id	sid	tid	token	lemma	pos
iajs-2681	1	1	87	87	NUM
iajs-2681	1	2	fibrewise	fibrewise	NOUN
iajs-2681	1	3	fuzzy	fuzzy	ADJ
iajs-2681	1	4	topological	topological	ADJ
iajs-2681	1	5	spaces	space	NOUN
iajs-2681	1	6	yousif	yousif	PROPN
iajs-2681	1	7	y.	y.	PROPN
iajs-2681	1	8	yousif	yousif	PROPN
iajs-2681	1	9	yoyayousif@yahoo.com	yoyayousif@yahoo.com	PROPN
iajs-2681	2	1	yousif.y.y@ihcoedu.uobaghdad.edu.iq	yousif.y.y@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-2681	2	2	department	department	PROPN
iajs-2681	2	3	of	of	ADP
iajs-2681	2	4	mathematics	mathematics	PROPN
iajs-2681	2	5	,	,	PUNCT
iajs-2681	2	6	college	college	NOUN
iajs-2681	2	7	of	of	ADP
iajs-2681	2	8	education	education	NOUN
iajs-2681	2	9	for	for	ADP
iajs-2681	2	10	pure	pure	ADJ
iajs-2681	2	11	science	science	NOUN
iajs-2681	2	12	(	(	PUNCT
iajs-2681	2	13	ibn	ibn	PROPN
iajs-2681	2	14	al	al	PROPN
iajs-2681	2	15	-	-	PUNCT
iajs-2681	2	16	haitham	haitham	PROPN
iajs-2681	2	17	)	)	PUNCT
iajs-2681	2	18	,	,	PUNCT
iajs-2681	2	19	university	university	NOUN
iajs-2681	2	20	of	of	ADP
iajs-2681	2	21	baghdad	baghdad	PROPN
iajs-2681	2	22	abstract	abstract	NOUN
iajs-2681	2	23	we	we	PRON
iajs-2681	2	24	introduce	introduce	VERB
iajs-2681	2	25	and	and	CCONJ
iajs-2681	2	26	discuss	discuss	VERB
iajs-2681	2	27	the	the	DET
iajs-2681	2	28	modern	modern	ADJ
iajs-2681	2	29	type	type	NOUN
iajs-2681	2	30	of	of	ADP
iajs-2681	2	31	fibrewise	fibrewise	NOUN
iajs-2681	2	32	topological	topological	ADJ
iajs-2681	2	33	spaces	space	NOUN
iajs-2681	2	34	,	,	PUNCT
iajs-2681	2	35	namely	namely	ADV
iajs-2681	2	36	fibrewise	fibrewise	VERB
iajs-2681	2	37	fuzzy	fuzzy	ADJ
iajs-2681	2	38	topological	topological	ADJ
iajs-2681	2	39	spaces	space	NOUN
iajs-2681	2	40	.	.	PUNCT
iajs-2681	3	1	also	also	ADV
iajs-2681	3	2	,	,	PUNCT
iajs-2681	3	3	we	we	PRON
iajs-2681	3	4	introduce	introduce	VERB
iajs-2681	3	5	the	the	DET
iajs-2681	3	6	concepts	concept	NOUN
iajs-2681	3	7	of	of	ADP
iajs-2681	3	8	fibrewise	fibrewise	NOUN
iajs-2681	3	9	closed	close	VERB
iajs-2681	3	10	fuzzy	fuzzy	ADJ
iajs-2681	3	11	topological	topological	ADJ
iajs-2681	3	12	spaces	space	NOUN
iajs-2681	3	13	,	,	PUNCT
iajs-2681	3	14	fibrewise	fibrewise	ADV
iajs-2681	3	15	open	open	VERB
iajs-2681	3	16	fuzzy	fuzzy	ADJ
iajs-2681	3	17	topological	topological	ADJ
iajs-2681	3	18	spaces	space	NOUN
iajs-2681	3	19	,	,	PUNCT
iajs-2681	3	20	fibrewise	fibrewise	ADV
iajs-2681	3	21	locally	locally	ADV
iajs-2681	3	22	sliceable	sliceable	ADJ
iajs-2681	3	23	fuzzy	fuzzy	ADJ
iajs-2681	3	24	topological	topological	ADJ
iajs-2681	3	25	spaces	space	NOUN
iajs-2681	3	26	and	and	CCONJ
iajs-2681	3	27	fibrewise	fibrewise	ADV
iajs-2681	3	28	locally	locally	ADV
iajs-2681	3	29	sectionable	sectionable	ADJ
iajs-2681	3	30	fuzzy	fuzzy	ADJ
iajs-2681	3	31	topological	topological	ADJ
iajs-2681	3	32	spaces	space	NOUN
iajs-2681	3	33	.	.	PUNCT
iajs-2681	4	1	furthermore	furthermore	ADV
iajs-2681	4	2	,	,	PUNCT
iajs-2681	4	3	we	we	PRON
iajs-2681	4	4	state	state	VERB
iajs-2681	4	5	and	and	CCONJ
iajs-2681	4	6	prove	prove	VERB
iajs-2681	4	7	several	several	ADJ
iajs-2681	4	8	theorems	theorem	NOUN
iajs-2681	4	9	concerning	concern	VERB
iajs-2681	4	10	these	these	DET
iajs-2681	4	11	concepts	concept	NOUN
iajs-2681	4	12	.	.	PUNCT
iajs-2681	5	1	keywords	keyword	NOUN
iajs-2681	5	2	:	:	PUNCT
iajs-2681	5	3	fuzzy	fuzzy	ADJ
iajs-2681	5	4	open	open	ADJ
iajs-2681	5	5	,	,	PUNCT
iajs-2681	5	6	fwfts	fwft	NOUN
iajs-2681	5	7	’s	’s	PART
iajs-2681	5	8	,	,	PUNCT
iajs-2681	5	9	fwcfts	fwcfts	PROPN
iajs-2681	5	10	’s	’s	PART
iajs-2681	5	11	,	,	PUNCT
iajs-2681	5	12	fwofts	fwoft	NOUN
iajs-2681	5	13	’s	’s	PART
iajs-2681	5	14	,	,	PUNCT
iajs-2681	5	15	fw	fw	PROPN
iajs-2681	5	16	-	-	PUNCT
iajs-2681	5	17	lsl	lsl	NOUN
iajs-2681	5	18	-	-	PUNCT
iajs-2681	5	19	fts	fts	X
iajs-2681	5	20	’s	’s	NOUN
iajs-2681	5	21	and	and	CCONJ
iajs-2681	5	22	fw	fw	NOUN
iajs-2681	5	23	-	-	PUNCT
iajs-2681	5	24	lsefts	lseft	NOUN
iajs-2681	5	25	’s	’s	PART
iajs-2681	5	26	.	.	PUNCT
iajs-2681	6	1	ams	am	NOUN
iajs-2681	6	2	subject	subject	ADJ
iajs-2681	6	3	classification	classification	NOUN
iajs-2681	6	4	:	:	PUNCT
iajs-2681	6	5	55r70	55r70	NUM
iajs-2681	6	6	,	,	PUNCT
iajs-2681	6	7	54a40	54a40	NUM
iajs-2681	6	8	,	,	PUNCT
iajs-2681	6	9	54c08	54c08	NUM
iajs-2681	6	10	,	,	PUNCT
iajs-2681	6	11	54c10	54c10	NUM
iajs-2681	6	12	.	.	PUNCT
iajs-2681	7	1	1.introduction	1.introduction	NUM
iajs-2681	7	2	the	the	DET
iajs-2681	7	3	notion	notion	NOUN
iajs-2681	7	4	of	of	ADP
iajs-2681	7	5	fibrewise	fibrewise	NOUN
iajs-2681	7	6	topology	topology	NOUN
iajs-2681	7	7	was	be	AUX
iajs-2681	7	8	introduced	introduce	VERB
iajs-2681	7	9	by	by	ADP
iajs-2681	7	10	james	james	PROPN
iajs-2681	8	1	[	[	X
iajs-2681	8	2	6	6	NUM
iajs-2681	8	3	]	]	PUNCT
iajs-2681	8	4	who	who	PRON
iajs-2681	8	5	studied	study	VERB
iajs-2681	8	6	a	a	DET
iajs-2681	8	7	good	good	ADJ
iajs-2681	8	8	number	number	NOUN
iajs-2681	8	9	of	of	ADP
iajs-2681	8	10	concepts	concept	NOUN
iajs-2681	8	11	and	and	CCONJ
iajs-2681	8	12	results	result	NOUN
iajs-2681	8	13	.	.	PUNCT
iajs-2681	9	1	in	in	ADP
iajs-2681	9	2	recent	recent	ADJ
iajs-2681	9	3	times	time	NOUN
iajs-2681	9	4	,	,	PUNCT
iajs-2681	9	5	many	many	ADJ
iajs-2681	9	6	researchers	researcher	NOUN
iajs-2681	9	7	studied	study	VERB
iajs-2681	9	8	this	this	DET
iajs-2681	9	9	notion	notion	NOUN
iajs-2681	9	10	[	[	X
iajs-2681	9	11	1	1	NUM
iajs-2681	9	12	,	,	PUNCT
iajs-2681	9	13	7	7	NUM
iajs-2681	9	14	,	,	PUNCT
iajs-2681	9	15	16	16	NUM
iajs-2681	9	16	,	,	PUNCT
iajs-2681	9	17	17	17	NUM
iajs-2681	9	18	]	]	PUNCT
iajs-2681	9	19	.	.	PUNCT
iajs-2681	10	1	contributions	contribution	NOUN
iajs-2681	10	2	of	of	ADP
iajs-2681	10	3	yousif	yousif	PROPN
iajs-2681	10	4	and	and	CCONJ
iajs-2681	10	5	hussain	hussain	PROPN
iajs-2681	10	6	[	[	X
iajs-2681	10	7	1012	1012	NUM
iajs-2681	10	8	]	]	PUNCT
iajs-2681	10	9	,	,	PUNCT
iajs-2681	10	10	yousif	yousif	PROPN
iajs-2681	10	11	and	and	CCONJ
iajs-2681	10	12	hussain	hussain	PROPN
iajs-2681	11	1	[	[	X
iajs-2681	11	2	1315	1315	NUM
iajs-2681	11	3	]	]	PUNCT
iajs-2681	11	4	and	and	CCONJ
iajs-2681	11	5	mohammed	mohammed	PROPN
iajs-2681	11	6	and	and	CCONJ
iajs-2681	11	7	yousif	yousif	PROPN
iajs-2681	12	1	[	[	X
iajs-2681	12	2	8	8	X
iajs-2681	12	3	]	]	PUNCT
iajs-2681	12	4	in	in	ADP
iajs-2681	12	5	the	the	DET
iajs-2681	12	6	field	field	NOUN
iajs-2681	12	7	of	of	ADP
iajs-2681	12	8	fibrewise	fibrewise	NOUN
iajs-2681	12	9	topology	topology	NOUN
iajs-2681	12	10	and	and	CCONJ
iajs-2681	12	11	related	related	ADJ
iajs-2681	12	12	concepts	concept	NOUN
iajs-2681	12	13	are	be	AUX
iajs-2681	12	14	important	important	ADJ
iajs-2681	12	15	to	to	PART
iajs-2681	12	16	be	be	AUX
iajs-2681	12	17	mentioned	mention	VERB
iajs-2681	12	18	.	.	PUNCT
iajs-2681	13	1	the	the	DET
iajs-2681	13	2	fibrewise	fibrewise	NOUN
iajs-2681	13	3	(	(	PUNCT
iajs-2681	13	4	written	write	VERB
iajs-2681	13	5	as	as	ADP
iajs-2681	13	6	fw	fw	NOUN
iajs-2681	13	7	)	)	PUNCT
iajs-2681	13	8	sets	set	NOUN
iajs-2681	13	9	over	over	ADP
iajs-2681	13	10	an	an	DET
iajs-2681	13	11	explicit	explicit	ADJ
iajs-2681	13	12	set	set	NOUN
iajs-2681	13	13	,	,	PUNCT
iajs-2681	13	14	called	call	VERB
iajs-2681	13	15	the	the	DET
iajs-2681	13	16	base	base	NOUN
iajs-2681	13	17	set	set	NOUN
iajs-2681	13	18	,	,	PUNCT
iajs-2681	13	19	say	say	VERB
iajs-2681	13	20	b.	b.	PROPN
iajs-2681	14	1	a	a	DET
iajs-2681	14	2	fw	fw	PROPN
iajs-2681	14	3	set	set	NOUN
iajs-2681	14	4	over	over	ADP
iajs-2681	14	5	b	b	NOUN
iajs-2681	14	6	push	push	NOUN
iajs-2681	14	7	back	back	ADV
iajs-2681	14	8	of	of	ADP
iajs-2681	14	9	a	a	DET
iajs-2681	14	10	set	set	NOUN
iajs-2681	14	11	m	m	VERB
iajs-2681	14	12	jointly	jointly	ADV
iajs-2681	14	13	with	with	ADP
iajs-2681	14	14	a	a	DET
iajs-2681	14	15	mapping	mapping	NOUN
iajs-2681	14	16	þ	þ	NOUN
iajs-2681	14	17	:	:	PUNCT
iajs-2681	14	18	m	m	VERB
iajs-2681	14	19			NOUN
iajs-2681	14	20	b	b	X
iajs-2681	14	21	,	,	PUNCT
iajs-2681	14	22	called	call	VERB
iajs-2681	14	23	the	the	DET
iajs-2681	14	24	projection	projection	NOUN
iajs-2681	14	25	(	(	PUNCT
iajs-2681	14	26	written	write	VERB
iajs-2681	14	27	as	as	ADP
iajs-2681	14	28	proj	proj	PROPN
iajs-2681	14	29	.	.	PUNCT
iajs-2681	14	30	)	)	PUNCT
iajs-2681	14	31	.	.	PUNCT
iajs-2681	15	1	the	the	DET
iajs-2681	15	2	subset	subset	NOUN
iajs-2681	15	3	mb	mb	ADP
iajs-2681	15	4	=	=	SYM
iajs-2681	15	5	þ–1(b	þ–1(b	NOUN
iajs-2681	15	6	)	)	PUNCT
iajs-2681	15	7	of	of	ADP
iajs-2681	15	8	m	m	PROPN
iajs-2681	15	9	is	be	AUX
iajs-2681	15	10	the	the	DET
iajs-2681	15	11	fibre	fibre	NOUN
iajs-2681	15	12	over	over	ADP
iajs-2681	15	13	b	b	NOUN
iajs-2681	15	14	for	for	ADP
iajs-2681	15	15	every	every	DET
iajs-2681	15	16	point	point	NOUN
iajs-2681	15	17	b	b	PROPN
iajs-2681	15	18			PROPN
iajs-2681	15	19	b.	b.	PROPN
iajs-2681	15	20	possibly	possibly	ADV
iajs-2681	15	21	,	,	PUNCT
iajs-2681	15	22	fibre	fibre	NOUN
iajs-2681	15	23	will	will	AUX
iajs-2681	15	24	be	be	AUX
iajs-2681	15	25	empty	empty	ADJ
iajs-2681	15	26	since	since	SCONJ
iajs-2681	15	27	we	we	PRON
iajs-2681	15	28	do	do	AUX
iajs-2681	15	29	not	not	PART
iajs-2681	15	30	require	require	VERB
iajs-2681	15	31	þ	þ	NOUN
iajs-2681	15	32	is	be	AUX
iajs-2681	15	33	a	a	DET
iajs-2681	15	34	surjectve	surjectve	PROPN
iajs-2681	15	35	,	,	PUNCT
iajs-2681	15	36	also	also	ADV
iajs-2681	15	37	,	,	PUNCT
iajs-2681	15	38	the	the	DET
iajs-2681	15	39	subset	subset	NOUN
iajs-2681	15	40	mb	mb	NOUN
iajs-2681	15	41	*	*	PROPN
iajs-2681	15	42	=	=	PUNCT
iajs-2681	15	43	þ–1(b	þ–1(b	NOUN
iajs-2681	15	44	*	*	NOUN
iajs-2681	15	45	)	)	PUNCT
iajs-2681	15	46	as	as	ADP
iajs-2681	15	47	a	a	DET
iajs-2681	15	48	fw	fw	NOUN
iajs-2681	15	49	set	set	NOUN
iajs-2681	15	50	over	over	ADP
iajs-2681	15	51	b	b	PROPN
iajs-2681	15	52	*	*	VERB
iajs-2681	15	53	for	for	ADP
iajs-2681	15	54	every	every	DET
iajs-2681	15	55	subset	subset	NOUN
iajs-2681	15	56	b	b	NOUN
iajs-2681	15	57	*	*	PROPN
iajs-2681	15	58			PROPN
iajs-2681	15	59	b	b	PROPN
iajs-2681	15	60	with	with	ADP
iajs-2681	15	61	the	the	DET
iajs-2681	15	62	proj	proj	NOUN
iajs-2681	15	63	.	.	PUNCT
iajs-2681	16	1	fixed	fix	VERB
iajs-2681	16	2	by	by	ADP
iajs-2681	16	3	þ	þ	PROPN
iajs-2681	16	4	.	.	PUNCT
iajs-2681	17	1	the	the	DET
iajs-2681	17	2	notation	notation	NOUN
iajs-2681	17	3	m	m	VERB
iajs-2681	17	4	|	|	ADV
iajs-2681	17	5	b	b	X
iajs-2681	17	6	*	*	VERB
iajs-2681	17	7	is	be	AUX
iajs-2681	17	8	sometime	sometime	ADV
iajs-2681	17	9	suitable	suitable	ADJ
iajs-2681	17	10	instead	instead	ADV
iajs-2681	17	11	of	of	ADP
iajs-2681	17	12	mb	mb	ADP
iajs-2681	17	13	*	*	PROPN
iajs-2681	17	14	=	=	SYM
iajs-2681	17	15	þ–1(b	þ–1(b	NOUN
iajs-2681	17	16	)	)	PUNCT
iajs-2681	17	17	.	.	PUNCT
iajs-2681	18	1	the	the	DET
iajs-2681	18	2	cartesian	cartesian	ADJ
iajs-2681	18	3	product	product	NOUN
iajs-2681	18	4	b	b	PROPN
iajs-2681	18	5			PROPN
iajs-2681	18	6	t	t	PROPN
iajs-2681	18	7	,	,	PUNCT
iajs-2681	18	8	for	for	ADP
iajs-2681	18	9	every	every	DET
iajs-2681	18	10	set	set	NOUN
iajs-2681	18	11	t	t	PROPN
iajs-2681	18	12	,	,	PUNCT
iajs-2681	18	13	like	like	ADP
iajs-2681	18	14	a	a	DET
iajs-2681	18	15	fw	fw	PROPN
iajs-2681	18	16	set	set	NOUN
iajs-2681	18	17	b	b	PROPN
iajs-2681	18	18	by	by	ADP
iajs-2681	18	19	the	the	DET
iajs-2681	18	20	first	first	ADJ
iajs-2681	18	21	proj	proj	PROPN
iajs-2681	18	22	..	..	PUNCT
iajs-2681	19	1	ibn	ibn	PROPN
iajs-2681	19	2	al	al	PROPN
iajs-2681	19	3	haitham	haitham	PROPN
iajs-2681	19	4	journal	journal	PROPN
iajs-2681	19	5	for	for	ADP
iajs-2681	19	6	pure	pure	ADJ
iajs-2681	19	7	and	and	CCONJ
iajs-2681	19	8	applied	apply	VERB
iajs-2681	19	9	science	science	NOUN
iajs-2681	19	10	journal	journal	PROPN
iajs-2681	19	11	homepage	homepage	NOUN
iajs-2681	19	12	:	:	PUNCT
iajs-2681	19	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2681	19	14	doi	doi	NOUN
iajs-2681	19	15	:	:	PUNCT
iajs-2681	19	16	10.30526/34.3.2681	10.30526/34.3.2681	PROPN
iajs-2681	19	17	article	article	NOUN
iajs-2681	19	18	history	history	NOUN
iajs-2681	19	19	:	:	PUNCT
iajs-2681	19	20	received	receive	VERB
iajs-2681	19	21	28	28	NUM
iajs-2681	19	22	september	september	PROPN
iajs-2681	19	23	2020	2020	NUM
iajs-2681	19	24	,	,	PUNCT
iajs-2681	19	25	accepted	accept	VERB
iajs-2681	19	26	8	8	NUM
iajs-2681	19	27	november	november	NOUN
iajs-2681	19	28	2020	2020	NUM
iajs-2681	19	29	,	,	PUNCT
iajs-2681	19	30	published	publish	VERB
iajs-2681	19	31	in	in	ADP
iajs-2681	19	32	july	july	PROPN
iajs-2681	19	33	2021	2021	NUM
iajs-2681	19	34	.	.	PUNCT
iajs-2681	20	1	mailto:yoyayousif@yahoo.com	mailto:yoyayousif@yahoo.com	PROPN
iajs-2681	20	2	mailto:yousif.y.y@ihcoedu.uobaghdad.edu.iq	mailto:yousif.y.y@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-2681	20	3	ibn	ibn	PROPN
iajs-2681	20	4	al	al	PROPN
iajs-2681	20	5	-	-	PUNCT
iajs-2681	20	6	haitham	haitham	PROPN
iajs-2681	20	7	jour	jour	X
iajs-2681	20	8	.	.	PROPN
iajs-2681	21	1	for	for	ADP
iajs-2681	21	2	pure	pure	ADJ
iajs-2681	21	3	&	&	CCONJ
iajs-2681	21	4	appl	appl	PROPN
iajs-2681	21	5	.	.	PUNCT
iajs-2681	22	1	sci	sci	PROPN
iajs-2681	22	2	.	.	PROPN
iajs-2681	23	1	34(3)2021	34(3)2021	NUM
iajs-2681	23	2	88	88	NUM
iajs-2681	23	3	definition	definition	NOUN
iajs-2681	23	4	1.1	1.1	NUM
iajs-2681	23	5	.	.	PUNCT
iajs-2681	24	1	[	[	X
iajs-2681	24	2	6	6	NUM
iajs-2681	24	3	]	]	PUNCT
iajs-2681	24	4	a	a	DET
iajs-2681	24	5	mapping	mapping	NOUN
iajs-2681	24	6			X
iajs-2681	24	7	:	:	PUNCT
iajs-2681	24	8	m	m	AUX
iajs-2681	24	9			NOUN
iajs-2681	24	10	n	n	CCONJ
iajs-2681	24	11	,	,	PUNCT
iajs-2681	24	12	where	where	SCONJ
iajs-2681	24	13	m	m	VERB
iajs-2681	24	14	and	and	CCONJ
iajs-2681	24	15	n	n	PRON
iajs-2681	24	16	are	be	AUX
iajs-2681	24	17	fw	fw	ADJ
iajs-2681	24	18	sets	set	NOUN
iajs-2681	24	19	over	over	ADP
iajs-2681	24	20	b	b	NOUN
iajs-2681	24	21	,	,	PUNCT
iajs-2681	24	22	with	with	ADP
iajs-2681	24	23	proj	proj	PROPN
iajs-2681	24	24	.	.	PUNCT
iajs-2681	24	25	’s	’s	PROPN
iajs-2681	25	1	þm	þm	PROPN
iajs-2681	25	2	:	:	PUNCT
iajs-2681	25	3	m	m	VERB
iajs-2681	25	4			NOUN
iajs-2681	26	1	b	b	NOUN
iajs-2681	26	2	and	and	CCONJ
iajs-2681	26	3	þn	þn	INTJ
iajs-2681	26	4	:	:	PUNCT
iajs-2681	26	5	n	n	CCONJ
iajs-2681	26	6			NOUN
iajs-2681	26	7	b	b	X
iajs-2681	26	8	,	,	PUNCT
iajs-2681	26	9	is	be	AUX
iajs-2681	26	10	said	say	VERB
iajs-2681	26	11	to	to	PART
iajs-2681	26	12	be	be	AUX
iajs-2681	26	13	fw	fw	ADJ
iajs-2681	26	14	mapping	mapping	NOUN
iajs-2681	26	15	(	(	PUNCT
iajs-2681	26	16	written	write	VERB
iajs-2681	26	17	as	as	ADP
iajs-2681	26	18	fw	fw	PROPN
iajs-2681	26	19	-	-	PUNCT
iajs-2681	26	20	m	m	NOUN
iajs-2681	26	21	)	)	PUNCT
iajs-2681	26	22	if	if	SCONJ
iajs-2681	26	23	þn	þn	ADP
iajs-2681	26	24			X
iajs-2681	26	25			X
iajs-2681	26	26	=	=	SYM
iajs-2681	26	27	þm	þm	PROPN
iajs-2681	26	28	,	,	PUNCT
iajs-2681	26	29	or	or	CCONJ
iajs-2681	26	30	(mb	(mb	PROPN
iajs-2681	26	31	)	)	PUNCT
iajs-2681	26	32			PROPN
iajs-2681	26	33	nb	nb	PROPN
iajs-2681	26	34	,	,	PUNCT
iajs-2681	26	35	for	for	ADP
iajs-2681	26	36	every	every	DET
iajs-2681	26	37	point	point	NOUN
iajs-2681	26	38	b	b	PROPN
iajs-2681	26	39			PROPN
iajs-2681	26	40	b.	b.	PROPN
iajs-2681	26	41	observe	observe	VERB
iajs-2681	26	42	that	that	SCONJ
iajs-2681	26	43	a	a	DET
iajs-2681	26	44	fw	fw	PROPN
iajs-2681	26	45	-	-	PUNCT
iajs-2681	26	46	m	m	NOUN
iajs-2681	26	47			NOUN
iajs-2681	26	48	:	:	PUNCT
iajs-2681	26	49	m	m	VERB
iajs-2681	26	50			NOUN
iajs-2681	27	1	n	n	CCONJ
iajs-2681	27	2	over	over	ADP
iajs-2681	27	3	b	b	NOUN
iajs-2681	27	4	limited	limit	VERB
iajs-2681	27	5	by	by	ADP
iajs-2681	27	6	restriction	restriction	NOUN
iajs-2681	27	7	,	,	PUNCT
iajs-2681	27	8	a	a	DET
iajs-2681	27	9	fw	fw	PROPN
iajs-2681	27	10	-	-	PUNCT
iajs-2681	27	11	m	m	NOUN
iajs-2681	27	12			NOUN
iajs-2681	27	13	:	:	PUNCT
iajs-2681	27	14	mb	mb	PART
iajs-2681	27	15	*	*	NOUN
iajs-2681	27	16			NOUN
iajs-2681	27	17	nb	nb	INTJ
iajs-2681	27	18	*	*	PROPN
iajs-2681	27	19	over	over	ADP
iajs-2681	27	20	b	b	PROPN
iajs-2681	27	21	*	*	VERB
iajs-2681	27	22	for	for	ADP
iajs-2681	27	23	every	every	DET
iajs-2681	27	24	subset	subset	NOUN
iajs-2681	27	25	b	b	PROPN
iajs-2681	27	26	*	*	PROPN
iajs-2681	27	27			PROPN
iajs-2681	27	28	b.	b.	PROPN
iajs-2681	27	29	definition	definition	NOUN
iajs-2681	27	30	1.2	1.2	NUM
iajs-2681	27	31	.	.	PUNCT
iajs-2681	28	1	[	[	X
iajs-2681	28	2	6	6	NUM
iajs-2681	28	3	]	]	PUNCT
iajs-2681	28	4	the	the	DET
iajs-2681	28	5	fibrewise	fibrewise	NOUN
iajs-2681	28	6	topology	topology	NOUN
iajs-2681	28	7	(	(	PUNCT
iajs-2681	28	8	written	write	VERB
iajs-2681	28	9	as	as	ADP
iajs-2681	28	10	fwt	fwt	PROPN
iajs-2681	28	11	)	)	PUNCT
iajs-2681	28	12	on	on	ADP
iajs-2681	28	13	a	a	DET
iajs-2681	28	14	fw	fw	PROPN
iajs-2681	28	15	set	set	NOUN
iajs-2681	28	16	m	m	NOUN
iajs-2681	28	17	over	over	ADP
iajs-2681	28	18	a	a	DET
iajs-2681	28	19	topological	topological	ADJ
iajs-2681	28	20	space	space	NOUN
iajs-2681	28	21	(	(	PUNCT
iajs-2681	28	22	b	b	NOUN
iajs-2681	28	23	,	,	PUNCT
iajs-2681	28	24			NOUN
iajs-2681	28	25	)	)	PUNCT
iajs-2681	28	26	signifies	signify	VERB
iajs-2681	28	27	any	any	DET
iajs-2681	28	28	topology	topology	NOUN
iajs-2681	28	29	on	on	ADP
iajs-2681	28	30	m	m	PROPN
iajs-2681	28	31	for	for	ADP
iajs-2681	28	32	which	which	PRON
iajs-2681	28	33	the	the	DET
iajs-2681	28	34	proj	proj	NOUN
iajs-2681	28	35	.	.	PUNCT
iajs-2681	29	1	þ	þ	PROPN
iajs-2681	29	2	is	be	AUX
iajs-2681	29	3	continuous	continuous	ADJ
iajs-2681	29	4	(	(	PUNCT
iajs-2681	29	5	written	write	VERB
iajs-2681	29	6	as	as	ADP
iajs-2681	29	7	fwts	fwts	NOUN
iajs-2681	29	8	)	)	PUNCT
iajs-2681	29	9	.	.	PUNCT
iajs-2681	30	1	definition	definition	NOUN
iajs-2681	30	2	1.3	1.3	NUM
iajs-2681	30	3	.	.	PUNCT
iajs-2681	31	1	[	[	X
iajs-2681	31	2	6	6	NUM
iajs-2681	31	3	]	]	PUNCT
iajs-2681	31	4	let	let	AUX
iajs-2681	31	5	m	m	PRON
iajs-2681	31	6	and	and	CCONJ
iajs-2681	31	7	n	n	ADV
iajs-2681	31	8	be	be	AUX
iajs-2681	31	9	fwts	fwts	NOUN
iajs-2681	31	10	's	's	PART
iajs-2681	31	11	over	over	ADP
iajs-2681	31	12	b	b	PROPN
iajs-2681	31	13	,	,	PUNCT
iajs-2681	31	14	the	the	DET
iajs-2681	31	15	fw	fw	PROPN
iajs-2681	31	16	-	-	PUNCT
iajs-2681	31	17	m	m	NOUN
iajs-2681	31	18			NOUN
iajs-2681	31	19	:	:	PUNCT
iajs-2681	32	1	m	m	VERB
iajs-2681	32	2			NOUN
iajs-2681	32	3	n	n	ADV
iajs-2681	32	4	is	be	AUX
iajs-2681	32	5	said	say	VERB
iajs-2681	32	6	to	to	PART
iajs-2681	32	7	be	be	AUX
iajs-2681	32	8	:	:	PUNCT
iajs-2681	32	9	(	(	PUNCT
iajs-2681	32	10	a	a	X
iajs-2681	32	11	)	)	PUNCT
iajs-2681	32	12	continuous	continuous	ADJ
iajs-2681	32	13	if	if	SCONJ
iajs-2681	32	14	b	b	PROPN
iajs-2681	32	15			PROPN
iajs-2681	32	16	b	b	NOUN
iajs-2681	32	17	and	and	CCONJ
iajs-2681	32	18	for	for	ADP
iajs-2681	32	19	every	every	DET
iajs-2681	32	20	point	point	NOUN
iajs-2681	32	21	m	m	VERB
iajs-2681	32	22			NOUN
iajs-2681	32	23	mb	mb	ADP
iajs-2681	32	24	,	,	PUNCT
iajs-2681	32	25	the	the	DET
iajs-2681	32	26	pre	pre	ADJ
iajs-2681	32	27	image	image	NOUN
iajs-2681	32	28	of	of	ADP
iajs-2681	32	29	every	every	DET
iajs-2681	32	30	open	open	ADJ
iajs-2681	32	31	set	set	NOUN
iajs-2681	32	32	of	of	ADP
iajs-2681	32	33	(m	(m	PROPN
iajs-2681	32	34	)	)	PUNCT
iajs-2681	32	35	is	be	AUX
iajs-2681	32	36	an	an	DET
iajs-2681	32	37	open	open	ADJ
iajs-2681	32	38	set	set	NOUN
iajs-2681	32	39	of	of	ADP
iajs-2681	32	40	m.	m.	NOUN
iajs-2681	32	41	(	(	PUNCT
iajs-2681	32	42	b	b	X
iajs-2681	32	43	)	)	PUNCT
iajs-2681	32	44	open	open	ADJ
iajs-2681	32	45	if	if	SCONJ
iajs-2681	32	46	b	b	PROPN
iajs-2681	32	47			PROPN
iajs-2681	32	48	b	b	NOUN
iajs-2681	32	49	and	and	CCONJ
iajs-2681	32	50	for	for	ADP
iajs-2681	32	51	every	every	DET
iajs-2681	32	52	point	point	NOUN
iajs-2681	32	53	m	m	VERB
iajs-2681	32	54			NOUN
iajs-2681	32	55	mb	mb	ADP
iajs-2681	32	56	,	,	PUNCT
iajs-2681	32	57	the	the	DET
iajs-2681	32	58	image	image	NOUN
iajs-2681	32	59	of	of	ADP
iajs-2681	32	60	every	every	DET
iajs-2681	32	61	open	open	ADJ
iajs-2681	32	62	set	set	NOUN
iajs-2681	32	63	of	of	ADP
iajs-2681	32	64	m	m	PROPN
iajs-2681	32	65	is	be	AUX
iajs-2681	32	66	an	an	DET
iajs-2681	32	67	open	open	ADJ
iajs-2681	32	68	set	set	NOUN
iajs-2681	32	69	of	of	ADP
iajs-2681	32	70	(m	(m	PROPN
iajs-2681	32	71	)	)	PUNCT
iajs-2681	32	72	.	.	PUNCT
iajs-2681	33	1	definition	definition	NOUN
iajs-2681	33	2	1.4	1.4	NUM
iajs-2681	33	3	.	.	PUNCT
iajs-2681	34	1	[	[	X
iajs-2681	34	2	6	6	NUM
iajs-2681	34	3	]	]	PUNCT
iajs-2681	34	4	the	the	DET
iajs-2681	34	5	fwts	fwts	NOUN
iajs-2681	34	6	(	(	PUNCT
iajs-2681	34	7	m	m	PROPN
iajs-2681	34	8	,	,	PUNCT
iajs-2681	34	9			PROPN
iajs-2681	34	10	)	)	PUNCT
iajs-2681	34	11	over	over	ADP
iajs-2681	34	12	(	(	PUNCT
iajs-2681	34	13	b	b	NOUN
iajs-2681	34	14	,	,	PUNCT
iajs-2681	34	15			NOUN
iajs-2681	34	16	)	)	PUNCT
iajs-2681	34	17	is	be	AUX
iajs-2681	34	18	said	say	VERB
iajs-2681	34	19	to	to	PART
iajs-2681	34	20	be	be	AUX
iajs-2681	34	21	:	:	PUNCT
iajs-2681	34	22	(	(	PUNCT
iajs-2681	34	23	a	a	X
iajs-2681	34	24	)	)	PUNCT
iajs-2681	34	25	fw	fw	NOUN
iajs-2681	34	26	closed	closed	ADJ
iajs-2681	34	27	(	(	PUNCT
iajs-2681	34	28	written	write	VERB
iajs-2681	34	29	as	as	ADP
iajs-2681	34	30	fwc	fwc	NOUN
iajs-2681	34	31	)	)	PUNCT
iajs-2681	34	32	if	if	SCONJ
iajs-2681	34	33	the	the	DET
iajs-2681	34	34	proj	proj	NOUN
iajs-2681	34	35	.	.	PUNCT
iajs-2681	35	1	þ	þ	PROPN
iajs-2681	35	2	is	be	AUX
iajs-2681	35	3	a	a	DET
iajs-2681	35	4	closed	closed	ADJ
iajs-2681	35	5	mapping	mapping	NOUN
iajs-2681	35	6	.	.	PUNCT
iajs-2681	36	1	(	(	PUNCT
iajs-2681	36	2	b	b	X
iajs-2681	36	3	)	)	PUNCT
iajs-2681	36	4	fw	fw	NOUN
iajs-2681	36	5	open	open	ADJ
iajs-2681	36	6	(	(	PUNCT
iajs-2681	36	7	written	write	VERB
iajs-2681	36	8	as	as	ADP
iajs-2681	36	9	fwo	fwo	PROPN
iajs-2681	36	10	)	)	PUNCT
iajs-2681	36	11	if	if	SCONJ
iajs-2681	36	12	the	the	DET
iajs-2681	36	13	proj	proj	NOUN
iajs-2681	36	14	.	.	PUNCT
iajs-2681	37	1	þ	þ	PROPN
iajs-2681	37	2	is	be	AUX
iajs-2681	37	3	a	a	DET
iajs-2681	37	4	open	open	ADJ
iajs-2681	37	5	mapping	mapping	NOUN
iajs-2681	37	6	.	.	PUNCT
iajs-2681	38	1	the	the	DET
iajs-2681	38	2	concept	concept	NOUN
iajs-2681	38	3	of	of	ADP
iajs-2681	38	4	fuzzy	fuzzy	ADJ
iajs-2681	38	5	sets	set	NOUN
iajs-2681	38	6	was	be	AUX
iajs-2681	38	7	introduced	introduce	VERB
iajs-2681	38	8	by	by	ADP
iajs-2681	38	9	zadeh	zadeh	PROPN
iajs-2681	38	10	[	[	X
iajs-2681	38	11	18	18	NUM
iajs-2681	38	12	]	]	PUNCT
iajs-2681	38	13	.	.	PUNCT
iajs-2681	39	1	the	the	DET
iajs-2681	39	2	idea	idea	NOUN
iajs-2681	39	3	of	of	ADP
iajs-2681	39	4	fuzzy	fuzzy	ADJ
iajs-2681	39	5	topological	topological	ADJ
iajs-2681	39	6	spaces	space	NOUN
iajs-2681	39	7	was	be	AUX
iajs-2681	39	8	introduced	introduce	VERB
iajs-2681	39	9	by	by	ADP
iajs-2681	39	10	chang	chang	PROPN
iajs-2681	40	1	[	[	X
iajs-2681	40	2	2	2	NUM
iajs-2681	40	3	]	]	PUNCT
iajs-2681	40	4	.	.	PUNCT
iajs-2681	41	1	different	different	ADJ
iajs-2681	41	2	aspects	aspect	NOUN
iajs-2681	41	3	of	of	ADP
iajs-2681	41	4	such	such	ADJ
iajs-2681	41	5	spaces	space	NOUN
iajs-2681	41	6	have	have	AUX
iajs-2681	41	7	been	be	AUX
iajs-2681	41	8	developed	develop	VERB
iajs-2681	41	9	by	by	ADP
iajs-2681	41	10	several	several	ADJ
iajs-2681	41	11	investigators	investigator	NOUN
iajs-2681	41	12	.	.	PUNCT
iajs-2681	42	1	in	in	ADP
iajs-2681	42	2	this	this	DET
iajs-2681	42	3	work	work	NOUN
iajs-2681	42	4	,	,	PUNCT
iajs-2681	42	5	by	by	ADP
iajs-2681	42	6	(	(	PUNCT
iajs-2681	42	7	m	m	PROPN
iajs-2681	42	8	,	,	PUNCT
iajs-2681	42	9			PROPN
iajs-2681	42	10	)	)	PUNCT
iajs-2681	42	11	we	we	PRON
iajs-2681	42	12	will	will	AUX
iajs-2681	42	13	denote	denote	VERB
iajs-2681	42	14	a	a	DET
iajs-2681	42	15	fuzzy	fuzzy	ADJ
iajs-2681	42	16	topological	topological	ADJ
iajs-2681	42	17	space	space	NOUN
iajs-2681	42	18	(	(	PUNCT
iajs-2681	42	19	written	write	VERB
iajs-2681	42	20	as	as	ADP
iajs-2681	42	21	fts	fts	PROPN
iajs-2681	42	22	)	)	PUNCT
iajs-2681	42	23	definition	definition	NOUN
iajs-2681	42	24	1.5	1.5	NUM
iajs-2681	42	25	.	.	PUNCT
iajs-2681	43	1	[	[	X
iajs-2681	43	2	2	2	X
iajs-2681	43	3	]	]	PUNCT
iajs-2681	43	4	a	a	DET
iajs-2681	43	5	mapping	mapping	NOUN
iajs-2681	43	6			X
iajs-2681	43	7	:	:	PUNCT
iajs-2681	43	8	(	(	PUNCT
iajs-2681	43	9	m	m	NOUN
iajs-2681	43	10	,	,	PUNCT
iajs-2681	43	11			NOUN
iajs-2681	43	12	)	)	PUNCT
iajs-2681	43	13			PUNCT
iajs-2681	43	14	(	(	PUNCT
iajs-2681	43	15	n	n	X
iajs-2681	43	16	,	,	PUNCT
iajs-2681	43	17			NUM
iajs-2681	43	18	)	)	PUNCT
iajs-2681	43	19	is	be	AUX
iajs-2681	43	20	said	say	VERB
iajs-2681	43	21	to	to	PART
iajs-2681	43	22	be	be	AUX
iajs-2681	43	23	fuzzy	fuzzy	ADJ
iajs-2681	43	24	continuous	continuous	ADJ
iajs-2681	43	25	if	if	SCONJ
iajs-2681	43	26	the	the	DET
iajs-2681	43	27	pre	pre	ADJ
iajs-2681	43	28	image	image	NOUN
iajs-2681	43	29	of	of	ADP
iajs-2681	43	30	every	every	DET
iajs-2681	43	31	fuzzy	fuzzy	ADJ
iajs-2681	43	32	open	open	ADJ
iajs-2681	43	33	set	set	NOUN
iajs-2681	43	34	of	of	ADP
iajs-2681	43	35	n	n	PRON
iajs-2681	43	36	is	be	AUX
iajs-2681	43	37	a	a	DET
iajs-2681	43	38	fuzzy	fuzzy	ADJ
iajs-2681	43	39	open	open	NOUN
iajs-2681	43	40	set	set	VERB
iajs-2681	43	41	in	in	ADP
iajs-2681	43	42	m.	m.	NOUN
iajs-2681	43	43	this	this	DET
iajs-2681	43	44	paper	paper	NOUN
iajs-2681	43	45	is	be	AUX
iajs-2681	43	46	mixed	mixed	ADJ
iajs-2681	43	47	and	and	CCONJ
iajs-2681	43	48	devoted	devote	VERB
iajs-2681	43	49	to	to	ADP
iajs-2681	43	50	the	the	DET
iajs-2681	43	51	development	development	NOUN
iajs-2681	43	52	of	of	ADP
iajs-2681	43	53	the	the	DET
iajs-2681	43	54	theory	theory	NOUN
iajs-2681	43	55	of	of	ADP
iajs-2681	43	56	fibrewise	fibrewise	NOUN
iajs-2681	43	57	topological	topological	ADJ
iajs-2681	43	58	spaces	space	NOUN
iajs-2681	43	59	and	and	CCONJ
iajs-2681	43	60	fuzzy	fuzzy	ADJ
iajs-2681	43	61	topological	topological	ADJ
iajs-2681	43	62	spaces	space	NOUN
iajs-2681	43	63	.	.	PUNCT
iajs-2681	44	1	for	for	ADP
iajs-2681	44	2	other	other	ADJ
iajs-2681	44	3	notions	notion	NOUN
iajs-2681	44	4	or	or	CCONJ
iajs-2681	44	5	notations	notation	NOUN
iajs-2681	44	6	not	not	PART
iajs-2681	44	7	defined	define	VERB
iajs-2681	44	8	here	here	ADV
iajs-2681	44	9	,	,	PUNCT
iajs-2681	44	10	we	we	PRON
iajs-2681	44	11	follow	follow	VERB
iajs-2681	44	12	closely	closely	ADV
iajs-2681	44	13	in	in	ADP
iajs-2681	44	14	[	[	X
iajs-2681	44	15	2	2	NUM
iajs-2681	44	16	,	,	PUNCT
iajs-2681	44	17	3	3	NUM
iajs-2681	44	18	,	,	PUNCT
iajs-2681	44	19	4	4	NUM
iajs-2681	44	20	,	,	PUNCT
iajs-2681	44	21	5	5	NUM
iajs-2681	44	22	,	,	PUNCT
iajs-2681	44	23	6	6	NUM
iajs-2681	44	24	,	,	PUNCT
iajs-2681	44	25	9	9	NUM
iajs-2681	44	26	,	,	PUNCT
iajs-2681	44	27	18	18	NUM
iajs-2681	44	28	]	]	PUNCT
iajs-2681	44	29	.	.	PUNCT
iajs-2681	45	1	2.fibrewise	2.fibrewise	NUM
iajs-2681	45	2	fuzzy	fuzzy	ADJ
iajs-2681	45	3	topological	topological	ADJ
iajs-2681	45	4	spaces	space	NOUN
iajs-2681	45	5	we	we	PRON
iajs-2681	45	6	will	will	AUX
iajs-2681	45	7	introduce	introduce	VERB
iajs-2681	45	8	the	the	DET
iajs-2681	45	9	ideas	idea	NOUN
iajs-2681	45	10	of	of	ADP
iajs-2681	45	11	fibrewise	fibrewise	NOUN
iajs-2681	45	12	fuzzy	fuzzy	ADJ
iajs-2681	45	13	topological	topological	ADJ
iajs-2681	45	14	spaces	space	NOUN
iajs-2681	45	15	,	,	PUNCT
iajs-2681	45	16	several	several	ADJ
iajs-2681	45	17	properties	property	NOUN
iajs-2681	45	18	on	on	ADP
iajs-2681	45	19	the	the	DET
iajs-2681	45	20	obtained	obtain	VERB
iajs-2681	45	21	fibrewise	fibrewise	NOUN
iajs-2681	45	22	concepts	concept	NOUN
iajs-2681	45	23	are	be	AUX
iajs-2681	45	24	studied	study	VERB
iajs-2681	45	25	.	.	PUNCT
iajs-2681	46	1	definition	definition	NOUN
iajs-2681	46	2	2.1	2.1	NUM
iajs-2681	46	3	.	.	PUNCT
iajs-2681	47	1	the	the	DET
iajs-2681	47	2	fibrewise	fibrewise	ADJ
iajs-2681	47	3	fuzzy	fuzzy	ADJ
iajs-2681	47	4	topology	topology	NOUN
iajs-2681	47	5	(	(	PUNCT
iajs-2681	47	6	written	write	VERB
iajs-2681	47	7	as	as	ADP
iajs-2681	47	8	fwfts	fwft	NOUN
iajs-2681	47	9	)	)	PUNCT
iajs-2681	47	10	on	on	ADP
iajs-2681	47	11	a	a	DET
iajs-2681	47	12	fw	fw	PROPN
iajs-2681	47	13	set	set	NOUN
iajs-2681	47	14	m	m	NOUN
iajs-2681	47	15	over	over	ADP
iajs-2681	47	16	fts	fts	PROPN
iajs-2681	47	17	(	(	PUNCT
iajs-2681	47	18	b	b	NOUN
iajs-2681	47	19	,	,	PUNCT
iajs-2681	47	20			NOUN
iajs-2681	47	21	)	)	PUNCT
iajs-2681	47	22	signifies	signify	VERB
iajs-2681	47	23	any	any	DET
iajs-2681	47	24	fuzzy	fuzzy	ADJ
iajs-2681	47	25	topology	topology	NOUN
iajs-2681	47	26	on	on	ADP
iajs-2681	47	27	m	m	PROPN
iajs-2681	47	28	for	for	ADP
iajs-2681	47	29	which	which	PRON
iajs-2681	47	30	the	the	DET
iajs-2681	47	31	proj	proj	NOUN
iajs-2681	47	32	.	.	PUNCT
iajs-2681	48	1	þ	þ	PROPN
iajs-2681	48	2	is	be	AUX
iajs-2681	48	3	a	a	DET
iajs-2681	48	4	fuzzy	fuzzy	ADJ
iajs-2681	48	5	continuous	continuous	ADJ
iajs-2681	48	6	.	.	PUNCT
iajs-2681	49	1	for	for	ADP
iajs-2681	49	2	example	example	NOUN
iajs-2681	49	3	,	,	PUNCT
iajs-2681	49	4	we	we	PRON
iajs-2681	49	5	can	can	AUX
iajs-2681	49	6	assume	assume	VERB
iajs-2681	49	7	that	that	SCONJ
iajs-2681	49	8	(	(	PUNCT
iajs-2681	49	9	b	b	NOUN
iajs-2681	49	10	,	,	PUNCT
iajs-2681	49	11			NOUN
iajs-2681	49	12	)	)	PUNCT
iajs-2681	49	13	like	like	ADP
iajs-2681	49	14	a	a	DET
iajs-2681	49	15	fwfts	fwft	NOUN
iajs-2681	49	16	over	over	ADP
iajs-2681	49	17	itself	itself	PRON
iajs-2681	49	18	by	by	ADP
iajs-2681	49	19	the	the	DET
iajs-2681	49	20	identity	identity	NOUN
iajs-2681	49	21	as	as	ADP
iajs-2681	49	22	proj	proj	PROPN
iajs-2681	49	23	..	..	PUNCT
iajs-2681	49	24	also	also	ADV
iajs-2681	49	25	,	,	PUNCT
iajs-2681	49	26	the	the	DET
iajs-2681	49	27	fuzzy	fuzzy	ADJ
iajs-2681	49	28	topological	topological	ADJ
iajs-2681	49	29	product	product	NOUN
iajs-2681	49	30	(	(	PUNCT
iajs-2681	49	31	see	see	VERB
iajs-2681	49	32	[	[	X
iajs-2681	49	33	5	5	NUM
iajs-2681	49	34	]	]	SYM
iajs-2681	49	35	)	)	PUNCT
iajs-2681	49	36	b	b	PROPN
iajs-2681	49	37			PROPN
iajs-2681	49	38	t	t	PROPN
iajs-2681	49	39	,	,	PUNCT
iajs-2681	49	40	for	for	ADP
iajs-2681	49	41	every	every	DET
iajs-2681	49	42	fts	fts	PROPN
iajs-2681	49	43	t	t	PROPN
iajs-2681	49	44	,	,	PUNCT
iajs-2681	49	45	can	can	AUX
iajs-2681	49	46	be	be	AUX
iajs-2681	49	47	regarded	regard	VERB
iajs-2681	49	48	like	like	ADP
iajs-2681	49	49	a	a	DET
iajs-2681	49	50	fwfts	fwft	NOUN
iajs-2681	49	51	's	be	AUX
iajs-2681	49	52	over	over	ADP
iajs-2681	49	53	b	b	NOUN
iajs-2681	49	54	,	,	PUNCT
iajs-2681	49	55	by	by	ADP
iajs-2681	49	56	the	the	DET
iajs-2681	49	57	first	first	ADJ
iajs-2681	49	58	proj	proj	NOUN
iajs-2681	49	59	.	.	PUNCT
iajs-2681	50	1	and	and	CCONJ
iajs-2681	50	2	in	in	ADP
iajs-2681	50	3	the	the	DET
iajs-2681	50	4	same	same	ADJ
iajs-2681	50	5	way	way	NOUN
iajs-2681	50	6	for	for	ADP
iajs-2681	50	7	every	every	DET
iajs-2681	50	8	fuzzy	fuzzy	ADJ
iajs-2681	50	9	subspace	subspace	NOUN
iajs-2681	50	10	(	(	PUNCT
iajs-2681	50	11	see	see	VERB
iajs-2681	50	12	[	[	X
iajs-2681	50	13	4	4	NUM
iajs-2681	50	14	]	]	PUNCT
iajs-2681	50	15	)	)	PUNCT
iajs-2681	50	16	of	of	ADP
iajs-2681	50	17	b	b	PROPN
iajs-2681	50	18			PROPN
iajs-2681	50	19	t.	t.	PROPN
iajs-2681	50	20	remark	remark	PROPN
iajs-2681	50	21	2.2	2.2	NUM
iajs-2681	50	22	.	.	PUNCT
iajs-2681	51	1	(	(	PUNCT
iajs-2681	51	2	a	a	X
iajs-2681	51	3	)	)	PUNCT
iajs-2681	51	4	in	in	ADP
iajs-2681	51	5	fwfts	fwft	NOUN
iajs-2681	51	6	,	,	PUNCT
iajs-2681	51	7	we	we	PRON
iajs-2681	51	8	carry	carry	VERB
iajs-2681	51	9	out	out	ADP
iajs-2681	51	10	over	over	ADP
iajs-2681	51	11	fts	fts	PROPN
iajs-2681	51	12	(	(	PUNCT
iajs-2681	51	13	b	b	NOUN
iajs-2681	51	14	,	,	PUNCT
iajs-2681	51	15			NOUN
iajs-2681	51	16	)	)	PUNCT
iajs-2681	51	17	as	as	ADP
iajs-2681	51	18	a	a	DET
iajs-2681	51	19	base	base	NOUN
iajs-2681	51	20	space	space	NOUN
iajs-2681	51	21	.	.	PUNCT
iajs-2681	52	1	if	if	SCONJ
iajs-2681	52	2	b	b	PROPN
iajs-2681	52	3	is	be	AUX
iajs-2681	52	4	a	a	DET
iajs-2681	52	5	point	point	NOUN
iajs-2681	52	6	–	–	PUNCT
iajs-2681	52	7	space	space	NOUN
iajs-2681	52	8	,	,	PUNCT
iajs-2681	52	9	the	the	DET
iajs-2681	52	10	theory	theory	NOUN
iajs-2681	52	11	changes	change	VERB
iajs-2681	52	12	to	to	ADP
iajs-2681	52	13	that	that	PRON
iajs-2681	52	14	of	of	ADP
iajs-2681	52	15	ordinary	ordinary	ADJ
iajs-2681	52	16	fuzzy	fuzzy	ADJ
iajs-2681	52	17	topology	topology	NOUN
iajs-2681	52	18	.	.	PUNCT
iajs-2681	53	1	(	(	PUNCT
iajs-2681	53	2	b	b	X
iajs-2681	53	3	)	)	PUNCT
iajs-2681	53	4	a	a	DET
iajs-2681	53	5	fwfts	fwft	NOUN
iajs-2681	53	6	's	's	PART
iajs-2681	53	7	over	over	ADP
iajs-2681	53	8	b	b	NOUN
iajs-2681	53	9	is	be	AUX
iajs-2681	53	10	just	just	ADV
iajs-2681	53	11	a	a	DET
iajs-2681	53	12	fts	fts	PROPN
iajs-2681	53	13	(	(	PUNCT
iajs-2681	53	14	m	m	PROPN
iajs-2681	53	15	,	,	PUNCT
iajs-2681	53	16			PROPN
iajs-2681	53	17	)	)	PUNCT
iajs-2681	53	18	with	with	ADP
iajs-2681	53	19	a	a	DET
iajs-2681	53	20	fuzzy	fuzzy	ADJ
iajs-2681	53	21	continuous	continuous	ADJ
iajs-2681	53	22	proj	proj	NOUN
iajs-2681	53	23	.	.	PUNCT
iajs-2681	54	1	mapping	mapping	NOUN
iajs-2681	54	2	þ	þ	NOUN
iajs-2681	54	3	:	:	PUNCT
iajs-2681	54	4	(	(	PUNCT
iajs-2681	54	5	m	m	NOUN
iajs-2681	54	6	,	,	PUNCT
iajs-2681	54	7			NOUN
iajs-2681	54	8	)	)	PUNCT
iajs-2681	54	9			PUNCT
iajs-2681	55	1	(	(	PUNCT
iajs-2681	55	2	b	b	NOUN
iajs-2681	55	3	,	,	PUNCT
iajs-2681	55	4			NOUN
iajs-2681	55	5	)	)	PUNCT
iajs-2681	55	6	.	.	PUNCT
iajs-2681	56	1	(	(	PUNCT
iajs-2681	56	2	c	c	X
iajs-2681	56	3	)	)	PUNCT
iajs-2681	56	4	the	the	DET
iajs-2681	56	5	coarsest	coarse	ADJ
iajs-2681	56	6	fuzzy	fuzzy	ADJ
iajs-2681	56	7	topology	topology	NOUN
iajs-2681	56	8	got	get	VERB
iajs-2681	56	9	by	by	ADP
iajs-2681	56	10	þ	þ	PROPN
iajs-2681	56	11	,	,	PUNCT
iajs-2681	56	12	in	in	ADP
iajs-2681	56	13	which	which	PRON
iajs-2681	56	14	the	the	DET
iajs-2681	56	15	fuzzy	fuzzy	ADJ
iajs-2681	56	16	open	open	ADJ
iajs-2681	56	17	sets	set	NOUN
iajs-2681	56	18	of	of	ADP
iajs-2681	56	19	(	(	PUNCT
iajs-2681	56	20	m	m	PROPN
iajs-2681	56	21	,	,	PUNCT
iajs-2681	56	22			PROPN
iajs-2681	56	23	)	)	PUNCT
iajs-2681	56	24	are	be	AUX
iajs-2681	56	25	the	the	DET
iajs-2681	56	26	exactly	exactly	ADV
iajs-2681	56	27	the	the	DET
iajs-2681	56	28	pre	pre	ADJ
iajs-2681	56	29	image	image	NOUN
iajs-2681	56	30	of	of	ADP
iajs-2681	56	31	the	the	DET
iajs-2681	56	32	fuzzy	fuzzy	ADJ
iajs-2681	56	33	open	open	ADJ
iajs-2681	56	34	set	set	NOUN
iajs-2681	56	35	of	of	ADP
iajs-2681	56	36	(	(	PUNCT
iajs-2681	56	37	b	b	NOUN
iajs-2681	56	38	,	,	PUNCT
iajs-2681	56	39			NOUN
iajs-2681	56	40	)	)	PUNCT
iajs-2681	56	41	.	.	PUNCT
iajs-2681	57	1	ibn	ibn	PROPN
iajs-2681	57	2	al	al	PROPN
iajs-2681	57	3	-	-	PUNCT
iajs-2681	57	4	haitham	haitham	PROPN
iajs-2681	57	5	jour	jour	X
iajs-2681	57	6	.	.	PROPN
iajs-2681	57	7	for	for	ADP
iajs-2681	57	8	pure	pure	ADJ
iajs-2681	57	9	&	&	CCONJ
iajs-2681	57	10	appl	appl	PROPN
iajs-2681	57	11	.	.	PUNCT
iajs-2681	58	1	sci	sci	PROPN
iajs-2681	58	2	.	.	PROPN
iajs-2681	59	1	34(3)2021	34(3)2021	NUM
iajs-2681	59	2	89	89	NUM
iajs-2681	59	3	(	(	PUNCT
iajs-2681	59	4	d	d	X
iajs-2681	59	5	)	)	PUNCT
iajs-2681	59	6	the	the	DET
iajs-2681	59	7	fwfts	fwft	NOUN
iajs-2681	59	8	over	over	ADP
iajs-2681	59	9	(	(	PUNCT
iajs-2681	59	10	b	b	NOUN
iajs-2681	59	11	,	,	PUNCT
iajs-2681	59	12			NOUN
iajs-2681	59	13	)	)	PUNCT
iajs-2681	59	14	is	be	AUX
iajs-2681	59	15	defined	define	VERB
iajs-2681	59	16	to	to	PART
iajs-2681	59	17	be	be	AUX
iajs-2681	59	18	a	a	DET
iajs-2681	59	19	fw	fw	NOUN
iajs-2681	59	20	set	set	NOUN
iajs-2681	59	21	over	over	ADP
iajs-2681	59	22	b	b	NOUN
iajs-2681	59	23	with	with	ADP
iajs-2681	59	24	fwfts	fwft	NOUN
iajs-2681	59	25	.	.	PUNCT
iajs-2681	60	1	(	(	PUNCT
iajs-2681	60	2	e	e	X
iajs-2681	60	3	)	)	PUNCT
iajs-2681	60	4	we	we	PRON
iajs-2681	60	5	consider	consider	VERB
iajs-2681	60	6	the	the	DET
iajs-2681	60	7	fuzzy	fuzzy	ADJ
iajs-2681	60	8	topological	topological	ADJ
iajs-2681	60	9	product	product	NOUN
iajs-2681	60	10	(	(	PUNCT
iajs-2681	60	11	written	write	VERB
iajs-2681	60	12	as	as	ADP
iajs-2681	60	13	ftp	ftp	NOUN
iajs-2681	60	14	)	)	PUNCT
iajs-2681	60	15	b	b	PROPN
iajs-2681	60	16			PROPN
iajs-2681	60	17	t	t	PROPN
iajs-2681	60	18	,	,	PUNCT
iajs-2681	60	19	for	for	ADP
iajs-2681	60	20	every	every	DET
iajs-2681	60	21	fts	fts	PROPN
iajs-2681	60	22	t	t	PROPN
iajs-2681	60	23	,	,	PUNCT
iajs-2681	60	24	like	like	ADP
iajs-2681	60	25	a	a	DET
iajs-2681	60	26	fwfts	fwft	NOUN
iajs-2681	60	27	's	's	PART
iajs-2681	60	28	over	over	ADP
iajs-2681	60	29	b	b	NOUN
iajs-2681	60	30	by	by	ADP
iajs-2681	60	31	the	the	DET
iajs-2681	60	32	first	first	ADJ
iajs-2681	60	33	proj	proj	PROPN
iajs-2681	60	34	..	..	PUNCT
iajs-2681	60	35	definition	definition	NOUN
iajs-2681	60	36	2.3	2.3	NUM
iajs-2681	60	37	.	.	PUNCT
iajs-2681	61	1	the	the	DET
iajs-2681	61	2	fw	fw	PROPN
iajs-2681	61	3	-	-	PUNCT
iajs-2681	61	4	m	m	NOUN
iajs-2681	61	5			NOUN
iajs-2681	61	6	:	:	PUNCT
iajs-2681	61	7	m	m	VERB
iajs-2681	61	8			NOUN
iajs-2681	61	9	n	n	CCONJ
iajs-2681	61	10	where	where	SCONJ
iajs-2681	61	11	(	(	PUNCT
iajs-2681	61	12	m	m	NOUN
iajs-2681	61	13	,	,	PUNCT
iajs-2681	61	14			PROPN
iajs-2681	61	15	)	)	PUNCT
iajs-2681	61	16	and	and	CCONJ
iajs-2681	61	17	(	(	PUNCT
iajs-2681	61	18	n	n	CCONJ
iajs-2681	61	19	,	,	PUNCT
iajs-2681	61	20			NUM
iajs-2681	61	21	)	)	PUNCT
iajs-2681	61	22	are	be	AUX
iajs-2681	61	23	fwfts	fwft	NOUN
iajs-2681	61	24	's	's	PART
iajs-2681	61	25	over	over	ADP
iajs-2681	61	26	(	(	PUNCT
iajs-2681	61	27	b	b	NOUN
iajs-2681	61	28	,	,	PUNCT
iajs-2681	61	29			NOUN
iajs-2681	61	30	)	)	PUNCT
iajs-2681	61	31	is	be	AUX
iajs-2681	61	32	said	say	VERB
iajs-2681	61	33	to	to	PART
iajs-2681	61	34	be	be	AUX
iajs-2681	61	35	:	:	PUNCT
iajs-2681	61	36	(	(	PUNCT
iajs-2681	61	37	a	a	X
iajs-2681	61	38	)	)	PUNCT
iajs-2681	61	39	fuzzy	fuzzy	ADJ
iajs-2681	61	40	continuous	continuous	ADJ
iajs-2681	61	41	if	if	SCONJ
iajs-2681	61	42	b	b	PROPN
iajs-2681	61	43	b	b	PROPN
iajs-2681	61	44	and	and	CCONJ
iajs-2681	61	45	for	for	ADP
iajs-2681	61	46	every	every	DET
iajs-2681	61	47	point	point	NOUN
iajs-2681	61	48	m	m	VERB
iajs-2681	61	49			NOUN
iajs-2681	61	50	mb	mb	ADP
iajs-2681	61	51	,	,	PUNCT
iajs-2681	61	52	the	the	DET
iajs-2681	61	53	pre	pre	ADJ
iajs-2681	61	54	image	image	NOUN
iajs-2681	61	55	of	of	ADP
iajs-2681	61	56	every	every	DET
iajs-2681	61	57	fuzzy	fuzzy	ADJ
iajs-2681	61	58	open	open	ADJ
iajs-2681	61	59	set	set	NOUN
iajs-2681	61	60	of	of	ADP
iajs-2681	61	61	(m	(m	PROPN
iajs-2681	61	62	)	)	PUNCT
iajs-2681	61	63	is	be	AUX
iajs-2681	61	64	a	a	DET
iajs-2681	61	65	fuzzy	fuzzy	ADJ
iajs-2681	61	66	open	open	ADJ
iajs-2681	61	67	set	set	NOUN
iajs-2681	61	68	of	of	ADP
iajs-2681	61	69	m.	m.	NOUN
iajs-2681	61	70	(	(	PUNCT
iajs-2681	61	71	b	b	NOUN
iajs-2681	61	72	)	)	PUNCT
iajs-2681	61	73	fuzzy	fuzzy	ADJ
iajs-2681	61	74	open	open	ADJ
iajs-2681	61	75	if	if	SCONJ
iajs-2681	61	76	b	b	PROPN
iajs-2681	61	77			PROPN
iajs-2681	61	78	b	b	NOUN
iajs-2681	61	79	and	and	CCONJ
iajs-2681	61	80	for	for	ADP
iajs-2681	61	81	every	every	DET
iajs-2681	61	82	point	point	NOUN
iajs-2681	61	83	m	m	VERB
iajs-2681	61	84			NOUN
iajs-2681	61	85	mb	mb	ADP
iajs-2681	61	86	,	,	PUNCT
iajs-2681	61	87	the	the	DET
iajs-2681	61	88	image	image	NOUN
iajs-2681	61	89	of	of	ADP
iajs-2681	61	90	every	every	DET
iajs-2681	61	91	fuzzy	fuzzy	ADJ
iajs-2681	61	92	open	open	ADJ
iajs-2681	61	93	set	set	NOUN
iajs-2681	61	94	of	of	ADP
iajs-2681	61	95	m	m	PROPN
iajs-2681	61	96	is	be	AUX
iajs-2681	61	97	a	a	DET
iajs-2681	61	98	fuzzy	fuzzy	ADJ
iajs-2681	61	99	open	open	ADJ
iajs-2681	61	100	set	set	NOUN
iajs-2681	61	101	of	of	ADP
iajs-2681	61	102	(m	(m	PROPN
iajs-2681	61	103	)	)	PUNCT
iajs-2681	61	104	.	.	PUNCT
iajs-2681	62	1	(	(	PUNCT
iajs-2681	62	2	c	c	X
iajs-2681	62	3	)	)	PUNCT
iajs-2681	62	4	fuzzy	fuzzy	ADJ
iajs-2681	62	5	closed	close	VERB
iajs-2681	62	6	if	if	SCONJ
iajs-2681	62	7	b	b	NUM
iajs-2681	62	8			PROPN
iajs-2681	62	9	b	b	NOUN
iajs-2681	62	10	and	and	CCONJ
iajs-2681	62	11	for	for	ADP
iajs-2681	62	12	every	every	DET
iajs-2681	62	13	point	point	NOUN
iajs-2681	62	14	m	m	VERB
iajs-2681	62	15			NOUN
iajs-2681	62	16	mb	mb	ADP
iajs-2681	62	17	,	,	PUNCT
iajs-2681	62	18	the	the	DET
iajs-2681	62	19	image	image	NOUN
iajs-2681	62	20	of	of	ADP
iajs-2681	62	21	every	every	DET
iajs-2681	62	22	fuzzy	fuzzy	NOUN
iajs-2681	62	23	closed	close	VERB
iajs-2681	62	24	set	set	NOUN
iajs-2681	62	25	of	of	ADP
iajs-2681	62	26	m	m	PROPN
iajs-2681	62	27	is	be	AUX
iajs-2681	62	28	a	a	DET
iajs-2681	62	29	fuzzy	fuzzy	ADJ
iajs-2681	62	30	closed	close	VERB
iajs-2681	62	31	set	set	NOUN
iajs-2681	62	32	of	of	ADP
iajs-2681	62	33	(m	(m	NOUN
iajs-2681	62	34	)	)	PUNCT
iajs-2681	62	35	.	.	PUNCT
iajs-2681	63	1	if	if	SCONJ
iajs-2681	63	2			X
iajs-2681	63	3	:	:	PUNCT
iajs-2681	63	4	m	m	VERB
iajs-2681	63	5			NOUN
iajs-2681	64	1	n	n	PRON
iajs-2681	64	2	is	be	AUX
iajs-2681	64	3	a	a	DET
iajs-2681	64	4	fw	fw	NOUN
iajs-2681	64	5	-	-	PUNCT
iajs-2681	64	6	m	m	NOUN
iajs-2681	64	7	where	where	SCONJ
iajs-2681	64	8	m	m	NOUN
iajs-2681	64	9	is	be	AUX
iajs-2681	64	10	a	a	DET
iajs-2681	64	11	fw	fw	NOUN
iajs-2681	64	12	set	set	NOUN
iajs-2681	64	13	and	and	CCONJ
iajs-2681	64	14	(	(	PUNCT
iajs-2681	64	15	n	n	CCONJ
iajs-2681	64	16	,	,	PUNCT
iajs-2681	64	17			NUM
iajs-2681	64	18	)	)	PUNCT
iajs-2681	64	19	is	be	AUX
iajs-2681	64	20	a	a	DET
iajs-2681	64	21	fwfts	fwft	NOUN
iajs-2681	64	22	over	over	ADP
iajs-2681	64	23	(	(	PUNCT
iajs-2681	64	24	b	b	NOUN
iajs-2681	64	25	,	,	PUNCT
iajs-2681	64	26			NOUN
iajs-2681	64	27	)	)	PUNCT
iajs-2681	64	28	.	.	PUNCT
iajs-2681	65	1	we	we	PRON
iajs-2681	65	2	can	can	AUX
iajs-2681	65	3	give	give	VERB
iajs-2681	65	4	m	m	PRON
iajs-2681	65	5	the	the	DET
iajs-2681	65	6	induced	induce	VERB
iajs-2681	65	7	fuzzy	fuzzy	ADJ
iajs-2681	65	8	topology	topology	NOUN
iajs-2681	65	9	(	(	PUNCT
iajs-2681	65	10	see	see	VERB
iajs-2681	65	11	[	[	X
iajs-2681	65	12	4	4	NUM
iajs-2681	65	13	]	]	NUM
iajs-2681	65	14	)	)	PUNCT
iajs-2681	65	15	,	,	PUNCT
iajs-2681	65	16	in	in	ADP
iajs-2681	65	17	the	the	DET
iajs-2681	65	18	ordinary	ordinary	ADJ
iajs-2681	65	19	sense	sense	NOUN
iajs-2681	65	20	and	and	CCONJ
iajs-2681	65	21	this	this	PRON
iajs-2681	65	22	is	be	AUX
iajs-2681	65	23	necessarily	necessarily	ADV
iajs-2681	65	24	a	a	DET
iajs-2681	65	25	fwftopology	fwftopology	NOUN
iajs-2681	65	26	.	.	PUNCT
iajs-2681	66	1	we	we	PRON
iajs-2681	66	2	may	may	AUX
iajs-2681	66	3	refer	refer	VERB
iajs-2681	66	4	to	to	ADP
iajs-2681	66	5	it	it	PRON
iajs-2681	66	6	,	,	PUNCT
iajs-2681	66	7	therefore	therefore	ADV
iajs-2681	66	8	,	,	PUNCT
iajs-2681	66	9	like	like	ADP
iajs-2681	66	10	the	the	DET
iajs-2681	66	11	induced	induced	ADJ
iajs-2681	66	12	fwf	fwf	ADJ
iajs-2681	66	13	-	-	PUNCT
iajs-2681	66	14	topology	topology	NOUN
iajs-2681	66	15	and	and	CCONJ
iajs-2681	66	16	note	note	VERB
iajs-2681	66	17	the	the	DET
iajs-2681	66	18	next	next	ADJ
iajs-2681	66	19	characterizations	characterization	NOUN
iajs-2681	66	20	.	.	PUNCT
iajs-2681	67	1	theorem	theorem	VERB
iajs-2681	67	2	2.4	2.4	NUM
iajs-2681	67	3	.	.	PUNCT
iajs-2681	68	1	let	let	VERB
iajs-2681	68	2			X
iajs-2681	68	3	:	:	PUNCT
iajs-2681	68	4	m	m	VERB
iajs-2681	68	5			NOUN
iajs-2681	68	6	n	n	AUX
iajs-2681	68	7	be	be	AUX
iajs-2681	68	8	a	a	DET
iajs-2681	68	9	fw	fw	ADJ
iajs-2681	68	10	-	-	PUNCT
iajs-2681	68	11	m	m	NOUN
iajs-2681	68	12	,	,	PUNCT
iajs-2681	68	13	where	where	SCONJ
iajs-2681	68	14	(	(	PUNCT
iajs-2681	68	15	n	n	X
iajs-2681	68	16	,	,	PUNCT
iajs-2681	68	17			PROPN
iajs-2681	68	18	)	)	PUNCT
iajs-2681	68	19	a	a	DET
iajs-2681	68	20	fwfts	fwft	NOUN
iajs-2681	68	21	over	over	ADP
iajs-2681	68	22	(	(	PUNCT
iajs-2681	68	23	b	b	NOUN
iajs-2681	68	24	,	,	PUNCT
iajs-2681	68	25			NOUN
iajs-2681	68	26	)	)	PUNCT
iajs-2681	68	27	and	and	CCONJ
iajs-2681	68	28	m	m	PROPN
iajs-2681	68	29	has	have	VERB
iajs-2681	68	30	the	the	DET
iajs-2681	68	31	induced	induced	ADJ
iajs-2681	68	32	fwf	fwf	ADJ
iajs-2681	68	33	-	-	PUNCT
iajs-2681	68	34	topology	topology	NOUN
iajs-2681	68	35	.	.	PUNCT
iajs-2681	69	1	then	then	ADV
iajs-2681	69	2	,	,	PUNCT
iajs-2681	69	3	for	for	ADP
iajs-2681	69	4	every	every	DET
iajs-2681	69	5	fwfts	fwft	NOUN
iajs-2681	69	6	(	(	PUNCT
iajs-2681	69	7	o	o	NOUN
iajs-2681	69	8	,	,	PUNCT
iajs-2681	69	9			NUM
iajs-2681	69	10	)	)	PUNCT
iajs-2681	69	11	a	a	DET
iajs-2681	69	12	fw	fw	PROPN
iajs-2681	69	13	-	-	PUNCT
iajs-2681	69	14	m	m	NOUN
iajs-2681	69	15			ADJ
iajs-2681	69	16	:	:	PUNCT
iajs-2681	69	17	o	o	NOUN
iajs-2681	69	18			X
iajs-2681	69	19	(	(	PUNCT
iajs-2681	69	20	m	m	NOUN
iajs-2681	69	21	,	,	PUNCT
iajs-2681	69	22			PROPN
iajs-2681	69	23	)	)	PUNCT
iajs-2681	69	24	is	be	AUX
iajs-2681	69	25	a	a	DET
iajs-2681	69	26	fuzzy	fuzzy	ADJ
iajs-2681	69	27	continuous	continuous	ADJ
iajs-2681	69	28	iff	iff	NOUN
iajs-2681	69	29	the	the	DET
iajs-2681	69	30	composition	composition	NOUN
iajs-2681	69	31			X
iajs-2681	69	32			PROPN
iajs-2681	69	33			PROPN
iajs-2681	69	34	:	:	PUNCT
iajs-2681	69	35	o	o	NOUN
iajs-2681	69	36			NOUN
iajs-2681	70	1	n	n	PRON
iajs-2681	70	2	is	be	AUX
iajs-2681	70	3	a	a	DET
iajs-2681	70	4	fuzzy	fuzzy	ADJ
iajs-2681	70	5	continuous	continuous	ADJ
iajs-2681	70	6	.	.	PUNCT
iajs-2681	71	1	proof	proof	NOUN
iajs-2681	71	2	.	.	PUNCT
iajs-2681	72	1	(	(	PUNCT
iajs-2681	72	2			NOUN
iajs-2681	72	3	)	)	PUNCT
iajs-2681	72	4	suppose	suppose	VERB
iajs-2681	72	5	that	that	SCONJ
iajs-2681	72	6			ADJ
iajs-2681	72	7	is	be	AUX
iajs-2681	72	8	a	a	DET
iajs-2681	72	9	fuzzy	fuzzy	ADJ
iajs-2681	72	10	continuous	continuous	ADJ
iajs-2681	72	11	.	.	PUNCT
iajs-2681	73	1	let	let	VERB
iajs-2681	73	2	q	q	PROPN
iajs-2681	73	3			NOUN
iajs-2681	73	4	ob	ob	ADP
iajs-2681	73	5	;	;	PUNCT
iajs-2681	73	6	b	b	X
iajs-2681	73	7			PROPN
iajs-2681	73	8	b	b	NOUN
iajs-2681	73	9	and	and	CCONJ
iajs-2681	73	10	let	let	VERB
iajs-2681	73	11	v	v	PART
iajs-2681	73	12	be	be	AUX
iajs-2681	73	13	fuzzy	fuzzy	ADJ
iajs-2681	73	14	open	open	ADJ
iajs-2681	73	15	set	set	NOUN
iajs-2681	73	16	of	of	ADP
iajs-2681	73	17	(	(	PUNCT
iajs-2681	73	18			PROPN
iajs-2681	73	19			PROPN
iajs-2681	73	20	)(q	)(q	PROPN
iajs-2681	73	21	)	)	PUNCT
iajs-2681	73	22	=	=	PUNCT
iajs-2681	74	1	n	n	PROPN
iajs-2681	74	2			NOUN
iajs-2681	74	3	nb	nb	PROPN
iajs-2681	74	4	in	in	ADP
iajs-2681	74	5	n.	n.	NOUN
iajs-2681	74	6	since	since	SCONJ
iajs-2681	74	7			PROPN
iajs-2681	74	8	is	be	AUX
iajs-2681	74	9	a	a	DET
iajs-2681	74	10	fuzzy	fuzzy	ADJ
iajs-2681	74	11	continuous	continuous	ADJ
iajs-2681	74	12	,	,	PUNCT
iajs-2681	74	13	then	then	ADV
iajs-2681	74	14	1(v	1(v	PROPN
iajs-2681	74	15	)	)	PUNCT
iajs-2681	74	16	is	be	AUX
iajs-2681	74	17	a	a	DET
iajs-2681	74	18	fuzzy	fuzzy	ADJ
iajs-2681	74	19	open	open	ADJ
iajs-2681	74	20	set	set	NOUN
iajs-2681	74	21	containing	contain	VERB
iajs-2681	74	22	(q	(q	ADV
iajs-2681	74	23	)	)	PUNCT
iajs-2681	75	1	=	=	PUNCT
iajs-2681	75	2	m	m	PROPN
iajs-2681	75	3			NOUN
iajs-2681	75	4	mb	mb	ADP
iajs-2681	75	5	in	in	ADP
iajs-2681	75	6	m.	m.	NOUN
iajs-2681	75	7	since	since	SCONJ
iajs-2681	75	8			PROPN
iajs-2681	75	9	is	be	AUX
iajs-2681	75	10	a	a	DET
iajs-2681	75	11	fuzzy	fuzzy	ADJ
iajs-2681	75	12	continuous	continuous	ADJ
iajs-2681	75	13	,	,	PUNCT
iajs-2681	75	14	then	then	ADV
iajs-2681	75	15			ADJ
iajs-2681	75	16	1(1(v	1(1(v	NOUN
iajs-2681	75	17	)	)	PUNCT
iajs-2681	75	18	)	)	PUNCT
iajs-2681	76	1	is	be	AUX
iajs-2681	76	2	a	a	DET
iajs-2681	76	3	fuzzy	fuzzy	ADJ
iajs-2681	76	4	open	open	ADJ
iajs-2681	76	5	set	set	NOUN
iajs-2681	76	6	containing	contain	VERB
iajs-2681	76	7	q	q	PROPN
iajs-2681	76	8			NOUN
iajs-2681	76	9	ob	ob	ADJ
iajs-2681	76	10	in	in	ADP
iajs-2681	76	11	o	o	NOUN
iajs-2681	76	12	and	and	CCONJ
iajs-2681	76	13			ADJ
iajs-2681	76	14	1(1(v	1(1(v	NOUN
iajs-2681	76	15	)	)	PUNCT
iajs-2681	76	16	)	)	PUNCT
iajs-2681	77	1	=	=	PUNCT
iajs-2681	77	2	(	(	PUNCT
iajs-2681	77	3			X
iajs-2681	77	4			PROPN
iajs-2681	77	5	)1(v	)1(v	PROPN
iajs-2681	77	6	)	)	PUNCT
iajs-2681	77	7	is	be	AUX
iajs-2681	77	8	a	a	DET
iajs-2681	77	9	fuzzy	fuzzy	ADJ
iajs-2681	77	10	open	open	ADJ
iajs-2681	77	11	set	set	NOUN
iajs-2681	77	12	containing	contain	VERB
iajs-2681	77	13	q	q	PROPN
iajs-2681	77	14			NOUN
iajs-2681	77	15	ob	ob	ADJ
iajs-2681	77	16	in	in	ADP
iajs-2681	77	17	o.	o.	PROPN
iajs-2681	77	18	(	(	PUNCT
iajs-2681	77	19			NOUN
iajs-2681	77	20	)	)	PUNCT
iajs-2681	77	21	suppose	suppose	VERB
iajs-2681	77	22	that	that	SCONJ
iajs-2681	77	23			PROPN
iajs-2681	77	24			PROPN
iajs-2681	77	25			PROPN
iajs-2681	77	26	is	be	AUX
iajs-2681	77	27	a	a	DET
iajs-2681	77	28	fuzzy	fuzzy	ADJ
iajs-2681	77	29	continuous	continuous	ADJ
iajs-2681	77	30	.	.	PUNCT
iajs-2681	78	1	let	let	VERB
iajs-2681	78	2	q	q	PROPN
iajs-2681	78	3			NOUN
iajs-2681	78	4	ob	ob	ADP
iajs-2681	78	5	;	;	PUNCT
iajs-2681	78	6	b	b	X
iajs-2681	78	7			PROPN
iajs-2681	78	8	b	b	NOUN
iajs-2681	78	9	and	and	CCONJ
iajs-2681	78	10	u	u	NOUN
iajs-2681	78	11	be	be	VERB
iajs-2681	78	12	a	a	DET
iajs-2681	78	13	fuzzy	fuzzy	ADJ
iajs-2681	78	14	open	open	ADJ
iajs-2681	78	15	set	set	NOUN
iajs-2681	78	16	of	of	ADP
iajs-2681	78	17	(q	(q	ADJ
iajs-2681	78	18	)	)	PUNCT
iajs-2681	79	1	=	=	PUNCT
iajs-2681	79	2	m	m	PROPN
iajs-2681	79	3			NOUN
iajs-2681	79	4	mb	mb	ADP
iajs-2681	79	5	in	in	ADP
iajs-2681	79	6	m.	m.	NOUN
iajs-2681	79	7	since	since	SCONJ
iajs-2681	79	8			PROPN
iajs-2681	79	9	is	be	AUX
iajs-2681	79	10	a	a	DET
iajs-2681	79	11	fuzzy	fuzzy	ADJ
iajs-2681	79	12	open	open	ADJ
iajs-2681	79	13	then	then	ADV
iajs-2681	79	14	,	,	PUNCT
iajs-2681	79	15	(u	(u	ADJ
iajs-2681	79	16	)	)	PUNCT
iajs-2681	79	17	is	be	AUX
iajs-2681	79	18	a	a	DET
iajs-2681	79	19	fuzzy	fuzzy	ADJ
iajs-2681	79	20	open	open	ADJ
iajs-2681	79	21	set	set	NOUN
iajs-2681	79	22	containing	contain	VERB
iajs-2681	79	23	(m	(m	PRON
iajs-2681	79	24	)	)	PUNCT
iajs-2681	79	25	=	=	SYM
iajs-2681	80	1	((q	((q	NOUN
iajs-2681	80	2	)	)	PUNCT
iajs-2681	80	3	)	)	PUNCT
iajs-2681	81	1	=	=	SYM
iajs-2681	81	2	n	n	PROPN
iajs-2681	81	3			NOUN
iajs-2681	81	4	nb	nb	PROPN
iajs-2681	81	5	in	in	ADP
iajs-2681	81	6	n.	n.	NOUN
iajs-2681	81	7	since	since	SCONJ
iajs-2681	81	8			PROPN
iajs-2681	81	9			PROPN
iajs-2681	81	10			PROPN
iajs-2681	81	11	is	be	AUX
iajs-2681	81	12	a	a	DET
iajs-2681	81	13	fuzzy	fuzzy	ADJ
iajs-2681	81	14	continuous	continuous	ADJ
iajs-2681	81	15	,	,	PUNCT
iajs-2681	81	16	then	then	ADV
iajs-2681	81	17	(	(	PUNCT
iajs-2681	81	18			PROPN
iajs-2681	81	19			PROPN
iajs-2681	81	20	)1((u	)1((u	PROPN
iajs-2681	81	21	)	)	PUNCT
iajs-2681	81	22	)	)	PUNCT
iajs-2681	82	1	=	=	SYM
iajs-2681	82	2	1(u	1(u	X
iajs-2681	82	3	)	)	PUNCT
iajs-2681	82	4	is	be	AUX
iajs-2681	82	5	a	a	DET
iajs-2681	82	6	fuzzy	fuzzy	ADJ
iajs-2681	82	7	open	open	ADJ
iajs-2681	82	8	set	set	NOUN
iajs-2681	82	9	containing	contain	VERB
iajs-2681	82	10	q	q	PROPN
iajs-2681	82	11			NOUN
iajs-2681	82	12	ob	ob	NOUN
iajs-2681	82	13	in	in	ADP
iajs-2681	82	14	o.	o.	PROPN
iajs-2681	82	15	theorem	theorem	VERB
iajs-2681	82	16	2.5	2.5	NUM
iajs-2681	82	17	.	.	PUNCT
iajs-2681	83	1	let	let	VERB
iajs-2681	83	2			X
iajs-2681	83	3	:	:	PUNCT
iajs-2681	83	4	m	m	VERB
iajs-2681	83	5			NOUN
iajs-2681	83	6	n	n	AUX
iajs-2681	83	7	be	be	AUX
iajs-2681	83	8	a	a	DET
iajs-2681	83	9	fw	fw	PROPN
iajs-2681	83	10	-	-	PUNCT
iajs-2681	83	11	m	m	NOUN
iajs-2681	83	12	where	where	SCONJ
iajs-2681	83	13	,	,	PUNCT
iajs-2681	83	14	(	(	PUNCT
iajs-2681	83	15	n	n	X
iajs-2681	83	16	,	,	PUNCT
iajs-2681	83	17			PROPN
iajs-2681	83	18	)	)	PUNCT
iajs-2681	83	19	a	a	DET
iajs-2681	83	20	fwfts	fwft	NOUN
iajs-2681	83	21	over	over	ADP
iajs-2681	83	22	(	(	PUNCT
iajs-2681	83	23	b	b	NOUN
iajs-2681	83	24	,	,	PUNCT
iajs-2681	83	25			NOUN
iajs-2681	83	26	)	)	PUNCT
iajs-2681	83	27	and	and	CCONJ
iajs-2681	83	28	m	m	PROPN
iajs-2681	83	29	has	have	VERB
iajs-2681	83	30	the	the	DET
iajs-2681	83	31	induced	induced	ADJ
iajs-2681	83	32	fwf	fwf	ADJ
iajs-2681	83	33	-	-	PUNCT
iajs-2681	83	34	topology	topology	NOUN
iajs-2681	83	35	.	.	PUNCT
iajs-2681	84	1	if	if	SCONJ
iajs-2681	84	2	for	for	ADP
iajs-2681	84	3	every	every	DET
iajs-2681	84	4	fwfts	fwft	NOUN
iajs-2681	84	5	(	(	PUNCT
iajs-2681	84	6	o	o	NOUN
iajs-2681	84	7	,	,	PUNCT
iajs-2681	84	8			NUM
iajs-2681	84	9	)	)	PUNCT
iajs-2681	84	10	a	a	DET
iajs-2681	84	11	subjective	subjective	ADJ
iajs-2681	84	12	fw	fw	ADJ
iajs-2681	84	13	-	-	PUNCT
iajs-2681	84	14	m	m	NOUN
iajs-2681	84	15			ADJ
iajs-2681	84	16	:	:	PUNCT
iajs-2681	84	17	o	o	NOUN
iajs-2681	84	18			X
iajs-2681	84	19	(	(	PUNCT
iajs-2681	84	20	m	m	NOUN
iajs-2681	84	21	,	,	PUNCT
iajs-2681	84	22			PROPN
iajs-2681	84	23	)	)	PUNCT
iajs-2681	84	24	is	be	AUX
iajs-2681	84	25	a	a	DET
iajs-2681	84	26	fuzzy	fuzzy	ADJ
iajs-2681	84	27	open	open	NOUN
iajs-2681	84	28	iff	iff	VERB
iajs-2681	84	29	the	the	DET
iajs-2681	84	30	composition	composition	NOUN
iajs-2681	84	31			X
iajs-2681	84	32			PROPN
iajs-2681	84	33			PROPN
iajs-2681	84	34	:	:	PUNCT
iajs-2681	84	35	o	o	NOUN
iajs-2681	84	36			NOUN
iajs-2681	84	37	n	n	PRON
iajs-2681	84	38	is	be	AUX
iajs-2681	84	39	a	a	DET
iajs-2681	84	40	fuzzy	fuzzy	ADJ
iajs-2681	84	41	open	open	ADJ
iajs-2681	84	42	.	.	PUNCT
iajs-2681	85	1	proof	proof	NOUN
iajs-2681	85	2	.	.	PUNCT
iajs-2681	86	1	(	(	PUNCT
iajs-2681	86	2			NOUN
iajs-2681	86	3	)	)	PUNCT
iajs-2681	86	4	suppose	suppose	VERB
iajs-2681	86	5	that	that	SCONJ
iajs-2681	86	6			ADJ
iajs-2681	86	7	is	be	AUX
iajs-2681	86	8	a	a	DET
iajs-2681	86	9	fuzzy	fuzzy	ADJ
iajs-2681	86	10	open	open	ADJ
iajs-2681	86	11	.	.	PUNCT
iajs-2681	87	1	let	let	VERB
iajs-2681	87	2	q	q	PROPN
iajs-2681	87	3			NOUN
iajs-2681	87	4	ob	ob	ADP
iajs-2681	87	5	;	;	PUNCT
iajs-2681	87	6	b	b	X
iajs-2681	87	7			PROPN
iajs-2681	87	8	b	b	NOUN
iajs-2681	87	9	and	and	CCONJ
iajs-2681	87	10	let	let	VERB
iajs-2681	87	11	u	u	PRON
iajs-2681	87	12	be	be	AUX
iajs-2681	87	13	fuzzy	fuzzy	ADJ
iajs-2681	87	14	open	open	ADJ
iajs-2681	87	15	set	set	NOUN
iajs-2681	87	16	of	of	ADP
iajs-2681	87	17	q	q	NOUN
iajs-2681	87	18	in	in	ADP
iajs-2681	87	19	o.	o.	NOUN
iajs-2681	87	20	since	since	SCONJ
iajs-2681	87	21			PROPN
iajs-2681	87	22	is	be	AUX
iajs-2681	87	23	a	a	DET
iajs-2681	87	24	fuzzy	fuzzy	ADJ
iajs-2681	87	25	open	open	ADJ
iajs-2681	87	26	,	,	PUNCT
iajs-2681	87	27	(u	(u	PROPN
iajs-2681	87	28	)	)	PUNCT
iajs-2681	87	29	is	be	AUX
iajs-2681	87	30	a	a	DET
iajs-2681	87	31	fuzzy	fuzzy	ADJ
iajs-2681	87	32	open	open	ADJ
iajs-2681	87	33	set	set	NOUN
iajs-2681	87	34	containing	contain	VERB
iajs-2681	87	35	(q	(q	ADV
iajs-2681	87	36	)	)	PUNCT
iajs-2681	88	1	=	=	PUNCT
iajs-2681	88	2	m	m	PROPN
iajs-2681	88	3			NOUN
iajs-2681	88	4	mb	mb	ADP
iajs-2681	88	5	in	in	ADP
iajs-2681	88	6	m.	m.	NOUN
iajs-2681	88	7	since	since	SCONJ
iajs-2681	88	8			PROPN
iajs-2681	88	9	is	be	AUX
iajs-2681	88	10	a	a	DET
iajs-2681	88	11	fuzzy	fuzzy	ADJ
iajs-2681	88	12	open	open	NOUN
iajs-2681	88	13	,	,	PUNCT
iajs-2681	88	14	then	then	ADV
iajs-2681	88	15	((u	((u	PROPN
iajs-2681	88	16	)	)	PUNCT
iajs-2681	88	17	)	)	PUNCT
iajs-2681	88	18	is	be	AUX
iajs-2681	88	19	a	a	DET
iajs-2681	88	20	fuzzy	fuzzy	ADJ
iajs-2681	88	21	open	open	ADJ
iajs-2681	88	22	set	set	NOUN
iajs-2681	88	23	containing	contain	VERB
iajs-2681	88	24	(m	(m	PRON
iajs-2681	88	25	)	)	PUNCT
iajs-2681	89	1	=	=	SYM
iajs-2681	89	2	((q	((q	NOUN
iajs-2681	89	3	)	)	PUNCT
iajs-2681	89	4	)	)	PUNCT
iajs-2681	90	1	=	=	SYM
iajs-2681	90	2	(	(	PUNCT
iajs-2681	90	3			X
iajs-2681	90	4			PROPN
iajs-2681	90	5	)(q	)(q	PROPN
iajs-2681	90	6	)	)	PUNCT
iajs-2681	90	7	=	=	PUNCT
iajs-2681	91	1	n	n	PROPN
iajs-2681	91	2			NOUN
iajs-2681	91	3	nb	nb	INTJ
iajs-2681	91	4	in	in	ADP
iajs-2681	91	5	n	n	PROPN
iajs-2681	91	6	and	and	CCONJ
iajs-2681	91	7	((u	((u	PROPN
iajs-2681	91	8	)	)	PUNCT
iajs-2681	91	9	)	)	PUNCT
iajs-2681	92	1	=	=	PUNCT
iajs-2681	92	2	(	(	PUNCT
iajs-2681	92	3			X
iajs-2681	92	4			X
iajs-2681	92	5	)(u	)(u	VERB
iajs-2681	92	6	)	)	PUNCT
iajs-2681	92	7	.	.	PUNCT
iajs-2681	93	1	(	(	PUNCT
iajs-2681	93	2			NOUN
iajs-2681	93	3	)	)	PUNCT
iajs-2681	93	4	suppose	suppose	VERB
iajs-2681	93	5	that	that	SCONJ
iajs-2681	93	6			PROPN
iajs-2681	93	7			PROPN
iajs-2681	93	8			PROPN
iajs-2681	93	9	is	be	AUX
iajs-2681	93	10	a	a	DET
iajs-2681	93	11	fuzzy	fuzzy	ADJ
iajs-2681	93	12	open	open	ADJ
iajs-2681	93	13	.	.	PUNCT
iajs-2681	94	1	let	let	VERB
iajs-2681	94	2	q	q	PROPN
iajs-2681	94	3			NOUN
iajs-2681	94	4	ob	ob	ADP
iajs-2681	94	5	;	;	PUNCT
iajs-2681	94	6	b	b	X
iajs-2681	94	7			PROPN
iajs-2681	94	8	b	b	NOUN
iajs-2681	94	9	and	and	CCONJ
iajs-2681	94	10	u	u	NOUN
iajs-2681	94	11	be	be	VERB
iajs-2681	94	12	a	a	DET
iajs-2681	94	13	fuzzy	fuzzy	ADJ
iajs-2681	94	14	open	open	ADJ
iajs-2681	94	15	set	set	NOUN
iajs-2681	94	16	of	of	ADP
iajs-2681	94	17	q	q	PROPN
iajs-2681	94	18			PROPN
iajs-2681	94	19	qb	qb	PROPN
iajs-2681	94	20	in	in	ADP
iajs-2681	94	21	q.	q.	PROPN
iajs-2681	94	22	since	since	SCONJ
iajs-2681	94	23			PROPN
iajs-2681	94	24			PROPN
iajs-2681	94	25			PROPN
iajs-2681	94	26	is	be	AUX
iajs-2681	94	27	a	a	DET
iajs-2681	94	28	fuzzy	fuzzy	ADJ
iajs-2681	94	29	open	open	ADJ
iajs-2681	94	30	then	then	ADV
iajs-2681	94	31	,	,	PUNCT
iajs-2681	94	32	(	(	PUNCT
iajs-2681	94	33			X
iajs-2681	94	34			X
iajs-2681	94	35	)(u	)(u	ADJ
iajs-2681	94	36	)	)	PUNCT
iajs-2681	94	37	is	be	AUX
iajs-2681	94	38	a	a	DET
iajs-2681	94	39	fuzzy	fuzzy	ADJ
iajs-2681	94	40	open	open	ADJ
iajs-2681	94	41	set	set	NOUN
iajs-2681	94	42	containing	contain	VERB
iajs-2681	94	43			PROPN
iajs-2681	94	44			PROPN
iajs-2681	94	45	(q	(q	PROPN
iajs-2681	94	46	)	)	PUNCT
iajs-2681	94	47	)	)	PUNCT
iajs-2681	95	1	=	=	PUNCT
iajs-2681	95	2	n	n	PROPN
iajs-2681	95	3			NOUN
iajs-2681	95	4	nb	nb	PROPN
iajs-2681	95	5	in	in	ADP
iajs-2681	95	6	n.	n.	NOUN
iajs-2681	95	7	since	since	SCONJ
iajs-2681	95	8	m	m	PROPN
iajs-2681	95	9	has	have	VERB
iajs-2681	95	10	the	the	DET
iajs-2681	95	11	induced	induced	ADJ
iajs-2681	95	12	fwf	fwf	ADJ
iajs-2681	95	13	-	-	PUNCT
iajs-2681	95	14	topology	topology	NOUN
iajs-2681	95	15	then	then	ADV
iajs-2681	95	16	1(	1(	X
iajs-2681	95	17			X
iajs-2681	95	18	)(u	)(u	NOUN
iajs-2681	95	19	)	)	PUNCT
iajs-2681	95	20	)	)	PUNCT
iajs-2681	96	1	=	=	SYM
iajs-2681	96	2	(u	(u	NOUN
iajs-2681	96	3	)	)	PUNCT
iajs-2681	96	4	is	be	AUX
iajs-2681	96	5	a	a	DET
iajs-2681	96	6	fuzzy	fuzzy	ADJ
iajs-2681	96	7	open	open	NOUN
iajs-2681	96	8	containing	contain	VERB
iajs-2681	96	9	1(	1(	PUNCT
iajs-2681	96	10			PROPN
iajs-2681	96	11	)(q	)(q	PROPN
iajs-2681	96	12	)	)	PUNCT
iajs-2681	96	13	)	)	PUNCT
iajs-2681	97	1	=	=	PUNCT
iajs-2681	97	2	(q	(q	ADJ
iajs-2681	97	3	)	)	PUNCT
iajs-2681	97	4	=	=	PUNCT
iajs-2681	97	5	m	m	PROPN
iajs-2681	97	6			NOUN
iajs-2681	97	7	mb	mb	ADP
iajs-2681	97	8	in	in	ADP
iajs-2681	97	9	m.	m.	PROPN
iajs-2681	97	10	ibn	ibn	PROPN
iajs-2681	97	11	al	al	PROPN
iajs-2681	97	12	-	-	PUNCT
iajs-2681	97	13	haitham	haitham	PROPN
iajs-2681	97	14	jour	jour	X
iajs-2681	97	15	.	.	PROPN
iajs-2681	98	1	for	for	ADP
iajs-2681	98	2	pure	pure	ADJ
iajs-2681	98	3	&	&	CCONJ
iajs-2681	98	4	appl	appl	PROPN
iajs-2681	98	5	.	.	PUNCT
iajs-2681	99	1	sci	sci	PROPN
iajs-2681	99	2	.	.	PROPN
iajs-2681	100	1	34(3)2021	34(3)2021	NUM
iajs-2681	100	2	90	90	NUM
iajs-2681	100	3	let	let	VERB
iajs-2681	100	4	us	we	PRON
iajs-2681	100	5	pass	pass	VERB
iajs-2681	100	6	the	the	DET
iajs-2681	100	7	general	general	ADJ
iajs-2681	100	8	cases	case	NOUN
iajs-2681	100	9	of	of	ADP
iajs-2681	100	10	theorems	theorem	NOUN
iajs-2681	100	11	(	(	PUNCT
iajs-2681	100	12	2.4	2.4	NUM
iajs-2681	100	13	)	)	PUNCT
iajs-2681	100	14	and	and	CCONJ
iajs-2681	100	15	(	(	PUNCT
iajs-2681	100	16	2.5	2.5	NUM
iajs-2681	100	17	)	)	PUNCT
iajs-2681	100	18	as	as	SCONJ
iajs-2681	100	19	follows	follow	VERB
iajs-2681	100	20	:	:	PUNCT
iajs-2681	100	21	similarly	similarly	ADV
iajs-2681	100	22	in	in	ADP
iajs-2681	100	23	case	case	NOUN
iajs-2681	100	24	of	of	ADP
iajs-2681	100	25	families	family	NOUN
iajs-2681	100	26	{	{	PUNCT
iajs-2681	100	27	r	r	NOUN
iajs-2681	100	28	}	}	PUNCT
iajs-2681	100	29	of	of	ADP
iajs-2681	100	30	fw	fw	PROPN
iajs-2681	100	31	-	-	PUNCT
iajs-2681	100	32	m	m	NOUN
iajs-2681	100	33	's	's	PART
iajs-2681	100	34	,	,	PUNCT
iajs-2681	100	35	where	where	SCONJ
iajs-2681	100	36	r	r	NUM
iajs-2681	100	37	:	:	PUNCT
iajs-2681	100	38	m	m	VERB
iajs-2681	100	39			NOUN
iajs-2681	100	40	nr	nr	NOUN
iajs-2681	100	41	with	with	ADP
iajs-2681	100	42	(	(	PUNCT
iajs-2681	100	43	nr	nr	PROPN
iajs-2681	100	44	,	,	PUNCT
iajs-2681	100	45	r	r	NOUN
iajs-2681	100	46	)	)	PUNCT
iajs-2681	100	47	fwfts	fwft	NOUN
iajs-2681	100	48	over	over	ADP
iajs-2681	100	49	b	b	NOUN
iajs-2681	100	50	for	for	ADP
iajs-2681	100	51	every	every	DET
iajs-2681	100	52	r.	r.	PROPN
iajs-2681	100	53	specially	specially	ADV
iajs-2681	100	54	,	,	PUNCT
iajs-2681	100	55	given	give	VERB
iajs-2681	100	56	a	a	DET
iajs-2681	100	57	family	family	NOUN
iajs-2681	100	58	{	{	PUNCT
iajs-2681	100	59	(	(	PUNCT
iajs-2681	100	60	mr	mr	PROPN
iajs-2681	100	61	,	,	PUNCT
iajs-2681	100	62	r	r	NOUN
iajs-2681	100	63	)	)	PUNCT
iajs-2681	100	64	}	}	PUNCT
iajs-2681	100	65	of	of	ADP
iajs-2681	100	66	fwfts	fwft	NOUN
iajs-2681	100	67	over	over	ADP
iajs-2681	100	68	b	b	NOUN
iajs-2681	100	69	,	,	PUNCT
iajs-2681	100	70	the	the	DET
iajs-2681	100	71	fwf	fwf	ADJ
iajs-2681	100	72	-	-	PUNCT
iajs-2681	100	73	topological	topological	ADJ
iajs-2681	100	74	product	product	NOUN
iajs-2681	100	75	∏b	∏b	NOUN
iajs-2681	101	1	mr	mr	PROPN
iajs-2681	101	2	is	be	AUX
iajs-2681	101	3	defined	define	VERB
iajs-2681	101	4	to	to	PART
iajs-2681	101	5	be	be	AUX
iajs-2681	101	6	the	the	DET
iajs-2681	101	7	fw	fw	ADJ
iajs-2681	101	8	-	-	PUNCT
iajs-2681	101	9	product	product	NOUN
iajs-2681	101	10	with	with	ADP
iajs-2681	101	11	the	the	DET
iajs-2681	101	12	fwf	fwf	ADJ
iajs-2681	101	13	-	-	PUNCT
iajs-2681	101	14	topology	topology	NOUN
iajs-2681	101	15	generated	generate	VERB
iajs-2681	101	16	by	by	ADP
iajs-2681	101	17	the	the	DET
iajs-2681	101	18	family	family	NOUN
iajs-2681	101	19	of	of	ADP
iajs-2681	101	20	proj’sr	proj’sr	PRON
iajs-2681	101	21	:	:	PUNCT
iajs-2681	101	22	∏b	∏b	X
iajs-2681	102	1	mr	mr	PROPN
iajs-2681	102	2			PROPN
iajs-2681	102	3	mr	mr	PROPN
iajs-2681	102	4	.	.	PROPN
iajs-2681	102	5	then	then	ADV
iajs-2681	102	6	for	for	ADP
iajs-2681	102	7	every	every	DET
iajs-2681	102	8	fwfts	fwft	NOUN
iajs-2681	102	9	(	(	PUNCT
iajs-2681	102	10	o	o	NOUN
iajs-2681	102	11	,	,	PUNCT
iajs-2681	102	12			NUM
iajs-2681	102	13	)	)	PUNCT
iajs-2681	102	14	over	over	ADP
iajs-2681	102	15	b	b	PROPN
iajs-2681	102	16	a	a	DET
iajs-2681	102	17	fw	fw	ADJ
iajs-2681	102	18	-	-	PUNCT
iajs-2681	102	19	m	m	NOUN
iajs-2681	102	20			NOUN
iajs-2681	102	21	:	:	PUNCT
iajs-2681	102	22	o	o	X
iajs-2681	102	23			NOUN
iajs-2681	102	24	∏b	∏b	X
iajs-2681	103	1	mr	mr	PROPN
iajs-2681	103	2	is	be	AUX
iajs-2681	103	3	a	a	DET
iajs-2681	103	4	fuzzy	fuzzy	ADJ
iajs-2681	103	5	continuous	continuous	ADJ
iajs-2681	103	6	(	(	PUNCT
iajs-2681	103	7	resp	resp	NOUN
iajs-2681	103	8	.	.	PUNCT
iajs-2681	104	1	fuzzy	fuzzy	ADJ
iajs-2681	104	2	open	open	ADJ
iajs-2681	104	3	)	)	PUNCT
iajs-2681	104	4	.	.	PUNCT
iajs-2681	105	1	for	for	ADP
iajs-2681	105	2	example	example	NOUN
iajs-2681	105	3	when	when	SCONJ
iajs-2681	105	4	mr	mr	PROPN
iajs-2681	105	5	=	=	PROPN
iajs-2681	105	6	m	m	VERB
iajs-2681	105	7	for	for	ADP
iajs-2681	105	8	every	every	DET
iajs-2681	105	9	index	index	NOUN
iajs-2681	105	10	r	r	NOUN
iajs-2681	105	11	we	we	PRON
iajs-2681	105	12	see	see	VERB
iajs-2681	105	13	that	that	SCONJ
iajs-2681	105	14	the	the	DET
iajs-2681	105	15	diagonal	diagonal	ADJ
iajs-2681	105	16			NOUN
iajs-2681	105	17	:	:	PUNCT
iajs-2681	105	18	m	m	VERB
iajs-2681	105	19			NOUN
iajs-2681	105	20	∏b	∏b	X
iajs-2681	106	1	m	m	NOUN
iajs-2681	106	2	is	be	AUX
iajs-2681	106	3	a	a	DET
iajs-2681	106	4	fuzzy	fuzzy	ADJ
iajs-2681	106	5	continuous	continuous	ADJ
iajs-2681	106	6	(	(	PUNCT
iajs-2681	106	7	resp	resp	NOUN
iajs-2681	106	8	.	.	PUNCT
iajs-2681	107	1	fuzzy	fuzzy	ADJ
iajs-2681	107	2	open	open	ADJ
iajs-2681	107	3	)	)	PUNCT
iajs-2681	107	4	iff	iff	VERB
iajs-2681	107	5	the	the	DET
iajs-2681	107	6	composition	composition	NOUN
iajs-2681	107	7	r	r	X
iajs-2681	107	8			PROPN
iajs-2681	107	9			NOUN
iajs-2681	107	10	=	=	SYM
iajs-2681	108	1	idm	idm	NOUN
iajs-2681	108	2	is	be	AUX
iajs-2681	108	3	a	a	DET
iajs-2681	108	4	fuzzy	fuzzy	ADJ
iajs-2681	108	5	continuous	continuous	ADJ
iajs-2681	108	6	(	(	PUNCT
iajs-2681	108	7	resp	resp	NOUN
iajs-2681	108	8	.	.	PUNCT
iajs-2681	109	1	fuzzy	fuzzy	ADJ
iajs-2681	109	2	open	open	ADJ
iajs-2681	109	3	)	)	PUNCT
iajs-2681	109	4	.	.	PUNCT
iajs-2681	110	1	again	again	ADV
iajs-2681	110	2	if	if	SCONJ
iajs-2681	110	3	{	{	PUNCT
iajs-2681	110	4	(	(	PUNCT
iajs-2681	110	5	mr	mr	PROPN
iajs-2681	110	6	,	,	PUNCT
iajs-2681	110	7	r	r	NOUN
iajs-2681	110	8	)	)	PUNCT
iajs-2681	110	9	}	}	PUNCT
iajs-2681	110	10	is	be	AUX
iajs-2681	110	11	a	a	DET
iajs-2681	110	12	family	family	NOUN
iajs-2681	110	13	of	of	ADP
iajs-2681	110	14	fwfts	fwft	NOUN
iajs-2681	110	15	's	's	PART
iajs-2681	110	16	over	over	ADP
iajs-2681	110	17	b	b	NOUN
iajs-2681	110	18	and	and	CCONJ
iajs-2681	110	19			PROPN
iajs-2681	110	20	:	:	PUNCT
iajs-2681	110	21	∐b	∐b	VERB
iajs-2681	110	22	mr	mr	PROPN
iajs-2681	110	23			PROPN
iajs-2681	110	24	m	m	VERB
iajs-2681	110	25	is	be	AUX
iajs-2681	110	26	a	a	DET
iajs-2681	110	27	fw	fw	NOUN
iajs-2681	110	28	-	-	PUNCT
iajs-2681	110	29	m	m	NOUN
iajs-2681	110	30	where	where	SCONJ
iajs-2681	110	31	(	(	PUNCT
iajs-2681	110	32	m	m	NOUN
iajs-2681	110	33	,	,	PUNCT
iajs-2681	110	34			PROPN
iajs-2681	110	35	)	)	PUNCT
iajs-2681	110	36	a	a	DET
iajs-2681	110	37	fwf	fwf	ADJ
iajs-2681	110	38	-	-	PUNCT
iajs-2681	110	39	topology	topology	NOUN
iajs-2681	110	40	over	over	ADP
iajs-2681	110	41	b	b	NOUN
iajs-2681	110	42	and	and	CCONJ
iajs-2681	110	43	∐b	∐b	VERB
iajs-2681	110	44	mr	mr	PROPN
iajs-2681	110	45	is	be	AUX
iajs-2681	110	46	a	a	DET
iajs-2681	110	47	fwf	fwf	ADJ
iajs-2681	110	48	-	-	PUNCT
iajs-2681	110	49	topological	topological	ADJ
iajs-2681	110	50	coproduct	coproduct	NOUN
iajs-2681	110	51	at	at	ADP
iajs-2681	110	52	the	the	DET
iajs-2681	110	53	set	set	NOUN
iajs-2681	110	54	-	-	PUNCT
iajs-2681	110	55	theoretic	theoretic	NOUN
iajs-2681	110	56	level	level	NOUN
iajs-2681	110	57	with	with	ADP
iajs-2681	110	58	the	the	DET
iajs-2681	110	59	ordinary	ordinary	ADJ
iajs-2681	110	60	coproduct	coproduct	NOUN
iajs-2681	110	61	fuzzy	fuzzy	ADJ
iajs-2681	110	62	topology	topology	NOUN
iajs-2681	110	63	,	,	PUNCT
iajs-2681	110	64	also	also	ADV
iajs-2681	110	65	for	for	ADP
iajs-2681	110	66	every	every	DET
iajs-2681	110	67	fwf	fwf	ADJ
iajs-2681	110	68	-	-	PUNCT
iajs-2681	110	69	topology	topology	NOUN
iajs-2681	110	70	(	(	PUNCT
iajs-2681	110	71	mr	mr	PROPN
iajs-2681	110	72	,	,	PUNCT
iajs-2681	110	73	r	r	PROPN
iajs-2681	110	74	)	)	PUNCT
iajs-2681	110	75	with	with	ADP
iajs-2681	110	76	the	the	DET
iajs-2681	110	77	family	family	NOUN
iajs-2681	110	78	of	of	ADP
iajs-2681	110	79	fw	fw	PROPN
iajs-2681	110	80	insertions	insertion	NOUN
iajs-2681	110	81	r	r	NOUN
iajs-2681	110	82	:	:	PUNCT
iajs-2681	110	83	mr	mr	PROPN
iajs-2681	110	84			PROPN
iajs-2681	110	85	∐b	∐b	VERB
iajs-2681	110	86	mr	mr	PROPN
iajs-2681	110	87	is	be	AUX
iajs-2681	110	88	a	a	DET
iajs-2681	110	89	fuzzy	fuzzy	ADJ
iajs-2681	110	90	continuous	continuous	ADJ
iajs-2681	110	91	(	(	PUNCT
iajs-2681	110	92	resp	resp	NOUN
iajs-2681	110	93	.	.	PUNCT
iajs-2681	111	1	fuzzy	fuzzy	ADJ
iajs-2681	111	2	open	open	ADJ
iajs-2681	111	3	)	)	PUNCT
iajs-2681	111	4	iff	iff	VERB
iajs-2681	111	5	the	the	DET
iajs-2681	111	6	composition	composition	NOUN
iajs-2681	111	7	r	r	NOUN
iajs-2681	111	8	=	=	SYM
iajs-2681	111	9			PROPN
iajs-2681	111	10			PROPN
iajs-2681	111	11	r	r	NOUN
iajs-2681	111	12	:	:	PUNCT
iajs-2681	112	1	mr	mr	PROPN
iajs-2681	112	2			PROPN
iajs-2681	112	3	m	m	VERB
iajs-2681	112	4	is	be	AUX
iajs-2681	112	5	a	a	DET
iajs-2681	112	6	fuzzy	fuzzy	ADJ
iajs-2681	112	7	continuous	continuous	ADJ
iajs-2681	112	8	(	(	PUNCT
iajs-2681	112	9	resp	resp	NOUN
iajs-2681	112	10	.	.	PUNCT
iajs-2681	113	1	fuzzy	fuzzy	ADJ
iajs-2681	113	2	open	open	ADJ
iajs-2681	113	3	)	)	PUNCT
iajs-2681	113	4	.	.	PUNCT
iajs-2681	114	1	for	for	ADP
iajs-2681	114	2	example	example	NOUN
iajs-2681	114	3	when	when	SCONJ
iajs-2681	114	4	mr	mr	PROPN
iajs-2681	114	5	=	=	PROPN
iajs-2681	114	6	m	m	VERB
iajs-2681	114	7	for	for	ADP
iajs-2681	114	8	every	every	DET
iajs-2681	114	9	index	index	NOUN
iajs-2681	114	10	r	r	NOUN
iajs-2681	114	11	we	we	PRON
iajs-2681	114	12	see	see	VERB
iajs-2681	114	13	that	that	SCONJ
iajs-2681	114	14	the	the	DET
iajs-2681	114	15	codiagonal	codiagonal	ADJ
iajs-2681	114	16			NOUN
iajs-2681	114	17	:	:	PUNCT
iajs-2681	114	18	∐b	∐b	VERB
iajs-2681	114	19	m	m	PROPN
iajs-2681	114	20	r	r	NOUN
iajs-2681	114	21			NOUN
iajs-2681	114	22	m	m	VERB
iajs-2681	114	23	is	be	AUX
iajs-2681	114	24	a	a	DET
iajs-2681	114	25	fuzzy	fuzzy	ADJ
iajs-2681	114	26	continuous	continuous	ADJ
iajs-2681	114	27	(	(	PUNCT
iajs-2681	114	28	resp	resp	NOUN
iajs-2681	114	29	.	.	PUNCT
iajs-2681	115	1	fuzzy	fuzzy	ADJ
iajs-2681	115	2	open	open	ADJ
iajs-2681	115	3	)	)	PUNCT
iajs-2681	115	4	.	.	PUNCT
iajs-2681	116	1	3.fibrewise	3.fibrewise	NUM
iajs-2681	116	2	closed	closed	ADJ
iajs-2681	116	3	and	and	CCONJ
iajs-2681	116	4	fibrewise	fibrewise	ADV
iajs-2681	116	5	open	open	ADJ
iajs-2681	116	6	fuzzy	fuzzy	ADJ
iajs-2681	116	7	topological	topological	ADJ
iajs-2681	116	8	spaces	space	NOUN
iajs-2681	116	9	we	we	PRON
iajs-2681	116	10	present	present	VERB
iajs-2681	116	11	the	the	DET
iajs-2681	116	12	ideas	idea	NOUN
iajs-2681	116	13	of	of	ADP
iajs-2681	116	14	fibrewise	fibrewise	NOUN
iajs-2681	116	15	closed	closed	ADJ
iajs-2681	116	16	and	and	CCONJ
iajs-2681	116	17	fibrewise	fibrewise	ADV
iajs-2681	116	18	open	open	ADJ
iajs-2681	116	19	fts	fts	PROPN
iajs-2681	116	20	’s	’s	PART
iajs-2681	116	21	fuzzy	fuzzy	ADJ
iajs-2681	116	22	topological	topological	ADJ
iajs-2681	116	23	spaces	space	NOUN
iajs-2681	116	24	over	over	ADP
iajs-2681	116	25	b	b	NOUN
iajs-2681	116	26	,	,	PUNCT
iajs-2681	116	27	several	several	ADJ
iajs-2681	116	28	property	property	NOUN
iajs-2681	116	29	on	on	ADP
iajs-2681	116	30	the	the	DET
iajs-2681	116	31	obtained	obtain	VERB
iajs-2681	116	32	concepts	concept	NOUN
iajs-2681	116	33	are	be	AUX
iajs-2681	116	34	studies	study	NOUN
iajs-2681	116	35	.	.	PUNCT
iajs-2681	117	1	definition	definition	NOUN
iajs-2681	117	2	3.1	3.1	NUM
iajs-2681	117	3	.	.	PUNCT
iajs-2681	118	1	the	the	DET
iajs-2681	118	2	fwfts	fwft	NOUN
iajs-2681	118	3	(	(	PUNCT
iajs-2681	118	4	m	m	NOUN
iajs-2681	118	5	,	,	PUNCT
iajs-2681	118	6			PROPN
iajs-2681	118	7	)	)	PUNCT
iajs-2681	118	8	over	over	ADP
iajs-2681	118	9	(	(	PUNCT
iajs-2681	118	10	b	b	NOUN
iajs-2681	118	11	,	,	PUNCT
iajs-2681	118	12			NOUN
iajs-2681	118	13	)	)	PUNCT
iajs-2681	118	14	is	be	AUX
iajs-2681	118	15	said	say	VERB
iajs-2681	118	16	to	to	PART
iajs-2681	118	17	be	be	AUX
iajs-2681	118	18	fibrewise	fibrewise	ADV
iajs-2681	118	19	closed	close	VERB
iajs-2681	118	20	(	(	PUNCT
iajs-2681	118	21	written	write	VERB
iajs-2681	118	22	as	as	ADP
iajs-2681	118	23	fwcfts	fwcft	NOUN
iajs-2681	118	24	)	)	PUNCT
iajs-2681	118	25	if	if	SCONJ
iajs-2681	118	26	the	the	DET
iajs-2681	118	27	proj	proj	NOUN
iajs-2681	118	28	.	.	PUNCT
iajs-2681	119	1	þ	þ	PROPN
iajs-2681	119	2	is	be	AUX
iajs-2681	119	3	a	a	DET
iajs-2681	119	4	fuzzy	fuzzy	ADJ
iajs-2681	119	5	closed	closed	ADJ
iajs-2681	119	6	.	.	PUNCT
iajs-2681	120	1	for	for	ADP
iajs-2681	120	2	example	example	NOUN
iajs-2681	120	3	,	,	PUNCT
iajs-2681	120	4	trivial	trivial	ADJ
iajs-2681	120	5	fwfts	fwft	NOUN
iajs-2681	120	6	with	with	ADP
iajs-2681	120	7	fuzzy	fuzzy	ADJ
iajs-2681	120	8	compact	compact	ADJ
iajs-2681	120	9	fibre	fibre	NOUN
iajs-2681	120	10	(	(	PUNCT
iajs-2681	120	11	see	see	VERB
iajs-2681	120	12	[	[	X
iajs-2681	120	13	4	4	NUM
iajs-2681	120	14	]	]	PUNCT
iajs-2681	120	15	)	)	PUNCT
iajs-2681	120	16	is	be	AUX
iajs-2681	120	17	a	a	DET
iajs-2681	120	18	fwcfts	fwcft	NOUN
iajs-2681	120	19	.	.	PUNCT
iajs-2681	121	1	theorem	theorem	NOUN
iajs-2681	121	2	3.2	3.2	NUM
iajs-2681	121	3	.	.	PUNCT
iajs-2681	122	1	let	let	VERB
iajs-2681	122	2			X
iajs-2681	122	3	:	:	PUNCT
iajs-2681	122	4	m	m	VERB
iajs-2681	122	5			NOUN
iajs-2681	122	6	n	n	AUX
iajs-2681	122	7	be	be	AUX
iajs-2681	122	8	fuzzy	fuzzy	ADJ
iajs-2681	122	9	closed	closed	ADJ
iajs-2681	122	10	fw	fw	NOUN
iajs-2681	122	11	-	-	PUNCT
iajs-2681	122	12	m	m	NOUN
iajs-2681	122	13	where	where	SCONJ
iajs-2681	122	14	(	(	PUNCT
iajs-2681	122	15	m	m	NOUN
iajs-2681	122	16	,	,	PUNCT
iajs-2681	122	17			PROPN
iajs-2681	122	18	)	)	PUNCT
iajs-2681	122	19	and	and	CCONJ
iajs-2681	122	20	(	(	PUNCT
iajs-2681	122	21	n	n	CCONJ
iajs-2681	122	22	,	,	PUNCT
iajs-2681	122	23			NUM
iajs-2681	122	24	)	)	PUNCT
iajs-2681	122	25	are	be	AUX
iajs-2681	122	26	fwcfts	fwcft	NOUN
iajs-2681	122	27	's	's	PART
iajs-2681	122	28	over	over	ADP
iajs-2681	122	29	(	(	PUNCT
iajs-2681	122	30	b	b	NOUN
iajs-2681	122	31	,	,	PUNCT
iajs-2681	122	32			NOUN
iajs-2681	122	33	)	)	PUNCT
iajs-2681	122	34	.	.	PUNCT
iajs-2681	123	1	then	then	ADV
iajs-2681	123	2	m	m	PROPN
iajs-2681	123	3	is	be	AUX
iajs-2681	123	4	a	a	DET
iajs-2681	123	5	fwcfts	fwcft	NOUN
iajs-2681	123	6	if	if	SCONJ
iajs-2681	123	7	n	n	NOUN
iajs-2681	123	8	is	be	AUX
iajs-2681	123	9	a	a	DET
iajs-2681	123	10	fwcfts	fwcft	NOUN
iajs-2681	123	11	.	.	PUNCT
iajs-2681	124	1	proof	proof	NOUN
iajs-2681	124	2	.	.	PUNCT
iajs-2681	125	1	assume	assume	VERB
iajs-2681	125	2	that	that	SCONJ
iajs-2681	125	3			PROPN
iajs-2681	125	4	:	:	PUNCT
iajs-2681	126	1	m	m	VERB
iajs-2681	126	2			NOUN
iajs-2681	126	3	n	n	PRON
iajs-2681	126	4	is	be	AUX
iajs-2681	126	5	a	a	DET
iajs-2681	126	6	closed	closed	ADJ
iajs-2681	126	7	fw	fw	NOUN
iajs-2681	126	8	-	-	PUNCT
iajs-2681	126	9	m	m	NOUN
iajs-2681	126	10	and	and	CCONJ
iajs-2681	126	11	n	n	PRON
iajs-2681	126	12	is	be	AUX
iajs-2681	126	13	a	a	DET
iajs-2681	126	14	fwcfts	fwcft	NOUN
iajs-2681	126	15	i.e.	i.e.	X
iajs-2681	126	16	the	the	DET
iajs-2681	126	17	proj	proj	NOUN
iajs-2681	126	18	.	.	PUNCT
iajs-2681	127	1	þn	þn	ADP
iajs-2681	127	2	:	:	PUNCT
iajs-2681	127	3	n	n	CCONJ
iajs-2681	127	4			NOUN
iajs-2681	127	5	b	b	NOUN
iajs-2681	127	6	is	be	AUX
iajs-2681	127	7	a	a	DET
iajs-2681	127	8	fuzzy	fuzzy	ADJ
iajs-2681	127	9	closed	closed	ADJ
iajs-2681	127	10	.	.	PUNCT
iajs-2681	128	1	to	to	PART
iajs-2681	128	2	prove	prove	VERB
iajs-2681	128	3	that	that	SCONJ
iajs-2681	128	4	m	m	PROPN
iajs-2681	128	5	is	be	AUX
iajs-2681	128	6	a	a	DET
iajs-2681	128	7	fwcfts	fwcft	NOUN
iajs-2681	128	8	i.e.	i.e.	X
iajs-2681	128	9	the	the	DET
iajs-2681	128	10	proj	proj	NOUN
iajs-2681	128	11	.	.	PUNCT
iajs-2681	129	1	þm	þm	VERB
iajs-2681	129	2	:	:	PUNCT
iajs-2681	130	1	m	m	VERB
iajs-2681	130	2			NOUN
iajs-2681	130	3	b	b	NOUN
iajs-2681	130	4	is	be	AUX
iajs-2681	130	5	a	a	DET
iajs-2681	130	6	fuzzy	fuzzy	ADJ
iajs-2681	130	7	closed	closed	ADJ
iajs-2681	130	8	.	.	PUNCT
iajs-2681	131	1	now	now	ADV
iajs-2681	131	2	,	,	PUNCT
iajs-2681	131	3	let	let	VERB
iajs-2681	131	4	m	m	PRON
iajs-2681	131	5			NOUN
iajs-2681	131	6	mb	mb	ADP
iajs-2681	131	7	;	;	PUNCT
iajs-2681	131	8	b	b	X
iajs-2681	131	9			PROPN
iajs-2681	131	10	b	b	NUM
iajs-2681	131	11	,	,	PUNCT
iajs-2681	131	12	and	and	CCONJ
iajs-2681	131	13	let	let	VERB
iajs-2681	131	14	f	f	PRON
iajs-2681	131	15	be	be	AUX
iajs-2681	131	16	a	a	DET
iajs-2681	131	17	fuzzy	fuzzy	ADJ
iajs-2681	131	18	closed	close	VERB
iajs-2681	131	19	set	set	NOUN
iajs-2681	131	20	of	of	ADP
iajs-2681	131	21	m.	m.	NOUN
iajs-2681	131	22	since	since	SCONJ
iajs-2681	131	23			PROPN
iajs-2681	131	24	is	be	AUX
iajs-2681	131	25	a	a	DET
iajs-2681	131	26	fuzzy	fuzzy	ADJ
iajs-2681	131	27	closed	close	VERB
iajs-2681	132	1	so	so	SCONJ
iajs-2681	132	2	that	that	SCONJ
iajs-2681	132	3	(f	(f	NOUN
iajs-2681	132	4	)	)	PUNCT
iajs-2681	132	5	is	be	AUX
iajs-2681	132	6	a	a	DET
iajs-2681	132	7	fuzzy	fuzzy	ADJ
iajs-2681	132	8	closed	close	VERB
iajs-2681	132	9	set	set	NOUN
iajs-2681	132	10	of	of	ADP
iajs-2681	132	11	(m	(m	NOUN
iajs-2681	132	12	)	)	PUNCT
iajs-2681	132	13	=	=	SYM
iajs-2681	132	14	n	n	NOUN
iajs-2681	132	15			NOUN
iajs-2681	133	1	n	n	PROPN
iajs-2681	133	2	b	b	PROPN
iajs-2681	133	3	in	in	ADP
iajs-2681	133	4	n.	n.	NOUN
iajs-2681	133	5	since	since	SCONJ
iajs-2681	133	6	þn	þn	ADV
iajs-2681	133	7	is	be	AUX
iajs-2681	133	8	a	a	DET
iajs-2681	133	9	fuzzy	fuzzy	ADJ
iajs-2681	133	10	closed	close	VERB
iajs-2681	133	11	so	so	ADV
iajs-2681	133	12	þn((f	þn((f	ADJ
iajs-2681	133	13	)	)	PUNCT
iajs-2681	133	14	)	)	PUNCT
iajs-2681	134	1	a	a	DET
iajs-2681	134	2	fuzzy	fuzzy	ADJ
iajs-2681	134	3	closed	close	VERB
iajs-2681	134	4	set	set	VERB
iajs-2681	134	5	in	in	ADP
iajs-2681	134	6	b.	b.	PROPN
iajs-2681	134	7	but	but	CCONJ
iajs-2681	134	8	,	,	PUNCT
iajs-2681	134	9	þn((f	þn((f	PROPN
iajs-2681	134	10	)	)	PUNCT
iajs-2681	134	11	)	)	PUNCT
iajs-2681	135	1	=	=	PUNCT
iajs-2681	135	2	þn	þn	ADP
iajs-2681	135	3			PROPN
iajs-2681	135	4	(f	(f	NOUN
iajs-2681	135	5	)	)	PUNCT
iajs-2681	135	6	=	=	SYM
iajs-2681	135	7	þm(f	þm(f	X
iajs-2681	135	8	)	)	PUNCT
iajs-2681	135	9	is	be	AUX
iajs-2681	135	10	a	a	DET
iajs-2681	135	11	fuzzy	fuzzy	ADJ
iajs-2681	135	12	closed	close	VERB
iajs-2681	135	13	set	set	NOUN
iajs-2681	135	14	of	of	ADP
iajs-2681	135	15	b.	b.	PROPN
iajs-2681	135	16	thus	thus	ADV
iajs-2681	135	17	,	,	PUNCT
iajs-2681	135	18	þm	þm	VERB
iajs-2681	135	19	is	be	AUX
iajs-2681	135	20	a	a	DET
iajs-2681	135	21	fuzzy	fuzzy	ADJ
iajs-2681	135	22	closed	closed	ADJ
iajs-2681	135	23	and	and	CCONJ
iajs-2681	135	24	m	m	VERB
iajs-2681	135	25	is	be	AUX
iajs-2681	135	26	a	a	DET
iajs-2681	135	27	fwcfts	fwcft	NOUN
iajs-2681	135	28	.	.	PUNCT
iajs-2681	136	1	theorem	theorem	VERB
iajs-2681	136	2	3.3	3.3	NUM
iajs-2681	136	3	.	.	PUNCT
iajs-2681	137	1	if	if	SCONJ
iajs-2681	137	2	(	(	PUNCT
iajs-2681	137	3	m	m	NOUN
iajs-2681	137	4	,	,	PUNCT
iajs-2681	137	5			PROPN
iajs-2681	137	6	)	)	PUNCT
iajs-2681	137	7	is	be	AUX
iajs-2681	137	8	a	a	DET
iajs-2681	137	9	fwfts	fwft	NOUN
iajs-2681	137	10	over	over	ADP
iajs-2681	137	11	(	(	PUNCT
iajs-2681	137	12	b	b	NOUN
iajs-2681	137	13	,	,	PUNCT
iajs-2681	137	14			NOUN
iajs-2681	137	15	)	)	PUNCT
iajs-2681	137	16	.	.	PUNCT
iajs-2681	138	1	assume	assume	VERB
iajs-2681	138	2	that	that	SCONJ
iajs-2681	138	3	mj	mj	PROPN
iajs-2681	138	4	is	be	AUX
iajs-2681	138	5	a	a	DET
iajs-2681	138	6	fwcfts	fwcft	NOUN
iajs-2681	138	7	for	for	ADP
iajs-2681	138	8	every	every	DET
iajs-2681	138	9	member	member	NOUN
iajs-2681	138	10	mj	mj	PROPN
iajs-2681	138	11	of	of	ADP
iajs-2681	138	12	a	a	DET
iajs-2681	138	13	finite	finite	NOUN
iajs-2681	138	14	covering	covering	NOUN
iajs-2681	138	15	of	of	ADP
iajs-2681	138	16	m.	m.	NOUN
iajs-2681	138	17	then	then	ADV
iajs-2681	138	18	m	m	VERB
iajs-2681	138	19	is	be	AUX
iajs-2681	138	20	a	a	DET
iajs-2681	138	21	fwcfts	fwcft	NOUN
iajs-2681	138	22	.	.	PUNCT
iajs-2681	139	1	proof	proof	NOUN
iajs-2681	139	2	.	.	PUNCT
iajs-2681	140	1	assume	assume	VERB
iajs-2681	140	2	that	that	SCONJ
iajs-2681	140	3	m	m	PROPN
iajs-2681	140	4	is	be	AUX
iajs-2681	140	5	a	a	DET
iajs-2681	140	6	fwfts	fwft	NOUN
iajs-2681	140	7	over	over	ADP
iajs-2681	140	8	b	b	NOUN
iajs-2681	140	9	,	,	PUNCT
iajs-2681	140	10	then	then	ADV
iajs-2681	140	11	the	the	DET
iajs-2681	140	12	proj	proj	NOUN
iajs-2681	140	13	.	.	PUNCT
iajs-2681	141	1	þm	þm	VERB
iajs-2681	141	2	:	:	PUNCT
iajs-2681	142	1	m	m	VERB
iajs-2681	142	2			NOUN
iajs-2681	142	3	b	b	AUX
iajs-2681	142	4	exist	exist	VERB
iajs-2681	142	5	.	.	PUNCT
iajs-2681	143	1	to	to	PART
iajs-2681	143	2	prove	prove	VERB
iajs-2681	143	3	that	that	SCONJ
iajs-2681	143	4	þ	þ	PROPN
iajs-2681	143	5	is	be	AUX
iajs-2681	143	6	a	a	DET
iajs-2681	143	7	fuzzy	fuzzy	ADJ
iajs-2681	143	8	closed	closed	ADJ
iajs-2681	143	9	.	.	PUNCT
iajs-2681	144	1	since	since	SCONJ
iajs-2681	144	2	mj	mj	PROPN
iajs-2681	144	3	is	be	AUX
iajs-2681	144	4	a	a	DET
iajs-2681	144	5	fwcfts	fwcft	NOUN
iajs-2681	144	6	,	,	PUNCT
iajs-2681	144	7	then	then	ADV
iajs-2681	144	8	the	the	DET
iajs-2681	144	9	proj	proj	NOUN
iajs-2681	144	10	.	.	PUNCT
iajs-2681	145	1	þmj	þmj	ADJ
iajs-2681	145	2	:	:	PUNCT
iajs-2681	145	3	mj	mj	PROPN
iajs-2681	145	4	b	b	PROPN
iajs-2681	145	5	is	be	AUX
iajs-2681	145	6	a	a	DET
iajs-2681	145	7	fuzzy	fuzzy	ADJ
iajs-2681	145	8	closed	close	VERB
iajs-2681	145	9	for	for	SCONJ
iajs-2681	145	10	every	every	DET
iajs-2681	145	11	member	member	NOUN
iajs-2681	145	12	mj	mj	PROPN
iajs-2681	145	13	of	of	ADP
iajs-2681	145	14	a	a	DET
iajs-2681	145	15	finite	finite	NOUN
iajs-2681	145	16	covering	covering	NOUN
iajs-2681	145	17	of	of	ADP
iajs-2681	145	18	m.	m.	NOUN
iajs-2681	145	19	let	let	VERB
iajs-2681	145	20	f	f	PROPN
iajs-2681	145	21			PROPN
iajs-2681	145	22	m	m	AUX
iajs-2681	145	23	be	be	VERB
iajs-2681	145	24	a	a	DET
iajs-2681	145	25	fuzzy	fuzzy	ADJ
iajs-2681	145	26	closed	close	VERB
iajs-2681	145	27	set	set	NOUN
iajs-2681	145	28	.	.	PUNCT
iajs-2681	146	1	then	then	ADV
iajs-2681	146	2	þ(f	þ(f	PROPN
iajs-2681	146	3	)	)	PUNCT
iajs-2681	146	4	=	=	SYM
iajs-2681	146	5	⋃	⋃	PROPN
iajs-2681	146	6	þj(mj	þj(mj	NOUN
iajs-2681	146	7	⋂	⋂	PROPN
iajs-2681	146	8	f	f	X
iajs-2681	146	9	)	)	PUNCT
iajs-2681	146	10	which	which	PRON
iajs-2681	146	11	is	be	AUX
iajs-2681	146	12	a	a	DET
iajs-2681	146	13	finite	finite	ADJ
iajs-2681	146	14	union	union	NOUN
iajs-2681	146	15	of	of	ADP
iajs-2681	146	16	fuzzy	fuzzy	ADJ
iajs-2681	146	17	closed	close	VERB
iajs-2681	146	18	sets	set	NOUN
iajs-2681	146	19	and	and	CCONJ
iajs-2681	146	20	so	so	ADV
iajs-2681	146	21	þ	þ	PROPN
iajs-2681	146	22	is	be	AUX
iajs-2681	146	23	a	a	DET
iajs-2681	146	24	fuzzy	fuzzy	ADJ
iajs-2681	146	25	closed	close	VERB
iajs-2681	146	26	,	,	PUNCT
iajs-2681	146	27	so	so	SCONJ
iajs-2681	146	28	that	that	SCONJ
iajs-2681	146	29	m	m	NOUN
iajs-2681	146	30	is	be	AUX
iajs-2681	146	31	a	a	DET
iajs-2681	146	32	fwcfts	fwcft	NOUN
iajs-2681	146	33	.	.	PUNCT
iajs-2681	147	1	theorem	theorem	VERB
iajs-2681	147	2	3.4	3.4	NUM
iajs-2681	147	3	.	.	PUNCT
iajs-2681	148	1	let	let	VERB
iajs-2681	148	2	(	(	PUNCT
iajs-2681	148	3	m	m	NOUN
iajs-2681	148	4	,	,	PUNCT
iajs-2681	148	5			PROPN
iajs-2681	148	6	)	)	PUNCT
iajs-2681	148	7	be	be	VERB
iajs-2681	148	8	a	a	DET
iajs-2681	148	9	fwfts	fwft	NOUN
iajs-2681	148	10	over	over	ADP
iajs-2681	148	11	(	(	PUNCT
iajs-2681	148	12	b	b	NOUN
iajs-2681	148	13	,	,	PUNCT
iajs-2681	148	14			NOUN
iajs-2681	148	15	)	)	PUNCT
iajs-2681	148	16	.	.	PUNCT
iajs-2681	149	1	then	then	ADV
iajs-2681	149	2	,	,	PUNCT
iajs-2681	149	3	(	(	PUNCT
iajs-2681	149	4	m	m	NOUN
iajs-2681	149	5	,	,	PUNCT
iajs-2681	149	6			PROPN
iajs-2681	149	7	)	)	PUNCT
iajs-2681	149	8	is	be	AUX
iajs-2681	149	9	a	a	DET
iajs-2681	149	10	fwcfts	fwcft	NOUN
iajs-2681	149	11	iff	iff	NOUN
iajs-2681	149	12	for	for	ADP
iajs-2681	149	13	every	every	DET
iajs-2681	149	14	fibre	fibre	NOUN
iajs-2681	149	15	mb	mb	NOUN
iajs-2681	149	16	of	of	ADP
iajs-2681	149	17	m	m	PROPN
iajs-2681	149	18	and	and	CCONJ
iajs-2681	149	19	every	every	PRON
iajs-2681	149	20	fuzzy	fuzzy	ADJ
iajs-2681	149	21	open	open	ADJ
iajs-2681	149	22	set	set	NOUN
iajs-2681	149	23	u	u	NOUN
iajs-2681	149	24	of	of	ADP
iajs-2681	149	25	mb	mb	ADP
iajs-2681	149	26			PROPN
iajs-2681	149	27	m	m	PROPN
iajs-2681	149	28	,	,	PUNCT
iajs-2681	149	29	there	there	PRON
iajs-2681	149	30	is	be	VERB
iajs-2681	149	31	a	a	DET
iajs-2681	149	32	fuzzy	fuzzy	ADJ
iajs-2681	149	33	open	open	NOUN
iajs-2681	149	34	set	set	NOUN
iajs-2681	149	35	o	o	NOUN
iajs-2681	149	36	of	of	ADP
iajs-2681	149	37	b	b	PROPN
iajs-2681	149	38	where	where	SCONJ
iajs-2681	149	39	mo	mo	PROPN
iajs-2681	149	40			PROPN
iajs-2681	149	41	u.	u.	PROPN
iajs-2681	149	42	ibn	ibn	PROPN
iajs-2681	149	43	al	al	PROPN
iajs-2681	149	44	-	-	PUNCT
iajs-2681	149	45	haitham	haitham	PROPN
iajs-2681	149	46	jour	jour	X
iajs-2681	149	47	.	.	PROPN
iajs-2681	150	1	for	for	ADP
iajs-2681	150	2	pure	pure	ADJ
iajs-2681	150	3	&	&	CCONJ
iajs-2681	150	4	appl	appl	PROPN
iajs-2681	150	5	.	.	PUNCT
iajs-2681	151	1	sci	sci	PROPN
iajs-2681	151	2	.	.	PROPN
iajs-2681	152	1	34(3)2021	34(3)2021	NUM
iajs-2681	152	2	91	91	NUM
iajs-2681	152	3	proof	proof	NOUN
iajs-2681	152	4	.	.	PUNCT
iajs-2681	153	1	(	(	PUNCT
iajs-2681	153	2			NOUN
iajs-2681	153	3	)	)	PUNCT
iajs-2681	153	4	assume	assume	VERB
iajs-2681	153	5	that	that	SCONJ
iajs-2681	153	6	m	m	PROPN
iajs-2681	153	7	is	be	AUX
iajs-2681	153	8	a	a	DET
iajs-2681	153	9	fefts	feft	NOUN
iajs-2681	153	10	i.e.	i.e.	X
iajs-2681	153	11	the	the	DET
iajs-2681	153	12	proj	proj	NOUN
iajs-2681	153	13	.	.	PUNCT
iajs-2681	154	1	þ	þ	NOUN
iajs-2681	154	2	:	:	PUNCT
iajs-2681	155	1	m	m	VERB
iajs-2681	155	2			NOUN
iajs-2681	155	3	b	b	X
iajs-2681	155	4	is	be	AUX
iajs-2681	155	5	a	a	DET
iajs-2681	155	6	fuzzy	fuzzy	ADJ
iajs-2681	155	7	closed	closed	ADJ
iajs-2681	155	8	.	.	PUNCT
iajs-2681	156	1	now	now	ADV
iajs-2681	156	2	,	,	PUNCT
iajs-2681	156	3	let	let	VERB
iajs-2681	156	4	b	b	NUM
iajs-2681	156	5			PROPN
iajs-2681	156	6	b	b	NOUN
iajs-2681	156	7	and	and	CCONJ
iajs-2681	156	8	u	u	NOUN
iajs-2681	156	9	be	be	VERB
iajs-2681	156	10	fuzzy	fuzzy	ADJ
iajs-2681	156	11	open	open	ADJ
iajs-2681	156	12	set	set	NOUN
iajs-2681	156	13	of	of	ADP
iajs-2681	156	14	mb	mb	NOUN
iajs-2681	156	15	,	,	PUNCT
iajs-2681	156	16	so	so	SCONJ
iajs-2681	156	17	we	we	PRON
iajs-2681	156	18	have	have	VERB
iajs-2681	156	19	m	m	PROPN
iajs-2681	156	20	–	–	PUNCT
iajs-2681	156	21	u	u	NOUN
iajs-2681	156	22	is	be	AUX
iajs-2681	156	23	a	a	DET
iajs-2681	156	24	fuzzy	fuzzy	ADJ
iajs-2681	156	25	closed	close	VERB
iajs-2681	156	26	set	set	ADJ
iajs-2681	156	27	and	and	CCONJ
iajs-2681	156	28	þ(m	þ(m	ADJ
iajs-2681	156	29	–	–	PUNCT
iajs-2681	156	30	u	u	NOUN
iajs-2681	156	31	)	)	PUNCT
iajs-2681	156	32	is	be	AUX
iajs-2681	156	33	a	a	DET
iajs-2681	156	34	fuzzy	fuzzy	ADJ
iajs-2681	156	35	closed	close	VERB
iajs-2681	156	36	set	set	NOUN
iajs-2681	156	37	.	.	PUNCT
iajs-2681	157	1	let	let	VERB
iajs-2681	157	2	o	o	NOUN
iajs-2681	157	3	=	=	SYM
iajs-2681	157	4	b	b	PROPN
iajs-2681	157	5	–	–	PUNCT
iajs-2681	157	6	þ(m	þ(m	ADJ
iajs-2681	157	7	–	–	PUNCT
iajs-2681	157	8	u	u	NOUN
iajs-2681	157	9	)	)	PUNCT
iajs-2681	157	10	is	be	AUX
iajs-2681	157	11	a	a	DET
iajs-2681	157	12	fuzzy	fuzzy	ADJ
iajs-2681	157	13	open	open	ADJ
iajs-2681	157	14	set	set	NOUN
iajs-2681	157	15	of	of	ADP
iajs-2681	157	16	b.	b.	PROPN
iajs-2681	157	17	hence	hence	PROPN
iajs-2681	157	18	,	,	PUNCT
iajs-2681	157	19	mo	mo	PROPN
iajs-2681	157	20	=	=	PROPN
iajs-2681	157	21	þ	þ	PROPN
iajs-2681	157	22	–	–	PUNCT
iajs-2681	157	23	1(b	1(b	NUM
iajs-2681	157	24	–	–	PUNCT
iajs-2681	157	25	þ(m	þ(m	PROPN
iajs-2681	157	26	–	–	PUNCT
iajs-2681	157	27	u	u	NOUN
iajs-2681	157	28	)	)	PUNCT
iajs-2681	157	29	)	)	PUNCT
iajs-2681	157	30	which	which	PRON
iajs-2681	157	31	is	be	AUX
iajs-2681	157	32	a	a	DET
iajs-2681	157	33	subset	subset	NOUN
iajs-2681	157	34	of	of	ADP
iajs-2681	157	35	u.	u.	NOUN
iajs-2681	157	36	thus	thus	ADV
iajs-2681	157	37	mo	mo	PROPN
iajs-2681	157	38			PROPN
iajs-2681	157	39	u.	u.	PROPN
iajs-2681	157	40	(	(	PUNCT
iajs-2681	157	41			NOUN
iajs-2681	157	42	)	)	PUNCT
iajs-2681	157	43	suppose	suppose	VERB
iajs-2681	157	44	that	that	SCONJ
iajs-2681	157	45	the	the	DET
iajs-2681	157	46	assumption	assumption	NOUN
iajs-2681	157	47	is	be	AUX
iajs-2681	157	48	hold	hold	NOUN
iajs-2681	157	49	,	,	PUNCT
iajs-2681	157	50	to	to	PART
iajs-2681	157	51	show	show	VERB
iajs-2681	157	52	that	that	SCONJ
iajs-2681	157	53	m	m	PROPN
iajs-2681	157	54	is	be	AUX
iajs-2681	157	55	a	a	DET
iajs-2681	157	56	fwcfts	fwcft	NOUN
iajs-2681	157	57	.	.	PUNCT
iajs-2681	158	1	let	let	VERB
iajs-2681	158	2	f	f	PRON
iajs-2681	158	3	be	be	AUX
iajs-2681	158	4	fuzzy	fuzzy	ADV
iajs-2681	158	5	closed	close	VERB
iajs-2681	158	6	set	set	VERB
iajs-2681	158	7	in	in	ADP
iajs-2681	158	8	m.	m.	NOUN
iajs-2681	158	9	let	let	VERB
iajs-2681	158	10	b	b	PROPN
iajs-2681	158	11			PROPN
iajs-2681	158	12	b	b	PROPN
iajs-2681	158	13	–	–	PUNCT
iajs-2681	158	14	þ(f	þ(f	NOUN
iajs-2681	158	15	)	)	PUNCT
iajs-2681	158	16	and	and	CCONJ
iajs-2681	158	17	every	every	DET
iajs-2681	158	18	fuzzy	fuzzy	ADJ
iajs-2681	158	19	open	open	ADJ
iajs-2681	158	20	set	set	NOUN
iajs-2681	158	21	u	u	NOUN
iajs-2681	158	22	of	of	ADP
iajs-2681	158	23	mb	mb	PROPN
iajs-2681	158	24			PROPN
iajs-2681	158	25	m.	m.	NOUN
iajs-2681	158	26	by	by	ADP
iajs-2681	158	27	assumption	assumption	NOUN
iajs-2681	158	28	there	there	PRON
iajs-2681	158	29	is	be	VERB
iajs-2681	158	30	a	a	DET
iajs-2681	158	31	fuzzy	fuzzy	ADJ
iajs-2681	158	32	open	open	NOUN
iajs-2681	158	33	set	set	NOUN
iajs-2681	158	34	o	o	NOUN
iajs-2681	158	35	of	of	ADP
iajs-2681	158	36	b	b	NOUN
iajs-2681	158	37	such	such	ADJ
iajs-2681	159	1	that	that	DET
iajs-2681	159	2	mo	mo	PROPN
iajs-2681	159	3			PROPN
iajs-2681	159	4	u.	u.	PROPN
iajs-2681	160	1	it	it	PRON
iajs-2681	160	2	’s	’	VERB
iajs-2681	160	3	easy	easy	ADJ
iajs-2681	160	4	to	to	PART
iajs-2681	160	5	show	show	VERB
iajs-2681	160	6	that	that	SCONJ
iajs-2681	160	7	o	o	NOUN
iajs-2681	160	8			PROPN
iajs-2681	160	9	b	b	PROPN
iajs-2681	160	10	–	–	PUNCT
iajs-2681	160	11	þ(f	þ(f	NOUN
iajs-2681	160	12	)	)	PUNCT
iajs-2681	160	13	.	.	PUNCT
iajs-2681	161	1	so	so	ADV
iajs-2681	161	2	that	that	PRON
iajs-2681	161	3	b	b	X
iajs-2681	161	4	–	–	PUNCT
iajs-2681	161	5	þ(f	þ(f	NOUN
iajs-2681	161	6	)	)	PUNCT
iajs-2681	161	7	is	be	AUX
iajs-2681	161	8	a	a	DET
iajs-2681	161	9	fuzzy	fuzzy	ADJ
iajs-2681	161	10	open	open	ADJ
iajs-2681	161	11	set	set	NOUN
iajs-2681	161	12	in	in	ADP
iajs-2681	161	13	b.	b.	PROPN
iajs-2681	161	14	hence	hence	ADV
iajs-2681	161	15	þ(f	þ(f	PROPN
iajs-2681	161	16	)	)	PUNCT
iajs-2681	161	17	is	be	AUX
iajs-2681	161	18	a	a	DET
iajs-2681	161	19	fuzzy	fuzzy	ADJ
iajs-2681	161	20	closed	close	VERB
iajs-2681	161	21	in	in	ADP
iajs-2681	161	22	b	b	PROPN
iajs-2681	161	23	,	,	PUNCT
iajs-2681	161	24	þ	þ	PROPN
iajs-2681	161	25	is	be	AUX
iajs-2681	161	26	a	a	DET
iajs-2681	161	27	fuzzy	fuzzy	ADJ
iajs-2681	161	28	closed	closed	ADJ
iajs-2681	161	29	and	and	CCONJ
iajs-2681	161	30	m	m	VERB
iajs-2681	161	31	is	be	AUX
iajs-2681	161	32	a	a	DET
iajs-2681	161	33	fwcfts	fwcft	NOUN
iajs-2681	161	34	.	.	PUNCT
iajs-2681	162	1	definition	definition	NOUN
iajs-2681	162	2	3.5	3.5	NUM
iajs-2681	162	3	.	.	PUNCT
iajs-2681	163	1	the	the	DET
iajs-2681	163	2	fwfts	fwft	NOUN
iajs-2681	163	3	(	(	PUNCT
iajs-2681	163	4	m	m	NOUN
iajs-2681	163	5	,	,	PUNCT
iajs-2681	163	6			PROPN
iajs-2681	163	7	)	)	PUNCT
iajs-2681	163	8	over	over	ADP
iajs-2681	163	9	(	(	PUNCT
iajs-2681	163	10	b	b	NOUN
iajs-2681	163	11	,	,	PUNCT
iajs-2681	163	12			NOUN
iajs-2681	163	13	)	)	PUNCT
iajs-2681	163	14	is	be	AUX
iajs-2681	163	15	said	say	VERB
iajs-2681	163	16	to	to	PART
iajs-2681	163	17	be	be	AUX
iajs-2681	163	18	fibrewise	fibrewise	ADV
iajs-2681	163	19	open	open	ADJ
iajs-2681	163	20	(	(	PUNCT
iajs-2681	163	21	written	write	VERB
iajs-2681	163	22	as	as	ADP
iajs-2681	163	23	fwofts	fwoft	NOUN
iajs-2681	163	24	)	)	PUNCT
iajs-2681	163	25	if	if	SCONJ
iajs-2681	163	26	the	the	DET
iajs-2681	163	27	proj	proj	NOUN
iajs-2681	163	28	.	.	PUNCT
iajs-2681	164	1	þ	þ	PROPN
iajs-2681	164	2	is	be	AUX
iajs-2681	164	3	a	a	DET
iajs-2681	164	4	fuzzy	fuzzy	ADJ
iajs-2681	164	5	open	open	NOUN
iajs-2681	164	6	.	.	PUNCT
iajs-2681	165	1	for	for	ADP
iajs-2681	165	2	example	example	NOUN
iajs-2681	165	3	,	,	PUNCT
iajs-2681	165	4	trivial	trivial	ADJ
iajs-2681	165	5	fwfts	fwft	NOUN
iajs-2681	165	6	's	's	PART
iajs-2681	165	7	are	be	AUX
iajs-2681	165	8	always	always	ADV
iajs-2681	165	9	fwofts	fwoft	NOUN
iajs-2681	165	10	.	.	PUNCT
iajs-2681	166	1	theorem	theorem	VERB
iajs-2681	166	2	3.6	3.6	NUM
iajs-2681	166	3	.	.	PUNCT
iajs-2681	167	1	let	let	VERB
iajs-2681	167	2			X
iajs-2681	167	3	:	:	PUNCT
iajs-2681	167	4	m	m	VERB
iajs-2681	167	5			NOUN
iajs-2681	167	6	n	n	AUX
iajs-2681	167	7	be	be	AUX
iajs-2681	167	8	a	a	DET
iajs-2681	167	9	fuzzy	fuzzy	ADJ
iajs-2681	167	10	open	open	ADJ
iajs-2681	167	11	fw	fw	NOUN
iajs-2681	167	12	-	-	PUNCT
iajs-2681	167	13	m	m	NOUN
iajs-2681	167	14	where	where	SCONJ
iajs-2681	167	15	(	(	PUNCT
iajs-2681	167	16	m	m	NOUN
iajs-2681	167	17	,	,	PUNCT
iajs-2681	167	18			PROPN
iajs-2681	167	19	)	)	PUNCT
iajs-2681	167	20	,	,	PUNCT
iajs-2681	167	21	(	(	PUNCT
iajs-2681	167	22	n	n	X
iajs-2681	167	23	,	,	PUNCT
iajs-2681	167	24			NUM
iajs-2681	167	25	)	)	PUNCT
iajs-2681	167	26	are	be	AUX
iajs-2681	167	27	fwfts	fwft	NOUN
iajs-2681	167	28	over	over	ADP
iajs-2681	167	29	(	(	PUNCT
iajs-2681	167	30	b	b	NOUN
iajs-2681	167	31	,	,	PUNCT
iajs-2681	167	32			NOUN
iajs-2681	167	33	)	)	PUNCT
iajs-2681	167	34	.	.	PUNCT
iajs-2681	168	1	if	if	SCONJ
iajs-2681	168	2	n	n	PRON
iajs-2681	168	3	is	be	AUX
iajs-2681	168	4	a	a	DET
iajs-2681	168	5	fwofts	fwoft	NOUN
iajs-2681	168	6	,	,	PUNCT
iajs-2681	168	7	then	then	ADV
iajs-2681	168	8	m	m	VERB
iajs-2681	168	9	is	be	AUX
iajs-2681	168	10	a	a	DET
iajs-2681	168	11	fwofts	fwoft	NOUN
iajs-2681	168	12	.	.	PUNCT
iajs-2681	169	1	proof	proof	NOUN
iajs-2681	169	2	.	.	PUNCT
iajs-2681	170	1	since	since	SCONJ
iajs-2681	170	2	n	n	NUM
iajs-2681	170	3	is	be	AUX
iajs-2681	170	4	a	a	DET
iajs-2681	170	5	fwofts	fwoft	NOUN
iajs-2681	170	6	,	,	PUNCT
iajs-2681	170	7	we	we	PRON
iajs-2681	170	8	have	have	AUX
iajs-2681	170	9	þn	þn	ADP
iajs-2681	170	10	:	:	PUNCT
iajs-2681	170	11	n	n	NUM
iajs-2681	170	12			NOUN
iajs-2681	170	13	b	b	NOUN
iajs-2681	170	14	is	be	AUX
iajs-2681	170	15	a	a	DET
iajs-2681	170	16	fuzzy	fuzzy	ADJ
iajs-2681	170	17	open	open	NOUN
iajs-2681	170	18	.	.	PUNCT
iajs-2681	171	1	to	to	PART
iajs-2681	171	2	prove	prove	VERB
iajs-2681	171	3	that	that	SCONJ
iajs-2681	171	4	þm	þm	PROPN
iajs-2681	171	5	is	be	AUX
iajs-2681	171	6	a	a	DET
iajs-2681	171	7	fuzzy	fuzzy	ADJ
iajs-2681	171	8	open	open	ADJ
iajs-2681	171	9	,	,	PUNCT
iajs-2681	171	10	i.e.	i.e.	X
iajs-2681	171	11	the	the	DET
iajs-2681	171	12	proj	proj	NOUN
iajs-2681	171	13	.	.	PUNCT
iajs-2681	172	1	þm	þm	VERB
iajs-2681	172	2	:	:	PUNCT
iajs-2681	173	1	m	m	VERB
iajs-2681	173	2			NOUN
iajs-2681	173	3	b	b	NOUN
iajs-2681	173	4	is	be	AUX
iajs-2681	173	5	a	a	DET
iajs-2681	173	6	fuzzy	fuzzy	ADJ
iajs-2681	173	7	open	open	ADJ
iajs-2681	173	8	.	.	PUNCT
iajs-2681	174	1	let	let	VERB
iajs-2681	174	2	m	m	PRON
iajs-2681	174	3			NOUN
iajs-2681	174	4	mb	mb	ADP
iajs-2681	174	5	;	;	PUNCT
iajs-2681	174	6	b	b	X
iajs-2681	174	7			PROPN
iajs-2681	174	8	b	b	NUM
iajs-2681	174	9	,	,	PUNCT
iajs-2681	174	10	and	and	CCONJ
iajs-2681	174	11	let	let	VERB
iajs-2681	174	12	u	u	PRON
iajs-2681	174	13	be	be	AUX
iajs-2681	174	14	a	a	DET
iajs-2681	174	15	fuzzy	fuzzy	ADJ
iajs-2681	174	16	open	open	ADJ
iajs-2681	174	17	set	set	NOUN
iajs-2681	174	18	of	of	ADP
iajs-2681	174	19	m	m	PROPN
iajs-2681	174	20	,	,	PUNCT
iajs-2681	174	21	(u	(u	ADJ
iajs-2681	174	22	)	)	PUNCT
iajs-2681	174	23	is	be	AUX
iajs-2681	174	24	a	a	DET
iajs-2681	174	25	fuzzy	fuzzy	ADJ
iajs-2681	174	26	open	open	ADJ
iajs-2681	174	27	set	set	NOUN
iajs-2681	174	28	of	of	ADP
iajs-2681	174	29	(m	(m	NOUN
iajs-2681	174	30	)	)	PUNCT
iajs-2681	174	31	=	=	SYM
iajs-2681	174	32	n	n	PROPN
iajs-2681	174	33			NOUN
iajs-2681	174	34	nb	nb	PROPN
iajs-2681	174	35			PROPN
iajs-2681	174	36	n	n	PROPN
iajs-2681	174	37	since	since	SCONJ
iajs-2681	174	38			PROPN
iajs-2681	174	39	is	be	AUX
iajs-2681	174	40	a	a	DET
iajs-2681	174	41	fuzzy	fuzzy	ADJ
iajs-2681	174	42	open	open	NOUN
iajs-2681	174	43	.	.	PUNCT
iajs-2681	175	1	also	also	ADV
iajs-2681	175	2	,	,	PUNCT
iajs-2681	175	3	since	since	SCONJ
iajs-2681	175	4	n	n	PRON
iajs-2681	175	5	is	be	AUX
iajs-2681	175	6	a	a	DET
iajs-2681	175	7	fwofts	fwoft	NOUN
iajs-2681	175	8	,	,	PUNCT
iajs-2681	175	9	then	then	ADV
iajs-2681	175	10	the	the	DET
iajs-2681	175	11	proj	proj	NOUN
iajs-2681	175	12	.	.	PUNCT
iajs-2681	176	1	þn	þn	ADP
iajs-2681	176	2	:	:	PUNCT
iajs-2681	176	3	n	n	CCONJ
iajs-2681	176	4			NOUN
iajs-2681	176	5	b	b	NOUN
iajs-2681	176	6	is	be	AUX
iajs-2681	176	7	a	a	DET
iajs-2681	176	8	fuzzy	fuzzy	ADJ
iajs-2681	176	9	open	open	ADJ
iajs-2681	176	10	and	and	CCONJ
iajs-2681	176	11	þn((u	þn((u	ADJ
iajs-2681	176	12	)	)	PUNCT
iajs-2681	176	13	)	)	PUNCT
iajs-2681	177	1	is	be	AUX
iajs-2681	177	2	a	a	DET
iajs-2681	177	3	fuzzy	fuzzy	ADJ
iajs-2681	177	4	open	open	NOUN
iajs-2681	177	5	set	set	NOUN
iajs-2681	177	6	in	in	ADP
iajs-2681	177	7	b	b	NOUN
iajs-2681	177	8	,	,	PUNCT
iajs-2681	177	9	but	but	CCONJ
iajs-2681	177	10	þn((u	þn((u	ADJ
iajs-2681	177	11	)	)	PUNCT
iajs-2681	177	12	)	)	PUNCT
iajs-2681	178	1	=	=	PUNCT
iajs-2681	178	2	þn	þn	ADP
iajs-2681	178	3			PROPN
iajs-2681	178	4	(u	(u	PROPN
iajs-2681	178	5	)	)	PUNCT
iajs-2681	178	6	=	=	SYM
iajs-2681	178	7	þm	þm	PROPN
iajs-2681	178	8	(	(	PUNCT
iajs-2681	178	9	u	u	NOUN
iajs-2681	178	10	)	)	PUNCT
iajs-2681	178	11	.	.	PUNCT
iajs-2681	179	1	so	so	ADV
iajs-2681	179	2	that	that	SCONJ
iajs-2681	179	3	þm	þm	PROPN
iajs-2681	179	4	is	be	AUX
iajs-2681	179	5	a	a	DET
iajs-2681	179	6	fuzzy	fuzzy	ADJ
iajs-2681	179	7	open	open	ADJ
iajs-2681	179	8	and	and	CCONJ
iajs-2681	179	9	m	m	VERB
iajs-2681	179	10	is	be	AUX
iajs-2681	179	11	a	a	DET
iajs-2681	179	12	fwofts	fwoft	NOUN
iajs-2681	179	13	.	.	PUNCT
iajs-2681	180	1	theorem	theorem	VERB
iajs-2681	180	2	3.7	3.7	NUM
iajs-2681	180	3	.	.	PUNCT
iajs-2681	181	1	let	let	VERB
iajs-2681	181	2			X
iajs-2681	181	3	:	:	PUNCT
iajs-2681	181	4	m	m	VERB
iajs-2681	181	5			NOUN
iajs-2681	181	6	n	n	AUX
iajs-2681	181	7	be	be	AUX
iajs-2681	181	8	a	a	DET
iajs-2681	181	9	fw	fw	ADJ
iajs-2681	181	10	-	-	PUNCT
iajs-2681	181	11	m	m	NOUN
iajs-2681	181	12	,	,	PUNCT
iajs-2681	181	13	where	where	SCONJ
iajs-2681	181	14	(	(	PUNCT
iajs-2681	181	15	m	m	NOUN
iajs-2681	181	16	,	,	PUNCT
iajs-2681	181	17			PROPN
iajs-2681	181	18	)	)	PUNCT
iajs-2681	181	19	,	,	PUNCT
iajs-2681	181	20	(	(	PUNCT
iajs-2681	181	21	n	n	X
iajs-2681	181	22	,	,	PUNCT
iajs-2681	181	23			NUM
iajs-2681	181	24	)	)	PUNCT
iajs-2681	181	25	are	be	AUX
iajs-2681	181	26	fwfts	fwft	NOUN
iajs-2681	181	27	's	's	PART
iajs-2681	181	28	over	over	ADP
iajs-2681	181	29	(	(	PUNCT
iajs-2681	181	30	b	b	NOUN
iajs-2681	181	31	,	,	PUNCT
iajs-2681	181	32			NOUN
iajs-2681	181	33	)	)	PUNCT
iajs-2681	181	34	.	.	PUNCT
iajs-2681	182	1	assume	assume	VERB
iajs-2681	182	2	that	that	SCONJ
iajs-2681	182	3	the	the	DET
iajs-2681	182	4	product	product	NOUN
iajs-2681	182	5	:	:	PUNCT
iajs-2681	182	6	idm	idm	PROPN
iajs-2681	182	7			VERB
iajs-2681	182	8			PROPN
iajs-2681	182	9	:	:	PUNCT
iajs-2681	182	10	(	(	PUNCT
iajs-2681	182	11	m	m	VERB
iajs-2681	182	12	b	b	PROPN
iajs-2681	182	13	m	m	PROPN
iajs-2681	182	14	,	,	PUNCT
iajs-2681	182	15			PROPN
iajs-2681	182	16			PROPN
iajs-2681	182	17			PROPN
iajs-2681	182	18	)	)	PUNCT
iajs-2681	182	19			PUNCT
iajs-2681	182	20	(	(	PUNCT
iajs-2681	182	21	m	m	PROPN
iajs-2681	182	22	b	b	PROPN
iajs-2681	182	23	n	n	CCONJ
iajs-2681	182	24	,	,	PUNCT
iajs-2681	182	25			PROPN
iajs-2681	182	26			NOUN
iajs-2681	182	27			PROPN
iajs-2681	182	28	)	)	PUNCT
iajs-2681	182	29	is	be	AUX
iajs-2681	182	30	a	a	DET
iajs-2681	182	31	fuzzy	fuzzy	ADJ
iajs-2681	182	32	open	open	ADJ
iajs-2681	182	33	and	and	CCONJ
iajs-2681	182	34	m	m	VERB
iajs-2681	182	35	is	be	AUX
iajs-2681	182	36	a	a	DET
iajs-2681	182	37	fwofts	fwoft	NOUN
iajs-2681	182	38	.	.	PUNCT
iajs-2681	183	1	then	then	ADV
iajs-2681	183	2			PROPN
iajs-2681	183	3	itself	itself	PRON
iajs-2681	183	4	fuzzy	fuzzy	ADV
iajs-2681	183	5	open	open	ADJ
iajs-2681	183	6	.	.	PUNCT
iajs-2681	184	1	proof	proof	NOUN
iajs-2681	184	2	.	.	PUNCT
iajs-2681	185	1	consider	consider	VERB
iajs-2681	185	2	the	the	DET
iajs-2681	185	3	following	follow	VERB
iajs-2681	185	4	figure	figure	NOUN
iajs-2681	185	5	:	:	PUNCT
iajs-2681	185	6	idm	idm	PROPN
iajs-2681	185	7			NOUN
iajs-2681	185	8			PROPN
iajs-2681	185	9	m	m	PROPN
iajs-2681	185	10	b	b	PROPN
iajs-2681	185	11	m	m	PROPN
iajs-2681	185	12	m	m	PROPN
iajs-2681	185	13	b	b	PROPN
iajs-2681	185	14	n	n	CCONJ
iajs-2681	185	15	2	2	ADV
iajs-2681	185	16	2	2	ADJ
iajs-2681	185	17			PROPN
iajs-2681	185	18	m	m	VERB
iajs-2681	185	19	n	n	PRON
iajs-2681	185	20	figure	figure	VERB
iajs-2681	185	21	1	1	NUM
iajs-2681	185	22	.	.	PUNCT
iajs-2681	186	1	diagraph	diagraph	NOUN
iajs-2681	186	2	of	of	ADP
iajs-2681	186	3	theorem	theorem	NOUN
iajs-2681	186	4	3.7	3.7	NUM
iajs-2681	186	5	.	.	PUNCT
iajs-2681	187	1	the	the	DET
iajs-2681	187	2	projection	projection	NOUN
iajs-2681	187	3	on	on	ADP
iajs-2681	187	4	the	the	DET
iajs-2681	187	5	right	right	NOUN
iajs-2681	187	6	is	be	AUX
iajs-2681	187	7	surjective	surjective	ADJ
iajs-2681	187	8	.	.	PUNCT
iajs-2681	188	1	while	while	SCONJ
iajs-2681	188	2	the	the	DET
iajs-2681	188	3	projection	projection	NOUN
iajs-2681	188	4	on	on	ADP
iajs-2681	188	5	the	the	DET
iajs-2681	188	6	left	left	NOUN
iajs-2681	188	7	is	be	AUX
iajs-2681	188	8	a	a	DET
iajs-2681	188	9	fuzzy	fuzzy	ADJ
iajs-2681	188	10	open	open	ADJ
iajs-2681	188	11	since	since	SCONJ
iajs-2681	188	12	m	m	PROPN
iajs-2681	188	13	is	be	AUX
iajs-2681	188	14	a	a	DET
iajs-2681	188	15	fwofts	fwoft	NOUN
iajs-2681	188	16	.	.	PUNCT
iajs-2681	189	1	thus	thus	ADV
iajs-2681	189	2	2	2	ADV
iajs-2681	189	3			NUM
iajs-2681	189	4	idm	idm	NOUN
iajs-2681	189	5			VERB
iajs-2681	189	6			PROPN
iajs-2681	190	1	=	=	PUNCT
iajs-2681	191	1			PROPN
iajs-2681	192	1			PROPN
iajs-2681	192	2	2	2	PROPN
iajs-2681	192	3	is	be	AUX
iajs-2681	192	4	a	a	DET
iajs-2681	192	5	fuzzy	fuzzy	ADJ
iajs-2681	192	6	open	open	ADJ
iajs-2681	192	7	and	and	CCONJ
iajs-2681	192	8	so	so	ADV
iajs-2681	192	9			PROPN
iajs-2681	192	10	is	be	AUX
iajs-2681	192	11	a	a	DET
iajs-2681	192	12	fuzzy	fuzzy	ADJ
iajs-2681	192	13	open	open	ADJ
iajs-2681	192	14	.	.	PUNCT
iajs-2681	193	1	our	our	PRON
iajs-2681	193	2	next	next	ADJ
iajs-2681	193	3	three	three	NUM
iajs-2681	193	4	results	result	NOUN
iajs-2681	193	5	apply	apply	VERB
iajs-2681	193	6	equally	equally	ADV
iajs-2681	193	7	to	to	ADP
iajs-2681	193	8	fwcfts	fwcft	NOUN
iajs-2681	193	9	's	's	PART
iajs-2681	193	10	and	and	CCONJ
iajs-2681	193	11	fwofts	fwoft	NOUN
iajs-2681	193	12	's	's	PART
iajs-2681	193	13	.	.	PUNCT
iajs-2681	194	1	theorem	theorem	VERB
iajs-2681	194	2	3.8	3.8	NUM
iajs-2681	194	3	.	.	PUNCT
iajs-2681	195	1	let	let	VERB
iajs-2681	195	2			X
iajs-2681	195	3	:	:	PUNCT
iajs-2681	195	4	m	m	VERB
iajs-2681	195	5			NOUN
iajs-2681	195	6	n	n	AUX
iajs-2681	195	7	be	be	AUX
iajs-2681	195	8	a	a	DET
iajs-2681	195	9	surjection	surjection	NOUN
iajs-2681	195	10	fw	fw	DET
iajs-2681	195	11	fuzzy	fuzzy	ADJ
iajs-2681	195	12	continuous	continuous	ADJ
iajs-2681	195	13	where	where	SCONJ
iajs-2681	195	14	(	(	PUNCT
iajs-2681	195	15	m	m	NOUN
iajs-2681	195	16	,	,	PUNCT
iajs-2681	195	17			PROPN
iajs-2681	195	18	)	)	PUNCT
iajs-2681	195	19	,	,	PUNCT
iajs-2681	195	20	(	(	PUNCT
iajs-2681	195	21	n	n	X
iajs-2681	195	22	,	,	PUNCT
iajs-2681	195	23			NUM
iajs-2681	195	24	)	)	PUNCT
iajs-2681	195	25	are	be	AUX
iajs-2681	195	26	fwfts	fwft	NOUN
iajs-2681	195	27	's	's	PART
iajs-2681	195	28	over	over	ADP
iajs-2681	195	29	(	(	PUNCT
iajs-2681	195	30	b	b	NOUN
iajs-2681	195	31	,	,	PUNCT
iajs-2681	195	32			NOUN
iajs-2681	195	33	)	)	PUNCT
iajs-2681	195	34	.	.	PUNCT
iajs-2681	196	1	then	then	ADV
iajs-2681	196	2	n	n	PRON
iajs-2681	196	3	is	be	AUX
iajs-2681	196	4	a	a	DET
iajs-2681	196	5	fwcfts	fwcft	NOUN
iajs-2681	196	6	(	(	PUNCT
iajs-2681	196	7	resp	resp	NOUN
iajs-2681	196	8	.	.	PUNCT
iajs-2681	197	1	fwofts	fwoft	NOUN
iajs-2681	197	2	)	)	PUNCT
iajs-2681	197	3	if	if	SCONJ
iajs-2681	197	4	m	m	NOUN
iajs-2681	197	5	is	be	AUX
iajs-2681	197	6	a	a	DET
iajs-2681	197	7	fwcfts	fwcft	NOUN
iajs-2681	197	8	(	(	PUNCT
iajs-2681	197	9	resp	resp	NOUN
iajs-2681	197	10	.	.	PUNCT
iajs-2681	198	1	fwofts	fwoft	NOUN
iajs-2681	198	2	)	)	PUNCT
iajs-2681	198	3	.	.	PUNCT
iajs-2681	199	1	ibn	ibn	PROPN
iajs-2681	199	2	al	al	PROPN
iajs-2681	199	3	-	-	PUNCT
iajs-2681	199	4	haitham	haitham	PROPN
iajs-2681	199	5	jour	jour	X
iajs-2681	199	6	.	.	PROPN
iajs-2681	199	7	for	for	ADP
iajs-2681	199	8	pure	pure	ADJ
iajs-2681	199	9	&	&	CCONJ
iajs-2681	199	10	appl	appl	PROPN
iajs-2681	199	11	.	.	PUNCT
iajs-2681	200	1	sci	sci	PROPN
iajs-2681	200	2	.	.	PROPN
iajs-2681	201	1	34(3)2021	34(3)2021	NUM
iajs-2681	201	2	92	92	NUM
iajs-2681	201	3	proof	proof	NOUN
iajs-2681	201	4	.	.	PUNCT
iajs-2681	202	1	suppose	suppose	VERB
iajs-2681	202	2	that	that	SCONJ
iajs-2681	202	3	m	m	PROPN
iajs-2681	202	4	is	be	AUX
iajs-2681	202	5	a	a	DET
iajs-2681	202	6	fwcfys	fwcfys	PROPN
iajs-2681	202	7	(	(	PUNCT
iajs-2681	202	8	resp	resp	NOUN
iajs-2681	202	9	.	.	PUNCT
iajs-2681	203	1	fwofts	fwoft	NOUN
iajs-2681	203	2	)	)	PUNCT
iajs-2681	203	3	.	.	PUNCT
iajs-2681	204	1	then	then	ADV
iajs-2681	204	2	the	the	DET
iajs-2681	204	3	proj	proj	NOUN
iajs-2681	204	4	.	.	PUNCT
iajs-2681	205	1	þm	þm	VERB
iajs-2681	205	2	:	:	PUNCT
iajs-2681	206	1	m	m	VERB
iajs-2681	206	2			NOUN
iajs-2681	206	3	b	b	NOUN
iajs-2681	206	4	is	be	AUX
iajs-2681	206	5	a	a	DET
iajs-2681	206	6	fuzzy	fuzzy	ADJ
iajs-2681	206	7	closed	close	VERB
iajs-2681	206	8	(	(	PUNCT
iajs-2681	206	9	resp	resp	NOUN
iajs-2681	206	10	.	.	PUNCT
iajs-2681	207	1	fuzzy	fuzzy	ADJ
iajs-2681	207	2	open	open	ADJ
iajs-2681	207	3	)	)	PUNCT
iajs-2681	207	4	.	.	PUNCT
iajs-2681	208	1	to	to	PART
iajs-2681	208	2	prove	prove	VERB
iajs-2681	208	3	that	that	SCONJ
iajs-2681	208	4	n	n	PRON
iajs-2681	208	5	is	be	AUX
iajs-2681	208	6	a	a	DET
iajs-2681	208	7	fwcfts	fwcft	NOUN
iajs-2681	208	8	(	(	PUNCT
iajs-2681	208	9	resp	resp	NOUN
iajs-2681	208	10	.	.	PUNCT
iajs-2681	209	1	fwofts	fwoft	NOUN
iajs-2681	209	2	)	)	PUNCT
iajs-2681	209	3	over	over	ADP
iajs-2681	209	4	b	b	NOUN
iajs-2681	209	5	i.e.	i.e.	X
iajs-2681	209	6	the	the	DET
iajs-2681	209	7	proj	proj	NOUN
iajs-2681	209	8	.	.	PUNCT
iajs-2681	210	1	þn	þn	ADP
iajs-2681	210	2	:	:	PUNCT
iajs-2681	210	3	(	(	PUNCT
iajs-2681	210	4	n	n	X
iajs-2681	210	5	,	,	PUNCT
iajs-2681	210	6			NUM
iajs-2681	210	7	)	)	PUNCT
iajs-2681	210	8			NOUN
iajs-2681	210	9	(	(	PUNCT
iajs-2681	210	10	b	b	NOUN
iajs-2681	210	11	,	,	PUNCT
iajs-2681	210	12			NOUN
iajs-2681	210	13	)	)	PUNCT
iajs-2681	210	14	is	be	AUX
iajs-2681	210	15	a	a	DET
iajs-2681	210	16	fuzzy	fuzzy	ADJ
iajs-2681	210	17	closed	close	VERB
iajs-2681	210	18	(	(	PUNCT
iajs-2681	210	19	resp	resp	NOUN
iajs-2681	210	20	.	.	PUNCT
iajs-2681	211	1	fuzzy	fuzzy	ADJ
iajs-2681	211	2	open	open	ADJ
iajs-2681	211	3	)	)	PUNCT
iajs-2681	211	4	.	.	PUNCT
iajs-2681	212	1	suppose	suppose	VERB
iajs-2681	212	2	that	that	SCONJ
iajs-2681	212	3	n	n	PROPN
iajs-2681	212	4			PROPN
iajs-2681	212	5	nb	nb	INTJ
iajs-2681	212	6	;	;	PUNCT
iajs-2681	212	7	b	b	X
iajs-2681	212	8			PROPN
iajs-2681	212	9	b.	b.	PROPN
iajs-2681	212	10	let	let	VERB
iajs-2681	212	11	v	v	PART
iajs-2681	212	12	be	be	AUX
iajs-2681	212	13	fuzzy	fuzzy	ADV
iajs-2681	212	14	closed	closed	ADJ
iajs-2681	212	15	(	(	PUNCT
iajs-2681	212	16	resp	resp	NOUN
iajs-2681	212	17	.	.	PUNCT
iajs-2681	213	1	fuzzy	fuzzy	ADJ
iajs-2681	213	2	open	open	ADJ
iajs-2681	213	3	)	)	PUNCT
iajs-2681	213	4	set	set	NOUN
iajs-2681	213	5	of	of	ADP
iajs-2681	213	6	n.	n.	NOUN
iajs-2681	213	7	since	since	SCONJ
iajs-2681	213	8			PROPN
iajs-2681	213	9	is	be	AUX
iajs-2681	213	10	a	a	DET
iajs-2681	213	11	fuzzy	fuzzy	ADJ
iajs-2681	213	12	continuous	continuous	ADJ
iajs-2681	213	13	so	so	SCONJ
iajs-2681	213	14	–1(v	–1(v	X
iajs-2681	213	15	)	)	PUNCT
iajs-2681	213	16	is	be	AUX
iajs-2681	213	17	a	a	DET
iajs-2681	213	18	fuzzy	fuzzy	ADJ
iajs-2681	213	19	closed	close	VERB
iajs-2681	213	20	(	(	PUNCT
iajs-2681	213	21	resp	resp	NOUN
iajs-2681	213	22	.	.	PUNCT
iajs-2681	214	1	fuzzy	fuzzy	ADJ
iajs-2681	214	2	open	open	ADJ
iajs-2681	214	3	)	)	PUNCT
iajs-2681	214	4	set	set	NOUN
iajs-2681	214	5	of	of	ADP
iajs-2681	214	6	–1(n	–1(n	NOUN
iajs-2681	214	7	)	)	PUNCT
iajs-2681	215	1	=	=	SYM
iajs-2681	215	2	m	m	PROPN
iajs-2681	215	3			NOUN
iajs-2681	215	4	mb	mb	ADP
iajs-2681	215	5			PROPN
iajs-2681	215	6	m.	m.	NOUN
iajs-2681	215	7	since	since	SCONJ
iajs-2681	215	8	þm	þm	PROPN
iajs-2681	215	9	is	be	AUX
iajs-2681	215	10	a	a	DET
iajs-2681	215	11	fuzzy	fuzzy	ADJ
iajs-2681	215	12	closed	close	VERB
iajs-2681	215	13	(	(	PUNCT
iajs-2681	215	14	resp	resp	NOUN
iajs-2681	215	15	.	.	PUNCT
iajs-2681	216	1	fuzzy	fuzzy	ADJ
iajs-2681	216	2	open	open	ADJ
iajs-2681	216	3	)	)	PUNCT
iajs-2681	216	4	,	,	PUNCT
iajs-2681	216	5	then	then	ADV
iajs-2681	216	6	þm(–1(v	þm(–1(v	PROPN
iajs-2681	216	7	)	)	PUNCT
iajs-2681	216	8	)	)	PUNCT
iajs-2681	216	9	is	be	AUX
iajs-2681	216	10	a	a	DET
iajs-2681	216	11	fuzzy	fuzzy	ADJ
iajs-2681	216	12	closed	close	VERB
iajs-2681	216	13	(	(	PUNCT
iajs-2681	216	14	resp	resp	NOUN
iajs-2681	216	15	.	.	PUNCT
iajs-2681	217	1	fuzzy	fuzzy	ADJ
iajs-2681	217	2	open	open	NOUN
iajs-2681	217	3	)	)	PUNCT
iajs-2681	217	4	in	in	ADP
iajs-2681	217	5	b	b	NUM
iajs-2681	217	6	,	,	PUNCT
iajs-2681	217	7	but	but	CCONJ
iajs-2681	217	8	þm(–1(v	þm(–1(v	NUM
iajs-2681	217	9	)	)	PUNCT
iajs-2681	217	10	)	)	PUNCT
iajs-2681	218	1	=	=	PRON
iajs-2681	218	2	þm	þm	PROPN
iajs-2681	218	3			PROPN
iajs-2681	218	4	–1(v	–1(v	X
iajs-2681	218	5	)	)	PUNCT
iajs-2681	219	1	=	=	PRON
iajs-2681	219	2	þn	þn	ADP
iajs-2681	219	3	(	(	PUNCT
iajs-2681	219	4	v	v	NOUN
iajs-2681	219	5	)	)	PUNCT
iajs-2681	219	6	.	.	PUNCT
iajs-2681	220	1	thus	thus	ADV
iajs-2681	220	2	þn	þn	INTJ
iajs-2681	220	3	is	be	AUX
iajs-2681	220	4	a	a	DET
iajs-2681	220	5	fuzzy	fuzzy	ADJ
iajs-2681	220	6	closed	close	VERB
iajs-2681	220	7	(	(	PUNCT
iajs-2681	220	8	resp	resp	NOUN
iajs-2681	220	9	.	.	PUNCT
iajs-2681	221	1	fuzzy	fuzzy	ADJ
iajs-2681	221	2	open	open	ADJ
iajs-2681	221	3	)	)	PUNCT
iajs-2681	221	4	,	,	PUNCT
iajs-2681	221	5	and	and	CCONJ
iajs-2681	221	6	n	n	PRON
iajs-2681	221	7	is	be	AUX
iajs-2681	221	8	a	a	DET
iajs-2681	221	9	fwcfts	fwcft	NOUN
iajs-2681	221	10	(	(	PUNCT
iajs-2681	221	11	resp	resp	NOUN
iajs-2681	221	12	.	.	PUNCT
iajs-2681	222	1	fwofts	fwoft	NOUN
iajs-2681	222	2	)	)	PUNCT
iajs-2681	222	3	.	.	PUNCT
iajs-2681	223	1	theorem	theorem	VERB
iajs-2681	223	2	3.9	3.9	NUM
iajs-2681	223	3	.	.	PUNCT
iajs-2681	224	1	if	if	SCONJ
iajs-2681	224	2	(	(	PUNCT
iajs-2681	224	3	m	m	NOUN
iajs-2681	224	4	,	,	PUNCT
iajs-2681	224	5			PROPN
iajs-2681	224	6	)	)	PUNCT
iajs-2681	224	7	is	be	AUX
iajs-2681	224	8	a	a	DET
iajs-2681	224	9	fwfts	fwft	NOUN
iajs-2681	224	10	over	over	ADP
iajs-2681	224	11	(	(	PUNCT
iajs-2681	224	12	b	b	NOUN
iajs-2681	224	13	,	,	PUNCT
iajs-2681	224	14			NOUN
iajs-2681	224	15	)	)	PUNCT
iajs-2681	224	16	.	.	PUNCT
iajs-2681	225	1	assume	assume	VERB
iajs-2681	225	2	that	that	SCONJ
iajs-2681	225	3	m	m	PROPN
iajs-2681	225	4	is	be	AUX
iajs-2681	225	5	a	a	DET
iajs-2681	225	6	fwcfts	fwcft	NOUN
iajs-2681	225	7	(	(	PUNCT
iajs-2681	225	8	resp	resp	NOUN
iajs-2681	225	9	.	.	PUNCT
iajs-2681	226	1	fwofts	fwoft	NOUN
iajs-2681	226	2	)	)	PUNCT
iajs-2681	226	3	over	over	ADP
iajs-2681	226	4	b	b	NOUN
iajs-2681	226	5	,	,	PUNCT
iajs-2681	226	6	then	then	ADV
iajs-2681	226	7	mb*is	mb*is	VERB
iajs-2681	226	8	a	a	DET
iajs-2681	226	9	fwcfts	fwcft	NOUN
iajs-2681	226	10	(	(	PUNCT
iajs-2681	226	11	resp	resp	NOUN
iajs-2681	226	12	.	.	PUNCT
iajs-2681	227	1	fwofts	fwoft	NOUN
iajs-2681	227	2	)	)	PUNCT
iajs-2681	227	3	over	over	ADP
iajs-2681	227	4	b	b	PROPN
iajs-2681	227	5	*	*	VERB
iajs-2681	227	6	for	for	ADP
iajs-2681	227	7	every	every	DET
iajs-2681	227	8	fuzzy	fuzzy	ADJ
iajs-2681	227	9	subspace	subspace	NOUN
iajs-2681	227	10	b	b	PROPN
iajs-2681	227	11	*	*	PROPN
iajs-2681	227	12			PROPN
iajs-2681	227	13	b.	b.	PROPN
iajs-2681	227	14	proof	proof	NOUN
iajs-2681	227	15	.	.	PUNCT
iajs-2681	228	1	assume	assume	VERB
iajs-2681	228	2	that	that	SCONJ
iajs-2681	228	3	m	m	PROPN
iajs-2681	228	4	is	be	AUX
iajs-2681	228	5	a	a	DET
iajs-2681	228	6	fwcfts	fwcft	NOUN
iajs-2681	228	7	(	(	PUNCT
iajs-2681	228	8	resp	resp	NOUN
iajs-2681	228	9	.	.	PUNCT
iajs-2681	228	10	fwofts	fwoft	NOUN
iajs-2681	228	11	)	)	PUNCT
iajs-2681	228	12	,	,	PUNCT
iajs-2681	228	13	so	so	SCONJ
iajs-2681	228	14	that	that	SCONJ
iajs-2681	228	15	the	the	DET
iajs-2681	228	16	proj	proj	NOUN
iajs-2681	228	17	.	.	PUNCT
iajs-2681	229	1	þ	þ	NOUN
iajs-2681	229	2	:	:	PUNCT
iajs-2681	230	1	m	m	VERB
iajs-2681	230	2			NOUN
iajs-2681	230	3	b	b	X
iajs-2681	230	4	is	be	AUX
iajs-2681	230	5	a	a	DET
iajs-2681	230	6	fuzzy	fuzzy	ADJ
iajs-2681	230	7	closed	close	VERB
iajs-2681	230	8	(	(	PUNCT
iajs-2681	230	9	resp	resp	NOUN
iajs-2681	230	10	.	.	PUNCT
iajs-2681	231	1	fuzzy	fuzzy	ADJ
iajs-2681	231	2	open	open	ADJ
iajs-2681	231	3	)	)	PUNCT
iajs-2681	231	4	.	.	PUNCT
iajs-2681	232	1	to	to	PART
iajs-2681	232	2	prove	prove	VERB
iajs-2681	232	3	that	that	SCONJ
iajs-2681	232	4	mb	mb	NOUN
iajs-2681	232	5	*	*	PROPN
iajs-2681	232	6	is	be	AUX
iajs-2681	232	7	a	a	DET
iajs-2681	232	8	fuzzy	fuzzy	ADJ
iajs-2681	232	9	closed	close	VERB
iajs-2681	232	10	(	(	PUNCT
iajs-2681	232	11	resp	resp	NOUN
iajs-2681	232	12	.	.	PUNCT
iajs-2681	233	1	fuzzy	fuzzy	ADJ
iajs-2681	233	2	open	open	ADJ
iajs-2681	233	3	)	)	PUNCT
iajs-2681	233	4	,	,	PUNCT
iajs-2681	233	5	i.e.	i.e.	X
iajs-2681	233	6	the	the	DET
iajs-2681	233	7	proj	proj	NOUN
iajs-2681	233	8	.	.	PUNCT
iajs-2681	234	1	þb	þb	PROPN
iajs-2681	234	2	*	*	PUNCT
iajs-2681	234	3	:	:	PUNCT
iajs-2681	234	4	mb	mb	ADP
iajs-2681	234	5	*	*	NOUN
iajs-2681	234	6			NOUN
iajs-2681	234	7	b	b	X
iajs-2681	234	8	*	*	PUNCT
iajs-2681	234	9	is	be	AUX
iajs-2681	234	10	a	a	DET
iajs-2681	234	11	fuzzy	fuzzy	ADJ
iajs-2681	234	12	closed	close	VERB
iajs-2681	234	13	(	(	PUNCT
iajs-2681	234	14	resp	resp	NOUN
iajs-2681	234	15	.	.	PUNCT
iajs-2681	235	1	fuzzy	fuzzy	ADJ
iajs-2681	235	2	open	open	ADJ
iajs-2681	235	3	)	)	PUNCT
iajs-2681	235	4	.	.	PUNCT
iajs-2681	236	1	let	let	VERB
iajs-2681	236	2	m	m	PRON
iajs-2681	236	3			NOUN
iajs-2681	236	4	m	m	VERB
iajs-2681	236	5	|	|	ADV
iajs-2681	236	6	b	b	NOUN
iajs-2681	236	7	*	*	PUNCT
iajs-2681	236	8	,	,	PUNCT
iajs-2681	236	9	and	and	CCONJ
iajs-2681	236	10	g	g	NOUN
iajs-2681	236	11	be	be	VERB
iajs-2681	236	12	fuzzy	fuzzy	ADV
iajs-2681	236	13	closed	closed	ADJ
iajs-2681	236	14	(	(	PUNCT
iajs-2681	236	15	resp	resp	NOUN
iajs-2681	236	16	.	.	PUNCT
iajs-2681	237	1	fuzzy	fuzzy	ADJ
iajs-2681	237	2	open	open	ADJ
iajs-2681	237	3	)	)	PUNCT
iajs-2681	237	4	set	set	NOUN
iajs-2681	237	5	of	of	ADP
iajs-2681	237	6	m	m	PROPN
iajs-2681	237	7	,	,	PUNCT
iajs-2681	237	8	we	we	PRON
iajs-2681	237	9	have	have	VERB
iajs-2681	237	10	g	g	PROPN
iajs-2681	237	11	⋂	⋂	PROPN
iajs-2681	237	12	mb	mb	X
iajs-2681	237	13	*	*	PROPN
iajs-2681	237	14	is	be	AUX
iajs-2681	237	15	a	a	DET
iajs-2681	237	16	fuzzy	fuzzy	ADJ
iajs-2681	237	17	closed	close	VERB
iajs-2681	237	18	(	(	PUNCT
iajs-2681	237	19	resp	resp	NOUN
iajs-2681	237	20	.	.	PUNCT
iajs-2681	238	1	fuzzy	fuzzy	ADJ
iajs-2681	238	2	open	open	ADJ
iajs-2681	238	3	)	)	PUNCT
iajs-2681	238	4	set	set	NOUN
iajs-2681	238	5	of	of	ADP
iajs-2681	238	6	mb	mb	NOUN
iajs-2681	238	7	*	*	PROPN
iajs-2681	238	8	.	.	PUNCT
iajs-2681	239	1	þb*(g	þb*(g	PROPN
iajs-2681	239	2	⋂	⋂	PROPN
iajs-2681	239	3	mb	mb	NOUN
iajs-2681	239	4	*	*	NOUN
iajs-2681	239	5	)	)	PUNCT
iajs-2681	240	1	=	=	SYM
iajs-2681	240	2	þ(g	þ(g	PROPN
iajs-2681	240	3	⋂	⋂	PROPN
iajs-2681	240	4	mb	mb	PROPN
iajs-2681	240	5	*	*	PROPN
iajs-2681	240	6	)	)	PUNCT
iajs-2681	240	7	=	=	SYM
iajs-2681	240	8	þ(g	þ(g	PROPN
iajs-2681	240	9	)	)	PUNCT
iajs-2681	240	10	⋂	⋂	PROPN
iajs-2681	240	11	þ(mb	þ(mb	NOUN
iajs-2681	240	12	*	*	X
iajs-2681	240	13	)	)	PUNCT
iajs-2681	240	14	=	=	SYM
iajs-2681	240	15	þ(g	þ(g	PROPN
iajs-2681	240	16	)	)	PUNCT
iajs-2681	240	17	⋂	⋂	PROPN
iajs-2681	241	1	b	b	X
iajs-2681	241	2	*	*	PROPN
iajs-2681	241	3	which	which	PRON
iajs-2681	241	4	is	be	AUX
iajs-2681	241	5	a	a	DET
iajs-2681	241	6	fuzzy	fuzzy	ADJ
iajs-2681	241	7	closed	close	VERB
iajs-2681	241	8	(	(	PUNCT
iajs-2681	241	9	resp	resp	NOUN
iajs-2681	241	10	.	.	PUNCT
iajs-2681	242	1	fuzzy	fuzzy	ADJ
iajs-2681	242	2	open	open	ADJ
iajs-2681	242	3	)	)	PUNCT
iajs-2681	243	1	set	set	VERB
iajs-2681	243	2	in	in	ADP
iajs-2681	243	3	b	b	PROPN
iajs-2681	243	4	*	*	PROPN
iajs-2681	243	5	.	.	PUNCT
iajs-2681	244	1	þb	þb	PROPN
iajs-2681	244	2	*	*	PROPN
iajs-2681	244	3	is	be	AUX
iajs-2681	244	4	a	a	DET
iajs-2681	244	5	fuzzy	fuzzy	ADJ
iajs-2681	244	6	closed	close	VERB
iajs-2681	244	7	(	(	PUNCT
iajs-2681	244	8	resp	resp	NOUN
iajs-2681	244	9	.	.	PUNCT
iajs-2681	245	1	fuzzy	fuzzy	ADJ
iajs-2681	245	2	open	open	ADJ
iajs-2681	245	3	)	)	PUNCT
iajs-2681	245	4	.	.	PUNCT
iajs-2681	246	1	so	so	ADV
iajs-2681	246	2	that	that	SCONJ
iajs-2681	246	3	mb	mb	NOUN
iajs-2681	246	4	*	*	PROPN
iajs-2681	246	5	is	be	AUX
iajs-2681	246	6	a	a	DET
iajs-2681	246	7	fwcfts	fwcft	NOUN
iajs-2681	246	8	(	(	PUNCT
iajs-2681	246	9	resp	resp	NOUN
iajs-2681	246	10	.	.	PUNCT
iajs-2681	247	1	fwofts	fwoft	NOUN
iajs-2681	247	2	)	)	PUNCT
iajs-2681	247	3	.	.	PUNCT
iajs-2681	248	1	theorem	theorem	VERB
iajs-2681	248	2	3.10	3.10	NUM
iajs-2681	248	3	.	.	PUNCT
iajs-2681	249	1	let	let	VERB
iajs-2681	249	2	(	(	PUNCT
iajs-2681	249	3	m	m	NOUN
iajs-2681	249	4	,	,	PUNCT
iajs-2681	249	5			PROPN
iajs-2681	249	6	)	)	PUNCT
iajs-2681	249	7	be	be	VERB
iajs-2681	249	8	a	a	DET
iajs-2681	249	9	fwfts	fwft	NOUN
iajs-2681	249	10	over	over	ADP
iajs-2681	249	11	(	(	PUNCT
iajs-2681	249	12	b	b	NOUN
iajs-2681	249	13	,	,	PUNCT
iajs-2681	249	14			NOUN
iajs-2681	249	15	)	)	PUNCT
iajs-2681	249	16	.	.	PUNCT
iajs-2681	250	1	assume	assume	VERB
iajs-2681	250	2	that	that	SCONJ
iajs-2681	250	3	(	(	PUNCT
iajs-2681	250	4	mbj	mbj	PROPN
iajs-2681	250	5	,	,	PUNCT
iajs-2681	250	6			PROPN
iajs-2681	250	7	)	)	PUNCT
iajs-2681	250	8	is	be	AUX
iajs-2681	250	9	a	a	DET
iajs-2681	250	10	fwcfts	fwcft	NOUN
iajs-2681	250	11	's	's	PART
iajs-2681	250	12	(	(	PUNCT
iajs-2681	250	13	resp	resp	NOUN
iajs-2681	250	14	.	.	PUNCT
iajs-2681	251	1	fwofts	fwoft	NOUN
iajs-2681	251	2	's	's	PART
iajs-2681	251	3	)	)	PUNCT
iajs-2681	251	4	over	over	ADP
iajs-2681	251	5	(	(	PUNCT
iajs-2681	251	6	bj	bj	NOUN
iajs-2681	251	7	,	,	PUNCT
iajs-2681	251	8	bj	bj	NUM
iajs-2681	251	9	)	)	PUNCT
iajs-2681	251	10	for	for	ADP
iajs-2681	251	11	every	every	DET
iajs-2681	251	12	member	member	NOUN
iajs-2681	251	13	of	of	ADP
iajs-2681	251	14	a	a	DET
iajs-2681	251	15	bj	bj	NUM
iajs-2681	251	16	-	-	PUNCT
iajs-2681	251	17	fuzzy	fuzzy	ADJ
iajs-2681	251	18	open	open	ADJ
iajs-2681	251	19	covering	covering	NOUN
iajs-2681	251	20	of	of	ADP
iajs-2681	251	21	b.	b.	PROPN
iajs-2681	252	1	so	so	ADV
iajs-2681	252	2	m	m	PROPN
iajs-2681	252	3	is	be	AUX
iajs-2681	252	4	a	a	DET
iajs-2681	252	5	fwcfts	fwcft	NOUN
iajs-2681	252	6	(	(	PUNCT
iajs-2681	252	7	resp	resp	NOUN
iajs-2681	252	8	.	.	PUNCT
iajs-2681	253	1	fwofts	fwoft	NOUN
iajs-2681	253	2	)	)	PUNCT
iajs-2681	253	3	over	over	ADP
iajs-2681	253	4	b.	b.	PROPN
iajs-2681	253	5	proof	proof	NOUN
iajs-2681	253	6	.	.	PUNCT
iajs-2681	254	1	assume	assume	VERB
iajs-2681	254	2	that	that	SCONJ
iajs-2681	254	3	m	m	PROPN
iajs-2681	254	4	is	be	AUX
iajs-2681	254	5	a	a	DET
iajs-2681	254	6	fwfts	fwft	NOUN
iajs-2681	254	7	over	over	ADP
iajs-2681	254	8	b	b	NOUN
iajs-2681	255	1	so	so	ADV
iajs-2681	255	2	,	,	PUNCT
iajs-2681	255	3	the	the	DET
iajs-2681	255	4	proj	proj	NOUN
iajs-2681	255	5	.	.	PUNCT
iajs-2681	256	1	þ	þ	NOUN
iajs-2681	256	2	:	:	PUNCT
iajs-2681	257	1	m	m	VERB
iajs-2681	257	2			NOUN
iajs-2681	257	3	b	b	NOUN
iajs-2681	257	4	is	be	AUX
iajs-2681	257	5	exist	exist	VERB
iajs-2681	257	6	.to	.to	PUNCT
iajs-2681	258	1	prove	prove	VERB
iajs-2681	258	2	that	that	SCONJ
iajs-2681	258	3	þ	þ	PROPN
iajs-2681	258	4	is	be	AUX
iajs-2681	258	5	a	a	DET
iajs-2681	258	6	fuzzy	fuzzy	ADJ
iajs-2681	258	7	closed	close	VERB
iajs-2681	258	8	(	(	PUNCT
iajs-2681	258	9	resp	resp	NOUN
iajs-2681	258	10	.	.	PUNCT
iajs-2681	259	1	fuzzy	fuzzy	ADJ
iajs-2681	259	2	open	open	ADJ
iajs-2681	259	3	)	)	PUNCT
iajs-2681	259	4	.	.	PUNCT
iajs-2681	260	1	since	since	SCONJ
iajs-2681	260	2	mb	mb	PROPN
iajs-2681	260	3	is	be	AUX
iajs-2681	260	4	a	a	DET
iajs-2681	260	5	fwcfts	fwcft	NOUN
iajs-2681	260	6	(	(	PUNCT
iajs-2681	260	7	resp	resp	NOUN
iajs-2681	260	8	.	.	PUNCT
iajs-2681	261	1	fwofts	fwoft	NOUN
iajs-2681	261	2	)	)	PUNCT
iajs-2681	261	3	over	over	ADP
iajs-2681	261	4	bj	bj	NOUN
iajs-2681	261	5	for	for	ADP
iajs-2681	261	6	every	every	DET
iajs-2681	261	7	member	member	NOUN
iajs-2681	261	8	of	of	ADP
iajs-2681	261	9	a	a	DET
iajs-2681	261	10	bj	bj	NUM
iajs-2681	261	11	-	-	PUNCT
iajs-2681	261	12	fuzzy	fuzzy	ADJ
iajs-2681	261	13	open	open	ADJ
iajs-2681	261	14	covering	covering	NOUN
iajs-2681	261	15	of	of	ADP
iajs-2681	261	16	b	b	NOUN
iajs-2681	261	17	,	,	PUNCT
iajs-2681	261	18	then	then	ADV
iajs-2681	261	19	the	the	DET
iajs-2681	261	20	proj	proj	NOUN
iajs-2681	261	21	.	.	PUNCT
iajs-2681	262	1	þmj	þmj	ADJ
iajs-2681	262	2	:	:	PUNCT
iajs-2681	262	3	mbj	mbj	PROPN
iajs-2681	262	4			PROPN
iajs-2681	262	5	bj	bj	VERB
iajs-2681	262	6	is	be	AUX
iajs-2681	262	7	a	a	DET
iajs-2681	262	8	fuzzy	fuzzy	ADJ
iajs-2681	262	9	closed	close	VERB
iajs-2681	262	10	(	(	PUNCT
iajs-2681	262	11	resp	resp	NOUN
iajs-2681	262	12	.	.	PUNCT
iajs-2681	263	1	fuzzy	fuzzy	ADJ
iajs-2681	263	2	open	open	ADJ
iajs-2681	263	3	)	)	PUNCT
iajs-2681	263	4	.	.	PUNCT
iajs-2681	264	1	now	now	ADV
iajs-2681	264	2	,	,	PUNCT
iajs-2681	264	3	let	let	VERB
iajs-2681	264	4	f	f	PRON
iajs-2681	264	5	be	be	AUX
iajs-2681	264	6	fuzzy	fuzzy	ADV
iajs-2681	264	7	closed	closed	ADJ
iajs-2681	264	8	(	(	PUNCT
iajs-2681	264	9	resp	resp	NOUN
iajs-2681	264	10	.	.	PUNCT
iajs-2681	265	1	fuzzy	fuzzy	ADJ
iajs-2681	265	2	open	open	ADJ
iajs-2681	265	3	)	)	PUNCT
iajs-2681	265	4	set	set	NOUN
iajs-2681	265	5	of	of	ADP
iajs-2681	265	6	mb	mb	NOUN
iajs-2681	265	7	;	;	PUNCT
iajs-2681	266	1	b	b	X
iajs-2681	266	2			PROPN
iajs-2681	266	3	b	b	NOUN
iajs-2681	266	4	,	,	PUNCT
iajs-2681	266	5	þ(f	þ(f	NOUN
iajs-2681	266	6	)	)	PUNCT
iajs-2681	266	7	=	=	PUNCT
iajs-2681	266	8	⋃	⋃	NOUN
iajs-2681	266	9	þbj	þbj	NOUN
iajs-2681	266	10	(	(	PUNCT
iajs-2681	266	11	f	f	PROPN
iajs-2681	266	12	⋂	⋂	PROPN
iajs-2681	266	13	mbj	mbj	PROPN
iajs-2681	266	14	)	)	PUNCT
iajs-2681	266	15	which	which	PRON
iajs-2681	266	16	is	be	AUX
iajs-2681	266	17	a	a	DET
iajs-2681	266	18	finite	finite	ADJ
iajs-2681	266	19	union	union	NOUN
iajs-2681	266	20	of	of	ADP
iajs-2681	266	21	fuzzy	fuzzy	ADJ
iajs-2681	266	22	closed	close	VERB
iajs-2681	266	23	(	(	PUNCT
iajs-2681	266	24	resp	resp	NOUN
iajs-2681	266	25	.	.	PUNCT
iajs-2681	266	26	fuzzy	fuzzy	ADJ
iajs-2681	266	27	open	open	ADJ
iajs-2681	266	28	)	)	PUNCT
iajs-2681	266	29	sets	set	NOUN
iajs-2681	266	30	of	of	ADP
iajs-2681	266	31	b.	b.	NOUN
iajs-2681	266	32	thus	thus	ADV
iajs-2681	266	33	þ	þ	PROPN
iajs-2681	266	34	is	be	AUX
iajs-2681	266	35	a	a	DET
iajs-2681	266	36	fuzzy	fuzzy	ADJ
iajs-2681	266	37	closed	close	VERB
iajs-2681	266	38	(	(	PUNCT
iajs-2681	266	39	resp	resp	NOUN
iajs-2681	266	40	.	.	PUNCT
iajs-2681	267	1	fuzzy	fuzzy	ADJ
iajs-2681	267	2	open	open	ADJ
iajs-2681	267	3	)	)	PUNCT
iajs-2681	267	4	and	and	CCONJ
iajs-2681	267	5	m	m	PROPN
iajs-2681	267	6	is	be	AUX
iajs-2681	267	7	a	a	DET
iajs-2681	267	8	fwcfts	fwcft	NOUN
iajs-2681	267	9	(	(	PUNCT
iajs-2681	267	10	resp	resp	NOUN
iajs-2681	267	11	.	.	PUNCT
iajs-2681	268	1	fwofts	fwoft	NOUN
iajs-2681	268	2	)	)	PUNCT
iajs-2681	268	3	.	.	PUNCT
iajs-2681	269	1	actually	actually	ADV
iajs-2681	269	2	,	,	PUNCT
iajs-2681	269	3	the	the	DET
iajs-2681	269	4	past	past	ADJ
iajs-2681	269	5	theorem	theorem	NOUN
iajs-2681	269	6	is	be	AUX
iajs-2681	269	7	true	true	ADJ
iajs-2681	269	8	to	to	AUX
iajs-2681	269	9	locally	locally	ADV
iajs-2681	269	10	finite	finite	VERB
iajs-2681	269	11	closed	closed	ADJ
iajs-2681	269	12	covering	covering	NOUN
iajs-2681	269	13	and	and	CCONJ
iajs-2681	269	14	there	there	PRON
iajs-2681	269	15	are	be	VERB
iajs-2681	269	16	several	several	ADJ
iajs-2681	269	17	subclasses	subclass	NOUN
iajs-2681	269	18	of	of	ADP
iajs-2681	269	19	the	the	DET
iajs-2681	269	20	class	class	NOUN
iajs-2681	269	21	of	of	ADP
iajs-2681	269	22	fwofts	fwoft	NOUN
iajs-2681	269	23	's	's	PART
iajs-2681	269	24	which	which	PRON
iajs-2681	269	25	induces	induce	VERB
iajs-2681	269	26	many	many	ADJ
iajs-2681	269	27	important	important	ADJ
iajs-2681	269	28	examples	example	NOUN
iajs-2681	269	29	and	and	CCONJ
iajs-2681	269	30	have	have	VERB
iajs-2681	269	31	interesting	interesting	ADJ
iajs-2681	269	32	properties	property	NOUN
iajs-2681	269	33	.	.	PUNCT
iajs-2681	270	1	4.fibrewise	4.fibrewise	NUM
iajs-2681	270	2	locally	locally	ADV
iajs-2681	270	3	sliceable	sliceable	ADJ
iajs-2681	270	4	and	and	CCONJ
iajs-2681	270	5	fibrewise	fibrewise	ADV
iajs-2681	270	6	locally	locally	ADV
iajs-2681	270	7	sectionable	sectionable	ADJ
iajs-2681	270	8	fuzzy	fuzzy	ADJ
iajs-2681	270	9	topological	topological	ADJ
iajs-2681	270	10	spaces	space	NOUN
iajs-2681	270	11	we	we	PRON
iajs-2681	270	12	present	present	VERB
iajs-2681	270	13	the	the	DET
iajs-2681	270	14	ideas	idea	NOUN
iajs-2681	270	15	of	of	ADP
iajs-2681	270	16	fibrewise	fibrewise	NOUN
iajs-2681	270	17	locally	locally	ADV
iajs-2681	270	18	sliceable	sliceable	ADJ
iajs-2681	270	19	and	and	CCONJ
iajs-2681	270	20	fibrewise	fibrewise	ADV
iajs-2681	270	21	locally	locally	ADV
iajs-2681	270	22	sectionable	sectionable	ADJ
iajs-2681	270	23	fuzzy	fuzzy	ADJ
iajs-2681	270	24	topological	topological	ADJ
iajs-2681	270	25	spaces	space	NOUN
iajs-2681	270	26	over	over	ADP
iajs-2681	270	27	(	(	PUNCT
iajs-2681	270	28	b	b	NOUN
iajs-2681	270	29	,	,	PUNCT
iajs-2681	270	30			NOUN
iajs-2681	270	31	)	)	PUNCT
iajs-2681	270	32	,	,	PUNCT
iajs-2681	270	33	several	several	ADJ
iajs-2681	270	34	properties	property	NOUN
iajs-2681	270	35	on	on	ADP
iajs-2681	270	36	the	the	DET
iajs-2681	270	37	obtained	obtain	VERB
iajs-2681	270	38	concepts	concept	NOUN
iajs-2681	270	39	are	be	AUX
iajs-2681	270	40	studied	study	VERB
iajs-2681	270	41	.	.	PUNCT
iajs-2681	271	1	definition	definition	NOUN
iajs-2681	271	2	4.1	4.1	NUM
iajs-2681	271	3	.	.	PUNCT
iajs-2681	272	1	the	the	DET
iajs-2681	272	2	fwfts	fwft	NOUN
iajs-2681	272	3	(	(	PUNCT
iajs-2681	272	4	m	m	NOUN
iajs-2681	272	5	,	,	PUNCT
iajs-2681	272	6			PROPN
iajs-2681	272	7	)	)	PUNCT
iajs-2681	272	8	over	over	ADP
iajs-2681	272	9	(	(	PUNCT
iajs-2681	272	10	b	b	NOUN
iajs-2681	272	11	,	,	PUNCT
iajs-2681	272	12			NOUN
iajs-2681	272	13	)	)	PUNCT
iajs-2681	272	14	is	be	AUX
iajs-2681	272	15	said	say	VERB
iajs-2681	272	16	to	to	PART
iajs-2681	272	17	be	be	AUX
iajs-2681	272	18	locally	locally	ADV
iajs-2681	272	19	sliceable	sliceable	ADJ
iajs-2681	272	20	(	(	PUNCT
iajs-2681	272	21	written	write	VERB
iajs-2681	272	22	as	as	ADP
iajs-2681	272	23	fw	fw	NOUN
iajs-2681	272	24	-	-	PUNCT
iajs-2681	272	25	lslfts	lslft	NOUN
iajs-2681	272	26	)	)	PUNCT
iajs-2681	272	27	if	if	SCONJ
iajs-2681	272	28	for	for	ADP
iajs-2681	272	29	every	every	DET
iajs-2681	272	30	point	point	NOUN
iajs-2681	272	31	m	m	VERB
iajs-2681	272	32			NOUN
iajs-2681	272	33	mb	mb	ADP
iajs-2681	272	34	;	;	PUNCT
iajs-2681	272	35	b	b	X
iajs-2681	272	36			PROPN
iajs-2681	272	37	b	b	NOUN
iajs-2681	272	38	,	,	PUNCT
iajs-2681	272	39	there	there	PRON
iajs-2681	272	40	is	be	VERB
iajs-2681	272	41	a	a	DET
iajs-2681	272	42	fuzzy	fuzzy	ADJ
iajs-2681	272	43	open	open	NOUN
iajs-2681	272	44	set	set	NOUN
iajs-2681	272	45	w	w	PROPN
iajs-2681	272	46	of	of	ADP
iajs-2681	272	47	b	b	PROPN
iajs-2681	272	48	and	and	CCONJ
iajs-2681	272	49	a	a	DET
iajs-2681	272	50	section	section	NOUN
iajs-2681	272	51	s	s	VERB
iajs-2681	272	52	:	:	PUNCT
iajs-2681	272	53	w	w	ADJ
iajs-2681	272	54			NOUN
iajs-2681	272	55	mw	mw	X
iajs-2681	272	56	and	and	CCONJ
iajs-2681	272	57	s(b	s(b	NOUN
iajs-2681	272	58	)	)	PUNCT
iajs-2681	273	1	=	=	VERB
iajs-2681	273	2	m.	m.	NOUN
iajs-2681	273	3	the	the	DET
iajs-2681	273	4	condition	condition	NOUN
iajs-2681	273	5	leads	lead	VERB
iajs-2681	273	6	to	to	ADP
iajs-2681	273	7	þ	þ	PROPN
iajs-2681	273	8	is	be	AUX
iajs-2681	273	9	a	a	DET
iajs-2681	273	10	fuzzy	fuzzy	ADJ
iajs-2681	273	11	open	open	ADJ
iajs-2681	273	12	for	for	SCONJ
iajs-2681	273	13	if	if	SCONJ
iajs-2681	273	14	u	u	NOUN
iajs-2681	273	15	is	be	AUX
iajs-2681	273	16	a	a	DET
iajs-2681	273	17	fuzzy	fuzzy	ADJ
iajs-2681	273	18	open	open	ADJ
iajs-2681	273	19	set	set	NOUN
iajs-2681	273	20	of	of	ADP
iajs-2681	273	21	m	m	PROPN
iajs-2681	273	22			PROPN
iajs-2681	273	23	m	m	PROPN
iajs-2681	273	24	,	,	PUNCT
iajs-2681	273	25	then	then	ADV
iajs-2681	273	26	s	s	PART
iajs-2681	273	27	–	–	PUNCT
iajs-2681	273	28	1(mw	1(mw	PROPN
iajs-2681	273	29	⋂	⋂	PROPN
iajs-2681	273	30	u	u	NOUN
iajs-2681	273	31	)	)	PUNCT
iajs-2681	273	32			PROPN
iajs-2681	273	33	þ(u	þ(u	PROPN
iajs-2681	273	34	)	)	PUNCT
iajs-2681	273	35	is	be	AUX
iajs-2681	273	36	a	a	DET
iajs-2681	273	37	fuzzy	fuzzy	ADJ
iajs-2681	273	38	open	open	ADJ
iajs-2681	273	39	set	set	NOUN
iajs-2681	273	40	of	of	ADP
iajs-2681	273	41	b	b	PROPN
iajs-2681	273	42			PROPN
iajs-2681	273	43	w	w	PROPN
iajs-2681	273	44	,	,	PUNCT
iajs-2681	273	45	and	and	CCONJ
iajs-2681	273	46	hence	hence	ADV
iajs-2681	273	47	in	in	ADP
iajs-2681	273	48	b.	b.	PROPN
iajs-2681	273	49	the	the	DET
iajs-2681	273	50	class	class	NOUN
iajs-2681	273	51	of	of	ADP
iajs-2681	273	52	b	b	PROPN
iajs-2681	273	53	fw	fw	PROPN
iajs-2681	273	54	-	-	PUNCT
iajs-2681	273	55	lsl	lsl	NOUN
iajs-2681	273	56	-	-	PUNCT
iajs-2681	273	57	fts	fts	PROPN
iajs-2681	273	58	is	be	AUX
iajs-2681	273	59	a	a	DET
iajs-2681	273	60	finitely	finitely	ADV
iajs-2681	273	61	multiplicative	multiplicative	ADJ
iajs-2681	273	62	stated	state	VERB
iajs-2681	273	63	in	in	ADP
iajs-2681	273	64	.	.	PUNCT
iajs-2681	274	1	ibn	ibn	PROPN
iajs-2681	274	2	al	al	PROPN
iajs-2681	274	3	-	-	PUNCT
iajs-2681	274	4	haitham	haitham	PROPN
iajs-2681	274	5	jour	jour	X
iajs-2681	274	6	.	.	PROPN
iajs-2681	274	7	for	for	ADP
iajs-2681	274	8	pure	pure	ADJ
iajs-2681	274	9	&	&	CCONJ
iajs-2681	274	10	appl	appl	PROPN
iajs-2681	274	11	.	.	PUNCT
iajs-2681	275	1	sci	sci	PROPN
iajs-2681	275	2	.	.	PROPN
iajs-2681	276	1	34(3)2021	34(3)2021	NUM
iajs-2681	276	2	93	93	NUM
iajs-2681	276	3	theorem	theorem	VERB
iajs-2681	276	4	4.2	4.2	NUM
iajs-2681	276	5	.	.	PUNCT
iajs-2681	277	1	let	let	VERB
iajs-2681	277	2	{	{	PUNCT
iajs-2681	277	3	(	(	PUNCT
iajs-2681	277	4	mr	mr	PROPN
iajs-2681	277	5	,	,	PUNCT
iajs-2681	277	6	r	r	PROPN
iajs-2681	277	7	)	)	PUNCT
iajs-2681	277	8	}	}	PUNCT
iajs-2681	278	1	𝑟=1	𝑟=1	VERB
iajs-2681	278	2	𝑘	𝑘	PRON
iajs-2681	278	3	be	be	AUX
iajs-2681	278	4	a	a	DET
iajs-2681	278	5	finite	finite	ADJ
iajs-2681	278	6	family	family	NOUN
iajs-2681	278	7	of	of	ADP
iajs-2681	278	8	fw	fw	PROPN
iajs-2681	278	9	-	-	PUNCT
iajs-2681	278	10	lsl	lsl	NOUN
iajs-2681	278	11	-	-	PUNCT
iajs-2681	278	12	fts	fts	PROPN
iajs-2681	278	13	's	's	PART
iajs-2681	278	14	over	over	ADP
iajs-2681	278	15	(	(	PUNCT
iajs-2681	278	16	b	b	NOUN
iajs-2681	278	17	,	,	PUNCT
iajs-2681	278	18			NOUN
iajs-2681	278	19	)	)	PUNCT
iajs-2681	278	20	.	.	PUNCT
iajs-2681	279	1	then	then	ADV
iajs-2681	279	2	the	the	DET
iajs-2681	279	3	fwftopological	fwftopological	ADJ
iajs-2681	279	4	product	product	NOUN
iajs-2681	279	5	(	(	PUNCT
iajs-2681	279	6	m	m	PROPN
iajs-2681	279	7	=	=	PUNCT
iajs-2681	279	8	∏b	∏b	X
iajs-2681	279	9	mr	mr	PROPN
iajs-2681	279	10	,	,	PUNCT
iajs-2681	279	11			PROPN
iajs-2681	279	12	)	)	PUNCT
iajs-2681	279	13	is	be	AUX
iajs-2681	279	14	a	a	DET
iajs-2681	279	15	fw	fw	PROPN
iajs-2681	279	16	-	-	PUNCT
iajs-2681	279	17	lsl	lsl	NOUN
iajs-2681	279	18	-	-	PUNCT
iajs-2681	279	19	fts	fts	ADJ
iajs-2681	279	20	.	.	PUNCT
iajs-2681	280	1	proof	proof	NOUN
iajs-2681	280	2	.	.	PUNCT
iajs-2681	281	1	let	let	VERB
iajs-2681	281	2	m	m	VERB
iajs-2681	281	3	=	=	SYM
iajs-2681	281	4	(	(	PUNCT
iajs-2681	281	5	mr	mr	PROPN
iajs-2681	281	6	)	)	PUNCT
iajs-2681	281	7	be	be	VERB
iajs-2681	281	8	a	a	DET
iajs-2681	281	9	point	point	NOUN
iajs-2681	281	10	of	of	ADP
iajs-2681	281	11	mb	mb	NOUN
iajs-2681	281	12	;	;	PUNCT
iajs-2681	281	13	b	b	X
iajs-2681	281	14			PROPN
iajs-2681	281	15	b	b	NOUN
iajs-2681	281	16	,	,	PUNCT
iajs-2681	281	17	so	so	SCONJ
iajs-2681	281	18	that	that	SCONJ
iajs-2681	281	19	mr	mr	PROPN
iajs-2681	281	20	=	=	PROPN
iajs-2681	281	21	r(m	r(m	PROPN
iajs-2681	281	22	)	)	PUNCT
iajs-2681	281	23	for	for	ADP
iajs-2681	281	24	every	every	DET
iajs-2681	281	25	index	index	NOUN
iajs-2681	281	26	r.	r.	NOUN
iajs-2681	281	27	since	since	SCONJ
iajs-2681	281	28	mr	mr	PROPN
iajs-2681	281	29	is	be	AUX
iajs-2681	281	30	a	a	DET
iajs-2681	281	31	fw	fw	PROPN
iajs-2681	281	32	-	-	PUNCT
iajs-2681	281	33	lsl	lsl	NOUN
iajs-2681	281	34	-	-	PUNCT
iajs-2681	281	35	fts	fts	X
iajs-2681	281	36	,	,	PUNCT
iajs-2681	281	37	there	there	PRON
iajs-2681	281	38	is	be	VERB
iajs-2681	281	39	a	a	DET
iajs-2681	281	40	fuzzy	fuzzy	ADJ
iajs-2681	281	41	open	open	NOUN
iajs-2681	281	42	set	set	VERB
iajs-2681	281	43	wr	wr	NOUN
iajs-2681	281	44	of	of	ADP
iajs-2681	281	45	b	b	PROPN
iajs-2681	281	46	and	and	CCONJ
iajs-2681	281	47	a	a	DET
iajs-2681	281	48	section	section	NOUN
iajs-2681	281	49	sr	sr	NOUN
iajs-2681	281	50	:	:	PUNCT
iajs-2681	281	51	wr	wr	PROPN
iajs-2681	281	52			VERB
iajs-2681	282	1	mr	mr	PROPN
iajs-2681	282	2	|	|	ADV
iajs-2681	282	3	wr	wr	PROPN
iajs-2681	282	4	,	,	PUNCT
iajs-2681	282	5	where	where	SCONJ
iajs-2681	282	6	sr(b	sr(b	PUNCT
iajs-2681	282	7	)	)	PUNCT
iajs-2681	282	8	=	=	SYM
iajs-2681	283	1	mr	mr	PROPN
iajs-2681	283	2	.	.	PROPN
iajs-2681	283	3	then	then	ADV
iajs-2681	283	4	,	,	PUNCT
iajs-2681	283	5	the	the	DET
iajs-2681	283	6	intersection	intersection	NOUN
iajs-2681	283	7	w	w	PROPN
iajs-2681	283	8	=	=	PROPN
iajs-2681	283	9	w1	w1	PROPN
iajs-2681	283	10	⋂	⋂	PROPN
iajs-2681	283	11	…	…	PUNCT
iajs-2681	283	12	⋂	⋂	PROPN
iajs-2681	283	13	wn	wn	PROPN
iajs-2681	283	14	is	be	AUX
iajs-2681	283	15	a	a	DET
iajs-2681	283	16	fuzzy	fuzzy	ADJ
iajs-2681	283	17	open	open	ADJ
iajs-2681	283	18	set	set	NOUN
iajs-2681	283	19	of	of	ADP
iajs-2681	283	20	b	b	NOUN
iajs-2681	283	21	and	and	CCONJ
iajs-2681	283	22	a	a	DET
iajs-2681	283	23	section	section	NOUN
iajs-2681	283	24	s	s	VERB
iajs-2681	283	25	:	:	PUNCT
iajs-2681	283	26	w	w	ADJ
iajs-2681	283	27			NOUN
iajs-2681	283	28	mw	mw	PROPN
iajs-2681	283	29	is	be	AUX
iajs-2681	283	30	given	give	VERB
iajs-2681	283	31	by	by	ADP
iajs-2681	283	32	(	(	PUNCT
iajs-2681	283	33	r	r	X
iajs-2681	283	34			PROPN
iajs-2681	283	35	s)(w	s)(w	X
iajs-2681	283	36	)	)	PUNCT
iajs-2681	283	37	=	=	SYM
iajs-2681	283	38	sr(w	sr(w	X
iajs-2681	283	39	)	)	PUNCT
iajs-2681	283	40	for	for	ADP
iajs-2681	283	41	every	every	DET
iajs-2681	283	42	index	index	NOUN
iajs-2681	283	43	r	r	NOUN
iajs-2681	283	44	and	and	CCONJ
iajs-2681	283	45	every	every	DET
iajs-2681	283	46	point	point	NOUN
iajs-2681	283	47	w	w	ADP
iajs-2681	283	48			PROPN
iajs-2681	283	49	w.	w.	PROPN
iajs-2681	283	50	theorem	theorem	VERB
iajs-2681	283	51	4.3	4.3	NUM
iajs-2681	283	52	.	.	PUNCT
iajs-2681	284	1	let	let	VERB
iajs-2681	284	2			X
iajs-2681	284	3	:	:	PUNCT
iajs-2681	284	4	m	m	VERB
iajs-2681	284	5			NOUN
iajs-2681	285	1	n	n	CCONJ
iajs-2681	285	2	fuzzy	fuzzy	ADJ
iajs-2681	285	3	continuous	continuous	ADJ
iajs-2681	285	4	,	,	PUNCT
iajs-2681	285	5	surjection	surjection	PROPN
iajs-2681	285	6	fw	fw	PROPN
iajs-2681	285	7	-	-	PUNCT
iajs-2681	285	8	m	m	NOUN
iajs-2681	285	9	,	,	PUNCT
iajs-2681	285	10	where	where	SCONJ
iajs-2681	285	11	(	(	PUNCT
iajs-2681	285	12	m	m	NOUN
iajs-2681	285	13	,	,	PUNCT
iajs-2681	285	14			PROPN
iajs-2681	285	15	)	)	PUNCT
iajs-2681	285	16	and	and	CCONJ
iajs-2681	285	17	(	(	PUNCT
iajs-2681	285	18	n	n	CCONJ
iajs-2681	285	19	,	,	PUNCT
iajs-2681	285	20			NUM
iajs-2681	285	21	)	)	PUNCT
iajs-2681	285	22	are	be	AUX
iajs-2681	285	23	fwfts	fwft	NOUN
iajs-2681	285	24	's	's	PART
iajs-2681	285	25	over	over	ADP
iajs-2681	285	26	(	(	PUNCT
iajs-2681	285	27	b	b	NOUN
iajs-2681	285	28	,	,	PUNCT
iajs-2681	285	29			NOUN
iajs-2681	285	30	)	)	PUNCT
iajs-2681	285	31	.	.	PUNCT
iajs-2681	286	1	if	if	SCONJ
iajs-2681	286	2	m	m	NOUN
iajs-2681	286	3	is	be	AUX
iajs-2681	286	4	a	a	DET
iajs-2681	286	5	fw	fw	PROPN
iajs-2681	286	6	-	-	PUNCT
iajs-2681	286	7	lsl	lsl	NOUN
iajs-2681	286	8	-	-	PUNCT
iajs-2681	286	9	tts	tts	NOUN
iajs-2681	286	10	,	,	PUNCT
iajs-2681	286	11	then	then	ADV
iajs-2681	286	12	n	n	PRON
iajs-2681	286	13	is	be	AUX
iajs-2681	286	14	so	so	ADV
iajs-2681	286	15	.	.	PUNCT
iajs-2681	287	1	proof	proof	NOUN
iajs-2681	287	2	.	.	PUNCT
iajs-2681	288	1	let	let	VERB
iajs-2681	288	2	n	n	PRON
iajs-2681	288	3			PROPN
iajs-2681	288	4	nb	nb	INTJ
iajs-2681	288	5	;	;	PUNCT
iajs-2681	288	6	b	b	X
iajs-2681	288	7			PROPN
iajs-2681	288	8	b.	b.	PROPN
iajs-2681	288	9	then	then	ADV
iajs-2681	288	10	n	n	PROPN
iajs-2681	288	11	=	=	SYM
iajs-2681	288	12	(m	(m	ADJ
iajs-2681	288	13	)	)	PUNCT
iajs-2681	288	14	,	,	PUNCT
iajs-2681	288	15	for	for	ADP
iajs-2681	288	16	some	some	DET
iajs-2681	288	17	m	m	PROPN
iajs-2681	288	18			NOUN
iajs-2681	288	19	mb	mb	NOUN
iajs-2681	288	20	.	.	PUNCT
iajs-2681	289	1	if	if	SCONJ
iajs-2681	289	2	m	m	NOUN
iajs-2681	289	3	is	be	AUX
iajs-2681	289	4	a	a	DET
iajs-2681	289	5	fw	fw	PROPN
iajs-2681	289	6	-	-	PUNCT
iajs-2681	289	7	lsl	lsl	NOUN
iajs-2681	289	8	-	-	PUNCT
iajs-2681	289	9	fts	fts	X
iajs-2681	289	10	,	,	PUNCT
iajs-2681	289	11	then	then	ADV
iajs-2681	289	12	there	there	PRON
iajs-2681	289	13	is	be	VERB
iajs-2681	289	14	a	a	DET
iajs-2681	289	15	fuzzy	fuzzy	ADJ
iajs-2681	289	16	open	open	NOUN
iajs-2681	289	17	set	set	NOUN
iajs-2681	289	18	w	w	PROPN
iajs-2681	289	19	of	of	ADP
iajs-2681	289	20	b	b	PROPN
iajs-2681	289	21	and	and	CCONJ
iajs-2681	289	22	a	a	DET
iajs-2681	289	23	section	section	NOUN
iajs-2681	289	24	s	s	VERB
iajs-2681	289	25	:	:	PUNCT
iajs-2681	289	26	w	w	NOUN
iajs-2681	289	27			NOUN
iajs-2681	289	28	mw	mw	VERB
iajs-2681	289	29	where	where	SCONJ
iajs-2681	289	30	s(b	s(b	NOUN
iajs-2681	289	31	)	)	PUNCT
iajs-2681	289	32	=	=	SYM
iajs-2681	289	33	m.	m.	NOUN
iajs-2681	290	1	then	then	ADV
iajs-2681	290	2			PROPN
iajs-2681	290	3			PROPN
iajs-2681	290	4	s	s	PART
iajs-2681	290	5	:	:	PUNCT
iajs-2681	290	6	w	w	NOUN
iajs-2681	290	7			NOUN
iajs-2681	291	1	nw	nw	PROPN
iajs-2681	291	2	is	be	AUX
iajs-2681	291	3	a	a	DET
iajs-2681	291	4	section	section	NOUN
iajs-2681	291	5	such	such	ADJ
iajs-2681	291	6	that	that	SCONJ
iajs-2681	291	7	s(b	s(b	NOUN
iajs-2681	291	8	)	)	PUNCT
iajs-2681	292	1	=	=	SYM
iajs-2681	292	2	n	n	CCONJ
iajs-2681	292	3	as	as	SCONJ
iajs-2681	292	4	required	require	VERB
iajs-2681	292	5	.	.	PUNCT
iajs-2681	293	1	definition	definition	NOUN
iajs-2681	293	2	4.4	4.4	NUM
iajs-2681	293	3	.	.	PUNCT
iajs-2681	294	1	the	the	DET
iajs-2681	294	2	fwfts	fwft	NOUN
iajs-2681	294	3	(	(	PUNCT
iajs-2681	294	4	m	m	NOUN
iajs-2681	294	5	,	,	PUNCT
iajs-2681	294	6			PROPN
iajs-2681	294	7	)	)	PUNCT
iajs-2681	294	8	over	over	ADP
iajs-2681	294	9	(	(	PUNCT
iajs-2681	294	10	b	b	NOUN
iajs-2681	294	11	,	,	PUNCT
iajs-2681	294	12			NOUN
iajs-2681	294	13	)	)	PUNCT
iajs-2681	294	14	is	be	AUX
iajs-2681	294	15	said	say	VERB
iajs-2681	294	16	to	to	PART
iajs-2681	294	17	be	be	AUX
iajs-2681	294	18	fibrewise	fibrewise	ADV
iajs-2681	294	19	discrete	discrete	ADJ
iajs-2681	294	20	(	(	PUNCT
iajs-2681	294	21	written	write	VERB
iajs-2681	294	22	as	as	ADP
iajs-2681	294	23	fw	fw	ADJ
iajs-2681	294	24	-	-	PUNCT
iajs-2681	294	25	dfts	dft	NOUN
iajs-2681	294	26	)	)	PUNCT
iajs-2681	294	27	if	if	SCONJ
iajs-2681	294	28	the	the	DET
iajs-2681	294	29	proj	proj	NOUN
iajs-2681	294	30	.	.	PUNCT
iajs-2681	295	1	þ	þ	PROPN
iajs-2681	295	2	is	be	AUX
iajs-2681	295	3	a	a	DET
iajs-2681	295	4	local	local	ADJ
iajs-2681	295	5	fuzzy	fuzzy	ADJ
iajs-2681	295	6	homeomorphism	homeomorphism	NOUN
iajs-2681	295	7	(	(	PUNCT
iajs-2681	295	8	i.e.	i.e.	X
iajs-2681	295	9	fuzzy	fuzzy	ADJ
iajs-2681	295	10	continuous	continuous	ADJ
iajs-2681	295	11	,	,	PUNCT
iajs-2681	295	12	fuzzy	fuzzy	ADJ
iajs-2681	295	13	open	open	ADJ
iajs-2681	295	14	,	,	PUNCT
iajs-2681	295	15	one	one	NUM
iajs-2681	295	16	to	to	ADP
iajs-2681	295	17	one	one	NUM
iajs-2681	295	18	,	,	PUNCT
iajs-2681	295	19	onto	onto	ADP
iajs-2681	295	20	)	)	PUNCT
iajs-2681	295	21	.	.	PUNCT
iajs-2681	296	1	this	this	PRON
iajs-2681	296	2	means	mean	VERB
iajs-2681	296	3	,	,	PUNCT
iajs-2681	296	4	we	we	PRON
iajs-2681	296	5	recall	recall	VERB
iajs-2681	296	6	,	,	PUNCT
iajs-2681	296	7	that	that	SCONJ
iajs-2681	296	8	for	for	ADP
iajs-2681	296	9	every	every	DET
iajs-2681	296	10	point	point	NOUN
iajs-2681	296	11	b	b	PROPN
iajs-2681	296	12			PROPN
iajs-2681	296	13	b	b	NOUN
iajs-2681	296	14	and	and	CCONJ
iajs-2681	296	15	every	every	DET
iajs-2681	296	16	point	point	NOUN
iajs-2681	296	17	m	m	VERB
iajs-2681	296	18			NOUN
iajs-2681	296	19	mb	mb	ADP
iajs-2681	296	20	;	;	PUNCT
iajs-2681	296	21	b	b	X
iajs-2681	296	22			PROPN
iajs-2681	296	23	b	b	NOUN
iajs-2681	296	24	there	there	PRON
iajs-2681	296	25	is	be	VERB
iajs-2681	296	26	a	a	DET
iajs-2681	296	27	fuzzy	fuzzy	ADJ
iajs-2681	296	28	open	open	NOUN
iajs-2681	296	29	set	set	VERB
iajs-2681	296	30	v	v	NOUN
iajs-2681	296	31	of	of	ADP
iajs-2681	296	32	m	m	PROPN
iajs-2681	296	33	in	in	ADP
iajs-2681	296	34	m	m	PROPN
iajs-2681	296	35	and	and	CCONJ
iajs-2681	296	36	a	a	DET
iajs-2681	296	37	fuzzy	fuzzy	ADJ
iajs-2681	296	38	open	open	NOUN
iajs-2681	296	39	set	set	NOUN
iajs-2681	296	40	w	w	PROPN
iajs-2681	296	41	of	of	ADP
iajs-2681	296	42	b	b	PROPN
iajs-2681	296	43	in	in	ADP
iajs-2681	296	44	b	b	PROPN
iajs-2681	296	45	where	where	SCONJ
iajs-2681	296	46	þ	þ	PROPN
iajs-2681	296	47	maps	map	VERB
iajs-2681	296	48	v	v	PRON
iajs-2681	296	49	fuzzy	fuzzy	ADJ
iajs-2681	296	50	homeomorphically	homeomorphically	ADV
iajs-2681	296	51	onto	onto	ADP
iajs-2681	296	52	w	w	PROPN
iajs-2681	296	53	,	,	PUNCT
iajs-2681	296	54	in	in	ADP
iajs-2681	296	55	that	that	DET
iajs-2681	296	56	case	case	NOUN
iajs-2681	296	57	we	we	PRON
iajs-2681	296	58	say	say	VERB
iajs-2681	296	59	that	that	SCONJ
iajs-2681	296	60	w	w	NOUN
iajs-2681	296	61	is	be	AUX
iajs-2681	296	62	evenly	evenly	ADV
iajs-2681	296	63	covered	cover	VERB
iajs-2681	296	64	by	by	ADP
iajs-2681	296	65	v.	v.	ADP
iajs-2681	296	66	it	it	PRON
iajs-2681	296	67	is	be	AUX
iajs-2681	296	68	clear	clear	ADJ
iajs-2681	296	69	that	that	SCONJ
iajs-2681	296	70	fwd	fwd	NOUN
iajs-2681	296	71	-	-	PUNCT
iajs-2681	296	72	fts	fts	PROPN
iajs-2681	296	73	's	's	PART
iajs-2681	296	74	are	be	AUX
iajs-2681	296	75	fw	fw	ADJ
iajs-2681	296	76	-	-	PUNCT
iajs-2681	296	77	lsl	lsl	NOUN
iajs-2681	296	78	-	-	ADJ
iajs-2681	296	79	fts	fts	X
iajs-2681	296	80	there	there	ADV
iajs-2681	296	81	for	for	ADP
iajs-2681	296	82	fwofts	fwoft	NOUN
iajs-2681	296	83	.	.	PUNCT
iajs-2681	297	1	the	the	DET
iajs-2681	297	2	class	class	NOUN
iajs-2681	297	3	of	of	ADP
iajs-2681	297	4	fw	fw	PROPN
iajs-2681	297	5	-	-	PUNCT
iajs-2681	297	6	d	d	NOUN
iajs-2681	297	7	-	-	PUNCT
iajs-2681	297	8	fts	fts	PROPN
iajs-2681	297	9	's	's	PART
iajs-2681	297	10	is	be	AUX
iajs-2681	297	11	a	a	DET
iajs-2681	297	12	finitely	finitely	ADV
iajs-2681	297	13	multiplicative	multiplicative	VERB
iajs-2681	297	14	.	.	PUNCT
iajs-2681	298	1	theorem	theorem	NOUN
iajs-2681	298	2	4.5	4.5	NUM
iajs-2681	298	3	.	.	PUNCT
iajs-2681	299	1	let	let	VERB
iajs-2681	299	2	{	{	PUNCT
iajs-2681	299	3	(	(	PUNCT
iajs-2681	299	4	mr	mr	PROPN
iajs-2681	299	5	,	,	PUNCT
iajs-2681	299	6	r	r	PROPN
iajs-2681	299	7	)	)	PUNCT
iajs-2681	299	8	}	}	PUNCT
iajs-2681	300	1	𝑟=1	𝑟=1	VERB
iajs-2681	300	2	𝑘	𝑘	PRON
iajs-2681	300	3	be	be	AUX
iajs-2681	300	4	a	a	DET
iajs-2681	300	5	finite	finite	ADJ
iajs-2681	300	6	family	family	NOUN
iajs-2681	300	7	of	of	ADP
iajs-2681	300	8	fw	fw	PROPN
iajs-2681	300	9	-	-	PUNCT
iajs-2681	300	10	d	d	NOUN
iajs-2681	300	11	-	-	PUNCT
iajs-2681	300	12	fts	fts	PROPN
iajs-2681	300	13	over	over	ADP
iajs-2681	300	14	(	(	PUNCT
iajs-2681	300	15	b	b	NOUN
iajs-2681	300	16	,	,	PUNCT
iajs-2681	300	17			NOUN
iajs-2681	300	18	)	)	PUNCT
iajs-2681	300	19	.	.	PUNCT
iajs-2681	301	1	then	then	ADV
iajs-2681	301	2	the	the	DET
iajs-2681	301	3	fwftproduct	fwftproduct	NOUN
iajs-2681	301	4	(	(	PUNCT
iajs-2681	301	5	m	m	NOUN
iajs-2681	301	6	=	=	PUNCT
iajs-2681	301	7	b	b	PROPN
iajs-2681	301	8	mr	mr	PROPN
iajs-2681	301	9	,	,	PUNCT
iajs-2681	301	10			PROPN
iajs-2681	301	11	)	)	PUNCT
iajs-2681	301	12	is	be	AUX
iajs-2681	301	13	a	a	DET
iajs-2681	301	14	fw	fw	ADJ
iajs-2681	301	15	-	-	PUNCT
iajs-2681	301	16	d	d	NOUN
iajs-2681	301	17	-	-	PUNCT
iajs-2681	301	18	fts	fts	ADJ
iajs-2681	301	19	.	.	PUNCT
iajs-2681	301	20	proof	proof	NOUN
iajs-2681	301	21	.	.	PUNCT
iajs-2681	302	1	given	give	VERB
iajs-2681	302	2	a	a	DET
iajs-2681	302	3	point	point	NOUN
iajs-2681	302	4	m	m	NOUN
iajs-2681	302	5			NOUN
iajs-2681	302	6	mb	mb	ADP
iajs-2681	302	7	;	;	PUNCT
iajs-2681	302	8	b	b	X
iajs-2681	302	9			PROPN
iajs-2681	302	10	b	b	NOUN
iajs-2681	302	11	,	,	PUNCT
iajs-2681	302	12	there	there	PRON
iajs-2681	302	13	is	be	VERB
iajs-2681	302	14	for	for	ADP
iajs-2681	302	15	every	every	DET
iajs-2681	302	16	index	index	NOUN
iajs-2681	302	17	r	r	NOUN
iajs-2681	302	18	an	an	DET
iajs-2681	302	19	open	open	ADJ
iajs-2681	302	20	set	set	NOUN
iajs-2681	302	21	ur	ur	INTJ
iajs-2681	302	22	of	of	ADP
iajs-2681	302	23	r(m	r(m	PROPN
iajs-2681	302	24	)	)	PUNCT
iajs-2681	302	25	in	in	ADP
iajs-2681	302	26	mr	mr	PROPN
iajs-2681	302	27	,	,	PUNCT
iajs-2681	302	28	where	where	SCONJ
iajs-2681	302	29	the	the	DET
iajs-2681	302	30	proj	proj	NOUN
iajs-2681	302	31	.	.	PUNCT
iajs-2681	303	1	þr	þr	PUNCT
iajs-2681	304	1	=	=	PUNCT
iajs-2681	304	2	þ	þ	PROPN
iajs-2681	304	3			PROPN
iajs-2681	304	4	𝜋𝑟	𝜋𝑟	PROPN
iajs-2681	304	5	−1	−1	NOUN
iajs-2681	304	6	maps	map	NOUN
iajs-2681	304	7	ur	ur	INTJ
iajs-2681	304	8	fuzzy	fuzzy	ADJ
iajs-2681	304	9	homeomorphically	homeomorphically	ADV
iajs-2681	304	10	onto	onto	ADP
iajs-2681	304	11	the	the	DET
iajs-2681	304	12	fuzzy	fuzzy	ADJ
iajs-2681	304	13	open	open	ADJ
iajs-2681	304	14	þr(ur	þr(ur	NOUN
iajs-2681	304	15	)	)	PUNCT
iajs-2681	305	1	=	=	SYM
iajs-2681	305	2	wr	wr	PROPN
iajs-2681	305	3	of	of	ADP
iajs-2681	305	4	b.	b.	PROPN
iajs-2681	305	5	then	then	ADV
iajs-2681	305	6	the	the	DET
iajs-2681	305	7	fuzzy	fuzzy	ADJ
iajs-2681	305	8	open	open	ADJ
iajs-2681	305	9	b	b	PRON
iajs-2681	305	10	ur	ur	INTJ
iajs-2681	305	11	of	of	ADP
iajs-2681	305	12	m	m	PROPN
iajs-2681	305	13	is	be	AUX
iajs-2681	305	14	mapped	map	VERB
iajs-2681	305	15	fuzzy	fuzzy	ADJ
iajs-2681	305	16	homeomorphically	homeomorphically	ADV
iajs-2681	305	17	onto	onto	ADP
iajs-2681	305	18	the	the	DET
iajs-2681	305	19	intersection	intersection	NOUN
iajs-2681	305	20	w	w	PROPN
iajs-2681	305	21	=	=	SYM
iajs-2681	305	22	⋂	⋂	PROPN
iajs-2681	305	23	wr	wr	NOUN
iajs-2681	305	24	which	which	PRON
iajs-2681	305	25	is	be	AUX
iajs-2681	305	26	a	a	DET
iajs-2681	305	27	fuzzy	fuzzy	ADJ
iajs-2681	305	28	open	open	NOUN
iajs-2681	305	29	of	of	ADP
iajs-2681	305	30	b.	b.	PROPN
iajs-2681	305	31	an	an	DET
iajs-2681	305	32	attractive	attractive	ADJ
iajs-2681	305	33	characterization	characterization	NOUN
iajs-2681	305	34	of	of	ADP
iajs-2681	305	35	fw	fw	PROPN
iajs-2681	305	36	-	-	PUNCT
iajs-2681	305	37	d	d	NOUN
iajs-2681	305	38	-	-	PUNCT
iajs-2681	305	39	fts	fts	PROPN
iajs-2681	305	40	's	's	PART
iajs-2681	305	41	is	be	AUX
iajs-2681	305	42	given	give	VERB
iajs-2681	305	43	by	by	ADP
iajs-2681	305	44	the	the	DET
iajs-2681	305	45	following	following	NOUN
iajs-2681	305	46	:	:	PUNCT
iajs-2681	305	47	theorem	theorem	VERB
iajs-2681	305	48	4.6	4.6	NUM
iajs-2681	305	49	.	.	PUNCT
iajs-2681	306	1	if	if	SCONJ
iajs-2681	306	2	(	(	PUNCT
iajs-2681	306	3	m	m	NOUN
iajs-2681	306	4	,	,	PUNCT
iajs-2681	306	5			PROPN
iajs-2681	306	6	)	)	PUNCT
iajs-2681	306	7	is	be	AUX
iajs-2681	306	8	a	a	DET
iajs-2681	306	9	fwfts	fwft	NOUN
iajs-2681	306	10	over	over	ADP
iajs-2681	306	11	(	(	PUNCT
iajs-2681	306	12	b	b	NOUN
iajs-2681	306	13	,	,	PUNCT
iajs-2681	306	14			NOUN
iajs-2681	306	15	)	)	PUNCT
iajs-2681	306	16	.	.	PUNCT
iajs-2681	307	1	then	then	ADV
iajs-2681	307	2	,	,	PUNCT
iajs-2681	307	3	m	m	PROPN
iajs-2681	307	4	is	be	AUX
iajs-2681	307	5	a	a	DET
iajs-2681	307	6	fw	fw	ADJ
iajs-2681	307	7	-	-	PUNCT
iajs-2681	307	8	d	d	NOUN
iajs-2681	307	9	-	-	ADJ
iajs-2681	307	10	fts	fts	PROPN
iajs-2681	307	11	iff	iff	PROPN
iajs-2681	307	12	(	(	PUNCT
iajs-2681	307	13	a	a	NOUN
iajs-2681	307	14	)	)	PUNCT
iajs-2681	307	15	m	m	VERB
iajs-2681	307	16	is	be	AUX
iajs-2681	307	17	a	a	DET
iajs-2681	307	18	fwofts	fwoft	NOUN
iajs-2681	307	19	(	(	PUNCT
iajs-2681	307	20	b	b	NOUN
iajs-2681	307	21	)	)	PUNCT
iajs-2681	307	22	the	the	DET
iajs-2681	307	23	diagonal	diagonal	ADJ
iajs-2681	307	24	embedding	embedding	NOUN
iajs-2681	307	25			NOUN
iajs-2681	307	26	:	:	PUNCT
iajs-2681	307	27	m	m	VERB
iajs-2681	307	28			NOUN
iajs-2681	308	1	m	m	VERB
iajs-2681	308	2	b	b	PROPN
iajs-2681	308	3	m	m	VERB
iajs-2681	308	4	is	be	AUX
iajs-2681	308	5	a	a	DET
iajs-2681	308	6	fuzzy	fuzzy	ADJ
iajs-2681	308	7	open	open	ADJ
iajs-2681	308	8	proof	proof	NOUN
iajs-2681	308	9	.	.	PUNCT
iajs-2681	309	1	(	(	PUNCT
iajs-2681	309	2			NOUN
iajs-2681	309	3	)	)	PUNCT
iajs-2681	309	4	suppose	suppose	VERB
iajs-2681	309	5	that	that	SCONJ
iajs-2681	309	6	(	(	PUNCT
iajs-2681	309	7	a	a	X
iajs-2681	309	8	)	)	PUNCT
iajs-2681	309	9	and	and	CCONJ
iajs-2681	309	10	(	(	PUNCT
iajs-2681	309	11	b	b	X
iajs-2681	309	12	)	)	PUNCT
iajs-2681	309	13	are	be	AUX
iajs-2681	309	14	satisfied	satisfied	ADJ
iajs-2681	309	15	.	.	PUNCT
iajs-2681	310	1	let	let	VERB
iajs-2681	310	2	m	m	PRON
iajs-2681	310	3			NOUN
iajs-2681	310	4	mb	mb	ADP
iajs-2681	310	5	;	;	PUNCT
iajs-2681	310	6	b	b	X
iajs-2681	310	7			PROPN
iajs-2681	310	8	b	b	PROPN
iajs-2681	310	9	,	,	PUNCT
iajs-2681	310	10	then	then	ADV
iajs-2681	310	11	(m	(m	PROPN
iajs-2681	310	12	)	)	PUNCT
iajs-2681	311	1	=	=	PUNCT
iajs-2681	311	2	(	(	PUNCT
iajs-2681	311	3	m	m	PROPN
iajs-2681	311	4	,	,	PUNCT
iajs-2681	311	5	m	m	PROPN
iajs-2681	311	6	)	)	PUNCT
iajs-2681	311	7	admits	admit	VERB
iajs-2681	311	8	a	a	DET
iajs-2681	311	9	fuzzy	fuzzy	ADJ
iajs-2681	311	10	open	open	NOUN
iajs-2681	311	11	set	set	NOUN
iajs-2681	311	12	in	in	ADP
iajs-2681	311	13	m	m	PROPN
iajs-2681	311	14	b	b	PROPN
iajs-2681	311	15	m	m	VERB
iajs-2681	311	16	which	which	PRON
iajs-2681	311	17	is	be	AUX
iajs-2681	311	18	entirely	entirely	ADV
iajs-2681	311	19	contained	contain	VERB
iajs-2681	311	20	in	in	ADP
iajs-2681	311	21	(m	(m	PROPN
iajs-2681	311	22	)	)	PUNCT
iajs-2681	311	23	.	.	PUNCT
iajs-2681	312	1	without	without	ADP
iajs-2681	312	2	real	real	ADJ
iajs-2681	312	3	lacking	lacking	NOUN
iajs-2681	312	4	in	in	ADP
iajs-2681	312	5	general	general	ADJ
iajs-2681	312	6	,	,	PUNCT
iajs-2681	312	7	we	we	PRON
iajs-2681	312	8	may	may	AUX
iajs-2681	312	9	suppose	suppose	VERB
iajs-2681	312	10	the	the	DET
iajs-2681	312	11	fuzzy	fuzzy	ADJ
iajs-2681	312	12	open	open	ADJ
iajs-2681	312	13	set	set	NOUN
iajs-2681	312	14	is	be	AUX
iajs-2681	312	15	of	of	ADP
iajs-2681	312	16	the	the	DET
iajs-2681	312	17	form	form	NOUN
iajs-2681	312	18	u	u	PROPN
iajs-2681	312	19	b	b	PROPN
iajs-2681	312	20	u	u	NOUN
iajs-2681	312	21	,	,	PUNCT
iajs-2681	312	22	where	where	SCONJ
iajs-2681	312	23	u	u	NOUN
iajs-2681	312	24	is	be	AUX
iajs-2681	312	25	a	a	DET
iajs-2681	312	26	fuzzy	fuzzy	ADJ
iajs-2681	312	27	open	open	ADJ
iajs-2681	312	28	set	set	NOUN
iajs-2681	312	29	of	of	ADP
iajs-2681	312	30	m	m	PROPN
iajs-2681	312	31	in	in	ADP
iajs-2681	312	32	m.	m.	NOUN
iajs-2681	312	33	then	then	ADV
iajs-2681	312	34	þ|u	þ|u	PRON
iajs-2681	312	35	is	be	AUX
iajs-2681	312	36	a	a	DET
iajs-2681	312	37	fuzzy	fuzzy	ADJ
iajs-2681	312	38	homeomorphism	homeomorphism	NOUN
iajs-2681	312	39	.	.	PUNCT
iajs-2681	313	1	therefore	therefore	ADV
iajs-2681	313	2	,	,	PUNCT
iajs-2681	313	3	m	m	VERB
iajs-2681	313	4	is	be	AUX
iajs-2681	313	5	a	a	DET
iajs-2681	313	6	fw	fw	ADJ
iajs-2681	313	7	-	-	PUNCT
iajs-2681	313	8	d	d	NOUN
iajs-2681	313	9	-	-	PUNCT
iajs-2681	313	10	fts	fts	X
iajs-2681	313	11	.	.	PUNCT
iajs-2681	314	1	(	(	PUNCT
iajs-2681	314	2			NOUN
iajs-2681	314	3	)	)	PUNCT
iajs-2681	314	4	assume	assume	VERB
iajs-2681	314	5	that	that	SCONJ
iajs-2681	314	6	m	m	PROPN
iajs-2681	314	7	is	be	AUX
iajs-2681	314	8	a	a	DET
iajs-2681	314	9	fw	fw	ADJ
iajs-2681	314	10	-	-	PUNCT
iajs-2681	314	11	d	d	NOUN
iajs-2681	314	12	-	-	PUNCT
iajs-2681	314	13	fts	fts	X
iajs-2681	314	14	.	.	PUNCT
iajs-2681	315	1	we	we	PRON
iajs-2681	315	2	have	have	AUX
iajs-2681	315	3	already	already	ADV
iajs-2681	315	4	seen	see	VERB
iajs-2681	315	5	that	that	SCONJ
iajs-2681	315	6	m	m	PROPN
iajs-2681	315	7	is	be	AUX
iajs-2681	315	8	a	a	DET
iajs-2681	315	9	fwofts	fwoft	NOUN
iajs-2681	315	10	.	.	PUNCT
iajs-2681	316	1	to	to	PART
iajs-2681	316	2	prove	prove	VERB
iajs-2681	316	3	that	that	PRON
iajs-2681	316	4			PUNCT
iajs-2681	316	5	is	be	AUX
iajs-2681	316	6	a	a	DET
iajs-2681	316	7	fuzzy	fuzzy	ADJ
iajs-2681	316	8	open	open	NOUN
iajs-2681	316	9	,	,	PUNCT
iajs-2681	316	10	it	it	PRON
iajs-2681	316	11	is	be	AUX
iajs-2681	316	12	sufficient	sufficient	ADJ
iajs-2681	316	13	to	to	PART
iajs-2681	316	14	prove	prove	VERB
iajs-2681	316	15	that	that	SCONJ
iajs-2681	316	16	(m	(m	PROPN
iajs-2681	316	17	)	)	PUNCT
iajs-2681	316	18	is	be	AUX
iajs-2681	316	19	a	a	DET
iajs-2681	316	20	fuzzy	fuzzy	ADJ
iajs-2681	316	21	open	open	ADJ
iajs-2681	316	22	in	in	ADP
iajs-2681	316	23	m	m	PROPN
iajs-2681	316	24	b	b	PROPN
iajs-2681	316	25	m.	m.	NOUN
iajs-2681	316	26	so	so	ADV
iajs-2681	316	27	let	let	VERB
iajs-2681	316	28	m	m	PRON
iajs-2681	316	29			NOUN
iajs-2681	316	30	mb	mb	ADP
iajs-2681	316	31	;	;	PUNCT
iajs-2681	316	32	b	b	X
iajs-2681	316	33			PROPN
iajs-2681	316	34	b	b	NUM
iajs-2681	316	35	,	,	PUNCT
iajs-2681	316	36	and	and	CCONJ
iajs-2681	316	37	let	let	VERB
iajs-2681	316	38	u	u	PRON
iajs-2681	316	39	be	be	AUX
iajs-2681	316	40	a	a	DET
iajs-2681	316	41	fuzzy	fuzzy	ADJ
iajs-2681	316	42	open	open	ADJ
iajs-2681	316	43	set	set	NOUN
iajs-2681	316	44	of	of	ADP
iajs-2681	316	45	m	m	PROPN
iajs-2681	316	46	in	in	ADP
iajs-2681	316	47	m	m	PROPN
iajs-2681	316	48	,	,	PUNCT
iajs-2681	316	49	where	where	SCONJ
iajs-2681	316	50	w	w	NOUN
iajs-2681	316	51	=	=	PUNCT
iajs-2681	316	52	þ(u	þ(u	PROPN
iajs-2681	316	53	)	)	PUNCT
iajs-2681	316	54	is	be	AUX
iajs-2681	316	55	a	a	DET
iajs-2681	316	56	fuzzy	fuzzy	ADJ
iajs-2681	316	57	open	open	ADJ
iajs-2681	316	58	set	set	NOUN
iajs-2681	316	59	of	of	ADP
iajs-2681	316	60	b	b	PROPN
iajs-2681	316	61	in	in	ADP
iajs-2681	316	62	b	b	PROPN
iajs-2681	316	63	and	and	CCONJ
iajs-2681	316	64	þ	þ	PROPN
iajs-2681	316	65	ibn	ibn	PROPN
iajs-2681	316	66	al	al	PROPN
iajs-2681	316	67	-	-	PUNCT
iajs-2681	316	68	haitham	haitham	PROPN
iajs-2681	316	69	jour	jour	X
iajs-2681	316	70	.	.	PROPN
iajs-2681	317	1	for	for	ADP
iajs-2681	317	2	pure	pure	ADJ
iajs-2681	317	3	&	&	CCONJ
iajs-2681	317	4	appl	appl	PROPN
iajs-2681	317	5	.	.	PUNCT
iajs-2681	318	1	sci	sci	PROPN
iajs-2681	318	2	.	.	PROPN
iajs-2681	319	1	34(3)2021	34(3)2021	NUM
iajs-2681	319	2	94	94	NUM
iajs-2681	319	3	maps	map	NOUN
iajs-2681	319	4	u	u	NOUN
iajs-2681	319	5	fuzzy	fuzzy	ADJ
iajs-2681	319	6	homeomorphically	homeomorphically	ADV
iajs-2681	319	7	onto	onto	ADP
iajs-2681	319	8	w.	w.	PROPN
iajs-2681	319	9	then	then	ADV
iajs-2681	319	10	u	u	PROPN
iajs-2681	319	11	b	b	PROPN
iajs-2681	319	12	u	u	NOUN
iajs-2681	319	13	is	be	AUX
iajs-2681	319	14	contained	contain	VERB
iajs-2681	319	15	in	in	ADP
iajs-2681	319	16	(m	(m	PROPN
iajs-2681	319	17	)	)	PUNCT
iajs-2681	319	18	since	since	SCONJ
iajs-2681	319	19	if	if	SCONJ
iajs-2681	319	20	not	not	PART
iajs-2681	319	21	then	then	ADV
iajs-2681	319	22	there	there	PRON
iajs-2681	319	23	exist	exist	VERB
iajs-2681	319	24	distinct	distinct	ADJ
iajs-2681	319	25			NOUN
iajs-2681	319	26	,	,	PUNCT
iajs-2681	319	27			X
iajs-2681	319	28	*	*	PROPN
iajs-2681	319	29			PROPN
iajs-2681	319	30	mw	mw	NOUN
iajs-2681	319	31	,	,	PUNCT
iajs-2681	319	32	where	where	SCONJ
iajs-2681	319	33	w	w	ADP
iajs-2681	319	34			PROPN
iajs-2681	319	35	w	w	PROPN
iajs-2681	319	36	and	and	CCONJ
iajs-2681	319	37			ADJ
iajs-2681	319	38	,	,	PUNCT
iajs-2681	319	39			X
iajs-2681	319	40	*	*	SYM
iajs-2681	319	41			PROPN
iajs-2681	319	42	u	u	NOUN
iajs-2681	319	43	,	,	PUNCT
iajs-2681	319	44	which	which	PRON
iajs-2681	319	45	is	be	AUX
iajs-2681	319	46	absurd	absurd	ADJ
iajs-2681	319	47	.	.	PUNCT
iajs-2681	320	1	fuzzy	fuzzy	ADJ
iajs-2681	320	2	open	open	ADJ
iajs-2681	320	3	subset	subset	NOUN
iajs-2681	320	4	of	of	ADP
iajs-2681	320	5	fw	fw	PROPN
iajs-2681	320	6	-	-	PUNCT
iajs-2681	320	7	d	d	NOUN
iajs-2681	320	8	-	-	PUNCT
iajs-2681	320	9	fts	fts	PROPN
iajs-2681	320	10	's	's	PART
iajs-2681	320	11	is	be	AUX
iajs-2681	320	12	also	also	ADV
iajs-2681	320	13	fw	fw	ADJ
iajs-2681	320	14	-	-	PUNCT
iajs-2681	320	15	d	d	NOUN
iajs-2681	320	16	-	-	PUNCT
iajs-2681	320	17	fts	fts	ADJ
iajs-2681	320	18	,	,	PUNCT
iajs-2681	320	19	actually	actually	ADV
iajs-2681	320	20	,	,	PUNCT
iajs-2681	320	21	we	we	PRON
iajs-2681	320	22	have	have	VERB
iajs-2681	320	23	.	.	PUNCT
iajs-2681	321	1	theorem	theorem	VERB
iajs-2681	321	2	4.7	4.7	NUM
iajs-2681	321	3	.	.	PUNCT
iajs-2681	322	1	let	let	VERB
iajs-2681	322	2			X
iajs-2681	322	3	:	:	PUNCT
iajs-2681	322	4	m	m	VERB
iajs-2681	322	5			NOUN
iajs-2681	322	6	n	n	AUX
iajs-2681	322	7	be	be	AUX
iajs-2681	322	8	a	a	DET
iajs-2681	322	9	fuzzy	fuzzy	ADJ
iajs-2681	322	10	continuous	continuous	ADJ
iajs-2681	322	11	,	,	PUNCT
iajs-2681	322	12	injection	injection	NOUN
iajs-2681	322	13	fw	fw	PROPN
iajs-2681	322	14	-	-	PUNCT
iajs-2681	322	15	m	m	NOUN
iajs-2681	322	16	,	,	PUNCT
iajs-2681	322	17	where	where	SCONJ
iajs-2681	322	18	(	(	PUNCT
iajs-2681	322	19	m	m	NOUN
iajs-2681	322	20	,	,	PUNCT
iajs-2681	322	21			PROPN
iajs-2681	322	22	)	)	PUNCT
iajs-2681	322	23	and	and	CCONJ
iajs-2681	322	24	(	(	PUNCT
iajs-2681	322	25	n	n	CCONJ
iajs-2681	322	26	,	,	PUNCT
iajs-2681	322	27			NUM
iajs-2681	322	28	)	)	PUNCT
iajs-2681	322	29	are	be	AUX
iajs-2681	322	30	fwofts	fwoft	NOUN
iajs-2681	322	31	's	's	PART
iajs-2681	322	32	over	over	ADP
iajs-2681	322	33	(	(	PUNCT
iajs-2681	322	34	b	b	NOUN
iajs-2681	322	35	,	,	PUNCT
iajs-2681	322	36			NOUN
iajs-2681	322	37	)	)	PUNCT
iajs-2681	322	38	.	.	PUNCT
iajs-2681	323	1	if	if	SCONJ
iajs-2681	323	2	n	n	PRON
iajs-2681	323	3	is	be	AUX
iajs-2681	323	4	a	a	DET
iajs-2681	323	5	fw	fw	ADJ
iajs-2681	323	6	-	-	PUNCT
iajs-2681	323	7	d	d	NOUN
iajs-2681	323	8	-	-	PUNCT
iajs-2681	323	9	fts	fts	X
iajs-2681	323	10	,	,	PUNCT
iajs-2681	323	11	then	then	ADV
iajs-2681	323	12	m	m	NOUN
iajs-2681	323	13	is	be	AUX
iajs-2681	323	14	so	so	ADV
iajs-2681	323	15	.	.	PUNCT
iajs-2681	324	1	proof	proof	NOUN
iajs-2681	324	2	.	.	PUNCT
iajs-2681	325	1	consider	consider	VERB
iajs-2681	325	2	the	the	DET
iajs-2681	325	3	diagram	diagram	NOUN
iajs-2681	325	4	shown	show	VERB
iajs-2681	325	5	below	below	ADP
iajs-2681	325	6	.	.	PUNCT
iajs-2681	326	1			X
iajs-2681	327	1	m	m	VERB
iajs-2681	327	2	m	m	VERB
iajs-2681	327	3	b	b	PROPN
iajs-2681	327	4	m	m	PROPN
iajs-2681	327	5			PROPN
iajs-2681	327	6			PROPN
iajs-2681	327	7			PROPN
iajs-2681	327	8			PROPN
iajs-2681	327	9			PROPN
iajs-2681	327	10	n	n	CCONJ
iajs-2681	327	11	n	n	PRON
iajs-2681	327	12	b	b	PROPN
iajs-2681	328	1	n	n	PRON
iajs-2681	328	2	figure	figure	VERB
iajs-2681	328	3	2	2	NUM
iajs-2681	328	4	.	.	PUNCT
iajs-2681	328	5	diagraph	diagraph	NOUN
iajs-2681	328	6	of	of	ADP
iajs-2681	328	7	theorem	theorem	NOUN
iajs-2681	328	8	4.7	4.7	NUM
iajs-2681	328	9	.	.	PUNCT
iajs-2681	329	1	since	since	SCONJ
iajs-2681	329	2			PROPN
iajs-2681	329	3	is	be	AUX
iajs-2681	329	4	a	a	DET
iajs-2681	329	5	fuzzy	fuzzy	ADJ
iajs-2681	329	6	continuous	continuous	ADJ
iajs-2681	329	7	so	so	ADV
iajs-2681	329	8	is	be	AUX
iajs-2681	329	9			PROPN
iajs-2681	329	10			PROPN
iajs-2681	329	11	.	.	PROPN
iajs-2681	329	12	now	now	ADV
iajs-2681	329	13	(n	(n	PROPN
iajs-2681	329	14	)	)	PUNCT
iajs-2681	329	15	is	be	AUX
iajs-2681	329	16	open	open	ADJ
iajs-2681	329	17	in	in	ADP
iajs-2681	329	18	n	n	DET
iajs-2681	329	19	b	b	PROPN
iajs-2681	329	20	n	n	CCONJ
iajs-2681	329	21	,	,	PUNCT
iajs-2681	329	22	by	by	ADP
iajs-2681	329	23	theorem	theorem	NOUN
iajs-2681	329	24	(	(	PUNCT
iajs-2681	329	25	4.6	4.6	NUM
iajs-2681	329	26	)	)	PUNCT
iajs-2681	329	27	.	.	PUNCT
iajs-2681	330	1	since	since	SCONJ
iajs-2681	330	2	n	n	NUM
iajs-2681	330	3	is	be	AUX
iajs-2681	330	4	a	a	DET
iajs-2681	330	5	fw	fw	ADJ
iajs-2681	330	6	-	-	PUNCT
iajs-2681	330	7	d	d	NOUN
iajs-2681	330	8	-	-	PUNCT
iajs-2681	330	9	fts	fts	X
iajs-2681	330	10	,	,	PUNCT
iajs-2681	330	11	then	then	ADV
iajs-2681	330	12	(m	(m	PROPN
iajs-2681	330	13	)	)	PUNCT
iajs-2681	331	1	=	=	SYM
iajs-2681	331	2	((–1	((–1	PROPN
iajs-2681	331	3	(	(	PUNCT
iajs-2681	331	4	n	n	CCONJ
iajs-2681	331	5	)	)	PUNCT
iajs-2681	331	6	)	)	PUNCT
iajs-2681	331	7	)	)	PUNCT
iajs-2681	332	1	=	=	PUNCT
iajs-2681	332	2	(	(	PUNCT
iajs-2681	332	3			X
iajs-2681	332	4			PROPN
iajs-2681	332	5	)–1((n	)–1((n	PROPN
iajs-2681	332	6	)	)	PUNCT
iajs-2681	332	7	)	)	PUNCT
iajs-2681	332	8	is	be	AUX
iajs-2681	332	9	a	a	DET
iajs-2681	332	10	fuzzy	fuzzy	ADJ
iajs-2681	332	11	open	open	ADJ
iajs-2681	332	12	in	in	ADP
iajs-2681	332	13	m	m	PROPN
iajs-2681	332	14	b	b	PROPN
iajs-2681	332	15	m.	m.	NOUN
iajs-2681	332	16	thus	thus	ADV
iajs-2681	332	17	,	,	PUNCT
iajs-2681	332	18	theorem	theorem	ADJ
iajs-2681	332	19	(	(	PUNCT
iajs-2681	332	20	4.7	4.7	NUM
iajs-2681	332	21	)	)	PUNCT
iajs-2681	332	22	follows	follow	VERB
iajs-2681	332	23	from	from	ADP
iajs-2681	332	24	theorem	theorem	NOUN
iajs-2681	332	25	(	(	PUNCT
iajs-2681	332	26	4.6	4.6	NUM
iajs-2681	332	27	)	)	PUNCT
iajs-2681	332	28	.	.	PUNCT
iajs-2681	333	1	theorem	theorem	NOUN
iajs-2681	333	2	4.8	4.8	NUM
iajs-2681	333	3	.	.	PUNCT
iajs-2681	334	1	assume	assume	VERB
iajs-2681	334	2	that	that	SCONJ
iajs-2681	334	3			PROPN
iajs-2681	334	4	:	:	PUNCT
iajs-2681	335	1	m	m	VERB
iajs-2681	335	2			NOUN
iajs-2681	335	3	n	n	ADV
iajs-2681	335	4	is	be	AUX
iajs-2681	335	5	a	a	DET
iajs-2681	335	6	fuzzy	fuzzy	ADJ
iajs-2681	335	7	open	open	NOUN
iajs-2681	335	8	,	,	PUNCT
iajs-2681	335	9	surjection	surjection	PROPN
iajs-2681	335	10	fw	fw	PROPN
iajs-2681	335	11	-	-	PUNCT
iajs-2681	335	12	m	m	NOUN
iajs-2681	335	13	,	,	PUNCT
iajs-2681	335	14	where	where	SCONJ
iajs-2681	335	15	(	(	PUNCT
iajs-2681	335	16	m	m	NOUN
iajs-2681	335	17	,	,	PUNCT
iajs-2681	335	18			PROPN
iajs-2681	335	19	)	)	PUNCT
iajs-2681	335	20	and	and	CCONJ
iajs-2681	335	21	(	(	PUNCT
iajs-2681	335	22	n	n	CCONJ
iajs-2681	335	23	,	,	PUNCT
iajs-2681	335	24			NUM
iajs-2681	335	25	)	)	PUNCT
iajs-2681	335	26	are	be	AUX
iajs-2681	335	27	fwofts	fwoft	NOUN
iajs-2681	335	28	's	's	PART
iajs-2681	335	29	over	over	ADP
iajs-2681	335	30	(	(	PUNCT
iajs-2681	335	31	b	b	NOUN
iajs-2681	335	32	,	,	PUNCT
iajs-2681	335	33			NOUN
iajs-2681	335	34	)	)	PUNCT
iajs-2681	335	35	.	.	PUNCT
iajs-2681	336	1	if	if	SCONJ
iajs-2681	336	2	m	m	NOUN
iajs-2681	336	3	is	be	AUX
iajs-2681	336	4	a	a	DET
iajs-2681	336	5	fw	fw	ADJ
iajs-2681	336	6	-	-	PUNCT
iajs-2681	336	7	d	d	NOUN
iajs-2681	336	8	-	-	PUNCT
iajs-2681	336	9	fts	fts	X
iajs-2681	336	10	,	,	PUNCT
iajs-2681	336	11	then	then	ADV
iajs-2681	336	12	n	n	PRON
iajs-2681	336	13	is	be	AUX
iajs-2681	336	14	so	so	ADV
iajs-2681	336	15	.	.	PUNCT
iajs-2681	337	1	proof	proof	NOUN
iajs-2681	337	2	.	.	PUNCT
iajs-2681	338	1	in	in	ADP
iajs-2681	338	2	the	the	DET
iajs-2681	338	3	above	above	ADJ
iajs-2681	338	4	figure	figure	NOUN
iajs-2681	338	5	,	,	PUNCT
iajs-2681	338	6	with	with	ADP
iajs-2681	338	7	these	these	DET
iajs-2681	338	8	fresh	fresh	ADJ
iajs-2681	338	9	hypotheses	hypothesis	NOUN
iajs-2681	338	10	on	on	ADP
iajs-2681	338	11			PROPN
iajs-2681	338	12	,	,	PUNCT
iajs-2681	338	13	if	if	SCONJ
iajs-2681	338	14	m	m	NOUN
iajs-2681	338	15	is	be	AUX
iajs-2681	338	16	a	a	DET
iajs-2681	338	17	fw	fw	ADJ
iajs-2681	338	18	-	-	PUNCT
iajs-2681	338	19	d	d	NOUN
iajs-2681	338	20	-	-	PUNCT
iajs-2681	338	21	fts	fts	X
iajs-2681	338	22	,	,	PUNCT
iajs-2681	338	23	then	then	ADV
iajs-2681	338	24	(m	(m	PROPN
iajs-2681	338	25	)	)	PUNCT
iajs-2681	338	26	is	be	AUX
iajs-2681	338	27	a	a	DET
iajs-2681	338	28	fuzzy	fuzzy	ADJ
iajs-2681	338	29	open	open	ADJ
iajs-2681	338	30	in	in	ADP
iajs-2681	338	31	m	m	PROPN
iajs-2681	338	32	b	b	PROPN
iajs-2681	338	33	m	m	PRON
iajs-2681	338	34	,	,	PUNCT
iajs-2681	338	35	by	by	ADP
iajs-2681	338	36	theorem	theorem	NOUN
iajs-2681	338	37	(	(	PUNCT
iajs-2681	338	38	4.6	4.6	NUM
iajs-2681	338	39	)	)	PUNCT
iajs-2681	338	40	,	,	PUNCT
iajs-2681	338	41	so	so	ADV
iajs-2681	338	42	(n	(n	ADJ
iajs-2681	338	43	)	)	PUNCT
iajs-2681	338	44	=	=	SYM
iajs-2681	338	45	(((m	(((m	PROPN
iajs-2681	338	46	)	)	PUNCT
iajs-2681	338	47	)	)	PUNCT
iajs-2681	338	48	)	)	PUNCT
iajs-2681	339	1	=	=	PUNCT
iajs-2681	339	2	(	(	PUNCT
iajs-2681	339	3			AUX
iajs-2681	339	4			VERB
iajs-2681	339	5	)((m	)((m	ADV
iajs-2681	339	6	)	)	PUNCT
iajs-2681	339	7	)	)	PUNCT
iajs-2681	339	8	is	be	AUX
iajs-2681	339	9	a	a	DET
iajs-2681	339	10	fuzzy	fuzzy	ADJ
iajs-2681	339	11	open	open	NOUN
iajs-2681	339	12	in	in	ADP
iajs-2681	339	13	n	n	DET
iajs-2681	339	14	b	b	PROPN
iajs-2681	339	15	n.	n.	PROPN
iajs-2681	339	16	thus	thus	ADV
iajs-2681	339	17	,	,	PUNCT
iajs-2681	339	18	theorem	theorem	ADJ
iajs-2681	339	19	(	(	PUNCT
iajs-2681	339	20	4.8	4.8	NUM
iajs-2681	339	21	)	)	PUNCT
iajs-2681	339	22	follows	follow	VERB
iajs-2681	339	23	from	from	ADP
iajs-2681	339	24	theorem	theorem	NOUN
iajs-2681	339	25	(	(	PUNCT
iajs-2681	339	26	4.6	4.6	NUM
iajs-2681	339	27	)	)	PUNCT
iajs-2681	339	28	again	again	ADV
iajs-2681	339	29	.	.	PUNCT
iajs-2681	340	1	theorem	theorem	VERB
iajs-2681	340	2	4.9	4.9	NUM
iajs-2681	340	3	.	.	PUNCT
iajs-2681	341	1	if	if	SCONJ
iajs-2681	341	2			PROPN
iajs-2681	341	3	,	,	PUNCT
iajs-2681	341	4			PROPN
iajs-2681	341	5	:	:	PUNCT
iajs-2681	341	6	m	m	VERB
iajs-2681	341	7			NOUN
iajs-2681	341	8	n	n	ADV
iajs-2681	341	9	is	be	AUX
iajs-2681	341	10	a	a	DET
iajs-2681	341	11	fuzzy	fuzzy	ADJ
iajs-2681	341	12	continuous	continuous	ADJ
iajs-2681	341	13	fw	fw	NOUN
iajs-2681	341	14	-	-	PUNCT
iajs-2681	341	15	m	m	NOUN
iajs-2681	341	16	,	,	PUNCT
iajs-2681	341	17	where	where	SCONJ
iajs-2681	341	18	(	(	PUNCT
iajs-2681	341	19	m	m	NOUN
iajs-2681	341	20	,	,	PUNCT
iajs-2681	341	21			PROPN
iajs-2681	341	22	)	)	PUNCT
iajs-2681	341	23	is	be	AUX
iajs-2681	341	24	a	a	DET
iajs-2681	341	25	fwfts	fwft	NOUN
iajs-2681	341	26	and	and	CCONJ
iajs-2681	341	27	(	(	PUNCT
iajs-2681	341	28	n	n	CCONJ
iajs-2681	341	29	,	,	PUNCT
iajs-2681	341	30			NUM
iajs-2681	341	31	)	)	PUNCT
iajs-2681	341	32	is	be	AUX
iajs-2681	341	33	a	a	DET
iajs-2681	341	34	fw	fw	ADJ
iajs-2681	341	35	-	-	PUNCT
iajs-2681	341	36	d	d	NOUN
iajs-2681	341	37	-	-	PUNCT
iajs-2681	341	38	fts	fts	PROPN
iajs-2681	341	39	over	over	ADP
iajs-2681	341	40	(	(	PUNCT
iajs-2681	341	41	b	b	NOUN
iajs-2681	341	42	,	,	PUNCT
iajs-2681	341	43			NOUN
iajs-2681	341	44	)	)	PUNCT
iajs-2681	341	45	.	.	PUNCT
iajs-2681	342	1	then	then	ADV
iajs-2681	342	2	the	the	DET
iajs-2681	342	3	coincidence	coincidence	NOUN
iajs-2681	342	4	set	set	VERB
iajs-2681	342	5	k(	k(	PROPN
iajs-2681	342	6	,	,	PUNCT
iajs-2681	342	7			PROPN
iajs-2681	342	8	)	)	PUNCT
iajs-2681	342	9	of	of	ADP
iajs-2681	342	10			PROPN
iajs-2681	342	11	and	and	CCONJ
iajs-2681	342	12			PROPN
iajs-2681	342	13	is	be	AUX
iajs-2681	342	14	a	a	DET
iajs-2681	342	15	fuzzy	fuzzy	ADJ
iajs-2681	342	16	open	open	ADJ
iajs-2681	342	17	in	in	ADP
iajs-2681	342	18	m.	m.	NOUN
iajs-2681	342	19	proof	proof	NOUN
iajs-2681	342	20	.	.	PUNCT
iajs-2681	343	1	the	the	DET
iajs-2681	343	2	coincidence	coincidence	NOUN
iajs-2681	343	3	set	set	NOUN
iajs-2681	343	4	is	be	AUX
iajs-2681	343	5	precisely	precisely	ADV
iajs-2681	343	6	–1(	–1(	PROPN
iajs-2681	343	7			PROPN
iajs-2681	343	8	)–1((n	)–1((n	PROPN
iajs-2681	343	9	)	)	PUNCT
iajs-2681	343	10	)	)	PUNCT
iajs-2681	343	11	,	,	PUNCT
iajs-2681	343	12	where	where	SCONJ
iajs-2681	343	13	:	:	PUNCT
iajs-2681	343	14			PUNCT
iajs-2681	343	15			X
iajs-2681	343	16			PROPN
iajs-2681	344	1			PROPN
iajs-2681	344	2			NOUN
iajs-2681	344	3	m	m	VERB
iajs-2681	344	4	m	m	VERB
iajs-2681	344	5	b	b	PROPN
iajs-2681	344	6	m	m	PROPN
iajs-2681	344	7	n	n	PRON
iajs-2681	344	8	b	b	PROPN
iajs-2681	344	9	n	n	CCONJ
iajs-2681	344	10	n	n	PRON
iajs-2681	344	11	figure	figure	NOUN
iajs-2681	344	12	3	3	NUM
iajs-2681	344	13	.	.	PUNCT
iajs-2681	345	1	diagraph	diagraph	NOUN
iajs-2681	345	2	of	of	ADP
iajs-2681	345	3	theorem	theorem	PROPN
iajs-2681	345	4	4.9.fig	4.9.fig	PROPN
iajs-2681	345	5	.	.	PROPN
iajs-2681	345	6	4.2	4.2	NUM
iajs-2681	345	7	.	.	PUNCT
iajs-2681	346	1	hence	hence	ADV
iajs-2681	346	2	theorem	theorem	ADJ
iajs-2681	346	3	(	(	PUNCT
iajs-2681	346	4	4.9	4.9	NUM
iajs-2681	346	5	)	)	PUNCT
iajs-2681	346	6	follows	follow	VERB
iajs-2681	346	7	at	at	ADP
iajs-2681	346	8	once	once	ADV
iajs-2681	346	9	from	from	ADP
iajs-2681	346	10	theorem	theorem	NOUN
iajs-2681	346	11	(	(	PUNCT
iajs-2681	346	12	4.6	4.6	NUM
iajs-2681	346	13	)	)	PUNCT
iajs-2681	346	14	.	.	PUNCT
iajs-2681	347	1	in	in	ADP
iajs-2681	347	2	particular	particular	ADJ
iajs-2681	347	3	,	,	PUNCT
iajs-2681	347	4	take	take	VERB
iajs-2681	347	5	m	m	NOUN
iajs-2681	347	6	=	=	SYM
iajs-2681	347	7	n	n	CCONJ
iajs-2681	347	8	,	,	PUNCT
iajs-2681	347	9	take	take	VERB
iajs-2681	347	10			NOUN
iajs-2681	347	11	=	=	SYM
iajs-2681	347	12	idm	idm	NOUN
iajs-2681	347	13	and	and	CCONJ
iajs-2681	347	14	take	take	VERB
iajs-2681	347	15			NOUN
iajs-2681	347	16	=	=	SYM
iajs-2681	347	17	s	s	X
iajs-2681	347	18			PROPN
iajs-2681	347	19			ADP
iajs-2681	347	20	where	where	SCONJ
iajs-2681	347	21	s	s	NOUN
iajs-2681	347	22	is	be	AUX
iajs-2681	347	23	a	a	DET
iajs-2681	347	24	section	section	NOUN
iajs-2681	347	25	,	,	PUNCT
iajs-2681	347	26	we	we	PRON
iajs-2681	347	27	conclude	conclude	VERB
iajs-2681	347	28	that	that	SCONJ
iajs-2681	347	29	s	s	VERB
iajs-2681	347	30	is	be	AUX
iajs-2681	347	31	a	a	DET
iajs-2681	347	32	fuzzy	fuzzy	ADJ
iajs-2681	347	33	open	open	ADJ
iajs-2681	347	34	embedding	embed	VERB
iajs-2681	347	35	when	when	SCONJ
iajs-2681	347	36	m	m	PROPN
iajs-2681	347	37	is	be	AUX
iajs-2681	347	38	a	a	DET
iajs-2681	347	39	fw	fw	ADJ
iajs-2681	347	40	-	-	PUNCT
iajs-2681	347	41	d	d	NOUN
iajs-2681	347	42	-	-	PUNCT
iajs-2681	347	43	fts	fts	X
iajs-2681	347	44	.	.	PUNCT
iajs-2681	347	45	theorem	theorem	VERB
iajs-2681	347	46	4.10	4.10	NUM
iajs-2681	347	47	.	.	PUNCT
iajs-2681	348	1	if	if	SCONJ
iajs-2681	348	2			X
iajs-2681	348	3	:	:	PUNCT
iajs-2681	348	4	m	m	VERB
iajs-2681	348	5			NOUN
iajs-2681	348	6	n	n	ADV
iajs-2681	348	7	is	be	AUX
iajs-2681	348	8	a	a	DET
iajs-2681	348	9	fuzzy	fuzzy	ADJ
iajs-2681	348	10	continuous	continuous	ADJ
iajs-2681	348	11	fw	fw	NOUN
iajs-2681	348	12	-	-	PUNCT
iajs-2681	348	13	m	m	NOUN
iajs-2681	348	14	,	,	PUNCT
iajs-2681	348	15	where	where	SCONJ
iajs-2681	348	16	(	(	PUNCT
iajs-2681	348	17	m	m	NOUN
iajs-2681	348	18	,	,	PUNCT
iajs-2681	348	19			PROPN
iajs-2681	348	20	)	)	PUNCT
iajs-2681	348	21	is	be	AUX
iajs-2681	348	22	a	a	DET
iajs-2681	348	23	fwofts	fwoft	NOUN
iajs-2681	348	24	and	and	CCONJ
iajs-2681	348	25	(	(	PUNCT
iajs-2681	348	26	n	n	CCONJ
iajs-2681	348	27	,	,	PUNCT
iajs-2681	348	28			NUM
iajs-2681	348	29	)	)	PUNCT
iajs-2681	348	30	is	be	AUX
iajs-2681	348	31	a	a	DET
iajs-2681	348	32	fw	fw	ADJ
iajs-2681	348	33	-	-	PUNCT
iajs-2681	348	34	d	d	NOUN
iajs-2681	348	35	-	-	PUNCT
iajs-2681	348	36	fts	fts	PROPN
iajs-2681	348	37	over	over	ADP
iajs-2681	348	38	(	(	PUNCT
iajs-2681	348	39	b	b	NOUN
iajs-2681	348	40	,	,	PUNCT
iajs-2681	348	41			NOUN
iajs-2681	348	42	)	)	PUNCT
iajs-2681	348	43	.	.	PUNCT
iajs-2681	349	1	then	then	ADV
iajs-2681	349	2	the	the	DET
iajs-2681	349	3	fw	fw	ADJ
iajs-2681	349	4	-	-	PUNCT
iajs-2681	349	5	graph	graph	NOUN
iajs-2681	349	6	:	:	PUNCT
iajs-2681	349	7			VERB
iajs-2681	349	8	:	:	PUNCT
iajs-2681	349	9	m	m	VERB
iajs-2681	349	10			NOUN
iajs-2681	349	11	m	m	VERB
iajs-2681	349	12	b	b	PROPN
iajs-2681	349	13	n	n	PROPN
iajs-2681	349	14	of	of	ADP
iajs-2681	349	15			PROPN
iajs-2681	349	16	is	be	AUX
iajs-2681	349	17	a	a	DET
iajs-2681	349	18	fuzzy	fuzzy	ADJ
iajs-2681	349	19	open	open	ADJ
iajs-2681	349	20	embedding	embed	VERB
iajs-2681	349	21	.	.	PUNCT
iajs-2681	350	1	ibn	ibn	PROPN
iajs-2681	350	2	al	al	PROPN
iajs-2681	350	3	-	-	PUNCT
iajs-2681	350	4	haitham	haitham	PROPN
iajs-2681	350	5	jour	jour	X
iajs-2681	350	6	.	.	PROPN
iajs-2681	350	7	for	for	ADP
iajs-2681	350	8	pure	pure	ADJ
iajs-2681	350	9	&	&	CCONJ
iajs-2681	350	10	appl	appl	PROPN
iajs-2681	350	11	.	.	PUNCT
iajs-2681	351	1	sci	sci	PROPN
iajs-2681	351	2	.	.	PROPN
iajs-2681	352	1	34(3)2021	34(3)2021	NUM
iajs-2681	352	2	95	95	NUM
iajs-2681	352	3	proof	proof	NOUN
iajs-2681	352	4	.	.	PUNCT
iajs-2681	353	1	the	the	DET
iajs-2681	353	2	fw	fw	ADJ
iajs-2681	353	3	-	-	PUNCT
iajs-2681	353	4	graph	graph	NOUN
iajs-2681	353	5	is	be	AUX
iajs-2681	353	6	defined	define	VERB
iajs-2681	353	7	in	in	ADP
iajs-2681	353	8	the	the	DET
iajs-2681	353	9	same	same	ADJ
iajs-2681	353	10	way	way	NOUN
iajs-2681	353	11	as	as	ADP
iajs-2681	353	12	the	the	DET
iajs-2681	353	13	ordinary	ordinary	ADJ
iajs-2681	353	14	graph	graph	NOUN
iajs-2681	353	15	,	,	PUNCT
iajs-2681	353	16	but	but	CCONJ
iajs-2681	353	17	with	with	ADP
iajs-2681	353	18	values	value	NOUN
iajs-2681	353	19	in	in	ADP
iajs-2681	353	20	the	the	DET
iajs-2681	353	21	fwft	fwft	NOUN
iajs-2681	353	22	-	-	PUNCT
iajs-2681	353	23	product	product	NOUN
iajs-2681	353	24	,	,	PUNCT
iajs-2681	353	25	therefore	therefore	ADV
iajs-2681	353	26	the	the	DET
iajs-2681	353	27	diagram	diagram	NOUN
iajs-2681	353	28	shown	show	VERB
iajs-2681	353	29	below	below	ADP
iajs-2681	353	30	is	be	AUX
iajs-2681	353	31	commutative	commutative	ADJ
iajs-2681	353	32	.	.	PUNCT
iajs-2681	354	1			VERB
iajs-2681	354	2	m	m	VERB
iajs-2681	354	3	m	m	NOUN
iajs-2681	354	4	b	b	PROPN
iajs-2681	354	5	n	n	CCONJ
iajs-2681	354	6			PROPN
iajs-2681	354	7			PROPN
iajs-2681	354	8			PROPN
iajs-2681	354	9	idn	idn	PROPN
iajs-2681	354	10			PROPN
iajs-2681	354	11	n	n	CCONJ
iajs-2681	354	12	n	n	PRON
iajs-2681	354	13	b	b	PROPN
iajs-2681	355	1	n	n	PRON
iajs-2681	355	2	figure	figure	VERB
iajs-2681	355	3	4	4	NUM
iajs-2681	355	4	.	.	PUNCT
iajs-2681	356	1	diagraph	diagraph	NOUN
iajs-2681	356	2	of	of	ADP
iajs-2681	356	3	theorem	theorem	NOUN
iajs-2681	356	4	4.10	4.10	NUM
iajs-2681	356	5	.	.	PUNCT
iajs-2681	357	1	since	since	SCONJ
iajs-2681	357	2	(n	(n	PROPN
iajs-2681	357	3	)	)	PUNCT
iajs-2681	357	4	is	be	AUX
iajs-2681	357	5	a	a	DET
iajs-2681	357	6	fuzzy	fuzzy	ADJ
iajs-2681	357	7	open	open	NOUN
iajs-2681	357	8	in	in	ADP
iajs-2681	357	9	n	n	DET
iajs-2681	357	10	b	b	PROPN
iajs-2681	357	11	n	n	CCONJ
iajs-2681	357	12	,	,	PUNCT
iajs-2681	357	13	by	by	ADP
iajs-2681	357	14	theorem	theorem	NOUN
iajs-2681	357	15	(	(	PUNCT
iajs-2681	357	16	4.6	4.6	NUM
iajs-2681	357	17	)	)	PUNCT
iajs-2681	357	18	,	,	PUNCT
iajs-2681	357	19	so	so	ADV
iajs-2681	357	20	(m	(m	NOUN
iajs-2681	357	21	)	)	PUNCT
iajs-2681	357	22	=	=	SYM
iajs-2681	358	1	(	(	PUNCT
iajs-2681	358	2			PROPN
iajs-2681	358	3			PROPN
iajs-2681	358	4	idn	idn	PROPN
iajs-2681	358	5	)	)	PUNCT
iajs-2681	358	6	–	–	PUNCT
iajs-2681	358	7	1((n	1((n	NUM
iajs-2681	358	8	)	)	PUNCT
iajs-2681	358	9	)	)	PUNCT
iajs-2681	358	10	is	be	AUX
iajs-2681	358	11	a	a	DET
iajs-2681	358	12	fuzzy	fuzzy	ADJ
iajs-2681	358	13	open	open	ADJ
iajs-2681	358	14	in	in	ADP
iajs-2681	358	15	m	m	PROPN
iajs-2681	358	16	b	b	PROPN
iajs-2681	358	17	n	n	ADV
iajs-2681	358	18	as	as	SCONJ
iajs-2681	358	19	asserted	assert	VERB
iajs-2681	358	20	.	.	PUNCT
iajs-2681	359	1	remark	remark	PROPN
iajs-2681	359	2	4.11	4.11	NUM
iajs-2681	359	3	.	.	PUNCT
iajs-2681	360	1	if	if	SCONJ
iajs-2681	360	2	(	(	PUNCT
iajs-2681	360	3	m	m	NOUN
iajs-2681	360	4	,	,	PUNCT
iajs-2681	360	5			PROPN
iajs-2681	360	6	)	)	PUNCT
iajs-2681	360	7	is	be	AUX
iajs-2681	360	8	a	a	DET
iajs-2681	360	9	fw	fw	ADJ
iajs-2681	360	10	-	-	PUNCT
iajs-2681	360	11	d	d	NOUN
iajs-2681	360	12	-	-	PUNCT
iajs-2681	360	13	fts	fts	PROPN
iajs-2681	360	14	over	over	ADP
iajs-2681	360	15	(	(	PUNCT
iajs-2681	360	16	b	b	NOUN
iajs-2681	360	17	,	,	PUNCT
iajs-2681	360	18			NOUN
iajs-2681	360	19	)	)	PUNCT
iajs-2681	360	20	then	then	ADV
iajs-2681	360	21	for	for	ADP
iajs-2681	360	22	every	every	DET
iajs-2681	360	23	point	point	NOUN
iajs-2681	360	24	m	m	VERB
iajs-2681	360	25			NOUN
iajs-2681	360	26	mb	mb	ADP
iajs-2681	360	27	;	;	PUNCT
iajs-2681	360	28	b	b	X
iajs-2681	360	29			PROPN
iajs-2681	360	30	b	b	NOUN
iajs-2681	360	31	,	,	PUNCT
iajs-2681	360	32	there	there	PRON
iajs-2681	360	33	is	be	VERB
iajs-2681	360	34	a	a	DET
iajs-2681	360	35	fuzzy	fuzzy	ADJ
iajs-2681	360	36	open	open	NOUN
iajs-2681	360	37	set	set	NOUN
iajs-2681	360	38	w	w	PROPN
iajs-2681	360	39	of	of	ADP
iajs-2681	360	40	b	b	PROPN
iajs-2681	360	41	a	a	DET
iajs-2681	360	42	unique	unique	ADJ
iajs-2681	360	43	section	section	NOUN
iajs-2681	360	44	s	s	PART
iajs-2681	360	45	:	:	PUNCT
iajs-2681	360	46	w	w	NOUN
iajs-2681	360	47			NOUN
iajs-2681	360	48	mw	mw	AUX
iajs-2681	360	49	exist	exist	VERB
iajs-2681	360	50	satisfying	satisfying	ADJ
iajs-2681	360	51	s(b	s(b	NOUN
iajs-2681	360	52	)	)	PUNCT
iajs-2681	361	1	=	=	SYM
iajs-2681	361	2	m	m	PROPN
iajs-2681	361	3	,	,	PUNCT
iajs-2681	361	4	we	we	PRON
iajs-2681	361	5	may	may	AUX
iajs-2681	361	6	refer	refer	VERB
iajs-2681	361	7	to	to	ADP
iajs-2681	361	8	s	s	PRON
iajs-2681	361	9	as	as	ADP
iajs-2681	361	10	the	the	DET
iajs-2681	361	11	section	section	NOUN
iajs-2681	361	12	through	through	ADP
iajs-2681	361	13	m.	m.	NOUN
iajs-2681	361	14	definition	definition	NOUN
iajs-2681	361	15	4.12	4.12	NUM
iajs-2681	361	16	.	.	PUNCT
iajs-2681	362	1	the	the	DET
iajs-2681	362	2	fwfts	fwft	NOUN
iajs-2681	362	3	(	(	PUNCT
iajs-2681	362	4	m	m	NOUN
iajs-2681	362	5	,	,	PUNCT
iajs-2681	362	6			PROPN
iajs-2681	362	7	)	)	PUNCT
iajs-2681	362	8	over	over	ADP
iajs-2681	362	9	(	(	PUNCT
iajs-2681	362	10	b	b	NOUN
iajs-2681	362	11	,	,	PUNCT
iajs-2681	362	12			NOUN
iajs-2681	362	13	)	)	PUNCT
iajs-2681	362	14	is	be	AUX
iajs-2681	362	15	said	say	VERB
iajs-2681	362	16	to	to	PART
iajs-2681	362	17	be	be	AUX
iajs-2681	362	18	locally	locally	ADV
iajs-2681	362	19	sectionable	sectionable	ADJ
iajs-2681	362	20	(	(	PUNCT
iajs-2681	362	21	written	write	VERB
iajs-2681	362	22	as	as	ADP
iajs-2681	362	23	fwlse	fwlse	ADJ
iajs-2681	362	24	-	-	PUNCT
iajs-2681	362	25	fts	fts	X
iajs-2681	362	26	)	)	PUNCT
iajs-2681	362	27	if	if	SCONJ
iajs-2681	362	28	for	for	ADP
iajs-2681	362	29	every	every	DET
iajs-2681	362	30	point	point	NOUN
iajs-2681	362	31	b	b	PROPN
iajs-2681	362	32			PROPN
iajs-2681	362	33	b	b	NOUN
iajs-2681	362	34	,	,	PUNCT
iajs-2681	362	35	it	it	PRON
iajs-2681	362	36	admits	admit	VERB
iajs-2681	362	37	a	a	DET
iajs-2681	362	38	fuzzy	fuzzy	ADJ
iajs-2681	362	39	open	open	NOUN
iajs-2681	362	40	set	set	VERB
iajs-2681	362	41	w	w	ADP
iajs-2681	362	42	and	and	CCONJ
iajs-2681	362	43	a	a	DET
iajs-2681	362	44	section	section	NOUN
iajs-2681	362	45	s	s	VERB
iajs-2681	362	46	:	:	PUNCT
iajs-2681	362	47	w	w	NOUN
iajs-2681	362	48			NOUN
iajs-2681	362	49	mw	mw	PROPN
iajs-2681	362	50	.	.	PROPN
iajs-2681	362	51	remark	remark	PROPN
iajs-2681	362	52	4.13	4.13	NUM
iajs-2681	362	53	.	.	PUNCT
iajs-2681	363	1	the	the	DET
iajs-2681	363	2	non	non	ADJ
iajs-2681	363	3	-	-	ADJ
iajs-2681	363	4	empty	empty	ADJ
iajs-2681	363	5	fw	fw	ADJ
iajs-2681	363	6	-	-	PUNCT
iajs-2681	363	7	lsl	lsl	NOUN
iajs-2681	363	8	-	-	PUNCT
iajs-2681	363	9	fts	fts	PROPN
iajs-2681	363	10	's	's	PART
iajs-2681	363	11	are	be	AUX
iajs-2681	363	12	fw	fw	ADJ
iajs-2681	363	13	-	-	PUNCT
iajs-2681	363	14	lse	lse	NOUN
iajs-2681	363	15	-	-	PUNCT
iajs-2681	363	16	fts	fts	PROPN
iajs-2681	363	17	's	's	PART
iajs-2681	363	18	,	,	PUNCT
iajs-2681	363	19	but	but	CCONJ
iajs-2681	363	20	the	the	DET
iajs-2681	363	21	converse	converse	NOUN
iajs-2681	363	22	is	be	AUX
iajs-2681	363	23	false	false	ADJ
iajs-2681	363	24	.	.	PUNCT
iajs-2681	364	1	in	in	ADP
iajs-2681	364	2	fact	fact	NOUN
iajs-2681	364	3	,	,	PUNCT
iajs-2681	364	4	fw	fw	ADJ
iajs-2681	364	5	-	-	PUNCT
iajs-2681	364	6	lse	lse	NOUN
iajs-2681	364	7	-	-	PUNCT
iajs-2681	364	8	fts	fts	PROPN
iajs-2681	364	9	's	's	PART
iajs-2681	364	10	are	be	AUX
iajs-2681	364	11	not	not	PART
iajs-2681	364	12	necessarily	necessarily	ADV
iajs-2681	364	13	fwofys	fwofy	NOUN
iajs-2681	364	14	,	,	PUNCT
iajs-2681	364	15	for	for	ADP
iajs-2681	364	16	example	example	NOUN
iajs-2681	364	17	take	take	VERB
iajs-2681	364	18	m	m	NOUN
iajs-2681	364	19	=	=	SYM
iajs-2681	364	20	(	(	PUNCT
iajs-2681	364	21	–	–	PUNCT
iajs-2681	364	22	1	1	NUM
iajs-2681	364	23	,	,	PUNCT
iajs-2681	364	24	1	1	NUM
iajs-2681	364	25	]	]	PUNCT
iajs-2681	364	26			PROPN
iajs-2681	364	27	ℝ	ℝ	PROPN
iajs-2681	364	28	with	with	ADP
iajs-2681	364	29	(	(	PUNCT
iajs-2681	364	30	m	m	PROPN
iajs-2681	364	31	,	,	PUNCT
iajs-2681	364	32			PROPN
iajs-2681	364	33	)	)	PUNCT
iajs-2681	364	34	,	,	PUNCT
iajs-2681	364	35	the	the	DET
iajs-2681	364	36	natural	natural	ADJ
iajs-2681	364	37	projection	projection	NOUN
iajs-2681	364	38	onto	onto	ADP
iajs-2681	364	39	b	b	NOUN
iajs-2681	364	40	=	=	SYM
iajs-2681	364	41	ℝ	ℝ	PROPN
iajs-2681	364	42	∣	∣	ADJ
iajs-2681	364	43	ℤ	ℤ	NOUN
iajs-2681	364	44	;	;	PUNCT
iajs-2681	364	45	(	(	PUNCT
iajs-2681	364	46	b	b	NOUN
iajs-2681	364	47	,	,	PUNCT
iajs-2681	364	48			NOUN
iajs-2681	364	49	)	)	PUNCT
iajs-2681	364	50	.	.	PUNCT
iajs-2681	365	1	the	the	DET
iajs-2681	365	2	class	class	NOUN
iajs-2681	365	3	of	of	ADP
iajs-2681	365	4	fw	fw	PROPN
iajs-2681	365	5	-	-	PUNCT
iajs-2681	365	6	lse	lse	NOUN
iajs-2681	365	7	-	-	PUNCT
iajs-2681	365	8	fts	fts	PROPN
iajs-2681	365	9	's	's	PART
iajs-2681	365	10	is	be	AUX
iajs-2681	365	11	a	a	DET
iajs-2681	365	12	finitely	finitely	ADV
iajs-2681	365	13	multiplicative	multiplicative	VERB
iajs-2681	365	14	.	.	PUNCT
iajs-2681	366	1	theorem	theorem	VERB
iajs-2681	366	2	4.14	4.14	NUM
iajs-2681	366	3	.	.	PUNCT
iajs-2681	367	1	if	if	SCONJ
iajs-2681	367	2	{	{	PUNCT
iajs-2681	367	3	(	(	PUNCT
iajs-2681	367	4	mr	mr	PROPN
iajs-2681	367	5	,	,	PUNCT
iajs-2681	367	6	r	r	PROPN
iajs-2681	367	7	)	)	PUNCT
iajs-2681	367	8	}	}	PUNCT
iajs-2681	367	9	𝑟=1	𝑟=1	PROPN
iajs-2681	367	10	𝑘	𝑘	PROPN
iajs-2681	367	11	is	be	AUX
iajs-2681	367	12	a	a	DET
iajs-2681	367	13	finite	finite	ADJ
iajs-2681	367	14	family	family	NOUN
iajs-2681	367	15	of	of	ADP
iajs-2681	367	16	fw	fw	PROPN
iajs-2681	367	17	-	-	PUNCT
iajs-2681	367	18	lse	lse	NOUN
iajs-2681	367	19	-	-	PUNCT
iajs-2681	367	20	fts	fts	PROPN
iajs-2681	367	21	's	's	PART
iajs-2681	367	22	over	over	ADP
iajs-2681	367	23	(	(	PUNCT
iajs-2681	367	24	b	b	NOUN
iajs-2681	367	25	,	,	PUNCT
iajs-2681	367	26			NOUN
iajs-2681	367	27	)	)	PUNCT
iajs-2681	367	28	.	.	PUNCT
iajs-2681	368	1	then	then	ADV
iajs-2681	368	2	the	the	DET
iajs-2681	368	3	fwft	fwft	NOUN
iajs-2681	368	4	-	-	PUNCT
iajs-2681	368	5	product	product	NOUN
iajs-2681	368	6	(	(	PUNCT
iajs-2681	368	7	m	m	NOUN
iajs-2681	368	8	=	=	PUNCT
iajs-2681	368	9	b	b	PROPN
iajs-2681	368	10	mr	mr	PROPN
iajs-2681	368	11	,	,	PUNCT
iajs-2681	368	12			PROPN
iajs-2681	368	13	)	)	PUNCT
iajs-2681	368	14	is	be	AUX
iajs-2681	368	15	a	a	DET
iajs-2681	368	16	fw	fw	ADJ
iajs-2681	368	17	-	-	PUNCT
iajs-2681	368	18	lse	lse	NOUN
iajs-2681	368	19	-	-	PUNCT
iajs-2681	368	20	fts	fts	PROPN
iajs-2681	368	21	.	.	PUNCT
iajs-2681	369	1	proof	proof	NOUN
iajs-2681	369	2	.	.	PUNCT
iajs-2681	370	1	given	give	VERB
iajs-2681	370	2	a	a	DET
iajs-2681	370	3	point	point	NOUN
iajs-2681	370	4	b	b	NOUN
iajs-2681	370	5	of	of	ADP
iajs-2681	370	6	b	b	NOUN
iajs-2681	370	7	,	,	PUNCT
iajs-2681	370	8	there	there	PRON
iajs-2681	370	9	exist	exist	VERB
iajs-2681	370	10	a	a	DET
iajs-2681	370	11	fuzzy	fuzzy	ADJ
iajs-2681	370	12	open	open	NOUN
iajs-2681	370	13	set	set	VERB
iajs-2681	370	14	wr	wr	NOUN
iajs-2681	370	15	of	of	ADP
iajs-2681	370	16	b	b	PROPN
iajs-2681	370	17	and	and	CCONJ
iajs-2681	370	18	a	a	DET
iajs-2681	370	19	section	section	NOUN
iajs-2681	370	20	sr	sr	NOUN
iajs-2681	370	21	:	:	PUNCT
iajs-2681	370	22	wr	wr	PROPN
iajs-2681	370	23			VERB
iajs-2681	371	1	mr	mr	PROPN
iajs-2681	371	2	|	|	ADV
iajs-2681	371	3	wr	wr	NOUN
iajs-2681	371	4	for	for	ADP
iajs-2681	371	5	every	every	DET
iajs-2681	371	6	index	index	NOUN
iajs-2681	371	7	r.	r.	NOUN
iajs-2681	371	8	since	since	SCONJ
iajs-2681	371	9	there	there	PRON
iajs-2681	371	10	are	be	VERB
iajs-2681	371	11	finite	finite	ADJ
iajs-2681	371	12	numbers	number	NOUN
iajs-2681	371	13	of	of	ADP
iajs-2681	371	14	indices	index	NOUN
iajs-2681	371	15	the	the	DET
iajs-2681	371	16	intersection	intersection	NOUN
iajs-2681	371	17	w	w	PROPN
iajs-2681	371	18	of	of	ADP
iajs-2681	371	19	the	the	DET
iajs-2681	371	20	fuzzy	fuzzy	ADJ
iajs-2681	371	21	open	open	ADJ
iajs-2681	371	22	sets	set	NOUN
iajs-2681	371	23	wr	wr	NOUN
iajs-2681	371	24	is	be	AUX
iajs-2681	371	25	also	also	ADV
iajs-2681	371	26	a	a	DET
iajs-2681	371	27	fuzzy	fuzzy	ADJ
iajs-2681	371	28	open	open	ADJ
iajs-2681	371	29	set	set	NOUN
iajs-2681	371	30	of	of	ADP
iajs-2681	371	31	b	b	NOUN
iajs-2681	371	32	,	,	PUNCT
iajs-2681	371	33	and	and	CCONJ
iajs-2681	371	34	a	a	DET
iajs-2681	371	35	section	section	NOUN
iajs-2681	371	36	s	s	VERB
iajs-2681	371	37	:	:	PUNCT
iajs-2681	371	38	w	w	NOUN
iajs-2681	371	39			NOUN
iajs-2681	371	40	(	(	PUNCT
iajs-2681	371	41	b	b	PROPN
iajs-2681	371	42	mr)w	mr)w	PROPN
iajs-2681	371	43	is	be	AUX
iajs-2681	371	44	given	give	VERB
iajs-2681	371	45	by	by	ADP
iajs-2681	371	46	(	(	PUNCT
iajs-2681	371	47	r	r	X
iajs-2681	371	48			PROPN
iajs-2681	371	49	s)(w	s)(w	X
iajs-2681	371	50	)	)	PUNCT
iajs-2681	371	51	=	=	SYM
iajs-2681	371	52	sr(w	sr(w	NOUN
iajs-2681	371	53	)	)	PUNCT
iajs-2681	371	54	,	,	PUNCT
iajs-2681	371	55	for	for	ADP
iajs-2681	371	56	w	w	PROPN
iajs-2681	371	57			PROPN
iajs-2681	371	58	w.	w.	NOUN
iajs-2681	371	59	our	our	PRON
iajs-2681	371	60	last	last	ADJ
iajs-2681	371	61	two	two	NUM
iajs-2681	371	62	result	result	NOUN
iajs-2681	371	63	apply	apply	VERB
iajs-2681	371	64	equally	equally	ADV
iajs-2681	371	65	well	well	ADV
iajs-2681	371	66	to	to	ADP
iajs-2681	371	67	every	every	PRON
iajs-2681	371	68	of	of	ADP
iajs-2681	371	69	the	the	DET
iajs-2681	371	70	above	above	ADJ
iajs-2681	371	71	three	three	NUM
iajs-2681	371	72	theorems	theorem	NOUN
iajs-2681	371	73	.	.	PUNCT
iajs-2681	372	1	theorem	theorem	NOUN
iajs-2681	372	2	4.15	4.15	NUM
iajs-2681	372	3	.	.	PUNCT
iajs-2681	373	1	if	if	SCONJ
iajs-2681	373	2	(	(	PUNCT
iajs-2681	373	3	m	m	NOUN
iajs-2681	373	4	,	,	PUNCT
iajs-2681	373	5			PROPN
iajs-2681	373	6	)	)	PUNCT
iajs-2681	373	7	is	be	AUX
iajs-2681	373	8	a	a	DET
iajs-2681	373	9	fw	fw	ADJ
iajs-2681	373	10	-	-	PUNCT
iajs-2681	373	11	d	d	NOUN
iajs-2681	373	12	-	-	PUNCT
iajs-2681	373	13	fts	fts	PROPN
iajs-2681	373	14	over	over	ADP
iajs-2681	373	15	(	(	PUNCT
iajs-2681	373	16	b	b	NOUN
iajs-2681	373	17	,	,	PUNCT
iajs-2681	373	18			NOUN
iajs-2681	373	19	)	)	PUNCT
iajs-2681	373	20	.	.	PUNCT
iajs-2681	374	1	suppose	suppose	VERB
iajs-2681	374	2	that	that	SCONJ
iajs-2681	374	3	(	(	PUNCT
iajs-2681	374	4	m	m	NOUN
iajs-2681	374	5	,	,	PUNCT
iajs-2681	374	6			PROPN
iajs-2681	374	7	)	)	PUNCT
iajs-2681	374	8	is	be	AUX
iajs-2681	374	9	a	a	DET
iajs-2681	374	10	fw	fw	PROPN
iajs-2681	374	11	-	-	PUNCT
iajs-2681	374	12	lsl	lsl	NOUN
iajs-2681	374	13	-	-	PUNCT
iajs-2681	374	14	fts	fts	X
iajs-2681	374	15	,	,	PUNCT
iajs-2681	374	16	fwd	fwd	PROPN
iajs-2681	374	17	-	-	PUNCT
iajs-2681	374	18	fts	fts	PROPN
iajs-2681	374	19	or	or	CCONJ
iajs-2681	374	20	fw	fw	ADJ
iajs-2681	374	21	-	-	PUNCT
iajs-2681	374	22	lse	lse	NOUN
iajs-2681	374	23	-	-	PUNCT
iajs-2681	374	24	fts	fts	PROPN
iajs-2681	374	25	's	's	PART
iajs-2681	374	26	over	over	ADP
iajs-2681	374	27	(	(	PUNCT
iajs-2681	374	28	b	b	NOUN
iajs-2681	374	29	,	,	PUNCT
iajs-2681	374	30			NOUN
iajs-2681	374	31	)	)	PUNCT
iajs-2681	374	32	.	.	PUNCT
iajs-2681	375	1	then	then	ADV
iajs-2681	375	2	so	so	ADV
iajs-2681	375	3	is	be	AUX
iajs-2681	375	4	mb	mb	ADP
iajs-2681	375	5	*	*	PROPN
iajs-2681	375	6	over	over	ADP
iajs-2681	375	7	b	b	PROPN
iajs-2681	375	8	*	*	VERB
iajs-2681	375	9	for	for	ADP
iajs-2681	375	10	every	every	DET
iajs-2681	375	11	fuzzy	fuzzy	ADJ
iajs-2681	375	12	open	open	NOUN
iajs-2681	375	13	set	set	ADJ
iajs-2681	375	14	b	b	PROPN
iajs-2681	375	15	*	*	PROPN
iajs-2681	375	16			PROPN
iajs-2681	375	17	b.	b.	PROPN
iajs-2681	375	18	theorem	theorem	VERB
iajs-2681	375	19	4.16	4.16	NUM
iajs-2681	375	20	.	.	PUNCT
iajs-2681	376	1	let	let	VERB
iajs-2681	376	2	(	(	PUNCT
iajs-2681	376	3	m	m	NOUN
iajs-2681	376	4	,	,	PUNCT
iajs-2681	376	5			PROPN
iajs-2681	376	6	)	)	PUNCT
iajs-2681	376	7	be	be	VERB
iajs-2681	376	8	fwfts	fwft	NOUN
iajs-2681	376	9	over	over	ADP
iajs-2681	376	10	(	(	PUNCT
iajs-2681	376	11	b	b	NOUN
iajs-2681	376	12	,	,	PUNCT
iajs-2681	376	13			NOUN
iajs-2681	376	14	)	)	PUNCT
iajs-2681	376	15	.	.	PUNCT
iajs-2681	377	1	assume	assume	VERB
iajs-2681	377	2	that	that	SCONJ
iajs-2681	377	3	mbj	mbj	PROPN
iajs-2681	377	4	is	be	AUX
iajs-2681	377	5	a	a	DET
iajs-2681	377	6	fw	fw	PROPN
iajs-2681	377	7	-	-	PUNCT
iajs-2681	377	8	lsl	lsl	NOUN
iajs-2681	377	9	-	-	PUNCT
iajs-2681	377	10	fts	fts	ADJ
iajs-2681	377	11	,	,	PUNCT
iajs-2681	377	12	fw	fw	ADJ
iajs-2681	377	13	-	-	PUNCT
iajs-2681	377	14	dfts	dfts	ADJ
iajs-2681	377	15	or	or	CCONJ
iajs-2681	377	16	fw	fw	ADJ
iajs-2681	377	17	-	-	PUNCT
iajs-2681	377	18	lse	lse	NOUN
iajs-2681	377	19	-	-	PUNCT
iajs-2681	377	20	fts	fts	PROPN
iajs-2681	377	21	over	over	ADP
iajs-2681	377	22	bj	bj	NOUN
iajs-2681	377	23	for	for	ADP
iajs-2681	377	24	every	every	DET
iajs-2681	377	25	member	member	NOUN
iajs-2681	377	26	bj	bj	NOUN
iajs-2681	377	27	of	of	ADP
iajs-2681	377	28	a	a	DET
iajs-2681	377	29	fuzzy	fuzzy	ADJ
iajs-2681	377	30	open	open	ADJ
iajs-2681	377	31	covering	covering	NOUN
iajs-2681	377	32	of	of	ADP
iajs-2681	377	33	b.	b.	PROPN
iajs-2681	377	34	so	so	ADV
iajs-2681	377	35	is	be	AUX
iajs-2681	377	36	m	m	PROPN
iajs-2681	377	37	over	over	ADP
iajs-2681	377	38	b.	b.	PROPN
iajs-2681	377	39	ibn	ibn	PROPN
iajs-2681	377	40	al	al	PROPN
iajs-2681	377	41	-	-	PUNCT
iajs-2681	377	42	haitham	haitham	PROPN
iajs-2681	377	43	jour	jour	X
iajs-2681	377	44	.	.	PROPN
iajs-2681	378	1	for	for	ADP
iajs-2681	378	2	pure	pure	ADJ
iajs-2681	378	3	&	&	CCONJ
iajs-2681	378	4	appl	appl	PROPN
iajs-2681	378	5	.	.	PUNCT
iajs-2681	379	1	sci	sci	PROPN
iajs-2681	379	2	.	.	PROPN
iajs-2681	380	1	34(3)2021	34(3)2021	NUM
iajs-2681	380	2	96	96	NUM
iajs-2681	380	3	remark	remark	NOUN
iajs-2681	380	4	4.17	4.17	NUM
iajs-2681	380	5	.	.	PUNCT
iajs-2681	381	1	it	it	PRON
iajs-2681	381	2	is	be	AUX
iajs-2681	381	3	not	not	PART
iajs-2681	381	4	difficult	difficult	ADJ
iajs-2681	381	5	to	to	PART
iajs-2681	381	6	give	give	VERB
iajs-2681	381	7	examples	example	NOUN
iajs-2681	381	8	of	of	ADP
iajs-2681	381	9	different	different	ADJ
iajs-2681	381	10	fw	fw	ADJ
iajs-2681	381	11	-	-	PUNCT
iajs-2681	381	12	d	d	NOUN
iajs-2681	381	13	-	-	PUNCT
iajs-2681	381	14	fts	fts	PROPN
iajs-2681	381	15	's	's	PART
iajs-2681	381	16	on	on	ADP
iajs-2681	381	17	the	the	DET
iajs-2681	381	18	same	same	ADJ
iajs-2681	381	19	fw	fw	NOUN
iajs-2681	381	20	-	-	PUNCT
iajs-2681	381	21	set	set	NOUN
iajs-2681	381	22	which	which	PRON
iajs-2681	381	23	are	be	AUX
iajs-2681	381	24	equivalent	equivalent	ADJ
iajs-2681	381	25	,	,	PUNCT
iajs-2681	381	26	to	to	ADP
iajs-2681	381	27	fwfts	fwft	NOUN
iajs-2681	381	28	's	's	PART
iajs-2681	381	29	.	.	PUNCT
iajs-2681	382	1	for	for	ADP
iajs-2681	382	2	this	this	DET
iajs-2681	382	3	reason	reason	NOUN
iajs-2681	382	4	,	,	PUNCT
iajs-2681	382	5	we	we	PRON
iajs-2681	382	6	must	must	AUX
iajs-2681	382	7	be	be	AUX
iajs-2681	382	8	careful	careful	ADJ
iajs-2681	382	9	not	not	PART
iajs-2681	382	10	to	to	PART
iajs-2681	382	11	say	say	VERB
iajs-2681	382	12	the	the	DET
iajs-2681	382	13	fw	fw	NOUN
iajs-2681	382	14	-	-	PUNCT
iajs-2681	382	15	dfts	dft	NOUN
iajs-2681	382	16	.	.	PUNCT
iajs-2681	383	1	references	reference	NOUN
iajs-2681	383	2	1	1	NUM
iajs-2681	383	3	.	.	PUNCT
iajs-2681	383	4	abo	abo	PROPN
iajs-2681	383	5	khadra	khadra	NOUN
iajs-2681	383	6	,	,	PUNCT
iajs-2681	383	7	a.	a.	NOUN
iajs-2681	383	8	a.	a.	PROPN
iajs-2681	383	9	;	;	PUNCT
iajs-2681	383	10	mahmoud	mahmoud	PROPN
iajs-2681	383	11	,	,	PUNCT
iajs-2681	383	12	s.	s.	PROPN
iajs-2681	383	13	s.	s.	PROPN
iajs-2681	383	14	;	;	PUNCT
iajs-2681	384	1	yousif	yousif	PROPN
iajs-2681	384	2	y.	y.	PROPN
iajs-2681	384	3	y.	y.	PROPN
iajs-2681	384	4	,	,	PUNCT
iajs-2681	384	5	fibrewise	fibrewise	ADV
iajs-2681	384	6	near	near	ADP
iajs-2681	384	7	topological	topological	ADJ
iajs-2681	384	8	spaces	space	NOUN
iajs-2681	384	9	,	,	PUNCT
iajs-2681	384	10	journal	journal	NOUN
iajs-2681	384	11	of	of	ADP
iajs-2681	384	12	computing	computing	PROPN
iajs-2681	384	13	,	,	PUNCT
iajs-2681	384	14	usa	usa	PROPN
iajs-2681	384	15	,	,	PUNCT
iajs-2681	384	16	2012	2012	NUM
iajs-2681	384	17	,	,	PUNCT
iajs-2681	384	18	4	4	NUM
iajs-2681	384	19	,	,	PUNCT
iajs-2681	384	20	5	5	NUM
iajs-2681	384	21	,	,	PUNCT
iajs-2681	384	22	may	may	AUX
iajs-2681	384	23	223	223	NUM
iajs-2681	384	24	-	-	SYM
iajs-2681	384	25	230	230	NUM
iajs-2681	384	26	.	.	PUNCT
iajs-2681	385	1	2	2	NUM
iajs-2681	385	2	.	.	X
iajs-2681	385	3	chang	chang	PROPN
iajs-2681	385	4	,	,	PUNCT
iajs-2681	385	5	c.	c.	PROPN
iajs-2681	385	6	l.	l.	PROPN
iajs-2681	385	7	;	;	PUNCT
iajs-2681	385	8	fuzz	fuzz	PROPN
iajs-2681	385	9	topological	topological	ADJ
iajs-2681	385	10	spaces	space	NOUN
iajs-2681	385	11	.	.	PUNCT
iajs-2681	386	1	j.	j.	PROPN
iajs-2681	386	2	math	math	PROPN
iajs-2681	386	3	.	.	PUNCT
iajs-2681	387	1	anal	anal	PROPN
iajs-2681	387	2	.	.	PUNCT
iajs-2681	388	1	appl	appl	PROPN
iajs-2681	388	2	.	.	PROPN
iajs-2681	389	1	24	24	NUM
iajs-2681	389	2	,	,	PUNCT
iajs-2681	389	3	1968,182	1968,182	NUM
iajs-2681	389	4	-	-	SYM
iajs-2681	389	5	190	190	NUM
iajs-2681	389	6	.	.	PUNCT
iajs-2681	390	1	3	3	X
iajs-2681	390	2	.	.	X
iajs-2681	390	3	englking	englking	NOUN
iajs-2681	390	4	,	,	PUNCT
iajs-2681	390	5	r.	r.	PROPN
iajs-2681	390	6	,	,	PUNCT
iajs-2681	390	7	outline	outline	NOUN
iajs-2681	390	8	of	of	ADP
iajs-2681	390	9	general	general	ADJ
iajs-2681	390	10	topology	topology	NOUN
iajs-2681	390	11	,	,	PUNCT
iajs-2681	390	12	amsterdam	amsterdam	PROPN
iajs-2681	390	13	,	,	PUNCT
iajs-2681	390	14	1989	1989	NUM
iajs-2681	390	15	.	.	PUNCT
iajs-2681	391	1	4	4	X
iajs-2681	391	2	.	.	X
iajs-2681	391	3	ghanim	ghanim	NOUN
iajs-2681	391	4	,	,	PUNCT
iajs-2681	391	5	m.	m.	PROPN
iajs-2681	391	6	h.	h.	PROPN
iajs-2681	391	7	;	;	PUNCT
iajs-2681	391	8	kerre	kerre	PROPN
iajs-2681	391	9	e.	e.	PROPN
iajs-2681	391	10	e.	e.	PROPN
iajs-2681	391	11	;	;	PUNCT
iajs-2681	392	1	mashhour	mashhour	PROPN
iajs-2681	392	2	,	,	PUNCT
iajs-2681	392	3	a.	a.	PROPN
iajs-2681	392	4	s.	s.	PROPN
iajs-2681	392	5	,	,	PUNCT
iajs-2681	392	6	separation	separation	NOUN
iajs-2681	392	7	axioms	axiom	NOUN
iajs-2681	392	8	,	,	PUNCT
iajs-2681	392	9	subspaces	subspace	NOUN
iajs-2681	392	10	and	and	CCONJ
iajs-2681	392	11	sums	sum	NOUN
iajs-2681	392	12	in	in	ADP
iajs-2681	392	13	fuzzy	fuzzy	ADJ
iajs-2681	392	14	topology	topology	NOUN
iajs-2681	392	15	,	,	PUNCT
iajs-2681	392	16	journal	journal	NOUN
iajs-2681	392	17	of	of	ADP
iajs-2681	392	18	mathematical	mathematical	ADJ
iajs-2681	392	19	analysis	analysis	NOUN
iajs-2681	392	20	and	and	CCONJ
iajs-2681	392	21	applications	application	NOUN
iajs-2681	392	22	,	,	PUNCT
iajs-2681	392	23	academic	academic	ADJ
iajs-2681	392	24	press	press	NOUN
iajs-2681	392	25	,	,	PUNCT
iajs-2681	392	26	inc	inc	PROPN
iajs-2681	392	27	.	.	PROPN
iajs-2681	392	28	,	,	PUNCT
iajs-2681	392	29	1984	1984	NUM
iajs-2681	392	30	,	,	PUNCT
iajs-2681	392	31	102	102	NUM
iajs-2681	392	32	,	,	PUNCT
iajs-2681	392	33	189	189	NUM
iajs-2681	392	34	-	-	SYM
iajs-2681	392	35	202	202	NUM
iajs-2681	392	36	.	.	PUNCT
iajs-2681	393	1	5	5	NUM
iajs-2681	393	2	.	.	X
iajs-2681	393	3	hutton	hutton	PROPN
iajs-2681	393	4	,	,	PUNCT
iajs-2681	393	5	b.	b.	PROPN
iajs-2681	393	6	,	,	PUNCT
iajs-2681	393	7	products	product	NOUN
iajs-2681	393	8	of	of	ADP
iajs-2681	393	9	fuzzy	fuzzy	ADJ
iajs-2681	393	10	topological	topological	ADJ
iajs-2681	393	11	spaces	space	NOUN
iajs-2681	393	12	,	,	PUNCT
iajs-2681	393	13	topology	topology	NOUN
iajs-2681	393	14	and	and	CCONJ
iajs-2681	393	15	its	its	PRON
iajs-2681	393	16	applications	application	NOUN
iajs-2681	393	17	,	,	PUNCT
iajs-2681	393	18	northholland	northholland	NOUN
iajs-2681	393	19	publishing	publish	VERB
iajs-2681	393	20	company	company	NOUN
iajs-2681	393	21	,	,	PUNCT
iajs-2681	393	22	1980	1980	NUM
iajs-2681	393	23	,	,	PUNCT
iajs-2681	393	24	11	11	NUM
iajs-2681	393	25	,	,	PUNCT
iajs-2681	393	26	59	59	NUM
iajs-2681	393	27	-	-	SYM
iajs-2681	393	28	67	67	NUM
iajs-2681	393	29	.	.	PUNCT
iajs-2681	393	30	6	6	NUM
iajs-2681	393	31	.	.	X
iajs-2681	394	1	james	james	PROPN
iajs-2681	394	2	,	,	PUNCT
iajs-2681	394	3	i.	i.	PROPN
iajs-2681	394	4	m.	m.	PROPN
iajs-2681	394	5	,	,	PUNCT
iajs-2681	394	6	fibrewise	fibrewise	NOUN
iajs-2681	394	7	topology	topology	NOUN
iajs-2681	394	8	,	,	PUNCT
iajs-2681	394	9	cambridge	cambridge	PROPN
iajs-2681	394	10	university	university	PROPN
iajs-2681	394	11	press	press	NOUN
iajs-2681	394	12	,	,	PUNCT
iajs-2681	394	13	london	london	PROPN
iajs-2681	394	14	1989	1989	NUM
iajs-2681	394	15	.	.	PUNCT
iajs-2681	395	1	7	7	X
iajs-2681	395	2	.	.	X
iajs-2681	395	3	mahmoud	mahmoud	PROPN
iajs-2681	395	4	,	,	PUNCT
iajs-2681	395	5	s.	s.	PROPN
iajs-2681	395	6	s.	s.	PROPN
iajs-2681	395	7	;	;	PUNCT
iajs-2681	395	8	yousif	yousif	PROPN
iajs-2681	395	9	,	,	PUNCT
iajs-2681	395	10	y.	y.	PROPN
iajs-2681	395	11	y.	y.	PROPN
iajs-2681	395	12	,	,	PUNCT
iajs-2681	395	13	fibrewise	fibrewise	ADV
iajs-2681	395	14	near	near	ADP
iajs-2681	395	15	separation	separation	NOUN
iajs-2681	395	16	axioms	axiom	NOUN
iajs-2681	395	17	,	,	PUNCT
iajs-2681	395	18	international	international	PROPN
iajs-2681	395	19	mathematical	mathematical	ADJ
iajs-2681	395	20	forum	forum	PROPN
iajs-2681	395	21	,	,	PUNCT
iajs-2681	395	22	hikari	hikari	PROPN
iajs-2681	395	23	ltd	ltd	PROPN
iajs-2681	395	24	,	,	PUNCT
iajs-2681	395	25	bulgaria	bulgaria	PROPN
iajs-2681	395	26	,	,	PUNCT
iajs-2681	395	27	2012	2012	NUM
iajs-2681	395	28	,	,	PUNCT
iajs-2681	395	29	7,35	7,35	NUM
iajs-2681	395	30	,	,	PUNCT
iajs-2681	395	31	1725	1725	NUM
iajs-2681	395	32	-	-	SYM
iajs-2681	395	33	1736	1736	NUM
iajs-2681	395	34	.	.	PUNCT
iajs-2681	396	1	8	8	NUM
iajs-2681	396	2	.	.	PUNCT
iajs-2681	397	1	mohammed	mohammed	PROPN
iajs-2681	397	2	,	,	PUNCT
iajs-2681	397	3	n.	n.	PROPN
iajs-2681	397	4	f.	f.	PROPN
iajs-2681	397	5	;	;	PUNCT
iajs-2681	397	6	yousif	yousif	PROPN
iajs-2681	397	7	,	,	PUNCT
iajs-2681	397	8	y.	y.	PROPN
iajs-2681	397	9	y.	y.	PROPN
iajs-2681	397	10	,	,	PUNCT
iajs-2681	397	11	connected	connect	VERB
iajs-2681	397	12	fibrewise	fibrewise	ADJ
iajs-2681	397	13	topological	topological	ADJ
iajs-2681	397	14	spaces	space	NOUN
iajs-2681	397	15	,	,	PUNCT
iajs-2681	397	16	2nd	2nd	PROPN
iajs-2681	397	17	.	.	PUNCT
iajs-2681	397	18	isc-2019	isc-2019	PROPN
iajs-2681	398	1	college	college	PROPN
iajs-2681	398	2	of	of	ADP
iajs-2681	398	3	science	science	NOUN
iajs-2681	398	4	,	,	PUNCT
iajs-2681	398	5	university	university	PROPN
iajs-2681	398	6	of	of	ADP
iajs-2681	398	7	al	al	PROPN
iajs-2681	398	8	-	-	PUNCT
iajs-2681	398	9	qadisiyah	qadisiyah	NOUN
iajs-2681	398	10	scientific	scientific	ADJ
iajs-2681	398	11	conference	conference	NOUN
iajs-2681	398	12	,	,	PUNCT
iajs-2681	398	13	iop	iop	PROPN
iajs-2681	398	14	conf	conf	NOUN
iajs-2681	398	15	.	.	PUNCT
iajs-2681	399	1	series	series	PROPN
iajs-2681	399	2	:	:	PUNCT
iajs-2681	399	3	journal	journal	PROPN
iajs-2681	399	4	of	of	ADP
iajs-2681	399	5	physics	physics	PROPN
iajs-2681	399	6	:	:	PUNCT
iajs-2681	399	7	conf	conf	PROPN
iajs-2681	399	8	.	.	PUNCT
iajs-2681	400	1	series	series	PROPN
iajs-2681	400	2	1294	1294	NUM
iajs-2681	400	3	(	(	PUNCT
iajs-2681	400	4	2019	2019	NUM
iajs-2681	400	5	)	)	PUNCT
iajs-2681	400	6	032022	032022	NUM
iajs-2681	400	7	doi	doi	NOUN
iajs-2681	400	8	:	:	PUNCT
iajs-2681	400	9	10.1088/17426596/1294/1/032022	10.1088/17426596/1294/1/032022	NUM
iajs-2681	400	10	,	,	PUNCT
iajs-2681	400	11	24	24	NUM
iajs-2681	400	12	-	-	SYM
iajs-2681	400	13	25	25	NUM
iajs-2681	400	14	april	april	PROPN
iajs-2681	400	15	2019	2019	NUM
iajs-2681	400	16	,	,	PUNCT
iajs-2681	400	17	pp	pp	ADJ
iajs-2681	400	18	.	.	PUNCT
iajs-2681	401	1	1	1	NUM
iajs-2681	401	2	-	-	SYM
iajs-2681	401	3	6	6	NUM
iajs-2681	401	4	.	.	NOUN
iajs-2681	401	5	9	9	NUM
iajs-2681	401	6	.	.	X
iajs-2681	402	1	willard	willard	PROPN
iajs-2681	402	2	,	,	PUNCT
iajs-2681	402	3	s.	s.	PROPN
iajs-2681	402	4	,	,	PUNCT
iajs-2681	402	5	general	general	ADJ
iajs-2681	402	6	topology	topology	NOUN
iajs-2681	402	7	,	,	PUNCT
iajs-2681	402	8	addison	addison	PROPN
iajs-2681	402	9	wesly	wesly	ADV
iajs-2681	402	10	,	,	PUNCT
iajs-2681	402	11	london	london	PROPN
iajs-2681	402	12	,	,	PUNCT
iajs-2681	402	13	1970	1970	NUM
iajs-2681	402	14	.	.	PUNCT
iajs-2681	403	1	10	10	NUM
iajs-2681	403	2	.	.	PUNCT
iajs-2681	404	1	yousif	yousif	PROPN
iajs-2681	404	2	,	,	PUNCT
iajs-2681	404	3	y.	y.	PROPN
iajs-2681	404	4	y.	y.	PROPN
iajs-2681	404	5	;	;	PUNCT
iajs-2681	404	6	hussain	hussain	PROPN
iajs-2681	404	7	l.	l.	PROPN
iajs-2681	404	8	a.	a.	PROPN
iajs-2681	404	9	,	,	PUNCT
iajs-2681	404	10	fibrewise	fibrewise	ADV
iajs-2681	404	11	bitopological	bitopological	ADJ
iajs-2681	404	12	spaces	space	NOUN
iajs-2681	404	13	,	,	PUNCT
iajs-2681	404	14	international	international	ADJ
iajs-2681	404	15	journal	journal	NOUN
iajs-2681	404	16	of	of	ADP
iajs-2681	404	17	science	science	NOUN
iajs-2681	404	18	and	and	CCONJ
iajs-2681	404	19	research	research	NOUN
iajs-2681	404	20	(	(	PUNCT
iajs-2681	404	21	ijsr	ijsr	NOUN
iajs-2681	404	22	)	)	PUNCT
iajs-2681	404	23	,	,	PUNCT
iajs-2681	404	24	https://www.ijsr.net/archive/v6i2/v6i2.pdf	https://www.ijsr.net/archive/v6i2/v6i2.pdf	NOUN
iajs-2681	404	25	,	,	PUNCT
iajs-2681	404	26	february	february	PROPN
iajs-2681	404	27	2017	2017	NUM
iajs-2681	404	28	,	,	PUNCT
iajs-2681	404	29	6	6	NUM
iajs-2681	404	30	,	,	PUNCT
iajs-2681	404	31	2	2	NUM
iajs-2681	404	32	,	,	PUNCT
iajs-2681	404	33	978	978	NUM
iajs-2681	404	34	–	–	PUNCT
iajs-2681	404	35	983	983	NUM
iajs-2681	404	36	.	.	PUNCT
iajs-2681	405	1	11	11	NUM
iajs-2681	405	2	.	.	PUNCT
iajs-2681	406	1	yousif	yousif	PROPN
iajs-2681	406	2	,	,	PUNCT
iajs-2681	406	3	y.	y.	PROPN
iajs-2681	406	4	y.	y.	PROPN
iajs-2681	406	5	;	;	PUNCT
iajs-2681	406	6	hussain	hussain	PROPN
iajs-2681	406	7	,	,	PUNCT
iajs-2681	406	8	l.	l.	PROPN
iajs-2681	406	9	a.	a.	PROPN
iajs-2681	406	10	,	,	PUNCT
iajs-2681	406	11	fibrewise	fibrewise	NOUN
iajs-2681	406	12	ij	ij	ADJ
iajs-2681	406	13	-	-	ADJ
iajs-2681	406	14	perfect	perfect	ADJ
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iajs-2681	406	20	1st	1st	NOUN
iajs-2681	406	21	.	.	PUNCT
iajs-2681	407	1	international	international	ADJ
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iajs-2681	408	5	physics	physics	PROPN
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iajs-2681	408	7	conf	conf	PROPN
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iajs-2681	409	6	012063	012063	NUM
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iajs-2681	409	10	-	-	SYM
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iajs-2681	409	22	.	.	PUNCT
iajs-2681	410	1	12	12	NUM
iajs-2681	410	2	.	.	PUNCT
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iajs-2681	411	19	.	.	PUNCT
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iajs-2681	412	8	,	,	PUNCT
iajs-2681	412	9	al	al	PROPN
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iajs-2681	412	13	.	.	PUNCT
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iajs-2681	413	7	-	-	SYM
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iajs-2681	413	11	-	-	SYM
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iajs-2681	413	15	.	.	PUNCT
iajs-2681	414	1	yousif	yousif	PROPN
iajs-2681	414	2	,	,	PUNCT
iajs-2681	414	3	y.	y.	PROPN
iajs-2681	414	4	y.	y.	PROPN
iajs-2681	414	5	;	;	PUNCT
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iajs-2681	414	7	,	,	PUNCT
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iajs-2681	414	9	a.	a.	PROPN
iajs-2681	414	10	,	,	PUNCT
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iajs-2681	414	16	,	,	PUNCT
iajs-2681	414	17	ibn	ibn	PROPN
iajs-2681	414	18	al	al	PROPN
iajs-2681	414	19	-	-	PUNCT
iajs-2681	414	20	aaitham	aaitham	PROPN
iajs-2681	414	21	1st	1st	NOUN
iajs-2681	414	22	.	.	PUNCT
iajs-2681	415	1	international	international	ADJ
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iajs-2681	415	4	,	,	PUNCT
iajs-2681	415	5	iop	iop	PROPN
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iajs-2681	415	7	.	.	PUNCT
iajs-2681	416	1	series	series	PROPN
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iajs-2681	416	3	journal	journal	PROPN
iajs-2681	416	4	of	of	ADP
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iajs-2681	416	6	:	:	PUNCT
iajs-2681	416	7	conf	conf	PROPN
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iajs-2681	417	7	doi	doi	NOUN
iajs-2681	417	8	:	:	PUNCT
iajs-2681	417	9	10.1088/1742	10.1088/1742	NUM
iajs-2681	417	10	-	-	SYM
iajs-2681	417	11	6596/1003/1/012050	6596/1003/1/012050	NUM
iajs-2681	417	12	,	,	PUNCT
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iajs-2681	417	18	-	-	SYM
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iajs-2681	417	20	.	.	PUNCT
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iajs-2681	418	2	.	.	PUNCT
iajs-2681	419	1	yousif	yousif	PROPN
iajs-2681	419	2	,	,	PUNCT
iajs-2681	419	3	y.	y.	PROPN
iajs-2681	419	4	y.	y.	PROPN
iajs-2681	419	5	;	;	PUNCT
iajs-2681	419	6	hussain	hussain	PROPN
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iajs-2681	419	9	a.	a.	PROPN
iajs-2681	419	10	,	,	PUNCT
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iajs-2681	419	15	axioms	axiom	NOUN
iajs-2681	419	16	,	,	PUNCT
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iajs-2681	419	25	,	,	PUNCT
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iajs-2681	419	30	,	,	PUNCT
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iajs-2681	420	15	,	,	PUNCT
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iajs-2681	420	17	journal	journal	NOUN
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iajs-2681	420	24	)	)	PUNCT
iajs-2681	420	25	,	,	PUNCT
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iajs-2681	420	30	,	,	PUNCT
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iajs-2681	420	32	,	,	PUNCT
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iajs-2681	420	34	–	–	PUNCT
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iajs-2681	421	2	.	.	PUNCT
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iajs-2681	422	3	y.	y.	PROPN
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iajs-2681	422	17	ibn	ibn	PROPN
iajs-2681	422	18	al	al	PROPN
iajs-2681	422	19	-	-	PUNCT
iajs-2681	422	20	haitham	haitham	PROPN
iajs-2681	422	21	journal	journal	PROPN
iajs-2681	422	22	science	science	PROPN
iajs-2681	422	23	,	,	PUNCT
iajs-2681	422	24	2009	2009	NUM
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iajs-2681	422	31	-	-	SYM
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iajs-2681	422	33	.	.	PUNCT
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iajs-2681	423	2	https://www.ijsr.net/archive/v6i2/v6i2.pdf	https://www.ijsr.net/archive/v6i2/v6i2.pdf	PROPN
iajs-2681	423	3	ibn	ibn	PROPN
iajs-2681	423	4	al	al	PROPN
iajs-2681	423	5	-	-	PUNCT
iajs-2681	423	6	haitham	haitham	PROPN
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iajs-2681	423	8	.	.	PROPN
iajs-2681	424	1	for	for	ADP
iajs-2681	424	2	pure	pure	ADJ
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iajs-2681	424	4	appl	appl	PROPN
iajs-2681	424	5	.	.	PUNCT
iajs-2681	425	1	sci	sci	PROPN
iajs-2681	425	2	.	.	PROPN
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iajs-2681	426	4	.	.	PUNCT
iajs-2681	427	1	yousif	yousif	PROPN
iajs-2681	427	2	,	,	PUNCT
iajs-2681	427	3	y.	y.	PROPN
iajs-2681	427	4	y.	y.	PROPN
iajs-2681	427	5	,	,	PUNCT
iajs-2681	427	6	some	some	DET
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iajs-2681	427	8	on	on	ADP
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iajs-2681	427	12	,	,	PUNCT
iajs-2681	427	13	ibn	ibn	PROPN
iajs-2681	427	14	al	al	PROPN
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iajs-2681	427	16	haitham	haitham	PROPN
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iajs-2681	428	10	-	-	PUNCT
iajs-2681	428	11	haitham	haitham	PROPN
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iajs-2681	428	24	.	.	X
iajs-2681	429	1	zadeh	zadeh	PROPN
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iajs-2681	430	4	,	,	PUNCT
iajs-2681	430	5	8,338	8,338	NUM
iajs-2681	430	6	-	-	SYM
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iajs-2681	430	8	.	.	PUNCT