id	sid	tid	token	lemma	pos
ejpam-5430	1	1	european	european	PROPN
ejpam-5430	1	2	journal	journal	PROPN
ejpam-5430	1	3	of	of	ADP
ejpam-5430	1	4	pure	pure	ADJ
ejpam-5430	1	5	and	and	CCONJ
ejpam-5430	1	6	applied	apply	VERB
ejpam-5430	1	7	mathematics	mathematic	NOUN
ejpam-5430	1	8	vol	vol	NOUN
ejpam-5430	1	9	.	.	PROPN
ejpam-5430	2	1	17	17	NUM
ejpam-5430	2	2	,	,	PUNCT
ejpam-5430	2	3	no	no	INTJ
ejpam-5430	2	4	.	.	NOUN
ejpam-5430	2	5	4	4	NUM
ejpam-5430	2	6	,	,	PUNCT
ejpam-5430	2	7	2024	2024	NUM
ejpam-5430	2	8	,	,	PUNCT
ejpam-5430	2	9	4147	4147	NUM
ejpam-5430	2	10	-	-	SYM
ejpam-5430	2	11	4163	4163	NUM
ejpam-5430	2	12	issn	issn	PROPN
ejpam-5430	2	13	1307	1307	NUM
ejpam-5430	2	14	-	-	SYM
ejpam-5430	2	15	5543	5543	NUM
ejpam-5430	2	16	–	–	PUNCT
ejpam-5430	2	17	ejpam.com	ejpam.com	X
ejpam-5430	2	18	published	publish	VERB
ejpam-5430	2	19	by	by	ADP
ejpam-5430	2	20	new	new	PROPN
ejpam-5430	2	21	york	york	PROPN
ejpam-5430	2	22	business	business	PROPN
ejpam-5430	2	23	global	global	PROPN
ejpam-5430	2	24	pythagorean	pythagorean	PROPN
ejpam-5430	2	25	fuzzy	fuzzy	ADJ
ejpam-5430	2	26	soft	soft	ADJ
ejpam-5430	2	27	somewhat	somewhat	ADV
ejpam-5430	2	28	continuous	continuous	ADJ
ejpam-5430	2	29	functions	function	NOUN
ejpam-5430	2	30	a.	a.	NOUN
ejpam-5430	2	31	a.	a.	PROPN
ejpam-5430	2	32	azzam1,2,∗	azzam1,2,∗	PROPN
ejpam-5430	2	33	,	,	PUNCT
ejpam-5430	2	34	m.	m.	NOUN
ejpam-5430	2	35	aldawood1	aldawood1	PROPN
ejpam-5430	2	36	,	,	PUNCT
ejpam-5430	2	37	radwan	radwan	VERB
ejpam-5430	2	38	abu	abu	PROPN
ejpam-5430	2	39	-	-	PUNCT
ejpam-5430	2	40	gdairi3	gdairi3	PROPN
ejpam-5430	2	41	1	1	NUM
ejpam-5430	2	42	mathematics	mathematics	PROPN
ejpam-5430	2	43	department	department	NOUN
ejpam-5430	2	44	,	,	PUNCT
ejpam-5430	2	45	faculty	faculty	NOUN
ejpam-5430	2	46	of	of	ADP
ejpam-5430	2	47	science	science	NOUN
ejpam-5430	2	48	and	and	CCONJ
ejpam-5430	2	49	humanities	humanity	NOUN
ejpam-5430	2	50	,	,	PUNCT
ejpam-5430	2	51	prince	prince	PROPN
ejpam-5430	2	52	sattam	sattam	PROPN
ejpam-5430	2	53	bin	bin	PROPN
ejpam-5430	2	54	abdulaziz	abdulaziz	PROPN
ejpam-5430	2	55	university	university	PROPN
ejpam-5430	2	56	,	,	PUNCT
ejpam-5430	2	57	alkharj	alkharj	VERB
ejpam-5430	2	58	11942	11942	NUM
ejpam-5430	2	59	,	,	PUNCT
ejpam-5430	2	60	saudi	saudi	PROPN
ejpam-5430	2	61	arabia	arabia	PROPN
ejpam-5430	2	62	2	2	NUM
ejpam-5430	2	63	mathematics	mathematics	PROPN
ejpam-5430	2	64	department	department	NOUN
ejpam-5430	2	65	,	,	PUNCT
ejpam-5430	2	66	faculty	faculty	NOUN
ejpam-5430	2	67	of	of	ADP
ejpam-5430	2	68	science	science	NOUN
ejpam-5430	2	69	,	,	PUNCT
ejpam-5430	2	70	new	new	ADJ
ejpam-5430	2	71	valley	valley	NOUN
ejpam-5430	2	72	university	university	NOUN
ejpam-5430	2	73	,	,	PUNCT
ejpam-5430	2	74	elkharga	elkharga	NOUN
ejpam-5430	2	75	72511	72511	NUM
ejpam-5430	2	76	,	,	PUNCT
ejpam-5430	2	77	egypt	egypt	PROPN
ejpam-5430	2	78	3	3	NUM
ejpam-5430	2	79	mathematics	mathematics	PROPN
ejpam-5430	2	80	department	department	NOUN
ejpam-5430	2	81	,	,	PUNCT
ejpam-5430	2	82	faculty	faculty	NOUN
ejpam-5430	2	83	of	of	ADP
ejpam-5430	2	84	science	science	NOUN
ejpam-5430	2	85	,	,	PUNCT
ejpam-5430	2	86	zarqa	zarqa	PROPN
ejpam-5430	2	87	university	university	PROPN
ejpam-5430	2	88	,	,	PUNCT
ejpam-5430	2	89	zarqa	zarqa	PROPN
ejpam-5430	2	90	13132	13132	NUM
ejpam-5430	2	91	,	,	PUNCT
ejpam-5430	2	92	jordan	jordan	PROPN
ejpam-5430	2	93	abstract	abstract	PROPN
ejpam-5430	2	94	.	.	PUNCT
ejpam-5430	3	1	in	in	ADP
ejpam-5430	3	2	this	this	DET
ejpam-5430	3	3	work	work	NOUN
ejpam-5430	3	4	,	,	PUNCT
ejpam-5430	3	5	we	we	PRON
ejpam-5430	3	6	introduce	introduce	VERB
ejpam-5430	3	7	the	the	DET
ejpam-5430	3	8	concept	concept	NOUN
ejpam-5430	3	9	of	of	ADP
ejpam-5430	3	10	pythagorean	pythagorean	PROPN
ejpam-5430	3	11	fuzzy	fuzzy	ADJ
ejpam-5430	3	12	soft	soft	ADJ
ejpam-5430	3	13	somewhat	somewhat	ADV
ejpam-5430	3	14	open	open	ADJ
ejpam-5430	3	15	sets	set	NOUN
ejpam-5430	3	16	utilizing	utilize	VERB
ejpam-5430	3	17	the	the	DET
ejpam-5430	3	18	pythagorean	pythagorean	PROPN
ejpam-5430	3	19	fuzzy	fuzzy	ADJ
ejpam-5430	3	20	soft	soft	ADJ
ejpam-5430	3	21	interior	interior	ADJ
ejpam-5430	3	22	operator	operator	NOUN
ejpam-5430	3	23	,	,	PUNCT
ejpam-5430	3	24	extending	extend	VERB
ejpam-5430	3	25	its	its	PRON
ejpam-5430	3	26	application	application	NOUN
ejpam-5430	3	27	to	to	PART
ejpam-5430	3	28	pythagorean	pythagorean	VERB
ejpam-5430	3	29	fuzzy	fuzzy	ADJ
ejpam-5430	3	30	soft	soft	ADJ
ejpam-5430	3	31	topological	topological	ADJ
ejpam-5430	3	32	spaces	space	NOUN
ejpam-5430	3	33	.	.	PUNCT
ejpam-5430	4	1	this	this	DET
ejpam-5430	4	2	study	study	NOUN
ejpam-5430	4	3	aims	aim	VERB
ejpam-5430	4	4	to	to	PART
ejpam-5430	4	5	enhance	enhance	VERB
ejpam-5430	4	6	decision	decision	NOUN
ejpam-5430	4	7	-	-	PUNCT
ejpam-5430	4	8	making	make	VERB
ejpam-5430	4	9	processes	process	NOUN
ejpam-5430	4	10	in	in	ADP
ejpam-5430	4	11	futureassisted	futureassiste	VERB
ejpam-5430	4	12	economies	economy	NOUN
ejpam-5430	4	13	by	by	ADP
ejpam-5430	4	14	addressing	address	VERB
ejpam-5430	4	15	the	the	DET
ejpam-5430	4	16	limitations	limitation	NOUN
ejpam-5430	4	17	of	of	ADP
ejpam-5430	4	18	existing	exist	VERB
ejpam-5430	4	19	fuzzy	fuzzy	ADJ
ejpam-5430	4	20	set	set	NOUN
ejpam-5430	4	21	theories	theory	NOUN
ejpam-5430	4	22	.	.	PUNCT
ejpam-5430	5	1	we	we	PRON
ejpam-5430	5	2	investigate	investigate	VERB
ejpam-5430	5	3	the	the	DET
ejpam-5430	5	4	distinctive	distinctive	ADJ
ejpam-5430	5	5	properties	property	NOUN
ejpam-5430	5	6	of	of	ADP
ejpam-5430	5	7	pythagorean	pythagorean	PROPN
ejpam-5430	5	8	fuzzy	fuzzy	ADJ
ejpam-5430	5	9	soft	soft	ADJ
ejpam-5430	5	10	somewhat	somewhat	ADV
ejpam-5430	5	11	open	open	ADJ
ejpam-5430	5	12	sets	set	NOUN
ejpam-5430	5	13	as	as	ADP
ejpam-5430	5	14	a	a	DET
ejpam-5430	5	15	subclass	subclass	NOUN
ejpam-5430	5	16	of	of	ADP
ejpam-5430	5	17	pythagorean	pythagorean	PROPN
ejpam-5430	5	18	fuzzy	fuzzy	ADJ
ejpam-5430	5	19	soft	soft	ADJ
ejpam-5430	5	20	somewhere	somewhere	ADV
ejpam-5430	5	21	dense	dense	ADJ
ejpam-5430	5	22	sets	set	NOUN
ejpam-5430	5	23	.	.	PUNCT
ejpam-5430	6	1	additionally	additionally	ADV
ejpam-5430	6	2	,	,	PUNCT
ejpam-5430	6	3	we	we	PRON
ejpam-5430	6	4	explore	explore	VERB
ejpam-5430	6	5	pythagorean	pythagorean	PROPN
ejpam-5430	6	6	fuzzy	fuzzy	ADJ
ejpam-5430	6	7	soft	soft	ADJ
ejpam-5430	6	8	somewhat	somewhat	ADV
ejpam-5430	6	9	metamorphism	metamorphism	NOUN
ejpam-5430	6	10	’s	’s	NOUN
ejpam-5430	6	11	within	within	ADP
ejpam-5430	6	12	the	the	DET
ejpam-5430	6	13	context	context	NOUN
ejpam-5430	6	14	of	of	ADP
ejpam-5430	6	15	pythagorean	pythagorean	PROPN
ejpam-5430	6	16	fuzzy	fuzzy	ADJ
ejpam-5430	6	17	soft	soft	ADJ
ejpam-5430	6	18	somewhat	somewhat	ADV
ejpam-5430	6	19	continuous	continuous	ADJ
ejpam-5430	6	20	functions	function	NOUN
ejpam-5430	6	21	,	,	PUNCT
ejpam-5430	6	22	offering	offer	VERB
ejpam-5430	6	23	new	new	ADJ
ejpam-5430	6	24	insights	insight	NOUN
ejpam-5430	6	25	into	into	ADP
ejpam-5430	6	26	their	their	PRON
ejpam-5430	6	27	topological	topological	ADJ
ejpam-5430	6	28	invariant	invariant	NOUN
ejpam-5430	6	29	.	.	PUNCT
ejpam-5430	7	1	through	through	ADP
ejpam-5430	7	2	detailed	detailed	ADJ
ejpam-5430	7	3	analysis	analysis	NOUN
ejpam-5430	7	4	and	and	CCONJ
ejpam-5430	7	5	examples	example	NOUN
ejpam-5430	7	6	,	,	PUNCT
ejpam-5430	7	7	we	we	PRON
ejpam-5430	7	8	demonstrate	demonstrate	VERB
ejpam-5430	7	9	the	the	DET
ejpam-5430	7	10	applicability	applicability	NOUN
ejpam-5430	7	11	of	of	ADP
ejpam-5430	7	12	these	these	DET
ejpam-5430	7	13	concepts	concept	NOUN
ejpam-5430	7	14	in	in	ADP
ejpam-5430	7	15	various	various	ADJ
ejpam-5430	7	16	scientific	scientific	ADJ
ejpam-5430	7	17	and	and	CCONJ
ejpam-5430	7	18	engineering	engineering	NOUN
ejpam-5430	7	19	problems	problem	NOUN
ejpam-5430	7	20	.	.	PUNCT
ejpam-5430	8	1	this	this	DET
ejpam-5430	8	2	work	work	NOUN
ejpam-5430	8	3	provides	provide	VERB
ejpam-5430	8	4	a	a	DET
ejpam-5430	8	5	comprehensive	comprehensive	ADJ
ejpam-5430	8	6	framework	framework	NOUN
ejpam-5430	8	7	for	for	ADP
ejpam-5430	8	8	understanding	understanding	NOUN
ejpam-5430	8	9	and	and	CCONJ
ejpam-5430	8	10	utilizing	utilize	VERB
ejpam-5430	8	11	pythagorean	pythagorean	PROPN
ejpam-5430	8	12	fuzzy	fuzzy	ADJ
ejpam-5430	8	13	soft	soft	ADJ
ejpam-5430	8	14	sets	set	NOUN
ejpam-5430	8	15	in	in	ADP
ejpam-5430	8	16	complex	complex	ADJ
ejpam-5430	8	17	decision	decision	NOUN
ejpam-5430	8	18	-	-	PUNCT
ejpam-5430	8	19	making	make	VERB
ejpam-5430	8	20	scenarios	scenario	NOUN
ejpam-5430	8	21	.	.	PUNCT
ejpam-5430	9	1	finally	finally	ADV
ejpam-5430	9	2	,	,	PUNCT
ejpam-5430	9	3	we	we	PRON
ejpam-5430	9	4	compare	compare	VERB
ejpam-5430	9	5	various	various	ADJ
ejpam-5430	9	6	relationships	relationship	NOUN
ejpam-5430	9	7	across	across	ADP
ejpam-5430	9	8	some	some	DET
ejpam-5430	9	9	generalizations	generalization	NOUN
ejpam-5430	9	10	of	of	ADP
ejpam-5430	9	11	pythagorean	pythagorean	PROPN
ejpam-5430	9	12	fuzzy	fuzzy	ADJ
ejpam-5430	9	13	soft	soft	ADJ
ejpam-5430	9	14	continuous	continuous	ADJ
ejpam-5430	9	15	functions	function	NOUN
ejpam-5430	9	16	.	.	PUNCT
ejpam-5430	10	1	2020	2020	NUM
ejpam-5430	10	2	mathematics	mathematic	NOUN
ejpam-5430	10	3	subject	subject	NOUN
ejpam-5430	10	4	classifications	classification	NOUN
ejpam-5430	10	5	:	:	PUNCT
ejpam-5430	10	6	54c08	54c08	NUM
ejpam-5430	10	7	,	,	PUNCT
ejpam-5430	10	8	03e99	03e99	NUM
ejpam-5430	10	9	,	,	PUNCT
ejpam-5430	10	10	54c10	54c10	NUM
ejpam-5430	10	11	,	,	PUNCT
ejpam-5430	10	12	03e72	03e72	X
ejpam-5430	10	13	key	key	ADJ
ejpam-5430	10	14	words	word	NOUN
ejpam-5430	10	15	and	and	CCONJ
ejpam-5430	10	16	phrases	phrase	NOUN
ejpam-5430	10	17	:	:	PUNCT
ejpam-5430	10	18	fuzzy	fuzzy	ADJ
ejpam-5430	10	19	soft	soft	ADJ
ejpam-5430	10	20	,	,	PUNCT
ejpam-5430	10	21	pythagorean	pythagorean	ADJ
ejpam-5430	10	22	fuzzy	fuzzy	ADJ
ejpam-5430	10	23	soft	soft	ADJ
ejpam-5430	10	24	,	,	PUNCT
ejpam-5430	10	25	somewhat	somewhat	ADV
ejpam-5430	10	26	open	open	ADJ
ejpam-5430	10	27	set	set	NOUN
ejpam-5430	10	28	,	,	PUNCT
ejpam-5430	10	29	pythagorean	pythagorean	PROPN
ejpam-5430	10	30	fuzzy	fuzzy	ADJ
ejpam-5430	10	31	soft	soft	ADJ
ejpam-5430	10	32	somewhat	somewhat	ADV
ejpam-5430	10	33	open	open	ADJ
ejpam-5430	10	34	sets	set	NOUN
ejpam-5430	10	35	1	1	NUM
ejpam-5430	10	36	.	.	PUNCT
ejpam-5430	11	1	introduction	introduction	NOUN
ejpam-5430	11	2	many	many	ADJ
ejpam-5430	11	3	researchers	researcher	NOUN
ejpam-5430	11	4	in	in	ADP
ejpam-5430	11	5	the	the	DET
ejpam-5430	11	6	fields	field	NOUN
ejpam-5430	11	7	of	of	ADP
ejpam-5430	11	8	economics	economic	NOUN
ejpam-5430	11	9	,	,	PUNCT
ejpam-5430	11	10	engineering	engineering	NOUN
ejpam-5430	11	11	,	,	PUNCT
ejpam-5430	11	12	medicine	medicine	NOUN
ejpam-5430	11	13	,	,	PUNCT
ejpam-5430	11	14	and	and	CCONJ
ejpam-5430	11	15	other	other	ADJ
ejpam-5430	11	16	sciences	science	NOUN
ejpam-5430	11	17	face	face	VERB
ejpam-5430	11	18	the	the	DET
ejpam-5430	11	19	daily	daily	ADJ
ejpam-5430	11	20	challenge	challenge	NOUN
ejpam-5430	11	21	of	of	ADP
ejpam-5430	11	22	lacking	lack	VERB
ejpam-5430	11	23	sufficient	sufficient	ADJ
ejpam-5430	11	24	data	datum	NOUN
ejpam-5430	11	25	to	to	PART
ejpam-5430	11	26	make	make	VERB
ejpam-5430	11	27	decisions	decision	NOUN
ejpam-5430	11	28	due	due	ADJ
ejpam-5430	11	29	to	to	ADP
ejpam-5430	11	30	the	the	DET
ejpam-5430	11	31	emergence	emergence	NOUN
ejpam-5430	11	32	of	of	ADP
ejpam-5430	11	33	new	new	ADJ
ejpam-5430	11	34	problems	problem	NOUN
ejpam-5430	11	35	in	in	ADP
ejpam-5430	11	36	our	our	PRON
ejpam-5430	11	37	daily	daily	ADJ
ejpam-5430	11	38	lives	life	NOUN
ejpam-5430	11	39	that	that	PRON
ejpam-5430	11	40	did	do	AUX
ejpam-5430	11	41	not	not	PART
ejpam-5430	11	42	previously	previously	ADV
ejpam-5430	11	43	exist	exist	VERB
ejpam-5430	11	44	and	and	CCONJ
ejpam-5430	11	45	for	for	ADP
ejpam-5430	11	46	which	which	PRON
ejpam-5430	11	47	innovative	innovative	ADJ
ejpam-5430	11	48	and	and	CCONJ
ejpam-5430	11	49	modern	modern	ADJ
ejpam-5430	11	50	approaches	approach	NOUN
ejpam-5430	11	51	are	be	AUX
ejpam-5430	11	52	needed	need	VERB
ejpam-5430	11	53	to	to	PART
ejpam-5430	11	54	find	find	VERB
ejpam-5430	11	55	solutions	solution	NOUN
ejpam-5430	11	56	.	.	PUNCT
ejpam-5430	12	1	a	a	DET
ejpam-5430	12	2	topology	topology	NOUN
ejpam-5430	12	3	is	be	AUX
ejpam-5430	12	4	an	an	DET
ejpam-5430	12	5	important	important	ADJ
ejpam-5430	12	6	branch	branch	NOUN
ejpam-5430	12	7	of	of	ADP
ejpam-5430	12	8	mathematics	mathematic	NOUN
ejpam-5430	12	9	called	call	VERB
ejpam-5430	12	10	rubber	rubber	NOUN
ejpam-5430	12	11	geometry	geometry	NOUN
ejpam-5430	12	12	that	that	PRON
ejpam-5430	12	13	helps	help	VERB
ejpam-5430	12	14	solve	solve	VERB
ejpam-5430	12	15	these	these	DET
ejpam-5430	12	16	problems	problem	NOUN
ejpam-5430	12	17	.	.	PUNCT
ejpam-5430	13	1	as	as	ADP
ejpam-5430	13	2	a	a	DET
ejpam-5430	13	3	result	result	NOUN
ejpam-5430	13	4	,	,	PUNCT
ejpam-5430	13	5	scientists	scientist	NOUN
ejpam-5430	13	6	are	be	AUX
ejpam-5430	13	7	trying	try	VERB
ejpam-5430	13	8	to	to	PART
ejpam-5430	13	9	expand	expand	VERB
ejpam-5430	13	10	the	the	DET
ejpam-5430	13	11	topological	topological	ADJ
ejpam-5430	13	12	space	space	NOUN
ejpam-5430	13	13	in	in	ADP
ejpam-5430	13	14	order	order	NOUN
ejpam-5430	13	15	to	to	PART
ejpam-5430	13	16	help	help	VERB
ejpam-5430	13	17	with	with	ADP
ejpam-5430	13	18	∗corresponding	∗corresponde	VERB
ejpam-5430	13	19	author	author	NOUN
ejpam-5430	13	20	.	.	PUNCT
ejpam-5430	14	1	doi	doi	NOUN
ejpam-5430	14	2	:	:	PUNCT
ejpam-5430	14	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5430	https://doi.org/10.29020/nybg.ejpam.v17i4.5430	PROPN
ejpam-5430	14	4	email	email	NOUN
ejpam-5430	14	5	addresses	address	NOUN
ejpam-5430	14	6	:	:	PUNCT
ejpam-5430	14	7	aa.azzam@psau.edu.sa	aa.azzam@psau.edu.sa	PROPN
ejpam-5430	14	8	(	(	PUNCT
ejpam-5430	14	9	a.	a.	NOUN
ejpam-5430	14	10	a.	a.	PROPN
ejpam-5430	14	11	azzam	azzam	PROPN
ejpam-5430	14	12	)	)	PUNCT
ejpam-5430	14	13	,	,	PUNCT
ejpam-5430	14	14	rgdairi@zu.edu.jo	rgdairi@zu.edu.jo	PROPN
ejpam-5430	14	15	(	(	PUNCT
ejpam-5430	14	16	r.	r.	PROPN
ejpam-5430	14	17	abu	abu	PROPN
ejpam-5430	14	18	-	-	PUNCT
ejpam-5430	14	19	gdairi	gdairi	PROPN
ejpam-5430	14	20	)	)	PUNCT
ejpam-5430	14	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5430	15	1	4147	4147	NUM
ejpam-5430	15	2	copyright	copyright	NOUN
ejpam-5430	15	3	:	:	PUNCT
ejpam-5430	15	4	©	©	PROPN
ejpam-5430	15	5	2024	2024	NUM
ejpam-5430	15	6	the	the	DET
ejpam-5430	15	7	author(s	author(s	NOUN
ejpam-5430	15	8	)	)	PUNCT
ejpam-5430	15	9	.	.	PUNCT
ejpam-5430	16	1	(	(	PUNCT
ejpam-5430	16	2	cc	cc	NOUN
ejpam-5430	16	3	by	by	ADP
ejpam-5430	16	4	-	-	PUNCT
ejpam-5430	16	5	nc	nc	PROPN
ejpam-5430	16	6	4.0	4.0	NUM
ejpam-5430	16	7	)	)	PUNCT
ejpam-5430	16	8	a.	a.	NOUN
ejpam-5430	16	9	a.	a.	PROPN
ejpam-5430	16	10	azzam	azzam	PROPN
ejpam-5430	16	11	,	,	PUNCT
ejpam-5430	16	12	m.	m.	NOUN
ejpam-5430	16	13	aldawood	aldawood	PROPN
ejpam-5430	16	14	,	,	PUNCT
ejpam-5430	16	15	r.	r.	PROPN
ejpam-5430	16	16	abu	abu	PROPN
ejpam-5430	16	17	-	-	PUNCT
ejpam-5430	16	18	gdairi	gdairi	PROPN
ejpam-5430	16	19	/	/	SYM
ejpam-5430	16	20	eur	eur	PROPN
ejpam-5430	16	21	.	.	PUNCT
ejpam-5430	17	1	j.	j.	PROPN
ejpam-5430	17	2	pure	pure	PROPN
ejpam-5430	17	3	appl	appl	PROPN
ejpam-5430	17	4	.	.	PROPN
ejpam-5430	17	5	math	math	PROPN
ejpam-5430	17	6	,	,	PUNCT
ejpam-5430	17	7	17	17	NUM
ejpam-5430	17	8	(	(	PUNCT
ejpam-5430	17	9	4	4	NUM
ejpam-5430	17	10	)	)	PUNCT
ejpam-5430	17	11	(	(	PUNCT
ejpam-5430	17	12	2024	2024	NUM
ejpam-5430	17	13	)	)	PUNCT
ejpam-5430	17	14	,	,	PUNCT
ejpam-5430	17	15	4147	4147	NUM
ejpam-5430	17	16	-	-	SYM
ejpam-5430	17	17	4163	4163	NUM
ejpam-5430	17	18	4148	4148	NUM
ejpam-5430	17	19	everyday	everyday	NOUN
ejpam-5430	17	20	problems	problem	NOUN
ejpam-5430	17	21	related	relate	VERB
ejpam-5430	17	22	to	to	ADP
ejpam-5430	17	23	the	the	DET
ejpam-5430	17	24	environment	environment	NOUN
ejpam-5430	17	25	,	,	PUNCT
ejpam-5430	17	26	economy	economy	NOUN
ejpam-5430	17	27	,	,	PUNCT
ejpam-5430	17	28	health	health	NOUN
ejpam-5430	17	29	,	,	PUNCT
ejpam-5430	17	30	and	and	CCONJ
ejpam-5430	17	31	even	even	ADV
ejpam-5430	17	32	human	human	ADJ
ejpam-5430	17	33	needs	need	NOUN
ejpam-5430	17	34	.	.	PUNCT
ejpam-5430	18	1	to	to	PART
ejpam-5430	18	2	get	get	VERB
ejpam-5430	18	3	beyond	beyond	ADP
ejpam-5430	18	4	these	these	DET
ejpam-5430	18	5	obstacles	obstacle	NOUN
ejpam-5430	18	6	,	,	PUNCT
ejpam-5430	18	7	a	a	DET
ejpam-5430	18	8	number	number	NOUN
ejpam-5430	18	9	of	of	ADP
ejpam-5430	18	10	theories	theory	NOUN
ejpam-5430	18	11	have	have	AUX
ejpam-5430	18	12	been	be	AUX
ejpam-5430	18	13	put	put	VERB
ejpam-5430	18	14	forward	forward	ADV
ejpam-5430	18	15	,	,	PUNCT
ejpam-5430	18	16	similar	similar	ADJ
ejpam-5430	18	17	to	to	ADP
ejpam-5430	18	18	the	the	DET
ejpam-5430	18	19	1999	1999	NUM
ejpam-5430	18	20	introduction	introduction	NOUN
ejpam-5430	18	21	of	of	ADP
ejpam-5430	18	22	the	the	DET
ejpam-5430	18	23	notion	notion	NOUN
ejpam-5430	18	24	of	of	ADP
ejpam-5430	18	25	soft	soft	ADJ
ejpam-5430	18	26	sets	set	NOUN
ejpam-5430	18	27	(	(	PUNCT
ejpam-5430	18	28	brevity	brevity	NOUN
ejpam-5430	18	29	sss	sss	NOUN
ejpam-5430	18	30	)	)	PUNCT
ejpam-5430	18	31	by	by	ADP
ejpam-5430	18	32	molodtsov	molodtsov	NOUN
ejpam-5430	18	33	[	[	X
ejpam-5430	18	34	23	23	NUM
ejpam-5430	18	35	]	]	PUNCT
ejpam-5430	18	36	and	and	CCONJ
ejpam-5430	18	37	which	which	PRON
ejpam-5430	18	38	has	have	AUX
ejpam-5430	18	39	been	be	AUX
ejpam-5430	18	40	used	use	VERB
ejpam-5430	18	41	in	in	ADP
ejpam-5430	18	42	a	a	DET
ejpam-5430	18	43	number	number	NOUN
ejpam-5430	18	44	of	of	ADP
ejpam-5430	18	45	sectors	sector	NOUN
ejpam-5430	18	46	.	.	PUNCT
ejpam-5430	19	1	the	the	DET
ejpam-5430	19	2	character	character	NOUN
ejpam-5430	19	3	of	of	ADP
ejpam-5430	19	4	parameter	parameter	NOUN
ejpam-5430	19	5	sets	set	NOUN
ejpam-5430	19	6	is	be	AUX
ejpam-5430	19	7	central	central	ADJ
ejpam-5430	19	8	to	to	ADP
ejpam-5430	19	9	the	the	DET
ejpam-5430	19	10	notion	notion	NOUN
ejpam-5430	19	11	of	of	ADP
ejpam-5430	19	12	sss	sss	PROPN
ejpam-5430	19	13	,	,	PUNCT
ejpam-5430	19	14	it	it	PRON
ejpam-5430	19	15	offers	offer	VERB
ejpam-5430	19	16	an	an	DET
ejpam-5430	19	17	extensive	extensive	ADJ
ejpam-5430	19	18	structure	structure	NOUN
ejpam-5430	19	19	for	for	ADP
ejpam-5430	19	20	modeling	model	VERB
ejpam-5430	19	21	ambiguous	ambiguous	ADJ
ejpam-5430	19	22	data	datum	NOUN
ejpam-5430	19	23	.	.	PUNCT
ejpam-5430	20	1	in	in	ADP
ejpam-5430	20	2	a	a	DET
ejpam-5430	20	3	short	short	ADJ
ejpam-5430	20	4	time	time	NOUN
ejpam-5430	20	5	,	,	PUNCT
ejpam-5430	20	6	this	this	PRON
ejpam-5430	20	7	essentially	essentially	ADV
ejpam-5430	20	8	advances	advance	VERB
ejpam-5430	20	9	the	the	DET
ejpam-5430	20	10	topic	topic	NOUN
ejpam-5430	20	11	of	of	ADP
ejpam-5430	20	12	soft	soft	ADJ
ejpam-5430	20	13	set	set	NOUN
ejpam-5430	20	14	(	(	PUNCT
ejpam-5430	20	15	brevity	brevity	NOUN
ejpam-5430	20	16	ss	ss	NOUN
ejpam-5430	20	17	)	)	PUNCT
ejpam-5430	20	18	theory	theory	NOUN
ejpam-5430	20	19	.	.	PUNCT
ejpam-5430	21	1	the	the	DET
ejpam-5430	21	2	theoretical	theoretical	ADJ
ejpam-5430	21	3	basis	basis	NOUN
ejpam-5430	21	4	of	of	ADP
ejpam-5430	21	5	the	the	DET
ejpam-5430	21	6	ss	ss	PROPN
ejpam-5430	21	7	theory	theory	NOUN
ejpam-5430	21	8	has	have	AUX
ejpam-5430	21	9	been	be	AUX
ejpam-5430	21	10	extensively	extensively	ADV
ejpam-5430	21	11	examined	examine	VERB
ejpam-5430	21	12	by	by	ADP
ejpam-5430	21	13	maji	maji	PROPN
ejpam-5430	21	14	et	et	PROPN
ejpam-5430	21	15	al	al	PROPN
ejpam-5430	21	16	.	.	PUNCT
ejpam-5430	22	1	[	[	X
ejpam-5430	22	2	22	22	NUM
ejpam-5430	22	3	]	]	PUNCT
ejpam-5430	22	4	and	and	CCONJ
ejpam-5430	22	5	azzam	azzam	PROPN
ejpam-5430	22	6	et	et	PROPN
ejpam-5430	22	7	al	al	PROPN
ejpam-5430	22	8	.	.	PUNCT
ejpam-5430	23	1	[	[	X
ejpam-5430	23	2	10–12	10–12	NUM
ejpam-5430	23	3	]	]	PUNCT
ejpam-5430	23	4	.	.	PUNCT
ejpam-5430	24	1	in	in	ADP
ejpam-5430	24	2	addition	addition	NOUN
ejpam-5430	24	3	,	,	PUNCT
ejpam-5430	24	4	radwan	radwan	NOUN
ejpam-5430	24	5	and	and	CCONJ
ejpam-5430	24	6	et	et	NOUN
ejpam-5430	24	7	al	al	PROPN
ejpam-5430	24	8	.	.	PUNCT
ejpam-5430	25	1	[	[	X
ejpam-5430	25	2	1	1	X
ejpam-5430	25	3	]	]	PUNCT
ejpam-5430	25	4	proposed	propose	VERB
ejpam-5430	25	5	soft	soft	ADJ
ejpam-5430	25	6	ditopological	ditopological	ADJ
ejpam-5430	25	7	spaces	space	NOUN
ejpam-5430	25	8	to	to	PART
ejpam-5430	25	9	achieve	achieve	VERB
ejpam-5430	25	10	nearly	nearly	ADV
ejpam-5430	25	11	soft	soft	ADJ
ejpam-5430	25	12	β	β	ADJ
ejpam-5430	25	13	-	-	ADJ
ejpam-5430	25	14	open	open	ADJ
ejpam-5430	25	15	sets	set	NOUN
ejpam-5430	25	16	.	.	PUNCT
ejpam-5430	26	1	to	to	PART
ejpam-5430	26	2	address	address	VERB
ejpam-5430	26	3	this	this	DET
ejpam-5430	26	4	problem	problem	NOUN
ejpam-5430	26	5	,	,	PUNCT
ejpam-5430	26	6	zadeh	zadeh	PROPN
ejpam-5430	27	1	[	[	X
ejpam-5430	27	2	32	32	NUM
ejpam-5430	27	3	]	]	PUNCT
ejpam-5430	27	4	developed	develop	VERB
ejpam-5430	27	5	the	the	DET
ejpam-5430	27	6	fuzzy	fuzzy	ADJ
ejpam-5430	27	7	set	set	NOUN
ejpam-5430	27	8	(	(	PUNCT
ejpam-5430	27	9	brevity	brevity	NOUN
ejpam-5430	27	10	fs	fs	NOUN
ejpam-5430	27	11	)	)	PUNCT
ejpam-5430	27	12	theory	theory	NOUN
ejpam-5430	27	13	.	.	PUNCT
ejpam-5430	28	1	following	follow	VERB
ejpam-5430	28	2	fs	fs	ADP
ejpam-5430	28	3	theory	theory	NOUN
ejpam-5430	28	4	concept	concept	NOUN
ejpam-5430	28	5	for	for	ADP
ejpam-5430	28	6	various	various	ADJ
ejpam-5430	28	7	specific	specific	ADJ
ejpam-5430	28	8	purposes	purpose	NOUN
ejpam-5430	28	9	,	,	PUNCT
ejpam-5430	28	10	higher	high	ADJ
ejpam-5430	28	11	order	order	NOUN
ejpam-5430	28	12	and	and	CCONJ
ejpam-5430	28	13	nonclassical	nonclassical	ADJ
ejpam-5430	28	14	fuzzy	fuzzy	ADJ
ejpam-5430	28	15	sets	set	NOUN
ejpam-5430	28	16	(	(	PUNCT
ejpam-5430	28	17	abbreviated	abbreviate	VERB
ejpam-5430	28	18	fss	fss	NOUN
ejpam-5430	28	19	)	)	PUNCT
ejpam-5430	28	20	have	have	AUX
ejpam-5430	28	21	been	be	AUX
ejpam-5430	28	22	presented	present	VERB
ejpam-5430	28	23	.	.	PUNCT
ejpam-5430	29	1	atanassov	atanassov	PROPN
ejpam-5430	30	1	[	[	X
ejpam-5430	30	2	8	8	NUM
ejpam-5430	30	3	]	]	PUNCT
ejpam-5430	30	4	established	establish	VERB
ejpam-5430	30	5	the	the	DET
ejpam-5430	30	6	idea	idea	NOUN
ejpam-5430	30	7	of	of	ADP
ejpam-5430	30	8	the	the	DET
ejpam-5430	30	9	intuitionistic	intuitionistic	ADJ
ejpam-5430	30	10	fuzzy	fuzzy	ADJ
ejpam-5430	30	11	set	set	NOUN
ejpam-5430	30	12	(	(	PUNCT
ejpam-5430	30	13	abbreviated	abbreviate	VERB
ejpam-5430	30	14	ifs	ifs	PROPN
ejpam-5430	30	15	)	)	PUNCT
ejpam-5430	30	16	.	.	PUNCT
ejpam-5430	31	1	a	a	DET
ejpam-5430	31	2	growth	growth	NOUN
ejpam-5430	31	3	of	of	ADP
ejpam-5430	31	4	theory	theory	NOUN
ejpam-5430	31	5	fs	fs	ADP
ejpam-5430	31	6	that	that	DET
ejpam-5430	31	7	addresses	address	NOUN
ejpam-5430	31	8	both	both	CCONJ
ejpam-5430	31	9	membership	membership	NOUN
ejpam-5430	31	10	and	and	CCONJ
ejpam-5430	31	11	non	non	ADJ
ejpam-5430	31	12	-	-	ADJ
ejpam-5430	31	13	membership	membership	ADJ
ejpam-5430	31	14	values	value	NOUN
ejpam-5430	31	15	(	(	PUNCT
ejpam-5430	31	16	abbreviated	abbreviate	VERB
ejpam-5430	31	17	m	m	NOUN
ejpam-5430	31	18	-	-	NOUN
ejpam-5430	31	19	values	value	NOUN
ejpam-5430	31	20	and	and	CCONJ
ejpam-5430	31	21	n	n	CCONJ
ejpam-5430	31	22	-	-	PUNCT
ejpam-5430	31	23	m	m	NOUN
ejpam-5430	31	24	-	-	PUNCT
ejpam-5430	31	25	values	value	NOUN
ejpam-5430	31	26	consequently	consequently	ADV
ejpam-5430	31	27	)	)	PUNCT
ejpam-5430	32	1	[	[	X
ejpam-5430	32	2	7	7	NUM
ejpam-5430	32	3	,	,	PUNCT
ejpam-5430	32	4	17	17	NUM
ejpam-5430	32	5	]	]	PUNCT
ejpam-5430	32	6	.	.	PUNCT
ejpam-5430	33	1	yager	yager	PROPN
ejpam-5430	33	2	invented	invent	VERB
ejpam-5430	33	3	the	the	DET
ejpam-5430	33	4	pythagorean	pythagorean	PROPN
ejpam-5430	33	5	fuzzy	fuzzy	ADJ
ejpam-5430	33	6	set	set	NOUN
ejpam-5430	33	7	(	(	PUNCT
ejpam-5430	33	8	abbreviated	abbreviate	VERB
ejpam-5430	33	9	pyfs	pyfs	NOUN
ejpam-5430	33	10	)	)	PUNCT
ejpam-5430	33	11	in	in	ADP
ejpam-5430	33	12	two	two	NUM
ejpam-5430	33	13	thousand	thousand	NUM
ejpam-5430	33	14	thirteen	thirteen	NUM
ejpam-5430	33	15	,	,	PUNCT
ejpam-5430	33	16	which	which	PRON
ejpam-5430	33	17	is	be	AUX
ejpam-5430	33	18	an	an	DET
ejpam-5430	33	19	additional	additional	ADJ
ejpam-5430	33	20	extension	extension	NOUN
ejpam-5430	33	21	of	of	ADP
ejpam-5430	33	22	fs	f	NOUN
ejpam-5430	33	23	and	and	CCONJ
ejpam-5430	33	24	ifs	ifs	PROPN
ejpam-5430	33	25	[	[	X
ejpam-5430	33	26	30	30	NUM
ejpam-5430	33	27	]	]	PUNCT
ejpam-5430	33	28	.	.	PUNCT
ejpam-5430	34	1	numerous	numerous	ADJ
ejpam-5430	34	2	applications	application	NOUN
ejpam-5430	34	3	in	in	ADP
ejpam-5430	34	4	the	the	DET
ejpam-5430	34	5	scientific	scientific	ADJ
ejpam-5430	34	6	and	and	CCONJ
ejpam-5430	34	7	social	social	ADJ
ejpam-5430	34	8	sciences	science	NOUN
ejpam-5430	34	9	have	have	AUX
ejpam-5430	34	10	been	be	AUX
ejpam-5430	34	11	made	make	VERB
ejpam-5430	34	12	possible	possible	ADJ
ejpam-5430	34	13	by	by	ADP
ejpam-5430	34	14	this	this	DET
ejpam-5430	34	15	set	set	NOUN
ejpam-5430	34	16	theory	theory	NOUN
ejpam-5430	34	17	.	.	PUNCT
ejpam-5430	35	1	for	for	ADP
ejpam-5430	35	2	instance	instance	NOUN
ejpam-5430	35	3	,	,	PUNCT
ejpam-5430	35	4	the	the	DET
ejpam-5430	35	5	work	work	NOUN
ejpam-5430	35	6	by	by	ADP
ejpam-5430	35	7	akram	akram	PROPN
ejpam-5430	35	8	and	and	CCONJ
ejpam-5430	35	9	et	et	NOUN
ejpam-5430	35	10	al	al	PROPN
ejpam-5430	35	11	.	.	PUNCT
ejpam-5430	36	1	[	[	X
ejpam-5430	36	2	2	2	X
ejpam-5430	36	3	]	]	PUNCT
ejpam-5430	36	4	introduced	introduce	VERB
ejpam-5430	36	5	significant	significant	ADJ
ejpam-5430	36	6	advancements	advancement	NOUN
ejpam-5430	36	7	in	in	ADP
ejpam-5430	36	8	fuzzy	fuzzy	ADJ
ejpam-5430	36	9	subsets	subset	NOUN
ejpam-5430	36	10	.	.	PUNCT
ejpam-5430	37	1	similarly	similarly	ADV
ejpam-5430	37	2	,	,	PUNCT
ejpam-5430	37	3	azzam	azzam	PROPN
ejpam-5430	38	1	[	[	X
ejpam-5430	38	2	9	9	NUM
ejpam-5430	38	3	]	]	PUNCT
ejpam-5430	38	4	explored	explore	VERB
ejpam-5430	38	5	its	its	PRON
ejpam-5430	38	6	applications	application	NOUN
ejpam-5430	38	7	in	in	ADP
ejpam-5430	38	8	social	social	ADJ
ejpam-5430	38	9	sciences	science	NOUN
ejpam-5430	38	10	,	,	PUNCT
ejpam-5430	38	11	while	while	SCONJ
ejpam-5430	38	12	cuong	cuong	PROPN
ejpam-5430	38	13	and	and	CCONJ
ejpam-5430	38	14	et	et	PROPN
ejpam-5430	38	15	al	al	PROPN
ejpam-5430	38	16	.	.	PUNCT
ejpam-5430	39	1	[	[	X
ejpam-5430	39	2	15	15	NUM
ejpam-5430	39	3	]	]	PUNCT
ejpam-5430	39	4	and	and	CCONJ
ejpam-5430	39	5	garg	garg	NOUN
ejpam-5430	40	1	[	[	X
ejpam-5430	40	2	16	16	NUM
ejpam-5430	40	3	]	]	PUNCT
ejpam-5430	40	4	provided	provide	VERB
ejpam-5430	40	5	critical	critical	ADJ
ejpam-5430	40	6	insights	insight	NOUN
ejpam-5430	40	7	into	into	ADP
ejpam-5430	40	8	its	its	PRON
ejpam-5430	40	9	mathematical	mathematical	ADJ
ejpam-5430	40	10	underpinnings	underpinning	NOUN
ejpam-5430	40	11	.	.	PUNCT
ejpam-5430	41	1	further	further	ADJ
ejpam-5430	41	2	contributions	contribution	NOUN
ejpam-5430	41	3	by	by	ADP
ejpam-5430	41	4	garg	garg	NOUN
ejpam-5430	41	5	[	[	X
ejpam-5430	41	6	18	18	NUM
ejpam-5430	41	7	]	]	PUNCT
ejpam-5430	41	8	and	and	CCONJ
ejpam-5430	41	9	yager	yager	NOUN
ejpam-5430	41	10	[	[	X
ejpam-5430	41	11	30	30	NUM
ejpam-5430	41	12	]	]	PUNCT
ejpam-5430	41	13	expanded	expand	VERB
ejpam-5430	41	14	its	its	PRON
ejpam-5430	41	15	practical	practical	ADJ
ejpam-5430	41	16	applications	application	NOUN
ejpam-5430	41	17	,	,	PUNCT
ejpam-5430	41	18	and	and	CCONJ
ejpam-5430	41	19	zadeh	zadeh	NOUN
ejpam-5430	42	1	[	[	X
ejpam-5430	42	2	32	32	NUM
ejpam-5430	42	3	]	]	PUNCT
ejpam-5430	42	4	developed	develop	VERB
ejpam-5430	42	5	foundational	foundational	ADJ
ejpam-5430	42	6	theories	theory	NOUN
ejpam-5430	42	7	that	that	PRON
ejpam-5430	42	8	underpin	underpin	VERB
ejpam-5430	42	9	the	the	DET
ejpam-5430	42	10	current	current	ADJ
ejpam-5430	42	11	study	study	NOUN
ejpam-5430	42	12	.	.	PUNCT
ejpam-5430	43	1	olgun	olgun	NOUN
ejpam-5430	43	2	et	et	PROPN
ejpam-5430	43	3	al	al	PROPN
ejpam-5430	43	4	.	.	PUNCT
ejpam-5430	44	1	[	[	X
ejpam-5430	44	2	25	25	NUM
ejpam-5430	44	3	]	]	PUNCT
ejpam-5430	44	4	suggested	suggest	VERB
ejpam-5430	44	5	and	and	CCONJ
ejpam-5430	44	6	studied	study	VERB
ejpam-5430	44	7	pythagorean	pythagorean	PROPN
ejpam-5430	44	8	fuzzy	fuzzy	ADJ
ejpam-5430	44	9	topological	topological	ADJ
ejpam-5430	44	10	spaces	space	NOUN
ejpam-5430	44	11	(	(	PUNCT
ejpam-5430	44	12	abbreviated	abbreviate	VERB
ejpam-5430	44	13	pyftss	pyftss	NOUN
ejpam-5430	44	14	)	)	PUNCT
ejpam-5430	44	15	in	in	ADP
ejpam-5430	44	16	2019	2019	NUM
ejpam-5430	44	17	.	.	PUNCT
ejpam-5430	45	1	independent	independent	ADJ
ejpam-5430	45	2	definitions	definition	NOUN
ejpam-5430	45	3	of	of	ADP
ejpam-5430	45	4	soft	soft	ADJ
ejpam-5430	45	5	(	(	PUNCT
ejpam-5430	45	6	generic	generic	ADJ
ejpam-5430	45	7	)	)	PUNCT
ejpam-5430	45	8	topology	topology	NOUN
ejpam-5430	45	9	were	be	AUX
ejpam-5430	45	10	provided	provide	VERB
ejpam-5430	45	11	in	in	ADP
ejpam-5430	45	12	two	two	NUM
ejpam-5430	45	13	thousand	thousand	NUM
ejpam-5430	45	14	eleven	eleven	NUM
ejpam-5430	45	15	by	by	ADP
ejpam-5430	45	16	cağman	cağman	PROPN
ejpam-5430	45	17	et	et	PROPN
ejpam-5430	45	18	al	al	PROPN
ejpam-5430	45	19	.	.	PUNCT
ejpam-5430	46	1	[	[	X
ejpam-5430	46	2	13	13	NUM
ejpam-5430	46	3	]	]	PUNCT
ejpam-5430	46	4	and	and	CCONJ
ejpam-5430	46	5	shabir	shabir	PROPN
ejpam-5430	46	6	and	and	CCONJ
ejpam-5430	46	7	naz	naz	PROPN
ejpam-5430	46	8	[	[	X
ejpam-5430	46	9	27	27	NUM
ejpam-5430	46	10	]	]	PUNCT
ejpam-5430	46	11	.	.	PUNCT
ejpam-5430	47	1	nazmul	nazmul	PROPN
ejpam-5430	47	2	and	and	CCONJ
ejpam-5430	47	3	samanta	samanta	PROPN
ejpam-5430	48	1	[	[	X
ejpam-5430	48	2	24	24	NUM
ejpam-5430	48	3	]	]	PUNCT
ejpam-5430	48	4	provided	provide	VERB
ejpam-5430	48	5	a	a	DET
ejpam-5430	48	6	definition	definition	NOUN
ejpam-5430	48	7	of	of	ADP
ejpam-5430	48	8	soft	soft	ADJ
ejpam-5430	48	9	continuity	continuity	NOUN
ejpam-5430	48	10	(	(	PUNCT
ejpam-5430	48	11	abbreviated	abbreviate	VERB
ejpam-5430	48	12	sc	sc	NOUN
ejpam-5430	48	13	)	)	PUNCT
ejpam-5430	48	14	of	of	ADP
ejpam-5430	48	15	functions	function	NOUN
ejpam-5430	48	16	in	in	ADP
ejpam-5430	48	17	2013	2013	NUM
ejpam-5430	48	18	.	.	PUNCT
ejpam-5430	49	1	next	next	ADV
ejpam-5430	49	2	,	,	PUNCT
ejpam-5430	49	3	a	a	DET
ejpam-5430	49	4	number	number	NOUN
ejpam-5430	49	5	of	of	ADP
ejpam-5430	49	6	sc	sc	PROPN
ejpam-5430	49	7	and	and	CCONJ
ejpam-5430	49	8	soft	soft	ADJ
ejpam-5430	49	9	openness	openness	NOUN
ejpam-5430	49	10	generalizations	generalization	NOUN
ejpam-5430	49	11	functions	function	NOUN
ejpam-5430	49	12	that	that	PRON
ejpam-5430	49	13	were	be	AUX
ejpam-5430	49	14	documented	document	VERB
ejpam-5430	49	15	in	in	ADP
ejpam-5430	49	16	the	the	DET
ejpam-5430	49	17	literature	literature	NOUN
ejpam-5430	49	18	.	.	PUNCT
ejpam-5430	50	1	pyfts	pyft	NOUN
ejpam-5430	50	2	was	be	AUX
ejpam-5430	50	3	first	first	ADV
ejpam-5430	50	4	described	describe	VERB
ejpam-5430	50	5	in	in	ADP
ejpam-5430	50	6	[	[	X
ejpam-5430	50	7	25	25	NUM
ejpam-5430	50	8	]	]	PUNCT
ejpam-5430	50	9	and	and	CCONJ
ejpam-5430	50	10	pythagorean	pythagorean	VERB
ejpam-5430	50	11	fuzzy	fuzzy	ADJ
ejpam-5430	50	12	soft	soft	ADJ
ejpam-5430	50	13	topological	topological	ADJ
ejpam-5430	50	14	space	space	NOUN
ejpam-5430	50	15	(	(	PUNCT
ejpam-5430	50	16	pyfsts	pyfst	NOUN
ejpam-5430	50	17	)	)	PUNCT
ejpam-5430	51	1	[	[	X
ejpam-5430	51	2	7	7	NUM
ejpam-5430	51	3	,	,	PUNCT
ejpam-5430	51	4	26	26	NUM
ejpam-5430	51	5	]	]	PUNCT
ejpam-5430	51	6	.	.	PUNCT
ejpam-5430	52	1	in	in	ADP
ejpam-5430	52	2	recent	recent	ADJ
ejpam-5430	52	3	years	year	NOUN
ejpam-5430	52	4	,	,	PUNCT
ejpam-5430	52	5	the	the	DET
ejpam-5430	52	6	need	need	NOUN
ejpam-5430	52	7	for	for	ADP
ejpam-5430	52	8	advanced	advanced	ADJ
ejpam-5430	52	9	fuzzy	fuzzy	ADJ
ejpam-5430	52	10	set	set	NOUN
ejpam-5430	52	11	theories	theory	NOUN
ejpam-5430	52	12	has	have	AUX
ejpam-5430	52	13	grown	grow	VERB
ejpam-5430	52	14	significantly	significantly	ADV
ejpam-5430	52	15	due	due	ADP
ejpam-5430	52	16	to	to	ADP
ejpam-5430	52	17	the	the	DET
ejpam-5430	52	18	increasing	increase	VERB
ejpam-5430	52	19	complexity	complexity	NOUN
ejpam-5430	52	20	of	of	ADP
ejpam-5430	52	21	problems	problem	NOUN
ejpam-5430	52	22	in	in	ADP
ejpam-5430	52	23	economics	economic	NOUN
ejpam-5430	52	24	,	,	PUNCT
ejpam-5430	52	25	engineering	engineering	NOUN
ejpam-5430	52	26	,	,	PUNCT
ejpam-5430	52	27	and	and	CCONJ
ejpam-5430	52	28	decision	decision	NOUN
ejpam-5430	52	29	-	-	PUNCT
ejpam-5430	52	30	making	make	VERB
ejpam-5430	52	31	processes	process	NOUN
ejpam-5430	52	32	.	.	PUNCT
ejpam-5430	53	1	the	the	DET
ejpam-5430	53	2	motivation	motivation	NOUN
ejpam-5430	53	3	behind	behind	ADP
ejpam-5430	53	4	this	this	DET
ejpam-5430	53	5	study	study	NOUN
ejpam-5430	53	6	is	be	AUX
ejpam-5430	53	7	to	to	PART
ejpam-5430	53	8	address	address	VERB
ejpam-5430	53	9	these	these	DET
ejpam-5430	53	10	challenges	challenge	NOUN
ejpam-5430	53	11	by	by	ADP
ejpam-5430	53	12	developing	develop	VERB
ejpam-5430	53	13	a	a	DET
ejpam-5430	53	14	robust	robust	ADJ
ejpam-5430	53	15	framework	framework	NOUN
ejpam-5430	53	16	using	use	VERB
ejpam-5430	53	17	pythagorean	pythagorean	PROPN
ejpam-5430	53	18	fuzzy	fuzzy	ADJ
ejpam-5430	53	19	soft	soft	ADJ
ejpam-5430	53	20	sets	set	NOUN
ejpam-5430	53	21	.	.	PUNCT
ejpam-5430	54	1	our	our	PRON
ejpam-5430	54	2	main	main	ADJ
ejpam-5430	54	3	contribution	contribution	NOUN
ejpam-5430	54	4	lies	lie	VERB
ejpam-5430	54	5	in	in	ADP
ejpam-5430	54	6	defining	define	VERB
ejpam-5430	54	7	and	and	CCONJ
ejpam-5430	54	8	exploring	explore	VERB
ejpam-5430	54	9	the	the	DET
ejpam-5430	54	10	properties	property	NOUN
ejpam-5430	54	11	of	of	ADP
ejpam-5430	54	12	pythagorean	pythagorean	PROPN
ejpam-5430	54	13	fuzzy	fuzzy	ADJ
ejpam-5430	54	14	soft	soft	ADJ
ejpam-5430	54	15	somewhat	somewhat	ADV
ejpam-5430	54	16	open	open	ADJ
ejpam-5430	54	17	sets	set	NOUN
ejpam-5430	54	18	and	and	CCONJ
ejpam-5430	54	19	their	their	PRON
ejpam-5430	54	20	applications	application	NOUN
ejpam-5430	54	21	in	in	ADP
ejpam-5430	54	22	topological	topological	ADJ
ejpam-5430	54	23	spaces	space	NOUN
ejpam-5430	54	24	.	.	PUNCT
ejpam-5430	55	1	this	this	DET
ejpam-5430	55	2	approach	approach	NOUN
ejpam-5430	55	3	provides	provide	VERB
ejpam-5430	55	4	a	a	DET
ejpam-5430	55	5	more	more	ADV
ejpam-5430	55	6	nuanced	nuanced	ADJ
ejpam-5430	55	7	understanding	understanding	NOUN
ejpam-5430	55	8	of	of	ADP
ejpam-5430	55	9	fuzzy	fuzzy	ADJ
ejpam-5430	55	10	environments	environment	NOUN
ejpam-5430	55	11	,	,	PUNCT
ejpam-5430	55	12	enabling	enable	VERB
ejpam-5430	55	13	more	more	ADV
ejpam-5430	55	14	precise	precise	ADJ
ejpam-5430	55	15	modeling	modeling	NOUN
ejpam-5430	55	16	of	of	ADP
ejpam-5430	55	17	uncertainty	uncertainty	NOUN
ejpam-5430	55	18	and	and	CCONJ
ejpam-5430	55	19	imprecision	imprecision	NOUN
ejpam-5430	55	20	in	in	ADP
ejpam-5430	55	21	real	real	ADJ
ejpam-5430	55	22	-	-	PUNCT
ejpam-5430	55	23	world	world	NOUN
ejpam-5430	55	24	scenarios	scenario	NOUN
ejpam-5430	55	25	.	.	PUNCT
ejpam-5430	56	1	following	follow	VERB
ejpam-5430	56	2	this	this	DET
ejpam-5430	56	3	quick	quick	ADJ
ejpam-5430	56	4	introduction	introduction	NOUN
ejpam-5430	56	5	,	,	PUNCT
ejpam-5430	56	6	we	we	PRON
ejpam-5430	56	7	will	will	AUX
ejpam-5430	56	8	review	review	VERB
ejpam-5430	56	9	some	some	DET
ejpam-5430	56	10	preliminary	preliminary	ADJ
ejpam-5430	56	11	principles	principle	NOUN
ejpam-5430	56	12	in	in	ADP
ejpam-5430	56	13	part	part	NOUN
ejpam-5430	56	14	2	2	NUM
ejpam-5430	56	15	.	.	PUNCT
ejpam-5430	56	16	part	part	NOUN
ejpam-5430	56	17	3	3	NUM
ejpam-5430	56	18	then	then	ADV
ejpam-5430	56	19	introduces	introduce	VERB
ejpam-5430	56	20	the	the	DET
ejpam-5430	56	21	idea	idea	NOUN
ejpam-5430	56	22	that	that	PRON
ejpam-5430	56	23	pythagorean	pythagorean	VERB
ejpam-5430	56	24	fuzzy	fuzzy	ADJ
ejpam-5430	56	25	soft	soft	ADJ
ejpam-5430	56	26	somewhat	somewhat	ADV
ejpam-5430	56	27	open	open	ADJ
ejpam-5430	56	28	(	(	PUNCT
ejpam-5430	56	29	brevity	brevity	NOUN
ejpam-5430	56	30	pyfssw	pyfssw	ADV
ejpam-5430	56	31	-	-	PUNCT
ejpam-5430	56	32	open	open	ADJ
ejpam-5430	56	33	)	)	PUNCT
ejpam-5430	56	34	sets	set	NOUN
ejpam-5430	56	35	and	and	CCONJ
ejpam-5430	56	36	looks	look	VERB
ejpam-5430	56	37	at	at	ADP
ejpam-5430	56	38	how	how	SCONJ
ejpam-5430	56	39	it	it	PRON
ejpam-5430	56	40	relates	relate	VERB
ejpam-5430	56	41	to	to	ADP
ejpam-5430	56	42	a	a	DET
ejpam-5430	56	43	few	few	ADJ
ejpam-5430	56	44	soft	soft	ADJ
ejpam-5430	56	45	open	open	ADJ
ejpam-5430	56	46	set	set	VERB
ejpam-5430	56	47	assumptions	assumption	NOUN
ejpam-5430	56	48	.	.	PUNCT
ejpam-5430	57	1	the	the	DET
ejpam-5430	57	2	objectives	objective	NOUN
ejpam-5430	57	3	of	of	ADP
ejpam-5430	57	4	part	part	NOUN
ejpam-5430	57	5	4	4	NUM
ejpam-5430	57	6	is	be	AUX
ejpam-5430	57	7	to	to	PART
ejpam-5430	57	8	examine	examine	VERB
ejpam-5430	57	9	pyfssw	pyfssw	ADJ
ejpam-5430	57	10	-	-	PUNCT
ejpam-5430	57	11	c	c	NOUN
ejpam-5430	57	12	functions	function	NOUN
ejpam-5430	57	13	,	,	PUNCT
ejpam-5430	57	14	which	which	PRON
ejpam-5430	57	15	are	be	AUX
ejpam-5430	57	16	stronger	strong	ADJ
ejpam-5430	57	17	than	than	ADP
ejpam-5430	57	18	pyfssw	pyfssw	ADV
ejpam-5430	57	19	-	-	PUNCT
ejpam-5430	57	20	dense	dense	ADJ
ejpam-5430	57	21	c	c	NOUN
ejpam-5430	57	22	,	,	PUNCT
ejpam-5430	57	23	but	but	CCONJ
ejpam-5430	57	24	weaker	weak	ADJ
ejpam-5430	57	25	than	than	ADP
ejpam-5430	57	26	soft	soft	ADJ
ejpam-5430	57	27	semicontinuous	semicontinuous	NOUN
ejpam-5430	57	28	.	.	PUNCT
ejpam-5430	58	1	we	we	PRON
ejpam-5430	58	2	wrap	wrap	VERB
ejpam-5430	58	3	up	up	ADP
ejpam-5430	58	4	and	and	CCONJ
ejpam-5430	58	5	offer	offer	VERB
ejpam-5430	58	6	some	some	DET
ejpam-5430	58	7	suggestions	suggestion	NOUN
ejpam-5430	58	8	for	for	ADP
ejpam-5430	58	9	next	next	ADJ
ejpam-5430	58	10	works	work	NOUN
ejpam-5430	58	11	in	in	ADP
ejpam-5430	58	12	part	part	NOUN
ejpam-5430	58	13	5	5	NUM
ejpam-5430	58	14	.	.	PUNCT
ejpam-5430	58	15	a.	a.	NOUN
ejpam-5430	58	16	a.	a.	PROPN
ejpam-5430	58	17	azzam	azzam	PROPN
ejpam-5430	58	18	,	,	PUNCT
ejpam-5430	58	19	m.	m.	NOUN
ejpam-5430	58	20	aldawood	aldawood	PROPN
ejpam-5430	58	21	,	,	PUNCT
ejpam-5430	58	22	r.	r.	PROPN
ejpam-5430	58	23	abu	abu	PROPN
ejpam-5430	58	24	-	-	PUNCT
ejpam-5430	58	25	gdairi	gdairi	PROPN
ejpam-5430	58	26	/	/	SYM
ejpam-5430	58	27	eur	eur	PROPN
ejpam-5430	58	28	.	.	PUNCT
ejpam-5430	59	1	j.	j.	PROPN
ejpam-5430	59	2	pure	pure	PROPN
ejpam-5430	59	3	appl	appl	PROPN
ejpam-5430	59	4	.	.	PROPN
ejpam-5430	59	5	math	math	PROPN
ejpam-5430	59	6	,	,	PUNCT
ejpam-5430	59	7	17	17	NUM
ejpam-5430	59	8	(	(	PUNCT
ejpam-5430	59	9	4	4	NUM
ejpam-5430	59	10	)	)	PUNCT
ejpam-5430	59	11	(	(	PUNCT
ejpam-5430	59	12	2024	2024	NUM
ejpam-5430	59	13	)	)	PUNCT
ejpam-5430	59	14	,	,	PUNCT
ejpam-5430	59	15	4147	4147	NUM
ejpam-5430	59	16	-	-	SYM
ejpam-5430	59	17	4163	4163	NUM
ejpam-5430	59	18	4149	4149	NUM
ejpam-5430	59	19	2	2	NUM
ejpam-5430	59	20	.	.	PUNCT
ejpam-5430	59	21	preliminaries	preliminary	NOUN
ejpam-5430	59	22	various	various	ADJ
ejpam-5430	59	23	fundamental	fundamental	ADJ
ejpam-5430	59	24	ideas	idea	NOUN
ejpam-5430	59	25	and	and	CCONJ
ejpam-5430	59	26	symbols	symbol	NOUN
ejpam-5430	59	27	will	will	AUX
ejpam-5430	59	28	be	be	AUX
ejpam-5430	59	29	used	use	VERB
ejpam-5430	59	30	in	in	ADP
ejpam-5430	59	31	the	the	DET
ejpam-5430	59	32	sequel	sequel	NOUN
ejpam-5430	59	33	are	be	AUX
ejpam-5430	59	34	contained	contain	VERB
ejpam-5430	59	35	in	in	ADP
ejpam-5430	59	36	this	this	DET
ejpam-5430	59	37	part	part	NOUN
ejpam-5430	59	38	.	.	PUNCT
ejpam-5430	60	1	we	we	PRON
ejpam-5430	60	2	will	will	AUX
ejpam-5430	60	3	henceforth	henceforth	ADV
ejpam-5430	60	4	refer	refer	VERB
ejpam-5430	60	5	to	to	ADP
ejpam-5430	60	6	an	an	DET
ejpam-5430	60	7	original	original	ADJ
ejpam-5430	60	8	universe	universe	NOUN
ejpam-5430	60	9	x	x	NOUN
ejpam-5430	60	10	,	,	PUNCT
ejpam-5430	60	11	a	a	DET
ejpam-5430	60	12	collection	collection	NOUN
ejpam-5430	60	13	of	of	ADP
ejpam-5430	60	14	parameters	parameter	NOUN
ejpam-5430	60	15	η	η	PROPN
ejpam-5430	60	16	,	,	PUNCT
ejpam-5430	60	17	an	an	DET
ejpam-5430	60	18	exponential	exponential	ADJ
ejpam-5430	60	19	set	set	NOUN
ejpam-5430	60	20	of	of	ADP
ejpam-5430	60	21	x	x	INTJ
ejpam-5430	60	22	(	(	PUNCT
ejpam-5430	60	23	℘(x	℘(x	ADJ
ejpam-5430	60	24	)	)	PUNCT
ejpam-5430	60	25	)	)	PUNCT
ejpam-5430	60	26	,	,	PUNCT
ejpam-5430	60	27	soft	soft	ADJ
ejpam-5430	60	28	topology	topology	NOUN
ejpam-5430	60	29	st	st	PROPN
ejpam-5430	60	30	,	,	PUNCT
ejpam-5430	60	31	a	a	DET
ejpam-5430	60	32	soft	soft	ADJ
ejpam-5430	60	33	topological	topological	ADJ
ejpam-5430	60	34	space	space	NOUN
ejpam-5430	60	35	sts	st	NOUN
ejpam-5430	60	36	,	,	PUNCT
ejpam-5430	60	37	picture	picture	NOUN
ejpam-5430	60	38	fuzzy	fuzzy	ADJ
ejpam-5430	60	39	set	set	VERB
ejpam-5430	60	40	pfs	pfs	PROPN
ejpam-5430	60	41	,	,	PUNCT
ejpam-5430	60	42	positive	positive	ADJ
ejpam-5430	60	43	membership	membership	NOUN
ejpam-5430	60	44	function	function	NOUN
ejpam-5430	60	45	pmf	pmf	NOUN
ejpam-5430	60	46	,	,	PUNCT
ejpam-5430	60	47	negative	negative	ADJ
ejpam-5430	60	48	membership	membership	NOUN
ejpam-5430	60	49	function	function	NOUN
ejpam-5430	60	50	nmf	nmf	PROPN
ejpam-5430	60	51	,	,	PUNCT
ejpam-5430	60	52	and	and	CCONJ
ejpam-5430	60	53	continuous	continuous	ADJ
ejpam-5430	60	54	c.	c.	NOUN
ejpam-5430	60	55	definition	definition	NOUN
ejpam-5430	60	56	1	1	NUM
ejpam-5430	60	57	.	.	PUNCT
ejpam-5430	61	1	[	[	X
ejpam-5430	61	2	32	32	NUM
ejpam-5430	61	3	]	]	PUNCT
ejpam-5430	61	4	a	a	DET
ejpam-5430	61	5	membership	membership	NOUN
ejpam-5430	61	6	function	function	NOUN
ejpam-5430	61	7	ξd(x	ξd(x	PUNCT
ejpam-5430	61	8	)	)	PUNCT
ejpam-5430	61	9	that	that	PRON
ejpam-5430	61	10	assigns	assign	VERB
ejpam-5430	61	11	a	a	DET
ejpam-5430	61	12	real	real	ADJ
ejpam-5430	61	13	number	number	NOUN
ejpam-5430	61	14	in	in	ADP
ejpam-5430	61	15	the	the	DET
ejpam-5430	61	16	range	range	NOUN
ejpam-5430	62	1	[	[	X
ejpam-5430	62	2	0	0	NUM
ejpam-5430	62	3	,	,	PUNCT
ejpam-5430	62	4	1	1	NUM
ejpam-5430	62	5	]	]	PUNCT
ejpam-5430	62	6	to	to	ADP
ejpam-5430	62	7	each	each	DET
ejpam-5430	62	8	point	point	NOUN
ejpam-5430	62	9	in	in	ADP
ejpam-5430	62	10	x	x	PUNCT
ejpam-5430	62	11	characterizes	characterize	VERB
ejpam-5430	62	12	a	a	DET
ejpam-5430	62	13	fuzzy	fuzzy	ADJ
ejpam-5430	62	14	set	set	NOUN
ejpam-5430	62	15	d	d	NOUN
ejpam-5430	62	16	in	in	ADP
ejpam-5430	62	17	x.	x.	NOUN
ejpam-5430	62	18	the	the	DET
ejpam-5430	62	19	”	"	PUNCT
ejpam-5430	62	20	grade	grade	NOUN
ejpam-5430	62	21	of	of	ADP
ejpam-5430	62	22	m	m	PROPN
ejpam-5430	62	23	”	"	PUNCT
ejpam-5430	62	24	of	of	ADP
ejpam-5430	62	25	x	x	PUNCT
ejpam-5430	62	26	in	in	ADP
ejpam-5430	62	27	d	d	PROPN
ejpam-5430	62	28	is	be	AUX
ejpam-5430	62	29	indicated	indicate	VERB
ejpam-5430	62	30	by	by	ADP
ejpam-5430	62	31	the	the	DET
ejpam-5430	62	32	value	value	NOUN
ejpam-5430	62	33	of	of	ADP
ejpam-5430	62	34	ξd(x	ξd(x	NOUN
ejpam-5430	62	35	)	)	PUNCT
ejpam-5430	62	36	at	at	ADP
ejpam-5430	62	37	x.	x.	NOUN
ejpam-5430	62	38	definition	definition	NOUN
ejpam-5430	62	39	2	2	NUM
ejpam-5430	62	40	.	.	PUNCT
ejpam-5430	63	1	[	[	X
ejpam-5430	63	2	29	29	NUM
ejpam-5430	63	3	]	]	PUNCT
ejpam-5430	63	4	let	let	VERB
ejpam-5430	63	5	x	x	PRON
ejpam-5430	63	6	represent	represent	VERB
ejpam-5430	63	7	the	the	DET
ejpam-5430	63	8	universe	universe	NOUN
ejpam-5430	63	9	,	,	PUNCT
ejpam-5430	63	10	then	then	ADV
ejpam-5430	63	11	the	the	DET
ejpam-5430	63	12	set	set	NOUN
ejpam-5430	63	13	d	d	X
ejpam-5430	63	14	=	=	SYM
ejpam-5430	63	15	{	{	PUNCT
ejpam-5430	63	16	(	(	PUNCT
ejpam-5430	63	17	x	x	NOUN
ejpam-5430	63	18	,	,	PUNCT
ejpam-5430	63	19	ξd(x	ξd(x	NOUN
ejpam-5430	63	20	)	)	PUNCT
ejpam-5430	63	21	,	,	PUNCT
ejpam-5430	63	22	ψd(x	ψd(x	NOUN
ejpam-5430	63	23	)	)	PUNCT
ejpam-5430	63	24	)	)	PUNCT
ejpam-5430	63	25	:	:	PUNCT
ejpam-5430	64	1	x	x	X
ejpam-5430	64	2	∈	∈	NOUN
ejpam-5430	64	3	x	x	VERB
ejpam-5430	64	4	}	}	PUNCT
ejpam-5430	64	5	is	be	AUX
ejpam-5430	64	6	referred	refer	VERB
ejpam-5430	64	7	to	to	ADP
ejpam-5430	64	8	as	as	ADP
ejpam-5430	64	9	ifs	ifs	PROPN
ejpam-5430	64	10	of	of	ADP
ejpam-5430	64	11	x	x	PRON
ejpam-5430	64	12	,	,	PUNCT
ejpam-5430	64	13	ξd	ξd	X
ejpam-5430	64	14	:	:	PUNCT
ejpam-5430	64	15	x	x	X
ejpam-5430	64	16	→	→	PUNCT
ejpam-5430	65	1	[	[	X
ejpam-5430	65	2	0	0	NUM
ejpam-5430	65	3	,	,	PUNCT
ejpam-5430	65	4	1	1	NUM
ejpam-5430	65	5	]	]	PUNCT
ejpam-5430	65	6	and	and	CCONJ
ejpam-5430	65	7	ψd	ψd	ADP
ejpam-5430	65	8	:	:	PUNCT
ejpam-5430	65	9	x	x	X
ejpam-5430	65	10	→	→	SYM
ejpam-5430	65	11	[	[	X
ejpam-5430	65	12	0	0	NUM
ejpam-5430	65	13	,	,	PUNCT
ejpam-5430	65	14	1	1	NUM
ejpam-5430	65	15	]	]	PUNCT
ejpam-5430	65	16	are	be	AUX
ejpam-5430	65	17	referred	refer	VERB
ejpam-5430	65	18	to	to	ADP
ejpam-5430	65	19	as	as	SCONJ
ejpam-5430	65	20	x	x	NOUN
ejpam-5430	65	21	’s	’s	NOUN
ejpam-5430	65	22	pmf	pmf	NOUN
ejpam-5430	65	23	in	in	ADP
ejpam-5430	65	24	x	x	PROPN
ejpam-5430	65	25	,	,	PUNCT
ejpam-5430	65	26	and	and	CCONJ
ejpam-5430	65	27	within	within	ADP
ejpam-5430	65	28	x	x	PROPN
ejpam-5430	65	29	,	,	PUNCT
ejpam-5430	65	30	x	x	PRON
ejpam-5430	65	31	has	have	VERB
ejpam-5430	65	32	a	a	DET
ejpam-5430	65	33	nmf	nmf	NOUN
ejpam-5430	65	34	effectively	effectively	ADV
ejpam-5430	65	35	under	under	ADP
ejpam-5430	65	36	the	the	DET
ejpam-5430	65	37	circumstances	circumstance	NOUN
ejpam-5430	65	38	0	0	NUM
ejpam-5430	65	39	≤	≤	NOUN
ejpam-5430	65	40	ξd(x	ξd(x	PUNCT
ejpam-5430	65	41	)	)	PUNCT
ejpam-5430	66	1	+	+	CCONJ
ejpam-5430	66	2	ψd(x	ψd(x	NOUN
ejpam-5430	66	3	)	)	PUNCT
ejpam-5430	66	4	≤	≤	NUM
ejpam-5430	66	5	1	1	NUM
ejpam-5430	66	6	,	,	PUNCT
ejpam-5430	66	7	∀x	∀x	X
ejpam-5430	66	8	∈	∈	PROPN
ejpam-5430	66	9	x.	x.	NOUN
ejpam-5430	66	10	definition	definition	NOUN
ejpam-5430	66	11	3	3	NUM
ejpam-5430	66	12	.	.	PUNCT
ejpam-5430	67	1	[	[	X
ejpam-5430	67	2	15	15	NUM
ejpam-5430	67	3	]	]	X
ejpam-5430	67	4	assume	assume	VERB
ejpam-5430	67	5	x	x	SYM
ejpam-5430	67	6	is	be	AUX
ejpam-5430	67	7	the	the	DET
ejpam-5430	67	8	universe	universe	ADJ
ejpam-5430	67	9	setting	setting	NOUN
ejpam-5430	67	10	,	,	PUNCT
ejpam-5430	67	11	then	then	ADV
ejpam-5430	67	12	the	the	DET
ejpam-5430	67	13	set	set	NOUN
ejpam-5430	67	14	d	d	X
ejpam-5430	67	15	=	=	SYM
ejpam-5430	67	16	{	{	PUNCT
ejpam-5430	67	17	(	(	PUNCT
ejpam-5430	67	18	x	x	NOUN
ejpam-5430	67	19	,	,	PUNCT
ejpam-5430	67	20	ξd(x	ξd(x	NOUN
ejpam-5430	67	21	)	)	PUNCT
ejpam-5430	67	22	,	,	PUNCT
ejpam-5430	67	23	υd(x	υd(x	NUM
ejpam-5430	67	24	)	)	PUNCT
ejpam-5430	67	25	,	,	PUNCT
ejpam-5430	67	26	ψd(x	ψd(x	NOUN
ejpam-5430	67	27	)	)	PUNCT
ejpam-5430	67	28	)	)	PUNCT
ejpam-5430	67	29	:	:	PUNCT
ejpam-5430	68	1	x	x	X
ejpam-5430	68	2	∈	∈	NOUN
ejpam-5430	68	3	x	x	VERB
ejpam-5430	68	4	}	}	PUNCT
ejpam-5430	68	5	is	be	AUX
ejpam-5430	68	6	referred	refer	VERB
ejpam-5430	68	7	to	to	ADP
ejpam-5430	68	8	as	as	ADP
ejpam-5430	68	9	pfs	pfs	PROPN
ejpam-5430	68	10	of	of	ADP
ejpam-5430	68	11	x	x	PRON
ejpam-5430	68	12	,	,	PUNCT
ejpam-5430	68	13	ξd	ξd	X
ejpam-5430	68	14	:	:	PUNCT
ejpam-5430	68	15	x	x	X
ejpam-5430	68	16	→	→	PUNCT
ejpam-5430	69	1	[	[	X
ejpam-5430	69	2	0	0	NUM
ejpam-5430	69	3	,	,	PUNCT
ejpam-5430	69	4	1	1	NUM
ejpam-5430	69	5	]	]	PUNCT
ejpam-5430	69	6	,	,	PUNCT
ejpam-5430	69	7	ψd	ψd	ADP
ejpam-5430	69	8	:	:	PUNCT
ejpam-5430	69	9	x	x	X
ejpam-5430	69	10	→	→	SYM
ejpam-5430	70	1	[	[	X
ejpam-5430	70	2	0	0	NUM
ejpam-5430	70	3	,	,	PUNCT
ejpam-5430	70	4	1	1	NUM
ejpam-5430	70	5	]	]	PUNCT
ejpam-5430	70	6	and	and	CCONJ
ejpam-5430	70	7	ψd	ψd	INTJ
ejpam-5430	70	8	:	:	PUNCT
ejpam-5430	70	9	ω	ω	PROPN
ejpam-5430	70	10	→	→	PUNCT
ejpam-5430	70	11	[	[	X
ejpam-5430	70	12	0	0	NUM
ejpam-5430	70	13	,	,	PUNCT
ejpam-5430	70	14	1	1	NUM
ejpam-5430	70	15	]	]	PUNCT
ejpam-5430	70	16	the	the	DET
ejpam-5430	70	17	degrees	degree	NOUN
ejpam-5430	70	18	of	of	ADP
ejpam-5430	70	19	positive	positive	ADJ
ejpam-5430	70	20	,	,	PUNCT
ejpam-5430	70	21	neutral	neutral	ADJ
ejpam-5430	70	22	,	,	PUNCT
ejpam-5430	70	23	and	and	CCONJ
ejpam-5430	70	24	negative	negative	ADJ
ejpam-5430	70	25	m	m	NOUN
ejpam-5430	70	26	of	of	ADP
ejpam-5430	70	27	x	x	PUNCT
ejpam-5430	70	28	in	in	ADP
ejpam-5430	70	29	x	x	NOUN
ejpam-5430	70	30	,	,	PUNCT
ejpam-5430	70	31	as	as	ADV
ejpam-5430	70	32	well	well	ADV
ejpam-5430	70	33	as	as	ADP
ejpam-5430	70	34	their	their	PRON
ejpam-5430	70	35	respective	respective	ADJ
ejpam-5430	70	36	conditions	condition	NOUN
ejpam-5430	70	37	0	0	NUM
ejpam-5430	70	38	≤	≤	NOUN
ejpam-5430	70	39	ξd(x	ξd(x	PUNCT
ejpam-5430	70	40	)	)	PUNCT
ejpam-5430	70	41	+	+	CCONJ
ejpam-5430	70	42	υd(x	υd(x	PUNCT
ejpam-5430	70	43	)	)	PUNCT
ejpam-5430	70	44	+	+	ADJ
ejpam-5430	70	45	ψd(x	ψd(x	NUM
ejpam-5430	70	46	)	)	PUNCT
ejpam-5430	70	47	)	)	PUNCT
ejpam-5430	70	48	≤	≤	NUM
ejpam-5430	70	49	1	1	NUM
ejpam-5430	70	50	,	,	PUNCT
ejpam-5430	70	51	∀x	∀x	VERB
ejpam-5430	70	52	∈	∈	PROPN
ejpam-5430	70	53	x	x	PRON
ejpam-5430	70	54	,	,	PUNCT
ejpam-5430	70	55	are	be	AUX
ejpam-5430	70	56	designated	designate	VERB
ejpam-5430	70	57	accordingly	accordingly	ADV
ejpam-5430	70	58	.	.	PUNCT
ejpam-5430	71	1	definition	definition	NOUN
ejpam-5430	71	2	4	4	NUM
ejpam-5430	71	3	.	.	PUNCT
ejpam-5430	72	1	[	[	X
ejpam-5430	72	2	29	29	NUM
ejpam-5430	72	3	]	]	PUNCT
ejpam-5430	72	4	let	let	VERB
ejpam-5430	72	5	x	x	PRON
ejpam-5430	72	6	represent	represent	VERB
ejpam-5430	72	7	the	the	DET
ejpam-5430	72	8	cosmos	cosmos	PROPN
ejpam-5430	72	9	,	,	PUNCT
ejpam-5430	72	10	then	then	ADV
ejpam-5430	72	11	the	the	DET
ejpam-5430	72	12	set	set	NOUN
ejpam-5430	72	13	d	d	X
ejpam-5430	72	14	=	=	SYM
ejpam-5430	72	15	{	{	PUNCT
ejpam-5430	72	16	(	(	PUNCT
ejpam-5430	72	17	x	x	NOUN
ejpam-5430	72	18	,	,	PUNCT
ejpam-5430	72	19	ξ(x	ξ(x	NOUN
ejpam-5430	72	20	)	)	PUNCT
ejpam-5430	72	21	,	,	PUNCT
ejpam-5430	72	22	ψ(x	ψ(x	NOUN
ejpam-5430	72	23	)	)	PUNCT
ejpam-5430	72	24	)	)	PUNCT
ejpam-5430	72	25	:	:	PUNCT
ejpam-5430	73	1	x	x	X
ejpam-5430	73	2	∈	∈	NOUN
ejpam-5430	73	3	x	x	VERB
ejpam-5430	73	4	}	}	PUNCT
ejpam-5430	73	5	is	be	AUX
ejpam-5430	73	6	named	name	VERB
ejpam-5430	73	7	pyfs	pyfs	ADJ
ejpam-5430	73	8	of	of	ADP
ejpam-5430	73	9	x	x	PROPN
ejpam-5430	73	10	,	,	PUNCT
ejpam-5430	73	11	ξ	ξ	PROPN
ejpam-5430	73	12	:	:	PUNCT
ejpam-5430	73	13	x	x	SYM
ejpam-5430	73	14	→	→	SYM
ejpam-5430	74	1	[	[	X
ejpam-5430	74	2	0	0	NUM
ejpam-5430	74	3	,	,	PUNCT
ejpam-5430	74	4	1	1	NUM
ejpam-5430	74	5	]	]	PUNCT
ejpam-5430	74	6	and	and	CCONJ
ejpam-5430	74	7	ψ	ψ	X
ejpam-5430	74	8	:	:	PUNCT
ejpam-5430	74	9	x	x	X
ejpam-5430	74	10	→	→	SYM
ejpam-5430	75	1	[	[	X
ejpam-5430	75	2	0	0	NUM
ejpam-5430	75	3	,	,	PUNCT
ejpam-5430	75	4	1	1	NUM
ejpam-5430	75	5	]	]	PUNCT
ejpam-5430	75	6	are	be	AUX
ejpam-5430	75	7	referred	refer	VERB
ejpam-5430	75	8	to	to	ADP
ejpam-5430	75	9	the	the	DET
ejpam-5430	75	10	degree	degree	NOUN
ejpam-5430	75	11	of	of	ADP
ejpam-5430	75	12	pmf	pmf	NOUN
ejpam-5430	75	13	of	of	ADP
ejpam-5430	75	14	x	x	PROPN
ejpam-5430	75	15	in	in	ADP
ejpam-5430	75	16	x	x	SYM
ejpam-5430	75	17	and	and	CCONJ
ejpam-5430	75	18	nmf	nmf	NOUN
ejpam-5430	75	19	degree	degree	NOUN
ejpam-5430	75	20	of	of	ADP
ejpam-5430	75	21	x	x	PUNCT
ejpam-5430	75	22	in	in	ADP
ejpam-5430	75	23	x	x	PUNCT
ejpam-5430	75	24	effectively	effectively	ADV
ejpam-5430	75	25	under	under	ADP
ejpam-5430	75	26	the	the	DET
ejpam-5430	75	27	circumstances	circumstance	NOUN
ejpam-5430	75	28	0	0	NUM
ejpam-5430	75	29	≤	≤	NUM
ejpam-5430	75	30	ξ2	ξ2	NOUN
ejpam-5430	75	31	+	+	NUM
ejpam-5430	75	32	ψ2	ψ2	NOUN
ejpam-5430	75	33	≤	≤	NUM
ejpam-5430	75	34	1	1	NUM
ejpam-5430	75	35	,	,	PUNCT
ejpam-5430	75	36	∀x	∀x	X
ejpam-5430	75	37	∈	∈	PROPN
ejpam-5430	75	38	x.	x.	NOUN
ejpam-5430	75	39	definition	definition	NOUN
ejpam-5430	75	40	5	5	NUM
ejpam-5430	75	41	.	.	PUNCT
ejpam-5430	76	1	[	[	X
ejpam-5430	76	2	29	29	NUM
ejpam-5430	76	3	]	]	PUNCT
ejpam-5430	76	4	let	let	VERB
ejpam-5430	76	5	d1	d1	PROPN
ejpam-5430	76	6	=	=	SYM
ejpam-5430	76	7	{	{	PUNCT
ejpam-5430	76	8	(	(	PUNCT
ejpam-5430	76	9	x	x	NOUN
ejpam-5430	76	10	,	,	PUNCT
ejpam-5430	76	11	ξd1(x	ξd1(x	NUM
ejpam-5430	76	12	)	)	PUNCT
ejpam-5430	76	13	,	,	PUNCT
ejpam-5430	76	14	ψd1(x	ψd1(x	NOUN
ejpam-5430	76	15	)	)	PUNCT
ejpam-5430	76	16	)	)	PUNCT
ejpam-5430	76	17	:	:	PUNCT
ejpam-5430	77	1	x	x	X
ejpam-5430	77	2	∈	∈	NOUN
ejpam-5430	77	3	x	x	NOUN
ejpam-5430	77	4	}	}	PUNCT
ejpam-5430	77	5	and	and	CCONJ
ejpam-5430	77	6	d2	d2	PROPN
ejpam-5430	77	7	=	=	SYM
ejpam-5430	77	8	{	{	PUNCT
ejpam-5430	77	9	(	(	PUNCT
ejpam-5430	77	10	x	x	NOUN
ejpam-5430	77	11	,	,	PUNCT
ejpam-5430	77	12	ξd2(x	ξd2(x	PROPN
ejpam-5430	77	13	)	)	PUNCT
ejpam-5430	77	14	,	,	PUNCT
ejpam-5430	77	15	ψd2(x	ψd2(x	PROPN
ejpam-5430	77	16	)	)	PUNCT
ejpam-5430	77	17	)	)	PUNCT
ejpam-5430	77	18	:	:	PUNCT
ejpam-5430	77	19	x	x	X
ejpam-5430	77	20	∈	∈	NOUN
ejpam-5430	77	21	x	x	PRON
ejpam-5430	77	22	}	}	PUNCT
ejpam-5430	77	23	are	be	AUX
ejpam-5430	77	24	two	two	NUM
ejpam-5430	77	25	fyfs	fyfs	NOUN
ejpam-5430	77	26	on	on	ADP
ejpam-5430	77	27	x	x	NOUN
ejpam-5430	77	28	,	,	PUNCT
ejpam-5430	77	29	then	then	ADV
ejpam-5430	77	30	i	i	PRON
ejpam-5430	77	31	)	)	PUNCT
ejpam-5430	77	32	d1	d1	VERB
ejpam-5430	77	33	⊓d2	⊓d2	NOUN
ejpam-5430	78	1	=	=	SYM
ejpam-5430	78	2	{	{	PUNCT
ejpam-5430	78	3	(	(	PUNCT
ejpam-5430	78	4	x	x	NOUN
ejpam-5430	78	5	,	,	PUNCT
ejpam-5430	78	6	ξd1(x	ξd1(x	NUM
ejpam-5430	78	7	)	)	PUNCT
ejpam-5430	78	8	∧	∧	PROPN
ejpam-5430	78	9	ξd2(x	ξd2(x	PROPN
ejpam-5430	78	10	)	)	PUNCT
ejpam-5430	78	11	,	,	PUNCT
ejpam-5430	78	12	ξd1(x	ξd1(x	NUM
ejpam-5430	78	13	)	)	PUNCT
ejpam-5430	78	14	∨	∨	PROPN
ejpam-5430	78	15	ξd2(x	ξd2(x	PROPN
ejpam-5430	78	16	)	)	PUNCT
ejpam-5430	78	17	:	:	PUNCT
ejpam-5430	79	1	x	x	X
ejpam-5430	79	2	∈	∈	NOUN
ejpam-5430	79	3	x	x	X
ejpam-5430	79	4	}	}	PUNCT
ejpam-5430	79	5	,	,	PUNCT
ejpam-5430	79	6	ii	ii	NOUN
ejpam-5430	79	7	)	)	PUNCT
ejpam-5430	79	8	d1	d1	NOUN
ejpam-5430	79	9	⊔d2	⊔d2	PROPN
ejpam-5430	79	10	=	=	SYM
ejpam-5430	79	11	{	{	PUNCT
ejpam-5430	79	12	(	(	PUNCT
ejpam-5430	79	13	x	x	NOUN
ejpam-5430	79	14	,	,	PUNCT
ejpam-5430	79	15	ξd1(x	ξd1(x	NUM
ejpam-5430	79	16	)	)	PUNCT
ejpam-5430	79	17	∨	∨	PROPN
ejpam-5430	79	18	ξd2(x	ξd2(x	PROPN
ejpam-5430	79	19	)	)	PUNCT
ejpam-5430	79	20	,	,	PUNCT
ejpam-5430	79	21	ξd1(x	ξd1(x	NUM
ejpam-5430	79	22	)	)	PUNCT
ejpam-5430	79	23	∧	∧	PROPN
ejpam-5430	79	24	ξd2(x	ξd2(x	PROPN
ejpam-5430	79	25	)	)	PUNCT
ejpam-5430	79	26	:	:	PUNCT
ejpam-5430	80	1	x	x	X
ejpam-5430	80	2	∈	∈	NOUN
ejpam-5430	80	3	x	x	X
ejpam-5430	80	4	}	}	PUNCT
ejpam-5430	80	5	,	,	PUNCT
ejpam-5430	80	6	iii	iii	X
ejpam-5430	80	7	)	)	PUNCT
ejpam-5430	80	8	d1	d1	PROPN
ejpam-5430	80	9	⊑	⊑	PROPN
ejpam-5430	80	10	d2	d2	PROPN
ejpam-5430	80	11	if	if	SCONJ
ejpam-5430	80	12	and	and	CCONJ
ejpam-5430	80	13	only	only	ADV
ejpam-5430	80	14	if	if	SCONJ
ejpam-5430	80	15	ξd1(x	ξd1(x	NUM
ejpam-5430	80	16	)	)	PUNCT
ejpam-5430	80	17	≤	≤	NOUN
ejpam-5430	80	18	ξd2(x	ξd2(x	PROPN
ejpam-5430	80	19	)	)	PUNCT
ejpam-5430	80	20	,	,	PUNCT
ejpam-5430	80	21	ψd1(x	ψd1(x	NOUN
ejpam-5430	80	22	)	)	PUNCT
ejpam-5430	80	23	≥	≥	NOUN
ejpam-5430	80	24	ψd2(x	ψd2(x	PROPN
ejpam-5430	80	25	)	)	PUNCT
ejpam-5430	80	26	:	:	PUNCT
ejpam-5430	81	1	x	x	X
ejpam-5430	81	2	∈	∈	NOUN
ejpam-5430	81	3	x.	x.	NOUN
ejpam-5430	81	4	definition	definition	NOUN
ejpam-5430	81	5	6	6	NUM
ejpam-5430	81	6	.	.	PUNCT
ejpam-5430	82	1	[	[	X
ejpam-5430	82	2	25	25	NUM
ejpam-5430	82	3	]	]	PUNCT
ejpam-5430	82	4	pyfts	pyft	NOUN
ejpam-5430	82	5	is	be	AUX
ejpam-5430	82	6	the	the	DET
ejpam-5430	82	7	pyf	pyf	PROPN
ejpam-5430	82	8	family	family	PROPN
ejpam-5430	82	9	τ	τ	PROPN
ejpam-5430	82	10	that	that	SCONJ
ejpam-5430	82	11	subsets	subset	NOUN
ejpam-5430	82	12	of	of	ADP
ejpam-5430	82	13	a	a	DET
ejpam-5430	82	14	non	non	ADJ
ejpam-5430	82	15	-	-	ADJ
ejpam-5430	82	16	empty	empty	ADJ
ejpam-5430	82	17	set	set	NOUN
ejpam-5430	82	18	x	x	PUNCT
ejpam-5430	82	19	if	if	SCONJ
ejpam-5430	82	20	i	i	PRON
ejpam-5430	82	21	)	)	PUNCT
ejpam-5430	82	22	0x	0x	NOUN
ejpam-5430	82	23	,	,	PUNCT
ejpam-5430	82	24	and	and	CCONJ
ejpam-5430	82	25	1x	1x	NUM
ejpam-5430	82	26	belong	belong	VERB
ejpam-5430	82	27	to	to	ADP
ejpam-5430	82	28	τ	τ	PROPN
ejpam-5430	82	29	,	,	PUNCT
ejpam-5430	82	30	ii	ii	PROPN
ejpam-5430	82	31	)	)	PUNCT
ejpam-5430	82	32	we	we	PRON
ejpam-5430	82	33	have	have	VERB
ejpam-5430	82	34	x1	x1	DET
ejpam-5430	82	35	⊓	⊓	PROPN
ejpam-5430	82	36	x2	x2	NOUN
ejpam-5430	82	37	belong	belong	VERB
ejpam-5430	82	38	to	to	ADP
ejpam-5430	82	39	τ	τ	PROPN
ejpam-5430	82	40	for	for	ADP
ejpam-5430	82	41	any	any	DET
ejpam-5430	82	42	pair	pair	NOUN
ejpam-5430	83	1	x1	x1	PROPN
ejpam-5430	83	2	,	,	PUNCT
ejpam-5430	83	3	x2	x2	PROPN
ejpam-5430	83	4	∈	∈	PROPN
ejpam-5430	83	5	τ	τ	PROPN
ejpam-5430	83	6	,	,	PUNCT
ejpam-5430	83	7	iii	iii	X
ejpam-5430	83	8	)	)	PUNCT
ejpam-5430	83	9	we	we	PRON
ejpam-5430	83	10	have	have	VERB
ejpam-5430	83	11	⊔ixi	⊔ixi	NOUN
ejpam-5430	83	12	belong	belong	VERB
ejpam-5430	83	13	to	to	ADP
ejpam-5430	83	14	τ	τ	PROPN
ejpam-5430	83	15	for	for	ADP
ejpam-5430	83	16	any	any	DET
ejpam-5430	83	17	xi	xi	ADP
ejpam-5430	83	18	∈	∈	PROPN
ejpam-5430	83	19	τ	τ	X
ejpam-5430	83	20	.	.	PUNCT
ejpam-5430	84	1	definition	definition	NOUN
ejpam-5430	84	2	7	7	NUM
ejpam-5430	84	3	.	.	PUNCT
ejpam-5430	85	1	[	[	X
ejpam-5430	85	2	23	23	NUM
ejpam-5430	85	3	]	]	PUNCT
ejpam-5430	85	4	when	when	SCONJ
ejpam-5430	85	5	ξ	ξ	X
ejpam-5430	85	6	:	:	PUNCT
ejpam-5430	85	7	η	η	PROPN
ejpam-5430	85	8	→	→	SYM
ejpam-5430	85	9	℘(x	℘(x	VERB
ejpam-5430	85	10	)	)	PUNCT
ejpam-5430	85	11	is	be	AUX
ejpam-5430	85	12	a	a	DET
ejpam-5430	85	13	(	(	PUNCT
ejpam-5430	85	14	crisp	crisp	ADJ
ejpam-5430	85	15	)	)	PUNCT
ejpam-5430	85	16	map	map	NOUN
ejpam-5430	85	17	,	,	PUNCT
ejpam-5430	85	18	then	then	ADV
ejpam-5430	85	19	a	a	DET
ejpam-5430	85	20	ss	ss	NOUN
ejpam-5430	85	21	over	over	ADV
ejpam-5430	85	22	x	x	VERB
ejpam-5430	85	23	is	be	AUX
ejpam-5430	85	24	a	a	DET
ejpam-5430	85	25	pair	pair	NOUN
ejpam-5430	85	26	(	(	PUNCT
ejpam-5430	85	27	ξ	ξ	PROPN
ejpam-5430	85	28	,	,	PUNCT
ejpam-5430	85	29	η	η	NOUN
ejpam-5430	85	30	)	)	PUNCT
ejpam-5430	85	31	=	=	PRON
ejpam-5430	85	32	{	{	PUNCT
ejpam-5430	85	33	(	(	PUNCT
ejpam-5430	85	34	a	a	PRON
ejpam-5430	85	35	,	,	PUNCT
ejpam-5430	85	36	η(a	η(a	NOUN
ejpam-5430	85	37	)	)	PUNCT
ejpam-5430	85	38	)	)	PUNCT
ejpam-5430	85	39	:	:	PUNCT
ejpam-5430	85	40	a	a	DET
ejpam-5430	85	41	∈	∈	PROPN
ejpam-5430	85	42	η	η	PROPN
ejpam-5430	85	43	}	}	PUNCT
ejpam-5430	85	44	.	.	PUNCT
ejpam-5430	86	1	instead	instead	ADV
ejpam-5430	86	2	of	of	ADP
ejpam-5430	86	3	writing	write	VERB
ejpam-5430	86	4	the	the	DET
ejpam-5430	86	5	soft	soft	ADJ
ejpam-5430	86	6	set	set	NOUN
ejpam-5430	86	7	(	(	PUNCT
ejpam-5430	86	8	ξ	ξ	PROPN
ejpam-5430	86	9	,	,	PUNCT
ejpam-5430	86	10	η	η	NOUN
ejpam-5430	86	11	)	)	PUNCT
ejpam-5430	86	12	,	,	PUNCT
ejpam-5430	86	13	we	we	PRON
ejpam-5430	86	14	write	write	VERB
ejpam-5430	86	15	ξη	ξη	PRON
ejpam-5430	86	16	.	.	PUNCT
ejpam-5430	87	1	ssη(x	ssη(x	PROPN
ejpam-5430	87	2	)	)	PUNCT
ejpam-5430	87	3	or	or	CCONJ
ejpam-5430	87	4	for	for	ADP
ejpam-5430	87	5	all	all	DET
ejpam-5430	87	6	sss	sss	VERB
ejpam-5430	87	7	on	on	ADP
ejpam-5430	87	8	x	x	PRON
ejpam-5430	87	9	,	,	PUNCT
ejpam-5430	87	10	the	the	DET
ejpam-5430	87	11	class	class	NOUN
ejpam-5430	87	12	is	be	AUX
ejpam-5430	87	13	represented	represent	VERB
ejpam-5430	87	14	by	by	ADP
ejpam-5430	87	15	just	just	ADV
ejpam-5430	87	16	ss(x	ss(x	NOUN
ejpam-5430	87	17	)	)	PUNCT
ejpam-5430	87	18	.	.	PUNCT
ejpam-5430	88	1	when	when	SCONJ
ejpam-5430	88	2	a	a	DET
ejpam-5430	88	3	⊑	⊑	DET
ejpam-5430	88	4	η	η	PROPN
ejpam-5430	88	5	,	,	PUNCT
ejpam-5430	88	6	then	then	ADV
ejpam-5430	88	7	ssa(x	ssa(x	PROPN
ejpam-5430	88	8	)	)	PUNCT
ejpam-5430	88	9	will	will	AUX
ejpam-5430	88	10	serve	serve	VERB
ejpam-5430	88	11	as	as	ADP
ejpam-5430	88	12	its	its	PRON
ejpam-5430	88	13	symbol	symbol	NOUN
ejpam-5430	88	14	.	.	PUNCT
ejpam-5430	89	1	definition	definition	NOUN
ejpam-5430	89	2	8	8	NUM
ejpam-5430	89	3	.	.	PUNCT
ejpam-5430	90	1	[	[	X
ejpam-5430	90	2	6	6	NUM
ejpam-5430	90	3	]	]	PUNCT
ejpam-5430	90	4	the	the	DET
ejpam-5430	90	5	term	term	NOUN
ejpam-5430	90	6	for	for	ADP
ejpam-5430	90	7	a	a	DET
ejpam-5430	90	8	ss	ss	NOUN
ejpam-5430	90	9	ξη	ξη	ADV
ejpam-5430	90	10	on	on	ADP
ejpam-5430	90	11	x	x	X
ejpam-5430	90	12	is	be	AUX
ejpam-5430	90	13	:	:	PUNCT
ejpam-5430	90	14	(	(	PUNCT
ejpam-5430	90	15	1	1	X
ejpam-5430	90	16	)	)	PUNCT
ejpam-5430	90	17	a	a	DET
ejpam-5430	90	18	soft	soft	ADJ
ejpam-5430	90	19	element	element	NOUN
ejpam-5430	90	20	if	if	SCONJ
ejpam-5430	90	21	ξ(a	ξ(a	NUM
ejpam-5430	90	22	)	)	PUNCT
ejpam-5430	90	23	=	=	PRON
ejpam-5430	90	24	{	{	PUNCT
ejpam-5430	90	25	x	x	NOUN
ejpam-5430	90	26	}	}	PUNCT
ejpam-5430	90	27	for	for	ADP
ejpam-5430	90	28	every	every	DET
ejpam-5430	90	29	a	a	DET
ejpam-5430	90	30	∈	∈	PROPN
ejpam-5430	90	31	η	η	PROPN
ejpam-5430	90	32	,	,	PUNCT
ejpam-5430	90	33	for	for	ADP
ejpam-5430	90	34	x	x	PROPN
ejpam-5430	90	35	∈	∈	PROPN
ejpam-5430	90	36	x	x	X
ejpam-5430	90	37	,	,	PUNCT
ejpam-5430	90	38	{	{	PUNCT
ejpam-5430	90	39	x}η	x}η	PROPN
ejpam-5430	90	40	is	be	AUX
ejpam-5430	90	41	used	use	VERB
ejpam-5430	90	42	to	to	PART
ejpam-5430	90	43	represent	represent	VERB
ejpam-5430	90	44	a.	a.	NOUN
ejpam-5430	90	45	a.	a.	PROPN
ejpam-5430	90	46	azzam	azzam	PROPN
ejpam-5430	90	47	,	,	PUNCT
ejpam-5430	90	48	m.	m.	NOUN
ejpam-5430	90	49	aldawood	aldawood	PROPN
ejpam-5430	90	50	,	,	PUNCT
ejpam-5430	90	51	r.	r.	PROPN
ejpam-5430	90	52	abu	abu	PROPN
ejpam-5430	90	53	-	-	PUNCT
ejpam-5430	90	54	gdairi	gdairi	PROPN
ejpam-5430	90	55	/	/	SYM
ejpam-5430	90	56	eur	eur	PROPN
ejpam-5430	90	57	.	.	PUNCT
ejpam-5430	91	1	j.	j.	PROPN
ejpam-5430	91	2	pure	pure	PROPN
ejpam-5430	91	3	appl	appl	PROPN
ejpam-5430	91	4	.	.	PROPN
ejpam-5430	91	5	math	math	PROPN
ejpam-5430	91	6	,	,	PUNCT
ejpam-5430	91	7	17	17	NUM
ejpam-5430	91	8	(	(	PUNCT
ejpam-5430	91	9	4	4	NUM
ejpam-5430	91	10	)	)	PUNCT
ejpam-5430	91	11	(	(	PUNCT
ejpam-5430	91	12	2024	2024	NUM
ejpam-5430	91	13	)	)	PUNCT
ejpam-5430	91	14	,	,	PUNCT
ejpam-5430	91	15	4147	4147	NUM
ejpam-5430	91	16	-	-	SYM
ejpam-5430	91	17	4163	4163	NUM
ejpam-5430	91	18	4150	4150	NUM
ejpam-5430	92	1	it(maybe	it(maybe	ADV
ejpam-5430	92	2	soon	soon	ADV
ejpam-5430	92	3	x	x	NOUN
ejpam-5430	92	4	)	)	PUNCT
ejpam-5430	92	5	.	.	PUNCT
ejpam-5430	93	1	(	(	PUNCT
ejpam-5430	93	2	2	2	X
ejpam-5430	93	3	)	)	PUNCT
ejpam-5430	93	4	a	a	DET
ejpam-5430	93	5	soft	soft	ADJ
ejpam-5430	93	6	point	point	NOUN
ejpam-5430	93	7	if	if	SCONJ
ejpam-5430	93	8	for	for	ADP
ejpam-5430	93	9	every	every	DET
ejpam-5430	93	10	a	a	DET
ejpam-5430	93	11	̸=	̸=	PROPN
ejpam-5430	93	12	á	á	PROPN
ejpam-5430	93	13	,	,	PUNCT
ejpam-5430	93	14	ξ(a	ξ(a	NUM
ejpam-5430	93	15	)	)	PUNCT
ejpam-5430	93	16	=	=	PRON
ejpam-5430	94	1	{	{	PUNCT
ejpam-5430	94	2	x	x	NOUN
ejpam-5430	94	3	}	}	PUNCT
ejpam-5430	94	4	and	and	CCONJ
ejpam-5430	94	5	ξ(á	ξ(á	NUM
ejpam-5430	94	6	)	)	PUNCT
ejpam-5430	95	1	=	=	SYM
ejpam-5430	95	2	ϕ	ϕ	PROPN
ejpam-5430	95	3	for	for	ADP
ejpam-5430	95	4	every	every	DET
ejpam-5430	95	5	a	a	DET
ejpam-5430	95	6	∈	∈	PROPN
ejpam-5430	95	7	η	η	PROPN
ejpam-5430	95	8	and	and	CCONJ
ejpam-5430	95	9	x	x	SYM
ejpam-5430	95	10	∈	∈	PROPN
ejpam-5430	95	11	x.	x.	NOUN
ejpam-5430	96	1	it	it	PRON
ejpam-5430	96	2	’s	’s	AUX
ejpam-5430	96	3	indicated	indicate	VERB
ejpam-5430	96	4	by	by	ADP
ejpam-5430	96	5	pxa	pxa	NOUN
ejpam-5430	96	6	.	.	PUNCT
ejpam-5430	97	1	if	if	SCONJ
ejpam-5430	97	2	x	x	PROPN
ejpam-5430	97	3	∈	∈	PROPN
ejpam-5430	97	4	ξ(a	ξ(a	PROPN
ejpam-5430	97	5	)	)	PUNCT
ejpam-5430	97	6	,	,	PUNCT
ejpam-5430	97	7	then	then	ADV
ejpam-5430	97	8	the	the	DET
ejpam-5430	97	9	expression	expression	NOUN
ejpam-5430	97	10	pxa	pxa	NOUN
ejpam-5430	97	11	∈	∈	PROPN
ejpam-5430	97	12	ξ(a	ξ(a	PROPN
ejpam-5430	97	13	)	)	PUNCT
ejpam-5430	97	14	.	.	PUNCT
ejpam-5430	98	1	definition	definition	NOUN
ejpam-5430	98	2	9	9	NUM
ejpam-5430	98	3	.	.	PUNCT
ejpam-5430	99	1	[	[	X
ejpam-5430	99	2	5	5	NUM
ejpam-5430	99	3	]	]	PUNCT
ejpam-5430	99	4	a	a	DET
ejpam-5430	99	5	soft	soft	ADJ
ejpam-5430	99	6	set	set	NOUN
ejpam-5430	99	7	xη	xη	PRON
ejpam-5430	99	8	−	−	PROPN
ejpam-5430	99	9	ξη	ξη	CCONJ
ejpam-5430	99	10	(	(	PUNCT
ejpam-5430	99	11	or	or	CCONJ
ejpam-5430	99	12	simply	simply	ADV
ejpam-5430	99	13	ξcη	ξcη	ADJ
ejpam-5430	99	14	is	be	AUX
ejpam-5430	99	15	the	the	DET
ejpam-5430	99	16	complement	complement	NOUN
ejpam-5430	99	17	of	of	ADP
ejpam-5430	99	18	ξη	ξη	PROPN
ejpam-5430	99	19	,	,	PUNCT
ejpam-5430	99	20	ξ	ξ	PROPN
ejpam-5430	99	21	c	c	NOUN
ejpam-5430	99	22	:	:	PUNCT
ejpam-5430	99	23	η	η	PROPN
ejpam-5430	99	24	→	→	SYM
ejpam-5430	99	25	℘(x	℘(x	VERB
ejpam-5430	99	26	)	)	PUNCT
ejpam-5430	99	27	is	be	AUX
ejpam-5430	99	28	defined	define	VERB
ejpam-5430	99	29	as	as	ADP
ejpam-5430	99	30	ξc(a	ξc(a	NOUN
ejpam-5430	99	31	)	)	PUNCT
ejpam-5430	99	32	=	=	SYM
ejpam-5430	100	1	x	x	X
ejpam-5430	100	2	−	−	PROPN
ejpam-5430	100	3	ξ(a	ξ(a	NUM
ejpam-5430	100	4	)	)	PUNCT
ejpam-5430	100	5	for	for	ADP
ejpam-5430	100	6	every	every	DET
ejpam-5430	100	7	a	a	DET
ejpam-5430	100	8	∈	∈	PROPN
ejpam-5430	100	9	η	η	PROPN
ejpam-5430	100	10	.	.	PROPN
ejpam-5430	100	11	definition	definition	NOUN
ejpam-5430	100	12	10	10	NUM
ejpam-5430	100	13	.	.	PUNCT
ejpam-5430	101	1	[	[	X
ejpam-5430	101	2	23	23	NUM
ejpam-5430	101	3	]	]	PUNCT
ejpam-5430	101	4	the	the	DET
ejpam-5430	101	5	term	term	NOUN
ejpam-5430	101	6	for	for	ADP
ejpam-5430	101	7	a	a	DET
ejpam-5430	101	8	soft	soft	ADJ
ejpam-5430	101	9	subset	subset	NOUN
ejpam-5430	101	10	ξη	ξη	PRON
ejpam-5430	101	11	over	over	ADV
ejpam-5430	101	12	x	x	VERB
ejpam-5430	101	13	is	be	AUX
ejpam-5430	101	14	null	null	ADJ
ejpam-5430	101	15	for	for	ADP
ejpam-5430	101	16	any	any	DET
ejpam-5430	101	17	a	a	DET
ejpam-5430	101	18	∈	∈	PROPN
ejpam-5430	101	19	η	η	PROPN
ejpam-5430	101	20	if	if	SCONJ
ejpam-5430	101	21	ξ(a	ξ(a	VERB
ejpam-5430	101	22	)	)	PUNCT
ejpam-5430	101	23	=	=	SYM
ejpam-5430	101	24	ϕ	ϕ	NOUN
ejpam-5430	101	25	,	,	PUNCT
ejpam-5430	101	26	and	and	CCONJ
ejpam-5430	101	27	absolute	absolute	ADJ
ejpam-5430	101	28	if	if	SCONJ
ejpam-5430	101	29	ξ(a	ξ(a	NUM
ejpam-5430	101	30	)	)	PUNCT
ejpam-5430	101	31	=	=	SYM
ejpam-5430	101	32	x.	x.	NOUN
ejpam-5430	101	33	both	both	CCONJ
ejpam-5430	101	34	empty	empty	ADJ
ejpam-5430	101	35	and	and	CCONJ
ejpam-5430	101	36	absolute	absolute	ADJ
ejpam-5430	101	37	sss	sss	NOUN
ejpam-5430	101	38	are	be	AUX
ejpam-5430	101	39	denoted	denote	VERB
ejpam-5430	101	40	by	by	ADP
ejpam-5430	101	41	ϕη	ϕη	ADV
ejpam-5430	101	42	and	and	CCONJ
ejpam-5430	101	43	xη	xη	PROPN
ejpam-5430	101	44	,	,	PUNCT
ejpam-5430	101	45	respectively	respectively	ADV
ejpam-5430	101	46	.	.	PUNCT
ejpam-5430	102	1	it	it	PRON
ejpam-5430	102	2	is	be	AUX
ejpam-5430	102	3	evident	evident	ADJ
ejpam-5430	102	4	that	that	SCONJ
ejpam-5430	102	5	ϕcη	ϕcη	NOUN
ejpam-5430	102	6	=	=	PUNCT
ejpam-5430	102	7	xη	xη	PROPN
ejpam-5430	102	8	and	and	CCONJ
ejpam-5430	102	9	xc	xc	PROPN
ejpam-5430	102	10	η	η	PROPN
ejpam-5430	102	11	=	=	PROPN
ejpam-5430	102	12	ϕη	ϕη	PROPN
ejpam-5430	102	13	.	.	PUNCT
ejpam-5430	103	1	definition	definition	NOUN
ejpam-5430	103	2	11	11	NUM
ejpam-5430	103	3	.	.	PUNCT
ejpam-5430	104	1	[	[	X
ejpam-5430	104	2	22	22	NUM
ejpam-5430	104	3	]	]	PUNCT
ejpam-5430	104	4	assume	assume	VERB
ejpam-5430	104	5	c	c	NOUN
ejpam-5430	104	6	,	,	PUNCT
ejpam-5430	104	7	d	d	PROPN
ejpam-5430	104	8	⊑	⊑	PRON
ejpam-5430	104	9	η	η	PROPN
ejpam-5430	104	10	.	.	PROPN
ejpam-5430	105	1	if	if	SCONJ
ejpam-5430	105	2	c	c	PROPN
ejpam-5430	105	3	⊑	⊑	X
ejpam-5430	105	4	d	d	PROPN
ejpam-5430	105	5	and	and	CCONJ
ejpam-5430	105	6	ξ(a	ξ(a	NUM
ejpam-5430	105	7	)	)	PUNCT
ejpam-5430	105	8	⊑	⊑	PROPN
ejpam-5430	105	9	g(a	g(a	PROPN
ejpam-5430	105	10	)	)	PUNCT
ejpam-5430	105	11	for	for	ADP
ejpam-5430	105	12	each	each	PRON
ejpam-5430	105	13	a	a	DET
ejpam-5430	105	14	∈	∈	PROPN
ejpam-5430	105	15	c	c	NOUN
ejpam-5430	105	16	,	,	PUNCT
ejpam-5430	105	17	then	then	ADV
ejpam-5430	105	18	gc	gc	PROPN
ejpam-5430	105	19	is	be	AUX
ejpam-5430	105	20	a	a	DET
ejpam-5430	105	21	soft	soft	ADJ
ejpam-5430	105	22	subset	subset	NOUN
ejpam-5430	105	23	of	of	ADP
ejpam-5430	105	24	hd	hd	PROPN
ejpam-5430	105	25	(	(	PUNCT
ejpam-5430	105	26	written	write	VERB
ejpam-5430	105	27	as	as	ADP
ejpam-5430	105	28	gc	gc	PROPN
ejpam-5430	105	29	⊑	⊑	PROPN
ejpam-5430	105	30	hd	hd	PROPN
ejpam-5430	105	31	)	)	PUNCT
ejpam-5430	105	32	.	.	PUNCT
ejpam-5430	106	1	if	if	SCONJ
ejpam-5430	106	2	gc	gc	PROPN
ejpam-5430	106	3	⊑	⊑	PROPN
ejpam-5430	106	4	hd	hd	PROPN
ejpam-5430	106	5	and	and	CCONJ
ejpam-5430	106	6	hd	hd	VERB
ejpam-5430	106	7	⊑	⊑	DET
ejpam-5430	106	8	gc	gc	PROPN
ejpam-5430	106	9	,	,	PUNCT
ejpam-5430	106	10	we	we	PRON
ejpam-5430	106	11	refer	refer	VERB
ejpam-5430	106	12	to	to	ADP
ejpam-5430	106	13	gc	gc	PROPN
ejpam-5430	106	14	soft	soft	ADJ
ejpam-5430	106	15	equates	equate	VERB
ejpam-5430	106	16	to	to	AUX
ejpam-5430	106	17	hd	hd	PROPN
ejpam-5430	106	18	.	.	PUNCT
ejpam-5430	107	1	maji	maji	PROPN
ejpam-5430	107	2	et	et	PROPN
ejpam-5430	107	3	al	al	PROPN
ejpam-5430	107	4	.	.	PUNCT
ejpam-5430	108	1	[	[	X
ejpam-5430	108	2	22	22	NUM
ejpam-5430	108	3	]	]	PUNCT
ejpam-5430	108	4	defined	define	VERB
ejpam-5430	108	5	the	the	DET
ejpam-5430	108	6	soft	soft	ADJ
ejpam-5430	108	7	union	union	NOUN
ejpam-5430	108	8	and	and	CCONJ
ejpam-5430	108	9	soft	soft	ADJ
ejpam-5430	108	10	overlap	overlap	NOUN
ejpam-5430	108	11	of	of	ADP
ejpam-5430	108	12	two	two	NUM
ejpam-5430	108	13	sss	sss	VERB
ejpam-5430	108	14	with	with	ADP
ejpam-5430	108	15	respect	respect	NOUN
ejpam-5430	108	16	to	to	ADP
ejpam-5430	108	17	arbitrary	arbitrary	ADJ
ejpam-5430	108	18	subsets	subset	NOUN
ejpam-5430	108	19	of	of	ADP
ejpam-5430	108	20	η	η	PROPN
ejpam-5430	108	21	.	.	PROPN
ejpam-5430	108	22	however	however	ADV
ejpam-5430	108	23	,	,	PUNCT
ejpam-5430	108	24	as	as	SCONJ
ejpam-5430	108	25	noted	note	VERB
ejpam-5430	108	26	by	by	ADP
ejpam-5430	108	27	ali	ali	PROPN
ejpam-5430	108	28	et	et	PROPN
ejpam-5430	108	29	al	al	PROPN
ejpam-5430	108	30	.	.	PUNCT
ejpam-5430	109	1	[	[	X
ejpam-5430	109	2	5	5	NUM
ejpam-5430	109	3	]	]	PUNCT
ejpam-5430	109	4	,	,	PUNCT
ejpam-5430	109	5	these	these	DET
ejpam-5430	109	6	definitions	definition	NOUN
ejpam-5430	109	7	are	be	AUX
ejpam-5430	109	8	imprecise	imprecise	ADJ
ejpam-5430	109	9	and	and	CCONJ
ejpam-5430	109	10	ambiguous	ambiguous	ADJ
ejpam-5430	109	11	.	.	PUNCT
ejpam-5430	110	1	consequently	consequently	ADV
ejpam-5430	110	2	,	,	PUNCT
ejpam-5430	110	3	we	we	PRON
ejpam-5430	110	4	adhere	adhere	VERB
ejpam-5430	110	5	to	to	ADP
ejpam-5430	110	6	the	the	DET
ejpam-5430	110	7	definitions	definition	NOUN
ejpam-5430	110	8	provided	provide	VERB
ejpam-5430	110	9	by	by	ADP
ejpam-5430	110	10	ali	ali	PROPN
ejpam-5430	110	11	et	et	PROPN
ejpam-5430	110	12	al	al	PROPN
ejpam-5430	110	13	.	.	PUNCT
ejpam-5430	111	1	[	[	X
ejpam-5430	111	2	5	5	NUM
ejpam-5430	111	3	]	]	PUNCT
ejpam-5430	111	4	and	and	CCONJ
ejpam-5430	111	5	m.	m.	NOUN
ejpam-5430	111	6	terepeta	terepeta	NOUN
ejpam-5430	112	1	[	[	X
ejpam-5430	112	2	28	28	NUM
ejpam-5430	112	3	]	]	PUNCT
ejpam-5430	112	4	.	.	PUNCT
ejpam-5430	113	1	definition	definition	NOUN
ejpam-5430	113	2	12	12	NUM
ejpam-5430	113	3	.	.	PUNCT
ejpam-5430	114	1	[	[	X
ejpam-5430	114	2	27	27	NUM
ejpam-5430	114	3	]	]	X
ejpam-5430	114	4	a	a	DET
ejpam-5430	114	5	subfamily	subfamily	ADV
ejpam-5430	114	6	τ	τ	X
ejpam-5430	114	7	of	of	ADP
ejpam-5430	114	8	ssη	ssη	NOUN
ejpam-5430	114	9	is	be	AUX
ejpam-5430	114	10	said	say	VERB
ejpam-5430	114	11	to	to	PART
ejpam-5430	114	12	be	be	AUX
ejpam-5430	114	13	a	a	DET
ejpam-5430	114	14	st	st	NOUN
ejpam-5430	114	15	on	on	ADP
ejpam-5430	114	16	x	x	SYM
ejpam-5430	114	17	if	if	SCONJ
ejpam-5430	114	18	(	(	PUNCT
ejpam-5430	114	19	i	i	NOUN
ejpam-5430	114	20	)	)	PUNCT
ejpam-5430	114	21	xη	xη	PRON
ejpam-5430	114	22	and	and	CCONJ
ejpam-5430	114	23	ϕη	ϕη	ADV
ejpam-5430	114	24	elements	element	NOUN
ejpam-5430	114	25	in	in	ADP
ejpam-5430	114	26	τ	τ	PROPN
ejpam-5430	114	27	,	,	PUNCT
ejpam-5430	114	28	(	(	PUNCT
ejpam-5430	114	29	ii	ii	NOUN
ejpam-5430	114	30	)	)	PUNCT
ejpam-5430	114	31	τ	τ	PROPN
ejpam-5430	114	32	owns	own	VERB
ejpam-5430	114	33	the	the	DET
ejpam-5430	114	34	finite	finite	ADJ
ejpam-5430	114	35	intersection	intersection	NOUN
ejpam-5430	114	36	of	of	ADP
ejpam-5430	114	37	sets	set	NOUN
ejpam-5430	114	38	from	from	ADP
ejpam-5430	114	39	τ	τ	PROPN
ejpam-5430	114	40	,	,	PUNCT
ejpam-5430	114	41	and	and	CCONJ
ejpam-5430	114	42	(	(	PUNCT
ejpam-5430	114	43	iii	iii	X
ejpam-5430	114	44	)	)	PUNCT
ejpam-5430	114	45	τ	τ	PROPN
ejpam-5430	114	46	owns	own	VERB
ejpam-5430	114	47	any	any	DET
ejpam-5430	114	48	union	union	NOUN
ejpam-5430	114	49	of	of	ADP
ejpam-5430	114	50	sets	set	NOUN
ejpam-5430	114	51	from	from	ADP
ejpam-5430	114	52	τ	τ	PROPN
ejpam-5430	114	53	.	.	PUNCT
ejpam-5430	115	1	we	we	PRON
ejpam-5430	115	2	refer	refer	VERB
ejpam-5430	115	3	to	to	ADP
ejpam-5430	115	4	(	(	PUNCT
ejpam-5430	115	5	x	x	X
ejpam-5430	115	6	,	,	PUNCT
ejpam-5430	115	7	τ	τ	PROPN
ejpam-5430	115	8	,	,	PUNCT
ejpam-5430	115	9	η	η	PROPN
ejpam-5430	115	10	)	)	PUNCT
ejpam-5430	115	11	as	as	SCONJ
ejpam-5430	115	12	a	a	DET
ejpam-5430	115	13	sts	st	NOUN
ejpam-5430	115	14	on	on	ADP
ejpam-5430	115	15	x.	x.	PROPN
ejpam-5430	115	16	τ	τ	PROPN
ejpam-5430	115	17	’s	’s	PART
ejpam-5430	115	18	elements	element	NOUN
ejpam-5430	115	19	are	be	AUX
ejpam-5430	115	20	known	know	VERB
ejpam-5430	115	21	as	as	ADP
ejpam-5430	115	22	soft	soft	ADJ
ejpam-5430	115	23	open	open	ADJ
ejpam-5430	115	24	sets	set	NOUN
ejpam-5430	115	25	,	,	PUNCT
ejpam-5430	115	26	while	while	SCONJ
ejpam-5430	115	27	their	their	PRON
ejpam-5430	115	28	complements	complement	NOUN
ejpam-5430	115	29	are	be	AUX
ejpam-5430	115	30	known	know	VERB
ejpam-5430	115	31	as	as	ADP
ejpam-5430	115	32	soft	soft	ADJ
ejpam-5430	115	33	closed	closed	ADJ
ejpam-5430	115	34	sets	set	NOUN
ejpam-5430	115	35	.	.	PUNCT
ejpam-5430	116	1	definition	definition	NOUN
ejpam-5430	116	2	13	13	NUM
ejpam-5430	116	3	.	.	PUNCT
ejpam-5430	117	1	[	[	X
ejpam-5430	117	2	27	27	NUM
ejpam-5430	117	3	]	]	PUNCT
ejpam-5430	117	4	suppose	suppose	VERB
ejpam-5430	117	5	zη	zη	PART
ejpam-5430	117	6	is	be	AUX
ejpam-5430	117	7	a	a	DET
ejpam-5430	117	8	non	non	ADJ
ejpam-5430	117	9	-	-	ADJ
ejpam-5430	117	10	null	null	ADJ
ejpam-5430	117	11	soft	soft	ADJ
ejpam-5430	117	12	subset	subset	NOUN
ejpam-5430	117	13	of	of	ADP
ejpam-5430	117	14	(	(	PUNCT
ejpam-5430	117	15	x	x	PROPN
ejpam-5430	117	16	,	,	PUNCT
ejpam-5430	117	17	τ	τ	PROPN
ejpam-5430	117	18	,	,	PUNCT
ejpam-5430	117	19	η	η	PROPN
ejpam-5430	117	20	)	)	PUNCT
ejpam-5430	117	21	.	.	PUNCT
ejpam-5430	118	1	in	in	ADP
ejpam-5430	118	2	that	that	DET
ejpam-5430	118	3	case	case	NOUN
ejpam-5430	118	4	,	,	PUNCT
ejpam-5430	118	5	(	(	PUNCT
ejpam-5430	118	6	z	z	NOUN
ejpam-5430	118	7	,	,	PUNCT
ejpam-5430	118	8	τz	τz	ADP
ejpam-5430	118	9	,	,	PUNCT
ejpam-5430	118	10	η	η	PROPN
ejpam-5430	118	11	)	)	PUNCT
ejpam-5430	118	12	represents	represent	VERB
ejpam-5430	118	13	a	a	DET
ejpam-5430	118	14	soft	soft	ADJ
ejpam-5430	118	15	subspace	subspace	NOUN
ejpam-5430	118	16	of	of	ADP
ejpam-5430	118	17	(	(	PUNCT
ejpam-5430	118	18	x	x	PROPN
ejpam-5430	118	19	,	,	PUNCT
ejpam-5430	118	20	τ	τ	PROPN
ejpam-5430	118	21	,	,	PUNCT
ejpam-5430	118	22	η	η	PROPN
ejpam-5430	118	23	)	)	PUNCT
ejpam-5430	118	24	,	,	PUNCT
ejpam-5430	118	25	a	a	DET
ejpam-5430	118	26	soft	soft	ADJ
ejpam-5430	118	27	relative	relative	ADJ
ejpam-5430	118	28	topology	topology	NOUN
ejpam-5430	118	29	on	on	ADP
ejpam-5430	118	30	z	z	PROPN
ejpam-5430	118	31	is	be	AUX
ejpam-5430	118	32	denoted	denote	VERB
ejpam-5430	118	33	by	by	ADP
ejpam-5430	118	34	τz	τz	ADP
ejpam-5430	118	35	=	=	VERB
ejpam-5430	118	36	{	{	PUNCT
ejpam-5430	118	37	gη	gη	PRON
ejpam-5430	118	38	⊓	⊓	PROPN
ejpam-5430	118	39	zη	zη	NOUN
ejpam-5430	118	40	:	:	PUNCT
ejpam-5430	118	41	gη	gη	ADP
ejpam-5430	118	42	∈	∈	PROPN
ejpam-5430	118	43	τ	τ	PROPN
ejpam-5430	118	44	}	}	PUNCT
ejpam-5430	118	45	.	.	PUNCT
ejpam-5430	119	1	definition	definition	NOUN
ejpam-5430	119	2	14	14	NUM
ejpam-5430	119	3	.	.	PUNCT
ejpam-5430	120	1	[	[	X
ejpam-5430	120	2	27	27	NUM
ejpam-5430	120	3	]	]	PUNCT
ejpam-5430	120	4	ξη	ξη	X
ejpam-5430	120	5	is	be	AUX
ejpam-5430	120	6	a	a	DET
ejpam-5430	120	7	soft	soft	ADJ
ejpam-5430	120	8	subset	subset	NOUN
ejpam-5430	120	9	of	of	ADP
ejpam-5430	120	10	(	(	PUNCT
ejpam-5430	120	11	x	x	PROPN
ejpam-5430	120	12	,	,	PUNCT
ejpam-5430	120	13	τ	τ	PROPN
ejpam-5430	120	14	,	,	PUNCT
ejpam-5430	120	15	η	η	PROPN
ejpam-5430	120	16	)	)	PUNCT
ejpam-5430	120	17	.	.	PUNCT
ejpam-5430	121	1	denoted	denote	VERB
ejpam-5430	121	2	by	by	ADP
ejpam-5430	121	3	intξη	intξη	PROPN
ejpam-5430	121	4	,	,	PUNCT
ejpam-5430	121	5	the	the	DET
ejpam-5430	121	6	largest	large	ADJ
ejpam-5430	121	7	soft	soft	ADJ
ejpam-5430	121	8	open	open	ADJ
ejpam-5430	121	9	set	set	NOUN
ejpam-5430	121	10	contained	contain	VERB
ejpam-5430	121	11	in	in	ADP
ejpam-5430	121	12	ξη	ξη	PRON
ejpam-5430	121	13	is	be	AUX
ejpam-5430	121	14	the	the	DET
ejpam-5430	121	15	soft	soft	ADJ
ejpam-5430	121	16	interior	interior	NOUN
ejpam-5430	121	17	of	of	ADP
ejpam-5430	121	18	ξη	ξη	PRON
ejpam-5430	121	19	.	.	PUNCT
ejpam-5430	122	1	the	the	DET
ejpam-5430	122	2	soft	soft	ADJ
ejpam-5430	122	3	closure	closure	NOUN
ejpam-5430	122	4	of	of	ADP
ejpam-5430	122	5	ξη	ξη	PRON
ejpam-5430	122	6	is	be	AUX
ejpam-5430	122	7	clξη	clξη	NOUN
ejpam-5430	122	8	,	,	PUNCT
ejpam-5430	122	9	which	which	PRON
ejpam-5430	122	10	is	be	AUX
ejpam-5430	122	11	the	the	DET
ejpam-5430	122	12	smallest	small	ADJ
ejpam-5430	122	13	soft	soft	ADJ
ejpam-5430	122	14	closed	closed	ADJ
ejpam-5430	122	15	set	set	NOUN
ejpam-5430	122	16	containing	contain	VERB
ejpam-5430	122	17	ξη	ξη	PRON
ejpam-5430	122	18	.	.	PUNCT
ejpam-5430	123	1	definition	definition	NOUN
ejpam-5430	123	2	15	15	NUM
ejpam-5430	123	3	.	.	PUNCT
ejpam-5430	124	1	the	the	DET
ejpam-5430	124	2	terms	term	NOUN
ejpam-5430	124	3	”	"	PUNCT
ejpam-5430	124	4	soft	soft	ADJ
ejpam-5430	124	5	dense	dense	ADJ
ejpam-5430	124	6	,	,	PUNCT
ejpam-5430	124	7	”	"	PUNCT
ejpam-5430	124	8	”	"	PUNCT
ejpam-5430	124	9	soft	soft	ADJ
ejpam-5430	124	10	co	co	NOUN
ejpam-5430	124	11	-	-	ADJ
ejpam-5430	124	12	dense	dense	ADJ
ejpam-5430	124	13	,	,	PUNCT
ejpam-5430	124	14	”	"	PUNCT
ejpam-5430	124	15	”	"	PUNCT
ejpam-5430	124	16	soft	soft	ADJ
ejpam-5430	124	17	semiopen	semiopen	ADJ
ejpam-5430	125	1	[	[	X
ejpam-5430	125	2	14	14	NUM
ejpam-5430	125	3	]	]	PUNCT
ejpam-5430	125	4	,	,	PUNCT
ejpam-5430	125	5	”	"	PUNCT
ejpam-5430	125	6	”	"	PUNCT
ejpam-5430	125	7	soft	soft	ADJ
ejpam-5430	125	8	β	β	NOUN
ejpam-5430	125	9	-	-	NOUN
ejpam-5430	125	10	c	c	NOUN
ejpam-5430	126	1	[	[	X
ejpam-5430	126	2	31	31	NUM
ejpam-5430	126	3	]	]	PUNCT
ejpam-5430	126	4	,	,	PUNCT
ejpam-5430	126	5	”	"	PUNCT
ejpam-5430	126	6	”	"	PUNCT
ejpam-5430	126	7	soft	soft	ADJ
ejpam-5430	126	8	somewhat	somewhat	ADV
ejpam-5430	126	9	open	open	ADJ
ejpam-5430	126	10	[	[	X
ejpam-5430	126	11	4	4	NUM
ejpam-5430	126	12	]	]	PUNCT
ejpam-5430	126	13	,	,	PUNCT
ejpam-5430	126	14	”	"	PUNCT
ejpam-5430	126	15	and	and	CCONJ
ejpam-5430	127	1	”	"	PUNCT
ejpam-5430	127	2	soft	soft	ADJ
ejpam-5430	127	3	somewhere	somewhere	ADV
ejpam-5430	127	4	dense	dense	ADJ
ejpam-5430	127	5	[	[	X
ejpam-5430	127	6	3	3	NUM
ejpam-5430	127	7	]	]	PUNCT
ejpam-5430	127	8	,	,	PUNCT
ejpam-5430	127	9	”	"	PUNCT
ejpam-5430	127	10	if	if	SCONJ
ejpam-5430	127	11	”	"	PUNCT
ejpam-5430	127	12	cl(gη	cl(gη	NOUN
ejpam-5430	127	13	)	)	PUNCT
ejpam-5430	127	14	=	=	SYM
ejpam-5430	127	15	xη	xη	PROPN
ejpam-5430	127	16	,	,	PUNCT
ejpam-5430	127	17	”	"	PUNCT
ejpam-5430	127	18	”	"	PUNCT
ejpam-5430	127	19	int(gη	int(gη	NOUN
ejpam-5430	127	20	)	)	PUNCT
ejpam-5430	127	21	=	=	PUNCT
ejpam-5430	127	22	ϕη	ϕη	ADV
ejpam-5430	127	23	,	,	PUNCT
ejpam-5430	127	24	”	"	PUNCT
ejpam-5430	127	25	”	"	PUNCT
ejpam-5430	127	26	gη	gη	ADP
ejpam-5430	127	27	⊑	⊑	X
ejpam-5430	127	28	cl(int(gη	cl(int(gη	PROPN
ejpam-5430	127	29	)	)	PUNCT
ejpam-5430	127	30	)	)	PUNCT
ejpam-5430	127	31	,	,	PUNCT
ejpam-5430	127	32	”	"	PUNCT
ejpam-5430	127	33	”	"	PUNCT
ejpam-5430	127	34	gη	gη	ADP
ejpam-5430	127	35	⊑	⊑	DET
ejpam-5430	127	36	cl(int(clgη	cl(int(clgη	PROPN
ejpam-5430	127	37	)	)	PUNCT
ejpam-5430	127	38	)	)	PUNCT
ejpam-5430	127	39	,	,	PUNCT
ejpam-5430	127	40	”	"	PUNCT
ejpam-5430	127	41	”	"	PUNCT
ejpam-5430	127	42	int(gη	int(gη	NOUN
ejpam-5430	127	43	)	)	PUNCT
ejpam-5430	127	44	̸=	̸=	PROPN
ejpam-5430	127	45	ϕη	ϕη	ADV
ejpam-5430	127	46	,	,	PUNCT
ejpam-5430	127	47	”	"	PUNCT
ejpam-5430	127	48	”	"	PUNCT
ejpam-5430	127	49	int(cl(gη	int(cl(gη	NOUN
ejpam-5430	127	50	)	)	PUNCT
ejpam-5430	127	51	)	)	PUNCT
ejpam-5430	127	52	̸=	̸=	PROPN
ejpam-5430	127	53	ϕη	ϕη	ADV
ejpam-5430	127	54	,	,	PUNCT
ejpam-5430	127	55	”	"	PUNCT
ejpam-5430	127	56	respectively	respectively	ADV
ejpam-5430	127	57	”	"	PUNCT
ejpam-5430	127	58	referring	refer	VERB
ejpam-5430	127	59	to	to	ADP
ejpam-5430	127	60	the	the	DET
ejpam-5430	127	61	different	different	ADJ
ejpam-5430	127	62	states	state	NOUN
ejpam-5430	127	63	of	of	ADP
ejpam-5430	127	64	a	a	DET
ejpam-5430	127	65	soft	soft	ADJ
ejpam-5430	127	66	subset	subset	NOUN
ejpam-5430	127	67	ge	ge	PROPN
ejpam-5430	127	68	of	of	ADP
ejpam-5430	127	69	(	(	PUNCT
ejpam-5430	127	70	x	x	PROPN
ejpam-5430	127	71	,	,	PUNCT
ejpam-5430	127	72	τ	τ	PROPN
ejpam-5430	127	73	,	,	PUNCT
ejpam-5430	127	74	η	η	PROPN
ejpam-5430	127	75	)	)	PUNCT
ejpam-5430	127	76	.	.	PUNCT
ejpam-5430	128	1	(	(	PUNCT
ejpam-5430	128	2	we	we	PRON
ejpam-5430	128	3	compel	compel	VERB
ejpam-5430	128	4	ϕη	ϕη	ADV
ejpam-5430	128	5	to	to	PART
ejpam-5430	128	6	be	be	AUX
ejpam-5430	128	7	soft	soft	ADJ
ejpam-5430	128	8	somewhere	somewhere	ADV
ejpam-5430	128	9	dense	dense	ADJ
ejpam-5430	128	10	in	in	ADP
ejpam-5430	128	11	order	order	NOUN
ejpam-5430	128	12	to	to	PART
ejpam-5430	128	13	improve	improve	VERB
ejpam-5430	128	14	the	the	DET
ejpam-5430	128	15	connectivity	connectivity	NOUN
ejpam-5430	128	16	between	between	ADP
ejpam-5430	128	17	these	these	DET
ejpam-5430	128	18	soft	soft	ADJ
ejpam-5430	128	19	sets	set	NOUN
ejpam-5430	128	20	)	)	PUNCT
ejpam-5430	128	21	.	.	PUNCT
ejpam-5430	129	1	a.	a.	PROPN
ejpam-5430	129	2	a.	a.	PROPN
ejpam-5430	129	3	azzam	azzam	PROPN
ejpam-5430	129	4	,	,	PUNCT
ejpam-5430	129	5	m.	m.	NOUN
ejpam-5430	129	6	aldawood	aldawood	PROPN
ejpam-5430	129	7	,	,	PUNCT
ejpam-5430	129	8	r.	r.	PROPN
ejpam-5430	129	9	abu	abu	PROPN
ejpam-5430	129	10	-	-	PUNCT
ejpam-5430	129	11	gdairi	gdairi	PROPN
ejpam-5430	129	12	/	/	SYM
ejpam-5430	129	13	eur	eur	PROPN
ejpam-5430	129	14	.	.	PUNCT
ejpam-5430	130	1	j.	j.	PROPN
ejpam-5430	130	2	pure	pure	PROPN
ejpam-5430	130	3	appl	appl	PROPN
ejpam-5430	130	4	.	.	PROPN
ejpam-5430	130	5	math	math	PROPN
ejpam-5430	130	6	,	,	PUNCT
ejpam-5430	130	7	17	17	NUM
ejpam-5430	130	8	(	(	PUNCT
ejpam-5430	130	9	4	4	NUM
ejpam-5430	130	10	)	)	PUNCT
ejpam-5430	130	11	(	(	PUNCT
ejpam-5430	130	12	2024	2024	NUM
ejpam-5430	130	13	)	)	PUNCT
ejpam-5430	130	14	,	,	PUNCT
ejpam-5430	130	15	4147	4147	NUM
ejpam-5430	130	16	-	-	SYM
ejpam-5430	130	17	4163	4163	NUM
ejpam-5430	130	18	4151	4151	NUM
ejpam-5430	130	19	definition	definition	NOUN
ejpam-5430	130	20	16	16	NUM
ejpam-5430	130	21	.	.	PUNCT
ejpam-5430	131	1	suppose	suppose	VERB
ejpam-5430	131	2	(	(	PUNCT
ejpam-5430	131	3	x	x	X
ejpam-5430	131	4	,	,	PUNCT
ejpam-5430	131	5	τ	τ	PROPN
ejpam-5430	131	6	,	,	PUNCT
ejpam-5430	131	7	η	η	PROPN
ejpam-5430	131	8	)	)	PUNCT
ejpam-5430	131	9	and	and	CCONJ
ejpam-5430	131	10	(	(	PUNCT
ejpam-5430	131	11	z	z	PROPN
ejpam-5430	131	12	,	,	PUNCT
ejpam-5430	131	13	ρ	ρ	PROPN
ejpam-5430	131	14	,	,	PUNCT
ejpam-5430	131	15	ή	ή	PROPN
ejpam-5430	131	16	)	)	PUNCT
ejpam-5430	131	17	be	be	VERB
ejpam-5430	131	18	sts	st	NOUN
ejpam-5430	131	19	.	.	PUNCT
ejpam-5430	132	1	a	a	DET
ejpam-5430	132	2	soft	soft	ADJ
ejpam-5430	132	3	function	function	NOUN
ejpam-5430	132	4	ξ	ξ	PROPN
ejpam-5430	132	5	:	:	PUNCT
ejpam-5430	132	6	(	(	PUNCT
ejpam-5430	132	7	x	x	X
ejpam-5430	132	8	,	,	PUNCT
ejpam-5430	132	9	τ	τ	PROPN
ejpam-5430	132	10	,	,	PUNCT
ejpam-5430	132	11	η	η	PROPN
ejpam-5430	132	12	)	)	PUNCT
ejpam-5430	132	13	→	→	SYM
ejpam-5430	132	14	(	(	PUNCT
ejpam-5430	132	15	z	z	PROPN
ejpam-5430	132	16	,	,	PUNCT
ejpam-5430	132	17	ρ	ρ	PROPN
ejpam-5430	132	18	,	,	PUNCT
ejpam-5430	132	19	ή	ή	PROPN
ejpam-5430	132	20	)	)	PUNCT
ejpam-5430	132	21	is	be	AUX
ejpam-5430	132	22	called	call	VERB
ejpam-5430	132	23	i	i	PRON
ejpam-5430	132	24	)	)	PUNCT
ejpam-5430	132	25	sc	sc	PROPN
ejpam-5430	133	1	[	[	X
ejpam-5430	133	2	24	24	NUM
ejpam-5430	133	3	]	]	PUNCT
ejpam-5430	133	4	(	(	PUNCT
ejpam-5430	133	5	resp	resp	NOUN
ejpam-5430	133	6	.	.	PUNCT
ejpam-5430	133	7	,	,	PUNCT
ejpam-5430	133	8	soft	soft	ADJ
ejpam-5430	133	9	semi	semi	NOUN
ejpam-5430	133	10	-	-	NOUN
ejpam-5430	133	11	c	c	NOUN
ejpam-5430	133	12	[	[	X
ejpam-5430	133	13	20	20	NUM
ejpam-5430	133	14	]	]	PUNCT
ejpam-5430	133	15	,	,	PUNCT
ejpam-5430	133	16	soft	soft	ADJ
ejpam-5430	133	17	sd	sd	NOUN
ejpam-5430	133	18	-	-	PUNCT
ejpam-5430	133	19	c	c	NOUN
ejpam-5430	134	1	[	[	X
ejpam-5430	134	2	4	4	NUM
ejpam-5430	134	3	]	]	PUNCT
ejpam-5430	134	4	,	,	PUNCT
ejpam-5430	134	5	soft	soft	ADJ
ejpam-5430	134	6	β	β	NOUN
ejpam-5430	134	7	-	-	NOUN
ejpam-5430	134	8	c	c	NOUN
ejpam-5430	135	1	[	[	X
ejpam-5430	135	2	31	31	NUM
ejpam-5430	135	3	]	]	SYM
ejpam-5430	135	4	)	)	PUNCT
ejpam-5430	135	5	if	if	SCONJ
ejpam-5430	135	6	every	every	DET
ejpam-5430	135	7	soft	soft	ADJ
ejpam-5430	135	8	open	open	ADJ
ejpam-5430	135	9	subset	subset	NOUN
ejpam-5430	135	10	of	of	ADP
ejpam-5430	135	11	(	(	PUNCT
ejpam-5430	135	12	z	z	PROPN
ejpam-5430	135	13	,	,	PUNCT
ejpam-5430	135	14	ρ	ρ	PROPN
ejpam-5430	135	15	,	,	PUNCT
ejpam-5430	135	16	ή	ή	PROPN
ejpam-5430	135	17	)	)	PUNCT
ejpam-5430	135	18	has	have	VERB
ejpam-5430	135	19	a	a	DET
ejpam-5430	135	20	soft	soft	ADJ
ejpam-5430	135	21	open	open	NOUN
ejpam-5430	135	22	as	as	ADP
ejpam-5430	135	23	its	its	PRON
ejpam-5430	135	24	inverse	inverse	NOUN
ejpam-5430	135	25	image	image	NOUN
ejpam-5430	135	26	(	(	PUNCT
ejpam-5430	135	27	resp	resp	NOUN
ejpam-5430	135	28	.	.	PUNCT
ejpam-5430	135	29	,	,	PUNCT
ejpam-5430	135	30	soft	soft	ADJ
ejpam-5430	135	31	semiopen	semiopen	ADJ
ejpam-5430	135	32	,	,	PUNCT
ejpam-5430	135	33	soft	soft	ADJ
ejpam-5430	135	34	somewhere	somewhere	ADV
ejpam-5430	135	35	dense	dense	ADJ
ejpam-5430	135	36	,	,	PUNCT
ejpam-5430	135	37	β	β	ADJ
ejpam-5430	135	38	-	-	ADJ
ejpam-5430	135	39	open	open	ADJ
ejpam-5430	135	40	)	)	PUNCT
ejpam-5430	135	41	subset	subset	NOUN
ejpam-5430	135	42	of	of	ADP
ejpam-5430	135	43	(	(	PUNCT
ejpam-5430	135	44	x	x	PROPN
ejpam-5430	135	45	,	,	PUNCT
ejpam-5430	135	46	τ	τ	PROPN
ejpam-5430	135	47	,	,	PUNCT
ejpam-5430	135	48	η	η	PROPN
ejpam-5430	135	49	)	)	PUNCT
ejpam-5430	135	50	.	.	PUNCT
ejpam-5430	136	1	ii	ii	X
ejpam-5430	136	2	)	)	PUNCT
ejpam-5430	136	3	soft	soft	ADJ
ejpam-5430	136	4	open	open	ADJ
ejpam-5430	136	5	[	[	X
ejpam-5430	136	6	23	23	NUM
ejpam-5430	136	7	]	]	PUNCT
ejpam-5430	136	8	(	(	PUNCT
ejpam-5430	136	9	resp	resp	NOUN
ejpam-5430	136	10	.	.	PUNCT
ejpam-5430	136	11	,	,	PUNCT
ejpam-5430	136	12	soft	soft	ADJ
ejpam-5430	136	13	semiopen	semiopen	ADJ
ejpam-5430	137	1	[	[	X
ejpam-5430	137	2	20	20	NUM
ejpam-5430	137	3	]	]	PUNCT
ejpam-5430	137	4	,	,	PUNCT
ejpam-5430	137	5	soft	soft	ADJ
ejpam-5430	137	6	sd	sd	NOUN
ejpam-5430	137	7	-	-	PUNCT
ejpam-5430	137	8	open	open	NOUN
ejpam-5430	138	1	[	[	X
ejpam-5430	138	2	4	4	NUM
ejpam-5430	138	3	]	]	PUNCT
ejpam-5430	138	4	,	,	PUNCT
ejpam-5430	138	5	soft	soft	ADJ
ejpam-5430	138	6	β	β	NOUN
ejpam-5430	138	7	-	-	ADJ
ejpam-5430	138	8	open	open	ADJ
ejpam-5430	138	9	[	[	X
ejpam-5430	138	10	31	31	NUM
ejpam-5430	138	11	]	]	SYM
ejpam-5430	138	12	)	)	PUNCT
ejpam-5430	138	13	if	if	SCONJ
ejpam-5430	138	14	the	the	DET
ejpam-5430	138	15	image	image	NOUN
ejpam-5430	138	16	of	of	ADP
ejpam-5430	138	17	each	each	DET
ejpam-5430	138	18	soft	soft	ADJ
ejpam-5430	138	19	open	open	ADJ
ejpam-5430	138	20	subset	subset	NOUN
ejpam-5430	138	21	of	of	ADP
ejpam-5430	138	22	(	(	PUNCT
ejpam-5430	138	23	x	x	PROPN
ejpam-5430	138	24	,	,	PUNCT
ejpam-5430	138	25	τ	τ	PROPN
ejpam-5430	138	26	,	,	PUNCT
ejpam-5430	138	27	η	η	NOUN
ejpam-5430	138	28	)	)	PUNCT
ejpam-5430	138	29	is	be	AUX
ejpam-5430	138	30	a	a	DET
ejpam-5430	138	31	soft	soft	ADJ
ejpam-5430	138	32	open	open	ADJ
ejpam-5430	138	33	(	(	PUNCT
ejpam-5430	138	34	resp	resp	NOUN
ejpam-5430	138	35	.	.	PUNCT
ejpam-5430	138	36	,	,	PUNCT
ejpam-5430	138	37	soft	soft	ADJ
ejpam-5430	138	38	semiopen	semiopen	ADJ
ejpam-5430	138	39	,	,	PUNCT
ejpam-5430	138	40	soft	soft	ADJ
ejpam-5430	138	41	somewhere	somewhere	ADV
ejpam-5430	138	42	dense	dense	ADJ
ejpam-5430	138	43	,	,	PUNCT
ejpam-5430	138	44	β	β	ADJ
ejpam-5430	138	45	-	-	ADJ
ejpam-5430	138	46	open	open	ADJ
ejpam-5430	138	47	)	)	PUNCT
ejpam-5430	138	48	subset	subset	NOUN
ejpam-5430	138	49	of	of	ADP
ejpam-5430	138	50	(	(	PUNCT
ejpam-5430	138	51	z	z	PROPN
ejpam-5430	138	52	,	,	PUNCT
ejpam-5430	138	53	ρ	ρ	PROPN
ejpam-5430	138	54	,	,	PUNCT
ejpam-5430	138	55	ή	ή	PROPN
ejpam-5430	138	56	)	)	PUNCT
ejpam-5430	138	57	.	.	PUNCT
ejpam-5430	139	1	iii	iii	X
ejpam-5430	139	2	)	)	PUNCT
ejpam-5430	139	3	if	if	SCONJ
ejpam-5430	139	4	it	it	PRON
ejpam-5430	139	5	is	be	AUX
ejpam-5430	139	6	one	one	NUM
ejpam-5430	139	7	to	to	ADP
ejpam-5430	139	8	one	one	NUM
ejpam-5430	139	9	soft	soft	ADJ
ejpam-5430	139	10	open	open	ADJ
ejpam-5430	139	11	and	and	CCONJ
ejpam-5430	139	12	sc	sc	NOUN
ejpam-5430	139	13	from	from	ADP
ejpam-5430	139	14	(	(	PUNCT
ejpam-5430	139	15	x	x	NOUN
ejpam-5430	139	16	,	,	PUNCT
ejpam-5430	139	17	τ	τ	PROPN
ejpam-5430	139	18	,	,	PUNCT
ejpam-5430	139	19	η	η	PROPN
ejpam-5430	139	20	)	)	PUNCT
ejpam-5430	139	21	onto	onto	ADP
ejpam-5430	139	22	(	(	PUNCT
ejpam-5430	139	23	z	z	PROPN
ejpam-5430	139	24	,	,	PUNCT
ejpam-5430	139	25	ρ	ρ	PROPN
ejpam-5430	139	26	,	,	PUNCT
ejpam-5430	139	27	ή	ή	PROPN
ejpam-5430	139	28	)	)	PUNCT
ejpam-5430	139	29	,	,	PUNCT
ejpam-5430	139	30	then	then	ADV
ejpam-5430	139	31	it	it	PRON
ejpam-5430	139	32	is	be	AUX
ejpam-5430	139	33	a	a	DET
ejpam-5430	139	34	soft	soft	ADJ
ejpam-5430	139	35	homeomorphism	homeomorphism	NOUN
ejpam-5430	140	1	[	[	X
ejpam-5430	140	2	24	24	NUM
ejpam-5430	140	3	]	]	PUNCT
ejpam-5430	140	4	.	.	PUNCT
ejpam-5430	141	1	the	the	DET
ejpam-5430	141	2	reader	reader	NOUN
ejpam-5430	141	3	is	be	AUX
ejpam-5430	141	4	referred	refer	VERB
ejpam-5430	141	5	to	to	ADP
ejpam-5430	141	6	[	[	X
ejpam-5430	141	7	19	19	NUM
ejpam-5430	141	8	]	]	PUNCT
ejpam-5430	141	9	for	for	ADP
ejpam-5430	141	10	a	a	DET
ejpam-5430	141	11	definition	definition	NOUN
ejpam-5430	141	12	of	of	ADP
ejpam-5430	141	13	soft	soft	ADJ
ejpam-5430	141	14	functions	function	NOUN
ejpam-5430	141	15	spanning	span	VERB
ejpam-5430	141	16	collections	collection	NOUN
ejpam-5430	141	17	of	of	ADP
ejpam-5430	141	18	all	all	DET
ejpam-5430	141	19	sss	sss	NOUN
ejpam-5430	141	20	.	.	PUNCT
ejpam-5430	141	21	from	from	ADP
ejpam-5430	141	22	here	here	ADV
ejpam-5430	141	23	on	on	ADV
ejpam-5430	141	24	,	,	PUNCT
ejpam-5430	141	25	we	we	PRON
ejpam-5430	141	26	refer	refer	VERB
ejpam-5430	141	27	to	to	ADP
ejpam-5430	141	28	”	"	PUNCT
ejpam-5430	141	29	soft	soft	ADJ
ejpam-5430	141	30	function	function	NOUN
ejpam-5430	141	31	”	"	PUNCT
ejpam-5430	141	32	when	when	SCONJ
ejpam-5430	141	33	we	we	PRON
ejpam-5430	141	34	use	use	VERB
ejpam-5430	141	35	the	the	DET
ejpam-5430	141	36	term	term	NOUN
ejpam-5430	141	37	”	"	PUNCT
ejpam-5430	141	38	function	function	NOUN
ejpam-5430	141	39	.	.	PUNCT
ejpam-5430	141	40	”	"	PUNCT
ejpam-5430	142	1	definition	definition	NOUN
ejpam-5430	142	2	17	17	NUM
ejpam-5430	142	3	.	.	PUNCT
ejpam-5430	143	1	[	[	X
ejpam-5430	143	2	29	29	NUM
ejpam-5430	143	3	]	]	PUNCT
ejpam-5430	143	4	the	the	DET
ejpam-5430	143	5	pyfss	pyfss	NOUN
ejpam-5430	143	6	may	may	AUX
ejpam-5430	143	7	be	be	AUX
ejpam-5430	143	8	expressed	express	VERB
ejpam-5430	143	9	as	as	ADP
ejpam-5430	143	10	a	a	DET
ejpam-5430	143	11	collection	collection	NOUN
ejpam-5430	143	12	of	of	ADP
ejpam-5430	143	13	ordered	order	VERB
ejpam-5430	143	14	pairs	pair	NOUN
ejpam-5430	143	15	(	(	PUNCT
ejpam-5430	143	16	ξ̃	ξ̃	PROPN
ejpam-5430	143	17	,	,	PUNCT
ejpam-5430	143	18	η̃	η̃	PROPN
ejpam-5430	143	19	)	)	PUNCT
ejpam-5430	143	20	=	=	PRON
ejpam-5430	143	21	{	{	PUNCT
ejpam-5430	143	22	(	(	PUNCT
ejpam-5430	143	23	a	a	PRON
ejpam-5430	143	24	,	,	PUNCT
ejpam-5430	143	25	{	{	PUNCT
ejpam-5430	143	26	(	(	PUNCT
ejpam-5430	143	27	x	x	NOUN
ejpam-5430	143	28	,	,	PUNCT
ejpam-5430	143	29	ξξ̃(a)(x	ξξ̃(a)(x	NOUN
ejpam-5430	143	30	)	)	PUNCT
ejpam-5430	143	31	,	,	PUNCT
ejpam-5430	143	32	ψξ̃(a)(x	ψξ̃(a)(x	NOUN
ejpam-5430	143	33	)	)	PUNCT
ejpam-5430	143	34	)	)	PUNCT
ejpam-5430	143	35	:	:	PUNCT
ejpam-5430	143	36	a	a	DET
ejpam-5430	143	37	∈	∈	PROPN
ejpam-5430	143	38	η̃	η̃	PROPN
ejpam-5430	143	39	}	}	PUNCT
ejpam-5430	143	40	}	}	PUNCT
ejpam-5430	143	41	because	because	SCONJ
ejpam-5430	143	42	it	it	PRON
ejpam-5430	143	43	is	be	AUX
ejpam-5430	143	44	not	not	PART
ejpam-5430	143	45	a	a	DET
ejpam-5430	143	46	set	set	NOUN
ejpam-5430	143	47	but	but	CCONJ
ejpam-5430	143	48	rather	rather	ADV
ejpam-5430	143	49	a	a	DET
ejpam-5430	143	50	specified	specified	ADJ
ejpam-5430	143	51	unit	unit	NOUN
ejpam-5430	143	52	of	of	ADP
ejpam-5430	143	53	certain	certain	ADJ
ejpam-5430	143	54	components	component	NOUN
ejpam-5430	143	55	of	of	ADP
ejpam-5430	143	56	the	the	DET
ejpam-5430	143	57	set	set	VERB
ejpam-5430	143	58	pyf	pyf	PROPN
ejpam-5430	143	59	(	(	PUNCT
ejpam-5430	143	60	x̃	x̃	PROPN
ejpam-5430	143	61	)	)	PUNCT
ejpam-5430	143	62	,	,	PUNCT
ejpam-5430	143	63	where	where	SCONJ
ejpam-5430	143	64	ξξ̃(a)(x	ξξ̃(a)(x	NOUN
ejpam-5430	143	65	)	)	PUNCT
ejpam-5430	143	66	and	and	CCONJ
ejpam-5430	143	67	ψξ̃(a)(x	ψξ̃(a)(x	NOUN
ejpam-5430	143	68	)	)	PUNCT
ejpam-5430	143	69	are	be	AUX
ejpam-5430	143	70	the	the	DET
ejpam-5430	143	71	pmfs	pmfs	NOUN
ejpam-5430	143	72	and	and	CCONJ
ejpam-5430	143	73	nmfs	nmfs	NOUN
ejpam-5430	143	74	,	,	PUNCT
ejpam-5430	143	75	successively	successively	ADV
ejpam-5430	143	76	.	.	PUNCT
ejpam-5430	144	1	if	if	SCONJ
ejpam-5430	144	2	x	x	PROPN
ejpam-5430	144	3	∈	∈	PROPN
ejpam-5430	144	4	x̃	x̃	PROPN
ejpam-5430	144	5	,	,	PUNCT
ejpam-5430	144	6	0	0	NUM
ejpam-5430	144	7	≤	≤	NUM
ejpam-5430	144	8	ξ2	ξ2	NOUN
ejpam-5430	144	9	ξ̃(a	ξ̃(a	NOUN
ejpam-5430	144	10	)	)	PUNCT
ejpam-5430	144	11	(	(	PUNCT
ejpam-5430	144	12	x	x	X
ejpam-5430	144	13	)	)	PUNCT
ejpam-5430	144	14	+	+	NUM
ejpam-5430	144	15	ψ2	ψ2	NOUN
ejpam-5430	144	16	ξ̃(a	ξ̃(a	NOUN
ejpam-5430	144	17	)	)	PUNCT
ejpam-5430	144	18	(	(	PUNCT
ejpam-5430	144	19	x	x	X
ejpam-5430	144	20	)	)	PUNCT
ejpam-5430	144	21	≤	≤	NUM
ejpam-5430	144	22	1	1	NUM
ejpam-5430	144	23	.	.	PUNCT
ejpam-5430	145	1	we	we	PRON
ejpam-5430	145	2	introduced	introduce	VERB
ejpam-5430	145	3	the	the	DET
ejpam-5430	145	4	idea	idea	NOUN
ejpam-5430	145	5	of	of	ADP
ejpam-5430	145	6	pyfsts	pyfst	NOUN
ejpam-5430	145	7	and	and	CCONJ
ejpam-5430	145	8	looked	look	VERB
ejpam-5430	145	9	into	into	ADP
ejpam-5430	145	10	its	its	PRON
ejpam-5430	145	11	properties	property	NOUN
ejpam-5430	145	12	in	in	ADP
ejpam-5430	145	13	more	more	ADJ
ejpam-5430	145	14	detail	detail	NOUN
ejpam-5430	145	15	.	.	PUNCT
ejpam-5430	146	1	let	let	VERB
ejpam-5430	146	2	pyf	pyf	PROPN
ejpam-5430	146	3	(	(	PUNCT
ejpam-5430	146	4	x̃	x̃	PROPN
ejpam-5430	146	5	,	,	PUNCT
ejpam-5430	146	6	η̃	η̃	PROPN
ejpam-5430	146	7	)	)	PUNCT
ejpam-5430	146	8	and	and	CCONJ
ejpam-5430	146	9	x̃	x̃	PROPN
ejpam-5430	146	10	represent	represent	PROPN
ejpam-5430	146	11	,	,	PUNCT
ejpam-5430	146	12	respectively	respectively	ADV
ejpam-5430	146	13	,	,	PUNCT
ejpam-5430	146	14	the	the	DET
ejpam-5430	146	15	family	family	NOUN
ejpam-5430	146	16	of	of	ADP
ejpam-5430	146	17	pyfss	pyfss	NOUN
ejpam-5430	146	18	on	on	ADP
ejpam-5430	146	19	x̃	x̃	PROPN
ejpam-5430	146	20	and	and	CCONJ
ejpam-5430	146	21	the	the	DET
ejpam-5430	146	22	origin	origin	NOUN
ejpam-5430	146	23	of	of	ADP
ejpam-5430	146	24	the	the	DET
ejpam-5430	146	25	universal	universal	ADJ
ejpam-5430	146	26	set	set	NOUN
ejpam-5430	146	27	.	.	PUNCT
ejpam-5430	147	1	definition	definition	NOUN
ejpam-5430	147	2	18	18	NUM
ejpam-5430	147	3	.	.	PUNCT
ejpam-5430	148	1	[	[	X
ejpam-5430	148	2	7	7	X
ejpam-5430	148	3	]	]	X
ejpam-5430	148	4	a	a	DET
ejpam-5430	148	5	void	void	ADJ
ejpam-5430	148	6	pyfsss	pyfsss	NOUN
ejpam-5430	148	7	(	(	PUNCT
ejpam-5430	148	8	or	or	CCONJ
ejpam-5430	148	9	0̃	0̃	NOUN
ejpam-5430	148	10	)	)	PUNCT
ejpam-5430	148	11	is	be	AUX
ejpam-5430	148	12	defined	define	VERB
ejpam-5430	148	13	as	as	ADP
ejpam-5430	148	14	a	a	DET
ejpam-5430	148	15	pyfsss(ξ̃	pyfsss(ξ̃	NOUN
ejpam-5430	148	16	,	,	PUNCT
ejpam-5430	148	17	η̃	η̃	PROPN
ejpam-5430	148	18	)	)	PUNCT
ejpam-5430	148	19	over	over	ADP
ejpam-5430	148	20	x̃	x̃	PROPN
ejpam-5430	149	1	if	if	SCONJ
ejpam-5430	149	2	and	and	CCONJ
ejpam-5430	149	3	only	only	ADV
ejpam-5430	149	4	if	if	SCONJ
ejpam-5430	149	5	∀a	∀a	NOUN
ejpam-5430	149	6	∈	∈	PROPN
ejpam-5430	149	7	η̃	η̃	PROPN
ejpam-5430	149	8	,	,	PUNCT
ejpam-5430	149	9	(	(	PUNCT
ejpam-5430	149	10	ξ̃	ξ̃	PROPN
ejpam-5430	149	11	,	,	PUNCT
ejpam-5430	149	12	η̃)(a	η̃)(a	NOUN
ejpam-5430	149	13	)	)	PUNCT
ejpam-5430	149	14	=	=	PRON
ejpam-5430	149	15	(	(	PUNCT
ejpam-5430	149	16	0̃	0̃	PROPN
ejpam-5430	149	17	,	,	PUNCT
ejpam-5430	149	18	1̃	1̃	NUM
ejpam-5430	149	19	)	)	PUNCT
ejpam-5430	149	20	,	,	PUNCT
ejpam-5430	149	21	where	where	SCONJ
ejpam-5430	149	22	0̃	0̃	NOUN
ejpam-5430	149	23	,	,	PUNCT
ejpam-5430	149	24	1̃	1̃	NUM
ejpam-5430	149	25	are	be	AUX
ejpam-5430	149	26	the	the	DET
ejpam-5430	149	27	pmf	pmf	NOUN
ejpam-5430	149	28	and	and	CCONJ
ejpam-5430	149	29	the	the	DET
ejpam-5430	149	30	value	value	NOUN
ejpam-5430	149	31	of	of	ADP
ejpam-5430	149	32	the	the	DET
ejpam-5430	149	33	nmfs	nmfs	NOUN
ejpam-5430	149	34	,	,	PUNCT
ejpam-5430	149	35	the	the	DET
ejpam-5430	149	36	null	null	ADJ
ejpam-5430	149	37	and	and	CCONJ
ejpam-5430	149	38	absolute	absolute	ADJ
ejpam-5430	149	39	,	,	PUNCT
ejpam-5430	149	40	respectively	respectively	ADV
ejpam-5430	149	41	pyfss	pyfss	NOUN
ejpam-5430	149	42	pythagorean	pythagorean	NOUN
ejpam-5430	149	43	over	over	ADP
ejpam-5430	149	44	x̃.	x̃.	ADJ
ejpam-5430	149	45	definition	definition	NOUN
ejpam-5430	149	46	19	19	NUM
ejpam-5430	149	47	.	.	PUNCT
ejpam-5430	150	1	[	[	X
ejpam-5430	150	2	7	7	X
ejpam-5430	150	3	]	]	X
ejpam-5430	150	4	an	an	DET
ejpam-5430	150	5	absolute	absolute	ADJ
ejpam-5430	150	6	pyfsss	pyfsss	NOUN
ejpam-5430	150	7	,	,	PUNCT
ejpam-5430	150	8	or(1̃	or(1̃	NUM
ejpam-5430	150	9	)	)	PUNCT
ejpam-5430	150	10	,	,	PUNCT
ejpam-5430	150	11	is	be	AUX
ejpam-5430	150	12	a	a	DET
ejpam-5430	150	13	pyfsss(ξ̃	pyfsss(ξ̃	NOUN
ejpam-5430	150	14	,	,	PUNCT
ejpam-5430	150	15	η̃	η̃	PROPN
ejpam-5430	150	16	)	)	PUNCT
ejpam-5430	150	17	over	over	ADP
ejpam-5430	150	18	x̃	x̃	PROPN
ejpam-5430	150	19	if	if	SCONJ
ejpam-5430	150	20	and	and	CCONJ
ejpam-5430	150	21	only	only	ADV
ejpam-5430	150	22	if	if	SCONJ
ejpam-5430	150	23	∀a	∀a	NOUN
ejpam-5430	150	24	∈	∈	PROPN
ejpam-5430	150	25	η̃	η̃	PROPN
ejpam-5430	150	26	,	,	PUNCT
ejpam-5430	150	27	(	(	PUNCT
ejpam-5430	150	28	ξ̃	ξ̃	PROPN
ejpam-5430	150	29	,	,	PUNCT
ejpam-5430	150	30	η̃)(a	η̃)(a	NOUN
ejpam-5430	150	31	)	)	PUNCT
ejpam-5430	150	32	=	=	PRON
ejpam-5430	150	33	(	(	PUNCT
ejpam-5430	150	34	0̃	0̃	PROPN
ejpam-5430	150	35	,	,	PUNCT
ejpam-5430	150	36	1̃	1̃	NUM
ejpam-5430	150	37	)	)	PUNCT
ejpam-5430	150	38	,	,	PUNCT
ejpam-5430	150	39	where	where	SCONJ
ejpam-5430	150	40	0̃	0̃	NOUN
ejpam-5430	150	41	,	,	PUNCT
ejpam-5430	150	42	1̃	1̃	NUM
ejpam-5430	150	43	are	be	AUX
ejpam-5430	150	44	the	the	DET
ejpam-5430	150	45	pmf	pmf	NOUN
ejpam-5430	150	46	and	and	CCONJ
ejpam-5430	150	47	the	the	DET
ejpam-5430	150	48	value	value	NOUN
ejpam-5430	150	49	of	of	ADP
ejpam-5430	150	50	the	the	DET
ejpam-5430	150	51	nmfs	nmfs	NOUN
ejpam-5430	150	52	,	,	PUNCT
ejpam-5430	150	53	the	the	DET
ejpam-5430	150	54	null	null	ADJ
ejpam-5430	150	55	and	and	CCONJ
ejpam-5430	150	56	absolute	absolute	ADJ
ejpam-5430	150	57	,	,	PUNCT
ejpam-5430	150	58	respectively	respectively	ADV
ejpam-5430	150	59	,	,	PUNCT
ejpam-5430	150	60	of	of	ADP
ejpam-5430	150	61	the	the	DET
ejpam-5430	150	62	absolute	absolute	ADJ
ejpam-5430	150	63	and	and	CCONJ
ejpam-5430	150	64	null	null	ADJ
ejpam-5430	150	65	function	function	NOUN
ejpam-5430	150	66	.	.	PUNCT
ejpam-5430	151	1	definition	definition	NOUN
ejpam-5430	151	2	20	20	NUM
ejpam-5430	151	3	.	.	PUNCT
ejpam-5430	152	1	[	[	X
ejpam-5430	152	2	7	7	X
ejpam-5430	152	3	]	]	X
ejpam-5430	152	4	let	let	VERB
ejpam-5430	152	5	ω̃	ω̃	PROPN
ejpam-5430	152	6	⊑	⊑	PRON
ejpam-5430	152	7	pyf	pyf	PROPN
ejpam-5430	152	8	(	(	PUNCT
ejpam-5430	152	9	x̃	x̃	PROPN
ejpam-5430	152	10	,	,	PUNCT
ejpam-5430	152	11	η̃	η̃	PROPN
ejpam-5430	152	12	)	)	PUNCT
ejpam-5430	152	13	,	,	PUNCT
ejpam-5430	152	14	at	at	ADP
ejpam-5430	152	15	hence	hence	ADV
ejpam-5430	152	16	,	,	PUNCT
ejpam-5430	152	17	ω̃	ω̃	PROPN
ejpam-5430	152	18	is	be	AUX
ejpam-5430	152	19	claimed	claim	VERB
ejpam-5430	152	20	to	to	PART
ejpam-5430	152	21	be	be	AUX
ejpam-5430	152	22	a	a	DET
ejpam-5430	152	23	pyfsts	pyfst	NOUN
ejpam-5430	152	24	if	if	SCONJ
ejpam-5430	152	25	i	i	PRON
ejpam-5430	152	26	)	)	PUNCT
ejpam-5430	152	27	ω̃	ω̃	PROPN
ejpam-5430	152	28	includes	include	VERB
ejpam-5430	152	29	0̃	0̃	NOUN
ejpam-5430	152	30	and	and	CCONJ
ejpam-5430	152	31	1̃	1̃	NUM
ejpam-5430	152	32	as	as	SCONJ
ejpam-5430	152	33	members	member	NOUN
ejpam-5430	152	34	,	,	PUNCT
ejpam-5430	152	35	ii	ii	NOUN
ejpam-5430	152	36	)	)	PUNCT
ejpam-5430	152	37	any	any	DET
ejpam-5430	152	38	two	two	NUM
ejpam-5430	152	39	pyfss	pyfss	NOUN
ejpam-5430	152	40	that	that	SCONJ
ejpam-5430	152	41	intersect	intersect	NOUN
ejpam-5430	152	42	in	in	ADP
ejpam-5430	152	43	ω̃	ω̃	NUM
ejpam-5430	152	44	are	be	AUX
ejpam-5430	152	45	related	relate	VERB
ejpam-5430	152	46	to	to	ADP
ejpam-5430	152	47	ω̃	ω̃	PROPN
ejpam-5430	152	48	,	,	PUNCT
ejpam-5430	152	49	ii	ii	NOUN
ejpam-5430	152	50	)	)	PUNCT
ejpam-5430	152	51	any	any	DET
ejpam-5430	152	52	number	number	NOUN
ejpam-5430	152	53	of	of	ADP
ejpam-5430	152	54	pyfss	pyfss	NOUN
ejpam-5430	152	55	in	in	ADP
ejpam-5430	152	56	ω̃	ω̃	NUM
ejpam-5430	152	57	that	that	PRON
ejpam-5430	152	58	is	be	AUX
ejpam-5430	152	59	united	unite	VERB
ejpam-5430	152	60	belongs	belong	VERB
ejpam-5430	152	61	to	to	ADP
ejpam-5430	152	62	ω̃	ω̃	PROPN
ejpam-5430	152	63	,	,	PUNCT
ejpam-5430	152	64	it	it	PRON
ejpam-5430	152	65	is	be	AUX
ejpam-5430	152	66	argued	argue	VERB
ejpam-5430	152	67	that	that	SCONJ
ejpam-5430	152	68	the	the	DET
ejpam-5430	152	69	triple	triple	ADJ
ejpam-5430	152	70	(	(	PUNCT
ejpam-5430	152	71	x̃	x̃	PROPN
ejpam-5430	152	72	,	,	PUNCT
ejpam-5430	152	73	ω̃	ω̃	PROPN
ejpam-5430	152	74	,	,	PUNCT
ejpam-5430	152	75	η̃	η̃	PROPN
ejpam-5430	152	76	)	)	PUNCT
ejpam-5430	152	77	is	be	AUX
ejpam-5430	152	78	a	a	DET
ejpam-5430	152	79	pyfsts	pyfst	NOUN
ejpam-5430	152	80	over	over	ADP
ejpam-5430	152	81	x̃.	x̃.	PROPN
ejpam-5430	152	82	∗.	∗.	NOUN
ejpam-5430	152	83	all	all	DET
ejpam-5430	152	84	ω̃	ω̃	NUM
ejpam-5430	152	85	members	member	NOUN
ejpam-5430	152	86	are	be	AUX
ejpam-5430	152	87	considered	consider	VERB
ejpam-5430	152	88	to	to	PART
ejpam-5430	152	89	be	be	AUX
ejpam-5430	152	90	ω̃-open	ω̃-open	ADJ
ejpam-5430	152	91	pyfss	pyfss	NOUN
ejpam-5430	152	92	.	.	PUNCT
ejpam-5430	153	1	∗∗.	∗∗.	PROPN
ejpam-5430	153	2	a	a	DET
ejpam-5430	153	3	ω̃-closed	ω̃-close	VERB
ejpam-5430	153	4	pyfss	pyfss	NOUN
ejpam-5430	153	5	is	be	AUX
ejpam-5430	153	6	considered	consider	VERB
ejpam-5430	153	7	to	to	PART
ejpam-5430	153	8	be	be	AUX
ejpam-5430	153	9	the	the	DET
ejpam-5430	153	10	complement	complement	NOUN
ejpam-5430	153	11	of	of	ADP
ejpam-5430	153	12	a	a	DET
ejpam-5430	153	13	ω̃-open	ω̃-open	PROPN
ejpam-5430	153	14	.	.	PUNCT
ejpam-5430	153	15	a.	a.	PROPN
ejpam-5430	153	16	a.	a.	PROPN
ejpam-5430	153	17	azzam	azzam	PROPN
ejpam-5430	153	18	,	,	PUNCT
ejpam-5430	153	19	m.	m.	NOUN
ejpam-5430	153	20	aldawood	aldawood	PROPN
ejpam-5430	153	21	,	,	PUNCT
ejpam-5430	153	22	r.	r.	PROPN
ejpam-5430	153	23	abu	abu	PROPN
ejpam-5430	153	24	-	-	PUNCT
ejpam-5430	153	25	gdairi	gdairi	PROPN
ejpam-5430	153	26	/	/	SYM
ejpam-5430	153	27	eur	eur	PROPN
ejpam-5430	153	28	.	.	PUNCT
ejpam-5430	154	1	j.	j.	PROPN
ejpam-5430	154	2	pure	pure	PROPN
ejpam-5430	154	3	appl	appl	PROPN
ejpam-5430	154	4	.	.	PROPN
ejpam-5430	154	5	math	math	PROPN
ejpam-5430	154	6	,	,	PUNCT
ejpam-5430	154	7	17	17	NUM
ejpam-5430	154	8	(	(	PUNCT
ejpam-5430	154	9	4	4	NUM
ejpam-5430	154	10	)	)	PUNCT
ejpam-5430	154	11	(	(	PUNCT
ejpam-5430	154	12	2024	2024	NUM
ejpam-5430	154	13	)	)	PUNCT
ejpam-5430	154	14	,	,	PUNCT
ejpam-5430	154	15	4147	4147	NUM
ejpam-5430	154	16	-	-	SYM
ejpam-5430	154	17	4163	4163	NUM
ejpam-5430	154	18	4152	4152	NUM
ejpam-5430	154	19	3	3	X
ejpam-5430	154	20	.	.	PUNCT
ejpam-5430	155	1	pythagorean	pythagorean	PROPN
ejpam-5430	155	2	fuzzy	fuzzy	ADJ
ejpam-5430	155	3	soft	soft	ADJ
ejpam-5430	155	4	somewhat	somewhat	ADV
ejpam-5430	155	5	open	open	ADJ
ejpam-5430	155	6	sets	set	NOUN
ejpam-5430	155	7	we	we	PRON
ejpam-5430	155	8	create	create	VERB
ejpam-5430	155	9	key	key	ADJ
ejpam-5430	155	10	properties	property	NOUN
ejpam-5430	155	11	and	and	CCONJ
ejpam-5430	155	12	introduce	introduce	VERB
ejpam-5430	155	13	the	the	DET
ejpam-5430	155	14	concept	concept	NOUN
ejpam-5430	155	15	of	of	ADP
ejpam-5430	155	16	pyfssw	pyfssw	ADV
ejpam-5430	155	17	-	-	PUNCT
ejpam-5430	155	18	open	open	ADJ
ejpam-5430	155	19	sets	set	NOUN
ejpam-5430	155	20	in	in	ADP
ejpam-5430	155	21	this	this	DET
ejpam-5430	155	22	section	section	NOUN
ejpam-5430	155	23	.	.	PUNCT
ejpam-5430	156	1	we	we	PRON
ejpam-5430	156	2	provide	provide	VERB
ejpam-5430	156	3	examples	example	NOUN
ejpam-5430	156	4	to	to	PART
ejpam-5430	156	5	show	show	VERB
ejpam-5430	156	6	the	the	DET
ejpam-5430	156	7	relationships	relationship	NOUN
ejpam-5430	156	8	between	between	ADP
ejpam-5430	156	9	pyfs	pyfs	NOUN
ejpam-5430	156	10	semiopen	semiopen	ADJ
ejpam-5430	156	11	and	and	CCONJ
ejpam-5430	156	12	pyfs	pyfs	ADJ
ejpam-5430	156	13	somewhere	somewhere	ADV
ejpam-5430	156	14	dense	dense	ADJ
ejpam-5430	156	15	sets	set	NOUN
ejpam-5430	156	16	,	,	PUNCT
ejpam-5430	156	17	as	as	ADV
ejpam-5430	156	18	well	well	ADV
ejpam-5430	156	19	as	as	ADP
ejpam-5430	156	20	various	various	ADJ
ejpam-5430	156	21	generalizations	generalization	NOUN
ejpam-5430	156	22	of	of	ADP
ejpam-5430	156	23	pyfssw	pyfssw	ADV
ejpam-5430	156	24	-	-	PUNCT
ejpam-5430	156	25	open	open	ADJ
ejpam-5430	156	26	sets	set	NOUN
ejpam-5430	156	27	.	.	PUNCT
ejpam-5430	157	1	definition	definition	NOUN
ejpam-5430	157	2	21	21	NUM
ejpam-5430	157	3	.	.	PUNCT
ejpam-5430	158	1	a	a	DET
ejpam-5430	158	2	subset	subset	NOUN
ejpam-5430	158	3	gη̃	gη̃	PROPN
ejpam-5430	158	4	of	of	ADP
ejpam-5430	158	5	a	a	DET
ejpam-5430	158	6	pyfsts	pyfst	NOUN
ejpam-5430	158	7	(	(	PUNCT
ejpam-5430	158	8	x̃	x̃	PROPN
ejpam-5430	158	9	,	,	PUNCT
ejpam-5430	158	10	ω̃	ω̃	PROPN
ejpam-5430	158	11	,	,	PUNCT
ejpam-5430	158	12	η̃	η̃	PROPN
ejpam-5430	158	13	)	)	PUNCT
ejpam-5430	158	14	is	be	AUX
ejpam-5430	158	15	claimed	claim	VERB
ejpam-5430	158	16	to	to	PART
ejpam-5430	158	17	be	be	AUX
ejpam-5430	158	18	pyfssw	pyfssw	ADV
ejpam-5430	158	19	-	-	PUNCT
ejpam-5430	158	20	open	open	ADJ
ejpam-5430	158	21	if	if	SCONJ
ejpam-5430	158	22	int(gη̃	int(gη̃	NOUN
ejpam-5430	158	23	)	)	PUNCT
ejpam-5430	158	24	̸=	̸=	PROPN
ejpam-5430	158	25	ϕη̃	ϕη̃	NUM
ejpam-5430	158	26	or	or	CCONJ
ejpam-5430	158	27	gη̃	gη̃	PROPN
ejpam-5430	158	28	is	be	AUX
ejpam-5430	158	29	null	null	ADJ
ejpam-5430	158	30	.	.	PUNCT
ejpam-5430	159	1	pyfssw	pyfssw	ADV
ejpam-5430	159	2	-	-	PUNCT
ejpam-5430	159	3	closed	close	VERB
ejpam-5430	159	4	is	be	AUX
ejpam-5430	159	5	the	the	DET
ejpam-5430	159	6	complement	complement	NOUN
ejpam-5430	159	7	of	of	ADP
ejpam-5430	159	8	pyfssw	pyfssw	ADV
ejpam-5430	159	9	-	-	PUNCT
ejpam-5430	159	10	open	open	ADJ
ejpam-5430	159	11	set	set	NOUN
ejpam-5430	159	12	.	.	PUNCT
ejpam-5430	160	1	that	that	PRON
ejpam-5430	160	2	is	is	ADV
ejpam-5430	160	3	,	,	PUNCT
ejpam-5430	160	4	a	a	DET
ejpam-5430	160	5	set	set	NOUN
ejpam-5430	160	6	ξη̃	ξη̃	NUM
ejpam-5430	160	7	is	be	AUX
ejpam-5430	160	8	pyfssw	pyfssw	ADV
ejpam-5430	160	9	-	-	PUNCT
ejpam-5430	160	10	closed	closed	ADJ
ejpam-5430	160	11	if	if	SCONJ
ejpam-5430	160	12	cl(ξη̃	cl(ξη̃	ADJ
ejpam-5430	160	13	)	)	PUNCT
ejpam-5430	160	14	̸=	̸=	PROPN
ejpam-5430	160	15	hη̃	hη̃	NOUN
ejpam-5430	160	16	or	or	CCONJ
ejpam-5430	160	17	ξη̃	ξη̃	NUM
ejpam-5430	160	18	=	=	SYM
ejpam-5430	160	19	x̃η̃.	x̃η̃.	X
ejpam-5430	160	20	remark	remark	NOUN
ejpam-5430	160	21	1	1	NUM
ejpam-5430	160	22	.	.	PUNCT
ejpam-5430	161	1	let	let	AUX
ejpam-5430	161	2	(	(	PUNCT
ejpam-5430	161	3	x̃	x̃	PROPN
ejpam-5430	161	4	,	,	PUNCT
ejpam-5430	161	5	ω̃	ω̃	PROPN
ejpam-5430	161	6	,	,	PUNCT
ejpam-5430	161	7	η̃	η̃	PROPN
ejpam-5430	161	8	)	)	PUNCT
ejpam-5430	161	9	be	be	AUX
ejpam-5430	161	10	a	a	DET
ejpam-5430	161	11	pyfsts	pyfst	NOUN
ejpam-5430	161	12	.	.	PUNCT
ejpam-5430	162	1	i	i	PRON
ejpam-5430	162	2	)	)	PUNCT
ejpam-5430	162	3	if	if	SCONJ
ejpam-5430	162	4	and	and	CCONJ
ejpam-5430	162	5	only	only	ADV
ejpam-5430	162	6	if	if	SCONJ
ejpam-5430	162	7	there	there	PRON
ejpam-5430	162	8	is	be	VERB
ejpam-5430	162	9	a	a	DET
ejpam-5430	162	10	pyfs	pyfs	ADJ
ejpam-5430	162	11	-	-	PUNCT
ejpam-5430	162	12	open	open	NOUN
ejpam-5430	162	13	set	set	NOUN
ejpam-5430	162	14	uη̃	uη̃	PUNCT
ejpam-5430	162	15	that	that	SCONJ
ejpam-5430	162	16	ϕη̃	ϕη̃	NUM
ejpam-5430	162	17	̸=	̸=	PROPN
ejpam-5430	162	18	uη̃	uη̃	NUM
ejpam-5430	162	19	⊑	⊑	DET
ejpam-5430	162	20	gη̃	gη̃	PROPN
ejpam-5430	162	21	,	,	PUNCT
ejpam-5430	162	22	the	the	DET
ejpam-5430	162	23	non	non	ADJ
ejpam-5430	162	24	-	-	ADJ
ejpam-5430	162	25	null	null	ADJ
ejpam-5430	162	26	set	set	NOUN
ejpam-5430	162	27	gη̃	gη̃	NOUN
ejpam-5430	162	28	over	over	ADP
ejpam-5430	162	29	x̃	x̃	PROPN
ejpam-5430	162	30	is	be	AUX
ejpam-5430	162	31	pyfssw	pyfssw	ADV
ejpam-5430	162	32	-	-	PUNCT
ejpam-5430	162	33	open	open	ADJ
ejpam-5430	162	34	.	.	PUNCT
ejpam-5430	163	1	ii	ii	X
ejpam-5430	163	2	)	)	PUNCT
ejpam-5430	163	3	if	if	SCONJ
ejpam-5430	163	4	ξη̃	ξη̃	NUM
ejpam-5430	163	5	is	be	AUX
ejpam-5430	163	6	a	a	DET
ejpam-5430	163	7	pyfssw	pyfssw	ADV
ejpam-5430	163	8	-	-	PUNCT
ejpam-5430	163	9	closed	close	VERB
ejpam-5430	163	10	set	set	NOUN
ejpam-5430	163	11	that	that	SCONJ
ejpam-5430	163	12	hη̃	hη̃	PROPN
ejpam-5430	163	13	⊑	⊑	DET
ejpam-5430	163	14	ξη̃	ξη̃	NUM
ejpam-5430	163	15	̸=	̸=	PROPN
ejpam-5430	163	16	x̃η̃	x̃η̃	PROPN
ejpam-5430	163	17	,	,	PUNCT
ejpam-5430	163	18	then	then	ADV
ejpam-5430	163	19	a	a	DET
ejpam-5430	163	20	valid	valid	ADJ
ejpam-5430	163	21	set	set	NOUN
ejpam-5430	163	22	hη̃	hη̃	INTJ
ejpam-5430	163	23	over	over	ADP
ejpam-5430	163	24	x̃	x̃	PROPN
ejpam-5430	163	25	is	be	AUX
ejpam-5430	163	26	pyfssw	pyfssw	ADV
ejpam-5430	163	27	-	-	PUNCT
ejpam-5430	163	28	closed	closed	ADJ
ejpam-5430	163	29	.	.	PUNCT
ejpam-5430	164	1	proposition	proposition	NOUN
ejpam-5430	164	2	1	1	NUM
ejpam-5430	164	3	.	.	PUNCT
ejpam-5430	165	1	i	i	PRON
ejpam-5430	165	2	)	)	PUNCT
ejpam-5430	165	3	each	each	DET
ejpam-5430	165	4	superset	superset	NOUN
ejpam-5430	165	5	of	of	ADP
ejpam-5430	165	6	a	a	DET
ejpam-5430	165	7	pyfssw	pyfssw	ADV
ejpam-5430	165	8	-	-	PUNCT
ejpam-5430	165	9	open	open	ADJ
ejpam-5430	165	10	set	set	NOUN
ejpam-5430	165	11	is	be	AUX
ejpam-5430	165	12	pyfssw	pyfssw	ADV
ejpam-5430	165	13	-	-	PUNCT
ejpam-5430	165	14	open	open	ADJ
ejpam-5430	165	15	.	.	PUNCT
ejpam-5430	166	1	ii	ii	X
ejpam-5430	166	2	)	)	PUNCT
ejpam-5430	166	3	each	each	DET
ejpam-5430	166	4	subset	subset	NOUN
ejpam-5430	166	5	of	of	ADP
ejpam-5430	166	6	a	a	DET
ejpam-5430	166	7	pyfssw	pyfssw	ADV
ejpam-5430	166	8	-	-	PUNCT
ejpam-5430	166	9	closed	close	VERB
ejpam-5430	166	10	set	set	NOUN
ejpam-5430	166	11	is	be	AUX
ejpam-5430	166	12	pyfssw	pyfssw	ADV
ejpam-5430	166	13	-	-	PUNCT
ejpam-5430	166	14	closed	closed	ADJ
ejpam-5430	166	15	.	.	PUNCT
ejpam-5430	167	1	proof	proof	NOUN
ejpam-5430	167	2	.	.	PUNCT
ejpam-5430	168	1	obvious	obvious	ADJ
ejpam-5430	168	2	.	.	PUNCT
ejpam-5430	169	1	proposition	proposition	NOUN
ejpam-5430	169	2	2	2	NUM
ejpam-5430	169	3	.	.	PUNCT
ejpam-5430	169	4	a	a	DET
ejpam-5430	169	5	non	non	ADJ
ejpam-5430	169	6	-	-	ADJ
ejpam-5430	169	7	null	null	ADJ
ejpam-5430	169	8	pyfss	pyfss	NOUN
ejpam-5430	169	9	is	be	AUX
ejpam-5430	169	10	pyfssw	pyfssw	ADV
ejpam-5430	169	11	-	-	PUNCT
ejpam-5430	169	12	open	open	ADJ
ejpam-5430	169	13	if	if	SCONJ
ejpam-5430	169	14	and	and	CCONJ
ejpam-5430	169	15	only	only	ADV
ejpam-5430	169	16	if	if	SCONJ
ejpam-5430	169	17	it	it	PRON
ejpam-5430	169	18	is	be	AUX
ejpam-5430	169	19	a	a	DET
ejpam-5430	169	20	pyfs	pyfs	ADJ
ejpam-5430	169	21	neighborhood	neighborhood	NOUN
ejpam-5430	169	22	of	of	ADP
ejpam-5430	169	23	a	a	DET
ejpam-5430	169	24	pyfs	pyfs	ADJ
ejpam-5430	169	25	point	point	NOUN
ejpam-5430	169	26	.	.	PUNCT
ejpam-5430	170	1	proof	proof	NOUN
ejpam-5430	170	2	.	.	PUNCT
ejpam-5430	171	1	let	let	VERB
ejpam-5430	171	2	gη̃	gη̃	PRON
ejpam-5430	171	3	be	be	AUX
ejpam-5430	171	4	a	a	DET
ejpam-5430	171	5	pyfssw	pyfssw	ADV
ejpam-5430	171	6	-	-	PUNCT
ejpam-5430	171	7	open	open	ADJ
ejpam-5430	171	8	set	set	NOUN
ejpam-5430	171	9	that	that	PRON
ejpam-5430	171	10	is	be	AUX
ejpam-5430	171	11	n’t	not	PART
ejpam-5430	171	12	null	null	ADJ
ejpam-5430	171	13	.	.	PUNCT
ejpam-5430	172	1	next	next	ADV
ejpam-5430	172	2	,	,	PUNCT
ejpam-5430	172	3	there	there	PRON
ejpam-5430	172	4	exists	exist	VERB
ejpam-5430	172	5	a	a	DET
ejpam-5430	172	6	pyfs	pyfs	ADJ
ejpam-5430	172	7	open	open	ADJ
ejpam-5430	172	8	set	set	NOUN
ejpam-5430	172	9	uη̃	uη̃	SYM
ejpam-5430	172	10	,	,	PUNCT
ejpam-5430	172	11	where	where	SCONJ
ejpam-5430	172	12	ϕη̃	ϕη̃	PROPN
ejpam-5430	172	13	̸=	̸=	PROPN
ejpam-5430	172	14	uη̃	uη̃	PUNCT
ejpam-5430	172	15	⊑	⊑	PRON
ejpam-5430	172	16	gη̃.	gη̃.	VERB
ejpam-5430	172	17	as	as	ADP
ejpam-5430	172	18	a	a	DET
ejpam-5430	172	19	result	result	NOUN
ejpam-5430	172	20	,	,	PUNCT
ejpam-5430	172	21	gη̃	gη̃	PROPN
ejpam-5430	172	22	is	be	AUX
ejpam-5430	172	23	every	every	DET
ejpam-5430	172	24	soft	soft	ADJ
ejpam-5430	172	25	point	point	NOUN
ejpam-5430	172	26	in	in	ADP
ejpam-5430	172	27	uη̃	uη̃	NOUN
ejpam-5430	172	28	’s	’s	PART
ejpam-5430	172	29	soft	soft	ADJ
ejpam-5430	172	30	neighborhood	neighborhood	NOUN
ejpam-5430	172	31	.	.	PUNCT
ejpam-5430	173	1	let	let	VERB
ejpam-5430	173	2	gη̃	gη̃	NOUN
ejpam-5430	173	3	,	,	PUNCT
ejpam-5430	173	4	on	on	ADP
ejpam-5430	173	5	the	the	DET
ejpam-5430	173	6	other	other	ADJ
ejpam-5430	173	7	hand	hand	NOUN
ejpam-5430	173	8	,	,	PUNCT
ejpam-5430	173	9	be	be	AUX
ejpam-5430	173	10	the	the	DET
ejpam-5430	173	11	pyfs	pyfs	ADJ
ejpam-5430	173	12	neighborhood	neighborhood	NOUN
ejpam-5430	173	13	of	of	ADP
ejpam-5430	173	14	a	a	DET
ejpam-5430	173	15	pyf	pyf	NOUN
ejpam-5430	173	16	soft	soft	ADJ
ejpam-5430	173	17	point	point	NOUN
ejpam-5430	173	18	pxa	pxa	NOUN
ejpam-5430	173	19	.	.	PUNCT
ejpam-5430	174	1	after	after	ADP
ejpam-5430	174	2	that	that	PRON
ejpam-5430	174	3	,	,	PUNCT
ejpam-5430	174	4	uη̃	uη̃	PROPN
ejpam-5430	174	5	is	be	AUX
ejpam-5430	174	6	pyf	pyf	PROPN
ejpam-5430	174	7	softly	softly	ADV
ejpam-5430	174	8	opened	open	VERB
ejpam-5430	174	9	so	so	SCONJ
ejpam-5430	174	10	that	that	SCONJ
ejpam-5430	174	11	pxa	pxa	NOUN
ejpam-5430	174	12	∈	∈	NOUN
ejpam-5430	174	13	uη̃	uη̃	PUNCT
ejpam-5430	174	14	⊑	⊑	PRON
ejpam-5430	174	15	gη̃.	gη̃.	VERB
ejpam-5430	174	16	as	as	ADP
ejpam-5430	174	17	a	a	DET
ejpam-5430	174	18	result	result	NOUN
ejpam-5430	174	19	,	,	PUNCT
ejpam-5430	174	20	we	we	PRON
ejpam-5430	174	21	get	get	VERB
ejpam-5430	174	22	intgη̃	intgη̃	ADJ
ejpam-5430	174	23	̸=	̸=	PROPN
ejpam-5430	174	24	ϕη̃	ϕη̃	NUM
ejpam-5430	174	25	,	,	PUNCT
ejpam-5430	174	26	as	as	SCONJ
ejpam-5430	174	27	needed	need	VERB
ejpam-5430	174	28	.	.	PUNCT
ejpam-5430	175	1	proposition	proposition	NOUN
ejpam-5430	175	2	3	3	NUM
ejpam-5430	175	3	.	.	PUNCT
ejpam-5430	176	1	a	a	DET
ejpam-5430	176	2	union	union	NOUN
ejpam-5430	176	3	of	of	ADP
ejpam-5430	176	4	pyfssw	pyfssw	ADV
ejpam-5430	176	5	-	-	PUNCT
ejpam-5430	176	6	open	open	ADJ
ejpam-5430	176	7	sets	set	NOUN
ejpam-5430	176	8	is	be	AUX
ejpam-5430	176	9	pyfssw	pyfssw	ADV
ejpam-5430	176	10	-	-	PUNCT
ejpam-5430	176	11	open	open	ADJ
ejpam-5430	176	12	.	.	PUNCT
ejpam-5430	177	1	proof	proof	NOUN
ejpam-5430	177	2	.	.	PUNCT
ejpam-5430	178	1	suppose	suppose	VERB
ejpam-5430	178	2	that	that	SCONJ
ejpam-5430	178	3	{	{	PUNCT
ejpam-5430	178	4	gβ	gβ	PROPN
ejpam-5430	178	5	η̃	η̃	PROPN
ejpam-5430	178	6	:	:	PUNCT
ejpam-5430	178	7	β	β	X
ejpam-5430	178	8	∈	∈	PROPN
ejpam-5430	178	9	λ	λ	PROPN
ejpam-5430	178	10	}	}	PUNCT
ejpam-5430	178	11	is	be	AUX
ejpam-5430	178	12	the	the	DET
ejpam-5430	178	13	collection	collection	NOUN
ejpam-5430	178	14	of	of	ADP
ejpam-5430	178	15	pyfssw	pyfssw	ADV
ejpam-5430	178	16	-	-	PUNCT
ejpam-5430	178	17	open	open	ADJ
ejpam-5430	178	18	subsets	subset	NOUN
ejpam-5430	178	19	of	of	ADP
ejpam-5430	178	20	a	a	DET
ejpam-5430	178	21	pyfsts	pyfst	NOUN
ejpam-5430	178	22	(	(	PUNCT
ejpam-5430	178	23	x̃	x̃	PROPN
ejpam-5430	178	24	,	,	PUNCT
ejpam-5430	178	25	ω̃	ω̃	PROPN
ejpam-5430	178	26	,	,	PUNCT
ejpam-5430	178	27	η̃	η̃	PROPN
ejpam-5430	178	28	)	)	PUNCT
ejpam-5430	178	29	.	.	PUNCT
ejpam-5430	179	1	at	at	ADP
ejpam-5430	179	2	hence	hence	ADV
ejpam-5430	179	3	,	,	PUNCT
ejpam-5430	179	4	int(∪β∈λg	int(∪β∈λg	ADP
ejpam-5430	179	5	β	β	X
ejpam-5430	179	6	η̃	η̃	PROPN
ejpam-5430	179	7	)	)	PUNCT
ejpam-5430	179	8	⊒	⊒	PUNCT
ejpam-5430	180	1	∪β∈λint(g	∪β∈λint(g	PROPN
ejpam-5430	180	2	β	β	X
ejpam-5430	180	3	η̃	η̃	PROPN
ejpam-5430	180	4	)	)	PUNCT
ejpam-5430	181	1	̸=	̸=	PROPN
ejpam-5430	181	2	ϕη̃.	ϕη̃.	VERB
ejpam-5430	181	3	thus	thus	ADV
ejpam-5430	181	4	∪β∈λg	∪β∈λg	NOUN
ejpam-5430	181	5	β	β	ADP
ejpam-5430	181	6	η̃	η̃	PROPN
ejpam-5430	181	7	is	be	AUX
ejpam-5430	181	8	pyfssw	pyfssw	ADV
ejpam-5430	181	9	-	-	PUNCT
ejpam-5430	181	10	open	open	ADJ
ejpam-5430	181	11	.	.	PUNCT
ejpam-5430	182	1	corollary	corollary	ADJ
ejpam-5430	182	2	1	1	NUM
ejpam-5430	182	3	.	.	PUNCT
ejpam-5430	183	1	the	the	DET
ejpam-5430	183	2	intersection	intersection	NOUN
ejpam-5430	183	3	of	of	ADP
ejpam-5430	183	4	pyfssw	pyfssw	ADV
ejpam-5430	183	5	-	-	PUNCT
ejpam-5430	183	6	closed	close	VERB
ejpam-5430	183	7	sets	set	NOUN
ejpam-5430	183	8	is	be	AUX
ejpam-5430	183	9	pyfssw	pyfssw	ADV
ejpam-5430	183	10	-	-	PUNCT
ejpam-5430	183	11	closed	closed	ADJ
ejpam-5430	183	12	.	.	PUNCT
ejpam-5430	184	1	as	as	SCONJ
ejpam-5430	184	2	demonstrated	demonstrate	VERB
ejpam-5430	184	3	by	by	ADP
ejpam-5430	184	4	the	the	DET
ejpam-5430	184	5	example	example	NOUN
ejpam-5430	184	6	that	that	PRON
ejpam-5430	184	7	follows	follow	VERB
ejpam-5430	184	8	,	,	PUNCT
ejpam-5430	184	9	the	the	DET
ejpam-5430	184	10	intersection	intersection	NOUN
ejpam-5430	184	11	of	of	ADP
ejpam-5430	184	12	two	two	NUM
ejpam-5430	184	13	pyfssw	pyfssw	ADV
ejpam-5430	184	14	-	-	PUNCT
ejpam-5430	184	15	open	open	ADJ
ejpam-5430	184	16	sets	set	NOUN
ejpam-5430	184	17	need	need	AUX
ejpam-5430	184	18	not	not	PART
ejpam-5430	184	19	be	be	AUX
ejpam-5430	184	20	pyfssw	pyfssw	ADV
ejpam-5430	184	21	-	-	PUNCT
ejpam-5430	184	22	open	open	ADJ
ejpam-5430	184	23	.	.	PUNCT
ejpam-5430	185	1	example	example	NOUN
ejpam-5430	186	1	1	1	NUM
ejpam-5430	186	2	.	.	PUNCT
ejpam-5430	186	3	let	let	VERB
ejpam-5430	186	4	η̃	η̃	PROPN
ejpam-5430	186	5	=	=	SYM
ejpam-5430	186	6	{	{	PUNCT
ejpam-5430	186	7	a1	a1	PROPN
ejpam-5430	186	8	,	,	PUNCT
ejpam-5430	186	9	a2	a2	PROPN
ejpam-5430	186	10	,	,	PUNCT
ejpam-5430	186	11	a3	a3	NOUN
ejpam-5430	186	12	,	,	PUNCT
ejpam-5430	186	13	a4	a4	PROPN
ejpam-5430	186	14	}	}	PUNCT
ejpam-5430	186	15	be	be	VERB
ejpam-5430	186	16	the	the	DET
ejpam-5430	186	17	parameters	parameter	NOUN
ejpam-5430	186	18	or	or	CCONJ
ejpam-5430	186	19	characteristics	characteristic	NOUN
ejpam-5430	186	20	set	set	VERB
ejpam-5430	186	21	and	and	CCONJ
ejpam-5430	186	22	as	as	SCONJ
ejpam-5430	186	23	the	the	DET
ejpam-5430	186	24	reference	reference	NOUN
ejpam-5430	186	25	set	set	NOUN
ejpam-5430	186	26	,	,	PUNCT
ejpam-5430	186	27	let	let	VERB
ejpam-5430	186	28	x̃	x̃	PROPN
ejpam-5430	186	29	=	=	PRON
ejpam-5430	186	30	{	{	PUNCT
ejpam-5430	186	31	x1	x1	PROPN
ejpam-5430	186	32	,	,	PUNCT
ejpam-5430	186	33	x2	x2	PROPN
ejpam-5430	186	34	,	,	PUNCT
ejpam-5430	186	35	x3	x3	ADJ
ejpam-5430	186	36	}	}	PUNCT
ejpam-5430	186	37	represent	represent	VERB
ejpam-5430	186	38	the	the	DET
ejpam-5430	186	39	applicants	applicant	NOUN
ejpam-5430	186	40	who	who	PRON
ejpam-5430	186	41	have	have	AUX
ejpam-5430	186	42	been	be	AUX
ejpam-5430	186	43	recommended	recommend	VERB
ejpam-5430	186	44	for	for	ADP
ejpam-5430	186	45	promotion	promotion	NOUN
ejpam-5430	186	46	,	,	PUNCT
ejpam-5430	186	47	in	in	ADP
ejpam-5430	186	48	which	which	PRON
ejpam-5430	186	49	a1	a1	NOUN
ejpam-5430	186	50	denotes	denote	NOUN
ejpam-5430	186	51	intelligence	intelligence	NOUN
ejpam-5430	186	52	,	,	PUNCT
ejpam-5430	186	53	a2	a2	PROPN
ejpam-5430	186	54	experience	experience	NOUN
ejpam-5430	186	55	,	,	PUNCT
ejpam-5430	186	56	a3	a3	NOUN
ejpam-5430	186	57	attitude	attitude	NOUN
ejpam-5430	186	58	,	,	PUNCT
ejpam-5430	186	59	and	and	CCONJ
ejpam-5430	186	60	a4	a4	NUM
ejpam-5430	186	61	competence	competence	NOUN
ejpam-5430	186	62	.	.	PUNCT
ejpam-5430	187	1	let	let	VERB
ejpam-5430	187	2	d1	d1	PROPN
ejpam-5430	187	3	=	=	SYM
ejpam-5430	187	4	{	{	PUNCT
ejpam-5430	187	5	a1	a1	PROPN
ejpam-5430	187	6	,	,	PUNCT
ejpam-5430	187	7	a2	a2	PROPN
ejpam-5430	187	8	}	}	PUNCT
ejpam-5430	187	9	⊑	⊑	PROPN
ejpam-5430	187	10	η̃	η̃	PROPN
ejpam-5430	187	11	,	,	PUNCT
ejpam-5430	187	12	d2	d2	PROPN
ejpam-5430	187	13	=	=	SYM
ejpam-5430	187	14	{	{	PUNCT
ejpam-5430	187	15	a2	a2	PROPN
ejpam-5430	187	16	}	}	PUNCT
ejpam-5430	187	17	⊑	⊑	PRON
ejpam-5430	187	18	η̃.	η̃.	PROPN
ejpam-5430	187	19	next	next	ADV
ejpam-5430	187	20	,	,	PUNCT
ejpam-5430	187	21	two	two	NUM
ejpam-5430	187	22	pyfssw(ξ̃1	pyfssw(ξ̃1	NOUN
ejpam-5430	187	23	,	,	PUNCT
ejpam-5430	187	24	d1	d1	PROPN
ejpam-5430	187	25	)	)	PUNCT
ejpam-5430	187	26	and	and	CCONJ
ejpam-5430	187	27	(	(	PUNCT
ejpam-5430	187	28	ξ̃2	ξ̃2	PROPN
ejpam-5430	187	29	,	,	PUNCT
ejpam-5430	187	30	d2	d2	PROPN
ejpam-5430	187	31	)	)	PUNCT
ejpam-5430	187	32	are	be	AUX
ejpam-5430	187	33	examined	examine	VERB
ejpam-5430	187	34	.	.	PUNCT
ejpam-5430	188	1	these	these	PRON
ejpam-5430	188	2	are	be	AUX
ejpam-5430	188	3	represented	represent	VERB
ejpam-5430	188	4	as	as	SCONJ
ejpam-5430	188	5	follows	follow	VERB
ejpam-5430	188	6	:	:	PUNCT
ejpam-5430	188	7	a.	a.	NOUN
ejpam-5430	188	8	a.	a.	PROPN
ejpam-5430	188	9	azzam	azzam	PROPN
ejpam-5430	188	10	,	,	PUNCT
ejpam-5430	188	11	m.	m.	NOUN
ejpam-5430	188	12	aldawood	aldawood	PROPN
ejpam-5430	188	13	,	,	PUNCT
ejpam-5430	188	14	r.	r.	PROPN
ejpam-5430	188	15	abu	abu	PROPN
ejpam-5430	188	16	-	-	PUNCT
ejpam-5430	188	17	gdairi	gdairi	PROPN
ejpam-5430	188	18	/	/	SYM
ejpam-5430	188	19	eur	eur	PROPN
ejpam-5430	188	20	.	.	PUNCT
ejpam-5430	189	1	j.	j.	PROPN
ejpam-5430	189	2	pure	pure	PROPN
ejpam-5430	189	3	appl	appl	PROPN
ejpam-5430	189	4	.	.	PROPN
ejpam-5430	189	5	math	math	PROPN
ejpam-5430	189	6	,	,	PUNCT
ejpam-5430	189	7	17	17	NUM
ejpam-5430	189	8	(	(	PUNCT
ejpam-5430	189	9	4	4	NUM
ejpam-5430	189	10	)	)	PUNCT
ejpam-5430	189	11	(	(	PUNCT
ejpam-5430	189	12	2024	2024	NUM
ejpam-5430	189	13	)	)	PUNCT
ejpam-5430	189	14	,	,	PUNCT
ejpam-5430	189	15	4147	4147	NUM
ejpam-5430	189	16	-	-	SYM
ejpam-5430	189	17	4163	4163	NUM
ejpam-5430	189	18	4153	4153	NUM
ejpam-5430	189	19	(	(	PUNCT
ejpam-5430	189	20	ξ̃1	ξ̃1	NOUN
ejpam-5430	189	21	,	,	PUNCT
ejpam-5430	189	22	d1	d1	NOUN
ejpam-5430	189	23	)	)	PUNCT
ejpam-5430	189	24	=	=	PRON
ejpam-5430	189	25	{	{	PUNCT
ejpam-5430	189	26	(	(	PUNCT
ejpam-5430	189	27	a1	a1	NOUN
ejpam-5430	189	28	,	,	PUNCT
ejpam-5430	189	29	ξ̃1(a1	ξ̃1(a1	NOUN
ejpam-5430	189	30	)	)	PUNCT
ejpam-5430	189	31	)	)	PUNCT
ejpam-5430	189	32	,	,	PUNCT
ejpam-5430	189	33	(	(	PUNCT
ejpam-5430	189	34	a2	a2	PROPN
ejpam-5430	189	35	,	,	PUNCT
ejpam-5430	189	36	ξ̃1(a2	ξ̃1(a2	NUM
ejpam-5430	189	37	)	)	PUNCT
ejpam-5430	189	38	)	)	PUNCT
ejpam-5430	189	39	}	}	PUNCT
ejpam-5430	189	40	,	,	PUNCT
ejpam-5430	189	41	and	and	CCONJ
ejpam-5430	189	42	(	(	PUNCT
ejpam-5430	189	43	ξ̃2	ξ̃2	PROPN
ejpam-5430	189	44	,	,	PUNCT
ejpam-5430	189	45	d2	d2	PROPN
ejpam-5430	189	46	)	)	PUNCT
ejpam-5430	189	47	=	=	PRON
ejpam-5430	189	48	{	{	PUNCT
ejpam-5430	189	49	(	(	PUNCT
ejpam-5430	189	50	a2	a2	PROPN
ejpam-5430	189	51	,	,	PUNCT
ejpam-5430	189	52	ξ̃2(a2	ξ̃2(a2	NOUN
ejpam-5430	189	53	)	)	PUNCT
ejpam-5430	189	54	)	)	PUNCT
ejpam-5430	189	55	}	}	PUNCT
ejpam-5430	189	56	,	,	PUNCT
ejpam-5430	189	57	where	where	SCONJ
ejpam-5430	189	58	ξ̃1(a1	ξ̃1(a1	NOUN
ejpam-5430	189	59	)	)	PUNCT
ejpam-5430	189	60	)	)	PUNCT
ejpam-5430	190	1	=	=	PRON
ejpam-5430	190	2	{	{	PUNCT
ejpam-5430	190	3	x1	x1	PROPN
ejpam-5430	190	4	=	=	SYM
ejpam-5430	190	5	(	(	PUNCT
ejpam-5430	190	6	0.5	0.5	NUM
ejpam-5430	190	7	,	,	PUNCT
ejpam-5430	190	8	0.6	0.6	NUM
ejpam-5430	190	9	)	)	PUNCT
ejpam-5430	190	10	,	,	PUNCT
ejpam-5430	190	11	x2	x2	PROPN
ejpam-5430	190	12	=	=	PUNCT
ejpam-5430	190	13	(	(	PUNCT
ejpam-5430	190	14	0.4	0.4	NUM
ejpam-5430	190	15	,	,	PUNCT
ejpam-5430	190	16	0.7	0.7	NUM
ejpam-5430	190	17	)	)	PUNCT
ejpam-5430	190	18	,	,	PUNCT
ejpam-5430	190	19	x3	x3	NOUN
ejpam-5430	190	20	=	=	PUNCT
ejpam-5430	190	21	(	(	PUNCT
ejpam-5430	190	22	0.1	0.1	NUM
ejpam-5430	190	23	,	,	PUNCT
ejpam-5430	190	24	0.7	0.7	NUM
ejpam-5430	190	25	)	)	PUNCT
ejpam-5430	190	26	}	}	PUNCT
ejpam-5430	190	27	,	,	PUNCT
ejpam-5430	190	28	ξ̃1(a2	ξ̃1(a2	NUM
ejpam-5430	190	29	)	)	PUNCT
ejpam-5430	190	30	)	)	PUNCT
ejpam-5430	191	1	=	=	PRON
ejpam-5430	192	1	{	{	PUNCT
ejpam-5430	192	2	x1	x1	PROPN
ejpam-5430	192	3	=	=	X
ejpam-5430	192	4	(	(	PUNCT
ejpam-5430	192	5	0.3	0.3	NUM
ejpam-5430	192	6	,	,	PUNCT
ejpam-5430	192	7	0.2	0.2	NUM
ejpam-5430	192	8	)	)	PUNCT
ejpam-5430	192	9	,	,	PUNCT
ejpam-5430	192	10	x2	x2	NOUN
ejpam-5430	192	11	=	=	PRON
ejpam-5430	192	12	(	(	PUNCT
ejpam-5430	192	13	0.6	0.6	NUM
ejpam-5430	192	14	,	,	PUNCT
ejpam-5430	192	15	0.5	0.5	NUM
ejpam-5430	192	16	)	)	PUNCT
ejpam-5430	192	17	,	,	PUNCT
ejpam-5430	192	18	x3	x3	NOUN
ejpam-5430	192	19	=	=	PUNCT
ejpam-5430	192	20	(	(	PUNCT
ejpam-5430	192	21	0.2	0.2	NUM
ejpam-5430	192	22	,	,	PUNCT
ejpam-5430	192	23	0.7	0.7	NUM
ejpam-5430	192	24	)	)	PUNCT
ejpam-5430	192	25	}	}	PUNCT
ejpam-5430	192	26	,	,	PUNCT
ejpam-5430	192	27	ξ̃2(a2	ξ̃2(a2	NOUN
ejpam-5430	192	28	)	)	PUNCT
ejpam-5430	192	29	)	)	PUNCT
ejpam-5430	193	1	=	=	PRON
ejpam-5430	193	2	{	{	PUNCT
ejpam-5430	193	3	x1	x1	PROPN
ejpam-5430	193	4	=	=	X
ejpam-5430	193	5	(	(	PUNCT
ejpam-5430	193	6	0.8	0.8	NUM
ejpam-5430	193	7	,	,	PUNCT
ejpam-5430	193	8	0.4	0.4	NUM
ejpam-5430	193	9	)	)	PUNCT
ejpam-5430	193	10	,	,	PUNCT
ejpam-5430	193	11	x2	x2	PROPN
ejpam-5430	193	12	=	=	PUNCT
ejpam-5430	193	13	(	(	PUNCT
ejpam-5430	193	14	0.8	0.8	NUM
ejpam-5430	193	15	,	,	PUNCT
ejpam-5430	193	16	0.3	0.3	NUM
ejpam-5430	193	17	)	)	PUNCT
ejpam-5430	193	18	,	,	PUNCT
ejpam-5430	194	1	x3	x3	NOUN
ejpam-5430	194	2	=	=	PUNCT
ejpam-5430	194	3	(	(	PUNCT
ejpam-5430	194	4	0.4	0.4	NUM
ejpam-5430	194	5	,	,	PUNCT
ejpam-5430	194	6	0.3	0.3	NUM
ejpam-5430	194	7	)	)	PUNCT
ejpam-5430	194	8	}	}	PUNCT
ejpam-5430	194	9	ω̃1	ω̃1	NOUN
ejpam-5430	194	10	=	=	PUNCT
ejpam-5430	194	11	{	{	PUNCT
ejpam-5430	194	12	1̃	1̃	NUM
ejpam-5430	194	13	,	,	PUNCT
ejpam-5430	194	14	0̃	0̃	PROPN
ejpam-5430	194	15	,	,	PUNCT
ejpam-5430	194	16	(	(	PUNCT
ejpam-5430	194	17	ξ̃1	ξ̃1	NOUN
ejpam-5430	194	18	,	,	PUNCT
ejpam-5430	194	19	d1	d1	PROPN
ejpam-5430	194	20	)	)	PUNCT
ejpam-5430	194	21	}	}	PUNCT
ejpam-5430	194	22	and	and	CCONJ
ejpam-5430	194	23	ω̃2	ω̃2	PROPN
ejpam-5430	194	24	=	=	SYM
ejpam-5430	194	25	{	{	PUNCT
ejpam-5430	194	26	1̃	1̃	NUM
ejpam-5430	194	27	,	,	PUNCT
ejpam-5430	194	28	0̃	0̃	PROPN
ejpam-5430	194	29	,	,	PUNCT
ejpam-5430	194	30	(	(	PUNCT
ejpam-5430	194	31	ξ̃1	ξ̃1	NOUN
ejpam-5430	194	32	,	,	PUNCT
ejpam-5430	194	33	d1	d1	PROPN
ejpam-5430	194	34	)	)	PUNCT
ejpam-5430	194	35	,	,	PUNCT
ejpam-5430	194	36	(	(	PUNCT
ejpam-5430	194	37	ξ̃2	ξ̃2	PROPN
ejpam-5430	194	38	,	,	PUNCT
ejpam-5430	194	39	d2	d2	PROPN
ejpam-5430	194	40	)	)	PUNCT
ejpam-5430	194	41	}	}	PUNCT
ejpam-5430	194	42	}	}	PUNCT
ejpam-5430	194	43	are	be	AUX
ejpam-5430	194	44	two	two	NUM
ejpam-5430	194	45	pyfstss	pyfstss	NOUN
ejpam-5430	194	46	and	and	CCONJ
ejpam-5430	194	47	ω̃	ω̃	NUM
ejpam-5430	194	48	=	=	SYM
ejpam-5430	194	49	{	{	PUNCT
ejpam-5430	194	50	1̃	1̃	NUM
ejpam-5430	194	51	,	,	PUNCT
ejpam-5430	194	52	0̃	0̃	PROPN
ejpam-5430	194	53	,	,	PUNCT
ejpam-5430	194	54	(	(	PUNCT
ejpam-5430	194	55	ξ̃1	ξ̃1	NOUN
ejpam-5430	194	56	,	,	PUNCT
ejpam-5430	194	57	d1	d1	PROPN
ejpam-5430	194	58	)	)	PUNCT
ejpam-5430	194	59	,	,	PUNCT
ejpam-5430	194	60	(	(	PUNCT
ejpam-5430	194	61	ξ̃2	ξ̃2	PROPN
ejpam-5430	194	62	,	,	PUNCT
ejpam-5430	194	63	d2	d2	PROPN
ejpam-5430	194	64	)	)	PUNCT
ejpam-5430	194	65	}	}	PUNCT
ejpam-5430	194	66	is	be	AUX
ejpam-5430	194	67	a	a	DET
ejpam-5430	194	68	pyfst	pyfst	NOUN
ejpam-5430	194	69	over	over	ADP
ejpam-5430	194	70	x̃	x̃	PROPN
ejpam-5430	194	71	,	,	PUNCT
ejpam-5430	194	72	(	(	PUNCT
ejpam-5430	194	73	ξ̃1	ξ̃1	NOUN
ejpam-5430	194	74	,	,	PUNCT
ejpam-5430	194	75	d1	d1	NOUN
ejpam-5430	194	76	)	)	PUNCT
ejpam-5430	195	1	⊓	⊓	PROPN
ejpam-5430	195	2	(	(	PUNCT
ejpam-5430	195	3	ξ̃2	ξ̃2	PROPN
ejpam-5430	195	4	,	,	PUNCT
ejpam-5430	195	5	d2	d2	PROPN
ejpam-5430	195	6	)	)	PUNCT
ejpam-5430	195	7	̸=	̸=	PROPN
ejpam-5430	195	8	ϕη̃	ϕη̃	NUM
ejpam-5430	195	9	but	but	CCONJ
ejpam-5430	195	10	int((ξ̃1	int((ξ̃1	PROPN
ejpam-5430	195	11	,	,	PUNCT
ejpam-5430	195	12	d1	d1	PROPN
ejpam-5430	195	13	)	)	PUNCT
ejpam-5430	195	14	⊓	⊓	PROPN
ejpam-5430	195	15	(	(	PUNCT
ejpam-5430	195	16	̃ξ̃2	̃ξ̃2	PROPN
ejpam-5430	195	17	,	,	PUNCT
ejpam-5430	195	18	d2	d2	PROPN
ejpam-5430	195	19	)	)	PUNCT
ejpam-5430	195	20	)	)	PUNCT
ejpam-5430	196	1	=	=	PRON
ejpam-5430	196	2	ϕη̃.	ϕη̃.	NOUN
ejpam-5430	196	3	there	there	PRON
ejpam-5430	196	4	are	be	VERB
ejpam-5430	196	5	several	several	ADJ
ejpam-5430	196	6	examples	example	NOUN
ejpam-5430	196	7	when	when	SCONJ
ejpam-5430	196	8	the	the	DET
ejpam-5430	196	9	intersection	intersection	NOUN
ejpam-5430	196	10	of	of	ADP
ejpam-5430	196	11	a	a	DET
ejpam-5430	196	12	pyfssw	pyfssw	ADV
ejpam-5430	196	13	-	-	PUNCT
ejpam-5430	196	14	open	open	NOUN
ejpam-5430	196	15	set	set	NOUN
ejpam-5430	196	16	with	with	ADP
ejpam-5430	196	17	another	another	DET
ejpam-5430	196	18	pyfs	pyfs	ADJ
ejpam-5430	196	19	open	open	ADJ
ejpam-5430	196	20	,	,	PUNCT
ejpam-5430	196	21	pyfs	pyfs	NOUN
ejpam-5430	196	22	closed	closed	ADJ
ejpam-5430	196	23	,	,	PUNCT
ejpam-5430	196	24	or	or	CCONJ
ejpam-5430	196	25	pyfs	pyfs	ADJ
ejpam-5430	196	26	dense	dense	ADJ
ejpam-5430	196	27	set	set	NOUN
ejpam-5430	196	28	is	be	AUX
ejpam-5430	196	29	not	not	PART
ejpam-5430	196	30	a	a	DET
ejpam-5430	196	31	pyfssw	pyfssw	ADV
ejpam-5430	196	32	-	-	PUNCT
ejpam-5430	196	33	open	open	ADJ
ejpam-5430	196	34	set	set	NOUN
ejpam-5430	196	35	.	.	PUNCT
ejpam-5430	197	1	the	the	DET
ejpam-5430	197	2	following	follow	VERB
ejpam-5430	197	3	result	result	NOUN
ejpam-5430	197	4	shows	show	VERB
ejpam-5430	197	5	when	when	SCONJ
ejpam-5430	197	6	the	the	DET
ejpam-5430	197	7	intersection	intersection	NOUN
ejpam-5430	197	8	of	of	ADP
ejpam-5430	197	9	pyfssw	pyfssw	ADV
ejpam-5430	197	10	-	-	PUNCT
ejpam-5430	197	11	open	open	ADJ
ejpam-5430	197	12	and	and	CCONJ
ejpam-5430	197	13	pyfs	pyfs	ADJ
ejpam-5430	197	14	open	open	ADJ
ejpam-5430	197	15	sets	set	NOUN
ejpam-5430	197	16	is	be	AUX
ejpam-5430	197	17	a	a	DET
ejpam-5430	197	18	pyfssw	pyfssw	ADV
ejpam-5430	197	19	-	-	PUNCT
ejpam-5430	197	20	open	open	ADJ
ejpam-5430	197	21	set	set	NOUN
ejpam-5430	197	22	.	.	PUNCT
ejpam-5430	198	1	definition	definition	NOUN
ejpam-5430	198	2	22	22	NUM
ejpam-5430	198	3	.	.	PUNCT
ejpam-5430	199	1	a	a	DET
ejpam-5430	199	2	pyfsts	pyfst	NOUN
ejpam-5430	199	3	(	(	PUNCT
ejpam-5430	199	4	x̃	x̃	PROPN
ejpam-5430	199	5	,	,	PUNCT
ejpam-5430	199	6	ω̃	ω̃	PROPN
ejpam-5430	199	7	,	,	PUNCT
ejpam-5430	199	8	η̃	η̃	PROPN
ejpam-5430	199	9	)	)	PUNCT
ejpam-5430	199	10	is	be	AUX
ejpam-5430	199	11	named	name	VERB
ejpam-5430	199	12	i	i	PRON
ejpam-5430	199	13	)	)	PUNCT
ejpam-5430	199	14	pyfs	pyfs	ADJ
ejpam-5430	199	15	separable	separable	NOUN
ejpam-5430	199	16	if	if	SCONJ
ejpam-5430	199	17	it	it	PRON
ejpam-5430	199	18	has	have	VERB
ejpam-5430	199	19	a	a	DET
ejpam-5430	199	20	countable	countable	ADJ
ejpam-5430	199	21	pyfs	pyfs	ADJ
ejpam-5430	199	22	dense	dense	ADJ
ejpam-5430	199	23	subset	subset	NOUN
ejpam-5430	199	24	.	.	PUNCT
ejpam-5430	200	1	ii	ii	PROPN
ejpam-5430	200	2	)	)	PUNCT
ejpam-5430	200	3	pyfs	pyfs	NOUN
ejpam-5430	200	4	hyperconnected	hyperconnecte	VERB
ejpam-5430	200	5	if	if	SCONJ
ejpam-5430	200	6	any	any	DET
ejpam-5430	200	7	pair	pair	NOUN
ejpam-5430	200	8	of	of	ADP
ejpam-5430	200	9	non	non	ADJ
ejpam-5430	200	10	-	-	ADJ
ejpam-5430	200	11	null	null	ADJ
ejpam-5430	200	12	pyfs	pyfs	ADJ
ejpam-5430	200	13	open	open	ADJ
ejpam-5430	200	14	subsets	subset	NOUN
ejpam-5430	200	15	intersect	intersect	ADJ
ejpam-5430	200	16	.	.	PUNCT
ejpam-5430	201	1	proposition	proposition	NOUN
ejpam-5430	201	2	4	4	NUM
ejpam-5430	201	3	.	.	PUNCT
ejpam-5430	201	4	in	in	ADP
ejpam-5430	201	5	a	a	DET
ejpam-5430	201	6	pyfs	pyfs	ADJ
ejpam-5430	201	7	hyperconnected	hyperconnecte	VERB
ejpam-5430	201	8	space	space	NOUN
ejpam-5430	201	9	(	(	PUNCT
ejpam-5430	201	10	x̃	x̃	PROPN
ejpam-5430	201	11	,	,	PUNCT
ejpam-5430	201	12	ω̃	ω̃	PROPN
ejpam-5430	201	13	,	,	PUNCT
ejpam-5430	201	14	η̃	η̃	PROPN
ejpam-5430	201	15	)	)	PUNCT
ejpam-5430	201	16	,	,	PUNCT
ejpam-5430	201	17	a	a	DET
ejpam-5430	201	18	pyfssw	pyfssw	ADV
ejpam-5430	201	19	-	-	PUNCT
ejpam-5430	201	20	open	open	ADJ
ejpam-5430	201	21	set	set	NOUN
ejpam-5430	201	22	is	be	AUX
ejpam-5430	201	23	the	the	DET
ejpam-5430	201	24	intersection	intersection	NOUN
ejpam-5430	201	25	of	of	ADP
ejpam-5430	201	26	two	two	NUM
ejpam-5430	201	27	pyfssw	pyfssw	ADV
ejpam-5430	201	28	-	-	PUNCT
ejpam-5430	201	29	open	open	ADJ
ejpam-5430	201	30	sets	set	NOUN
ejpam-5430	201	31	.	.	PUNCT
ejpam-5430	202	1	proof	proof	NOUN
ejpam-5430	202	2	.	.	PUNCT
ejpam-5430	203	1	the	the	DET
ejpam-5430	203	2	evidence	evidence	NOUN
ejpam-5430	203	3	is	be	AUX
ejpam-5430	203	4	easy	easy	ADJ
ejpam-5430	203	5	to	to	PART
ejpam-5430	203	6	understand	understand	VERB
ejpam-5430	203	7	if	if	SCONJ
ejpam-5430	203	8	one	one	NUM
ejpam-5430	203	9	of	of	ADP
ejpam-5430	203	10	the	the	DET
ejpam-5430	203	11	two	two	NUM
ejpam-5430	203	12	pyfssw	pyfssw	ADV
ejpam-5430	203	13	-	-	PUNCT
ejpam-5430	203	14	open	open	ADJ
ejpam-5430	203	15	sets	set	NOUN
ejpam-5430	203	16	is	be	AUX
ejpam-5430	203	17	null	null	ADJ
ejpam-5430	203	18	.	.	PUNCT
ejpam-5430	204	1	assume	assume	VERB
ejpam-5430	204	2	that	that	SCONJ
ejpam-5430	204	3	there	there	PRON
ejpam-5430	204	4	are	be	VERB
ejpam-5430	204	5	two	two	NUM
ejpam-5430	204	6	pyfssw	pyfssw	ADV
ejpam-5430	204	7	-	-	PUNCT
ejpam-5430	204	8	open	open	ADJ
ejpam-5430	204	9	sets	set	NOUN
ejpam-5430	204	10	,	,	PUNCT
ejpam-5430	204	11	gη̃	gη̃	PROPN
ejpam-5430	204	12	and	and	CCONJ
ejpam-5430	204	13	hη̃.	hη̃.	PROPN
ejpam-5430	204	14	next	next	ADJ
ejpam-5430	204	15	,	,	PUNCT
ejpam-5430	204	16	int(gη̃	int(gη̃	NOUN
ejpam-5430	204	17	)	)	PUNCT
ejpam-5430	204	18	=	=	PUNCT
ejpam-5430	205	1	uη̃	uη̃	PROPN
ejpam-5430	205	2	̸=	̸=	PROPN
ejpam-5430	205	3	ϕη̃	ϕη̃	X
ejpam-5430	205	4	and	and	CCONJ
ejpam-5430	205	5	int(hη̃	int(hη̃	NOUN
ejpam-5430	205	6	)	)	PUNCT
ejpam-5430	205	7	=	=	PRON
ejpam-5430	206	1	vη̃	vη̃	ADV
ejpam-5430	206	2	̸=	̸=	PROPN
ejpam-5430	206	3	ϕη̃	ϕη̃	NUM
ejpam-5430	206	4	are	be	AUX
ejpam-5430	206	5	obtained	obtain	VERB
ejpam-5430	206	6	.	.	PUNCT
ejpam-5430	207	1	now	now	ADV
ejpam-5430	207	2	,	,	PUNCT
ejpam-5430	207	3	int(gη̃	int(gη̃	PROPN
ejpam-5430	207	4	⊓	⊓	PROPN
ejpam-5430	207	5	hη̃	hη̃	NOUN
ejpam-5430	207	6	)	)	PUNCT
ejpam-5430	207	7	=	=	SYM
ejpam-5430	207	8	int(gη̃	int(gη̃	NOUN
ejpam-5430	207	9	)	)	PUNCT
ejpam-5430	207	10	⊓	⊓	PROPN
ejpam-5430	207	11	int(hη̃	int(hη̃	NOUN
ejpam-5430	207	12	)	)	PUNCT
ejpam-5430	207	13	=	=	SYM
ejpam-5430	208	1	uη̃	uη̃	NUM
ejpam-5430	208	2	⊓	⊓	NOUN
ejpam-5430	208	3	vη̃.	vη̃.	X
ejpam-5430	208	4	then	then	ADV
ejpam-5430	208	5	,	,	PUNCT
ejpam-5430	208	6	uη̃	uη̃	NUM
ejpam-5430	208	7	⊓vη̃	⊓vη̃	ADV
ejpam-5430	208	8	̸=	̸=	PROPN
ejpam-5430	208	9	ϕη̃	ϕη̃	PUNCT
ejpam-5430	208	10	since	since	SCONJ
ejpam-5430	208	11	(	(	PUNCT
ejpam-5430	208	12	x̃	x̃	PROPN
ejpam-5430	208	13	,	,	PUNCT
ejpam-5430	208	14	ω̃	ω̃	PROPN
ejpam-5430	208	15	,	,	PUNCT
ejpam-5430	208	16	η̃	η̃	PROPN
ejpam-5430	208	17	)	)	PUNCT
ejpam-5430	208	18	is	be	AUX
ejpam-5430	208	19	a	a	DET
ejpam-5430	208	20	pyfs	pyfs	NOUN
ejpam-5430	208	21	hyperconnected	hyperconnecte	VERB
ejpam-5430	208	22	.	.	PUNCT
ejpam-5430	209	1	hence	hence	ADV
ejpam-5430	209	2	,	,	PUNCT
ejpam-5430	209	3	int(gη̃	int(gη̃	PROPN
ejpam-5430	209	4	⊓hη̃	⊓hη̃	NOUN
ejpam-5430	209	5	)	)	PUNCT
ejpam-5430	209	6	̸=	̸=	PROPN
ejpam-5430	209	7	ϕη̃	ϕη̃	NUM
ejpam-5430	209	8	,	,	PUNCT
ejpam-5430	209	9	and	and	CCONJ
ejpam-5430	209	10	we	we	PRON
ejpam-5430	209	11	achieve	achieve	VERB
ejpam-5430	209	12	the	the	DET
ejpam-5430	209	13	intended	intended	ADJ
ejpam-5430	209	14	outcome	outcome	NOUN
ejpam-5430	209	15	.	.	PUNCT
ejpam-5430	210	1	corollary	corollary	ADJ
ejpam-5430	210	2	2	2	NUM
ejpam-5430	210	3	.	.	PUNCT
ejpam-5430	211	1	in	in	ADP
ejpam-5430	211	2	a	a	DET
ejpam-5430	211	3	pyfs	pyfs	ADJ
ejpam-5430	211	4	hyperconnected	hyperconnecte	VERB
ejpam-5430	211	5	space	space	NOUN
ejpam-5430	211	6	(	(	PUNCT
ejpam-5430	211	7	x̃	x̃	PROPN
ejpam-5430	211	8	,	,	PUNCT
ejpam-5430	211	9	ω̃	ω̃	PROPN
ejpam-5430	211	10	,	,	PUNCT
ejpam-5430	211	11	η̃	η̃	PROPN
ejpam-5430	211	12	)	)	PUNCT
ejpam-5430	211	13	,	,	PUNCT
ejpam-5430	211	14	the	the	DET
ejpam-5430	211	15	intersection	intersection	NOUN
ejpam-5430	211	16	of	of	ADP
ejpam-5430	211	17	pyfsswopen	pyfsswopen	NOUN
ejpam-5430	211	18	and	and	CCONJ
ejpam-5430	211	19	pyfs	pyfs	ADJ
ejpam-5430	211	20	open	open	ADJ
ejpam-5430	211	21	sets	set	NOUN
ejpam-5430	211	22	is	be	AUX
ejpam-5430	211	23	a	a	DET
ejpam-5430	211	24	pyfssw	pyfssw	ADV
ejpam-5430	211	25	-	-	PUNCT
ejpam-5430	211	26	open	open	ADJ
ejpam-5430	211	27	.	.	PUNCT
ejpam-5430	212	1	corollary	corollary	ADJ
ejpam-5430	212	2	3	3	NUM
ejpam-5430	212	3	.	.	PUNCT
ejpam-5430	213	1	a	a	DET
ejpam-5430	213	2	pyfs	pyfs	ADJ
ejpam-5430	213	3	topology	topology	NOUN
ejpam-5430	213	4	is	be	AUX
ejpam-5430	213	5	formed	form	VERB
ejpam-5430	213	6	by	by	ADP
ejpam-5430	213	7	the	the	DET
ejpam-5430	213	8	family	family	NOUN
ejpam-5430	213	9	of	of	ADP
ejpam-5430	213	10	pyfssw	pyfssw	ADV
ejpam-5430	213	11	-	-	PUNCT
ejpam-5430	213	12	open	open	ADJ
ejpam-5430	213	13	subsets	subset	NOUN
ejpam-5430	213	14	of	of	ADP
ejpam-5430	213	15	a	a	DET
ejpam-5430	213	16	pyfs	pyfs	ADJ
ejpam-5430	213	17	hyperconnected	hyperconnecte	VERB
ejpam-5430	213	18	space	space	NOUN
ejpam-5430	213	19	(	(	PUNCT
ejpam-5430	213	20	x̃	x̃	PROPN
ejpam-5430	213	21	,	,	PUNCT
ejpam-5430	213	22	ω̃	ω̃	PROPN
ejpam-5430	213	23	,	,	PUNCT
ejpam-5430	213	24	η̃	η̃	PROPN
ejpam-5430	213	25	)	)	PUNCT
ejpam-5430	213	26	.	.	PUNCT
ejpam-5430	214	1	lemma	lemma	PROPN
ejpam-5430	214	2	1	1	X
ejpam-5430	214	3	.	.	PUNCT
ejpam-5430	214	4	suppose	suppose	VERB
ejpam-5430	214	5	gη̃	gη̃	PROPN
ejpam-5430	214	6	and	and	CCONJ
ejpam-5430	214	7	hη̃	hη̃	PROPN
ejpam-5430	214	8	are	be	AUX
ejpam-5430	214	9	subsets	subset	NOUN
ejpam-5430	214	10	of	of	ADP
ejpam-5430	214	11	(	(	PUNCT
ejpam-5430	214	12	x̃	x̃	PROPN
ejpam-5430	214	13	,	,	PUNCT
ejpam-5430	214	14	ω̃	ω̃	PROPN
ejpam-5430	214	15	,	,	PUNCT
ejpam-5430	214	16	η̃	η̃	PROPN
ejpam-5430	214	17	)	)	PUNCT
ejpam-5430	214	18	.	.	PUNCT
ejpam-5430	215	1	if	if	SCONJ
ejpam-5430	215	2	gη̃	gη̃	PROPN
ejpam-5430	215	3	is	be	AUX
ejpam-5430	215	4	sw	sw	NOUN
ejpam-5430	215	5	-	-	PUNCT
ejpam-5430	215	6	open	open	ADJ
ejpam-5430	215	7	and	and	CCONJ
ejpam-5430	215	8	hη̃	hη̃	PRON
ejpam-5430	215	9	is	be	AUX
ejpam-5430	215	10	a	a	DET
ejpam-5430	215	11	pyfs	pyfs	ADJ
ejpam-5430	215	12	dense	dense	ADJ
ejpam-5430	215	13	over	over	ADP
ejpam-5430	215	14	x̃	x̃	PROPN
ejpam-5430	215	15	,	,	PUNCT
ejpam-5430	215	16	then	then	ADV
ejpam-5430	215	17	gη̃	gη̃	PROPN
ejpam-5430	215	18	⊓hη̃	⊓hη̃	PROPN
ejpam-5430	215	19	is	be	AUX
ejpam-5430	215	20	pyfssw	pyfssw	ADV
ejpam-5430	215	21	-	-	PUNCT
ejpam-5430	215	22	open	open	ADJ
ejpam-5430	215	23	over	over	ADP
ejpam-5430	215	24	x̃.	x̃.	ADJ
ejpam-5430	215	25	proof	proof	NOUN
ejpam-5430	215	26	.	.	PUNCT
ejpam-5430	216	1	since	since	SCONJ
ejpam-5430	216	2	inth(gη̃	inth(gη̃	PROPN
ejpam-5430	216	3	⊓	⊓	PROPN
ejpam-5430	216	4	hη̃	hη̃	NOUN
ejpam-5430	216	5	)	)	PUNCT
ejpam-5430	216	6	=	=	SYM
ejpam-5430	216	7	inth(gη̃	inth(gη̃	NOUN
ejpam-5430	216	8	)	)	PUNCT
ejpam-5430	216	9	⊓	⊓	PROPN
ejpam-5430	216	10	hη̃	hη̃	NUM
ejpam-5430	216	11	⊒	⊒	SYM
ejpam-5430	216	12	int(gη̃	int(gη̃	NOUN
ejpam-5430	216	13	)	)	PUNCT
ejpam-5430	216	14	⊓	⊓	PROPN
ejpam-5430	216	15	hη̃	hη̃	PROPN
ejpam-5430	216	16	̸=	̸=	PROPN
ejpam-5430	216	17	ϕη̃	ϕη̃	NUM
ejpam-5430	216	18	,	,	PUNCT
ejpam-5430	216	19	hence	hence	ADV
ejpam-5430	216	20	gη̃	gη̃	PUNCT
ejpam-5430	216	21	⊓	⊓	NOUN
ejpam-5430	216	22	hη̃	hη̃	INTJ
ejpam-5430	216	23	is	be	AUX
ejpam-5430	216	24	pyfssw	pyfssw	ADV
ejpam-5430	216	25	-	-	PUNCT
ejpam-5430	216	26	open	open	ADJ
ejpam-5430	216	27	over	over	ADP
ejpam-5430	216	28	x̃.	x̃.	ADJ
ejpam-5430	216	29	lemma	lemma	PROPN
ejpam-5430	216	30	2	2	X
ejpam-5430	216	31	.	.	X
ejpam-5430	216	32	assume	assume	VERB
ejpam-5430	216	33	that	that	SCONJ
ejpam-5430	216	34	gη̃	gη̃	PROPN
ejpam-5430	216	35	⊑	⊑	DET
ejpam-5430	216	36	yη̃	yη̃	NOUN
ejpam-5430	217	1	and	and	CCONJ
ejpam-5430	217	2	that	that	SCONJ
ejpam-5430	217	3	(	(	PUNCT
ejpam-5430	217	4	ỹ	ỹ	PROPN
ejpam-5430	217	5	,	,	PUNCT
ejpam-5430	217	6	ω̃y	ω̃y	NOUN
ejpam-5430	217	7	,	,	PUNCT
ejpam-5430	217	8	η̃	η̃	PROPN
ejpam-5430	217	9	)	)	PUNCT
ejpam-5430	217	10	is	be	AUX
ejpam-5430	217	11	a	a	DET
ejpam-5430	217	12	pyfs	pyfs	ADJ
ejpam-5430	217	13	open	open	ADJ
ejpam-5430	217	14	subspace	subspace	NOUN
ejpam-5430	217	15	of	of	ADP
ejpam-5430	217	16	(	(	PUNCT
ejpam-5430	217	17	x̃	x̃	PROPN
ejpam-5430	217	18	,	,	PUNCT
ejpam-5430	217	19	ω̃	ω̃	PROPN
ejpam-5430	217	20	,	,	PUNCT
ejpam-5430	217	21	η̃	η̃	PROPN
ejpam-5430	217	22	)	)	PUNCT
ejpam-5430	217	23	.	.	PUNCT
ejpam-5430	218	1	if	if	SCONJ
ejpam-5430	218	2	and	and	CCONJ
ejpam-5430	218	3	only	only	ADV
ejpam-5430	218	4	if	if	SCONJ
ejpam-5430	218	5	gη̃	gη̃	PROPN
ejpam-5430	218	6	is	be	AUX
ejpam-5430	218	7	pyfssw	pyfssw	ADV
ejpam-5430	218	8	-	-	PUNCT
ejpam-5430	218	9	open	open	ADJ
ejpam-5430	218	10	over	over	ADP
ejpam-5430	218	11	x̃	x̃	PROPN
ejpam-5430	218	12	,	,	PUNCT
ejpam-5430	218	13	then	then	ADV
ejpam-5430	218	14	it	it	PRON
ejpam-5430	218	15	is	be	AUX
ejpam-5430	218	16	also	also	ADV
ejpam-5430	218	17	pyfssw	pyfssw	ADV
ejpam-5430	218	18	-	-	PUNCT
ejpam-5430	218	19	open	open	ADJ
ejpam-5430	218	20	over	over	ADP
ejpam-5430	218	21	ỹ	ỹ	PROPN
ejpam-5430	218	22	.	.	PUNCT
ejpam-5430	219	1	a.	a.	PROPN
ejpam-5430	219	2	a.	a.	PROPN
ejpam-5430	219	3	azzam	azzam	PROPN
ejpam-5430	219	4	,	,	PUNCT
ejpam-5430	219	5	m.	m.	NOUN
ejpam-5430	219	6	aldawood	aldawood	PROPN
ejpam-5430	219	7	,	,	PUNCT
ejpam-5430	219	8	r.	r.	PROPN
ejpam-5430	219	9	abu	abu	PROPN
ejpam-5430	219	10	-	-	PUNCT
ejpam-5430	219	11	gdairi	gdairi	PROPN
ejpam-5430	219	12	/	/	SYM
ejpam-5430	219	13	eur	eur	PROPN
ejpam-5430	219	14	.	.	PUNCT
ejpam-5430	220	1	j.	j.	PROPN
ejpam-5430	220	2	pure	pure	PROPN
ejpam-5430	220	3	appl	appl	PROPN
ejpam-5430	220	4	.	.	PROPN
ejpam-5430	220	5	math	math	PROPN
ejpam-5430	220	6	,	,	PUNCT
ejpam-5430	220	7	17	17	NUM
ejpam-5430	220	8	(	(	PUNCT
ejpam-5430	220	9	4	4	NUM
ejpam-5430	220	10	)	)	PUNCT
ejpam-5430	220	11	(	(	PUNCT
ejpam-5430	220	12	2024	2024	NUM
ejpam-5430	220	13	)	)	PUNCT
ejpam-5430	220	14	,	,	PUNCT
ejpam-5430	220	15	4147	4147	NUM
ejpam-5430	220	16	-	-	SYM
ejpam-5430	220	17	4163	4163	NUM
ejpam-5430	220	18	4154	4154	NUM
ejpam-5430	220	19	proof	proof	NOUN
ejpam-5430	220	20	.	.	PUNCT
ejpam-5430	221	1	let	let	VERB
ejpam-5430	221	2	’s	’s	PRON
ejpam-5430	221	3	say	say	VERB
ejpam-5430	221	4	that	that	SCONJ
ejpam-5430	221	5	gη̃	gη̃	PROPN
ejpam-5430	221	6	is	be	AUX
ejpam-5430	221	7	pyfssw	pyfssw	ADV
ejpam-5430	221	8	-	-	PUNCT
ejpam-5430	221	9	open	open	ADJ
ejpam-5430	221	10	over	over	ADP
ejpam-5430	221	11	ỹ	ỹ	PROPN
ejpam-5430	221	12	.	.	PUNCT
ejpam-5430	222	1	it	it	PRON
ejpam-5430	222	2	is	be	AUX
ejpam-5430	222	3	possible	possible	ADJ
ejpam-5430	222	4	to	to	PART
ejpam-5430	222	5	have	have	VERB
ejpam-5430	222	6	a	a	DET
ejpam-5430	222	7	pyfs	pyfs	ADJ
ejpam-5430	222	8	open	open	NOUN
ejpam-5430	222	9	set	set	VERB
ejpam-5430	222	10	uη̃	uη̃	INTJ
ejpam-5430	222	11	over	over	ADP
ejpam-5430	222	12	ỹ	ỹ	NUM
ejpam-5430	222	13	such	such	ADJ
ejpam-5430	222	14	that	that	SCONJ
ejpam-5430	222	15	ϕη̃	ϕη̃	NUM
ejpam-5430	222	16	̸=	̸=	PROPN
ejpam-5430	222	17	uη̃	uη̃	NUM
ejpam-5430	222	18	⊑	⊑	PRON
ejpam-5430	222	19	gη̃.	gη̃.	NOUN
ejpam-5430	222	20	because	because	SCONJ
ejpam-5430	222	21	yη̃	yη̃	NOUN
ejpam-5430	222	22	is	be	AUX
ejpam-5430	222	23	pyfs	pyfs	ADJ
ejpam-5430	222	24	open	open	ADJ
ejpam-5430	222	25	over	over	ADP
ejpam-5430	222	26	x̃	x̃	PROPN
ejpam-5430	222	27	,	,	PUNCT
ejpam-5430	222	28	uη̃	uη̃	PRON
ejpam-5430	222	29	is	be	AUX
ejpam-5430	222	30	also	also	ADV
ejpam-5430	222	31	pyfs	pyfs	ADJ
ejpam-5430	222	32	open	open	ADJ
ejpam-5430	222	33	over	over	ADP
ejpam-5430	222	34	x̃.	x̃.	ADJ
ejpam-5430	222	35	as	as	ADP
ejpam-5430	222	36	a	a	DET
ejpam-5430	222	37	result	result	NOUN
ejpam-5430	222	38	,	,	PUNCT
ejpam-5430	222	39	gη̃	gη̃	PROPN
ejpam-5430	222	40	is	be	AUX
ejpam-5430	222	41	pyfssw	pyfssw	ADV
ejpam-5430	222	42	-	-	PUNCT
ejpam-5430	222	43	open	open	ADJ
ejpam-5430	222	44	over	over	ADP
ejpam-5430	222	45	x̃.	x̃.	ADJ
ejpam-5430	222	46	in	in	ADP
ejpam-5430	222	47	contrast	contrast	NOUN
ejpam-5430	222	48	,	,	PUNCT
ejpam-5430	222	49	let	let	VERB
ejpam-5430	222	50	’s	’s	PRON
ejpam-5430	222	51	say	say	VERB
ejpam-5430	222	52	that	that	SCONJ
ejpam-5430	222	53	gη̃	gη̃	PROPN
ejpam-5430	222	54	is	be	AUX
ejpam-5430	222	55	pyfssw	pyfssw	ADV
ejpam-5430	222	56	-	-	PUNCT
ejpam-5430	222	57	open	open	ADJ
ejpam-5430	222	58	over	over	ADP
ejpam-5430	222	59	x̃.	x̃.	ADJ
ejpam-5430	222	60	this	this	PRON
ejpam-5430	222	61	is	be	AUX
ejpam-5430	222	62	equivalent	equivalent	ADJ
ejpam-5430	222	63	to	to	ADP
ejpam-5430	222	64	intx̃(gη̃	intx̃(gη̃	PROPN
ejpam-5430	222	65	)	)	PUNCT
ejpam-5430	222	66	̸=	̸=	PROPN
ejpam-5430	222	67	ϕη̃.	ϕη̃.	VERB
ejpam-5430	222	68	according	accord	VERB
ejpam-5430	222	69	to	to	ADP
ejpam-5430	222	70	theorem	theorem	NOUN
ejpam-5430	222	71	2	2	NUM
ejpam-5430	222	72	in	in	ADP
ejpam-5430	222	73	[	[	X
ejpam-5430	222	74	19	19	NUM
ejpam-5430	222	75	]	]	PUNCT
ejpam-5430	222	76	,	,	PUNCT
ejpam-5430	222	77	and	and	CCONJ
ejpam-5430	222	78	remark	remark	NOUN
ejpam-5430	222	79	3.2	3.2	NUM
ejpam-5430	222	80	,	,	PUNCT
ejpam-5430	222	81	intx̃(gη̃	intx̃(gη̃	PROPN
ejpam-5430	222	82	)	)	PUNCT
ejpam-5430	222	83	⊑	⊑	PROPN
ejpam-5430	222	84	intỹ	intỹ	PROPN
ejpam-5430	222	85	(	(	PUNCT
ejpam-5430	222	86	gη̃	gη̃	NOUN
ejpam-5430	222	87	)	)	PUNCT
ejpam-5430	222	88	,	,	PUNCT
ejpam-5430	222	89	hence	hence	ADV
ejpam-5430	222	90	gη̃	gη̃	PROPN
ejpam-5430	222	91	is	be	AUX
ejpam-5430	222	92	pyfssw	pyfssw	ADV
ejpam-5430	222	93	-	-	PUNCT
ejpam-5430	222	94	open	open	ADJ
ejpam-5430	222	95	over	over	ADP
ejpam-5430	222	96	ỹ	ỹ	PROPN
ejpam-5430	222	97	.	.	PUNCT
ejpam-5430	223	1	if	if	SCONJ
ejpam-5430	223	2	yη̃	yη̃	NOUN
ejpam-5430	223	3	is	be	AUX
ejpam-5430	223	4	pyfs	pyf	VERB
ejpam-5430	223	5	dense	dense	ADJ
ejpam-5430	223	6	in	in	ADP
ejpam-5430	223	7	x̃	x̃	PROPN
ejpam-5430	223	8	,	,	PUNCT
ejpam-5430	223	9	as	as	SCONJ
ejpam-5430	223	10	the	the	DET
ejpam-5430	223	11	following	following	ADJ
ejpam-5430	223	12	example	example	NOUN
ejpam-5430	223	13	demonstrates	demonstrate	VERB
ejpam-5430	223	14	,	,	PUNCT
ejpam-5430	223	15	then	then	ADV
ejpam-5430	223	16	the	the	DET
ejpam-5430	223	17	previous	previous	ADJ
ejpam-5430	223	18	result	result	NOUN
ejpam-5430	223	19	is	be	AUX
ejpam-5430	223	20	not	not	PART
ejpam-5430	223	21	valid	valid	ADJ
ejpam-5430	223	22	.	.	PUNCT
ejpam-5430	223	23	example	example	NOUN
ejpam-5430	224	1	2	2	NUM
ejpam-5430	224	2	.	.	PUNCT
ejpam-5430	224	3	suppose	suppose	VERB
ejpam-5430	224	4	x̃	x̃	PROPN
ejpam-5430	224	5	=	=	PRON
ejpam-5430	224	6	{	{	PUNCT
ejpam-5430	224	7	x1	x1	PROPN
ejpam-5430	224	8	,	,	PUNCT
ejpam-5430	224	9	x2	x2	PROPN
ejpam-5430	224	10	,	,	PUNCT
ejpam-5430	224	11	x3	x3	ADJ
ejpam-5430	224	12	,	,	PUNCT
ejpam-5430	224	13	x4	x4	PROPN
ejpam-5430	224	14	}	}	PUNCT
ejpam-5430	224	15	,	,	PUNCT
ejpam-5430	224	16	η	η	PROPN
ejpam-5430	224	17	=	=	SYM
ejpam-5430	224	18	{	{	PUNCT
ejpam-5430	224	19	a1	a1	PROPN
ejpam-5430	224	20	,	,	PUNCT
ejpam-5430	224	21	a2	a2	PROPN
ejpam-5430	224	22	}	}	PUNCT
ejpam-5430	224	23	,	,	PUNCT
ejpam-5430	224	24	and	and	CCONJ
ejpam-5430	224	25	ω̃	ω̃	NUM
ejpam-5430	224	26	=	=	SYM
ejpam-5430	224	27	{	{	PUNCT
ejpam-5430	224	28	0̃	0̃	NOUN
ejpam-5430	224	29	,	,	PUNCT
ejpam-5430	224	30	fη̃	fη̃	PRON
ejpam-5430	224	31	,	,	PUNCT
ejpam-5430	224	32	gη̃	gη̃	PROPN
ejpam-5430	224	33	,	,	PUNCT
ejpam-5430	224	34	hη̃	hη̃	NOUN
ejpam-5430	224	35	,	,	PUNCT
ejpam-5430	224	36	1̃	1̃	NUM
ejpam-5430	224	37	}	}	PUNCT
ejpam-5430	224	38	,	,	PUNCT
ejpam-5430	224	39	where	where	SCONJ
ejpam-5430	224	40	fη̃	fη̃	NOUN
ejpam-5430	224	41	=	=	SYM
ejpam-5430	224	42	{	{	PUNCT
ejpam-5430	224	43	(	(	PUNCT
ejpam-5430	224	44	a1	a1	NOUN
ejpam-5430	224	45	,	,	PUNCT
ejpam-5430	224	46	{	{	PUNCT
ejpam-5430	224	47	x2	x2	PROPN
ejpam-5430	224	48	,	,	PUNCT
ejpam-5430	224	49	x4	x4	PROPN
ejpam-5430	224	50	}	}	PUNCT
ejpam-5430	224	51	)	)	PUNCT
ejpam-5430	224	52	,	,	PUNCT
ejpam-5430	224	53	(	(	PUNCT
ejpam-5430	224	54	a2	a2	PROPN
ejpam-5430	224	55	,	,	PUNCT
ejpam-5430	224	56	{	{	PUNCT
ejpam-5430	224	57	x1	x1	PROPN
ejpam-5430	224	58	,	,	PUNCT
ejpam-5430	224	59	x2	x2	PROPN
ejpam-5430	224	60	}	}	PUNCT
ejpam-5430	224	61	)	)	PUNCT
ejpam-5430	224	62	}	}	PUNCT
ejpam-5430	224	63	gη̃	gη̃	X
ejpam-5430	224	64	=	=	SYM
ejpam-5430	224	65	{	{	PUNCT
ejpam-5430	224	66	(	(	PUNCT
ejpam-5430	224	67	a1	a1	PROPN
ejpam-5430	224	68	,	,	PUNCT
ejpam-5430	224	69	x̃	x̃	PROPN
ejpam-5430	224	70	)	)	PUNCT
ejpam-5430	224	71	,	,	PUNCT
ejpam-5430	224	72	(	(	PUNCT
ejpam-5430	224	73	a2	a2	PROPN
ejpam-5430	224	74	,	,	PUNCT
ejpam-5430	224	75	{	{	PUNCT
ejpam-5430	224	76	x3	x3	ADJ
ejpam-5430	224	77	,	,	PUNCT
ejpam-5430	224	78	x4	x4	PROPN
ejpam-5430	224	79	}	}	PUNCT
ejpam-5430	224	80	)	)	PUNCT
ejpam-5430	224	81	}	}	PUNCT
ejpam-5430	224	82	hη̃	hη̃	PROPN
ejpam-5430	224	83	=	=	SYM
ejpam-5430	224	84	{	{	PUNCT
ejpam-5430	224	85	(	(	PUNCT
ejpam-5430	224	86	a1	a1	NOUN
ejpam-5430	224	87	,	,	PUNCT
ejpam-5430	224	88	{	{	PUNCT
ejpam-5430	224	89	x2	x2	PROPN
ejpam-5430	224	90	,	,	PUNCT
ejpam-5430	224	91	x4	x4	PROPN
ejpam-5430	224	92	}	}	PUNCT
ejpam-5430	224	93	)	)	PUNCT
ejpam-5430	224	94	,	,	PUNCT
ejpam-5430	224	95	(	(	PUNCT
ejpam-5430	224	96	a2	a2	PROPN
ejpam-5430	224	97	,	,	PUNCT
ejpam-5430	224	98	ϕη̃	ϕη̃	NUM
ejpam-5430	224	99	)	)	PUNCT
ejpam-5430	224	100	}	}	PUNCT
ejpam-5430	224	101	let	let	VERB
ejpam-5430	224	102	ỹ	ỹ	PROPN
ejpam-5430	224	103	=	=	SYM
ejpam-5430	224	104	{	{	PUNCT
ejpam-5430	224	105	x2	x2	PROPN
ejpam-5430	224	106	,	,	PUNCT
ejpam-5430	224	107	x3	x3	ADJ
ejpam-5430	224	108	}	}	PUNCT
ejpam-5430	224	109	at	at	ADP
ejpam-5430	224	110	hence	hence	ADV
ejpam-5430	224	111	,	,	PUNCT
ejpam-5430	224	112	ω̃y	ω̃y	NOUN
ejpam-5430	224	113	=	=	SYM
ejpam-5430	224	114	{	{	PUNCT
ejpam-5430	224	115	0̃	0̃	PROPN
ejpam-5430	224	116	,	,	PUNCT
ejpam-5430	224	117	iη̃	iη̃	NUM
ejpam-5430	224	118	,	,	PUNCT
ejpam-5430	224	119	jη̃,kη̃	jη̃,kη̃	PROPN
ejpam-5430	224	120	,	,	PUNCT
ejpam-5430	224	121	1̃	1̃	NUM
ejpam-5430	224	122	}	}	PUNCT
ejpam-5430	224	123	,	,	PUNCT
ejpam-5430	224	124	where	where	SCONJ
ejpam-5430	224	125	iη̃	iη̃	ADV
ejpam-5430	224	126	=	=	SYM
ejpam-5430	224	127	{	{	PUNCT
ejpam-5430	224	128	(	(	PUNCT
ejpam-5430	224	129	a1	a1	NOUN
ejpam-5430	224	130	,	,	PUNCT
ejpam-5430	224	131	{	{	PUNCT
ejpam-5430	224	132	x2	x2	ADJ
ejpam-5430	224	133	}	}	PUNCT
ejpam-5430	224	134	)	)	PUNCT
ejpam-5430	224	135	,	,	PUNCT
ejpam-5430	224	136	(	(	PUNCT
ejpam-5430	224	137	a2	a2	PROPN
ejpam-5430	224	138	,	,	PUNCT
ejpam-5430	224	139	{	{	PUNCT
ejpam-5430	224	140	x2	x2	ADJ
ejpam-5430	224	141	}	}	PUNCT
ejpam-5430	224	142	)	)	PUNCT
ejpam-5430	224	143	}	}	PUNCT
ejpam-5430	224	144	jη̃	jη̃	PUNCT
ejpam-5430	225	1	=	=	PRON
ejpam-5430	225	2	{	{	PUNCT
ejpam-5430	225	3	(	(	PUNCT
ejpam-5430	225	4	a1	a1	NOUN
ejpam-5430	225	5	,	,	PUNCT
ejpam-5430	225	6	ỹ	ỹ	PROPN
ejpam-5430	225	7	)	)	PUNCT
ejpam-5430	225	8	,	,	PUNCT
ejpam-5430	225	9	(	(	PUNCT
ejpam-5430	225	10	a2	a2	PROPN
ejpam-5430	225	11	,	,	PUNCT
ejpam-5430	225	12	{	{	PUNCT
ejpam-5430	225	13	x3	x3	ADJ
ejpam-5430	225	14	}	}	PUNCT
ejpam-5430	225	15	)	)	PUNCT
ejpam-5430	225	16	}	}	PUNCT
ejpam-5430	225	17	kη̃	kη̃	X
ejpam-5430	226	1	=	=	PUNCT
ejpam-5430	226	2	{	{	PUNCT
ejpam-5430	226	3	(	(	PUNCT
ejpam-5430	226	4	a1	a1	NOUN
ejpam-5430	226	5	,	,	PUNCT
ejpam-5430	226	6	{	{	PUNCT
ejpam-5430	226	7	x2	x2	ADJ
ejpam-5430	226	8	}	}	PUNCT
ejpam-5430	226	9	)	)	PUNCT
ejpam-5430	226	10	,	,	PUNCT
ejpam-5430	226	11	(	(	PUNCT
ejpam-5430	226	12	a2	a2	PROPN
ejpam-5430	226	13	,	,	PUNCT
ejpam-5430	226	14	ϕη̃	ϕη̃	NUM
ejpam-5430	226	15	)	)	PUNCT
ejpam-5430	226	16	}	}	PUNCT
ejpam-5430	226	17	ỹη̃	ỹη̃	NOUN
ejpam-5430	226	18	=	=	SYM
ejpam-5430	226	19	{	{	PUNCT
ejpam-5430	226	20	(	(	PUNCT
ejpam-5430	226	21	a1	a1	NOUN
ejpam-5430	226	22	,	,	PUNCT
ejpam-5430	226	23	{	{	PUNCT
ejpam-5430	226	24	x2	x2	PROPN
ejpam-5430	226	25	,	,	PUNCT
ejpam-5430	226	26	x4	x4	PROPN
ejpam-5430	226	27	}	}	PUNCT
ejpam-5430	226	28	)	)	PUNCT
ejpam-5430	226	29	,	,	PUNCT
ejpam-5430	226	30	(	(	PUNCT
ejpam-5430	226	31	a2	a2	PROPN
ejpam-5430	226	32	,	,	PUNCT
ejpam-5430	226	33	{	{	PUNCT
ejpam-5430	226	34	x2	x2	PROPN
ejpam-5430	226	35	,	,	PUNCT
ejpam-5430	226	36	x4	x4	PROPN
ejpam-5430	226	37	}	}	PUNCT
ejpam-5430	226	38	)	)	PUNCT
ejpam-5430	226	39	}	}	PUNCT
ejpam-5430	226	40	.	.	PUNCT
ejpam-5430	227	1	over	over	ADP
ejpam-5430	227	2	the	the	DET
ejpam-5430	227	3	pyfs	pyfs	ADJ
ejpam-5430	227	4	dense	dense	ADJ
ejpam-5430	227	5	set	set	NOUN
ejpam-5430	227	6	ỹ	ỹ	PROPN
ejpam-5430	227	7	,	,	PUNCT
ejpam-5430	227	8	the	the	DET
ejpam-5430	227	9	set	set	NOUN
ejpam-5430	227	10	iη̃	iη̃	NOUN
ejpam-5430	227	11	is	be	AUX
ejpam-5430	227	12	pyfssw	pyfssw	ADV
ejpam-5430	227	13	-	-	PUNCT
ejpam-5430	227	14	open	open	ADJ
ejpam-5430	227	15	,	,	PUNCT
ejpam-5430	227	16	but	but	CCONJ
ejpam-5430	227	17	not	not	PART
ejpam-5430	227	18	over	over	ADP
ejpam-5430	227	19	x̃.	x̃.	ADJ
ejpam-5430	227	20	lemma	lemma	PROPN
ejpam-5430	227	21	3	3	X
ejpam-5430	227	22	.	.	PUNCT
ejpam-5430	227	23	suppose	suppose	VERB
ejpam-5430	227	24	gη̃	gη̃	PROPN
ejpam-5430	227	25	that	that	SCONJ
ejpam-5430	227	26	a	a	DET
ejpam-5430	227	27	subset	subset	NOUN
ejpam-5430	227	28	of	of	ADP
ejpam-5430	227	29	(	(	PUNCT
ejpam-5430	227	30	x̃	x̃	PROPN
ejpam-5430	227	31	,	,	PUNCT
ejpam-5430	227	32	ω̃	ω̃	PROPN
ejpam-5430	227	33	,	,	PUNCT
ejpam-5430	227	34	η̃	η̃	PROPN
ejpam-5430	227	35	)	)	PUNCT
ejpam-5430	227	36	.	.	PUNCT
ejpam-5430	228	1	hence	hence	ADV
ejpam-5430	228	2	,	,	PUNCT
ejpam-5430	228	3	gη̃	gη̃	PROPN
ejpam-5430	228	4	is	be	AUX
ejpam-5430	228	5	pyfs	pyf	VERB
ejpam-5430	228	6	semiopen	semiopen	ADJ
ejpam-5430	228	7	if	if	SCONJ
ejpam-5430	228	8	and	and	CCONJ
ejpam-5430	228	9	only	only	ADV
ejpam-5430	228	10	if	if	SCONJ
ejpam-5430	228	11	cl(gη̃	cl(gη̃	NOUN
ejpam-5430	228	12	)	)	PUNCT
ejpam-5430	228	13	=	=	SYM
ejpam-5430	228	14	cl(int(gη̃	cl(int(gη̃	NOUN
ejpam-5430	228	15	)	)	PUNCT
ejpam-5430	228	16	)	)	PUNCT
ejpam-5430	228	17	.	.	PUNCT
ejpam-5430	229	1	proof	proof	NOUN
ejpam-5430	229	2	.	.	PUNCT
ejpam-5430	230	1	suppose	suppose	VERB
ejpam-5430	230	2	gη̃	gη̃	PROPN
ejpam-5430	230	3	is	be	AUX
ejpam-5430	230	4	pyfs	pyfs	ADJ
ejpam-5430	230	5	semiopen	semiopen	ADJ
ejpam-5430	230	6	,	,	PUNCT
ejpam-5430	230	7	that	that	SCONJ
ejpam-5430	230	8	gη̃	gη̃	PROPN
ejpam-5430	230	9	⊑	⊑	PROPN
ejpam-5430	230	10	cl(int(gη̃	cl(int(gη̃	PROPN
ejpam-5430	230	11	)	)	PUNCT
ejpam-5430	230	12	)	)	PUNCT
ejpam-5430	230	13	,	,	PUNCT
ejpam-5430	230	14	and	and	CCONJ
ejpam-5430	230	15	then	then	ADV
ejpam-5430	230	16	cl(gη̃	cl(gη̃	PROPN
ejpam-5430	230	17	)	)	PUNCT
ejpam-5430	230	18	⊑	⊑	PRON
ejpam-5430	230	19	cl(int(gη̃	cl(int(gη̃	PROPN
ejpam-5430	230	20	)	)	PUNCT
ejpam-5430	230	21	)	)	PUNCT
ejpam-5430	230	22	.	.	PUNCT
ejpam-5430	231	1	for	for	ADP
ejpam-5430	231	2	the	the	DET
ejpam-5430	231	3	opposite	opposite	ADJ
ejpam-5430	231	4	side	side	NOUN
ejpam-5430	231	5	of	of	ADP
ejpam-5430	231	6	inclusion	inclusion	NOUN
ejpam-5430	231	7	,	,	PUNCT
ejpam-5430	231	8	there	there	PRON
ejpam-5430	231	9	is	be	VERB
ejpam-5430	231	10	always	always	ADV
ejpam-5430	231	11	int(gη̃	int(gη̃	NOUN
ejpam-5430	231	12	)	)	PUNCT
ejpam-5430	231	13	⊑	⊑	PRON
ejpam-5430	231	14	gη̃.	gη̃.	VERB
ejpam-5430	231	15	so	so	ADV
ejpam-5430	231	16	,	,	PUNCT
ejpam-5430	231	17	cl(gη̃	cl(gη̃	NOUN
ejpam-5430	231	18	)	)	PUNCT
ejpam-5430	231	19	=	=	SYM
ejpam-5430	231	20	cl(int(gη̃	cl(int(gη̃	NOUN
ejpam-5430	231	21	)	)	PUNCT
ejpam-5430	231	22	)	)	PUNCT
ejpam-5430	231	23	.	.	PUNCT
ejpam-5430	232	1	in	in	ADP
ejpam-5430	232	2	contrast	contrast	NOUN
ejpam-5430	232	3	,	,	PUNCT
ejpam-5430	232	4	let	let	VERB
ejpam-5430	232	5	’s	’s	PRON
ejpam-5430	232	6	say	say	VERB
ejpam-5430	232	7	that	that	SCONJ
ejpam-5430	232	8	cl(gη̃	cl(gη̃	NOUN
ejpam-5430	232	9	)	)	PUNCT
ejpam-5430	232	10	=	=	SYM
ejpam-5430	232	11	cl(int(gη̃	cl(int(gη̃	NOUN
ejpam-5430	232	12	)	)	PUNCT
ejpam-5430	232	13	)	)	PUNCT
ejpam-5430	232	14	,	,	PUNCT
ejpam-5430	232	15	but	but	CCONJ
ejpam-5430	232	16	gη̃	gη̃	PROPN
ejpam-5430	232	17	⊑	⊑	DET
ejpam-5430	232	18	cl(gη̃	cl(gη̃	NOUN
ejpam-5430	232	19	)	)	PUNCT
ejpam-5430	232	20	always	always	ADV
ejpam-5430	232	21	,	,	PUNCT
ejpam-5430	232	22	at	at	ADP
ejpam-5430	232	23	hence	hence	ADV
ejpam-5430	232	24	gη̃	gη̃	PROPN
ejpam-5430	232	25	⊑	⊑	PROPN
ejpam-5430	232	26	cl(int(gη̃	cl(int(gη̃	PROPN
ejpam-5430	232	27	)	)	PUNCT
ejpam-5430	232	28	)	)	PUNCT
ejpam-5430	232	29	.	.	PUNCT
ejpam-5430	233	1	so	so	ADV
ejpam-5430	233	2	,	,	PUNCT
ejpam-5430	233	3	gη̃	gη̃	PROPN
ejpam-5430	233	4	is	be	AUX
ejpam-5430	233	5	pyfs	pyfs	ADJ
ejpam-5430	233	6	semiopen	semiopen	ADJ
ejpam-5430	233	7	.	.	PUNCT
ejpam-5430	234	1	lemma	lemma	PROPN
ejpam-5430	234	2	4	4	X
ejpam-5430	234	3	.	.	PUNCT
ejpam-5430	234	4	consider	consider	VERB
ejpam-5430	234	5	gη̃	gη̃	PROPN
ejpam-5430	234	6	as	as	ADP
ejpam-5430	234	7	a	a	DET
ejpam-5430	234	8	non	non	ADJ
ejpam-5430	234	9	-	-	ADJ
ejpam-5430	234	10	null	null	ADJ
ejpam-5430	234	11	subset	subset	NOUN
ejpam-5430	234	12	of	of	ADP
ejpam-5430	234	13	(	(	PUNCT
ejpam-5430	234	14	x̃	x̃	PROPN
ejpam-5430	234	15	,	,	PUNCT
ejpam-5430	234	16	ω̃	ω̃	PROPN
ejpam-5430	234	17	,	,	PUNCT
ejpam-5430	234	18	η̃	η̃	PROPN
ejpam-5430	234	19	)	)	PUNCT
ejpam-5430	234	20	.	.	PUNCT
ejpam-5430	235	1	hence	hence	ADV
ejpam-5430	235	2	,	,	PUNCT
ejpam-5430	235	3	gη̃	gη̃	PROPN
ejpam-5430	235	4	is	be	AUX
ejpam-5430	235	5	pyfs	pyf	VERB
ejpam-5430	235	6	semiopen	semiopen	ADJ
ejpam-5430	235	7	if	if	SCONJ
ejpam-5430	235	8	int(gη̃	int(gη̃	NOUN
ejpam-5430	235	9	)	)	PUNCT
ejpam-5430	235	10	̸=	̸=	PROPN
ejpam-5430	235	11	ϕη̃.	ϕη̃.	VERB
ejpam-5430	235	12	proof	proof	NOUN
ejpam-5430	235	13	.	.	PUNCT
ejpam-5430	236	1	suppose	suppose	VERB
ejpam-5430	236	2	otherwise	otherwise	ADV
ejpam-5430	236	3	that	that	SCONJ
ejpam-5430	236	4	,	,	PUNCT
ejpam-5430	236	5	if	if	SCONJ
ejpam-5430	236	6	gη̃	gη̃	PROPN
ejpam-5430	236	7	is	be	AUX
ejpam-5430	236	8	a	a	DET
ejpam-5430	236	9	non	non	ADJ
ejpam-5430	236	10	-	-	ADJ
ejpam-5430	236	11	null	null	ADJ
ejpam-5430	236	12	soft	soft	ADJ
ejpam-5430	236	13	semiopen	semiopen	NOUN
ejpam-5430	236	14	set	set	VERB
ejpam-5430	236	15	with	with	ADP
ejpam-5430	236	16	int(gη̃	int(gη̃	NOUN
ejpam-5430	236	17	)	)	PUNCT
ejpam-5430	236	18	=	=	SYM
ejpam-5430	237	1	ϕη̃	ϕη̃	PROPN
ejpam-5430	237	2	,	,	PUNCT
ejpam-5430	237	3	then	then	ADV
ejpam-5430	237	4	gη̃	gη̃	PROPN
ejpam-5430	237	5	=	=	SYM
ejpam-5430	237	6	ϕη̃	ϕη̃	PROPN
ejpam-5430	237	7	is	be	AUX
ejpam-5430	237	8	implied	imply	VERB
ejpam-5430	237	9	by	by	ADP
ejpam-5430	237	10	lemma	lemma	PROPN
ejpam-5430	237	11	3.14	3.14	NUM
ejpam-5430	237	12	since	since	SCONJ
ejpam-5430	237	13	cl(gη̃	cl(gη̃	NUM
ejpam-5430	237	14	)	)	PUNCT
ejpam-5430	238	1	=	=	PRON
ejpam-5430	238	2	ϕη̃.	ϕη̃.	NOUN
ejpam-5430	238	3	inconsistency	inconsistency	NOUN
ejpam-5430	238	4	.	.	PUNCT
ejpam-5430	239	1	remark	remark	NOUN
ejpam-5430	239	2	2	2	NUM
ejpam-5430	239	3	.	.	PUNCT
ejpam-5430	239	4	since	since	SCONJ
ejpam-5430	239	5	int(gη̃	int(gη̃	NOUN
ejpam-5430	239	6	)	)	PUNCT
ejpam-5430	239	7	=	=	SYM
ejpam-5430	239	8	int(cl(gη̃	int(cl(gη̃	NOUN
ejpam-5430	239	9	)	)	PUNCT
ejpam-5430	239	10	)	)	PUNCT
ejpam-5430	239	11	for	for	ADP
ejpam-5430	239	12	each	each	DET
ejpam-5430	239	13	pyfs	pyfs	NOUN
ejpam-5430	239	14	gη̃	gη̃	PROPN
ejpam-5430	239	15	in	in	ADP
ejpam-5430	239	16	a	a	DET
ejpam-5430	239	17	pyfsts	pyfst	NOUN
ejpam-5430	239	18	(	(	PUNCT
ejpam-5430	239	19	x̃	x̃	PROPN
ejpam-5430	239	20	,	,	PUNCT
ejpam-5430	239	21	ω̃	ω̃	PROPN
ejpam-5430	239	22	,	,	PUNCT
ejpam-5430	239	23	η̃	η̃	PROPN
ejpam-5430	239	24	)	)	PUNCT
ejpam-5430	239	25	,	,	PUNCT
ejpam-5430	239	26	so	so	CCONJ
ejpam-5430	239	27	each	each	DET
ejpam-5430	239	28	pyfssw	pyfssw	ADV
ejpam-5430	239	29	-	-	PUNCT
ejpam-5430	239	30	open	open	ADJ
ejpam-5430	239	31	set	set	NOUN
ejpam-5430	239	32	is	be	AUX
ejpam-5430	239	33	pyfs	pyfs	ADJ
ejpam-5430	239	34	somewhere	somewhere	ADV
ejpam-5430	239	35	dense	dense	ADJ
ejpam-5430	239	36	.	.	PUNCT
ejpam-5430	240	1	the	the	DET
ejpam-5430	240	2	following	follow	VERB
ejpam-5430	240	3	figure	figure	NOUN
ejpam-5430	240	4	depicts	depict	VERB
ejpam-5430	240	5	the	the	DET
ejpam-5430	240	6	relation	relation	NOUN
ejpam-5430	240	7	between	between	ADP
ejpam-5430	240	8	different	different	ADJ
ejpam-5430	240	9	extensions	extension	NOUN
ejpam-5430	240	10	of	of	ADP
ejpam-5430	240	11	pyfs	pyfs	ADJ
ejpam-5430	240	12	open	open	ADJ
ejpam-5430	240	13	sets	set	NOUN
ejpam-5430	240	14	.	.	PUNCT
ejpam-5430	241	1	as	as	SCONJ
ejpam-5430	241	2	demonstrated	demonstrate	VERB
ejpam-5430	241	3	below	below	ADV
ejpam-5430	241	4	,	,	PUNCT
ejpam-5430	241	5	none	none	NOUN
ejpam-5430	241	6	of	of	ADP
ejpam-5430	241	7	these	these	DET
ejpam-5430	241	8	implications	implication	NOUN
ejpam-5430	241	9	can	can	AUX
ejpam-5430	241	10	,	,	PUNCT
ejpam-5430	241	11	in	in	ADP
ejpam-5430	241	12	general	general	ADJ
ejpam-5430	241	13	,	,	PUNCT
ejpam-5430	241	14	be	be	AUX
ejpam-5430	241	15	replaced	replace	VERB
ejpam-5430	241	16	by	by	ADP
ejpam-5430	241	17	equivalency	equivalency	NOUN
ejpam-5430	241	18	.	.	PUNCT
ejpam-5430	242	1	a.	a.	NOUN
ejpam-5430	242	2	a.	a.	PROPN
ejpam-5430	242	3	azzam	azzam	PROPN
ejpam-5430	242	4	,	,	PUNCT
ejpam-5430	242	5	m.	m.	NOUN
ejpam-5430	242	6	aldawood	aldawood	PROPN
ejpam-5430	242	7	,	,	PUNCT
ejpam-5430	242	8	r.	r.	PROPN
ejpam-5430	242	9	abu	abu	PROPN
ejpam-5430	242	10	-	-	PUNCT
ejpam-5430	242	11	gdairi	gdairi	PROPN
ejpam-5430	242	12	/	/	SYM
ejpam-5430	242	13	eur	eur	PROPN
ejpam-5430	242	14	.	.	PUNCT
ejpam-5430	243	1	j.	j.	PROPN
ejpam-5430	243	2	pure	pure	PROPN
ejpam-5430	243	3	appl	appl	PROPN
ejpam-5430	243	4	.	.	PROPN
ejpam-5430	243	5	math	math	PROPN
ejpam-5430	243	6	,	,	PUNCT
ejpam-5430	243	7	17	17	NUM
ejpam-5430	243	8	(	(	PUNCT
ejpam-5430	243	9	4	4	NUM
ejpam-5430	243	10	)	)	PUNCT
ejpam-5430	243	11	(	(	PUNCT
ejpam-5430	243	12	2024	2024	NUM
ejpam-5430	243	13	)	)	PUNCT
ejpam-5430	243	14	,	,	PUNCT
ejpam-5430	243	15	4147	4147	NUM
ejpam-5430	243	16	-	-	SYM
ejpam-5430	243	17	4163	4163	NUM
ejpam-5430	243	18	4155	4155	NUM
ejpam-5430	243	19	figure	figure	NOUN
ejpam-5430	243	20	1	1	NUM
ejpam-5430	243	21	:	:	PUNCT
ejpam-5430	243	22	the	the	DET
ejpam-5430	243	23	relationships	relationship	NOUN
ejpam-5430	243	24	between	between	ADP
ejpam-5430	243	25	some	some	DET
ejpam-5430	243	26	generalizations	generalization	NOUN
ejpam-5430	243	27	of	of	ADP
ejpam-5430	243	28	pyfs	pyfs	ADJ
ejpam-5430	243	29	open	open	ADJ
ejpam-5430	243	30	sets	set	NOUN
ejpam-5430	243	31	.	.	PUNCT
ejpam-5430	244	1	example	example	NOUN
ejpam-5430	244	2	3	3	X
ejpam-5430	244	3	.	.	X
ejpam-5430	244	4	think	think	VERB
ejpam-5430	244	5	about	about	ADP
ejpam-5430	244	6	pyfst	pyfst	NOUN
ejpam-5430	244	7	over	over	ADP
ejpam-5430	244	8	x̃	x̃	PROPN
ejpam-5430	244	9	that	that	DET
ejpam-5430	244	10	example	example	NOUN
ejpam-5430	244	11	3.7	3.7	NUM
ejpam-5430	244	12	.	.	PUNCT
ejpam-5430	245	1	the	the	DET
ejpam-5430	245	2	pyfss	pyfss	NOUN
ejpam-5430	245	3	over	over	ADP
ejpam-5430	245	4	x̃	x̃	PROPN
ejpam-5430	245	5	is	be	AUX
ejpam-5430	245	6	not	not	PART
ejpam-5430	245	7	pyfssw	pyfssw	ADV
ejpam-5430	245	8	-	-	PUNCT
ejpam-5430	245	9	open	open	ADJ
ejpam-5430	245	10	,	,	PUNCT
ejpam-5430	245	11	meaning	mean	VERB
ejpam-5430	245	12	it	it	PRON
ejpam-5430	245	13	is	be	AUX
ejpam-5430	245	14	not	not	PART
ejpam-5430	245	15	pyfs	pyfs	ADJ
ejpam-5430	245	16	semiopen	semiopen	ADJ
ejpam-5430	245	17	,	,	PUNCT
ejpam-5430	245	18	but	but	CCONJ
ejpam-5430	245	19	is	be	AUX
ejpam-5430	245	20	pyfsβ	pyfsβ	ADJ
ejpam-5430	245	21	-	-	PUNCT
ejpam-5430	245	22	open	open	ADJ
ejpam-5430	245	23	,	,	PUNCT
ejpam-5430	245	24	meaning	mean	VERB
ejpam-5430	245	25	it	it	PRON
ejpam-5430	245	26	is	be	AUX
ejpam-5430	245	27	pyfs	pyfs	ADJ
ejpam-5430	245	28	somewhere	somewhere	ADV
ejpam-5430	245	29	dense	dense	ADJ
ejpam-5430	245	30	.	.	PUNCT
ejpam-5430	246	1	however	however	ADV
ejpam-5430	246	2	,	,	PUNCT
ejpam-5430	246	3	it	it	PRON
ejpam-5430	246	4	is	be	AUX
ejpam-5430	246	5	evident	evident	ADJ
ejpam-5430	246	6	that	that	SCONJ
ejpam-5430	246	7	the	the	DET
ejpam-5430	246	8	set	set	NOUN
ejpam-5430	246	9	{	{	PUNCT
ejpam-5430	246	10	(	(	PUNCT
ejpam-5430	246	11	a1	a1	PROPN
ejpam-5430	246	12	,	,	PUNCT
ejpam-5430	246	13	ξ̃1(a1	ξ̃1(a1	NOUN
ejpam-5430	246	14	)	)	PUNCT
ejpam-5430	246	15	)	)	PUNCT
ejpam-5430	246	16	,	,	PUNCT
ejpam-5430	246	17	(	(	PUNCT
ejpam-5430	246	18	a2	a2	PROPN
ejpam-5430	246	19	,	,	PUNCT
ejpam-5430	246	20	ξ̃1(a2	ξ̃1(a2	NUM
ejpam-5430	246	21	)	)	PUNCT
ejpam-5430	246	22	)	)	PUNCT
ejpam-5430	246	23	}	}	PUNCT
ejpam-5430	246	24	is	be	AUX
ejpam-5430	246	25	not	not	PART
ejpam-5430	246	26	pyfs	pyfs	ADJ
ejpam-5430	246	27	semiopen	semiopen	ADJ
ejpam-5430	246	28	,	,	PUNCT
ejpam-5430	246	29	but	but	CCONJ
ejpam-5430	246	30	rather	rather	ADV
ejpam-5430	246	31	pyfssw	pyfssw	ADV
ejpam-5430	246	32	-	-	PUNCT
ejpam-5430	246	33	open	open	ADJ
ejpam-5430	246	34	.	.	PUNCT
ejpam-5430	247	1	lemma	lemma	PROPN
ejpam-5430	247	2	5	5	NUM
ejpam-5430	247	3	.	.	PUNCT
ejpam-5430	247	4	suppose	suppose	VERB
ejpam-5430	247	5	gη̃	gη̃	PROPN
ejpam-5430	247	6	that	that	SCONJ
ejpam-5430	247	7	a	a	DET
ejpam-5430	247	8	non	non	ADJ
ejpam-5430	247	9	-	-	ADJ
ejpam-5430	247	10	null	null	ADJ
ejpam-5430	247	11	subset	subset	NOUN
ejpam-5430	247	12	of	of	ADP
ejpam-5430	247	13	(	(	PUNCT
ejpam-5430	247	14	x̃	x̃	PROPN
ejpam-5430	247	15	,	,	PUNCT
ejpam-5430	247	16	ω̃	ω̃	PROPN
ejpam-5430	247	17	,	,	PUNCT
ejpam-5430	247	18	η̃	η̃	PROPN
ejpam-5430	247	19	)	)	PUNCT
ejpam-5430	247	20	.	.	PUNCT
ejpam-5430	248	1	then	then	ADV
ejpam-5430	248	2	cl(gη̃)⊓hη̃	cl(gη̃)⊓hη̃	PROPN
ejpam-5430	248	3	⊑	⊑	X
ejpam-5430	248	4	cl(gη̃⊓hη̃	cl(gη̃⊓hη̃	PROPN
ejpam-5430	248	5	)	)	PUNCT
ejpam-5430	248	6	for	for	ADP
ejpam-5430	248	7	all	all	DET
ejpam-5430	248	8	pyfs	pyfs	ADJ
ejpam-5430	248	9	open	open	ADJ
ejpam-5430	248	10	set	set	VERB
ejpam-5430	248	11	hη̃	hη̃	PROPN
ejpam-5430	248	12	on	on	ADP
ejpam-5430	248	13	x̃.	x̃.	PROPN
ejpam-5430	248	14	lemma	lemma	PROPN
ejpam-5430	248	15	6	6	X
ejpam-5430	248	16	.	.	PUNCT
ejpam-5430	248	17	assume	assume	VERB
ejpam-5430	248	18	that	that	SCONJ
ejpam-5430	248	19	gη̃	gη̃	PROPN
ejpam-5430	248	20	,	,	PUNCT
ejpam-5430	248	21	hη̃	hη̃	PROPN
ejpam-5430	248	22	is	be	AUX
ejpam-5430	248	23	a	a	DET
ejpam-5430	248	24	subset	subset	NOUN
ejpam-5430	248	25	of	of	ADP
ejpam-5430	248	26	(	(	PUNCT
ejpam-5430	248	27	x̃	x̃	PROPN
ejpam-5430	248	28	,	,	PUNCT
ejpam-5430	248	29	ω̃	ω̃	PROPN
ejpam-5430	248	30	,	,	PUNCT
ejpam-5430	248	31	η̃	η̃	PROPN
ejpam-5430	248	32	)	)	PUNCT
ejpam-5430	248	33	.	.	PUNCT
ejpam-5430	249	1	gη̃	gη̃	PROPN
ejpam-5430	249	2	⊓hη̃	⊓hη̃	PROPN
ejpam-5430	249	3	is	be	AUX
ejpam-5430	249	4	pyfs	pyf	VERB
ejpam-5430	249	5	semiopen	semiopen	ADJ
ejpam-5430	249	6	over	over	ADP
ejpam-5430	249	7	x̃	x̃	PROPN
ejpam-5430	249	8	if	if	SCONJ
ejpam-5430	249	9	gη̃	gη̃	PROPN
ejpam-5430	249	10	is	be	AUX
ejpam-5430	249	11	pyfs	pyfs	ADJ
ejpam-5430	249	12	open	open	ADJ
ejpam-5430	249	13	and	and	CCONJ
ejpam-5430	249	14	hη̃	hη̃	PRON
ejpam-5430	249	15	is	be	AUX
ejpam-5430	249	16	pyfs	pyfs	ADJ
ejpam-5430	249	17	semiopen	semiopen	ADJ
ejpam-5430	249	18	.	.	PUNCT
ejpam-5430	250	1	proof	proof	NOUN
ejpam-5430	250	2	.	.	PUNCT
ejpam-5430	251	1	suppose	suppose	VERB
ejpam-5430	251	2	that	that	SCONJ
ejpam-5430	251	3	gη̃	gη̃	PROPN
ejpam-5430	251	4	is	be	AUX
ejpam-5430	251	5	pyfs	pyfs	ADJ
ejpam-5430	251	6	open	open	ADJ
ejpam-5430	251	7	and	and	CCONJ
ejpam-5430	251	8	hη̃	hη̃	PRON
ejpam-5430	251	9	is	be	AUX
ejpam-5430	251	10	pyfs	pyfs	ADJ
ejpam-5430	251	11	semiopen	semiopen	ADJ
ejpam-5430	251	12	.	.	PUNCT
ejpam-5430	252	1	then	then	ADV
ejpam-5430	252	2	there	there	PRON
ejpam-5430	252	3	’s	’	VERB
ejpam-5430	252	4	a	a	DET
ejpam-5430	252	5	pyfs	pyfs	ADJ
ejpam-5430	252	6	open	open	ADJ
ejpam-5430	252	7	set	set	NOUN
ejpam-5430	252	8	.	.	PUNCT
ejpam-5430	253	1	uη̃	uη̃	PUNCT
ejpam-5430	254	1	over	over	ADP
ejpam-5430	254	2	x̃	x̃	PROPN
ejpam-5430	254	3	with	with	ADP
ejpam-5430	254	4	uη̃	uη̃	PRON
ejpam-5430	254	5	⊑	⊑	PRON
ejpam-5430	254	6	hη̃	hη̃	PROPN
ejpam-5430	254	7	⊑	⊑	X
ejpam-5430	254	8	cl(uη̃	cl(uη̃	PROPN
ejpam-5430	254	9	)	)	PUNCT
ejpam-5430	254	10	.	.	PUNCT
ejpam-5430	255	1	now	now	ADV
ejpam-5430	255	2	uη̃⊓gη̃	uη̃⊓gη̃	NOUN
ejpam-5430	255	3	⊑	⊑	PRON
ejpam-5430	255	4	hη̃⊓gη̃	hη̃⊓gη̃	NOUN
ejpam-5430	255	5	⊑	⊑	ADP
ejpam-5430	255	6	cl(uη̃)⊓gη̃.	cl(uη̃)⊓gη̃.	PROPN
ejpam-5430	255	7	by	by	ADP
ejpam-5430	255	8	lemma	lemma	PROPN
ejpam-5430	255	9	3.18	3.18	NUM
ejpam-5430	255	10	,	,	PUNCT
ejpam-5430	255	11	uη̃	uη̃	PRON
ejpam-5430	255	12	⊓gη̃	⊓gη̃	NOUN
ejpam-5430	255	13	⊑	⊑	PRON
ejpam-5430	255	14	hη̃	hη̃	INTJ
ejpam-5430	255	15	⊓gη̃	⊓gη̃	NOUN
ejpam-5430	255	16	⊑	⊑	X
ejpam-5430	255	17	cl(uη̃	cl(uη̃	PROPN
ejpam-5430	255	18	⊓gη̃	⊓gη̃	NOUN
ejpam-5430	255	19	)	)	PUNCT
ejpam-5430	255	20	and	and	CCONJ
ejpam-5430	255	21	since	since	SCONJ
ejpam-5430	255	22	uη̃	uη̃	NUM
ejpam-5430	255	23	⊓gη̃	⊓gη̃	NOUN
ejpam-5430	255	24	is	be	AUX
ejpam-5430	255	25	pyfs	pyfs	ADJ
ejpam-5430	255	26	open	open	ADJ
ejpam-5430	255	27	,	,	PUNCT
ejpam-5430	255	28	then	then	ADV
ejpam-5430	255	29	hη̃	hη̃	INTJ
ejpam-5430	255	30	⊓gη̃	⊓gη̃	NOUN
ejpam-5430	255	31	is	be	AUX
ejpam-5430	255	32	pyfs	pyf	VERB
ejpam-5430	255	33	semiopen	semiopen	ADJ
ejpam-5430	255	34	over	over	ADP
ejpam-5430	255	35	x̃.	x̃.	PROPN
ejpam-5430	255	36	lemma	lemma	PROPN
ejpam-5430	255	37	7	7	X
ejpam-5430	255	38	.	.	X
ejpam-5430	255	39	assume	assume	VERB
ejpam-5430	255	40	that	that	SCONJ
ejpam-5430	255	41	gη̃	gη̃	PROPN
ejpam-5430	255	42	,	,	PUNCT
ejpam-5430	255	43	hη̃	hη̃	PROPN
ejpam-5430	255	44	is	be	AUX
ejpam-5430	255	45	a	a	DET
ejpam-5430	255	46	subset	subset	NOUN
ejpam-5430	255	47	of	of	ADP
ejpam-5430	255	48	(	(	PUNCT
ejpam-5430	255	49	x̃	x̃	PROPN
ejpam-5430	255	50	,	,	PUNCT
ejpam-5430	255	51	ω̃	ω̃	PROPN
ejpam-5430	255	52	,	,	PUNCT
ejpam-5430	255	53	η̃	η̃	PROPN
ejpam-5430	255	54	)	)	PUNCT
ejpam-5430	255	55	.	.	PUNCT
ejpam-5430	256	1	gη̃	gη̃	PROPN
ejpam-5430	256	2	⊓hη̃	⊓hη̃	PROPN
ejpam-5430	256	3	is	be	AUX
ejpam-5430	256	4	pyfs	pyf	VERB
ejpam-5430	256	5	semiopen	semiopen	ADJ
ejpam-5430	256	6	over	over	ADP
ejpam-5430	256	7	gη̃	gη̃	PROPN
ejpam-5430	256	8	if	if	SCONJ
ejpam-5430	256	9	gη̃	gη̃	PROPN
ejpam-5430	256	10	is	be	AUX
ejpam-5430	256	11	pyfs	pyfs	ADJ
ejpam-5430	256	12	open	open	ADJ
ejpam-5430	256	13	and	and	CCONJ
ejpam-5430	256	14	hη̃	hη̃	PRON
ejpam-5430	256	15	is	be	AUX
ejpam-5430	256	16	pyfs	pyfs	ADJ
ejpam-5430	256	17	semiopen	semiopen	ADJ
ejpam-5430	256	18	.	.	PUNCT
ejpam-5430	257	1	proof	proof	NOUN
ejpam-5430	257	2	.	.	PUNCT
ejpam-5430	258	1	utilizing	utilize	VERB
ejpam-5430	258	2	the	the	DET
ejpam-5430	258	3	same	same	ADJ
ejpam-5430	258	4	procedures	procedure	NOUN
ejpam-5430	258	5	as	as	ADP
ejpam-5430	258	6	in	in	ADP
ejpam-5430	258	7	the	the	DET
ejpam-5430	258	8	lemma	lemma	PROPN
ejpam-5430	258	9	proof	proof	NOUN
ejpam-5430	258	10	above	above	ADV
ejpam-5430	258	11	,	,	PUNCT
ejpam-5430	258	12	apply	apply	VERB
ejpam-5430	258	13	the	the	DET
ejpam-5430	258	14	assertion	assertion	NOUN
ejpam-5430	258	15	that	that	SCONJ
ejpam-5430	258	16	cl(uη̃	cl(uη̃	NOUN
ejpam-5430	258	17	)	)	PUNCT
ejpam-5430	258	18	⊓gη̃	⊓gη̃	NOUN
ejpam-5430	258	19	=	=	NOUN
ejpam-5430	258	20	clgη̃(uη̃	clgη̃(uη̃	PROPN
ejpam-5430	258	21	)	)	PUNCT
ejpam-5430	258	22	.	.	PUNCT
ejpam-5430	259	1	lemma	lemma	PROPN
ejpam-5430	259	2	8	8	NUM
ejpam-5430	259	3	.	.	PUNCT
ejpam-5430	260	1	a	a	DET
ejpam-5430	260	2	subset	subset	NOUN
ejpam-5430	260	3	gη̃	gη̃	PROPN
ejpam-5430	260	4	of	of	ADP
ejpam-5430	260	5	(	(	PUNCT
ejpam-5430	260	6	x̃	x̃	PROPN
ejpam-5430	260	7	,	,	PUNCT
ejpam-5430	260	8	ω̃	ω̃	PROPN
ejpam-5430	260	9	,	,	PUNCT
ejpam-5430	260	10	η̃	η̃	PROPN
ejpam-5430	260	11	)	)	PUNCT
ejpam-5430	260	12	is	be	AUX
ejpam-5430	260	13	pyfs	pyf	VERB
ejpam-5430	260	14	semiopen	semiopen	ADJ
ejpam-5430	260	15	if	if	SCONJ
ejpam-5430	260	16	and	and	CCONJ
ejpam-5430	260	17	only	only	ADV
ejpam-5430	260	18	if	if	SCONJ
ejpam-5430	260	19	gη̃⊓uη̃	gη̃⊓uη̃	NOUN
ejpam-5430	260	20	is	be	AUX
ejpam-5430	260	21	pyfssw	pyfssw	ADV
ejpam-5430	260	22	open	open	ADJ
ejpam-5430	260	23	for	for	ADP
ejpam-5430	260	24	each	each	DET
ejpam-5430	260	25	pyfs	pyfs	ADJ
ejpam-5430	260	26	open	open	ADJ
ejpam-5430	260	27	set	set	VERB
ejpam-5430	260	28	uη̃	uη̃	INTJ
ejpam-5430	260	29	over	over	ADP
ejpam-5430	260	30	x̃.	x̃.	ADJ
ejpam-5430	260	31	a.	a.	NOUN
ejpam-5430	260	32	a.	a.	PROPN
ejpam-5430	260	33	azzam	azzam	PROPN
ejpam-5430	260	34	,	,	PUNCT
ejpam-5430	260	35	m.	m.	NOUN
ejpam-5430	260	36	aldawood	aldawood	PROPN
ejpam-5430	260	37	,	,	PUNCT
ejpam-5430	260	38	r.	r.	PROPN
ejpam-5430	260	39	abu	abu	PROPN
ejpam-5430	260	40	-	-	PUNCT
ejpam-5430	260	41	gdairi	gdairi	PROPN
ejpam-5430	260	42	/	/	SYM
ejpam-5430	260	43	eur	eur	PROPN
ejpam-5430	260	44	.	.	PUNCT
ejpam-5430	261	1	j.	j.	PROPN
ejpam-5430	261	2	pure	pure	PROPN
ejpam-5430	261	3	appl	appl	PROPN
ejpam-5430	261	4	.	.	PROPN
ejpam-5430	261	5	math	math	PROPN
ejpam-5430	261	6	,	,	PUNCT
ejpam-5430	261	7	17	17	NUM
ejpam-5430	261	8	(	(	PUNCT
ejpam-5430	261	9	4	4	NUM
ejpam-5430	261	10	)	)	PUNCT
ejpam-5430	261	11	(	(	PUNCT
ejpam-5430	261	12	2024	2024	NUM
ejpam-5430	261	13	)	)	PUNCT
ejpam-5430	261	14	,	,	PUNCT
ejpam-5430	261	15	4147	4147	NUM
ejpam-5430	261	16	-	-	SYM
ejpam-5430	261	17	4163	4163	NUM
ejpam-5430	261	18	4156	4156	NUM
ejpam-5430	261	19	proof	proof	NOUN
ejpam-5430	261	20	.	.	PUNCT
ejpam-5430	262	1	the	the	DET
ejpam-5430	262	2	first	first	ADJ
ejpam-5430	262	3	part	part	NOUN
ejpam-5430	262	4	follows	follow	VERB
ejpam-5430	262	5	because	because	SCONJ
ejpam-5430	262	6	each	each	DET
ejpam-5430	262	7	pyfs	pyfs	ADJ
ejpam-5430	262	8	semiopen	semiopen	VERB
ejpam-5430	262	9	set	set	NOUN
ejpam-5430	262	10	is	be	AUX
ejpam-5430	262	11	pyfssw	pyfssw	ADV
ejpam-5430	262	12	open	open	ADJ
ejpam-5430	262	13	and	and	CCONJ
ejpam-5430	262	14	because	because	SCONJ
ejpam-5430	262	15	the	the	DET
ejpam-5430	262	16	intersection	intersection	NOUN
ejpam-5430	262	17	of	of	ADP
ejpam-5430	262	18	a	a	DET
ejpam-5430	262	19	pyfs	pyfs	ADJ
ejpam-5430	262	20	semiopen	semiopen	NOUN
ejpam-5430	262	21	set	set	VERB
ejpam-5430	262	22	with	with	ADP
ejpam-5430	262	23	a	a	DET
ejpam-5430	262	24	pyfs	pyfs	ADJ
ejpam-5430	262	25	open	open	ADJ
ejpam-5430	262	26	set	set	NOUN
ejpam-5430	262	27	is	be	AUX
ejpam-5430	262	28	semiopen	semiopen	ADJ
ejpam-5430	262	29	according	accord	VERB
ejpam-5430	262	30	to	to	ADP
ejpam-5430	262	31	lemma	lemma	PROPN
ejpam-5430	262	32	3.19	3.19	NUM
ejpam-5430	262	33	.	.	PUNCT
ejpam-5430	263	1	on	on	ADP
ejpam-5430	263	2	the	the	DET
ejpam-5430	263	3	other	other	ADJ
ejpam-5430	263	4	hand	hand	NOUN
ejpam-5430	263	5	,	,	PUNCT
ejpam-5430	263	6	suppose	suppose	VERB
ejpam-5430	263	7	that	that	SCONJ
ejpam-5430	263	8	pxa	pxa	NOUN
ejpam-5430	263	9	∈	∈	PROPN
ejpam-5430	263	10	gη̃	gη̃	PROPN
ejpam-5430	263	11	and	and	CCONJ
ejpam-5430	263	12	that	that	PRON
ejpam-5430	263	13	for	for	SCONJ
ejpam-5430	263	14	any	any	DET
ejpam-5430	263	15	pyfs	pyfs	ADJ
ejpam-5430	263	16	open	open	ADJ
ejpam-5430	263	17	set	set	VERB
ejpam-5430	263	18	uη̃	uη̃	INTJ
ejpam-5430	263	19	over	over	ADP
ejpam-5430	263	20	x̃	x̃	PROPN
ejpam-5430	263	21	,	,	PUNCT
ejpam-5430	263	22	gη̃	gη̃	PUNCT
ejpam-5430	263	23	⊓	⊓	PROPN
ejpam-5430	263	24	uη̃	uη̃	PRON
ejpam-5430	263	25	is	be	AUX
ejpam-5430	263	26	pyfssw	pyfssw	ADV
ejpam-5430	263	27	open	open	ADJ
ejpam-5430	263	28	.	.	PUNCT
ejpam-5430	264	1	that	that	PRON
ejpam-5430	264	2	is	be	AUX
ejpam-5430	264	3	int(gη̃	int(gη̃	ADJ
ejpam-5430	264	4	⊓	⊓	PROPN
ejpam-5430	264	5	uη̃	uη̃	SYM
ejpam-5430	264	6	)	)	PUNCT
ejpam-5430	264	7	̸=	̸=	PROPN
ejpam-5430	264	8	ϕη̃.	ϕη̃.	NOUN
ejpam-5430	265	1	but	but	CCONJ
ejpam-5430	265	2	ϕη̃	ϕη̃	NUM
ejpam-5430	265	3	̸=	̸=	PROPN
ejpam-5430	265	4	int(gη̃	int(gη̃	NUM
ejpam-5430	265	5	⊓	⊓	PROPN
ejpam-5430	265	6	uη̃	uη̃	PRON
ejpam-5430	265	7	)	)	PUNCT
ejpam-5430	265	8	=	=	SYM
ejpam-5430	265	9	int(gη̃	int(gη̃	NOUN
ejpam-5430	265	10	)	)	PUNCT
ejpam-5430	265	11	⊓	⊓	NOUN
ejpam-5430	265	12	int(uη̃	int(uη̃	NOUN
ejpam-5430	265	13	)	)	PUNCT
ejpam-5430	265	14	=	=	SYM
ejpam-5430	266	1	int(gη̃	int(gη̃	NOUN
ejpam-5430	266	2	)	)	PUNCT
ejpam-5430	266	3	⊓	⊓	PROPN
ejpam-5430	266	4	uη̃	uη̃	PROPN
ejpam-5430	266	5	,	,	PUNCT
ejpam-5430	266	6	that	that	PRON
ejpam-5430	266	7	is	be	AUX
ejpam-5430	266	8	p	p	X
ejpam-5430	266	9	x	x	DET
ejpam-5430	266	10	a	a	DET
ejpam-5430	266	11	∈	∈	PROPN
ejpam-5430	266	12	cl(int(gη̃	cl(int(gη̃	NOUN
ejpam-5430	266	13	)	)	PUNCT
ejpam-5430	266	14	)	)	PUNCT
ejpam-5430	267	1	and	and	CCONJ
ejpam-5430	267	2	then	then	ADV
ejpam-5430	267	3	gη̃	gη̃	PROPN
ejpam-5430	267	4	⊑	⊑	PROPN
ejpam-5430	267	5	cl(int(gη̃	cl(int(gη̃	PROPN
ejpam-5430	267	6	)	)	PUNCT
ejpam-5430	267	7	)	)	PUNCT
ejpam-5430	267	8	.	.	PUNCT
ejpam-5430	268	1	this	this	PRON
ejpam-5430	268	2	demonstrates	demonstrate	VERB
ejpam-5430	268	3	gη̃	gη̃	PROPN
ejpam-5430	268	4	’s	’s	PART
ejpam-5430	268	5	pyfs	pyfs	ADJ
ejpam-5430	268	6	semiopenness	semiopenness	NOUN
ejpam-5430	268	7	.	.	PUNCT
ejpam-5430	269	1	lemma	lemma	PROPN
ejpam-5430	269	2	9	9	NUM
ejpam-5430	269	3	.	.	PUNCT
ejpam-5430	269	4	consider	consider	VERB
ejpam-5430	269	5	fη̃.	fη̃.	NOUN
ejpam-5430	269	6	is	be	AUX
ejpam-5430	269	7	a	a	DET
ejpam-5430	269	8	subset	subset	NOUN
ejpam-5430	269	9	of	of	ADP
ejpam-5430	269	10	(	(	PUNCT
ejpam-5430	269	11	x̃	x̃	PROPN
ejpam-5430	269	12	,	,	PUNCT
ejpam-5430	269	13	ω̃	ω̃	PROPN
ejpam-5430	269	14	,	,	PUNCT
ejpam-5430	269	15	η̃	η̃	PROPN
ejpam-5430	269	16	)	)	PUNCT
ejpam-5430	269	17	.	.	PUNCT
ejpam-5430	270	1	if	if	SCONJ
ejpam-5430	270	2	fη̃	fη̃	PRON
ejpam-5430	270	3	is	be	AUX
ejpam-5430	270	4	pyfs	pyfs	ADJ
ejpam-5430	270	5	semiclosed	semiclose	VERB
ejpam-5430	270	6	and	and	CCONJ
ejpam-5430	270	7	pyfs	pyfs	ADJ
ejpam-5430	270	8	somewhere	somewhere	ADV
ejpam-5430	270	9	dense	dense	ADJ
ejpam-5430	270	10	,	,	PUNCT
ejpam-5430	270	11	it	it	PRON
ejpam-5430	270	12	is	be	AUX
ejpam-5430	270	13	pyfssw	pyfssw	ADV
ejpam-5430	270	14	open	open	ADJ
ejpam-5430	270	15	.	.	PUNCT
ejpam-5430	271	1	proof	proof	NOUN
ejpam-5430	271	2	.	.	PUNCT
ejpam-5430	272	1	it	it	PRON
ejpam-5430	272	2	may	may	AUX
ejpam-5430	272	3	be	be	AUX
ejpam-5430	272	4	inferred	infer	VERB
ejpam-5430	272	5	directly	directly	ADV
ejpam-5430	272	6	from	from	ADP
ejpam-5430	272	7	lemma	lemma	PROPN
ejpam-5430	272	8	3.15	3.15	NUM
ejpam-5430	272	9	that	that	PRON
ejpam-5430	272	10	fη̃	fη̃	PRON
ejpam-5430	272	11	is	be	AUX
ejpam-5430	272	12	semiclosed	semiclose	VERB
ejpam-5430	272	13	if	if	SCONJ
ejpam-5430	272	14	and	and	CCONJ
ejpam-5430	272	15	only	only	ADV
ejpam-5430	272	16	if	if	SCONJ
ejpam-5430	272	17	int(cl(fη̃))=int(fη̃	int(cl(fη̃))=int(fη̃	NOUN
ejpam-5430	272	18	)	)	PUNCT
ejpam-5430	272	19	.	.	PUNCT
ejpam-5430	273	1	4	4	X
ejpam-5430	273	2	.	.	X
ejpam-5430	273	3	pyfssw	pyfssw	ADJ
ejpam-5430	273	4	-	-	PUNCT
ejpam-5430	273	5	continuous	continuous	ADJ
ejpam-5430	273	6	functions	function	NOUN
ejpam-5430	273	7	this	this	DET
ejpam-5430	273	8	part	part	NOUN
ejpam-5430	273	9	focuses	focus	VERB
ejpam-5430	273	10	on	on	ADP
ejpam-5430	273	11	outlining	outline	VERB
ejpam-5430	273	12	the	the	DET
ejpam-5430	273	13	ideas	idea	NOUN
ejpam-5430	273	14	behind	behind	ADP
ejpam-5430	273	15	pyfssw	pyfssw	PROPN
ejpam-5430	273	16	c	c	PROPN
ejpam-5430	273	17	functions	function	NOUN
ejpam-5430	273	18	,	,	PUNCT
ejpam-5430	273	19	also	also	ADV
ejpam-5430	273	20	known	know	VERB
ejpam-5430	273	21	as	as	ADP
ejpam-5430	273	22	pyfssw	pyfssw	NOUN
ejpam-5430	273	23	c	c	NOUN
ejpam-5430	273	24	,	,	PUNCT
ejpam-5430	273	25	and	and	CCONJ
ejpam-5430	273	26	providing	provide	VERB
ejpam-5430	273	27	several	several	ADJ
ejpam-5430	273	28	characterizations	characterization	NOUN
ejpam-5430	273	29	of	of	ADP
ejpam-5430	273	30	them	they	PRON
ejpam-5430	273	31	.	.	PUNCT
ejpam-5430	274	1	furthermore	furthermore	ADV
ejpam-5430	274	2	,	,	PUNCT
ejpam-5430	274	3	we	we	PRON
ejpam-5430	274	4	demonstrate	demonstrate	VERB
ejpam-5430	274	5	its	its	PRON
ejpam-5430	274	6	connections	connection	NOUN
ejpam-5430	274	7	to	to	ADP
ejpam-5430	274	8	various	various	ADJ
ejpam-5430	274	9	forms	form	NOUN
ejpam-5430	274	10	of	of	ADP
ejpam-5430	274	11	pyfs	pyfs	ADJ
ejpam-5430	274	12	continuity	continuity	NOUN
ejpam-5430	274	13	.	.	PUNCT
ejpam-5430	275	1	in	in	ADP
ejpam-5430	275	2	conclusion	conclusion	NOUN
ejpam-5430	275	3	,	,	PUNCT
ejpam-5430	275	4	we	we	PRON
ejpam-5430	275	5	obtain	obtain	VERB
ejpam-5430	275	6	certain	certain	ADJ
ejpam-5430	275	7	findings	finding	NOUN
ejpam-5430	275	8	about	about	ADP
ejpam-5430	275	9	hyperconnected	hyperconnected	ADJ
ejpam-5430	275	10	and	and	CCONJ
ejpam-5430	275	11	pyfs	pyfs	ADJ
ejpam-5430	275	12	separable	separable	ADJ
ejpam-5430	275	13	spaces	space	NOUN
ejpam-5430	275	14	.	.	PUNCT
ejpam-5430	276	1	definition	definition	NOUN
ejpam-5430	276	2	23	23	NUM
ejpam-5430	276	3	.	.	PUNCT
ejpam-5430	277	1	consider	consider	VERB
ejpam-5430	277	2	(	(	PUNCT
ejpam-5430	277	3	x̃	x̃	PROPN
ejpam-5430	277	4	,	,	PUNCT
ejpam-5430	277	5	ω̃1	ω̃1	PROPN
ejpam-5430	277	6	,	,	PUNCT
ejpam-5430	277	7	η̃1	η̃1	PROPN
ejpam-5430	277	8	)	)	PUNCT
ejpam-5430	277	9	and	and	CCONJ
ejpam-5430	277	10	(	(	PUNCT
ejpam-5430	277	11	ỹ	ỹ	PROPN
ejpam-5430	277	12	,	,	PUNCT
ejpam-5430	277	13	ω̃2	ω̃2	PROPN
ejpam-5430	277	14	,	,	PUNCT
ejpam-5430	277	15	η̃2	η̃2	PROPN
ejpam-5430	277	16	)	)	PUNCT
ejpam-5430	277	17	are	be	AUX
ejpam-5430	277	18	a	a	DET
ejpam-5430	277	19	pyfstss	pyfstss	NOUN
ejpam-5430	277	20	.	.	PUNCT
ejpam-5430	278	1	if	if	SCONJ
ejpam-5430	278	2	every	every	DET
ejpam-5430	278	3	pyfs	pyfs	ADJ
ejpam-5430	278	4	open	open	NOUN
ejpam-5430	278	5	set	set	VERB
ejpam-5430	278	6	over	over	ADP
ejpam-5430	278	7	ỹ	ỹ	PROPN
ejpam-5430	278	8	has	have	VERB
ejpam-5430	278	9	an	an	DET
ejpam-5430	278	10	inverse	inverse	ADJ
ejpam-5430	278	11	image	image	NOUN
ejpam-5430	278	12	that	that	PRON
ejpam-5430	278	13	is	be	AUX
ejpam-5430	278	14	also	also	ADV
ejpam-5430	278	15	pyfssw	pyfssw	ADV
ejpam-5430	278	16	open	open	ADJ
ejpam-5430	278	17	over	over	ADP
ejpam-5430	278	18	x̃	x̃	PROPN
ejpam-5430	278	19	,	,	PUNCT
ejpam-5430	278	20	then	then	ADV
ejpam-5430	278	21	the	the	DET
ejpam-5430	278	22	function	function	NOUN
ejpam-5430	278	23	f	f	NOUN
ejpam-5430	278	24	:	:	PUNCT
ejpam-5430	278	25	(	(	PUNCT
ejpam-5430	278	26	x̃	x̃	PROPN
ejpam-5430	278	27	,	,	PUNCT
ejpam-5430	278	28	ω̃1	ω̃1	PROPN
ejpam-5430	278	29	,	,	PUNCT
ejpam-5430	278	30	η̃1	η̃1	PROPN
ejpam-5430	278	31	)	)	PUNCT
ejpam-5430	278	32	→	→	PUNCT
ejpam-5430	278	33	(	(	PUNCT
ejpam-5430	278	34	ỹ	ỹ	PROPN
ejpam-5430	278	35	,	,	PUNCT
ejpam-5430	278	36	ω̃2	ω̃2	PROPN
ejpam-5430	278	37	,	,	PUNCT
ejpam-5430	278	38	η̃2	η̃2	PROPN
ejpam-5430	278	39	)	)	PUNCT
ejpam-5430	278	40	is	be	AUX
ejpam-5430	278	41	considered	consider	VERB
ejpam-5430	278	42	pyfssw	pyfssw	ADJ
ejpam-5430	278	43	-	-	PUNCT
ejpam-5430	278	44	c.	c.	NOUN
ejpam-5430	278	45	remark	remark	NOUN
ejpam-5430	278	46	3	3	NUM
ejpam-5430	278	47	.	.	PUNCT
ejpam-5430	279	1	a	a	DET
ejpam-5430	279	2	function	function	NOUN
ejpam-5430	279	3	f	f	NOUN
ejpam-5430	279	4	:	:	PUNCT
ejpam-5430	279	5	(	(	PUNCT
ejpam-5430	279	6	x̃	x̃	PROPN
ejpam-5430	279	7	,	,	PUNCT
ejpam-5430	279	8	ω̃1	ω̃1	PROPN
ejpam-5430	279	9	,	,	PUNCT
ejpam-5430	279	10	η̃1	η̃1	PROPN
ejpam-5430	279	11	)	)	PUNCT
ejpam-5430	279	12	→	→	PUNCT
ejpam-5430	279	13	(	(	PUNCT
ejpam-5430	279	14	ỹ	ỹ	PROPN
ejpam-5430	279	15	,	,	PUNCT
ejpam-5430	279	16	ω̃2	ω̃2	PROPN
ejpam-5430	279	17	,	,	PUNCT
ejpam-5430	279	18	η̃2	η̃2	PROPN
ejpam-5430	279	19	)	)	PUNCT
ejpam-5430	279	20	is	be	AUX
ejpam-5430	279	21	pyfssw	pyfssw	ADJ
ejpam-5430	279	22	-	-	PUNCT
ejpam-5430	279	23	c	c	NOUN
ejpam-5430	279	24	if	if	SCONJ
ejpam-5430	279	25	each	each	DET
ejpam-5430	279	26	pxa	pxa	NOUN
ejpam-5430	279	27	∈	∈	PROPN
ejpam-5430	279	28	x̃	x̃	PROPN
ejpam-5430	279	29	and	and	CCONJ
ejpam-5430	279	30	each	each	DET
ejpam-5430	279	31	pyfs	pyfs	ADJ
ejpam-5430	279	32	open	open	ADJ
ejpam-5430	279	33	set	set	VERB
ejpam-5430	279	34	vη̃2	vη̃2	NOUN
ejpam-5430	279	35	over	over	ADP
ejpam-5430	279	36	ỹ	ỹ	PROPN
ejpam-5430	279	37	⊒	⊒	SYM
ejpam-5430	279	38	f(pxa	f(pxa	PROPN
ejpam-5430	279	39	)	)	PUNCT
ejpam-5430	279	40	,	,	PUNCT
ejpam-5430	279	41	there	there	PRON
ejpam-5430	279	42	is	be	VERB
ejpam-5430	279	43	a	a	DET
ejpam-5430	279	44	pyfssw	pyfssw	ADJ
ejpam-5430	279	45	open	open	NOUN
ejpam-5430	279	46	set	set	VERB
ejpam-5430	279	47	uη̃	uη̃	INTJ
ejpam-5430	279	48	on	on	ADP
ejpam-5430	279	49	x̃	x̃	PROPN
ejpam-5430	279	50	⊒	⊒	PROPN
ejpam-5430	279	51	pxa	pxa	VERB
ejpam-5430	279	52	that	that	SCONJ
ejpam-5430	279	53	f(uη̃	f(uη̃	PROPN
ejpam-5430	279	54	)	)	PUNCT
ejpam-5430	280	1	⊑	⊑	PRON
ejpam-5430	280	2	vη̃2	vη̃2	PROPN
ejpam-5430	280	3	.	.	PUNCT
ejpam-5430	281	1	based	base	VERB
ejpam-5430	281	2	on	on	ADP
ejpam-5430	281	3	figure	figure	NOUN
ejpam-5430	281	4	1	1	NUM
ejpam-5430	281	5	,	,	PUNCT
ejpam-5430	281	6	we	we	PRON
ejpam-5430	281	7	deduce	deduce	VERB
ejpam-5430	281	8	that	that	SCONJ
ejpam-5430	281	9	the	the	DET
ejpam-5430	281	10	ramifications	ramification	NOUN
ejpam-5430	281	11	shown	show	VERB
ejpam-5430	281	12	in	in	ADP
ejpam-5430	281	13	the	the	DET
ejpam-5430	281	14	above	above	ADJ
ejpam-5430	281	15	graphic	graphic	NOUN
ejpam-5430	281	16	are	be	AUX
ejpam-5430	281	17	all	all	ADV
ejpam-5430	281	18	irreversible	irreversible	ADJ
ejpam-5430	281	19	.	.	PUNCT
ejpam-5430	282	1	example	example	NOUN
ejpam-5430	283	1	4	4	X
ejpam-5430	283	2	.	.	PUNCT
ejpam-5430	283	3	let	let	VERB
ejpam-5430	283	4	x̃	x̃	PROPN
ejpam-5430	283	5	=	=	PRON
ejpam-5430	283	6	{	{	PUNCT
ejpam-5430	283	7	x1	x1	PROPN
ejpam-5430	283	8	,	,	PUNCT
ejpam-5430	283	9	x2	x2	PROPN
ejpam-5430	283	10	,	,	PUNCT
ejpam-5430	283	11	x3	x3	ADJ
ejpam-5430	283	12	}	}	PUNCT
ejpam-5430	283	13	,	,	PUNCT
ejpam-5430	283	14	η	η	PROPN
ejpam-5430	283	15	=	=	SYM
ejpam-5430	283	16	{	{	PUNCT
ejpam-5430	283	17	a1	a1	PROPN
ejpam-5430	283	18	,	,	PUNCT
ejpam-5430	283	19	a2	a2	PROPN
ejpam-5430	283	20	}	}	PUNCT
ejpam-5430	283	21	,	,	PUNCT
ejpam-5430	283	22	and	and	CCONJ
ejpam-5430	283	23	ω̃	ω̃	NUM
ejpam-5430	283	24	=	=	SYM
ejpam-5430	283	25	{	{	PUNCT
ejpam-5430	283	26	0̃	0̃	NOUN
ejpam-5430	283	27	,	,	PUNCT
ejpam-5430	283	28	fη̃	fη̃	PRON
ejpam-5430	283	29	,	,	PUNCT
ejpam-5430	283	30	gη̃	gη̃	PROPN
ejpam-5430	283	31	,	,	PUNCT
ejpam-5430	283	32	1̃	1̃	NUM
ejpam-5430	283	33	}	}	PUNCT
ejpam-5430	283	34	,	,	PUNCT
ejpam-5430	283	35	where	where	SCONJ
ejpam-5430	283	36	fη̃	fη̃	NOUN
ejpam-5430	283	37	=	=	SYM
ejpam-5430	283	38	{	{	PUNCT
ejpam-5430	283	39	(	(	PUNCT
ejpam-5430	283	40	a1	a1	NOUN
ejpam-5430	283	41	,	,	PUNCT
ejpam-5430	283	42	{	{	PUNCT
ejpam-5430	283	43	x2	x2	ADJ
ejpam-5430	283	44	}	}	PUNCT
ejpam-5430	283	45	)	)	PUNCT
ejpam-5430	283	46	,	,	PUNCT
ejpam-5430	283	47	(	(	PUNCT
ejpam-5430	283	48	a2	a2	PROPN
ejpam-5430	283	49	,	,	PUNCT
ejpam-5430	283	50	{	{	PUNCT
ejpam-5430	283	51	x2	x2	ADJ
ejpam-5430	283	52	}	}	PUNCT
ejpam-5430	283	53	)	)	PUNCT
ejpam-5430	283	54	}	}	PUNCT
ejpam-5430	283	55	gη̃	gη̃	X
ejpam-5430	283	56	=	=	SYM
ejpam-5430	283	57	{	{	PUNCT
ejpam-5430	283	58	(	(	PUNCT
ejpam-5430	283	59	a1	a1	NOUN
ejpam-5430	283	60	,	,	PUNCT
ejpam-5430	283	61	{	{	PUNCT
ejpam-5430	283	62	x1	x1	ADJ
ejpam-5430	283	63	,	,	PUNCT
ejpam-5430	283	64	x3	x3	ADJ
ejpam-5430	283	65	}	}	PUNCT
ejpam-5430	283	66	)	)	PUNCT
ejpam-5430	283	67	,	,	PUNCT
ejpam-5430	283	68	(	(	PUNCT
ejpam-5430	283	69	a2	a2	PROPN
ejpam-5430	283	70	,	,	PUNCT
ejpam-5430	283	71	{	{	PUNCT
ejpam-5430	283	72	x1	x1	PROPN
ejpam-5430	283	73	,	,	PUNCT
ejpam-5430	283	74	x3	x3	ADJ
ejpam-5430	283	75	}	}	PUNCT
ejpam-5430	283	76	)	)	PUNCT
ejpam-5430	283	77	}	}	PUNCT
ejpam-5430	283	78	and	and	CCONJ
ejpam-5430	283	79	ω̃1	ω̃1	PROPN
ejpam-5430	283	80	=	=	SYM
ejpam-5430	283	81	{	{	PUNCT
ejpam-5430	283	82	0̃	0̃	PROPN
ejpam-5430	283	83	,	,	PUNCT
ejpam-5430	283	84	hη̃	hη̃	NOUN
ejpam-5430	283	85	,	,	PUNCT
ejpam-5430	283	86	1̃	1̃	NUM
ejpam-5430	283	87	}	}	PUNCT
ejpam-5430	283	88	where	where	SCONJ
ejpam-5430	283	89	hη̃	hη̃	PROPN
ejpam-5430	283	90	=	=	SYM
ejpam-5430	283	91	{	{	PUNCT
ejpam-5430	283	92	(	(	PUNCT
ejpam-5430	283	93	a1	a1	PROPN
ejpam-5430	283	94	,	,	PUNCT
ejpam-5430	283	95	x̃	x̃	PROPN
ejpam-5430	283	96	}	}	PUNCT
ejpam-5430	283	97	)	)	PUNCT
ejpam-5430	283	98	,	,	PUNCT
ejpam-5430	283	99	(	(	PUNCT
ejpam-5430	283	100	a2	a2	PROPN
ejpam-5430	283	101	,	,	PUNCT
ejpam-5430	283	102	{	{	PUNCT
ejpam-5430	283	103	x1	x1	PROPN
ejpam-5430	283	104	,	,	PUNCT
ejpam-5430	283	105	x2	x2	PROPN
ejpam-5430	283	106	}	}	PUNCT
ejpam-5430	283	107	)	)	PUNCT
ejpam-5430	283	108	}	}	PUNCT
ejpam-5430	283	109	.	.	PUNCT
ejpam-5430	284	1	let	let	VERB
ejpam-5430	284	2	f	f	NOUN
ejpam-5430	284	3	:	:	PUNCT
ejpam-5430	284	4	(	(	PUNCT
ejpam-5430	284	5	x̃	x̃	PROPN
ejpam-5430	284	6	,	,	PUNCT
ejpam-5430	284	7	ω̃1	ω̃1	PROPN
ejpam-5430	284	8	,	,	PUNCT
ejpam-5430	284	9	η̃	η̃	PROPN
ejpam-5430	284	10	)	)	PUNCT
ejpam-5430	284	11	→	→	SYM
ejpam-5430	284	12	(	(	PUNCT
ejpam-5430	284	13	x̃	x̃	PROPN
ejpam-5430	284	14	,	,	PUNCT
ejpam-5430	284	15	ω̃2	ω̃2	PROPN
ejpam-5430	284	16	,	,	PUNCT
ejpam-5430	284	17	η̃	η̃	PROPN
ejpam-5430	284	18	)	)	PUNCT
ejpam-5430	284	19	be	be	VERB
ejpam-5430	284	20	the	the	DET
ejpam-5430	284	21	pyfs	pyfs	ADJ
ejpam-5430	284	22	identity	identity	NOUN
ejpam-5430	284	23	function	function	NOUN
ejpam-5430	284	24	.	.	PUNCT
ejpam-5430	285	1	at	at	ADP
ejpam-5430	285	2	hence	hence	ADV
ejpam-5430	285	3	,	,	PUNCT
ejpam-5430	285	4	f	f	PROPN
ejpam-5430	285	5	is	be	AUX
ejpam-5430	285	6	pyfssw	pyfssw	ADJ
ejpam-5430	285	7	-	-	PUNCT
ejpam-5430	285	8	c	c	NOUN
ejpam-5430	285	9	but	but	CCONJ
ejpam-5430	285	10	not	not	PART
ejpam-5430	285	11	pyfssw	pyfssw	ADV
ejpam-5430	285	12	-	-	PUNCT
ejpam-5430	285	13	semicontinuous	semicontinuous	ADJ
ejpam-5430	285	14	.	.	PUNCT
ejpam-5430	286	1	example	example	NOUN
ejpam-5430	287	1	5	5	NUM
ejpam-5430	287	2	.	.	PUNCT
ejpam-5430	288	1	let	let	VERB
ejpam-5430	288	2	x̃	x̃	PROPN
ejpam-5430	288	3	=	=	SYM
ejpam-5430	288	4	ℜ	ℜ	PROPN
ejpam-5430	288	5	be	be	AUX
ejpam-5430	288	6	the	the	DET
ejpam-5430	288	7	set	set	NOUN
ejpam-5430	288	8	of	of	ADP
ejpam-5430	288	9	real	real	ADJ
ejpam-5430	288	10	numbers	number	NOUN
ejpam-5430	288	11	and	and	CCONJ
ejpam-5430	288	12	η	η	PROPN
ejpam-5430	288	13	=	=	PROPN
ejpam-5430	288	14	{	{	PUNCT
ejpam-5430	288	15	a	a	PRON
ejpam-5430	288	16	}	}	PUNCT
ejpam-5430	288	17	be	be	AUX
ejpam-5430	288	18	a	a	DET
ejpam-5430	288	19	collection	collection	NOUN
ejpam-5430	288	20	of	of	ADP
ejpam-5430	288	21	parameters	parameter	NOUN
ejpam-5430	288	22	.	.	PUNCT
ejpam-5430	289	1	let	let	VERB
ejpam-5430	289	2	ω̃	ω̃	PRON
ejpam-5430	289	3	be	be	AUX
ejpam-5430	289	4	the	the	DET
ejpam-5430	289	5	pyfst	pyfst	NOUN
ejpam-5430	289	6	on	on	ADP
ejpam-5430	289	7	ℜ	ℜ	PROPN
ejpam-5430	289	8	generated	generate	VERB
ejpam-5430	289	9	by	by	ADP
ejpam-5430	289	10	{	{	PUNCT
ejpam-5430	289	11	(	(	PUNCT
ejpam-5430	289	12	a	a	PRON
ejpam-5430	289	13	,	,	PUNCT
ejpam-5430	289	14	ξ(a	ξ(a	NUM
ejpam-5430	289	15	)	)	PUNCT
ejpam-5430	289	16	)	)	PUNCT
ejpam-5430	289	17	:	:	PUNCT
ejpam-5430	290	1	(	(	PUNCT
ejpam-5430	290	2	x1	x1	ADJ
ejpam-5430	290	3	,	,	PUNCT
ejpam-5430	290	4	x2	x2	ADJ
ejpam-5430	290	5	)	)	PUNCT
ejpam-5430	290	6	∈	∈	PROPN
ejpam-5430	290	7	ℜ;x1	ℜ;x1	VERB
ejpam-5430	290	8	<	<	X
ejpam-5430	290	9	x2	x2	X
ejpam-5430	290	10	}	}	PUNCT
ejpam-5430	290	11	.	.	PUNCT
ejpam-5430	291	1	define	define	VERB
ejpam-5430	291	2	a	a	DET
ejpam-5430	291	3	pyfs	pyfs	ADJ
ejpam-5430	291	4	function	function	NOUN
ejpam-5430	291	5	f	f	NOUN
ejpam-5430	291	6	:	:	PUNCT
ejpam-5430	291	7	(	(	PUNCT
ejpam-5430	291	8	x̃	x̃	PROPN
ejpam-5430	291	9	,	,	PUNCT
ejpam-5430	291	10	ω̃	ω̃	PROPN
ejpam-5430	291	11	,	,	PUNCT
ejpam-5430	291	12	η̃	η̃	PROPN
ejpam-5430	291	13	)	)	PUNCT
ejpam-5430	291	14	→	→	SYM
ejpam-5430	291	15	(	(	PUNCT
ejpam-5430	291	16	x̃	x̃	PROPN
ejpam-5430	291	17	,	,	PUNCT
ejpam-5430	291	18	ω̃	ω̃	PROPN
ejpam-5430	291	19	,	,	PUNCT
ejpam-5430	291	20	η̃	η̃	PROPN
ejpam-5430	291	21	)	)	PUNCT
ejpam-5430	291	22	by	by	ADP
ejpam-5430	291	23	a.	a.	PROPN
ejpam-5430	291	24	a.	a.	PROPN
ejpam-5430	291	25	azzam	azzam	PROPN
ejpam-5430	291	26	,	,	PUNCT
ejpam-5430	291	27	m.	m.	NOUN
ejpam-5430	291	28	aldawood	aldawood	PROPN
ejpam-5430	291	29	,	,	PUNCT
ejpam-5430	291	30	r.	r.	PROPN
ejpam-5430	291	31	abu	abu	PROPN
ejpam-5430	291	32	-	-	PUNCT
ejpam-5430	291	33	gdairi	gdairi	PROPN
ejpam-5430	291	34	/	/	SYM
ejpam-5430	291	35	eur	eur	PROPN
ejpam-5430	291	36	.	.	PUNCT
ejpam-5430	292	1	j.	j.	PROPN
ejpam-5430	292	2	pure	pure	PROPN
ejpam-5430	292	3	appl	appl	PROPN
ejpam-5430	292	4	.	.	PROPN
ejpam-5430	292	5	math	math	PROPN
ejpam-5430	292	6	,	,	PUNCT
ejpam-5430	292	7	17	17	NUM
ejpam-5430	292	8	(	(	PUNCT
ejpam-5430	292	9	4	4	NUM
ejpam-5430	292	10	)	)	PUNCT
ejpam-5430	292	11	(	(	PUNCT
ejpam-5430	292	12	2024	2024	NUM
ejpam-5430	292	13	)	)	PUNCT
ejpam-5430	292	14	,	,	PUNCT
ejpam-5430	292	15	4147	4147	NUM
ejpam-5430	292	16	-	-	SYM
ejpam-5430	292	17	4163	4163	NUM
ejpam-5430	292	18	4157	4157	NUM
ejpam-5430	292	19	figure	figure	NOUN
ejpam-5430	292	20	2	2	NUM
ejpam-5430	292	21	:	:	PUNCT
ejpam-5430	292	22	the	the	DET
ejpam-5430	292	23	relationships	relationship	NOUN
ejpam-5430	292	24	between	between	ADP
ejpam-5430	292	25	some	some	DET
ejpam-5430	292	26	generalizations	generalization	NOUN
ejpam-5430	292	27	of	of	ADP
ejpam-5430	292	28	pyfs	pyfs	ADJ
ejpam-5430	292	29	continuous	continuous	ADJ
ejpam-5430	292	30	.	.	PUNCT
ejpam-5430	293	1	f(x	f(x	NOUN
ejpam-5430	293	2	)	)	PUNCT
ejpam-5430	294	1	=	=	PUNCT
ejpam-5430	295	1			NOUN
ejpam-5430	295	2	x	x	PUNCT
ejpam-5430	295	3	if	if	SCONJ
ejpam-5430	295	4	x	x	X
ejpam-5430	295	5	/∈	/∈	PUNCT
ejpam-5430	295	6	{	{	PUNCT
ejpam-5430	295	7	0̃	0̃	NOUN
ejpam-5430	295	8	,	,	PUNCT
ejpam-5430	295	9	1̃}η̃	1̃}η̃	NUM
ejpam-5430	295	10	,	,	PUNCT
ejpam-5430	295	11	0	0	PUNCT
ejpam-5430	295	12	if	if	SCONJ
ejpam-5430	295	13	x	x	X
ejpam-5430	295	14	=	=	SYM
ejpam-5430	295	15	1	1	NUM
ejpam-5430	295	16	,	,	PUNCT
ejpam-5430	295	17	1	1	NUM
ejpam-5430	295	18	if	if	SCONJ
ejpam-5430	295	19	x	x	X
ejpam-5430	295	20	=	=	NOUN
ejpam-5430	295	21	0	0	NUM
ejpam-5430	295	22	.	.	PUNCT
ejpam-5430	296	1	given	give	VERB
ejpam-5430	296	2	that	that	SCONJ
ejpam-5430	296	3	every	every	DET
ejpam-5430	296	4	pyfs	pyfs	ADJ
ejpam-5430	296	5	basic	basic	ADJ
ejpam-5430	296	6	open	open	ADJ
ejpam-5430	296	7	set	set	NOUN
ejpam-5430	296	8	has	have	AUX
ejpam-5430	296	9	an	an	DET
ejpam-5430	296	10	inverse	inverse	ADJ
ejpam-5430	296	11	image	image	NOUN
ejpam-5430	296	12	that	that	PRON
ejpam-5430	296	13	also	also	ADV
ejpam-5430	296	14	contains	contain	VERB
ejpam-5430	296	15	another	another	DET
ejpam-5430	296	16	pyfs	pyfs	ADJ
ejpam-5430	296	17	basic	basic	ADJ
ejpam-5430	296	18	open	open	NOUN
ejpam-5430	296	19	,	,	PUNCT
ejpam-5430	296	20	one	one	PRON
ejpam-5430	296	21	can	can	AUX
ejpam-5430	296	22	simply	simply	ADV
ejpam-5430	296	23	demonstrate	demonstrate	VERB
ejpam-5430	296	24	that	that	SCONJ
ejpam-5430	296	25	f	f	PROPN
ejpam-5430	296	26	is	be	AUX
ejpam-5430	296	27	pyfssw	pyfssw	ADJ
ejpam-5430	296	28	-	-	PUNCT
ejpam-5430	296	29	c	c	NOUN
ejpam-5430	296	30	(	(	PUNCT
ejpam-5430	296	31	and	and	CCONJ
ejpam-5430	296	32	hence	hence	ADV
ejpam-5430	296	33	,	,	PUNCT
ejpam-5430	296	34	pyfs	pyfs	ADJ
ejpam-5430	296	35	sd	sd	NOUN
ejpam-5430	296	36	-	-	PUNCT
ejpam-5430	296	37	c	c	NOUN
ejpam-5430	296	38	)	)	PUNCT
ejpam-5430	296	39	,	,	PUNCT
ejpam-5430	296	40	since	since	SCONJ
ejpam-5430	296	41	its	its	PRON
ejpam-5430	296	42	pyfs	pyfs	ADJ
ejpam-5430	296	43	interior	interior	NOUN
ejpam-5430	296	44	can	can	AUX
ejpam-5430	296	45	not	not	PART
ejpam-5430	296	46	be	be	AUX
ejpam-5430	296	47	null	null	ADJ
ejpam-5430	296	48	.	.	PUNCT
ejpam-5430	297	1	however	however	ADV
ejpam-5430	297	2	,	,	PUNCT
ejpam-5430	297	3	f	f	PROPN
ejpam-5430	297	4	is	be	AUX
ejpam-5430	297	5	not	not	PART
ejpam-5430	297	6	pyfsβ	pyfsβ	ADJ
ejpam-5430	297	7	-	-	PUNCT
ejpam-5430	297	8	c.	c.	NOUN
ejpam-5430	297	9	let	let	VERB
ejpam-5430	297	10	gη̃	gη̃	X
ejpam-5430	297	11	=	=	PRON
ejpam-5430	297	12	{	{	PUNCT
ejpam-5430	297	13	(	(	PUNCT
ejpam-5430	297	14	a	a	PRON
ejpam-5430	297	15	,	,	PUNCT
ejpam-5430	297	16	(	(	PUNCT
ejpam-5430	297	17	−ε	−ε	NOUN
ejpam-5430	297	18	,	,	PUNCT
ejpam-5430	297	19	ε	ε	PROPN
ejpam-5430	297	20	)	)	PUNCT
ejpam-5430	297	21	)	)	PUNCT
ejpam-5430	297	22	}	}	PUNCT
ejpam-5430	297	23	be	be	AUX
ejpam-5430	297	24	the	the	DET
ejpam-5430	297	25	pyfs	pyfs	ADJ
ejpam-5430	297	26	open	open	ADJ
ejpam-5430	297	27	set	set	NOUN
ejpam-5430	297	28	,	,	PUNCT
ejpam-5430	297	29	with	with	ADP
ejpam-5430	297	30	ε	ε	PROPN
ejpam-5430	297	31	<	<	X
ejpam-5430	297	32	1	1	NUM
ejpam-5430	297	33	.	.	PUNCT
ejpam-5430	297	34	therefore	therefore	ADV
ejpam-5430	297	35	f−1(gη̃	f−1(gη̃	NOUN
ejpam-5430	297	36	)	)	PUNCT
ejpam-5430	297	37	=	=	SYM
ejpam-5430	297	38	{	{	PUNCT
ejpam-5430	297	39	(	(	PUNCT
ejpam-5430	297	40	a	a	PRON
ejpam-5430	297	41	,	,	PUNCT
ejpam-5430	297	42	(	(	PUNCT
ejpam-5430	297	43	−ε	−ε	NOUN
ejpam-5430	297	44	,	,	PUNCT
ejpam-5430	297	45	0	0	NUM
ejpam-5430	297	46	)	)	PUNCT
ejpam-5430	297	47	)	)	PUNCT
ejpam-5430	297	48	}	}	PUNCT
ejpam-5430	298	1	⊔	⊔	NUM
ejpam-5430	298	2	{	{	PUNCT
ejpam-5430	298	3	(	(	PUNCT
ejpam-5430	298	4	a	a	DET
ejpam-5430	298	5	,	,	PUNCT
ejpam-5430	298	6	(	(	PUNCT
ejpam-5430	298	7	0	0	NUM
ejpam-5430	298	8	,	,	PUNCT
ejpam-5430	298	9	ε	ε	PROPN
ejpam-5430	298	10	)	)	PUNCT
ejpam-5430	298	11	)	)	PUNCT
ejpam-5430	298	12	}	}	PUNCT
ejpam-5430	298	13	⊔	⊔	NUM
ejpam-5430	298	14	{	{	PUNCT
ejpam-5430	298	15	(	(	PUNCT
ejpam-5430	298	16	a	a	PROPN
ejpam-5430	298	17	,	,	PUNCT
ejpam-5430	298	18	{	{	PUNCT
ejpam-5430	298	19	1	1	NUM
ejpam-5430	298	20	}	}	PUNCT
ejpam-5430	298	21	)	)	PUNCT
ejpam-5430	298	22	}	}	PUNCT
ejpam-5430	298	23	.	.	PUNCT
ejpam-5430	299	1	but	but	CCONJ
ejpam-5430	299	2	cl(int((cl(f−1(gη̃	cl(int((cl(f−1(gη̃	PROPN
ejpam-5430	299	3	)	)	PUNCT
ejpam-5430	299	4	)	)	PUNCT
ejpam-5430	299	5	)	)	PUNCT
ejpam-5430	300	1	=	=	PRON
ejpam-5430	300	2	{	{	PUNCT
ejpam-5430	300	3	(	(	PUNCT
ejpam-5430	300	4	a	a	NOUN
ejpam-5430	300	5	,	,	PUNCT
ejpam-5430	300	6	[	[	X
ejpam-5430	300	7	−ε	−ε	NOUN
ejpam-5430	300	8	,	,	PUNCT
ejpam-5430	300	9	ε	ε	PROPN
ejpam-5430	300	10	]	]	PUNCT
ejpam-5430	300	11	)	)	PUNCT
ejpam-5430	300	12	}	}	PUNCT
ejpam-5430	300	13	and	and	CCONJ
ejpam-5430	300	14	so	so	ADV
ejpam-5430	300	15	f−1(gη̃	f−1(gη̃	NOUN
ejpam-5430	300	16	)	)	PUNCT
ejpam-5430	300	17	⊈	⊈	PROPN
ejpam-5430	300	18	cl(int((cl(f−1(gη̃	cl(int((cl(f−1(gη̃	NOUN
ejpam-5430	300	19	)	)	PUNCT
ejpam-5430	300	20	)	)	PUNCT
ejpam-5430	300	21	)	)	PUNCT
ejpam-5430	300	22	.	.	PUNCT
ejpam-5430	301	1	as	as	ADP
ejpam-5430	301	2	a	a	DET
ejpam-5430	301	3	result	result	NOUN
ejpam-5430	301	4	,	,	PUNCT
ejpam-5430	301	5	f	f	PROPN
ejpam-5430	301	6	is	be	AUX
ejpam-5430	301	7	not	not	PART
ejpam-5430	301	8	pyfs	pyfs	ADJ
ejpam-5430	301	9	semicontinuous	semicontinuous	ADJ
ejpam-5430	301	10	and	and	CCONJ
ejpam-5430	301	11	can	can	AUX
ejpam-5430	301	12	not	not	PART
ejpam-5430	301	13	be	be	AUX
ejpam-5430	301	14	pyfsβ	pyfsβ	ADJ
ejpam-5430	301	15	-	-	PUNCT
ejpam-5430	301	16	c.	c.	NOUN
ejpam-5430	301	17	example	example	NOUN
ejpam-5430	301	18	6	6	NUM
ejpam-5430	301	19	.	.	PUNCT
ejpam-5430	302	1	consider	consider	VERB
ejpam-5430	302	2	the	the	DET
ejpam-5430	302	3	pyfsts	pyfst	NOUN
ejpam-5430	302	4	(	(	PUNCT
ejpam-5430	302	5	x̃	x̃	PROPN
ejpam-5430	302	6	,	,	PUNCT
ejpam-5430	302	7	ω̃	ω̃	PROPN
ejpam-5430	302	8	,	,	PUNCT
ejpam-5430	302	9	η̃	η̃	PROPN
ejpam-5430	302	10	)	)	PUNCT
ejpam-5430	302	11	as	as	SCONJ
ejpam-5430	302	12	described	describe	VERB
ejpam-5430	302	13	in	in	ADP
ejpam-5430	302	14	example	example	NOUN
ejpam-5430	302	15	4.4	4.4	NUM
ejpam-5430	302	16	.	.	PUNCT
ejpam-5430	303	1	define	define	VERB
ejpam-5430	303	2	f	f	NOUN
ejpam-5430	303	3	:	:	PUNCT
ejpam-5430	303	4	(	(	PUNCT
ejpam-5430	303	5	x̃	x̃	PROPN
ejpam-5430	303	6	,	,	PUNCT
ejpam-5430	303	7	ω̃	ω̃	PROPN
ejpam-5430	303	8	,	,	PUNCT
ejpam-5430	303	9	η̃	η̃	PROPN
ejpam-5430	303	10	)	)	PUNCT
ejpam-5430	303	11	→	→	SYM
ejpam-5430	303	12	(	(	PUNCT
ejpam-5430	303	13	x̃	x̃	PROPN
ejpam-5430	303	14	,	,	PUNCT
ejpam-5430	303	15	ω̃	ω̃	PROPN
ejpam-5430	303	16	,	,	PUNCT
ejpam-5430	303	17	η̃	η̃	PROPN
ejpam-5430	303	18	)	)	PUNCT
ejpam-5430	303	19	as	as	SCONJ
ejpam-5430	303	20	follows	follow	VERB
ejpam-5430	303	21	:	:	PUNCT
ejpam-5430	303	22	f(x	f(x	PROPN
ejpam-5430	303	23	)	)	PUNCT
ejpam-5430	304	1	=	=	PRON
ejpam-5430	304	2	{	{	PUNCT
ejpam-5430	304	3	0	0	NUM
ejpam-5430	304	4	if	if	SCONJ
ejpam-5430	304	5	x	x	X
ejpam-5430	304	6	/∈	/∈	PUNCT
ejpam-5430	304	7	qη̃	qη̃	NOUN
ejpam-5430	304	8	,	,	PUNCT
ejpam-5430	304	9	1	1	NUM
ejpam-5430	304	10	if	if	SCONJ
ejpam-5430	304	11	x	x	SYM
ejpam-5430	304	12	∈	∈	PROPN
ejpam-5430	304	13	qη̃.	qη̃.	NOUN
ejpam-5430	304	14	in	in	ADP
ejpam-5430	304	15	such	such	ADJ
ejpam-5430	304	16	case	case	NOUN
ejpam-5430	304	17	,	,	PUNCT
ejpam-5430	304	18	f	f	PROPN
ejpam-5430	304	19	is	be	AUX
ejpam-5430	304	20	not	not	PART
ejpam-5430	304	21	pyfssw	pyfssw	ADV
ejpam-5430	304	22	-	-	PUNCT
ejpam-5430	304	23	continuous	continuous	ADJ
ejpam-5430	304	24	but	but	CCONJ
ejpam-5430	304	25	soft	soft	ADJ
ejpam-5430	304	26	sd	sd	NOUN
ejpam-5430	304	27	-	-	PUNCT
ejpam-5430	304	28	continuous	continuous	ADJ
ejpam-5430	304	29	.	.	PUNCT
ejpam-5430	305	1	any	any	DET
ejpam-5430	305	2	pyfs	pyfs	ADJ
ejpam-5430	305	3	open	open	NOUN
ejpam-5430	305	4	set	set	VERB
ejpam-5430	305	5	with	with	ADP
ejpam-5430	305	6	only	only	ADV
ejpam-5430	305	7	one	one	NUM
ejpam-5430	305	8	element	element	NOUN
ejpam-5430	305	9	is	be	AUX
ejpam-5430	305	10	its	its	PRON
ejpam-5430	305	11	inverse	inverse	NOUN
ejpam-5430	305	12	image	image	NOUN
ejpam-5430	305	13	,	,	PUNCT
ejpam-5430	305	14	and	and	CCONJ
ejpam-5430	305	15	qη̃	qη̃	VERB
ejpam-5430	305	16	is	be	AUX
ejpam-5430	305	17	not	not	PART
ejpam-5430	305	18	a	a	DET
ejpam-5430	305	19	pyfssw	pyfssw	ADV
ejpam-5430	305	20	-	-	PUNCT
ejpam-5430	305	21	open	open	NOUN
ejpam-5430	305	22	set	set	NOUN
ejpam-5430	305	23	over	over	ADP
ejpam-5430	305	24	x̃.	x̃.	PROPN
ejpam-5430	305	25	a.	a.	NOUN
ejpam-5430	305	26	a.	a.	PROPN
ejpam-5430	305	27	azzam	azzam	PROPN
ejpam-5430	305	28	,	,	PUNCT
ejpam-5430	305	29	m.	m.	NOUN
ejpam-5430	305	30	aldawood	aldawood	PROPN
ejpam-5430	305	31	,	,	PUNCT
ejpam-5430	305	32	r.	r.	PROPN
ejpam-5430	305	33	abu	abu	PROPN
ejpam-5430	305	34	-	-	PUNCT
ejpam-5430	305	35	gdairi	gdairi	PROPN
ejpam-5430	305	36	/	/	SYM
ejpam-5430	305	37	eur	eur	PROPN
ejpam-5430	305	38	.	.	PUNCT
ejpam-5430	306	1	j.	j.	PROPN
ejpam-5430	306	2	pure	pure	PROPN
ejpam-5430	306	3	appl	appl	PROPN
ejpam-5430	306	4	.	.	PROPN
ejpam-5430	306	5	math	math	PROPN
ejpam-5430	306	6	,	,	PUNCT
ejpam-5430	306	7	17	17	NUM
ejpam-5430	306	8	(	(	PUNCT
ejpam-5430	306	9	4	4	NUM
ejpam-5430	306	10	)	)	PUNCT
ejpam-5430	306	11	(	(	PUNCT
ejpam-5430	306	12	2024	2024	NUM
ejpam-5430	306	13	)	)	PUNCT
ejpam-5430	306	14	,	,	PUNCT
ejpam-5430	306	15	4147	4147	NUM
ejpam-5430	306	16	-	-	SYM
ejpam-5430	306	17	4163	4163	NUM
ejpam-5430	306	18	4158	4158	NUM
ejpam-5430	306	19	definition	definition	NOUN
ejpam-5430	306	20	24	24	NUM
ejpam-5430	306	21	.	.	PUNCT
ejpam-5430	307	1	we	we	PRON
ejpam-5430	307	2	introduce	introduce	VERB
ejpam-5430	307	3	the	the	DET
ejpam-5430	307	4	following	following	NOUN
ejpam-5430	307	5	for	for	ADP
ejpam-5430	307	6	a	a	DET
ejpam-5430	307	7	subset	subset	NOUN
ejpam-5430	307	8	gη̃	gη̃	PROPN
ejpam-5430	307	9	of	of	ADP
ejpam-5430	307	10	a	a	DET
ejpam-5430	307	11	pyfsts	pyfst	NOUN
ejpam-5430	307	12	(	(	PUNCT
ejpam-5430	307	13	x̃	x̃	PROPN
ejpam-5430	307	14	,	,	PUNCT
ejpam-5430	307	15	ω̃	ω̃	PROPN
ejpam-5430	307	16	,	,	PUNCT
ejpam-5430	307	17	η̃	η̃	PROPN
ejpam-5430	307	18	):	):	PUNCT
ejpam-5430	307	19	1	1	NUM
ejpam-5430	307	20	-	-	PUNCT
ejpam-5430	307	21	clsw(gη̃	clsw(gη̃	NUM
ejpam-5430	307	22	)	)	PUNCT
ejpam-5430	308	1	=	=	SYM
ejpam-5430	308	2	⊓{fη̃	⊓{fη̃	NOUN
ejpam-5430	308	3	:	:	PUNCT
ejpam-5430	308	4	fη̃	fη̃	PRON
ejpam-5430	308	5	is	be	AUX
ejpam-5430	308	6	pyfssw	pyfssw	ADV
ejpam-5430	308	7	-	-	PUNCT
ejpam-5430	308	8	closed	close	VERB
ejpam-5430	308	9	over	over	ADP
ejpam-5430	308	10	x̃	x̃	PROPN
ejpam-5430	308	11	and	and	CCONJ
ejpam-5430	308	12	gη̃	gη̃	PROPN
ejpam-5430	308	13	⊑	⊑	PRON
ejpam-5430	308	14	fη̃	fη̃	NOUN
ejpam-5430	308	15	}	}	PUNCT
ejpam-5430	308	16	.	.	PUNCT
ejpam-5430	309	1	2	2	NUM
ejpam-5430	309	2	-	-	PUNCT
ejpam-5430	309	3	intsw(gη̃	intsw(gη̃	NOUN
ejpam-5430	309	4	)	)	PUNCT
ejpam-5430	310	1	=	=	VERB
ejpam-5430	310	2	⊔{oη̃	⊔{oη̃	ADJ
ejpam-5430	310	3	:	:	PUNCT
ejpam-5430	310	4	oη̃	oη̃	ADV
ejpam-5430	310	5	is	be	AUX
ejpam-5430	310	6	pyfssw	pyfssw	ADV
ejpam-5430	310	7	-	-	PUNCT
ejpam-5430	310	8	open	open	ADJ
ejpam-5430	310	9	over	over	ADP
ejpam-5430	310	10	x̃	x̃	PROPN
ejpam-5430	310	11	and	and	CCONJ
ejpam-5430	310	12	oη̃	oη̃	ADP
ejpam-5430	310	13	⊑	⊑	PRON
ejpam-5430	310	14	gη̃	gη̃	NOUN
ejpam-5430	310	15	}	}	PUNCT
ejpam-5430	310	16	.	.	PUNCT
ejpam-5430	311	1	proposition	proposition	NOUN
ejpam-5430	311	2	5	5	NUM
ejpam-5430	311	3	.	.	PUNCT
ejpam-5430	312	1	consider	consider	VERB
ejpam-5430	312	2	(	(	PUNCT
ejpam-5430	312	3	x̃	x̃	PROPN
ejpam-5430	312	4	,	,	PUNCT
ejpam-5430	312	5	ω̃1	ω̃1	PROPN
ejpam-5430	312	6	,	,	PUNCT
ejpam-5430	312	7	η̃1	η̃1	PROPN
ejpam-5430	312	8	)	)	PUNCT
ejpam-5430	312	9	and	and	CCONJ
ejpam-5430	312	10	(	(	PUNCT
ejpam-5430	312	11	ỹ	ỹ	PROPN
ejpam-5430	312	12	,	,	PUNCT
ejpam-5430	312	13	ω̃2	ω̃2	PROPN
ejpam-5430	312	14	,	,	PUNCT
ejpam-5430	312	15	η̃2	η̃2	PROPN
ejpam-5430	312	16	)	)	PUNCT
ejpam-5430	313	1	that	that	SCONJ
ejpam-5430	313	2	a	a	DET
ejpam-5430	313	3	pyfstss	pyfstss	NOUN
ejpam-5430	313	4	.	.	PUNCT
ejpam-5430	314	1	the	the	DET
ejpam-5430	314	2	function	function	NOUN
ejpam-5430	314	3	f	f	NOUN
ejpam-5430	314	4	:	:	PUNCT
ejpam-5430	314	5	(	(	PUNCT
ejpam-5430	314	6	x̃	x̃	PROPN
ejpam-5430	314	7	,	,	PUNCT
ejpam-5430	314	8	ω̃1	ω̃1	PROPN
ejpam-5430	314	9	,	,	PUNCT
ejpam-5430	314	10	η̃1	η̃1	PROPN
ejpam-5430	314	11	)	)	PUNCT
ejpam-5430	314	12	→	→	PUNCT
ejpam-5430	314	13	(	(	PUNCT
ejpam-5430	314	14	ỹ	ỹ	PROPN
ejpam-5430	314	15	,	,	PUNCT
ejpam-5430	314	16	ω̃2	ω̃2	PROPN
ejpam-5430	314	17	,	,	PUNCT
ejpam-5430	314	18	η̃2	η̃2	PROPN
ejpam-5430	314	19	)	)	PUNCT
ejpam-5430	314	20	can	can	AUX
ejpam-5430	314	21	be	be	AUX
ejpam-5430	314	22	represented	represent	VERB
ejpam-5430	314	23	by	by	ADP
ejpam-5430	314	24	the	the	DET
ejpam-5430	314	25	following	follow	VERB
ejpam-5430	314	26	functions	function	NOUN
ejpam-5430	314	27	:	:	PUNCT
ejpam-5430	314	28	1f	1f	PROPN
ejpam-5430	314	29	is	be	AUX
ejpam-5430	314	30	pyfssw	pyfssw	ADJ
ejpam-5430	314	31	-	-	PUNCT
ejpam-5430	314	32	c	c	NOUN
ejpam-5430	314	33	,	,	PUNCT
ejpam-5430	314	34	2f−1(fη̃2	2f−1(fη̃2	NUM
ejpam-5430	314	35	)	)	PUNCT
ejpam-5430	314	36	is	be	AUX
ejpam-5430	314	37	pyfssw	pyfssw	ADV
ejpam-5430	314	38	-	-	PUNCT
ejpam-5430	314	39	closed	close	VERB
ejpam-5430	314	40	set	set	NOUN
ejpam-5430	314	41	over	over	ADP
ejpam-5430	314	42	x̃	x̃	PROPN
ejpam-5430	314	43	,	,	PUNCT
ejpam-5430	314	44	for	for	ADP
ejpam-5430	314	45	every	every	DET
ejpam-5430	314	46	pyfs	pyfs	ADJ
ejpam-5430	314	47	closed	close	VERB
ejpam-5430	314	48	set	set	NOUN
ejpam-5430	314	49	fη̃2	fη̃2	NOUN
ejpam-5430	314	50	over	over	ADP
ejpam-5430	314	51	ỹ	ỹ	PROPN
ejpam-5430	314	52	,	,	PUNCT
ejpam-5430	314	53	3f(clsw(gη̃	3f(clsw(gη̃	NUM
ejpam-5430	314	54	)	)	PUNCT
ejpam-5430	314	55	)	)	PUNCT
ejpam-5430	315	1	⊑	⊑	PRON
ejpam-5430	315	2	cl(f(gη̃	cl(f(gη̃	NOUN
ejpam-5430	315	3	)	)	PUNCT
ejpam-5430	315	4	)	)	PUNCT
ejpam-5430	316	1	for	for	ADP
ejpam-5430	316	2	every	every	DET
ejpam-5430	316	3	set	set	NOUN
ejpam-5430	316	4	gη̃	gη̃	PROPN
ejpam-5430	316	5	on	on	ADP
ejpam-5430	316	6	x̃	x̃	PROPN
ejpam-5430	316	7	,	,	PUNCT
ejpam-5430	316	8	4clsw(f	4clsw(f	NUM
ejpam-5430	316	9	−1(hη̃2	−1(hη̃2	NOUN
ejpam-5430	316	10	)	)	PUNCT
ejpam-5430	316	11	)	)	PUNCT
ejpam-5430	316	12	⊑	⊑	PRON
ejpam-5430	316	13	f−1(cl(hη̃2	f−1(cl(hη̃2	NOUN
ejpam-5430	316	14	)	)	PUNCT
ejpam-5430	316	15	)	)	PUNCT
ejpam-5430	316	16	,	,	PUNCT
ejpam-5430	316	17	for	for	ADP
ejpam-5430	316	18	every	every	DET
ejpam-5430	316	19	set	set	NOUN
ejpam-5430	316	20	hη̃2	hη̃2	NOUN
ejpam-5430	316	21	on	on	ADP
ejpam-5430	316	22	ỹ	ỹ	PROPN
ejpam-5430	316	23	,	,	PUNCT
ejpam-5430	316	24	5f−1(int(hη̃2	5f−1(int(hη̃2	NUM
ejpam-5430	316	25	)	)	PUNCT
ejpam-5430	316	26	)	)	PUNCT
ejpam-5430	316	27	⊑	⊑	PROPN
ejpam-5430	316	28	intsw(f	intsw(f	PROPN
ejpam-5430	316	29	−1(hη̃2	−1(hη̃2	NOUN
ejpam-5430	316	30	)	)	PUNCT
ejpam-5430	316	31	)	)	PUNCT
ejpam-5430	316	32	,	,	PUNCT
ejpam-5430	316	33	for	for	ADP
ejpam-5430	316	34	every	every	DET
ejpam-5430	316	35	set	set	NOUN
ejpam-5430	316	36	hη̃2	hη̃2	NOUN
ejpam-5430	316	37	on	on	ADP
ejpam-5430	316	38	ỹ	ỹ	PROPN
ejpam-5430	316	39	.	.	PUNCT
ejpam-5430	317	1	proof	proof	NOUN
ejpam-5430	317	2	.	.	PUNCT
ejpam-5430	318	1	straightforward	straightforward	ADJ
ejpam-5430	318	2	.	.	PUNCT
ejpam-5430	319	1	definition	definition	NOUN
ejpam-5430	319	2	25	25	NUM
ejpam-5430	319	3	.	.	PUNCT
ejpam-5430	319	4	assume	assume	VERB
ejpam-5430	319	5	that	that	SCONJ
ejpam-5430	319	6	pyf	pyf	PROPN
ejpam-5430	319	7	(	(	PUNCT
ejpam-5430	319	8	x̃	x̃	PROPN
ejpam-5430	319	9	,	,	PUNCT
ejpam-5430	319	10	η̃1	η̃1	PROPN
ejpam-5430	319	11	)	)	PUNCT
ejpam-5430	319	12	and	and	CCONJ
ejpam-5430	319	13	pyf	pyf	PROPN
ejpam-5430	319	14	(	(	PUNCT
ejpam-5430	319	15	ỹ	ỹ	PROPN
ejpam-5430	319	16	,	,	PUNCT
ejpam-5430	319	17	η̃2	η̃2	PROPN
ejpam-5430	319	18	)	)	PUNCT
ejpam-5430	319	19	be	be	AUX
ejpam-5430	319	20	pyfsss	pyfsss	NOUN
ejpam-5430	319	21	and	and	CCONJ
ejpam-5430	319	22	let	let	VERB
ejpam-5430	319	23	dη̃1	dη̃1	PROPN
ejpam-5430	319	24	∈	∈	PROPN
ejpam-5430	319	25	(	(	PUNCT
ejpam-5430	319	26	x̃	x̃	PROPN
ejpam-5430	319	27	,	,	PUNCT
ejpam-5430	319	28	η̃1	η̃1	PROPN
ejpam-5430	319	29	)	)	PUNCT
ejpam-5430	319	30	.	.	PUNCT
ejpam-5430	320	1	the	the	DET
ejpam-5430	320	2	restriction	restriction	NOUN
ejpam-5430	320	3	of	of	ADP
ejpam-5430	320	4	f	f	PROPN
ejpam-5430	320	5	:	:	PUNCT
ejpam-5430	320	6	pyf	pyf	PROPN
ejpam-5430	320	7	(	(	PUNCT
ejpam-5430	320	8	x̃	x̃	PROPN
ejpam-5430	320	9	,	,	PUNCT
ejpam-5430	320	10	η̃1	η̃1	PROPN
ejpam-5430	320	11	)	)	PUNCT
ejpam-5430	320	12	→	→	SYM
ejpam-5430	320	13	pyf	pyf	PROPN
ejpam-5430	320	14	(	(	PUNCT
ejpam-5430	320	15	ỹ	ỹ	PROPN
ejpam-5430	320	16	,	,	PUNCT
ejpam-5430	320	17	η̃2	η̃2	PROPN
ejpam-5430	320	18	)	)	PUNCT
ejpam-5430	320	19	is	be	AUX
ejpam-5430	320	20	the	the	DET
ejpam-5430	320	21	fyfs	fyfs	NOUN
ejpam-5430	320	22	function	function	NOUN
ejpam-5430	320	23	fdη̃1	fdη̃1	NOUN
ejpam-5430	320	24	:	:	PUNCT
ejpam-5430	321	1	pyf	pyf	PROPN
ejpam-5430	321	2	(	(	PUNCT
ejpam-5430	321	3	x̃	x̃	PROPN
ejpam-5430	321	4	,	,	PUNCT
ejpam-5430	321	5	η̃1	η̃1	PROPN
ejpam-5430	321	6	)	)	PUNCT
ejpam-5430	321	7	→	→	SYM
ejpam-5430	321	8	pyf	pyf	PROPN
ejpam-5430	321	9	(	(	PUNCT
ejpam-5430	321	10	ỹ	ỹ	PROPN
ejpam-5430	321	11	,	,	PUNCT
ejpam-5430	321	12	η̃2	η̃2	PROPN
ejpam-5430	321	13	)	)	PUNCT
ejpam-5430	321	14	defined	define	VERB
ejpam-5430	321	15	by	by	ADP
ejpam-5430	321	16	fdη̃1	fdη̃1	NOUN
ejpam-5430	321	17	(	(	PUNCT
ejpam-5430	321	18	p	p	X
ejpam-5430	321	19	x	x	X
ejpam-5430	321	20	a	a	NOUN
ejpam-5430	321	21	)	)	PUNCT
ejpam-5430	321	22	=	=	SYM
ejpam-5430	321	23	f(p	f(p	PROPN
ejpam-5430	321	24	x	x	SYM
ejpam-5430	321	25	a	a	NOUN
ejpam-5430	321	26	)	)	PUNCT
ejpam-5430	321	27	for	for	ADP
ejpam-5430	321	28	all	all	DET
ejpam-5430	321	29	p	p	NOUN
ejpam-5430	321	30	x	x	DET
ejpam-5430	321	31	a	a	DET
ejpam-5430	321	32	∈	∈	PROPN
ejpam-5430	321	33	dη̃1	dη̃1	NOUN
ejpam-5430	321	34	.	.	PUNCT
ejpam-5430	322	1	a	a	DET
ejpam-5430	322	2	pyfs	pyfs	ADJ
ejpam-5430	322	3	function	function	NOUN
ejpam-5430	322	4	’s	’s	PART
ejpam-5430	322	5	expansion	expansion	NOUN
ejpam-5430	322	6	f	f	PROPN
ejpam-5430	322	7	is	be	AUX
ejpam-5430	322	8	a	a	DET
ejpam-5430	322	9	pyfs	pyfs	ADJ
ejpam-5430	322	10	function	function	NOUN
ejpam-5430	322	11	of	of	ADP
ejpam-5430	322	12	g	g	NOUN
ejpam-5430	322	13	,	,	PUNCT
ejpam-5430	322	14	meaning	mean	VERB
ejpam-5430	322	15	that	that	SCONJ
ejpam-5430	322	16	f	f	PROPN
ejpam-5430	322	17	restricts	restrict	VERB
ejpam-5430	322	18	g.	g.	PROPN
ejpam-5430	322	19	theorem	theorem	PROPN
ejpam-5430	322	20	1	1	X
ejpam-5430	322	21	.	.	X
ejpam-5430	322	22	consider	consider	VERB
ejpam-5430	322	23	(	(	PUNCT
ejpam-5430	322	24	x̃	x̃	PROPN
ejpam-5430	322	25	,	,	PUNCT
ejpam-5430	322	26	ω̃1	ω̃1	PROPN
ejpam-5430	322	27	,	,	PUNCT
ejpam-5430	322	28	η̃1	η̃1	PROPN
ejpam-5430	322	29	)	)	PUNCT
ejpam-5430	322	30	and	and	CCONJ
ejpam-5430	322	31	(	(	PUNCT
ejpam-5430	322	32	ỹ	ỹ	PROPN
ejpam-5430	322	33	,	,	PUNCT
ejpam-5430	322	34	ω̃2	ω̃2	PROPN
ejpam-5430	322	35	,	,	PUNCT
ejpam-5430	322	36	η̃2	η̃2	PROPN
ejpam-5430	322	37	)	)	PUNCT
ejpam-5430	323	1	that	that	SCONJ
ejpam-5430	323	2	a	a	DET
ejpam-5430	323	3	pyfstss	pyfstss	NOUN
ejpam-5430	323	4	,	,	PUNCT
ejpam-5430	323	5	and	and	CCONJ
ejpam-5430	323	6	let	let	VERB
ejpam-5430	323	7	dη̃1	dη̃1	PROPN
ejpam-5430	323	8	be	be	AUX
ejpam-5430	323	9	a	a	DET
ejpam-5430	323	10	pyfs	pyfs	ADJ
ejpam-5430	323	11	dense	dense	ADJ
ejpam-5430	323	12	subspace	subspace	NOUN
ejpam-5430	323	13	over	over	ADP
ejpam-5430	323	14	x̃.	x̃.	PROPN
ejpam-5430	323	15	if	if	SCONJ
ejpam-5430	323	16	f	f	X
ejpam-5430	323	17	:	:	PUNCT
ejpam-5430	323	18	(	(	PUNCT
ejpam-5430	323	19	x̃	x̃	PROPN
ejpam-5430	323	20	,	,	PUNCT
ejpam-5430	323	21	ω̃1	ω̃1	PROPN
ejpam-5430	323	22	,	,	PUNCT
ejpam-5430	323	23	η̃1	η̃1	PROPN
ejpam-5430	323	24	)	)	PUNCT
ejpam-5430	323	25	→	→	PUNCT
ejpam-5430	323	26	(	(	PUNCT
ejpam-5430	323	27	ỹ	ỹ	PROPN
ejpam-5430	323	28	,	,	PUNCT
ejpam-5430	323	29	ω̃2	ω̃2	PROPN
ejpam-5430	323	30	,	,	PUNCT
ejpam-5430	323	31	η̃2	η̃2	PROPN
ejpam-5430	323	32	)	)	PUNCT
ejpam-5430	323	33	is	be	AUX
ejpam-5430	323	34	pyfssw	pyfssw	ADJ
ejpam-5430	323	35	-	-	PUNCT
ejpam-5430	323	36	c	c	NOUN
ejpam-5430	323	37	over	over	ADP
ejpam-5430	323	38	x̃	x̃	PROPN
ejpam-5430	323	39	,	,	PUNCT
ejpam-5430	323	40	then	then	ADV
ejpam-5430	323	41	f	f	PROPN
ejpam-5430	323	42	|	|	ADV
ejpam-5430	323	43	dη̃1	dη̃1	PROPN
ejpam-5430	323	44	is	be	AUX
ejpam-5430	323	45	pyfssw	pyfssw	ADJ
ejpam-5430	323	46	-	-	PUNCT
ejpam-5430	323	47	c	c	NOUN
ejpam-5430	323	48	over	over	ADP
ejpam-5430	323	49	d.	d.	PROPN
ejpam-5430	323	50	proof	proof	PROPN
ejpam-5430	323	51	.	.	PUNCT
ejpam-5430	324	1	straightforward	straightforward	ADJ
ejpam-5430	324	2	(	(	PUNCT
ejpam-5430	324	3	with	with	ADP
ejpam-5430	324	4	the	the	DET
ejpam-5430	324	5	aid	aid	NOUN
ejpam-5430	324	6	of	of	ADP
ejpam-5430	324	7	lemma	lemma	PROPN
ejpam-5430	324	8	3.12	3.12	NUM
ejpam-5430	324	9	)	)	PUNCT
ejpam-5430	324	10	.	.	PUNCT
ejpam-5430	325	1	theorem	theorem	NOUN
ejpam-5430	325	2	2	2	NUM
ejpam-5430	325	3	.	.	PUNCT
ejpam-5430	326	1	let	let	VERB
ejpam-5430	326	2	(	(	PUNCT
ejpam-5430	326	3	x̃	x̃	PROPN
ejpam-5430	326	4	,	,	PUNCT
ejpam-5430	326	5	ω̃1	ω̃1	PROPN
ejpam-5430	326	6	,	,	PUNCT
ejpam-5430	326	7	η̃1	η̃1	PROPN
ejpam-5430	326	8	)	)	PUNCT
ejpam-5430	326	9	and	and	CCONJ
ejpam-5430	326	10	(	(	PUNCT
ejpam-5430	326	11	ỹ	ỹ	PROPN
ejpam-5430	326	12	,	,	PUNCT
ejpam-5430	326	13	ω̃2	ω̃2	PROPN
ejpam-5430	326	14	,	,	PUNCT
ejpam-5430	326	15	η̃2	η̃2	PROPN
ejpam-5430	326	16	)	)	PUNCT
ejpam-5430	326	17	be	be	AUX
ejpam-5430	326	18	a	a	DET
ejpam-5430	326	19	pyfstss	pyfstss	NOUN
ejpam-5430	326	20	,	,	PUNCT
ejpam-5430	326	21	and	and	CCONJ
ejpam-5430	326	22	let	let	VERB
ejpam-5430	326	23	f	f	X
ejpam-5430	326	24	:	:	PUNCT
ejpam-5430	326	25	(	(	PUNCT
ejpam-5430	326	26	x̃	x̃	PROPN
ejpam-5430	326	27	,	,	PUNCT
ejpam-5430	326	28	ω̃1	ω̃1	PROPN
ejpam-5430	326	29	,	,	PUNCT
ejpam-5430	326	30	η̃1	η̃1	PROPN
ejpam-5430	326	31	)	)	PUNCT
ejpam-5430	326	32	→	→	PUNCT
ejpam-5430	326	33	(	(	PUNCT
ejpam-5430	326	34	ỹ	ỹ	PROPN
ejpam-5430	326	35	,	,	PUNCT
ejpam-5430	326	36	ω̃2	ω̃2	PROPN
ejpam-5430	326	37	,	,	PUNCT
ejpam-5430	326	38	η̃2	η̃2	PROPN
ejpam-5430	326	39	)	)	PUNCT
ejpam-5430	326	40	be	be	AUX
ejpam-5430	326	41	a	a	DET
ejpam-5430	326	42	function	function	NOUN
ejpam-5430	326	43	and	and	CCONJ
ejpam-5430	326	44	{	{	PUNCT
ejpam-5430	326	45	gβ	gβ	PROPN
ejpam-5430	326	46	η̃1	η̃1	PROPN
ejpam-5430	326	47	:	:	PUNCT
ejpam-5430	326	48	β	β	X
ejpam-5430	326	49	∈	∈	PROPN
ejpam-5430	326	50	λ	λ	PROPN
ejpam-5430	326	51	}	}	PUNCT
ejpam-5430	326	52	be	be	VERB
ejpam-5430	326	53	a	a	DET
ejpam-5430	326	54	pyfs	pyfs	ADJ
ejpam-5430	326	55	open	open	ADJ
ejpam-5430	326	56	cover	cover	NOUN
ejpam-5430	326	57	of	of	ADP
ejpam-5430	326	58	x̃.	x̃.	ADJ
ejpam-5430	326	59	at	at	ADP
ejpam-5430	326	60	hence	hence	ADV
ejpam-5430	326	61	,	,	PUNCT
ejpam-5430	326	62	f	f	PROPN
ejpam-5430	326	63	is	be	AUX
ejpam-5430	326	64	pyfssw	pyfssw	ADJ
ejpam-5430	326	65	-	-	PUNCT
ejpam-5430	326	66	c	c	NOUN
ejpam-5430	326	67	,	,	PUNCT
ejpam-5430	326	68	if	if	SCONJ
ejpam-5430	326	69	f	f	PROPN
ejpam-5430	326	70	|	|	ADV
ejpam-5430	326	71	gβ	gβ	INTJ
ejpam-5430	326	72	η̃1	η̃1	PROPN
ejpam-5430	326	73	is	be	AUX
ejpam-5430	326	74	pyfssw	pyfssw	ADJ
ejpam-5430	326	75	-	-	PUNCT
ejpam-5430	326	76	c	c	NOUN
ejpam-5430	326	77	for	for	ADP
ejpam-5430	326	78	each	each	DET
ejpam-5430	326	79	β	β	X
ejpam-5430	326	80	∈	∈	PROPN
ejpam-5430	326	81	λ	λ	PROPN
ejpam-5430	326	82	.	.	PUNCT
ejpam-5430	326	83	proof	proof	NOUN
ejpam-5430	326	84	.	.	PUNCT
ejpam-5430	327	1	suppose	suppose	VERB
ejpam-5430	327	2	vη̃2	vη̃2	NOUN
ejpam-5430	327	3	is	be	AUX
ejpam-5430	327	4	a	a	DET
ejpam-5430	327	5	pyfs	pyfs	ADJ
ejpam-5430	327	6	open	open	NOUN
ejpam-5430	327	7	set	set	VERB
ejpam-5430	327	8	across	across	ADP
ejpam-5430	327	9	ỹ	ỹ	PROPN
ejpam-5430	327	10	.	.	PUNCT
ejpam-5430	328	1	by	by	ADP
ejpam-5430	328	2	presumption	presumption	NOUN
ejpam-5430	328	3	,	,	PUNCT
ejpam-5430	328	4	(	(	PUNCT
ejpam-5430	328	5	f	f	X
ejpam-5430	328	6	|	|	ADV
ejpam-5430	328	7	gβ	gβ	ADP
ejpam-5430	328	8	η̃1	η̃1	PROPN
ejpam-5430	328	9	)	)	PUNCT
ejpam-5430	328	10	−1(vη̃2	−1(vη̃2	NOUN
ejpam-5430	328	11	)	)	PUNCT
ejpam-5430	328	12	is	be	AUX
ejpam-5430	328	13	pyfssw	pyfssw	ADV
ejpam-5430	328	14	open	open	ADJ
ejpam-5430	328	15	over	over	ADP
ejpam-5430	328	16	gβ	gβ	ADP
ejpam-5430	328	17	η̃1	η̃1	PROPN
ejpam-5430	328	18	.	.	PUNCT
ejpam-5430	329	1	by	by	ADP
ejpam-5430	329	2	lemma	lemma	PROPN
ejpam-5430	329	3	3.13	3.13	NUM
ejpam-5430	329	4	,	,	PUNCT
ejpam-5430	329	5	(	(	PUNCT
ejpam-5430	329	6	f	f	X
ejpam-5430	329	7	|	|	ADV
ejpam-5430	329	8	gβ	gβ	ADP
ejpam-5430	329	9	η̃1	η̃1	PROPN
ejpam-5430	329	10	)	)	PUNCT
ejpam-5430	329	11	−1(vη̃2	−1(vη̃2	NOUN
ejpam-5430	329	12	)	)	PUNCT
ejpam-5430	329	13	is	be	AUX
ejpam-5430	329	14	pyfssw	pyfssw	ADV
ejpam-5430	329	15	open	open	ADJ
ejpam-5430	329	16	over	over	ADP
ejpam-5430	329	17	x̃	x̃	PROPN
ejpam-5430	329	18	foe	foe	VERB
ejpam-5430	329	19	all	all	DET
ejpam-5430	329	20	β	β	NOUN
ejpam-5430	329	21	∈	∈	PROPN
ejpam-5430	329	22	λ	λ	PROPN
ejpam-5430	329	23	.	.	PROPN
ejpam-5430	330	1	but	but	CCONJ
ejpam-5430	330	2	f−1(vη̃2	f−1(vη̃2	PROPN
ejpam-5430	330	3	)	)	PUNCT
ejpam-5430	331	1	=	=	NOUN
ejpam-5430	332	1	⊔β∈λ[(f	⊔β∈λ[(f	X
ejpam-5430	332	2	|	|	ADV
ejpam-5430	332	3	gβ	gβ	ADP
ejpam-5430	332	4	η̃1	η̃1	PROPN
ejpam-5430	332	5	)	)	PUNCT
ejpam-5430	332	6	−1(vη̃2	−1(vη̃2	NOUN
ejpam-5430	332	7	)	)	PUNCT
ejpam-5430	332	8	]	]	PUNCT
ejpam-5430	332	9	,	,	PUNCT
ejpam-5430	332	10	this	this	PRON
ejpam-5430	332	11	is	be	AUX
ejpam-5430	332	12	the	the	DET
ejpam-5430	332	13	union	union	NOUN
ejpam-5430	332	14	of	of	ADP
ejpam-5430	332	15	pyfssw	pyfssw	ADJ
ejpam-5430	332	16	open	open	ADJ
ejpam-5430	332	17	sets	set	NOUN
ejpam-5430	332	18	,	,	PUNCT
ejpam-5430	332	19	and	and	CCONJ
ejpam-5430	332	20	f−1(vη̃2	f−1(vη̃2	NOUN
ejpam-5430	332	21	)	)	PUNCT
ejpam-5430	332	22	is	be	AUX
ejpam-5430	332	23	pyfssw	pyfssw	ADV
ejpam-5430	332	24	open	open	ADJ
ejpam-5430	332	25	over	over	ADP
ejpam-5430	332	26	x̃.	x̃.	PROPN
ejpam-5430	332	27	f	f	PROPN
ejpam-5430	332	28	is	be	AUX
ejpam-5430	332	29	hence	hence	ADV
ejpam-5430	332	30	pyfssw	pyfssw	ADJ
ejpam-5430	332	31	-	-	PUNCT
ejpam-5430	332	32	c.	c.	NOUN
ejpam-5430	332	33	theorem	theorem	NOUN
ejpam-5430	332	34	3	3	X
ejpam-5430	332	35	.	.	PUNCT
ejpam-5430	333	1	let	let	AUX
ejpam-5430	333	2	(	(	PUNCT
ejpam-5430	333	3	x̃	x̃	PROPN
ejpam-5430	333	4	,	,	PUNCT
ejpam-5430	333	5	ω̃1	ω̃1	PROPN
ejpam-5430	333	6	,	,	PUNCT
ejpam-5430	333	7	η̃1	η̃1	PROPN
ejpam-5430	333	8	)	)	PUNCT
ejpam-5430	333	9	and	and	CCONJ
ejpam-5430	333	10	(	(	PUNCT
ejpam-5430	333	11	ỹ	ỹ	PROPN
ejpam-5430	333	12	,	,	PUNCT
ejpam-5430	333	13	ω̃2	ω̃2	PROPN
ejpam-5430	333	14	,	,	PUNCT
ejpam-5430	333	15	η̃2	η̃2	PROPN
ejpam-5430	333	16	)	)	PUNCT
ejpam-5430	333	17	be	be	AUX
ejpam-5430	333	18	a	a	DET
ejpam-5430	333	19	pyfstss	pyfstss	NOUN
ejpam-5430	333	20	,	,	PUNCT
ejpam-5430	333	21	and	and	CCONJ
ejpam-5430	333	22	let	let	VERB
ejpam-5430	333	23	uη̃1	uη̃1	NOUN
ejpam-5430	333	24	be	be	AUX
ejpam-5430	333	25	a	a	DET
ejpam-5430	333	26	pyfs	pyfs	ADJ
ejpam-5430	333	27	open	open	NOUN
ejpam-5430	333	28	set	set	VERB
ejpam-5430	333	29	over	over	ADP
ejpam-5430	333	30	x̃.	x̃.	PROPN
ejpam-5430	333	31	if	if	SCONJ
ejpam-5430	333	32	f	f	X
ejpam-5430	333	33	:	:	PUNCT
ejpam-5430	333	34	(	(	PUNCT
ejpam-5430	333	35	ũ	ũ	PROPN
ejpam-5430	333	36	,	,	PUNCT
ejpam-5430	333	37	ω̃1	ω̃1	PROPN
ejpam-5430	333	38	,	,	PUNCT
ejpam-5430	333	39	η̃1	η̃1	PROPN
ejpam-5430	333	40	)	)	PUNCT
ejpam-5430	333	41	→	→	PUNCT
ejpam-5430	333	42	(	(	PUNCT
ejpam-5430	333	43	ỹ	ỹ	PROPN
ejpam-5430	333	44	,	,	PUNCT
ejpam-5430	333	45	ω̃2	ω̃2	PROPN
ejpam-5430	333	46	,	,	PUNCT
ejpam-5430	333	47	η̃2	η̃2	PROPN
ejpam-5430	333	48	)	)	PUNCT
ejpam-5430	333	49	is	be	AUX
ejpam-5430	333	50	a	a	DET
ejpam-5430	333	51	pyfssw	pyfssw	ADJ
ejpam-5430	333	52	-	-	PUNCT
ejpam-5430	333	53	c	c	NOUN
ejpam-5430	333	54	function	function	NOUN
ejpam-5430	333	55	that	that	PRON
ejpam-5430	333	56	f(uη̃1	f(uη̃1	NOUN
ejpam-5430	333	57	)	)	PUNCT
ejpam-5430	333	58	is	be	AUX
ejpam-5430	333	59	fys	fys	PROPN
ejpam-5430	333	60	dense	dense	ADJ
ejpam-5430	333	61	over	over	ADP
ejpam-5430	333	62	ỹ	ỹ	PROPN
ejpam-5430	333	63	,	,	PUNCT
ejpam-5430	333	64	then	then	ADV
ejpam-5430	333	65	pyfssw	pyfssw	ADJ
ejpam-5430	333	66	-	-	PUNCT
ejpam-5430	333	67	c	c	NOUN
ejpam-5430	333	68	is	be	AUX
ejpam-5430	333	69	the	the	DET
ejpam-5430	333	70	extension	extension	NOUN
ejpam-5430	333	71	function	function	NOUN
ejpam-5430	333	72	of	of	ADP
ejpam-5430	333	73	each	each	DET
ejpam-5430	333	74	f	f	NOUN
ejpam-5430	333	75	over	over	ADP
ejpam-5430	333	76	x̃.	x̃.	ADJ
ejpam-5430	333	77	proof	proof	NOUN
ejpam-5430	333	78	.	.	PUNCT
ejpam-5430	334	1	let	let	VERB
ejpam-5430	334	2	vη̃2	vη̃2	NOUN
ejpam-5430	334	3	be	be	AUX
ejpam-5430	334	4	a	a	DET
ejpam-5430	334	5	(	(	PUNCT
ejpam-5430	334	6	non	non	ADJ
ejpam-5430	334	7	-	-	ADJ
ejpam-5430	334	8	null	null	ADJ
ejpam-5430	334	9	)	)	PUNCT
ejpam-5430	334	10	pyfs	pyfs	ADJ
ejpam-5430	334	11	open	open	ADJ
ejpam-5430	334	12	set	set	NOUN
ejpam-5430	334	13	on	on	ADP
ejpam-5430	334	14	ỹ	ỹ	PROPN
ejpam-5430	334	15	and	and	CCONJ
ejpam-5430	334	16	let	let	VERB
ejpam-5430	334	17	g	g	PRON
ejpam-5430	334	18	be	be	AUX
ejpam-5430	334	19	an	an	DET
ejpam-5430	334	20	extension	extension	NOUN
ejpam-5430	334	21	of	of	ADP
ejpam-5430	334	22	f	f	PROPN
ejpam-5430	334	23	.	.	PUNCT
ejpam-5430	335	1	if	if	SCONJ
ejpam-5430	335	2	g−1(vη̃2	g−1(vη̃2	NOUN
ejpam-5430	335	3	)	)	PUNCT
ejpam-5430	335	4	=	=	SYM
ejpam-5430	336	1	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	336	2	,	,	PUNCT
ejpam-5430	336	3	then	then	ADV
ejpam-5430	336	4	g	g	PROPN
ejpam-5430	336	5	is	be	AUX
ejpam-5430	336	6	simply	simply	ADV
ejpam-5430	336	7	pyfssw	pyfssw	ADJ
ejpam-5430	336	8	-	-	PUNCT
ejpam-5430	336	9	c.	c.	NOUN
ejpam-5430	336	10	let	let	VERB
ejpam-5430	336	11	g−1(vη̃2	g−1(vη̃2	NOUN
ejpam-5430	336	12	)	)	PUNCT
ejpam-5430	336	13	̸=	̸=	PROPN
ejpam-5430	336	14	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	336	15	.	.	PUNCT
ejpam-5430	337	1	by	by	ADP
ejpam-5430	337	2	density	density	NOUN
ejpam-5430	337	3	of	of	ADP
ejpam-5430	337	4	f(uη̃1	f(uη̃1	NOUN
ejpam-5430	337	5	)	)	PUNCT
ejpam-5430	337	6	,	,	PUNCT
ejpam-5430	337	7	f(uη̃1	f(uη̃1	NOUN
ejpam-5430	337	8	)	)	PUNCT
ejpam-5430	337	9	⊓	⊓	PROPN
ejpam-5430	337	10	vη̃2	vη̃2	NOUN
ejpam-5430	337	11	̸=	̸=	PROPN
ejpam-5430	337	12	ϕη̃2	ϕη̃2	NOUN
ejpam-5430	337	13	it	it	PRON
ejpam-5430	337	14	suggests	suggest	VERB
ejpam-5430	337	15	that	that	SCONJ
ejpam-5430	337	16	uη̃1	uη̃1	PROPN
ejpam-5430	337	17	⊓	⊓	PROPN
ejpam-5430	337	18	f−1(vη̃2	f−1(vη̃2	PROPN
ejpam-5430	337	19	)	)	PUNCT
ejpam-5430	337	20	̸=	̸=	PROPN
ejpam-5430	337	21	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	337	22	.	.	PUNCT
ejpam-5430	338	1	therefore	therefore	ADV
ejpam-5430	338	2	f−1(vη̃2	f−1(vη̃2	PROPN
ejpam-5430	338	3	)	)	PUNCT
ejpam-5430	338	4	̸=	̸=	PROPN
ejpam-5430	338	5	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	338	6	.	.	PUNCT
ejpam-5430	339	1	presumably	presumably	ADV
ejpam-5430	339	2	,	,	PUNCT
ejpam-5430	339	3	a	a	DET
ejpam-5430	339	4	non	non	ADJ
ejpam-5430	339	5	-	-	ADJ
ejpam-5430	339	6	null	null	ADJ
ejpam-5430	339	7	pyfs	pyfs	ADJ
ejpam-5430	339	8	open	open	ADJ
ejpam-5430	339	9	set	set	VERB
ejpam-5430	339	10	wη̃1	wη̃1	NOUN
ejpam-5430	339	11	on	on	ADP
ejpam-5430	339	12	u	u	NOUN
ejpam-5430	339	13	exists	exist	VERB
ejpam-5430	339	14	such	such	ADJ
ejpam-5430	339	15	that	that	DET
ejpam-5430	339	16	wη̃1	wη̃1	NOUN
ejpam-5430	339	17	=	=	NOUN
ejpam-5430	339	18	wη̃1	wη̃1	NOUN
ejpam-5430	340	1	⊓	⊓	PROPN
ejpam-5430	340	2	uη̃1	uη̃1	NOUN
ejpam-5430	340	3	⊑	⊑	X
ejpam-5430	340	4	f−1(vη̃2	f−1(vη̃2	PROPN
ejpam-5430	340	5	)	)	PUNCT
ejpam-5430	340	6	⊓	⊓	PROPN
ejpam-5430	340	7	uη̃1	uη̃1	NOUN
ejpam-5430	340	8	=	=	SYM
ejpam-5430	340	9	g−1(vη̃2	g−1(vη̃2	PROPN
ejpam-5430	340	10	)	)	PUNCT
ejpam-5430	340	11	⊓	⊓	PROPN
ejpam-5430	340	12	uη̃1	uη̃1	NOUN
ejpam-5430	340	13	⊑	⊑	X
ejpam-5430	340	14	g−1(vη̃2	g−1(vη̃2	PROPN
ejpam-5430	340	15	)	)	PUNCT
ejpam-5430	340	16	.	.	PUNCT
ejpam-5430	341	1	since	since	SCONJ
ejpam-5430	341	2	wη̃1	wη̃1	PROPN
ejpam-5430	341	3	is	be	AUX
ejpam-5430	341	4	a	a	DET
ejpam-5430	341	5	pyfs	pyfs	ADJ
ejpam-5430	341	6	open	open	NOUN
ejpam-5430	341	7	set	set	VERB
ejpam-5430	341	8	over	over	ADP
ejpam-5430	341	9	x̃	x̃	PROPN
ejpam-5430	341	10	according	accord	VERB
ejpam-5430	341	11	to	to	ADP
ejpam-5430	341	12	lemma	lemma	PROPN
ejpam-5430	341	13	3.13	3.13	NUM
ejpam-5430	341	14	,	,	PUNCT
ejpam-5430	341	15	ϕη̃1	ϕη̃1	PROPN
ejpam-5430	341	16	̸=	̸=	PROPN
ejpam-5430	341	17	wη̃1	wη̃1	PROPN
ejpam-5430	341	18	⊑	⊑	DET
ejpam-5430	341	19	g−1(vη̃2	g−1(vη̃2	PROPN
ejpam-5430	341	20	)	)	PUNCT
ejpam-5430	341	21	.	.	PUNCT
ejpam-5430	342	1	consequently	consequently	ADV
ejpam-5430	342	2	,	,	PUNCT
ejpam-5430	342	3	across	across	ADP
ejpam-5430	342	4	x̃	x̃	PROPN
ejpam-5430	342	5	,	,	PUNCT
ejpam-5430	342	6	g	g	PROPN
ejpam-5430	342	7	is	be	AUX
ejpam-5430	342	8	pyfssw	pyfssw	ADJ
ejpam-5430	342	9	-	-	PUNCT
ejpam-5430	342	10	c.	c.	NOUN
ejpam-5430	342	11	a.	a.	PROPN
ejpam-5430	342	12	a.	a.	PROPN
ejpam-5430	342	13	azzam	azzam	PROPN
ejpam-5430	342	14	,	,	PUNCT
ejpam-5430	342	15	m.	m.	NOUN
ejpam-5430	342	16	aldawood	aldawood	PROPN
ejpam-5430	342	17	,	,	PUNCT
ejpam-5430	342	18	r.	r.	PROPN
ejpam-5430	342	19	abu	abu	PROPN
ejpam-5430	342	20	-	-	PUNCT
ejpam-5430	342	21	gdairi	gdairi	PROPN
ejpam-5430	342	22	/	/	SYM
ejpam-5430	342	23	eur	eur	PROPN
ejpam-5430	342	24	.	.	PUNCT
ejpam-5430	343	1	j.	j.	PROPN
ejpam-5430	343	2	pure	pure	PROPN
ejpam-5430	343	3	appl	appl	PROPN
ejpam-5430	343	4	.	.	PROPN
ejpam-5430	343	5	math	math	PROPN
ejpam-5430	343	6	,	,	PUNCT
ejpam-5430	343	7	17	17	NUM
ejpam-5430	343	8	(	(	PUNCT
ejpam-5430	343	9	4	4	NUM
ejpam-5430	343	10	)	)	PUNCT
ejpam-5430	343	11	(	(	PUNCT
ejpam-5430	343	12	2024	2024	NUM
ejpam-5430	343	13	)	)	PUNCT
ejpam-5430	343	14	,	,	PUNCT
ejpam-5430	343	15	4147	4147	NUM
ejpam-5430	343	16	-	-	SYM
ejpam-5430	343	17	4163	4163	NUM
ejpam-5430	343	18	4159	4159	NUM
ejpam-5430	343	19	theorem	theorem	NOUN
ejpam-5430	343	20	4	4	NUM
ejpam-5430	343	21	.	.	X
ejpam-5430	344	1	consider	consider	VERB
ejpam-5430	344	2	(	(	PUNCT
ejpam-5430	344	3	x̃	x̃	PROPN
ejpam-5430	344	4	,	,	PUNCT
ejpam-5430	344	5	ω̃1	ω̃1	PROPN
ejpam-5430	344	6	,	,	PUNCT
ejpam-5430	344	7	η̃1	η̃1	PROPN
ejpam-5430	344	8	)	)	PUNCT
ejpam-5430	344	9	and	and	CCONJ
ejpam-5430	344	10	(	(	PUNCT
ejpam-5430	344	11	ỹ	ỹ	PROPN
ejpam-5430	344	12	,	,	PUNCT
ejpam-5430	344	13	ω̃2	ω̃2	PROPN
ejpam-5430	344	14	,	,	PUNCT
ejpam-5430	344	15	η̃2	η̃2	PROPN
ejpam-5430	344	16	)	)	PUNCT
ejpam-5430	344	17	be	be	AUX
ejpam-5430	344	18	a	a	DET
ejpam-5430	344	19	pyfstss	pyfstss	NOUN
ejpam-5430	344	20	.	.	PUNCT
ejpam-5430	345	1	a	a	DET
ejpam-5430	345	2	function	function	NOUN
ejpam-5430	345	3	f	f	NOUN
ejpam-5430	345	4	:	:	PUNCT
ejpam-5430	345	5	(	(	PUNCT
ejpam-5430	345	6	ũ	ũ	PROPN
ejpam-5430	345	7	,	,	PUNCT
ejpam-5430	345	8	ω̃1	ω̃1	PROPN
ejpam-5430	345	9	,	,	PUNCT
ejpam-5430	345	10	η̃1	η̃1	PROPN
ejpam-5430	345	11	)	)	PUNCT
ejpam-5430	345	12	→	→	PUNCT
ejpam-5430	345	13	(	(	PUNCT
ejpam-5430	345	14	ỹ	ỹ	PROPN
ejpam-5430	345	15	,	,	PUNCT
ejpam-5430	345	16	ω̃2	ω̃2	PROPN
ejpam-5430	345	17	,	,	PUNCT
ejpam-5430	345	18	η̃2	η̃2	PROPN
ejpam-5430	345	19	)	)	PUNCT
ejpam-5430	345	20	is	be	AUX
ejpam-5430	345	21	a	a	DET
ejpam-5430	345	22	pyfs	pyfs	ADJ
ejpam-5430	345	23	-	-	PUNCT
ejpam-5430	345	24	semicontinuous	semicontinuous	ADJ
ejpam-5430	345	25	if	if	SCONJ
ejpam-5430	345	26	and	and	CCONJ
ejpam-5430	345	27	only	only	ADV
ejpam-5430	345	28	if	if	SCONJ
ejpam-5430	345	29	f	f	PROPN
ejpam-5430	345	30	|	|	ADV
ejpam-5430	345	31	wη̃1	wη̃1	NOUN
ejpam-5430	345	32	is	be	AUX
ejpam-5430	345	33	sw	sw	PROPN
ejpam-5430	345	34	-	-	PUNCT
ejpam-5430	345	35	c	c	PROPN
ejpam-5430	345	36	for	for	ADP
ejpam-5430	345	37	all	all	DET
ejpam-5430	345	38	pyfs	pyfs	ADJ
ejpam-5430	345	39	open	open	ADJ
ejpam-5430	345	40	set	set	VERB
ejpam-5430	345	41	wη̃1	wη̃1	NOUN
ejpam-5430	345	42	over	over	ADP
ejpam-5430	345	43	x̃.	x̃.	ADJ
ejpam-5430	345	44	proof	proof	NOUN
ejpam-5430	345	45	.	.	PUNCT
ejpam-5430	346	1	let	let	VERB
ejpam-5430	346	2	f	f	PRON
ejpam-5430	346	3	be	be	AUX
ejpam-5430	346	4	a	a	DET
ejpam-5430	346	5	pyfs	pyfs	ADJ
ejpam-5430	346	6	-	-	PUNCT
ejpam-5430	346	7	semicontinuous	semicontinuous	ADJ
ejpam-5430	346	8	,	,	PUNCT
ejpam-5430	346	9	wη̃1	wη̃1	NOUN
ejpam-5430	346	10	is	be	AUX
ejpam-5430	346	11	any	any	DET
ejpam-5430	346	12	pyfs	pyfs	ADJ
ejpam-5430	346	13	open	open	ADJ
ejpam-5430	346	14	set	set	VERB
ejpam-5430	346	15	on	on	ADP
ejpam-5430	346	16	x̃.	x̃.	PROPN
ejpam-5430	346	17	let	let	VERB
ejpam-5430	346	18	gη̃2	gη̃2	NOUN
ejpam-5430	346	19	be	be	AUX
ejpam-5430	346	20	a	a	DET
ejpam-5430	346	21	pyfs	pyfs	ADJ
ejpam-5430	346	22	open	open	ADJ
ejpam-5430	346	23	set	set	NOUN
ejpam-5430	346	24	on	on	ADP
ejpam-5430	346	25	ỹ	ỹ	PROPN
ejpam-5430	346	26	.	.	PUNCT
ejpam-5430	347	1	then	then	ADV
ejpam-5430	347	2	f−1(gη̃2	f−1(gη̃2	VERB
ejpam-5430	347	3	)	)	PUNCT
ejpam-5430	347	4	is	be	AUX
ejpam-5430	347	5	pyfs	pyf	VERB
ejpam-5430	347	6	semiopen	semiopen	ADJ
ejpam-5430	347	7	and	and	CCONJ
ejpam-5430	347	8	from	from	ADP
ejpam-5430	347	9	lemma	lemma	PROPN
ejpam-5430	347	10	3.19	3.19	NUM
ejpam-5430	347	11	,	,	PUNCT
ejpam-5430	347	12	(	(	PUNCT
ejpam-5430	347	13	f	f	PROPN
ejpam-5430	347	14	|	|	ADV
ejpam-5430	347	15	wη̃1	wη̃1	NOUN
ejpam-5430	347	16	)	)	PUNCT
ejpam-5430	347	17	−1(gη̃2	−1(gη̃2	NOUN
ejpam-5430	347	18	)	)	PUNCT
ejpam-5430	347	19	=	=	SYM
ejpam-5430	347	20	f−1(gη̃2	f−1(gη̃2	PROPN
ejpam-5430	347	21	)	)	PUNCT
ejpam-5430	347	22	⊓wη̃1	⊓wη̃1	PROPN
ejpam-5430	347	23	is	be	AUX
ejpam-5430	347	24	pyfs	pyfs	ADJ
ejpam-5430	347	25	semiopen	semiopen	ADJ
ejpam-5430	347	26	over	over	ADP
ejpam-5430	347	27	w	w	PROPN
ejpam-5430	347	28	.	.	PUNCT
ejpam-5430	348	1	then	then	ADV
ejpam-5430	348	2	f	f	PROPN
ejpam-5430	348	3	|	|	ADV
ejpam-5430	348	4	wη̃1	wη̃1	NOUN
ejpam-5430	348	5	is	be	AUX
ejpam-5430	348	6	pyfssemicontinuous	pyfssemicontinuous	ADJ
ejpam-5430	348	7	and	and	CCONJ
ejpam-5430	348	8	hence	hence	ADV
ejpam-5430	348	9	pyfssw	pyfssw	ADJ
ejpam-5430	348	10	-	-	PUNCT
ejpam-5430	348	11	c.	c.	NOUN
ejpam-5430	348	12	conversely	conversely	ADV
ejpam-5430	348	13	,	,	PUNCT
ejpam-5430	348	14	let	let	VERB
ejpam-5430	348	15	f	f	PRON
ejpam-5430	348	16	|	|	ADV
ejpam-5430	348	17	wη̃1	wη̃1	NOUN
ejpam-5430	348	18	is	be	AUX
ejpam-5430	348	19	sw	sw	PROPN
ejpam-5430	348	20	-	-	PUNCT
ejpam-5430	348	21	c	c	PROPN
ejpam-5430	348	22	for	for	ADP
ejpam-5430	348	23	all	all	DET
ejpam-5430	348	24	pyfs	pyfs	ADJ
ejpam-5430	348	25	open	open	ADJ
ejpam-5430	348	26	set	set	VERB
ejpam-5430	348	27	wη̃1	wη̃1	NOUN
ejpam-5430	348	28	over	over	ADP
ejpam-5430	348	29	x̃	x̃	PROPN
ejpam-5430	348	30	,	,	PUNCT
ejpam-5430	348	31	and	and	CCONJ
ejpam-5430	348	32	hη̃2	hη̃2	VERB
ejpam-5430	348	33	be	be	AUX
ejpam-5430	348	34	pyfs	pyf	VERB
ejpam-5430	348	35	open	open	ADJ
ejpam-5430	348	36	set	set	VERB
ejpam-5430	348	37	over	over	ADP
ejpam-5430	348	38	ỹ	ỹ	PROPN
ejpam-5430	348	39	.	.	PUNCT
ejpam-5430	349	1	then	then	ADV
ejpam-5430	349	2	(	(	PUNCT
ejpam-5430	349	3	f	f	X
ejpam-5430	349	4	|	|	ADV
ejpam-5430	349	5	wη̃1	wη̃1	NOUN
ejpam-5430	349	6	)	)	PUNCT
ejpam-5430	349	7	−1(hη̃2	−1(hη̃2	NOUN
ejpam-5430	349	8	)	)	PUNCT
ejpam-5430	349	9	=	=	SYM
ejpam-5430	349	10	f−1(hη̃2	f−1(hη̃2	PROPN
ejpam-5430	349	11	)	)	PUNCT
ejpam-5430	349	12	⊓wη̃1	⊓wη̃1	PROPN
ejpam-5430	349	13	is	be	AUX
ejpam-5430	349	14	pyfssw	pyfssw	ADV
ejpam-5430	349	15	-	-	PUNCT
ejpam-5430	349	16	open	open	ADJ
ejpam-5430	349	17	over	over	ADP
ejpam-5430	349	18	w	w	PROPN
ejpam-5430	349	19	.	.	PUNCT
ejpam-5430	350	1	since	since	SCONJ
ejpam-5430	350	2	wη̃1	wη̃1	PROPN
ejpam-5430	350	3	is	be	AUX
ejpam-5430	350	4	a	a	DET
ejpam-5430	350	5	pyfssw	pyfssw	ADV
ejpam-5430	350	6	-	-	PUNCT
ejpam-5430	350	7	open	open	ADJ
ejpam-5430	350	8	over	over	ADP
ejpam-5430	350	9	x̃	x̃	PROPN
ejpam-5430	350	10	by	by	ADP
ejpam-5430	350	11	lemma	lemma	PROPN
ejpam-5430	350	12	3.12	3.12	NUM
ejpam-5430	350	13	,	,	PUNCT
ejpam-5430	350	14	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	350	15	)	)	PUNCT
ejpam-5430	350	16	⊓	⊓	NOUN
ejpam-5430	350	17	wη̃1	wη̃1	NOUN
ejpam-5430	350	18	is	be	AUX
ejpam-5430	350	19	a	a	DET
ejpam-5430	350	20	pyfsswopen	pyfsswopen	NOUN
ejpam-5430	350	21	over	over	ADP
ejpam-5430	350	22	x̃	x̃	PROPN
ejpam-5430	350	23	and	and	CCONJ
ejpam-5430	350	24	so	so	ADV
ejpam-5430	350	25	,	,	PUNCT
ejpam-5430	350	26	by	by	ADP
ejpam-5430	350	27	lemma	lemma	PROPN
ejpam-5430	350	28	3.22	3.22	NUM
ejpam-5430	350	29	,	,	PUNCT
ejpam-5430	350	30	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	350	31	)	)	PUNCT
ejpam-5430	350	32	is	be	AUX
ejpam-5430	350	33	pyfs	pyf	VERB
ejpam-5430	350	34	semiopen	semiopen	ADJ
ejpam-5430	350	35	over	over	ADP
ejpam-5430	350	36	x̃.	x̃.	ADJ
ejpam-5430	350	37	thus	thus	ADV
ejpam-5430	350	38	f	f	PROPN
ejpam-5430	350	39	is	be	AUX
ejpam-5430	350	40	pyfs	pyfs	ADJ
ejpam-5430	350	41	-	-	PUNCT
ejpam-5430	350	42	semicontinuous	semicontinuous	ADJ
ejpam-5430	350	43	.	.	PUNCT
ejpam-5430	351	1	theorem	theorem	NOUN
ejpam-5430	351	2	5	5	NUM
ejpam-5430	351	3	.	.	X
ejpam-5430	352	1	consider	consider	VERB
ejpam-5430	352	2	(	(	PUNCT
ejpam-5430	352	3	x̃	x̃	PROPN
ejpam-5430	352	4	,	,	PUNCT
ejpam-5430	352	5	ω̃1	ω̃1	PROPN
ejpam-5430	352	6	,	,	PUNCT
ejpam-5430	352	7	η̃1	η̃1	PROPN
ejpam-5430	352	8	)	)	PUNCT
ejpam-5430	352	9	and	and	CCONJ
ejpam-5430	352	10	(	(	PUNCT
ejpam-5430	352	11	ỹ	ỹ	PROPN
ejpam-5430	352	12	,	,	PUNCT
ejpam-5430	352	13	ω̃2	ω̃2	PROPN
ejpam-5430	352	14	,	,	PUNCT
ejpam-5430	352	15	η̃2	η̃2	PROPN
ejpam-5430	352	16	)	)	PUNCT
ejpam-5430	352	17	be	be	AUX
ejpam-5430	352	18	a	a	DET
ejpam-5430	352	19	pyfsts	pyfst	NOUN
ejpam-5430	352	20	.	.	PUNCT
ejpam-5430	353	1	the	the	DET
ejpam-5430	353	2	function	function	NOUN
ejpam-5430	353	3	f	f	NOUN
ejpam-5430	353	4	:	:	PUNCT
ejpam-5430	353	5	(	(	PUNCT
ejpam-5430	353	6	ũ	ũ	PROPN
ejpam-5430	353	7	,	,	PUNCT
ejpam-5430	353	8	ω̃1	ω̃1	PROPN
ejpam-5430	353	9	,	,	PUNCT
ejpam-5430	353	10	η̃1	η̃1	PROPN
ejpam-5430	353	11	)	)	PUNCT
ejpam-5430	353	12	→	→	PUNCT
ejpam-5430	353	13	(	(	PUNCT
ejpam-5430	353	14	ỹ	ỹ	PROPN
ejpam-5430	353	15	,	,	PUNCT
ejpam-5430	353	16	ω̃2	ω̃2	PROPN
ejpam-5430	353	17	,	,	PUNCT
ejpam-5430	353	18	η̃2	η̃2	PROPN
ejpam-5430	353	19	)	)	PUNCT
ejpam-5430	353	20	can	can	AUX
ejpam-5430	353	21	be	be	AUX
ejpam-5430	353	22	represented	represent	VERB
ejpam-5430	353	23	by	by	ADP
ejpam-5430	353	24	the	the	DET
ejpam-5430	353	25	following	follow	VERB
ejpam-5430	353	26	function	function	NOUN
ejpam-5430	353	27	:	:	PUNCT
ejpam-5430	353	28	1f	1f	PROPN
ejpam-5430	353	29	is	be	AUX
ejpam-5430	353	30	pyfssw	pyfssw	ADV
ejpam-5430	353	31	-	-	PUNCT
ejpam-5430	353	32	continuous	continuous	ADJ
ejpam-5430	353	33	,	,	PUNCT
ejpam-5430	353	34	2	2	NUM
ejpam-5430	353	35	-	-	PUNCT
ejpam-5430	353	36	there	there	PRON
ejpam-5430	353	37	is	be	VERB
ejpam-5430	353	38	a	a	DET
ejpam-5430	353	39	non	non	ADJ
ejpam-5430	353	40	-	-	ADJ
ejpam-5430	353	41	null	null	ADJ
ejpam-5430	353	42	pyfs	pyfs	ADJ
ejpam-5430	353	43	open	open	ADJ
ejpam-5430	353	44	set	set	VERB
ejpam-5430	353	45	wη̃1	wη̃1	NOUN
ejpam-5430	353	46	on	on	ADP
ejpam-5430	353	47	x̃	x̃	PROPN
ejpam-5430	353	48	that	that	PRON
ejpam-5430	353	49	wη̃1	wη̃1	NOUN
ejpam-5430	353	50	⊑	⊑	PRON
ejpam-5430	353	51	f−1(vη̃2	f−1(vη̃2	PROPN
ejpam-5430	353	52	)	)	PUNCT
ejpam-5430	353	53	,	,	PUNCT
ejpam-5430	353	54	for	for	ADP
ejpam-5430	353	55	any	any	DET
ejpam-5430	353	56	pyfs	pyfs	ADJ
ejpam-5430	353	57	open	open	ADJ
ejpam-5430	353	58	set	set	VERB
ejpam-5430	353	59	f−1(vη̃2	f−1(vη̃2	NOUN
ejpam-5430	353	60	)	)	PUNCT
ejpam-5430	353	61	on	on	ADP
ejpam-5430	353	62	y	y	PROPN
ejpam-5430	353	63	with	with	ADP
ejpam-5430	353	64	f−1(vη̃2	f−1(vη̃2	NOUN
ejpam-5430	353	65	)	)	PUNCT
ejpam-5430	353	66	̸=	̸=	PROPN
ejpam-5430	353	67	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	353	68	,	,	PUNCT
ejpam-5430	353	69	3	3	NUM
ejpam-5430	353	70	-	-	PUNCT
ejpam-5430	353	71	there	there	PRON
ejpam-5430	353	72	is	be	VERB
ejpam-5430	353	73	a	a	DET
ejpam-5430	353	74	proper	proper	ADJ
ejpam-5430	353	75	pyfs	pyfs	NOUN
ejpam-5430	353	76	closed	closed	ADJ
ejpam-5430	353	77	kη̃1	kη̃1	NOUN
ejpam-5430	353	78	on	on	ADP
ejpam-5430	353	79	x̃	x̃	PROPN
ejpam-5430	353	80	that	that	SCONJ
ejpam-5430	353	81	f−1(fη̃2	f−1(fη̃2	ADV
ejpam-5430	353	82	)	)	PUNCT
ejpam-5430	353	83	⊑	⊑	PROPN
ejpam-5430	353	84	kη̃1	kη̃1	PROPN
ejpam-5430	353	85	,	,	PUNCT
ejpam-5430	353	86	for	for	ADP
ejpam-5430	353	87	any	any	DET
ejpam-5430	353	88	pyfs	pyfs	ADJ
ejpam-5430	353	89	closed	close	VERB
ejpam-5430	353	90	set	set	NOUN
ejpam-5430	353	91	fη̃2	fη̃2	NOUN
ejpam-5430	353	92	on	on	ADP
ejpam-5430	353	93	y	y	PROPN
ejpam-5430	353	94	with	with	ADP
ejpam-5430	353	95	f−1(fη̃2	f−1(fη̃2	NOUN
ejpam-5430	353	96	)	)	PUNCT
ejpam-5430	353	97	̸=	̸=	PROPN
ejpam-5430	353	98	x̃η̃1	x̃η̃1	NUM
ejpam-5430	353	99	,	,	PUNCT
ejpam-5430	353	100	4f(dη̃1	4f(dη̃1	PROPN
ejpam-5430	353	101	)	)	PUNCT
ejpam-5430	353	102	is	be	AUX
ejpam-5430	353	103	pyfs	pyf	VERB
ejpam-5430	353	104	dense	dense	ADJ
ejpam-5430	353	105	over	over	ADP
ejpam-5430	353	106	f(x̃	f(x̃	NOUN
ejpam-5430	353	107	)	)	PUNCT
ejpam-5430	353	108	for	for	ADP
ejpam-5430	353	109	any	any	DET
ejpam-5430	353	110	pyfs	pyfs	ADJ
ejpam-5430	353	111	dense	dense	ADJ
ejpam-5430	353	112	set	set	VERB
ejpam-5430	353	113	dη̃1	dη̃1	NOUN
ejpam-5430	353	114	over	over	ADP
ejpam-5430	353	115	x̃.	x̃.	ADJ
ejpam-5430	353	116	proof	proof	NOUN
ejpam-5430	353	117	.	.	PUNCT
ejpam-5430	354	1	1	1	NUM
ejpam-5430	354	2	⇒	⇒	NOUN
ejpam-5430	354	3	2	2	NUM
ejpam-5430	354	4	the	the	DET
ejpam-5430	354	5	definition	definition	NOUN
ejpam-5430	354	6	of	of	ADP
ejpam-5430	354	7	sw	sw	NOUN
ejpam-5430	354	8	-	-	PUNCT
ejpam-5430	354	9	continuity	continuity	NOUN
ejpam-5430	354	10	and	and	CCONJ
ejpam-5430	354	11	remark	remark	NOUN
ejpam-5430	354	12	3.2	3.2	NUM
ejpam-5430	354	13	.	.	NOUN
ejpam-5430	354	14	2	2	NUM
ejpam-5430	354	15	⇒	⇒	NOUN
ejpam-5430	354	16	3	3	NUM
ejpam-5430	354	17	given	give	VERB
ejpam-5430	354	18	a	a	DET
ejpam-5430	354	19	pyfs	pyfs	ADJ
ejpam-5430	354	20	closed	close	VERB
ejpam-5430	354	21	set	set	NOUN
ejpam-5430	354	22	fη̃2	fη̃2	NOUN
ejpam-5430	354	23	over	over	ADP
ejpam-5430	354	24	ỹ	ỹ	PROPN
ejpam-5430	354	25	,	,	PUNCT
ejpam-5430	354	26	f−1(fη̃2	f−1(fη̃2	PROPN
ejpam-5430	354	27	)	)	PUNCT
ejpam-5430	354	28	̸=	̸=	PROPN
ejpam-5430	354	29	x̃η̃1	x̃η̃1	NUM
ejpam-5430	354	30	.	.	PUNCT
ejpam-5430	355	1	f	f	PROPN
ejpam-5430	355	2	−1(ỹη̃2	−1(ỹη̃2	PROPN
ejpam-5430	355	3	\	\	PROPN
ejpam-5430	355	4	fη̃2	fη̃2	PROPN
ejpam-5430	355	5	)	)	PUNCT
ejpam-5430	355	6	̸=	̸=	PROPN
ejpam-5430	355	7	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	355	8	indicates	indicate	VERB
ejpam-5430	355	9	that	that	SCONJ
ejpam-5430	355	10	ỹη̃2	ỹη̃2	NOUN
ejpam-5430	355	11	\fη̃2	\fη̃2	PROPN
ejpam-5430	355	12	is	be	AUX
ejpam-5430	355	13	pyfs	pyfs	ADJ
ejpam-5430	355	14	open	open	ADJ
ejpam-5430	355	15	over	over	ADP
ejpam-5430	355	16	ỹ	ỹ	PROPN
ejpam-5430	355	17	.	.	PUNCT
ejpam-5430	356	1	a	a	DET
ejpam-5430	356	2	pyfs	pyfs	ADJ
ejpam-5430	356	3	open	open	ADJ
ejpam-5430	356	4	set	set	VERB
ejpam-5430	356	5	wη̃1	wη̃1	NOUN
ejpam-5430	356	6	over	over	ADP
ejpam-5430	356	7	x̃	x̃	PROPN
ejpam-5430	356	8	exists	exist	VERB
ejpam-5430	356	9	according	accord	VERB
ejpam-5430	356	10	to	to	ADP
ejpam-5430	356	11	(	(	PUNCT
ejpam-5430	356	12	2	2	NUM
ejpam-5430	356	13	)	)	PUNCT
ejpam-5430	356	14	in	in	ADP
ejpam-5430	356	15	such	such	DET
ejpam-5430	356	16	a	a	DET
ejpam-5430	356	17	way	way	NOUN
ejpam-5430	356	18	that	that	PRON
ejpam-5430	356	19	ϕη̃1	ϕη̃1	PROPN
ejpam-5430	356	20	̸=wη̃1	̸=wη̃1	VERB
ejpam-5430	356	21	⊑	⊑	PRON
ejpam-5430	356	22	f−1(ỹη̃2	f−1(ỹη̃2	PROPN
ejpam-5430	356	23	\fη̃2	\fη̃2	NOUN
ejpam-5430	356	24	)	)	PUNCT
ejpam-5430	357	1	=	=	SYM
ejpam-5430	357	2	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	357	3	\f−1(fη̃2	\f−1(fη̃2	PROPN
ejpam-5430	357	4	)	)	PUNCT
ejpam-5430	357	5	.	.	PUNCT
ejpam-5430	358	1	this	this	PRON
ejpam-5430	358	2	suggests	suggest	VERB
ejpam-5430	358	3	that	that	SCONJ
ejpam-5430	358	4	f−1(fη̃2	f−1(fη̃2	ADV
ejpam-5430	358	5	)	)	PUNCT
ejpam-5430	358	6	⊑	⊑	X
ejpam-5430	358	7	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	358	8	\wη̃1	\wη̃1	PROPN
ejpam-5430	358	9	̸=	̸=	PROPN
ejpam-5430	358	10	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	358	11	.	.	PUNCT
ejpam-5430	359	1	kη̃1	kη̃1	PROPN
ejpam-5430	359	2	is	be	AUX
ejpam-5430	359	3	a	a	DET
ejpam-5430	359	4	proper	proper	ADJ
ejpam-5430	359	5	pyfs	pyfs	ADJ
ejpam-5430	359	6	closed	close	VERB
ejpam-5430	359	7	set	set	NOUN
ejpam-5430	359	8	that	that	PRON
ejpam-5430	359	9	meets	meet	VERB
ejpam-5430	359	10	the	the	DET
ejpam-5430	359	11	necessary	necessary	ADJ
ejpam-5430	359	12	property	property	NOUN
ejpam-5430	359	13	if	if	SCONJ
ejpam-5430	359	14	kη̃1	kη̃1	PROPN
ejpam-5430	359	15	=	=	SYM
ejpam-5430	360	1	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	360	2	|wη̃1	|wη̃1	NOUN
ejpam-5430	360	3	.	.	PUNCT
ejpam-5430	361	1	3	3	NUM
ejpam-5430	361	2	⇒	⇒	NOUN
ejpam-5430	361	3	4	4	NUM
ejpam-5430	361	4	over	over	ADP
ejpam-5430	361	5	x̃	x̃	PROPN
ejpam-5430	361	6	,	,	PUNCT
ejpam-5430	361	7	let	let	VERB
ejpam-5430	361	8	dη̃1	dη̃1	PROPN
ejpam-5430	361	9	be	be	AUX
ejpam-5430	361	10	pyfs	pyf	VERB
ejpam-5430	361	11	dense	dense	ADJ
ejpam-5430	361	12	.	.	PUNCT
ejpam-5430	362	1	the	the	DET
ejpam-5430	362	2	claim	claim	NOUN
ejpam-5430	362	3	that	that	SCONJ
ejpam-5430	362	4	f(dη̃1	f(dη̃1	NOUN
ejpam-5430	362	5	)	)	PUNCT
ejpam-5430	362	6	is	be	AUX
ejpam-5430	362	7	pyfs	pyf	VERB
ejpam-5430	362	8	dense	dense	ADJ
ejpam-5430	362	9	over	over	ADP
ejpam-5430	362	10	f(x̃	f(x̃	NOUN
ejpam-5430	362	11	)	)	PUNCT
ejpam-5430	362	12	must	must	AUX
ejpam-5430	362	13	be	be	AUX
ejpam-5430	362	14	proven	prove	VERB
ejpam-5430	362	15	.	.	PUNCT
ejpam-5430	363	1	assume	assume	VERB
ejpam-5430	363	2	that	that	SCONJ
ejpam-5430	363	3	over	over	ADP
ejpam-5430	363	4	f(x̃	f(x̃	NOUN
ejpam-5430	363	5	)	)	PUNCT
ejpam-5430	363	6	,	,	PUNCT
ejpam-5430	363	7	c	c	PROPN
ejpam-5430	363	8	is	be	AUX
ejpam-5430	363	9	not	not	PART
ejpam-5430	363	10	pyfs	pyfs	ADJ
ejpam-5430	363	11	dense	dense	ADJ
ejpam-5430	363	12	.	.	PUNCT
ejpam-5430	364	1	a	a	DET
ejpam-5430	364	2	proper	proper	ADJ
ejpam-5430	364	3	pyfs	pyfs	ADJ
ejpam-5430	364	4	closed	closed	ADJ
ejpam-5430	364	5	set	set	NOUN
ejpam-5430	364	6	fη̃2	fη̃2	NOUN
ejpam-5430	364	7	,	,	PUNCT
ejpam-5430	364	8	exists	exist	VERB
ejpam-5430	364	9	such	such	ADJ
ejpam-5430	364	10	that	that	DET
ejpam-5430	364	11	f(dη̃1	f(dη̃1	NOUN
ejpam-5430	364	12	)	)	PUNCT
ejpam-5430	364	13	⊑	⊑	PRON
ejpam-5430	364	14	fη̃2	fη̃2	VERB
ejpam-5430	364	15	⊏	⊏	PROPN
ejpam-5430	364	16	f(x̃η̃1	f(x̃η̃1	VERB
ejpam-5430	364	17	)	)	PUNCT
ejpam-5430	364	18	.	.	PUNCT
ejpam-5430	365	1	so	so	ADV
ejpam-5430	365	2	,	,	PUNCT
ejpam-5430	365	3	dη̃1	dη̃1	PROPN
ejpam-5430	365	4	⊑	⊑	PRON
ejpam-5430	365	5	f(fη̃2	f(fη̃2	NOUN
ejpam-5430	365	6	)	)	PUNCT
ejpam-5430	365	7	.	.	PUNCT
ejpam-5430	366	1	according	accord	VERB
ejpam-5430	366	2	to	to	ADP
ejpam-5430	366	3	(	(	PUNCT
ejpam-5430	366	4	3	3	NUM
ejpam-5430	366	5	)	)	PUNCT
ejpam-5430	366	6	,	,	PUNCT
ejpam-5430	366	7	there	there	PRON
ejpam-5430	366	8	is	be	VERB
ejpam-5430	366	9	a	a	DET
ejpam-5430	366	10	pyfs	pyfs	ADJ
ejpam-5430	366	11	closed	close	VERB
ejpam-5430	366	12	set	set	VERB
ejpam-5430	366	13	kη̃1	kη̃1	NOUN
ejpam-5430	366	14	over	over	ADP
ejpam-5430	366	15	x̃	x̃	PROPN
ejpam-5430	366	16	such	such	ADJ
ejpam-5430	366	17	that	that	SCONJ
ejpam-5430	366	18	dη̃1	dη̃1	PROPN
ejpam-5430	366	19	⊑	⊑	PRON
ejpam-5430	366	20	f−1(fη̃2	f−1(fη̃2	PROPN
ejpam-5430	366	21	)	)	PUNCT
ejpam-5430	366	22	⊑	⊑	PROPN
ejpam-5430	366	23	kη̃1	kη̃1	PROPN
ejpam-5430	367	1	̸=	̸=	PROPN
ejpam-5430	367	2	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	367	3	.	.	PUNCT
ejpam-5430	368	1	that	that	SCONJ
ejpam-5430	368	2	dη̃1	dη̃1	PROPN
ejpam-5430	368	3	is	be	AUX
ejpam-5430	368	4	pyfs	pyf	VERB
ejpam-5430	368	5	dense	dense	ADJ
ejpam-5430	368	6	over	over	ADP
ejpam-5430	368	7	x̃	x̃	PROPN
ejpam-5430	368	8	is	be	AUX
ejpam-5430	368	9	contradicted	contradict	VERB
ejpam-5430	368	10	by	by	ADP
ejpam-5430	368	11	this	this	PRON
ejpam-5430	368	12	.	.	PUNCT
ejpam-5430	369	1	therefore	therefore	ADV
ejpam-5430	369	2	,	,	PUNCT
ejpam-5430	369	3	(	(	PUNCT
ejpam-5430	369	4	4	4	X
ejpam-5430	369	5	)	)	PUNCT
ejpam-5430	369	6	is	be	AUX
ejpam-5430	369	7	true	true	ADJ
ejpam-5430	369	8	.	.	PUNCT
ejpam-5430	370	1	4	4	NUM
ejpam-5430	370	2	⇒	⇒	NOUN
ejpam-5430	370	3	1	1	NUM
ejpam-5430	370	4	let	let	VERB
ejpam-5430	370	5	hη̃2	hη̃2	NOUN
ejpam-5430	370	6	be	be	AUX
ejpam-5430	370	7	a	a	DET
ejpam-5430	370	8	pyfs	pyfs	ADJ
ejpam-5430	370	9	open	open	NOUN
ejpam-5430	370	10	set	set	VERB
ejpam-5430	370	11	over	over	ADP
ejpam-5430	370	12	ỹ	ỹ	PROPN
ejpam-5430	370	13	with	with	ADP
ejpam-5430	370	14	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	370	15	)	)	PUNCT
ejpam-5430	370	16	̸=	̸=	PROPN
ejpam-5430	370	17	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	370	18	without	without	ADP
ejpam-5430	370	19	losing	lose	VERB
ejpam-5430	370	20	generality	generality	NOUN
ejpam-5430	370	21	,	,	PUNCT
ejpam-5430	370	22	since	since	SCONJ
ejpam-5430	370	23	it	it	PRON
ejpam-5430	370	24	is	be	AUX
ejpam-5430	370	25	trivially	trivially	ADV
ejpam-5430	370	26	pyfssw	pyfssw	ADV
ejpam-5430	370	27	-	-	PUNCT
ejpam-5430	370	28	open	open	ADJ
ejpam-5430	370	29	if	if	SCONJ
ejpam-5430	370	30	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	370	31	)	)	PUNCT
ejpam-5430	371	1	=	=	SYM
ejpam-5430	371	2	ϕη̃1	ϕη̃1	PROPN
ejpam-5430	371	3	.	.	PUNCT
ejpam-5430	372	1	assume	assume	VERB
ejpam-5430	372	2	that	that	SCONJ
ejpam-5430	372	3	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	372	4	)	)	PUNCT
ejpam-5430	372	5	is	be	AUX
ejpam-5430	372	6	not	not	PART
ejpam-5430	372	7	pyfssw	pyfssw	ADV
ejpam-5430	372	8	-	-	PUNCT
ejpam-5430	372	9	open	open	ADJ
ejpam-5430	372	10	,	,	PUNCT
ejpam-5430	372	11	i.e.	i.e.	X
ejpam-5430	372	12	int(f−1(hη̃2	int(f−1(hη̃2	NOUN
ejpam-5430	372	13	)	)	PUNCT
ejpam-5430	372	14	)	)	PUNCT
ejpam-5430	373	1	=	=	SYM
ejpam-5430	374	1	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	374	2	.	.	PUNCT
ejpam-5430	375	1	at	at	ADP
ejpam-5430	375	2	hence	hence	ADV
ejpam-5430	375	3	,	,	PUNCT
ejpam-5430	375	4	cl(x̃η̃1	cl(x̃η̃1	PROPN
ejpam-5430	375	5	\	\	PROPN
ejpam-5430	375	6	f−1(hη̃2	f−1(hη̃2	PROPN
ejpam-5430	375	7	)	)	PUNCT
ejpam-5430	375	8	=	=	SYM
ejpam-5430	375	9	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	375	10	.	.	PUNCT
ejpam-5430	376	1	this	this	PRON
ejpam-5430	376	2	suggests	suggest	VERB
ejpam-5430	376	3	that	that	SCONJ
ejpam-5430	376	4	on	on	ADP
ejpam-5430	376	5	x̃	x̃	PROPN
ejpam-5430	376	6	,	,	PUNCT
ejpam-5430	376	7	x̃η̃1	x̃η̃1	PROPN
ejpam-5430	376	8	\	\	PROPN
ejpam-5430	376	9	f−1(hη̃2	f−1(hη̃2	PROPN
ejpam-5430	376	10	)	)	PUNCT
ejpam-5430	376	11	is	be	AUX
ejpam-5430	376	12	pyfs	pyf	VERB
ejpam-5430	376	13	dense	dense	ADJ
ejpam-5430	376	14	.	.	PUNCT
ejpam-5430	377	1	from	from	ADP
ejpam-5430	377	2	4	4	NUM
ejpam-5430	377	3	,	,	PUNCT
ejpam-5430	377	4	f(x̃η̃1	f(x̃η̃1	VERB
ejpam-5430	377	5	\	\	PROPN
ejpam-5430	377	6	f−1(hη̃2	f−1(hη̃2	PROPN
ejpam-5430	377	7	)	)	PUNCT
ejpam-5430	377	8	)	)	PUNCT
ejpam-5430	377	9	is	be	AUX
ejpam-5430	377	10	pyfs	pyf	VERB
ejpam-5430	377	11	dense	dense	ADJ
ejpam-5430	377	12	over	over	ADP
ejpam-5430	377	13	f(x̃	f(x̃	NOUN
ejpam-5430	377	14	)	)	PUNCT
ejpam-5430	377	15	,	,	PUNCT
ejpam-5430	377	16	this	this	PRON
ejpam-5430	377	17	means	mean	VERB
ejpam-5430	377	18	that	that	SCONJ
ejpam-5430	377	19	cl(f(x̃η̃1	cl(f(x̃η̃1	NOUN
ejpam-5430	377	20	)	)	PUNCT
ejpam-5430	377	21	\	\	NOUN
ejpam-5430	377	22	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	377	23	)	)	PUNCT
ejpam-5430	377	24	)	)	PUNCT
ejpam-5430	378	1	=	=	SYM
ejpam-5430	378	2	f(x̃η̃1	f(x̃η̃1	PROPN
ejpam-5430	378	3	)	)	PUNCT
ejpam-5430	378	4	.	.	PUNCT
ejpam-5430	379	1	this	this	DET
ejpam-5430	379	2	results	result	NOUN
ejpam-5430	379	3	in	in	ADP
ejpam-5430	379	4	cl(f(x̃η̃1	cl(f(x̃η̃1	NOUN
ejpam-5430	379	5	)	)	PUNCT
ejpam-5430	379	6	\	\	NOUN
ejpam-5430	379	7	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	379	8	)	)	PUNCT
ejpam-5430	379	9	=	=	SYM
ejpam-5430	379	10	f(x̃η̃1	f(x̃η̃1	PROPN
ejpam-5430	379	11	)	)	PUNCT
ejpam-5430	379	12	\hη̃2	\hη̃2	PROPN
ejpam-5430	379	13	=	=	PUNCT
ejpam-5430	379	14	f(x̃η̃1	f(x̃η̃1	PROPN
ejpam-5430	379	15	)	)	PUNCT
ejpam-5430	379	16	and	and	CCONJ
ejpam-5430	379	17	so	so	ADV
ejpam-5430	379	18	hη̃2	hη̃2	VERB
ejpam-5430	379	19	=	=	ADJ
ejpam-5430	379	20	ϕη̃2	ϕη̃2	NOUN
ejpam-5430	379	21	.	.	PUNCT
ejpam-5430	380	1	in	in	ADP
ejpam-5430	380	2	contrast	contrast	NOUN
ejpam-5430	380	3	to	to	ADP
ejpam-5430	380	4	the	the	DET
ejpam-5430	380	5	selection	selection	NOUN
ejpam-5430	380	6	of	of	ADP
ejpam-5430	380	7	hη̃2	hη̃2	NOUN
ejpam-5430	380	8	.	.	PUNCT
ejpam-5430	381	1	as	as	ADP
ejpam-5430	381	2	a	a	DET
ejpam-5430	381	3	result	result	NOUN
ejpam-5430	381	4	,	,	PUNCT
ejpam-5430	381	5	int(f−1(h	int(f−1(h	PROPN
ejpam-5430	381	6	)	)	PUNCT
ejpam-5430	381	7	)	)	PUNCT
ejpam-5430	381	8	can	can	AUX
ejpam-5430	381	9	not	not	PART
ejpam-5430	381	10	be	be	AUX
ejpam-5430	381	11	null	null	ADJ
ejpam-5430	381	12	.	.	PUNCT
ejpam-5430	382	1	as	as	ADP
ejpam-5430	382	2	a	a	DET
ejpam-5430	382	3	result	result	NOUN
ejpam-5430	382	4	,	,	PUNCT
ejpam-5430	382	5	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	382	6	)	)	PUNCT
ejpam-5430	382	7	is	be	AUX
ejpam-5430	382	8	pyfssw	pyfssw	ADJ
ejpam-5430	382	9	on	on	ADP
ejpam-5430	382	10	x̃.	x̃.	ADJ
ejpam-5430	382	11	corollary	corollary	ADJ
ejpam-5430	382	12	4	4	NUM
ejpam-5430	382	13	.	.	PUNCT
ejpam-5430	383	1	consider	consider	VERB
ejpam-5430	383	2	(	(	PUNCT
ejpam-5430	383	3	x̃	x̃	PROPN
ejpam-5430	383	4	,	,	PUNCT
ejpam-5430	383	5	ω̃1	ω̃1	PROPN
ejpam-5430	383	6	,	,	PUNCT
ejpam-5430	383	7	η̃1	η̃1	PROPN
ejpam-5430	383	8	)	)	PUNCT
ejpam-5430	383	9	and	and	CCONJ
ejpam-5430	383	10	(	(	PUNCT
ejpam-5430	383	11	ỹ	ỹ	PROPN
ejpam-5430	383	12	,	,	PUNCT
ejpam-5430	383	13	ω̃2	ω̃2	PROPN
ejpam-5430	383	14	,	,	PUNCT
ejpam-5430	383	15	η̃2	η̃2	PROPN
ejpam-5430	383	16	)	)	PUNCT
ejpam-5430	383	17	be	be	AUX
ejpam-5430	383	18	a	a	DET
ejpam-5430	383	19	pyfsts	pyfst	NOUN
ejpam-5430	383	20	.	.	PUNCT
ejpam-5430	384	1	the	the	DET
ejpam-5430	384	2	corresponding	correspond	VERB
ejpam-5430	384	3	values	value	NOUN
ejpam-5430	384	4	for	for	ADP
ejpam-5430	384	5	a	a	DET
ejpam-5430	384	6	one	one	NUM
ejpam-5430	384	7	-	-	PUNCT
ejpam-5430	384	8	to	to	ADP
ejpam-5430	384	9	-	-	PUNCT
ejpam-5430	384	10	one	one	NUM
ejpam-5430	384	11	function	function	NOUN
ejpam-5430	384	12	are	be	AUX
ejpam-5430	384	13	as	as	SCONJ
ejpam-5430	384	14	follows	follow	VERB
ejpam-5430	384	15	:	:	PUNCT
ejpam-5430	384	16	f	f	X
ejpam-5430	384	17	:	:	PUNCT
ejpam-5430	384	18	(	(	PUNCT
ejpam-5430	384	19	ũ	ũ	PROPN
ejpam-5430	384	20	,	,	PUNCT
ejpam-5430	384	21	ω̃1	ω̃1	PROPN
ejpam-5430	384	22	,	,	PUNCT
ejpam-5430	384	23	η̃1	η̃1	PROPN
ejpam-5430	384	24	)	)	PUNCT
ejpam-5430	384	25	→	→	PUNCT
ejpam-5430	384	26	(	(	PUNCT
ejpam-5430	384	27	ỹ	ỹ	PROPN
ejpam-5430	384	28	,	,	PUNCT
ejpam-5430	384	29	ω̃2	ω̃2	PROPN
ejpam-5430	384	30	,	,	PUNCT
ejpam-5430	384	31	η̃2	η̃2	PROPN
ejpam-5430	384	32	):	):	PUNCT
ejpam-5430	384	33	a.	a.	PROPN
ejpam-5430	384	34	a.	a.	PROPN
ejpam-5430	384	35	azzam	azzam	PROPN
ejpam-5430	384	36	,	,	PUNCT
ejpam-5430	384	37	m.	m.	NOUN
ejpam-5430	384	38	aldawood	aldawood	PROPN
ejpam-5430	384	39	,	,	PUNCT
ejpam-5430	384	40	r.	r.	PROPN
ejpam-5430	384	41	abu	abu	PROPN
ejpam-5430	384	42	-	-	PUNCT
ejpam-5430	384	43	gdairi	gdairi	PROPN
ejpam-5430	384	44	/	/	SYM
ejpam-5430	384	45	eur	eur	PROPN
ejpam-5430	384	46	.	.	PUNCT
ejpam-5430	385	1	j.	j.	PROPN
ejpam-5430	385	2	pure	pure	PROPN
ejpam-5430	385	3	appl	appl	PROPN
ejpam-5430	385	4	.	.	PROPN
ejpam-5430	385	5	math	math	PROPN
ejpam-5430	385	6	,	,	PUNCT
ejpam-5430	385	7	17	17	NUM
ejpam-5430	385	8	(	(	PUNCT
ejpam-5430	385	9	4	4	NUM
ejpam-5430	385	10	)	)	PUNCT
ejpam-5430	385	11	(	(	PUNCT
ejpam-5430	385	12	2024	2024	NUM
ejpam-5430	385	13	)	)	PUNCT
ejpam-5430	385	14	,	,	PUNCT
ejpam-5430	385	15	4147	4147	NUM
ejpam-5430	385	16	-	-	SYM
ejpam-5430	385	17	4163	4163	NUM
ejpam-5430	385	18	4160	4160	NUM
ejpam-5430	385	19	a	a	X
ejpam-5430	385	20	-	-	PUNCT
ejpam-5430	385	21	f	f	PROPN
ejpam-5430	385	22	is	be	AUX
ejpam-5430	385	23	pyfssw	pyfssw	ADJ
ejpam-5430	385	24	-	-	PUNCT
ejpam-5430	385	25	c	c	NOUN
ejpam-5430	385	26	,	,	PUNCT
ejpam-5430	385	27	b	b	X
ejpam-5430	385	28	-	-	PUNCT
ejpam-5430	385	29	f(mη̃1	f(mη̃1	NOUN
ejpam-5430	385	30	)	)	PUNCT
ejpam-5430	385	31	is	be	AUX
ejpam-5430	385	32	pyfs	pyfs	ADJ
ejpam-5430	385	33	co	co	ADJ
ejpam-5430	385	34	-	-	NOUN
ejpam-5430	385	35	dense	dense	ADJ
ejpam-5430	385	36	over	over	ADP
ejpam-5430	385	37	ỹ	ỹ	PROPN
ejpam-5430	385	38	for	for	ADP
ejpam-5430	385	39	any	any	DET
ejpam-5430	385	40	soft	soft	ADJ
ejpam-5430	385	41	co	co	ADJ
ejpam-5430	385	42	-	-	ADJ
ejpam-5430	385	43	dense	dense	ADJ
ejpam-5430	385	44	set	set	NOUN
ejpam-5430	385	45	mη̃1	mη̃1	NOUN
ejpam-5430	385	46	over	over	ADP
ejpam-5430	385	47	x̃.	x̃.	ADJ
ejpam-5430	385	48	this	this	DET
ejpam-5430	385	49	section	section	NOUN
ejpam-5430	385	50	concludes	conclude	VERB
ejpam-5430	385	51	with	with	ADP
ejpam-5430	385	52	two	two	NUM
ejpam-5430	385	53	results	result	NOUN
ejpam-5430	385	54	about	about	ADP
ejpam-5430	385	55	soft	soft	ADJ
ejpam-5430	385	56	separable	separable	NOUN
ejpam-5430	385	57	and	and	CCONJ
ejpam-5430	385	58	hyperconnected	hyperconnected	ADJ
ejpam-5430	385	59	space	space	NOUN
ejpam-5430	385	60	.	.	PUNCT
ejpam-5430	386	1	theorem	theorem	ADJ
ejpam-5430	386	2	6	6	NUM
ejpam-5430	386	3	.	.	PUNCT
ejpam-5430	387	1	consider	consider	VERB
ejpam-5430	387	2	(	(	PUNCT
ejpam-5430	387	3	x̃	x̃	PROPN
ejpam-5430	387	4	,	,	PUNCT
ejpam-5430	387	5	ω̃1	ω̃1	PROPN
ejpam-5430	387	6	,	,	PUNCT
ejpam-5430	387	7	η̃1	η̃1	PROPN
ejpam-5430	387	8	)	)	PUNCT
ejpam-5430	387	9	and	and	CCONJ
ejpam-5430	387	10	(	(	PUNCT
ejpam-5430	387	11	ỹ	ỹ	PROPN
ejpam-5430	387	12	,	,	PUNCT
ejpam-5430	387	13	ω̃2	ω̃2	PROPN
ejpam-5430	387	14	,	,	PUNCT
ejpam-5430	387	15	η̃2	η̃2	PROPN
ejpam-5430	387	16	)	)	PUNCT
ejpam-5430	387	17	be	be	AUX
ejpam-5430	387	18	a	a	DET
ejpam-5430	387	19	pyfstss	pyfstss	NOUN
ejpam-5430	387	20	,	,	PUNCT
ejpam-5430	387	21	and	and	CCONJ
ejpam-5430	387	22	f	f	X
ejpam-5430	387	23	:	:	PUNCT
ejpam-5430	387	24	(	(	PUNCT
ejpam-5430	387	25	ũ	ũ	PROPN
ejpam-5430	387	26	,	,	PUNCT
ejpam-5430	387	27	ω̃1	ω̃1	PROPN
ejpam-5430	387	28	,	,	PUNCT
ejpam-5430	387	29	η̃1	η̃1	PROPN
ejpam-5430	387	30	)	)	PUNCT
ejpam-5430	387	31	→	→	PUNCT
ejpam-5430	387	32	(	(	PUNCT
ejpam-5430	387	33	ỹ	ỹ	PROPN
ejpam-5430	387	34	,	,	PUNCT
ejpam-5430	387	35	ω̃2	ω̃2	PROPN
ejpam-5430	387	36	,	,	PUNCT
ejpam-5430	387	37	η̃2	η̃2	PROPN
ejpam-5430	387	38	)	)	PUNCT
ejpam-5430	387	39	.	.	PUNCT
ejpam-5430	388	1	if	if	SCONJ
ejpam-5430	388	2	f	f	PROPN
ejpam-5430	388	3	is	be	AUX
ejpam-5430	388	4	pyfssw	pyfssw	ADJ
ejpam-5430	388	5	-	-	PUNCT
ejpam-5430	388	6	c	c	NOUN
ejpam-5430	388	7	and	and	CCONJ
ejpam-5430	388	8	(	(	PUNCT
ejpam-5430	388	9	x̃	x̃	PROPN
ejpam-5430	388	10	,	,	PUNCT
ejpam-5430	388	11	ω̃1	ω̃1	PROPN
ejpam-5430	388	12	,	,	PUNCT
ejpam-5430	388	13	η̃1	η̃1	PROPN
ejpam-5430	388	14	)	)	PUNCT
ejpam-5430	388	15	is	be	AUX
ejpam-5430	388	16	pyfs	pyfs	ADJ
ejpam-5430	388	17	separable	separable	NOUN
ejpam-5430	388	18	,	,	PUNCT
ejpam-5430	388	19	then	then	ADV
ejpam-5430	388	20	(	(	PUNCT
ejpam-5430	388	21	ỹ	ỹ	PROPN
ejpam-5430	388	22	,	,	PUNCT
ejpam-5430	388	23	ω̃2	ω̃2	PROPN
ejpam-5430	388	24	,	,	PUNCT
ejpam-5430	388	25	η̃2	η̃2	PROPN
ejpam-5430	388	26	)	)	PUNCT
ejpam-5430	388	27	is	be	AUX
ejpam-5430	388	28	pyfs	pyfs	ADJ
ejpam-5430	388	29	separable	separable	NOUN
ejpam-5430	388	30	.	.	PUNCT
ejpam-5430	389	1	proof	proof	NOUN
ejpam-5430	389	2	.	.	PUNCT
ejpam-5430	390	1	allow	allow	VERB
ejpam-5430	390	2	dη̃1	dη̃1	PROPN
ejpam-5430	390	3	to	to	PART
ejpam-5430	390	4	be	be	AUX
ejpam-5430	390	5	a	a	DET
ejpam-5430	390	6	countable	countable	ADJ
ejpam-5430	390	7	pyfs	pyfs	ADJ
ejpam-5430	390	8	dense	dense	ADJ
ejpam-5430	390	9	set	set	NOUN
ejpam-5430	390	10	on	on	ADP
ejpam-5430	390	11	x̃.	x̃.	ADJ
ejpam-5430	390	12	f(dη̃1	f(dη̃1	NOUN
ejpam-5430	390	13	)	)	PUNCT
ejpam-5430	390	14	is	be	AUX
ejpam-5430	390	15	clearly	clearly	ADV
ejpam-5430	390	16	countable	countable	ADJ
ejpam-5430	390	17	.	.	PUNCT
ejpam-5430	391	1	according	accord	VERB
ejpam-5430	391	2	to	to	ADP
ejpam-5430	391	3	f(dη̃1	f(dη̃1	NOUN
ejpam-5430	391	4	)	)	PUNCT
ejpam-5430	391	5	is	be	AUX
ejpam-5430	391	6	pyfs	pyf	VERB
ejpam-5430	391	7	dense	dense	ADJ
ejpam-5430	391	8	over	over	ADP
ejpam-5430	391	9	f(x̃	f(x̃	NOUN
ejpam-5430	391	10	)	)	PUNCT
ejpam-5430	391	11	=	=	SYM
ejpam-5430	391	12	ỹ	ỹ	PROPN
ejpam-5430	391	13	.	.	PUNCT
ejpam-5430	392	1	as	as	ADP
ejpam-5430	392	2	a	a	DET
ejpam-5430	392	3	result	result	NOUN
ejpam-5430	392	4	,	,	PUNCT
ejpam-5430	392	5	(	(	PUNCT
ejpam-5430	392	6	ỹ	ỹ	PROPN
ejpam-5430	392	7	,	,	PUNCT
ejpam-5430	392	8	ω̃2	ω̃2	PROPN
ejpam-5430	392	9	,	,	PUNCT
ejpam-5430	392	10	η̃2	η̃2	PROPN
ejpam-5430	392	11	)	)	PUNCT
ejpam-5430	392	12	is	be	AUX
ejpam-5430	392	13	pyfs	pyfs	ADJ
ejpam-5430	392	14	separable	separable	NOUN
ejpam-5430	392	15	.	.	PUNCT
ejpam-5430	393	1	theorem	theorem	VERB
ejpam-5430	393	2	7	7	NUM
ejpam-5430	393	3	.	.	PUNCT
ejpam-5430	394	1	let	let	VERB
ejpam-5430	394	2	(	(	PUNCT
ejpam-5430	394	3	x̃	x̃	PROPN
ejpam-5430	394	4	,	,	PUNCT
ejpam-5430	394	5	ω̃1	ω̃1	PROPN
ejpam-5430	394	6	,	,	PUNCT
ejpam-5430	394	7	η̃1	η̃1	PROPN
ejpam-5430	394	8	)	)	PUNCT
ejpam-5430	394	9	and	and	CCONJ
ejpam-5430	394	10	(	(	PUNCT
ejpam-5430	394	11	ỹ	ỹ	PROPN
ejpam-5430	394	12	,	,	PUNCT
ejpam-5430	394	13	ω̃2	ω̃2	PROPN
ejpam-5430	394	14	,	,	PUNCT
ejpam-5430	394	15	η̃2	η̃2	PROPN
ejpam-5430	394	16	)	)	PUNCT
ejpam-5430	394	17	be	be	AUX
ejpam-5430	394	18	a	a	DET
ejpam-5430	394	19	pyfstss	pyfstss	NOUN
ejpam-5430	394	20	,	,	PUNCT
ejpam-5430	394	21	and	and	CCONJ
ejpam-5430	394	22	f	f	X
ejpam-5430	394	23	:	:	PUNCT
ejpam-5430	394	24	(	(	PUNCT
ejpam-5430	394	25	ũ	ũ	PROPN
ejpam-5430	394	26	,	,	PUNCT
ejpam-5430	394	27	ω̃1	ω̃1	PROPN
ejpam-5430	394	28	,	,	PUNCT
ejpam-5430	394	29	η̃1	η̃1	PROPN
ejpam-5430	394	30	)	)	PUNCT
ejpam-5430	394	31	→	→	PUNCT
ejpam-5430	394	32	(	(	PUNCT
ejpam-5430	394	33	ỹ	ỹ	PROPN
ejpam-5430	394	34	,	,	PUNCT
ejpam-5430	394	35	ω̃2	ω̃2	PROPN
ejpam-5430	394	36	,	,	PUNCT
ejpam-5430	394	37	η̃2	η̃2	PROPN
ejpam-5430	394	38	)	)	PUNCT
ejpam-5430	394	39	.	.	PUNCT
ejpam-5430	395	1	if	if	SCONJ
ejpam-5430	395	2	f	f	PROPN
ejpam-5430	395	3	is	be	AUX
ejpam-5430	395	4	pyfssw	pyfssw	ADJ
ejpam-5430	395	5	-	-	PUNCT
ejpam-5430	395	6	c	c	NOUN
ejpam-5430	395	7	and	and	CCONJ
ejpam-5430	395	8	(	(	PUNCT
ejpam-5430	395	9	x̃	x̃	PROPN
ejpam-5430	395	10	,	,	PUNCT
ejpam-5430	395	11	ω̃1	ω̃1	PROPN
ejpam-5430	395	12	,	,	PUNCT
ejpam-5430	395	13	η̃1	η̃1	PROPN
ejpam-5430	395	14	)	)	PUNCT
ejpam-5430	395	15	is	be	AUX
ejpam-5430	395	16	pyfs	pyfs	ADJ
ejpam-5430	395	17	hyperconnected	hyperconnecte	VERB
ejpam-5430	395	18	,	,	PUNCT
ejpam-5430	395	19	then	then	ADV
ejpam-5430	395	20	(	(	PUNCT
ejpam-5430	395	21	ỹ	ỹ	PROPN
ejpam-5430	395	22	,	,	PUNCT
ejpam-5430	395	23	ω̃2	ω̃2	PROPN
ejpam-5430	395	24	,	,	PUNCT
ejpam-5430	395	25	η̃2	η̃2	PROPN
ejpam-5430	395	26	)	)	PUNCT
ejpam-5430	395	27	is	be	AUX
ejpam-5430	395	28	pyfs	pyfs	ADJ
ejpam-5430	395	29	hyperconnected	hyperconnecte	VERB
ejpam-5430	395	30	.	.	PUNCT
ejpam-5430	396	1	proof	proof	NOUN
ejpam-5430	396	2	.	.	PUNCT
ejpam-5430	397	1	allow	allow	VERB
ejpam-5430	397	2	gη̃2	gη̃2	NOUN
ejpam-5430	397	3	,	,	PUNCT
ejpam-5430	397	4	hη̃2	hη̃2	NOUN
ejpam-5430	397	5	be	be	VERB
ejpam-5430	397	6	any	any	DET
ejpam-5430	397	7	two	two	NUM
ejpam-5430	397	8	pyfs	pyfs	ADJ
ejpam-5430	397	9	open	open	ADJ
ejpam-5430	397	10	sets	set	NOUN
ejpam-5430	397	11	over	over	ADP
ejpam-5430	397	12	ỹ	ỹ	PROPN
ejpam-5430	397	13	with	with	ADP
ejpam-5430	397	14	gη̃2	gη̃2	NOUN
ejpam-5430	397	15	̸=	̸=	PROPN
ejpam-5430	397	16	hη̃2	hη̃2	VERB
ejpam-5430	397	17	̸=	̸=	PROPN
ejpam-5430	397	18	ϕη̃2	ϕη̃2	NOUN
ejpam-5430	397	19	.	.	PUNCT
ejpam-5430	398	1	since	since	SCONJ
ejpam-5430	398	2	f	f	PROPN
ejpam-5430	398	3	is	be	AUX
ejpam-5430	398	4	pyfssw	pyfssw	ADJ
ejpam-5430	398	5	-	-	PUNCT
ejpam-5430	398	6	c	c	NOUN
ejpam-5430	398	7	,	,	PUNCT
ejpam-5430	398	8	then	then	ADV
ejpam-5430	398	9	int(f−1(gη̃2	int(f−1(gη̃2	NOUN
ejpam-5430	398	10	)	)	PUNCT
ejpam-5430	398	11	̸=	̸=	PROPN
ejpam-5430	398	12	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	398	13	̸=	̸=	PROPN
ejpam-5430	398	14	int(f−1(hη̃2	int(f−1(hη̃2	PROPN
ejpam-5430	398	15	)	)	PUNCT
ejpam-5430	398	16	.	.	PUNCT
ejpam-5430	399	1	but	but	CCONJ
ejpam-5430	399	2	(	(	PUNCT
ejpam-5430	399	3	x̃	x̃	PROPN
ejpam-5430	399	4	,	,	PUNCT
ejpam-5430	399	5	ω̃1	ω̃1	PROPN
ejpam-5430	399	6	,	,	PUNCT
ejpam-5430	399	7	η̃1	η̃1	PROPN
ejpam-5430	399	8	)	)	PUNCT
ejpam-5430	399	9	is	be	AUX
ejpam-5430	399	10	pyfs	pyfs	ADJ
ejpam-5430	399	11	hyperconnected	hyperconnecte	VERB
ejpam-5430	399	12	,	,	PUNCT
ejpam-5430	399	13	then	then	ADV
ejpam-5430	399	14	int(f−1(gη̃2	int(f−1(gη̃2	NOUN
ejpam-5430	399	15	)	)	PUNCT
ejpam-5430	399	16	)	)	PUNCT
ejpam-5430	400	1	⊓	⊓	PROPN
ejpam-5430	400	2	int(f−1(hη̃2	int(f−1(hη̃2	NOUN
ejpam-5430	400	3	)	)	PUNCT
ejpam-5430	400	4	̸=	̸=	PROPN
ejpam-5430	400	5	ϕη̃1	ϕη̃1	NOUN
ejpam-5430	400	6	.	.	PUNCT
ejpam-5430	401	1	if	if	SCONJ
ejpam-5430	401	2	x	x	SYM
ejpam-5430	401	3	∈	∈	PROPN
ejpam-5430	401	4	int(f−1(gη̃2	int(f−1(gη̃2	NOUN
ejpam-5430	401	5	)	)	PUNCT
ejpam-5430	401	6	)	)	PUNCT
ejpam-5430	402	1	⊓	⊓	PROPN
ejpam-5430	402	2	int(f−1(hη̃2	int(f−1(hη̃2	NOUN
ejpam-5430	402	3	)	)	PUNCT
ejpam-5430	402	4	)	)	PUNCT
ejpam-5430	402	5	⊑	⊑	PRON
ejpam-5430	402	6	f−1(gη̃2	f−1(gη̃2	VERB
ejpam-5430	402	7	)	)	PUNCT
ejpam-5430	403	1	⊓	⊓	PROPN
ejpam-5430	403	2	f−1(hη̃2	f−1(hη̃2	NOUN
ejpam-5430	403	3	)	)	PUNCT
ejpam-5430	404	1	,	,	PUNCT
ejpam-5430	404	2	at	at	ADP
ejpam-5430	404	3	hence	hence	ADV
ejpam-5430	404	4	f(x	f(x	NOUN
ejpam-5430	404	5	)	)	PUNCT
ejpam-5430	404	6	∈	∈	NOUN
ejpam-5430	404	7	gη̃2	gη̃2	NOUN
ejpam-5430	404	8	⊓hη̃2	⊓hη̃2	PROPN
ejpam-5430	404	9	.	.	PUNCT
ejpam-5430	405	1	thus	thus	ADV
ejpam-5430	405	2	(	(	PUNCT
ejpam-5430	405	3	ỹ	ỹ	PROPN
ejpam-5430	405	4	,	,	PUNCT
ejpam-5430	405	5	ω̃2	ω̃2	PROPN
ejpam-5430	405	6	,	,	PUNCT
ejpam-5430	405	7	η̃2	η̃2	PROPN
ejpam-5430	405	8	)	)	PUNCT
ejpam-5430	405	9	is	be	AUX
ejpam-5430	405	10	pyfs	pyfs	ADJ
ejpam-5430	405	11	hyperconnected	hyperconnecte	VERB
ejpam-5430	405	12	.	.	PUNCT
ejpam-5430	406	1	5	5	X
ejpam-5430	406	2	.	.	X
ejpam-5430	406	3	conclusion	conclusion	VERB
ejpam-5430	406	4	numerous	numerous	ADJ
ejpam-5430	406	5	aspects	aspect	NOUN
ejpam-5430	406	6	of	of	ADP
ejpam-5430	406	7	everyday	everyday	ADJ
ejpam-5430	406	8	existence	existence	NOUN
ejpam-5430	406	9	are	be	AUX
ejpam-5430	406	10	uncertain	uncertain	ADJ
ejpam-5430	406	11	.	.	PUNCT
ejpam-5430	407	1	the	the	DET
ejpam-5430	407	2	pyfss	pyfss	NOUN
ejpam-5430	407	3	theory	theory	NOUN
ejpam-5430	407	4	is	be	AUX
ejpam-5430	407	5	one	one	NUM
ejpam-5430	407	6	theory	theory	NOUN
ejpam-5430	407	7	developed	develop	VERB
ejpam-5430	407	8	to	to	PART
ejpam-5430	407	9	deal	deal	VERB
ejpam-5430	407	10	with	with	ADP
ejpam-5430	407	11	uncertainty	uncertainty	NOUN
ejpam-5430	407	12	.	.	PUNCT
ejpam-5430	408	1	this	this	DET
ejpam-5430	408	2	study	study	NOUN
ejpam-5430	408	3	is	be	AUX
ejpam-5430	408	4	based	base	VERB
ejpam-5430	408	5	on	on	ADP
ejpam-5430	408	6	a	a	DET
ejpam-5430	408	7	novel	novel	ADJ
ejpam-5430	408	8	mathematical	mathematical	ADJ
ejpam-5430	408	9	structure	structure	NOUN
ejpam-5430	408	10	called	call	VERB
ejpam-5430	408	11	pyfst	pyfst	PROPN
ejpam-5430	408	12	,	,	PUNCT
ejpam-5430	408	13	which	which	PRON
ejpam-5430	408	14	was	be	AUX
ejpam-5430	408	15	initiated	initiate	VERB
ejpam-5430	408	16	by	by	ADP
ejpam-5430	408	17	typologists	typologist	NOUN
ejpam-5430	408	18	using	use	VERB
ejpam-5430	408	19	pyfsss	pyfsss	NOUN
ejpam-5430	408	20	.	.	PUNCT
ejpam-5430	409	1	in	in	ADP
ejpam-5430	409	2	this	this	DET
ejpam-5430	409	3	work	work	NOUN
ejpam-5430	409	4	,	,	PUNCT
ejpam-5430	409	5	we	we	PRON
ejpam-5430	409	6	presented	present	VERB
ejpam-5430	409	7	the	the	DET
ejpam-5430	409	8	idea	idea	NOUN
ejpam-5430	409	9	of	of	ADP
ejpam-5430	409	10	pyfssw	pyfssw	ADJ
ejpam-5430	409	11	open	open	ADJ
ejpam-5430	409	12	sets	set	NOUN
ejpam-5430	409	13	as	as	ADP
ejpam-5430	409	14	a	a	DET
ejpam-5430	409	15	new	new	ADJ
ejpam-5430	409	16	extension	extension	NOUN
ejpam-5430	409	17	of	of	ADP
ejpam-5430	409	18	pyfs	pyfs	ADJ
ejpam-5430	409	19	open	open	ADJ
ejpam-5430	409	20	sets	set	NOUN
ejpam-5430	409	21	.	.	PUNCT
ejpam-5430	410	1	on	on	ADP
ejpam-5430	410	2	the	the	DET
ejpam-5430	410	3	one	one	NUM
ejpam-5430	410	4	hand	hand	NOUN
ejpam-5430	410	5	,	,	PUNCT
ejpam-5430	410	6	the	the	DET
ejpam-5430	410	7	family	family	NOUN
ejpam-5430	410	8	of	of	ADP
ejpam-5430	410	9	pyfs	pyf	VERB
ejpam-5430	410	10	open	open	ADJ
ejpam-5430	410	11	to	to	ADP
ejpam-5430	410	12	some	some	DET
ejpam-5430	410	13	extent	extent	NOUN
ejpam-5430	410	14	sets	set	NOUN
ejpam-5430	410	15	is	be	AUX
ejpam-5430	410	16	located	locate	VERB
ejpam-5430	410	17	between	between	ADP
ejpam-5430	410	18	the	the	DET
ejpam-5430	410	19	families	family	NOUN
ejpam-5430	410	20	of	of	ADP
ejpam-5430	410	21	pyfs	pyfs	ADJ
ejpam-5430	410	22	semiopen	semiopen	ADJ
ejpam-5430	410	23	sets	set	NOUN
ejpam-5430	410	24	and	and	CCONJ
ejpam-5430	410	25	pyfs	pyf	VERB
ejpam-5430	410	26	somewhere	somewhere	ADV
ejpam-5430	410	27	dense	dense	ADJ
ejpam-5430	410	28	sets	set	NOUN
ejpam-5430	410	29	.	.	PUNCT
ejpam-5430	411	1	the	the	DET
ejpam-5430	411	2	families	family	NOUN
ejpam-5430	411	3	of	of	ADP
ejpam-5430	411	4	pyfssw	pyfssw	ADJ
ejpam-5430	411	5	open	open	ADJ
ejpam-5430	411	6	sets	set	NOUN
ejpam-5430	411	7	and	and	CCONJ
ejpam-5430	411	8	pyfsβ	pyfsβ	ADJ
ejpam-5430	411	9	-	-	PUNCT
ejpam-5430	411	10	open	open	ADJ
ejpam-5430	411	11	sets	set	NOUN
ejpam-5430	411	12	,	,	PUNCT
ejpam-5430	411	13	on	on	ADP
ejpam-5430	411	14	the	the	DET
ejpam-5430	411	15	other	other	ADJ
ejpam-5430	411	16	hand	hand	NOUN
ejpam-5430	411	17	,	,	PUNCT
ejpam-5430	411	18	are	be	AUX
ejpam-5430	411	19	independent	independent	ADJ
ejpam-5430	411	20	of	of	ADP
ejpam-5430	411	21	one	one	NUM
ejpam-5430	411	22	another	another	DET
ejpam-5430	411	23	.	.	PUNCT
ejpam-5430	412	1	with	with	ADP
ejpam-5430	412	2	the	the	DET
ejpam-5430	412	3	help	help	NOUN
ejpam-5430	412	4	of	of	ADP
ejpam-5430	412	5	examples	example	NOUN
ejpam-5430	412	6	,	,	PUNCT
ejpam-5430	412	7	these	these	DET
ejpam-5430	412	8	linkages	linkage	NOUN
ejpam-5430	412	9	have	have	AUX
ejpam-5430	412	10	been	be	AUX
ejpam-5430	412	11	explained	explain	VERB
ejpam-5430	412	12	and	and	CCONJ
ejpam-5430	412	13	main	main	ADJ
ejpam-5430	412	14	attributes	attribute	NOUN
ejpam-5430	412	15	established	establish	VERB
ejpam-5430	412	16	.	.	PUNCT
ejpam-5430	413	1	then	then	ADV
ejpam-5430	413	2	,	,	PUNCT
ejpam-5430	413	3	to	to	PART
ejpam-5430	413	4	define	define	VERB
ejpam-5430	413	5	pyfssw	pyfssw	ADV
ejpam-5430	413	6	-	-	PUNCT
ejpam-5430	413	7	continuous	continuous	ADJ
ejpam-5430	413	8	,	,	PUNCT
ejpam-5430	413	9	we	we	PRON
ejpam-5430	413	10	used	use	VERB
ejpam-5430	413	11	pyfssw	pyfssw	NOUN
ejpam-5430	413	12	open	open	ADJ
ejpam-5430	413	13	sets	set	NOUN
ejpam-5430	413	14	.	.	PUNCT
ejpam-5430	414	1	we	we	PRON
ejpam-5430	414	2	defined	define	VERB
ejpam-5430	414	3	these	these	DET
ejpam-5430	414	4	two	two	NUM
ejpam-5430	414	5	functions	function	NOUN
ejpam-5430	414	6	and	and	CCONJ
ejpam-5430	414	7	explored	explore	VERB
ejpam-5430	414	8	their	their	PRON
ejpam-5430	414	9	key	key	ADJ
ejpam-5430	414	10	characteristics	characteristic	NOUN
ejpam-5430	414	11	.	.	PUNCT
ejpam-5430	415	1	investigates	investigate	VERB
ejpam-5430	415	2	some	some	DET
ejpam-5430	415	3	intriguing	intriguing	ADJ
ejpam-5430	415	4	relationships	relationship	NOUN
ejpam-5430	415	5	in	in	ADP
ejpam-5430	415	6	a	a	DET
ejpam-5430	415	7	certain	certain	ADJ
ejpam-5430	415	8	pyfst	pyfst	NOUN
ejpam-5430	415	9	in	in	ADP
ejpam-5430	415	10	[	[	X
ejpam-5430	415	11	8	8	NUM
ejpam-5430	415	12	]	]	PUNCT
ejpam-5430	415	13	.	.	PUNCT
ejpam-5430	416	1	the	the	DET
ejpam-5430	416	2	purpose	purpose	NOUN
ejpam-5430	416	3	of	of	ADP
ejpam-5430	416	4	developing	develop	VERB
ejpam-5430	416	5	these	these	DET
ejpam-5430	416	6	categories	category	NOUN
ejpam-5430	416	7	was	be	AUX
ejpam-5430	416	8	to	to	PART
ejpam-5430	416	9	analyze	analyze	VERB
ejpam-5430	416	10	the	the	DET
ejpam-5430	416	11	distinctions	distinction	NOUN
ejpam-5430	416	12	betweenpyfs	betweenpyfs	ADJ
ejpam-5430	416	13	homeomorphism	homeomorphism	PROPN
ejpam-5430	416	14	and	and	CCONJ
ejpam-5430	416	15	pyfs	pyfs	ADJ
ejpam-5430	416	16	partly	partly	ADV
ejpam-5430	416	17	homeomorphism	homeomorphism	NOUN
ejpam-5430	416	18	in	in	ADP
ejpam-5430	416	19	terms	term	NOUN
ejpam-5430	416	20	of	of	ADP
ejpam-5430	416	21	preserving	preserve	VERB
ejpam-5430	416	22	certain	certain	ADJ
ejpam-5430	416	23	pyfst	pyfst	ADJ
ejpam-5430	416	24	features	feature	NOUN
ejpam-5430	416	25	.	.	PUNCT
ejpam-5430	417	1	in	in	ADP
ejpam-5430	417	2	the	the	DET
ejpam-5430	417	3	following	follow	VERB
ejpam-5430	417	4	work	work	NOUN
ejpam-5430	417	5	,	,	PUNCT
ejpam-5430	417	6	we	we	PRON
ejpam-5430	417	7	intend	intend	VERB
ejpam-5430	417	8	to	to	PART
ejpam-5430	417	9	investigate	investigate	VERB
ejpam-5430	417	10	some	some	DET
ejpam-5430	417	11	topological	topological	ADJ
ejpam-5430	417	12	concepts	concept	NOUN
ejpam-5430	417	13	such	such	ADJ
ejpam-5430	417	14	as	as	ADP
ejpam-5430	417	15	pyfs	pyfs	ADJ
ejpam-5430	417	16	compactness	compactness	NOUN
ejpam-5430	417	17	,	,	PUNCT
ejpam-5430	417	18	pyfs	pyfs	ADJ
ejpam-5430	417	19	lindelofness	lindelofness	NOUN
ejpam-5430	417	20	,	,	PUNCT
ejpam-5430	417	21	and	and	CCONJ
ejpam-5430	417	22	pyfs	pyfs	ADJ
ejpam-5430	417	23	connectedness	connectedness	NOUN
ejpam-5430	417	24	using	use	VERB
ejpam-5430	417	25	pyfssw	pyfssw	ADJ
ejpam-5430	417	26	open	open	ADJ
ejpam-5430	417	27	sets	set	NOUN
ejpam-5430	417	28	.	.	PUNCT
ejpam-5430	418	1	it	it	PRON
ejpam-5430	418	2	is	be	AUX
ejpam-5430	418	3	also	also	ADV
ejpam-5430	418	4	planned	plan	VERB
ejpam-5430	418	5	to	to	PART
ejpam-5430	418	6	investigate	investigate	VERB
ejpam-5430	418	7	certain	certain	ADJ
ejpam-5430	418	8	applications	application	NOUN
ejpam-5430	418	9	of	of	ADP
ejpam-5430	418	10	pyfssw	pyfssw	ADJ
ejpam-5430	418	11	homeomorphisms	homeomorphism	NOUN
ejpam-5430	418	12	.	.	PUNCT
ejpam-5430	419	1	in	in	ADP
ejpam-5430	419	2	addition	addition	NOUN
ejpam-5430	419	3	,	,	PUNCT
ejpam-5430	419	4	we	we	PRON
ejpam-5430	419	5	investigate	investigate	VERB
ejpam-5430	419	6	pyfssw	pyfssw	ADJ
ejpam-5430	419	7	open	open	ADJ
ejpam-5430	419	8	sets	set	NOUN
ejpam-5430	419	9	in	in	ADP
ejpam-5430	419	10	the	the	DET
ejpam-5430	419	11	context	context	NOUN
ejpam-5430	419	12	of	of	ADP
ejpam-5430	419	13	supra	supra	PROPN
ejpam-5430	419	14	pyfsts	pyfst	NOUN
ejpam-5430	419	15	.	.	PUNCT
ejpam-5430	420	1	this	this	DET
ejpam-5430	420	2	study	study	NOUN
ejpam-5430	420	3	has	have	AUX
ejpam-5430	420	4	laid	lay	VERB
ejpam-5430	420	5	the	the	DET
ejpam-5430	420	6	groundwork	groundwork	NOUN
ejpam-5430	420	7	for	for	ADP
ejpam-5430	420	8	further	further	ADJ
ejpam-5430	420	9	exploration	exploration	NOUN
ejpam-5430	420	10	of	of	ADP
ejpam-5430	420	11	pyfss	pyfss	NOUN
ejpam-5430	420	12	and	and	CCONJ
ejpam-5430	420	13	their	their	PRON
ejpam-5430	420	14	applications	application	NOUN
ejpam-5430	420	15	.	.	PUNCT
ejpam-5430	421	1	future	future	ADJ
ejpam-5430	421	2	research	research	NOUN
ejpam-5430	421	3	should	should	AUX
ejpam-5430	421	4	investigate	investigate	VERB
ejpam-5430	421	5	the	the	DET
ejpam-5430	421	6	potential	potential	NOUN
ejpam-5430	421	7	of	of	ADP
ejpam-5430	421	8	t	t	PROPN
ejpam-5430	421	9	-	-	PUNCT
ejpam-5430	421	10	bipolar	bipolar	ADJ
ejpam-5430	421	11	sss	sss	NOUN
ejpam-5430	421	12	[	[	X
ejpam-5430	421	13	3	3	NUM
ejpam-5430	421	14	]	]	PUNCT
ejpam-5430	421	15	,	,	PUNCT
ejpam-5430	421	16	spherical	spherical	ADJ
ejpam-5430	421	17	and	and	CCONJ
ejpam-5430	421	18	t	t	NOUN
ejpam-5430	421	19	-	-	PUNCT
ejpam-5430	421	20	spherical	spherical	ADJ
ejpam-5430	421	21	fss	fss	NOUN
ejpam-5430	422	1	[	[	X
ejpam-5430	422	2	9	9	NUM
ejpam-5430	422	3	]	]	PUNCT
ejpam-5430	422	4	,	,	PUNCT
ejpam-5430	422	5	complex	complex	ADJ
ejpam-5430	422	6	pyfss	pyfss	NOUN
ejpam-5430	422	7	[	[	X
ejpam-5430	422	8	7	7	NUM
ejpam-5430	422	9	,	,	PUNCT
ejpam-5430	422	10	16	16	NUM
ejpam-5430	422	11	]	]	PUNCT
ejpam-5430	422	12	,	,	PUNCT
ejpam-5430	422	13	and	and	CCONJ
ejpam-5430	422	14	bipolar	bipolar	ADJ
ejpam-5430	422	15	complex	complex	ADJ
ejpam-5430	422	16	fss	fss	NOUN
ejpam-5430	423	1	[	[	X
ejpam-5430	423	2	21	21	NUM
ejpam-5430	423	3	]	]	PUNCT
ejpam-5430	423	4	.	.	PUNCT
ejpam-5430	424	1	these	these	DET
ejpam-5430	424	2	directions	direction	NOUN
ejpam-5430	424	3	offer	offer	VERB
ejpam-5430	424	4	promising	promise	VERB
ejpam-5430	424	5	avenues	avenue	NOUN
ejpam-5430	424	6	for	for	ADP
ejpam-5430	424	7	developing	develop	VERB
ejpam-5430	424	8	more	more	ADV
ejpam-5430	424	9	sophisticated	sophisticated	ADJ
ejpam-5430	424	10	models	model	NOUN
ejpam-5430	424	11	and	and	CCONJ
ejpam-5430	424	12	decision	decision	NOUN
ejpam-5430	424	13	-	-	PUNCT
ejpam-5430	424	14	making	make	VERB
ejpam-5430	424	15	tools	tool	NOUN
ejpam-5430	424	16	in	in	ADP
ejpam-5430	424	17	various	various	ADJ
ejpam-5430	424	18	scientific	scientific	ADJ
ejpam-5430	424	19	and	and	CCONJ
ejpam-5430	424	20	engineering	engineering	NOUN
ejpam-5430	424	21	domains	domain	NOUN
ejpam-5430	424	22	.	.	PUNCT
ejpam-5430	425	1	references	reference	NOUN
ejpam-5430	425	2	4161	4161	NUM
ejpam-5430	425	3	declaration	declaration	NOUN
ejpam-5430	425	4	competing	compete	VERB
ejpam-5430	425	5	interests	interest	NOUN
ejpam-5430	425	6	:	:	PUNCT
ejpam-5430	425	7	no	no	DET
ejpam-5430	425	8	competing	compete	VERB
ejpam-5430	425	9	interests	interest	NOUN
ejpam-5430	425	10	have	have	AUX
ejpam-5430	425	11	been	be	AUX
ejpam-5430	425	12	disclosed	disclose	VERB
ejpam-5430	425	13	by	by	ADP
ejpam-5430	425	14	the	the	DET
ejpam-5430	425	15	authors	author	NOUN
ejpam-5430	425	16	.	.	PUNCT
ejpam-5430	426	1	availability	availability	NOUN
ejpam-5430	426	2	of	of	ADP
ejpam-5430	426	3	data	datum	NOUN
ejpam-5430	426	4	and	and	CCONJ
ejpam-5430	426	5	material	material	NOUN
ejpam-5430	426	6	:	:	PUNCT
ejpam-5430	426	7	there	there	PRON
ejpam-5430	426	8	were	be	VERB
ejpam-5430	426	9	no	no	DET
ejpam-5430	426	10	data	datum	NOUN
ejpam-5430	426	11	used	use	VERB
ejpam-5430	426	12	in	in	ADP
ejpam-5430	426	13	this	this	DET
ejpam-5430	426	14	investigation	investigation	NOUN
ejpam-5430	426	15	.	.	PUNCT
ejpam-5430	427	1	authors	author	NOUN
ejpam-5430	427	2	’	'	PUNCT
ejpam-5430	427	3	contributions	contribution	NOUN
ejpam-5430	427	4	:	:	PUNCT
ejpam-5430	427	5	the	the	DET
ejpam-5430	427	6	author	author	NOUN
ejpam-5430	427	7	conducted	conduct	VERB
ejpam-5430	427	8	the	the	DET
ejpam-5430	427	9	research	research	NOUN
ejpam-5430	427	10	,	,	PUNCT
ejpam-5430	427	11	wrote	write	VERB
ejpam-5430	427	12	the	the	DET
ejpam-5430	427	13	paper	paper	NOUN
ejpam-5430	427	14	,	,	PUNCT
ejpam-5430	427	15	and	and	CCONJ
ejpam-5430	427	16	came	come	VERB
ejpam-5430	427	17	to	to	ADP
ejpam-5430	427	18	the	the	DET
ejpam-5430	427	19	conclusions	conclusion	NOUN
ejpam-5430	427	20	on	on	ADP
ejpam-5430	427	21	his	his	PRON
ejpam-5430	427	22	own	own	ADJ
ejpam-5430	427	23	.	.	PUNCT
ejpam-5430	428	1	acknowledgements	acknowledgement	NOUN
ejpam-5430	428	2	the	the	DET
ejpam-5430	428	3	authors	author	NOUN
ejpam-5430	428	4	extend	extend	VERB
ejpam-5430	428	5	their	their	PRON
ejpam-5430	428	6	appreciation	appreciation	NOUN
ejpam-5430	428	7	to	to	ADP
ejpam-5430	428	8	prince	prince	PROPN
ejpam-5430	428	9	sattam	sattam	PROPN
ejpam-5430	428	10	bin	bin	PROPN
ejpam-5430	428	11	abdulaziz	abdulaziz	PROPN
ejpam-5430	428	12	university	university	PROPN
ejpam-5430	428	13	for	for	ADP
ejpam-5430	428	14	funding	fund	VERB
ejpam-5430	428	15	this	this	DET
ejpam-5430	428	16	research	research	NOUN
ejpam-5430	428	17	work	work	NOUN
ejpam-5430	428	18	through	through	ADP
ejpam-5430	428	19	the	the	DET
ejpam-5430	428	20	project	project	NOUN
ejpam-5430	428	21	number	number	NOUN
ejpam-5430	428	22	(	(	PUNCT
ejpam-5430	428	23	psau/2024/01/29167	psau/2024/01/29167	PROPN
ejpam-5430	428	24	)	)	PUNCT
ejpam-5430	428	25	.	.	PUNCT
ejpam-5430	429	1	references	reference	NOUN
ejpam-5430	429	2	[	[	X
ejpam-5430	429	3	1	1	X
ejpam-5430	429	4	]	]	PUNCT
ejpam-5430	429	5	radwan	radwan	VERB
ejpam-5430	429	6	abu	abu	PROPN
ejpam-5430	429	7	-	-	PUNCT
ejpam-5430	429	8	gdairi	gdairi	PROPN
ejpam-5430	429	9	,	,	PUNCT
ejpam-5430	429	10	a.	a.	PROPN
ejpam-5430	429	11	a.	a.	PROPN
ejpam-5430	429	12	azzam	azzam	PROPN
ejpam-5430	429	13	,	,	PUNCT
ejpam-5430	429	14	and	and	CCONJ
ejpam-5430	429	15	ibrahim	ibrahim	PROPN
ejpam-5430	429	16	noaman	noaman	PROPN
ejpam-5430	429	17	.	.	PUNCT
ejpam-5430	430	1	nearly	nearly	ADV
ejpam-5430	430	2	soft	soft	ADJ
ejpam-5430	430	3	β	β	ADJ
ejpam-5430	430	4	-	-	ADJ
ejpam-5430	430	5	open	open	ADJ
ejpam-5430	430	6	sets	set	NOUN
ejpam-5430	430	7	via	via	ADP
ejpam-5430	430	8	soft	soft	ADJ
ejpam-5430	430	9	ditopological	ditopological	ADJ
ejpam-5430	430	10	spaces	space	NOUN
ejpam-5430	430	11	.	.	PUNCT
ejpam-5430	431	1	european	european	ADJ
ejpam-5430	431	2	journal	journal	PROPN
ejpam-5430	431	3	of	of	ADP
ejpam-5430	431	4	pure	pure	ADJ
ejpam-5430	431	5	and	and	CCONJ
ejpam-5430	431	6	applied	applied	ADJ
ejpam-5430	431	7	mathematics	mathematic	NOUN
ejpam-5430	431	8	,	,	PUNCT
ejpam-5430	431	9	15(1):126–134	15(1):126–134	PROPN
ejpam-5430	431	10	,	,	PUNCT
ejpam-5430	431	11	2022	2022	NUM
ejpam-5430	431	12	.	.	PUNCT
ejpam-5430	432	1	[	[	X
ejpam-5430	432	2	2	2	NUM
ejpam-5430	432	3	]	]	PUNCT
ejpam-5430	432	4	m.	m.	NOUN
ejpam-5430	432	5	akram	akram	PROPN
ejpam-5430	432	6	,	,	PUNCT
ejpam-5430	432	7	x.	x.	PROPN
ejpam-5430	432	8	peng	peng	PROPN
ejpam-5430	432	9	,	,	PUNCT
ejpam-5430	432	10	and	and	CCONJ
ejpam-5430	432	11	a.	a.	PROPN
ejpam-5430	432	12	sattar	sattar	PROPN
ejpam-5430	432	13	.	.	PUNCT
ejpam-5430	433	1	multi	multi	ADJ
ejpam-5430	433	2	-	-	ADJ
ejpam-5430	433	3	criteria	criterion	NOUN
ejpam-5430	433	4	decision	decision	NOUN
ejpam-5430	433	5	-	-	PUNCT
ejpam-5430	433	6	making	make	VERB
ejpam-5430	433	7	model	model	NOUN
ejpam-5430	433	8	using	use	VERB
ejpam-5430	433	9	complex	complex	ADJ
ejpam-5430	433	10	pythagorean	pythagorean	ADJ
ejpam-5430	433	11	fuzzy	fuzzy	ADJ
ejpam-5430	433	12	yager	yager	NOUN
ejpam-5430	433	13	aggregation	aggregation	NOUN
ejpam-5430	433	14	operators	operator	NOUN
ejpam-5430	433	15	.	.	PUNCT
ejpam-5430	434	1	arabian	arabian	ADJ
ejpam-5430	434	2	journal	journal	PROPN
ejpam-5430	434	3	for	for	ADP
ejpam-5430	434	4	science	science	NOUN
ejpam-5430	434	5	and	and	CCONJ
ejpam-5430	434	6	engineering	engineering	NOUN
ejpam-5430	434	7	,	,	PUNCT
ejpam-5430	434	8	pages	page	NOUN
ejpam-5430	434	9	1–27	1–27	NUM
ejpam-5430	434	10	,	,	PUNCT
ejpam-5430	434	11	2020	2020	NUM
ejpam-5430	434	12	.	.	PUNCT
ejpam-5430	435	1	[	[	X
ejpam-5430	435	2	3	3	X
ejpam-5430	435	3	]	]	PUNCT
ejpam-5430	435	4	t.	t.	PROPN
ejpam-5430	435	5	m.	m.	PROPN
ejpam-5430	435	6	al	al	PROPN
ejpam-5430	435	7	-	-	PUNCT
ejpam-5430	435	8	shami	shami	PROPN
ejpam-5430	435	9	.	.	PUNCT
ejpam-5430	436	1	soft	soft	ADJ
ejpam-5430	436	2	somewhere	somewhere	ADV
ejpam-5430	436	3	dense	dense	ADJ
ejpam-5430	436	4	sets	set	NOUN
ejpam-5430	436	5	on	on	ADP
ejpam-5430	436	6	soft	soft	ADJ
ejpam-5430	436	7	topological	topological	ADJ
ejpam-5430	436	8	spaces	space	NOUN
ejpam-5430	436	9	.	.	PUNCT
ejpam-5430	437	1	commun	commun	PROPN
ejpam-5430	437	2	.	.	PUNCT
ejpam-5430	438	1	korean	korean	ADJ
ejpam-5430	438	2	math	math	PROPN
ejpam-5430	438	3	.	.	PUNCT
ejpam-5430	439	1	soc	soc	PROPN
ejpam-5430	439	2	,	,	PUNCT
ejpam-5430	439	3	33(4):1341–1356	33(4):1341–1356	NUM
ejpam-5430	439	4	,	,	PUNCT
ejpam-5430	439	5	2018	2018	NUM
ejpam-5430	439	6	.	.	PUNCT
ejpam-5430	440	1	[	[	X
ejpam-5430	440	2	4	4	X
ejpam-5430	440	3	]	]	PUNCT
ejpam-5430	440	4	t.	t.	PROPN
ejpam-5430	440	5	m.	m.	PROPN
ejpam-5430	440	6	al	al	PROPN
ejpam-5430	440	7	-	-	PUNCT
ejpam-5430	440	8	shami	shami	PROPN
ejpam-5430	440	9	,	,	PUNCT
ejpam-5430	440	10	i.	i.	PROPN
ejpam-5430	440	11	alshammari	alshammari	PROPN
ejpam-5430	440	12	,	,	PUNCT
ejpam-5430	440	13	and	and	CCONJ
ejpam-5430	440	14	b.	b.	PROPN
ejpam-5430	440	15	a.	a.	PROPN
ejpam-5430	440	16	asaad	asaad	PROPN
ejpam-5430	440	17	.	.	PUNCT
ejpam-5430	441	1	soft	soft	ADJ
ejpam-5430	441	2	maps	map	NOUN
ejpam-5430	441	3	via	via	ADP
ejpam-5430	441	4	soft	soft	ADJ
ejpam-5430	441	5	somewhere	somewhere	ADV
ejpam-5430	441	6	dense	dense	ADJ
ejpam-5430	441	7	sets	set	NOUN
ejpam-5430	441	8	.	.	PUNCT
ejpam-5430	442	1	filomat	filomat	NOUN
ejpam-5430	442	2	,	,	PUNCT
ejpam-5430	442	3	34(10):3429–3440	34(10):3429–3440	NUM
ejpam-5430	442	4	,	,	PUNCT
ejpam-5430	442	5	2020	2020	NUM
ejpam-5430	442	6	.	.	PUNCT
ejpam-5430	443	1	[	[	X
ejpam-5430	443	2	5	5	NUM
ejpam-5430	443	3	]	]	PUNCT
ejpam-5430	443	4	m.	m.	PROPN
ejpam-5430	443	5	ali	ali	PROPN
ejpam-5430	443	6	,	,	PUNCT
ejpam-5430	443	7	f.	f.	PROPN
ejpam-5430	443	8	feng	feng	PROPN
ejpam-5430	443	9	,	,	PUNCT
ejpam-5430	443	10	x.	x.	PROPN
ejpam-5430	443	11	liu	liu	PROPN
ejpam-5430	443	12	,	,	PUNCT
ejpam-5430	443	13	w.	w.	PROPN
ejpam-5430	443	14	k.	k.	PROPN
ejpam-5430	443	15	min	min	PROPN
ejpam-5430	443	16	,	,	PUNCT
ejpam-5430	443	17	and	and	CCONJ
ejpam-5430	443	18	m.	m.	NOUN
ejpam-5430	443	19	shabir	shabir	PROPN
ejpam-5430	443	20	.	.	PUNCT
ejpam-5430	444	1	on	on	ADP
ejpam-5430	444	2	some	some	DET
ejpam-5430	444	3	new	new	ADJ
ejpam-5430	444	4	operations	operation	NOUN
ejpam-5430	444	5	in	in	ADP
ejpam-5430	444	6	soft	soft	ADJ
ejpam-5430	444	7	set	set	NOUN
ejpam-5430	444	8	theory	theory	NOUN
ejpam-5430	444	9	.	.	PUNCT
ejpam-5430	445	1	comput	comput	PROPN
ejpam-5430	445	2	math	math	PROPN
ejpam-5430	445	3	appl	appl	PROPN
ejpam-5430	445	4	,	,	PUNCT
ejpam-5430	445	5	57:1547–1553	57:1547–1553	NUM
ejpam-5430	445	6	,	,	PUNCT
ejpam-5430	445	7	2009	2009	NUM
ejpam-5430	445	8	.	.	PUNCT
ejpam-5430	446	1	[	[	X
ejpam-5430	446	2	6	6	NUM
ejpam-5430	446	3	]	]	PUNCT
ejpam-5430	446	4	a.	a.	NOUN
ejpam-5430	446	5	allam	allam	PROPN
ejpam-5430	446	6	,	,	PUNCT
ejpam-5430	446	7	t.	t.	PROPN
ejpam-5430	446	8	ismail	ismail	PROPN
ejpam-5430	446	9	,	,	PUNCT
ejpam-5430	446	10	and	and	CCONJ
ejpam-5430	446	11	r.	r.	PROPN
ejpam-5430	446	12	muhammed	muhammed	PROPN
ejpam-5430	446	13	.	.	PUNCT
ejpam-5430	447	1	a	a	DET
ejpam-5430	447	2	new	new	ADJ
ejpam-5430	447	3	approach	approach	NOUN
ejpam-5430	447	4	to	to	ADP
ejpam-5430	447	5	soft	soft	ADJ
ejpam-5430	447	6	belonging	belonging	NOUN
ejpam-5430	447	7	.	.	PUNCT
ejpam-5430	448	1	ann	ann	PROPN
ejpam-5430	448	2	.	.	PUNCT
ejpam-5430	448	3	fuzzy	fuzzy	ADJ
ejpam-5430	448	4	math	math	NOUN
ejpam-5430	448	5	.	.	PUNCT
ejpam-5430	449	1	inform	inform	NOUN
ejpam-5430	449	2	.	.	PUNCT
ejpam-5430	449	3	,	,	PUNCT
ejpam-5430	449	4	13:145–152	13:145–152	NUM
ejpam-5430	449	5	,	,	PUNCT
ejpam-5430	449	6	2017	2017	NUM
ejpam-5430	449	7	.	.	PUNCT
ejpam-5430	450	1	[	[	X
ejpam-5430	450	2	7	7	NUM
ejpam-5430	450	3	]	]	X
ejpam-5430	450	4	i.	i.	NOUN
ejpam-5430	450	5	alshammari	alshammari	PROPN
ejpam-5430	450	6	,	,	PUNCT
ejpam-5430	450	7	m.	m.	NOUN
ejpam-5430	450	8	parimala	parimala	NOUN
ejpam-5430	450	9	,	,	PUNCT
ejpam-5430	450	10	and	and	CCONJ
ejpam-5430	450	11	s.	s.	PROPN
ejpam-5430	450	12	jafari	jafari	PROPN
ejpam-5430	450	13	.	.	PUNCT
ejpam-5430	451	1	on	on	ADP
ejpam-5430	451	2	pythagorean	pythagorean	PROPN
ejpam-5430	451	3	fuzzy	fuzzy	ADJ
ejpam-5430	451	4	soft	soft	ADJ
ejpam-5430	451	5	topological	topological	ADJ
ejpam-5430	451	6	spaces	space	NOUN
ejpam-5430	451	7	.	.	PUNCT
ejpam-5430	452	1	journal	journal	NOUN
ejpam-5430	452	2	of	of	ADP
ejpam-5430	452	3	intelligent	intelligent	ADJ
ejpam-5430	452	4	and	and	CCONJ
ejpam-5430	452	5	fuzzy	fuzzy	ADJ
ejpam-5430	452	6	systems	system	NOUN
ejpam-5430	452	7	,	,	PUNCT
ejpam-5430	452	8	41(6):6889–6897	41(6):6889–6897	PROPN
ejpam-5430	452	9	,	,	PUNCT
ejpam-5430	452	10	2021	2021	NUM
ejpam-5430	452	11	.	.	PUNCT
ejpam-5430	453	1	[	[	X
ejpam-5430	453	2	8	8	NUM
ejpam-5430	453	3	]	]	PUNCT
ejpam-5430	453	4	k.	k.	PROPN
ejpam-5430	453	5	t.	t.	PROPN
ejpam-5430	453	6	atanassov	atanassov	PROPN
ejpam-5430	453	7	.	.	PUNCT
ejpam-5430	454	1	intuitionistic	intuitionistic	ADJ
ejpam-5430	454	2	fuzzy	fuzzy	ADJ
ejpam-5430	454	3	sets	set	NOUN
ejpam-5430	454	4	.	.	PUNCT
ejpam-5430	455	1	fuzzy	fuzzy	ADJ
ejpam-5430	455	2	sets	set	NOUN
ejpam-5430	455	3	and	and	CCONJ
ejpam-5430	455	4	systems	system	NOUN
ejpam-5430	455	5	,	,	PUNCT
ejpam-5430	455	6	20:87–96	20:87–96	NUM
ejpam-5430	455	7	,	,	PUNCT
ejpam-5430	455	8	1986	1986	NUM
ejpam-5430	455	9	.	.	PUNCT
ejpam-5430	456	1	[	[	X
ejpam-5430	456	2	9	9	NUM
ejpam-5430	456	3	]	]	PUNCT
ejpam-5430	456	4	a.	a.	NOUN
ejpam-5430	456	5	a.	a.	PROPN
ejpam-5430	456	6	azzam	azzam	PROPN
ejpam-5430	456	7	.	.	PUNCT
ejpam-5430	456	8	spherical	spherical	ADJ
ejpam-5430	456	9	fuzzy	fuzzy	ADJ
ejpam-5430	456	10	and	and	CCONJ
ejpam-5430	456	11	soft	soft	ADJ
ejpam-5430	456	12	topology	topology	NOUN
ejpam-5430	456	13	:	:	PUNCT
ejpam-5430	456	14	some	some	DET
ejpam-5430	456	15	applications	application	NOUN
ejpam-5430	456	16	.	.	PUNCT
ejpam-5430	457	1	j.	j.	PROPN
ejpam-5430	457	2	math	math	PROPN
ejpam-5430	457	3	.	.	PUNCT
ejpam-5430	458	1	computer	computer	NOUN
ejpam-5430	458	2	sci	sci	PROPN
ejpam-5430	458	3	.	.	PROPN
ejpam-5430	458	4	,	,	PUNCT
ejpam-5430	458	5	32:152–159	32:152–159	PROPN
ejpam-5430	458	6	,	,	PUNCT
ejpam-5430	458	7	2024	2024	NUM
ejpam-5430	458	8	.	.	PUNCT
ejpam-5430	459	1	[	[	X
ejpam-5430	459	2	10	10	NUM
ejpam-5430	459	3	]	]	PUNCT
ejpam-5430	459	4	a.	a.	NOUN
ejpam-5430	459	5	a.	a.	PROPN
ejpam-5430	459	6	azzam	azzam	PROPN
ejpam-5430	459	7	,	,	PUNCT
ejpam-5430	459	8	d.	d.	PROPN
ejpam-5430	459	9	breaz	breaz	PROPN
ejpam-5430	459	10	,	,	PUNCT
ejpam-5430	459	11	a.	a.	PROPN
ejpam-5430	459	12	s.	s.	PROPN
ejpam-5430	459	13	shah	shah	PROPN
ejpam-5430	459	14	,	,	PUNCT
ejpam-5430	459	15	and	and	CCONJ
ejpam-5430	459	16	l.	l.	PROPN
ejpam-5430	459	17	cot̆ırlă.	cot̆ırlă.	PROPN
ejpam-5430	459	18	study	study	NOUN
ejpam-5430	459	19	of	of	ADP
ejpam-5430	459	20	the	the	DET
ejpam-5430	459	21	fuzzy	fuzzy	ADJ
ejpam-5430	459	22	q	q	ADJ
ejpam-5430	459	23	-	-	ADJ
ejpam-5430	459	24	spiral	spiral	ADJ
ejpam-5430	459	25	like	like	ADP
ejpam-5430	459	26	functions	function	NOUN
ejpam-5430	459	27	associated	associate	VERB
ejpam-5430	459	28	with	with	ADP
ejpam-5430	459	29	the	the	DET
ejpam-5430	459	30	generalized	generalize	VERB
ejpam-5430	459	31	linear	linear	NOUN
ejpam-5430	459	32	operator	operator	NOUN
ejpam-5430	459	33	.	.	PUNCT
ejpam-5430	460	1	aims	aim	VERB
ejpam-5430	460	2	mathematics	mathematic	NOUN
ejpam-5430	460	3	,	,	PUNCT
ejpam-5430	460	4	8(11):26290–26300	8(11):26290–26300	NUM
ejpam-5430	460	5	,	,	PUNCT
ejpam-5430	460	6	2023	2023	NUM
ejpam-5430	460	7	.	.	PUNCT
ejpam-5430	461	1	references	reference	NOUN
ejpam-5430	461	2	4162	4162	NUM
ejpam-5430	462	1	[	[	X
ejpam-5430	462	2	11	11	NUM
ejpam-5430	462	3	]	]	PUNCT
ejpam-5430	462	4	a.	a.	NOUN
ejpam-5430	462	5	a.	a.	PROPN
ejpam-5430	462	6	azzam	azzam	PROPN
ejpam-5430	462	7	and	and	CCONJ
ejpam-5430	462	8	ibrahim	ibrahim	PROPN
ejpam-5430	462	9	noaman	noaman	PROPN
ejpam-5430	462	10	.	.	PUNCT
ejpam-5430	463	1	a	a	DET
ejpam-5430	463	2	soft	soft	ADJ
ejpam-5430	463	3	ideal	ideal	ADJ
ejpam-5430	463	4	topological	topological	ADJ
ejpam-5430	463	5	space	space	NOUN
ejpam-5430	463	6	:	:	PUNCT
ejpam-5430	463	7	new	new	ADJ
ejpam-5430	463	8	closed	closed	ADJ
ejpam-5430	463	9	set	set	NOUN
ejpam-5430	463	10	.	.	PUNCT
ejpam-5430	464	1	appl	appl	PROPN
ejpam-5430	464	2	.	.	PROPN
ejpam-5430	465	1	math	math	PROPN
ejpam-5430	465	2	.	.	PUNCT
ejpam-5430	466	1	inf	inf	PROPN
ejpam-5430	466	2	.	.	PUNCT
ejpam-5430	467	1	sci	sci	PROPN
ejpam-5430	467	2	.	.	PROPN
ejpam-5430	467	3	,	,	PUNCT
ejpam-5430	467	4	17(6):1065–1071	17(6):1065–1071	NUM
ejpam-5430	467	5	,	,	PUNCT
ejpam-5430	467	6	2023	2023	NUM
ejpam-5430	467	7	.	.	PUNCT
ejpam-5430	468	1	[	[	X
ejpam-5430	468	2	12	12	NUM
ejpam-5430	468	3	]	]	PUNCT
ejpam-5430	468	4	a.	a.	NOUN
ejpam-5430	468	5	a.	a.	PROPN
ejpam-5430	468	6	azzam	azzam	PROPN
ejpam-5430	468	7	,	,	PUNCT
ejpam-5430	468	8	a.	a.	PROPN
ejpam-5430	468	9	s.	s.	PROPN
ejpam-5430	468	10	shah	shah	PROPN
ejpam-5430	468	11	,	,	PUNCT
ejpam-5430	468	12	a.	a.	NOUN
ejpam-5430	468	13	cătas	căta	NOUN
ejpam-5430	468	14	,	,	PUNCT
ejpam-5430	468	15	and	and	CCONJ
ejpam-5430	468	16	l.-i	l.-i	PROPN
ejpam-5430	468	17	.	.	PUNCT
ejpam-5430	469	1	cot̆ırlă.	cot̆ırlă.	NOUN
ejpam-5430	469	2	on	on	ADP
ejpam-5430	469	3	fuzzy	fuzzy	ADJ
ejpam-5430	469	4	spiral	spiral	ADJ
ejpam-5430	469	5	-	-	PUNCT
ejpam-5430	469	6	like	like	ADJ
ejpam-5430	469	7	functions	function	NOUN
ejpam-5430	469	8	associated	associate	VERB
ejpam-5430	469	9	with	with	ADP
ejpam-5430	469	10	the	the	DET
ejpam-5430	469	11	family	family	NOUN
ejpam-5430	469	12	of	of	ADP
ejpam-5430	469	13	linear	linear	PROPN
ejpam-5430	469	14	operators	operator	NOUN
ejpam-5430	469	15	.	.	PUNCT
ejpam-5430	470	1	fractal	fractal	ADJ
ejpam-5430	470	2	fract	fract	PROPN
ejpam-5430	470	3	.	.	PUNCT
ejpam-5430	470	4	,	,	PUNCT
ejpam-5430	470	5	7(145	7(145	NUM
ejpam-5430	470	6	)	)	PUNCT
ejpam-5430	470	7	,	,	PUNCT
ejpam-5430	470	8	2023	2023	NUM
ejpam-5430	470	9	.	.	PUNCT
ejpam-5430	471	1	[	[	X
ejpam-5430	471	2	13	13	NUM
ejpam-5430	471	3	]	]	X
ejpam-5430	471	4	n.	n.	PROPN
ejpam-5430	471	5	cağman	cağman	PROPN
ejpam-5430	471	6	,	,	PUNCT
ejpam-5430	471	7	s.	s.	PROPN
ejpam-5430	471	8	karatas	karatas	PROPN
ejpam-5430	471	9	,	,	PUNCT
ejpam-5430	471	10	and	and	CCONJ
ejpam-5430	471	11	s.	s.	PROPN
ejpam-5430	471	12	enginoglu	enginoglu	PROPN
ejpam-5430	471	13	.	.	PUNCT
ejpam-5430	471	14	soft	soft	ADJ
ejpam-5430	471	15	topology	topology	NOUN
ejpam-5430	471	16	.	.	PUNCT
ejpam-5430	472	1	comput	comput	PROPN
ejpam-5430	472	2	math	math	PROPN
ejpam-5430	472	3	appl	appl	PROPN
ejpam-5430	472	4	,	,	PUNCT
ejpam-5430	472	5	62:351	62:351	NUM
ejpam-5430	472	6	–	–	PUNCT
ejpam-5430	472	7	358	358	NUM
ejpam-5430	472	8	,	,	PUNCT
ejpam-5430	472	9	2011	2011	NUM
ejpam-5430	472	10	.	.	PUNCT
ejpam-5430	473	1	[	[	X
ejpam-5430	473	2	14	14	NUM
ejpam-5430	473	3	]	]	PUNCT
ejpam-5430	473	4	b.	b.	PROPN
ejpam-5430	473	5	chen	chen	PROPN
ejpam-5430	473	6	.	.	PUNCT
ejpam-5430	474	1	soft	soft	ADJ
ejpam-5430	474	2	semi	semi	ADJ
ejpam-5430	474	3	-	-	ADJ
ejpam-5430	474	4	open	open	ADJ
ejpam-5430	474	5	sets	set	NOUN
ejpam-5430	474	6	and	and	CCONJ
ejpam-5430	474	7	related	related	ADJ
ejpam-5430	474	8	properties	property	NOUN
ejpam-5430	474	9	in	in	ADP
ejpam-5430	474	10	soft	soft	ADJ
ejpam-5430	474	11	topological	topological	ADJ
ejpam-5430	474	12	spaces	space	NOUN
ejpam-5430	474	13	.	.	PUNCT
ejpam-5430	475	1	appl	appl	PROPN
ejpam-5430	475	2	.	.	PROPN
ejpam-5430	476	1	math	math	PROPN
ejpam-5430	476	2	.	.	PUNCT
ejpam-5430	477	1	inf	inf	PROPN
ejpam-5430	477	2	.	.	PUNCT
ejpam-5430	478	1	sci	sci	PROPN
ejpam-5430	478	2	.	.	PROPN
ejpam-5430	478	3	,	,	PUNCT
ejpam-5430	478	4	7:287–294	7:287–294	NUM
ejpam-5430	478	5	,	,	PUNCT
ejpam-5430	478	6	2013	2013	NUM
ejpam-5430	478	7	.	.	PUNCT
ejpam-5430	479	1	[	[	X
ejpam-5430	479	2	15	15	NUM
ejpam-5430	479	3	]	]	X
ejpam-5430	479	4	b.	b.	PROPN
ejpam-5430	479	5	c.	c.	PROPN
ejpam-5430	479	6	cuong	cuong	PROPN
ejpam-5430	479	7	and	and	CCONJ
ejpam-5430	479	8	v.	v.	ADP
ejpam-5430	479	9	kreinovich	kreinovich	ADJ
ejpam-5430	479	10	.	.	PUNCT
ejpam-5430	480	1	picture	picture	NOUN
ejpam-5430	480	2	fuzzy	fuzzy	ADJ
ejpam-5430	480	3	sets	set	NOUN
ejpam-5430	480	4	-	-	PUNCT
ejpam-5430	480	5	a	a	DET
ejpam-5430	480	6	new	new	ADJ
ejpam-5430	480	7	concept	concept	NOUN
ejpam-5430	480	8	for	for	ADP
ejpam-5430	480	9	computational	computational	ADJ
ejpam-5430	480	10	intelligence	intelligence	NOUN
ejpam-5430	480	11	problems	problem	NOUN
ejpam-5430	480	12	.	.	PUNCT
ejpam-5430	481	1	in	in	ADP
ejpam-5430	481	2	proceedings	proceeding	NOUN
ejpam-5430	481	3	of	of	ADP
ejpam-5430	481	4	the	the	DET
ejpam-5430	481	5	third	third	ADJ
ejpam-5430	481	6	world	world	NOUN
ejpam-5430	481	7	congress	congress	PROPN
ejpam-5430	481	8	on	on	ADP
ejpam-5430	481	9	information	information	NOUN
ejpam-5430	481	10	and	and	CCONJ
ejpam-5430	481	11	communication	communication	NOUN
ejpam-5430	481	12	technologies	technology	NOUN
ejpam-5430	481	13	,	,	PUNCT
ejpam-5430	481	14	pages	page	NOUN
ejpam-5430	481	15	1–6	1–6	NUM
ejpam-5430	481	16	.	.	PUNCT
ejpam-5430	481	17	ieee	ieee	PROPN
ejpam-5430	481	18	,	,	PUNCT
ejpam-5430	481	19	2013	2013	NUM
ejpam-5430	481	20	.	.	PUNCT
ejpam-5430	482	1	[	[	X
ejpam-5430	482	2	16	16	NUM
ejpam-5430	482	3	]	]	X
ejpam-5430	482	4	h.	h.	PROPN
ejpam-5430	482	5	garg	garg	PROPN
ejpam-5430	482	6	.	.	PUNCT
ejpam-5430	483	1	generalised	generalise	VERB
ejpam-5430	483	2	pythagorean	pythagorean	PROPN
ejpam-5430	483	3	fuzzy	fuzzy	ADJ
ejpam-5430	483	4	geometric	geometric	ADJ
ejpam-5430	483	5	interactive	interactive	ADJ
ejpam-5430	483	6	aggregation	aggregation	NOUN
ejpam-5430	483	7	operators	operator	NOUN
ejpam-5430	483	8	using	use	VERB
ejpam-5430	483	9	einstein	einstein	ADJ
ejpam-5430	483	10	operations	operation	NOUN
ejpam-5430	483	11	and	and	CCONJ
ejpam-5430	483	12	their	their	PRON
ejpam-5430	483	13	application	application	NOUN
ejpam-5430	483	14	to	to	ADP
ejpam-5430	483	15	decision	decision	NOUN
ejpam-5430	483	16	making	making	NOUN
ejpam-5430	483	17	.	.	PUNCT
ejpam-5430	484	1	journal	journal	NOUN
ejpam-5430	484	2	of	of	ADP
ejpam-5430	484	3	experimental	experimental	ADJ
ejpam-5430	484	4	and	and	CCONJ
ejpam-5430	484	5	theoretical	theoretical	ADJ
ejpam-5430	484	6	artificial	artificial	ADJ
ejpam-5430	484	7	intelligence	intelligence	NOUN
ejpam-5430	484	8	,	,	PUNCT
ejpam-5430	484	9	30:1–32	30:1–32	NUM
ejpam-5430	484	10	,	,	PUNCT
ejpam-5430	484	11	2018	2018	NUM
ejpam-5430	484	12	.	.	PUNCT
ejpam-5430	485	1	[	[	X
ejpam-5430	485	2	17	17	NUM
ejpam-5430	485	3	]	]	X
ejpam-5430	485	4	h.	h.	PROPN
ejpam-5430	485	5	garg	garg	PROPN
ejpam-5430	485	6	.	.	PUNCT
ejpam-5430	486	1	new	new	ADJ
ejpam-5430	486	2	exponential	exponential	ADJ
ejpam-5430	486	3	operational	operational	ADJ
ejpam-5430	486	4	laws	law	NOUN
ejpam-5430	486	5	and	and	CCONJ
ejpam-5430	486	6	their	their	PRON
ejpam-5430	486	7	aggregation	aggregation	NOUN
ejpam-5430	486	8	operators	operator	NOUN
ejpam-5430	486	9	for	for	ADP
ejpam-5430	486	10	interval	interval	NOUN
ejpam-5430	486	11	-	-	PUNCT
ejpam-5430	486	12	valued	value	VERB
ejpam-5430	486	13	pythagorean	pythagorean	PROPN
ejpam-5430	486	14	fuzzy	fuzzy	ADJ
ejpam-5430	486	15	multi	multi	ADJ
ejpam-5430	486	16	-	-	ADJ
ejpam-5430	486	17	criteria	criterion	NOUN
ejpam-5430	486	18	decision	decision	NOUN
ejpam-5430	486	19	-	-	PUNCT
ejpam-5430	486	20	making	making	NOUN
ejpam-5430	486	21	.	.	PUNCT
ejpam-5430	487	1	journal	journal	NOUN
ejpam-5430	487	2	of	of	ADP
ejpam-5430	487	3	intelligent	intelligent	ADJ
ejpam-5430	487	4	systems	system	NOUN
ejpam-5430	487	5	,	,	PUNCT
ejpam-5430	487	6	33(3):653–683	33(3):653–683	PROPN
ejpam-5430	487	7	,	,	PUNCT
ejpam-5430	487	8	2018	2018	NUM
ejpam-5430	487	9	.	.	PUNCT
ejpam-5430	488	1	[	[	X
ejpam-5430	488	2	18	18	NUM
ejpam-5430	488	3	]	]	X
ejpam-5430	488	4	h.	h.	PROPN
ejpam-5430	488	5	garg	garg	PROPN
ejpam-5430	488	6	.	.	PUNCT
ejpam-5430	489	1	new	new	ADJ
ejpam-5430	489	2	logarithmic	logarithmic	ADJ
ejpam-5430	489	3	operational	operational	ADJ
ejpam-5430	489	4	laws	law	NOUN
ejpam-5430	489	5	and	and	CCONJ
ejpam-5430	489	6	their	their	PRON
ejpam-5430	489	7	aggregation	aggregation	NOUN
ejpam-5430	489	8	operators	operator	NOUN
ejpam-5430	489	9	for	for	ADP
ejpam-5430	489	10	pythagorean	pythagorean	PROPN
ejpam-5430	489	11	fuzzy	fuzzy	ADJ
ejpam-5430	489	12	set	set	NOUN
ejpam-5430	489	13	and	and	CCONJ
ejpam-5430	489	14	their	their	PRON
ejpam-5430	489	15	applications	application	NOUN
ejpam-5430	489	16	.	.	PUNCT
ejpam-5430	490	1	international	international	ADJ
ejpam-5430	490	2	journal	journal	NOUN
ejpam-5430	490	3	of	of	ADP
ejpam-5430	490	4	intelligent	intelligent	ADJ
ejpam-5430	490	5	systems	system	NOUN
ejpam-5430	490	6	,	,	PUNCT
ejpam-5430	490	7	34(1):82–106	34(1):82–106	NUM
ejpam-5430	490	8	,	,	PUNCT
ejpam-5430	490	9	2019	2019	NUM
ejpam-5430	490	10	.	.	PUNCT
ejpam-5430	491	1	[	[	X
ejpam-5430	491	2	19	19	NUM
ejpam-5430	491	3	]	]	PUNCT
ejpam-5430	491	4	a.	a.	NOUN
ejpam-5430	491	5	kharal	kharal	PROPN
ejpam-5430	491	6	and	and	CCONJ
ejpam-5430	491	7	b.	b.	PROPN
ejpam-5430	491	8	ahmad	ahmad	PROPN
ejpam-5430	491	9	.	.	PUNCT
ejpam-5430	492	1	mappings	mapping	NOUN
ejpam-5430	492	2	of	of	ADP
ejpam-5430	492	3	soft	soft	ADJ
ejpam-5430	492	4	classes	class	NOUN
ejpam-5430	492	5	.	.	PUNCT
ejpam-5430	493	1	new	new	ADJ
ejpam-5430	493	2	math	math	NOUN
ejpam-5430	493	3	.	.	PUNCT
ejpam-5430	494	1	nat	nat	PROPN
ejpam-5430	494	2	.	.	PUNCT
ejpam-5430	495	1	comput	comput	PROPN
ejpam-5430	495	2	.	.	PUNCT
ejpam-5430	495	3	,	,	PUNCT
ejpam-5430	495	4	7(3):471–481	7(3):471–481	NUM
ejpam-5430	495	5	,	,	PUNCT
ejpam-5430	495	6	2011	2011	NUM
ejpam-5430	495	7	.	.	PUNCT
ejpam-5430	496	1	[	[	X
ejpam-5430	496	2	20	20	NUM
ejpam-5430	496	3	]	]	PUNCT
ejpam-5430	496	4	j.	j.	PROPN
ejpam-5430	496	5	mahanta	mahanta	PROPN
ejpam-5430	496	6	and	and	CCONJ
ejpam-5430	496	7	p.	p.	PROPN
ejpam-5430	496	8	k.	k.	PUNCT
ejpam-5430	497	1	das	das	PROPN
ejpam-5430	497	2	.	.	PUNCT
ejpam-5430	498	1	on	on	ADP
ejpam-5430	498	2	soft	soft	ADJ
ejpam-5430	498	3	topological	topological	ADJ
ejpam-5430	498	4	space	space	NOUN
ejpam-5430	498	5	via	via	ADP
ejpam-5430	498	6	semiopen	semiopen	VERB
ejpam-5430	498	7	and	and	CCONJ
ejpam-5430	498	8	semiclosed	semiclose	VERB
ejpam-5430	498	9	soft	soft	ADJ
ejpam-5430	498	10	sets	set	NOUN
ejpam-5430	498	11	.	.	PUNCT
ejpam-5430	499	1	kyungpook	kyungpook	PROPN
ejpam-5430	499	2	math	math	PROPN
ejpam-5430	499	3	j.	j.	PROPN
ejpam-5430	499	4	,	,	PUNCT
ejpam-5430	499	5	4:221–223	4:221–223	PROPN
ejpam-5430	499	6	,	,	PUNCT
ejpam-5430	499	7	2014	2014	NUM
ejpam-5430	499	8	.	.	PUNCT
ejpam-5430	500	1	[	[	X
ejpam-5430	500	2	21	21	NUM
ejpam-5430	500	3	]	]	PUNCT
ejpam-5430	500	4	t.	t.	PROPN
ejpam-5430	500	5	mahmood	mahmood	PROPN
ejpam-5430	500	6	,	,	PUNCT
ejpam-5430	500	7	u.	u.	PROPN
ejpam-5430	500	8	ur	ur	PROPN
ejpam-5430	500	9	rehman	rehman	PROPN
ejpam-5430	500	10	,	,	PUNCT
ejpam-5430	500	11	j.	j.	PROPN
ejpam-5430	500	12	ahmmad	ahmmad	PROPN
ejpam-5430	500	13	,	,	PUNCT
ejpam-5430	500	14	abdul	abdul	PROPN
ejpam-5430	500	15	jaleel	jaleel	PROPN
ejpam-5430	500	16	,	,	PUNCT
ejpam-5430	500	17	and	and	CCONJ
ejpam-5430	500	18	ronnason	ronnason	PROPN
ejpam-5430	500	19	chinram	chinram	PROPN
ejpam-5430	500	20	.	.	PUNCT
ejpam-5430	501	1	bipolar	bipolar	ADJ
ejpam-5430	501	2	complex	complex	ADJ
ejpam-5430	501	3	fuzzy	fuzzy	ADJ
ejpam-5430	501	4	soft	soft	ADJ
ejpam-5430	501	5	sets	set	NOUN
ejpam-5430	501	6	and	and	CCONJ
ejpam-5430	501	7	their	their	PRON
ejpam-5430	501	8	applications	application	NOUN
ejpam-5430	501	9	in	in	ADP
ejpam-5430	501	10	decision	decision	NOUN
ejpam-5430	501	11	-	-	PUNCT
ejpam-5430	501	12	making	making	NOUN
ejpam-5430	501	13	.	.	PUNCT
ejpam-5430	502	1	mathematics	mathematic	NOUN
ejpam-5430	502	2	,	,	PUNCT
ejpam-5430	502	3	10(7	10(7	NUM
ejpam-5430	502	4	)	)	PUNCT
ejpam-5430	502	5	,	,	PUNCT
ejpam-5430	502	6	2022	2022	NUM
ejpam-5430	502	7	.	.	PUNCT
ejpam-5430	503	1	[	[	X
ejpam-5430	503	2	22	22	NUM
ejpam-5430	503	3	]	]	PUNCT
ejpam-5430	503	4	p.	p.	PROPN
ejpam-5430	503	5	k.	k.	PROPN
ejpam-5430	504	1	maji	maji	PROPN
ejpam-5430	504	2	,	,	PUNCT
ejpam-5430	504	3	r.	r.	PROPN
ejpam-5430	504	4	biswas	biswas	PROPN
ejpam-5430	504	5	,	,	PUNCT
ejpam-5430	504	6	and	and	CCONJ
ejpam-5430	504	7	a.	a.	PROPN
ejpam-5430	504	8	r.	r.	PROPN
ejpam-5430	504	9	roy	roy	PROPN
ejpam-5430	504	10	.	.	PROPN
ejpam-5430	504	11	soft	soft	ADJ
ejpam-5430	504	12	set	set	NOUN
ejpam-5430	504	13	theory	theory	NOUN
ejpam-5430	504	14	.	.	PUNCT
ejpam-5430	505	1	computers	computer	NOUN
ejpam-5430	505	2	and	and	CCONJ
ejpam-5430	505	3	mathematics	mathematic	NOUN
ejpam-5430	505	4	with	with	ADP
ejpam-5430	505	5	applications	application	NOUN
ejpam-5430	505	6	,	,	PUNCT
ejpam-5430	505	7	45:555–562	45:555–562	PROPN
ejpam-5430	505	8	,	,	PUNCT
ejpam-5430	505	9	2003	2003	NUM
ejpam-5430	505	10	.	.	PUNCT
ejpam-5430	506	1	[	[	X
ejpam-5430	506	2	23	23	NUM
ejpam-5430	506	3	]	]	X
ejpam-5430	506	4	d.	d.	PROPN
ejpam-5430	506	5	molodtsov	molodtsov	PROPN
ejpam-5430	506	6	.	.	PUNCT
ejpam-5430	507	1	soft	soft	ADJ
ejpam-5430	507	2	set	set	ADJ
ejpam-5430	507	3	theory	theory	NOUN
ejpam-5430	507	4	first	first	ADJ
ejpam-5430	507	5	results	result	NOUN
ejpam-5430	507	6	.	.	PUNCT
ejpam-5430	508	1	comput	comput	PROPN
ejpam-5430	508	2	math	math	PROPN
ejpam-5430	508	3	appl	appl	PROPN
ejpam-5430	508	4	,	,	PUNCT
ejpam-5430	508	5	37:19–31	37:19–31	PROPN
ejpam-5430	508	6	,	,	PUNCT
ejpam-5430	508	7	1999	1999	NUM
ejpam-5430	508	8	.	.	PUNCT
ejpam-5430	509	1	[	[	X
ejpam-5430	509	2	24	24	NUM
ejpam-5430	509	3	]	]	PUNCT
ejpam-5430	509	4	s.	s.	PROPN
ejpam-5430	509	5	k.	k.	PROPN
ejpam-5430	509	6	nazmul	nazmul	PROPN
ejpam-5430	509	7	and	and	CCONJ
ejpam-5430	509	8	s.	s.	PROPN
ejpam-5430	509	9	k.	k.	PROPN
ejpam-5430	509	10	samanta	samanta	PROPN
ejpam-5430	509	11	.	.	PUNCT
ejpam-5430	510	1	neighbourhood	neighbourhood	NOUN
ejpam-5430	510	2	properties	property	NOUN
ejpam-5430	510	3	of	of	ADP
ejpam-5430	510	4	soft	soft	ADJ
ejpam-5430	510	5	topological	topological	ADJ
ejpam-5430	510	6	spaces	space	NOUN
ejpam-5430	510	7	.	.	PUNCT
ejpam-5430	511	1	ann	ann	PROPN
ejpam-5430	511	2	.	.	PUNCT
ejpam-5430	511	3	fuzzy	fuzzy	ADJ
ejpam-5430	511	4	math	math	NOUN
ejpam-5430	511	5	.	.	PUNCT
ejpam-5430	512	1	inform	inform	NOUN
ejpam-5430	512	2	.	.	PUNCT
ejpam-5430	512	3	,	,	PUNCT
ejpam-5430	512	4	6:1–15	6:1–15	NUM
ejpam-5430	512	5	,	,	PUNCT
ejpam-5430	512	6	2013	2013	NUM
ejpam-5430	512	7	.	.	PUNCT
ejpam-5430	513	1	[	[	X
ejpam-5430	513	2	25	25	NUM
ejpam-5430	513	3	]	]	PUNCT
ejpam-5430	513	4	m.	m.	NOUN
ejpam-5430	513	5	olgun	olgun	NOUN
ejpam-5430	513	6	,	,	PUNCT
ejpam-5430	513	7	m.	m.	NOUN
ejpam-5430	513	8	unver	unver	ADJ
ejpam-5430	513	9	,	,	PUNCT
ejpam-5430	513	10	and	and	CCONJ
ejpam-5430	513	11	s.	s.	PROPN
ejpam-5430	513	12	yard	yard	PROPN
ejpam-5430	513	13	.	.	PUNCT
ejpam-5430	514	1	pythagorean	pythagorean	PROPN
ejpam-5430	514	2	fuzzy	fuzzy	ADJ
ejpam-5430	514	3	topological	topological	ADJ
ejpam-5430	514	4	spaces	space	NOUN
ejpam-5430	514	5	.	.	PUNCT
ejpam-5430	515	1	complex	complex	ADJ
ejpam-5430	515	2	and	and	CCONJ
ejpam-5430	515	3	intelligent	intelligent	ADJ
ejpam-5430	515	4	systems	system	NOUN
ejpam-5430	515	5	,	,	PUNCT
ejpam-5430	515	6	pages	page	NOUN
ejpam-5430	515	7	1–7	1–7	NUM
ejpam-5430	515	8	,	,	PUNCT
ejpam-5430	515	9	2019	2019	NUM
ejpam-5430	515	10	.	.	PUNCT
ejpam-5430	516	1	references	reference	NOUN
ejpam-5430	516	2	4163	4163	NUM
ejpam-5430	516	3	[	[	X
ejpam-5430	516	4	26	26	NUM
ejpam-5430	516	5	]	]	PUNCT
ejpam-5430	516	6	m.	m.	NOUN
ejpam-5430	516	7	parimala	parimala	PROPN
ejpam-5430	516	8	,	,	PUNCT
ejpam-5430	516	9	ibtesam	ibtesam	PROPN
ejpam-5430	516	10	alshammari	alshammari	NOUN
ejpam-5430	516	11	,	,	PUNCT
ejpam-5430	516	12	and	and	CCONJ
ejpam-5430	516	13	saeid	saeid	PROPN
ejpam-5430	516	14	jafari	jafari	PROPN
ejpam-5430	516	15	.	.	PUNCT
ejpam-5430	517	1	on	on	ADP
ejpam-5430	517	2	pythagorean	pythagorean	PROPN
ejpam-5430	517	3	fuzzy	fuzzy	ADJ
ejpam-5430	517	4	soft	soft	ADJ
ejpam-5430	517	5	topological	topological	ADJ
ejpam-5430	517	6	spaces	space	NOUN
ejpam-5430	517	7	.	.	PUNCT
ejpam-5430	518	1	journal	journal	NOUN
ejpam-5430	518	2	of	of	ADP
ejpam-5430	518	3	intelligent	intelligent	ADJ
ejpam-5430	518	4	and	and	CCONJ
ejpam-5430	518	5	fuzzy	fuzzy	ADJ
ejpam-5430	518	6	systems	system	NOUN
ejpam-5430	518	7	,	,	PUNCT
ejpam-5430	518	8	41(6):6889–6897	41(6):6889–6897	PROPN
ejpam-5430	518	9	,	,	PUNCT
ejpam-5430	518	10	2021	2021	NUM
ejpam-5430	518	11	.	.	PUNCT
ejpam-5430	519	1	[	[	X
ejpam-5430	519	2	27	27	NUM
ejpam-5430	519	3	]	]	PUNCT
ejpam-5430	519	4	m.	m.	NOUN
ejpam-5430	519	5	shabir	shabir	PROPN
ejpam-5430	519	6	and	and	CCONJ
ejpam-5430	519	7	m.	m.	PROPN
ejpam-5430	519	8	naz	naz	PROPN
ejpam-5430	519	9	.	.	PUNCT
ejpam-5430	520	1	on	on	ADP
ejpam-5430	520	2	soft	soft	ADJ
ejpam-5430	520	3	topological	topological	ADJ
ejpam-5430	520	4	spaces	space	NOUN
ejpam-5430	520	5	.	.	PUNCT
ejpam-5430	521	1	comput	comput	PROPN
ejpam-5430	521	2	math	math	PROPN
ejpam-5430	521	3	appl	appl	PROPN
ejpam-5430	521	4	,	,	PUNCT
ejpam-5430	521	5	61:1786–1799	61:1786–1799	NUM
ejpam-5430	521	6	,	,	PUNCT
ejpam-5430	521	7	2011	2011	NUM
ejpam-5430	521	8	.	.	PUNCT
ejpam-5430	522	1	[	[	X
ejpam-5430	522	2	28	28	NUM
ejpam-5430	522	3	]	]	X
ejpam-5430	522	4	m.	m.	NOUN
ejpam-5430	522	5	terepeta	terepeta	PROPN
ejpam-5430	522	6	.	.	PUNCT
ejpam-5430	523	1	on	on	ADP
ejpam-5430	523	2	separating	separate	VERB
ejpam-5430	523	3	axioms	axiom	NOUN
ejpam-5430	523	4	and	and	CCONJ
ejpam-5430	523	5	similarity	similarity	NOUN
ejpam-5430	523	6	of	of	ADP
ejpam-5430	523	7	soft	soft	ADJ
ejpam-5430	523	8	topological	topological	ADJ
ejpam-5430	523	9	spaces	space	NOUN
ejpam-5430	523	10	.	.	PUNCT
ejpam-5430	524	1	soft	soft	ADJ
ejpam-5430	524	2	comput	comput	NOUN
ejpam-5430	524	3	,	,	PUNCT
ejpam-5430	524	4	23:1049–1057	23:1049–1057	NUM
ejpam-5430	524	5	,	,	PUNCT
ejpam-5430	524	6	2019	2019	NUM
ejpam-5430	524	7	.	.	PUNCT
ejpam-5430	525	1	[	[	X
ejpam-5430	525	2	29	29	NUM
ejpam-5430	525	3	]	]	PUNCT
ejpam-5430	525	4	l.	l.	PROPN
ejpam-5430	525	5	wang	wang	PROPN
ejpam-5430	525	6	,	,	PUNCT
ejpam-5430	525	7	h.	h.	PROPN
ejpam-5430	525	8	garg	garg	PROPN
ejpam-5430	525	9	,	,	PUNCT
ejpam-5430	525	10	and	and	CCONJ
ejpam-5430	525	11	n.	n.	PROPN
ejpam-5430	525	12	li	li	PROPN
ejpam-5430	525	13	.	.	PROPN
ejpam-5430	526	1	pythagorean	pythagorean	PROPN
ejpam-5430	526	2	fuzzy	fuzzy	PROPN
ejpam-5430	526	3	interactive	interactive	ADJ
ejpam-5430	526	4	hamacher	hamacher	NOUN
ejpam-5430	526	5	power	power	NOUN
ejpam-5430	526	6	aggregation	aggregation	NOUN
ejpam-5430	526	7	operators	operator	NOUN
ejpam-5430	526	8	for	for	ADP
ejpam-5430	526	9	assessment	assessment	NOUN
ejpam-5430	526	10	of	of	ADP
ejpam-5430	526	11	express	express	ADJ
ejpam-5430	526	12	service	service	NOUN
ejpam-5430	526	13	quality	quality	NOUN
ejpam-5430	526	14	with	with	ADP
ejpam-5430	526	15	entropy	entropy	NOUN
ejpam-5430	526	16	weight	weight	NOUN
ejpam-5430	526	17	.	.	PUNCT
ejpam-5430	527	1	soft	soft	ADJ
ejpam-5430	527	2	computing	computing	NOUN
ejpam-5430	527	3	,	,	PUNCT
ejpam-5430	527	4	27:1–21	27:1–21	NUM
ejpam-5430	527	5	,	,	PUNCT
ejpam-5430	527	6	2020	2020	NUM
ejpam-5430	527	7	.	.	PUNCT
ejpam-5430	528	1	[	[	X
ejpam-5430	528	2	30	30	NUM
ejpam-5430	528	3	]	]	X
ejpam-5430	528	4	r.	r.	PROPN
ejpam-5430	528	5	r.	r.	PROPN
ejpam-5430	528	6	yager	yager	PROPN
ejpam-5430	528	7	.	.	PUNCT
ejpam-5430	529	1	pythagorean	pythagorean	PROPN
ejpam-5430	529	2	fuzzy	fuzzy	ADJ
ejpam-5430	529	3	subsets	subset	NOUN
ejpam-5430	529	4	.	.	PUNCT
ejpam-5430	530	1	in	in	ADP
ejpam-5430	530	2	2013	2013	NUM
ejpam-5430	530	3	joint	joint	ADJ
ejpam-5430	530	4	ifsa	ifsa	PROPN
ejpam-5430	530	5	world	world	PROPN
ejpam-5430	530	6	congress	congress	PROPN
ejpam-5430	530	7	and	and	CCONJ
ejpam-5430	530	8	nafips	nafip	NOUN
ejpam-5430	530	9	annual	annual	ADJ
ejpam-5430	530	10	meeting	meeting	NOUN
ejpam-5430	530	11	(	(	PUNCT
ejpam-5430	530	12	ifsa	ifsa	PROPN
ejpam-5430	530	13	/	/	SYM
ejpam-5430	530	14	nafips	nafip	NOUN
ejpam-5430	530	15	)	)	PUNCT
ejpam-5430	530	16	,	,	PUNCT
ejpam-5430	530	17	pages	page	NOUN
ejpam-5430	530	18	57–61	57–61	NUM
ejpam-5430	530	19	,	,	PUNCT
ejpam-5430	530	20	edmonton	edmonton	PROPN
ejpam-5430	530	21	,	,	PUNCT
ejpam-5430	530	22	ab	ab	PROPN
ejpam-5430	530	23	,	,	PUNCT
ejpam-5430	530	24	canada	canada	PROPN
ejpam-5430	530	25	,	,	PUNCT
ejpam-5430	530	26	2013	2013	NUM
ejpam-5430	530	27	.	.	PUNCT
ejpam-5430	531	1	ieee	ieee	NOUN
ejpam-5430	531	2	.	.	PUNCT
ejpam-5430	532	1	[	[	X
ejpam-5430	532	2	31	31	NUM
ejpam-5430	532	3	]	]	X
ejpam-5430	532	4	y.	y.	PROPN
ejpam-5430	532	5	yumak	yumak	PROPN
ejpam-5430	532	6	and	and	CCONJ
ejpam-5430	532	7	a.	a.	PROPN
ejpam-5430	532	8	k.	k.	PROPN
ejpam-5430	532	9	kaymakci	kaymakci	PROPN
ejpam-5430	532	10	.	.	PUNCT
ejpam-5430	533	1	soft	soft	ADJ
ejpam-5430	533	2	β	β	ADJ
ejpam-5430	533	3	-	-	ADJ
ejpam-5430	533	4	open	open	ADJ
ejpam-5430	533	5	sets	set	NOUN
ejpam-5430	533	6	and	and	CCONJ
ejpam-5430	533	7	their	their	PRON
ejpam-5430	533	8	applications	application	NOUN
ejpam-5430	533	9	.	.	PUNCT
ejpam-5430	534	1	j.	j.	PROPN
ejpam-5430	534	2	new	new	PROPN
ejpam-5430	534	3	theory	theory	NOUN
ejpam-5430	534	4	,	,	PUNCT
ejpam-5430	534	5	4:80–89	4:80–89	NUM
ejpam-5430	534	6	,	,	PUNCT
ejpam-5430	534	7	2015	2015	NUM
ejpam-5430	534	8	.	.	PUNCT
ejpam-5430	535	1	[	[	X
ejpam-5430	535	2	32	32	NUM
ejpam-5430	535	3	]	]	PUNCT
ejpam-5430	535	4	l.	l.	PROPN
ejpam-5430	535	5	a.	a.	PROPN
ejpam-5430	535	6	zadeh	zadeh	PROPN
ejpam-5430	535	7	.	.	PUNCT
ejpam-5430	535	8	fuzzy	fuzzy	ADJ
ejpam-5430	535	9	sets	set	NOUN
ejpam-5430	535	10	.	.	PUNCT
ejpam-5430	536	1	information	information	NOUN
ejpam-5430	536	2	and	and	CCONJ
ejpam-5430	536	3	control	control	NOUN
ejpam-5430	536	4	,	,	PUNCT
ejpam-5430	536	5	18:338–353	18:338–353	NUM
ejpam-5430	536	6	,	,	PUNCT
ejpam-5430	536	7	1965	1965	NUM
ejpam-5430	536	8	.	.	PUNCT