajs-2289	221	9	on	on	ADP
iajs-2289	221	10	g	g	NOUN
iajs-2289	221	11	,	,	PUNCT
iajs-2289	221	12	(alj	(alj	PROPN
iajs-2289	221	13	-	-	PUNCT
iajs-2289	221	14	ω	ω	NOUN
iajs-2289	221	15	-	-	PUNCT
iajs-2289	221	16	c	c	NOUN
iajs-2289	221	17	)	)	PUNCT
iajs-2289	221	18			PROPN
iajs-2289	221	19	(	(	PUNCT
iajs-2289	221	20	alj	alj	PROPN
iajs-2289	221	21	-	-	PUNCT
iajs-2289	221	22	ω	ω	NOUN
iajs-2289	221	23	-	-	PUNCT
iajs-2289	221	24	c	c	NOUN
iajs-2289	221	25			X
iajs-2289	221	26	(	(	PUNCT
iajs-2289	221	27			NOUN
iajs-2289	221	28	)	)	PUNCT
iajs-2289	221	29	)	)	PUNCT
iajs-2289	221	30	.	.	PUNCT
iajs-2289	222	1	(	(	PUNCT
iajs-2289	222	2	d	d	X
iajs-2289	222	3	)	)	PUNCT
iajs-2289	222	4	for	for	ADP
iajs-2289	222	5	all	all	DET
iajs-2289	222	6	open	open	ADJ
iajs-2289	222	7	s	s	VERB
iajs-2289	222	8			PROPN
iajs-2289	222	9	h	h	NOUN
iajs-2289	222	10	,	,	PUNCT
iajs-2289	222	11	–1	–1	PROPN
iajs-2289	222	12	(	(	PUNCT
iajs-2289	222	13	s	s	NOUN
iajs-2289	222	14	)	)	PUNCT
iajs-2289	222	15			PROPN
iajs-2289	222	16	int	int	PROPN
iajs-2289	222	17			X
iajs-2289	222	18	–	–	PUNCT
iajs-2289	222	19	1	1	NUM
iajs-2289	222	20	(	(	PUNCT
iajs-2289	222	21	cl	cl	NOUN
iajs-2289	222	22	j	j	NOUN
iajs-2289	222	23	-	-	PROPN
iajs-2289	222	24	ω-(s	ω-(s	NUM
iajs-2289	222	25	)	)	PUNCT
iajs-2289	222	26	)	)	PUNCT
iajs-2289	222	27	.	.	PUNCT
iajs-2289	223	1	where	where	SCONJ
iajs-2289	223	2	j	j	PROPN
iajs-2289	223	3	{	{	PROPN
iajs-2289	223	4	,	,	PUNCT
iajs-2289	223	5	δ	δ	PROPN
iajs-2289	223	6	,	,	PUNCT
iajs-2289	223	7			NOUN
iajs-2289	223	8	,	,	PUNCT
iajs-2289	223	9	pre	pre	AUX
iajs-2289	223	10	,	,	PUNCT
iajs-2289	223	11	b	b	NOUN
iajs-2289	223	12	,	,	PUNCT
iajs-2289	223	13			PROPN
iajs-2289	223	14	}	}	PUNCT
iajs-2289	223	15	.	.	PUNCT
iajs-2289	224	1	172	172	NUM
iajs-2289	224	2	ibn	ibn	PROPN
iajs-2289	224	3	al	al	PROPN
iajs-2289	224	4	-	-	PUNCT
iajs-2289	224	5	haitham	haitham	PROPN
iajs-2289	224	6	jour	jour	X
iajs-2289	224	7	.	.	PROPN
iajs-2289	224	8	for	for	ADP
iajs-2289	224	9	pure	pure	ADJ
iajs-2289	224	10	&	&	CCONJ
iajs-2289	224	11	appl	appl	PROPN
iajs-2289	224	12	.	.	PUNCT
iajs-2289	225	1	sci	sci	PROPN
iajs-2289	225	2	.	.	PROPN
iajs-2289	225	3	32	32	NUM
iajs-2289	225	4	(	(	PUNCT
iajs-2289	225	5	3	3	NUM
iajs-2289	225	6	)	)	PUNCT
iajs-2289	225	7	2019	2019	NUM
iajs-2289	225	8	theorem	theorem	VERB
iajs-2289	225	9	26	26	NUM
iajs-2289	225	10	if	if	SCONJ
iajs-2289	225	11			ADJ
iajs-2289	225	12	:	:	PUNCT
iajs-2289	225	13	g	g	PROPN
iajs-2289	225	14			NOUN
iajs-2289	225	15	h	h	NOUN
iajs-2289	225	16	is	be	AUX
iajs-2289	225	17	j	j	PROPN
iajs-2289	225	18	-	-	PUNCT
iajs-2289	225	19	ω	ω	VERB
iajs-2289	225	20	-	-	ADJ
iajs-2289	225	21	weakly	weakly	ADJ
iajs-2289	225	22	continuous	continuous	ADJ
iajs-2289	225	23	mapping	mapping	NOUN
iajs-2289	225	24	,	,	PUNCT
iajs-2289	225	25	then	then	ADV
iajs-2289	225	26	(	(	PUNCT
iajs-2289	225	27	a	a	X
iajs-2289	225	28	)	)	PUNCT
iajs-2289	225	29	for	for	ADP
iajs-2289	225	30	all	all	PRON
iajs-2289	225	31	k	k	PROPN
iajs-2289	225	32			PROPN
iajs-2289	225	33	g	g	PROPN
iajs-2289	225	34	,	,	PUNCT
iajs-2289	225	35	(cl	(cl	PROPN
iajs-2289	225	36	j	j	PROPN
iajs-2289	225	37	-	-	PUNCT
iajs-2289	225	38	ω-(k	ω-(k	NOUN
iajs-2289	225	39	)	)	PUNCT
iajs-2289	225	40	)	)	PUNCT
iajs-2289	226	1			PROPN
iajs-2289	226	2	(	(	PUNCT
iajs-2289	226	3	alj	alj	PROPN
iajs-2289	226	4	-	-	PUNCT
iajs-2289	226	5	ω	ω	NOUN
iajs-2289	226	6	-	-	PUNCT
iajs-2289	226	7	cl	cl	NOUN
iajs-2289	226	8	(k	(k	NOUN
iajs-2289	226	9	)	)	PUNCT
iajs-2289	226	10	)	)	PUNCT
iajs-2289	226	11	.	.	PUNCT
iajs-2289	227	1	(	(	PUNCT
iajs-2289	227	2	b	b	X
iajs-2289	227	3	)	)	PUNCT
iajs-2289	227	4	for	for	ADP
iajs-2289	227	5	all	all	DET
iajs-2289	227	6	l	l	NOUN
iajs-2289	227	7			PROPN
iajs-2289	227	8	h	h	NOUN
iajs-2289	227	9	,	,	PUNCT
iajs-2289	227	10	(cl	(cl	PROPN
iajs-2289	227	11	j	j	PROPN
iajs-2289	227	12	-	-	PUNCT
iajs-2289	227	13	ω-(int(cl	ω-(int(cl	PROPN
iajs-2289	227	14	j	j	PROPN
iajs-2289	227	15	-	-	PUNCT
iajs-2289	227	16	ω-	ω-	PROPN
iajs-2289	227	17	–	–	PUNCT
iajs-2289	227	18	1	1	NUM
iajs-2289	227	19	(	(	PUNCT
iajs-2289	227	20	l	l	NOUN
iajs-2289	227	21	)	)	PUNCT
iajs-2289	227	22	)	)	PUNCT
iajs-2289	227	23	)	)	PUNCT
iajs-2289	227	24	)	)	PUNCT
iajs-2289	228	1			PROPN
iajs-2289	228	2	cl	cl	INTJ
iajs-2289	228	3	j	j	NOUN
iajs-2289	228	4	-	-	NOUN
iajs-2289	228	5	ω-(l	ω-(l	NOUN
iajs-2289	228	6	)	)	PUNCT
iajs-2289	228	7	.	.	PUNCT
iajs-2289	229	1	(	(	PUNCT
iajs-2289	229	2	c	c	X
iajs-2289	229	3	)	)	PUNCT
iajs-2289	229	4	for	for	ADP
iajs-2289	229	5	all	all	DET
iajs-2289	229	6	open	open	ADJ
iajs-2289	229	7	s	s	VERB
iajs-2289	229	8			PROPN
iajs-2289	229	9	h	h	NOUN
iajs-2289	229	10	,	,	PUNCT
iajs-2289	229	11			X
iajs-2289	229	12	(	(	PUNCT
iajs-2289	229	13	cl	cl	INTJ
iajs-2289	229	14	j	j	NOUN
iajs-2289	229	15	-	-	PROPN
iajs-2289	229	16	ω-(s	ω-(s	NUM
iajs-2289	229	17	)	)	PUNCT
iajs-2289	229	18	)	)	PUNCT
iajs-2289	230	1			PROPN
iajs-2289	230	2	cl	cl	INTJ
iajs-2289	230	3	j	j	NOUN
iajs-2289	230	4	-	-	NOUN
iajs-2289	230	5	ω-(s	ω-(s	NOUN
iajs-2289	230	6	)	)	PUNCT
iajs-2289	230	7	.	.	PUNCT
iajs-2289	231	1	where	where	SCONJ
iajs-2289	231	2	j	j	PROPN
iajs-2289	231	3			NOUN
iajs-2289	231	4	{	{	PUNCT
iajs-2289	231	5			PROPN
iajs-2289	231	6	,	,	PUNCT
iajs-2289	231	7	δ	δ	PROPN
iajs-2289	231	8	,	,	PUNCT
iajs-2289	231	9			NOUN
iajs-2289	231	10	,	,	PUNCT
iajs-2289	231	11	pre	pre	ADJ
iajs-2289	231	12	,	,	PUNCT
iajs-2289	231	13	b	b	NOUN
iajs-2289	231	14	,	,	PUNCT
iajs-2289	231	15			NOUN
iajs-2289	231	16	}	}	PUNCT
iajs-2289	231	17	.	.	PUNCT
iajs-2289	232	1	now	now	ADV
iajs-2289	232	2	,	,	PUNCT
iajs-2289	232	3	we	we	PRON
iajs-2289	232	4	introduce	introduce	VERB
iajs-2289	232	5	the	the	DET
iajs-2289	232	6	definitions	definition	NOUN
iajs-2289	232	7	of	of	ADP
iajs-2289	232	8	j	j	PROPN
iajs-2289	232	9	-	-	PUNCT
iajs-2289	232	10	ω	ω	NOUN
iajs-2289	232	11	-	-	ADJ
iajs-2289	232	12	compact	compact	ADJ
iajs-2289	232	13	,	,	PUNCT
iajs-2289	232	14	j	j	PROPN
iajs-2289	232	15	-	-	PUNCT
iajs-2289	232	16	ω	ω	VERB
iajs-2289	232	17	-	-	ADJ
iajs-2289	232	18	rigid	rigid	ADJ
iajs-2289	232	19	set	set	NOUN
iajs-2289	232	20	,	,	PUNCT
iajs-2289	232	21	almost	almost	ADV
iajs-2289	232	22	j	j	PROPN
iajs-2289	232	23	-	-	PUNCT
iajs-2289	232	24	ω	ω	NOUN
iajs-2289	232	25	-	-	PUNCT
iajs-2289	232	26	closed	closed	ADJ
iajs-2289	232	27	,	,	PUNCT
iajs-2289	232	28	and	and	CCONJ
iajs-2289	232	29	jω	jω	ADJ
iajs-2289	232	30	-	-	ADJ
iajs-2289	232	31	urysohn	urysohn	ADJ
iajs-2289	232	32	space	space	NOUN
iajs-2289	232	33	as	as	SCONJ
iajs-2289	232	34	follows	follow	VERB
iajs-2289	232	35	.	.	PUNCT
iajs-2289	233	1	definition	definition	NOUN
iajs-2289	233	2	27	27	NUM
iajs-2289	233	3	a	a	DET
iajs-2289	233	4	mapping	mapping	NOUN
iajs-2289	233	5			ADJ
iajs-2289	233	6	:	:	PUNCT
iajs-2289	233	7	g	g	PROPN
iajs-2289	233	8			NOUN
iajs-2289	233	9	h	h	NOUN
iajs-2289	233	10	is	be	AUX
iajs-2289	233	11	said	say	VERB
iajs-2289	233	12	to	to	PART
iajs-2289	233	13	be	be	AUX
iajs-2289	233	14	j	j	NOUN
iajs-2289	233	15	-	-	ADJ
iajs-2289	233	16	ωcompact	ωcompact	ADJ
iajs-2289	233	17	if	if	SCONJ
iajs-2289	233	18	for	for	ADP
iajs-2289	233	19	every	every	DET
iajs-2289	233	20	subset	subset	NOUN
iajs-2289	233	21	c	c	PROPN
iajs-2289	233	22	quasij	quasij	PROPN
iajs-2289	233	23	-	-	PUNCT
iajs-2289	233	24	ω	ω	VERB
iajs-2289	233	25	-	-	PUNCT
iajs-2289	233	26	h	h	NOUN
iajs-2289	233	27	-	-	PUNCT
iajs-2289	233	28	closed	closed	ADJ
iajs-2289	233	29	relative	relative	ADJ
iajs-2289	233	30	to	to	ADP
iajs-2289	233	31	h	h	NOUN
iajs-2289	233	32	,	,	PUNCT
iajs-2289	233	33	–1	–1	PROPN
iajs-2289	233	34	(	(	PUNCT
iajs-2289	233	35	c	c	X
iajs-2289	233	36	)	)	PUNCT
iajs-2289	233	37	is	be	AUX
iajs-2289	233	38	quasij	quasij	NOUN
iajs-2289	233	39	-	-	PUNCT
iajs-2289	233	40	ω	ω	NUM
iajs-2289	233	41	-	-	PUNCT
iajs-2289	233	42	h	h	NOUN
iajs-2289	233	43	-	-	PUNCT
iajs-2289	233	44	closed	closed	ADJ
iajs-2289	233	45	relative	relative	ADJ
iajs-2289	233	46	to	to	ADP
iajs-2289	233	47	g	g	NOUN
iajs-2289	233	48	,	,	PUNCT
iajs-2289	233	49	where	where	SCONJ
iajs-2289	233	50	j	j	PROPN
iajs-2289	233	51			NOUN
iajs-2289	233	52	{	{	PUNCT
iajs-2289	233	53			PROPN
iajs-2289	233	54	,	,	PUNCT
iajs-2289	233	55	δ	δ	PROPN
iajs-2289	233	56	,	,	PUNCT
iajs-2289	233	57			NOUN
iajs-2289	233	58	,	,	PUNCT
iajs-2289	233	59	pre	pre	ADJ
iajs-2289	233	60	,	,	PUNCT
iajs-2289	233	61	b	b	NOUN
iajs-2289	233	62	,	,	PUNCT
iajs-2289	233	63			NOUN
iajs-2289	233	64	}	}	PUNCT
iajs-2289	233	65	.	.	PUNCT
iajs-2289	234	1	definition	definition	NOUN
iajs-2289	234	2	28	28	NUM
iajs-2289	234	3	a	a	DET
iajs-2289	234	4	subset	subset	NOUN
iajs-2289	234	5	k	k	PROPN
iajs-2289	234	6	of	of	ADP
iajs-2289	234	7	a	a	DET
iajs-2289	234	8	space	space	NOUN
iajs-2289	234	9	g	g	NOUN
iajs-2289	234	10	is	be	AUX
iajs-2289	234	11	said	say	VERB
iajs-2289	234	12	to	to	PART
iajs-2289	234	13	be	be	AUX
iajs-2289	234	14	j	j	PROPN
iajs-2289	234	15	-	-	PUNCT
iajs-2289	234	16	ω	ω	VERB
iajs-2289	234	17	-	-	ADJ
iajs-2289	234	18	rigid	rigid	ADJ
iajs-2289	234	19	provided	provide	VERB
iajs-2289	234	20	whenever	whenever	SCONJ
iajs-2289	234	21			NOUN
iajs-2289	234	22	is	be	AUX
iajs-2289	234	23	a	a	DET
iajs-2289	234	24	filter	filter	NOUN
iajs-2289	234	25	base	base	NOUN
iajs-2289	234	26	on	on	ADP
iajs-2289	234	27	g	g	PROPN
iajs-2289	234	28	and	and	CCONJ
iajs-2289	234	29	k	k	PROPN
iajs-2289	234	30	∩	∩	NOUN
iajs-2289	234	31	(	(	PUNCT
iajs-2289	234	32	alj	alj	PROPN
iajs-2289	234	33	-	-	PUNCT
iajs-2289	234	34	ω	ω	NOUN
iajs-2289	234	35	-	-	NOUN
iajs-2289	234	36	cg	cg	NOUN
iajs-2289	234	37	)	)	PUNCT
iajs-2289	234	38	=	=	SYM
iajs-2289	234	39			NOUN
iajs-2289	234	40	,	,	PUNCT
iajs-2289	234	41	there	there	PRON
iajs-2289	234	42	is	be	VERB
iajs-2289	234	43	an	an	DET
iajs-2289	234	44	open	open	NOUN
iajs-2289	234	45	s	s	AUX
iajs-2289	234	46	containing	contain	VERB
iajs-2289	234	47	k	k	PROPN
iajs-2289	234	48	and	and	CCONJ
iajs-2289	234	49	m	m	PROPN
iajs-2289	234	50			NOUN
iajs-2289	234	51			NOUN
iajs-2289	234	52	such	such	ADJ
iajs-2289	234	53	that	that	DET
iajs-2289	234	54	cl	cl	NOUN
iajs-2289	234	55	j	j	NOUN
iajs-2289	234	56	-	-	ADJ
iajs-2289	234	57	ω-(s	ω-(s	NUM
iajs-2289	234	58	)	)	PUNCT
iajs-2289	234	59	∩	∩	NOUN
iajs-2289	234	60	m	m	NOUN
iajs-2289	234	61	=	=	SYM
iajs-2289	234	62			NOUN
iajs-2289	234	63	,	,	PUNCT
iajs-2289	234	64	where	where	SCONJ
iajs-2289	234	65	j	j	PROPN
iajs-2289	234	66	{	{	PUNCT
iajs-2289	234	67			PROPN
iajs-2289	234	68	,	,	PUNCT
iajs-2289	234	69	δ	δ	PROPN
iajs-2289	234	70	,	,	PUNCT
iajs-2289	234	71			NOUN
iajs-2289	234	72	,	,	PUNCT
iajs-2289	234	73	pre	pre	ADJ
iajs-2289	234	74	,	,	PUNCT
iajs-2289	234	75	b	b	NOUN
iajs-2289	234	76	,	,	PUNCT
iajs-2289	234	77			NOUN
iajs-2289	234	78	}	}	PUNCT
iajs-2289	234	79	.	.	PUNCT
iajs-2289	235	1	definition	definition	NOUN
iajs-2289	235	2	29	29	NUM
iajs-2289	235	3	a	a	DET
iajs-2289	235	4	mapping	mapping	NOUN
iajs-2289	235	5			ADJ
iajs-2289	235	6	:	:	PUNCT
iajs-2289	235	7	g	g	PROPN
iajs-2289	235	8			NOUN
iajs-2289	235	9	h	h	NOUN
iajs-2289	235	10	is	be	AUX
iajs-2289	235	11	said	say	VERB
iajs-2289	235	12	to	to	PART
iajs-2289	235	13	be	be	AUX
iajs-2289	235	14	almost	almost	ADV
iajs-2289	235	15	j	j	PROPN
iajs-2289	235	16	-	-	PUNCT
iajs-2289	235	17	ω	ω	NOUN
iajs-2289	235	18	-	-	PUNCT
iajs-2289	235	19	closed	closed	ADJ
iajs-2289	235	20	if	if	SCONJ
iajs-2289	235	21	for	for	ADP
iajs-2289	235	22	any	any	DET
iajs-2289	235	23	set	set	NOUN
iajs-2289	235	24	k	k	PROPN
iajs-2289	235	25			PROPN
iajs-2289	235	26	g	g	PROPN
iajs-2289	235	27	,	,	PUNCT
iajs-2289	235	28	(alj	(alj	PROPN
iajs-2289	235	29	-	-	PUNCT
iajs-2289	235	30	ω	ω	NOUN
iajs-2289	235	31	-	-	NOUN
iajs-2289	235	32	cl(k	cl(k	NOUN
iajs-2289	235	33	)	)	PUNCT
iajs-2289	235	34	)	)	PUNCT
iajs-2289	236	1	=	=	PRON
iajs-2289	236	2	(	(	PUNCT
iajs-2289	236	3	alj	alj	PROPN
iajs-2289	236	4	-	-	PUNCT
iajs-2289	236	5	ω	ω	NOUN
iajs-2289	236	6	-	-	PUNCT
iajs-2289	236	7	cl	cl	NOUN
iajs-2289	236	8	(k	(k	NOUN
iajs-2289	236	9	)	)	PUNCT
iajs-2289	236	10	)	)	PUNCT
iajs-2289	236	11	,	,	PUNCT
iajs-2289	236	12	where	where	SCONJ
iajs-2289	236	13	j	j	PROPN
iajs-2289	236	14	{	{	PUNCT
iajs-2289	236	15			PROPN
iajs-2289	236	16	,	,	PUNCT
iajs-2289	236	17	δ	δ	PROPN
iajs-2289	236	18	,	,	PUNCT
iajs-2289	236	19			NOUN
iajs-2289	236	20	,	,	PUNCT
iajs-2289	236	21	pre	pre	ADJ
iajs-2289	236	22	,	,	PUNCT
iajs-2289	236	23	b	b	NOUN
iajs-2289	236	24	,	,	PUNCT
iajs-2289	236	25			NOUN
iajs-2289	236	26	}	}	PUNCT
iajs-2289	236	27	.	.	PUNCT
iajs-2289	237	1	definition	definition	NOUN
iajs-2289	237	2	30	30	NUM
iajs-2289	237	3	a	a	DET
iajs-2289	237	4	space	space	NOUN
iajs-2289	237	5	g	g	NOUN
iajs-2289	237	6	is	be	AUX
iajs-2289	237	7	said	say	VERB
iajs-2289	237	8	to	to	PART
iajs-2289	237	9	be	be	AUX
iajs-2289	237	10	j	j	PROPN
iajs-2289	237	11	-	-	PUNCT
iajs-2289	237	12	ω	ω	NOUN
iajs-2289	237	13	-	-	NOUN
iajs-2289	237	14	urysohn	urysohn	NOUN
iajs-2289	237	15	if	if	SCONJ
iajs-2289	237	16	every	every	DET
iajs-2289	237	17	pair	pair	NOUN
iajs-2289	237	18	of	of	ADP
iajs-2289	237	19	distinct	distinct	ADJ
iajs-2289	237	20	points	point	NOUN
iajs-2289	237	21	are	be	AUX
iajs-2289	237	22	contained	contain	VERB
iajs-2289	237	23	in	in	ADP
iajs-2289	237	24	disjoint	disjoint	PROPN
iajs-2289	237	25	j	j	PROPN
iajs-2289	237	26	-	-	PUNCT
iajs-2289	237	27	ω	ω	VERB
iajs-2289	237	28	-	-	PUNCT
iajs-2289	237	29	closed	closed	ADJ
iajs-2289	237	30	nbds	nbds	NOUN
iajs-2289	237	31	,	,	PUNCT
iajs-2289	237	32	where	where	SCONJ
iajs-2289	237	33	j	j	PROPN
iajs-2289	237	34	{	{	PROPN
iajs-2289	237	35	,	,	PUNCT
iajs-2289	237	36	δ	δ	PROPN
iajs-2289	237	37	,	,	PUNCT
iajs-2289	237	38			NOUN
iajs-2289	237	39	,	,	PUNCT
iajs-2289	237	40	pre	pre	ADJ
iajs-2289	237	41	,	,	PUNCT
iajs-2289	237	42	b	b	NOUN
iajs-2289	237	43	,	,	PUNCT
iajs-2289	237	44			NOUN
iajs-2289	237	45	}	}	PUNCT
iajs-2289	237	46	.	.	PUNCT
iajs-2289	238	1	before	before	ADP
iajs-2289	238	2	characterizing	characterize	VERB
iajs-2289	238	3	j	j	PROPN
iajs-2289	238	4	-	-	PUNCT
iajs-2289	238	5	ω	ω	NOUN
iajs-2289	238	6	-	-	PUNCT
iajs-2289	238	7	rigidity	rigidity	NOUN
iajs-2289	238	8	,	,	PUNCT
iajs-2289	238	9	we	we	PRON
iajs-2289	238	10	can	can	AUX
iajs-2289	238	11	show	show	VERB
iajs-2289	238	12	that	that	SCONJ
iajs-2289	238	13	a	a	DET
iajs-2289	238	14	j	j	PROPN
iajs-2289	238	15	-	-	PUNCT
iajs-2289	238	16	ω	ω	NOUN
iajs-2289	238	17	-	-	PUNCT
iajs-2289	238	18	closure	closure	NOUN
iajs-2289	238	19	continuous	continuous	ADJ
iajs-2289	238	20	,	,	PUNCT
iajs-2289	238	21	j	j	PROPN
iajs-2289	238	22	-	-	PUNCT
iajs-2289	238	23	ω	ω	VERB
iajs-2289	238	24	-	-	ADJ
iajs-2289	238	25	compact	compact	ADJ
iajs-2289	238	26	mapping	mapping	NOUN
iajs-2289	238	27	into	into	ADP
iajs-2289	238	28	a	a	DET
iajs-2289	238	29	j	j	PROPN
iajs-2289	238	30	-	-	PUNCT
iajs-2289	238	31	ω	ω	VERB
iajs-2289	238	32	-	-	PUNCT
iajs-2289	238	33	urysohn	urysohn	ADJ
iajs-2289	238	34	space	space	NOUN
iajs-2289	238	35	with	with	ADP
iajs-2289	238	36	a	a	DET
iajs-2289	238	37	certain	certain	ADJ
iajs-2289	238	38	property	property	NOUN
iajs-2289	238	39	(	(	PUNCT
iajs-2289	238	40	the	the	DET
iajs-2289	238	41	“	"	PUNCT
iajs-2289	238	42	j	j	PROPN
iajs-2289	238	43	-	-	PUNCT
iajs-2289	238	44	ω	ω	NOUN
iajs-2289	238	45	-	-	PUNCT
iajs-2289	238	46	closure	closure	NOUN
iajs-2289	238	47	”	"	PUNCT
iajs-2289	238	48	and	and	CCONJ
iajs-2289	238	49	“	"	PUNCT
iajs-2289	238	50	quasij	quasij	PROPN
iajs-2289	238	51	-	-	PUNCT
iajs-2289	238	52	ωh	ωh	NOUN
iajs-2289	238	53	-	-	PUNCT
iajs-2289	238	54	closed	closed	ADJ
iajs-2289	238	55	relative	relative	ADJ
iajs-2289	238	56	”	"	PUNCT
iajs-2289	238	57	analogue	analogue	NOUN
iajs-2289	238	58	of	of	ADP
iajs-2289	238	59	property	property	NOUN
iajs-2289	238	60			NOUN
iajs-2289	238	61	in	in	ADP
iajs-2289	238	62	[	[	X
iajs-2289	238	63	15	15	NUM
iajs-2289	238	64	]	]	X
iajs-2289	238	65	.	.	PUNCT
iajs-2289	238	66	)	)	PUNCT
iajs-2289	238	67	is	be	AUX
iajs-2289	238	68	almost	almost	ADV
iajs-2289	238	69	j	j	PROPN
iajs-2289	238	70	-	-	PUNCT
iajs-2289	238	71	ω	ω	NOUN
iajs-2289	238	72	-	-	PUNCT
iajs-2289	238	73	closed	closed	ADJ
iajs-2289	238	74	.	.	PUNCT
iajs-2289	239	1	theorem	theorem	ADJ
iajs-2289	239	2	31	31	NUM
iajs-2289	239	3	suppose	suppose	VERB
iajs-2289	239	4			ADJ
iajs-2289	239	5	:	:	PUNCT
iajs-2289	239	6	g	g	PROPN
iajs-2289	239	7			NOUN
iajs-2289	239	8	h	h	NOUN
iajs-2289	239	9	is	be	AUX
iajs-2289	239	10	a	a	DET
iajs-2289	239	11	j	j	PROPN
iajs-2289	239	12	-	-	PUNCT
iajs-2289	239	13	ω	ω	NOUN
iajs-2289	239	14	-	-	PUNCT
iajs-2289	239	15	closure	closure	NOUN
iajs-2289	239	16	continuous	continuous	ADJ
iajs-2289	239	17	mapping	mapping	NOUN
iajs-2289	239	18	and	and	CCONJ
iajs-2289	239	19	j	j	PROPN
iajs-2289	239	20	-	-	PUNCT
iajs-2289	239	21	ω	ω	NOUN
iajs-2289	239	22	-	-	ADJ
iajs-2289	239	23	compact	compact	ADJ
iajs-2289	240	1	and	and	CCONJ
iajs-2289	240	2	h	h	NOUN
iajs-2289	240	3	is	be	AUX
iajs-2289	240	4	j	j	NOUN
iajs-2289	240	5	-	-	NOUN
iajs-2289	240	6	ωurysohn	ωurysohn	ADJ
iajs-2289	240	7	with	with	ADP
iajs-2289	240	8	this	this	DET
iajs-2289	240	9	property	property	NOUN
iajs-2289	240	10	:	:	PUNCT
iajs-2289	240	11	for	for	ADP
iajs-2289	240	12	each	each	DET
iajs-2289	240	13	l	l	NOUN
iajs-2289	240	14			PROPN
iajs-2289	240	15	h	h	PROPN
iajs-2289	240	16	and	and	CCONJ
iajs-2289	240	17	h	h	NOUN
iajs-2289	240	18			NOUN
iajs-2289	240	19	(	(	PUNCT
iajs-2289	240	20	alj	alj	PROPN
iajs-2289	240	21	-	-	PUNCT
iajs-2289	240	22	ω	ω	NOUN
iajs-2289	240	23	-	-	PUNCT
iajs-2289	240	24	cl(l	cl(l	NUM
iajs-2289	240	25	)	)	PUNCT
iajs-2289	240	26	,	,	PUNCT
iajs-2289	240	27	there	there	PRON
iajs-2289	240	28	is	be	VERB
iajs-2289	240	29	a	a	DET
iajs-2289	240	30	subset	subset	NOUN
iajs-2289	240	31	c	c	ADP
iajs-2289	240	32	quasi	quasi	ADJ
iajs-2289	240	33	-	-	ADJ
iajs-2289	240	34	jω	jω	ADJ
iajs-2289	240	35	-	-	ADJ
iajs-2289	240	36	h	h	NOUN
iajs-2289	240	37	-	-	PUNCT
iajs-2289	240	38	closed	closed	ADJ
iajs-2289	240	39	relative	relative	ADJ
iajs-2289	240	40	to	to	ADP
iajs-2289	240	41	h	h	NOUN
iajs-2289	240	42	such	such	ADJ
iajs-2289	240	43	that	that	DET
iajs-2289	240	44	h	h	NOUN
iajs-2289	240	45			NOUN
iajs-2289	240	46	(	(	PUNCT
iajs-2289	240	47	alj	alj	PROPN
iajs-2289	240	48	-	-	PUNCT
iajs-2289	240	49	ω	ω	VERB
iajs-2289	240	50	-	-	PUNCT
iajs-2289	240	51	cl(c	cl(c	NOUN
iajs-2289	240	52	∩	∩	ADJ
iajs-2289	240	53	l	l	NOUN
iajs-2289	240	54	)	)	PUNCT
iajs-2289	240	55	)	)	PUNCT
iajs-2289	240	56	.	.	PUNCT
iajs-2289	241	1	then	then	ADV
iajs-2289	241	2			X
iajs-2289	241	3	is	be	AUX
iajs-2289	241	4	almost	almost	ADV
iajs-2289	241	5	j	j	PROPN
iajs-2289	241	6	-	-	PUNCT
iajs-2289	241	7	ω	ω	NOUN
iajs-2289	241	8	-	-	PUNCT
iajs-2289	241	9	closed	closed	ADJ
iajs-2289	241	10	,	,	PUNCT
iajs-2289	241	11	where	where	SCONJ
iajs-2289	241	12	j	j	PROPN
iajs-2289	241	13	{	{	PUNCT
iajs-2289	241	14			PROPN
iajs-2289	241	15	,	,	PUNCT
iajs-2289	241	16	δ	δ	PROPN
iajs-2289	241	17	,	,	PUNCT
iajs-2289	241	18			NOUN
iajs-2289	241	19	,	,	PUNCT
iajs-2289	241	20	pre	pre	ADJ
iajs-2289	241	21	,	,	PUNCT
iajs-2289	241	22	b	b	NOUN
iajs-2289	241	23	,	,	PUNCT
iajs-2289	241	24			NOUN
iajs-2289	241	25	}	}	PUNCT
iajs-2289	241	26	.	.	PUNCT
iajs-2289	242	1	proof	proof	NOUN
iajs-2289	242	2	:	:	PUNCT
iajs-2289	242	3	let	let	VERB
iajs-2289	242	4	k	k	PROPN
iajs-2289	242	5			PROPN
iajs-2289	242	6	h.	h.	PROPN
iajs-2289	242	7	by	by	ADP
iajs-2289	242	8	corollary	corollary	ADJ
iajs-2289	242	9	(	(	PUNCT
iajs-2289	242	10	24	24	NUM
iajs-2289	242	11	)	)	PUNCT
iajs-2289	242	12	,	,	PUNCT
iajs-2289	242	13			X
iajs-2289	242	14	(	(	PUNCT
iajs-2289	242	15	alj	alj	PROPN
iajs-2289	242	16	-	-	PUNCT
iajs-2289	242	17	ω	ω	NOUN
iajs-2289	242	18	-	-	NOUN
iajs-2289	242	19	cl	cl	NOUN
iajs-2289	242	20	(	(	PUNCT
iajs-2289	242	21	k	k	NOUN
iajs-2289	242	22	)	)	PUNCT
iajs-2289	242	23	)	)	PUNCT
iajs-2289	243	1			PROPN
iajs-2289	243	2	(	(	PUNCT
iajs-2289	243	3	alj	alj	PROPN
iajs-2289	243	4	-	-	PUNCT
iajs-2289	243	5	ω	ω	NOUN
iajs-2289	243	6	-	-	ADJ
iajs-2289	243	7	cl	cl	ADJ
iajs-2289	243	8	(	(	PUNCT
iajs-2289	243	9	k	k	NOUN
iajs-2289	243	10	)	)	PUNCT
iajs-2289	243	11	)	)	PUNCT
iajs-2289	243	12	.	.	PUNCT
iajs-2289	244	1	suppose	suppose	VERB
iajs-2289	244	2	h	h	PROPN
iajs-2289	244	3			PROPN
iajs-2289	244	4	(	(	PUNCT
iajs-2289	244	5	aljω	aljω	NOUN
iajs-2289	244	6	-	-	ADJ
iajs-2289	244	7	cl	cl	ADJ
iajs-2289	244	8	(	(	PUNCT
iajs-2289	244	9	k)).yond	k)).yond	NOUN
iajs-2289	244	10	is	be	AUX
iajs-2289	244	11	a	a	DET
iajs-2289	244	12	subset	subset	NOUN
iajs-2289	244	13	c	c	NOUN
iajs-2289	244	14	quasij	quasij	NOUN
iajs-2289	244	15	-	-	PUNCT
iajs-2289	244	16	ω	ω	VERB
iajs-2289	244	17	-	-	PUNCT
iajs-2289	244	18	h	h	NOUN
iajs-2289	244	19	-	-	PUNCT
iajs-2289	244	20	closed	closed	ADJ
iajs-2289	244	21	relative	relative	ADJ
iajs-2289	244	22	to	to	ADP
iajs-2289	244	23	h	h	NOUN
iajs-2289	244	24	such	such	ADJ
iajs-2289	244	25	that	that	SCONJ
iajs-2289	244	26	h	h	NOUN
iajs-2289	244	27	(alj	(alj	ADV
iajs-2289	244	28	-	-	PUNCT
iajs-2289	244	29	ω	ω	NUM
iajs-2289	244	30	-	-	PUNCT
iajs-2289	244	31	cl(c	cl(c	NOUN
iajs-2289	244	32	∩	∩	ADJ
iajs-2289	244	33	(k	(k	PROPN
iajs-2289	244	34	)	)	PUNCT
iajs-2289	244	35	)	)	PUNCT
iajs-2289	244	36	.	.	PUNCT
iajs-2289	245	1	then	then	ADV
iajs-2289	245	2			VERB
iajs-2289	245	3	=	=	PUNCT
iajs-2289	245	4	{	{	PUNCT
iajs-2289	245	5	cl	cl	INTJ
iajs-2289	245	6	j	j	NOUN
iajs-2289	245	7	-	-	ADJ
iajs-2289	245	8	ω-(s	ω-(s	NUM
iajs-2289	245	9	)	)	PUNCT
iajs-2289	245	10	∩	∩	NOUN
iajs-2289	245	11	c	c	NOUN
iajs-2289	245	12	∩	∩	X
iajs-2289	245	13	(k	(k	PROPN
iajs-2289	245	14	):	):	PUNCT
iajs-2289	245	15	s	s	AUX
iajs-2289	245	16			NOUN
iajs-2289	245	17	h	h	NUM
iajs-2289	245	18	}	}	PUNCT
iajs-2289	245	19	,	,	PUNCT
iajs-2289	245	20	is	be	AUX
iajs-2289	245	21	a	a	DET
iajs-2289	245	22	filter	filter	NOUN
iajs-2289	245	23	base	base	NOUN
iajs-2289	245	24	on	on	ADP
iajs-2289	245	25	h	h	NOUN
iajs-2289	245	26	such	such	ADJ
iajs-2289	245	27	that	that	SCONJ
iajs-2289	245	28			VERB
iajs-2289	245	29	j	j	PROPN
iajs-2289	245	30	-	-	PUNCT
iajs-2289	245	31	ω	ω	PROPN
iajs-2289	245	32	⇝	⇝	PROPN
iajs-2289	245	33	h.	h.	PROPN
iajs-2289	245	34	now	now	ADV
iajs-2289	245	35	,	,	PUNCT
iajs-2289	245	36			PROPN
iajs-2289	245	37	=	=	SYM
iajs-2289	245	38	{	{	PUNCT
iajs-2289	245	39	k	k	PROPN
iajs-2289	245	40	∩	∩	PROPN
iajs-2289	245	41			X
iajs-2289	245	42	–	–	PUNCT
iajs-2289	245	43	1	1	NUM
iajs-2289	245	44	(	(	PUNCT
iajs-2289	245	45	m	m	PROPN
iajs-2289	245	46	):	):	PUNCT
iajs-2289	245	47	m	m	VERB
iajs-2289	245	48			NOUN
iajs-2289	245	49			NOUN
iajs-2289	245	50	}	}	PUNCT
iajs-2289	245	51	is	be	AUX
iajs-2289	245	52	a	a	DET
iajs-2289	245	53	filter	filter	NOUN
iajs-2289	245	54	base	base	NOUN
iajs-2289	245	55	on	on	ADP
iajs-2289	245	56	k	k	PROPN
iajs-2289	245	57	∩	∩	NOUN
iajs-2289	245	58	–1	–1	PROPN
iajs-2289	245	59	(	(	PUNCT
iajs-2289	245	60	c	c	NOUN
iajs-2289	245	61	)	)	PUNCT
iajs-2289	245	62	.	.	PUNCT
iajs-2289	246	1	since	since	SCONJ
iajs-2289	246	2	–1	–1	PROPN
iajs-2289	246	3	(	(	PUNCT
iajs-2289	246	4	c	c	X
iajs-2289	246	5	)	)	PUNCT
iajs-2289	246	6	is	be	AUX
iajs-2289	246	7	quasij	quasij	NOUN
iajs-2289	246	8	-	-	PUNCT
iajs-2289	246	9	ω	ω	VERB
iajs-2289	246	10	-	-	PUNCT
iajs-2289	246	11	hclosed	hclosed	ADJ
iajs-2289	246	12	relative	relative	NOUN
iajs-2289	246	13	to	to	ADP
iajs-2289	246	14	h	h	NOUN
iajs-2289	246	15	,	,	PUNCT
iajs-2289	246	16	then	then	ADV
iajs-2289	246	17	there	there	PRON
iajs-2289	246	18	is	be	VERB
iajs-2289	246	19	g	g	PROPN
iajs-2289	246	20			NOUN
iajs-2289	246	21	(	(	PUNCT
iajs-2289	246	22	al	al	PROPN
iajs-2289	246	23	-j	-j	PROPN
iajs-2289	246	24	-	-	PUNCT
iajs-2289	246	25	ω	ω	NOUN
iajs-2289	246	26	-	-	PUNCT
iajs-2289	246	27	cg	cg	NOUN
iajs-2289	246	28	)	)	PUNCT
iajs-2289	246	29	∩	∩	NOUN
iajs-2289	247	1	–1	–1	PROPN
iajs-2289	247	2	(	(	PUNCT
iajs-2289	247	3	c	c	NOUN
iajs-2289	247	4	)	)	PUNCT
iajs-2289	247	5	.	.	PUNCT
iajs-2289	248	1	by	by	ADP
iajs-2289	248	2	theorem	theorem	NOUN
iajs-2289	248	3	23	23	NUM
iajs-2289	248	4	,	,	PUNCT
iajs-2289	248	5	(g	(g	NUM
iajs-2289	248	6	)	)	PUNCT
iajs-2289	248	7			NOUN
iajs-2289	248	8	(	(	PUNCT
iajs-2289	248	9	alj	alj	NOUN
iajs-2289	248	10	-	-	NOUN
iajs-2289	248	11	ωch(	ωch(	NOUN
iajs-2289	248	12	)	)	PUNCT
iajs-2289	248	13	)	)	PUNCT
iajs-2289	248	14			PROPN
iajs-2289	248	15	(	(	PUNCT
iajs-2289	248	16	alj	alj	PROPN
iajs-2289	248	17	-	-	PUNCT
iajs-2289	248	18	ω	ω	NOUN
iajs-2289	248	19	ch	ch	ADJ
iajs-2289	248	20	)	)	PUNCT
iajs-2289	248	21	.	.	PUNCT
iajs-2289	249	1	since	since	SCONJ
iajs-2289	249	2			NOUN
iajs-2289	249	3	j	j	PROPN
iajs-2289	249	4	-	-	PUNCT
iajs-2289	249	5	ω	ω	PROPN
iajs-2289	249	6	⇝	⇝	NOUN
iajs-2289	249	7	h	h	NOUN
iajs-2289	249	8	and	and	CCONJ
iajs-2289	249	9	h	h	NOUN
iajs-2289	249	10	is	be	AUX
iajs-2289	249	11	j	j	PROPN
iajs-2289	249	12	-	-	PUNCT
iajs-2289	249	13	ω	ω	NOUN
iajs-2289	249	14	-	-	NOUN
iajs-2289	249	15	urysohn	urysohn	ADJ
iajs-2289	249	16	,	,	PUNCT
iajs-2289	249	17	(	(	PUNCT
iajs-2289	249	18	alj	alj	PROPN
iajs-2289	249	19	-	-	PUNCT
iajs-2289	249	20	ω	ω	NOUN
iajs-2289	249	21	-	-	PUNCT
iajs-2289	249	22	ch	ch	ADJ
iajs-2289	249	23	)	)	PUNCT
iajs-2289	250	1	=	=	PRON
iajs-2289	250	2	{	{	PUNCT
iajs-2289	250	3	h	h	NOUN
iajs-2289	250	4	}	}	PUNCT
iajs-2289	250	5	.	.	PUNCT
iajs-2289	251	1	so	so	ADV
iajs-2289	251	2	,	,	PUNCT
iajs-2289	251	3	h	h	NOUN
iajs-2289	251	4			PROPN
iajs-2289	251	5	(alj	(alj	PROPN
iajs-2289	251	6	-	-	PUNCT
iajs-2289	251	7	ω	ω	NOUN
iajs-2289	251	8	-	-	NOUN
iajs-2289	251	9	cl	cl	NOUN
iajs-2289	251	10	(	(	PUNCT
iajs-2289	251	11	k	k	NOUN
iajs-2289	251	12	)	)	PUNCT
iajs-2289	251	13	)	)	PUNCT
iajs-2289	251	14	,	,	PUNCT
iajs-2289	251	15	where	where	SCONJ
iajs-2289	251	16	j	j	PROPN
iajs-2289	251	17	{	{	PUNCT
iajs-2289	251	18			PROPN
iajs-2289	251	19	,	,	PUNCT
iajs-2289	251	20	δ	δ	PROPN
iajs-2289	251	21	,	,	PUNCT
iajs-2289	251	22			NOUN
iajs-2289	251	23	,	,	PUNCT
iajs-2289	251	24	pre	pre	ADJ
iajs-2289	251	25	,	,	PUNCT
iajs-2289	251	26	b	b	NOUN
iajs-2289	251	27	,	,	PUNCT
iajs-2289	251	28			NOUN
iajs-2289	251	29	}	}	PUNCT
iajs-2289	251	30	.	.	PUNCT
iajs-2289	252	1	theorem	theorem	ADJ
iajs-2289	252	2	32	32	NUM
iajs-2289	252	3	let	let	VERB
iajs-2289	252	4	k	k	PROPN
iajs-2289	252	5	be	be	AUX
iajs-2289	252	6	a	a	DET
iajs-2289	252	7	subset	subset	NOUN
iajs-2289	252	8	of	of	ADP
iajs-2289	252	9	a	a	DET
iajs-2289	252	10	space	space	NOUN
iajs-2289	252	11	g.	g.	NOUN
iajs-2289	252	12	the	the	DET
iajs-2289	252	13	following	following	NOUN
iajs-2289	252	14	are	be	AUX
iajs-2289	252	15	equivalent	equivalent	ADJ
iajs-2289	252	16	:	:	PUNCT
iajs-2289	252	17	(	(	PUNCT
iajs-2289	252	18	a	a	X
iajs-2289	252	19	)	)	PUNCT
iajs-2289	252	20	k	k	PROPN
iajs-2289	252	21	is	be	AUX
iajs-2289	252	22	j	j	PROPN
iajs-2289	252	23	-	-	PUNCT
iajs-2289	252	24	ω	ω	NOUN
iajs-2289	252	25	-	-	ADJ
iajs-2289	252	26	rigid	rigid	ADJ
iajs-2289	252	27	in	in	ADP
iajs-2289	252	28	g.	g.	PROPN
iajs-2289	252	29	173	173	NUM
iajs-2289	253	1	ibn	ibn	PROPN
iajs-2289	253	2	al	al	PROPN
iajs-2289	253	3	-	-	PUNCT
iajs-2289	253	4	haitham	haitham	PROPN
iajs-2289	253	5	jour	jour	X
iajs-2289	253	6	.	.	PROPN
iajs-2289	253	7	for	for	ADP
iajs-2289	253	8	pure	pure	ADJ
iajs-2289	253	9	&	&	CCONJ
iajs-2289	253	10	appl	appl	PROPN
iajs-2289	253	11	.	.	PUNCT
iajs-2289	254	1	sci	sci	PROPN
iajs-2289	254	2	.	.	PROPN
iajs-2289	254	3	32	32	NUM
iajs-2289	254	4	(	(	PUNCT
iajs-2289	254	5	3	3	NUM
iajs-2289	254	6	)	)	PUNCT
iajs-2289	254	7	2019	2019	NUM
iajs-2289	254	8	(	(	PUNCT
iajs-2289	254	9	b	b	NOUN
iajs-2289	254	10	)	)	PUNCT
iajs-2289	254	11	for	for	ADP
iajs-2289	254	12	all	all	DET
iajs-2289	254	13	filter	filter	NOUN
iajs-2289	254	14	base	base	NOUN
iajs-2289	254	15			NOUN
iajs-2289	254	16	on	on	ADP
iajs-2289	254	17	g	g	NOUN
iajs-2289	254	18	,	,	PUNCT
iajs-2289	254	19	if	if	SCONJ
iajs-2289	254	20	k	k	PROPN
iajs-2289	254	21	∩	∩	X
iajs-2289	254	22	(	(	PUNCT
iajs-2289	254	23	alj	alj	PROPN
iajs-2289	254	24	-	-	PUNCT
iajs-2289	254	25	ω	ω	NOUN
iajs-2289	254	26	-	-	PUNCT
iajs-2289	254	27	cg	cg	NOUN
iajs-2289	254	28	)	)	PUNCT
iajs-2289	254	29	=	=	SYM
iajs-2289	254	30			NOUN
iajs-2289	254	31	,	,	PUNCT
iajs-2289	254	32	then	then	ADV
iajs-2289	254	33	for	for	ADP
iajs-2289	254	34	some	some	DET
iajs-2289	254	35	m	m	NOUN
iajs-2289	254	36			NOUN
iajs-2289	254	37			NOUN
iajs-2289	254	38	,	,	PUNCT
iajs-2289	254	39	k	k	PROPN
iajs-2289	254	40	∩	∩	X
iajs-2289	254	41	(	(	PUNCT
iajs-2289	254	42	alj	alj	PROPN
iajs-2289	254	43	-	-	PROPN
iajs-2289	254	44	ωcl(m	ωcl(m	PROPN
iajs-2289	254	45	)	)	PUNCT
iajs-2289	254	46	=	=	SYM
iajs-2289	254	47	.	.	X
iajs-2289	254	48	(	(	PUNCT
iajs-2289	254	49	c	c	NOUN
iajs-2289	254	50	)	)	PUNCT
iajs-2289	254	51	for	for	ADP
iajs-2289	254	52	all	all	DET
iajs-2289	254	53	cover	cover	NOUN
iajs-2289	254	54	k	k	PROPN
iajs-2289	254	55	of	of	ADP
iajs-2289	254	56	k	k	X
iajs-2289	254	57	by	by	ADP
iajs-2289	254	58	open	open	ADJ
iajs-2289	254	59	subsets	subset	NOUN
iajs-2289	254	60	of	of	ADP
iajs-2289	254	61	g	g	NOUN
iajs-2289	254	62	,	,	PUNCT
iajs-2289	254	63	there	there	PRON
iajs-2289	254	64	is	be	VERB
iajs-2289	254	65	a	a	DET
iajs-2289	254	66	finite	finite	NOUN
iajs-2289	254	67	subfamily	subfamily	ADV
iajs-2289	254	68	b	b	PROPN
iajs-2289	254	69			PROPN
iajs-2289	254	70	k	k	X
iajs-2289	254	71	such	such	ADJ
iajs-2289	254	72	that	that	SCONJ
iajs-2289	254	73	k	k	PROPN
iajs-2289	254	74			PROPN
iajs-2289	254	75	int	int	PROPN
iajs-2289	254	76	cl	cl	INTJ
iajs-2289	254	77	j	j	PROPN
iajs-2289	254	78	-	-	PROPN
iajs-2289	254	79	ω-(	ω-(	NUM
iajs-2289	254	80	b	b	NOUN
iajs-2289	254	81	)	)	PUNCT
iajs-2289	254	82	.	.	PUNCT
iajs-2289	255	1	where	where	SCONJ
iajs-2289	255	2	j	j	PROPN
iajs-2289	255	3	{	{	PROPN
iajs-2289	255	4	,	,	PUNCT
iajs-2289	255	5	δ	δ	PROPN
iajs-2289	255	6	,	,	PUNCT
iajs-2289	255	7			NOUN
iajs-2289	255	8	,	,	PUNCT
iajs-2289	255	9	pre	pre	AUX
iajs-2289	255	10	,	,	PUNCT
iajs-2289	255	11	b	b	NOUN
iajs-2289	255	12	,	,	PUNCT
iajs-2289	255	13			NOUN
iajs-2289	255	14	}	}	PUNCT
iajs-2289	255	15	.	.	PUNCT
iajs-2289	256	1	proof	proof	NOUN
iajs-2289	256	2	:	:	PUNCT
iajs-2289	256	3	the	the	DET
iajs-2289	256	4	proof	proof	NOUN
iajs-2289	256	5	that	that	SCONJ
iajs-2289	256	6	(	(	PUNCT
iajs-2289	256	7	a	a	X
iajs-2289	256	8	)	)	PUNCT
iajs-2289	256	9			NOUN
iajs-2289	256	10	(	(	PUNCT
iajs-2289	256	11	b	b	NOUN
iajs-2289	256	12	)	)	PUNCT
iajs-2289	256	13	is	be	AUX
iajs-2289	256	14	straightforward	straightforward	ADJ
iajs-2289	256	15	.	.	PUNCT
iajs-2289	257	1	(	(	PUNCT
iajs-2289	257	2	b	b	X
iajs-2289	257	3	)	)	PUNCT
iajs-2289	257	4			NOUN
iajs-2289	257	5	(	(	PUNCT
iajs-2289	257	6	c	c	X
iajs-2289	257	7	)	)	PUNCT
iajs-2289	257	8	let	let	VERB
iajs-2289	257	9	k	k	X
iajs-2289	257	10	be	be	AUX
iajs-2289	257	11	a	a	DET
iajs-2289	257	12	cover	cover	NOUN
iajs-2289	257	13	of	of	ADP
iajs-2289	257	14	k	k	X
iajs-2289	257	15	by	by	ADP
iajs-2289	257	16	open	open	ADJ
iajs-2289	257	17	subsets	subset	NOUN
iajs-2289	257	18	of	of	ADP
iajs-2289	257	19	g	g	NOUN
iajs-2289	257	20	and	and	CCONJ
iajs-2289	257	21			NOUN
iajs-2289	257	22	=	=	SYM
iajs-2289	257	23	{	{	PUNCT
iajs-2289	257	24	∩sb	∩sb	PROPN
iajs-2289	257	25	(	(	PUNCT
iajs-2289	257	26	g	g	PROPN
iajs-2289	257	27			PROPN
iajs-2289	257	28	cl	cl	PROPN
iajs-2289	257	29	j	j	PROPN
iajs-2289	257	30	-	-	PROPN
iajs-2289	257	31	ω-(s	ω-(s	NUM
iajs-2289	257	32	)	)	PUNCT
iajs-2289	257	33	):	):	PUNCT
iajs-2289	257	34	b	b	X
iajs-2289	257	35	is	be	AUX
iajs-2289	257	36	a	a	DET
iajs-2289	257	37	finite	finite	NOUN
iajs-2289	257	38	subset	subset	NOUN
iajs-2289	257	39	of	of	ADP
iajs-2289	257	40	k	k	NOUN
iajs-2289	257	41	}	}	PUNCT
iajs-2289	257	42	.	.	PUNCT
iajs-2289	258	1	if	if	SCONJ
iajs-2289	258	2			NOUN
iajs-2289	258	3	is	be	AUX
iajs-2289	258	4	not	not	PART
iajs-2289	258	5	a	a	DET
iajs-2289	258	6	filter	filter	NOUN
iajs-2289	258	7	base	base	NOUN
iajs-2289	258	8	,	,	PUNCT
iajs-2289	258	9	then	then	ADV
iajs-2289	258	10	for	for	ADP
iajs-2289	258	11	some	some	DET
iajs-2289	258	12	finite	finite	NOUN
iajs-2289	258	13	subfamily	subfamily	ADV
iajs-2289	258	14	b	b	PROPN
iajs-2289	258	15			PROPN
iajs-2289	258	16	k	k	PROPN
iajs-2289	258	17	,	,	PUNCT
iajs-2289	258	18	g	g	PROPN
iajs-2289	258	19			PROPN
iajs-2289	258	20	{cl	{cl	PROPN
iajs-2289	258	21	j	j	PROPN
iajs-2289	258	22	-	-	PROPN
iajs-2289	258	23	ω-(s	ω-(s	NUM
iajs-2289	258	24	)	)	PUNCT
iajs-2289	258	25	:	:	PUNCT
iajs-2289	258	26	s	s	VERB
iajs-2289	258	27			PROPN
iajs-2289	258	28	b	b	PROPN
iajs-2289	258	29	}	}	PUNCT
iajs-2289	258	30	;	;	PUNCT
iajs-2289	258	31	thus	thus	ADV
iajs-2289	258	32	,	,	PUNCT
iajs-2289	258	33	k	k	PROPN
iajs-2289	258	34			PROPN
iajs-2289	258	35	g	g	PROPN
iajs-2289	258	36			PROPN
iajs-2289	258	37	int	int	NOUN
iajs-2289	258	38	cl	cl	INTJ
iajs-2289	258	39	j	j	NOUN
iajs-2289	258	40	-	-	PUNCT
iajs-2289	258	41	ω(	ω(	PROPN
iajs-2289	258	42	b	b	NOUN
iajs-2289	258	43	)	)	PUNCT
iajs-2289	258	44	which	which	PRON
iajs-2289	258	45	completes	complete	VERB
iajs-2289	258	46	the	the	DET
iajs-2289	258	47	proof	proof	NOUN
iajs-2289	258	48	in	in	ADP
iajs-2289	258	49	the	the	DET
iajs-2289	258	50	case	case	NOUN
iajs-2289	258	51	that	that	SCONJ
iajs-2289	258	52			NOUN
iajs-2289	258	53	is	be	AUX
iajs-2289	258	54	not	not	PART
iajs-2289	258	55	a	a	DET
iajs-2289	258	56	filter	filter	NOUN
iajs-2289	258	57	base	base	NOUN
iajs-2289	258	58	.	.	PUNCT
iajs-2289	259	1	so	so	ADV
iajs-2289	259	2	,	,	PUNCT
iajs-2289	259	3	suppose	suppose	VERB
iajs-2289	259	4			NOUN
iajs-2289	259	5	is	be	AUX
iajs-2289	259	6	a	a	DET
iajs-2289	259	7	filter	filter	NOUN
iajs-2289	259	8	base	base	NOUN
iajs-2289	259	9	.	.	PUNCT
iajs-2289	260	1	then	then	ADV
iajs-2289	260	2	k	k	PROPN
iajs-2289	260	3	∩	∩	PROPN
iajs-2289	260	4	(	(	PUNCT
iajs-2289	260	5	alj	alj	PROPN
iajs-2289	260	6	-	-	PUNCT
iajs-2289	260	7	ω	ω	NOUN
iajs-2289	260	8	-	-	PUNCT
iajs-2289	260	9	c	c	NOUN
iajs-2289	260	10	)	)	PUNCT
iajs-2289	261	1	=	=	NOUN
iajs-2289	261	2			NOUN
iajs-2289	261	3	and	and	CCONJ
iajs-2289	261	4	there	there	PRON
iajs-2289	261	5	is	be	VERB
iajs-2289	261	6	an	an	DET
iajs-2289	261	7	m	m	NOUN
iajs-2289	261	8			NOUN
iajs-2289	261	9			NOUN
iajs-2289	261	10	such	such	ADJ
iajs-2289	261	11	that	that	SCONJ
iajs-2289	261	12	k	k	PROPN
iajs-2289	261	13	∩	∩	X
iajs-2289	261	14	(	(	PUNCT
iajs-2289	261	15	alj	alj	PROPN
iajs-2289	261	16	-	-	PUNCT
iajs-2289	261	17	ω	ω	NOUN
iajs-2289	261	18	-	-	NOUN
iajs-2289	261	19	cl	cl	NOUN
iajs-2289	261	20	(	(	PUNCT
iajs-2289	261	21	m	m	NOUN
iajs-2289	261	22	)	)	PUNCT
iajs-2289	261	23	)	)	PUNCT
iajs-2289	261	24	=	=	SYM
iajs-2289	262	1	.	.	X
iajs-2289	262	2	for	for	ADP
iajs-2289	262	3	each	each	DET
iajs-2289	262	4	x	x	ADJ
iajs-2289	262	5			NOUN
iajs-2289	262	6	k	k	PROPN
iajs-2289	262	7	,	,	PUNCT
iajs-2289	262	8	yond	yond	PROPN
iajs-2289	262	9	is	be	AUX
iajs-2289	262	10	open	open	ADJ
iajs-2289	262	11	tg	tg	ADP
iajs-2289	262	12	of	of	ADP
iajs-2289	262	13	g	g	PROPN
iajs-2289	262	14	such	such	ADJ
iajs-2289	262	15	that	that	DET
iajs-2289	262	16	cl	cl	PROPN
iajs-2289	262	17	j	j	PROPN
iajs-2289	262	18	-	-	PUNCT
iajs-2289	262	19	ω-(tg	ω-(tg	PROPN
iajs-2289	262	20	)	)	PUNCT
iajs-2289	262	21	∩	∩	NOUN
iajs-2289	262	22	m	m	NOUN
iajs-2289	262	23	=	=	PUNCT
iajs-2289	262	24	.	.	NOUN
iajs-2289	262	25	let	let	VERB
iajs-2289	262	26	t	t	PROPN
iajs-2289	262	27	=	=	SYM
iajs-2289	262	28	{tg	{tg	PROPN
iajs-2289	262	29	:	:	PUNCT
iajs-2289	262	30	g	g	PROPN
iajs-2289	262	31			PROPN
iajs-2289	262	32	k	k	X
iajs-2289	262	33	}	}	PUNCT
iajs-2289	262	34	.	.	PUNCT
iajs-2289	263	1	now	now	ADV
iajs-2289	263	2	,	,	PUNCT
iajs-2289	263	3	t	t	PROPN
iajs-2289	263	4	∩	∩	PROPN
iajs-2289	263	5	m	m	NOUN
iajs-2289	263	6	=	=	SYM
iajs-2289	263	7	.	.	X
iajs-2289	263	8	since	since	SCONJ
iajs-2289	263	9	m	m	PROPN
iajs-2289	263	10			NOUN
iajs-2289	263	11			NOUN
iajs-2289	263	12	,	,	PUNCT
iajs-2289	263	13	then	then	ADV
iajs-2289	263	14	for	for	ADP
iajs-2289	263	15	some	some	DET
iajs-2289	263	16	finite	finite	NOUN
iajs-2289	263	17	subfamily	subfamily	ADV
iajs-2289	263	18	b	b	PROPN
iajs-2289	263	19			PROPN
iajs-2289	263	20	k	k	PROPN
iajs-2289	263	21	,	,	PUNCT
iajs-2289	263	22	m	m	VERB
iajs-2289	263	23	=	=	X
iajs-2289	263	24	∩{g	∩{g	PRON
iajs-2289	263	25			PROPN
iajs-2289	263	26	cl	cl	PROPN
iajs-2289	263	27	j	j	PROPN
iajs-2289	263	28	-	-	PROPN
iajs-2289	263	29	ω-(s	ω-(s	NUM
iajs-2289	263	30	)	)	PUNCT
iajs-2289	263	31	:	:	PUNCT
iajs-2289	263	32	s	s	VERB
iajs-2289	263	33			PROPN
iajs-2289	263	34	b	b	PROPN
iajs-2289	263	35	}	}	PUNCT
iajs-2289	263	36	.	.	PUNCT
iajs-2289	264	1	it	it	PRON
iajs-2289	264	2	follows	follow	VERB
iajs-2289	264	3	that	that	SCONJ
iajs-2289	264	4	t	t	PROPN
iajs-2289	264	5			PROPN
iajs-2289	264	6	cl	cl	PROPN
iajs-2289	264	7	j	j	PROPN
iajs-2289	264	8	-	-	PUNCT
iajs-2289	264	9	ω(b	ω(b	PROPN
iajs-2289	264	10	)	)	PUNCT
iajs-2289	264	11	and	and	CCONJ
iajs-2289	264	12	hence	hence	ADV
iajs-2289	264	13	,	,	PUNCT
iajs-2289	264	14	k	k	PROPN
iajs-2289	264	15			PROPN
iajs-2289	264	16	int	int	PROPN
iajs-2289	264	17	cl	cl	INTJ
iajs-2289	264	18	j	j	PROPN
iajs-2289	264	19	-	-	PROPN
iajs-2289	264	20	ω-(	ω-(	NUM
iajs-2289	264	21	b	b	NOUN
iajs-2289	264	22	)	)	PUNCT
iajs-2289	264	23	,	,	PUNCT
iajs-2289	264	24	where	where	SCONJ
iajs-2289	264	25	j	j	PROPN
iajs-2289	264	26	{	{	PROPN
iajs-2289	264	27	,	,	PUNCT
iajs-2289	264	28	δ	δ	PROPN
iajs-2289	264	29	,	,	PUNCT
iajs-2289	264	30			NOUN
iajs-2289	264	31	,	,	PUNCT
iajs-2289	264	32	pre	pre	ADJ
iajs-2289	264	33	,	,	PUNCT
iajs-2289	264	34	b	b	NOUN
iajs-2289	264	35	,	,	PUNCT
iajs-2289	264	36			NOUN
iajs-2289	264	37	}	}	PUNCT
iajs-2289	264	38	.	.	PUNCT
iajs-2289	265	1	(	(	PUNCT
iajs-2289	265	2	c	c	X
iajs-2289	265	3	)	)	PUNCT
iajs-2289	265	4			NOUN
iajs-2289	265	5	(	(	PUNCT
iajs-2289	265	6	a	a	X
iajs-2289	265	7	)	)	PUNCT
iajs-2289	265	8	let	let	VERB
iajs-2289	265	9			NOUN
iajs-2289	265	10	be	be	AUX
iajs-2289	265	11	a	a	DET
iajs-2289	265	12	filter	filter	NOUN
iajs-2289	265	13	base	base	NOUN
iajs-2289	265	14	on	on	ADP
iajs-2289	265	15	g	g	PROPN
iajs-2289	265	16	such	such	ADJ
iajs-2289	265	17	that	that	SCONJ
iajs-2289	265	18	k	k	PROPN
iajs-2289	265	19	∩	∩	PROPN
iajs-2289	265	20	(	(	PUNCT
iajs-2289	265	21	al	al	PROPN
iajs-2289	265	22	-j	-j	PROPN
iajs-2289	265	23	-	-	PUNCT
iajs-2289	265	24	ω	ω	NOUN
iajs-2289	265	25	-	-	PUNCT
iajs-2289	265	26	c	c	NOUN
iajs-2289	265	27	)	)	PUNCT
iajs-2289	265	28	=	=	SYM
iajs-2289	265	29	.	.	X
iajs-2289	265	30	for	for	ADP
iajs-2289	265	31	all	all	DET
iajs-2289	265	32	g	g	PROPN
iajs-2289	265	33			NOUN
iajs-2289	265	34	k	k	PROPN
iajs-2289	265	35	yond	yond	PROPN
iajs-2289	265	36	is	be	AUX
iajs-2289	265	37	open	open	ADJ
iajs-2289	265	38	tg	tg	ADP
iajs-2289	265	39	of	of	ADP
iajs-2289	265	40	g	g	PROPN
iajs-2289	265	41	and	and	CCONJ
iajs-2289	265	42	mg	mg	PROPN
iajs-2289	265	43			NOUN
iajs-2289	265	44			NOUN
iajs-2289	265	45	such	such	ADJ
iajs-2289	265	46	that	that	DET
iajs-2289	265	47	cl	cl	PROPN
iajs-2289	265	48	j	j	PROPN
iajs-2289	265	49	-	-	PUNCT
iajs-2289	265	50	ω-(tg	ω-(tg	PROPN
iajs-2289	265	51	)	)	PUNCT
iajs-2289	265	52	∩	∩	NOUN
iajs-2289	265	53	mg	mg	PROPN
iajs-2289	265	54	=	=	SYM
iajs-2289	265	55	.	.	X
iajs-2289	265	56	now	now	ADV
iajs-2289	265	57	{	{	PUNCT
iajs-2289	265	58	tg	tg	X
iajs-2289	265	59	:	:	PUNCT
iajs-2289	265	60	g	g	PROPN
iajs-2289	265	61			PROPN
iajs-2289	265	62	k	k	VERB
iajs-2289	265	63	}	}	PUNCT
iajs-2289	265	64	is	be	AUX
iajs-2289	265	65	a	a	DET
iajs-2289	265	66	cover	cover	NOUN
iajs-2289	265	67	of	of	ADP
iajs-2289	265	68	k	k	X
iajs-2289	265	69	by	by	ADP
iajs-2289	265	70	open	open	ADJ
iajs-2289	265	71	subsets	subset	NOUN
iajs-2289	265	72	of	of	ADP
iajs-2289	265	73	g	g	NOUN
iajs-2289	265	74	;	;	PUNCT
iajs-2289	265	75	so	so	ADV
iajs-2289	265	76	,	,	PUNCT
iajs-2289	265	77	there	there	PRON
iajs-2289	265	78	is	be	VERB
iajs-2289	265	79	finite	finite	NOUN
iajs-2289	265	80	subset	subset	NOUN
iajs-2289	265	81	l	l	PROPN
iajs-2289	265	82			PROPN
iajs-2289	266	1	k	k	PROPN
iajs-2289	266	2	such	such	ADJ
iajs-2289	266	3	that	that	SCONJ
iajs-2289	266	4	k	k	PROPN
iajs-2289	266	5			PROPN
iajs-2289	266	6	int	int	PROPN
iajs-2289	266	7	cl	cl	INTJ
iajs-2289	266	8	j	j	PROPN
iajs-2289	266	9	-	-	PUNCT
iajs-2289	266	10	ω({tg	ω({tg	ADJ
iajs-2289	266	11	:	:	PUNCT
iajs-2289	266	12	g	g	PROPN
iajs-2289	266	13			PROPN
iajs-2289	266	14	t	t	PROPN
iajs-2289	266	15	}	}	PUNCT
iajs-2289	266	16	)	)	PUNCT
iajs-2289	266	17	.	.	PUNCT
iajs-2289	267	1	let	let	VERB
iajs-2289	267	2	s	s	NOUN
iajs-2289	267	3	=	=	NOUN
iajs-2289	267	4	int	int	PROPN
iajs-2289	267	5	cl	cl	INTJ
iajs-2289	267	6	j	j	PROPN
iajs-2289	267	7	-	-	PUNCT
iajs-2289	267	8	ω-({tg	ω-({tg	PROPN
iajs-2289	267	9	:	:	PUNCT
iajs-2289	267	10	g	g	PROPN
iajs-2289	267	11			PROPN
iajs-2289	267	12	l	l	NOUN
iajs-2289	267	13	}	}	PUNCT
iajs-2289	267	14	)	)	PUNCT
iajs-2289	267	15	.	.	PUNCT
iajs-2289	268	1	yond	yond	PROPN
iajs-2289	268	2	is	be	AUX
iajs-2289	268	3	m	m	PROPN
iajs-2289	268	4			NOUN
iajs-2289	268	5			NOUN
iajs-2289	268	6	such	such	ADJ
iajs-2289	268	7	that	that	SCONJ
iajs-2289	268	8	m	m	PROPN
iajs-2289	268	9			PROPN
iajs-2289	268	10	∩	∩	NOUN
iajs-2289	268	11	{	{	PUNCT
iajs-2289	268	12	mg	mg	NOUN
iajs-2289	268	13	:	:	PUNCT
iajs-2289	268	14	g	g	PROPN
iajs-2289	268	15			PROPN
iajs-2289	268	16	l	l	NOUN
iajs-2289	268	17	}	}	PUNCT
iajs-2289	268	18	.	.	PUNCT
iajs-2289	269	1	since	since	SCONJ
iajs-2289	269	2	cl	cl	NOUN
iajs-2289	269	3	j	j	PROPN
iajs-2289	269	4	-	-	PUNCT
iajs-2289	269	5	ω(s	ω(s	PROPN
iajs-2289	269	6	)	)	PUNCT
iajs-2289	269	7	=	=	PUNCT
iajs-2289	269	8	{cl	{cl	PROPN
iajs-2289	269	9	j	j	PROPN
iajs-2289	269	10	-	-	PUNCT
iajs-2289	269	11	ω-(tg	ω-(tg	PROPN
iajs-2289	269	12	):	):	PUNCT
iajs-2289	269	13	g	g	PROPN
iajs-2289	269	14			PROPN
iajs-2289	269	15	l	l	NOUN
iajs-2289	269	16	}	}	PUNCT
iajs-2289	269	17	,	,	PUNCT
iajs-2289	269	18	then	then	ADV
iajs-2289	269	19	cl	cl	VERB
iajs-2289	269	20	j	j	PROPN
iajs-2289	269	21	-	-	ADJ
iajs-2289	269	22	ω-(s	ω-(s	NUM
iajs-2289	269	23	)	)	PUNCT
iajs-2289	269	24	∩	∩	NOUN
iajs-2289	269	25	m	m	NOUN
iajs-2289	269	26	=	=	SYM
iajs-2289	269	27	.	.	X
iajs-2289	269	28	so	so	ADV
iajs-2289	269	29	k	k	PROPN
iajs-2289	269	30	is	be	AUX
iajs-2289	269	31	j	j	PROPN
iajs-2289	269	32	-	-	PUNCT
iajs-2289	269	33	ω	ω	NOUN
iajs-2289	269	34	-	-	NOUN
iajs-2289	269	35	rigid	rigid	ADJ
iajs-2289	269	36	in	in	ADP
iajs-2289	269	37	g	g	PROPN
iajs-2289	269	38	,	,	PUNCT
iajs-2289	269	39	where	where	SCONJ
iajs-2289	269	40	j	j	PROPN
iajs-2289	269	41	{	{	PROPN
iajs-2289	269	42	,	,	PUNCT
iajs-2289	269	43	δ	δ	PROPN
iajs-2289	269	44	,	,	PUNCT
iajs-2289	269	45			NOUN
iajs-2289	269	46	,	,	PUNCT
iajs-2289	269	47	pre	pre	ADJ
iajs-2289	269	48	,	,	PUNCT
iajs-2289	269	49	b	b	NOUN
iajs-2289	269	50	,	,	PUNCT
iajs-2289	269	51			PROPN
iajs-2289	269	52	}	}	PUNCT
iajs-2289	269	53	.	.	PUNCT
iajs-2289	270	1	6	6	X
iajs-2289	270	2	.	.	X
iajs-2289	270	3	filter	filter	NOUN
iajs-2289	270	4	bases	basis	NOUN
iajs-2289	270	5	and	and	CCONJ
iajs-2289	270	6	j	j	PROPN
iajs-2289	270	7	-	-	PUNCT
iajs-2289	270	8	ω	ω	VERB
iajs-2289	270	9	-	-	PUNCT
iajs-2289	270	10	perfect	perfect	ADJ
iajs-2289	270	11	mappings	mapping	NOUN
iajs-2289	270	12	in	in	ADP
iajs-2289	270	13	the	the	DET
iajs-2289	270	14	section	section	NOUN
iajs-2289	270	15	,	,	PUNCT
iajs-2289	270	16	we	we	PRON
iajs-2289	270	17	defined	define	VERB
iajs-2289	270	18	filter	filter	NOUN
iajs-2289	270	19	bases	basis	NOUN
iajs-2289	270	20	,	,	PUNCT
iajs-2289	270	21	j	j	PROPN
iajs-2289	270	22	-	-	PUNCT
iajs-2289	270	23	ω	ω	VERB
iajs-2289	270	24	-	-	PUNCT
iajs-2289	270	25	perfect	perfect	ADJ
iajs-2289	270	26	mappings	mapping	NOUN
iajs-2289	270	27	,	,	PUNCT
iajs-2289	270	28	and	and	CCONJ
iajs-2289	270	29	the	the	DET
iajs-2289	270	30	some	some	DET
iajs-2289	270	31	theorems	theorem	NOUN
iajs-2289	270	32	about	about	ADP
iajs-2289	270	33	them	they	PRON
iajs-2289	270	34	.	.	PUNCT
iajs-2289	271	1	in	in	ADP
iajs-2289	271	2	corollary	corollary	ADJ
iajs-2289	271	3	14	14	NUM
iajs-2289	271	4	,	,	PUNCT
iajs-2289	271	5	we	we	PRON
iajs-2289	271	6	show	show	VERB
iajs-2289	271	7	that	that	SCONJ
iajs-2289	271	8	a	a	DET
iajs-2289	271	9	mapping	mapping	NOUN
iajs-2289	271	10			ADJ
iajs-2289	271	11	:	:	PUNCT
iajs-2289	271	12	g	g	PROPN
iajs-2289	271	13			NOUN
iajs-2289	271	14	h	h	NOUN
iajs-2289	271	15	is	be	AUX
iajs-2289	271	16	perfect	perfect	ADJ
iajs-2289	271	17	(	(	PUNCT
iajs-2289	271	18	i.e.	i.e.	X
iajs-2289	271	19	closed	closed	ADJ
iajs-2289	271	20	and	and	CCONJ
iajs-2289	271	21			ADJ
iajs-2289	271	22	–	–	PUNCT
iajs-2289	271	23	1	1	NUM
iajs-2289	271	24	(	(	PUNCT
iajs-2289	271	25	y	y	NOUN
iajs-2289	271	26	)	)	PUNCT
iajs-2289	271	27	compact	compact	NOUN
iajs-2289	271	28	for	for	ADP
iajs-2289	271	29	each	each	DET
iajs-2289	271	30	h	h	NOUN
iajs-2289	271	31			PROPN
iajs-2289	271	32	h	h	PROPN
iajs-2289	271	33	)	)	PUNCT
iajs-2289	271	34	iff	iff	NOUN
iajs-2289	271	35	for	for	ADP
iajs-2289	271	36	all	all	DET
iajs-2289	271	37	filter	filter	NOUN
iajs-2289	271	38	base	base	NOUN
iajs-2289	271	39			NOUN
iajs-2289	271	40	on	on	ADP
iajs-2289	271	41	(g	(g	PROPN
iajs-2289	271	42	)	)	PUNCT
iajs-2289	271	43	,	,	PUNCT
iajs-2289	271	44			ADJ
iajs-2289	271	45	⇝	⇝	NOUN
iajs-2289	271	46	h	h	PROPN
iajs-2289	271	47			NOUN
iajs-2289	271	48	h	h	NOUN
iajs-2289	271	49	,	,	PUNCT
iajs-2289	271	50	implies	imply	VERB
iajs-2289	271	51			ADJ
iajs-2289	271	52	–	–	PUNCT
iajs-2289	271	53	1	1	NUM
iajs-2289	271	54	(	(	PUNCT
iajs-2289	271	55			NOUN
iajs-2289	271	56	)	)	PUNCT
iajs-2289	271	57	is	be	AUX
iajs-2289	271	58	(	(	PUNCT
iajs-2289	271	59	cl	cl	NOUN
iajs-2289	271	60	-	-	PUNCT
iajs-2289	271	61	dirtow	dirtow	NOUN
iajs-2289	271	62	)	)	PUNCT
iajs-2289	272	1	–1	–1	PROPN
iajs-2289	272	2	(	(	PUNCT
iajs-2289	272	3	y	y	NOUN
iajs-2289	272	4	)	)	PUNCT
iajs-2289	272	5	and	and	CCONJ
iajs-2289	272	6	in	in	ADP
iajs-2289	272	7	corollary	corollary	ADJ
iajs-2289	272	8	15	15	NUM
iajs-2289	272	9	,	,	PUNCT
iajs-2289	272	10	proved	prove	VERB
iajs-2289	272	11	that	that	SCONJ
iajs-2289	272	12	a	a	DET
iajs-2289	272	13	perfect	perfect	ADJ
iajs-2289	272	14	mapping	mapping	NOUN
iajs-2289	272	15	is	be	AUX
iajs-2289	272	16	compact	compact	ADJ
iajs-2289	272	17	(	(	PUNCT
iajs-2289	272	18	i.e.	i.e.	X
iajs-2289	272	19	inverse	inverse	ADJ
iajs-2289	272	20	image	image	NOUN
iajs-2289	272	21	of	of	ADP
iajs-2289	272	22	compact	compact	ADJ
iajs-2289	272	23	sets	set	NOUN
iajs-2289	272	24	are	be	AUX
iajs-2289	272	25	compact	compact	ADJ
iajs-2289	272	26	)	)	PUNCT
iajs-2289	272	27	.	.	PUNCT
iajs-2289	273	1	in	in	ADP
iajs-2289	273	2	view	view	NOUN
iajs-2289	273	3	theorem	theorem	VERB
iajs-2289	273	4	21	21	NUM
iajs-2289	273	5	,	,	PUNCT
iajs-2289	273	6	we	we	PRON
iajs-2289	273	7	say	say	VERB
iajs-2289	273	8	that	that	SCONJ
iajs-2289	273	9	a	a	DET
iajs-2289	273	10	mapping	mapping	NOUN
iajs-2289	273	11			ADJ
iajs-2289	273	12	:	:	PUNCT
iajs-2289	273	13	g	g	PROPN
iajs-2289	273	14			NOUN
iajs-2289	273	15	h	h	NOUN
iajs-2289	273	16	is	be	AUX
iajs-2289	273	17	j	j	NOUN
iajs-2289	273	18	-	-	PUNCT
iajs-2289	273	19	ωperfect	ωperfect	NOUN
iajs-2289	273	20	if	if	SCONJ
iajs-2289	273	21	for	for	ADP
iajs-2289	273	22	every	every	DET
iajs-2289	273	23	filter	filter	NOUN
iajs-2289	273	24	base	base	NOUN
iajs-2289	273	25			NOUN
iajs-2289	273	26	on	on	ADP
iajs-2289	273	27	(g	(g	PROPN
iajs-2289	273	28	)	)	PUNCT
iajs-2289	273	29	,	,	PUNCT
iajs-2289	273	30			VERB
iajs-2289	273	31	j	j	PROPN
iajs-2289	273	32	-	-	PUNCT
iajs-2289	273	33	ω	ω	PROPN
iajs-2289	273	34	⇝	⇝	NOUN
iajs-2289	273	35	h	h	NOUN
iajs-2289	273	36			PROPN
iajs-2289	273	37	h	h	PROPN
iajs-2289	273	38	implies	imply	VERB
iajs-2289	273	39			ADJ
iajs-2289	273	40	–	–	PUNCT
iajs-2289	273	41	1	1	NUM
iajs-2289	273	42	(	(	PUNCT
iajs-2289	273	43	)j	)j	PROPN
iajs-2289	273	44	-	-	PUNCT
iajs-2289	273	45	ω	ω	NUM
iajs-2289	273	46	⇝	⇝	NOUN
iajs-2289	273	47			X
iajs-2289	273	48	–	–	PUNCT
iajs-2289	273	49	1	1	NUM
iajs-2289	273	50	(	(	PUNCT
iajs-2289	273	51	h	h	NOUN
iajs-2289	273	52	)	)	PUNCT
iajs-2289	273	53	,	,	PUNCT
iajs-2289	273	54	where	where	SCONJ
iajs-2289	273	55	j	j	PROPN
iajs-2289	273	56	{	{	PROPN
iajs-2289	273	57	,	,	PUNCT
iajs-2289	273	58	δ	δ	PROPN
iajs-2289	273	59	,	,	PUNCT
iajs-2289	273	60			NOUN
iajs-2289	273	61	,	,	PUNCT
iajs-2289	273	62	pre	pre	ADJ
iajs-2289	273	63	,	,	PUNCT
iajs-2289	273	64	b	b	NOUN
iajs-2289	273	65	,	,	PUNCT
iajs-2289	273	66			PROPN
iajs-2289	273	67	}	}	PUNCT
iajs-2289	273	68	.	.	PUNCT
iajs-2289	274	1	theorem	theorem	VERB
iajs-2289	274	2	33	33	NUM
iajs-2289	274	3	let	let	VERB
iajs-2289	274	4			ADJ
iajs-2289	274	5	:	:	PUNCT
iajs-2289	274	6	g	g	PROPN
iajs-2289	274	7			NOUN
iajs-2289	274	8	h	h	NOUN
iajs-2289	274	9	be	be	VERB
iajs-2289	274	10	a	a	DET
iajs-2289	274	11	mapping	mapping	NOUN
iajs-2289	274	12	.	.	PUNCT
iajs-2289	275	1	the	the	DET
iajs-2289	275	2	following	follow	VERB
iajs-2289	275	3	are	be	AUX
iajs-2289	275	4	equivalent	equivalent	ADJ
iajs-2289	275	5	:	:	PUNCT
iajs-2289	275	6	(	(	PUNCT
iajs-2289	275	7	a	a	X
iajs-2289	275	8	)	)	PUNCT
iajs-2289	275	9			X
iajs-2289	275	10	is	be	AUX
iajs-2289	275	11	j	j	PROPN
iajs-2289	275	12	-	-	PUNCT
iajs-2289	275	13	ω	ω	NOUN
iajs-2289	275	14	-	-	NOUN
iajs-2289	275	15	perfect	perfect	ADJ
iajs-2289	275	16	.	.	PUNCT
iajs-2289	276	1	(	(	PUNCT
iajs-2289	276	2	b	b	X
iajs-2289	276	3	)	)	PUNCT
iajs-2289	276	4	for	for	ADP
iajs-2289	276	5	all	all	DET
iajs-2289	276	6	filter	filter	NOUN
iajs-2289	276	7	base	base	NOUN
iajs-2289	276	8			NOUN
iajs-2289	276	9	on	on	ADP
iajs-2289	276	10	g	g	PROPN
iajs-2289	276	11	,	,	PUNCT
iajs-2289	276	12	(	(	PUNCT
iajs-2289	276	13	alj	alj	PROPN
iajs-2289	276	14	-	-	PUNCT
iajs-2289	276	15	ω-(c	ω-(c	NOUN
iajs-2289	276	16	(	(	NOUN
iajs-2289	276	17	)	)	PUNCT
iajs-2289	276	18	)	)	PUNCT
iajs-2289	276	19			PROPN
iajs-2289	276	20	(alj	(alj	ADJ
iajs-2289	276	21	-	-	PUNCT
iajs-2289	276	22	ω-(c	ω-(c	NOUN
iajs-2289	276	23	)	)	PUNCT
iajs-2289	276	24	.	.	PUNCT
iajs-2289	277	1	(	(	PUNCT
iajs-2289	277	2	c	c	X
iajs-2289	277	3	)	)	PUNCT
iajs-2289	277	4	for	for	ADP
iajs-2289	277	5	all	all	DET
iajs-2289	277	6	filter	filter	NOUN
iajs-2289	277	7	base	base	NOUN
iajs-2289	277	8			NOUN
iajs-2289	277	9	on	on	ADP
iajs-2289	277	10	(g	(g	PROPN
iajs-2289	277	11	)	)	PUNCT
iajs-2289	277	12	,	,	PUNCT
iajs-2289	277	13			VERB
iajs-2289	277	14	j	j	PROPN
iajs-2289	277	15	-	-	PUNCT
iajs-2289	277	16	ω	ω	NUM
iajs-2289	277	17	⇝	⇝	NOUN
iajs-2289	277	18	l	l	NOUN
iajs-2289	277	19			PROPN
iajs-2289	277	20	h	h	NOUN
iajs-2289	277	21	,	,	PUNCT
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iajs-2289	277	23	–1	–1	PROPN
iajs-2289	277	24	(	(	PUNCT
iajs-2289	277	25			NOUN
iajs-2289	277	26	)	)	PUNCT
iajs-2289	277	27	j	j	PROPN
iajs-2289	277	28	-	-	PUNCT
iajs-2289	277	29	ω	ω	PROPN
iajs-2289	277	30	⇝	⇝	X
iajs-2289	277	31	–1	–1	PROPN
iajs-2289	277	32	(	(	PUNCT
iajs-2289	277	33	l	l	NOUN
iajs-2289	277	34	)	)	PUNCT
iajs-2289	277	35	.	.	PUNCT
iajs-2289	278	1	where	where	SCONJ
iajs-2289	278	2	j	j	PROPN
iajs-2289	278	3			NOUN
iajs-2289	278	4	{	{	PUNCT
iajs-2289	278	5			PROPN
iajs-2289	278	6	,	,	PUNCT
iajs-2289	278	7	δ	δ	PROPN
iajs-2289	278	8	,	,	PUNCT
iajs-2289	278	9			NOUN
iajs-2289	278	10	,	,	PUNCT
iajs-2289	278	11	pre	pre	ADJ
iajs-2289	278	12	,	,	PUNCT
iajs-2289	278	13	b	b	NOUN
iajs-2289	278	14	,	,	PUNCT
iajs-2289	278	15			NOUN
iajs-2289	278	16	}	}	PUNCT
iajs-2289	278	17	.	.	PUNCT
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iajs-2289	279	2	:	:	PUNCT
iajs-2289	279	3	(	(	PUNCT
iajs-2289	279	4	a	a	X
iajs-2289	279	5	)	)	PUNCT
iajs-2289	279	6			NOUN
iajs-2289	279	7	(	(	PUNCT
iajs-2289	279	8	b	b	NOUN
iajs-2289	279	9	)	)	PUNCT
iajs-2289	279	10	assume	assume	VERB
iajs-2289	279	11			NOUN
iajs-2289	279	12	is	be	AUX
iajs-2289	279	13	a	a	DET
iajs-2289	279	14	filter	filter	NOUN
iajs-2289	279	15	base	base	NOUN
iajs-2289	279	16	on	on	ADP
iajs-2289	279	17	g	g	PROPN
iajs-2289	279	18	and	and	CCONJ
iajs-2289	279	19	h	h	PROPN
iajs-2289	279	20			NOUN
iajs-2289	279	21	(	(	PUNCT
iajs-2289	279	22	alj	alj	PROPN
iajs-2289	279	23	-	-	PUNCT
iajs-2289	279	24	ω	ω	PROPN
iajs-2289	279	25	-	-	PUNCT
iajs-2289	279	26	c	c	NOUN
iajs-2289	279	27	(	(	NOUN
iajs-2289	279	28	)	)	PUNCT
iajs-2289	279	29	)	)	PUNCT
iajs-2289	279	30	.	.	PUNCT
iajs-2289	280	1	for	for	ADP
iajs-2289	280	2	if	if	SCONJ
iajs-2289	280	3	not	not	PART
iajs-2289	280	4	.	.	PUNCT
iajs-2289	281	1	assume	assume	VERB
iajs-2289	281	2	that	that	SCONJ
iajs-2289	281	3	–1	–1	PROPN
iajs-2289	281	4	(	(	PUNCT
iajs-2289	281	5	h	h	NOUN
iajs-2289	281	6	)	)	PUNCT
iajs-2289	281	7	∩	∩	NOUN
iajs-2289	281	8	(	(	PUNCT
iajs-2289	281	9	alj	alj	NOUN
iajs-2289	281	10	-	-	PUNCT
iajs-2289	281	11	ω-(c	ω-(c	NOUN
iajs-2289	281	12	)	)	PUNCT
iajs-2289	281	13	=	=	NOUN
iajs-2289	281	14	.	.	X
iajs-2289	281	15	for	for	ADP
iajs-2289	281	16	each	each	DET
iajs-2289	281	17	g	g	PROPN
iajs-2289	281	18			PROPN
iajs-2289	281	19			ADJ
iajs-2289	281	20	–	–	PUNCT
iajs-2289	281	21	1	1	NUM
iajs-2289	281	22	(	(	PUNCT
iajs-2289	281	23	h	h	NOUN
iajs-2289	281	24	)	)	PUNCT
iajs-2289	281	25	,	,	PUNCT
iajs-2289	281	26	yond	yond	PROPN
iajs-2289	281	27	is	be	AUX
iajs-2289	281	28	open	open	ADJ
iajs-2289	281	29	sg	sg	ADP
iajs-2289	281	30	of	of	ADP
iajs-2289	281	31	g	g	PROPN
iajs-2289	281	32	and	and	CCONJ
iajs-2289	281	33	mg	mg	PROPN
iajs-2289	281	34			NOUN
iajs-2289	281	35			NOUN
iajs-2289	281	36	such	such	ADJ
iajs-2289	281	37	that	that	SCONJ
iajs-2289	281	38	cl	cl	PROPN
iajs-2289	281	39	j	j	PROPN
iajs-2289	281	40	-	-	PUNCT
iajs-2289	281	41	ω-(sg	ω-(sg	PROPN
iajs-2289	281	42	)	)	PUNCT
iajs-2289	281	43	∩	∩	NOUN
iajs-2289	281	44	mg	mg	PROPN
iajs-2289	281	45	=	=	SYM
iajs-2289	281	46	.	.	X
iajs-2289	281	47	since	since	SCONJ
iajs-2289	281	48	–1	–1	PROPN
iajs-2289	281	49	(	(	PUNCT
iajs-2289	281	50	cl	cl	INTJ
iajs-2289	281	51	j	j	PROPN
iajs-2289	281	52	-	-	PUNCT
iajs-2289	281	53	ω-(h	ω-(h	PROPN
iajs-2289	281	54	)	)	PUNCT
iajs-2289	281	55	)	)	PUNCT
iajs-2289	282	1	j	j	PROPN
iajs-2289	282	2	-	-	PUNCT
iajs-2289	282	3	ω	ω	PROPN
iajs-2289	282	4	⇝	⇝	NOUN
iajs-2289	282	5	–1	–1	PROPN
iajs-2289	282	6	(	(	PUNCT
iajs-2289	282	7	y	y	NOUN
iajs-2289	282	8	)	)	PUNCT
iajs-2289	282	9	and	and	CCONJ
iajs-2289	282	10	{	{	PUNCT
iajs-2289	282	11	sg	sg	INTJ
iajs-2289	282	12	:	:	PUNCT
iajs-2289	282	13	g	g	PROPN
iajs-2289	282	14			PROPN
iajs-2289	282	15			ADJ
iajs-2289	282	16	–	–	PUNCT
iajs-2289	282	17	1	1	NUM
iajs-2289	282	18	(	(	PUNCT
iajs-2289	282	19	h	h	NOUN
iajs-2289	282	20	)	)	PUNCT
iajs-2289	282	21	}	}	PUNCT
iajs-2289	282	22	is	be	AUX
iajs-2289	282	23	an	an	DET
iajs-2289	282	24	open	open	ADJ
iajs-2289	282	25	cover	cover	NOUN
iajs-2289	282	26	of	of	ADP
iajs-2289	282	27	–1	–1	PROPN
iajs-2289	282	28	(	(	PUNCT
iajs-2289	282	29	y	y	NOUN
iajs-2289	282	30	)	)	PUNCT
iajs-2289	282	31	,	,	PUNCT
iajs-2289	282	32	yond	yond	PROPN
iajs-2289	282	33	is	be	AUX
iajs-2289	282	34	a	a	DET
iajs-2289	282	35	v	v	NOUN
iajs-2289	282	36			NOUN
iajs-2289	282	37	h	h	PUNCT
iajs-2289	282	38	and	and	CCONJ
iajs-2289	282	39	a	a	DET
iajs-2289	282	40	finite	finite	NOUN
iajs-2289	282	41	subset	subset	NOUN
iajs-2289	282	42	b	b	X
iajs-2289	282	43			PROPN
iajs-2289	282	44	–1	–1	PROPN
iajs-2289	282	45	(	(	PUNCT
iajs-2289	282	46	y	y	NOUN
iajs-2289	282	47	)	)	PUNCT
iajs-2289	282	48	such	such	ADJ
iajs-2289	282	49	that	that	SCONJ
iajs-2289	282	50	–1	–1	PROPN
iajs-2289	282	51	(	(	PUNCT
iajs-2289	282	52	cl	cl	INTJ
iajs-2289	282	53	j	j	NOUN
iajs-2289	282	54	-	-	NOUN
iajs-2289	282	55	ω-(t	ω-(t	NUM
iajs-2289	282	56	)	)	PUNCT
iajs-2289	282	57	)	)	PUNCT
iajs-2289	283	1			PROPN
iajs-2289	283	2	{cl	{cl	PROPN
iajs-2289	283	3	j	j	PROPN
iajs-2289	283	4	-	-	PUNCT
iajs-2289	283	5	ω-(tg	ω-(tg	PROPN
iajs-2289	283	6	):	):	PUNCT
iajs-2289	283	7	g	g	PROPN
iajs-2289	283	8			PROPN
iajs-2289	283	9	l	l	NOUN
iajs-2289	283	10	}	}	PUNCT
iajs-2289	283	11	.	.	PUNCT
iajs-2289	284	1	yond	yond	NOUN
iajs-2289	284	2	is	be	AUX
iajs-2289	284	3	an	an	DET
iajs-2289	284	4	m	m	NOUN
iajs-2289	284	5			NOUN
iajs-2289	284	6			NOUN
iajs-2289	284	7	such	such	ADJ
iajs-2289	284	8	that	that	SCONJ
iajs-2289	284	9	m	m	PROPN
iajs-2289	284	10			PROPN
iajs-2289	284	11	∩	∩	NOUN
iajs-2289	284	12	{	{	PUNCT
iajs-2289	284	13	mg	mg	NOUN
iajs-2289	284	14	:	:	PUNCT
iajs-2289	284	15	g	g	PROPN
iajs-2289	284	16			PROPN
iajs-2289	284	17	l	l	NOUN
iajs-2289	284	18	}	}	PUNCT
iajs-2289	284	19	.	.	PUNCT
iajs-2289	285	1	thus	thus	ADV
iajs-2289	285	2	,	,	PUNCT
iajs-2289	285	3	m	m	VERB
iajs-2289	285	4	∩	∩	ADJ
iajs-2289	285	5	–1	–1	PROPN
iajs-2289	285	6	(	(	PUNCT
iajs-2289	285	7	cl	cl	INTJ
iajs-2289	285	8	j	j	PROPN
iajs-2289	285	9	174	174	NUM
iajs-2289	285	10	ibn	ibn	PROPN
iajs-2289	285	11	al	al	PROPN
iajs-2289	285	12	-	-	PUNCT
iajs-2289	285	13	haitham	haitham	PROPN
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iajs-2289	285	15	.	.	PROPN
iajs-2289	285	16	for	for	ADP
iajs-2289	285	17	pure	pure	ADJ
iajs-2289	285	18	&	&	CCONJ
iajs-2289	285	19	appl	appl	PROPN
iajs-2289	285	20	.	.	PUNCT
iajs-2289	286	1	sci	sci	PROPN
iajs-2289	286	2	.	.	PROPN
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iajs-2289	286	4	(	(	PUNCT
iajs-2289	286	5	3	3	NUM
iajs-2289	286	6	)	)	PUNCT
iajs-2289	286	7	2019	2019	NUM
iajs-2289	286	8	ω-(t	ω-(t	NUM
iajs-2289	286	9	)	)	PUNCT
iajs-2289	286	10	)	)	PUNCT
iajs-2289	287	1	=	=	SYM
iajs-2289	287	2			NOUN
iajs-2289	287	3	implying	imply	VERB
iajs-2289	287	4	cl	cl	NOUN
iajs-2289	287	5	j	j	NOUN
iajs-2289	287	6	-	-	ADJ
iajs-2289	287	7	ω-(t	ω-(t	ADJ
iajs-2289	287	8	)	)	PUNCT
iajs-2289	287	9	∩	∩	ADJ
iajs-2289	287	10	(m	(m	NOUN
iajs-2289	287	11	)	)	PUNCT
iajs-2289	287	12	=	=	SYM
iajs-2289	287	13			NOUN
iajs-2289	287	14	,	,	PUNCT
iajs-2289	287	15	a	a	DET
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iajs-2289	287	17	as	as	ADP
iajs-2289	287	18	h	h	PROPN
iajs-2289	287	19			PROPN
iajs-2289	287	20	(	(	PUNCT
iajs-2289	287	21	alj	alj	PROPN
iajs-2289	287	22	-	-	PUNCT
iajs-2289	287	23	ω	ω	PROPN
iajs-2289	287	24	-	-	PUNCT
iajs-2289	287	25	c	c	NOUN
iajs-2289	287	26	(	(	NOUN
iajs-2289	287	27	)	)	PUNCT
iajs-2289	287	28	)	)	PUNCT
iajs-2289	287	29	.	.	PUNCT
iajs-2289	288	1	this	this	PRON
iajs-2289	288	2	shows	show	VERB
iajs-2289	288	3	that	that	SCONJ
iajs-2289	288	4	h	h	PROPN
iajs-2289	288	5			PROPN
iajs-2289	288	6	(alj	(alj	PROPN
iajs-2289	288	7	-	-	PUNCT
iajs-2289	288	8	ω	ω	NOUN
iajs-2289	288	9	-	-	PROPN
iajs-2289	288	10	c	c	NOUN
iajs-2289	288	11	)	)	PUNCT
iajs-2289	288	12	,	,	PUNCT
iajs-2289	288	13	where	where	SCONJ
iajs-2289	288	14	j{pre	j{pre	PROPN
iajs-2289	288	15	,	,	PUNCT
iajs-2289	288	16	,	,	PUNCT
iajs-2289	288	17	b	b	X
iajs-2289	288	18	,	,	PUNCT
iajs-2289	288	19			NOUN
iajs-2289	288	20	,	,	PUNCT
iajs-2289	288	21			NOUN
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iajs-2289	288	23	.	.	PUNCT
iajs-2289	289	1	(	(	PUNCT
iajs-2289	289	2	b	b	X
iajs-2289	289	3	)	)	PUNCT
iajs-2289	289	4			NOUN
iajs-2289	289	5	(	(	PUNCT
iajs-2289	289	6	c	c	X
iajs-2289	289	7	)	)	PUNCT
iajs-2289	289	8	assume	assume	VERB
iajs-2289	289	9			NOUN
iajs-2289	289	10	is	be	AUX
iajs-2289	289	11	a	a	DET
iajs-2289	289	12	filter	filter	NOUN
iajs-2289	289	13	base	base	NOUN
iajs-2289	289	14	on	on	ADP
iajs-2289	289	15	(g	(g	PROPN
iajs-2289	289	16	)	)	PUNCT
iajs-2289	289	17	and	and	CCONJ
iajs-2289	289	18			VERB
iajs-2289	289	19	j	j	PROPN
iajs-2289	289	20	-	-	PUNCT
iajs-2289	289	21	ω	ω	NUM
iajs-2289	289	22	⇝	⇝	NOUN
iajs-2289	289	23	l	l	NOUN
iajs-2289	289	24			PROPN
iajs-2289	289	25	h.	h.	PROPN
iajs-2289	289	26	let	let	NOUN
iajs-2289	289	27	be	be	AUX
iajs-2289	289	28	a	a	DET
iajs-2289	289	29	filter	filter	NOUN
iajs-2289	289	30	base	base	NOUN
iajs-2289	289	31	on	on	ADP
iajs-2289	289	32	g	g	PROPN
iajs-2289	289	33	such	such	ADJ
iajs-2289	289	34	that	that	SCONJ
iajs-2289	289	35	–1	–1	PROPN
iajs-2289	289	36	(	(	PUNCT
iajs-2289	289	37			NOUN
iajs-2289	289	38	)	)	PUNCT
iajs-2289	289	39	<	<	X
iajs-2289	289	40	.	.	X
iajs-2289	289	41	then	then	ADV
iajs-2289	289	42			VERB
iajs-2289	289	43	<	<	X
iajs-2289	289	44	(	(	PROPN
iajs-2289	289	45	)	)	PUNCT
iajs-2289	289	46	and	and	CCONJ
iajs-2289	289	47	(	(	PUNCT
iajs-2289	289	48	alj	alj	PROPN
iajs-2289	289	49	-	-	PROPN
iajs-2289	289	50	ω	ω	PROPN
iajs-2289	289	51	c	c	NOUN
iajs-2289	289	52	(	(	PROPN
iajs-2289	289	53	)	)	PUNCT
iajs-2289	289	54	)	)	PUNCT
iajs-2289	290	1	∩	∩	NOUN
iajs-2289	290	2	l	l	PROPN
iajs-2289	290	3			NOUN
iajs-2289	290	4	.	.	PUNCT
iajs-2289	290	5	therefore	therefore	ADV
iajs-2289	290	6	(alj	(alj	PROPN
iajs-2289	290	7	-	-	PUNCT
iajs-2289	290	8	ω	ω	NOUN
iajs-2289	290	9	-	-	PUNCT
iajs-2289	290	10	c	c	NOUN
iajs-2289	290	11	)	)	PUNCT
iajs-2289	290	12	∩	∩	PROPN
iajs-2289	290	13	l	l	NOUN
iajs-2289	290	14			NOUN
iajs-2289	290	15			NOUN
iajs-2289	290	16	and	and	CCONJ
iajs-2289	290	17	(	(	PUNCT
iajs-2289	290	18	alj	alj	PROPN
iajs-2289	290	19	-	-	PUNCT
iajs-2289	290	20	ω	ω	NOUN
iajs-2289	290	21	-	-	PUNCT
iajs-2289	290	22	c	c	NOUN
iajs-2289	290	23	)	)	PUNCT
iajs-2289	290	24	∩	∩	NOUN
iajs-2289	290	25			X
iajs-2289	290	26	–	–	PUNCT
iajs-2289	290	27	1	1	NUM
iajs-2289	290	28	(	(	PUNCT
iajs-2289	290	29	l	l	NOUN
iajs-2289	290	30	)	)	PUNCT
iajs-2289	290	31			NOUN
iajs-2289	290	32	.	.	PUNCT
iajs-2289	290	33	by	by	ADP
iajs-2289	290	34	theorem	theorem	NOUN
iajs-2289	290	35	(	(	PUNCT
iajs-2289	290	36	3.6	3.6	NUM
iajs-2289	290	37	,	,	PUNCT
iajs-2289	290	38	b	b	NOUN
iajs-2289	290	39	)	)	PUNCT
iajs-2289	290	40	,	,	PUNCT
iajs-2289	290	41	–1	–1	PROPN
iajs-2289	290	42	(	(	PUNCT
iajs-2289	290	43			NOUN
iajs-2289	290	44	)	)	PUNCT
iajs-2289	290	45	j	j	PROPN
iajs-2289	290	46	-	-	PUNCT
iajs-2289	290	47	ω	ω	PROPN
iajs-2289	290	48	⇝	⇝	NOUN
iajs-2289	290	49	–1	–1	PROPN
iajs-2289	290	50	(	(	PUNCT
iajs-2289	290	51	l	l	NOUN
iajs-2289	290	52	)	)	PUNCT
iajs-2289	290	53	,	,	PUNCT
iajs-2289	290	54	where	where	SCONJ
iajs-2289	290	55	j	j	PROPN
iajs-2289	290	56	{	{	PROPN
iajs-2289	290	57	,	,	PUNCT
iajs-2289	290	58	δ	δ	PROPN
iajs-2289	290	59	,	,	PUNCT
iajs-2289	290	60			NOUN
iajs-2289	290	61	,	,	PUNCT
iajs-2289	290	62	pre	pre	ADJ
iajs-2289	290	63	,	,	PUNCT
iajs-2289	290	64	b	b	NOUN
iajs-2289	290	65	,	,	PUNCT
iajs-2289	290	66			NOUN
iajs-2289	290	67	}	}	PUNCT
iajs-2289	290	68	.	.	PUNCT
iajs-2289	291	1	(	(	PUNCT
iajs-2289	291	2	c	c	X
iajs-2289	291	3	)	)	PUNCT
iajs-2289	291	4			NOUN
iajs-2289	291	5	(	(	PUNCT
iajs-2289	291	6	a	a	X
iajs-2289	291	7	)	)	PUNCT
iajs-2289	291	8	clearly	clearly	ADV
iajs-2289	291	9	.	.	PUNCT
iajs-2289	292	1	corollary	corollary	ADJ
iajs-2289	292	2	34	34	NUM
iajs-2289	292	3	if	if	SCONJ
iajs-2289	292	4			ADJ
iajs-2289	292	5	:	:	PUNCT
iajs-2289	292	6	g	g	PROPN
iajs-2289	292	7			NOUN
iajs-2289	292	8	h	h	NOUN
iajs-2289	292	9	is	be	AUX
iajs-2289	292	10	j	j	PROPN
iajs-2289	292	11	-	-	PUNCT
iajs-2289	292	12	ω	ω	VERB
iajs-2289	292	13	-	-	PUNCT
iajs-2289	292	14	perfect	perfect	ADJ
iajs-2289	292	15	mapping	mapping	NOUN
iajs-2289	292	16	,	,	PUNCT
iajs-2289	292	17	then	then	ADV
iajs-2289	292	18	:	:	PUNCT
iajs-2289	292	19	(	(	PUNCT
iajs-2289	292	20	a	a	X
iajs-2289	292	21	)	)	PUNCT
iajs-2289	292	22	for	for	ADP
iajs-2289	292	23	all	all	PRON
iajs-2289	292	24	k	k	PROPN
iajs-2289	292	25			PROPN
iajs-2289	292	26	g	g	PROPN
iajs-2289	292	27	,	,	PUNCT
iajs-2289	292	28	(	(	PUNCT
iajs-2289	292	29	alj	alj	PROPN
iajs-2289	292	30	-	-	PUNCT
iajs-2289	292	31	ω	ω	NOUN
iajs-2289	292	32	-	-	PUNCT
iajs-2289	292	33	cl	cl	NOUN
iajs-2289	292	34	(k	(k	NOUN
iajs-2289	292	35	)	)	PUNCT
iajs-2289	292	36	)	)	PUNCT
iajs-2289	293	1			PROPN
iajs-2289	293	2	(alj	(alj	PROPN
iajs-2289	293	3	-	-	PUNCT
iajs-2289	293	4	ω	ω	NOUN
iajs-2289	293	5	-	-	NOUN
iajs-2289	293	6	cl	cl	NOUN
iajs-2289	293	7	(	(	PUNCT
iajs-2289	293	8	k	k	NOUN
iajs-2289	293	9	)	)	PUNCT
iajs-2289	293	10	)	)	PUNCT
iajs-2289	293	11	.	.	PUNCT
iajs-2289	294	1	(	(	PUNCT
iajs-2289	294	2	b	b	X
iajs-2289	294	3	)	)	PUNCT
iajs-2289	294	4	for	for	ADP
iajs-2289	294	5	all	all	PRON
iajs-2289	294	6	almost	almost	ADV
iajs-2289	294	7	j	j	PROPN
iajs-2289	294	8	-	-	PUNCT
iajs-2289	294	9	ω	ω	NOUN
iajs-2289	294	10	-	-	PUNCT
iajs-2289	294	11	closed	closed	ADJ
iajs-2289	294	12	k	k	PROPN
iajs-2289	294	13			PROPN
iajs-2289	294	14	g	g	PROPN
iajs-2289	294	15	,	,	PUNCT
iajs-2289	294	16	(k	(k	PROPN
iajs-2289	294	17	)	)	PUNCT
iajs-2289	294	18	is	be	AUX
iajs-2289	294	19	almost	almost	ADV
iajs-2289	294	20	j	j	PROPN
iajs-2289	294	21	-	-	PUNCT
iajs-2289	294	22	ω	ω	NOUN
iajs-2289	294	23	-	-	PUNCT
iajs-2289	294	24	closed	closed	ADJ
iajs-2289	294	25	.	.	PUNCT
iajs-2289	295	1	(	(	PUNCT
iajs-2289	295	2	c	c	X
iajs-2289	295	3	)	)	PUNCT
iajs-2289	295	4			X
iajs-2289	295	5	is	be	AUX
iajs-2289	295	6	j	j	PROPN
iajs-2289	295	7	-	-	PUNCT
iajs-2289	295	8	ω	ω	NOUN
iajs-2289	295	9	-	-	ADJ
iajs-2289	295	10	compact	compact	ADJ
iajs-2289	295	11	.	.	PUNCT
iajs-2289	296	1	where	where	SCONJ
iajs-2289	296	2	j	j	PROPN
iajs-2289	296	3	{	{	PROPN
iajs-2289	296	4	,	,	PUNCT
iajs-2289	296	5	δ	δ	PROPN
iajs-2289	296	6	,	,	PUNCT
iajs-2289	296	7			NOUN
iajs-2289	296	8	,	,	PUNCT
iajs-2289	296	9	pre	pre	AUX
iajs-2289	296	10	,	,	PUNCT
iajs-2289	296	11	b	b	NOUN
iajs-2289	296	12	,	,	PUNCT
iajs-2289	296	13			NOUN
iajs-2289	296	14	}	}	PUNCT
iajs-2289	296	15	.	.	PUNCT
iajs-2289	297	1	proof	proof	NOUN
iajs-2289	297	2	:	:	PUNCT
iajs-2289	297	3	(	(	PUNCT
iajs-2289	297	4	a	a	X
iajs-2289	297	5	)	)	PUNCT
iajs-2289	297	6	is	be	AUX
iajs-2289	297	7	an	an	DET
iajs-2289	297	8	immediate	immediate	ADJ
iajs-2289	297	9	consequence	consequence	NOUN
iajs-2289	297	10	of	of	ADP
iajs-2289	297	11	theorem	theorem	NOUN
iajs-2289	297	12	33	33	NUM
iajs-2289	297	13	,	,	PUNCT
iajs-2289	297	14	and	and	CCONJ
iajs-2289	297	15	(	(	PUNCT
iajs-2289	297	16	b	b	X
iajs-2289	297	17	)	)	PUNCT
iajs-2289	297	18	follows	follow	VERB
iajs-2289	297	19	easily	easily	ADV
iajs-2289	297	20	from	from	ADP
iajs-2289	297	21	(	(	PUNCT
iajs-2289	297	22	a	a	NOUN
iajs-2289	297	23	)	)	PUNCT
iajs-2289	297	24	.	.	PUNCT
iajs-2289	298	1	to	to	PART
iajs-2289	298	2	prove	prove	VERB
iajs-2289	298	3	(	(	PUNCT
iajs-2289	298	4	c	c	X
iajs-2289	298	5	)	)	PUNCT
iajs-2289	298	6	let	let	VERB
iajs-2289	298	7	c	c	PRON
iajs-2289	298	8	be	be	AUX
iajs-2289	298	9	quasij	quasij	NOUN
iajs-2289	298	10	-	-	PUNCT
iajs-2289	298	11	ω	ω	NUM
iajs-2289	298	12	-	-	PUNCT
iajs-2289	298	13	h	h	NOUN
iajs-2289	298	14	-	-	PUNCT
iajs-2289	298	15	closed	closed	ADJ
iajs-2289	298	16	relative	relative	ADJ
iajs-2289	298	17	to	to	ADP
iajs-2289	298	18	h	h	NOUN
iajs-2289	298	19	,	,	PUNCT
iajs-2289	298	20	and	and	CCONJ
iajs-2289	298	21			NOUN
iajs-2289	298	22	be	be	VERB
iajs-2289	298	23	a	a	DET
iajs-2289	298	24	filter	filter	NOUN
iajs-2289	298	25	base	base	NOUN
iajs-2289	298	26	on	on	ADP
iajs-2289	298	27	–1	–1	PROPN
iajs-2289	298	28	(	(	PUNCT
iajs-2289	298	29	c	c	NOUN
iajs-2289	298	30	)	)	PUNCT
iajs-2289	298	31	,	,	PUNCT
iajs-2289	298	32	then	then	ADV
iajs-2289	298	33	(	(	PROPN
iajs-2289	298	34	)	)	PUNCT
iajs-2289	298	35	is	be	AUX
iajs-2289	298	36	a	a	DET
iajs-2289	298	37	filter	filter	NOUN
iajs-2289	298	38	base	base	NOUN
iajs-2289	298	39	on	on	ADP
iajs-2289	298	40	c.	c.	NOUN
iajs-2289	298	41	by	by	ADP
iajs-2289	298	42	theorem	theorem	NOUN
iajs-2289	298	43	20	20	NUM
iajs-2289	298	44	,	,	PUNCT
iajs-2289	298	45	(	(	PUNCT
iajs-2289	298	46	alj	alj	PROPN
iajs-2289	298	47	-	-	PUNCT
iajs-2289	298	48	ω	ω	NOUN
iajs-2289	298	49	-	-	PUNCT
iajs-2289	298	50	c(	c(	NOUN
iajs-2289	298	51	)	)	PUNCT
iajs-2289	298	52	)	)	PUNCT
iajs-2289	299	1	∩	∩	PROPN
iajs-2289	299	2	c	c	PROPN
iajs-2289	299	3			NOUN
iajs-2289	299	4			NOUN
iajs-2289	299	5	and	and	CCONJ
iajs-2289	299	6	by	by	ADP
iajs-2289	299	7	theorem	theorem	NOUN
iajs-2289	299	8	(	(	PUNCT
iajs-2289	299	9	33	33	NUM
iajs-2289	299	10	,	,	PUNCT
iajs-2289	299	11	b	b	NOUN
iajs-2289	299	12	)	)	PUNCT
iajs-2289	299	13	,	,	PUNCT
iajs-2289	299	14	(	(	PUNCT
iajs-2289	299	15	alj	alj	PROPN
iajs-2289	299	16	-	-	PUNCT
iajs-2289	299	17	ω	ω	NOUN
iajs-2289	299	18	-	-	PUNCT
iajs-2289	299	19	c	c	NOUN
iajs-2289	299	20	)	)	PUNCT
iajs-2289	299	21	∩	∩	NOUN
iajs-2289	299	22	–1	–1	PROPN
iajs-2289	299	23	(	(	PUNCT
iajs-2289	299	24	c	c	NOUN
iajs-2289	299	25	)	)	PUNCT
iajs-2289	299	26			NOUN
iajs-2289	299	27	.	.	PUNCT
iajs-2289	299	28	by	by	ADP
iajs-2289	299	29	theorem	theorem	NOUN
iajs-2289	299	30	20	20	NUM
iajs-2289	299	31	,	,	PUNCT
iajs-2289	299	32	–1	–1	PROPN
iajs-2289	299	33	(	(	PUNCT
iajs-2289	299	34	c	c	X
iajs-2289	299	35	)	)	PUNCT
iajs-2289	299	36	is	be	AUX
iajs-2289	299	37	quasij	quasij	NOUN
iajs-2289	299	38	-	-	PUNCT
iajs-2289	299	39	ω	ω	NUM
iajs-2289	299	40	-	-	PUNCT
iajs-2289	299	41	h	h	NOUN
iajs-2289	299	42	-	-	PUNCT
iajs-2289	299	43	closed	closed	ADJ
iajs-2289	299	44	relative	relative	ADJ
iajs-2289	299	45	to	to	ADP
iajs-2289	299	46	g	g	NOUN
iajs-2289	299	47	,	,	PUNCT
iajs-2289	299	48	where	where	SCONJ
iajs-2289	299	49	j{	j{	PROPN
iajs-2289	299	50	,	,	PUNCT
iajs-2289	299	51	δ	δ	PROPN
iajs-2289	299	52	,	,	PUNCT
iajs-2289	299	53			NOUN
iajs-2289	299	54	,	,	PUNCT
iajs-2289	299	55	pre	pre	ADJ
iajs-2289	299	56	,	,	PUNCT
iajs-2289	299	57	b	b	NOUN
iajs-2289	299	58	,	,	PUNCT
iajs-2289	299	59			NOUN
iajs-2289	299	60	}	}	PUNCT
iajs-2289	299	61	.	.	PUNCT
iajs-2289	300	1	theorem	theorem	VERB
iajs-2289	300	2	35	35	NUM
iajs-2289	300	3	an	an	DET
iajs-2289	300	4	j	j	PROPN
iajs-2289	300	5	-	-	PUNCT
iajs-2289	300	6	ω	ω	NOUN
iajs-2289	300	7	-	-	PUNCT
iajs-2289	300	8	closure	closure	NOUN
iajs-2289	300	9	continuous	continuous	ADJ
iajs-2289	300	10	mapping	mapping	NOUN
iajs-2289	300	11			ADJ
iajs-2289	300	12	:	:	PUNCT
iajs-2289	300	13	g	g	PROPN
iajs-2289	300	14			NOUN
iajs-2289	300	15	h	h	NOUN
iajs-2289	300	16	is	be	AUX
iajs-2289	300	17	j	j	PROPN
iajs-2289	300	18	-	-	PUNCT
iajs-2289	300	19	ω	ω	NOUN
iajs-2289	300	20	-	-	NOUN
iajs-2289	300	21	perfect	perfect	ADJ
iajs-2289	300	22	if	if	SCONJ
iajs-2289	301	1	and	and	CCONJ
iajs-2289	301	2	only	only	ADV
iajs-2289	301	3	if	if	SCONJ
iajs-2289	301	4	(	(	PUNCT
iajs-2289	301	5	a	a	X
iajs-2289	301	6	)	)	PUNCT
iajs-2289	301	7			X
iajs-2289	301	8	is	be	AUX
iajs-2289	301	9	almost	almost	ADV
iajs-2289	301	10	j	j	PROPN
iajs-2289	301	11	-	-	PUNCT
iajs-2289	301	12	ω	ω	NOUN
iajs-2289	301	13	-	-	PUNCT
iajs-2289	301	14	closed	closed	ADJ
iajs-2289	301	15	,	,	PUNCT
iajs-2289	301	16	and	and	CCONJ
iajs-2289	301	17	(	(	PUNCT
iajs-2289	301	18	b	b	NOUN
iajs-2289	301	19	)	)	PUNCT
iajs-2289	301	20			X
iajs-2289	301	21	–	–	PUNCT
iajs-2289	301	22	1	1	NUM
iajs-2289	301	23	(	(	PUNCT
iajs-2289	301	24	y	y	NOUN
iajs-2289	301	25	)	)	PUNCT
iajs-2289	301	26	j	j	PROPN
iajs-2289	301	27	-	-	PUNCT
iajs-2289	301	28	ω	ω	NOUN
iajs-2289	301	29	-	-	NOUN
iajs-2289	301	30	rigid	rigid	ADJ
iajs-2289	301	31	for	for	ADP
iajs-2289	301	32	each	each	DET
iajs-2289	301	33	h	h	NOUN
iajs-2289	301	34			PROPN
iajs-2289	301	35	h	h	NOUN
iajs-2289	301	36	,	,	PUNCT
iajs-2289	301	37	where	where	SCONJ
iajs-2289	301	38	j	j	PROPN
iajs-2289	301	39	{	{	PUNCT
iajs-2289	301	40			PROPN
iajs-2289	301	41	,	,	PUNCT
iajs-2289	301	42	δ	δ	PROPN
iajs-2289	301	43	,	,	PUNCT
iajs-2289	301	44			NOUN
iajs-2289	301	45	,	,	PUNCT
iajs-2289	301	46	pre	pre	ADJ
iajs-2289	301	47	,	,	PUNCT
iajs-2289	301	48	b	b	NOUN
iajs-2289	301	49	,	,	PUNCT
iajs-2289	301	50			NOUN
iajs-2289	301	51	}	}	PUNCT
iajs-2289	301	52	.	.	PUNCT
iajs-2289	302	1	proof	proof	NOUN
iajs-2289	302	2	:	:	PUNCT
iajs-2289	302	3	(	(	PUNCT
iajs-2289	302	4			NOUN
iajs-2289	302	5	)	)	PUNCT
iajs-2289	302	6	if	if	SCONJ
iajs-2289	302	7			ADJ
iajs-2289	302	8	is	be	AUX
iajs-2289	302	9	j	j	PROPN
iajs-2289	302	10	-	-	PUNCT
iajs-2289	302	11	ω	ω	NOUN
iajs-2289	302	12	-	-	PUNCT
iajs-2289	302	13	closure	closure	NOUN
iajs-2289	302	14	continuous	continuous	ADJ
iajs-2289	302	15	and	and	CCONJ
iajs-2289	302	16	j	j	PROPN
iajs-2289	302	17	-	-	PUNCT
iajs-2289	302	18	ω	ω	VERB
iajs-2289	302	19	-	-	PUNCT
iajs-2289	302	20	perfect	perfect	ADJ
iajs-2289	302	21	mapping	mapping	NOUN
iajs-2289	302	22	,	,	PUNCT
iajs-2289	302	23	then	then	ADV
iajs-2289	302	24	by	by	ADP
iajs-2289	302	25	corollaries	corollary	NOUN
iajs-2289	302	26	34	34	NUM
iajs-2289	302	27	and	and	CCONJ
iajs-2289	302	28	24	24	NUM
iajs-2289	302	29	,	,	PUNCT
iajs-2289	302	30			X
iajs-2289	302	31	is	be	AUX
iajs-2289	302	32	almost	almost	ADV
iajs-2289	302	33	j	j	PROPN
iajs-2289	302	34	-	-	PUNCT
iajs-2289	302	35	ω	ω	NOUN
iajs-2289	302	36	-	-	PUNCT
iajs-2289	302	37	closed	closed	ADJ
iajs-2289	302	38	.	.	PUNCT
iajs-2289	303	1	to	to	PART
iajs-2289	303	2	show	show	VERB
iajs-2289	303	3	–1	–1	PROPN
iajs-2289	303	4	(	(	PUNCT
iajs-2289	303	5	h	h	NOUN
iajs-2289	303	6	)	)	PUNCT
iajs-2289	303	7	,	,	PUNCT
iajs-2289	303	8	for	for	ADP
iajs-2289	303	9	h	h	PROPN
iajs-2289	303	10			PROPN
iajs-2289	303	11	h	h	NOUN
iajs-2289	303	12	,	,	PUNCT
iajs-2289	303	13	is	be	AUX
iajs-2289	303	14	j	j	PROPN
iajs-2289	303	15	-	-	PUNCT
iajs-2289	303	16	ω	ω	NOUN
iajs-2289	303	17	-	-	ADJ
iajs-2289	303	18	rigid	rigid	ADJ
iajs-2289	303	19	,	,	PUNCT
iajs-2289	303	20	let	let	VERB
iajs-2289	303	21			NOUN
iajs-2289	303	22	be	be	AUX
iajs-2289	303	23	a	a	DET
iajs-2289	303	24	filter	filter	NOUN
iajs-2289	303	25	base	base	NOUN
iajs-2289	303	26	on	on	ADP
iajs-2289	303	27	g	g	PROPN
iajs-2289	303	28	such	such	ADJ
iajs-2289	303	29	that	that	SCONJ
iajs-2289	303	30	–1	–1	PROPN
iajs-2289	303	31	(	(	PUNCT
iajs-2289	303	32	h	h	NOUN
iajs-2289	303	33	)	)	PUNCT
iajs-2289	303	34	∩	∩	NOUN
iajs-2289	303	35	(	(	PUNCT
iajs-2289	303	36	al	al	PROPN
iajs-2289	303	37	-j	-j	PROPN
iajs-2289	303	38	-	-	PUNCT
iajs-2289	303	39	ω	ω	NOUN
iajs-2289	303	40	-	-	PUNCT
iajs-2289	303	41	c	c	NOUN
iajs-2289	303	42	)	)	PUNCT
iajs-2289	303	43	=	=	NOUN
iajs-2289	304	1	.	.	X
iajs-2289	304	2	so	so	ADV
iajs-2289	304	3	,	,	PUNCT
iajs-2289	304	4	h	h	NOUN
iajs-2289	304	5			VERB
iajs-2289	304	6	(alj	(alj	PROPN
iajs-2289	304	7	-	-	PUNCT
iajs-2289	304	8	ω	ω	NOUN
iajs-2289	304	9	-	-	NOUN
iajs-2289	304	10	c	c	NOUN
iajs-2289	304	11	)	)	PUNCT
iajs-2289	304	12	and	and	CCONJ
iajs-2289	304	13	by	by	ADP
iajs-2289	304	14	theorem	theorem	NOUN
iajs-2289	304	15	(	(	PUNCT
iajs-2289	304	16	33	33	NUM
iajs-2289	304	17	,	,	PUNCT
iajs-2289	304	18	b	b	NOUN
iajs-2289	304	19	)	)	PUNCT
iajs-2289	304	20	,	,	PUNCT
iajs-2289	304	21	h	h	NOUN
iajs-2289	304	22			PROPN
iajs-2289	304	23	(	(	PUNCT
iajs-2289	304	24	al	al	PROPN
iajs-2289	304	25	j	j	PROPN
iajs-2289	304	26	-	-	PROPN
iajs-2289	304	27	ω	ω	PROPN
iajs-2289	304	28	c	c	PROPN
iajs-2289	304	29	(	(	NOUN
iajs-2289	304	30	)	)	PUNCT
iajs-2289	304	31	)	)	PUNCT
iajs-2289	304	32	.	.	PUNCT
iajs-2289	305	1	yond	yond	NOUN
iajs-2289	305	2	is	be	AUX
iajs-2289	305	3	open	open	ADJ
iajs-2289	305	4	s	s	PROPN
iajs-2289	305	5	of	of	ADP
iajs-2289	305	6	h	h	NOUN
iajs-2289	305	7	and	and	CCONJ
iajs-2289	305	8	m	m	PROPN
iajs-2289	305	9			NOUN
iajs-2289	305	10			NOUN
iajs-2289	305	11	such	such	ADJ
iajs-2289	305	12	that	that	DET
iajs-2289	305	13	cl	cl	NOUN
iajs-2289	305	14	j	j	NOUN
iajs-2289	305	15	-	-	ADJ
iajs-2289	305	16	ω-(s	ω-(s	NUM
iajs-2289	305	17	)	)	PUNCT
iajs-2289	305	18	∩	∩	ADJ
iajs-2289	305	19	(m	(m	NOUN
iajs-2289	305	20	)	)	PUNCT
iajs-2289	305	21	=	=	NOUN
iajs-2289	305	22	.	.	X
iajs-2289	305	23	so	so	ADV
iajs-2289	305	24	,	,	PUNCT
iajs-2289	305	25	–1	–1	PROPN
iajs-2289	305	26	(	(	PUNCT
iajs-2289	305	27	cl	cl	INTJ
iajs-2289	305	28	j	j	NOUN
iajs-2289	305	29	-	-	PUNCT
iajs-2289	305	30	ω(s	ω(s	PROPN
iajs-2289	305	31	)	)	PUNCT
iajs-2289	305	32	)	)	PUNCT
iajs-2289	305	33	∩	∩	NOUN
iajs-2289	305	34	m	m	NOUN
iajs-2289	305	35	=	=	X
iajs-2289	305	36	.	.	X
iajs-2289	305	37	since	since	SCONJ
iajs-2289	305	38			ADJ
iajs-2289	305	39	is	be	AUX
iajs-2289	305	40	j	j	PROPN
iajs-2289	305	41	-	-	PUNCT
iajs-2289	305	42	ω	ω	NOUN
iajs-2289	305	43	-	-	PUNCT
iajs-2289	305	44	closure	closure	NOUN
iajs-2289	305	45	continuous	continuous	ADJ
iajs-2289	305	46	,	,	PUNCT
iajs-2289	305	47	then	then	ADV
iajs-2289	305	48	for	for	ADP
iajs-2289	305	49	any	any	DET
iajs-2289	305	50	g	g	NOUN
iajs-2289	305	51			NOUN
iajs-2289	305	52	–1	–1	PROPN
iajs-2289	305	53	(	(	PUNCT
iajs-2289	305	54	h	h	NOUN
iajs-2289	305	55	)	)	PUNCT
iajs-2289	305	56	,	,	PUNCT
iajs-2289	305	57	yond	yond	PROPN
iajs-2289	305	58	is	be	AUX
iajs-2289	305	59	open	open	ADJ
iajs-2289	305	60	t	t	NOUN
iajs-2289	305	61	of	of	ADP
iajs-2289	305	62	g	g	PROPN
iajs-2289	305	63	such	such	ADJ
iajs-2289	305	64	that	that	DET
iajs-2289	305	65	cl	cl	NOUN
iajs-2289	305	66	j	j	NOUN
iajs-2289	305	67	-	-	PUNCT
iajs-2289	305	68	ω-(t	ω-(t	ADJ
iajs-2289	305	69	)	)	PUNCT
iajs-2289	305	70			PROPN
iajs-2289	305	71	–1	–1	PROPN
iajs-2289	305	72	(	(	PUNCT
iajs-2289	305	73	cl	cl	INTJ
iajs-2289	305	74	j	j	NOUN
iajs-2289	305	75	-	-	PROPN
iajs-2289	305	76	ω-(s	ω-(s	NUM
iajs-2289	305	77	)	)	PUNCT
iajs-2289	305	78	)	)	PUNCT
iajs-2289	305	79	.	.	PUNCT
iajs-2289	306	1	so	so	ADV
iajs-2289	306	2	,	,	PUNCT
iajs-2289	306	3			ADJ
iajs-2289	306	4	–	–	PUNCT
iajs-2289	306	5	1	1	NUM
iajs-2289	306	6	(	(	PUNCT
iajs-2289	306	7	h	h	NOUN
iajs-2289	306	8	)	)	PUNCT
iajs-2289	306	9	∩	∩	ADJ
iajs-2289	306	10	cl	cl	PROPN
iajs-2289	306	11	j	j	PROPN
iajs-2289	306	12	-	-	PUNCT
iajs-2289	306	13	ω-(m	ω-(m	NUM
iajs-2289	306	14	)	)	PUNCT
iajs-2289	306	15	=	=	SYM
iajs-2289	306	16			NOUN
iajs-2289	306	17	,	,	PUNCT
iajs-2289	306	18	where	where	SCONJ
iajs-2289	306	19	j	j	PROPN
iajs-2289	306	20	{	{	PUNCT
iajs-2289	306	21			PROPN
iajs-2289	306	22	,	,	PUNCT
iajs-2289	306	23	δ	δ	PROPN
iajs-2289	306	24	,	,	PUNCT
iajs-2289	306	25			NOUN
iajs-2289	306	26	,	,	PUNCT
iajs-2289	306	27	pre	pre	ADJ
iajs-2289	306	28	,	,	PUNCT
iajs-2289	306	29	b	b	NOUN
iajs-2289	306	30	,	,	PUNCT
iajs-2289	306	31			NOUN
iajs-2289	306	32	}	}	PUNCT
iajs-2289	306	33	.	.	PUNCT
iajs-2289	307	1	(	(	PUNCT
iajs-2289	307	2			NOUN
iajs-2289	307	3	)	)	PUNCT
iajs-2289	307	4	assume	assume	VERB
iajs-2289	307	5	that	that	SCONJ
iajs-2289	307	6	j	j	PROPN
iajs-2289	307	7	-	-	PUNCT
iajs-2289	307	8	ω	ω	NOUN
iajs-2289	307	9	-	-	PUNCT
iajs-2289	307	10	closure	closure	NOUN
iajs-2289	307	11	continuous	continuous	ADJ
iajs-2289	307	12	mapping	mapping	NOUN
iajs-2289	307	13			ADJ
iajs-2289	307	14	satisfies	satisfie	NOUN
iajs-2289	307	15	(	(	PUNCT
iajs-2289	307	16	a	a	X
iajs-2289	307	17	)	)	PUNCT
iajs-2289	307	18	and	and	CCONJ
iajs-2289	307	19	(	(	PUNCT
iajs-2289	307	20	b	b	NOUN
iajs-2289	307	21	)	)	PUNCT
iajs-2289	307	22	.	.	PUNCT
iajs-2289	308	1	let	let	VERB
iajs-2289	308	2			NOUN
iajs-2289	308	3	be	be	AUX
iajs-2289	308	4	a	a	DET
iajs-2289	308	5	filter	filter	NOUN
iajs-2289	308	6	base	base	NOUN
iajs-2289	308	7	on	on	ADP
iajs-2289	308	8	(g	(g	NOUN
iajs-2289	308	9	)	)	PUNCT
iajs-2289	308	10	such	such	ADJ
iajs-2289	308	11	that	that	SCONJ
iajs-2289	308	12			VERB
iajs-2289	308	13	j	j	PROPN
iajs-2289	308	14	-	-	PUNCT
iajs-2289	308	15	ω	ω	PROPN
iajs-2289	308	16	⇝	⇝	PROPN
iajs-2289	308	17	h.	h.	PROPN
iajs-2289	308	18	let	let	VERB
iajs-2289	308	19			PROPN
iajs-2289	308	20	be	be	AUX
iajs-2289	308	21	a	a	DET
iajs-2289	308	22	filter	filter	NOUN
iajs-2289	308	23	base	base	NOUN
iajs-2289	308	24	on	on	ADP
iajs-2289	308	25	g	g	PROPN
iajs-2289	308	26	such	such	ADJ
iajs-2289	308	27	that	that	SCONJ
iajs-2289	308	28	–1	–1	PROPN
iajs-2289	308	29	(	(	PUNCT
iajs-2289	308	30			NOUN
iajs-2289	308	31	)	)	PUNCT
iajs-2289	308	32	<	<	X
iajs-2289	308	33	.	.	X
iajs-2289	309	1	so	so	ADV
iajs-2289	309	2	,	,	PUNCT
iajs-2289	309	3			VERB
iajs-2289	309	4	<	<	X
iajs-2289	309	5	(	(	PROPN
iajs-2289	309	6	)	)	PUNCT
iajs-2289	309	7	implying	imply	VERB
iajs-2289	309	8	that	that	SCONJ
iajs-2289	309	9	h	h	NOUN
iajs-2289	309	10			NOUN
iajs-2289	309	11	(	(	PUNCT
iajs-2289	309	12	alj	alj	PROPN
iajs-2289	309	13	-	-	PUNCT
iajs-2289	309	14	ω	ω	NOUN
iajs-2289	309	15	-	-	PUNCT
iajs-2289	309	16	c	c	NOUN
iajs-2289	309	17	(	(	PROPN
iajs-2289	309	18	)	)	PUNCT
iajs-2289	309	19	)	)	PUNCT
iajs-2289	309	20	.	.	PUNCT
iajs-2289	310	1	therefore	therefore	ADV
iajs-2289	310	2	,	,	PUNCT
iajs-2289	310	3	for	for	ADP
iajs-2289	310	4	each	each	DET
iajs-2289	310	5	g	g	PROPN
iajs-2289	310	6			PROPN
iajs-2289	310	7			PROPN
iajs-2289	310	8	,	,	PUNCT
iajs-2289	310	9	h	h	NOUN
iajs-2289	310	10			NOUN
iajs-2289	310	11	(	(	PUNCT
iajs-2289	310	12	alj	alj	PROPN
iajs-2289	310	13	-	-	PUNCT
iajs-2289	310	14	ω	ω	NOUN
iajs-2289	310	15	-	-	PUNCT
iajs-2289	310	16	cl	cl	ADJ
iajs-2289	310	17	(	(	PUNCT
iajs-2289	310	18	g	g	NOUN
iajs-2289	310	19	)	)	PUNCT
iajs-2289	310	20	)	)	PUNCT
iajs-2289	310	21			PROPN
iajs-2289	310	22	(alj	(alj	PROPN
iajs-2289	310	23	-	-	PUNCT
iajs-2289	310	24	ω	ω	NOUN
iajs-2289	310	25	-	-	NOUN
iajs-2289	310	26	cl	cl	NOUN
iajs-2289	310	27	g	g	NOUN
iajs-2289	310	28	)	)	PUNCT
iajs-2289	310	29	.	.	PUNCT
iajs-2289	311	1	hence	hence	ADV
iajs-2289	311	2	,	,	PUNCT
iajs-2289	311	3			X
iajs-2289	311	4	–	–	PUNCT
iajs-2289	311	5	1	1	NUM
iajs-2289	311	6	(	(	PUNCT
iajs-2289	311	7	h	h	NOUN
iajs-2289	311	8	)	)	PUNCT
iajs-2289	311	9	∩	∩	NOUN
iajs-2289	311	10	(	(	PUNCT
iajs-2289	311	11	alj	alj	PROPN
iajs-2289	311	12	-	-	PUNCT
iajs-2289	311	13	ω	ω	NOUN
iajs-2289	311	14	-	-	NOUN
iajs-2289	311	15	cl	cl	NOUN
iajs-2289	311	16	g	g	NOUN
iajs-2289	311	17	)	)	PUNCT
iajs-2289	311	18			NOUN
iajs-2289	311	19			NOUN
iajs-2289	311	20	for	for	ADP
iajs-2289	311	21	each	each	DET
iajs-2289	311	22	g	g	NOUN
iajs-2289	311	23	.	.	PROPN
iajs-2289	311	24	by	by	ADP
iajs-2289	311	25	(	(	PUNCT
iajs-2289	311	26	b	b	NOUN
iajs-2289	311	27	)	)	PUNCT
iajs-2289	311	28	,	,	PUNCT
iajs-2289	311	29	–1	–1	PROPN
iajs-2289	311	30	(	(	PUNCT
iajs-2289	311	31	h	h	NOUN
iajs-2289	311	32	)	)	PUNCT
iajs-2289	311	33	∩	∩	NOUN
iajs-2289	311	34	(	(	PUNCT
iajs-2289	311	35	alj	alj	PROPN
iajs-2289	311	36	-	-	PUNCT
iajs-2289	311	37	ωc	ωc	NOUN
iajs-2289	311	38	)	)	PUNCT
iajs-2289	311	39			NOUN
iajs-2289	311	40	.	.	PUNCT
iajs-2289	311	41	by	by	ADP
iajs-2289	311	42	theorem	theorem	NOUN
iajs-2289	311	43	33	33	NUM
iajs-2289	311	44	,	,	PUNCT
iajs-2289	311	45			X
iajs-2289	311	46	is	be	AUX
iajs-2289	311	47	j	j	PROPN
iajs-2289	311	48	-	-	PUNCT
iajs-2289	311	49	ω	ω	VERB
iajs-2289	311	50	-	-	PUNCT
iajs-2289	311	51	perfect	perfect	ADJ
iajs-2289	311	52	mapping	mapping	NOUN
iajs-2289	311	53	,	,	PUNCT
iajs-2289	311	54	where	where	SCONJ
iajs-2289	311	55	j	j	PROPN
iajs-2289	311	56			NOUN
iajs-2289	311	57	{	{	PUNCT
iajs-2289	311	58			PROPN
iajs-2289	311	59	,	,	PUNCT
iajs-2289	311	60	δ	δ	PROPN
iajs-2289	311	61	,	,	PUNCT
iajs-2289	311	62			NOUN
iajs-2289	311	63	,	,	PUNCT
iajs-2289	311	64	pre	pre	ADJ
iajs-2289	311	65	,	,	PUNCT
iajs-2289	311	66	b	b	NOUN
iajs-2289	311	67	,	,	PUNCT
iajs-2289	311	68			NOUN
iajs-2289	311	69	}	}	PUNCT
iajs-2289	311	70	.	.	PUNCT
iajs-2289	312	1	actually	actually	ADV
iajs-2289	312	2	,	,	PUNCT
iajs-2289	312	3	in	in	ADP
iajs-2289	312	4	the	the	DET
iajs-2289	312	5	proof	proof	NOUN
iajs-2289	312	6	of	of	ADP
iajs-2289	312	7	the	the	DET
iajs-2289	312	8	converse	converse	NOUN
iajs-2289	312	9	of	of	ADP
iajs-2289	312	10	theorem	theorem	NOUN
iajs-2289	312	11	35	35	NUM
iajs-2289	312	12	,	,	PUNCT
iajs-2289	312	13	we	we	PRON
iajs-2289	312	14	have	have	AUX
iajs-2289	312	15	shown	show	VERB
iajs-2289	312	16	that	that	SCONJ
iajs-2289	312	17	property	property	NOUN
iajs-2289	312	18	(	(	PUNCT
iajs-2289	312	19	a	a	NOUN
iajs-2289	312	20	)	)	PUNCT
iajs-2289	312	21	of	of	ADP
iajs-2289	312	22	theorem	theorem	ADJ
iajs-2289	312	23	35	35	NUM
iajs-2289	312	24	can	can	AUX
iajs-2289	312	25	reduced	reduce	VERB
iajs-2289	312	26	to	to	ADP
iajs-2289	312	27	this	this	DET
iajs-2289	312	28	statement	statement	NOUN
iajs-2289	312	29	:	:	PUNCT
iajs-2289	312	30	for	for	ADP
iajs-2289	312	31	each	each	DET
iajs-2289	312	32	k	k	PROPN
iajs-2289	312	33			PROPN
iajs-2289	312	34	g	g	PROPN
iajs-2289	312	35	,	,	PUNCT
iajs-2289	312	36	al	al	PROPN
iajs-2289	312	37	j	j	PROPN
iajs-2289	312	38	-	-	PUNCT
iajs-2289	312	39	ω	ω	PROPN
iajs-2289	312	40	-	-	PUNCT
iajs-2289	312	41	cl	cl	NOUN
iajs-2289	312	42	(k	(k	NOUN
iajs-2289	312	43	)	)	PUNCT
iajs-2289	312	44			PROPN
iajs-2289	312	45			X
iajs-2289	312	46	(	(	PUNCT
iajs-2289	312	47	al	al	PROPN
iajs-2289	312	48	j	j	PROPN
iajs-2289	312	49	-	-	PUNCT
iajs-2289	312	50	ω	ω	NOUN
iajs-2289	312	51	-	-	NOUN
iajs-2289	312	52	cl	cl	NOUN
iajs-2289	312	53	(	(	PUNCT
iajs-2289	312	54	k	k	NOUN
iajs-2289	312	55	)	)	PUNCT
iajs-2289	312	56	;	;	PUNCT
iajs-2289	312	57	in	in	ADP
iajs-2289	312	58	fact	fact	NOUN
iajs-2289	312	59	,	,	PUNCT
iajs-2289	312	60	we	we	PRON
iajs-2289	312	61	have	have	AUX
iajs-2289	312	62	shown	show	VERB
iajs-2289	312	63	the	the	DET
iajs-2289	312	64	next	next	ADJ
iajs-2289	312	65	corollary	corollary	NOUN
iajs-2289	312	66	(	(	PUNCT
iajs-2289	312	67	the	the	DET
iajs-2289	312	68	mapping	mapping	NOUN
iajs-2289	312	69	is	be	AUX
iajs-2289	312	70	not	not	PART
iajs-2289	312	71	necessarily	necessarily	ADV
iajs-2289	312	72	j	j	PROPN
iajs-2289	312	73	-	-	PUNCT
iajs-2289	312	74	ω	ω	VERB
iajs-2289	312	75	-	-	PUNCT
iajs-2289	312	76	closure	closure	NOUN
iajs-2289	312	77	continuous	continuous	ADJ
iajs-2289	312	78	)	)	PUNCT
iajs-2289	312	79	.	.	PUNCT
iajs-2289	313	1	corollary	corollary	ADJ
iajs-2289	313	2	36	36	NUM
iajs-2289	313	3	let	let	VERB
iajs-2289	313	4			ADJ
iajs-2289	313	5	:	:	PUNCT
iajs-2289	313	6	g	g	PROPN
iajs-2289	313	7			NOUN
iajs-2289	313	8	h	h	NOUN
iajs-2289	313	9	be	be	AUX
iajs-2289	313	10	a	a	DET
iajs-2289	313	11	mapping	mapping	NOUN
iajs-2289	313	12	if	if	SCONJ
iajs-2289	313	13	(	(	PUNCT
iajs-2289	313	14	a	a	NOUN
iajs-2289	313	15	)	)	PUNCT
iajs-2289	313	16	for	for	ADP
iajs-2289	313	17	all	all	DET
iajs-2289	313	18	k	k	PROPN
iajs-2289	313	19			PROPN
iajs-2289	313	20	g	g	PROPN
iajs-2289	313	21	,	,	PUNCT
iajs-2289	313	22	(	(	PUNCT
iajs-2289	313	23	alj	alj	PROPN
iajs-2289	313	24	-	-	PUNCT
iajs-2289	313	25	ω	ω	NOUN
iajs-2289	313	26	-	-	PUNCT
iajs-2289	313	27	cl	cl	NOUN
iajs-2289	313	28	(k	(k	NOUN
iajs-2289	313	29	)	)	PUNCT
iajs-2289	313	30	)	)	PUNCT
iajs-2289	314	1			PROPN
iajs-2289	314	2	(alj	(alj	PROPN
iajs-2289	314	3	-	-	PUNCT
iajs-2289	314	4	ω	ω	NOUN
iajs-2289	314	5	-	-	NOUN
iajs-2289	314	6	cl	cl	NOUN
iajs-2289	314	7	(	(	PUNCT
iajs-2289	314	8	k	k	NOUN
iajs-2289	314	9	)	)	PUNCT
iajs-2289	314	10	175	175	NUM
iajs-2289	314	11	ibn	ibn	PROPN
iajs-2289	314	12	al	al	PROPN
iajs-2289	314	13	-	-	PUNCT
iajs-2289	314	14	haitham	haitham	PROPN
iajs-2289	314	15	jour	jour	X
iajs-2289	314	16	.	.	PROPN
iajs-2289	315	1	for	for	ADP
iajs-2289	315	2	pure	pure	ADJ
iajs-2289	315	3	&	&	CCONJ
iajs-2289	315	4	appl	appl	PROPN
iajs-2289	315	5	.	.	PUNCT
iajs-2289	316	1	sci	sci	PROPN
iajs-2289	316	2	.	.	PROPN
iajs-2289	316	3	32	32	NUM
iajs-2289	316	4	(	(	PUNCT
iajs-2289	316	5	3	3	NUM
iajs-2289	316	6	)	)	PUNCT
iajs-2289	316	7	2019	2019	NUM
iajs-2289	316	8	(	(	PUNCT
iajs-2289	316	9	b	b	X
iajs-2289	316	10	)	)	PUNCT
iajs-2289	316	11	–1	–1	PROPN
iajs-2289	316	12	(	(	PUNCT
iajs-2289	316	13	h	h	NOUN
iajs-2289	316	14	)	)	PUNCT
iajs-2289	316	15	j	j	PROPN
iajs-2289	316	16	-	-	PUNCT
iajs-2289	316	17	ω	ω	NOUN
iajs-2289	316	18	-	-	NOUN
iajs-2289	316	19	rigid	rigid	ADJ
iajs-2289	316	20	for	for	ADP
iajs-2289	316	21	each	each	DET
iajs-2289	316	22	h	h	NOUN
iajs-2289	316	23			PROPN
iajs-2289	316	24	h	h	NOUN
iajs-2289	316	25	,	,	PUNCT
iajs-2289	316	26	then	then	ADV
iajs-2289	316	27			X
iajs-2289	316	28	is	be	AUX
iajs-2289	316	29	j	j	PROPN
iajs-2289	316	30	-	-	PUNCT
iajs-2289	316	31	ω	ω	NOUN
iajs-2289	316	32	-	-	NOUN
iajs-2289	316	33	perfect	perfect	ADJ
iajs-2289	316	34	,	,	PUNCT
iajs-2289	316	35	where	where	SCONJ
iajs-2289	316	36	j	j	PROPN
iajs-2289	316	37	{	{	PROPN
iajs-2289	316	38	,	,	PUNCT
iajs-2289	316	39	δ	δ	PROPN
iajs-2289	316	40	,	,	PUNCT
iajs-2289	316	41			NOUN
iajs-2289	316	42	,	,	PUNCT
iajs-2289	316	43	pre	pre	ADJ
iajs-2289	316	44	,	,	PUNCT
iajs-2289	316	45	b	b	NOUN
iajs-2289	316	46	,	,	PUNCT
iajs-2289	316	47			NOUN
iajs-2289	316	48	}	}	PUNCT
iajs-2289	316	49	.	.	PUNCT
iajs-2289	317	1	corollary	corollary	ADJ
iajs-2289	317	2	37	37	NUM
iajs-2289	317	3	let	let	VERB
iajs-2289	317	4			ADJ
iajs-2289	317	5	:	:	PUNCT
iajs-2289	317	6	g	g	PROPN
iajs-2289	317	7			NOUN
iajs-2289	317	8	h	h	NOUN
iajs-2289	317	9	be	be	VERB
iajs-2289	317	10	a	a	DET
iajs-2289	317	11	mapping	mapping	NOUN
iajs-2289	317	12	.	.	PUNCT
iajs-2289	318	1	(	(	PUNCT
iajs-2289	318	2	a	a	X
iajs-2289	318	3	)	)	PUNCT
iajs-2289	318	4			X
iajs-2289	318	5	is	be	AUX
iajs-2289	318	6	almost	almost	ADV
iajs-2289	318	7	j	j	PROPN
iajs-2289	318	8	-	-	PUNCT
iajs-2289	318	9	ω	ω	PROPN
iajs-2289	318	10	closed	closed	ADJ
iajs-2289	318	11	(	(	PUNCT
iajs-2289	318	12	b	b	NOUN
iajs-2289	318	13	)	)	PUNCT
iajs-2289	318	14	–1	–1	PROPN
iajs-2289	318	15	(	(	PUNCT
iajs-2289	318	16	h	h	NOUN
iajs-2289	318	17	)	)	PUNCT
iajs-2289	318	18	j	j	PROPN
iajs-2289	318	19	-	-	PROPN
iajs-2289	318	20	ω	ω	PROPN
iajs-2289	318	21	rigid	rigid	ADJ
iajs-2289	318	22	for	for	ADP
iajs-2289	318	23	each	each	DET
iajs-2289	318	24	h	h	NOUN
iajs-2289	318	25			PROPN
iajs-2289	318	26	h	h	NOUN
iajs-2289	318	27	,	,	PUNCT
iajs-2289	318	28	then	then	ADV
iajs-2289	318	29	–1	–1	PROPN
iajs-2289	318	30	preserves	preserve	VERB
iajs-2289	318	31	j	j	PROPN
iajs-2289	318	32	-	-	PUNCT
iajs-2289	318	33	ω	ω	NUM
iajs-2289	318	34	rigidity	rigidity	NOUN
iajs-2289	318	35	,	,	PUNCT
iajs-2289	318	36	where	where	SCONJ
iajs-2289	318	37	j{	j{	PROPN
iajs-2289	318	38	,	,	PUNCT
iajs-2289	318	39	δ	δ	PROPN
iajs-2289	318	40	,	,	PUNCT
iajs-2289	318	41			NOUN
iajs-2289	318	42	,	,	PUNCT
iajs-2289	318	43	pre	pre	ADJ
iajs-2289	318	44	,	,	PUNCT
iajs-2289	318	45	b	b	AUX
iajs-2289	318	46	,	,	PUNCT
iajs-2289	318	47			NOUN
iajs-2289	318	48	}	}	PUNCT
iajs-2289	318	49	.	.	PUNCT
iajs-2289	319	1	proof	proof	NOUN
iajs-2289	319	2	.	.	PUNCT
iajs-2289	320	1	let	let	VERB
iajs-2289	320	2	c	c	PROPN
iajs-2289	320	3			VERB
iajs-2289	320	4	h	h	PROPN
iajs-2289	320	5	be	be	AUX
iajs-2289	320	6	j	j	PROPN
iajs-2289	320	7	-	-	PROPN
iajs-2289	320	8	ω	ω	PROPN
iajs-2289	320	9	rigid	rigid	ADJ
iajs-2289	320	10	and	and	CCONJ
iajs-2289	320	11			NOUN
iajs-2289	320	12	be	be	VERB
iajs-2289	320	13	a	a	DET
iajs-2289	320	14	filter	filter	NOUN
iajs-2289	320	15	base	base	NOUN
iajs-2289	320	16	on	on	ADP
iajs-2289	320	17	g	g	PROPN
iajs-2289	320	18	such	such	ADJ
iajs-2289	320	19	that	that	SCONJ
iajs-2289	320	20	al	al	PROPN
iajs-2289	320	21	j	j	PROPN
iajs-2289	320	22	-	-	PUNCT
iajs-2289	320	23	ω	ω	PROPN
iajs-2289	320	24	cg	cg	NOUN
iajs-2289	320	25	∩	∩	NOUN
iajs-2289	320	26	–1	–1	PROPN
iajs-2289	320	27	(	(	PUNCT
iajs-2289	320	28	c	c	NOUN
iajs-2289	320	29	)	)	PUNCT
iajs-2289	320	30	=	=	NOUN
iajs-2289	320	31	.	.	PUNCT
iajs-2289	320	32	by	by	ADP
iajs-2289	320	33	corollary	corollary	ADJ
iajs-2289	320	34	36	36	NUM
iajs-2289	320	35	and	and	CCONJ
iajs-2289	320	36	theorem	theorem	VERB
iajs-2289	320	37	33	33	NUM
iajs-2289	320	38	,	,	PUNCT
iajs-2289	320	39	(	(	PUNCT
iajs-2289	320	40	alj	alj	PROPN
iajs-2289	320	41	-	-	PUNCT
iajs-2289	320	42	ω	ω	NUM
iajs-2289	320	43	c(	c(	NOUN
iajs-2289	320	44	)	)	PUNCT
iajs-2289	320	45	)	)	PUNCT
iajs-2289	321	1	∩	∩	NOUN
iajs-2289	321	2	c	c	NOUN
iajs-2289	321	3	=	=	SYM
iajs-2289	321	4	.	.	X
iajs-2289	321	5	so	so	ADV
iajs-2289	321	6	,	,	PUNCT
iajs-2289	321	7	there	there	PRON
iajs-2289	321	8	is	be	VERB
iajs-2289	321	9	m	m	PROPN
iajs-2289	321	10			NOUN
iajs-2289	321	11			NOUN
iajs-2289	321	12	such	such	ADJ
iajs-2289	321	13	that	that	SCONJ
iajs-2289	321	14	(	(	PUNCT
iajs-2289	321	15	aljω	aljω	NOUN
iajs-2289	321	16	cl	cl	NOUN
iajs-2289	321	17	(m	(m	NOUN
iajs-2289	321	18	)	)	PUNCT
iajs-2289	321	19	)	)	PUNCT
iajs-2289	321	20	∩	∩	NOUN
iajs-2289	321	21	c	c	NOUN
iajs-2289	321	22	=	=	SYM
iajs-2289	321	23	.	.	X
iajs-2289	321	24	nevertheless	nevertheless	ADV
iajs-2289	321	25	(	(	PUNCT
iajs-2289	321	26	alj	alj	PROPN
iajs-2289	321	27	-	-	PUNCT
iajs-2289	321	28	ω	ω	PROPN
iajs-2289	321	29	cl	cl	ADJ
iajs-2289	321	30	(	(	PUNCT
iajs-2289	321	31	m	m	NOUN
iajs-2289	321	32	)	)	PUNCT
iajs-2289	321	33	)	)	PUNCT
iajs-2289	322	1	=	=	SYM
iajs-2289	322	2	(alj	(alj	ADJ
iajs-2289	322	3	-	-	PUNCT
iajs-2289	322	4	ω	ω	NUM
iajs-2289	322	5	cl	cl	NOUN
iajs-2289	322	6	(	(	PUNCT
iajs-2289	322	7	m	m	NOUN
iajs-2289	322	8	)	)	PUNCT
iajs-2289	322	9	)	)	PUNCT
iajs-2289	322	10	.	.	PUNCT
iajs-2289	323	1	so	so	ADV
iajs-2289	323	2	,	,	PUNCT
iajs-2289	323	3	(	(	PUNCT
iajs-2289	323	4	alj	alj	PROPN
iajs-2289	323	5	-	-	PUNCT
iajs-2289	323	6	ω	ω	NUM
iajs-2289	323	7	cl	cl	NOUN
iajs-2289	323	8	(	(	PUNCT
iajs-2289	323	9	m	m	NOUN
iajs-2289	323	10	)	)	PUNCT
iajs-2289	323	11	)	)	PUNCT
iajs-2289	323	12	∩	∩	NOUN
iajs-2289	323	13	–1	–1	PROPN
iajs-2289	323	14	(	(	PUNCT
iajs-2289	323	15	c	c	NOUN
iajs-2289	323	16	)	)	PUNCT
iajs-2289	323	17	=	=	NOUN
iajs-2289	323	18	.	.	X
iajs-2289	323	19	so	so	ADV
iajs-2289	323	20	,	,	PUNCT
iajs-2289	323	21	by	by	ADP
iajs-2289	323	22	theorem	theorem	NOUN
iajs-2289	323	23	32	32	NUM
iajs-2289	323	24	,	,	PUNCT
iajs-2289	323	25			X
iajs-2289	323	26	–	–	PUNCT
iajs-2289	323	27	1	1	NUM
iajs-2289	323	28	(	(	PUNCT
iajs-2289	323	29	c	c	NOUN
iajs-2289	323	30	)	)	PUNCT
iajs-2289	323	31	is	be	AUX
iajs-2289	323	32	j	j	PROPN
iajs-2289	323	33	-	-	PUNCT
iajs-2289	323	34	ω	ω	PROPN
iajs-2289	323	35	rigid	rigid	ADJ
iajs-2289	323	36	,	,	PUNCT
iajs-2289	323	37	where	where	SCONJ
iajs-2289	323	38	j	j	PROPN
iajs-2289	323	39	{	{	PUNCT
iajs-2289	323	40			PROPN
iajs-2289	323	41	,	,	PUNCT
iajs-2289	323	42	δ	δ	PROPN
iajs-2289	323	43	,	,	PUNCT
iajs-2289	323	44			NOUN
iajs-2289	323	45	,	,	PUNCT
iajs-2289	323	46	pre	pre	ADJ
iajs-2289	323	47	,	,	PUNCT
iajs-2289	323	48	b	b	NOUN
iajs-2289	323	49	,	,	PUNCT
iajs-2289	323	50			NOUN
iajs-2289	323	51	}	}	PUNCT
iajs-2289	323	52	.	.	PUNCT
iajs-2289	324	1	theorem	theorem	VERB
iajs-2289	324	2	38	38	NUM
iajs-2289	324	3	suppose	suppose	VERB
iajs-2289	324	4			ADJ
iajs-2289	324	5	:	:	PUNCT
iajs-2289	324	6	g	g	PROPN
iajs-2289	324	7			NOUN
iajs-2289	324	8	h	h	NOUN
iajs-2289	324	9	has	have	VERB
iajs-2289	324	10	j	j	PROPN
iajs-2289	324	11	-	-	PUNCT
iajs-2289	324	12	ω	ω	PROPN
iajs-2289	324	13	rigid	rigid	ADJ
iajs-2289	324	14	point	point	NOUN
iajs-2289	324	15	-	-	PUNCT
iajs-2289	324	16	inverses	inverse	NOUN
iajs-2289	324	17	.	.	PUNCT
iajs-2289	325	1	then	then	ADV
iajs-2289	325	2	:	:	PUNCT
iajs-2289	325	3	(	(	PUNCT
iajs-2289	325	4	a	a	X
iajs-2289	325	5	)	)	PUNCT
iajs-2289	325	6			X
iajs-2289	325	7	is	be	AUX
iajs-2289	325	8	j	j	PROPN
iajs-2289	325	9	-	-	PUNCT
iajs-2289	325	10	ω	ω	PROPN
iajs-2289	325	11	closure	closure	NOUN
iajs-2289	325	12	continuous	continuous	ADJ
iajs-2289	325	13	iff	iff	PROPN
iajs-2289	325	14	for	for	ADP
iajs-2289	325	15	each	each	DET
iajs-2289	325	16	h	h	NOUN
iajs-2289	325	17			PROPN
iajs-2289	325	18	h	h	NOUN
iajs-2289	325	19	and	and	CCONJ
iajs-2289	325	20	open	open	VERB
iajs-2289	325	21	set	set	VERB
iajs-2289	325	22	t	t	NOUN
iajs-2289	325	23	containing	contain	VERB
iajs-2289	325	24	h	h	NOUN
iajs-2289	325	25	,	,	PUNCT
iajs-2289	325	26	there	there	PRON
iajs-2289	325	27	is	be	VERB
iajs-2289	325	28	an	an	DET
iajs-2289	325	29	open	open	ADJ
iajs-2289	325	30	set	set	NOUN
iajs-2289	325	31	s	s	AUX
iajs-2289	325	32	containing	contain	VERB
iajs-2289	325	33	–1	–1	PROPN
iajs-2289	325	34	(	(	PUNCT
iajs-2289	325	35	h	h	NOUN
iajs-2289	325	36	)	)	PUNCT
iajs-2289	325	37	such	such	ADJ
iajs-2289	325	38	that	that	SCONJ
iajs-2289	325	39	(cl	(cl	PROPN
iajs-2289	325	40	j	j	PROPN
iajs-2289	325	41	-	-	PUNCT
iajs-2289	325	42	ω	ω	PROPN
iajs-2289	325	43	(	(	PUNCT
iajs-2289	325	44	s	s	NOUN
iajs-2289	325	45	)	)	PUNCT
iajs-2289	325	46	)	)	PUNCT
iajs-2289	325	47			PROPN
iajs-2289	325	48	cl	cl	INTJ
iajs-2289	325	49	j	j	PROPN
iajs-2289	325	50	-	-	PUNCT
iajs-2289	325	51	ω(t	ω(t	NOUN
iajs-2289	325	52	)	)	PUNCT
iajs-2289	325	53	,	,	PUNCT
iajs-2289	325	54	where	where	SCONJ
iajs-2289	325	55	j	j	PROPN
iajs-2289	325	56	{	{	PUNCT
iajs-2289	325	57			PROPN
iajs-2289	325	58	,	,	PUNCT
iajs-2289	325	59	δ	δ	PROPN
iajs-2289	325	60	,	,	PUNCT
iajs-2289	325	61			NOUN
iajs-2289	325	62	,	,	PUNCT
iajs-2289	325	63	pre	pre	ADJ
iajs-2289	325	64	,	,	PUNCT
iajs-2289	325	65	b	b	NOUN
iajs-2289	325	66	,	,	PUNCT
iajs-2289	325	67			NOUN
iajs-2289	325	68	}	}	PUNCT
iajs-2289	325	69	.	.	PUNCT
iajs-2289	326	1	(	(	PUNCT
iajs-2289	326	2	b	b	X
iajs-2289	326	3	)	)	PUNCT
iajs-2289	326	4	if	if	SCONJ
iajs-2289	326	5	for	for	ADP
iajs-2289	326	6	each	each	DET
iajs-2289	326	7	h	h	NOUN
iajs-2289	326	8			PROPN
iajs-2289	326	9	g	g	PROPN
iajs-2289	326	10	and	and	CCONJ
iajs-2289	326	11	open	open	VERB
iajs-2289	326	12	set	set	NOUN
iajs-2289	326	13	s	s	AUX
iajs-2289	326	14	containing	contain	VERB
iajs-2289	326	15	–1	–1	PROPN
iajs-2289	326	16	(	(	PUNCT
iajs-2289	326	17	h	h	NOUN
iajs-2289	326	18	)	)	PUNCT
iajs-2289	326	19	,	,	PUNCT
iajs-2289	326	20	there	there	PRON
iajs-2289	326	21	is	be	VERB
iajs-2289	326	22	an	an	DET
iajs-2289	326	23	open	open	ADJ
iajs-2289	326	24	set	set	VERB
iajs-2289	326	25	t	t	PROPN
iajs-2289	326	26	of	of	ADP
iajs-2289	326	27	h	h	NOUN
iajs-2289	327	1	such	such	ADJ
iajs-2289	327	2	that	that	SCONJ
iajs-2289	327	3			ADJ
iajs-2289	327	4	–	–	PUNCT
iajs-2289	327	5	1	1	NUM
iajs-2289	327	6	(	(	PUNCT
iajs-2289	327	7	cl	cl	INTJ
iajs-2289	327	8	j	j	PROPN
iajs-2289	327	9	-	-	PROPN
iajs-2289	327	10	ω	ω	PROPN
iajs-2289	327	11	(	(	PUNCT
iajs-2289	327	12	t	t	PROPN
iajs-2289	327	13	)	)	PUNCT
iajs-2289	327	14	)	)	PUNCT
iajs-2289	327	15			PROPN
iajs-2289	327	16	cl	cl	INTJ
iajs-2289	327	17	j	j	PROPN
iajs-2289	327	18	-	-	PROPN
iajs-2289	327	19	ω	ω	PROPN
iajs-2289	327	20	(	(	PUNCT
iajs-2289	327	21	s	s	NOUN
iajs-2289	327	22	)	)	PUNCT
iajs-2289	327	23	,	,	PUNCT
iajs-2289	327	24	then	then	ADV
iajs-2289	327	25	for	for	ADP
iajs-2289	327	26	each	each	DET
iajs-2289	327	27	k	k	PROPN
iajs-2289	327	28			PROPN
iajs-2289	327	29	g	g	PROPN
iajs-2289	327	30	,	,	PUNCT
iajs-2289	327	31	(	(	PUNCT
iajs-2289	327	32	alj	alj	PROPN
iajs-2289	327	33	-	-	PUNCT
iajs-2289	327	34	ω	ω	NOUN
iajs-2289	327	35	cl((k	cl((k	NOUN
iajs-2289	327	36	)	)	PUNCT
iajs-2289	327	37	)	)	PUNCT
iajs-2289	327	38			PROPN
iajs-2289	327	39	(alj	(alj	PROPN
iajs-2289	327	40	-	-	PUNCT
iajs-2289	327	41	ω	ω	NOUN
iajs-2289	327	42	cl(k	cl(k	NOUN
iajs-2289	327	43	)	)	PUNCT
iajs-2289	327	44	)	)	PUNCT
iajs-2289	327	45	,	,	PUNCT
iajs-2289	327	46	where	where	SCONJ
iajs-2289	327	47	j{	j{	PROPN
iajs-2289	327	48	,	,	PUNCT
iajs-2289	327	49	δ	δ	PROPN
iajs-2289	327	50	,	,	PUNCT
iajs-2289	327	51			NOUN
iajs-2289	327	52	,	,	PUNCT
iajs-2289	327	53	pre	pre	AUX
iajs-2289	327	54	,	,	PUNCT
iajs-2289	327	55	b	b	AUX
iajs-2289	327	56	,	,	PUNCT
iajs-2289	327	57			NOUN
iajs-2289	327	58	}	}	PUNCT
iajs-2289	327	59	.	.	PUNCT
iajs-2289	328	1	proof	proof	NOUN
iajs-2289	328	2	.	.	PUNCT
iajs-2289	329	1	(	(	PUNCT
iajs-2289	329	2	a	a	X
iajs-2289	329	3	)	)	PUNCT
iajs-2289	329	4	(	(	PUNCT
iajs-2289	329	5			NOUN
iajs-2289	329	6	)	)	PUNCT
iajs-2289	329	7	is	be	AUX
iajs-2289	329	8	obvious	obvious	ADJ
iajs-2289	329	9	.	.	PUNCT
iajs-2289	330	1	(	(	PUNCT
iajs-2289	330	2			NOUN
iajs-2289	330	3	)	)	PUNCT
iajs-2289	330	4	is	be	AUX
iajs-2289	330	5	straightforward	straightforward	ADJ
iajs-2289	330	6	using	use	VERB
iajs-2289	330	7	theorem	theorem	NOUN
iajs-2289	330	8	(	(	PUNCT
iajs-2289	330	9	32	32	NUM
iajs-2289	330	10	,	,	PUNCT
iajs-2289	330	11	c	c	NOUN
iajs-2289	330	12	)	)	PUNCT
iajs-2289	330	13	(	(	PUNCT
iajs-2289	330	14	b	b	X
iajs-2289	330	15	)	)	PUNCT
iajs-2289	330	16	let	let	VERB
iajs-2289	330	17			NOUN
iajs-2289	330	18			NOUN
iajs-2289	330	19	k	k	NOUN
iajs-2289	330	20			PROPN
iajs-2289	330	21	g	g	PROPN
iajs-2289	330	22	and	and	CCONJ
iajs-2289	330	23	h	h	NOUN
iajs-2289	330	24			VERB
iajs-2289	330	25	(alj	(alj	PROPN
iajs-2289	330	26	-	-	PUNCT
iajs-2289	330	27	ω	ω	NUM
iajs-2289	330	28	cl	cl	NOUN
iajs-2289	330	29	(	(	PUNCT
iajs-2289	330	30	k	k	NOUN
iajs-2289	330	31	)	)	PUNCT
iajs-2289	330	32	)	)	PUNCT
iajs-2289	330	33	.	.	PUNCT
iajs-2289	331	1	then	then	ADV
iajs-2289	331	2	–1	–1	PROPN
iajs-2289	331	3	(	(	PUNCT
iajs-2289	331	4	h	h	NOUN
iajs-2289	331	5	)	)	PUNCT
iajs-2289	331	6	∩	∩	NOUN
iajs-2289	331	7	(	(	PUNCT
iajs-2289	331	8	alj	alj	PROPN
iajs-2289	331	9	-	-	PUNCT
iajs-2289	331	10	ω	ω	NUM
iajs-2289	331	11	cl	cl	NOUN
iajs-2289	331	12	(	(	PUNCT
iajs-2289	331	13	k	k	NOUN
iajs-2289	331	14	)	)	PUNCT
iajs-2289	331	15	)	)	PUNCT
iajs-2289	332	1	=	=	SYM
iajs-2289	332	2	.	.	X
iajs-2289	332	3	now	now	ADV
iajs-2289	332	4	,	,	PUNCT
iajs-2289	332	5			VERB
iajs-2289	332	6	=	=	SYM
iajs-2289	332	7	{	{	PUNCT
iajs-2289	332	8	k	k	NOUN
iajs-2289	332	9	}	}	PUNCT
iajs-2289	332	10	is	be	AUX
iajs-2289	332	11	a	a	DET
iajs-2289	332	12	filter	filter	NOUN
iajs-2289	332	13	base	base	NOUN
iajs-2289	332	14	and	and	CCONJ
iajs-2289	332	15	(	(	PUNCT
iajs-2289	332	16	al	al	PROPN
iajs-2289	332	17	-j	-j	PROPN
iajs-2289	332	18	-	-	PUNCT
iajs-2289	332	19	ω	ω	PROPN
iajs-2289	332	20	c	c	NOUN
iajs-2289	332	21	)	)	PUNCT
iajs-2289	332	22	∩	∩	NOUN
iajs-2289	332	23	–1	–1	PROPN
iajs-2289	332	24	(	(	PUNCT
iajs-2289	332	25	h	h	NOUN
iajs-2289	332	26	)	)	PUNCT
iajs-2289	332	27	=	=	NOUN
iajs-2289	332	28	.	.	X
iajs-2289	332	29	so	so	ADV
iajs-2289	332	30	,	,	PUNCT
iajs-2289	332	31	yond	yond	PROPN
iajs-2289	332	32	is	be	AUX
iajs-2289	332	33	open	open	ADJ
iajs-2289	332	34	set	set	ADJ
iajs-2289	332	35	s	s	AUX
iajs-2289	332	36	continuing	continue	VERB
iajs-2289	332	37	–1	–1	PROPN
iajs-2289	332	38	(	(	PUNCT
iajs-2289	332	39	h	h	NOUN
iajs-2289	332	40	)	)	PUNCT
iajs-2289	332	41	such	such	ADJ
iajs-2289	332	42	that	that	SCONJ
iajs-2289	332	43	cl	cl	PROPN
iajs-2289	332	44	j	j	PROPN
iajs-2289	332	45	-	-	PROPN
iajs-2289	332	46	ω	ω	PROPN
iajs-2289	332	47	(	(	PUNCT
iajs-2289	332	48	s	s	NOUN
iajs-2289	332	49	)	)	PUNCT
iajs-2289	332	50	∩	∩	NOUN
iajs-2289	332	51	k	k	NOUN
iajs-2289	332	52	=	=	SYM
iajs-2289	332	53			NOUN
iajs-2289	332	54	,	,	PUNCT
iajs-2289	332	55	yond	yond	PROPN
iajs-2289	332	56	is	be	AUX
iajs-2289	332	57	open	open	ADJ
iajs-2289	332	58	t	t	NOUN
iajs-2289	332	59	of	of	ADP
iajs-2289	332	60	h	h	PRON
iajs-2289	332	61	such	such	ADJ
iajs-2289	332	62	that	that	SCONJ
iajs-2289	332	63	–1	–1	PROPN
iajs-2289	332	64	(	(	PUNCT
iajs-2289	332	65	cl	cl	INTJ
iajs-2289	332	66	j	j	PROPN
iajs-2289	332	67	-	-	PUNCT
iajs-2289	332	68	ω(t	ω(t	NOUN
iajs-2289	332	69	)	)	PUNCT
iajs-2289	332	70	)	)	PUNCT
iajs-2289	333	1			PROPN
iajs-2289	333	2	cl	cl	INTJ
iajs-2289	333	3	j	j	NOUN
iajs-2289	333	4	-	-	PUNCT
iajs-2289	333	5	ω(s	ω(s	PROPN
iajs-2289	333	6	)	)	PUNCT
iajs-2289	333	7	.	.	PUNCT
iajs-2289	334	1	therefore	therefore	ADV
iajs-2289	334	2	,	,	PUNCT
iajs-2289	334	3	cl	cl	INTJ
iajs-2289	334	4	j	j	PROPN
iajs-2289	334	5	-	-	PROPN
iajs-2289	334	6	ω	ω	PROPN
iajs-2289	334	7	(	(	PUNCT
iajs-2289	334	8	t	t	PROPN
iajs-2289	334	9	)	)	PUNCT
iajs-2289	334	10	∩	∩	NOUN
iajs-2289	334	11			X
iajs-2289	334	12	(	(	PUNCT
iajs-2289	334	13	k	k	NOUN
iajs-2289	334	14	)	)	PUNCT
iajs-2289	334	15	=	=	NOUN
iajs-2289	334	16	.	.	X
iajs-2289	334	17	hence	hence	ADV
iajs-2289	334	18	h	h	NOUN
iajs-2289	334	19			PROPN
iajs-2289	334	20	(	(	PUNCT
iajs-2289	334	21	alj	alj	PROPN
iajs-2289	334	22	-	-	PUNCT
iajs-2289	334	23	ω	ω	NUM
iajs-2289	334	24	cl	cl	NOUN
iajs-2289	334	25	(k	(k	PROPN
iajs-2289	334	26	)	)	PUNCT
iajs-2289	334	27	)	)	PUNCT
iajs-2289	334	28	,	,	PUNCT
iajs-2289	334	29	where	where	SCONJ
iajs-2289	334	30	j{	j{	PROPN
iajs-2289	334	31	,	,	PUNCT
iajs-2289	334	32	δ	δ	PROPN
iajs-2289	334	33	,	,	PUNCT
iajs-2289	334	34			NOUN
iajs-2289	334	35	,	,	PUNCT
iajs-2289	334	36	pre	pre	AUX
iajs-2289	334	37	,	,	PUNCT
iajs-2289	334	38	b	b	AUX
iajs-2289	334	39	,	,	PUNCT
iajs-2289	334	40			PROPN
iajs-2289	334	41	}	}	PUNCT
iajs-2289	334	42	.	.	PUNCT
iajs-2289	335	1	the	the	DET
iajs-2289	335	2	next	next	ADJ
iajs-2289	335	3	result	result	NOUN
iajs-2289	335	4	related	relate	VERB
iajs-2289	335	5	to	to	ADP
iajs-2289	335	6	theorem	theorem	NOUN
iajs-2289	335	7	(	(	PUNCT
iajs-2289	335	8	38	38	NUM
iajs-2289	335	9	,	,	PUNCT
iajs-2289	335	10	b	b	NOUN
iajs-2289	335	11	)	)	PUNCT
iajs-2289	335	12	;	;	PUNCT
iajs-2289	335	13	the	the	DET
iajs-2289	335	14	proof	proof	NOUN
iajs-2289	335	15	is	be	AUX
iajs-2289	335	16	straightforward	straightforward	ADJ
iajs-2289	335	17	.	.	PUNCT
iajs-2289	336	1	theorem	theorem	ADJ
iajs-2289	336	2	39	39	NUM
iajs-2289	336	3	let	let	VERB
iajs-2289	336	4			ADJ
iajs-2289	336	5	:	:	PUNCT
iajs-2289	336	6	g	g	PROPN
iajs-2289	336	7			PROPN
iajs-2289	336	8	h.	h.	NOUN
iajs-2289	336	9	the	the	DET
iajs-2289	336	10	following	following	NOUN
iajs-2289	336	11	are	be	AUX
iajs-2289	336	12	equivalent	equivalent	ADJ
iajs-2289	336	13	:	:	PUNCT
iajs-2289	336	14	(	(	PUNCT
iajs-2289	336	15	a	a	X
iajs-2289	336	16	)	)	PUNCT
iajs-2289	336	17	for	for	ADP
iajs-2289	336	18	all	all	DET
iajs-2289	336	19	j	j	PROPN
iajs-2289	336	20	-	-	PUNCT
iajs-2289	336	21	ω	ω	NOUN
iajs-2289	336	22	-	-	PUNCT
iajs-2289	336	23	closed	closed	ADJ
iajs-2289	336	24	k	k	PROPN
iajs-2289	336	25			PROPN
iajs-2289	336	26	g	g	PROPN
iajs-2289	336	27	,	,	PUNCT
iajs-2289	336	28	(k	(k	PROPN
iajs-2289	336	29	)	)	PUNCT
iajs-2289	336	30	is	be	AUX
iajs-2289	336	31	j	j	PROPN
iajs-2289	336	32	-	-	PUNCT
iajs-2289	336	33	ω	ω	NOUN
iajs-2289	336	34	-	-	PUNCT
iajs-2289	336	35	closed	closed	ADJ
iajs-2289	336	36	,	,	PUNCT
iajs-2289	336	37	where	where	SCONJ
iajs-2289	336	38	j	j	PROPN
iajs-2289	336	39	{	{	PROPN
iajs-2289	336	40	,	,	PUNCT
iajs-2289	336	41	δ	δ	PROPN
iajs-2289	336	42	,	,	PUNCT
iajs-2289	336	43			NOUN
iajs-2289	336	44	,	,	PUNCT
iajs-2289	336	45	pre	pre	ADJ
iajs-2289	336	46	,	,	PUNCT
iajs-2289	336	47	b	b	NOUN
iajs-2289	336	48	,	,	PUNCT
iajs-2289	336	49			NOUN
iajs-2289	336	50	}	}	PUNCT
iajs-2289	336	51	.	.	PUNCT
iajs-2289	337	1	(	(	PUNCT
iajs-2289	337	2	b	b	X
iajs-2289	337	3	)	)	PUNCT
iajs-2289	337	4	for	for	ADP
iajs-2289	337	5	all	all	DET
iajs-2289	337	6	l	l	NOUN
iajs-2289	337	7			PROPN
iajs-2289	337	8	h	h	PROPN
iajs-2289	337	9	and	and	CCONJ
iajs-2289	337	10	j	j	PROPN
iajs-2289	337	11	-	-	PROPN
iajs-2289	337	12	ω	ω	PROPN
iajs-2289	337	13	open	open	NOUN
iajs-2289	337	14	s	s	AUX
iajs-2289	337	15	containing	contain	VERB
iajs-2289	337	16	–1	–1	PROPN
iajs-2289	337	17	(	(	PUNCT
iajs-2289	337	18	l	l	NOUN
iajs-2289	337	19	)	)	PUNCT
iajs-2289	337	20	,	,	PUNCT
iajs-2289	337	21	there	there	PRON
iajs-2289	337	22	is	be	VERB
iajs-2289	337	23	j	j	PROPN
iajs-2289	337	24	-	-	PUNCT
iajs-2289	337	25	ω	ω	VERB
iajs-2289	337	26	-	-	PUNCT
iajs-2289	337	27	open	open	ADJ
iajs-2289	337	28	t	t	NOUN
iajs-2289	337	29	containing	contain	VERB
iajs-2289	337	30	l	l	NOUN
iajs-2289	337	31	such	such	ADJ
iajs-2289	337	32	that	that	SCONJ
iajs-2289	337	33	–1	–1	PROPN
iajs-2289	337	34	(	(	PUNCT
iajs-2289	337	35	t	t	PROPN
iajs-2289	337	36	)	)	PUNCT
iajs-2289	337	37			PROPN
iajs-2289	337	38	s	s	PROPN
iajs-2289	337	39	,	,	PUNCT
iajs-2289	337	40	where	where	SCONJ
iajs-2289	337	41	j	j	PROPN
iajs-2289	337	42	{	{	PROPN
iajs-2289	337	43	,	,	PUNCT
iajs-2289	337	44	δ	δ	PROPN
iajs-2289	337	45	,	,	PUNCT
iajs-2289	337	46			NOUN
iajs-2289	337	47	,	,	PUNCT
iajs-2289	337	48	pre	pre	ADJ
iajs-2289	337	49	,	,	PUNCT
iajs-2289	337	50	b	b	NOUN
iajs-2289	337	51	,	,	PUNCT
iajs-2289	337	52			NOUN
iajs-2289	337	53	}	}	PUNCT
iajs-2289	337	54	.	.	PUNCT
iajs-2289	338	1	theorem	theorem	VERB
iajs-2289	338	2	40	40	NUM
iajs-2289	338	3	if	if	SCONJ
iajs-2289	338	4			ADJ
iajs-2289	338	5	:	:	PUNCT
iajs-2289	338	6	g	g	PROPN
iajs-2289	338	7			NOUN
iajs-2289	338	8	h	h	NOUN
iajs-2289	338	9	is	be	AUX
iajs-2289	338	10	j	j	PROPN
iajs-2289	338	11	-	-	PUNCT
iajs-2289	338	12	ω	ω	PROPN
iajs-2289	338	13	closure	closure	NOUN
iajs-2289	338	14	continuous	continuous	ADJ
iajs-2289	338	15	and	and	CCONJ
iajs-2289	338	16	h	h	NOUN
iajs-2289	338	17	is	be	AUX
iajs-2289	338	18	j	j	PROPN
iajs-2289	338	19	-	-	PROPN
iajs-2289	338	20	ω	ω	NUM
iajs-2289	338	21	urysohn	urysohn	NOUN
iajs-2289	338	22	,	,	PUNCT
iajs-2289	338	23	then	then	ADV
iajs-2289	338	24			X
iajs-2289	338	25	is	be	AUX
iajs-2289	338	26	j	j	PROPN
iajs-2289	338	27	-	-	PUNCT
iajs-2289	338	28	ω	ω	NUM
iajs-2289	338	29	perfect	perfect	ADJ
iajs-2289	339	1	if	if	SCONJ
iajs-2289	339	2	and	and	CCONJ
iajs-2289	339	3	only	only	ADV
iajs-2289	339	4	if	if	SCONJ
iajs-2289	339	5	for	for	ADP
iajs-2289	339	6	all	all	DET
iajs-2289	339	7	filter	filter	NOUN
iajs-2289	339	8	base	base	NOUN
iajs-2289	339	9			NOUN
iajs-2289	339	10	on	on	ADP
iajs-2289	339	11	g	g	NOUN
iajs-2289	339	12	,	,	PUNCT
iajs-2289	339	13	if	if	SCONJ
iajs-2289	339	14	(	(	NUM
iajs-2289	339	15	)	)	PUNCT
iajs-2289	339	16	j	j	PROPN
iajs-2289	339	17	-	-	PUNCT
iajs-2289	339	18	ω	ω	NUM
iajs-2289	339	19	⇝	⇝	NOUN
iajs-2289	339	20	h	h	PROPN
iajs-2289	339	21			NOUN
iajs-2289	339	22	h	h	NOUN
iajs-2289	339	23	,	,	PUNCT
iajs-2289	339	24	then	then	ADV
iajs-2289	339	25	(	(	PUNCT
iajs-2289	339	26	alj	alj	PROPN
iajs-2289	339	27	-	-	PUNCT
iajs-2289	339	28	ω	ω	NUM
iajs-2289	339	29	cg	cg	NOUN
iajs-2289	339	30	)	)	PUNCT
iajs-2289	339	31			NOUN
iajs-2289	339	32			NOUN
iajs-2289	339	33	,	,	PUNCT
iajs-2289	339	34	where	where	SCONJ
iajs-2289	339	35	j{	j{	PROPN
iajs-2289	339	36	,	,	PUNCT
iajs-2289	339	37	δ	δ	PROPN
iajs-2289	339	38	,	,	PUNCT
iajs-2289	339	39			NOUN
iajs-2289	339	40	,	,	PUNCT
iajs-2289	339	41	pre	pre	ADJ
iajs-2289	339	42	,	,	PUNCT
iajs-2289	339	43	b	b	NOUN
iajs-2289	339	44	,	,	PUNCT
iajs-2289	339	45			NOUN
iajs-2289	339	46	}	}	PUNCT
iajs-2289	339	47	.	.	PUNCT
iajs-2289	340	1	proof	proof	NOUN
iajs-2289	340	2	.	.	PUNCT
iajs-2289	341	1	(	(	PUNCT
iajs-2289	341	2			NOUN
iajs-2289	341	3	)	)	PUNCT
iajs-2289	341	4	assume	assume	VERB
iajs-2289	341	5	that	that	SCONJ
iajs-2289	341	6			NOUN
iajs-2289	341	7	is	be	AUX
iajs-2289	341	8	j	j	PROPN
iajs-2289	341	9	-	-	PUNCT
iajs-2289	341	10	ω	ω	NUM
iajs-2289	341	11	perfect	perfect	ADJ
iajs-2289	341	12	and	and	CCONJ
iajs-2289	341	13	(	(	NOUN
iajs-2289	341	14	)	)	PUNCT
iajs-2289	341	15	j	j	PROPN
iajs-2289	341	16	-	-	PUNCT
iajs-2289	341	17	ω	ω	PROPN
iajs-2289	341	18	⇝	⇝	PROPN
iajs-2289	341	19	h.	h.	PROPN
iajs-2289	341	20	therefore	therefore	ADV
iajs-2289	341	21	,	,	PUNCT
iajs-2289	341	22	–1	–1	PROPN
iajs-2289	341	23	(	(	PUNCT
iajs-2289	341	24			NOUN
iajs-2289	341	25	)	)	PUNCT
iajs-2289	341	26	j	j	PROPN
iajs-2289	341	27	-	-	PUNCT
iajs-2289	341	28	ω	ω	PROPN
iajs-2289	341	29	⇝	⇝	NOUN
iajs-2289	341	30	–1	–1	NOUN
iajs-2289	341	31	(	(	PUNCT
iajs-2289	341	32	h	h	NOUN
iajs-2289	341	33	)	)	PUNCT
iajs-2289	341	34	.	.	PUNCT
iajs-2289	342	1	since	since	SCONJ
iajs-2289	342	2	–1(	–1(	NUM
iajs-2289	342	3	)	)	PUNCT
iajs-2289	342	4	<	<	X
iajs-2289	342	5			NOUN
iajs-2289	342	6	,	,	PUNCT
iajs-2289	342	7	then	then	ADV
iajs-2289	342	8	by	by	ADP
iajs-2289	342	9	theorem	theorem	NOUN
iajs-2289	342	10	(	(	PUNCT
iajs-2289	342	11	18	18	NUM
iajs-2289	342	12	,	,	PUNCT
iajs-2289	342	13	d	d	NOUN
iajs-2289	342	14	)	)	PUNCT
iajs-2289	342	15	,	,	PUNCT
iajs-2289	342	16			VERB
iajs-2289	342	17	j	j	PROPN
iajs-2289	342	18	-	-	PUNCT
iajs-2289	342	19	ω	ω	NOUN
iajs-2289	342	20	⇝	⇝	NOUN
iajs-2289	342	21	–1	–1	NOUN
iajs-2289	342	22	(	(	PUNCT
iajs-2289	342	23	h	h	NOUN
iajs-2289	342	24	)	)	PUNCT
iajs-2289	342	25	,	,	PUNCT
iajs-2289	342	26	by	by	ADP
iajs-2289	342	27	theorem	theorem	NOUN
iajs-2289	342	28	(	(	PUNCT
iajs-2289	342	29	18	18	NUM
iajs-2289	342	30	,	,	PUNCT
iajs-2289	342	31	h	h	NOUN
iajs-2289	342	32	)	)	PUNCT
iajs-2289	342	33	,	,	PUNCT
iajs-2289	342	34	(	(	PUNCT
iajs-2289	342	35	al	al	PROPN
iajs-2289	342	36	j	j	PROPN
iajs-2289	342	37	-	-	PROPN
iajs-2289	342	38	ω	ω	PROPN
iajs-2289	342	39	c	c	NOUN
iajs-2289	342	40			PROPN
iajs-2289	342	41	)	)	PUNCT
iajs-2289	342	42			NOUN
iajs-2289	342	43	.	.	PUNCT
iajs-2289	342	44	(	(	PUNCT
iajs-2289	342	45			NOUN
iajs-2289	342	46	)	)	PUNCT
iajs-2289	342	47	assume	assume	VERB
iajs-2289	342	48	that	that	SCONJ
iajs-2289	342	49	for	for	ADP
iajs-2289	342	50	each	each	DET
iajs-2289	342	51	filter	filter	NOUN
iajs-2289	342	52	base	base	NOUN
iajs-2289	342	53			NOUN
iajs-2289	342	54	on	on	ADP
iajs-2289	342	55	g	g	NOUN
iajs-2289	342	56	,	,	PUNCT
iajs-2289	342	57	if	if	SCONJ
iajs-2289	342	58	(	(	NUM
iajs-2289	342	59	)	)	PUNCT
iajs-2289	342	60	j	j	PROPN
iajs-2289	342	61	-	-	PUNCT
iajs-2289	342	62	ω	ω	NUM
iajs-2289	342	63	⇝	⇝	NOUN
iajs-2289	342	64	h	h	NOUN
iajs-2289	342	65			NOUN
iajs-2289	342	66	g	g	PROPN
iajs-2289	342	67	,	,	PUNCT
iajs-2289	342	68	then	then	ADV
iajs-2289	342	69	(	(	PUNCT
iajs-2289	342	70	alj	alj	PROPN
iajs-2289	342	71	-	-	PUNCT
iajs-2289	342	72	ω	ω	PROPN
iajs-2289	342	73	cg)	cg)	NOUN
iajs-2289	342	74	.	.	X
iajs-2289	342	75	suppose	suppose	VERB
iajs-2289	342	76			NOUN
iajs-2289	342	77	is	be	AUX
iajs-2289	342	78	a	a	DET
iajs-2289	342	79	filter	filter	NOUN
iajs-2289	342	80	base	base	NOUN
iajs-2289	342	81	on	on	ADP
iajs-2289	342	82	(g	(g	PROPN
iajs-2289	342	83	)	)	PUNCT
iajs-2289	342	84	such	such	ADJ
iajs-2289	342	85	that	that	DET
iajs-2289	342	86			PROPN
iajs-2289	342	87	j	j	PROPN
iajs-2289	342	88	-	-	PUNCT
iajs-2289	342	89	ω	ω	NUM
iajs-2289	342	90	⇝	⇝	NOUN
iajs-2289	342	91	h	h	PROPN
iajs-2289	342	92			NOUN
iajs-2289	342	93	h	h	NOUN
iajs-2289	342	94	,	,	PUNCT
iajs-2289	342	95	and	and	CCONJ
iajs-2289	342	96	assume	assume	VERB
iajs-2289	342	97	l	l	NOUN
iajs-2289	342	98	is	be	AUX
iajs-2289	342	99	a	a	DET
iajs-2289	342	100	filter	filter	NOUN
iajs-2289	342	101	base	base	NOUN
iajs-2289	342	102	on	on	ADP
iajs-2289	342	103	g	g	PROPN
iajs-2289	342	104	such	such	ADJ
iajs-2289	342	105	that	that	SCONJ
iajs-2289	342	106	–1	–1	PROPN
iajs-2289	342	107	(	(	PUNCT
iajs-2289	342	108			PROPN
iajs-2289	342	109	)	)	PUNCT
iajs-2289	342	110	<	<	X
iajs-2289	342	111	l.	l.	PROPN
iajs-2289	342	112	then	then	ADV
iajs-2289	342	113			PROPN
iajs-2289	342	114	=	=	SYM
iajs-2289	342	115	–1	–1	PROPN
iajs-2289	342	116	(	(	PUNCT
iajs-2289	342	117	g	g	NOUN
iajs-2289	342	118	)	)	PUNCT
iajs-2289	342	119	<	<	X
iajs-2289	342	120			X
iajs-2289	342	121	(	(	PUNCT
iajs-2289	342	122	l	l	NOUN
iajs-2289	342	123	)	)	PUNCT
iajs-2289	342	124	.	.	PUNCT
iajs-2289	343	1	so	so	ADV
iajs-2289	343	2	,	,	PUNCT
iajs-2289	343	3	(l	(l	PROPN
iajs-2289	343	4	)	)	PUNCT
iajs-2289	343	5	j	j	PROPN
iajs-2289	343	6	-	-	PUNCT
iajs-2289	343	7	ω	ω	PROPN
iajs-2289	343	8	⇝	⇝	PROPN
iajs-2289	343	9	h.	h.	PROPN
iajs-2289	343	10	therefore	therefore	ADV
iajs-2289	343	11	,	,	PUNCT
iajs-2289	343	12	(	(	PUNCT
iajs-2289	343	13	alj	alj	PROPN
iajs-2289	343	14	-	-	PUNCT
iajs-2289	343	15	ω	ω	NOUN
iajs-2289	343	16	-	-	NOUN
iajs-2289	343	17	cg	cg	NOUN
iajs-2289	343	18	176	176	NUM
iajs-2289	343	19	ibn	ibn	PROPN
iajs-2289	343	20	al	al	PROPN
iajs-2289	343	21	-	-	PUNCT
iajs-2289	343	22	haitham	haitham	PROPN
iajs-2289	343	23	jour	jour	X
iajs-2289	343	24	.	.	PROPN
iajs-2289	344	1	for	for	ADP
iajs-2289	344	2	pure	pure	ADJ
iajs-2289	344	3	&	&	CCONJ
iajs-2289	344	4	appl	appl	PROPN
iajs-2289	344	5	.	.	PUNCT
iajs-2289	345	1	sci	sci	PROPN
iajs-2289	345	2	.	.	PROPN
iajs-2289	345	3	32	32	NUM
iajs-2289	345	4	(	(	PUNCT
iajs-2289	345	5	3	3	NUM
iajs-2289	345	6	)	)	PUNCT
iajs-2289	345	7	2019	2019	NUM
iajs-2289	345	8	l	l	NOUN
iajs-2289	345	9	)	)	PUNCT
iajs-2289	345	10			NOUN
iajs-2289	345	11	.	.	PUNCT
iajs-2289	345	12	let	let	VERB
iajs-2289	345	13	i	i	PRON
iajs-2289	345	14			NOUN
iajs-2289	345	15	h	h	PROPN
iajs-2289	345	16			PROPN
iajs-2289	345	17	{	{	PUNCT
iajs-2289	345	18	h	h	NOUN
iajs-2289	345	19	}	}	PUNCT
iajs-2289	345	20	.	.	PUNCT
iajs-2289	346	1	because	because	SCONJ
iajs-2289	346	2	of	of	ADP
iajs-2289	346	3	h	h	PROPN
iajs-2289	346	4	j	j	PROPN
iajs-2289	346	5	-	-	PUNCT
iajs-2289	346	6	ω	ω	NOUN
iajs-2289	346	7	-	-	NOUN
iajs-2289	346	8	urysohn	urysohn	PROPN
iajs-2289	346	9	,	,	PUNCT
iajs-2289	346	10	yond	yond	PROPN
iajs-2289	346	11	are	be	AUX
iajs-2289	346	12	open	open	ADJ
iajs-2289	346	13	sets	set	NOUN
iajs-2289	346	14	si	si	INTJ
iajs-2289	346	15	of	of	ADP
iajs-2289	346	16	i	i	PRON
iajs-2289	346	17	and	and	CCONJ
iajs-2289	346	18	sh	sh	INTJ
iajs-2289	346	19	of	of	ADP
iajs-2289	346	20	h	h	PROPN
iajs-2289	346	21	such	such	ADJ
iajs-2289	347	1	that	that	PRON
iajs-2289	347	2	cl	cl	PROPN
iajs-2289	347	3	j	j	PROPN
iajs-2289	347	4	-	-	PUNCT
iajs-2289	347	5	ω-(si	ω-(si	PROPN
iajs-2289	347	6	)	)	PUNCT
iajs-2289	347	7	∩	∩	PROPN
iajs-2289	347	8	cl	cl	ADP
iajs-2289	347	9	j	j	PROPN
iajs-2289	347	10	-	-	PUNCT
iajs-2289	347	11	ω-(sh	ω-(sh	PROPN
iajs-2289	347	12	)	)	PUNCT
iajs-2289	347	13	=	=	PUNCT
iajs-2289	347	14	.	.	VERB
iajs-2289	347	15	yond	yond	NOUN
iajs-2289	347	16	is	be	AUX
iajs-2289	347	17	h	h	PROPN
iajs-2289	347	18			NOUN
iajs-2289	347	19	l	l	NOUN
iajs-2289	347	20	such	such	ADJ
iajs-2289	347	21	that	that	SCONJ
iajs-2289	347	22	(h	(h	PROPN
iajs-2289	347	23	)	)	PUNCT
iajs-2289	347	24			PROPN
iajs-2289	347	25	cl	cl	INTJ
iajs-2289	347	26	j	j	NOUN
iajs-2289	347	27	-	-	PUNCT
iajs-2289	347	28	ω(sh	ω(sh	ADJ
iajs-2289	347	29	)	)	PUNCT
iajs-2289	347	30	.	.	PUNCT
iajs-2289	348	1	for	for	ADP
iajs-2289	348	2	every	every	DET
iajs-2289	348	3	g	g	NOUN
iajs-2289	348	4			NOUN
iajs-2289	348	5	–1	–1	PROPN
iajs-2289	348	6	(	(	PUNCT
iajs-2289	348	7	i	i	NOUN
iajs-2289	348	8	)	)	PUNCT
iajs-2289	348	9	,	,	PUNCT
iajs-2289	348	10	there	there	PRON
iajs-2289	348	11	is	be	VERB
iajs-2289	348	12	open	open	ADJ
iajs-2289	348	13	ti	ti	NOUN
iajs-2289	348	14	of	of	ADP
iajs-2289	348	15	i	i	PRON
iajs-2289	348	16	such	such	ADJ
iajs-2289	348	17	that	that	SCONJ
iajs-2289	348	18			ADJ
iajs-2289	348	19	(	(	PUNCT
iajs-2289	348	20	cl	cl	INTJ
iajs-2289	348	21	j	j	PROPN
iajs-2289	348	22	-	-	PUNCT
iajs-2289	348	23	ω(ti	ω(ti	NOUN
iajs-2289	348	24	)	)	PUNCT
iajs-2289	348	25	)	)	PUNCT
iajs-2289	349	1			PROPN
iajs-2289	349	2	cl	cl	INTJ
iajs-2289	349	3	j	j	PROPN
iajs-2289	349	4	-	-	PUNCT
iajs-2289	349	5	ω(si	ω(si	PROPN
iajs-2289	349	6	)	)	PUNCT
iajs-2289	349	7	.	.	PUNCT
iajs-2289	350	1	so	so	ADV
iajs-2289	350	2	,	,	PUNCT
iajs-2289	350	3	cl	cl	INTJ
iajs-2289	350	4	j	j	PROPN
iajs-2289	350	5	-	-	PUNCT
iajs-2289	350	6	ω(tg	ω(tg	PROPN
iajs-2289	350	7	)	)	PUNCT
iajs-2289	350	8	∩	∩	ADJ
iajs-2289	350	9	h	h	NOUN
iajs-2289	350	10	=	=	PUNCT
iajs-2289	350	11	.	.	PUNCT
iajs-2289	350	12	it	it	PRON
iajs-2289	350	13	follows	follow	VERB
iajs-2289	350	14	that	that	SCONJ
iajs-2289	350	15	–1	–1	PROPN
iajs-2289	350	16	(	(	PUNCT
iajs-2289	350	17	i	i	NOUN
iajs-2289	350	18	)	)	PUNCT
iajs-2289	350	19	∩	∩	NOUN
iajs-2289	350	20	(	(	PUNCT
iajs-2289	350	21	alj	alj	PROPN
iajs-2289	350	22	-	-	PUNCT
iajs-2289	350	23	ω	ω	NOUN
iajs-2289	350	24	-	-	PUNCT
iajs-2289	350	25	cg	cg	NOUN
iajs-2289	350	26	l	l	NOUN
iajs-2289	350	27	)	)	PUNCT
iajs-2289	351	1	=	=	NOUN
iajs-2289	351	2			NOUN
iajs-2289	351	3	for	for	ADP
iajs-2289	351	4	each	each	DET
iajs-2289	351	5	i	i	PRON
iajs-2289	351	6			PROPN
iajs-2289	351	7	h	h	PROPN
iajs-2289	351	8			PROPN
iajs-2289	351	9	{	{	PUNCT
iajs-2289	351	10	h	h	NOUN
iajs-2289	351	11	}	}	PUNCT
iajs-2289	351	12	.	.	PUNCT
iajs-2289	352	1	so	so	ADV
iajs-2289	352	2	,	,	PUNCT
iajs-2289	352	3	(	(	PUNCT
iajs-2289	352	4	alj	alj	PROPN
iajs-2289	352	5	-	-	PUNCT
iajs-2289	352	6	ω	ω	NOUN
iajs-2289	352	7	-	-	PUNCT
iajs-2289	352	8	cg	cg	NOUN
iajs-2289	352	9	l	l	NOUN
iajs-2289	352	10	)	)	PUNCT
iajs-2289	352	11	∩	∩	NOUN
iajs-2289	352	12	–1	–1	PROPN
iajs-2289	352	13	(	(	PUNCT
iajs-2289	352	14	h	h	NOUN
iajs-2289	352	15	)	)	PUNCT
iajs-2289	352	16			NOUN
iajs-2289	352	17			NOUN
iajs-2289	352	18	and	and	CCONJ
iajs-2289	352	19			NOUN
iajs-2289	352	20	is	be	AUX
iajs-2289	352	21	j	j	PROPN
iajs-2289	352	22	-	-	PUNCT
iajs-2289	352	23	ω	ω	NOUN
iajs-2289	352	24	-	-	NOUN
iajs-2289	352	25	perfect	perfect	ADJ
iajs-2289	352	26	,	,	PUNCT
iajs-2289	352	27	where	where	SCONJ
iajs-2289	352	28	j{	j{	PROPN
iajs-2289	352	29	,	,	PUNCT
iajs-2289	352	30	δ	δ	PROPN
iajs-2289	352	31	,	,	PUNCT
iajs-2289	352	32			NOUN
iajs-2289	352	33	,	,	PUNCT
iajs-2289	352	34	pre	pre	AUX
iajs-2289	352	35	,	,	PUNCT
iajs-2289	352	36	b	b	NOUN
iajs-2289	352	37	,	,	PUNCT
iajs-2289	352	38			NOUN
iajs-2289	352	39	}	}	PUNCT
iajs-2289	352	40	.	.	PUNCT
iajs-2289	353	1	corollary	corollary	ADJ
iajs-2289	353	2	41	41	NUM
iajs-2289	353	3	if	if	SCONJ
iajs-2289	353	4			ADJ
iajs-2289	353	5	:	:	PUNCT
iajs-2289	353	6	g	g	PROPN
iajs-2289	353	7			NOUN
iajs-2289	353	8	h	h	NOUN
iajs-2289	353	9	be	be	VERB
iajs-2289	353	10	a	a	DET
iajs-2289	353	11	mapping	mapping	NOUN
iajs-2289	353	12	is	be	AUX
iajs-2289	353	13	j	j	PROPN
iajs-2289	353	14	-	-	PUNCT
iajs-2289	353	15	ω	ω	VERB
iajs-2289	353	16	-	-	PUNCT
iajs-2289	353	17	closure	closure	NOUN
iajs-2289	353	18	continuous	continuous	ADJ
iajs-2289	353	19	,	,	PUNCT
iajs-2289	353	20	g	g	PROPN
iajs-2289	353	21	is	be	AUX
iajs-2289	353	22	quasij	quasij	NOUN
iajs-2289	353	23	-	-	PUNCT
iajs-2289	353	24	ω	ω	NUM
iajs-2289	353	25	-	-	PUNCT
iajs-2289	353	26	h	h	NOUN
iajs-2289	353	27	-	-	PUNCT
iajs-2289	353	28	closed	closed	ADJ
iajs-2289	353	29	,	,	PUNCT
iajs-2289	353	30	and	and	CCONJ
iajs-2289	353	31	h	h	NOUN
iajs-2289	353	32	is	be	AUX
iajs-2289	353	33	j	j	PROPN
iajs-2289	353	34	-	-	PUNCT
iajs-2289	353	35	ω	ω	NOUN
iajs-2289	353	36	-	-	NOUN
iajs-2289	353	37	urysohn	urysohn	ADJ
iajs-2289	353	38	,	,	PUNCT
iajs-2289	353	39	then	then	ADV
iajs-2289	353	40			X
iajs-2289	353	41	is	be	AUX
iajs-2289	353	42	j	j	PROPN
iajs-2289	353	43	-	-	PUNCT
iajs-2289	353	44	ω	ω	NOUN
iajs-2289	353	45	-	-	NOUN
iajs-2289	353	46	perfect	perfect	ADJ
iajs-2289	353	47	,	,	PUNCT
iajs-2289	353	48	where	where	SCONJ
iajs-2289	353	49	j{	j{	PROPN
iajs-2289	353	50	,	,	PUNCT
iajs-2289	353	51	δ	δ	PROPN
iajs-2289	353	52	,	,	PUNCT
iajs-2289	353	53			NOUN
iajs-2289	353	54	,	,	PUNCT
iajs-2289	353	55	pre	pre	ADJ
iajs-2289	353	56	,	,	PUNCT
iajs-2289	353	57	b	b	NOUN
iajs-2289	353	58	,	,	PUNCT
iajs-2289	353	59			NOUN
iajs-2289	353	60	}	}	PUNCT
iajs-2289	353	61	.	.	PUNCT
iajs-2289	354	1	proof	proof	NOUN
iajs-2289	354	2	.	.	PUNCT
iajs-2289	355	1	since	since	SCONJ
iajs-2289	355	2	g	g	PROPN
iajs-2289	355	3	is	be	AUX
iajs-2289	355	4	quasij	quasij	NOUN
iajs-2289	355	5	-	-	PUNCT
iajs-2289	355	6	ω	ω	NUM
iajs-2289	355	7	-	-	PUNCT
iajs-2289	355	8	h	h	NOUN
iajs-2289	355	9	-	-	PUNCT
iajs-2289	355	10	closed	closed	ADJ
iajs-2289	355	11	,	,	PUNCT
iajs-2289	355	12	then	then	ADV
iajs-2289	355	13	all	all	DET
iajs-2289	355	14	filter	filter	NOUN
iajs-2289	355	15	base	base	NOUN
iajs-2289	355	16	on	on	ADP
iajs-2289	355	17	g	g	PROPN
iajs-2289	355	18	has	have	VERB
iajs-2289	355	19	non	non	NOUN
iajs-2289	355	20	void	void	VERB
iajs-2289	355	21	almost	almost	ADV
iajs-2289	355	22	j	j	NOUN
iajs-2289	355	23	-	-	NOUN
iajs-2289	355	24	ωcluster	ωcluster	NOUN
iajs-2289	355	25	;	;	PUNCT
iajs-2289	355	26	now	now	ADV
iajs-2289	355	27	,	,	PUNCT
iajs-2289	355	28	the	the	DET
iajs-2289	355	29	corollary	corollary	NOUN
iajs-2289	355	30	follows	follow	VERB
iajs-2289	355	31	directly	directly	ADV
iajs-2289	355	32	from	from	ADP
iajs-2289	355	33	theorem	theorem	ADJ
iajs-2289	355	34	35	35	NUM
iajs-2289	355	35	,	,	PUNCT
iajs-2289	355	36	where	where	SCONJ
iajs-2289	355	37	j{	j{	PROPN
iajs-2289	355	38	,	,	PUNCT
iajs-2289	355	39	δ	δ	PROPN
iajs-2289	355	40	,	,	PUNCT
iajs-2289	355	41			NOUN
iajs-2289	355	42	,	,	PUNCT
iajs-2289	355	43	pre	pre	ADJ
iajs-2289	355	44	,	,	PUNCT
iajs-2289	355	45	,	,	PUNCT
iajs-2289	355	46	b	b	X
iajs-2289	355	47	,	,	PUNCT
iajs-2289	355	48			PROPN
iajs-2289	355	49	}	}	PUNCT
iajs-2289	355	50	.	.	PUNCT
iajs-2289	356	1	7	7	X
iajs-2289	356	2	.	.	X
iajs-2289	356	3	conclusions	conclusion	NOUN
iajs-2289	356	4	the	the	DET
iajs-2289	356	5	starting	starting	NOUN
iajs-2289	356	6	point	point	NOUN
iajs-2289	356	7	for	for	ADP
iajs-2289	356	8	the	the	DET
iajs-2289	356	9	application	application	NOUN
iajs-2289	356	10	of	of	ADP
iajs-2289	356	11	abstract	abstract	ADJ
iajs-2289	356	12	topological	topological	ADJ
iajs-2289	356	13	structures	structure	NOUN
iajs-2289	356	14	in	in	ADP
iajs-2289	356	15	j	j	PROPN
iajs-2289	356	16	-	-	PUNCT
iajs-2289	356	17	ω	ω	VERB
iajs-2289	356	18	-	-	PUNCT
iajs-2289	356	19	perfect	perfect	ADJ
iajs-2289	356	20	mapping	mapping	NOUN
iajs-2289	356	21	is	be	AUX
iajs-2289	356	22	presented	present	VERB
iajs-2289	356	23	in	in	ADP
iajs-2289	356	24	this	this	DET
iajs-2289	356	25	paper	paper	NOUN
iajs-2289	356	26	.	.	PUNCT
iajs-2289	357	1	we	we	PRON
iajs-2289	357	2	use	use	VERB
iajs-2289	357	3	filter	filter	NOUN
iajs-2289	357	4	base	base	NOUN
iajs-2289	357	5	to	to	PART
iajs-2289	357	6	introduce	introduce	VERB
iajs-2289	357	7	a	a	DET
iajs-2289	357	8	new	new	ADJ
iajs-2289	357	9	notion	notion	NOUN
iajs-2289	357	10	namely	namely	ADV
iajs-2289	357	11	filter	filter	NOUN
iajs-2289	357	12	base	base	NOUN
iajs-2289	357	13	and	and	CCONJ
iajs-2289	357	14	j	j	PROPN
iajs-2289	357	15	-	-	PUNCT
iajs-2289	357	16	ω	ω	VERB
iajs-2289	357	17	-	-	PUNCT
iajs-2289	357	18	perfect	perfect	ADJ
iajs-2289	357	19	mapping	mapping	NOUN
iajs-2289	357	20	.	.	PUNCT
iajs-2289	358	1	finally	finally	ADV
iajs-2289	358	2	,	,	PUNCT
iajs-2289	358	3	certain	certain	ADJ
iajs-2289	358	4	theorems	theorem	NOUN
iajs-2289	358	5	and	and	CCONJ
iajs-2289	358	6	generalization	generalization	NOUN
iajs-2289	358	7	concerning	concern	VERB
iajs-2289	358	8	these	these	DET
iajs-2289	358	9	concepts	concept	NOUN
iajs-2289	358	10	of	of	ADP
iajs-2289	358	11	studied	studied	ADJ
iajs-2289	358	12	;	;	PUNCT
iajs-2289	358	13	j	j	PROPN
iajs-2289	358	14	{	{	PROPN
iajs-2289	358	15	,	,	PUNCT
iajs-2289	358	16	δ	δ	PROPN
iajs-2289	358	17	,	,	PUNCT
iajs-2289	358	18			NOUN
iajs-2289	358	19	,	,	PUNCT
iajs-2289	358	20	pre	pre	ADJ
iajs-2289	358	21	,	,	PUNCT
iajs-2289	358	22	b	b	NOUN
iajs-2289	358	23	,	,	PUNCT
iajs-2289	358	24			NOUN
iajs-2289	358	25	}	}	PUNCT
iajs-2289	358	26	.	.	PUNCT
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iajs-2289	359	2	1	1	NUM
iajs-2289	359	3	.	.	PUNCT
iajs-2289	359	4	riesz	riesz	PROPN
iajs-2289	359	5	,	,	PUNCT
iajs-2289	359	6	f.	f.	PROPN
iajs-2289	359	7	stetigkeitsbegriff	stetigkeitsbegriff	PROPN
iajs-2289	359	8	and	and	CCONJ
iajs-2289	359	9	und	und	VERB
iajs-2289	359	10	abstrakte	abstrakte	PROPN
iajs-2289	359	11	mengenlehre	mengenlehre	PROPN
iajs-2289	359	12	.	.	PUNCT
iajs-2289	360	1	atti	atti	PROPN
iajs-2289	360	2	ael	ael	PROPN
iajs-2289	360	3	iv	iv	PROPN
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iajs-2289	360	5	internazionale	internazionale	NOUN
iajs-2289	360	6	dei	dei	PROPN
iajs-2289	360	7	matematici.1909	matematici.1909	PROPN
iajs-2289	360	8	,	,	PUNCT
iajs-2289	360	9	2	2	NUM
iajs-2289	360	10	,	,	PUNCT
iajs-2289	360	11	18	18	NUM
iajs-2289	360	12	-	-	SYM
iajs-2289	360	13	24	24	NUM
iajs-2289	360	14	.	.	PUNCT
iajs-2289	361	1	2	2	NUM
iajs-2289	361	2	.	.	X
iajs-2289	361	3	cartan	cartan	PROPN
iajs-2289	361	4	,	,	PUNCT
iajs-2289	361	5	h.	h.	PROPN
iajs-2289	361	6	theorie	theorie	PROPN
iajs-2289	361	7	des	des	PROPN
iajs-2289	361	8	filters	filter	NOUN
iajs-2289	361	9	.	.	PUNCT
iajs-2289	362	1	acad	acad	PROPN
iajs-2289	362	2	.	.	PUNCT
iajs-2289	363	1	paris	paris	PROPN
iajs-2289	363	2	.	.	PUNCT
iajs-2289	364	1	1	1	NUM
iajs-2289	364	2	st	st	PROPN
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iajs-2289	364	4	.	.	PUNCT
iajs-2289	365	1	3	3	X
iajs-2289	365	2	.	.	X
iajs-2289	365	3	cartan	cartan	PROPN
iajs-2289	365	4	,	,	PUNCT
iajs-2289	365	5	h.	h.	PROPN
iajs-2289	365	6	filters	filter	VERB
iajs-2289	365	7	ultrafilters	ultrafilter	NOUN
iajs-2289	365	8	.	.	PUNCT
iajs-2289	366	1	acad	acad	PROPN
iajs-2289	366	2	.	.	PUNCT
iajs-2289	367	1	paris	paris	PROPN
iajs-2289	367	2	.	.	PUNCT
iajs-2289	368	1	2	2	NUM
iajs-2289	368	2	nd	nd	NUM
iajs-2289	368	3	edition,1937a	edition,1937a	NOUN
iajs-2289	368	4	.	.	PUNCT
iajs-2289	369	1	4	4	X
iajs-2289	369	2	.	.	X
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iajs-2289	369	4	,	,	PUNCT
iajs-2289	369	5	n.	n.	PROPN
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iajs-2289	369	7	topology	topology	PROPN
iajs-2289	369	8	.	.	PUNCT
iajs-2289	370	1	part	part	PROPN
iajs-2289	370	2	i.	i.	PROPN
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iajs-2289	370	4	-	-	PUNCT
iajs-2289	370	5	wesly	wesly	ADV
iajs-2289	370	6	.	.	PUNCT
iajs-2289	371	1	reding	rede	VERB
iajs-2289	371	2	.	.	PUNCT
iajs-2289	372	1	mass,1975	mass,1975	NOUN
iajs-2289	372	2	.	.	PROPN
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iajs-2289	372	4	.	.	X
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iajs-2289	372	6	,	,	PUNCT
iajs-2289	372	7	g.t	g.t	PROPN
iajs-2289	372	8	.	.	PROPN
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iajs-2289	372	11	of	of	ADP
iajs-2289	372	12	sets	set	NOUN
iajs-2289	372	13	and	and	CCONJ
iajs-2289	372	14	closedness	closedness	NOUN
iajs-2289	372	15	of	of	ADP
iajs-2289	372	16	functions	function	NOUN
iajs-2289	372	17	.	.	PUNCT
iajs-2289	373	1	proc	proc	NOUN
iajs-2289	373	2	.	.	PUNCT
iajs-2289	374	1	nat	nat	PROPN
iajs-2289	374	2	.	.	PUNCT
iajs-2289	375	1	acad	acad	PROPN
iajs-2289	375	2	.	.	PUNCT
iajs-2289	376	1	sci.1965	sci.1965	NOUN
iajs-2289	376	2	,	,	PUNCT
iajs-2289	376	3	54	54	NUM
iajs-2289	376	4	,	,	PUNCT
iajs-2289	376	5	688692	688692	NUM
iajs-2289	376	6	.	.	PUNCT
iajs-2289	377	1	6	6	NUM
iajs-2289	377	2	.	.	X
iajs-2289	377	3	dickman	dickman	PROPN
iajs-2289	377	4	,	,	PUNCT
iajs-2289	377	5	r.f	r.f	PROPN
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iajs-2289	377	8	porter	porter	PROPN
iajs-2289	377	9	,	,	PUNCT
iajs-2289	377	10	j.r	j.r	PROPN
iajs-2289	377	11	.	.	PROPN
iajs-2289	377	12	-perfect	-perfect	PROPN
iajs-2289	377	13	and	and	CCONJ
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iajs-2289	377	15	functions	function	NOUN
iajs-2289	377	16	.	.	PUNCT
iajs-2289	378	1	illinois	illinois	PROPN
iajs-2289	378	2	jour	jour	PROPN
iajs-2289	378	3	.	.	PUNCT
iajs-2289	379	1	math.1977	math.1977	PROPN
iajs-2289	379	2	,	,	PUNCT
iajs-2289	379	3	21	21	NUM
iajs-2289	379	4	,	,	PUNCT
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iajs-2289	379	6	-	-	SYM
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iajs-2289	379	8	.	.	PUNCT
iajs-2289	380	1	7	7	X
iajs-2289	380	2	.	.	X
iajs-2289	380	3	porter	porter	PROPN
iajs-2289	380	4	,	,	PUNCT
iajs-2289	380	5	j.r	j.r	PROPN
iajs-2289	380	6	.	.	PROPN
iajs-2289	380	7	;	;	PUNCT
iajs-2289	381	1	thomas	thomas	PROPN
iajs-2289	381	2	,	,	PUNCT
iajs-2289	381	3	j.d	j.d	PROPN
iajs-2289	381	4	.	.	PROPN
iajs-2289	381	5	on	on	ADP
iajs-2289	381	6	h	h	NOUN
iajs-2289	381	7	-	-	PUNCT
iajs-2289	381	8	closed	closed	ADJ
iajs-2289	381	9	and	and	CCONJ
iajs-2289	381	10	minimal	minimal	ADJ
iajs-2289	381	11	hausdorff	hausdorff	NOUN
iajs-2289	381	12	spaces	space	NOUN
iajs-2289	381	13	.	.	PUNCT
iajs-2289	382	1	trans	trans	PROPN
iajs-2289	382	2	.	.	PUNCT
iajs-2289	383	1	amer	amer	PROPN
iajs-2289	383	2	.	.	PUNCT
iajs-2289	383	3	math	math	PROPN
iajs-2289	383	4	.	.	PUNCT
iajs-2289	384	1	soc.1969	soc.1969	PROPN
iajs-2289	384	2	,	,	PUNCT
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iajs-2289	384	4	,	,	PUNCT
iajs-2289	384	5	159170	159170	NUM
iajs-2289	384	6	.	.	PUNCT
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iajs-2289	384	8	.	.	X
iajs-2289	384	9	levine	levine	PROPN
iajs-2289	384	10	,	,	PUNCT
iajs-2289	384	11	n.a	n.a	PROPN
iajs-2289	384	12	.	.	PROPN
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iajs-2289	384	14	of	of	ADP
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iajs-2289	384	16	in	in	ADP
iajs-2289	384	17	topological	topological	ADJ
iajs-2289	384	18	spaces	space	NOUN
iajs-2289	384	19	.	.	PUNCT
iajs-2289	385	1	american	american	PROPN
iajs-2289	385	2	mathematical	mathematical	PROPN
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iajs-2289	385	4	,	,	PUNCT
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iajs-2289	385	6	,	,	PUNCT
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iajs-2289	385	8	-	-	SYM
iajs-2289	385	9	418	418	NUM
iajs-2289	385	10	.	.	PUNCT
iajs-2289	386	1	9	9	NUM
iajs-2289	386	2	.	.	X
iajs-2289	386	3	andrew	andrew	PROPN
iajs-2289	386	4	,	,	PUNCT
iajs-2289	386	5	d.r	d.r	PROPN
iajs-2289	386	6	;	;	PUNCT
iajs-2289	386	7	whittlesy	whittlesy	NOUN
iajs-2289	386	8	,	,	PUNCT
iajs-2289	386	9	e.k	e.k	PROPN
iajs-2289	386	10	.	.	PROPN
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iajs-2289	386	12	continuity	continuity	NOUN
iajs-2289	386	13	.	.	PUNCT
iajs-2289	387	1	american	american	PROPN
iajs-2289	387	2	mathematical	mathematical	PROPN
iajs-2289	387	3	monthly	monthly	ADV
iajs-2289	387	4	.	.	PUNCT
iajs-2289	388	1	1966	1966	NUM
iajs-2289	388	2	,	,	PUNCT
iajs-2289	388	3	73	73	NUM
iajs-2289	388	4	,	,	PUNCT
iajs-2289	388	5	758	758	NUM
iajs-2289	388	6	-	-	SYM
iajs-2289	388	7	759	759	NUM
iajs-2289	388	8	.	.	PUNCT
iajs-2289	389	1	10	10	NUM
iajs-2289	389	2	.	.	X
iajs-2289	390	1	willard	willard	PROPN
iajs-2289	390	2	,	,	PUNCT
iajs-2289	390	3	s.	s.	PROPN
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iajs-2289	390	5	topology	topology	PROPN
iajs-2289	390	6	.	.	PUNCT
iajs-2289	391	1	addison	addison	PROPN
iajs-2289	391	2	wesley	wesley	PROPN
iajs-2289	391	3	publishing	publishing	PROPN
iajs-2289	391	4	company	company	PROPN
iajs-2289	391	5	,	,	PUNCT
iajs-2289	391	6	inc	inc	PROPN
iajs-2289	391	7	.	.	PROPN
iajs-2289	391	8	1	1	NUM
iajs-2289	391	9	st	st	PROPN
iajs-2289	391	10	edition,1970	edition,1970	PROPN
iajs-2289	391	11	.	.	PROPN
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iajs-2289	391	13	.	.	X
iajs-2289	392	1	hdeib	hdeib	PROPN
iajs-2289	392	2	,	,	PUNCT
iajs-2289	392	3	h.z	h.z	PROPN
iajs-2289	392	4	.	.	PROPN
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iajs-2289	392	9	.	.	PUNCT
iajs-2289	393	1	revista	revista	PROPN
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iajs-2289	393	3	a	a	DET
iajs-2289	393	4	de	de	X
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iajs-2289	393	6	,	,	PUNCT
iajs-2289	393	7	xvi	xvi	NOUN
iajs-2289	393	8	,	,	PUNCT
iajs-2289	393	9	65	65	NUM
iajs-2289	393	10	-	-	SYM
iajs-2289	393	11	78	78	NUM
iajs-2289	393	12	.	.	PUNCT
iajs-2289	394	1	12	12	NUM
iajs-2289	394	2	.	.	PUNCT
iajs-2289	395	1	yousif	yousif	PROPN
iajs-2289	395	2	,	,	PUNCT
iajs-2289	395	3	y.y	y.y	PROPN
iajs-2289	395	4	.	.	PROPN
iajs-2289	395	5	-perfect	-perfect	NOUN
iajs-2289	395	6	mappings	mapping	NOUN
iajs-2289	395	7	.	.	PUNCT
iajs-2289	396	1	ibn	ibn	PROPN
iajs-2289	396	2	al	al	PROPN
iajs-2289	396	3	–	–	PUNCT
iajs-2289	396	4	haitham	haitham	PROPN
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iajs-2289	396	11	,	,	PUNCT
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iajs-2289	396	13	,	,	PUNCT
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iajs-2289	396	15	,	,	PUNCT
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iajs-2289	396	17	-	-	SYM
iajs-2289	396	18	149	149	NUM
iajs-2289	396	19	.	.	PUNCT
iajs-2289	397	1	13	13	NUM
iajs-2289	397	2	.	.	PUNCT
iajs-2289	398	1	mashhour	mashhour	PROPN
iajs-2289	398	2	,	,	PUNCT
iajs-2289	398	3	a.s	a.s	PROPN
iajs-2289	398	4	.	.	PROPN
iajs-2289	398	5	;	;	PUNCT
iajs-2289	399	1	abd	abd	PROPN
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iajs-2289	399	3	-	-	PUNCT
iajs-2289	399	4	monsef	monsef	ADJ
iajs-2289	399	5	,	,	PUNCT
iajs-2289	399	6	m.e	m.e	PROPN
iajs-2289	399	7	.	.	PROPN
iajs-2289	399	8	;	;	PUNCT
iajs-2289	399	9	el	el	PROPN
iajs-2289	399	10	-	-	PUNCT
iajs-2289	399	11	deeb	deeb	PROPN
iajs-2289	399	12	,	,	PUNCT
iajs-2289	399	13	s.n	s.n	PROPN
iajs-2289	399	14	.	.	PROPN
iajs-2289	399	15	on	on	ADP
iajs-2289	399	16	pre	pre	VERB
iajs-2289	399	17	continuous	continuous	ADJ
iajs-2289	399	18	and	and	CCONJ
iajs-2289	399	19	weak	weak	ADJ
iajs-2289	399	20	pre	pre	ADJ
iajs-2289	399	21	continuous	continuous	ADJ
iajs-2289	399	22	mappings	mapping	NOUN
iajs-2289	399	23	.	.	PUNCT
iajs-2289	400	1	proc	proc	NOUN
iajs-2289	400	2	.	.	PUNCT
iajs-2289	401	1	math	math	NOUN
iajs-2289	401	2	.	.	PUNCT
iajs-2289	402	1	phys	phy	NOUN
iajs-2289	402	2	.	.	PUNCT
iajs-2289	403	1	soc.1982	soc.1982	ADP
iajs-2289	403	2	,	,	PUNCT
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iajs-2289	403	4	,	,	PUNCT
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iajs-2289	403	6	-	-	SYM
iajs-2289	403	7	53	53	NUM
iajs-2289	403	8	.	.	PUNCT
iajs-2289	404	1	14	14	NUM
iajs-2289	404	2	.	.	PUNCT
iajs-2289	405	1	abd	abd	PROPN
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iajs-2289	405	29	.	.	PUNCT
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iajs-2289	406	2	.	.	PUNCT
iajs-2289	407	1	fac	fac	PROPN
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iajs-2289	408	2	,	,	PUNCT
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iajs-2289	408	4	,	,	PUNCT
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iajs-2289	408	6	-	-	SYM
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iajs-2289	408	8	.	.	NOUN
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iajs-2289	408	10	.	.	PUNCT
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iajs-2289	409	6	-	-	PUNCT
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iajs-2289	409	9	.	.	PUNCT
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iajs-2289	410	2	.	.	PUNCT
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iajs-2289	411	2	,	,	PUNCT
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iajs-2289	411	6	-	-	SYM
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iajs-2289	411	8	.	.	PUNCT
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iajs-2289	412	2	.	.	PUNCT
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iajs-2289	413	10	.	.	PUNCT
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iajs-2289	414	5	,	,	PUNCT
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iajs-2289	414	7	,	,	PUNCT
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iajs-2289	414	9	,	,	PUNCT
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iajs-2289	414	11	.	.	PUNCT
iajs-2289	415	1	177	177	NUM
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iajs-2289	415	7	.	.	PROPN
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iajs-2289	416	9	.	.	PUNCT
iajs-2289	417	1	yousif	yousif	PROPN
iajs-2289	417	2	,	,	PUNCT
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iajs-2289	418	3	,	,	PUNCT
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iajs-2289	418	9	-	-	SYM
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iajs-2289	418	11	.	.	PUNCT
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iajs-2289	419	2	.	.	PUNCT
iajs-2289	420	1	yousif	yousif	PROPN
iajs-2289	420	2	,	,	PUNCT
iajs-2289	420	3	y.y	y.y	PROPN
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iajs-2289	420	5	;	;	PUNCT
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iajs-2289	420	16	.	.	PUNCT
iajs-2289	421	1	conf	conf	PROPN
iajs-2289	421	2	.	.	PUNCT
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iajs-2289	422	6	,	,	PUNCT
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iajs-2289	422	10	,	,	PUNCT
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iajs-2289	422	12	-	-	SYM
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iajs-2289	422	14	,	,	PUNCT
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iajs-2289	422	16	-	-	PUNCT
iajs-2289	422	17	6596/1003/1/012063	6596/1003/1/012063	NUM
iajs-2289	422	18	.	.	PUNCT
iajs-2289	423	1	19	19	NUM
iajs-2289	423	2	.	.	X
iajs-2289	423	3	yousif	yousif	PROPN
iajs-2289	423	4	,	,	PUNCT
iajs-2289	423	5	y.y	y.y	PROPN
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iajs-2289	423	7	;	;	PUNCT
iajs-2289	423	8	jassim	jassim	PROPN
iajs-2289	423	9	,	,	PUNCT
iajs-2289	423	10	n.s	n.s	PROPN
iajs-2289	423	11	.	.	PROPN
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iajs-2289	423	17	.	.	PUNCT
iajs-2289	424	1	ibn	ibn	PROPN
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iajs-2289	424	11	,	,	PUNCT
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iajs-2289	424	15	,	,	PUNCT
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iajs-2289	424	17	-	-	SYM
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iajs-2289	424	19	.	.	PUNCT