id	sid	tid	token	lemma	pos
iajs-1956	1	1	microsoft	microsoft	PROPN
iajs-1956	1	2	word	word	NOUN
iajs-1956	1	3	179	179	NUM
iajs-1956	1	4	-	-	SYM
iajs-1956	1	5	185	185	NUM
iajs-1956	1	6	  	  	SPACE
iajs-1956	1	7	179	179	NUM
iajs-1956	1	8	mathematics	mathematic	NOUN
iajs-1956	1	9	|	|	ADV
iajs-1956	1	10	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	1	11	2018	2018	NUM
iajs-1956	1	12	)	)	PUNCT
iajs-1956	1	13	عام	عام	ADP
iajs-1956	1	14	2العدد	2العدد	NUM
iajs-1956	1	15	(	(	PUNCT
iajs-1956	1	16	31المجلد	31المجلد	NUM
iajs-1956	1	17	مجلة	مجلة	VERB
iajs-1956	1	18	إبن	إبن	VERB
iajs-1956	1	19	الهيثم	الهيثم	ADJ
iajs-1956	1	20	للعلوم	للعلوم	NOUN
iajs-1956	1	21	الصرفة	الصرفة	NOUN
iajs-1956	1	22	و	و	PRON
iajs-1956	1	23	التطبيقية	التطبيقية	ADJ
iajs-1956	1	24	ibn	ibn	PROPN
iajs-1956	1	25	al	al	PROPN
iajs-1956	1	26	-	-	PUNCT
iajs-1956	1	27	haitham	haitham	PROPN
iajs-1956	1	28	jour	jour	X
iajs-1956	1	29	.	.	PROPN
iajs-1956	1	30	for	for	ADP
iajs-1956	1	31	pure	pure	ADJ
iajs-1956	1	32	&	&	CCONJ
iajs-1956	1	33	appl	appl	PROPN
iajs-1956	1	34	.	.	PUNCT
iajs-1956	2	1	sci	sci	PROPN
iajs-1956	2	2	.	.	PUNCT
iajs-1956	2	3	vol	vol	NOUN
iajs-1956	2	4	.	.	PROPN
iajs-1956	3	1	31	31	NUM
iajs-1956	3	2	(	(	PUNCT
iajs-1956	3	3	2	2	NUM
iajs-1956	3	4	)	)	PUNCT
iajs-1956	3	5	2018	2018	NUM
iajs-1956	3	6	on	on	ADP
iajs-1956	3	7	𝛉-totally	𝛉-totally	ADV
iajs-1956	3	8	disconnected	disconnected	ADJ
iajs-1956	3	9	and	and	CCONJ
iajs-1956	3	10	𝛉-light	𝛉-light	NOUN
iajs-1956	3	11	mappings	mapping	NOUN
iajs-1956	3	12	haider	haider	PROPN
iajs-1956	3	13	jebur	jebur	PROPN
iajs-1956	3	14	ali	ali	PROPN
iajs-1956	3	15	huda	huda	PROPN
iajs-1956	3	16	fadel	fadel	PROPN
iajs-1956	3	17	abass	abass	PROPN
iajs-1956	3	18	dept	dept	PROPN
iajs-1956	3	19	of	of	ADP
iajs-1956	3	20	mathematics	mathematics	PROPN
iajs-1956	3	21	/	/	SYM
iajs-1956	3	22	college	college	NOUN
iajs-1956	3	23	of	of	ADP
iajs-1956	3	24	science	science	PROPN
iajs-1956	3	25	/	/	SYM
iajs-1956	3	26	al	al	PROPN
iajs-1956	3	27	-	-	PUNCT
iajs-1956	3	28	mustansiriyah	mustansiriyah	PROPN
iajs-1956	3	29	university	university	NOUN
iajs-1956	3	30	,	,	PUNCT
iajs-1956	3	31	haiderali89@yahoo.com	haiderali89@yahoo.com	X
iajs-1956	4	1	huda.fadel91@gmail.com	huda.fadel91@gmail.com	PROPN
iajs-1956	4	2	received	receive	VERB
iajs-1956	4	3	in:24	in:24	PROPN
iajs-1956	4	4	/	/	SYM
iajs-1956	4	5	january/2018	january/2018	NOUN
iajs-1956	4	6	,	,	PUNCT
iajs-1956	4	7	accepted:27	accepted:27	PROPN
iajs-1956	4	8	/	/	SYM
iajs-1956	4	9	march/2018	march/2018	NOUN
iajs-1956	4	10	abstract	abstract	ADV
iajs-1956	4	11	in	in	ADP
iajs-1956	4	12	our	our	PRON
iajs-1956	4	13	research	research	NOUN
iajs-1956	4	14	,	,	PUNCT
iajs-1956	4	15	we	we	PRON
iajs-1956	4	16	introduced	introduce	VERB
iajs-1956	4	17	new	new	ADJ
iajs-1956	4	18	concepts	concept	NOUN
iajs-1956	4	19	,	,	PUNCT
iajs-1956	4	20	namely	namely	ADV
iajs-1956	4	21	𝜃	𝜃	NOUN
iajs-1956	4	22	,	,	PUNCT
iajs-1956	4	23	𝜃*and	𝜃*and	NUM
iajs-1956	4	24	𝜃**-light	𝜃**-light	NUM
iajs-1956	4	25	mappings	mapping	NOUN
iajs-1956	4	26	,	,	PUNCT
iajs-1956	4	27	after	after	SCONJ
iajs-1956	4	28	we	we	PRON
iajs-1956	4	29	knew	know	VERB
iajs-1956	4	30	𝜃	𝜃	NOUN
iajs-1956	4	31	,	,	PUNCT
iajs-1956	4	32	𝜃*and	𝜃*and	X
iajs-1956	4	33	𝜃**-totally	𝜃**-totally	ADV
iajs-1956	4	34	disconnected	disconnect	VERB
iajs-1956	4	35	mappings	mapping	NOUN
iajs-1956	4	36	through	through	ADP
iajs-1956	4	37	the	the	DET
iajs-1956	4	38	use	use	NOUN
iajs-1956	4	39	of	of	ADP
iajs-1956	4	40	𝜃-open	𝜃-open	NOUN
iajs-1956	4	41	sets	set	NOUN
iajs-1956	4	42	.	.	PUNCT
iajs-1956	5	1	many	many	ADJ
iajs-1956	5	2	examples	example	NOUN
iajs-1956	5	3	,	,	PUNCT
iajs-1956	5	4	facts	fact	NOUN
iajs-1956	5	5	,	,	PUNCT
iajs-1956	5	6	relationships	relationship	NOUN
iajs-1956	5	7	and	and	CCONJ
iajs-1956	5	8	results	result	NOUN
iajs-1956	5	9	have	have	AUX
iajs-1956	5	10	been	be	AUX
iajs-1956	5	11	given	give	VERB
iajs-1956	5	12	to	to	PART
iajs-1956	5	13	support	support	VERB
iajs-1956	5	14	our	our	PRON
iajs-1956	5	15	work	work	NOUN
iajs-1956	5	16	.	.	PUNCT
iajs-1956	6	1	keywords	keyword	NOUN
iajs-1956	6	2	:	:	PUNCT
iajs-1956	6	3	𝜃-open	𝜃-open	NOUN
iajs-1956	6	4	set	set	NOUN
iajs-1956	6	5	,	,	PUNCT
iajs-1956	6	6	light	light	ADJ
iajs-1956	6	7	mapping	mapping	NOUN
iajs-1956	6	8	,	,	PUNCT
iajs-1956	6	9	𝜃-homeomorphism	𝜃-homeomorphism	NOUN
iajs-1956	6	10	function	function	NOUN
iajs-1956	6	11	,	,	PUNCT
iajs-1956	6	12	𝜃-totally	𝜃-totally	ADV
iajs-1956	6	13	disconnected	disconnect	VERB
iajs-1956	6	14	set	set	NOUN
iajs-1956	6	15	,	,	PUNCT
iajs-1956	6	16	𝜃-light	𝜃-light	NUM
iajs-1956	6	17	mapping	mapping	NOUN
iajs-1956	6	18	.	.	PUNCT
iajs-1956	6	19	  	  	SPACE
iajs-1956	7	1	180	180	NUM
iajs-1956	7	2	mathematics	mathematic	NOUN
iajs-1956	7	3	|	|	ADV
iajs-1956	7	4	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	7	5	2018	2018	NUM
iajs-1956	7	6	)	)	PUNCT
iajs-1956	7	7	عام	عام	ADP
iajs-1956	7	8	2العدد	2العدد	NUM
iajs-1956	7	9	(	(	PUNCT
iajs-1956	7	10	31لمجلد	31لمجلد	NUM
iajs-1956	7	11	ا	ا	NOUN
iajs-1956	7	12	مجلة	مجلة	NOUN
iajs-1956	7	13	إبن	إبن	VERB
iajs-1956	7	14	الهيثم	الهيثم	ADJ
iajs-1956	7	15	للعلوم	للعلوم	NOUN
iajs-1956	7	16	الصرفة	الصرفة	NOUN
iajs-1956	8	1	و	و	PRON
iajs-1956	8	2	التطبيقية	التطبيقية	ADJ
iajs-1956	8	3	ibn	ibn	PROPN
iajs-1956	8	4	al	al	PROPN
iajs-1956	8	5	-	-	PUNCT
iajs-1956	8	6	haitham	haitham	PROPN
iajs-1956	8	7	jour	jour	X
iajs-1956	8	8	.	.	PROPN
iajs-1956	8	9	for	for	ADP
iajs-1956	8	10	pure	pure	ADJ
iajs-1956	8	11	&	&	CCONJ
iajs-1956	8	12	appl	appl	PROPN
iajs-1956	8	13	.	.	PUNCT
iajs-1956	9	1	sci	sci	PROPN
iajs-1956	9	2	.	.	PUNCT
iajs-1956	9	3	vol	vol	NOUN
iajs-1956	9	4	.	.	PROPN
iajs-1956	10	1	31	31	NUM
iajs-1956	10	2	(	(	PUNCT
iajs-1956	10	3	2	2	NUM
iajs-1956	10	4	)	)	PUNCT
iajs-1956	10	5	2018	2018	NUM
iajs-1956	10	6	introduction	introduction	NOUN
iajs-1956	10	7	many	many	ADJ
iajs-1956	10	8	researchers	researcher	NOUN
iajs-1956	10	9	studied	study	VERB
iajs-1956	10	10	the	the	DET
iajs-1956	10	11	light	light	ADJ
iajs-1956	10	12	mappings	mapping	NOUN
iajs-1956	10	13	such	such	ADJ
iajs-1956	10	14	as	as	ADP
iajs-1956	10	15	the	the	DET
iajs-1956	10	16	world	world	NOUN
iajs-1956	10	17	’s	’s	PART
iajs-1956	10	18	j.j.charatonic	j.j.charatonic	ADJ
iajs-1956	10	19	and	and	CCONJ
iajs-1956	10	20	k.omiljanowski[2	k.omiljanowski[2	PROPN
iajs-1956	10	21	]	]	PUNCT
iajs-1956	10	22	.	.	PUNCT
iajs-1956	11	1	in	in	ADP
iajs-1956	11	2	this	this	DET
iajs-1956	11	3	paper	paper	NOUN
iajs-1956	11	4	,	,	PUNCT
iajs-1956	11	5	we	we	PRON
iajs-1956	11	6	provide	provide	VERB
iajs-1956	11	7	other	other	ADJ
iajs-1956	11	8	types	type	NOUN
iajs-1956	11	9	of	of	ADP
iajs-1956	11	10	light	light	ADJ
iajs-1956	11	11	mappings	mapping	NOUN
iajs-1956	11	12	namely	namely	ADV
iajs-1956	11	13	𝜃light	𝜃light	VERB
iajs-1956	11	14	open	open	ADJ
iajs-1956	11	15	mapping	mapping	NOUN
iajs-1956	11	16	.	.	PUNCT
iajs-1956	12	1	other	other	ADJ
iajs-1956	12	2	scientists	scientist	NOUN
iajs-1956	12	3	who	who	PRON
iajs-1956	12	4	studied	study	VERB
iajs-1956	12	5	the	the	DET
iajs-1956	12	6	light	light	ADJ
iajs-1956	12	7	mappings	mapping	NOUN
iajs-1956	12	8	are	be	AUX
iajs-1956	12	9	the	the	DET
iajs-1956	12	10	word	word	NOUN
iajs-1956	12	11	m.	m.	NOUN
iajs-1956	12	12	wldyslaw	wldyslaw	NOUN
iajs-1956	13	1	[	[	X
iajs-1956	13	2	5	5	NUM
iajs-1956	13	3	]	]	PUNCT
iajs-1956	13	4	,	,	PUNCT
iajs-1956	13	5	m.	m.	PROPN
iajs-1956	13	6	k.	k.	PROPN
iajs-1956	13	7	fort	fort	PROPN
iajs-1956	14	1	[	[	X
iajs-1956	14	2	3	3	NUM
iajs-1956	14	3	]	]	PUNCT
iajs-1956	14	4	and	and	CCONJ
iajs-1956	14	5	g.	g.	PROPN
iajs-1956	14	6	sh	sh	PROPN
iajs-1956	14	7	.	.	PROPN
iajs-1956	14	8	mohammed	mohammed	PROPN
iajs-1956	15	1	[	[	X
iajs-1956	15	2	1	1	X
iajs-1956	15	3	]	]	PUNCT
iajs-1956	15	4	and	and	CCONJ
iajs-1956	15	5	others	other	NOUN
iajs-1956	15	6	.	.	PUNCT
iajs-1956	16	1	in	in	ADP
iajs-1956	16	2	our	our	PRON
iajs-1956	16	3	work	work	NOUN
iajs-1956	16	4	,	,	PUNCT
iajs-1956	16	5	we	we	PRON
iajs-1956	16	6	needed	need	VERB
iajs-1956	16	7	some	some	DET
iajs-1956	16	8	basic	basic	ADJ
iajs-1956	16	9	definitions	definition	NOUN
iajs-1956	16	10	.	.	PUNCT
iajs-1956	17	1	let	let	VERB
iajs-1956	17	2	(	(	PUNCT
iajs-1956	17	3	x	x	NOUN
iajs-1956	17	4	,	,	PUNCT
iajs-1956	17	5	ʈ	ʈ	AUX
iajs-1956	17	6	)	)	PUNCT
iajs-1956	17	7	be	be	AUX
iajs-1956	17	8	topological	topological	ADJ
iajs-1956	17	9	space	space	NOUN
iajs-1956	17	10	and	and	CCONJ
iajs-1956	17	11	a	a	DET
iajs-1956	17	12	be	be	AUX
iajs-1956	17	13	a	a	DET
iajs-1956	17	14	subset	subset	NOUN
iajs-1956	17	15	of	of	ADP
iajs-1956	17	16	x	x	PRON
iajs-1956	17	17	,	,	PUNCT
iajs-1956	17	18	a	a	DET
iajs-1956	17	19	point	point	NOUN
iajs-1956	17	20	x∈a	x∈a	NOUN
iajs-1956	17	21	is	be	AUX
iajs-1956	17	22	said	say	VERB
iajs-1956	17	23	to	to	PART
iajs-1956	17	24	be	be	AUX
iajs-1956	17	25	𝜃-interior	𝜃-interior	ADJ
iajs-1956	17	26	point	point	NOUN
iajs-1956	17	27	to	to	ADP
iajs-1956	17	28	a	a	DET
iajs-1956	17	29	if	if	SCONJ
iajs-1956	17	30	x∈	x∈	PROPN
iajs-1956	17	31	𝑈	𝑈	PROPN
iajs-1956	17	32	⊆	⊆	NUM
iajs-1956	17	33	𝐴	𝐴	PROPN
iajs-1956	17	34	for	for	ADP
iajs-1956	17	35	some	some	DET
iajs-1956	17	36	u∈	u∈	NOUN
iajs-1956	17	37	𝜏	𝜏	NOUN
iajs-1956	17	38	containing	contain	VERB
iajs-1956	17	39	x.	x.	NOUN
iajs-1956	17	40	the	the	DET
iajs-1956	17	41	set	set	NOUN
iajs-1956	17	42	of	of	ADP
iajs-1956	17	43	all	all	DET
iajs-1956	17	44	𝜃-interior	𝜃-interior	ADJ
iajs-1956	17	45	points	point	NOUN
iajs-1956	17	46	are	be	AUX
iajs-1956	17	47	called	call	VERB
iajs-1956	17	48	𝜃-interior	𝜃-interior	PROPN
iajs-1956	17	49	set	set	NOUN
iajs-1956	17	50	and	and	CCONJ
iajs-1956	17	51	we	we	PRON
iajs-1956	17	52	denoted	denote	VERB
iajs-1956	17	53	by	by	ADP
iajs-1956	17	54	𝜃	𝜃	PROPN
iajs-1956	17	55	𝑖𝑛𝑡	𝑖𝑛𝑡	NUM
iajs-1956	17	56	a	a	PRON
iajs-1956	17	57	,	,	PUNCT
iajs-1956	17	58	a	a	DET
iajs-1956	17	59	subset	subset	ADJ
iajs-1956	17	60	u	u	NOUN
iajs-1956	17	61	of	of	ADP
iajs-1956	17	62	topological	topological	ADJ
iajs-1956	17	63	pace	pace	NOUN
iajs-1956	17	64	x	x	PUNCT
iajs-1956	17	65	is	be	AUX
iajs-1956	17	66	𝜃-open	𝜃-open	NOUN
iajs-1956	17	67	if	if	SCONJ
iajs-1956	17	68	and	and	CCONJ
iajs-1956	17	69	only	only	ADV
iajs-1956	17	70	if	if	SCONJ
iajs-1956	17	71	every	every	DET
iajs-1956	17	72	point	point	NOUN
iajs-1956	17	73	in	in	ADP
iajs-1956	17	74	u	u	NOUN
iajs-1956	17	75	is	be	AUX
iajs-1956	17	76	a	a	DET
iajs-1956	17	77	interior	interior	ADJ
iajs-1956	17	78	point	point	NOUN
iajs-1956	17	79	[	[	X
iajs-1956	17	80	7	7	NUM
iajs-1956	17	81	]	]	PUNCT
iajs-1956	17	82	.	.	PUNCT
iajs-1956	18	1	every	every	DET
iajs-1956	18	2	𝜃-open	𝜃-open	NOUN
iajs-1956	18	3	set	set	NOUN
iajs-1956	18	4	is	be	AUX
iajs-1956	18	5	an	an	DET
iajs-1956	18	6	open	open	ADJ
iajs-1956	18	7	set	set	NOUN
iajs-1956	18	8	but	but	CCONJ
iajs-1956	18	9	the	the	DET
iajs-1956	18	10	converse	converse	NOUN
iajs-1956	18	11	may	may	AUX
iajs-1956	18	12	not	not	PART
iajs-1956	18	13	be	be	AUX
iajs-1956	18	14	true	true	ADJ
iajs-1956	18	15	in	in	ADP
iajs-1956	18	16	general	general	ADJ
iajs-1956	18	17	.	.	PUNCT
iajs-1956	18	18	 	 	SPACE
iajs-1956	19	1	a	a	DET
iajs-1956	19	2	space	space	NOUN
iajs-1956	19	3	x	x	PUNCT
iajs-1956	19	4	is	be	AUX
iajs-1956	19	5	said	say	VERB
iajs-1956	19	6	to	to	PART
iajs-1956	19	7	be	be	AUX
iajs-1956	19	8	𝜃-hausdorff	𝜃-hausdorff	VERB
iajs-1956	19	9	if	if	SCONJ
iajs-1956	19	10	for	for	ADP
iajs-1956	19	11	every	every	DET
iajs-1956	19	12	distinct	distinct	ADJ
iajs-1956	19	13	point	point	NOUN
iajs-1956	19	14	x	x	SYM
iajs-1956	19	15	,	,	PUNCT
iajs-1956	19	16	y∈x	y∈x	NOUN
iajs-1956	19	17	there	there	PRON
iajs-1956	19	18	exist	exist	VERB
iajs-1956	19	19	𝜃-open	𝜃-open	NOUN
iajs-1956	19	20	sets	set	NOUN
iajs-1956	19	21	ux	ux	PROPN
iajs-1956	19	22	,	,	PUNCT
iajs-1956	20	1	vy	vy	PROPN
iajs-1956	20	2	containing	contain	VERB
iajs-1956	20	3	x	x	PROPN
iajs-1956	20	4	and	and	CCONJ
iajs-1956	20	5	y	y	PROPN
iajs-1956	20	6	respectively	respectively	ADV
iajs-1956	20	7	such	such	ADJ
iajs-1956	20	8	that	that	SCONJ
iajs-1956	20	9	ux∩	ux∩	PROPN
iajs-1956	20	10	vy	vy	NOUN
iajs-1956	20	11	=	=	PROPN
iajs-1956	20	12	∅[4	∅[4	PROPN
iajs-1956	20	13	]	]	PUNCT
iajs-1956	20	14	.	.	PUNCT
iajs-1956	21	1	a	a	DET
iajs-1956	21	2	mapping	mapping	NOUN
iajs-1956	21	3	f	f	X
iajs-1956	21	4	:	:	PUNCT
iajs-1956	21	5	x→y	x→y	NUM
iajs-1956	21	6	is	be	AUX
iajs-1956	21	7	said	say	VERB
iajs-1956	21	8	to	to	PART
iajs-1956	21	9	be	be	AUX
iajs-1956	21	10	𝜃-open(𝜃*-open	𝜃-open(𝜃*-open	PUNCT
iajs-1956	21	11	and	and	CCONJ
iajs-1956	21	12	𝜃**-open	𝜃**-open	PRON
iajs-1956	21	13	)	)	PUNCT
iajs-1956	21	14	if	if	SCONJ
iajs-1956	21	15	f(v	f(v	NOUN
iajs-1956	21	16	)	)	PUNCT
iajs-1956	21	17	is	be	AUX
iajs-1956	21	18	𝜃-open(open	𝜃-open(open	ADJ
iajs-1956	21	19	and	and	CCONJ
iajs-1956	21	20	𝜃-open	𝜃-open	NOUN
iajs-1956	21	21	)	)	PUNCT
iajs-1956	21	22	in	in	ADP
iajs-1956	21	23	y	y	PROPN
iajs-1956	21	24	,	,	PUNCT
iajs-1956	21	25	whenever	whenever	SCONJ
iajs-1956	21	26	v	v	NOUN
iajs-1956	21	27	is	be	AUX
iajs-1956	21	28	open	open	ADJ
iajs-1956	21	29	(	(	PUNCT
iajs-1956	21	30	𝜃-open	𝜃-open	NOUN
iajs-1956	21	31	)	)	PUNCT
iajs-1956	21	32	in	in	ADP
iajs-1956	21	33	x	x	PUNCT
iajs-1956	22	1	[	[	X
iajs-1956	22	2	6	6	NUM
iajs-1956	22	3	]	]	PUNCT
iajs-1956	22	4	.	.	PUNCT
iajs-1956	22	5	 	 	SPACE
iajs-1956	22	6	let	let	VERB
iajs-1956	22	7	x	x	PRON
iajs-1956	22	8	and	and	CCONJ
iajs-1956	22	9	y	y	PROPN
iajs-1956	22	10	be	be	AUX
iajs-1956	22	11	spaces	space	NOUN
iajs-1956	22	12	and	and	CCONJ
iajs-1956	22	13	let	let	VERB
iajs-1956	22	14	f	f	PRON
iajs-1956	22	15	be	be	AUX
iajs-1956	22	16	a	a	DET
iajs-1956	22	17	mapping	mapping	NOUN
iajs-1956	22	18	from	from	ADP
iajs-1956	22	19	x	x	PUNCT
iajs-1956	22	20	into	into	ADP
iajs-1956	22	21	y	y	PROPN
iajs-1956	22	22	then	then	ADV
iajs-1956	22	23	f	f	PROPN
iajs-1956	22	24	is	be	AUX
iajs-1956	22	25	said	say	VERB
iajs-1956	22	26	to	to	PART
iajs-1956	22	27	be	be	AUX
iajs-1956	22	28	𝜃-homeomorphism	𝜃-homeomorphism	NOUN
iajs-1956	22	29	if	if	SCONJ
iajs-1956	22	30	f	f	PROPN
iajs-1956	22	31	is	be	AUX
iajs-1956	22	32	bijective	bijective	ADJ
iajs-1956	22	33	,	,	PUNCT
iajs-1956	22	34	continuous	continuous	ADJ
iajs-1956	22	35	and	and	CCONJ
iajs-1956	22	36	𝜃-closed	𝜃-closed	ADJ
iajs-1956	22	37	(	(	PUNCT
iajs-1956	22	38	𝜃-open	𝜃-open	NOUN
iajs-1956	22	39	)	)	PUNCT
iajs-1956	23	1	[	[	X
iajs-1956	23	2	6	6	NUM
iajs-1956	23	3	]	]	PUNCT
iajs-1956	23	4	.	.	PUNCT
iajs-1956	24	1	a	a	DET
iajs-1956	24	2	space	space	NOUN
iajs-1956	24	3	x	x	PUNCT
iajs-1956	24	4	is	be	AUX
iajs-1956	24	5	said	say	VERB
iajs-1956	24	6	to	to	PART
iajs-1956	24	7	be	be	AUX
iajs-1956	24	8	totally	totally	ADV
iajs-1956	24	9	disconnected	disconnected	ADJ
iajs-1956	24	10	space	space	NOUN
iajs-1956	24	11	if	if	SCONJ
iajs-1956	24	12	for	for	ADP
iajs-1956	24	13	every	every	DET
iajs-1956	24	14	pair	pair	NOUN
iajs-1956	24	15	of	of	ADP
iajs-1956	24	16	distinct	distinct	ADJ
iajs-1956	24	17	points	point	NOUN
iajs-1956	24	18	,	,	PUNCT
iajs-1956	24	19	a	a	PRON
iajs-1956	24	20	,	,	PUNCT
iajs-1956	24	21	b	b	NOUN
iajs-1956	24	22	∈x	∈x	NOUN
iajs-1956	24	23	has	have	VERB
iajs-1956	24	24	a	a	DET
iajs-1956	24	25	disconnection	disconnection	NOUN
iajs-1956	24	26	a∪b	a∪b	NOUN
iajs-1956	24	27	to	to	ADP
iajs-1956	24	28	x	x	SYM
iajs-1956	24	29	such	such	ADJ
iajs-1956	24	30	that	that	SCONJ
iajs-1956	24	31	a	a	DET
iajs-1956	24	32	∈	∈	PROPN
iajs-1956	24	33	a	a	PRON
iajs-1956	24	34	and	and	CCONJ
iajs-1956	24	35	b	b	NOUN
iajs-1956	24	36	∈	∈	ADP
iajs-1956	24	37	b	b	PROPN
iajs-1956	25	1	[	[	X
iajs-1956	25	2	8	8	NUM
iajs-1956	25	3	]	]	PUNCT
iajs-1956	25	4	.	.	PUNCT
iajs-1956	26	1	a	a	DET
iajs-1956	26	2	surjective	surjective	ADJ
iajs-1956	26	3	mapping	mapping	NOUN
iajs-1956	26	4	f	f	X
iajs-1956	26	5	:	:	PUNCT
iajs-1956	26	6	x→y	x→y	NUM
iajs-1956	26	7	is	be	AUX
iajs-1956	26	8	said	say	VERB
iajs-1956	26	9	to	to	PART
iajs-1956	26	10	be	be	AUX
iajs-1956	26	11	totally	totally	ADV
iajs-1956	26	12	disconnected	disconnected	ADJ
iajs-1956	26	13	mapping	mapping	NOUN
iajs-1956	26	14	if	if	SCONJ
iajs-1956	26	15	and	and	CCONJ
iajs-1956	26	16	only	only	ADV
iajs-1956	26	17	if	if	SCONJ
iajs-1956	26	18	for	for	ADP
iajs-1956	26	19	every	every	DET
iajs-1956	26	20	totally	totally	ADV
iajs-1956	26	21	disconnected	disconnected	ADJ
iajs-1956	26	22	set	set	VERB
iajs-1956	26	23	u	u	NOUN
iajs-1956	26	24	in	in	ADP
iajs-1956	26	25	x	x	PROPN
iajs-1956	26	26	,	,	PUNCT
iajs-1956	26	27	f(u	f(u	PROPN
iajs-1956	26	28	)	)	PUNCT
iajs-1956	26	29	is	be	AUX
iajs-1956	26	30	totally	totally	ADV
iajs-1956	26	31	disconnected	disconnect	VERB
iajs-1956	26	32	set	set	VERB
iajs-1956	26	33	in	in	ADP
iajs-1956	26	34	y	y	PROPN
iajs-1956	27	1	[	[	X
iajs-1956	27	2	1	1	NUM
iajs-1956	27	3	]	]	PUNCT
iajs-1956	27	4	.	.	PUNCT
iajs-1956	28	1	definition(1	definition(1	NOUN
iajs-1956	28	2	):	):	PUNCT
iajs-1956	28	3	let	let	VERB
iajs-1956	28	4	x	x	PRON
iajs-1956	28	5	be	be	AUX
iajs-1956	28	6	topological	topological	ADJ
iajs-1956	28	7	space	space	NOUN
iajs-1956	28	8	,	,	PUNCT
iajs-1956	28	9	and	and	CCONJ
iajs-1956	28	10	let	let	VERB
iajs-1956	28	11	a	a	PRON
iajs-1956	28	12	and	and	CCONJ
iajs-1956	28	13	b	b	NOUN
iajs-1956	28	14	are	be	AUX
iajs-1956	28	15	nonempty	nonempty	ADJ
iajs-1956	28	16	𝜃-open	𝜃-open	NOUN
iajs-1956	28	17	sets	set	NOUN
iajs-1956	28	18	in	in	ADP
iajs-1956	28	19	x	x	NOUN
iajs-1956	28	20	,	,	PUNCT
iajs-1956	28	21	then	then	ADV
iajs-1956	28	22	a∪b	a∪b	NOUN
iajs-1956	28	23	is	be	AUX
iajs-1956	28	24	said	say	VERB
iajs-1956	28	25	to	to	PART
iajs-1956	28	26	be	be	AUX
iajs-1956	28	27	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	28	28	in	in	ADP
iajs-1956	28	29	x	x	PUNCT
iajs-1956	28	30	if	if	SCONJ
iajs-1956	28	31	and	and	CCONJ
iajs-1956	28	32	only	only	ADV
iajs-1956	28	33	if	if	SCONJ
iajs-1956	28	34	a∪b	a∪b	ADJ
iajs-1956	28	35	=	=	NOUN
iajs-1956	28	36	x	x	X
iajs-1956	28	37	and	and	CCONJ
iajs-1956	28	38	a∩b	a∩b	X
iajs-1956	28	39	=	=	NOUN
iajs-1956	28	40	∅.	∅.	VERB
iajs-1956	28	41	definition(2	definition(2	NOUN
iajs-1956	28	42	):	):	PUNCT
iajs-1956	28	43	let	let	VERB
iajs-1956	28	44	x	x	PRON
iajs-1956	28	45	be	be	AUX
iajs-1956	28	46	topology	topology	NOUN
iajs-1956	28	47	space	space	NOUN
iajs-1956	28	48	,	,	PUNCT
iajs-1956	28	49	g⊆x	g⊆x	PROPN
iajs-1956	28	50	,	,	PUNCT
iajs-1956	28	51	let	let	VERB
iajs-1956	28	52	a	a	DET
iajs-1956	28	53	,	,	PUNCT
iajs-1956	28	54	b	b	NOUN
iajs-1956	28	55	are	be	AUX
iajs-1956	28	56	nonempty	nonempty	ADJ
iajs-1956	28	57	𝜃-open	𝜃-open	NOUN
iajs-1956	28	58	sets	set	NOUN
iajs-1956	28	59	in	in	ADP
iajs-1956	28	60	x	x	NOUN
iajs-1956	28	61	,	,	PUNCT
iajs-1956	28	62	then	then	ADV
iajs-1956	28	63	a∪b	a∪b	NOUN
iajs-1956	28	64	is	be	AUX
iajs-1956	28	65	said	say	VERB
iajs-1956	28	66	to	to	PART
iajs-1956	28	67	be	be	AUX
iajs-1956	28	68	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	28	69	in	in	ADP
iajs-1956	28	70	g	g	PROPN
iajs-1956	28	71	if	if	SCONJ
iajs-1956	29	1	and	and	CCONJ
iajs-1956	29	2	only	only	ADV
iajs-1956	29	3	if	if	SCONJ
iajs-1956	29	4	satisfy	satisfy	VERB
iajs-1956	29	5	the	the	DET
iajs-1956	29	6	following	following	NOUN
iajs-1956	29	7	:	:	PUNCT
iajs-1956	29	8	1g∩a	1g∩a	NUM
iajs-1956	29	9	∅.	∅.	NOUN
iajs-1956	29	10	2g∩b	2g∩b	NUM
iajs-1956	29	11	∅.	∅.	PRON
iajs-1956	29	12	3-(g∩a)∩(g∩b)=∅.	3-(g∩a)∩(g∩b)=∅.	NUM
iajs-1956	29	13	4-(g∩	4-(g∩	NUM
iajs-1956	29	14	a)∪(g∩b)=g	a)∪(g∩b)=g	PROPN
iajs-1956	29	15	.	.	PUNCT
iajs-1956	30	1	example	example	NOUN
iajs-1956	30	2	(	(	PUNCT
iajs-1956	30	3	3	3	NUM
iajs-1956	30	4	):	):	PUNCT
iajs-1956	30	5	let	let	VERB
iajs-1956	30	6	x={a	x={a	PROPN
iajs-1956	30	7	,	,	PUNCT
iajs-1956	30	8	b	b	PROPN
iajs-1956	30	9	,	,	PUNCT
iajs-1956	30	10	c	c	NOUN
iajs-1956	30	11	}	}	PUNCT
iajs-1956	30	12	and	and	CCONJ
iajs-1956	30	13	let	let	VERB
iajs-1956	30	14	ʈd	ʈd	PRON
iajs-1956	30	15	is	be	AUX
iajs-1956	30	16	discrete	discrete	ADJ
iajs-1956	30	17	topology	topology	NOUN
iajs-1956	30	18	define	define	VERB
iajs-1956	30	19	to	to	PART
iajs-1956	30	20	x.	x.	NOUN
iajs-1956	30	21	then	then	ADV
iajs-1956	30	22	{	{	PUNCT
iajs-1956	30	23	a	a	X
iajs-1956	30	24	}	}	PUNCT
iajs-1956	30	25	,	,	PUNCT
iajs-1956	30	26	{	{	PUNCT
iajs-1956	30	27	b	b	X
iajs-1956	30	28	,	,	PUNCT
iajs-1956	30	29	c	c	NOUN
iajs-1956	30	30	}	}	PUNCT
iajs-1956	30	31	are	be	AUX
iajs-1956	30	32	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	30	33	to	to	ADP
iajs-1956	30	34	x	x	PUNCT
iajs-1956	30	35	and	and	CCONJ
iajs-1956	30	36	{	{	PUNCT
iajs-1956	30	37	a	a	X
iajs-1956	30	38	}	}	PUNCT
iajs-1956	30	39	,	,	PUNCT
iajs-1956	30	40	{	{	PUNCT
iajs-1956	30	41	b	b	X
iajs-1956	30	42	,	,	PUNCT
iajs-1956	30	43	c	c	NOUN
iajs-1956	30	44	}	}	PUNCT
iajs-1956	30	45	are	be	AUX
iajs-1956	30	46	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	30	47	to	to	PART
iajs-1956	30	48	subset	subset	VERB
iajs-1956	30	49	{	{	PUNCT
iajs-1956	30	50	a	a	DET
iajs-1956	30	51	,	,	PUNCT
iajs-1956	30	52	b	b	NOUN
iajs-1956	30	53	}	}	PUNCT
iajs-1956	30	54	to	to	ADP
iajs-1956	30	55	x.	x.	NOUN
iajs-1956	30	56	*	*	PUNCT
iajs-1956	30	57	its	its	PRON
iajs-1956	30	58	known	know	VERB
iajs-1956	30	59	that	that	SCONJ
iajs-1956	30	60	every	every	DET
iajs-1956	30	61	𝜃	𝜃	NOUN
iajs-1956	30	62	open	open	ADJ
iajs-1956	30	63	set	set	NOUN
iajs-1956	30	64	s	s	VERB
iajs-1956	30	65	is	be	AUX
iajs-1956	30	66	open	open	ADJ
iajs-1956	30	67	but	but	CCONJ
iajs-1956	30	68	the	the	DET
iajs-1956	30	69	converse	converse	NOUN
iajs-1956	30	70	may	may	AUX
iajs-1956	30	71	be	be	AUX
iajs-1956	30	72	not	not	PART
iajs-1956	30	73	true	true	ADJ
iajs-1956	30	74	.	.	PUNCT
iajs-1956	31	1	example	example	NOUN
iajs-1956	31	2	(	(	PUNCT
iajs-1956	31	3	4	4	NUM
iajs-1956	31	4	):	):	PUNCT
iajs-1956	31	5	(	(	PUNCT
iajs-1956	31	6	r	r	NOUN
iajs-1956	31	7	,	,	PUNCT
iajs-1956	31	8	ʈcof	ʈcof	NOUN
iajs-1956	31	9	)	)	PUNCT
iajs-1956	31	10	the	the	DET
iajs-1956	31	11	open	open	ADJ
iajs-1956	31	12	subsets	subset	NOUN
iajs-1956	31	13	of	of	ADP
iajs-1956	31	14	r	r	NOUN
iajs-1956	31	15	is	be	AUX
iajs-1956	31	16	open	open	ADJ
iajs-1956	31	17	set	set	ADJ
iajs-1956	31	18	but	but	CCONJ
iajs-1956	31	19	not	not	PART
iajs-1956	31	20	𝜃-open	𝜃-open	NOUN
iajs-1956	31	21	.	.	PUNCT
iajs-1956	32	1	definition(5	definition(5	NOUN
iajs-1956	32	2	):	):	PUNCT
iajs-1956	32	3	a	a	DET
iajs-1956	32	4	topology	topology	NOUN
iajs-1956	32	5	space	space	NOUN
iajs-1956	32	6	x	x	PRON
iajs-1956	32	7	is	be	AUX
iajs-1956	32	8	said	say	VERB
iajs-1956	32	9	to	to	PART
iajs-1956	32	10	be	be	AUX
iajs-1956	32	11	𝜃-totally	𝜃-totally	ADV
iajs-1956	32	12	disconnected	disconnect	VERB
iajs-1956	32	13	if	if	SCONJ
iajs-1956	32	14	for	for	ADP
iajs-1956	32	15	every	every	DET
iajs-1956	32	16	two	two	NUM
iajs-1956	32	17	distinct	distinct	ADJ
iajs-1956	32	18	point	point	NOUN
iajs-1956	32	19	p	p	PROPN
iajs-1956	32	20	&	&	CCONJ
iajs-1956	32	21	q	q	NOUN
iajs-1956	32	22	there	there	PRON
iajs-1956	32	23	exist	exist	VERB
iajs-1956	32	24	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	32	25	g∪h	g∪h	NOUN
iajs-1956	32	26	to	to	ADP
iajs-1956	32	27	x	x	SYM
iajs-1956	32	28	such	such	ADJ
iajs-1956	32	29	that	that	DET
iajs-1956	32	30	p∈g	p∈g	ADJ
iajs-1956	32	31	&	&	CCONJ
iajs-1956	32	32	q∈h	q∈h	PROPN
iajs-1956	32	33	.	.	PUNCT
iajs-1956	32	34	  	  	SPACE
iajs-1956	33	1	181	181	NUM
iajs-1956	33	2	mathematics	mathematic	NOUN
iajs-1956	33	3	|	|	ADV
iajs-1956	33	4	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	33	5	2018	2018	NUM
iajs-1956	33	6	)	)	PUNCT
iajs-1956	33	7	عام	عام	ADP
iajs-1956	33	8	2العدد	2العدد	NUM
iajs-1956	33	9	(	(	PUNCT
iajs-1956	33	10	31لمجلد	31لمجلد	NUM
iajs-1956	33	11	ا	ا	NOUN
iajs-1956	33	12	مجلة	مجلة	NOUN
iajs-1956	33	13	إبن	إبن	VERB
iajs-1956	33	14	الهيثم	الهيثم	ADJ
iajs-1956	33	15	للعلوم	للعلوم	NOUN
iajs-1956	33	16	الصرفة	الصرفة	NOUN
iajs-1956	34	1	و	و	PRON
iajs-1956	34	2	التطبيقية	التطبيقية	ADJ
iajs-1956	34	3	ibn	ibn	PROPN
iajs-1956	34	4	al	al	PROPN
iajs-1956	34	5	-	-	PUNCT
iajs-1956	34	6	haitham	haitham	PROPN
iajs-1956	34	7	jour	jour	X
iajs-1956	34	8	.	.	PROPN
iajs-1956	34	9	for	for	ADP
iajs-1956	34	10	pure	pure	ADJ
iajs-1956	34	11	&	&	CCONJ
iajs-1956	34	12	appl	appl	PROPN
iajs-1956	34	13	.	.	PUNCT
iajs-1956	35	1	sci	sci	PROPN
iajs-1956	35	2	.	.	PUNCT
iajs-1956	35	3	vol	vol	NOUN
iajs-1956	35	4	.	.	PROPN
iajs-1956	36	1	31	31	NUM
iajs-1956	36	2	(	(	PUNCT
iajs-1956	36	3	2	2	NUM
iajs-1956	36	4	)	)	PUNCT
iajs-1956	36	5	2018	2018	NUM
iajs-1956	36	6	example	example	NOUN
iajs-1956	36	7	(	(	PUNCT
iajs-1956	36	8	6	6	NUM
iajs-1956	36	9	):	):	PUNCT
iajs-1956	36	10	the	the	DET
iajs-1956	36	11	rational	rational	ADJ
iajs-1956	36	12	numbers	number	NOUN
iajs-1956	36	13	with	with	ADP
iajs-1956	36	14	relative	relative	ADJ
iajs-1956	36	15	usual	usual	ADJ
iajs-1956	36	16	topology	topology	NOUN
iajs-1956	36	17	is	be	AUX
iajs-1956	36	18	a	a	DET
iajs-1956	36	19	𝜃-totally	𝜃-totally	ADV
iajs-1956	36	20	disconnected	disconnect	VERB
iajs-1956	36	21	.	.	PUNCT
iajs-1956	37	1	since	since	SCONJ
iajs-1956	37	2	if	if	SCONJ
iajs-1956	37	3	we	we	PRON
iajs-1956	37	4	take	take	VERB
iajs-1956	37	5	q1&q2	q1&q2	PROPN
iajs-1956	37	6	∈q	∈q	NOUN
iajs-1956	37	7	where	where	SCONJ
iajs-1956	37	8	q1	q1	PROPN
iajs-1956	37	9	q2	q2	PROPN
iajs-1956	37	10	there	there	ADV
iajs-1956	37	11	exist	exist	VERB
iajs-1956	37	12	r∈qc	r∈qc	PROPN
iajs-1956	37	13	such	such	ADJ
iajs-1956	37	14	that	that	DET
iajs-1956	37	15	q1	q1	PROPN
iajs-1956	37	16	r	r	PROPN
iajs-1956	37	17	q2	q2	NOUN
iajs-1956	37	18	g={x∈q	g={x∈q	PROPN
iajs-1956	37	19	:x	:x	PROPN
iajs-1956	37	20	𝑟	𝑟	NOUN
iajs-1956	37	21	}	}	PUNCT
iajs-1956	37	22	and	and	CCONJ
iajs-1956	37	23	h=	h=	NOUN
iajs-1956	37	24	{	{	PUNCT
iajs-1956	37	25	x∈q	x∈q	PROPN
iajs-1956	37	26	:x	:x	PROPN
iajs-1956	37	27	r	r	AUX
iajs-1956	37	28	}	}	PUNCT
iajs-1956	37	29	then	then	ADV
iajs-1956	37	30	g∪h	g∪h	NOUN
iajs-1956	37	31	is	be	AUX
iajs-1956	37	32	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	37	33	to	to	ADP
iajs-1956	37	34	q	q	NOUN
iajs-1956	37	35	such	such	ADJ
iajs-1956	37	36	that	that	SCONJ
iajs-1956	37	37	q1∈	q1∈	PROPN
iajs-1956	37	38	𝐺	𝐺	PROPN
iajs-1956	37	39	&	&	CCONJ
iajs-1956	37	40	q2∈h	q2∈h	PROPN
iajs-1956	38	1	𝐺ing	𝐺ing	PROPN
iajs-1956	38	2	=	=	SYM
iajs-1956	38	3	g	g	PROPN
iajs-1956	38	4	&	&	CCONJ
iajs-1956	38	5	𝐻inh	𝐻inh	PROPN
iajs-1956	38	6	=	=	PROPN
iajs-1956	38	7	h	h	NOUN
iajs-1956	38	8	so	so	ADV
iajs-1956	38	9	q	q	X
iajs-1956	38	10	is	be	AUX
iajs-1956	38	11	a	a	DET
iajs-1956	38	12	𝜃-totally	𝜃-totally	ADV
iajs-1956	38	13	disconnected	disconnect	VERB
iajs-1956	38	14	.	.	PUNCT
iajs-1956	39	1	proposition	proposition	NOUN
iajs-1956	39	2	(	(	PUNCT
iajs-1956	39	3	7	7	NUM
iajs-1956	39	4	):	):	PUNCT
iajs-1956	39	5	every	every	DET
iajs-1956	39	6	𝜃-totally	𝜃-totally	ADV
iajs-1956	39	7	disconnected	disconnected	ADJ
iajs-1956	39	8	set	set	NOUN
iajs-1956	39	9	is	be	AUX
iajs-1956	39	10	totally	totally	ADV
iajs-1956	39	11	disconnected	disconnected	ADJ
iajs-1956	39	12	.	.	PUNCT
iajs-1956	40	1	proof	proof	NOUN
iajs-1956	40	2	:	:	PUNCT
iajs-1956	40	3	let	let	VERB
iajs-1956	40	4	x	x	PRON
iajs-1956	40	5	be	be	AUX
iajs-1956	40	6	𝜃-totally	𝜃-totally	ADV
iajs-1956	40	7	disconnected	disconnect	VERB
iajs-1956	40	8	space	space	NOUN
iajs-1956	40	9	to	to	PART
iajs-1956	40	10	prove	prove	VERB
iajs-1956	40	11	x	x	PUNCT
iajs-1956	40	12	is	be	AUX
iajs-1956	40	13	totally	totally	ADV
iajs-1956	40	14	disconnected	disconnected	ADJ
iajs-1956	40	15	space	space	NOUN
iajs-1956	40	16	.	.	PUNCT
iajs-1956	41	1	let	let	VERB
iajs-1956	41	2	x	x	X
iajs-1956	41	3	,	,	PUNCT
iajs-1956	41	4	y∈x	y∈x	NOUN
iajs-1956	41	5	with	with	ADP
iajs-1956	41	6	x	x	PROPN
iajs-1956	42	1	y.	y.	NOUN
iajs-1956	43	1	so	so	ADV
iajs-1956	43	2	there	there	PRON
iajs-1956	43	3	exist	exist	VERB
iajs-1956	43	4	a	a	DET
iajs-1956	43	5	𝜃-totally	𝜃-totally	ADJ
iajs-1956	43	6	disconnection	disconnection	NOUN
iajs-1956	43	7	to	to	ADP
iajs-1956	43	8	x	x	SYM
iajs-1956	43	9	(	(	PUNCT
iajs-1956	43	10	i	i	PRON
iajs-1956	43	11	mean	mean	VERB
iajs-1956	43	12	there	there	PRON
iajs-1956	43	13	exist	exist	VERB
iajs-1956	43	14	g	g	NOUN
iajs-1956	43	15	and	and	CCONJ
iajs-1956	43	16	h	h	NOUN
iajs-1956	43	17	which	which	PRON
iajs-1956	43	18	are	be	AUX
iajs-1956	43	19	𝜃-open	𝜃-open	NOUN
iajs-1956	43	20	sets	set	NOUN
iajs-1956	43	21	and	and	CCONJ
iajs-1956	43	22	g	g	NOUN
iajs-1956	43	23	,	,	PUNCT
iajs-1956	43	24	h	h	NOUN
iajs-1956	43	25	∅	∅	NOUN
iajs-1956	43	26	and	and	CCONJ
iajs-1956	43	27	g∪h	g∪h	NOUN
iajs-1956	43	28	=	=	NOUN
iajs-1956	43	29	x	x	NOUN
iajs-1956	43	30	,	,	PUNCT
iajs-1956	43	31	g∩h=∅	g∩h=∅	NOUN
iajs-1956	43	32	with	with	ADP
iajs-1956	43	33	x∈g	x∈g	PROPN
iajs-1956	43	34	,	,	PUNCT
iajs-1956	43	35	y∈h	y∈h	NUM
iajs-1956	43	36	)	)	PUNCT
iajs-1956	43	37	.	.	PUNCT
iajs-1956	44	1	but	but	CCONJ
iajs-1956	44	2	every	every	DET
iajs-1956	44	3	𝜃-open	𝜃-open	NOUN
iajs-1956	44	4	set	set	VERB
iajs-1956	44	5	is	be	AUX
iajs-1956	44	6	open	open	ADJ
iajs-1956	44	7	set	set	ADJ
iajs-1956	44	8	sox	sox	PROPN
iajs-1956	44	9	is	be	AUX
iajs-1956	44	10	totally	totally	ADV
iajs-1956	44	11	disconnected	disconnected	ADJ
iajs-1956	44	12	space	space	NOUN
iajs-1956	44	13	.	.	PUNCT
iajs-1956	45	1	remark	remark	NOUN
iajs-1956	45	2	(	(	PUNCT
iajs-1956	45	3	8)	8)	NUM
iajs-1956	45	4	:	:	PUNCT
iajs-1956	45	5	the	the	DET
iajs-1956	45	6	converse	converse	NOUN
iajs-1956	45	7	of	of	ADP
iajs-1956	45	8	above	above	ADJ
iajs-1956	45	9	proposition	proposition	NOUN
iajs-1956	45	10	is	be	AUX
iajs-1956	45	11	not	not	PART
iajs-1956	45	12	true	true	ADJ
iajs-1956	45	13	in	in	ADP
iajs-1956	45	14	general	general	ADJ
iajs-1956	45	15	but	but	CCONJ
iajs-1956	45	16	in	in	ADP
iajs-1956	45	17	discrete	discrete	ADJ
iajs-1956	45	18	space	space	NOUN
iajs-1956	45	19	it	it	PRON
iajs-1956	45	20	is	be	AUX
iajs-1956	45	21	availed	avail	VERB
iajs-1956	45	22	.	.	PUNCT
iajs-1956	46	1	definition	definition	NOUN
iajs-1956	46	2	(	(	PUNCT
iajs-1956	46	3	9	9	NUM
iajs-1956	46	4	):	):	PUNCT
iajs-1956	46	5	a	a	DET
iajs-1956	46	6	surjective	surjective	ADJ
iajs-1956	46	7	mapping	mapping	NOUN
iajs-1956	46	8	f	f	X
iajs-1956	46	9	:	:	PUNCT
iajs-1956	46	10	x→y	x→y	NUM
iajs-1956	46	11	is	be	AUX
iajs-1956	46	12	said	say	VERB
iajs-1956	46	13	to	to	PART
iajs-1956	46	14	be	be	AUX
iajs-1956	46	15	𝜃-light	𝜃-light	VERB
iajs-1956	46	16	mapping	mapping	NOUN
iajs-1956	46	17	if	if	SCONJ
iajs-1956	46	18	for	for	ADP
iajs-1956	46	19	every	every	DET
iajs-1956	46	20	y∈y	y∈y	NOUN
iajs-1956	46	21	,	,	PUNCT
iajs-1956	46	22	f-1(y	f-1(y	PROPN
iajs-1956	46	23	)	)	PUNCT
iajs-1956	46	24	is	be	AUX
iajs-1956	46	25	𝜃-totally	𝜃-totally	ADV
iajs-1956	46	26	disconnected	disconnect	VERB
iajs-1956	46	27	set	set	NOUN
iajs-1956	46	28	.	.	PUNCT
iajs-1956	47	1	example(10	example(10	NOUN
iajs-1956	47	2	):	):	PUNCT
iajs-1956	47	3	let(q	let(q	PROPN
iajs-1956	47	4	,	,	PUNCT
iajs-1956	47	5	ʈd	ʈd	PROPN
iajs-1956	47	6	)	)	PUNCT
iajs-1956	47	7	to	to	ADP
iajs-1956	47	8	topological	topological	ADJ
iajs-1956	47	9	space	space	NOUN
iajs-1956	47	10	such	such	ADJ
iajs-1956	47	11	that	that	SCONJ
iajs-1956	47	12	ʈd	ʈd	PROPN
iajs-1956	47	13	is	be	AUX
iajs-1956	47	14	the	the	DET
iajs-1956	47	15	discrete	discrete	ADJ
iajs-1956	47	16	topology	topology	NOUN
iajs-1956	47	17	define	define	VERB
iajs-1956	47	18	to	to	ADP
iajs-1956	47	19	the	the	DET
iajs-1956	47	20	rational	rational	ADJ
iajs-1956	47	21	number	number	NOUN
iajs-1956	47	22	q	q	PUNCT
iajs-1956	47	23	and	and	CCONJ
iajs-1956	47	24	let	let	VERB
iajs-1956	47	25	(	(	PUNCT
iajs-1956	47	26	q	q	ADJ
iajs-1956	47	27	,	,	PUNCT
iajs-1956	47	28	ʈind	ʈind	ADJ
iajs-1956	47	29	)	)	PUNCT
iajs-1956	47	30	is	be	AUX
iajs-1956	47	31	the	the	DET
iajs-1956	47	32	indiscrete	indiscrete	ADJ
iajs-1956	47	33	topology	topology	NOUN
iajs-1956	47	34	such	such	ADJ
iajs-1956	47	35	that	that	DET
iajs-1956	47	36	k∈r.let	k∈r.let	PROPN
iajs-1956	47	37	f:(q	f:(q	PROPN
iajs-1956	47	38	,	,	PUNCT
iajs-1956	47	39	ʈd)→(q	ʈd)→(q	PROPN
iajs-1956	47	40	,	,	PUNCT
iajs-1956	47	41	ʈind	ʈind	NOUN
iajs-1956	47	42	)	)	PUNCT
iajs-1956	47	43	is	be	AUX
iajs-1956	47	44	a	a	DET
iajs-1956	47	45	mapping	mapping	NOUN
iajs-1956	47	46	define	define	VERB
iajs-1956	47	47	the	the	DET
iajs-1956	47	48	following	following	NOUN
iajs-1956	47	49	:	:	PUNCT
iajs-1956	47	50	f(x)=0.5	f(x)=0.5	X
iajs-1956	47	51	for	for	ADP
iajs-1956	47	52	each	each	DET
iajs-1956	47	53	x∈q	x∈q	NOUN
iajs-1956	47	54	note	note	NOUN
iajs-1956	47	55	that	that	SCONJ
iajs-1956	47	56	f-1(x)=q	f-1(x)=q	VERB
iajs-1956	47	57	if	if	SCONJ
iajs-1956	47	58	x	x	ADP
iajs-1956	47	59	=	=	NOUN
iajs-1956	47	60	0.5	0.5	NUM
iajs-1956	47	61	and	and	CCONJ
iajs-1956	47	62	f-1(x)=∅	f-1(x)=∅	NOUN
iajs-1956	47	63	when	when	SCONJ
iajs-1956	47	64	x	x	X
iajs-1956	47	65	0.5	0.5	NUM
iajs-1956	47	66	where	where	SCONJ
iajs-1956	47	67	∅	∅	NOUN
iajs-1956	47	68	and	and	CCONJ
iajs-1956	47	69	q	q	NOUN
iajs-1956	47	70	are	be	AUX
iajs-1956	47	71	𝜃-totally	𝜃-totally	ADV
iajs-1956	47	72	disconnected	disconnect	VERB
iajs-1956	47	73	.	.	PUNCT
iajs-1956	48	1	then	then	ADV
iajs-1956	48	2	f	f	PROPN
iajs-1956	48	3	is	be	AUX
iajs-1956	48	4	𝜃-light	𝜃-light	VERB
iajs-1956	48	5	mapping	mapping	NOUN
iajs-1956	48	6	.	.	PUNCT
iajs-1956	49	1	remark	remark	NOUN
iajs-1956	49	2	(	(	PUNCT
iajs-1956	49	3	11	11	NUM
iajs-1956	49	4	):	):	PUNCT
iajs-1956	49	5	every	every	DET
iajs-1956	49	6	𝜃-totally	𝜃-totally	ADV
iajs-1956	49	7	disconnected	disconnect	VERB
iajs-1956	49	8	is	be	AUX
iajs-1956	49	9	𝜃-hausdorff	𝜃-hausdorff	NOUN
iajs-1956	49	10	but	but	CCONJ
iajs-1956	49	11	the	the	DET
iajs-1956	49	12	converse	converse	NOUN
iajs-1956	49	13	may	may	AUX
iajs-1956	49	14	be	be	AUX
iajs-1956	49	15	not	not	PART
iajs-1956	49	16	true	true	ADJ
iajs-1956	49	17	in	in	ADP
iajs-1956	49	18	general	general	ADJ
iajs-1956	49	19	for	for	ADP
iajs-1956	49	20	example	example	NOUN
iajs-1956	49	21	:	:	PUNCT
iajs-1956	50	1	example	example	NOUN
iajs-1956	50	2	(	(	PUNCT
iajs-1956	50	3	12	12	NUM
iajs-1956	50	4	):	):	PUNCT
iajs-1956	50	5	(	(	PUNCT
iajs-1956	50	6	r	r	NOUN
iajs-1956	50	7	,	,	PUNCT
iajs-1956	50	8	ʈu	ʈu	NOUN
iajs-1956	50	9	)	)	PUNCT
iajs-1956	50	10	is	be	AUX
iajs-1956	50	11	𝜃-hausdorff	𝜃-hausdorff	ADJ
iajs-1956	50	12	but	but	CCONJ
iajs-1956	50	13	not	not	PART
iajs-1956	50	14	𝜃-totally	𝜃-totally	ADV
iajs-1956	50	15	disconnected	disconnect	VERB
iajs-1956	50	16	,	,	PUNCT
iajs-1956	50	17	where	where	SCONJ
iajs-1956	50	18	r	r	NOUN
iajs-1956	50	19	is	be	AUX
iajs-1956	50	20	the	the	DET
iajs-1956	50	21	set	set	NOUN
iajs-1956	50	22	of	of	ADP
iajs-1956	50	23	real	real	ADJ
iajs-1956	50	24	number	number	NOUN
iajs-1956	50	25	.to	.to	PUNCT
iajs-1956	50	26	show	show	VERB
iajs-1956	50	27	that	that	SCONJ
iajs-1956	50	28	(	(	PUNCT
iajs-1956	50	29	r	r	NOUN
iajs-1956	50	30	,	,	PUNCT
iajs-1956	50	31	ʈu	ʈu	NOUN
iajs-1956	50	32	)	)	PUNCT
iajs-1956	50	33	is	be	AUX
iajs-1956	50	34	not	not	PART
iajs-1956	50	35	𝜃-totally	𝜃-totally	ADV
iajs-1956	50	36	disconnected	disconnect	VERB
iajs-1956	50	37	.	.	PUNCT
iajs-1956	51	1	let	let	VERB
iajs-1956	51	2	x	x	PROPN
iajs-1956	51	3	&	&	CCONJ
iajs-1956	51	4	y	y	PROPN
iajs-1956	51	5	∈q⊆r	∈q⊆r	PUNCT
iajs-1956	51	6	such	such	ADJ
iajs-1956	51	7	that	that	SCONJ
iajs-1956	51	8	x	x	SYM
iajs-1956	51	9	y	y	NOUN
iajs-1956	51	10	,	,	PUNCT
iajs-1956	51	11	x	x	X
iajs-1956	51	12	y.	y.	NOUN
iajs-1956	51	13	then	then	ADV
iajs-1956	51	14	∃	∃	PROPN
iajs-1956	51	15	p∈qc	p∈qc	NOUN
iajs-1956	51	16	such	such	ADJ
iajs-1956	51	17	that	that	SCONJ
iajs-1956	51	18	x	x	PROPN
iajs-1956	51	19	p	p	X
iajs-1956	51	20	y	y	PROPN
iajs-1956	51	21	,	,	PUNCT
iajs-1956	51	22	(	(	PUNCT
iajs-1956	51	23	p	p	X
iajs-1956	51	24	,	,	PUNCT
iajs-1956	51	25	∞)&(-∞	∞)&(-∞	NOUN
iajs-1956	51	26	,	,	PUNCT
iajs-1956	51	27	p	p	NOUN
iajs-1956	51	28	)	)	PUNCT
iajs-1956	51	29	are	be	AUX
iajs-1956	51	30	𝜃-open	𝜃-open	NOUN
iajs-1956	51	31	sets	set	NOUN
iajs-1956	51	32	in	in	ADP
iajs-1956	51	33	r	r	NOUN
iajs-1956	51	34	since	since	SCONJ
iajs-1956	51	35	p-1∈(-∞	p-1∈(-∞	NOUN
iajs-1956	51	36	,	,	PUNCT
iajs-1956	51	37	p	p	NOUN
iajs-1956	51	38	)	)	PUNCT
iajs-1956	51	39	there	there	PRON
iajs-1956	51	40	exist	exist	VERB
iajs-1956	51	41	(	(	PUNCT
iajs-1956	51	42	-∞	-∞	PROPN
iajs-1956	51	43	,	,	PUNCT
iajs-1956	51	44	p-1	p-1	NOUN
iajs-1956	51	45	]	]	PUNCT
iajs-1956	51	46	,	,	PUNCT
iajs-1956	51	47	p-1	p-1	PROPN
iajs-1956	51	48	∈	∈	PROPN
iajs-1956	51	49	(	(	PUNCT
iajs-1956	51	50	-∞	-∞	PROPN
iajs-1956	51	51	,	,	PUNCT
iajs-1956	51	52	p-1	p-1	NOUN
iajs-1956	51	53	]	]	X
iajs-1956	51	54	⊆	⊆	NUM
iajs-1956	51	55	(	(	PUNCT
iajs-1956	51	56	-∞	-∞	NUM
iajs-1956	51	57	,	,	PUNCT
iajs-1956	51	58	p	p	NOUN
iajs-1956	51	59	)	)	PUNCT
iajs-1956	51	60	where	where	SCONJ
iajs-1956	51	61	∞	∞	PROPN
iajs-1956	51	62	,	,	PUNCT
iajs-1956	51	63	𝑝	𝑝	PROPN
iajs-1956	51	64	=(	=(	NOUN
iajs-1956	51	65	-∞	-∞	PROPN
iajs-1956	51	66	,	,	PUNCT
iajs-1956	51	67	p	p	X
iajs-1956	51	68	]	]	X
iajs-1956	51	69	the	the	DET
iajs-1956	51	70	set	set	NOUN
iajs-1956	51	71	(	(	PUNCT
iajs-1956	51	72	p	p	X
iajs-1956	51	73	,	,	PUNCT
iajs-1956	51	74	∞	∞	PROPN
iajs-1956	51	75	)	)	PUNCT
iajs-1956	51	76	is	be	AUX
iajs-1956	51	77	similar	similar	ADJ
iajs-1956	51	78	.	.	PUNCT
iajs-1956	52	1	(	(	PUNCT
iajs-1956	52	2	p	p	X
iajs-1956	52	3	,	,	PUNCT
iajs-1956	52	4	∞)∩(-∞	∞)∩(-∞	NOUN
iajs-1956	52	5	,	,	PUNCT
iajs-1956	52	6	p)=∅	p)=∅	PROPN
iajs-1956	52	7	,	,	PUNCT
iajs-1956	52	8	but	but	CCONJ
iajs-1956	52	9	(	(	PUNCT
iajs-1956	52	10	p,∞)∪(-∞	p,∞)∪(-∞	PROPN
iajs-1956	52	11	,	,	PUNCT
iajs-1956	52	12	p	p	NOUN
iajs-1956	52	13	)	)	PUNCT
iajs-1956	52	14	r	r	NOUN
iajs-1956	52	15	(	(	PUNCT
iajs-1956	52	16	r	r	NOUN
iajs-1956	52	17	has	have	AUX
iajs-1956	52	18	no	no	DET
iajs-1956	52	19	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	52	20	)	)	PUNCT
iajs-1956	52	21	  	  	SPACE
iajs-1956	52	22	182	182	NUM
iajs-1956	52	23	mathematics	mathematic	NOUN
iajs-1956	53	1	|	|	ADV
iajs-1956	53	2	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	53	3	2018	2018	NUM
iajs-1956	53	4	)	)	PUNCT
iajs-1956	53	5	عام	عام	ADP
iajs-1956	53	6	2العدد	2العدد	NUM
iajs-1956	53	7	(	(	PUNCT
iajs-1956	53	8	31لمجلد	31لمجلد	NUM
iajs-1956	53	9	ا	ا	NOUN
iajs-1956	53	10	مجلة	مجلة	NOUN
iajs-1956	53	11	إبن	إبن	VERB
iajs-1956	53	12	الهيثم	الهيثم	ADJ
iajs-1956	53	13	للعلوم	للعلوم	NOUN
iajs-1956	53	14	الصرفة	الصرفة	NOUN
iajs-1956	54	1	و	و	PRON
iajs-1956	54	2	التطبيقية	التطبيقية	ADJ
iajs-1956	54	3	ibn	ibn	PROPN
iajs-1956	54	4	al	al	PROPN
iajs-1956	54	5	-	-	PUNCT
iajs-1956	54	6	haitham	haitham	PROPN
iajs-1956	54	7	jour	jour	X
iajs-1956	54	8	.	.	PROPN
iajs-1956	54	9	for	for	ADP
iajs-1956	54	10	pure	pure	ADJ
iajs-1956	54	11	&	&	CCONJ
iajs-1956	54	12	appl	appl	PROPN
iajs-1956	54	13	.	.	PUNCT
iajs-1956	55	1	sci	sci	PROPN
iajs-1956	55	2	.	.	PUNCT
iajs-1956	55	3	vol	vol	NOUN
iajs-1956	55	4	.	.	PROPN
iajs-1956	56	1	31	31	NUM
iajs-1956	56	2	(	(	PUNCT
iajs-1956	56	3	2	2	NUM
iajs-1956	56	4	)	)	PUNCT
iajs-1956	56	5	2018	2018	NUM
iajs-1956	57	1	so	so	CCONJ
iajs-1956	57	2	(	(	PUNCT
iajs-1956	57	3	r	r	NOUN
iajs-1956	57	4	,	,	PUNCT
iajs-1956	57	5	ʈu	ʈu	NOUN
iajs-1956	57	6	)	)	PUNCT
iajs-1956	57	7	is	be	AUX
iajs-1956	57	8	not	not	PART
iajs-1956	57	9	𝜃-totally	𝜃-totally	ADV
iajs-1956	57	10	disconnected	disconnect	VERB
iajs-1956	57	11	.	.	PUNCT
iajs-1956	58	1	definition	definition	NOUN
iajs-1956	58	2	(	(	PUNCT
iajs-1956	58	3	13	13	NUM
iajs-1956	58	4	):	):	PUNCT
iajs-1956	58	5	a	a	DET
iajs-1956	58	6	surjective	surjective	ADJ
iajs-1956	58	7	mapping	mapping	NOUN
iajs-1956	58	8	f	f	X
iajs-1956	58	9	:	:	PUNCT
iajs-1956	58	10	x→y	x→y	NUM
iajs-1956	58	11	is	be	AUX
iajs-1956	58	12	said	say	VERB
iajs-1956	58	13	to	to	PART
iajs-1956	58	14	be	be	AUX
iajs-1956	58	15	𝜃-totally	𝜃-totally	ADV
iajs-1956	58	16	disconnected	disconnect	VERB
iajs-1956	58	17	if	if	SCONJ
iajs-1956	58	18	and	and	CCONJ
iajs-1956	58	19	only	only	ADV
iajs-1956	58	20	if	if	SCONJ
iajs-1956	58	21	for	for	ADP
iajs-1956	58	22	every	every	DET
iajs-1956	58	23	totally	totally	ADV
iajs-1956	58	24	disconnected	disconnected	ADJ
iajs-1956	58	25	set	set	NOUN
iajs-1956	58	26	u⊆x	u⊆x	PROPN
iajs-1956	58	27	then	then	ADV
iajs-1956	58	28	f(u	f(u	PROPN
iajs-1956	58	29	)	)	PUNCT
iajs-1956	58	30	is	be	AUX
iajs-1956	58	31	𝜃-totally	𝜃-totally	ADV
iajs-1956	58	32	disconnected	disconnect	VERB
iajs-1956	58	33	in	in	ADP
iajs-1956	58	34	y.	y.	PROPN
iajs-1956	58	35	definition	definition	NOUN
iajs-1956	58	36	(	(	PUNCT
iajs-1956	58	37	14	14	NUM
iajs-1956	58	38	):	):	PUNCT
iajs-1956	58	39	a	a	DET
iajs-1956	58	40	surjective	surjective	ADJ
iajs-1956	58	41	mapping	mapping	NOUN
iajs-1956	58	42	f	f	X
iajs-1956	58	43	:	:	PUNCT
iajs-1956	58	44	x→y	x→y	NUM
iajs-1956	58	45	is	be	AUX
iajs-1956	58	46	said	say	VERB
iajs-1956	58	47	to	to	PART
iajs-1956	58	48	be	be	AUX
iajs-1956	58	49	𝜃*-totally	𝜃*-totally	ADV
iajs-1956	58	50	disconnected	disconnect	VERB
iajs-1956	58	51	mapping	mapping	NOUN
iajs-1956	58	52	if	if	SCONJ
iajs-1956	58	53	and	and	CCONJ
iajs-1956	58	54	only	only	ADV
iajs-1956	58	55	if	if	SCONJ
iajs-1956	58	56	for	for	ADP
iajs-1956	58	57	every	every	DET
iajs-1956	58	58	𝜃totally	𝜃totally	ADV
iajs-1956	58	59	disconnected	disconnect	VERB
iajs-1956	58	60	set	set	VERB
iajs-1956	58	61	u⊆x	u⊆x	PROPN
iajs-1956	58	62	then	then	ADV
iajs-1956	58	63	f(u	f(u	PROPN
iajs-1956	58	64	)	)	PUNCT
iajs-1956	58	65	is	be	AUX
iajs-1956	58	66	totally	totally	ADV
iajs-1956	58	67	disconnected	disconnected	ADJ
iajs-1956	58	68	examples	example	NOUN
iajs-1956	58	69	(	(	PUNCT
iajs-1956	58	70	15):1	15):1	ADV
iajs-1956	58	71	-	-	PUNCT
iajs-1956	58	72	let	let	VERB
iajs-1956	58	73	f	f	X
iajs-1956	58	74	:	:	PUNCT
iajs-1956	58	75	(	(	PUNCT
iajs-1956	58	76	r	r	NOUN
iajs-1956	58	77	,	,	PUNCT
iajs-1956	58	78	ʈu)→(r	ʈu)→(r	PROPN
iajs-1956	58	79	,	,	PUNCT
iajs-1956	58	80	ʈd	ʈd	PROPN
iajs-1956	58	81	)	)	PUNCT
iajs-1956	58	82	such	such	ADJ
iajs-1956	58	83	that	that	SCONJ
iajs-1956	58	84	f(x)=x	f(x)=x	PROPN
iajs-1956	58	85	for	for	ADP
iajs-1956	58	86	each	each	DET
iajs-1956	58	87	x∈r	x∈r	PROPN
iajs-1956	58	88	.	.	PUNCT
iajs-1956	59	1	since	since	SCONJ
iajs-1956	59	2	(	(	PUNCT
iajs-1956	59	3	q	q	NOUN
iajs-1956	59	4	,	,	PUNCT
iajs-1956	59	5	ʈu	ʈu	NOUN
iajs-1956	59	6	)	)	PUNCT
iajs-1956	59	7	is	be	AUX
iajs-1956	59	8	totally	totally	ADV
iajs-1956	59	9	disconnected	disconnect	VERB
iajs-1956	59	10	set	set	VERB
iajs-1956	59	11	in	in	ADP
iajs-1956	59	12	(	(	PUNCT
iajs-1956	59	13	r	r	NOUN
iajs-1956	59	14	,	,	PUNCT
iajs-1956	59	15	ʈu	ʈu	NOUN
iajs-1956	59	16	)	)	PUNCT
iajs-1956	59	17	and	and	CCONJ
iajs-1956	59	18	f(q)=q⊆(r	f(q)=q⊆(r	NOUN
iajs-1956	59	19	,	,	PUNCT
iajs-1956	59	20	ʈd	ʈd	PROPN
iajs-1956	59	21	)	)	PUNCT
iajs-1956	59	22	for	for	ADP
iajs-1956	59	23	each	each	DET
iajs-1956	59	24	x	x	NOUN
iajs-1956	59	25	,	,	PUNCT
iajs-1956	59	26	y∈q	y∈q	VERB
iajs-1956	59	27	there	there	PRON
iajs-1956	59	28	exist	exist	VERB
iajs-1956	59	29	p∈qc	p∈qc	ADJ
iajs-1956	59	30	such	such	ADJ
iajs-1956	59	31	that	that	SCONJ
iajs-1956	59	32	x	x	X
iajs-1956	59	33	<	<	X
iajs-1956	59	34	p	p	X
iajs-1956	59	35	<	<	X
iajs-1956	59	36	y	y	PROPN
iajs-1956	59	37	g={x	g={x	PROPN
iajs-1956	59	38	∈q	∈q	NOUN
iajs-1956	59	39	:x	:x	PROPN
iajs-1956	59	40	<	<	X
iajs-1956	59	41	p	p	X
iajs-1956	59	42	}	}	PUNCT
iajs-1956	59	43	and	and	CCONJ
iajs-1956	59	44	h={x∈q	h={x∈q	NOUN
iajs-1956	59	45	:x	:x	PROPN
iajs-1956	59	46	>	>	X
iajs-1956	59	47	p	p	X
iajs-1956	59	48	}	}	PUNCT
iajs-1956	59	49	are	be	AUX
iajs-1956	59	50	two	two	NUM
iajs-1956	59	51	open	open	ADJ
iajs-1956	59	52	sets	set	NOUN
iajs-1956	59	53	in	in	ADP
iajs-1956	59	54	(	(	PUNCT
iajs-1956	59	55	q	q	NOUN
iajs-1956	59	56	,	,	PUNCT
iajs-1956	59	57	ʈu	ʈu	NOUN
iajs-1956	59	58	)	)	PUNCT
iajs-1956	59	59	such	such	ADJ
iajs-1956	59	60	that	that	DET
iajs-1956	59	61	g∪h	g∪h	NOUN
iajs-1956	60	1	=	=	SYM
iajs-1956	60	2	q	q	NOUN
iajs-1956	60	3	,	,	PUNCT
iajs-1956	60	4	g∩h=∅	g∩h=∅	PROPN
iajs-1956	60	5	now	now	ADV
iajs-1956	60	6	to	to	PART
iajs-1956	60	7	prove	prove	VERB
iajs-1956	60	8	(	(	PUNCT
iajs-1956	60	9	q	q	NOUN
iajs-1956	60	10	,	,	PUNCT
iajs-1956	60	11	ʈd	ʈd	PROPN
iajs-1956	60	12	)	)	PUNCT
iajs-1956	60	13	is	be	AUX
iajs-1956	60	14	𝜃-totally	𝜃-totally	ADV
iajs-1956	60	15	disconnected	disconnect	VERB
iajs-1956	60	16	in	in	ADP
iajs-1956	60	17	(	(	PUNCT
iajs-1956	60	18	r	r	NOUN
iajs-1956	60	19	,	,	PUNCT
iajs-1956	60	20	ʈd	ʈd	PROPN
iajs-1956	60	21	)	)	PUNCT
iajs-1956	61	1	where	where	SCONJ
iajs-1956	61	2	f(q)=q	f(q)=q	PROPN
iajs-1956	61	3	.	.	PUNCT
iajs-1956	61	4	g={x∈q	g={x∈q	PROPN
iajs-1956	61	5	:	:	PUNCT
iajs-1956	61	6	x≤0	x≤0	VERB
iajs-1956	61	7	}	}	PUNCT
iajs-1956	61	8	is	be	AUX
iajs-1956	61	9	𝜃-open	𝜃-open	NOUN
iajs-1956	61	10	set	set	VERB
iajs-1956	61	11	in	in	ADP
iajs-1956	61	12	(	(	PUNCT
iajs-1956	61	13	q	q	NOUN
iajs-1956	61	14	,	,	PUNCT
iajs-1956	61	15	ʈd	ʈd	PROPN
iajs-1956	61	16	)	)	PUNCT
iajs-1956	62	1	h={x∈q	h={x∈q	NOUN
iajs-1956	62	2	:	:	PUNCT
iajs-1956	62	3	x>0	x>0	NOUN
iajs-1956	62	4	}	}	PUNCT
iajs-1956	62	5	is	be	AUX
iajs-1956	62	6	𝜃-open	𝜃-open	NOUN
iajs-1956	62	7	set	set	VERB
iajs-1956	62	8	in	in	ADP
iajs-1956	62	9	(	(	PUNCT
iajs-1956	62	10	q	q	NOUN
iajs-1956	62	11	,	,	PUNCT
iajs-1956	62	12	ʈd	ʈd	NOUN
iajs-1956	62	13	)	)	PUNCT
iajs-1956	62	14	h∪g	h∪g	NOUN
iajs-1956	62	15	=	=	SYM
iajs-1956	62	16	q	q	NOUN
iajs-1956	62	17	,	,	PUNCT
iajs-1956	62	18	h∩g=∅	h∩g=∅	NOUN
iajs-1956	62	19	so	so	ADV
iajs-1956	62	20	(	(	PUNCT
iajs-1956	62	21	q	q	X
iajs-1956	62	22	,	,	PUNCT
iajs-1956	62	23	ʈd	ʈd	PROPN
iajs-1956	62	24	)	)	PUNCT
iajs-1956	62	25	is	be	AUX
iajs-1956	62	26	𝜃-totally	𝜃-totally	ADV
iajs-1956	62	27	disconnected	disconnect	VERB
iajs-1956	62	28	in	in	ADP
iajs-1956	62	29	(	(	PUNCT
iajs-1956	62	30	r	r	NOUN
iajs-1956	62	31	,	,	PUNCT
iajs-1956	62	32	ʈd	ʈd	PROPN
iajs-1956	62	33	)	)	PUNCT
iajs-1956	62	34	.	.	PUNCT
iajs-1956	63	1	2if	2if	NOUN
iajs-1956	63	2	we	we	PRON
iajs-1956	63	3	replace	replace	VERB
iajs-1956	63	4	q	q	PUNCT
iajs-1956	63	5	by	by	ADP
iajs-1956	63	6	(	(	PUNCT
iajs-1956	63	7	a	a	DET
iajs-1956	63	8	,	,	PUNCT
iajs-1956	63	9	b	b	NOUN
iajs-1956	63	10	]	]	X
iajs-1956	63	11	then	then	ADV
iajs-1956	63	12	the	the	DET
iajs-1956	63	13	sets	set	NOUN
iajs-1956	63	14	g={x	g={x	ADJ
iajs-1956	63	15	∈(a	∈(a	NOUN
iajs-1956	63	16	,	,	PUNCT
iajs-1956	63	17	b]:x	b]:x	NOUN
iajs-1956	63	18	p	p	X
iajs-1956	63	19	}	}	PUNCT
iajs-1956	63	20	and	and	CCONJ
iajs-1956	63	21	h={x∈(a	h={x∈(a	PROPN
iajs-1956	63	22	,	,	PUNCT
iajs-1956	63	23	b]:x	b]:x	PROPN
iajs-1956	63	24	>	>	X
iajs-1956	63	25	p	p	X
iajs-1956	63	26	}	}	PUNCT
iajs-1956	63	27	where	where	SCONJ
iajs-1956	63	28	p∈qc	p∈qc	ADV
iajs-1956	63	29	such	such	ADJ
iajs-1956	63	30	that	that	SCONJ
iajs-1956	63	31	a	a	DET
iajs-1956	63	32	<	<	X
iajs-1956	63	33	p	p	X
iajs-1956	63	34	b	b	NOUN
iajs-1956	63	35	then	then	ADV
iajs-1956	63	36	(	(	PUNCT
iajs-1956	63	37	(	(	PUNCT
iajs-1956	63	38	a	a	PRON
iajs-1956	63	39	,	,	PUNCT
iajs-1956	63	40	b	b	NOUN
iajs-1956	63	41	]	]	X
iajs-1956	63	42	,	,	PUNCT
iajs-1956	63	43	ʈu	ʈu	NOUN
iajs-1956	63	44	)	)	PUNCT
iajs-1956	63	45	is	be	AUX
iajs-1956	63	46	totally	totally	ADV
iajs-1956	63	47	disconnected	disconnect	VERB
iajs-1956	63	48	set	set	VERB
iajs-1956	63	49	in	in	ADP
iajs-1956	63	50	(	(	PUNCT
iajs-1956	63	51	r	r	NOUN
iajs-1956	63	52	,	,	PUNCT
iajs-1956	63	53	ʈu	ʈu	NOUN
iajs-1956	63	54	)	)	PUNCT
iajs-1956	63	55	definition	definition	NOUN
iajs-1956	63	56	(	(	PUNCT
iajs-1956	63	57	16	16	NUM
iajs-1956	63	58	):	):	PUNCT
iajs-1956	63	59	a	a	DET
iajs-1956	63	60	surjective	surjective	ADJ
iajs-1956	63	61	mapping	mapping	NOUN
iajs-1956	64	1	f	f	X
iajs-1956	64	2	:	:	PUNCT
iajs-1956	64	3	x→y	x→y	NUM
iajs-1956	64	4	is	be	AUX
iajs-1956	64	5	said	say	VERB
iajs-1956	64	6	to	to	PART
iajs-1956	64	7	be	be	AUX
iajs-1956	64	8	𝜃**-totally	𝜃**-totally	ADV
iajs-1956	64	9	disconnected	disconnect	VERB
iajs-1956	64	10	mapping	mapping	NOUN
iajs-1956	64	11	if	if	SCONJ
iajs-1956	64	12	and	and	CCONJ
iajs-1956	64	13	only	only	ADV
iajs-1956	64	14	if	if	SCONJ
iajs-1956	64	15	for	for	ADP
iajs-1956	64	16	every	every	DET
iajs-1956	64	17	𝜃totally	𝜃totally	ADV
iajs-1956	64	18	disconnected	disconnect	VERB
iajs-1956	64	19	set	set	VERB
iajs-1956	64	20	u⊆x	u⊆x	PROPN
iajs-1956	64	21	then	then	ADV
iajs-1956	64	22	f(u	f(u	PROPN
iajs-1956	64	23	)	)	PUNCT
iajs-1956	64	24	is	be	AUX
iajs-1956	64	25	𝜃-totally	𝜃-totally	ADV
iajs-1956	64	26	disconnected	disconnected	ADJ
iajs-1956	64	27	proposition	proposition	NOUN
iajs-1956	64	28	(	(	PUNCT
iajs-1956	64	29	17	17	NUM
iajs-1956	64	30	):	):	PUNCT
iajs-1956	64	31	1	1	NUM
iajs-1956	64	32	-	-	NUM
iajs-1956	64	33	every	every	DET
iajs-1956	64	34	𝜃-totally	𝜃-totally	ADV
iajs-1956	64	35	disconnected	disconnected	ADJ
iajs-1956	64	36	mapping	mapping	NOUN
iajs-1956	64	37	is	be	AUX
iajs-1956	64	38	totally	totally	ADV
iajs-1956	64	39	disconnected	disconnected	ADJ
iajs-1956	64	40	mapping	mapping	NOUN
iajs-1956	64	41	.	.	PUNCT
iajs-1956	65	1	2	2	NUM
iajs-1956	65	2	-	-	NUM
iajs-1956	65	3	every	every	DET
iajs-1956	65	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	65	5	disconnected	disconnected	ADJ
iajs-1956	65	6	mapping	mapping	NOUN
iajs-1956	65	7	is	be	AUX
iajs-1956	65	8	𝜃**-totally	𝜃**-totally	ADV
iajs-1956	65	9	disconnected	disconnect	VERB
iajs-1956	65	10	mapping	mapping	NOUN
iajs-1956	65	11	.	.	PUNCT
iajs-1956	66	1	3	3	NUM
iajs-1956	66	2	-	-	X
iajs-1956	66	3	every	every	DET
iajs-1956	66	4	𝜃**-totally	𝜃**-totally	ADV
iajs-1956	66	5	disconnected	disconnected	ADJ
iajs-1956	66	6	mapping	mapping	NOUN
iajs-1956	66	7	is	be	AUX
iajs-1956	66	8	𝜃*-totally	𝜃*-totally	ADV
iajs-1956	66	9	disconnected	disconnect	VERB
iajs-1956	66	10	mapping	mapping	NOUN
iajs-1956	66	11	.	.	PUNCT
iajs-1956	67	1	proof	proof	NOUN
iajs-1956	67	2	:	:	PUNCT
iajs-1956	67	3	1	1	NUM
iajs-1956	67	4	-	-	PUNCT
iajs-1956	67	5	let	let	VERB
iajs-1956	67	6	u	u	PRON
iajs-1956	67	7	be	be	AUX
iajs-1956	67	8	totally	totally	ADV
iajs-1956	67	9	disconnected	disconnect	VERB
iajs-1956	67	10	set	set	VERB
iajs-1956	67	11	in	in	ADP
iajs-1956	67	12	x	x	NOUN
iajs-1956	67	13	,	,	PUNCT
iajs-1956	67	14	but	but	CCONJ
iajs-1956	67	15	f	f	PROPN
iajs-1956	67	16	is	be	AUX
iajs-1956	67	17	𝜃-totally	𝜃-totally	ADV
iajs-1956	67	18	disconnected	disconnect	VERB
iajs-1956	67	19	mapping	mapping	NOUN
iajs-1956	67	20	then	then	ADV
iajs-1956	67	21	f(u	f(u	PROPN
iajs-1956	67	22	)	)	PUNCT
iajs-1956	67	23	is	be	AUX
iajs-1956	67	24	𝜃-totally	𝜃-totally	ADV
iajs-1956	67	25	disconnection	disconnection	NOUN
iajs-1956	67	26	set	set	VERB
iajs-1956	67	27	in	in	ADP
iajs-1956	67	28	y	y	PROPN
iajs-1956	67	29	,	,	PUNCT
iajs-1956	67	30	but	but	CCONJ
iajs-1956	67	31	every	every	DET
iajs-1956	67	32	𝜃-totally	𝜃-totally	ADV
iajs-1956	67	33	disconnected	disconnect	VERB
iajs-1956	67	34	set	set	NOUN
iajs-1956	67	35	is	be	AUX
iajs-1956	67	36	totally	totally	ADV
iajs-1956	67	37	disconnected	disconnected	ADJ
iajs-1956	67	38	so	so	SCONJ
iajs-1956	67	39	f	f	PROPN
iajs-1956	67	40	(	(	PUNCT
iajs-1956	67	41	u	u	NOUN
iajs-1956	67	42	)	)	PUNCT
iajs-1956	67	43	is	be	AUX
iajs-1956	67	44	totally	totally	ADV
iajs-1956	67	45	disconnected	disconnected	ADJ
iajs-1956	67	46	in	in	ADP
iajs-1956	67	47	y	y	PROPN
iajs-1956	67	48	,	,	PUNCT
iajs-1956	67	49	then	then	ADV
iajs-1956	67	50	f	f	PROPN
iajs-1956	67	51	is	be	AUX
iajs-1956	67	52	totally	totally	ADV
iajs-1956	67	53	disconnected	disconnected	ADJ
iajs-1956	67	54	mapping	mapping	NOUN
iajs-1956	67	55	.	.	PUNCT
iajs-1956	68	1	the	the	DET
iajs-1956	68	2	proof	proof	NOUN
iajs-1956	68	3	of	of	ADP
iajs-1956	68	4	2	2	NUM
iajs-1956	68	5	and	and	CCONJ
iajs-1956	68	6	3	3	NUM
iajs-1956	68	7	are	be	AUX
iajs-1956	68	8	similar	similar	ADJ
iajs-1956	68	9	.	.	PUNCT
iajs-1956	68	10	  	  	SPACE
iajs-1956	69	1	183	183	NUM
iajs-1956	69	2	mathematics	mathematic	NOUN
iajs-1956	69	3	|	|	ADV
iajs-1956	69	4	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	69	5	2018	2018	NUM
iajs-1956	69	6	)	)	PUNCT
iajs-1956	69	7	عام	عام	ADP
iajs-1956	69	8	2العدد	2العدد	NUM
iajs-1956	69	9	(	(	PUNCT
iajs-1956	69	10	31لمجلد	31لمجلد	NUM
iajs-1956	69	11	ا	ا	NOUN
iajs-1956	69	12	مجلة	مجلة	NOUN
iajs-1956	69	13	إبن	إبن	VERB
iajs-1956	69	14	الهيثم	الهيثم	ADJ
iajs-1956	69	15	للعلوم	للعلوم	NOUN
iajs-1956	69	16	الصرفة	الصرفة	NOUN
iajs-1956	70	1	و	و	PRON
iajs-1956	70	2	التطبيقية	التطبيقية	ADJ
iajs-1956	70	3	ibn	ibn	PROPN
iajs-1956	70	4	al	al	PROPN
iajs-1956	70	5	-	-	PUNCT
iajs-1956	70	6	haitham	haitham	PROPN
iajs-1956	70	7	jour	jour	X
iajs-1956	70	8	.	.	PROPN
iajs-1956	70	9	for	for	ADP
iajs-1956	70	10	pure	pure	ADJ
iajs-1956	70	11	&	&	CCONJ
iajs-1956	70	12	appl	appl	PROPN
iajs-1956	70	13	.	.	PUNCT
iajs-1956	71	1	sci	sci	PROPN
iajs-1956	71	2	.	.	PUNCT
iajs-1956	71	3	vol	vol	NOUN
iajs-1956	71	4	.	.	PROPN
iajs-1956	72	1	31	31	NUM
iajs-1956	72	2	(	(	PUNCT
iajs-1956	72	3	2	2	NUM
iajs-1956	72	4	)	)	SYM
iajs-1956	72	5	2018	2018	NUM
iajs-1956	72	6	proposition	proposition	NOUN
iajs-1956	72	7	(	(	PUNCT
iajs-1956	72	8	18	18	NUM
iajs-1956	72	9	):	):	PUNCT
iajs-1956	72	10	let	let	VERB
iajs-1956	72	11	f	f	X
iajs-1956	72	12	:	:	PUNCT
iajs-1956	72	13	x→y	x→y	NUM
iajs-1956	72	14	be	be	AUX
iajs-1956	72	15	bijective	bijective	ADJ
iajs-1956	72	16	𝜃-open	𝜃-open	NOUN
iajs-1956	72	17	mapping	mapping	NOUN
iajs-1956	72	18	.	.	PUNCT
iajs-1956	73	1	then	then	ADV
iajs-1956	73	2	y	y	PROPN
iajs-1956	73	3	is	be	AUX
iajs-1956	73	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	73	5	disconnected	disconnect	VERB
iajs-1956	73	6	set	set	VERB
iajs-1956	73	7	whenever	whenever	SCONJ
iajs-1956	73	8	x	x	PRON
iajs-1956	73	9	is	be	AUX
iajs-1956	73	10	totally	totally	ADV
iajs-1956	73	11	disconnected	disconnected	ADJ
iajs-1956	73	12	proof	proof	NOUN
iajs-1956	73	13	:	:	PUNCT
iajs-1956	73	14	let	let	VERB
iajs-1956	73	15	y1	y1	INTJ
iajs-1956	73	16	,	,	PUNCT
iajs-1956	73	17	y2	y2	PROPN
iajs-1956	73	18	∈y	∈y	NOUN
iajs-1956	73	19	with	with	ADP
iajs-1956	73	20	y1	y1	ADJ
iajs-1956	73	21	y2	y2	PROPN
iajs-1956	73	22	since	since	SCONJ
iajs-1956	73	23	f	f	PROPN
iajs-1956	73	24	is	be	AUX
iajs-1956	73	25	bijective	bijective	ADJ
iajs-1956	73	26	,	,	PUNCT
iajs-1956	73	27	then	then	ADV
iajs-1956	73	28	there	there	PRON
iajs-1956	73	29	exist	exist	VERB
iajs-1956	73	30	two	two	NUM
iajs-1956	73	31	distinct	distinct	ADJ
iajs-1956	73	32	points	point	NOUN
iajs-1956	73	33	x1	x1	PROPN
iajs-1956	73	34	,	,	PUNCT
iajs-1956	73	35	x2	x2	PROPN
iajs-1956	73	36	∈	∈	PROPN
iajs-1956	73	37	x	x	PUNCT
iajs-1956	73	38	such	such	ADJ
iajs-1956	73	39	that	that	DET
iajs-1956	73	40	f(x1)=y1	f(x1)=y1	NOUN
iajs-1956	73	41	,	,	PUNCT
iajs-1956	73	42	f(x2)=y2	f(x2)=y2	PROPN
iajs-1956	73	43	.	.	PUNCT
iajs-1956	74	1	but	but	CCONJ
iajs-1956	74	2	x	x	X
iajs-1956	74	3	is	be	AUX
iajs-1956	74	4	totally	totally	ADV
iajs-1956	74	5	disconnected	disconnected	ADJ
iajs-1956	74	6	space	space	NOUN
iajs-1956	74	7	,	,	PUNCT
iajs-1956	74	8	then	then	ADV
iajs-1956	74	9	there	there	PRON
iajs-1956	74	10	exist	exist	VERB
iajs-1956	74	11	disconnection	disconnection	NOUN
iajs-1956	74	12	g∪h	g∪h	NOUN
iajs-1956	74	13	to	to	ADP
iajs-1956	74	14	x	x	SYM
iajs-1956	74	15	such	such	ADJ
iajs-1956	74	16	that	that	SCONJ
iajs-1956	74	17	x1∈g	x1∈g	PROPN
iajs-1956	74	18	&	&	CCONJ
iajs-1956	74	19	x2∈h	x2∈h	PROPN
iajs-1956	74	20	.	.	PUNCT
iajs-1956	75	1	also	also	ADV
iajs-1956	75	2	f	f	PROPN
iajs-1956	75	3	is	be	AUX
iajs-1956	75	4	𝜃open	𝜃open	ADJ
iajs-1956	75	5	mapping	mapping	NOUN
iajs-1956	75	6	and	and	CCONJ
iajs-1956	75	7	g	g	NOUN
iajs-1956	75	8	,	,	PUNCT
iajs-1956	75	9	h	h	NOUN
iajs-1956	75	10	are	be	AUX
iajs-1956	75	11	open	open	ADJ
iajs-1956	75	12	sets	set	NOUN
iajs-1956	75	13	in	in	ADP
iajs-1956	75	14	x.	x.	NOUN
iajs-1956	75	15	so	so	SCONJ
iajs-1956	75	16	f(g	f(g	PROPN
iajs-1956	75	17	)	)	PUNCT
iajs-1956	75	18	and	and	CCONJ
iajs-1956	75	19	f(h	f(h	PROPN
iajs-1956	75	20	)	)	PUNCT
iajs-1956	75	21	are	be	AUX
iajs-1956	75	22	𝜃open	𝜃open	NOUN
iajs-1956	75	23	sets	set	NOUN
iajs-1956	75	24	in	in	ADP
iajs-1956	75	25	y.	y.	PROPN
iajs-1956	75	26	but	but	CCONJ
iajs-1956	75	27	f(g)∪f(h)=f(g∪h)=f(x)=y	f(g)∪f(h)=f(g∪h)=f(x)=y	NOUN
iajs-1956	75	28	and	and	CCONJ
iajs-1956	75	29	f	f	PROPN
iajs-1956	75	30	is	be	AUX
iajs-1956	75	31	one	one	NUM
iajs-1956	75	32	to	to	ADP
iajs-1956	75	33	one	one	NUM
iajs-1956	75	34	mapping	mapping	NOUN
iajs-1956	75	35	.	.	PUNCT
iajs-1956	76	1	so	so	ADV
iajs-1956	76	2	f(g)∩f(h)=f(g∩h)=f(∅)=∅	f(g)∩f(h)=f(g∩h)=f(∅)=∅	PROPN
iajs-1956	76	3	such	such	ADJ
iajs-1956	76	4	that	that	SCONJ
iajs-1956	76	5	y1∈f(g	y1∈f(g	PROPN
iajs-1956	76	6	)	)	PUNCT
iajs-1956	76	7	,	,	PUNCT
iajs-1956	76	8	y2∈f(h	y2∈f(h	NOUN
iajs-1956	76	9	)	)	PUNCT
iajs-1956	76	10	so	so	ADV
iajs-1956	76	11	f(g)∪f(h	f(g)∪f(h	NUM
iajs-1956	76	12	)	)	PUNCT
iajs-1956	76	13	is	be	AUX
iajs-1956	76	14	𝜃disconnection	𝜃disconnection	NOUN
iajs-1956	76	15	to	to	ADP
iajs-1956	76	16	y.	y.	PROPN
iajs-1956	76	17	therefor	therefor	PROPN
iajs-1956	76	18	y	y	PROPN
iajs-1956	76	19	is	be	AUX
iajs-1956	76	20	𝜃-totally	𝜃-totally	ADV
iajs-1956	76	21	disconnected	disconnect	VERB
iajs-1956	76	22	set	set	NOUN
iajs-1956	76	23	.	.	PUNCT
iajs-1956	77	1	corollary	corollary	ADJ
iajs-1956	77	2	(	(	PUNCT
iajs-1956	77	3	19	19	NUM
iajs-1956	77	4	):	):	PUNCT
iajs-1956	77	5	a	a	DET
iajs-1956	77	6	property	property	NOUN
iajs-1956	77	7	of	of	ADP
iajs-1956	77	8	space	space	NOUN
iajs-1956	77	9	being	be	AUX
iajs-1956	77	10	𝜃-totally	𝜃-totally	ADV
iajs-1956	77	11	disconnected	disconnect	VERB
iajs-1956	77	12	a	a	DET
iajs-1956	77	13	topological	topological	ADJ
iajs-1956	77	14	property	property	NOUN
iajs-1956	77	15	.	.	PUNCT
iajs-1956	78	1	proposition	proposition	NOUN
iajs-1956	78	2	(	(	PUNCT
iajs-1956	78	3	20	20	NUM
iajs-1956	78	4	):	):	PUNCT
iajs-1956	78	5	let	let	VERB
iajs-1956	78	6	x	x	PRON
iajs-1956	78	7	and	and	CCONJ
iajs-1956	78	8	y	y	PROPN
iajs-1956	78	9	be	be	AUX
iajs-1956	78	10	topological	topological	ADJ
iajs-1956	78	11	space	space	NOUN
iajs-1956	78	12	,	,	PUNCT
iajs-1956	78	13	let	let	VERB
iajs-1956	78	14	f	f	X
iajs-1956	78	15	:	:	PUNCT
iajs-1956	78	16	x→y	x→y	NUM
iajs-1956	78	17	be	be	AUX
iajs-1956	78	18	homeomorphism	homeomorphism	X
iajs-1956	78	19	.	.	PUNCT
iajs-1956	79	1	so	so	ADV
iajs-1956	79	2	if	if	SCONJ
iajs-1956	79	3	x	x	PRON
iajs-1956	79	4	is	be	AUX
iajs-1956	79	5	𝜃totally	𝜃totally	ADV
iajs-1956	79	6	disconnected	disconnect	VERB
iajs-1956	79	7	then	then	ADV
iajs-1956	79	8	y	y	PROPN
iajs-1956	79	9	is	be	AUX
iajs-1956	79	10	totally	totally	ADV
iajs-1956	79	11	disconnected	disconnected	ADJ
iajs-1956	79	12	set	set	NOUN
iajs-1956	79	13	.	.	PUNCT
iajs-1956	80	1	proof	proof	NOUN
iajs-1956	80	2	:	:	PUNCT
iajs-1956	80	3	let	let	VERB
iajs-1956	80	4	y1	y1	INTJ
iajs-1956	80	5	,	,	PUNCT
iajs-1956	80	6	y2	y2	PROPN
iajs-1956	80	7	∈y	∈y	NOUN
iajs-1956	80	8	with	with	ADP
iajs-1956	80	9	y1	y1	ADJ
iajs-1956	80	10	y2.since	y2.since	NOUN
iajs-1956	80	11	f	f	PROPN
iajs-1956	80	12	is	be	AUX
iajs-1956	80	13	bijective	bijective	ADJ
iajs-1956	80	14	,	,	PUNCT
iajs-1956	80	15	then	then	ADV
iajs-1956	80	16	there	there	PRON
iajs-1956	80	17	exist	exist	VERB
iajs-1956	80	18	two	two	NUM
iajs-1956	80	19	distinct	distinct	ADJ
iajs-1956	80	20	points	point	NOUN
iajs-1956	80	21	x1	x1	PROPN
iajs-1956	80	22	,	,	PUNCT
iajs-1956	80	23	x2	x2	PROPN
iajs-1956	80	24	∈xsuch	∈xsuch	PROPN
iajs-1956	80	25	that	that	DET
iajs-1956	80	26	f(x1)=y1	f(x1)=y1	NOUN
iajs-1956	80	27	,	,	PUNCT
iajs-1956	80	28	f(x2)=y2	f(x2)=y2	PROPN
iajs-1956	80	29	.	.	PUNCT
iajs-1956	81	1	but	but	CCONJ
iajs-1956	81	2	x	x	X
iajs-1956	81	3	is	be	AUX
iajs-1956	81	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	81	5	disconnected	disconnect	VERB
iajs-1956	81	6	set	set	NOUN
iajs-1956	81	7	,	,	PUNCT
iajs-1956	81	8	then	then	ADV
iajs-1956	81	9	there	there	PRON
iajs-1956	81	10	exist	exist	VERB
iajs-1956	81	11	𝜃disconnection	𝜃disconnection	NOUN
iajs-1956	81	12	g∪h	g∪h	NOUN
iajs-1956	81	13	to	to	ADP
iajs-1956	81	14	x	x	SYM
iajs-1956	81	15	such	such	ADJ
iajs-1956	81	16	that	that	SCONJ
iajs-1956	81	17	x1∈g	x1∈g	PROPN
iajs-1956	81	18	&	&	CCONJ
iajs-1956	81	19	x2∈h	x2∈h	PROPN
iajs-1956	81	20	.	.	PUNCT
iajs-1956	82	1	also	also	ADV
iajs-1956	82	2	f	f	PROPN
iajs-1956	82	3	is	be	AUX
iajs-1956	82	4	homeomorphism	homeomorphism	PROPN
iajs-1956	82	5	,	,	PUNCT
iajs-1956	82	6	so	so	CCONJ
iajs-1956	82	7	f	f	PROPN
iajs-1956	82	8	is	be	AUX
iajs-1956	82	9	open	open	ADJ
iajs-1956	82	10	mapping	mapping	NOUN
iajs-1956	82	11	.	.	PUNCT
iajs-1956	83	1	since	since	SCONJ
iajs-1956	83	2	g	g	PROPN
iajs-1956	83	3	and	and	CCONJ
iajs-1956	83	4	h	h	NOUN
iajs-1956	83	5	are	be	AUX
iajs-1956	83	6	𝜃-open	𝜃-open	NOUN
iajs-1956	83	7	sets	set	NOUN
iajs-1956	83	8	in	in	ADP
iajs-1956	83	9	x.	x.	NOUN
iajs-1956	83	10	so	so	SCONJ
iajs-1956	83	11	f(g	f(g	PROPN
iajs-1956	83	12	)	)	PUNCT
iajs-1956	83	13	and	and	CCONJ
iajs-1956	83	14	f(h	f(h	PROPN
iajs-1956	83	15	)	)	PUNCT
iajs-1956	83	16	are	be	AUX
iajs-1956	83	17	open	open	ADJ
iajs-1956	83	18	sets	set	NOUN
iajs-1956	83	19	in	in	ADP
iajs-1956	83	20	y.	y.	PROPN
iajs-1956	83	21	but	but	CCONJ
iajs-1956	83	22	f(g)∪f(h)=f(g∪h)=f(x)=y	f(g)∪f(h)=f(g∪h)=f(x)=y	NOUN
iajs-1956	83	23	.	.	PUNCT
iajs-1956	84	1	since	since	SCONJ
iajs-1956	84	2	f	f	PROPN
iajs-1956	84	3	is	be	AUX
iajs-1956	84	4	bijective	bijective	ADJ
iajs-1956	84	5	mapping	mapping	NOUN
iajs-1956	84	6	.	.	PUNCT
iajs-1956	85	1	so	so	ADV
iajs-1956	85	2	f(g)∩f(h)=f(g∩h)=f(∅)=∅	f(g)∩f(h)=f(g∩h)=f(∅)=∅	PROPN
iajs-1956	85	3	such	such	ADJ
iajs-1956	85	4	that	that	SCONJ
iajs-1956	85	5	y1∈f(g	y1∈f(g	PROPN
iajs-1956	85	6	)	)	PUNCT
iajs-1956	85	7	,	,	PUNCT
iajs-1956	85	8	y2∈f(h	y2∈f(h	PROPN
iajs-1956	85	9	)	)	PUNCT
iajs-1956	85	10	which	which	PRON
iajs-1956	85	11	implies	imply	VERB
iajs-1956	85	12	f(g)∪f(h	f(g)∪f(h	NUM
iajs-1956	85	13	)	)	PUNCT
iajs-1956	85	14	is	be	AUX
iajs-1956	85	15	disconnection	disconnection	NOUN
iajs-1956	85	16	to	to	ADP
iajs-1956	85	17	y.	y.	PROPN
iajs-1956	85	18	therefor	therefor	PROPN
iajs-1956	85	19	y	y	PROPN
iajs-1956	85	20	is	be	AUX
iajs-1956	85	21	totally	totally	ADV
iajs-1956	85	22	disconnected	disconnected	ADJ
iajs-1956	85	23	set	set	NOUN
iajs-1956	85	24	.	.	PUNCT
iajs-1956	86	1	proposition	proposition	NOUN
iajs-1956	86	2	(	(	PUNCT
iajs-1956	86	3	21	21	NUM
iajs-1956	86	4	):	):	PUNCT
iajs-1956	86	5	let	let	VERB
iajs-1956	86	6	f	f	X
iajs-1956	86	7	:	:	PUNCT
iajs-1956	86	8	x→y	x→y	NUM
iajs-1956	86	9	be	be	AUX
iajs-1956	86	10	bijective	bijective	ADJ
iajs-1956	86	11	𝜃**-open	𝜃**-open	ADJ
iajs-1956	86	12	mapping	mapping	NOUN
iajs-1956	86	13	.	.	PUNCT
iajs-1956	87	1	then	then	ADV
iajs-1956	87	2	y	y	PROPN
iajs-1956	87	3	is	be	AUX
iajs-1956	87	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	87	5	disconnected	disconnect	VERB
iajs-1956	87	6	set	set	VERB
iajs-1956	87	7	whenever	whenever	SCONJ
iajs-1956	87	8	x	x	PRON
iajs-1956	87	9	is	be	AUX
iajs-1956	87	10	𝜃-totally	𝜃-totally	ADV
iajs-1956	87	11	disconnected	disconnected	ADJ
iajs-1956	87	12	proof	proof	NOUN
iajs-1956	87	13	:	:	PUNCT
iajs-1956	87	14	let	let	VERB
iajs-1956	87	15	y1	y1	INTJ
iajs-1956	87	16	,	,	PUNCT
iajs-1956	87	17	y2	y2	PROPN
iajs-1956	87	18	∈y	∈y	NOUN
iajs-1956	87	19	with	with	ADP
iajs-1956	87	20	y1	y1	ADJ
iajs-1956	87	21	y2.since	y2.since	NOUN
iajs-1956	87	22	f	f	PROPN
iajs-1956	87	23	is	be	AUX
iajs-1956	87	24	bijective	bijective	ADJ
iajs-1956	87	25	,	,	PUNCT
iajs-1956	87	26	then	then	ADV
iajs-1956	87	27	there	there	PRON
iajs-1956	87	28	exist	exist	VERB
iajs-1956	87	29	two	two	NUM
iajs-1956	87	30	distinct	distinct	ADJ
iajs-1956	87	31	points	point	NOUN
iajs-1956	87	32	x1	x1	PROPN
iajs-1956	87	33	,	,	PUNCT
iajs-1956	87	34	x2	x2	PROPN
iajs-1956	87	35	∈xsuch	∈xsuch	PROPN
iajs-1956	87	36	that	that	DET
iajs-1956	87	37	f(x1)=y1	f(x1)=y1	NOUN
iajs-1956	87	38	,	,	PUNCT
iajs-1956	87	39	f(x2)=y2	f(x2)=y2	PROPN
iajs-1956	87	40	.	.	PUNCT
iajs-1956	88	1	but	but	CCONJ
iajs-1956	88	2	x	x	X
iajs-1956	88	3	is	be	AUX
iajs-1956	88	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	88	5	disconnected	disconnect	VERB
iajs-1956	88	6	set	set	NOUN
iajs-1956	88	7	,	,	PUNCT
iajs-1956	88	8	then	then	ADV
iajs-1956	88	9	there	there	PRON
iajs-1956	88	10	exist	exist	VERB
iajs-1956	88	11	𝜃disconnection	𝜃disconnection	NOUN
iajs-1956	88	12	g∪h	g∪h	NOUN
iajs-1956	88	13	to	to	ADP
iajs-1956	88	14	x	x	SYM
iajs-1956	88	15	such	such	ADJ
iajs-1956	88	16	that	that	SCONJ
iajs-1956	88	17	x1∈g	x1∈g	PROPN
iajs-1956	88	18	&	&	CCONJ
iajs-1956	88	19	x2∈h	x2∈h	PROPN
iajs-1956	88	20	.	.	PUNCT
iajs-1956	89	1	also	also	ADV
iajs-1956	89	2	f	f	PROPN
iajs-1956	89	3	is	be	AUX
iajs-1956	89	4	𝜃homeomorphism	𝜃homeomorphism	NOUN
iajs-1956	89	5	,	,	PUNCT
iajs-1956	89	6	so	so	CCONJ
iajs-1956	89	7	f	f	PROPN
iajs-1956	89	8	is	be	AUX
iajs-1956	89	9	𝜃	𝜃	PRON
iajs-1956	89	10	open	open	ADJ
iajs-1956	89	11	mapping	mapping	NOUN
iajs-1956	89	12	.	.	PUNCT
iajs-1956	90	1	since	since	SCONJ
iajs-1956	90	2	g	g	PROPN
iajs-1956	90	3	and	and	CCONJ
iajs-1956	90	4	h	h	NOUN
iajs-1956	90	5	are	be	AUX
iajs-1956	90	6	𝜃open	𝜃open	ADJ
iajs-1956	90	7	sets	set	NOUN
iajs-1956	90	8	in	in	ADP
iajs-1956	90	9	x.	x.	NOUN
iajs-1956	90	10	so	so	SCONJ
iajs-1956	90	11	f(g	f(g	PROPN
iajs-1956	90	12	)	)	PUNCT
iajs-1956	90	13	and	and	CCONJ
iajs-1956	90	14	f(h	f(h	PROPN
iajs-1956	90	15	)	)	PUNCT
iajs-1956	90	16	are	be	AUX
iajs-1956	90	17	𝜃open	𝜃open	NOUN
iajs-1956	90	18	sets	set	NOUN
iajs-1956	90	19	in	in	ADP
iajs-1956	90	20	y.	y.	PROPN
iajs-1956	90	21	but	but	CCONJ
iajs-1956	90	22	f(g)∪f(h)=f(g∪h)=f(x)=y	f(g)∪f(h)=f(g∪h)=f(x)=y	NOUN
iajs-1956	90	23	.	.	PUNCT
iajs-1956	91	1	since	since	SCONJ
iajs-1956	91	2	f	f	PROPN
iajs-1956	91	3	is	be	AUX
iajs-1956	91	4	bijective	bijective	ADJ
iajs-1956	91	5	mapping	mapping	NOUN
iajs-1956	91	6	.	.	PUNCT
iajs-1956	92	1	so	so	ADV
iajs-1956	92	2	f(g)∩f(h)=f(g∩h)=f(∅)=∅	f(g)∩f(h)=f(g∩h)=f(∅)=∅	PROPN
iajs-1956	92	3	such	such	ADJ
iajs-1956	92	4	that	that	DET
iajs-1956	92	5	f(g)∪f(h	f(g)∪f(h	NOUN
iajs-1956	92	6	)	)	PUNCT
iajs-1956	92	7	is	be	AUX
iajs-1956	92	8	𝜃-disconnection	𝜃-disconnection	NOUN
iajs-1956	92	9	to	to	ADP
iajs-1956	92	10	y.	y.	PROPN
iajs-1956	92	11	therefore	therefore	ADV
iajs-1956	92	12	y	y	PROPN
iajs-1956	92	13	is	be	AUX
iajs-1956	92	14	also	also	ADV
iajs-1956	92	15	𝜃-totally	𝜃-totally	ADV
iajs-1956	92	16	disconnected	disconnect	VERB
iajs-1956	92	17	.	.	PUNCT
iajs-1956	93	1	corollary	corollary	ADJ
iajs-1956	93	2	(	(	PUNCT
iajs-1956	93	3	22	22	NUM
iajs-1956	93	4	):	):	PUNCT
iajs-1956	93	5	let	let	VERB
iajs-1956	93	6	x	x	PRON
iajs-1956	93	7	and	and	CCONJ
iajs-1956	93	8	y	y	PROPN
iajs-1956	93	9	be	be	AUX
iajs-1956	93	10	topological	topological	ADJ
iajs-1956	93	11	space	space	NOUN
iajs-1956	93	12	,	,	PUNCT
iajs-1956	93	13	let	let	VERB
iajs-1956	93	14	f	f	X
iajs-1956	93	15	:	:	PUNCT
iajs-1956	93	16	x→y	x→y	NUM
iajs-1956	93	17	be	be	AUX
iajs-1956	93	18	𝜃-homeomorphism	𝜃-homeomorphism	NOUN
iajs-1956	93	19	.	.	PUNCT
iajs-1956	94	1	so	so	ADV
iajs-1956	94	2	if	if	SCONJ
iajs-1956	94	3	x	x	PRON
iajs-1956	94	4	is	be	AUX
iajs-1956	94	5	𝜃totally	𝜃totally	ADV
iajs-1956	94	6	disconnected	disconnect	VERB
iajs-1956	94	7	then	then	ADV
iajs-1956	94	8	y	y	PROPN
iajs-1956	94	9	is	be	AUX
iajs-1956	94	10	𝜃-totally	𝜃-totally	ADV
iajs-1956	94	11	disconnected	disconnect	VERB
iajs-1956	94	12	set	set	VERB
iajs-1956	94	13	again	again	ADV
iajs-1956	94	14	.	.	PUNCT
iajs-1956	94	15	  	  	SPACE
iajs-1956	95	1	184	184	NUM
iajs-1956	95	2	mathematics	mathematic	NOUN
iajs-1956	95	3	|	|	ADV
iajs-1956	95	4	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	95	5	2018	2018	NUM
iajs-1956	95	6	)	)	PUNCT
iajs-1956	95	7	عام	عام	ADP
iajs-1956	95	8	2العدد	2العدد	NUM
iajs-1956	95	9	(	(	PUNCT
iajs-1956	95	10	31لمجلد	31لمجلد	NUM
iajs-1956	95	11	ا	ا	NOUN
iajs-1956	95	12	مجلة	مجلة	NOUN
iajs-1956	95	13	إبن	إبن	VERB
iajs-1956	95	14	الهيثم	الهيثم	ADJ
iajs-1956	95	15	للعلوم	للعلوم	NOUN
iajs-1956	95	16	الصرفة	الصرفة	NOUN
iajs-1956	96	1	و	و	PRON
iajs-1956	96	2	التطبيقية	التطبيقية	ADJ
iajs-1956	96	3	ibn	ibn	PROPN
iajs-1956	96	4	al	al	PROPN
iajs-1956	96	5	-	-	PUNCT
iajs-1956	96	6	haitham	haitham	PROPN
iajs-1956	96	7	jour	jour	X
iajs-1956	96	8	.	.	PROPN
iajs-1956	96	9	for	for	ADP
iajs-1956	96	10	pure	pure	ADJ
iajs-1956	96	11	&	&	CCONJ
iajs-1956	96	12	appl	appl	PROPN
iajs-1956	96	13	.	.	PUNCT
iajs-1956	97	1	sci	sci	PROPN
iajs-1956	97	2	.	.	PUNCT
iajs-1956	97	3	vol	vol	NOUN
iajs-1956	97	4	.	.	PROPN
iajs-1956	98	1	31	31	NUM
iajs-1956	98	2	(	(	PUNCT
iajs-1956	98	3	2	2	NUM
iajs-1956	98	4	)	)	SYM
iajs-1956	98	5	2018	2018	NUM
iajs-1956	98	6	definition	definition	NOUN
iajs-1956	98	7	(	(	PUNCT
iajs-1956	98	8	23	23	NUM
iajs-1956	98	9	):	):	PUNCT
iajs-1956	98	10	a	a	DET
iajs-1956	98	11	surjective	surjective	ADJ
iajs-1956	98	12	mapping	mapping	NOUN
iajs-1956	98	13	f	f	X
iajs-1956	98	14	:	:	PUNCT
iajs-1956	98	15	x→y	x→y	NUM
iajs-1956	98	16	is	be	AUX
iajs-1956	98	17	𝜃	𝜃	NOUN
iajs-1956	98	18	𝜃	𝜃	NOUN
iajs-1956	98	19	∗	∗	NOUN
iajs-1956	98	20	,	,	PUNCT
iajs-1956	98	21	𝜃	𝜃	PRON
iajs-1956	98	22	∗∗	∗∗	NOUN
iajs-1956	98	23	-inversely	-inversely	ADV
iajs-1956	98	24	totally	totally	ADV
iajs-1956	98	25	disconnected	disconnected	ADJ
iajs-1956	98	26	,	,	PUNCT
iajs-1956	98	27	if	if	SCONJ
iajs-1956	98	28	f-1(u	f-1(u	NOUN
iajs-1956	98	29	)	)	PUNCT
iajs-1956	98	30	is	be	AUX
iajs-1956	98	31	𝜃-totally	𝜃-totally	ADV
iajs-1956	98	32	disconnected	disconnected	ADJ
iajs-1956	98	33	(	(	PUNCT
iajs-1956	98	34	totally	totally	ADV
iajs-1956	98	35	disconnected	disconnected	ADJ
iajs-1956	98	36	,	,	PUNCT
iajs-1956	98	37	𝜃-totally	𝜃-totally	ADV
iajs-1956	98	38	disconnected	disconnect	VERB
iajs-1956	98	39	)	)	PUNCT
iajs-1956	98	40	set	set	VERB
iajs-1956	98	41	for	for	ADP
iajs-1956	98	42	every	every	PRON
iajs-1956	98	43	totally	totally	ADV
iajs-1956	98	44	disconnected	disconnected	ADJ
iajs-1956	98	45	(	(	PUNCT
iajs-1956	98	46	𝜃-totally	𝜃-totally	ADV
iajs-1956	98	47	disconnected	disconnected	ADJ
iajs-1956	98	48	)	)	PUNCT
iajs-1956	98	49	set	set	VERB
iajs-1956	98	50	u	u	NOUN
iajs-1956	98	51	in	in	ADP
iajs-1956	98	52	y.	y.	PROPN
iajs-1956	98	53	proposition	proposition	PROPN
iajs-1956	98	54	(	(	PUNCT
iajs-1956	98	55	24	24	NUM
iajs-1956	98	56	):	):	PUNCT
iajs-1956	98	57	1	1	NUM
iajs-1956	98	58	-	-	NUM
iajs-1956	98	59	every	every	DET
iajs-1956	98	60	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	98	61	totally	totally	ADV
iajs-1956	98	62	disconnected	disconnected	ADJ
iajs-1956	98	63	mapping	mapping	NOUN
iajs-1956	98	64	is	be	AUX
iajs-1956	98	65	𝜃*-inversely	𝜃*-inversely	ADV
iajs-1956	98	66	totally	totally	ADV
iajs-1956	98	67	disconnected	disconnected	ADJ
iajs-1956	98	68	mapping	mapping	NOUN
iajs-1956	98	69	.	.	PUNCT
iajs-1956	99	1	2	2	NUM
iajs-1956	99	2	-	-	X
iajs-1956	99	3	every	every	DET
iajs-1956	99	4	𝜃-inversely	𝜃-inversely	ADV
iajs-1956	99	5	totally	totally	ADV
iajs-1956	99	6	disconnected	disconnected	ADJ
iajs-1956	99	7	mapping	mapping	NOUN
iajs-1956	99	8	is	be	AUX
iajs-1956	99	9	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	99	10	totally	totally	ADV
iajs-1956	99	11	disconnected	disconnected	ADJ
iajs-1956	99	12	mapping	mapping	NOUN
iajs-1956	99	13	.	.	PUNCT
iajs-1956	100	1	3	3	NUM
iajs-1956	100	2	-	-	X
iajs-1956	100	3	every	every	DET
iajs-1956	100	4	𝜃-inversely	𝜃-inversely	ADV
iajs-1956	100	5	totally	totally	ADV
iajs-1956	100	6	disconnected	disconnected	ADJ
iajs-1956	100	7	mapping	mapping	NOUN
iajs-1956	100	8	is	be	AUX
iajs-1956	100	9	𝜃*-inversely	𝜃*-inversely	ADV
iajs-1956	100	10	totally	totally	ADV
iajs-1956	100	11	disconnected	disconnected	ADJ
iajs-1956	100	12	mapping	mapping	NOUN
iajs-1956	100	13	.	.	PUNCT
iajs-1956	101	1	proof	proof	NOUN
iajs-1956	101	2	:	:	PUNCT
iajs-1956	101	3	1	1	NUM
iajs-1956	101	4	-	-	PUNCT
iajs-1956	101	5	let	let	VERB
iajs-1956	101	6	u	u	NOUN
iajs-1956	101	7	is	be	AUX
iajs-1956	101	8	𝜃-totally	𝜃-totally	ADV
iajs-1956	101	9	disconnected	disconnect	VERB
iajs-1956	101	10	set	set	VERB
iajs-1956	101	11	in	in	ADP
iajs-1956	101	12	y.	y.	NOUN
iajs-1956	101	13	since	since	SCONJ
iajs-1956	101	14	f	f	PROPN
iajs-1956	101	15	is	be	AUX
iajs-1956	101	16	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	101	17	totally	totally	ADV
iajs-1956	101	18	disconnected	disconnected	ADJ
iajs-1956	101	19	mapping	mapping	NOUN
iajs-1956	101	20	.	.	PUNCT
iajs-1956	102	1	f-1(u	f-1(u	NOUN
iajs-1956	102	2	)	)	PUNCT
iajs-1956	102	3	is	be	AUX
iajs-1956	102	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	102	5	disconnected	disconnect	VERB
iajs-1956	102	6	in	in	ADP
iajs-1956	102	7	x	x	PROPN
iajs-1956	102	8	(	(	PUNCT
iajs-1956	102	9	proposition	proposition	NOUN
iajs-1956	102	10	7	7	NUM
iajs-1956	102	11	)	)	PUNCT
iajs-1956	102	12	so	so	ADV
iajs-1956	102	13	f-1(u	f-1(u	NOUN
iajs-1956	102	14	)	)	PUNCT
iajs-1956	102	15	is	be	AUX
iajs-1956	102	16	totally	totally	ADV
iajs-1956	102	17	disconnected	disconnected	ADJ
iajs-1956	102	18	in	in	ADP
iajs-1956	102	19	x	x	NOUN
iajs-1956	102	20	,	,	PUNCT
iajs-1956	102	21	then	then	ADV
iajs-1956	102	22	f	f	PROPN
iajs-1956	102	23	is	be	AUX
iajs-1956	102	24	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	102	25	totally	totally	ADV
iajs-1956	102	26	disconnected	disconnected	ADJ
iajs-1956	102	27	mapping	mapping	NOUN
iajs-1956	102	28	.	.	PUNCT
iajs-1956	103	1	2	2	NUM
iajs-1956	103	2	-	-	PUNCT
iajs-1956	103	3	let	let	VERB
iajs-1956	103	4	u	u	NOUN
iajs-1956	103	5	is	be	AUX
iajs-1956	103	6	𝜃-totally	𝜃-totally	ADV
iajs-1956	103	7	disconnected	disconnect	VERB
iajs-1956	103	8	set	set	VERB
iajs-1956	103	9	in	in	ADP
iajs-1956	103	10	y.	y.	PROPN
iajs-1956	103	11	then	then	ADV
iajs-1956	103	12	u	u	NOUN
iajs-1956	103	13	is	be	AUX
iajs-1956	103	14	totally	totally	ADV
iajs-1956	103	15	disconnected	disconnect	VERB
iajs-1956	103	16	set	set	VERB
iajs-1956	103	17	in	in	ADP
iajs-1956	103	18	y.	y.	NOUN
iajs-1956	103	19	to	to	PART
iajs-1956	103	20	prove	prove	VERB
iajs-1956	103	21	f-1(u	f-1(u	NOUN
iajs-1956	103	22	)	)	PUNCT
iajs-1956	103	23	is	be	AUX
iajs-1956	103	24	𝜃-totally	𝜃-totally	ADV
iajs-1956	103	25	disconnected	disconnect	VERB
iajs-1956	103	26	set	set	VERB
iajs-1956	103	27	in	in	ADP
iajs-1956	103	28	y.	y.	NOUN
iajs-1956	103	29	since	since	SCONJ
iajs-1956	103	30	f	f	PROPN
iajs-1956	103	31	is	be	AUX
iajs-1956	103	32	𝜃-inversely	𝜃-inversely	ADV
iajs-1956	103	33	totally	totally	ADV
iajs-1956	103	34	disconnected	disconnected	ADJ
iajs-1956	103	35	mapping	mapping	NOUN
iajs-1956	103	36	,	,	PUNCT
iajs-1956	103	37	f-1(u	f-1(u	PROPN
iajs-1956	103	38	)	)	PUNCT
iajs-1956	103	39	is	be	AUX
iajs-1956	103	40	𝜃-totally	𝜃-totally	ADV
iajs-1956	103	41	disconnected	disconnect	VERB
iajs-1956	103	42	in	in	ADP
iajs-1956	103	43	x	x	PROPN
iajs-1956	103	44	(	(	PUNCT
iajs-1956	103	45	proposition	proposition	NOUN
iajs-1956	103	46	7	7	NUM
iajs-1956	103	47	)	)	PUNCT
iajs-1956	103	48	.	.	PUNCT
iajs-1956	104	1	then	then	ADV
iajs-1956	104	2	f	f	PROPN
iajs-1956	104	3	is	be	AUX
iajs-1956	104	4	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	104	5	totally	totally	ADV
iajs-1956	104	6	disconnected	disconnected	ADJ
iajs-1956	104	7	mapping	mapping	NOUN
iajs-1956	104	8	3	3	NUM
iajs-1956	104	9	-	-	PUNCT
iajs-1956	104	10	let	let	VERB
iajs-1956	104	11	u	u	NOUN
iajs-1956	104	12	is	be	AUX
iajs-1956	104	13	𝜃-totally	𝜃-totally	ADV
iajs-1956	104	14	disconnected	disconnect	VERB
iajs-1956	104	15	set	set	VERB
iajs-1956	104	16	in	in	ADP
iajs-1956	104	17	y.	y.	PROPN
iajs-1956	104	18	then	then	ADV
iajs-1956	104	19	u	u	NOUN
iajs-1956	104	20	is	be	AUX
iajs-1956	104	21	totally	totally	ADV
iajs-1956	104	22	disconnected	disconnect	VERB
iajs-1956	104	23	set	set	VERB
iajs-1956	104	24	in	in	ADP
iajs-1956	104	25	y(proposition	y(proposition	NOUN
iajs-1956	104	26	7	7	NUM
iajs-1956	104	27	)	)	PUNCT
iajs-1956	104	28	.	.	PUNCT
iajs-1956	105	1	since	since	SCONJ
iajs-1956	105	2	f	f	PROPN
iajs-1956	105	3	is	be	AUX
iajs-1956	105	4	𝜃*-inversely	𝜃*-inversely	ADV
iajs-1956	105	5	totally	totally	ADV
iajs-1956	105	6	disconnected	disconnected	ADJ
iajs-1956	105	7	mapping	mapping	NOUN
iajs-1956	105	8	.	.	PUNCT
iajs-1956	106	1	but	but	CCONJ
iajs-1956	106	2	f-1(u	f-1(u	NOUN
iajs-1956	106	3	)	)	PUNCT
iajs-1956	106	4	is	be	AUX
iajs-1956	106	5	𝜃totally	𝜃totally	ADV
iajs-1956	106	6	disconnected	disconnect	VERB
iajs-1956	106	7	in	in	ADP
iajs-1956	106	8	x	x	PROPN
iajs-1956	106	9	so	so	ADV
iajs-1956	106	10	f-1(u	f-1(u	NOUN
iajs-1956	106	11	)	)	PUNCT
iajs-1956	106	12	is	be	AUX
iajs-1956	106	13	totally	totally	ADV
iajs-1956	106	14	disconnected	disconnected	ADJ
iajs-1956	106	15	in	in	ADP
iajs-1956	106	16	x.	x.	PROPN
iajs-1956	106	17	then	then	ADV
iajs-1956	106	18	f	f	PROPN
iajs-1956	106	19	is	be	AUX
iajs-1956	106	20	𝜃*-inversely	𝜃*-inversely	ADV
iajs-1956	106	21	totally	totally	ADV
iajs-1956	106	22	disconnected	disconnected	ADJ
iajs-1956	106	23	mapping	mapping	NOUN
iajs-1956	106	24	theorem	theorem	NOUN
iajs-1956	106	25	(	(	PUNCT
iajs-1956	106	26	25	25	NUM
iajs-1956	106	27	):	):	PUNCT
iajs-1956	106	28	if	if	SCONJ
iajs-1956	106	29	f	f	X
iajs-1956	106	30	:	:	PUNCT
iajs-1956	106	31	x→y	x→y	NUM
iajs-1956	106	32	is	be	AUX
iajs-1956	106	33	𝜃-inversely	𝜃-inversely	ADV
iajs-1956	106	34	totally	totally	ADV
iajs-1956	106	35	disconnected	disconnected	ADJ
iajs-1956	106	36	mapping	mapping	NOUN
iajs-1956	106	37	then	then	ADV
iajs-1956	106	38	f	f	PROPN
iajs-1956	106	39	is	be	AUX
iajs-1956	106	40	𝜃-light	𝜃-light	VERB
iajs-1956	106	41	mapping	mapping	NOUN
iajs-1956	106	42	.	.	PUNCT
iajs-1956	107	1	proof	proof	NOUN
iajs-1956	107	2	:	:	PUNCT
iajs-1956	107	3	since	since	SCONJ
iajs-1956	107	4	f	f	PROPN
iajs-1956	107	5	is	be	AUX
iajs-1956	107	6	𝜃-inversely	𝜃-inversely	ADV
iajs-1956	107	7	totally	totally	ADV
iajs-1956	107	8	disconnected	disconnected	ADJ
iajs-1956	107	9	mapping	mapping	NOUN
iajs-1956	107	10	to	to	PART
iajs-1956	107	11	prove	prove	VERB
iajs-1956	107	12	f	f	PROPN
iajs-1956	107	13	is	be	AUX
iajs-1956	107	14	𝜃-light	𝜃-light	VERB
iajs-1956	107	15	mapping	mapping	NOUN
iajs-1956	107	16	.	.	PUNCT
iajs-1956	108	1	let	let	VERB
iajs-1956	108	2	y∈y	y∈y	NOUN
iajs-1956	108	3	to	to	PART
iajs-1956	108	4	prove	prove	VERB
iajs-1956	108	5	f-1(y	f-1(y	NOUN
iajs-1956	108	6	)	)	PUNCT
iajs-1956	108	7	is	be	AUX
iajs-1956	108	8	𝜃-totally	𝜃-totally	ADV
iajs-1956	108	9	disconnected	disconnect	VERB
iajs-1956	108	10	set	set	NOUN
iajs-1956	108	11	.	.	PUNCT
iajs-1956	109	1	since	since	SCONJ
iajs-1956	109	2	f	f	PROPN
iajs-1956	109	3	is	be	AUX
iajs-1956	109	4	𝜃-inversely	𝜃-inversely	ADV
iajs-1956	109	5	totally	totally	ADV
iajs-1956	109	6	disconnected	disconnected	ADJ
iajs-1956	109	7	mapping	mapping	NOUN
iajs-1956	109	8	,	,	PUNCT
iajs-1956	109	9	and	and	CCONJ
iajs-1956	109	10	{	{	PUNCT
iajs-1956	109	11	y	y	NOUN
iajs-1956	109	12	}	}	PUNCT
iajs-1956	109	13	is	be	AUX
iajs-1956	109	14	totally	totally	ADV
iajs-1956	109	15	disconnected	disconnected	ADJ
iajs-1956	109	16	in	in	ADP
iajs-1956	109	17	y	y	PROPN
iajs-1956	109	18	,	,	PUNCT
iajs-1956	109	19	then	then	ADV
iajs-1956	109	20	f-1({y	f-1({y	NOUN
iajs-1956	109	21	}	}	PUNCT
iajs-1956	109	22	)	)	PUNCT
iajs-1956	109	23	is	be	AUX
iajs-1956	109	24	𝜃-totally	𝜃-totally	ADV
iajs-1956	109	25	disconnected	disconnect	VERB
iajs-1956	109	26	set	set	VERB
iajs-1956	109	27	in	in	ADP
iajs-1956	109	28	x	x	PROPN
iajs-1956	110	1	so	so	ADV
iajs-1956	110	2	f	f	PROPN
iajs-1956	110	3	is	be	AUX
iajs-1956	110	4	𝜃-light	𝜃-light	VERB
iajs-1956	110	5	mapping	mapping	NOUN
iajs-1956	110	6	.	.	PUNCT
iajs-1956	111	1	proposition	proposition	NOUN
iajs-1956	111	2	(	(	PUNCT
iajs-1956	111	3	26	26	NUM
iajs-1956	111	4	):	):	PUNCT
iajs-1956	111	5	let	let	VERB
iajs-1956	111	6	f	f	X
iajs-1956	111	7	:	:	PUNCT
iajs-1956	111	8	x→z	x→z	NUM
iajs-1956	111	9	and	and	CCONJ
iajs-1956	111	10	g	g	NOUN
iajs-1956	111	11	:	:	PUNCT
iajs-1956	111	12	z→y	z→y	NUM
iajs-1956	111	13	be	be	AUX
iajs-1956	111	14	surjective	surjective	ADJ
iajs-1956	111	15	mapping	mapping	NOUN
iajs-1956	111	16	if	if	SCONJ
iajs-1956	111	17	f	f	PROPN
iajs-1956	111	18	is	be	AUX
iajs-1956	111	19	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	111	20	totally	totally	ADV
iajs-1956	111	21	disconnected	disconnected	ADJ
iajs-1956	111	22	and	and	CCONJ
iajs-1956	111	23	g	g	PROPN
iajs-1956	111	24	is	be	AUX
iajs-1956	111	25	𝜃-light	𝜃-light	NUM
iajs-1956	111	26	mappings	mapping	NOUN
iajs-1956	111	27	,	,	PUNCT
iajs-1956	111	28	then	then	ADV
iajs-1956	111	29	h	h	NOUN
iajs-1956	111	30	:	:	PUNCT
iajs-1956	111	31	x→y	x→y	NUM
iajs-1956	111	32	is	be	AUX
iajs-1956	111	33	𝜃-light	𝜃-light	VERB
iajs-1956	111	34	mapping	mapping	NOUN
iajs-1956	111	35	proof	proof	NOUN
iajs-1956	111	36	:	:	PUNCT
iajs-1956	111	37	let	let	AUX
iajs-1956	111	38	c∈y	c∈y	VERB
iajs-1956	112	1	so	so	ADV
iajs-1956	112	2	h-1(c)=(g∘f)-1(c)=(f-1∘g-1)(c)=	h-1(c)=(g∘f)-1(c)=(f-1∘g-1)(c)=	PROPN
iajs-1956	112	3	f-1(g-1(c	f-1(g-1(c	NUM
iajs-1956	112	4	)	)	PUNCT
iajs-1956	112	5	)	)	PUNCT
iajs-1956	112	6	.	.	PUNCT
iajs-1956	113	1	as	as	SCONJ
iajs-1956	113	2	g	g	PROPN
iajs-1956	113	3	is	be	AUX
iajs-1956	113	4	𝜃-light	𝜃-light	VERB
iajs-1956	113	5	mapping	map	VERB
iajs-1956	113	6	so	so	SCONJ
iajs-1956	113	7	g-1(c	g-1(c	NOUN
iajs-1956	113	8	)	)	PUNCT
iajs-1956	113	9	is	be	AUX
iajs-1956	113	10	𝜃-totally	𝜃-totally	ADV
iajs-1956	113	11	disconnected	disconnect	VERB
iajs-1956	113	12	.	.	PUNCT
iajs-1956	114	1	also	also	ADV
iajs-1956	114	2	as	as	SCONJ
iajs-1956	114	3	f	f	PROPN
iajs-1956	114	4	is	be	AUX
iajs-1956	114	5	𝜃**-inversely	𝜃**-inversely	ADV
iajs-1956	114	6	totally	totally	ADV
iajs-1956	114	7	disconnected	disconnected	ADJ
iajs-1956	114	8	mapping	mapping	NOUN
iajs-1956	114	9	so	so	SCONJ
iajs-1956	114	10	f-1(g1(c	f-1(g1(c	NOUN
iajs-1956	114	11	)	)	PUNCT
iajs-1956	114	12	)	)	PUNCT
iajs-1956	114	13	is	be	AUX
iajs-1956	114	14	𝜃-totally	𝜃-totally	ADV
iajs-1956	114	15	disconnected	disconnect	VERB
iajs-1956	114	16	.	.	PUNCT
iajs-1956	115	1	h-1(c	h-1(c	X
iajs-1956	115	2	)	)	PUNCT
iajs-1956	115	3	is	be	AUX
iajs-1956	115	4	𝜃-totally	𝜃-totally	ADV
iajs-1956	115	5	disconnected	disconnect	VERB
iajs-1956	115	6	then	then	ADV
iajs-1956	115	7	h	h	PROPN
iajs-1956	115	8	is	be	AUX
iajs-1956	115	9	𝜃-light	𝜃-light	VERB
iajs-1956	115	10	mapping	mapping	NOUN
iajs-1956	115	11	.	.	PUNCT
iajs-1956	116	1	  	  	SPACE
iajs-1956	117	1	185	185	NUM
iajs-1956	117	2	mathematics	mathematic	NOUN
iajs-1956	117	3	|	|	ADV
iajs-1956	117	4	https://doi.org/10.30526/31.2.1956	https://doi.org/10.30526/31.2.1956	NOUN
iajs-1956	117	5	2018	2018	NUM
iajs-1956	117	6	)	)	PUNCT
iajs-1956	117	7	عام	عام	ADP
iajs-1956	117	8	2العدد	2العدد	NUM
iajs-1956	117	9	(	(	PUNCT
iajs-1956	117	10	31لمجلد	31لمجلد	NUM
iajs-1956	117	11	ا	ا	NOUN
iajs-1956	117	12	مجلة	مجلة	NOUN
iajs-1956	117	13	إبن	إبن	VERB
iajs-1956	117	14	الهيثم	الهيثم	ADJ
iajs-1956	117	15	للعلوم	للعلوم	NOUN
iajs-1956	117	16	الصرفة	الصرفة	NOUN
iajs-1956	118	1	و	و	PRON
iajs-1956	118	2	التطبيقية	التطبيقية	ADJ
iajs-1956	118	3	ibn	ibn	PROPN
iajs-1956	118	4	al	al	PROPN
iajs-1956	118	5	-	-	PUNCT
iajs-1956	118	6	haitham	haitham	PROPN
iajs-1956	118	7	jour	jour	X
iajs-1956	118	8	.	.	PROPN
iajs-1956	118	9	for	for	ADP
iajs-1956	118	10	pure	pure	ADJ
iajs-1956	118	11	&	&	CCONJ
iajs-1956	118	12	appl	appl	PROPN
iajs-1956	118	13	.	.	PUNCT
iajs-1956	119	1	sci	sci	PROPN
iajs-1956	119	2	.	.	PUNCT
iajs-1956	119	3	vol	vol	NOUN
iajs-1956	119	4	.	.	PROPN
iajs-1956	120	1	31	31	NUM
iajs-1956	120	2	(	(	PUNCT
iajs-1956	120	3	2	2	NUM
iajs-1956	120	4	)	)	SYM
iajs-1956	120	5	2018	2018	NUM
iajs-1956	120	6	theorem	theorem	NOUN
iajs-1956	120	7	(	(	PUNCT
iajs-1956	120	8	27	27	NUM
iajs-1956	120	9	):	):	PUNCT
iajs-1956	120	10	let	let	VERB
iajs-1956	120	11	h	h	PRON
iajs-1956	120	12	:	:	PUNCT
iajs-1956	120	13	x→y	x→y	NUM
iajs-1956	120	14	be	be	AUX
iajs-1956	120	15	a	a	DET
iajs-1956	120	16	suriective	suriective	ADJ
iajs-1956	120	17	mapping	mapping	NOUN
iajs-1956	120	18	and	and	CCONJ
iajs-1956	120	19	h	h	NOUN
iajs-1956	120	20	=	=	NOUN
iajs-1956	120	21	g∘f	g∘f	NOUN
iajs-1956	120	22	such	such	ADJ
iajs-1956	120	23	that	that	PRON
iajs-1956	120	24	for	for	ADP
iajs-1956	120	25	every	every	DET
iajs-1956	120	26	f	f	NOUN
iajs-1956	120	27	:	:	PUNCT
iajs-1956	120	28	x→z	x→z	NUM
iajs-1956	120	29	,	,	PUNCT
iajs-1956	120	30	g	g	NOUN
iajs-1956	120	31	:	:	PUNCT
iajs-1956	120	32	z→y	z→y	NUM
iajs-1956	120	33	be	be	AUX
iajs-1956	120	34	a	a	DET
iajs-1956	120	35	surjective	surjective	ADJ
iajs-1956	120	36	mappings	mapping	NOUN
iajs-1956	120	37	then	then	ADV
iajs-1956	120	38	:	:	PUNCT
iajs-1956	120	39	1	1	NUM
iajs-1956	120	40	-	-	PUNCT
iajs-1956	120	41	if	if	SCONJ
iajs-1956	120	42	h	h	NOUN
iajs-1956	120	43	is	be	AUX
iajs-1956	120	44	𝜃-light	𝜃-light	VERB
iajs-1956	120	45	mapping	mapping	NOUN
iajs-1956	120	46	and	and	CCONJ
iajs-1956	120	47	f	f	PROPN
iajs-1956	120	48	is	be	AUX
iajs-1956	120	49	𝜃**-totally	𝜃**-totally	ADV
iajs-1956	120	50	disconnected	disconnect	VERB
iajs-1956	120	51	mapping	mapping	NOUN
iajs-1956	120	52	then	then	ADV
iajs-1956	120	53	g	g	PROPN
iajs-1956	120	54	is	be	AUX
iajs-1956	120	55	𝜃-light	𝜃-light	NUM
iajs-1956	120	56	mapping	mapping	NOUN
iajs-1956	120	57	.	.	PUNCT
iajs-1956	121	1	2	2	NUM
iajs-1956	121	2	-	-	PUNCT
iajs-1956	121	3	if	if	SCONJ
iajs-1956	121	4	g	g	PROPN
iajs-1956	121	5	is	be	AUX
iajs-1956	121	6	injective	injective	ADJ
iajs-1956	121	7	mapping	mapping	NOUN
iajs-1956	121	8	and	and	CCONJ
iajs-1956	121	9	h	h	NOUN
iajs-1956	121	10	is	be	AUX
iajs-1956	121	11	𝜃-light	𝜃-light	NUM
iajs-1956	121	12	mapping	mapping	NOUN
iajs-1956	121	13	then	then	ADV
iajs-1956	121	14	f	f	PROPN
iajs-1956	121	15	is	be	AUX
iajs-1956	121	16	𝜃-light	𝜃-light	VERB
iajs-1956	121	17	mapping	mapping	NOUN
iajs-1956	121	18	.	.	PUNCT
iajs-1956	122	1	3	3	NUM
iajs-1956	122	2	-	-	PUNCT
iajs-1956	122	3	if	if	SCONJ
iajs-1956	122	4	g	g	NOUN
iajs-1956	122	5	be	be	VERB
iajs-1956	122	6	a	a	DET
iajs-1956	122	7	surjective	surjective	ADJ
iajs-1956	122	8	mapping	mapping	NOUN
iajs-1956	122	9	and	and	CCONJ
iajs-1956	122	10	f	f	PROPN
iajs-1956	122	11	is	be	AUX
iajs-1956	122	12	𝜃-light	𝜃-light	NUM
iajs-1956	122	13	mapping	mapping	NOUN
iajs-1956	122	14	then	then	ADV
iajs-1956	122	15	h	h	PROPN
iajs-1956	122	16	is	be	AUX
iajs-1956	122	17	also	also	ADV
iajs-1956	122	18	𝜃-light	𝜃-light	VERB
iajs-1956	122	19	mapping	mapping	NOUN
iajs-1956	122	20	.	.	PUNCT
iajs-1956	123	1	proof	proof	NOUN
iajs-1956	123	2	:	:	PUNCT
iajs-1956	123	3	1	1	NUM
iajs-1956	123	4	-	-	PUNCT
iajs-1956	123	5	let	let	VERB
iajs-1956	123	6	y∈y	y∈y	NOUN
iajs-1956	123	7	,	,	PUNCT
iajs-1956	123	8	so	so	ADV
iajs-1956	123	9	h-1(y	h-1(y	PROPN
iajs-1956	123	10	)	)	PUNCT
iajs-1956	123	11	is	be	AUX
iajs-1956	123	12	𝜃-totally	𝜃-totally	ADV
iajs-1956	123	13	disconnected	disconnect	VERB
iajs-1956	123	14	set	set	VERB
iajs-1956	123	15	in	in	ADP
iajs-1956	123	16	x	x	PUNCT
iajs-1956	123	17	as	as	SCONJ
iajs-1956	123	18	f	f	PROPN
iajs-1956	123	19	is	be	AUX
iajs-1956	123	20	𝜃**-totally	𝜃**-totally	ADV
iajs-1956	123	21	disconnected	disconnect	VERB
iajs-1956	123	22	mapping	mapping	NOUN
iajs-1956	123	23	then	then	ADV
iajs-1956	123	24	f(h-1(y	f(h-1(y	NOUN
iajs-1956	123	25	)	)	PUNCT
iajs-1956	123	26	)	)	PUNCT
iajs-1956	123	27	is	be	AUX
iajs-1956	123	28	𝜃-totally	𝜃-totally	ADV
iajs-1956	123	29	disconnected	disconnect	VERB
iajs-1956	123	30	set	set	VERB
iajs-1956	123	31	to	to	ADP
iajs-1956	123	32	z	z	NOUN
iajs-1956	123	33	,	,	PUNCT
iajs-1956	123	34	let	let	VERB
iajs-1956	123	35	f(h-1(y	f(h-1(y	NOUN
iajs-1956	123	36	)	)	PUNCT
iajs-1956	123	37	)	)	PUNCT
iajs-1956	124	1	=	=	PRON
iajs-1956	124	2	f((g∘f)1(y))=f((f-1∘g-1)(y))=	f((g∘f)1(y))=f((f-1∘g-1)(y))=	PROPN
iajs-1956	124	3	f((f-1(g-1(y)))=g-1(y	f((f-1(g-1(y)))=g-1(y	NUM
iajs-1956	124	4	)	)	PUNCT
iajs-1956	124	5	.	.	PUNCT
iajs-1956	125	1	so	so	ADV
iajs-1956	125	2	g-1(y	g-1(y	ADV
iajs-1956	125	3	)	)	PUNCT
iajs-1956	125	4	is	be	AUX
iajs-1956	125	5	𝜃-totally	𝜃-totally	ADV
iajs-1956	125	6	disconnected	disconnect	VERB
iajs-1956	125	7	set	set	VERB
iajs-1956	125	8	to	to	ADP
iajs-1956	125	9	z.	z.	PROPN
iajs-1956	125	10	in	in	ADP
iajs-1956	125	11	other	other	ADJ
iajs-1956	125	12	words	word	NOUN
iajs-1956	125	13	g	g	PROPN
iajs-1956	125	14	is	be	AUX
iajs-1956	125	15	𝜃-light	𝜃-light	VERB
iajs-1956	125	16	mapping	mapping	NOUN
iajs-1956	125	17	.	.	PUNCT
iajs-1956	126	1	2	2	NUM
iajs-1956	126	2	-	-	PUNCT
iajs-1956	126	3	let	let	VERB
iajs-1956	126	4	z∈z	z∈z	NOUN
iajs-1956	126	5	so	so	ADV
iajs-1956	126	6	g(z)∈y	g(z)∈y	PROPN
iajs-1956	126	7	since	since	SCONJ
iajs-1956	126	8	h	h	NOUN
iajs-1956	126	9	is	be	AUX
iajs-1956	126	10	𝜃-light	𝜃-light	NUM
iajs-1956	126	11	mapping	mapping	NOUN
iajs-1956	126	12	,	,	PUNCT
iajs-1956	126	13	h-1(g(z	h-1(g(z	NOUN
iajs-1956	126	14	)	)	PUNCT
iajs-1956	126	15	)	)	PUNCT
iajs-1956	126	16	is	be	AUX
iajs-1956	126	17	𝜃-totally	𝜃-totally	ADV
iajs-1956	126	18	disconnected	disconnect	VERB
iajs-1956	126	19	set	set	VERB
iajs-1956	126	20	to	to	PART
iajs-1956	126	21	x.	x.	NOUN
iajs-1956	126	22	but	but	CCONJ
iajs-1956	126	23	h-1(g(z))=(g∘f)-1(g(z))=(f-1∘g-1)(g(z))=f-1(z	h-1(g(z))=(g∘f)-1(g(z))=(f-1∘g-1)(g(z))=f-1(z	PROPN
iajs-1956	126	24	)	)	PUNCT
iajs-1956	126	25	,	,	PUNCT
iajs-1956	126	26	so	so	ADV
iajs-1956	126	27	f-1(z	f-1(z	NOUN
iajs-1956	126	28	)	)	PUNCT
iajs-1956	126	29	is	be	AUX
iajs-1956	126	30	𝜃-totally	𝜃-totally	ADV
iajs-1956	126	31	disconnected	disconnect	VERB
iajs-1956	126	32	set	set	VERB
iajs-1956	126	33	in	in	ADP
iajs-1956	126	34	x.	x.	NOUN
iajs-1956	126	35	in	in	ADP
iajs-1956	126	36	other	other	ADJ
iajs-1956	126	37	words	word	NOUN
iajs-1956	126	38	f	f	X
iajs-1956	126	39	is	be	AUX
iajs-1956	126	40	𝜃-light	𝜃-light	VERB
iajs-1956	126	41	mapping	mapping	NOUN
iajs-1956	126	42	.	.	PUNCT
iajs-1956	127	1	3	3	X
iajs-1956	127	2	-	-	PUNCT
iajs-1956	127	3	let	let	VERB
iajs-1956	127	4	y∈y	y∈y	NOUN
iajs-1956	127	5	as	as	SCONJ
iajs-1956	127	6	g	g	PROPN
iajs-1956	127	7	is	be	AUX
iajs-1956	127	8	bijective	bijective	ADJ
iajs-1956	127	9	mapping	mapping	NOUN
iajs-1956	127	10	,	,	PUNCT
iajs-1956	127	11	then	then	ADV
iajs-1956	127	12	there	there	PRON
iajs-1956	127	13	exist	exist	VERB
iajs-1956	127	14	only	only	ADV
iajs-1956	127	15	one	one	NUM
iajs-1956	127	16	point	point	NOUN
iajs-1956	127	17	z∈z	z∈z	NOUN
iajs-1956	127	18	such	such	ADJ
iajs-1956	127	19	that	that	DET
iajs-1956	127	20	g(z)=y	g(z)=y	NOUN
iajs-1956	127	21	.	.	PROPN
iajs-1956	128	1	as	as	SCONJ
iajs-1956	128	2	f	f	PROPN
iajs-1956	128	3	is	be	AUX
iajs-1956	128	4	𝜃-light	𝜃-light	NUM
iajs-1956	128	5	mapping	mapping	NOUN
iajs-1956	128	6	,	,	PUNCT
iajs-1956	128	7	then	then	ADV
iajs-1956	128	8	f-1(z	f-1(z	NOUN
iajs-1956	128	9	)	)	PUNCT
iajs-1956	128	10	is	be	AUX
iajs-1956	128	11	𝜃-totally	𝜃-totally	ADV
iajs-1956	128	12	disconnected	disconnect	VERB
iajs-1956	128	13	set	set	VERB
iajs-1956	128	14	to	to	PART
iajs-1956	128	15	x.	x.	VERB
iajs-1956	128	16	as	as	ADP
iajs-1956	128	17	f1(z)=h-1(y	f1(z)=h-1(y	ADV
iajs-1956	128	18	)	)	PUNCT
iajs-1956	128	19	,	,	PUNCT
iajs-1956	128	20	then	then	ADV
iajs-1956	128	21	h-1(y	h-1(y	PROPN
iajs-1956	128	22	)	)	PUNCT
iajs-1956	128	23	is	be	AUX
iajs-1956	128	24	also	also	ADV
iajs-1956	128	25	𝜃-totally	𝜃-totally	ADV
iajs-1956	128	26	disconnected	disconnect	VERB
iajs-1956	128	27	set	set	VERB
iajs-1956	128	28	to	to	PART
iajs-1956	128	29	x.	x.	VERB
iajs-1956	129	1	so	so	ADV
iajs-1956	129	2	h	h	PROPN
iajs-1956	129	3	is	be	AUX
iajs-1956	129	4	𝜃-light	𝜃-light	VERB
iajs-1956	129	5	mapping	mapping	NOUN
iajs-1956	129	6	.	.	PUNCT
iajs-1956	130	1	references	reference	NOUN
iajs-1956	130	2	1	1	NUM
iajs-1956	130	3	.	.	PUNCT
iajs-1956	131	1	mohammed	mohammed	PROPN
iajs-1956	131	2	,	,	PUNCT
iajs-1956	131	3	g.	g.	PROPN
iajs-1956	131	4	sh	sh	PROPN
iajs-1956	131	5	.	.	PROPN
iajs-1956	131	6	,	,	PUNCT
iajs-1956	131	7	(	(	PUNCT
iajs-1956	131	8	2001	2001	NUM
iajs-1956	131	9	)	)	PUNCT
iajs-1956	131	10	.	.	PUNCT
iajs-1956	132	1	“	"	PUNCT
iajs-1956	132	2	open	open	ADJ
iajs-1956	132	3	light	light	ADJ
iajs-1956	132	4	mappings	mapping	NOUN
iajs-1956	132	5	”	"	PUNCT
iajs-1956	132	6	m.sc	m.sc	PROPN
iajs-1956	132	7	.	.	PUNCT
iajs-1956	133	1	thesis	thesis	NOUN
iajs-1956	133	2	,	,	PUNCT
iajs-1956	133	3	college	college	NOUN
iajs-1956	133	4	of	of	ADP
iajs-1956	133	5	education	education	NOUN
iajs-1956	133	6	,	,	PUNCT
iajs-1956	133	7	the	the	DET
iajs-1956	133	8	university	university	NOUN
iajs-1956	133	9	of	of	ADP
iajs-1956	133	10	almustansiriyah	almustansiriyah	NOUN
iajs-1956	133	11	2	2	NUM
iajs-1956	133	12	.	.	PUNCT
iajs-1956	133	13	charatonic	charatonic	PROPN
iajs-1956	133	14	,	,	PUNCT
iajs-1956	133	15	j.j	j.j	PROPN
iajs-1956	133	16	and	and	CCONJ
iajs-1956	133	17	omiljanowski	omiljanowski	PROPN
iajs-1956	133	18	,	,	PUNCT
iajs-1956	133	19	k.	k.	PROPN
iajs-1956	133	20	(	(	PUNCT
iajs-1956	133	21	1989	1989	NUM
iajs-1956	133	22	)	)	PUNCT
iajs-1956	133	23	.	.	PUNCT
iajs-1956	133	24	,	,	PUNCT
iajs-1956	133	25	"	"	PUNCT
iajs-1956	133	26	on	on	ADP
iajs-1956	133	27	light	light	ADJ
iajs-1956	133	28	open	open	ADJ
iajs-1956	133	29	mappings	mapping	NOUN
iajs-1956	133	30	"	"	PUNCT
iajs-1956	133	31	,	,	PUNCT
iajs-1956	133	32	baku	baku	PROPN
iajs-1956	133	33	international	international	PROPN
iajs-1956	133	34	topology	topology	PROPN
iajs-1956	133	35	conference	conference	NOUN
iajs-1956	133	36	proceed	proceed	VERB
iajs-1956	133	37	,	,	PUNCT
iajs-1956	133	38	elm	elm	PROPN
iajs-1956	133	39	,	,	PUNCT
iajs-1956	133	40	baku	baku	PROPN
iajs-1956	133	41	3	3	NUM
iajs-1956	133	42	.	.	PUNCT
iajs-1956	134	1	fort	fort	NOUN
iajs-1956	134	2	,	,	PUNCT
iajs-1956	134	3	m.	m.	PROPN
iajs-1956	134	4	k.	k.	PROPN
iajs-1956	134	5	(	(	PUNCT
iajs-1956	134	6	1951	1951	NUM
iajs-1956	134	7	)	)	PUNCT
iajs-1956	134	8	.	.	PUNCT
iajs-1956	135	1	"	"	PUNCT
iajs-1956	135	2	a	a	DET
iajs-1956	135	3	characterization	characterization	NOUN
iajs-1956	135	4	of	of	ADP
iajs-1956	135	5	plane	plane	NOUN
iajs-1956	135	6	light	light	NOUN
iajs-1956	135	7	open	open	ADJ
iajs-1956	135	8	mappings	mapping	NOUN
iajs-1956	135	9	,	,	PUNCT
iajs-1956	135	10	amer	amer	PROPN
iajs-1956	135	11	.	.	PROPN
iajs-1956	135	12	math	math	PROPN
iajs-1956	135	13	.	.	PUNCT
iajs-1956	136	1	soc	soc	PROPN
iajs-1956	136	2	.	.	PUNCT
iajs-1956	137	1	3	3	NUM
iajs-1956	137	2	4	4	NUM
iajs-1956	137	3	saleh	saleh	NOUN
iajs-1956	137	4	,	,	PUNCT
iajs-1956	137	5	m.	m.	NOUN
iajs-1956	137	6	(	(	PUNCT
iajs-1956	137	7	2004	2004	NUM
iajs-1956	137	8	)	)	PUNCT
iajs-1956	137	9	,	,	PUNCT
iajs-1956	137	10	“	"	PUNCT
iajs-1956	137	11	on	on	ADP
iajs-1956	137	12	𝜃-closed	𝜃-close	VERB
iajs-1956	137	13	sets	set	NOUN
iajs-1956	137	14	and	and	CCONJ
iajs-1956	137	15	some	some	DET
iajs-1956	137	16	forms	form	NOUN
iajs-1956	137	17	of	of	ADP
iajs-1956	137	18	continuity	continuity	NOUN
iajs-1956	137	19	”	"	PUNCT
iajs-1956	137	20	,	,	PUNCT
iajs-1956	137	21	archivum	archivum	PROPN
iajs-1956	137	22	mathematicum	mathematicum	NOUN
iajs-1956	137	23	(	(	PUNCT
iajs-1956	137	24	brno	brno	NOUN
iajs-1956	137	25	)	)	PUNCT
iajs-1956	137	26	,	,	PUNCT
iajs-1956	137	27	40	40	NUM
iajs-1956	137	28	,	,	PUNCT
iajs-1956	137	29	383	383	NUM
iajs-1956	137	30	-	-	SYM
iajs-1956	137	31	393	393	NUM
iajs-1956	137	32	.	.	PUNCT
iajs-1956	137	33	5	5	NUM
iajs-1956	137	34	.	.	X
iajs-1956	137	35	wladyslaw	wladyslaw	NOUN
iajs-1956	137	36	,	,	PUNCT
iajs-1956	137	37	m.	m.	NOUN
iajs-1956	137	38	(	(	PUNCT
iajs-1956	137	39	1994	1994	NUM
iajs-1956	137	40	)	)	PUNCT
iajs-1956	137	41	.	.	PUNCT
iajs-1956	138	1	"	"	PUNCT
iajs-1956	138	2	on	on	ADP
iajs-1956	138	3	open	open	ADJ
iajs-1956	138	4	light	light	ADJ
iajs-1956	138	5	mappings	mapping	NOUN
iajs-1956	138	6	"	"	PUNCT
iajs-1956	138	7	,	,	PUNCT
iajs-1956	138	8	comment	comment	NOUN
iajs-1956	138	9	.	.	PUNCT
iajs-1956	139	1	m	m	AUX
iajs-1956	139	2	ath	ath	PROPN
iajs-1956	139	3	.	.	PROPN
iajs-1956	139	4	,	,	PUNCT
iajs-1956	139	5	university	university	NOUN
iajs-1956	139	6	carulinae.35	carulinae.35	NOUN
iajs-1956	139	7	6	6	NUM
iajs-1956	139	8	.	.	PUNCT
iajs-1956	140	1	mohammed	mohammed	PROPN
iajs-1956	140	2	,	,	PUNCT
iajs-1956	140	3	n.	n.	PROPN
iajs-1956	140	4	s.	s.	PROPN
iajs-1956	140	5	(	(	PUNCT
iajs-1956	140	6	2015	2015	NUM
iajs-1956	140	7	)	)	PUNCT
iajs-1956	140	8	.	.	PUNCT
iajs-1956	141	1	“	"	PUNCT
iajs-1956	141	2	certain	certain	ADJ
iajs-1956	141	3	types	type	NOUN
iajs-1956	141	4	of	of	ADP
iajs-1956	141	5	perfect	perfect	ADJ
iajs-1956	141	6	mappings	mapping	NOUN
iajs-1956	141	7	"	"	PUNCT
iajs-1956	141	8	,	,	PUNCT
iajs-1956	141	9	m.sc	m.sc	PROPN
iajs-1956	141	10	.	.	PUNCT
iajs-1956	142	1	thesis	thesis	NOUN
iajs-1956	142	2	,	,	PUNCT
iajs-1956	142	3	college	college	NOUN
iajs-1956	142	4	of	of	ADP
iajs-1956	142	5	since	since	SCONJ
iajs-1956	142	6	,	,	PUNCT
iajs-1956	142	7	al	al	PROPN
iajs-1956	142	8	-	-	PUNCT
iajs-1956	142	9	mustansiriyah	mustansiriyah	PROPN
iajs-1956	142	10	university	university	NOUN
iajs-1956	142	11	.	.	PUNCT
iajs-1956	143	1	7	7	X
iajs-1956	143	2	.	.	X
iajs-1956	143	3	veliko	veliko	NOUN
iajs-1956	143	4	,	,	PUNCT
iajs-1956	143	5	n.	n.	PROPN
iajs-1956	143	6	v.	v.	PROPN
iajs-1956	143	7	(	(	PUNCT
iajs-1956	143	8	1968	1968	NUM
iajs-1956	143	9	)	)	PUNCT
iajs-1956	143	10	,	,	PUNCT
iajs-1956	143	11	"	"	PUNCT
iajs-1956	143	12	h	h	X
iajs-1956	143	13	-	-	PUNCT
iajs-1956	143	14	closed	closed	ADJ
iajs-1956	143	15	topological	topological	ADJ
iajs-1956	143	16	spaces	space	NOUN
iajs-1956	143	17	,	,	PUNCT
iajs-1956	143	18	amer	amer	PROPN
iajs-1956	143	19	.	.	PROPN
iajs-1956	143	20	math	math	PROPN
iajs-1956	143	21	.	.	PUNCT
iajs-1956	144	1	soc	soc	PROPN
iajs-1956	144	2	.	.	PUNCT
iajs-1956	145	1	transl	transl	PROPN
iajs-1956	145	2	.	.	PUNCT
iajs-1956	146	1	ams.78103	ams.78103	PROPN
iajs-1956	146	2	-	-	X
iajs-1956	146	3	118	118	NUM
iajs-1956	146	4	.	.	NOUN
iajs-1956	146	5	8	8	NUM
iajs-1956	146	6	.	.	X
iajs-1956	147	1	lipschutz	lipschutz	PROPN
iajs-1956	147	2	,	,	PUNCT
iajs-1956	147	3	s.	s.	PROPN
iajs-1956	147	4	(	(	PUNCT
iajs-1956	147	5	1965	1965	NUM
iajs-1956	147	6	)	)	PUNCT
iajs-1956	147	7	.	.	PUNCT
iajs-1956	148	1	"	"	PUNCT
iajs-1956	148	2	general	general	ADJ
iajs-1956	148	3	topology	topology	NOUN
iajs-1956	148	4	"	"	PUNCT
iajs-1956	148	5	,	,	PUNCT
iajs-1956	148	6	professor	professor	NOUN
iajs-1956	148	7	of	of	ADP
iajs-1956	148	8	mathematics	mathematics	PROPN
iajs-1956	148	9	temple	temple	PROPN
iajs-1956	148	10	university	university	PROPN