id	sid	tid	token	lemma	pos
iajs-1867	1	1	microsoft	microsoft	PROPN
iajs-1867	1	2	word	word	NOUN
iajs-1867	1	3	330	330	NUM
iajs-1867	1	4	-	-	SYM
iajs-1867	1	5	336	336	NUM
iajs-1867	1	6	ihsciconf	ihsciconf	NOUN
iajs-1867	1	7	2017	2017	NUM
iajs-1867	1	8	special	special	ADJ
iajs-1867	1	9	issue	issue	NOUN
iajs-1867	1	10	ibn	ibn	PROPN
iajs-1867	1	11	al	al	PROPN
iajs-1867	1	12	-	-	PUNCT
iajs-1867	1	13	haitham	haitham	PROPN
iajs-1867	1	14	journal	journal	PROPN
iajs-1867	1	15	for	for	ADP
iajs-1867	1	16	pure	pure	ADJ
iajs-1867	1	17	and	and	CCONJ
iajs-1867	1	18	applied	apply	VERB
iajs-1867	1	19	science	science	NOUN
iajs-1867	1	20	https://doi.org/	https://doi.org/	NOUN
iajs-1867	1	21	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	1	22	for	for	ADP
iajs-1867	1	23	more	more	ADJ
iajs-1867	1	24	information	information	NOUN
iajs-1867	1	25	about	about	ADP
iajs-1867	1	26	the	the	DET
iajs-1867	1	27	conference	conference	NOUN
iajs-1867	1	28	please	please	INTJ
iajs-1867	1	29	visit	visit	VERB
iajs-1867	1	30	the	the	DET
iajs-1867	1	31	websites	website	NOUN
iajs-1867	1	32	:	:	PUNCT
iajs-1867	1	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1867	1	34	      	      	SPACE
iajs-1867	1	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	1	36	                                                                            	                                                                            	SPACE
iajs-1867	1	37	mathematics	mathematic	NOUN
iajs-1867	1	38	|330	|330	X
iajs-1867	1	39	  	  	SPACE
iajs-1867	1	40	on	on	ADP
iajs-1867	1	41	contractible	contractible	ADJ
iajs-1867	1	42	j	j	NOUN
iajs-1867	1	43	-	-	PUNCT
iajs-1867	1	44	saces	sace	NOUN
iajs-1867	1	45	narjis	narjis	PROPN
iajs-1867	1	46	a.	a.	PROPN
iajs-1867	1	47	dawood	dawood	PROPN
iajs-1867	1	48	narjisabduljabbar@yahoo.com	narjisabduljabbar@yahoo.com	PROPN
iajs-1867	1	49	dept	dept	PROPN
iajs-1867	1	50	.	.	PROPN
iajs-1867	1	51	of	of	ADP
iajs-1867	1	52	mathematics	mathematics	PROPN
iajs-1867	1	53	/	/	SYM
iajs-1867	1	54	college	college	NOUN
iajs-1867	1	55	of	of	ADP
iajs-1867	1	56	education	education	NOUN
iajs-1867	1	57	for	for	ADP
iajs-1867	1	58	pure	pure	ADJ
iajs-1867	1	59	science/	science/	NOUN
iajs-1867	1	60	ibn	ibn	PROPN
iajs-1867	1	61	al	al	PROPN
iajs-1867	1	62	–	–	PUNCT
iajs-1867	1	63	haithamuniversity	haithamuniversity	NOUN
iajs-1867	1	64	of	of	ADP
iajs-1867	1	65	baghdad	baghdad	PROPN
iajs-1867	1	66	suaad	suaad	PROPN
iajs-1867	1	67	g.	g.	PROPN
iajs-1867	1	68	gasim	gasim	PROPN
iajs-1867	1	69	suaad.gedaan@yahoo.com	suaad.gedaan@yahoo.com	PROPN
iajs-1867	1	70	dept	dept	PROPN
iajs-1867	1	71	.	.	PROPN
iajs-1867	1	72	of	of	ADP
iajs-1867	1	73	mathematics	mathematics	PROPN
iajs-1867	1	74	/	/	SYM
iajs-1867	1	75	college	college	NOUN
iajs-1867	1	76	of	of	ADP
iajs-1867	1	77	education	education	NOUN
iajs-1867	1	78	for	for	ADP
iajs-1867	1	79	pure	pure	ADJ
iajs-1867	1	80	science/	science/	NOUN
iajs-1867	1	81	ibn	ibn	PROPN
iajs-1867	1	82	al	al	PROPN
iajs-1867	1	83	–	–	PUNCT
iajs-1867	1	84	haithamuniversity	haithamuniversity	NOUN
iajs-1867	1	85	of	of	ADP
iajs-1867	1	86	baghdad	baghdad	PROPN
iajs-1867	1	87	abstract	abstract	PROPN
iajs-1867	1	88	jordan	jordan	PROPN
iajs-1867	1	89	curve	curve	PROPN
iajs-1867	1	90	theorem	theorem	PROPN
iajs-1867	1	91	is	be	AUX
iajs-1867	1	92	one	one	NUM
iajs-1867	1	93	of	of	ADP
iajs-1867	1	94	the	the	DET
iajs-1867	1	95	classical	classical	ADJ
iajs-1867	1	96	theorems	theorem	NOUN
iajs-1867	1	97	of	of	ADP
iajs-1867	1	98	mathematics	mathematic	NOUN
iajs-1867	1	99	,	,	PUNCT
iajs-1867	1	100	it	it	PRON
iajs-1867	1	101	states	state	VERB
iajs-1867	1	102	the	the	DET
iajs-1867	1	103	following	follow	VERB
iajs-1867	1	104	:	:	PUNCT
iajs-1867	1	105	if	if	SCONJ
iajs-1867	1	106	c	c	PROPN
iajs-1867	1	107	is	be	AUX
iajs-1867	1	108	a	a	DET
iajs-1867	1	109	graph	graph	NOUN
iajs-1867	1	110	of	of	ADP
iajs-1867	1	111	a	a	DET
iajs-1867	1	112	simple	simple	ADJ
iajs-1867	1	113	closed	closed	ADJ
iajs-1867	1	114	curve	curve	NOUN
iajs-1867	1	115	in	in	ADP
iajs-1867	1	116	the	the	DET
iajs-1867	1	117	complex	complex	ADJ
iajs-1867	1	118	plane	plane	NOUN
iajs-1867	1	119	the	the	DET
iajs-1867	1	120	complement	complement	NOUN
iajs-1867	1	121	of	of	ADP
iajs-1867	1	122	c	c	PROPN
iajs-1867	1	123	is	be	AUX
iajs-1867	1	124	the	the	DET
iajs-1867	1	125	union	union	NOUN
iajs-1867	1	126	of	of	ADP
iajs-1867	1	127	two	two	NUM
iajs-1867	1	128	regions	region	NOUN
iajs-1867	1	129	,	,	PUNCT
iajs-1867	1	130	c	c	ADP
iajs-1867	1	131	being	be	AUX
iajs-1867	1	132	the	the	DET
iajs-1867	1	133	common	common	ADJ
iajs-1867	1	134	boundary	boundary	NOUN
iajs-1867	1	135	of	of	ADP
iajs-1867	1	136	the	the	DET
iajs-1867	1	137	two	two	NUM
iajs-1867	1	138	regions	region	NOUN
iajs-1867	1	139	.	.	PUNCT
iajs-1867	2	1	one	one	NUM
iajs-1867	2	2	of	of	ADP
iajs-1867	2	3	the	the	DET
iajs-1867	2	4	region	region	NOUN
iajs-1867	2	5	is	be	AUX
iajs-1867	2	6	bounded	bound	VERB
iajs-1867	2	7	and	and	CCONJ
iajs-1867	2	8	the	the	DET
iajs-1867	2	9	other	other	ADJ
iajs-1867	2	10	is	be	AUX
iajs-1867	2	11	unbounded	unbounded	ADJ
iajs-1867	2	12	.	.	PUNCT
iajs-1867	3	1	we	we	PRON
iajs-1867	3	2	introduced	introduce	VERB
iajs-1867	3	3	in	in	ADP
iajs-1867	3	4	this	this	DET
iajs-1867	3	5	paper	paper	NOUN
iajs-1867	3	6	one	one	NUM
iajs-1867	3	7	of	of	ADP
iajs-1867	3	8	jordan	jordan	PROPN
iajs-1867	3	9	's	's	PART
iajs-1867	3	10	theorem	theorem	ADJ
iajs-1867	3	11	generalizations	generalization	NOUN
iajs-1867	3	12	.	.	PUNCT
iajs-1867	4	1	a	a	DET
iajs-1867	4	2	new	new	ADJ
iajs-1867	4	3	type	type	NOUN
iajs-1867	4	4	of	of	ADP
iajs-1867	4	5	space	space	NOUN
iajs-1867	4	6	is	be	AUX
iajs-1867	4	7	discussed	discuss	VERB
iajs-1867	4	8	with	with	ADP
iajs-1867	4	9	some	some	DET
iajs-1867	4	10	properties	property	NOUN
iajs-1867	4	11	and	and	CCONJ
iajs-1867	4	12	new	new	ADJ
iajs-1867	4	13	examples	example	NOUN
iajs-1867	4	14	.	.	PUNCT
iajs-1867	5	1	this	this	DET
iajs-1867	5	2	new	new	ADJ
iajs-1867	5	3	space	space	NOUN
iajs-1867	5	4	called	call	VERB
iajs-1867	5	5	contractible	contractible	ADJ
iajs-1867	5	6	j	j	NOUN
iajs-1867	5	7	-	-	NOUN
iajs-1867	5	8	space	space	NOUN
iajs-1867	5	9	.	.	PUNCT
iajs-1867	6	1	key	key	ADJ
iajs-1867	6	2	words	word	NOUN
iajs-1867	6	3	:	:	PUNCT
iajs-1867	6	4	contractible	contractible	ADJ
iajs-1867	6	5	jspace	jspace	NOUN
iajs-1867	6	6	,	,	PUNCT
iajs-1867	6	7	compact	compact	ADJ
iajs-1867	6	8	space	space	NOUN
iajs-1867	6	9	and	and	CCONJ
iajs-1867	6	10	contractible	contractible	ADJ
iajs-1867	6	11	map	map	NOUN
iajs-1867	6	12	.	.	PUNCT
iajs-1867	7	1	ihsciconf	ihsciconf	PROPN
iajs-1867	7	2	2017	2017	NUM
iajs-1867	7	3	special	special	ADJ
iajs-1867	7	4	issue	issue	NOUN
iajs-1867	7	5	ibn	ibn	PROPN
iajs-1867	7	6	al	al	PROPN
iajs-1867	7	7	-	-	PUNCT
iajs-1867	7	8	haitham	haitham	PROPN
iajs-1867	7	9	journal	journal	PROPN
iajs-1867	7	10	for	for	ADP
iajs-1867	7	11	pure	pure	ADJ
iajs-1867	7	12	and	and	CCONJ
iajs-1867	7	13	applied	apply	VERB
iajs-1867	7	14	science	science	NOUN
iajs-1867	7	15	https://doi.org/	https://doi.org/	NOUN
iajs-1867	7	16	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	7	17	for	for	ADP
iajs-1867	7	18	more	more	ADJ
iajs-1867	7	19	information	information	NOUN
iajs-1867	7	20	about	about	ADP
iajs-1867	7	21	the	the	DET
iajs-1867	7	22	conference	conference	NOUN
iajs-1867	7	23	please	please	INTJ
iajs-1867	7	24	visit	visit	VERB
iajs-1867	7	25	the	the	DET
iajs-1867	7	26	websites	website	NOUN
iajs-1867	7	27	:	:	PUNCT
iajs-1867	7	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1867	7	29	      	      	SPACE
iajs-1867	7	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	7	31	                                                                            	                                                                            	SPACE
iajs-1867	7	32	mathematics	mathematic	NOUN
iajs-1867	7	33	|331	|331	PROPN
iajs-1867	7	34	  	  	SPACE
iajs-1867	7	35	1	1	NUM
iajs-1867	7	36	.	.	PUNCT
iajs-1867	8	1	introduction	introduction	NOUN
iajs-1867	8	2	recall	recall	VERB
iajs-1867	8	3	the	the	DET
iajs-1867	8	4	jordan	jordan	PROPN
iajs-1867	8	5	curve	curve	PROPN
iajs-1867	8	6	theorem	theorem	PROPN
iajs-1867	8	7	which	which	PRON
iajs-1867	8	8	states	state	VERB
iajs-1867	8	9	that	that	SCONJ
iajs-1867	8	10	,	,	PUNCT
iajs-1867	8	11	if	if	SCONJ
iajs-1867	8	12	c	c	PROPN
iajs-1867	8	13	is	be	AUX
iajs-1867	8	14	a	a	DET
iajs-1867	8	15	simple	simple	ADJ
iajs-1867	8	16	closed	closed	ADJ
iajs-1867	8	17	curve	curve	NOUN
iajs-1867	8	18	in	in	ADP
iajs-1867	8	19	the	the	DET
iajs-1867	8	20	plane	plane	NOUN
iajs-1867	8	21	ℝ	ℝ	NOUN
iajs-1867	8	22	,	,	PUNCT
iajs-1867	8	23	then	then	ADV
iajs-1867	8	24	ℝ	ℝ	PROPN
iajs-1867	8	25	\c	\c	NOUN
iajs-1867	8	26	is	be	AUX
iajs-1867	8	27	disconnected	disconnect	VERB
iajs-1867	8	28	and	and	CCONJ
iajs-1867	8	29	consists	consist	VERB
iajs-1867	8	30	of	of	ADP
iajs-1867	8	31	two	two	NUM
iajs-1867	8	32	components	component	NOUN
iajs-1867	8	33	with	with	ADP
iajs-1867	8	34	c	c	PROPN
iajs-1867	8	35	as	as	ADP
iajs-1867	8	36	their	their	PRON
iajs-1867	8	37	common	common	ADJ
iajs-1867	8	38	boundary	boundary	NOUN
iajs-1867	8	39	,	,	PUNCT
iajs-1867	8	40	exactly	exactly	ADV
iajs-1867	8	41	one	one	NUM
iajs-1867	8	42	of	of	ADP
iajs-1867	8	43	these	these	DET
iajs-1867	8	44	components	component	NOUN
iajs-1867	8	45	is	be	AUX
iajs-1867	8	46	bounded	bound	VERB
iajs-1867	8	47	(	(	PUNCT
iajs-1867	8	48	see	see	VERB
iajs-1867	8	49	,	,	PUNCT
iajs-1867	8	50	[	[	X
iajs-1867	8	51	1	1	NUM
iajs-1867	8	52	]	]	PUNCT
iajs-1867	8	53	)	)	PUNCT
iajs-1867	8	54	.	.	PUNCT
iajs-1867	9	1	many	many	ADJ
iajs-1867	9	2	generalizations	generalization	NOUN
iajs-1867	9	3	of	of	ADP
iajs-1867	9	4	jordan	jordan	PROPN
iajs-1867	9	5	curve	curve	PROPN
iajs-1867	9	6	theorem	theorem	PROPN
iajs-1867	9	7	are	be	AUX
iajs-1867	9	8	discussed	discuss	VERB
iajs-1867	9	9	by	by	ADP
iajs-1867	9	10	many	many	ADJ
iajs-1867	9	11	researchers	researcher	NOUN
iajs-1867	9	12	,	,	PUNCT
iajs-1867	9	13	for	for	ADP
iajs-1867	9	14	example	example	NOUN
iajs-1867	9	15	not	not	PART
iajs-1867	9	16	limited	limited	ADJ
iajs-1867	9	17	,	,	PUNCT
iajs-1867	9	18	we	we	PRON
iajs-1867	9	19	recall	recall	VERB
iajs-1867	9	20	some	some	PRON
iajs-1867	9	21	of	of	ADP
iajs-1867	9	22	these	these	DET
iajs-1867	9	23	generalizations	generalization	NOUN
iajs-1867	9	24	.	.	PUNCT
iajs-1867	10	1	in	in	ADP
iajs-1867	10	2	1967	1967	NUM
iajs-1867	10	3	,	,	PUNCT
iajs-1867	10	4	kopperman	kopperman	NOUN
iajs-1867	10	5	,	,	PUNCT
iajs-1867	10	6	khalimsky	khalimsky	PROPN
iajs-1867	10	7	and	and	CCONJ
iajs-1867	10	8	meyer	meyer	PROPN
iajs-1867	10	9	stated	state	VERB
iajs-1867	10	10	a	a	DET
iajs-1867	10	11	generalization	generalization	NOUN
iajs-1867	10	12	in	in	ADP
iajs-1867	10	13	ℤ	ℤ	PROPN
iajs-1867	10	14	equipped	equip	VERB
iajs-1867	10	15	with	with	ADP
iajs-1867	10	16	the	the	DET
iajs-1867	10	17	khalimsky	khalimsky	ADJ
iajs-1867	10	18	topology	topology	NOUN
iajs-1867	10	19	,	,	PUNCT
iajs-1867	10	20	(	(	PUNCT
iajs-1867	10	21	see[2	see[2	X
iajs-1867	10	22	]	]	PUNCT
iajs-1867	10	23	)	)	PUNCT
iajs-1867	10	24	.	.	PUNCT
iajs-1867	11	1	in	in	ADP
iajs-1867	11	2	1991	1991	NUM
iajs-1867	11	3	,	,	PUNCT
iajs-1867	11	4	kong	kong	PROPN
iajs-1867	11	5	,	,	PUNCT
iajs-1867	11	6	kopperman	kopperman	NOUN
iajs-1867	11	7	and	and	CCONJ
iajs-1867	11	8	meyer	meyer	PROPN
iajs-1867	11	9	introduced	introduce	VERB
iajs-1867	11	10	the	the	DET
iajs-1867	11	11	following	following	ADJ
iajs-1867	11	12	result	result	NOUN
iajs-1867	11	13	:	:	PUNCT
iajs-1867	11	14	if	if	SCONJ
iajs-1867	11	15	γ	γ	X
iajs-1867	11	16	is	be	AUX
iajs-1867	11	17	an	an	DET
iajs-1867	11	18	nconnected	nconnecte	VERB
iajs-1867	11	19	closed	closed	ADJ
iajs-1867	11	20	curve	curve	NOUN
iajs-1867	11	21	in	in	ADP
iajs-1867	11	22	ℤ	ℤ	PROPN
iajs-1867	11	23	,	,	PUNCT
iajs-1867	11	24	then	then	ADV
iajs-1867	11	25	ℤ	ℤ	PROPN
iajs-1867	11	26	\𝛤	\𝛤	PROPN
iajs-1867	11	27	has	have	AUX
iajs-1867	11	28	two	two	NUM
iajs-1867	11	29	and	and	CCONJ
iajs-1867	11	30	only	only	ADV
iajs-1867	11	31	two	two	NUM
iajs-1867	11	32	n	n	ADJ
iajs-1867	11	33	–	–	PUNCT
iajs-1867	11	34	connectivity	connectivity	NOUN
iajs-1867	11	35	components	component	NOUN
iajs-1867	11	36	n	n	CCONJ
iajs-1867	11	37	n	n	ADV
iajs-1867	11	38	12	12	NUM
iajs-1867	11	39	,	,	PUNCT
iajs-1867	11	40	n	n	ADV
iajs-1867	11	41	4,8	4,8	NUM
iajs-1867	11	42	.	.	PUNCT
iajs-1867	12	1	this	this	DET
iajs-1867	12	2	result	result	NOUN
iajs-1867	12	3	is	be	AUX
iajs-1867	12	4	a	a	DET
iajs-1867	12	5	kind	kind	NOUN
iajs-1867	12	6	of	of	ADP
iajs-1867	12	7	generalization	generalization	NOUN
iajs-1867	12	8	of	of	ADP
iajs-1867	12	9	the	the	DET
iajs-1867	12	10	classical	classical	ADJ
iajs-1867	12	11	jordan	jordan	PROPN
iajs-1867	12	12	curve	curve	PROPN
iajs-1867	12	13	theorem	theorem	NOUN
iajs-1867	12	14	in	in	ADP
iajs-1867	12	15	ℝ	ℝ	PROPN
iajs-1867	12	16	,	,	PUNCT
iajs-1867	12	17	(	(	PUNCT
iajs-1867	12	18	see	see	VERB
iajs-1867	12	19	[	[	X
iajs-1867	12	20	3	3	NUM
iajs-1867	12	21	]	]	NUM
iajs-1867	12	22	)	)	PUNCT
iajs-1867	12	23	.	.	PUNCT
iajs-1867	13	1	in	in	ADP
iajs-1867	13	2	1999	1999	NUM
iajs-1867	13	3	,	,	PUNCT
iajs-1867	13	4	e.micael	e.micael	PROPN
iajs-1867	13	5	introduced	introduce	VERB
iajs-1867	13	6	and	and	CCONJ
iajs-1867	13	7	studied	study	VERB
iajs-1867	13	8	jspaces	jspace	NOUN
iajs-1867	13	9	and	and	CCONJ
iajs-1867	13	10	strong	strong	ADJ
iajs-1867	13	11	jspaces	jspace	NOUN
iajs-1867	13	12	which	which	PRON
iajs-1867	13	13	are	be	AUX
iajs-1867	13	14	considered	consider	VERB
iajs-1867	13	15	to	to	PART
iajs-1867	13	16	be	be	AUX
iajs-1867	13	17	generalizations	generalization	NOUN
iajs-1867	13	18	of	of	ADP
iajs-1867	13	19	properties	property	NOUN
iajs-1867	13	20	of	of	ADP
iajs-1867	13	21	jordan	jordan	PROPN
iajs-1867	13	22	curve	curve	PROPN
iajs-1867	13	23	theorem	theorem	PROPN
iajs-1867	13	24	,	,	PUNCT
iajs-1867	13	25	(	(	PUNCT
iajs-1867	13	26	see	see	VERB
iajs-1867	13	27	[	[	X
iajs-1867	13	28	4	4	NUM
iajs-1867	13	29	]	]	NUM
iajs-1867	13	30	)	)	PUNCT
iajs-1867	13	31	.	.	PUNCT
iajs-1867	14	1	in	in	ADP
iajs-1867	14	2	2007	2007	NUM
iajs-1867	14	3	,	,	PUNCT
iajs-1867	14	4	y.nanjing	y.nanjing	NOUN
iajs-1867	14	5	introduced	introduce	VERB
iajs-1867	14	6	the	the	DET
iajs-1867	14	7	concept	concept	NOUN
iajs-1867	14	8	of	of	ADP
iajs-1867	14	9	ljspaces	ljspace	NOUN
iajs-1867	14	10	exploited	exploit	VERB
iajs-1867	14	11	the	the	DET
iajs-1867	14	12	common	common	ADJ
iajs-1867	14	13	generalization	generalization	NOUN
iajs-1867	14	14	of	of	ADP
iajs-1867	14	15	lindelöf	lindelöf	NOUN
iajs-1867	14	16	spaces	space	NOUN
iajs-1867	14	17	and	and	CCONJ
iajs-1867	14	18	jspaces	jspace	NOUN
iajs-1867	14	19	,	,	PUNCT
iajs-1867	14	20	(	(	PUNCT
iajs-1867	14	21	see	see	VERB
iajs-1867	14	22	[	[	X
iajs-1867	14	23	5	5	NUM
iajs-1867	14	24	]	]	NUM
iajs-1867	14	25	)	)	PUNCT
iajs-1867	14	26	.	.	PUNCT
iajs-1867	15	1	in	in	ADP
iajs-1867	15	2	2007	2007	NUM
iajs-1867	15	3	,	,	PUNCT
iajs-1867	15	4	a.kornitowicz	a.kornitowicz	PROPN
iajs-1867	15	5	worked	work	VERB
iajs-1867	15	6	hard	hard	ADV
iajs-1867	15	7	to	to	PART
iajs-1867	15	8	mark	mark	VERB
iajs-1867	15	9	crucial	crucial	ADJ
iajs-1867	15	10	points	point	NOUN
iajs-1867	15	11	in	in	ADP
iajs-1867	15	12	the	the	DET
iajs-1867	15	13	proof	proof	NOUN
iajs-1867	15	14	of	of	ADP
iajs-1867	15	15	jordan	jordan	PROPN
iajs-1867	15	16	curve	curve	PROPN
iajs-1867	15	17	theorem	theorem	PROPN
iajs-1867	15	18	,	,	PUNCT
iajs-1867	15	19	(	(	PUNCT
iajs-1867	15	20	see[6	see[6	X
iajs-1867	15	21	]	]	PUNCT
iajs-1867	15	22	)	)	PUNCT
iajs-1867	15	23	.	.	PUNCT
iajs-1867	16	1	in	in	ADP
iajs-1867	16	2	2008	2008	NUM
iajs-1867	16	3	,	,	PUNCT
iajs-1867	16	4	e.bouassida	e.bouassida	PROPN
iajs-1867	16	5	introduced	introduce	VERB
iajs-1867	16	6	a	a	DET
iajs-1867	16	7	new	new	ADJ
iajs-1867	16	8	proof	proof	NOUN
iajs-1867	16	9	of	of	ADP
iajs-1867	16	10	the	the	DET
iajs-1867	16	11	khalimsky	khalimsky	PROPN
iajs-1867	16	12	's	's	PART
iajs-1867	16	13	jordan	jordan	PROPN
iajs-1867	16	14	curve	curve	PROPN
iajs-1867	16	15	theorem	theorem	VERB
iajs-1867	16	16	using	use	VERB
iajs-1867	16	17	the	the	DET
iajs-1867	16	18	specificity	specificity	NOUN
iajs-1867	16	19	of	of	ADP
iajs-1867	16	20	the	the	DET
iajs-1867	16	21	khalimsky	khalimsky	PROPN
iajs-1867	16	22	's	's	PART
iajs-1867	16	23	plane	plane	NOUN
iajs-1867	16	24	as	as	ADP
iajs-1867	16	25	an	an	DET
iajs-1867	16	26	alexandroff	alexandroff	ADJ
iajs-1867	16	27	topological	topological	ADJ
iajs-1867	16	28	space	space	NOUN
iajs-1867	16	29	and	and	CCONJ
iajs-1867	16	30	the	the	DET
iajs-1867	16	31	specific	specific	ADJ
iajs-1867	16	32	properties	property	NOUN
iajs-1867	16	33	of	of	ADP
iajs-1867	16	34	connectivity	connectivity	NOUN
iajs-1867	16	35	on	on	ADP
iajs-1867	16	36	these	these	DET
iajs-1867	16	37	spaces	space	NOUN
iajs-1867	16	38	,	,	PUNCT
iajs-1867	16	39	(	(	PUNCT
iajs-1867	16	40	see	see	VERB
iajs-1867	16	41	[	[	X
iajs-1867	16	42	7	7	NUM
iajs-1867	16	43	]	]	NUM
iajs-1867	16	44	)	)	PUNCT
iajs-1867	16	45	.	.	PUNCT
iajs-1867	17	1	in	in	ADP
iajs-1867	17	2	this	this	DET
iajs-1867	17	3	paper	paper	NOUN
iajs-1867	17	4	we	we	PRON
iajs-1867	17	5	introduced	introduce	VERB
iajs-1867	17	6	another	another	DET
iajs-1867	17	7	generalization	generalization	NOUN
iajs-1867	17	8	of	of	ADP
iajs-1867	17	9	jordan	jordan	PROPN
iajs-1867	17	10	curve	curve	PROPN
iajs-1867	17	11	theorem	theorem	VERB
iajs-1867	17	12	by	by	ADP
iajs-1867	17	13	using	use	VERB
iajs-1867	17	14	the	the	DET
iajs-1867	17	15	concept	concept	NOUN
iajs-1867	17	16	of	of	ADP
iajs-1867	17	17	contractible	contractible	ADJ
iajs-1867	17	18	space	space	NOUN
iajs-1867	17	19	.	.	PUNCT
iajs-1867	18	1	suitability	suitability	NOUN
iajs-1867	18	2	with	with	ADP
iajs-1867	18	3	our	our	PRON
iajs-1867	18	4	work	work	NOUN
iajs-1867	18	5	,	,	PUNCT
iajs-1867	18	6	we	we	PRON
iajs-1867	18	7	assumed	assume	VERB
iajs-1867	18	8	all	all	DET
iajs-1867	18	9	functions	function	NOUN
iajs-1867	18	10	are	be	AUX
iajs-1867	18	11	continuous	continuous	ADJ
iajs-1867	18	12	and	and	CCONJ
iajs-1867	18	13	all	all	DET
iajs-1867	18	14	spaces	space	NOUN
iajs-1867	18	15	are	be	AUX
iajs-1867	18	16	t	t	NOUN
iajs-1867	18	17	,	,	PUNCT
iajs-1867	18	18	in	in	ADP
iajs-1867	18	19	spite	spite	NOUN
iajs-1867	18	20	of	of	ADP
iajs-1867	18	21	most	most	ADJ
iajs-1867	18	22	of	of	ADP
iajs-1867	18	23	our	our	PRON
iajs-1867	18	24	results	result	NOUN
iajs-1867	18	25	are	be	AUX
iajs-1867	18	26	useful	useful	ADJ
iajs-1867	18	27	wanting	want	VERB
iajs-1867	18	28	that	that	DET
iajs-1867	18	29	presumption	presumption	NOUN
iajs-1867	18	30	.	.	PUNCT
iajs-1867	19	1	2	2	X
iajs-1867	19	2	.	.	NUM
iajs-1867	19	3	preliminaries	preliminary	NOUN
iajs-1867	19	4	in	in	ADP
iajs-1867	19	5	this	this	DET
iajs-1867	19	6	section	section	NOUN
iajs-1867	19	7	,	,	PUNCT
iajs-1867	19	8	we	we	PRON
iajs-1867	19	9	give	give	VERB
iajs-1867	19	10	some	some	DET
iajs-1867	19	11	important	important	ADJ
iajs-1867	19	12	definitions	definition	NOUN
iajs-1867	19	13	and	and	CCONJ
iajs-1867	19	14	properties	property	NOUN
iajs-1867	19	15	that	that	PRON
iajs-1867	19	16	we	we	PRON
iajs-1867	19	17	need	need	VERB
iajs-1867	19	18	in	in	ADP
iajs-1867	19	19	our	our	PRON
iajs-1867	19	20	work	work	NOUN
iajs-1867	19	21	.	.	PUNCT
iajs-1867	20	1	definition	definition	NOUN
iajs-1867	20	2	(	(	PUNCT
iajs-1867	20	3	2.1	2.1	NUM
iajs-1867	20	4	)	)	PUNCT
iajs-1867	21	1	[	[	X
iajs-1867	21	2	1	1	NUM
iajs-1867	21	3	]	]	PUNCT
iajs-1867	21	4	:	:	PUNCT
iajs-1867	21	5	two	two	NUM
iajs-1867	21	6	continuous	continuous	ADJ
iajs-1867	21	7	maps	map	NOUN
iajs-1867	21	8	f	f	PROPN
iajs-1867	21	9	,	,	PUNCT
iajs-1867	21	10	f	f	X
iajs-1867	21	11	:	:	PUNCT
iajs-1867	21	12	x	x	X
iajs-1867	21	13	→	→	SYM
iajs-1867	21	14	y	y	PROPN
iajs-1867	21	15	are	be	AUX
iajs-1867	21	16	said	say	VERB
iajs-1867	21	17	to	to	PART
iajs-1867	21	18	be	be	AUX
iajs-1867	21	19	homotopic	homotopic	ADJ
iajs-1867	21	20	if	if	SCONJ
iajs-1867	21	21	there	there	PRON
iajs-1867	21	22	is	be	VERB
iajs-1867	21	23	a	a	DET
iajs-1867	21	24	continuous	continuous	ADJ
iajs-1867	21	25	map	map	NOUN
iajs-1867	22	1	f	f	X
iajs-1867	22	2	:	:	PUNCT
iajs-1867	22	3	x	x	SYM
iajs-1867	22	4	i	i	PRON
iajs-1867	22	5	→	→	SYM
iajs-1867	22	6	y	y	PROPN
iajs-1867	22	7	(	(	PUNCT
iajs-1867	22	8	i	i	PRON
iajs-1867	22	9	is	be	AUX
iajs-1867	22	10	the	the	DET
iajs-1867	22	11	closed	closed	ADJ
iajs-1867	22	12	interval	interval	NOUN
iajs-1867	22	13	0,1	0,1	NUM
iajs-1867	22	14	)	)	PUNCT
iajs-1867	22	15	,	,	PUNCT
iajs-1867	22	16	such	such	ADJ
iajs-1867	22	17	that	that	SCONJ
iajs-1867	22	18	f	f	PROPN
iajs-1867	22	19	x	x	X
iajs-1867	22	20	,	,	PUNCT
iajs-1867	22	21	0	0	NUM
iajs-1867	22	22	f	f	PROPN
iajs-1867	22	23	x	x	X
iajs-1867	22	24	and	and	CCONJ
iajs-1867	22	25	f	f	PROPN
iajs-1867	22	26	x	x	PROPN
iajs-1867	22	27	,	,	PUNCT
iajs-1867	22	28	1	1	NUM
iajs-1867	22	29	f	f	NOUN
iajs-1867	22	30	x	x	PROPN
iajs-1867	22	31	.	.	PUNCT
iajs-1867	23	1	this	this	DET
iajs-1867	23	2	homotopic	homotopic	PROPN
iajs-1867	23	3	denoted	denote	VERB
iajs-1867	23	4	by	by	ADP
iajs-1867	23	5	f	f	PROPN
iajs-1867	23	6	≅	≅	PROPN
iajs-1867	23	7	f	f	PROPN
iajs-1867	23	8	.	.	PUNCT
iajs-1867	24	1	definition	definition	NOUN
iajs-1867	24	2	(	(	PUNCT
iajs-1867	24	3	2.2	2.2	NUM
iajs-1867	24	4	)	)	PUNCT
iajs-1867	25	1	[	[	X
iajs-1867	25	2	1	1	NUM
iajs-1867	25	3	]	]	PUNCT
iajs-1867	25	4	:	:	PUNCT
iajs-1867	25	5	two	two	NUM
iajs-1867	25	6	spaces	space	NOUN
iajs-1867	25	7	x	x	PUNCT
iajs-1867	25	8	and	and	CCONJ
iajs-1867	25	9	y	y	PROPN
iajs-1867	25	10	are	be	AUX
iajs-1867	25	11	of	of	ADP
iajs-1867	25	12	the	the	DET
iajs-1867	25	13	same	same	ADJ
iajs-1867	25	14	homotopic	homotopic	ADJ
iajs-1867	25	15	type	type	NOUN
iajs-1867	25	16	if	if	SCONJ
iajs-1867	25	17	there	there	PRON
iajs-1867	25	18	exist	exist	VERB
iajs-1867	25	19	continuous	continuous	ADJ
iajs-1867	25	20	maps	map	NOUN
iajs-1867	25	21	f	f	NOUN
iajs-1867	25	22	:	:	PUNCT
iajs-1867	25	23	x	x	X
iajs-1867	25	24	→	→	SYM
iajs-1867	25	25	y	y	PROPN
iajs-1867	25	26	and	and	CCONJ
iajs-1867	25	27	g	g	NOUN
iajs-1867	25	28	:	:	PUNCT
iajs-1867	25	29	x	x	X
iajs-1867	25	30	→	→	PUNCT
iajs-1867	25	31	y	y	PROPN
iajs-1867	25	32	such	such	ADJ
iajs-1867	25	33	that	that	PRON
iajs-1867	25	34	gf	gf	PROPN
iajs-1867	25	35	≅	≅	PROPN
iajs-1867	25	36	i	i	PROPN
iajs-1867	25	37	:	:	PUNCT
iajs-1867	25	38	x	x	X
iajs-1867	25	39	→	→	SYM
iajs-1867	25	40	x	x	X
iajs-1867	25	41	and	and	CCONJ
iajs-1867	25	42	fg	fg	PROPN
iajs-1867	25	43	≅	≅	PROPN
iajs-1867	25	44	i	i	PROPN
iajs-1867	25	45	:	:	PUNCT
iajs-1867	25	46	y	y	PROPN
iajs-1867	25	47	→	→	PUNCT
iajs-1867	25	48	y.	y.	VERB
iajs-1867	25	49	the	the	DET
iajs-1867	25	50	maps	maps	PROPN
iajs-1867	25	51	f	f	PROPN
iajs-1867	25	52	and	and	CCONJ
iajs-1867	25	53	g	g	PROPN
iajs-1867	25	54	are	be	AUX
iajs-1867	25	55	then	then	ADV
iajs-1867	25	56	called	call	VERB
iajs-1867	25	57	homotopy	homotopy	NOUN
iajs-1867	25	58	equivalences	equivalence	NOUN
iajs-1867	25	59	,	,	PUNCT
iajs-1867	25	60	we	we	PRON
iajs-1867	25	61	also	also	ADV
iajs-1867	25	62	say	say	VERB
iajs-1867	25	63	that	that	SCONJ
iajs-1867	25	64	x	x	PROPN
iajs-1867	25	65	and	and	CCONJ
iajs-1867	25	66	y	y	PROPN
iajs-1867	25	67	are	be	AUX
iajs-1867	25	68	homotopy	homotopy	NOUN
iajs-1867	25	69	equivalent	equivalent	ADJ
iajs-1867	25	70	.	.	PUNCT
iajs-1867	26	1	definition	definition	NOUN
iajs-1867	26	2	(	(	PUNCT
iajs-1867	26	3	2.3	2.3	NUM
iajs-1867	26	4	)	)	PUNCT
iajs-1867	27	1	[	[	X
iajs-1867	27	2	8	8	NUM
iajs-1867	27	3	]	]	X
iajs-1867	27	4	:	:	PUNCT
iajs-1867	27	5	if	if	SCONJ
iajs-1867	27	6	y	y	PROPN
iajs-1867	27	7	is	be	AUX
iajs-1867	27	8	a	a	DET
iajs-1867	27	9	subspace	subspace	NOUN
iajs-1867	27	10	of	of	ADP
iajs-1867	27	11	a	a	DET
iajs-1867	27	12	topological	topological	ADJ
iajs-1867	27	13	space	space	NOUN
iajs-1867	27	14	x	x	NOUN
iajs-1867	27	15	,	,	PUNCT
iajs-1867	27	16	a	a	DET
iajs-1867	27	17	retraction	retraction	NOUN
iajs-1867	27	18	from	from	ADP
iajs-1867	27	19	x	x	PUNCT
iajs-1867	27	20	to	to	ADP
iajs-1867	27	21	y	y	PROPN
iajs-1867	27	22	is	be	AUX
iajs-1867	27	23	a	a	DET
iajs-1867	27	24	continuous	continuous	ADJ
iajs-1867	27	25	mapping	mapping	NOUN
iajs-1867	27	26	r	r	NOUN
iajs-1867	27	27	:	:	PUNCT
iajs-1867	27	28	x	x	SYM
iajs-1867	27	29	→	→	SYM
iajs-1867	27	30	y	y	NUM
iajs-1867	27	31	such	such	ADJ
iajs-1867	27	32	that	that	DET
iajs-1867	27	33	r	r	NOUN
iajs-1867	27	34	p	p	X
iajs-1867	27	35	p	p	NOUN
iajs-1867	27	36	,	,	PUNCT
iajs-1867	27	37	∀	∀	PUNCT
iajs-1867	27	38	p	p	NOUN
iajs-1867	27	39	∈	∈	PROPN
iajs-1867	27	40	y.	y.	NOUN
iajs-1867	27	41	in	in	ADP
iajs-1867	27	42	this	this	DET
iajs-1867	27	43	case	case	NOUN
iajs-1867	27	44	y	y	NOUN
iajs-1867	27	45	is	be	AUX
iajs-1867	27	46	called	call	VERB
iajs-1867	27	47	a	a	DET
iajs-1867	27	48	retract	retract	NOUN
iajs-1867	27	49	of	of	ADP
iajs-1867	27	50	x.	x.	NOUN
iajs-1867	27	51	definition	definition	NOUN
iajs-1867	27	52	(	(	PUNCT
iajs-1867	27	53	2.4	2.4	NUM
iajs-1867	27	54	)	)	PUNCT
iajs-1867	28	1	[	[	X
iajs-1867	28	2	8	8	NUM
iajs-1867	28	3	]	]	X
iajs-1867	28	4	:	:	PUNCT
iajs-1867	28	5	a	a	DET
iajs-1867	28	6	subspace	subspace	NOUN
iajs-1867	28	7	y	y	PROPN
iajs-1867	28	8	of	of	ADP
iajs-1867	28	9	a	a	DET
iajs-1867	28	10	space	space	NOUN
iajs-1867	28	11	x	x	PUNCT
iajs-1867	28	12	is	be	AUX
iajs-1867	28	13	called	call	VERB
iajs-1867	28	14	a	a	DET
iajs-1867	28	15	deformation	deformation	NOUN
iajs-1867	28	16	retract	retract	NOUN
iajs-1867	28	17	if	if	SCONJ
iajs-1867	28	18	there	there	PRON
iajs-1867	28	19	is	be	VERB
iajs-1867	28	20	a	a	DET
iajs-1867	28	21	continuous	continuous	ADJ
iajs-1867	28	22	retract	retract	NOUN
iajs-1867	29	1	r	r	NOUN
iajs-1867	29	2	:	:	PUNCT
iajs-1867	29	3	x	x	SYM
iajs-1867	29	4	→	→	SYM
iajs-1867	29	5	y	y	PROPN
iajs-1867	29	6	such	such	ADJ
iajs-1867	29	7	that	that	SCONJ
iajs-1867	29	8	the	the	DET
iajs-1867	29	9	identity	identity	NOUN
iajs-1867	29	10	map	map	NOUN
iajs-1867	29	11	from	from	ADP
iajs-1867	29	12	x	x	PUNCT
iajs-1867	29	13	to	to	ADP
iajs-1867	29	14	x	x	X
iajs-1867	29	15	homotopic	homotopic	ADJ
iajs-1867	29	16	to	to	ADP
iajs-1867	29	17	the	the	DET
iajs-1867	29	18	map	map	NOUN
iajs-1867	30	1	i	i	PRON
iajs-1867	30	2	∘	∘	VERB
iajs-1867	30	3	r	r	NOUN
iajs-1867	30	4	,	,	PUNCT
iajs-1867	30	5	where	where	SCONJ
iajs-1867	30	6	i	i	PRON
iajs-1867	30	7	is	be	AUX
iajs-1867	30	8	the	the	DET
iajs-1867	30	9	inclusion	inclusion	NOUN
iajs-1867	30	10	of	of	ADP
iajs-1867	30	11	y	y	PROPN
iajs-1867	30	12	in	in	ADP
iajs-1867	30	13	x.	x.	PROPN
iajs-1867	30	14	definition	definition	NOUN
iajs-1867	30	15	(	(	PUNCT
iajs-1867	30	16	2.5	2.5	NUM
iajs-1867	30	17	)	)	PUNCT
iajs-1867	31	1	[	[	X
iajs-1867	31	2	9	9	NUM
iajs-1867	31	3	]	]	PUNCT
iajs-1867	31	4	:	:	PUNCT
iajs-1867	31	5	let	let	VERB
iajs-1867	31	6	x	x	PRON
iajs-1867	31	7	be	be	AUX
iajs-1867	31	8	a	a	DET
iajs-1867	31	9	topological	topological	ADJ
iajs-1867	31	10	space	space	NOUN
iajs-1867	31	11	and	and	CCONJ
iajs-1867	31	12	a	a	DET
iajs-1867	31	13	the	the	DET
iajs-1867	31	14	subset	subset	NOUN
iajs-1867	31	15	of	of	ADP
iajs-1867	31	16	x	x	SYM
iajs-1867	31	17	0,1	0,1	NUM
iajs-1867	31	18	given	give	VERB
iajs-1867	31	19	by	by	ADP
iajs-1867	31	20	x	x	PROPN
iajs-1867	31	21	1	1	NUM
iajs-1867	31	22	.	.	PUNCT
iajs-1867	32	1	by	by	ADP
iajs-1867	32	2	the	the	DET
iajs-1867	32	3	cone	cone	NOUN
iajs-1867	32	4	over	over	ADP
iajs-1867	32	5	x	x	NOUN
iajs-1867	32	6	,	,	PUNCT
iajs-1867	32	7	mean	mean	VERB
iajs-1867	32	8	the	the	DET
iajs-1867	32	9	space	space	NOUN
iajs-1867	32	10	x	x	NOUN
iajs-1867	32	11	0,1	0,1	NUM
iajs-1867	32	12	/a	/a	PUNCT
iajs-1867	32	13	and	and	CCONJ
iajs-1867	32	14	denoted	denote	VERB
iajs-1867	32	15	by	by	ADP
iajs-1867	32	16	tx	tx	PROPN
iajs-1867	32	17	.	.	PUNCT
iajs-1867	33	1	definition	definition	NOUN
iajs-1867	33	2	(	(	PUNCT
iajs-1867	33	3	2.6	2.6	NUM
iajs-1867	33	4	)	)	PUNCT
iajs-1867	34	1	[	[	X
iajs-1867	34	2	10	10	NUM
iajs-1867	34	3	]	]	X
iajs-1867	34	4	:	:	PUNCT
iajs-1867	34	5	a	a	DET
iajs-1867	34	6	space	space	NOUN
iajs-1867	34	7	x	x	PUNCT
iajs-1867	34	8	is	be	AUX
iajs-1867	34	9	path	path	NOUN
iajs-1867	34	10	connected	connect	VERB
iajs-1867	34	11	if	if	SCONJ
iajs-1867	34	12	,	,	PUNCT
iajs-1867	34	13	for	for	ADP
iajs-1867	34	14	every	every	DET
iajs-1867	34	15	𝑎	𝑎	NOUN
iajs-1867	34	16	,	,	PUNCT
iajs-1867	34	17	𝑏	𝑏	PROPN
iajs-1867	34	18	∊	∊	NOUN
iajs-1867	34	19	x	x	NOUN
iajs-1867	34	20	,	,	PUNCT
iajs-1867	34	21	there	there	PRON
iajs-1867	34	22	exists	exist	VERB
iajs-1867	34	23	a	a	DET
iajs-1867	34	24	path	path	NOUN
iajs-1867	34	25	in	in	ADP
iajs-1867	34	26	x	x	PUNCT
iajs-1867	34	27	from	from	ADP
iajs-1867	34	28	𝑎	𝑎	PRON
iajs-1867	34	29	to	to	PART
iajs-1867	34	30	𝑏.	𝑏.	VERB
iajs-1867	34	31	definition	definition	NOUN
iajs-1867	34	32	(	(	PUNCT
iajs-1867	34	33	2.7	2.7	NUM
iajs-1867	34	34	)	)	PUNCT
iajs-1867	35	1	[	[	X
iajs-1867	35	2	10	10	NUM
iajs-1867	35	3	]	]	X
iajs-1867	35	4	:	:	PUNCT
iajs-1867	35	5	a	a	DET
iajs-1867	35	6	space	space	NOUN
iajs-1867	35	7	x	x	PUNCT
iajs-1867	35	8	is	be	AUX
iajs-1867	35	9	simply	simply	ADV
iajs-1867	35	10	connected	connect	VERB
iajs-1867	35	11	if	if	SCONJ
iajs-1867	35	12	it	it	PRON
iajs-1867	35	13	is	be	AUX
iajs-1867	35	14	path	path	NOUN
iajs-1867	35	15	connected	connect	VERB
iajs-1867	35	16	and	and	CCONJ
iajs-1867	35	17	π	π	NOUN
iajs-1867	35	18	x	x	PROPN
iajs-1867	35	19	,	,	PUNCT
iajs-1867	35	20	x	x	NOUN
iajs-1867	35	21	°	°	ADP
iajs-1867	35	22	e	e	X
iajs-1867	35	23	,	,	PUNCT
iajs-1867	35	24	∀x	∀x	NUM
iajs-1867	35	25	°	°	ADP
iajs-1867	35	26	∈	∈	PROPN
iajs-1867	36	1	x	x	NOUN
iajs-1867	36	2	,	,	PUNCT
iajs-1867	36	3	where	where	SCONJ
iajs-1867	36	4	π	π	PROPN
iajs-1867	36	5	x	x	X
iajs-1867	36	6	,	,	PUNCT
iajs-1867	36	7	x	x	PROPN
iajs-1867	36	8	°	°	PRON
iajs-1867	36	9	is	be	AUX
iajs-1867	36	10	the	the	DET
iajs-1867	36	11	fundamental	fundamental	ADJ
iajs-1867	36	12	group	group	NOUN
iajs-1867	36	13	of	of	ADP
iajs-1867	36	14	a	a	DET
iajs-1867	36	15	space	space	NOUN
iajs-1867	36	16	x	x	NOUN
iajs-1867	36	17	at	at	ADP
iajs-1867	36	18	the	the	DET
iajs-1867	36	19	basepoint	basepoint	PROPN
iajs-1867	36	20	𝑥	𝑥	PROPN
iajs-1867	36	21	°	°	PROPN
iajs-1867	36	22	.	.	PUNCT
iajs-1867	36	23	ihsciconf	ihsciconf	PROPN
iajs-1867	36	24	2017	2017	NUM
iajs-1867	36	25	special	special	ADJ
iajs-1867	36	26	issue	issue	NOUN
iajs-1867	36	27	ibn	ibn	PROPN
iajs-1867	36	28	al	al	PROPN
iajs-1867	36	29	-	-	PUNCT
iajs-1867	36	30	haitham	haitham	PROPN
iajs-1867	36	31	journal	journal	PROPN
iajs-1867	36	32	for	for	ADP
iajs-1867	36	33	pure	pure	ADJ
iajs-1867	36	34	and	and	CCONJ
iajs-1867	36	35	applied	apply	VERB
iajs-1867	36	36	science	science	NOUN
iajs-1867	36	37	https://doi.org/	https://doi.org/	NOUN
iajs-1867	36	38	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	36	39	for	for	ADP
iajs-1867	36	40	more	more	ADJ
iajs-1867	36	41	information	information	NOUN
iajs-1867	36	42	about	about	ADP
iajs-1867	36	43	the	the	DET
iajs-1867	36	44	conference	conference	NOUN
iajs-1867	36	45	please	please	INTJ
iajs-1867	36	46	visit	visit	VERB
iajs-1867	36	47	the	the	DET
iajs-1867	36	48	websites	website	NOUN
iajs-1867	36	49	:	:	PUNCT
iajs-1867	36	50	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1867	36	51	      	      	SPACE
iajs-1867	36	52	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	36	53	                                                                            	                                                                            	SPACE
iajs-1867	36	54	mathematics	mathematic	NOUN
iajs-1867	36	55	|332	|332	PROPN
iajs-1867	36	56	  	  	SPACE
iajs-1867	36	57	examples	example	NOUN
iajs-1867	36	58	(	(	PUNCT
iajs-1867	36	59	2.8	2.8	NUM
iajs-1867	36	60	)	)	PUNCT
iajs-1867	37	1	[	[	X
iajs-1867	37	2	11	11	NUM
iajs-1867	37	3	]	]	SYM
iajs-1867	37	4	:	:	PUNCT
iajs-1867	37	5	1	1	X
iajs-1867	37	6	.	.	X
iajs-1867	37	7	the	the	DET
iajs-1867	37	8	unite	unite	NOUN
iajs-1867	37	9	sphere	sphere	ADV
iajs-1867	37	10	s	s	PROPN
iajs-1867	37	11	in	in	ADP
iajs-1867	37	12	ℝ	ℝ	PROPN
iajs-1867	37	13	is	be	AUX
iajs-1867	37	14	path	path	NOUN
iajs-1867	37	15	connected	connect	VERB
iajs-1867	37	16	∀	∀	NOUN
iajs-1867	37	17	n	n	PRON
iajs-1867	37	18	1	1	NUM
iajs-1867	37	19	.	.	X
iajs-1867	38	1	2	2	NUM
iajs-1867	38	2	.	.	X
iajs-1867	38	3	the	the	DET
iajs-1867	38	4	unite	unite	NOUN
iajs-1867	38	5	ball	ball	PROPN
iajs-1867	38	6	b	b	PROPN
iajs-1867	38	7	in	in	ADP
iajs-1867	38	8	ℝ	ℝ	PROPN
iajs-1867	38	9	is	be	AUX
iajs-1867	38	10	path	path	NOUN
iajs-1867	38	11	connected	connect	VERB
iajs-1867	38	12	.	.	PUNCT
iajs-1867	39	1	3	3	X
iajs-1867	39	2	.	.	X
iajs-1867	39	3	every	every	DET
iajs-1867	39	4	open	open	ADJ
iajs-1867	39	5	ball	ball	NOUN
iajs-1867	39	6	and	and	CCONJ
iajs-1867	39	7	every	every	DET
iajs-1867	39	8	closed	close	VERB
iajs-1867	39	9	ball	ball	NOUN
iajs-1867	39	10	in	in	ADP
iajs-1867	39	11	ℝ	ℝ	PROPN
iajs-1867	39	12	is	be	AUX
iajs-1867	39	13	path	path	NOUN
iajs-1867	39	14	connected	connect	VERB
iajs-1867	39	15	.	.	PUNCT
iajs-1867	40	1	definition	definition	NOUN
iajs-1867	40	2	(	(	PUNCT
iajs-1867	40	3	2.9	2.9	NUM
iajs-1867	40	4	)	)	PUNCT
iajs-1867	41	1	[	[	X
iajs-1867	41	2	12	12	NUM
iajs-1867	41	3	]	]	X
iajs-1867	41	4	:	:	PUNCT
iajs-1867	41	5	a	a	DET
iajs-1867	41	6	function	function	NOUN
iajs-1867	41	7	from	from	ADP
iajs-1867	41	8	x	x	PUNCT
iajs-1867	41	9	to	to	ADP
iajs-1867	41	10	y	y	PROPN
iajs-1867	41	11	is	be	AUX
iajs-1867	41	12	said	say	VERB
iajs-1867	41	13	to	to	PART
iajs-1867	41	14	be	be	AUX
iajs-1867	41	15	nullhomotopic	nullhomotopic	ADJ
iajs-1867	41	16	if	if	SCONJ
iajs-1867	41	17	it	it	PRON
iajs-1867	41	18	is	be	AUX
iajs-1867	41	19	homotopic	homotopic	ADJ
iajs-1867	41	20	to	to	ADP
iajs-1867	41	21	some	some	DET
iajs-1867	41	22	constant	constant	ADJ
iajs-1867	41	23	function	function	NOUN
iajs-1867	41	24	.	.	PUNCT
iajs-1867	42	1	definition	definition	NOUN
iajs-1867	42	2	(	(	PUNCT
iajs-1867	42	3	2.10	2.10	NUM
iajs-1867	42	4	)	)	PUNCT
iajs-1867	43	1	[	[	X
iajs-1867	43	2	11	11	NUM
iajs-1867	43	3	]	]	X
iajs-1867	43	4	:	:	PUNCT
iajs-1867	43	5	a	a	DET
iajs-1867	43	6	space	space	NOUN
iajs-1867	43	7	x	x	PUNCT
iajs-1867	43	8	is	be	AUX
iajs-1867	43	9	called	call	VERB
iajs-1867	43	10	contractible	contractible	ADJ
iajs-1867	43	11	space	space	NOUN
iajs-1867	43	12	if	if	SCONJ
iajs-1867	43	13	the	the	DET
iajs-1867	43	14	identity	identity	NOUN
iajs-1867	43	15	function	function	VERB
iajs-1867	43	16	i	i	PRON
iajs-1867	43	17	:	:	PUNCT
iajs-1867	43	18	x	x	X
iajs-1867	43	19	→	→	PUNCT
iajs-1867	43	20	x	x	X
iajs-1867	43	21	is	be	AUX
iajs-1867	43	22	nullhomotopic	nullhomotopic	ADJ
iajs-1867	43	23	.	.	PUNCT
iajs-1867	44	1	examples	example	NOUN
iajs-1867	44	2	(	(	PUNCT
iajs-1867	44	3	2.11	2.11	NUM
iajs-1867	44	4	):	):	PUNCT
iajs-1867	44	5	1	1	NUM
iajs-1867	44	6	.	.	PUNCT
iajs-1867	45	1	the	the	DET
iajs-1867	45	2	euclidean	euclidean	ADJ
iajs-1867	45	3	space	space	NOUN
iajs-1867	45	4	ℝ𝒏	ℝ𝒏	PROPN
iajs-1867	45	5	is	be	AUX
iajs-1867	45	6	contractible	contractible	ADJ
iajs-1867	45	7	[	[	PUNCT
iajs-1867	45	8	13	13	NUM
iajs-1867	45	9	]	]	SYM
iajs-1867	45	10	.	.	PUNCT
iajs-1867	46	1	2	2	X
iajs-1867	46	2	.	.	X
iajs-1867	46	3	a	a	DET
iajs-1867	46	4	discrete	discrete	ADJ
iajs-1867	46	5	space	space	NOUN
iajs-1867	46	6	with	with	ADP
iajs-1867	46	7	more	more	ADJ
iajs-1867	46	8	than	than	ADP
iajs-1867	46	9	one	one	NUM
iajs-1867	46	10	point	point	NOUN
iajs-1867	46	11	is	be	AUX
iajs-1867	46	12	not	not	PART
iajs-1867	46	13	contractible	contractible	ADJ
iajs-1867	46	14	[	[	X
iajs-1867	46	15	14	14	NUM
iajs-1867	46	16	]	]	PUNCT
iajs-1867	46	17	.	.	PUNCT
iajs-1867	47	1	in	in	ADP
iajs-1867	47	2	the	the	DET
iajs-1867	47	3	following	following	NOUN
iajs-1867	47	4	we	we	PRON
iajs-1867	47	5	give	give	VERB
iajs-1867	47	6	some	some	DET
iajs-1867	47	7	results	result	NOUN
iajs-1867	47	8	about	about	ADP
iajs-1867	47	9	trivial	trivial	ADJ
iajs-1867	47	10	spaces	space	NOUN
iajs-1867	47	11	:	:	PUNCT
iajs-1867	47	12	remarks	remark	NOUN
iajs-1867	47	13	(	(	PUNCT
iajs-1867	47	14	2.12	2.12	NUM
iajs-1867	47	15	):	):	PUNCT
iajs-1867	47	16	1	1	NUM
iajs-1867	47	17	.	.	X
iajs-1867	48	1	any	any	DET
iajs-1867	48	2	subspace	subspace	NOUN
iajs-1867	48	3	(	(	PUNCT
iajs-1867	48	4	with	with	ADP
iajs-1867	48	5	more	more	ADJ
iajs-1867	48	6	than	than	ADP
iajs-1867	48	7	one	one	NUM
iajs-1867	48	8	element	element	NOUN
iajs-1867	48	9	)	)	PUNCT
iajs-1867	48	10	of	of	ADP
iajs-1867	48	11	a	a	DET
iajs-1867	48	12	discrete	discrete	ADJ
iajs-1867	48	13	space	space	NOUN
iajs-1867	48	14	is	be	AUX
iajs-1867	48	15	not	not	PART
iajs-1867	48	16	contractible	contractible	ADJ
iajs-1867	48	17	since	since	SCONJ
iajs-1867	48	18	every	every	DET
iajs-1867	48	19	subspace	subspace	NOUN
iajs-1867	48	20	of	of	ADP
iajs-1867	48	21	a	a	DET
iajs-1867	48	22	discrete	discrete	ADJ
iajs-1867	48	23	space	space	NOUN
iajs-1867	48	24	is	be	AUX
iajs-1867	48	25	also	also	ADV
iajs-1867	48	26	discrete	discrete	ADJ
iajs-1867	48	27	.	.	PUNCT
iajs-1867	49	1	2	2	X
iajs-1867	49	2	.	.	X
iajs-1867	49	3	a	a	DET
iajs-1867	49	4	subset	subset	NOUN
iajs-1867	49	5	y	y	NOUN
iajs-1867	49	6	of	of	ADP
iajs-1867	49	7	ℝ	ℝ	PROPN
iajs-1867	49	8	is	be	AUX
iajs-1867	49	9	contractible	contractible	ADJ
iajs-1867	49	10	if	if	SCONJ
iajs-1867	49	11	y	y	PROPN
iajs-1867	49	12	is	be	AUX
iajs-1867	49	13	not	not	PART
iajs-1867	49	14	discrete	discrete	ADJ
iajs-1867	49	15	space	space	NOUN
iajs-1867	49	16	(	(	PUNCT
iajs-1867	49	17	with	with	ADP
iajs-1867	49	18	more	more	ADJ
iajs-1867	49	19	than	than	ADP
iajs-1867	49	20	one	one	NUM
iajs-1867	49	21	element	element	NOUN
iajs-1867	49	22	)	)	PUNCT
iajs-1867	49	23	.	.	PUNCT
iajs-1867	50	1	3	3	X
iajs-1867	50	2	.	.	X
iajs-1867	50	3	an	an	DET
iajs-1867	50	4	indiscrete	indiscrete	ADJ
iajs-1867	50	5	space	space	NOUN
iajs-1867	50	6	is	be	AUX
iajs-1867	50	7	a	a	DET
iajs-1867	50	8	contractible	contractible	ADJ
iajs-1867	50	9	space	space	NOUN
iajs-1867	50	10	;	;	PUNCT
iajs-1867	50	11	this	this	PRON
iajs-1867	50	12	follows	follow	VERB
iajs-1867	50	13	from	from	ADP
iajs-1867	50	14	the	the	DET
iajs-1867	50	15	fact	fact	NOUN
iajs-1867	50	16	says	say	VERB
iajs-1867	50	17	that	that	SCONJ
iajs-1867	50	18	any	any	DET
iajs-1867	50	19	function	function	NOUN
iajs-1867	50	20	with	with	ADP
iajs-1867	50	21	indiscrete	indiscrete	ADJ
iajs-1867	50	22	codomain	codomain	NOUN
iajs-1867	50	23	is	be	AUX
iajs-1867	50	24	continuous	continuous	ADJ
iajs-1867	50	25	.	.	PUNCT
iajs-1867	51	1	4	4	X
iajs-1867	51	2	.	.	X
iajs-1867	51	3	any	any	DET
iajs-1867	51	4	subspace	subspace	NOUN
iajs-1867	51	5	of	of	ADP
iajs-1867	51	6	an	an	DET
iajs-1867	51	7	indiscrete	indiscrete	ADJ
iajs-1867	51	8	space	space	NOUN
iajs-1867	51	9	is	be	AUX
iajs-1867	51	10	contractible	contractible	ADJ
iajs-1867	51	11	since	since	SCONJ
iajs-1867	51	12	every	every	DET
iajs-1867	51	13	subspace	subspace	NOUN
iajs-1867	51	14	of	of	ADP
iajs-1867	51	15	an	an	DET
iajs-1867	51	16	indiscrete	indiscrete	ADJ
iajs-1867	51	17	space	space	NOUN
iajs-1867	51	18	is	be	AUX
iajs-1867	51	19	also	also	ADV
iajs-1867	51	20	indiscrete	indiscrete	ADJ
iajs-1867	51	21	.	.	PUNCT
iajs-1867	52	1	definition	definition	NOUN
iajs-1867	52	2	(	(	PUNCT
iajs-1867	52	3	2.13	2.13	NUM
iajs-1867	52	4	)	)	PUNCT
iajs-1867	53	1	[	[	X
iajs-1867	53	2	15	15	NUM
iajs-1867	53	3	]	]	X
iajs-1867	53	4	:	:	PUNCT
iajs-1867	53	5	a	a	DET
iajs-1867	53	6	subset	subset	NOUN
iajs-1867	53	7	y	y	NOUN
iajs-1867	53	8	of	of	ADP
iajs-1867	53	9	ℝ	ℝ	PROPN
iajs-1867	53	10	is	be	AUX
iajs-1867	53	11	said	say	VERB
iajs-1867	53	12	to	to	PART
iajs-1867	53	13	be	be	AUX
iajs-1867	53	14	convex	convex	ADJ
iajs-1867	53	15	if	if	SCONJ
iajs-1867	53	16	for	for	ADP
iajs-1867	53	17	every	every	DET
iajs-1867	53	18	pair	pair	NOUN
iajs-1867	53	19	of	of	ADP
iajs-1867	53	20	points	point	NOUN
iajs-1867	53	21	in	in	ADP
iajs-1867	53	22	x	x	PRON
iajs-1867	53	23	,	,	PUNCT
iajs-1867	53	24	the	the	DET
iajs-1867	53	25	line	line	NOUN
iajs-1867	53	26	segment	segment	NOUN
iajs-1867	53	27	connecting	connect	VERB
iajs-1867	53	28	the	the	DET
iajs-1867	53	29	points	point	NOUN
iajs-1867	53	30	is	be	AUX
iajs-1867	53	31	also	also	ADV
iajs-1867	53	32	in	in	ADP
iajs-1867	53	33	x.	x.	NOUN
iajs-1867	53	34	propositions	proposition	NOUN
iajs-1867	53	35	(	(	PUNCT
iajs-1867	53	36	2.14	2.14	NUM
iajs-1867	53	37	)	)	PUNCT
iajs-1867	54	1	[	[	X
iajs-1867	54	2	15	15	NUM
iajs-1867	54	3	]	]	SYM
iajs-1867	54	4	:	:	PUNCT
iajs-1867	54	5	1	1	X
iajs-1867	54	6	.	.	X
iajs-1867	54	7	every	every	DET
iajs-1867	54	8	convex	convex	NOUN
iajs-1867	54	9	subset	subset	NOUN
iajs-1867	54	10	of	of	ADP
iajs-1867	54	11	ℝ	ℝ	PROPN
iajs-1867	54	12	is	be	AUX
iajs-1867	54	13	contractible	contractible	ADJ
iajs-1867	54	14	.	.	PUNCT
iajs-1867	55	1	2	2	X
iajs-1867	55	2	.	.	X
iajs-1867	55	3	any	any	DET
iajs-1867	55	4	open	open	ADJ
iajs-1867	55	5	ball	ball	NOUN
iajs-1867	55	6	in	in	ADP
iajs-1867	55	7	ℝ	ℝ	PROPN
iajs-1867	55	8	is	be	AUX
iajs-1867	55	9	contractible	contractible	ADJ
iajs-1867	55	10	.	.	PUNCT
iajs-1867	56	1	theorem	theorem	NOUN
iajs-1867	56	2	(	(	PUNCT
iajs-1867	56	3	2.15	2.15	NUM
iajs-1867	56	4	):	):	PUNCT
iajs-1867	56	5	the	the	DET
iajs-1867	56	6	following	follow	VERB
iajs-1867	56	7	conditions	condition	NOUN
iajs-1867	56	8	are	be	AUX
iajs-1867	56	9	equivalent	equivalent	ADJ
iajs-1867	56	10	for	for	ADP
iajs-1867	56	11	any	any	DET
iajs-1867	56	12	space	space	NOUN
iajs-1867	56	13	x	x	NOUN
iajs-1867	56	14	1	1	X
iajs-1867	56	15	.	.	X
iajs-1867	57	1	x	x	PUNCT
iajs-1867	57	2	is	be	AUX
iajs-1867	57	3	a	a	DET
iajs-1867	57	4	contractible	contractible	ADJ
iajs-1867	57	5	space	space	NOUN
iajs-1867	57	6	.	.	PUNCT
iajs-1867	58	1	2	2	X
iajs-1867	58	2	.	.	X
iajs-1867	58	3	x	x	PUNCT
iajs-1867	58	4	is	be	AUX
iajs-1867	58	5	a	a	DET
iajs-1867	58	6	homotopy	homotopy	NOUN
iajs-1867	58	7	equivalent	equivalent	NOUN
iajs-1867	58	8	to	to	ADP
iajs-1867	58	9	a	a	DET
iajs-1867	58	10	point	point	NOUN
iajs-1867	58	11	[	[	X
iajs-1867	58	12	16	16	NUM
iajs-1867	58	13	]	]	PUNCT
iajs-1867	58	14	.	.	PUNCT
iajs-1867	59	1	3	3	X
iajs-1867	59	2	.	.	X
iajs-1867	59	3	there	there	PRON
iajs-1867	59	4	exists	exist	VERB
iajs-1867	59	5	a	a	DET
iajs-1867	59	6	point	point	NOUN
iajs-1867	59	7	x	x	SYM
iajs-1867	59	8	°	°	ADP
iajs-1867	59	9	∈	∈	X
iajs-1867	59	10	x	x	PUNCT
iajs-1867	59	11	such	such	ADJ
iajs-1867	59	12	that	that	SCONJ
iajs-1867	59	13	𝑥	𝑥	PROPN
iajs-1867	59	14	°	°	PROPN
iajs-1867	59	15	is	be	AUX
iajs-1867	59	16	a	a	DET
iajs-1867	59	17	deformation	deformation	NOUN
iajs-1867	59	18	retract	retract	NOUN
iajs-1867	59	19	of	of	ADP
iajs-1867	59	20	x	x	PUNCT
iajs-1867	60	1	[	[	X
iajs-1867	60	2	17	17	NUM
iajs-1867	60	3	]	]	SYM
iajs-1867	60	4	.	.	PUNCT
iajs-1867	61	1	4	4	X
iajs-1867	61	2	.	.	X
iajs-1867	61	3	x	x	PUNCT
iajs-1867	61	4	is	be	AUX
iajs-1867	61	5	a	a	DET
iajs-1867	61	6	retract	retract	NOUN
iajs-1867	61	7	of	of	ADP
iajs-1867	61	8	any	any	DET
iajs-1867	61	9	cone	cone	NOUN
iajs-1867	61	10	over	over	ADP
iajs-1867	61	11	it	it	PRON
iajs-1867	62	1	[	[	X
iajs-1867	62	2	16	16	NUM
iajs-1867	62	3	]	]	PUNCT
iajs-1867	62	4	.	.	PUNCT
iajs-1867	63	1	5	5	X
iajs-1867	63	2	.	.	X
iajs-1867	63	3	every	every	DET
iajs-1867	63	4	map	map	NOUN
iajs-1867	64	1	f	f	X
iajs-1867	64	2	:	:	PUNCT
iajs-1867	64	3	x	x	SYM
iajs-1867	64	4	→	→	SYM
iajs-1867	64	5	y	y	PROPN
iajs-1867	64	6	,	,	PUNCT
iajs-1867	64	7	for	for	ADP
iajs-1867	64	8	arbitrary	arbitrary	ADJ
iajs-1867	64	9	y	y	PROPN
iajs-1867	64	10	,	,	PUNCT
iajs-1867	64	11	is	be	AUX
iajs-1867	64	12	null	null	ADJ
iajs-1867	64	13	-	-	PUNCT
iajs-1867	64	14	homotopic	homotopic	NOUN
iajs-1867	64	15	[	[	X
iajs-1867	64	16	18	18	NUM
iajs-1867	64	17	]	]	PUNCT
iajs-1867	64	18	.	.	PUNCT
iajs-1867	65	1	6	6	NUM
iajs-1867	65	2	.	.	X
iajs-1867	66	1	every	every	DET
iajs-1867	66	2	map	map	NOUN
iajs-1867	66	3	f	f	X
iajs-1867	66	4	:	:	PUNCT
iajs-1867	66	5	y	y	PROPN
iajs-1867	66	6	→	→	SYM
iajs-1867	66	7	x	x	X
iajs-1867	66	8	,	,	PUNCT
iajs-1867	66	9	for	for	ADP
iajs-1867	66	10	arbitrary	arbitrary	ADJ
iajs-1867	66	11	y	y	PROPN
iajs-1867	66	12	,	,	PUNCT
iajs-1867	66	13	is	be	AUX
iajs-1867	66	14	null	null	ADJ
iajs-1867	66	15	-	-	PUNCT
iajs-1867	66	16	homotopic	homotopic	NOUN
iajs-1867	66	17	[	[	X
iajs-1867	66	18	18	18	NUM
iajs-1867	66	19	]	]	PUNCT
iajs-1867	66	20	.	.	PUNCT
iajs-1867	67	1	proposition	proposition	NOUN
iajs-1867	67	2	(	(	PUNCT
iajs-1867	67	3	2.16	2.16	NUM
iajs-1867	67	4	)	)	PUNCT
iajs-1867	68	1	[	[	X
iajs-1867	68	2	10	10	NUM
iajs-1867	68	3	]	]	X
iajs-1867	68	4	:	:	PUNCT
iajs-1867	68	5	every	every	DET
iajs-1867	68	6	contractible	contractible	ADJ
iajs-1867	68	7	space	space	NOUN
iajs-1867	68	8	is	be	AUX
iajs-1867	68	9	path	path	NOUN
iajs-1867	68	10	connected	connected	ADJ
iajs-1867	68	11	space	space	NOUN
iajs-1867	68	12	.	.	PUNCT
iajs-1867	69	1	proposition	proposition	NOUN
iajs-1867	69	2	(	(	PUNCT
iajs-1867	69	3	2.17	2.17	NUM
iajs-1867	69	4	)	)	PUNCT
iajs-1867	70	1	[	[	X
iajs-1867	70	2	10	10	NUM
iajs-1867	70	3	]	]	X
iajs-1867	70	4	:	:	PUNCT
iajs-1867	70	5	every	every	DET
iajs-1867	70	6	contractible	contractible	ADJ
iajs-1867	70	7	space	space	NOUN
iajs-1867	70	8	is	be	AUX
iajs-1867	70	9	simply	simply	ADV
iajs-1867	70	10	connected	connected	ADJ
iajs-1867	70	11	space	space	NOUN
iajs-1867	70	12	.	.	PUNCT
iajs-1867	71	1	remark	remark	NOUN
iajs-1867	71	2	(	(	PUNCT
iajs-1867	71	3	2.18	2.18	NUM
iajs-1867	71	4	)	)	PUNCT
iajs-1867	72	1	[	[	X
iajs-1867	72	2	19	19	NUM
iajs-1867	72	3	]	]	X
iajs-1867	72	4	:	:	PUNCT
iajs-1867	72	5	the	the	DET
iajs-1867	72	6	convers	conver	NOUN
iajs-1867	72	7	of	of	ADP
iajs-1867	72	8	propositions	proposition	NOUN
iajs-1867	72	9	(	(	PUNCT
iajs-1867	72	10	14.1	14.1	NUM
iajs-1867	72	11	)	)	PUNCT
iajs-1867	72	12	and	and	CCONJ
iajs-1867	72	13	(	(	PUNCT
iajs-1867	72	14	15.1	15.1	NUM
iajs-1867	72	15	)	)	PUNCT
iajs-1867	72	16	is	be	AUX
iajs-1867	72	17	not	not	PART
iajs-1867	72	18	true	true	ADJ
iajs-1867	72	19	in	in	ADP
iajs-1867	72	20	general	general	ADJ
iajs-1867	72	21	.	.	PUNCT
iajs-1867	73	1	for	for	ADP
iajs-1867	73	2	example	example	NOUN
iajs-1867	73	3	,	,	PUNCT
iajs-1867	73	4	s	s	VERB
iajs-1867	73	5	is	be	AUX
iajs-1867	73	6	path	path	NOUN
iajs-1867	73	7	connected	connect	VERB
iajs-1867	73	8	for	for	ADP
iajs-1867	73	9	every	every	DET
iajs-1867	73	10	integer	integer	NOUN
iajs-1867	73	11	n	n	PRON
iajs-1867	73	12	1	1	NUM
iajs-1867	73	13	,	,	PUNCT
iajs-1867	73	14	and	and	CCONJ
iajs-1867	73	15	simply	simply	ADV
iajs-1867	73	16	connected	connect	VERB
iajs-1867	73	17	for	for	ADP
iajs-1867	73	18	every	every	DET
iajs-1867	73	19	integer	integer	NOUN
iajs-1867	73	20	n	n	NOUN
iajs-1867	73	21	2	2	NUM
iajs-1867	73	22	.	.	PUNCT
iajs-1867	74	1	yet	yet	ADV
iajs-1867	74	2	these	these	DET
iajs-1867	74	3	spheres	sphere	NOUN
iajs-1867	74	4	are	be	AUX
iajs-1867	74	5	not	not	PART
iajs-1867	74	6	contractible	contractible	ADJ
iajs-1867	74	7	.	.	PUNCT
iajs-1867	75	1	remark	remark	NOUN
iajs-1867	75	2	(	(	PUNCT
iajs-1867	75	3	2.19	2.19	NUM
iajs-1867	75	4	)	)	PUNCT
iajs-1867	76	1	[	[	X
iajs-1867	76	2	1	1	NUM
iajs-1867	76	3	]	]	PUNCT
iajs-1867	76	4	:	:	PUNCT
iajs-1867	76	5	the	the	DET
iajs-1867	76	6	continuous	continuous	ADJ
iajs-1867	76	7	image	image	NOUN
iajs-1867	76	8	of	of	ADP
iajs-1867	76	9	a	a	DET
iajs-1867	76	10	contractible	contractible	ADJ
iajs-1867	76	11	space	space	NOUN
iajs-1867	76	12	need	need	AUX
iajs-1867	76	13	not	not	PART
iajs-1867	76	14	be	be	AUX
iajs-1867	76	15	contractible	contractible	ADJ
iajs-1867	76	16	.	.	PUNCT
iajs-1867	77	1	for	for	ADP
iajs-1867	77	2	example	example	NOUN
iajs-1867	77	3	:	:	PUNCT
iajs-1867	77	4	f	f	X
iajs-1867	77	5	:	:	PUNCT
iajs-1867	77	6	a	a	DET
iajs-1867	77	7	,	,	PUNCT
iajs-1867	77	8	b	b	PROPN
iajs-1867	77	9	→	→	SYM
iajs-1867	77	10	s	s	PART
iajs-1867	77	11	is	be	AUX
iajs-1867	77	12	continuous	continuous	ADJ
iajs-1867	77	13	and	and	CCONJ
iajs-1867	77	14	onto	onto	ADP
iajs-1867	77	15	,	,	PUNCT
iajs-1867	77	16	since	since	SCONJ
iajs-1867	77	17	s	s	NOUN
iajs-1867	77	18	is	be	AUX
iajs-1867	77	19	a	a	DET
iajs-1867	77	20	quotient	quotient	NOUN
iajs-1867	77	21	space	space	NOUN
iajs-1867	77	22	for	for	ADP
iajs-1867	77	23	a	a	DET
iajs-1867	77	24	,	,	PUNCT
iajs-1867	77	25	b	b	NOUN
iajs-1867	77	26	by	by	ADP
iajs-1867	77	27	the	the	DET
iajs-1867	77	28	relation	relation	NOUN
iajs-1867	77	29	x	x	PUNCT
iajs-1867	77	30	~	~	PUNCT
iajs-1867	77	31	y	y	PROPN
iajs-1867	77	32	if	if	SCONJ
iajs-1867	77	33	x	x	PROPN
iajs-1867	77	34	a	a	PROPN
iajs-1867	77	35	and	and	CCONJ
iajs-1867	77	36	y	y	PROPN
iajs-1867	77	37	b.	b.	PROPN
iajs-1867	77	38	note	note	VERB
iajs-1867	77	39	that	that	SCONJ
iajs-1867	77	40	a	a	X
iajs-1867	77	41	,	,	PUNCT
iajs-1867	77	42	b	b	NOUN
iajs-1867	77	43	is	be	AUX
iajs-1867	77	44	contractible	contractible	ADJ
iajs-1867	77	45	,	,	PUNCT
iajs-1867	77	46	but	but	CCONJ
iajs-1867	77	47	s	s	NOUN
iajs-1867	77	48	is	be	AUX
iajs-1867	77	49	not	not	PART
iajs-1867	77	50	.	.	PUNCT
iajs-1867	78	1	theorem	theorem	NOUN
iajs-1867	78	2	(	(	PUNCT
iajs-1867	78	3	2.20	2.20	NUM
iajs-1867	78	4	)	)	PUNCT
iajs-1867	79	1	[	[	X
iajs-1867	79	2	20	20	NUM
iajs-1867	79	3	]	]	X
iajs-1867	79	4	:	:	PUNCT
iajs-1867	79	5	if	if	SCONJ
iajs-1867	79	6	x	x	PRON
iajs-1867	79	7	is	be	AUX
iajs-1867	79	8	a	a	DET
iajs-1867	79	9	contractible	contractible	ADJ
iajs-1867	79	10	space	space	NOUN
iajs-1867	79	11	,	,	PUNCT
iajs-1867	79	12	then	then	ADV
iajs-1867	79	13	π	π	PROPN
iajs-1867	79	14	x	x	X
iajs-1867	79	15	,	,	PUNCT
iajs-1867	79	16	x	x	NOUN
iajs-1867	79	17	°	°	ADP
iajs-1867	79	18	e	e	X
iajs-1867	79	19	for	for	ADP
iajs-1867	79	20	all	all	DET
iajs-1867	79	21	x	x	NOUN
iajs-1867	79	22	°	°	ADP
iajs-1867	79	23	∈	∈	PROPN
iajs-1867	79	24	x.	x.	NOUN
iajs-1867	79	25	ihsciconf	ihsciconf	PROPN
iajs-1867	79	26	2017	2017	NUM
iajs-1867	79	27	special	special	ADJ
iajs-1867	79	28	issue	issue	NOUN
iajs-1867	79	29	ibn	ibn	PROPN
iajs-1867	79	30	al	al	PROPN
iajs-1867	79	31	-	-	PUNCT
iajs-1867	79	32	haitham	haitham	PROPN
iajs-1867	79	33	journal	journal	PROPN
iajs-1867	79	34	for	for	ADP
iajs-1867	79	35	pure	pure	ADJ
iajs-1867	79	36	and	and	CCONJ
iajs-1867	79	37	applied	apply	VERB
iajs-1867	79	38	science	science	NOUN
iajs-1867	79	39	https://doi.org/	https://doi.org/	NOUN
iajs-1867	79	40	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	79	41	for	for	ADP
iajs-1867	79	42	more	more	ADJ
iajs-1867	79	43	information	information	NOUN
iajs-1867	79	44	about	about	ADP
iajs-1867	79	45	the	the	DET
iajs-1867	79	46	conference	conference	NOUN
iajs-1867	79	47	please	please	INTJ
iajs-1867	79	48	visit	visit	VERB
iajs-1867	79	49	the	the	DET
iajs-1867	79	50	websites	website	NOUN
iajs-1867	79	51	:	:	PUNCT
iajs-1867	79	52	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1867	79	53	      	      	SPACE
iajs-1867	79	54	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	79	55	                                                                            	                                                                            	SPACE
iajs-1867	79	56	mathematics	mathematic	NOUN
iajs-1867	79	57	|333	|333	NOUN
iajs-1867	79	58	  	  	SPACE
iajs-1867	79	59	proposition	proposition	NOUN
iajs-1867	79	60	(	(	PUNCT
iajs-1867	79	61	2.21	2.21	NUM
iajs-1867	79	62	)	)	PUNCT
iajs-1867	80	1	[	[	X
iajs-1867	80	2	18	18	NUM
iajs-1867	80	3	]	]	X
iajs-1867	80	4	:	:	PUNCT
iajs-1867	80	5	a	a	DET
iajs-1867	80	6	retract	retract	NOUN
iajs-1867	80	7	of	of	ADP
iajs-1867	80	8	a	a	DET
iajs-1867	80	9	contractible	contractible	ADJ
iajs-1867	80	10	space	space	NOUN
iajs-1867	80	11	is	be	AUX
iajs-1867	80	12	contractible	contractible	ADJ
iajs-1867	80	13	.	.	PUNCT
iajs-1867	81	1	proposition	proposition	NOUN
iajs-1867	81	2	(	(	PUNCT
iajs-1867	81	3	2.22	2.22	NUM
iajs-1867	81	4	)	)	PUNCT
iajs-1867	82	1	[	[	X
iajs-1867	82	2	10	10	NUM
iajs-1867	82	3	]	]	X
iajs-1867	82	4	:	:	PUNCT
iajs-1867	82	5	if	if	SCONJ
iajs-1867	82	6	x	x	PRON
iajs-1867	82	7	is	be	AUX
iajs-1867	82	8	a	a	DET
iajs-1867	82	9	contractible	contractible	ADJ
iajs-1867	82	10	and	and	CCONJ
iajs-1867	82	11	y	y	PROPN
iajs-1867	82	12	is	be	AUX
iajs-1867	82	13	path	path	NOUN
iajs-1867	82	14	connected	connect	VERB
iajs-1867	82	15	,	,	PUNCT
iajs-1867	82	16	then	then	ADV
iajs-1867	82	17	any	any	DET
iajs-1867	82	18	two	two	NUM
iajs-1867	82	19	continuous	continuous	ADJ
iajs-1867	82	20	maps	map	NOUN
iajs-1867	82	21	from	from	ADP
iajs-1867	82	22	x	x	PUNCT
iajs-1867	82	23	onto	onto	ADP
iajs-1867	82	24	y	y	PROPN
iajs-1867	82	25	are	be	AUX
iajs-1867	82	26	homotopic	homotopic	ADJ
iajs-1867	82	27	(	(	PUNCT
iajs-1867	82	28	and	and	CCONJ
iajs-1867	82	29	each	each	PRON
iajs-1867	82	30	is	be	AUX
iajs-1867	82	31	nullhomotopic	nullhomotopic	NOUN
iajs-1867	82	32	)	)	PUNCT
iajs-1867	82	33	.	.	PUNCT
iajs-1867	83	1	proposition	proposition	NOUN
iajs-1867	83	2	(	(	PUNCT
iajs-1867	83	3	2.23	2.23	NUM
iajs-1867	83	4	)	)	PUNCT
iajs-1867	84	1	[	[	X
iajs-1867	84	2	16	16	NUM
iajs-1867	84	3	]	]	X
iajs-1867	84	4	:	:	PUNCT
iajs-1867	84	5	two	two	NUM
iajs-1867	84	6	homeomorphic	homeomorphic	ADJ
iajs-1867	84	7	spaces	space	NOUN
iajs-1867	84	8	are	be	AUX
iajs-1867	84	9	homotopy	homotopy	NOUN
iajs-1867	84	10	equivalent	equivalent	NOUN
iajs-1867	84	11	.	.	PUNCT
iajs-1867	85	1	thus	thus	ADV
iajs-1867	85	2	the	the	DET
iajs-1867	85	3	classification	classification	NOUN
iajs-1867	85	4	of	of	ADP
iajs-1867	85	5	spaces	space	NOUN
iajs-1867	85	6	up	up	ADP
iajs-1867	85	7	to	to	PART
iajs-1867	85	8	homotopy	homotopy	VERB
iajs-1867	85	9	equivalence	equivalence	NOUN
iajs-1867	85	10	is	be	AUX
iajs-1867	85	11	coarser	coarse	ADJ
iajs-1867	85	12	than	than	ADP
iajs-1867	85	13	the	the	DET
iajs-1867	85	14	homeomorphism	homeomorphism	PROPN
iajs-1867	85	15	classification	classification	NOUN
iajs-1867	85	16	.	.	PUNCT
iajs-1867	86	1	remarks	remark	NOUN
iajs-1867	86	2	(	(	PUNCT
iajs-1867	86	3	2.24	2.24	NUM
iajs-1867	86	4	)	)	PUNCT
iajs-1867	87	1	[	[	X
iajs-1867	87	2	21	21	NUM
iajs-1867	87	3	]	]	SYM
iajs-1867	87	4	:	:	PUNCT
iajs-1867	87	5	1	1	X
iajs-1867	87	6	.	.	X
iajs-1867	87	7	homotopy	homotopy	NOUN
iajs-1867	87	8	relation	relation	NOUN
iajs-1867	87	9	on	on	ADP
iajs-1867	87	10	the	the	DET
iajs-1867	87	11	collection	collection	NOUN
iajs-1867	87	12	of	of	ADP
iajs-1867	87	13	all	all	DET
iajs-1867	87	14	topological	topological	ADJ
iajs-1867	87	15	spaces	space	NOUN
iajs-1867	87	16	is	be	AUX
iajs-1867	87	17	an	an	DET
iajs-1867	87	18	equivalence	equivalence	NOUN
iajs-1867	87	19	relation	relation	NOUN
iajs-1867	87	20	.	.	PUNCT
iajs-1867	88	1	2	2	X
iajs-1867	88	2	.	.	X
iajs-1867	88	3	homotopy	homotopy	NOUN
iajs-1867	88	4	relation	relation	NOUN
iajs-1867	88	5	is	be	AUX
iajs-1867	88	6	an	an	DET
iajs-1867	88	7	equivalence	equivalence	NOUN
iajs-1867	88	8	relation	relation	NOUN
iajs-1867	88	9	on	on	ADP
iajs-1867	88	10	the	the	DET
iajs-1867	88	11	collection	collection	NOUN
iajs-1867	88	12	of	of	ADP
iajs-1867	88	13	all	all	DET
iajs-1867	88	14	maps	map	NOUN
iajs-1867	88	15	from	from	ADP
iajs-1867	88	16	x	x	PUNCT
iajs-1867	88	17	to	to	ADP
iajs-1867	88	18	y.	y.	NOUN
iajs-1867	88	19	definition	definition	NOUN
iajs-1867	88	20	(	(	PUNCT
iajs-1867	88	21	2.25	2.25	NUM
iajs-1867	88	22	)	)	PUNCT
iajs-1867	89	1	[	[	X
iajs-1867	89	2	22	22	NUM
iajs-1867	89	3	]	]	X
iajs-1867	89	4	:	:	PUNCT
iajs-1867	89	5	a	a	DET
iajs-1867	89	6	closed	closed	ADJ
iajs-1867	89	7	continuous	continuous	ADJ
iajs-1867	89	8	function	function	NOUN
iajs-1867	89	9	with	with	ADP
iajs-1867	89	10	compact	compact	ADJ
iajs-1867	89	11	preimages	preimage	NOUN
iajs-1867	89	12	of	of	ADP
iajs-1867	89	13	points	point	NOUN
iajs-1867	89	14	is	be	AUX
iajs-1867	89	15	called	call	VERB
iajs-1867	89	16	perfect	perfect	ADJ
iajs-1867	89	17	.	.	PUNCT
iajs-1867	90	1	theorem	theorem	NOUN
iajs-1867	90	2	(	(	PUNCT
iajs-1867	90	3	2.26	2.26	NUM
iajs-1867	90	4	)	)	PUNCT
iajs-1867	91	1	[	[	X
iajs-1867	91	2	22	22	NUM
iajs-1867	91	3	]	]	X
iajs-1867	91	4	:	:	PUNCT
iajs-1867	91	5	if	if	SCONJ
iajs-1867	91	6	a	a	DET
iajs-1867	91	7	function	function	NOUN
iajs-1867	91	8	f	f	X
iajs-1867	91	9	:	:	PUNCT
iajs-1867	91	10	x	x	X
iajs-1867	91	11	→	→	SYM
iajs-1867	91	12	y	y	PROPN
iajs-1867	91	13	is	be	AUX
iajs-1867	91	14	a	a	DET
iajs-1867	91	15	perfect	perfect	ADJ
iajs-1867	91	16	function	function	NOUN
iajs-1867	91	17	,	,	PUNCT
iajs-1867	91	18	then	then	ADV
iajs-1867	91	19	for	for	ADP
iajs-1867	91	20	any	any	DET
iajs-1867	91	21	compact	compact	ADJ
iajs-1867	91	22	subset	subset	NOUN
iajs-1867	91	23	f	f	PROPN
iajs-1867	91	24	of	of	ADP
iajs-1867	91	25	y	y	PROPN
iajs-1867	91	26	,	,	PUNCT
iajs-1867	91	27	the	the	DET
iajs-1867	91	28	preimage	preimage	NOUN
iajs-1867	91	29	f	f	PROPN
iajs-1867	91	30	f	f	PROPN
iajs-1867	91	31	is	be	AUX
iajs-1867	91	32	a	a	DET
iajs-1867	91	33	compact	compact	ADJ
iajs-1867	91	34	subset	subset	NOUN
iajs-1867	91	35	of	of	ADP
iajs-1867	91	36	x.	x.	NOUN
iajs-1867	91	37	3	3	X
iajs-1867	91	38	.	.	PUNCT
iajs-1867	91	39	contractible	contractible	ADJ
iajs-1867	91	40	𝐉space	𝐉space	PROPN
iajs-1867	91	41	definition	definition	NOUN
iajs-1867	91	42	(	(	PUNCT
iajs-1867	91	43	3.1	3.1	NUM
iajs-1867	91	44	):	):	PUNCT
iajs-1867	91	45	by	by	ADP
iajs-1867	91	46	a	a	DET
iajs-1867	91	47	contractible	contractible	ADJ
iajs-1867	91	48	jspace	jspace	NOUN
iajs-1867	91	49	we	we	PRON
iajs-1867	91	50	mean	mean	VERB
iajs-1867	91	51	the	the	DET
iajs-1867	91	52	space	space	NOUN
iajs-1867	91	53	satisfies	satisfy	VERB
iajs-1867	91	54	the	the	DET
iajs-1867	91	55	property	property	NOUN
iajs-1867	91	56	which	which	PRON
iajs-1867	91	57	provides	provide	VERB
iajs-1867	91	58	;	;	PUNCT
iajs-1867	91	59	for	for	ADP
iajs-1867	91	60	every	every	DET
iajs-1867	91	61	proper	proper	ADJ
iajs-1867	91	62	closed	closed	ADJ
iajs-1867	91	63	subsets	subset	NOUN
iajs-1867	91	64	e	e	NOUN
iajs-1867	91	65	,	,	PUNCT
iajs-1867	91	66	f	f	PROPN
iajs-1867	91	67	of	of	ADP
iajs-1867	91	68	x	x	PUNCT
iajs-1867	91	69	with	with	ADP
iajs-1867	91	70	e	e	NOUN
iajs-1867	91	71	∪	∪	VERB
iajs-1867	91	72	f	f	PROPN
iajs-1867	91	73	x	x	PUNCT
iajs-1867	91	74	and	and	CCONJ
iajs-1867	91	75	e	e	PROPN
iajs-1867	91	76	∩	∩	X
iajs-1867	91	77	f	f	PROPN
iajs-1867	91	78	compact	compact	ADJ
iajs-1867	91	79	,	,	PUNCT
iajs-1867	91	80	either	either	CCONJ
iajs-1867	91	81	e	e	NOUN
iajs-1867	91	82	or	or	CCONJ
iajs-1867	91	83	f	f	PROPN
iajs-1867	91	84	is	be	AUX
iajs-1867	91	85	contractible	contractible	ADJ
iajs-1867	91	86	.	.	PUNCT
iajs-1867	92	1	remark	remark	NOUN
iajs-1867	92	2	(	(	PUNCT
iajs-1867	92	3	3.2	3.2	NUM
iajs-1867	92	4	):	):	PUNCT
iajs-1867	92	5	if	if	SCONJ
iajs-1867	92	6	the	the	DET
iajs-1867	92	7	closed	closed	ADJ
iajs-1867	92	8	cover	cover	NOUN
iajs-1867	92	9	in	in	ADP
iajs-1867	92	10	definition	definition	NOUN
iajs-1867	92	11	(	(	PUNCT
iajs-1867	92	12	3.1	3.1	NUM
iajs-1867	92	13	)	)	PUNCT
iajs-1867	92	14	is	be	AUX
iajs-1867	92	15	not	not	PART
iajs-1867	92	16	proper	proper	ADJ
iajs-1867	92	17	,	,	PUNCT
iajs-1867	92	18	then	then	ADV
iajs-1867	92	19	every	every	DET
iajs-1867	92	20	contractible	contractible	ADJ
iajs-1867	92	21	j	j	NOUN
iajs-1867	92	22	space	space	NOUN
iajs-1867	92	23	must	must	AUX
iajs-1867	92	24	be	be	AUX
iajs-1867	92	25	contractible	contractible	ADJ
iajs-1867	92	26	.	.	PUNCT
iajs-1867	93	1	remark	remark	NOUN
iajs-1867	93	2	(	(	PUNCT
iajs-1867	93	3	3.3	3.3	NUM
iajs-1867	93	4	):	):	PUNCT
iajs-1867	93	5	if	if	SCONJ
iajs-1867	93	6	a	a	DET
iajs-1867	93	7	topological	topological	ADJ
iajs-1867	93	8	space	space	NOUN
iajs-1867	93	9	x	x	PRON
iajs-1867	93	10	has	have	VERB
iajs-1867	93	11	no	no	DET
iajs-1867	93	12	proper	proper	ADJ
iajs-1867	93	13	closed	closed	ADJ
iajs-1867	93	14	cover	cover	NOUN
iajs-1867	93	15	,	,	PUNCT
iajs-1867	93	16	then	then	ADV
iajs-1867	93	17	x	x	PUNCT
iajs-1867	93	18	is	be	AUX
iajs-1867	93	19	a	a	DET
iajs-1867	93	20	contractible	contractible	ADJ
iajs-1867	93	21	j	j	NOUN
iajs-1867	93	22	space	space	NOUN
iajs-1867	93	23	.	.	PUNCT
iajs-1867	94	1	it	it	PRON
iajs-1867	94	2	follows	follow	VERB
iajs-1867	94	3	from	from	ADP
iajs-1867	94	4	this	this	DET
iajs-1867	94	5	fact	fact	NOUN
iajs-1867	94	6	that	that	SCONJ
iajs-1867	94	7	every	every	DET
iajs-1867	94	8	indiscrete	indiscrete	ADJ
iajs-1867	94	9	space	space	NOUN
iajs-1867	94	10	is	be	AUX
iajs-1867	94	11	a	a	DET
iajs-1867	94	12	contractible	contractible	ADJ
iajs-1867	94	13	jspace	jspace	NOUN
iajs-1867	94	14	.	.	PUNCT
iajs-1867	95	1	remark	remark	NOUN
iajs-1867	95	2	(	(	PUNCT
iajs-1867	95	3	3.4):a	3.4):a	NUM
iajs-1867	95	4	space	space	NOUN
iajs-1867	95	5	x	x	PUNCT
iajs-1867	95	6	is	be	AUX
iajs-1867	95	7	a	a	DET
iajs-1867	95	8	contractible	contractible	ADJ
iajs-1867	95	9	jspace	jspace	NOUN
iajs-1867	95	10	if	if	SCONJ
iajs-1867	95	11	,	,	PUNCT
iajs-1867	95	12	whenever	whenever	SCONJ
iajs-1867	95	13	every	every	DET
iajs-1867	95	14	subspace	subspace	NOUN
iajs-1867	95	15	of	of	ADP
iajs-1867	95	16	it	it	PRON
iajs-1867	95	17	is	be	AUX
iajs-1867	95	18	contractible	contractible	ADJ
iajs-1867	95	19	.	.	PUNCT
iajs-1867	96	1	example	example	NOUN
iajs-1867	96	2	(	(	PUNCT
iajs-1867	96	3	3.5	3.5	NUM
iajs-1867	96	4	):	):	PUNCT
iajs-1867	96	5	the	the	DET
iajs-1867	96	6	usual	usual	ADJ
iajs-1867	96	7	space	space	NOUN
iajs-1867	96	8	ℝ	ℝ	PROPN
iajs-1867	96	9	is	be	AUX
iajs-1867	96	10	a	a	DET
iajs-1867	96	11	contractible	contractible	ADJ
iajs-1867	96	12	jspace	jspace	NOUN
iajs-1867	96	13	,	,	PUNCT
iajs-1867	96	14	for	for	SCONJ
iajs-1867	96	15	if	if	SCONJ
iajs-1867	96	16	e	e	NOUN
iajs-1867	96	17	,	,	PUNCT
iajs-1867	96	18	f	f	PROPN
iajs-1867	96	19	is	be	AUX
iajs-1867	96	20	a	a	DET
iajs-1867	96	21	closed	closed	ADJ
iajs-1867	96	22	cover	cover	NOUN
iajs-1867	96	23	of	of	ADP
iajs-1867	96	24	ℝ	ℝ	PROPN
iajs-1867	96	25	with	with	ADP
iajs-1867	96	26	e⋂f	e⋂f	PROPN
iajs-1867	96	27	compact	compact	NOUN
iajs-1867	96	28	,	,	PUNCT
iajs-1867	96	29	then	then	ADV
iajs-1867	96	30	e	e	PROPN
iajs-1867	96	31	and	and	CCONJ
iajs-1867	96	32	f	f	PROPN
iajs-1867	96	33	can	can	AUX
iajs-1867	96	34	not	not	PART
iajs-1867	96	35	be	be	AUX
iajs-1867	96	36	both	both	ADV
iajs-1867	96	37	discrete	discrete	ADJ
iajs-1867	96	38	,	,	PUNCT
iajs-1867	96	39	thus	thus	ADV
iajs-1867	96	40	e	e	NOUN
iajs-1867	96	41	or	or	CCONJ
iajs-1867	96	42	f	f	PROPN
iajs-1867	96	43	is	be	AUX
iajs-1867	96	44	contractible	contractible	ADJ
iajs-1867	96	45	(	(	PUNCT
iajs-1867	96	46	see	see	INTJ
iajs-1867	96	47	remark	remark	NOUN
iajs-1867	96	48	(	(	PUNCT
iajs-1867	96	49	2.12	2.12	NUM
iajs-1867	96	50	)	)	PUNCT
iajs-1867	96	51	,	,	PUNCT
iajs-1867	96	52	no2	no2	NOUN
iajs-1867	96	53	)	)	PUNCT
iajs-1867	96	54	.	.	PUNCT
iajs-1867	97	1	example	example	NOUN
iajs-1867	97	2	(	(	PUNCT
iajs-1867	97	3	3.6	3.6	NUM
iajs-1867	97	4	):	):	PUNCT
iajs-1867	97	5	a	a	DET
iajs-1867	97	6	discrete	discrete	ADJ
iajs-1867	97	7	space	space	NOUN
iajs-1867	97	8	with	with	ADP
iajs-1867	97	9	more	more	ADJ
iajs-1867	97	10	than	than	ADP
iajs-1867	97	11	two	two	NUM
iajs-1867	97	12	points	point	NOUN
iajs-1867	97	13	is	be	AUX
iajs-1867	97	14	not	not	PART
iajs-1867	97	15	contractible	contractible	ADJ
iajs-1867	97	16	jspace	jspace	NOUN
iajs-1867	97	17	,	,	PUNCT
iajs-1867	97	18	follows	follow	VERB
iajs-1867	97	19	from	from	ADP
iajs-1867	97	20	example	example	NOUN
iajs-1867	97	21	(	(	PUNCT
iajs-1867	97	22	2.11	2.11	NUM
iajs-1867	97	23	)	)	PUNCT
iajs-1867	97	24	,	,	PUNCT
iajs-1867	97	25	no2	no2	PROPN
iajs-1867	97	26	.	.	PUNCT
iajs-1867	98	1	remark	remark	NOUN
iajs-1867	98	2	(	(	PUNCT
iajs-1867	98	3	3.7	3.7	NUM
iajs-1867	98	4	):	):	PUNCT
iajs-1867	98	5	a	a	DET
iajs-1867	98	6	subspace	subspace	NOUN
iajs-1867	98	7	y	y	PROPN
iajs-1867	98	8	of	of	ADP
iajs-1867	98	9	ℝ	ℝ	PROPN
iajs-1867	98	10	is	be	AUX
iajs-1867	98	11	a	a	DET
iajs-1867	98	12	contractible	contractible	ADJ
iajs-1867	98	13	jspace	jspace	NOUN
iajs-1867	98	14	if	if	SCONJ
iajs-1867	98	15	it	it	PRON
iajs-1867	98	16	is	be	AUX
iajs-1867	98	17	not	not	PART
iajs-1867	98	18	discrete	discrete	ADJ
iajs-1867	98	19	space	space	NOUN
iajs-1867	98	20	(	(	PUNCT
iajs-1867	98	21	with	with	ADP
iajs-1867	98	22	more	more	ADJ
iajs-1867	98	23	than	than	ADP
iajs-1867	98	24	two	two	NUM
iajs-1867	98	25	elements	element	NOUN
iajs-1867	98	26	)	)	PUNCT
iajs-1867	98	27	follows	follow	VERB
iajs-1867	98	28	from	from	ADP
iajs-1867	98	29	(	(	PUNCT
iajs-1867	98	30	remark	remark	NOUN
iajs-1867	98	31	(	(	PUNCT
iajs-1867	98	32	2.12	2.12	NUM
iajs-1867	98	33	)	)	PUNCT
iajs-1867	98	34	,	,	PUNCT
iajs-1867	98	35	no2	no2	NOUN
iajs-1867	98	36	)	)	PUNCT
iajs-1867	98	37	.	.	PUNCT
iajs-1867	99	1	example	example	NOUN
iajs-1867	99	2	(	(	PUNCT
iajs-1867	99	3	3.8	3.8	NUM
iajs-1867	99	4	):	):	PUNCT
iajs-1867	99	5	let	let	VERB
iajs-1867	99	6	x	x	PRON
iajs-1867	99	7	be	be	AUX
iajs-1867	99	8	a	a	DET
iajs-1867	99	9	non	non	X
iajs-1867	99	10	empty	empty	ADJ
iajs-1867	99	11	set	set	NOUN
iajs-1867	99	12	and	and	CCONJ
iajs-1867	99	13	a	a	PRON
iajs-1867	99	14	is	be	AUX
iajs-1867	99	15	a	a	DET
iajs-1867	99	16	proper	proper	ADJ
iajs-1867	99	17	subset	subset	NOUN
iajs-1867	99	18	of	of	ADP
iajs-1867	99	19	x	x	X
iajs-1867	99	20	.	.	PUNCT
iajs-1867	99	21	define	define	VERB
iajs-1867	99	22	a	a	DET
iajs-1867	99	23	topology	topology	NOUN
iajs-1867	99	24	on	on	ADP
iajs-1867	99	25	x	x	PUNCT
iajs-1867	99	26	by	by	ADP
iajs-1867	99	27	τ	τ	PROPN
iajs-1867	99	28	x	x	SYM
iajs-1867	99	29	,	,	PUNCT
iajs-1867	99	30	∅	∅	NOUN
iajs-1867	99	31	,	,	PUNCT
iajs-1867	99	32	a	a	PRON
iajs-1867	99	33	,	,	PUNCT
iajs-1867	99	34	then	then	ADV
iajs-1867	99	35	x	x	X
iajs-1867	99	36	,	,	PUNCT
iajs-1867	99	37	τ	τ	PROPN
iajs-1867	99	38	is	be	AUX
iajs-1867	99	39	a	a	DET
iajs-1867	99	40	contractible	contractible	ADJ
iajs-1867	99	41	jspace	jspace	NOUN
iajs-1867	99	42	since	since	SCONJ
iajs-1867	99	43	x	x	PRON
iajs-1867	99	44	has	have	VERB
iajs-1867	99	45	no	no	DET
iajs-1867	99	46	proper	proper	ADJ
iajs-1867	99	47	closed	closed	ADJ
iajs-1867	99	48	cover	cover	NOUN
iajs-1867	99	49	.	.	PUNCT
iajs-1867	100	1	remark	remark	NOUN
iajs-1867	100	2	(	(	PUNCT
iajs-1867	100	3	3.9	3.9	NUM
iajs-1867	100	4	):	):	PUNCT
iajs-1867	100	5	if	if	SCONJ
iajs-1867	100	6	x	x	PRON
iajs-1867	100	7	is	be	AUX
iajs-1867	100	8	a	a	DET
iajs-1867	100	9	contractible	contractible	ADJ
iajs-1867	100	10	space	space	NOUN
iajs-1867	100	11	,	,	PUNCT
iajs-1867	100	12	then	then	ADV
iajs-1867	100	13	it	it	PRON
iajs-1867	100	14	is	be	AUX
iajs-1867	100	15	not	not	PART
iajs-1867	100	16	contractible	contractible	ADJ
iajs-1867	100	17	jspace	jspace	NOUN
iajs-1867	100	18	in	in	ADP
iajs-1867	100	19	general	general	ADJ
iajs-1867	100	20	.	.	PUNCT
iajs-1867	101	1	for	for	ADP
iajs-1867	101	2	instance	instance	NOUN
iajs-1867	101	3	:	:	PUNCT
iajs-1867	101	4	let	let	VERB
iajs-1867	101	5	x	x	PRON
iajs-1867	101	6	be	be	AUX
iajs-1867	101	7	a	a	DET
iajs-1867	101	8	subspace	subspace	NOUN
iajs-1867	101	9	of	of	ADP
iajs-1867	101	10	euclidian	euclidian	ADJ
iajs-1867	101	11	space	space	NOUN
iajs-1867	101	12	ℝ	ℝ	PROPN
iajs-1867	101	13	such	such	ADJ
iajs-1867	101	14	that	that	SCONJ
iajs-1867	101	15	x	x	SYM
iajs-1867	101	16	x	x	X
iajs-1867	101	17	,	,	PUNCT
iajs-1867	101	18	y	y	PROPN
iajs-1867	101	19	∈	∈	PROPN
iajs-1867	101	20	ℝ	ℝ	PROPN
iajs-1867	101	21	,	,	PUNCT
iajs-1867	101	22	x	x	PROPN
iajs-1867	101	23	1	1	NUM
iajs-1867	101	24	y	y	PROPN
iajs-1867	101	25	1	1	NUM
iajs-1867	101	26	∪	∪	ADP
iajs-1867	101	27	x	x	X
iajs-1867	101	28	,	,	PUNCT
iajs-1867	101	29	y	y	PROPN
iajs-1867	101	30	∈	∈	PROPN
iajs-1867	101	31	ℝ	ℝ	PROPN
iajs-1867	101	32	,	,	PUNCT
iajs-1867	101	33	x	x	PROPN
iajs-1867	101	34	1	1	NUM
iajs-1867	101	35	y	y	PROPN
iajs-1867	101	36	1	1	NUM
iajs-1867	101	37	.	.	PUNCT
iajs-1867	102	1	let	let	VERB
iajs-1867	102	2	e	e	X
iajs-1867	102	3	,	,	PUNCT
iajs-1867	102	4	f	f	X
iajs-1867	102	5	be	be	VERB
iajs-1867	102	6	two	two	NUM
iajs-1867	102	7	subsets	subset	NOUN
iajs-1867	102	8	of	of	ADP
iajs-1867	102	9	x	x	SYM
iajs-1867	102	10	such	such	ADJ
iajs-1867	102	11	that	that	SCONJ
iajs-1867	102	12	e	e	NOUN
iajs-1867	102	13	x	x	PROPN
iajs-1867	102	14	,	,	PUNCT
iajs-1867	102	15	y	y	PROPN
iajs-1867	102	16	∈	∈	PROPN
iajs-1867	102	17	ℝ	ℝ	PROPN
iajs-1867	102	18	,	,	PUNCT
iajs-1867	102	19	x	x	PROPN
iajs-1867	102	20	1	1	NUM
iajs-1867	102	21	y	y	PROPN
iajs-1867	102	22	1	1	NUM
iajs-1867	102	23	∪	∪	ADP
iajs-1867	102	24	x	x	X
iajs-1867	102	25	,	,	PUNCT
iajs-1867	102	26	y	y	PROPN
iajs-1867	102	27	∈	∈	PROPN
iajs-1867	102	28	ℝ	ℝ	PROPN
iajs-1867	102	29	,	,	PUNCT
iajs-1867	102	30	x	x	PROPN
iajs-1867	102	31	1	1	NUM
iajs-1867	102	32	y	y	PROPN
iajs-1867	102	33	1	1	NUM
iajs-1867	102	34	,	,	PUNCT
iajs-1867	102	35	f	f	PROPN
iajs-1867	102	36	x	x	PROPN
iajs-1867	102	37	,	,	PUNCT
iajs-1867	102	38	y	y	PROPN
iajs-1867	102	39	∈	∈	PROPN
iajs-1867	102	40	ℝ	ℝ	PROPN
iajs-1867	102	41	,	,	PUNCT
iajs-1867	102	42	x	x	PROPN
iajs-1867	102	43	1	1	NUM
iajs-1867	102	44	y	y	PROPN
iajs-1867	102	45	1	1	NUM
iajs-1867	102	46	∪	∪	ADP
iajs-1867	102	47	x	x	X
iajs-1867	102	48	,	,	PUNCT
iajs-1867	102	49	y	y	PROPN
iajs-1867	102	50	∈	∈	PROPN
iajs-1867	102	51	ℝ	ℝ	PROPN
iajs-1867	102	52	,	,	PUNCT
iajs-1867	102	53	x	x	PROPN
iajs-1867	102	54	1	1	NUM
iajs-1867	102	55	y	y	NOUN
iajs-1867	102	56	1	1	NUM
iajs-1867	102	57	then	then	ADV
iajs-1867	102	58	e	e	PROPN
iajs-1867	102	59	and	and	CCONJ
iajs-1867	102	60	f	f	PROPN
iajs-1867	102	61	are	be	AUX
iajs-1867	102	62	closed	close	VERB
iajs-1867	102	63	subsets	subset	NOUN
iajs-1867	102	64	of	of	ADP
iajs-1867	102	65	x	x	PUNCT
iajs-1867	102	66	with	with	ADP
iajs-1867	102	67	a	a	DET
iajs-1867	102	68	∪	∪	X
iajs-1867	102	69	b	b	NOUN
iajs-1867	102	70	x	x	NOUN
iajs-1867	102	71	and	and	CCONJ
iajs-1867	102	72	e⋂f	e⋂f	PROPN
iajs-1867	102	73	x	x	NOUN
iajs-1867	102	74	,	,	PUNCT
iajs-1867	102	75	y	y	PROPN
iajs-1867	102	76	∈	∈	PROPN
iajs-1867	102	77	ℝ	ℝ	PROPN
iajs-1867	102	78	,	,	PUNCT
iajs-1867	102	79	x	x	PROPN
iajs-1867	102	80	1	1	NUM
iajs-1867	102	81	y	y	PROPN
iajs-1867	102	82	1	1	NUM
iajs-1867	102	83	∪	∪	ADP
iajs-1867	102	84	x	x	X
iajs-1867	102	85	,	,	PUNCT
iajs-1867	102	86	y	y	PROPN
iajs-1867	102	87	∈	∈	PROPN
iajs-1867	102	88	ℝ	ℝ	PROPN
iajs-1867	102	89	,	,	PUNCT
iajs-1867	102	90	x	x	PROPN
iajs-1867	102	91	1	1	NUM
iajs-1867	102	92	y	y	PROPN
iajs-1867	102	93	1	1	NUM
iajs-1867	102	94	which	which	PRON
iajs-1867	102	95	is	be	AUX
iajs-1867	102	96	compact	compact	ADJ
iajs-1867	102	97	subset	subset	NOUN
iajs-1867	102	98	of	of	ADP
iajs-1867	102	99	x	x	PRON
iajs-1867	102	100	,	,	PUNCT
iajs-1867	102	101	but	but	CCONJ
iajs-1867	102	102	neither	neither	CCONJ
iajs-1867	102	103	e	e	NOUN
iajs-1867	102	104	nor	nor	CCONJ
iajs-1867	102	105	f	f	PROPN
iajs-1867	102	106	is	be	AUX
iajs-1867	102	107	contractible	contractible	ADJ
iajs-1867	102	108	.	.	PUNCT
iajs-1867	103	1	hence	hence	ADV
iajs-1867	103	2	x	x	VERB
iajs-1867	103	3	is	be	AUX
iajs-1867	103	4	not	not	PART
iajs-1867	103	5	contractible	contractible	ADJ
iajs-1867	103	6	jspace	jspace	NOUN
iajs-1867	103	7	,	,	PUNCT
iajs-1867	103	8	but	but	CCONJ
iajs-1867	103	9	x	x	X
iajs-1867	103	10	is	be	AUX
iajs-1867	103	11	contractible	contractible	ADJ
iajs-1867	103	12	since	since	SCONJ
iajs-1867	103	13	x	x	PRON
iajs-1867	103	14	is	be	AUX
iajs-1867	103	15	closed	close	VERB
iajs-1867	103	16	ball	ball	NOUN
iajs-1867	103	17	in	in	ADP
iajs-1867	103	18	ℝ	ℝ	PROPN
iajs-1867	103	19	.	.	PUNCT
iajs-1867	104	1	ihsciconf	ihsciconf	PROPN
iajs-1867	104	2	2017	2017	NUM
iajs-1867	104	3	special	special	ADJ
iajs-1867	104	4	issue	issue	NOUN
iajs-1867	104	5	ibn	ibn	PROPN
iajs-1867	104	6	al	al	PROPN
iajs-1867	104	7	-	-	PUNCT
iajs-1867	104	8	haitham	haitham	PROPN
iajs-1867	104	9	journal	journal	PROPN
iajs-1867	104	10	for	for	ADP
iajs-1867	104	11	pure	pure	ADJ
iajs-1867	104	12	and	and	CCONJ
iajs-1867	104	13	applied	apply	VERB
iajs-1867	104	14	science	science	NOUN
iajs-1867	104	15	https://doi.org/	https://doi.org/	NOUN
iajs-1867	104	16	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	104	17	for	for	ADP
iajs-1867	104	18	more	more	ADJ
iajs-1867	104	19	information	information	NOUN
iajs-1867	104	20	about	about	ADP
iajs-1867	104	21	the	the	DET
iajs-1867	104	22	conference	conference	NOUN
iajs-1867	104	23	please	please	INTJ
iajs-1867	104	24	visit	visit	VERB
iajs-1867	104	25	the	the	DET
iajs-1867	104	26	websites	website	NOUN
iajs-1867	104	27	:	:	PUNCT
iajs-1867	104	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1867	104	29	      	      	SPACE
iajs-1867	104	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	104	31	                                                                            	                                                                            	SPACE
iajs-1867	104	32	mathematics	mathematic	NOUN
iajs-1867	104	33	|334	|334	PROPN
iajs-1867	104	34	  	  	SPACE
iajs-1867	104	35	remark	remark	NOUN
iajs-1867	104	36	(	(	PUNCT
iajs-1867	104	37	3.10	3.10	NUM
iajs-1867	104	38	):	):	PUNCT
iajs-1867	104	39	a	a	DET
iajs-1867	104	40	contractible	contractible	ADJ
iajs-1867	104	41	jspace	jspace	NOUN
iajs-1867	104	42	need	need	AUX
iajs-1867	104	43	not	not	PART
iajs-1867	104	44	be	be	AUX
iajs-1867	104	45	contractible	contractible	ADJ
iajs-1867	104	46	.	.	PUNCT
iajs-1867	105	1	for	for	ADP
iajs-1867	105	2	example	example	NOUN
iajs-1867	105	3	:	:	PUNCT
iajs-1867	105	4	the	the	DET
iajs-1867	105	5	unite	unite	NOUN
iajs-1867	105	6	circle	circle	NOUN
iajs-1867	105	7	s	s	PRON
iajs-1867	105	8	as	as	ADP
iajs-1867	105	9	a	a	DET
iajs-1867	105	10	subspace	subspace	NOUN
iajs-1867	105	11	of	of	ADP
iajs-1867	105	12	ℝ	ℝ	PROPN
iajs-1867	105	13	is	be	AUX
iajs-1867	105	14	not	not	PART
iajs-1867	105	15	contractible	contractible	ADJ
iajs-1867	105	16	,	,	PUNCT
iajs-1867	105	17	but	but	CCONJ
iajs-1867	105	18	it	it	PRON
iajs-1867	105	19	is	be	AUX
iajs-1867	105	20	contractible	contractible	ADJ
iajs-1867	105	21	jspace	jspace	NOUN
iajs-1867	105	22	since	since	SCONJ
iajs-1867	105	23	every	every	DET
iajs-1867	105	24	proper	proper	ADJ
iajs-1867	105	25	subset	subset	NOUN
iajs-1867	105	26	of	of	ADP
iajs-1867	105	27	s	s	PROPN
iajs-1867	105	28	is	be	AUX
iajs-1867	105	29	contractible	contractible	ADJ
iajs-1867	105	30	.	.	PUNCT
iajs-1867	106	1	theorem	theorem	NOUN
iajs-1867	106	2	(	(	PUNCT
iajs-1867	106	3	3.11	3.11	NUM
iajs-1867	106	4	):	):	PUNCT
iajs-1867	106	5	for	for	ADP
iajs-1867	106	6	any	any	DET
iajs-1867	106	7	space	space	NOUN
iajs-1867	106	8	x	x	NOUN
iajs-1867	106	9	,	,	PUNCT
iajs-1867	106	10	these	these	DET
iajs-1867	106	11	following	follow	VERB
iajs-1867	106	12	conditions	condition	NOUN
iajs-1867	106	13	are	be	AUX
iajs-1867	106	14	valent	valent	NOUN
iajs-1867	106	15	:	:	PUNCT
iajs-1867	107	1	1	1	X
iajs-1867	107	2	.	.	X
iajs-1867	107	3	x	x	PRON
iajs-1867	107	4	is	be	AUX
iajs-1867	107	5	a	a	DET
iajs-1867	107	6	contractible	contractible	ADJ
iajs-1867	107	7	jspace	jspace	NOUN
iajs-1867	107	8	.	.	PUNCT
iajs-1867	108	1	2	2	X
iajs-1867	108	2	.	.	X
iajs-1867	108	3	for	for	ADP
iajs-1867	108	4	every	every	DET
iajs-1867	108	5	proper	proper	ADJ
iajs-1867	108	6	closed	closed	ADJ
iajs-1867	108	7	cover	cover	NOUN
iajs-1867	108	8	e	e	NOUN
iajs-1867	108	9	,	,	PUNCT
iajs-1867	108	10	f	f	PROPN
iajs-1867	108	11	with	with	ADP
iajs-1867	108	12	e	e	PROPN
iajs-1867	108	13	∩	∩	X
iajs-1867	108	14	f	f	X
iajs-1867	108	15	compact	compact	ADJ
iajs-1867	108	16	e	e	PROPN
iajs-1867	108	17	or	or	CCONJ
iajs-1867	108	18	f	f	PROPN
iajs-1867	108	19	is	be	AUX
iajs-1867	108	20	homotopy	homotopy	VERB
iajs-1867	108	21	equivalent	equivalent	ADJ
iajs-1867	108	22	to	to	ADP
iajs-1867	108	23	a	a	DET
iajs-1867	108	24	point	point	NOUN
iajs-1867	108	25	.	.	PUNCT
iajs-1867	109	1	3	3	X
iajs-1867	109	2	.	.	X
iajs-1867	109	3	for	for	ADP
iajs-1867	109	4	every	every	DET
iajs-1867	109	5	proper	proper	ADJ
iajs-1867	109	6	closed	closed	ADJ
iajs-1867	109	7	cover	cover	NOUN
iajs-1867	109	8	e	e	NOUN
iajs-1867	109	9	,	,	PUNCT
iajs-1867	109	10	f	f	PROPN
iajs-1867	109	11	with	with	ADP
iajs-1867	109	12	e	e	PROPN
iajs-1867	109	13	∩	∩	PROPN
iajs-1867	109	14	f	f	PROPN
iajs-1867	109	15	compact	compact	ADJ
iajs-1867	109	16	,	,	PUNCT
iajs-1867	109	17	there	there	PRON
iajs-1867	109	18	exists	exist	VERB
iajs-1867	109	19	x	x	X
iajs-1867	109	20	°	°	ADP
iajs-1867	109	21	∈	∈	PROPN
iajs-1867	109	22	e	e	NOUN
iajs-1867	109	23	or	or	CCONJ
iajs-1867	109	24	x	x	PROPN
iajs-1867	109	25	°	°	PROPN
iajs-1867	109	26	∈	∈	PROPN
iajs-1867	110	1	f	f	PROPN
iajs-1867	110	2	such	such	ADJ
iajs-1867	110	3	that	that	SCONJ
iajs-1867	110	4	x	x	PROPN
iajs-1867	110	5	°	°	PRON
iajs-1867	110	6	is	be	AUX
iajs-1867	110	7	a	a	DET
iajs-1867	110	8	deformation	deformation	NOUN
iajs-1867	110	9	retract	retract	NOUN
iajs-1867	110	10	of	of	ADP
iajs-1867	110	11	e	e	NOUN
iajs-1867	110	12	(	(	PUNCT
iajs-1867	110	13	or	or	CCONJ
iajs-1867	110	14	of	of	ADP
iajs-1867	110	15	f	f	PROPN
iajs-1867	110	16	)	)	PUNCT
iajs-1867	110	17	.	.	PUNCT
iajs-1867	111	1	4	4	X
iajs-1867	111	2	.	.	X
iajs-1867	111	3	for	for	ADP
iajs-1867	111	4	every	every	DET
iajs-1867	111	5	proper	proper	ADJ
iajs-1867	111	6	closed	closed	ADJ
iajs-1867	111	7	cover	cover	NOUN
iajs-1867	111	8	e	e	NOUN
iajs-1867	111	9	,	,	PUNCT
iajs-1867	111	10	f	f	PROPN
iajs-1867	111	11	with	with	ADP
iajs-1867	111	12	e	e	PROPN
iajs-1867	111	13	∩	∩	PROPN
iajs-1867	111	14	f	f	PROPN
iajs-1867	111	15	compact	compact	ADJ
iajs-1867	111	16	,	,	PUNCT
iajs-1867	111	17	e	e	NOUN
iajs-1867	111	18	or	or	CCONJ
iajs-1867	111	19	f	f	PROPN
iajs-1867	111	20	is	be	AUX
iajs-1867	111	21	a	a	DET
iajs-1867	111	22	retract	retract	NOUN
iajs-1867	111	23	of	of	ADP
iajs-1867	111	24	any	any	DET
iajs-1867	111	25	cone	cone	NOUN
iajs-1867	111	26	over	over	ADP
iajs-1867	111	27	it	it	PRON
iajs-1867	111	28	.	.	PUNCT
iajs-1867	112	1	5	5	X
iajs-1867	112	2	.	.	X
iajs-1867	112	3	for	for	ADP
iajs-1867	112	4	every	every	DET
iajs-1867	112	5	proper	proper	ADJ
iajs-1867	112	6	closed	closed	ADJ
iajs-1867	112	7	cover	cover	NOUN
iajs-1867	112	8	e	e	NOUN
iajs-1867	112	9	,	,	PUNCT
iajs-1867	112	10	f	f	PROPN
iajs-1867	112	11	with	with	ADP
iajs-1867	112	12	e	e	PROPN
iajs-1867	112	13	∩	∩	PROPN
iajs-1867	112	14	f	f	PROPN
iajs-1867	112	15	compact	compact	ADJ
iajs-1867	112	16	,	,	PUNCT
iajs-1867	112	17	every	every	DET
iajs-1867	112	18	map	map	NOUN
iajs-1867	112	19	f	f	PROPN
iajs-1867	112	20	from	from	ADP
iajs-1867	112	21	e	e	PROPN
iajs-1867	112	22	or	or	CCONJ
iajs-1867	112	23	f	f	PROPN
iajs-1867	112	24	to	to	ADP
iajs-1867	112	25	an	an	DET
iajs-1867	112	26	arbitrary	arbitrary	ADJ
iajs-1867	112	27	space	space	NOUN
iajs-1867	112	28	y	y	NOUN
iajs-1867	112	29	,	,	PUNCT
iajs-1867	112	30	is	be	AUX
iajs-1867	112	31	nullhomotopic	nullhomotopic	ADJ
iajs-1867	112	32	.	.	PUNCT
iajs-1867	113	1	6	6	NUM
iajs-1867	113	2	.	.	X
iajs-1867	113	3	for	for	ADP
iajs-1867	113	4	every	every	DET
iajs-1867	113	5	proper	proper	ADJ
iajs-1867	113	6	closed	closed	ADJ
iajs-1867	113	7	cover	cover	NOUN
iajs-1867	113	8	e	e	NOUN
iajs-1867	113	9	,	,	PUNCT
iajs-1867	113	10	f	f	PROPN
iajs-1867	113	11	with	with	ADP
iajs-1867	113	12	e	e	PROPN
iajs-1867	113	13	∩	∩	PROPN
iajs-1867	113	14	f	f	PROPN
iajs-1867	113	15	compact	compact	ADJ
iajs-1867	113	16	,	,	PUNCT
iajs-1867	113	17	every	every	DET
iajs-1867	113	18	map	map	NOUN
iajs-1867	113	19	f	f	NOUN
iajs-1867	113	20	from	from	ADP
iajs-1867	113	21	an	an	DET
iajs-1867	113	22	arbitrary	arbitrary	ADJ
iajs-1867	113	23	space	space	NOUN
iajs-1867	113	24	y	y	NOUN
iajs-1867	113	25	to	to	ADP
iajs-1867	113	26	e	e	PROPN
iajs-1867	113	27	or	or	CCONJ
iajs-1867	113	28	f	f	PROPN
iajs-1867	113	29	is	be	AUX
iajs-1867	113	30	nullhomotopic	nullhomotopic	ADJ
iajs-1867	113	31	.	.	PUNCT
iajs-1867	114	1	proof	proof	NOUN
iajs-1867	114	2	:	:	PUNCT
iajs-1867	114	3	follows	follow	VERB
iajs-1867	114	4	from	from	ADP
iajs-1867	114	5	theorem	theorem	NOUN
iajs-1867	114	6	(	(	PUNCT
iajs-1867	114	7	2.15	2.15	NUM
iajs-1867	114	8	)	)	PUNCT
iajs-1867	114	9	and	and	CCONJ
iajs-1867	114	10	definition	definition	NOUN
iajs-1867	114	11	(	(	PUNCT
iajs-1867	114	12	3.1	3.1	NUM
iajs-1867	114	13	)	)	PUNCT
iajs-1867	114	14	.	.	PUNCT
iajs-1867	115	1	proposition	proposition	NOUN
iajs-1867	115	2	(	(	PUNCT
iajs-1867	115	3	3.12	3.12	NUM
iajs-1867	115	4	):	):	PUNCT
iajs-1867	115	5	if	if	SCONJ
iajs-1867	115	6	x	x	PRON
iajs-1867	115	7	is	be	AUX
iajs-1867	115	8	a	a	DET
iajs-1867	115	9	contractible	contractible	ADJ
iajs-1867	115	10	jspace	jspace	NOUN
iajs-1867	115	11	,	,	PUNCT
iajs-1867	115	12	then	then	ADV
iajs-1867	115	13	for	for	ADP
iajs-1867	115	14	every	every	DET
iajs-1867	115	15	proper	proper	ADJ
iajs-1867	115	16	closed	closed	ADJ
iajs-1867	115	17	cover	cover	NOUN
iajs-1867	115	18	e	e	NOUN
iajs-1867	115	19	,	,	PUNCT
iajs-1867	115	20	f	f	PROPN
iajs-1867	115	21	with	with	ADP
iajs-1867	115	22	e	e	PROPN
iajs-1867	115	23	∩	∩	PROPN
iajs-1867	115	24	f	f	PROPN
iajs-1867	115	25	compact	compact	ADJ
iajs-1867	115	26	,	,	PUNCT
iajs-1867	115	27	e	e	NOUN
iajs-1867	115	28	or	or	CCONJ
iajs-1867	115	29	f	f	PROPN
iajs-1867	115	30	is	be	AUX
iajs-1867	115	31	path	path	NOUN
iajs-1867	115	32	connected	connect	VERB
iajs-1867	115	33	.	.	PUNCT
iajs-1867	116	1	proof	proof	NOUN
iajs-1867	116	2	:	:	PUNCT
iajs-1867	116	3	follows	follow	VERB
iajs-1867	116	4	from	from	ADP
iajs-1867	116	5	proposition	proposition	NOUN
iajs-1867	116	6	(	(	PUNCT
iajs-1867	116	7	2.16	2.16	NUM
iajs-1867	116	8	)	)	PUNCT
iajs-1867	116	9	and	and	CCONJ
iajs-1867	116	10	definition	definition	NOUN
iajs-1867	116	11	(	(	PUNCT
iajs-1867	116	12	3.1	3.1	NUM
iajs-1867	116	13	)	)	PUNCT
iajs-1867	116	14	.	.	PUNCT
iajs-1867	117	1	remark	remark	NOUN
iajs-1867	117	2	(	(	PUNCT
iajs-1867	117	3	3.13	3.13	NUM
iajs-1867	117	4	):	):	PUNCT
iajs-1867	117	5	if	if	SCONJ
iajs-1867	117	6	for	for	ADP
iajs-1867	117	7	every	every	DET
iajs-1867	117	8	proper	proper	ADJ
iajs-1867	117	9	closed	closed	ADJ
iajs-1867	117	10	cover	cover	NOUN
iajs-1867	117	11	e	e	NOUN
iajs-1867	117	12	,	,	PUNCT
iajs-1867	117	13	f	f	PROPN
iajs-1867	117	14	of	of	ADP
iajs-1867	117	15	a	a	DET
iajs-1867	117	16	space	space	NOUN
iajs-1867	117	17	x	x	PUNCT
iajs-1867	117	18	with	with	ADP
iajs-1867	117	19	e	e	NOUN
iajs-1867	117	20	∩	∩	X
iajs-1867	117	21	f	f	PROPN
iajs-1867	117	22	compact	compact	ADJ
iajs-1867	117	23	,	,	PUNCT
iajs-1867	117	24	e	e	NOUN
iajs-1867	117	25	or	or	CCONJ
iajs-1867	117	26	f	f	PROPN
iajs-1867	117	27	is	be	AUX
iajs-1867	117	28	path	path	NOUN
iajs-1867	117	29	connected	connect	VERB
iajs-1867	117	30	,	,	PUNCT
iajs-1867	117	31	then	then	ADV
iajs-1867	117	32	x	x	PRON
iajs-1867	117	33	need	need	AUX
iajs-1867	117	34	not	not	PART
iajs-1867	117	35	be	be	AUX
iajs-1867	117	36	contractible	contractible	ADJ
iajs-1867	117	37	jspace	jspace	NOUN
iajs-1867	117	38	.	.	PUNCT
iajs-1867	118	1	for	for	ADP
iajs-1867	118	2	example	example	NOUN
iajs-1867	118	3	:	:	PUNCT
iajs-1867	118	4	let	let	VERB
iajs-1867	118	5	us	we	PRON
iajs-1867	118	6	take	take	VERB
iajs-1867	118	7	the	the	DET
iajs-1867	118	8	example	example	NOUN
iajs-1867	118	9	of	of	ADP
iajs-1867	118	10	remark	remark	NOUN
iajs-1867	118	11	(	(	PUNCT
iajs-1867	118	12	3.9	3.9	NUM
iajs-1867	118	13	)	)	PUNCT
iajs-1867	118	14	,	,	PUNCT
iajs-1867	118	15	as	as	SCONJ
iajs-1867	118	16	we	we	PRON
iajs-1867	118	17	saw	see	VERB
iajs-1867	118	18	in	in	ADP
iajs-1867	118	19	this	this	DET
iajs-1867	118	20	example	example	NOUN
iajs-1867	118	21	x	x	PUNCT
iajs-1867	118	22	is	be	AUX
iajs-1867	118	23	not	not	PART
iajs-1867	118	24	contractible	contractible	ADJ
iajs-1867	118	25	jspace	jspace	NOUN
iajs-1867	118	26	,	,	PUNCT
iajs-1867	118	27	but	but	CCONJ
iajs-1867	118	28	for	for	ADP
iajs-1867	118	29	every	every	DET
iajs-1867	118	30	proper	proper	ADJ
iajs-1867	118	31	closed	closed	ADJ
iajs-1867	118	32	cover	cover	NOUN
iajs-1867	118	33	e	e	NOUN
iajs-1867	118	34	,	,	PUNCT
iajs-1867	118	35	f	f	PROPN
iajs-1867	118	36	of	of	ADP
iajs-1867	118	37	x	x	PUNCT
iajs-1867	118	38	with	with	ADP
iajs-1867	118	39	e	e	NOUN
iajs-1867	118	40	∩	∩	X
iajs-1867	118	41	f	f	PROPN
iajs-1867	118	42	compact	compact	ADJ
iajs-1867	118	43	,	,	PUNCT
iajs-1867	118	44	e	e	NOUN
iajs-1867	118	45	or	or	CCONJ
iajs-1867	118	46	f	f	PROPN
iajs-1867	118	47	is	be	AUX
iajs-1867	118	48	path	path	NOUN
iajs-1867	118	49	connected	connect	VERB
iajs-1867	118	50	.	.	PUNCT
iajs-1867	119	1	proposition	proposition	NOUN
iajs-1867	119	2	(	(	PUNCT
iajs-1867	119	3	3.14	3.14	NUM
iajs-1867	119	4	):	):	PUNCT
iajs-1867	119	5	if	if	SCONJ
iajs-1867	119	6	x	x	PRON
iajs-1867	119	7	is	be	AUX
iajs-1867	119	8	a	a	DET
iajs-1867	119	9	contractible	contractible	ADJ
iajs-1867	119	10	jspace	jspace	NOUN
iajs-1867	119	11	,	,	PUNCT
iajs-1867	119	12	then	then	ADV
iajs-1867	119	13	for	for	ADP
iajs-1867	119	14	every	every	DET
iajs-1867	119	15	proper	proper	ADJ
iajs-1867	119	16	closed	closed	ADJ
iajs-1867	119	17	cover	cover	NOUN
iajs-1867	119	18	e	e	NOUN
iajs-1867	119	19	,	,	PUNCT
iajs-1867	119	20	f	f	PROPN
iajs-1867	119	21	with	with	ADP
iajs-1867	119	22	e	e	PROPN
iajs-1867	119	23	∩	∩	PROPN
iajs-1867	119	24	f	f	PROPN
iajs-1867	119	25	compact	compact	ADJ
iajs-1867	119	26	,	,	PUNCT
iajs-1867	119	27	e	e	PROPN
iajs-1867	119	28	or	or	CCONJ
iajs-1867	119	29	f	f	PROPN
iajs-1867	119	30	is	be	AUX
iajs-1867	119	31	simply	simply	ADV
iajs-1867	119	32	connected	connect	VERB
iajs-1867	119	33	.	.	PUNCT
iajs-1867	120	1	proof	proof	NOUN
iajs-1867	120	2	:	:	PUNCT
iajs-1867	120	3	follows	follow	VERB
iajs-1867	120	4	from	from	ADP
iajs-1867	120	5	proposition	proposition	NOUN
iajs-1867	120	6	(	(	PUNCT
iajs-1867	120	7	2.17	2.17	NUM
iajs-1867	120	8	)	)	PUNCT
iajs-1867	120	9	and	and	CCONJ
iajs-1867	120	10	definition	definition	NOUN
iajs-1867	120	11	(	(	PUNCT
iajs-1867	120	12	3.1	3.1	NUM
iajs-1867	120	13	)	)	PUNCT
iajs-1867	120	14	.	.	PUNCT
iajs-1867	121	1	remark	remark	NOUN
iajs-1867	121	2	(	(	PUNCT
iajs-1867	121	3	3.15	3.15	NUM
iajs-1867	121	4	):	):	PUNCT
iajs-1867	121	5	the	the	DET
iajs-1867	121	6	opposite	opposite	ADJ
iajs-1867	121	7	direction	direction	NOUN
iajs-1867	121	8	of	of	ADP
iajs-1867	121	9	proposition	proposition	NOUN
iajs-1867	121	10	(	(	PUNCT
iajs-1867	121	11	3.14	3.14	NUM
iajs-1867	121	12	)	)	PUNCT
iajs-1867	121	13	is	be	AUX
iajs-1867	121	14	not	not	PART
iajs-1867	121	15	true	true	ADJ
iajs-1867	121	16	in	in	ADP
iajs-1867	121	17	general	general	ADJ
iajs-1867	121	18	.	.	PUNCT
iajs-1867	122	1	for	for	ADP
iajs-1867	122	2	example	example	NOUN
iajs-1867	122	3	:	:	PUNCT
iajs-1867	122	4	let	let	VERB
iajs-1867	122	5	x	x	PRON
iajs-1867	122	6	be	be	AUX
iajs-1867	122	7	a	a	DET
iajs-1867	122	8	subspace	subspace	NOUN
iajs-1867	122	9	of	of	ADP
iajs-1867	122	10	ℝ	ℝ	PROPN
iajs-1867	122	11	such	such	DET
iajs-1867	122	12	that	that	SCONJ
iajs-1867	122	13	x	x	SYM
iajs-1867	122	14	e	e	NOUN
iajs-1867	122	15	∪	∪	ADP
iajs-1867	122	16	f	f	PROPN
iajs-1867	122	17	,	,	PUNCT
iajs-1867	122	18	where	where	SCONJ
iajs-1867	122	19	e	e	PROPN
iajs-1867	122	20	x	x	PROPN
iajs-1867	122	21	,	,	PUNCT
iajs-1867	122	22	y	y	PROPN
iajs-1867	122	23	,	,	PUNCT
iajs-1867	122	24	z	z	PROPN
iajs-1867	122	25	∈	∈	PROPN
iajs-1867	122	26	ℝ	ℝ	PROPN
iajs-1867	122	27	,	,	PUNCT
iajs-1867	122	28	x	x	PROPN
iajs-1867	122	29	1	1	NUM
iajs-1867	122	30	y	y	PROPN
iajs-1867	122	31	z	z	PROPN
iajs-1867	122	32	1	1	NUM
iajs-1867	122	33	and	and	CCONJ
iajs-1867	122	34	f	f	PROPN
iajs-1867	122	35	x	x	PROPN
iajs-1867	122	36	,	,	PUNCT
iajs-1867	122	37	y	y	PROPN
iajs-1867	122	38	,	,	PUNCT
iajs-1867	122	39	z	z	PROPN
iajs-1867	122	40	∈	∈	PROPN
iajs-1867	122	41	ℝ	ℝ	PROPN
iajs-1867	122	42	,	,	PUNCT
iajs-1867	122	43	x	x	PROPN
iajs-1867	122	44	3	3	NUM
iajs-1867	122	45	y	y	PROPN
iajs-1867	122	46	z	z	PROPN
iajs-1867	122	47	1	1	NUM
iajs-1867	122	48	,	,	PUNCT
iajs-1867	122	49	then	then	ADV
iajs-1867	122	50	e	e	X
iajs-1867	122	51	,	,	PUNCT
iajs-1867	122	52	f	f	PROPN
iajs-1867	122	53	is	be	AUX
iajs-1867	122	54	a	a	DET
iajs-1867	122	55	closed	closed	ADJ
iajs-1867	122	56	cover	cover	NOUN
iajs-1867	122	57	of	of	ADP
iajs-1867	122	58	x	x	PUNCT
iajs-1867	122	59	with	with	ADP
iajs-1867	122	60	e	e	NOUN
iajs-1867	122	61	∩	∩	NOUN
iajs-1867	122	62	f	f	PROPN
iajs-1867	122	63	2,0,0	2,0,0	NUM
iajs-1867	122	64	which	which	PRON
iajs-1867	122	65	is	be	AUX
iajs-1867	122	66	compact	compact	ADJ
iajs-1867	122	67	,	,	PUNCT
iajs-1867	122	68	but	but	CCONJ
iajs-1867	122	69	neither	neither	CCONJ
iajs-1867	122	70	e	e	NOUN
iajs-1867	122	71	nor	nor	CCONJ
iajs-1867	122	72	f	f	PROPN
iajs-1867	122	73	is	be	AUX
iajs-1867	122	74	contractible	contractible	ADJ
iajs-1867	122	75	.	.	PUNCT
iajs-1867	123	1	hence	hence	ADV
iajs-1867	123	2	x	x	VERB
iajs-1867	123	3	is	be	AUX
iajs-1867	123	4	not	not	PART
iajs-1867	123	5	contractible	contractible	ADJ
iajs-1867	123	6	j	j	NOUN
iajs-1867	123	7	space	space	NOUN
iajs-1867	123	8	,	,	PUNCT
iajs-1867	123	9	but	but	CCONJ
iajs-1867	123	10	e	e	X
iajs-1867	123	11	and	and	CCONJ
iajs-1867	123	12	f	f	PROPN
iajs-1867	123	13	are	be	AUX
iajs-1867	123	14	simply	simply	ADV
iajs-1867	123	15	connected	connect	VERB
iajs-1867	123	16	since	since	SCONJ
iajs-1867	123	17	both	both	PRON
iajs-1867	123	18	of	of	ADP
iajs-1867	123	19	them	they	PRON
iajs-1867	123	20	are	be	AUX
iajs-1867	123	21	homotopic	homotopic	ADJ
iajs-1867	123	22	equivalent	equivalent	ADJ
iajs-1867	123	23	to	to	ADP
iajs-1867	123	24	s	s	PROPN
iajs-1867	123	25	.	.	PUNCT
iajs-1867	124	1	remark	remark	PROPN
iajs-1867	124	2	(	(	PUNCT
iajs-1867	124	3	3.16	3.16	NUM
iajs-1867	124	4	):	):	PUNCT
iajs-1867	124	5	the	the	DET
iajs-1867	124	6	property	property	NOUN
iajs-1867	124	7	of	of	ADP
iajs-1867	124	8	being	be	AUX
iajs-1867	124	9	contractible	contractible	ADJ
iajs-1867	124	10	jspace	jspace	NOUN
iajs-1867	124	11	is	be	AUX
iajs-1867	124	12	not	not	PART
iajs-1867	124	13	a	a	DET
iajs-1867	124	14	weak	weak	ADJ
iajs-1867	124	15	hereditary	hereditary	ADJ
iajs-1867	124	16	property	property	NOUN
iajs-1867	124	17	,	,	PUNCT
iajs-1867	124	18	and	and	CCONJ
iajs-1867	124	19	thus	thus	ADV
iajs-1867	124	20	not	not	PART
iajs-1867	124	21	hereditary	hereditary	ADJ
iajs-1867	124	22	property	property	NOUN
iajs-1867	124	23	.	.	PUNCT
iajs-1867	125	1	for	for	ADP
iajs-1867	125	2	example	example	NOUN
iajs-1867	125	3	:	:	PUNCT
iajs-1867	125	4	the	the	DET
iajs-1867	125	5	usual	usual	ADJ
iajs-1867	125	6	space	space	NOUN
iajs-1867	125	7	ℝ	ℝ	PROPN
iajs-1867	125	8	is	be	AUX
iajs-1867	125	9	a	a	DET
iajs-1867	125	10	contractible	contractible	ADJ
iajs-1867	125	11	jspace	jspace	NOUN
iajs-1867	125	12	,	,	PUNCT
iajs-1867	125	13	but	but	CCONJ
iajs-1867	125	14	the	the	DET
iajs-1867	125	15	natural	natural	ADJ
iajs-1867	125	16	numbers	number	NOUN
iajs-1867	125	17	ℕ	ℕ	PROPN
iajs-1867	125	18	as	as	ADP
iajs-1867	125	19	a	a	DET
iajs-1867	125	20	subspace	subspace	NOUN
iajs-1867	125	21	of	of	ADP
iajs-1867	125	22	ℝ	ℝ	PROPN
iajs-1867	125	23	is	be	AUX
iajs-1867	125	24	not	not	PART
iajs-1867	125	25	contractible	contractible	ADJ
iajs-1867	125	26	jspace	jspace	NOUN
iajs-1867	125	27	since	since	SCONJ
iajs-1867	125	28	the	the	DET
iajs-1867	125	29	induced	induced	ADJ
iajs-1867	125	30	topology	topology	NOUN
iajs-1867	125	31	of	of	ADP
iajs-1867	125	32	the	the	DET
iajs-1867	125	33	usual	usual	ADJ
iajs-1867	125	34	topology	topology	NOUN
iajs-1867	125	35	with	with	ADP
iajs-1867	125	36	respect	respect	NOUN
iajs-1867	125	37	to	to	ADP
iajs-1867	125	38	ℕ	ℕ	PROPN
iajs-1867	125	39	is	be	AUX
iajs-1867	125	40	the	the	DET
iajs-1867	125	41	discrete	discrete	ADJ
iajs-1867	125	42	topology	topology	NOUN
iajs-1867	125	43	.	.	PUNCT
iajs-1867	126	1	proposition	proposition	NOUN
iajs-1867	126	2	(	(	PUNCT
iajs-1867	126	3	3.17	3.17	NUM
iajs-1867	126	4	):	):	PUNCT
iajs-1867	126	5	if	if	SCONJ
iajs-1867	126	6	a	a	PRON
iajs-1867	126	7	is	be	AUX
iajs-1867	126	8	a	a	DET
iajs-1867	126	9	subset	subset	NOUN
iajs-1867	126	10	of	of	ADP
iajs-1867	126	11	a	a	DET
iajs-1867	126	12	contractible	contractible	ADJ
iajs-1867	126	13	jspace	jspace	NOUN
iajs-1867	126	14	with	with	ADP
iajs-1867	126	15	compact	compact	ADJ
iajs-1867	126	16	boundary	boundary	NOUN
iajs-1867	126	17	,	,	PUNCT
iajs-1867	126	18	then	then	ADV
iajs-1867	126	19	cl	cl	VERB
iajs-1867	126	20	a	a	PRON
iajs-1867	126	21	or	or	CCONJ
iajs-1867	126	22	cl	cl	NOUN
iajs-1867	126	23	x\a	x\a	PUNCT
iajs-1867	126	24	is	be	AUX
iajs-1867	126	25	contractible	contractible	ADJ
iajs-1867	126	26	.	.	PUNCT
iajs-1867	127	1	proof	proof	NOUN
iajs-1867	127	2	:	:	PUNCT
iajs-1867	127	3	consider	consider	VERB
iajs-1867	127	4	the	the	DET
iajs-1867	127	5	closed	closed	ADJ
iajs-1867	127	6	cover	cover	NOUN
iajs-1867	127	7	cl	cl	NOUN
iajs-1867	127	8	a	a	DET
iajs-1867	127	9	,	,	PUNCT
iajs-1867	127	10	cl	cl	NOUN
iajs-1867	127	11	x\a	x\a	PUNCT
iajs-1867	127	12	of	of	ADP
iajs-1867	127	13	x	x	PRON
iajs-1867	127	14	,	,	PUNCT
iajs-1867	127	15	such	such	ADJ
iajs-1867	127	16	that	that	DET
iajs-1867	127	17	cl	cl	NOUN
iajs-1867	127	18	a	a	DET
iajs-1867	127	19	∩	∩	ADJ
iajs-1867	127	20	cl	cl	NOUN
iajs-1867	127	21	x\a	x\a	PUNCT
iajs-1867	128	1	∂a	∂a	ADP
iajs-1867	128	2	which	which	PRON
iajs-1867	128	3	is	be	AUX
iajs-1867	128	4	compact	compact	ADJ
iajs-1867	128	5	,	,	PUNCT
iajs-1867	128	6	it	it	PRON
iajs-1867	128	7	follows	follow	VERB
iajs-1867	128	8	by	by	ADP
iajs-1867	128	9	definition	definition	NOUN
iajs-1867	128	10	of	of	ADP
iajs-1867	128	11	contractible	contractible	ADJ
iajs-1867	128	12	jspace	jspace	NOUN
iajs-1867	128	13	that	that	PRON
iajs-1867	128	14	cl	cl	VERB
iajs-1867	128	15	a	a	PRON
iajs-1867	128	16	or	or	CCONJ
iajs-1867	128	17	cl	cl	NOUN
iajs-1867	128	18	x\a	x\a	PUNCT
iajs-1867	128	19	is	be	AUX
iajs-1867	128	20	contractible	contractible	ADJ
iajs-1867	128	21	.	.	PUNCT
iajs-1867	129	1	remark	remark	NOUN
iajs-1867	129	2	(	(	PUNCT
iajs-1867	129	3	3.18	3.18	NUM
iajs-1867	129	4	):	):	PUNCT
iajs-1867	129	5	if	if	SCONJ
iajs-1867	129	6	x	x	PRON
iajs-1867	129	7	and	and	CCONJ
iajs-1867	129	8	y	y	PROPN
iajs-1867	129	9	are	be	AUX
iajs-1867	129	10	two	two	NUM
iajs-1867	129	11	contractible	contractible	ADJ
iajs-1867	129	12	jspaces	jspace	NOUN
iajs-1867	129	13	,	,	PUNCT
iajs-1867	129	14	then	then	ADV
iajs-1867	129	15	x	x	SYM
iajs-1867	129	16	y	y	PROPN
iajs-1867	129	17	need	need	AUX
iajs-1867	129	18	not	not	PART
iajs-1867	129	19	be	be	AUX
iajs-1867	129	20	so	so	ADV
iajs-1867	129	21	.	.	PUNCT
iajs-1867	130	1	for	for	ADP
iajs-1867	130	2	example	example	NOUN
iajs-1867	130	3	:	:	PUNCT
iajs-1867	130	4	let	let	VERB
iajs-1867	130	5	x	x	X
iajs-1867	130	6	1,2	1,2	NUM
iajs-1867	130	7	and	and	CCONJ
iajs-1867	130	8	τ	τ	PROPN
iajs-1867	130	9	d	d	NOUN
iajs-1867	130	10	the	the	DET
iajs-1867	130	11	discrete	discrete	ADJ
iajs-1867	130	12	topology	topology	NOUN
iajs-1867	130	13	,	,	PUNCT
iajs-1867	130	14	then	then	ADV
iajs-1867	130	15	x	x	PUNCT
iajs-1867	130	16	is	be	AUX
iajs-1867	130	17	contractible	contractible	ADJ
iajs-1867	130	18	j	j	NOUN
iajs-1867	130	19	space	space	NOUN
iajs-1867	130	20	since	since	SCONJ
iajs-1867	130	21	1	1	NUM
iajs-1867	130	22	,	,	PUNCT
iajs-1867	130	23	2	2	NUM
iajs-1867	130	24	is	be	AUX
iajs-1867	130	25	the	the	DET
iajs-1867	130	26	only	only	ADJ
iajs-1867	130	27	proper	proper	ADJ
iajs-1867	130	28	closed	closed	ADJ
iajs-1867	130	29	cover	cover	NOUN
iajs-1867	130	30	of	of	ADP
iajs-1867	130	31	x	x	PUNCT
iajs-1867	130	32	with	with	ADP
iajs-1867	130	33	1	1	NUM
iajs-1867	130	34	⋂	⋂	PROPN
iajs-1867	130	35	2	2	NUM
iajs-1867	130	36	∅	∅	NOUN
iajs-1867	130	37	which	which	PRON
iajs-1867	130	38	is	be	AUX
iajs-1867	130	39	ihsciconf	ihsciconf	ADJ
iajs-1867	130	40	2017	2017	NUM
iajs-1867	130	41	special	special	ADJ
iajs-1867	130	42	issue	issue	NOUN
iajs-1867	130	43	ibn	ibn	PROPN
iajs-1867	130	44	al	al	PROPN
iajs-1867	130	45	-	-	PUNCT
iajs-1867	130	46	haitham	haitham	PROPN
iajs-1867	130	47	journal	journal	PROPN
iajs-1867	130	48	for	for	ADP
iajs-1867	130	49	pure	pure	ADJ
iajs-1867	130	50	and	and	CCONJ
iajs-1867	130	51	applied	apply	VERB
iajs-1867	130	52	science	science	NOUN
iajs-1867	130	53	https://doi.org/	https://doi.org/	NOUN
iajs-1867	130	54	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	130	55	for	for	ADP
iajs-1867	130	56	more	more	ADJ
iajs-1867	130	57	information	information	NOUN
iajs-1867	130	58	about	about	ADP
iajs-1867	130	59	the	the	DET
iajs-1867	130	60	conference	conference	NOUN
iajs-1867	130	61	please	please	INTJ
iajs-1867	130	62	visit	visit	VERB
iajs-1867	130	63	the	the	DET
iajs-1867	130	64	websites	website	NOUN
iajs-1867	130	65	:	:	PUNCT
iajs-1867	130	66	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	AUX
iajs-1867	130	67	      	      	SPACE
iajs-1867	130	68	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	130	69	                                                                            	                                                                            	SPACE
iajs-1867	130	70	mathematics	mathematic	NOUN
iajs-1867	130	71	|335	|335	NOUN
iajs-1867	130	72	  	  	SPACE
iajs-1867	130	73	compact	compact	ADJ
iajs-1867	130	74	and	and	CCONJ
iajs-1867	130	75	1	1	NUM
iajs-1867	130	76	and	and	CCONJ
iajs-1867	130	77	2	2	NUM
iajs-1867	130	78	are	be	AUX
iajs-1867	130	79	contractible	contractible	ADJ
iajs-1867	130	80	.	.	PUNCT
iajs-1867	131	1	but	but	CCONJ
iajs-1867	131	2	x	x	X
iajs-1867	131	3	x	x	SYM
iajs-1867	131	4	1,1	1,1	NUM
iajs-1867	131	5	,	,	PUNCT
iajs-1867	131	6	1,2	1,2	NUM
iajs-1867	131	7	,	,	PUNCT
iajs-1867	131	8	2,1	2,1	NUM
iajs-1867	131	9	,	,	PUNCT
iajs-1867	131	10	2,2	2,2	NUM
iajs-1867	131	11	,	,	PUNCT
iajs-1867	131	12	is	be	AUX
iajs-1867	131	13	not	not	PART
iajs-1867	131	14	contractible	contractible	ADJ
iajs-1867	131	15	jspace	jspace	NOUN
iajs-1867	131	16	since	since	SCONJ
iajs-1867	131	17	it	it	PRON
iajs-1867	131	18	has	have	VERB
iajs-1867	131	19	more	more	ADJ
iajs-1867	131	20	than	than	ADP
iajs-1867	131	21	two	two	NUM
iajs-1867	131	22	elements	element	NOUN
iajs-1867	131	23	and	and	CCONJ
iajs-1867	131	24	by	by	ADP
iajs-1867	131	25	example	example	NOUN
iajs-1867	131	26	(	(	PUNCT
iajs-1867	131	27	3.6	3.6	NUM
iajs-1867	131	28	)	)	PUNCT
iajs-1867	131	29	.	.	PUNCT
iajs-1867	132	1	definition	definition	NOUN
iajs-1867	132	2	(	(	PUNCT
iajs-1867	132	3	3.19	3.19	NUM
iajs-1867	132	4	):	):	PUNCT
iajs-1867	132	5	a	a	DET
iajs-1867	132	6	continuous	continuous	ADJ
iajs-1867	132	7	function	function	NOUN
iajs-1867	132	8	f	f	NOUN
iajs-1867	132	9	:	:	PUNCT
iajs-1867	132	10	x	x	X
iajs-1867	132	11	→	→	SYM
iajs-1867	132	12	y	y	PROPN
iajs-1867	132	13	is	be	AUX
iajs-1867	132	14	said	say	VERB
iajs-1867	132	15	to	to	PART
iajs-1867	132	16	be	be	AUX
iajs-1867	132	17	contractible	contractible	ADJ
iajs-1867	132	18	if	if	SCONJ
iajs-1867	132	19	f	f	PROPN
iajs-1867	132	20	a	a	PRON
iajs-1867	132	21	is	be	AUX
iajs-1867	132	22	a	a	DET
iajs-1867	132	23	contractible	contractible	ADJ
iajs-1867	132	24	subspace	subspace	NOUN
iajs-1867	132	25	of	of	ADP
iajs-1867	132	26	y	y	PROPN
iajs-1867	132	27	for	for	ADP
iajs-1867	132	28	each	each	DET
iajs-1867	132	29	contractible	contractible	ADJ
iajs-1867	132	30	subspace	subspace	NOUN
iajs-1867	132	31	a	a	PRON
iajs-1867	132	32	of	of	ADP
iajs-1867	132	33	x.	x.	NOUN
iajs-1867	132	34	remarks	remark	NOUN
iajs-1867	132	35	(	(	PUNCT
iajs-1867	132	36	3.20	3.20	NUM
iajs-1867	132	37	):	):	PUNCT
iajs-1867	132	38	a	a	X
iajs-1867	132	39	)	)	PUNCT
iajs-1867	132	40	the	the	DET
iajs-1867	132	41	identity	identity	NOUN
iajs-1867	132	42	function	function	NOUN
iajs-1867	132	43	on	on	ADP
iajs-1867	132	44	any	any	DET
iajs-1867	132	45	topological	topological	ADJ
iajs-1867	132	46	space	space	NOUN
iajs-1867	132	47	is	be	AUX
iajs-1867	132	48	a	a	DET
iajs-1867	132	49	contractible	contractible	ADJ
iajs-1867	132	50	function	function	NOUN
iajs-1867	132	51	.	.	PUNCT
iajs-1867	133	1	b	b	X
iajs-1867	133	2	)	)	PUNCT
iajs-1867	133	3	any	any	DET
iajs-1867	133	4	constant	constant	ADJ
iajs-1867	133	5	function	function	NOUN
iajs-1867	133	6	is	be	AUX
iajs-1867	133	7	a	a	DET
iajs-1867	133	8	contractible	contractible	ADJ
iajs-1867	133	9	function	function	NOUN
iajs-1867	133	10	.	.	PUNCT
iajs-1867	134	1	c	c	X
iajs-1867	134	2	)	)	PUNCT
iajs-1867	134	3	any	any	DET
iajs-1867	134	4	function	function	NOUN
iajs-1867	134	5	defined	define	VERB
iajs-1867	134	6	from	from	ADP
iajs-1867	134	7	any	any	DET
iajs-1867	134	8	topological	topological	ADJ
iajs-1867	134	9	space	space	NOUN
iajs-1867	134	10	to	to	ADP
iajs-1867	134	11	an	an	DET
iajs-1867	134	12	indiscrete	indiscrete	ADJ
iajs-1867	134	13	space	space	NOUN
iajs-1867	134	14	is	be	AUX
iajs-1867	134	15	contractible	contractible	ADJ
iajs-1867	134	16	function	function	NOUN
iajs-1867	134	17	.	.	PUNCT
iajs-1867	135	1	example	example	NOUN
iajs-1867	135	2	(	(	PUNCT
iajs-1867	135	3	3.21	3.21	NUM
iajs-1867	135	4	):	):	PUNCT
iajs-1867	135	5	a	a	DET
iajs-1867	135	6	function	function	NOUN
iajs-1867	135	7	f	f	NOUN
iajs-1867	135	8	:	:	PUNCT
iajs-1867	135	9	ℝ	ℝ	PROPN
iajs-1867	135	10	,	,	PUNCT
iajs-1867	135	11	i	i	PRON
iajs-1867	135	12	→	→	SYM
iajs-1867	135	13	ℝ	ℝ	PROPN
iajs-1867	135	14	such	such	ADJ
iajs-1867	135	15	that	that	SCONJ
iajs-1867	135	16	f	f	NOUN
iajs-1867	135	17	x	x	SYM
iajs-1867	135	18	x	x	PROPN
iajs-1867	135	19	,	,	PUNCT
iajs-1867	135	20	∀x	∀x	X
iajs-1867	135	21	∈	∈	PROPN
iajs-1867	135	22	ℝ	ℝ	PROPN
iajs-1867	135	23	,	,	PUNCT
iajs-1867	135	24	is	be	AUX
iajs-1867	135	25	not	not	PART
iajs-1867	135	26	contractible	contractible	ADJ
iajs-1867	135	27	function	function	NOUN
iajs-1867	135	28	since	since	SCONJ
iajs-1867	135	29	ℕ	ℕ	PROPN
iajs-1867	135	30	is	be	AUX
iajs-1867	135	31	a	a	DET
iajs-1867	135	32	contractible	contractible	ADJ
iajs-1867	135	33	subspace	subspace	NOUN
iajs-1867	135	34	of	of	ADP
iajs-1867	135	35	ℝ	ℝ	PROPN
iajs-1867	135	36	with	with	ADP
iajs-1867	135	37	the	the	DET
iajs-1867	135	38	indiscrete	indiscrete	ADJ
iajs-1867	135	39	topology	topology	NOUN
iajs-1867	135	40	,	,	PUNCT
iajs-1867	135	41	but	but	CCONJ
iajs-1867	135	42	f	f	PROPN
iajs-1867	135	43	ℕ	ℕ	PROPN
iajs-1867	135	44	ℕ	ℕ	PROPN
iajs-1867	135	45	is	be	AUX
iajs-1867	135	46	not	not	PART
iajs-1867	135	47	contractible	contractible	ADJ
iajs-1867	135	48	subset	subset	NOUN
iajs-1867	135	49	of	of	ADP
iajs-1867	135	50	ℝ	ℝ	PROPN
iajs-1867	135	51	with	with	ADP
iajs-1867	135	52	the	the	DET
iajs-1867	135	53	usual	usual	ADJ
iajs-1867	135	54	topology	topology	NOUN
iajs-1867	135	55	.	.	PUNCT
iajs-1867	136	1	remark	remark	NOUN
iajs-1867	136	2	(	(	PUNCT
iajs-1867	136	3	3.22	3.22	NUM
iajs-1867	136	4	):	):	PUNCT
iajs-1867	136	5	a	a	DET
iajs-1867	136	6	continuous	continuous	ADJ
iajs-1867	136	7	function	function	NOUN
iajs-1867	136	8	need	need	AUX
iajs-1867	136	9	not	not	PART
iajs-1867	136	10	be	be	AUX
iajs-1867	136	11	contractible	contractible	ADJ
iajs-1867	136	12	function	function	NOUN
iajs-1867	136	13	.	.	PUNCT
iajs-1867	137	1	for	for	ADP
iajs-1867	137	2	example	example	NOUN
iajs-1867	137	3	:	:	PUNCT
iajs-1867	137	4	let	let	VERB
iajs-1867	137	5	f	f	X
iajs-1867	137	6	:	:	PUNCT
iajs-1867	137	7	a	a	DET
iajs-1867	137	8	,	,	PUNCT
iajs-1867	137	9	b	b	X
iajs-1867	137	10	→	→	SYM
iajs-1867	137	11	s	s	VERB
iajs-1867	137	12	such	such	ADJ
iajs-1867	137	13	that	that	SCONJ
iajs-1867	137	14	f	f	PROPN
iajs-1867	137	15	x	x	SYM
iajs-1867	137	16	e	e	NOUN
iajs-1867	137	17	,	,	PUNCT
iajs-1867	137	18	∀x	∀x	X
iajs-1867	137	19	∈	∈	PROPN
iajs-1867	137	20	a	a	DET
iajs-1867	137	21	,	,	PUNCT
iajs-1867	137	22	b	b	NOUN
iajs-1867	137	23	,	,	PUNCT
iajs-1867	137	24	clear	clear	ADJ
iajs-1867	137	25	that	that	SCONJ
iajs-1867	137	26	f	f	PROPN
iajs-1867	137	27	is	be	AUX
iajs-1867	137	28	continuous	continuous	ADJ
iajs-1867	137	29	onto	onto	ADP
iajs-1867	137	30	function	function	NOUN
iajs-1867	137	31	,	,	PUNCT
iajs-1867	137	32	but	but	CCONJ
iajs-1867	137	33	not	not	PART
iajs-1867	137	34	contractible	contractible	ADJ
iajs-1867	137	35	function	function	NOUN
iajs-1867	137	36	since	since	SCONJ
iajs-1867	137	37	a	a	PRON
iajs-1867	137	38	,	,	PUNCT
iajs-1867	137	39	b	b	NOUN
iajs-1867	137	40	is	be	AUX
iajs-1867	137	41	a	a	DET
iajs-1867	137	42	contractible	contractible	ADJ
iajs-1867	137	43	set	set	NOUN
iajs-1867	137	44	while	while	SCONJ
iajs-1867	137	45	s	s	NOUN
iajs-1867	137	46	is	be	AUX
iajs-1867	137	47	not	not	PART
iajs-1867	137	48	.	.	PUNCT
iajs-1867	138	1	remark	remark	NOUN
iajs-1867	138	2	(	(	PUNCT
iajs-1867	138	3	3.23	3.23	NUM
iajs-1867	138	4	):	):	PUNCT
iajs-1867	138	5	a	a	DET
iajs-1867	138	6	contractible	contractible	ADJ
iajs-1867	138	7	function	function	NOUN
iajs-1867	138	8	is	be	AUX
iajs-1867	138	9	not	not	PART
iajs-1867	138	10	necessary	necessary	ADJ
iajs-1867	138	11	to	to	PART
iajs-1867	138	12	be	be	AUX
iajs-1867	138	13	continuous	continuous	ADJ
iajs-1867	138	14	function	function	NOUN
iajs-1867	138	15	.	.	PUNCT
iajs-1867	139	1	for	for	ADP
iajs-1867	139	2	example	example	NOUN
iajs-1867	139	3	:	:	PUNCT
iajs-1867	139	4	let	let	VERB
iajs-1867	139	5	x	x	SYM
iajs-1867	139	6	1,2,3	1,2,3	NUM
iajs-1867	139	7	,	,	PUNCT
iajs-1867	139	8	and	and	CCONJ
iajs-1867	139	9	τ	τ	PROPN
iajs-1867	139	10	x	x	PROPN
iajs-1867	139	11	,	,	PUNCT
iajs-1867	139	12	∅	∅	NOUN
iajs-1867	139	13	,	,	PUNCT
iajs-1867	139	14	1	1	NUM
iajs-1867	139	15	,	,	PUNCT
iajs-1867	139	16	and	and	CCONJ
iajs-1867	139	17	let	let	VERB
iajs-1867	139	18	f	f	X
iajs-1867	139	19	:	:	PUNCT
iajs-1867	139	20	x	x	SYM
iajs-1867	139	21	→	→	PUNCT
iajs-1867	139	22	x	x	X
iajs-1867	139	23	such	such	ADJ
iajs-1867	139	24	that	that	SCONJ
iajs-1867	139	25	f	f	PROPN
iajs-1867	139	26	2	2	NUM
iajs-1867	139	27	f	f	PROPN
iajs-1867	139	28	3	3	NUM
iajs-1867	139	29	1	1	NUM
iajs-1867	139	30	and	and	CCONJ
iajs-1867	139	31	f	f	PROPN
iajs-1867	139	32	1	1	NUM
iajs-1867	139	33	2	2	NUM
iajs-1867	139	34	,	,	PUNCT
iajs-1867	139	35	then	then	ADV
iajs-1867	139	36	f	f	PROPN
iajs-1867	139	37	is	be	AUX
iajs-1867	139	38	a	a	DET
iajs-1867	139	39	contractible	contractible	ADJ
iajs-1867	139	40	function	function	NOUN
iajs-1867	139	41	since	since	SCONJ
iajs-1867	139	42	every	every	DET
iajs-1867	139	43	subset	subset	NOUN
iajs-1867	139	44	of	of	ADP
iajs-1867	139	45	x	x	PUNCT
iajs-1867	139	46	is	be	AUX
iajs-1867	139	47	contractible	contractible	ADJ
iajs-1867	139	48	,	,	PUNCT
iajs-1867	139	49	and	and	CCONJ
iajs-1867	139	50	thus	thus	ADV
iajs-1867	139	51	f	f	PROPN
iajs-1867	139	52	a	a	DET
iajs-1867	139	53	⊆	⊆	NUM
iajs-1867	139	54	x	x	PUNCT
iajs-1867	139	55	is	be	AUX
iajs-1867	139	56	contractible	contractible	ADJ
iajs-1867	139	57	for	for	SCONJ
iajs-1867	139	58	each	each	PRON
iajs-1867	139	59	contractible	contractible	ADJ
iajs-1867	139	60	a	a	DET
iajs-1867	139	61	⊆	⊆	NUM
iajs-1867	139	62	x.	x.	NOUN
iajs-1867	140	1	but	but	CCONJ
iajs-1867	140	2	f	f	PROPN
iajs-1867	140	3	is	be	AUX
iajs-1867	140	4	not	not	PART
iajs-1867	140	5	continuous	continuous	ADJ
iajs-1867	140	6	function	function	NOUN
iajs-1867	140	7	since	since	SCONJ
iajs-1867	140	8	1	1	NUM
iajs-1867	140	9	∈	∈	PROPN
iajs-1867	140	10	τ	τ	X
iajs-1867	140	11	while	while	SCONJ
iajs-1867	140	12	f	f	PROPN
iajs-1867	140	13	1	1	NUM
iajs-1867	140	14	2,3	2,3	NUM
iajs-1867	140	15	∉	∉	PROPN
iajs-1867	140	16	τ	τ	PROPN
iajs-1867	140	17	.	.	PUNCT
iajs-1867	140	18	proposition	proposition	NOUN
iajs-1867	140	19	(	(	PUNCT
iajs-1867	140	20	3.24	3.24	NUM
iajs-1867	140	21	):	):	PUNCT
iajs-1867	140	22	the	the	DET
iajs-1867	140	23	property	property	NOUN
iajs-1867	140	24	of	of	ADP
iajs-1867	140	25	being	be	AUX
iajs-1867	140	26	contractible	contractible	ADJ
iajs-1867	140	27	jspace	jspace	NOUN
iajs-1867	140	28	is	be	AUX
iajs-1867	140	29	preserved	preserve	VERB
iajs-1867	140	30	by	by	ADP
iajs-1867	140	31	the	the	DET
iajs-1867	140	32	perfect	perfect	ADJ
iajs-1867	140	33	and	and	CCONJ
iajs-1867	140	34	contractible	contractible	ADJ
iajs-1867	140	35	function	function	NOUN
iajs-1867	140	36	from	from	ADP
iajs-1867	140	37	x	x	PRON
iajs-1867	140	38	onto	onto	ADP
iajs-1867	140	39	y.	y.	NOUN
iajs-1867	140	40	proof	proof	NOUN
iajs-1867	140	41	:	:	PUNCT
iajs-1867	140	42	let	let	VERB
iajs-1867	140	43	e	e	X
iajs-1867	140	44	,	,	PUNCT
iajs-1867	140	45	f	f	PROPN
iajs-1867	140	46	be	be	AUX
iajs-1867	140	47	closed	close	VERB
iajs-1867	140	48	subset	subset	NOUN
iajs-1867	140	49	of	of	ADP
iajs-1867	140	50	y	y	PROPN
iajs-1867	140	51	with	with	ADP
iajs-1867	140	52	e	e	PROPN
iajs-1867	140	53	∪	∪	PROPN
iajs-1867	140	54	f	f	PROPN
iajs-1867	140	55	y	y	PROPN
iajs-1867	140	56	and	and	CCONJ
iajs-1867	140	57	e	e	PROPN
iajs-1867	140	58	∩	∩	PROPN
iajs-1867	140	59	f	f	PROPN
iajs-1867	140	60	compact	compact	ADJ
iajs-1867	140	61	,	,	PUNCT
iajs-1867	140	62	then	then	ADV
iajs-1867	140	63	f	f	PROPN
iajs-1867	140	64	e	e	PROPN
iajs-1867	140	65	,	,	PUNCT
iajs-1867	140	66	f	f	PROPN
iajs-1867	140	67	f	f	PROPN
iajs-1867	140	68	are	be	AUX
iajs-1867	140	69	closed	close	VERB
iajs-1867	140	70	subsets	subset	NOUN
iajs-1867	140	71	of	of	ADP
iajs-1867	140	72	x	x	PRON
iajs-1867	140	73	since	since	SCONJ
iajs-1867	140	74	f	f	PROPN
iajs-1867	140	75	is	be	AUX
iajs-1867	140	76	continuous	continuous	ADJ
iajs-1867	140	77	,	,	PUNCT
iajs-1867	140	78	and	and	CCONJ
iajs-1867	140	79	f	f	PROPN
iajs-1867	140	80	e	e	PROPN
iajs-1867	140	81	∩	∩	PROPN
iajs-1867	140	82	f	f	PROPN
iajs-1867	140	83	f	f	PROPN
iajs-1867	140	84	f	f	PROPN
iajs-1867	140	85	e	e	PROPN
iajs-1867	140	86	∩	∩	PROPN
iajs-1867	140	87	f	f	X
iajs-1867	140	88	which	which	PRON
iajs-1867	140	89	is	be	AUX
iajs-1867	140	90	compact	compact	ADJ
iajs-1867	140	91	since	since	SCONJ
iajs-1867	140	92	f	f	PROPN
iajs-1867	140	93	is	be	AUX
iajs-1867	140	94	perfect	perfect	ADJ
iajs-1867	140	95	,	,	PUNCT
iajs-1867	140	96	and	and	CCONJ
iajs-1867	140	97	f	f	PROPN
iajs-1867	140	98	e	e	PROPN
iajs-1867	140	99	∪	∪	VERB
iajs-1867	140	100	f	f	PROPN
iajs-1867	140	101	f	f	PROPN
iajs-1867	140	102	x	x	PROPN
iajs-1867	140	103	,	,	PUNCT
iajs-1867	140	104	but	but	CCONJ
iajs-1867	140	105	x	x	X
iajs-1867	140	106	is	be	AUX
iajs-1867	140	107	contractible	contractible	ADJ
iajs-1867	140	108	j	j	NOUN
iajs-1867	140	109	-	-	NOUN
iajs-1867	140	110	space	space	NOUN
iajs-1867	140	111	,	,	PUNCT
iajs-1867	140	112	so	so	SCONJ
iajs-1867	140	113	f	f	PROPN
iajs-1867	140	114	e	e	PROPN
iajs-1867	140	115	or	or	CCONJ
iajs-1867	140	116	f	f	PROPN
iajs-1867	140	117	f	f	PROPN
iajs-1867	140	118	is	be	AUX
iajs-1867	140	119	contractible	contractible	ADJ
iajs-1867	140	120	,	,	PUNCT
iajs-1867	140	121	it	it	PRON
iajs-1867	140	122	follows	follow	VERB
iajs-1867	140	123	by	by	ADP
iajs-1867	140	124	definition	definition	NOUN
iajs-1867	140	125	of	of	ADP
iajs-1867	140	126	contractible	contractible	ADJ
iajs-1867	140	127	function	function	NOUN
iajs-1867	140	128	that	that	PRON
iajs-1867	140	129	f	f	PROPN
iajs-1867	140	130	f	f	PROPN
iajs-1867	140	131	e	e	PROPN
iajs-1867	140	132	or	or	CCONJ
iajs-1867	140	133	f	f	PROPN
iajs-1867	140	134	f	f	PROPN
iajs-1867	140	135	f	f	PROPN
iajs-1867	140	136	is	be	AUX
iajs-1867	140	137	contractible	contractible	ADJ
iajs-1867	140	138	,	,	PUNCT
iajs-1867	140	139	but	but	CCONJ
iajs-1867	140	140	f	f	PROPN
iajs-1867	140	141	is	be	AUX
iajs-1867	140	142	surjective	surjective	ADJ
iajs-1867	140	143	,	,	PUNCT
iajs-1867	140	144	so	so	CCONJ
iajs-1867	140	145	e	e	PROPN
iajs-1867	140	146	or	or	CCONJ
iajs-1867	140	147	f	f	PROPN
iajs-1867	140	148	is	be	AUX
iajs-1867	140	149	contractible	contractible	ADJ
iajs-1867	140	150	.	.	PUNCT
iajs-1867	141	1	hence	hence	ADV
iajs-1867	141	2	y	y	PROPN
iajs-1867	141	3	is	be	AUX
iajs-1867	141	4	contractible	contractible	ADJ
iajs-1867	141	5	jspace	jspace	NOUN
iajs-1867	141	6	.	.	PUNCT
iajs-1867	142	1	proposition	proposition	NOUN
iajs-1867	142	2	(	(	PUNCT
iajs-1867	142	3	3.25	3.25	NUM
iajs-1867	142	4	):	):	PUNCT
iajs-1867	142	5	every	every	DET
iajs-1867	142	6	homeomorphism	homeomorphism	PROPN
iajs-1867	142	7	function	function	NOUN
iajs-1867	142	8	is	be	AUX
iajs-1867	142	9	a	a	DET
iajs-1867	142	10	contractible	contractible	ADJ
iajs-1867	142	11	function	function	NOUN
iajs-1867	142	12	.	.	PUNCT
iajs-1867	143	1	proof	proof	NOUN
iajs-1867	143	2	:	:	PUNCT
iajs-1867	144	1	f	f	X
iajs-1867	144	2	:	:	PUNCT
iajs-1867	144	3	x	x	X
iajs-1867	144	4	→	→	SYM
iajs-1867	144	5	y	y	X
iajs-1867	144	6	be	be	AUX
iajs-1867	144	7	a	a	DET
iajs-1867	144	8	homeomorphism	homeomorphism	NOUN
iajs-1867	144	9	function	function	NOUN
iajs-1867	144	10	,	,	PUNCT
iajs-1867	144	11	and	and	CCONJ
iajs-1867	144	12	let	let	VERB
iajs-1867	144	13	a	a	PRON
iajs-1867	144	14	be	be	AUX
iajs-1867	144	15	a	a	DET
iajs-1867	144	16	contractible	contractible	ADJ
iajs-1867	144	17	subset	subset	NOUN
iajs-1867	144	18	of	of	ADP
iajs-1867	144	19	x	x	PRON
iajs-1867	144	20	,	,	PUNCT
iajs-1867	144	21	we	we	PRON
iajs-1867	144	22	have	have	VERB
iajs-1867	144	23	to	to	PART
iajs-1867	144	24	show	show	VERB
iajs-1867	144	25	that	that	SCONJ
iajs-1867	144	26	f	f	PROPN
iajs-1867	144	27	a	a	PRON
iajs-1867	144	28	is	be	AUX
iajs-1867	144	29	contractible	contractible	ADJ
iajs-1867	144	30	subset	subset	NOUN
iajs-1867	144	31	of	of	ADP
iajs-1867	144	32	y.	y.	PROPN
iajs-1867	144	33	note	note	VERB
iajs-1867	144	34	that	that	SCONJ
iajs-1867	144	35	a	a	DET
iajs-1867	144	36	and	and	CCONJ
iajs-1867	144	37	f	f	PROPN
iajs-1867	144	38	a	a	PRON
iajs-1867	144	39	are	be	AUX
iajs-1867	144	40	homeomorphic	homeomorphic	ADJ
iajs-1867	144	41	spaces	space	NOUN
iajs-1867	144	42	,	,	PUNCT
iajs-1867	144	43	it	it	PRON
iajs-1867	144	44	follows	follow	VERB
iajs-1867	144	45	by	by	ADP
iajs-1867	144	46	proposition	proposition	NOUN
iajs-1867	144	47	(	(	PUNCT
iajs-1867	144	48	2.23	2.23	NUM
iajs-1867	144	49	)	)	PUNCT
iajs-1867	145	1	that	that	PRON
iajs-1867	145	2	a	a	PRON
iajs-1867	145	3	and	and	CCONJ
iajs-1867	145	4	f	f	PROPN
iajs-1867	145	5	a	a	PRON
iajs-1867	145	6	are	be	AUX
iajs-1867	145	7	homotopy	homotopy	NOUN
iajs-1867	145	8	equivalent	equivalent	NOUN
iajs-1867	145	9	.	.	PUNCT
iajs-1867	146	1	since	since	SCONJ
iajs-1867	146	2	a	a	PRON
iajs-1867	146	3	is	be	AUX
iajs-1867	146	4	contractible	contractible	ADJ
iajs-1867	146	5	,	,	PUNCT
iajs-1867	146	6	it	it	PRON
iajs-1867	146	7	follows	follow	VERB
iajs-1867	146	8	by	by	ADP
iajs-1867	146	9	theorem	theorem	NOUN
iajs-1867	146	10	(	(	PUNCT
iajs-1867	146	11	2.15	2.15	NUM
iajs-1867	146	12	)	)	PUNCT
iajs-1867	146	13	and	and	CCONJ
iajs-1867	146	14	remark	remark	NOUN
iajs-1867	146	15	(	(	PUNCT
iajs-1867	146	16	2.24	2.24	NUM
iajs-1867	146	17	)	)	PUNCT
iajs-1867	147	1	that	that	PRON
iajs-1867	147	2	f	f	PROPN
iajs-1867	147	3	a	a	PRON
iajs-1867	147	4	contractible	contractible	ADJ
iajs-1867	147	5	.	.	PUNCT
iajs-1867	148	1	corollary	corollary	ADJ
iajs-1867	148	2	(	(	PUNCT
iajs-1867	148	3	3.26	3.26	NUM
iajs-1867	148	4	):	):	PUNCT
iajs-1867	148	5	if	if	SCONJ
iajs-1867	148	6	the	the	DET
iajs-1867	148	7	topological	topological	ADJ
iajs-1867	148	8	spaces	space	NOUN
iajs-1867	148	9	x	x	PUNCT
iajs-1867	148	10	and	and	CCONJ
iajs-1867	148	11	y	y	PROPN
iajs-1867	148	12	are	be	AUX
iajs-1867	148	13	homeomorphic	homeomorphic	ADJ
iajs-1867	148	14	spaces	space	NOUN
iajs-1867	148	15	and	and	CCONJ
iajs-1867	148	16	one	one	NUM
iajs-1867	148	17	of	of	ADP
iajs-1867	148	18	them	they	PRON
iajs-1867	148	19	is	be	AUX
iajs-1867	148	20	contractible	contractible	ADJ
iajs-1867	148	21	jspace	jspace	NOUN
iajs-1867	148	22	,	,	PUNCT
iajs-1867	148	23	then	then	ADV
iajs-1867	148	24	so	so	ADV
iajs-1867	148	25	is	be	AUX
iajs-1867	148	26	the	the	DET
iajs-1867	148	27	other	other	ADJ
iajs-1867	148	28	.	.	PUNCT
iajs-1867	149	1	proof	proof	NOUN
iajs-1867	149	2	:	:	PUNCT
iajs-1867	149	3	follows	follow	VERB
iajs-1867	149	4	from	from	ADP
iajs-1867	149	5	propositions	proposition	NOUN
iajs-1867	149	6	(	(	PUNCT
iajs-1867	149	7	3.24	3.24	NUM
iajs-1867	149	8	)	)	PUNCT
iajs-1867	149	9	and	and	CCONJ
iajs-1867	149	10	(	(	PUNCT
iajs-1867	149	11	3.25	3.25	NUM
iajs-1867	149	12	)	)	PUNCT
iajs-1867	149	13	.	.	PUNCT
iajs-1867	150	1	references	reference	NOUN
iajs-1867	150	2	[	[	X
iajs-1867	150	3	1	1	NUM
iajs-1867	150	4	]	]	PUNCT
iajs-1867	150	5	c.	c.	PROPN
iajs-1867	150	6	kosniowski	kosniowski	PROPN
iajs-1867	150	7	,	,	PUNCT
iajs-1867	150	8	a	a	DET
iajs-1867	150	9	first	first	ADJ
iajs-1867	150	10	cours	cour	NOUN
iajs-1867	150	11	in	in	ADP
iajs-1867	150	12	algebraic	algebraic	PROPN
iajs-1867	150	13	topology	topology	NOUN
iajs-1867	150	14	,	,	PUNCT
iajs-1867	150	15	cambridge	cambridge	PROPN
iajs-1867	150	16	university	university	PROPN
iajs-1867	150	17	press	press	NOUN
iajs-1867	150	18	,	,	PUNCT
iajs-1867	150	19	first	first	ADV
iajs-1867	150	20	published	publish	VERB
iajs-1867	150	21	,	,	PUNCT
iajs-1867	150	22	1980	1980	NUM
iajs-1867	150	23	.	.	PUNCT
iajs-1867	151	1	[	[	X
iajs-1867	151	2	2	2	X
iajs-1867	151	3	]	]	PUNCT
iajs-1867	151	4	e.	e.	PROPN
iajs-1867	151	5	d.	d.	PROPN
iajs-1867	151	6	khalimsky	khalimsky	PROPN
iajs-1867	151	7	;	;	PUNCT
iajs-1867	151	8	r.	r.	PROPN
iajs-1867	151	9	kopperman	kopperman	NOUN
iajs-1867	151	10	and	and	CCONJ
iajs-1867	151	11	p.	p.	PROPN
iajs-1867	151	12	r.	r.	PROPN
iajs-1867	151	13	meyer	meyer	PROPN
iajs-1867	151	14	,	,	PUNCT
iajs-1867	151	15	computer	computer	NOUN
iajs-1867	151	16	graphics	graphic	NOUN
iajs-1867	151	17	and	and	CCONJ
iajs-1867	151	18	connected	connected	ADJ
iajs-1867	151	19	topologies	topology	NOUN
iajs-1867	151	20	on	on	ADP
iajs-1867	151	21	finite	finite	ADJ
iajs-1867	151	22	closed	close	VERB
iajs-1867	151	23	sets	set	NOUN
iajs-1867	151	24	,	,	PUNCT
iajs-1867	151	25	topology	topology	NOUN
iajs-1867	151	26	appl	appl	NOUN
iajs-1867	151	27	.	.	PUNCT
iajs-1867	152	1	36,1	36,1	NUM
iajs-1867	152	2	-	-	SYM
iajs-1867	152	3	7	7	NUM
iajs-1867	152	4	.	.	NUM
iajs-1867	152	5	1967	1967	NUM
iajs-1867	153	1	[	[	X
iajs-1867	153	2	3	3	X
iajs-1867	153	3	]	]	PUNCT
iajs-1867	153	4	t.	t.	PROPN
iajs-1867	153	5	y.	y.	PROPN
iajs-1867	153	6	kong	kong	PROPN
iajs-1867	153	7	;	;	PUNCT
iajs-1867	153	8	r.	r.	PROPN
iajs-1867	153	9	kopperman	kopperman	NOUN
iajs-1867	153	10	and	and	CCONJ
iajs-1867	153	11	p.	p.	PROPN
iajs-1867	153	12	r.	r.	PROPN
iajs-1867	153	13	meyer	meyer	PROPN
iajs-1867	153	14	,	,	PUNCT
iajs-1867	153	15	a	a	DET
iajs-1867	153	16	topological	topological	ADJ
iajs-1867	153	17	approach	approach	NOUN
iajs-1867	153	18	to	to	ADP
iajs-1867	153	19	digital	digital	ADJ
iajs-1867	153	20	topology	topology	NOUN
iajs-1867	153	21	,	,	PUNCT
iajs-1867	153	22	american	american	PROPN
iajs-1867	153	23	math	math	PROPN
iajs-1867	153	24	.	.	PUNCT
iajs-1867	154	1	monthly	monthly	ADJ
iajs-1867	154	2	,	,	PUNCT
iajs-1867	154	3	98	98	NUM
iajs-1867	154	4	,	,	PUNCT
iajs-1867	154	5	901	901	NUM
iajs-1867	154	6	-	-	SYM
iajs-1867	154	7	917	917	NUM
iajs-1867	154	8	.	.	PUNCT
iajs-1867	154	9	1991	1991	NUM
iajs-1867	155	1	[	[	X
iajs-1867	155	2	4	4	X
iajs-1867	155	3	]	]	X
iajs-1867	155	4	e.	e.	PROPN
iajs-1867	155	5	michael	michael	PROPN
iajs-1867	155	6	;	;	PUNCT
iajs-1867	155	7	jspaces	jspace	NOUN
iajs-1867	155	8	,	,	PUNCT
iajs-1867	155	9	topology	topology	NOUN
iajs-1867	155	10	and	and	CCONJ
iajs-1867	155	11	its	its	PRON
iajs-1867	155	12	application	application	NOUN
iajs-1867	155	13	102,315	102,315	NUM
iajs-1867	155	14	-	-	SYM
iajs-1867	155	15	339	339	NUM
iajs-1867	155	16	.	.	PUNCT
iajs-1867	155	17	2000	2000	NUM
iajs-1867	156	1	[	[	X
iajs-1867	156	2	5	5	X
iajs-1867	156	3	]	]	X
iajs-1867	156	4	y.	y.	PROPN
iajs-1867	156	5	nanjing	nanjing	PROPN
iajs-1867	156	6	;	;	PUNCT
iajs-1867	156	7	ljspaces	ljspace	NOUN
iajs-1867	156	8	,	,	PUNCT
iajs-1867	156	9	czechoslovak	czechoslovak	ADJ
iajs-1867	156	10	math	math	NOUN
iajs-1867	156	11	.	.	PUNCT
iajs-1867	157	1	journal	journal	PROPN
iajs-1867	157	2	,	,	PUNCT
iajs-1867	157	3	57(132	57(132	PROPN
iajs-1867	157	4	)	)	PUNCT
iajs-1867	157	5	1223	1223	NUM
iajs-1867	157	6	-	-	SYM
iajs-1867	157	7	1237	1237	NUM
iajs-1867	157	8	.	.	PUNCT
iajs-1867	158	1	2007	2007	NUM
iajs-1867	158	2	.	.	PUNCT
iajs-1867	159	1	ihsciconf	ihsciconf	PROPN
iajs-1867	159	2	2017	2017	NUM
iajs-1867	159	3	special	special	ADJ
iajs-1867	159	4	issue	issue	NOUN
iajs-1867	159	5	ibn	ibn	PROPN
iajs-1867	159	6	al	al	PROPN
iajs-1867	159	7	-	-	PUNCT
iajs-1867	159	8	haitham	haitham	PROPN
iajs-1867	159	9	journal	journal	PROPN
iajs-1867	159	10	for	for	ADP
iajs-1867	159	11	pure	pure	ADJ
iajs-1867	159	12	and	and	CCONJ
iajs-1867	159	13	applied	apply	VERB
iajs-1867	159	14	science	science	NOUN
iajs-1867	159	15	https://doi.org/	https://doi.org/	NOUN
iajs-1867	159	16	10.30526/2017.ihsciconf.1867	10.30526/2017.ihsciconf.1867	NUM
iajs-1867	159	17	for	for	ADP
iajs-1867	159	18	more	more	ADJ
iajs-1867	159	19	information	information	NOUN
iajs-1867	159	20	about	about	ADP
iajs-1867	159	21	the	the	DET
iajs-1867	159	22	conference	conference	NOUN
iajs-1867	159	23	please	please	INTJ
iajs-1867	159	24	visit	visit	VERB
iajs-1867	159	25	the	the	DET
iajs-1867	159	26	websites	website	NOUN
iajs-1867	159	27	:	:	PUNCT
iajs-1867	159	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1867	159	29	      	      	SPACE
iajs-1867	159	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1867	159	31	                                                                            	                                                                            	SPACE
iajs-1867	159	32	mathematics	mathematic	NOUN
iajs-1867	159	33	|336	|336	ADV
iajs-1867	159	34	  	  	SPACE
iajs-1867	160	1	[	[	X
iajs-1867	160	2	6	6	NUM
iajs-1867	160	3	]	]	PUNCT
iajs-1867	160	4	a.	a.	NOUN
iajs-1867	160	5	kornitowicz	kornitowicz	NOUN
iajs-1867	160	6	,	,	PUNCT
iajs-1867	160	7	a	a	DET
iajs-1867	160	8	proof	proof	NOUN
iajs-1867	160	9	of	of	ADP
iajs-1867	160	10	the	the	DET
iajs-1867	160	11	jordan	jordan	PROPN
iajs-1867	160	12	curve	curve	PROPN
iajs-1867	160	13	theorem	theorem	VERB
iajs-1867	160	14	via	via	ADP
iajs-1867	160	15	the	the	DET
iajs-1867	160	16	brouwer	brouwer	PROPN
iajs-1867	160	17	fixed	fix	VERB
iajs-1867	160	18	point	point	NOUN
iajs-1867	160	19	theorem	theorem	VERB
iajs-1867	160	20	,	,	PUNCT
iajs-1867	160	21	6(1)33	6(1)33	NUM
iajs-1867	160	22	-	-	SYM
iajs-1867	160	23	40	40	NUM
iajs-1867	160	24	.	.	PUNCT
iajs-1867	160	25	2007	2007	NUM
iajs-1867	160	26	.	.	PUNCT
iajs-1867	161	1	[	[	X
iajs-1867	161	2	7	7	X
iajs-1867	161	3	]	]	X
iajs-1867	161	4	e.	e.	PROPN
iajs-1867	161	5	bouassida	bouassida	PROPN
iajs-1867	161	6	,	,	PUNCT
iajs-1867	161	7	the	the	DET
iajs-1867	161	8	jordan	jordan	PROPN
iajs-1867	161	9	curve	curve	PROPN
iajs-1867	161	10	theorem	theorem	VERB
iajs-1867	161	11	in	in	ADP
iajs-1867	161	12	the	the	DET
iajs-1867	161	13	khalimsky	khalimsky	ADJ
iajs-1867	161	14	plane	plane	NOUN
iajs-1867	161	15	,	,	PUNCT
iajs-1867	161	16	applied	apply	VERB
iajs-1867	161	17	general	general	ADJ
iajs-1867	161	18	topology	topology	NOUN
iajs-1867	161	19	,	,	PUNCT
iajs-1867	161	20	9(2	9(2	NUM
iajs-1867	161	21	)	)	PUNCT
iajs-1867	161	22	253262	253262	NUM
iajs-1867	161	23	.	.	PUNCT
iajs-1867	162	1	2008	2008	NUM
iajs-1867	162	2	.	.	PUNCT
iajs-1867	163	1	[	[	X
iajs-1867	163	2	8	8	NUM
iajs-1867	163	3	]	]	X
iajs-1867	163	4	w.	w.	PROPN
iajs-1867	163	5	fulton	fulton	PROPN
iajs-1867	163	6	,	,	PUNCT
iajs-1867	163	7	a	a	DET
iajs-1867	163	8	first	first	ADJ
iajs-1867	163	9	cours	cours	ADJ
iajs-1867	163	10	:	:	PUNCT
iajs-1867	163	11	algebraic	algebraic	ADJ
iajs-1867	163	12	topology	topology	NOUN
iajs-1867	163	13	,	,	PUNCT
iajs-1867	163	14	springer	springer	NOUN
iajs-1867	163	15	science	science	PROPN
iajs-1867	163	16	&	&	CCONJ
iajs-1867	163	17	business	business	NOUN
iajs-1867	163	18	media	medium	NOUN
iajs-1867	163	19	,	,	PUNCT
iajs-1867	163	20	1997	1997	NUM
iajs-1867	163	21	.	.	PUNCT
iajs-1867	164	1	[	[	X
iajs-1867	164	2	9	9	NUM
iajs-1867	164	3	]	]	PUNCT
iajs-1867	164	4	b.	b.	PROPN
iajs-1867	164	5	mendelson	mendelson	PROPN
iajs-1867	164	6	,	,	PUNCT
iajs-1867	164	7	introduction	introduction	NOUN
iajs-1867	164	8	to	to	ADP
iajs-1867	164	9	topology	topology	NOUN
iajs-1867	164	10	,	,	PUNCT
iajs-1867	164	11	third	third	ADJ
iajs-1867	164	12	edition	edition	NOUN
iajs-1867	164	13	,	,	PUNCT
iajs-1867	164	14	courier	courier	NOUN
iajs-1867	164	15	corporation	corporation	NOUN
iajs-1867	164	16	,	,	PUNCT
iajs-1867	164	17	1990	1990	NUM
iajs-1867	164	18	.	.	PUNCT
iajs-1867	165	1	[	[	X
iajs-1867	165	2	10	10	NUM
iajs-1867	165	3	]	]	PUNCT
iajs-1867	165	4	j.	j.	PROPN
iajs-1867	165	5	j.	j.	PROPN
iajs-1867	165	6	rotman	rotman	PROPN
iajs-1867	165	7	,	,	PUNCT
iajs-1867	165	8	an	an	DET
iajs-1867	165	9	introduction	introduction	NOUN
iajs-1867	165	10	to	to	ADP
iajs-1867	165	11	algebraic	algebraic	ADJ
iajs-1867	165	12	topology	topology	NOUN
iajs-1867	165	13	,	,	PUNCT
iajs-1867	165	14	springer	springer	NOUN
iajs-1867	165	15	science	science	PROPN
iajs-1867	165	16	&	&	CCONJ
iajs-1867	165	17	business	business	NOUN
iajs-1867	165	18	media	medium	NOUN
iajs-1867	165	19	,	,	PUNCT
iajs-1867	165	20	2013	2013	NUM
iajs-1867	165	21	.	.	PUNCT
iajs-1867	166	1	[	[	X
iajs-1867	166	2	11	11	NUM
iajs-1867	166	3	]	]	X
iajs-1867	166	4	james	james	PROPN
iajs-1867	166	5	r.	r.	PROPN
iajs-1867	166	6	munkres	munkres	PROPN
iajs-1867	166	7	,	,	PUNCT
iajs-1867	166	8	topology	topology	NOUN
iajs-1867	166	9	a	a	DET
iajs-1867	166	10	first	first	ADJ
iajs-1867	166	11	course	course	NOUN
iajs-1867	166	12	,	,	PUNCT
iajs-1867	166	13	prenticehall	prenticehall	NOUN
iajs-1867	166	14	,	,	PUNCT
iajs-1867	166	15	1974	1974	NUM
iajs-1867	166	16	.	.	PUNCT
iajs-1867	167	1	[	[	X
iajs-1867	167	2	12	12	NUM
iajs-1867	167	3	]	]	X
iajs-1867	167	4	e.	e.	PROPN
iajs-1867	167	5	h.	h.	PROPN
iajs-1867	167	6	spanier	spanier	PROPN
iajs-1867	167	7	,	,	PUNCT
iajs-1867	167	8	algebraic	algebraic	ADJ
iajs-1867	167	9	topology	topology	NOUN
iajs-1867	167	10	,	,	PUNCT
iajs-1867	167	11	springer	springer	NOUN
iajs-1867	167	12	science	science	PROPN
iajs-1867	167	13	&	&	CCONJ
iajs-1867	167	14	business	business	NOUN
iajs-1867	167	15	media	medium	NOUN
iajs-1867	167	16	,	,	PUNCT
iajs-1867	167	17	1994	1994	NUM
iajs-1867	167	18	.	.	PUNCT
iajs-1867	168	1	[	[	X
iajs-1867	168	2	13	13	NUM
iajs-1867	168	3	]	]	SYM
iajs-1867	168	4	a.r	a.r	PROPN
iajs-1867	168	5	.	.	PROPN
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iajs-1867	168	7	,	,	PUNCT
iajs-1867	168	8	basic	basic	ADJ
iajs-1867	168	9	algebraic	algebraic	ADJ
iajs-1867	168	10	topology	topology	NOUN
iajs-1867	168	11	,	,	PUNCT
iajs-1867	168	12	crc	crc	NOUN
iajs-1867	168	13	press	press	NOUN
iajs-1867	168	14	,	,	PUNCT
iajs-1867	168	15	2016	2016	NUM
iajs-1867	168	16	.	.	PUNCT
iajs-1867	169	1	[	[	X
iajs-1867	169	2	14	14	NUM
iajs-1867	169	3	]	]	PUNCT
iajs-1867	169	4	s.	s.	PROPN
iajs-1867	169	5	t.	t.	PROPN
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iajs-1867	169	7	,	,	PUNCT
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iajs-1867	169	11	,	,	PUNCT
iajs-1867	169	12	crc	crc	NOUN
iajs-1867	169	13	press	press	PROPN
iajs-1867	169	14	,	,	PUNCT
iajs-1867	169	15	taylor	taylor	PROPN
iajs-1867	169	16	&	&	CCONJ
iajs-1867	169	17	francis	francis	PROPN
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iajs-1867	169	19	,	,	PUNCT
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iajs-1867	169	21	.	.	PUNCT
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iajs-1867	170	2	15	15	NUM
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iajs-1867	170	4	w.	w.	PROPN
iajs-1867	170	5	f.	f.	PROPN
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iajs-1867	170	7	,	,	PUNCT
iajs-1867	170	8	topology	topology	NOUN
iajs-1867	170	9	and	and	CCONJ
iajs-1867	170	10	its	its	PRON
iajs-1867	170	11	applications	application	NOUN
iajs-1867	170	12	,	,	PUNCT
iajs-1867	170	13	john	john	PROPN
iajs-1867	170	14	wiley	wiley	PROPN
iajs-1867	170	15	&	&	CCONJ
iajs-1867	170	16	sons	son	NOUN
iajs-1867	170	17	,	,	PUNCT
iajs-1867	170	18	2006	2006	NUM
iajs-1867	170	19	.	.	PUNCT
iajs-1867	171	1	[	[	X
iajs-1867	171	2	16	16	NUM
iajs-1867	171	3	]	]	X
iajs-1867	171	4	c.	c.	PROPN
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iajs-1867	171	6	f.	f.	PROPN
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iajs-1867	171	8	,	,	PUNCT
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iajs-1867	171	10	topology	topology	NOUN
iajs-1867	171	11	,	,	PUNCT
iajs-1867	171	12	courier	courier	NOUN
iajs-1867	171	13	corporation	corporation	NOUN
iajs-1867	171	14	,	,	PUNCT
iajs-1867	171	15	1996	1996	NUM
iajs-1867	171	16	.	.	PUNCT
iajs-1867	172	1	[	[	X
iajs-1867	172	2	17	17	NUM
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iajs-1867	172	4	w.	w.	PROPN
iajs-1867	172	5	s.massey	s.massey	PROPN
iajs-1867	172	6	,	,	PUNCT
iajs-1867	172	7	a	a	DET
iajs-1867	172	8	basic	basic	ADJ
iajs-1867	172	9	course	course	NOUN
iajs-1867	172	10	in	in	ADP
iajs-1867	172	11	algebraic	algebraic	PROPN
iajs-1867	172	12	topology	topology	NOUN
iajs-1867	172	13	,	,	PUNCT
iajs-1867	172	14	springer	springer	NOUN
iajs-1867	172	15	science	science	PROPN
iajs-1867	172	16	&	&	CCONJ
iajs-1867	172	17	business	business	NOUN
iajs-1867	172	18	media	medium	NOUN
iajs-1867	172	19	,	,	PUNCT
iajs-1867	172	20	1991	1991	NUM
iajs-1867	172	21	.	.	PUNCT
iajs-1867	173	1	[	[	X
iajs-1867	173	2	18	18	NUM
iajs-1867	173	3	]	]	PUNCT
iajs-1867	173	4	a.hatcher	a.hatcher	NOUN
iajs-1867	173	5	,	,	PUNCT
iajs-1867	173	6	algebraic	algebraic	ADJ
iajs-1867	173	7	topology	topology	NOUN
iajs-1867	173	8	,	,	PUNCT
iajs-1867	173	9	cambridge	cambridge	PROPN
iajs-1867	173	10	university	university	PROPN
iajs-1867	173	11	press	press	NOUN
iajs-1867	173	12	,	,	PUNCT
iajs-1867	173	13	2002	2002	NUM
iajs-1867	173	14	.	.	PUNCT
iajs-1867	174	1	[	[	X
iajs-1867	174	2	19	19	NUM
iajs-1867	174	3	]	]	PUNCT
iajs-1867	174	4	a.	a.	NOUN
iajs-1867	174	5	ouahab	ouahab	PROPN
iajs-1867	174	6	;	;	PUNCT
iajs-1867	174	7	l.	l.	PROPN
iajs-1867	174	8	go’miewicz	go’miewicz	PROPN
iajs-1867	174	9	and	and	CCONJ
iajs-1867	174	10	s.	s.	PROPN
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iajs-1867	174	12	,	,	PUNCT
iajs-1867	174	13	solution	solution	NOUN
iajs-1867	174	14	sets	set	NOUN
iajs-1867	174	15	for	for	ADP
iajs-1867	174	16	differential	differential	ADJ
iajs-1867	174	17	equations	equation	NOUN
iajs-1867	174	18	and	and	CCONJ
iajs-1867	174	19	inclusions	inclusion	NOUN
iajs-1867	174	20	,	,	PUNCT
iajs-1867	174	21	walter	walter	PROPN
iajs-1867	174	22	de	de	PROPN
iajs-1867	174	23	gruyter	gruyter	NOUN
iajs-1867	174	24	,	,	PUNCT
iajs-1867	174	25	2012	2012	NUM
iajs-1867	174	26	.	.	PUNCT
iajs-1867	175	1	[	[	X
iajs-1867	175	2	20	20	NUM
iajs-1867	175	3	]	]	PUNCT
iajs-1867	175	4	m.	m.	NOUN
iajs-1867	175	5	s.	s.	PROPN
iajs-1867	175	6	nakahara	nakahara	PROPN
iajs-1867	175	7	,	,	PUNCT
iajs-1867	175	8	geometry	geometry	NOUN
iajs-1867	175	9	topology	topology	NOUN
iajs-1867	175	10	and	and	CCONJ
iajs-1867	175	11	physics	physics	NOUN
iajs-1867	175	12	,	,	PUNCT
iajs-1867	175	13	second	second	ADJ
iajs-1867	175	14	edition	edition	NOUN
iajs-1867	175	15	,	,	PUNCT
iajs-1867	175	16	taylor	taylor	PROPN
iajs-1867	175	17	and	and	CCONJ
iajs-1867	175	18	francis	francis	PROPN
iajs-1867	175	19	group	group	PROPN
iajs-1867	175	20	,	,	PUNCT
iajs-1867	175	21	new	new	PROPN
iajs-1867	175	22	york	york	PROPN
iajs-1867	175	23	london	london	PROPN
iajs-1867	175	24	,	,	PUNCT
iajs-1867	175	25	2003	2003	NUM
iajs-1867	175	26	.	.	PUNCT
iajs-1867	176	1	[	[	X
iajs-1867	176	2	21	21	NUM
iajs-1867	176	3	]	]	X
iajs-1867	176	4	r.	r.	PROPN
iajs-1867	176	5	anant	anant	PROPN
iajs-1867	176	6	shastri	shastri	PROPN
iajs-1867	176	7	.	.	PROPN
iajs-1867	176	8	,	,	PUNCT
iajs-1867	176	9	algebraic	algebraic	PROPN
iajs-1867	176	10	topology	topology	NOUN
iajs-1867	176	11	,	,	PUNCT
iajs-1867	176	12	crc	crc	NOUN
iajs-1867	176	13	press	press	NOUN
iajs-1867	176	14	,	,	PUNCT
iajs-1867	176	15	2013	2013	NUM
iajs-1867	176	16	.	.	PUNCT
iajs-1867	177	1	[	[	X
iajs-1867	177	2	22	22	NUM
iajs-1867	177	3	]	]	PUNCT
iajs-1867	177	4	m.	m.	NOUN
iajs-1867	177	5	tkachenko	tkachenko	PROPN
iajs-1867	177	6	and	and	CCONJ
iajs-1867	177	7	arhangel	arhangel	NOUN
iajs-1867	177	8	's	's	PART
iajs-1867	177	9	kii	kii	PROPN
iajs-1867	177	10	a.	a.	PROPN
iajs-1867	177	11	,	,	PUNCT
iajs-1867	177	12	topological	topological	ADJ
iajs-1867	177	13	groups	group	NOUN
iajs-1867	177	14	and	and	CCONJ
iajs-1867	177	15	related	related	ADJ
iajs-1867	177	16	structures	structure	NOUN
iajs-1867	177	17	,	,	PUNCT
iajs-1867	177	18	an	an	DET
iajs-1867	177	19	introduction	introduction	NOUN
iajs-1867	177	20	to	to	ADP
iajs-1867	177	21	topological	topological	ADJ
iajs-1867	177	22	algebra	algebra	NOUN
iajs-1867	177	23	,	,	PUNCT
iajs-1867	177	24	springer	springer	NOUN
iajs-1867	177	25	science	science	PROPN
iajs-1867	177	26	&	&	CCONJ
iajs-1867	177	27	business	business	NOUN
iajs-1867	177	28	media	medium	NOUN
iajs-1867	177	29	,	,	PUNCT
iajs-1867	177	30	2008	2008	NUM
iajs-1867	177	31	.	.	PUNCT