id	sid	tid	token	lemma	pos
iajs-4071	1	1	363	363	NUM
iajs-4071	1	2	©	©	PROPN
iajs-4071	1	3	2025	2025	NUM
iajs-4071	1	4	the	the	DET
iajs-4071	1	5	author(s	author(s	NOUN
iajs-4071	1	6	)	)	PUNCT
iajs-4071	1	7	.	.	PUNCT
iajs-4071	2	1	published	publish	VERB
iajs-4071	2	2	by	by	ADP
iajs-4071	2	3	college	college	NOUN
iajs-4071	2	4	of	of	ADP
iajs-4071	2	5	education	education	NOUN
iajs-4071	2	6	for	for	ADP
iajs-4071	2	7	pure	pure	ADJ
iajs-4071	2	8	science	science	NOUN
iajs-4071	2	9	(	(	PUNCT
iajs-4071	2	10	ibn	ibn	PROPN
iajs-4071	2	11	al	al	PROPN
iajs-4071	2	12	-	-	PUNCT
iajs-4071	2	13	haitham	haitham	PROPN
iajs-4071	2	14	)	)	PUNCT
iajs-4071	2	15	,	,	PUNCT
iajs-4071	2	16	university	university	NOUN
iajs-4071	2	17	of	of	ADP
iajs-4071	2	18	baghdad	baghdad	PROPN
iajs-4071	2	19	.	.	PUNCT
iajs-4071	3	1	this	this	PRON
iajs-4071	3	2	is	be	AUX
iajs-4071	3	3	an	an	DET
iajs-4071	3	4	open	open	ADJ
iajs-4071	3	5	-	-	PUNCT
iajs-4071	3	6	access	access	NOUN
iajs-4071	3	7	article	article	NOUN
iajs-4071	3	8	distributed	distribute	VERB
iajs-4071	3	9	under	under	ADP
iajs-4071	3	10	the	the	DET
iajs-4071	3	11	terms	term	NOUN
iajs-4071	3	12	of	of	ADP
iajs-4071	3	13	the	the	DET
iajs-4071	3	14	creative	creative	ADJ
iajs-4071	3	15	commons	common	NOUN
iajs-4071	3	16	attribution	attribution	NOUN
iajs-4071	3	17	4.0	4.0	NUM
iajs-4071	3	18	international	international	ADJ
iajs-4071	3	19	license	license	NOUN
iajs-4071	3	20	̃	̃	NOUN
iajs-4071	3	21	open	open	ADJ
iajs-4071	3	22	sets	set	NOUN
iajs-4071	3	23	and	and	CCONJ
iajs-4071	3	24	̃	̃	NOUN
iajs-4071	3	25	continuous	continuous	ADJ
iajs-4071	3	26	in	in	ADP
iajs-4071	3	27	soft	soft	ADJ
iajs-4071	3	28	topological	topological	ADJ
iajs-4071	3	29	spaces	space	NOUN
iajs-4071	3	30	nehmat	nehmat	PROPN
iajs-4071	3	31	k.	k.	PROPN
iajs-4071	3	32	ahmed	ahmed	PROPN
iajs-4071	3	33	1	1	PROPN
iajs-4071	3	34	and	and	CCONJ
iajs-4071	3	35	shaymaa	shaymaa	NOUN
iajs-4071	3	36	m.	m.	NOUN
iajs-4071	3	37	mohammed	mohammed	PROPN
iajs-4071	4	1	2	2	NUM
iajs-4071	4	2	*	*	SYM
iajs-4071	4	3	1,2	1,2	NUM
iajs-4071	4	4	department	department	NOUN
iajs-4071	4	5	of	of	ADP
iajs-4071	4	6	mathematics	mathematic	NOUN
iajs-4071	4	7	,	,	PUNCT
iajs-4071	4	8	college	college	NOUN
iajs-4071	4	9	of	of	ADP
iajs-4071	4	10	education	education	NOUN
iajs-4071	4	11	,	,	PUNCT
iajs-4071	4	12	salahaddin	salahaddin	VERB
iajs-4071	4	13	university	university	NOUN
iajs-4071	4	14	,	,	PUNCT
iajs-4071	4	15	erbil	erbil	PROPN
iajs-4071	4	16	,	,	PUNCT
iajs-4071	4	17	iraq	iraq	PROPN
iajs-4071	4	18	.	.	PUNCT
iajs-4071	5	1	*	*	PUNCT
iajs-4071	5	2	corresponding	correspond	VERB
iajs-4071	5	3	author	author	NOUN
iajs-4071	5	4	.	.	PUNCT
iajs-4071	6	1	received	receive	VERB
iajs-4071	6	2	:	:	PUNCT
iajs-4071	6	3	15	15	NUM
iajs-4071	6	4	december	december	PROPN
iajs-4071	6	5	2024	2024	NUM
iajs-4071	6	6	accepted	accept	VERB
iajs-4071	6	7	:	:	PUNCT
iajs-4071	6	8	16	16	NUM
iajs-4071	6	9	june	june	PROPN
iajs-4071	6	10	2025	2025	NUM
iajs-4071	6	11	published	publish	VERB
iajs-4071	6	12	:	:	PUNCT
iajs-4071	6	13	20	20	NUM
iajs-4071	6	14	october	october	NOUN
iajs-4071	6	15	2025	2025	NUM
iajs-4071	6	16	doi.org/10.30526/38.4.4071	doi.org/10.30526/38.4.4071	ADJ
iajs-4071	6	17	abstract	abstract	NOUN
iajs-4071	6	18	our	our	PRON
iajs-4071	6	19	work	work	NOUN
iajs-4071	6	20	introduces	introduce	VERB
iajs-4071	6	21	the	the	DET
iajs-4071	6	22	notion	notion	NOUN
iajs-4071	6	23	of	of	ADP
iajs-4071	6	24	-open	-open	ADJ
iajs-4071	6	25	set	set	NOUN
iajs-4071	6	26	.	.	PUNCT
iajs-4071	7	1	this	this	DET
iajs-4071	7	2	class	class	NOUN
iajs-4071	7	3	of	of	ADP
iajs-4071	7	4	̃	̃	PROPN
iajs-4071	7	5	open	open	ADJ
iajs-4071	7	6	sets	set	NOUN
iajs-4071	7	7	is	be	AUX
iajs-4071	7	8	not	not	PART
iajs-4071	7	9	directly	directly	ADV
iajs-4071	7	10	comparable	comparable	ADJ
iajs-4071	7	11	to	to	ADP
iajs-4071	7	12	the	the	DET
iajs-4071	7	13	categories	category	NOUN
iajs-4071	7	14	of	of	ADP
iajs-4071	7	15	soft	soft	ADJ
iajs-4071	7	16	open	open	ADJ
iajs-4071	7	17	,	,	PUNCT
iajs-4071	7	18	-closed	-closed	ADJ
iajs-4071	7	19	.	.	PUNCT
iajs-4071	8	1	we	we	PRON
iajs-4071	8	2	demonstrate	demonstrate	VERB
iajs-4071	8	3	that	that	SCONJ
iajs-4071	8	4	the	the	DET
iajs-4071	8	5	category	category	NOUN
iajs-4071	8	6	of	of	ADP
iajs-4071	8	7	̃	̃	NOUN
iajs-4071	8	8	-open	-open	NOUN
iajs-4071	8	9	sets	set	NOUN
iajs-4071	8	10	lies	lie	VERB
iajs-4071	8	11	strictly	strictly	ADV
iajs-4071	8	12	between	between	ADP
iajs-4071	8	13	the	the	DET
iajs-4071	8	14	class	class	NOUN
iajs-4071	8	15	of	of	ADP
iajs-4071	8	16	̃	̃	NOUN
iajs-4071	8	17	-open	-open	NOUN
iajs-4071	8	18	sets	set	NOUN
iajs-4071	8	19	and	and	CCONJ
iajs-4071	8	20	̃	̃	NOUN
iajs-4071	8	21	-open	-open	NOUN
iajs-4071	8	22	sets	set	NOUN
iajs-4071	8	23	.	.	PUNCT
iajs-4071	9	1	additionally	additionally	ADV
iajs-4071	9	2	,	,	PUNCT
iajs-4071	9	3	we	we	PRON
iajs-4071	9	4	investigate	investigate	VERB
iajs-4071	9	5	the	the	DET
iajs-4071	9	6	connections	connection	NOUN
iajs-4071	9	7	that	that	PRON
iajs-4071	9	8	exist	exist	VERB
iajs-4071	9	9	between	between	ADP
iajs-4071	9	10	̃	̃	ADJ
iajs-4071	9	11	-open	-open	ADJ
iajs-4071	9	12	sets	set	NOUN
iajs-4071	9	13	along	along	ADP
iajs-4071	9	14	with	with	ADP
iajs-4071	9	15	other	other	ADJ
iajs-4071	9	16	kinds	kind	NOUN
iajs-4071	9	17	of	of	ADP
iajs-4071	9	18	soft	soft	ADJ
iajs-4071	9	19	sets	set	NOUN
iajs-4071	9	20	.	.	PUNCT
iajs-4071	10	1	moreover	moreover	ADV
iajs-4071	10	2	,	,	PUNCT
iajs-4071	10	3	we	we	PRON
iajs-4071	10	4	provide	provide	VERB
iajs-4071	10	5	several	several	ADJ
iajs-4071	10	6	criteria	criterion	NOUN
iajs-4071	10	7	that	that	PRON
iajs-4071	10	8	are	be	AUX
iajs-4071	10	9	sufficient	sufficient	ADJ
iajs-4071	10	10	for	for	ADP
iajs-4071	10	11	determining	determine	VERB
iajs-4071	10	12	the	the	DET
iajs-4071	10	13	equivalence	equivalence	NOUN
iajs-4071	10	14	between	between	ADP
iajs-4071	10	15	̃	̃	NOUN
iajs-4071	10	16	-open	-open	NOUN
iajs-4071	10	17	sets	set	NOUN
iajs-4071	10	18	and	and	CCONJ
iajs-4071	10	19	every	every	DET
iajs-4071	10	20	one	one	NUM
iajs-4071	10	21	of	of	ADP
iajs-4071	10	22	̃	̃	NOUN
iajs-4071	10	23	-open	-open	NOUN
iajs-4071	10	24	sets	set	NOUN
iajs-4071	10	25	and	and	CCONJ
iajs-4071	10	26	̃	̃	NOUN
iajs-4071	10	27	-open	-open	NOUN
iajs-4071	10	28	sets	set	NOUN
iajs-4071	10	29	.	.	PUNCT
iajs-4071	11	1	also	also	ADV
iajs-4071	11	2	,	,	PUNCT
iajs-4071	11	3	according	accord	VERB
iajs-4071	11	4	to	to	ADP
iajs-4071	11	5	our	our	PRON
iajs-4071	11	6	findings	finding	NOUN
iajs-4071	11	7	,	,	PUNCT
iajs-4071	11	8	the	the	DET
iajs-4071	11	9	family	family	NOUN
iajs-4071	11	10	of	of	ADP
iajs-4071	11	11	̃	̃	PROPN
iajs-4071	11	12	-open	-open	NOUN
iajs-4071	11	13	sets	set	NOUN
iajs-4071	11	14	is	be	AUX
iajs-4071	11	15	a	a	DET
iajs-4071	11	16	supra	supra	ADJ
iajs-4071	11	17	soft	soft	ADJ
iajs-4071	11	18	topology	topology	NOUN
iajs-4071	11	19	.	.	PUNCT
iajs-4071	12	1	furthermore	furthermore	ADV
iajs-4071	12	2	,	,	PUNCT
iajs-4071	12	3	we	we	PRON
iajs-4071	12	4	make	make	VERB
iajs-4071	12	5	it	it	PRON
iajs-4071	12	6	clear	clear	ADJ
iajs-4071	12	7	the	the	DET
iajs-4071	12	8	correlation	correlation	NOUN
iajs-4071	12	9	that	that	PRON
iajs-4071	12	10	exists	exist	VERB
iajs-4071	12	11	between	between	ADP
iajs-4071	12	12	the	the	DET
iajs-4071	12	13	respective	respective	ADJ
iajs-4071	12	14	categories	category	NOUN
iajs-4071	12	15	of	of	ADP
iajs-4071	12	16	̃	̃	PROPN
iajs-4071	12	17	-open	-open	ADJ
iajs-4071	12	18	sets	set	NOUN
iajs-4071	12	19	in	in	ADP
iajs-4071	12	20	a	a	DET
iajs-4071	12	21	soft	soft	ADJ
iajs-4071	12	22	topological	topological	ADJ
iajs-4071	12	23	space	space	NOUN
iajs-4071	12	24	and	and	CCONJ
iajs-4071	12	25	in	in	ADP
iajs-4071	12	26	its	its	PRON
iajs-4071	12	27	soft	soft	ADJ
iajs-4071	12	28	topological	topological	ADJ
iajs-4071	12	29	subspace	subspace	NOUN
iajs-4071	12	30	.	.	PUNCT
iajs-4071	13	1	finally	finally	ADV
iajs-4071	13	2	,	,	PUNCT
iajs-4071	13	3	the	the	DET
iajs-4071	13	4	class	class	NOUN
iajs-4071	13	5	of	of	ADP
iajs-4071	13	6	̃	̃	ADJ
iajs-4071	13	7	-continuous	-continuous	ADJ
iajs-4071	13	8	function	function	NOUN
iajs-4071	13	9	is	be	AUX
iajs-4071	13	10	introduced	introduce	VERB
iajs-4071	13	11	,	,	PUNCT
iajs-4071	13	12	it	it	PRON
iajs-4071	13	13	is	be	AUX
iajs-4071	13	14	main	main	ADJ
iajs-4071	13	15	properties	property	NOUN
iajs-4071	13	16	are	be	AUX
iajs-4071	13	17	studied	study	VERB
iajs-4071	13	18	and	and	CCONJ
iajs-4071	13	19	derive	derive	VERB
iajs-4071	13	20	some	some	PRON
iajs-4071	13	21	of	of	ADP
iajs-4071	13	22	the	the	DET
iajs-4071	13	23	properties	property	NOUN
iajs-4071	13	24	of	of	ADP
iajs-4071	13	25	these	these	DET
iajs-4071	13	26	soft	soft	ADJ
iajs-4071	13	27	functions	function	NOUN
iajs-4071	13	28	under	under	ADP
iajs-4071	13	29	the	the	DET
iajs-4071	13	30	soft	soft	ADJ
iajs-4071	13	31	composition	composition	NOUN
iajs-4071	13	32	of	of	ADP
iajs-4071	13	33	soft	soft	ADJ
iajs-4071	13	34	functions	function	NOUN
iajs-4071	13	35	.	.	PUNCT
iajs-4071	14	1	keywords	keyword	NOUN
iajs-4071	14	2	:	:	PUNCT
iajs-4071	14	3	open	open	ADJ
iajs-4071	14	4	,	,	PUNCT
iajs-4071	14	5	soft	soft	ADJ
iajs-4071	14	6	soft	soft	ADJ
iajs-4071	14	7	semi	semi	ADJ
iajs-4071	14	8	-	-	ADJ
iajs-4071	14	9	closed	closed	ADJ
iajs-4071	14	10	,	,	PUNCT
iajs-4071	14	11	-continuous	-continuous	ADJ
iajs-4071	14	12	function	function	NOUN
iajs-4071	14	13	.	.	PUNCT
iajs-4071	15	1	1	1	X
iajs-4071	15	2	.	.	X
iajs-4071	15	3	introduction	introduction	NOUN
iajs-4071	15	4	the	the	DET
iajs-4071	15	5	concept	concept	NOUN
iajs-4071	15	6	of	of	ADP
iajs-4071	15	7	first	first	ADV
iajs-4071	15	8	using	use	VERB
iajs-4071	15	9	soft	soft	ADJ
iajs-4071	15	10	set	set	NOUN
iajs-4071	15	11	theory	theory	NOUN
iajs-4071	15	12	by	by	ADP
iajs-4071	15	13	(	(	PUNCT
iajs-4071	15	14	1	1	X
iajs-4071	15	15	)	)	PUNCT
iajs-4071	15	16	was	be	AUX
iajs-4071	15	17	presented	present	VERB
iajs-4071	15	18	as	as	ADP
iajs-4071	15	19	a	a	DET
iajs-4071	15	20	novel	novel	ADJ
iajs-4071	15	21	tool	tool	NOUN
iajs-4071	15	22	in	in	ADP
iajs-4071	15	23	mathematics	mathematic	NOUN
iajs-4071	15	24	for	for	ADP
iajs-4071	15	25	dealing	deal	VERB
iajs-4071	15	26	with	with	ADP
iajs-4071	15	27	several	several	ADJ
iajs-4071	15	28	forms	form	NOUN
iajs-4071	15	29	of	of	ADP
iajs-4071	15	30	ambiguity	ambiguity	NOUN
iajs-4071	15	31	in	in	ADP
iajs-4071	15	32	complicated	complicated	ADJ
iajs-4071	15	33	scientific	scientific	ADJ
iajs-4071	15	34	problems	problem	NOUN
iajs-4071	15	35	and	and	CCONJ
iajs-4071	15	36	solving	solve	VERB
iajs-4071	15	37	these	these	DET
iajs-4071	15	38	problems	problem	NOUN
iajs-4071	15	39	.	.	PUNCT
iajs-4071	16	1	soft	soft	ADJ
iajs-4071	16	2	sets	set	NOUN
iajs-4071	16	3	research	research	NOUN
iajs-4071	16	4	and	and	CCONJ
iajs-4071	16	5	its	its	PRON
iajs-4071	16	6	characteristics	characteristic	NOUN
iajs-4071	16	7	were	be	AUX
iajs-4071	16	8	used	use	VERB
iajs-4071	16	9	to	to	ADP
iajs-4071	16	10	several	several	ADJ
iajs-4071	16	11	areas	area	NOUN
iajs-4071	16	12	of	of	ADP
iajs-4071	16	13	mathematics	mathematic	NOUN
iajs-4071	16	14	,	,	PUNCT
iajs-4071	16	15	including	include	VERB
iajs-4071	16	16	theory	theory	NOUN
iajs-4071	16	17	,	,	PUNCT
iajs-4071	16	18	probability	probability	NOUN
iajs-4071	16	19	,	,	PUNCT
iajs-4071	16	20	operations	operation	NOUN
iajs-4071	16	21	research	research	NOUN
iajs-4071	16	22	,	,	PUNCT
iajs-4071	16	23	algebra	algebra	NOUN
iajs-4071	16	24	,	,	PUNCT
iajs-4071	16	25	mathematical	mathematical	ADJ
iajs-4071	16	26	analysis	analysis	NOUN
iajs-4071	16	27	,	,	PUNCT
iajs-4071	16	28	etc	etc	X
iajs-4071	16	29	.	.	X
iajs-4071	16	30	in	in	ADP
iajs-4071	16	31	2011	2011	NUM
iajs-4071	16	32	,	,	PUNCT
iajs-4071	16	33	the	the	DET
iajs-4071	16	34	main	main	ADJ
iajs-4071	16	35	concepts	concept	NOUN
iajs-4071	16	36	of	of	ADP
iajs-4071	16	37	soft	soft	ADJ
iajs-4071	16	38	topologies	topology	NOUN
iajs-4071	16	39	were	be	AUX
iajs-4071	16	40	investigated	investigate	VERB
iajs-4071	16	41	by	by	ADP
iajs-4071	16	42	(	(	PUNCT
iajs-4071	16	43	2	2	NUM
iajs-4071	16	44	)	)	PUNCT
iajs-4071	16	45	.	.	PUNCT
iajs-4071	17	1	they	they	PRON
iajs-4071	17	2	presented	present	VERB
iajs-4071	17	3	the	the	DET
iajs-4071	17	4	ideas	idea	NOUN
iajs-4071	17	5	of	of	ADP
iajs-4071	17	6	a	a	DET
iajs-4071	17	7	soft	soft	ADJ
iajs-4071	17	8	open	open	ADJ
iajs-4071	17	9	set	set	NOUN
iajs-4071	17	10	and	and	CCONJ
iajs-4071	17	11	showed	show	VERB
iajs-4071	17	12	that	that	SCONJ
iajs-4071	17	13	a	a	DET
iajs-4071	17	14	soft	soft	ADJ
iajs-4071	17	15	topological	topological	ADJ
iajs-4071	17	16	space	space	NOUN
iajs-4071	17	17	produces	produce	VERB
iajs-4071	17	18	a	a	DET
iajs-4071	17	19	parameterized	parameterized	ADJ
iajs-4071	17	20	family	family	NOUN
iajs-4071	17	21	of	of	ADP
iajs-4071	17	22	topological	topological	ADJ
iajs-4071	17	23	spaces	space	NOUN
iajs-4071	17	24	,	,	PUNCT
iajs-4071	17	25	soft	soft	ADJ
iajs-4071	17	26	closed	closed	ADJ
iajs-4071	17	27	set	set	NOUN
iajs-4071	17	28	,	,	PUNCT
iajs-4071	17	29	soft	soft	ADJ
iajs-4071	17	30	interior	interior	ADJ
iajs-4071	17	31	point	point	NOUN
iajs-4071	17	32	,	,	PUNCT
iajs-4071	17	33	soft	soft	ADJ
iajs-4071	17	34	closure	closure	NOUN
iajs-4071	17	35	and	and	CCONJ
iajs-4071	17	36	soft	soft	ADJ
iajs-4071	17	37	separation	separation	NOUN
iajs-4071	17	38	axioms	axiom	NOUN
iajs-4071	17	39	.	.	PUNCT
iajs-4071	18	1	a	a	DET
iajs-4071	18	2	multitude	multitude	NOUN
iajs-4071	18	3	of	of	ADP
iajs-4071	18	4	contributions	contribution	NOUN
iajs-4071	18	5	has	have	AUX
iajs-4071	18	6	been	be	AUX
iajs-4071	18	7	made	make	VERB
iajs-4071	18	8	to	to	ADP
iajs-4071	18	9	the	the	DET
iajs-4071	18	10	research	research	NOUN
iajs-4071	18	11	of	of	ADP
iajs-4071	18	12	topological	topological	ADJ
iajs-4071	18	13	principles	principle	NOUN
iajs-4071	18	14	in	in	ADP
iajs-4071	18	15	soft	soft	ADJ
iajs-4071	18	16	environments	environment	NOUN
iajs-4071	18	17	after	after	SCONJ
iajs-4071	18	18	soft	soft	ADJ
iajs-4071	18	19	topology	topology	NOUN
iajs-4071	18	20	was	be	AUX
iajs-4071	18	21	developed	develop	VERB
iajs-4071	18	22	(	(	PUNCT
iajs-4071	18	23	36	36	NUM
iajs-4071	18	24	)	)	PUNCT
iajs-4071	18	25	.	.	PUNCT
iajs-4071	19	1	athar	athar	PROPN
iajs-4071	19	2	kharal	kharal	PROPN
iajs-4071	19	3	,	,	PUNCT
iajs-4071	19	4	a.	a.	NOUN
iajs-4071	19	5	and	and	CCONJ
iajs-4071	19	6	ahmad	ahmad	PROPN
iajs-4071	19	7	,	,	PUNCT
iajs-4071	19	8	b.	b.	PROPN
iajs-4071	19	9	(	(	PUNCT
iajs-4071	19	10	7	7	X
iajs-4071	19	11	)	)	PUNCT
iajs-4071	19	12	explained	explain	VERB
iajs-4071	19	13	what	what	PRON
iajs-4071	19	14	soft	soft	ADJ
iajs-4071	19	15	mapping	mapping	NOUN
iajs-4071	19	16	is	be	AUX
iajs-4071	19	17	in	in	ADP
iajs-4071	19	18	the	the	DET
iajs-4071	19	19	context	context	NOUN
iajs-4071	19	20	of	of	ADP
iajs-4071	19	21	soft	soft	ADJ
iajs-4071	19	22	classes	class	NOUN
iajs-4071	19	23	and	and	CCONJ
iajs-4071	19	24	investigated	investigate	VERB
iajs-4071	19	25	several	several	ADJ
iajs-4071	19	26	properties	property	NOUN
iajs-4071	19	27	of	of	ADP
iajs-4071	19	28	soft	soft	ADJ
iajs-4071	19	29	set	set	VERB
iajs-4071	19	30	images	image	NOUN
iajs-4071	19	31	and	and	CCONJ
iajs-4071	19	32	inverse	inverse	NOUN
iajs-4071	19	33	images	image	NOUN
iajs-4071	19	34	.	.	PUNCT
iajs-4071	20	1	chen	chen	PROPN
iajs-4071	20	2	(	(	PUNCT
iajs-4071	20	3	8)	8)	NUM
iajs-4071	20	4	introduced	introduce	VERB
iajs-4071	20	5	and	and	CCONJ
iajs-4071	20	6	investigated	investigate	VERB
iajs-4071	20	7	soft	soft	ADJ
iajs-4071	20	8	semi	semi	ADJ
iajs-4071	20	9	-	-	ADJ
iajs-4071	20	10	open	open	ADJ
iajs-4071	20	11	sets	set	NOUN
iajs-4071	20	12	and	and	CCONJ
iajs-4071	20	13	their	their	PRON
iajs-4071	20	14	properties	property	NOUN
iajs-4071	20	15	.	.	PUNCT
iajs-4071	21	1	mahanta	mahanta	ADJ
iajs-4071	21	2	and	and	CCONJ
iajs-4071	21	3	das	das	PROPN
iajs-4071	21	4	(	(	PUNCT
iajs-4071	21	5	9	9	NUM
iajs-4071	21	6	)	)	PUNCT
iajs-4071	21	7	also	also	ADV
iajs-4071	21	8	introduced	introduce	VERB
iajs-4071	21	9	and	and	CCONJ
iajs-4071	21	10	defined	define	VERB
iajs-4071	21	11	soft	soft	ADJ
iajs-4071	21	12	semi	semi	ADJ
iajs-4071	21	13	-	-	ADJ
iajs-4071	21	14	open	open	ADJ
iajs-4071	21	15	sets	set	NOUN
iajs-4071	21	16	and	and	CCONJ
iajs-4071	21	17	soft	soft	ADJ
iajs-4071	21	18	semi	semi	ADJ
iajs-4071	21	19	-	-	ADJ
iajs-4071	21	20	continuous	continuous	ADJ
iajs-4071	21	21	functions	function	NOUN
iajs-4071	21	22	.	.	PUNCT
iajs-4071	22	1	the	the	DET
iajs-4071	22	2	authors	author	NOUN
iajs-4071	22	3	of	of	ADP
iajs-4071	22	4	(	(	PUNCT
iajs-4071	22	5	10	10	NUM
iajs-4071	22	6	)	)	PUNCT
iajs-4071	22	7	introduced	introduce	VERB
iajs-4071	22	8	the	the	DET
iajs-4071	22	9	concept	concept	NOUN
iajs-4071	22	10	of	of	ADP
iajs-4071	22	11	soft	soft	ADJ
iajs-4071	22	12	-open	-open	ADJ
iajs-4071	22	13	subsets	subset	NOUN
iajs-4071	22	14	.	.	PUNCT
iajs-4071	23	1	however	however	ADV
iajs-4071	23	2	,	,	PUNCT
iajs-4071	23	3	this	this	DET
iajs-4071	23	4	work	work	NOUN
iajs-4071	23	5	introduces	introduce	VERB
iajs-4071	23	6	a	a	DET
iajs-4071	23	7	novel	novel	ADJ
iajs-4071	23	8	kind	kind	NOUN
iajs-4071	23	9	of	of	ADP
iajs-4071	23	10	soft	soft	ADJ
iajs-4071	23	11	open	open	ADJ
iajs-4071	23	12	sets	set	NOUN
iajs-4071	23	13	(	(	PUNCT
iajs-4071	23	14	respectively	respectively	ADV
iajs-4071	23	15	soft	soft	ADJ
iajs-4071	23	16	functions	function	NOUN
iajs-4071	23	17	)	)	PUNCT
iajs-4071	23	18	called	call	VERB
iajs-4071	23	19	̃	̃	PROPN
iajs-4071	23	20	open	open	ADJ
iajs-4071	23	21	sets	set	NOUN
iajs-4071	23	22	(	(	PUNCT
iajs-4071	23	23	resp	resp	NOUN
iajs-4071	23	24	.	.	PUNCT
iajs-4071	23	25	;	;	PUNCT
iajs-4071	24	1	̃	̃	NOUN
iajs-4071	24	2	-continuous	-continuous	ADJ
iajs-4071	24	3	functions	function	NOUN
iajs-4071	24	4	)	)	PUNCT
iajs-4071	24	5	,	,	PUNCT
iajs-4071	24	6	which	which	PRON
iajs-4071	24	7	are	be	AUX
iajs-4071	24	8	strictly	strictly	ADV
iajs-4071	24	9	placed	place	VERB
iajs-4071	24	10	between	between	ADP
iajs-4071	24	11	the	the	DET
iajs-4071	24	12	https://orcid.org/0000-0002-7134-3348	https://orcid.org/0000-0002-7134-3348	ADJ
iajs-4071	24	13	mailto:nehmat.ahmed@su.edu.krd	mailto:nehmat.ahmed@su.edu.krd	NOUN
iajs-4071	24	14	https://orcid.org/0009-0006-7522-2953	https://orcid.org/0009-0006-7522-2953	NOUN
iajs-4071	24	15	mailto:shaymaa.mohammed@su.edu.krd	mailto:shaymaa.mohammed@su.edu.krd	PROPN
iajs-4071	24	16	https://orcid.org/0000-0002-7134-3348	https://orcid.org/0000-0002-7134-3348	ADJ
iajs-4071	24	17	mailto:nehmat.ahmed@su.edu.krd	mailto:nehmat.ahmed@su.edu.krd	NOUN
iajs-4071	24	18	https://orcid.org/0009-0006-7522-2953	https://orcid.org/0009-0006-7522-2953	NOUN
iajs-4071	24	19	mailto:shaymaa.mohammed@su.edu.krd	mailto:shaymaa.mohammed@su.edu.krd	PROPN
iajs-4071	24	20	https://orcid.org/0000-0002-7134-3348	https://orcid.org/0000-0002-7134-3348	ADJ
iajs-4071	24	21	mailto:nehmat.ahmed@su.edu.krd	mailto:nehmat.ahmed@su.edu.krd	NOUN
iajs-4071	24	22	https://orcid.org/0009-0006-7522-2953	https://orcid.org/0009-0006-7522-2953	NOUN
iajs-4071	24	23	mailto:shaymaa.mohammed@su.edu.krd	mailto:shaymaa.mohammed@su.edu.krd	PROPN
iajs-4071	24	24	https://orcid.org/0000-0002-7134-3348	https://orcid.org/0000-0002-7134-3348	ADJ
iajs-4071	24	25	mailto:nehmat.ahmed@su.edu.krd	mailto:nehmat.ahmed@su.edu.krd	NOUN
iajs-4071	24	26	https://orcid.org/0009-0006-7522-2953	https://orcid.org/0009-0006-7522-2953	NOUN
iajs-4071	24	27	mailto:shaymaa.mohammed@su.edu.krd	mailto:shaymaa.mohammed@su.edu.krd	PROPN
iajs-4071	24	28	https://orcid.org/0000-0002-7134-3348	https://orcid.org/0000-0002-7134-3348	ADJ
iajs-4071	24	29	mailto:nehmat.ahmed@su.edu.krd	mailto:nehmat.ahmed@su.edu.krd	NOUN
iajs-4071	24	30	https://orcid.org/0009-0006-7522-2953	https://orcid.org/0009-0006-7522-2953	NOUN
iajs-4071	24	31	mailto:shaymaa.mohammed@su.edu.krd	mailto:shaymaa.mohammed@su.edu.krd	PROPN
iajs-4071	24	32	https://orcid.org/0000-0002-7134-3348	https://orcid.org/0000-0002-7134-3348	ADJ
iajs-4071	24	33	mailto:nehmat.ahmed@su.edu.krd	mailto:nehmat.ahmed@su.edu.krd	NOUN
iajs-4071	24	34	https://orcid.org/0009-0006-7522-2953	https://orcid.org/0009-0006-7522-2953	NOUN
iajs-4071	24	35	mailto:shaymaa.mohammed@su.edu.krd	mailto:shaymaa.mohammed@su.edu.krd	PROPN
iajs-4071	24	36	ihjpas	ihjpas	PROPN
iajs-4071	24	37	.	.	PUNCT
iajs-4071	25	1	2025,38(4	2025,38(4	X
iajs-4071	25	2	)	)	PUNCT
iajs-4071	25	3	364	364	NUM
iajs-4071	25	4	soft	soft	ADJ
iajs-4071	25	5	classes	class	NOUN
iajs-4071	25	6	of	of	ADP
iajs-4071	25	7	̃	̃	ADJ
iajs-4071	25	8	open	open	ADJ
iajs-4071	25	9	sets	set	NOUN
iajs-4071	25	10	and	and	CCONJ
iajs-4071	25	11	̃	̃	NOUN
iajs-4071	25	12	open	open	ADJ
iajs-4071	25	13	sets	set	NOUN
iajs-4071	25	14	̃	̃	PROPN
iajs-4071	25	15	-continuous	-continuous	ADJ
iajs-4071	25	16	functions	function	NOUN
iajs-4071	25	17	and	and	CCONJ
iajs-4071	25	18	soft	soft	ADJ
iajs-4071	25	19	continuous	continuous	ADJ
iajs-4071	25	20	functions	function	NOUN
iajs-4071	25	21	)	)	PUNCT
iajs-4071	25	22	.	.	PUNCT
iajs-4071	26	1	some	some	PRON
iajs-4071	26	2	of	of	ADP
iajs-4071	26	3	̃	̃	ADJ
iajs-4071	26	4	-continuous	-continuous	ADJ
iajs-4071	26	5	functions	function	NOUN
iajs-4071	26	6	basic	basic	ADJ
iajs-4071	26	7	properties	property	NOUN
iajs-4071	26	8	and	and	CCONJ
iajs-4071	26	9	relationships	relationship	NOUN
iajs-4071	26	10	with	with	ADP
iajs-4071	26	11	some	some	DET
iajs-4071	26	12	other	other	ADJ
iajs-4071	26	13	types	type	NOUN
iajs-4071	26	14	of	of	ADP
iajs-4071	26	15	soft	soft	ADJ
iajs-4071	26	16	functions	function	NOUN
iajs-4071	26	17	are	be	AUX
iajs-4071	26	18	given	give	VERB
iajs-4071	26	19	.	.	PUNCT
iajs-4071	27	1	throughout	throughout	ADP
iajs-4071	27	2	this	this	DET
iajs-4071	27	3	work	work	NOUN
iajs-4071	27	4	,	,	PUNCT
iajs-4071	27	5	will	will	AUX
iajs-4071	27	6	be	be	AUX
iajs-4071	27	7	a	a	DET
iajs-4071	27	8	nonempty	nonempty	ADJ
iajs-4071	27	9	initial	initial	ADJ
iajs-4071	27	10	universal	universal	ADJ
iajs-4071	27	11	set	set	NOUN
iajs-4071	27	12	and	and	CCONJ
iajs-4071	27	13	will	will	AUX
iajs-4071	27	14	be	be	AUX
iajs-4071	27	15	a	a	DET
iajs-4071	27	16	set	set	NOUN
iajs-4071	27	17	of	of	ADP
iajs-4071	27	18	parameters	parameter	NOUN
iajs-4071	27	19	.	.	PUNCT
iajs-4071	28	1	(	(	PUNCT
iajs-4071	28	2	̃	̃	NOUN
iajs-4071	28	3	̃	̃	ADJ
iajs-4071	28	4	)	)	PUNCT
iajs-4071	28	5	̃	̃	NOUN
iajs-4071	28	6	̃	̃	NOUN
iajs-4071	28	7	)	)	PUNCT
iajs-4071	28	8	or	or	CCONJ
iajs-4071	28	9	basically	basically	ADV
iajs-4071	28	10	̃	̃	PROPN
iajs-4071	28	11	and	and	CCONJ
iajs-4071	28	12	̃	̃	PROPN
iajs-4071	28	13	show	show	VERB
iajs-4071	28	14	soft	soft	ADJ
iajs-4071	28	15	topological	topological	ADJ
iajs-4071	28	16	spaces	space	NOUN
iajs-4071	28	17	(	(	PUNCT
iajs-4071	28	18	simply	simply	ADV
iajs-4071	28	19	,	,	PUNCT
iajs-4071	28	20	sts	st	NOUN
iajs-4071	28	21	)	)	PUNCT
iajs-4071	28	22	,	,	PUNCT
iajs-4071	28	23	the	the	DET
iajs-4071	28	24	family	family	NOUN
iajs-4071	28	25	of	of	ADP
iajs-4071	28	26	all	all	DET
iajs-4071	28	27	soft	soft	ADJ
iajs-4071	28	28	clopen	clopen	ADJ
iajs-4071	28	29	sets	set	NOUN
iajs-4071	28	30	(	(	PUNCT
iajs-4071	28	31	resp	resp	NOUN
iajs-4071	28	32	.	.	PUNCT
iajs-4071	28	33	;	;	PUNCT
iajs-4071	28	34	semi	semi	ADV
iajs-4071	28	35	closed	closed	ADJ
iajs-4071	28	36	)	)	PUNCT
iajs-4071	28	37	in	in	ADP
iajs-4071	28	38	̃	̃	PROPN
iajs-4071	28	39	is	be	AUX
iajs-4071	28	40	denoted	denote	VERB
iajs-4071	28	41	by	by	ADP
iajs-4071	28	42	̃	̃	PROPN
iajs-4071	28	43	(	(	PUNCT
iajs-4071	28	44	̃	̃	NOUN
iajs-4071	28	45	)	)	PUNCT
iajs-4071	28	46	̃	̃	PROPN
iajs-4071	28	47	̃	̃	NOUN
iajs-4071	28	48	)	)	PUNCT
iajs-4071	28	49	)	)	PUNCT
iajs-4071	28	50	.	.	PUNCT
iajs-4071	29	1	a	a	DET
iajs-4071	29	2	pair	pair	NOUN
iajs-4071	29	3	(	(	PUNCT
iajs-4071	29	4	)	)	PUNCT
iajs-4071	29	5	is	be	AUX
iajs-4071	29	6	known	know	VERB
iajs-4071	29	7	as	as	ADP
iajs-4071	29	8	a	a	DET
iajs-4071	29	9	soft	soft	ADJ
iajs-4071	29	10	set	set	NOUN
iajs-4071	29	11	over	over	ADP
iajs-4071	29	12	,	,	PUNCT
iajs-4071	29	13	in	in	ADP
iajs-4071	29	14	which	which	PRON
iajs-4071	29	15	is	be	AUX
iajs-4071	29	16	a	a	DET
iajs-4071	29	17	function	function	NOUN
iajs-4071	29	18	therefore	therefore	ADV
iajs-4071	29	19	)	)	PUNCT
iajs-4071	29	20	the	the	DET
iajs-4071	29	21	collection	collection	NOUN
iajs-4071	29	22	of	of	ADP
iajs-4071	29	23	soft	soft	ADJ
iajs-4071	29	24	sets	set	NOUN
iajs-4071	29	25	(	(	PUNCT
iajs-4071	29	26	)	)	PUNCT
iajs-4071	29	27	over	over	ADP
iajs-4071	29	28	a	a	DET
iajs-4071	29	29	universal	universal	ADJ
iajs-4071	29	30	set	set	NOUN
iajs-4071	29	31	with	with	ADP
iajs-4071	29	32	the	the	DET
iajs-4071	29	33	parameter	parameter	NOUN
iajs-4071	29	34	set	set	NOUN
iajs-4071	29	35	is	be	AUX
iajs-4071	29	36	indicated	indicate	VERB
iajs-4071	29	37	by	by	ADP
iajs-4071	29	38	̃	̃	PROPN
iajs-4071	29	39	̃	̃	PROPN
iajs-4071	29	40	)	)	PUNCT
iajs-4071	29	41	.	.	PUNCT
iajs-4071	30	1	2.preliminaries	2.preliminaries	NUM
iajs-4071	30	2	2.1	2.1	NUM
iajs-4071	30	3	.	.	PUNCT
iajs-4071	31	1	definition	definition	NOUN
iajs-4071	31	2	(	(	PUNCT
iajs-4071	31	3	11	11	NUM
iajs-4071	31	4	)	)	PUNCT
iajs-4071	31	5	for	for	ADP
iajs-4071	31	6	any	any	DET
iajs-4071	31	7	two	two	NUM
iajs-4071	31	8	soft	soft	ADJ
iajs-4071	31	9	subsets	subset	NOUN
iajs-4071	31	10	)	)	PUNCT
iajs-4071	31	11	)	)	PUNCT
iajs-4071	31	12	over	over	ADP
iajs-4071	31	13	a	a	DET
iajs-4071	31	14	common	common	ADJ
iajs-4071	31	15	universe	universe	NOUN
iajs-4071	31	16	,	,	PUNCT
iajs-4071	31	17	we	we	PRON
iajs-4071	31	18	say	say	VERB
iajs-4071	31	19	that	that	PRON
iajs-4071	31	20	)	)	PUNCT
iajs-4071	31	21	is	be	AUX
iajs-4071	31	22	a	a	DET
iajs-4071	31	23	soft	soft	ADJ
iajs-4071	31	24	subset	subset	NOUN
iajs-4071	31	25	of	of	ADP
iajs-4071	31	26	)	)	PUNCT
iajs-4071	31	27	indicated	indicate	VERB
iajs-4071	31	28	as	as	ADP
iajs-4071	31	29	)	)	PUNCT
iajs-4071	31	30	̃	̃	PROPN
iajs-4071	31	31	)	)	PUNCT
iajs-4071	31	32	,	,	PUNCT
iajs-4071	31	33	if	if	SCONJ
iajs-4071	31	34	)	)	PUNCT
iajs-4071	31	35	)	)	PUNCT
iajs-4071	31	36	.	.	PUNCT
iajs-4071	32	1	2.2	2.2	NUM
iajs-4071	32	2	.	.	PUNCT
iajs-4071	32	3	definition	definition	NOUN
iajs-4071	32	4	(	(	PUNCT
iajs-4071	32	5	12	12	NUM
iajs-4071	32	6	)	)	PUNCT
iajs-4071	32	7	the	the	DET
iajs-4071	32	8	soft	soft	ADJ
iajs-4071	32	9	complement	complement	NOUN
iajs-4071	32	10	of	of	ADP
iajs-4071	32	11	a	a	DET
iajs-4071	32	12	soft	soft	ADJ
iajs-4071	32	13	set	set	NOUN
iajs-4071	32	14	)	)	PUNCT
iajs-4071	32	15	is	be	AUX
iajs-4071	32	16	indicated	indicate	VERB
iajs-4071	32	17	by	by	ADP
iajs-4071	32	18	)	)	PUNCT
iajs-4071	32	19	or	or	CCONJ
iajs-4071	32	20	̃	̃	PROPN
iajs-4071	32	21	)	)	PUNCT
iajs-4071	32	22	and	and	CCONJ
iajs-4071	32	23	is	be	AUX
iajs-4071	32	24	described	describe	VERB
iajs-4071	32	25	as	as	ADP
iajs-4071	32	26	)	)	PUNCT
iajs-4071	32	27	)	)	PUNCT
iajs-4071	32	28	in	in	ADP
iajs-4071	32	29	which	which	PRON
iajs-4071	32	30	)	)	PUNCT
iajs-4071	32	31	is	be	AUX
iajs-4071	32	32	a	a	DET
iajs-4071	32	33	function	function	NOUN
iajs-4071	32	34	provided	provide	VERB
iajs-4071	32	35	by	by	ADP
iajs-4071	32	36	)	)	PUNCT
iajs-4071	32	37	)	)	PUNCT
iajs-4071	32	38	,	,	PUNCT
iajs-4071	32	39	2.3	2.3	NUM
iajs-4071	32	40	.	.	PUNCT
iajs-4071	33	1	definition	definition	NOUN
iajs-4071	33	2	(	(	PUNCT
iajs-4071	33	3	13	13	NUM
iajs-4071	33	4	)	)	PUNCT
iajs-4071	33	5	a	a	DET
iajs-4071	33	6	soft	soft	ADJ
iajs-4071	33	7	set	set	NOUN
iajs-4071	33	8	)	)	PUNCT
iajs-4071	33	9	is	be	AUX
iajs-4071	33	10	said	say	VERB
iajs-4071	33	11	to	to	PART
iajs-4071	33	12	be	be	AUX
iajs-4071	33	13	.	.	PUNCT
iajs-4071	34	1	1	1	X
iajs-4071	34	2	.	.	X
iajs-4071	34	3	a	a	DET
iajs-4071	34	4	null	null	ADJ
iajs-4071	34	5	soft	soft	ADJ
iajs-4071	34	6	set	set	NOUN
iajs-4071	34	7	indicated	indicate	VERB
iajs-4071	34	8	by	by	ADP
iajs-4071	34	9	̃	̃	PROPN
iajs-4071	34	10	if	if	SCONJ
iajs-4071	34	11	.	.	PUNCT
iajs-4071	34	12	,	,	PUNCT
iajs-4071	34	13	)	)	PUNCT
iajs-4071	34	14	.	.	PUNCT
iajs-4071	35	1	2	2	X
iajs-4071	35	2	.	.	X
iajs-4071	35	3	an	an	DET
iajs-4071	35	4	absolute	absolute	ADJ
iajs-4071	35	5	soft	soft	ADJ
iajs-4071	35	6	set	set	NOUN
iajs-4071	35	7	indicated	indicate	VERB
iajs-4071	35	8	by	by	ADP
iajs-4071	35	9	̃	̃	PROPN
iajs-4071	35	10	if	if	SCONJ
iajs-4071	35	11	)	)	PUNCT
iajs-4071	35	12	.	.	PUNCT
iajs-4071	36	1	3	3	X
iajs-4071	36	2	.	.	X
iajs-4071	36	3	a	a	DET
iajs-4071	36	4	soft	soft	ADJ
iajs-4071	36	5	point	point	NOUN
iajs-4071	36	6	indicated	indicate	VERB
iajs-4071	36	7	by	by	ADP
iajs-4071	36	8	,	,	PUNCT
iajs-4071	36	9	if	if	SCONJ
iajs-4071	36	10	)	)	PUNCT
iajs-4071	36	11	{	{	PUNCT
iajs-4071	36	12	we	we	PRON
iajs-4071	36	13	say	say	VERB
iajs-4071	36	14	that	that	SCONJ
iajs-4071	36	15	)	)	PUNCT
iajs-4071	36	16	if	if	SCONJ
iajs-4071	36	17	)	)	PUNCT
iajs-4071	36	18	2.4	2.4	NUM
iajs-4071	36	19	.	.	PUNCT
iajs-4071	37	1	definition	definition	NOUN
iajs-4071	37	2	(	(	PUNCT
iajs-4071	37	3	13	13	NUM
iajs-4071	37	4	)	)	PUNCT
iajs-4071	37	5	let	let	NOUN
iajs-4071	37	6	)	)	PUNCT
iajs-4071	37	7	)	)	PUNCT
iajs-4071	37	8	1	1	X
iajs-4071	37	9	.	.	PUNCT
iajs-4071	37	10	)	)	PUNCT
iajs-4071	37	11	)	)	PUNCT
iajs-4071	38	1	̃	̃	ADV
iajs-4071	38	2	)	)	PUNCT
iajs-4071	38	3	)	)	PUNCT
iajs-4071	38	4	)	)	PUNCT
iajs-4071	38	5	)	)	PUNCT
iajs-4071	38	6	.	.	PUNCT
iajs-4071	39	1	2	2	X
iajs-4071	39	2	.	.	NUM
iajs-4071	39	3	)	)	PUNCT
iajs-4071	39	4	)	)	PUNCT
iajs-4071	40	1	̃	̃	ADV
iajs-4071	40	2	)	)	PUNCT
iajs-4071	40	3	)	)	PUNCT
iajs-4071	40	4	)	)	PUNCT
iajs-4071	40	5	)	)	PUNCT
iajs-4071	40	6	.	.	PUNCT
iajs-4071	41	1	2.5	2.5	NUM
iajs-4071	41	2	.	.	PUNCT
iajs-4071	42	1	definition	definition	NOUN
iajs-4071	42	2	(	(	PUNCT
iajs-4071	42	3	14	14	NUM
iajs-4071	42	4	)	)	PUNCT
iajs-4071	42	5	let	let	VERB
iajs-4071	42	6	̃	̃	PROPN
iajs-4071	42	7	̃	̃	NOUN
iajs-4071	42	8	̃	̃	PROPN
iajs-4071	42	9	̃	̃	NUM
iajs-4071	42	10	)	)	PUNCT
iajs-4071	42	11	,	,	PUNCT
iajs-4071	42	12	then	then	ADV
iajs-4071	42	13	̃	̃	PROPN
iajs-4071	42	14	is	be	AUX
iajs-4071	42	15	described	describe	VERB
iajs-4071	42	16	as	as	ADP
iajs-4071	42	17	a	a	DET
iajs-4071	42	18	soft	soft	ADJ
iajs-4071	42	19	topology	topology	NOUN
iajs-4071	42	20	on	on	ADP
iajs-4071	42	21	̃	̃	ADJ
iajs-4071	42	22	if	if	SCONJ
iajs-4071	42	23	1	1	NUM
iajs-4071	42	24	.	.	X
iajs-4071	43	1	̃	̃	ADJ
iajs-4071	43	2	̃	̃	ADP
iajs-4071	43	3	̃	̃	NOUN
iajs-4071	43	4	̃.	̃.	ADJ
iajs-4071	43	5	2	2	NUM
iajs-4071	43	6	.	.	PUNCT
iajs-4071	43	7	)	)	PUNCT
iajs-4071	43	8	)	)	PUNCT
iajs-4071	44	1	̃	̃	PROPN
iajs-4071	44	2	̃	̃	PROPN
iajs-4071	44	3	,	,	PUNCT
iajs-4071	44	4	then	then	ADV
iajs-4071	44	5	)	)	PUNCT
iajs-4071	44	6	̃	̃	ADJ
iajs-4071	44	7	)	)	PUNCT
iajs-4071	45	1	̃	̃	ADV
iajs-4071	45	2	̃.	̃.	NOUN
iajs-4071	45	3	3	3	NUM
iajs-4071	45	4	.	.	PUNCT
iajs-4071	46	1	if	if	SCONJ
iajs-4071	46	2	)	)	PUNCT
iajs-4071	46	3	̃	̃	ADV
iajs-4071	46	4	̃	̃	NOUN
iajs-4071	46	5	,	,	PUNCT
iajs-4071	46	6	then	then	ADV
iajs-4071	46	7	̃	̃	PROPN
iajs-4071	46	8	)	)	PUNCT
iajs-4071	46	9	̃	̃	ADV
iajs-4071	46	10	̃.	̃.	ADP
iajs-4071	46	11	the	the	DET
iajs-4071	46	12	triple	triple	ADJ
iajs-4071	46	13	(	(	PUNCT
iajs-4071	46	14	̃	̃	NOUN
iajs-4071	46	15	̃	̃	NOUN
iajs-4071	46	16	)	)	PUNCT
iajs-4071	46	17	)	)	PUNCT
iajs-4071	46	18	(	(	PUNCT
iajs-4071	46	19	simply	simply	ADV
iajs-4071	46	20	,	,	PUNCT
iajs-4071	46	21	̃	̃	PROPN
iajs-4071	46	22	)	)	PUNCT
iajs-4071	46	23	is	be	AUX
iajs-4071	46	24	known	know	VERB
iajs-4071	46	25	as	as	ADP
iajs-4071	46	26	a	a	DET
iajs-4071	46	27	sts	st	NOUN
iajs-4071	46	28	over	over	ADP
iajs-4071	46	29	̃	̃	PROPN
iajs-4071	46	30	.	.	PUNCT
iajs-4071	46	31	)	)	PUNCT
iajs-4071	46	32	is	be	AUX
iajs-4071	46	33	soft	soft	ADJ
iajs-4071	46	34	open	open	ADJ
iajs-4071	46	35	set	set	VERB
iajs-4071	46	36	if	if	SCONJ
iajs-4071	46	37	)	)	PUNCT
iajs-4071	46	38	̃	̃	ADJ
iajs-4071	46	39	̃.	̃.	NOUN
iajs-4071	46	40	)	)	PUNCT
iajs-4071	46	41	is	be	AUX
iajs-4071	46	42	soft	soft	ADJ
iajs-4071	46	43	closed	closed	ADJ
iajs-4071	46	44	set	set	VERB
iajs-4071	46	45	if	if	SCONJ
iajs-4071	46	46	)	)	PUNCT
iajs-4071	46	47	̃	̃	NOUN
iajs-4071	46	48	̃	̃	NOUN
iajs-4071	46	49	.	.	PUNCT
iajs-4071	47	1	the	the	DET
iajs-4071	47	2	triple	triple	ADJ
iajs-4071	47	3	(	(	PUNCT
iajs-4071	47	4	̃	̃	PROPN
iajs-4071	47	5	̃	̃	NOUN
iajs-4071	47	6	̃	̃	NOUN
iajs-4071	47	7	)	)	PUNCT
iajs-4071	47	8	is	be	AUX
iajs-4071	47	9	a	a	DET
iajs-4071	47	10	soft	soft	ADJ
iajs-4071	47	11	subspace	subspace	NOUN
iajs-4071	47	12	of	of	ADP
iajs-4071	47	13	(	(	PUNCT
iajs-4071	47	14	̃	̃	PROPN
iajs-4071	47	15	̃	̃	PROPN
iajs-4071	47	16	)	)	PUNCT
iajs-4071	47	17	where	where	SCONJ
iajs-4071	47	18	w	w	NOUN
iajs-4071	47	19	,	,	PUNCT
iajs-4071	47	20	̃	̃	PROPN
iajs-4071	47	21	)	)	PUNCT
iajs-4071	47	22	̃	̃	NOUN
iajs-4071	47	23	̃	̃	NOUN
iajs-4071	47	24	)	)	PUNCT
iajs-4071	47	25	)	)	PUNCT
iajs-4071	48	1	̃	̃	NOUN
iajs-4071	48	2	is	be	AUX
iajs-4071	48	3	known	know	VERB
iajs-4071	48	4	as	as	ADP
iajs-4071	48	5	―the	―the	DET
iajs-4071	48	6	soft	soft	ADJ
iajs-4071	48	7	relative	relative	ADJ
iajs-4071	48	8	topology‖	topology‖	X
iajs-4071	48	9	on	on	ADP
iajs-4071	48	10	̃	̃	PROPN
iajs-4071	48	11	,	,	PUNCT
iajs-4071	48	12	and	and	CCONJ
iajs-4071	48	13	)	)	PUNCT
iajs-4071	48	14	̃	̃	NOUN
iajs-4071	48	15	̃	̃	NOUN
iajs-4071	48	16	)	)	PUNCT
iajs-4071	48	17	.	.	PUNCT
iajs-4071	49	1	2.6	2.6	NUM
iajs-4071	49	2	.	.	PUNCT
iajs-4071	49	3	definition	definition	NOUN
iajs-4071	49	4	(	(	PUNCT
iajs-4071	49	5	14	14	NUM
iajs-4071	49	6	)	)	PUNCT
iajs-4071	49	7	let	let	VERB
iajs-4071	49	8	̃	̃	SCONJ
iajs-4071	49	9	be	be	AUX
iajs-4071	49	10	a	a	DET
iajs-4071	49	11	collection	collection	NOUN
iajs-4071	49	12	of	of	ADP
iajs-4071	49	13	soft	soft	ADJ
iajs-4071	49	14	subsets	subset	NOUN
iajs-4071	49	15	over	over	ADP
iajs-4071	49	16	a	a	DET
iajs-4071	49	17	̃	̃	NOUN
iajs-4071	49	18	.then	.then	X
iajs-4071	49	19	̃	̃	NOUN
iajs-4071	49	20	is	be	AUX
iajs-4071	49	21	described	describe	VERB
iajs-4071	49	22	as	as	ADP
iajs-4071	49	23	a	a	DET
iajs-4071	49	24	soft	soft	ADJ
iajs-4071	49	25	supra	supra	ADJ
iajs-4071	49	26	topology	topology	NOUN
iajs-4071	49	27	on	on	ADP
iajs-4071	49	28	̃	̃	PROPN
iajs-4071	49	29	if	if	SCONJ
iajs-4071	49	30	1	1	NUM
iajs-4071	49	31	.	.	X
iajs-4071	50	1	̃	̃	ADJ
iajs-4071	50	2	̃	̃	ADP
iajs-4071	50	3	̃	̃	NOUN
iajs-4071	50	4	̃.	̃.	NOUN
iajs-4071	50	5	2	2	NUM
iajs-4071	50	6	.	.	PUNCT
iajs-4071	51	1	the	the	DET
iajs-4071	51	2	union	union	NOUN
iajs-4071	51	3	of	of	ADP
iajs-4071	51	4	any	any	DET
iajs-4071	51	5	number	number	NOUN
iajs-4071	51	6	of	of	ADP
iajs-4071	51	7	soft	soft	ADJ
iajs-4071	51	8	sets	set	NOUN
iajs-4071	51	9	in	in	ADP
iajs-4071	51	10	̃	̃	ADJ
iajs-4071	51	11	belonges	belonge	NOUN
iajs-4071	51	12	to	to	PART
iajs-4071	51	13	̃.	̃.	VERB
iajs-4071	51	14	the	the	DET
iajs-4071	51	15	triple	triple	ADJ
iajs-4071	51	16	(	(	PUNCT
iajs-4071	51	17	̃	̃	NOUN
iajs-4071	51	18	̃	̃	PROPN
iajs-4071	51	19	)	)	PUNCT
iajs-4071	51	20	is	be	AUX
iajs-4071	51	21	called	call	VERB
iajs-4071	51	22	supra	supra	PROPN
iajs-4071	51	23	soft	soft	ADJ
iajs-4071	51	24	topological	topological	ADJ
iajs-4071	51	25	space	space	NOUN
iajs-4071	51	26	and	and	CCONJ
iajs-4071	51	27	the	the	DET
iajs-4071	51	28	elements	element	NOUN
iajs-4071	51	29	of	of	ADP
iajs-4071	51	30	̃	̃	PROPN
iajs-4071	51	31	are	be	AUX
iajs-4071	51	32	called	call	VERB
iajs-4071	51	33	supra	supra	PROPN
iajs-4071	51	34	open	open	ADJ
iajs-4071	51	35	sets	set	NOUN
iajs-4071	51	36	.	.	PUNCT
iajs-4071	52	1	the	the	DET
iajs-4071	52	2	soft	soft	ADJ
iajs-4071	52	3	complement	complement	NOUN
iajs-4071	52	4	of	of	ADP
iajs-4071	52	5	any	any	DET
iajs-4071	52	6	soft	soft	ADJ
iajs-4071	52	7	supra	supra	NOUN
iajs-4071	52	8	open	open	ADJ
iajs-4071	52	9	set	set	NOUN
iajs-4071	52	10	is	be	AUX
iajs-4071	52	11	called	call	VERB
iajs-4071	52	12	supra	supra	PROPN
iajs-4071	52	13	soft	soft	ADJ
iajs-4071	52	14	closed	closed	ADJ
iajs-4071	52	15	.	.	PUNCT
iajs-4071	53	1	2.7.definition	2.7.definition	NUM
iajs-4071	53	2	̃	̃	NOUN
iajs-4071	53	3	)	)	PUNCT
iajs-4071	53	4	is	be	AUX
iajs-4071	53	5	a	a	DET
iajs-4071	53	6	soft	soft	ADJ
iajs-4071	53	7	interior	interior	NOUN
iajs-4071	53	8	of	of	ADP
iajs-4071	53	9	the	the	DET
iajs-4071	53	10	soft	soft	ADJ
iajs-4071	53	11	subset	subset	NOUN
iajs-4071	53	12	)	)	PUNCT
iajs-4071	53	13	and	and	CCONJ
iajs-4071	53	14	is	be	AUX
iajs-4071	53	15	defined	define	VERB
iajs-4071	53	16	as	as	ADP
iajs-4071	53	17	follows	follow	VERB
iajs-4071	53	18	.	.	PUNCT
iajs-4071	54	1	̃	̃	ADV
iajs-4071	54	2	)	)	PUNCT
iajs-4071	54	3	̃	̃	PROPN
iajs-4071	54	4	)	)	PUNCT
iajs-4071	54	5	)	)	PUNCT
iajs-4071	55	1	̃	̃	ADV
iajs-4071	55	2	)	)	PUNCT
iajs-4071	55	3	)	)	PUNCT
iajs-4071	56	1	̃	̃	NOUN
iajs-4071	56	2	̃	̃	NOUN
iajs-4071	56	3	}	}	PUNCT
iajs-4071	56	4	.	.	PUNCT
iajs-4071	57	1	ihjpas	ihjpas	PROPN
iajs-4071	57	2	.	.	PUNCT
iajs-4071	58	1	2025,38(4	2025,38(4	NOUN
iajs-4071	58	2	)	)	PUNCT
iajs-4071	59	1	365	365	NUM
iajs-4071	59	2	2.8	2.8	NUM
iajs-4071	59	3	.	.	PUNCT
iajs-4071	60	1	definition	definition	NOUN
iajs-4071	60	2	̃	̃	PROPN
iajs-4071	60	3	)	)	PUNCT
iajs-4071	60	4	is	be	AUX
iajs-4071	60	5	a	a	DET
iajs-4071	60	6	soft	soft	ADJ
iajs-4071	60	7	closure	closure	NOUN
iajs-4071	60	8	of	of	ADP
iajs-4071	60	9	the	the	DET
iajs-4071	60	10	soft	soft	ADJ
iajs-4071	60	11	subset	subset	NOUN
iajs-4071	60	12	)	)	PUNCT
iajs-4071	60	13	and	and	CCONJ
iajs-4071	60	14	is	be	AUX
iajs-4071	60	15	defined	define	VERB
iajs-4071	60	16	as	as	ADP
iajs-4071	60	17	follows	follow	VERB
iajs-4071	60	18	.	.	PUNCT
iajs-4071	61	1	̃	̃	ADV
iajs-4071	61	2	)	)	PUNCT
iajs-4071	61	3	̃	̃	PROPN
iajs-4071	61	4	)	)	PUNCT
iajs-4071	61	5	)	)	PUNCT
iajs-4071	62	1	̃	̃	ADV
iajs-4071	62	2	)	)	PUNCT
iajs-4071	62	3	)	)	PUNCT
iajs-4071	63	1	̃	̃	NOUN
iajs-4071	63	2	̃	̃	NOUN
iajs-4071	63	3	}	}	PUNCT
iajs-4071	63	4	.	.	PUNCT
iajs-4071	64	1	2.9	2.9	NUM
iajs-4071	64	2	.	.	PUNCT
iajs-4071	64	3	definition	definition	NOUN
iajs-4071	64	4	(	(	PUNCT
iajs-4071	64	5	15	15	NUM
iajs-4071	64	6	)	)	PUNCT
iajs-4071	64	7	a	a	DET
iajs-4071	64	8	soft	soft	ADJ
iajs-4071	64	9	subset	subset	NOUN
iajs-4071	64	10	)	)	PUNCT
iajs-4071	64	11	of	of	ADP
iajs-4071	64	12	a	a	DET
iajs-4071	64	13	sts	st	NOUN
iajs-4071	64	14	(	(	PUNCT
iajs-4071	64	15	̃	̃	NOUN
iajs-4071	64	16	̃	̃	PROPN
iajs-4071	64	17	)	)	PUNCT
iajs-4071	64	18	become	become	VERB
iajs-4071	64	19	a	a	DET
iajs-4071	64	20	soft	soft	ADJ
iajs-4071	64	21	pre	pre	ADJ
iajs-4071	64	22	-	-	ADJ
iajs-4071	64	23	open	open	ADJ
iajs-4071	64	24	(	(	PUNCT
iajs-4071	64	25	resp	resp	NOUN
iajs-4071	64	26	.	.	PUNCT
iajs-4071	64	27	,	,	PUNCT
iajs-4071	64	28	soft	soft	ADJ
iajs-4071	64	29	semi	semi	ADJ
iajs-4071	64	30	-	-	ADJ
iajs-4071	64	31	open	open	ADJ
iajs-4071	64	32	,	,	PUNCT
iajs-4071	64	33	soft	soft	ADJ
iajs-4071	64	34	α	α	NOUN
iajs-4071	64	35	-	-	ADJ
iajs-4071	64	36	open	open	ADJ
iajs-4071	64	37	,	,	PUNCT
iajs-4071	64	38	soft	soft	ADJ
iajs-4071	64	39	-open	-open	NOUN
iajs-4071	64	40	,	,	PUNCT
iajs-4071	64	41	soft	soft	ADJ
iajs-4071	64	42	b	b	NOUN
iajs-4071	64	43	-	-	PUNCT
iajs-4071	64	44	open	open	ADJ
iajs-4071	64	45	,	,	PUNCT
iajs-4071	64	46	and	and	CCONJ
iajs-4071	64	47	soft	soft	ADJ
iajs-4071	64	48	regular	regular	ADJ
iajs-4071	64	49	-	-	PUNCT
iajs-4071	64	50	open	open	ADJ
iajs-4071	64	51	)	)	PUNCT
iajs-4071	64	52	if	if	SCONJ
iajs-4071	64	53	)	)	PUNCT
iajs-4071	64	54	̃	̃	NOUN
iajs-4071	64	55	̃	̃	NOUN
iajs-4071	64	56	)	)	PUNCT
iajs-4071	64	57	)	)	PUNCT
iajs-4071	64	58	(	(	PUNCT
iajs-4071	64	59	resp	resp	NOUN
iajs-4071	64	60	.	.	PUNCT
iajs-4071	64	61	,	,	PUNCT
iajs-4071	64	62	)	)	PUNCT
iajs-4071	65	1	̃	̃	PROPN
iajs-4071	65	2	(	(	PUNCT
iajs-4071	65	3	̃	̃	NOUN
iajs-4071	65	4	)	)	PUNCT
iajs-4071	65	5	)	)	PUNCT
iajs-4071	65	6	)	)	PUNCT
iajs-4071	66	1	̃	̃	PROPN
iajs-4071	66	2	(	(	PUNCT
iajs-4071	66	3	̃	̃	PROPN
iajs-4071	66	4	(	(	PUNCT
iajs-4071	66	5	̃	̃	PROPN
iajs-4071	66	6	)	)	PUNCT
iajs-4071	66	7	)	)	PUNCT
iajs-4071	66	8	)	)	PUNCT
iajs-4071	66	9	)	)	PUNCT
iajs-4071	67	1	̃	̃	PROPN
iajs-4071	67	2	(	(	PUNCT
iajs-4071	67	3	̃	̃	PROPN
iajs-4071	67	4	(	(	PUNCT
iajs-4071	67	5	̃	̃	PROPN
iajs-4071	67	6	)	)	PUNCT
iajs-4071	67	7	)	)	PUNCT
iajs-4071	67	8	)	)	PUNCT
iajs-4071	67	9	)	)	PUNCT
iajs-4071	68	1	̃	̃	NOUN
iajs-4071	68	2	̃	̃	NOUN
iajs-4071	68	3	)	)	PUNCT
iajs-4071	68	4	)	)	PUNCT
iajs-4071	69	1	̃	̃	NOUN
iajs-4071	69	2	̃	̃	PROPN
iajs-4071	69	3	(	(	PUNCT
iajs-4071	69	4	̃	̃	NOUN
iajs-4071	69	5	)	)	PUNCT
iajs-4071	69	6	)	)	PUNCT
iajs-4071	69	7	)	)	PUNCT
iajs-4071	70	1	̃	̃	NOUN
iajs-4071	70	2	̃	̃	NOUN
iajs-4071	70	3	)	)	PUNCT
iajs-4071	70	4	)	)	PUNCT
iajs-4071	70	5	)	)	PUNCT
iajs-4071	71	1	the	the	DET
iajs-4071	71	2	family	family	NOUN
iajs-4071	71	3	of	of	ADP
iajs-4071	71	4	all	all	DET
iajs-4071	71	5	soft	soft	ADJ
iajs-4071	71	6	pre	pre	ADJ
iajs-4071	71	7	-	-	ADJ
iajs-4071	71	8	open	open	ADJ
iajs-4071	71	9	(	(	PUNCT
iajs-4071	71	10	resp	resp	NOUN
iajs-4071	71	11	.	.	PUNCT
iajs-4071	71	12	,	,	PUNCT
iajs-4071	71	13	soft	soft	ADJ
iajs-4071	71	14	semi	semi	ADJ
iajs-4071	71	15	-	-	ADJ
iajs-4071	71	16	open	open	ADJ
iajs-4071	71	17	,	,	PUNCT
iajs-4071	71	18	soft	soft	ADJ
iajs-4071	71	19	α	α	NOUN
iajs-4071	71	20	-	-	ADJ
iajs-4071	71	21	open	open	ADJ
iajs-4071	71	22	,	,	PUNCT
iajs-4071	71	23	soft	soft	ADJ
iajs-4071	71	24	open	open	ADJ
iajs-4071	71	25	,	,	PUNCT
iajs-4071	71	26	soft	soft	ADJ
iajs-4071	71	27	b	b	NOUN
iajs-4071	71	28	-	-	ADJ
iajs-4071	71	29	open	open	ADJ
iajs-4071	71	30	,	,	PUNCT
iajs-4071	71	31	and	and	CCONJ
iajs-4071	71	32	soft	soft	ADJ
iajs-4071	71	33	regular	regular	ADJ
iajs-4071	71	34	-	-	PUNCT
iajs-4071	71	35	open	open	ADJ
iajs-4071	71	36	)	)	PUNCT
iajs-4071	71	37	subsets	subset	NOUN
iajs-4071	71	38	of	of	ADP
iajs-4071	71	39	̃	̃	PROPN
iajs-4071	71	40	is	be	AUX
iajs-4071	71	41	indicated	indicate	VERB
iajs-4071	71	42	by	by	ADP
iajs-4071	71	43	̃	̃	PROPN
iajs-4071	71	44	̃)(resp	̃)(resp	ADJ
iajs-4071	71	45	.	.	PUNCT
iajs-4071	71	46	,	,	PUNCT
iajs-4071	72	1	̃	̃	PROPN
iajs-4071	72	2	(	(	PUNCT
iajs-4071	72	3	̃	̃	NOUN
iajs-4071	72	4	)	)	PUNCT
iajs-4071	72	5	̃	̃	PROPN
iajs-4071	72	6	(	(	PUNCT
iajs-4071	72	7	̃	̃	NOUN
iajs-4071	72	8	)	)	PUNCT
iajs-4071	72	9	̃	̃	PROPN
iajs-4071	72	10	(	(	PUNCT
iajs-4071	72	11	̃	̃	NOUN
iajs-4071	72	12	)	)	PUNCT
iajs-4071	72	13	̃	̃	PROPN
iajs-4071	72	14	(	(	PUNCT
iajs-4071	72	15	̃	̃	NOUN
iajs-4071	72	16	)	)	PUNCT
iajs-4071	72	17	̃	̃	PROPN
iajs-4071	72	18	̃	̃	NOUN
iajs-4071	72	19	)	)	PUNCT
iajs-4071	72	20	)	)	PUNCT
iajs-4071	72	21	2.10	2.10	NUM
iajs-4071	72	22	.	.	PUNCT
iajs-4071	72	23	definition	definition	NOUN
iajs-4071	72	24	a	a	DET
iajs-4071	72	25	soft	soft	ADJ
iajs-4071	72	26	subset	subset	NOUN
iajs-4071	72	27	)	)	PUNCT
iajs-4071	72	28	of	of	ADP
iajs-4071	72	29	sts	st	NOUN
iajs-4071	72	30	(	(	PUNCT
iajs-4071	72	31	̃	̃	NOUN
iajs-4071	72	32	̃	̃	PROPN
iajs-4071	72	33	)	)	PUNCT
iajs-4071	72	34	is	be	AUX
iajs-4071	72	35	recognized	recognize	VERB
iajs-4071	72	36	as	as	ADP
iajs-4071	72	37	a	a	DET
iajs-4071	72	38	soft	soft	ADJ
iajs-4071	72	39	-open	-open	NOUN
iajs-4071	72	40	(	(	PUNCT
iajs-4071	72	41	13	13	NUM
iajs-4071	72	42	)	)	PUNCT
iajs-4071	72	43	(	(	PUNCT
iajs-4071	72	44	resp	resp	NOUN
iajs-4071	72	45	.	.	PUNCT
iajs-4071	72	46	,	,	PUNCT
iajs-4071	72	47	soft	soft	ADJ
iajs-4071	72	48	open	open	ADJ
iajs-4071	72	49	(	(	PUNCT
iajs-4071	72	50	14	14	NUM
iajs-4071	72	51	)	)	PUNCT
iajs-4071	72	52	,	,	PUNCT
iajs-4071	72	53	soft	soft	ADJ
iajs-4071	72	54	-open	-open	NOUN
iajs-4071	72	55	(	(	PUNCT
iajs-4071	72	56	14),soft	14),soft	NUM
iajs-4071	72	57	-open	-open	ADJ
iajs-4071	72	58	(	(	PUNCT
iajs-4071	72	59	15	15	NUM
iajs-4071	72	60	)	)	PUNCT
iajs-4071	72	61	,	,	PUNCT
iajs-4071	72	62	soft	soft	ADJ
iajs-4071	72	63	-open	-open	NOUN
iajs-4071	72	64	(	(	PUNCT
iajs-4071	72	65	16	16	NUM
iajs-4071	72	66	)	)	PUNCT
iajs-4071	72	67	and	and	CCONJ
iajs-4071	72	68	soft	soft	ADJ
iajs-4071	72	69	-open	-open	NOUN
iajs-4071	72	70	(	(	PUNCT
iajs-4071	72	71	17	17	NUM
iajs-4071	72	72	)	)	PUNCT
iajs-4071	72	73	)	)	PUNCT
iajs-4071	73	1	set	set	VERB
iajs-4071	73	2	,	,	PUNCT
iajs-4071	73	3	if	if	SCONJ
iajs-4071	73	4	)	)	PUNCT
iajs-4071	73	5	̃	̃	PROPN
iajs-4071	73	6	̃	̃	NOUN
iajs-4071	73	7	̃	̃	NUM
iajs-4071	73	8	)	)	PUNCT
iajs-4071	73	9	(	(	PUNCT
iajs-4071	73	10	resp	resp	NOUN
iajs-4071	73	11	.	.	PUNCT
iajs-4071	73	12	,	,	PUNCT
iajs-4071	73	13	̃	̃	PROPN
iajs-4071	73	14	̃	̃	NOUN
iajs-4071	73	15	̃	̃	NOUN
iajs-4071	73	16	)	)	PUNCT
iajs-4071	73	17	̃	̃	ADP
iajs-4071	73	18	̃	̃	NOUN
iajs-4071	73	19	)	)	PUNCT
iajs-4071	73	20	̃	̃	PROPN
iajs-4071	73	21	̃	̃	NOUN
iajs-4071	73	22	)	)	PUNCT
iajs-4071	73	23	,	,	PUNCT
iajs-4071	73	24	and	and	CCONJ
iajs-4071	73	25	̃	̃	PROPN
iajs-4071	73	26	̃	̃	NOUN
iajs-4071	73	27	)	)	PUNCT
iajs-4071	73	28	)	)	PUNCT
iajs-4071	73	29	and	and	CCONJ
iajs-4071	73	30	̃	̃	PROPN
iajs-4071	73	31	)	)	PUNCT
iajs-4071	73	32	a	a	DET
iajs-4071	73	33	soft	soft	ADJ
iajs-4071	73	34	closed	closed	ADJ
iajs-4071	73	35	(	(	PUNCT
iajs-4071	73	36	resp	resp	NOUN
iajs-4071	73	37	.	.	PUNCT
iajs-4071	73	38	,	,	PUNCT
iajs-4071	73	39	soft	soft	ADJ
iajs-4071	73	40	semi	semi	ADJ
iajs-4071	73	41	-	-	ADJ
iajs-4071	73	42	closed	closed	ADJ
iajs-4071	73	43	,	,	PUNCT
iajs-4071	73	44	soft	soft	ADJ
iajs-4071	73	45	regular	regular	ADJ
iajs-4071	73	46	open	open	ADJ
iajs-4071	73	47	,	,	PUNCT
iajs-4071	73	48	soft	soft	ADJ
iajs-4071	73	49	closed	closed	ADJ
iajs-4071	73	50	,	,	PUNCT
iajs-4071	73	51	soft	soft	ADJ
iajs-4071	73	52	closed	closed	ADJ
iajs-4071	73	53	and	and	CCONJ
iajs-4071	73	54	soft	soft	ADJ
iajs-4071	73	55	closed	closed	ADJ
iajs-4071	73	56	)	)	PUNCT
iajs-4071	73	57	subset	subset	NOUN
iajs-4071	73	58	)	)	PUNCT
iajs-4071	73	59	of	of	ADP
iajs-4071	73	60	̃	̃	PROPN
iajs-4071	73	61	s.t	s.t	PROPN
iajs-4071	73	62	.	.	PUNCT
iajs-4071	73	63	̃	̃	ADV
iajs-4071	73	64	)	)	PUNCT
iajs-4071	73	65	̃	̃	PROPN
iajs-4071	73	66	)	)	PUNCT
iajs-4071	73	67	.	.	PUNCT
iajs-4071	74	1	the	the	DET
iajs-4071	74	2	family	family	NOUN
iajs-4071	74	3	of	of	ADP
iajs-4071	74	4	all	all	DET
iajs-4071	74	5	soft	soft	ADJ
iajs-4071	74	6	open	open	ADJ
iajs-4071	74	7	(	(	PUNCT
iajs-4071	74	8	resp	resp	NOUN
iajs-4071	74	9	.	.	PUNCT
iajs-4071	74	10	,	,	PUNCT
iajs-4071	74	11	soft	soft	ADJ
iajs-4071	74	12	-open	-open	NOUN
iajs-4071	74	13	,	,	PUNCT
iajs-4071	74	14	soft	soft	ADJ
iajs-4071	74	15	-open	-open	ADJ
iajs-4071	74	16	,	,	PUNCT
iajs-4071	74	17	soft	soft	ADJ
iajs-4071	74	18	-open	-open	NOUN
iajs-4071	74	19	,	,	PUNCT
iajs-4071	74	20	soft	soft	ADJ
iajs-4071	74	21	-open	-open	ADJ
iajs-4071	74	22	and	and	CCONJ
iajs-4071	74	23	soft	soft	ADJ
iajs-4071	74	24	-open	-open	NOUN
iajs-4071	74	25	)	)	PUNCT
iajs-4071	74	26	subsets	subset	NOUN
iajs-4071	74	27	of	of	ADP
iajs-4071	74	28	̃	̃	PROPN
iajs-4071	74	29	is	be	AUX
iajs-4071	74	30	indicated	indicate	VERB
iajs-4071	74	31	by	by	ADP
iajs-4071	74	32	̃	̃	PROPN
iajs-4071	74	33	̃	̃	PROPN
iajs-4071	74	34	)	)	PUNCT
iajs-4071	74	35	(	(	PUNCT
iajs-4071	74	36	resp	resp	NOUN
iajs-4071	74	37	.	.	PUNCT
iajs-4071	74	38	,	,	PUNCT
iajs-4071	75	1	̃	̃	PROPN
iajs-4071	75	2	(	(	PUNCT
iajs-4071	75	3	̃	̃	NOUN
iajs-4071	75	4	)	)	PUNCT
iajs-4071	75	5	̃	̃	PROPN
iajs-4071	75	6	(	(	PUNCT
iajs-4071	75	7	̃	̃	NOUN
iajs-4071	75	8	)	)	PUNCT
iajs-4071	75	9	̃	̃	NOUN
iajs-4071	75	10	̃	̃	NOUN
iajs-4071	75	11	)	)	PUNCT
iajs-4071	75	12	̃	̃	NOUN
iajs-4071	75	13	̃	̃	NOUN
iajs-4071	75	14	)	)	PUNCT
iajs-4071	75	15	and	and	CCONJ
iajs-4071	75	16	̃	̃	PROPN
iajs-4071	75	17	̃	̃	PROPN
iajs-4071	75	18	)	)	PUNCT
iajs-4071	75	19	)	)	PUNCT
iajs-4071	75	20	.	.	PUNCT
iajs-4071	76	1	2.11	2.11	NUM
iajs-4071	76	2	.	.	PUNCT
iajs-4071	76	3	definition	definition	NOUN
iajs-4071	76	4	(	(	PUNCT
iajs-4071	76	5	15,16	15,16	NUM
iajs-4071	76	6	)	)	PUNCT
iajs-4071	76	7	a	a	DET
iajs-4071	76	8	sts	st	NOUN
iajs-4071	76	9	(	(	PUNCT
iajs-4071	76	10	̃	̃	NOUN
iajs-4071	76	11	̃	̃	PROPN
iajs-4071	76	12	)	)	PUNCT
iajs-4071	76	13	is	be	AUX
iajs-4071	76	14	recognized	recognize	VERB
iajs-4071	76	15	as	as	ADP
iajs-4071	76	16	.	.	PROPN
iajs-4071	76	17	1	1	X
iajs-4071	76	18	.	.	X
iajs-4071	76	19	soft	soft	ADJ
iajs-4071	76	20	extremally	extremally	ADV
iajs-4071	76	21	disconnected	disconnect	VERB
iajs-4071	76	22	space	space	NOUN
iajs-4071	76	23	(	(	PUNCT
iajs-4071	76	24	simply	simply	ADV
iajs-4071	76	25	,	,	PUNCT
iajs-4071	76	26	seds	sed	NOUN
iajs-4071	76	27	)	)	PUNCT
iajs-4071	76	28	,	,	PUNCT
iajs-4071	76	29	if	if	SCONJ
iajs-4071	76	30	̃	̃	ADJ
iajs-4071	76	31	)	)	PUNCT
iajs-4071	76	32	̃	̃	NOUN
iajs-4071	76	33	̃	̃	ADJ
iajs-4071	76	34	)	)	PUNCT
iajs-4071	77	1	̃	̃	ADV
iajs-4071	77	2	̃.	̃.	ADJ
iajs-4071	77	3	2	2	NUM
iajs-4071	77	4	.	.	PUNCT
iajs-4071	77	5	soft	soft	ADJ
iajs-4071	77	6	locally	locally	ADV
iajs-4071	77	7	indiscrete	indiscrete	ADJ
iajs-4071	77	8	,	,	PUNCT
iajs-4071	77	9	if	if	SCONJ
iajs-4071	77	10	)	)	PUNCT
iajs-4071	77	11	̃	̃	NOUN
iajs-4071	77	12	̃	̃	NOUN
iajs-4071	77	13	,	,	PUNCT
iajs-4071	77	14	then	then	ADV
iajs-4071	77	15	)	)	PUNCT
iajs-4071	78	1	̃	̃	NOUN
iajs-4071	78	2	̃	̃	NOUN
iajs-4071	78	3	.	.	PUNCT
iajs-4071	79	1	3	3	X
iajs-4071	79	2	.	.	NOUN
iajs-4071	79	3	soft	soft	ADJ
iajs-4071	79	4	-space	-space	NOUN
iajs-4071	79	5	,	,	PUNCT
iajs-4071	79	6	if	if	SCONJ
iajs-4071	79	7	̃	̃	PROPN
iajs-4071	79	8	̃	̃	NOUN
iajs-4071	79	9	̃	̃	NOUN
iajs-4071	79	10	)	)	PUNCT
iajs-4071	79	11	such	such	ADJ
iajs-4071	79	12	that	that	SCONJ
iajs-4071	79	13	,	,	PUNCT
iajs-4071	79	14	there	there	PRON
iajs-4071	79	15	are	be	VERB
iajs-4071	79	16	soft	soft	ADJ
iajs-4071	79	17	open	open	ADJ
iajs-4071	79	18	sets	set	NOUN
iajs-4071	79	19	)	)	PUNCT
iajs-4071	79	20	and	and	CCONJ
iajs-4071	79	21	)	)	PUNCT
iajs-4071	79	22	s.t	s.t	PROPN
iajs-4071	79	23	̃	̃	PROPN
iajs-4071	79	24	)	)	PUNCT
iajs-4071	80	1	̃	̃	PROPN
iajs-4071	80	2	)	)	PUNCT
iajs-4071	80	3	and	and	CCONJ
iajs-4071	80	4	̃	̃	PROPN
iajs-4071	80	5	)	)	PUNCT
iajs-4071	80	6	̃	̃	NOUN
iajs-4071	80	7	)	)	PUNCT
iajs-4071	80	8	.	.	PUNCT
iajs-4071	81	1	2.12	2.12	NUM
iajs-4071	81	2	.	.	PUNCT
iajs-4071	81	3	definition	definition	NOUN
iajs-4071	81	4	(	(	PUNCT
iajs-4071	81	5	15	15	NUM
iajs-4071	81	6	)	)	PUNCT
iajs-4071	81	7	let	let	VERB
iajs-4071	81	8	̃	̃	PROPN
iajs-4071	81	9	̃	̃	PROPN
iajs-4071	81	10	)	)	PUNCT
iajs-4071	81	11	be	be	AUX
iajs-4071	81	12	a	a	DET
iajs-4071	81	13	sts	st	NOUN
iajs-4071	81	14	.	.	PUNCT
iajs-4071	82	1	the	the	DET
iajs-4071	82	2	soft	soft	ADJ
iajs-4071	82	3	-interior	-interior	NOUN
iajs-4071	82	4	of	of	ADP
iajs-4071	82	5	a	a	DET
iajs-4071	82	6	soft	soft	ADJ
iajs-4071	82	7	subset	subset	NOUN
iajs-4071	82	8	)	)	PUNCT
iajs-4071	83	1	̃	̃	NOUN
iajs-4071	83	2	̃	̃	NOUN
iajs-4071	83	3	)	)	PUNCT
iajs-4071	83	4	is	be	AUX
iajs-4071	83	5	the	the	DET
iajs-4071	83	6	union	union	NOUN
iajs-4071	83	7	of	of	ADP
iajs-4071	83	8	all	all	DET
iajs-4071	83	9	soft	soft	ADJ
iajs-4071	83	10	open	open	ADJ
iajs-4071	83	11	sets	set	NOUN
iajs-4071	83	12	over	over	ADP
iajs-4071	83	13	̃	̃	ADP
iajs-4071	83	14	whose	whose	DET
iajs-4071	83	15	soft	soft	ADJ
iajs-4071	83	16	closures	closure	NOUN
iajs-4071	83	17	are	be	AUX
iajs-4071	83	18	located	locate	VERB
iajs-4071	83	19	within	within	ADP
iajs-4071	83	20	)	)	PUNCT
iajs-4071	83	21	,	,	PUNCT
iajs-4071	83	22	and	and	CCONJ
iajs-4071	83	23	is	be	AUX
iajs-4071	83	24	indicated	indicate	VERB
iajs-4071	83	25	by	by	ADP
iajs-4071	83	26	̃	̃	PROPN
iajs-4071	83	27	)	)	PUNCT
iajs-4071	83	28	.	.	PUNCT
iajs-4071	84	1	the	the	DET
iajs-4071	84	2	soft	soft	ADJ
iajs-4071	84	3	subset	subset	NOUN
iajs-4071	84	4	)	)	PUNCT
iajs-4071	84	5	is	be	AUX
iajs-4071	84	6	known	know	VERB
iajs-4071	84	7	as	as	ADP
iajs-4071	84	8	soft	soft	ADJ
iajs-4071	84	9	open	open	ADJ
iajs-4071	84	10	if	if	SCONJ
iajs-4071	84	11	̃	̃	PROPN
iajs-4071	84	12	)	)	PUNCT
iajs-4071	84	13	)	)	PUNCT
iajs-4071	84	14	.	.	PUNCT
iajs-4071	85	1	the	the	DET
iajs-4071	85	2	complement	complement	NOUN
iajs-4071	85	3	of	of	ADP
iajs-4071	85	4	a	a	DET
iajs-4071	85	5	soft	soft	ADJ
iajs-4071	85	6	-open	-open	ADJ
iajs-4071	85	7	set	set	NOUN
iajs-4071	85	8	is	be	AUX
iajs-4071	85	9	called	call	VERB
iajs-4071	85	10	soft	soft	ADJ
iajs-4071	85	11	-closed	-close	VERB
iajs-4071	85	12	.	.	PUNCT
iajs-4071	86	1	2.13	2.13	NUM
iajs-4071	86	2	.	.	PUNCT
iajs-4071	87	1	definition	definition	NOUN
iajs-4071	87	2	(	(	PUNCT
iajs-4071	87	3	14	14	NUM
iajs-4071	87	4	)	)	PUNCT
iajs-4071	87	5	suppose	suppose	VERB
iajs-4071	87	6	that	that	SCONJ
iajs-4071	87	7	̃	̃	PROPN
iajs-4071	87	8	̃	̃	PROPN
iajs-4071	87	9	)	)	PUNCT
iajs-4071	87	10	and	and	CCONJ
iajs-4071	87	11	̃	̃	PROPN
iajs-4071	87	12	̃	̃	PROPN
iajs-4071	87	13	)	)	PUNCT
iajs-4071	87	14	be	be	AUX
iajs-4071	87	15	soft	soft	ADJ
iajs-4071	87	16	categories	category	NOUN
iajs-4071	87	17	.	.	PUNCT
iajs-4071	88	1	suppose	suppose	VERB
iajs-4071	88	2	and	and	CCONJ
iajs-4071	88	3	be	be	AUX
iajs-4071	88	4	functions	function	NOUN
iajs-4071	88	5	.	.	PUNCT
iajs-4071	89	1	next	next	ADV
iajs-4071	89	2	,	,	PUNCT
iajs-4071	89	3	a	a	DET
iajs-4071	89	4	soft	soft	ADJ
iajs-4071	89	5	function	function	NOUN
iajs-4071	89	6	̃	̃	PROPN
iajs-4071	89	7	̃	̃	PROPN
iajs-4071	89	8	)	)	PUNCT
iajs-4071	89	9	̃	̃	NOUN
iajs-4071	89	10	̃	̃	PROPN
iajs-4071	89	11	)	)	PUNCT
iajs-4071	89	12	is	be	AUX
iajs-4071	89	13	described	describe	VERB
iajs-4071	89	14	as	as	ADP
iajs-4071	89	15	the	the	DET
iajs-4071	89	16	following	following	NOUN
iajs-4071	89	17	.	.	PUNCT
iajs-4071	90	1	1	1	X
iajs-4071	90	2	.	.	X
iajs-4071	90	3	for	for	ADP
iajs-4071	90	4	a	a	DET
iajs-4071	90	5	soft	soft	ADJ
iajs-4071	90	6	set	set	NOUN
iajs-4071	90	7	)	)	PUNCT
iajs-4071	90	8	̃	̃	PROPN
iajs-4071	90	9	̃	̃	NOUN
iajs-4071	90	10	)	)	PUNCT
iajs-4071	90	11	,	,	PUNCT
iajs-4071	90	12	)	)	PUNCT
iajs-4071	90	13	)	)	PUNCT
iajs-4071	90	14	)	)	PUNCT
iajs-4071	90	15	is	be	AUX
iajs-4071	90	16	a	a	DET
iajs-4071	90	17	soft	soft	ADJ
iajs-4071	90	18	set	set	NOUN
iajs-4071	90	19	in	in	ADP
iajs-4071	90	20	̃	̃	PROPN
iajs-4071	90	21	̃	̃	PROPN
iajs-4071	90	22	)	)	PUNCT
iajs-4071	90	23	provided	provide	VERB
iajs-4071	90	24	by	by	ADP
iajs-4071	90	25	)	)	PUNCT
iajs-4071	90	26	)	)	PUNCT
iajs-4071	90	27	{	{	PUNCT
iajs-4071	90	28	(	(	PUNCT
iajs-4071	90	29	)	)	PUNCT
iajs-4071	90	30	(	(	PUNCT
iajs-4071	90	31	)	)	PUNCT
iajs-4071	90	32	)	)	PUNCT
iajs-4071	90	33	)	)	PUNCT
iajs-4071	90	34	)	)	PUNCT
iajs-4071	90	35	for	for	ADP
iajs-4071	90	36	.	.	PUNCT
iajs-4071	90	37	)	)	PUNCT
iajs-4071	90	38	)	)	PUNCT
iajs-4071	90	39	is	be	AUX
iajs-4071	90	40	called	call	VERB
iajs-4071	90	41	a	a	DET
iajs-4071	90	42	soft	soft	ADJ
iajs-4071	90	43	image	image	NOUN
iajs-4071	90	44	of	of	ADP
iajs-4071	90	45	a	a	DET
iajs-4071	90	46	soft	soft	ADJ
iajs-4071	90	47	set	set	NOUN
iajs-4071	90	48	)	)	PUNCT
iajs-4071	90	49	.	.	PUNCT
iajs-4071	91	1	if	if	SCONJ
iajs-4071	91	2	,	,	PUNCT
iajs-4071	91	3	afterward	afterward	ADV
iajs-4071	91	4	,	,	PUNCT
iajs-4071	91	5	we	we	PRON
iajs-4071	91	6	’ll	’ll	AUX
iajs-4071	91	7	write	write	VERB
iajs-4071	91	8	)	)	PUNCT
iajs-4071	91	9	)	)	PUNCT
iajs-4071	91	10	as	as	ADP
iajs-4071	91	11	)	)	PUNCT
iajs-4071	91	12	2	2	X
iajs-4071	91	13	.	.	X
iajs-4071	92	1	for	for	ADP
iajs-4071	92	2	a	a	DET
iajs-4071	92	3	soft	soft	ADJ
iajs-4071	92	4	set	set	NOUN
iajs-4071	92	5	)	)	PUNCT
iajs-4071	92	6	in	in	ADP
iajs-4071	92	7	̃	̃	PROPN
iajs-4071	92	8	̃	̃	PROPN
iajs-4071	92	9	)	)	PUNCT
iajs-4071	92	10	where	where	SCONJ
iajs-4071	92	11	)	)	PUNCT
iajs-4071	92	12	)	)	PUNCT
iajs-4071	92	13	)	)	PUNCT
iajs-4071	92	14	is	be	AUX
iajs-4071	92	15	a	a	DET
iajs-4071	92	16	soft	soft	ADJ
iajs-4071	92	17	set	set	NOUN
iajs-4071	92	18	in	in	ADP
iajs-4071	92	19	̃	̃	PROPN
iajs-4071	92	20	̃	̃	PROPN
iajs-4071	92	21	)	)	PUNCT
iajs-4071	92	22	provided	provide	VERB
iajs-4071	92	23	by	by	ADP
iajs-4071	92	24	)	)	PUNCT
iajs-4071	92	25	)	)	PUNCT
iajs-4071	92	26	{	{	PUNCT
iajs-4071	92	27	(	(	PUNCT
iajs-4071	92	28	(	(	PUNCT
iajs-4071	92	29	)	)	PUNCT
iajs-4071	92	30	)	)	PUNCT
iajs-4071	92	31	)	)	PUNCT
iajs-4071	92	32	)	)	PUNCT
iajs-4071	92	33	for	for	ADP
iajs-4071	92	34	,	,	PUNCT
iajs-4071	92	35	)	)	PUNCT
iajs-4071	92	36	)	)	PUNCT
iajs-4071	92	37	is	be	AUX
iajs-4071	92	38	known	know	VERB
iajs-4071	92	39	as	as	ADP
iajs-4071	92	40	a	a	DET
iajs-4071	92	41	soft	soft	ADJ
iajs-4071	92	42	inverse	inverse	NOUN
iajs-4071	92	43	image	image	NOUN
iajs-4071	92	44	of	of	ADP
iajs-4071	92	45	a	a	DET
iajs-4071	92	46	soft	soft	ADJ
iajs-4071	92	47	set	set	NOUN
iajs-4071	92	48	)	)	PUNCT
iajs-4071	92	49	.	.	PUNCT
iajs-4071	93	1	we	we	PRON
iajs-4071	93	2	’ll	’ll	AUX
iajs-4071	93	3	write	write	VERB
iajs-4071	93	4	)	)	PUNCT
iajs-4071	93	5	)	)	PUNCT
iajs-4071	93	6	as	as	ADP
iajs-4071	93	7	)	)	PUNCT
iajs-4071	93	8	.	.	PUNCT
iajs-4071	94	1	the	the	DET
iajs-4071	94	2	soft	soft	ADJ
iajs-4071	94	3	function	function	NOUN
iajs-4071	94	4	is	be	AUX
iajs-4071	94	5	called	call	VERB
iajs-4071	94	6	surjective	surjective	ADJ
iajs-4071	94	7	if	if	SCONJ
iajs-4071	94	8	and	and	CCONJ
iajs-4071	94	9	are	be	AUX
iajs-4071	94	10	surjective	surjective	ADJ
iajs-4071	94	11	.	.	PUNCT
iajs-4071	95	1	the	the	DET
iajs-4071	95	2	soft	soft	ADJ
iajs-4071	95	3	function	function	NOUN
iajs-4071	95	4	is	be	AUX
iajs-4071	95	5	called	call	VERB
iajs-4071	95	6	injective	injective	ADJ
iajs-4071	95	7	if	if	SCONJ
iajs-4071	95	8	and	and	CCONJ
iajs-4071	95	9	are	be	AUX
iajs-4071	95	10	injective	injective	ADJ
iajs-4071	95	11	functions	function	NOUN
iajs-4071	95	12	.	.	PUNCT
iajs-4071	96	1	ihjpas	ihjpas	PROPN
iajs-4071	96	2	.	.	PUNCT
iajs-4071	97	1	2025,38(4	2025,38(4	X
iajs-4071	97	2	)	)	PUNCT
iajs-4071	98	1	366	366	NUM
iajs-4071	98	2	2.14	2.14	NUM
iajs-4071	98	3	.	.	PUNCT
iajs-4071	99	1	definition	definition	NOUN
iajs-4071	99	2	(	(	PUNCT
iajs-4071	99	3	15	15	NUM
iajs-4071	99	4	)	)	PUNCT
iajs-4071	99	5	suppose	suppose	VERB
iajs-4071	99	6	that	that	SCONJ
iajs-4071	99	7	(	(	PUNCT
iajs-4071	99	8	̃	̃	PROPN
iajs-4071	99	9	̃	̃	ADJ
iajs-4071	99	10	)	)	PUNCT
iajs-4071	99	11	̃	̃	NOUN
iajs-4071	99	12	̃	̃	PROPN
iajs-4071	99	13	)	)	PUNCT
iajs-4071	99	14	be	be	AUX
iajs-4071	99	15	a	a	DET
iajs-4071	99	16	soft	soft	ADJ
iajs-4071	99	17	mapping	mapping	NOUN
iajs-4071	99	18	and	and	CCONJ
iajs-4071	99	19	.	.	PUNCT
iajs-4071	100	1	then	then	ADV
iajs-4071	100	2	the	the	DET
iajs-4071	100	3	restriction	restriction	NOUN
iajs-4071	100	4	of	of	ADP
iajs-4071	100	5	to	to	ADP
iajs-4071	100	6	̃	̃	PROPN
iajs-4071	100	7	̃	̃	PROPN
iajs-4071	100	8	)	)	PUNCT
iajs-4071	100	9	is	be	AUX
iajs-4071	100	10	the	the	DET
iajs-4071	100	11	soft	soft	ADJ
iajs-4071	100	12	mapping	mapping	NOUN
iajs-4071	100	13	̃	̃	PROPN
iajs-4071	100	14	̃	̃	PROPN
iajs-4071	100	15	)	)	PUNCT
iajs-4071	100	16	from	from	ADP
iajs-4071	100	17	̃	̃	PROPN
iajs-4071	100	18	̃	̃	PROPN
iajs-4071	100	19	)	)	PUNCT
iajs-4071	100	20	to	to	ADP
iajs-4071	100	21	̃	̃	PROPN
iajs-4071	100	22	̃	̃	PROPN
iajs-4071	100	23	)	)	PUNCT
iajs-4071	100	24	which	which	PRON
iajs-4071	100	25	is	be	AUX
iajs-4071	100	26	defined	define	VERB
iajs-4071	100	27	by	by	ADP
iajs-4071	100	28	the	the	DET
iajs-4071	100	29	functions	function	NOUN
iajs-4071	100	30	and	and	CCONJ
iajs-4071	100	31	where	where	SCONJ
iajs-4071	100	32	is	be	AUX
iajs-4071	100	33	the	the	DET
iajs-4071	100	34	restriction	restriction	NOUN
iajs-4071	100	35	of	of	ADP
iajs-4071	100	36	to	to	PART
iajs-4071	100	37	.	.	PUNCT
iajs-4071	101	1	2.15	2.15	NUM
iajs-4071	101	2	.	.	PUNCT
iajs-4071	101	3	definition	definition	NOUN
iajs-4071	101	4	(	(	PUNCT
iajs-4071	101	5	18)a	18)a	NUM
iajs-4071	101	6	soft	soft	ADJ
iajs-4071	101	7	function	function	NOUN
iajs-4071	101	8	̃	̃	PROPN
iajs-4071	101	9	(	(	PUNCT
iajs-4071	101	10	̃	̃	NOUN
iajs-4071	101	11	̃	̃	ADJ
iajs-4071	101	12	)	)	PUNCT
iajs-4071	101	13	̃	̃	NOUN
iajs-4071	101	14	̃	̃	PROPN
iajs-4071	101	15	)	)	PUNCT
iajs-4071	101	16	is	be	AUX
iajs-4071	101	17	known	know	VERB
iajs-4071	101	18	as	as	ADP
iajs-4071	101	19	.	.	PROPN
iajs-4071	101	20	1	1	X
iajs-4071	101	21	.	.	PUNCT
iajs-4071	101	22	soft	soft	ADJ
iajs-4071	101	23	continuous	continuous	ADJ
iajs-4071	101	24	,	,	PUNCT
iajs-4071	101	25	if	if	SCONJ
iajs-4071	101	26	̃	̃	ADJ
iajs-4071	101	27	)	)	PUNCT
iajs-4071	102	1	̃	̃	NOUN
iajs-4071	102	2	̃	̃	ADJ
iajs-4071	102	3	)	)	PUNCT
iajs-4071	103	1	̃	̃	ADV
iajs-4071	103	2	̃.	̃.	ADJ
iajs-4071	103	3	2	2	NUM
iajs-4071	103	4	.	.	PUNCT
iajs-4071	103	5	soft	soft	ADJ
iajs-4071	103	6	perfectly	perfectly	ADV
iajs-4071	103	7	continuous	continuous	ADJ
iajs-4071	103	8	,	,	PUNCT
iajs-4071	103	9	if	if	SCONJ
iajs-4071	103	10	̃	̃	PROPN
iajs-4071	103	11	)	)	PUNCT
iajs-4071	103	12	is	be	AUX
iajs-4071	103	13	a	a	DET
iajs-4071	103	14	soft	soft	ADJ
iajs-4071	103	15	clopen	clopen	ADJ
iajs-4071	103	16	set	set	NOUN
iajs-4071	103	17	in	in	ADP
iajs-4071	103	18	̃	̃	PROPN
iajs-4071	103	19	)	)	PUNCT
iajs-4071	104	1	̃	̃	ADV
iajs-4071	104	2	̃.	̃.	ADJ
iajs-4071	104	3	3	3	NUM
iajs-4071	104	4	.	.	PUNCT
iajs-4071	104	5	soft	soft	ADJ
iajs-4071	104	6	-continuous	-continuous	ADJ
iajs-4071	104	7	,	,	PUNCT
iajs-4071	104	8	if	if	SCONJ
iajs-4071	104	9	̃	̃	ADJ
iajs-4071	104	10	)	)	PUNCT
iajs-4071	105	1	̃	̃	PROPN
iajs-4071	105	2	̃	̃	PROPN
iajs-4071	105	3	̃	̃	NOUN
iajs-4071	105	4	)	)	PUNCT
iajs-4071	105	5	)	)	PUNCT
iajs-4071	106	1	̃	̃	ADV
iajs-4071	106	2	̃.	̃.	ADJ
iajs-4071	106	3	4	4	NUM
iajs-4071	106	4	.	.	PUNCT
iajs-4071	106	5	soft	soft	ADJ
iajs-4071	106	6	regular	regular	ADJ
iajs-4071	106	7	continuous	continuous	ADJ
iajs-4071	106	8	,	,	PUNCT
iajs-4071	106	9	if	if	SCONJ
iajs-4071	106	10	̃	̃	ADJ
iajs-4071	106	11	)	)	PUNCT
iajs-4071	107	1	̃	̃	SYM
iajs-4071	107	2	̃	̃	PROPN
iajs-4071	107	3	(	(	PUNCT
iajs-4071	107	4	̃	̃	NOUN
iajs-4071	107	5	)	)	PUNCT
iajs-4071	107	6	)	)	PUNCT
iajs-4071	108	1	̃	̃	NOUN
iajs-4071	108	2	̃	̃	NOUN
iajs-4071	108	3	5	5	NUM
iajs-4071	108	4	.	.	PUNCT
iajs-4071	108	5	̃	̃	NOUN
iajs-4071	108	6	-continuous	-continuous	ADJ
iajs-4071	108	7	,	,	PUNCT
iajs-4071	108	8	if	if	SCONJ
iajs-4071	108	9	̃	̃	ADJ
iajs-4071	108	10	)	)	PUNCT
iajs-4071	108	11	̃	̃	PROPN
iajs-4071	108	12	̃	̃	PROPN
iajs-4071	108	13	̃	̃	NOUN
iajs-4071	108	14	)	)	PUNCT
iajs-4071	108	15	)	)	PUNCT
iajs-4071	109	1	̃	̃	ADV
iajs-4071	109	2	̃.	̃.	ADJ
iajs-4071	109	3	6	6	NUM
iajs-4071	109	4	.	.	PUNCT
iajs-4071	109	5	soft	soft	ADJ
iajs-4071	109	6	-continuous	-continuous	ADJ
iajs-4071	109	7	,	,	PUNCT
iajs-4071	109	8	if	if	SCONJ
iajs-4071	109	9	̃	̃	ADJ
iajs-4071	109	10	)	)	PUNCT
iajs-4071	109	11	̃	̃	PROPN
iajs-4071	109	12	̃	̃	PROPN
iajs-4071	109	13	̃	̃	NOUN
iajs-4071	109	14	)	)	PUNCT
iajs-4071	109	15	)	)	PUNCT
iajs-4071	110	1	̃	̃	ADV
iajs-4071	110	2	̃.	̃.	ADJ
iajs-4071	110	3	7	7	NUM
iajs-4071	110	4	.	.	PUNCT
iajs-4071	110	5	soft	soft	ADJ
iajs-4071	110	6	-continuous	-continuous	ADJ
iajs-4071	110	7	,	,	PUNCT
iajs-4071	110	8	if	if	SCONJ
iajs-4071	110	9	̃	̃	ADJ
iajs-4071	110	10	)	)	PUNCT
iajs-4071	110	11	̃	̃	PROPN
iajs-4071	110	12	̃	̃	PROPN
iajs-4071	110	13	̃	̃	NOUN
iajs-4071	110	14	)	)	PUNCT
iajs-4071	110	15	)	)	PUNCT
iajs-4071	111	1	̃	̃	ADV
iajs-4071	111	2	̃.	̃.	ADJ
iajs-4071	111	3	8	8	NUM
iajs-4071	111	4	.	.	PUNCT
iajs-4071	112	1	̃	̃	ADV
iajs-4071	112	2	-continuous	-continuous	ADJ
iajs-4071	112	3	,	,	PUNCT
iajs-4071	112	4	if	if	SCONJ
iajs-4071	112	5	̃	̃	ADJ
iajs-4071	112	6	)	)	PUNCT
iajs-4071	112	7	̃	̃	PROPN
iajs-4071	112	8	̃	̃	PROPN
iajs-4071	112	9	̃	̃	NOUN
iajs-4071	112	10	)	)	PUNCT
iajs-4071	112	11	)	)	PUNCT
iajs-4071	113	1	̃	̃	ADV
iajs-4071	113	2	̃.	̃.	ADJ
iajs-4071	113	3	9	9	NUM
iajs-4071	113	4	.	.	PUNCT
iajs-4071	113	5	soft	soft	ADJ
iajs-4071	113	6	irresolute	irresolute	ADJ
iajs-4071	113	7	,	,	PUNCT
iajs-4071	113	8	̃	̃	ADJ
iajs-4071	113	9	)	)	PUNCT
iajs-4071	113	10	̃	̃	PROPN
iajs-4071	113	11	̃	̃	NOUN
iajs-4071	113	12	̃	̃	NOUN
iajs-4071	113	13	)	)	PUNCT
iajs-4071	113	14	)	)	PUNCT
iajs-4071	114	1	̃	̃	PROPN
iajs-4071	114	2	̃	̃	NOUN
iajs-4071	114	3	̃	̃	NOUN
iajs-4071	114	4	)	)	PUNCT
iajs-4071	114	5	.	.	PUNCT
iajs-4071	115	1	10	10	NUM
iajs-4071	115	2	.	.	PUNCT
iajs-4071	115	3	soft	soft	ADJ
iajs-4071	115	4	open	open	ADJ
iajs-4071	115	5	.	.	PUNCT
iajs-4071	116	1	if	if	SCONJ
iajs-4071	116	2	̃	̃	ADJ
iajs-4071	116	3	)	)	PUNCT
iajs-4071	116	4	̃	̃	NOUN
iajs-4071	116	5	̃	̃	ADJ
iajs-4071	116	6	)	)	PUNCT
iajs-4071	117	1	̃	̃	NOUN
iajs-4071	117	2	̃.	̃.	ADJ
iajs-4071	117	3	2.16	2.16	NUM
iajs-4071	117	4	.	.	PUNCT
iajs-4071	118	1	proposition	proposition	NOUN
iajs-4071	118	2	(	(	PUNCT
iajs-4071	118	3	16	16	NUM
iajs-4071	118	4	)	)	PUNCT
iajs-4071	118	5	a	a	DET
iajs-4071	118	6	sts	st	NOUN
iajs-4071	118	7	(	(	PUNCT
iajs-4071	118	8	̃	̃	NOUN
iajs-4071	118	9	̃	̃	PROPN
iajs-4071	118	10	)	)	PUNCT
iajs-4071	118	11	is	be	AUX
iajs-4071	118	12	-space	-space	PROPN
iajs-4071	118	13	iff	iff	PROPN
iajs-4071	118	14	̃	̃	PROPN
iajs-4071	118	15	̃	̃	PROPN
iajs-4071	118	16	̃	̃	PROPN
iajs-4071	118	17	̃	̃	NOUN
iajs-4071	118	18	)	)	PUNCT
iajs-4071	118	19	is	be	AUX
iajs-4071	118	20	soft	soft	ADJ
iajs-4071	118	21	closed	closed	ADJ
iajs-4071	118	22	set	set	NOUN
iajs-4071	118	23	.	.	PUNCT
iajs-4071	119	1	2.17	2.17	NUM
iajs-4071	119	2	.	.	PUNCT
iajs-4071	120	1	proposition	proposition	NOUN
iajs-4071	120	2	(	(	PUNCT
iajs-4071	120	3	16	16	NUM
iajs-4071	120	4	)	)	PUNCT
iajs-4071	120	5	let	let	VERB
iajs-4071	120	6	(	(	PUNCT
iajs-4071	120	7	̃	̃	NOUN
iajs-4071	120	8	̃	̃	PROPN
iajs-4071	120	9	)	)	PUNCT
iajs-4071	120	10	be	be	VERB
iajs-4071	120	11	a	a	DET
iajs-4071	120	12	sts	st	NOUN
iajs-4071	120	13	,	,	PUNCT
iajs-4071	120	14	then	then	ADV
iajs-4071	120	15	̃	̃	PROPN
iajs-4071	120	16	̃	̃	NOUN
iajs-4071	120	17	)	)	PUNCT
iajs-4071	120	18	forms	form	VERB
iajs-4071	120	19	a	a	DET
iajs-4071	120	20	soft	soft	ADJ
iajs-4071	120	21	supra	supra	NOUN
iajs-4071	120	22	topology	topology	NOUN
iajs-4071	120	23	.	.	PUNCT
iajs-4071	121	1	2.18	2.18	NUM
iajs-4071	121	2	.	.	PUNCT
iajs-4071	121	3	proposition	proposition	NOUN
iajs-4071	121	4	(	(	PUNCT
iajs-4071	121	5	19	19	NUM
iajs-4071	121	6	)	)	PUNCT
iajs-4071	121	7	if	if	SCONJ
iajs-4071	121	8	(	(	PUNCT
iajs-4071	121	9	̃	̃	NOUN
iajs-4071	121	10	̃	̃	NOUN
iajs-4071	121	11	)	)	PUNCT
iajs-4071	121	12	be	be	VERB
iajs-4071	121	13	a	a	DET
iajs-4071	121	14	seds	sed	NOUN
iajs-4071	121	15	,	,	PUNCT
iajs-4071	121	16	then	then	ADV
iajs-4071	121	17	1	1	NUM
iajs-4071	121	18	.	.	X
iajs-4071	122	1	̃	̃	PROPN
iajs-4071	122	2	(	(	PUNCT
iajs-4071	122	3	̃	̃	NOUN
iajs-4071	122	4	)	)	PUNCT
iajs-4071	122	5	̃	̃	NOUN
iajs-4071	122	6	̃	̃	PROPN
iajs-4071	122	7	(	(	PUNCT
iajs-4071	122	8	̃	̃	PROPN
iajs-4071	122	9	)	)	PUNCT
iajs-4071	122	10	2	2	NUM
iajs-4071	122	11	.	.	X
iajs-4071	123	1	̃	̃	PROPN
iajs-4071	123	2	(	(	PUNCT
iajs-4071	123	3	̃	̃	NOUN
iajs-4071	123	4	)	)	PUNCT
iajs-4071	123	5	̃	̃	NOUN
iajs-4071	123	6	̃	̃	PROPN
iajs-4071	123	7	(	(	PUNCT
iajs-4071	123	8	̃	̃	PROPN
iajs-4071	123	9	)	)	PUNCT
iajs-4071	123	10	2.19	2.19	NUM
iajs-4071	123	11	.	.	PUNCT
iajs-4071	124	1	proposition	proposition	NOUN
iajs-4071	124	2	(	(	PUNCT
iajs-4071	124	3	10	10	NUM
iajs-4071	124	4	)	)	PUNCT
iajs-4071	124	5	if	if	SCONJ
iajs-4071	124	6	)	)	PUNCT
iajs-4071	124	7	̃	̃	NOUN
iajs-4071	124	8	̃	̃	PROPN
iajs-4071	124	9	(	(	PUNCT
iajs-4071	124	10	)	)	PUNCT
iajs-4071	124	11	̃	̃	NOUN
iajs-4071	124	12	̃	̃	PROPN
iajs-4071	124	13	(	(	PUNCT
iajs-4071	124	14	̃	̃	PROPN
iajs-4071	124	15	)	)	PUNCT
iajs-4071	124	16	in	in	ADP
iajs-4071	124	17	a	a	DET
iajs-4071	124	18	sts	st	NOUN
iajs-4071	124	19	(	(	PUNCT
iajs-4071	124	20	̃	̃	NOUN
iajs-4071	124	21	̃	̃	PROPN
iajs-4071	124	22	)	)	PUNCT
iajs-4071	124	23	,	,	PUNCT
iajs-4071	124	24	then	then	ADV
iajs-4071	124	25	)	)	PUNCT
iajs-4071	124	26	̃	̃	PROPN
iajs-4071	124	27	(	(	PUNCT
iajs-4071	124	28	)	)	PUNCT
iajs-4071	124	29	̃	̃	NOUN
iajs-4071	124	30	̃	̃	PROPN
iajs-4071	124	31	(	(	PUNCT
iajs-4071	124	32	̃	̃	NOUN
iajs-4071	124	33	)	)	PUNCT
iajs-4071	124	34	.	.	PUNCT
iajs-4071	125	1	2.20	2.20	NUM
iajs-4071	125	2	.	.	PUNCT
iajs-4071	125	3	proposition	proposition	NOUN
iajs-4071	125	4	(	(	PUNCT
iajs-4071	125	5	14	14	NUM
iajs-4071	125	6	)	)	PUNCT
iajs-4071	125	7	let	let	VERB
iajs-4071	125	8	(	(	PUNCT
iajs-4071	125	9	̃	̃	NOUN
iajs-4071	125	10	̃	̃	PROPN
iajs-4071	125	11	)	)	PUNCT
iajs-4071	125	12	be	be	VERB
iajs-4071	125	13	a	a	DET
iajs-4071	125	14	sts	st	NOUN
iajs-4071	125	15	,	,	PUNCT
iajs-4071	125	16	̃	̃	PROPN
iajs-4071	125	17	̃	̃	PROPN
iajs-4071	125	18	(	(	PUNCT
iajs-4071	125	19	̃	̃	NOUN
iajs-4071	125	20	)	)	PUNCT
iajs-4071	125	21	iff	iff	PROPN
iajs-4071	125	22	̃	̃	PROPN
iajs-4071	125	23	̃	̃	PROPN
iajs-4071	125	24	(	(	PUNCT
iajs-4071	125	25	̃	̃	PROPN
iajs-4071	125	26	)	)	PUNCT
iajs-4071	125	27	2.21	2.21	NUM
iajs-4071	125	28	.	.	PUNCT
iajs-4071	126	1	proposition	proposition	NOUN
iajs-4071	126	2	(	(	PUNCT
iajs-4071	126	3	15	15	NUM
iajs-4071	126	4	)	)	PUNCT
iajs-4071	126	5	let	let	VERB
iajs-4071	126	6	(	(	PUNCT
iajs-4071	126	7	̃	̃	NOUN
iajs-4071	126	8	̃	̃	PROPN
iajs-4071	126	9	)	)	PUNCT
iajs-4071	126	10	be	be	AUX
iajs-4071	126	11	a	a	DET
iajs-4071	126	12	soft	soft	ADJ
iajs-4071	126	13	regular	regular	ADJ
iajs-4071	126	14	space	space	NOUN
iajs-4071	126	15	iff	iff	PROPN
iajs-4071	126	16	̃	̃	PROPN
iajs-4071	126	17	and	and	CCONJ
iajs-4071	126	18	̃	̃	PROPN
iajs-4071	126	19	)	)	PUNCT
iajs-4071	126	20	,	,	PUNCT
iajs-4071	126	21	)	)	PUNCT
iajs-4071	127	1	̃	̃	PROPN
iajs-4071	127	2	̃	̃	PROPN
iajs-4071	127	3	s.t	s.t	PROPN
iajs-4071	127	4	.	.	PUNCT
iajs-4071	127	5	̃	̃	ADJ
iajs-4071	127	6	)	)	PUNCT
iajs-4071	128	1	̃	̃	NOUN
iajs-4071	128	2	̃	̃	ADJ
iajs-4071	128	3	)	)	PUNCT
iajs-4071	129	1	̃	̃	PROPN
iajs-4071	129	2	)	)	PUNCT
iajs-4071	129	3	2.22	2.22	NUM
iajs-4071	129	4	.	.	PUNCT
iajs-4071	130	1	proposition	proposition	NOUN
iajs-4071	130	2	(	(	PUNCT
iajs-4071	130	3	18	18	NUM
iajs-4071	130	4	)	)	PUNCT
iajs-4071	130	5	let	let	AUX
iajs-4071	130	6	̃	̃	PROPN
iajs-4071	130	7	̃	̃	PROPN
iajs-4071	130	8	)	)	PUNCT
iajs-4071	130	9	be	be	AUX
iajs-4071	130	10	a	a	DET
iajs-4071	130	11	soft	soft	ADJ
iajs-4071	130	12	subspace	subspace	NOUN
iajs-4071	130	13	of	of	ADP
iajs-4071	130	14	(	(	PUNCT
iajs-4071	130	15	̃	̃	PROPN
iajs-4071	130	16	̃	̃	PROPN
iajs-4071	130	17	)	)	PUNCT
iajs-4071	130	18	and	and	CCONJ
iajs-4071	130	19	)	)	PUNCT
iajs-4071	130	20	̃	̃	NOUN
iajs-4071	130	21	̃	̃	ADV
iajs-4071	130	22	then	then	ADV
iajs-4071	130	23	,	,	PUNCT
iajs-4071	130	24	̃	̃	PROPN
iajs-4071	130	25	̃	̃	ADJ
iajs-4071	130	26	)	)	PUNCT
iajs-4071	131	1	̃	̃	NOUN
iajs-4071	131	2	)	)	PUNCT
iajs-4071	132	1	if	if	SCONJ
iajs-4071	132	2	̃	̃	PROPN
iajs-4071	132	3	̃	̃	ADP
iajs-4071	132	4	̃	̃	NOUN
iajs-4071	132	5	2.23	2.23	NUM
iajs-4071	132	6	.	.	PUNCT
iajs-4071	133	1	proposition	proposition	NOUN
iajs-4071	133	2	(	(	PUNCT
iajs-4071	133	3	16	16	NUM
iajs-4071	133	4	)	)	PUNCT
iajs-4071	133	5	let	let	AUX
iajs-4071	133	6	̃	̃	PROPN
iajs-4071	133	7	̃	̃	PROPN
iajs-4071	133	8	)	)	PUNCT
iajs-4071	133	9	be	be	AUX
iajs-4071	133	10	a	a	DET
iajs-4071	133	11	soft	soft	ADJ
iajs-4071	133	12	subspace	subspace	NOUN
iajs-4071	133	13	of	of	ADP
iajs-4071	133	14	(	(	PUNCT
iajs-4071	133	15	̃	̃	PROPN
iajs-4071	133	16	̃	̃	PROPN
iajs-4071	133	17	)	)	PUNCT
iajs-4071	133	18	and	and	CCONJ
iajs-4071	133	19	)	)	PUNCT
iajs-4071	134	1	̃	̃	PROPN
iajs-4071	134	2	̃	̃	ADJ
iajs-4071	134	3	s.t	s.t	PROPN
iajs-4071	134	4	.	.	PUNCT
iajs-4071	134	5	̃	̃	PROPN
iajs-4071	134	6	̃	̃	PROPN
iajs-4071	134	7	̃	̃	PROPN
iajs-4071	134	8	(	(	PUNCT
iajs-4071	134	9	̃	̃	NOUN
iajs-4071	134	10	)	)	PUNCT
iajs-4071	134	11	)	)	PUNCT
iajs-4071	135	1	̃	̃	NOUN
iajs-4071	135	2	̃	̃	PROPN
iajs-4071	135	3	(	(	PUNCT
iajs-4071	135	4	̃	̃	PROPN
iajs-4071	135	5	)	)	PUNCT
iajs-4071	135	6	,	,	PUNCT
iajs-4071	135	7	then	then	ADV
iajs-4071	135	8	)	)	PUNCT
iajs-4071	135	9	̃	̃	NOUN
iajs-4071	135	10	̃	̃	PROPN
iajs-4071	135	11	(	(	PUNCT
iajs-4071	135	12	̃	̃	NOUN
iajs-4071	135	13	)	)	PUNCT
iajs-4071	135	14	.	.	PUNCT
iajs-4071	136	1	3	3	X
iajs-4071	136	2	.	.	X
iajs-4071	136	3	̃	̃	ADJ
iajs-4071	136	4	open	open	ADJ
iajs-4071	136	5	sets	set	NOUN
iajs-4071	136	6	.	.	PUNCT
iajs-4071	137	1	in	in	ADP
iajs-4071	137	2	this	this	DET
iajs-4071	137	3	section	section	NOUN
iajs-4071	137	4	,	,	PUNCT
iajs-4071	137	5	we	we	PRON
iajs-4071	137	6	study	study	VERB
iajs-4071	137	7	a	a	DET
iajs-4071	137	8	new	new	ADJ
iajs-4071	137	9	type	type	NOUN
iajs-4071	137	10	of	of	ADP
iajs-4071	137	11	soft	soft	ADJ
iajs-4071	137	12	sets	set	NOUN
iajs-4071	137	13	called	call	VERB
iajs-4071	137	14	̃	̃	PROPN
iajs-4071	137	15	open	open	ADJ
iajs-4071	137	16	set	set	VERB
iajs-4071	137	17	in	in	ADP
iajs-4071	137	18	soft	soft	ADJ
iajs-4071	137	19	topological	topological	ADJ
iajs-4071	137	20	spaces	space	NOUN
iajs-4071	137	21	.	.	PUNCT
iajs-4071	138	1	some	some	DET
iajs-4071	138	2	properties	property	NOUN
iajs-4071	138	3	of	of	ADP
iajs-4071	138	4	this	this	DET
iajs-4071	138	5	type	type	NOUN
iajs-4071	138	6	of	of	ADP
iajs-4071	138	7	soft	soft	ADJ
iajs-4071	138	8	set	set	NOUN
iajs-4071	138	9	are	be	AUX
iajs-4071	138	10	given	give	VERB
iajs-4071	138	11	,	,	PUNCT
iajs-4071	138	12	and	and	CCONJ
iajs-4071	138	13	the	the	DET
iajs-4071	138	14	relationships	relationship	NOUN
iajs-4071	138	15	with	with	ADP
iajs-4071	138	16	a	a	DET
iajs-4071	138	17	few	few	ADJ
iajs-4071	138	18	other	other	ADJ
iajs-4071	138	19	kinds	kind	NOUN
iajs-4071	138	20	of	of	ADP
iajs-4071	138	21	soft	soft	ADJ
iajs-4071	138	22	sets	set	NOUN
iajs-4071	138	23	are	be	AUX
iajs-4071	138	24	introduced	introduce	VERB
iajs-4071	138	25	.	.	PUNCT
iajs-4071	139	1	3.1	3.1	NUM
iajs-4071	139	2	.	.	PUNCT
iajs-4071	139	3	definition	definition	NOUN
iajs-4071	139	4	a	a	DET
iajs-4071	139	5	soft	soft	ADJ
iajs-4071	139	6	set	set	NOUN
iajs-4071	139	7	)	)	PUNCT
iajs-4071	139	8	of	of	ADP
iajs-4071	139	9	sts	st	NOUN
iajs-4071	139	10	(	(	PUNCT
iajs-4071	139	11	̃	̃	NOUN
iajs-4071	139	12	̃	̃	PROPN
iajs-4071	139	13	)	)	PUNCT
iajs-4071	139	14	is	be	AUX
iajs-4071	139	15	called	call	VERB
iajs-4071	139	16	̃	̃	ADV
iajs-4071	139	17	-open	-open	ADJ
iajs-4071	139	18	if	if	SCONJ
iajs-4071	139	19	)	)	PUNCT
iajs-4071	139	20	̃	̃	PROPN
iajs-4071	139	21	̃	̃	ADP
iajs-4071	139	22	̃	̃	NOUN
iajs-4071	139	23	)	)	PUNCT
iajs-4071	139	24	̃	̃	NOUN
iajs-4071	139	25	)	)	PUNCT
iajs-4071	139	26	(	(	PUNCT
iajs-4071	139	27	)	)	PUNCT
iajs-4071	140	1	̃	̃	PROPN
iajs-4071	140	2	̃	̃	PROPN
iajs-4071	140	3	̃	̃	PROPN
iajs-4071	140	4	)	)	PUNCT
iajs-4071	140	5	s.t	s.t	PROPN
iajs-4071	140	6	.	.	PUNCT
iajs-4071	140	7	̃	̃	ADV
iajs-4071	140	8	)	)	PUNCT
iajs-4071	141	1	̃	̃	PROPN
iajs-4071	141	2	)	)	PUNCT
iajs-4071	141	3	the	the	DET
iajs-4071	141	4	family	family	NOUN
iajs-4071	141	5	of	of	ADP
iajs-4071	141	6	all	all	DET
iajs-4071	141	7	̃	̃	PROPN
iajs-4071	141	8	-open	-open	ADJ
iajs-4071	141	9	subsets	subset	NOUN
iajs-4071	141	10	of	of	ADP
iajs-4071	141	11	(	(	PUNCT
iajs-4071	141	12	̃	̃	PROPN
iajs-4071	141	13	̃	̃	PROPN
iajs-4071	141	14	)	)	PUNCT
iajs-4071	141	15	is	be	AUX
iajs-4071	141	16	indicated	indicate	VERB
iajs-4071	141	17	by	by	ADP
iajs-4071	141	18	̃	̃	PROPN
iajs-4071	141	19	̃	̃	NOUN
iajs-4071	141	20	̃	̃	PROPN
iajs-4071	141	21	)	)	PUNCT
iajs-4071	141	22	or	or	CCONJ
iajs-4071	141	23	̃	̃	PROPN
iajs-4071	141	24	̃	̃	PROPN
iajs-4071	141	25	)	)	PUNCT
iajs-4071	141	26	.	.	PUNCT
iajs-4071	142	1	3.2	3.2	NUM
iajs-4071	142	2	.	.	PUNCT
iajs-4071	143	1	proposition	proposition	VERB
iajs-4071	143	2	a	a	DET
iajs-4071	143	3	soft	soft	ADJ
iajs-4071	143	4	set	set	NOUN
iajs-4071	143	5	)	)	PUNCT
iajs-4071	143	6	of	of	ADP
iajs-4071	143	7	sts	st	NOUN
iajs-4071	143	8	(	(	PUNCT
iajs-4071	143	9	̃	̃	NOUN
iajs-4071	143	10	̃	̃	PROPN
iajs-4071	143	11	)	)	PUNCT
iajs-4071	143	12	is	be	AUX
iajs-4071	143	13	̃	̃	PROPN
iajs-4071	143	14	-open	-open	ADJ
iajs-4071	143	15	iff	iff	NOUN
iajs-4071	143	16	)	)	PUNCT
iajs-4071	143	17	(	(	PUNCT
iajs-4071	143	18	)	)	PUNCT
iajs-4071	144	1	where	where	SCONJ
iajs-4071	144	2	)	)	PUNCT
iajs-4071	144	3	̃	̃	PROPN
iajs-4071	144	4	̃	̃	PROPN
iajs-4071	144	5	̃	̃	NOUN
iajs-4071	144	6	)	)	PUNCT
iajs-4071	144	7	and	and	CCONJ
iajs-4071	144	8	)	)	PUNCT
iajs-4071	144	9	̃	̃	PROPN
iajs-4071	144	10	̃	̃	ADP
iajs-4071	144	11	̃	̃	ADJ
iajs-4071	144	12	)	)	PUNCT
iajs-4071	144	13	̃	̃	ADJ
iajs-4071	144	14	proof	proof	NOUN
iajs-4071	144	15	:	:	PUNCT
iajs-4071	144	16	obvious	obvious	ADJ
iajs-4071	144	17	.	.	PUNCT
iajs-4071	145	1	corollary	corollary	ADJ
iajs-4071	145	2	a	a	DET
iajs-4071	145	3	soft	soft	ADJ
iajs-4071	145	4	set	set	NOUN
iajs-4071	145	5	)	)	PUNCT
iajs-4071	145	6	of	of	ADP
iajs-4071	145	7	sts	st	NOUN
iajs-4071	145	8	(	(	PUNCT
iajs-4071	145	9	̃	̃	NOUN
iajs-4071	145	10	̃	̃	PROPN
iajs-4071	145	11	)	)	PUNCT
iajs-4071	145	12	is	be	AUX
iajs-4071	145	13	̃	̃	NOUN
iajs-4071	145	14	-open	-open	ADJ
iajs-4071	145	15	.	.	PUNCT
iajs-4071	146	1	if	if	SCONJ
iajs-4071	146	2	)	)	PUNCT
iajs-4071	146	3	̃	̃	ADV
iajs-4071	146	4	̃	̃	PROPN
iajs-4071	146	5	(	(	PUNCT
iajs-4071	146	6	̃	̃	NOUN
iajs-4071	146	7	)	)	PUNCT
iajs-4071	146	8	̃	̃	NOUN
iajs-4071	146	9	̃	̃	PROPN
iajs-4071	146	10	(	(	PUNCT
iajs-4071	146	11	̃	̃	NOUN
iajs-4071	146	12	)	)	PUNCT
iajs-4071	146	13	proof	proof	NOUN
iajs-4071	146	14	:	:	PUNCT
iajs-4071	146	15	directly	directly	ADV
iajs-4071	146	16	from	from	ADP
iajs-4071	146	17	definition	definition	NOUN
iajs-4071	146	18	3.1	3.1	NUM
iajs-4071	146	19	.	.	PUNCT
iajs-4071	146	20	ihjpas	ihjpas	PROPN
iajs-4071	146	21	.	.	PUNCT
iajs-4071	147	1	2025,38(4	2025,38(4	X
iajs-4071	147	2	)	)	PUNCT
iajs-4071	147	3	367	367	NUM
iajs-4071	147	4	remark	remark	NOUN
iajs-4071	147	5	1	1	NUM
iajs-4071	147	6	̃	̃	PROPN
iajs-4071	147	7	(	(	PUNCT
iajs-4071	147	8	̃	̃	NOUN
iajs-4071	147	9	)	)	PUNCT
iajs-4071	147	10	̃	̃	NOUN
iajs-4071	147	11	̃	̃	PROPN
iajs-4071	147	12	(	(	PUNCT
iajs-4071	147	13	̃	̃	PROPN
iajs-4071	147	14	)	)	PUNCT
iajs-4071	147	15	but	but	CCONJ
iajs-4071	147	16	̃	̃	PROPN
iajs-4071	147	17	(	(	PUNCT
iajs-4071	147	18	̃	̃	NOUN
iajs-4071	147	19	)	)	PUNCT
iajs-4071	147	20	̃	̃	NOUN
iajs-4071	147	21	̃	̃	PROPN
iajs-4071	147	22	(	(	PUNCT
iajs-4071	147	23	̃	̃	NOUN
iajs-4071	147	24	)	)	PUNCT
iajs-4071	147	25	is	be	AUX
iajs-4071	147	26	not	not	PART
iajs-4071	147	27	true	true	ADJ
iajs-4071	147	28	in	in	ADP
iajs-4071	147	29	general	general	ADJ
iajs-4071	147	30	.	.	PUNCT
iajs-4071	148	1	2	2	NUM
iajs-4071	148	2	̃	̃	PROPN
iajs-4071	148	3	(	(	PUNCT
iajs-4071	148	4	̃	̃	NOUN
iajs-4071	148	5	)	)	PUNCT
iajs-4071	148	6	̃	̃	PROPN
iajs-4071	148	7	(	(	PUNCT
iajs-4071	148	8	̃	̃	PROPN
iajs-4071	148	9	)	)	PUNCT
iajs-4071	148	10	3	3	NUM
iajs-4071	148	11	̃	̃	NOUN
iajs-4071	148	12	̃	̃	PROPN
iajs-4071	148	13	(	(	PUNCT
iajs-4071	148	14	̃	̃	NOUN
iajs-4071	148	15	)	)	PUNCT
iajs-4071	148	16	4	4	NUM
iajs-4071	148	17	̃	̃	NOUN
iajs-4071	148	18	̃	̃	PROPN
iajs-4071	148	19	(	(	PUNCT
iajs-4071	148	20	̃	̃	PROPN
iajs-4071	148	21	)	)	PUNCT
iajs-4071	148	22	the	the	DET
iajs-4071	148	23	examples	example	NOUN
iajs-4071	148	24	that	that	PRON
iajs-4071	148	25	follow	follow	VERB
iajs-4071	148	26	demonstrate	demonstrate	VERB
iajs-4071	148	27	the	the	DET
iajs-4071	148	28	earlier	early	ADJ
iajs-4071	148	29	point	point	NOUN
iajs-4071	148	30	.	.	PUNCT
iajs-4071	149	1	example	example	NOUN
iajs-4071	149	2	consider	consider	VERB
iajs-4071	149	3	,	,	PUNCT
iajs-4071	149	4	with	with	ADP
iajs-4071	149	5	the	the	DET
iajs-4071	149	6	two	two	NUM
iajs-4071	149	7	soft	soft	ADJ
iajs-4071	149	8	topological	topological	ADJ
iajs-4071	149	9	̃	̃	PROPN
iajs-4071	149	10	{	{	PUNCT
iajs-4071	149	11	̃	̃	NOUN
iajs-4071	149	12	̃	̃	PROPN
iajs-4071	149	13	(	(	PUNCT
iajs-4071	149	14	)	)	PUNCT
iajs-4071	149	15	(	(	PUNCT
iajs-4071	149	16	)	)	PUNCT
iajs-4071	149	17	}	}	PUNCT
iajs-4071	149	18	̃	̃	PROPN
iajs-4071	149	19	{	{	PUNCT
iajs-4071	149	20	̃	̃	NOUN
iajs-4071	149	21	̃	̃	PROPN
iajs-4071	149	22	(	(	PUNCT
iajs-4071	149	23	)	)	PUNCT
iajs-4071	149	24	(	(	PUNCT
iajs-4071	149	25	)	)	PUNCT
iajs-4071	149	26	)	)	PUNCT
iajs-4071	149	27	}	}	PUNCT
iajs-4071	149	28	where	where	SCONJ
iajs-4071	149	29	̃	̃	NOUN
iajs-4071	149	30	)	)	PUNCT
iajs-4071	149	31	)	)	PUNCT
iajs-4071	150	1	̃	̃	ADV
iajs-4071	150	2	)	)	PUNCT
iajs-4071	150	3	)	)	PUNCT
iajs-4071	150	4	,	,	PUNCT
iajs-4071	150	5	)	)	PUNCT
iajs-4071	150	6	)	)	PUNCT
iajs-4071	150	7	)	)	PUNCT
iajs-4071	150	8	)	)	PUNCT
iajs-4071	150	9	)	)	PUNCT
iajs-4071	150	10	)	)	PUNCT
iajs-4071	150	11	)	)	PUNCT
iajs-4071	150	12	)	)	PUNCT
iajs-4071	150	13	)	)	PUNCT
iajs-4071	151	1	(	(	PUNCT
iajs-4071	151	2	)	)	PUNCT
iajs-4071	151	3	)	)	PUNCT
iajs-4071	151	4	)	)	PUNCT
iajs-4071	152	1	(	(	PUNCT
iajs-4071	152	2	)	)	PUNCT
iajs-4071	152	3	)	)	PUNCT
iajs-4071	152	4	)	)	PUNCT
iajs-4071	152	5	)	)	PUNCT
iajs-4071	152	6	)	)	PUNCT
iajs-4071	152	7	)	)	PUNCT
iajs-4071	153	1	,	,	PUNCT
iajs-4071	153	2	(	(	PUNCT
iajs-4071	153	3	)	)	PUNCT
iajs-4071	153	4	)	)	PUNCT
iajs-4071	153	5	)	)	PUNCT
iajs-4071	154	1	(	(	PUNCT
iajs-4071	154	2	)	)	PUNCT
iajs-4071	154	3	)	)	PUNCT
iajs-4071	154	4	)	)	PUNCT
iajs-4071	155	1	(	(	PUNCT
iajs-4071	155	2	)	)	PUNCT
iajs-4071	155	3	)	)	PUNCT
iajs-4071	155	4	)	)	PUNCT
iajs-4071	156	1	(	(	PUNCT
iajs-4071	156	2	)	)	PUNCT
iajs-4071	156	3	)	)	PUNCT
iajs-4071	156	4	)	)	PUNCT
iajs-4071	157	1	(	(	PUNCT
iajs-4071	157	2	)	)	PUNCT
iajs-4071	157	3	)	)	PUNCT
iajs-4071	157	4	)	)	PUNCT
iajs-4071	158	1	(	(	PUNCT
iajs-4071	158	2	)	)	PUNCT
iajs-4071	158	3	)	)	PUNCT
iajs-4071	158	4	)	)	PUNCT
iajs-4071	159	1	(	(	PUNCT
iajs-4071	159	2	)	)	PUNCT
iajs-4071	159	3	)	)	PUNCT
iajs-4071	159	4	)	)	PUNCT
iajs-4071	160	1	(	(	PUNCT
iajs-4071	160	2	)	)	PUNCT
iajs-4071	160	3	)	)	PUNCT
iajs-4071	160	4	)	)	PUNCT
iajs-4071	160	5	̃.	̃.	NOUN
iajs-4071	160	6	(	(	PUNCT
iajs-4071	160	7	̃	̃	NOUN
iajs-4071	160	8	̃	̃	PROPN
iajs-4071	160	9	)	)	PUNCT
iajs-4071	160	10	and	and	CCONJ
iajs-4071	160	11	(	(	PUNCT
iajs-4071	160	12	̃	̃	NOUN
iajs-4071	160	13	̃	̃	PROPN
iajs-4071	160	14	)	)	PUNCT
iajs-4071	160	15	are	be	AUX
iajs-4071	160	16	two	two	NUM
iajs-4071	160	17	stss	stss	NOUN
iajs-4071	160	18	over	over	ADP
iajs-4071	160	19	.	.	PUNCT
iajs-4071	161	1	1	1	NUM
iajs-4071	161	2	(	(	PUNCT
iajs-4071	161	3	)	)	PUNCT
iajs-4071	161	4	̃	̃	NOUN
iajs-4071	161	5	̃	̃	PROPN
iajs-4071	161	6	(	(	PUNCT
iajs-4071	161	7	̃	̃	NOUN
iajs-4071	161	8	̃	̃	NOUN
iajs-4071	161	9	)	)	PUNCT
iajs-4071	161	10	(	(	PUNCT
iajs-4071	161	11	)	)	PUNCT
iajs-4071	161	12	̃	̃	PROPN
iajs-4071	161	13	̃	̃	ADP
iajs-4071	161	14	̃	̃	NOUN
iajs-4071	161	15	̃	̃	NOUN
iajs-4071	161	16	)	)	PUNCT
iajs-4071	161	17	2	2	NUM
iajs-4071	161	18	(	(	PUNCT
iajs-4071	161	19	)	)	PUNCT
iajs-4071	161	20	̃	̃	NOUN
iajs-4071	161	21	̃	̃	PROPN
iajs-4071	161	22	(	(	PUNCT
iajs-4071	161	23	̃	̃	NOUN
iajs-4071	161	24	̃	̃	NOUN
iajs-4071	161	25	)	)	PUNCT
iajs-4071	161	26	(	(	PUNCT
iajs-4071	161	27	)	)	PUNCT
iajs-4071	161	28	̃	̃	ADV
iajs-4071	161	29	̃	̃	PROPN
iajs-4071	161	30	(	(	PUNCT
iajs-4071	161	31	̃	̃	NOUN
iajs-4071	161	32	̃	̃	NOUN
iajs-4071	161	33	)	)	PUNCT
iajs-4071	161	34	(	(	PUNCT
iajs-4071	161	35	)	)	PUNCT
iajs-4071	161	36	̃	̃	ADV
iajs-4071	161	37	̃	̃	PROPN
iajs-4071	161	38	(	(	PUNCT
iajs-4071	161	39	̃	̃	NOUN
iajs-4071	161	40	̃	̃	NOUN
iajs-4071	161	41	)	)	PUNCT
iajs-4071	161	42	(	(	PUNCT
iajs-4071	161	43	)	)	PUNCT
iajs-4071	161	44	̃	̃	ADV
iajs-4071	161	45	̃	̃	PROPN
iajs-4071	161	46	(	(	PUNCT
iajs-4071	161	47	̃	̃	NOUN
iajs-4071	161	48	̃	̃	NOUN
iajs-4071	161	49	)	)	PUNCT
iajs-4071	161	50	3	3	NUM
iajs-4071	161	51	(	(	PUNCT
iajs-4071	161	52	)	)	PUNCT
iajs-4071	161	53	̃	̃	NOUN
iajs-4071	161	54	̃	̃	PROPN
iajs-4071	161	55	(	(	PUNCT
iajs-4071	161	56	)	)	PUNCT
iajs-4071	161	57	̃	̃	PROPN
iajs-4071	161	58	̃	̃	NOUN
iajs-4071	161	59	̃	̃	NOUN
iajs-4071	161	60	̃	̃	NOUN
iajs-4071	161	61	)	)	PUNCT
iajs-4071	161	62	(	(	PUNCT
iajs-4071	161	63	)	)	PUNCT
iajs-4071	161	64	̃	̃	ADV
iajs-4071	161	65	̃	̃	PROPN
iajs-4071	161	66	(	(	PUNCT
iajs-4071	161	67	̃	̃	NOUN
iajs-4071	161	68	̃	̃	NOUN
iajs-4071	161	69	)	)	PUNCT
iajs-4071	161	70	(	(	PUNCT
iajs-4071	161	71	)	)	PUNCT
iajs-4071	162	1	̃	̃	ADV
iajs-4071	162	2	̃	̃	NOUN
iajs-4071	162	3	4	4	NUM
iajs-4071	162	4	(	(	PUNCT
iajs-4071	162	5	)	)	PUNCT
iajs-4071	162	6	̃	̃	NOUN
iajs-4071	162	7	̃	̃	PROPN
iajs-4071	162	8	(	(	PUNCT
iajs-4071	162	9	)	)	PUNCT
iajs-4071	162	10	̃	̃	SYM
iajs-4071	162	11	̃	̃	PROPN
iajs-4071	162	12	(	(	PUNCT
iajs-4071	162	13	̃	̃	NOUN
iajs-4071	162	14	̃	̃	NOUN
iajs-4071	162	15	)	)	PUNCT
iajs-4071	162	16	(	(	PUNCT
iajs-4071	162	17	)	)	PUNCT
iajs-4071	162	18	̃	̃	ADV
iajs-4071	162	19	̃	̃	PROPN
iajs-4071	162	20	(	(	PUNCT
iajs-4071	162	21	̃	̃	NOUN
iajs-4071	162	22	̃	̃	NOUN
iajs-4071	162	23	)	)	PUNCT
iajs-4071	162	24	(	(	PUNCT
iajs-4071	162	25	)	)	PUNCT
iajs-4071	162	26	̃	̃	NOUN
iajs-4071	162	27	̃	̃	NOUN
iajs-4071	162	28	the	the	DET
iajs-4071	162	29	following	follow	VERB
iajs-4071	162	30	diagram	diagram	NOUN
iajs-4071	162	31	shows	show	VERB
iajs-4071	162	32	the	the	DET
iajs-4071	162	33	relations	relation	NOUN
iajs-4071	162	34	between	between	ADP
iajs-4071	162	35	̃	̃	PROPN
iajs-4071	162	36	(	(	PUNCT
iajs-4071	162	37	̃	̃	NOUN
iajs-4071	162	38	)	)	PUNCT
iajs-4071	162	39	̃	̃	PROPN
iajs-4071	162	40	(	(	PUNCT
iajs-4071	162	41	̃	̃	NOUN
iajs-4071	162	42	)	)	PUNCT
iajs-4071	162	43	̃	̃	PROPN
iajs-4071	162	44	(	(	PUNCT
iajs-4071	162	45	̃	̃	NOUN
iajs-4071	162	46	)	)	PUNCT
iajs-4071	162	47	̃	̃	PROPN
iajs-4071	162	48	(	(	PUNCT
iajs-4071	162	49	̃	̃	PROPN
iajs-4071	162	50	)	)	PUNCT
iajs-4071	162	51	,	,	PUNCT
iajs-4071	162	52	̃	̃	PROPN
iajs-4071	162	53	(	(	PUNCT
iajs-4071	162	54	̃	̃	NOUN
iajs-4071	162	55	)	)	PUNCT
iajs-4071	162	56	̃	̃	NOUN
iajs-4071	162	57	̃	̃	NOUN
iajs-4071	162	58	)	)	PUNCT
iajs-4071	163	1	̃	̃	PROPN
iajs-4071	163	2	(	(	PUNCT
iajs-4071	163	3	̃	̃	NOUN
iajs-4071	163	4	)	)	PUNCT
iajs-4071	163	5	̃	̃	PROPN
iajs-4071	163	6	(	(	PUNCT
iajs-4071	163	7	̃	̃	NOUN
iajs-4071	163	8	)	)	PUNCT
iajs-4071	163	9	̃	̃	PROPN
iajs-4071	163	10	(	(	PUNCT
iajs-4071	163	11	̃	̃	NOUN
iajs-4071	163	12	)	)	PUNCT
iajs-4071	163	13	̃	̃	NOUN
iajs-4071	163	14	̃	̃	NOUN
iajs-4071	163	15	)	)	PUNCT
iajs-4071	163	16	̃	̃	PROPN
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iajs-4071	164	10	̃	̃	NOUN
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iajs-4071	165	1	̃	̃	ADV
iajs-4071	165	2	̃	̃	PROPN
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iajs-4071	165	4	̃	̃	NOUN
iajs-4071	165	5	)	)	PUNCT
iajs-4071	165	6	)	)	PUNCT
iajs-4071	166	1	̃	̃	NOUN
iajs-4071	166	2	̃	̃	PROPN
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iajs-4071	166	4	̃	̃	PROPN
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iajs-4071	166	8	)	)	PUNCT
iajs-4071	167	1	̃	̃	NOUN
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iajs-4071	167	3	(	(	PUNCT
iajs-4071	167	4	̃	̃	NOUN
iajs-4071	167	5	)	)	PUNCT
iajs-4071	167	6	)	)	PUNCT
iajs-4071	168	1	̃	̃	NOUN
iajs-4071	168	2	̃	̃	PROPN
iajs-4071	168	3	(	(	PUNCT
iajs-4071	168	4	̃	̃	NOUN
iajs-4071	168	5	)	)	PUNCT
iajs-4071	168	6	.	.	PUNCT
iajs-4071	169	1	3	3	X
iajs-4071	169	2	.	.	X
iajs-4071	169	3	)	)	PUNCT
iajs-4071	170	1	̃	̃	NOUN
iajs-4071	170	2	̃	̃	PROPN
iajs-4071	170	3	(	(	PUNCT
iajs-4071	170	4	̃	̃	NOUN
iajs-4071	170	5	)	)	PUNCT
iajs-4071	170	6	)	)	PUNCT
iajs-4071	171	1	̃	̃	NOUN
iajs-4071	171	2	̃	̃	PROPN
iajs-4071	171	3	(	(	PUNCT
iajs-4071	171	4	̃	̃	PROPN
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iajs-4071	171	6	4	4	NUM
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iajs-4071	171	8	)	)	PUNCT
iajs-4071	172	1	̃	̃	ADV
iajs-4071	172	2	̃	̃	PROPN
iajs-4071	172	3	(	(	PUNCT
iajs-4071	172	4	̃	̃	NOUN
iajs-4071	172	5	)	)	PUNCT
iajs-4071	172	6	)	)	PUNCT
iajs-4071	173	1	̃	̃	NOUN
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iajs-4071	173	8	)	)	PUNCT
iajs-4071	174	1	̃	̃	ADV
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iajs-4071	174	4	̃	̃	NOUN
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iajs-4071	175	8	)	)	PUNCT
iajs-4071	176	1	̃	̃	ADV
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iajs-4071	177	4	̃	̃	PROPN
iajs-4071	177	5	)	)	PUNCT
iajs-4071	177	6	7	7	NUM
iajs-4071	177	7	.	.	PUNCT
iajs-4071	177	8	)	)	PUNCT
iajs-4071	178	1	̃	̃	ADV
iajs-4071	178	2	̃	̃	PROPN
iajs-4071	178	3	(	(	PUNCT
iajs-4071	178	4	̃	̃	NOUN
iajs-4071	178	5	)	)	PUNCT
iajs-4071	178	6	)	)	PUNCT
iajs-4071	179	1	̃	̃	NOUN
iajs-4071	179	2	̃	̃	PROPN
iajs-4071	179	3	(	(	PUNCT
iajs-4071	179	4	̃	̃	PROPN
iajs-4071	179	5	)	)	PUNCT
iajs-4071	179	6	8	8	NUM
iajs-4071	179	7	.	.	PUNCT
iajs-4071	179	8	)	)	PUNCT
iajs-4071	180	1	̃	̃	ADV
iajs-4071	180	2	̃	̃	PROPN
iajs-4071	180	3	(	(	PUNCT
iajs-4071	180	4	̃	̃	NOUN
iajs-4071	180	5	)	)	PUNCT
iajs-4071	180	6	)	)	PUNCT
iajs-4071	181	1	̃	̃	NOUN
iajs-4071	181	2	̃	̃	PROPN
iajs-4071	181	3	(	(	PUNCT
iajs-4071	181	4	̃	̃	PROPN
iajs-4071	181	5	)	)	PUNCT
iajs-4071	181	6	9	9	NUM
iajs-4071	181	7	.	.	PUNCT
iajs-4071	181	8	)	)	PUNCT
iajs-4071	182	1	̃	̃	ADV
iajs-4071	182	2	̃	̃	PROPN
iajs-4071	182	3	(	(	PUNCT
iajs-4071	182	4	̃	̃	NOUN
iajs-4071	182	5	)	)	PUNCT
iajs-4071	182	6	)	)	PUNCT
iajs-4071	183	1	̃	̃	NOUN
iajs-4071	183	2	̃	̃	PROPN
iajs-4071	183	3	(	(	PUNCT
iajs-4071	183	4	̃	̃	NOUN
iajs-4071	183	5	)	)	PUNCT
iajs-4071	183	6	ihjpas	ihjpa	NOUN
iajs-4071	183	7	.	.	PUNCT
iajs-4071	184	1	2025,38(4	2025,38(4	X
iajs-4071	184	2	)	)	PUNCT
iajs-4071	185	1	368	368	NUM
iajs-4071	185	2	10	10	NUM
iajs-4071	185	3	.	.	PUNCT
iajs-4071	185	4	)	)	PUNCT
iajs-4071	186	1	̃	̃	ADV
iajs-4071	186	2	̃	̃	PROPN
iajs-4071	186	3	(	(	PUNCT
iajs-4071	186	4	̃	̃	NOUN
iajs-4071	186	5	)	)	PUNCT
iajs-4071	186	6	)	)	PUNCT
iajs-4071	187	1	̃	̃	NOUN
iajs-4071	187	2	̃	̃	PROPN
iajs-4071	187	3	(	(	PUNCT
iajs-4071	187	4	̃	̃	PROPN
iajs-4071	187	5	)	)	PUNCT
iajs-4071	187	6	the	the	DET
iajs-4071	187	7	following	follow	VERB
iajs-4071	187	8	example	example	NOUN
iajs-4071	187	9	illustrates	illustrate	VERB
iajs-4071	187	10	above	above	ADP
iajs-4071	187	11	proposition	proposition	NOUN
iajs-4071	187	12	.	.	PUNCT
iajs-4071	188	1	example	example	NOUN
iajs-4071	188	2	consider	consider	VERB
iajs-4071	188	3	the	the	DET
iajs-4071	188	4	sts	st	NOUN
iajs-4071	188	5	(	(	PUNCT
iajs-4071	188	6	̃	̃	NOUN
iajs-4071	188	7	̃	̃	PROPN
iajs-4071	188	8	)	)	PUNCT
iajs-4071	188	9	in	in	ADP
iajs-4071	188	10	example	example	NOUN
iajs-4071	188	11	,	,	PUNCT
iajs-4071	188	12	let	let	VERB
iajs-4071	188	13	(	(	PUNCT
iajs-4071	188	14	)	)	PUNCT
iajs-4071	189	1	̃	̃	ADV
iajs-4071	189	2	̃	̃	PROPN
iajs-4071	189	3	(	(	PUNCT
iajs-4071	189	4	̃	̃	NOUN
iajs-4071	189	5	̃	̃	ADJ
iajs-4071	189	6	)	)	PUNCT
iajs-4071	189	7	̃	̃	PROPN
iajs-4071	189	8	(	(	PUNCT
iajs-4071	189	9	̃	̃	NOUN
iajs-4071	189	10	̃	̃	ADJ
iajs-4071	189	11	)	)	PUNCT
iajs-4071	189	12	̃	̃	PROPN
iajs-4071	189	13	(	(	PUNCT
iajs-4071	189	14	̃	̃	NOUN
iajs-4071	189	15	̃	̃	ADJ
iajs-4071	189	16	)	)	PUNCT
iajs-4071	189	17	̃	̃	PROPN
iajs-4071	189	18	(	(	PUNCT
iajs-4071	189	19	̃	̃	NOUN
iajs-4071	189	20	̃	̃	ADJ
iajs-4071	189	21	)	)	PUNCT
iajs-4071	189	22	̃	̃	PROPN
iajs-4071	189	23	(	(	PUNCT
iajs-4071	189	24	̃	̃	NOUN
iajs-4071	189	25	̃	̃	NOUN
iajs-4071	189	26	)	)	PUNCT
iajs-4071	189	27	(	(	PUNCT
iajs-4071	189	28	)	)	PUNCT
iajs-4071	189	29	̃	̃	ADV
iajs-4071	189	30	̃	̃	PROPN
iajs-4071	189	31	(	(	PUNCT
iajs-4071	189	32	̃	̃	NOUN
iajs-4071	189	33	̃	̃	PROPN
iajs-4071	189	34	)	)	PUNCT
iajs-4071	189	35	,	,	PUNCT
iajs-4071	189	36	but	but	CCONJ
iajs-4071	189	37	(	(	PUNCT
iajs-4071	189	38	)	)	PUNCT
iajs-4071	189	39	̃	̃	NOUN
iajs-4071	189	40	̃	̃	PROPN
iajs-4071	189	41	(	(	PUNCT
iajs-4071	189	42	̃	̃	NOUN
iajs-4071	189	43	̃	̃	ADJ
iajs-4071	189	44	)	)	PUNCT
iajs-4071	189	45	,	,	PUNCT
iajs-4071	189	46	̃	̃	PROPN
iajs-4071	189	47	(	(	PUNCT
iajs-4071	189	48	̃	̃	NOUN
iajs-4071	189	49	̃	̃	ADJ
iajs-4071	189	50	)	)	PUNCT
iajs-4071	190	1	̃	̃	PROPN
iajs-4071	190	2	(	(	PUNCT
iajs-4071	190	3	̃	̃	NOUN
iajs-4071	190	4	̃	̃	PROPN
iajs-4071	190	5	)	)	PUNCT
iajs-4071	190	6	and	and	CCONJ
iajs-4071	190	7	̃	̃	PROPN
iajs-4071	190	8	(	(	PUNCT
iajs-4071	190	9	̃	̃	NOUN
iajs-4071	190	10	̃	̃	NOUN
iajs-4071	190	11	)	)	PUNCT
iajs-4071	190	12	.	.	PUNCT
iajs-4071	191	1	3.4.proposition	3.4.proposition	NUM
iajs-4071	191	2	if	if	SCONJ
iajs-4071	191	3	a	a	DET
iajs-4071	191	4	space	space	NOUN
iajs-4071	191	5	̃	̃	NOUN
iajs-4071	191	6	̃	̃	PROPN
iajs-4071	191	7	)	)	PUNCT
iajs-4071	191	8	is	be	AUX
iajs-4071	191	9	a	a	DET
iajs-4071	191	10	soft	soft	ADJ
iajs-4071	191	11	t1	t1	NOUN
iajs-4071	191	12	-	-	PUNCT
iajs-4071	191	13	space	space	NOUN
iajs-4071	191	14	,	,	PUNCT
iajs-4071	191	15	subsequently	subsequently	ADV
iajs-4071	191	16	̃	̃	PROPN
iajs-4071	191	17	(	(	PUNCT
iajs-4071	191	18	̃	̃	NOUN
iajs-4071	191	19	)	)	PUNCT
iajs-4071	191	20	̃	̃	NOUN
iajs-4071	191	21	̃	̃	NOUN
iajs-4071	191	22	)	)	PUNCT
iajs-4071	191	23	̃	̃	PROPN
iajs-4071	191	24	̃	̃	NOUN
iajs-4071	191	25	)	)	PUNCT
iajs-4071	191	26	proof	proof	NOUN
iajs-4071	191	27	:	:	PUNCT
iajs-4071	191	28	)	)	PUNCT
iajs-4071	191	29	̃	̃	PROPN
iajs-4071	191	30	̃	̃	NOUN
iajs-4071	191	31	̃	̃	NOUN
iajs-4071	191	32	)	)	PUNCT
iajs-4071	191	33	if	if	SCONJ
iajs-4071	191	34	)	)	PUNCT
iajs-4071	191	35	̃	̃	ADV
iajs-4071	191	36	then	then	ADV
iajs-4071	191	37	)	)	PUNCT
iajs-4071	191	38	̃	̃	PROPN
iajs-4071	191	39	̃	̃	PROPN
iajs-4071	191	40	̃	̃	NOUN
iajs-4071	191	41	)	)	PUNCT
iajs-4071	192	1	if	if	SCONJ
iajs-4071	192	2	(	(	PUNCT
iajs-4071	192	3	)	)	PUNCT
iajs-4071	192	4	̃	̃	PROPN
iajs-4071	192	5	,	,	PUNCT
iajs-4071	192	6	then	then	ADV
iajs-4071	192	7	for	for	ADP
iajs-4071	192	8	each	each	DET
iajs-4071	192	9	̃	̃	PROPN
iajs-4071	192	10	)	)	PUNCT
iajs-4071	193	1	̃	̃	NOUN
iajs-4071	193	2	̃	̃	NOUN
iajs-4071	193	3	.	.	PUNCT
iajs-4071	194	1	hence	hence	ADV
iajs-4071	194	2	,	,	PUNCT
iajs-4071	194	3	̃	̃	PROPN
iajs-4071	194	4	̃	̃	PROPN
iajs-4071	194	5	)	)	PUNCT
iajs-4071	194	6	therefore	therefore	ADV
iajs-4071	194	7	,	,	PUNCT
iajs-4071	194	8	)	)	PUNCT
iajs-4071	195	1	̃	̃	SYM
iajs-4071	195	2	̃	̃	PROPN
iajs-4071	195	3	(	(	PUNCT
iajs-4071	195	4	̃	̃	NOUN
iajs-4071	195	5	)	)	PUNCT
iajs-4071	195	6	since	since	SCONJ
iajs-4071	195	7	̃	̃	NOUN
iajs-4071	195	8	̃	̃	NOUN
iajs-4071	195	9	̃	̃	PROPN
iajs-4071	195	10	(	(	PUNCT
iajs-4071	195	11	̃)then	̃)then	PROPN
iajs-4071	195	12	)	)	PUNCT
iajs-4071	195	13	̃	̃	PROPN
iajs-4071	195	14	̃	̃	PROPN
iajs-4071	195	15	(	(	PUNCT
iajs-4071	195	16	̃	̃	NOUN
iajs-4071	195	17	)	)	PUNCT
iajs-4071	195	18	hence	hence	ADV
iajs-4071	195	19	̃	̃	PROPN
iajs-4071	195	20	̃	̃	ADJ
iajs-4071	195	21	)	)	PUNCT
iajs-4071	195	22	̃	̃	PROPN
iajs-4071	195	23	̃	̃	ADP
iajs-4071	195	24	̃	̃	NOUN
iajs-4071	195	25	)	)	PUNCT
iajs-4071	195	26	̃	̃	PROPN
iajs-4071	195	27	̃	̃	NOUN
iajs-4071	195	28	̃	̃	NOUN
iajs-4071	195	29	)	)	PUNCT
iajs-4071	195	30	but	but	CCONJ
iajs-4071	195	31	̃	̃	PROPN
iajs-4071	195	32	̃	̃	ADJ
iajs-4071	195	33	)	)	PUNCT
iajs-4071	195	34	̃	̃	PROPN
iajs-4071	195	35	̃	̃	NOUN
iajs-4071	195	36	̃	̃	NOUN
iajs-4071	195	37	)	)	PUNCT
iajs-4071	195	38	and	and	CCONJ
iajs-4071	195	39	̃	̃	PROPN
iajs-4071	195	40	̃	̃	ADJ
iajs-4071	195	41	)	)	PUNCT
iajs-4071	195	42	̃	̃	PROPN
iajs-4071	195	43	̃	̃	PROPN
iajs-4071	195	44	̃	̃	NOUN
iajs-4071	195	45	)	)	PUNCT
iajs-4071	195	46	generally	generally	ADV
iajs-4071	195	47	,	,	PUNCT
iajs-4071	195	48	therefore	therefore	ADV
iajs-4071	195	49	̃	̃	PROPN
iajs-4071	195	50	(	(	PUNCT
iajs-4071	195	51	̃	̃	NOUN
iajs-4071	195	52	)	)	PUNCT
iajs-4071	195	53	̃	̃	NOUN
iajs-4071	195	54	̃	̃	NOUN
iajs-4071	195	55	)	)	PUNCT
iajs-4071	195	56	̃	̃	PROPN
iajs-4071	195	57	̃	̃	NOUN
iajs-4071	195	58	)	)	PUNCT
iajs-4071	195	59	corollary	corollary	NOUN
iajs-4071	195	60	if	if	SCONJ
iajs-4071	195	61	(	(	PUNCT
iajs-4071	195	62	̃	̃	NOUN
iajs-4071	195	63	̃	̃	NOUN
iajs-4071	195	64	)	)	PUNCT
iajs-4071	195	65	is	be	AUX
iajs-4071	195	66	soft	soft	ADJ
iajs-4071	195	67	t1	t1	NOUN
iajs-4071	195	68	-	-	PUNCT
iajs-4071	195	69	space	space	NOUN
iajs-4071	195	70	,	,	PUNCT
iajs-4071	195	71	then	then	ADV
iajs-4071	195	72	̃	̃	PROPN
iajs-4071	195	73	̃	̃	NOUN
iajs-4071	195	74	̃	̃	PROPN
iajs-4071	195	75	(	(	PUNCT
iajs-4071	195	76	̃	̃	NOUN
iajs-4071	195	77	)	)	PUNCT
iajs-4071	195	78	̃	̃	PROPN
iajs-4071	195	79	(	(	PUNCT
iajs-4071	195	80	̃	̃	NOUN
iajs-4071	195	81	)	)	PUNCT
iajs-4071	195	82	̃	̃	NOUN
iajs-4071	195	83	̃	̃	PROPN
iajs-4071	195	84	(	(	PUNCT
iajs-4071	195	85	̃	̃	NOUN
iajs-4071	195	86	)	)	PUNCT
iajs-4071	195	87	the	the	DET
iajs-4071	195	88	following	follow	VERB
iajs-4071	195	89	findings	finding	NOUN
iajs-4071	195	90	demonstrate	demonstrate	VERB
iajs-4071	195	91	that	that	SCONJ
iajs-4071	195	92	any	any	DET
iajs-4071	195	93	union	union	NOUN
iajs-4071	195	94	of	of	ADP
iajs-4071	195	95	̃	̃	PROPN
iajs-4071	195	96	-open	-open	ADJ
iajs-4071	195	97	sets	set	NOUN
iajs-4071	195	98	of	of	ADP
iajs-4071	195	99	(	(	PUNCT
iajs-4071	195	100	̃	̃	NOUN
iajs-4071	195	101	̃	̃	PROPN
iajs-4071	195	102	)	)	PUNCT
iajs-4071	195	103	is	be	AUX
iajs-4071	195	104	̃	̃	PROPN
iajs-4071	195	105	.	.	PUNCT
iajs-4071	196	1	3.5	3.5	NUM
iajs-4071	196	2	.	.	PUNCT
iajs-4071	197	1	proposition	proposition	NOUN
iajs-4071	197	2	arbitrary	arbitrary	ADJ
iajs-4071	197	3	soft	soft	ADJ
iajs-4071	197	4	union	union	NOUN
iajs-4071	197	5	of	of	ADP
iajs-4071	197	6	soft	soft	ADJ
iajs-4071	197	7	-open	-open	ADJ
iajs-4071	197	8	sets	set	NOUN
iajs-4071	197	9	in	in	ADP
iajs-4071	197	10	a	a	DET
iajs-4071	197	11	sts	st	NOUN
iajs-4071	197	12	(	(	PUNCT
iajs-4071	197	13	̃	̃	NOUN
iajs-4071	197	14	̃	̃	PROPN
iajs-4071	197	15	)	)	PUNCT
iajs-4071	197	16	is	be	AUX
iajs-4071	197	17	a	a	DET
iajs-4071	197	18	soft	soft	ADJ
iajs-4071	197	19	-open	-open	ADJ
iajs-4071	197	20	set	set	NOUN
iajs-4071	197	21	.	.	PUNCT
iajs-4071	198	1	proof	proof	NOUN
iajs-4071	198	2	:	:	PUNCT
iajs-4071	198	3	let	let	VERB
iajs-4071	198	4	)	)	PUNCT
iajs-4071	198	5	-open	-open	VERB
iajs-4071	198	6	sets	set	NOUN
iajs-4071	198	7	in	in	ADP
iajs-4071	198	8	sts	st	NOUN
iajs-4071	198	9	(	(	PUNCT
iajs-4071	198	10	̃	̃	NOUN
iajs-4071	198	11	̃	̃	PROPN
iajs-4071	198	12	)	)	PUNCT
iajs-4071	198	13	then	then	ADV
iajs-4071	198	14	)	)	PUNCT
iajs-4071	198	15	̃	̃	PROPN
iajs-4071	198	16	̃	̃	PROPN
iajs-4071	198	17	̃	̃	NUM
iajs-4071	198	18	)	)	PUNCT
iajs-4071	198	19	and	and	CCONJ
iajs-4071	198	20	by	by	ADP
iajs-4071	198	21	proposition	proposition	NOUN
iajs-4071	198	22	2.14	2.14	NUM
iajs-4071	198	23	,	,	PUNCT
iajs-4071	198	24	̃	̃	PROPN
iajs-4071	198	25	)	)	PUNCT
iajs-4071	198	26	}	}	PUNCT
iajs-4071	198	27	̃	̃	PROPN
iajs-4071	198	28	̃	̃	NOUN
iajs-4071	198	29	̃	̃	NUM
iajs-4071	198	30	)	)	PUNCT
iajs-4071	198	31	.	.	PUNCT
iajs-4071	199	1	let	let	VERB
iajs-4071	199	2	̃	̃	NOUN
iajs-4071	199	3	̃	̃	PROPN
iajs-4071	199	4	)	)	PUNCT
iajs-4071	199	5	,	,	PUNCT
iajs-4071	199	6	hence	hence	ADV
iajs-4071	199	7	)	)	PUNCT
iajs-4071	199	8	for	for	ADP
iajs-4071	199	9	some	some	DET
iajs-4071	199	10	λ	λ	PROPN
iajs-4071	199	11	λ	λ	PROPN
iajs-4071	199	12	.	.	PUNCT
iajs-4071	200	1	since	since	SCONJ
iajs-4071	200	2	)	)	PUNCT
iajs-4071	200	3	̃	̃	NOUN
iajs-4071	200	4	̃	̃	PROPN
iajs-4071	200	5	(	(	PUNCT
iajs-4071	200	6	̃	̃	NOUN
iajs-4071	200	7	)	)	PUNCT
iajs-4071	200	8	λ	λ	NOUN
iajs-4071	200	9	,	,	PUNCT
iajs-4071	200	10	so	so	SCONJ
iajs-4071	200	11	there	there	PRON
iajs-4071	200	12	is	be	VERB
iajs-4071	200	13	)	)	PUNCT
iajs-4071	200	14	̃	̃	PROPN
iajs-4071	200	15	̃	̃	PROPN
iajs-4071	200	16	(	(	PUNCT
iajs-4071	200	17	̃	̃	PROPN
iajs-4071	200	18	)	)	PUNCT
iajs-4071	200	19	s.t	s.t	PROPN
iajs-4071	200	20	.	.	PUNCT
iajs-4071	200	21	̃	̃	ADV
iajs-4071	200	22	)	)	PUNCT
iajs-4071	201	1	̃	̃	ADJ
iajs-4071	201	2	)	)	PUNCT
iajs-4071	201	3	̃	̃	NOUN
iajs-4071	201	4	̃	̃	NOUN
iajs-4071	201	5	)	)	PUNCT
iajs-4071	201	6	so	so	ADV
iajs-4071	201	7	̃	̃	ADJ
iajs-4071	201	8	)	)	PUNCT
iajs-4071	201	9	̃	̃	NOUN
iajs-4071	201	10	̃	̃	PROPN
iajs-4071	201	11	)	)	PUNCT
iajs-4071	201	12	therefore	therefore	ADV
iajs-4071	201	13	,	,	PUNCT
iajs-4071	201	14	̃	̃	PROPN
iajs-4071	201	15	)	)	PUNCT
iajs-4071	201	16	̃	̃	NOUN
iajs-4071	202	1	̃	̃	NOUN
iajs-4071	202	2	o	o	X
iajs-4071	202	3	(	(	PUNCT
iajs-4071	202	4	̃	̃	PROPN
iajs-4071	202	5	)	)	PUNCT
iajs-4071	202	6	.	.	PUNCT
iajs-4071	203	1	the	the	DET
iajs-4071	203	2	soft	soft	ADJ
iajs-4071	203	3	intersection	intersection	NOUN
iajs-4071	203	4	of	of	ADP
iajs-4071	203	5	two	two	NUM
iajs-4071	203	6	soft	soft	ADJ
iajs-4071	203	7	-open	-open	NOUN
iajs-4071	203	8	sets	set	NOUN
iajs-4071	203	9	need	need	AUX
iajs-4071	203	10	not	not	PART
iajs-4071	203	11	be	be	AUX
iajs-4071	203	12	a	a	DET
iajs-4071	203	13	soft	soft	ADJ
iajs-4071	203	14	-open	-open	ADJ
iajs-4071	203	15	sets	set	NOUN
iajs-4071	203	16	in	in	ADP
iajs-4071	203	17	general	general	ADJ
iajs-4071	203	18	as	as	ADP
iajs-4071	203	19	an	an	DET
iajs-4071	203	20	exam	exam	NOUN
iajs-4071	203	21	:	:	PUNCT
iajs-4071	203	22	example	example	NOUN
iajs-4071	203	23	if	if	SCONJ
iajs-4071	203	24	)	)	PUNCT
iajs-4071	203	25	,	,	PUNCT
iajs-4071	203	26	(	(	PUNCT
iajs-4071	203	27	)	)	PUNCT
iajs-4071	204	1	̃	̃	NOUN
iajs-4071	204	2	̃	̃	NOUN
iajs-4071	204	3	o	o	X
iajs-4071	204	4	(	(	PUNCT
iajs-4071	204	5	̃	̃	PROPN
iajs-4071	204	6	)	)	PUNCT
iajs-4071	204	7	then	then	ADV
iajs-4071	204	8	)	)	PUNCT
iajs-4071	204	9	(	(	PUNCT
iajs-4071	204	10	)	)	PUNCT
iajs-4071	204	11	̃	̃	PROPN
iajs-4071	204	12	(	(	PUNCT
iajs-4071	204	13	̃	̃	NOUN
iajs-4071	204	14	̃	̃	ADV
iajs-4071	204	15	)	)	PUNCT
iajs-4071	204	16	let	let	VERB
iajs-4071	204	17	)	)	PUNCT
iajs-4071	204	18	,	,	PUNCT
iajs-4071	204	19	)	)	PUNCT
iajs-4071	205	1	̃	̃	NOUN
iajs-4071	205	2	̃	̃	ADJ
iajs-4071	205	3	o	o	NOUN
iajs-4071	205	4	(	(	PUNCT
iajs-4071	205	5	̃	̃	NOUN
iajs-4071	205	6	̃	̃	ADJ
iajs-4071	205	7	)	)	PUNCT
iajs-4071	205	8	.	.	PUNCT
iajs-4071	206	1	now	now	ADV
iajs-4071	206	2	we	we	PRON
iajs-4071	206	3	have	have	VERB
iajs-4071	206	4	)	)	PUNCT
iajs-4071	206	5	)	)	PUNCT
iajs-4071	207	1	=	=	PUNCT
iajs-4071	207	2	)	)	PUNCT
iajs-4071	208	1	it	it	PRON
iajs-4071	208	2	is	be	AUX
iajs-4071	208	3	clear	clear	ADJ
iajs-4071	208	4	that	that	SCONJ
iajs-4071	208	5	)	)	PUNCT
iajs-4071	209	1	̃	̃	NOUN
iajs-4071	209	2	̃	̃	NOUN
iajs-4071	209	3	o	o	NOUN
iajs-4071	209	4	(	(	PUNCT
iajs-4071	209	5	̃	̃	NOUN
iajs-4071	209	6	̃	̃	PROPN
iajs-4071	209	7	)	)	PUNCT
iajs-4071	209	8	and	and	CCONJ
iajs-4071	209	9	hence	hence	ADV
iajs-4071	209	10	)	)	PUNCT
iajs-4071	209	11	)	)	PUNCT
iajs-4071	210	1	̃	̃	NOUN
iajs-4071	210	2	̃	̃	NOUN
iajs-4071	210	3	o	o	NOUN
iajs-4071	210	4	(	(	PUNCT
iajs-4071	210	5	̃	̃	NOUN
iajs-4071	210	6	̃	̃	NOUN
iajs-4071	210	7	)	)	PUNCT
iajs-4071	210	8	3.6	3.6	NUM
iajs-4071	210	9	.	.	PUNCT
iajs-4071	211	1	proposition	proposition	NOUN
iajs-4071	211	2	if	if	SCONJ
iajs-4071	211	3	̃	̃	ADJ
iajs-4071	211	4	o	o	NOUN
iajs-4071	211	5	̃)is	̃)is	DET
iajs-4071	211	6	a	a	DET
iajs-4071	211	7	soft	soft	ADJ
iajs-4071	211	8	topology	topology	NOUN
iajs-4071	211	9	on	on	ADP
iajs-4071	211	10	̃	̃	PROPN
iajs-4071	211	11	,	,	PUNCT
iajs-4071	211	12	then	then	ADV
iajs-4071	211	13	̃	̃	PROPN
iajs-4071	211	14	o	o	X
iajs-4071	211	15	̃	̃	PROPN
iajs-4071	211	16	)	)	PUNCT
iajs-4071	211	17	is	be	AUX
iajs-4071	211	18	also	also	ADV
iajs-4071	211	19	a	a	DET
iajs-4071	211	20	soft	soft	ADJ
iajs-4071	211	21	topology	topology	NOUN
iajs-4071	211	22	on	on	ADP
iajs-4071	211	23	̃.	̃.	ADJ
iajs-4071	211	24	proof	proof	NOUN
iajs-4071	211	25	:	:	PUNCT
iajs-4071	211	26	this	this	PRON
iajs-4071	211	27	is	be	AUX
iajs-4071	211	28	sufficient	sufficient	ADJ
iajs-4071	211	29	evidence	evidence	NOUN
iajs-4071	211	30	to	to	PART
iajs-4071	211	31	demonstrate	demonstrate	VERB
iajs-4071	211	32	whether	whether	SCONJ
iajs-4071	211	33	the	the	DET
iajs-4071	211	34	intersection	intersection	NOUN
iajs-4071	211	35	of	of	ADP
iajs-4071	211	36	two	two	NUM
iajs-4071	211	37	̃	̃	PROPN
iajs-4071	211	38	open	open	ADJ
iajs-4071	211	39	subsets	subset	NOUN
iajs-4071	211	40	is	be	AUX
iajs-4071	211	41	̃	̃	ADV
iajs-4071	211	42	open	open	ADJ
iajs-4071	211	43	.	.	PUNCT
iajs-4071	212	1	suppose	suppose	VERB
iajs-4071	212	2	)	)	PUNCT
iajs-4071	212	3	,	,	PUNCT
iajs-4071	212	4	(	(	PUNCT
iajs-4071	212	5	)	)	PUNCT
iajs-4071	212	6	̃	̃	NOUN
iajs-4071	212	7	̃	̃	PROPN
iajs-4071	212	8	o	o	X
iajs-4071	212	9	̃	̃	PROPN
iajs-4071	212	10	)	)	PUNCT
iajs-4071	212	11	,	,	PUNCT
iajs-4071	212	12	then	then	ADV
iajs-4071	212	13	)	)	PUNCT
iajs-4071	212	14	,	,	PUNCT
iajs-4071	212	15	)	)	PUNCT
iajs-4071	213	1	̃	̃	SYM
iajs-4071	213	2	̃	̃	ADJ
iajs-4071	213	3	o	o	X
iajs-4071	213	4	̃	̃	PROPN
iajs-4071	213	5	)	)	PUNCT
iajs-4071	213	6	.	.	PUNCT
iajs-4071	214	1	since	since	SCONJ
iajs-4071	214	2	̃	̃	PROPN
iajs-4071	214	3	̃	̃	PROPN
iajs-4071	214	4	)	)	PUNCT
iajs-4071	214	5	is	be	AUX
iajs-4071	214	6	a	a	DET
iajs-4071	214	7	soft	soft	ADJ
iajs-4071	214	8	topology	topology	NOUN
iajs-4071	214	9	on	on	ADP
iajs-4071	214	10	̃	̃	PROPN
iajs-4071	214	11	,	,	PUNCT
iajs-4071	214	12	so	so	ADV
iajs-4071	214	13	)	)	PUNCT
iajs-4071	214	14	)	)	PUNCT
iajs-4071	215	1	̃	̃	NOUN
iajs-4071	215	2	̃	̃	ADJ
iajs-4071	215	3	o	o	X
iajs-4071	215	4	̃	̃	PROPN
iajs-4071	215	5	)	)	PUNCT
iajs-4071	215	6	.	.	PUNCT
iajs-4071	216	1	let	let	VERB
iajs-4071	216	2	̃	̃	ADV
iajs-4071	216	3	)	)	PUNCT
iajs-4071	216	4	)	)	PUNCT
iajs-4071	217	1	then	then	ADV
iajs-4071	217	2	̃	̃	PROPN
iajs-4071	217	3	)	)	PUNCT
iajs-4071	217	4	and	and	CCONJ
iajs-4071	217	5	̃	̃	PROPN
iajs-4071	217	6	)	)	PUNCT
iajs-4071	218	1	so	so	ADV
iajs-4071	218	2	there	there	PRON
iajs-4071	218	3	exist	exist	VERB
iajs-4071	218	4	)	)	PUNCT
iajs-4071	218	5	)	)	PUNCT
iajs-4071	219	1	̃	̃	PROPN
iajs-4071	219	2	̃	̃	NOUN
iajs-4071	219	3	̃	̃	NUM
iajs-4071	219	4	)	)	PUNCT
iajs-4071	219	5	.	.	PUNCT
iajs-4071	220	1	s.t	s.t	PROPN
iajs-4071	220	2	.	.	PUNCT
iajs-4071	220	3	̃	̃	ADV
iajs-4071	220	4	)	)	PUNCT
iajs-4071	220	5	̃	̃	PROPN
iajs-4071	220	6	)	)	PUNCT
iajs-4071	220	7	nd	nd	NUM
iajs-4071	220	8	̃	̃	ADV
iajs-4071	220	9	)	)	PUNCT
iajs-4071	220	10	̃	̃	PROPN
iajs-4071	220	11	)	)	PUNCT
iajs-4071	220	12	which	which	PRON
iajs-4071	220	13	implies	imply	VERB
iajs-4071	220	14	that	that	SCONJ
iajs-4071	220	15	̃	̃	NOUN
iajs-4071	220	16	)	)	PUNCT
iajs-4071	220	17	)	)	PUNCT
iajs-4071	221	1	̃	̃	ADV
iajs-4071	221	2	)	)	PUNCT
iajs-4071	221	3	)	)	PUNCT
iajs-4071	221	4	then	then	ADV
iajs-4071	221	5	)	)	PUNCT
iajs-4071	221	6	)	)	PUNCT
iajs-4071	222	1	̃	̃	NOUN
iajs-4071	222	2	̃	̃	NOUN
iajs-4071	222	3	̃	̃	NOUN
iajs-4071	222	4	)	)	PUNCT
iajs-4071	222	5	.	.	PUNCT
iajs-4071	223	1	thus	thus	ADV
iajs-4071	223	2	,	,	PUNCT
iajs-4071	223	3	)	)	PUNCT
iajs-4071	223	4	)	)	PUNCT
iajs-4071	224	1	̃	̃	NOUN
iajs-4071	224	2	̃	̃	NOUN
iajs-4071	224	3	̃	̃	NOUN
iajs-4071	224	4	)	)	PUNCT
iajs-4071	224	5	.	.	PUNCT
iajs-4071	225	1	3.7	3.7	NUM
iajs-4071	225	2	.	.	PUNCT
iajs-4071	225	3	proposition	proposition	VERB
iajs-4071	225	4	a	a	DET
iajs-4071	225	5	sts	st	NOUN
iajs-4071	225	6	(	(	PUNCT
iajs-4071	225	7	̃	̃	NOUN
iajs-4071	225	8	̃	̃	PROPN
iajs-4071	225	9	)	)	PUNCT
iajs-4071	225	10	is	be	AUX
iajs-4071	225	11	seds	sed	NOUN
iajs-4071	225	12	if	if	SCONJ
iajs-4071	225	13	̃	̃	PROPN
iajs-4071	225	14	(	(	PUNCT
iajs-4071	225	15	̃	̃	NOUN
iajs-4071	225	16	)	)	PUNCT
iajs-4071	225	17	̃	̃	PROPN
iajs-4071	225	18	(	(	PUNCT
iajs-4071	225	19	̃	̃	NOUN
iajs-4071	225	20	)	)	PUNCT
iajs-4071	225	21	.	.	PUNCT
iajs-4071	226	1	proof	proof	NOUN
iajs-4071	226	2	:	:	PUNCT
iajs-4071	226	3	by	by	ADP
iajs-4071	226	4	remark	remark	NOUN
iajs-4071	226	5	3.4(1	3.4(1	NUM
iajs-4071	226	6	)	)	PUNCT
iajs-4071	226	7	and	and	CCONJ
iajs-4071	226	8	proposition	proposition	VERB
iajs-4071	226	9	2.18(1),the	2.18(1),the	PRON
iajs-4071	226	10	prove	prove	VERB
iajs-4071	226	11	only	only	ADV
iajs-4071	226	12	if	if	SCONJ
iajs-4071	226	13	part	part	NOUN
iajs-4071	226	14	will	will	AUX
iajs-4071	226	15	follow	follow	VERB
iajs-4071	226	16	.	.	PUNCT
iajs-4071	227	1	conversely	conversely	ADV
iajs-4071	227	2	,	,	PUNCT
iajs-4071	227	3	let	let	VERB
iajs-4071	227	4	)	)	PUNCT
iajs-4071	228	1	̃	̃	ADV
iajs-4071	228	2	̃.	̃.	NOUN
iajs-4071	228	3	then	then	ADV
iajs-4071	228	4	,	,	PUNCT
iajs-4071	228	5	̃	̃	PROPN
iajs-4071	228	6	)	)	PUNCT
iajs-4071	228	7	̃	̃	PROPN
iajs-4071	228	8	(	(	PUNCT
iajs-4071	228	9	̃	̃	NOUN
iajs-4071	228	10	)	)	PUNCT
iajs-4071	228	11	)	)	PUNCT
iajs-4071	228	12	.	.	PUNCT
iajs-4071	229	1	that	that	PRON
iajs-4071	229	2	is	be	AUX
iajs-4071	229	3	,	,	PUNCT
iajs-4071	229	4	̃	̃	ADJ
iajs-4071	229	5	)	)	PUNCT
iajs-4071	230	1	̃	̃	NOUN
iajs-4071	230	2	̃	̃	PROPN
iajs-4071	230	3	(	(	PUNCT
iajs-4071	230	4	̃	̃	NOUN
iajs-4071	230	5	)	)	PUNCT
iajs-4071	230	6	,	,	PUNCT
iajs-4071	230	7	so	so	ADV
iajs-4071	230	8	by	by	ADP
iajs-4071	230	9	proposition	proposition	NOUN
iajs-4071	230	10	3.6(6	3.6(6	NUM
iajs-4071	230	11	)	)	PUNCT
iajs-4071	230	12	,	,	PUNCT
iajs-4071	230	13	̃	̃	PROPN
iajs-4071	230	14	)	)	PUNCT
iajs-4071	231	1	̃	̃	NOUN
iajs-4071	231	2	̃	̃	PROPN
iajs-4071	231	3	(	(	PUNCT
iajs-4071	231	4	̃	̃	NOUN
iajs-4071	231	5	)	)	PUNCT
iajs-4071	231	6	.	.	PUNCT
iajs-4071	232	1	by	by	ADP
iajs-4071	232	2	hypothesis	hypothesis	NOUN
iajs-4071	232	3	,	,	PUNCT
iajs-4071	232	4	̃	̃	PROPN
iajs-4071	232	5	)	)	PUNCT
iajs-4071	232	6	̃	̃	NOUN
iajs-4071	232	7	̃	̃	PROPN
iajs-4071	232	8	(	(	PUNCT
iajs-4071	232	9	̃	̃	NOUN
iajs-4071	232	10	)	)	PUNCT
iajs-4071	232	11	.	.	PUNCT
iajs-4071	233	1	that	that	PRON
iajs-4071	233	2	is	be	AUX
iajs-4071	233	3	,	,	PUNCT
iajs-4071	233	4	ihjpas	ihjpas	PROPN
iajs-4071	233	5	.	.	PUNCT
iajs-4071	234	1	2025,38(4	2025,38(4	X
iajs-4071	234	2	)	)	PUNCT
iajs-4071	235	1	369	369	NUM
iajs-4071	235	2	̃	̃	PROPN
iajs-4071	235	3	)	)	PUNCT
iajs-4071	236	1	̃	̃	NOUN
iajs-4071	236	2	̃	̃	PROPN
iajs-4071	236	3	(	(	PUNCT
iajs-4071	236	4	̃	̃	PROPN
iajs-4071	236	5	(	(	PUNCT
iajs-4071	236	6	̃	̃	PROPN
iajs-4071	236	7	)	)	PUNCT
iajs-4071	236	8	)	)	PUNCT
iajs-4071	236	9	)	)	PUNCT
iajs-4071	237	1	then	then	ADV
iajs-4071	237	2	̃	̃	X
iajs-4071	237	3	)	)	PUNCT
iajs-4071	237	4	̃	̃	SYM
iajs-4071	237	5	̃	̃	NOUN
iajs-4071	237	6	̃	̃	NOUN
iajs-4071	237	7	)	)	PUNCT
iajs-4071	237	8	)	)	PUNCT
iajs-4071	237	9	,	,	PUNCT
iajs-4071	237	10	but	but	CCONJ
iajs-4071	237	11	̃	̃	PROPN
iajs-4071	237	12	̃	̃	NOUN
iajs-4071	237	13	)	)	PUNCT
iajs-4071	237	14	)	)	PUNCT
iajs-4071	238	1	̃	̃	NOUN
iajs-4071	238	2	̃	̃	NOUN
iajs-4071	238	3	)	)	PUNCT
iajs-4071	238	4	.	.	PUNCT
iajs-4071	239	1	hence	hence	ADV
iajs-4071	239	2	,	,	PUNCT
iajs-4071	239	3	̃	̃	PROPN
iajs-4071	239	4	)	)	PUNCT
iajs-4071	239	5	̃	̃	NOUN
iajs-4071	239	6	̃	̃	NOUN
iajs-4071	239	7	)	)	PUNCT
iajs-4071	239	8	)	)	PUNCT
iajs-4071	239	9	.	.	PUNCT
iajs-4071	240	1	this	this	PRON
iajs-4071	240	2	means	mean	VERB
iajs-4071	240	3	that	that	SCONJ
iajs-4071	240	4	,	,	PUNCT
iajs-4071	240	5	̃	̃	ADJ
iajs-4071	240	6	)	)	PUNCT
iajs-4071	240	7	̃	̃	PROPN
iajs-4071	240	8	̃.	̃.	NOUN
iajs-4071	240	9	thus	thus	ADV
iajs-4071	240	10	,	,	PUNCT
iajs-4071	240	11	̃	̃	PROPN
iajs-4071	240	12	̃	̃	PROPN
iajs-4071	240	13	)	)	PUNCT
iajs-4071	240	14	is	be	AUX
iajs-4071	240	15	a	a	DET
iajs-4071	240	16	seds	sed	NOUN
iajs-4071	240	17	.	.	PUNCT
iajs-4071	241	1	3.8	3.8	NUM
iajs-4071	241	2	.	.	PUNCT
iajs-4071	241	3	proposition	proposition	VERB
iajs-4071	241	4	a	a	DET
iajs-4071	241	5	̃	̃	NOUN
iajs-4071	241	6	̃	̃	PROPN
iajs-4071	241	7	)	)	PUNCT
iajs-4071	241	8	is	be	AUX
iajs-4071	241	9	seds	sed	NOUN
iajs-4071	241	10	iff	iff	PROPN
iajs-4071	241	11	̃	̃	PROPN
iajs-4071	241	12	̃	̃	PROPN
iajs-4071	241	13	)	)	PUNCT
iajs-4071	241	14	̃	̃	PROPN
iajs-4071	241	15	̃	̃	PROPN
iajs-4071	241	16	̃	̃	NOUN
iajs-4071	241	17	)	)	PUNCT
iajs-4071	241	18	.	.	PUNCT
iajs-4071	242	1	3.9	3.9	NUM
iajs-4071	242	2	.	.	PUNCT
iajs-4071	242	3	proposition	proposition	NOUN
iajs-4071	242	4	if	if	SCONJ
iajs-4071	242	5	a	a	DET
iajs-4071	242	6	space	space	NOUN
iajs-4071	242	7	̃	̃	NOUN
iajs-4071	242	8	̃	̃	PROPN
iajs-4071	242	9	)	)	PUNCT
iajs-4071	242	10	is	be	AUX
iajs-4071	242	11	a	a	DET
iajs-4071	242	12	soft	soft	ADJ
iajs-4071	242	13	locally	locally	ADV
iajs-4071	242	14	indiscrete	indiscrete	ADJ
iajs-4071	242	15	space	space	NOUN
iajs-4071	242	16	,	,	PUNCT
iajs-4071	242	17	then	then	ADV
iajs-4071	242	18	̃	̃	PROPN
iajs-4071	242	19	(	(	PUNCT
iajs-4071	242	20	̃	̃	NOUN
iajs-4071	242	21	)	)	PUNCT
iajs-4071	242	22	̃	̃	NOUN
iajs-4071	242	23	̃	̃	NOUN
iajs-4071	242	24	)	)	PUNCT
iajs-4071	242	25	̃	̃	PROPN
iajs-4071	242	26	̃	̃	NOUN
iajs-4071	242	27	)	)	PUNCT
iajs-4071	242	28	corollary	corollary	NOUN
iajs-4071	242	29	let	let	VERB
iajs-4071	242	30	̃	̃	NOUN
iajs-4071	242	31	̃	̃	PROPN
iajs-4071	242	32	)	)	PUNCT
iajs-4071	242	33	is	be	AUX
iajs-4071	242	34	a	a	DET
iajs-4071	242	35	soft	soft	ADJ
iajs-4071	242	36	locally	locally	ADV
iajs-4071	242	37	indiscrete	indiscrete	ADJ
iajs-4071	242	38	space	space	NOUN
iajs-4071	242	39	,	,	PUNCT
iajs-4071	242	40	then	then	ADV
iajs-4071	242	41	.	.	PUNCT
iajs-4071	243	1	1	1	X
iajs-4071	243	2	.	.	X
iajs-4071	243	3	̃	̃	ADV
iajs-4071	243	4	(	(	PUNCT
iajs-4071	243	5	̃	̃	NOUN
iajs-4071	243	6	)	)	PUNCT
iajs-4071	243	7	̃.	̃.	NOUN
iajs-4071	243	8	2	2	NUM
iajs-4071	243	9	.	.	PUNCT
iajs-4071	244	1	̃	̃	PROPN
iajs-4071	244	2	(	(	PUNCT
iajs-4071	244	3	̃	̃	NOUN
iajs-4071	244	4	)	)	PUNCT
iajs-4071	244	5	̃	̃	PROPN
iajs-4071	244	6	(	(	PUNCT
iajs-4071	244	7	̃	̃	PROPN
iajs-4071	244	8	)	)	PUNCT
iajs-4071	244	9	3.10	3.10	NUM
iajs-4071	244	10	.	.	PUNCT
iajs-4071	245	1	proposition	proposition	VERB
iajs-4071	245	2	a	a	DET
iajs-4071	245	3	subset	subset	NOUN
iajs-4071	245	4	)	)	PUNCT
iajs-4071	245	5	of	of	ADP
iajs-4071	245	6	̃	̃	PROPN
iajs-4071	245	7	̃	̃	PROPN
iajs-4071	245	8	)	)	PUNCT
iajs-4071	245	9	is	be	AUX
iajs-4071	245	10	̃	̃	ADV
iajs-4071	245	11	open	open	ADJ
iajs-4071	245	12	iff	iff	NOUN
iajs-4071	245	13	for	for	ADP
iajs-4071	245	14	each	each	DET
iajs-4071	245	15	̃	̃	PROPN
iajs-4071	245	16	)	)	PUNCT
iajs-4071	245	17	,	,	PUNCT
iajs-4071	245	18	)	)	PUNCT
iajs-4071	246	1	̃	̃	SYM
iajs-4071	246	2	̃	̃	PROPN
iajs-4071	246	3	(	(	PUNCT
iajs-4071	246	4	̃	̃	PROPN
iajs-4071	246	5	)	)	PUNCT
iajs-4071	246	6	s.t	s.t	PROPN
iajs-4071	246	7	.	.	PUNCT
iajs-4071	246	8	̃	̃	ADV
iajs-4071	246	9	)	)	PUNCT
iajs-4071	246	10	̃	̃	ADJ
iajs-4071	246	11	)	)	PUNCT
iajs-4071	246	12	proof	proof	NOUN
iajs-4071	246	13	:	:	PUNCT
iajs-4071	246	14	assume	assume	VERB
iajs-4071	246	15	that	that	SCONJ
iajs-4071	246	16	)	)	PUNCT
iajs-4071	247	1	̃	̃	ADV
iajs-4071	247	2	̃	̃	PROPN
iajs-4071	247	3	(	(	PUNCT
iajs-4071	247	4	̃	̃	PROPN
iajs-4071	247	5	)	)	PUNCT
iajs-4071	247	6	.	.	PUNCT
iajs-4071	248	1	then	then	ADV
iajs-4071	248	2	for	for	ADP
iajs-4071	248	3	each	each	DET
iajs-4071	248	4	̃	̃	NOUN
iajs-4071	248	5	)	)	PUNCT
iajs-4071	248	6	)	)	PUNCT
iajs-4071	248	7	)	)	PUNCT
iajs-4071	249	1	̃	̃	ADV
iajs-4071	249	2	̃	̃	PROPN
iajs-4071	249	3	(	(	PUNCT
iajs-4071	249	4	̃	̃	NOUN
iajs-4071	249	5	)	)	PUNCT
iajs-4071	249	6	containing	contain	VERB
iajs-4071	249	7	s.t	s.t	PROPN
iajs-4071	249	8	.	.	PUNCT
iajs-4071	250	1	̃	̃	ADV
iajs-4071	250	2	)	)	PUNCT
iajs-4071	250	3	̃	̃	NOUN
iajs-4071	250	4	)	)	PUNCT
iajs-4071	250	5	.	.	PUNCT
iajs-4071	251	1	conversely	conversely	ADV
iajs-4071	251	2	,	,	PUNCT
iajs-4071	251	3	suppose	suppose	VERB
iajs-4071	251	4	that	that	SCONJ
iajs-4071	251	5	̃	̃	PROPN
iajs-4071	251	6	)	)	PUNCT
iajs-4071	251	7	here	here	ADV
iajs-4071	251	8	exists	exist	VERB
iajs-4071	251	9	)	)	PUNCT
iajs-4071	251	10	̃	̃	SYM
iajs-4071	251	11	̃	̃	PROPN
iajs-4071	251	12	(	(	PUNCT
iajs-4071	251	13	̃	̃	PROPN
iajs-4071	251	14	)	)	PUNCT
iajs-4071	251	15	s.t	s.t	PROPN
iajs-4071	251	16	.	.	PUNCT
iajs-4071	251	17	̃	̃	ADV
iajs-4071	251	18	)	)	PUNCT
iajs-4071	251	19	̃	̃	PROPN
iajs-4071	251	20	)	)	PUNCT
iajs-4071	251	21	thus	thus	ADV
iajs-4071	251	22	)	)	PUNCT
iajs-4071	251	23	̃	̃	ADJ
iajs-4071	251	24	)	)	PUNCT
iajs-4071	251	25	̃	̃	PROPN
iajs-4071	251	26	)	)	PUNCT
iajs-4071	251	27	for	for	ADP
iajs-4071	251	28	each	each	DET
iajs-4071	251	29	̃	̃	PROPN
iajs-4071	251	30	)	)	PUNCT
iajs-4071	251	31	this	this	PRON
iajs-4071	251	32	implies	imply	VERB
iajs-4071	251	33	that	that	PRON
iajs-4071	251	34	)	)	PUNCT
iajs-4071	251	35	)	)	PUNCT
iajs-4071	251	36	therefore	therefore	ADV
iajs-4071	251	37	)	)	PUNCT
iajs-4071	251	38	is	be	AUX
iajs-4071	251	39	̃	̃	PROPN
iajs-4071	251	40	-open	-open	NOUN
iajs-4071	251	41	set	set	NOUN
iajs-4071	251	42	.	.	PUNCT
iajs-4071	252	1	3.11.proposition	3.11.proposition	NOUN
iajs-4071	252	2	if	if	SCONJ
iajs-4071	252	3	̃	̃	NOUN
iajs-4071	252	4	̃	̃	PROPN
iajs-4071	252	5	)	)	PUNCT
iajs-4071	252	6	is	be	AUX
iajs-4071	252	7	soft	soft	ADJ
iajs-4071	252	8	regular	regular	ADJ
iajs-4071	252	9	space	space	NOUN
iajs-4071	252	10	,	,	PUNCT
iajs-4071	252	11	then	then	ADV
iajs-4071	252	12	̃	̃	PROPN
iajs-4071	252	13	̃	̃	PROPN
iajs-4071	252	14	̃	̃	PROPN
iajs-4071	252	15	o	o	X
iajs-4071	252	16	(	(	PUNCT
iajs-4071	252	17	̃	̃	PROPN
iajs-4071	252	18	)	)	PUNCT
iajs-4071	252	19	.	.	PUNCT
iajs-4071	253	1	proof	proof	NOUN
iajs-4071	253	2	:	:	PUNCT
iajs-4071	253	3	let	let	VERB
iajs-4071	253	4	)	)	PUNCT
iajs-4071	253	5	̃	̃	ADV
iajs-4071	253	6	̃	̃	PROPN
iajs-4071	253	7	,	,	PUNCT
iajs-4071	253	8	then	then	ADV
iajs-4071	253	9	)	)	PUNCT
iajs-4071	253	10	̃	̃	PROPN
iajs-4071	253	11	̃	̃	PROPN
iajs-4071	253	12	(	(	PUNCT
iajs-4071	253	13	̃	̃	NOUN
iajs-4071	253	14	)	)	PUNCT
iajs-4071	253	15	.	.	PUNCT
iajs-4071	254	1	since	since	SCONJ
iajs-4071	254	2	̃	̃	PROPN
iajs-4071	254	3	is	be	AUX
iajs-4071	254	4	regular	regular	ADJ
iajs-4071	254	5	,	,	PUNCT
iajs-4071	254	6	then	then	ADV
iajs-4071	254	7	by	by	ADP
iajs-4071	254	8	proposition	proposition	NOUN
iajs-4071	254	9	2.21	2.21	NUM
iajs-4071	254	10	,	,	PUNCT
iajs-4071	254	11	for	for	ADP
iajs-4071	254	12	each	each	DET
iajs-4071	254	13	̃	̃	PROPN
iajs-4071	254	14	)	)	PUNCT
iajs-4071	254	15	,	,	PUNCT
iajs-4071	254	16	)	)	PUNCT
iajs-4071	255	1	̃	̃	PROPN
iajs-4071	255	2	̃	̃	PROPN
iajs-4071	255	3	s.t	s.t	PROPN
iajs-4071	255	4	.	.	PUNCT
iajs-4071	255	5	̃	̃	ADJ
iajs-4071	255	6	)	)	PUNCT
iajs-4071	255	7	̃	̃	NOUN
iajs-4071	255	8	̃	̃	ADJ
iajs-4071	255	9	)	)	PUNCT
iajs-4071	255	10	̃	̃	PROPN
iajs-4071	255	11	)	)	PUNCT
iajs-4071	256	1	so	so	SCONJ
iajs-4071	256	2	that	that	SCONJ
iajs-4071	256	3	,	,	PUNCT
iajs-4071	256	4	̃	̃	PROPN
iajs-4071	256	5	̃	̃	ADJ
iajs-4071	256	6	)	)	PUNCT
iajs-4071	256	7	̃	̃	NOUN
iajs-4071	256	8	)	)	PUNCT
iajs-4071	256	9	.since	.since	PUNCT
iajs-4071	257	1	̃	̃	ADJ
iajs-4071	257	2	)	)	PUNCT
iajs-4071	258	1	̃	̃	PROPN
iajs-4071	258	2	̃	̃	PROPN
iajs-4071	258	3	̃	̃	NUM
iajs-4071	258	4	)	)	PUNCT
iajs-4071	258	5	,	,	PUNCT
iajs-4071	258	6	then	then	ADV
iajs-4071	258	7	(	(	PUNCT
iajs-4071	258	8	)	)	PUNCT
iajs-4071	259	1	̃	̃	ADV
iajs-4071	259	2	̃	̃	PROPN
iajs-4071	259	3	(	(	PUNCT
iajs-4071	259	4	̃	̃	PROPN
iajs-4071	259	5	)	)	PUNCT
iajs-4071	259	6	.	.	PUNCT
iajs-4071	260	1	3.12.proposition	3.12.proposition	PROPN
iajs-4071	260	2	let	let	VERB
iajs-4071	260	3	̃	̃	PROPN
iajs-4071	260	4	̃	̃	PROPN
iajs-4071	260	5	)	)	PUNCT
iajs-4071	260	6	be	be	AUX
iajs-4071	260	7	a	a	DET
iajs-4071	260	8	seds	sed	NOUN
iajs-4071	260	9	.	.	PUNCT
iajs-4071	261	1	if	if	SCONJ
iajs-4071	261	2	)	)	PUNCT
iajs-4071	261	3	̃	̃	NOUN
iajs-4071	261	4	̃	̃	NOUN
iajs-4071	261	5	o	o	X
iajs-4071	261	6	(	(	PUNCT
iajs-4071	261	7	̃	̃	PROPN
iajs-4071	261	8	)	)	PUNCT
iajs-4071	261	9	and	and	CCONJ
iajs-4071	261	10	)	)	PUNCT
iajs-4071	261	11	̃	̃	NOUN
iajs-4071	261	12	̃	̃	ADJ
iajs-4071	261	13	o	o	X
iajs-4071	261	14	(	(	PUNCT
iajs-4071	261	15	̃	̃	PROPN
iajs-4071	261	16	)	)	PUNCT
iajs-4071	261	17	.	.	PUNCT
iajs-4071	262	1	then	then	ADV
iajs-4071	262	2	)	)	PUNCT
iajs-4071	262	3	)	)	PUNCT
iajs-4071	263	1	̃	̃	NOUN
iajs-4071	263	2	̃	̃	PROPN
iajs-4071	263	3	(	(	PUNCT
iajs-4071	263	4	̃	̃	NOUN
iajs-4071	263	5	)	)	PUNCT
iajs-4071	263	6	.	.	PUNCT
iajs-4071	264	1	proof	proof	NOUN
iajs-4071	264	2	:	:	PUNCT
iajs-4071	264	3	let	let	VERB
iajs-4071	264	4	)	)	PUNCT
iajs-4071	265	1	̃	̃	ADV
iajs-4071	265	2	̃	̃	NOUN
iajs-4071	265	3	o	o	X
iajs-4071	265	4	(	(	PUNCT
iajs-4071	265	5	̃	̃	PROPN
iajs-4071	265	6	)	)	PUNCT
iajs-4071	265	7	and	and	CCONJ
iajs-4071	265	8	)	)	PUNCT
iajs-4071	265	9	̃	̃	NOUN
iajs-4071	265	10	̃	̃	ADJ
iajs-4071	265	11	o	o	X
iajs-4071	265	12	(	(	PUNCT
iajs-4071	265	13	̃	̃	PROPN
iajs-4071	265	14	)	)	PUNCT
iajs-4071	265	15	then	then	ADV
iajs-4071	265	16	,	,	PUNCT
iajs-4071	265	17	)	)	PUNCT
iajs-4071	265	18	̃	̃	PROPN
iajs-4071	265	19	̃	̃	ADV
iajs-4071	265	20	then	then	ADV
iajs-4071	265	21	by	by	ADP
iajs-4071	265	22	proposition	proposition	NOUN
iajs-4071	265	23	2.19	2.19	NUM
iajs-4071	265	24	)	)	PUNCT
iajs-4071	265	25	)	)	PUNCT
iajs-4071	266	1	̃	̃	NOUN
iajs-4071	266	2	̃	̃	PROPN
iajs-4071	266	3	(	(	PUNCT
iajs-4071	266	4	̃	̃	NOUN
iajs-4071	266	5	)	)	PUNCT
iajs-4071	266	6	.	.	PUNCT
iajs-4071	267	1	if	if	SCONJ
iajs-4071	267	2	̃	̃	PROPN
iajs-4071	267	3	)	)	PUNCT
iajs-4071	267	4	)	)	PUNCT
iajs-4071	268	1	then	then	ADV
iajs-4071	268	2	,	,	PUNCT
iajs-4071	268	3	since	since	SCONJ
iajs-4071	268	4	)	)	PUNCT
iajs-4071	268	5	̃	̃	NOUN
iajs-4071	268	6	̃	̃	PROPN
iajs-4071	268	7	(	(	PUNCT
iajs-4071	268	8	̃	̃	NOUN
iajs-4071	268	9	)	)	PUNCT
iajs-4071	268	10	,	,	PUNCT
iajs-4071	268	11	)	)	PUNCT
iajs-4071	268	12	̃	̃	SYM
iajs-4071	268	13	̃	̃	PROPN
iajs-4071	268	14	(	(	PUNCT
iajs-4071	268	15	̃	̃	PROPN
iajs-4071	268	16	)	)	PUNCT
iajs-4071	268	17	s.t	s.t	PROPN
iajs-4071	268	18	.	.	PUNCT
iajs-4071	268	19	̃	̃	ADV
iajs-4071	268	20	)	)	PUNCT
iajs-4071	268	21	̃	̃	PROPN
iajs-4071	268	22	)	)	PUNCT
iajs-4071	268	23	and	and	CCONJ
iajs-4071	268	24	so	so	ADV
iajs-4071	268	25	,	,	PUNCT
iajs-4071	268	26	̃	̃	PROPN
iajs-4071	268	27	)	)	PUNCT
iajs-4071	268	28	)	)	PUNCT
iajs-4071	268	29	̃	̃	ADV
iajs-4071	268	30	)	)	PUNCT
iajs-4071	268	31	)	)	PUNCT
iajs-4071	268	32	.	.	PUNCT
iajs-4071	269	1	since	since	SCONJ
iajs-4071	269	2	)	)	PUNCT
iajs-4071	269	3	̃	̃	NOUN
iajs-4071	269	4	̃	̃	PROPN
iajs-4071	269	5	(	(	PUNCT
iajs-4071	269	6	̃	̃	PROPN
iajs-4071	269	7	)	)	PUNCT
iajs-4071	269	8	in	in	ADP
iajs-4071	269	9	a	a	DET
iajs-4071	269	10	seds	sed	NOUN
iajs-4071	269	11	so	so	ADV
iajs-4071	269	12	by	by	ADP
iajs-4071	269	13	proposition	proposition	NOUN
iajs-4071	269	14	2.18(2	2.18(2	NUM
iajs-4071	269	15	)	)	PUNCT
iajs-4071	269	16	,	,	PUNCT
iajs-4071	269	17	(	(	PUNCT
iajs-4071	269	18	g	g	NOUN
iajs-4071	269	19	,	,	PUNCT
iajs-4071	269	20	)	)	PUNCT
iajs-4071	270	1	̃	̃	SYM
iajs-4071	270	2	̃	̃	PROPN
iajs-4071	270	3	(	(	PUNCT
iajs-4071	270	4	̃	̃	PROPN
iajs-4071	270	5	)	)	PUNCT
iajs-4071	270	6	then	then	ADV
iajs-4071	270	7	it	it	PRON
iajs-4071	270	8	is	be	AUX
iajs-4071	270	9	soft	soft	ADJ
iajs-4071	270	10	semi	semi	ADJ
iajs-4071	270	11	-	-	ADJ
iajs-4071	270	12	closed	closed	ADJ
iajs-4071	270	13	and	and	CCONJ
iajs-4071	270	14	hence	hence	ADV
iajs-4071	270	15	)	)	PUNCT
iajs-4071	270	16	)	)	PUNCT
iajs-4071	271	1	̃	̃	NOUN
iajs-4071	271	2	̃	̃	PROPN
iajs-4071	271	3	(	(	PUNCT
iajs-4071	271	4	̃	̃	PROPN
iajs-4071	271	5	)	)	PUNCT
iajs-4071	271	6	.	.	PUNCT
iajs-4071	272	1	therefore	therefore	ADV
iajs-4071	272	2	,	,	PUNCT
iajs-4071	272	3	)	)	PUNCT
iajs-4071	272	4	)	)	PUNCT
iajs-4071	273	1	̃	̃	NOUN
iajs-4071	273	2	̃	̃	PROPN
iajs-4071	273	3	(	(	PUNCT
iajs-4071	273	4	̃	̃	NOUN
iajs-4071	273	5	)	)	PUNCT
iajs-4071	273	6	3.13.proposition	3.13.proposition	NOUN
iajs-4071	273	7	let	let	VERB
iajs-4071	273	8	̃	̃	PROPN
iajs-4071	273	9	be	be	AUX
iajs-4071	273	10	a	a	DET
iajs-4071	273	11	seds	sed	NOUN
iajs-4071	273	12	.	.	PUNCT
iajs-4071	274	1	if	if	SCONJ
iajs-4071	274	2	)	)	PUNCT
iajs-4071	274	3	̃	̃	NOUN
iajs-4071	274	4	̃	̃	NOUN
iajs-4071	274	5	o	o	X
iajs-4071	274	6	(	(	PUNCT
iajs-4071	274	7	̃	̃	PROPN
iajs-4071	274	8	)	)	PUNCT
iajs-4071	274	9	and	and	CCONJ
iajs-4071	274	10	)	)	PUNCT
iajs-4071	274	11	̃	̃	NOUN
iajs-4071	274	12	̃	̃	ADJ
iajs-4071	274	13	o	o	X
iajs-4071	274	14	(	(	PUNCT
iajs-4071	274	15	̃	̃	PROPN
iajs-4071	274	16	)	)	PUNCT
iajs-4071	274	17	.	.	PUNCT
iajs-4071	275	1	then	then	ADV
iajs-4071	275	2	)	)	PUNCT
iajs-4071	275	3	)	)	PUNCT
iajs-4071	276	1	̃	̃	NOUN
iajs-4071	276	2	̃	̃	PROPN
iajs-4071	276	3	(	(	PUNCT
iajs-4071	276	4	̃	̃	NOUN
iajs-4071	276	5	)	)	PUNCT
iajs-4071	276	6	.	.	PUNCT
iajs-4071	277	1	proof	proof	NOUN
iajs-4071	277	2	:	:	PUNCT
iajs-4071	277	3	by	by	ADP
iajs-4071	277	4	proposition	proposition	NOUN
iajs-4071	277	5	2.20	2.20	NUM
iajs-4071	277	6	and	and	CCONJ
iajs-4071	277	7	proposition	proposition	NOUN
iajs-4071	277	8	3.19	3.19	NUM
iajs-4071	277	9	.	.	PUNCT
iajs-4071	278	1	3.14	3.14	NUM
iajs-4071	278	2	.	.	PUNCT
iajs-4071	279	1	proposition	proposition	NOUN
iajs-4071	279	2	let	let	VERB
iajs-4071	279	3	(	(	PUNCT
iajs-4071	279	4	̃	̃	NOUN
iajs-4071	279	5	̃	̃	PROPN
iajs-4071	279	6	)	)	PUNCT
iajs-4071	279	7	be	be	AUX
iajs-4071	279	8	a	a	DET
iajs-4071	279	9	sts	st	NOUN
iajs-4071	279	10	and	and	CCONJ
iajs-4071	279	11	)	)	PUNCT
iajs-4071	279	12	)	)	PUNCT
iajs-4071	280	1	̃	̃	NOUN
iajs-4071	280	2	̃	̃	NOUN
iajs-4071	280	3	̃	̃	NOUN
iajs-4071	280	4	)	)	PUNCT
iajs-4071	280	5	.	.	PUNCT
iajs-4071	281	1	if	if	SCONJ
iajs-4071	281	2	)	)	PUNCT
iajs-4071	281	3	̃	̃	ADV
iajs-4071	281	4	̃	̃	PROPN
iajs-4071	281	5	(	(	PUNCT
iajs-4071	281	6	̃	̃	PROPN
iajs-4071	281	7	)	)	PUNCT
iajs-4071	281	8	and	and	CCONJ
iajs-4071	281	9	)	)	PUNCT
iajs-4071	281	10	̃	̃	NOUN
iajs-4071	281	11	̃	̃	PROPN
iajs-4071	281	12	(	(	PUNCT
iajs-4071	281	13	̃	̃	PROPN
iajs-4071	281	14	)	)	PUNCT
iajs-4071	281	15	,	,	PUNCT
iajs-4071	281	16	then	then	ADV
iajs-4071	281	17	)	)	PUNCT
iajs-4071	281	18	)	)	PUNCT
iajs-4071	281	19	̃	̃	PROPN
iajs-4071	281	20	̃	̃	ADP
iajs-4071	281	21	̃	̃	NOUN
iajs-4071	281	22	)	)	PUNCT
iajs-4071	281	23	proof	proof	NOUN
iajs-4071	281	24	:	:	PUNCT
iajs-4071	281	25	let	let	VERB
iajs-4071	281	26	)	)	PUNCT
iajs-4071	281	27	̃	̃	ADV
iajs-4071	281	28	̃	̃	PROPN
iajs-4071	281	29	̃	̃	NOUN
iajs-4071	281	30	)	)	PUNCT
iajs-4071	281	31	and	and	CCONJ
iajs-4071	281	32	)	)	PUNCT
iajs-4071	282	1	̃	̃	NOUN
iajs-4071	282	2	̃	̃	PROPN
iajs-4071	282	3	(	(	PUNCT
iajs-4071	282	4	̃	̃	PROPN
iajs-4071	282	5	)	)	PUNCT
iajs-4071	282	6	,	,	PUNCT
iajs-4071	282	7	then	then	ADV
iajs-4071	282	8	)	)	PUNCT
iajs-4071	282	9	̃	̃	NOUN
iajs-4071	282	10	̃	̃	PROPN
iajs-4071	282	11	(	(	PUNCT
iajs-4071	282	12	̃	̃	PROPN
iajs-4071	282	13	)	)	PUNCT
iajs-4071	282	14	then	then	ADV
iajs-4071	282	15	by	by	ADP
iajs-4071	282	16	proposition	proposition	NOUN
iajs-4071	282	17	2.19	2.19	NUM
iajs-4071	282	18	)	)	PUNCT
iajs-4071	282	19	)	)	PUNCT
iajs-4071	283	1	̃	̃	PROPN
iajs-4071	283	2	̃	̃	NOUN
iajs-4071	283	3	̃	̃	NOUN
iajs-4071	283	4	)	)	PUNCT
iajs-4071	283	5	.	.	PUNCT
iajs-4071	284	1	after	after	ADP
iajs-4071	284	2	that	that	PRON
iajs-4071	284	3	,	,	PUNCT
iajs-4071	284	4	let	let	VERB
iajs-4071	284	5	's	us	PRON
iajs-4071	284	6	̃	̃	PROPN
iajs-4071	284	7	)	)	PUNCT
iajs-4071	284	8	)	)	PUNCT
iajs-4071	284	9	,	,	PUNCT
iajs-4071	284	10	therefore	therefore	ADV
iajs-4071	284	11	̃	̃	PROPN
iajs-4071	284	12	)	)	PUNCT
iajs-4071	284	13	and	and	CCONJ
iajs-4071	284	14	̃	̃	PROPN
iajs-4071	284	15	)	)	PUNCT
iajs-4071	285	1	so	so	ADV
iajs-4071	285	2	)	)	PUNCT
iajs-4071	285	3	̃	̃	NOUN
iajs-4071	285	4	̃	̃	PROPN
iajs-4071	285	5	(	(	PUNCT
iajs-4071	285	6	̃	̃	NOUN
iajs-4071	285	7	)	)	PUNCT
iajs-4071	285	8	such	such	ADJ
iajs-4071	285	9	that	that	SCONJ
iajs-4071	285	10	̃	̃	PROPN
iajs-4071	285	11	)	)	PUNCT
iajs-4071	285	12	̃	̃	NOUN
iajs-4071	285	13	)	)	PUNCT
iajs-4071	285	14	.	.	PUNCT
iajs-4071	286	1	since	since	SCONJ
iajs-4071	286	2	)	)	PUNCT
iajs-4071	286	3	̃	̃	NOUN
iajs-4071	286	4	̃	̃	PROPN
iajs-4071	286	5	(	(	PUNCT
iajs-4071	286	6	̃	̃	PROPN
iajs-4071	286	7	)	)	PUNCT
iajs-4071	286	8	then	then	ADV
iajs-4071	286	9	)	)	PUNCT
iajs-4071	287	1	̃	̃	SYM
iajs-4071	287	2	̃	̃	PROPN
iajs-4071	287	3	(	(	PUNCT
iajs-4071	287	4	̃	̃	NOUN
iajs-4071	287	5	)	)	PUNCT
iajs-4071	287	6	implying	imply	VERB
iajs-4071	287	7	that	that	SCONJ
iajs-4071	287	8	(	(	PUNCT
iajs-4071	287	9	k	k	NOUN
iajs-4071	287	10	,	,	PUNCT
iajs-4071	287	11	)	)	PUNCT
iajs-4071	287	12	∩(g	∩(g	PROPN
iajs-4071	287	13	,	,	PUNCT
iajs-4071	287	14	)	)	PUNCT
iajs-4071	287	15	̃	̃	SYM
iajs-4071	287	16	̃	̃	PROPN
iajs-4071	287	17	(	(	PUNCT
iajs-4071	287	18	̃	̃	PROPN
iajs-4071	287	19	)	)	PUNCT
iajs-4071	287	20	.	.	PUNCT
iajs-4071	288	1	therefore	therefore	ADV
iajs-4071	288	2	,	,	PUNCT
iajs-4071	288	3	̃	̃	PROPN
iajs-4071	288	4	)	)	PUNCT
iajs-4071	288	5	)	)	PUNCT
iajs-4071	289	1	̃	̃	ADV
iajs-4071	289	2	)	)	PUNCT
iajs-4071	289	3	)	)	PUNCT
iajs-4071	290	1	thus	thus	ADV
iajs-4071	290	2	,	,	PUNCT
iajs-4071	290	3	)	)	PUNCT
iajs-4071	290	4	)	)	PUNCT
iajs-4071	290	5	is	be	AUX
iajs-4071	290	6	̃	̃	ADV
iajs-4071	290	7	)	)	PUNCT
iajs-4071	290	8	corollary	corollary	NOUN
iajs-4071	290	9	suppose	suppose	VERB
iajs-4071	290	10	̃	̃	NOUN
iajs-4071	290	11	be	be	AUX
iajs-4071	290	12	a	a	DET
iajs-4071	290	13	sts	st	NOUN
iajs-4071	290	14	,	,	PUNCT
iajs-4071	290	15	let	let	VERB
iajs-4071	290	16	)	)	PUNCT
iajs-4071	290	17	)	)	PUNCT
iajs-4071	291	1	̃	̃	ADV
iajs-4071	291	2	̃.	̃.	NOUN
iajs-4071	291	3	if	if	SCONJ
iajs-4071	291	4	)	)	PUNCT
iajs-4071	291	5	̃	̃	PROPN
iajs-4071	291	6	̃	̃	PROPN
iajs-4071	291	7	̃	̃	NOUN
iajs-4071	291	8	)	)	PUNCT
iajs-4071	291	9	,	,	PUNCT
iajs-4071	291	10	)	)	PUNCT
iajs-4071	292	1	̃	̃	SYM
iajs-4071	292	2	̃	̃	PROPN
iajs-4071	292	3	(	(	PUNCT
iajs-4071	292	4	̃	̃	NOUN
iajs-4071	292	5	)	)	PUNCT
iajs-4071	292	6	)	)	PUNCT
iajs-4071	293	1	̃	̃	NOUN
iajs-4071	293	2	̃	̃	PROPN
iajs-4071	293	3	(	(	PUNCT
iajs-4071	293	4	̃	̃	PROPN
iajs-4071	293	5	)	)	PUNCT
iajs-4071	293	6	,	,	PUNCT
iajs-4071	293	7	then	then	ADV
iajs-4071	293	8	)	)	PUNCT
iajs-4071	293	9	)	)	PUNCT
iajs-4071	294	1	̃	̃	NOUN
iajs-4071	294	2	̃	̃	NOUN
iajs-4071	294	3	̃	̃	NOUN
iajs-4071	294	4	)	)	PUNCT
iajs-4071	295	1	3.15	3.15	NUM
iajs-4071	295	2	.	.	PUNCT
iajs-4071	296	1	proposition	proposition	NOUN
iajs-4071	296	2	let	let	VERB
iajs-4071	296	3	(	(	PUNCT
iajs-4071	296	4	̃	̃	ADV
iajs-4071	296	5	̃	̃	NOUN
iajs-4071	296	6	)	)	PUNCT
iajs-4071	296	7	be	be	AUX
iajs-4071	296	8	a	a	DET
iajs-4071	296	9	soft	soft	ADJ
iajs-4071	296	10	subspace	subspace	NOUN
iajs-4071	296	11	of	of	ADP
iajs-4071	296	12	a	a	DET
iajs-4071	296	13	soft	soft	ADJ
iajs-4071	296	14	space	space	NOUN
iajs-4071	296	15	(	(	PUNCT
iajs-4071	296	16	̃	̃	NOUN
iajs-4071	296	17	̃	̃	ADJ
iajs-4071	296	18	)	)	PUNCT
iajs-4071	296	19	̃	̃	SYM
iajs-4071	296	20	̃	̃	NOUN
iajs-4071	296	21	̃	̃	PROPN
iajs-4071	296	22	.	.	PUNCT
iajs-4071	297	1	if	if	SCONJ
iajs-4071	297	2	)	)	PUNCT
iajs-4071	297	3	̃	̃	PROPN
iajs-4071	297	4	̃	̃	PROPN
iajs-4071	297	5	̃	̃	PROPN
iajs-4071	297	6	)	)	PUNCT
iajs-4071	297	7	,	,	PUNCT
iajs-4071	297	8	then	then	ADV
iajs-4071	297	9	)	)	PUNCT
iajs-4071	298	1	̃	̃	SYM
iajs-4071	298	2	̃	̃	ADP
iajs-4071	298	3	̃	̃	ADP
iajs-4071	298	4	̃	̃	PROPN
iajs-4071	298	5	̃	̃	NUM
iajs-4071	298	6	)	)	PUNCT
iajs-4071	298	7	.	.	PUNCT
iajs-4071	299	1	ihjpas	ihjpas	PROPN
iajs-4071	299	2	.	.	PUNCT
iajs-4071	300	1	2025,38(4	2025,38(4	NOUN
iajs-4071	300	2	)	)	PUNCT
iajs-4071	300	3	370	370	NUM
iajs-4071	300	4	proof	proof	NOUN
iajs-4071	300	5	:	:	PUNCT
iajs-4071	301	1	since	since	SCONJ
iajs-4071	301	2	̃	̃	PROPN
iajs-4071	301	3	̃	̃	NOUN
iajs-4071	301	4	̃	̃	PROPN
iajs-4071	301	5	and	and	CCONJ
iajs-4071	301	6	by	by	ADP
iajs-4071	301	7	proposition	proposition	NOUN
iajs-4071	301	8	2.22	2.22	NUM
iajs-4071	301	9	then	then	ADV
iajs-4071	301	10	̃	̃	PROPN
iajs-4071	301	11	̃	̃	PROPN
iajs-4071	301	12	)	)	PUNCT
iajs-4071	301	13	̃	̃	PROPN
iajs-4071	301	14	)	)	PUNCT
iajs-4071	301	15	for	for	ADP
iajs-4071	301	16	all	all	PRON
iajs-4071	301	17	)	)	PUNCT
iajs-4071	301	18	̃	̃	ADV
iajs-4071	301	19	̃.	̃.	NOUN
iajs-4071	301	20	hence	hence	ADV
iajs-4071	301	21	,	,	PUNCT
iajs-4071	301	22	we	we	PRON
iajs-4071	301	23	obtain	obtain	VERB
iajs-4071	301	24	̃	̃	NOUN
iajs-4071	301	25	̃	̃	NOUN
iajs-4071	301	26	̃	̃	NOUN
iajs-4071	301	27	̃	̃	ADJ
iajs-4071	301	28	)	)	PUNCT
iajs-4071	301	29	̃	̃	PROPN
iajs-4071	301	30	̃	̃	NOUN
iajs-4071	301	31	)	)	PUNCT
iajs-4071	301	32	)	)	PUNCT
iajs-4071	302	1	̃	̃	NOUN
iajs-4071	302	2	̃	̃	ADJ
iajs-4071	302	3	)	)	PUNCT
iajs-4071	302	4	̃	̃	PROPN
iajs-4071	302	5	̃	̃	ADJ
iajs-4071	302	6	)	)	PUNCT
iajs-4071	302	7	̃	̃	NOUN
iajs-4071	302	8	̃	̃	ADP
iajs-4071	302	9	̃	̃	ADP
iajs-4071	302	10	̃	̃	NOUN
iajs-4071	302	11	̃	̃	ADJ
iajs-4071	302	12	)	)	PUNCT
iajs-4071	302	13	̃	̃	PROPN
iajs-4071	302	14	̃	̃	PROPN
iajs-4071	302	15	̃	̃	NOUN
iajs-4071	302	16	)	)	PUNCT
iajs-4071	302	17	)	)	PUNCT
iajs-4071	303	1	̃	̃	PROPN
iajs-4071	303	2	̃	̃	ADP
iajs-4071	303	3	̃	̃	NOUN
iajs-4071	303	4	̃	̃	PROPN
iajs-4071	303	5	(	(	PUNCT
iajs-4071	303	6	̃	̃	NOUN
iajs-4071	303	7	)	)	PUNCT
iajs-4071	303	8	)	)	PUNCT
iajs-4071	304	1	̃	̃	NOUN
iajs-4071	304	2	̃	̃	PROPN
iajs-4071	304	3	(	(	PUNCT
iajs-4071	304	4	̃	̃	PROPN
iajs-4071	304	5	(	(	PUNCT
iajs-4071	304	6	̃	̃	NOUN
iajs-4071	304	7	)	)	PUNCT
iajs-4071	304	8	)	)	PUNCT
iajs-4071	305	1	̃	̃	PROPN
iajs-4071	305	2	̃	̃	ADP
iajs-4071	305	3	̃	̃	NOUN
iajs-4071	305	4	̃	̃	PROPN
iajs-4071	305	5	(	(	PUNCT
iajs-4071	305	6	̃	̃	NOUN
iajs-4071	305	7	)	)	PUNCT
iajs-4071	305	8	)	)	PUNCT
iajs-4071	305	9	̃	̃	NOUN
iajs-4071	305	10	̃	̃	ADJ
iajs-4071	305	11	)	)	PUNCT
iajs-4071	306	1	̃	̃	NOUN
iajs-4071	306	2	̃	̃	PROPN
iajs-4071	306	3	(	(	PUNCT
iajs-4071	306	4	̃	̃	PROPN
iajs-4071	306	5	)	)	PUNCT
iajs-4071	306	6	̃	̃	PROPN
iajs-4071	306	7	(	(	PUNCT
iajs-4071	306	8	̃	̃	NOUN
iajs-4071	306	9	)	)	PUNCT
iajs-4071	306	10	)	)	PUNCT
iajs-4071	307	1	̃	̃	ADJ
iajs-4071	307	2	)	)	PUNCT
iajs-4071	308	1	̃	̃	NOUN
iajs-4071	308	2	̃	̃	PROPN
iajs-4071	308	3	(	(	PUNCT
iajs-4071	308	4	̃	̃	NOUN
iajs-4071	308	5	̃	̃	PROPN
iajs-4071	308	6	(	(	PUNCT
iajs-4071	308	7	)	)	PUNCT
iajs-4071	308	8	̃	̃	PROPN
iajs-4071	308	9	̃	̃	NOUN
iajs-4071	308	10	)	)	PUNCT
iajs-4071	308	11	)	)	PUNCT
iajs-4071	309	1	̃	̃	ADJ
iajs-4071	309	2	)	)	PUNCT
iajs-4071	310	1	̃	̃	NOUN
iajs-4071	310	2	̃	̃	ADJ
iajs-4071	310	3	)	)	PUNCT
iajs-4071	311	1	̃	̃	SYM
iajs-4071	311	2	̃	̃	ADP
iajs-4071	311	3	̃	̃	NOUN
iajs-4071	311	4	̃	̃	NOUN
iajs-4071	311	5	̃	̃	NOUN
iajs-4071	311	6	)	)	PUNCT
iajs-4071	311	7	.	.	PUNCT
iajs-4071	312	1	3.16.proposition	3.16.proposition	NOUN
iajs-4071	312	2	let	let	VERB
iajs-4071	312	3	(	(	PUNCT
iajs-4071	312	4	̃	̃	NOUN
iajs-4071	312	5	̃	̃	PROPN
iajs-4071	312	6	)	)	PUNCT
iajs-4071	312	7	be	be	AUX
iajs-4071	312	8	a	a	DET
iajs-4071	312	9	soft	soft	ADJ
iajs-4071	312	10	subspace	subspace	NOUN
iajs-4071	312	11	of	of	ADP
iajs-4071	312	12	a	a	DET
iajs-4071	312	13	soft	soft	ADJ
iajs-4071	312	14	space	space	NOUN
iajs-4071	312	15	(	(	PUNCT
iajs-4071	312	16	̃	̃	NOUN
iajs-4071	312	17	̃	̃	ADJ
iajs-4071	312	18	)	)	PUNCT
iajs-4071	312	19	̃	̃	SYM
iajs-4071	312	20	̃	̃	NOUN
iajs-4071	312	21	̃	̃	NOUN
iajs-4071	312	22	)	)	PUNCT
iajs-4071	312	23	.	.	PUNCT
iajs-4071	313	1	if	if	SCONJ
iajs-4071	313	2	)	)	PUNCT
iajs-4071	313	3	̃	̃	NOUN
iajs-4071	313	4	̃	̃	NOUN
iajs-4071	313	5	̃	̃	PROPN
iajs-4071	313	6	)	)	PUNCT
iajs-4071	313	7	,	,	PUNCT
iajs-4071	313	8	then	then	ADV
iajs-4071	313	9	)	)	PUNCT
iajs-4071	314	1	̃	̃	SYM
iajs-4071	314	2	̃	̃	ADP
iajs-4071	314	3	̃	̃	NOUN
iajs-4071	314	4	̃	̃	NOUN
iajs-4071	314	5	̃	̃	NOUN
iajs-4071	314	6	)	)	PUNCT
iajs-4071	314	7	.	.	PUNCT
iajs-4071	315	1	proof	proof	NOUN
iajs-4071	315	2	:	:	PUNCT
iajs-4071	315	3	since	since	SCONJ
iajs-4071	315	4	̃	̃	PROPN
iajs-4071	315	5	̃	̃	NOUN
iajs-4071	315	6	̃	̃	ADJ
iajs-4071	315	7	)	)	PUNCT
iajs-4071	316	1	̃	̃	PROPN
iajs-4071	316	2	̃	̃	NOUN
iajs-4071	316	3	̃	̃	PROPN
iajs-4071	316	4	)	)	PUNCT
iajs-4071	316	5	by	by	ADP
iajs-4071	316	6	proposition	proposition	NOUN
iajs-4071	316	7	2.19	2.19	NUM
iajs-4071	316	8	)	)	PUNCT
iajs-4071	317	1	̃	̃	PROPN
iajs-4071	317	2	̃	̃	ADP
iajs-4071	317	3	̃	̃	NOUN
iajs-4071	317	4	̃	̃	NOUN
iajs-4071	317	5	̃	̃	NOUN
iajs-4071	317	6	)	)	PUNCT
iajs-4071	317	7	since	since	SCONJ
iajs-4071	317	8	)	)	PUNCT
iajs-4071	317	9	̃	̃	NOUN
iajs-4071	317	10	̃	̃	ADP
iajs-4071	317	11	̃	̃	PROPN
iajs-4071	317	12	̃and	̃and	PROPN
iajs-4071	317	13	̃	̃	PROPN
iajs-4071	317	14	̃	̃	PROPN
iajs-4071	318	1	̃	̃	PROPN
iajs-4071	318	2	then	then	ADV
iajs-4071	318	3	̃	̃	PROPN
iajs-4071	318	4	̃	̃	PROPN
iajs-4071	318	5	̃	̃	PROPN
iajs-4071	318	6	̃	̃	NOUN
iajs-4071	318	7	)	)	PUNCT
iajs-4071	318	8	then	then	ADV
iajs-4071	318	9	by	by	ADP
iajs-4071	318	10	proposition	proposition	NOUN
iajs-4071	318	11	2.20	2.20	NUM
iajs-4071	318	12	)	)	PUNCT
iajs-4071	318	13	̃	̃	PROPN
iajs-4071	318	14	̃	̃	ADP
iajs-4071	318	15	̃	̃	NOUN
iajs-4071	318	16	̃	̃	NOUN
iajs-4071	318	17	̃	̃	NOUN
iajs-4071	318	18	)	)	PUNCT
iajs-4071	318	19	.but	.but	PUNCT
iajs-4071	318	20	)	)	PUNCT
iajs-4071	319	1	̃	̃	NOUN
iajs-4071	319	2	̃	̃	NOUN
iajs-4071	319	3	̃	̃	PROPN
iajs-4071	319	4	)	)	PUNCT
iajs-4071	319	5	then	then	ADV
iajs-4071	319	6	̃	̃	PROPN
iajs-4071	319	7	)	)	PUNCT
iajs-4071	319	8	(	(	PUNCT
iajs-4071	319	9	g	g	NOUN
iajs-4071	319	10	,	,	PUNCT
iajs-4071	319	11	)	)	PUNCT
iajs-4071	319	12	̃	̃	SYM
iajs-4071	319	13	̃	̃	PROPN
iajs-4071	319	14	(	(	PUNCT
iajs-4071	319	15	̃	̃	PROPN
iajs-4071	319	16	)	)	PUNCT
iajs-4071	319	17	s.t	s.t	PROPN
iajs-4071	319	18	.	.	PUNCT
iajs-4071	319	19	̃	̃	ADV
iajs-4071	319	20	)	)	PUNCT
iajs-4071	319	21	̃	̃	NOUN
iajs-4071	319	22	)	)	PUNCT
iajs-4071	319	23	.	.	PUNCT
iajs-4071	320	1	hence	hence	ADV
iajs-4071	320	2	̃	̃	ADV
iajs-4071	320	3	)	)	PUNCT
iajs-4071	320	4	̃	̃	SYM
iajs-4071	320	5	̃	̃	ADP
iajs-4071	320	6	̃	̃	ADJ
iajs-4071	320	7	)	)	PUNCT
iajs-4071	320	8	̃	̃	NOUN
iajs-4071	320	9	̃	̃	NOUN
iajs-4071	320	10	,	,	PUNCT
iajs-4071	320	11	since	since	SCONJ
iajs-4071	320	12	̃	̃	PROPN
iajs-4071	320	13	̃	̃	NOUN
iajs-4071	320	14	̃	̃	PROPN
iajs-4071	320	15	and	and	CCONJ
iajs-4071	320	16	(	(	PUNCT
iajs-4071	320	17	g	g	NOUN
iajs-4071	320	18	,	,	PUNCT
iajs-4071	320	19	)	)	PUNCT
iajs-4071	320	20	̃	̃	PROPN
iajs-4071	320	21	̃	̃	NOUN
iajs-4071	320	22	̃	̃	PROPN
iajs-4071	320	23	)	)	PUNCT
iajs-4071	320	24	,	,	PUNCT
iajs-4071	320	25	then	then	ADV
iajs-4071	320	26	by	by	ADP
iajs-4071	320	27	proposition	proposition	NOUN
iajs-4071	320	28	3.23	3.23	NUM
iajs-4071	320	29	(	(	PUNCT
iajs-4071	320	30	g	g	NOUN
iajs-4071	320	31	,	,	PUNCT
iajs-4071	320	32	)	)	PUNCT
iajs-4071	321	1	̃	̃	SYM
iajs-4071	321	2	̃	̃	ADP
iajs-4071	321	3	̃	̃	NOUN
iajs-4071	321	4	̃	̃	NOUN
iajs-4071	321	5	̃	̃	PROPN
iajs-4071	321	6	)	)	PUNCT
iajs-4071	321	7	therefor	therefor	ADP
iajs-4071	321	8	)	)	PUNCT
iajs-4071	321	9	̃	̃	PROPN
iajs-4071	321	10	̃	̃	ADP
iajs-4071	321	11	̃	̃	NOUN
iajs-4071	321	12	̃	̃	NOUN
iajs-4071	321	13	̃	̃	PROPN
iajs-4071	321	14	)	)	PUNCT
iajs-4071	321	15	.	.	PUNCT
iajs-4071	322	1	shown	show	VERB
iajs-4071	322	2	by	by	ADP
iajs-4071	322	3	the	the	DET
iajs-4071	322	4	example	example	NOUN
iajs-4071	322	5	following	following	NOUN
iajs-4071	322	6	,	,	PUNCT
iajs-4071	322	7	the	the	DET
iajs-4071	322	8	converse	converse	NOUN
iajs-4071	322	9	of	of	ADP
iajs-4071	322	10	proposition	proposition	NOUN
iajs-4071	322	11	3.24	3.24	NUM
iajs-4071	322	12	is	be	AUX
iajs-4071	322	13	incorrect	incorrect	ADJ
iajs-4071	322	14	,	,	PUNCT
iajs-4071	322	15	if	if	SCONJ
iajs-4071	322	16	̃	̃	PROPN
iajs-4071	322	17	̃	̃	PROPN
iajs-4071	322	18	̃.	̃.	ADJ
iajs-4071	322	19	example	example	NOUN
iajs-4071	322	20	examine	examine	VERB
iajs-4071	322	21	,	,	PUNCT
iajs-4071	322	22	and	and	CCONJ
iajs-4071	322	23	}	}	PUNCT
iajs-4071	322	24	.	.	PUNCT
iajs-4071	323	1	we	we	PRON
iajs-4071	323	2	consider	consider	VERB
iajs-4071	323	3	̃	̃	ADV
iajs-4071	323	4	)	)	PUNCT
iajs-4071	323	5	̃	̃	NOUN
iajs-4071	323	6	̃	̃	NOUN
iajs-4071	323	7	where	where	SCONJ
iajs-4071	323	8	)	)	PUNCT
iajs-4071	323	9	{	{	PUNCT
iajs-4071	323	10	)	)	PUNCT
iajs-4071	323	11	{	{	PUNCT
iajs-4071	323	12	)	)	PUNCT
iajs-4071	323	13	{	{	PUNCT
iajs-4071	323	14	)	)	PUNCT
iajs-4071	323	15	{	{	PUNCT
iajs-4071	323	16	)	)	PUNCT
iajs-4071	323	17	{	{	PUNCT
iajs-4071	323	18	)	)	PUNCT
iajs-4071	323	19	{	{	PUNCT
iajs-4071	323	20	then	then	ADV
iajs-4071	323	21	̃	̃	PROPN
iajs-4071	323	22	)	)	PUNCT
iajs-4071	323	23	̃	̃	PROPN
iajs-4071	323	24	and	and	CCONJ
iajs-4071	323	25	̃	̃	PROPN
iajs-4071	323	26	̃	̃	NOUN
iajs-4071	323	27	̃	̃	NOUN
iajs-4071	323	28	̃	̃	PROPN
iajs-4071	323	29	)	)	PUNCT
iajs-4071	323	30	where	where	SCONJ
iajs-4071	323	31	)	)	PUNCT
iajs-4071	323	32	{	{	PUNCT
iajs-4071	323	33	)	)	PUNCT
iajs-4071	323	34	{	{	PUNCT
iajs-4071	323	35	)	)	PUNCT
iajs-4071	323	36	{	{	PUNCT
iajs-4071	323	37	)	)	PUNCT
iajs-4071	323	38	{	{	PUNCT
iajs-4071	323	39	)	)	PUNCT
iajs-4071	323	40	{	{	PUNCT
iajs-4071	323	41	)	)	PUNCT
iajs-4071	323	42	{	{	PUNCT
iajs-4071	323	43	so	so	ADV
iajs-4071	323	44	)	)	PUNCT
iajs-4071	323	45	̃	̃	PROPN
iajs-4071	323	46	̃	̃	NOUN
iajs-4071	323	47	̃	̃	NOUN
iajs-4071	323	48	)	)	PUNCT
iajs-4071	323	49	but	but	CCONJ
iajs-4071	323	50	)	)	PUNCT
iajs-4071	323	51	̃	̃	PROPN
iajs-4071	323	52	̃	̃	PROPN
iajs-4071	323	53	̃	̃	NOUN
iajs-4071	323	54	)	)	PUNCT
iajs-4071	323	55	3.17	3.17	NUM
iajs-4071	323	56	.	.	PUNCT
iajs-4071	324	1	proposition	proposition	NOUN
iajs-4071	324	2	let	let	VERB
iajs-4071	324	3	̃	̃	PROPN
iajs-4071	324	4	̃	̃	PROPN
iajs-4071	324	5	)	)	PUNCT
iajs-4071	324	6	be	be	AUX
iajs-4071	324	7	a	a	DET
iajs-4071	324	8	subspace	subspace	NOUN
iajs-4071	324	9	of	of	ADP
iajs-4071	324	10	a	a	DET
iajs-4071	324	11	space	space	NOUN
iajs-4071	324	12	̃	̃	NOUN
iajs-4071	324	13	̃	̃	PROPN
iajs-4071	324	14	)	)	PUNCT
iajs-4071	324	15	and	and	CCONJ
iajs-4071	324	16	)	)	PUNCT
iajs-4071	324	17	̃	̃	ADV
iajs-4071	324	18	̃.	̃.	NOUN
iajs-4071	324	19	if	if	SCONJ
iajs-4071	324	20	)	)	PUNCT
iajs-4071	324	21	̃	̃	PROPN
iajs-4071	324	22	̃	̃	NOUN
iajs-4071	324	23	̃	̃	NOUN
iajs-4071	324	24	)	)	PUNCT
iajs-4071	324	25	and	and	CCONJ
iajs-4071	324	26	̃	̃	PROPN
iajs-4071	324	27	̃	̃	PROPN
iajs-4071	324	28	̃	̃	PROPN
iajs-4071	324	29	̃	̃	PROPN
iajs-4071	324	30	)	)	PUNCT
iajs-4071	324	31	,	,	PUNCT
iajs-4071	324	32	then	then	ADV
iajs-4071	324	33	)	)	PUNCT
iajs-4071	324	34	̃	̃	PROPN
iajs-4071	324	35	̃	̃	PROPN
iajs-4071	324	36	̃	̃	NOUN
iajs-4071	324	37	)	)	PUNCT
iajs-4071	324	38	.	.	PUNCT
iajs-4071	325	1	proof	proof	NOUN
iajs-4071	325	2	:	:	PUNCT
iajs-4071	325	3	let	let	VERB
iajs-4071	325	4	(	(	PUNCT
iajs-4071	325	5	)	)	PUNCT
iajs-4071	325	6	̃	̃	PROPN
iajs-4071	325	7	̃	̃	PROPN
iajs-4071	325	8	̃	̃	PROPN
iajs-4071	325	9	)	)	PUNCT
iajs-4071	325	10	,	,	PUNCT
iajs-4071	325	11	then	then	ADV
iajs-4071	325	12	)	)	PUNCT
iajs-4071	325	13	̃	̃	PROPN
iajs-4071	325	14	̃	̃	PROPN
iajs-4071	325	15	̃	̃	NUM
iajs-4071	325	16	)	)	PUNCT
iajs-4071	325	17	and	and	CCONJ
iajs-4071	325	18	for	for	ADP
iajs-4071	325	19	̃	̃	PROPN
iajs-4071	325	20	)	)	PUNCT
iajs-4071	325	21	,	,	PUNCT
iajs-4071	325	22	there	there	PRON
iajs-4071	325	23	is	be	VERB
iajs-4071	325	24	)	)	PUNCT
iajs-4071	326	1	̃	̃	PROPN
iajs-4071	326	2	̃	̃	PROPN
iajs-4071	326	3	̃	̃	PROPN
iajs-4071	326	4	)	)	PUNCT
iajs-4071	327	1	s.t	s.t	PROPN
iajs-4071	327	2	.	.	PUNCT
iajs-4071	327	3	̃	̃	ADV
iajs-4071	327	4	)	)	PUNCT
iajs-4071	327	5	̃	̃	PROPN
iajs-4071	327	6	)	)	PUNCT
iajs-4071	327	7	since	since	SCONJ
iajs-4071	327	8	̃	̃	PROPN
iajs-4071	327	9	̃	̃	PROPN
iajs-4071	327	10	̃	̃	PROPN
iajs-4071	327	11	,	,	PUNCT
iajs-4071	327	12	and	and	CCONJ
iajs-4071	327	13	)	)	PUNCT
iajs-4071	327	14	̃	̃	NOUN
iajs-4071	327	15	̃	̃	ADJ
iajs-4071	327	16	)	)	PUNCT
iajs-4071	328	1	̃	̃	SYM
iajs-4071	328	2	̃	̃	ADP
iajs-4071	328	3	̃	̃	ADP
iajs-4071	328	4	̃	̃	ADP
iajs-4071	328	5	̃	̃	ADP
iajs-4071	328	6	̃	̃	NOUN
iajs-4071	328	7	̃	̃	NOUN
iajs-4071	328	8	)	)	PUNCT
iajs-4071	328	9	)	)	PUNCT
iajs-4071	328	10	)	)	PUNCT
iajs-4071	329	1	̃	̃	NOUN
iajs-4071	329	2	̃	̃	NOUN
iajs-4071	329	3	̃	̃	NOUN
iajs-4071	329	4	)	)	PUNCT
iajs-4071	329	5	)	)	PUNCT
iajs-4071	329	6	)	)	PUNCT
iajs-4071	329	7	,	,	PUNCT
iajs-4071	329	8	)	)	PUNCT
iajs-4071	329	9	̃	̃	NOUN
iajs-4071	329	10	̃	̃	NOUN
iajs-4071	329	11	̃).since	̃).since	NOUN
iajs-4071	329	12	)	)	PUNCT
iajs-4071	329	13	̃	̃	NOUN
iajs-4071	329	14	̃	̃	PROPN
iajs-4071	329	15	(	(	PUNCT
iajs-4071	329	16	̃	̃	NOUN
iajs-4071	329	17	)	)	PUNCT
iajs-4071	329	18	)	)	PUNCT
iajs-4071	330	1	̃	̃	NOUN
iajs-4071	330	2	̃	̃	PROPN
iajs-4071	330	3	(	(	PUNCT
iajs-4071	330	4	̃	̃	PROPN
iajs-4071	330	5	)	)	PUNCT
iajs-4071	330	6	s.t	s.t	PROPN
iajs-4071	330	7	.	.	PROPN
iajs-4071	330	8	)	)	PUNCT
iajs-4071	330	9	)	)	PUNCT
iajs-4071	331	1	̃	̃	NOUN
iajs-4071	331	2	̃	̃	ADJ
iajs-4071	331	3	but	but	CCONJ
iajs-4071	331	4	̃	̃	PROPN
iajs-4071	331	5	̃	̃	NOUN
iajs-4071	331	6	̃	̃	ADV
iajs-4071	331	7	then	then	ADV
iajs-4071	331	8	it	it	PRON
iajs-4071	331	9	is	be	AUX
iajs-4071	331	10	soft	soft	ADJ
iajs-4071	331	11	semi	semi	ADJ
iajs-4071	331	12	-	-	ADJ
iajs-4071	331	13	closed	closed	ADJ
iajs-4071	331	14	therefore	therefore	ADV
iajs-4071	331	15	)	)	PUNCT
iajs-4071	331	16	̃	̃	PROPN
iajs-4071	331	17	̃	̃	PROPN
iajs-4071	331	18	̃	̃	NOUN
iajs-4071	331	19	)	)	PUNCT
iajs-4071	331	20	the	the	DET
iajs-4071	331	21	following	follow	VERB
iajs-4071	331	22	corollary	corollary	NOUN
iajs-4071	331	23	is	be	AUX
iajs-4071	331	24	derived	derive	VERB
iajs-4071	331	25	directly	directly	ADV
iajs-4071	331	26	from	from	ADP
iajs-4071	331	27	proposition	proposition	NOUN
iajs-4071	331	28	3.26	3.26	NUM
iajs-4071	331	29	.	.	PUNCT
iajs-4071	332	1	and	and	CCONJ
iajs-4071	332	2	proposition	proposition	NOUN
iajs-4071	332	3	3.24	3.24	NUM
iajs-4071	332	4	.	.	PUNCT
iajs-4071	333	1	corollary	corollary	ADJ
iajs-4071	333	2	let	let	VERB
iajs-4071	333	3	̃	̃	PROPN
iajs-4071	333	4	̃	̃	PROPN
iajs-4071	333	5	)	)	PUNCT
iajs-4071	333	6	be	be	AUX
iajs-4071	333	7	a	a	DET
iajs-4071	333	8	sts	st	NOUN
iajs-4071	333	9	,	,	PUNCT
iajs-4071	333	10	and	and	CCONJ
iajs-4071	333	11	)	)	PUNCT
iajs-4071	334	1	̃	̃	NOUN
iajs-4071	334	2	be	be	VERB
iajs-4071	334	3	soft	soft	ADJ
iajs-4071	334	4	subsets	subset	NOUN
iajs-4071	334	5	of	of	ADP
iajs-4071	334	6	̃	̃	PROPN
iajs-4071	334	7	s.t	s.t	PROPN
iajs-4071	334	8	.	.	PUNCT
iajs-4071	334	9	)	)	PUNCT
iajs-4071	335	1	̃	̃	PROPN
iajs-4071	335	2	̃	̃	ADP
iajs-4071	335	3	̃	̃	NOUN
iajs-4071	335	4	̃	̃	PROPN
iajs-4071	335	5	and	and	CCONJ
iajs-4071	335	6	̃	̃	PROPN
iajs-4071	335	7	̃	̃	NOUN
iajs-4071	335	8	̃	̃	PROPN
iajs-4071	335	9	(	(	PUNCT
iajs-4071	335	10	̃	̃	PROPN
iajs-4071	335	11	)	)	PUNCT
iajs-4071	335	12	.	.	PUNCT
iajs-4071	336	1	therefore	therefore	ADV
iajs-4071	336	2	)	)	PUNCT
iajs-4071	336	3	̃	̃	NOUN
iajs-4071	336	4	̃	̃	ADP
iajs-4071	336	5	̃	̃	PROPN
iajs-4071	336	6	)	)	PUNCT
iajs-4071	336	7	iff	iff	PROPN
iajs-4071	336	8	)	)	PUNCT
iajs-4071	336	9	̃	̃	PROPN
iajs-4071	336	10	̃	̃	NOUN
iajs-4071	336	11	̃	̃	NOUN
iajs-4071	336	12	)	)	PUNCT
iajs-4071	336	13	.	.	PUNCT
iajs-4071	337	1	corollary	corollary	ADJ
iajs-4071	337	2	let	let	VERB
iajs-4071	337	3	)	)	PUNCT
iajs-4071	338	1	̃	̃	ADV
iajs-4071	338	2	̃	̃	PROPN
iajs-4071	338	3	(	(	PUNCT
iajs-4071	338	4	̃	̃	NOUN
iajs-4071	338	5	)	)	PUNCT
iajs-4071	338	6	)	)	PUNCT
iajs-4071	339	1	̃	̃	ADV
iajs-4071	339	2	̃and	̃and	NUM
iajs-4071	339	3	̃	̃	PROPN
iajs-4071	339	4	̃	̃	PROPN
iajs-4071	339	5	̃	̃	PROPN
iajs-4071	339	6	(	(	PUNCT
iajs-4071	339	7	̃	̃	PROPN
iajs-4071	339	8	)	)	PUNCT
iajs-4071	339	9	,	,	PUNCT
iajs-4071	339	10	then	then	ADV
iajs-4071	339	11	)	)	PUNCT
iajs-4071	339	12	̃	̃	PROPN
iajs-4071	339	13	̃	̃	ADP
iajs-4071	339	14	̃	̃	PROPN
iajs-4071	339	15	̃	̃	NOUN
iajs-4071	339	16	)	)	PUNCT
iajs-4071	339	17	ihjpas	ihjpa	NOUN
iajs-4071	339	18	.	.	PUNCT
iajs-4071	340	1	2025,38(4	2025,38(4	NOUN
iajs-4071	340	2	)	)	PUNCT
iajs-4071	340	3	371	371	NUM
iajs-4071	340	4	proof	proof	NOUN
iajs-4071	340	5	:	:	PUNCT
iajs-4071	340	6	let	let	VERB
iajs-4071	340	7	)	)	PUNCT
iajs-4071	340	8	̃	̃	ADV
iajs-4071	340	9	̃	̃	PROPN
iajs-4071	340	10	̃	̃	PROPN
iajs-4071	340	11	)	)	PUNCT
iajs-4071	340	12	,	,	PUNCT
iajs-4071	340	13	then	then	ADV
iajs-4071	340	14	)	)	PUNCT
iajs-4071	340	15	̃	̃	PROPN
iajs-4071	340	16	̃	̃	PROPN
iajs-4071	340	17	̃	̃	NOUN
iajs-4071	340	18	)	)	PUNCT
iajs-4071	340	19	.	.	PUNCT
iajs-4071	341	1	since	since	SCONJ
iajs-4071	341	2	̃	̃	PROPN
iajs-4071	341	3	̃	̃	PROPN
iajs-4071	341	4	̃	̃	PROPN
iajs-4071	341	5	,	,	PUNCT
iajs-4071	341	6	by	by	ADP
iajs-4071	341	7	proposition	proposition	NOUN
iajs-4071	341	8	2.19	2.19	NUM
iajs-4071	341	9	,	,	PUNCT
iajs-4071	341	10	)	)	PUNCT
iajs-4071	341	11	̃	̃	PROPN
iajs-4071	341	12	̃	̃	ADP
iajs-4071	341	13	̃	̃	NOUN
iajs-4071	341	14	̃	̃	NOUN
iajs-4071	341	15	)	)	PUNCT
iajs-4071	341	16	.	.	PUNCT
iajs-4071	342	1	since	since	SCONJ
iajs-4071	342	2	̃	̃	PROPN
iajs-4071	342	3	̃	̃	PROPN
iajs-4071	342	4	̃	̃	PROPN
iajs-4071	342	5	(	(	PUNCT
iajs-4071	342	6	̃	̃	PROPN
iajs-4071	342	7	)	)	PUNCT
iajs-4071	342	8	)	)	PUNCT
iajs-4071	342	9	)	)	PUNCT
iajs-4071	343	1	̃	̃	NOUN
iajs-4071	343	2	̃	̃	ADP
iajs-4071	343	3	̃	̃	NOUN
iajs-4071	343	4	̃	̃	NOUN
iajs-4071	343	5	)	)	PUNCT
iajs-4071	343	6	.	.	PUNCT
iajs-4071	344	1	and	and	CCONJ
iajs-4071	344	2	̃	̃	PROPN
iajs-4071	344	3	)	)	PUNCT
iajs-4071	344	4	,	,	PUNCT
iajs-4071	344	5	there	there	PRON
iajs-4071	344	6	is	be	VERB
iajs-4071	344	7	)	)	PUNCT
iajs-4071	344	8	̃	̃	PROPN
iajs-4071	344	9	̃	̃	PROPN
iajs-4071	344	10	(	(	PUNCT
iajs-4071	344	11	̃	̃	NOUN
iajs-4071	344	12	)	)	PUNCT
iajs-4071	344	13	̃	̃	PROPN
iajs-4071	344	14	)	)	PUNCT
iajs-4071	344	15	̃	̃	PROPN
iajs-4071	344	16	)	)	PUNCT
iajs-4071	344	17	hence	hence	ADV
iajs-4071	344	18	,	,	PUNCT
iajs-4071	344	19	̃	̃	PROPN
iajs-4071	344	20	)	)	PUNCT
iajs-4071	344	21	̃	̃	NOUN
iajs-4071	344	22	̃	̃	NOUN
iajs-4071	344	23	)	)	PUNCT
iajs-4071	345	1	̃	̃	NOUN
iajs-4071	345	2	by	by	ADP
iajs-4071	345	3	proposition	proposition	NOUN
iajs-4071	345	4	3.23	3.23	NUM
iajs-4071	345	5	.	.	PUNCT
iajs-4071	345	6	)	)	PUNCT
iajs-4071	346	1	̃	̃	NOUN
iajs-4071	346	2	̃	̃	NOUN
iajs-4071	346	3	̃	̃	PROPN
iajs-4071	346	4	(	(	PUNCT
iajs-4071	346	5	̃	̃	PROPN
iajs-4071	346	6	)	)	PUNCT
iajs-4071	346	7	and	and	CCONJ
iajs-4071	346	8	therefore	therefore	ADV
iajs-4071	346	9	,	,	PUNCT
iajs-4071	346	10	)	)	PUNCT
iajs-4071	347	1	̃	̃	SYM
iajs-4071	347	2	̃	̃	NOUN
iajs-4071	347	3	̃	̃	NOUN
iajs-4071	347	4	̃	̃	NOUN
iajs-4071	347	5	)	)	PUNCT
iajs-4071	347	6	.	.	PUNCT
iajs-4071	348	1	4	4	X
iajs-4071	348	2	.	.	X
iajs-4071	348	3	̃	̃	ADV
iajs-4071	348	4	-continuity	-continuity	ADJ
iajs-4071	348	5	in	in	ADP
iajs-4071	348	6	this	this	DET
iajs-4071	348	7	section	section	NOUN
iajs-4071	348	8	we	we	PRON
iajs-4071	348	9	define	define	VERB
iajs-4071	348	10	the	the	DET
iajs-4071	348	11	concept	concept	NOUN
iajs-4071	348	12	of	of	ADP
iajs-4071	348	13	soft	soft	ADJ
iajs-4071	348	14	̃	̃	PROPN
iajs-4071	348	15	-continuous	-continuous	ADJ
iajs-4071	348	16	function	function	NOUN
iajs-4071	348	17	by	by	ADP
iajs-4071	348	18	using	use	VERB
iajs-4071	348	19	soft	soft	ADJ
iajs-4071	348	20	-open	-open	ADJ
iajs-4071	348	21	sets	set	NOUN
iajs-4071	348	22	.	.	PUNCT
iajs-4071	349	1	we	we	PRON
iajs-4071	349	2	then	then	ADV
iajs-4071	349	3	explain	explain	VERB
iajs-4071	349	4	various	various	ADJ
iajs-4071	349	5	properties	property	NOUN
iajs-4071	349	6	of	of	ADP
iajs-4071	349	7	this	this	DET
iajs-4071	349	8	concept	concept	NOUN
iajs-4071	349	9	as	as	ADV
iajs-4071	349	10	well	well	ADV
iajs-4071	349	11	as	as	ADP
iajs-4071	349	12	compare	compare	VERB
iajs-4071	349	13	it	it	PRON
iajs-4071	349	14	to	to	ADP
iajs-4071	349	15	several	several	ADJ
iajs-4071	349	16	other	other	ADJ
iajs-4071	349	17	forms	form	NOUN
iajs-4071	349	18	of	of	ADP
iajs-4071	349	19	soft	soft	ADJ
iajs-4071	349	20	continuous	continuous	ADJ
iajs-4071	349	21	functions	function	NOUN
iajs-4071	349	22	.	.	PUNCT
iajs-4071	350	1	4.1.definition	4.1.definition	NUM
iajs-4071	350	2	4.1	4.1	NUM
iajs-4071	350	3	.	.	PUNCT
iajs-4071	351	1	a	a	DET
iajs-4071	351	2	soft	soft	ADJ
iajs-4071	351	3	function	function	NOUN
iajs-4071	351	4	(	(	PUNCT
iajs-4071	351	5	̃	̃	NOUN
iajs-4071	351	6	̃	̃	ADJ
iajs-4071	351	7	)	)	PUNCT
iajs-4071	351	8	̃	̃	NOUN
iajs-4071	351	9	̃	̃	PROPN
iajs-4071	351	10	)	)	PUNCT
iajs-4071	351	11	is	be	AUX
iajs-4071	351	12	called	call	VERB
iajs-4071	351	13	̃	̃	ADV
iajs-4071	351	14	-continuous	-continuous	ADJ
iajs-4071	351	15	at	at	ADP
iajs-4071	351	16	a	a	DET
iajs-4071	351	17	soft	soft	ADJ
iajs-4071	351	18	point	point	NOUN
iajs-4071	351	19	̃	̃	PROPN
iajs-4071	351	20	̃	̃	PROPN
iajs-4071	351	21	̃	̃	PROPN
iajs-4071	351	22	)	)	PUNCT
iajs-4071	351	23	,	,	PUNCT
iajs-4071	351	24	if	if	SCONJ
iajs-4071	351	25	)	)	PUNCT
iajs-4071	351	26	̃	̃	NOUN
iajs-4071	351	27	̃	̃	NOUN
iajs-4071	351	28	containing	contain	VERB
iajs-4071	351	29	)	)	PUNCT
iajs-4071	351	30	,	,	PUNCT
iajs-4071	351	31	)	)	PUNCT
iajs-4071	352	1	̃	̃	NOUN
iajs-4071	352	2	̃	̃	ADJ
iajs-4071	352	3	o	o	X
iajs-4071	352	4	(	(	PUNCT
iajs-4071	352	5	̃	̃	PROPN
iajs-4071	352	6	)	)	PUNCT
iajs-4071	352	7	containing	contain	VERB
iajs-4071	352	8	s.t	s.t	PROPN
iajs-4071	352	9	.	.	PUNCT
iajs-4071	352	10	)	)	PUNCT
iajs-4071	353	1	̃	̃	ADV
iajs-4071	353	2	)	)	PUNCT
iajs-4071	353	3	and	and	CCONJ
iajs-4071	353	4	it	it	PRON
iajs-4071	353	5	is	be	AUX
iajs-4071	353	6	called	call	VERB
iajs-4071	353	7	̃	̃	PROPN
iajs-4071	353	8	continuous	continuous	ADJ
iajs-4071	353	9	function	function	NOUN
iajs-4071	353	10	,	,	PUNCT
iajs-4071	353	11	if	if	SCONJ
iajs-4071	353	12	is	be	AUX
iajs-4071	353	13	̃	̃	ADV
iajs-4071	353	14	continuous	continuous	ADJ
iajs-4071	353	15	at	at	ADP
iajs-4071	353	16	every	every	DET
iajs-4071	353	17	soft	soft	ADJ
iajs-4071	353	18	point	point	NOUN
iajs-4071	353	19	of	of	ADP
iajs-4071	353	20	̃.	̃.	NOUN
iajs-4071	353	21	4.2	4.2	NUM
iajs-4071	353	22	.	.	PUNCT
iajs-4071	354	1	proposition	proposition	NOUN
iajs-4071	354	2	4.2	4.2	NUM
iajs-4071	354	3	.	.	PUNCT
iajs-4071	355	1	a	a	DET
iajs-4071	355	2	soft	soft	ADJ
iajs-4071	355	3	function	function	NOUN
iajs-4071	355	4	(	(	PUNCT
iajs-4071	355	5	̃	̃	NOUN
iajs-4071	355	6	̃	̃	ADJ
iajs-4071	355	7	)	)	PUNCT
iajs-4071	355	8	̃	̃	NOUN
iajs-4071	355	9	̃	̃	NOUN
iajs-4071	355	10	)	)	PUNCT
iajs-4071	355	11	is	be	AUX
iajs-4071	355	12	̃	̃	ADV
iajs-4071	355	13	-continuous	-continuous	ADJ
iajs-4071	355	14	iff	iff	VERB
iajs-4071	355	15	the	the	DET
iajs-4071	355	16	inverse	inverse	NOUN
iajs-4071	355	17	image	image	NOUN
iajs-4071	355	18	)	)	PUNCT
iajs-4071	356	1	̃	̃	NOUN
iajs-4071	356	2	̃	̃	NOUN
iajs-4071	356	3	o	o	X
iajs-4071	356	4	(	(	PUNCT
iajs-4071	356	5	̃	̃	PROPN
iajs-4071	356	6	)	)	PUNCT
iajs-4071	356	7	,	,	PUNCT
iajs-4071	356	8	)	)	PUNCT
iajs-4071	356	9	̃	̃	NOUN
iajs-4071	356	10	̃	̃	NOUN
iajs-4071	356	11	proof	proof	NOUN
iajs-4071	356	12	:	:	PUNCT
iajs-4071	356	13	suppose	suppose	VERB
iajs-4071	356	14	is	be	AUX
iajs-4071	356	15	̃	̃	ADV
iajs-4071	356	16	-continuous	-continuous	ADJ
iajs-4071	356	17	and	and	CCONJ
iajs-4071	356	18	let	let	VERB
iajs-4071	356	19	)	)	PUNCT
iajs-4071	356	20	̃	̃	ADV
iajs-4071	356	21	̃.	̃.	NOUN
iajs-4071	356	22	we	we	PRON
iajs-4071	356	23	show	show	VERB
iajs-4071	356	24	that	that	PRON
iajs-4071	356	25	)	)	PUNCT
iajs-4071	356	26	)	)	PUNCT
iajs-4071	357	1	̃	̃	NOUN
iajs-4071	357	2	̃	̃	NOUN
iajs-4071	357	3	o	o	X
iajs-4071	357	4	(	(	PUNCT
iajs-4071	357	5	̃	̃	PROPN
iajs-4071	357	6	)	)	PUNCT
iajs-4071	357	7	if	if	SCONJ
iajs-4071	357	8	)	)	PUNCT
iajs-4071	357	9	)	)	PUNCT
iajs-4071	358	1	̃	̃	PROPN
iajs-4071	358	2	,	,	PUNCT
iajs-4071	358	3	then	then	ADV
iajs-4071	358	4	)	)	PUNCT
iajs-4071	358	5	)	)	PUNCT
iajs-4071	359	1	̃	̃	NOUN
iajs-4071	359	2	̃	̃	NOUN
iajs-4071	359	3	o	o	X
iajs-4071	359	4	(	(	PUNCT
iajs-4071	359	5	̃	̃	PROPN
iajs-4071	359	6	)	)	PUNCT
iajs-4071	359	7	if	if	SCONJ
iajs-4071	359	8	)	)	PUNCT
iajs-4071	359	9	)	)	PUNCT
iajs-4071	360	1	̃	̃	PROPN
iajs-4071	360	2	,	,	PUNCT
iajs-4071	360	3	then	then	ADV
iajs-4071	360	4	̃	̃	PROPN
iajs-4071	360	5	)	)	PUNCT
iajs-4071	360	6	)	)	PUNCT
iajs-4071	360	7	which	which	PRON
iajs-4071	360	8	implies	imply	VERB
iajs-4071	360	9	that	that	SCONJ
iajs-4071	360	10	)	)	PUNCT
iajs-4071	361	1	̃	̃	ADV
iajs-4071	361	2	)	)	PUNCT
iajs-4071	361	3	.	.	PUNCT
iajs-4071	362	1	since	since	SCONJ
iajs-4071	362	2	is	be	AUX
iajs-4071	362	3	̃	̃	ADV
iajs-4071	362	4	continuous	continuous	ADJ
iajs-4071	362	5	,	,	PUNCT
iajs-4071	362	6	̃	̃	ADJ
iajs-4071	362	7	)	)	PUNCT
iajs-4071	363	1	̃	̃	NOUN
iajs-4071	363	2	̃	̃	NOUN
iajs-4071	363	3	o	o	X
iajs-4071	363	4	(	(	PUNCT
iajs-4071	363	5	̃	̃	PROPN
iajs-4071	363	6	)	)	PUNCT
iajs-4071	363	7	s.t	s.t	PROPN
iajs-4071	363	8	.	.	PROPN
iajs-4071	363	9	)	)	PUNCT
iajs-4071	363	10	)	)	PUNCT
iajs-4071	364	1	̃	̃	ADV
iajs-4071	364	2	)	)	PUNCT
iajs-4071	364	3	.	.	PUNCT
iajs-4071	365	1	this	this	PRON
iajs-4071	365	2	implies	imply	VERB
iajs-4071	365	3	that	that	SCONJ
iajs-4071	365	4	̃	̃	PROPN
iajs-4071	365	5	)	)	PUNCT
iajs-4071	365	6	̃	̃	NOUN
iajs-4071	365	7	)	)	PUNCT
iajs-4071	365	8	)	)	PUNCT
iajs-4071	365	9	.	.	PUNCT
iajs-4071	366	1	this	this	PRON
iajs-4071	366	2	shows	show	VERB
iajs-4071	366	3	that	that	PRON
iajs-4071	366	4	)	)	PUNCT
iajs-4071	366	5	)	)	PUNCT
iajs-4071	367	1	̃	̃	NOUN
iajs-4071	367	2	̃	̃	NOUN
iajs-4071	367	3	o	o	X
iajs-4071	367	4	(	(	PUNCT
iajs-4071	367	5	̃	̃	NOUN
iajs-4071	367	6	)	)	PUNCT
iajs-4071	367	7	conversely	conversely	ADV
iajs-4071	367	8	,	,	PUNCT
iajs-4071	367	9	let	let	VERB
iajs-4071	367	10	̃	̃	PROPN
iajs-4071	367	11	̃	̃	NOUN
iajs-4071	367	12	̃	̃	NUM
iajs-4071	367	13	)	)	PUNCT
iajs-4071	367	14	)	)	PUNCT
iajs-4071	368	1	̃	̃	ADJ
iajs-4071	368	2	)	)	PUNCT
iajs-4071	368	3	̃	̃	PROPN
iajs-4071	368	4	̃	̃	PROPN
iajs-4071	368	5	,	,	PUNCT
iajs-4071	368	6	then	then	ADV
iajs-4071	368	7	̃	̃	PROPN
iajs-4071	368	8	)	)	PUNCT
iajs-4071	368	9	)	)	PUNCT
iajs-4071	369	1	̃	̃	NOUN
iajs-4071	369	2	̃	̃	PROPN
iajs-4071	369	3	(	(	PUNCT
iajs-4071	369	4	̃	̃	NOUN
iajs-4071	369	5	)	)	PUNCT
iajs-4071	369	6	)	)	PUNCT
iajs-4071	369	7	)	)	PUNCT
iajs-4071	369	8	)	)	PUNCT
iajs-4071	370	1	s.t	s.t	PROPN
iajs-4071	370	2	.	.	PROPN
iajs-4071	370	3	)	)	PUNCT
iajs-4071	370	4	)	)	PUNCT
iajs-4071	370	5	)	)	PUNCT
iajs-4071	370	6	)	)	PUNCT
iajs-4071	370	7	)	)	PUNCT
iajs-4071	371	1	̃	̃	NOUN
iajs-4071	371	2	)	)	PUNCT
iajs-4071	371	3	.	.	PUNCT
iajs-4071	372	1	hence	hence	ADV
iajs-4071	372	2	,	,	PUNCT
iajs-4071	372	3	is	be	AUX
iajs-4071	372	4	̃	̃	ADV
iajs-4071	372	5	-continuous	-continuous	ADJ
iajs-4071	372	6	.	.	PUNCT
iajs-4071	373	1	4.3	4.3	NUM
iajs-4071	373	2	.	.	PUNCT
iajs-4071	373	3	proposition	proposition	NOUN
iajs-4071	373	4	let	let	VERB
iajs-4071	373	5	(	(	PUNCT
iajs-4071	373	6	̃	̃	NOUN
iajs-4071	373	7	̃	̃	ADJ
iajs-4071	373	8	)	)	PUNCT
iajs-4071	373	9	̃	̃	NOUN
iajs-4071	373	10	̃	̃	NOUN
iajs-4071	373	11	)	)	PUNCT
iajs-4071	373	12	1	1	X
iajs-4071	373	13	.	.	PUNCT
iajs-4071	373	14	is	be	AUX
iajs-4071	373	15	̃	̃	ADV
iajs-4071	373	16	continuous	continuous	ADJ
iajs-4071	373	17	,	,	PUNCT
iajs-4071	373	18	if	if	SCONJ
iajs-4071	373	19	is	be	AUX
iajs-4071	373	20	a	a	DET
iajs-4071	373	21	̃	̃	ADV
iajs-4071	373	22	-continuous	-continuous	ADJ
iajs-4071	373	23	.	.	PUNCT
iajs-4071	374	1	2	2	X
iajs-4071	374	2	.	.	X
iajs-4071	374	3	is	be	AUX
iajs-4071	374	4	̃	̃	ADV
iajs-4071	374	5	-continuous	-continuous	ADJ
iajs-4071	374	6	,	,	PUNCT
iajs-4071	374	7	if	if	SCONJ
iajs-4071	374	8	is	be	AUX
iajs-4071	374	9	a	a	DET
iajs-4071	374	10	̃	̃	PROPN
iajs-4071	374	11	(	(	PUNCT
iajs-4071	374	12	resp	resp	NOUN
iajs-4071	374	13	.	.	PUNCT
iajs-4071	375	1	̃	̃	ADJ
iajs-4071	375	2	-continuous	-continuous	ADJ
iajs-4071	375	3	,	,	PUNCT
iajs-4071	375	4	̃	̃	PROPN
iajs-4071	375	5	̃	̃	NOUN
iajs-4071	375	6	̃	̃	NOUN
iajs-4071	375	7	c	c	X
iajs-4071	376	1	̃	̃	NOUN
iajs-4071	376	2	̃	̃	ADP
iajs-4071	376	3	̃	̃	PROPN
iajs-4071	376	4	and	and	CCONJ
iajs-4071	376	5	soft	soft	ADJ
iajs-4071	376	6	perfectly	perfectly	ADV
iajs-4071	376	7	continuous	continuous	ADJ
iajs-4071	376	8	)	)	PUNCT
iajs-4071	376	9	proof	proof	NOUN
iajs-4071	376	10	:	:	PUNCT
iajs-4071	376	11	by	by	ADP
iajs-4071	376	12	̃	̃	PROPN
iajs-4071	376	13	(	(	PUNCT
iajs-4071	376	14	̃	̃	NOUN
iajs-4071	376	15	)	)	PUNCT
iajs-4071	376	16	̃	̃	NOUN
iajs-4071	376	17	̃	̃	PROPN
iajs-4071	376	18	(	(	PUNCT
iajs-4071	376	19	̃	̃	NOUN
iajs-4071	376	20	)	)	PUNCT
iajs-4071	376	21	and	and	CCONJ
iajs-4071	376	22	proposition	proposition	NOUN
iajs-4071	376	23	4.2	4.2	NUM
iajs-4071	376	24	.	.	PUNCT
iajs-4071	377	1	we	we	PRON
iajs-4071	377	2	get	get	VERB
iajs-4071	377	3	prove	prove	ADJ
iajs-4071	377	4	(	(	PUNCT
iajs-4071	377	5	1	1	NUM
iajs-4071	377	6	)	)	PUNCT
iajs-4071	377	7	.	.	PUNCT
iajs-4071	378	1	and	and	CCONJ
iajs-4071	378	2	by	by	ADP
iajs-4071	378	3	proposition	proposition	NOUN
iajs-4071	378	4	3.6	3.6	NUM
iajs-4071	378	5	.	.	PUNCT
iajs-4071	379	1	and	and	CCONJ
iajs-4071	379	2	proposition	proposition	NOUN
iajs-4071	379	3	4.2	4.2	NUM
iajs-4071	379	4	.	.	PUNCT
iajs-4071	380	1	prove	prove	VERB
iajs-4071	380	2	(	(	PUNCT
iajs-4071	380	3	2	2	X
iajs-4071	380	4	)	)	PUNCT
iajs-4071	380	5	will	will	AUX
iajs-4071	380	6	follow	follow	VERB
iajs-4071	380	7	.	.	PUNCT
iajs-4071	381	1	the	the	DET
iajs-4071	381	2	following	follow	VERB
iajs-4071	381	3	examples	example	NOUN
iajs-4071	381	4	illustrate	illustrate	VERB
iajs-4071	381	5	the	the	DET
iajs-4071	381	6	previous	previous	ADJ
iajs-4071	381	7	remark	remark	NOUN
iajs-4071	381	8	.	.	PUNCT
iajs-4071	382	1	example	example	NOUN
iajs-4071	382	2	consider	consider	VERB
iajs-4071	382	3	the	the	DET
iajs-4071	382	4	soft	soft	ADJ
iajs-4071	382	5	topology	topology	NOUN
iajs-4071	382	6	̃	̃	PROPN
iajs-4071	382	7	{	{	PUNCT
iajs-4071	382	8	̃	̃	NOUN
iajs-4071	382	9	̃	̃	PROPN
iajs-4071	382	10	(	(	PUNCT
iajs-4071	382	11	)	)	PUNCT
iajs-4071	382	12	(	(	PUNCT
iajs-4071	382	13	)	)	PUNCT
iajs-4071	382	14	}	}	PUNCT
iajs-4071	383	1	in	in	ADP
iajs-4071	383	2	example	example	NOUN
iajs-4071	383	3	3.5	3.5	NUM
iajs-4071	383	4	.	.	PUNCT
iajs-4071	384	1	then	then	ADV
iajs-4071	384	2	the	the	DET
iajs-4071	384	3	identity	identity	NOUN
iajs-4071	384	4	function	function	NOUN
iajs-4071	384	5	(	(	PUNCT
iajs-4071	384	6	̃	̃	NOUN
iajs-4071	384	7	̃	̃	ADJ
iajs-4071	384	8	)	)	PUNCT
iajs-4071	384	9	̃	̃	NOUN
iajs-4071	384	10	̃	̃	NOUN
iajs-4071	384	11	)	)	PUNCT
iajs-4071	384	12	is	be	AUX
iajs-4071	384	13	̃	̃	ADV
iajs-4071	384	14	-continuous	-continuous	ADJ
iajs-4071	384	15	but	but	CCONJ
iajs-4071	384	16	not	not	PART
iajs-4071	384	17	̃	̃	NOUN
iajs-4071	384	18	-continuous	-continuous	ADJ
iajs-4071	384	19	since	since	SCONJ
iajs-4071	384	20	(	(	PUNCT
iajs-4071	384	21	)	)	PUNCT
iajs-4071	384	22	̃	̃	ADV
iajs-4071	384	23	̃	̃	PROPN
iajs-4071	384	24	,	,	PUNCT
iajs-4071	384	25	but	but	CCONJ
iajs-4071	384	26	(	(	PUNCT
iajs-4071	384	27	)	)	PUNCT
iajs-4071	384	28	(	(	PUNCT
iajs-4071	384	29	)	)	PUNCT
iajs-4071	384	30	̃	̃	NOUN
iajs-4071	384	31	̃	̃	NOUN
iajs-4071	384	32	o	o	X
iajs-4071	384	33	(	(	PUNCT
iajs-4071	384	34	̃	̃	PROPN
iajs-4071	384	35	)	)	PUNCT
iajs-4071	384	36	.	.	PUNCT
iajs-4071	385	1	1	1	X
iajs-4071	385	2	.	.	X
iajs-4071	385	3	consider	consider	VERB
iajs-4071	385	4	the	the	DET
iajs-4071	385	5	soft	soft	ADJ
iajs-4071	385	6	topology	topology	NOUN
iajs-4071	385	7	̃	̃	PROPN
iajs-4071	385	8	{	{	PUNCT
iajs-4071	385	9	̃	̃	NOUN
iajs-4071	385	10	̃	̃	PROPN
iajs-4071	385	11	(	(	PUNCT
iajs-4071	385	12	)	)	PUNCT
iajs-4071	385	13	(	(	PUNCT
iajs-4071	385	14	)	)	PUNCT
iajs-4071	385	15	)	)	PUNCT
iajs-4071	385	16	}	}	PUNCT
iajs-4071	385	17	in	in	ADP
iajs-4071	385	18	example	example	NOUN
iajs-4071	385	19	3.5	3.5	NUM
iajs-4071	385	20	.	.	PUNCT
iajs-4071	386	1	then	then	ADV
iajs-4071	386	2	the	the	DET
iajs-4071	386	3	identity	identity	NOUN
iajs-4071	386	4	function	function	NOUN
iajs-4071	386	5	(	(	PUNCT
iajs-4071	386	6	̃	̃	NOUN
iajs-4071	386	7	̃	̃	ADJ
iajs-4071	386	8	)	)	PUNCT
iajs-4071	386	9	̃	̃	NOUN
iajs-4071	386	10	̃	̃	NOUN
iajs-4071	386	11	)	)	PUNCT
iajs-4071	386	12	is	be	AUX
iajs-4071	386	13	̃	̃	ADV
iajs-4071	386	14	-continuous	-continuous	ADJ
iajs-4071	386	15	but	but	CCONJ
iajs-4071	386	16	is	be	AUX
iajs-4071	386	17	not	not	PART
iajs-4071	386	18	̃	̃	ADJ
iajs-4071	386	19	,	,	PUNCT
iajs-4071	386	20	̃	̃	NOUN
iajs-4071	386	21	continuous	continuous	ADJ
iajs-4071	386	22	,	,	PUNCT
iajs-4071	386	23	̃	̃	PROPN
iajs-4071	386	24	̃	̃	NOUN
iajs-4071	386	25	̃	̃	NOUN
iajs-4071	386	26	c	c	X
iajs-4071	386	27	̃	̃	ADJ
iajs-4071	386	28	and	and	CCONJ
iajs-4071	386	29	soft	soft	ADJ
iajs-4071	386	30	perfectly	perfectly	ADV
iajs-4071	386	31	continuous	continuous	ADJ
iajs-4071	386	32	.	.	PUNCT
iajs-4071	387	1	since	since	SCONJ
iajs-4071	387	2	(	(	PUNCT
iajs-4071	387	3	)	)	PUNCT
iajs-4071	387	4	̃	̃	ADV
iajs-4071	387	5	̃,then	̃,then	NOUN
iajs-4071	387	6	(	(	PUNCT
iajs-4071	387	7	)	)	PUNCT
iajs-4071	387	8	̃	̃	NOUN
iajs-4071	387	9	̃	̃	ADJ
iajs-4071	387	10	o	o	NOUN
iajs-4071	387	11	(	(	PUNCT
iajs-4071	387	12	̃)but	̃)but	PROPN
iajs-4071	387	13	(	(	PUNCT
iajs-4071	387	14	)	)	PUNCT
iajs-4071	387	15	is	be	AUX
iajs-4071	387	16	not	not	PART
iajs-4071	387	17	̃	̃	ADJ
iajs-4071	387	18	,	,	PUNCT
iajs-4071	387	19	̃	̃	NOUN
iajs-4071	387	20	-open	-open	ADJ
iajs-4071	387	21	,	,	PUNCT
iajs-4071	387	22	̃	̃	PROPN
iajs-4071	387	23	̃	̃	NOUN
iajs-4071	387	24	̃	̃	NOUN
iajs-4071	387	25	̃	̃	NOUN
iajs-4071	387	26	c	c	X
iajs-4071	387	27	̃	̃	ADJ
iajs-4071	387	28	and	and	CCONJ
iajs-4071	387	29	soft	soft	ADJ
iajs-4071	387	30	clopen	clopen	ADJ
iajs-4071	387	31	.	.	PUNCT
iajs-4071	388	1	ihjpas	ihjpas	PROPN
iajs-4071	388	2	.	.	PUNCT
iajs-4071	389	1	2025,38(4	2025,38(4	NOUN
iajs-4071	389	2	)	)	PUNCT
iajs-4071	389	3	372	372	NUM
iajs-4071	389	4	2	2	NUM
iajs-4071	389	5	.	.	PUNCT
iajs-4071	389	6	consider	consider	VERB
iajs-4071	389	7	the	the	DET
iajs-4071	389	8	soft	soft	ADJ
iajs-4071	389	9	topology	topology	NOUN
iajs-4071	389	10	̃	̃	PROPN
iajs-4071	389	11	{	{	PUNCT
iajs-4071	389	12	̃	̃	NOUN
iajs-4071	389	13	̃	̃	PROPN
iajs-4071	389	14	(	(	PUNCT
iajs-4071	389	15	)	)	PUNCT
iajs-4071	389	16	(	(	PUNCT
iajs-4071	389	17	)	)	PUNCT
iajs-4071	389	18	}	}	PUNCT
iajs-4071	389	19	̃	̃	PROPN
iajs-4071	389	20	{	{	PUNCT
iajs-4071	389	21	̃	̃	NOUN
iajs-4071	389	22	̃	̃	PROPN
iajs-4071	389	23	(	(	PUNCT
iajs-4071	389	24	)	)	PUNCT
iajs-4071	389	25	(	(	PUNCT
iajs-4071	389	26	)	)	PUNCT
iajs-4071	389	27	)	)	PUNCT
iajs-4071	389	28	}	}	PUNCT
iajs-4071	390	1	in	in	ADP
iajs-4071	390	2	example	example	NOUN
iajs-4071	390	3	3.5	3.5	NUM
iajs-4071	390	4	.	.	PUNCT
iajs-4071	391	1	then	then	ADV
iajs-4071	391	2	(	(	PUNCT
iajs-4071	391	3	̃	̃	NOUN
iajs-4071	391	4	̃	̃	NOUN
iajs-4071	391	5	)	)	PUNCT
iajs-4071	391	6	(	(	PUNCT
iajs-4071	391	7	̃	̃	NOUN
iajs-4071	391	8	̃	̃	PROPN
iajs-4071	391	9	)	)	PUNCT
iajs-4071	391	10	is	be	AUX
iajs-4071	391	11	̃	̃	ADV
iajs-4071	391	12	-continuous	-continuous	ADJ
iajs-4071	391	13	but	but	CCONJ
iajs-4071	391	14	is	be	AUX
iajs-4071	391	15	not	not	PART
iajs-4071	391	16	̃	̃	ADV
iajs-4071	391	17	̃	̃	ADJ
iajs-4071	391	18	since	since	SCONJ
iajs-4071	391	19	(	(	PUNCT
iajs-4071	391	20	)	)	PUNCT
iajs-4071	391	21	̃	̃	PROPN
iajs-4071	391	22	̃	̃	PROPN
iajs-4071	391	23	,	,	PUNCT
iajs-4071	391	24	but	but	CCONJ
iajs-4071	391	25	(	(	PUNCT
iajs-4071	391	26	)	)	PUNCT
iajs-4071	391	27	(	(	PUNCT
iajs-4071	391	28	)	)	PUNCT
iajs-4071	391	29	is	be	AUX
iajs-4071	391	30	not	not	PART
iajs-4071	391	31	̃	̃	ADV
iajs-4071	391	32	and	and	CCONJ
iajs-4071	391	33	̃	̃	ADV
iajs-4071	391	34	open	open	ADJ
iajs-4071	391	35	.	.	PUNCT
iajs-4071	392	1	4.4.proposition	4.4.proposition	NOUN
iajs-4071	392	2	a	a	DET
iajs-4071	392	3	soft	soft	ADJ
iajs-4071	392	4	function	function	NOUN
iajs-4071	392	5	(	(	PUNCT
iajs-4071	392	6	̃	̃	NOUN
iajs-4071	392	7	̃	̃	ADJ
iajs-4071	392	8	)	)	PUNCT
iajs-4071	392	9	̃	̃	NOUN
iajs-4071	392	10	̃	̃	NOUN
iajs-4071	392	11	)	)	PUNCT
iajs-4071	392	12	is	be	AUX
iajs-4071	392	13	̃	̃	ADV
iajs-4071	392	14	continuous	continuous	ADJ
iajs-4071	392	15	iff	iff	PROPN
iajs-4071	392	16	is	be	AUX
iajs-4071	392	17	a	a	DET
iajs-4071	392	18	soft	soft	ADJ
iajs-4071	392	19	-continuous	-continuous	ADJ
iajs-4071	392	20	and	and	CCONJ
iajs-4071	392	21	̃	̃	NOUN
iajs-4071	392	22	̃	̃	PROPN
iajs-4071	392	23	and	and	CCONJ
iajs-4071	392	24	)	)	PUNCT
iajs-4071	393	1	̃	̃	NOUN
iajs-4071	393	2	̃	̃	NOUN
iajs-4071	393	3	containing	contain	VERB
iajs-4071	393	4	)	)	PUNCT
iajs-4071	393	5	,	,	PUNCT
iajs-4071	393	6	)	)	PUNCT
iajs-4071	394	1	̃	̃	PROPN
iajs-4071	394	2	̃	̃	PROPN
iajs-4071	394	3	̃	̃	PROPN
iajs-4071	394	4	)	)	PUNCT
iajs-4071	394	5	s.t	s.t	PROPN
iajs-4071	394	6	)	)	PUNCT
iajs-4071	394	7	)	)	PUNCT
iajs-4071	395	1	̃	̃	ADV
iajs-4071	395	2	)	)	PUNCT
iajs-4071	395	3	.	.	PUNCT
iajs-4071	396	1	proof	proof	NOUN
iajs-4071	396	2	:	:	PUNCT
iajs-4071	396	3	let	let	VERB
iajs-4071	396	4	(	(	PUNCT
iajs-4071	396	5	̃	̃	ADV
iajs-4071	396	6	̃	̃	ADJ
iajs-4071	396	7	)	)	PUNCT
iajs-4071	396	8	̃	̃	NOUN
iajs-4071	396	9	̃	̃	PROPN
iajs-4071	396	10	)	)	PUNCT
iajs-4071	396	11	be	be	VERB
iajs-4071	396	12	a	a	DET
iajs-4071	396	13	̃	̃	ADV
iajs-4071	396	14	continuous	continuous	ADJ
iajs-4071	396	15	function	function	NOUN
iajs-4071	396	16	and	and	CCONJ
iajs-4071	396	17	also	also	ADV
iajs-4071	396	18	let	let	VERB
iajs-4071	396	19	̃	̃	PROPN
iajs-4071	396	20	̃	̃	NOUN
iajs-4071	396	21	̃	̃	NUM
iajs-4071	396	22	)	)	PUNCT
iajs-4071	396	23	and	and	CCONJ
iajs-4071	396	24	)	)	PUNCT
iajs-4071	396	25	̃	̃	NOUN
iajs-4071	396	26	̃	̃	NOUN
iajs-4071	396	27	containing	contain	VERB
iajs-4071	396	28	)	)	PUNCT
iajs-4071	396	29	.	.	PUNCT
iajs-4071	397	1	by	by	ADP
iajs-4071	397	2	assumption	assumption	NOUN
iajs-4071	397	3	,	,	PUNCT
iajs-4071	397	4	̃	̃	PROPN
iajs-4071	397	5	)	)	PUNCT
iajs-4071	397	6	̃	̃	PROPN
iajs-4071	397	7	̃	̃	PROPN
iajs-4071	397	8	̃	̃	PROPN
iajs-4071	397	9	)	)	PUNCT
iajs-4071	397	10	s.t	s.t	PROPN
iajs-4071	397	11	.	.	PROPN
iajs-4071	397	12	)	)	PUNCT
iajs-4071	397	13	)	)	PUNCT
iajs-4071	398	1	̃	̃	ADV
iajs-4071	398	2	)	)	PUNCT
iajs-4071	398	3	.	.	PUNCT
iajs-4071	399	1	since	since	SCONJ
iajs-4071	399	2	)	)	PUNCT
iajs-4071	399	3	̃	̃	PROPN
iajs-4071	399	4	̃	̃	PROPN
iajs-4071	399	5	̃	̃	NOUN
iajs-4071	399	6	)	)	PUNCT
iajs-4071	399	7	)	)	PUNCT
iajs-4071	400	1	̃	̃	PROPN
iajs-4071	400	2	̃	̃	PROPN
iajs-4071	400	3	̃	̃	NOUN
iajs-4071	400	4	)	)	PUNCT
iajs-4071	400	5	s.t	s.t	PROPN
iajs-4071	400	6	̃	̃	ADV
iajs-4071	400	7	)	)	PUNCT
iajs-4071	400	8	̃	̃	PROPN
iajs-4071	400	9	)	)	PUNCT
iajs-4071	400	10	.	.	PUNCT
iajs-4071	401	1	this	this	PRON
iajs-4071	401	2	implies	imply	VERB
iajs-4071	401	3	that	that	SCONJ
iajs-4071	401	4	)	)	PUNCT
iajs-4071	402	1	̃	̃	ADV
iajs-4071	402	2	)	)	PUNCT
iajs-4071	402	3	.	.	PUNCT
iajs-4071	403	1	therefore	therefore	ADV
iajs-4071	403	2	,	,	PUNCT
iajs-4071	403	3	is	be	AUX
iajs-4071	403	4	̃	̃	ADV
iajs-4071	403	5	continuous	continuous	ADJ
iajs-4071	403	6	.	.	PUNCT
iajs-4071	404	1	then	then	ADV
iajs-4071	404	2	is	be	AUX
iajs-4071	404	3	soft	soft	ADJ
iajs-4071	404	4	continuous	continuous	ADJ
iajs-4071	404	5	.	.	PUNCT
iajs-4071	405	1	conversely	conversely	ADV
iajs-4071	405	2	,	,	PUNCT
iajs-4071	405	3	suppose	suppose	VERB
iajs-4071	405	4	)	)	PUNCT
iajs-4071	406	1	̃	̃	ADV
iajs-4071	406	2	̃.	̃.	NOUN
iajs-4071	406	3	we	we	PRON
iajs-4071	406	4	have	have	VERB
iajs-4071	406	5	to	to	PART
iajs-4071	406	6	show	show	VERB
iajs-4071	406	7	that	that	PRON
iajs-4071	406	8	)	)	PUNCT
iajs-4071	406	9	)	)	PUNCT
iajs-4071	407	1	̃	̃	PROPN
iajs-4071	407	2	̃	̃	NOUN
iajs-4071	407	3	̃	̃	NOUN
iajs-4071	407	4	)	)	PUNCT
iajs-4071	407	5	.	.	PUNCT
iajs-4071	408	1	since	since	SCONJ
iajs-4071	408	2	is	be	AUX
iajs-4071	408	3	soft	soft	ADJ
iajs-4071	408	4	-continuous	-continuous	ADJ
iajs-4071	408	5	,	,	PUNCT
iajs-4071	408	6	then	then	ADV
iajs-4071	408	7	)	)	PUNCT
iajs-4071	408	8	)	)	PUNCT
iajs-4071	409	1	̃	̃	PROPN
iajs-4071	409	2	̃	̃	NOUN
iajs-4071	409	3	̃	̃	NUM
iajs-4071	409	4	)	)	PUNCT
iajs-4071	409	5	.	.	PUNCT
iajs-4071	410	1	let	let	VERB
iajs-4071	410	2	̃	̃	ADV
iajs-4071	410	3	)	)	PUNCT
iajs-4071	410	4	)	)	PUNCT
iajs-4071	410	5	.	.	PUNCT
iajs-4071	411	1	then	then	ADV
iajs-4071	411	2	)	)	PUNCT
iajs-4071	411	3	̃	̃	NOUN
iajs-4071	411	4	)	)	PUNCT
iajs-4071	411	5	.	.	PUNCT
iajs-4071	412	1	by	by	ADP
iajs-4071	412	2	hypothesis	hypothesis	NOUN
iajs-4071	412	3	̃	̃	PROPN
iajs-4071	412	4	)	)	PUNCT
iajs-4071	413	1	̃	̃	PROPN
iajs-4071	413	2	̃	̃	PROPN
iajs-4071	413	3	̃	̃	PROPN
iajs-4071	413	4	)	)	PUNCT
iajs-4071	413	5	s.t	s.t	PROPN
iajs-4071	413	6	.	.	PROPN
iajs-4071	413	7	)	)	PUNCT
iajs-4071	413	8	)	)	PUNCT
iajs-4071	414	1	̃	̃	ADV
iajs-4071	414	2	)	)	PUNCT
iajs-4071	414	3	,	,	PUNCT
iajs-4071	414	4	which	which	PRON
iajs-4071	414	5	implies	imply	VERB
iajs-4071	414	6	that	that	SCONJ
iajs-4071	414	7	̃	̃	PROPN
iajs-4071	414	8	)	)	PUNCT
iajs-4071	414	9	̃	̃	NOUN
iajs-4071	414	10	)	)	PUNCT
iajs-4071	414	11	)	)	PUNCT
iajs-4071	414	12	,	,	PUNCT
iajs-4071	414	13	therefore	therefore	ADV
iajs-4071	414	14	)	)	PUNCT
iajs-4071	414	15	)	)	PUNCT
iajs-4071	415	1	̃	̃	PROPN
iajs-4071	415	2	̃	̃	PROPN
iajs-4071	415	3	̃	̃	NOUN
iajs-4071	415	4	)	)	PUNCT
iajs-4071	415	5	.hence	.hence	ADP
iajs-4071	415	6	by	by	ADP
iajs-4071	415	7	proposition	proposition	NOUN
iajs-4071	415	8	4.2	4.2	NUM
iajs-4071	415	9	is	be	AUX
iajs-4071	415	10	̃	̃	ADV
iajs-4071	415	11	-continuous	-continuous	ADJ
iajs-4071	415	12	.	.	PUNCT
iajs-4071	416	1	4.5	4.5	NUM
iajs-4071	416	2	.	.	PUNCT
iajs-4071	416	3	proposition	proposition	NOUN
iajs-4071	416	4	if	if	SCONJ
iajs-4071	416	5	̃	̃	NOUN
iajs-4071	416	6	is	be	AUX
iajs-4071	416	7	soft	soft	ADJ
iajs-4071	416	8	-space	-space	NOUN
iajs-4071	416	9	in	in	ADP
iajs-4071	416	10	(	(	PUNCT
iajs-4071	416	11	̃	̃	NOUN
iajs-4071	416	12	̃	̃	ADJ
iajs-4071	416	13	)	)	PUNCT
iajs-4071	416	14	̃	̃	NOUN
iajs-4071	416	15	̃	̃	NOUN
iajs-4071	416	16	)	)	PUNCT
iajs-4071	416	17	the	the	DET
iajs-4071	416	18	following	follow	VERB
iajs-4071	416	19	properties	property	NOUN
iajs-4071	416	20	are	be	AUX
iajs-4071	416	21	equivalent	equivalent	ADJ
iajs-4071	416	22	.	.	PUNCT
iajs-4071	417	1	1	1	X
iajs-4071	417	2	.	.	X
iajs-4071	417	3	is	be	AUX
iajs-4071	417	4	̃	̃	ADV
iajs-4071	417	5	-continuous	-continuous	ADJ
iajs-4071	417	6	.	.	PUNCT
iajs-4071	418	1	2	2	X
iajs-4071	418	2	.	.	X
iajs-4071	418	3	is	be	AUX
iajs-4071	418	4	̃	̃	ADV
iajs-4071	418	5	-continuous	-continuous	ADJ
iajs-4071	418	6	.	.	PUNCT
iajs-4071	419	1	3	3	X
iajs-4071	419	2	.	.	X
iajs-4071	419	3	is	be	AUX
iajs-4071	419	4	̃	̃	ADV
iajs-4071	419	5	-continuous	-continuous	ADJ
iajs-4071	419	6	.	.	PUNCT
iajs-4071	420	1	proof	proof	NOUN
iajs-4071	420	2	:	:	PUNCT
iajs-4071	420	3	by	by	ADP
iajs-4071	420	4	proposition	proposition	NOUN
iajs-4071	420	5	3.8	3.8	NUM
iajs-4071	420	6	4.6.proposition	4.6.proposition	NUM
iajs-4071	420	7	if	if	SCONJ
iajs-4071	420	8	a	a	DET
iajs-4071	420	9	soft	soft	ADJ
iajs-4071	420	10	function	function	NOUN
iajs-4071	420	11	(	(	PUNCT
iajs-4071	420	12	̃	̃	NOUN
iajs-4071	420	13	̃	̃	ADJ
iajs-4071	420	14	)	)	PUNCT
iajs-4071	420	15	̃	̃	NOUN
iajs-4071	420	16	̃	̃	PROPN
iajs-4071	420	17	)	)	PUNCT
iajs-4071	420	18	,	,	PUNCT
iajs-4071	420	19	is	be	AUX
iajs-4071	420	20	soft	soft	ADJ
iajs-4071	420	21	continuous	continuous	ADJ
iajs-4071	420	22	,	,	PUNCT
iajs-4071	420	23	and	and	CCONJ
iajs-4071	420	24	̃	̃	NOUN
iajs-4071	420	25	is	be	AUX
iajs-4071	420	26	soft	soft	ADJ
iajs-4071	420	27	space	space	NOUN
iajs-4071	420	28	,	,	PUNCT
iajs-4071	420	29	then	then	ADV
iajs-4071	420	30	is	be	AUX
iajs-4071	420	31	̃	̃	ADV
iajs-4071	420	32	-continuous	-continuous	ADJ
iajs-4071	420	33	.	.	PUNCT
iajs-4071	421	1	4.7.proposition	4.7.proposition	NOUN
iajs-4071	421	2	if	if	SCONJ
iajs-4071	421	3	(	(	PUNCT
iajs-4071	421	4	̃	̃	NOUN
iajs-4071	421	5	̃	̃	ADJ
iajs-4071	421	6	)	)	PUNCT
iajs-4071	421	7	̃	̃	NOUN
iajs-4071	421	8	̃	̃	PROPN
iajs-4071	421	9	)	)	PUNCT
iajs-4071	421	10	,	,	PUNCT
iajs-4071	421	11	is	be	AUX
iajs-4071	421	12	soft	soft	ADJ
iajs-4071	421	13	continuous	continuous	ADJ
iajs-4071	421	14	,	,	PUNCT
iajs-4071	421	15	and	and	CCONJ
iajs-4071	421	16	̃	̃	NOUN
iajs-4071	421	17	is	be	AUX
iajs-4071	421	18	soft	soft	ADJ
iajs-4071	421	19	regular	regular	ADJ
iajs-4071	421	20	space	space	NOUN
iajs-4071	421	21	,	,	PUNCT
iajs-4071	421	22	then	then	ADV
iajs-4071	421	23	is	be	AUX
iajs-4071	421	24	̃	̃	ADV
iajs-4071	421	25	-continuous	-continuous	ADJ
iajs-4071	421	26	.	.	PUNCT
iajs-4071	422	1	proof	proof	NOUN
iajs-4071	422	2	:	:	PUNCT
iajs-4071	422	3	by	by	ADP
iajs-4071	422	4	proposition	proposition	NOUN
iajs-4071	422	5	4.2	4.2	NUM
iajs-4071	422	6	and	and	CCONJ
iajs-4071	422	7	proposition	proposition	NOUN
iajs-4071	422	8	3.18	3.18	NUM
iajs-4071	422	9	we	we	PRON
iajs-4071	422	10	get	get	VERB
iajs-4071	422	11	the	the	DET
iajs-4071	422	12	prove	prove	NOUN
iajs-4071	422	13	.	.	PUNCT
iajs-4071	423	1	4.8	4.8	NUM
iajs-4071	423	2	.	.	PUNCT
iajs-4071	423	3	proposition	proposition	NOUN
iajs-4071	423	4	if	if	SCONJ
iajs-4071	423	5	(	(	PUNCT
iajs-4071	423	6	̃	̃	NOUN
iajs-4071	423	7	̃	̃	ADJ
iajs-4071	423	8	)	)	PUNCT
iajs-4071	423	9	̃	̃	NOUN
iajs-4071	423	10	̃	̃	PROPN
iajs-4071	423	11	)	)	PUNCT
iajs-4071	423	12	,	,	PUNCT
iajs-4071	423	13	is	be	AUX
iajs-4071	423	14	soft	soft	ADJ
iajs-4071	423	15	continuous	continuous	ADJ
iajs-4071	423	16	,	,	PUNCT
iajs-4071	423	17	and	and	CCONJ
iajs-4071	423	18	̃	̃	NOUN
iajs-4071	423	19	is	be	AUX
iajs-4071	423	20	seds	sed	NOUN
iajs-4071	423	21	,	,	PUNCT
iajs-4071	423	22	then	then	ADV
iajs-4071	423	23	is	be	AUX
iajs-4071	423	24	̃	̃	ADV
iajs-4071	423	25	-continuous	-continuous	ADJ
iajs-4071	423	26	(	(	PUNCT
iajs-4071	423	27	resp	resp	NOUN
iajs-4071	423	28	.	.	PUNCT
iajs-4071	423	29	,	,	PUNCT
iajs-4071	424	1	̃	̃	NOUN
iajs-4071	424	2	continuous	continuous	ADJ
iajs-4071	424	3	)	)	PUNCT
iajs-4071	424	4	.	.	PUNCT
iajs-4071	425	1	proof	proof	NOUN
iajs-4071	425	2	:	:	PUNCT
iajs-4071	425	3	by	by	ADP
iajs-4071	425	4	proposition	proposition	NOUN
iajs-4071	425	5	4.2	4.2	NUM
iajs-4071	425	6	and	and	CCONJ
iajs-4071	425	7	proposition	proposition	NOUN
iajs-4071	425	8	3.13(resp	3.13(resp	NUM
iajs-4071	425	9	.	.	NUM
iajs-4071	425	10	,	,	PUNCT
iajs-4071	425	11	proposition	proposition	NOUN
iajs-4071	425	12	3.14	3.14	NUM
iajs-4071	425	13	)	)	PUNCT
iajs-4071	425	14	we	we	PRON
iajs-4071	425	15	get	get	VERB
iajs-4071	425	16	the	the	DET
iajs-4071	425	17	prove	prove	NOUN
iajs-4071	425	18	.	.	PUNCT
iajs-4071	426	1	4.9.proposition	4.9.proposition	PRON
iajs-4071	426	2	if	if	SCONJ
iajs-4071	426	3	̃	̃	PROPN
iajs-4071	426	4	is	be	AUX
iajs-4071	426	5	soft	soft	ADJ
iajs-4071	426	6	locally	locally	ADV
iajs-4071	426	7	indiscrete	indiscrete	ADJ
iajs-4071	426	8	space	space	NOUN
iajs-4071	426	9	in	in	ADP
iajs-4071	426	10	(	(	PUNCT
iajs-4071	426	11	̃	̃	NOUN
iajs-4071	426	12	̃	̃	ADJ
iajs-4071	426	13	)	)	PUNCT
iajs-4071	426	14	̃	̃	NOUN
iajs-4071	426	15	̃	̃	NOUN
iajs-4071	426	16	)	)	PUNCT
iajs-4071	426	17	the	the	DET
iajs-4071	426	18	following	follow	VERB
iajs-4071	426	19	properties	property	NOUN
iajs-4071	426	20	are	be	AUX
iajs-4071	426	21	equivalent	equivalent	ADJ
iajs-4071	426	22	.	.	PUNCT
iajs-4071	427	1	1	1	X
iajs-4071	427	2	.	.	X
iajs-4071	427	3	is	be	AUX
iajs-4071	427	4	̃	̃	ADV
iajs-4071	427	5	-continuous	-continuous	ADJ
iajs-4071	427	6	.	.	PUNCT
iajs-4071	428	1	2	2	X
iajs-4071	428	2	.	.	X
iajs-4071	428	3	is	be	AUX
iajs-4071	428	4	̃	̃	ADV
iajs-4071	428	5	-continuous	-continuous	ADJ
iajs-4071	428	6	.	.	PUNCT
iajs-4071	429	1	3	3	X
iajs-4071	429	2	.	.	X
iajs-4071	429	3	is	be	AUX
iajs-4071	429	4	̃	̃	ADV
iajs-4071	429	5	-continuous	-continuous	ADJ
iajs-4071	429	6	.	.	PUNCT
iajs-4071	430	1	proof	proof	NOUN
iajs-4071	430	2	:	:	PUNCT
iajs-4071	430	3	by	by	ADP
iajs-4071	430	4	proposition	proposition	NOUN
iajs-4071	430	5	3.15	3.15	NUM
iajs-4071	430	6	.	.	PUNCT
iajs-4071	431	1	corollary	corollary	ADJ
iajs-4071	431	2	let	let	VERB
iajs-4071	431	3	(	(	PUNCT
iajs-4071	431	4	̃	̃	NOUN
iajs-4071	431	5	̃	̃	ADJ
iajs-4071	431	6	)	)	PUNCT
iajs-4071	431	7	̃	̃	NOUN
iajs-4071	431	8	̃	̃	PROPN
iajs-4071	431	9	)	)	PUNCT
iajs-4071	431	10	be	be	AUX
iajs-4071	431	11	a	a	DET
iajs-4071	431	12	soft	soft	ADJ
iajs-4071	431	13	function	function	NOUN
iajs-4071	431	14	s.t	s.t	PROPN
iajs-4071	431	15	.	.	PUNCT
iajs-4071	432	1	(	(	PUNCT
iajs-4071	432	2	̃	̃	NOUN
iajs-4071	432	3	̃	̃	PROPN
iajs-4071	432	4	)	)	PUNCT
iajs-4071	432	5	is	be	AUX
iajs-4071	432	6	a	a	DET
iajs-4071	432	7	soft	soft	ADJ
iajs-4071	432	8	locally	locally	ADV
iajs-4071	432	9	indiscrete	indiscrete	ADJ
iajs-4071	432	10	space	space	NOUN
iajs-4071	432	11	.	.	PUNCT
iajs-4071	433	1	then	then	ADV
iajs-4071	433	2	(	(	PUNCT
iajs-4071	433	3	1	1	X
iajs-4071	433	4	)	)	PUNCT
iajs-4071	433	5	is	be	AUX
iajs-4071	433	6	a	a	DET
iajs-4071	433	7	soft	soft	ADJ
iajs-4071	433	8	-continuous	-continuous	ADJ
iajs-4071	433	9	function	function	NOUN
iajs-4071	433	10	,	,	PUNCT
iajs-4071	433	11	iff	iff	PROPN
iajs-4071	433	12	is	be	AUX
iajs-4071	433	13	a	a	DET
iajs-4071	433	14	soft	soft	ADJ
iajs-4071	433	15	continuous	continuous	ADJ
iajs-4071	433	16	function	function	NOUN
iajs-4071	433	17	.	.	PUNCT
iajs-4071	434	1	(	(	PUNCT
iajs-4071	434	2	2	2	X
iajs-4071	434	3	)	)	PUNCT
iajs-4071	434	4	is	be	AUX
iajs-4071	434	5	a	a	DET
iajs-4071	434	6	soft	soft	ADJ
iajs-4071	434	7	-continuous	-continuous	ADJ
iajs-4071	434	8	function	function	NOUN
iajs-4071	434	9	,	,	PUNCT
iajs-4071	434	10	iff	iff	PROPN
iajs-4071	434	11	is	be	AUX
iajs-4071	434	12	a	a	DET
iajs-4071	434	13	soft	soft	ADJ
iajs-4071	434	14	-continuous	-continuous	ADJ
iajs-4071	434	15	function	function	NOUN
iajs-4071	434	16	.	.	PUNCT
iajs-4071	435	1	proof	proof	NOUN
iajs-4071	435	2	:	:	PUNCT
iajs-4071	435	3	(	(	PUNCT
iajs-4071	435	4	1	1	X
iajs-4071	435	5	)	)	PUNCT
iajs-4071	435	6	and	and	CCONJ
iajs-4071	435	7	(	(	PUNCT
iajs-4071	435	8	2	2	X
iajs-4071	435	9	)	)	PUNCT
iajs-4071	435	10	direct	direct	ADJ
iajs-4071	435	11	by	by	ADP
iajs-4071	435	12	using	use	VERB
iajs-4071	435	13	corollary	corollary	ADJ
iajs-4071	435	14	3.16	3.16	NUM
iajs-4071	435	15	and	and	CCONJ
iajs-4071	435	16	by	by	ADP
iajs-4071	435	17	proposition	proposition	NOUN
iajs-4071	435	18	4.2	4.2	NUM
iajs-4071	435	19	.	.	PUNCT
iajs-4071	436	1	ihjpas	ihjpas	PROPN
iajs-4071	436	2	.	.	PUNCT
iajs-4071	437	1	2025,38(4	2025,38(4	NOUN
iajs-4071	437	2	)	)	PUNCT
iajs-4071	437	3	373	373	NUM
iajs-4071	437	4	5	5	NUM
iajs-4071	437	5	.	.	PUNCT
iajs-4071	438	1	properties	property	NOUN
iajs-4071	438	2	and	and	CCONJ
iajs-4071	438	3	comparisons	comparison	NOUN
iajs-4071	438	4	5.1.proposition	5.1.proposition	NUM
iajs-4071	438	5	let	let	VERB
iajs-4071	438	6	(	(	PUNCT
iajs-4071	438	7	̃	̃	NOUN
iajs-4071	438	8	̃	̃	ADJ
iajs-4071	438	9	)	)	PUNCT
iajs-4071	438	10	̃	̃	NOUN
iajs-4071	438	11	̃	̃	NOUN
iajs-4071	438	12	)	)	PUNCT
iajs-4071	438	13	be	be	VERB
iajs-4071	438	14	̃	̃	ADV
iajs-4071	438	15	continuous	continuous	ADJ
iajs-4071	438	16	function	function	NOUN
iajs-4071	438	17	.	.	PUNCT
iajs-4071	439	1	if	if	SCONJ
iajs-4071	439	2	̃	̃	PROPN
iajs-4071	439	3	̃	̃	NOUN
iajs-4071	439	4	̃	̃	PROPN
iajs-4071	439	5	(	(	PUNCT
iajs-4071	439	6	resp	resp	NOUN
iajs-4071	439	7	.	.	PUNCT
iajs-4071	439	8	,	,	PUNCT
iajs-4071	439	9	soft	soft	ADJ
iajs-4071	439	10	clopen	clopen	NOUN
iajs-4071	439	11	)	)	PUNCT
iajs-4071	439	12	,	,	PUNCT
iajs-4071	439	13	then	then	ADV
iajs-4071	439	14	̃	̃	PROPN
iajs-4071	439	15	̃	̃	ADJ
iajs-4071	439	16	)	)	PUNCT
iajs-4071	439	17	̃	̃	NOUN
iajs-4071	439	18	̃	̃	ADJ
iajs-4071	439	19	)	)	PUNCT
iajs-4071	439	20	̃	̃	NOUN
iajs-4071	439	21	̃	̃	NOUN
iajs-4071	439	22	)	)	PUNCT
iajs-4071	439	23	is	be	AUX
iajs-4071	439	24	̃	̃	ADV
iajs-4071	439	25	-continuous	-continuous	ADJ
iajs-4071	439	26	function	function	NOUN
iajs-4071	439	27	in	in	ADP
iajs-4071	439	28	the	the	DET
iajs-4071	439	29	subspace	subspace	NOUN
iajs-4071	439	30	̃.	̃.	PROPN
iajs-4071	439	31	proof	proof	NOUN
iajs-4071	439	32	:	:	PUNCT
iajs-4071	439	33	let	let	VERB
iajs-4071	439	34	)	)	PUNCT
iajs-4071	439	35	̃	̃	ADV
iajs-4071	439	36	̃.	̃.	NOUN
iajs-4071	439	37	since	since	SCONJ
iajs-4071	439	38	is	be	AUX
iajs-4071	439	39	̃	̃	PROPN
iajs-4071	439	40	-continuous	-continuous	ADJ
iajs-4071	439	41	function	function	NOUN
iajs-4071	439	42	,	,	PUNCT
iajs-4071	439	43	then	then	ADV
iajs-4071	439	44	by	by	ADP
iajs-4071	439	45	proposition	proposition	NOUN
iajs-4071	439	46	4.2	4.2	NUM
iajs-4071	439	47	)	)	PUNCT
iajs-4071	439	48	is	be	AUX
iajs-4071	439	49	̃	̃	PROPN
iajs-4071	439	50	o	o	NOUN
iajs-4071	439	51	(	(	PUNCT
iajs-4071	439	52	̃	̃	PROPN
iajs-4071	439	53	)	)	PUNCT
iajs-4071	439	54	.	.	PUNCT
iajs-4071	440	1	since	since	SCONJ
iajs-4071	440	2	̃	̃	PROPN
iajs-4071	440	3	̃	̃	PROPN
iajs-4071	440	4	̃	̃	PROPN
iajs-4071	440	5	,	,	PUNCT
iajs-4071	440	6	then	then	ADV
iajs-4071	440	7	by	by	ADP
iajs-4071	440	8	proposition	proposition	NOUN
iajs-4071	440	9	3.24	3.24	NUM
iajs-4071	440	10	|	|	NOUN
iajs-4071	440	11	̃	̃	PROPN
iajs-4071	440	12	(	(	PUNCT
iajs-4071	440	13	̃	̃	PROPN
iajs-4071	440	14	)	)	PUNCT
iajs-4071	440	15	)	)	PUNCT
iajs-4071	440	16	)	)	PUNCT
iajs-4071	440	17	)	)	PUNCT
iajs-4071	440	18	)	)	PUNCT
iajs-4071	441	1	̃	̃	NOUN
iajs-4071	441	2	̃	̃	ADP
iajs-4071	441	3	̃	̃	NOUN
iajs-4071	441	4	o	o	X
iajs-4071	441	5	(	(	PUNCT
iajs-4071	441	6	̃	̃	PROPN
iajs-4071	441	7	)	)	PUNCT
iajs-4071	441	8	.	.	PUNCT
iajs-4071	442	1	this	this	PRON
iajs-4071	442	2	shows	show	VERB
iajs-4071	442	3	that	that	SCONJ
iajs-4071	442	4	̃	̃	PROPN
iajs-4071	442	5	̃	̃	ADJ
iajs-4071	442	6	)	)	PUNCT
iajs-4071	442	7	̃	̃	NOUN
iajs-4071	442	8	̃	̃	ADJ
iajs-4071	442	9	)	)	PUNCT
iajs-4071	442	10	̃	̃	NOUN
iajs-4071	442	11	̃	̃	NOUN
iajs-4071	442	12	)	)	PUNCT
iajs-4071	442	13	is	be	AUX
iajs-4071	442	14	̃	̃	ADV
iajs-4071	442	15	continuous	continuous	ADJ
iajs-4071	442	16	function	function	NOUN
iajs-4071	442	17	.	.	PUNCT
iajs-4071	443	1	5.2.proposition	5.2.proposition	NUM
iajs-4071	443	2	let	let	VERB
iajs-4071	443	3	(	(	PUNCT
iajs-4071	443	4	̃	̃	NOUN
iajs-4071	443	5	̃	̃	ADJ
iajs-4071	443	6	)	)	PUNCT
iajs-4071	443	7	̃	̃	NOUN
iajs-4071	443	8	̃	̃	NOUN
iajs-4071	443	9	)	)	PUNCT
iajs-4071	443	10	be	be	VERB
iajs-4071	443	11	̃	̃	ADV
iajs-4071	443	12	-continuous	-continuous	ADJ
iajs-4071	443	13	function	function	NOUN
iajs-4071	443	14	.	.	PUNCT
iajs-4071	444	1	if	if	SCONJ
iajs-4071	444	2	̃	̃	PROPN
iajs-4071	444	3	̃	̃	PROPN
iajs-4071	444	4	̃	̃	NOUN
iajs-4071	444	5	o	o	NOUN
iajs-4071	444	6	(	(	PUNCT
iajs-4071	444	7	̃)then	̃)then	PROPN
iajs-4071	444	8	̃	̃	PROPN
iajs-4071	444	9	(	(	PUNCT
iajs-4071	444	10	̃	̃	PROPN
iajs-4071	444	11	)	)	PUNCT
iajs-4071	444	12	)	)	PUNCT
iajs-4071	444	13	̃	̃	NOUN
iajs-4071	444	14	̃	̃	ADJ
iajs-4071	444	15	)	)	PUNCT
iajs-4071	444	16	̃	̃	NOUN
iajs-4071	444	17	̃	̃	NOUN
iajs-4071	444	18	)	)	PUNCT
iajs-4071	444	19	is	be	AUX
iajs-4071	444	20	̃	̃	ADV
iajs-4071	444	21	-continuous	-continuous	ADJ
iajs-4071	444	22	function	function	NOUN
iajs-4071	444	23	in	in	ADP
iajs-4071	444	24	the	the	DET
iajs-4071	444	25	subspace	subspace	NOUN
iajs-4071	444	26	̃.	̃.	PROPN
iajs-4071	444	27	proof	proof	NOUN
iajs-4071	444	28	:	:	PUNCT
iajs-4071	444	29	since	since	SCONJ
iajs-4071	444	30	every	every	DET
iajs-4071	444	31	soft	soft	ADJ
iajs-4071	444	32	regular	regular	ADJ
iajs-4071	444	33	open	open	NOUN
iajs-4071	444	34	is	be	AUX
iajs-4071	444	35	soft	soft	ADJ
iajs-4071	444	36	open	open	ADJ
iajs-4071	444	37	,	,	PUNCT
iajs-4071	444	38	this	this	PRON
iajs-4071	444	39	is	be	AUX
iajs-4071	444	40	a	a	DET
iajs-4071	444	41	direct	direct	ADJ
iajs-4071	444	42	result	result	NOUN
iajs-4071	444	43	of	of	ADP
iajs-4071	444	44	proposition	proposition	NOUN
iajs-4071	444	45	4.2	4.2	NUM
iajs-4071	444	46	and	and	CCONJ
iajs-4071	444	47	proposition	proposition	NOUN
iajs-4071	444	48	5.1	5.1	NUM
iajs-4071	444	49	.	.	PUNCT
iajs-4071	445	1	5.3.proposition	5.3.proposition	NUM
iajs-4071	445	2	let	let	VERB
iajs-4071	445	3	(	(	PUNCT
iajs-4071	445	4	̃	̃	NOUN
iajs-4071	445	5	̃	̃	ADJ
iajs-4071	445	6	)	)	PUNCT
iajs-4071	445	7	̃	̃	NOUN
iajs-4071	445	8	̃	̃	NOUN
iajs-4071	445	9	)	)	PUNCT
iajs-4071	445	10	and	and	CCONJ
iajs-4071	445	11	̃	̃	PROPN
iajs-4071	445	12	̃	̃	PROPN
iajs-4071	445	13	)	)	PUNCT
iajs-4071	445	14	(	(	PUNCT
iajs-4071	445	15	̃	̃	NOUN
iajs-4071	445	16	̃	̃	PROPN
iajs-4071	445	17	)	)	PUNCT
iajs-4071	445	18	be	be	VERB
iajs-4071	445	19	two	two	NUM
iajs-4071	445	20	soft	soft	ADJ
iajs-4071	445	21	functions	function	NOUN
iajs-4071	445	22	,	,	PUNCT
iajs-4071	445	23	then	then	ADV
iajs-4071	445	24	the	the	DET
iajs-4071	445	25	following	follow	VERB
iajs-4071	445	26	properties	property	NOUN
iajs-4071	445	27	hold	hold	VERB
iajs-4071	445	28	.	.	PUNCT
iajs-4071	446	1	(	(	PUNCT
iajs-4071	446	2	1	1	X
iajs-4071	446	3	)	)	PUNCT
iajs-4071	446	4	if	if	SCONJ
iajs-4071	446	5	is	be	AUX
iajs-4071	446	6	a	a	DET
iajs-4071	446	7	̃	̃	ADV
iajs-4071	446	8	continuous	continuous	ADJ
iajs-4071	446	9	and	and	CCONJ
iajs-4071	446	10	is	be	AUX
iajs-4071	446	11	a	a	DET
iajs-4071	446	12	soft	soft	ADJ
iajs-4071	446	13	continuous	continuous	ADJ
iajs-4071	446	14	,	,	PUNCT
iajs-4071	446	15	then	then	ADV
iajs-4071	446	16	is	be	AUX
iajs-4071	446	17	a	a	DET
iajs-4071	446	18	̃	̃	ADV
iajs-4071	446	19	continuous	continuous	ADJ
iajs-4071	446	20	.	.	PUNCT
iajs-4071	447	1	(	(	PUNCT
iajs-4071	447	2	2	2	X
iajs-4071	447	3	)	)	PUNCT
iajs-4071	447	4	if	if	SCONJ
iajs-4071	447	5	is	be	AUX
iajs-4071	447	6	a	a	DET
iajs-4071	447	7	̃	̃	NOUN
iajs-4071	447	8	irresolute	irresolute	ADJ
iajs-4071	447	9	and	and	CCONJ
iajs-4071	447	10	is	be	AUX
iajs-4071	447	11	a	a	DET
iajs-4071	447	12	̃	̃	ADV
iajs-4071	447	13	continuous	continuous	ADJ
iajs-4071	447	14	,	,	PUNCT
iajs-4071	447	15	then	then	ADV
iajs-4071	447	16	is	be	AUX
iajs-4071	447	17	a	a	DET
iajs-4071	447	18	̃	̃	ADV
iajs-4071	447	19	continuous	continuous	ADJ
iajs-4071	447	20	.	.	PUNCT
iajs-4071	448	1	proof	proof	NOUN
iajs-4071	448	2	:	:	PUNCT
iajs-4071	448	3	(	(	PUNCT
iajs-4071	448	4	1	1	X
iajs-4071	448	5	)	)	PUNCT
iajs-4071	448	6	let	let	VERB
iajs-4071	448	7	)	)	PUNCT
iajs-4071	449	1	̃	̃	ADV
iajs-4071	449	2	̃.	̃.	NOUN
iajs-4071	449	3	then	then	ADV
iajs-4071	449	4	)	)	PUNCT
iajs-4071	449	5	̃	̃	PROPN
iajs-4071	449	6	̃	̃	NOUN
iajs-4071	449	7	by	by	ADP
iajs-4071	449	8	continuity	continuity	NOUN
iajs-4071	449	9	of	of	ADP
iajs-4071	449	10	.	.	PUNCT
iajs-4071	450	1	since	since	SCONJ
iajs-4071	450	2	is	be	AUX
iajs-4071	450	3	a	a	DET
iajs-4071	450	4	̃	̃	ADV
iajs-4071	450	5	continuous	continuous	ADJ
iajs-4071	450	6	,	,	PUNCT
iajs-4071	450	7	(	(	PUNCT
iajs-4071	450	8	)	)	PUNCT
iajs-4071	450	9	)	)	PUNCT
iajs-4071	451	1	̃	̃	PROPN
iajs-4071	451	2	̃	̃	NOUN
iajs-4071	451	3	̃	̃	NOUN
iajs-4071	451	4	)	)	PUNCT
iajs-4071	451	5	and	and	CCONJ
iajs-4071	451	6	hence	hence	ADV
iajs-4071	451	7	,	,	PUNCT
iajs-4071	451	8	(	(	PUNCT
iajs-4071	451	9	)	)	PUNCT
iajs-4071	451	10	)	)	PUNCT
iajs-4071	451	11	(	(	PUNCT
iajs-4071	451	12	)	)	PUNCT
iajs-4071	451	13	)	)	PUNCT
iajs-4071	452	1	̃	̃	PROPN
iajs-4071	452	2	̃	̃	PROPN
iajs-4071	452	3	̃	̃	NUM
iajs-4071	452	4	)	)	PUNCT
iajs-4071	452	5	.	.	PUNCT
iajs-4071	453	1	therefore	therefore	ADV
iajs-4071	453	2	,	,	PUNCT
iajs-4071	453	3	is	be	AUX
iajs-4071	453	4	a	a	DET
iajs-4071	453	5	̃	̃	ADV
iajs-4071	453	6	-continuous	-continuous	ADJ
iajs-4071	453	7	.	.	PUNCT
iajs-4071	454	1	(	(	PUNCT
iajs-4071	454	2	2	2	X
iajs-4071	454	3	)	)	PUNCT
iajs-4071	454	4	let	let	VERB
iajs-4071	454	5	)	)	PUNCT
iajs-4071	455	1	̃	̃	ADV
iajs-4071	455	2	̃.	̃.	NOUN
iajs-4071	455	3	since	since	SCONJ
iajs-4071	455	4	is	be	AUX
iajs-4071	455	5	a	a	DET
iajs-4071	455	6	̃	̃	ADV
iajs-4071	455	7	-continuous	-continuous	ADJ
iajs-4071	455	8	,	,	PUNCT
iajs-4071	455	9	)	)	PUNCT
iajs-4071	455	10	̃	̃	PROPN
iajs-4071	455	11	̃	̃	NOUN
iajs-4071	455	12	̃	̃	NOUN
iajs-4071	455	13	)	)	PUNCT
iajs-4071	455	14	.	.	PUNCT
iajs-4071	456	1	since	since	SCONJ
iajs-4071	456	2	is	be	AUX
iajs-4071	456	3	a	a	DET
iajs-4071	456	4	̃	̃	NOUN
iajs-4071	456	5	irresolute	irresolute	ADJ
iajs-4071	456	6	,	,	PUNCT
iajs-4071	456	7	(	(	PUNCT
iajs-4071	456	8	)	)	PUNCT
iajs-4071	456	9	)	)	PUNCT
iajs-4071	457	1	̃	̃	PROPN
iajs-4071	457	2	̃	̃	NOUN
iajs-4071	457	3	̃	̃	NOUN
iajs-4071	457	4	)	)	PUNCT
iajs-4071	457	5	and	and	CCONJ
iajs-4071	457	6	hence	hence	ADV
iajs-4071	457	7	,	,	PUNCT
iajs-4071	457	8	(	(	PUNCT
iajs-4071	457	9	)	)	PUNCT
iajs-4071	457	10	)	)	PUNCT
iajs-4071	457	11	(	(	PUNCT
iajs-4071	457	12	)	)	PUNCT
iajs-4071	457	13	)	)	PUNCT
iajs-4071	458	1	̃	̃	PROPN
iajs-4071	458	2	̃	̃	PROPN
iajs-4071	458	3	̃	̃	NUM
iajs-4071	458	4	)	)	PUNCT
iajs-4071	458	5	.	.	PUNCT
iajs-4071	459	1	therefore	therefore	ADV
iajs-4071	459	2	,	,	PUNCT
iajs-4071	459	3	is	be	AUX
iajs-4071	459	4	a	a	DET
iajs-4071	459	5	̃	̃	ADV
iajs-4071	459	6	-continuous	-continuous	ADJ
iajs-4071	459	7	.	.	PUNCT
iajs-4071	460	1	5.4.proposition	5.4.proposition	NUM
iajs-4071	460	2	let	let	VERB
iajs-4071	460	3	(	(	PUNCT
iajs-4071	460	4	̃	̃	NOUN
iajs-4071	460	5	̃	̃	ADJ
iajs-4071	460	6	)	)	PUNCT
iajs-4071	460	7	̃	̃	NOUN
iajs-4071	460	8	̃	̃	NOUN
iajs-4071	460	9	)	)	PUNCT
iajs-4071	460	10	and	and	CCONJ
iajs-4071	460	11	̃	̃	PROPN
iajs-4071	460	12	̃	̃	PROPN
iajs-4071	460	13	)	)	PUNCT
iajs-4071	460	14	(	(	PUNCT
iajs-4071	460	15	̃	̃	NOUN
iajs-4071	460	16	̃	̃	PROPN
iajs-4071	460	17	)	)	PUNCT
iajs-4071	460	18	be	be	VERB
iajs-4071	460	19	two	two	NUM
iajs-4071	460	20	soft	soft	ADJ
iajs-4071	460	21	functions	function	NOUN
iajs-4071	460	22	.	.	PUNCT
iajs-4071	461	1	if	if	SCONJ
iajs-4071	461	2	is	be	AUX
iajs-4071	461	3	a	a	DET
iajs-4071	461	4	̃	̃	ADV
iajs-4071	461	5	-open	-open	ADJ
iajs-4071	461	6	and	and	CCONJ
iajs-4071	461	7	surjective	surjective	ADJ
iajs-4071	461	8	and	and	CCONJ
iajs-4071	461	9	is	be	AUX
iajs-4071	461	10	a	a	DET
iajs-4071	461	11	̃	̃	ADV
iajs-4071	461	12	-continuous	-continuous	ADJ
iajs-4071	461	13	,	,	PUNCT
iajs-4071	461	14	then	then	ADV
iajs-4071	461	15	is	be	AUX
iajs-4071	461	16	a	a	DET
iajs-4071	461	17	̃	̃	ADV
iajs-4071	461	18	-continuous	-continuous	ADJ
iajs-4071	461	19	.	.	PUNCT
iajs-4071	462	1	proof	proof	NOUN
iajs-4071	462	2	:	:	PUNCT
iajs-4071	462	3	let	let	VERB
iajs-4071	462	4	)	)	PUNCT
iajs-4071	463	1	̃	̃	ADV
iajs-4071	463	2	̃.	̃.	NOUN
iajs-4071	463	3	since	since	SCONJ
iajs-4071	463	4	is	be	AUX
iajs-4071	463	5	a	a	DET
iajs-4071	463	6	̃	̃	ADV
iajs-4071	463	7	-continuous	-continuous	ADJ
iajs-4071	463	8	,	,	PUNCT
iajs-4071	463	9	(	(	PUNCT
iajs-4071	463	10	)	)	PUNCT
iajs-4071	463	11	)	)	PUNCT
iajs-4071	463	12	(	(	PUNCT
iajs-4071	463	13	)	)	PUNCT
iajs-4071	463	14	)	)	PUNCT
iajs-4071	464	1	̃	̃	PROPN
iajs-4071	464	2	̃	̃	NOUN
iajs-4071	464	3	̃	̃	NOUN
iajs-4071	464	4	)	)	PUNCT
iajs-4071	464	5	.	.	PUNCT
iajs-4071	465	1	since	since	SCONJ
iajs-4071	465	2	is	be	AUX
iajs-4071	465	3	a	a	DET
iajs-4071	465	4	̃	̃	ADV
iajs-4071	465	5	-open	-open	ADJ
iajs-4071	465	6	and	and	CCONJ
iajs-4071	465	7	surjective	surjective	ADJ
iajs-4071	465	8	,	,	PUNCT
iajs-4071	465	9	then	then	ADV
iajs-4071	465	10	(	(	PUNCT
iajs-4071	465	11	(	(	PUNCT
iajs-4071	465	12	)	)	PUNCT
iajs-4071	465	13	)	)	PUNCT
iajs-4071	465	14	)	)	PUNCT
iajs-4071	465	15	)	)	PUNCT
iajs-4071	466	1	̃	̃	NOUN
iajs-4071	466	2	̃	̃	NOUN
iajs-4071	466	3	̃	̃	NOUN
iajs-4071	466	4	)	)	PUNCT
iajs-4071	466	5	.	.	PUNCT
iajs-4071	467	1	hence	hence	ADV
iajs-4071	467	2	,	,	PUNCT
iajs-4071	467	3	is	be	AUX
iajs-4071	467	4	a	a	DET
iajs-4071	467	5	̃	̃	ADV
iajs-4071	467	6	-continuous	-continuous	ADJ
iajs-4071	467	7	.	.	PUNCT
iajs-4071	468	1	5.5.proposition	5.5.proposition	NUM
iajs-4071	468	2	a	a	DET
iajs-4071	468	3	function	function	NOUN
iajs-4071	468	4	(	(	PUNCT
iajs-4071	468	5	̃	̃	NOUN
iajs-4071	468	6	̃	̃	ADJ
iajs-4071	468	7	)	)	PUNCT
iajs-4071	468	8	̃	̃	NOUN
iajs-4071	468	9	̃	̃	NOUN
iajs-4071	468	10	)	)	PUNCT
iajs-4071	468	11	is	be	AUX
iajs-4071	468	12	̃	̃	ADV
iajs-4071	468	13	-continuous	-continuous	ADJ
iajs-4071	468	14	.	.	PUNCT
iajs-4071	469	1	if	if	SCONJ
iajs-4071	469	2	̃	̃	PROPN
iajs-4071	469	3	̃	̃	PROPN
iajs-4071	469	4	̃	̃	PROPN
iajs-4071	469	5	)	)	PUNCT
iajs-4071	469	6	,	,	PUNCT
iajs-4071	469	7	a	a	DET
iajs-4071	469	8	soft	soft	ADJ
iajs-4071	469	9	clopen	clopen	ADJ
iajs-4071	469	10	set	set	NOUN
iajs-4071	469	11	)	)	PUNCT
iajs-4071	469	12	of	of	ADP
iajs-4071	469	13	̃	̃	PROPN
iajs-4071	469	14	containing	contain	VERB
iajs-4071	469	15	s.t	s.t	PROPN
iajs-4071	469	16	.	.	PUNCT
iajs-4071	469	17	)	)	PUNCT
iajs-4071	469	18	)	)	PUNCT
iajs-4071	470	1	̃	̃	ADV
iajs-4071	470	2	is	be	AUX
iajs-4071	470	3	̃	̃	ADV
iajs-4071	470	4	-continuous	-continuous	ADJ
iajs-4071	470	5	.	.	PUNCT
iajs-4071	471	1	proof	proof	NOUN
iajs-4071	471	2	:	:	PUNCT
iajs-4071	471	3	let	let	VERB
iajs-4071	471	4	̃	̃	PROPN
iajs-4071	471	5	̃	̃	NOUN
iajs-4071	471	6	̃	̃	NUM
iajs-4071	471	7	)	)	PUNCT
iajs-4071	471	8	,	,	PUNCT
iajs-4071	471	9	then	then	ADV
iajs-4071	471	10	by	by	ADP
iajs-4071	471	11	hypothesis	hypothesis	NOUN
iajs-4071	471	12	,	,	PUNCT
iajs-4071	471	13	)	)	PUNCT
iajs-4071	471	14	̃	̃	PROPN
iajs-4071	471	15	̃	̃	PROPN
iajs-4071	471	16	̃	̃	NOUN
iajs-4071	471	17	)	)	PUNCT
iajs-4071	471	18	containing	contain	VERB
iajs-4071	471	19	s.t	s.t	PROPN
iajs-4071	471	20	.	.	PROPN
iajs-4071	471	21	)	)	PUNCT
iajs-4071	471	22	)	)	PUNCT
iajs-4071	472	1	̃	̃	ADV
iajs-4071	472	2	is	be	AUX
iajs-4071	472	3	̃	̃	ADV
iajs-4071	472	4	-continuous	-continuous	ADJ
iajs-4071	472	5	.	.	PUNCT
iajs-4071	473	1	let	let	VERB
iajs-4071	473	2	)	)	PUNCT
iajs-4071	473	3	̃	̃	NOUN
iajs-4071	473	4	̃	̃	NOUN
iajs-4071	473	5	)	)	PUNCT
iajs-4071	473	6	containing	contain	VERB
iajs-4071	473	7	)	)	PUNCT
iajs-4071	473	8	,	,	PUNCT
iajs-4071	473	9	a	a	DET
iajs-4071	473	10	̃	̃	PROPN
iajs-4071	473	11	open	open	ADJ
iajs-4071	473	12	subset	subset	NOUN
iajs-4071	473	13	)	)	PUNCT
iajs-4071	473	14	of	of	ADP
iajs-4071	473	15	)	)	PUNCT
iajs-4071	473	16	containing	contain	VERB
iajs-4071	473	17	s.t	s.t	PROPN
iajs-4071	473	18	.	.	PROPN
iajs-4071	473	19	(	(	PUNCT
iajs-4071	473	20	)	)	PUNCT
iajs-4071	473	21	)	)	PUNCT
iajs-4071	473	22	)	)	PUNCT
iajs-4071	474	1	̃	̃	ADV
iajs-4071	474	2	)	)	PUNCT
iajs-4071	474	3	.	.	PUNCT
iajs-4071	475	1	since	since	SCONJ
iajs-4071	475	2	)	)	PUNCT
iajs-4071	475	3	̃	̃	PROPN
iajs-4071	475	4	̃	̃	PROPN
iajs-4071	475	5	̃	̃	NOUN
iajs-4071	475	6	)	)	PUNCT
iajs-4071	475	7	.	.	PUNCT
iajs-4071	476	1	by	by	ADP
iajs-4071	476	2	proposition	proposition	NOUN
iajs-4071	476	3	3.26	3.26	NUM
iajs-4071	476	4	)	)	PUNCT
iajs-4071	476	5	̃	̃	PROPN
iajs-4071	476	6	̃	̃	NOUN
iajs-4071	476	7	̃	̃	NUM
iajs-4071	476	8	)	)	PUNCT
iajs-4071	476	9	and	and	CCONJ
iajs-4071	476	10	hence	hence	ADV
iajs-4071	476	11	)	)	PUNCT
iajs-4071	476	12	)	)	PUNCT
iajs-4071	476	13	̃	̃	NOUN
iajs-4071	476	14	)	)	PUNCT
iajs-4071	476	15	.	.	PUNCT
iajs-4071	477	1	this	this	PRON
iajs-4071	477	2	implies	imply	VERB
iajs-4071	477	3	that	that	PRON
iajs-4071	477	4	is	be	AUX
iajs-4071	477	5	̃	̃	ADV
iajs-4071	477	6	-continuous	-continuous	ADJ
iajs-4071	477	7	.	.	PUNCT
iajs-4071	478	1	5.6.proposition	5.6.proposition	NUM
iajs-4071	478	2	if	if	SCONJ
iajs-4071	478	3	̃	̃	PROPN
iajs-4071	478	4	)	)	PUNCT
iajs-4071	478	5	)	)	PUNCT
iajs-4071	479	1	,	,	PUNCT
iajs-4071	479	2	where	where	SCONJ
iajs-4071	479	3	)	)	PUNCT
iajs-4071	479	4	)	)	PUNCT
iajs-4071	480	1	̃	̃	NOUN
iajs-4071	480	2	̃	̃	NOUN
iajs-4071	480	3	̃	̃	NUM
iajs-4071	480	4	)	)	PUNCT
iajs-4071	480	5	and	and	CCONJ
iajs-4071	480	6	(	(	PUNCT
iajs-4071	480	7	̃	̃	NOUN
iajs-4071	480	8	̃	̃	ADJ
iajs-4071	480	9	)	)	PUNCT
iajs-4071	480	10	̃	̃	NOUN
iajs-4071	480	11	̃	̃	PROPN
iajs-4071	480	12	)	)	PUNCT
iajs-4071	480	13	is	be	AUX
iajs-4071	480	14	a	a	DET
iajs-4071	480	15	function	function	NOUN
iajs-4071	480	16	s.t	s.t	PROPN
iajs-4071	480	17	.	.	PROPN
iajs-4071	480	18	both	both	PRON
iajs-4071	480	19	)	)	PUNCT
iajs-4071	480	20	and	and	CCONJ
iajs-4071	480	21	)	)	PUNCT
iajs-4071	480	22	are	be	AUX
iajs-4071	480	23	both	both	PRON
iajs-4071	480	24	̃	̃	ADV
iajs-4071	480	25	-continuous	-continuous	ADJ
iajs-4071	480	26	,	,	PUNCT
iajs-4071	480	27	then	then	ADV
iajs-4071	480	28	is	be	AUX
iajs-4071	480	29	̃	̃	PROPN
iajs-4071	480	30	-continuous	-continuous	ADJ
iajs-4071	480	31	.	.	PUNCT
iajs-4071	481	1	ihjpas	ihjpas	PROPN
iajs-4071	481	2	.	.	PUNCT
iajs-4071	482	1	2025,38(4	2025,38(4	NOUN
iajs-4071	482	2	)	)	PUNCT
iajs-4071	482	3	374	374	NUM
iajs-4071	482	4	proof	proof	NOUN
iajs-4071	482	5	:	:	PUNCT
iajs-4071	482	6	let	let	VERB
iajs-4071	482	7	)	)	PUNCT
iajs-4071	483	1	̃	̃	ADV
iajs-4071	483	2	̃.then	̃.then	PROPN
iajs-4071	483	3	)	)	PUNCT
iajs-4071	483	4	)	)	PUNCT
iajs-4071	483	5	)	)	PUNCT
iajs-4071	483	6	)	)	PUNCT
iajs-4071	483	7	)	)	PUNCT
iajs-4071	483	8	)	)	PUNCT
iajs-4071	483	9	)	)	PUNCT
iajs-4071	483	10	)	)	PUNCT
iajs-4071	483	11	)	)	PUNCT
iajs-4071	483	12	)	)	PUNCT
iajs-4071	483	13	.	.	PUNCT
iajs-4071	484	1	since	since	SCONJ
iajs-4071	484	2	)	)	PUNCT
iajs-4071	484	3	and	and	CCONJ
iajs-4071	484	4	)	)	PUNCT
iajs-4071	484	5	are	be	AUX
iajs-4071	484	6	̃	̃	ADV
iajs-4071	484	7	-continuous	-continuous	ADJ
iajs-4071	484	8	.	.	PUNCT
iajs-4071	485	1	then	then	ADV
iajs-4071	485	2	by	by	ADP
iajs-4071	485	3	proposition	proposition	NOUN
iajs-4071	485	4	4.2	4.2	NUM
iajs-4071	485	5	)	)	PUNCT
iajs-4071	485	6	)	)	PUNCT
iajs-4071	485	7	)	)	PUNCT
iajs-4071	485	8	)	)	PUNCT
iajs-4071	485	9	and	and	CCONJ
iajs-4071	485	10	)	)	PUNCT
iajs-4071	485	11	)	)	PUNCT
iajs-4071	485	12	)	)	PUNCT
iajs-4071	485	13	)	)	PUNCT
iajs-4071	485	14	are	be	AUX
iajs-4071	485	15	̃	̃	NOUN
iajs-4071	485	16	-open	-open	ADJ
iajs-4071	485	17	sets	set	NOUN
iajs-4071	485	18	in	in	ADP
iajs-4071	485	19	)	)	PUNCT
iajs-4071	485	20	and	and	CCONJ
iajs-4071	485	21	)	)	PUNCT
iajs-4071	485	22	respectively	respectively	ADV
iajs-4071	485	23	.	.	PUNCT
iajs-4071	486	1	since	since	SCONJ
iajs-4071	486	2	)	)	PUNCT
iajs-4071	486	3	)	)	PUNCT
iajs-4071	487	1	̃	̃	NOUN
iajs-4071	487	2	̃	̃	PROPN
iajs-4071	487	3	̃	̃	PROPN
iajs-4071	487	4	)	)	PUNCT
iajs-4071	487	5	,	,	PUNCT
iajs-4071	487	6	then	then	ADV
iajs-4071	487	7	by	by	ADP
iajs-4071	487	8	corollary	corollary	ADJ
iajs-4071	487	9	3.26	3.26	NUM
iajs-4071	487	10	)	)	PUNCT
iajs-4071	487	11	)	)	PUNCT
iajs-4071	487	12	)	)	PUNCT
iajs-4071	487	13	)	)	PUNCT
iajs-4071	487	14	,	,	PUNCT
iajs-4071	487	15	)	)	PUNCT
iajs-4071	487	16	)	)	PUNCT
iajs-4071	487	17	)	)	PUNCT
iajs-4071	487	18	)	)	PUNCT
iajs-4071	488	1	̃	̃	PROPN
iajs-4071	488	2	̃	̃	NOUN
iajs-4071	488	3	̃	̃	NOUN
iajs-4071	488	4	)	)	PUNCT
iajs-4071	488	5	.	.	PUNCT
iajs-4071	489	1	since	since	SCONJ
iajs-4071	489	2	the	the	DET
iajs-4071	489	3	union	union	NOUN
iajs-4071	489	4	of	of	ADP
iajs-4071	489	5	two	two	NUM
iajs-4071	489	6	̃	̃	PROPN
iajs-4071	489	7	-open	-open	NOUN
iajs-4071	489	8	sets	set	NOUN
iajs-4071	489	9	are	be	AUX
iajs-4071	489	10	̃	̃	ADV
iajs-4071	489	11	open	open	ADJ
iajs-4071	489	12	.	.	PUNCT
iajs-4071	490	1	hence	hence	ADV
iajs-4071	490	2	)	)	PUNCT
iajs-4071	490	3	)	)	PUNCT
iajs-4071	491	1	̃	̃	PROPN
iajs-4071	491	2	̃	̃	PROPN
iajs-4071	491	3	̃	̃	NUM
iajs-4071	491	4	)	)	PUNCT
iajs-4071	491	5	.	.	PUNCT
iajs-4071	492	1	therefore	therefore	ADV
iajs-4071	492	2	,	,	PUNCT
iajs-4071	492	3	by	by	ADP
iajs-4071	492	4	proposition	proposition	NOUN
iajs-4071	492	5	4.2	4.2	NUM
iajs-4071	492	6	is	be	AUX
iajs-4071	492	7	̃	̃	ADV
iajs-4071	492	8	continuous	continuous	ADJ
iajs-4071	492	9	.	.	PUNCT
iajs-4071	493	1	in	in	ADP
iajs-4071	493	2	general	general	ADJ
iajs-4071	493	3	,	,	PUNCT
iajs-4071	493	4	if	if	SCONJ
iajs-4071	493	5	̃	̃	PROPN
iajs-4071	493	6	)	)	PUNCT
iajs-4071	493	7	̃	̃	PROPN
iajs-4071	493	8	,	,	PUNCT
iajs-4071	493	9	where	where	SCONJ
iajs-4071	493	10	each	each	PRON
iajs-4071	493	11	)	)	PUNCT
iajs-4071	493	12	is	be	AUX
iajs-4071	493	13	a	a	DET
iajs-4071	493	14	soft	soft	ADJ
iajs-4071	493	15	clopen	clopen	ADJ
iajs-4071	493	16	set	set	NOUN
iajs-4071	493	17	and	and	CCONJ
iajs-4071	493	18	(	(	PUNCT
iajs-4071	493	19	̃	̃	PROPN
iajs-4071	493	20	̃	̃	ADJ
iajs-4071	493	21	)	)	PUNCT
iajs-4071	493	22	̃	̃	NOUN
iajs-4071	493	23	̃	̃	PROPN
iajs-4071	493	24	)	)	PUNCT
iajs-4071	493	25	is	be	AUX
iajs-4071	493	26	a	a	DET
iajs-4071	493	27	function	function	NOUN
iajs-4071	493	28	s.t	s.t	PROPN
iajs-4071	493	29	.	.	PUNCT
iajs-4071	493	30	)	)	PUNCT
iajs-4071	493	31	is	be	AUX
iajs-4071	493	32	̃	̃	ADV
iajs-4071	493	33	-continuous	-continuous	ADJ
iajs-4071	493	34	for	for	ADP
iajs-4071	493	35	each	each	PRON
iajs-4071	493	36	,	,	PUNCT
iajs-4071	493	37	then	then	ADV
iajs-4071	493	38	is	be	AUX
iajs-4071	493	39	̃	̃	ADV
iajs-4071	493	40	-continuous	-continuous	ADJ
iajs-4071	493	41	.	.	PUNCT
iajs-4071	494	1	5.7.proposition	5.7.proposition	NUM
iajs-4071	494	2	let	let	VERB
iajs-4071	494	3	̃	̃	PROPN
iajs-4071	494	4	)	)	PUNCT
iajs-4071	494	5	)	)	PUNCT
iajs-4071	494	6	,	,	PUNCT
iajs-4071	494	7	where	where	SCONJ
iajs-4071	494	8	)	)	PUNCT
iajs-4071	494	9	)	)	PUNCT
iajs-4071	495	1	̃	̃	NOUN
iajs-4071	495	2	̃	̃	PROPN
iajs-4071	495	3	(	(	PUNCT
iajs-4071	495	4	̃	̃	NOUN
iajs-4071	495	5	)	)	PUNCT
iajs-4071	495	6	.	.	PUNCT
iajs-4071	496	1	let	let	VERB
iajs-4071	496	2	)	)	PUNCT
iajs-4071	496	3	̃	̃	ADV
iajs-4071	496	4	̃	̃	PROPN
iajs-4071	496	5	)	)	PUNCT
iajs-4071	496	6	and	and	CCONJ
iajs-4071	496	7	)	)	PUNCT
iajs-4071	496	8	̃	̃	NOUN
iajs-4071	496	9	̃	̃	PROPN
iajs-4071	496	10	)	)	PUNCT
iajs-4071	496	11	be	be	VERB
iajs-4071	496	12	a	a	DET
iajs-4071	496	13	̃	̃	ADV
iajs-4071	496	14	-continuous	-continuous	ADJ
iajs-4071	496	15	.	.	PUNCT
iajs-4071	497	1	if	if	SCONJ
iajs-4071	497	2	)	)	PUNCT
iajs-4071	497	3	)	)	PUNCT
iajs-4071	497	4	,	,	PUNCT
iajs-4071	497	5	̃	̃	PROPN
iajs-4071	497	6	)	)	PUNCT
iajs-4071	497	7	)	)	PUNCT
iajs-4071	497	8	.	.	PUNCT
iajs-4071	498	1	then	then	ADV
iajs-4071	498	2	the	the	DET
iajs-4071	498	3	function	function	NOUN
iajs-4071	498	4	)	)	PUNCT
iajs-4071	498	5	)	)	PUNCT
iajs-4071	499	1	̃	̃	PROPN
iajs-4071	499	2	s.t	s.t	PROPN
iajs-4071	499	3	.	.	PROPN
iajs-4071	499	4	)	)	PUNCT
iajs-4071	499	5	{	{	PUNCT
iajs-4071	499	6	)	)	PUNCT
iajs-4071	499	7	̃	̃	PROPN
iajs-4071	499	8	)	)	PUNCT
iajs-4071	499	9	)	)	PUNCT
iajs-4071	500	1	̃	̃	ADV
iajs-4071	500	2	)	)	PUNCT
iajs-4071	500	3	is	be	AUX
iajs-4071	500	4	̃	̃	ADV
iajs-4071	500	5	-continuous	-continuous	ADJ
iajs-4071	500	6	.	.	PUNCT
iajs-4071	501	1	proof	proof	NOUN
iajs-4071	501	2	:	:	PUNCT
iajs-4071	501	3	let	let	AUX
iajs-4071	501	4	)	)	PUNCT
iajs-4071	501	5	be	be	AUX
iajs-4071	501	6	a	a	DET
iajs-4071	501	7	soft	soft	ADJ
iajs-4071	501	8	open	open	ADJ
iajs-4071	501	9	set	set	NOUN
iajs-4071	501	10	of	of	ADP
iajs-4071	501	11	̃.	̃.	NOUN
iajs-4071	501	12	now	now	ADV
iajs-4071	501	13	(	(	PUNCT
iajs-4071	501	14	)	)	PUNCT
iajs-4071	501	15	)	)	PUNCT
iajs-4071	501	16	)	)	PUNCT
iajs-4071	501	17	)	)	PUNCT
iajs-4071	501	18	)	)	PUNCT
iajs-4071	501	19	)	)	PUNCT
iajs-4071	501	20	.	.	PUNCT
iajs-4071	502	1	since	since	SCONJ
iajs-4071	502	2	is	be	AUX
iajs-4071	502	3	̃	̃	PROPN
iajs-4071	502	4	-continuous	-continuous	ADJ
iajs-4071	502	5	,	,	PUNCT
iajs-4071	502	6	then	then	ADV
iajs-4071	502	7	by	by	ADP
iajs-4071	502	8	proposition	proposition	NOUN
iajs-4071	502	9	4.2	4.2	NUM
iajs-4071	502	10	,	,	PUNCT
iajs-4071	502	11	)	)	PUNCT
iajs-4071	502	12	is	be	AUX
iajs-4071	502	13	̃	̃	PROPN
iajs-4071	502	14	-open	-open	NOUN
iajs-4071	502	15	set	set	VERB
iajs-4071	502	16	in	in	ADP
iajs-4071	502	17	)	)	PUNCT
iajs-4071	502	18	.	.	PUNCT
iajs-4071	503	1	but	but	CCONJ
iajs-4071	503	2	)	)	PUNCT
iajs-4071	503	3	is	be	AUX
iajs-4071	503	4	soft	soft	ADJ
iajs-4071	503	5	clopen	clopen	ADJ
iajs-4071	503	6	set	set	NOUN
iajs-4071	503	7	in	in	ADP
iajs-4071	503	8	̃.	̃.	NOUN
iajs-4071	503	9	then	then	ADV
iajs-4071	503	10	by	by	ADP
iajs-4071	503	11	corollary	corollary	ADJ
iajs-4071	503	12	3.26	3.26	NUM
iajs-4071	503	13	,	,	PUNCT
iajs-4071	503	14	)	)	PUNCT
iajs-4071	503	15	is	be	AUX
iajs-4071	503	16	̃	̃	PROPN
iajs-4071	503	17	-open	-open	NOUN
iajs-4071	503	18	set	set	VERB
iajs-4071	503	19	in	in	ADP
iajs-4071	503	20	̃.	̃.	NOUN
iajs-4071	503	21	similarly	similarly	ADV
iajs-4071	503	22	,	,	PUNCT
iajs-4071	503	23	)	)	PUNCT
iajs-4071	503	24	is	be	AUX
iajs-4071	503	25	̃	̃	PROPN
iajs-4071	503	26	-open	-open	NOUN
iajs-4071	503	27	set	set	VERB
iajs-4071	503	28	in	in	ADP
iajs-4071	503	29	)	)	PUNCT
iajs-4071	503	30	,	,	PUNCT
iajs-4071	503	31	and	and	CCONJ
iajs-4071	503	32	hence	hence	ADV
iajs-4071	503	33	̃	̃	ADV
iajs-4071	503	34	-open	-open	NOUN
iajs-4071	503	35	set	set	VERB
iajs-4071	503	36	in	in	ADP
iajs-4071	503	37	̃.	̃.	NOUN
iajs-4071	503	38	since	since	SCONJ
iajs-4071	503	39	the	the	DET
iajs-4071	503	40	union	union	NOUN
iajs-4071	503	41	of	of	ADP
iajs-4071	503	42	two	two	NUM
iajs-4071	503	43	̃	̃	PROPN
iajs-4071	503	44	-open	-open	NOUN
iajs-4071	503	45	set	set	NOUN
iajs-4071	503	46	is	be	AUX
iajs-4071	503	47	̃	̃	NOUN
iajs-4071	503	48	-open	-open	ADJ
iajs-4071	503	49	.	.	PUNCT
iajs-4071	504	1	therefore	therefore	ADV
iajs-4071	504	2	,	,	PUNCT
iajs-4071	504	3	(	(	PUNCT
iajs-4071	504	4	)	)	PUNCT
iajs-4071	504	5	)	)	PUNCT
iajs-4071	504	6	)	)	PUNCT
iajs-4071	504	7	)	)	PUNCT
iajs-4071	504	8	is	be	AUX
iajs-4071	504	9	̃	̃	ADV
iajs-4071	504	10	open	open	ADJ
iajs-4071	504	11	set	set	VERB
iajs-4071	504	12	in	in	ADP
iajs-4071	504	13	̃.	̃.	NOUN
iajs-4071	504	14	hence	hence	ADV
iajs-4071	504	15	by	by	ADP
iajs-4071	504	16	proposition	proposition	NOUN
iajs-4071	504	17	4.2	4.2	NUM
iajs-4071	504	18	is	be	AUX
iajs-4071	504	19	̃	̃	ADV
iajs-4071	504	20	-continuous	-continuous	ADJ
iajs-4071	504	21	.	.	PUNCT
iajs-4071	505	1	5.8	5.8	NUM
iajs-4071	505	2	.	.	PUNCT
iajs-4071	505	3	proposition	proposition	NOUN
iajs-4071	505	4	let	let	VERB
iajs-4071	505	5	(	(	PUNCT
iajs-4071	505	6	̃	̃	NOUN
iajs-4071	505	7	̃	̃	ADJ
iajs-4071	505	8	)	)	PUNCT
iajs-4071	505	9	̃	̃	NOUN
iajs-4071	505	10	̃	̃	NOUN
iajs-4071	505	11	)	)	PUNCT
iajs-4071	505	12	be	be	VERB
iajs-4071	505	13	̃	̃	ADV
iajs-4071	505	14	-continuous	-continuous	ADJ
iajs-4071	505	15	.	.	PUNCT
iajs-4071	506	1	if	if	SCONJ
iajs-4071	506	2	̃	̃	PROPN
iajs-4071	506	3	is	be	AUX
iajs-4071	506	4	a	a	DET
iajs-4071	506	5	soft	soft	ADJ
iajs-4071	506	6	clopen	clopen	ADJ
iajs-4071	506	7	subset	subset	NOUN
iajs-4071	506	8	of	of	ADP
iajs-4071	506	9	a	a	DET
iajs-4071	506	10	sts	st	NOUN
iajs-4071	506	11	̃	̃	PROPN
iajs-4071	506	12	,	,	PUNCT
iajs-4071	506	13	then	then	ADV
iajs-4071	506	14	(	(	PUNCT
iajs-4071	506	15	̃	̃	PROPN
iajs-4071	506	16	̃	̃	NOUN
iajs-4071	506	17	)	)	PUNCT
iajs-4071	506	18	(	(	PUNCT
iajs-4071	506	19	̃	̃	NOUN
iajs-4071	506	20	̃	̃	PROPN
iajs-4071	506	21	)	)	PUNCT
iajs-4071	506	22	is	be	AUX
iajs-4071	506	23	̃	̃	ADV
iajs-4071	506	24	-continuous	-continuous	ADJ
iajs-4071	506	25	.	.	PUNCT
iajs-4071	507	1	proof	proof	NOUN
iajs-4071	507	2	:	:	PUNCT
iajs-4071	507	3	suppose	suppose	VERB
iajs-4071	507	4	̃	̃	PROPN
iajs-4071	507	5	̃	̃	NOUN
iajs-4071	507	6	̃	̃	NUM
iajs-4071	507	7	)	)	PUNCT
iajs-4071	507	8	and	and	CCONJ
iajs-4071	507	9	)	)	PUNCT
iajs-4071	507	10	be	be	AUX
iajs-4071	507	11	any	any	DET
iajs-4071	507	12	soft	soft	ADJ
iajs-4071	507	13	open	open	ADJ
iajs-4071	507	14	set	set	NOUN
iajs-4071	507	15	of	of	ADP
iajs-4071	507	16	̃	̃	PROPN
iajs-4071	507	17	containing	contain	VERB
iajs-4071	507	18	)	)	PUNCT
iajs-4071	507	19	,	,	PUNCT
iajs-4071	507	20	then	then	ADV
iajs-4071	507	21	)	)	PUNCT
iajs-4071	508	1	̃	̃	NOUN
iajs-4071	508	2	is	be	AUX
iajs-4071	508	3	a	a	DET
iajs-4071	508	4	soft	soft	ADJ
iajs-4071	508	5	open	open	ADJ
iajs-4071	508	6	set	set	NOUN
iajs-4071	508	7	in	in	ADP
iajs-4071	508	8	̃.	̃.	NOUN
iajs-4071	508	9	but	but	CCONJ
iajs-4071	508	10	)	)	PUNCT
iajs-4071	509	1	̃	̃	PROPN
iajs-4071	509	2	̃	̃	NOUN
iajs-4071	509	3	̃	̃	ADJ
iajs-4071	509	4	)	)	PUNCT
iajs-4071	509	5	̃	̃	PROPN
iajs-4071	509	6	̃	̃	PROPN
iajs-4071	509	7	̃	̃	NUM
iajs-4071	509	8	)	)	PUNCT
iajs-4071	509	9	,	,	PUNCT
iajs-4071	509	10	then	then	ADV
iajs-4071	509	11	)	)	PUNCT
iajs-4071	509	12	̃	̃	PROPN
iajs-4071	509	13	)	)	PUNCT
iajs-4071	509	14	̃.	̃.	NOUN
iajs-4071	509	15	since	since	SCONJ
iajs-4071	509	16	(	(	PUNCT
iajs-4071	509	17	̃	̃	NOUN
iajs-4071	509	18	̃	̃	ADJ
iajs-4071	509	19	)	)	PUNCT
iajs-4071	509	20	̃	̃	NOUN
iajs-4071	509	21	̃	̃	NOUN
iajs-4071	509	22	)	)	PUNCT
iajs-4071	509	23	is	be	AUX
iajs-4071	509	24	̃	̃	ADV
iajs-4071	509	25	-continuous	-continuous	ADJ
iajs-4071	509	26	,	,	PUNCT
iajs-4071	509	27	then	then	ADV
iajs-4071	509	28	a	a	DET
iajs-4071	509	29	̃	̃	ADV
iajs-4071	509	30	-open	-open	NOUN
iajs-4071	509	31	set	set	NOUN
iajs-4071	509	32	)	)	PUNCT
iajs-4071	509	33	containing	contain	VERB
iajs-4071	509	34	s.t	s.t	PROPN
iajs-4071	509	35	.	.	PROPN
iajs-4071	509	36	)	)	PUNCT
iajs-4071	509	37	)	)	PUNCT
iajs-4071	510	1	̃	̃	PROPN
iajs-4071	510	2	(	(	PUNCT
iajs-4071	510	3	)	)	PUNCT
iajs-4071	510	4	̃	̃	ADJ
iajs-4071	510	5	)	)	PUNCT
iajs-4071	510	6	̃	̃	NOUN
iajs-4071	510	7	)	)	PUNCT
iajs-4071	510	8	.	.	PUNCT
iajs-4071	511	1	therefore	therefore	ADV
iajs-4071	511	2	(	(	PUNCT
iajs-4071	511	3	̃	̃	NOUN
iajs-4071	511	4	̃	̃	NOUN
iajs-4071	511	5	)	)	PUNCT
iajs-4071	511	6	(	(	PUNCT
iajs-4071	511	7	̃	̃	NOUN
iajs-4071	511	8	̃	̃	PROPN
iajs-4071	511	9	)	)	PUNCT
iajs-4071	511	10	is	be	AUX
iajs-4071	511	11	̃	̃	ADV
iajs-4071	511	12	-continuous	-continuous	ADJ
iajs-4071	511	13	.	.	PUNCT
iajs-4071	512	1	6	6	NUM
iajs-4071	512	2	.	.	X
iajs-4071	512	3	conclusion	conclusion	NOUN
iajs-4071	512	4	through	through	ADP
iajs-4071	512	5	the	the	DET
iajs-4071	512	6	current	current	ADJ
iajs-4071	512	7	research	research	NOUN
iajs-4071	512	8	work	work	NOUN
iajs-4071	512	9	,	,	PUNCT
iajs-4071	512	10	we	we	PRON
iajs-4071	512	11	have	have	AUX
iajs-4071	512	12	continued	continue	VERB
iajs-4071	512	13	to	to	PART
iajs-4071	512	14	investigate	investigate	VERB
iajs-4071	512	15	the	the	DET
iajs-4071	512	16	properties	property	NOUN
iajs-4071	512	17	of	of	ADP
iajs-4071	512	18	soft	soft	ADJ
iajs-4071	512	19	beta	beta	NOUN
iajs-4071	512	20	open	open	ADJ
iajs-4071	512	21	sets	set	NOUN
iajs-4071	512	22	in	in	ADP
iajs-4071	512	23	soft	soft	ADJ
iajs-4071	512	24	topological	topological	ADJ
iajs-4071	512	25	spaces	space	NOUN
iajs-4071	512	26	.	.	PUNCT
iajs-4071	513	1	̃	̃	ADJ
iajs-4071	513	2	-open	-open	NOUN
iajs-4071	513	3	sets	set	NOUN
iajs-4071	513	4	is	be	AUX
iajs-4071	513	5	defined	define	VERB
iajs-4071	513	6	as	as	ADP
iajs-4071	513	7	a	a	DET
iajs-4071	513	8	new	new	ADJ
iajs-4071	513	9	kind	kind	NOUN
iajs-4071	513	10	of	of	ADP
iajs-4071	513	11	soft	soft	ADJ
iajs-4071	513	12	sets	set	NOUN
iajs-4071	513	13	which	which	PRON
iajs-4071	513	14	is	be	AUX
iajs-4071	513	15	a	a	DET
iajs-4071	513	16	stronger	strong	ADJ
iajs-4071	513	17	form	form	NOUN
iajs-4071	513	18	of	of	ADP
iajs-4071	513	19	soft	soft	ADJ
iajs-4071	513	20	-open	-open	ADJ
iajs-4071	513	21	sets	set	NOUN
iajs-4071	513	22	and	and	CCONJ
iajs-4071	513	23	weaker	weak	ADJ
iajs-4071	513	24	than	than	ADP
iajs-4071	513	25	each	each	PRON
iajs-4071	513	26	of	of	ADP
iajs-4071	513	27	̃	̃	PROPN
iajs-4071	513	28	-open	-open	ADJ
iajs-4071	513	29	,	,	PUNCT
iajs-4071	513	30	soft	soft	ADJ
iajs-4071	513	31	clopen	clopen	ADJ
iajs-4071	513	32	sets	set	NOUN
iajs-4071	513	33	and	and	CCONJ
iajs-4071	513	34	some	some	DET
iajs-4071	513	35	other	other	ADJ
iajs-4071	513	36	.	.	PUNCT
iajs-4071	514	1	we	we	PRON
iajs-4071	514	2	presented	present	VERB
iajs-4071	514	3	and	and	CCONJ
iajs-4071	514	4	examined	examine	VERB
iajs-4071	514	5	̃	̃	PROPN
iajs-4071	514	6	-continuous	-continuous	ADJ
iajs-4071	514	7	functions	function	NOUN
iajs-4071	514	8	in	in	ADP
iajs-4071	514	9	a	a	DET
iajs-4071	514	10	sts	st	NOUN
iajs-4071	514	11	.	.	PUNCT
iajs-4071	515	1	we	we	PRON
iajs-4071	515	2	also	also	ADV
iajs-4071	515	3	identified	identify	VERB
iajs-4071	515	4	some	some	DET
iajs-4071	515	5	characterizations	characterization	NOUN
iajs-4071	515	6	and	and	CCONJ
iajs-4071	515	7	basic	basic	ADJ
iajs-4071	515	8	properties	property	NOUN
iajs-4071	515	9	of	of	ADP
iajs-4071	515	10	these	these	DET
iajs-4071	515	11	soft	soft	ADJ
iajs-4071	515	12	functions	function	NOUN
iajs-4071	515	13	as	as	ADV
iajs-4071	515	14	well	well	ADV
iajs-4071	515	15	as	as	ADP
iajs-4071	515	16	their	their	PRON
iajs-4071	515	17	relationships	relationship	NOUN
iajs-4071	515	18	to	to	ADP
iajs-4071	515	19	certain	certain	ADJ
iajs-4071	515	20	other	other	ADJ
iajs-4071	515	21	categories	category	NOUN
iajs-4071	515	22	of	of	ADP
iajs-4071	515	23	soft	soft	ADJ
iajs-4071	515	24	functions	function	NOUN
iajs-4071	515	25	and	and	CCONJ
iajs-4071	515	26	documented	document	VERB
iajs-4071	515	27	with	with	ADP
iajs-4071	515	28	some	some	DET
iajs-4071	515	29	illustrative	illustrative	ADJ
iajs-4071	515	30	examples	example	NOUN
iajs-4071	515	31	.	.	PUNCT
iajs-4071	516	1	acknowledgments	acknowledgment	NOUN
iajs-4071	516	2	no	no	DET
iajs-4071	516	3	thanks	thank	NOUN
iajs-4071	516	4	.	.	PUNCT
iajs-4071	517	1	conflict	conflict	NOUN
iajs-4071	517	2	of	of	ADP
iajs-4071	517	3	interest	interest	NOUN
iajs-4071	517	4	the	the	DET
iajs-4071	517	5	publication	publication	NOUN
iajs-4071	517	6	fee	fee	NOUN
iajs-4071	517	7	for	for	ADP
iajs-4071	517	8	this	this	DET
iajs-4071	517	9	article	article	NOUN
iajs-4071	517	10	was	be	AUX
iajs-4071	517	11	funded	fund	VERB
iajs-4071	517	12	by	by	ADP
iajs-4071	517	13	the	the	DET
iajs-4071	517	14	university	university	NOUN
iajs-4071	517	15	of	of	ADP
iajs-4071	517	16	salahaddin	salahaddin	VERB
iajs-4071	517	17	erbil	erbil	PROPN
iajs-4071	517	18	.	.	PUNCT
iajs-4071	518	1	ihjpas	ihjpas	PROPN
iajs-4071	518	2	.	.	PUNCT
iajs-4071	519	1	2025,38(4	2025,38(4	NOUN
iajs-4071	519	2	)	)	PUNCT
iajs-4071	519	3	375	375	NUM
iajs-4071	519	4	funding	fund	VERB
iajs-4071	519	5	no	no	DET
iajs-4071	519	6	funding	funding	NOUN
iajs-4071	519	7	.	.	PUNCT
iajs-4071	520	1	references	reference	NOUN
iajs-4071	520	2	1	1	NUM
iajs-4071	520	3	.	.	PUNCT
iajs-4071	521	1	molodtsov	molodtsov	PROPN
iajs-4071	521	2	d.	d.	PROPN
iajs-4071	521	3	soft	soft	ADJ
iajs-4071	521	4	set	set	PROPN
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iajs-4071	521	6	—	—	PUNCT
iajs-4071	521	7	first	first	ADJ
iajs-4071	521	8	results	result	NOUN
iajs-4071	521	9	.	.	PUNCT
iajs-4071	522	1	comput	comput	PROPN
iajs-4071	522	2	math	math	PROPN
iajs-4071	522	3	appl	appl	PROPN
iajs-4071	522	4	.	.	PUNCT
iajs-4071	523	1	1999;37:19–31	1999;37:19–31	NUM
iajs-4071	523	2	.	.	PUNCT
iajs-4071	524	1	https.//doi.org/10.1016	https.//doi.org/10.1016	PROPN
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iajs-4071	524	3	s0898	s0898	PROPN
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iajs-4071	524	6	-	-	SYM
iajs-4071	524	7	5	5	NUM
iajs-4071	524	8	2	2	NUM
iajs-4071	524	9	.	.	PUNCT
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iajs-4071	525	2	m	m	PROPN
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iajs-4071	525	6	on	on	ADP
iajs-4071	525	7	soft	soft	ADJ
iajs-4071	525	8	topological	topological	ADJ
iajs-4071	525	9	spaces	space	NOUN
iajs-4071	525	10	.	.	PUNCT
iajs-4071	526	1	comput	comput	PROPN
iajs-4071	526	2	math	math	PROPN
iajs-4071	526	3	appl	appl	PROPN
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iajs-4071	527	1	2011;61(7):1786–1799	2011;61(7):1786–1799	NUM
iajs-4071	527	2	.	.	PUNCT
iajs-4071	528	1	https.//doi.org/10.1016	https.//doi.org/10.1016	PROPN
iajs-4071	528	2	/	/	SYM
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iajs-4071	528	5	.	.	PUNCT
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iajs-4071	529	2	-	-	PUNCT
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iajs-4071	529	18	of	of	ADP
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iajs-4071	529	20	open	open	ADJ
iajs-4071	529	21	sets	set	NOUN
iajs-4071	529	22	and	and	CCONJ
iajs-4071	529	23	its	its	PRON
iajs-4071	529	24	applications	application	NOUN
iajs-4071	529	25	via	via	ADP
iajs-4071	529	26	soft	soft	ADJ
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iajs-4071	529	28	.	.	PUNCT
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iajs-4071	530	2	.	.	PUNCT
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iajs-4071	531	2	:	:	PUNCT
iajs-4071	531	3	840	840	NUM
iajs-4071	531	4	.	.	PUNCT
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iajs-4071	535	2	.	.	PUNCT
iajs-4071	536	1	https.//doi.org/10.24996	https.//doi.org/10.24996	PROPN
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iajs-4071	536	5	.	.	PUNCT
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iajs-4071	555	5	.	.	PUNCT
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iajs-4071	559	5	.	.	PUNCT
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iajs-4071	571	4	.	.	PUNCT
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